LMFDB - Embedded newform 231.2.w.a.118.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(13,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 1]))

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

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

chi := DirichletCharacter("231.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			118.4
Character	$\chi$	$=$	231.118
Dual form			231.2.w.a.139.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.917545 - 1.26289i) q^{2} +(0.951057 - 0.309017i) q^{3} +(-0.134974 + 0.415407i) q^{4} +(-0.118521 + 0.163130i) q^{5} +(-1.26289 - 0.917545i) q^{6} +(-1.29844 - 2.30523i) q^{7} +(-2.32078 + 0.754067i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.917545 - 1.26289i) q^{2} +(0.951057 - 0.309017i) q^{3} +(-0.134974 + 0.415407i) q^{4} +(-0.118521 + 0.163130i) q^{5} +(-1.26289 - 0.917545i) q^{6} +(-1.29844 - 2.30523i) q^{7} +(-2.32078 + 0.754067i) q^{8} +(0.809017 - 0.587785i) q^{9} +0.314765 q^{10} +(-2.08955 - 2.57561i) q^{11} +0.436785i q^{12} +(2.99372 - 2.17507i) q^{13} +(-1.71988 + 3.75493i) q^{14} +(-0.0623103 + 0.191771i) q^{15} +(3.78846 + 2.75247i) q^{16} +(2.75177 + 1.99928i) q^{17} +(-1.48462 - 0.482382i) q^{18} +(-2.21568 - 6.81916i) q^{19} +(-0.0517682 - 0.0712529i) q^{20} +(-1.94724 - 1.79116i) q^{21} +(-1.33547 + 5.00212i) q^{22} -5.47270 q^{23} +(-1.97417 + 1.43432i) q^{24} +(1.53252 + 4.71661i) q^{25} +(-5.49375 - 1.78503i) q^{26} +(0.587785 - 0.809017i) q^{27} +(1.13286 - 0.228234i) q^{28} +(0.476871 + 0.154945i) q^{29} +(0.299359 - 0.0972676i) q^{30} +(6.47776 + 8.91587i) q^{31} -2.42951i q^{32} +(-2.78319 - 1.80385i) q^{33} -5.30962i q^{34} +(0.529944 + 0.0614037i) q^{35} +(0.134974 + 0.415407i) q^{36} +(2.29658 - 7.06815i) q^{37} +(-6.57888 + 9.05505i) q^{38} +(2.17507 - 2.99372i) q^{39} +(0.152050 - 0.467962i) q^{40} +(0.00258650 + 0.00796044i) q^{41} +(-0.475364 + 4.10262i) q^{42} -0.303537i q^{43} +(1.35196 - 0.520373i) q^{44} +0.201640i q^{45} +(5.02145 + 6.91143i) q^{46} +(3.52634 - 1.14578i) q^{47} +(4.45360 + 1.44706i) q^{48} +(-3.62813 + 5.98637i) q^{49} +(4.55042 - 6.26311i) q^{50} +(3.23491 + 1.05108i) q^{51} +(0.499463 + 1.53719i) q^{52} +(8.63924 - 6.27678i) q^{53} -1.56102 q^{54} +(0.667817 - 0.0356044i) q^{55} +(4.75168 + 4.37081i) q^{56} +(-4.21448 - 5.80073i) q^{57} +(-0.241872 - 0.744406i) q^{58} +(11.3604 + 3.69120i) q^{59} +(-0.0712529 - 0.0517682i) q^{60} +(9.17982 + 6.66953i) q^{61} +(5.31615 - 16.3614i) q^{62} +(-2.40543 - 1.10177i) q^{63} +(4.50871 - 3.27577i) q^{64} +0.746158i q^{65} +(0.275635 + 5.16998i) q^{66} -9.00999 q^{67} +(-1.20193 + 0.873256i) q^{68} +(-5.20484 + 1.69116i) q^{69} +(-0.408702 - 0.725603i) q^{70} +(7.99556 + 5.80911i) q^{71} +(-1.43432 + 1.97417i) q^{72} +(-0.608021 + 1.87130i) q^{73} +(-11.0335 + 3.58501i) q^{74} +(2.91503 + 4.01219i) q^{75} +3.13179 q^{76} +(-3.22422 + 8.16115i) q^{77} -5.77647 q^{78} +(-2.00132 - 2.75459i) q^{79} +(-0.898024 + 0.291786i) q^{80} +(0.309017 - 0.951057i) q^{81} +(0.00767994 - 0.0105705i) q^{82} +(-3.53003 - 2.56472i) q^{83} +(1.00689 - 0.567137i) q^{84} +(-0.652287 + 0.211941i) q^{85} +(-0.383335 + 0.278509i) q^{86} +0.501412 q^{87} +(6.79157 + 4.40177i) q^{88} -12.6584i q^{89} +(0.254650 - 0.185014i) q^{90} +(-8.90117 - 4.07702i) q^{91} +(0.738671 - 2.27340i) q^{92} +(8.91587 + 6.47776i) q^{93} +(-4.68256 - 3.40208i) q^{94} +(1.37502 + 0.446770i) q^{95} +(-0.750759 - 2.31060i) q^{96} +(-2.02452 - 2.78652i) q^{97} +(10.8891 - 0.910831i) q^{98} +(-3.20439 - 0.855508i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 12 q^{4} + 10 q^{7} - 20 q^{8} + 16 q^{9}+O(q^{10}) $ 64 * q + 12 * q^4 + 10 * q^7 - 20 * q^8 + 16 * q^9	$ 64 q + 12 q^{4} + 10 q^{7} - 20 q^{8} + 16 q^{9} - 16 q^{11} + 12 q^{14} - 12 q^{15} - 16 q^{16} + 10 q^{18} - 40 q^{22} - 24 q^{23} + 44 q^{25} - 30 q^{28} - 40 q^{29} - 40 q^{35} - 12 q^{36} + 32 q^{37} - 2 q^{42} + 22 q^{44} - 70 q^{46} - 50 q^{49} - 40 q^{51} - 64 q^{53} + 80 q^{56} + 2 q^{58} - 36 q^{60} + 10 q^{63} + 72 q^{64} - 8 q^{67} - 26 q^{70} + 68 q^{71} - 10 q^{72} + 80 q^{74} + 90 q^{77} - 72 q^{78} + 40 q^{79} - 16 q^{81} + 60 q^{84} - 40 q^{85} - 62 q^{86} + 140 q^{88} + 54 q^{91} + 18 q^{92} - 20 q^{93} + 20 q^{95} - 4 q^{99}+O(q^{100}) $ 64 * q + 12 * q^4 + 10 * q^7 - 20 * q^8 + 16 * q^9 - 16 * q^11 + 12 * q^14 - 12 * q^15 - 16 * q^16 + 10 * q^18 - 40 * q^22 - 24 * q^23 + 44 * q^25 - 30 * q^28 - 40 * q^29 - 40 * q^35 - 12 * q^36 + 32 * q^37 - 2 * q^42 + 22 * q^44 - 70 * q^46 - 50 * q^49 - 40 * q^51 - 64 * q^53 + 80 * q^56 + 2 * q^58 - 36 * q^60 + 10 * q^63 + 72 * q^64 - 8 * q^67 - 26 * q^70 + 68 * q^71 - 10 * q^72 + 80 * q^74 + 90 * q^77 - 72 * q^78 + 40 * q^79 - 16 * q^81 + 60 * q^84 - 40 * q^85 - 62 * q^86 + 140 * q^88 + 54 * q^91 + 18 * q^92 - 20 * q^93 + 20 * q^95 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−0.917545	−	1.26289i	−0.648802	−	0.893000i	0.350244	−	0.936658i	$-0.386099\pi$
$2$	−0.917545	−	1.26289i	−0.648802	−	0.893000i	−0.999046	+	0.0436588i	$0.986099\pi$
$3$	0.951057	−	0.309017i	0.549093	−	0.178411i
$3$	0.951057	−	0.309017i	0.549093	−	0.178411i
$4$	−0.134974	+	0.415407i	−0.0674870	+	0.207704i
$5$	−0.118521	+	0.163130i	−0.0530043	+	0.0729541i	−0.834696	−	0.550710i	$-0.814357\pi$
$5$	−0.118521	+	0.163130i	−0.0530043	+	0.0729541i	0.781692	+	0.623665i	$0.214357\pi$
$6$	−1.26289	−	0.917545i	−0.515574	−	0.374586i
$7$	−1.29844	−	2.30523i	−0.490763	−	0.871293i
$7$	−1.29844	−	2.30523i	−0.490763	−	0.871293i
$8$	−2.32078	+	0.754067i	−0.820519	+	0.266603i
$9$	0.809017	−	0.587785i	0.269672	−	0.195928i
$10$	0.314765			0.0995373
$11$	−2.08955	−	2.57561i	−0.630023	−	0.776577i
$11$	−2.08955	−	2.57561i	−0.630023	−	0.776577i
$12$			0.436785i			0.126089i
$13$	2.99372	−	2.17507i	0.830309	−	0.603255i	−0.0893379	−	0.996001i	$-0.528475\pi$
$13$	2.99372	−	2.17507i	0.830309	−	0.603255i	0.919647	+	0.392747i	$0.128475\pi$
$14$	−1.71988	+	3.75493i	−0.459657	+	1.00355i
$15$	−0.0623103	+	0.191771i	−0.0160884	+	0.0495151i
$16$	3.78846	+	2.75247i	0.947114	+	0.688119i
$17$	2.75177	+	1.99928i	0.667403	+	0.484897i	0.869155	−	0.494540i	$-0.164663\pi$
$17$	2.75177	+	1.99928i	0.667403	+	0.484897i	−0.201752	+	0.979437i	$0.564663\pi$
$18$	−1.48462	−	0.482382i	−0.349928	−	0.113698i
$19$	−2.21568	−	6.81916i	−0.508312	−	1.56442i	−0.795130	−	0.606439i	$-0.792598\pi$
$19$	−2.21568	−	6.81916i	−0.508312	−	1.56442i	0.286818	−	0.957985i	$-0.407402\pi$
$20$	−0.0517682	−	0.0712529i	−0.0115757	−	0.0159326i
$21$	−1.94724	−	1.79116i	−0.424923	−	0.390863i
$22$	−1.33547	+	5.00212i	−0.284722	+	1.06645i
$23$	−5.47270			−1.14114			−0.570568	−	0.821250i	$-0.693277\pi$
$23$	−5.47270			−1.14114			−0.570568	+	0.821250i	$0.693277\pi$
$24$	−1.97417	+	1.43432i	−0.402976	+	0.292779i
$25$	1.53252	+	4.71661i	0.306504	+	0.943323i
$26$	−5.49375	−	1.78503i	−1.07741	−	0.350072i
$27$	0.587785	−	0.809017i	0.113119	−	0.155695i
$28$	1.13286	−	0.228234i	0.214091	−	0.0431322i
$29$	0.476871	+	0.154945i	0.0885527	+	0.0287725i	0.352958	−	0.935639i	$-0.385176\pi$
$29$	0.476871	+	0.154945i	0.0885527	+	0.0287725i	−0.264406	+	0.964412i	$0.585176\pi$
$30$	0.299359	−	0.0972676i	0.0546552	−	0.0177586i
$31$	6.47776	+	8.91587i	1.16344	+	1.60134i	0.697640	+	0.716449i	$0.254234\pi$
$31$	6.47776	+	8.91587i	1.16344	+	1.60134i	0.465800	+	0.884890i	$0.345766\pi$
$32$		−	2.42951i		−	0.429480i
$33$	−2.78319	−	1.80385i	−0.484491	−	0.314009i
$34$		−	5.30962i		−	0.910593i
$35$	0.529944	+	0.0614037i	0.0895770	+	0.0103791i
$36$	0.134974	+	0.415407i	0.0224957	+	0.0692345i
$37$	2.29658	−	7.06815i	0.377555	−	1.16200i	−0.564183	−	0.825650i	$-0.690809\pi$
$37$	2.29658	−	7.06815i	0.377555	−	1.16200i	0.941738	−	0.336346i	$-0.109191\pi$
$38$	−6.57888	+	9.05505i	−1.06724	+	1.46892i
$39$	2.17507	−	2.99372i	0.348289	−	0.479379i
$40$	0.152050	−	0.467962i	0.0240412	−	0.0739914i
$41$	0.00258650	+	0.00796044i	0.000403944	+	0.00124321i	0.951258	−	0.308395i	$-0.0997920\pi$
$41$	0.00258650	+	0.00796044i	0.000403944	+	0.00124321i	−0.950854	+	0.309639i	$0.899792\pi$
$42$	−0.475364	+	4.10262i	−0.0733502	+	0.633049i
$43$		−	0.303537i		−	0.0462890i	−0.999732	−	0.0231445i	$-0.992632\pi$
$43$		−	0.303537i		−	0.0462890i	0.999732	−	0.0231445i	$-0.00736779\pi$
$44$	1.35196	−	0.520373i	0.203816	−	0.0784492i
$45$			0.201640i			0.0300588i
$46$	5.02145	+	6.91143i	0.740372	+	1.01903i
$47$	3.52634	−	1.14578i	0.514369	−	0.167129i	−0.0403192	−	0.999187i	$-0.512837\pi$
$47$	3.52634	−	1.14578i	0.514369	−	0.167129i	0.554688	+	0.832058i	$0.312837\pi$
$48$	4.45360	+	1.44706i	0.642821	+	0.208865i
$49$	−3.62813	+	5.98637i	−0.518304	+	0.855196i
$50$	4.55042	−	6.26311i	0.643526	−	0.885738i
$51$	3.23491	+	1.05108i	0.452977	+	0.147181i
$52$	0.499463	+	1.53719i	0.0692631	+	0.213170i
$53$	8.63924	−	6.27678i	1.18669	−	0.862181i	0.193780	−	0.981045i	$-0.437925\pi$
$53$	8.63924	−	6.27678i	1.18669	−	0.862181i	0.992911	+	0.118863i	$0.0379251\pi$
$54$	−1.56102			−0.212428
$55$	0.667817	−	0.0356044i	0.0900484	−	0.00480090i
$56$	4.75168	+	4.37081i	0.634969	+	0.584074i
$57$	−4.21448	−	5.80073i	−0.558221	−	0.768325i
$58$	−0.241872	−	0.744406i	−0.0317594	−	0.0977452i
$59$	11.3604	+	3.69120i	1.47899	+	0.480554i	0.933812	−	0.357765i	$-0.116461\pi$
$59$	11.3604	+	3.69120i	1.47899	+	0.480554i	0.545181	+	0.838319i	$0.316461\pi$
$60$	−0.0712529	−	0.0517682i	−0.00919871	−	0.00668325i
$61$	9.17982	+	6.66953i	1.17535	+	0.853945i	0.991640	−	0.129034i	$-0.0411877\pi$
$61$	9.17982	+	6.66953i	1.17535	+	0.853945i	0.183715	+	0.982980i	$0.441188\pi$
$62$	5.31615	−	16.3614i	0.675152	−	2.07790i
$63$	−2.40543	−	1.10177i	−0.303056	−	0.138809i
$64$	4.50871	−	3.27577i	0.563588	−	0.409471i
$65$			0.746158i			0.0925495i
$66$	0.275635	+	5.16998i	0.0339284	+	0.636380i
$67$	−9.00999			−1.10075			−0.550373	−	0.834919i	$-0.685514\pi$
$67$	−9.00999			−1.10075			−0.550373	+	0.834919i	$0.685514\pi$
$68$	−1.20193	+	0.873256i	−0.145756	+	0.105898i
$69$	−5.20484	+	1.69116i	−0.626590	+	0.203591i
$70$	−0.408702	−	0.725603i	−0.0488492	−	0.0867262i
$71$	7.99556	+	5.80911i	0.948898	+	0.689415i	0.950546	−	0.310584i	$-0.100524\pi$
$71$	7.99556	+	5.80911i	0.948898	+	0.689415i	−0.00164769	+	0.999999i	$0.500524\pi$
$72$	−1.43432	+	1.97417i	−0.169036	+	0.232658i
$73$	−0.608021	+	1.87130i	−0.0711635	+	0.219019i	−0.980313	−	0.197452i	$-0.936733\pi$
$73$	−0.608021	+	1.87130i	−0.0711635	+	0.219019i	0.909149	+	0.416471i	$0.136733\pi$
$74$	−11.0335	+	3.58501i	−1.28262	+	0.416749i
$75$	2.91503	+	4.01219i	0.336598	+	0.463288i
$76$	3.13179			0.359241
$77$	−3.22422	+	8.16115i	−0.367434	+	0.930049i
$78$	−5.77647			−0.654056
$79$	−2.00132	−	2.75459i	−0.225167	−	0.309915i	0.681455	−	0.731860i	$-0.261348\pi$
$79$	−2.00132	−	2.75459i	−0.225167	−	0.309915i	−0.906621	+	0.421945i	$0.861348\pi$
$80$	−0.898024	+	0.291786i	−0.100402	+	0.0326226i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	0.00767994	−	0.0105705i	0.000848108	−	0.00116732i
$83$	−3.53003	−	2.56472i	−0.387471	−	0.281514i	0.376947	−	0.926235i	$-0.376974\pi$
$83$	−3.53003	−	2.56472i	−0.387471	−	0.281514i	−0.764418	+	0.644721i	$0.776974\pi$
$84$	1.00689	−	0.567137i	0.109860	−	0.0618797i
$85$	−0.652287	+	0.211941i	−0.0707505	+	0.0229882i
$86$	−0.383335	+	0.278509i	−0.0413361	+	0.0300324i
$87$	0.501412			0.0537570
$88$	6.79157	+	4.40177i	0.723983	+	0.469230i
$89$		−	12.6584i		−	1.34179i	−0.741553	−	0.670895i	$-0.765910\pi$
$89$		−	12.6584i		−	1.34179i	0.741553	−	0.670895i	$-0.234090\pi$
$90$	0.254650	−	0.185014i	0.0268425	−	0.0195022i
$91$	−8.90117	−	4.07702i	−0.933096	−	0.427388i
$92$	0.738671	−	2.27340i	0.0770118	−	0.237018i
$93$	8.91587	+	6.47776i	0.924533	+	0.671713i
$94$	−4.68256	−	3.40208i	−0.482970	−	0.350898i
$95$	1.37502	+	0.446770i	0.141074	+	0.0458377i
$96$	−0.750759	−	2.31060i	−0.0766240	−	0.235824i
$97$	−2.02452	−	2.78652i	−0.205559	−	0.282928i	0.693773	−	0.720193i	$-0.255947\pi$
$97$	−2.02452	−	2.78652i	−0.205559	−	0.282928i	−0.899332	+	0.437266i	$0.855947\pi$
$98$	10.8891	−	0.910831i	1.09997	−	0.0920078i
$99$	−3.20439	−	0.855508i	−0.322053	−	0.0859818i
$100$	−2.16616			−0.216616
$101$	−4.79881	+	3.48654i	−0.477499	+	0.346924i	−0.800357	−	0.599524i	$-0.795357\pi$
$101$	−4.79881	+	3.48654i	−0.477499	+	0.346924i	0.322857	+	0.946448i	$0.395357\pi$
$102$	−1.64076	−	5.04975i	−0.162460	−	0.500000i
$103$	−11.7416	−	3.81507i	−1.15693	−	0.375910i	−0.333183	−	0.942862i	$-0.608123\pi$
$103$	−11.7416	−	3.81507i	−1.15693	−	0.375910i	−0.823751	+	0.566952i	$0.808123\pi$
$104$	−5.30762	+	7.30531i	−0.520455	+	0.716345i
$105$	0.522982	−	0.105363i	0.0510378	−	0.0102824i
$106$	−15.8538	−	5.15121i	−1.53986	−	0.500329i
$107$	−9.64121	+	3.13262i	−0.932051	+	0.302842i	−0.735401	−	0.677632i	$-0.763006\pi$
$107$	−9.64121	+	3.13262i	−0.932051	+	0.302842i	−0.196650	+	0.980474i	$0.563006\pi$
$108$	0.256736	+	0.353366i	0.0247044	+	0.0340027i
$109$			6.46440i			0.619177i	0.950871	+	0.309589i	$0.100191\pi$
$109$			6.46440i			0.619177i	−0.950871	+	0.309589i	$0.899809\pi$
$110$	−0.657716	−	0.810712i	−0.0627108	−	0.0772983i
$111$		−	7.43189i		−	0.705404i
$112$	1.42601	−	12.3072i	0.134745	−	1.16292i
$113$	3.47746	+	10.7025i	0.327132	+	1.00681i	0.970469	+	0.241225i	$0.0775491\pi$
$113$	3.47746	+	10.7025i	0.327132	+	1.00681i	−0.643338	+	0.765583i	$0.722451\pi$
$114$	−3.45872	+	10.6449i	−0.323939	+	0.996982i
$115$	0.648631	−	0.892763i	0.0604851	−	0.0832506i
$116$	−0.128730	+	0.177182i	−0.0119523	+	0.0164509i
$117$	1.14350	−	3.51933i	0.105717	−	0.325362i
$118$	−5.76204	−	17.7337i	−0.530439	−	1.63252i
$119$	1.03579	−	8.93940i	0.0949509	−	0.819473i
$120$		−	0.492045i		−	0.0449173i
$121$	−2.26756	+	10.7637i	−0.206142	+	0.978522i
$122$		−	17.7127i		−	1.60363i
$123$	0.00491982	+	0.00677155i	0.000443605	+	0.000610570i
$124$	−4.57805	+	1.48750i	−0.411121	+	0.133581i
$125$	−1.90992	−	0.620569i	−0.170828	−	0.0555054i
$126$	0.815683	+	4.04872i	0.0726668	+	0.360689i
$127$	0.947169	−	1.30367i	0.0840476	−	0.115682i	−0.764923	−	0.644122i	$-0.777223\pi$
$127$	0.947169	−	1.30367i	0.0840476	−	0.115682i	0.848970	+	0.528440i	$0.177223\pi$
$128$	−12.8951	−	4.18986i	−1.13977	−	0.370335i
$129$	−0.0937982	−	0.288681i	−0.00825847	−	0.0254170i
$130$	0.942317	−	0.684634i	0.0826467	−	0.0600463i
$131$	6.33693			0.553660			0.276830	−	0.960919i	$-0.410716\pi$
$131$	6.33693			0.553660			0.276830	+	0.960919i	$0.410716\pi$
$132$	1.12499	−	0.912684i	0.0979177	−	0.0794389i
$133$	−12.8428	+	13.9619i	−1.11361	+	1.21065i
$134$	8.26707	+	11.3786i	0.714166	+	0.982965i
$135$	0.0623103	+	0.191771i	0.00536281	+	0.0165050i
$136$	−7.89385	−	2.56487i	−0.676892	−	0.219936i
$137$	−14.4122	−	10.4711i	−1.23132	−	0.894603i	−0.234328	−	0.972158i	$-0.575289\pi$
$137$	−14.4122	−	10.4711i	−1.23132	−	0.894603i	−0.996988	+	0.0775542i	$0.975289\pi$
$138$	6.91143	+	5.02145i	0.588340	+	0.427454i
$139$	−2.95842	+	9.10507i	−0.250930	+	0.772282i	0.743675	+	0.668542i	$0.233081\pi$
$139$	−2.95842	+	9.10507i	−0.250930	+	0.772282i	−0.994604	+	0.103741i	$0.966919\pi$
$140$	−0.0970362	+	0.211855i	−0.00820106	+	0.0179050i
$141$	2.99968	−	2.17940i	0.252619	−	0.183538i
$142$		−	15.4277i		−	1.29466i
$143$	−11.8577	−	3.16576i	−0.991587	−	0.264734i
$144$	4.68279			0.390232
$145$	−0.0817955	+	0.0594279i	−0.00679275	+	0.00493522i
$146$	2.92113	−	0.949133i	0.241755	−	0.0785508i
$147$	−1.60066	+	6.81453i	−0.132021	+	0.562053i
$148$	2.62618	+	1.90803i	0.215871	+	0.156839i
$149$	1.72858	−	2.37919i	0.141611	−	0.194911i	−0.732320	−	0.680961i	$-0.761563\pi$
$149$	1.72858	−	2.37919i	0.141611	−	0.194911i	0.873931	+	0.486049i	$0.161563\pi$
$150$	2.39230	−	7.36273i	0.195330	−	0.601164i
$151$	4.57337	−	1.48598i	0.372176	−	0.120927i	−0.116956	−	0.993137i	$-0.537314\pi$
$151$	4.57337	−	1.48598i	0.372176	−	0.120927i	0.489132	+	0.872210i	$0.337314\pi$
$152$	10.2842	+	14.1550i	0.834159	+	1.14812i
$153$	3.40138			0.274985
$154$	13.2650	−	3.41638i	1.06893	−	0.275299i
$155$	−2.22220			−0.178492
$156$	0.950036	+	1.30761i	0.0760637	+	0.104693i
$157$	−0.689478	+	0.224025i	−0.0550264	+	0.0178791i	−0.336401	−	0.941719i	$-0.609210\pi$
$157$	−0.689478	+	0.224025i	−0.0550264	+	0.0178791i	0.281374	+	0.959598i	$0.409210\pi$
$158$	−1.64244	+	5.05491i	−0.130666	+	0.402147i
$159$	6.27678	−	8.63924i	0.497781	−	0.685136i
$160$	0.396326	+	0.287948i	0.0313324	+	0.0227643i
$161$	7.10595	+	12.6158i	0.560027	+	0.994264i
$162$	−1.48462	+	0.482382i	−0.116643	+	0.0378995i
$163$	1.65304	−	1.20100i	0.129476	−	0.0940696i	−0.521162	−	0.853457i	$-0.674501\pi$
$163$	1.65304	−	1.20100i	0.129476	−	0.0940696i	0.650638	+	0.759388i	$0.274501\pi$
$164$	−0.00365593			−0.000285480
$165$	0.624129	−	0.240228i	0.0485884	−	0.0187018i
$166$			6.81129i			0.528658i
$167$	19.0175	−	13.8170i	1.47162	−	1.06919i	0.491480	−	0.870889i	$-0.336456\pi$
$167$	19.0175	−	13.8170i	1.47162	−	1.06919i	0.980140	−	0.198305i	$-0.0635438\pi$
$168$	5.86977	+	2.68854i	0.452862	+	0.207425i
$169$	0.214234	−	0.659344i	0.0164795	−	0.0507187i
$170$	0.866161	+	0.629303i	0.0664315	+	0.0482653i
$171$	−5.80073	−	4.21448i	−0.443593	−	0.322289i
$172$	0.126092	+	0.0409696i	0.00961439	+	0.00312391i
$173$	3.27411	+	10.0767i	0.248926	+	0.766116i	0.994966	+	0.100215i	$0.0319529\pi$
$173$	3.27411	+	10.0767i	0.248926	+	0.766116i	−0.746040	+	0.665902i	$0.768047\pi$
$174$	−0.460068	−	0.633229i	−0.0348777	−	0.0480050i
$175$	8.88298	−	9.65703i	0.671490	−	0.730003i
$176$	−0.826858	−	15.5090i	−0.0623268	−	1.16904i
$177$	11.9450			0.897840
$178$	−15.9862	+	11.6147i	−1.19822	+	0.870556i
$179$	2.37602	+	7.31265i	0.177592	+	0.546573i	0.999742	−	0.0226979i	$-0.00722559\pi$
$179$	2.37602	+	7.31265i	0.177592	+	0.546573i	−0.822150	+	0.569271i	$0.807226\pi$
$180$	−0.0837628	−	0.0272162i	−0.00624331	−	0.00202857i
$181$	−3.53199	+	4.86137i	−0.262531	+	0.361343i	−0.919850	−	0.392269i	$-0.871690\pi$
$181$	−3.53199	+	4.86137i	−0.262531	+	0.361343i	0.657320	+	0.753612i	$0.271690\pi$
$182$	3.01839	+	14.9821i	0.223738	+	1.11054i
$183$	10.7915	+	3.50638i	0.797732	+	0.259199i
$184$	12.7009	−	4.12678i	0.936324	−	0.304230i
$185$	0.880836	+	1.21237i	0.0647604	+	0.0891350i
$186$		−	17.2034i		−	1.26142i
$187$	−0.600595	−	11.2651i	−0.0439198	−	0.823786i
$188$			1.61952i			0.118115i
$189$	−2.62817	−	0.304521i	−0.191171	−	0.0221506i
$190$	−0.697418	−	2.14643i	−0.0505960	−	0.155718i
$191$	−2.54188	+	7.82311i	−0.183924	+	0.566060i	−0.999928	−	0.0119859i	$-0.996185\pi$
$191$	−2.54188	+	7.82311i	−0.183924	+	0.566060i	0.816004	+	0.578046i	$0.196185\pi$
$192$	3.27577	−	4.50871i	0.236408	−	0.325388i
$193$	−10.5305	+	14.4940i	−0.758004	+	1.04330i	0.239373	+	0.970928i	$0.423058\pi$
$193$	−10.5305	+	14.4940i	−0.758004	+	1.04330i	−0.997377	+	0.0723759i	$0.976942\pi$
$194$	−1.66148	+	5.11351i	−0.119287	+	0.367128i
$195$	0.230576	+	0.709639i	0.0165119	+	0.0508183i
$196$	−1.99708	−	2.31515i	−0.142649	−	0.165368i
$197$		−	6.44353i		−	0.459083i	−0.973299	−	0.229541i	$-0.926277\pi$
$197$		−	6.44353i		−	0.459083i	0.973299	−	0.229541i	$-0.0737226\pi$
$198$	1.85976	+	4.83176i	0.132167	+	0.343379i
$199$		−	9.88850i		−	0.700977i	−0.936567	−	0.350489i	$-0.886016\pi$
$199$		−	9.88850i		−	0.700977i	0.936567	−	0.350489i	$-0.113984\pi$
$200$	−7.11328	−	9.79059i	−0.502985	−	0.692299i
$201$	−8.56901	+	2.78424i	−0.604411	+	0.196385i
$202$	8.80624	+	2.86132i	0.619605	+	0.201322i
$203$	−0.262004	−	1.30048i	−0.0183891	−	0.0912759i
$204$	−0.873256	+	1.20193i	−0.0611401	+	0.0841522i
$205$	−0.00160515		0.000521543i	−0.000112108		3.64262e-5i
$206$	5.95541	+	18.3289i	0.414933	+	1.27703i
$207$	−4.42751	+	3.21677i	−0.307733	+	0.223581i
$208$	17.3284			1.20151
$209$	−12.9338	+	19.9557i	−0.894646	+	1.38037i
$210$	−0.612922	−	0.563794i	−0.0422956	−	0.0389055i
$211$	−3.55076	−	4.88721i	−0.244445	−	0.336449i	0.669111	−	0.743162i	$-0.266675\pi$
$211$	−3.55076	−	4.88721i	−0.244445	−	0.336449i	−0.913556	+	0.406713i	$0.866675\pi$
$212$	1.44134	+	4.43600i	0.0989919	+	0.304666i
$213$	9.39934	+	3.05403i	0.644032	+	0.209259i
$214$	12.8024	+	9.30149i	0.875154	+	0.635837i
$215$	0.0495162	+	0.0359756i	0.00337698	+	0.00245352i
$216$	−0.754067	+	2.32078i	−0.0513077	+	0.157909i
$217$	12.1421	−	26.5094i	0.824262	−	1.79957i
$218$	8.16384	−	5.93137i	0.552925	−	0.401723i
$219$			1.96760i			0.132958i
$220$	−0.0753475	+	0.282221i	−0.00507993	+	0.0190274i
$221$	12.5866			0.846667
$222$	−9.38567	+	6.81909i	−0.629925	+	0.457667i
$223$	−11.3519	+	3.68845i	−0.760178	+	0.246997i	−0.663355	−	0.748305i	$-0.730868\pi$
$223$	−11.3519	+	3.68845i	−0.760178	+	0.246997i	−0.0968228	+	0.995302i	$0.530868\pi$
$224$	−5.60056	+	3.15456i	−0.374203	+	0.210773i
$225$	4.01219	+	2.91503i	0.267479	+	0.194335i
$226$	10.3254	−	14.2117i	0.686835	−	0.945347i
$227$	0.419459	−	1.29096i	0.0278405	−	0.0856842i	−0.936171	−	0.351545i	$-0.885656\pi$
$227$	0.419459	−	1.29096i	0.0278405	−	0.0856842i	0.964011	+	0.265861i	$0.0856563\pi$
$228$	2.97851	−	0.967776i	0.197256	−	0.0640925i
$229$	10.8646	+	14.9538i	0.717951	+	0.988175i	0.999589	+	0.0286541i	$0.00912212\pi$
$229$	10.8646	+	14.9538i	0.717951	+	0.988175i	−0.281638	+	0.959521i	$0.590878\pi$
$230$	−1.72261			−0.113586
$231$	−0.544484	+	8.75806i	−0.0358244	+	0.576238i
$232$	−1.22355			−0.0803301
$233$	1.15906	+	1.59532i	0.0759328	+	0.104513i	0.845294	−	0.534302i	$-0.179425\pi$
$233$	1.15906	+	1.59532i	0.0759328	+	0.104513i	−0.769361	+	0.638814i	$0.779425\pi$
$234$	−5.49375	+	1.78503i	−0.359137	+	0.116691i
$235$	−0.231035	+	0.711052i	−0.0150710	+	0.0463839i
$236$	−3.06670	+	4.22096i	−0.199625	+	0.274761i
$237$	−2.75459	−	2.00132i	−0.178930	−	0.130000i
$238$	−12.2399	+	6.89421i	−0.793394	+	0.446885i
$239$	−19.4221	+	6.31063i	−1.25631	+	0.408200i	−0.860179	−	0.509993i	$-0.829648\pi$
$239$	−19.4221	+	6.31063i	−1.25631	+	0.408200i	−0.396133	+	0.918193i	$0.629648\pi$
$240$	−0.763905	+	0.555010i	−0.0493099	+	0.0358257i
$241$	4.29052			0.276377			0.138188	−	0.990406i	$-0.455872\pi$
$241$	4.29052			0.276377			0.138188	+	0.990406i	$0.455872\pi$
$242$	15.6740	−	7.01253i	1.00757	−	0.450782i
$243$		−	1.00000i		−	0.0641500i
$244$	−4.00960	+	2.91315i	−0.256689	+	0.186495i
$245$	−0.546549	−	1.30137i	−0.0349178	−	0.0831415i
$246$	0.00403758	−	0.0124264i	0.000257427	−	0.000792279i
$247$	−21.4653	−	15.5954i	−1.36580	−	0.992313i
$248$	−21.7566	−	15.8071i	−1.38155	−	1.00375i
$249$	−4.14980	−	1.34835i	−0.262983	−	0.0854483i
$250$	0.968721	+	2.98142i	0.0612673	+	0.188561i
$251$	−7.96362	−	10.9610i	−0.502659	−	0.691851i	0.480000	−	0.877268i	$-0.340636\pi$
$251$	−7.96362	−	10.9610i	−0.502659	−	0.691851i	−0.982660	+	0.185417i	$0.940636\pi$
$252$	0.782352	−	0.850525i	0.0492835	−	0.0535780i
$253$	11.4355	+	14.0956i	0.718942	+	0.886180i
$254$	−2.51546			−0.157834
$255$	−0.554869	+	0.403136i	−0.0347472	+	0.0252453i
$256$	3.09612	+	9.52887i	0.193507	+	0.595555i
$257$	−22.0307	−	7.15820i	−1.37424	−	0.446516i	−0.473465	−	0.880812i	$-0.656997\pi$
$257$	−22.0307	−	7.15820i	−1.37424	−	0.446516i	−0.900770	+	0.434296i	$0.856997\pi$
$258$	−0.278509	+	0.383335i	−0.0173392	+	0.0238654i
$259$	−19.2756	+	3.88340i	−1.19773	+	0.241303i
$260$	−0.309959	−	0.100712i	−0.0192229	−	0.00624589i
$261$	0.476871	−	0.154945i	0.0295176	−	0.00959084i
$262$	−5.81441	−	8.00285i	−0.359216	−	0.494418i
$263$		−	15.3433i		−	0.946107i	−0.881034	−	0.473053i	$-0.843152\pi$
$263$		−	15.3433i		−	0.946107i	0.881034	−	0.473053i	$-0.156848\pi$
$264$	7.81938	+	2.08762i	0.481250	+	0.128484i
$265$			2.15325i			0.132273i
$266$	29.4162	+	3.40840i	1.80362	+	0.208982i
$267$	−3.91167	−	12.0389i	−0.239390	−	0.736767i
$268$	1.21611	−	3.74281i	0.0742860	−	0.228629i
$269$	16.9441	−	23.3216i	1.03310	−	1.42194i	0.130506	−	0.991448i	$-0.458340\pi$
$269$	16.9441	−	23.3216i	1.03310	−	1.42194i	0.902594	−	0.430493i	$-0.141660\pi$
$270$	0.185014	−	0.254650i	0.0112596	−	0.0154975i
$271$	−4.84326	+	14.9060i	−0.294207	+	0.905476i	0.689280	+	0.724495i	$0.257927\pi$
$271$	−4.84326	+	14.9060i	−0.294207	+	0.905476i	−0.983487	+	0.180981i	$0.942073\pi$
$272$	4.92201	+	15.1484i	0.298440	+	0.918505i
$273$	−9.72538	−	1.12686i	−0.588607	−	0.0682008i
$274$			27.8087i			1.67999i
$275$	8.94589	−	13.8028i	0.539458	−	0.832339i
$276$		−	2.39039i		−	0.143885i
$277$	9.06801	+	12.4810i	0.544844	+	0.749913i	0.989301	−	0.145887i	$-0.0466035\pi$
$277$	9.06801	+	12.4810i	0.544844	+	0.749913i	−0.444457	+	0.895800i	$0.646603\pi$
$278$	14.2132	−	4.61815i	0.852451	−	0.276978i
$279$	10.4812	+	3.40556i	0.627495	+	0.203886i
$280$	−1.27619	+	0.257109i	−0.0762667	+	0.0153652i
$281$	−8.78258	+	12.0882i	−0.523925	+	0.721120i	−0.986189	−	0.165622i	$-0.947037\pi$
$281$	−8.78258	+	12.0882i	−0.523925	+	0.721120i	0.462265	+	0.886742i	$0.347037\pi$
$282$	−5.50468	−	1.78858i	−0.327799	−	0.106508i
$283$	−1.22037	−	3.75590i	−0.0725433	−	0.223265i	0.908211	−	0.418513i	$-0.137449\pi$
$283$	−1.22037	−	3.75590i	−0.0725433	−	0.223265i	−0.980754	+	0.195248i	$0.937449\pi$
$284$	−3.49234	+	2.53733i	−0.207232	+	0.150563i
$285$	1.44578			0.0856406
$286$	6.88192	+	17.8797i	0.406936	+	1.05725i
$287$	0.0149922	−	0.0162986i	0.000884962	−	0.000962075i
$288$	−1.42803	−	1.96551i	−0.0841474	−	0.115819i
$289$	−1.67815	−	5.16482i	−0.0987147	−	0.303813i
$290$	0.150102	+	0.0487711i	0.00881430	+	0.00286394i
$291$	−2.78652	−	2.02452i	−0.163349	−	0.118680i
$292$	−0.695283	−	0.505153i	−0.0406883	−	0.0295618i
$293$	−6.30903	+	19.4172i	−0.368577	+	1.13436i	0.579133	+	0.815233i	$0.303391\pi$
$293$	−6.30903	+	19.4172i	−0.368577	+	1.13436i	−0.947710	+	0.319132i	$0.896609\pi$
$294$	10.0747	−	4.23117i	0.587569	−	0.246767i
$295$	−1.94859	+	1.41573i	−0.113451	+	0.0824272i
$296$			18.1354i			1.05410i
$297$	−3.31192	+	0.176574i	−0.192177	+	0.0102459i
$298$	−4.59072			−0.265933
$299$	−16.3837	+	11.9035i	−0.947495	+	0.688396i
$300$	−2.06015	+	0.669382i	−0.118943	+	0.0386468i
$301$	−0.699722	+	0.394124i	−0.0403313	+	0.0227169i
$302$	−6.07290	−	4.41222i	−0.349456	−	0.253895i
$303$	−3.48654	+	4.79881i	−0.200296	+	0.275684i
$304$	10.3756	−	31.9327i	0.595079	−	1.83147i
$305$	−2.17600	+	0.707027i	−0.124598	+	0.0404842i
$306$	−3.12092	−	4.29558i	−0.178411	−	0.245562i
$307$	6.24612			0.356485			0.178242	−	0.983987i	$-0.442959\pi$
$307$	6.24612			0.356485			0.178242	+	0.983987i	$0.442959\pi$
$308$	−2.95501	−	2.44091i	−0.168378	−	0.139084i
$309$	−12.3458			−0.702330
$310$	2.03897	+	2.80640i	0.115806	+	0.159393i
$311$	13.3923	−	4.35144i	0.759410	−	0.246747i	0.0963846	−	0.995344i	$-0.469272\pi$
$311$	13.3923	−	4.35144i	0.759410	−	0.246747i	0.663025	+	0.748597i	$0.269272\pi$
$312$	−2.79038	+	8.58791i	−0.157974	+	0.486195i
$313$	11.6221	−	15.9964i	0.656920	−	0.904173i	−0.342455	−	0.939534i	$-0.611258\pi$
$313$	11.6221	−	15.9964i	0.656920	−	0.904173i	0.999375	+	0.0353618i	$0.0112584\pi$
$314$	0.915547	+	0.665184i	0.0516673	+	0.0375385i
$315$	0.464826	−	0.261817i	0.0261900	−	0.0147517i
$316$	1.41440	−	0.459567i	0.0795663	−	0.0258526i
$317$	6.96870	−	5.06305i	0.391401	−	0.284369i	−0.374628	−	0.927175i	$-0.622230\pi$
$317$	6.96870	−	5.06305i	0.391401	−	0.284369i	0.766029	+	0.642806i	$0.222230\pi$
$318$	−16.6697			−0.934788
$319$	−0.597368	−	1.55200i	−0.0334462	−	0.0868953i
$320$			1.12375i			0.0628198i
$321$	−8.20130	+	5.95860i	−0.457752	+	0.332576i
$322$	9.41237	−	20.5496i	0.524531	−	1.14518i
$323$	7.53637	−	23.1946i	0.419335	−	1.29058i
$324$	0.353366	+	0.256736i	0.0196315	+	0.0142631i
$325$	14.8469	+	10.7869i	0.823557	+	0.598349i
$326$	−3.03347	−	0.985634i	−0.168008	−	0.0545892i
$327$	1.99761	+	6.14801i	0.110468	+	0.339986i
$328$	−0.0120054	−	0.0165240i	−0.000662887	−	0.000912386i
$329$	−7.21999	−	6.64129i	−0.398051	−	0.366146i
$330$	−0.876049	−	0.567787i	−0.0482249	−	0.0312557i
$331$	−10.7809			−0.592571			−0.296286	−	0.955099i	$-0.595748\pi$
$331$	−10.7809			−0.592571			−0.296286	+	0.955099i	$0.595748\pi$
$332$	1.54186	−	1.12023i	0.0846207	−	0.0614805i
$333$	−2.29658	−	7.06815i	−0.125852	−	0.387332i
$334$	−34.8989	−	11.3393i	−1.90958	−	0.620460i
$335$	1.06787	−	1.46980i	0.0583442	−	0.0803039i
$336$	−2.44691	−	12.1455i	−0.133490	−	0.662589i
$337$	1.55692	+	0.505873i	0.0848106	+	0.0275566i	0.351115	−	0.936332i	$-0.385803\pi$
$337$	1.55692	+	0.505873i	0.0848106	+	0.0275566i	−0.266304	+	0.963889i	$0.585803\pi$
$338$	−1.02925	+	0.334423i	−0.0559838	+	0.0181902i
$339$	6.61451	+	9.10410i	0.359251	+	0.494467i
$340$		−	0.299571i		−	0.0162465i
$341$	9.42824	−	35.3144i	0.510568	−	1.91238i
$342$			11.1927i			0.605230i
$343$	18.5108	+	0.590735i	0.999491	+	0.0318967i
$344$	0.228887	+	0.704443i	0.0123408	+	0.0379810i
$345$	0.341005	−	1.04951i	0.0183591	−	0.0565035i
$346$	9.72162	−	13.3807i	0.522637	−	0.719349i
$347$	4.48485	−	6.17286i	0.240759	−	0.331377i	−0.671489	−	0.741015i	$-0.734345\pi$
$347$	4.48485	−	6.17286i	0.240759	−	0.331377i	0.912248	+	0.409638i	$0.134345\pi$
$348$	−0.0676775	+	0.208290i	−0.00362790	+	0.0111655i
$349$	7.70757	+	23.7214i	0.412577	+	1.26978i	0.914401	+	0.404810i	$0.132662\pi$
$349$	7.70757	+	23.7214i	0.412577	+	1.26978i	−0.501824	+	0.864970i	$0.667338\pi$
$350$	−20.3463	−	2.35749i	−1.08756	−	0.126013i
$351$		−	3.70044i		−	0.197515i
$352$	−6.25747	+	5.07658i	−0.333524	+	0.270582i
$353$			1.33192i			0.0708908i	0.999372	+	0.0354454i	$0.0112850\pi$
$353$			1.33192i			0.0708908i	−0.999372	+	0.0354454i	$0.988715\pi$
$354$	−10.9601	−	15.0852i	−0.582521	−	0.801771i
$355$	−1.89529	+	0.615816i	−0.100591	+	0.0326841i
$356$	5.25839	+	1.70856i	0.278694	+	0.0905533i
$357$	−1.77733	−	8.82195i	−0.0940663	−	0.466907i
$358$	7.05498	−	9.71034i	0.372867	−	0.513208i
$359$	32.8398	+	10.6703i	1.73322	+	0.563156i	0.993908	−	0.110212i	$-0.0351528\pi$
$359$	32.8398	+	10.6703i	1.73322	+	0.563156i	0.739308	+	0.673368i	$0.235153\pi$
$360$	−0.152050	−	0.467962i	−0.00801375	−	0.0246638i
$361$	−26.2204	+	19.0503i	−1.38002	+	1.00265i
$362$	9.38015			0.493010
$363$	1.16960	+	10.9376i	0.0613879	+	0.574077i
$364$	2.89505	−	3.14732i	0.151742	−	0.164964i
$365$	−0.233202	−	0.320975i	−0.0122064	−	0.0168006i
$366$	−5.47353	−	16.8458i	−0.286106	−	0.880543i
$367$	29.7738	+	9.67411i	1.55418	+	0.504984i	0.955246	−	0.295813i	$-0.0955904\pi$
$367$	29.7738	+	9.67411i	1.55418	+	0.504984i	0.598936	+	0.800797i	$0.295590\pi$
$368$	−20.7331	−	15.0635i	−1.08079	−	0.785237i
$369$	0.00677155	+	0.00491982i	0.000352513	+	0.000256116i
$370$	0.722882	−	2.22480i	0.0375808	−	0.115662i
$371$	−25.6869	−	11.7654i	−1.33360	−	0.610830i
$372$	−3.89432	+	2.82939i	−0.201911	+	0.146697i
$373$		−	7.91010i		−	0.409569i	−0.978807	−	0.204785i	$-0.934351\pi$
$373$		−	7.91010i		−	0.409569i	0.978807	−	0.204785i	$-0.0656494\pi$
$374$	−13.6755	+	11.0947i	−0.707145	+	0.573695i
$375$	−2.00820			−0.103703
$376$	−7.31986	+	5.31819i	−0.377493	+	0.274265i
$377$	1.76463	−	0.573364i	0.0908833	−	0.0295298i
$378$	2.02688	+	3.59850i	0.104252	+	0.185087i
$379$	−7.45995	−	5.41997i	−0.383192	−	0.278405i	0.379468	−	0.925205i	$-0.376107\pi$
$379$	−7.45995	−	5.41997i	−0.383192	−	0.278405i	−0.762660	+	0.646800i	$0.776107\pi$
$380$	−0.371183	+	0.510890i	−0.0190413	+	0.0262081i
$381$	0.497956	−	1.53255i	0.0255111	−	0.0785150i
$382$	12.2120	−	3.96793i	0.624822	−	0.203017i
$383$	−4.04094	−	5.56187i	−0.206482	−	0.284198i	0.693199	−	0.720747i	$-0.256201\pi$
$383$	−4.04094	−	5.56187i	−0.206482	−	0.284198i	−0.899681	+	0.436548i	$0.856201\pi$
$384$	−13.5587			−0.691914
$385$	−0.949193	−	1.49324i	−0.0483754	−	0.0761025i
$386$	27.9666			1.42346
$387$	−0.178415	−	0.245567i	−0.00906934	−	0.0124829i
$388$	1.43080	−	0.464894i	0.0726377	−	0.0236014i
$389$	5.11516	−	15.7429i	0.259349	−	0.798194i	−0.733592	−	0.679590i	$-0.762158\pi$
$389$	5.11516	−	15.7429i	0.259349	−	0.798194i	0.992942	−	0.118605i	$-0.0378421\pi$
$390$	0.684634	−	0.942317i	0.0346678	−	0.0477161i
$391$	−15.0596	−	10.9415i	−0.761598	−	0.553334i
$392$	3.90596	−	16.6289i	0.197281	−	0.839886i
$393$	6.02678	−	1.95822i	0.304011	−	0.0987790i
$394$	−8.13749	+	5.91223i	−0.409961	+	0.297854i
$395$	0.686556			0.0345444
$396$	0.787893	−	1.21565i	0.0395931	−	0.0610889i
$397$		−	4.34880i		−	0.218260i	−0.994027	−	0.109130i	$-0.965194\pi$
$397$		−	4.34880i		−	0.218260i	0.994027	−	0.109130i	$-0.0348065\pi$
$398$	−12.4881	+	9.07314i	−0.625973	+	0.454796i
$399$	−7.89976	+	17.2472i	−0.395483	+	0.863439i
$400$	−7.17647	+	22.0869i	−0.358824	+	1.10435i
$401$	−4.62963	−	3.36363i	−0.231193	−	0.167971i	0.466158	−	0.884702i	$-0.345638\pi$
$401$	−4.62963	−	3.36363i	−0.231193	−	0.167971i	−0.697351	+	0.716730i	$0.745638\pi$
$402$	11.3786	+	8.26707i	0.567515	+	0.412324i
$403$	38.7852	+	12.6021i	1.93203	+	0.627754i
$404$	−0.800618	−	2.46405i	−0.0398323	−	0.122591i
$405$	0.118521	+	0.163130i	0.00588936	+	0.00810601i
$406$	−1.40197	+	1.52413i	−0.0695785	+	0.0756414i
$407$	−23.0036	+	8.85414i	−1.14025	+	0.438883i
$408$	−8.30009			−0.410916
$409$	−4.77922	+	3.47231i	−0.236317	+	0.171695i	−0.699641	−	0.714495i	$-0.746657\pi$
$409$	−4.77922	+	3.47231i	−0.236317	+	0.171695i	0.463324	+	0.886189i	$0.346657\pi$
$410$	0.000814140		0.00250566i	4.02075e−5		0.000123746i
$411$	−16.9425	−	5.50496i	−0.835714	−	0.271540i
$412$	3.16962	−	4.36260i	0.156156	−	0.214930i
$413$	−6.24164	−	30.9810i	−0.307131	−	1.52447i
$414$	8.12487	+	2.63993i	0.399316	+	0.129745i
$415$	0.836766	−	0.271882i	0.0410752	−	0.0133462i
$416$	−5.28434	−	7.27327i	−0.259086	−	0.356601i
$417$			9.57364i			0.468823i
$418$	37.0692	−	1.97633i	1.81311	−	0.0966655i
$419$			13.0400i			0.637047i	0.947915	+	0.318524i	$0.103187\pi$
$419$			13.0400i			0.637047i	−0.947915	+	0.318524i	$0.896813\pi$
$420$	−0.0268202	+	0.231472i	−0.00130869	+	0.0112947i
$421$	4.36960	+	13.4482i	0.212961	+	0.655427i	0.999292	+	0.0376213i	$0.0119781\pi$
$421$	4.36960	+	13.4482i	0.212961	+	0.655427i	−0.786331	+	0.617805i	$0.788022\pi$
$422$	−2.91403	+	8.96846i	−0.141853	+	0.436578i
$423$	2.17940	−	2.99968i	0.105966	−	0.145850i
$424$	−15.3167	+	21.0816i	−0.743843	+	1.02381i
$425$	−5.21269	+	16.0430i	−0.252852	+	0.778200i
$426$	−4.76741	−	14.6726i	−0.230982	−	0.710888i
$427$	3.45536	−	29.8215i	0.167217	−	1.44316i
$428$		−	4.42785i		−	0.214028i
$429$	−12.2556	+	0.653401i	−0.591705	+	0.0315465i
$430$		−	0.0955428i		−	0.00460749i
$431$	3.83272	+	5.27529i	0.184616	+	0.254102i	0.891286	−	0.453441i	$-0.149804\pi$
$431$	3.83272	+	5.27529i	0.184616	+	0.254102i	−0.706671	+	0.707543i	$0.749804\pi$
$432$	4.45360	−	1.44706i	0.214274	−	0.0696218i
$433$	18.8950	+	6.13935i	0.908035	+	0.295038i	0.725549	−	0.688170i	$-0.241586\pi$
$433$	18.8950	+	6.13935i	0.908035	+	0.295038i	0.182485	+	0.983209i	$0.441586\pi$
$434$	−44.6195	+	8.98934i	−2.14180	+	0.431502i
$435$	−0.0594279	+	0.0817955i	−0.00284935	+	0.00392180i
$436$	−2.68536	−	0.872525i	−0.128605	−	0.0417864i
$437$	12.1258	+	37.3192i	0.580053	+	1.78522i
$438$	2.48486	−	1.80536i	0.118731	−	0.0862634i
$439$	−24.5836			−1.17331			−0.586656	−	0.809836i	$-0.699556\pi$
$439$	−24.5836			−1.17331			−0.586656	+	0.809836i	$0.699556\pi$
$440$	−1.52301	+	0.586208i	−0.0726065	+	0.0279464i
$441$	0.583484	+	6.97564i	0.0277850	+	0.332173i
$442$	−11.5488	−	15.8955i	−0.549320	−	0.756073i
$443$	7.24774	+	22.3063i	0.344351	+	1.05980i	0.961931	+	0.273294i	$0.0881132\pi$
$443$	7.24774	+	22.3063i	0.344351	+	1.05980i	−0.617580	+	0.786508i	$0.711887\pi$
$444$	3.08726	+	1.00311i	0.146515	+	0.0476055i
$445$	2.06497	+	1.50029i	0.0978891	+	0.0711206i
$446$	15.0740	+	10.9519i	0.713773	+	0.518586i
$447$	0.908771	−	2.79691i	0.0429834	−	0.132289i
$448$	−13.4056	−	6.14021i	−0.633357	−	0.290098i
$449$	−3.91214	+	2.84234i	−0.184625	+	0.134138i	−0.676259	−	0.736664i	$-0.736400\pi$
$449$	−3.91214	+	2.84234i	−0.184625	+	0.134138i	0.491634	+	0.870802i	$0.336400\pi$
$450$		−	7.74163i		−	0.364944i
$451$	0.0150984	−	0.0232956i	0.000710955	−	0.00109695i
$452$	−4.91526			−0.231195
$453$	3.89034	−	2.82650i	0.182784	−	0.132800i
$454$	−2.01522	+	0.654785i	−0.0945790	+	0.0307306i
$455$	1.72006	−	0.968838i	0.0806378	−	0.0454198i
$456$	14.1550	+	10.2842i	0.662869	+	0.481602i
$457$	−8.38559	+	11.5418i	−0.392262	+	0.539902i	−0.958781	−	0.284147i	$-0.908290\pi$
$457$	−8.38559	+	11.5418i	−0.392262	+	0.539902i	0.566519	+	0.824048i	$0.308290\pi$
$458$	8.91630	−	27.4416i	0.416631	−	1.28226i
$459$	3.23491	−	1.05108i	0.150992	−	0.0490604i
$460$	0.283312	+	0.389945i	0.0132095	+	0.0181813i
$461$	0.352080			0.0163980			0.00819901	−	0.999966i	$-0.497390\pi$
$461$	0.352080			0.0163980			0.00819901	+	0.999966i	$0.497390\pi$
$462$	11.5601	−	7.34828i	0.537823	−	0.341873i
$463$	32.5594			1.51316			0.756581	−	0.653900i	$-0.226868\pi$
$463$	32.5594			1.51316			0.756581	+	0.653900i	$0.226868\pi$
$464$	1.38012	+	1.89958i	0.0640706	+	0.0881857i
$465$	−2.11344	+	0.686698i	−0.0980084	+	0.0318449i
$466$	0.951218	−	2.92755i	0.0440643	−	0.135616i
$467$	−18.7216	+	25.7681i	−0.866332	+	1.19240i	0.113691	+	0.993516i	$0.463733\pi$
$467$	−18.7216	+	25.7681i	−0.866332	+	1.19240i	−0.980022	+	0.198887i	$0.936267\pi$
$468$	1.30761	+	0.950036i	0.0604444	+	0.0439154i
$469$	11.6989	+	20.7701i	0.540205	+	0.959072i
$470$	1.10997	−	0.360650i	0.0511989	−	0.0166355i
$471$	−0.586505	+	0.426121i	−0.0270247	+	0.0196346i
$472$	−29.1483			−1.34166
$473$	−0.781795	+	0.634257i	−0.0359470	+	0.0291632i
$474$			5.31505i			0.244128i
$475$	28.7678	−	20.9010i	1.31996	−	0.959005i
$476$	3.57368	+	1.63686i	0.163800	+	0.0750254i
$477$	3.29990	−	10.1560i	0.151092	−	0.465013i
$478$	25.7903	+	18.7377i	1.17962	+	0.857044i
$479$	16.0258	+	11.6435i	0.732240	+	0.532003i	0.890271	−	0.455431i	$-0.150515\pi$
$479$	16.0258	+	11.6435i	0.732240	+	0.532003i	−0.158032	+	0.987434i	$0.550515\pi$
$480$	0.465910	+	0.151383i	0.0212658	+	0.00690967i
$481$	−8.49836	−	26.1553i	−0.387492	−	1.19258i
$482$	−3.93675	−	5.41847i	−0.179314	−	0.246804i
$483$	10.6567	+	9.80248i	0.484895	+	0.446028i
$484$	−4.16527	−	2.39479i	−0.189331	−	0.108854i
$485$	0.694514			0.0315363
$486$	−1.26289	+	0.917545i	−0.0572859	+	0.0416207i
$487$	−10.4853	−	32.2706i	−0.475136	−	1.46232i	−0.845774	−	0.533541i	$-0.820861\pi$
$487$	−10.4853	−	32.2706i	−0.475136	−	1.46232i	0.370638	−	0.928777i	$-0.379139\pi$
$488$	−26.3336	−	8.55630i	−1.19207	−	0.387326i
$489$	1.20100	−	1.65304i	0.0543111	−	0.0747529i
$490$	−1.14201	+	1.88430i	−0.0515906	+	0.0851239i
$491$	−21.2781	−	6.91368i	−0.960268	−	0.312010i	−0.213387	−	0.976968i	$-0.568450\pi$
$491$	−21.2781	−	6.91368i	−0.960268	−	0.312010i	−0.746881	+	0.664958i	$0.768450\pi$
$492$	−0.00347700	+	0.00112975i	−0.000156755	+	5.09329e-5i
$493$	1.00246	+	1.37977i	0.0451487	+	0.0621418i
$494$			41.4178i			1.86348i
$495$	0.519347	−	0.421337i	0.0233429	−	0.0189377i
$496$			51.6073i			2.31723i
$497$	3.00960	−	25.9743i	0.134999	−	1.16511i
$498$	2.10480	+	6.47792i	0.0943185	+	0.290282i
$499$	6.65048	−	20.4681i	0.297716	−	0.916276i	−0.684579	−	0.728938i	$-0.740014\pi$
$499$	6.65048	−	20.4681i	0.297716	−	0.916276i	0.982296	−	0.187338i	$-0.0599859\pi$
$500$	0.515578	−	0.709632i	0.0230573	−	0.0317357i
$501$	13.8170	−	19.0175i	0.617300	−	0.849640i
$502$	−6.53556	+	20.1144i	−0.291696	+	0.897749i
$503$	8.65278	+	26.6305i	0.385809	+	1.18740i	0.935892	+	0.352287i	$0.114596\pi$
$503$	8.65278	+	26.6305i	0.385809	+	1.18740i	−0.550084	+	0.835110i	$0.685404\pi$
$504$	6.41328	+	0.743095i	0.285670	+	0.0331001i
$505$		−	1.19606i		−	0.0532240i
$506$	7.30860	−	27.3751i	0.324907	−	1.21697i
$507$		−	0.693275i		−	0.0307894i
$508$	0.413709	+	0.569421i	0.0183554	+	0.0252640i
$509$	15.0298	−	4.88349i	0.666185	−	0.216457i	0.0436483	−	0.999047i	$-0.486102\pi$
$509$	15.0298	−	4.88349i	0.666185	−	0.216457i	0.622537	+	0.782590i	$0.286102\pi$
$510$	1.01823	+	0.330844i	0.0450881	+	0.0146500i
$511$	5.10324	−	1.02813i	0.225754	−	0.0454819i
$512$	−6.74608	+	9.28518i	−0.298137	+	0.410351i
$513$	−6.81916	−	2.21568i	−0.301073	−	0.0978247i
$514$	11.1741	+	34.3903i	0.492868	+	1.51689i
$515$	2.01398	−	1.46324i	0.0887466	−	0.0644782i
$516$	0.132581			0.00583653
$517$	−10.3195	−	6.68832i	−0.453853	−	0.294152i
$518$	22.5906	+	20.7798i	0.992573	+	0.913014i
$519$	6.22773	+	8.57174i	0.273367	+	0.376258i
$520$	−0.562653	−	1.73167i	−0.0246740	−	0.0759387i
$521$	−0.835592	−	0.271500i	−0.0366080	−	0.0118946i	0.290656	−	0.956828i	$-0.406127\pi$
$521$	−0.835592	−	0.271500i	−0.0366080	−	0.0118946i	−0.327264	+	0.944933i	$0.606127\pi$
$522$	−0.633229	−	0.460068i	−0.0277157	−	0.0201366i
$523$	19.2638	+	13.9960i	0.842347	+	0.612001i	0.923025	−	0.384739i	$-0.125709\pi$
$523$	19.2638	+	13.9960i	0.842347	+	0.612001i	−0.0806782	+	0.996740i	$0.525709\pi$
$524$	−0.855320	+	2.63240i	−0.0373648	+	0.114997i
$525$	5.46403	−	11.9294i	0.238470	−	0.520640i
$526$	−19.3769	+	14.0781i	−0.844873	+	0.613836i
$527$			37.4853i			1.63289i
$528$	−5.57894	−	14.4944i	−0.242792	−	0.630790i
$529$	6.95042			0.302192
$530$	2.71933	−	1.97571i	0.118120	−	0.0858192i
$531$	11.3604	−	3.69120i	0.492998	−	0.160185i
$532$	−4.06643	−	7.21948i	−0.176302	−	0.313004i
$533$	0.0250577	+	0.0182055i	0.00108537	+	0.000788569i
$534$	−11.6147	+	15.9862i	−0.502616	+	0.691791i
$535$	0.631662	−	1.94406i	0.0273091	−	0.0840489i
$536$	20.9102	−	6.79413i	0.903183	−	0.293462i
$537$	4.51946	+	6.22051i	0.195029	+	0.268435i
$538$	−44.9996			−1.94007
$539$	22.9997	−	3.16417i	0.990669	−	0.136290i
$540$	−0.0880734			−0.00379008
$541$	−5.25382	−	7.23126i	−0.225879	−	0.310896i	0.681003	−	0.732281i	$-0.261544\pi$
$541$	−5.25382	−	7.23126i	−0.225879	−	0.310896i	−0.906882	+	0.421385i	$0.861544\pi$
$542$	23.2686	−	7.56042i	0.999472	−	0.324748i
$543$	−1.85688	+	5.71488i	−0.0796863	+	0.245249i
$544$	4.85727	−	6.68546i	0.208254	−	0.286637i
$545$	−1.05454	−	0.766168i	−0.0451715	−	0.0328190i
$546$	7.50037	+	13.3161i	0.320986	+	0.569875i
$547$	42.4544	−	13.7943i	1.81522	−	0.589801i	0.815279	−	0.579069i	$-0.196584\pi$
$547$	42.4544	−	13.7943i	1.81522	−	0.589801i	0.999942	−	0.0107321i	$-0.00341621\pi$
$548$	6.29502	−	4.57360i	0.268910	−	0.195375i
$549$	11.3469			0.484273
$550$	−25.6397	+	1.36697i	−1.09328	+	0.0582878i
$551$		−	3.59517i		−	0.153159i
$552$	10.8040	−	7.84960i	0.459851	−	0.334101i
$553$	−3.75135	+	8.19016i	−0.159524	+	0.348281i
$554$	7.44191	−	22.9038i	0.316176	−	0.973091i
$555$	1.21237	+	0.880836i	0.0514621	+	0.0373894i
$556$	−3.38300	−	2.45789i	−0.143471	−	0.104238i
$557$	−13.6936	−	4.44932i	−0.580216	−	0.188524i	0.00418123	−	0.999991i	$-0.498669\pi$
$557$	−13.6936	−	4.44932i	−0.580216	−	0.188524i	−0.584397	+	0.811468i	$0.698669\pi$
$558$	−5.31615	−	16.3614i	−0.225051	−	0.692634i
$559$	−0.660214	−	0.908707i	−0.0279241	−	0.0384342i
$560$	1.83866	+	1.69128i	0.0776975	+	0.0714698i
$561$	−4.05231	−	10.5282i	−0.171089	−	0.444499i
$562$	23.3245			0.983883
$563$	−21.2946	+	15.4714i	−0.897461	+	0.652043i	−0.937813	−	0.347142i	$-0.887152\pi$
$563$	−21.2946	+	15.4714i	−0.897461	+	0.652043i	0.0403518	+	0.999186i	$0.487152\pi$
$564$	0.500458	+	1.54025i	0.0210731	+	0.0648562i
$565$	−2.15806	−	0.701195i	−0.0907901	−	0.0294995i
$566$	−3.62356	+	4.98740i	−0.152310	+	0.209636i
$567$	−2.59364	+	0.522532i	−0.108923	+	0.0219443i
$568$	−22.9364	−	7.45248i	−0.962389	−	0.312699i
$569$	7.88033	−	2.56047i	0.330361	−	0.107341i	−0.139140	−	0.990273i	$-0.544434\pi$
$569$	7.88033	−	2.56047i	0.330361	−	0.107341i	0.469501	+	0.882932i	$0.344434\pi$
$570$	−1.32657	−	1.82586i	−0.0555638	−	0.0764770i
$571$		−	22.7598i		−	0.952469i	−0.879318	−	0.476234i	$-0.842001\pi$
$571$		−	22.7598i		−	0.952469i	0.879318	−	0.476234i	$-0.157999\pi$
$572$	2.91555	−	4.49846i	0.121905	−	0.188090i
$573$			8.22570i			0.343634i
$574$	−0.0343394	−	0.00397884i	−0.00143330	−	0.000166074i
$575$	−8.38702	−	25.8126i	−0.349763	−	1.07646i
$576$	1.72217	−	5.30030i	0.0717572	−	0.220846i
$577$	10.3084	−	14.1883i	0.429143	−	0.590665i	−0.538613	−	0.842553i	$-0.681052\pi$
$577$	10.3084	−	14.1883i	0.429143	−	0.590665i	0.967756	+	0.251888i	$0.0810516\pi$
$578$	−4.98283	+	6.85827i	−0.207258	+	0.285267i
$579$	−5.53623	+	17.0388i	−0.230078	+	0.708107i
$580$	−0.0136465	−	0.0419997i	−0.000566641	−	0.00174394i
$581$	−1.32873	+	11.4676i	−0.0551251	+	0.475757i
$582$			5.37666i			0.222870i
$583$	−34.2187	−	9.13571i	−1.41719	−	0.378362i
$584$		−	4.80135i		−	0.198681i
$585$	0.438581	+	0.603655i	0.0181331	+	0.0249580i
$586$	30.3106	−	9.84852i	1.25212	−	0.406839i
$587$	38.8792	+	12.6326i	1.60472	+	0.521404i	0.968268	−	0.249915i	$-0.0804026\pi$
$587$	38.8792	+	12.6326i	1.60472	+	0.521404i	0.636449	+	0.771319i	$0.280403\pi$
$588$	−2.61476	−	1.58471i	−0.107831	−	0.0653524i
$589$	46.4462	−	63.9277i	1.91378	−	2.63409i
$590$	3.57584	+	1.16186i	0.147215	+	0.0478330i
$591$	−1.99116	−	6.12816i	−0.0819054	−	0.252079i
$592$	28.1554	−	20.4561i	1.15718	−	0.840740i
$593$	−14.7340			−0.605052			−0.302526	−	0.953141i	$-0.597830\pi$
$593$	−14.7340			−0.605052			−0.302526	+	0.953141i	$0.597830\pi$
$594$	3.26183	+	4.02058i	0.133834	+	0.164967i
$595$	1.33552	+	1.22848i	0.0547512	+	0.0503627i
$596$	0.755020	+	1.03920i	0.0309268	+	0.0425671i
$597$	−3.05572	−	9.40453i	−0.125062	−	0.384902i
$598$	30.0656	+	9.76891i	1.22947	+	0.399480i
$599$	22.3203	+	16.2167i	0.911983	+	0.662594i	0.941516	−	0.336969i	$-0.109402\pi$
$599$	22.3203	+	16.2167i	0.911983	+	0.662594i	−0.0295326	+	0.999564i	$0.509402\pi$
$600$	−9.79059	−	7.11328i	−0.399699	−	0.290399i
$601$	8.04689	−	24.7658i	0.328240	−	1.01022i	−0.641717	−	0.766941i	$-0.721778\pi$
$601$	8.04689	−	24.7658i	0.328240	−	1.01022i	0.969957	−	0.243276i	$-0.0782222\pi$
$602$	1.13976	+	0.522047i	0.0464533	+	0.0212771i
$603$	−7.28923	+	5.29594i	−0.296841	+	0.215667i
$604$			2.10038i			0.0854632i
$605$	−1.48714	−	1.64564i	−0.0604608	−	0.0669048i
$606$	9.25943			0.376139
$607$	−36.6562	+	26.6323i	−1.48783	+	1.08097i	−0.512902	+	0.858447i	$0.671429\pi$
$607$	−36.6562	+	26.6323i	−1.48783	+	1.08097i	−0.974927	+	0.222524i	$0.928571\pi$
$608$	−16.5672	+	5.38301i	−0.671889	+	0.218310i
$609$	−0.651051	−	1.15587i	−0.0263819	−	0.0468381i
$610$	2.88948	+	2.09933i	0.116992	+	0.0849994i
$611$	8.06473	−	11.1001i	0.326264	−	0.449064i
$612$	−0.459098	+	1.41296i	−0.0185579	+	0.0571154i
$613$	−24.3899	+	7.92476i	−0.985099	+	0.320078i	−0.756896	−	0.653536i	$-0.773285\pi$
$613$	−24.3899	+	7.92476i	−0.985099	+	0.320078i	−0.228203	+	0.973614i	$0.573285\pi$
$614$	−5.73109	−	7.88817i	−0.231288	−	0.318341i
$615$	−0.00168775			−6.80566e−5
$616$	1.32866	−	21.3715i	0.0535331	−	0.861082i
$617$	−42.9784			−1.73025			−0.865123	−	0.501559i	$-0.832760\pi$
$617$	−42.9784			−1.73025			−0.865123	+	0.501559i	$0.832760\pi$
$618$	11.3279	+	15.5915i	0.455673	+	0.627181i
$619$	−18.6100	+	6.04677i	−0.748001	+	0.243040i	−0.658121	−	0.752912i	$-0.728648\pi$
$619$	−18.6100	+	6.04677i	−0.748001	+	0.243040i	−0.0898800	+	0.995953i	$0.528648\pi$
$620$	0.299939	−	0.923118i	0.0120459	−	0.0370733i
$621$	−3.21677	+	4.42751i	−0.129085	+	0.177670i
$622$	−17.7835	−	12.9204i	−0.713052	−	0.518063i
$623$	−29.1805	+	16.4361i	−1.16909	+	0.658500i
$624$	16.4803	−	5.35477i	0.659739	−	0.214362i
$625$	−19.7334	+	14.3371i	−0.789334	+	0.573485i
$626$	−30.8656			−1.23364
$627$	−6.13407	+	22.9758i	−0.244971	+	0.917564i
$628$		−	0.316652i		−	0.0126358i
$629$	20.4509	−	14.8584i	0.815430	−	0.592445i
$630$	−0.757145	−	0.346797i	−0.0301654	−	0.0138167i
$631$	−12.4349	+	38.2708i	−0.495027	+	1.52354i	0.321889	+	0.946778i	$0.395682\pi$
$631$	−12.4349	+	38.2708i	−0.495027	+	1.52354i	−0.816915	+	0.576758i	$0.804318\pi$
$632$	6.72177	+	4.88365i	0.267378	+	0.194261i
$633$	−4.88721	−	3.55076i	−0.194249	−	0.141130i
$634$	−12.7882	−	4.15513i	−0.507884	−	0.165021i
$635$	0.100408	+	0.309024i	0.00398457	+	0.0122632i
$636$	2.74160	+	3.77349i	0.108712	+	0.149629i
$637$	2.15915	+	25.8130i	0.0855486	+	1.02275i
$638$	−1.41190	+	2.17844i	−0.0558975	+	0.0862453i
$639$	9.88306			0.390968
$640$	2.21183	−	1.60699i	0.0874304	−	0.0635219i
$641$	12.7764	+	39.3218i	0.504638	+	1.55312i	0.801378	+	0.598158i	$0.204100\pi$
$641$	12.7764	+	39.3218i	0.504638	+	1.55312i	−0.296740	+	0.954958i	$0.595900\pi$
$642$	15.0501	+	4.89008i	0.593981	+	0.192996i
$643$	−10.3056	+	14.1845i	−0.406414	+	0.559381i	−0.962339	−	0.271852i	$-0.912364\pi$
$643$	−10.3056	+	14.1845i	−0.406414	+	0.559381i	0.555925	+	0.831232i	$0.312364\pi$
$644$	−6.19981	+	1.24906i	−0.244307	+	0.0492197i
$645$	0.0582098	+	0.0189135i	0.00229201	+	0.000744718i
$646$	−36.2072	+	11.7644i	−1.42455	+	0.462865i
$647$	−3.44311	−	4.73903i	−0.135363	−	0.186311i	0.735955	−	0.677031i	$-0.236734\pi$
$647$	−3.44311	−	4.73903i	−0.135363	−	0.186311i	−0.871317	+	0.490720i	$0.836734\pi$
$648$			2.44021i			0.0958605i
$649$	−14.2309	−	36.9728i	−0.558612	−	1.45131i
$650$		−	28.6475i		−	1.12365i
$651$	3.35601	−	28.9641i	0.131532	−	1.13519i
$652$	0.275787	+	0.848786i	0.0108007	+	0.0332410i
$653$	7.91231	−	24.3516i	0.309633	−	0.952952i	−0.668275	−	0.743914i	$-0.732967\pi$
$653$	7.91231	−	24.3516i	0.309633	−	0.952952i	0.977908	−	0.209037i	$-0.0670330\pi$
$654$	5.93137	−	8.16384i	0.231935	−	0.319231i
$655$	−0.751060	+	1.03375i	−0.0293463	+	0.0403918i
$656$	−0.0121120	+	0.0372771i	−0.000472896	+	0.00145542i
$657$	0.608021	+	1.87130i	0.0237212	+	0.0730062i
$658$	−1.76256	+	15.2118i	−0.0687117	+	0.593016i
$659$			22.2740i			0.867671i	0.900992	+	0.433835i	$0.142840\pi$
$659$			22.2740i			0.867671i	−0.900992	+	0.433835i	$0.857160\pi$
$660$	0.0155515	+	0.291692i	0.000605340	+	0.0113541i
$661$		−	20.7076i		−	0.805433i	−0.915325	−	0.402717i	$-0.868066\pi$
$661$		−	20.7076i		−	0.805433i	0.915325	−	0.402717i	$-0.131934\pi$
$662$	9.89194	+	13.6151i	0.384461	+	0.529166i
$663$	11.9706	−	3.88948i	0.464899	−	0.151055i
$664$	10.1264	+	3.29026i	0.392980	+	0.127687i
$665$	−0.755466	−	3.74983i	−0.0292957	−	0.145412i
$666$	−6.81909	+	9.38567i	−0.264234	+	0.363687i
$667$	−2.60977	−	0.847966i	−0.101051	−	0.0328334i
$668$	3.17283	+	9.76495i	0.122760	+	0.377817i
$669$	−9.65648	+	7.01584i	−0.373341	+	0.271248i
$670$	−2.83603			−0.109565
$671$	−2.00356	−	37.5800i	−0.0773466	−	1.45076i
$672$	−4.35164	+	4.73083i	−0.167868	+	0.182496i
$673$	−8.31978	−	11.4512i	−0.320704	−	0.441411i	0.617978	−	0.786195i	$-0.287952\pi$
$673$	−8.31978	−	11.4512i	−0.320704	−	0.441411i	−0.938682	+	0.344784i	$0.887952\pi$
$674$	−0.789677	−	2.43038i	−0.0304172	−	0.0936146i
$675$	4.71661	+	1.53252i	0.181543	+	0.0589867i
$676$	0.244980	+	0.177988i	0.00942231	+	0.00684571i
$677$	27.1743	+	19.7433i	1.04439	+	0.758796i	0.971138	−	0.238517i	$-0.0766613\pi$
$677$	27.1743	+	19.7433i	1.04439	+	0.758796i	0.0732550	+	0.997313i	$0.476661\pi$
$678$	5.42838	−	16.7068i	0.208476	−	0.641622i
$679$	−3.79484	+	8.28509i	−0.145632	+	0.317953i
$680$	1.35400	−	0.983736i	0.0519234	−	0.0377246i
$681$		−	1.35740i		−	0.0520156i
$682$	−53.2491	+	20.4957i	−2.03901	+	0.784820i
$683$	−7.87822			−0.301452			−0.150726	−	0.988576i	$-0.548161\pi$
$683$	−7.87822			−0.301452			−0.150726	+	0.988576i	$0.548161\pi$
$684$	2.53367	−	1.84082i	0.0968773	−	0.0703855i
$685$	3.41630	−	1.11002i	0.130530	−	0.0424118i
$686$	−16.2385	−	23.9192i	−0.619988	−	0.913240i
$687$	14.9538	+	10.8646i	0.570523	+	0.414509i
$688$	0.835479	−	1.14994i	0.0318523	−	0.0438410i
$689$	12.2111	−	37.5818i	0.465205	−	1.43175i
$690$	−1.63830	+	0.532316i	−0.0623690	+	0.0202649i
$691$	7.31139	+	10.0633i	0.278138	+	0.382825i	0.925116	−	0.379684i	$-0.123967\pi$
$691$	7.31139	+	10.0633i	0.278138	+	0.382825i	−0.646978	+	0.762509i	$0.723967\pi$
$692$	−4.62785			−0.175924
$693$	2.18855	+	8.49766i	0.0831363	+	0.322799i
$694$	−11.9107			−0.452124
$695$	−1.13468	−	1.56175i	−0.0430408	−	0.0592406i
$696$	−1.16367	+	0.378098i	−0.0441087	+	0.0143318i
$697$	−0.00879768	+	0.0270765i	−0.000333236	+	0.00102559i
$698$	22.8856	−	31.4993i	0.866232	−	1.19227i
$699$	1.59532	+	1.15906i	0.0603404	+	0.0438398i
$700$	2.81263	+	4.99350i	0.106307	+	0.188737i
$701$	−32.2693	+	10.4849i	−1.21880	+	0.396011i	−0.846643	−	0.532161i	$-0.821380\pi$
$701$	−32.2693	+	10.4849i	−1.21880	+	0.396011i	−0.372152	+	0.928172i	$0.621380\pi$
$702$	−4.67326	+	3.39532i	−0.176381	+	0.128148i
$703$	−53.2873			−2.00977
$704$	−17.8583	−	4.76780i	−0.673059	−	0.179693i
$705$			0.747644i			0.0281579i
$706$	1.68207	−	1.22209i	0.0633055	−	0.0459941i
$707$	14.2682	+	6.53529i	0.536611	+	0.245785i
$708$	−1.61226	+	4.96203i	−0.0605925	+	0.186485i
$709$	−24.6992	−	17.9450i	−0.927599	−	0.673940i	0.0178051	−	0.999841i	$-0.494332\pi$
$709$	−24.6992	−	17.9450i	−0.927599	−	0.673940i	−0.945404	+	0.325902i	$0.894332\pi$
$710$	2.51672	+	1.82850i	0.0944508	+	0.0686225i
$711$	−3.23821	−	1.05216i	−0.121442	−	0.0394590i
$712$	9.54529	+	29.3774i	0.357725	+	1.10096i
$713$	−35.4508	−	48.7939i	−1.32764	−	1.82735i
$714$	−9.51039	+	10.3391i	−0.355918	+	0.386932i
$715$	1.92181	−	1.55913i	0.0718718	−	0.0583083i
$716$	−3.35843			−0.125510
$717$	−16.5214	+	12.0035i	−0.617004	+	0.448280i
$718$	−16.6565	−	51.2635i	−0.621616	−	1.91314i
$719$	0.425024	+	0.138099i	0.0158507	+	0.00515021i	0.316932	−	0.948448i	$-0.397347\pi$
$719$	0.425024	+	0.138099i	0.0158507	+	0.00515021i	−0.301081	+	0.953599i	$0.597347\pi$
$720$	−0.555010	+	0.763905i	−0.0206840	+	0.0284691i
$721$	6.45109	+	32.0206i	0.240251	+	1.19251i
$722$	48.1168	+	15.6341i	1.79072	+	0.581841i
$723$	4.08053	−	1.32584i	0.151756	−	0.0493087i
$724$	−1.54272	−	2.12337i	−0.0573348	−	0.0789145i
$725$			2.48667i			0.0923527i
$726$	12.7399	−	11.5129i	0.472822	−	0.427282i
$727$		−	37.6722i		−	1.39719i	−0.715519	−	0.698593i	$-0.753810\pi$
$727$		−	37.6722i		−	1.39719i	0.715519	−	0.698593i	$-0.246190\pi$
$728$	23.7320	+	2.74978i	0.879566	+	0.101914i
$729$	−0.309017	−	0.951057i	−0.0114451	−	0.0352243i
$730$	−0.191384	+	0.589018i	−0.00708342	+	0.0218005i
$731$	0.606857	−	0.835267i	0.0224454	−	0.0308935i
$732$	−2.91315	+	4.00960i	−0.107673	+	0.148199i
$733$	6.71983	−	20.6815i	0.248203	−	0.763889i	−0.746891	−	0.664947i	$-0.768454\pi$
$733$	6.71983	−	20.6815i	0.248203	−	0.763889i	0.995093	−	0.0989421i	$-0.0315459\pi$
$734$	−15.1015	−	46.4776i	−0.557406	−	1.71552i
$735$	−0.921945	−	1.06878i	−0.0340065	−	0.0394227i
$736$			13.2960i			0.490095i
$737$	18.8268	+	23.2062i	0.693495	+	0.854813i
$738$		−	0.0130659i		−	0.000480962i
$739$	−14.0686	−	19.3638i	−0.517524	−	0.712310i	0.467642	−	0.883918i	$-0.345104\pi$
$739$	−14.0686	−	19.3638i	−0.517524	−	0.712310i	−0.985165	+	0.171608i	$0.945104\pi$
$740$	−0.622516	+	0.202268i	−0.0228841	+	0.00743550i
$741$	−25.2339	−	8.19900i	−0.926991	−	0.301198i
$742$	8.71042	+	43.2350i	0.319770	+	1.58721i
$743$	−18.2302	+	25.0917i	−0.668800	+	0.920524i	−0.999732	−	0.0231301i	$-0.992637\pi$
$743$	−18.2302	+	25.0917i	−0.668800	+	0.920524i	0.330932	+	0.943654i	$0.392637\pi$
$744$	−25.5764	−	8.31029i	−0.937678	−	0.304670i
$745$	0.183245	+	0.563969i	0.00671357	+	0.0206622i
$746$	−9.98960	+	7.25787i	−0.365745	+	0.265729i
$747$	−4.36335			−0.159647
$748$	4.76067	+	1.27100i	0.174067	+	0.0464725i
$749$	19.7399	+	18.1577i	0.721280	+	0.663466i
$750$	1.84262	+	2.53615i	0.0672829	+	0.0926069i
$751$	1.76456	+	5.43076i	0.0643897	+	0.198171i	0.978076	−	0.208250i	$-0.0667767\pi$
$751$	1.76456	+	5.43076i	0.0643897	+	0.198171i	−0.913686	+	0.406421i	$0.866777\pi$
$752$	16.5131	+	5.36543i	0.602170	+	0.195657i
$753$	−10.9610	−	7.96362i	−0.399441	−	0.290211i
$754$	−2.34323	−	1.70246i	−0.0853353	−	0.0619998i
$755$	−0.299633	+	0.922175i	−0.0109048	+	0.0335614i
$756$	0.481234	−	1.05066i	0.0175023	−	0.0382120i
$757$	−5.61537	+	4.07981i	−0.204094	+	0.148283i	−0.685138	−	0.728414i	$-0.740258\pi$
$757$	−5.61537	+	4.07981i	−0.204094	+	0.148283i	0.481043	+	0.876697i	$0.340258\pi$
$758$			14.3942i			0.522820i
$759$	15.2315	+	9.87191i	0.552870	+	0.358328i
$760$	−3.52801			−0.127974
$761$	17.2551	−	12.5366i	0.625497	−	0.454450i	−0.229341	−	0.973346i	$-0.573657\pi$
$761$	17.2551	−	12.5366i	0.625497	−	0.454450i	0.854837	+	0.518896i	$0.173657\pi$
$762$	−2.39234	+	0.777320i	−0.0866655	+	0.0281593i
$763$	14.9019	−	8.39360i	0.539485	−	0.303869i
$764$	−2.90669	−	2.11183i	−0.105160	−	0.0764034i
$765$	−0.403136	+	0.554869i	−0.0145754	+	0.0200613i
$766$	−3.31631	+	10.2065i	−0.119823	+	0.368777i
$767$	42.0383	−	13.6591i	1.51792	−	0.493201i
$768$	5.88917	+	8.10574i	0.212507	+	0.292491i
$769$	5.00134			0.180353			0.0901764	−	0.995926i	$-0.471257\pi$
$769$	5.00134			0.180353			0.0901764	+	0.995926i	$0.471257\pi$
$770$	−1.01487	+	2.56884i	−0.0365734	+	0.0925746i
$771$	−23.1644			−0.834246
$772$	−4.59958	−	6.33077i	−0.165542	−	0.227850i
$773$	−33.0945	+	10.7530i	−1.19033	+	0.386760i	−0.836193	−	0.548435i	$-0.815224\pi$
$773$	−33.0945	+	10.7530i	−1.19033	+	0.386760i	−0.354132	+	0.935195i	$0.615224\pi$
$774$	−0.146421	+	0.450637i	−0.00526299	+	0.0161978i
$775$	−32.1254	+	44.2169i	−1.15398	+	1.58832i
$776$	6.79969	+	4.94026i	0.244095	+	0.177345i
$777$	−17.1322	+	9.64983i	−0.614613	+	0.346186i
$778$	−24.5749	+	7.98488i	−0.881054	+	0.286272i
$779$	0.0485527	−	0.0352756i	0.00173958	−	0.00126388i
$780$	−0.325911			−0.0116695
$781$	−1.74509	−	32.7319i	−0.0624442	−	1.17124i
$782$			29.0580i			1.03911i
$783$	0.405651	−	0.294723i	0.0144968	−	0.0105325i
$784$	−30.2223	+	12.6928i	−1.07937	+	0.453314i
$785$	0.0451725	−	0.139027i	0.00161227	−	0.00496207i
$786$	−8.00285	−	5.81441i	−0.285452	−	0.207393i
$787$	−27.7856	−	20.1874i	−0.990448	−	0.719603i	−0.0304289	−	0.999537i	$-0.509687\pi$
$787$	−27.7856	−	20.1874i	−0.990448	−	0.719603i	−0.960019	+	0.279934i	$0.909687\pi$
$788$	2.67669	+	0.869709i	0.0953531	+	0.0309821i
$789$	−4.74133	−	14.5923i	−0.168796	−	0.519500i
$790$	−0.629946	−	0.867046i	−0.0224125	−	0.0308481i
$791$	20.1564	−	21.9128i	0.716681	−	0.779131i
$792$	8.08179	−	0.430877i	0.287174	−	0.0153106i
$793$	41.9885			1.49105
$794$	−5.49207	+	3.99022i	−0.194906	+	0.141608i
$795$	0.665392	+	2.04787i	0.0235990	+	0.0726303i
$796$	4.10775	+	1.33469i	0.145595	+	0.0473068i
$797$	−9.94844	+	13.6928i	−0.352392	+	0.485026i	−0.948009	−	0.318243i	$-0.896907\pi$
$797$	−9.94844	+	13.6928i	−0.352392	+	0.485026i	0.595618	+	0.803268i	$0.296907\pi$
$798$	29.0297	−	5.84852i	1.02764	−	0.207035i
$799$	11.9944	+	3.89722i	0.424332	+	0.137874i
$800$	11.4590	−	3.72327i	0.405138	−	0.131637i
$801$	−7.44043	−	10.2409i	−0.262895	−	0.361843i
$802$			8.93300i			0.315435i
$803$	6.09023	−	2.34414i	0.214919	−	0.0827229i
$804$		−	3.93543i		−	0.138792i
$805$	−2.90023	−	0.336044i	−0.102220	−	0.0118440i
$806$	−19.6721	−	60.5445i	−0.692920	−	2.13259i
$807$	8.90804	−	27.4161i	0.313578	−	0.965093i
$808$	8.50789	−	11.7101i	0.299306	−	0.411960i
$809$	22.8325	−	31.4263i	0.802749	−	1.10489i	−0.189653	−	0.981851i	$-0.560736\pi$
$809$	22.8325	−	31.4263i	0.802749	−	1.10489i	0.992402	−	0.123038i	$-0.0392638\pi$
$810$	0.0972676	−	0.299359i	0.00341764	−	0.0105184i
$811$	−7.09386	−	21.8326i	−0.249099	−	0.766648i	−0.994935	−	0.100518i	$-0.967950\pi$
$811$	−7.09386	−	21.8326i	−0.249099	−	0.766648i	0.745836	−	0.666129i	$-0.232050\pi$
$812$	0.575593	+	0.0666929i	0.0201993	+	0.00234046i
$813$			15.6731i			0.549680i
$814$	32.2887	+	20.9270i	1.13172	+	0.733492i
$815$			0.412004i			0.0144319i
$816$	9.36221	+	12.8860i	0.327743	+	0.451100i
$817$	−2.06987	+	0.672542i	−0.0724157	+	0.0235293i
$818$	8.77030	+	2.84964i	0.306646	+	0.0996354i
$819$	−9.59761	+	1.93360i	−0.335368	+	0.0675654i
$820$	0.000433305	0	0.000596394i	1.51317e−5	0	2.08270e-5i
$821$	−12.1584	−	3.95051i	−0.424331	−	0.137874i	0.0890638	−	0.996026i	$-0.471612\pi$
$821$	−12.1584	−	3.95051i	−0.424331	−	0.137874i	−0.513395	+	0.858152i	$0.671612\pi$
$822$	8.59336	+	26.4476i	0.299728	+	0.922468i
$823$	−10.1496	+	7.37413i	−0.353793	+	0.257046i	−0.750459	−	0.660917i	$-0.770167\pi$
$823$	−10.1496	+	7.37413i	−0.353793	+	0.257046i	0.396665	+	0.917963i	$0.370167\pi$
$824$	30.1265			1.04950
$825$	4.24276	−	15.8917i	0.147714	−	0.553276i
$826$	−33.3986	+	36.3089i	−1.16209	+	1.26335i
$827$	27.7792	+	38.2348i	0.965978	+	1.32955i	0.944053	+	0.329795i	$0.106980\pi$
$827$	27.7792	+	38.2348i	0.965978	+	1.32955i	0.0219255	+	0.999760i	$0.493020\pi$
$828$	−0.738671	−	2.27340i	−0.0256706	−	0.0790060i
$829$	47.4074	+	15.4036i	1.64653	+	0.534989i	0.977983	−	0.208684i	$-0.0669180\pi$
$829$	47.4074	+	15.4036i	1.64653	+	0.534989i	0.668544	+	0.743673i	$0.266918\pi$
$830$	−1.11113	−	0.807282i	−0.0385678	−	0.0280212i
$831$	12.4810	+	9.06801i	0.432963	+	0.314566i
$832$	6.37280	−	19.6135i	0.220937	−	0.679974i
$833$	−21.9522	+	9.21950i	−0.760600	+	0.319437i
$834$	12.0905	−	8.78424i	0.418659	−	0.304173i
$835$			4.73995i			0.164033i
$836$	−6.54403	−	8.06627i	−0.226330	−	0.278978i
$837$	11.0206			0.380929
$838$	16.4682	−	11.9648i	0.568883	−	0.413318i
$839$	20.3265	−	6.60449i	0.701750	−	0.228012i	0.0636571	−	0.997972i	$-0.479724\pi$
$839$	20.3265	−	6.60449i	0.701750	−	0.228012i	0.638093	+	0.769959i	$0.279724\pi$
$840$	−1.13427	+	0.638889i	−0.0391362	+	0.0220437i
$841$	−23.2581	−	16.8980i	−0.802003	−	0.582689i
$842$	12.9744	−	17.8577i	0.447126	−	0.615416i
$843$	−4.61727	+	14.2105i	−0.159027	+	0.489436i
$844$	2.50944	−	0.815367i	0.0863785	−	0.0280661i
$845$	0.0821678	+	0.113094i	0.00282666	+	0.00389056i
$846$	−5.78797			−0.198994
$847$	27.7571	−	8.74878i	0.953747	−	0.300612i
$848$	50.0060			1.71721
$849$	−2.32128	−	3.19496i	−0.0796660	−	0.109651i
$850$	25.0434	−	8.13711i	0.858983	−	0.279101i
$851$	−12.5685	+	38.6818i	−0.430842	+	1.32600i
$852$	−2.53733	+	3.49234i	−0.0869276	+	0.119646i
$853$	22.5721	+	16.3996i	0.772853	+	0.561511i	0.902826	−	0.430007i	$-0.141489\pi$
$853$	22.5721	+	16.3996i	0.772853	+	0.561511i	−0.129972	+	0.991518i	$0.541489\pi$
$854$	−40.8318	+	22.9988i	−1.39723	+	0.787003i
$855$	1.37502	−	0.446770i	0.0470246	−	0.0152792i
$856$	20.0129	−	14.5402i	0.684027	−	0.496975i
$857$	−47.5491			−1.62425			−0.812124	−	0.583485i	$-0.801689\pi$
$857$	−47.5491			−1.62425			−0.812124	+	0.583485i	$0.801689\pi$
$858$	12.0702	+	14.8779i	0.412070	+	0.507925i
$859$		−	6.77933i		−	0.231308i	−0.993290	−	0.115654i	$-0.963104\pi$
$859$		−	6.77933i		−	0.231308i	0.993290	−	0.115654i	$-0.0368964\pi$
$860$	−0.0216279	+	0.0157136i	−0.000737506	+	0.000535829i
$861$	0.00922189	−	0.0201337i	0.000314281	−	0.000686156i
$862$	3.14542	−	9.68062i	0.107134	−	0.329723i
$863$	−1.30457	−	0.947823i	−0.0444080	−	0.0322643i	0.565360	−	0.824844i	$-0.308737\pi$
$863$	−1.30457	−	0.947823i	−0.0444080	−	0.0322643i	−0.609768	+	0.792580i	$0.708737\pi$
$864$	−1.96551	−	1.42803i	−0.0668681	−	0.0485825i
$865$	−2.03187	−	0.660193i	−0.0690855	−	0.0224472i
$866$	−9.58365	−	29.4954i	−0.325666	−	1.00230i
$867$	−3.19203	−	4.39346i	−0.108407	−	0.149210i
$868$	9.37331	+	8.62201i	0.318151	+	0.292650i
$869$	−2.91288	+	10.9105i	−0.0988128	+	0.370113i
$870$	0.157827			0.00535083
$871$	−26.9734	+	19.5973i	−0.913959	+	0.664030i
$872$	−4.87459	−	15.0024i	−0.165074	−	0.508047i
$873$	−3.27575	−	1.06435i	−0.110867	−	0.0360229i
$874$	36.0042	−	49.5556i	1.21786	−	1.67624i
$875$	1.04935	+	5.20856i	0.0354745	+	0.176081i
$876$	−0.817354	−	0.265574i	−0.0276158	−	0.00897293i
$877$	13.7407	−	4.46463i	0.463991	−	0.150760i	−0.0676864	−	0.997707i	$-0.521562\pi$
$877$	13.7407	−	4.46463i	0.463991	−	0.150760i	0.531678	+	0.846947i	$0.321562\pi$
$878$	22.5566	+	31.0464i	0.761247	+	1.04777i
$879$			20.4165i			0.688630i
$880$	2.62799	+	1.70326i	0.0885897	+	0.0574170i
$881$			13.6216i			0.458923i	0.973318	+	0.229462i	$0.0736965\pi$
$881$			13.6216i			0.458923i	−0.973318	+	0.229462i	$0.926303\pi$
$882$	8.27411	−	7.13734i	0.278604	−	0.240327i
$883$	11.6220	+	35.7687i	0.391110	+	1.20371i	0.931950	+	0.362588i	$0.118107\pi$
$883$	11.6220	+	35.7687i	0.391110	+	1.20371i	−0.540839	+	0.841126i	$0.681893\pi$
$884$	−1.69886	+	5.22857i	−0.0571390	+	0.175856i
$885$	−1.41573	+	1.94859i	−0.0475894	+	0.0655012i
$886$	21.5203	−	29.6201i	0.722987	−	0.995107i
$887$	−13.6151	+	41.9029i	−0.457150	+	1.40696i	0.411443	+	0.911436i	$0.365025\pi$
$887$	−13.6151	+	41.9029i	−0.457150	+	1.40696i	−0.868593	+	0.495527i	$0.834975\pi$
$888$	5.60414	+	17.2478i	0.188063	+	0.578797i
$889$	−4.23508	−	0.490711i	−0.142040	−	0.0164579i
$890$		−	3.98442i		−	0.133558i
$891$	−3.09526	+	1.19137i	−0.103695	+	0.0399125i
$892$		−	5.21349i		−	0.174561i
$893$	−15.6265	−	21.5080i	−0.522920	−	0.719738i
$894$	−4.36603	+	1.41861i	−0.146022	+	0.0474454i
$895$	−1.47452	−	0.479102i	−0.0492879	−	0.0160146i
$896$	7.08485	+	35.1663i	0.236688	+	1.17482i
$897$	−11.9035	+	16.3837i	−0.397445	+	0.547037i
$898$	7.17913	+	2.33264i	0.239571	+	0.0778413i
$899$	1.70759	+	5.25542i	0.0569513	+	0.175278i
$900$	−1.75246	+	1.27324i	−0.0584155	+	0.0424413i
$901$	36.3223			1.21007
$902$	−0.0432732	+	0.00230710i	−0.00144084	+	7.68179e-5i
$903$	−0.543685	+	0.591060i	−0.0180927	+	0.0196693i
$904$	−16.1408	−	22.2159i	−0.536835	−	0.738890i
$905$	−0.374421	−	1.15235i	−0.0124462	−	0.0383054i
$906$	−7.13912	−	2.31964i	−0.237181	−	0.0770649i
$907$	41.1895	+	29.9259i	1.36768	+	0.993675i	0.997915	+	0.0645476i	$0.0205604\pi$
$907$	41.1895	+	29.9259i	1.36768	+	0.993675i	0.369761	+	0.929127i	$0.379440\pi$
$908$	0.479659	+	0.348493i	0.0159180	+	0.0115651i
$909$	−1.83298	+	5.64134i	−0.0607962	+	0.187111i
$910$	−2.80177	−	1.28330i	−0.0928779	−	0.0425410i
$911$	41.4368	−	30.1056i	1.37286	−	0.997442i	0.375354	−	0.926882i	$-0.377521\pi$
$911$	41.4368	−	30.1056i	1.37286	−	0.997442i	0.997507	−	0.0705606i	$-0.0224788\pi$
$912$		−	33.5760i		−	1.11181i
$913$	0.770454	+	14.4511i	0.0254983	+	0.478261i
$914$	22.2702			0.736632
$915$	−1.85102	+	1.34485i	−0.0611928	+	0.0444592i
$916$	−7.67835	+	2.49485i	−0.253700	+	0.0824320i
$917$	−8.22809	−	14.6080i	−0.271716	−	0.482400i
$918$	−4.29558	−	3.12092i	−0.141775	−	0.103006i
$919$	6.47401	−	8.91071i	0.213558	−	0.293937i	−0.688777	−	0.724974i	$-0.741852\pi$
$919$	6.47401	−	8.91071i	0.213558	−	0.293937i	0.902335	+	0.431036i	$0.141852\pi$
$920$	−0.832125	+	2.56102i	−0.0274343	+	0.0844342i
$921$	5.94041	−	1.93016i	0.195743	−	0.0636008i
$922$	−0.323049	−	0.444639i	−0.0106391	−	0.0146434i
$923$	36.5717			1.20377
$924$	−3.56467	−	1.40829i	−0.117269	−	0.0463294i
$925$	36.8573			1.21186
$926$	−29.8747	−	41.1190i	−0.981743	−	1.35125i
$927$	−11.7416	+	3.81507i	−0.385644	+	0.125303i
$928$	0.376440	−	1.15856i	0.0123572	−	0.0380317i
$929$	16.0609	−	22.1059i	0.526940	−	0.725270i	−0.459721	−	0.888064i	$-0.652050\pi$
$929$	16.0609	−	22.1059i	0.526940	−	0.725270i	0.986660	+	0.162794i	$0.0520504\pi$
$930$	2.80640	+	2.03897i	0.0920255	+	0.0668605i
$931$	48.8608	+	11.4769i	1.60135	+	0.376141i
$932$	−0.819149	+	0.266158i	−0.0268321	+	0.00871828i
$933$	11.3922	−	8.27692i	0.372964	−	0.270974i
$934$	49.7202			1.62689
$935$	1.90886	+	1.23718i	0.0624265	+	0.0404601i
$936$			9.02986i			0.295150i
$937$	−36.6105	+	26.5991i	−1.19601	+	0.868955i	−0.993887	−	0.110404i	$-0.964785\pi$
$937$	−36.6105	+	26.5991i	−1.19601	+	0.868955i	−0.202127	+	0.979359i	$0.564785\pi$
$938$	15.4961	−	33.8319i	0.505965	−	1.10465i
$939$	6.11010	−	18.8049i	0.199396	−	0.613676i
$940$	−0.264192	−	0.191947i	−0.00861700	−	0.00626062i
$941$	7.12435	+	5.17614i	0.232247	+	0.168737i	0.697822	−	0.716271i	$-0.254153\pi$
$941$	7.12435	+	5.17614i	0.232247	+	0.168737i	−0.465575	+	0.885008i	$0.654153\pi$
$942$	1.07629	+	0.349708i	0.0350674	+	0.0113941i
$943$	−0.0141552	−	0.0435651i	−0.000460955	−	0.00141867i
$944$	32.8783	+	45.2530i	1.07010	+	1.47286i
$945$	0.361170	−	0.392642i	0.0117489	−	0.0127726i
$946$	1.51833	+	0.405364i	0.0493652	+	0.0131795i
$947$	−47.4464			−1.54180			−0.770901	−	0.636955i	$-0.780194\pi$
$947$	−47.4464			−1.54180			−0.770901	+	0.636955i	$0.780194\pi$
$948$	1.20316	−	0.874148i	0.0390769	−	0.0283910i
$949$	2.24995	+	6.92463i	0.0730364	+	0.224783i
$950$	−52.7915	−	17.1530i	−1.71278	−	0.556516i
$951$	5.06305	−	6.96870i	0.164181	−	0.225975i
$952$	4.33706	+	21.5274i	0.140565	+	0.697708i
$953$	2.96011	+	0.961797i	0.0958873	+	0.0311557i	0.356568	−	0.934269i	$-0.383947\pi$
$953$	2.96011	+	0.961797i	0.0958873	+	0.0311557i	−0.260680	+	0.965425i	$0.583947\pi$
$954$	−15.8538	+	5.15121i	−0.513285	+	0.166776i
$955$	−0.974920	−	1.34186i	−0.0315477	−	0.0434217i
$956$		−	8.91985i		−	0.288489i
$957$	−1.04773	−	1.29144i	−0.0338681	−	0.0417464i
$958$		−	30.9223i		−	0.999055i
$959$	−5.42487	+	46.8193i	−0.175178	+	1.51188i
$960$	0.347259	+	1.06875i	0.0112077	+	0.0344939i
$961$	−27.9519	+	86.0271i	−0.901674	+	2.77507i
$962$	−25.2337	+	34.7311i	−0.813566	+	1.11978i
$963$	−5.95860	+	8.20130i	−0.192013	+	0.264283i
$964$	−0.579109	+	1.78231i	−0.0186518	+	0.0574044i
$965$	−1.11633	−	3.43570i	−0.0359358	−	0.110599i
$966$	2.60152	−	22.4524i	0.0837026	−	0.722395i
$967$		−	36.4221i		−	1.17125i	−0.810580	−	0.585627i	$-0.800848\pi$
$967$		−	36.4221i		−	1.17125i	0.810580	−	0.585627i	$-0.199152\pi$
$968$	−2.85406	−	26.6902i	−0.0917331	−	0.857854i
$969$		−	24.3882i		−	0.783462i
$970$	−0.637248	−	0.877097i	−0.0204608	−	0.0281619i
$971$	−42.0367	+	13.6585i	−1.34902	+	0.438324i	−0.892363	−	0.451319i	$-0.850954\pi$
$971$	−42.0367	+	13.6585i	−1.34902	+	0.438324i	−0.456658	+	0.889642i	$0.650954\pi$
$972$	0.415407	+	0.134974i	0.0133242	+	0.00432929i
$973$	24.8306	−	5.00253i	0.796031	−	0.160374i
$974$	−31.1335	+	42.8515i	−0.997580	+	1.37305i
$975$	17.4536	+	5.67100i	0.558961	+	0.181618i
$976$	16.4196	+	50.5344i	0.525579	+	1.61757i
$977$	−11.5534	+	8.39404i	−0.369626	+	0.268549i	−0.757056	−	0.653350i	$-0.773363\pi$
$977$	−11.5534	+	8.39404i	−0.369626	+	0.268549i	0.387430	+	0.921899i	$0.373363\pi$
$978$	−3.18958			−0.101991
$979$	−32.6032	+	26.4504i	−1.04200	+	0.845358i
$980$	0.614368	−	0.0513894i	0.0196253	−	0.00164158i
$981$	3.79968	+	5.22981i	0.121314	+	0.166975i
$982$	10.7924	+	33.2156i	0.344399	+	1.05995i
$983$	16.0501	+	5.21499i	0.511919	+	0.166332i	0.553575	−	0.832800i	$-0.313263\pi$
$983$	16.0501	+	5.21499i	0.511919	+	0.166332i	−0.0416561	+	0.999132i	$0.513263\pi$
$984$	−0.0165240	−	0.0120054i	−0.000526767	−	0.000382718i
$985$	1.05114	+	0.763695i	0.0334920	+	0.0243333i
$986$	0.822699	−	2.53201i	0.0262001	−	0.0806355i
$987$	−8.91889	−	4.08514i	−0.283891	−	0.130031i
$988$	9.37570	−	6.81184i	0.298281	−	0.216714i
$989$			1.66117i			0.0528221i
$990$	−1.00863	−	0.269284i	−0.0320563	−	0.00855840i
$991$	−51.8232			−1.64622			−0.823109	−	0.567883i	$-0.807763\pi$
$991$	−51.8232			−1.64622			−0.823109	+	0.567883i	$0.807763\pi$
$992$	21.6612	−	15.7378i	0.687743	−	0.499675i
$993$	−10.2532	+	3.33148i	−0.325376	+	0.105721i
$994$	−35.5642	+	20.0318i	−1.12803	+	0.635371i
$995$	1.61312	+	1.17200i	0.0511392	+	0.0371548i
$996$	1.12023	−	1.54186i	0.0354958	−	0.0488558i
$997$	13.3528	−	41.0956i	0.422886	−	1.30151i	−0.482118	−	0.876106i	$-0.660132\pi$
$997$	13.3528	−	41.0956i	0.422886	−	1.30151i	0.905004	−	0.425403i	$-0.139868\pi$
$998$	−31.9511	+	10.3815i	−1.01139	+	0.328622i
$999$	−4.36835	−	6.01252i	−0.138209	−	0.190228i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.w.a.118.4	yes	64
3.2	odd	2		693.2.bu.f.118.14		64
7.6	odd	2	inner	231.2.w.a.118.3	✓	64
11.7	odd	10	inner	231.2.w.a.139.3	yes	64
21.20	even	2		693.2.bu.f.118.13		64
33.29	even	10		693.2.bu.f.370.13		64
77.62	even	10	inner	231.2.w.a.139.4	yes	64
231.62	odd	10		693.2.bu.f.370.14		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.w.a.118.3	✓	64	7.6	odd	2	inner
231.2.w.a.118.4	yes	64	1.1	even	1	trivial
231.2.w.a.139.3	yes	64	11.7	odd	10	inner
231.2.w.a.139.4	yes	64	77.62	even	10	inner
693.2.bu.f.118.13		64	21.20	even	2
693.2.bu.f.118.14		64	3.2	odd	2
693.2.bu.f.370.13		64	33.29	even	10
693.2.bu.f.370.14		64	231.62	odd	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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.w (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.917545 - 1.26289i) q^{2} +(0.951057 - 0.309017i) q^{3} +(-0.134974 + 0.415407i) q^{4} +(-0.118521 + 0.163130i) q^{5} +(-1.26289 - 0.917545i) q^{6} +(-1.29844 - 2.30523i) q^{7} +(-2.32078 + 0.754067i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.917545 - 1.26289i) q^{2} +(0.951057 - 0.309017i) q^{3} +(-0.134974 + 0.415407i) q^{4} +(-0.118521 + 0.163130i) q^{5} +(-1.26289 - 0.917545i) q^{6} +(-1.29844 - 2.30523i) q^{7} +(-2.32078 + 0.754067i) q^{8} +(0.809017 - 0.587785i) q^{9} +0.314765 q^{10} +(-2.08955 - 2.57561i) q^{11} +0.436785i q^{12} +(2.99372 - 2.17507i) q^{13} +(-1.71988 + 3.75493i) q^{14} +(-0.0623103 + 0.191771i) q^{15} +(3.78846 + 2.75247i) q^{16} +(2.75177 + 1.99928i) q^{17} +(-1.48462 - 0.482382i) q^{18} +(-2.21568 - 6.81916i) q^{19} +(-0.0517682 - 0.0712529i) q^{20} +(-1.94724 - 1.79116i) q^{21} +(-1.33547 + 5.00212i) q^{22} -5.47270 q^{23} +(-1.97417 + 1.43432i) q^{24} +(1.53252 + 4.71661i) q^{25} +(-5.49375 - 1.78503i) q^{26} +(0.587785 - 0.809017i) q^{27} +(1.13286 - 0.228234i) q^{28} +(0.476871 + 0.154945i) q^{29} +(0.299359 - 0.0972676i) q^{30} +(6.47776 + 8.91587i) q^{31} -2.42951i q^{32} +(-2.78319 - 1.80385i) q^{33} -5.30962i q^{34} +(0.529944 + 0.0614037i) q^{35} +(0.134974 + 0.415407i) q^{36} +(2.29658 - 7.06815i) q^{37} +(-6.57888 + 9.05505i) q^{38} +(2.17507 - 2.99372i) q^{39} +(0.152050 - 0.467962i) q^{40} +(0.00258650 + 0.00796044i) q^{41} +(-0.475364 + 4.10262i) q^{42} -0.303537i q^{43} +(1.35196 - 0.520373i) q^{44} +0.201640i q^{45} +(5.02145 + 6.91143i) q^{46} +(3.52634 - 1.14578i) q^{47} +(4.45360 + 1.44706i) q^{48} +(-3.62813 + 5.98637i) q^{49} +(4.55042 - 6.26311i) q^{50} +(3.23491 + 1.05108i) q^{51} +(0.499463 + 1.53719i) q^{52} +(8.63924 - 6.27678i) q^{53} -1.56102 q^{54} +(0.667817 - 0.0356044i) q^{55} +(4.75168 + 4.37081i) q^{56} +(-4.21448 - 5.80073i) q^{57} +(-0.241872 - 0.744406i) q^{58} +(11.3604 + 3.69120i) q^{59} +(-0.0712529 - 0.0517682i) q^{60} +(9.17982 + 6.66953i) q^{61} +(5.31615 - 16.3614i) q^{62} +(-2.40543 - 1.10177i) q^{63} +(4.50871 - 3.27577i) q^{64} +0.746158i q^{65} +(0.275635 + 5.16998i) q^{66} -9.00999 q^{67} +(-1.20193 + 0.873256i) q^{68} +(-5.20484 + 1.69116i) q^{69} +(-0.408702 - 0.725603i) q^{70} +(7.99556 + 5.80911i) q^{71} +(-1.43432 + 1.97417i) q^{72} +(-0.608021 + 1.87130i) q^{73} +(-11.0335 + 3.58501i) q^{74} +(2.91503 + 4.01219i) q^{75} +3.13179 q^{76} +(-3.22422 + 8.16115i) q^{77} -5.77647 q^{78} +(-2.00132 - 2.75459i) q^{79} +(-0.898024 + 0.291786i) q^{80} +(0.309017 - 0.951057i) q^{81} +(0.00767994 - 0.0105705i) q^{82} +(-3.53003 - 2.56472i) q^{83} +(1.00689 - 0.567137i) q^{84} +(-0.652287 + 0.211941i) q^{85} +(-0.383335 + 0.278509i) q^{86} +0.501412 q^{87} +(6.79157 + 4.40177i) q^{88} -12.6584i q^{89} +(0.254650 - 0.185014i) q^{90} +(-8.90117 - 4.07702i) q^{91} +(0.738671 - 2.27340i) q^{92} +(8.91587 + 6.47776i) q^{93} +(-4.68256 - 3.40208i) q^{94} +(1.37502 + 0.446770i) q^{95} +(-0.750759 - 2.31060i) q^{96} +(-2.02452 - 2.78652i) q^{97} +(10.8891 - 0.910831i) q^{98} +(-3.20439 - 0.855508i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 12 q^{4} + 10 q^{7} - 20 q^{8} + 16 q^{9}+O(q^{10}) \) 64 * q + 12 * q^4 + 10 * q^7 - 20 * q^8 + 16 * q^9	\( 64 q + 12 q^{4} + 10 q^{7} - 20 q^{8} + 16 q^{9} - 16 q^{11} + 12 q^{14} - 12 q^{15} - 16 q^{16} + 10 q^{18} - 40 q^{22} - 24 q^{23} + 44 q^{25} - 30 q^{28} - 40 q^{29} - 40 q^{35} - 12 q^{36} + 32 q^{37} - 2 q^{42} + 22 q^{44} - 70 q^{46} - 50 q^{49} - 40 q^{51} - 64 q^{53} + 80 q^{56} + 2 q^{58} - 36 q^{60} + 10 q^{63} + 72 q^{64} - 8 q^{67} - 26 q^{70} + 68 q^{71} - 10 q^{72} + 80 q^{74} + 90 q^{77} - 72 q^{78} + 40 q^{79} - 16 q^{81} + 60 q^{84} - 40 q^{85} - 62 q^{86} + 140 q^{88} + 54 q^{91} + 18 q^{92} - 20 q^{93} + 20 q^{95} - 4 q^{99}+O(q^{100}) \) 64 * q + 12 * q^4 + 10 * q^7 - 20 * q^8 + 16 * q^9 - 16 * q^11 + 12 * q^14 - 12 * q^15 - 16 * q^16 + 10 * q^18 - 40 * q^22 - 24 * q^23 + 44 * q^25 - 30 * q^28 - 40 * q^29 - 40 * q^35 - 12 * q^36 + 32 * q^37 - 2 * q^42 + 22 * q^44 - 70 * q^46 - 50 * q^49 - 40 * q^51 - 64 * q^53 + 80 * q^56 + 2 * q^58 - 36 * q^60 + 10 * q^63 + 72 * q^64 - 8 * q^67 - 26 * q^70 + 68 * q^71 - 10 * q^72 + 80 * q^74 + 90 * q^77 - 72 * q^78 + 40 * q^79 - 16 * q^81 + 60 * q^84 - 40 * q^85 - 62 * q^86 + 140 * q^88 + 54 * q^91 + 18 * q^92 - 20 * q^93 + 20 * q^95 - 4 * q^99

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