LMFDB - Embedded newform 731.2.m.c.689.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(87,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([7, 0]))

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

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

chi := DirichletCharacter("731.87");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.m (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			689.18
Character	$\chi$	$=$	731.689
Dual form			731.2.m.c.87.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.493410 - 0.493410i) q^{2} +(2.20257 + 0.912334i) q^{3} +1.51309i q^{4} +(-1.26013 + 3.04222i) q^{5} +(1.53692 - 0.636615i) q^{6} +(-1.60257 - 3.86896i) q^{7} +(1.73339 + 1.73339i) q^{8} +(1.89764 + 1.89764i) q^{9} +O(q^{10})$	\(q+(0.493410 - 0.493410i) q^{2} +(2.20257 + 0.912334i) q^{3} +1.51309i q^{4} +(-1.26013 + 3.04222i) q^{5} +(1.53692 - 0.636615i) q^{6} +(-1.60257 - 3.86896i) q^{7} +(1.73339 + 1.73339i) q^{8} +(1.89764 + 1.89764i) q^{9} +(0.879301 + 2.12282i) q^{10} +(0.798554 - 0.330772i) q^{11} +(-1.38045 + 3.33269i) q^{12} +4.97189i q^{13} +(-2.69971 - 1.11826i) q^{14} +(-5.55104 + 5.55104i) q^{15} -1.31564 q^{16} +(-0.463963 + 4.09692i) q^{17} +1.87263 q^{18} +(0.523830 - 0.523830i) q^{19} +(-4.60316 - 1.90669i) q^{20} -9.98374i q^{21} +(0.230808 - 0.557221i) q^{22} +(6.47869 - 2.68356i) q^{23} +(2.23649 + 5.39936i) q^{24} +(-4.13164 - 4.13164i) q^{25} +(2.45318 + 2.45318i) q^{26} +(-0.288600 - 0.696741i) q^{27} +(5.85410 - 2.42485i) q^{28} +(-0.419969 + 1.01389i) q^{29} +5.47788i q^{30} +(-1.54250 - 0.638926i) q^{31} +(-4.11594 + 4.11594i) q^{32} +2.06065 q^{33} +(1.79254 + 2.25038i) q^{34} +13.7897 q^{35} +(-2.87131 + 2.87131i) q^{36} +(1.02087 + 0.422858i) q^{37} -0.516926i q^{38} +(-4.53603 + 10.9509i) q^{39} +(-7.45767 + 3.08907i) q^{40} +(-1.36744 - 3.30130i) q^{41} +(-4.92607 - 4.92607i) q^{42} +(-0.707107 - 0.707107i) q^{43} +(0.500489 + 1.20829i) q^{44} +(-8.16431 + 3.38177i) q^{45} +(1.87255 - 4.52075i) q^{46} -4.76167i q^{47} +(-2.89779 - 1.20030i) q^{48} +(-7.45084 + 7.45084i) q^{49} -4.07718 q^{50} +(-4.75967 + 8.60046i) q^{51} -7.52294 q^{52} +(0.708903 - 0.708903i) q^{53} +(-0.486177 - 0.201381i) q^{54} +2.84619i q^{55} +(3.92854 - 9.48433i) q^{56} +(1.63168 - 0.675864i) q^{57} +(0.293049 + 0.707482i) q^{58} +(5.32071 + 5.32071i) q^{59} +(-8.39925 - 8.39925i) q^{60} +(0.461102 + 1.11320i) q^{61} +(-1.07634 + 0.445834i) q^{62} +(4.30078 - 10.3830i) q^{63} +1.43041i q^{64} +(-15.1256 - 6.26523i) q^{65} +(1.01674 - 1.01674i) q^{66} +14.3801 q^{67} +(-6.19902 - 0.702020i) q^{68} +16.7181 q^{69} +(6.80396 - 6.80396i) q^{70} +(9.57871 + 3.96763i) q^{71} +6.57872i q^{72} +(3.54002 - 8.54636i) q^{73} +(0.712349 - 0.295065i) q^{74} +(-5.33079 - 12.8697i) q^{75} +(0.792604 + 0.792604i) q^{76} +(-2.55949 - 2.55949i) q^{77} +(3.16518 + 7.64143i) q^{78} +(5.43583 - 2.25160i) q^{79} +(1.65787 - 4.00246i) q^{80} -9.84893i q^{81} +(-2.30360 - 0.954184i) q^{82} +(7.05417 - 7.05417i) q^{83} +15.1063 q^{84} +(-11.8791 - 6.57412i) q^{85} -0.697787 q^{86} +(-1.85002 + 1.85002i) q^{87} +(1.95757 + 0.810851i) q^{88} +6.34024i q^{89} +(-2.35975 + 5.69695i) q^{90} +(19.2361 - 7.96783i) q^{91} +(4.06048 + 9.80287i) q^{92} +(-2.81456 - 2.81456i) q^{93} +(-2.34946 - 2.34946i) q^{94} +(0.933512 + 2.25370i) q^{95} +(-12.8208 + 5.31053i) q^{96} +(-0.907902 + 2.19187i) q^{97} +7.35264i q^{98} +(2.14305 + 0.887682i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9}+O(q^{10}) $ 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9	$ 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9} - 8 q^{10} - 4 q^{11} + 12 q^{12} + 12 q^{14} - 12 q^{15} - 144 q^{16} - 12 q^{17} + 64 q^{18} - 28 q^{19} - 8 q^{20} - 12 q^{22} + 16 q^{23} - 16 q^{24} - 20 q^{25} + 16 q^{26} - 8 q^{27} + 20 q^{28} + 12 q^{31} - 4 q^{32} - 104 q^{33} + 20 q^{34} + 32 q^{35} - 96 q^{36} - 12 q^{37} + 8 q^{39} + 216 q^{40} + 24 q^{41} - 4 q^{42} + 24 q^{44} - 28 q^{45} - 48 q^{46} + 28 q^{48} - 80 q^{50} - 20 q^{51} + 56 q^{52} - 36 q^{53} - 12 q^{54} - 8 q^{56} + 72 q^{57} - 32 q^{58} + 48 q^{59} - 40 q^{60} - 76 q^{61} - 44 q^{62} + 36 q^{65} - 68 q^{66} - 48 q^{67} + 32 q^{68} + 216 q^{69} - 196 q^{70} + 4 q^{71} + 20 q^{73} + 88 q^{74} + 80 q^{75} + 72 q^{76} + 28 q^{77} - 120 q^{78} + 68 q^{79} - 68 q^{80} + 28 q^{82} - 36 q^{83} - 152 q^{84} + 28 q^{85} - 24 q^{86} - 56 q^{87} + 20 q^{88} - 112 q^{90} + 96 q^{91} - 28 q^{92} + 24 q^{93} - 36 q^{94} - 108 q^{95} + 272 q^{96} + 8 q^{97} - 20 q^{99}+O(q^{100}) $ 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9 - 8 * q^10 - 4 * q^11 + 12 * q^12 + 12 * q^14 - 12 * q^15 - 144 * q^16 - 12 * q^17 + 64 * q^18 - 28 * q^19 - 8 * q^20 - 12 * q^22 + 16 * q^23 - 16 * q^24 - 20 * q^25 + 16 * q^26 - 8 * q^27 + 20 * q^28 + 12 * q^31 - 4 * q^32 - 104 * q^33 + 20 * q^34 + 32 * q^35 - 96 * q^36 - 12 * q^37 + 8 * q^39 + 216 * q^40 + 24 * q^41 - 4 * q^42 + 24 * q^44 - 28 * q^45 - 48 * q^46 + 28 * q^48 - 80 * q^50 - 20 * q^51 + 56 * q^52 - 36 * q^53 - 12 * q^54 - 8 * q^56 + 72 * q^57 - 32 * q^58 + 48 * q^59 - 40 * q^60 - 76 * q^61 - 44 * q^62 + 36 * q^65 - 68 * q^66 - 48 * q^67 + 32 * q^68 + 216 * q^69 - 196 * q^70 + 4 * q^71 + 20 * q^73 + 88 * q^74 + 80 * q^75 + 72 * q^76 + 28 * q^77 - 120 * q^78 + 68 * q^79 - 68 * q^80 + 28 * q^82 - 36 * q^83 - 152 * q^84 + 28 * q^85 - 24 * q^86 - 56 * q^87 + 20 * q^88 - 112 * q^90 + 96 * q^91 - 28 * q^92 + 24 * q^93 - 36 * q^94 - 108 * q^95 + 272 * q^96 + 8 * q^97 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.493410	−	0.493410i	0.348893	−	0.348893i	−0.510804	−	0.859697i	$-0.670652\pi$
$2$	0.493410	−	0.493410i	0.348893	−	0.348893i	0.859697	+	0.510804i	$0.170652\pi$
$3$	2.20257	+	0.912334i	1.27165	+	0.526737i	0.913467	−	0.406913i	$-0.133395\pi$
$3$	2.20257	+	0.912334i	1.27165	+	0.526737i	0.358188	+	0.933650i	$0.383395\pi$
$4$			1.51309i			0.756547i
$5$	−1.26013	+	3.04222i	−0.563547	+	1.36052i	0.343365	+	0.939202i	$0.388433\pi$
$5$	−1.26013	+	3.04222i	−0.563547	+	1.36052i	−0.906912	+	0.421320i	$0.861567\pi$
$6$	1.53692	−	0.636615i	0.627447	−	0.259897i
$7$	−1.60257	−	3.86896i	−0.605716	−	1.46233i	−0.867617	−	0.497234i	$-0.834349\pi$
$7$	−1.60257	−	3.86896i	−0.605716	−	1.46233i	0.261900	−	0.965095i	$-0.415651\pi$
$8$	1.73339	+	1.73339i	0.612848	+	0.612848i
$9$	1.89764	+	1.89764i	0.632547	+	0.632547i
$10$	0.879301	+	2.12282i	0.278059	+	0.671295i
$11$	0.798554	−	0.330772i	0.240773	−	0.0997315i	−0.259034	−	0.965868i	$-0.583404\pi$
$11$	0.798554	−	0.330772i	0.240773	−	0.0997315i	0.499807	+	0.866137i	$0.333404\pi$
$12$	−1.38045	+	3.33269i	−0.398501	+	0.962066i
$13$			4.97189i			1.37896i	0.724307	+	0.689478i	$0.242160\pi$
$13$			4.97189i			1.37896i	−0.724307	+	0.689478i	$0.757840\pi$
$14$	−2.69971	−	1.11826i	−0.721527	−	0.298866i
$15$	−5.55104	+	5.55104i	−1.43327	+	1.43327i
$16$	−1.31564			−0.328910
$17$	−0.463963	+	4.09692i	−0.112528	+	0.993649i
$17$	−0.463963	+	4.09692i	−0.112528	+	0.993649i
$18$	1.87263			0.441383
$19$	0.523830	−	0.523830i	0.120175	−	0.120175i	−0.644462	−	0.764637i	$-0.722919\pi$
$19$	0.523830	−	0.523830i	0.120175	−	0.120175i	0.764637	+	0.644462i	$0.222919\pi$
$20$	−4.60316	−	1.90669i	−1.02930	−	0.426349i
$21$		−	9.98374i		−	2.17863i
$22$	0.230808	−	0.557221i	0.0492085	−	0.118800i
$23$	6.47869	−	2.68356i	1.35090	−	0.559561i	0.414358	−	0.910114i	$-0.364006\pi$
$23$	6.47869	−	2.68356i	1.35090	−	0.559561i	0.936543	+	0.350553i	$0.114006\pi$
$24$	2.23649	+	5.39936i	0.456521	+	1.10214i
$25$	−4.13164	−	4.13164i	−0.826328	−	0.826328i
$26$	2.45318	+	2.45318i	0.481108	+	0.481108i
$27$	−0.288600	−	0.696741i	−0.0555410	−	0.134088i
$28$	5.85410	−	2.42485i	1.10632	−	0.458253i
$29$	−0.419969	+	1.01389i	−0.0779863	+	0.188275i	−0.958064	−	0.286554i	$-0.907490\pi$
$29$	−0.419969	+	1.01389i	−0.0779863	+	0.188275i	0.880078	+	0.474829i	$0.157490\pi$
$30$			5.47788i			1.00012i
$31$	−1.54250	−	0.638926i	−0.277042	−	0.114755i	0.239837	−	0.970813i	$-0.422906\pi$
$31$	−1.54250	−	0.638926i	−0.277042	−	0.114755i	−0.516879	+	0.856059i	$0.672906\pi$
$32$	−4.11594	+	4.11594i	−0.727602	+	0.727602i
$33$	2.06065			0.358712
$34$	1.79254	+	2.25038i	0.307417	+	0.385938i
$35$	13.7897			2.33088
$36$	−2.87131	+	2.87131i	−0.478551	+	0.478551i
$37$	1.02087	+	0.422858i	0.167830	+	0.0695174i	0.465017	−	0.885302i	$-0.346048\pi$
$37$	1.02087	+	0.422858i	0.167830	+	0.0695174i	−0.297187	+	0.954819i	$0.596048\pi$
$38$		−	0.516926i		−	0.0838564i
$39$	−4.53603	+	10.9509i	−0.726346	+	1.75355i
$40$	−7.45767	+	3.08907i	−1.17916	+	0.488424i
$41$	−1.36744	−	3.30130i	−0.213559	−	0.515576i	0.780406	−	0.625273i	$-0.215012\pi$
$41$	−1.36744	−	3.30130i	−0.213559	−	0.515576i	−0.993965	+	0.109696i	$0.965012\pi$
$42$	−4.92607	−	4.92607i	−0.760110	−	0.760110i
$43$	−0.707107	−	0.707107i	−0.107833	−	0.107833i
$43$	−0.707107	−	0.707107i	−0.107833	−	0.107833i
$44$	0.500489	+	1.20829i	0.0754515	+	0.182156i
$45$	−8.16431	+	3.38177i	−1.21706	+	0.504124i
$46$	1.87255	−	4.52075i	0.276093	−	0.666548i
$47$		−	4.76167i		−	0.694561i	−0.937761	−	0.347281i	$-0.887105\pi$
$47$		−	4.76167i		−	0.694561i	0.937761	−	0.347281i	$-0.112895\pi$
$48$	−2.89779	−	1.20030i	−0.418260	−	0.173249i
$49$	−7.45084	+	7.45084i	−1.06441	+	1.06441i
$50$	−4.07718			−0.576601
$51$	−4.75967	+	8.60046i	−0.666487	+	1.20431i
$52$	−7.52294			−1.04324
$53$	0.708903	−	0.708903i	0.0973754	−	0.0973754i	−0.656741	−	0.754116i	$-0.728065\pi$
$53$	0.708903	−	0.708903i	0.0973754	−	0.0973754i	0.754116	+	0.656741i	$0.228065\pi$
$54$	−0.486177	−	0.201381i	−0.0661603	−	0.0274045i
$55$			2.84619i			0.383780i
$56$	3.92854	−	9.48433i	0.524973	−	1.26740i
$57$	1.63168	−	0.675864i	0.216121	−	0.0895204i
$58$	0.293049	+	0.707482i	0.0384792	+	0.0928970i
$59$	5.32071	+	5.32071i	0.692697	+	0.692697i	0.962825	−	0.270127i	$-0.0870658\pi$
$59$	5.32071	+	5.32071i	0.692697	+	0.692697i	−0.270127	+	0.962825i	$0.587066\pi$
$60$	−8.39925	−	8.39925i	−1.08434	−	1.08434i
$61$	0.461102	+	1.11320i	0.0590380	+	0.142530i	0.950646	−	0.310278i	$-0.100422\pi$
$61$	0.461102	+	1.11320i	0.0590380	+	0.142530i	−0.891608	+	0.452808i	$0.850422\pi$
$62$	−1.07634	+	0.445834i	−0.136695	+	0.0566210i
$63$	4.30078	−	10.3830i	0.541847	−	1.30814i
$64$			1.43041i			0.178801i
$65$	−15.1256	−	6.26523i	−1.87610	−	0.777106i
$66$	1.01674	−	1.01674i	0.125152	−	0.125152i
$67$	14.3801			1.75681			0.878406	−	0.477916i	$-0.158608\pi$
$67$	14.3801			1.75681			0.878406	+	0.477916i	$0.158608\pi$
$68$	−6.19902	−	0.702020i	−0.751742	−	0.0851324i
$69$	16.7181			2.01262
$70$	6.80396	−	6.80396i	0.813229	−	0.813229i
$71$	9.57871	+	3.96763i	1.13678	+	0.470871i	0.870082	−	0.492908i	$-0.164066\pi$
$71$	9.57871	+	3.96763i	1.13678	+	0.470871i	0.266702	+	0.963779i	$0.414066\pi$
$72$			6.57872i			0.775310i
$73$	3.54002	−	8.54636i	0.414328	−	1.00028i	−0.569634	−	0.821898i	$-0.692915\pi$
$73$	3.54002	−	8.54636i	0.414328	−	1.00028i	0.983962	−	0.178378i	$-0.0570849\pi$
$74$	0.712349	−	0.295065i	0.0828089	−	0.0343006i
$75$	−5.33079	−	12.8697i	−0.615547	−	1.48606i
$76$	0.792604	+	0.792604i	0.0909179	+	0.0909179i
$77$	−2.55949	−	2.55949i	−0.291680	−	0.291680i
$78$	3.16518	+	7.64143i	0.358386	+	0.865221i
$79$	5.43583	−	2.25160i	0.611579	−	0.253324i	−0.0553244	−	0.998468i	$-0.517619\pi$
$79$	5.43583	−	2.25160i	0.611579	−	0.253324i	0.666904	+	0.745144i	$0.267619\pi$
$80$	1.65787	−	4.00246i	0.185356	−	0.447489i
$81$		−	9.84893i		−	1.09433i
$82$	−2.30360	−	0.954184i	−0.254390	−	0.105372i
$83$	7.05417	−	7.05417i	0.774296	−	0.774296i	−0.204559	−	0.978854i	$-0.565576\pi$
$83$	7.05417	−	7.05417i	0.774296	−	0.774296i	0.978854	+	0.204559i	$0.0655759\pi$
$84$	15.1063			1.64824
$85$	−11.8791	−	6.57412i	−1.28847	−	0.713064i
$86$	−0.697787			−0.0752443
$87$	−1.85002	+	1.85002i	−0.198343	+	0.198343i
$88$	1.95757	+	0.810851i	0.208677	+	0.0864370i
$89$			6.34024i			0.672064i	0.941850	+	0.336032i	$0.109085\pi$
$89$			6.34024i			0.672064i	−0.941850	+	0.336032i	$0.890915\pi$
$90$	−2.35975	+	5.69695i	−0.248740	+	0.600511i
$91$	19.2361	−	7.96783i	2.01649	−	0.835256i
$92$	4.06048	+	9.80287i	0.423334	+	1.02202i
$93$	−2.81456	−	2.81456i	−0.291856	−	0.291856i
$94$	−2.34946	−	2.34946i	−0.242328	−	0.242328i
$95$	0.933512	+	2.25370i	0.0957764	+	0.231225i
$96$	−12.8208	+	5.31053i	−1.30851	+	0.542004i
$97$	−0.907902	+	2.19187i	−0.0921835	+	0.222551i	−0.963246	−	0.268622i	$-0.913432\pi$
$97$	−0.907902	+	2.19187i	−0.0921835	+	0.222551i	0.871062	+	0.491173i	$0.163432\pi$
$98$			7.35264i			0.742729i
$99$	2.14305	+	0.887682i	0.215385	+	0.0892154i
$100$	6.25156	−	6.25156i	0.625156	−	0.625156i
$101$	4.88521			0.486097			0.243048	−	0.970014i	$-0.421853\pi$
$101$	4.88521			0.486097			0.243048	+	0.970014i	$0.421853\pi$
$102$	1.89508	+	6.59202i	0.187641	+	0.652707i
$103$	−17.9635			−1.76999			−0.884996	−	0.465599i	$-0.845839\pi$
$103$	−17.9635			−1.76999			−0.884996	+	0.465599i	$0.845839\pi$
$104$	−8.61826	+	8.61826i	−0.845090	+	0.845090i
$105$	30.3727	+	12.5808i	2.96407	+	1.22776i
$106$		−	0.699560i		−	0.0679473i
$107$	7.28425	−	17.5857i	0.704195	−	1.70008i	−0.00982415	−	0.999952i	$-0.503127\pi$
$107$	7.28425	−	17.5857i	0.704195	−	1.70008i	0.714019	−	0.700126i	$-0.246873\pi$
$108$	1.05423	−	0.436678i	0.101444	−	0.0420194i
$109$	−4.96245	−	11.9804i	−0.475316	−	1.14752i	−0.961782	−	0.273816i	$-0.911714\pi$
$109$	−4.96245	−	11.9804i	−0.475316	−	1.14752i	0.486466	−	0.873700i	$-0.338286\pi$
$110$	1.40434	+	1.40434i	0.133898	+	0.133898i
$111$	1.86275	+	1.86275i	0.176804	+	0.176804i
$112$	2.10841	+	5.09015i	0.199226	+	0.480974i
$113$	0.740888	−	0.306886i	0.0696969	−	0.0288694i	−0.347563	−	0.937657i	$-0.612991\pi$
$113$	0.740888	−	0.306886i	0.0696969	−	0.0288694i	0.417260	+	0.908787i	$0.362991\pi$
$114$	0.471609	−	1.13856i	0.0441702	−	0.106636i
$115$			23.0912i			2.15327i
$116$	−1.53412	−	0.635452i	−0.142439	−	0.0590002i
$117$	−9.43487	+	9.43487i	−0.872254	+	0.872254i
$118$	5.25058			0.483355
$119$	16.5943	−	4.77056i	1.52120	−	0.437317i
$120$	−19.2443			−1.75676
$121$	−7.24990	+	7.24990i	−0.659081	+	0.659081i
$122$	0.776775	+	0.321751i	0.0703259	+	0.0291299i
$123$		−	8.51891i		−	0.768124i
$124$	0.966755	−	2.33395i	0.0868172	−	0.209595i
$125$	2.56466	−	1.06232i	0.229390	−	0.0950166i
$126$	−3.00103	−	7.24512i	−0.267353	−	0.645447i
$127$	−7.11232	−	7.11232i	−0.631116	−	0.631116i	0.317232	−	0.948348i	$-0.397247\pi$
$127$	−7.11232	−	7.11232i	−0.631116	−	0.631116i	−0.948348	+	0.317232i	$0.897247\pi$
$128$	−7.52610	−	7.52610i	−0.665219	−	0.665219i
$129$	−0.912334	−	2.20257i	−0.0803266	−	0.193925i
$130$	−10.5544	+	4.37179i	−0.925686	+	0.383432i
$131$	0.639274	−	1.54334i	0.0558536	−	0.134843i	−0.893489	−	0.449084i	$-0.851750\pi$
$131$	0.639274	−	1.54334i	0.0558536	−	0.134843i	0.949343	+	0.314242i	$0.101750\pi$
$132$			3.11795i			0.271383i
$133$	−2.86615	−	1.18720i	−0.248527	−	0.102943i
$134$	7.09529	−	7.09529i	0.612940	−	0.612940i
$135$	2.48331			0.213730
$136$	−7.90581	+	6.29734i	−0.677917	+	0.539993i
$137$	20.1168			1.71869			0.859346	−	0.511395i	$-0.170871\pi$
$137$	20.1168			1.71869			0.859346	+	0.511395i	$0.170871\pi$
$138$	8.24886	−	8.24886i	0.702190	−	0.702190i
$139$	12.6486	+	5.23921i	1.07284	+	0.444384i	0.847991	−	0.530010i	$-0.177812\pi$
$139$	12.6486	+	5.23921i	1.07284	+	0.444384i	0.224846	+	0.974394i	$0.427812\pi$
$140$			20.8651i			1.76342i
$141$	4.34424	−	10.4879i	0.365851	−	0.883242i
$142$	6.68390	−	2.76856i	0.560900	−	0.232333i
$143$	1.64456	+	3.97033i	0.137525	+	0.332015i
$144$	−2.49661	−	2.49661i	−0.208051	−	0.208051i
$145$	−2.55527	−	2.55527i	−0.212204	−	0.212204i
$146$	−2.47018	−	5.96354i	−0.204433	−	0.493546i
$147$	−23.2087	+	9.61334i	−1.91422	+	0.792895i
$148$	−0.639824	+	1.54467i	−0.0525932	+	0.126971i
$149$			12.4345i			1.01868i	0.860566	+	0.509338i	$0.170110\pi$
$149$			12.4345i			1.01868i	−0.860566	+	0.509338i	$0.829890\pi$
$150$	−8.98028	−	3.71976i	−0.733237	−	0.303717i
$151$	5.65632	−	5.65632i	0.460305	−	0.460305i	−0.438451	−	0.898755i	$-0.644473\pi$
$151$	5.65632	−	5.65632i	0.460305	−	0.460305i	0.898755	+	0.438451i	$0.144473\pi$
$152$	1.81601			0.147298
$153$	−8.65491	+	6.89404i	−0.699708	+	0.557350i
$154$	−2.52575			−0.203531
$155$	3.88751	−	3.88751i	0.312252	−	0.312252i
$156$	−16.5698	−	6.86344i	−1.32665	−	0.549515i
$157$			12.1765i			0.971792i	0.874017	+	0.485896i	$0.161507\pi$
$157$			12.1765i			0.971792i	−0.874017	+	0.485896i	$0.838493\pi$
$158$	1.57113	−	3.79305i	0.124993	−	0.301759i
$159$	2.20817	−	0.914653i	0.175119	−	0.0725367i
$160$	−7.33498	−	17.7082i	−0.579881	−	1.39996i
$161$	−20.7652	−	20.7652i	−1.63653	−	1.63653i
$162$	−4.85956	−	4.85956i	−0.381803	−	0.381803i
$163$	8.58330	+	20.7219i	0.672296	+	1.62307i	0.777700	+	0.628636i	$0.216386\pi$
$163$	8.58330	+	20.7219i	0.672296	+	1.62307i	−0.105404	+	0.994430i	$0.533614\pi$
$164$	4.99518	−	2.06907i	0.390058	−	0.161567i
$165$	−2.59668	+	6.26894i	−0.202151	+	0.488036i
$166$		−	6.96119i		−	0.540293i
$167$	−17.7664	−	7.35908i	−1.37480	−	0.569463i	−0.431718	−	0.902009i	$-0.642092\pi$
$167$	−17.7664	−	7.35908i	−1.37480	−	0.569463i	−0.943087	+	0.332546i	$0.892092\pi$
$168$	17.3058	−	17.3058i	1.33517	−	1.33517i
$169$	−11.7197			−0.901518
$170$	−9.10499	+	2.61751i	−0.698321	+	0.200754i
$171$	1.98808			0.152032
$172$	1.06992	−	1.06992i	0.0815805	−	0.0815805i
$173$	−20.4762	−	8.48153i	−1.55678	−	0.644839i	−0.572253	−	0.820077i	$-0.693930\pi$
$173$	−20.4762	−	8.48153i	−1.55678	−	0.644839i	−0.984526	+	0.175238i	$0.943930\pi$
$174$			1.82564i			0.138401i
$175$	−9.36388	+	22.6064i	−0.707843	+	1.70888i
$176$	−1.05061	+	0.435176i	−0.0791926	+	0.0328027i
$177$	6.86497	+	16.5735i	0.516003	+	1.24574i
$178$	3.12834	+	3.12834i	0.234479	+	0.234479i
$179$	−16.7400	−	16.7400i	−1.25120	−	1.25120i	−0.955181	−	0.296021i	$-0.904340\pi$
$179$	−16.7400	−	16.7400i	−1.25120	−	1.25120i	−0.296021	−	0.955181i	$-0.595660\pi$
$180$	−5.11693	−	12.3534i	−0.381394	−	0.920765i
$181$	−10.3020	+	4.26723i	−0.765742	+	0.317181i	−0.731146	−	0.682221i	$-0.761014\pi$
$181$	−10.3020	+	4.26723i	−0.765742	+	0.317181i	−0.0345958	+	0.999401i	$0.511014\pi$
$182$	5.55985	−	13.4227i	0.412123	−	0.994954i
$183$			2.87257i			0.212347i
$184$	15.8818	+	6.57846i	1.17082	+	0.484970i
$185$	−2.57285	+	2.57285i	−0.189160	+	0.189160i
$186$	−2.77746			−0.203653
$187$	0.984646	+	3.42508i	0.0720044	+	0.250466i
$188$	7.20486			0.525468
$189$	−2.23316	+	2.23316i	−0.162438	+	0.162438i
$190$	1.57260	+	0.651393i	0.114088	+	0.0472570i
$191$		−	20.5429i		−	1.48643i	−0.669052	−	0.743216i	$-0.733300\pi$
$191$		−	20.5429i		−	1.48643i	0.669052	−	0.743216i	$-0.266700\pi$
$192$	−1.30501	+	3.15058i	−0.0941812	+	0.227374i
$193$	18.9208	−	7.83726i	1.36195	−	0.564138i	0.422356	−	0.906430i	$-0.361203\pi$
$193$	18.9208	−	7.83726i	1.36195	−	0.564138i	0.939594	+	0.342292i	$0.111203\pi$
$194$	0.633522	+	1.52946i	0.0454843	+	0.109809i
$195$	−27.5992	−	27.5992i	−1.97642	−	1.97642i
$196$	−11.2738	−	11.2738i	−0.805273	−	0.805273i
$197$	4.37960	+	10.5733i	0.312033	+	0.753315i	0.999629	+	0.0272218i	$0.00866603\pi$
$197$	4.37960	+	10.5733i	0.312033	+	0.753315i	−0.687596	+	0.726093i	$0.741334\pi$
$198$	1.49540	−	0.619413i	0.106273	−	0.0440198i
$199$	−9.10677	+	21.9857i	−0.645562	+	1.55852i	0.173510	+	0.984832i	$0.444489\pi$
$199$	−9.10677	+	21.9857i	−0.645562	+	1.55852i	−0.819071	+	0.573692i	$0.805511\pi$
$200$		−	14.3235i		−	1.01283i
$201$	31.6732	+	13.1195i	2.23406	+	0.925377i
$202$	2.41041	−	2.41041i	0.169596	−	0.169596i
$203$	4.59575			0.322558
$204$	−13.0133	−	7.20183i	−0.911113	−	0.504229i
$205$	11.7664			0.821803
$206$	−8.86334	+	8.86334i	−0.617538	+	0.617538i
$207$	17.3867	+	7.20179i	1.20846	+	0.500559i
$208$		−	6.54122i		−	0.453552i
$209$	0.245038	−	0.591575i	0.0169497	−	0.0409201i
$210$	21.1937	−	8.77871i	1.46250	−	0.605789i
$211$	−0.597832	−	1.44329i	−0.0411565	−	0.0993605i	0.901965	−	0.431810i	$-0.142125\pi$
$211$	−0.597832	−	1.44329i	−0.0411565	−	0.0993605i	−0.943121	+	0.332450i	$0.892125\pi$
$212$	1.07264	+	1.07264i	0.0736690	+	0.0736690i
$213$	17.4780	+	17.4780i	1.19757	+	1.19757i
$214$	−5.08286	−	12.2711i	−0.347457	−	0.838835i
$215$	3.04222	−	1.26013i	0.207478	−	0.0859401i
$216$	0.707470	−	1.70798i	0.0481373	−	0.116214i
$217$			6.99181i			0.474635i
$218$	−8.35977	−	3.46273i	−0.566195	−	0.234526i
$219$	15.5943	−	15.5943i	1.05376	−	1.05376i
$220$	−4.30655			−0.290348
$221$	−20.3694	−	2.30678i	−1.37020	−	0.155171i
$222$	1.83820			0.123372
$223$	−19.2534	+	19.2534i	−1.28930	+	1.28930i	−0.354090	+	0.935211i	$0.615209\pi$
$223$	−19.2534	+	19.2534i	−1.28930	+	1.28930i	−0.935211	+	0.354090i	$0.884791\pi$
$224$	22.5205	+	9.32829i	1.50471	+	0.623273i
$225$		−	15.6807i		−	1.04538i
$226$	0.214141	−	0.516982i	0.0142444	−	0.0343891i
$227$	2.08090	−	0.861939i	0.138114	−	0.0572089i	−0.312556	−	0.949899i	$-0.601185\pi$
$227$	2.08090	−	0.861939i	0.138114	−	0.0572089i	0.450670	+	0.892691i	$0.351185\pi$
$228$	1.02265	+	2.46888i	0.0677264	+	0.163506i
$229$	3.77452	+	3.77452i	0.249427	+	0.249427i	0.820736	−	0.571308i	$-0.193564\pi$
$229$	3.77452	+	3.77452i	0.249427	+	0.249427i	−0.571308	+	0.820736i	$0.693564\pi$
$230$	11.3934	+	11.3934i	0.751261	+	0.751261i
$231$	−3.30234	−	7.97255i	−0.217278	−	0.524555i
$232$	−2.48545	+	1.02951i	−0.163178	+	0.0675905i
$233$	−5.63286	+	13.5989i	−0.369021	+	0.890896i	0.624890	+	0.780713i	$0.285144\pi$
$233$	−5.63286	+	13.5989i	−0.369021	+	0.890896i	−0.993911	+	0.110183i	$0.964856\pi$
$234$			9.31051i			0.608647i
$235$	14.4861	+	6.00032i	0.944966	+	0.391418i
$236$	−8.05073	+	8.05073i	−0.524058	+	0.524058i
$237$	14.0270			0.911152
$238$	5.83397	−	10.5417i	0.378160	−	0.683314i
$239$	−11.2997			−0.730916			−0.365458	−	0.930828i	$-0.619088\pi$
$239$	−11.2997			−0.730916			−0.365458	+	0.930828i	$0.619088\pi$
$240$	7.30317	−	7.30317i	0.471418	−	0.471418i
$241$	12.9254	+	5.35387i	0.832598	+	0.344873i	0.757931	−	0.652335i	$-0.226211\pi$
$241$	12.9254	+	5.35387i	0.832598	+	0.344873i	0.0746672	+	0.997209i	$0.476211\pi$
$242$			7.15434i			0.459898i
$243$	8.11972	−	19.6027i	0.520880	−	1.25752i
$244$	−1.68437	+	0.697690i	−0.107831	+	0.0446650i
$245$	−13.2781	−	32.0561i	−0.848305	−	2.04799i
$246$	−4.20331	−	4.20331i	−0.267993	−	0.267993i
$247$	2.60443	+	2.60443i	0.165716	+	0.165716i
$248$	−1.56626	−	3.78128i	−0.0994574	−	0.240111i
$249$	21.9731	−	9.10154i	1.39249	−	0.576787i
$250$	0.741271	−	1.78959i	0.0468821	−	0.113183i
$251$		−	22.2513i		−	1.40449i	−0.711936	−	0.702245i	$-0.752181\pi$
$251$		−	22.2513i		−	1.40449i	0.711936	−	0.702245i	$-0.247819\pi$
$252$	15.7105	+	6.50748i	0.989666	+	0.409933i
$253$	4.28594	−	4.28594i	0.269455	−	0.269455i
$254$	−7.01858			−0.440385
$255$	−20.1667	−	25.3176i	−1.26289	−	1.58545i
$256$	−10.2877			−0.642983
$257$	0.547062	−	0.547062i	0.0341248	−	0.0341248i	−0.689838	−	0.723963i	$-0.742318\pi$
$257$	0.547062	−	0.547062i	0.0341248	−	0.0341248i	0.723963	+	0.689838i	$0.242318\pi$
$258$	−1.53692	−	0.636615i	−0.0956847	−	0.0396339i
$259$		−	4.62736i		−	0.287530i
$260$	9.47987	−	22.8864i	0.587917	−	1.41936i
$261$	−2.72096	+	1.12706i	−0.168423	+	0.0697631i
$262$	−0.446077	−	1.07692i	−0.0275587	−	0.0665326i
$263$	−11.5750	−	11.5750i	−0.713748	−	0.713748i	0.253570	−	0.967317i	$-0.418395\pi$
$263$	−11.5750	−	11.5750i	−0.713748	−	0.713748i	−0.967317	+	0.253570i	$0.918395\pi$
$264$	3.57191	+	3.57191i	0.219836	+	0.219836i
$265$	1.26333	+	3.04995i	0.0776058	+	0.187357i
$266$	−1.99996	+	0.828412i	−0.122626	+	0.0507932i
$267$	−5.78442	+	13.9648i	−0.354001	+	0.854634i
$268$			21.7585i			1.32911i
$269$	−11.2996	−	4.68047i	−0.688952	−	0.285373i	0.0106117	−	0.999944i	$-0.496622\pi$
$269$	−11.2996	−	4.68047i	−0.688952	−	0.285373i	−0.699563	+	0.714571i	$0.746622\pi$
$270$	1.22529	−	1.22529i	0.0745688	−	0.0745688i
$271$	−28.9720			−1.75993			−0.879963	−	0.475043i	$-0.842433\pi$
$271$	−28.9720			−1.75993			−0.879963	+	0.475043i	$0.842433\pi$
$272$	0.610408	−	5.39007i	0.0370114	−	0.326821i
$273$	49.6381			3.00423
$274$	9.92581	−	9.92581i	0.599640	−	0.599640i
$275$	−4.66597	−	1.93271i	−0.281369	−	0.116547i
$276$			25.2960i			1.52264i
$277$	−12.0297	+	29.0423i	−0.722795	+	1.74498i	−0.0575667	+	0.998342i	$0.518334\pi$
$277$	−12.0297	+	29.0423i	−0.722795	+	1.74498i	−0.665228	+	0.746640i	$0.731666\pi$
$278$	8.82600	−	3.65585i	0.529349	−	0.219263i
$279$	−1.71467	−	4.13957i	−0.102654	−	0.247830i
$280$	23.9029	+	23.9029i	1.42847	+	1.42847i
$281$	−7.93647	−	7.93647i	−0.473450	−	0.473450i	0.429579	−	0.903029i	$-0.358662\pi$
$281$	−7.93647	−	7.93647i	−0.473450	−	0.473450i	−0.903029	+	0.429579i	$0.858662\pi$
$282$	−3.03135	−	7.31833i	−0.180514	−	0.435800i
$283$	2.88169	−	1.19364i	0.171299	−	0.0709542i	−0.295386	−	0.955378i	$-0.595448\pi$
$283$	2.88169	−	1.19364i	0.171299	−	0.0709542i	0.466685	+	0.884424i	$0.345448\pi$
$284$	−6.00340	+	14.4935i	−0.356236	+	0.860030i
$285$			5.81560i			0.344487i
$286$	2.77044	+	1.14755i	0.163820	+	0.0678563i
$287$	−10.5812	+	10.5812i	−0.624586	+	0.624586i
$288$	−15.6211			−0.920485
$289$	−16.5695	−	3.80164i	−0.974675	−	0.223626i
$290$	−2.52160			−0.148073
$291$	−3.99944	+	3.99944i	−0.234451	+	0.234451i
$292$	12.9314	+	5.35638i	0.756756	+	0.313458i
$293$		−	18.7640i		−	1.09620i	−0.836412	−	0.548101i	$-0.815351\pi$
$293$		−	18.7640i		−	1.09620i	0.836412	−	0.548101i	$-0.184649\pi$
$294$	−6.70806	+	16.1947i	−0.391222	+	0.944494i
$295$	−22.8915	+	9.48198i	−1.33280	+	0.552062i
$296$	1.03659	+	2.50255i	0.0602506	+	0.145458i
$297$	−0.460925	−	0.460925i	−0.0267456	−	0.0267456i
$298$	6.13532	+	6.13532i	0.355409	+	0.355409i
$299$	13.3424	+	32.2114i	0.771610	+	1.86283i
$300$	19.4730	−	8.06599i	1.12427	−	0.465690i
$301$	−1.60257	+	3.86896i	−0.0923709	+	0.223003i
$302$		−	5.58176i		−	0.321194i
$303$	10.7600	+	4.45694i	0.618147	+	0.256045i
$304$	−0.689171	+	0.689171i	−0.0395267	+	0.0395267i
$305$	−3.96764			−0.227186
$306$	−0.868831	+	7.67201i	−0.0496678	+	0.438579i
$307$	−28.2956			−1.61492			−0.807458	−	0.589926i	$-0.799157\pi$
$307$	−28.2956			−1.61492			−0.807458	+	0.589926i	$0.799157\pi$
$308$	3.87274	−	3.87274i	0.220670	−	0.220670i
$309$	−39.5658	−	16.3887i	−2.25082	−	0.932319i
$310$		−	3.83627i		−	0.217885i
$311$	8.44991	−	20.3999i	0.479150	−	1.15677i	−0.480858	−	0.876799i	$-0.659675\pi$
$311$	8.44991	−	20.3999i	0.479150	−	1.15677i	0.960008	−	0.279972i	$-0.0903253\pi$
$312$	−26.8450	+	11.1196i	−1.51980	+	0.629522i
$313$	3.13665	+	7.57255i	0.177294	+	0.428026i	0.987397	−	0.158262i	$-0.0505890\pi$
$313$	3.13665	+	7.57255i	0.177294	+	0.428026i	−0.810103	+	0.586287i	$0.800589\pi$
$314$	6.00801	+	6.00801i	0.339052	+	0.339052i
$315$	26.1678	+	26.1678i	1.47439	+	1.47439i
$316$	3.40688	+	8.22493i	0.191652	+	0.462688i
$317$	10.7210	−	4.44079i	0.602152	−	0.249420i	−0.0607166	−	0.998155i	$-0.519339\pi$
$317$	10.7210	−	4.44079i	0.602152	−	0.249420i	0.662869	+	0.748735i	$0.269339\pi$
$318$	0.638233	−	1.54083i	0.0357903	−	0.0864054i
$319$			0.948563i			0.0531094i
$320$	−4.35162	−	1.80250i	−0.243263	−	0.100763i
$321$	32.0882	−	32.0882i	1.79099	−	1.79099i
$322$	−20.4915			−1.14195
$323$	1.90305	+	2.38913i	0.105889	+	0.132935i
$324$	14.9023			0.827908
$325$	20.5421	−	20.5421i	1.13947	−	1.13947i
$326$	14.4595	+	5.98931i	0.800836	+	0.331717i
$327$		−	30.9151i		−	1.70961i
$328$	3.35214	−	8.09278i	0.185091	−	0.446849i
$329$	−18.4227	+	7.63094i	−1.01568	+	0.420707i
$330$	1.81193	+	4.37438i	0.0997434	+	0.240802i
$331$	−3.94127	−	3.94127i	−0.216632	−	0.216632i	0.590446	−	0.807077i	$-0.298952\pi$
$331$	−3.94127	−	3.94127i	−0.216632	−	0.216632i	−0.807077	+	0.590446i	$0.798952\pi$
$332$	10.6736	+	10.6736i	0.585791	+	0.585791i
$333$	1.13481	+	2.73968i	0.0621873	+	0.150133i
$334$	−12.3972	+	5.13507i	−0.678342	+	0.280979i
$335$	−18.1208	+	43.7475i	−0.990045	+	2.39018i
$336$			13.1350i			0.716573i
$337$	−5.62406	−	2.32956i	−0.306362	−	0.126899i	0.224206	−	0.974542i	$-0.428021\pi$
$337$	−5.62406	−	2.32956i	−0.306362	−	0.126899i	−0.530568	+	0.847643i	$0.678021\pi$
$338$	−5.78263	+	5.78263i	−0.314534	+	0.314534i
$339$	1.91184			0.103837
$340$	9.94726	−	17.9741i	0.539466	−	0.974785i
$341$	−1.44311			−0.0781489
$342$	0.980939	−	0.980939i	0.0530431	−	0.0530431i
$343$	13.6848	+	5.66844i	0.738911	+	0.306067i
$344$		−	2.45139i		−	0.132170i
$345$	−21.0669	+	50.8601i	−1.13421	+	2.73821i
$346$	−14.2880	+	5.91830i	−0.768130	+	0.318170i
$347$	−9.59765	−	23.1708i	−0.515229	−	1.24387i	−0.940805	−	0.338949i	$-0.889928\pi$
$347$	−9.59765	−	23.1708i	−0.515229	−	1.24387i	0.425576	−	0.904923i	$-0.360072\pi$
$348$	−2.79926	−	2.79926i	−0.150056	−	0.150056i
$349$	−18.3680	−	18.3680i	−0.983218	−	0.983218i	0.0166439	−	0.999861i	$-0.494702\pi$
$349$	−18.3680	−	18.3680i	−0.983218	−	0.983218i	−0.999861	+	0.0166439i	$0.994702\pi$
$350$	6.53399	+	15.7745i	0.349257	+	0.843180i
$351$	3.46412	−	1.43489i	0.184901	−	0.0765886i
$352$	−1.92536	+	4.64824i	−0.102622	+	0.247752i
$353$		−	1.30967i		−	0.0697069i	−0.999392	−	0.0348535i	$-0.988904\pi$
$353$		−	1.30967i		−	0.0697069i	0.999392	−	0.0348535i	$-0.0110965\pi$
$354$	11.5648	+	4.79028i	0.614660	+	0.254601i
$355$	−24.1408	+	24.1408i	−1.28126	+	1.28126i
$356$	−9.59338			−0.508448
$357$	40.9025	+	4.63209i	2.16479	+	0.245156i
$358$	−16.5193			−0.873073
$359$	−16.4436	+	16.4436i	−0.867859	+	0.867859i	−0.992235	−	0.124376i	$-0.960307\pi$
$359$	−16.4436	+	16.4436i	−0.867859	+	0.867859i	0.124376	+	0.992235i	$0.460307\pi$
$360$	−20.0139	−	8.29003i	−1.05483	−	0.436923i
$361$			18.4512i			0.971116i
$362$	−2.97762	+	7.18861i	−0.156500	+	0.377825i
$363$	−22.5827	+	9.35407i	−1.18529	+	0.490962i
$364$	12.0561	+	29.1059i	0.631910	+	1.52557i
$365$	21.5390	+	21.5390i	1.12740	+	1.12740i
$366$	1.41736	+	1.41736i	0.0740864	+	0.0740864i
$367$	0.966966	+	2.33446i	0.0504752	+	0.121858i	0.947106	−	0.320921i	$-0.103993\pi$
$367$	0.966966	+	2.33446i	0.0504752	+	0.121858i	−0.896631	+	0.442779i	$0.853993\pi$
$368$	−8.52362	+	3.53060i	−0.444324	+	0.184045i
$369$	3.66976	−	8.85960i	0.191040	−	0.461212i
$370$			2.53894i			0.131993i
$371$	−3.87879	−	1.60665i	−0.201377	−	0.0834130i
$372$	4.25869	−	4.25869i	0.220803	−	0.220803i
$373$	2.69393			0.139487			0.0697433	−	0.997565i	$-0.477782\pi$
$373$	2.69393			0.139487			0.0697433	+	0.997565i	$0.477782\pi$
$374$	2.17580	+	1.20413i	0.112508	+	0.0622642i
$375$	6.61803			0.341754
$376$	8.25386	−	8.25386i	0.425660	−	0.425660i
$377$	−5.04098	−	2.08804i	−0.259623	−	0.107540i
$378$			2.20373i			0.113347i
$379$	12.6177	−	30.4617i	0.648126	−	1.56471i	−0.167334	−	0.985900i	$-0.553516\pi$
$379$	12.6177	−	30.4617i	0.648126	−	1.56471i	0.815460	−	0.578814i	$-0.196484\pi$
$380$	−3.41006	+	1.41249i	−0.174932	+	0.0724593i
$381$	−9.17657	−	22.1542i	−0.470130	−	1.13499i
$382$	−10.1361	−	10.1361i	−0.518606	−	0.518606i
$383$	18.8344	+	18.8344i	0.962395	+	0.962395i	0.999318	−	0.0369228i	$-0.0117556\pi$
$383$	18.8344	+	18.8344i	0.962395	+	0.962395i	−0.0369228	+	0.999318i	$0.511756\pi$
$384$	−9.71044	−	23.4431i	−0.495534	−	1.19632i
$385$	11.0118	−	4.56124i	0.561213	−	0.232462i
$386$	5.46874	−	13.2027i	0.278351	−	0.672000i
$387$		−	2.68367i		−	0.136419i
$388$	−3.31650	−	1.37374i	−0.168370	−	0.0697411i
$389$	7.54968	−	7.54968i	0.382784	−	0.382784i	−0.489320	−	0.872104i	$-0.662755\pi$
$389$	7.54968	−	7.54968i	0.382784	−	0.382784i	0.872104	+	0.489320i	$0.162755\pi$
$390$	−27.2354			−1.37912
$391$	7.98846	+	27.7877i	0.403994	+	1.40529i
$392$	−25.8305			−1.30464
$393$	2.81609	−	2.81609i	0.142053	−	0.142053i
$394$	7.37790	+	3.05603i	0.371693	+	0.153960i
$395$			19.3743i			0.974827i
$396$	−1.34315	+	3.24264i	−0.0674957	+	0.162949i
$397$	14.2267	−	5.89287i	0.714016	−	0.295755i	0.00405044	−	0.999992i	$-0.498711\pi$
$397$	14.2267	−	5.89287i	0.714016	−	0.295755i	0.709965	+	0.704237i	$0.248711\pi$
$398$	6.35458	+	15.3413i	0.318526	+	0.768991i
$399$	−5.22978	−	5.22978i	−0.261816	−	0.261816i
$400$	5.43575	+	5.43575i	0.271787	+	0.271787i
$401$	14.0886	+	34.0129i	0.703551	+	1.69852i	0.715519	+	0.698594i	$0.246190\pi$
$401$	14.0886	+	34.0129i	0.703551	+	1.69852i	−0.0119678	+	0.999928i	$0.503810\pi$
$402$	22.1012	−	9.15460i	1.10231	−	0.456590i
$403$	3.17667	−	7.66917i	0.158241	−	0.382028i
$404$			7.39178i			0.367755i
$405$	29.9626	+	12.4109i	1.48885	+	0.616703i
$406$	2.26759	−	2.26759i	0.112538	−	0.112538i
$407$	0.955089			0.0473420
$408$	−23.1584	+	6.65760i	−1.14651	+	0.329600i
$409$	7.07974			0.350071			0.175035	−	0.984562i	$-0.443996\pi$
$409$	7.07974			0.350071			0.175035	+	0.984562i	$0.443996\pi$
$410$	5.80567	−	5.80567i	0.286722	−	0.286722i
$411$	44.3086	+	18.3532i	2.18558	+	0.905298i
$412$		−	27.1804i		−	1.33908i
$413$	12.0588	−	29.1124i	0.593373	−	1.43253i
$414$	12.1322	−	5.02532i	0.596264	−	0.246981i
$415$	12.5712	+	30.3495i	0.617095	+	1.48980i
$416$	−20.4640	−	20.4640i	−1.00333	−	1.00333i
$417$	23.0794	+	23.0794i	1.13021	+	1.13021i
$418$	−0.170984	−	0.412793i	−0.00836312	−	0.0201904i
$419$	−6.77868	+	2.80782i	−0.331160	+	0.137171i	−0.542067	−	0.840335i	$-0.682358\pi$
$419$	−6.77868	+	2.80782i	−0.331160	+	0.137171i	0.210907	+	0.977506i	$0.432358\pi$
$420$	−19.0359	+	45.9568i	−0.928857	+	2.24246i
$421$		−	5.54226i		−	0.270113i	−0.990838	−	0.135057i	$-0.956878\pi$
$421$		−	5.54226i		−	0.270113i	0.990838	−	0.135057i	$-0.0431217\pi$
$422$	−1.00711	−	0.417159i	−0.0490254	−	0.0203070i
$423$	9.03594	−	9.03594i	0.439343	−	0.439343i
$424$	2.45762			0.119353
$425$	18.8439	−	15.0101i	0.914065	−	0.728095i
$426$	17.2476			0.835649
$427$	3.56797	−	3.56797i	0.172666	−	0.172666i
$428$	26.6089	+	11.0218i	1.28619	+	0.532757i
$429$			10.2453i			0.494648i
$430$	0.879301	−	2.12282i	0.0424037	−	0.102372i
$431$	19.9233	−	8.25251i	0.959673	−	0.397509i	0.152815	−	0.988255i	$-0.451166\pi$
$431$	19.9233	−	8.25251i	0.959673	−	0.397509i	0.806858	+	0.590746i	$0.201166\pi$
$432$	0.379693	+	0.916660i	0.0182680	+	0.0441028i
$433$	9.39245	+	9.39245i	0.451373	+	0.451373i	0.895810	−	0.444437i	$-0.146596\pi$
$433$	9.39245	+	9.39245i	0.451373	+	0.451373i	−0.444437	+	0.895810i	$0.646596\pi$
$434$	3.44983	+	3.44983i	0.165597	+	0.165597i
$435$	−3.29691	−	7.95944i	−0.158075	−	0.381626i
$436$	18.1275	−	7.50865i	0.868149	−	0.359599i
$437$	1.98800	−	4.79946i	0.0950991	−	0.229589i
$438$		−	15.3887i		−	0.735302i
$439$	−5.13843	−	2.12841i	−0.245244	−	0.101583i	0.256676	−	0.966498i	$-0.417373\pi$
$439$	−5.13843	−	2.12841i	−0.245244	−	0.101583i	−0.501920	+	0.864914i	$0.667373\pi$
$440$	−4.93357	+	4.93357i	−0.235199	+	0.235199i
$441$	−28.2780			−1.34657
$442$	−11.1887	+	8.91230i	−0.532191	+	0.423915i
$443$	16.5604			0.786810			0.393405	−	0.919365i	$-0.371297\pi$
$443$	16.5604			0.786810			0.393405	+	0.919365i	$0.371297\pi$
$444$	−2.81851	+	2.81851i	−0.133761	+	0.133761i
$445$	−19.2884	−	7.98952i	−0.914358	−	0.378740i
$446$			18.9996i			0.899658i
$447$	−11.3444	+	27.3879i	−0.536574	+	1.29540i
$448$	5.53420	−	2.29234i	0.261466	−	0.108303i
$449$	−7.10203	−	17.1458i	−0.335166	−	0.809162i	−0.998166	−	0.0605421i	$-0.980717\pi$
$449$	−7.10203	−	17.1458i	−0.335166	−	0.809162i	0.663000	−	0.748619i	$-0.269283\pi$
$450$	−7.73703	−	7.73703i	−0.364727	−	0.364727i
$451$	−2.18395	−	2.18395i	−0.102838	−	0.102838i
$452$	0.464347	+	1.12103i	0.0218410	+	0.0527289i
$453$	17.6189	−	7.29798i	0.827808	−	0.342889i
$454$	0.601449	−	1.45203i	0.0282274	−	0.0681470i
$455$			68.5608i			3.21418i
$456$	3.99989	+	1.65681i	0.187312	+	0.0775871i
$457$	−3.92622	+	3.92622i	−0.183661	+	0.183661i	−0.792949	−	0.609288i	$-0.791455\pi$
$457$	−3.92622	+	3.92622i	−0.183661	+	0.183661i	0.609288	+	0.792949i	$0.291455\pi$
$458$	3.72477			0.174047
$459$	2.98839	−	0.859107i	0.139486	−	0.0400997i
$460$	−34.9392			−1.62905
$461$	5.00301	−	5.00301i	0.233013	−	0.233013i	−0.580936	−	0.813949i	$-0.697313\pi$
$461$	5.00301	−	5.00301i	0.233013	−	0.233013i	0.813949	+	0.580936i	$0.197313\pi$
$462$	−5.56314	−	2.30433i	−0.258821	−	0.107207i
$463$			11.5955i			0.538888i	0.963016	+	0.269444i	$0.0868398\pi$
$463$			11.5955i			0.538888i	−0.963016	+	0.269444i	$0.913160\pi$
$464$	0.552527	−	1.33392i	0.0256504	−	0.0619256i
$465$	12.1092	−	5.01580i	0.561551	−	0.232602i
$466$	3.93054	+	9.48916i	0.182079	+	0.439577i
$467$	4.73985	+	4.73985i	0.219334	+	0.219334i	0.808218	−	0.588884i	$-0.200432\pi$
$467$	4.73985	+	4.73985i	0.219334	+	0.219334i	−0.588884	+	0.808218i	$0.700432\pi$
$468$	−14.2758	−	14.2758i	−0.659901	−	0.659901i
$469$	−23.0452	−	55.6361i	−1.06413	−	2.56904i
$470$	10.1082	−	4.18694i	0.466256	−	0.193129i
$471$	−11.1091	+	26.8196i	−0.511878	+	1.23578i
$472$			18.4458i			0.849036i
$473$	−0.798554	−	0.330772i	−0.0367176	−	0.0152089i
$474$	6.92107	−	6.92107i	0.317895	−	0.317895i
$475$	−4.32855			−0.198608
$476$	7.21831	+	25.1088i	0.330851	+	1.15086i
$477$	2.69049			0.123189
$478$	−5.57538	+	5.57538i	−0.255012	+	0.255012i
$479$	22.9360	+	9.50042i	1.04797	+	0.434085i	0.839168	−	0.543872i	$-0.183042\pi$
$479$	22.9360	+	9.50042i	1.04797	+	0.434085i	0.208806	+	0.977957i	$0.433042\pi$
$480$		−	45.6955i		−	2.08570i
$481$	−2.10241	+	5.07566i	−0.0958614	+	0.231430i
$482$	9.01917	−	3.73586i	0.410812	−	0.170164i
$483$	−26.7920	−	64.6815i	−1.21908	−	2.94311i
$484$	−10.9698	−	10.9698i	−0.498626	−	0.498626i
$485$	−5.52408	−	5.52408i	−0.250835	−	0.250835i
$486$	−5.66583	−	13.6785i	−0.257007	−	0.620471i
$487$	−8.88432	+	3.68001i	−0.402587	+	0.166757i	−0.574783	−	0.818306i	$-0.694914\pi$
$487$	−8.88432	+	3.68001i	−0.402587	+	0.166757i	0.172196	+	0.985063i	$0.444914\pi$
$488$	−1.13034	+	2.72888i	−0.0511681	+	0.123531i
$489$			53.4723i			2.41810i
$490$	−22.3683	−	9.26527i	−1.01050	−	0.418562i
$491$	−11.5347	+	11.5347i	−0.520554	+	0.520554i	−0.917739	−	0.397185i	$-0.869987\pi$
$491$	−11.5347	+	11.5347i	−0.520554	+	0.520554i	0.397185	+	0.917739i	$0.369987\pi$
$492$	12.8899			0.581122
$493$	−3.95899	−	2.19099i	−0.178304	−	0.0986771i
$494$	2.57010			0.115634
$495$	−5.40105	+	5.40105i	−0.242759	+	0.242759i
$496$	2.02938	+	0.840596i	0.0911218	+	0.0377439i
$497$		−	43.4181i		−	1.94757i
$498$	6.35094	−	15.3325i	0.284592	−	0.687067i
$499$	11.6573	−	4.82861i	0.521852	−	0.216158i	−0.106178	−	0.994347i	$-0.533861\pi$
$499$	11.6573	−	4.82861i	0.521852	−	0.216158i	0.628030	+	0.778189i	$0.283861\pi$
$500$	1.60739	+	3.88057i	0.0718845	+	0.173544i
$501$	−32.4178	−	32.4178i	−1.44832	−	1.44832i
$502$	−10.9790	−	10.9790i	−0.490017	−	0.490017i
$503$	−0.171212	−	0.413344i	−0.00763399	−	0.0184301i	0.920017	−	0.391879i	$-0.128175\pi$
$503$	−0.171212	−	0.413344i	−0.00763399	−	0.0184301i	−0.927651	+	0.373449i	$0.878175\pi$
$504$	25.4528	−	10.5429i	1.13376	−	0.469618i
$505$	−6.15599	+	14.8619i	−0.273938	+	0.661345i
$506$		−	4.22945i		−	0.188022i
$507$	−25.8135	−	10.6923i	−1.14642	−	0.474863i
$508$	10.7616	−	10.7616i	0.477469	−	0.477469i
$509$	−35.7666			−1.58533			−0.792663	−	0.609660i	$-0.791306\pi$
$509$	−35.7666			−1.58533			−0.792663	+	0.609660i	$0.791306\pi$
$510$	−22.4424	−	2.54153i	−0.993767	−	0.112541i
$511$	−38.7387			−1.71370
$512$	9.97613	−	9.97613i	0.440887	−	0.440887i
$513$	−0.516151	−	0.213797i	−0.0227886	−	0.00943936i
$514$		−	0.539852i		−	0.0238118i
$515$	22.6363	−	54.6488i	0.997473	−	2.40811i
$516$	3.33269	−	1.38045i	0.146714	−	0.0607708i
$517$	−1.57503	−	3.80245i	−0.0692697	−	0.167232i
$518$	−2.28319	−	2.28319i	−0.100317	−	0.100317i
$519$	−37.3623	−	37.3623i	−1.64002	−	1.64002i
$520$	−15.3585	−	37.0787i	−0.673515	−	1.62601i
$521$	−3.54688	+	1.46917i	−0.155392	+	0.0643653i	−0.459024	−	0.888424i	$-0.651801\pi$
$521$	−3.54688	+	1.46917i	−0.155392	+	0.0643653i	0.303632	+	0.952789i	$0.401801\pi$
$522$	−0.786446	+	1.89865i	−0.0344218	+	0.0831016i
$523$		−	13.3596i		−	0.584176i	−0.956391	−	0.292088i	$-0.905650\pi$
$523$		−	13.3596i		−	0.584176i	0.956391	−	0.292088i	$-0.0943500\pi$
$524$	2.33522	+	0.967281i	0.102015	+	0.0422559i
$525$	−41.2492	+	41.2492i	−1.80026	+	1.80026i
$526$	−11.4225			−0.498044
$527$	3.33329	−	6.02307i	0.145201	−	0.262369i
$528$	−2.71107			−0.117984
$529$	18.5085	−	18.5085i	0.804717	−	0.804717i
$530$	2.12821	+	0.881535i	0.0924437	+	0.0382914i
$531$			20.1936i			0.876327i
$532$	1.79634	−	4.33676i	0.0778814	−	0.188022i
$533$	16.4137	−	6.79878i	0.710957	−	0.294488i
$534$	4.03629	+	9.74447i	0.174668	+	0.421685i
$535$	44.3206	+	44.3206i	1.91615	+	1.91615i
$536$	24.9264	+	24.9264i	1.07666	+	1.07666i
$537$	−21.5985	−	52.1433i	−0.932043	−	2.25015i
$538$	−7.88475	+	3.26597i	−0.339936	+	0.140806i
$539$	−3.48537	+	8.41443i	−0.150126	+	0.362435i
$540$			3.75748i			0.161696i
$541$	18.3423	+	7.59763i	0.788597	+	0.326647i	0.740379	−	0.672189i	$-0.234646\pi$
$541$	18.3423	+	7.59763i	0.788597	+	0.326647i	0.0482175	+	0.998837i	$0.484646\pi$
$542$	−14.2951	+	14.2951i	−0.614026	+	0.614026i
$543$	−26.5840			−1.14083
$544$	−14.9530	−	18.7723i	−0.641105	−	0.804856i
$545$	42.7004			1.82908
$546$	24.4919	−	24.4919i	1.04816	−	1.04816i
$547$	−8.97745	−	3.71858i	−0.383848	−	0.158995i	0.182411	−	0.983222i	$-0.441610\pi$
$547$	−8.97745	−	3.71858i	−0.383848	−	0.158995i	−0.566259	+	0.824227i	$0.691610\pi$
$548$			30.4386i			1.30027i
$549$	−1.23744	+	2.98745i	−0.0528128	+	0.127501i
$550$	−3.25585	+	1.34862i	−0.138830	+	0.0575053i
$551$	0.311116	+	0.751100i	0.0132540	+	0.0319980i
$552$	28.9790	+	28.9790i	1.23343	+	1.23343i
$553$	−17.4227	−	17.4227i	−0.740887	−	0.740887i
$554$	8.39417	+	20.2653i	0.356634	+	0.860991i
$555$	−8.01419	+	3.31959i	−0.340184	+	0.140909i
$556$	−7.92741	+	19.1385i	−0.336197	+	0.811652i
$557$		−	4.15170i		−	0.175913i	−0.996124	−	0.0879566i	$-0.971966\pi$
$557$		−	4.15170i		−	0.175913i	0.996124	−	0.0879566i	$-0.0280337\pi$
$558$	−2.88854	−	1.19647i	−0.122282	−	0.0506507i
$559$	3.51566	−	3.51566i	0.148697	−	0.148697i
$560$	−18.1422			−0.766649
$561$	−0.956064	+	8.44230i	−0.0403651	+	0.356434i
$562$	−7.83187			−0.330367
$563$	−2.29138	+	2.29138i	−0.0965700	+	0.0965700i	−0.753741	−	0.657171i	$-0.771753\pi$
$563$	−2.29138	+	2.29138i	−0.0965700	+	0.0965700i	0.657171	+	0.753741i	$0.271753\pi$
$564$	15.8692	+	6.57324i	0.668214	+	0.276783i
$565$			2.64066i			0.111093i
$566$	0.832903	−	2.01081i	0.0350095	−	0.0845205i
$567$	−38.1051	+	15.7836i	−1.60026	+	0.662851i
$568$	9.72622	+	23.4812i	0.408103	+	0.985248i
$569$	26.5233	+	26.5233i	1.11191	+	1.11191i	0.992892	+	0.119022i	$0.0379759\pi$
$569$	26.5233	+	26.5233i	1.11191	+	1.11191i	0.119022	+	0.992892i	$0.462024\pi$
$570$	2.86948	+	2.86948i	0.120189	+	0.120189i
$571$	6.02699	+	14.5504i	0.252222	+	0.608917i	0.998383	−	0.0568482i	$-0.0181051\pi$
$571$	6.02699	+	14.5504i	0.252222	+	0.608917i	−0.746161	+	0.665766i	$0.768105\pi$
$572$	−6.00748	+	2.48838i	−0.251185	+	0.104044i
$573$	18.7420	−	45.2472i	0.782958	−	1.89023i
$574$			10.4417i			0.435828i
$575$	−37.8551	−	15.6801i	−1.57867	−	0.653906i
$576$	−2.71441	+	2.71441i	−0.113100	+	0.113100i
$577$	−13.2294			−0.550748			−0.275374	−	0.961337i	$-0.588802\pi$
$577$	−13.2294			−0.550748			−0.275374	+	0.961337i	$0.588802\pi$
$578$	−10.0513	+	6.29978i	−0.418079	+	0.262036i
$579$	48.8246			2.02908
$580$	3.86637	−	3.86637i	0.160542	−	0.160542i
$581$	−38.5971	−	15.9875i	−1.60128	−	0.663271i
$582$			3.94672i			0.163597i
$583$	0.331612	−	0.800583i	0.0137340	−	0.0331568i
$584$	20.9505	−	8.67797i	0.866937	−	0.359097i
$585$	−16.8138	−	40.5921i	−0.695165	−	1.67828i
$586$	−9.25833	−	9.25833i	−0.382458	−	0.382458i
$587$	17.8849	+	17.8849i	0.738188	+	0.738188i	0.972227	−	0.234039i	$-0.0751943\pi$
$587$	17.8849	+	17.8849i	0.738188	+	0.738188i	−0.234039	+	0.972227i	$0.575194\pi$
$588$	−14.5459	−	35.1169i	−0.599862	−	1.44820i
$589$	−1.14270	+	0.473321i	−0.0470841	+	0.0195029i
$590$	−6.61640	+	15.9734i	−0.272393	+	0.657615i
$591$			27.2841i			1.12232i
$592$	−1.34310	−	0.556328i	−0.0552009	−	0.0228650i
$593$	−7.46590	+	7.46590i	−0.306588	+	0.306588i	−0.843584	−	0.536997i	$-0.819559\pi$
$593$	−7.46590	+	7.46590i	−0.306588	+	0.306588i	0.536997	+	0.843584i	$0.319559\pi$
$594$	−0.454850			−0.0186627
$595$	−6.39790	+	56.4951i	−0.262288	+	2.31608i
$596$	−18.8146			−0.770676
$597$	−40.1166	+	40.1166i	−1.64186	+	1.64186i
$598$	22.4767	+	9.31014i	0.919139	+	0.380720i
$599$			4.54677i			0.185776i	0.995677	+	0.0928880i	$0.0296098\pi$
$599$			4.54677i			0.185776i	−0.995677	+	0.0928880i	$0.970390\pi$
$600$	13.0678	−	31.5486i	0.533493	−	1.28797i
$601$	−2.14879	+	0.890056i	−0.0876508	+	0.0363061i	−0.426078	−	0.904686i	$-0.640105\pi$
$601$	−2.14879	+	0.890056i	−0.0876508	+	0.0363061i	0.338427	+	0.940993i	$0.390105\pi$
$602$	1.11826	+	2.69971i	0.0455767	+	0.110032i
$603$	27.2883	+	27.2883i	1.11127	+	1.11127i
$604$	8.55854	+	8.55854i	0.348242	+	0.348242i
$605$	−12.9200	−	31.1916i	−0.525272	−	1.26812i
$606$	7.50820	−	3.11000i	0.305000	−	0.126335i
$607$	0.331060	−	0.799249i	0.0134373	−	0.0324405i	−0.917018	−	0.398845i	$-0.869411\pi$
$607$	0.331060	−	0.799249i	0.0134373	−	0.0324405i	0.930456	+	0.366404i	$0.119411\pi$
$608$			4.31210i			0.174879i
$609$	10.1225	+	4.19286i	0.410183	+	0.169903i
$610$	−1.95767	+	1.95767i	−0.0792638	+	0.0792638i
$611$	23.6745			0.957769
$612$	−10.4313	−	13.0957i	−0.421662	−	0.529362i
$613$	0.635418			0.0256643			0.0128322	−	0.999918i	$-0.495915\pi$
$613$	0.635418			0.0256643			0.0128322	+	0.999918i	$0.495915\pi$
$614$	−13.9613	+	13.9613i	−0.563433	+	0.563433i
$615$	25.9164	+	10.7349i	1.04505	+	0.432874i
$616$		−	8.87320i		−	0.357511i
$617$	−0.591191	+	1.42726i	−0.0238005	+	0.0574594i	−0.935333	−	0.353769i	$-0.884900\pi$
$617$	−0.591191	+	1.42726i	−0.0238005	+	0.0574594i	0.911532	+	0.411228i	$0.134900\pi$
$618$	−27.6085	+	11.4358i	−1.11058	+	0.460015i
$619$	−11.2387	−	27.1327i	−0.451723	−	1.09056i	−0.971667	−	0.236356i	$-0.924047\pi$
$619$	−11.2387	−	27.1327i	−0.451723	−	1.09056i	0.519943	−	0.854201i	$-0.325953\pi$
$620$	5.88216	+	5.88216i	0.236233	+	0.236233i
$621$	−3.73950	−	3.73950i	−0.150061	−	0.150061i
$622$	−5.89623	−	14.2348i	−0.236417	−	0.570762i
$623$	24.5301	−	10.1607i	0.982779	−	0.407080i
$624$	5.96778	−	14.4075i	0.238902	−	0.576761i
$625$		−	20.0742i		−	0.802968i
$626$	5.28402	+	2.18871i	0.211192	+	0.0874786i
$627$	1.07943	−	1.07943i	0.0431082	−	0.0431082i
$628$	−18.4242			−0.735206
$629$	−2.20606	+	3.98623i	−0.0879614	+	0.158941i
$630$	25.8229			1.02881
$631$	2.30075	−	2.30075i	0.0915915	−	0.0915915i	−0.659827	−	0.751418i	$-0.729370\pi$
$631$	2.30075	−	2.30075i	0.0915915	−	0.0915915i	0.751418	+	0.659827i	$0.229370\pi$
$632$	13.3254	+	5.51954i	0.530054	+	0.219556i
$633$		−	3.72438i		−	0.148031i
$634$	3.09873	−	7.48099i	0.123066	−	0.297108i
$635$	30.5997	−	12.6748i	1.21431	−	0.502984i
$636$	1.38395	+	3.34116i	0.0548774	+	0.132486i
$637$	−37.0448	−	37.0448i	−1.46777	−	1.46777i
$638$	0.468031	+	0.468031i	0.0185295	+	0.0185295i
$639$	10.6478	+	25.7061i	0.421221	+	1.01692i
$640$	32.3799	−	13.4122i	1.27993	−	0.530163i
$641$	−3.86829	+	9.33888i	−0.152788	+	0.368864i	−0.981678	−	0.190549i	$-0.938973\pi$
$641$	−3.86829	+	9.33888i	−0.152788	+	0.368864i	0.828889	+	0.559413i	$0.188973\pi$
$642$		−	31.6652i		−	1.24973i
$643$	−17.2467	−	7.14382i	−0.680144	−	0.281725i	0.0157431	−	0.999876i	$-0.494989\pi$
$643$	−17.2467	−	7.14382i	−0.680144	−	0.281725i	−0.695887	+	0.718151i	$0.744989\pi$
$644$	31.4197	−	31.4197i	1.23811	−	1.23811i
$645$	7.85036			0.309108
$646$	2.11780	+	0.239835i	0.0833238	+	0.00943616i
$647$	−2.66177			−0.104645			−0.0523225	−	0.998630i	$-0.516662\pi$
$647$	−2.66177			−0.104645			−0.0523225	+	0.998630i	$0.516662\pi$
$648$	17.0721	−	17.0721i	0.670655	−	0.670655i
$649$	6.00881	+	2.48893i	0.235867	+	0.0976991i
$650$		−	20.2713i		−	0.795107i
$651$	−6.37887	+	15.4000i	−0.250008	+	0.603572i
$652$	−31.3542	+	12.9873i	−1.22793	+	0.508623i
$653$	7.53266	+	18.1855i	0.294776	+	0.711652i	0.999996	+	0.00266397i	$0.000847968\pi$
$653$	7.53266	+	18.1855i	0.294776	+	0.711652i	−0.705221	+	0.708988i	$0.749152\pi$
$654$	−15.2538	−	15.2538i	−0.596471	−	0.596471i
$655$	3.88962	+	3.88962i	0.151980	+	0.151980i
$656$	1.79906	+	4.34332i	0.0702416	+	0.169578i
$657$	22.9356	−	9.50024i	0.894803	−	0.370640i
$658$	−5.32477	+	12.8551i	−0.207581	+	0.501145i
$659$		−	30.6816i		−	1.19519i	−0.801800	−	0.597593i	$-0.796124\pi$
$659$		−	30.6816i		−	1.19519i	0.801800	−	0.597593i	$-0.203876\pi$
$660$	−9.48549	−	3.92902i	−0.369222	−	0.152937i
$661$	21.9308	−	21.9308i	0.853008	−	0.853008i	−0.137494	−	0.990503i	$-0.543905\pi$
$661$	21.9308	−	21.9308i	0.853008	−	0.853008i	0.990503	+	0.137494i	$0.0439049\pi$
$662$	−3.88932			−0.151163
$663$	−42.7606	−	23.6646i	−1.66068	−	0.919056i
$664$	24.4553			0.949051
$665$	7.22344	−	7.22344i	0.280113	−	0.280113i
$666$	1.91171	+	0.791856i	0.0740772	+	0.0306838i
$667$			7.69572i			0.297980i
$668$	11.1350	−	26.8822i	0.430825	−	1.04010i
$669$	−59.9724	+	24.8414i	−2.31867	+	0.960424i
$670$	12.6445	+	30.5264i	0.488498	+	1.17934i
$671$	0.736429	+	0.736429i	0.0284295	+	0.0284295i
$672$	41.0924	+	41.0924i	1.58518	+	1.58518i
$673$	−15.1828	−	36.6546i	−0.585256	−	1.41293i	−0.887992	−	0.459858i	$-0.847900\pi$
$673$	−15.1828	−	36.6546i	−0.585256	−	1.41293i	0.302737	−	0.953074i	$-0.402100\pi$
$674$	−3.92439	+	1.62554i	−0.151162	+	0.0626133i
$675$	−1.68629	+	4.07108i	−0.0649055	+	0.156696i
$676$		−	17.7331i		−	0.682041i
$677$	44.8187	+	18.5645i	1.72252	+	0.713492i	0.999749	+	0.0224055i	$0.00713248\pi$
$677$	44.8187	+	18.5645i	1.72252	+	0.713492i	0.722772	+	0.691086i	$0.242868\pi$
$678$	0.943320	−	0.943320i	0.0362280	−	0.0362280i
$679$	9.93524			0.381279
$680$	−9.19557	−	31.9867i	−0.352634	−	1.22663i
$681$	5.36971			0.205768
$682$	−0.712045	+	0.712045i	−0.0272656	+	0.0272656i
$683$	−0.319156	−	0.132199i	−0.0122122	−	0.00505845i	0.376569	−	0.926389i	$-0.377104\pi$
$683$	−0.319156	−	0.132199i	−0.0122122	−	0.00505845i	−0.388781	+	0.921330i	$0.627104\pi$
$684$			3.00815i			0.115020i
$685$	−25.3497	+	61.1996i	−0.968563	+	2.33832i
$686$	9.54909	−	3.95536i	0.364586	−	0.151016i
$687$	4.87002	+	11.7573i	0.185803	+	0.448568i
$688$	0.930297	+	0.930297i	0.0354673	+	0.0354673i
$689$	3.52459	+	3.52459i	0.134276	+	0.134276i
$690$	14.7002	+	35.4895i	0.559628	+	1.35106i
$691$	22.6800	−	9.39437i	0.862789	−	0.357379i	0.0929913	−	0.995667i	$-0.470357\pi$
$691$	22.6800	−	9.39437i	0.862789	−	0.357379i	0.769798	+	0.638288i	$0.220357\pi$
$692$	12.8333	−	30.9824i	0.487851	−	1.17778i
$693$		−	9.71397i		−	0.369003i
$694$	−16.1683	−	6.69711i	−0.613739	−	0.254219i
$695$	−31.8776	+	31.8776i	−1.20919	+	1.20919i
$696$	−6.41364			−0.243108
$697$	14.1596	−	4.07062i	0.536333	−	0.154186i
$698$	−18.1259			−0.686076
$699$	−24.8136	+	24.8136i	−0.938535	+	0.938535i
$700$	−34.2056	−	14.1684i	−1.29285	−	0.535516i
$701$			2.57726i			0.0973418i	0.998815	+	0.0486709i	$0.0154985\pi$
$701$			2.57726i			0.0973418i	−0.998815	+	0.0486709i	$0.984501\pi$
$702$	1.00125	−	2.41722i	0.0377896	−	0.0912321i
$703$	0.756268	−	0.313256i	0.0285232	−	0.0118147i
$704$	0.473140	+	1.14226i	0.0178321	+	0.0430506i
$705$	26.4323	+	26.4323i	0.995496	+	0.995496i
$706$	−0.646206	−	0.646206i	−0.0243203	−	0.0243203i
$707$	−7.82891	−	18.9007i	−0.294437	−	0.710833i
$708$	−25.0772	+	10.3873i	−0.942461	+	0.390380i
$709$	16.0701	−	38.7967i	0.603527	−	1.45704i	−0.266401	−	0.963862i	$-0.585834\pi$
$709$	16.0701	−	38.7967i	0.603527	−	1.45704i	0.869927	−	0.493180i	$-0.164166\pi$
$710$			23.8226i			0.894047i
$711$	14.5880	+	6.04254i	0.547092	+	0.226613i
$712$	−10.9901	+	10.9901i	−0.411873	+	0.411873i
$713$	−11.7080			−0.438468
$714$	22.4672	−	17.8962i	0.840815	−	0.669748i
$715$	−14.1510			−0.529216
$716$	25.3291	−	25.3291i	0.946593	−	0.946593i
$717$	−24.8884	−	10.3091i	−0.929473	−	0.385000i
$718$			16.2268i			0.605580i
$719$	8.87506	−	21.4263i	0.330984	−	0.799066i	−0.667531	−	0.744582i	$-0.732649\pi$
$719$	8.87506	−	21.4263i	0.330984	−	0.799066i	0.998515	−	0.0544838i	$-0.0173513\pi$
$720$	10.7413	−	4.44919i	0.400304	−	0.165811i
$721$	28.7878	+	69.4998i	1.07211	+	2.58831i
$722$	9.10401	+	9.10401i	0.338816	+	0.338816i
$723$	23.5846	+	23.5846i	0.877119	+	0.877119i
$724$	−6.45672	−	15.5879i	−0.239962	−	0.579320i
$725$	5.92421	−	2.45389i	0.220020	−	0.0911351i
$726$	−6.52715	+	15.7579i	−0.242245	+	0.584832i
$727$		−	42.6594i		−	1.58215i	−0.611721	−	0.791074i	$-0.709522\pi$
$727$		−	42.6594i		−	1.58215i	0.611721	−	0.791074i	$-0.290478\pi$
$728$	47.1551	+	19.5323i	1.74768	+	0.723914i
$729$	14.8758	−	14.8758i	0.550954	−	0.550954i
$730$	21.2551			0.786688
$731$	3.22503	−	2.56889i	0.119282	−	0.0950137i
$732$	−4.34647			−0.160650
$733$	−24.6931	+	24.6931i	−0.912061	+	0.912061i	−0.996434	−	0.0843732i	$-0.973111\pi$
$733$	−24.6931	+	24.6931i	−0.912061	+	0.912061i	0.0843732	+	0.996434i	$0.473111\pi$
$734$	1.62896	+	0.674736i	0.0601259	+	0.0249050i
$735$		−	82.7199i		−	3.05117i
$736$	−15.6205	+	37.7113i	−0.575780	+	1.39006i
$737$	11.4833	−	4.75654i	0.422993	−	0.175209i
$738$	−2.56071	−	6.18211i	−0.0942612	−	0.227567i
$739$	5.28062	+	5.28062i	0.194251	+	0.194251i	0.797530	−	0.603279i	$-0.206140\pi$
$739$	5.28062	+	5.28062i	0.194251	+	0.194251i	−0.603279	+	0.797530i	$0.706140\pi$
$740$	−3.89297	−	3.89297i	−0.143108	−	0.143108i
$741$	3.36032	+	8.11254i	0.123445	+	0.298022i
$742$	−2.70657	+	1.12110i	−0.0993612	+	0.0411568i
$743$	20.2083	−	48.7872i	0.741372	−	1.78983i	0.141163	−	0.989986i	$-0.454916\pi$
$743$	20.2083	−	48.7872i	0.741372	−	1.78983i	0.600208	−	0.799844i	$-0.295084\pi$
$744$		−	9.75748i		−	0.357727i
$745$	−37.8286	−	15.6691i	−1.38593	−	0.574072i
$746$	1.32921	−	1.32921i	0.0486660	−	0.0486660i
$747$	26.7726			0.979557
$748$	−5.18246	+	1.48986i	−0.189490	+	0.0544747i
$749$	−79.7121			−2.91261
$750$	3.26540	−	3.26540i	0.119236	−	0.119236i
$751$	−21.4631	−	8.89031i	−0.783200	−	0.324412i	−0.0449937	−	0.998987i	$-0.514327\pi$
$751$	−21.4631	−	8.89031i	−0.783200	−	0.324412i	−0.738206	+	0.674575i	$0.764327\pi$
$752$			6.26464i			0.228448i
$753$	20.3006	−	49.0100i	0.739796	−	1.78602i
$754$	−3.51753	+	1.45701i	−0.128101	+	0.0530611i
$755$	10.0801	+	24.3354i	0.366851	+	0.885657i
$756$	−3.37898	−	3.37898i	−0.122892	−	0.122892i
$757$	−3.46078	−	3.46078i	−0.125784	−	0.125784i	0.641412	−	0.767196i	$-0.278349\pi$
$757$	−3.46078	−	3.46078i	−0.125784	−	0.125784i	−0.767196	+	0.641412i	$0.778349\pi$
$758$	−8.80444	−	21.2558i	−0.319792	−	0.772045i
$759$	13.3503	−	5.52987i	0.484585	−	0.200722i
$760$	−2.28840	+	5.52470i	−0.0830091	+	0.200402i
$761$		−	3.85748i		−	0.139833i	−0.997553	−	0.0699167i	$-0.977727\pi$
$761$		−	3.85748i		−	0.139833i	0.997553	−	0.0699167i	$-0.0222733\pi$
$762$	−15.4589	−	6.40329i	−0.560017	−	0.231967i
$763$	−38.3990	+	38.3990i	−1.39014	+	1.39014i
$764$	31.0833			1.12455
$765$	−10.0669	−	35.0175i	−0.363969	−	1.26606i
$766$	18.5862			0.671547
$767$	−26.4540	+	26.4540i	−0.955199	+	0.955199i
$768$	−22.6594	−	9.38584i	−0.817652	−	0.338682i
$769$		−	8.73276i		−	0.314912i	−0.987526	−	0.157456i	$-0.949671\pi$
$769$		−	8.73276i		−	0.314912i	0.987526	−	0.157456i	$-0.0503292\pi$
$770$	3.18277	−	7.68389i	0.114699	−	0.276908i
$771$	1.70405	−	0.705839i	0.0613697	−	0.0254202i
$772$	11.8585	+	28.6290i	0.426797	+	1.03038i
$773$	1.43380	+	1.43380i	0.0515701	+	0.0515701i	0.732422	−	0.680851i	$-0.238390\pi$
$773$	1.43380	+	1.43380i	0.0515701	+	0.0515701i	−0.680851	+	0.732422i	$0.738390\pi$
$774$	−1.32415	−	1.32415i	−0.0475955	−	0.0475955i
$775$	3.73326	+	9.01289i	0.134103	+	0.323752i
$776$	−5.37313	+	2.22562i	−0.192884	+	0.0798952i
$777$	4.22170	−	10.1921i	0.151453	−	0.365639i
$778$		−	7.45017i		−	0.267102i
$779$	−2.44563	−	1.01301i	−0.0876237	−	0.0362949i
$780$	41.7602	−	41.7602i	1.49525	−	1.49525i
$781$	8.96150			0.320668
$782$	17.6523	+	9.76916i	0.631246	+	0.349345i
$783$	0.827625			0.0295769
$784$	9.80262	−	9.80262i	0.350094	−	0.350094i
$785$	−37.0436	−	15.3440i	−1.32214	−	0.547650i
$786$		−	2.77897i		−	0.0991227i
$787$	−15.3327	+	37.0163i	−0.546550	+	1.31949i	0.373479	+	0.927639i	$0.378165\pi$
$787$	−15.3327	+	37.0163i	−0.546550	+	1.31949i	−0.920029	+	0.391850i	$0.871835\pi$
$788$	−15.9984	+	6.62674i	−0.569918	+	0.236068i
$789$	−14.9345	−	36.0551i	−0.531683	−	1.28360i
$790$	9.55947	+	9.55947i	0.340111	+	0.340111i
$791$	−2.37466	−	2.37466i	−0.0844331	−	0.0844331i
$792$	2.17606	+	5.25346i	0.0773228	+	0.186674i
$793$	−5.53470	+	2.29255i	−0.196543	+	0.0814108i
$794$	4.11197	−	9.92718i	0.145928	−	0.352302i
$795$			7.87031i			0.279131i
$796$	−33.2664	−	13.7794i	−1.17910	−	0.488398i
$797$	−25.8022	+	25.8022i	−0.913960	+	0.913960i	−0.996581	−	0.0826208i	$-0.973671\pi$
$797$	−25.8022	+	25.8022i	−0.913960	+	0.913960i	0.0826208	+	0.996581i	$0.473671\pi$
$798$	−5.16085			−0.182692
$799$	19.5082	+	2.20924i	0.690150	+	0.0781574i
$800$	34.0112			1.20248
$801$	−12.0315	+	12.0315i	−0.425112	+	0.425112i
$802$	23.7337	+	9.83084i	0.838067	+	0.347139i
$803$		−	7.99567i		−	0.282161i
$804$	−19.8510	+	47.9245i	−0.700091	+	1.69017i
$805$	89.3390	−	37.0054i	3.14879	−	1.30427i
$806$	−2.21664	−	5.35144i	−0.0780778	−	0.188497i
$807$	−20.6181	−	20.6181i	−0.725792	−	0.725792i
$808$	8.46800	+	8.46800i	0.297903	+	0.297903i
$809$	−2.84872	−	6.87742i	−0.100156	−	0.241797i	0.865857	−	0.500291i	$-0.166774\pi$
$809$	−2.84872	−	6.87742i	−0.100156	−	0.241797i	−0.966013	+	0.258494i	$0.916774\pi$
$810$	20.9075	−	8.66017i	0.734615	−	0.304287i
$811$	18.6212	−	44.9556i	0.653880	−	1.57861i	−0.153222	−	0.988192i	$-0.548965\pi$
$811$	18.6212	−	44.9556i	0.653880	−	1.57861i	0.807101	−	0.590413i	$-0.201035\pi$
$812$			6.95379i			0.244030i
$813$	−63.8129	−	26.4322i	−2.23802	−	0.927017i
$814$	0.471250	−	0.471250i	0.0165173	−	0.0165173i
$815$	−73.8567			−2.58709
$816$	6.26201	−	11.3151i	0.219214	−	0.396108i
$817$	−0.740807			−0.0259176
$818$	3.49321	−	3.49321i	0.122137	−	0.122137i
$819$	51.6232	+	21.3830i	1.80386	+	0.747183i
$820$			17.8037i			0.621733i
$821$	5.02362	−	12.1281i	0.175325	−	0.423273i	−0.811650	−	0.584144i	$-0.801430\pi$
$821$	5.02362	−	12.1281i	0.175325	−	0.423273i	0.986975	+	0.160871i	$0.0514303\pi$
$822$	30.9180	−	12.8066i	1.07839	−	0.446683i
$823$	18.8412	+	45.4866i	0.656762	+	1.58556i	0.802776	+	0.596281i	$0.203356\pi$
$823$	18.8412	+	45.4866i	0.656762	+	1.58556i	−0.146013	+	0.989283i	$0.546644\pi$
$824$	−31.1378	−	31.1378i	−1.08473	−	1.08473i
$825$	−8.51385	−	8.51385i	−0.296414	−	0.296414i
$826$	−8.41445	−	20.3143i	−0.292776	−	0.706824i
$827$	−9.20242	+	3.81177i	−0.319999	+	0.132548i	−0.536901	−	0.843645i	$-0.680405\pi$
$827$	−9.20242	+	3.81177i	−0.319999	+	0.132548i	0.216901	+	0.976194i	$0.430405\pi$
$828$	−10.8970	+	26.3076i	−0.378696	+	0.914254i
$829$		−	16.4898i		−	0.572714i	−0.958123	−	0.286357i	$-0.907556\pi$
$829$		−	16.4898i		−	0.572714i	0.958123	−	0.286357i	$-0.0924443\pi$
$830$	21.1775	+	8.77200i	0.735081	+	0.304481i
$831$	−52.9925	+	52.9925i	−1.83829	+	1.83829i
$832$	−7.11185			−0.246559
$833$	−27.0686	−	33.9824i	−0.937871	−	1.17742i
$834$	22.7753			0.788642
$835$	44.7759	−	44.7759i	1.54953	−	1.54953i
$836$	0.895108	+	0.370766i	0.0309580	+	0.0128232i
$837$			1.25912i			0.0435216i
$838$	−1.95926	+	4.73007i	−0.0676816	+	0.163398i
$839$	−31.8931	+	13.2105i	−1.10107	+	0.456079i	−0.857854	−	0.513893i	$-0.828203\pi$
$839$	−31.8931	+	13.2105i	−1.10107	+	0.456079i	−0.243217	+	0.969972i	$0.578203\pi$
$840$	30.8404	+	74.4554i	1.06410	+	2.56895i
$841$	19.6545	+	19.6545i	0.677741	+	0.677741i
$842$	−2.73461	−	2.73461i	−0.0942408	−	0.0942408i
$843$	−10.2399	−	24.7214i	−0.352682	−	0.851449i
$844$	2.18384	−	0.904576i	0.0751709	−	0.0311368i
$845$	14.7684	−	35.6540i	0.508048	−	1.22654i
$846$		−	8.91685i		−	0.306568i
$847$	39.6680	+	16.4310i	1.36301	+	0.564577i
$848$	−0.932661	+	0.932661i	−0.0320277	+	0.0320277i
$849$	7.43612			0.255207
$850$	1.89166	−	16.7039i	0.0648836	−	0.572939i
$851$	7.74866			0.265621
$852$	−26.4458	+	26.4458i	−0.906019	+	0.906019i
$853$	21.5239	+	8.91551i	0.736966	+	0.305261i	0.719411	−	0.694585i	$-0.244412\pi$
$853$	21.5239	+	8.91551i	0.736966	+	0.305261i	0.0175549	+	0.999846i	$0.494412\pi$
$854$		−	3.52094i		−	0.120484i
$855$	−2.50524	+	6.04818i	−0.0856773	+	0.206843i
$856$	43.1095	−	17.8565i	1.47345	−	0.610324i
$857$	1.58089	+	3.81661i	0.0540023	+	0.130373i	0.948578	−	0.316543i	$-0.102522\pi$
$857$	1.58089	+	3.81661i	0.0540023	+	0.130373i	−0.894576	+	0.446916i	$0.852522\pi$
$858$	5.05514	+	5.05514i	0.172580	+	0.172580i
$859$	−3.61915	−	3.61915i	−0.123484	−	0.123484i	0.642664	−	0.766148i	$-0.277829\pi$
$859$	−3.61915	−	3.61915i	−0.123484	−	0.123484i	−0.766148	+	0.642664i	$0.777829\pi$
$860$	1.90669	+	4.60316i	0.0650177	+	0.156967i
$861$	−32.9593	+	13.6522i	−1.12325	+	0.465265i
$862$	5.75849	−	13.9022i	0.196135	−	0.473512i
$863$			37.9201i			1.29081i	0.763839	+	0.645407i	$0.223312\pi$
$863$			37.9201i			1.29081i	−0.763839	+	0.645407i	$0.776688\pi$
$864$	4.05560	+	1.67989i	0.137974	+	0.0571509i
$865$	51.6054	−	51.6054i	1.75463	−	1.75463i
$866$	9.26866			0.314962
$867$	−33.0271	−	23.4903i	−1.12166	−	0.797772i
$868$	−10.5793			−0.359084
$869$	3.59604	−	3.59604i	0.121987	−	0.121987i
$870$	−5.55399	−	2.30054i	−0.188298	−	0.0779955i
$871$			71.4964i			2.42256i
$872$	12.1649	−	29.3687i	0.411955	−	0.994549i
$873$	−5.88225	+	2.43651i	−0.199084	+	0.0824634i
$874$	−1.38720	−	3.34900i	−0.0469228	−	0.113282i
$875$	−8.22012	−	8.22012i	−0.277891	−	0.277891i
$876$	23.5956	+	23.5956i	0.797222	+	0.797222i
$877$	−1.05535	−	2.54785i	−0.0356367	−	0.0860347i	0.905059	−	0.425286i	$-0.139826\pi$
$877$	−1.05535	−	2.54785i	−0.0356367	−	0.0860347i	−0.940696	+	0.339251i	$0.889826\pi$
$878$	−3.58553	+	1.48518i	−0.121006	+	0.0501222i
$879$	17.1190	−	41.3290i	0.577410	−	1.39399i
$880$		−	3.74456i		−	0.126229i
$881$	−3.74617	−	1.55171i	−0.126212	−	0.0522786i	0.318684	−	0.947861i	$-0.396759\pi$
$881$	−3.74617	−	1.55171i	−0.126212	−	0.0522786i	−0.444896	+	0.895582i	$0.646759\pi$
$882$	−13.9527	+	13.9527i	−0.469811	+	0.469811i
$883$	−27.7834			−0.934985			−0.467493	−	0.883997i	$-0.654843\pi$
$883$	−27.7834			−0.934985			−0.467493	+	0.883997i	$0.654843\pi$
$884$	3.49037	−	30.8209i	0.117394	−	1.03662i
$885$	−59.0710			−1.98565
$886$	8.17108	−	8.17108i	0.274513	−	0.274513i
$887$	29.9555	+	12.4080i	1.00581	+	0.416619i	0.823923	−	0.566701i	$-0.191781\pi$
$887$	29.9555	+	12.4080i	1.00581	+	0.416619i	0.181883	+	0.983320i	$0.441781\pi$
$888$			6.45776i			0.216708i
$889$	−16.1192	+	38.9153i	−0.540622	+	1.30518i
$890$	−13.4592	+	5.57498i	−0.451153	+	0.186874i
$891$	−3.25775	−	7.86490i	−0.109139	−	0.263484i
$892$	−29.1322	−	29.1322i	−0.975417	−	0.975417i
$893$	−2.49431	−	2.49431i	−0.0834688	−	0.0834688i
$894$	7.91601	+	19.1109i	0.264751	+	0.639165i
$895$	72.0211	−	29.8321i	2.40740	−	0.997178i
$896$	−17.0570	+	41.1793i	−0.569835	+	1.37570i
$897$			83.1205i			2.77531i
$898$	−11.9641	−	4.95571i	−0.399248	−	0.165374i
$899$	1.29561	−	1.29561i	0.0432109	−	0.0432109i
$900$	23.7264			0.790881
$901$	2.57541	+	3.23322i	0.0857995	+	0.107714i
$902$	−2.15517			−0.0717593
$903$	−7.05957	+	7.05957i	−0.234928	+	0.234928i
$904$	1.81621	+	0.752297i	0.0604061	+	0.0250210i
$905$		−	36.7182i		−	1.22056i
$906$	5.09244	−	12.2942i	0.169185	−	0.408448i
$907$	−16.9524	+	7.02190i	−0.562894	+	0.233158i	−0.645941	−	0.763387i	$-0.723535\pi$
$907$	−16.9524	+	7.02190i	−0.562894	+	0.233158i	0.0830470	+	0.996546i	$0.473535\pi$
$908$	1.30419	+	3.14860i	0.0432812	+	0.104490i
$909$	9.27037	+	9.27037i	0.307479	+	0.307479i
$910$	33.8286	+	33.8286i	1.12141	+	1.12141i
$911$	4.64499	+	11.2140i	0.153895	+	0.371537i	0.981958	−	0.189099i	$-0.0605568\pi$
$911$	4.64499	+	11.2140i	0.153895	+	0.371537i	−0.828063	+	0.560636i	$0.810557\pi$
$912$	−2.14670	+	0.889193i	−0.0710844	+	0.0294441i
$913$	3.29982	−	7.96646i	0.109208	−	0.263651i
$914$			3.87447i			0.128156i
$915$	−8.73900	−	3.61981i	−0.288903	−	0.119667i
$916$	−5.71120	+	5.71120i	−0.188703	+	0.188703i
$917$	−6.99562			−0.231016
$918$	1.05061	−	1.89839i	0.0346753	−	0.0626563i
$919$	−41.6449			−1.37374			−0.686869	−	0.726781i	$-0.741015\pi$
$919$	−41.6449			−1.37374			−0.686869	+	0.726781i	$0.741015\pi$
$920$	−40.0262	+	40.0262i	−1.31963	+	1.31963i
$921$	−62.3230	−	25.8150i	−2.05361	−	0.850635i
$922$		−	4.93707i		−	0.162594i
$923$	−19.7266	+	47.6243i	−0.649311	+	1.56757i
$924$	12.0632	−	4.99675i	0.396851	−	0.164381i
$925$	−2.47077	−	5.96496i	−0.0812384	−	0.196127i
$926$	5.72132	+	5.72132i	0.188014	+	0.188014i
$927$	−34.0882	−	34.0882i	−1.11960	−	1.11960i
$928$	−2.44456	−	5.90169i	−0.0802467	−	0.193733i
$929$	−26.4770	+	10.9671i	−0.868682	+	0.359820i	−0.772097	−	0.635505i	$-0.780792\pi$
$929$	−26.4770	+	10.9671i	−0.868682	+	0.359820i	−0.0965852	+	0.995325i	$0.530792\pi$
$930$	3.49996	−	8.44965i	0.114768	−	0.277075i
$931$			7.80595i			0.255830i
$932$	−20.5765	−	8.52305i	−0.674004	−	0.279182i
$933$	37.2230	−	37.2230i	1.21863	−	1.21863i
$934$	4.67738			0.153048
$935$	−11.6606	−	1.32053i	−0.381343	−	0.0431859i
$936$	−32.7087			−1.06912
$937$	−38.0586	+	38.0586i	−1.24332	+	1.24332i	−0.284705	+	0.958615i	$0.591896\pi$
$937$	−38.0586	+	38.0586i	−1.24332	+	1.24332i	−0.958615	+	0.284705i	$0.908104\pi$
$938$	−38.8221	−	16.0807i	−1.26759	−	0.525052i
$939$			19.5407i			0.637688i
$940$	−9.07905	+	21.9188i	−0.296126	+	0.714911i
$941$	39.4612	−	16.3454i	1.28640	−	0.532844i	0.368489	−	0.929632i	$-0.379875\pi$
$941$	39.4612	−	16.3454i	1.28640	−	0.532844i	0.917910	+	0.396788i	$0.129875\pi$
$942$	7.75175	+	18.7144i	0.252566	+	0.609747i
$943$	−17.7185	−	17.7185i	−0.576993	−	0.576993i
$944$	−7.00013	−	7.00013i	−0.227835	−	0.227835i
$945$	−3.97969	−	9.60783i	−0.129459	−	0.312543i
$946$	−0.557221	+	0.230808i	−0.0181168	+	0.00750423i
$947$	3.90520	−	9.42798i	0.126902	−	0.306368i	−0.847641	−	0.530571i	$-0.821978\pi$
$947$	3.90520	−	9.42798i	0.126902	−	0.306368i	0.974543	+	0.224202i	$0.0719777\pi$
$948$			21.2242i			0.689329i
$949$	42.4916	+	17.6006i	1.37934	+	0.571340i
$950$	−2.13575	+	2.13575i	−0.0692929	+	0.0692929i
$951$	27.6653			0.897108
$952$	37.0338	+	20.4953i	1.20027	+	0.664256i
$953$	32.9574			1.06759			0.533797	−	0.845613i	$-0.320765\pi$
$953$	32.9574			1.06759			0.533797	+	0.845613i	$0.320765\pi$
$954$	1.32751	−	1.32751i	0.0429798	−	0.0429798i
$955$	62.4960	+	25.8867i	2.02232	+	0.837673i
$956$		−	17.0975i		−	0.552972i
$957$	−0.865407	+	2.08928i	−0.0279746	+	0.0675368i
$958$	16.0045	−	6.62927i	0.517081	−	0.214182i
$959$	−32.2386	−	77.8310i	−1.04104	−	2.51329i
$960$	−7.94027	−	7.94027i	−0.256271	−	0.256271i
$961$	−19.9492	−	19.9492i	−0.643523	−	0.643523i
$962$	1.46703	+	3.54173i	0.0472990	+	0.114190i
$963$	47.1943	−	19.5485i	1.52082	−	0.629942i
$964$	−8.10091	+	19.5573i	−0.260913	+	0.629899i
$965$			67.4372i			2.17088i
$966$	−45.1339	−	18.6951i	−1.45216	−	0.601505i
$967$	11.7662	−	11.7662i	0.378374	−	0.378374i	−0.492141	−	0.870515i	$-0.663786\pi$
$967$	11.7662	−	11.7662i	0.378374	−	0.378374i	0.870515	+	0.492141i	$0.163786\pi$
$968$	−25.1339			−0.807833
$969$	2.01192	+	6.99844i	0.0646322	+	0.224822i
$970$	−5.45127			−0.175030
$971$	−32.6313	+	32.6313i	−1.04719	+	1.04719i	−0.0483571	+	0.998830i	$0.515399\pi$
$971$	−32.6313	+	32.6313i	−1.04719	+	1.04719i	−0.998830	+	0.0483571i	$0.984601\pi$
$972$	29.6608	+	12.2859i	0.951369	+	0.394070i
$973$		−	57.3330i		−	1.83801i
$974$	−2.56786	+	6.19937i	−0.0822796	+	0.198640i
$975$	63.9866	−	26.5041i	2.04921	−	0.848811i
$976$	−0.606643	−	1.46457i	−0.0194182	−	0.0468796i
$977$	27.2003	+	27.2003i	0.870214	+	0.870214i	0.992495	−	0.122282i	$-0.0390211\pi$
$977$	27.2003	+	27.2003i	0.870214	+	0.870214i	−0.122282	+	0.992495i	$0.539021\pi$
$978$	26.3838	+	26.3838i	0.843660	+	0.843660i
$979$	2.09717	+	5.06303i	0.0670260	+	0.161815i
$980$	48.5039	−	20.0910i	1.54940	−	0.641783i
$981$	13.3176	−	32.1515i	0.425197	−	1.02652i
$982$			11.3827i			0.363236i
$983$	45.0627	+	18.6656i	1.43728	+	0.595339i	0.959136	−	0.282945i	$-0.0913114\pi$
$983$	45.0627	+	18.6656i	1.43728	+	0.595339i	0.478139	+	0.878284i	$0.341311\pi$
$984$	14.7666	−	14.7666i	0.470743	−	0.470743i
$985$	−37.6851			−1.20075
$986$	−3.03446	+	0.872351i	−0.0966369	+	0.0277813i
$987$	−47.5393			−1.51319
$988$	−3.94074	+	3.94074i	−0.125372	+	0.125372i
$989$	−6.47869	−	2.68356i	−0.206010	−	0.0853323i
$990$			5.32986i			0.169394i
$991$	−12.9828	+	31.3432i	−0.412412	+	0.995651i	0.572076	+	0.820200i	$0.306138\pi$
$991$	−12.9828	+	31.3432i	−0.412412	+	0.995651i	−0.984488	+	0.175450i	$0.943862\pi$
$992$	8.97863	−	3.71907i	0.285072	−	0.118081i
$993$	−5.08516	−	12.2767i	−0.161373	−	0.389588i
$994$	−21.4229	−	21.4229i	−0.679493	−	0.679493i
$995$	−55.4096	−	55.4096i	−1.75660	−	1.75660i
$996$	13.7715	+	33.2473i	0.436366	+	1.05348i
$997$	−0.382275	+	0.158344i	−0.0121068	+	0.00501479i	−0.388729	−	0.921352i	$-0.627086\pi$
$997$	−0.382275	+	0.158344i	−0.0121068	+	0.00501479i	0.376622	+	0.926367i	$0.377086\pi$
$998$	3.36934	−	8.13431i	0.106655	−	0.257487i
$999$		−	0.833319i		−	0.0263650i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.m.c.689.18	yes	128
17.2	even	8	inner	731.2.m.c.87.18	✓	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.m.c.87.18	✓	128	17.2	even	8	inner
731.2.m.c.689.18	yes	128	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.m (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.493410 - 0.493410i) q^{2} +(2.20257 + 0.912334i) q^{3} +1.51309i q^{4} +(-1.26013 + 3.04222i) q^{5} +(1.53692 - 0.636615i) q^{6} +(-1.60257 - 3.86896i) q^{7} +(1.73339 + 1.73339i) q^{8} +(1.89764 + 1.89764i) q^{9} +O(q^{10})\)	\(q+(0.493410 - 0.493410i) q^{2} +(2.20257 + 0.912334i) q^{3} +1.51309i q^{4} +(-1.26013 + 3.04222i) q^{5} +(1.53692 - 0.636615i) q^{6} +(-1.60257 - 3.86896i) q^{7} +(1.73339 + 1.73339i) q^{8} +(1.89764 + 1.89764i) q^{9} +(0.879301 + 2.12282i) q^{10} +(0.798554 - 0.330772i) q^{11} +(-1.38045 + 3.33269i) q^{12} +4.97189i q^{13} +(-2.69971 - 1.11826i) q^{14} +(-5.55104 + 5.55104i) q^{15} -1.31564 q^{16} +(-0.463963 + 4.09692i) q^{17} +1.87263 q^{18} +(0.523830 - 0.523830i) q^{19} +(-4.60316 - 1.90669i) q^{20} -9.98374i q^{21} +(0.230808 - 0.557221i) q^{22} +(6.47869 - 2.68356i) q^{23} +(2.23649 + 5.39936i) q^{24} +(-4.13164 - 4.13164i) q^{25} +(2.45318 + 2.45318i) q^{26} +(-0.288600 - 0.696741i) q^{27} +(5.85410 - 2.42485i) q^{28} +(-0.419969 + 1.01389i) q^{29} +5.47788i q^{30} +(-1.54250 - 0.638926i) q^{31} +(-4.11594 + 4.11594i) q^{32} +2.06065 q^{33} +(1.79254 + 2.25038i) q^{34} +13.7897 q^{35} +(-2.87131 + 2.87131i) q^{36} +(1.02087 + 0.422858i) q^{37} -0.516926i q^{38} +(-4.53603 + 10.9509i) q^{39} +(-7.45767 + 3.08907i) q^{40} +(-1.36744 - 3.30130i) q^{41} +(-4.92607 - 4.92607i) q^{42} +(-0.707107 - 0.707107i) q^{43} +(0.500489 + 1.20829i) q^{44} +(-8.16431 + 3.38177i) q^{45} +(1.87255 - 4.52075i) q^{46} -4.76167i q^{47} +(-2.89779 - 1.20030i) q^{48} +(-7.45084 + 7.45084i) q^{49} -4.07718 q^{50} +(-4.75967 + 8.60046i) q^{51} -7.52294 q^{52} +(0.708903 - 0.708903i) q^{53} +(-0.486177 - 0.201381i) q^{54} +2.84619i q^{55} +(3.92854 - 9.48433i) q^{56} +(1.63168 - 0.675864i) q^{57} +(0.293049 + 0.707482i) q^{58} +(5.32071 + 5.32071i) q^{59} +(-8.39925 - 8.39925i) q^{60} +(0.461102 + 1.11320i) q^{61} +(-1.07634 + 0.445834i) q^{62} +(4.30078 - 10.3830i) q^{63} +1.43041i q^{64} +(-15.1256 - 6.26523i) q^{65} +(1.01674 - 1.01674i) q^{66} +14.3801 q^{67} +(-6.19902 - 0.702020i) q^{68} +16.7181 q^{69} +(6.80396 - 6.80396i) q^{70} +(9.57871 + 3.96763i) q^{71} +6.57872i q^{72} +(3.54002 - 8.54636i) q^{73} +(0.712349 - 0.295065i) q^{74} +(-5.33079 - 12.8697i) q^{75} +(0.792604 + 0.792604i) q^{76} +(-2.55949 - 2.55949i) q^{77} +(3.16518 + 7.64143i) q^{78} +(5.43583 - 2.25160i) q^{79} +(1.65787 - 4.00246i) q^{80} -9.84893i q^{81} +(-2.30360 - 0.954184i) q^{82} +(7.05417 - 7.05417i) q^{83} +15.1063 q^{84} +(-11.8791 - 6.57412i) q^{85} -0.697787 q^{86} +(-1.85002 + 1.85002i) q^{87} +(1.95757 + 0.810851i) q^{88} +6.34024i q^{89} +(-2.35975 + 5.69695i) q^{90} +(19.2361 - 7.96783i) q^{91} +(4.06048 + 9.80287i) q^{92} +(-2.81456 - 2.81456i) q^{93} +(-2.34946 - 2.34946i) q^{94} +(0.933512 + 2.25370i) q^{95} +(-12.8208 + 5.31053i) q^{96} +(-0.907902 + 2.19187i) q^{97} +7.35264i q^{98} +(2.14305 + 0.887682i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9}+O(q^{10}) \) 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9	\( 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9} - 8 q^{10} - 4 q^{11} + 12 q^{12} + 12 q^{14} - 12 q^{15} - 144 q^{16} - 12 q^{17} + 64 q^{18} - 28 q^{19} - 8 q^{20} - 12 q^{22} + 16 q^{23} - 16 q^{24} - 20 q^{25} + 16 q^{26} - 8 q^{27} + 20 q^{28} + 12 q^{31} - 4 q^{32} - 104 q^{33} + 20 q^{34} + 32 q^{35} - 96 q^{36} - 12 q^{37} + 8 q^{39} + 216 q^{40} + 24 q^{41} - 4 q^{42} + 24 q^{44} - 28 q^{45} - 48 q^{46} + 28 q^{48} - 80 q^{50} - 20 q^{51} + 56 q^{52} - 36 q^{53} - 12 q^{54} - 8 q^{56} + 72 q^{57} - 32 q^{58} + 48 q^{59} - 40 q^{60} - 76 q^{61} - 44 q^{62} + 36 q^{65} - 68 q^{66} - 48 q^{67} + 32 q^{68} + 216 q^{69} - 196 q^{70} + 4 q^{71} + 20 q^{73} + 88 q^{74} + 80 q^{75} + 72 q^{76} + 28 q^{77} - 120 q^{78} + 68 q^{79} - 68 q^{80} + 28 q^{82} - 36 q^{83} - 152 q^{84} + 28 q^{85} - 24 q^{86} - 56 q^{87} + 20 q^{88} - 112 q^{90} + 96 q^{91} - 28 q^{92} + 24 q^{93} - 36 q^{94} - 108 q^{95} + 272 q^{96} + 8 q^{97} - 20 q^{99}+O(q^{100}) \) 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9 - 8 * q^10 - 4 * q^11 + 12 * q^12 + 12 * q^14 - 12 * q^15 - 144 * q^16 - 12 * q^17 + 64 * q^18 - 28 * q^19 - 8 * q^20 - 12 * q^22 + 16 * q^23 - 16 * q^24 - 20 * q^25 + 16 * q^26 - 8 * q^27 + 20 * q^28 + 12 * q^31 - 4 * q^32 - 104 * q^33 + 20 * q^34 + 32 * q^35 - 96 * q^36 - 12 * q^37 + 8 * q^39 + 216 * q^40 + 24 * q^41 - 4 * q^42 + 24 * q^44 - 28 * q^45 - 48 * q^46 + 28 * q^48 - 80 * q^50 - 20 * q^51 + 56 * q^52 - 36 * q^53 - 12 * q^54 - 8 * q^56 + 72 * q^57 - 32 * q^58 + 48 * q^59 - 40 * q^60 - 76 * q^61 - 44 * q^62 + 36 * q^65 - 68 * q^66 - 48 * q^67 + 32 * q^68 + 216 * q^69 - 196 * q^70 + 4 * q^71 + 20 * q^73 + 88 * q^74 + 80 * q^75 + 72 * q^76 + 28 * q^77 - 120 * q^78 + 68 * q^79 - 68 * q^80 + 28 * q^82 - 36 * q^83 - 152 * q^84 + 28 * q^85 - 24 * q^86 - 56 * q^87 + 20 * q^88 - 112 * q^90 + 96 * q^91 - 28 * q^92 + 24 * q^93 - 36 * q^94 - 108 * q^95 + 272 * q^96 + 8 * q^97 - 20 * q^99

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