LMFDB - Embedded newform 273.2.cg.b.124.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(19,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 10, 5]))

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

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

chi := DirichletCharacter("273.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.cg (of order $12$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			124.10
Character	$\chi$	$=$	273.124
Dual form			273.2.cg.b.262.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.680470 - 2.53955i) q^{2} -1.00000i q^{3} +(-4.25421 - 2.45617i) q^{4} +(0.134776 + 0.502992i) q^{5} +(-2.53955 - 0.680470i) q^{6} +(-2.56445 + 0.650845i) q^{7} +(-5.41427 + 5.41427i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(0.680470 - 2.53955i) q^{2} -1.00000i q^{3} +(-4.25421 - 2.45617i) q^{4} +(0.134776 + 0.502992i) q^{5} +(-2.53955 - 0.680470i) q^{6} +(-2.56445 + 0.650845i) q^{7} +(-5.41427 + 5.41427i) q^{8} -1.00000 q^{9} +1.36908 q^{10} +(1.41413 - 1.41413i) q^{11} +(-2.45617 + 4.25421i) q^{12} +(-2.40655 - 2.68487i) q^{13} +(-0.0921792 + 6.95542i) q^{14} +(0.502992 - 0.134776i) q^{15} +(5.15321 + 8.92562i) q^{16} +(2.54630 - 4.41032i) q^{17} +(-0.680470 + 2.53955i) q^{18} +(5.09679 - 5.09679i) q^{19} +(0.662067 - 2.47087i) q^{20} +(0.650845 + 2.56445i) q^{21} +(-2.62897 - 4.55351i) q^{22} +(-4.14570 + 2.39352i) q^{23} +(5.41427 + 5.41427i) q^{24} +(4.09529 - 2.36442i) q^{25} +(-8.45594 + 4.28458i) q^{26} +1.00000i q^{27} +(12.5083 + 3.52989i) q^{28} +(-1.35547 + 2.34774i) q^{29} -1.36908i q^{30} +(3.23806 + 0.867635i) q^{31} +(11.3816 - 3.04969i) q^{32} +(-1.41413 - 1.41413i) q^{33} +(-9.46754 - 9.46754i) q^{34} +(-0.672997 - 1.20218i) q^{35} +(4.25421 + 2.45617i) q^{36} +(7.17752 + 1.92321i) q^{37} +(-9.47532 - 16.4117i) q^{38} +(-2.68487 + 2.40655i) q^{39} +(-3.45305 - 1.99362i) q^{40} +(-0.938828 - 3.50375i) q^{41} +(6.95542 + 0.0921792i) q^{42} +(-3.62298 + 2.09173i) q^{43} +(-9.48933 + 2.54266i) q^{44} +(-0.134776 - 0.502992i) q^{45} +(3.25743 + 12.1569i) q^{46} +(0.0803226 - 0.0215224i) q^{47} +(8.92562 - 5.15321i) q^{48} +(6.15280 - 3.33812i) q^{49} +(-3.21783 - 12.0091i) q^{50} +(-4.41032 - 2.54630i) q^{51} +(3.64348 + 17.3329i) q^{52} +(6.85585 + 11.8747i) q^{53} +(2.53955 + 0.680470i) q^{54} +(0.901885 + 0.520704i) q^{55} +(10.3608 - 17.4085i) q^{56} +(-5.09679 - 5.09679i) q^{57} +(5.03985 + 5.03985i) q^{58} +(-5.34294 + 1.43164i) q^{59} +(-2.47087 - 0.662067i) q^{60} -0.753473i q^{61} +(4.40680 - 7.63280i) q^{62} +(2.56445 - 0.650845i) q^{63} -10.3665i q^{64} +(1.02612 - 1.57233i) q^{65} +(-4.55351 + 2.62897i) q^{66} +(-7.68466 - 7.68466i) q^{67} +(-21.6650 + 12.5083i) q^{68} +(2.39352 + 4.14570i) q^{69} +(-3.51095 + 0.891061i) q^{70} +(-1.34000 + 5.00093i) q^{71} +(5.41427 - 5.41427i) q^{72} +(0.551150 - 2.05692i) q^{73} +(9.76817 - 16.9190i) q^{74} +(-2.36442 - 4.09529i) q^{75} +(-34.2014 + 9.16424i) q^{76} +(-2.70608 + 4.54683i) q^{77} +(4.28458 + 8.45594i) q^{78} +(6.17212 - 10.6904i) q^{79} +(-3.79499 + 3.79499i) q^{80} +1.00000 q^{81} -9.53679 q^{82} +(-7.09696 + 7.09696i) q^{83} +(3.52989 - 12.5083i) q^{84} +(2.56154 + 0.686362i) q^{85} +(2.84672 + 10.6241i) q^{86} +(2.34774 + 1.35547i) q^{87} +15.3129i q^{88} +(3.53214 - 13.1821i) q^{89} -1.36908 q^{90} +(7.91891 + 5.31892i) q^{91} +23.5156 q^{92} +(0.867635 - 3.23806i) q^{93} -0.218629i q^{94} +(3.25057 + 1.87672i) q^{95} +(-3.04969 - 11.3816i) q^{96} +(3.28692 + 0.880729i) q^{97} +(-4.29051 - 17.8968i) q^{98} +(-1.41413 + 1.41413i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 8 q^{7} - 40 q^{9}+O(q^{10}) $ 40 * q - 8 * q^7 - 40 * q^9	$ 40 q - 8 q^{7} - 40 q^{9} + 4 q^{11} - 24 q^{12} - 18 q^{14} + 32 q^{16} + 4 q^{17} + 14 q^{19} + 14 q^{20} + 2 q^{21} + 4 q^{22} + 12 q^{23} + 24 q^{25} - 32 q^{26} + 16 q^{28} + 8 q^{29} + 14 q^{31} - 26 q^{32} - 4 q^{33} - 24 q^{34} + 26 q^{35} + 36 q^{37} - 8 q^{38} + 18 q^{39} - 30 q^{40} - 2 q^{41} - 66 q^{43} - 32 q^{44} - 26 q^{46} - 4 q^{47} + 24 q^{48} - 14 q^{49} - 20 q^{50} + 2 q^{52} - 8 q^{53} - 42 q^{55} + 46 q^{56} - 14 q^{57} + 24 q^{58} + 14 q^{59} + 2 q^{60} + 24 q^{62} + 8 q^{63} + 28 q^{65} - 18 q^{66} - 44 q^{67} - 18 q^{68} + 4 q^{69} - 4 q^{70} - 6 q^{71} + 14 q^{73} - 20 q^{74} + 24 q^{75} - 64 q^{76} + 24 q^{77} + 8 q^{78} + 20 q^{80} + 40 q^{81} + 48 q^{82} - 12 q^{83} + 22 q^{84} + 2 q^{85} - 60 q^{86} + 18 q^{87} - 2 q^{89} - 14 q^{91} + 236 q^{92} - 8 q^{93} + 24 q^{95} + 16 q^{96} - 62 q^{97} - 88 q^{98} - 4 q^{99}+O(q^{100}) $ 40 * q - 8 * q^7 - 40 * q^9 + 4 * q^11 - 24 * q^12 - 18 * q^14 + 32 * q^16 + 4 * q^17 + 14 * q^19 + 14 * q^20 + 2 * q^21 + 4 * q^22 + 12 * q^23 + 24 * q^25 - 32 * q^26 + 16 * q^28 + 8 * q^29 + 14 * q^31 - 26 * q^32 - 4 * q^33 - 24 * q^34 + 26 * q^35 + 36 * q^37 - 8 * q^38 + 18 * q^39 - 30 * q^40 - 2 * q^41 - 66 * q^43 - 32 * q^44 - 26 * q^46 - 4 * q^47 + 24 * q^48 - 14 * q^49 - 20 * q^50 + 2 * q^52 - 8 * q^53 - 42 * q^55 + 46 * q^56 - 14 * q^57 + 24 * q^58 + 14 * q^59 + 2 * q^60 + 24 * q^62 + 8 * q^63 + 28 * q^65 - 18 * q^66 - 44 * q^67 - 18 * q^68 + 4 * q^69 - 4 * q^70 - 6 * q^71 + 14 * q^73 - 20 * q^74 + 24 * q^75 - 64 * q^76 + 24 * q^77 + 8 * q^78 + 20 * q^80 + 40 * q^81 + 48 * q^82 - 12 * q^83 + 22 * q^84 + 2 * q^85 - 60 * q^86 + 18 * q^87 - 2 * q^89 - 14 * q^91 + 236 * q^92 - 8 * q^93 + 24 * q^95 + 16 * q^96 - 62 * q^97 - 88 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.680470	−	2.53955i	0.481165	−	1.79573i	−0.115577	−	0.993298i	$-0.536872\pi$
$2$	0.680470	−	2.53955i	0.481165	−	1.79573i	0.596742	−	0.802433i	$-0.296461\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−4.25421	−	2.45617i	−2.12711	−	1.22809i
$5$	0.134776	+	0.502992i	0.0602738	+	0.224945i	0.989492	−	0.144586i	$-0.0461851\pi$
$5$	0.134776	+	0.502992i	0.0602738	+	0.224945i	−0.929218	+	0.369531i	$0.879518\pi$
$6$	−2.53955	−	0.680470i	−1.03677	−	0.277801i
$7$	−2.56445	+	0.650845i	−0.969271	+	0.245996i
$7$	−2.56445	+	0.650845i	−0.969271	+	0.245996i
$8$	−5.41427	+	5.41427i	−1.91423	+	1.91423i
$9$	−1.00000			−0.333333
$10$	1.36908			0.432942
$11$	1.41413	−	1.41413i	0.426375	−	0.426375i	−0.461016	−	0.887392i	$-0.652515\pi$
$11$	1.41413	−	1.41413i	0.426375	−	0.426375i	0.887392	+	0.461016i	$0.152515\pi$
$12$	−2.45617	+	4.25421i	−0.709036	+	1.22809i
$13$	−2.40655	−	2.68487i	−0.667457	−	0.744648i
$13$	−2.40655	−	2.68487i	−0.667457	−	0.744648i
$14$	−0.0921792	+	6.95542i	−0.0246359	+	1.85891i
$15$	0.502992	−	0.134776i	0.129872	−	0.0347991i
$16$	5.15321	+	8.92562i	1.28830	+	2.23141i
$17$	2.54630	−	4.41032i	0.617569	−	1.06966i	−0.372359	−	0.928089i	$-0.621451\pi$
$17$	2.54630	−	4.41032i	0.617569	−	1.06966i	0.989928	−	0.141572i	$-0.0452156\pi$
$18$	−0.680470	+	2.53955i	−0.160388	+	0.598577i
$19$	5.09679	−	5.09679i	1.16928	−	1.16928i	0.186905	−	0.982378i	$-0.440154\pi$
$19$	5.09679	−	5.09679i	1.16928	−	1.16928i	0.982378	−	0.186905i	$-0.0598457\pi$
$20$	0.662067	−	2.47087i	0.148043	−	0.552503i
$21$	0.650845	+	2.56445i	0.142026	+	0.559609i
$22$	−2.62897	−	4.55351i	−0.560499	−	0.970812i
$23$	−4.14570	+	2.39352i	−0.864437	+	0.499083i	−0.865496	−	0.500916i	$-0.832996\pi$
$23$	−4.14570	+	2.39352i	−0.864437	+	0.499083i	0.00105850	+	0.999999i	$0.499663\pi$
$24$	5.41427	+	5.41427i	1.10518	+	1.10518i
$25$	4.09529	−	2.36442i	0.819058	−	0.472883i
$26$	−8.45594	+	4.28458i	−1.65835	+	0.840275i
$27$			1.00000i			0.192450i
$28$	12.5083	+	3.52989i	2.36385	+	0.667087i
$29$	−1.35547	+	2.34774i	−0.251704	+	0.435965i	−0.963995	−	0.265920i	$-0.914324\pi$
$29$	−1.35547	+	2.34774i	−0.251704	+	0.435965i	0.712291	+	0.701884i	$0.247658\pi$
$30$		−	1.36908i		−	0.249959i
$31$	3.23806	+	0.867635i	0.581572	+	0.155832i	0.537599	−	0.843201i	$-0.319332\pi$
$31$	3.23806	+	0.867635i	0.581572	+	0.155832i	0.0439736	+	0.999033i	$0.485998\pi$
$32$	11.3816	−	3.04969i	2.01200	−	0.539114i
$33$	−1.41413	−	1.41413i	−0.246168	−	0.246168i
$34$	−9.46754	−	9.46754i	−1.62367	−	1.62367i
$35$	−0.672997	−	1.20218i	−0.113757	−	0.203205i
$36$	4.25421	+	2.45617i	0.709036	+	0.409362i
$37$	7.17752	+	1.92321i	1.17998	+	0.316174i	0.794917	−	0.606718i	$-0.207514\pi$
$37$	7.17752	+	1.92321i	1.17998	+	0.316174i	0.385060	+	0.922892i	$0.374181\pi$
$38$	−9.47532	−	16.4117i	−1.53710	−	2.66234i
$39$	−2.68487	+	2.40655i	−0.429923	+	0.385356i
$40$	−3.45305	−	1.99362i	−0.545975	−	0.315219i
$41$	−0.938828	−	3.50375i	−0.146620	−	0.547194i	−0.999678	−	0.0253776i	$-0.991921\pi$
$41$	−0.938828	−	3.50375i	−0.146620	−	0.547194i	0.853058	−	0.521817i	$-0.174745\pi$
$42$	6.95542	+	0.0921792i	1.07324	+	0.0142236i
$43$	−3.62298	+	2.09173i	−0.552500	+	0.318986i	−0.750130	−	0.661291i	$-0.770009\pi$
$43$	−3.62298	+	2.09173i	−0.552500	+	0.318986i	0.197630	+	0.980277i	$0.436676\pi$
$44$	−9.48933	+	2.54266i	−1.43057	+	0.383320i
$45$	−0.134776	−	0.502992i	−0.0200913	−	0.0749816i
$46$	3.25743	+	12.1569i	0.480282	+	1.79244i
$47$	0.0803226	−	0.0215224i	0.0117163	−	0.00313936i	−0.252956	−	0.967478i	$-0.581403\pi$
$47$	0.0803226	−	0.0215224i	0.0117163	−	0.00313936i	0.264672	+	0.964338i	$0.414736\pi$
$48$	8.92562	−	5.15321i	1.28830	−	0.743802i
$49$	6.15280	−	3.33812i	0.878972	−	0.476874i
$50$	−3.21783	−	12.0091i	−0.455070	−	1.69834i
$51$	−4.41032	−	2.54630i	−0.617569	−	0.356553i
$52$	3.64348	+	17.3329i	0.505260	+	2.40364i
$53$	6.85585	+	11.8747i	0.941723	+	1.63111i	0.762183	+	0.647362i	$0.224128\pi$
$53$	6.85585	+	11.8747i	0.941723	+	1.63111i	0.179541	+	0.983751i	$0.442539\pi$
$54$	2.53955	+	0.680470i	0.345589	+	0.0926002i
$55$	0.901885	+	0.520704i	0.121610	+	0.0702117i
$56$	10.3608	−	17.4085i	1.38452	−	2.32631i
$57$	−5.09679	−	5.09679i	−0.675086	−	0.675086i
$58$	5.03985	+	5.03985i	0.661764	+	0.661764i
$59$	−5.34294	+	1.43164i	−0.695591	+	0.186383i	−0.589255	−	0.807947i	$-0.700579\pi$
$59$	−5.34294	+	1.43164i	−0.695591	+	0.186383i	−0.106336	+	0.994330i	$0.533912\pi$
$60$	−2.47087	−	0.662067i	−0.318988	−	0.0854725i
$61$		−	0.753473i		−	0.0964723i	−0.998836	−	0.0482361i	$-0.984640\pi$
$61$		−	0.753473i		−	0.0964723i	0.998836	−	0.0482361i	$-0.0153600\pi$
$62$	4.40680	−	7.63280i	0.559664	−	0.969367i
$63$	2.56445	−	0.650845i	0.323090	−	0.0819987i
$64$		−	10.3665i		−	1.29581i
$65$	1.02612	−	1.57233i	0.127275	−	0.195024i
$66$	−4.55351	+	2.62897i	−0.560499	+	0.323604i
$67$	−7.68466	−	7.68466i	−0.938831	−	0.938831i	0.0594033	−	0.998234i	$-0.481080\pi$
$67$	−7.68466	−	7.68466i	−0.938831	−	0.938831i	−0.998234	+	0.0594033i	$0.981080\pi$
$68$	−21.6650	+	12.5083i	−2.62727	+	1.51685i
$69$	2.39352	+	4.14570i	0.288146	+	0.499083i
$70$	−3.51095	+	0.891061i	−0.419638	+	0.106502i
$71$	−1.34000	+	5.00093i	−0.159028	+	0.593502i	0.839698	+	0.543053i	$0.182732\pi$
$71$	−1.34000	+	5.00093i	−0.159028	+	0.593502i	−0.998727	+	0.0504485i	$0.983935\pi$
$72$	5.41427	−	5.41427i	0.638078	−	0.638078i
$73$	0.551150	−	2.05692i	0.0645072	−	0.240744i	−0.926143	−	0.377174i	$-0.876896\pi$
$73$	0.551150	−	2.05692i	0.0645072	−	0.240744i	0.990650	+	0.136429i	$0.0435627\pi$
$74$	9.76817	−	16.9190i	1.13553	−	1.96679i
$75$	−2.36442	−	4.09529i	−0.273019	−	0.472883i
$76$	−34.2014	+	9.16424i	−3.92317	+	1.05121i
$77$	−2.70608	+	4.54683i	−0.308386	+	0.518160i
$78$	4.28458	+	8.45594i	0.485133	+	0.957446i
$79$	6.17212	−	10.6904i	0.694418	−	1.20277i	−0.275959	−	0.961169i	$-0.588995\pi$
$79$	6.17212	−	10.6904i	0.694418	−	1.20277i	0.970377	−	0.241597i	$-0.0776713\pi$
$80$	−3.79499	+	3.79499i	−0.424292	+	0.424292i
$81$	1.00000			0.111111
$82$	−9.53679			−1.05316
$83$	−7.09696	+	7.09696i	−0.778993	+	0.778993i	−0.979660	−	0.200667i	$-0.935689\pi$
$83$	−7.09696	+	7.09696i	−0.778993	+	0.778993i	0.200667	+	0.979660i	$0.435689\pi$
$84$	3.52989	−	12.5083i	0.385143	−	1.36477i
$85$	2.56154	+	0.686362i	0.277838	+	0.0744464i
$86$	2.84672	+	10.6241i	0.306970	+	1.14563i
$87$	2.34774	+	1.35547i	0.251704	+	0.145322i
$88$			15.3129i			1.63236i
$89$	3.53214	−	13.1821i	0.374406	−	1.39730i	−0.479805	−	0.877375i	$-0.659293\pi$
$89$	3.53214	−	13.1821i	0.374406	−	1.39730i	0.854211	−	0.519927i	$-0.174041\pi$
$90$	−1.36908			−0.144314
$91$	7.91891	+	5.31892i	0.830127	+	0.557574i
$92$	23.5156			2.45167
$93$	0.867635	−	3.23806i	0.0899695	−	0.335771i
$94$		−	0.218629i		−	0.0225498i
$95$	3.25057	+	1.87672i	0.333501	+	0.192547i
$96$	−3.04969	−	11.3816i	−0.311257	−	1.16163i
$97$	3.28692	+	0.880729i	0.333737	+	0.0894244i	0.421796	−	0.906691i	$-0.361400\pi$
$97$	3.28692	+	0.880729i	0.333737	+	0.0894244i	−0.0880594	+	0.996115i	$0.528067\pi$
$98$	−4.29051	−	17.8968i	−0.433407	−	1.80785i
$99$	−1.41413	+	1.41413i	−0.142125	+	0.142125i
$100$	−23.2297			−2.32297
$101$	12.0952			1.20352			0.601760	−	0.798677i	$-0.294466\pi$
$101$	12.0952			1.20352			0.601760	+	0.798677i	$0.294466\pi$
$102$	−9.46754	+	9.46754i	−0.937426	+	0.937426i
$103$	−4.04418	+	7.00473i	−0.398485	+	0.690196i	−0.993539	−	0.113489i	$-0.963797\pi$
$103$	−4.04418	+	7.00473i	−0.398485	+	0.690196i	0.595054	+	0.803686i	$0.297131\pi$
$104$	27.5663	+	1.50689i	2.70310	+	0.147762i
$105$	−1.20218	+	0.672997i	−0.117321	+	0.0656777i
$106$	34.8215	−	9.33040i	3.38216	−	0.906248i
$107$	2.82363	+	4.89066i	0.272970	+	0.472798i	0.969621	−	0.244612i	$-0.0786606\pi$
$107$	2.82363	+	4.89066i	0.272970	+	0.472798i	−0.696651	+	0.717410i	$0.745327\pi$
$108$	2.45617	−	4.25421i	0.236345	−	0.409362i
$109$	2.50644	−	9.35415i	0.240073	−	0.895965i	−0.735723	−	0.677282i	$-0.763158\pi$
$109$	2.50644	−	9.35415i	0.240073	−	0.895965i	0.975796	−	0.218682i	$-0.0701758\pi$
$110$	1.93606	−	1.93606i	0.184596	−	0.184596i
$111$	1.92321	−	7.17752i	0.182543	−	0.681260i
$112$	−19.0243	−	19.5354i	−1.79763	−	1.84592i
$113$	9.60923	+	16.6437i	0.903960	+	1.56570i	0.822307	+	0.569044i	$0.192686\pi$
$113$	9.60923	+	16.6437i	0.903960	+	1.56570i	0.0816525	+	0.996661i	$0.473980\pi$
$114$	−16.4117	+	9.47532i	−1.53710	+	0.887445i
$115$	−1.76266	−	1.76266i	−0.164369	−	0.164369i
$116$	11.5329	−	6.65853i	1.07080	−	0.618229i
$117$	2.40655	+	2.68487i	0.222486	+	0.248216i
$118$			14.5428i			1.33878i
$119$	−3.65942	+	12.9673i	−0.335459	+	1.18871i
$120$	−1.99362	+	3.45305i	−0.181992	+	0.315219i
$121$			7.00049i			0.636408i
$122$	−1.91348	−	0.512715i	−0.173238	−	0.0464191i
$123$	−3.50375	+	0.938828i	−0.315923	+	0.0846512i
$124$	−11.6443	−	11.6443i	−1.04569	−	1.04569i
$125$	3.58231	+	3.58231i	0.320411	+	0.320411i
$126$	0.0921792	−	6.95542i	0.00821197	−	0.619638i
$127$	−5.78281	−	3.33871i	−0.513141	−	0.296262i	0.220983	−	0.975278i	$-0.429074\pi$
$127$	−5.78281	−	3.33871i	−0.513141	−	0.296262i	−0.734124	+	0.679015i	$0.762407\pi$
$128$	−3.56294	−	0.954687i	−0.314923	−	0.0843832i
$129$	2.09173	+	3.62298i	0.184167	+	0.318986i
$130$	−3.29477	−	3.67581i	−0.288970	−	0.322390i
$131$	−0.269003	−	0.155309i	−0.0235029	−	0.0135694i	0.488203	−	0.872730i	$-0.337653\pi$
$131$	−0.269003	−	0.155309i	−0.0235029	−	0.0135694i	−0.511705	+	0.859161i	$0.670986\pi$
$132$	2.54266	+	9.48933i	0.221310	+	0.825940i
$133$	−9.75324	+	16.3877i	−0.845713	+	1.42099i
$134$	−24.7447	+	14.2864i	−2.13762	+	1.23416i
$135$	−0.502992	+	0.134776i	−0.0432907	+	0.0115997i
$136$	10.0923	+	37.6650i	0.865409	+	3.22975i
$137$	−1.25362	−	4.67858i	−0.107104	−	0.399718i	0.891471	−	0.453077i	$-0.149674\pi$
$137$	−1.25362	−	4.67858i	−0.107104	−	0.399718i	−0.998575	+	0.0533594i	$0.983007\pi$
$138$	12.1569	−	3.25743i	1.03486	−	0.277291i
$139$	9.26980	−	5.35192i	0.786254	−	0.453944i	−0.0523882	−	0.998627i	$-0.516683\pi$
$139$	9.26980	−	5.35192i	0.786254	−	0.453944i	0.838642	+	0.544683i	$0.183350\pi$
$140$	−0.0896863	+	6.76732i	−0.00757988	+	0.571943i
$141$	−0.0215224	−	0.0803226i	−0.00181251	−	0.00676439i
$142$	11.7883	+	6.80597i	0.989251	+	0.571144i
$143$	−7.19991	−	0.393577i	−0.602087	−	0.0329125i
$144$	−5.15321	−	8.92562i	−0.429434	−	0.743802i
$145$	−1.36358	−	0.365370i	−0.113239	−	0.0303424i
$146$	−4.84860	−	2.79934i	−0.401273	−	0.231675i
$147$	−3.33812	−	6.15280i	−0.275323	−	0.507475i
$148$	−25.8110	−	25.8110i	−2.12165	−	2.12165i
$149$	−12.0380	−	12.0380i	−0.986188	−	0.986188i	0.0137184	−	0.999906i	$-0.495633\pi$
$149$	−12.0380	−	12.0380i	−0.986188	−	0.986188i	−0.999906	+	0.0137184i	$0.995633\pi$
$150$	−12.0091	+	3.21783i	−0.980539	+	0.262735i
$151$	17.6453	+	4.72803i	1.43595	+	0.384762i	0.891114	−	0.453780i	$-0.149925\pi$
$151$	17.6453	+	4.72803i	1.43595	+	0.384762i	0.544837	+	0.838542i	$0.316592\pi$
$152$			55.1908i			4.47656i
$153$	−2.54630	+	4.41032i	−0.205856	+	0.356553i
$154$	9.70549	+	9.96620i	0.782091	+	0.803099i
$155$			1.74565i			0.140214i
$156$	17.3329	−	3.64348i	1.38774	−	0.291712i
$157$	−4.25722	+	2.45791i	−0.339763	+	0.196162i	−0.660167	−	0.751119i	$-0.729515\pi$
$157$	−4.25722	+	2.45791i	−0.339763	+	0.196162i	0.320404	+	0.947281i	$0.396181\pi$
$158$	−22.9489	−	22.9489i	−1.82572	−	1.82572i
$159$	11.8747	−	6.85585i	0.941723	−	0.543704i
$160$	3.06794	+	5.31382i	0.242542	+	0.420094i
$161$	9.07362	−	8.83626i	0.715101	−	0.696395i
$162$	0.680470	−	2.53955i	0.0534628	−	0.199526i
$163$	2.14574	−	2.14574i	0.168067	−	0.168067i	−0.618062	−	0.786129i	$-0.712082\pi$
$163$	2.14574	−	2.14574i	0.168067	−	0.168067i	0.786129	+	0.618062i	$0.212082\pi$
$164$	−4.61184	+	17.2116i	−0.360124	+	1.34400i
$165$	0.520704	−	0.901885i	0.0405367	−	0.0702117i
$166$	13.1938	+	22.8523i	1.02404	+	1.77369i
$167$	−9.12053	+	2.44384i	−0.705768	+	0.189110i	−0.593813	−	0.804603i	$-0.702378\pi$
$167$	−9.12053	+	2.44384i	−0.705768	+	0.189110i	−0.111955	+	0.993713i	$0.535711\pi$
$168$	−17.4085	−	10.3608i	−1.34309	−	0.799351i
$169$	−1.41703	+	12.9225i	−0.109002	+	0.994041i
$170$	3.48610	−	6.03810i	0.267372	−	0.463101i
$171$	−5.09679	+	5.09679i	−0.389761	+	0.389761i
$172$	20.5506			1.56697
$173$	21.9790			1.67103			0.835515	−	0.549468i	$-0.185169\pi$
$173$	21.9790			1.67103			0.835515	+	0.549468i	$0.185169\pi$
$174$	5.03985	−	5.03985i	0.382070	−	0.382070i
$175$	−8.96330	+	8.72883i	−0.677562	+	0.659837i
$176$	19.9093	+	5.33467i	1.50072	+	0.402116i
$177$	1.43164	+	5.34294i	0.107608	+	0.401600i
$178$	−31.0731	−	17.9401i	−2.32903	−	1.34467i
$179$			17.0783i			1.27649i	0.769832	+	0.638247i	$0.220340\pi$
$179$			17.0783i			1.27649i	−0.769832	+	0.638247i	$0.779660\pi$
$180$	−0.662067	+	2.47087i	−0.0493476	+	0.184168i
$181$	−18.0173			−1.33922			−0.669608	−	0.742714i	$-0.733538\pi$
$181$	−18.0173			−1.33922			−0.669608	+	0.742714i	$0.733538\pi$
$182$	18.8962	−	16.4911i	1.40068	−	1.22240i
$183$	−0.753473			−0.0556983
$184$	9.48676	−	35.4051i	0.699373	−	2.61010i
$185$			3.86944i			0.284487i
$186$	−7.63280	−	4.40680i	−0.559664	−	0.323122i
$187$	−2.63596	−	9.83755i	−0.192761	−	0.719393i
$188$	−0.394572	−	0.105725i	−0.0287771	−	0.00771081i
$189$	−0.650845	−	2.56445i	−0.0473420	−	0.186536i
$190$	6.97793	−	6.97793i	0.506232	−	0.506232i
$191$	−22.0698			−1.59692			−0.798458	−	0.602050i	$-0.794351\pi$
$191$	−22.0698			−1.59692			−0.798458	+	0.602050i	$0.794351\pi$
$192$	−10.3665			−0.748135
$193$	5.16659	−	5.16659i	0.371899	−	0.371899i	−0.496269	−	0.868169i	$-0.665297\pi$
$193$	5.16659	−	5.16659i	0.371899	−	0.371899i	0.868169	+	0.496269i	$0.165297\pi$
$194$	4.47330	−	7.74799i	0.321165	−	0.556273i
$195$	−1.57233	−	1.02612i	−0.112597	−	0.0734821i
$196$	−34.3743	−	0.911276i	−2.45531	−	0.0650911i
$197$	−22.5188	+	6.03390i	−1.60440	+	0.429898i	−0.946368	−	0.323092i	$-0.895278\pi$
$197$	−22.5188	+	6.03390i	−1.60440	+	0.429898i	−0.658033	+	0.752989i	$0.728611\pi$
$198$	2.62897	+	4.55351i	0.186833	+	0.323604i
$199$	8.87911	−	15.3791i	0.629423	−	1.09019i	−0.358244	−	0.933628i	$-0.616625\pi$
$199$	8.87911	−	15.3791i	0.629423	−	1.09019i	0.987668	−	0.156565i	$-0.0500421\pi$
$200$	−9.37142	+	34.9746i	−0.662659	+	2.47308i
$201$	−7.68466	+	7.68466i	−0.542034	+	0.542034i
$202$	8.23044	−	30.7164i	0.579092	−	2.16120i
$203$	1.94802	−	6.90287i	0.136724	−	0.484486i
$204$	12.5083	+	21.6650i	0.875756	+	1.51685i
$205$	1.63583	−	0.944445i	0.114251	−	0.0659629i
$206$	15.0369	+	15.0369i	1.04767	+	1.04767i
$207$	4.14570	−	2.39352i	0.288146	−	0.166361i
$208$	11.5627	−	35.3156i	0.801726	−	2.44870i
$209$		−	14.4150i		−	0.997107i
$210$	0.891061	+	3.51095i	0.0614890	+	0.242278i
$211$	−2.69516	+	4.66816i	−0.185543	+	0.321370i	−0.943759	−	0.330633i	$-0.892738\pi$
$211$	−2.69516	+	4.66816i	−0.185543	+	0.321370i	0.758217	+	0.652003i	$0.226071\pi$
$212$		−	67.3566i		−	4.62607i
$213$	5.00093	+	1.34000i	0.342658	+	0.0918150i
$214$	14.3415	−	3.84278i	0.980362	−	0.262687i
$215$	−1.54042	−	1.54042i	−0.105055	−	0.105055i
$216$	−5.41427	−	5.41427i	−0.368395	−	0.368395i
$217$	−8.86853	−	0.117533i	−0.602035	−	0.00797868i
$218$	−22.0497	−	12.7304i	−1.49340	−	0.862213i
$219$	−2.05692	−	0.551150i	−0.138994	−	0.0372432i
$220$	−2.55787	−	4.43037i	−0.172452	−	0.298695i
$221$	−17.9689	+	3.77718i	−1.20872	+	0.254081i
$222$	−16.9190	−	9.76817i	−1.13553	−	0.655597i
$223$	−3.70617	−	13.8316i	−0.248183	−	0.926233i	−0.971757	−	0.235986i	$-0.924168\pi$
$223$	−3.70617	−	13.8316i	−0.248183	−	0.926233i	0.723573	−	0.690248i	$-0.242498\pi$
$224$	−27.2026	+	15.2284i	−1.81755	+	1.01749i
$225$	−4.09529	+	2.36442i	−0.273019	+	0.157628i
$226$	48.8062	−	13.0776i	3.24654	−	0.869907i
$227$	−1.53180	−	5.71677i	−0.101669	−	0.379435i	0.896277	−	0.443495i	$-0.146262\pi$
$227$	−1.53180	−	5.71677i	−0.101669	−	0.379435i	−0.997946	+	0.0640600i	$0.979595\pi$
$228$	9.16424	+	34.2014i	0.606916	+	2.26504i
$229$	28.5531	−	7.65078i	1.88684	−	0.505578i	0.887877	−	0.460081i	$-0.152179\pi$
$229$	28.5531	−	7.65078i	1.88684	−	0.505578i	0.998964	−	0.0454971i	$-0.0144872\pi$
$230$	−5.67580	+	3.27693i	−0.374251	+	0.216074i
$231$	4.54683	+	2.70608i	0.299160	+	0.178047i
$232$	−5.37243	−	20.0502i	−0.352718	−	1.31636i
$233$	−2.20932	−	1.27555i	−0.144737	−	0.0835641i	0.425883	−	0.904778i	$-0.359964\pi$
$233$	−2.20932	−	1.27555i	−0.144737	−	0.0835641i	−0.570620	+	0.821214i	$0.693297\pi$
$234$	8.45594	−	4.28458i	0.552782	−	0.280092i
$235$	0.0216512	+	0.0375009i	0.00141237	+	0.00244629i
$236$	26.2463	+	7.03269i	1.70849	+	0.457789i
$237$	−10.6904	−	6.17212i	−0.694418	−	0.400922i
$238$	30.4409	+	18.1171i	1.97319	+	1.17436i
$239$	7.35563	+	7.35563i	0.475796	+	0.475796i	0.903784	−	0.427988i	$-0.140778\pi$
$239$	7.35563	+	7.35563i	0.475796	+	0.475796i	−0.427988	+	0.903784i	$0.640778\pi$
$240$	3.79499	+	3.79499i	0.244965	+	0.244965i
$241$	−3.49299	+	0.935943i	−0.225003	+	0.0602894i	−0.369559	−	0.929207i	$-0.620491\pi$
$241$	−3.49299	+	0.935943i	−0.225003	+	0.0602894i	0.144556	+	0.989497i	$0.453825\pi$
$242$	17.7781	+	4.76362i	1.14282	+	0.306217i
$243$		−	1.00000i		−	0.0641500i
$244$	−1.85066	+	3.20543i	−0.118476	+	0.205207i
$245$	2.50830	+	2.64491i	0.160249	+	0.168977i
$246$			9.53679i			0.608044i
$247$	−25.9499	−	1.41853i	−1.65115	−	0.0902587i
$248$	−22.2293	+	12.8341i	−1.41156	+	0.814967i
$249$	7.09696	+	7.09696i	0.449752	+	0.449752i
$250$	11.5351	−	6.65979i	0.729544	−	0.421202i
$251$	0.0388167	+	0.0672326i	0.00245009	+	0.00424368i	0.867248	−	0.497877i	$-0.165887\pi$
$251$	0.0388167	+	0.0672326i	0.00245009	+	0.00424368i	−0.864798	+	0.502120i	$0.832553\pi$
$252$	−12.5083	−	3.52989i	−0.787949	−	0.222362i
$253$	−2.47780	+	9.24728i	−0.155778	+	0.581371i
$254$	−12.4138	+	12.4138i	−0.778913	+	0.778913i
$255$	0.686362	−	2.56154i	0.0429817	−	0.160410i
$256$	5.51751	−	9.55660i	0.344844	−	0.597288i
$257$	1.14492	+	1.98305i	0.0714179	+	0.123699i	0.899523	−	0.436874i	$-0.143914\pi$
$257$	1.14492	+	1.98305i	0.0714179	+	0.123699i	−0.828105	+	0.560573i	$0.810581\pi$
$258$	10.6241	−	2.84672i	0.661428	−	0.177229i
$259$	−19.6581	−	0.260526i	−1.22149	−	0.0161883i
$260$	−8.22725	+	4.16871i	−0.510233	+	0.258532i
$261$	1.35547	−	2.34774i	0.0839015	−	0.145322i
$262$	−0.577463	+	0.577463i	−0.0356758	+	0.0356758i
$263$	−5.04181			−0.310891			−0.155446	−	0.987844i	$-0.549681\pi$
$263$	−5.04181			−0.310891			−0.155446	+	0.987844i	$0.549681\pi$
$264$	15.3129			0.942446
$265$	−5.04886	+	5.04886i	−0.310149	+	0.310149i
$266$	34.9805	+	35.9201i	2.14479	+	2.20240i
$267$	−13.1821	−	3.53214i	−0.806733	−	0.216163i
$268$	13.8173	+	51.5670i	0.844029	+	3.14996i
$269$	14.1938	+	8.19481i	0.865413	+	0.499646i	0.865821	−	0.500353i	$-0.166797\pi$
$269$	14.1938	+	8.19481i	0.865413	+	0.499646i	−0.000408161		1.00000i	$0.500130\pi$
$270$			1.36908i			0.0833198i
$271$	1.70008	−	6.34477i	0.103272	−	0.385418i	−0.894871	−	0.446325i	$-0.852733\pi$
$271$	1.70008	−	6.34477i	0.103272	−	0.385418i	0.998143	+	0.0609071i	$0.0193993\pi$
$272$	52.4865			3.18246
$273$	5.31892	−	7.91891i	0.321916	−	0.479274i
$274$	−12.7345			−0.769320
$275$	2.44767	−	9.13484i	0.147600	−	0.550852i
$276$		−	23.5156i		−	1.41547i
$277$	1.35080	+	0.779884i	0.0811616	+	0.0468587i	0.540032	−	0.841645i	$-0.318412\pi$
$277$	1.35080	+	0.779884i	0.0811616	+	0.0468587i	−0.458870	+	0.888503i	$0.651746\pi$
$278$	−7.28364	−	27.1829i	−0.436844	−	1.63032i
$279$	−3.23806	−	0.867635i	−0.193857	−	0.0519439i
$280$	10.1527	+	2.86514i	0.606740	+	0.171225i
$281$	0.519129	−	0.519129i	0.0309687	−	0.0309687i	−0.691453	−	0.722422i	$-0.743029\pi$
$281$	0.519129	−	0.519129i	0.0309687	−	0.0309687i	0.722422	+	0.691453i	$0.243029\pi$
$282$	−0.218629			−0.0130191
$283$	−27.5291			−1.63644			−0.818218	−	0.574908i	$-0.805038\pi$
$283$	−27.5291			−1.63644			−0.818218	+	0.574908i	$0.805038\pi$
$284$	17.9838	−	17.9838i	1.06714	−	1.06714i
$285$	1.87672	−	3.25057i	0.111167	−	0.192547i
$286$	−5.89883	+	18.0167i	−0.348805	+	1.06535i
$287$	4.68797	+	8.37416i	0.276722	+	0.494311i
$288$	−11.3816	+	3.04969i	−0.670666	+	0.179705i
$289$	−4.46730	−	7.73758i	−0.262782	−	0.455152i
$290$	−1.85575	+	3.21425i	−0.108973	+	0.188748i
$291$	0.880729	−	3.28692i	0.0516292	−	0.192683i
$292$	−7.39685	+	7.39685i	−0.432868	+	0.432868i
$293$	2.78349	−	10.3881i	0.162613	−	0.606881i	−0.835719	−	0.549157i	$-0.814949\pi$
$293$	2.78349	−	10.3881i	0.162613	−	0.606881i	0.998333	−	0.0577244i	$-0.0183845\pi$
$294$	−17.8968	+	4.29051i	−1.04376	+	0.250228i
$295$	−1.44020	−	2.49450i	−0.0838518	−	0.145236i
$296$	−49.2738	+	28.4482i	−2.86398	+	1.65352i
$297$	1.41413	+	1.41413i	0.0820559	+	0.0820559i
$298$	−38.7624	+	22.3795i	−2.24545	+	1.29641i
$299$	16.4031	+	5.37052i	0.948616	+	0.310585i
$300$			23.2297i			1.34116i
$301$	7.92957	−	7.72214i	0.457053	−	0.445097i
$302$	24.0141	−	41.5937i	1.38186	−	2.39345i
$303$		−	12.0952i		−	0.694853i
$304$	71.7568	+	19.2272i	4.11554	+	1.10275i
$305$	0.378991	−	0.101550i	0.0217009	−	0.00581475i
$306$	9.46754	+	9.46754i	0.541223	+	0.541223i
$307$	2.62443	+	2.62443i	0.149784	+	0.149784i	0.778022	−	0.628237i	$-0.216223\pi$
$307$	2.62443	+	2.62443i	0.149784	+	0.149784i	−0.628237	+	0.778022i	$0.716223\pi$
$308$	22.6800	−	12.6966i	1.29232	−	0.723456i
$309$	7.00473	+	4.04418i	0.398485	+	0.230065i
$310$	4.43317	+	1.18786i	0.251787	+	0.0674662i
$311$	2.68970	+	4.65870i	0.152519	+	0.264171i	0.932153	−	0.362065i	$-0.117928\pi$
$311$	2.68970	+	4.65870i	0.152519	+	0.264171i	−0.779634	+	0.626236i	$0.784595\pi$
$312$	1.50689	−	27.5663i	0.0853107	−	1.56064i
$313$	27.3358	+	15.7824i	1.54511	+	0.892072i	0.998504	+	0.0546842i	$0.0174152\pi$
$313$	27.3358	+	15.7824i	1.54511	+	0.892072i	0.546610	+	0.837387i	$0.315918\pi$
$314$	3.34506	+	12.4839i	0.188773	+	0.704510i
$315$	0.672997	+	1.20218i	0.0379191	+	0.0677351i
$316$	−52.5150	+	30.3196i	−2.95420	+	1.70561i
$317$	10.9296	−	2.92857i	0.613866	−	0.164485i	0.0615283	−	0.998105i	$-0.480403\pi$
$317$	10.9296	−	2.92857i	0.613866	−	0.164485i	0.552338	+	0.833620i	$0.313736\pi$
$318$	−9.33040	−	34.8215i	−0.523223	−	1.95269i
$319$	1.40320	+	5.23681i	0.0785641	+	0.293205i
$320$	5.21424	−	1.39715i	0.291485	−	0.0781032i
$321$	4.89066	−	2.82363i	0.272970	−	0.157599i
$322$	−16.2658	−	29.0557i	−0.906457	−	1.61921i
$323$	−9.50052	−	35.4564i	−0.528623	−	1.97285i
$324$	−4.25421	−	2.45617i	−0.236345	−	0.136454i
$325$	−16.2037	−	5.30523i	−0.898818	−	0.294281i
$326$	−3.98909	−	6.90931i	−0.220935	−	0.382672i
$327$	−9.35415	−	2.50644i	−0.517285	−	0.138606i
$328$	24.0533	+	13.8872i	1.32812	+	0.766792i
$329$	−0.191976	+	0.107471i	−0.0105840	+	0.00592505i
$330$	−1.93606	−	1.93606i	−0.106576	−	0.106576i
$331$	−12.8446	−	12.8446i	−0.706004	−	0.706004i	0.259688	−	0.965692i	$-0.416380\pi$
$331$	−12.8446	−	12.8446i	−0.706004	−	0.706004i	−0.965692	+	0.259688i	$0.916380\pi$
$332$	47.6233	−	12.7606i	2.61367	−	0.700331i
$333$	−7.17752	−	1.92321i	−0.393326	−	0.105391i
$334$			24.8250i			1.35836i
$335$	2.82961	−	4.90103i	0.154598	−	0.267772i
$336$	−19.5354	+	19.0243i	−1.06574	+	1.03786i
$337$			20.1380i			1.09698i	0.836156	+	0.548492i	$0.184798\pi$
$337$			20.1380i			1.09698i	−0.836156	+	0.548492i	$0.815202\pi$
$338$	31.8532	+	12.3920i	1.73258	+	0.674037i
$339$	16.6437	−	9.60923i	0.903960	−	0.521901i
$340$	−9.21150	−	9.21150i	−0.499564	−	0.499564i
$341$	5.80597	−	3.35208i	0.314411	−	0.181525i
$342$	9.47532	+	16.4117i	0.512367	+	0.887445i
$343$	−13.6060	+	12.5650i	−0.734653	+	0.678444i
$344$	8.29062	−	30.9410i	0.447000	−	1.66823i
$345$	−1.76266	+	1.76266i	−0.0948985	+	0.0948985i
$346$	14.9560	−	55.8166i	0.804041	−	3.00072i
$347$	4.81207	−	8.33476i	0.258326	−	0.447433i	−0.707468	−	0.706746i	$-0.750163\pi$
$347$	4.81207	−	8.33476i	0.258326	−	0.447433i	0.965794	+	0.259312i	$0.0834959\pi$
$348$	−6.65853	−	11.5329i	−0.356935	−	0.618229i
$349$	−24.0092	+	6.43324i	−1.28518	+	0.344364i	−0.835829	−	0.548990i	$-0.815012\pi$
$349$	−24.0092	+	6.43324i	−1.28518	+	0.344364i	−0.449354	+	0.893354i	$0.648346\pi$
$350$	16.0680	+	28.7024i	0.858872	+	1.53421i
$351$	2.68487	−	2.40655i	0.143308	−	0.128452i
$352$	11.7824	−	20.4076i	0.628002	−	1.08773i
$353$	6.44715	−	6.44715i	0.343147	−	0.343147i	−0.514402	−	0.857549i	$-0.671986\pi$
$353$	6.44715	−	6.44715i	0.343147	−	0.343147i	0.857549	+	0.514402i	$0.171986\pi$
$354$	14.5428			0.772943
$355$	−2.69603			−0.143090
$356$	−47.4040	+	47.4040i	−2.51241	+	2.51241i
$357$	12.9673	+	3.65942i	0.686302	+	0.193677i
$358$	43.3712	+	11.6213i	2.29224	+	0.614204i
$359$	0.911092	+	3.40024i	0.0480856	+	0.179458i	0.985792	−	0.167971i	$-0.0537215\pi$
$359$	0.911092	+	3.40024i	0.0480856	+	0.179458i	−0.937706	+	0.347429i	$0.887055\pi$
$360$	3.45305	+	1.99362i	0.181992	+	0.105073i
$361$		−	32.9545i		−	1.73445i
$362$	−12.2602	+	45.7558i	−0.644384	+	2.40487i
$363$	7.00049			0.367431
$364$	−20.6246	−	42.0780i	−1.08102	−	2.20549i
$365$	1.10890			0.0580422
$366$	−0.512715	+	1.91348i	−0.0268001	+	0.100019i
$367$			1.44234i			0.0752895i	0.999291	+	0.0376448i	$0.0119855\pi$
$367$			1.44234i			0.0752895i	−0.999291	+	0.0376448i	$0.988014\pi$
$368$	−42.7273	−	24.6686i	−2.22731	−	1.28594i
$369$	0.938828	+	3.50375i	0.0488734	+	0.182398i
$370$	9.82662	+	2.63304i	0.510862	+	0.136885i
$371$	−25.3101	−	25.9899i	−1.31403	−	1.34933i
$372$	−11.6443	+	11.6443i	−0.603730	+	0.603730i
$373$	7.38975			0.382627			0.191313	−	0.981529i	$-0.438725\pi$
$373$	7.38975			0.382627			0.191313	+	0.981529i	$0.438725\pi$
$374$	−26.7766			−1.38459
$375$	3.58231	−	3.58231i	0.184990	−	0.184990i
$376$	−0.318361	+	0.551417i	−0.0164182	+	0.0284371i
$377$	9.56538	−	2.01070i	0.492642	−	0.103556i
$378$	−6.95542	−	0.0921792i	−0.357748	−	0.00474119i
$379$	−12.7292	+	3.41078i	−0.653855	+	0.175200i	−0.570471	−	0.821318i	$-0.693239\pi$
$379$	−12.7292	+	3.41078i	−0.653855	+	0.175200i	−0.0833836	+	0.996518i	$0.526573\pi$
$380$	−9.21908	−	15.9679i	−0.472929	−	0.819136i
$381$	−3.33871	+	5.78281i	−0.171047	+	0.296262i
$382$	−15.0178	+	56.0474i	−0.768380	+	2.86763i
$383$	−14.5825	+	14.5825i	−0.745133	+	0.745133i	−0.973561	−	0.228427i	$-0.926642\pi$
$383$	−14.5825	+	14.5825i	−0.745133	+	0.745133i	0.228427	+	0.973561i	$0.426642\pi$
$384$	−0.954687	+	3.56294i	−0.0487187	+	0.181821i
$385$	−2.65174	−	0.748331i	−0.135145	−	0.0381385i
$386$	−9.60509	−	16.6365i	−0.488886	−	0.846776i
$387$	3.62298	−	2.09173i	0.184167	−	0.106329i
$388$	−11.8201	−	11.8201i	−0.600072	−	0.600072i
$389$	−31.3755	+	18.1147i	−1.59080	+	0.918449i	−0.597631	+	0.801771i	$0.703891\pi$
$389$	−31.3755	+	18.1147i	−1.59080	+	0.918449i	−0.993170	+	0.116678i	$0.962775\pi$
$390$	−3.67581	+	3.29477i	−0.186132	+	0.166837i
$391$			24.3785i			1.23287i
$392$	−15.2395	+	51.3864i	−0.769710	+	2.59541i
$393$	−0.155309	+	0.269003i	−0.00783431	+	0.0135694i
$394$			61.2935i			3.08792i
$395$	6.20905	+	1.66371i	0.312411	+	0.0837104i
$396$	9.48933	−	2.54266i	0.476857	−	0.127773i
$397$	−19.3303	−	19.3303i	−0.970161	−	0.970161i	0.0294069	−	0.999568i	$-0.490638\pi$
$397$	−19.3303	−	19.3303i	−0.970161	−	0.970161i	−0.999568	+	0.0294069i	$0.990638\pi$
$398$	−33.0139	−	33.0139i	−1.65484	−	1.65484i
$399$	16.3877	+	9.75324i	0.820410	+	0.488272i
$400$	42.2078	+	24.3687i	2.11039	+	1.21843i
$401$	−13.2850	−	3.55970i	−0.663421	−	0.177763i	−0.0886316	−	0.996064i	$-0.528249\pi$
$401$	−13.2850	−	3.55970i	−0.663421	−	0.177763i	−0.574789	+	0.818301i	$0.694916\pi$
$402$	14.2864	+	24.7447i	0.712540	+	1.23416i
$403$	−5.46306	−	10.7818i	−0.272135	−	0.537078i
$404$	−51.4557	−	29.7080i	−2.56002	−	1.47803i
$405$	0.134776	+	0.502992i	0.00669709	+	0.0249939i
$406$	−16.2046	−	9.64428i	−0.804220	−	0.478637i
$407$	12.8696	−	7.43026i	0.637922	−	0.368304i
$408$	37.6650	−	10.0923i	1.86470	−	0.499644i
$409$	4.02721	+	15.0297i	0.199133	+	0.743173i	0.991158	+	0.132685i	$0.0423599\pi$
$409$	4.02721	+	15.0297i	0.199133	+	0.743173i	−0.792026	+	0.610488i	$0.790973\pi$
$410$	−1.28533	−	4.79693i	−0.0634781	−	0.236903i
$411$	−4.67858	+	1.25362i	−0.230777	+	0.0618365i
$412$	34.4096	−	19.8664i	1.69524	−	0.978748i
$413$	12.7699	−	7.14878i	0.628367	−	0.351768i
$414$	−3.25743	−	12.1569i	−0.160094	−	0.597479i
$415$	−4.52622	−	2.61321i	−0.222183	−	0.128278i
$416$	−35.5784	−	23.2188i	−1.74437	−	1.13840i
$417$	−5.35192	−	9.26980i	−0.262085	−	0.453944i
$418$	−36.6076	−	9.80897i	−1.79054	−	0.479773i
$419$	17.5367	+	10.1248i	0.856726	+	0.494631i	0.862914	−	0.505350i	$-0.168637\pi$
$419$	17.5367	+	10.1248i	0.856726	+	0.494631i	−0.00618874	+	0.999981i	$0.501970\pi$
$420$	6.76732	+	0.0896863i	0.330211	+	0.00437624i
$421$	14.0732	+	14.0732i	0.685887	+	0.685887i	0.961320	−	0.275433i	$-0.0888213\pi$
$421$	14.0732	+	14.0732i	0.685887	+	0.685887i	−0.275433	+	0.961320i	$0.588821\pi$
$422$	10.0210	+	10.0210i	0.487817	+	0.487817i
$423$	−0.0803226	+	0.0215224i	−0.00390542	+	0.00104645i
$424$	−101.412	−	27.1733i	−4.92501	−	1.31965i
$425$		−	24.0821i		−	1.16815i
$426$	6.80597	−	11.7883i	0.329750	−	0.571144i
$427$	0.490394	+	1.93224i	0.0237318	+	0.0935078i
$428$		−	27.7412i		−	1.34092i
$429$	−0.393577	+	7.19991i	−0.0190021	+	0.347615i
$430$	−4.96017	+	2.86375i	−0.239200	+	0.138102i
$431$	9.14707	+	9.14707i	0.440599	+	0.440599i	0.892213	−	0.451614i	$-0.149152\pi$
$431$	9.14707	+	9.14707i	0.440599	+	0.440599i	−0.451614	+	0.892213i	$0.649152\pi$
$432$	−8.92562	+	5.15321i	−0.429434	+	0.247934i
$433$	10.1407	+	17.5642i	0.487331	+	0.844082i	0.999894	−	0.0145673i	$-0.00463709\pi$
$433$	10.1407	+	17.5642i	0.487331	+	0.844082i	−0.512563	+	0.858650i	$0.671304\pi$
$434$	−6.33325	+	22.4421i	−0.304006	+	1.07725i
$435$	−0.365370	+	1.36358i	−0.0175182	+	0.0653787i
$436$	−33.6383	+	33.6383i	−1.61098	+	1.61098i
$437$	−8.93047	+	33.3290i	−0.427202	+	1.59434i
$438$	−2.79934	+	4.84860i	−0.133758	+	0.231675i
$439$	10.7585	+	18.6343i	0.513475	+	0.889365i	0.999878	+	0.0156304i	$0.00497550\pi$
$439$	10.7585	+	18.6343i	0.513475	+	0.889365i	−0.486403	+	0.873735i	$0.661691\pi$
$440$	−7.70228	+	2.06382i	−0.367192	+	0.0983888i
$441$	−6.15280	+	3.33812i	−0.292991	+	0.158958i
$442$	−2.63499	+	48.2032i	−0.125333	+	2.29279i
$443$	−12.3515	+	21.3934i	−0.586836	+	1.01643i	0.407808	+	0.913068i	$0.366293\pi$
$443$	−12.3515	+	21.3934i	−0.586836	+	1.01643i	−0.994644	+	0.103362i	$0.967040\pi$
$444$	−25.8110	+	25.8110i	−1.22493	+	1.22493i
$445$	7.10655			0.336883
$446$	−37.6480			−1.78268
$447$	−12.0380	+	12.0380i	−0.569376	+	0.569376i
$448$	6.74695	+	26.5843i	0.318764	+	1.25599i
$449$	36.3730	+	9.74613i	1.71655	+	0.459948i	0.977015	−	0.213170i	$-0.0683787\pi$
$449$	36.3730	+	9.74613i	1.71655	+	0.459948i	0.739535	+	0.673118i	$0.235045\pi$
$450$	3.21783	+	12.0091i	0.151690	+	0.566114i
$451$	−6.28237	−	3.62713i	−0.295825	−	0.170795i
$452$		−	94.4076i		−	4.44056i
$453$	4.72803	−	17.6453i	0.222142	−	0.829047i
$454$	−15.5604			−0.730284
$455$	−1.60809	+	4.70001i	−0.0753885	+	0.220340i
$456$	55.1908			2.58454
$457$	−6.91179	+	25.7951i	−0.323320	+	1.20665i	0.592670	+	0.805445i	$0.298074\pi$
$457$	−6.91179	+	25.7951i	−0.323320	+	1.20665i	−0.915990	+	0.401201i	$0.868593\pi$
$458$		−	77.7181i		−	3.63153i
$459$	4.41032	+	2.54630i	0.205856	+	0.118851i
$460$	3.16934	+	11.8281i	0.147771	+	0.551490i
$461$	−4.97413	−	1.33281i	−0.231668	−	0.0620754i	0.141117	−	0.989993i	$-0.454931\pi$
$461$	−4.97413	−	1.33281i	−0.231668	−	0.0620754i	−0.372785	+	0.927918i	$0.621597\pi$
$462$	9.96620	−	9.70549i	0.463670	−	0.451540i
$463$	13.3125	−	13.3125i	0.618683	−	0.618683i	−0.326511	−	0.945193i	$-0.605873\pi$
$463$	13.3125	−	13.3125i	0.618683	−	0.618683i	0.945193	+	0.326511i	$0.105873\pi$
$464$	−27.9401			−1.29709
$465$	1.74565			0.0809527
$466$	−4.74270	+	4.74270i	−0.219701	+	0.219701i
$467$	9.27178	−	16.0592i	0.429047	−	0.743131i	−0.567742	−	0.823207i	$-0.692183\pi$
$467$	9.27178	−	16.0592i	0.429047	−	0.743131i	0.996789	+	0.0800755i	$0.0255161\pi$
$468$	−3.64348	−	17.3329i	−0.168420	−	0.801214i
$469$	24.7084	+	14.7054i	1.14093	+	0.679032i
$470$	0.109968	−	0.0294659i	0.00507246	−	0.00135916i
$471$	2.45791	+	4.25722i	0.113254	+	0.196162i
$472$	21.1768	−	36.6794i	0.974744	−	1.68831i
$473$	−2.16539	+	8.08133i	−0.0995645	+	0.371580i
$474$	−22.9489	+	22.9489i	−1.05408	+	1.05408i
$475$	8.82189	−	32.9238i	0.404776	−	1.51065i
$476$	47.4179	−	46.1775i	2.17339	−	2.11654i
$477$	−6.85585	−	11.8747i	−0.313908	−	0.543704i
$478$	23.6853	−	13.6747i	1.08334	−	0.625466i
$479$	15.9594	+	15.9594i	0.729202	+	0.729202i	0.970461	−	0.241259i	$-0.0775602\pi$
$479$	15.9594	+	15.9594i	0.729202	+	0.729202i	−0.241259	+	0.970461i	$0.577560\pi$
$480$	5.31382	−	3.06794i	0.242542	−	0.140031i
$481$	−12.1095	−	23.8990i	−0.552145	−	1.08970i
$482$			9.50748i			0.433054i
$483$	−8.83626	−	9.07362i	−0.402064	−	0.412864i
$484$	17.1944	−	29.7816i	0.781564	−	1.35371i
$485$			1.77200i			0.0804623i
$486$	−2.53955	−	0.680470i	−0.115196	−	0.0308667i
$487$	14.4863	−	3.88160i	0.656439	−	0.175892i	0.0848003	−	0.996398i	$-0.472975\pi$
$487$	14.4863	−	3.88160i	0.656439	−	0.175892i	0.571638	+	0.820506i	$0.306308\pi$
$488$	4.07951	+	4.07951i	0.184671	+	0.184671i
$489$	−2.14574	−	2.14574i	−0.0970336	−	0.0970336i
$490$	8.42370	−	4.57016i	0.380544	−	0.206459i
$491$	0.576104	+	0.332614i	0.0259992	+	0.0150106i	0.512943	−	0.858423i	$-0.328555\pi$
$491$	0.576104	+	0.332614i	0.0259992	+	0.0150106i	−0.486944	+	0.873433i	$0.661888\pi$
$492$	17.2116	+	4.61184i	0.775960	+	0.207918i
$493$	6.90287	+	11.9561i	0.310889	+	0.538476i
$494$	−21.2605	+	64.9357i	−0.956556	+	2.92159i
$495$	−0.901885	−	0.520704i	−0.0405367	−	0.0234039i
$496$	8.94221	+	33.3728i	0.401517	+	1.49848i
$497$	0.181521	−	13.6968i	0.00814234	−	0.614384i
$498$	22.8523	−	13.1938i	1.02404	−	0.591228i
$499$	18.9600	−	5.08032i	0.848767	−	0.227426i	0.191883	−	0.981418i	$-0.438541\pi$
$499$	18.9600	−	5.08032i	0.848767	−	0.227426i	0.656884	+	0.753992i	$0.271874\pi$
$500$	−6.44114	−	24.0387i	−0.288057	−	1.07504i
$501$	2.44384	+	9.12053i	0.109183	+	0.407475i
$502$	0.197154	−	0.0528272i	0.00879941	−	0.00235779i
$503$	18.5259	−	10.6959i	0.826028	−	0.476907i	−0.0264628	−	0.999650i	$-0.508424\pi$
$503$	18.5259	−	10.6959i	0.826028	−	0.476907i	0.852491	+	0.522742i	$0.175091\pi$
$504$	−10.3608	+	17.4085i	−0.461506	+	0.775435i
$505$	1.63015	+	6.08380i	0.0725407	+	0.270726i
$506$	21.7978	+	12.5850i	0.969032	+	0.559471i
$507$	12.9225	+	1.41703i	0.573910	+	0.0629326i
$508$	16.4009	+	28.4071i	0.727671	+	1.26036i
$509$	−32.7976	−	8.78810i	−1.45373	−	0.389526i	−0.556410	−	0.830908i	$-0.687822\pi$
$509$	−32.7976	−	8.78810i	−1.45373	−	0.389526i	−0.897319	+	0.441382i	$0.854488\pi$
$510$	−6.03810	−	3.48610i	−0.267372	−	0.154367i
$511$	−0.0746609	+	5.63358i	−0.00330281	+	0.249215i
$512$	−25.7315	−	25.7315i	−1.13718	−	1.13718i
$513$	5.09679	+	5.09679i	0.225029	+	0.225029i
$514$	5.81514	−	1.55816i	0.256495	−	0.0687275i
$515$	−4.06838	−	1.09012i	−0.179274	−	0.0480364i
$516$		−	20.5506i		−	0.904689i
$517$	0.0831510	−	0.144022i	0.00365698	−	0.00633407i
$518$	−14.0384	+	49.7454i	−0.616810	+	2.18569i
$519$		−	21.9790i		−	0.964770i
$520$	2.95733	+	14.0687i	0.129688	+	0.616955i
$521$	3.73842	−	2.15838i	0.163783	−	0.0945602i	−0.415868	−	0.909425i	$-0.636522\pi$
$521$	3.73842	−	2.15838i	0.163783	−	0.0945602i	0.579651	+	0.814865i	$0.303189\pi$
$522$	−5.03985	−	5.03985i	−0.220588	−	0.220588i
$523$	−30.6798	+	17.7130i	−1.34154	+	0.774536i	−0.987033	−	0.160519i	$-0.948683\pi$
$523$	−30.6798	+	17.7130i	−1.34154	+	0.774536i	−0.354503	+	0.935055i	$0.615350\pi$
$524$	0.762931	+	1.32144i	0.0333288	+	0.0577272i
$525$	8.72883	+	8.96330i	0.380957	+	0.391190i
$526$	−3.43080	+	12.8039i	−0.149590	+	0.558277i
$527$	12.0716	−	12.0716i	0.525848	−	0.525848i
$528$	5.33467	−	19.9093i	0.232162	−	0.866439i
$529$	−0.0421417	+	0.0729916i	−0.00183225	+	0.00317355i
$530$	9.38623	+	16.2574i	0.407712	+	0.706177i
$531$	5.34294	−	1.43164i	0.231864	−	0.0621277i
$532$	81.7433	−	45.7610i	3.54402	−	1.98399i
$533$	−7.14778	+	10.9526i	−0.309605	+	0.474409i
$534$	−17.9401	+	31.0731i	−0.776343	+	1.34467i
$535$	−2.07941	+	2.07941i	−0.0899006	+	0.0899006i
$536$	83.2137			3.59428
$537$	17.0783			0.736984
$538$	30.4696	−	30.4696i	1.31364	−	1.31364i
$539$	3.98032	−	13.4214i	0.171445	−	0.578099i
$540$	2.47087	+	0.662067i	0.106329	+	0.0284908i
$541$	−0.765699	−	2.85763i	−0.0329200	−	0.122859i	0.947511	−	0.319725i	$-0.103590\pi$
$541$	−0.765699	−	2.85763i	−0.0329200	−	0.122859i	−0.980430	+	0.196866i	$0.936924\pi$
$542$	−14.9560	−	8.63485i	−0.642416	−	0.370899i
$543$			18.0173i			0.773197i
$544$	15.5308	−	57.9619i	0.665879	−	2.48509i
$545$	5.04287			0.216013
$546$	−16.4911	−	18.8962i	−0.705753	−	0.808684i
$547$	14.0808			0.602052			0.301026	−	0.953616i	$-0.402671\pi$
$547$	14.0808			0.602052			0.301026	+	0.953616i	$0.402671\pi$
$548$	−6.15821	+	22.9828i	−0.263066	+	0.981775i
$549$			0.753473i			0.0321574i
$550$	−21.5328	−	12.4320i	−0.918162	−	0.530101i
$551$	5.05740	+	18.8745i	0.215453	+	0.804080i
$552$	−35.4051	−	9.48676i	−1.50694	−	0.403783i
$553$	−8.87028	+	31.4321i	−0.377203	+	1.33663i
$554$	2.89973	−	2.89973i	0.123198	−	0.123198i
$555$	3.86944			0.164248
$556$	−52.5809			−2.22993
$557$	26.3249	−	26.3249i	1.11542	−	1.11542i	0.123018	−	0.992404i	$-0.460743\pi$
$557$	26.3249	−	26.3249i	1.11542	−	1.11542i	0.992404	−	0.123018i	$-0.0392572\pi$
$558$	−4.40680	+	7.63280i	−0.186555	+	0.323122i
$559$	14.3349	+	4.69338i	0.606302	+	0.198509i
$560$	7.26210	−	12.2020i	0.306880	−	0.515628i
$561$	−9.83755	+	2.63596i	−0.415342	+	0.111290i
$562$	−0.965102	−	1.67161i	−0.0407104	−	0.0705124i
$563$	−22.1262	+	38.3237i	−0.932508	+	1.61515i	−0.153489	+	0.988150i	$0.549051\pi$
$563$	−22.1262	+	38.3237i	−0.932508	+	1.61515i	−0.779019	+	0.627001i	$0.784282\pi$
$564$	−0.105725	+	0.394572i	−0.00445184	+	0.0166145i
$565$	−7.07653	+	7.07653i	−0.297712	+	0.297712i
$566$	−18.7327	+	69.9115i	−0.787395	+	2.93860i
$567$	−2.56445	+	0.650845i	−0.107697	+	0.0273329i
$568$	−19.8213	−	34.3315i	−0.831684	−	1.44052i
$569$	7.20021	−	4.15704i	0.301848	−	0.174272i	−0.341425	−	0.939909i	$-0.610909\pi$
$569$	7.20021	−	4.15704i	0.301848	−	0.174272i	0.643273	+	0.765637i	$0.277576\pi$
$570$	−6.97793	−	6.97793i	−0.292273	−	0.292273i
$571$	21.7326	−	12.5473i	0.909481	−	0.525089i	0.0292166	−	0.999573i	$-0.490699\pi$
$571$	21.7326	−	12.5473i	0.909481	−	0.525089i	0.880264	+	0.474484i	$0.157365\pi$
$572$	29.6633	+	19.3586i	1.24028	+	0.809422i
$573$			22.0698i			0.921980i
$574$	24.4566	−	6.20697i	1.02080	−	0.259074i
$575$	−11.3186	+	19.6043i	−0.472016	+	0.817556i
$576$			10.3665i			0.431936i
$577$	−25.5733	−	6.85235i	−1.06463	−	0.285267i	−0.316346	−	0.948644i	$-0.602456\pi$
$577$	−25.5733	−	6.85235i	−1.06463	−	0.285267i	−0.748285	+	0.663377i	$0.769123\pi$
$578$	−22.6898	+	6.07972i	−0.943772	+	0.252883i
$579$	−5.16659	−	5.16659i	−0.214716	−	0.214716i
$580$	4.90355	+	4.90355i	0.203609	+	0.203609i
$581$	13.5808	−	22.8188i	0.563426	−	0.946684i
$582$	−7.74799	−	4.47330i	−0.321165	−	0.185424i
$583$	26.4873	+	7.09726i	1.09699	+	0.293939i
$584$	8.15264	+	14.1208i	0.337359	+	0.584322i
$585$	−1.02612	+	1.57233i	−0.0424249	+	0.0650079i
$586$	−24.4871	−	14.1376i	−1.01155	−	0.584020i
$587$	0.317942	+	1.18658i	0.0131229	+	0.0489752i	0.972177	−	0.234248i	$-0.0752629\pi$
$587$	0.317942	+	1.18658i	0.0131229	+	0.0489752i	−0.959054	+	0.283223i	$0.908596\pi$
$588$	−0.911276	+	34.3743i	−0.0375804	+	1.41757i
$589$	20.9258	−	12.0815i	0.862234	−	0.497811i
$590$	−7.31493	+	1.96003i	−0.301151	+	0.0806931i
$591$	6.03390	+	22.5188i	0.248202	+	0.926301i
$592$	19.8214	+	73.9745i	0.814655	+	3.04033i
$593$	22.0301	−	5.90295i	0.904669	−	0.242405i	0.223648	−	0.974670i	$-0.428203\pi$
$593$	22.0301	−	5.90295i	0.904669	−	0.242405i	0.681020	+	0.732265i	$0.261537\pi$
$594$	4.55351	−	2.62897i	0.186833	−	0.107868i
$595$	−7.01565	−	0.0929774i	−0.287614	−	0.00381170i
$596$	21.6447	+	80.7793i	0.886603	+	3.30885i
$597$	−15.3791	−	8.87911i	−0.629423	−	0.363398i
$598$	24.8005	−	38.0020i	1.01417	−	1.55402i
$599$	4.86660	+	8.42920i	0.198844	+	0.344408i	0.948154	−	0.317812i	$-0.102948\pi$
$599$	4.86660	+	8.42920i	0.198844	+	0.344408i	−0.749310	+	0.662220i	$0.769615\pi$
$600$	34.9746	+	9.37142i	1.42783	+	0.382587i
$601$	7.28411	+	4.20549i	0.297125	+	0.171545i	0.641151	−	0.767415i	$-0.278457\pi$
$601$	7.28411	+	4.20549i	0.297125	+	0.171545i	−0.344025	+	0.938960i	$0.611791\pi$
$602$	−14.2149	−	25.3922i	−0.579356	−	1.03491i
$603$	7.68466	+	7.68466i	0.312944	+	0.312944i
$604$	−63.4538	−	63.4538i	−2.58190	−	2.58190i
$605$	−3.52119	+	0.943500i	−0.143157	+	0.0383587i
$606$	−30.7164	−	8.23044i	−1.24777	−	0.334339i
$607$			26.6604i			1.08211i	0.840987	+	0.541056i	$0.181975\pi$
$607$			26.6604i			1.08211i	−0.840987	+	0.541056i	$0.818025\pi$
$608$	42.4659	−	73.5531i	1.72222	−	2.98297i
$609$	−6.90287	−	1.94802i	−0.279718	−	0.0789377i
$610$		−	1.03157i		−	0.0417669i
$611$	−0.251085	−	0.163861i	−0.0101578	−	0.00662911i
$612$	21.6650	−	12.5083i	0.875756	−	0.505618i
$613$	6.71483	+	6.71483i	0.271209	+	0.271209i	0.829587	−	0.558378i	$-0.188576\pi$
$613$	6.71483	+	6.71483i	0.271209	+	0.271209i	−0.558378	+	0.829587i	$0.688576\pi$
$614$	8.45072	−	4.87902i	0.341043	−	0.196901i
$615$	−0.944445	−	1.63583i	−0.0380837	−	0.0659629i
$616$	−9.96634	−	39.2692i	−0.401555	−	1.58220i
$617$	−2.76556	+	10.3212i	−0.111337	+	0.415516i	−0.998987	−	0.0450034i	$-0.985670\pi$
$617$	−2.76556	+	10.3212i	−0.111337	+	0.415516i	0.887650	+	0.460519i	$0.152337\pi$
$618$	15.0369	−	15.0369i	0.604873	−	0.604873i
$619$	−4.64947	+	17.3520i	−0.186878	+	0.697438i	0.807343	+	0.590083i	$0.200905\pi$
$619$	−4.64947	+	17.3520i	−0.186878	+	0.697438i	−0.994221	+	0.107355i	$0.965762\pi$
$620$	4.28762	−	7.42638i	0.172195	−	0.298251i
$621$	−2.39352	−	4.14570i	−0.0960486	−	0.166361i
$622$	13.6613	−	3.66052i	0.547767	−	0.146774i
$623$	−0.478478	+	36.1038i	−0.0191698	+	1.44647i
$624$	−35.3156	−	11.5627i	−1.41376	−	0.462877i
$625$	10.5030	−	18.1918i	0.420121	−	0.727671i
$626$	58.6813	−	58.6813i	2.34538	−	2.34538i
$627$	−14.4150			−0.575680
$628$	24.1482			0.963616
$629$	26.7581	−	26.7581i	1.06692	−	1.06692i
$630$	3.51095	−	0.891061i	0.139879	−	0.0355007i
$631$	17.3537	+	4.64990i	0.690838	+	0.185110i	0.587123	−	0.809497i	$-0.300260\pi$
$631$	17.3537	+	4.64990i	0.690838	+	0.185110i	0.103715	+	0.994607i	$0.466927\pi$
$632$	24.4633	+	91.2984i	0.973099	+	3.63165i
$633$	4.66816	+	2.69516i	0.185543	+	0.107123i
$634$		−	29.7490i		−	1.18148i
$635$	0.899957	−	3.35869i	0.0357137	−	0.133285i
$636$	−67.3566			−2.67086
$637$	−23.7694	−	8.48612i	−0.941779	−	0.336232i
$638$	14.2540			0.564320
$639$	1.34000	−	5.00093i	0.0530094	−	0.197834i
$640$		−	1.92080i		−	0.0759263i
$641$	6.20731	+	3.58379i	0.245174	+	0.141551i	0.617552	−	0.786530i	$-0.288124\pi$
$641$	6.20731	+	3.58379i	0.245174	+	0.141551i	−0.372378	+	0.928081i	$0.621458\pi$
$642$	−3.84278	−	14.3415i	−0.151663	−	0.566012i
$643$	41.0624	+	11.0026i	1.61934	+	0.433902i	0.950809	−	0.309779i	$-0.100255\pi$
$643$	41.0624	+	11.0026i	1.61934	+	0.433902i	0.668535	+	0.743681i	$0.266922\pi$
$644$	−60.3045	+	15.3050i	−2.37633	+	0.603101i
$645$	−1.54042	+	1.54042i	−0.0606538	+	0.0606538i
$646$	−96.5081			−3.79706
$647$	−4.72974			−0.185945			−0.0929726	−	0.995669i	$-0.529637\pi$
$647$	−4.72974			−0.185945			−0.0929726	+	0.995669i	$0.529637\pi$
$648$	−5.41427	+	5.41427i	−0.212693	+	0.212693i
$649$	−5.53108	+	9.58010i	−0.217114	+	0.376052i
$650$	−24.4990	+	37.5400i	−0.960929	+	1.47244i
$651$	−0.117533	+	8.86853i	−0.00460649	+	0.347585i
$652$	−14.3987	+	3.85813i	−0.563898	+	0.151096i
$653$	−0.0818691	−	0.141801i	−0.00320379	−	0.00554912i	0.864419	−	0.502772i	$-0.167686\pi$
$653$	−0.0818691	−	0.141801i	−0.00320379	−	0.00554912i	−0.867623	+	0.497223i	$0.834353\pi$
$654$	−12.7304	+	22.0497i	−0.497799	+	0.862213i
$655$	0.0418640	−	0.156238i	0.00163576	−	0.00610474i
$656$	26.4352	−	26.4352i	1.03212	−	1.03212i
$657$	−0.551150	+	2.05692i	−0.0215024	+	0.0802480i
$658$	0.142293	+	0.560662i	0.00554717	+	0.0218569i
$659$	−11.4177	−	19.7761i	−0.444772	−	0.770367i	0.553265	−	0.833006i	$-0.313382\pi$
$659$	−11.4177	−	19.7761i	−0.444772	−	0.770367i	−0.998036	+	0.0626385i	$0.980048\pi$
$660$	−4.43037	+	2.55787i	−0.172452	+	0.0995651i
$661$	−22.4488	−	22.4488i	−0.873158	−	0.873158i	0.119657	−	0.992815i	$-0.461821\pi$
$661$	−22.4488	−	22.4488i	−0.873158	−	0.873158i	−0.992815	+	0.119657i	$0.961821\pi$
$662$	−41.3599	+	23.8791i	−1.60750	+	0.928089i
$663$	3.77718	+	17.9689i	0.146694	+	0.697856i
$664$		−	76.8497i		−	2.98235i
$665$	−9.55737	−	2.69713i	−0.370619	−	0.104590i
$666$	−9.76817	+	16.9190i	−0.378509	+	0.655597i
$667$		−	12.9774i		−	0.502486i
$668$	44.8032	+	12.0050i	1.73349	+	0.464486i
$669$	−13.8316	+	3.70617i	−0.534761	+	0.143289i
$670$	−10.5209	−	10.5209i	−0.406459	−	0.406459i
$671$	−1.06551	−	1.06551i	−0.0411334	−	0.0411334i
$672$	15.2284	+	27.2026i	0.587449	+	1.04936i
$673$	−31.2839	−	18.0618i	−1.20591	−	0.696231i	−0.244044	−	0.969764i	$-0.578474\pi$
$673$	−31.2839	−	18.0618i	−1.20591	−	0.696231i	−0.961862	+	0.273534i	$0.911808\pi$
$674$	51.1413	+	13.7033i	1.96989	+	0.527830i
$675$	2.36442	+	4.09529i	0.0910065	+	0.157628i
$676$	37.7683	−	51.4948i	1.45263	−	1.98057i
$677$	−34.8720	−	20.1334i	−1.34024	−	0.773788i	−0.353398	−	0.935473i	$-0.614974\pi$
$677$	−34.8720	−	20.1334i	−1.34024	−	0.773788i	−0.986842	+	0.161685i	$0.948307\pi$
$678$	−13.0776	−	48.8062i	−0.502241	−	1.87439i
$679$	−9.00237	−	0.119307i	−0.345479	−	0.00457858i
$680$	−17.5850	+	10.1527i	−0.674354	+	0.389339i
$681$	−5.71677	+	1.53180i	−0.219067	+	0.0586989i
$682$	−4.56197	−	17.0255i	−0.174687	−	0.651941i
$683$	−8.55543	−	31.9293i	−0.327364	−	1.22174i	−0.911914	−	0.410382i	$-0.865395\pi$
$683$	−8.55543	−	31.9293i	−0.327364	−	1.22174i	0.584549	−	0.811358i	$-0.301271\pi$
$684$	34.2014	−	9.16424i	1.30772	−	0.350403i
$685$	2.18433	−	1.26112i	0.0834589	−	0.0481850i
$686$	22.6509	+	43.1030i	0.864813	+	1.64568i
$687$	−7.65078	−	28.5531i	−0.291895	−	1.08937i
$688$	−37.3400	−	21.5583i	−1.42357	−	0.821901i
$689$	15.3830	−	46.9841i	0.586046	−	1.78995i
$690$	3.27693	+	5.67580i	0.124750	+	0.216074i
$691$	−13.4764	−	3.61100i	−0.512668	−	0.137369i	−0.00679506	−	0.999977i	$-0.502163\pi$
$691$	−13.4764	−	3.61100i	−0.512668	−	0.137369i	−0.505873	+	0.862608i	$0.668830\pi$
$692$	−93.5032	−	53.9841i	−3.55446	−	2.05217i
$693$	2.70608	−	4.54683i	0.102795	−	0.172720i
$694$	−17.8920	−	17.8920i	−0.679173	−	0.679173i
$695$	3.94132	+	3.94132i	0.149503	+	0.149503i
$696$	−20.0502	+	5.37243i	−0.760001	+	0.203642i
$697$	−17.8432	−	4.78107i	−0.675860	−	0.181096i
$698$			65.3501i			2.47354i
$699$	−1.27555	+	2.20932i	−0.0482458	+	0.0835641i
$700$	59.5713	−	15.1189i	2.25158	−	0.571441i
$701$		−	26.0431i		−	0.983633i	−0.870699	−	0.491817i	$-0.836333\pi$
$701$		−	26.0431i		−	0.983633i	0.870699	−	0.491817i	$-0.163667\pi$
$702$	−4.28458	−	8.45594i	−0.161711	−	0.319149i
$703$	46.3845	−	26.7801i	1.74942	−	1.01003i
$704$	−14.6595	−	14.6595i	−0.552500	−	0.552500i
$705$	0.0375009	−	0.0216512i	0.00141237	−	0.000815430i
$706$	−11.9857	−	20.7599i	−0.451090	−	0.781310i
$707$	−31.0176	+	7.87212i	−1.16654	+	0.296061i
$708$	7.03269	−	26.2463i	0.264304	−	0.986398i
$709$	−3.04089	+	3.04089i	−0.114203	+	0.114203i	−0.761899	−	0.647696i	$-0.775733\pi$
$709$	−3.04089	+	3.04089i	−0.114203	+	0.114203i	0.647696	+	0.761899i	$0.275733\pi$
$710$	−1.83457	+	6.84669i	−0.0688500	+	0.256952i
$711$	−6.17212	+	10.6904i	−0.231473	+	0.400922i
$712$	52.2476	+	90.4955i	1.95806	+	3.39146i
$713$	−15.5007	+	4.15340i	−0.580506	+	0.155546i
$714$	18.1171	−	30.4409i	0.678017	−	1.13922i
$715$	−0.772411	−	3.67454i	−0.0288865	−	0.137420i
$716$	41.9473	−	72.6548i	1.56764	−	2.71524i
$717$	7.35563	−	7.35563i	0.274701	−	0.274701i
$718$	9.25504			0.345395
$719$	4.51154			0.168252			0.0841260	−	0.996455i	$-0.473190\pi$
$719$	4.51154			0.168252			0.0841260	+	0.996455i	$0.473190\pi$
$720$	3.79499	−	3.79499i	0.141431	−	0.141431i
$721$	5.81211	−	20.5954i	0.216454	−	0.767013i
$722$	−83.6895	−	22.4245i	−3.11460	−	0.834554i
$723$	0.935943	+	3.49299i	0.0348081	+	0.129906i
$724$	76.6495	+	44.2536i	2.84866	+	1.64467i
$725$			12.8196i			0.476107i
$726$	4.76362	−	17.7781i	0.176795	−	0.659807i
$727$	6.85388			0.254196			0.127098	−	0.991890i	$-0.459434\pi$
$727$	6.85388			0.254196			0.127098	+	0.991890i	$0.459434\pi$
$728$	−71.6732	+	14.0771i	−2.65638	+	0.521730i
$729$	−1.00000			−0.0370370
$730$	0.754570	−	2.81609i	0.0279279	−	0.104228i
$731$			21.3047i			0.787983i
$732$	3.20543	+	1.85066i	0.118476	+	0.0684023i
$733$	−5.06911	−	18.9182i	−0.187232	−	0.698758i	−0.994142	−	0.108084i	$-0.965528\pi$
$733$	−5.06911	−	18.9182i	−0.187232	−	0.698758i	0.806910	−	0.590674i	$-0.201138\pi$
$734$	3.66289	+	0.981468i	0.135200	+	0.0362267i
$735$	2.64491	−	2.50830i	0.0975590	−	0.0925200i
$736$	−39.8851	+	39.8851i	−1.47018	+	1.47018i
$737$	−21.7342			−0.800588
$738$	9.53679			0.351054
$739$	−6.73165	+	6.73165i	−0.247628	+	0.247628i	−0.819996	−	0.572369i	$-0.806025\pi$
$739$	−6.73165	+	6.73165i	−0.247628	+	0.247628i	0.572369	+	0.819996i	$0.306025\pi$
$740$	9.50400	−	16.4614i	0.349374	−	0.605133i
$741$	−1.41853	+	25.9499i	−0.0521109	+	0.953292i
$742$	−83.2254	+	46.5907i	−3.05530	+	1.71040i
$743$	33.4189	−	8.95458i	1.22602	−	0.328512i	0.412993	−	0.910734i	$-0.364484\pi$
$743$	33.4189	−	8.95458i	1.22602	−	0.328512i	0.813029	+	0.582223i	$0.197817\pi$
$744$	12.8341	+	22.2293i	0.470521	+	0.814967i
$745$	4.43256	−	7.67742i	0.162397	−	0.281279i
$746$	5.02850	−	18.7666i	0.184106	−	0.687095i
$747$	7.09696	−	7.09696i	0.259664	−	0.259664i
$748$	−12.9487	+	48.3254i	−0.473453	+	1.76695i
$749$	−10.4241	−	10.7041i	−0.380889	−	0.391120i
$750$	−6.65979	−	11.5351i	−0.243181	−	0.421202i
$751$	37.0313	−	21.3801i	1.35129	−	0.780169i	0.362862	−	0.931843i	$-0.381800\pi$
$751$	37.0313	−	21.3801i	1.35129	−	0.780169i	0.988431	+	0.151674i	$0.0484662\pi$
$752$	0.606020	+	0.606020i	0.0220993	+	0.0220993i
$753$	0.0672326	−	0.0388167i	0.00245009	−	0.00141456i
$754$	1.40268	−	25.6600i	0.0510826	−	0.934481i
$755$			9.51265i			0.346201i
$756$	−3.52989	+	12.5083i	−0.128381	+	0.454922i
$757$	0.327683	−	0.567563i	0.0119098	−	0.0206284i	−0.860009	−	0.510279i	$-0.829542\pi$
$757$	0.327683	−	0.567563i	0.0119098	−	0.0206284i	0.871919	+	0.489650i	$0.162876\pi$
$758$			34.6473i			1.25845i
$759$	9.24728	+	2.47780i	0.335655	+	0.0899384i
$760$	−27.7605	+	7.43841i	−1.00698	+	0.269819i
$761$	8.57390	+	8.57390i	0.310803	+	0.310803i	0.845221	−	0.534417i	$-0.179469\pi$
$761$	8.57390	+	8.57390i	0.310803	+	0.310803i	−0.534417	+	0.845221i	$0.679469\pi$
$762$	12.4138	+	12.4138i	0.449706	+	0.449706i
$763$	−0.339532	+	25.6195i	−0.0122919	+	0.927489i
$764$	93.8897	+	54.2073i	3.39681	+	1.96115i
$765$	−2.56154	−	0.686362i	−0.0926126	−	0.0248155i
$766$	27.1101	+	46.9561i	0.979528	+	1.69659i
$767$	16.7018	+	10.8998i	0.603067	+	0.393568i
$768$	−9.55660	−	5.51751i	−0.344844	−	0.199096i
$769$	1.93954	+	7.23846i	0.0699416	+	0.261025i	0.992039	−	0.125933i	$-0.0401924\pi$
$769$	1.93954	+	7.23846i	0.0699416	+	0.261025i	−0.922097	+	0.386958i	$0.873526\pi$
$770$	−3.70485	+	6.22499i	−0.133513	+	0.224333i
$771$	1.98305	−	1.14492i	0.0714179	−	0.0412331i
$772$	−34.6698	+	9.28974i	−1.24779	+	0.334345i
$773$	−7.93706	−	29.6215i	−0.285476	−	1.06541i	−0.948491	−	0.316805i	$-0.897390\pi$
$773$	−7.93706	−	29.6215i	−0.285476	−	1.06541i	0.663015	−	0.748606i	$-0.269277\pi$
$774$	−2.84672	−	10.6241i	−0.102323	−	0.381875i
$775$	15.3122	−	4.10290i	0.550032	−	0.147381i
$776$	−22.5648	+	13.0278i	−0.810029	+	0.467671i
$777$	−0.260526	+	19.6581i	−0.00934631	+	0.705230i
$778$	24.6529	+	92.0061i	0.883851	+	3.29858i
$779$	−22.6429	−	13.0729i	−0.811265	−	0.468384i
$780$	4.16871	+	8.22725i	0.149264	+	0.294583i
$781$	5.17703	+	8.96688i	0.185249	+	0.320860i
$782$	61.9103	+	16.5888i	2.21391	+	0.593215i
$783$	−2.34774	−	1.35547i	−0.0839015	−	0.0484405i
$784$	61.5015	+	37.7156i	2.19648	+	1.34698i
$785$	−1.81008	−	1.81008i	−0.0646045	−	0.0646045i
$786$	0.577463	+	0.577463i	0.0205974	+	0.0205974i
$787$	4.40030	−	1.17906i	0.156854	−	0.0420289i	−0.179538	−	0.983751i	$-0.557460\pi$
$787$	4.40030	−	1.17906i	0.156854	−	0.0420289i	0.336391	+	0.941722i	$0.390793\pi$
$788$	110.620	+	29.6406i	3.94068	+	1.05590i
$789$			5.04181i			0.179493i
$790$	8.45015	−	14.6361i	0.300643	−	0.520728i
$791$	−35.4748	−	36.4277i	−1.26134	−	1.29522i
$792$		−	15.3129i		−	0.544121i
$793$	−2.02297	+	1.81327i	−0.0718379	+	0.0643911i
$794$	−62.2440	+	35.9366i	−2.20896	+	1.27534i
$795$	5.04886	+	5.04886i	0.179065	+	0.179065i
$796$	−75.5472	+	43.6172i	−2.67770	+	1.54597i
$797$	−16.9732	−	29.3985i	−0.601222	−	1.04135i	−0.992636	−	0.121133i	$-0.961347\pi$
$797$	−16.9732	−	29.3985i	−0.601222	−	1.04135i	0.391414	−	0.920215i	$-0.371986\pi$
$798$	35.9201	−	34.9805i	1.27156	−	1.23830i
$799$	0.109605	−	0.409051i	0.00387754	−	0.0144712i
$800$	39.4002	−	39.4002i	1.39301	−	1.39301i
$801$	−3.53214	+	13.1821i	−0.124802	+	0.465767i
$802$	−18.0801	+	31.3156i	−0.638430	+	1.10579i
$803$	−2.12935	−	3.68814i	−0.0751430	−	0.130152i
$804$	51.5670	−	13.8173i	1.81863	−	0.487300i
$805$	5.66748	+	3.37304i	0.199752	+	0.118884i
$806$	−31.0983	+	6.53704i	−1.09539	+	0.230258i
$807$	8.19481	−	14.1938i	0.288471	−	0.499646i
$808$	−65.4869	+	65.4869i	−2.30382	+	2.30382i
$809$	28.6673			1.00789			0.503945	−	0.863736i	$-0.331881\pi$
$809$	28.6673			1.00789			0.503945	+	0.863736i	$0.331881\pi$
$810$	1.36908			0.0481047
$811$	3.29098	−	3.29098i	0.115562	−	0.115562i	−0.646961	−	0.762523i	$-0.723960\pi$
$811$	3.29098	−	3.29098i	0.115562	−	0.115562i	0.762523	+	0.646961i	$0.223960\pi$
$812$	−25.2419	+	24.5816i	−0.885817	+	0.862645i
$813$	−6.34477	−	1.70008i	−0.222521	−	0.0596243i
$814$	−10.1121	−	37.7390i	−0.354430	−	1.32275i
$815$	1.36848	+	0.790094i	0.0479359	+	0.0276758i
$816$		−	52.4865i		−	1.83739i
$817$	−7.80447	+	29.1267i	−0.273044	+	1.01901i
$818$	40.9091			1.43035
$819$	−7.91891	−	5.31892i	−0.276709	−	0.185858i
$820$	−9.27888			−0.324032
$821$	−7.71032	+	28.7753i	−0.269092	+	1.00426i	0.690606	+	0.723231i	$0.257344\pi$
$821$	−7.71032	+	28.7753i	−0.269092	+	1.00426i	−0.959698	+	0.281034i	$0.909323\pi$
$822$			12.7345i			0.444167i
$823$	−28.7199	−	16.5814i	−1.00111	−	0.577993i	−0.0925357	−	0.995709i	$-0.529497\pi$
$823$	−28.7199	−	16.5814i	−1.00111	−	0.577993i	−0.908577	+	0.417716i	$0.862831\pi$
$824$	−16.0292	−	59.8218i	−0.558404	−	2.08399i
$825$	−9.13484	−	2.44767i	−0.318034	−	0.0852171i
$826$	−9.46512	−	37.2944i	−0.329334	−	1.29764i
$827$	−13.0460	+	13.0460i	−0.453653	+	0.453653i	−0.896565	−	0.442912i	$-0.853945\pi$
$827$	−13.0460	+	13.0460i	−0.453653	+	0.453653i	0.442912	+	0.896565i	$0.353945\pi$
$828$	−23.5156			−0.817222
$829$	−25.1378			−0.873070			−0.436535	−	0.899687i	$-0.643795\pi$
$829$	−25.1378			−0.873070			−0.436535	+	0.899687i	$0.643795\pi$
$830$	−9.71633	+	9.71633i	−0.337259	+	0.337259i
$831$	0.779884	−	1.35080i	0.0270539	−	0.0468587i
$832$	−27.8326	+	24.9474i	−0.964921	+	0.864895i
$833$	0.944715	−	35.6357i	0.0327324	−	1.23470i
$834$	−27.1829	+	7.28364i	−0.941267	+	0.252212i
$835$	−2.45846	−	4.25818i	−0.0850786	−	0.147360i
$836$	−35.4057	+	61.3245i	−1.22453	+	2.12095i
$837$	−0.867635	+	3.23806i	−0.0299898	+	0.111924i
$838$	37.6457	−	37.6457i	1.30045	−	1.30045i
$839$	1.98291	−	7.40032i	0.0684577	−	0.255488i	−0.923213	−	0.384289i	$-0.874446\pi$
$839$	1.98291	−	7.40032i	0.0684577	−	0.255488i	0.991670	+	0.128802i	$0.0411131\pi$
$840$	2.86514	−	10.1527i	0.0988566	−	0.350302i
$841$	10.8254	+	18.7502i	0.373290	+	0.646557i
$842$	45.3160	−	26.1632i	1.56169	−	0.901644i
$843$	−0.519129	−	0.519129i	−0.0178798	−	0.0178798i
$844$	22.9316	−	13.2396i	0.789339	−	0.455725i
$845$	−6.69092	+	1.02890i	−0.230175	+	0.0353951i
$846$			0.218629i			0.00751660i
$847$	−4.55623	−	17.9524i	−0.156554	−	0.616852i
$848$	−70.6593	+	122.385i	−2.42645	+	4.20273i
$849$			27.5291i			0.944797i
$850$	−61.1576	−	16.3871i	−2.09769	−	0.562074i
$851$	−34.3590	+	9.20648i	−1.17781	+	0.315594i
$852$	−17.9838	−	17.9838i	−0.616114	−	0.616114i
$853$	18.8489	+	18.8489i	0.645373	+	0.645373i	0.951871	−	0.306498i	$-0.0991574\pi$
$853$	18.8489	+	18.8489i	0.645373	+	0.645373i	−0.306498	+	0.951871i	$0.599157\pi$
$854$	5.24072	+	0.0694545i	0.179334	+	0.00237668i
$855$	−3.25057	−	1.87672i	−0.111167	−	0.0641824i
$856$	−41.7672	−	11.1915i	−1.42758	−	0.382518i
$857$	−9.97165	−	17.2714i	−0.340625	−	0.589980i	0.643924	−	0.765090i	$-0.277305\pi$
$857$	−9.97165	−	17.2714i	−0.340625	−	0.589980i	−0.984549	+	0.175110i	$0.943972\pi$
$858$	18.0167	+	5.89883i	0.615080	+	0.201383i
$859$	0.354309	+	0.204560i	0.0120889	+	0.00697950i	0.506032	−	0.862515i	$-0.331112\pi$
$859$	0.354309	+	0.204560i	0.0120889	+	0.00697950i	−0.493943	+	0.869494i	$0.664445\pi$
$860$	2.76973	+	10.3368i	0.0944471	+	0.352481i
$861$	8.37416	−	4.68797i	0.285391	−	0.159766i
$862$	29.4537	−	17.0051i	1.00320	−	0.579196i
$863$	−10.6641	+	2.85743i	−0.363010	+	0.0972682i	−0.435714	−	0.900085i	$-0.643504\pi$
$863$	−10.6641	+	2.85743i	−0.363010	+	0.0972682i	0.0727037	+	0.997354i	$0.476837\pi$
$864$	3.04969	+	11.3816i	0.103752	+	0.387209i
$865$	2.96224	+	11.0552i	0.100719	+	0.375890i
$866$	51.5056	−	13.8009i	1.75023	−	0.468973i
$867$	−7.73758	+	4.46730i	−0.262782	+	0.151717i
$868$	37.4399	+	22.2826i	1.27079	+	0.756322i
$869$	−6.38945	−	23.8458i	−0.216747	−	0.808912i
$870$	3.21425	+	1.85575i	0.108973	+	0.0629158i
$871$	−2.13878	+	39.1258i	−0.0724697	+	1.32573i
$872$	37.0754	+	64.2164i	1.25553	+	2.17464i
$873$	−3.28692	−	0.880729i	−0.111246	−	0.0298081i
$874$	78.5636	+	45.3587i	2.65745	+	1.53428i
$875$	−11.5182	−	6.85512i	−0.389386	−	0.231746i
$876$	7.39685	+	7.39685i	0.249916	+	0.249916i
$877$	−19.3771	−	19.3771i	−0.654318	−	0.654318i	0.299712	−	0.954030i	$-0.403110\pi$
$877$	−19.3771	−	19.3771i	−0.654318	−	0.654318i	−0.954030	+	0.299712i	$0.903110\pi$
$878$	54.6435	−	14.6417i	1.84413	−	0.494132i
$879$	−10.3881	−	2.78349i	−0.350383	−	0.0938849i
$880$			10.7332i			0.361815i
$881$	−15.9556	+	27.6359i	−0.537557	+	0.931077i	0.461478	+	0.887152i	$0.347319\pi$
$881$	−15.9556	+	27.6359i	−0.537557	+	0.931077i	−0.999035	+	0.0439247i	$0.986014\pi$
$882$	4.29051	+	17.8968i	0.144469	+	0.602617i
$883$		−	32.9852i		−	1.11004i	−0.831837	−	0.555019i	$-0.812711\pi$
$883$		−	32.9852i		−	1.11004i	0.831837	−	0.555019i	$-0.187289\pi$
$884$	85.7211	+	28.0658i	2.88311	+	0.943956i
$885$	−2.49450	+	1.44020i	−0.0838518	+	0.0484119i
$886$	45.9247	+	45.9247i	1.54287	+	1.54287i
$887$	−19.5103	+	11.2643i	−0.655091	+	0.378217i	−0.790404	−	0.612586i	$-0.790129\pi$
$887$	−19.5103	+	11.2643i	−0.655091	+	0.378217i	0.135313	+	0.990803i	$0.456796\pi$
$888$	28.4482	+	49.2738i	0.954661	+	1.65352i
$889$	17.0027	+	4.79823i	0.570252	+	0.160928i
$890$	4.83579	−	18.0474i	0.162096	−	0.604951i
$891$	1.41413	−	1.41413i	0.0473750	−	0.0473750i
$892$	−18.2060	+	67.9456i	−0.609581	+	2.27499i
$893$	0.299692	−	0.519082i	0.0100288	−	0.0173704i
$894$	22.3795	+	38.7624i	0.748482	+	1.29641i
$895$	−8.59026	+	2.30175i	−0.287141	+	0.0769391i
$896$	9.75834	+	0.129326i	0.326003	+	0.00432047i
$897$	5.37052	−	16.4031i	0.179317	−	0.547684i
$898$	49.5015	−	85.7392i	1.65189	−	2.86115i
$899$	−6.42607	+	6.42607i	−0.214321	+	0.214321i
$900$	23.2297			0.774322
$901$	69.8282			2.32632
$902$	−13.4862	+	13.4862i	−0.449042	+	0.449042i
$903$	−7.72214	−	7.92957i	−0.256977	−	0.263879i
$904$	−142.140	−	38.0864i	−4.72752	−	1.26673i
$905$	−2.42831	−	9.06256i	−0.0807197	−	0.301250i
$906$	−41.5937	−	24.0141i	−1.38186	−	0.797816i
$907$		−	26.2585i		−	0.871900i	−0.899971	−	0.435950i	$-0.856413\pi$
$907$		−	26.2585i		−	0.871900i	0.899971	−	0.435950i	$-0.143587\pi$
$908$	−7.52474	+	28.0827i	−0.249717	+	0.931958i
$909$	−12.0952			−0.401173
$910$	10.8416	+	7.28204i	0.359397	+	0.241397i
$911$	−6.71393			−0.222442			−0.111221	−	0.993796i	$-0.535476\pi$
$911$	−6.71393			−0.222442			−0.111221	+	0.993796i	$0.535476\pi$
$912$	19.2272	−	71.7568i	0.636676	−	2.37611i
$913$			20.0720i			0.664286i
$914$	60.8047	+	35.1056i	2.01124	+	1.16119i
$915$	−0.101550	−	0.378991i	−0.00335715	−	0.0125290i
$916$	−140.263	−	37.5832i	−4.63441	−	1.24179i
$917$	0.790927	+	0.223203i	0.0261187	+	0.00737081i
$918$	9.46754	−	9.46754i	0.312475	−	0.312475i
$919$	47.9672			1.58229			0.791146	−	0.611627i	$-0.209485\pi$
$919$	47.9672			1.58229			0.791146	+	0.611627i	$0.209485\pi$
$920$	19.0871			0.629282
$921$	2.62443	−	2.62443i	0.0864780	−	0.0864780i
$922$	−6.76949	+	11.7251i	−0.222941	+	0.386146i
$923$	16.6516	−	8.43728i	0.548094	−	0.277717i
$924$	−12.6966	−	22.6800i	−0.417688	−	0.746118i
$925$	33.9413	−	9.09454i	1.11598	−	0.299027i
$926$	−24.7489	−	42.8664i	−0.813300	−	1.40868i
$927$	4.04418	−	7.00473i	0.132828	−	0.230065i
$928$	−8.26751	+	30.8548i	−0.271394	+	1.01286i
$929$	−7.96550	+	7.96550i	−0.261339	+	0.261339i	−0.825598	−	0.564259i	$-0.809162\pi$
$929$	−7.96550	+	7.96550i	−0.261339	+	0.261339i	0.564259	+	0.825598i	$0.309162\pi$
$930$	1.18786	−	4.43317i	0.0389516	−	0.145369i
$931$	14.3459	−	48.3732i	0.470166	−	1.58537i
$932$	6.26594	+	10.8529i	0.205248	+	0.355500i
$933$	4.65870	−	2.68970i	0.152519	−	0.0880569i
$934$	−34.4739	−	34.4739i	−1.12802	−	1.12802i
$935$	4.59294	−	2.65174i	0.150205	−	0.0867210i
$936$	−27.5663	−	1.50689i	−0.901033	−	0.0492542i
$937$		−	15.4167i		−	0.503641i	−0.967774	−	0.251820i	$-0.918971\pi$
$937$		−	15.4167i		−	0.503641i	0.967774	−	0.251820i	$-0.0810292\pi$
$938$	54.1584	−	52.7417i	1.76834	−	1.72208i
$939$	15.7824	−	27.3358i	0.515038	−	0.892072i
$940$		−	0.212716i		−	0.00693803i
$941$	−7.84684	−	2.10255i	−0.255800	−	0.0685413i	0.128640	−	0.991691i	$-0.458939\pi$
$941$	−7.84684	−	2.10255i	−0.255800	−	0.0685413i	−0.384440	+	0.923150i	$0.625605\pi$
$942$	12.4839	−	3.34506i	0.406749	−	0.108988i
$943$	12.2784	+	12.2784i	0.399839	+	0.399839i
$944$	−40.3115	−	40.3115i	−1.31203	−	1.31203i
$945$	1.20218	−	0.672997i	0.0391069	−	0.0218926i
$946$	19.0494	+	10.9982i	0.619351	+	0.357582i
$947$	1.40726	+	0.377073i	0.0457297	+	0.0122532i	0.281611	−	0.959529i	$-0.409131\pi$
$947$	1.40726	+	0.377073i	0.0457297	+	0.0122532i	−0.235882	+	0.971782i	$0.575798\pi$
$948$	30.3196	+	52.5150i	0.984734	+	1.70561i
$949$	−6.84892	+	3.47031i	−0.222325	+	0.112651i
$950$	−77.6084	−	44.8072i	−2.51795	−	1.45374i
$951$	−2.92857	−	10.9296i	−0.0949654	−	0.354416i
$952$	−50.3953	−	90.0216i	−1.63332	−	2.91762i
$953$	21.4785	−	12.4006i	0.695756	−	0.401695i	−0.110009	−	0.993931i	$-0.535088\pi$
$953$	21.4785	−	12.4006i	0.695756	−	0.401695i	0.805765	+	0.592236i	$0.201755\pi$
$954$	−34.8215	+	9.33040i	−1.12739	+	0.302083i
$955$	−2.97449	−	11.1009i	−0.0962522	−	0.359218i
$956$	−13.2257	−	49.3591i	−0.427751	−	1.59639i
$957$	5.23681	−	1.40320i	0.169282	−	0.0453590i
$958$	51.3895	−	29.6697i	1.66032	−	0.958585i
$959$	6.25987	+	11.1821i	0.202142	+	0.361088i
$960$	−1.39715	−	5.21424i	−0.0450929	−	0.168289i
$961$	−17.1146	−	9.88110i	−0.552083	−	0.318745i
$962$	−68.9328	+	14.4901i	−2.22248	+	0.467179i
$963$	−2.82363	−	4.89066i	−0.0909901	−	0.157599i
$964$	17.1587	+	4.59767i	0.552646	+	0.148081i
$965$	3.29508	+	1.90242i	0.106073	+	0.0612410i
$966$	−29.0557	+	16.2658i	−0.934852	+	0.523343i
$967$	−4.62828	−	4.62828i	−0.148835	−	0.148835i	0.628762	−	0.777598i	$-0.283562\pi$
$967$	−4.62828	−	4.62828i	−0.148835	−	0.148835i	−0.777598	+	0.628762i	$0.783562\pi$
$968$	−37.9026	−	37.9026i	−1.21823	−	1.21823i
$969$	−35.4564	+	9.50052i	−1.13902	+	0.305201i
$970$	4.50007	+	1.20579i	0.144489	+	0.0387156i
$971$			16.7974i			0.539054i	0.962993	+	0.269527i	$0.0868674\pi$
$971$			16.7974i			0.539054i	−0.962993	+	0.269527i	$0.913133\pi$
$972$	−2.45617	+	4.25421i	−0.0787817	+	0.136454i
$973$	−20.2887	+	19.7579i	−0.650424	+	0.633410i
$974$		−	39.4301i		−	1.26342i
$975$	−5.30523	+	16.2037i	−0.169903	+	0.518933i
$976$	6.72521	−	3.88280i	0.215269	−	0.124285i
$977$	−17.3829	−	17.3829i	−0.556127	−	0.556127i	0.372076	−	0.928202i	$-0.378646\pi$
$977$	−17.3829	−	17.3829i	−0.556127	−	0.556127i	−0.928202	+	0.372076i	$0.878646\pi$
$978$	−6.90931	+	3.98909i	−0.220935	+	0.127557i
$979$	−13.6463	−	23.6361i	−0.436138	−	0.755412i
$980$	−4.17448	−	17.4128i	−0.133349	−	0.556232i
$981$	−2.50644	+	9.35415i	−0.0800243	+	0.298655i
$982$	1.23671	−	1.23671i	0.0394650	−	0.0394650i
$983$	−6.01359	+	22.4430i	−0.191804	+	0.715822i	0.801267	+	0.598307i	$0.204160\pi$
$983$	−6.01359	+	22.4430i	−0.191804	+	0.715822i	−0.993071	+	0.117515i	$0.962507\pi$
$984$	13.8872	−	24.0533i	0.442708	−	0.766792i
$985$	−6.07001	−	10.5136i	−0.193407	−	0.334990i
$986$	35.0603	−	9.39438i	1.11655	−	0.299178i
$987$	0.107471	+	0.191976i	0.00342083	+	0.00611065i
$988$	106.912	+	69.7720i	3.40133	+	2.21974i
$989$	10.0132	−	17.3434i	0.318401	−	0.551487i
$990$	−1.93606	+	1.93606i	−0.0615319	+	0.0615319i
$991$	−49.7853			−1.58148			−0.790741	−	0.612151i	$-0.790304\pi$
$991$	−49.7853			−1.58148			−0.790741	+	0.612151i	$0.790304\pi$
$992$	39.5002			1.25413
$993$	−12.8446	+	12.8446i	−0.407612	+	0.407612i
$994$	−34.6601	−	9.78122i	−1.09935	−	0.310241i
$995$	8.93224	+	2.39339i	0.283171	+	0.0758754i
$996$	−12.7606	−	47.6233i	−0.404336	−	1.50900i
$997$	2.73713	+	1.58028i	0.0866856	+	0.0500480i	0.542716	−	0.839916i	$-0.317396\pi$
$997$	2.73713	+	1.58028i	0.0866856	+	0.0500480i	−0.456031	+	0.889964i	$0.650729\pi$
$998$		−	51.6069i		−	1.63359i
$999$	−1.92321	+	7.17752i	−0.0608477	+	0.227087i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.cg.b.124.10	yes	40
3.2	odd	2		819.2.gh.d.397.1		40
7.3	odd	6		273.2.bt.b.241.10	yes	40
13.2	odd	12		273.2.bt.b.145.10	✓	40
21.17	even	6		819.2.et.d.514.1		40
39.2	even	12		819.2.et.d.145.1		40
91.80	even	12	inner	273.2.cg.b.262.10	yes	40
273.80	odd	12		819.2.gh.d.262.1		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.b.145.10	✓	40	13.2	odd	12
273.2.bt.b.241.10	yes	40	7.3	odd	6
273.2.cg.b.124.10	yes	40	1.1	even	1	trivial
273.2.cg.b.262.10	yes	40	91.80	even	12	inner
819.2.et.d.145.1		40	39.2	even	12
819.2.et.d.514.1		40	21.17	even	6
819.2.gh.d.262.1		40	273.80	odd	12
819.2.gh.d.397.1		40	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.cg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.680470 - 2.53955i) q^{2} -1.00000i q^{3} +(-4.25421 - 2.45617i) q^{4} +(0.134776 + 0.502992i) q^{5} +(-2.53955 - 0.680470i) q^{6} +(-2.56445 + 0.650845i) q^{7} +(-5.41427 + 5.41427i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(0.680470 - 2.53955i) q^{2} -1.00000i q^{3} +(-4.25421 - 2.45617i) q^{4} +(0.134776 + 0.502992i) q^{5} +(-2.53955 - 0.680470i) q^{6} +(-2.56445 + 0.650845i) q^{7} +(-5.41427 + 5.41427i) q^{8} -1.00000 q^{9} +1.36908 q^{10} +(1.41413 - 1.41413i) q^{11} +(-2.45617 + 4.25421i) q^{12} +(-2.40655 - 2.68487i) q^{13} +(-0.0921792 + 6.95542i) q^{14} +(0.502992 - 0.134776i) q^{15} +(5.15321 + 8.92562i) q^{16} +(2.54630 - 4.41032i) q^{17} +(-0.680470 + 2.53955i) q^{18} +(5.09679 - 5.09679i) q^{19} +(0.662067 - 2.47087i) q^{20} +(0.650845 + 2.56445i) q^{21} +(-2.62897 - 4.55351i) q^{22} +(-4.14570 + 2.39352i) q^{23} +(5.41427 + 5.41427i) q^{24} +(4.09529 - 2.36442i) q^{25} +(-8.45594 + 4.28458i) q^{26} +1.00000i q^{27} +(12.5083 + 3.52989i) q^{28} +(-1.35547 + 2.34774i) q^{29} -1.36908i q^{30} +(3.23806 + 0.867635i) q^{31} +(11.3816 - 3.04969i) q^{32} +(-1.41413 - 1.41413i) q^{33} +(-9.46754 - 9.46754i) q^{34} +(-0.672997 - 1.20218i) q^{35} +(4.25421 + 2.45617i) q^{36} +(7.17752 + 1.92321i) q^{37} +(-9.47532 - 16.4117i) q^{38} +(-2.68487 + 2.40655i) q^{39} +(-3.45305 - 1.99362i) q^{40} +(-0.938828 - 3.50375i) q^{41} +(6.95542 + 0.0921792i) q^{42} +(-3.62298 + 2.09173i) q^{43} +(-9.48933 + 2.54266i) q^{44} +(-0.134776 - 0.502992i) q^{45} +(3.25743 + 12.1569i) q^{46} +(0.0803226 - 0.0215224i) q^{47} +(8.92562 - 5.15321i) q^{48} +(6.15280 - 3.33812i) q^{49} +(-3.21783 - 12.0091i) q^{50} +(-4.41032 - 2.54630i) q^{51} +(3.64348 + 17.3329i) q^{52} +(6.85585 + 11.8747i) q^{53} +(2.53955 + 0.680470i) q^{54} +(0.901885 + 0.520704i) q^{55} +(10.3608 - 17.4085i) q^{56} +(-5.09679 - 5.09679i) q^{57} +(5.03985 + 5.03985i) q^{58} +(-5.34294 + 1.43164i) q^{59} +(-2.47087 - 0.662067i) q^{60} -0.753473i q^{61} +(4.40680 - 7.63280i) q^{62} +(2.56445 - 0.650845i) q^{63} -10.3665i q^{64} +(1.02612 - 1.57233i) q^{65} +(-4.55351 + 2.62897i) q^{66} +(-7.68466 - 7.68466i) q^{67} +(-21.6650 + 12.5083i) q^{68} +(2.39352 + 4.14570i) q^{69} +(-3.51095 + 0.891061i) q^{70} +(-1.34000 + 5.00093i) q^{71} +(5.41427 - 5.41427i) q^{72} +(0.551150 - 2.05692i) q^{73} +(9.76817 - 16.9190i) q^{74} +(-2.36442 - 4.09529i) q^{75} +(-34.2014 + 9.16424i) q^{76} +(-2.70608 + 4.54683i) q^{77} +(4.28458 + 8.45594i) q^{78} +(6.17212 - 10.6904i) q^{79} +(-3.79499 + 3.79499i) q^{80} +1.00000 q^{81} -9.53679 q^{82} +(-7.09696 + 7.09696i) q^{83} +(3.52989 - 12.5083i) q^{84} +(2.56154 + 0.686362i) q^{85} +(2.84672 + 10.6241i) q^{86} +(2.34774 + 1.35547i) q^{87} +15.3129i q^{88} +(3.53214 - 13.1821i) q^{89} -1.36908 q^{90} +(7.91891 + 5.31892i) q^{91} +23.5156 q^{92} +(0.867635 - 3.23806i) q^{93} -0.218629i q^{94} +(3.25057 + 1.87672i) q^{95} +(-3.04969 - 11.3816i) q^{96} +(3.28692 + 0.880729i) q^{97} +(-4.29051 - 17.8968i) q^{98} +(-1.41413 + 1.41413i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 8 q^{7} - 40 q^{9}+O(q^{10}) \) 40 * q - 8 * q^7 - 40 * q^9	\( 40 q - 8 q^{7} - 40 q^{9} + 4 q^{11} - 24 q^{12} - 18 q^{14} + 32 q^{16} + 4 q^{17} + 14 q^{19} + 14 q^{20} + 2 q^{21} + 4 q^{22} + 12 q^{23} + 24 q^{25} - 32 q^{26} + 16 q^{28} + 8 q^{29} + 14 q^{31} - 26 q^{32} - 4 q^{33} - 24 q^{34} + 26 q^{35} + 36 q^{37} - 8 q^{38} + 18 q^{39} - 30 q^{40} - 2 q^{41} - 66 q^{43} - 32 q^{44} - 26 q^{46} - 4 q^{47} + 24 q^{48} - 14 q^{49} - 20 q^{50} + 2 q^{52} - 8 q^{53} - 42 q^{55} + 46 q^{56} - 14 q^{57} + 24 q^{58} + 14 q^{59} + 2 q^{60} + 24 q^{62} + 8 q^{63} + 28 q^{65} - 18 q^{66} - 44 q^{67} - 18 q^{68} + 4 q^{69} - 4 q^{70} - 6 q^{71} + 14 q^{73} - 20 q^{74} + 24 q^{75} - 64 q^{76} + 24 q^{77} + 8 q^{78} + 20 q^{80} + 40 q^{81} + 48 q^{82} - 12 q^{83} + 22 q^{84} + 2 q^{85} - 60 q^{86} + 18 q^{87} - 2 q^{89} - 14 q^{91} + 236 q^{92} - 8 q^{93} + 24 q^{95} + 16 q^{96} - 62 q^{97} - 88 q^{98} - 4 q^{99}+O(q^{100}) \) 40 * q - 8 * q^7 - 40 * q^9 + 4 * q^11 - 24 * q^12 - 18 * q^14 + 32 * q^16 + 4 * q^17 + 14 * q^19 + 14 * q^20 + 2 * q^21 + 4 * q^22 + 12 * q^23 + 24 * q^25 - 32 * q^26 + 16 * q^28 + 8 * q^29 + 14 * q^31 - 26 * q^32 - 4 * q^33 - 24 * q^34 + 26 * q^35 + 36 * q^37 - 8 * q^38 + 18 * q^39 - 30 * q^40 - 2 * q^41 - 66 * q^43 - 32 * q^44 - 26 * q^46 - 4 * q^47 + 24 * q^48 - 14 * q^49 - 20 * q^50 + 2 * q^52 - 8 * q^53 - 42 * q^55 + 46 * q^56 - 14 * q^57 + 24 * q^58 + 14 * q^59 + 2 * q^60 + 24 * q^62 + 8 * q^63 + 28 * q^65 - 18 * q^66 - 44 * q^67 - 18 * q^68 + 4 * q^69 - 4 * q^70 - 6 * q^71 + 14 * q^73 - 20 * q^74 + 24 * q^75 - 64 * q^76 + 24 * q^77 + 8 * q^78 + 20 * q^80 + 40 * q^81 + 48 * q^82 - 12 * q^83 + 22 * q^84 + 2 * q^85 - 60 * q^86 + 18 * q^87 - 2 * q^89 - 14 * q^91 + 236 * q^92 - 8 * q^93 + 24 * q^95 + 16 * q^96 - 62 * q^97 - 88 * q^98 - 4 * q^99

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