LMFDB - Embedded newform 13.9.d.a.5.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [13,9,Mod(5,13)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(13, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("13.5");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 13 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	13.d (of order $4$, degree $2$, 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:	$5.29592193079$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 2 x^{17} + 2 x^{16} + 3828 x^{15} + 1204401 x^{14} + 47082 x^{13} + 4823826 x^{12} + \cdots + 18\!\cdots\!48 $ x^18 - 2x^17 + 2x^16 + 3828x^15 + 1204401x^14 + 47082x^13 + 4823826x^12 + 3014328096x^11 + 324100560576x^10 + 1243720573056x^9 + 2594493183360x^8 + 67426704543744x^7 + 16374511738433536x^6 + 38893585626849280x^5 + 61002122197950464x^4 + 4754717719118610432x^3 + 119869629126769115136x^2 + 658222091640736579584*x + 1807198057923881730048
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{16}\cdot 3^{2}\cdot 13^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			5.9
Root			$-21.3021 - 21.3021i$ of defining polynomial
Character	$\chi$	$=$	13.5
Dual form			13.9.d.a.8.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(21.3021 - 21.3021i) q^{2} +58.3050 q^{3} -651.562i q^{4} +(-310.371 + 310.371i) q^{5} +(1242.02 - 1242.02i) q^{6} +(2550.45 + 2550.45i) q^{7} +(-8426.31 - 8426.31i) q^{8} -3161.53 q^{9} +O(q^{10})$	\(q+(21.3021 - 21.3021i) q^{2} +58.3050 q^{3} -651.562i q^{4} +(-310.371 + 310.371i) q^{5} +(1242.02 - 1242.02i) q^{6} +(2550.45 + 2550.45i) q^{7} +(-8426.31 - 8426.31i) q^{8} -3161.53 q^{9} +13223.1i q^{10} +(-5774.38 - 5774.38i) q^{11} -37989.3i q^{12} +(26421.9 + 10845.0i) q^{13} +108660. q^{14} +(-18096.2 + 18096.2i) q^{15} -192197. q^{16} +91222.3i q^{17} +(-67347.3 + 67347.3i) q^{18} +(71340.6 - 71340.6i) q^{19} +(202226. + 202226. i) q^{20} +(148704. + 148704. i) q^{21} -246013. q^{22} -215310. i q^{23} +(-491296. - 491296. i) q^{24} +197965. i q^{25} +(793864. - 331822. i) q^{26} -566872. q^{27} +(1.66177e6 - 1.66177e6i) q^{28} -916133. q^{29} +770974. i q^{30} +(200402. - 200402. i) q^{31} +(-1.93707e6 + 1.93707e6i) q^{32} +(-336675. - 336675. i) q^{33} +(1.94323e6 + 1.94323e6i) q^{34} -1.58317e6 q^{35} +2.05993e6i q^{36} +(-1.78299e6 - 1.78299e6i) q^{37} -3.03941e6i q^{38} +(1.54053e6 + 632316. i) q^{39} +5.23057e6 q^{40} +(-2.16221e6 + 2.16221e6i) q^{41} +6.33542e6 q^{42} -2.68300e6i q^{43} +(-3.76236e6 + 3.76236e6i) q^{44} +(981247. - 981247. i) q^{45} +(-4.58657e6 - 4.58657e6i) q^{46} +(-1.53089e6 - 1.53089e6i) q^{47} -1.12060e7 q^{48} +7.24476e6i q^{49} +(4.21707e6 + 4.21707e6i) q^{50} +5.31871e6i q^{51} +(7.06618e6 - 1.72155e7i) q^{52} +1.09754e7 q^{53} +(-1.20756e7 + 1.20756e7i) q^{54} +3.58440e6 q^{55} -4.29817e7i q^{56} +(4.15951e6 - 4.15951e6i) q^{57} +(-1.95156e7 + 1.95156e7i) q^{58} +(4.08405e6 + 4.08405e6i) q^{59} +(1.17908e7 + 1.17908e7i) q^{60} +1.40493e7 q^{61} -8.53799e6i q^{62} +(-8.06332e6 - 8.06332e6i) q^{63} +3.33251e7i q^{64} +(-1.15666e7 + 4.83463e6i) q^{65} -1.43438e7 q^{66} +(-653233. + 653233. i) q^{67} +5.94370e7 q^{68} -1.25537e7i q^{69} +(-3.37249e7 + 3.37249e7i) q^{70} +(-6.95378e6 + 6.95378e6i) q^{71} +(2.66400e7 + 2.66400e7i) q^{72} +(-7.01379e6 - 7.01379e6i) q^{73} -7.59629e7 q^{74} +1.15423e7i q^{75} +(-4.64828e7 - 4.64828e7i) q^{76} -2.94545e7i q^{77} +(4.62862e7 - 1.93469e7i) q^{78} +4.87918e7 q^{79} +(5.96524e7 - 5.96524e7i) q^{80} -1.23087e7 q^{81} +9.21195e7i q^{82} +(1.56170e7 - 1.56170e7i) q^{83} +(9.68897e7 - 9.68897e7i) q^{84} +(-2.83128e7 - 2.83128e7i) q^{85} +(-5.71537e7 - 5.71537e7i) q^{86} -5.34151e7 q^{87} +9.73134e7i q^{88} +(-2.63507e6 - 2.63507e6i) q^{89} -4.18053e7i q^{90} +(3.97281e7 + 9.50472e7i) q^{91} -1.40288e8 q^{92} +(1.16844e7 - 1.16844e7i) q^{93} -6.52223e7 q^{94} +4.42841e7i q^{95} +(-1.12941e8 + 1.12941e8i) q^{96} +(2.21991e7 - 2.21991e7i) q^{97} +(1.54329e8 + 1.54329e8i) q^{98} +(1.82559e7 + 1.82559e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 2 q^{2} - 4 q^{3} + 166 q^{5} + 2720 q^{6} + 5308 q^{7} + 10464 q^{8} + 39362 q^{9}+O(q^{10}) $ 18 * q - 2 * q^2 - 4 * q^3 + 166 * q^5 + 2720 * q^6 + 5308 * q^7 + 10464 * q^8 + 39362 * q^9	\( 18 q - 2 q^{2} - 4 q^{3} + 166 q^{5} + 2720 q^{6} + 5308 q^{7} + 10464 q^{8} + 39362 q^{9} - 31556 q^{11} + 71300 q^{13} - 110260 q^{14} + 121124 q^{15} - 522860 q^{16} - 308962 q^{18} + 100288 q^{19} + 736268 q^{20} + 279416 q^{21} - 977312 q^{22} - 986232 q^{24} + 2952238 q^{26} + 364916 q^{27} + 4497084 q^{28} - 2479024 q^{29} - 1892664 q^{31} + 947212 q^{32} + 1368644 q^{33} - 531576 q^{34} - 2918284 q^{35} - 8343978 q^{37} - 1101268 q^{39} - 12691908 q^{40} + 1140178 q^{41} + 15137212 q^{42} - 3867188 q^{44} + 6565370 q^{45} + 2006148 q^{46} - 13368572 q^{47} - 10106716 q^{48} + 37369598 q^{50} - 14821220 q^{52} + 50561348 q^{53} - 4995928 q^{54} + 76994128 q^{55} - 34755760 q^{57} + 22505716 q^{58} + 2127976 q^{59} - 161134196 q^{60} - 52016516 q^{61} - 15210112 q^{63} + 10413082 q^{65} - 51097328 q^{66} + 960292 q^{67} + 283187508 q^{68} - 166635032 q^{70} + 67412140 q^{71} + 96846900 q^{72} - 145213226 q^{73} - 233620024 q^{74} - 150533640 q^{76} + 212071160 q^{78} - 76829120 q^{79} + 524889520 q^{80} + 293280674 q^{81} - 241951556 q^{83} + 345496184 q^{84} + 260737764 q^{85} - 579480384 q^{86} - 618300656 q^{87} - 89187110 q^{89} + 232660948 q^{91} - 122690376 q^{92} + 669553400 q^{93} + 1069637380 q^{94} - 1324092400 q^{96} + 331183146 q^{97} + 588677614 q^{98} - 1125076336 q^{99}+O(q^{100}) \) 18 * q - 2 * q^2 - 4 * q^3 + 166 * q^5 + 2720 * q^6 + 5308 * q^7 + 10464 * q^8 + 39362 * q^9 - 31556 * q^11 + 71300 * q^13 - 110260 * q^14 + 121124 * q^15 - 522860 * q^16 - 308962 * q^18 + 100288 * q^19 + 736268 * q^20 + 279416 * q^21 - 977312 * q^22 - 986232 * q^24 + 2952238 * q^26 + 364916 * q^27 + 4497084 * q^28 - 2479024 * q^29 - 1892664 * q^31 + 947212 * q^32 + 1368644 * q^33 - 531576 * q^34 - 2918284 * q^35 - 8343978 * q^37 - 1101268 * q^39 - 12691908 * q^40 + 1140178 * q^41 + 15137212 * q^42 - 3867188 * q^44 + 6565370 * q^45 + 2006148 * q^46 - 13368572 * q^47 - 10106716 * q^48 + 37369598 * q^50 - 14821220 * q^52 + 50561348 * q^53 - 4995928 * q^54 + 76994128 * q^55 - 34755760 * q^57 + 22505716 * q^58 + 2127976 * q^59 - 161134196 * q^60 - 52016516 * q^61 - 15210112 * q^63 + 10413082 * q^65 - 51097328 * q^66 + 960292 * q^67 + 283187508 * q^68 - 166635032 * q^70 + 67412140 * q^71 + 96846900 * q^72 - 145213226 * q^73 - 233620024 * q^74 - 150533640 * q^76 + 212071160 * q^78 - 76829120 * q^79 + 524889520 * q^80 + 293280674 * q^81 - 241951556 * q^83 + 345496184 * q^84 + 260737764 * q^85 - 579480384 * q^86 - 618300656 * q^87 - 89187110 * q^89 + 232660948 * q^91 - 122690376 * q^92 + 669553400 * q^93 + 1069637380 * q^94 - 1324092400 * q^96 + 331183146 * q^97 + 588677614 * q^98 - 1125076336 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/13\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	21.3021	−	21.3021i	1.33138	−	1.33138i	0.427250	−	0.904134i	$-0.359482\pi$
$2$	21.3021	−	21.3021i	1.33138	−	1.33138i	0.904134	−	0.427250i	$-0.140518\pi$
$3$	58.3050			0.719814			0.359907	−	0.932988i	$-0.382808\pi$
$3$	58.3050			0.719814			0.359907	+	0.932988i	$0.382808\pi$
$4$		−	651.562i		−	2.54516i
$5$	−310.371	+	310.371i	−0.496594	+	0.496594i	−0.910376	−	0.413782i	$-0.864207\pi$
$5$	−310.371	+	310.371i	−0.496594	+	0.496594i	0.413782	+	0.910376i	$0.364207\pi$
$6$	1242.02	−	1242.02i	0.958349	−	0.958349i
$7$	2550.45	+	2550.45i	1.06224	+	1.06224i	0.997930	+	0.0643140i	$0.0204859\pi$
$7$	2550.45	+	2550.45i	1.06224	+	1.06224i	0.0643140	+	0.997930i	$0.479514\pi$
$8$	−8426.31	−	8426.31i	−2.05721	−	2.05721i
$9$	−3161.53			−0.481867
$10$			13223.1i			1.32231i
$11$	−5774.38	−	5774.38i	−0.394398	−	0.394398i	0.481854	−	0.876252i	$-0.339964\pi$
$11$	−5774.38	−	5774.38i	−0.394398	−	0.394398i	−0.876252	+	0.481854i	$0.839964\pi$
$12$		−	37989.3i		−	1.83205i
$13$	26421.9	+	10845.0i	0.925104	+	0.379713i
$13$	26421.9	+	10845.0i	0.925104	+	0.379713i
$14$	108660.			2.82851
$15$	−18096.2	+	18096.2i	−0.357455	+	0.357455i
$16$	−192197.			−2.93270
$17$			91222.3i			1.09221i	0.837717	+	0.546104i	$0.183890\pi$
$17$			91222.3i			1.09221i	−0.837717	+	0.546104i	$0.816110\pi$
$18$	−67347.3	+	67347.3i	−0.641550	+	0.641550i
$19$	71340.6	−	71340.6i	0.547422	−	0.547422i	−0.378272	−	0.925694i	$-0.623482\pi$
$19$	71340.6	−	71340.6i	0.547422	−	0.547422i	0.925694	+	0.378272i	$0.123482\pi$
$20$	202226.	+	202226.i	1.26391	+	1.26391i
$21$	148704.	+	148704.i	0.764618	+	0.764618i
$22$	−246013.			−1.05019
$23$		−	215310.i		−	0.769402i	−0.923041	−	0.384701i	$-0.874305\pi$
$23$		−	215310.i		−	0.769402i	0.923041	−	0.384701i	$-0.125695\pi$
$24$	−491296.	−	491296.i	−1.48081	−	1.48081i
$25$			197965.i			0.506789i
$26$	793864.	−	331822.i	1.73721	−	0.726125i
$27$	−566872.			−1.06667
$28$	1.66177e6	−	1.66177e6i	2.70358	−	2.70358i
$29$	−916133.			−1.29529			−0.647645	−	0.761943i	$-0.724246\pi$
$29$	−916133.			−1.29529			−0.647645	+	0.761943i	$0.724246\pi$
$30$			770974.i			0.951820i
$31$	200402.	−	200402.i	0.216998	−	0.216998i	−0.590234	−	0.807232i	$-0.700965\pi$
$31$	200402.	−	200402.i	0.216998	−	0.216998i	0.807232	+	0.590234i	$0.200965\pi$
$32$	−1.93707e6	+	1.93707e6i	−1.84734	+	1.84734i
$33$	−336675.	−	336675.i	−0.283893	−	0.283893i
$34$	1.94323e6	+	1.94323e6i	1.45415	+	1.45415i
$35$	−1.58317e6			−1.05501
$36$			2.05993e6i			1.22643i
$37$	−1.78299e6	−	1.78299e6i	−0.951352	−	0.951352i	0.0475181	−	0.998870i	$-0.484869\pi$
$37$	−1.78299e6	−	1.78299e6i	−0.951352	−	0.951352i	−0.998870	+	0.0475181i	$0.984869\pi$
$38$		−	3.03941e6i		−	1.45766i
$39$	1.54053e6	+	632316.i	0.665904	+	0.273323i
$40$	5.23057e6			2.04319
$41$	−2.16221e6	+	2.16221e6i	−0.765179	+	0.765179i	−0.977253	−	0.212075i	$-0.931978\pi$
$41$	−2.16221e6	+	2.16221e6i	−0.765179	+	0.765179i	0.212075	+	0.977253i	$0.431978\pi$
$42$	6.33542e6			2.03600
$43$		−	2.68300e6i		−	0.784779i	−0.919799	−	0.392389i	$-0.871649\pi$
$43$		−	2.68300e6i		−	0.784779i	0.919799	−	0.392389i	$-0.128351\pi$
$44$	−3.76236e6	+	3.76236e6i	−1.00381	+	1.00381i
$45$	981247.	−	981247.i	0.239292	−	0.239292i
$46$	−4.58657e6	−	4.58657e6i	−1.02437	−	1.02437i
$47$	−1.53089e6	−	1.53089e6i	−0.313727	−	0.313727i	0.532625	−	0.846352i	$-0.321206\pi$
$47$	−1.53089e6	−	1.53089e6i	−0.313727	−	0.313727i	−0.846352	+	0.532625i	$0.821206\pi$
$48$	−1.12060e7			−2.11100
$49$			7.24476e6i			1.25672i
$50$	4.21707e6	+	4.21707e6i	0.674731	+	0.674731i
$51$			5.31871e6i			0.786187i
$52$	7.06618e6	−	1.72155e7i	0.966431	−	2.35454i
$53$	1.09754e7			1.39096			0.695481	−	0.718545i	$-0.255191\pi$
$53$	1.09754e7			1.39096			0.695481	+	0.718545i	$0.255191\pi$
$54$	−1.20756e7	+	1.20756e7i	−1.42015	+	1.42015i
$55$	3.58440e6			0.391711
$56$		−	4.29817e7i		−	4.37051i
$57$	4.15951e6	−	4.15951e6i	0.394042	−	0.394042i
$58$	−1.95156e7	+	1.95156e7i	−1.72453	+	1.72453i
$59$	4.08405e6	+	4.08405e6i	0.337041	+	0.337041i	0.855253	−	0.518211i	$-0.173402\pi$
$59$	4.08405e6	+	4.08405e6i	0.337041	+	0.337041i	−0.518211	+	0.855253i	$0.673402\pi$
$60$	1.17908e7	+	1.17908e7i	0.909782	+	0.909782i
$61$	1.40493e7			1.01469			0.507346	−	0.861742i	$-0.330627\pi$
$61$	1.40493e7			1.01469			0.507346	+	0.861742i	$0.330627\pi$
$62$		−	8.53799e6i		−	0.577815i
$63$	−8.06332e6	−	8.06332e6i	−0.511860	−	0.511860i
$64$			3.33251e7i			1.98633i
$65$	−1.15666e7	+	4.83463e6i	−0.647964	+	0.270838i
$66$	−1.43438e7			−0.755942
$67$	−653233.	+	653233.i	−0.0324167	+	0.0324167i	−0.723129	−	0.690713i	$-0.757297\pi$
$67$	−653233.	+	653233.i	−0.0324167	+	0.0324167i	0.690713	+	0.723129i	$0.257297\pi$
$68$	5.94370e7			2.77985
$69$		−	1.25537e7i		−	0.553826i
$70$	−3.37249e7	+	3.37249e7i	−1.40462	+	1.40462i
$71$	−6.95378e6	+	6.95378e6i	−0.273645	+	0.273645i	−0.830566	−	0.556921i	$-0.811983\pi$
$71$	−6.95378e6	+	6.95378e6i	−0.273645	+	0.273645i	0.556921	+	0.830566i	$0.311983\pi$
$72$	2.66400e7	+	2.66400e7i	0.991300	+	0.991300i
$73$	−7.01379e6	−	7.01379e6i	−0.246980	−	0.246980i	0.572750	−	0.819730i	$-0.305876\pi$
$73$	−7.01379e6	−	7.01379e6i	−0.246980	−	0.246980i	−0.819730	+	0.572750i	$0.805876\pi$
$74$	−7.59629e7			−2.53323
$75$			1.15423e7i			0.364794i
$76$	−4.64828e7	−	4.64828e7i	−1.39328	−	1.39328i
$77$		−	2.94545e7i		−	0.837893i
$78$	4.62862e7	−	1.93469e7i	1.25047	−	0.522676i
$79$	4.87918e7			1.25267			0.626337	−	0.779552i	$-0.284553\pi$
$79$	4.87918e7			1.25267			0.626337	+	0.779552i	$0.284553\pi$
$80$	5.96524e7	−	5.96524e7i	1.45636	−	1.45636i
$81$	−1.23087e7			−0.285937
$82$			9.21195e7i			2.03749i
$83$	1.56170e7	−	1.56170e7i	0.329067	−	0.329067i	−0.523165	−	0.852232i	$-0.675249\pi$
$83$	1.56170e7	−	1.56170e7i	0.329067	−	0.329067i	0.852232	+	0.523165i	$0.175249\pi$
$84$	9.68897e7	−	9.68897e7i	1.94608	−	1.94608i
$85$	−2.83128e7	−	2.83128e7i	−0.542384	−	0.542384i
$86$	−5.71537e7	−	5.71537e7i	−1.04484	−	1.04484i
$87$	−5.34151e7			−0.932368
$88$			9.73134e7i			1.62271i
$89$	−2.63507e6	−	2.63507e6i	−0.0419983	−	0.0419983i	0.685796	−	0.727794i	$-0.259454\pi$
$89$	−2.63507e6	−	2.63507e6i	−0.0419983	−	0.0419983i	−0.727794	+	0.685796i	$0.759454\pi$
$90$		−	4.18053e7i		−	0.637179i
$91$	3.97281e7	+	9.50472e7i	0.579339	+	1.38603i
$92$	−1.40288e8			−1.95825
$93$	1.16844e7	−	1.16844e7i	0.156198	−	0.156198i
$94$	−6.52223e7			−0.835382
$95$			4.42841e7i			0.543693i
$96$	−1.12941e8	+	1.12941e8i	−1.32974	+	1.32974i
$97$	2.21991e7	−	2.21991e7i	0.250754	−	0.250754i	−0.570526	−	0.821280i	$-0.693261\pi$
$97$	2.21991e7	−	2.21991e7i	0.250754	−	0.250754i	0.821280	+	0.570526i	$0.193261\pi$
$98$	1.54329e8	+	1.54329e8i	1.67318	+	1.67318i
$99$	1.82559e7	+	1.82559e7i	0.190047	+	0.190047i
$100$	1.28986e8			1.28986
$101$		−	1.02310e8i		−	0.983181i	−0.870826	−	0.491591i	$-0.836416\pi$
$101$		−	1.02310e8i		−	0.983181i	0.870826	−	0.491591i	$-0.163584\pi$
$102$	1.13300e8	+	1.13300e8i	1.04672	+	1.04672i
$103$			1.19723e8i			1.06372i	0.846831	+	0.531861i	$0.178507\pi$
$103$			1.19723e8i			1.06372i	−0.846831	+	0.531861i	$0.821493\pi$
$104$	−1.31256e8	−	3.14022e8i	−1.12198	−	2.68428i
$105$	−9.23067e7			−0.759409
$106$	2.33799e8	−	2.33799e8i	1.85190	−	1.85190i
$107$	3.75321e7			0.286331			0.143165	−	0.989699i	$-0.454272\pi$
$107$	3.75321e7			0.286331			0.143165	+	0.989699i	$0.454272\pi$
$108$			3.69352e8i			2.71485i
$109$	−6.08202e7	+	6.08202e7i	−0.430865	+	0.430865i	−0.888923	−	0.458057i	$-0.848545\pi$
$109$	−6.08202e7	+	6.08202e7i	−0.430865	+	0.430865i	0.458057	+	0.888923i	$0.348545\pi$
$110$	7.63554e7	−	7.63554e7i	0.521517	−	0.521517i
$111$	−1.03957e8	−	1.03957e8i	−0.684797	−	0.684797i
$112$	−4.90189e8	−	4.90189e8i	−3.11524	−	3.11524i
$113$	2.05572e8			1.26081			0.630407	−	0.776265i	$-0.282888\pi$
$113$	2.05572e8			1.26081			0.630407	+	0.776265i	$0.282888\pi$
$114$		−	1.77213e8i		−	1.04924i
$115$	6.68260e7	+	6.68260e7i	0.382080	+	0.382080i
$116$			5.96918e8i			3.29672i
$117$	−8.35337e7	−	3.42867e7i	−0.445777	−	0.182971i
$118$	1.73998e8			0.897462
$119$	−2.32658e8	+	2.32658e8i	−1.16019	+	1.16019i
$120$	3.04968e8			1.47072
$121$		−	1.47672e8i		−	0.688901i
$122$	2.99279e8	−	2.99279e8i	1.35094	−	1.35094i
$123$	−1.26068e8	+	1.26068e8i	−0.550787	+	0.550787i
$124$	−1.30574e8	−	1.30574e8i	−0.552295	−	0.552295i
$125$	−1.82681e8	−	1.82681e8i	−0.748262	−	0.748262i
$126$	−3.43532e8			−1.36296
$127$		−	3.50063e7i		−	0.134565i	−0.997734	−	0.0672824i	$-0.978567\pi$
$127$		−	3.50063e7i		−	0.134565i	0.997734	−	0.0672824i	$-0.0214329\pi$
$128$	2.14005e8	+	2.14005e8i	0.797232	+	0.797232i
$129$		−	1.56432e8i		−	0.564895i
$130$	−1.43405e8	+	3.49380e8i	−0.502099	+	1.22328i
$131$	−1.75652e8			−0.596441			−0.298221	−	0.954497i	$-0.596393\pi$
$131$	−1.75652e8			−0.596441			−0.298221	+	0.954497i	$0.596393\pi$
$132$	−2.19365e8	+	2.19365e8i	−0.722555	+	0.722555i
$133$	3.63901e8			1.16299
$134$			2.78305e7i			0.0863181i
$135$	1.75941e8	−	1.75941e8i	0.529701	−	0.529701i
$136$	7.68668e8	−	7.68668e8i	2.24690	−	2.24690i
$137$	−6.62889e7	−	6.62889e7i	−0.188174	−	0.188174i	0.606733	−	0.794906i	$-0.292480\pi$
$137$	−6.62889e7	−	6.62889e7i	−0.188174	−	0.188174i	−0.794906	+	0.606733i	$0.792480\pi$
$138$	−2.67420e8	−	2.67420e8i	−0.737355	−	0.737355i
$139$	3.73308e8			1.00002			0.500009	−	0.866020i	$-0.333330\pi$
$139$	3.73308e8			1.00002			0.500009	+	0.866020i	$0.333330\pi$
$140$			1.03153e9i			2.68517i
$141$	−8.92584e7	−	8.92584e7i	−0.225825	−	0.225825i
$142$			2.96261e8i			0.728653i
$143$	−8.99471e7	−	2.15193e8i	−0.215101	−	0.514617i
$144$	6.07637e8			1.41317
$145$	2.84341e8	−	2.84341e8i	0.643232	−	0.643232i
$146$	−2.98817e8			−0.657649
$147$			4.22406e8i			0.904608i
$148$	−1.16173e9	+	1.16173e9i	−2.42135	+	2.42135i
$149$	−5.45472e8	+	5.45472e8i	−1.10669	+	1.10669i	−0.113112	+	0.993582i	$0.536082\pi$
$149$	−5.45472e8	+	5.45472e8i	−1.10669	+	1.10669i	−0.993582	+	0.113112i	$0.963918\pi$
$150$	2.45876e8	+	2.45876e8i	0.485681	+	0.485681i
$151$	3.44294e8	+	3.44294e8i	0.662250	+	0.662250i	0.955910	−	0.293660i	$-0.0948733\pi$
$151$	3.44294e8	+	3.44294e8i	0.662250	+	0.662250i	−0.293660	+	0.955910i	$0.594873\pi$
$152$	−1.20228e9			−2.25232
$153$		−	2.88402e8i		−	0.526299i
$154$	−6.27444e8	−	6.27444e8i	−1.11556	−	1.11556i
$155$			1.24398e8i			0.215520i
$156$	4.11993e8	−	1.00375e9i	0.695651	−	1.69483i
$157$	−5.24918e8			−0.863959			−0.431979	−	0.901883i	$-0.642185\pi$
$157$	−5.24918e8			−0.863959			−0.431979	+	0.901883i	$0.642185\pi$
$158$	1.03937e9	−	1.03937e9i	1.66779	−	1.66779i
$159$	6.39918e8			1.00123
$160$		−	1.20242e9i		−	1.83475i
$161$	5.49137e8	−	5.49137e8i	0.817292	−	0.817292i
$162$	−2.62201e8	+	2.62201e8i	−0.380692	+	0.380692i
$163$	5.08593e8	+	5.08593e8i	0.720477	+	0.720477i	0.968702	−	0.248225i	$-0.0798472\pi$
$163$	5.08593e8	+	5.08593e8i	0.720477	+	0.720477i	−0.248225	+	0.968702i	$0.579847\pi$
$164$	1.40882e9	+	1.40882e9i	1.94751	+	1.94751i
$165$	2.08988e8			0.281959
$166$		−	6.65349e8i		−	0.876229i
$167$	−1.23124e8	−	1.23124e8i	−0.158299	−	0.158299i	0.623514	−	0.781813i	$-0.285705\pi$
$167$	−1.23124e8	−	1.23124e8i	−0.158299	−	0.158299i	−0.781813	+	0.623514i	$0.785705\pi$
$168$		−	2.50605e9i		−	3.14595i
$169$	5.80504e8	+	5.73090e8i	0.711636	+	0.702548i
$170$	−1.20624e9			−1.44424
$171$	−2.25545e8	+	2.25545e8i	−0.263785	+	0.263785i
$172$	−1.74814e9			−1.99739
$173$		−	7.09558e8i		−	0.792143i	−0.918220	−	0.396072i	$-0.870373\pi$
$173$		−	7.09558e8i		−	0.792143i	0.918220	−	0.396072i	$-0.129627\pi$
$174$	−1.13786e9	+	1.13786e9i	−1.24134	+	1.24134i
$175$	−5.04898e8	+	5.04898e8i	−0.538334	+	0.538334i
$176$	1.10982e9	+	1.10982e9i	1.15665	+	1.15665i
$177$	2.38120e8	+	2.38120e8i	0.242607	+	0.242607i
$178$	−1.12265e8			−0.111832
$179$		−	6.09452e8i		−	0.593646i	−0.954933	−	0.296823i	$-0.904073\pi$
$179$		−	6.09452e8i		−	0.593646i	0.954933	−	0.296823i	$-0.0959271\pi$
$180$	−6.39343e8	−	6.39343e8i	−0.609038	−	0.609038i
$181$			1.31806e9i			1.22806i	0.789281	+	0.614032i	$0.210453\pi$
$181$			1.31806e9i			1.22806i	−0.789281	+	0.614032i	$0.789547\pi$
$182$	2.87100e9	+	1.17841e9i	2.61666	+	1.07402i
$183$	8.19142e8			0.730390
$184$	−1.81427e9	+	1.81427e9i	−1.58282	+	1.58282i
$185$	1.10678e9			0.944871
$186$		−	4.97807e8i		−	0.415920i
$187$	5.26752e8	−	5.26752e8i	0.430764	−	0.430764i
$188$	−9.97468e8	+	9.97468e8i	−0.798487	+	0.798487i
$189$	−1.44578e9	−	1.44578e9i	−1.13306	−	1.13306i
$190$	9.43346e8	+	9.43346e8i	0.723863	+	0.723863i
$191$	−2.39534e9			−1.79984			−0.899920	−	0.436055i	$-0.856375\pi$
$191$	−2.39534e9			−1.79984			−0.899920	+	0.436055i	$0.856375\pi$
$192$			1.94302e9i			1.42979i
$193$	−1.42491e9	−	1.42491e9i	−1.02697	−	1.02697i	−0.999626	−	0.0273419i	$-0.991296\pi$
$193$	−1.42491e9	−	1.42491e9i	−1.02697	−	1.02697i	−0.0273419	−	0.999626i	$-0.508704\pi$
$194$		−	9.45775e8i		−	0.667700i
$195$	−6.74388e8	+	2.81883e8i	−0.466414	+	0.194953i
$196$	4.72041e9			3.19857
$197$	4.38693e7	−	4.38693e7i	0.0291270	−	0.0291270i	−0.692393	−	0.721520i	$-0.743444\pi$
$197$	4.38693e7	−	4.38693e7i	0.0291270	−	0.0291270i	0.721520	+	0.692393i	$0.243444\pi$
$198$	7.77778e8			0.506052
$199$			2.08596e9i			1.33013i	0.746785	+	0.665066i	$0.231596\pi$
$199$			2.08596e9i			1.33013i	−0.746785	+	0.665066i	$0.768404\pi$
$200$	1.66811e9	−	1.66811e9i	1.04257	−	1.04257i
$201$	−3.80867e7	+	3.80867e7i	−0.0233340	+	0.0233340i
$202$	−2.17943e9	−	2.17943e9i	−1.30899	−	1.30899i
$203$	−2.33655e9	−	2.33655e9i	−1.37591	−	1.37591i
$204$	3.46547e9			2.00098
$205$		−	1.34218e9i		−	0.759966i
$206$	2.55035e9	+	2.55035e9i	1.41622	+	1.41622i
$207$			6.80709e8i			0.370749i
$208$	−5.07821e9	−	2.08437e9i	−2.71305	−	1.11358i
$209$	−8.23895e8			−0.431804
$210$	−1.96633e9	+	1.96633e9i	−1.01107	+	1.01107i
$211$	2.22720e9			1.12364			0.561822	−	0.827258i	$-0.310100\pi$
$211$	2.22720e9			1.12364			0.561822	+	0.827258i	$0.310100\pi$
$212$		−	7.15113e9i		−	3.54023i
$213$	−4.05440e8	+	4.05440e8i	−0.196974	+	0.196974i
$214$	7.99515e8	−	7.99515e8i	0.381216	−	0.381216i
$215$	8.32726e8	+	8.32726e8i	0.389716	+	0.389716i
$216$	4.77664e9	+	4.77664e9i	2.19436	+	2.19436i
$217$	1.02223e9			0.461009
$218$			2.59120e9i			1.14729i
$219$	−4.08939e8	−	4.08939e8i	−0.177780	−	0.177780i
$220$		−	2.33546e9i		−	0.996968i
$221$	−9.89304e8	+	2.41027e9i	−0.414725	+	1.01041i
$222$	−4.42901e9			−1.82346
$223$	−4.04757e8	+	4.04757e8i	−0.163672	+	0.163672i	−0.784191	−	0.620519i	$-0.786922\pi$
$223$	−4.04757e8	+	4.04757e8i	−0.163672	+	0.163672i	0.620519	+	0.784191i	$0.286922\pi$
$224$	−9.88080e9			−3.92464
$225$		−	6.25871e8i		−	0.244205i
$226$	4.37913e9	−	4.37913e9i	1.67863	−	1.67863i
$227$	−2.82714e9	+	2.82714e9i	−1.06474	+	1.06474i	−0.0669870	+	0.997754i	$0.521339\pi$
$227$	−2.82714e9	+	2.82714e9i	−1.06474	+	1.06474i	−0.997754	+	0.0669870i	$0.978661\pi$
$228$	−2.71018e9	−	2.71018e9i	−1.00290	−	1.00290i
$229$	−8.00115e7	−	8.00115e7i	−0.0290945	−	0.0290945i	0.692410	−	0.721504i	$-0.256549\pi$
$229$	−8.00115e7	−	8.00115e7i	−0.0290945	−	0.0290945i	−0.721504	+	0.692410i	$0.756549\pi$
$230$	2.84707e9			1.01739
$231$		−	1.71734e9i		−	0.603128i
$232$	7.71963e9	+	7.71963e9i	2.66468	+	2.66468i
$233$			1.57796e9i			0.535391i	0.963504	+	0.267695i	$0.0862621\pi$
$233$			1.57796e9i			0.535391i	−0.963504	+	0.267695i	$0.913738\pi$
$234$	−2.50983e9	+	1.04906e9i	−0.837105	+	0.349896i
$235$	9.50286e8			0.311590
$236$	2.66101e9	−	2.66101e9i	0.857825	−	0.857825i
$237$	2.84480e9			0.901693
$238$			9.91221e9i			3.08932i
$239$	3.25040e9	−	3.25040e9i	0.996197	−	0.996197i	−0.00379604	−	0.999993i	$-0.501208\pi$
$239$	3.25040e9	−	3.25040e9i	0.996197	−	0.996197i	0.999993	+	0.00379604i	$0.00120832\pi$
$240$	3.47803e9	−	3.47803e9i	1.04831	−	1.04831i
$241$	1.57378e9	+	1.57378e9i	0.466526	+	0.466526i	0.900787	−	0.434261i	$-0.142991\pi$
$241$	1.57378e9	+	1.57378e9i	0.466526	+	0.466526i	−0.434261	+	0.900787i	$0.642991\pi$
$242$	−3.14573e9	−	3.14573e9i	−0.917191	−	0.917191i
$243$	3.00159e9			0.860848
$244$		−	9.15396e9i		−	2.58256i
$245$	−2.24856e9	−	2.24856e9i	−0.624081	−	0.624081i
$246$			5.37102e9i			1.46662i
$247$	2.65864e9	−	1.11127e9i	0.714286	−	0.298559i
$248$	−3.37730e9			−0.892819
$249$	9.10547e8	−	9.10547e8i	0.236867	−	0.236867i
$250$	−7.78300e9			−1.99245
$251$			4.88988e9i			1.23198i	0.787755	+	0.615989i	$0.211244\pi$
$251$			4.88988e9i			1.23198i	−0.787755	+	0.615989i	$0.788756\pi$
$252$	−5.25375e9	+	5.25375e9i	−1.30277	+	1.30277i
$253$	−1.24328e9	+	1.24328e9i	−0.303450	+	0.303450i
$254$	−7.45710e8	−	7.45710e8i	−0.179157	−	0.179157i
$255$	−1.65077e9	−	1.65077e9i	−0.390416	−	0.390416i
$256$	5.86311e8			0.136511
$257$			6.26216e9i			1.43546i	0.696320	+	0.717731i	$0.254819\pi$
$257$			6.26216e9i			1.43546i	−0.696320	+	0.717731i	$0.745181\pi$
$258$	−3.33234e9	−	3.33234e9i	−0.752092	−	0.752092i
$259$		−	9.09483e9i		−	2.02114i
$260$	3.15006e9	+	7.53633e9i	0.689327	+	1.64917i
$261$	2.89638e9			0.624157
$262$	−3.74176e9	+	3.74176e9i	−0.794092	+	0.794092i
$263$	2.97057e9			0.620892			0.310446	−	0.950591i	$-0.399522\pi$
$263$	2.97057e9			0.620892			0.310446	+	0.950591i	$0.399522\pi$
$264$			5.67386e9i			1.16805i
$265$	−3.40643e9	+	3.40643e9i	−0.690743	+	0.690743i
$266$	7.75187e9	−	7.75187e9i	1.54839	−	1.54839i
$267$	−1.53638e8	−	1.53638e8i	−0.0302310	−	0.0302310i
$268$	4.25622e8	+	4.25622e8i	0.0825058	+	0.0825058i
$269$	7.17468e9			1.37023			0.685115	−	0.728435i	$-0.259752\pi$
$269$	7.17468e9			1.37023			0.685115	+	0.728435i	$0.259752\pi$
$270$		−	7.49582e9i		−	1.41047i
$271$	−6.82278e9	−	6.82278e9i	−1.26498	−	1.26498i	−0.948648	−	0.316333i	$-0.897548\pi$
$271$	−6.82278e9	−	6.82278e9i	−1.26498	−	1.26498i	−0.316333	−	0.948648i	$-0.602452\pi$
$272$		−	1.75327e10i		−	3.20311i
$273$	2.31635e9	+	5.54173e9i	0.417016	+	0.997687i
$274$	−2.82419e9			−0.501062
$275$	1.14312e9	−	1.14312e9i	0.199877	−	0.199877i
$276$	−8.17948e9			−1.40958
$277$			7.81379e9i			1.32722i	0.748079	+	0.663609i	$0.230976\pi$
$277$			7.81379e9i			1.32722i	−0.748079	+	0.663609i	$0.769024\pi$
$278$	7.95226e9	−	7.95226e9i	1.33141	−	1.33141i
$279$	−6.33577e8	+	6.33577e8i	−0.104564	+	0.104564i
$280$	1.33403e10	+	1.33403e10i	2.17037	+	2.17037i
$281$	−3.42031e9	−	3.42031e9i	−0.548580	−	0.548580i	0.377450	−	0.926030i	$-0.376801\pi$
$281$	−3.42031e9	−	3.42031e9i	−0.548580	−	0.548580i	−0.926030	+	0.377450i	$0.876801\pi$
$282$	−3.80279e9			−0.601320
$283$		−	1.03762e10i		−	1.61768i	−0.588029	−	0.808840i	$-0.700096\pi$
$283$		−	1.03762e10i		−	1.61768i	0.588029	−	0.808840i	$-0.299904\pi$
$284$	4.53082e9	+	4.53082e9i	0.696472	+	0.696472i
$285$			2.58198e9i			0.391358i
$286$	−6.50014e9	−	2.66801e9i	−0.971535	−	0.398770i
$287$	−1.10292e10			−1.62561
$288$	6.12411e9	−	6.12411e9i	0.890171	−	0.890171i
$289$	−1.34575e9			−0.192918
$290$		−	1.21142e10i		−	1.71278i
$291$	1.29432e9	−	1.29432e9i	0.180496	−	0.180496i
$292$	−4.56992e9	+	4.56992e9i	−0.628604	+	0.628604i
$293$	−6.31754e9	−	6.31754e9i	−0.857191	−	0.857191i	0.133815	−	0.991006i	$-0.457277\pi$
$293$	−6.31754e9	−	6.31754e9i	−0.857191	−	0.857191i	−0.991006	+	0.133815i	$0.957277\pi$
$294$	8.99814e9	+	8.99814e9i	1.20438	+	1.20438i
$295$	−2.53514e9			−0.334745
$296$			3.00480e10i			3.91425i
$297$	3.27333e9	+	3.27333e9i	0.420692	+	0.420692i
$298$			2.32394e10i			2.94687i
$299$	2.33503e9	−	5.68890e9i	0.292152	−	0.711777i
$300$	7.52054e9			0.928462
$301$	6.84286e9	−	6.84286e9i	0.833626	−	0.833626i
$302$	1.46684e10			1.76342
$303$		−	5.96520e9i		−	0.707708i
$304$	−1.37115e10	+	1.37115e10i	−1.60542	+	1.60542i
$305$	−4.36048e9	+	4.36048e9i	−0.503890	+	0.503890i
$306$	−6.14358e9	−	6.14358e9i	−0.700706	−	0.700706i
$307$	4.92009e9	+	4.92009e9i	0.553885	+	0.553885i	0.927560	−	0.373675i	$-0.121902\pi$
$307$	4.92009e9	+	4.92009e9i	0.553885	+	0.553885i	−0.373675	+	0.927560i	$0.621902\pi$
$308$	−1.91914e10			−2.13258
$309$			6.98044e9i			0.765683i
$310$	2.64994e9	+	2.64994e9i	0.286939	+	0.286939i
$311$			9.96443e9i			1.06515i	0.846383	+	0.532575i	$0.178776\pi$
$311$			9.96443e9i			1.06515i	−0.846383	+	0.532575i	$0.821224\pi$
$312$	−7.65288e9	−	1.83091e10i	−0.807619	−	1.93218i
$313$	−4.96093e9			−0.516876			−0.258438	−	0.966028i	$-0.583208\pi$
$313$	−4.96093e9			−0.516876			−0.258438	+	0.966028i	$0.583208\pi$
$314$	−1.11819e10	+	1.11819e10i	−1.15026	+	1.15026i
$315$	5.00524e9			0.508373
$316$		−	3.17909e10i		−	3.18826i
$317$	−1.66881e9	+	1.66881e9i	−0.165260	+	0.165260i	−0.784892	−	0.619632i	$-0.787282\pi$
$317$	−1.66881e9	+	1.66881e9i	−0.165260	+	0.165260i	0.619632	+	0.784892i	$0.287282\pi$
$318$	1.36316e10	−	1.36316e10i	1.33303	−	1.33303i
$319$	5.29010e9	+	5.29010e9i	0.510859	+	0.510859i
$320$	−1.03431e10	−	1.03431e10i	−0.986399	−	0.986399i
$321$	2.18831e9			0.206105
$322$		−	2.33956e10i		−	2.17626i
$323$	6.50785e9	+	6.50785e9i	0.597899	+	0.597899i
$324$			8.01985e9i			0.727757i
$325$	−2.14692e9	+	5.23060e9i	−0.192434	+	0.468833i
$326$	2.16683e10			1.91846
$327$	−3.54612e9	+	3.54612e9i	−0.310143	+	0.310143i
$328$	3.64390e10			3.14826
$329$		−	7.80890e9i		−	0.666509i
$330$	4.45190e9	−	4.45190e9i	0.375396	−	0.375396i
$331$	−8.58995e9	+	8.58995e9i	−0.715614	+	0.715614i	−0.967704	−	0.252090i	$-0.918882\pi$
$331$	−8.58995e9	+	8.58995e9i	−0.715614	+	0.715614i	0.252090	+	0.967704i	$0.418882\pi$
$332$	−1.01754e10	−	1.01754e10i	−0.837529	−	0.837529i
$333$	5.63697e9	+	5.63697e9i	0.458425	+	0.458425i
$334$	−5.24563e9			−0.421514
$335$		−	4.05489e8i		−	0.0321958i
$336$	−2.85804e10	−	2.85804e10i	−2.24239	−	2.24239i
$337$		−	2.16829e10i		−	1.68112i	−0.541722	−	0.840558i	$-0.682227\pi$
$337$		−	2.16829e10i		−	1.68112i	0.541722	−	0.840558i	$-0.317773\pi$
$338$	2.45740e10	−	1.57925e8i	1.88282	−	0.0121000i
$339$	1.19859e10			0.907552
$340$	−1.84475e10	+	1.84475e10i	−1.38046	+	1.38046i
$341$	−2.31440e9			−0.171167
$342$			9.60920e9i			0.702397i
$343$	−3.77456e9	+	3.77456e9i	−0.272703	+	0.272703i
$344$	−2.26078e10	+	2.26078e10i	−1.61445	+	1.61445i
$345$	3.89629e9	+	3.89629e9i	0.275027	+	0.275027i
$346$	−1.51151e10	−	1.51151e10i	−1.05465	−	1.05465i
$347$	−6.39722e9			−0.441238			−0.220619	−	0.975360i	$-0.570808\pi$
$347$	−6.39722e9			−0.441238			−0.220619	+	0.975360i	$0.570808\pi$
$348$			3.48033e10i			2.37303i
$349$	−7.95340e9	−	7.95340e9i	−0.536107	−	0.536107i	0.386276	−	0.922383i	$-0.373761\pi$
$349$	−7.95340e9	−	7.95340e9i	−0.536107	−	0.536107i	−0.922383	+	0.386276i	$0.873761\pi$
$350$			2.15108e10i			1.43346i
$351$	−1.49778e10	−	6.14771e9i	−0.986781	−	0.405028i
$352$	2.23708e10			1.45717
$353$	3.10735e9	−	3.10735e9i	0.200120	−	0.200120i	−0.599931	−	0.800052i	$-0.704805\pi$
$353$	3.10735e9	−	3.10735e9i	0.200120	−	0.200120i	0.800052	+	0.599931i	$0.204805\pi$
$354$	1.01449e10			0.646006
$355$		−	4.31650e9i		−	0.271781i
$356$	−1.71691e9	+	1.71691e9i	−0.106893	+	0.106893i
$357$	−1.35651e10	+	1.35651e10i	−0.835122	+	0.835122i
$358$	−1.29826e10	−	1.29826e10i	−0.790370	−	0.790370i
$359$	−1.00990e10	−	1.00990e10i	−0.607997	−	0.607997i	0.334425	−	0.942422i	$-0.391458\pi$
$359$	−1.00990e10	−	1.00990e10i	−0.607997	−	0.607997i	−0.942422	+	0.334425i	$0.891458\pi$
$360$	−1.65366e10			−0.984546
$361$			6.80460e9i			0.400658i
$362$	2.80775e10	+	2.80775e10i	1.63502	+	1.63502i
$363$		−	8.61001e9i		−	0.495881i
$364$	6.19292e10	−	2.58853e10i	3.52768	−	1.47451i
$365$	4.35375e9			0.245297
$366$	1.74495e10	−	1.74495e10i	0.972429	−	0.972429i
$367$	−2.52192e10			−1.39017			−0.695085	−	0.718928i	$-0.744633\pi$
$367$	−2.52192e10			−1.39017			−0.695085	+	0.718928i	$0.744633\pi$
$368$			4.13820e10i			2.25642i
$369$	6.83590e9	−	6.83590e9i	0.368714	−	0.368714i
$370$	2.35767e10	−	2.35767e10i	1.25799	−	1.25799i
$371$	2.79921e10	+	2.79921e10i	1.47754	+	1.47754i
$372$	−7.61314e9	−	7.61314e9i	−0.397550	−	0.397550i
$373$	1.89331e10			0.978108			0.489054	−	0.872254i	$-0.337342\pi$
$373$	1.89331e10			0.978108			0.489054	+	0.872254i	$0.337342\pi$
$374$		−	2.24419e10i		−	1.14703i
$375$	−1.06512e10	−	1.06512e10i	−0.538610	−	0.538610i
$376$			2.57995e10i			1.29080i
$377$	−2.42060e10	−	9.93545e9i	−1.19828	−	0.491838i
$378$	−6.15963e10			−3.01708
$379$	1.15400e10	−	1.15400e10i	0.559306	−	0.559306i	−0.369804	−	0.929110i	$-0.620575\pi$
$379$	1.15400e10	−	1.15400e10i	0.559306	−	0.559306i	0.929110	+	0.369804i	$0.120575\pi$
$380$	2.88538e10			1.38379
$381$		−	2.04104e9i		−	0.0968618i
$382$	−5.10259e10	+	5.10259e10i	−2.39628	+	2.39628i
$383$	1.08429e10	−	1.08429e10i	0.503906	−	0.503906i	−0.408744	−	0.912649i	$-0.634033\pi$
$383$	1.08429e10	−	1.08429e10i	0.503906	−	0.503906i	0.912649	+	0.408744i	$0.134033\pi$
$384$	1.24776e10	+	1.24776e10i	0.573859	+	0.573859i
$385$	9.14182e9	+	9.14182e9i	0.416092	+	0.416092i
$386$	−6.07071e10			−2.73458
$387$			8.48239e9i			0.378159i
$388$	−1.44641e10	−	1.44641e10i	−0.638210	−	0.638210i
$389$		−	2.35898e10i		−	1.03021i	−0.857127	−	0.515105i	$-0.827753\pi$
$389$		−	2.35898e10i		−	1.03021i	0.857127	−	0.515105i	$-0.172247\pi$
$390$	−8.36120e9	+	2.03706e10i	−0.361418	+	0.880533i
$391$	1.96411e10			0.840347
$392$	6.10466e10	−	6.10466e10i	2.58534	−	2.58534i
$393$	−1.02414e10			−0.429327
$394$		−	1.86902e9i		−	0.0775584i
$395$	−1.51436e10	+	1.51436e10i	−0.622070	+	0.622070i
$396$	1.18948e10	−	1.18948e10i	0.483702	−	0.483702i
$397$	1.79391e9	+	1.79391e9i	0.0722169	+	0.0722169i	0.742293	−	0.670076i	$-0.233738\pi$
$397$	1.79391e9	+	1.79391e9i	0.0722169	+	0.0722169i	−0.670076	+	0.742293i	$0.733738\pi$
$398$	4.44355e10	+	4.44355e10i	1.77092	+	1.77092i
$399$	2.12172e10			0.837138
$400$		−	3.80482e10i		−	1.48626i
$401$	−1.03090e9	−	1.03090e9i	−0.0398691	−	0.0398691i	0.686891	−	0.726760i	$-0.258975\pi$
$401$	−1.03090e9	−	1.03090e9i	−0.0398691	−	0.0398691i	−0.726760	+	0.686891i	$0.758975\pi$
$402$			1.62266e9i			0.0621330i
$403$	7.46836e9	−	3.12165e9i	0.283143	−	0.118349i
$404$	−6.66615e10			−2.50236
$405$	3.82025e9	−	3.82025e9i	0.141995	−	0.141995i
$406$	−9.95470e10			−3.66374
$407$			2.05913e10i			0.750422i
$408$	4.48172e10	−	4.48172e10i	1.61735	−	1.61735i
$409$	6.83671e9	−	6.83671e9i	0.244317	−	0.244317i	−0.574316	−	0.818634i	$-0.694732\pi$
$409$	6.83671e9	−	6.83671e9i	0.244317	−	0.244317i	0.818634	+	0.574316i	$0.194732\pi$
$410$	−2.85912e10	−	2.85912e10i	−1.01181	−	1.01181i
$411$	−3.86497e9	−	3.86497e9i	−0.135450	−	0.135450i
$412$	7.80069e10			2.70735
$413$			2.08323e10i			0.716040i
$414$	1.45006e10	+	1.45006e10i	0.493610	+	0.493610i
$415$			9.69411e9i			0.326825i
$416$	−7.21887e10	+	3.01736e10i	−2.41044	+	1.00752i
$417$	2.17657e10			0.719828
$418$	−1.75507e10	+	1.75507e10i	−0.574897	+	0.574897i
$419$	6.77187e9			0.219711			0.109856	−	0.993948i	$-0.464961\pi$
$419$	6.77187e9			0.219711			0.109856	+	0.993948i	$0.464961\pi$
$420$			6.01435e10i			1.93282i
$421$	2.61602e10	−	2.61602e10i	0.832747	−	0.832747i	−0.155145	−	0.987892i	$-0.549584\pi$
$421$	2.61602e10	−	2.61602e10i	0.832747	−	0.832747i	0.987892	+	0.155145i	$0.0495844\pi$
$422$	4.74441e10	−	4.74441e10i	1.49600	−	1.49600i
$423$	4.83995e9	+	4.83995e9i	0.151175	+	0.151175i
$424$	−9.24818e10	−	9.24818e10i	−2.86149	−	2.86149i
$425$	−1.80588e10			−0.553520
$426$			1.72735e10i			0.524495i
$427$	3.58319e10	+	3.58319e10i	1.07785	+	1.07785i
$428$		−	2.44545e10i		−	0.728759i
$429$	−5.24436e9	−	1.25468e10i	−0.154833	−	0.370429i
$430$	3.54777e10			1.03772
$431$	−2.12347e10	+	2.12347e10i	−0.615372	+	0.615372i	−0.944341	−	0.328969i	$-0.893299\pi$
$431$	−2.12347e10	+	2.12347e10i	−0.615372	+	0.615372i	0.328969	+	0.944341i	$0.393299\pi$
$432$	1.08951e11			3.12822
$433$		−	1.66730e10i		−	0.474310i	−0.971472	−	0.237155i	$-0.923785\pi$
$433$		−	1.66730e10i		−	0.474310i	0.971472	−	0.237155i	$-0.0762149\pi$
$434$	2.17757e10	−	2.17757e10i	0.613780	−	0.613780i
$435$	1.65785e10	−	1.65785e10i	0.463008	−	0.463008i
$436$	3.96281e10	+	3.96281e10i	1.09662	+	1.09662i
$437$	−1.53604e10	−	1.53604e10i	−0.421188	−	0.421188i
$438$	−1.74225e10			−0.473385
$439$			6.06828e10i			1.63383i	0.576757	+	0.816916i	$0.304318\pi$
$439$			6.06828e10i			1.63383i	−0.576757	+	0.816916i	$0.695682\pi$
$440$	−3.02033e10	−	3.02033e10i	−0.805830	−	0.805830i
$441$		−	2.29045e10i		−	0.605574i
$442$	3.02696e10	+	7.24181e10i	0.793080	+	1.89740i
$443$	6.47087e9			0.168015			0.0840074	−	0.996465i	$-0.473228\pi$
$443$	6.47087e9			0.168015			0.0840074	+	0.996465i	$0.473228\pi$
$444$	−6.77344e10	+	6.77344e10i	−1.74292	+	1.74292i
$445$	1.63570e9			0.0417122
$446$			1.72444e10i			0.435820i
$447$	−3.18037e10	+	3.18037e10i	−0.796614	+	0.796614i
$448$	−8.49939e10	+	8.49939e10i	−2.10997	+	2.10997i
$449$	−5.76730e9	−	5.76730e9i	−0.141901	−	0.141901i	0.632587	−	0.774489i	$-0.281993\pi$
$449$	−5.76730e9	−	5.76730e9i	−0.141901	−	0.141901i	−0.774489	+	0.632587i	$0.781993\pi$
$450$	−1.33324e10	−	1.33324e10i	−0.325131	−	0.325131i
$451$	2.49709e10			0.603570
$452$		−	1.33943e11i		−	3.20898i
$453$	2.00741e10	+	2.00741e10i	0.476697	+	0.476697i
$454$			1.20448e11i			2.83516i
$455$	−4.18304e10	−	1.71694e10i	−0.975992	−	0.400600i
$456$	−7.00987e10			−1.62125
$457$	−5.48826e10	+	5.48826e10i	−1.25826	+	1.25826i	−0.306335	+	0.951924i	$0.599103\pi$
$457$	−5.48826e10	+	5.48826e10i	−1.25826	+	1.25826i	−0.951924	+	0.306335i	$0.900897\pi$
$458$	−3.40883e9			−0.0774718
$459$		−	5.17114e10i		−	1.16502i
$460$	4.35413e10	−	4.35413e10i	0.972456	−	0.972456i
$461$	3.66014e10	−	3.66014e10i	0.810391	−	0.810391i	−0.174302	−	0.984692i	$-0.555767\pi$
$461$	3.66014e10	−	3.66014e10i	0.810391	−	0.810391i	0.984692	+	0.174302i	$0.0557667\pi$
$462$	−3.65831e10	−	3.65831e10i	−0.802994	−	0.802994i
$463$	−4.67917e10	−	4.67917e10i	−1.01823	−	1.01823i	−0.999831	−	0.0183966i	$-0.994144\pi$
$463$	−4.67917e10	−	4.67917e10i	−1.01823	−	1.01823i	−0.0183966	−	0.999831i	$-0.505856\pi$
$464$	1.76078e11			3.79869
$465$			7.25303e9i			0.155134i
$466$	3.36138e10	+	3.36138e10i	0.712811	+	0.712811i
$467$		−	2.21919e10i		−	0.466580i	−0.972407	−	0.233290i	$-0.925051\pi$
$467$		−	2.21919e10i		−	0.466580i	0.972407	−	0.233290i	$-0.0749492\pi$
$468$	−2.23399e10	+	5.44273e10i	−0.465691	+	1.13458i
$469$	−3.33207e9			−0.0688689
$470$	2.02431e10	−	2.02431e10i	0.414845	−	0.414845i
$471$	−3.06053e10			−0.621890
$472$		−	6.88270e10i		−	1.38673i
$473$	−1.54927e10	+	1.54927e10i	−0.309515	+	0.309515i
$474$	6.06004e10	−	6.06004e10i	1.20050	−	1.20050i
$475$	1.41229e10	+	1.41229e10i	0.277428	+	0.277428i
$476$	1.51591e11	+	1.51591e11i	2.95288	+	2.95288i
$477$	−3.46989e10			−0.670259
$478$		−	1.38481e11i		−	2.65264i
$479$	−1.26550e10	−	1.26550e10i	−0.240393	−	0.240393i	0.576620	−	0.817013i	$-0.304371\pi$
$479$	−1.26550e10	−	1.26550e10i	−0.240393	−	0.240393i	−0.817013	+	0.576620i	$0.804371\pi$
$480$		−	7.01072e10i		−	1.32068i
$481$	−2.77735e10	−	6.64464e10i	−0.518860	−	1.24134i
$482$	6.70497e10			1.24225
$483$	3.20174e10	−	3.20174e10i	0.588299	−	0.588299i
$484$	−9.62175e10			−1.75337
$485$			1.37799e10i			0.249046i
$486$	6.39403e10	−	6.39403e10i	1.14612	−	1.14612i
$487$	−6.95971e10	+	6.95971e10i	−1.23730	+	1.23730i	−0.276200	+	0.961100i	$0.589075\pi$
$487$	−6.95971e10	+	6.95971e10i	−1.23730	+	1.23730i	−0.961100	+	0.276200i	$0.910925\pi$
$488$	−1.18383e11	−	1.18383e11i	−2.08743	−	2.08743i
$489$	2.96535e10	+	2.96535e10i	0.518610	+	0.518610i
$490$	−9.57984e10			−1.66178
$491$			4.86806e10i			0.837588i	0.908081	+	0.418794i	$0.137547\pi$
$491$			4.86806e10i			0.837588i	−0.908081	+	0.418794i	$0.862453\pi$
$492$	8.21409e10	+	8.21409e10i	1.40184	+	1.40184i
$493$		−	8.35718e10i		−	1.41473i
$494$	3.29624e10	−	8.03071e10i	0.553491	−	1.34849i
$495$	−1.13322e10			−0.188753
$496$	−3.85167e10	+	3.85167e10i	−0.636389	+	0.636389i
$497$	−3.54705e10			−0.581356
$498$		−	3.87932e10i		−	0.630722i
$499$	−3.67791e10	+	3.67791e10i	−0.593196	+	0.593196i	−0.938493	−	0.345297i	$-0.887778\pi$
$499$	−3.67791e10	+	3.67791e10i	−0.593196	+	0.593196i	0.345297	+	0.938493i	$0.387778\pi$
$500$	−1.19028e11	+	1.19028e11i	−1.90445	+	1.90445i
$501$	−7.17877e9	−	7.17877e9i	−0.113946	−	0.113946i
$502$	1.04165e11	+	1.04165e11i	1.64024	+	1.64024i
$503$	6.00767e10			0.938499			0.469249	−	0.883066i	$-0.344524\pi$
$503$	6.00767e10			0.938499			0.469249	+	0.883066i	$0.344524\pi$
$504$			1.35888e11i			2.10600i
$505$	3.17541e10	+	3.17541e10i	0.488242	+	0.488242i
$506$			5.29691e10i			0.808017i
$507$	3.38462e10	+	3.34140e10i	0.512246	+	0.505704i
$508$	−2.28088e10			−0.342490
$509$	5.70227e10	−	5.70227e10i	0.849526	−	0.849526i	−0.140547	−	0.990074i	$-0.544886\pi$
$509$	5.70227e10	−	5.70227e10i	0.849526	−	0.849526i	0.990074	+	0.140547i	$0.0448863\pi$
$510$	−7.03301e10			−1.03959
$511$		−	3.57766e10i		−	0.524705i
$512$	−4.22957e10	+	4.22957e10i	−0.615483	+	0.615483i
$513$	−4.04410e10	+	4.04410e10i	−0.583918	+	0.583918i
$514$	1.33397e11	+	1.33397e11i	1.91115	+	1.91115i
$515$	−3.71585e10	−	3.71585e10i	−0.528238	−	0.528238i
$516$	−1.01925e11			−1.43775
$517$			1.76798e10i			0.247466i
$518$	−1.93739e11	−	1.93739e11i	−2.69091	−	2.69091i
$519$		−	4.13708e10i		−	0.570196i
$520$	1.38202e11	+	5.67254e10i	1.89016	+	0.775826i
$521$	4.82687e10			0.655110			0.327555	−	0.944832i	$-0.393775\pi$
$521$	4.82687e10			0.655110			0.327555	+	0.944832i	$0.393775\pi$
$522$	6.16992e10	−	6.16992e10i	0.830993	−	0.830993i
$523$	8.50162e10			1.13631			0.568153	−	0.822923i	$-0.307658\pi$
$523$	8.50162e10			1.13631			0.568153	+	0.822923i	$0.307658\pi$
$524$			1.14448e11i			1.51804i
$525$	−2.94381e10	+	2.94381e10i	−0.387501	+	0.387501i
$526$	6.32794e10	−	6.32794e10i	0.826646	−	0.826646i
$527$	1.82811e10	+	1.82811e10i	0.237007	+	0.237007i
$528$	6.47080e10	+	6.47080e10i	0.832572	+	0.832572i
$529$	3.19525e10			0.408021
$530$			1.45129e11i			1.83929i
$531$	−1.29118e10	−	1.29118e10i	−0.162409	−	0.162409i
$532$		−	2.37104e11i		−	2.96000i
$533$	−8.05789e10	+	3.36806e10i	−0.998418	+	0.417322i
$534$	−6.54562e9			−0.0804981
$535$	−1.16489e10	+	1.16489e10i	−0.142190	+	0.142190i
$536$	1.10087e10			0.133376
$537$		−	3.55341e10i		−	0.427315i
$538$	1.52836e11	−	1.52836e11i	1.82430	−	1.82430i
$539$	4.18340e10	−	4.18340e10i	0.495649	−	0.495649i
$540$	−1.14636e11	−	1.14636e11i	−1.34818	−	1.34818i
$541$	1.57802e10	+	1.57802e10i	0.184215	+	0.184215i	0.793189	−	0.608975i	$-0.208419\pi$
$541$	1.57802e10	+	1.57802e10i	0.184215	+	0.184215i	−0.608975	+	0.793189i	$0.708419\pi$
$542$	−2.90679e11			−3.36835
$543$			7.68494e10i			0.883978i
$544$	−1.76704e11	−	1.76704e11i	−2.01768	−	2.01768i
$545$		−	3.77536e10i		−	0.427930i
$546$	1.67394e11	+	6.87074e10i	1.88351	+	0.773096i
$547$	1.19273e11			1.33227			0.666134	−	0.745832i	$-0.267948\pi$
$547$	1.19273e11			1.33227			0.666134	+	0.745832i	$0.267948\pi$
$548$	−4.31913e10	+	4.31913e10i	−0.478933	+	0.478933i
$549$	−4.44172e10			−0.488947
$550$		−	4.87019e10i		−	0.532225i
$551$	−6.53575e10	+	6.53575e10i	−0.709070	+	0.709070i
$552$	−1.05781e11	+	1.05781e11i	−1.13933	+	1.13933i
$553$	1.24441e11	+	1.24441e11i	1.33065	+	1.33065i
$554$	1.66450e11	+	1.66450e11i	1.76704	+	1.76704i
$555$	6.45305e10			0.680132
$556$		−	2.43233e11i		−	2.54521i
$557$	3.41753e10	+	3.41753e10i	0.355052	+	0.355052i	0.861985	−	0.506933i	$-0.169221\pi$
$557$	3.41753e10	+	3.41753e10i	0.355052	+	0.355052i	−0.506933	+	0.861985i	$0.669221\pi$
$558$			2.69931e10i			0.278430i
$559$	2.90971e10	−	7.08901e10i	0.297991	−	0.726002i
$560$	3.04281e11			3.09401
$561$	3.07123e10	−	3.07123e10i	0.310070	−	0.310070i
$562$	−1.45720e11			−1.46074
$563$			1.95881e10i			0.194966i	0.995237	+	0.0974832i	$0.0310792\pi$
$563$			1.95881e10i			0.194966i	−0.995237	+	0.0974832i	$0.968921\pi$
$564$	−5.81573e10	+	5.81573e10i	−0.574762	+	0.574762i
$565$	−6.38037e10	+	6.38037e10i	−0.626112	+	0.626112i
$566$	−2.21035e11	−	2.21035e11i	−2.15375	−	2.15375i
$567$	−3.13926e10	−	3.13926e10i	−0.303735	−	0.303735i
$568$	1.17189e11			1.12589
$569$		−	9.06111e10i		−	0.864435i	−0.901769	−	0.432218i	$-0.857731\pi$
$569$		−	9.06111e10i		−	0.864435i	0.901769	−	0.432218i	$-0.142269\pi$
$570$	5.50018e10	+	5.50018e10i	0.521047	+	0.521047i
$571$			1.64318e11i			1.54575i	0.634558	+	0.772875i	$0.281182\pi$
$571$			1.64318e11i			1.54575i	−0.634558	+	0.772875i	$0.718818\pi$
$572$	−1.40212e11	+	5.86061e10i	−1.30978	+	0.547468i
$573$	−1.39660e11			−1.29555
$574$	−2.34946e11	+	2.34946e11i	−2.16431	+	2.16431i
$575$	4.26238e10			0.389925
$576$		−	1.05358e11i		−	0.957147i
$577$	1.05830e11	−	1.05830e11i	0.954787	−	0.954787i	−0.0442340	−	0.999021i	$-0.514085\pi$
$577$	1.05830e11	−	1.05830e11i	0.954787	−	0.954787i	0.999021	+	0.0442340i	$0.0140847\pi$
$578$	−2.86674e10	+	2.86674e10i	−0.256848	+	0.256848i
$579$	−8.30791e10	−	8.30791e10i	−0.739227	−	0.739227i
$580$	−1.85266e11	−	1.85266e11i	−1.63713	−	1.63713i
$581$	7.96605e10			0.699099
$582$		−	5.51434e10i		−	0.480620i
$583$	−6.33759e10	−	6.33759e10i	−0.548592	−	0.548592i
$584$			1.18201e11i			1.01618i
$585$	3.65680e10	−	1.52848e10i	0.312233	−	0.130508i
$586$	−2.69154e11			−2.28250
$587$	1.47280e11	−	1.47280e11i	1.24048	−	1.24048i	0.280684	−	0.959800i	$-0.409439\pi$
$587$	1.47280e11	−	1.47280e11i	1.24048	−	1.24048i	0.959800	−	0.280684i	$-0.0905612\pi$
$588$	2.75223e11			2.30238
$589$		−	2.85936e10i		−	0.237579i
$590$	−5.40039e10	+	5.40039e10i	−0.445674	+	0.445674i
$591$	2.55780e9	−	2.55780e9i	0.0209660	−	0.0209660i
$592$	3.42685e11	+	3.42685e11i	2.79003	+	2.79003i
$593$	8.28440e10	+	8.28440e10i	0.669950	+	0.669950i	0.957704	−	0.287755i	$-0.0929087\pi$
$593$	8.28440e10	+	8.28440e10i	0.669950	+	0.669950i	−0.287755	+	0.957704i	$0.592909\pi$
$594$	1.39458e11			1.12020
$595$		−	1.44420e11i		−	1.15229i
$596$	3.55409e11	+	3.55409e11i	2.81672	+	2.81672i
$597$			1.21622e11i			0.957448i
$598$	−7.14446e10	−	1.70927e11i	−0.558682	−	1.33661i
$599$	−8.55656e10			−0.664648			−0.332324	−	0.943165i	$-0.607833\pi$
$599$	−8.55656e10			−0.664648			−0.332324	+	0.943165i	$0.607833\pi$
$600$	9.72592e10	−	9.72592e10i	0.750457	−	0.750457i
$601$	−9.68522e9			−0.0742355			−0.0371177	−	0.999311i	$-0.511818\pi$
$601$	−9.68522e9			−0.0742355			−0.0371177	+	0.999311i	$0.511818\pi$
$602$		−	2.91535e11i		−	2.21975i
$603$	2.06521e9	−	2.06521e9i	0.0156205	−	0.0156205i
$604$	2.24329e11	−	2.24329e11i	1.68553	−	1.68553i
$605$	4.58331e10	+	4.58331e10i	0.342104	+	0.342104i
$606$	−1.27071e11	−	1.27071e11i	−0.942231	−	0.942231i
$607$	−2.33218e11			−1.71794			−0.858968	−	0.512030i	$-0.828894\pi$
$607$	−2.33218e11			−1.71794			−0.858968	+	0.512030i	$0.828894\pi$
$608$			2.76384e11i			2.02255i
$609$	−1.36232e11	−	1.36232e11i	−0.990402	−	0.990402i
$610$			1.85775e11i			1.34174i
$611$	−2.38465e10	−	5.70514e10i	−0.171104	−	0.409356i
$612$	−1.87912e11			−1.33952
$613$	−1.94651e11	+	1.94651e11i	−1.37852	+	1.37852i	−0.531405	+	0.847118i	$0.678336\pi$
$613$	−1.94651e11	+	1.94651e11i	−1.37852	+	1.37852i	−0.847118	+	0.531405i	$0.821664\pi$
$614$	2.09617e11			1.47487
$615$		−	7.82555e10i		−	0.547034i
$616$	−2.48193e11	+	2.48193e11i	−1.72372	+	1.72372i
$617$	−5.21712e10	+	5.21712e10i	−0.359990	+	0.359990i	−0.863809	−	0.503819i	$-0.831928\pi$
$617$	−5.21712e10	+	5.21712e10i	−0.359990	+	0.359990i	0.503819	+	0.863809i	$0.331928\pi$
$618$	1.48698e11	+	1.48698e11i	1.01942	+	1.01942i
$619$	−4.99981e9	−	4.99981e9i	−0.0340558	−	0.0340558i	0.689874	−	0.723930i	$-0.257666\pi$
$619$	−4.99981e9	−	4.99981e9i	−0.0340558	−	0.0340558i	−0.723930	+	0.689874i	$0.757666\pi$
$620$	8.10530e10			0.548533
$621$			1.22053e11i			0.820697i
$622$	2.12264e11	+	2.12264e11i	1.41812	+	1.41812i
$623$		−	1.34412e10i		−	0.0892249i
$624$	−2.96085e11	−	1.21529e11i	−1.95289	−	0.801572i
$625$	3.60680e10			0.236375
$626$	−1.05678e11	+	1.05678e11i	−0.688160	+	0.688160i
$627$	−4.80372e10			−0.310819
$628$			3.42017e11i			2.19892i
$629$	1.62648e11	−	1.62648e11i	1.03907	−	1.03907i
$630$	1.06622e11	−	1.06622e11i	0.676840	−	0.676840i
$631$	−1.76095e11	−	1.76095e11i	−1.11079	−	1.11079i	−0.993044	−	0.117742i	$-0.962434\pi$
$631$	−1.76095e11	−	1.76095e11i	−1.11079	−	1.11079i	−0.117742	−	0.993044i	$-0.537566\pi$
$632$	−4.11135e11	−	4.11135e11i	−2.57701	−	2.57701i
$633$	1.29857e11			0.808816
$634$			7.10983e10i			0.440050i
$635$	1.08650e10	+	1.08650e10i	0.0668241	+	0.0668241i
$636$		−	4.16946e11i		−	2.54831i
$637$	−7.85693e10	+	1.91420e11i	−0.477194	+	1.16260i
$638$	2.25381e11			1.36030
$639$	2.19846e10	−	2.19846e10i	0.131861	−	0.131861i
$640$	−1.32842e11			−0.791800
$641$			3.15548e11i			1.86910i	0.355831	+	0.934550i	$0.384198\pi$
$641$			3.15548e11i			1.86910i	−0.355831	+	0.934550i	$0.615802\pi$
$642$	4.66157e10	−	4.66157e10i	0.274405	−	0.274405i
$643$	4.71431e10	−	4.71431e10i	0.275787	−	0.275787i	−0.555638	−	0.831425i	$-0.687526\pi$
$643$	4.71431e10	−	4.71431e10i	0.275787	−	0.275787i	0.831425	+	0.555638i	$0.187526\pi$
$644$	−3.57797e11	−	3.57797e11i	−2.08014	−	2.08014i
$645$	4.85521e10	+	4.85521e10i	0.280523	+	0.280523i
$646$	2.77262e11			1.59207
$647$		−	6.69539e10i		−	0.382084i	−0.981582	−	0.191042i	$-0.938813\pi$
$647$		−	6.69539e10i		−	0.382084i	0.981582	−	0.191042i	$-0.0611867\pi$
$648$	1.03717e11	+	1.03717e11i	0.588231	+	0.588231i
$649$		−	4.71657e10i		−	0.265857i
$650$	6.56890e10	+	1.57157e11i	0.367993	+	0.880401i
$651$	5.96011e10			0.331841
$652$	3.31380e11	−	3.31380e11i	1.83373	−	1.83373i
$653$	3.78472e10			0.208152			0.104076	−	0.994569i	$-0.466811\pi$
$653$	3.78472e10			0.208152			0.104076	+	0.994569i	$0.466811\pi$
$654$			1.51080e11i			0.825839i
$655$	5.45173e10	−	5.45173e10i	0.296189	−	0.296189i
$656$	4.15571e11	−	4.15571e11i	2.24404	−	2.24404i
$657$	2.21743e10	+	2.21743e10i	0.119011	+	0.119011i
$658$	−1.66346e11	−	1.66346e11i	−0.887379	−	0.887379i
$659$	1.81460e10			0.0962141			0.0481071	−	0.998842i	$-0.484681\pi$
$659$	1.81460e10			0.0962141			0.0481071	+	0.998842i	$0.484681\pi$
$660$		−	1.36169e11i		−	0.717632i
$661$	−9.69134e10	−	9.69134e10i	−0.507666	−	0.507666i	0.406143	−	0.913809i	$-0.366873\pi$
$661$	−9.69134e10	−	9.69134e10i	−0.507666	−	0.507666i	−0.913809	+	0.406143i	$0.866873\pi$
$662$			3.65969e11i			1.90551i
$663$	−5.76813e10	+	1.40531e11i	−0.298525	+	0.727305i
$664$	−2.63187e11			−1.35392
$665$	−1.12944e11	+	1.12944e11i	−0.577534	+	0.577534i
$666$	2.40159e11			1.22068
$667$			1.97253e11i			0.996598i
$668$	−8.02232e10	+	8.02232e10i	−0.402897	+	0.402897i
$669$	−2.35993e10	+	2.35993e10i	−0.117814	+	0.117814i
$670$	−8.63778e9	−	8.63778e9i	−0.0428650	−	0.0428650i
$671$	−8.11257e10	−	8.11257e10i	−0.400192	−	0.400192i
$672$	−5.76100e11			−2.82501
$673$		−	1.38521e11i		−	0.675237i	−0.941283	−	0.337618i	$-0.890379\pi$
$673$		−	1.38521e11i		−	0.675237i	0.941283	−	0.337618i	$-0.109621\pi$
$674$	−4.61892e11	−	4.61892e11i	−2.23821	−	2.23821i
$675$		−	1.12221e11i		−	0.540577i
$676$	3.73404e11	−	3.78234e11i	1.78810	−	1.81123i
$677$	−8.74542e10			−0.416319			−0.208159	−	0.978095i	$-0.566747\pi$
$677$	−8.74542e10			−0.416319			−0.208159	+	0.978095i	$0.566747\pi$
$678$	2.55325e11	−	2.55325e11i	1.20830	−	1.20830i
$679$	1.13235e11			0.532724
$680$			4.77144e11i			2.23159i
$681$	−1.64836e11	+	1.64836e11i	−0.766416	+	0.766416i
$682$	−4.93016e10	+	4.93016e10i	−0.227889	+	0.227889i
$683$	3.01967e11	+	3.01967e11i	1.38764	+	1.38764i	0.830257	+	0.557380i	$0.188194\pi$
$683$	3.01967e11	+	3.01967e11i	1.38764	+	1.38764i	0.557380	+	0.830257i	$0.311806\pi$
$684$	1.46957e11	+	1.46957e11i	0.671375	+	0.671375i
$685$	4.11483e10			0.186892
$686$			1.60812e11i			0.726145i
$687$	−4.66507e9	−	4.66507e9i	−0.0209426	−	0.0209426i
$688$			5.15665e11i			2.30152i
$689$	2.89990e11	+	1.19028e11i	1.28678	+	0.528166i
$690$	1.65999e11			0.732332
$691$	2.36911e11	−	2.36911e11i	1.03914	−	1.03914i	0.0399336	−	0.999202i	$-0.487285\pi$
$691$	2.36911e11	−	2.36911e11i	1.03914	−	1.03914i	0.999202	−	0.0399336i	$-0.0127147\pi$
$692$	−4.62321e11			−2.01613
$693$			9.31213e10i			0.403753i
$694$	−1.36274e11	+	1.36274e11i	−0.587457	+	0.587457i
$695$	−1.15864e11	+	1.15864e11i	−0.496603	+	0.496603i
$696$	4.50093e11	+	4.50093e11i	1.91807	+	1.91807i
$697$	−1.97242e11	−	1.97242e11i	−0.835734	−	0.835734i
$698$	−3.38849e11			−1.42753
$699$			9.20026e10i			0.385382i
$700$	3.28973e11	+	3.28973e11i	1.37015	+	1.37015i
$701$		−	2.94371e11i		−	1.21905i	−0.792765	−	0.609527i	$-0.791359\pi$
$701$		−	2.94371e11i		−	1.21905i	0.792765	−	0.609527i	$-0.208641\pi$
$702$	−4.50019e11	+	1.88100e11i	−1.85303	+	0.774536i
$703$	−2.54399e11			−1.04158
$704$	1.92432e11	−	1.92432e11i	0.783404	−	0.783404i
$705$	5.54064e10			0.224287
$706$		−	1.32386e11i		−	0.532874i
$707$	2.60937e11	−	2.60937e11i	1.04438	−	1.04438i
$708$	1.55150e11	−	1.55150e11i	0.617475	−	0.617475i
$709$	−1.56098e11	−	1.56098e11i	−0.617750	−	0.617750i	0.327204	−	0.944954i	$-0.393894\pi$
$709$	−1.56098e11	−	1.56098e11i	−0.617750	−	0.617750i	−0.944954	+	0.327204i	$0.893894\pi$
$710$	−9.19508e10	−	9.19508e10i	−0.361844	−	0.361844i
$711$	−1.54257e11			−0.603623
$712$			4.44078e10i			0.172798i
$713$	−4.31486e10	−	4.31486e10i	−0.166959	−	0.166959i
$714$			5.77931e11i			2.22374i
$715$	9.47067e10	+	3.88727e10i	0.362373	+	0.148738i
$716$	−3.97096e11			−1.51093
$717$	1.89514e11	−	1.89514e11i	0.717077	−	0.717077i
$718$	−4.30261e11			−1.61895
$719$			1.24976e11i			0.467639i	0.972280	+	0.233820i	$0.0751226\pi$
$719$			1.24976e11i			0.467639i	−0.972280	+	0.233820i	$0.924877\pi$
$720$	−1.88593e11	+	1.88593e11i	−0.701771	+	0.701771i
$721$	−3.05347e11	+	3.05347e11i	−1.12993	+	1.12993i
$722$	1.44953e11	+	1.44953e11i	0.533429	+	0.533429i
$723$	9.17591e10	+	9.17591e10i	0.335812	+	0.335812i
$724$	8.58798e11			3.12562
$725$		−	1.81362e11i		−	0.656439i
$726$	−1.83412e11	−	1.83412e11i	−0.660207	−	0.660207i
$727$		−	2.74225e10i		−	0.0981679i	−0.998795	−	0.0490839i	$-0.984370\pi$
$727$		−	2.74225e10i		−	0.0981679i	0.998795	−	0.0490839i	$-0.0156302\pi$
$728$	4.66136e11	−	1.13566e12i	1.65954	−	4.04318i
$729$	2.55765e11			0.905588
$730$	9.27442e10	−	9.27442e10i	0.326584	−	0.326584i
$731$	2.44750e11			0.857142
$732$		−	5.33722e11i		−	1.85896i
$733$	−8.13245e10	+	8.13245e10i	−0.281712	+	0.281712i	−0.833792	−	0.552079i	$-0.813835\pi$
$733$	−8.13245e10	+	8.13245e10i	−0.281712	+	0.281712i	0.552079	+	0.833792i	$0.313835\pi$
$734$	−5.37224e11	+	5.37224e11i	−1.85085	+	1.85085i
$735$	−1.31102e11	−	1.31102e11i	−0.449223	−	0.449223i
$736$	4.17071e11	+	4.17071e11i	1.42134	+	1.42134i
$737$	7.54402e9			0.0255701
$738$		−	2.91238e11i		−	0.981801i
$739$	−2.00152e11	−	2.00152e11i	−0.671093	−	0.671093i	0.286875	−	0.957968i	$-0.407384\pi$
$739$	−2.00152e11	−	2.00152e11i	−0.671093	−	0.671093i	−0.957968	+	0.286875i	$0.907384\pi$
$740$		−	7.21133e11i		−	2.40485i
$741$	1.55012e11	−	6.47924e10i	0.514153	−	0.214907i
$742$	1.19258e12			3.93435
$743$	−2.81094e11	+	2.81094e11i	−0.922351	+	0.922351i	−0.997195	−	0.0748440i	$-0.976154\pi$
$743$	−2.81094e11	+	2.81094e11i	−0.922351	+	0.922351i	0.0748440	+	0.997195i	$0.476154\pi$
$744$	−1.96914e11			−0.642664
$745$		−	3.38598e11i		−	1.09915i
$746$	4.03316e11	−	4.03316e11i	1.30224	−	1.30224i
$747$	−4.93735e10	+	4.93735e10i	−0.158567	+	0.158567i
$748$	−3.43212e11	−	3.43212e11i	−1.09637	−	1.09637i
$749$	9.57238e10	+	9.57238e10i	0.304153	+	0.304153i
$750$	−4.53788e11			−1.43419
$751$		−	2.60439e11i		−	0.818740i	−0.912369	−	0.409370i	$-0.865749\pi$
$751$		−	2.60439e11i		−	0.818740i	0.912369	−	0.409370i	$-0.134251\pi$
$752$	2.94232e11	+	2.94232e11i	0.920066	+	0.920066i
$753$			2.85104e11i			0.886796i
$754$	−7.27286e11	+	3.03993e11i	−2.25019	+	0.940542i
$755$	−2.13718e11			−0.657738
$756$	−9.42013e11	+	9.42013e11i	−2.88383	+	2.88383i
$757$	3.10598e11			0.945836			0.472918	−	0.881106i	$-0.343201\pi$
$757$	3.10598e11			0.945836			0.472918	+	0.881106i	$0.343201\pi$
$758$		−	4.91654e11i		−	1.48930i
$759$	−7.24895e10	+	7.24895e10i	−0.218428	+	0.218428i
$760$	3.73152e11	−	3.73152e11i	1.11849	−	1.11849i
$761$	−2.42734e11	−	2.42734e11i	−0.723755	−	0.723755i	0.245613	−	0.969368i	$-0.421011\pi$
$761$	−2.42734e11	−	2.42734e11i	−0.723755	−	0.723755i	−0.969368	+	0.245613i	$0.921011\pi$
$762$	−4.34786e10	−	4.34786e10i	−0.128960	−	0.128960i
$763$	−3.10237e11			−0.915368
$764$			1.56071e12i			4.58089i
$765$	8.95116e10	+	8.95116e10i	0.261357	+	0.261357i
$766$		−	4.61953e11i		−	1.34178i
$767$	6.36169e10	+	1.52200e11i	0.183819	+	0.439777i
$768$	3.41849e10			0.0982627
$769$	−2.88622e11	+	2.88622e11i	−0.825323	+	0.825323i	−0.986866	−	0.161542i	$-0.948353\pi$
$769$	−2.88622e11	+	2.88622e11i	−0.825323	+	0.825323i	0.161542	+	0.986866i	$0.448353\pi$
$770$	3.89481e11			1.10796
$771$			3.65115e11i			1.03327i
$772$	−9.28414e11	+	9.28414e11i	−2.61380	+	2.61380i
$773$	4.80550e11	−	4.80550e11i	1.34592	−	1.34592i	0.455884	−	0.890039i	$-0.349323\pi$
$773$	4.80550e11	−	4.80550e11i	1.34592	−	1.34592i	0.890039	−	0.455884i	$-0.150677\pi$
$774$	1.80693e11	+	1.80693e11i	0.503475	+	0.503475i
$775$	3.96725e10	+	3.96725e10i	0.109972	+	0.109972i
$776$	−3.74113e11			−1.03171
$777$		−	5.30274e11i		−	1.45484i
$778$	−5.02513e11	−	5.02513e11i	−1.37160	−	1.37160i
$779$			3.08507e11i			0.837752i
$780$	1.83664e11	+	4.39406e11i	0.496188	+	1.18710i
$781$	8.03075e10			0.215850
$782$	4.18397e11	−	4.18397e11i	1.11882	−	1.11882i
$783$	5.19330e11			1.38165
$784$		−	1.39242e12i		−	3.68559i
$785$	1.62919e11	−	1.62919e11i	0.429037	−	0.429037i
$786$	−2.18163e11	+	2.18163e11i	−0.571599	+	0.571599i
$787$	4.04395e10	+	4.04395e10i	0.105416	+	0.105416i	0.757848	−	0.652432i	$-0.226251\pi$
$787$	4.04395e10	+	4.04395e10i	0.105416	+	0.105416i	−0.652432	+	0.757848i	$0.726251\pi$
$788$	−2.85836e10	−	2.85836e10i	−0.0741330	−	0.0741330i
$789$	1.73199e11			0.446927
$790$			6.45180e11i			1.65643i
$791$	5.24301e11	+	5.24301e11i	1.33929	+	1.33929i
$792$		−	3.07659e11i		−	0.781933i
$793$	3.71208e11	+	1.52364e11i	0.938696	+	0.385292i
$794$	7.64282e10			0.192297
$795$	−1.98612e11	+	1.98612e11i	−0.497207	+	0.497207i
$796$	1.35913e12			3.38540
$797$		−	2.53880e11i		−	0.629209i	−0.949223	−	0.314605i	$-0.898128\pi$
$797$		−	2.53880e11i		−	0.629209i	0.949223	−	0.314605i	$-0.101872\pi$
$798$	4.51972e11	−	4.51972e11i	1.11455	−	1.11455i
$799$	1.39651e11	−	1.39651e11i	0.342655	−	0.342655i
$800$	−3.83472e11	−	3.83472e11i	−0.936211	−	0.936211i
$801$	8.33085e9	+	8.33085e9i	0.0202376	+	0.0202376i
$802$	−4.39205e10			−0.106162
$803$			8.10005e10i			0.194816i
$804$	2.48159e10	+	2.48159e10i	0.0593889	+	0.0593889i
$805$			3.40873e11i			0.811724i
$806$	9.25943e10	−	2.25590e11i	0.219404	−	0.534539i
$807$	4.18320e11			0.986312
$808$	−8.62098e11	+	8.62098e11i	−2.02261	+	2.02261i
$809$	−6.79676e11			−1.58675			−0.793374	−	0.608735i	$-0.791677\pi$
$809$	−6.79676e11			−1.58675			−0.793374	+	0.608735i	$0.791677\pi$
$810$		−	1.62759e11i		−	0.378098i
$811$	7.91580e10	−	7.91580e10i	0.182983	−	0.182983i	−0.609671	−	0.792654i	$-0.708698\pi$
$811$	7.91580e10	−	7.91580e10i	0.182983	−	0.182983i	0.792654	+	0.609671i	$0.208698\pi$
$812$	−1.52241e12	+	1.52241e12i	−3.50192	+	3.50192i
$813$	−3.97802e11	−	3.97802e11i	−0.910552	−	0.910552i
$814$	4.38638e11	+	4.38638e11i	0.999100	+	0.999100i
$815$	−3.15705e11			−0.715569
$816$		−	1.02224e12i		−	2.30565i
$817$	−1.91407e11	−	1.91407e11i	−0.429605	−	0.429605i
$818$		−	2.91273e11i		−	0.650560i
$819$	−1.25602e11	−	3.00495e11i	−0.279164	−	0.667884i
$820$	−8.74511e11			−1.93424
$821$	1.89360e11	−	1.89360e11i	0.416788	−	0.416788i	−0.467307	−	0.884095i	$-0.654776\pi$
$821$	1.89360e11	−	1.89360e11i	0.416788	−	0.416788i	0.884095	+	0.467307i	$0.154776\pi$
$822$	−1.64664e11			−0.360672
$823$			3.91534e11i			0.853434i	0.904385	+	0.426717i	$0.140330\pi$
$823$			3.91534e11i			0.853434i	−0.904385	+	0.426717i	$0.859670\pi$
$824$	1.00882e12	−	1.00882e12i	2.18830	−	2.18830i
$825$	6.66497e10	−	6.66497e10i	0.143874	−	0.143874i
$826$	4.43773e11	+	4.43773e11i	0.953323	+	0.953323i
$827$	1.83197e11	+	1.83197e11i	0.391648	+	0.391648i	0.875274	−	0.483627i	$-0.160681\pi$
$827$	1.83197e11	+	1.83197e11i	0.391648	+	0.391648i	−0.483627	+	0.875274i	$0.660681\pi$
$828$	4.43524e11			0.943618
$829$			4.24504e11i			0.898802i	0.893330	+	0.449401i	$0.148363\pi$
$829$			4.24504e11i			0.898802i	−0.893330	+	0.449401i	$0.851637\pi$
$830$	2.06505e11	+	2.06505e11i	0.435130	+	0.435130i
$831$			4.55583e11i			0.955351i
$832$	−3.61410e11	+	8.80513e11i	−0.754235	+	1.83756i
$833$	−6.60884e11			−1.37260
$834$	4.63656e11	−	4.63656e11i	0.958367	−	0.958367i
$835$	7.64285e10			0.157221
$836$			5.36819e11i			1.09901i
$837$	−1.13602e11	+	1.13602e11i	−0.231465	+	0.231465i
$838$	1.44255e11	−	1.44255e11i	0.292520	−	0.292520i
$839$	−2.06537e10	−	2.06537e10i	−0.0416822	−	0.0416822i	0.685958	−	0.727641i	$-0.259383\pi$
$839$	−2.06537e10	−	2.06537e10i	−0.0416822	−	0.0416822i	−0.727641	+	0.685958i	$0.759383\pi$
$840$	7.77805e11	+	7.77805e11i	1.56226	+	1.56226i
$841$	3.39054e11			0.677774
$842$		−	1.11454e12i		−	2.21741i
$843$	−1.99421e11	−	1.99421e11i	−0.394876	−	0.394876i
$844$		−	1.45116e12i		−	2.85986i
$845$	−3.58042e11	+	2.30096e9i	−0.702275	+	0.00451318i
$846$	2.06202e11			0.402543
$847$	3.76630e11	−	3.76630e11i	0.731781	−	0.731781i
$848$	−2.10943e12			−4.07927
$849$		−	6.04984e11i		−	1.16443i
$850$	−3.84691e11	+	3.84691e11i	−0.736947	+	0.736947i
$851$	−3.83895e11	+	3.83895e11i	−0.731972	+	0.731972i
$852$	2.64169e11	+	2.64169e11i	0.501330	+	0.501330i
$853$	2.78861e11	+	2.78861e11i	0.526735	+	0.526735i	0.919597	−	0.392862i	$-0.128515\pi$
$853$	2.78861e11	+	2.78861e11i	0.526735	+	0.526735i	−0.392862	+	0.919597i	$0.628515\pi$
$854$	1.52659e12			2.87006
$855$		−	1.40006e11i		−	0.261988i
$856$	−3.16258e11	−	3.16258e11i	−0.589042	−	0.589042i
$857$			4.19806e11i			0.778261i	0.921183	+	0.389130i	$0.127224\pi$
$857$			4.19806e11i			0.778261i	−0.921183	+	0.389130i	$0.872776\pi$
$858$	−3.78990e11	−	1.55558e11i	−0.699325	−	0.287041i
$859$	−5.67694e11			−1.04266			−0.521329	−	0.853356i	$-0.674563\pi$
$859$	−5.67694e11			−1.04266			−0.521329	+	0.853356i	$0.674563\pi$
$860$	5.42573e11	−	5.42573e11i	0.991892	−	0.991892i
$861$	−6.43058e11			−1.17014
$862$			9.04691e11i			1.63859i
$863$	−2.35148e11	+	2.35148e11i	−0.423934	+	0.423934i	−0.886556	−	0.462622i	$-0.846909\pi$
$863$	−2.35148e11	+	2.35148e11i	−0.423934	+	0.423934i	0.462622	+	0.886556i	$0.346909\pi$
$864$	1.09807e12	−	1.09807e12i	1.97050	−	1.97050i
$865$	2.20226e11	+	2.20226e11i	0.393373	+	0.393373i
$866$	−3.55170e11	−	3.55170e11i	−0.631488	−	0.631488i
$867$	−7.84640e10			−0.138865
$868$		−	6.66046e11i		−	1.17334i
$869$	−2.81742e11	−	2.81742e11i	−0.494052	−	0.494052i
$870$		−	7.06315e11i		−	1.23288i
$871$	−2.43439e10	+	1.01754e10i	−0.0422979	+	0.0176798i
$872$	1.02498e12			1.77276
$873$	−7.01830e10	+	7.01830e10i	−0.120830	+	0.120830i
$874$	−6.54417e11			−1.12152
$875$		−	9.31837e11i		−	1.58967i
$876$	−2.66449e11	+	2.66449e11i	−0.452478	+	0.452478i
$877$	4.21435e11	−	4.21435e11i	0.712414	−	0.712414i	−0.254626	−	0.967040i	$-0.581952\pi$
$877$	4.21435e11	−	4.21435e11i	0.712414	−	0.712414i	0.967040	+	0.254626i	$0.0819522\pi$
$878$	1.29267e12	+	1.29267e12i	2.17526	+	2.17526i
$879$	−3.68344e11	−	3.68344e11i	−0.617018	−	0.617018i
$880$	−6.88911e11			−1.14877
$881$			4.29405e10i			0.0712792i	0.999365	+	0.0356396i	$0.0113468\pi$
$881$			4.29405e10i			0.0712792i	−0.999365	+	0.0356396i	$0.988653\pi$
$882$	−4.87915e11	−	4.87915e11i	−0.806251	−	0.806251i
$883$		−	2.77366e11i		−	0.456258i	−0.973631	−	0.228129i	$-0.926739\pi$
$883$		−	2.77366e11i		−	0.456258i	0.973631	−	0.228129i	$-0.0732609\pi$
$884$	1.57044e12	+	6.44593e11i	2.57165	+	1.05554i
$885$	−1.47811e11			−0.240954
$886$	1.37843e11	−	1.37843e11i	0.223692	−	0.223692i
$887$	−9.45206e10			−0.152697			−0.0763487	−	0.997081i	$-0.524326\pi$
$887$	−9.45206e10			−0.152697			−0.0763487	+	0.997081i	$0.524326\pi$
$888$			1.75195e12i			2.81754i
$889$	8.92818e10	−	8.92818e10i	0.142941	−	0.142941i
$890$	3.48438e10	−	3.48438e10i	0.0555349	−	0.0555349i
$891$	7.10748e10	+	7.10748e10i	0.112773	+	0.112773i
$892$	2.63724e11	+	2.63724e11i	0.416572	+	0.416572i
$893$	−2.18429e11			−0.343482
$894$			1.35498e12i			2.12120i
$895$	1.89156e11	+	1.89156e11i	0.294801	+	0.294801i
$896$			1.09162e12i			1.69371i
$897$	1.36144e11	−	3.31691e11i	0.210295	−	0.512347i
$898$	−2.45711e11			−0.377851
$899$	−1.83595e11	+	1.83595e11i	−0.281075	+	0.281075i
$900$	−4.07794e11			−0.621542
$901$			1.00120e12i			1.51922i
$902$	5.31933e11	−	5.31933e11i	0.803583	−	0.803583i
$903$	3.98973e11	−	3.98973e11i	0.600056	−	0.600056i
$904$	−1.73222e12	−	1.73222e12i	−2.59375	−	2.59375i
$905$	−4.09088e11	−	4.09088e11i	−0.609849	−	0.609849i
$906$	8.55241e11			1.26933
$907$			6.11013e10i			0.0902862i	0.998981	+	0.0451431i	$0.0143744\pi$
$907$			6.11013e10i			0.0902862i	−0.998981	+	0.0451431i	$0.985626\pi$
$908$	1.84206e12	+	1.84206e12i	2.70994	+	2.70994i
$909$			3.23457e11i			0.473763i
$910$	−1.25682e12	+	5.25330e11i	−1.83277	+	0.766067i
$911$	5.01820e11			0.728575			0.364287	−	0.931287i	$-0.381313\pi$
$911$	5.01820e11			0.728575			0.364287	+	0.931287i	$0.381313\pi$
$912$	−7.99446e11	+	7.99446e11i	−1.15561	+	1.15561i
$913$	−1.80357e11			−0.259567
$914$			2.33823e12i			3.35045i
$915$	−2.54238e11	+	2.54238e11i	−0.362707	+	0.362707i
$916$	−5.21324e10	+	5.21324e10i	−0.0740502	+	0.0740502i
$917$	−4.47991e11	−	4.47991e11i	−0.633566	−	0.633566i
$918$	−1.10156e12	−	1.10156e12i	−1.55109	−	1.55109i
$919$	−5.41291e11			−0.758872			−0.379436	−	0.925218i	$-0.623882\pi$
$919$	−5.41291e11			−0.758872			−0.379436	+	0.925218i	$0.623882\pi$
$920$		−	1.12619e12i		−	1.57203i
$921$	2.86866e11	+	2.86866e11i	0.398695	+	0.398695i
$922$		−	1.55938e12i		−	2.15788i
$923$	−2.59146e11	+	1.08319e11i	−0.357057	+	0.149244i
$924$	−1.11896e12			−1.53506
$925$	3.52968e11	−	3.52968e11i	0.482135	−	0.482135i
$926$	−1.99353e12			−2.71130
$927$		−	3.78508e11i		−	0.512573i
$928$	1.77462e12	−	1.77462e12i	2.39283	−	2.39283i
$929$	2.86966e11	−	2.86966e11i	0.385272	−	0.385272i	−0.487725	−	0.872997i	$-0.662173\pi$
$929$	2.86966e11	−	2.86966e11i	0.385272	−	0.385272i	0.872997	+	0.487725i	$0.162173\pi$
$930$	1.54505e11	+	1.54505e11i	0.206543	+	0.206543i
$931$	5.16846e11	+	5.16846e11i	0.687958	+	0.687958i
$932$	1.02814e12			1.36266
$933$			5.80976e11i			0.766711i
$934$	−4.72734e11	−	4.72734e11i	−0.621197	−	0.621197i
$935$			3.26977e11i			0.427830i
$936$	4.14970e11	+	9.92792e11i	0.540646	+	1.29346i
$937$	8.58706e11			1.11400			0.557001	−	0.830512i	$-0.311952\pi$
$937$	8.58706e11			1.11400			0.557001	+	0.830512i	$0.311952\pi$
$938$	−7.09802e10	+	7.09802e10i	−0.0916909	+	0.0916909i
$939$	−2.89247e11			−0.372055
$940$		−	6.19170e11i		−	0.793047i
$941$	3.63130e11	−	3.63130e11i	0.463131	−	0.463131i	−0.436549	−	0.899680i	$-0.643800\pi$
$941$	3.63130e11	−	3.63130e11i	0.463131	−	0.463131i	0.899680	+	0.436549i	$0.143800\pi$
$942$	−6.51959e11	+	6.51959e11i	−0.827974	+	0.827974i
$943$	4.65546e11	+	4.65546e11i	0.588730	+	0.588730i
$944$	−7.84942e11	−	7.84942e11i	−0.988439	−	0.988439i
$945$	8.97454e11			1.12534
$946$			6.60054e11i			0.824166i
$947$	8.13984e11	+	8.13984e11i	1.01208	+	1.01208i	0.999926	+	0.0121560i	$0.00386948\pi$
$947$	8.13984e11	+	8.13984e11i	1.01208	+	1.01208i	0.0121560	+	0.999926i	$0.496131\pi$
$948$		−	1.85357e12i		−	2.29496i
$949$	−1.09253e11	−	2.61382e11i	−0.134701	−	0.322263i
$950$	6.01697e11			0.738726
$951$	−9.72997e10	+	9.72997e10i	−0.118957	+	0.118957i
$952$	3.92089e12			4.77350
$953$		−	9.08572e11i		−	1.10151i	−0.834667	−	0.550754i	$-0.814340\pi$
$953$		−	9.08572e11i		−	1.10151i	0.834667	−	0.550754i	$-0.185660\pi$
$954$	−7.39161e11	+	7.39161e11i	−0.892371	+	0.892371i
$955$	7.43444e11	−	7.43444e11i	0.893789	−	0.893789i
$956$	−2.11784e12	−	2.11784e12i	−2.53548	−	2.53548i
$957$	3.08439e11	+	3.08439e11i	0.367724	+	0.367724i
$958$	−5.39159e11			−0.640110
$959$		−	3.38133e11i		−	0.399772i
$960$	−6.03057e11	−	6.03057e11i	−0.710024	−	0.710024i
$961$			7.72569e11i			0.905824i
$962$	−2.00708e12	−	8.23816e11i	−2.34350	−	0.961900i
$963$	−1.18659e11			−0.137973
$964$	1.02541e12	−	1.02541e12i	1.18738	−	1.18738i
$965$	8.84499e11			1.01997
$966$		−	1.36408e12i		−	1.56650i
$967$	4.49757e11	−	4.49757e11i	0.514365	−	0.514365i	−0.401496	−	0.915861i	$-0.631510\pi$
$967$	4.49757e11	−	4.49757e11i	0.514365	−	0.514365i	0.915861	+	0.401496i	$0.131510\pi$
$968$	−1.24433e12	+	1.24433e12i	−1.41721	+	1.41721i
$969$	3.79440e11	+	3.79440e11i	0.430376	+	0.430376i
$970$	2.93541e11	+	2.93541e11i	0.331575	+	0.331575i
$971$	−7.84366e11			−0.882352			−0.441176	−	0.897421i	$-0.645439\pi$
$971$	−7.84366e11			−0.882352			−0.441176	+	0.897421i	$0.645439\pi$
$972$		−	1.95572e12i		−	2.19100i
$973$	9.52103e11	+	9.52103e11i	1.06226	+	1.06226i
$974$			2.96513e12i			3.29464i
$975$	−1.25176e11	+	3.04970e11i	−0.138517	+	0.337473i
$976$	−2.70023e12			−2.97578
$977$	−7.59681e11	+	7.59681e11i	−0.833783	+	0.833783i	−0.988032	−	0.154249i	$-0.950704\pi$
$977$	−7.59681e11	+	7.59681e11i	−0.833783	+	0.833783i	0.154249	+	0.988032i	$0.450704\pi$
$978$	1.26337e12			1.38094
$979$			3.04318e10i			0.0331281i
$980$	−1.46508e12	+	1.46508e12i	−1.58839	+	1.58839i
$981$	1.92285e11	−	1.92285e11i	0.207620	−	0.207620i
$982$	1.03700e12	+	1.03700e12i	1.11515	+	1.11515i
$983$	4.81884e11	+	4.81884e11i	0.516094	+	0.516094i	0.916387	−	0.400293i	$-0.131092\pi$
$983$	4.81884e11	+	4.81884e11i	0.516094	+	0.516094i	−0.400293	+	0.916387i	$0.631092\pi$
$984$	2.12457e12			2.26616
$985$			2.72315e10i			0.0289286i
$986$	−1.78026e12	−	1.78026e12i	−1.88354	−	1.88354i
$987$		−	4.55297e11i		−	0.479763i
$988$	−7.24060e11	−	1.73227e12i	−0.759883	−	1.81797i
$989$	−5.77678e11			−0.603810
$990$	−2.41400e11	+	2.41400e11i	−0.251302	+	0.251302i
$991$	−9.53860e11			−0.988986			−0.494493	−	0.869182i	$-0.664646\pi$
$991$	−9.53860e11			−0.988986			−0.494493	+	0.869182i	$0.664646\pi$
$992$			7.76387e11i			0.801736i
$993$	−5.00837e11	+	5.00837e11i	−0.515109	+	0.515109i
$994$	−7.55597e11	+	7.55597e11i	−0.774007	+	0.774007i
$995$	−6.47423e11	−	6.47423e11i	−0.660535	−	0.660535i
$996$	−5.93278e11	−	5.93278e11i	−0.602866	−	0.602866i
$997$	−1.65336e12			−1.67335			−0.836676	−	0.547698i	$-0.815504\pi$
$997$	−1.65336e12			−1.67335			−0.836676	+	0.547698i	$0.815504\pi$
$998$			1.56695e12i			1.57954i
$999$	1.01073e12	+	1.01073e12i	1.01478	+	1.01478i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.9.d.a.5.9	✓	18
3.2	odd	2		117.9.j.a.109.1		18
13.8	odd	4	inner	13.9.d.a.8.9	yes	18
39.8	even	4		117.9.j.a.73.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.9.d.a.5.9	✓	18	1.1	even	1	trivial
13.9.d.a.8.9	yes	18	13.8	odd	4	inner
117.9.j.a.73.1		18	39.8	even	4
117.9.j.a.109.1		18	3.2	odd	2

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:	\( N \)	\(=\)	\( 13 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	13.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(21.3021 - 21.3021i) q^{2} +58.3050 q^{3} -651.562i q^{4} +(-310.371 + 310.371i) q^{5} +(1242.02 - 1242.02i) q^{6} +(2550.45 + 2550.45i) q^{7} +(-8426.31 - 8426.31i) q^{8} -3161.53 q^{9} +O(q^{10})\)	\(q+(21.3021 - 21.3021i) q^{2} +58.3050 q^{3} -651.562i q^{4} +(-310.371 + 310.371i) q^{5} +(1242.02 - 1242.02i) q^{6} +(2550.45 + 2550.45i) q^{7} +(-8426.31 - 8426.31i) q^{8} -3161.53 q^{9} +13223.1i q^{10} +(-5774.38 - 5774.38i) q^{11} -37989.3i q^{12} +(26421.9 + 10845.0i) q^{13} +108660. q^{14} +(-18096.2 + 18096.2i) q^{15} -192197. q^{16} +91222.3i q^{17} +(-67347.3 + 67347.3i) q^{18} +(71340.6 - 71340.6i) q^{19} +(202226. + 202226. i) q^{20} +(148704. + 148704. i) q^{21} -246013. q^{22} -215310. i q^{23} +(-491296. - 491296. i) q^{24} +197965. i q^{25} +(793864. - 331822. i) q^{26} -566872. q^{27} +(1.66177e6 - 1.66177e6i) q^{28} -916133. q^{29} +770974. i q^{30} +(200402. - 200402. i) q^{31} +(-1.93707e6 + 1.93707e6i) q^{32} +(-336675. - 336675. i) q^{33} +(1.94323e6 + 1.94323e6i) q^{34} -1.58317e6 q^{35} +2.05993e6i q^{36} +(-1.78299e6 - 1.78299e6i) q^{37} -3.03941e6i q^{38} +(1.54053e6 + 632316. i) q^{39} +5.23057e6 q^{40} +(-2.16221e6 + 2.16221e6i) q^{41} +6.33542e6 q^{42} -2.68300e6i q^{43} +(-3.76236e6 + 3.76236e6i) q^{44} +(981247. - 981247. i) q^{45} +(-4.58657e6 - 4.58657e6i) q^{46} +(-1.53089e6 - 1.53089e6i) q^{47} -1.12060e7 q^{48} +7.24476e6i q^{49} +(4.21707e6 + 4.21707e6i) q^{50} +5.31871e6i q^{51} +(7.06618e6 - 1.72155e7i) q^{52} +1.09754e7 q^{53} +(-1.20756e7 + 1.20756e7i) q^{54} +3.58440e6 q^{55} -4.29817e7i q^{56} +(4.15951e6 - 4.15951e6i) q^{57} +(-1.95156e7 + 1.95156e7i) q^{58} +(4.08405e6 + 4.08405e6i) q^{59} +(1.17908e7 + 1.17908e7i) q^{60} +1.40493e7 q^{61} -8.53799e6i q^{62} +(-8.06332e6 - 8.06332e6i) q^{63} +3.33251e7i q^{64} +(-1.15666e7 + 4.83463e6i) q^{65} -1.43438e7 q^{66} +(-653233. + 653233. i) q^{67} +5.94370e7 q^{68} -1.25537e7i q^{69} +(-3.37249e7 + 3.37249e7i) q^{70} +(-6.95378e6 + 6.95378e6i) q^{71} +(2.66400e7 + 2.66400e7i) q^{72} +(-7.01379e6 - 7.01379e6i) q^{73} -7.59629e7 q^{74} +1.15423e7i q^{75} +(-4.64828e7 - 4.64828e7i) q^{76} -2.94545e7i q^{77} +(4.62862e7 - 1.93469e7i) q^{78} +4.87918e7 q^{79} +(5.96524e7 - 5.96524e7i) q^{80} -1.23087e7 q^{81} +9.21195e7i q^{82} +(1.56170e7 - 1.56170e7i) q^{83} +(9.68897e7 - 9.68897e7i) q^{84} +(-2.83128e7 - 2.83128e7i) q^{85} +(-5.71537e7 - 5.71537e7i) q^{86} -5.34151e7 q^{87} +9.73134e7i q^{88} +(-2.63507e6 - 2.63507e6i) q^{89} -4.18053e7i q^{90} +(3.97281e7 + 9.50472e7i) q^{91} -1.40288e8 q^{92} +(1.16844e7 - 1.16844e7i) q^{93} -6.52223e7 q^{94} +4.42841e7i q^{95} +(-1.12941e8 + 1.12941e8i) q^{96} +(2.21991e7 - 2.21991e7i) q^{97} +(1.54329e8 + 1.54329e8i) q^{98} +(1.82559e7 + 1.82559e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 2 q^{2} - 4 q^{3} + 166 q^{5} + 2720 q^{6} + 5308 q^{7} + 10464 q^{8} + 39362 q^{9}+O(q^{10}) \) 18 * q - 2 * q^2 - 4 * q^3 + 166 * q^5 + 2720 * q^6 + 5308 * q^7 + 10464 * q^8 + 39362 * q^9	\( 18 q - 2 q^{2} - 4 q^{3} + 166 q^{5} + 2720 q^{6} + 5308 q^{7} + 10464 q^{8} + 39362 q^{9} - 31556 q^{11} + 71300 q^{13} - 110260 q^{14} + 121124 q^{15} - 522860 q^{16} - 308962 q^{18} + 100288 q^{19} + 736268 q^{20} + 279416 q^{21} - 977312 q^{22} - 986232 q^{24} + 2952238 q^{26} + 364916 q^{27} + 4497084 q^{28} - 2479024 q^{29} - 1892664 q^{31} + 947212 q^{32} + 1368644 q^{33} - 531576 q^{34} - 2918284 q^{35} - 8343978 q^{37} - 1101268 q^{39} - 12691908 q^{40} + 1140178 q^{41} + 15137212 q^{42} - 3867188 q^{44} + 6565370 q^{45} + 2006148 q^{46} - 13368572 q^{47} - 10106716 q^{48} + 37369598 q^{50} - 14821220 q^{52} + 50561348 q^{53} - 4995928 q^{54} + 76994128 q^{55} - 34755760 q^{57} + 22505716 q^{58} + 2127976 q^{59} - 161134196 q^{60} - 52016516 q^{61} - 15210112 q^{63} + 10413082 q^{65} - 51097328 q^{66} + 960292 q^{67} + 283187508 q^{68} - 166635032 q^{70} + 67412140 q^{71} + 96846900 q^{72} - 145213226 q^{73} - 233620024 q^{74} - 150533640 q^{76} + 212071160 q^{78} - 76829120 q^{79} + 524889520 q^{80} + 293280674 q^{81} - 241951556 q^{83} + 345496184 q^{84} + 260737764 q^{85} - 579480384 q^{86} - 618300656 q^{87} - 89187110 q^{89} + 232660948 q^{91} - 122690376 q^{92} + 669553400 q^{93} + 1069637380 q^{94} - 1324092400 q^{96} + 331183146 q^{97} + 588677614 q^{98} - 1125076336 q^{99}+O(q^{100}) \) 18 * q - 2 * q^2 - 4 * q^3 + 166 * q^5 + 2720 * q^6 + 5308 * q^7 + 10464 * q^8 + 39362 * q^9 - 31556 * q^11 + 71300 * q^13 - 110260 * q^14 + 121124 * q^15 - 522860 * q^16 - 308962 * q^18 + 100288 * q^19 + 736268 * q^20 + 279416 * q^21 - 977312 * q^22 - 986232 * q^24 + 2952238 * q^26 + 364916 * q^27 + 4497084 * q^28 - 2479024 * q^29 - 1892664 * q^31 + 947212 * q^32 + 1368644 * q^33 - 531576 * q^34 - 2918284 * q^35 - 8343978 * q^37 - 1101268 * q^39 - 12691908 * q^40 + 1140178 * q^41 + 15137212 * q^42 - 3867188 * q^44 + 6565370 * q^45 + 2006148 * q^46 - 13368572 * q^47 - 10106716 * q^48 + 37369598 * q^50 - 14821220 * q^52 + 50561348 * q^53 - 4995928 * q^54 + 76994128 * q^55 - 34755760 * q^57 + 22505716 * q^58 + 2127976 * q^59 - 161134196 * q^60 - 52016516 * q^61 - 15210112 * q^63 + 10413082 * q^65 - 51097328 * q^66 + 960292 * q^67 + 283187508 * q^68 - 166635032 * q^70 + 67412140 * q^71 + 96846900 * q^72 - 145213226 * q^73 - 233620024 * q^74 - 150533640 * q^76 + 212071160 * q^78 - 76829120 * q^79 + 524889520 * q^80 + 293280674 * q^81 - 241951556 * q^83 + 345496184 * q^84 + 260737764 * q^85 - 579480384 * q^86 - 618300656 * q^87 - 89187110 * q^89 + 232660948 * q^91 - 122690376 * q^92 + 669553400 * q^93 + 1069637380 * q^94 - 1324092400 * q^96 + 331183146 * q^97 + 588677614 * q^98 - 1125076336 * q^99

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