LMFDB - Embedded newform 770.2.w.a.139.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(139,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 5, 7]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("770.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.w (of order $10$, 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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			139.7
Character	$\chi$	$=$	770.139
Dual form			770.2.w.a.349.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(-0.463552 + 1.42667i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.23591 - 0.0266895i) q^{5} +(1.21359 - 0.881728i) q^{6} +(-1.05163 - 2.42777i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.606556 + 0.440689i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.463552 + 1.42667i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.23591 - 0.0266895i) q^{5} +(1.21359 - 0.881728i) q^{6} +(-1.05163 - 2.42777i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.606556 + 0.440689i) q^{9} +(1.79320 + 1.33583i) q^{10} +(3.30041 - 0.327560i) q^{11} -1.50009 q^{12} +(0.191420 - 0.263467i) q^{13} +(-0.576225 + 2.58224i) q^{14} +(1.07454 - 3.17752i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(0.316463 + 0.435574i) q^{17} +(-0.231684 - 0.713050i) q^{18} +(-0.758164 + 2.33339i) q^{19} +(-0.665551 - 2.13472i) q^{20} +(3.95110 - 0.374922i) q^{21} +(-2.86262 - 1.67493i) q^{22} +4.70703i q^{23} +(1.21359 + 0.881728i) q^{24} +(4.99858 + 0.119350i) q^{25} +(-0.309724 + 0.100636i) q^{26} +(-4.55067 + 3.30625i) q^{27} +(1.98398 - 1.75038i) q^{28} +(-2.28218 + 0.741525i) q^{29} +(-2.73702 + 1.93907i) q^{30} +(-0.248208 + 0.341629i) q^{31} +1.00000 q^{32} +(-1.06259 + 4.86042i) q^{33} -0.538400i q^{34} +(2.28655 + 5.45635i) q^{35} +(-0.231684 + 0.713050i) q^{36} +(-3.07763 + 0.999984i) q^{37} +(1.98490 - 1.44211i) q^{38} +(0.287147 + 0.395224i) q^{39} +(-0.716317 + 2.11823i) q^{40} +(-1.25713 + 3.86905i) q^{41} +(-3.41688 - 2.01908i) q^{42} +0.787474 q^{43} +(1.33141 + 3.03765i) q^{44} +(-1.34444 - 1.00153i) q^{45} +(2.76672 - 3.80807i) q^{46} +(-1.98291 + 6.10277i) q^{47} +(-0.463552 - 1.42667i) q^{48} +(-4.78816 + 5.10622i) q^{49} +(-3.97378 - 3.03465i) q^{50} +(-0.768116 + 0.249576i) q^{51} +(0.309724 + 0.100636i) q^{52} +(-5.90889 + 8.13289i) q^{53} +5.62494 q^{54} +(-7.38816 + 0.644309i) q^{55} +(-2.63392 + 0.249934i) q^{56} +(-2.97752 - 2.16329i) q^{57} +(2.28218 + 0.741525i) q^{58} +(-3.34774 + 1.08775i) q^{59} +(3.35405 + 0.0400365i) q^{60} +(-2.60559 + 1.89307i) q^{61} +(0.401609 - 0.130491i) q^{62} +(0.432022 - 1.93602i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-0.435030 + 0.583980i) q^{65} +(3.71654 - 3.30759i) q^{66} -3.10205i q^{67} +(-0.316463 + 0.435574i) q^{68} +(-6.71536 - 2.18195i) q^{69} +(1.35731 - 5.75827i) q^{70} +(-4.55615 + 3.31024i) q^{71} +(0.606556 - 0.440689i) q^{72} +(13.4882 - 4.38258i) q^{73} +(3.07763 + 0.999984i) q^{74} +(-2.48737 + 7.07597i) q^{75} -2.45347 q^{76} +(-4.26604 - 7.66817i) q^{77} -0.488523i q^{78} +(0.136261 - 0.187547i) q^{79} +(1.82458 - 1.29264i) q^{80} +(-1.91240 - 5.88575i) q^{81} +(3.29121 - 2.39121i) q^{82} +(6.56779 + 9.03978i) q^{83} +(1.57753 + 3.64187i) q^{84} +(-0.695958 - 0.982351i) q^{85} +(-0.637080 - 0.462866i) q^{86} -3.59964i q^{87} +(0.708354 - 3.24010i) q^{88} +9.96145i q^{89} +(0.498993 + 1.60050i) q^{90} +(-0.840942 - 0.187656i) q^{91} +(-4.47665 + 1.45455i) q^{92} +(-0.372333 - 0.512472i) q^{93} +(5.19133 - 3.77172i) q^{94} +(1.75746 - 5.19701i) q^{95} +(-0.463552 + 1.42667i) q^{96} +(9.86605 + 7.16810i) q^{97} +(6.87507 - 1.31661i) q^{98} +(2.14624 + 1.25577i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 24 q^{2} - 24 q^{4} - 3 q^{7} - 24 q^{8} - 18 q^{9}+O(q^{10}) $ 96 * q - 24 * q^2 - 24 * q^4 - 3 * q^7 - 24 * q^8 - 18 * q^9	$ 96 q - 24 q^{2} - 24 q^{4} - 3 q^{7} - 24 q^{8} - 18 q^{9} + 4 q^{11} - 3 q^{14} - 6 q^{15} - 24 q^{16} - 28 q^{18} + 4 q^{22} - 42 q^{25} + 2 q^{28} - 6 q^{30} + 96 q^{32} + 14 q^{35} - 28 q^{36} + 10 q^{39} + 24 q^{43} - 16 q^{44} + 37 q^{49} + 8 q^{50} - 30 q^{51} - 40 q^{53} + 2 q^{56} + 20 q^{57} - 6 q^{60} - 63 q^{63} - 24 q^{64} + 40 q^{65} + 9 q^{70} - 20 q^{71} - 18 q^{72} + 16 q^{77} - 126 q^{81} + 100 q^{85} - 36 q^{86} + 14 q^{88} - 31 q^{91} + 10 q^{92} - 20 q^{93} - 16 q^{95} - 18 q^{98} + 100 q^{99}+O(q^{100}) $ 96 * q - 24 * q^2 - 24 * q^4 - 3 * q^7 - 24 * q^8 - 18 * q^9 + 4 * q^11 - 3 * q^14 - 6 * q^15 - 24 * q^16 - 28 * q^18 + 4 * q^22 - 42 * q^25 + 2 * q^28 - 6 * q^30 + 96 * q^32 + 14 * q^35 - 28 * q^36 + 10 * q^39 + 24 * q^43 - 16 * q^44 + 37 * q^49 + 8 * q^50 - 30 * q^51 - 40 * q^53 + 2 * q^56 + 20 * q^57 - 6 * q^60 - 63 * q^63 - 24 * q^64 + 40 * q^65 + 9 * q^70 - 20 * q^71 - 18 * q^72 + 16 * q^77 - 126 * q^81 + 100 * q^85 - 36 * q^86 + 14 * q^88 - 31 * q^91 + 10 * q^92 - 20 * q^93 - 16 * q^95 - 18 * q^98 + 100 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$	$-1$

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 $

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$	−0.463552	+	1.42667i	−0.267632	+	0.823686i	0.723444	+	0.690383i	$0.242558\pi$
$3$	−0.463552	+	1.42667i	−0.267632	+	0.823686i	−0.991075	+	0.133302i	$0.957442\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−2.23591	−	0.0266895i	−0.999929	−	0.0119359i
$5$	−2.23591	−	0.0266895i	−0.999929	−	0.0119359i
$6$	1.21359	−	0.881728i	0.495448	−	0.359964i
$7$	−1.05163	−	2.42777i	−0.397478	−	0.917612i
$7$	−1.05163	−	2.42777i	−0.397478	−	0.917612i
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	0.606556	+	0.440689i	0.202185	+	0.146896i
$10$	1.79320	+	1.33583i	0.567060	+	0.422425i
$11$	3.30041	−	0.327560i	0.995111	−	0.0987632i
$11$	3.30041	−	0.327560i	0.995111	−	0.0987632i
$12$	−1.50009			−0.433037
$13$	0.191420	−	0.263467i	0.0530904	−	0.0730727i	−0.781646	−	0.623722i	$-0.785620\pi$
$13$	0.191420	−	0.263467i	0.0530904	−	0.0730727i	0.834737	+	0.550649i	$0.185620\pi$
$14$	−0.576225	+	2.58224i	−0.154003	+	0.690133i
$15$	1.07454	−	3.17752i	0.277444	−	0.820433i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	0.316463	+	0.435574i	0.0767536	+	0.105642i	0.845668	−	0.533710i	$-0.179203\pi$
$17$	0.316463	+	0.435574i	0.0767536	+	0.105642i	−0.768914	+	0.639352i	$0.779203\pi$
$18$	−0.231684	−	0.713050i	−0.0546084	−	0.168067i
$19$	−0.758164	+	2.33339i	−0.173935	+	0.535316i	−0.999583	−	0.0288690i	$-0.990809\pi$
$19$	−0.758164	+	2.33339i	−0.173935	+	0.535316i	0.825649	+	0.564185i	$0.190809\pi$
$20$	−0.665551	−	2.13472i	−0.148822	−	0.477339i
$21$	3.95110	−	0.374922i	0.862202	−	0.0818146i
$22$	−2.86262	−	1.67493i	−0.610313	−	0.357096i
$23$			4.70703i			0.981484i	0.871305	+	0.490742i	$0.163274\pi$
$23$			4.70703i			0.981484i	−0.871305	+	0.490742i	$0.836726\pi$
$24$	1.21359	+	0.881728i	0.247724	+	0.179982i
$25$	4.99858	+	0.119350i	0.999715	+	0.0238701i
$26$	−0.309724	+	0.100636i	−0.0607420	+	0.0197363i
$27$	−4.55067	+	3.30625i	−0.875777	+	0.636289i
$28$	1.98398	−	1.75038i	0.374937	−	0.330791i
$29$	−2.28218	+	0.741525i	−0.423790	+	0.137698i	−0.513145	−	0.858302i	$-0.671520\pi$
$29$	−2.28218	+	0.741525i	−0.423790	+	0.137698i	0.0893546	+	0.996000i	$0.471520\pi$
$30$	−2.73702	+	1.93907i	−0.499709	+	0.354025i
$31$	−0.248208	+	0.341629i	−0.0445795	+	0.0613584i	−0.830725	−	0.556683i	$-0.812074\pi$
$31$	−0.248208	+	0.341629i	−0.0445795	+	0.0613584i	0.786145	+	0.618042i	$0.212074\pi$
$32$	1.00000			0.176777
$33$	−1.06259	+	4.86042i	−0.184973	+	0.846091i
$34$		−	0.538400i		−	0.0923348i
$35$	2.28655	+	5.45635i	0.386497	+	0.922291i
$36$	−0.231684	+	0.713050i	−0.0386140	+	0.118842i
$37$	−3.07763	+	0.999984i	−0.505960	+	0.164396i	−0.550864	−	0.834595i	$-0.685702\pi$
$37$	−3.07763	+	0.999984i	−0.505960	+	0.164396i	0.0449041	+	0.998991i	$0.485702\pi$
$38$	1.98490	−	1.44211i	0.321993	−	0.233942i
$39$	0.287147	+	0.395224i	0.0459803	+	0.0632864i
$40$	−0.716317	+	2.11823i	−0.113260	+	0.334921i
$41$	−1.25713	+	3.86905i	−0.196331	+	0.604244i	0.803628	+	0.595133i	$0.202900\pi$
$41$	−1.25713	+	3.86905i	−0.196331	+	0.604244i	−0.999958	+	0.00911194i	$0.997100\pi$
$42$	−3.41688	−	2.01908i	−0.527237	−	0.311551i
$43$	0.787474			0.120089			0.0600444	−	0.998196i	$-0.480876\pi$
$43$	0.787474			0.120089			0.0600444	+	0.998196i	$0.480876\pi$
$44$	1.33141	+	3.03765i	0.200718	+	0.457944i
$45$	−1.34444	−	1.00153i	−0.200418	−	0.149299i
$46$	2.76672	−	3.80807i	0.407931	−	0.561469i
$47$	−1.98291	+	6.10277i	−0.289237	+	0.890181i	0.695859	+	0.718178i	$0.255024\pi$
$47$	−1.98291	+	6.10277i	−0.289237	+	0.890181i	−0.985097	+	0.172002i	$0.944976\pi$
$48$	−0.463552	−	1.42667i	−0.0669079	−	0.205921i
$49$	−4.78816	+	5.10622i	−0.684023	+	0.729460i
$50$	−3.97378	−	3.03465i	−0.561977	−	0.429164i
$51$	−0.768116	+	0.249576i	−0.107558	+	0.0349476i
$52$	0.309724	+	0.100636i	0.0429511	+	0.0139556i
$53$	−5.90889	+	8.13289i	−0.811648	+	1.11714i	0.179419	+	0.983773i	$0.442578\pi$
$53$	−5.90889	+	8.13289i	−0.811648	+	1.11714i	−0.991067	+	0.133365i	$0.957422\pi$
$54$	5.62494			0.765457
$55$	−7.38816	+	0.644309i	−0.996219	+	0.0868786i
$56$	−2.63392	+	0.249934i	−0.351972	+	0.0333988i
$57$	−2.97752	−	2.16329i	−0.394382	−	0.286535i
$58$	2.28218	+	0.741525i	0.299665	+	0.0973670i
$59$	−3.34774	+	1.08775i	−0.435839	+	0.141613i	−0.518715	−	0.854947i	$-0.673589\pi$
$59$	−3.34774	+	1.08775i	−0.435839	+	0.141613i	0.0828760	+	0.996560i	$0.473589\pi$
$60$	3.35405	+	0.0400365i	0.433006	+	0.00516869i
$61$	−2.60559	+	1.89307i	−0.333612	+	0.242383i	−0.741962	−	0.670442i	$-0.766104\pi$
$61$	−2.60559	+	1.89307i	−0.333612	+	0.242383i	0.408350	+	0.912825i	$0.366104\pi$
$62$	0.401609	−	0.130491i	0.0510044	−	0.0165723i
$63$	0.432022	−	1.93602i	0.0544296	−	0.243916i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−0.435030	+	0.583980i	−0.0539588	+	0.0724338i
$66$	3.71654	−	3.30759i	0.457474	−	0.407136i
$67$		−	3.10205i		−	0.378976i	−0.981883	−	0.189488i	$-0.939317\pi$
$67$		−	3.10205i		−	0.378976i	0.981883	−	0.189488i	$-0.0606828\pi$
$68$	−0.316463	+	0.435574i	−0.0383768	+	0.0528212i
$69$	−6.71536	−	2.18195i	−0.808435	−	0.262676i
$70$	1.35731	−	5.75827i	0.162229	−	0.688245i
$71$	−4.55615	+	3.31024i	−0.540716	+	0.392853i	−0.824351	−	0.566079i	$-0.808460\pi$
$71$	−4.55615	+	3.31024i	−0.540716	+	0.392853i	0.283635	+	0.958932i	$0.408460\pi$
$72$	0.606556	−	0.440689i	0.0714833	−	0.0519357i
$73$	13.4882	−	4.38258i	1.57867	−	0.512942i	0.616959	−	0.786995i	$-0.288365\pi$
$73$	13.4882	−	4.38258i	1.57867	−	0.512942i	0.961714	+	0.274053i	$0.0883645\pi$
$74$	3.07763	+	0.999984i	0.357768	+	0.116246i
$75$	−2.48737	+	7.07597i	−0.287217	+	0.817063i
$76$	−2.45347			−0.281432
$77$	−4.26604	−	7.66817i	−0.486161	−	0.873869i
$78$		−	0.488523i		−	0.0553144i
$79$	0.136261	−	0.187547i	0.0153305	−	0.0211007i	−0.801283	−	0.598286i	$-0.795849\pi$
$79$	0.136261	−	0.187547i	0.0153305	−	0.0211007i	0.816613	+	0.577185i	$0.195849\pi$
$80$	1.82458	−	1.29264i	0.203994	−	0.144522i
$81$	−1.91240	−	5.88575i	−0.212489	−	0.653973i
$82$	3.29121	−	2.39121i	0.363454	−	0.264065i
$83$	6.56779	+	9.03978i	0.720908	+	0.992245i	0.999493	+	0.0318335i	$0.0101346\pi$
$83$	6.56779	+	9.03978i	0.720908	+	0.992245i	−0.278585	+	0.960412i	$0.589865\pi$
$84$	1.57753	+	3.64187i	0.172123	+	0.397360i
$85$	−0.695958	−	0.982351i	−0.0754872	−	0.106551i
$86$	−0.637080	−	0.462866i	−0.0686981	−	0.0499121i
$87$		−	3.59964i		−	0.385922i
$88$	0.708354	−	3.24010i	0.0755108	−	0.345396i
$89$			9.96145i			1.05591i	0.849272	+	0.527956i	$0.177041\pi$
$89$			9.96145i			1.05591i	−0.849272	+	0.527956i	$0.822959\pi$
$90$	0.498993	+	1.60050i	0.0525985	+	0.168707i
$91$	−0.840942	−	0.187656i	−0.0881546	−	0.0196716i
$92$	−4.47665	+	1.45455i	−0.466723	+	0.151648i
$93$	−0.372333	−	0.512472i	−0.0386091	−	0.0531409i
$94$	5.19133	−	3.77172i	0.535444	−	0.389023i
$95$	1.75746	−	5.19701i	0.180312	−	0.533202i
$96$	−0.463552	+	1.42667i	−0.0473111	+	0.145608i
$97$	9.86605	+	7.16810i	1.00175	+	0.727811i	0.962462	−	0.271418i	$-0.0874924\pi$
$97$	9.86605	+	7.16810i	1.00175	+	0.727811i	0.0392836	+	0.999228i	$0.487492\pi$
$98$	6.87507	−	1.31661i	0.694487	−	0.132998i
$99$	2.14624	+	1.25577i	0.215705	+	0.126210i
$100$	1.43114	+	4.79081i	0.143114	+	0.479081i
$101$	13.2251	+	9.60858i	1.31594	+	0.956090i	0.999973	+	0.00732117i	$0.00233042\pi$
$101$	13.2251	+	9.60858i	1.31594	+	0.956090i	0.315972	+	0.948769i	$0.397670\pi$
$102$	0.768116	+	0.249576i	0.0760548	+	0.0247117i
$103$	−3.86155	−	11.8846i	−0.380490	−	1.17103i	−0.939699	−	0.342002i	$-0.888895\pi$
$103$	−3.86155	−	11.8846i	−0.380490	−	1.17103i	0.559209	−	0.829026i	$-0.311105\pi$
$104$	−0.191420	−	0.263467i	−0.0187703	−	0.0258351i
$105$	−8.84431	+	0.732838i	−0.863117	+	0.0715176i
$106$	9.56078	−	3.10649i	0.928625	−	0.301729i
$107$	1.00057	−	3.07944i	0.0967288	−	0.297701i	−0.890972	−	0.454059i	$-0.849976\pi$
$107$	1.00057	−	3.07944i	0.0967288	−	0.297701i	0.987700	+	0.156358i	$0.0499755\pi$
$108$	−4.55067	−	3.30625i	−0.437888	−	0.318144i
$109$			18.1305i			1.73659i	0.496052	+	0.868293i	$0.334783\pi$
$109$			18.1305i			1.73659i	−0.496052	+	0.868293i	$0.665217\pi$
$110$	6.35586	+	3.82139i	0.606007	+	0.364356i
$111$		−	4.85430i		−	0.460750i
$112$	2.27779	+	1.34598i	0.215231	+	0.127183i
$113$	7.95856	+	2.58589i	0.748679	+	0.243260i	0.658413	−	0.752657i	$-0.271228\pi$
$113$	7.95856	+	2.58589i	0.748679	+	0.243260i	0.0902662	+	0.995918i	$0.471228\pi$
$114$	1.13731	+	3.50028i	0.106519	+	0.327831i
$115$	0.125628	−	10.5245i	0.0117149	−	0.981414i
$116$	−1.41046	−	1.94134i	−0.130958	−	0.180249i
$117$	0.232214	−	0.0754510i	0.0214682	−	0.00697545i
$118$	3.34774	+	1.08775i	0.308185	+	0.100135i
$119$	0.724674	−	1.22636i	0.0664308	−	0.112420i
$120$	−2.68995	−	2.00385i	−0.245558	−	0.182926i
$121$	10.7854	−	2.16217i	0.980492	−	0.196561i
$122$	3.22069			0.291587
$123$	−4.93710	−	3.58701i	−0.445163	−	0.323430i
$124$	−0.401609	−	0.130491i	−0.0360655	−	0.0117184i
$125$	−11.1732	−	0.400266i	−0.999359	−	0.0358009i
$126$	−1.48748	+	1.31234i	−0.132515	+	0.116912i
$127$	9.69463	−	7.04356i	0.860260	−	0.625015i	−0.0676959	−	0.997706i	$-0.521565\pi$
$127$	9.69463	−	7.04356i	0.860260	−	0.625015i	0.927956	+	0.372691i	$0.121565\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	−0.365035	+	1.12346i	−0.0321395	+	0.0989154i
$130$	0.695202	−	0.216746i	0.0609732	−	0.0190098i
$131$	−10.1962			−0.890848			−0.445424	−	0.895320i	$-0.646947\pi$
$131$	−10.1962			−0.890848			−0.445424	+	0.895320i	$0.646947\pi$
$132$	−4.95090	+	0.491368i	−0.430920	+	0.0427681i
$133$	6.46224	−	0.613204i	0.560347	−	0.0531715i
$134$	−1.82334	+	2.50961i	−0.157513	+	0.216797i
$135$	10.2631	−	7.27103i	0.883309	−	0.625790i
$136$	0.512048	−	0.166375i	0.0439078	−	0.0142665i
$137$	5.32725	+	7.33233i	0.455138	+	0.626443i	0.973492	−	0.228723i	$-0.0734550\pi$
$137$	5.32725	+	7.33233i	0.455138	+	0.626443i	−0.518354	+	0.855166i	$0.673455\pi$
$138$	4.15032	+	5.71243i	0.353299	+	0.486274i
$139$	−6.56257	−	20.1975i	−0.556630	−	1.71313i	−0.691599	−	0.722282i	$-0.743093\pi$
$139$	−6.56257	−	20.1975i	−0.556630	−	1.71313i	0.134969	−	0.990850i	$-0.456907\pi$
$140$	−4.48271	+	3.86074i	−0.378858	+	0.326292i
$141$	−7.78743	−	5.65790i	−0.655820	−	0.476481i
$142$	5.63171			0.472603
$143$	0.545464	−	0.932252i	0.0456140	−	0.0779588i
$144$	−0.749745			−0.0624787
$145$	5.12254	−	1.59707i	0.425403	−	0.132630i
$146$	−13.4882	−	4.38258i	−1.11629	−	0.362705i
$147$	−5.06531	−	9.19810i	−0.417780	−	0.758647i
$148$	−1.90208	−	2.61799i	−0.156350	−	0.215198i
$149$	5.72621	+	7.88145i	0.469109	+	0.645673i	0.976367	−	0.216121i	$-0.0693406\pi$
$149$	5.72621	+	7.88145i	0.469109	+	0.645673i	−0.507257	+	0.861795i	$0.669341\pi$
$150$	6.17148	−	4.26254i	0.503899	−	0.348035i
$151$	−5.36781	−	1.74411i	−0.436826	−	0.141933i	0.0823448	−	0.996604i	$-0.473759\pi$
$151$	−5.36781	−	1.74411i	−0.436826	−	0.141933i	−0.519171	+	0.854671i	$0.673759\pi$
$152$	1.98490	+	1.44211i	0.160996	+	0.116971i
$153$			0.403662i			0.0326342i
$154$	−1.05594	+	8.71120i	−0.0850900	+	0.701968i
$155$	0.564088	−	0.757226i	0.0453086	−	0.0608219i
$156$	−0.287147	+	0.395224i	−0.0229901	+	0.0316432i
$157$	5.92810	−	18.2448i	0.473114	−	1.45610i	−0.375370	−	0.926875i	$-0.622484\pi$
$157$	5.92810	−	18.2448i	0.473114	−	1.45610i	0.848484	−	0.529221i	$-0.177516\pi$
$158$	−0.220474	+	0.0716365i	−0.0175400	+	0.00569909i
$159$	−8.86383	−	12.2000i	−0.702948	−	0.967525i
$160$	−2.23591	−	0.0266895i	−0.176764	−	0.00210999i
$161$	11.4276	−	4.95004i	0.900622	−	0.390118i
$162$	−1.91240	+	5.88575i	−0.150252	+	0.462429i
$163$	−6.31611	+	8.69338i	−0.494716	+	0.680918i	−0.981249	−	0.192744i	$-0.938261\pi$
$163$	−6.31611	+	8.69338i	−0.494716	+	0.680918i	0.486533	+	0.873662i	$0.338261\pi$
$164$	−4.06816			−0.317670
$165$	2.50558	−	10.8391i	0.195059	−	0.843823i
$166$		−	11.1738i		−	0.867254i
$167$	−4.64921	+	6.39909i	−0.359767	+	0.495177i	−0.950084	−	0.311995i	$-0.899003\pi$
$167$	−4.64921	+	6.39909i	−0.359767	+	0.495177i	0.590317	+	0.807172i	$0.299003\pi$
$168$	0.864387	−	3.87358i	0.0666889	−	0.298853i
$169$	3.98445	+	12.2629i	0.306496	+	0.943298i
$170$	−0.0143696	+	1.20381i	−0.00110210	+	0.0923282i
$171$	−1.48817	+	1.08122i	−0.113803	+	0.0826827i
$172$	0.243343	+	0.748933i	0.0185547	+	0.0571056i
$173$	−18.8572	−	6.12709i	−1.43369	−	0.465834i	−0.513766	−	0.857931i	$-0.671750\pi$
$173$	−18.8572	−	6.12709i	−1.43369	−	0.465834i	−0.919924	+	0.392097i	$0.871750\pi$
$174$	−2.11582	+	2.91217i	−0.160400	+	0.220771i
$175$	−4.96688	−	12.2609i	−0.375461	−	0.926838i
$176$	−2.47755	+	2.20493i	−0.186753	+	0.166203i
$177$		−	5.28034i		−	0.396895i
$178$	5.85519	−	8.05898i	0.438865	−	0.604046i
$179$	−3.44282	+	10.5959i	−0.257329	+	0.791977i	0.736033	+	0.676946i	$0.236697\pi$
$179$	−3.44282	+	10.5959i	−0.257329	+	0.791977i	−0.993362	+	0.115031i	$0.963303\pi$
$180$	0.537055	−	1.58813i	0.0400297	−	0.118372i
$181$	−10.0233	−	13.7959i	−0.745028	−	1.02544i	−0.998314	−	0.0580511i	$-0.981511\pi$
$181$	−10.0233	−	13.7959i	−0.745028	−	1.02544i	0.253286	−	0.967391i	$-0.418489\pi$
$182$	0.570035	+	0.646110i	0.0422538	+	0.0478928i
$183$	−1.49296	−	4.59484i	−0.110362	−	0.339661i
$184$	4.47665	+	1.45455i	0.330023	+	0.107231i
$185$	6.90800	−	2.15373i	0.507886	−	0.158346i
$186$			0.633451i			0.0464469i
$187$	1.18714	+	1.33391i	0.0868119	+	0.0975454i
$188$	−6.41683			−0.467996
$189$	12.8124	+	7.57104i	0.931968	+	0.550712i
$190$	−4.47654	+	3.17146i	−0.324762	+	0.230082i
$191$	−5.55713	−	17.1031i	−0.402100	−	1.23754i	−0.923293	−	0.384097i	$-0.874513\pi$
$191$	−5.55713	−	17.1031i	−0.402100	−	1.23754i	0.521193	−	0.853439i	$-0.325487\pi$
$192$	1.21359	−	0.881728i	0.0875836	−	0.0636332i
$193$	−9.96613	+	7.24082i	−0.717378	+	0.521205i	−0.885545	−	0.464553i	$-0.846215\pi$
$193$	−9.96613	+	7.24082i	−0.717378	+	0.521205i	0.168168	+	0.985758i	$0.446215\pi$
$194$	−3.76849	−	11.5982i	−0.270562	−	0.832705i
$195$	−0.631485	−	0.891347i	−0.0452216	−	0.0638307i
$196$	−6.33593	−	2.97590i	−0.452566	−	0.212565i
$197$	−0.206405			−0.0147057			−0.00735287	−	0.999973i	$-0.502341\pi$
$197$	−0.206405			−0.0147057			−0.00735287	+	0.999973i	$0.502341\pi$
$198$	−0.998219	−	2.27747i	−0.0709403	−	0.161852i
$199$		−	22.2925i		−	1.58028i	−0.612929	−	0.790138i	$-0.710009\pi$
$199$		−	22.2925i		−	1.58028i	0.612929	−	0.790138i	$-0.289991\pi$
$200$	1.65815	−	4.71705i	0.117249	−	0.333546i
$201$	4.42559	+	1.43796i	0.312157	+	0.101426i
$202$	−5.05153	−	15.5470i	−0.355425	−	1.09388i
$203$	4.20026	+	4.76080i	0.294800	+	0.334143i
$204$	−0.474722	−	0.653399i	−0.0332372	−	0.0457471i
$205$	2.91409	−	8.61730i	0.203529	−	0.601858i
$206$	−3.86155	+	11.8846i	−0.269047	+	0.828042i
$207$	−2.07434	+	2.85508i	−0.144176	+	0.198442i
$208$			0.325664i			0.0225807i
$209$	−1.73793	+	7.94948i	−0.120215	+	0.549877i
$210$	7.58595	+	4.60568i	0.523480	+	0.317822i
$211$	−2.55703	+	3.51945i	−0.176033	+	0.242289i	−0.887912	−	0.460013i	$-0.847845\pi$
$211$	−2.55703	+	3.51945i	−0.176033	+	0.242289i	0.711879	+	0.702302i	$0.247845\pi$
$212$	−9.56078	−	3.10649i	−0.656637	−	0.213354i
$213$	−2.61059	−	8.03457i	−0.178875	−	0.550520i
$214$	−2.61953	+	1.90320i	−0.179067	+	0.130100i
$215$	−1.76072	−	0.0210173i	−0.120080	−	0.00143337i
$216$	1.73820	+	5.34963i	0.118270	+	0.363996i
$217$	1.09042	+	0.243326i	0.0740225	+	0.0165181i
$218$	10.6568	−	14.6679i	0.721772	−	0.993434i
$219$			21.2747i			1.43761i
$220$	−2.89584	−	6.82745i	−0.195238	−	0.460307i
$221$	0.175337			0.0117945
$222$	−2.85329	+	3.92721i	−0.191500	+	0.263577i
$223$	−4.73537	+	14.5740i	−0.317104	+	0.975944i	0.657776	+	0.753213i	$0.271497\pi$
$223$	−4.73537	+	14.5740i	−0.317104	+	0.975944i	−0.974880	+	0.222731i	$0.928503\pi$
$224$	−1.05163	−	2.42777i	−0.0702648	−	0.162212i
$225$	2.97932	+	2.27521i	0.198621	+	0.151681i
$226$	−4.91866	−	6.76996i	−0.327185	−	0.450331i
$227$	21.9096	−	7.11887i	1.45419	−	0.472496i	0.527902	−	0.849305i	$-0.322979\pi$
$227$	21.9096	−	7.11887i	1.45419	−	0.472496i	0.926291	+	0.376810i	$0.122979\pi$
$228$	1.13731	−	3.50028i	0.0753202	−	0.231812i
$229$	−9.19600	+	12.6572i	−0.607688	+	0.836411i	−0.996385	−	0.0849545i	$-0.972926\pi$
$229$	−9.19600	+	12.6572i	−0.607688	+	0.836411i	0.388696	+	0.921366i	$0.372926\pi$
$230$	−6.28778	+	8.44065i	−0.414604	+	0.556560i
$231$	12.9175	−	2.53162i	0.849906	−	0.166568i
$232$			2.39963i			0.157543i
$233$	−0.682122	−	0.495591i	−0.0446873	−	0.0324672i	0.565217	−	0.824942i	$-0.308792\pi$
$233$	−0.682122	−	0.495591i	−0.0446873	−	0.0324672i	−0.609905	+	0.792475i	$0.708792\pi$
$234$	−0.232214	−	0.0754510i	−0.0151803	−	0.00493239i
$235$	4.59649	−	13.5923i	0.299842	−	0.886665i
$236$	−2.06902	−	2.84776i	−0.134682	−	0.185373i
$237$	0.204403	+	0.281336i	0.0132774	+	0.0182747i
$238$	−1.30711	+	0.566195i	−0.0847275	+	0.0367010i
$239$	7.92025	+	2.57344i	0.512318	+	0.166462i	0.553756	−	0.832679i	$-0.313194\pi$
$239$	7.92025	+	2.57344i	0.512318	+	0.166462i	−0.0414381	+	0.999141i	$0.513194\pi$
$240$	0.998383	+	3.20227i	0.0644453	+	0.206705i
$241$	14.2248			0.916298			0.458149	−	0.888875i	$-0.348513\pi$
$241$	14.2248			0.916298			0.458149	+	0.888875i	$0.348513\pi$
$242$	−9.99647	−	4.59027i	−0.642597	−	0.295074i
$243$	−7.59131			−0.486983
$244$	−2.60559	−	1.89307i	−0.166806	−	0.121192i
$245$	10.8422	−	11.2893i	0.692681	−	0.721244i
$246$	1.88580	+	5.80391i	0.120234	+	0.370044i
$247$	0.469644	+	0.646409i	0.0298827	+	0.0411300i
$248$	0.248208	+	0.341629i	0.0157612	+	0.0216935i
$249$	−15.9413	+	5.17963i	−1.01024	+	0.328246i
$250$	8.80402	+	6.89125i	0.556815	+	0.435841i
$251$	−5.64976	+	7.77623i	−0.356610	+	0.490831i	−0.949200	−	0.314673i	$-0.898105\pi$
$251$	−5.64976	+	7.77623i	−0.356610	+	0.490831i	0.592591	+	0.805504i	$0.298105\pi$
$252$	1.97477	−	0.187386i	0.124399	−	0.0118042i
$253$	1.54184	+	15.5351i	0.0969345	+	0.976686i
$254$	−11.9832			−0.751895
$255$	1.72410	−	0.537529i	0.107967	−	0.0336614i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−4.72111	−	14.5301i	−0.294495	−	0.906362i	−0.983391	−	0.181502i	$-0.941904\pi$
$257$	−4.72111	−	14.5301i	−0.294495	−	0.906362i	0.688896	−	0.724860i	$-0.258096\pi$
$258$	0.955674	−	0.694338i	0.0594977	−	0.0432276i
$259$	5.66426	+	6.42019i	0.351960	+	0.398931i
$260$	−0.689830	−	0.233278i	−0.0427814	−	0.0144673i
$261$	−1.71105	−	0.555954i	−0.105911	−	0.0344127i
$262$	8.24892	+	5.99319i	0.509620	+	0.370260i
$263$	1.40139			0.0864132			0.0432066	−	0.999066i	$-0.486243\pi$
$263$	1.40139			0.0864132			0.0432066	+	0.999066i	$0.486243\pi$
$264$	4.29418	+	2.51254i	0.264288	+	0.154636i
$265$	13.4288	−	18.0267i	0.824924	−	1.10737i
$266$	−5.58849	−	3.30232i	−0.342653	−	0.202478i
$267$	−14.2117	−	4.61765i	−0.869739	−	0.282595i
$268$	2.95023	−	0.958586i	0.180214	−	0.0585550i
$269$	7.05324	+	9.70795i	0.430043	+	0.591904i	0.967963	−	0.251092i	$-0.0807897\pi$
$269$	7.05324	+	9.70795i	0.430043	+	0.591904i	−0.537920	+	0.842996i	$0.680790\pi$
$270$	−12.5768	−	0.150127i	−0.765402	−	0.00913641i
$271$	−7.70500	−	23.7135i	−0.468045	−	1.44050i	−0.855112	−	0.518444i	$-0.826512\pi$
$271$	−7.70500	−	23.7135i	−0.468045	−	1.44050i	0.387066	−	0.922052i	$-0.373488\pi$
$272$	−0.512048	−	0.166375i	−0.0310475	−	0.0100879i
$273$	0.657542	−	1.11275i	0.0397962	−	0.0673470i
$274$		−	9.06326i		−	0.547531i
$275$	16.5364	−	1.24343i	0.997185	−	0.0749816i
$276$		−	7.06095i		−	0.425019i
$277$	6.22158	+	4.52024i	0.373818	+	0.271595i	0.758793	−	0.651332i	$-0.225790\pi$
$277$	6.22158	+	4.52024i	0.373818	+	0.271595i	−0.384974	+	0.922927i	$0.625790\pi$
$278$	−6.56257	+	20.1975i	−0.393597	+	1.21137i
$279$	−0.301104	+	0.0978346i	−0.0180266	+	0.00585721i
$280$	5.89587	−	0.488531i	0.352346	−	0.0291953i
$281$	−7.30485	−	10.0543i	−0.435771	−	0.599787i	0.533495	−	0.845803i	$-0.320878\pi$
$281$	−7.30485	−	10.0543i	−0.435771	−	0.599787i	−0.969266	+	0.246016i	$0.920878\pi$
$282$	2.97453	+	9.15467i	0.177131	+	0.545153i
$283$	−21.3217	−	6.92784i	−1.26744	−	0.411817i	−0.403302	−	0.915067i	$-0.632138\pi$
$283$	−21.3217	−	6.92784i	−1.26744	−	0.411817i	−0.864141	+	0.503250i	$0.832138\pi$
$284$	−4.55615	−	3.31024i	−0.270358	−	0.196426i
$285$	6.59972	+	4.91639i	0.390933	+	0.291222i
$286$	−0.989253	+	0.433592i	−0.0584958	+	0.0256388i
$287$	10.7152	−	1.01677i	0.632499	−	0.0600181i
$288$	0.606556	+	0.440689i	0.0357417	+	0.0259678i
$289$	5.16371	−	15.8923i	0.303748	−	0.934840i
$290$	−5.08295	−	1.71889i	−0.298481	−	0.100937i
$291$	−14.7999	+	10.7528i	−0.867586	+	0.630338i
$292$	8.33616	+	11.4737i	0.487837	+	0.671450i
$293$	7.66041	−	2.48902i	0.447526	−	0.145410i	−0.0765794	−	0.997063i	$-0.524400\pi$
$293$	7.66041	−	2.48902i	0.447526	−	0.145410i	0.524105	+	0.851654i	$0.324400\pi$
$294$	−1.30859	+	10.4187i	−0.0763184	+	0.607633i
$295$	7.51428	−	2.34276i	0.437498	−	0.136400i
$296$			3.23602i			0.188090i
$297$	−13.9361	+	12.4026i	−0.808653	+	0.719673i
$298$		−	9.74201i		−	0.564339i
$299$	1.24015	+	0.901021i	0.0717197	+	0.0521074i
$300$	−7.49829	−	0.179036i	−0.432914	−	0.0103366i
$301$	−0.828129	−	1.91181i	−0.0477326	−	0.110195i
$302$	3.31749	+	4.56613i	0.190900	+	0.262751i
$303$	−19.8387	+	14.4137i	−1.13971	+	0.828045i
$304$	−0.758164	−	2.33339i	−0.0434837	−	0.133829i
$305$	5.87639	−	4.16320i	0.336481	−	0.238384i
$306$	0.237267	−	0.326570i	0.0135636	−	0.0186687i
$307$			25.7572i			1.47004i	0.678044	+	0.735021i	$0.262828\pi$
$307$			25.7572i			1.47004i	−0.678044	+	0.735021i	$0.737172\pi$
$308$	5.97459	−	6.42684i	0.340434	−	0.366203i
$309$	18.7454			1.06639
$310$	−0.901443	+	0.281046i	−0.0511985	+	0.0159624i
$311$	24.6295	+	8.00260i	1.39661	+	0.453786i	0.908093	−	0.418769i	$-0.137538\pi$
$311$	24.6295	+	8.00260i	1.39661	+	0.453786i	0.488517	+	0.872555i	$0.337538\pi$
$312$	0.464613	−	0.150962i	0.0263035	−	0.00854654i
$313$	−0.756757	+	0.549816i	−0.0427745	+	0.0310775i	−0.608967	−	0.793196i	$-0.708416\pi$
$313$	−0.756757	+	0.549816i	−0.0427745	+	0.0310775i	0.566193	+	0.824273i	$0.308416\pi$
$314$	−15.5200	+	11.2759i	−0.875843	+	0.636337i
$315$	−1.01763	+	4.31724i	−0.0573371	+	0.243249i
$316$	0.220474	+	0.0716365i	0.0124027	+	0.00402987i
$317$	11.7119	−	16.1200i	0.657805	−	0.905391i	−0.341602	−	0.939845i	$-0.610969\pi$
$317$	11.7119	−	16.1200i	0.657805	−	0.905391i	0.999406	+	0.0344544i	$0.0109693\pi$
$318$			15.0801i			0.845648i
$319$	−7.28923	+	3.19489i	−0.408119	+	0.178879i
$320$	1.79320	+	1.33583i	0.100243	+	0.0746750i
$321$	3.92951	+	2.85496i	0.219324	+	0.159348i
$322$	−12.1547	−	2.71231i	−0.677354	−	0.151151i
$323$	−1.25629	+	0.408195i	−0.0699021	+	0.0227126i
$324$	5.00672	−	3.63760i	0.278151	−	0.202089i
$325$	0.988274	−	1.29412i	0.0548196	−	0.0717846i
$326$	10.2197	−	3.32057i	0.566016	−	0.183910i
$327$	−25.8661	−	8.40442i	−1.43040	−	0.464765i
$328$	3.29121	+	2.39121i	0.181727	+	0.132032i
$329$	16.9014	−	1.60378i	0.931806	−	0.0884193i
$330$	−8.39812	+	7.29627i	−0.462301	+	0.401647i
$331$	−14.4420			−0.793804			−0.396902	−	0.917861i	$-0.629915\pi$
$331$	−14.4420			−0.793804			−0.396902	+	0.917861i	$0.629915\pi$
$332$	−6.56779	+	9.03978i	−0.360454	+	0.496123i
$333$	−2.30744	−	0.749733i	−0.126447	−	0.0410851i
$334$	7.52258	−	2.44424i	0.411617	−	0.133743i
$335$	−0.0827921	+	6.93590i	−0.00452341	+	0.378949i
$336$	−2.97614	+	2.62572i	−0.162362	+	0.143245i
$337$	9.72849	+	29.9412i	0.529945	+	1.63100i	0.754326	+	0.656500i	$0.227964\pi$
$337$	9.72849	+	29.9412i	0.529945	+	1.63100i	−0.224381	+	0.974501i	$0.572036\pi$
$338$	3.98445	−	12.2629i	0.216725	−	0.667012i
$339$	−7.37841	+	10.1555i	−0.400740	+	0.551572i
$340$	0.719208	−	0.965458i	0.0390045	−	0.0523593i
$341$	−0.707284	+	1.20882i	−0.0383016	+	0.0654612i
$342$	1.83948			0.0994674
$343$	17.4321	+	6.25473i	0.941245	+	0.337724i
$344$	0.243343	−	0.748933i	0.0131202	−	0.0403797i
$345$	14.9567	+	5.05788i	0.805242	+	0.272307i
$346$	11.6544	+	16.0409i	0.626545	+	0.862366i
$347$	−4.16413	+	3.02541i	−0.223542	+	0.162413i	−0.693920	−	0.720052i	$-0.744118\pi$
$347$	−4.16413	+	3.02541i	−0.223542	+	0.162413i	0.470378	+	0.882465i	$0.344118\pi$
$348$	3.42346	−	1.11235i	0.183517	−	0.0596282i
$349$	−1.58171	+	4.86800i	−0.0846670	+	0.260578i	−0.984423	−	0.175814i	$-0.943744\pi$
$349$	−1.58171	+	4.86800i	−0.0846670	+	0.260578i	0.899756	+	0.436393i	$0.143744\pi$
$350$	−3.18850	+	12.8387i	−0.170432	+	0.686260i
$351$			1.83184i			0.0977762i
$352$	3.30041	−	0.327560i	0.175912	−	0.0174590i
$353$	−3.35238			−0.178429			−0.0892147	−	0.996012i	$-0.528436\pi$
$353$	−3.35238			−0.178429			−0.0892147	+	0.996012i	$0.528436\pi$
$354$	−3.10370	+	4.27188i	−0.164960	+	0.227048i
$355$	10.2755	−	7.27979i	0.545366	−	0.386371i
$356$	−9.47390	+	3.07826i	−0.502116	+	0.163147i
$357$	1.41369	+	1.60235i	0.0748202	+	0.0848054i
$358$	9.01343	−	6.54864i	0.476375	−	0.346106i
$359$	−14.6734	+	4.76767i	−0.774431	+	0.251628i	−0.669461	−	0.742847i	$-0.733475\pi$
$359$	−14.6734	+	4.76767i	−0.774431	+	0.251628i	−0.104971	+	0.994475i	$0.533475\pi$
$360$	−1.36797	+	0.969152i	−0.0720981	+	0.0510788i
$361$	10.5014	+	7.62974i	0.552707	+	0.401565i
$362$			17.0527i			0.896270i
$363$	−1.91491	+	16.3894i	−0.100506	+	0.860223i
$364$	−0.0813943	−	0.857772i	−0.00426622	−	0.0449595i
$365$	−30.2753	+	9.43905i	−1.58468	+	0.494063i
$366$	−1.49296	+	4.59484i	−0.0780380	+	0.240176i
$367$	−3.88417	−	11.9542i	−0.202752	−	0.624006i	−0.999798	−	0.0200878i	$-0.993605\pi$
$367$	−3.88417	−	11.9542i	−0.202752	−	0.624006i	0.797046	−	0.603918i	$-0.206395\pi$
$368$	−2.76672	−	3.80807i	−0.144225	−	0.198509i
$369$	−2.46757	+	1.79279i	−0.128457	+	0.0933291i
$370$	−6.85462	−	2.31801i	−0.356355	−	0.120508i
$371$	25.9587	+	5.79268i	1.34771	+	0.300741i
$372$	0.372333	−	0.512472i	0.0193046	−	0.0265705i
$373$	−37.4219			−1.93763			−0.968815	−	0.247784i	$-0.920298\pi$
$373$	−37.4219			−1.93763			−0.968815	+	0.247784i	$0.920298\pi$
$374$	−0.176358	−	1.77694i	−0.00911927	−	0.0918833i
$375$	5.75039	−	15.7548i	0.296949	−	0.813576i
$376$	5.19133	+	3.77172i	0.267722	+	0.194512i
$377$	−0.241488	+	0.743223i	−0.0124372	+	0.0382779i
$378$	−5.91533	−	13.6561i	−0.304252	−	0.702392i
$379$	20.3040	−	14.7517i	1.04295	−	0.757744i	0.0720868	−	0.997398i	$-0.477034\pi$
$379$	20.3040	−	14.7517i	1.04295	−	0.757744i	0.970858	+	0.239654i	$0.0770341\pi$
$380$	5.48573	+	0.0654818i	0.281412	+	0.00335914i
$381$	5.55485	+	17.0961i	0.284583	+	0.875858i
$382$	−5.55713	+	17.1031i	−0.284327	+	0.875070i
$383$	−15.3530	−	11.1546i	−0.784501	−	0.569974i	0.121825	−	0.992552i	$-0.461125\pi$
$383$	−15.3530	−	11.1546i	−0.784501	−	0.569974i	−0.906327	+	0.422578i	$0.861125\pi$
$384$	−1.50009			−0.0765509
$385$	9.33382	+	17.2592i	0.475696	+	0.879610i
$386$	12.3188			0.627011
$387$	0.477647	+	0.347031i	0.0242802	+	0.0176406i
$388$	−3.76849	+	11.5982i	−0.191316	+	0.588811i
$389$	4.11649	+	12.6693i	0.208714	+	0.642357i	0.999540	+	0.0303158i	$0.00965129\pi$
$389$	4.11649	+	12.6693i	0.208714	+	0.642357i	−0.790826	+	0.612041i	$0.790349\pi$
$390$	−0.0130384	+	1.09229i	−0.000660226	+	0.0553104i
$391$	−2.05026	+	1.48960i	−0.103686	+	0.0753325i
$392$	3.37668	+	6.13172i	0.170548	+	0.309699i
$393$	4.72648	−	14.5466i	0.238419	−	0.733779i
$394$	0.166985	+	0.121322i	0.00841259	+	0.00611210i
$395$	−0.309672	+	0.415701i	−0.0155813	+	0.0209162i
$396$	−0.531085	+	2.42925i	−0.0266880	+	0.122074i
$397$	32.5495			1.63361			0.816805	−	0.576914i	$-0.195743\pi$
$397$	32.5495			1.63361			0.816805	+	0.576914i	$0.195743\pi$
$398$	−13.1032	+	18.0350i	−0.656806	+	0.904015i
$399$	−2.12075	+	9.50371i	−0.106170	+	0.475780i
$400$	−4.11408	+	2.84153i	−0.205704	+	0.142077i
$401$	14.7964	−	10.7502i	0.738896	−	0.536839i	−0.153469	−	0.988153i	$-0.549045\pi$
$401$	14.7964	−	10.7502i	0.738896	−	0.536839i	0.892365	+	0.451314i	$0.149045\pi$
$402$	−2.73516	−	3.76463i	−0.136418	−	0.187763i
$403$	0.0424960	+	0.130789i	0.00211688	+	0.00651508i
$404$	−5.05153	+	15.5470i	−0.251323	+	0.773493i
$405$	4.11886	+	13.2111i	0.204668	+	0.656462i
$406$	−0.599747	−	6.32042i	−0.0297649	−	0.313677i
$407$	−9.82990	+	4.30847i	−0.487250	+	0.213563i
$408$			0.807645i			0.0399844i
$409$	20.7913	+	15.1058i	1.02806	+	0.746933i	0.967920	−	0.251257i	$-0.0808440\pi$
$409$	20.7913	+	15.1058i	1.02806	+	0.746933i	0.0601441	+	0.998190i	$0.480844\pi$
$410$	−7.42267	+	5.25868i	−0.366580	+	0.259708i
$411$	−12.9302	+	4.20129i	−0.637802	+	0.207234i
$412$	10.1097	−	7.34511i	0.498068	−	0.361868i
$413$	6.16138	+	6.98366i	0.303182	+	0.343643i
$414$	3.35635	−	1.09054i	0.164956	−	0.0535973i
$415$	−14.4437	−	20.3874i	−0.709014	−	1.00078i
$416$	0.191420	−	0.263467i	0.00938515	−	0.0129176i
$417$	31.8572			1.56005
$418$	6.07860	−	5.40974i	0.297314	−	0.264599i
$419$			0.0761591i			0.00372062i	0.999998	+	0.00186031i	$0.000592155\pi$
$419$			0.0761591i			0.00372062i	−0.999998	+	0.00186031i	$0.999408\pi$
$420$	−3.43001	−	8.18498i	−0.167368	−	0.399386i
$421$	−0.783099	+	2.41013i	−0.0381659	+	0.117463i	−0.968324	−	0.249696i	$-0.919669\pi$
$421$	−0.783099	+	2.41013i	−0.0381659	+	0.117463i	0.930158	+	0.367159i	$0.119669\pi$
$422$	4.13736	−	1.34431i	0.201404	−	0.0654400i
$423$	−3.89217	+	2.82783i	−0.189244	+	0.137494i
$424$	5.90889	+	8.13289i	0.286961	+	0.394968i
$425$	1.52988	+	2.21502i	0.0742101	+	0.107444i
$426$	−2.61059	+	8.03457i	−0.126484	+	0.389276i
$427$	7.33606	+	4.33498i	0.355017	+	0.209784i
$428$	3.23791			0.156510
$429$	1.07716	+	1.21034i	0.0520058	+	0.0584358i
$430$	1.41210	+	1.05193i	0.0680975	+	0.0507285i
$431$	10.5070	−	14.4616i	0.506104	−	0.696592i	−0.477152	−	0.878821i	$-0.658331\pi$
$431$	10.5070	−	14.4616i	0.506104	−	0.696592i	0.983256	+	0.182228i	$0.0583310\pi$
$432$	1.73820	−	5.34963i	0.0836292	−	0.257384i
$433$	−0.0743891	−	0.228946i	−0.00357491	−	0.0110024i	0.949253	−	0.314513i	$-0.101841\pi$
$433$	−0.0743891	−	0.228946i	−0.00357491	−	0.0110024i	−0.952828	+	0.303511i	$0.901841\pi$
$434$	−0.739144	−	0.837787i	−0.0354801	−	0.0402151i
$435$	−0.0960725	+	8.04847i	−0.00460632	+	0.385895i
$436$	−17.2431	+	5.60263i	−0.825796	+	0.268317i
$437$	−10.9833	−	3.56870i	−0.525404	−	0.170714i
$438$	12.5049	−	17.2116i	0.597510	−	0.822401i
$439$	15.0509			0.718341			0.359171	−	0.933272i	$-0.383060\pi$
$439$	15.0509			0.718341			0.359171	+	0.933272i	$0.383060\pi$
$440$	−1.67029	+	7.22566i	−0.0796280	+	0.344470i
$441$	−5.15455	+	0.987121i	−0.245455	+	0.0470058i
$442$	−0.141851	−	0.103061i	−0.00674715	−	0.00490209i
$443$	−20.5775	−	6.68605i	−0.977668	−	0.317664i	−0.223761	−	0.974644i	$-0.571833\pi$
$443$	−20.5775	−	6.68605i	−0.977668	−	0.317664i	−0.753908	+	0.656981i	$0.771833\pi$
$444$	4.61671	−	1.50006i	0.219100	−	0.0711898i
$445$	0.265866	−	22.2729i	0.0126032	−	1.05584i
$446$	12.3973	−	9.00720i	0.587031	−	0.426503i
$447$	−13.8986	+	4.51592i	−0.657381	+	0.213596i
$448$	−0.576225	+	2.58224i	−0.0272241	+	0.121999i
$449$	−28.1981	−	20.4871i	−1.33075	−	0.966846i	−0.999730	−	0.0232212i	$-0.992608\pi$
$449$	−28.1981	−	20.4871i	−1.33075	−	0.966846i	−0.331018	−	0.943624i	$-0.607392\pi$
$450$	−1.07299	−	3.59188i	−0.0505811	−	0.169323i
$451$	−2.88170	+	13.1812i	−0.135694	+	0.620681i
$452$			8.36813i			0.393604i
$453$	4.97651	−	6.84958i	0.233817	−	0.321822i
$454$	−21.9096	−	7.11887i	−1.02827	−	0.334105i
$455$	1.87526	+	0.442025i	0.0879136	+	0.0207224i
$456$	−2.97752	+	2.16329i	−0.139435	+	0.101305i
$457$	31.1079	−	22.6012i	1.45517	−	1.05724i	0.470576	−	0.882359i	$-0.344046\pi$
$457$	31.1079	−	22.6012i	1.45517	−	1.05724i	0.984590	−	0.174881i	$-0.0559540\pi$
$458$	14.8794	−	4.83462i	0.695270	−	0.225907i
$459$	−2.88024	−	0.935847i	−0.134438	−	0.0436816i
$460$	10.0482	−	3.13277i	0.468500	−	0.146066i
$461$	21.6531			1.00849			0.504243	−	0.863562i	$-0.331772\pi$
$461$	21.6531			1.00849			0.504243	+	0.863562i	$0.331772\pi$
$462$	−11.9385	−	5.54456i	−0.555429	−	0.257956i
$463$			11.3856i			0.529136i	0.964367	+	0.264568i	$0.0852293\pi$
$463$			11.3856i			0.529136i	−0.964367	+	0.264568i	$0.914771\pi$
$464$	1.41046	−	1.94134i	0.0654792	−	0.0901243i
$465$	0.818825	+	1.15578i	0.0379721	+	0.0535980i
$466$	0.260547	+	0.801883i	0.0120696	+	0.0371465i
$467$	−8.29340	+	6.02551i	−0.383773	+	0.278827i	−0.762899	−	0.646518i	$-0.776225\pi$
$467$	−8.29340	+	6.02551i	−0.383773	+	0.278827i	0.379126	+	0.925345i	$0.376225\pi$
$468$	0.143516	+	0.197533i	0.00663405	+	0.00913098i
$469$	−7.53107	+	3.26220i	−0.347753	+	0.150634i
$470$	−11.7080	+	8.29467i	−0.540050	+	0.382604i
$471$	23.2813	+	16.9148i	1.07274	+	0.779395i
$472$			3.52003i			0.162022i
$473$	2.59899	−	0.257945i	0.119502	−	0.0118603i
$474$		−	0.347751i		−	0.0159727i
$475$	−4.06823	+	11.5731i	−0.186663	+	0.531011i
$476$	1.39028	+	0.310239i	0.0637232	+	0.0142198i
$477$	−7.16815	+	2.32907i	−0.328207	+	0.106641i
$478$	−4.89498	−	6.73736i	−0.223891	−	0.308160i
$479$	23.8610	−	17.3360i	1.09023	−	0.792102i	0.110796	−	0.993843i	$-0.464660\pi$
$479$	23.8610	−	17.3360i	1.09023	−	0.792102i	0.979439	+	0.201741i	$0.0646600\pi$
$480$	1.07454	−	3.17752i	0.0490457	−	0.145033i
$481$	−0.325658	+	1.00227i	−0.0148487	+	0.0456997i
$482$	−11.5081	−	8.36111i	−0.524179	−	0.380838i
$483$	1.76477	+	18.5980i	0.0802997	+	0.846237i
$484$	5.38922	+	9.58939i	0.244964	+	0.435881i
$485$	−21.8683	−	16.2905i	−0.992987	−	0.739715i
$486$	6.14150	+	4.46206i	0.278584	+	0.202403i
$487$	−17.6380	−	5.73095i	−0.799256	−	0.259694i	−0.119215	−	0.992868i	$-0.538038\pi$
$487$	−17.6380	−	5.73095i	−0.799256	−	0.259694i	−0.680041	+	0.733175i	$0.738038\pi$
$488$	0.995247	+	3.06306i	0.0450527	+	0.138658i
$489$	−9.47470	−	13.0408i	−0.428461	−	0.589726i
$490$	−15.4072	+	2.76033i	−0.696025	+	0.124699i
$491$	−0.239562	+	0.0778386i	−0.0108113	+	0.00351280i	−0.314418	−	0.949285i	$-0.601809\pi$
$491$	−0.239562	+	0.0778386i	−0.0108113	+	0.00351280i	0.303606	+	0.952798i	$0.401809\pi$
$492$	1.88580	−	5.80391i	0.0850186	−	0.261660i
$493$	−1.04522	−	0.759393i	−0.0470741	−	0.0342014i
$494$		−	0.799005i		−	0.0359490i
$495$	−4.76527	−	2.86507i	−0.214183	−	0.128775i
$496$		−	0.422276i		−	0.0189608i
$497$	12.8279	+	7.58017i	0.575409	+	0.340017i
$498$	15.9413	+	5.17963i	0.714345	+	0.232105i
$499$	−6.64170	−	20.4410i	−0.297323	−	0.915067i	−0.982431	−	0.186625i	$-0.940245\pi$
$499$	−6.64170	−	20.4410i	−0.297323	−	0.915067i	0.685108	−	0.728441i	$-0.259755\pi$
$500$	−3.07202	−	10.7500i	−0.137385	−	0.480755i
$501$	−6.97421	−	9.59918i	−0.311585	−	0.428860i
$502$	9.14150	−	2.97025i	0.408005	−	0.132569i
$503$	−34.9094	−	11.3427i	−1.55653	−	0.505748i	−0.600653	−	0.799510i	$-0.705093\pi$
$503$	−34.9094	−	11.3427i	−1.55653	−	0.505748i	−0.955879	+	0.293762i	$0.905093\pi$
$504$	−1.70776	−	1.00914i	−0.0760698	−	0.0449507i
$505$	−29.3136	−	21.8369i	−1.30444	−	0.971729i
$506$	7.88395	−	13.4745i	0.350484	−	0.599013i
$507$	−19.3420			−0.859009
$508$	9.69463	+	7.04356i	0.430130	+	0.312508i
$509$	13.7937	+	4.48183i	0.611394	+	0.198654i	0.598315	−	0.801261i	$-0.295837\pi$
$509$	13.7937	+	4.48183i	0.611394	+	0.198654i	0.0130782	+	0.999914i	$0.495837\pi$
$510$	−1.71078	−	0.578530i	−0.0757545	−	0.0256177i
$511$	−24.8244	−	28.1374i	−1.09817	−	1.24473i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−4.26462	−	13.1252i	−0.188288	−	0.579490i
$514$	−4.72111	+	14.5301i	−0.208239	+	0.640895i
$515$	8.31688	+	26.6760i	0.366486	+	1.17549i
$516$	−1.18128			−0.0520029
$517$	−4.54539	+	20.7912i	−0.199906	+	0.914394i
$518$	−0.808789	−	8.52341i	−0.0355361	−	0.374497i
$519$	17.4826	−	24.0628i	0.767402	−	1.05624i
$520$	0.420966	+	0.594198i	0.0184606	+	0.0260573i
$521$	−29.1844	+	9.48260i	−1.27859	+	0.415440i	−0.868085	−	0.496416i	$-0.834649\pi$
$521$	−29.1844	+	9.48260i	−1.27859	+	0.415440i	−0.410509	+	0.911856i	$0.634649\pi$
$522$	1.05749	+	1.45551i	0.0462850	+	0.0637058i
$523$	23.6685	+	32.5769i	1.03495	+	1.42449i	0.901165	+	0.433477i	$0.142713\pi$
$523$	23.6685	+	32.5769i	1.03495	+	1.42449i	0.133786	+	0.991010i	$0.457287\pi$
$524$	−3.15081	−	9.69718i	−0.137644	−	0.423623i
$525$	19.7946	−	1.40251i	0.863909	−	0.0612105i
$526$	−1.13375	−	0.823714i	−0.0494336	−	0.0359156i
$527$	−0.227353			−0.00990367
$528$	−1.99723	−	4.55674i	−0.0869183	−	0.198307i
$529$	0.843844			0.0366889
$530$	−21.4599	+	6.69065i	−0.932160	+	0.290623i
$531$	−2.50995	−	0.815533i	−0.108923	−	0.0353911i
$532$	2.58013	+	5.95646i	0.111863	+	0.258246i
$533$	0.778729	+	1.07183i	0.0337305	+	0.0464260i
$534$	8.78329	+	12.0892i	0.380090	+	0.523149i
$535$	−2.31937	+	6.85864i	−0.100275	+	0.296525i
$536$	−2.95023	−	0.958586i	−0.127430	−	0.0414046i
$537$	−13.5209	−	9.82352i	−0.583471	−	0.423916i
$538$		−	11.9997i		−	0.517343i
$539$	−14.1303	+	18.4210i	−0.608635	+	0.793450i
$540$	10.0866	+	7.51394i	0.434060	+	0.323348i
$541$	−24.4152	+	33.6046i	−1.04969	+	1.44478i	−0.160615	+	0.987017i	$0.551348\pi$
$541$	−24.4152	+	33.6046i	−1.04969	+	1.44478i	−0.889076	+	0.457759i	$0.848652\pi$
$542$	−7.70500	+	23.7135i	−0.330958	+	1.01858i
$543$	24.3285	−	7.90481i	1.04404	−	0.339228i
$544$	0.316463	+	0.435574i	0.0135683	+	0.0186751i
$545$	0.483893	−	40.5381i	0.0207277	−	1.73646i
$546$	−1.18602	+	0.513744i	−0.0507571	+	0.0219862i
$547$	−2.75033	+	8.46466i	−0.117596	+	0.361923i	−0.992480	−	0.122410i	$-0.960938\pi$
$547$	−2.75033	+	8.46466i	−0.117596	+	0.361923i	0.874884	+	0.484333i	$0.160938\pi$
$548$	−5.32725	+	7.33233i	−0.227569	+	0.313222i
$549$	−2.41469			−0.103057
$550$	−14.1091	−	8.71392i	−0.601615	−	0.371563i
$551$		−	5.88741i		−	0.250812i
$552$	−4.15032	+	5.71243i	−0.176649	+	0.243137i
$553$	−0.598616	−	0.133581i	−0.0254558	−	0.00568043i
$554$	−2.37643	−	7.31391i	−0.100965	−	0.310738i
$555$	−0.129559	+	10.8538i	−0.00549946	+	0.460717i
$556$	17.1810	−	12.4828i	0.728638	−	0.529387i
$557$	5.59276	+	17.2127i	0.236973	+	0.729327i	0.996854	+	0.0792649i	$0.0252573\pi$
$557$	5.59276	+	17.2127i	0.236973	+	0.729327i	−0.759881	+	0.650062i	$0.774743\pi$
$558$	0.301104	+	0.0978346i	0.0127468	+	0.00414167i
$559$	0.150739	−	0.207474i	0.00637556	−	0.00877521i
$560$	−5.05701	−	3.07028i	−0.213698	−	0.129743i
$561$	−2.45335	+	1.07531i	−0.103580	+	0.0453995i
$562$			12.4278i			0.524233i
$563$	5.96933	−	8.21608i	0.251577	−	0.346267i	−0.664486	−	0.747301i	$-0.731349\pi$
$563$	5.96933	−	8.21608i	0.251577	−	0.346267i	0.916063	+	0.401035i	$0.131349\pi$
$564$	2.97453	−	9.15467i	0.125250	−	0.385481i
$565$	−17.7256	−	5.99423i	−0.745722	−	0.252179i
$566$	13.1775	+	18.1373i	0.553893	+	0.762368i
$567$	−12.2781	+	10.8325i	−0.515634	+	0.454922i
$568$	1.74030	+	5.35608i	0.0730212	+	0.224736i
$569$	−27.2023	−	8.83856i	−1.14038	−	0.370532i	−0.322868	−	0.946444i	$-0.604647\pi$
$569$	−27.2023	−	8.83856i	−1.14038	−	0.370532i	−0.817511	+	0.575912i	$0.804647\pi$
$570$	−2.44950	−	7.85666i	−0.102598	−	0.329079i
$571$		−	8.74654i		−	0.366031i	−0.983110	−	0.183016i	$-0.941414\pi$
$571$		−	8.74654i		−	0.366031i	0.983110	−	0.183016i	$-0.0585859\pi$
$572$	1.05518	+	0.230685i	0.0441194	+	0.00964543i
$573$	26.9764			1.12696
$574$	−9.26643	−	5.47566i	−0.386773	−	0.228550i
$575$	−0.561786	+	23.5285i	−0.0234281	+	0.981204i
$576$	−0.231684	−	0.713050i	−0.00965349	−	0.0297104i
$577$	13.4356	−	9.76153i	0.559331	−	0.406378i	−0.271883	−	0.962330i	$-0.587646\pi$
$577$	13.4356	−	9.76153i	0.559331	−	0.406378i	0.831214	+	0.555952i	$0.187646\pi$
$578$	−13.5188	+	9.82197i	−0.562307	+	0.408540i
$579$	−5.71041	−	17.5748i	−0.237316	−	0.730385i
$580$	3.10186	+	4.37830i	0.128798	+	0.181799i
$581$	15.0397	−	25.4516i	0.623951	−	1.05591i
$582$	18.2937			0.758298
$583$	−16.8377	+	28.7774i	−0.697348	+	1.19184i
$584$		−	14.1823i		−	0.586869i
$585$	−0.521224	+	0.162504i	−0.0215500	+	0.00671871i
$586$	−7.66041	−	2.48902i	−0.316448	−	0.102820i
$587$	3.69244	+	11.3642i	0.152403	+	0.469049i	0.997889	−	0.0649498i	$-0.0206887\pi$
$587$	3.69244	+	11.3642i	0.152403	+	0.469049i	−0.845485	+	0.533999i	$0.820689\pi$
$588$	7.18265	−	7.65977i	0.296207	−	0.315884i
$589$	−0.608970	−	0.838176i	−0.0250922	−	0.0345364i
$590$	−7.45622	−	2.52145i	−0.306968	−	0.103807i
$591$	0.0956794	−	0.294471i	0.00393572	−	0.0121129i
$592$	1.90208	−	2.61799i	0.0781751	−	0.107599i
$593$		−	27.5376i		−	1.13083i	−0.824805	−	0.565417i	$-0.808715\pi$
$593$		−	27.5376i		−	1.13083i	0.824805	−	0.565417i	$-0.191285\pi$
$594$	18.5646	−	1.84251i	0.761715	−	0.0755989i
$595$	−1.65304	+	2.72269i	−0.0677679	+	0.111620i
$596$	−5.72621	+	7.88145i	−0.234555	+	0.322837i
$597$	31.8040	+	10.3337i	1.30165	+	0.422932i
$598$	−0.473695	−	1.45788i	−0.0193708	−	0.0596173i
$599$	22.5834	−	16.4078i	0.922731	−	0.670404i	−0.0214710	−	0.999769i	$-0.506835\pi$
$599$	22.5834	−	16.4078i	0.922731	−	0.670404i	0.944202	+	0.329366i	$0.106835\pi$
$600$	5.96101	+	4.55223i	0.243357	+	0.185844i
$601$	−5.00782	−	15.4125i	−0.204273	−	0.628689i	−0.999742	−	0.0226947i	$-0.992775\pi$
$601$	−5.00782	−	15.4125i	−0.204273	−	0.628689i	0.795469	−	0.605994i	$-0.207225\pi$
$602$	−0.453762	+	2.03345i	−0.0184940	+	0.0828771i
$603$	1.36704	−	1.88157i	0.0556701	−	0.0766234i
$604$		−	5.64405i		−	0.229653i
$605$	−24.1729	+	4.54655i	−0.982768	+	0.184844i
$606$	24.5220			0.996140
$607$	5.97460	−	8.22333i	0.242501	−	0.333775i	−0.670366	−	0.742031i	$-0.733863\pi$
$607$	5.97460	−	8.22333i	0.242501	−	0.333775i	0.912867	+	0.408256i	$0.133863\pi$
$608$	−0.758164	+	2.33339i	−0.0307476	+	0.0946314i
$609$	−8.73911	+	3.78548i	−0.354127	+	0.153395i
$610$	−7.20116	−	0.0859584i	−0.291567	−	0.00348035i
$611$	1.22831	+	1.69063i	0.0496922	+	0.0683954i
$612$	−0.383906	+	0.124738i	−0.0155185	+	0.00504225i
$613$	−3.52773	+	10.8572i	−0.142484	+	0.438520i	−0.996679	−	0.0814326i	$-0.974050\pi$
$613$	−3.52773	+	10.8572i	−0.142484	+	0.438520i	0.854195	+	0.519953i	$0.174050\pi$
$614$	15.1397	−	20.8380i	0.610989	−	0.840955i
$615$	10.9432	+	8.15200i	0.441271	+	0.328720i
$616$	−8.61115	+	1.68765i	−0.346953	+	0.0679974i
$617$			22.6358i			0.911285i	0.890163	+	0.455642i	$0.150590\pi$
$617$			22.6358i			0.911285i	−0.890163	+	0.455642i	$0.849410\pi$
$618$	−15.1654	−	11.0183i	−0.610041	−	0.443221i
$619$	−23.5446	−	7.65009i	−0.946336	−	0.307483i	−0.205110	−	0.978739i	$-0.565755\pi$
$619$	−23.5446	−	7.65009i	−0.946336	−	0.307483i	−0.741226	+	0.671256i	$0.765755\pi$
$620$	0.894478	+	0.302484i	0.0359231	+	0.0121480i
$621$	−15.5626	−	21.4201i	−0.624508	−	0.859561i
$622$	−15.2219	−	20.9511i	−0.610341	−	0.840062i
$623$	24.1841	−	10.4757i	0.968917	−	0.419701i
$624$	−0.464613	−	0.150962i	−0.0185994	−	0.00604331i
$625$	24.9715	+	1.19316i	0.998860	+	0.0477266i
$626$	0.935404			0.0373862
$627$	−10.5356	−	6.16443i	−0.420753	−	0.246184i
$628$	19.1837			0.765515
$629$	−1.40953	−	1.02408i	−0.0562015	−	0.0408328i
$630$	3.36089	−	2.89457i	0.133901	−	0.115322i
$631$	9.51865	+	29.2954i	0.378932	+	1.16623i	0.940788	+	0.338996i	$0.110087\pi$
$631$	9.51865	+	29.2954i	0.378932	+	1.16623i	−0.561856	+	0.827235i	$0.689913\pi$
$632$	−0.136261	−	0.187547i	−0.00542016	−	0.00746021i
$633$	−3.83576	−	5.27948i	−0.152458	−	0.209840i
$634$	−18.9502	+	6.15730i	−0.752609	+	0.244538i
$635$	−21.8643	+	15.4900i	−0.867659	+	0.614703i
$636$	8.86383	−	12.2000i	0.351474	−	0.483762i
$637$	0.428772	+	2.23896i	0.0169886	+	0.0887108i
$638$	7.77502	+	1.69978i	0.307816	+	0.0672951i
$639$	−4.22235			−0.167033
$640$	−0.665551	−	2.13472i	−0.0263082	−	0.0843823i
$641$	5.84241	−	17.9811i	0.230761	−	0.710210i	−0.766894	−	0.641774i	$-0.778199\pi$
$641$	5.84241	−	17.9811i	0.230761	−	0.710210i	0.997655	−	0.0684367i	$-0.0218011\pi$
$642$	−1.50094	−	4.61942i	−0.0592374	−	0.182314i
$643$	23.5788	−	17.1310i	0.929856	−	0.675580i	−0.0161016	−	0.999870i	$-0.505126\pi$
$643$	23.5788	−	17.1310i	0.929856	−	0.675580i	0.945958	+	0.324290i	$0.105126\pi$
$644$	8.23909	+	9.33865i	0.324666	+	0.367994i
$645$	0.846170	−	2.50222i	0.0333179	−	0.0985247i
$646$	1.25629	+	0.408195i	0.0494283	+	0.0160602i
$647$	−4.93972	−	3.58891i	−0.194200	−	0.141095i	0.486436	−	0.873716i	$-0.338297\pi$
$647$	−4.93972	−	3.58891i	−0.194200	−	0.141095i	−0.680636	+	0.732621i	$0.738297\pi$
$648$	−6.18865			−0.243113
$649$	−10.6926	+	4.68660i	−0.419722	+	0.183965i
$650$	−1.56019	+	0.466069i	−0.0611958	+	0.0182807i
$651$	−0.852611	+	1.44287i	−0.0334165	+	0.0565505i
$652$	−10.2197	−	3.32057i	−0.400233	−	0.130044i
$653$	−34.6497	+	11.2584i	−1.35595	+	0.440574i	−0.894688	−	0.446691i	$-0.852602\pi$
$653$	−34.6497	+	11.2584i	−1.35595	+	0.440574i	−0.461259	+	0.887265i	$0.652602\pi$
$654$	15.9862	+	22.0031i	0.625108	+	0.860388i
$655$	22.7978	+	0.272132i	0.890785	+	0.0106331i
$656$	−1.25713	−	3.86905i	−0.0490827	−	0.151061i
$657$	10.1127	+	3.28582i	0.394534	+	0.128192i
$658$	−14.6162	−	8.63692i	−0.569799	−	0.336702i
$659$		−	22.5251i		−	0.877454i	−0.898620	−	0.438727i	$-0.855430\pi$
$659$		−	22.5251i		−	0.877454i	0.898620	−	0.438727i	$-0.144570\pi$
$660$	11.0829	−	0.966518i	0.431400	−	0.0376217i
$661$			15.4324i			0.600250i	0.953900	+	0.300125i	$0.0970283\pi$
$661$			15.4324i			0.600250i	−0.953900	+	0.300125i	$0.902972\pi$
$662$	11.6838	+	8.48879i	0.454105	+	0.329926i
$663$	−0.0812778	+	0.250147i	−0.00315657	+	0.00971492i
$664$	10.6269	−	3.45289i	0.412404	−	0.133998i
$665$	−14.4653	+	1.19859i	−0.560942	+	0.0464795i
$666$	1.42608	+	1.96283i	0.0552593	+	0.0760580i
$667$	−3.49038	−	10.7423i	−0.135148	−	0.415943i
$668$	−7.52258	−	2.44424i	−0.291057	−	0.0945703i
$669$	−18.5971	−	13.5116i	−0.719004	−	0.522387i
$670$	4.14380	−	5.56260i	0.160089	−	0.214902i
$671$	−7.97942	+	7.10140i	−0.308042	+	0.274147i
$672$	3.95110	−	0.374922i	0.152417	−	0.0144629i
$673$	−2.86608	−	2.08233i	−0.110479	−	0.0802678i	0.531174	−	0.847263i	$-0.321751\pi$
$673$	−2.86608	−	2.08233i	−0.110479	−	0.0802678i	−0.641653	+	0.766995i	$0.721751\pi$
$674$	9.72849	−	29.9412i	0.374727	−	1.15329i
$675$	−23.1415	+	15.9834i	−0.890715	+	0.615203i
$676$	−10.4314	+	7.57887i	−0.401208	+	0.291495i
$677$	6.39270	+	8.79880i	0.245692	+	0.338165i	0.913997	−	0.405722i	$-0.132980\pi$
$677$	6.39270	+	8.79880i	0.245692	+	0.338165i	−0.668305	+	0.743887i	$0.732980\pi$
$678$	11.9385	−	3.87906i	0.458496	−	0.148974i
$679$	7.02712	−	31.4907i	0.269676	−	1.20850i
$680$	−1.14933	+	0.358332i	−0.0440749	+	0.0137414i
$681$			34.5577i			1.32425i
$682$	1.28273	−	0.562224i	0.0491183	−	0.0215287i
$683$		−	2.39383i		−	0.0915974i	−0.998951	−	0.0457987i	$-0.985417\pi$
$683$		−	2.39383i		−	0.0915974i	0.998951	−	0.0457987i	$-0.0145833\pi$
$684$	−1.48817	−	1.08122i	−0.0569015	−	0.0413413i
$685$	−11.7155	−	16.5366i	−0.447628	−	0.631831i
$686$	−10.4264	−	15.3065i	−0.398083	−	0.584406i
$687$	−13.7948	−	18.9869i	−0.526304	−	0.724395i
$688$	−0.637080	+	0.462866i	−0.0242884	+	0.0176466i
$689$	1.01167	+	3.11360i	0.0385415	+	0.118619i
$690$	−9.12728	−	12.8832i	−0.347470	−	0.490456i
$691$	−22.4766	+	30.9364i	−0.855049	+	1.17687i	0.127678	+	0.991816i	$0.459248\pi$
$691$	−22.4766	+	30.9364i	−0.855049	+	1.17687i	−0.982727	+	0.185059i	$0.940752\pi$
$692$		−	19.8277i		−	0.753735i
$693$	0.791685	−	6.53118i	0.0300736	−	0.248099i
$694$	5.14714			0.195383
$695$	14.1343	+	45.3350i	0.536143	+	1.71965i
$696$	−3.42346	−	1.11235i	−0.129766	−	0.0421635i
$697$	−2.08310	+	0.676839i	−0.0789029	+	0.0256371i
$698$	4.14097	−	3.00859i	0.156738	−	0.113877i
$699$	1.02324	−	0.743428i	0.0387025	−	0.0281190i
$700$	10.1260	−	8.51262i	0.382726	−	0.321747i
$701$	−10.0187	−	3.25527i	−0.378401	−	0.122950i	0.113640	−	0.993522i	$-0.463749\pi$
$701$	−10.0187	−	3.25527i	−0.378401	−	0.122950i	−0.492041	+	0.870572i	$0.663749\pi$
$702$	1.07673	−	1.48199i	0.0406384	−	0.0559340i
$703$		−	7.93947i		−	0.299443i
$704$	−2.86262	−	1.67493i	−0.107889	−	0.0631263i
$705$	17.2610	+	12.8584i	0.650086	+	0.484275i
$706$	2.71214	+	1.97048i	0.102073	+	0.0741601i
$707$	9.41961	−	42.2121i	0.354261	−	1.58755i
$708$	5.02190	−	1.63171i	0.188735	−	0.0613236i
$709$	39.3761	−	28.6084i	1.47880	−	1.07441i	0.500861	−	0.865528i	$-0.333017\pi$
$709$	39.3761	−	28.6084i	1.47880	−	1.07441i	0.977940	−	0.208884i	$-0.0669832\pi$
$710$	−12.5920	−	0.150307i	−0.472569	−	0.00564094i
$711$	0.165300	−	0.0537091i	0.00619922	−	0.00201425i
$712$	9.47390	+	3.07826i	0.355049	+	0.115363i
$713$	−1.60806	−	1.16832i	−0.0602222	−	0.0437540i
$714$	−0.201858	−	2.12727i	−0.00755433	−	0.0796112i
$715$	−1.24449	+	2.06987i	−0.0465412	+	0.0774088i
$716$	−11.1412			−0.416367
$717$	−7.34289	+	10.1066i	−0.274225	+	0.377439i
$718$	14.6734	+	4.76767i	0.547606	+	0.177928i
$719$	−20.8648	+	6.77937i	−0.778124	+	0.252828i	−0.671039	−	0.741422i	$-0.734152\pi$
$719$	−20.8648	+	6.77937i	−0.778124	+	0.252828i	−0.107085	+	0.994250i	$0.534152\pi$
$720$	1.67636	+	0.0200103i	0.0624743	+	0.000745739i
$721$	−24.7923	+	21.8732i	−0.923313	+	0.814600i
$722$	−4.01119	−	12.3452i	−0.149281	−	0.459440i
$723$	−6.59392	+	20.2940i	−0.245230	+	0.754741i
$724$	10.0233	−	13.7959i	0.372514	−	0.512721i
$725$	−11.4961	+	3.43419i	−0.426956	+	0.127543i
$726$	11.1827	−	12.1338i	0.415028	−	0.450327i
$727$	19.2838			0.715197			0.357599	−	0.933875i	$-0.383596\pi$
$727$	19.2838			0.715197			0.357599	+	0.933875i	$0.383596\pi$
$728$	−0.438336	+	0.741794i	−0.0162458	+	0.0274927i
$729$	9.25616	−	28.4875i	0.342821	−	1.05509i
$730$	30.0414	+	10.1590i	1.11188	+	0.376003i
$731$	0.249207	+	0.343004i	0.00921724	+	0.0126864i
$732$	3.90861	−	2.83977i	0.144466	−	0.104961i
$733$	20.2610	−	6.58320i	0.748357	−	0.243156i	0.0900830	−	0.995934i	$-0.471287\pi$
$733$	20.2610	−	6.58320i	0.748357	−	0.243156i	0.658274	+	0.752778i	$0.271287\pi$
$734$	−3.88417	+	11.9542i	−0.143367	+	0.441239i
$735$	11.0801	+	20.7013i	0.408695	+	0.763579i
$736$			4.70703i			0.173504i
$737$	−1.01611	−	10.2380i	−0.0374289	−	0.377123i
$738$	3.05008			0.112275
$739$	29.1699	−	40.1489i	1.07303	−	1.47690i	0.206062	−	0.978539i	$-0.433935\pi$
$739$	29.1699	−	40.1489i	1.07303	−	1.47690i	0.866969	−	0.498362i	$-0.166065\pi$
$740$	4.18301	+	5.90436i	0.153771	+	0.217048i
$741$	−1.13991	+	0.370380i	−0.0418758	+	0.0136063i
$742$	−17.5962	−	19.9445i	−0.645977	−	0.732187i
$743$	36.3102	−	26.3809i	1.33209	−	0.967822i	0.332397	−	0.943140i	$-0.392143\pi$
$743$	36.3102	−	26.3809i	1.33209	−	0.967822i	0.999695	−	0.0246822i	$-0.00785740\pi$
$744$	−0.602447	+	0.195747i	−0.0220868	+	0.00717643i
$745$	−12.5929	−	17.7750i	−0.461369	−	0.651227i
$746$	30.2749	+	21.9960i	1.10844	+	0.805331i
$747$			8.37749i			0.306516i
$748$	−0.901782	+	1.54123i	−0.0329724	+	0.0563531i
$749$	−8.52840	+	0.809263i	−0.311621	+	0.0295698i
$750$	−13.9126	+	9.36594i	−0.508017	+	0.341996i
$751$	−1.54932	+	4.76832i	−0.0565355	+	0.173998i	−0.975337	−	0.220722i	$-0.929159\pi$
$751$	−1.54932	+	4.76832i	−0.0565355	+	0.173998i	0.918801	+	0.394721i	$0.129159\pi$
$752$	−1.98291	−	6.10277i	−0.0723093	−	0.222545i
$753$	−8.47512	−	11.6650i	−0.308851	−	0.425096i
$754$	0.632223	−	0.459337i	0.0230242	−	0.0167281i
$755$	11.9554	+	4.04293i	0.435101	+	0.147137i
$756$	−3.24123	+	14.5249i	−0.117882	+	0.528267i
$757$	24.1802	−	33.2812i	0.878843	−	1.20962i	−0.0978964	−	0.995197i	$-0.531211\pi$
$757$	24.1802	−	33.2812i	0.878843	−	1.20962i	0.976740	−	0.214428i	$-0.0687886\pi$
$758$	−25.0971			−0.911567
$759$	−22.8782	−	5.00165i	−0.830425	−	0.181549i
$760$	−4.39956	−	3.27741i	−0.159589	−	0.118884i
$761$	−36.0123	−	26.1645i	−1.30544	−	0.948461i	−0.305452	−	0.952208i	$-0.598807\pi$
$761$	−36.0123	−	26.1645i	−1.30544	−	0.948461i	−0.999993	+	0.00374636i	$0.998807\pi$
$762$	5.55485	−	17.0961i	0.201231	−	0.619325i
$763$	44.0167	−	19.0665i	1.59351	−	0.690254i
$764$	14.5488	−	10.5703i	0.526355	−	0.382420i
$765$	0.0107735	−	0.902552i	0.000389518	−	0.0326318i
$766$	5.86432	+	18.0485i	0.211887	+	0.652120i
$767$	−0.354240	+	1.09024i	−0.0127909	+	0.0393662i
$768$	1.21359	+	0.881728i	0.0437918	+	0.0318166i
$769$	19.1126			0.689217			0.344609	−	0.938746i	$-0.388012\pi$
$769$	19.1126			0.689217			0.344609	+	0.938746i	$0.388012\pi$
$770$	2.59348	−	19.4493i	0.0934626	−	0.700903i
$771$	22.9181			0.825374
$772$	−9.96613	−	7.24082i	−0.358689	−	0.260603i
$773$	−13.2208	+	40.6895i	−0.475520	+	1.46350i	0.369736	+	0.929137i	$0.379448\pi$
$773$	−13.2208	+	40.6895i	−0.475520	+	1.46350i	−0.845256	+	0.534362i	$0.820552\pi$
$774$	−0.182445	−	0.561508i	−0.00655785	−	0.0201830i
$775$	−1.28146	+	1.67803i	−0.0460314	+	0.0602768i
$776$	9.86605	−	7.16810i	0.354170	−	0.257320i
$777$	−11.7851	+	5.10491i	−0.422789	+	0.183138i
$778$	4.11649	−	12.6693i	0.147583	−	0.454215i
$779$	−8.07489	−	5.86675i	−0.289313	−	0.210198i
$780$	0.652582	−	0.876020i	0.0233662	−	0.0313665i
$781$	−13.9529	+	12.4176i	−0.499273	+	0.444335i
$782$	2.53426			0.0906251
$783$	7.93377	−	10.9199i	0.283530	−	0.390245i
$784$	0.872342	−	6.94543i	0.0311551	−	0.248051i
$785$	−13.7416	+	40.6355i	−0.490460	+	1.45034i
$786$	−12.3741	+	8.99029i	−0.441369	+	0.320673i
$787$	−4.14868	−	5.71017i	−0.147885	−	0.203546i	0.728648	−	0.684889i	$-0.240149\pi$
$787$	−4.14868	−	5.71017i	−0.147885	−	0.203546i	−0.876532	+	0.481343i	$0.840149\pi$
$788$	−0.0637826	−	0.196303i	−0.00227216	−	0.00699300i
$789$	−0.649615	+	1.99931i	−0.0231269	+	0.0711773i
$790$	0.494873	−	0.154288i	0.0176068	−	0.00548933i
$791$	−2.09148	−	22.0410i	−0.0743643	−	0.783687i
$792$	1.85753	−	1.65314i	0.0660045	−	0.0587417i
$793$			1.04886i			0.0372461i
$794$	−26.3331	−	19.1321i	−0.934525	−	0.678972i
$795$	19.4931	+	27.5147i	0.691349	+	0.975846i
$796$	21.2015	−	6.88878i	0.751466	−	0.244166i
$797$	4.11659	−	2.99088i	0.145817	−	0.105942i	−0.512485	−	0.858696i	$-0.671275\pi$
$797$	4.11659	−	2.99088i	0.145817	−	0.105942i	0.658302	+	0.752754i	$0.271275\pi$
$798$	7.30186	−	6.44212i	0.258483	−	0.228049i
$799$	−3.28573	+	1.06760i	−0.116241	+	0.0377689i
$800$	4.99858	+	0.119350i	0.176726	+	0.00421967i
$801$	−4.38990	+	6.04218i	−0.155109	+	0.213490i
$802$	−18.2893			−0.645819
$803$	43.0810	−	18.8825i	1.52030	−	0.666349i
$804$			4.65334i			0.164111i
$805$	−25.6832	+	10.7628i	−0.905214	+	0.379340i
$806$	0.0424960	−	0.130789i	0.00149686	−	0.00460686i
$807$	−17.1195	+	5.56247i	−0.602636	+	0.195808i
$808$	13.2251	−	9.60858i	0.465257	−	0.338029i
$809$	8.93070	+	12.2921i	0.313987	+	0.432166i	0.936619	−	0.350349i	$-0.113937\pi$
$809$	8.93070	+	12.2921i	0.313987	+	0.432166i	−0.622633	+	0.782514i	$0.713937\pi$
$810$	4.43303	−	13.1090i	0.155761	−	0.460602i
$811$	5.34308	−	16.4443i	0.187621	−	0.577438i	−0.812363	−	0.583152i	$-0.801819\pi$
$811$	5.34308	−	16.4443i	0.187621	−	0.577438i	0.999984	+	0.00571471i	$0.00181906\pi$
$812$	−3.22984	+	5.46585i	−0.113345	+	0.191814i
$813$	37.4030			1.31178
$814$	10.4850	+	2.29225i	0.367499	+	0.0803432i
$815$	14.3543	−	19.2690i	0.502808	−	0.674965i
$816$	0.474722	−	0.653399i	0.0166186	−	0.0228735i
$817$	−0.597034	+	1.83748i	−0.0208876	+	0.0642854i
$818$	−7.94158	−	24.4417i	−0.277671	−	0.854583i
$819$	−0.427381	−	0.484417i	−0.0149339	−	0.0169269i
$820$	9.09604	+	0.108577i	0.317648	+	0.00379168i
$821$	48.4617	−	15.7462i	1.69132	−	0.549545i	0.704271	−	0.709932i	$-0.251274\pi$
$821$	48.4617	−	15.7462i	1.69132	−	0.549545i	0.987054	+	0.160387i	$0.0512741\pi$
$822$	12.9302	+	4.20129i	0.450994	+	0.146537i
$823$	−26.8446	+	36.9484i	−0.935743	+	1.28794i	0.0218344	+	0.999762i	$0.493049\pi$
$823$	−26.8446	+	36.9484i	−0.935743	+	1.28794i	−0.957577	+	0.288178i	$0.906951\pi$
$824$	−12.4962			−0.435327
$825$	−5.89154	+	24.1684i	−0.205117	+	0.841435i
$826$	−0.879772	−	9.27147i	−0.0306112	−	0.322596i
$827$	−34.3516	−	24.9579i	−1.19452	−	0.867872i	−0.200788	−	0.979635i	$-0.564350\pi$
$827$	−34.3516	−	24.9579i	−1.19452	−	0.867872i	−0.993735	+	0.111763i	$0.964350\pi$
$828$	−3.35635	−	1.09054i	−0.116641	−	0.0378990i
$829$	−39.6396	+	12.8797i	−1.37674	+	0.447331i	−0.901597	−	0.432577i	$-0.857604\pi$
$829$	−39.6396	+	12.8797i	−1.37674	+	0.447331i	−0.475145	+	0.879908i	$0.657604\pi$
$830$	−0.298222	+	24.9836i	−0.0103515	+	0.867192i
$831$	−9.33290	+	6.78075i	−0.323755	+	0.235222i
$832$	−0.309724	+	0.100636i	−0.0107378	+	0.00348891i
$833$	−3.73942	−	0.469669i	−0.129563	−	0.0162731i
$834$	−25.7730	−	18.7252i	−0.892447	−	0.648400i
$835$	10.5660	−	14.1837i	0.365652	−	0.490847i
$836$	−8.09745	+	0.803659i	−0.280056	+	0.0277951i
$837$		−	2.37528i		−	0.0821016i
$838$	0.0447652	−	0.0616140i	0.00154639	−	0.00212842i
$839$	39.9478	+	12.9798i	1.37915	+	0.448113i	0.902390	−	0.430920i	$-0.141811\pi$
$839$	39.9478	+	12.9798i	1.37915	+	0.448113i	0.476761	+	0.879033i	$0.341811\pi$
$840$	−2.03607	+	8.63790i	−0.0702512	+	0.298036i
$841$	−18.8030	+	13.6612i	−0.648380	+	0.471075i
$842$	2.05018	−	1.48954i	0.0706539	−	0.0513330i
$843$	17.7302	−	5.76091i	0.610662	−	0.198416i
$844$	−4.13736	−	1.34431i	−0.142414	−	0.0462731i
$845$	−8.58157	−	27.5250i	−0.295215	−	0.946889i
$846$	4.81099			0.165405
$847$	−16.5915	−	23.9107i	−0.570090	−	0.821582i
$848$		−	10.0528i		−	0.345215i
$849$	19.7674	−	27.2075i	0.678416	−	0.933760i
$850$	0.0642582	−	2.69123i	0.00220404	−	0.0923085i
$851$	−4.70696	−	14.4865i	−0.161352	−	0.496592i
$852$	6.83462	−	4.96564i	0.234150	−	0.170120i
$853$	−4.59884	−	6.32976i	−0.157461	−	0.216727i	0.722996	−	0.690852i	$-0.242764\pi$
$853$	−4.59884	−	6.32976i	−0.157461	−	0.216727i	−0.880457	+	0.474125i	$0.842764\pi$
$854$	−3.38696	−	7.81910i	−0.115899	−	0.267564i
$855$	3.35626	−	2.37778i	0.114782	−	0.0813185i
$856$	−2.61953	−	1.90320i	−0.0895336	−	0.0650500i
$857$		−	7.83870i		−	0.267765i	−0.990997	−	0.133882i	$-0.957256\pi$
$857$		−	7.83870i		−	0.267765i	0.990997	−	0.133882i	$-0.0427445\pi$
$858$	−0.160021	−	1.61233i	−0.00546302	−	0.0550439i
$859$			39.2036i			1.33761i	0.743438	+	0.668805i	$0.233194\pi$
$859$			39.2036i			1.33761i	−0.743438	+	0.668805i	$0.766806\pi$
$860$	−0.524104	−	1.68104i	−0.0178718	−	0.0573230i
$861$	−3.51647	+	15.7584i	−0.119841	+	0.537043i
$862$	−17.0007	+	5.52385i	−0.579045	+	0.188143i
$863$	11.4844	+	15.8070i	0.390935	+	0.538075i	0.958440	−	0.285294i	$-0.0920914\pi$
$863$	11.4844	+	15.8070i	0.390935	+	0.538075i	−0.567505	+	0.823370i	$0.692091\pi$
$864$	−4.55067	+	3.30625i	−0.154817	+	0.112481i
$865$	41.9995	+	14.2029i	1.42803	+	0.482913i
$866$	−0.0743891	+	0.228946i	−0.00252784	+	0.00777991i
$867$	20.2793	+	14.7338i	0.688722	+	0.500386i
$868$	0.105541	+	1.11224i	0.00358230	+	0.0377520i
$869$	0.388283	−	0.663615i	0.0131716	−	0.0225116i
$870$	4.80850	−	6.45488i	0.163023	−	0.218841i
$871$	−0.817289	−	0.593795i	−0.0276928	−	0.0201200i
$872$	17.2431	+	5.60263i	0.583926	+	0.189729i
$873$	2.82541	+	8.69572i	0.0956256	+	0.294305i
$874$	6.78807	+	9.34298i	0.229610	+	0.316031i
$875$	10.7783	+	27.5469i	0.364371	+	0.931254i
$876$	−20.2334	+	6.57424i	−0.683624	+	0.222123i
$877$	−6.70334	+	20.6308i	−0.226356	+	0.696651i	0.771795	+	0.635871i	$0.219359\pi$
$877$	−6.70334	+	20.6308i	−0.226356	+	0.696651i	−0.998151	+	0.0607804i	$0.980641\pi$
$878$	−12.1765	−	8.84671i	−0.410935	−	0.298562i
$879$			12.0826i			0.407537i
$880$	5.59843	−	4.86391i	0.188723	−	0.163962i
$881$			20.0203i			0.674503i	0.941415	+	0.337251i	$0.109497\pi$
$881$			20.0203i			0.674503i	−0.941415	+	0.337251i	$0.890503\pi$
$882$	4.75033	+	2.23117i	0.159952	+	0.0751273i
$883$	26.8896	+	8.73697i	0.904908	+	0.294023i	0.724261	−	0.689525i	$-0.242181\pi$
$883$	26.8896	+	8.73697i	0.904908	+	0.294023i	0.180647	+	0.983548i	$0.442181\pi$
$884$	0.0541822	+	0.166756i	0.00182234	+	0.00560860i
$885$	−0.140929	+	11.8064i	−0.00473729	+	0.396866i
$886$	12.7176	+	17.5043i	0.427257	+	0.588068i
$887$	3.39804	−	1.10409i	0.114095	−	0.0370717i	−0.251413	−	0.967880i	$-0.580895\pi$
$887$	3.39804	−	1.10409i	0.114095	−	0.0370717i	0.365508	+	0.930808i	$0.380895\pi$
$888$	−4.61671	−	1.50006i	−0.154927	−	0.0503388i
$889$	−27.2953	−	16.1292i	−0.915455	−	0.540955i
$890$	−13.3068	+	17.8629i	−0.446044	+	0.598765i
$891$	−8.23964	−	18.7990i	−0.276038	−	0.629789i
$892$	−15.3240			−0.513084
$893$	−12.7368	−	9.25380i	−0.426219	−	0.309666i
$894$	13.8986	+	4.51592i	0.464838	+	0.151035i
$895$	7.98064	−	23.5996i	0.266763	−	0.788849i
$896$	1.98398	−	1.75038i	0.0662801	−	0.0584761i
$897$	−1.86033	+	1.35161i	−0.0621146	+	0.0451289i
$898$	10.7707	+	33.1488i	0.359423	+	1.10619i
$899$	0.313129	−	0.963711i	0.0104434	−	0.0321415i
$900$	−1.24319	+	3.53658i	−0.0414397	+	0.117886i
$901$	−5.41242			−0.180314
$902$	10.0791	−	8.97003i	0.335597	−	0.298669i
$903$	3.11139	−	0.295241i	0.103541	−	0.00982501i
$904$	4.91866	−	6.76996i	0.163592	−	0.225166i
$905$	22.0430	+	31.1139i	0.732735	+	1.03426i
$906$	−8.05217	+	2.61631i	−0.267515	+	0.0869210i
$907$	−29.8232	−	41.0481i	−0.990263	−	1.36298i	−0.931113	−	0.364732i	$-0.881161\pi$
$907$	−29.8232	−	41.0481i	−0.990263	−	1.36298i	−0.0591508	−	0.998249i	$-0.518839\pi$
$908$	13.5409	+	18.6374i	0.449370	+	0.618505i
$909$	3.78736	+	11.6563i	0.125619	+	0.386615i
$910$	−1.25730	−	1.45986i	−0.0416791	−	0.0483938i
$911$	−6.36351	−	4.62336i	−0.210832	−	0.153179i	0.477358	−	0.878709i	$-0.341595\pi$
$911$	−6.36351	−	4.62336i	−0.210832	−	0.153179i	−0.688190	+	0.725530i	$0.741595\pi$
$912$	3.68041			0.121871
$913$	24.6375	+	27.6836i	0.815381	+	0.916195i
$914$	−38.4515			−1.27186
$915$	3.21548	+	10.3135i	0.106300	+	0.340954i
$916$	−14.8794	−	4.83462i	−0.491630	−	0.159740i
$917$	10.7226	+	24.7541i	0.354092	+	0.817453i
$918$	1.78009	+	2.45008i	0.0587516	+	0.0808646i
$919$	−5.87938	−	8.09228i	−0.193943	−	0.266940i	0.700960	−	0.713201i	$-0.252755\pi$
$919$	−5.87938	−	8.09228i	−0.193943	−	0.266940i	−0.894903	+	0.446261i	$0.852755\pi$
$920$	−9.97057	−	3.37173i	−0.328720	−	0.111163i
$921$	−36.7470	−	11.9398i	−1.21085	−	0.393430i
$922$	−17.5177	−	12.7274i	−0.576916	−	0.419154i
$923$			1.83404i			0.0603683i
$924$	6.39943	+	11.5029i	0.210526	+	0.378418i
$925$	−15.5031	+	4.63118i	−0.509740	+	0.152272i
$926$	6.69231	−	9.21118i	0.219923	−	0.302698i
$927$	2.89518	−	8.91044i	0.0950901	−	0.292657i
$928$	−2.28218	+	0.741525i	−0.0749162	+	0.0243417i
$929$	−14.4883	−	19.9414i	−0.475345	−	0.654256i	0.502257	−	0.864718i	$-0.332503\pi$
$929$	−14.4883	−	19.9414i	−0.475345	−	0.654256i	−0.977602	+	0.210462i	$0.932503\pi$
$930$	0.0169065	−	1.41634i	0.000554385	−	0.0464435i
$931$	−8.28459	−	15.0440i	−0.271516	−	0.493047i
$932$	0.260547	−	0.801883i	0.00853452	−	0.0262665i
$933$	−22.8341	+	31.4284i	−0.747554	+	1.02892i
$934$	10.2512			0.335430
$935$	−2.61873	−	3.01419i	−0.0856415	−	0.0985746i
$936$		−	0.244165i		−	0.00798077i
$937$	−5.55066	+	7.63983i	−0.181332	+	0.249582i	−0.890001	−	0.455959i	$-0.849296\pi$
$937$	−5.55066	+	7.63983i	−0.181332	+	0.249582i	0.708668	+	0.705542i	$0.249296\pi$
$938$	8.01024	+	1.78748i	0.261544	+	0.0583633i
$939$	−0.433608	−	1.33451i	−0.0141503	−	0.0435500i
$940$	14.3475	+	0.171262i	0.467962	+	0.00558595i
$941$	29.7671	−	21.6271i	0.970380	−	0.705022i	0.0148418	−	0.999890i	$-0.495276\pi$
$941$	29.7671	−	21.6271i	0.970380	−	0.705022i	0.955538	+	0.294868i	$0.0952755\pi$
$942$	−8.89266	−	27.3688i	−0.289738	−	0.891723i
$943$	−18.2118	−	5.91736i	−0.593056	−	0.192696i
$944$	2.06902	−	2.84776i	0.0673408	−	0.0926867i
$945$	−28.4454	−	17.2701i	−0.925328	−	0.561797i
$946$	−2.25424	−	1.31896i	−0.0732917	−	0.0428832i
$947$			36.4830i			1.18554i	0.805372	+	0.592770i	$0.201966\pi$
$947$			36.4830i			1.18554i	−0.805372	+	0.592770i	$0.798034\pi$
$948$	−0.204403	+	0.281336i	−0.00663869	+	0.00913737i
$949$	1.42725	−	4.39261i	0.0463304	−	0.142590i
$950$	10.0938	−	6.97161i	0.327485	−	0.226189i
$951$	17.5688	+	24.1814i	0.569708	+	0.784136i
$952$	−0.942404	−	1.06817i	−0.0305435	−	0.0346197i
$953$	−0.742332	−	2.28466i	−0.0240465	−	0.0740075i	0.938313	−	0.345787i	$-0.112388\pi$
$953$	−0.742332	−	2.28466i	−0.0240465	−	0.0740075i	−0.962360	+	0.271779i	$0.912388\pi$
$954$	7.16815	+	2.32907i	0.232077	+	0.0754065i
$955$	11.9688	+	38.3893i	0.387300	+	1.24225i
$956$			8.32784i			0.269342i
$957$	−1.17910	−	11.8803i	−0.0381149	−	0.384035i
$958$	−29.4938			−0.952900
$959$	12.1990	−	20.6442i	0.393925	−	0.666637i
$960$	−2.73702	+	1.93907i	−0.0883369	+	0.0625833i
$961$	9.52442	+	29.3132i	0.307239	+	0.945586i
$962$	0.852585	−	0.619439i	0.0274884	−	0.0199715i
$963$	1.96398	−	1.42691i	0.0632883	−	0.0459816i
$964$	4.39569	+	13.5286i	0.141576	+	0.435725i
$965$	22.4766	−	15.9238i	0.723548	−	0.512606i
$966$	9.50389	−	16.0834i	0.305783	−	0.517474i
$967$	5.56857			0.179073			0.0895366	−	0.995984i	$-0.471461\pi$
$967$	5.56857			0.179073			0.0895366	+	0.995984i	$0.471461\pi$
$968$	1.27653	−	10.9257i	0.0410293	−	0.351165i
$969$		−	1.98153i		−	0.0636560i
$970$	8.11646	+	26.0332i	0.260604	+	0.835875i
$971$	55.5827	+	18.0599i	1.78373	+	0.579570i	0.999180	−	0.0404922i	$-0.0128926\pi$
$971$	55.5827	+	18.0599i	1.78373	+	0.579570i	0.784553	+	0.620062i	$0.212893\pi$
$972$	−2.34584	−	7.21976i	−0.0752430	−	0.231574i
$973$	−42.1336	+	37.1727i	−1.35074	+	1.19170i
$974$	10.9009	+	15.0038i	0.349288	+	0.480753i
$975$	1.38815	+	2.00983i	0.0444565	+	0.0643659i
$976$	0.995247	−	3.06306i	0.0318571	−	0.0980460i
$977$	−1.27013	+	1.74818i	−0.0406351	+	0.0559294i	−0.828851	−	0.559469i	$-0.811005\pi$
$977$	−1.27013	+	1.74818i	−0.0406351	+	0.0559294i	0.788216	+	0.615399i	$0.211005\pi$
$978$			16.1193i			0.515439i
$979$	3.26298	+	32.8769i	0.104285	+	1.05075i
$980$	14.0871	+	6.82295i	0.449997	+	0.217951i
$981$	−7.98991	+	10.9972i	−0.255098	+	0.351112i
$982$	0.239562	+	0.0778386i	0.00764474	+	0.00248393i
$983$	12.6820	+	39.0311i	0.404492	+	1.24490i	0.921318	+	0.388809i	$0.127113\pi$
$983$	12.6820	+	39.0311i	0.404492	+	1.24490i	−0.516826	+	0.856090i	$0.672887\pi$
$984$	−4.93710	+	3.58701i	−0.157389	+	0.114350i
$985$	0.461503	+	0.00550884i	0.0147047	+	0.000175526i
$986$	0.399237	+	1.22872i	0.0127143	+	0.0391306i
$987$	−5.54662	+	24.8561i	−0.176551	+	0.791179i
$988$	−0.469644	+	0.646409i	−0.0149414	+	0.0205650i
$989$			3.70667i			0.117865i
$990$	2.17114	+	5.11885i	0.0690034	+	0.162688i
$991$	−38.7228			−1.23007			−0.615035	−	0.788499i	$-0.710858\pi$
$991$	−38.7228			−1.23007			−0.615035	+	0.788499i	$0.710858\pi$
$992$	−0.248208	+	0.341629i	−0.00788061	+	0.0108467i
$993$	6.69461	−	20.6039i	0.212447	−	0.653845i
$994$	−5.92246	−	13.6725i	−0.187849	−	0.433666i
$995$	−0.594976	+	49.8441i	−0.0188620	+	1.58016i
$996$	−9.85224	−	13.5604i	−0.312180	−	0.429679i
$997$	−24.4555	+	7.94609i	−0.774515	+	0.251655i	−0.669496	−	0.742815i	$-0.733490\pi$
$997$	−24.4555	+	7.94609i	−0.774515	+	0.251655i	−0.105018	+	0.994470i	$0.533490\pi$
$998$	−6.64170	+	20.4410i	−0.210239	+	0.647050i
$999$	10.6991	−	14.7260i	0.338504	−	0.465911i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.w.a.139.7	✓	96
5.4	even	2		770.2.w.b.139.18	yes	96
7.6	odd	2	inner	770.2.w.a.139.18	yes	96
11.8	odd	10		770.2.w.b.349.7	yes	96
35.34	odd	2		770.2.w.b.139.7	yes	96
55.19	odd	10	inner	770.2.w.a.349.18	yes	96
77.41	even	10		770.2.w.b.349.18	yes	96
385.349	even	10	inner	770.2.w.a.349.7	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.w.a.139.7	✓	96	1.1	even	1	trivial
770.2.w.a.139.18	yes	96	7.6	odd	2	inner
770.2.w.a.349.7	yes	96	385.349	even	10	inner
770.2.w.a.349.18	yes	96	55.19	odd	10	inner
770.2.w.b.139.7	yes	96	35.34	odd	2
770.2.w.b.139.18	yes	96	5.4	even	2
770.2.w.b.349.7	yes	96	11.8	odd	10
770.2.w.b.349.18	yes	96	77.41	even	10

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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.w (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.463552 + 1.42667i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.23591 - 0.0266895i) q^{5} +(1.21359 - 0.881728i) q^{6} +(-1.05163 - 2.42777i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.606556 + 0.440689i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.463552 + 1.42667i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.23591 - 0.0266895i) q^{5} +(1.21359 - 0.881728i) q^{6} +(-1.05163 - 2.42777i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.606556 + 0.440689i) q^{9} +(1.79320 + 1.33583i) q^{10} +(3.30041 - 0.327560i) q^{11} -1.50009 q^{12} +(0.191420 - 0.263467i) q^{13} +(-0.576225 + 2.58224i) q^{14} +(1.07454 - 3.17752i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(0.316463 + 0.435574i) q^{17} +(-0.231684 - 0.713050i) q^{18} +(-0.758164 + 2.33339i) q^{19} +(-0.665551 - 2.13472i) q^{20} +(3.95110 - 0.374922i) q^{21} +(-2.86262 - 1.67493i) q^{22} +4.70703i q^{23} +(1.21359 + 0.881728i) q^{24} +(4.99858 + 0.119350i) q^{25} +(-0.309724 + 0.100636i) q^{26} +(-4.55067 + 3.30625i) q^{27} +(1.98398 - 1.75038i) q^{28} +(-2.28218 + 0.741525i) q^{29} +(-2.73702 + 1.93907i) q^{30} +(-0.248208 + 0.341629i) q^{31} +1.00000 q^{32} +(-1.06259 + 4.86042i) q^{33} -0.538400i q^{34} +(2.28655 + 5.45635i) q^{35} +(-0.231684 + 0.713050i) q^{36} +(-3.07763 + 0.999984i) q^{37} +(1.98490 - 1.44211i) q^{38} +(0.287147 + 0.395224i) q^{39} +(-0.716317 + 2.11823i) q^{40} +(-1.25713 + 3.86905i) q^{41} +(-3.41688 - 2.01908i) q^{42} +0.787474 q^{43} +(1.33141 + 3.03765i) q^{44} +(-1.34444 - 1.00153i) q^{45} +(2.76672 - 3.80807i) q^{46} +(-1.98291 + 6.10277i) q^{47} +(-0.463552 - 1.42667i) q^{48} +(-4.78816 + 5.10622i) q^{49} +(-3.97378 - 3.03465i) q^{50} +(-0.768116 + 0.249576i) q^{51} +(0.309724 + 0.100636i) q^{52} +(-5.90889 + 8.13289i) q^{53} +5.62494 q^{54} +(-7.38816 + 0.644309i) q^{55} +(-2.63392 + 0.249934i) q^{56} +(-2.97752 - 2.16329i) q^{57} +(2.28218 + 0.741525i) q^{58} +(-3.34774 + 1.08775i) q^{59} +(3.35405 + 0.0400365i) q^{60} +(-2.60559 + 1.89307i) q^{61} +(0.401609 - 0.130491i) q^{62} +(0.432022 - 1.93602i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-0.435030 + 0.583980i) q^{65} +(3.71654 - 3.30759i) q^{66} -3.10205i q^{67} +(-0.316463 + 0.435574i) q^{68} +(-6.71536 - 2.18195i) q^{69} +(1.35731 - 5.75827i) q^{70} +(-4.55615 + 3.31024i) q^{71} +(0.606556 - 0.440689i) q^{72} +(13.4882 - 4.38258i) q^{73} +(3.07763 + 0.999984i) q^{74} +(-2.48737 + 7.07597i) q^{75} -2.45347 q^{76} +(-4.26604 - 7.66817i) q^{77} -0.488523i q^{78} +(0.136261 - 0.187547i) q^{79} +(1.82458 - 1.29264i) q^{80} +(-1.91240 - 5.88575i) q^{81} +(3.29121 - 2.39121i) q^{82} +(6.56779 + 9.03978i) q^{83} +(1.57753 + 3.64187i) q^{84} +(-0.695958 - 0.982351i) q^{85} +(-0.637080 - 0.462866i) q^{86} -3.59964i q^{87} +(0.708354 - 3.24010i) q^{88} +9.96145i q^{89} +(0.498993 + 1.60050i) q^{90} +(-0.840942 - 0.187656i) q^{91} +(-4.47665 + 1.45455i) q^{92} +(-0.372333 - 0.512472i) q^{93} +(5.19133 - 3.77172i) q^{94} +(1.75746 - 5.19701i) q^{95} +(-0.463552 + 1.42667i) q^{96} +(9.86605 + 7.16810i) q^{97} +(6.87507 - 1.31661i) q^{98} +(2.14624 + 1.25577i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 24 q^{2} - 24 q^{4} - 3 q^{7} - 24 q^{8} - 18 q^{9}+O(q^{10}) \) 96 * q - 24 * q^2 - 24 * q^4 - 3 * q^7 - 24 * q^8 - 18 * q^9	\( 96 q - 24 q^{2} - 24 q^{4} - 3 q^{7} - 24 q^{8} - 18 q^{9} + 4 q^{11} - 3 q^{14} - 6 q^{15} - 24 q^{16} - 28 q^{18} + 4 q^{22} - 42 q^{25} + 2 q^{28} - 6 q^{30} + 96 q^{32} + 14 q^{35} - 28 q^{36} + 10 q^{39} + 24 q^{43} - 16 q^{44} + 37 q^{49} + 8 q^{50} - 30 q^{51} - 40 q^{53} + 2 q^{56} + 20 q^{57} - 6 q^{60} - 63 q^{63} - 24 q^{64} + 40 q^{65} + 9 q^{70} - 20 q^{71} - 18 q^{72} + 16 q^{77} - 126 q^{81} + 100 q^{85} - 36 q^{86} + 14 q^{88} - 31 q^{91} + 10 q^{92} - 20 q^{93} - 16 q^{95} - 18 q^{98} + 100 q^{99}+O(q^{100}) \) 96 * q - 24 * q^2 - 24 * q^4 - 3 * q^7 - 24 * q^8 - 18 * q^9 + 4 * q^11 - 3 * q^14 - 6 * q^15 - 24 * q^16 - 28 * q^18 + 4 * q^22 - 42 * q^25 + 2 * q^28 - 6 * q^30 + 96 * q^32 + 14 * q^35 - 28 * q^36 + 10 * q^39 + 24 * q^43 - 16 * q^44 + 37 * q^49 + 8 * q^50 - 30 * q^51 - 40 * q^53 + 2 * q^56 + 20 * q^57 - 6 * q^60 - 63 * q^63 - 24 * q^64 + 40 * q^65 + 9 * q^70 - 20 * q^71 - 18 * q^72 + 16 * q^77 - 126 * q^81 + 100 * q^85 - 36 * q^86 + 14 * q^88 - 31 * q^91 + 10 * q^92 - 20 * q^93 - 16 * q^95 - 18 * q^98 + 100 * q^99

Introduction

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