LMFDB - Embedded newform 29.10.e.a.4.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,10,Mod(4,29)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 10, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("29.4");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	29.e (of order $14$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$14.9360392488$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			4.16
Character	$\chi$	$=$	29.4
Dual form			29.10.e.a.22.16

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(25.0876 + 5.72609i) q^{2} +(18.6267 + 38.6787i) q^{3} +(135.306 + 65.1598i) q^{4} +(-277.936 + 1217.72i) q^{5} +(245.822 + 1077.02i) q^{6} +(-7762.93 + 3738.43i) q^{7} +(-7279.40 - 5805.13i) q^{8} +(11123.1 - 13947.9i) q^{9} +O(q^{10})$	\(q+(25.0876 + 5.72609i) q^{2} +(18.6267 + 38.6787i) q^{3} +(135.306 + 65.1598i) q^{4} +(-277.936 + 1217.72i) q^{5} +(245.822 + 1077.02i) q^{6} +(-7762.93 + 3738.43i) q^{7} +(-7279.40 - 5805.13i) q^{8} +(11123.1 - 13947.9i) q^{9} +(-13945.5 + 28958.2i) q^{10} +(-45950.1 + 36644.0i) q^{11} +6447.17i q^{12} +(18195.7 + 22816.6i) q^{13} +(-216160. + 49337.2i) q^{14} +(-52276.9 + 11931.9i) q^{15} +(-197323. - 247435. i) q^{16} +374734. i q^{17} +(358918. - 286228. i) q^{18} +(-82253.5 + 170801. i) q^{19} +(-116953. + 146654. i) q^{20} +(-289195. - 230626. i) q^{21} +(-1.36261e6 + 656197. i) q^{22} +(-172424. - 755438. i) q^{23} +(88943.8 - 389688. i) q^{24} +(354113. + 170532. i) q^{25} +(325836. + 676606. i) q^{26} +(1.57048e6 + 358452. i) q^{27} -1.29396e6 q^{28} +(988845. + 3.67822e6i) q^{29} -1.37983e6 q^{30} +(-9.75340e6 - 2.22615e6i) q^{31} +(-1.46518e6 - 3.04247e6i) q^{32} +(-2.27324e6 - 1.09474e6i) q^{33} +(-2.14576e6 + 9.40120e6i) q^{34} +(-2.39476e6 - 1.04921e7i) q^{35} +(2.41385e6 - 1.16245e6i) q^{36} +(1.63131e7 + 1.30092e7i) q^{37} +(-3.04157e6 + 3.81401e6i) q^{38} +(-543594. + 1.12878e6i) q^{39} +(9.09222e6 - 7.25081e6i) q^{40} +1.53001e6i q^{41} +(-5.93465e6 - 7.44181e6i) q^{42} +(3.77903e7 - 8.62538e6i) q^{43} +(-8.60503e6 + 1.96404e6i) q^{44} +(1.38931e7 + 1.74214e7i) q^{45} -1.99395e7i q^{46} +(2.46270e7 - 1.96394e7i) q^{47} +(5.89501e6 - 1.22411e7i) q^{48} +(2.11271e7 - 2.64926e7i) q^{49} +(7.90738e6 + 6.30593e6i) q^{50} +(-1.44942e7 + 6.98006e6i) q^{51} +(975250. + 4.27285e6i) q^{52} +(-457777. + 2.00565e6i) q^{53} +(3.73471e7 + 1.79854e7i) q^{54} +(-3.18509e7 - 6.61390e7i) q^{55} +(7.82115e7 + 1.78513e7i) q^{56} -8.13849e6 q^{57} +(3.74594e6 + 9.79402e7i) q^{58} -7.44150e7 q^{59} +(-7.85084e6 - 1.79190e6i) q^{60} +(-4.82579e6 - 1.00209e7i) q^{61} +(-2.31943e8 - 1.11698e8i) q^{62} +(-3.42044e7 + 1.49859e8i) q^{63} +(1.67206e7 + 7.32578e7i) q^{64} +(-3.28415e7 + 1.58156e7i) q^{65} +(-5.07617e7 - 4.04811e7i) q^{66} +(-1.19588e8 + 1.49958e8i) q^{67} +(-2.44176e7 + 5.07037e7i) q^{68} +(2.60077e7 - 2.07405e7i) q^{69} -2.76935e8i q^{70} +(-3.91074e7 - 4.90391e7i) q^{71} +(-1.61938e8 + 3.69614e7i) q^{72} +(-3.04035e8 + 6.93940e7i) q^{73} +(3.34764e8 + 4.19781e8i) q^{74} +1.68731e7i q^{75} +(-2.22588e7 + 1.77508e7i) q^{76} +(2.19716e8 - 4.56246e8i) q^{77} +(-2.01010e7 + 2.52059e7i) q^{78} +(3.44673e8 + 2.74868e8i) q^{79} +(3.56150e8 - 1.71513e8i) q^{80} +(-6.27487e7 - 2.74920e8i) q^{81} +(-8.76099e6 + 3.83844e7i) q^{82} +(-6.33325e8 - 3.04993e8i) q^{83} +(-2.41023e7 - 5.00489e7i) q^{84} +(-4.56321e8 - 1.04152e8i) q^{85} +9.97459e8 q^{86} +(-1.23850e8 + 1.06760e8i) q^{87} +5.47212e8 q^{88} +(3.78821e7 + 8.64633e6i) q^{89} +(2.48789e8 + 5.16615e8i) q^{90} +(-2.26550e8 - 1.09101e8i) q^{91} +(2.58943e7 - 1.13450e8i) q^{92} +(-9.55689e7 - 4.18715e8i) q^{93} +(7.30290e8 - 3.51689e8i) q^{94} +(-1.85127e8 - 1.47634e8i) q^{95} +(9.03875e7 - 1.13342e8i) q^{96} +(-6.29030e8 + 1.30619e9i) q^{97} +(6.81729e8 - 5.43661e8i) q^{98} +1.04850e9i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 7 q^{2} - 7 q^{3} + 5797 q^{4} + 1367 q^{5} - 7607 q^{6} + 4949 q^{7} + 31766 q^{8} + 112237 q^{9}+O(q^{10}) $ 132 * q - 7 * q^2 - 7 * q^3 + 5797 * q^4 + 1367 * q^5 - 7607 * q^6 + 4949 * q^7 + 31766 * q^8 + 112237 * q^9	\( 132 q - 7 q^{2} - 7 q^{3} + 5797 q^{4} + 1367 q^{5} - 7607 q^{6} + 4949 q^{7} + 31766 q^{8} + 112237 q^{9} - 7 q^{10} + 230503 q^{11} + 370719 q^{13} - 7 q^{14} - 134953 q^{15} - 942171 q^{16} + 2518152 q^{18} - 7 q^{19} + 2630005 q^{20} - 5671057 q^{21} - 1956426 q^{22} - 5580815 q^{23} + 3549677 q^{24} - 4029457 q^{25} + 9649689 q^{26} + 6835241 q^{27} - 24789228 q^{28} - 4235889 q^{29} + 34444162 q^{30} + 10383597 q^{31} + 8347164 q^{32} + 35912671 q^{33} - 11257679 q^{34} + 873325 q^{35} - 125256554 q^{36} - 32126087 q^{37} + 131520700 q^{38} + 192355527 q^{39} - 158097415 q^{40} + 127695676 q^{42} - 78365203 q^{43} - 238378098 q^{44} + 57884904 q^{45} + 6546071 q^{47} - 400523802 q^{48} - 221520647 q^{49} + 154918442 q^{50} + 278243026 q^{51} - 52352040 q^{52} + 352279862 q^{53} + 155358204 q^{54} + 143671997 q^{55} - 575895495 q^{56} - 298751838 q^{57} - 1211966547 q^{58} + 776098748 q^{59} + 112101752 q^{60} - 124049779 q^{61} + 669065875 q^{62} + 1929121403 q^{63} + 1625889382 q^{64} - 866654028 q^{65} - 852661411 q^{66} + 13275097 q^{67} - 1504278412 q^{68} - 1267751723 q^{69} + 1776837051 q^{71} + 6219206035 q^{72} - 1507755424 q^{73} - 4950184776 q^{74} + 422070887 q^{76} - 561272089 q^{77} - 1228370591 q^{78} - 973234717 q^{79} + 1423181574 q^{80} + 2306016039 q^{81} - 1386574594 q^{82} - 932915983 q^{83} + 261177525 q^{84} - 3402309596 q^{85} - 3486024644 q^{86} - 1597393079 q^{87} + 5582534 q^{88} + 2316401563 q^{89} - 4748880458 q^{90} + 659194133 q^{91} + 11318573556 q^{92} + 3911968919 q^{93} + 3703837052 q^{94} + 2797945913 q^{95} - 1910264674 q^{96} - 2438073624 q^{97} - 1034416404 q^{98}+O(q^{100}) \) 132 * q - 7 * q^2 - 7 * q^3 + 5797 * q^4 + 1367 * q^5 - 7607 * q^6 + 4949 * q^7 + 31766 * q^8 + 112237 * q^9 - 7 * q^10 + 230503 * q^11 + 370719 * q^13 - 7 * q^14 - 134953 * q^15 - 942171 * q^16 + 2518152 * q^18 - 7 * q^19 + 2630005 * q^20 - 5671057 * q^21 - 1956426 * q^22 - 5580815 * q^23 + 3549677 * q^24 - 4029457 * q^25 + 9649689 * q^26 + 6835241 * q^27 - 24789228 * q^28 - 4235889 * q^29 + 34444162 * q^30 + 10383597 * q^31 + 8347164 * q^32 + 35912671 * q^33 - 11257679 * q^34 + 873325 * q^35 - 125256554 * q^36 - 32126087 * q^37 + 131520700 * q^38 + 192355527 * q^39 - 158097415 * q^40 + 127695676 * q^42 - 78365203 * q^43 - 238378098 * q^44 + 57884904 * q^45 + 6546071 * q^47 - 400523802 * q^48 - 221520647 * q^49 + 154918442 * q^50 + 278243026 * q^51 - 52352040 * q^52 + 352279862 * q^53 + 155358204 * q^54 + 143671997 * q^55 - 575895495 * q^56 - 298751838 * q^57 - 1211966547 * q^58 + 776098748 * q^59 + 112101752 * q^60 - 124049779 * q^61 + 669065875 * q^62 + 1929121403 * q^63 + 1625889382 * q^64 - 866654028 * q^65 - 852661411 * q^66 + 13275097 * q^67 - 1504278412 * q^68 - 1267751723 * q^69 + 1776837051 * q^71 + 6219206035 * q^72 - 1507755424 * q^73 - 4950184776 * q^74 + 422070887 * q^76 - 561272089 * q^77 - 1228370591 * q^78 - 973234717 * q^79 + 1423181574 * q^80 + 2306016039 * q^81 - 1386574594 * q^82 - 932915983 * q^83 + 261177525 * q^84 - 3402309596 * q^85 - 3486024644 * q^86 - 1597393079 * q^87 + 5582534 * q^88 + 2316401563 * q^89 - 4748880458 * q^90 + 659194133 * q^91 + 11318573556 * q^92 + 3911968919 * q^93 + 3703837052 * q^94 + 2797945913 * q^95 - 1910264674 * q^96 - 2438073624 * q^97 - 1034416404 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{14}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	25.0876	+	5.72609i	1.10873	+	0.253060i	0.737410	−	0.675446i	$-0.236049\pi$
$2$	25.0876	+	5.72609i	1.10873	+	0.253060i	0.371318	+	0.928506i	$0.378906\pi$
$3$	18.6267	+	38.6787i	0.132767	+	0.275693i	0.956745	−	0.290929i	$-0.0939642\pi$
$3$	18.6267	+	38.6787i	0.132767	+	0.275693i	−0.823978	+	0.566622i	$0.808250\pi$
$4$	135.306	+	65.1598i	0.264269	+	0.127265i
$5$	−277.936	+	1217.72i	−0.198875	+	0.871329i	0.772733	+	0.634732i	$0.218889\pi$
$5$	−277.936	+	1217.72i	−0.198875	+	0.871329i	−0.971608	+	0.236597i	$0.923968\pi$
$6$	245.822	+	1077.02i	0.0774355	+	0.339267i
$7$	−7762.93	+	3738.43i	−1.22204	+	0.588502i	−0.929878	−	0.367868i	$-0.880088\pi$
$7$	−7762.93	+	3738.43i	−1.22204	+	0.588502i	−0.292159	+	0.956370i	$0.594374\pi$
$8$	−7279.40	−	5805.13i	−0.628334	−	0.501080i
$9$	11123.1	−	13947.9i	0.565110	−	0.708625i
$10$	−13945.5	+	28958.2i	−0.440997	+	0.915739i
$11$	−45950.1	+	36644.0i	−0.946279	+	0.754633i	−0.969498	−	0.245098i	$-0.921180\pi$
$11$	−45950.1	+	36644.0i	−0.946279	+	0.754633i	0.0232189	+	0.999730i	$0.492609\pi$
$12$			6447.17i			0.0897539i
$13$	18195.7	+	22816.6i	0.176694	+	0.221568i	0.862290	−	0.506415i	$-0.169030\pi$
$13$	18195.7	+	22816.6i	0.176694	+	0.221568i	−0.685596	+	0.727983i	$0.740458\pi$
$14$	−216160.	+	49337.2i	−1.50383	+	0.343240i
$15$	−52276.9	+	11931.9i	−0.266624	+	0.0608551i
$16$	−197323.	−	247435.i	−0.752728	−	0.943891i
$17$			374734.i			1.08819i	0.839025	+	0.544093i	$0.183126\pi$
$17$			374734.i			1.08819i	−0.839025	+	0.544093i	$0.816874\pi$
$18$	358918.	−	286228.i	0.805878	−	0.642666i
$19$	−82253.5	+	170801.i	−0.144798	+	0.300677i	−0.960737	−	0.277462i	$-0.910507\pi$
$19$	−82253.5	+	170801.i	−0.144798	+	0.300677i	0.815938	+	0.578139i	$0.196221\pi$
$20$	−116953.	+	146654.i	−0.163446	+	0.204955i
$21$	−289195.	−	230626.i	−0.324492	−	0.258774i
$22$	−1.36261e6	+	656197.i	−1.24013	+	0.597217i
$23$	−172424.	−	755438.i	−0.128476	−	0.562890i	−0.997658	−	0.0683982i	$-0.978211\pi$
$23$	−172424.	−	755438.i	−0.128476	−	0.562890i	0.869182	−	0.494492i	$-0.164646\pi$
$24$	88943.8	−	389688.i	0.0547224	−	0.239754i
$25$	354113.	+	170532.i	0.181306	+	0.0873123i
$26$	325836.	+	676606.i	0.139836	+	0.290373i
$27$	1.57048e6	+	358452.i	0.568716	+	0.129806i
$28$	−1.29396e6			−0.397842
$29$	988845.	+	3.67822e6i	0.259619	+	0.965711i
$29$	988845.	+	3.67822e6i	0.259619	+	0.965711i
$30$	−1.37983e6			−0.311013
$31$	−9.75340e6	−	2.22615e6i	−1.89683	−	0.432939i	−0.896873	−	0.442288i	$-0.854167\pi$
$31$	−9.75340e6	−	2.22615e6i	−1.89683	−	0.432939i	−0.999956	+	0.00934879i	$0.997024\pi$
$32$	−1.46518e6	−	3.04247e6i	−0.247010	−	0.512922i
$33$	−2.27324e6	−	1.09474e6i	−0.333682	−	0.160693i
$34$	−2.14576e6	+	9.40120e6i	−0.275376	+	1.20650i
$35$	−2.39476e6	−	1.04921e7i	−0.269746	−	1.18183i
$36$	2.41385e6	−	1.16245e6i	0.239524	−	0.115349i
$37$	1.63131e7	+	1.30092e7i	1.43096	+	1.14115i	0.966840	+	0.255381i	$0.0822010\pi$
$37$	1.63131e7	+	1.30092e7i	1.43096	+	1.14115i	0.464120	+	0.885772i	$0.346370\pi$
$38$	−3.04157e6	+	3.81401e6i	−0.236631	+	0.296726i
$39$	−543594.	+	1.12878e6i	−0.0376256	+	0.0781304i
$40$	9.09222e6	−	7.25081e6i	0.561565	−	0.447833i
$41$			1.53001e6i			0.0845606i	0.999106	+	0.0422803i	$0.0134622\pi$
$41$			1.53001e6i			0.0845606i	−0.999106	+	0.0422803i	$0.986538\pi$
$42$	−5.93465e6	−	7.44181e6i	−0.294288	−	0.369026i
$43$	3.77903e7	−	8.62538e6i	1.68567	−	0.384743i	0.730991	−	0.682387i	$-0.239058\pi$
$43$	3.77903e7	−	8.62538e6i	1.68567	−	0.384743i	0.954677	+	0.297644i	$0.0962010\pi$
$44$	−8.60503e6	+	1.96404e6i	−0.346111	+	0.0789976i
$45$	1.38931e7	+	1.74214e7i	0.505060	+	0.633325i
$46$		−	1.99395e7i		−	0.656604i
$47$	2.46270e7	−	1.96394e7i	0.736158	−	0.587066i	−0.181992	−	0.983300i	$-0.558254\pi$
$47$	2.46270e7	−	1.96394e7i	0.736158	−	0.587066i	0.918150	+	0.396234i	$0.129683\pi$
$48$	5.89501e6	−	1.22411e7i	0.160287	−	0.332840i
$49$	2.11271e7	−	2.64926e7i	0.523550	−	0.656511i
$50$	7.90738e6	+	6.30593e6i	0.178924	+	0.142687i
$51$	−1.44942e7	+	6.98006e6i	−0.300006	+	0.144475i
$52$	975250.	+	4.27285e6i	0.0184970	+	0.0810406i
$53$	−457777.	+	2.00565e6i	−0.00796916	+	0.0349152i	−0.978756	−	0.205028i	$-0.934272\pi$
$53$	−457777.	+	2.00565e6i	−0.00796916	+	0.0349152i	0.970787	+	0.239943i	$0.0771287\pi$
$54$	3.73471e7	+	1.79854e7i	0.597703	+	0.287838i
$55$	−3.18509e7	−	6.61390e7i	−0.469342	−	0.974599i
$56$	7.82115e7	+	1.78513e7i	1.06273	+	0.242562i
$57$	−8.13849e6			−0.102119
$58$	3.74594e6	+	9.79402e7i	0.0434646	+	1.13641i
$59$	−7.44150e7			−0.799514			−0.399757	−	0.916621i	$-0.630906\pi$
$59$	−7.44150e7			−0.799514			−0.399757	+	0.916621i	$0.630906\pi$
$60$	−7.85084e6	−	1.79190e6i	−0.0782052	−	0.0178498i
$61$	−4.82579e6	−	1.00209e7i	−0.0446256	−	0.0926661i	0.877464	−	0.479643i	$-0.159234\pi$
$61$	−4.82579e6	−	1.00209e7i	−0.0446256	−	0.0926661i	−0.922090	+	0.386977i	$0.873519\pi$
$62$	−2.31943e8	−	1.11698e8i	−1.99351	−	0.960023i
$63$	−3.42044e7	+	1.49859e8i	−0.273558	+	1.19854i
$64$	1.67206e7	+	7.32578e7i	0.124578	+	0.545813i
$65$	−3.28415e7	+	1.58156e7i	−0.228199	+	0.109895i
$66$	−5.07617e7	−	4.04811e7i	−0.329298	−	0.262606i
$67$	−1.19588e8	+	1.49958e8i	−0.725020	+	0.909146i	−0.998610	−	0.0527001i	$-0.983217\pi$
$67$	−1.19588e8	+	1.49958e8i	−0.725020	+	0.909146i	0.273590	+	0.961846i	$0.411789\pi$
$68$	−2.44176e7	+	5.07037e7i	−0.138488	+	0.287574i
$69$	2.60077e7	−	2.07405e7i	0.138128	−	0.110153i
$70$		−	2.76935e8i		−	1.37860i
$71$	−3.91074e7	−	4.90391e7i	−0.182640	−	0.229023i	0.682080	−	0.731278i	$-0.261076\pi$
$71$	−3.91074e7	−	4.90391e7i	−0.182640	−	0.229023i	−0.864720	+	0.502254i	$0.832504\pi$
$72$	−1.61938e8	+	3.69614e7i	−0.710156	+	0.162088i
$73$	−3.04035e8	+	6.93940e7i	−1.25306	+	0.286002i	−0.797017	−	0.603957i	$-0.793590\pi$
$73$	−3.04035e8	+	6.93940e7i	−1.25306	+	0.286002i	−0.456040	+	0.889959i	$0.650733\pi$
$74$	3.34764e8	+	4.19781e8i	1.29777	+	1.62735i
$75$			1.68731e7i			0.0615770i
$76$	−2.22588e7	+	1.77508e7i	−0.0765314	+	0.0610318i
$77$	2.19716e8	−	4.56246e8i	0.712286	−	1.47908i
$78$	−2.01010e7	+	2.52059e7i	−0.0614882	+	0.0771038i
$79$	3.44673e8	+	2.74868e8i	0.995602	+	0.793966i	0.978575	−	0.205889i	$-0.0660087\pi$
$79$	3.44673e8	+	2.74868e8i	0.995602	+	0.793966i	0.0170263	+	0.999855i	$0.494580\pi$
$80$	3.56150e8	−	1.71513e8i	0.972139	−	0.468157i
$81$	−6.27487e7	−	2.74920e8i	−0.161965	−	0.709616i
$82$	−8.76099e6	+	3.83844e7i	−0.0213989	+	0.0937546i
$83$	−6.33325e8	−	3.04993e8i	−1.46479	−	0.705405i	−0.479697	−	0.877434i	$-0.659253\pi$
$83$	−6.33325e8	−	3.04993e8i	−1.46479	−	0.705405i	−0.985092	+	0.172029i	$0.944968\pi$
$84$	−2.41023e7	−	5.00489e7i	−0.0528203	−	0.109683i
$85$	−4.56321e8	−	1.04152e8i	−0.948168	−	0.216413i
$86$	9.97459e8			1.96631
$87$	−1.23850e8	+	1.06760e8i	−0.231771	+	0.199790i
$88$	5.47212e8			0.972711
$89$	3.78821e7	+	8.64633e6i	0.0639998	+	0.0146075i	0.254401	−	0.967099i	$-0.418122\pi$
$89$	3.78821e7	+	8.64633e6i	0.0639998	+	0.0146075i	−0.190401	+	0.981706i	$0.560979\pi$
$90$	2.48789e8	+	5.16615e8i	0.399705	+	0.829995i
$91$	−2.26550e8	−	1.09101e8i	−0.346320	−	0.166779i
$92$	2.58943e7	−	1.13450e8i	0.0376841	−	0.165105i
$93$	−9.55689e7	−	4.18715e8i	−0.132478	−	0.580424i
$94$	7.30290e8	−	3.51689e8i	0.964761	−	0.464605i
$95$	−1.85127e8	−	1.47634e8i	−0.233192	−	0.185964i
$96$	9.03875e7	−	1.13342e8i	0.108615	−	0.136198i
$97$	−6.29030e8	+	1.30619e9i	−0.721437	+	1.49808i	0.139966	+	0.990156i	$0.455301\pi$
$97$	−6.29030e8	+	1.30619e9i	−0.721437	+	1.49808i	−0.861403	+	0.507923i	$0.830414\pi$
$98$	6.81729e8	−	5.43661e8i	0.746611	−	0.595403i
$99$			1.04850e9i			1.09701i
$100$	3.68017e7	+	4.61479e7i	0.0368017	+	0.0461479i
$101$	−9.05884e8	+	2.06762e8i	−0.866216	+	0.197708i	−0.632466	−	0.774588i	$-0.717957\pi$
$101$	−9.05884e8	+	2.06762e8i	−0.866216	+	0.197708i	−0.233751	+	0.972297i	$0.575100\pi$
$102$	−4.03595e8	+	9.21179e7i	−0.369186	+	0.0842642i
$103$	1.40682e7	+	1.76410e7i	0.0123161	+	0.0154439i	0.787951	−	0.615737i	$-0.211142\pi$
$103$	1.40682e7	+	1.76410e7i	0.0123161	+	0.0154439i	−0.775635	+	0.631181i	$0.782570\pi$
$104$		−	2.71720e8i		−	0.227757i
$105$	3.61215e8	−	2.88060e8i	0.290011	−	0.231276i
$106$	−2.29691e7	+	4.76958e7i	−0.0176713	+	0.0366948i
$107$	5.26666e8	−	6.60418e8i	0.388426	−	0.487071i	−0.548721	−	0.836006i	$-0.684885\pi$
$107$	5.26666e8	−	6.60418e8i	0.388426	−	0.487071i	0.937147	+	0.348935i	$0.113456\pi$
$108$	1.89138e8	+	1.50833e8i	0.133774	+	0.106681i
$109$	−2.36297e8	+	1.13795e8i	−0.160339	+	0.0772152i	−0.512332	−	0.858787i	$-0.671218\pi$
$109$	−2.36297e8	+	1.13795e8i	−0.160339	+	0.0772152i	0.351993	+	0.936003i	$0.385504\pi$
$110$	−4.20345e8	−	1.84165e9i	−0.273741	−	1.19934i
$111$	−1.99322e8	+	8.73288e8i	−0.124624	+	0.546014i
$112$	2.45682e9	+	1.18314e9i	1.47534	+	0.710488i
$113$	−3.82995e8	−	7.95298e8i	−0.220974	−	0.458856i	0.760781	−	0.649009i	$-0.224816\pi$
$113$	−3.82995e8	−	7.95298e8i	−0.220974	−	0.458856i	−0.981755	+	0.190152i	$0.939102\pi$
$114$	−2.04175e8	−	4.66017e7i	−0.113222	−	0.0258422i
$115$	9.67835e8			0.516013
$116$	−1.05876e8	+	5.62118e8i	−0.0542921	+	0.288248i
$117$	5.20635e8			0.256860
$118$	−1.86690e9	−	4.26107e8i	−0.886444	−	0.202325i
$119$	−1.40092e9	−	2.90903e9i	−0.640400	−	1.32980i
$120$	4.49810e8	+	2.16617e8i	0.198022	+	0.0953624i
$121$	2.43938e8	−	1.06876e9i	0.103453	−	0.453259i
$122$	−6.36874e7	−	2.79033e8i	−0.0260276	−	0.114034i
$123$	−5.91790e7	+	2.84991e7i	−0.0233128	+	0.0112268i
$124$	−1.17464e9	−	9.36740e8i	−0.446175	−	0.355813i
$125$	−1.82710e9	+	2.29111e9i	−0.669371	+	0.839364i
$126$	−1.71621e9	+	3.56376e9i	−0.606602	+	1.25962i
$127$	2.93010e8	−	2.33667e8i	0.0999459	−	0.0797042i	−0.572242	−	0.820085i	$-0.693926\pi$
$127$	2.93010e8	−	2.33667e8i	0.0999459	−	0.0797042i	0.672188	+	0.740381i	$0.265355\pi$
$128$			3.66258e9i			1.20598i
$129$	1.03753e9	+	1.30102e9i	0.329872	+	0.413647i
$130$	−9.14478e8	+	2.08724e8i	−0.280820	+	0.0640953i
$131$	2.31614e9	−	5.28643e8i	0.687137	−	0.156835i	0.135323	−	0.990802i	$-0.456793\pi$
$131$	2.31614e9	−	5.28643e8i	0.687137	−	0.156835i	0.551814	+	0.833967i	$0.313936\pi$
$132$	−2.36250e8	−	2.96248e8i	−0.0677312	−	0.0849323i
$133$		−	1.63342e9i		−	0.452652i
$134$	−3.85885e9	+	3.07733e9i	−1.03392	+	0.824522i
$135$	−8.72988e8	+	1.81278e9i	−0.226207	+	0.469724i
$136$	2.17538e9	−	2.72784e9i	0.545268	−	0.683744i
$137$	−5.23511e8	−	4.17486e8i	−0.126965	−	0.101251i	0.557949	−	0.829875i	$-0.311589\pi$
$137$	−5.23511e8	−	4.17486e8i	−0.126965	−	0.101251i	−0.684913	+	0.728624i	$0.740160\pi$
$138$	7.71234e8	−	3.71407e8i	0.181022	−	0.0871754i
$139$	−8.29108e8	−	3.63256e9i	−0.188384	−	0.825365i	−0.977469	−	0.211080i	$-0.932302\pi$
$139$	−8.29108e8	−	3.63256e9i	−0.188384	−	0.825365i	0.789085	−	0.614285i	$-0.210555\pi$
$140$	3.59640e8	−	1.57569e9i	0.0791210	−	0.346652i
$141$	1.21834e9	+	5.86724e8i	0.259588	+	0.125011i
$142$	−7.00309e8	−	1.45421e9i	−0.144541	−	0.300143i
$143$	−1.67219e9	−	3.81665e8i	−0.334405	−	0.0763257i
$144$	−5.64603e9			−1.09424
$145$	−4.75388e9	+	1.81823e8i	−0.893084	+	0.0341580i
$146$	−8.02488e9			−1.46167
$147$	1.41823e9	+	3.23701e8i	0.250506	+	0.0571764i
$148$	1.35957e9	+	2.82318e9i	0.232929	+	0.483683i
$149$	4.54436e9	+	2.18845e9i	0.755326	+	0.363746i	0.771589	−	0.636122i	$-0.219462\pi$
$149$	4.54436e9	+	2.18845e9i	0.755326	+	0.363746i	−0.0162624	+	0.999868i	$0.505177\pi$
$150$	−9.66168e7	+	4.23306e8i	−0.0155827	+	0.0682722i
$151$	1.32423e9	+	5.80182e9i	0.207284	+	0.908171i	0.966365	+	0.257175i	$0.0827916\pi$
$151$	1.32423e9	+	5.80182e9i	0.207284	+	0.908171i	−0.759081	+	0.650996i	$0.774351\pi$
$152$	1.59028e9	−	7.65838e8i	0.241645	−	0.116370i
$153$	5.22675e9	+	4.16819e9i	0.771116	+	0.614945i
$154$	8.12467e9	−	1.01880e10i	1.16403	−	1.45964i
$155$	5.42165e9	−	1.12582e10i	0.754465	−	1.56666i
$156$	−1.47103e8	+	1.17310e8i	−0.0198866	+	0.0158590i
$157$			8.55850e9i			1.12422i	0.827064	+	0.562108i	$0.190009\pi$
$157$			8.55850e9i			1.12422i	−0.827064	+	0.562108i	$0.809991\pi$
$158$	7.07312e9	+	8.86941e9i	0.902930	+	1.13224i
$159$	−8.61030e7	+	1.96524e7i	−0.0106839	+	0.00243854i
$160$	4.11210e9	−	9.38561e8i	0.496048	−	0.113220i
$161$	4.16267e9	+	5.21982e9i	0.488265	+	0.612265i
$162$		−	7.25640e9i		−	0.827758i
$163$	9.71151e9	−	7.74467e9i	1.07756	−	0.859328i	0.0869758	−	0.996210i	$-0.472280\pi$
$163$	9.71151e9	−	7.74467e9i	1.07756	−	0.859328i	0.990587	+	0.136883i	$0.0437083\pi$
$164$	−9.96954e7	+	2.07020e8i	−0.0107616	+	0.0223467i
$165$	1.96490e9	−	2.46390e9i	0.206377	−	0.258789i
$166$	−1.41422e10	−	1.12780e10i	−1.44554	−	1.15278i
$167$	−1.98853e9	+	9.57625e8i	−0.197837	+	0.0952733i	−0.530179	−	0.847886i	$-0.677875\pi$
$167$	−1.98853e9	+	9.57625e8i	−0.197837	+	0.0952733i	0.332342	+	0.943159i	$0.392161\pi$
$168$	7.66357e8	+	3.35763e9i	0.0742232	+	0.325193i
$169$	2.17021e9	−	9.50829e9i	0.204650	−	0.896628i
$170$	−1.08516e10	−	5.22587e9i	−0.996495	−	0.479887i
$171$	1.46740e9	+	3.04709e9i	0.131240	+	0.272523i
$172$	5.67527e9	+	1.29534e9i	0.494434	+	0.112851i
$173$	1.45656e10			1.23629			0.618144	−	0.786065i	$-0.287885\pi$
$173$	1.45656e10			1.23629			0.618144	+	0.786065i	$0.287885\pi$
$174$	−3.71843e9	+	1.96919e9i	−0.307530	+	0.162861i
$175$	−3.38648e9			−0.272946
$176$	1.81340e10	+	4.13898e9i	1.42458	+	0.325152i
$177$	−1.38610e9	−	2.87828e9i	−0.106149	−	0.220421i
$178$	9.00862e8	+	4.33832e8i	0.0672618	+	0.0323916i
$179$	−2.73096e9	+	1.19651e10i	−0.198828	+	0.871122i	0.772808	+	0.634640i	$0.218852\pi$
$179$	−2.73096e9	+	1.19651e10i	−0.198828	+	0.871122i	−0.971636	+	0.236482i	$0.924006\pi$
$180$	7.44641e8	+	3.26249e9i	0.0528714	+	0.231645i
$181$	5.30643e9	−	2.55544e9i	0.367493	−	0.176975i	−0.241018	−	0.970521i	$-0.577481\pi$
$181$	5.30643e9	−	2.55544e9i	0.367493	−	0.176975i	0.608511	+	0.793545i	$0.291767\pi$
$182$	−5.05889e9	−	4.03433e9i	−0.341770	−	0.272552i
$183$	2.97706e8	−	3.73311e8i	0.0196226	−	0.0246060i
$184$	−3.13027e9	+	6.50008e9i	−0.201327	+	0.418060i
$185$	−2.03756e10	+	1.62490e10i	−1.27890	+	1.01989i
$186$		−	1.10518e10i		−	0.677057i
$187$	−1.37318e10	−	1.72191e10i	−0.821181	−	1.02973i
$188$	4.61187e9	−	1.05263e9i	0.269257	−	0.0614561i
$189$	−1.35316e10	+	3.08849e9i	−0.771383	+	0.176063i
$190$	−3.79903e9	−	4.76383e9i	−0.211486	−	0.265195i
$191$			2.42314e10i			1.31743i	0.752392	+	0.658715i	$0.228900\pi$
$191$			2.42314e10i			1.31743i	−0.752392	+	0.658715i	$0.771100\pi$
$192$	−2.52207e9	+	2.01128e9i	−0.133937	+	0.106811i
$193$	1.03151e10	−	2.14195e10i	0.535137	−	1.11122i	−0.441685	−	0.897170i	$-0.645619\pi$
$193$	1.03151e10	−	2.14195e10i	0.535137	−	1.11122i	0.976822	−	0.214053i	$-0.0686666\pi$
$194$	−2.32603e10	+	2.91674e10i	−1.17898	+	1.47839i
$195$	−1.22346e9	−	9.75675e8i	−0.0605945	−	0.0483225i
$196$	4.58488e9	−	2.20796e9i	0.221909	−	0.106866i
$197$	4.27417e9	+	1.87263e10i	0.202187	+	0.885840i	0.969602	+	0.244688i	$0.0786857\pi$
$197$	4.27417e9	+	1.87263e10i	0.202187	+	0.885840i	−0.767415	+	0.641151i	$0.778457\pi$
$198$	−6.00380e9	+	2.63044e10i	−0.277609	+	1.21628i
$199$	−1.81226e10	−	8.72737e9i	−0.819183	−	0.394498i	−0.0231361	−	0.999732i	$-0.507365\pi$
$199$	−1.81226e10	−	8.72737e9i	−0.819183	−	0.394498i	−0.796047	+	0.605234i	$0.793079\pi$
$200$	−1.58777e9	−	3.29704e9i	−0.0701702	−	0.145710i
$201$	−8.02772e9	−	1.83227e9i	−0.346904	−	0.0791787i
$202$	−2.39104e10			−1.01043
$203$	−2.14271e10	−	2.48571e10i	−0.885588	−	1.02735i
$204$	−2.41597e9			−0.0976689
$205$	−1.86313e9	−	4.25246e8i	−0.0736801	−	0.0168170i
$206$	2.51925e8	+	5.23128e8i	0.00974695	+	0.0202398i
$207$	−1.24546e10	−	5.99784e9i	−0.471482	−	0.227054i
$208$	2.05522e9	−	9.00450e9i	0.0761330	−	0.333561i
$209$	−2.47928e9	−	1.08624e10i	−0.0898809	−	0.393794i
$210$	1.07115e10	−	5.15838e9i	0.380070	−	0.183032i
$211$	3.52047e10	+	2.80748e10i	1.22273	+	0.975091i	1.00000		0.000209904i	$6.68146e-5\pi$
$211$	3.52047e10	+	2.80748e10i	1.22273	+	0.975091i	0.222726	+	0.974881i	$0.428505\pi$
$212$	−1.92628e8	+	2.41548e8i	−0.00654949	+	0.00821281i
$213$	1.16833e9	−	2.42606e9i	0.0388917	−	0.0807594i
$214$	1.69944e10	−	1.35526e10i	0.553917	−	0.441734i
$215$			4.84153e10i			1.54529i
$216$	−9.35129e9	−	1.17261e10i	−0.292301	−	0.366533i
$217$	8.40372e10	−	1.91809e10i	2.57278	−	0.587221i
$218$	−6.57974e9	+	1.50178e9i	−0.197312	+	0.0450352i
$219$	−8.34724e9	−	1.04671e10i	−0.245214	−	0.307488i
$220$		−	1.10244e10i		−	0.317287i
$221$	−8.55018e9	+	6.81854e9i	−0.241107	+	0.192276i
$222$	−1.00010e10	+	2.07674e10i	−0.276349	+	0.573844i
$223$	1.92665e10	−	2.41594e10i	0.521713	−	0.654207i	−0.449259	−	0.893402i	$-0.648312\pi$
$223$	1.92665e10	−	2.41594e10i	0.521713	−	0.654207i	0.970972	+	0.239195i	$0.0768834\pi$
$224$	2.27481e10	+	1.81410e10i	0.603712	+	0.481444i
$225$	6.31738e9	−	3.04229e9i	0.164330	−	0.0791369i
$226$	−5.05450e9	−	2.21452e10i	−0.128881	−	0.564666i
$227$	−1.90633e9	+	8.35218e9i	−0.0476521	+	0.208777i	−0.993149	−	0.116853i	$-0.962719\pi$
$227$	−1.90633e9	+	8.35218e9i	−0.0476521	+	0.208777i	0.945497	+	0.325630i	$0.105577\pi$
$228$	−1.10118e9	−	5.30302e8i	−0.0269869	−	0.0129962i
$229$	−6.92709e9	−	1.43842e10i	−0.166453	−	0.345643i	0.801012	−	0.598648i	$-0.204295\pi$
$229$	−6.92709e9	−	1.43842e10i	−0.166453	−	0.345643i	−0.967465	+	0.253006i	$0.918581\pi$
$230$	2.42807e10	+	5.54191e9i	0.572118	+	0.130582i
$231$	2.17396e10			0.502340
$232$	1.41544e10	−	3.25156e10i	0.320770	−	0.736879i
$233$	−6.08502e10			−1.35257			−0.676286	−	0.736639i	$-0.736412\pi$
$233$	−6.08502e10			−1.35257			−0.676286	+	0.736639i	$0.736412\pi$
$234$	1.30615e10	+	2.98120e9i	0.284788	+	0.0650011i
$235$	1.70705e10	+	3.54472e10i	0.365124	+	0.758188i
$236$	−1.00688e10	−	4.84887e9i	−0.211287	−	0.101750i
$237$	−4.21141e9	+	1.84514e10i	−0.0867082	+	0.379893i
$238$	−1.84883e10	−	8.10026e10i	−0.373509	−	1.63645i
$239$	−1.92393e10	+	9.26516e9i	−0.381416	+	0.183680i	−0.614760	−	0.788714i	$-0.710747\pi$
$239$	−1.92393e10	+	9.26516e9i	−0.381416	+	0.183680i	0.233345	+	0.972394i	$0.425033\pi$
$240$	1.32678e10	+	1.05807e10i	0.258136	+	0.205856i
$241$	2.91463e10	−	3.65483e10i	0.556554	−	0.697896i	−0.421363	−	0.906892i	$-0.638448\pi$
$241$	2.91463e10	−	3.65483e10i	0.556554	−	0.697896i	0.977917	+	0.208996i	$0.0670195\pi$
$242$	1.22396e10	−	2.54159e10i	0.229403	−	0.476361i
$243$	3.42541e10	−	2.73167e10i	0.630208	−	0.502574i
$244$		−	1.67033e9i		−	0.0301681i
$245$	2.63885e10	+	3.30902e10i	0.467916	+	0.586748i
$246$	−1.64785e9	+	3.76111e8i	−0.0286886	+	0.00654799i
$247$	−5.39377e9	+	1.23109e9i	−0.0922053	+	0.0210453i
$248$	5.80758e10	+	7.28247e10i	0.974905	+	1.22249i
$249$		−	3.01772e10i		−	0.497487i
$250$	−5.89567e10	+	4.70164e10i	−0.954559	+	0.761236i
$251$	2.10967e9	−	4.38077e9i	0.0335492	−	0.0696656i	−0.883521	−	0.468392i	$-0.844833\pi$
$251$	2.10967e9	−	4.38077e9i	0.0335492	−	0.0696656i	0.917070	+	0.398727i	$0.130548\pi$
$252$	−1.43928e10	+	1.80481e10i	−0.224825	+	0.281921i
$253$	3.56052e10	+	2.83942e10i	0.546350	+	0.435699i
$254$	8.68892e9	−	4.18436e9i	0.130983	−	0.0630780i
$255$	−4.47127e9	−	1.95899e10i	−0.0662217	−	0.290136i
$256$	−1.24113e10	+	5.43774e10i	−0.180608	+	0.791296i
$257$	−2.04690e10	−	9.85734e9i	−0.292683	−	0.140949i	0.281781	−	0.959479i	$-0.409075\pi$
$257$	−2.04690e10	−	9.85734e9i	−0.292683	−	0.140949i	−0.574463	+	0.818530i	$0.694789\pi$
$258$	1.85794e10	+	3.85804e10i	0.261061	+	0.542099i
$259$	−1.75271e11	−	4.00045e10i	−2.42026	−	0.552408i
$260$	−5.47419e9			−0.0742916
$261$	6.23024e10	+	2.71208e10i	0.831041	+	0.361760i
$262$	6.11335e10			0.801537
$263$	−1.00214e11	−	2.28732e10i	−1.29160	−	0.294800i	−0.479101	−	0.877760i	$-0.659037\pi$
$263$	−1.00214e11	−	2.28732e10i	−1.29160	−	0.294800i	−0.812501	+	0.582960i	$0.801894\pi$
$264$	1.01928e10	+	2.11655e10i	0.129144	+	0.268170i
$265$	−2.31509e9	−	1.11489e9i	−0.0288377	−	0.0138875i
$266$	9.35309e9	−	4.09786e10i	0.114548	−	0.501868i
$267$	3.71188e8	+	1.62628e9i	0.00446986	+	0.0195837i
$268$	−2.59522e10	+	1.24979e10i	−0.307303	+	0.147989i
$269$	1.48914e10	+	1.18755e10i	0.173400	+	0.138282i	0.706344	−	0.707868i	$-0.250343\pi$
$269$	1.48914e10	+	1.18755e10i	0.173400	+	0.138282i	−0.532944	+	0.846150i	$0.678914\pi$
$270$	−3.22813e10	+	4.04795e10i	−0.369670	+	0.463552i
$271$	2.43811e10	−	5.06279e10i	0.274594	−	0.570201i	−0.717374	−	0.696688i	$-0.754656\pi$
$271$	2.43811e10	−	5.06279e10i	0.274594	−	0.570201i	0.991968	+	0.126488i	$0.0403704\pi$
$272$	9.27225e10	−	7.39437e10i	1.02713	−	0.819108i
$273$		−	1.07949e10i		−	0.117621i
$274$	−1.07431e10	−	1.34714e10i	−0.115147	−	0.144390i
$275$	−2.25205e10	+	5.14016e9i	−0.237455	+	0.0541975i
$276$	4.87044e9	−	1.11165e9i	0.0505216	−	0.0115312i
$277$	3.14587e10	+	3.94479e10i	0.321056	+	0.402592i	0.916002	−	0.401174i	$-0.131398\pi$
$277$	3.14587e10	+	3.94479e10i	0.321056	+	0.402592i	−0.594945	+	0.803766i	$0.702826\pi$
$278$		−	9.58799e10i		−	0.962778i
$279$	−1.39538e11	+	1.11278e11i	−1.37871	+	1.09948i
$280$	−4.34757e10	+	9.02781e10i	−0.422703	+	0.877751i
$281$	7.59679e10	−	9.52607e10i	0.726861	−	0.911455i	−0.271843	−	0.962342i	$-0.587633\pi$
$281$	7.59679e10	−	9.52607e10i	0.726861	−	0.911455i	0.998704	+	0.0508865i	$0.0162047\pi$
$282$	2.72058e10	+	2.16959e10i	0.256177	+	0.204294i
$283$	1.15683e11	−	5.57100e10i	1.07209	−	0.516291i	0.187309	−	0.982301i	$-0.440023\pi$
$283$	1.15683e11	−	5.57100e10i	1.07209	−	0.516291i	0.884779	+	0.466010i	$0.154309\pi$
$284$	−2.09607e9	−	9.18350e9i	−0.0191194	−	0.0837675i
$285$	2.26198e9	−	9.91039e9i	0.0203089	−	0.0889793i
$286$	−3.97657e10	−	1.91502e10i	−0.351449	−	0.169249i
$287$	−5.71985e9	−	1.18774e10i	−0.0497641	−	0.103336i
$288$	−5.87333e10	−	1.34055e10i	−0.503058	−	0.114820i
$289$	−2.18378e10			−0.184149
$290$	−1.20305e11	−	2.26596e10i	−0.998831	−	0.188132i
$291$	−6.22386e10			−0.508794
$292$	−4.56594e10	−	1.04215e10i	−0.367542	−	0.0838891i
$293$	9.86177e10	+	2.04782e11i	0.781719	+	1.62326i	0.782018	+	0.623256i	$0.214191\pi$
$293$	9.86177e10	+	2.04782e11i	0.781719	+	1.62326i	−0.000299086		1.00000i	$0.500095\pi$
$294$	3.37265e10	+	1.62418e10i	0.263274	+	0.126786i
$295$	2.06826e10	−	9.06165e10i	0.159004	−	0.696640i
$296$	−4.32290e10	−	1.89399e11i	−0.327313	−	1.43405i
$297$	−8.52988e10	+	4.10778e10i	−0.636120	+	0.306339i
$298$	1.01476e11	+	8.09244e10i	0.745402	+	0.594438i
$299$	1.40992e10	−	1.76798e10i	0.102017	−	0.127926i
$300$	−1.09945e9	+	2.28303e9i	−0.00783662	+	0.0162729i
$301$	−2.61118e11	+	2.08235e11i	−1.83353	+	1.46219i
$302$			1.53137e11i			1.05937i
$303$	−2.48709e10	−	3.11871e10i	−0.169512	−	0.212561i
$304$	5.84928e10	−	1.33506e10i	0.392800	−	0.0896540i
$305$	1.35439e10	−	3.09130e9i	0.0896176	−	0.0204546i
$306$	1.07259e11	+	1.34499e11i	0.699340	+	0.876945i
$307$		−	2.13908e11i		−	1.37438i	−0.726480	−	0.687188i	$-0.758845\pi$
$307$		−	2.13908e11i		−	1.37438i	0.726480	−	0.687188i	$-0.241155\pi$
$308$	5.94578e10	−	4.74160e10i	0.376470	−	0.300225i
$309$	−4.20287e8	+	8.72736e8i	−0.00262261	+	0.00544590i
$310$	2.00482e11	−	2.51396e11i	1.23296	−	1.54608i
$311$	−6.16386e9	−	4.91551e9i	−0.0373621	−	0.0297953i	0.604631	−	0.796506i	$-0.293321\pi$
$311$	−6.16386e9	−	4.91551e9i	−0.0373621	−	0.0297953i	−0.641993	+	0.766711i	$0.721892\pi$
$312$	1.05098e10	−	5.06124e9i	0.0627910	−	0.0302386i
$313$	4.18715e10	+	1.83451e11i	0.246586	+	1.08036i	0.934889	+	0.354941i	$0.115499\pi$
$313$	4.18715e10	+	1.83451e11i	0.246586	+	1.08036i	−0.688303	+	0.725424i	$0.741644\pi$
$314$	−4.90068e10	+	2.14713e11i	−0.284494	+	1.24645i
$315$	−1.72980e11	−	8.33026e10i	−0.989915	−	0.476718i
$316$	2.87259e10	+	5.96500e10i	0.162062	+	0.336526i
$317$	−1.12518e11	−	2.56816e10i	−0.625831	−	0.142842i	−0.102168	−	0.994767i	$-0.532578\pi$
$317$	−1.12518e11	−	2.56816e10i	−0.625831	−	0.142842i	−0.523663	+	0.851925i	$0.675435\pi$
$318$	−2.27265e9			−0.0124627
$319$	−1.80222e11	−	1.32780e11i	−0.974430	−	0.717915i
$320$	−9.38547e10			−0.500358
$321$	3.53542e10	+	8.06936e9i	0.185852	+	0.0424196i
$322$	7.45424e10	+	1.54789e11i	0.386413	+	0.802395i
$323$	−6.40051e10	−	3.08232e10i	−0.327192	−	0.157567i
$324$	9.42347e9	−	4.12869e10i	0.0475071	−	0.208142i
$325$	2.55236e9	+	1.11826e10i	0.0126901	+	0.0555992i
$326$	2.87986e11	−	1.38687e11i	1.41219	−	0.680073i
$327$	−8.80287e9	−	7.02005e9i	−0.0425754	−	0.0339528i
$328$	8.88192e9	−	1.11376e10i	0.0423716	−	0.0531323i
$329$	−1.17757e11	+	2.44525e11i	−0.554122	+	1.15065i
$330$	6.34032e10	−	5.05623e10i	0.294305	−	0.234701i
$331$			2.87135e11i			1.31480i	0.753541	+	0.657401i	$0.228344\pi$
$331$			2.87135e11i			1.31480i	−0.753541	+	0.657401i	$0.771656\pi$
$332$	−6.58192e10	−	8.25346e10i	−0.297325	−	0.372833i
$333$	3.62902e11	−	8.28301e10i	1.61730	−	0.369138i
$334$	−5.53709e10	+	1.26381e10i	−0.243457	+	0.0555675i
$335$	−1.49369e11	−	1.87303e11i	−0.647977	−	0.812537i
$336$			1.17065e11i			0.501072i
$337$	1.85943e11	−	1.48285e11i	0.785319	−	0.626271i	−0.146493	−	0.989212i	$-0.546799\pi$
$337$	1.85943e11	−	1.48285e11i	0.785319	−	0.626271i	0.931812	+	0.362941i	$0.118227\pi$
$338$	1.08891e11	−	2.26114e11i	0.453801	−	0.942328i
$339$	2.36272e10	−	2.96275e10i	0.0971657	−	0.121842i
$340$	−5.49563e10	−	4.38262e10i	−0.223030	−	0.177860i
$341$	5.29745e11	−	2.55112e11i	2.12164	−	1.02173i
$342$	1.93658e10	+	8.48469e10i	0.0765450	+	0.335366i
$343$	1.24016e10	−	5.43349e10i	0.0483786	−	0.211961i
$344$	−3.25162e11	−	1.56590e11i	−1.25195	−	0.602907i
$345$	1.80276e10	+	3.74346e10i	0.0685095	+	0.142262i
$346$	3.65416e11	+	8.34038e10i	1.37071	+	0.312855i
$347$	3.54228e11			1.31160			0.655799	−	0.754936i	$-0.272332\pi$
$347$	3.54228e11			1.31160			0.655799	+	0.754936i	$0.272332\pi$
$348$	−2.37141e10	+	6.37525e9i	−0.0866763	+	0.0233019i
$349$	−2.69748e11			−0.973292			−0.486646	−	0.873599i	$-0.661780\pi$
$349$	−2.69748e11			−0.973292			−0.486646	+	0.873599i	$0.661780\pi$
$350$	−8.49587e10	−	1.93913e10i	−0.302623	−	0.0690717i
$351$	2.03973e10	+	4.23554e10i	0.0717282	+	0.148945i
$352$	1.78813e11	+	8.61120e10i	0.620809	+	0.298966i
$353$	−1.54440e10	+	6.76648e10i	−0.0529389	+	0.231941i	−0.994475	−	0.104971i	$-0.966525\pi$
$353$	−1.54440e10	+	6.76648e10i	−0.0529389	+	0.231941i	0.941536	+	0.336911i	$0.109382\pi$
$354$	−1.82928e10	−	8.01461e10i	−0.0619108	−	0.271249i
$355$	7.05852e10	−	3.39920e10i	0.235877	−	0.113593i
$356$	4.56227e9	+	3.63829e9i	0.0150541	+	0.0120053i
$357$	8.64233e10	−	1.08371e11i	0.281594	−	0.353108i
$358$	−1.37027e11	+	2.84539e11i	−0.440892	+	0.915522i
$359$	1.71041e11	−	1.36401e11i	0.543470	−	0.433403i	−0.312884	−	0.949791i	$-0.601295\pi$
$359$	1.71041e11	−	1.36401e11i	0.543470	−	0.433403i	0.856355	+	0.516388i	$0.172724\pi$
$360$		−	2.07468e11i		−	0.651015i
$361$	1.78785e11	+	2.24189e11i	0.554050	+	0.694757i
$362$	1.47759e11	−	3.37249e10i	0.452235	−	0.103220i
$363$	4.58821e10	−	1.04723e10i	0.138696	−	0.0316564i
$364$	−2.35445e10	−	2.95239e10i	−0.0702965	−	0.0881491i
$365$		−	3.89517e11i		−	1.14870i
$366$	9.60634e9	−	7.66080e9i	0.0279829	−	0.0223156i
$367$	−2.94433e11	+	6.11397e11i	−0.847207	+	1.75924i	−0.228643	+	0.973510i	$0.573429\pi$
$367$	−2.94433e11	+	6.11397e11i	−0.847207	+	1.75924i	−0.618565	+	0.785734i	$0.712285\pi$
$368$	−1.52899e11	+	1.91729e11i	−0.434600	+	0.544971i
$369$	2.13404e10	+	1.70184e10i	0.0599218	+	0.0477860i
$370$	−6.04219e11	+	2.90976e11i	−1.67605	+	0.807142i
$371$	−3.94430e9	−	1.72811e10i	−0.0108090	−	0.0473575i
$372$	1.43524e10	−	6.28818e10i	0.0388580	−	0.170248i
$373$	−5.22549e11	−	2.51646e11i	−1.39778	−	0.673133i	−0.425066	−	0.905162i	$-0.639749\pi$
$373$	−5.22549e11	−	2.51646e11i	−1.39778	−	0.673133i	−0.972709	+	0.232029i	$0.925464\pi$
$374$	−2.45899e11	−	5.10615e11i	−0.649883	−	1.34950i
$375$	−1.22650e11	−	2.79940e10i	−0.320278	−	0.0731013i
$376$	−2.93279e11			−0.756720
$377$	−6.59320e10	+	8.94899e10i	−0.168097	+	0.228159i
$378$	−3.57160e11			−0.899808
$379$	−1.48487e11	−	3.38911e10i	−0.369667	−	0.0843742i	0.0336516	−	0.999434i	$-0.489286\pi$
$379$	−1.48487e11	−	3.38911e10i	−0.369667	−	0.0843742i	−0.403319	+	0.915059i	$0.632143\pi$
$380$	−1.54289e10	−	3.20385e10i	−0.0379585	−	0.0788217i
$381$	1.44958e10	+	6.98079e9i	0.0352434	+	0.0169723i
$382$	−1.38751e11	+	6.07908e11i	−0.333389	+	1.46067i
$383$	1.09638e11	+	4.80355e11i	0.260355	+	1.14069i	0.920868	+	0.389876i	$0.127482\pi$
$383$	1.09638e11	+	4.80355e11i	0.260355	+	1.14069i	−0.660512	+	0.750815i	$0.729661\pi$
$384$	−1.41664e11	+	6.82217e10i	−0.332482	+	0.160115i
$385$	4.94512e11	+	3.94360e11i	1.14711	+	0.914787i
$386$	3.81431e11	−	4.78300e11i	0.874527	−	1.09662i
$387$	3.00038e11	−	6.23035e11i	0.679949	−	1.41193i
$388$	−1.70223e11	+	1.35748e11i	−0.381307	+	0.304082i
$389$			5.74770e11i			1.27268i	0.771407	+	0.636342i	$0.219553\pi$
$389$			5.74770e11i			1.27268i	−0.771407	+	0.636342i	$0.780447\pi$
$390$	−2.51069e10	−	3.14830e10i	−0.0549543	−	0.0689105i
$391$	2.83089e11	−	6.46131e10i	0.612529	−	0.139806i
$392$	−3.07586e11	+	7.02044e10i	−0.657929	+	0.150168i
$393$	6.35892e10	+	7.97384e10i	0.134467	+	0.168617i
$394$			4.94274e11i			1.03332i
$395$	−4.30509e11	+	3.43319e11i	−0.889806	+	0.709597i
$396$	−6.83200e10	+	1.41868e11i	−0.139611	+	0.289905i
$397$	2.92069e11	−	3.66243e11i	0.590104	−	0.739967i	−0.393695	−	0.919241i	$-0.628803\pi$
$397$	2.92069e11	−	3.66243e11i	0.590104	−	0.739967i	0.983799	+	0.179274i	$0.0573749\pi$
$398$	−4.04679e11	−	3.22721e11i	−0.808420	−	0.644693i
$399$	6.31785e10	−	3.04252e10i	0.124793	−	0.0600973i
$400$	−2.76791e10	−	1.21270e11i	−0.0540607	−	0.236855i
$401$	−1.59981e11	+	7.00920e11i	−0.308971	+	1.35369i	0.547202	+	0.837000i	$0.315693\pi$
$401$	−1.59981e11	+	7.00920e11i	−0.308971	+	1.35369i	−0.856173	+	0.516689i	$0.827164\pi$
$402$	−1.90905e11	−	9.19349e10i	−0.364586	−	0.175575i
$403$	−1.26676e11	−	2.63046e11i	−0.239234	−	0.496774i
$404$	−1.36044e11	−	3.10511e10i	−0.254076	−	0.0579911i
$405$	3.52215e11			0.650520
$406$	−3.95222e11	−	7.46299e11i	−0.721895	−	1.36316i
$407$	−1.22630e12			−2.21524
$408$	1.46029e11	+	3.33303e10i	0.260897	+	0.0595481i
$409$	7.42693e10	+	1.54222e11i	0.131236	+	0.272515i	0.956224	−	0.292635i	$-0.0945323\pi$
$409$	7.42693e10	+	1.54222e11i	0.131236	+	0.272515i	−0.824988	+	0.565151i	$0.808818\pi$
$410$	−4.43065e10	−	2.13369e10i	−0.0774354	−	0.0372909i
$411$	6.39655e9	−	2.80251e10i	0.0110575	−	0.0484462i
$412$	7.54029e8	+	3.30362e9i	0.00128929	+	0.00564875i
$413$	5.77678e11	−	2.78195e11i	0.977036	−	0.470516i
$414$	−2.78113e11	−	2.21788e11i	−0.465287	−	0.371054i
$415$	5.47420e11	−	6.86443e11i	0.905950	−	1.13603i
$416$	4.27591e10	−	8.87902e10i	0.0700017	−	0.145360i
$417$	1.25059e11	−	9.97314e10i	0.202537	−	0.161518i
$418$		−	2.86709e11i		−	0.459355i
$419$	2.97267e11	+	3.72761e11i	0.471177	+	0.590837i	0.959459	−	0.281849i	$-0.0909476\pi$
$419$	2.97267e11	+	3.72761e11i	0.471177	+	0.590837i	−0.488282	+	0.872686i	$0.662376\pi$
$420$	6.76444e10	−	1.54394e10i	0.106074	−	0.0242108i
$421$	1.09980e12	−	2.51023e11i	1.70626	−	0.389443i	0.745430	−	0.666583i	$-0.232244\pi$
$421$	1.09980e12	−	2.51023e11i	1.70626	−	0.389443i	0.960829	+	0.277141i	$0.0893868\pi$
$422$	7.22443e11	+	9.05915e11i	1.10891	+	1.39053i
$423$		−	5.61944e11i		−	0.853417i
$424$	1.49754e10	−	1.19425e10i	0.0225026	−	0.0179452i
$425$	−6.39041e10	+	1.32698e11i	−0.0950121	+	0.197295i
$426$	4.32024e10	−	5.41741e10i	0.0635573	−	0.0796983i
$427$	7.49246e10	+	5.97503e10i	0.109068	+	0.0869791i
$428$	1.14294e11	−	5.50409e10i	0.164636	−	0.0792846i
$429$	−1.63850e10	−	7.17872e10i	−0.0233554	−	0.102327i
$430$	−2.77230e11	+	1.21462e12i	−0.391050	+	1.71330i
$431$	2.49331e11	+	1.20072e11i	0.348040	+	0.167607i	0.599734	−	0.800200i	$-0.295273\pi$
$431$	2.49331e11	+	1.20072e11i	0.348040	+	0.167607i	−0.251694	+	0.967807i	$0.580988\pi$
$432$	−2.21198e11	−	4.59323e11i	−0.305566	−	0.634514i
$433$	4.21510e10	+	9.62070e9i	0.0576252	+	0.0131526i	0.251236	−	0.967926i	$-0.419163\pi$
$433$	4.21510e10	+	9.62070e9i	0.0576252	+	0.0131526i	−0.193611	+	0.981078i	$0.562020\pi$
$434$	2.21813e12			3.00112
$435$	−9.55817e10	−	1.80487e11i	−0.127989	−	0.241682i
$436$	−3.93872e10			−0.0521994
$437$	1.43212e11	+	3.26873e10i	0.187851	+	0.0428758i
$438$	−1.49477e11	−	3.10392e11i	−0.194062	−	0.402974i
$439$	4.58201e11	+	2.20658e11i	0.588797	+	0.283550i	0.704466	−	0.709738i	$-0.251187\pi$
$439$	4.58201e11	+	2.20658e11i	0.588797	+	0.283550i	−0.115668	+	0.993288i	$0.536901\pi$
$440$	−1.52090e11	+	6.66351e11i	−0.193448	+	0.847551i
$441$	−1.34517e11	−	5.89358e11i	−0.169357	−	0.742002i
$442$	−2.53547e11	+	1.22102e11i	−0.315979	+	0.152168i
$443$	−7.99292e11	−	6.37414e11i	−0.986027	−	0.786331i	−0.00911218	−	0.999958i	$-0.502901\pi$
$443$	−7.99292e11	−	6.37414e11i	−0.986027	−	0.786331i	−0.976915	+	0.213628i	$0.931472\pi$
$444$	−8.38727e10	+	1.05173e11i	−0.102423	+	0.128434i
$445$	−2.10576e10	+	4.37266e10i	−0.0254559	+	0.0528598i
$446$	6.21691e11	−	4.95782e11i	0.743991	−	0.593313i
$447$			2.16534e11i			0.256532i
$448$	−4.03670e11	−	5.06186e11i	−0.473451	−	0.593689i
$449$	4.51942e11	−	1.03153e11i	0.524776	−	0.119777i	0.0480777	−	0.998844i	$-0.484691\pi$
$449$	4.51942e11	−	1.03153e11i	0.524776	−	0.119777i	0.476698	+	0.879067i	$0.341833\pi$
$450$	1.75909e11	−	4.01500e10i	0.202223	−	0.0461561i
$451$	−5.60658e10	−	7.03043e10i	−0.0638122	−	0.0800179i
$452$		−	1.32564e11i		−	0.149384i
$453$	−1.99741e11	+	1.59288e11i	−0.222856	+	0.177722i
$454$	−9.56507e10	+	1.98621e11i	−0.105666	+	0.219418i
$455$	1.95821e11	−	2.45551e11i	0.214194	−	0.268591i
$456$	5.92433e10	+	4.72449e10i	0.0641649	+	0.0511698i
$457$	−5.47543e11	+	2.63683e11i	−0.587213	+	0.282787i	−0.703805	−	0.710393i	$-0.748517\pi$
$457$	−5.47543e11	+	2.63683e11i	−0.587213	+	0.282787i	0.116592	+	0.993180i	$0.462803\pi$
$458$	−9.14188e10	−	4.00532e11i	−0.0970825	−	0.425346i
$459$	−1.34324e11	+	5.88513e11i	−0.141253	+	0.618869i
$460$	1.30954e11	+	6.30639e10i	0.136366	+	0.0656706i
$461$	6.19125e11	+	1.28563e12i	0.638446	+	1.32575i	0.929423	+	0.369016i	$0.120305\pi$
$461$	6.19125e11	+	1.28563e12i	0.638446	+	1.32575i	−0.290978	+	0.956730i	$0.593980\pi$
$462$	5.45395e11	+	1.24483e11i	0.556958	+	0.127122i
$463$	−9.25166e11			−0.935632			−0.467816	−	0.883826i	$-0.654959\pi$
$463$	−9.25166e11			−0.935632			−0.467816	+	0.883826i	$0.654959\pi$
$464$	7.15001e11	−	9.70474e11i	0.716103	−	0.971970i
$465$	5.36439e11			0.532086
$466$	−1.52659e12	−	3.48434e11i	−1.49963	−	0.342282i
$467$	−4.47397e11	−	9.29029e11i	−0.435278	−	0.903864i	−0.997063	−	0.0765813i	$-0.975600\pi$
$467$	−4.47397e11	−	9.29029e11i	−0.435278	−	0.903864i	0.561785	−	0.827283i	$-0.310115\pi$
$468$	7.04449e10	+	3.39245e10i	0.0678802	+	0.0326894i
$469$	3.67743e11	−	1.61119e12i	0.350967	−	1.53769i
$470$	2.25284e11	+	9.87035e11i	0.212956	+	0.933023i
$471$	−3.31032e11	+	1.59417e11i	−0.309939	+	0.149259i
$472$	5.41696e11	+	4.31988e11i	0.502362	+	0.400620i
$473$	−1.42040e12	+	1.78112e12i	−1.30477	+	1.63613i
$474$	−2.11309e11	+	4.38787e11i	−0.192272	+	0.399256i
$475$	−5.82541e10	+	4.64561e10i	−0.0525056	+	0.0418718i
$476$		−	4.84893e11i		−	0.432927i
$477$	2.28827e10	+	2.86940e10i	0.0202383	+	0.0253781i
$478$	−5.35722e11	+	1.22275e11i	−0.469368	+	0.107130i
$479$	−9.85242e11	+	2.24875e11i	−0.855132	+	0.195178i	−0.627546	−	0.778580i	$-0.715940\pi$
$479$	−9.85242e11	+	2.24875e11i	−0.855132	+	0.195178i	−0.227586	+	0.973758i	$0.573083\pi$
$480$	1.12897e11	+	1.41569e11i	0.0970728	+	0.121725i
$481$			6.08921e11i			0.518690i
$482$	9.40492e11	−	7.50017e11i	0.793676	−	0.632936i
$483$	−1.24359e11	+	2.58235e11i	−0.103972	+	0.215900i
$484$	1.02646e11	−	1.28715e11i	0.0850237	−	0.106616i
$485$	−1.41575e12	−	1.12902e12i	−1.16184	−	0.926539i
$486$	1.01577e12	−	4.89170e11i	0.825910	−	0.397737i
$487$	5.73334e10	+	2.51194e11i	0.0461878	+	0.202362i	0.992757	−	0.120138i	$-0.0383338\pi$
$487$	5.73334e10	+	2.51194e11i	0.0461878	+	0.202362i	−0.946569	+	0.322500i	$0.895477\pi$
$488$	−2.30435e10	+	1.00960e11i	−0.0183933	+	0.0805862i
$489$	4.80447e11	+	2.31371e11i	0.379976	+	0.182987i
$490$	4.72549e11	+	9.81258e11i	0.370309	+	0.768955i
$491$	−1.97916e12	−	4.51731e11i	−1.53679	−	0.350763i	−0.631440	−	0.775424i	$-0.717536\pi$
$491$	−1.97916e12	−	4.51731e11i	−1.53679	−	0.350763i	−0.905352	+	0.424662i	$0.860393\pi$
$492$	−9.86425e9			−0.00758964
$493$	−1.37836e12	+	3.70554e11i	−1.05087	+	0.282514i
$494$	−1.42366e11			−0.107556
$495$	−1.27678e12	−	2.91416e11i	−0.955855	−	0.218168i
$496$	1.37374e12	+	2.85261e12i	1.01915	+	2.11629i
$497$	4.86917e11	+	2.34487e11i	0.357974	+	0.172391i
$498$	1.72797e11	−	7.57075e11i	0.125894	−	0.551578i
$499$	−1.51883e11	−	6.65444e11i	−0.109662	−	0.480462i	−0.999698	−	0.0245714i	$-0.992178\pi$
$499$	−1.51883e11	−	6.65444e11i	−0.109662	−	0.480462i	0.890036	−	0.455891i	$-0.150679\pi$
$500$	−3.96505e11	+	1.90947e11i	−0.283716	+	0.136630i
$501$	−7.40794e10	−	5.90764e10i	−0.0525325	−	0.0418932i
$502$	7.80112e10	−	9.78230e10i	0.0548265	−	0.0687502i
$503$	−7.08203e11	+	1.47060e12i	−0.493289	+	1.02433i	0.494594	+	0.869124i	$0.335317\pi$
$503$	−7.08203e11	+	1.47060e12i	−0.493289	+	1.02433i	−0.987883	+	0.155201i	$0.950397\pi$
$504$	1.11894e12	−	8.92324e11i	0.772447	−	0.616006i
$505$		−	1.16058e12i		−	0.794079i
$506$	7.30662e11	+	9.16222e11i	0.495495	+	0.621331i
$507$	4.08192e11	−	9.31673e10i	0.274365	−	0.0626221i
$508$	5.48716e10	−	1.25241e10i	0.0365562	−	0.00834371i
$509$	−5.32349e10	−	6.67544e10i	−0.0351533	−	0.0440809i	0.763944	−	0.645282i	$-0.223260\pi$
$509$	−5.32349e10	−	6.67544e10i	−0.0351533	−	0.0440809i	−0.799097	+	0.601202i	$0.794689\pi$
$510$		−	5.17068e11i		−	0.338440i
$511$	2.10078e12	−	1.67531e12i	1.36297	−	1.08693i
$512$	1.90896e11	−	3.96399e11i	0.122767	−	0.254928i
$513$	−1.90402e11	+	2.38756e11i	−0.121379	+	0.152204i
$514$	−4.57074e11	−	3.64505e11i	−0.288837	−	0.230340i
$515$	−2.53919e10	+	1.22281e10i	−0.0159061	+	0.00765995i
$516$	5.56093e10	+	2.43640e11i	0.0345321	+	0.151295i
$517$	−4.11948e11	+	1.80486e12i	−0.253592	+	1.11106i
$518$	−4.16807e12	−	2.00724e12i	−2.54362	−	1.22494i
$519$	2.71308e11	+	5.63378e11i	0.164138	+	0.340837i
$520$	3.30878e11	+	7.55208e10i	0.198451	+	0.0452951i
$521$	4.20735e11			0.250172			0.125086	−	0.992146i	$-0.460079\pi$
$521$	4.20735e11			0.250172			0.125086	+	0.992146i	$0.460079\pi$
$522$	1.40772e12	+	1.03715e12i	0.829851	+	0.611396i
$523$	−2.30931e11			−0.134966			−0.0674831	−	0.997720i	$-0.521497\pi$
$523$	−2.30931e11			−0.134966			−0.0674831	+	0.997720i	$0.521497\pi$
$524$	3.47833e11	+	7.93906e10i	0.201549	+	0.0460022i
$525$	−6.30788e10	−	1.30985e11i	−0.0362382	−	0.0752494i
$526$	−2.38316e12	−	1.14767e12i	−1.35743	−	0.653705i
$527$	8.34214e11	−	3.65493e12i	0.471118	−	2.06410i
$528$	1.77687e11	+	7.78497e11i	0.0994953	+	0.435917i
$529$	1.08183e12	−	5.20980e11i	0.600629	−	0.289248i
$530$	−5.16962e10	−	4.12263e10i	−0.0284588	−	0.0226952i
$531$	−8.27722e11	+	1.03793e12i	−0.451813	+	0.566556i
$532$	1.06433e11	−	2.21011e11i	0.0576069	−	0.119622i
$533$	−3.49098e10	+	2.78396e10i	−0.0187359	+	0.0149414i
$534$			4.29250e10i			0.0228442i
$535$	6.57825e11	+	8.24886e11i	0.347151	+	0.435313i
$536$	1.74105e12	−	3.97384e11i	0.911109	−	0.207955i
$537$	−5.13665e11	+	1.17241e11i	−0.266560	+	0.0608407i
$538$	3.05589e11	+	3.83196e11i	0.157260	+	0.197197i
$539$			1.99152e12i			1.01633i
$540$	−2.36240e11	+	1.88395e11i	−0.119559	+	0.0953451i
$541$	−6.16611e11	+	1.28041e12i	−0.309474	+	0.642628i	−0.996462	−	0.0840395i	$-0.973218\pi$
$541$	−6.16611e11	+	1.28041e12i	−0.309474	+	0.642628i	0.686989	+	0.726668i	$0.258932\pi$
$542$	9.01564e11	−	1.13053e12i	0.448745	−	0.562709i
$543$	1.97683e11	+	1.57647e11i	0.0975818	+	0.0778189i
$544$	1.14012e12	−	5.49052e11i	0.558155	−	0.268793i
$545$	−7.28944e10	−	3.19371e11i	−0.0353924	−	0.155064i
$546$	6.18123e10	−	2.70817e11i	0.0297652	−	0.130410i
$547$	2.11745e12	+	1.01971e12i	1.01128	+	0.487006i	0.864751	−	0.502201i	$-0.167476\pi$
$547$	2.11745e12	+	1.01971e12i	1.01128	+	0.487006i	0.146527	+	0.989207i	$0.453191\pi$
$548$	−4.36307e10	−	9.06002e10i	−0.0206671	−	0.0429157i
$549$	−1.93447e11	−	4.41531e10i	−0.0908839	−	0.0207437i
$550$	−5.94419e11			−0.276988
$551$	−7.09581e11	−	1.33651e11i	−0.327959	−	0.0617718i
$552$	−3.09721e11			−0.141986
$553$	−3.70325e12	−	8.45242e11i	−1.68391	−	0.384342i
$554$	5.63341e11	+	1.16979e12i	0.254084	+	0.527611i
$555$	−1.00802e12	−	4.85437e11i	−0.450973	−	0.217177i
$556$	1.24514e11	−	5.45531e11i	0.0552562	−	0.242093i
$557$	7.82861e11	+	3.42994e12i	0.344617	+	1.50986i	0.789205	+	0.614129i	$0.210493\pi$
$557$	7.82861e11	+	3.42994e12i	0.344617	+	1.50986i	−0.444589	+	0.895735i	$0.646650\pi$
$558$	−4.13786e12	+	1.99269e12i	−1.80685	+	0.870132i
$559$	8.84422e11	+	7.05303e11i	0.383095	+	0.305508i
$560$	−2.12358e12	+	2.66288e12i	−0.912478	+	1.14421i
$561$	4.10235e11	−	8.51861e11i	0.174864	−	0.363108i
$562$	2.45133e12	−	1.95487e12i	1.03654	−	0.826616i
$563$		−	4.15982e12i		−	1.74497i	−0.488644	−	0.872483i	$-0.662508\pi$
$563$		−	4.15982e12i		−	1.74497i	0.488644	−	0.872483i	$-0.337492\pi$
$564$	1.26618e11	+	1.58774e11i	0.0526915	+	0.0660730i
$565$	1.07490e12	−	2.45338e11i	0.443761	−	0.101286i
$566$	3.22122e12	−	7.35221e11i	1.31931	−	0.301123i
$567$	1.51488e12	+	1.89960e12i	0.615538	+	0.771861i
$568$			5.83998e11i			0.235420i
$569$	2.66491e12	−	2.12519e12i	1.06580	−	0.849950i	0.0766831	−	0.997056i	$-0.475567\pi$
$569$	2.66491e12	−	2.12519e12i	1.06580	−	0.849950i	0.989121	+	0.147105i	$0.0469956\pi$
$570$	1.13496e11	−	2.35676e11i	0.0450342	−	0.0935144i
$571$	5.37918e11	−	6.74527e11i	0.211765	−	0.265544i	−0.664593	−	0.747206i	$-0.731395\pi$
$571$	5.37918e11	−	6.74527e11i	0.211765	−	0.265544i	0.876357	+	0.481661i	$0.159966\pi$
$572$	−2.01387e11	−	1.60601e11i	−0.0786592	−	0.0627286i
$573$	−9.37239e11	+	4.51350e11i	−0.363207	+	0.174911i
$574$	−7.54865e10	−	3.30728e11i	−0.0290246	−	0.127165i
$575$	6.77688e10	−	2.96914e11i	0.0258538	−	0.113273i
$576$	1.20778e12	+	5.81634e11i	0.457178	+	0.220165i
$577$	−2.11327e12	−	4.38826e12i	−0.793715	−	1.64817i	−0.761043	−	0.648701i	$-0.775313\pi$
$577$	−2.11327e12	−	4.38826e12i	−0.793715	−	1.64817i	−0.0326720	−	0.999466i	$-0.510402\pi$
$578$	−5.47860e11	−	1.25045e11i	−0.204171	−	0.0466007i
$579$	1.02061e12			0.377406
$580$	−6.55075e11	−	2.85160e11i	−0.240362	−	0.104632i
$581$	6.05665e12			2.20516
$582$	−1.56142e12	−	3.56384e11i	−0.564114	−	0.128755i
$583$	−5.24602e10	−	1.08935e11i	−0.0188071	−	0.0390533i
$584$	2.61603e12	+	1.25982e12i	0.930648	+	0.448177i
$585$	−1.44704e11	+	6.33988e11i	−0.0510832	+	0.223810i
$586$	1.30149e12	+	5.70219e12i	0.455932	+	1.99757i
$587$	−4.34587e12	+	2.09286e12i	−1.51080	+	0.727561i	−0.991870	−	0.127258i	$-0.959382\pi$
$587$	−4.34587e12	+	2.09286e12i	−1.51080	+	0.727561i	−0.518926	+	0.854819i	$0.673668\pi$
$588$	1.70802e11	+	1.36210e11i	0.0589244	+	0.0469907i
$589$	1.18248e12	−	1.48278e12i	0.404832	−	0.507644i
$590$	1.03776e12	−	2.15492e12i	0.352583	−	0.732147i
$591$	−6.44698e11	+	5.14129e11i	−0.217376	+	0.173352i
$592$		−	6.60345e12i		−	2.20965i
$593$	−1.65931e12	−	2.08071e12i	−0.551038	−	0.690980i	0.425834	−	0.904801i	$-0.359981\pi$
$593$	−1.65931e12	−	2.08071e12i	−0.551038	−	0.690980i	−0.976873	+	0.213821i	$0.931409\pi$
$594$	−2.37516e12	+	5.42115e11i	−0.782806	+	0.178670i
$595$	3.93175e12	−	8.97397e11i	1.28606	−	0.293534i
$596$	4.72279e11	+	5.92219e11i	0.153317	+	0.192254i
$597$		−	8.63520e11i		−	0.278220i
$598$	4.54952e11	−	3.62812e11i	0.145482	−	0.116018i
$599$	−1.72575e11	+	3.58355e11i	−0.0547718	+	0.113735i	−0.926558	−	0.376151i	$-0.877247\pi$
$599$	−1.72575e11	+	3.58355e11i	−0.0547718	+	0.113735i	0.871787	+	0.489886i	$0.162962\pi$
$600$	9.79504e10	−	1.22826e11i	0.0308550	−	0.0386909i
$601$	−1.90116e12	−	1.51612e12i	−0.594406	−	0.474023i	0.279481	−	0.960151i	$-0.409837\pi$
$601$	−1.90116e12	−	1.51612e12i	−0.594406	−	0.474023i	−0.873888	+	0.486128i	$0.838409\pi$
$602$	−7.74320e12	+	3.72893e12i	−2.40290	+	1.15718i
$603$	7.61418e11	+	3.33599e12i	0.234528	+	1.02754i
$604$	−1.98870e11	+	8.71305e11i	−0.0607999	+	0.266382i
$605$	1.23365e12	+	5.94095e11i	0.374363	+	0.180284i
$606$	−4.45372e11	−	9.24825e11i	−0.134152	−	0.278569i
$607$	6.32358e12	+	1.44332e12i	1.89066	+	0.431532i	0.999744	−	0.0226300i	$-0.00720396\pi$
$607$	6.32358e12	+	1.44332e12i	1.89066	+	0.431532i	0.890919	+	0.454162i	$0.150061\pi$
$608$	6.40174e11			0.189991
$609$	5.62323e11	−	1.29178e12i	0.165656	−	0.380549i
$610$	3.57485e11			0.104538
$611$	8.96209e11	+	2.04554e11i	0.260150	+	0.0593775i
$612$	4.35610e11	+	9.04554e11i	0.125521	+	0.260647i
$613$	−9.02016e10	−	4.34388e10i	−0.0258013	−	0.0124253i	0.420939	−	0.907089i	$-0.361701\pi$
$613$	−9.02016e10	−	4.34388e10i	−0.0258013	−	0.0124253i	−0.446740	+	0.894664i	$0.647415\pi$
$614$	1.22486e12	−	5.36646e12i	0.347799	−	1.52381i
$615$	−1.82559e10	−	7.99843e10i	−0.00514594	−	0.0225459i
$616$	−4.24797e12	+	2.04571e12i	−1.18869	+	0.572442i
$617$	1.85729e12	+	1.48114e12i	0.515936	+	0.411445i	0.846540	−	0.532324i	$-0.178681\pi$
$617$	1.85729e12	+	1.48114e12i	0.515936	+	0.411445i	−0.330605	+	0.943769i	$0.607253\pi$
$618$	−1.55414e10	+	1.94883e10i	−0.00428590	+	0.00537434i
$619$	−1.30238e12	+	2.70441e12i	−0.356557	+	0.740397i	−0.999678	−	0.0253667i	$-0.991925\pi$
$619$	−1.30238e12	+	2.70441e12i	−0.356557	+	0.740397i	0.643122	+	0.765764i	$0.277639\pi$
$620$	1.46716e12	−	1.17002e12i	0.398763	−	0.318003i
$621$		−	1.24821e12i		−	0.336802i
$622$	−1.26490e11	−	1.58613e11i	−0.0338844	−	0.0424897i
$623$	−3.26399e11	+	7.44985e10i	−0.0868067	+	0.0198131i
$624$	3.86565e11	−	8.82309e10i	0.102068	−	0.0232965i
$625$	−1.80349e12	−	2.26150e12i	−0.472774	−	0.592840i
$626$			4.84211e12i			1.26023i
$627$	3.73964e11	−	2.98227e11i	0.0966332	−	0.0770624i
$628$	−5.57671e11	+	1.15801e12i	−0.143074	+	0.297095i
$629$	−4.87500e12	+	6.11306e12i	−1.24179	+	1.55715i
$630$	−3.86266e12	−	3.08036e12i	−0.976908	−	0.779058i
$631$	−1.13675e12	+	5.47430e11i	−0.285452	+	0.137466i	−0.571131	−	0.820859i	$-0.693495\pi$
$631$	−1.13675e12	+	5.47430e11i	−0.285452	+	0.137466i	0.285679	+	0.958325i	$0.407781\pi$
$632$	−9.13372e11	−	4.00174e12i	−0.227730	−	0.997751i
$633$	−4.30150e11	+	1.88461e12i	−0.106489	+	0.466557i
$634$	−2.67577e12	−	1.28858e12i	−0.657729	−	0.316745i
$635$	2.03103e11	+	4.21748e11i	0.0495718	+	0.102937i
$636$	−1.29308e10	−	2.95137e9i	−0.00313377	−	0.000715263i
$637$	9.88895e11			0.237970
$638$	−3.76105e12	−	4.36310e12i	−0.898702	−	1.04256i
$639$	−1.11898e12			−0.265503
$640$	−4.45999e12	−	1.01796e12i	−1.05081	−	0.239840i
$641$	−4.82935e11	−	1.00282e12i	−0.112987	−	0.234619i	0.836806	−	0.547500i	$-0.184420\pi$
$641$	−4.82935e11	−	1.00282e12i	−0.112987	−	0.234619i	−0.949792	+	0.312881i	$0.898706\pi$
$642$	8.40747e11	+	4.04883e11i	0.195325	+	0.0940636i
$643$	−3.61413e11	+	1.58345e12i	−0.0833785	+	0.365305i	−0.999354	−	0.0359283i	$-0.988561\pi$
$643$	−3.61413e11	+	1.58345e12i	−0.0833785	+	0.365305i	0.915976	+	0.401233i	$0.131418\pi$
$644$	2.23110e11	+	9.77510e11i	0.0511132	+	0.223942i
$645$	−1.87264e12	+	9.01816e11i	−0.426026	+	0.205163i
$646$	−1.42924e12	−	1.13978e12i	−0.322893	−	0.257499i
$647$	−4.61285e11	+	5.78433e11i	−0.103490	+	0.129773i	−0.830879	−	0.556452i	$-0.812162\pi$
$647$	−4.61285e11	+	5.78433e11i	−0.103490	+	0.129773i	0.727389	+	0.686225i	$0.240734\pi$
$648$	−1.13917e12	+	2.36552e12i	−0.253806	+	0.527034i
$649$	3.41938e12	−	2.72686e12i	0.756564	−	0.603340i
$650$			2.95160e11i			0.0648557i
$651$	2.30723e12	+	2.89318e12i	0.503473	+	0.631336i
$652$	1.81867e12	−	4.15098e11i	0.394129	−	0.0899574i
$653$	−3.14636e12	+	7.18136e11i	−0.677172	+	0.154560i	−0.547256	−	0.836965i	$-0.684328\pi$
$653$	−3.14636e12	+	7.18136e11i	−0.677172	+	0.154560i	−0.129915	+	0.991525i	$0.541471\pi$
$654$	−1.80646e11	−	2.26523e11i	−0.0386125	−	0.0484185i
$655$			2.96733e12i			0.629913i
$656$	3.78579e11	−	3.01907e11i	0.0798159	−	0.0636511i
$657$	−2.41390e12	+	5.01252e12i	−0.505447	+	1.04957i
$658$	−4.35442e12	+	5.46027e12i	−0.905553	+	1.13553i
$659$	−3.15689e12	−	2.51754e12i	−0.652041	−	0.519986i	0.240674	−	0.970606i	$-0.422631\pi$
$659$	−3.15689e12	−	2.51754e12i	−0.652041	−	0.519986i	−0.892716	+	0.450620i	$0.851203\pi$
$660$	4.26409e11	−	2.05348e11i	0.0874740	−	0.0421253i
$661$	−1.50416e12	−	6.59016e12i	−0.306470	−	1.34273i	−0.860166	−	0.510014i	$-0.829640\pi$
$661$	−1.50416e12	−	6.59016e12i	−0.306470	−	1.34273i	0.553696	−	0.832719i	$-0.313217\pi$
$662$	−1.64416e12	+	7.20354e12i	−0.332723	+	1.45776i
$663$	−4.22994e11	−	2.03703e11i	−0.0850204	−	0.0409437i
$664$	2.83970e12	+	5.89670e12i	0.566912	+	1.17721i
$665$	1.98904e12	+	4.53986e11i	0.394409	+	0.0900213i
$666$	9.57866e12			1.88656
$667$	2.60817e12	−	1.38123e12i	0.510235	−	0.270208i
$668$	−3.31458e11			−0.0644072
$669$	1.29333e12	+	2.95194e11i	0.249627	+	0.0569757i
$670$	−2.67481e12	−	5.55430e12i	−0.512809	−	1.06486i
$671$	5.88950e11	+	2.83623e11i	0.112157	+	0.0540120i
$672$	−2.77949e11	+	1.21778e12i	−0.0525780	+	0.230359i
$673$	−3.36197e10	−	1.47298e11i	−0.00631723	−	0.0276776i	0.971671	−	0.236337i	$-0.0759470\pi$
$673$	−3.36197e10	−	1.47298e11i	−0.00631723	−	0.0276776i	−0.977988	+	0.208660i	$0.933090\pi$
$674$	5.51397e12	−	2.65539e12i	1.02919	−	0.495631i
$675$	4.95000e11	+	3.94749e11i	0.0917779	+	0.0731905i
$676$	9.13200e11	−	1.14512e12i	0.168192	−	0.210906i
$677$	−3.04695e12	+	6.32706e12i	−0.557464	+	1.15759i	0.411735	+	0.911304i	$0.364923\pi$
$677$	−3.04695e12	+	6.32706e12i	−0.557464	+	1.15759i	−0.969198	+	0.246281i	$0.920791\pi$
$678$	7.62400e11	−	6.07994e11i	0.138564	−	0.110501i
$679$		−	1.24915e13i		−	2.25528i
$680$	2.71713e12	+	3.40717e12i	0.487326	+	0.611087i
$681$	−3.58560e11	+	8.18391e10i	−0.0638852	+	0.0145814i
$682$	1.47508e13	−	3.36678e12i	2.61088	−	0.595916i
$683$	5.16899e11	+	6.48171e11i	0.0908892	+	0.113971i	0.825197	−	0.564846i	$-0.191064\pi$
$683$	5.16899e11	+	6.48171e11i	0.0908892	+	0.113971i	−0.734307	+	0.678817i	$0.762493\pi$
$684$			5.07905e11i			0.0887218i
$685$	6.53884e11	−	5.21455e11i	0.113473	−	0.0904918i
$686$	6.22253e11	−	1.29212e12i	0.107277	−	0.222764i
$687$	4.27335e11	−	5.35862e11i	0.0731920	−	0.0917799i
$688$	−9.59112e12	−	7.64866e12i	−1.63200	−	1.30148i
$689$	−5.40918e10	+	2.60493e10i	−0.00914419	+	0.00440361i
$690$	2.37915e11	+	1.04237e12i	0.0399577	+	0.175066i
$691$	−3.46289e11	+	1.51719e12i	−0.0577813	+	0.253156i	−0.995567	−	0.0940594i	$-0.970016\pi$
$691$	−3.46289e11	+	1.51719e12i	−0.0577813	+	0.253156i	0.937785	+	0.347216i	$0.112873\pi$
$692$	1.97081e12	+	9.49090e11i	0.326713	+	0.157337i
$693$	−3.91974e12	−	8.13943e12i	−0.645592	−	1.34058i
$694$	8.88676e12	+	2.02834e12i	1.45421	+	0.331913i
$695$	4.65388e12			0.756629
$696$	1.52131e12	−	5.81860e10i	0.245740	−	0.00939890i
$697$	−5.73348e11			−0.0920176
$698$	−6.76733e12	−	1.54460e12i	−1.07912	−	0.246301i
$699$	−1.13344e12	−	2.35361e12i	−0.179577	−	0.372895i
$700$	−4.58210e11	−	2.20662e11i	−0.0721312	−	0.0347365i
$701$	2.14260e12	−	9.38734e12i	0.335127	−	1.46829i	−0.473931	−	0.880562i	$-0.657166\pi$
$701$	2.14260e12	−	9.38734e12i	0.335127	−	1.46829i	0.809059	−	0.587728i	$-0.199977\pi$
$702$	2.69189e11	+	1.17939e12i	0.0418350	+	0.183291i
$703$	−3.56380e12	+	1.71624e12i	−0.550319	+	0.265020i
$704$	−3.45277e12	−	2.75349e12i	−0.529774	−	0.422481i
$705$	−1.05309e12	+	1.32053e12i	−0.160551	+	0.201325i
$706$	−7.74910e11	+	1.60912e12i	−0.117390	+	0.243762i
$707$	6.25935e12	−	4.99166e12i	0.942197	−	0.751377i
$708$		−	4.79766e11i		−	0.0717595i
$709$	6.23928e12	+	7.82381e12i	0.927313	+	1.16281i	0.986367	+	0.164559i	$0.0526200\pi$
$709$	6.23928e12	+	7.82381e12i	0.927313	+	1.16281i	−0.0590545	+	0.998255i	$0.518809\pi$
$710$	1.96546e12	−	4.48603e11i	0.290269	−	0.0662521i
$711$	7.66764e12	−	1.75009e12i	1.12525	−	0.256831i
$712$	−2.25566e11	−	2.82850e11i	−0.0328937	−	0.0412474i
$713$			7.75193e12i			1.12333i
$714$	2.78870e12	−	2.22392e12i	0.401569	−	0.320241i
$715$	9.29523e11	−	1.93017e12i	0.133010	−	0.276197i
$716$	−1.14916e12	+	1.44100e12i	−0.163408	+	0.204907i
$717$	−7.16729e11	−	5.71572e11i	−0.101279	−	0.0807672i
$718$	5.07206e12	−	2.44258e12i	0.712237	−	0.342995i
$719$	2.18025e12	+	9.55230e12i	0.304247	+	1.33299i	0.863648	+	0.504096i	$0.168174\pi$
$719$	2.18025e12	+	9.55230e12i	0.304247	+	1.33299i	−0.559401	+	0.828897i	$0.688969\pi$
$720$	1.56924e12	−	6.87529e12i	0.217617	−	0.953443i
$721$	−1.75160e11	−	8.43528e10i	−0.0241395	−	0.0116249i
$722$	3.20157e12	+	6.64812e12i	0.438475	+	0.910504i
$723$	1.95654e12	+	4.46568e11i	0.266297	+	0.0607807i
$724$	8.84503e11			0.119640
$725$	−2.77092e11	+	1.47114e12i	−0.0372479	+	0.197757i
$726$	1.21104e12			0.161787
$727$	6.54121e12	+	1.49299e12i	0.868467	+	0.198222i	0.633464	−	0.773772i	$-0.281633\pi$
$727$	6.54121e12	+	1.49299e12i	0.868467	+	0.198222i	0.235004	+	0.971994i	$0.424490\pi$
$728$	1.01580e12	+	2.10934e12i	0.134035	+	0.278327i
$729$	−3.30613e12	−	1.59215e12i	−0.433557	−	0.208790i
$730$	2.23041e12	−	9.77205e12i	0.290691	−	1.27360i
$731$	3.23223e12	+	1.41613e13i	0.418672	+	1.83432i
$732$	6.46061e10	−	3.11127e10i	0.00831714	−	0.00400532i
$733$	−8.57707e12	−	6.83999e12i	−1.09742	−	0.875160i	−0.104565	−	0.994518i	$-0.533345\pi$
$733$	−8.57707e12	−	6.83999e12i	−1.09742	−	0.875160i	−0.992851	+	0.119358i	$0.961916\pi$
$734$	−1.08876e13	+	1.36526e13i	−1.38452	+	1.73613i
$735$	−7.88355e11	+	1.63704e12i	−0.0996389	+	0.206902i
$736$	−2.04577e12	+	1.63145e12i	−0.256984	+	0.204938i
$737$		−	1.12728e13i		−	1.40743i
$738$	4.37932e11	+	5.49150e11i	0.0543442	+	0.0681455i
$739$	−2.39732e11	+	5.47172e10i	−0.0295683	+	0.00674876i	−0.237279	−	0.971441i	$-0.576256\pi$
$739$	−2.39732e11	+	5.47172e10i	−0.0295683	+	0.00674876i	0.207711	+	0.978190i	$0.433399\pi$
$740$	−3.81572e12	+	8.70912e11i	−0.467771	+	0.106766i
$741$	−1.48085e11	−	1.85693e11i	−0.0180439	−	0.0226263i
$742$		−	4.56128e11i		−	0.0552419i
$743$	9.45739e12	−	7.54202e12i	1.13847	−	0.907900i	0.141837	−	0.989890i	$-0.454699\pi$
$743$	9.45739e12	−	7.54202e12i	1.13847	−	0.907900i	0.996633	+	0.0819899i	$0.0261275\pi$
$744$	−1.73501e12	+	3.60278e12i	−0.207598	+	0.431082i
$745$	−3.92796e12	+	4.92551e12i	−0.467158	+	0.585798i
$746$	−1.16686e13	−	9.30538e12i	−1.37941	−	1.10004i
$747$	−1.12985e13	+	5.44108e12i	−1.32763	+	0.639355i
$748$	−7.35994e11	−	3.22460e12i	−0.0859640	−	0.376633i
$749$	−1.61954e12	+	7.09568e12i	−0.188029	+	0.823808i
$750$	−2.91670e12	−	1.40461e12i	−0.336602	−	0.162099i
$751$	4.45453e11	+	9.24994e11i	0.0511002	+	0.106111i	0.924955	−	0.380075i	$-0.124102\pi$
$751$	4.45453e11	+	9.24994e11i	0.0511002	+	0.106111i	−0.873855	+	0.486186i	$0.838388\pi$
$752$	−9.71895e12	−	2.21829e12i	−1.10825	−	0.252951i
$753$	2.08739e11			0.0236606
$754$	−2.16651e12	+	1.86756e12i	−0.244112	+	0.210428i
$755$	−7.43303e12			−0.832539
$756$	−2.03215e12	−	4.63824e11i	−0.226259	−	0.0516422i
$757$	−1.65826e12	−	3.44342e12i	−0.183536	−	0.381117i	0.788818	−	0.614626i	$-0.210693\pi$
$757$	−1.65826e12	−	3.44342e12i	−0.183536	−	0.381117i	−0.972354	+	0.233510i	$0.924979\pi$
$758$	−3.53112e12	−	1.70050e12i	−0.388509	−	0.187096i
$759$	−4.35044e11	+	1.90605e12i	−0.0475823	+	0.208472i
$760$	4.90579e11	+	2.14937e12i	0.0533394	+	0.233695i
$761$	−1.20235e13	+	5.79022e12i	−1.29957	+	0.625841i	−0.950345	−	0.311197i	$-0.899270\pi$
$761$	−1.20235e13	+	5.79022e12i	−1.29957	+	0.625841i	−0.349227	+	0.937038i	$0.613556\pi$
$762$	3.23692e11	+	2.58135e11i	0.0347804	+	0.0277364i
$763$	1.40894e12	−	1.76676e12i	0.150499	−	0.188720i
$764$	−1.57891e12	+	3.27864e12i	−0.167663	+	0.348156i
$765$	−6.52839e12	+	5.20622e12i	−0.689175	+	0.549599i
$766$			1.26788e13i			1.33060i
$767$	−1.35403e12	−	1.69790e12i	−0.141270	−	0.177147i
$768$	−2.33443e12	+	5.32819e11i	−0.242134	+	0.0552655i
$769$	8.64451e12	−	1.97305e12i	0.891398	−	0.203456i	0.247793	−	0.968813i	$-0.420295\pi$
$769$	8.64451e12	−	1.97305e12i	0.891398	−	0.203456i	0.643606	+	0.765357i	$0.277438\pi$
$770$	1.01480e13	+	1.27252e13i	1.04033	+	1.30454i
$771$		−	9.75323e11i		−	0.0994040i
$772$	2.79138e12	−	2.22605e12i	0.282840	−	0.225558i
$773$	5.95183e12	−	1.23591e13i	0.599574	−	1.24503i	−0.351536	−	0.936175i	$-0.614340\pi$
$773$	5.95183e12	−	1.23591e13i	0.599574	−	1.24503i	0.951110	−	0.308854i	$-0.0999454\pi$
$774$	1.10948e13	−	1.39124e13i	1.11118	−	1.39338i
$775$	−3.07418e12	−	2.45157e12i	−0.306105	−	0.244111i
$776$	1.21616e13	−	5.85671e12i	1.20396	−	0.579797i
$777$	−1.71740e12	−	7.52442e12i	−0.169035	−	0.740591i
$778$	−3.29119e12	+	1.44196e13i	−0.322065	+	1.41106i
$779$	−2.61328e11	−	1.25849e11i	−0.0254254	−	0.0122442i
$780$	−1.01966e11	−	2.11735e11i	−0.00986347	−	0.0204817i
$781$	3.59397e12	+	8.20301e11i	0.345657	+	0.0788940i
$782$	7.47201e12			0.714508
$783$	2.34495e11	+	6.13103e12i	0.0222949	+	0.582915i
$784$	−1.07241e13			−1.01377
$785$	−1.04219e13	−	2.37872e12i	−0.979561	−	0.223578i
$786$	1.13871e12	+	2.36457e12i	0.106418	+	0.220978i
$787$	−1.12394e13	−	5.41261e12i	−1.04438	−	0.502945i	−0.168611	−	0.985683i	$-0.553928\pi$
$787$	−1.12394e13	−	5.41261e12i	−1.04438	−	0.502945i	−0.875765	+	0.482738i	$0.839642\pi$
$788$	−6.41886e11	+	2.81229e12i	−0.0593048	+	0.259831i
$789$	−9.81952e11	−	4.30221e12i	−0.0902077	−	0.395226i
$790$	−1.27663e13	+	6.14794e12i	−1.16612	+	0.561575i
$791$	5.94633e12	+	4.74204e12i	0.540076	+	0.430696i
$792$	6.08667e12	−	7.63245e12i	0.549688	−	0.689287i
$793$	1.40834e11	−	2.92445e11i	0.0126467	−	0.0262612i
$794$	9.42447e12	−	7.51576e12i	0.841520	−	0.671090i
$795$		−	1.10311e11i		−	0.00979418i
$796$	−1.88342e12	−	2.36173e12i	−0.166279	−	0.208507i
$797$	−4.78328e12	+	1.09175e12i	−0.419917	+	0.0958433i	−0.427258	−	0.904130i	$-0.640520\pi$
$797$	−4.78328e12	+	1.09175e12i	−0.419917	+	0.0958433i	0.00734112	+	0.999973i	$0.497663\pi$
$798$	1.75922e12	−	4.01530e11i	0.153570	−	0.0350513i
$799$	7.35954e12	+	9.22857e12i	0.638837	+	0.801077i
$800$		−	1.32724e12i		−	0.114563i
$801$	5.41962e11	−	4.32201e11i	0.0465182	−	0.0370970i
$802$	−8.02707e12	+	1.66684e13i	−0.685129	+	1.42268i
$803$	1.14276e13	−	1.43297e13i	0.969916	−	1.21624i
$804$	−9.66806e11	−	7.71002e11i	−0.0815994	−	0.0650733i
$805$	−7.51323e12	+	3.61818e12i	−0.630588	+	0.303675i
$806$	−1.67178e12	−	7.32457e12i	−0.139532	−	0.611328i
$807$	−1.81951e11	+	7.97179e11i	−0.0151016	+	0.0661645i
$808$	7.79457e12	+	3.75367e12i	0.643341	+	0.309817i
$809$	−5.70789e12	−	1.18525e13i	−0.468497	−	0.972844i	−0.992627	−	0.121206i	$-0.961324\pi$
$809$	−5.70789e12	−	1.18525e13i	−0.468497	−	0.972844i	0.524130	−	0.851638i	$-0.324390\pi$
$810$	8.83626e12	+	2.01682e12i	0.721250	+	0.164621i
$811$	2.25454e13			1.83005			0.915026	−	0.403394i	$-0.132170\pi$
$811$	2.25454e13			1.83005			0.915026	+	0.403394i	$0.132170\pi$
$812$	−1.27953e12	−	4.75949e12i	−0.103288	−	0.384201i
$813$	2.41236e12			0.193658
$814$	−3.07649e13	−	7.02189e12i	−2.45610	−	0.560588i
$815$	6.73166e12	+	1.39784e13i	0.534457	+	1.10981i
$816$	4.58716e12	+	2.20906e12i	0.362192	+	0.174422i
$817$	−1.63516e12	+	7.16409e12i	−0.128399	+	0.562551i
$818$	9.80154e11	+	4.29434e12i	0.0765428	+	0.335356i
$819$	−4.04165e12	+	1.94636e12i	−0.313893	+	0.151163i
$820$	−2.24383e11	−	1.78939e11i	−0.0173311	−	0.0138211i
$821$	4.56401e12	−	5.72308e12i	0.350592	−	0.439628i	−0.574999	−	0.818154i	$-0.694997\pi$
$821$	4.56401e12	−	5.72308e12i	0.350592	−	0.439628i	0.925591	+	0.378526i	$0.123569\pi$
$822$	3.20949e11	−	6.66457e11i	0.0245196	−	0.0509154i
$823$	9.41669e10	−	7.50956e10i	0.00715483	−	0.00570579i	−0.619906	−	0.784676i	$-0.712829\pi$
$823$	9.41669e10	−	7.50956e10i	0.00715483	−	0.00570579i	0.627061	+	0.778970i	$0.284258\pi$
$824$		−	2.10084e11i		−	0.0158752i
$825$	−6.18297e11	−	7.75320e11i	−0.0464681	−	0.0582691i
$826$	1.60856e13	−	3.67142e12i	1.20234	−	0.274425i
$827$	−1.18836e13	+	2.71236e12i	−0.883433	+	0.201638i	−0.640088	−	0.768302i	$-0.721102\pi$
$827$	−1.18836e13	+	2.71236e12i	−0.883433	+	0.201638i	−0.243346	+	0.969940i	$0.578245\pi$
$828$	−1.29437e12	−	1.62308e12i	−0.0957020	−	0.120006i
$829$		−	9.19792e12i		−	0.676386i	−0.941077	−	0.338193i	$-0.890184\pi$
$829$		−	9.19792e12i		−	0.676386i	0.941077	−	0.338193i	$-0.109816\pi$
$830$	1.76641e13	−	1.40867e13i	1.29193	−	1.03028i
$831$	−9.39824e11	+	1.95157e12i	−0.0683663	+	0.141964i
$832$	−1.36725e12	+	1.71448e12i	−0.0989223	+	0.124045i
$833$	9.92768e12	+	7.91706e12i	0.714406	+	0.569720i
$834$	3.70851e12	−	1.78593e12i	0.265431	−	0.127825i
$835$	−6.13434e11	−	2.68763e12i	−0.0436695	−	0.191329i
$836$	3.72333e11	−	1.63130e12i	0.0263635	−	0.115506i
$837$	−1.45195e13	−	6.99225e12i	−1.02256	−	0.492439i
$838$	5.32327e12	+	1.10539e13i	0.372890	+	0.774314i
$839$	−2.30214e13	−	5.25449e12i	−1.60400	−	0.366102i	−0.675476	−	0.737382i	$-0.736062\pi$
$839$	−2.30214e13	−	5.25449e12i	−1.60400	−	0.366102i	−0.928521	+	0.371280i	$0.878919\pi$
$840$	−4.30165e12			−0.298111
$841$	−1.25515e13	+	7.27439e12i	−0.865196	+	0.501435i
$842$	2.90288e13			1.99033
$843$	5.09959e12	+	1.16395e12i	0.347785	+	0.0793797i
$844$	2.93404e12	+	6.09261e12i	0.199033	+	0.413297i
$845$	1.09753e13	+	5.28540e12i	0.740559	+	0.356634i
$846$	3.21774e12	−	1.40978e13i	0.215966	−	0.946207i
$847$	2.10182e12	+	9.20866e12i	0.140320	+	0.614782i
$848$	5.86600e11	−	2.82491e11i	0.0389547	−	0.0187596i
$849$	4.30958e12	+	3.43678e12i	0.284676	+	0.227021i
$850$	−2.36305e12	+	2.96317e12i	−0.155270	+	0.194702i
$851$	7.01491e12	−	1.45666e13i	0.458500	−	0.952085i
$852$	3.16163e11	−	2.52132e11i	0.0205557	−	0.0163927i
$853$		−	1.11906e13i		−	0.723741i	−0.932228	−	0.361871i	$-0.882138\pi$
$853$		−	1.11906e13i		−	0.723741i	0.932228	−	0.361871i	$-0.117862\pi$
$854$	1.53754e12	+	1.92802e12i	0.0989162	+	0.124037i
$855$	−4.11835e12	+	9.39987e11i	−0.263558	+	0.0601553i
$856$	−7.66762e12	+	1.75009e12i	−0.488123	+	0.111411i
$857$	−3.48857e12	−	4.37453e12i	−0.220919	−	0.277024i	0.659004	−	0.752139i	$-0.270978\pi$
$857$	−3.48857e12	−	4.37453e12i	−0.220919	−	0.277024i	−0.879924	+	0.475115i	$0.842406\pi$
$858$		−	1.89479e12i		−	0.119363i
$859$	−5.99821e12	+	4.78341e12i	−0.375882	+	0.299756i	−0.793149	−	0.609028i	$-0.791560\pi$
$859$	−5.99821e12	+	4.78341e12i	−0.375882	+	0.299756i	0.417266	+	0.908784i	$0.362988\pi$
$860$	−3.15473e12	+	6.55086e12i	−0.196661	+	0.408372i
$861$	3.52860e11	−	4.42473e11i	0.0218821	−	0.0274393i
$862$	5.56760e12	+	4.44001e12i	0.343467	+	0.273906i
$863$	−1.26163e13	+	6.07569e12i	−0.774254	+	0.372861i	−0.778916	−	0.627128i	$-0.784230\pi$
$863$	−1.26163e13	+	6.07569e12i	−0.774254	+	0.372861i	0.00466195	+	0.999989i	$0.498516\pi$
$864$	−1.21045e12	−	5.30334e12i	−0.0738985	−	0.323771i
$865$	−4.04830e12	+	1.77368e13i	−0.245867	+	1.07721i
$866$	1.00238e12	+	4.82721e11i	0.0605623	+	0.0291653i
$867$	−4.06767e11	−	8.44660e11i	−0.0244489	−	0.0507687i
$868$	1.26205e13	+	2.88056e12i	0.754639	+	0.172241i
$869$	−2.59100e13			−1.54127
$870$	−1.36443e12	−	5.07531e12i	−0.0807451	−	0.300349i
$871$	−5.59752e12			−0.329545
$872$	2.38069e12	+	5.43378e11i	0.139437	+	0.0318257i
$873$	1.12219e13	+	2.33025e13i	0.653886	+	1.35781i
$874$	3.40569e12	+	1.64009e12i	0.197426	+	0.0950752i
$875$	5.61848e12	−	2.46162e13i	0.324028	−	1.41966i
$876$	−4.47395e11	−	1.96016e12i	−0.0256698	−	0.112467i
$877$	2.24977e13	−	1.08343e13i	1.28422	−	0.618449i	0.337750	−	0.941236i	$-0.390334\pi$
$877$	2.24977e13	−	1.08343e13i	1.28422	−	0.618449i	0.946472	+	0.322787i	$0.104620\pi$
$878$	1.02317e13	+	8.15949e12i	0.581061	+	0.463380i
$879$	−6.08378e12	+	7.62881e12i	−0.343735	+	0.431030i
$880$	−1.00802e13	+	2.09318e13i	−0.566628	+	1.17662i
$881$	2.40342e13	−	1.91666e13i	1.34412	−	1.07190i	0.353473	−	0.935445i	$-0.385001\pi$
$881$	2.40342e13	−	1.91666e13i	1.34412	−	1.07190i	0.990646	−	0.136455i	$-0.0435709\pi$
$882$		−	1.55558e13i		−	0.865536i
$883$	1.87622e12	+	2.35270e12i	0.103863	+	0.130240i	0.831046	−	0.556203i	$-0.187742\pi$
$883$	1.87622e12	+	2.35270e12i	0.103863	+	0.130240i	−0.727183	+	0.686443i	$0.759171\pi$
$884$	−1.60118e12	+	3.65460e11i	−0.0881872	+	0.0201282i
$885$	3.89018e12	−	8.87909e11i	0.213170	−	0.0486546i
$886$	−1.64025e13	−	2.05680e13i	−0.894247	−	1.12135i
$887$			1.35423e13i			0.734577i	0.930107	+	0.367289i	$0.119714\pi$
$887$			1.35423e13i			0.734577i	−0.930107	+	0.367289i	$0.880286\pi$
$888$	6.52049e12	−	5.19992e12i	0.351902	−	0.280633i
$889$	−1.40106e12	+	2.90934e12i	−0.0752315	+	0.156220i
$890$	−7.78668e11	+	9.76419e11i	−0.0416004	+	0.0521652i
$891$	1.29575e13	+	1.03332e13i	0.688764	+	0.549271i
$892$	4.18110e12	−	2.01351e12i	0.221130	−	0.106491i
$893$	1.32877e12	+	5.82173e12i	0.0699228	+	0.306352i
$894$	−1.23989e12	+	5.43232e12i	−0.0649180	+	0.284424i
$895$	−1.38111e13	−	6.65109e12i	−0.719492	−	0.346489i
$896$	−1.36923e13	−	2.84323e13i	−0.709725	−	1.47376i
$897$	9.46455e11	+	2.16022e11i	0.0488128	+	0.0111412i
$898$	1.19288e13			0.612145
$899$	−1.45632e12	−	3.80765e13i	−0.0743599	−	1.94419i
$900$	1.05301e12			0.0534986
$901$	−7.51587e11	−	1.71545e11i	−0.0379942	−	0.00867193i
$902$	−1.00399e12	−	2.08481e12i	−0.0505010	−	0.104866i
$903$	−1.29180e13	−	6.22098e12i	−0.646548	−	0.311361i
$904$	−1.82883e12	+	8.01262e12i	−0.0910784	+	0.399040i
$905$	1.63696e12	+	7.17199e12i	0.0811185	+	0.355403i
$906$	−5.92313e12	+	2.85243e12i	−0.292061	+	0.140649i
$907$	−4.68542e12	−	3.73650e12i	−0.229888	−	0.183329i	0.501771	−	0.865001i	$-0.332682\pi$
$907$	−4.68542e12	−	3.73650e12i	−0.229888	−	0.183329i	−0.731659	+	0.681671i	$0.761253\pi$
$908$	−8.02164e11	+	1.00588e12i	−0.0391631	+	0.0491090i
$909$	−7.19231e12	+	1.49350e13i	−0.349406	+	0.725550i
$910$	6.31873e12	−	5.03902e12i	0.305452	−	0.243590i
$911$			3.02546e13i			1.45532i	0.685936	+	0.727662i	$0.259393\pi$
$911$			3.02546e13i			1.45532i	−0.685936	+	0.727662i	$0.740607\pi$
$912$	1.60591e12	+	2.01375e12i	0.0768679	+	0.0963893i
$913$	4.02775e13	−	9.19308e12i	1.91842	−	0.437867i
$914$	−1.52464e13	+	3.47990e12i	−0.722621	+	0.164934i
$915$	3.71845e11	+	4.66279e11i	0.0175375	+	0.0219913i
$916$		−	2.39764e12i		−	0.112526i
$917$	−1.60037e13	+	1.27625e13i	−0.747410	+	0.596039i
$918$	−6.73975e12	+	1.39952e13i	−0.313222	+	0.650412i
$919$	−5.18106e12	+	6.49684e12i	−0.239607	+	0.300457i	−0.887066	−	0.461643i	$-0.847260\pi$
$919$	−5.18106e12	+	6.49684e12i	−0.239607	+	0.300457i	0.647459	+	0.762100i	$0.275832\pi$
$920$	−7.04526e12	−	5.61840e12i	−0.324229	−	0.258564i
$921$	8.27371e12	−	3.98441e12i	0.378906	−	0.182472i
$922$	8.17077e12	+	3.57985e13i	0.372369	+	1.63146i
$923$	4.07323e11	−	1.78460e12i	0.0184727	−	0.0809343i
$924$	2.94149e12	+	1.41655e12i	0.132753	+	0.0639304i
$925$	3.55818e12	+	7.38864e12i	0.159805	+	0.331838i
$926$	−2.32102e13	−	5.29758e12i	−1.03736	−	0.236771i
$927$	4.02537e11			0.0179039
$928$	9.74206e12	−	8.39778e12i	0.431206	−	0.371705i
$929$	−3.92166e13			−1.72742			−0.863712	−	0.503986i	$-0.831866\pi$
$929$	−3.92166e13			−1.72742			−0.863712	+	0.503986i	$0.831866\pi$
$930$	1.34580e13	+	3.07170e12i	0.589939	+	0.134650i
$931$	2.78719e12	+	5.78765e12i	0.121588	+	0.252481i
$932$	−8.23339e12	−	3.96499e12i	−0.357443	−	0.172135i
$933$	7.53135e10	−	3.29970e11i	0.00325391	−	0.0142563i
$934$	−5.90443e12	−	2.58690e13i	−0.253873	−	1.11229i
$935$	2.47846e13	−	1.19356e13i	1.06054	−	0.510731i
$936$	−3.78991e12	−	3.02235e12i	−0.161394	−	0.128708i
$937$	6.86883e11	−	8.61323e11i	0.0291108	−	0.0365038i	−0.767063	−	0.641572i	$-0.778283\pi$
$937$	6.86883e11	−	8.61323e11i	0.0291108	−	0.0365038i	0.796174	+	0.605068i	$0.206854\pi$
$938$	1.84516e13	−	3.83151e13i	0.778253	−	1.61606i
$939$	−6.31572e12	+	5.03662e12i	−0.265111	+	0.211419i
$940$			5.90853e12i			0.246833i
$941$	6.33705e11	+	7.94641e11i	0.0263472	+	0.0330383i	0.794831	−	0.606831i	$-0.207560\pi$
$941$	6.33705e11	+	7.94641e11i	0.0263472	+	0.0330383i	−0.768483	+	0.639870i	$0.778988\pi$
$942$	−9.21765e12	+	2.10387e12i	−0.381409	+	0.0870541i
$943$	1.15583e12	−	2.63811e11i	0.0475983	−	0.0108640i
$944$	1.46838e13	+	1.84129e13i	0.601817	+	0.754654i
$945$		−	1.73361e13i		−	0.707143i
$946$	−4.58333e13	+	3.65509e13i	−1.86068	+	1.48384i
$947$	5.61903e12	−	1.16680e13i	0.227032	−	0.471436i	−0.756071	−	0.654489i	$-0.772884\pi$
$947$	5.61903e12	−	1.16680e13i	0.227032	−	0.471436i	0.983103	+	0.183053i	$0.0585980\pi$
$948$	−1.77212e12	+	2.22217e12i	−0.0712615	+	0.0893591i
$949$	−7.11546e12	−	5.67439e12i	−0.284777	−	0.227102i
$950$	−1.72747e12	+	8.31906e11i	−0.0688105	+	0.0331374i
$951$	−1.10252e12	−	4.83043e12i	−0.0437091	−	0.191502i
$952$	−6.68948e12	+	2.93085e13i	−0.263953	+	1.15645i
$953$	−3.07696e13	−	1.48179e13i	−1.20838	−	0.581926i	−0.282328	−	0.959318i	$-0.591107\pi$
$953$	−3.07696e13	−	1.48179e13i	−1.20838	−	0.581926i	−0.926054	+	0.377392i	$0.876821\pi$
$954$	4.09769e11	+	8.50894e11i	0.0160166	+	0.0332589i
$955$	−2.95070e13	−	6.73478e12i	−1.14792	−	0.262004i
$956$	−3.20690e12			−0.124173
$957$	1.77880e12	−	9.44401e12i	0.0685525	−	0.363959i
$958$	−2.60051e13			−0.997500
$959$	5.62472e12	+	1.28381e12i	0.214742	+	0.0490135i
$960$	−1.74820e12	−	3.63018e12i	−0.0664311	−	0.137946i
$961$	6.63517e13	+	3.19533e13i	2.50956	+	1.20854i
$962$	−3.48674e12	+	1.52764e13i	−0.131260	+	0.575086i
$963$	−3.35330e12	−	1.46917e13i	−0.125647	−	0.550497i
$964$	6.32515e12	−	3.04603e12i	0.235898	−	0.113602i
$965$	2.32160e13	+	1.85141e13i	0.861816	+	0.687275i
$966$	−4.59856e12	+	5.76641e12i	−0.169912	+	0.213063i
$967$	−3.76647e11	+	7.82116e11i	−0.0138521	+	0.0287642i	−0.907780	−	0.419446i	$-0.862224\pi$
$967$	−3.76647e11	+	7.82116e11i	−0.0138521	+	0.0287642i	0.893928	+	0.448211i	$0.147939\pi$
$968$	−7.98001e12	+	6.36385e12i	−0.292122	+	0.232960i
$969$		−	3.04977e12i		−	0.111125i
$970$	−2.90529e13	−	3.64312e13i	−1.05370	−	1.32130i
$971$	−8.95328e11	+	2.04353e11i	−0.0323218	+	0.00737724i	−0.238651	−	0.971105i	$-0.576705\pi$
$971$	−8.95328e11	+	2.04353e11i	−0.0323218	+	0.00737724i	0.206329	+	0.978483i	$0.433848\pi$
$972$	6.41472e12	−	1.46412e12i	0.230505	−	0.0526112i
$973$	2.00164e13	+	2.50997e13i	0.715941	+	0.897762i
$974$			6.63016e12i			0.236053i
$975$	−3.84987e11	+	3.07017e11i	−0.0136435	+	0.0108803i
$976$	−1.52727e12	+	3.17142e12i	−0.0538757	+	0.111874i
$977$	3.37055e13	−	4.22653e13i	1.18352	−	1.48408i	0.345521	−	0.938411i	$-0.387702\pi$
$977$	3.37055e13	−	4.22653e13i	1.18352	−	1.48408i	0.837998	−	0.545674i	$-0.183726\pi$
$978$	1.07284e13	+	8.55565e12i	0.374983	+	0.299039i
$979$	−2.05752e12	+	9.90850e11i	−0.0715850	+	0.0344735i
$980$	1.41437e12	+	6.19677e12i	0.0489831	+	0.214609i
$981$	−1.04115e12	+	4.56159e12i	−0.0358925	+	0.157255i
$982$	−4.70659e13	−	2.26658e13i	−1.61512	−	0.777801i
$983$	1.58631e13	+	3.29401e13i	0.541873	+	1.12521i	0.974655	+	0.223712i	$0.0718174\pi$
$983$	1.58631e13	+	3.29401e13i	0.541873	+	1.12521i	−0.432783	+	0.901498i	$0.642468\pi$
$984$	5.96228e11	+	1.36085e11i	0.0202738	+	0.00462735i
$985$	−2.39914e13			−0.812068
$986$	−3.67015e13	+	1.40373e12i	−1.23663	+	0.0472975i
$987$	−1.16513e13			−0.390795
$988$	−8.10026e11	−	1.84883e11i	−0.0270453	−	0.00617292i
$989$	−1.30319e13	−	2.70610e13i	−0.433136	−	0.899416i
$990$	−3.03627e13	−	1.46219e13i	−1.00457	−	0.483777i
$991$	−4.53482e12	+	1.98684e13i	−0.149358	+	0.654381i	0.843706	+	0.536806i	$0.180369\pi$
$991$	−4.53482e12	+	1.98684e13i	−0.149358	+	0.654381i	−0.993064	+	0.117575i	$0.962488\pi$
$992$	7.51746e12	+	3.29361e13i	0.246473	+	1.07987i
$993$	−1.11060e13	+	5.34837e12i	−0.362482	+	0.174562i
$994$	1.08729e13	+	8.67085e12i	0.353270	+	0.281723i
$995$	1.56644e13	−	1.96426e13i	0.506653	−	0.635322i
$996$	1.96634e12	−	4.08315e12i	0.0633128	−	0.131470i
$997$	−1.94326e13	+	1.54969e13i	−0.622876	+	0.496727i	−0.883325	−	0.468760i	$-0.844701\pi$
$997$	−1.94326e13	+	1.54969e13i	−0.622876	+	0.496727i	0.260449	+	0.965488i	$0.416129\pi$
$998$		−	1.75641e13i		−	0.560453i
$999$	2.09562e13	+	2.62782e13i	0.665682	+	0.834739i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.10.e.a.4.16	✓	132
29.22	even	14	inner	29.10.e.a.22.16	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.10.e.a.4.16	✓	132	1.1	even	1	trivial
29.10.e.a.22.16	yes	132	29.22	even	14	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	29.e (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(25.0876 + 5.72609i) q^{2} +(18.6267 + 38.6787i) q^{3} +(135.306 + 65.1598i) q^{4} +(-277.936 + 1217.72i) q^{5} +(245.822 + 1077.02i) q^{6} +(-7762.93 + 3738.43i) q^{7} +(-7279.40 - 5805.13i) q^{8} +(11123.1 - 13947.9i) q^{9} +O(q^{10})\)	\(q+(25.0876 + 5.72609i) q^{2} +(18.6267 + 38.6787i) q^{3} +(135.306 + 65.1598i) q^{4} +(-277.936 + 1217.72i) q^{5} +(245.822 + 1077.02i) q^{6} +(-7762.93 + 3738.43i) q^{7} +(-7279.40 - 5805.13i) q^{8} +(11123.1 - 13947.9i) q^{9} +(-13945.5 + 28958.2i) q^{10} +(-45950.1 + 36644.0i) q^{11} +6447.17i q^{12} +(18195.7 + 22816.6i) q^{13} +(-216160. + 49337.2i) q^{14} +(-52276.9 + 11931.9i) q^{15} +(-197323. - 247435. i) q^{16} +374734. i q^{17} +(358918. - 286228. i) q^{18} +(-82253.5 + 170801. i) q^{19} +(-116953. + 146654. i) q^{20} +(-289195. - 230626. i) q^{21} +(-1.36261e6 + 656197. i) q^{22} +(-172424. - 755438. i) q^{23} +(88943.8 - 389688. i) q^{24} +(354113. + 170532. i) q^{25} +(325836. + 676606. i) q^{26} +(1.57048e6 + 358452. i) q^{27} -1.29396e6 q^{28} +(988845. + 3.67822e6i) q^{29} -1.37983e6 q^{30} +(-9.75340e6 - 2.22615e6i) q^{31} +(-1.46518e6 - 3.04247e6i) q^{32} +(-2.27324e6 - 1.09474e6i) q^{33} +(-2.14576e6 + 9.40120e6i) q^{34} +(-2.39476e6 - 1.04921e7i) q^{35} +(2.41385e6 - 1.16245e6i) q^{36} +(1.63131e7 + 1.30092e7i) q^{37} +(-3.04157e6 + 3.81401e6i) q^{38} +(-543594. + 1.12878e6i) q^{39} +(9.09222e6 - 7.25081e6i) q^{40} +1.53001e6i q^{41} +(-5.93465e6 - 7.44181e6i) q^{42} +(3.77903e7 - 8.62538e6i) q^{43} +(-8.60503e6 + 1.96404e6i) q^{44} +(1.38931e7 + 1.74214e7i) q^{45} -1.99395e7i q^{46} +(2.46270e7 - 1.96394e7i) q^{47} +(5.89501e6 - 1.22411e7i) q^{48} +(2.11271e7 - 2.64926e7i) q^{49} +(7.90738e6 + 6.30593e6i) q^{50} +(-1.44942e7 + 6.98006e6i) q^{51} +(975250. + 4.27285e6i) q^{52} +(-457777. + 2.00565e6i) q^{53} +(3.73471e7 + 1.79854e7i) q^{54} +(-3.18509e7 - 6.61390e7i) q^{55} +(7.82115e7 + 1.78513e7i) q^{56} -8.13849e6 q^{57} +(3.74594e6 + 9.79402e7i) q^{58} -7.44150e7 q^{59} +(-7.85084e6 - 1.79190e6i) q^{60} +(-4.82579e6 - 1.00209e7i) q^{61} +(-2.31943e8 - 1.11698e8i) q^{62} +(-3.42044e7 + 1.49859e8i) q^{63} +(1.67206e7 + 7.32578e7i) q^{64} +(-3.28415e7 + 1.58156e7i) q^{65} +(-5.07617e7 - 4.04811e7i) q^{66} +(-1.19588e8 + 1.49958e8i) q^{67} +(-2.44176e7 + 5.07037e7i) q^{68} +(2.60077e7 - 2.07405e7i) q^{69} -2.76935e8i q^{70} +(-3.91074e7 - 4.90391e7i) q^{71} +(-1.61938e8 + 3.69614e7i) q^{72} +(-3.04035e8 + 6.93940e7i) q^{73} +(3.34764e8 + 4.19781e8i) q^{74} +1.68731e7i q^{75} +(-2.22588e7 + 1.77508e7i) q^{76} +(2.19716e8 - 4.56246e8i) q^{77} +(-2.01010e7 + 2.52059e7i) q^{78} +(3.44673e8 + 2.74868e8i) q^{79} +(3.56150e8 - 1.71513e8i) q^{80} +(-6.27487e7 - 2.74920e8i) q^{81} +(-8.76099e6 + 3.83844e7i) q^{82} +(-6.33325e8 - 3.04993e8i) q^{83} +(-2.41023e7 - 5.00489e7i) q^{84} +(-4.56321e8 - 1.04152e8i) q^{85} +9.97459e8 q^{86} +(-1.23850e8 + 1.06760e8i) q^{87} +5.47212e8 q^{88} +(3.78821e7 + 8.64633e6i) q^{89} +(2.48789e8 + 5.16615e8i) q^{90} +(-2.26550e8 - 1.09101e8i) q^{91} +(2.58943e7 - 1.13450e8i) q^{92} +(-9.55689e7 - 4.18715e8i) q^{93} +(7.30290e8 - 3.51689e8i) q^{94} +(-1.85127e8 - 1.47634e8i) q^{95} +(9.03875e7 - 1.13342e8i) q^{96} +(-6.29030e8 + 1.30619e9i) q^{97} +(6.81729e8 - 5.43661e8i) q^{98} +1.04850e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 7 q^{2} - 7 q^{3} + 5797 q^{4} + 1367 q^{5} - 7607 q^{6} + 4949 q^{7} + 31766 q^{8} + 112237 q^{9}+O(q^{10}) \) 132 * q - 7 * q^2 - 7 * q^3 + 5797 * q^4 + 1367 * q^5 - 7607 * q^6 + 4949 * q^7 + 31766 * q^8 + 112237 * q^9	\( 132 q - 7 q^{2} - 7 q^{3} + 5797 q^{4} + 1367 q^{5} - 7607 q^{6} + 4949 q^{7} + 31766 q^{8} + 112237 q^{9} - 7 q^{10} + 230503 q^{11} + 370719 q^{13} - 7 q^{14} - 134953 q^{15} - 942171 q^{16} + 2518152 q^{18} - 7 q^{19} + 2630005 q^{20} - 5671057 q^{21} - 1956426 q^{22} - 5580815 q^{23} + 3549677 q^{24} - 4029457 q^{25} + 9649689 q^{26} + 6835241 q^{27} - 24789228 q^{28} - 4235889 q^{29} + 34444162 q^{30} + 10383597 q^{31} + 8347164 q^{32} + 35912671 q^{33} - 11257679 q^{34} + 873325 q^{35} - 125256554 q^{36} - 32126087 q^{37} + 131520700 q^{38} + 192355527 q^{39} - 158097415 q^{40} + 127695676 q^{42} - 78365203 q^{43} - 238378098 q^{44} + 57884904 q^{45} + 6546071 q^{47} - 400523802 q^{48} - 221520647 q^{49} + 154918442 q^{50} + 278243026 q^{51} - 52352040 q^{52} + 352279862 q^{53} + 155358204 q^{54} + 143671997 q^{55} - 575895495 q^{56} - 298751838 q^{57} - 1211966547 q^{58} + 776098748 q^{59} + 112101752 q^{60} - 124049779 q^{61} + 669065875 q^{62} + 1929121403 q^{63} + 1625889382 q^{64} - 866654028 q^{65} - 852661411 q^{66} + 13275097 q^{67} - 1504278412 q^{68} - 1267751723 q^{69} + 1776837051 q^{71} + 6219206035 q^{72} - 1507755424 q^{73} - 4950184776 q^{74} + 422070887 q^{76} - 561272089 q^{77} - 1228370591 q^{78} - 973234717 q^{79} + 1423181574 q^{80} + 2306016039 q^{81} - 1386574594 q^{82} - 932915983 q^{83} + 261177525 q^{84} - 3402309596 q^{85} - 3486024644 q^{86} - 1597393079 q^{87} + 5582534 q^{88} + 2316401563 q^{89} - 4748880458 q^{90} + 659194133 q^{91} + 11318573556 q^{92} + 3911968919 q^{93} + 3703837052 q^{94} + 2797945913 q^{95} - 1910264674 q^{96} - 2438073624 q^{97} - 1034416404 q^{98}+O(q^{100}) \) 132 * q - 7 * q^2 - 7 * q^3 + 5797 * q^4 + 1367 * q^5 - 7607 * q^6 + 4949 * q^7 + 31766 * q^8 + 112237 * q^9 - 7 * q^10 + 230503 * q^11 + 370719 * q^13 - 7 * q^14 - 134953 * q^15 - 942171 * q^16 + 2518152 * q^18 - 7 * q^19 + 2630005 * q^20 - 5671057 * q^21 - 1956426 * q^22 - 5580815 * q^23 + 3549677 * q^24 - 4029457 * q^25 + 9649689 * q^26 + 6835241 * q^27 - 24789228 * q^28 - 4235889 * q^29 + 34444162 * q^30 + 10383597 * q^31 + 8347164 * q^32 + 35912671 * q^33 - 11257679 * q^34 + 873325 * q^35 - 125256554 * q^36 - 32126087 * q^37 + 131520700 * q^38 + 192355527 * q^39 - 158097415 * q^40 + 127695676 * q^42 - 78365203 * q^43 - 238378098 * q^44 + 57884904 * q^45 + 6546071 * q^47 - 400523802 * q^48 - 221520647 * q^49 + 154918442 * q^50 + 278243026 * q^51 - 52352040 * q^52 + 352279862 * q^53 + 155358204 * q^54 + 143671997 * q^55 - 575895495 * q^56 - 298751838 * q^57 - 1211966547 * q^58 + 776098748 * q^59 + 112101752 * q^60 - 124049779 * q^61 + 669065875 * q^62 + 1929121403 * q^63 + 1625889382 * q^64 - 866654028 * q^65 - 852661411 * q^66 + 13275097 * q^67 - 1504278412 * q^68 - 1267751723 * q^69 + 1776837051 * q^71 + 6219206035 * q^72 - 1507755424 * q^73 - 4950184776 * q^74 + 422070887 * q^76 - 561272089 * q^77 - 1228370591 * q^78 - 973234717 * q^79 + 1423181574 * q^80 + 2306016039 * q^81 - 1386574594 * q^82 - 932915983 * q^83 + 261177525 * q^84 - 3402309596 * q^85 - 3486024644 * q^86 - 1597393079 * q^87 + 5582534 * q^88 + 2316401563 * q^89 - 4748880458 * q^90 + 659194133 * q^91 + 11318573556 * q^92 + 3911968919 * q^93 + 3703837052 * q^94 + 2797945913 * q^95 - 1910264674 * q^96 - 2438073624 * q^97 - 1034416404 * q^98

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