LMFDB - Embedded newform 32.8.g.a.21.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [32,8,Mod(5,32)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(32, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("32.5");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 32 = 2^{5} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	32.g (of order $8$, degree $4$, 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:	$9.99632081549$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$27$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			21.18
Character	$\chi$	$=$	32.21
Dual form			32.8.g.a.29.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.30805 + 9.99123i) q^{2} +(81.6081 - 33.8032i) q^{3} +(-71.6492 + 106.068i) q^{4} +(132.448 - 319.759i) q^{5} +(770.915 + 635.936i) q^{6} +(381.260 + 381.260i) q^{7} +(-1440.07 - 152.850i) q^{8} +(3970.78 - 3970.78i) q^{9} +O(q^{10})$	\(q+(5.30805 + 9.99123i) q^{2} +(81.6081 - 33.8032i) q^{3} +(-71.6492 + 106.068i) q^{4} +(132.448 - 319.759i) q^{5} +(770.915 + 635.936i) q^{6} +(381.260 + 381.260i) q^{7} +(-1440.07 - 152.850i) q^{8} +(3970.78 - 3970.78i) q^{9} +(3897.83 - 373.973i) q^{10} +(-2333.24 - 966.459i) q^{11} +(-2261.73 + 11078.0i) q^{12} +(-404.294 - 976.053i) q^{13} +(-1785.51 + 5833.00i) q^{14} -30572.1i q^{15} +(-6116.78 - 15199.4i) q^{16} +34786.9i q^{17} +(60750.1 + 18595.9i) q^{18} +(10993.9 + 26541.7i) q^{19} +(24426.3 + 36959.0i) q^{20} +(44001.7 + 18226.1i) q^{21} +(-2728.83 - 28441.9i) q^{22} +(-29360.9 + 29360.9i) q^{23} +(-122688. + 36205.0i) q^{24} +(-29460.4 - 29460.4i) q^{25} +(7605.95 - 9220.33i) q^{26} +(115895. - 279796. i) q^{27} +(-67756.4 + 13122.4i) q^{28} +(-52443.9 + 21723.0i) q^{29} +(305453. - 162278. i) q^{30} -312660. q^{31} +(119392. - 141793. i) q^{32} -223080. q^{33} +(-347564. + 184651. i) q^{34} +(172408. - 71413.9i) q^{35} +(136669. + 705676. i) q^{36} +(160357. - 387136. i) q^{37} +(-206828. + 250727. i) q^{38} +(-65987.4 - 65987.4i) q^{39} +(-239610. + 440229. i) q^{40} +(-5307.70 + 5307.70i) q^{41} +(51462.0 + 536376. i) q^{42} +(289812. + 120044. i) q^{43} +(269685. - 178235. i) q^{44} +(-743769. - 1.79562e6i) q^{45} +(-449200. - 137502. i) q^{46} +288244. i q^{47} +(-1.01296e6 - 1.03362e6i) q^{48} -532825. i q^{49} +(137968. - 450722. i) q^{50} +(1.17591e6 + 2.83889e6i) q^{51} +(132495. + 27050.8i) q^{52} +(-1.19353e6 - 494375. i) q^{53} +(3.41068e6 - 327235. i) q^{54} +(-618067. + 618067. i) q^{55} +(-490763. - 607315. i) q^{56} +(1.79438e6 + 1.79438e6i) q^{57} +(-495414. - 408673. i) q^{58} +(-224764. + 542627. i) q^{59} +(3.24271e6 + 2.19047e6i) q^{60} +(366711. - 151897. i) q^{61} +(-1.65962e6 - 3.12386e6i) q^{62} +3.02780e6 q^{63} +(2.05043e6 + 440229. i) q^{64} -365650. q^{65} +(-1.18412e6 - 2.22885e6i) q^{66} +(2.71125e6 - 1.12304e6i) q^{67} +(-3.68977e6 - 2.49246e6i) q^{68} +(-1.40359e6 + 3.38857e6i) q^{69} +(1.62866e6 + 1.34350e6i) q^{70} +(-1.18933e6 - 1.18933e6i) q^{71} +(-6.32512e6 + 5.11125e6i) q^{72} +(-3.76129e6 + 3.76129e6i) q^{73} +(4.71915e6 - 452775. i) q^{74} +(-3.40006e6 - 1.40835e6i) q^{75} +(-3.60292e6 - 735589. i) q^{76} +(-521098. - 1.25804e6i) q^{77} +(309031. - 1.00956e6i) q^{78} -934306. i q^{79} +(-5.67029e6 - 57238.2i) q^{80} -1.44701e7i q^{81} +(-81204.0 - 24856.9i) q^{82} +(2.62980e6 + 6.34889e6i) q^{83} +(-5.08589e6 + 3.36128e6i) q^{84} +(1.11234e7 + 4.60747e6i) q^{85} +(338948. + 3.53277e6i) q^{86} +(-3.54554e6 + 3.54554e6i) q^{87} +(3.21229e6 + 1.74840e6i) q^{88} +(-824518. - 824518. i) q^{89} +(1.39924e7 - 1.69624e7i) q^{90} +(217988. - 526271. i) q^{91} +(-1.01056e6 - 5.21792e6i) q^{92} +(-2.55156e7 + 1.05689e7i) q^{93} +(-2.87991e6 + 1.53001e6i) q^{94} +9.94306e6 q^{95} +(4.95030e6 - 1.56073e7i) q^{96} +1.07207e7 q^{97} +(5.32358e6 - 2.82826e6i) q^{98} +(-1.31024e7 + 5.42718e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) $ 108 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9	\( 108 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} - 13004 q^{10} - 4 q^{11} + 30668 q^{12} - 4 q^{13} - 26196 q^{14} - 52784 q^{16} + 102056 q^{18} - 4 q^{19} + 81996 q^{20} - 4 q^{21} - 374240 q^{22} - 143420 q^{23} + 380880 q^{24} - 4 q^{25} - 363984 q^{26} + 476084 q^{27} - 195464 q^{28} - 4 q^{29} + 870468 q^{30} - 714992 q^{31} + 535656 q^{32} - 8 q^{33} - 201072 q^{34} + 816500 q^{35} - 1669712 q^{36} - 4 q^{37} - 2533100 q^{38} - 283948 q^{39} + 2746344 q^{40} - 4 q^{41} + 4924936 q^{42} + 366180 q^{43} - 1585404 q^{44} + 8744 q^{45} - 2715812 q^{46} - 5044368 q^{48} - 1653804 q^{50} + 3002072 q^{51} + 8882212 q^{52} - 1815636 q^{53} + 6815776 q^{54} - 4191012 q^{55} - 3655000 q^{56} - 4 q^{57} - 12448736 q^{58} - 1835940 q^{59} - 6364808 q^{60} - 4559780 q^{61} + 12948600 q^{62} + 10001872 q^{63} + 16915544 q^{64} - 8 q^{65} - 11246068 q^{66} - 1940684 q^{67} - 8895536 q^{68} + 9580892 q^{69} - 8149480 q^{70} - 12348708 q^{71} + 12884564 q^{72} - 4 q^{73} + 10931436 q^{74} + 11573008 q^{75} + 14443516 q^{76} - 11914452 q^{77} - 38252364 q^{78} - 11333192 q^{80} + 15827196 q^{82} - 9565884 q^{83} + 8101984 q^{84} + 312496 q^{85} - 14812992 q^{86} + 40789108 q^{87} + 5716448 q^{88} - 4 q^{89} + 5335400 q^{90} - 3406996 q^{91} + 27562664 q^{92} - 8752 q^{93} - 14227032 q^{94} - 54872008 q^{95} - 25080448 q^{96} - 8 q^{97} + 57598104 q^{98} - 9738480 q^{99}+O(q^{100}) \) 108 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9 - 13004 * q^10 - 4 * q^11 + 30668 * q^12 - 4 * q^13 - 26196 * q^14 - 52784 * q^16 + 102056 * q^18 - 4 * q^19 + 81996 * q^20 - 4 * q^21 - 374240 * q^22 - 143420 * q^23 + 380880 * q^24 - 4 * q^25 - 363984 * q^26 + 476084 * q^27 - 195464 * q^28 - 4 * q^29 + 870468 * q^30 - 714992 * q^31 + 535656 * q^32 - 8 * q^33 - 201072 * q^34 + 816500 * q^35 - 1669712 * q^36 - 4 * q^37 - 2533100 * q^38 - 283948 * q^39 + 2746344 * q^40 - 4 * q^41 + 4924936 * q^42 + 366180 * q^43 - 1585404 * q^44 + 8744 * q^45 - 2715812 * q^46 - 5044368 * q^48 - 1653804 * q^50 + 3002072 * q^51 + 8882212 * q^52 - 1815636 * q^53 + 6815776 * q^54 - 4191012 * q^55 - 3655000 * q^56 - 4 * q^57 - 12448736 * q^58 - 1835940 * q^59 - 6364808 * q^60 - 4559780 * q^61 + 12948600 * q^62 + 10001872 * q^63 + 16915544 * q^64 - 8 * q^65 - 11246068 * q^66 - 1940684 * q^67 - 8895536 * q^68 + 9580892 * q^69 - 8149480 * q^70 - 12348708 * q^71 + 12884564 * q^72 - 4 * q^73 + 10931436 * q^74 + 11573008 * q^75 + 14443516 * q^76 - 11914452 * q^77 - 38252364 * q^78 - 11333192 * q^80 + 15827196 * q^82 - 9565884 * q^83 + 8101984 * q^84 + 312496 * q^85 - 14812992 * q^86 + 40789108 * q^87 + 5716448 * q^88 - 4 * q^89 + 5335400 * q^90 - 3406996 * q^91 + 27562664 * q^92 - 8752 * q^93 - 14227032 * q^94 - 54872008 * q^95 - 25080448 * q^96 - 8 * q^97 + 57598104 * q^98 - 9738480 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/32\mathbb{Z}\right)^\times$.

$n$	$5$	$31$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$1$

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 $

$2$	5.30805	+	9.99123i	0.469170	+	0.883108i
$2$	5.30805	+	9.99123i	0.469170	+	0.883108i
$3$	81.6081	−	33.8032i	1.74505	−	0.722825i	0.746719	−	0.665140i	$-0.231628\pi$
$3$	81.6081	−	33.8032i	1.74505	−	0.722825i	0.998335	−	0.0576850i	$-0.0183719\pi$
$4$	−71.6492	+	106.068i	−0.559760	+	0.828655i
$5$	132.448	−	319.759i	0.473862	−	1.14400i	−0.488581	−	0.872519i	$-0.662485\pi$
$5$	132.448	−	319.759i	0.473862	−	1.14400i	0.962443	−	0.271485i	$-0.0875148\pi$
$6$	770.915	+	635.936i	1.45706	+	1.20194i
$7$	381.260	+	381.260i	0.420124	+	0.420124i	0.885246	−	0.465122i	$-0.153990\pi$
$7$	381.260	+	381.260i	0.420124	+	0.420124i	−0.465122	+	0.885246i	$0.653990\pi$
$8$	−1440.07	−	152.850i	−0.994414	−	0.105548i
$9$	3970.78	−	3970.78i	1.81563	−	1.81563i
$10$	3897.83	−	373.973i	1.23260	−	0.118261i
$11$	−2333.24	−	966.459i	−0.528548	−	0.218932i	0.102419	−	0.994741i	$-0.467342\pi$
$11$	−2333.24	−	966.459i	−0.528548	−	0.218932i	−0.630967	+	0.775810i	$0.717342\pi$
$12$	−2261.73	+	11078.0i	−0.377838	+	1.85066i
$13$	−404.294	−	976.053i	−0.0510383	−	0.123217i	0.896304	−	0.443440i	$-0.146242\pi$
$13$	−404.294	−	976.053i	−0.0510383	−	0.123217i	−0.947342	+	0.320223i	$0.896242\pi$
$14$	−1785.51	+	5833.00i	−0.173906	+	0.568125i
$15$		−	30572.1i		−	2.33887i
$16$	−6116.78	−	15199.4i	−0.373338	−	0.927695i
$17$			34786.9i			1.71729i	0.512567	+	0.858647i	$0.328695\pi$
$17$			34786.9i			1.71729i	−0.512567	+	0.858647i	$0.671305\pi$
$18$	60750.1	+	18595.9i	2.45524	+	0.751559i
$19$	10993.9	+	26541.7i	0.367718	+	0.887750i	0.994123	+	0.108252i	$0.0345254\pi$
$19$	10993.9	+	26541.7i	0.367718	+	0.887750i	−0.626406	+	0.779497i	$0.715475\pi$
$20$	24426.3	+	36959.0i	0.682736	+	1.03304i
$21$	44001.7	+	18226.1i	1.03682	+	0.429463i
$22$	−2728.83	−	28441.9i	−0.0546383	−	0.569481i
$23$	−29360.9	+	29360.9i	−0.503178	+	0.503178i	−0.912424	−	0.409246i	$-0.865792\pi$
$23$	−29360.9	+	29360.9i	−0.503178	+	0.503178i	0.409246	+	0.912424i	$0.365792\pi$
$24$	−122688.	+	36205.0i	−1.81160	+	0.534600i
$25$	−29460.4	−	29460.4i	−0.377093	−	0.377093i
$26$	7605.95	−	9220.33i	0.0848685	−	0.102882i
$27$	115895.	−	279796.i	1.13316	−	2.73570i
$28$	−67756.4	+	13122.4i	−0.583307	+	0.112970i
$29$	−52443.9	+	21723.0i	−0.399303	+	0.165397i	−0.573292	−	0.819351i	$-0.694334\pi$
$29$	−52443.9	+	21723.0i	−0.399303	+	0.165397i	0.173990	+	0.984747i	$0.444334\pi$
$30$	305453.	−	162278.i	2.06547	−	1.09733i
$31$	−312660.			−1.88498			−0.942491	−	0.334232i	$-0.891523\pi$
$31$	−312660.			−1.88498			−0.942491	+	0.334232i	$0.891523\pi$
$32$	119392.	−	141793.i	0.644096	−	0.764945i
$33$	−223080.			−1.08059
$34$	−347564.	+	184651.i	−1.51656	+	0.805703i
$35$	172408.	−	71413.9i	0.679705	−	0.281543i
$36$	136669.	+	705676.i	0.488215	+	2.52085i
$37$	160357.	−	387136.i	0.520454	−	1.25649i	−0.417168	−	0.908830i	$-0.636977\pi$
$37$	160357.	−	387136.i	0.520454	−	1.25649i	0.937622	−	0.347658i	$-0.113023\pi$
$38$	−206828.	+	250727.i	−0.611457	+	0.741240i
$39$	−65987.4	−	65987.4i	−0.178129	−	0.178129i
$40$	−239610.	+	440229.i	−0.591963	+	1.08760i
$41$	−5307.70	+	5307.70i	−0.0120272	+	0.0120272i	−0.713095	−	0.701068i	$-0.752707\pi$
$41$	−5307.70	+	5307.70i	−0.0120272	+	0.0120272i	0.701068	+	0.713095i	$0.252707\pi$
$42$	51462.0	+	536376.i	0.107180	+	1.11711i
$43$	289812.	+	120044.i	0.555874	+	0.230250i	0.642893	−	0.765956i	$-0.277734\pi$
$43$	289812.	+	120044.i	0.555874	+	0.230250i	−0.0870190	+	0.996207i	$0.527734\pi$
$44$	269685.	−	178235.i	0.477279	−	0.315435i
$45$	−743769.	−	1.79562e6i	−1.21673	−	2.93744i
$46$	−449200.	−	137502.i	−0.680436	−	0.208284i
$47$			288244.i			0.404966i	0.979286	+	0.202483i	$0.0649010\pi$
$47$			288244.i			0.404966i	−0.979286	+	0.202483i	$0.935099\pi$
$48$	−1.01296e6	−	1.03362e6i	−1.32206	−	1.34902i
$49$		−	532825.i		−	0.646991i
$50$	137968.	−	450722.i	0.156093	−	0.509934i
$51$	1.17591e6	+	2.83889e6i	1.24130	+	2.99677i
$52$	132495.	+	27050.8i	0.130674	+	0.0266789i
$53$	−1.19353e6	−	494375.i	−1.10120	−	0.456132i	−0.243302	−	0.969951i	$-0.578231\pi$
$53$	−1.19353e6	−	494375.i	−1.10120	−	0.456132i	−0.857899	+	0.513818i	$0.828231\pi$
$54$	3.41068e6	−	327235.i	2.94756	−	0.282801i
$55$	−618067.	+	618067.i	−0.500918	+	0.500918i
$56$	−490763.	−	607315.i	−0.373434	−	0.462121i
$57$	1.79438e6	+	1.79438e6i	1.28338	+	1.28338i
$58$	−495414.	−	408673.i	−0.333404	−	0.275028i
$59$	−224764.	+	542627.i	−0.142477	+	0.343969i	−0.978969	−	0.204010i	$-0.934603\pi$
$59$	−224764.	+	542627.i	−0.142477	+	0.343969i	0.836492	+	0.547979i	$0.184603\pi$
$60$	3.24271e6	+	2.19047e6i	1.93811	+	1.30920i
$61$	366711.	−	151897.i	0.206857	−	0.0856828i	−0.276850	−	0.960913i	$-0.589290\pi$
$61$	366711.	−	151897.i	0.206857	−	0.0856828i	0.483706	+	0.875230i	$0.339290\pi$
$62$	−1.65962e6	−	3.12386e6i	−0.884376	−	1.66464i
$63$	3.02780e6			1.52558
$64$	2.05043e6	+	440229.i	0.977719	+	0.209918i
$65$	−365650.			−0.165146
$66$	−1.18412e6	−	2.22885e6i	−0.506982	−	0.954281i
$67$	2.71125e6	−	1.12304e6i	1.10131	−	0.456176i	0.243370	−	0.969934i	$-0.421747\pi$
$67$	2.71125e6	−	1.12304e6i	1.10131	−	0.456176i	0.857935	+	0.513758i	$0.171747\pi$
$68$	−3.68977e6	−	2.49246e6i	−1.42305	−	0.961272i
$69$	−1.40359e6	+	3.38857e6i	−0.514363	+	1.24178i
$70$	1.62866e6	+	1.34350e6i	0.567530	+	0.468161i
$71$	−1.18933e6	−	1.18933e6i	−0.394365	−	0.394365i	0.481875	−	0.876240i	$-0.339956\pi$
$71$	−1.18933e6	−	1.18933e6i	−0.394365	−	0.394365i	−0.876240	+	0.481875i	$0.839956\pi$
$72$	−6.32512e6	+	5.11125e6i	−1.99712	+	1.61385i
$73$	−3.76129e6	+	3.76129e6i	−1.13164	+	1.13164i	−0.141731	+	0.989905i	$0.545267\pi$
$73$	−3.76129e6	+	3.76129e6i	−1.13164	+	1.13164i	−0.989905	+	0.141731i	$0.954733\pi$
$74$	4.71915e6	−	452775.i	1.35380	−	0.129889i
$75$	−3.40006e6	−	1.40835e6i	−0.930619	−	0.385475i
$76$	−3.60292e6	−	735589.i	−0.941472	−	0.192215i
$77$	−521098.	−	1.25804e6i	−0.130077	−	0.314034i
$78$	309031.	−	1.00956e6i	0.0737344	−	0.240880i
$79$		−	934306.i		−	0.213203i	−0.994302	−	0.106602i	$-0.966003\pi$
$79$		−	934306.i		−	0.213203i	0.994302	−	0.106602i	$-0.0339970\pi$
$80$	−5.67029e6	−	57238.2i	−1.23820	−	0.0124989i
$81$		−	1.44701e7i		−	3.02533i
$82$	−81204.0	−	24856.9i	−0.0162641	−	0.00497850i
$83$	2.62980e6	+	6.34889e6i	0.504834	+	1.21878i	0.946822	+	0.321757i	$0.104273\pi$
$83$	2.62980e6	+	6.34889e6i	0.504834	+	1.21878i	−0.441988	+	0.897021i	$0.645727\pi$
$84$	−5.08589e6	+	3.36128e6i	−0.936244	+	0.618766i
$85$	1.11234e7	+	4.60747e6i	1.96459	+	0.813761i
$86$	338948.	+	3.53277e6i	0.0574631	+	0.598923i
$87$	−3.54554e6	+	3.54554e6i	−0.577252	+	0.577252i
$88$	3.21229e6	+	1.74840e6i	0.502488	+	0.273496i
$89$	−824518.	−	824518.i	−0.123975	−	0.123975i	0.642397	−	0.766372i	$-0.277940\pi$
$89$	−824518.	−	824518.i	−0.123975	−	0.123975i	−0.766372	+	0.642397i	$0.777940\pi$
$90$	1.39924e7	−	1.69624e7i	2.02323	−	2.45266i
$91$	217988.	−	526271.i	0.0303241	−	0.0732090i
$92$	−1.01056e6	−	5.21792e6i	−0.135302	−	0.698619i
$93$	−2.55156e7	+	1.05689e7i	−3.28939	+	1.36251i
$94$	−2.87991e6	+	1.53001e6i	−0.357628	+	0.189998i
$95$	9.94306e6			1.18984
$96$	4.95030e6	−	1.56073e7i	0.571061	−	1.80044i
$97$	1.07207e7			1.19268			0.596340	−	0.802732i	$-0.296621\pi$
$97$	1.07207e7			1.19268			0.596340	+	0.802732i	$0.296621\pi$
$98$	5.32358e6	−	2.82826e6i	0.571363	−	0.303549i
$99$	−1.31024e7	+	5.42718e6i	−1.35715	+	0.562149i
$100$	5.23561e6	−	1.01399e6i	0.523561	−	0.101399i
$101$	236403.	−	570727.i	0.0228312	−	0.0551193i	−0.912053	−	0.410073i	$-0.865503\pi$
$101$	236403.	−	570727.i	0.0228312	−	0.0551193i	0.934884	+	0.354953i	$0.115503\pi$
$102$	−2.21223e7	+	2.68178e7i	−2.06409	+	2.50220i
$103$	4.63576e6	+	4.63576e6i	0.418014	+	0.418014i	0.884519	−	0.466505i	$-0.154487\pi$
$103$	4.63576e6	+	4.63576e6i	0.418014	+	0.418014i	−0.466505	+	0.884519i	$0.654487\pi$
$104$	433020.	+	1.46738e6i	0.0377478	+	0.127916i
$105$	1.16559e7	−	1.16559e7i	0.982615	−	0.982615i
$106$	−1.39589e6	−	1.45490e7i	−0.113836	−	1.18648i
$107$	4.86507e6	+	2.01518e6i	0.383925	+	0.159027i	0.566294	−	0.824203i	$-0.308377\pi$
$107$	4.86507e6	+	2.01518e6i	0.383925	+	0.159027i	−0.182369	+	0.983230i	$0.558377\pi$
$108$	2.13736e7	+	3.23399e7i	1.63265	+	2.47034i
$109$	−2.79383e6	−	6.74491e6i	−0.206637	−	0.498865i	0.786253	−	0.617905i	$-0.212018\pi$
$109$	−2.79383e6	−	6.74491e6i	−0.206637	−	0.498865i	−0.992889	+	0.119040i	$0.962018\pi$
$110$	−9.45598e6	−	2.89452e6i	−0.677380	−	0.207349i
$111$		−	3.70140e7i		−	2.56883i
$112$	3.46282e6	−	8.12698e6i	0.232899	−	0.546596i
$113$		−	8.80821e6i		−	0.574266i	−0.957891	−	0.287133i	$-0.907298\pi$
$113$		−	8.80821e6i		−	0.574266i	0.957891	−	0.287133i	$-0.0927021\pi$
$114$	−8.40342e6	+	2.74528e7i	−0.531238	+	1.73548i
$115$	5.49959e6	+	1.32772e7i	0.337200	+	0.814074i
$116$	1.45346e6	−	7.11905e6i	0.0864568	−	0.423467i
$117$	−5.48106e6	−	2.27033e6i	−0.316383	−	0.131050i
$118$	−6.61457e6	+	634629.i	−0.370608	+	0.0355576i
$119$	−1.32629e7	+	1.32629e7i	−0.721477	+	0.721477i
$120$	−4.67295e6	+	4.40258e7i	−0.246864	+	2.32580i
$121$	−9.26956e6	−	9.26956e6i	−0.475675	−	0.475675i
$122$	3.46415e6	+	2.85762e6i	0.172718	+	0.142477i
$123$	−253734.	+	612569.i	−0.0122945	+	0.0296816i
$124$	2.24019e7	−	3.31632e7i	1.05514	−	1.56200i
$125$	1.16590e7	−	4.82930e6i	0.533918	−	0.221156i
$126$	1.60717e7	+	3.02514e7i	0.715756	+	1.34725i
$127$	2.78690e7			1.20728			0.603640	−	0.797257i	$-0.293716\pi$
$127$	2.78690e7			1.20728			0.603640	+	0.797257i	$0.293716\pi$
$128$	6.48533e6	+	2.28230e7i	0.273336	+	0.961919i
$129$	2.77088e7			1.13646
$130$	−1.94089e6	−	3.65329e6i	−0.0774815	−	0.145842i
$131$	1.93493e7	−	8.01474e6i	0.751996	−	0.311487i	0.0264403	−	0.999650i	$-0.491583\pi$
$131$	1.93493e7	−	8.01474e6i	0.751996	−	0.311487i	0.725556	+	0.688163i	$0.241583\pi$
$132$	1.59835e7	−	2.36617e7i	0.604873	−	0.895440i
$133$	−5.92773e6	+	1.43108e7i	−0.218478	+	0.527452i
$134$	2.56120e7	+	2.11276e7i	0.919551	+	0.758548i
$135$	−7.41171e7	−	7.41171e7i	−2.59269	−	2.59269i
$136$	5.31719e6	−	5.00955e7i	0.181258	−	1.70770i
$137$	−1.44421e7	+	1.44421e7i	−0.479854	+	0.479854i	−0.905085	−	0.425231i	$-0.860193\pi$
$137$	−1.44421e7	+	1.44421e7i	−0.479854	+	0.479854i	0.425231	+	0.905085i	$0.360193\pi$
$138$	−4.13063e7	+	3.96310e6i	−1.33795	+	0.128368i
$139$	−4.50543e6	−	1.86621e6i	−0.142293	−	0.0589398i	0.310400	−	0.950606i	$-0.399537\pi$
$139$	−4.50543e6	−	1.86621e6i	−0.142293	−	0.0589398i	−0.452694	+	0.891666i	$0.649537\pi$
$140$	−4.77821e6	+	2.34037e7i	−0.147169	+	0.720837i
$141$	9.74357e6	+	2.35231e7i	0.292719	+	0.706687i
$142$	5.56985e6	−	1.81959e7i	0.163243	−	0.533291i
$143$			2.66810e6i			0.0763001i
$144$	−8.46417e7	−	3.60650e7i	−2.36220	−	1.00651i
$145$			1.96466e7i			0.535179i
$146$	−5.75450e7	−	1.76148e7i	−1.53029	−	0.468428i
$147$	−1.80112e7	−	4.34828e7i	−0.467661	−	1.12903i
$148$	2.95733e7	+	4.47468e7i	0.749865	+	1.13461i
$149$	−5.94098e7	−	2.46084e7i	−1.47132	−	0.609440i	−0.504158	−	0.863611i	$-0.668197\pi$
$149$	−5.94098e7	−	2.46084e7i	−1.47132	−	0.609440i	−0.967159	+	0.254172i	$0.918197\pi$
$150$	−3.97653e6	−	4.14463e7i	−0.0962022	−	1.00269i
$151$	1.19952e7	−	1.19952e7i	0.283523	−	0.283523i	−0.550989	−	0.834512i	$-0.685750\pi$
$151$	1.19952e7	−	1.19952e7i	0.283523	−	0.283523i	0.834512	+	0.550989i	$0.185750\pi$
$152$	−1.17751e7	−	3.99022e7i	−0.271963	−	0.921603i
$153$	1.38131e8	+	1.38131e8i	3.11797	+	3.11797i
$154$	9.80336e6	−	1.18842e7i	0.216298	−	0.262208i
$155$	−4.14114e7	+	9.99759e7i	−0.893221	+	2.15643i
$156$	1.17271e7	−	2.27119e6i	0.247317	−	0.0478981i
$157$	1.56313e7	−	6.47471e6i	0.322365	−	0.133528i	−0.215632	−	0.976475i	$-0.569181\pi$
$157$	1.56313e7	−	6.47471e6i	0.322365	−	0.133528i	0.537997	+	0.842947i	$0.319181\pi$
$158$	9.33486e6	−	4.95934e6i	0.188282	−	0.100029i
$159$	−1.14113e8			−2.25136
$160$	−2.95263e7	−	5.69569e7i	−0.569887	−	1.09933i
$161$	−2.23882e7			−0.422794
$162$	1.44574e8	−	7.68079e7i	2.67170	−	1.41939i
$163$	3.99642e7	−	1.65537e7i	0.722793	−	0.299391i	0.00920655	−	0.999958i	$-0.497069\pi$
$163$	3.99642e7	−	1.65537e7i	0.722793	−	0.299391i	0.713587	+	0.700567i	$0.247069\pi$
$164$	−182684.	−	943269.i	−0.00323405	−	0.0166987i
$165$	−2.95466e7	+	7.13319e7i	−0.512052	+	1.23620i
$166$	−4.94741e7	+	5.99751e7i	−0.839460	+	1.01764i
$167$	−1.20723e7	−	1.20723e7i	−0.200577	−	0.200577i	0.599670	−	0.800247i	$-0.295299\pi$
$167$	−1.20723e7	−	1.20723e7i	−0.200577	−	0.200577i	−0.800247	+	0.599670i	$0.795299\pi$
$168$	−6.05794e7	−	3.29724e7i	−0.985695	−	0.536498i
$169$	4.35807e7	−	4.35807e7i	0.694529	−	0.694529i
$170$	1.30094e7	+	1.35593e8i	0.203088	+	2.11674i
$171$	1.49046e8	+	6.17367e7i	2.27946	+	0.944185i
$172$	−3.34976e7	+	2.21386e7i	−0.501954	+	0.331743i
$173$	−1.34790e7	−	3.25412e7i	−0.197923	−	0.477829i	0.793492	−	0.608581i	$-0.208261\pi$
$173$	−1.34790e7	−	3.25412e7i	−0.197923	−	0.477829i	−0.991415	+	0.130752i	$0.958261\pi$
$174$	−5.42442e7	−	1.66044e7i	−0.780605	−	0.238947i
$175$		−	2.24641e7i		−	0.316852i
$176$	−417659.	+	4.13753e7i	−0.00577468	+	0.572067i
$177$			5.18805e7i			0.703231i
$178$	3.86137e6	−	1.26145e7i	0.0513182	−	0.167649i
$179$	−2.71075e6	−	6.54434e6i	−0.0353268	−	0.0852865i	0.905231	−	0.424919i	$-0.139697\pi$
$179$	−2.71075e6	−	6.54434e6i	−0.0353268	−	0.0852865i	−0.940558	+	0.339632i	$0.889697\pi$
$180$	2.43748e8	+	4.97646e7i	3.11520	+	0.636014i
$181$	−8.05153e6	−	3.33505e6i	−0.100926	−	0.0418049i	0.331649	−	0.943403i	$-0.392395\pi$
$181$	−8.05153e6	−	3.33505e6i	−0.100926	−	0.0418049i	−0.432575	+	0.901598i	$0.642395\pi$
$182$	6.41518e6	−	615499.i	0.0788786	−	0.00756793i
$183$	2.47920e7	−	2.47920e7i	0.299042	−	0.299042i
$184$	4.67694e7	−	3.77937e7i	0.553476	−	0.447257i
$185$	−1.02551e8	−	1.02551e8i	−1.19080	−	1.19080i
$186$	−2.41035e8	−	1.98832e8i	−2.74653	−	2.26564i
$187$	3.36201e7	−	8.11662e7i	0.375970	−	0.907673i
$188$	−3.05734e7	−	2.06525e7i	−0.335577	−	0.226683i
$189$	1.50861e8	−	6.24887e7i	1.62540	−	0.673264i
$190$	5.27782e7	+	9.93433e7i	0.558235	+	1.05075i
$191$	1.07302e7			0.111427			0.0557134	−	0.998447i	$-0.482257\pi$
$191$	1.07302e7			0.111427			0.0557134	+	0.998447i	$0.482257\pi$
$192$	1.82212e8	−	3.33846e7i	1.85791	−	0.340402i
$193$	−1.20256e8			−1.20408			−0.602041	−	0.798465i	$-0.705646\pi$
$193$	−1.20256e8			−1.20408			−0.602041	+	0.798465i	$0.705646\pi$
$194$	5.69062e7	+	1.07113e8i	0.559569	+	1.05327i
$195$	−2.98400e7	+	1.23601e7i	−0.288189	+	0.119372i
$196$	5.65156e7	+	3.81765e7i	0.536133	+	0.362160i
$197$	−5.81872e7	+	1.40476e8i	−0.542245	+	1.30910i	0.380890	+	0.924620i	$0.375618\pi$
$197$	−5.81872e7	+	1.40476e8i	−0.542245	+	1.30910i	−0.923135	+	0.384475i	$0.874382\pi$
$198$	−1.23772e8	−	1.02101e8i	−1.13317	−	0.934764i
$199$	1.47371e8	+	1.47371e8i	1.32564	+	1.32564i	0.909130	+	0.416513i	$0.136748\pi$
$199$	1.47371e8	+	1.47371e8i	1.32564	+	1.32564i	0.416513	+	0.909130i	$0.363252\pi$
$200$	3.79218e7	+	4.69279e7i	0.335185	+	0.414788i
$201$	1.83298e8	−	1.83298e8i	1.59210	−	1.59210i
$202$	6.95710e6	−	667492.i	0.0593880	−	0.00569792i
$203$	−2.82769e7	−	1.17127e7i	−0.237244	−	0.0982696i
$204$	−3.85368e8	−	7.86785e7i	−3.17812	−	0.648859i
$205$	994188.	+	2.40018e6i	0.00805990	+	0.0194583i
$206$	−2.17101e7	+	7.09237e7i	−0.173032	+	0.565270i
$207$			2.33171e8i			1.82717i
$208$	−1.23624e7	+	1.21153e7i	−0.0952535	+	0.0933497i
$209$		−	7.25532e7i		−	0.549724i
$210$	1.78327e8	+	5.45867e7i	1.32877	+	0.406742i
$211$	−4.29373e7	−	1.03660e8i	−0.314664	−	0.759665i	−0.999520	−	0.0309869i	$-0.990135\pi$
$211$	−4.29373e7	−	1.03660e8i	−0.314664	−	0.759665i	0.684856	−	0.728678i	$-0.259865\pi$
$212$	1.37953e8	−	9.11732e7i	0.994384	−	0.657191i
$213$	−1.37262e8	−	5.68558e7i	−0.973245	−	0.403131i
$214$	5.68994e6	+	5.93047e7i	0.0396880	+	0.413658i
$215$	7.67702e7	−	7.67702e7i	0.526815	−	0.526815i
$216$	−2.09664e8	+	3.85210e8i	−1.41558	+	2.60081i
$217$	−1.19205e8	−	1.19205e8i	−0.791926	−	0.791926i
$218$	5.25601e7	−	6.37161e7i	0.343604	−	0.416535i
$219$	−1.79808e8	+	4.34095e8i	−1.15679	+	2.79274i
$220$	−2.12730e7	−	1.09841e8i	−0.134694	−	0.695481i
$221$	3.39539e7	−	1.40642e7i	0.211600	−	0.0876477i
$222$	3.69816e8	−	1.96472e8i	2.26856	−	1.20522i
$223$	5.43897e7			0.328435			0.164218	−	0.986424i	$-0.447490\pi$
$223$	5.43897e7			0.328435			0.164218	+	0.986424i	$0.447490\pi$
$224$	9.95794e7	−	8.54058e6i	0.591972	−	0.0507714i
$225$	−2.33961e8			−1.36932
$226$	8.80048e7	−	4.67544e7i	0.507139	−	0.269428i
$227$	−1.53342e8	+	6.35162e7i	−0.870101	+	0.360407i	−0.772650	−	0.634833i	$-0.781069\pi$
$227$	−1.53342e8	+	6.35162e7i	−0.870101	+	0.360407i	−0.0974511	+	0.995240i	$0.531069\pi$
$228$	−3.18893e8	+	6.17602e7i	−1.78186	+	0.345094i
$229$	2.80514e7	−	6.77220e7i	0.154358	−	0.372654i	−0.827716	−	0.561147i	$-0.810360\pi$
$229$	2.80514e7	−	6.77220e7i	0.154358	−	0.372654i	0.982075	+	0.188493i	$0.0603603\pi$
$230$	−1.03463e8	+	1.25424e8i	−0.560711	+	0.679723i
$231$	−8.50516e7	−	8.50516e7i	−0.453984	−	0.453984i
$232$	7.88431e7	−	2.32665e7i	0.414530	−	0.122327i
$233$	−5.40623e7	+	5.40623e7i	−0.279994	+	0.279994i	−0.833107	−	0.553112i	$-0.813440\pi$
$233$	−5.40623e7	+	5.40623e7i	−0.279994	+	0.279994i	0.553112	+	0.833107i	$0.313440\pi$
$234$	−6.41036e6	−	6.68135e7i	−0.0327059	−	0.340886i
$235$	9.21686e7	+	3.81775e7i	0.463282	+	0.191898i
$236$	−4.14512e7	−	6.27190e7i	−0.205279	−	0.310604i
$237$	−3.15825e7	−	7.62469e7i	−0.154109	−	0.372051i
$238$	−2.02912e8	−	6.21123e7i	−0.975638	−	0.298647i
$239$		−	3.74416e8i		−	1.77403i	−0.461737	−	0.887017i	$-0.652774\pi$
$239$		−	3.74416e8i		−	1.77403i	0.461737	−	0.887017i	$-0.347226\pi$
$240$	−4.64676e8	+	1.87003e8i	−2.16976	+	0.873189i
$241$		−	2.99463e8i		−	1.37811i	−0.724710	−	0.689054i	$-0.758026\pi$
$241$		−	2.99463e8i		−	1.37811i	0.724710	−	0.689054i	$-0.241974\pi$
$242$	4.34110e7	−	1.41817e8i	0.196900	−	0.643244i
$243$	−2.35671e8	−	5.68961e8i	−1.05362	−	2.54367i
$244$	−1.01632e7	+	4.97795e7i	−0.0447885	+	0.219375i
$245$	−1.70375e8	−	7.05718e7i	−0.740160	−	0.306584i
$246$	−7.46715e6	+	716428.i	−0.0319802	+	0.00306831i
$247$	2.14613e7	−	2.14613e7i	0.0906184	−	0.0906184i
$248$	4.50252e8	+	4.77903e7i	1.87445	+	0.198957i
$249$	4.29225e8	+	4.29225e8i	1.76193	+	1.76193i
$250$	1.10137e8	+	9.08532e7i	0.445803	+	0.367748i
$251$	9.16154e7	−	2.21179e8i	0.365688	−	0.882848i	−0.628758	−	0.777601i	$-0.716437\pi$
$251$	9.16154e7	−	2.21179e8i	0.365688	−	0.882848i	0.994446	−	0.105247i	$-0.0335634\pi$
$252$	−2.16939e8	+	3.21152e8i	−0.853958	+	1.26418i
$253$	9.68819e7	−	4.01298e7i	0.376115	−	0.155792i
$254$	1.47930e8	+	2.78445e8i	0.566419	+	1.06616i
$255$	1.06351e9			4.01652
$256$	−1.93606e8	+	1.85942e8i	−0.721237	+	0.692688i
$257$	8.94080e7			0.328557			0.164278	−	0.986414i	$-0.447470\pi$
$257$	8.94080e7			0.328557			0.164278	+	0.986414i	$0.447470\pi$
$258$	1.47080e8	+	2.76845e8i	0.533193	+	1.00362i
$259$	2.08737e8	−	8.64618e7i	0.746536	−	0.309225i
$260$	2.61985e7	−	3.87837e7i	0.0924421	−	0.136849i
$261$	−1.21986e8	+	2.94501e8i	−0.424687	+	1.02528i
$262$	1.82784e8	+	1.50781e8i	0.627890	+	0.517953i
$263$	−2.13062e8	−	2.13062e8i	−0.722207	−	0.722207i	0.246847	−	0.969054i	$-0.420605\pi$
$263$	−2.13062e8	−	2.13062e8i	−0.722207	−	0.722207i	−0.969054	+	0.246847i	$0.920605\pi$
$264$	3.21250e8	+	3.40979e7i	1.07456	+	0.114055i
$265$	−3.16161e8	+	3.16161e8i	−1.04363	+	1.04363i
$266$	−1.74447e8	+	1.67372e7i	−0.568301	+	0.0545251i
$267$	−9.51587e7	−	3.94160e7i	−0.305956	−	0.126731i
$268$	−7.51409e7	+	3.68041e8i	−0.238454	+	1.16795i
$269$	−4.37863e7	−	1.05709e8i	−0.137153	−	0.331116i	0.840348	−	0.542047i	$-0.182351\pi$
$269$	−4.37863e7	−	1.05709e8i	−0.137153	−	0.331116i	−0.977501	+	0.210931i	$0.932351\pi$
$270$	3.47103e8	−	1.13394e9i	1.07321	−	3.50603i
$271$			6.08686e8i			1.85781i	0.370320	+	0.928904i	$0.379248\pi$
$271$			6.08686e8i			1.85781i	−0.370320	+	0.928904i	$0.620752\pi$
$272$	5.28739e8	−	2.12784e8i	1.59313	−	0.641132i
$273$		−	5.03166e7i		−	0.149673i
$274$	−2.20954e8	−	6.76351e7i	−0.648896	−	0.198630i
$275$	4.02658e7	+	9.72103e7i	0.116754	+	0.281869i
$276$	−2.58852e8	−	3.91665e8i	−0.741089	−	1.12133i
$277$	3.86952e8	+	1.60281e8i	1.09390	+	0.453109i	0.855366	−	0.518025i	$-0.173333\pi$
$277$	3.86952e8	+	1.60281e8i	1.09390	+	0.453109i	0.238536	+	0.971134i	$0.423333\pi$
$278$	−5.26932e6	−	5.49207e7i	−0.0147095	−	0.153313i
$279$	−1.24151e9	+	1.24151e9i	−3.42243	+	3.42243i
$280$	−2.59195e8	+	7.64880e7i	−0.705624	+	0.208229i
$281$	−1.50212e8	−	1.50212e8i	−0.403861	−	0.403861i	0.475730	−	0.879591i	$-0.342184\pi$
$281$	−1.50212e8	−	1.50212e8i	−0.403861	−	0.403861i	−0.879591	+	0.475730i	$0.842184\pi$
$282$	−1.83305e8	+	2.22212e8i	−0.486746	+	0.590059i
$283$	−1.84040e8	+	4.44313e8i	−0.482682	+	1.16530i	0.475649	+	0.879635i	$0.342213\pi$
$283$	−1.84040e8	+	4.44313e8i	−0.482682	+	1.16530i	−0.958331	+	0.285661i	$0.907787\pi$
$284$	2.11364e8	−	4.09351e7i	0.547542	−	0.106043i
$285$	8.11434e8	−	3.36107e8i	2.07633	−	0.860043i
$286$	−2.66576e7	+	1.41624e7i	−0.0673813	+	0.0357977i
$287$	−4.04723e6			−0.0101058
$288$	−8.89493e7	−	1.03711e9i	−0.219416	−	2.55830i
$289$	−7.99792e8			−1.94910
$290$	−1.96293e8	+	1.04285e8i	−0.472621	+	0.251090i
$291$	8.74899e8	−	3.62395e8i	2.08129	−	0.862099i
$292$	−1.29458e8	−	6.68445e8i	−0.304292	−	1.57118i
$293$	2.08640e8	−	5.03702e8i	0.484575	−	1.16987i	−0.472839	−	0.881149i	$-0.656771\pi$
$293$	2.08640e8	−	5.03702e8i	0.484575	−	1.16987i	0.957414	−	0.288719i	$-0.0932292\pi$
$294$	3.38843e8	−	4.10763e8i	0.777647	−	0.942704i
$295$	1.43740e8	+	1.43740e8i	0.325988	+	0.325988i
$296$	−2.90099e8	+	5.32991e8i	−0.650167	+	1.19454i
$297$	−5.40823e8	+	5.40823e8i	−1.19786	+	1.19786i
$298$	−6.94826e7	−	7.24199e8i	−0.152096	−	1.58526i
$299$	4.05282e7	+	1.67873e7i	0.0876815	+	0.0363188i
$300$	3.92992e8	−	2.59730e8i	0.840349	−	0.555389i
$301$	6.47256e7	+	1.56261e8i	0.136802	+	0.330270i
$302$	1.83518e8	+	5.61756e7i	0.383401	+	0.117361i
$303$		−	5.45671e7i		−	0.112689i
$304$	3.36169e8	−	3.29450e8i	0.686278	−	0.672561i
$305$		−	1.37377e8i		−	0.277247i
$306$	−6.46893e8	+	2.11331e9i	−1.29065	+	4.21636i
$307$	1.13710e8	+	2.74519e8i	0.224292	+	0.541488i	0.995464	−	0.0951385i	$-0.0303294\pi$
$307$	1.13710e8	+	2.74519e8i	0.224292	+	0.541488i	−0.771172	+	0.636626i	$0.780329\pi$
$308$	1.70774e8	+	3.48660e7i	0.333038	+	0.0679946i
$309$	5.35018e8	+	2.21612e8i	1.03161	+	0.427305i
$310$	−1.21870e9	+	1.16927e8i	−2.32343	+	0.222919i
$311$	−2.56247e8	+	2.56247e8i	−0.483056	+	0.483056i	−0.906106	−	0.423050i	$-0.860959\pi$
$311$	−2.56247e8	+	2.56247e8i	−0.483056	+	0.483056i	0.423050	+	0.906106i	$0.360959\pi$
$312$	8.49399e7	+	1.05112e8i	0.158333	+	0.195935i
$313$	5.00037e8	+	5.00037e8i	0.921715	+	0.921715i	0.997151	−	0.0754359i	$-0.0240348\pi$
$313$	5.00037e8	+	5.00037e8i	0.921715	+	0.921715i	−0.0754359	+	0.997151i	$0.524035\pi$
$314$	1.47662e8	+	1.21808e8i	0.269163	+	0.222036i
$315$	4.01027e8	−	9.68165e8i	0.722914	−	1.74527i
$316$	9.90998e7	+	6.69423e7i	0.176672	+	0.119343i
$317$	−4.16716e8	+	1.72609e8i	−0.734739	+	0.304339i	−0.718498	−	0.695529i	$-0.755170\pi$
$317$	−4.16716e8	+	1.72609e8i	−0.734739	+	0.304339i	−0.0162410	+	0.999868i	$0.505170\pi$
$318$	−6.05717e8	−	1.14013e9i	−1.05627	−	1.98819i
$319$	1.43359e8			0.247261
$320$	4.12343e8	−	5.97334e8i	0.703450	−	1.01904i
$321$	4.65149e8			0.784918
$322$	−1.18838e8	−	2.23686e8i	−0.198362	−	0.373373i
$323$	−9.23303e8	+	3.82445e8i	−1.52453	+	0.631480i
$324$	1.53481e9	+	1.03677e9i	2.50696	+	1.69346i
$325$	−1.68442e7	+	4.06655e7i	−0.0272182	+	0.0657105i
$326$	3.77524e8	+	3.11423e8i	0.603507	+	0.497840i
$327$	−4.55999e8	−	4.55999e8i	−0.721184	−	0.721184i
$328$	8.45472e6	−	6.83216e6i	0.0132294	−	0.0106905i
$329$	−1.09896e8	+	1.09896e8i	−0.170136	+	0.170136i
$330$	−8.69528e8	+	8.34261e7i	−1.33194	+	0.127792i
$331$	−1.52739e8	−	6.32667e7i	−0.231501	−	0.0958908i	0.263918	−	0.964545i	$-0.414985\pi$
$331$	−1.52739e8	−	6.32667e7i	−0.231501	−	0.0958908i	−0.495419	+	0.868654i	$0.664985\pi$
$332$	−8.61836e8	−	1.75956e8i	−1.29253	−	0.263889i
$333$	−9.00491e8	−	2.17398e9i	−1.33636	−	3.22627i
$334$	5.65367e7	−	1.84697e8i	0.0830267	−	0.271236i
$335$		−	1.01569e9i		−	1.47606i
$336$	7.87648e6	−	7.80282e8i	0.0113278	−	1.12218i
$337$		−	4.64862e7i		−	0.0661636i	−0.999453	−	0.0330818i	$-0.989468\pi$
$337$		−	4.64862e7i		−	0.0661636i	0.999453	−	0.0330818i	$-0.0105322\pi$
$338$	6.66753e8	+	2.04096e8i	0.939196	+	0.287492i
$339$	−2.97745e8	−	7.18821e8i	−0.415094	−	1.00212i
$340$	−1.28569e9	+	8.49716e8i	−1.77403	+	1.17246i
$341$	7.29511e8	+	3.02173e8i	0.996303	+	0.412682i
$342$	1.74316e8	+	1.81685e9i	0.235638	+	2.45600i
$343$	5.17129e8	−	5.17129e8i	0.691941	−	0.691941i
$344$	−3.98999e8	−	2.17169e8i	−0.528466	−	0.287636i
$345$	8.97622e8	+	8.97622e8i	1.17687	+	1.17687i
$346$	2.53579e8	−	3.07402e8i	0.329115	−	0.398971i
$347$	5.21725e7	−	1.25956e8i	0.0670330	−	0.161832i	−0.886813	−	0.462129i	$-0.847086\pi$
$347$	5.21725e7	−	1.25956e8i	0.0670330	−	0.161832i	0.953846	+	0.300297i	$0.0970858\pi$
$348$	−1.22033e8	−	6.30103e8i	−0.155220	−	0.801465i
$349$	−6.84383e8	+	2.83481e8i	−0.861808	+	0.356972i	−0.769414	−	0.638750i	$-0.779452\pi$
$349$	−6.84383e8	+	2.83481e8i	−0.861808	+	0.356972i	−0.0923934	+	0.995723i	$0.529452\pi$
$350$	2.24444e8	−	1.19241e8i	0.279814	−	0.148657i
$351$	−3.19951e8			−0.394920
$352$	−4.15607e8	+	2.15449e8i	−0.507906	+	0.263297i
$353$	−3.97541e8			−0.481028			−0.240514	−	0.970646i	$-0.577316\pi$
$353$	−3.97541e8			−0.481028			−0.240514	+	0.970646i	$0.577316\pi$
$354$	−5.18350e8	+	2.75384e8i	−0.621029	+	0.329934i
$355$	−5.37824e8	+	2.22774e8i	−0.638029	+	0.264280i
$356$	1.46531e8	−	2.83788e7i	0.172129	−	0.0333364i
$357$	−6.34030e8	+	1.53068e9i	−0.737515	+	1.78052i
$358$	5.09971e7	−	6.18214e7i	0.0587429	−	0.0712112i
$359$	3.35367e8	+	3.35367e8i	0.382551	+	0.382551i	0.872020	−	0.489469i	$-0.162810\pi$
$359$	3.35367e8	+	3.35367e8i	0.382551	+	0.382551i	−0.489469	+	0.872020i	$0.662810\pi$
$360$	7.96615e8	+	2.69949e9i	0.899890	+	3.04946i
$361$	4.84692e7	−	4.84692e7i	0.0542239	−	0.0542239i
$362$	−9.41664e6	−	9.81472e7i	−0.0104332	−	0.108742i
$363$	−1.06981e9	−	4.43130e8i	−1.17391	−	0.486248i
$364$	4.02017e7	+	6.08285e7i	0.0436907	+	0.0661077i
$365$	7.04528e8	+	1.70088e9i	0.758357	+	1.83084i
$366$	3.79299e8	+	1.16105e8i	0.404388	+	0.123785i
$367$		−	2.04576e8i		−	0.216034i	−0.994149	−	0.108017i	$-0.965550\pi$
$367$		−	2.04576e8i		−	0.216034i	0.994149	−	0.108017i	$-0.0344501\pi$
$368$	6.25860e8	+	2.66672e8i	0.654651	+	0.278940i
$369$			4.21515e7i			0.0436737i
$370$	4.80266e8	−	1.56896e9i	0.492919	−	1.61030i
$371$	−2.66558e8	−	6.43529e8i	−0.271009	−	0.654273i
$372$	7.07152e8	−	3.46364e9i	0.712218	−	3.48845i
$373$	8.68542e8	+	3.59762e8i	0.866583	+	0.358950i	0.771278	−	0.636498i	$-0.219618\pi$
$373$	8.68542e8	+	3.59762e8i	0.866583	+	0.358950i	0.0953043	+	0.995448i	$0.469618\pi$
$374$	9.89407e8	−	9.49277e7i	0.977967	−	0.0938301i
$375$	7.88220e8	−	7.88220e8i	0.771859	−	0.771859i
$376$	4.40582e7	−	4.15091e8i	0.0427435	−	0.402704i
$377$	4.24056e7	+	4.24056e7i	0.0407594	+	0.0407594i
$378$	1.42512e9	+	1.17559e9i	1.35715	+	1.11953i
$379$	−1.94451e8	+	4.69446e8i	−0.183473	+	0.442944i	−0.988678	−	0.150053i	$-0.952055\pi$
$379$	−1.94451e8	+	4.69446e8i	−0.183473	+	0.442944i	0.805205	+	0.592997i	$0.202055\pi$
$380$	−7.12412e8	+	1.05464e9i	−0.666022	+	0.985964i
$381$	2.27433e9	−	9.42060e8i	2.10677	−	0.872652i
$382$	5.69563e7	+	1.07208e8i	0.0522781	+	0.0984019i
$383$	6.25944e8			0.569298			0.284649	−	0.958632i	$-0.408123\pi$
$383$	6.25944e8			0.569298			0.284649	+	0.958632i	$0.408123\pi$
$384$	1.30075e9	+	1.64332e9i	1.17229	+	1.48103i
$385$	−4.71288e8			−0.420895
$386$	−6.38324e8	−	1.20150e9i	−0.564919	−	1.06333i
$387$	1.62745e9	−	6.74110e8i	1.42731	−	0.591211i
$388$	−7.68133e8	+	1.13713e9i	−0.667614	+	0.988320i
$389$	−1.56705e8	+	3.78320e8i	−0.134977	+	0.325864i	−0.976888	−	0.213754i	$-0.931431\pi$
$389$	−1.56705e8	+	3.78320e8i	−0.134977	+	0.325864i	0.841910	+	0.539617i	$0.181431\pi$
$390$	−2.81885e8	−	2.32530e8i	−0.240628	−	0.198496i
$391$	−1.02137e9	−	1.02137e9i	−0.864104	−	0.864104i
$392$	−8.14425e7	+	7.67303e8i	−0.0682889	+	0.643377i
$393$	1.30813e9	−	1.30813e9i	1.08712	−	1.08712i
$394$	−1.71239e9	+	1.64294e8i	−1.41048	+	0.135327i
$395$	−2.98752e8	−	1.23747e8i	−0.243905	−	0.101029i
$396$	3.63126e8	−	1.77859e9i	0.293849	−	1.43927i
$397$	2.89232e8	+	6.98269e8i	0.231996	+	0.560088i	0.996412	−	0.0846357i	$-0.0269726\pi$
$397$	2.89232e8	+	6.98269e8i	0.231996	+	0.560088i	−0.764416	+	0.644723i	$0.776973\pi$
$398$	−6.90165e8	+	2.25467e9i	−0.548734	+	1.79264i
$399$			1.36825e9i			1.07835i
$400$	−2.67576e8	+	6.27981e8i	−0.209044	+	0.490610i
$401$		−	2.16728e9i		−	1.67845i	−0.543782	−	0.839226i	$-0.683008\pi$
$401$		−	2.16728e9i		−	1.67845i	0.543782	−	0.839226i	$-0.316992\pi$
$402$	2.80432e9	+	8.58416e8i	2.15296	+	0.659032i
$403$	1.26407e8	+	3.05173e8i	0.0962062	+	0.232262i
$404$	4.35977e7	+	6.59669e7i	0.0328949	+	0.0497727i
$405$	−4.62693e9	−	1.91654e9i	−3.46099	−	1.43359i
$406$	−3.30711e7	−	3.44692e8i	−0.0245249	−	0.255617i
$407$	−7.48303e8	+	7.48303e8i	−0.550170	+	0.550170i
$408$	−1.25946e9	−	4.26793e9i	−0.918065	−	3.11105i
$409$	−7.00540e8	−	7.00540e8i	−0.506292	−	0.506292i	0.407094	−	0.913386i	$-0.366542\pi$
$409$	−7.00540e8	−	7.00540e8i	−0.506292	−	0.506292i	−0.913386	+	0.407094i	$0.866542\pi$
$410$	−1.87036e7	+	2.26734e7i	−0.0134023	+	0.0162470i
$411$	−6.90405e8	+	1.66678e9i	−0.490521	+	1.18422i
$412$	−8.23853e8	+	1.59556e8i	−0.580376	+	0.112402i
$413$	−2.92575e8	+	1.21189e8i	−0.204368	+	0.0846519i
$414$	−2.32967e9	+	1.23768e9i	−1.61359	+	0.857252i
$415$	2.37843e9			1.63351
$416$	−1.86667e8	−	5.92069e7i	−0.127128	−	0.0403223i
$417$	−4.30764e8			−0.290913
$418$	7.24895e8	−	3.85116e8i	0.485465	−	0.257914i
$419$	−1.06378e9	+	4.40633e8i	−0.706486	+	0.292636i	−0.706850	−	0.707364i	$-0.749884\pi$
$419$	−1.06378e9	+	4.40633e8i	−0.706486	+	0.292636i	0.000363697		1.00000i	$0.499884\pi$
$420$	4.01180e8	+	2.07145e9i	0.264221	+	1.36428i
$421$	−2.82976e8	+	6.83166e8i	−0.184826	+	0.446209i	−0.988949	−	0.148253i	$-0.952635\pi$
$421$	−2.82976e8	+	6.83166e8i	−0.184826	+	0.446209i	0.804124	+	0.594462i	$0.202635\pi$
$422$	8.07776e8	−	9.79228e8i	0.523236	−	0.634294i
$423$	1.14456e9	+	1.14456e9i	0.735268	+	0.735268i
$424$	1.64319e9	+	8.94363e8i	1.04691	+	0.569814i
$425$	1.02484e9	−	1.02484e9i	0.647579	−	0.647579i
$426$	−1.60535e8	−	1.67321e9i	−0.100609	−	1.04862i
$427$	1.97724e8	+	8.19000e7i	0.122903	+	0.0509081i
$428$	−5.62325e8	+	3.71642e8i	−0.346684	+	0.229124i
$429$	9.01901e7	+	2.17738e8i	0.0551516	+	0.133148i
$430$	1.17453e9	+	3.59528e8i	0.712400	+	0.218069i
$431$			7.95551e8i			0.478628i	0.970942	+	0.239314i	$0.0769225\pi$
$431$			7.95551e8i			0.478628i	−0.970942	+	0.239314i	$0.923078\pi$
$432$	−4.96163e9	−	5.00847e7i	−2.96095	−	0.0298890i
$433$		−	1.06685e9i		−	0.631534i	−0.948837	−	0.315767i	$-0.897738\pi$
$433$		−	1.06685e9i		−	0.631534i	0.948837	−	0.315767i	$-0.102262\pi$
$434$	5.58258e8	−	1.82375e9i	0.327809	−	1.07090i
$435$	6.64117e8	+	1.60332e9i	0.386841	+	0.933916i
$436$	9.15594e8	+	1.86932e8i	0.529054	+	0.108014i
$437$	−1.10208e9	−	4.56495e8i	−0.631723	−	0.261668i
$438$	−5.29157e9	+	5.07695e8i	−3.00902	+	0.288698i
$439$	1.73709e9	−	1.73709e9i	0.979935	−	0.979935i	−0.0198675	−	0.999803i	$-0.506324\pi$
$439$	1.73709e9	−	1.73709e9i	0.979935	−	0.979935i	0.999803	+	0.0198675i	$0.00632445\pi$
$440$	9.84529e8	−	7.95586e8i	0.550991	−	0.445249i
$441$	−2.11573e9	−	2.11573e9i	−1.17470	−	1.17470i
$442$	3.20747e8	+	2.64588e8i	0.176679	+	0.145744i
$443$	−1.12738e9	+	2.72172e9i	−0.616106	+	1.48741i	0.240085	+	0.970752i	$0.422825\pi$
$443$	−1.12738e9	+	2.72172e9i	−0.616106	+	1.48741i	−0.856191	+	0.516659i	$0.827175\pi$
$444$	3.92600e9	+	2.65203e9i	2.12868	+	1.43793i
$445$	−3.72853e8	+	1.54441e8i	−0.200575	+	0.0830811i
$446$	2.88703e8	+	5.43420e8i	0.154092	+	0.290044i
$447$	−5.68016e9			−3.00805
$448$	6.13903e8	+	9.49586e8i	0.322572	+	0.498955i
$449$	2.09123e9			1.09028			0.545142	−	0.838344i	$-0.316476\pi$
$449$	2.09123e9			1.09028			0.545142	+	0.838344i	$0.316476\pi$
$450$	−1.24188e9	−	2.33756e9i	−0.642444	−	1.20926i
$451$	1.75138e7	−	7.25446e6i	0.00899006	−	0.00372381i
$452$	9.34268e8	+	6.31101e8i	0.475868	+	0.321451i
$453$	5.73429e8	−	1.38438e9i	0.289825	−	0.699700i
$454$	−1.44855e9	−	1.19492e9i	−0.726504	−	0.599301i
$455$	−1.39407e8	−	1.39407e8i	−0.0693819	−	0.0693819i
$456$	−2.30976e9	−	2.85830e9i	−1.14075	−	1.41166i
$457$	−5.27534e7	+	5.27534e7i	−0.0258550	+	0.0258550i	−0.719916	−	0.694061i	$-0.755820\pi$
$457$	−5.27534e7	+	5.27534e7i	−0.0258550	+	0.0258550i	0.694061	+	0.719916i	$0.255820\pi$
$458$	8.25524e8	−	7.92041e7i	0.401514	−	0.0385229i
$459$	9.73324e9	+	4.03164e9i	4.69800	+	1.94598i
$460$	−1.80232e9	−	3.67970e8i	−0.863337	−	0.176263i
$461$	7.50222e8	+	1.81120e9i	0.356645	+	0.861018i	0.995767	+	0.0919122i	$0.0292979\pi$
$461$	7.50222e8	+	1.81120e9i	0.356645	+	0.861018i	−0.639122	+	0.769105i	$0.720702\pi$
$462$	3.98312e8	−	1.30123e9i	0.187921	−	0.613912i
$463$		−	2.46169e9i		−	1.15266i	−0.817218	−	0.576329i	$-0.804485\pi$
$463$		−	2.46169e9i		−	1.15266i	0.817218	−	0.576329i	$-0.195515\pi$
$464$	6.50963e8	+	6.64239e8i	0.302513	+	0.308682i
$465$			9.55868e9i			4.40872i
$466$	−8.27115e8	−	2.53184e8i	−0.378630	−	0.115900i
$467$	−5.92582e8	−	1.43062e9i	−0.269240	−	0.650003i	0.730208	−	0.683225i	$-0.239423\pi$
$467$	−5.92582e8	−	1.43062e9i	−0.269240	−	0.650003i	−0.999448	+	0.0332221i	$0.989423\pi$
$468$	6.33522e8	−	4.18697e8i	0.285694	−	0.188816i
$469$	1.46186e9	+	6.05522e8i	0.654335	+	0.271035i
$470$	1.07796e8	+	1.12353e9i	0.0478915	+	0.499161i
$471$	1.05678e9	−	1.05678e9i	0.466026	−	0.466026i
$472$	4.06615e8	−	7.47064e8i	0.177986	−	0.327010i
$473$	−5.60182e8	−	5.60182e8i	−0.243397	−	0.243397i
$474$	5.94158e8	−	7.20270e8i	0.256258	−	0.310650i
$475$	4.58042e8	−	1.10581e9i	0.196100	−	0.473428i
$476$	−4.56489e8	−	2.35704e9i	−0.194002	−	1.00171i
$477$	−6.70229e9	+	2.77618e9i	−2.82754	+	1.17121i
$478$	3.74088e9	−	1.98742e9i	1.56666	−	0.832323i
$479$	−1.84538e9			−0.767205			−0.383603	−	0.923498i	$-0.625317\pi$
$479$	−1.84538e9			−0.767205			−0.383603	+	0.923498i	$0.625317\pi$
$480$	−4.33491e9	−	3.65006e9i	−1.78910	−	1.50646i
$481$	−4.42697e8			−0.181384
$482$	2.99200e9	−	1.58956e9i	1.21702	−	0.646567i
$483$	−1.82706e9	+	7.56793e8i	−0.737799	+	0.305606i
$484$	1.64736e9	−	3.19045e8i	0.660434	−	0.127907i
$485$	1.41995e9	−	3.42805e9i	0.565166	−	1.36443i
$486$	4.43366e9	−	5.37472e9i	1.75201	−	2.12387i
$487$	1.67225e9	+	1.67225e9i	0.656071	+	0.656071i	0.954448	−	0.298377i	$-0.0964453\pi$
$487$	1.67225e9	+	1.67225e9i	0.656071	+	0.656071i	−0.298377	+	0.954448i	$0.596445\pi$
$488$	−5.51305e8	+	1.62689e8i	−0.214745	+	0.0633708i
$489$	2.70183e9	−	2.70183e9i	1.04491	−	1.04491i
$490$	−1.99262e8	−	2.07686e9i	−0.0765136	−	0.797482i
$491$	−2.12563e9	−	8.80465e8i	−0.810406	−	0.335681i	−0.0612899	−	0.998120i	$-0.519521\pi$
$491$	−2.12563e9	−	8.80465e8i	−0.810406	−	0.335681i	−0.749116	+	0.662439i	$0.769521\pi$
$492$	−4.67940e7	−	7.08031e7i	−0.0177138	−	0.0268024i
$493$	−7.55676e8	−	1.82436e9i	−0.284035	−	0.685720i
$494$	3.28342e8	+	1.00507e8i	0.122541	+	0.0375104i
$495$			4.90842e9i			1.81896i
$496$	1.91247e9	+	4.75224e9i	0.703736	+	1.74869i
$497$		−	9.06888e8i		−	0.331365i
$498$	−2.01014e9	+	6.56684e9i	−0.729329	+	2.38261i
$499$	9.42525e8	+	2.27546e9i	0.339579	+	0.819817i	0.997756	+	0.0669533i	$0.0213279\pi$
$499$	9.42525e8	+	2.27546e9i	0.339579	+	0.819817i	−0.658177	+	0.752863i	$0.728672\pi$
$500$	−3.23122e8	+	1.58266e9i	−0.115604	+	0.566228i
$501$	−1.39328e9	−	5.77115e8i	−0.495001	−	0.205036i
$502$	2.69615e9	−	2.58679e8i	0.951220	−	0.0912639i
$503$	−1.15703e9	+	1.15703e9i	−0.405373	+	0.405373i	−0.880122	−	0.474748i	$-0.842539\pi$
$503$	−1.15703e9	+	1.15703e9i	−0.405373	+	0.405373i	0.474748	+	0.880122i	$0.342539\pi$
$504$	−4.36023e9	−	4.62800e8i	−1.51706	−	0.161022i
$505$	−1.51184e8	−	1.51184e8i	−0.0522378	−	0.0522378i
$506$	9.15200e8	+	7.54958e8i	0.314043	+	0.259057i
$507$	2.08337e9	−	5.02970e9i	0.709968	−	1.71401i
$508$	−1.99679e9	+	2.95600e9i	−0.675787	+	1.00042i
$509$	4.87148e9	−	2.01783e9i	1.63738	−	0.678224i	0.641348	−	0.767250i	$-0.278376\pi$
$509$	4.87148e9	−	2.01783e9i	1.63738	−	0.678224i	0.996029	+	0.0890263i	$0.0283755\pi$
$510$	5.64516e9	+	1.06258e10i	1.88443	+	3.54702i
$511$	−2.86806e9			−0.950856
$512$	−2.88546e9	−	9.47367e8i	−0.950101	−	0.311942i
$513$	8.70039e9			2.84530
$514$	4.74582e8	+	8.93296e8i	0.154149	+	0.290151i
$515$	2.09632e9	−	8.68325e8i	0.676290	−	0.280128i
$516$	−1.98532e9	+	2.93902e9i	−0.636144	+	0.941733i
$517$	2.78576e8	−	6.72542e8i	0.0886599	−	0.214044i
$518$	1.97185e9	+	1.62660e9i	0.623332	+	0.514193i
$519$	−2.19999e9	−	2.19999e9i	−0.690773	−	0.690773i
$520$	5.26559e8	+	5.58897e7i	0.164224	+	0.0174309i
$521$	−3.93023e9	+	3.93023e9i	−1.21755	+	1.21755i	−0.249059	+	0.968488i	$0.580121\pi$
$521$	−3.93023e9	+	3.93023e9i	−1.21755	+	1.21755i	−0.968488	+	0.249059i	$0.919879\pi$
$522$	−3.58993e9	+	3.44433e8i	−1.10469	+	0.105988i
$523$	−1.10412e9	−	4.57343e8i	−0.337490	−	0.139793i	0.207501	−	0.978235i	$-0.433467\pi$
$523$	−1.10412e9	−	4.57343e8i	−0.337490	−	0.139793i	−0.544991	+	0.838442i	$0.683467\pi$
$524$	−5.36256e8	+	2.62659e9i	−0.162822	+	0.797503i
$525$	−7.59358e8	−	1.83325e9i	−0.229028	−	0.552923i
$526$	9.97809e8	−	3.25970e9i	0.298949	−	0.976625i
$527$		−	1.08765e10i		−	3.23707i
$528$	1.36453e9	+	3.39068e9i	0.403427	+	1.00246i
$529$			1.68071e9i			0.493625i
$530$	−4.83704e9	−	1.48064e9i	−1.41128	−	0.432000i
$531$	1.26217e9	+	3.04714e9i	0.365836	+	0.883206i
$532$	−1.09320e9	−	1.65410e9i	−0.314781	−	0.476289i
$533$	7.32647e6	+	3.03472e6i	0.00209580	+	0.000868108i
$534$	−1.11293e8	−	1.15997e9i	−0.0316280	−	0.329651i
$535$	1.28874e9	−	1.28874e9i	0.363855	−	0.363855i
$536$	−4.07603e9	+	1.20283e9i	−1.14330	+	0.337386i
$537$	−4.42439e8	−	4.42439e8i	−0.123294	−	0.123294i
$538$	8.23747e8	−	9.98589e8i	0.228063	−	0.276470i
$539$	−5.14953e8	+	1.24321e9i	−0.141647	+	0.341966i
$540$	1.31719e10	−	2.55101e9i	3.59972	−	0.697162i
$541$	−5.59453e9	+	2.31733e9i	−1.51906	+	0.629213i	−0.977402	−	0.211389i	$-0.932201\pi$
$541$	−5.59453e9	+	2.31733e9i	−1.51906	+	0.629213i	−0.541653	+	0.840602i	$0.682201\pi$
$542$	−6.08152e9	+	3.23094e9i	−1.64065	+	0.871627i
$543$	−7.69805e8			−0.206339
$544$	4.93254e9	+	4.15328e9i	1.31364	+	1.10610i
$545$	−2.52678e9			−0.668621
$546$	5.02725e8	−	2.67083e8i	0.132177	−	0.0702219i
$547$	4.17456e9	−	1.72916e9i	1.09057	−	0.451730i	0.236366	−	0.971664i	$-0.424043\pi$
$547$	4.17456e9	−	1.72916e9i	1.09057	−	0.451730i	0.854206	+	0.519934i	$0.174043\pi$
$548$	−4.97078e8	−	2.56661e9i	−0.129031	−	0.666237i
$549$	8.52981e8	−	2.05928e9i	0.220007	−	0.531143i
$550$	−7.57517e8	+	9.18302e8i	−0.194144	+	0.235351i
$551$	−1.15313e9	−	1.15313e9i	−0.293662	−	0.293662i
$552$	2.53921e9	−	4.66523e9i	0.642557	−	1.18055i
$553$	3.56213e8	−	3.56213e8i	0.0895719	−	0.0895719i
$554$	4.52559e8	+	4.71691e9i	0.113081	+	1.17862i
$555$	−1.18356e10	−	4.90245e9i	−2.93876	−	1.21727i
$556$	5.20756e8	−	3.44169e8i	0.128491	−	0.0849200i
$557$	2.46032e9	+	5.93973e9i	0.603251	+	1.45638i	0.870216	+	0.492670i	$0.163979\pi$
$557$	2.46032e9	+	5.93973e9i	0.603251	+	1.45638i	−0.266965	+	0.963706i	$0.586021\pi$
$558$	−1.89942e10	−	5.81420e9i	−4.62807	−	1.41667i
$559$		−	3.31404e8i		−	0.0802448i
$560$	−2.14003e9	−	2.18367e9i	−0.514946	−	0.525448i
$561$		−	7.76028e9i		−	1.85570i
$562$	7.03468e8	−	2.29813e9i	0.167173	−	0.546132i
$563$	8.74413e8	+	2.11102e9i	0.206508	+	0.498555i	0.992869	−	0.119213i	$-0.0380371\pi$
$563$	8.74413e8	+	2.11102e9i	0.206508	+	0.498555i	−0.786360	+	0.617768i	$0.788037\pi$
$564$	−3.19316e9	−	6.51930e8i	−0.749452	−	0.153011i
$565$	−2.81650e9	−	1.16663e9i	−0.656962	−	0.272123i
$566$	−5.41613e9	+	5.19645e8i	−1.25554	+	0.120462i
$567$	5.51686e9	−	5.51686e9i	1.27102	−	1.27102i
$568$	1.53092e9	+	1.89450e9i	0.350538	+	0.433787i
$569$	1.76883e9	+	1.76883e9i	0.402525	+	0.402525i	0.879122	−	0.476597i	$-0.158130\pi$
$569$	1.76883e9	+	1.76883e9i	0.402525	+	0.402525i	−0.476597	+	0.879122i	$0.658130\pi$
$570$	7.66525e9	+	6.32315e9i	1.73366	+	1.43012i
$571$	−1.25698e9	+	3.03462e9i	−0.282555	+	0.682148i	−0.999894	−	0.0145766i	$-0.995360\pi$
$571$	−1.25698e9	+	3.03462e9i	−0.282555	+	0.682148i	0.717339	+	0.696724i	$0.245360\pi$
$572$	−2.82999e8	−	1.91167e8i	−0.0632265	−	0.0427097i
$573$	8.75668e8	−	3.62714e8i	0.194446	−	0.0805421i
$574$	−2.14829e7	−	4.04368e7i	−0.00474134	−	0.00892452i
$575$	1.72996e9			0.379489
$576$	9.88985e9	−	6.39374e9i	2.15631	−	1.39404i
$577$	−1.76351e9			−0.382176			−0.191088	−	0.981573i	$-0.561202\pi$
$577$	−1.76351e9			−0.382176			−0.191088	+	0.981573i	$0.561202\pi$
$578$	−4.24533e9	−	7.99090e9i	−0.914459	−	1.72127i
$579$	−9.81386e9	+	4.06503e9i	−2.10119	+	0.870340i
$580$	−2.08387e9	−	1.40766e9i	−0.443479	−	0.299572i
$581$	−1.41794e9	+	3.42321e9i	−0.299945	+	0.724132i
$582$	8.26478e9	+	6.81771e9i	1.73780	+	1.43353i
$583$	2.30699e9	+	2.30699e9i	0.482176	+	0.482176i
$584$	5.99142e9	−	4.84159e9i	1.24476	−	1.00587i
$585$	−1.45191e9	+	1.45191e9i	−0.299844	+	0.299844i
$586$	6.14007e9	−	5.89103e8i	1.26047	−	0.120934i
$587$	7.20612e8	+	2.98487e8i	0.147051	+	0.0609105i	0.454995	−	0.890494i	$-0.349641\pi$
$587$	7.20612e8	+	2.98487e8i	0.147051	+	0.0609105i	−0.307944	+	0.951404i	$0.599641\pi$
$588$	5.90262e9	+	1.20510e9i	1.19736	+	0.244458i
$589$	−3.43736e9	−	8.29853e9i	−0.693142	−	1.67339i
$590$	−6.73161e8	+	2.19912e9i	−0.134939	+	0.440826i
$591$			1.34309e10i			2.67639i
$592$	−6.86510e9	−	6.92991e7i	−1.35994	−	0.0137278i
$593$		−	4.74290e9i		−	0.934011i	−0.884254	−	0.467006i	$-0.845333\pi$
$593$		−	4.74290e9i		−	0.934011i	0.884254	−	0.467006i	$-0.154667\pi$
$594$	−8.27419e9	−	2.53277e9i	−1.61984	−	0.495842i
$595$	2.48427e9	+	5.99756e9i	0.483492	+	1.16725i
$596$	6.86682e9	−	4.53830e9i	1.32860	−	0.878075i
$597$	1.70083e10	+	7.04506e9i	3.27153	+	1.35511i
$598$	4.73996e7	+	4.94034e8i	0.00906402	+	0.0944719i
$599$	−6.56615e9	+	6.56615e9i	−1.24829	+	1.24829i	−0.291821	+	0.956473i	$0.594261\pi$
$599$	−6.56615e9	+	6.56615e9i	−1.24829	+	1.24829i	−0.956473	+	0.291821i	$0.905739\pi$
$600$	4.68104e9	+	2.54782e9i	0.884735	+	0.481547i
$601$	−9.78898e7	−	9.78898e7i	−0.0183940	−	0.0183940i	0.697850	−	0.716244i	$-0.254140\pi$
$601$	−9.78898e7	−	9.78898e7i	−0.0183940	−	0.0183940i	−0.716244	+	0.697850i	$0.754140\pi$
$602$	−1.21768e9	+	1.47613e9i	−0.227480	+	0.275764i
$603$	6.30645e9	−	1.52251e10i	1.17132	−	2.82781i
$604$	4.12858e8	+	2.13175e9i	0.0762380	+	0.393647i
$605$	−4.19176e9	+	1.73628e9i	−0.769578	+	0.318770i
$606$	5.45192e8	−	2.89645e8i	0.0995166	−	0.0528703i
$607$	7.75525e9			1.40746			0.703728	−	0.710469i	$-0.251517\pi$
$607$	7.75525e9			1.40746			0.703728	+	0.710469i	$0.251517\pi$
$608$	5.07601e9	+	1.61000e9i	0.915925	+	0.290512i
$609$	−2.70355e9			−0.485035
$610$	1.37257e9	−	7.29207e8i	0.244839	−	0.130076i
$611$	2.81342e8	−	1.16535e8i	0.0498988	−	0.0206687i
$612$	−2.45483e10	+	4.75429e9i	−4.32904	+	0.838408i
$613$	−1.20701e9	+	2.91398e9i	−0.211640	+	0.510945i	−0.993676	−	0.112289i	$-0.964182\pi$
$613$	−1.20701e9	+	2.91398e9i	−0.211640	+	0.510945i	0.782035	+	0.623234i	$0.214182\pi$
$614$	−2.13921e9	+	2.59326e9i	−0.372961	+	0.452123i
$615$	1.62267e8	+	1.62267e8i	0.0281299	+	0.0281299i
$616$	5.58123e8	+	1.89131e9i	0.0962049	+	0.326010i
$617$	−2.85390e9	+	2.85390e9i	−0.489148	+	0.489148i	−0.908037	−	0.418889i	$-0.862420\pi$
$617$	−2.85390e9	+	2.85390e9i	−0.489148	+	0.489148i	0.418889	+	0.908037i	$0.362420\pi$
$618$	6.25730e8	+	6.52182e9i	0.106642	+	1.11150i
$619$	−7.18401e9	−	2.97571e9i	−1.21745	−	0.504283i	−0.320849	−	0.947130i	$-0.603968\pi$
$619$	−7.18401e9	−	2.97571e9i	−1.21745	−	0.504283i	−0.896597	+	0.442848i	$0.853968\pi$
$620$	−7.63714e9	−	1.15556e10i	−1.28694	−	1.94725i
$621$	4.81226e9	+	1.16178e10i	0.806360	+	1.94672i
$622$	−3.92039e9	−	1.20005e9i	−0.653226	−	0.199955i
$623$		−	6.28711e8i		−	0.104170i
$624$	−5.99336e8	+	1.40660e9i	−0.0987470	+	0.231752i
$625$		−	7.62263e9i		−	1.24889i
$626$	−2.34176e9	+	7.65020e9i	−0.381533	+	1.24641i
$627$	−2.45253e9	−	5.92092e9i	−0.397354	−	0.959297i
$628$	−4.33214e8	+	2.12189e9i	−0.0697982	+	0.341872i
$629$	1.34673e10	+	5.57833e9i	2.15776	+	0.893773i
$630$	1.18018e10	−	1.13232e9i	1.88043	−	0.180416i
$631$	−1.44935e8	+	1.44935e8i	−0.0229652	+	0.0229652i	−0.718496	−	0.695531i	$-0.755169\pi$
$631$	−1.44935e8	+	1.44935e8i	−0.0229652	+	0.0229652i	0.695531	+	0.718496i	$0.255169\pi$
$632$	−1.42809e8	+	1.34546e9i	−0.0225033	+	0.212012i
$633$	−7.00807e9	−	7.00807e9i	−1.09821	−	1.09821i
$634$	−3.93653e9	−	3.24729e9i	−0.613481	−	0.506067i
$635$	3.69120e9	−	8.91135e9i	0.572084	−	1.38113i
$636$	8.17610e9	−	1.21037e10i	1.26022	−	1.86560i
$637$	−5.20065e8	+	2.15418e8i	−0.0797205	+	0.0330213i
$638$	7.60954e8	+	1.43233e9i	0.116008	+	0.218358i
$639$	−9.44514e9			−1.43204
$640$	8.15683e9	+	9.49132e8i	1.22996	+	0.143119i
$641$	1.25540e10			1.88268			0.941342	−	0.337454i	$-0.109566\pi$
$641$	1.25540e10			1.88268			0.941342	+	0.337454i	$0.109566\pi$
$642$	2.46903e9	+	4.64741e9i	0.368260	+	0.693167i
$643$	5.74288e9	−	2.37878e9i	0.851905	−	0.352871i	0.0863687	−	0.996263i	$-0.472474\pi$
$643$	5.74288e9	−	2.37878e9i	0.851905	−	0.352871i	0.765536	+	0.643393i	$0.222474\pi$
$644$	1.60410e9	−	2.37467e9i	0.236663	−	0.350351i
$645$	3.66999e9	−	8.86014e9i	0.538525	−	1.30011i
$646$	−8.72203e9	−	7.19489e9i	−1.27293	−	1.05005i
$647$	8.54013e9	+	8.54013e9i	1.23965	+	1.23965i	0.960144	+	0.279507i	$0.0901710\pi$
$647$	8.54013e9	+	8.54013e9i	1.23965	+	1.23965i	0.279507	+	0.960144i	$0.409829\pi$
$648$	−2.21176e9	+	2.08379e10i	−0.319319	+	3.00843i
$649$	1.04885e9	−	1.04885e9i	0.150612	−	0.150612i
$650$	−4.95708e8	+	4.75603e7i	−0.0707994	+	0.00679278i
$651$	−1.37576e10	−	5.69858e9i	−1.95438	−	0.809530i
$652$	−1.10759e9	+	5.42497e9i	−0.156499	+	0.766533i
$653$	2.42186e8	+	5.84689e8i	0.0340371	+	0.0821729i	0.939984	−	0.341218i	$-0.110840\pi$
$653$	2.42186e8	+	5.84689e8i	0.0340371	+	0.0821729i	−0.905947	+	0.423391i	$0.860840\pi$
$654$	2.13552e9	−	6.97645e9i	0.298526	−	0.975242i
$655$		−	7.24865e9i		−	1.00789i
$656$	1.13140e8	+	4.82076e7i	0.0156477	+	0.00666734i
$657$			2.98705e10i			4.10926i
$658$	−1.68133e9	−	5.14662e8i	−0.230071	−	0.0704258i
$659$	4.21381e9	+	1.01730e10i	0.573557	+	1.38469i	0.898508	+	0.438958i	$0.144652\pi$
$659$	4.21381e9	+	1.01730e10i	0.573557	+	1.38469i	−0.324951	+	0.945731i	$0.605348\pi$
$660$	−5.44903e9	−	8.24483e9i	−0.737760	−	1.11629i
$661$	−9.00493e9	−	3.72996e9i	−1.21276	−	0.502342i	−0.317660	−	0.948205i	$-0.602897\pi$
$661$	−9.00493e9	−	3.72996e9i	−1.21276	−	0.502342i	−0.895101	+	0.445863i	$0.852897\pi$
$662$	−1.78636e8	−	1.86188e9i	−0.0239313	−	0.249429i
$663$	2.29550e9	−	2.29550e9i	0.305900	−	0.305900i
$664$	−2.81665e9	−	9.54479e9i	−0.373375	−	1.26525i
$665$	3.79089e9	+	3.79089e9i	0.499879	+	0.499879i
$666$	1.69409e10	−	2.05366e10i	2.22216	−	2.69382i
$667$	9.01993e8	−	2.17760e9i	0.117696	−	0.284144i
$668$	2.14545e9	−	4.15511e8i	0.278485	−	0.0539343i
$669$	4.43864e9	−	1.83854e9i	0.573137	−	0.237401i
$670$	1.01480e10	−	5.39133e9i	1.30352	−	0.692523i
$671$	−1.00243e9			−0.128092
$672$	7.83778e9	−	4.06308e9i	0.996324	−	0.516491i
$673$	−1.12837e10			−1.42692			−0.713459	−	0.700697i	$-0.752873\pi$
$673$	−1.12837e10			−1.42692			−0.713459	+	0.700697i	$0.752873\pi$
$674$	4.64454e8	−	2.46751e8i	0.0584296	−	0.0310420i
$675$	−1.16572e10	+	4.82858e9i	−1.45892	+	0.604305i
$676$	1.49999e9	+	7.74503e9i	0.186756	+	0.964295i
$677$	1.05405e9	−	2.54469e9i	0.130557	−	0.315192i	−0.845061	−	0.534671i	$-0.820436\pi$
$677$	1.05405e9	−	2.54469e9i	0.130557	−	0.315192i	0.975617	+	0.219479i	$0.0704357\pi$
$678$	5.60146e9	−	6.79038e9i	0.690235	−	0.836739i
$679$	4.08739e9	+	4.08739e9i	0.501074	+	0.501074i
$680$	−1.53142e10	−	8.33528e9i	−1.86773	−	1.01657i
$681$	−1.03669e10	+	1.03669e10i	−1.25786	+	1.25786i
$682$	8.53198e8	+	8.89266e9i	0.102992	+	1.07346i
$683$	1.14181e10	+	4.72953e9i	1.37126	+	0.567996i	0.942131	−	0.335245i	$-0.108819\pi$
$683$	1.14181e10	+	4.72953e9i	1.37126	+	0.567996i	0.429133	+	0.903241i	$0.358819\pi$
$684$	−1.72273e10	+	1.13856e10i	−2.05836	+	1.36037i
$685$	2.70516e9	+	6.53084e9i	0.321570	+	0.776340i
$686$	7.91169e9	+	2.42180e9i	0.935696	+	0.286421i
$687$		−	6.47489e9i		−	0.761875i
$688$	5.18775e7	−	5.13923e9i	0.00607323	−	0.601643i
$689$			1.36482e9i			0.158967i
$690$	−4.20372e9	+	1.37330e10i	−0.487150	+	1.59145i
$691$	2.82662e9	+	6.82407e9i	0.325908	+	0.786811i	0.998888	+	0.0471504i	$0.0150140\pi$
$691$	2.82662e9	+	6.82407e9i	0.325908	+	0.786811i	−0.672980	+	0.739661i	$0.734986\pi$
$692$	4.41734e9	+	9.01863e8i	0.506745	+	0.103459i
$693$	−7.06457e9	−	2.92624e9i	−0.806343	−	0.333998i
$694$	1.53538e9	−	1.47311e8i	0.174365	−	0.0167293i
$695$	−1.19347e9	+	1.19347e9i	−0.134855	+	0.134855i
$696$	5.64775e9	−	4.56388e9i	0.634955	−	0.513099i
$697$	−1.84639e8	−	1.84639e8i	−0.0206542	−	0.0206542i
$698$	−6.46506e9	−	5.33310e9i	−0.719579	−	0.593589i
$699$	−2.58445e9	+	6.23940e9i	−0.286218	+	0.690992i
$700$	2.38272e9	+	1.60954e9i	0.262561	+	0.177361i
$701$	−1.09917e10	+	4.55290e9i	−1.20518	+	0.499200i	−0.892668	−	0.450715i	$-0.851169\pi$
$701$	−1.09917e10	+	4.55290e9i	−1.20518	+	0.499200i	−0.312508	+	0.949915i	$0.601169\pi$
$702$	−1.69832e9	−	3.19671e9i	−0.185285	−	0.348757i
$703$	1.20382e10			1.30683
$704$	−4.35867e9	−	3.00881e9i	−0.470814	−	0.325005i
$705$	8.81223e9			0.947161
$706$	−2.11017e9	−	3.97192e9i	−0.225684	−	0.424799i
$707$	3.07726e8	−	1.27464e8i	0.0327489	−	0.0135650i
$708$	−5.50285e9	−	3.71720e9i	−0.582736	−	0.393640i
$709$	6.61558e9	−	1.59714e10i	0.697118	−	1.68299i	−0.0328053	−	0.999462i	$-0.510444\pi$
$709$	6.61558e9	−	1.59714e10i	0.697118	−	1.68299i	0.729923	−	0.683529i	$-0.239556\pi$
$710$	−5.08058e9	−	4.19102e9i	−0.532732	−	0.439457i
$711$	−3.70992e9	−	3.70992e9i	−0.387098	−	0.387098i
$712$	1.06133e9	+	1.31339e9i	0.110197	+	0.136368i
$713$	9.17998e9	−	9.17998e9i	0.948480	−	0.948480i
$714$	−1.86589e10	+	1.79021e9i	−1.91841	+	0.184060i
$715$	8.53147e8	+	3.53385e8i	0.0872877	+	0.0361557i
$716$	8.88367e8	+	1.81373e8i	0.0904476	+	0.0184662i
$717$	−1.26565e10	−	3.05554e10i	−1.28232	−	3.09578i
$718$	−1.57058e9	+	5.13087e9i	−0.158353	+	0.517315i
$719$			1.03616e10i			1.03962i	0.854281	+	0.519811i	$0.173998\pi$
$719$			1.03616e10i			1.03962i	−0.854281	+	0.519811i	$0.826002\pi$
$720$	−2.27427e10	+	2.22882e10i	−2.27080	+	2.22541i
$721$			3.53485e9i			0.351235i
$722$	7.41543e8	+	2.26990e8i	0.0733257	+	0.0224453i
$723$	−1.01228e10	−	2.44386e10i	−0.996131	−	2.40487i
$724$	9.30627e8	−	6.15054e8i	0.0911362	−	0.0602322i
$725$	2.18499e9	+	9.05050e8i	0.212944	+	0.0882043i
$726$	−1.25119e9	−	1.30409e10i	−0.121352	−	1.26482i
$727$	−6.39034e9	+	6.39034e9i	−0.616813	+	0.616813i	−0.944713	−	0.327900i	$-0.893659\pi$
$727$	−6.39034e9	+	6.39034e9i	−0.616813	+	0.616813i	0.327900	+	0.944713i	$0.393659\pi$
$728$	−3.94358e8	+	7.24545e8i	−0.0378818	+	0.0695994i
$729$	−1.60882e10	−	1.60882e10i	−1.53802	−	1.53802i
$730$	−1.32542e10	+	1.60675e10i	−1.26103	+	1.52868i
$731$	−4.17596e9	+	1.00817e10i	−0.395408	+	0.954599i
$732$	8.53306e8	+	4.40596e9i	0.0804111	+	0.415195i
$733$	−1.01843e10	+	4.21849e9i	−0.955145	+	0.395634i	−0.805162	−	0.593055i	$-0.797922\pi$
$733$	−1.01843e10	+	4.21849e9i	−0.955145	+	0.395634i	−0.149982	+	0.988689i	$0.547922\pi$
$734$	2.04396e9	−	1.08590e9i	0.190782	−	0.101357i
$735$	−1.62896e10			−1.51323
$736$	6.57711e8	+	7.66862e9i	0.0608083	+	0.708998i
$737$	−7.41136e9			−0.681964
$738$	−4.21145e8	+	2.23742e8i	−0.0385686	+	0.0204904i
$739$	1.40881e10	−	5.83549e9i	1.28410	−	0.531890i	0.366875	−	0.930270i	$-0.380428\pi$
$739$	1.40881e10	−	5.83549e9i	1.28410	−	0.531890i	0.917220	+	0.398380i	$0.130428\pi$
$740$	1.82251e10	−	3.52967e9i	1.65333	−	0.320201i
$741$	1.02595e9	−	2.47687e9i	0.0926327	−	0.223635i
$742$	5.01474e9	−	6.07913e9i	0.450645	−	0.546295i
$743$	−3.90402e9	−	3.90402e9i	−0.349181	−	0.349181i	0.510623	−	0.859805i	$-0.329415\pi$
$743$	−3.90402e9	−	3.90402e9i	−0.349181	−	0.349181i	−0.859805	+	0.510623i	$0.829415\pi$
$744$	3.83596e10	−	1.13199e10i	3.41483	−	1.00771i
$745$	−1.57375e10	+	1.57375e10i	−1.39440	+	1.39440i
$746$	1.01580e9	+	1.05874e10i	0.0895825	+	0.933695i
$747$	3.56524e10	+	1.47677e10i	3.12944	+	1.29626i
$748$	6.20026e9	+	9.38151e9i	0.541695	+	0.819629i
$749$	1.08655e9	+	2.62316e9i	0.0944851	+	0.228107i
$750$	1.20592e10	+	3.69137e9i	1.04377	+	0.319502i
$751$			1.64562e10i			1.41772i	0.705349	+	0.708861i	$0.250790\pi$
$751$			1.64562e10i			1.41772i	−0.705349	+	0.708861i	$0.749210\pi$
$752$	4.38113e9	−	1.76313e9i	0.375685	−	0.151189i
$753$		−	2.11469e10i		−	1.80495i
$754$	−1.98593e8	+	6.48774e8i	−0.0168719	+	0.0551181i
$755$	−2.24682e9	−	5.42431e9i	−0.190000	−	0.458702i
$756$	−4.18104e9	+	2.04788e10i	−0.351931	+	1.72376i
$757$	−8.04378e9	−	3.33184e9i	−0.673945	−	0.279157i	0.0193483	−	0.999813i	$-0.493841\pi$
$757$	−8.04378e9	−	3.33184e9i	−0.673945	−	0.279157i	−0.693293	+	0.720656i	$0.743841\pi$
$758$	−5.72250e9	+	5.49039e8i	−0.477247	+	0.0457890i
$759$	6.54983e9	−	6.54983e9i	0.543731	−	0.543731i
$760$	−1.43187e10	−	1.51980e9i	−1.18319	−	0.125585i
$761$	4.75483e9	+	4.75483e9i	0.391101	+	0.391101i	0.875080	−	0.483979i	$-0.160809\pi$
$761$	4.75483e9	+	4.75483e9i	0.391101	+	0.391101i	−0.483979	+	0.875080i	$0.660809\pi$
$762$	2.14846e10	+	1.77229e10i	1.75908	+	1.45108i
$763$	1.50639e9	−	3.63674e9i	0.122772	−	0.296399i
$764$	−7.68808e8	+	1.13813e9i	−0.0623722	+	0.0923344i
$765$	6.24640e10	−	2.58734e10i	5.04446	−	2.08948i
$766$	3.32254e9	+	6.25395e9i	0.267097	+	0.502752i
$767$	6.20504e8			0.0496547
$768$	−9.51434e9	+	2.17189e10i	−0.757905	+	1.73011i
$769$	−1.56763e10			−1.24308			−0.621542	−	0.783381i	$-0.713493\pi$
$769$	−1.56763e10			−1.24308			−0.621542	+	0.783381i	$0.713493\pi$
$770$	−2.50162e9	−	4.70875e9i	−0.197471	−	0.371696i
$771$	7.29642e9	−	3.02227e9i	0.573349	−	0.237489i
$772$	8.61625e9	−	1.27553e10i	0.673996	−	0.997768i
$773$	4.26445e9	−	1.02953e10i	0.332074	−	0.801697i	−0.666353	−	0.745636i	$-0.732146\pi$
$773$	4.26445e9	−	1.02953e10i	0.332074	−	0.801697i	0.998427	−	0.0560612i	$-0.0178542\pi$
$774$	1.53738e10	+	1.26820e10i	1.19175	+	0.983091i
$775$	9.21109e9	+	9.21109e9i	0.710813	+	0.710813i
$776$	−1.54386e10	−	1.63867e9i	−1.18602	−	0.125885i
$777$	1.41120e10	−	1.41120e10i	1.07923	−	1.07923i
$778$	−4.61168e9	+	4.42463e8i	−0.351100	+	0.0336859i
$779$	−1.99228e8	−	8.25228e7i	−0.0150997	−	0.00625450i
$780$	8.26999e8	−	4.05065e9i	0.0623985	−	0.305629i
$781$	1.62555e9	+	3.92443e9i	0.122102	+	0.294780i
$782$	4.78328e9	−	1.56263e10i	0.357686	−	1.16851i
$783$			1.71912e10i			1.27979i
$784$	−8.09860e9	+	3.25917e9i	−0.600211	+	0.241547i
$785$		−	5.85582e9i		−	0.432060i
$786$	2.00135e10	+	6.12623e9i	1.47009	+	0.450002i
$787$	−7.84790e9	−	1.89465e10i	−0.573908	−	1.38554i	−0.898204	−	0.439580i	$-0.855127\pi$
$787$	−7.84790e9	−	1.89465e10i	−0.573908	−	1.38554i	0.324296	−	0.945956i	$-0.394873\pi$
$788$	−1.07310e10	−	1.62368e10i	−0.781262	−	1.18211i
$789$	−2.45898e10	−	1.01854e10i	−1.78232	−	0.738261i
$790$	−3.49405e8	−	3.64176e9i	−0.0252136	−	0.262795i
$791$	3.35821e9	−	3.35821e9i	0.241263	−	0.241263i
$792$	1.96978e10	−	5.81279e9i	1.40890	−	0.415764i
$793$	−2.96518e8	−	2.96518e8i	−0.0211152	−	0.0211152i
$794$	−5.44130e9	+	6.59623e9i	−0.385772	+	0.467653i
$795$	−1.51141e10	+	3.64886e10i	−1.06683	+	2.57556i
$796$	−2.61904e10	+	5.07231e9i	−1.84054	+	0.356459i
$797$	−1.62502e10	+	6.73107e9i	−1.13699	+	0.470956i	−0.870150	−	0.492786i	$-0.835979\pi$
$797$	−1.62502e10	+	6.73107e9i	−1.13699	+	0.470956i	−0.266837	+	0.963742i	$0.585979\pi$
$798$	−1.36705e10	+	7.26276e9i	−0.952303	+	0.505931i
$799$	−1.00271e10			−0.695445
$800$	−7.69461e9	+	6.59940e8i	−0.531339	+	0.0455711i
$801$	−6.54797e9			−0.450187
$802$	2.16538e10	−	1.15040e10i	1.48225	−	0.787479i
$803$	1.24111e10	−	5.14085e9i	0.845875	−	0.350373i
$804$	6.30885e9	+	3.25751e10i	0.428109	+	2.21050i
$805$	−2.96528e9	+	7.15883e9i	−0.200346	+	0.483678i
$806$	−2.37808e9	+	2.88283e9i	−0.159976	+	0.193931i
$807$	−7.14662e9	−	7.14662e9i	−0.478678	−	0.478678i
$808$	−4.27671e8	+	7.85750e8i	−0.0285214	+	0.0524016i
$809$	1.65376e10	−	1.65376e10i	1.09813	−	1.09813i	0.103499	−	0.994630i	$-0.466996\pi$
$809$	1.65376e10	−	1.65376e10i	1.09813	−	1.09813i	0.994630	−	0.103499i	$-0.0330039\pi$
$810$	−5.41142e9	−	5.64018e10i	−0.357778	−	3.72903i
$811$	−5.93392e9	−	2.45791e9i	−0.390633	−	0.161805i	0.178718	−	0.983900i	$-0.442805\pi$
$811$	−5.93392e9	−	2.45791e9i	−0.390633	−	0.161805i	−0.569350	+	0.822095i	$0.692805\pi$
$812$	3.26835e9	−	2.16006e9i	0.214231	−	0.141586i
$813$	2.05755e10	+	4.96737e10i	1.34287	+	3.24198i
$814$	−1.14485e10	−	3.50443e9i	−0.743983	−	0.227736i
$815$		−	1.49714e10i		−	0.968748i
$816$	3.59566e10	−	3.52379e10i	2.31666	−	2.27036i
$817$			9.01183e9i			0.578144i
$818$	3.28075e9	−	1.07178e10i	0.209574	−	0.684648i
$819$	−1.22412e9	−	2.95529e9i	−0.0778629	−	0.187978i
$820$	−3.25815e8	−	6.65198e7i	−0.0206359	−	0.00421311i
$821$	−1.90581e10	−	7.89412e9i	−1.20193	−	0.497855i	−0.310306	−	0.950637i	$-0.600432\pi$
$821$	−1.90581e10	−	7.89412e9i	−1.20193	−	0.497855i	−0.891621	+	0.452782i	$0.850432\pi$
$822$	−2.03179e10	+	1.94938e9i	−1.27593	+	0.122418i
$823$	−9.66585e9	+	9.66585e9i	−0.604423	+	0.604423i	−0.941483	−	0.337060i	$-0.890567\pi$
$823$	−9.66585e9	+	9.66585e9i	−0.604423	+	0.604423i	0.337060	+	0.941483i	$0.390567\pi$
$824$	−5.96722e9	−	7.38437e9i	−0.371558	−	0.459799i
$825$	6.57203e9	+	6.57203e9i	0.407484	+	0.407484i
$826$	−2.76383e9	−	2.27991e9i	−0.170640	−	0.140763i
$827$	4.74578e9	−	1.14573e10i	0.291768	−	0.704391i	−0.708230	−	0.705981i	$-0.750506\pi$
$827$	4.74578e9	−	1.14573e10i	0.291768	−	0.704391i	0.999999	+	0.00159042i	$0.000506248\pi$
$828$	−2.47320e10	−	1.67065e10i	−1.51409	−	1.02277i
$829$	−3.15108e9	+	1.30522e9i	−0.192096	+	0.0795688i	−0.476658	−	0.879089i	$-0.658152\pi$
$829$	−3.15108e9	+	1.30522e9i	−0.192096	+	0.0795688i	0.284562	+	0.958658i	$0.408152\pi$
$830$	1.26248e10	+	2.37634e10i	0.766393	+	1.44256i
$831$	3.69964e10			2.23644
$832$	−3.99289e8	−	2.17931e9i	−0.0240356	−	0.131186i
$833$	1.85353e10			1.11107
$834$	−2.28651e9	−	4.30386e9i	−0.136487	−	0.256907i
$835$	−5.45917e9	+	2.26126e9i	−0.324507	+	0.134415i
$836$	7.69556e9	+	5.19838e9i	0.455531	+	0.307713i
$837$	−3.62359e10	+	8.74812e10i	−2.13599	+	5.15674i
$838$	−1.00491e10	−	8.28958e9i	−0.589891	−	0.486607i
$839$	−1.14069e10	−	1.14069e10i	−0.666808	−	0.666808i	0.290168	−	0.956976i	$-0.406289\pi$
$839$	−1.14069e10	−	1.14069e10i	−0.666808	−	0.666808i	−0.956976	+	0.290168i	$0.906289\pi$
$840$	−1.85669e10	+	1.50037e10i	−1.08084	+	0.873413i
$841$	−9.91903e9	+	9.91903e9i	−0.575020	+	0.575020i
$842$	−8.32772e9	+	7.98995e8i	−0.480766	+	0.0461266i
$843$	−1.73361e10	−	7.18086e9i	−0.996679	−	0.412838i
$844$	1.40714e10	+	2.87288e9i	0.805636	+	0.164482i
$845$	−8.16311e9	−	1.97075e10i	−0.465433	−	1.12365i
$846$	−5.36015e9	+	1.75109e10i	−0.304355	+	0.994286i
$847$		−	7.06822e9i		−	0.399685i
$848$	−2.13646e8	+	2.11648e10i	−0.0120312	+	1.19187i
$849$			4.24807e10i			2.38240i
$850$	1.56792e10	+	4.79949e9i	0.875707	+	0.268058i
$851$	6.65843e9	+	1.60749e10i	0.370355	+	0.894117i
$852$	1.58653e10	−	1.04854e10i	0.878840	−	0.580828i
$853$	2.30378e10	+	9.54255e9i	1.27092	+	0.526433i	0.913244	−	0.407413i	$-0.133569\pi$
$853$	2.30378e10	+	9.54255e9i	1.27092	+	0.526433i	0.357677	+	0.933845i	$0.383569\pi$
$854$	2.31248e8	+	2.41024e9i	0.0127050	+	0.132421i
$855$	3.94817e10	−	3.94817e10i	2.16030	−	2.16030i
$856$	−6.69801e9	−	3.64562e9i	−0.364995	−	0.198661i
$857$	1.05227e10	+	1.05227e10i	0.571077	+	0.571077i	0.932429	−	0.361353i	$-0.117685\pi$
$857$	1.05227e10	+	1.05227e10i	0.571077	+	0.571077i	−0.361353	+	0.932429i	$0.617685\pi$
$858$	−1.69674e9	+	2.05688e9i	−0.0917085	+	0.111174i
$859$	6.92225e9	−	1.67118e10i	0.372624	−	0.899595i	−0.620680	−	0.784064i	$-0.713143\pi$
$859$	6.92225e9	−	1.67118e10i	0.372624	−	0.899595i	0.993304	−	0.115531i	$-0.0368568\pi$
$860$	2.64232e9	+	1.36434e10i	0.141658	+	0.731437i
$861$	−3.30286e8	+	1.36809e8i	−0.0176352	+	0.00730473i
$862$	−7.94853e9	+	4.22283e9i	−0.422680	+	0.224558i
$863$	−2.52403e10			−1.33677			−0.668384	−	0.743817i	$-0.733014\pi$
$863$	−2.52403e10			−1.33677			−0.668384	+	0.743817i	$0.733014\pi$
$864$	−2.58361e10	−	4.98386e10i	−1.36279	−	2.62886i
$865$	−1.21906e10			−0.640426
$866$	1.06592e10	−	5.66290e9i	0.557713	−	0.296296i
$867$	−6.52695e10	+	2.70355e10i	−3.40129	+	1.40886i
$868$	2.11847e10	−	4.10287e9i	1.09952	−	0.212945i
$869$	−9.02968e8	+	2.17996e9i	−0.0466770	+	0.112688i
$870$	−1.24940e10	+	1.51458e10i	−0.643255	+	0.779787i
$871$	−2.19228e9	−	2.19228e9i	−0.112417	−	0.112417i
$872$	2.99234e9	+	1.01401e10i	0.152828	+	0.517889i
$873$	4.25697e10	−	4.25697e10i	2.16546	−	2.16546i
$874$	−1.28893e9	−	1.34342e10i	−0.0653040	−	0.680647i
$875$	6.28631e9	+	2.60387e9i	0.317225	+	0.131399i
$876$	−3.31604e10	−	5.01744e10i	−1.66669	−	2.52184i
$877$	−8.36706e9	−	2.01999e10i	−0.418865	−	1.01123i	−0.982677	−	0.185327i	$-0.940666\pi$
$877$	−8.36706e9	−	2.01999e10i	−0.418865	−	1.01123i	0.563812	−	0.825903i	$-0.309334\pi$
$878$	2.65763e10	+	8.13512e9i	1.32514	+	0.405633i
$879$		−	4.81588e10i		−	2.39174i
$880$	1.31748e10	+	5.61365e9i	0.651711	+	0.277687i
$881$		−	3.27861e10i		−	1.61538i	−0.589608	−	0.807689i	$-0.700718\pi$
$881$		−	3.27861e10i		−	1.61538i	0.589608	−	0.807689i	$-0.299282\pi$
$882$	9.90835e9	−	3.23692e10i	0.486252	−	1.58852i
$883$	4.76820e9	+	1.15114e10i	0.233073	+	0.562688i	0.996536	−	0.0831640i	$-0.0265025\pi$
$883$	4.76820e9	+	1.15114e10i	0.233073	+	0.562688i	−0.763463	+	0.645851i	$0.776503\pi$
$884$	−9.41014e8	+	4.60910e9i	−0.0458156	+	0.224405i
$885$	1.65892e10	+	6.87149e9i	0.804498	+	0.333234i
$886$	−3.31775e10	+	3.18319e9i	−1.60260	+	0.153760i
$887$	−1.76558e10	+	1.76558e10i	−0.849481	+	0.849481i	−0.990068	−	0.140587i	$-0.955101\pi$
$887$	−1.76558e10	+	1.76558e10i	−0.849481	+	0.849481i	0.140587	+	0.990068i	$0.455101\pi$
$888$	−5.65761e9	+	5.33027e10i	−0.271136	+	2.55449i
$889$	1.06253e10	+	1.06253e10i	0.507208	+	0.507208i
$890$	−3.52218e9	−	2.90548e9i	−0.167473	−	0.138151i
$891$	−1.39847e10	+	3.37621e10i	−0.662342	+	1.59903i
$892$	−3.89698e9	+	5.76900e9i	−0.183845	+	0.272159i
$893$	−7.65048e9	+	3.16893e9i	−0.359508	+	0.148913i
$894$	−3.01506e10	−	5.67518e10i	−1.41128	−	2.65643i
$895$	−2.45164e9			−0.114308
$896$	−6.22890e9	+	1.11741e10i	−0.289290	+	0.518961i
$897$	3.87489e9			0.179261
$898$	1.11004e10	+	2.08940e10i	0.511528	+	0.962838i
$899$	1.63971e10	−	6.79192e9i	0.752678	−	0.311770i
$900$	1.67632e10	−	2.48158e10i	0.766491	−	1.13470i
$901$	1.71978e10	−	4.15191e10i	0.783314	−	1.89109i
$902$	1.65445e8	+	1.36477e8i	0.00750639	+	0.00619210i
$903$	1.05643e10	+	1.05643e10i	0.477455	+	0.477455i
$904$	−1.34634e9	+	1.26844e10i	−0.0606128	+	0.571058i
$905$	−2.13282e9	+	2.13282e9i	−0.0956500	+	0.0956500i
$906$	1.68754e10	−	1.61910e9i	0.753887	−	0.0723310i
$907$	−1.35817e10	−	5.62573e9i	−0.604407	−	0.250354i	0.0594282	−	0.998233i	$-0.481072\pi$
$907$	−1.35817e10	−	5.62573e9i	−0.604407	−	0.250354i	−0.663835	+	0.747879i	$0.731072\pi$
$908$	4.24978e9	−	2.08155e10i	0.188394	−	0.922755i
$909$	−1.32753e9	−	3.20494e9i	−0.0586233	−	0.141529i
$910$	6.52870e8	−	2.13283e9i	0.0287198	−	0.0938236i
$911$			1.20626e10i			0.528600i	0.964441	+	0.264300i	$0.0851409\pi$
$911$			1.20626e10i			0.528600i	−0.964441	+	0.264300i	$0.914859\pi$
$912$	1.62976e10	−	3.82493e10i	0.711448	−	1.66971i
$913$		−	1.73551e10i		−	0.754707i
$914$	−8.07089e8	−	2.47054e8i	−0.0349631	−	0.0107024i
$915$	−4.64380e9	−	1.12111e10i	−0.200401	−	0.483810i
$916$	5.17327e9	+	7.82758e9i	0.222398	+	0.336506i
$917$	1.04328e10	+	4.32141e9i	0.446795	+	0.185069i
$918$	1.13835e10	+	1.18647e11i	0.485653	+	5.06184i
$919$	−9.74904e9	+	9.74904e9i	−0.414341	+	0.414341i	−0.883248	−	0.468907i	$-0.844648\pi$
$919$	−9.74904e9	+	9.74904e9i	−0.414341	+	0.414341i	0.468907	+	0.883248i	$0.344648\pi$
$920$	−5.89035e9	−	1.99606e10i	−0.249393	−	0.845117i
$921$	1.85593e10	+	1.85593e10i	0.782802	+	0.782802i
$922$	−1.41139e10	+	1.71095e10i	−0.593045	+	0.718920i
$923$	−6.80010e8	+	1.64169e9i	−0.0284649	+	0.0687203i
$924$	1.51151e10	−	2.92736e9i	0.630318	−	0.122074i
$925$	−1.61294e10	+	6.68100e9i	−0.670072	+	0.277553i
$926$	2.45953e10	−	1.30668e10i	1.01792	−	0.540792i
$927$	3.68152e10			1.51792
$928$	−3.18122e9	+	1.00297e10i	−0.130670	+	0.411976i
$929$	−3.78576e10			−1.54917			−0.774583	−	0.632472i	$-0.782040\pi$
$929$	−3.78576e10			−1.54917			−0.774583	+	0.632472i	$0.782040\pi$
$930$	−9.55029e10	+	5.07379e10i	−3.89338	+	2.06844i
$931$	1.41421e10	−	5.85783e9i	0.574366	−	0.237910i
$932$	−1.86075e9	−	9.60780e9i	−0.0752892	−	0.388748i
$933$	−1.22499e10	+	2.95738e10i	−0.493793	+	1.19212i
$934$	1.11482e10	−	1.35144e10i	0.447703	−	0.542730i
$935$	−2.15007e10	−	2.15007e10i	−0.860223	−	0.860223i
$936$	7.54606e9	+	4.10720e9i	0.300784	+	0.163712i
$937$	−3.99170e9	+	3.99170e9i	−0.158515	+	0.158515i	−0.781908	−	0.623394i	$-0.785753\pi$
$937$	−3.99170e9	+	3.99170e9i	−0.158515	+	0.158515i	0.623394	+	0.781908i	$0.285753\pi$
$938$	1.70971e9	+	1.78199e10i	0.0676415	+	0.705010i
$939$	5.77098e10	+	2.39042e10i	2.27468	+	0.942203i
$940$	−1.06532e10	+	7.04074e9i	−0.418344	+	0.276485i
$941$	−1.63726e9	−	3.95269e9i	−0.0640551	−	0.154643i	0.888611	−	0.458662i	$-0.151671\pi$
$941$	−1.63726e9	−	3.95269e9i	−0.0640551	−	0.154643i	−0.952666	+	0.304020i	$0.901671\pi$
$942$	1.61679e10	+	4.94908e9i	0.630197	+	0.192906i
$943$		−	3.11677e8i		−	0.0121036i
$944$	9.62242e9	+	9.71326e7i	0.372291	+	0.00375805i
$945$		−	5.65157e10i		−	2.17850i
$946$	2.62343e9	−	8.57038e9i	0.100751	−	0.329140i
$947$	4.74695e9	+	1.14602e10i	0.181631	+	0.438496i	0.988303	−	0.152503i	$-0.0487335\pi$
$947$	4.74695e9	+	1.14602e10i	0.181631	+	0.438496i	−0.806672	+	0.590999i	$0.798734\pi$
$948$	1.03502e10	+	2.11314e9i	0.394566	+	0.0805563i
$949$	5.19188e9	+	2.15055e9i	0.197194	+	0.0816803i
$950$	1.34797e10	−	1.29330e9i	0.510092	−	0.0489403i
$951$	−2.81727e10	+	2.81727e10i	−1.06217	+	1.06217i
$952$	2.11266e10	−	1.70721e10i	0.793598	−	0.641296i
$953$	2.14279e10	+	2.14279e10i	0.801963	+	0.801963i	0.983402	−	0.181439i	$-0.0580756\pi$
$953$	2.14279e10	+	2.14279e10i	0.801963	+	0.801963i	−0.181439	+	0.983402i	$0.558076\pi$
$954$	−6.33135e10	−	5.22280e10i	−2.36090	−	1.94753i
$955$	1.42119e9	−	3.43107e9i	0.0528009	−	0.127473i
$956$	3.97135e10	+	2.68266e10i	1.47006	+	0.993032i
$957$	1.16992e10	−	4.84597e9i	0.431484	−	0.178727i
$958$	−9.79537e9	−	1.84376e10i	−0.359949	−	0.677525i
$959$	−1.10124e10			−0.403197
$960$	1.34587e10	−	6.26858e10i	0.490969	−	2.28675i
$961$	7.02440e10			2.55316
$962$	−2.34986e9	−	4.42309e9i	−0.0850999	−	0.160182i
$963$	2.73200e10	−	1.13163e10i	0.985799	−	0.408331i
$964$	3.17634e10	+	2.14563e10i	1.14198	+	0.771410i
$965$	−1.59277e10	+	3.84529e10i	−0.570568	+	1.37747i
$966$	−1.72594e10	−	1.42375e10i	−0.616036	−	0.508175i
$967$	−1.58738e9	−	1.58738e9i	−0.0564530	−	0.0564530i	0.678317	−	0.734770i	$-0.262710\pi$
$967$	−1.58738e9	−	1.58738e9i	−0.0564530	−	0.0564530i	−0.734770	+	0.678317i	$0.762710\pi$
$968$	1.19319e10	+	1.47656e10i	0.422811	+	0.523224i
$969$	−6.24211e10	+	6.24211e10i	−2.20393	+	2.20393i
$970$	4.17876e10	−	4.00927e9i	1.47010	−	0.141047i
$971$	−4.50110e10	−	1.86442e10i	−1.57780	−	0.653546i	−0.589736	−	0.807596i	$-0.700768\pi$
$971$	−4.50110e10	−	1.86442e10i	−1.57780	−	0.653546i	−0.988063	+	0.154050i	$0.950768\pi$
$972$	7.72341e10	+	1.57685e10i	2.69760	+	0.550754i
$973$	−1.00623e9	−	2.42925e9i	−0.0350188	−	0.0845430i
$974$	−7.83146e9	+	2.55843e10i	−0.271573	+	0.887190i
$975$			3.88802e9i			0.134342i
$976$	−4.55182e9	−	4.64465e9i	−0.156715	−	0.159911i
$977$		−	2.23044e10i		−	0.765172i	−0.923920	−	0.382586i	$-0.875034\pi$
$977$		−	2.23044e10i		−	0.765172i	0.923920	−	0.382586i	$-0.124966\pi$
$978$	4.13361e10	+	1.26532e10i	1.41300	+	0.432527i
$979$	1.12693e9	+	2.72066e9i	0.0383848	+	0.0926691i
$980$	1.96927e10	−	1.30149e10i	0.668365	−	0.441724i
$981$	−3.78763e10	−	1.56889e10i	−1.28093	−	0.530579i
$982$	−2.48603e9	−	2.59112e10i	−0.0837752	−	0.873167i
$983$	−2.48495e10	+	2.48495e10i	−0.834412	+	0.834412i	−0.988117	−	0.153705i	$-0.950879\pi$
$983$	−2.48495e10	+	2.48495e10i	−0.834412	+	0.834412i	0.153705	+	0.988117i	$0.450879\pi$
$984$	4.59025e8	−	8.43356e8i	0.0153587	−	0.0282181i
$985$	3.72117e10	+	3.72117e10i	1.24066	+	1.24066i
$986$	1.42165e10	−	1.72339e10i	0.472305	−	0.572553i
$987$	−5.25356e9	+	1.26832e10i	−0.173918	+	0.419875i
$988$	7.38668e8	+	3.81404e9i	0.0243669	+	0.125816i
$989$	−1.20337e10	+	4.98452e9i	−0.395560	+	0.163846i
$990$	−4.90411e10	+	2.60541e10i	−1.60634	+	0.853402i
$991$	4.05199e10			1.32254			0.661272	−	0.750146i	$-0.270017\pi$
$991$	4.05199e10			1.32254			0.661272	+	0.750146i	$0.270017\pi$
$992$	−3.73292e10	+	4.43331e10i	−1.21411	+	1.44191i
$993$	−1.46034e10			−0.473294
$994$	9.06092e9	−	4.81380e9i	0.292631	−	0.155466i
$995$	6.66423e10	−	2.76041e10i	2.14471	−	0.888369i
$996$	−7.62807e10	+	1.47733e10i	−2.44628	+	0.473774i
$997$	1.01964e10	−	2.46163e10i	0.325847	−	0.786664i	−0.673045	−	0.739602i	$-0.735014\pi$
$997$	1.01964e10	−	2.46163e10i	0.325847	−	0.786664i	0.998892	−	0.0470627i	$-0.0149861\pi$
$998$	−1.77316e10	+	2.14952e10i	−0.564666	+	0.684518i
$999$	−8.97346e10	−	8.97346e10i	−2.84761	−	2.84761i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	32.8.g.a.21.18	✓	108
32.29	even	8	inner	32.8.g.a.29.18	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.8.g.a.21.18	✓	108	1.1	even	1	trivial
32.8.g.a.29.18	yes	108	32.29	even	8	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:	\( N \)	\(=\)	\( 32 = 2^{5} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	32.g (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(5.30805 + 9.99123i) q^{2} +(81.6081 - 33.8032i) q^{3} +(-71.6492 + 106.068i) q^{4} +(132.448 - 319.759i) q^{5} +(770.915 + 635.936i) q^{6} +(381.260 + 381.260i) q^{7} +(-1440.07 - 152.850i) q^{8} +(3970.78 - 3970.78i) q^{9} +O(q^{10})\)	\(q+(5.30805 + 9.99123i) q^{2} +(81.6081 - 33.8032i) q^{3} +(-71.6492 + 106.068i) q^{4} +(132.448 - 319.759i) q^{5} +(770.915 + 635.936i) q^{6} +(381.260 + 381.260i) q^{7} +(-1440.07 - 152.850i) q^{8} +(3970.78 - 3970.78i) q^{9} +(3897.83 - 373.973i) q^{10} +(-2333.24 - 966.459i) q^{11} +(-2261.73 + 11078.0i) q^{12} +(-404.294 - 976.053i) q^{13} +(-1785.51 + 5833.00i) q^{14} -30572.1i q^{15} +(-6116.78 - 15199.4i) q^{16} +34786.9i q^{17} +(60750.1 + 18595.9i) q^{18} +(10993.9 + 26541.7i) q^{19} +(24426.3 + 36959.0i) q^{20} +(44001.7 + 18226.1i) q^{21} +(-2728.83 - 28441.9i) q^{22} +(-29360.9 + 29360.9i) q^{23} +(-122688. + 36205.0i) q^{24} +(-29460.4 - 29460.4i) q^{25} +(7605.95 - 9220.33i) q^{26} +(115895. - 279796. i) q^{27} +(-67756.4 + 13122.4i) q^{28} +(-52443.9 + 21723.0i) q^{29} +(305453. - 162278. i) q^{30} -312660. q^{31} +(119392. - 141793. i) q^{32} -223080. q^{33} +(-347564. + 184651. i) q^{34} +(172408. - 71413.9i) q^{35} +(136669. + 705676. i) q^{36} +(160357. - 387136. i) q^{37} +(-206828. + 250727. i) q^{38} +(-65987.4 - 65987.4i) q^{39} +(-239610. + 440229. i) q^{40} +(-5307.70 + 5307.70i) q^{41} +(51462.0 + 536376. i) q^{42} +(289812. + 120044. i) q^{43} +(269685. - 178235. i) q^{44} +(-743769. - 1.79562e6i) q^{45} +(-449200. - 137502. i) q^{46} +288244. i q^{47} +(-1.01296e6 - 1.03362e6i) q^{48} -532825. i q^{49} +(137968. - 450722. i) q^{50} +(1.17591e6 + 2.83889e6i) q^{51} +(132495. + 27050.8i) q^{52} +(-1.19353e6 - 494375. i) q^{53} +(3.41068e6 - 327235. i) q^{54} +(-618067. + 618067. i) q^{55} +(-490763. - 607315. i) q^{56} +(1.79438e6 + 1.79438e6i) q^{57} +(-495414. - 408673. i) q^{58} +(-224764. + 542627. i) q^{59} +(3.24271e6 + 2.19047e6i) q^{60} +(366711. - 151897. i) q^{61} +(-1.65962e6 - 3.12386e6i) q^{62} +3.02780e6 q^{63} +(2.05043e6 + 440229. i) q^{64} -365650. q^{65} +(-1.18412e6 - 2.22885e6i) q^{66} +(2.71125e6 - 1.12304e6i) q^{67} +(-3.68977e6 - 2.49246e6i) q^{68} +(-1.40359e6 + 3.38857e6i) q^{69} +(1.62866e6 + 1.34350e6i) q^{70} +(-1.18933e6 - 1.18933e6i) q^{71} +(-6.32512e6 + 5.11125e6i) q^{72} +(-3.76129e6 + 3.76129e6i) q^{73} +(4.71915e6 - 452775. i) q^{74} +(-3.40006e6 - 1.40835e6i) q^{75} +(-3.60292e6 - 735589. i) q^{76} +(-521098. - 1.25804e6i) q^{77} +(309031. - 1.00956e6i) q^{78} -934306. i q^{79} +(-5.67029e6 - 57238.2i) q^{80} -1.44701e7i q^{81} +(-81204.0 - 24856.9i) q^{82} +(2.62980e6 + 6.34889e6i) q^{83} +(-5.08589e6 + 3.36128e6i) q^{84} +(1.11234e7 + 4.60747e6i) q^{85} +(338948. + 3.53277e6i) q^{86} +(-3.54554e6 + 3.54554e6i) q^{87} +(3.21229e6 + 1.74840e6i) q^{88} +(-824518. - 824518. i) q^{89} +(1.39924e7 - 1.69624e7i) q^{90} +(217988. - 526271. i) q^{91} +(-1.01056e6 - 5.21792e6i) q^{92} +(-2.55156e7 + 1.05689e7i) q^{93} +(-2.87991e6 + 1.53001e6i) q^{94} +9.94306e6 q^{95} +(4.95030e6 - 1.56073e7i) q^{96} +1.07207e7 q^{97} +(5.32358e6 - 2.82826e6i) q^{98} +(-1.31024e7 + 5.42718e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) 108 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9	\( 108 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} - 13004 q^{10} - 4 q^{11} + 30668 q^{12} - 4 q^{13} - 26196 q^{14} - 52784 q^{16} + 102056 q^{18} - 4 q^{19} + 81996 q^{20} - 4 q^{21} - 374240 q^{22} - 143420 q^{23} + 380880 q^{24} - 4 q^{25} - 363984 q^{26} + 476084 q^{27} - 195464 q^{28} - 4 q^{29} + 870468 q^{30} - 714992 q^{31} + 535656 q^{32} - 8 q^{33} - 201072 q^{34} + 816500 q^{35} - 1669712 q^{36} - 4 q^{37} - 2533100 q^{38} - 283948 q^{39} + 2746344 q^{40} - 4 q^{41} + 4924936 q^{42} + 366180 q^{43} - 1585404 q^{44} + 8744 q^{45} - 2715812 q^{46} - 5044368 q^{48} - 1653804 q^{50} + 3002072 q^{51} + 8882212 q^{52} - 1815636 q^{53} + 6815776 q^{54} - 4191012 q^{55} - 3655000 q^{56} - 4 q^{57} - 12448736 q^{58} - 1835940 q^{59} - 6364808 q^{60} - 4559780 q^{61} + 12948600 q^{62} + 10001872 q^{63} + 16915544 q^{64} - 8 q^{65} - 11246068 q^{66} - 1940684 q^{67} - 8895536 q^{68} + 9580892 q^{69} - 8149480 q^{70} - 12348708 q^{71} + 12884564 q^{72} - 4 q^{73} + 10931436 q^{74} + 11573008 q^{75} + 14443516 q^{76} - 11914452 q^{77} - 38252364 q^{78} - 11333192 q^{80} + 15827196 q^{82} - 9565884 q^{83} + 8101984 q^{84} + 312496 q^{85} - 14812992 q^{86} + 40789108 q^{87} + 5716448 q^{88} - 4 q^{89} + 5335400 q^{90} - 3406996 q^{91} + 27562664 q^{92} - 8752 q^{93} - 14227032 q^{94} - 54872008 q^{95} - 25080448 q^{96} - 8 q^{97} + 57598104 q^{98} - 9738480 q^{99}+O(q^{100}) \) 108 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9 - 13004 * q^10 - 4 * q^11 + 30668 * q^12 - 4 * q^13 - 26196 * q^14 - 52784 * q^16 + 102056 * q^18 - 4 * q^19 + 81996 * q^20 - 4 * q^21 - 374240 * q^22 - 143420 * q^23 + 380880 * q^24 - 4 * q^25 - 363984 * q^26 + 476084 * q^27 - 195464 * q^28 - 4 * q^29 + 870468 * q^30 - 714992 * q^31 + 535656 * q^32 - 8 * q^33 - 201072 * q^34 + 816500 * q^35 - 1669712 * q^36 - 4 * q^37 - 2533100 * q^38 - 283948 * q^39 + 2746344 * q^40 - 4 * q^41 + 4924936 * q^42 + 366180 * q^43 - 1585404 * q^44 + 8744 * q^45 - 2715812 * q^46 - 5044368 * q^48 - 1653804 * q^50 + 3002072 * q^51 + 8882212 * q^52 - 1815636 * q^53 + 6815776 * q^54 - 4191012 * q^55 - 3655000 * q^56 - 4 * q^57 - 12448736 * q^58 - 1835940 * q^59 - 6364808 * q^60 - 4559780 * q^61 + 12948600 * q^62 + 10001872 * q^63 + 16915544 * q^64 - 8 * q^65 - 11246068 * q^66 - 1940684 * q^67 - 8895536 * q^68 + 9580892 * q^69 - 8149480 * q^70 - 12348708 * q^71 + 12884564 * q^72 - 4 * q^73 + 10931436 * q^74 + 11573008 * q^75 + 14443516 * q^76 - 11914452 * q^77 - 38252364 * q^78 - 11333192 * q^80 + 15827196 * q^82 - 9565884 * q^83 + 8101984 * q^84 + 312496 * q^85 - 14812992 * q^86 + 40789108 * q^87 + 5716448 * q^88 - 4 * q^89 + 5335400 * q^90 - 3406996 * q^91 + 27562664 * q^92 - 8752 * q^93 - 14227032 * q^94 - 54872008 * q^95 - 25080448 * q^96 - 8 * q^97 + 57598104 * q^98 - 9738480 * q^99

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