LMFDB - Embedded newform 546.2.by.a.397.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(19,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, 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("546.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.by (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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			397.2
Character	$\chi$	$=$	546.397
Dual form			546.2.by.a.535.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} -1.00000i q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.166844 - 0.622671i) q^{5} +(0.965926 + 0.258819i) q^{6} +(-2.38407 + 1.14726i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} -1.00000i q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.166844 - 0.622671i) q^{5} +(0.965926 + 0.258819i) q^{6} +(-2.38407 + 1.14726i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +0.644637 q^{10} +(0.137324 - 0.137324i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-2.76090 + 2.31893i) q^{13} +(-0.491121 - 2.59977i) q^{14} +(-0.622671 + 0.166844i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-2.33053 + 4.03659i) q^{17} +(0.258819 - 0.965926i) q^{18} +(0.494522 - 0.494522i) q^{19} +(-0.166844 + 0.622671i) q^{20} +(1.14726 + 2.38407i) q^{21} +(0.0971030 + 0.168187i) q^{22} +(-5.09246 + 2.94013i) q^{23} +(-0.707107 - 0.707107i) q^{24} +(3.97024 - 2.29222i) q^{25} +(-1.52534 - 3.26701i) q^{26} +1.00000i q^{27} +(2.63830 + 0.198484i) q^{28} +(-3.99977 + 6.92780i) q^{29} -0.644637i q^{30} +(-1.86727 - 0.500334i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-0.137324 - 0.137324i) q^{33} +(-3.29586 - 3.29586i) q^{34} +(1.11213 + 1.29308i) q^{35} +(0.866025 + 0.500000i) q^{36} +(-11.0903 - 2.97162i) q^{37} +(0.349680 + 0.605664i) q^{38} +(2.31893 + 2.76090i) q^{39} +(-0.558272 - 0.322318i) q^{40} +(3.14978 + 11.7551i) q^{41} +(-2.59977 + 0.491121i) q^{42} +(5.75363 - 3.32186i) q^{43} +(-0.187589 + 0.0502642i) q^{44} +(0.166844 + 0.622671i) q^{45} +(-1.52193 - 5.67990i) q^{46} +(-4.00985 + 1.07444i) q^{47} +(0.866025 - 0.500000i) q^{48} +(4.36761 - 5.47028i) q^{49} +(1.18654 + 4.42823i) q^{50} +(4.03659 + 2.33053i) q^{51} +(3.55047 - 0.627799i) q^{52} +(-6.01682 - 10.4214i) q^{53} +(-0.965926 - 0.258819i) q^{54} +(-0.108420 - 0.0625962i) q^{55} +(-0.874562 + 2.49703i) q^{56} +(-0.494522 - 0.494522i) q^{57} +(-5.65653 - 5.65653i) q^{58} +(-3.71896 + 0.996492i) q^{59} +(0.622671 + 0.166844i) q^{60} +4.08143i q^{61} +(0.966572 - 1.67415i) q^{62} +(2.38407 - 1.14726i) q^{63} -1.00000i q^{64} +(1.90457 + 1.33223i) q^{65} +(0.168187 - 0.0971030i) q^{66} +(-0.200320 - 0.200320i) q^{67} +(4.03659 - 2.33053i) q^{68} +(2.94013 + 5.09246i) q^{69} +(-1.53686 + 0.739564i) q^{70} +(2.34326 - 8.74517i) q^{71} +(-0.707107 + 0.707107i) q^{72} +(-0.228973 + 0.854539i) q^{73} +(5.74074 - 9.94325i) q^{74} +(-2.29222 - 3.97024i) q^{75} +(-0.675530 + 0.181008i) q^{76} +(-0.169845 + 0.484938i) q^{77} +(-3.26701 + 1.52534i) q^{78} +(6.95881 - 12.0530i) q^{79} +(0.455827 - 0.455827i) q^{80} +1.00000 q^{81} -12.1698 q^{82} +(-3.79021 + 3.79021i) q^{83} +(0.198484 - 2.63830i) q^{84} +(2.90231 + 0.777670i) q^{85} +(1.71952 + 6.41734i) q^{86} +(6.92780 + 3.99977i) q^{87} -0.194206i q^{88} +(-1.40377 + 5.23893i) q^{89} -0.644637 q^{90} +(3.92179 - 8.69595i) q^{91} +5.88027 q^{92} +(-0.500334 + 1.86727i) q^{93} -4.15130i q^{94} +(-0.390433 - 0.225417i) q^{95} +(0.258819 + 0.965926i) q^{96} +(-6.54551 - 1.75386i) q^{97} +(4.15347 + 5.63460i) q^{98} +(-0.137324 + 0.137324i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{7} - 32 q^{9}+O(q^{10}) $ 32 * q + 8 * q^7 - 32 * q^9	$ 32 q + 8 q^{7} - 32 q^{9} - 4 q^{11} - 16 q^{12} + 4 q^{14} + 16 q^{16} - 8 q^{17} - 12 q^{19} - 8 q^{21} - 4 q^{22} - 24 q^{23} - 24 q^{25} + 8 q^{26} - 4 q^{28} - 12 q^{29} - 28 q^{31} + 4 q^{33} - 8 q^{34} - 44 q^{35} - 36 q^{37} + 8 q^{38} - 20 q^{39} - 28 q^{41} + 12 q^{42} + 84 q^{43} + 8 q^{44} - 4 q^{46} + 16 q^{47} + 24 q^{49} - 16 q^{50} + 8 q^{52} - 4 q^{53} + 48 q^{55} + 12 q^{56} + 12 q^{57} + 24 q^{58} + 12 q^{59} - 40 q^{62} - 8 q^{63} - 4 q^{65} + 8 q^{67} - 8 q^{69} + 60 q^{70} + 20 q^{71} + 4 q^{73} + 20 q^{74} + 8 q^{75} + 36 q^{76} - 12 q^{77} - 20 q^{78} + 32 q^{81} - 48 q^{82} + 12 q^{83} - 16 q^{84} - 4 q^{85} + 52 q^{86} - 36 q^{87} - 36 q^{89} - 16 q^{92} + 4 q^{93} - 48 q^{95} + 76 q^{97} + 8 q^{98} + 4 q^{99}+O(q^{100}) $ 32 * q + 8 * q^7 - 32 * q^9 - 4 * q^11 - 16 * q^12 + 4 * q^14 + 16 * q^16 - 8 * q^17 - 12 * q^19 - 8 * q^21 - 4 * q^22 - 24 * q^23 - 24 * q^25 + 8 * q^26 - 4 * q^28 - 12 * q^29 - 28 * q^31 + 4 * q^33 - 8 * q^34 - 44 * q^35 - 36 * q^37 + 8 * q^38 - 20 * q^39 - 28 * q^41 + 12 * q^42 + 84 * q^43 + 8 * q^44 - 4 * q^46 + 16 * q^47 + 24 * q^49 - 16 * q^50 + 8 * q^52 - 4 * q^53 + 48 * q^55 + 12 * q^56 + 12 * q^57 + 24 * q^58 + 12 * q^59 - 40 * q^62 - 8 * q^63 - 4 * q^65 + 8 * q^67 - 8 * q^69 + 60 * q^70 + 20 * q^71 + 4 * q^73 + 20 * q^74 + 8 * q^75 + 36 * q^76 - 12 * q^77 - 20 * q^78 + 32 * q^81 - 48 * q^82 + 12 * q^83 - 16 * q^84 - 4 * q^85 + 52 * q^86 - 36 * q^87 - 36 * q^89 - 16 * q^92 + 4 * q^93 - 48 * q^95 + 76 * q^97 + 8 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{11}{12}\right)$

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 $

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	−0.166844	−	0.622671i	−0.0746150	−	0.278467i	0.918531	−	0.395350i	$-0.129377\pi$
$5$	−0.166844	−	0.622671i	−0.0746150	−	0.278467i	−0.993146	+	0.116883i	$0.962710\pi$
$6$	0.965926	+	0.258819i	0.394338	+	0.105662i
$7$	−2.38407	+	1.14726i	−0.901095	+	0.433622i
$7$	−2.38407	+	1.14726i	−0.901095	+	0.433622i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−1.00000			−0.333333
$10$	0.644637			0.203852
$11$	0.137324	−	0.137324i	0.0414049	−	0.0414049i	−0.686101	−	0.727506i	$-0.740679\pi$
$11$	0.137324	−	0.137324i	0.0414049	−	0.0414049i	0.727506	+	0.686101i	$0.240679\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−2.76090	+	2.31893i	−0.765736	+	0.643155i
$13$	−2.76090	+	2.31893i	−0.765736	+	0.643155i
$14$	−0.491121	−	2.59977i	−0.131258	−	0.694818i
$15$	−0.622671	+	0.166844i	−0.160773	+	0.0430790i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−2.33053	+	4.03659i	−0.565236	+	0.979017i	0.431792	+	0.901973i	$0.357882\pi$
$17$	−2.33053	+	4.03659i	−0.565236	+	0.979017i	−0.997028	+	0.0770440i	$0.975452\pi$
$18$	0.258819	−	0.965926i	0.0610042	−	0.227671i
$19$	0.494522	−	0.494522i	0.113451	−	0.113451i	−0.648102	−	0.761553i	$-0.724437\pi$
$19$	0.494522	−	0.494522i	0.113451	−	0.113451i	0.761553	+	0.648102i	$0.224437\pi$
$20$	−0.166844	+	0.622671i	−0.0373075	+	0.139234i
$21$	1.14726	+	2.38407i	0.250352	+	0.520247i
$22$	0.0971030	+	0.168187i	0.0207024	+	0.0358577i
$23$	−5.09246	+	2.94013i	−1.06185	+	0.613061i	−0.925944	−	0.377661i	$-0.876728\pi$
$23$	−5.09246	+	2.94013i	−1.06185	+	0.613061i	−0.135908	+	0.990721i	$0.543395\pi$
$24$	−0.707107	−	0.707107i	−0.144338	−	0.144338i
$25$	3.97024	−	2.29222i	0.794049	−	0.458444i
$26$	−1.52534	−	3.26701i	−0.299143	−	0.640713i
$27$			1.00000i			0.192450i
$28$	2.63830	+	0.198484i	0.498591	+	0.0375099i
$29$	−3.99977	+	6.92780i	−0.742738	+	1.28646i	0.208506	+	0.978021i	$0.433140\pi$
$29$	−3.99977	+	6.92780i	−0.742738	+	1.28646i	−0.951244	+	0.308439i	$0.900193\pi$
$30$		−	0.644637i		−	0.117694i
$31$	−1.86727	−	0.500334i	−0.335372	−	0.0898627i	0.0872031	−	0.996191i	$-0.472207\pi$
$31$	−1.86727	−	0.500334i	−0.335372	−	0.0898627i	−0.422575	+	0.906328i	$0.638874\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	−0.137324	−	0.137324i	−0.0239051	−	0.0239051i
$34$	−3.29586	−	3.29586i	−0.565236	−	0.565236i
$35$	1.11213	+	1.29308i	0.187985	+	0.218571i
$36$	0.866025	+	0.500000i	0.144338	+	0.0833333i
$37$	−11.0903	−	2.97162i	−1.82323	−	0.488532i	−0.826048	−	0.563600i	$-0.809416\pi$
$37$	−11.0903	−	2.97162i	−1.82323	−	0.488532i	−0.997178	+	0.0750679i	$0.976083\pi$
$38$	0.349680	+	0.605664i	0.0567256	+	0.0982516i
$39$	2.31893	+	2.76090i	0.371326	+	0.442098i
$40$	−0.558272	−	0.322318i	−0.0882705	−	0.0509630i
$41$	3.14978	+	11.7551i	0.491913	+	1.83584i	0.546675	+	0.837345i	$0.315893\pi$
$41$	3.14978	+	11.7551i	0.491913	+	1.83584i	−0.0547619	+	0.998499i	$0.517440\pi$
$42$	−2.59977	+	0.491121i	−0.401153	+	0.0757816i
$43$	5.75363	−	3.32186i	0.877420	−	0.506579i	0.00761309	−	0.999971i	$-0.497577\pi$
$43$	5.75363	−	3.32186i	0.877420	−	0.506579i	0.869807	+	0.493392i	$0.164243\pi$
$44$	−0.187589	+	0.0502642i	−0.0282801	+	0.00757762i
$45$	0.166844	+	0.622671i	0.0248717	+	0.0928224i
$46$	−1.52193	−	5.67990i	−0.224396	−	0.837456i
$47$	−4.00985	+	1.07444i	−0.584896	+	0.156723i	−0.539120	−	0.842229i	$-0.681243\pi$
$47$	−4.00985	+	1.07444i	−0.584896	+	0.156723i	−0.0457768	+	0.998952i	$0.514576\pi$
$48$	0.866025	−	0.500000i	0.125000	−	0.0721688i
$49$	4.36761	−	5.47028i	0.623944	−	0.781469i
$50$	1.18654	+	4.42823i	0.167802	+	0.626247i
$51$	4.03659	+	2.33053i	0.565236	+	0.326339i
$52$	3.55047	−	0.627799i	0.492362	−	0.0870601i
$53$	−6.01682	−	10.4214i	−0.826473	−	1.43149i	−0.900788	−	0.434259i	$-0.857010\pi$
$53$	−6.01682	−	10.4214i	−0.826473	−	1.43149i	0.0743148	−	0.997235i	$-0.476323\pi$
$54$	−0.965926	−	0.258819i	−0.131446	−	0.0352208i
$55$	−0.108420	−	0.0625962i	−0.0146193	−	0.00844047i
$56$	−0.874562	+	2.49703i	−0.116868	+	0.333679i
$57$	−0.494522	−	0.494522i	−0.0655011	−	0.0655011i
$58$	−5.65653	−	5.65653i	−0.742738	−	0.742738i
$59$	−3.71896	+	0.996492i	−0.484167	+	0.129732i	−0.492642	−	0.870232i	$-0.663969\pi$
$59$	−3.71896	+	0.996492i	−0.484167	+	0.129732i	0.00847517	+	0.999964i	$0.497302\pi$
$60$	0.622671	+	0.166844i	0.0803865	+	0.0215395i
$61$			4.08143i			0.522573i	0.965261	+	0.261287i	$0.0841468\pi$
$61$			4.08143i			0.522573i	−0.965261	+	0.261287i	$0.915853\pi$
$62$	0.966572	−	1.67415i	0.122755	−	0.212617i
$63$	2.38407	−	1.14726i	0.300365	−	0.144541i
$64$		−	1.00000i		−	0.125000i
$65$	1.90457	+	1.33223i	0.236233	+	0.165243i
$66$	0.168187	−	0.0971030i	0.0207024	−	0.0119526i
$67$	−0.200320	−	0.200320i	−0.0244730	−	0.0244730i	0.694764	−	0.719237i	$-0.255509\pi$
$67$	−0.200320	−	0.200320i	−0.0244730	−	0.0244730i	−0.719237	+	0.694764i	$0.755509\pi$
$68$	4.03659	−	2.33053i	0.489509	−	0.282618i
$69$	2.94013	+	5.09246i	0.353951	+	0.613061i
$70$	−1.53686	+	0.739564i	−0.183690	+	0.0883947i
$71$	2.34326	−	8.74517i	0.278094	−	1.03786i	−0.675645	−	0.737227i	$-0.736135\pi$
$71$	2.34326	−	8.74517i	0.278094	−	1.03786i	0.953739	−	0.300634i	$-0.0971984\pi$
$72$	−0.707107	+	0.707107i	−0.0833333	+	0.0833333i
$73$	−0.228973	+	0.854539i	−0.0267993	+	0.100016i	−0.978030	−	0.208464i	$-0.933154\pi$
$73$	−0.228973	+	0.854539i	−0.0267993	+	0.100016i	0.951231	+	0.308480i	$0.0998203\pi$
$74$	5.74074	−	9.94325i	0.667347	−	1.15588i
$75$	−2.29222	−	3.97024i	−0.264683	−	0.458444i
$76$	−0.675530	+	0.181008i	−0.0774886	+	0.0207630i
$77$	−0.169845	+	0.484938i	−0.0193557	+	0.0552638i
$78$	−3.26701	+	1.52534i	−0.369916	+	0.172711i
$79$	6.95881	−	12.0530i	0.782927	−	1.35607i	−0.147302	−	0.989091i	$-0.547059\pi$
$79$	6.95881	−	12.0530i	0.782927	−	1.35607i	0.930230	−	0.366978i	$-0.119608\pi$
$80$	0.455827	−	0.455827i	0.0509630	−	0.0509630i
$81$	1.00000			0.111111
$82$	−12.1698			−1.34393
$83$	−3.79021	+	3.79021i	−0.416029	+	0.416029i	−0.883833	−	0.467803i	$-0.845046\pi$
$83$	−3.79021	+	3.79021i	−0.416029	+	0.416029i	0.467803	+	0.883833i	$0.345046\pi$
$84$	0.198484	−	2.63830i	0.0216563	−	0.287862i
$85$	2.90231	+	0.777670i	0.314799	+	0.0843502i
$86$	1.71952	+	6.41734i	0.185421	+	0.691999i
$87$	6.92780	+	3.99977i	0.742738	+	0.428820i
$88$		−	0.194206i		−	0.0207024i
$89$	−1.40377	+	5.23893i	−0.148799	+	0.555326i	0.850758	+	0.525558i	$0.176143\pi$
$89$	−1.40377	+	5.23893i	−0.148799	+	0.555326i	−0.999557	+	0.0297678i	$0.990523\pi$
$90$	−0.644637			−0.0679507
$91$	3.92179	−	8.69595i	0.411115	−	0.911584i
$92$	5.88027			0.613061
$93$	−0.500334	+	1.86727i	−0.0518822	+	0.193627i
$94$		−	4.15130i		−	0.428174i
$95$	−0.390433	−	0.225417i	−0.0400576	−	0.0231273i
$96$	0.258819	+	0.965926i	0.0264156	+	0.0985844i
$97$	−6.54551	−	1.75386i	−0.664596	−	0.178078i	−0.0892767	−	0.996007i	$-0.528456\pi$
$97$	−6.54551	−	1.75386i	−0.664596	−	0.178078i	−0.575319	+	0.817929i	$0.695122\pi$
$98$	4.15347	+	5.63460i	0.419564	+	0.569180i
$99$	−0.137324	+	0.137324i	−0.0138016	+	0.0138016i
$100$	−4.58444			−0.458444
$101$	13.0803			1.30154			0.650768	−	0.759277i	$-0.274447\pi$
$101$	13.0803			1.30154			0.650768	+	0.759277i	$0.274447\pi$
$102$	−3.29586	+	3.29586i	−0.326339	+	0.326339i
$103$	6.00747	−	10.4052i	0.591934	−	1.02526i	−0.402038	−	0.915623i	$-0.631698\pi$
$103$	6.00747	−	10.4052i	0.591934	−	1.02526i	0.993972	−	0.109636i	$-0.0349686\pi$
$104$	−0.312523	+	3.59198i	−0.0306454	+	0.352223i
$105$	1.29308	−	1.11213i	0.126192	−	0.108533i
$106$	11.6236	−	3.11453i	1.12898	−	0.302510i
$107$	−4.16068	−	7.20651i	−0.402228	−	0.696680i	0.591766	−	0.806110i	$-0.298431\pi$
$107$	−4.16068	−	7.20651i	−0.402228	−	0.696680i	−0.993995	+	0.109430i	$0.965098\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−0.0885625	+	0.330520i	−0.00848275	+	0.0316580i	−0.970037	−	0.242955i	$-0.921883\pi$
$109$	−0.0885625	+	0.330520i	−0.00848275	+	0.0316580i	0.961555	+	0.274613i	$0.0885498\pi$
$110$	0.0885244	−	0.0885244i	0.00844047	−	0.00844047i
$111$	−2.97162	+	11.0903i	−0.282054	+	1.05264i
$112$	−2.18559	−	1.49104i	−0.206519	−	0.140890i
$113$	4.79806	+	8.31049i	0.451364	+	0.781785i	0.998471	−	0.0552776i	$-0.0176044\pi$
$113$	4.79806	+	8.31049i	0.451364	+	0.781785i	−0.547107	+	0.837062i	$0.684271\pi$
$114$	0.605664	−	0.349680i	0.0567256	−	0.0327505i
$115$	2.68039	+	2.68039i	0.249947	+	0.249947i
$116$	6.92780	−	3.99977i	0.643230	−	0.371369i
$117$	2.76090	−	2.31893i	0.255245	−	0.214385i
$118$		−	3.85015i		−	0.354435i
$119$	0.925143	−	12.2972i	0.0848077	−	1.12729i
$120$	−0.322318	+	0.558272i	−0.0294235	+	0.0509630i
$121$			10.9623i			0.996571i
$122$	−3.94236	−	1.05635i	−0.356924	−	0.0956376i
$123$	11.7551	−	3.14978i	1.05993	−	0.284006i
$124$	1.36694	+	1.36694i	0.122755	+	0.122755i
$125$	−4.36885	−	4.36885i	−0.390762	−	0.390762i
$126$	0.491121	+	2.59977i	0.0437525	+	0.231606i
$127$	18.0075	+	10.3966i	1.59791	+	0.922552i	0.991890	+	0.127099i	$0.0405666\pi$
$127$	18.0075	+	10.3966i	1.59791	+	0.922552i	0.606016	+	0.795452i	$0.292767\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	−3.32186	−	5.75363i	−0.292473	−	0.506579i
$130$	−1.77978	+	1.49487i	−0.156097	+	0.131108i
$131$	6.39529	+	3.69232i	0.558759	+	0.322600i	0.752647	−	0.658424i	$-0.228777\pi$
$131$	6.39529	+	3.69232i	0.558759	+	0.322600i	−0.193888	+	0.981024i	$0.562110\pi$
$132$	0.0502642	+	0.187589i	0.00437494	+	0.0163275i
$133$	−0.611633	+	1.74632i	−0.0530353	+	0.151425i
$134$	0.245341	−	0.141648i	0.0211942	−	0.0122365i
$135$	0.622671	−	0.166844i	0.0535910	−	0.0143597i
$136$	1.20637	+	4.50223i	0.103445	+	0.386063i
$137$	4.13082	+	15.4164i	0.352920	+	1.31711i	0.883082	+	0.469218i	$0.155464\pi$
$137$	4.13082	+	15.4164i	0.352920	+	1.31711i	−0.530163	+	0.847896i	$0.677869\pi$
$138$	−5.67990	+	1.52193i	−0.483506	+	0.129555i
$139$	−14.9928	+	8.65608i	−1.27167	+	0.734199i	−0.975302	−	0.220875i	$-0.929109\pi$
$139$	−14.9928	+	8.65608i	−1.27167	+	0.734199i	−0.296368	+	0.955074i	$0.595775\pi$
$140$	−0.316595	−	1.67591i	−0.0267571	−	0.141640i
$141$	1.07444	+	4.00985i	0.0904838	+	0.337690i
$142$	7.84071	+	4.52684i	0.657978	+	0.379884i
$143$	−0.0606938	+	0.697585i	−0.00507547	+	0.0583350i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	4.98108	+	1.33468i	0.413656	+	0.110839i
$146$	−0.766159	−	0.442342i	−0.0634077	−	0.0366085i
$147$	−5.47028	−	4.36761i	−0.451181	−	0.360234i
$148$	8.11863	+	8.11863i	0.667347	+	0.667347i
$149$	1.31568	+	1.31568i	0.107784	+	0.107784i	0.758942	−	0.651158i	$-0.225716\pi$
$149$	1.31568	+	1.31568i	0.107784	+	0.107784i	−0.651158	+	0.758942i	$0.725716\pi$
$150$	4.42823	−	1.18654i	0.361564	−	0.0968807i
$151$	−19.0362	−	5.10073i	−1.54914	−	0.415091i	−0.619936	−	0.784652i	$-0.712841\pi$
$151$	−19.0362	−	5.10073i	−1.54914	−	0.415091i	−0.929207	+	0.369561i	$0.879508\pi$
$152$		−	0.699360i		−	0.0567256i
$153$	2.33053	−	4.03659i	0.188412	−	0.326339i
$154$	−0.424455	−	0.289569i	−0.0342035	−	0.0233341i
$155$			1.24618i			0.100095i
$156$	−0.627799	−	3.55047i	−0.0502642	−	0.284265i
$157$	−6.16064	+	3.55685i	−0.491672	+	0.283867i	−0.725268	−	0.688467i	$-0.758284\pi$
$157$	−6.16064	+	3.55685i	−0.491672	+	0.283867i	0.233596	+	0.972334i	$0.424951\pi$
$158$	9.84124	+	9.84124i	0.782927	+	0.782927i
$159$	−10.4214	+	6.01682i	−0.826473	+	0.477165i
$160$	0.322318	+	0.558272i	0.0254815	+	0.0441353i
$161$	8.76772	−	12.8519i	0.690993	−	1.01287i
$162$	−0.258819	+	0.965926i	−0.0203347	+	0.0758903i
$163$	9.53104	−	9.53104i	0.746529	−	0.746529i	−0.227297	−	0.973826i	$-0.572989\pi$
$163$	9.53104	−	9.53104i	0.746529	−	0.746529i	0.973826	+	0.227297i	$0.0729887\pi$
$164$	3.14978	−	11.7551i	0.245957	−	0.917922i
$165$	−0.0625962	+	0.108420i	−0.00487311	+	0.00844047i
$166$	−2.68008	−	4.64204i	−0.208015	−	0.360292i
$167$	−9.84310	+	2.63745i	−0.761682	+	0.204092i	−0.618694	−	0.785632i	$-0.712338\pi$
$167$	−9.84310	+	2.63745i	−0.761682	+	0.204092i	−0.142988	+	0.989724i	$0.545671\pi$
$168$	2.49703	+	0.874562i	0.192650	+	0.0674739i
$169$	2.24515	−	12.8047i	0.172704	−	0.984974i
$170$	−1.50234	+	2.60214i	−0.115225	+	0.199575i
$171$	−0.494522	+	0.494522i	−0.0378171	+	0.0378171i
$172$	−6.64372			−0.506579
$173$	9.81322			0.746085			0.373043	−	0.927814i	$-0.378315\pi$
$173$	9.81322			0.746085			0.373043	+	0.927814i	$0.378315\pi$
$174$	−5.65653	+	5.65653i	−0.428820	+	0.428820i
$175$	−6.83559	+	10.0197i	−0.516722	+	0.757419i
$176$	0.187589	+	0.0502642i	0.0141400	+	0.00378881i
$177$	0.996492	+	3.71896i	0.0749009	+	0.279534i
$178$	−4.69710	−	2.71187i	−0.352063	−	0.203263i
$179$		−	4.56509i		−	0.341211i	−0.985339	−	0.170605i	$-0.945428\pi$
$179$		−	4.56509i		−	0.341211i	0.985339	−	0.170605i	$-0.0545723\pi$
$180$	0.166844	−	0.622671i	0.0124358	−	0.0464112i
$181$	12.9946			0.965885			0.482942	−	0.875652i	$-0.339568\pi$
$181$	12.9946			0.965885			0.482942	+	0.875652i	$0.339568\pi$
$182$	7.38461	+	6.03883i	0.547384	+	0.447628i
$183$	4.08143			0.301708
$184$	−1.52193	+	5.67990i	−0.112198	+	0.418728i
$185$			7.40138i			0.544160i
$186$	−1.67415	−	0.966572i	−0.122755	−	0.0708725i
$187$	0.234284	+	0.874361i	0.0171326	+	0.0639396i
$188$	4.00985	+	1.07444i	0.292448	+	0.0783613i
$189$	−1.14726	−	2.38407i	−0.0834506	−	0.173416i
$190$	0.318787	−	0.318787i	0.0231273	−	0.0231273i
$191$	0.933493			0.0675452			0.0337726	−	0.999430i	$-0.489248\pi$
$191$	0.933493			0.0675452			0.0337726	+	0.999430i	$0.489248\pi$
$192$	−1.00000			−0.0721688
$193$	1.59470	−	1.59470i	0.114789	−	0.114789i	−0.647379	−	0.762168i	$-0.724135\pi$
$193$	1.59470	−	1.59470i	0.114789	−	0.114789i	0.762168	+	0.647379i	$0.224135\pi$
$194$	3.38821	−	5.86854i	0.243259	−	0.421337i
$195$	1.33223	−	1.90457i	0.0954033	−	0.136389i
$196$	−6.51760	+	2.55360i	−0.465543	+	0.182400i
$197$	−19.1875	+	5.14128i	−1.36705	+	0.366301i	−0.866402	−	0.499348i	$-0.833573\pi$
$197$	−19.1875	+	5.14128i	−1.36705	+	0.366301i	−0.500652	+	0.865649i	$0.666906\pi$
$198$	−0.0971030	−	0.168187i	−0.00690081	−	0.0119526i
$199$	−2.59550	+	4.49554i	−0.183990	+	0.318680i	−0.943236	−	0.332124i	$-0.892235\pi$
$199$	−2.59550	+	4.49554i	−0.183990	+	0.318680i	0.759246	+	0.650804i	$0.225568\pi$
$200$	1.18654	−	4.42823i	0.0839011	−	0.313123i
$201$	−0.200320	+	0.200320i	−0.0141295	+	0.0141295i
$202$	−3.38542	+	12.6346i	−0.238197	+	0.888965i
$203$	1.58778	−	21.1051i	0.111440	−	1.48129i
$204$	−2.33053	−	4.03659i	−0.163170	−	0.282618i
$205$	6.79407	−	3.92256i	0.474518	−	0.273963i
$206$	8.49585	+	8.49585i	0.591934	+	0.591934i
$207$	5.09246	−	2.94013i	0.353951	−	0.204354i
$208$	−3.38870	−	1.23155i	−0.234964	−	0.0853924i
$209$		−	0.135820i		−	0.00939486i
$210$	0.739564	+	1.53686i	0.0510347	+	0.106053i
$211$	10.8041	−	18.7132i	0.743783	−	1.28827i	−0.206978	−	0.978346i	$-0.566363\pi$
$211$	10.8041	−	18.7132i	0.743783	−	1.28827i	0.950761	−	0.309925i	$-0.100304\pi$
$212$			12.0336i			0.826473i
$213$	−8.74517	−	2.34326i	−0.599209	−	0.160558i
$214$	8.03782	−	2.15373i	0.549454	−	0.147226i
$215$	−3.02839	−	3.02839i	−0.206534	−	0.206534i
$216$	0.707107	+	0.707107i	0.0481125	+	0.0481125i
$217$	5.02573	−	0.949407i	0.341169	−	0.0644499i
$218$	−0.296336	−	0.171090i	−0.0200704	−	0.0115877i
$219$	0.854539	+	0.228973i	0.0577444	+	0.0154726i
$220$	0.0625962	+	0.108420i	0.00422023	+	0.00730966i
$221$	−2.92621	−	16.5490i	−0.196838	−	1.11320i
$222$	−9.94325	−	5.74074i	−0.667347	−	0.385293i
$223$	3.24031	+	12.0930i	0.216987	+	0.809806i	0.985458	+	0.169921i	$0.0543513\pi$
$223$	3.24031	+	12.0930i	0.216987	+	0.809806i	−0.768471	+	0.639885i	$0.778982\pi$
$224$	2.00591	−	1.72521i	0.134025	−	0.115270i
$225$	−3.97024	+	2.29222i	−0.264683	+	0.152815i
$226$	−9.26914	+	2.48366i	−0.616574	+	0.165211i
$227$	−6.32296	−	23.5976i	−0.419669	−	1.56623i	−0.775295	−	0.631599i	$-0.782399\pi$
$227$	−6.32296	−	23.5976i	−0.419669	−	1.56623i	0.355626	−	0.934628i	$-0.384268\pi$
$228$	0.181008	+	0.675530i	0.0119875	+	0.0447381i
$229$	−18.3106	+	4.90630i	−1.21000	+	0.324218i	−0.806761	−	0.590879i	$-0.798781\pi$
$229$	−18.3106	+	4.90630i	−1.21000	+	0.324218i	−0.403236	+	0.915096i	$0.632115\pi$
$230$	−3.28279	+	1.89532i	−0.216461	+	0.124974i
$231$	0.484938	+	0.169845i	0.0319066	+	0.0111750i
$232$	2.07043	+	7.72696i	0.135931	+	0.507300i
$233$	3.27750	+	1.89226i	0.214716	+	0.123966i	0.603501	−	0.797362i	$-0.293772\pi$
$233$	3.27750	+	1.89226i	0.214716	+	0.123966i	−0.388785	+	0.921328i	$0.627105\pi$
$234$	1.52534	+	3.26701i	0.0997145	+	0.213571i
$235$	1.33804	+	2.31755i	0.0872841	+	0.151181i
$236$	3.71896	+	0.996492i	0.242084	+	0.0648661i
$237$	−12.0530	−	6.95881i	−0.782927	−	0.452023i
$238$	11.6388	+	4.07638i	0.754430	+	0.264232i
$239$	11.3575	+	11.3575i	0.734657	+	0.734657i	0.971538	−	0.236882i	$-0.0761254\pi$
$239$	11.3575	+	11.3575i	0.734657	+	0.734657i	−0.236882	+	0.971538i	$0.576125\pi$
$240$	−0.455827	−	0.455827i	−0.0294235	−	0.0294235i
$241$	−24.8332	+	6.65403i	−1.59965	+	0.428624i	−0.944936	−	0.327255i	$-0.893876\pi$
$241$	−24.8332	+	6.65403i	−1.59965	+	0.428624i	−0.654711	+	0.755880i	$0.727210\pi$
$242$	−10.5888	−	2.83725i	−0.680671	−	0.182385i
$243$		−	1.00000i		−	0.0641500i
$244$	2.04071	−	3.53462i	0.130643	−	0.226281i
$245$	−4.13490	−	1.80690i	−0.264169	−	0.115438i
$246$			12.1698i			0.775919i
$247$	−0.218566	+	2.51209i	−0.0139070	+	0.159840i
$248$	−1.67415	+	0.966572i	−0.106309	+	0.0613774i
$249$	3.79021	+	3.79021i	0.240195	+	0.240195i
$250$	5.35072	−	3.08924i	0.338410	−	0.195381i
$251$	3.33196	+	5.77112i	0.210311	+	0.364270i	0.951812	−	0.306682i	$-0.0992189\pi$
$251$	3.33196	+	5.77112i	0.210311	+	0.364270i	−0.741501	+	0.670952i	$0.765886\pi$
$252$	−2.63830	−	0.198484i	−0.166197	−	0.0125033i
$253$	−0.295567	+	1.10307i	−0.0185822	+	0.0693495i
$254$	−14.7031	+	14.7031i	−0.922552	+	0.922552i
$255$	0.777670	−	2.90231i	0.0486996	−	0.181749i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−2.29389	−	3.97314i	−0.143089	−	0.247838i	0.785569	−	0.618774i	$-0.212370\pi$
$257$	−2.29389	−	3.97314i	−0.143089	−	0.247838i	−0.928658	+	0.370936i	$0.879037\pi$
$258$	6.41734	−	1.71952i	0.399526	−	0.107053i
$259$	29.8492	−	5.63879i	1.85474	−	0.350377i
$260$	−0.983289	−	2.10603i	−0.0609810	−	0.130611i
$261$	3.99977	−	6.92780i	0.247579	−	0.428820i
$262$	−5.22173	+	5.22173i	−0.322600	+	0.322600i
$263$	−19.0460			−1.17443			−0.587213	−	0.809433i	$-0.699775\pi$
$263$	−19.0460			−1.17443			−0.587213	+	0.809433i	$0.699775\pi$
$264$	−0.194206			−0.0119526
$265$	−5.48526	+	5.48526i	−0.336957	+	0.336957i
$266$	−1.52851	−	1.04277i	−0.0937192	−	0.0639365i
$267$	5.23893	+	1.40377i	0.320618	+	0.0859092i
$268$	0.0733222	+	0.273642i	0.00447886	+	0.0167153i
$269$	−10.3988	−	6.00374i	−0.634025	−	0.366055i	0.148284	−	0.988945i	$-0.452625\pi$
$269$	−10.3988	−	6.00374i	−0.634025	−	0.366055i	−0.782309	+	0.622890i	$0.785958\pi$
$270$			0.644637i			0.0392313i
$271$	5.47560	−	20.4352i	0.332619	−	1.24135i	−0.573809	−	0.818989i	$-0.694535\pi$
$271$	5.47560	−	20.4352i	0.332619	−	1.24135i	0.906428	−	0.422361i	$-0.138799\pi$
$272$	−4.66105			−0.282618
$273$	−8.69595	−	3.92179i	−0.526303	−	0.237357i
$274$	−15.9603			−0.964194
$275$	0.230434	−	0.859990i	0.0138957	−	0.0518593i
$276$		−	5.88027i		−	0.353951i
$277$	−16.1906	−	9.34767i	−0.972801	−	0.561647i	−0.0727120	−	0.997353i	$-0.523165\pi$
$277$	−16.1906	−	9.34767i	−0.972801	−	0.561647i	−0.900089	+	0.435706i	$0.856499\pi$
$278$	−4.48072	−	16.7223i	−0.268736	−	1.00293i
$279$	1.86727	+	0.500334i	0.111791	+	0.0299542i
$280$	1.70074	+	0.127950i	0.101639	+	0.00764646i
$281$	−18.8108	+	18.8108i	−1.12216	+	1.12216i	−0.130744	+	0.991416i	$0.541736\pi$
$281$	−18.8108	+	18.8108i	−1.12216	+	1.12216i	−0.991416	+	0.130744i	$0.958264\pi$
$282$	−4.15130			−0.247206
$283$	−14.6008			−0.867929			−0.433965	−	0.900930i	$-0.642886\pi$
$283$	−14.6008			−0.867929			−0.433965	+	0.900930i	$0.642886\pi$
$284$	−6.40191	+	6.40191i	−0.379884	+	0.379884i
$285$	−0.225417	+	0.390433i	−0.0133525	+	0.0231273i
$286$	−0.658106	−	0.239174i	−0.0389146	−	0.0141427i
$287$	−20.9955	−	24.4115i	−1.23932	−	1.44097i
$288$	0.965926	−	0.258819i	0.0569177	−	0.0152511i
$289$	−2.36272	−	4.09234i	−0.138983	−	0.240726i
$290$	−2.57840	+	4.46592i	−0.151409	+	0.262248i
$291$	−1.75386	+	6.54551i	−0.102813	+	0.383705i
$292$	0.625566	−	0.625566i	0.0366085	−	0.0366085i
$293$	−7.21239	+	26.9170i	−0.421352	+	1.57251i	0.350409	+	0.936597i	$0.386043\pi$
$293$	−7.21239	+	26.9170i	−0.421352	+	1.57251i	−0.771762	+	0.635912i	$0.780624\pi$
$294$	5.63460	−	4.15347i	0.328616	−	0.242235i
$295$	1.24097	+	2.14943i	0.0722523	+	0.125145i
$296$	−9.94325	+	5.74074i	−0.577940	+	0.333674i
$297$	0.137324	+	0.137324i	0.00796837	+	0.00796837i
$298$	−1.61137	+	0.930324i	−0.0933441	+	0.0538922i
$299$	7.24183	−	19.9265i	0.418806	−	1.15238i
$300$			4.58444i			0.264683i
$301$	−9.90604	+	14.5204i	−0.570975	+	0.836944i
$302$	9.85385	−	17.0674i	0.567026	−	0.982117i
$303$		−	13.0803i		−	0.751442i
$304$	0.675530	+	0.181008i	0.0387443	+	0.0103815i
$305$	2.54139	−	0.680963i	0.145520	−	0.0389918i
$306$	3.29586	+	3.29586i	0.188412	+	0.188412i
$307$	1.42316	+	1.42316i	0.0812241	+	0.0812241i	0.746552	−	0.665327i	$-0.231708\pi$
$307$	1.42316	+	1.42316i	0.0812241	+	0.0812241i	−0.665327	+	0.746552i	$0.731708\pi$
$308$	0.389559	−	0.335046i	0.0221972	−	0.0190910i
$309$	−10.4052	−	6.00747i	−0.591934	−	0.341753i
$310$	−1.20371	−	0.322534i	−0.0683663	−	0.0183187i
$311$	−5.50785	−	9.53988i	−0.312322	−	0.540957i	0.666543	−	0.745467i	$-0.267773\pi$
$311$	−5.50785	−	9.53988i	−0.312322	−	0.540957i	−0.978865	+	0.204510i	$0.934440\pi$
$312$	3.59198	+	0.312523i	0.203356	+	0.0176931i
$313$	−5.06512	−	2.92435i	−0.286298	−	0.165294i	0.349973	−	0.936760i	$-0.386191\pi$
$313$	−5.06512	−	2.92435i	−0.286298	−	0.165294i	−0.636271	+	0.771466i	$0.719524\pi$
$314$	−1.84116	−	6.87130i	−0.103903	−	0.387770i
$315$	−1.11213	−	1.29308i	−0.0626616	−	0.0728568i
$316$	−12.0530	+	6.95881i	−0.678035	+	0.391464i
$317$	17.6975	−	4.74204i	0.993992	−	0.266339i	0.275066	−	0.961425i	$-0.411300\pi$
$317$	17.6975	−	4.74204i	0.993992	−	0.266339i	0.718927	+	0.695086i	$0.244634\pi$
$318$	−3.11453	−	11.6236i	−0.174654	−	0.651819i
$319$	0.402091	+	1.50062i	0.0225128	+	0.0840187i
$320$	−0.622671	+	0.166844i	−0.0348084	+	0.00932688i
$321$	−7.20651	+	4.16068i	−0.402228	+	0.232227i
$322$	10.1447	+	11.7953i	0.565341	+	0.657325i
$323$	0.843687	+	3.14868i	0.0469440	+	0.175197i
$324$	−0.866025	−	0.500000i	−0.0481125	−	0.0277778i
$325$	−5.64596	+	15.5353i	−0.313181	+	0.861744i
$326$	6.73947	+	11.6731i	0.373265	+	0.646513i
$327$	0.330520	+	0.0885625i	0.0182778	+	0.00489752i
$328$	10.5394	+	6.08491i	0.581939	+	0.335983i
$329$	8.32712	−	7.16186i	0.459089	−	0.394846i
$330$	−0.0885244	−	0.0885244i	−0.00487311	−	0.00487311i
$331$	11.5985	+	11.5985i	0.637511	+	0.637511i	0.949941	−	0.312430i	$-0.101143\pi$
$331$	11.5985	+	11.5985i	0.637511	+	0.637511i	−0.312430	+	0.949941i	$0.601143\pi$
$332$	5.17752	−	1.38731i	0.284153	−	0.0761386i
$333$	11.0903	+	2.97162i	0.607742	+	0.162844i
$334$		−	10.1903i		−	0.557590i
$335$	−0.0913112	+	0.158156i	−0.00498886	+	0.00864097i
$336$	−1.49104	+	2.18559i	−0.0813429	+	0.119234i
$337$			2.60165i			0.141721i	0.997486	+	0.0708603i	$0.0225745\pi$
$337$			2.60165i			0.141721i	−0.997486	+	0.0708603i	$0.977426\pi$
$338$	11.7873	+	5.48274i	0.641143	+	0.298222i
$339$	8.31049	−	4.79806i	0.451364	−	0.260595i
$340$	−2.12463	−	2.12463i	−0.115225	−	0.115225i
$341$	−0.325130	+	0.187714i	−0.0176068	+	0.0101653i
$342$	−0.349680	−	0.605664i	−0.0189085	−	0.0327505i
$343$	−4.13688	+	18.0523i	−0.223370	+	0.974734i
$344$	1.71952	−	6.41734i	0.0927103	−	0.346000i
$345$	2.68039	−	2.68039i	0.144307	−	0.144307i
$346$	−2.53985	+	9.47884i	−0.136543	+	0.509586i
$347$	−11.4820	+	19.8875i	−0.616388	+	1.06762i	0.373751	+	0.927529i	$0.378071\pi$
$347$	−11.4820	+	19.8875i	−0.616388	+	1.06762i	−0.990139	+	0.140087i	$0.955262\pi$
$348$	−3.99977	−	6.92780i	−0.214410	−	0.371369i
$349$	15.6485	−	4.19300i	0.837644	−	0.224446i	0.185598	−	0.982626i	$-0.440578\pi$
$349$	15.6485	−	4.19300i	0.837644	−	0.224446i	0.652046	+	0.758180i	$0.273911\pi$
$350$	−7.90912	−	9.19596i	−0.422760	−	0.491545i
$351$	−2.31893	−	2.76090i	−0.123775	−	0.147366i
$352$	−0.0971030	+	0.168187i	−0.00517561	+	0.00896442i
$353$	−11.6825	+	11.6825i	−0.621798	+	0.621798i	−0.945991	−	0.324193i	$-0.894907\pi$
$353$	−11.6825	+	11.6825i	−0.621798	+	0.621798i	0.324193	+	0.945991i	$0.394907\pi$
$354$	−3.85015			−0.204633
$355$	−5.83633			−0.309760
$356$	3.83517	−	3.83517i	0.203263	−	0.203263i
$357$	−12.2972	−	0.925143i	−0.650839	−	0.0489637i
$358$	4.40954	+	1.18153i	0.233051	+	0.0624459i
$359$	−3.19154	−	11.9110i	−0.168443	−	0.628638i	−0.997576	−	0.0695863i	$-0.977832\pi$
$359$	−3.19154	−	11.9110i	−0.168443	−	0.628638i	0.829133	−	0.559051i	$-0.188835\pi$
$360$	0.558272	+	0.322318i	0.0294235	+	0.0169877i
$361$			18.5109i			0.974258i
$362$	−3.36326	+	12.5519i	−0.176769	+	0.659712i
$363$	10.9623			0.575371
$364$	−7.74434	+	5.57002i	−0.405914	+	0.291949i
$365$	0.570300			0.0298509
$366$	−1.05635	+	3.94236i	−0.0552164	+	0.206070i
$367$			36.1948i			1.88935i	0.328004	+	0.944676i	$0.393624\pi$
$367$			36.1948i			1.88935i	−0.328004	+	0.944676i	$0.606376\pi$
$368$	−5.09246	−	2.94013i	−0.265463	−	0.153265i
$369$	−3.14978	−	11.7551i	−0.163971	−	0.611948i
$370$	−7.14919	−	1.91562i	−0.371668	−	0.0995883i
$371$	26.3006	+	17.9426i	1.36546	+	0.931535i
$372$	1.36694	−	1.36694i	0.0708725	−	0.0708725i
$373$	−2.61130			−0.135208			−0.0676041	−	0.997712i	$-0.521535\pi$
$373$	−2.61130			−0.135208			−0.0676041	+	0.997712i	$0.521535\pi$
$374$	−0.905205			−0.0468070
$375$	−4.36885	+	4.36885i	−0.225606	+	0.225606i
$376$	−2.07565	+	3.59513i	−0.107043	+	0.185405i
$377$	−5.02210	−	28.4022i	−0.258651	−	1.46279i
$378$	2.59977	−	0.491121i	0.133718	−	0.0252605i
$379$	15.9583	−	4.27602i	0.819724	−	0.219644i	0.175498	−	0.984480i	$-0.443846\pi$
$379$	15.9583	−	4.27602i	0.819724	−	0.219644i	0.644226	+	0.764835i	$0.277180\pi$
$380$	0.225417	+	0.390433i	0.0115636	+	0.0200288i
$381$	10.3966	−	18.0075i	0.532635	−	0.922552i
$382$	−0.241606	+	0.901685i	−0.0123616	+	0.0461342i
$383$	−4.41053	+	4.41053i	−0.225367	+	0.225367i	−0.810754	−	0.585387i	$-0.800943\pi$
$383$	−4.41053	+	4.41053i	−0.225367	+	0.225367i	0.585387	+	0.810754i	$0.300943\pi$
$384$	0.258819	−	0.965926i	0.0132078	−	0.0492922i
$385$	0.330295	+	0.0248486i	0.0168334	+	0.00126640i
$386$	1.12762	+	1.95310i	0.0573944	+	0.0994101i
$387$	−5.75363	+	3.32186i	−0.292473	+	0.168860i
$388$	4.79165	+	4.79165i	0.243259	+	0.243259i
$389$	16.0767	−	9.28186i	0.815119	−	0.470609i	−0.0336115	−	0.999435i	$-0.510701\pi$
$389$	16.0767	−	9.28186i	0.815119	−	0.470609i	0.848730	+	0.528826i	$0.177368\pi$
$390$	1.49487	+	1.77978i	0.0756955	+	0.0901226i
$391$		−	27.4083i		−	1.38610i
$392$	−0.779711	−	6.95644i	−0.0393813	−	0.351353i
$393$	3.69232	−	6.39529i	0.186253	−	0.322600i
$394$		−	19.8644i		−	1.00075i
$395$	−8.66610	−	2.32207i	−0.436039	−	0.116836i
$396$	0.187589	−	0.0502642i	0.00942669	−	0.00252587i
$397$	9.47036	+	9.47036i	0.475304	+	0.475304i	0.903626	−	0.428322i	$-0.140895\pi$
$397$	9.47036	+	9.47036i	0.475304	+	0.475304i	−0.428322	+	0.903626i	$0.640895\pi$
$398$	−3.67059	−	3.67059i	−0.183990	−	0.183990i
$399$	1.74632	+	0.611633i	0.0874254	+	0.0306200i
$400$	3.97024	+	2.29222i	0.198512	+	0.114611i
$401$	−8.13840	−	2.18068i	−0.406412	−	0.108898i	0.0498207	−	0.998758i	$-0.484135\pi$
$401$	−8.13840	−	2.18068i	−0.406412	−	0.108898i	−0.456233	+	0.889860i	$0.650802\pi$
$402$	−0.141648	−	0.245341i	−0.00706474	−	0.0122365i
$403$	6.31560	−	2.94870i	0.314602	−	0.146885i
$404$	−11.3278	−	6.54013i	−0.563581	−	0.325384i
$405$	−0.166844	−	0.622671i	−0.00829056	−	0.0309408i
$406$	19.9751	+	6.99609i	0.991345	+	0.347210i
$407$	−1.93104	+	1.11489i	−0.0957181	+	0.0552629i
$408$	4.50223	−	1.20637i	0.222894	−	0.0597242i
$409$	5.80258	+	21.6555i	0.286919	+	1.07080i	0.947426	+	0.319976i	$0.103675\pi$
$409$	5.80258	+	21.6555i	0.286919	+	1.07080i	−0.660507	+	0.750820i	$0.729659\pi$
$410$	2.03046	+	7.57780i	0.100277	+	0.374241i
$411$	15.4164	−	4.13082i	0.760436	−	0.203758i
$412$	−10.4052	+	6.00747i	−0.512630	+	0.295967i
$413$	7.72304	−	6.64231i	0.380026	−	0.326847i
$414$	1.52193	+	5.67990i	0.0747986	+	0.279152i
$415$	2.99243	+	1.72768i	0.146892	+	0.0848084i
$416$	2.06664	−	2.95449i	0.101326	−	0.144856i
$417$	8.65608	+	14.9928i	0.423890	+	0.734199i
$418$	0.131192	+	0.0351528i	0.00641681	+	0.00171938i
$419$	17.3858	+	10.0377i	0.849351	+	0.490373i	0.860432	−	0.509566i	$-0.170194\pi$
$419$	17.3858	+	10.0377i	0.849351	+	0.490373i	−0.0110810	+	0.999939i	$0.503527\pi$
$420$	−1.67591	+	0.316595i	−0.0817759	+	0.0154482i
$421$	5.85809	+	5.85809i	0.285506	+	0.285506i	0.835300	−	0.549794i	$-0.185294\pi$
$421$	5.85809	+	5.85809i	0.285506	+	0.285506i	−0.549794	+	0.835300i	$0.685294\pi$
$422$	15.2793	+	15.2793i	0.743783	+	0.743783i
$423$	4.00985	−	1.07444i	0.194965	−	0.0522408i
$424$	−11.6236	−	3.11453i	−0.564492	−	0.151255i
$425$			21.3683i			1.03652i
$426$	4.52684	−	7.84071i	0.219326	−	0.379884i
$427$	−4.68244	−	9.73042i	−0.226599	−	0.470888i
$428$			8.32137i			0.402228i
$429$	0.697585	+	0.0606938i	0.0336797	+	0.00293033i
$430$	3.70900	−	2.14139i	0.178864	−	0.103267i
$431$	13.9886	+	13.9886i	0.673806	+	0.673806i	0.958591	−	0.284785i	$-0.0919223\pi$
$431$	13.9886	+	13.9886i	0.673806	+	0.673806i	−0.284785	+	0.958591i	$0.591922\pi$
$432$	−0.866025	+	0.500000i	−0.0416667	+	0.0240563i
$433$	−1.55555	−	2.69429i	−0.0747549	−	0.129479i	0.826225	−	0.563341i	$-0.190484\pi$
$433$	−1.55555	−	2.69429i	−0.0747549	−	0.129479i	−0.900980	+	0.433861i	$0.857151\pi$
$434$	−0.383697	+	5.10020i	−0.0184180	+	0.244818i
$435$	1.33468	−	4.98108i	0.0639929	−	0.238825i
$436$	0.241957	−	0.241957i	0.0115877	−	0.0115877i
$437$	−1.06437	+	3.97230i	−0.0509159	+	0.190021i
$438$	−0.442342	+	0.766159i	−0.0211359	+	0.0366085i
$439$	12.0915	+	20.9431i	0.577095	+	0.999558i	0.995811	+	0.0914402i	$0.0291470\pi$
$439$	12.0915	+	20.9431i	0.577095	+	0.999558i	−0.418716	+	0.908117i	$0.637520\pi$
$440$	−0.120927	+	0.0324022i	−0.00576495	+	0.00154471i
$441$	−4.36761	+	5.47028i	−0.207981	+	0.260490i
$442$	16.7424	+	1.45669i	0.796356	+	0.0692875i
$443$	−3.54398	+	6.13836i	−0.168380	+	0.291642i	−0.937850	−	0.347040i	$-0.887187\pi$
$443$	−3.54398	+	6.13836i	−0.168380	+	0.291642i	0.769471	+	0.638682i	$0.220520\pi$
$444$	8.11863	−	8.11863i	0.385293	−	0.385293i
$445$	3.49635			0.165743
$446$	−12.5196			−0.592819
$447$	1.31568	−	1.31568i	0.0622294	−	0.0622294i
$448$	1.14726	+	2.38407i	0.0542028	+	0.112637i
$449$	5.40201	+	1.44746i	0.254936	+	0.0683100i	0.384024	−	0.923323i	$-0.374538\pi$
$449$	5.40201	+	1.44746i	0.254936	+	0.0683100i	−0.129087	+	0.991633i	$0.541205\pi$
$450$	−1.18654	−	4.42823i	−0.0559341	−	0.208749i
$451$	2.04681	+	1.18173i	0.0963805	+	0.0556453i
$452$		−	9.59612i		−	0.451364i
$453$	−5.10073	+	19.0362i	−0.239653	+	0.894398i
$454$	24.4300			1.14656
$455$	−6.06905	−	0.991114i	−0.284521	−	0.0464641i
$456$	−0.699360			−0.0327505
$457$	4.45808	−	16.6378i	0.208540	−	0.778283i	−0.779801	−	0.626027i	$-0.784680\pi$
$457$	4.45808	−	16.6378i	0.208540	−	0.778283i	0.988341	−	0.152255i	$-0.0486535\pi$
$458$		−	18.9565i		−	0.885779i
$459$	−4.03659	−	2.33053i	−0.188412	−	0.108780i
$460$	−0.981089	−	3.66148i	−0.0457435	−	0.170717i
$461$	1.99967	+	0.535809i	0.0931338	+	0.0249551i	0.305085	−	0.952325i	$-0.401315\pi$
$461$	1.99967	+	0.535809i	0.0931338	+	0.0249551i	−0.211951	+	0.977280i	$0.567982\pi$
$462$	−0.289569	+	0.424455i	−0.0134720	+	0.0197474i
$463$	0.348531	−	0.348531i	0.0161976	−	0.0161976i	−0.698962	−	0.715159i	$-0.746354\pi$
$463$	0.348531	−	0.348531i	0.0161976	−	0.0161976i	0.715159	+	0.698962i	$0.246354\pi$
$464$	−7.99954			−0.371369
$465$	1.24618			0.0577900
$466$	−2.67607	+	2.67607i	−0.123966	+	0.123966i
$467$	−8.23209	+	14.2584i	−0.380936	+	0.659800i	−0.991196	−	0.132401i	$-0.957731\pi$
$467$	−8.23209	+	14.2584i	−0.380936	+	0.659800i	0.610261	+	0.792201i	$0.291065\pi$
$468$	−3.55047	+	0.627799i	−0.164121	+	0.0290200i
$469$	0.707395	+	0.247759i	0.0326645	+	0.0114404i
$470$	−2.58490	+	0.692621i	−0.119232	+	0.0319482i
$471$	3.55685	+	6.16064i	0.163891	+	0.283867i
$472$	−1.92507	+	3.33433i	−0.0886087	+	0.153475i
$473$	0.333941	−	1.24629i	0.0153546	−	0.0573043i
$474$	9.84124	−	9.84124i	0.452023	−	0.452023i
$475$	0.829820	−	3.09693i	0.0380747	−	0.142097i
$476$	−6.94982	+	10.1872i	−0.318544	+	0.466927i
$477$	6.01682	+	10.4214i	0.275491	+	0.477165i
$478$	−13.9101	+	8.03098i	−0.636231	+	0.367328i
$479$	−9.59233	−	9.59233i	−0.438285	−	0.438285i	0.453150	−	0.891434i	$-0.350300\pi$
$479$	−9.59233	−	9.59233i	−0.438285	−	0.438285i	−0.891434	+	0.453150i	$0.850300\pi$
$480$	0.558272	−	0.322318i	0.0254815	−	0.0147118i
$481$	37.5101	−	17.5131i	1.71031	−	0.798530i
$482$		−	25.7092i		−	1.17102i
$483$	−12.8519	−	8.76772i	−0.584780	−	0.398945i
$484$	5.48114	−	9.49362i	0.249143	−	0.431528i
$485$			4.36832i			0.198355i
$486$	0.965926	+	0.258819i	0.0438153	+	0.0117403i
$487$	−19.6950	+	5.27725i	−0.892464	+	0.239135i	−0.675777	−	0.737106i	$-0.736192\pi$
$487$	−19.6950	+	5.27725i	−0.892464	+	0.239135i	−0.216687	+	0.976241i	$0.569525\pi$
$488$	2.88601	+	2.88601i	0.130643	+	0.130643i
$489$	−9.53104	−	9.53104i	−0.431009	−	0.431009i
$490$	2.81552	−	3.52635i	0.127192	−	0.159304i
$491$	−0.616449	−	0.355907i	−0.0278200	−	0.0160619i	0.486026	−	0.873945i	$-0.338446\pi$
$491$	−0.616449	−	0.355907i	−0.0278200	−	0.0160619i	−0.513845	+	0.857883i	$0.671780\pi$
$492$	−11.7551	−	3.14978i	−0.529963	−	0.142003i
$493$	−18.6431	−	32.2909i	−0.839645	−	1.45431i
$494$	−2.36992	−	0.861295i	−0.106628	−	0.0387515i
$495$	0.108420	+	0.0625962i	0.00487311	+	0.00281349i
$496$	−0.500334	−	1.86727i	−0.0224657	−	0.0838430i
$497$	4.44645	+	23.5375i	0.199450	+	1.05580i
$498$	−4.64204	+	2.68008i	−0.208015	+	0.120097i
$499$	10.1220	−	2.71218i	0.453122	−	0.121414i	−0.0250378	−	0.999687i	$-0.507971\pi$
$499$	10.1220	−	2.71218i	0.453122	−	0.121414i	0.478160	+	0.878273i	$0.341304\pi$
$500$	1.59911	+	5.96796i	0.0715144	+	0.266895i
$501$	2.63745	+	9.84310i	0.117833	+	0.439757i
$502$	−6.43685	+	1.72475i	−0.287291	+	0.0769793i
$503$	11.4031	−	6.58360i	0.508440	−	0.293548i	−0.223752	−	0.974646i	$-0.571831\pi$
$503$	11.4031	−	6.58360i	0.508440	−	0.293548i	0.732192	+	0.681098i	$0.238497\pi$
$504$	0.874562	−	2.49703i	0.0389561	−	0.111226i
$505$	−2.18237	−	8.14471i	−0.0971141	−	0.362435i
$506$	−0.988987	−	0.570992i	−0.0439658	−	0.0253837i
$507$	−12.8047	−	2.24515i	−0.568675	−	0.0997107i
$508$	−10.3966	−	18.0075i	−0.461276	−	0.798953i
$509$	8.92858	+	2.39241i	0.395752	+	0.106041i	0.451206	−	0.892420i	$-0.350994\pi$
$509$	8.92858	+	2.39241i	0.395752	+	0.106041i	−0.0554539	+	0.998461i	$0.517661\pi$
$510$	2.60214	+	1.50234i	0.115225	+	0.0665249i
$511$	−0.434487	−	2.29997i	−0.0192206	−	0.101745i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	0.494522	+	0.494522i	0.0218337	+	0.0218337i
$514$	4.43146	−	1.18741i	0.195463	−	0.0523743i
$515$	−7.48136	−	2.00462i	−0.329668	−	0.0883343i
$516$			6.64372i			0.292473i
$517$	−0.403104	+	0.698196i	−0.0177285	+	0.0307066i
$518$	−2.27888	+	30.2915i	−0.100128	+	1.33093i
$519$		−	9.81322i		−	0.430753i
$520$	2.28877	−	0.404703i	0.100369	−	0.0177474i
$521$	21.4893	−	12.4068i	0.941462	−	0.543553i	0.0510434	−	0.998696i	$-0.483745\pi$
$521$	21.4893	−	12.4068i	0.941462	−	0.543553i	0.890418	+	0.455143i	$0.150412\pi$
$522$	5.65653	+	5.65653i	0.247579	+	0.247579i
$523$	3.61957	−	2.08976i	0.158273	−	0.0913787i	−0.418772	−	0.908091i	$-0.637539\pi$
$523$	3.61957	−	2.08976i	0.158273	−	0.0913787i	0.577044	+	0.816713i	$0.304206\pi$
$524$	−3.69232	−	6.39529i	−0.161300	−	0.279380i
$525$	10.0197	+	6.83559i	0.437296	+	0.298329i
$526$	4.92946	−	18.3970i	0.214935	−	0.802147i
$527$	6.37138	−	6.37138i	0.277542	−	0.277542i
$528$	0.0502642	−	0.187589i	0.00218747	−	0.00816375i
$529$	5.78879	−	10.0265i	0.251686	−	0.435934i
$530$	−3.87866	−	6.71804i	−0.168478	−	0.291813i
$531$	3.71896	−	0.996492i	0.161389	−	0.0432441i
$532$	1.40285	−	1.20654i	0.0608213	−	0.0523102i
$533$	−35.9555	−	25.1507i	−1.55741	−	1.08940i
$534$	−2.71187	+	4.69710i	−0.117354	+	0.203263i
$535$	−3.79310	+	3.79310i	−0.163990	+	0.163990i
$536$	−0.283295			−0.0122365
$537$	−4.56509			−0.196998
$538$	8.49058	−	8.49058i	0.366055	−	0.366055i
$539$	−0.151425	−	1.35098i	−0.00652232	−	0.0581910i
$540$	−0.622671	−	0.166844i	−0.0267955	−	0.00717983i
$541$	−0.373703	−	1.39468i	−0.0160667	−	0.0599619i	0.957427	−	0.288675i	$-0.0932148\pi$
$541$	−0.373703	−	1.39468i	−0.0160667	−	0.0599619i	−0.973494	+	0.228713i	$0.926548\pi$
$542$	18.3217	+	10.5780i	0.786984	+	0.454366i
$543$		−	12.9946i		−	0.557654i
$544$	1.20637	−	4.50223i	0.0517227	−	0.193032i
$545$	0.220581			0.00944867
$546$	6.03883	−	7.38461i	0.258438	−	0.316032i
$547$	−7.40341			−0.316547			−0.158273	−	0.987395i	$-0.550593\pi$
$547$	−7.40341			−0.316547			−0.158273	+	0.987395i	$0.550593\pi$
$548$	4.13082	−	15.4164i	0.176460	−	0.658557i
$549$		−	4.08143i		−	0.174191i
$550$	0.771046	+	0.445163i	0.0328775	+	0.0189818i
$551$	1.44798	+	5.40393i	0.0616859	+	0.230215i
$552$	5.67990	+	1.52193i	0.241753	+	0.0647775i
$553$	−2.76242	+	36.7188i	−0.117470	+	1.56144i
$554$	13.2196	−	13.2196i	0.561647	−	0.561647i
$555$	7.40138			0.314171
$556$	17.3122			0.734199
$557$	6.16350	−	6.16350i	0.261156	−	0.261156i	−0.564368	−	0.825524i	$-0.690880\pi$
$557$	6.16350	−	6.16350i	0.261156	−	0.261156i	0.825524	+	0.564368i	$0.190880\pi$
$558$	−0.966572	+	1.67415i	−0.0409182	+	0.0708725i
$559$	−8.18205	+	22.5136i	−0.346064	+	0.952222i
$560$	−0.563775	+	1.60968i	−0.0238238	+	0.0680212i
$561$	0.874361	−	0.234284i	0.0369156	−	0.00989149i
$562$	−13.3013	−	23.0385i	−0.561080	−	0.971819i
$563$	18.0903	−	31.3333i	0.762414	−	1.32054i	−0.179189	−	0.983815i	$-0.557347\pi$
$563$	18.0903	−	31.3333i	0.762414	−	1.32054i	0.941603	−	0.336725i	$-0.109319\pi$
$564$	1.07444	−	4.00985i	0.0452419	−	0.168845i
$565$	4.37417	−	4.37417i	0.184023	−	0.184023i
$566$	3.77897	−	14.1033i	0.158842	−	0.592807i
$567$	−2.38407	+	1.14726i	−0.100122	+	0.0481802i
$568$	−4.52684	−	7.84071i	−0.189942	−	0.328989i
$569$	−25.7021	+	14.8391i	−1.07749	+	0.622088i	−0.930218	−	0.367008i	$-0.880382\pi$
$569$	−25.7021	+	14.8391i	−1.07749	+	0.622088i	−0.147271	+	0.989096i	$0.547049\pi$
$570$	−0.318787	−	0.318787i	−0.0133525	−	0.0133525i
$571$	13.1009	−	7.56384i	0.548258	−	0.316537i	−0.200161	−	0.979763i	$-0.564147\pi$
$571$	13.1009	−	7.56384i	0.548258	−	0.316537i	0.748419	+	0.663226i	$0.230813\pi$
$572$	0.401355	−	0.573779i	0.0167815	−	0.0239909i
$573$		−	0.933493i		−	0.0389972i
$574$	29.0137	−	13.9619i	1.21101	−	0.582758i
$575$	−13.4789	+	23.3461i	−0.562108	+	0.973600i
$576$			1.00000i			0.0416667i
$577$	19.2468	+	5.15718i	0.801257	+	0.214696i	0.636136	−	0.771577i	$-0.280532\pi$
$577$	19.2468	+	5.15718i	0.801257	+	0.214696i	0.165121	+	0.986273i	$0.447199\pi$
$578$	4.56442	−	1.22303i	0.189855	−	0.0508714i
$579$	−1.59470	−	1.59470i	−0.0662734	−	0.0662734i
$580$	−3.64641	−	3.64641i	−0.151409	−	0.151409i
$581$	4.68779	−	13.3845i	0.194482	−	0.555281i
$582$	−5.86854	−	3.38821i	−0.243259	−	0.140446i
$583$	−2.25737	−	0.604861i	−0.0934908	−	0.0250508i
$584$	0.442342	+	0.766159i	0.0183042	+	0.0317039i
$585$	−1.90457	−	1.33223i	−0.0787443	−	0.0550811i
$586$	−24.1331	−	13.9333i	−0.996931	−	0.575578i
$587$	7.35518	+	27.4499i	0.303581	+	1.13298i	0.934160	+	0.356854i	$0.116151\pi$
$587$	7.35518	+	27.4499i	0.303581	+	1.13298i	−0.630579	+	0.776125i	$0.717183\pi$
$588$	2.55360	+	6.51760i	0.105309	+	0.268781i
$589$	−1.17083	+	0.675982i	−0.0482434	+	0.0278533i
$590$	−2.39738	+	0.642375i	−0.0986985	+	0.0264462i
$591$	5.14128	+	19.1875i	0.211484	+	0.789269i
$592$	−2.97162	−	11.0903i	−0.122133	−	0.455807i
$593$	31.7417	−	8.50516i	1.30347	−	0.349265i	0.460712	−	0.887550i	$-0.347594\pi$
$593$	31.7417	−	8.50516i	1.30347	−	0.349265i	0.842763	+	0.538285i	$0.180928\pi$
$594$	−0.168187	+	0.0971030i	−0.00690081	+	0.00398419i
$595$	−7.81149	+	1.47566i	−0.320240	+	0.0604964i
$596$	−0.481571	−	1.79725i	−0.0197259	−	0.0736182i
$597$	4.49554	+	2.59550i	0.183990	+	0.106227i
$598$	17.3732	+	12.1524i	0.710442	+	0.496949i
$599$	16.9713	+	29.3952i	0.693429	+	1.20105i	0.970707	+	0.240265i	$0.0772343\pi$
$599$	16.9713	+	29.3952i	0.693429	+	1.20105i	−0.277278	+	0.960790i	$0.589432\pi$
$600$	−4.42823	−	1.18654i	−0.180782	−	0.0484403i
$601$	−34.5158	−	19.9277i	−1.40793	−	0.812868i	−0.412741	−	0.910848i	$-0.635429\pi$
$601$	−34.5158	−	19.9277i	−1.40793	−	0.812868i	−0.995188	+	0.0979799i	$0.968762\pi$
$602$	−11.4618	−	13.3267i	−0.467148	−	0.543155i
$603$	0.200320	+	0.200320i	0.00815766	+	0.00815766i
$604$	13.9355	+	13.9355i	0.567026	+	0.567026i
$605$	6.82590	−	1.82899i	0.277512	−	0.0743592i
$606$	12.6346	+	3.38542i	0.513244	+	0.137523i
$607$			45.3413i			1.84035i	0.391511	+	0.920174i	$0.371953\pi$
$607$			45.3413i			1.84035i	−0.391511	+	0.920174i	$0.628047\pi$
$608$	−0.349680	+	0.605664i	−0.0141814	+	0.0245629i
$609$	−21.1051	−	1.58778i	−0.855224	−	0.0643399i
$610$			2.63104i			0.106528i
$611$	8.57926	−	12.2650i	0.347080	−	0.496187i
$612$	−4.03659	+	2.33053i	−0.163170	+	0.0942060i
$613$	8.39485	+	8.39485i	0.339065	+	0.339065i	0.856015	−	0.516951i	$-0.172933\pi$
$613$	8.39485	+	8.39485i	0.339065	+	0.339065i	−0.516951	+	0.856015i	$0.672933\pi$
$614$	−1.74301	+	1.00633i	−0.0703422	+	0.0406121i
$615$	−3.92256	−	6.79407i	−0.158173	−	0.273963i
$616$	0.222804	+	0.463001i	0.00897703	+	0.0186549i
$617$	2.32942	−	8.69353i	0.0937791	−	0.349988i	−0.903052	−	0.429530i	$-0.858679\pi$
$617$	2.32942	−	8.69353i	0.0937791	−	0.349988i	0.996832	+	0.0795421i	$0.0253458\pi$
$618$	8.49585	−	8.49585i	0.341753	−	0.341753i
$619$	−11.3002	+	42.1728i	−0.454193	+	1.69507i	0.236258	+	0.971690i	$0.424079\pi$
$619$	−11.3002	+	42.1728i	−0.454193	+	1.69507i	−0.690451	+	0.723379i	$0.742588\pi$
$620$	0.623088	−	1.07922i	0.0250238	−	0.0433425i
$621$	−2.94013	−	5.09246i	−0.117984	−	0.204354i
$622$	10.6404	−	2.85107i	0.426639	−	0.114318i
$623$	−2.66371	−	14.1005i	−0.106719	−	0.564924i
$624$	−1.23155	+	3.38870i	−0.0493013	+	0.135657i
$625$	9.46967	−	16.4019i	0.378787	−	0.656078i
$626$	4.13566	−	4.13566i	0.165294	−	0.165294i
$627$	−0.135820			−0.00542413
$628$	7.11369			0.283867
$629$	37.8414	−	37.8414i	1.50883	−	1.50883i
$630$	1.53686	−	0.739564i	0.0612300	−	0.0294649i
$631$	−22.2577	−	5.96394i	−0.886066	−	0.237421i	−0.213044	−	0.977043i	$-0.568338\pi$
$631$	−22.2577	−	5.96394i	−0.886066	−	0.237421i	−0.673023	+	0.739622i	$0.735004\pi$
$632$	−3.60214	−	13.4434i	−0.143286	−	0.534749i
$633$	−18.7132	−	10.8041i	−0.743783	−	0.429423i
$634$			18.3218i			0.727653i
$635$	3.46924	−	12.9474i	0.137672	−	0.513800i
$636$	12.0336			0.477165
$637$	0.626660	+	25.2311i	0.0248292	+	0.999692i
$638$	−1.55356			−0.0615060
$639$	−2.34326	+	8.74517i	−0.0926980	+	0.345954i
$640$		−	0.644637i		−	0.0254815i
$641$	5.76869	+	3.33055i	0.227849	+	0.131549i	0.609580	−	0.792725i	$-0.291338\pi$
$641$	5.76869	+	3.33055i	0.227849	+	0.131549i	−0.381730	+	0.924274i	$0.624672\pi$
$642$	−2.15373	−	8.03782i	−0.0850009	−	0.317228i
$643$	23.5690	+	6.31530i	0.929471	+	0.249051i	0.691629	−	0.722253i	$-0.256893\pi$
$643$	23.5690	+	6.31530i	0.929471	+	0.249051i	0.237842	+	0.971304i	$0.423560\pi$
$644$	−14.0190	+	6.74618i	−0.552426	+	0.265837i
$645$	−3.02839	+	3.02839i	−0.119243	+	0.119243i
$646$	−3.25976			−0.128253
$647$	−33.5395			−1.31857			−0.659287	−	0.751892i	$-0.729142\pi$
$647$	−33.5395			−1.31857			−0.659287	+	0.751892i	$0.729142\pi$
$648$	0.707107	−	0.707107i	0.0277778	−	0.0277778i
$649$	−0.373861	+	0.647547i	−0.0146753	+	0.0254184i
$650$	−13.5447	−	9.47441i	−0.531266	−	0.371617i
$651$	−0.949407	−	5.02573i	−0.0372102	−	0.196974i
$652$	−13.0196	+	3.48860i	−0.509889	+	0.136624i
$653$	13.1376	+	22.7551i	0.514115	+	0.890474i	0.999866	+	0.0163766i	$0.00521306\pi$
$653$	13.1376	+	22.7551i	0.514115	+	0.890474i	−0.485750	+	0.874098i	$0.661454\pi$
$654$	−0.171090	+	0.296336i	−0.00669013	+	0.0115877i
$655$	1.23209	−	4.59821i	0.0481416	−	0.179667i
$656$	−8.60536	+	8.60536i	−0.335983	+	0.335983i
$657$	0.228973	−	0.854539i	0.00893309	−	0.0333387i
$658$	4.76260	+	9.89700i	0.185666	+	0.385825i
$659$	−10.6194	−	18.3934i	−0.413674	−	0.716504i	0.581614	−	0.813465i	$-0.302421\pi$
$659$	−10.6194	−	18.3934i	−0.413674	−	0.716504i	−0.995288	+	0.0969604i	$0.969088\pi$
$660$	0.108420	−	0.0625962i	0.00422023	−	0.00243655i
$661$	−30.8575	−	30.8575i	−1.20022	−	1.20022i	−0.974100	−	0.226118i	$-0.927397\pi$
$661$	−30.8575	−	30.8575i	−1.20022	−	1.20022i	−0.226118	−	0.974100i	$-0.572603\pi$
$662$	−14.2052	+	8.20137i	−0.552100	+	0.318755i
$663$	−16.5490	+	2.92621i	−0.642708	+	0.113644i
$664$			5.36016i			0.208015i
$665$	1.18943	+	0.0894830i	0.0461242	+	0.00347000i
$666$	−5.74074	+	9.94325i	−0.222449	+	0.385293i
$667$		−	47.0394i		−	1.82137i
$668$	9.84310	+	2.63745i	0.380841	+	0.102046i
$669$	12.0930	−	3.24031i	0.467542	−	0.125277i
$670$	−0.129134	−	0.129134i	−0.00498886	−	0.00498886i
$671$	0.560480	+	0.560480i	0.0216371	+	0.0216371i
$672$	−1.72521	−	2.00591i	−0.0665513	−	0.0773795i
$673$	0.332310	+	0.191859i	0.0128096	+	0.00739563i	0.506391	−	0.862304i	$-0.330979\pi$
$673$	0.332310	+	0.191859i	0.0128096	+	0.00739563i	−0.493582	+	0.869700i	$0.664313\pi$
$674$	−2.51300	−	0.673355i	−0.0967970	−	0.0259367i
$675$	2.29222	+	3.97024i	0.0882277	+	0.152815i
$676$	−8.34669	+	9.96658i	−0.321026	+	0.383330i
$677$	18.6386	+	10.7610i	0.716340	+	0.413579i	0.813404	−	0.581699i	$-0.197612\pi$
$677$	18.6386	+	10.7610i	0.716340	+	0.413579i	−0.0970639	+	0.995278i	$0.530945\pi$
$678$	2.48366	+	9.26914i	0.0953844	+	0.355979i
$679$	17.6171	−	3.32804i	0.676082	−	0.127718i
$680$	2.60214	−	1.50234i	0.0997874	−	0.0576123i
$681$	−23.5976	+	6.32296i	−0.904262	+	0.242296i
$682$	−0.0971680	−	0.362636i	−0.00372075	−	0.0138860i
$683$	−6.06410	−	22.6315i	−0.232036	−	0.865972i	−0.979462	−	0.201627i	$-0.935377\pi$
$683$	−6.06410	−	22.6315i	−0.232036	−	0.865972i	0.747426	−	0.664345i	$-0.231289\pi$
$684$	0.675530	−	0.181008i	0.0258295	−	0.00692100i
$685$	8.91016	−	5.14428i	0.340440	−	0.196553i
$686$	−16.3665	−	8.66820i	−0.624876	−	0.330953i
$687$	4.90630	+	18.3106i	0.187187	+	0.698592i
$688$	5.75363	+	3.32186i	0.219355	+	0.126645i
$689$	40.7784	+	14.8200i	1.55353	+	0.564596i
$690$	1.89532	+	3.28279i	0.0721536	+	0.124974i
$691$	−30.2799	−	8.11348i	−1.15190	−	0.308651i	−0.368175	−	0.929756i	$-0.620017\pi$
$691$	−30.2799	−	8.11348i	−1.15190	−	0.308651i	−0.783727	+	0.621105i	$0.786684\pi$
$692$	−8.49850	−	4.90661i	−0.323064	−	0.186521i
$693$	0.169845	−	0.484938i	0.00645188	−	0.0184213i
$694$	−16.2381	−	16.2381i	−0.616388	−	0.616388i
$695$	7.89135	+	7.89135i	0.299336	+	0.299336i
$696$	7.72696	−	2.07043i	0.292890	−	0.0784795i
$697$	−54.7914	−	14.6813i	−2.07537	−	0.556094i
$698$			16.2005i			0.613198i
$699$	1.89226	−	3.27750i	0.0715720	−	0.123966i
$700$	10.9296	−	5.25953i	0.413102	−	0.198792i
$701$			17.4358i			0.658542i	0.944235	+	0.329271i	$0.106803\pi$
$701$			17.4358i			0.658542i	−0.944235	+	0.329271i	$0.893197\pi$
$702$	3.26701	−	1.52534i	0.123305	−	0.0575702i
$703$	−6.95391	+	4.01484i	−0.262272	+	0.151423i
$704$	−0.137324	−	0.137324i	−0.00517561	−	0.00517561i
$705$	2.31755	−	1.33804i	0.0872841	−	0.0503935i
$706$	−8.26080	−	14.3081i	−0.310899	−	0.538493i
$707$	−31.1843	+	15.0064i	−1.17281	+	0.564374i
$708$	0.996492	−	3.71896i	0.0374505	−	0.139767i
$709$	6.67976	−	6.67976i	0.250864	−	0.250864i	−0.570461	−	0.821325i	$-0.693235\pi$
$709$	6.67976	−	6.67976i	0.250864	−	0.250864i	0.821325	+	0.570461i	$0.193235\pi$
$710$	1.51055	−	5.63746i	0.0566901	−	0.211570i
$711$	−6.95881	+	12.0530i	−0.260976	+	0.452023i
$712$	2.71187	+	4.69710i	0.101632	+	0.176031i
$713$	10.9801	−	2.94210i	0.411207	−	0.110183i
$714$	4.07638	−	11.6388i	0.152555	−	0.435570i
$715$	0.444492	−	0.0785957i	0.0166231	−	0.00293931i
$716$	−2.28254	+	3.95348i	−0.0853027	+	0.147749i
$717$	11.3575	−	11.3575i	0.424154	−	0.424154i
$718$	12.3312			0.460195
$719$	−31.4975			−1.17466			−0.587330	−	0.809348i	$-0.699821\pi$
$719$	−31.4975			−1.17466			−0.587330	+	0.809348i	$0.699821\pi$
$720$	−0.455827	+	0.455827i	−0.0169877	+	0.0169877i
$721$	−2.38477	+	31.6990i	−0.0888134	+	1.18053i
$722$	−17.8802	−	4.79097i	−0.665430	−	0.178302i
$723$	6.65403	+	24.8332i	0.247466	+	0.923556i
$724$	−11.2537	−	6.49732i	−0.418240	−	0.241471i
$725$			36.6734i			1.36202i
$726$	−2.83725	+	10.5888i	−0.105300	+	0.392985i
$727$	1.26745			0.0470072			0.0235036	−	0.999724i	$-0.492518\pi$
$727$	1.26745			0.0470072			0.0235036	+	0.999724i	$0.492518\pi$
$728$	−3.37585	−	8.92209i	−0.125117	−	0.330675i
$729$	−1.00000			−0.0370370
$730$	−0.147604	+	0.550867i	−0.00546309	+	0.0203885i
$731$			30.9667i			1.14535i
$732$	−3.53462	−	2.04071i	−0.130643	−	0.0754270i
$733$	8.01854	+	29.9256i	0.296172	+	1.10533i	0.940282	+	0.340396i	$0.110561\pi$
$733$	8.01854	+	29.9256i	0.296172	+	1.10533i	−0.644111	+	0.764932i	$0.722772\pi$
$734$	−34.9615	−	9.36790i	−1.29045	−	0.345776i
$735$	−1.80690	+	4.13490i	−0.0666484	+	0.152518i
$736$	4.15798	−	4.15798i	0.153265	−	0.153265i
$737$	−0.0550176			−0.00202660
$738$	12.1698			0.447977
$739$	15.1614	−	15.1614i	0.557721	−	0.557721i	−0.370937	−	0.928658i	$-0.620963\pi$
$739$	15.1614	−	15.1614i	0.557721	−	0.557721i	0.928658	+	0.370937i	$0.120963\pi$
$740$	3.70069	−	6.40978i	0.136040	−	0.235628i
$741$	2.51209	+	0.218566i	0.0922839	+	0.00802922i
$742$	−24.1383	+	20.7605i	−0.886146	+	0.762143i
$743$	−26.2331	+	7.02915i	−0.962401	+	0.257875i	−0.705616	−	0.708594i	$-0.749330\pi$
$743$	−26.2331	+	7.02915i	−0.962401	+	0.257875i	−0.256785	+	0.966469i	$0.582663\pi$
$744$	0.966572	+	1.67415i	0.0354362	+	0.0613774i
$745$	0.599721	−	1.03875i	0.0219721	−	0.0380568i
$746$	0.675855	−	2.52232i	0.0247448	−	0.0923489i
$747$	3.79021	−	3.79021i	0.138676	−	0.138676i
$748$	0.234284	−	0.874361i	0.00856628	−	0.0319698i
$749$	18.1871	+	12.4075i	0.664542	+	0.453360i
$750$	−3.08924	−	5.35072i	−0.112803	−	0.195381i
$751$	−37.6798	+	21.7545i	−1.37496	+	0.793832i	−0.991547	−	0.129746i	$-0.958584\pi$
$751$	−37.6798	+	21.7545i	−1.37496	+	0.793832i	−0.383410	+	0.923578i	$0.625250\pi$
$752$	−2.93541	−	2.93541i	−0.107043	−	0.107043i
$753$	5.77112	−	3.33196i	0.210311	−	0.121423i
$754$	28.7342	+	2.50004i	1.04644	+	0.0910460i
$755$			12.7043i			0.462357i
$756$	−0.198484	+	2.63830i	−0.00721878	+	0.0959539i
$757$	15.3805	−	26.6398i	0.559014	−	0.968240i	−0.438566	−	0.898699i	$-0.644513\pi$
$757$	15.3805	−	26.6398i	0.559014	−	0.968240i	0.997579	−	0.0695407i	$-0.0221534\pi$
$758$			16.5213i			0.600080i
$759$	1.10307	+	0.295567i	0.0400390	+	0.0107284i
$760$	−0.435471	+	0.116684i	−0.0157962	+	0.00423258i
$761$	27.7988	+	27.7988i	1.00771	+	1.00771i	0.999970	+	0.00773499i	$0.00246215\pi$
$761$	27.7988	+	27.7988i	1.00771	+	1.00771i	0.00773499	+	0.999970i	$0.497538\pi$
$762$	14.7031	+	14.7031i	0.532635	+	0.532635i
$763$	−0.168051	−	0.889587i	−0.00608387	−	0.0322052i
$764$	−0.808429	−	0.466746i	−0.0292479	−	0.0168863i
$765$	−2.90231	−	0.777670i	−0.104933	−	0.0281167i
$766$	−3.11871	−	5.40177i	−0.112684	−	0.195174i
$767$	7.95689	−	11.3752i	0.287306	−	0.410735i
$768$	0.866025	+	0.500000i	0.0312500	+	0.0180422i
$769$	−1.23726	−	4.61753i	−0.0446169	−	0.166513i	0.940023	−	0.341112i	$-0.110804\pi$
$769$	−1.23726	−	4.61753i	−0.0446169	−	0.166513i	−0.984640	+	0.174600i	$0.944137\pi$
$770$	−0.109488	+	0.312609i	−0.00394569	+	0.0112656i
$771$	−3.97314	+	2.29389i	−0.143089	+	0.0826126i
$772$	−2.17840	+	0.583700i	−0.0784023	+	0.0210078i
$773$	−6.71241	−	25.0510i	−0.241428	−	0.901023i	−0.975145	−	0.221568i	$-0.928883\pi$
$773$	−6.71241	−	25.0510i	−0.241428	−	0.901023i	0.733717	−	0.679456i	$-0.237784\pi$
$774$	−1.71952	−	6.41734i	−0.0618069	−	0.230666i
$775$	−8.56041	+	2.29375i	−0.307499	+	0.0823941i
$776$	−5.86854	+	3.38821i	−0.210668	+	0.121629i
$777$	−5.63879	−	29.8492i	−0.202291	−	1.07083i
$778$	4.80465	+	17.9312i	0.172255	+	0.642864i
$779$	7.37081	+	4.25554i	0.264087	+	0.152471i
$780$	−2.10603	+	0.983289i	−0.0754081	+	0.0352074i
$781$	−0.879139	−	1.52271i	−0.0314581	−	0.0544870i
$782$	26.4743	+	7.09378i	0.946721	+	0.253673i
$783$	−6.92780	−	3.99977i	−0.247579	−	0.142940i
$784$	6.92121	+	1.04732i	0.247186	+	0.0374042i
$785$	3.24261	+	3.24261i	0.115734	+	0.115734i
$786$	5.22173	+	5.22173i	0.186253	+	0.186253i
$787$	11.1483	−	2.98717i	0.397393	−	0.106481i	−0.0545872	−	0.998509i	$-0.517384\pi$
$787$	11.1483	−	2.98717i	0.397393	−	0.106481i	0.451981	+	0.892028i	$0.350718\pi$
$788$	19.1875	+	5.14128i	0.683527	+	0.183150i
$789$			19.0460i			0.678055i
$790$	4.48590	−	7.76981i	0.159601	−	0.276438i
$791$	−20.9732	−	14.3082i	−0.745721	−	0.508741i
$792$			0.194206i			0.00690081i
$793$	−9.46454	−	11.2684i	−0.336096	−	0.400153i
$794$	−11.5988	+	6.69656i	−0.411625	+	0.237652i
$795$	5.48526	+	5.48526i	0.194542	+	0.194542i
$796$	4.49554	−	2.59550i	0.159340	−	0.0919951i
$797$	25.0479	+	43.3843i	0.887244	+	1.53675i	0.843120	+	0.537725i	$0.180716\pi$
$797$	25.0479	+	43.3843i	0.887244	+	1.53675i	0.0441234	+	0.999026i	$0.485951\pi$
$798$	−1.04277	+	1.52851i	−0.0369138	+	0.0541088i
$799$	5.00800	−	18.6901i	0.177170	−	0.661209i
$800$	−3.24169	+	3.24169i	−0.114611	+	0.114611i
$801$	1.40377	−	5.23893i	0.0495997	−	0.185109i
$802$	4.21275	−	7.29669i	0.148757	−	0.257655i
$803$	0.0859055	+	0.148793i	0.00303154	+	0.00525078i
$804$	0.273642	−	0.0733222i	0.00965061	−	0.00258587i
$805$	−9.46533	−	3.31515i	−0.333609	−	0.116844i
$806$	1.21363	+	6.86358i	0.0427481	+	0.241759i
$807$	−6.00374	+	10.3988i	−0.211342	+	0.366055i
$808$	9.24915	−	9.24915i	0.325384	−	0.325384i
$809$	14.9123			0.524287			0.262143	−	0.965029i	$-0.415571\pi$
$809$	14.9123			0.524287			0.262143	+	0.965029i	$0.415571\pi$
$810$	0.644637			0.0226502
$811$	−20.0144	+	20.0144i	−0.702802	+	0.702802i	−0.965011	−	0.262209i	$-0.915549\pi$
$811$	−20.0144	+	20.0144i	−0.702802	+	0.702802i	0.262209	+	0.965011i	$0.415549\pi$
$812$	−11.9276	+	17.4837i	−0.418578	+	0.613558i
$813$	−20.4352	−	5.47560i	−0.716694	−	0.192038i
$814$	−0.577108	−	2.15379i	−0.0202276	−	0.0754905i
$815$	−7.52491	−	4.34451i	−0.263586	−	0.152181i
$816$			4.66105i			0.163170i
$817$	1.20256	−	4.48803i	0.0420724	−	0.157016i
$818$	−22.4194			−0.783877
$819$	−3.92179	+	8.69595i	−0.137038	+	0.303861i
$820$	−7.84511			−0.273963
$821$	12.2137	−	45.5821i	0.426260	−	1.59083i	−0.334895	−	0.942256i	$-0.608701\pi$
$821$	12.2137	−	45.5821i	0.426260	−	1.59083i	0.761155	−	0.648570i	$-0.224633\pi$
$822$			15.9603i			0.556678i
$823$	−41.0184	−	23.6820i	−1.42981	−	0.825502i	−0.432707	−	0.901535i	$-0.642441\pi$
$823$	−41.0184	−	23.6820i	−1.42981	−	0.825502i	−0.997105	+	0.0760326i	$0.975775\pi$
$824$	−3.10970	−	11.6055i	−0.108331	−	0.404298i
$825$	−0.859990	−	0.230434i	−0.0299410	−	0.00802267i
$826$	4.41711	+	9.17904i	0.153691	+	0.319380i
$827$	−3.14751	+	3.14751i	−0.109450	+	0.109450i	−0.759711	−	0.650261i	$-0.774659\pi$
$827$	−3.14751	+	3.14751i	−0.109450	+	0.109450i	0.650261	+	0.759711i	$0.274659\pi$
$828$	−5.88027			−0.204354
$829$	38.7681			1.34647			0.673235	−	0.739428i	$-0.264904\pi$
$829$	38.7681			1.34647			0.673235	+	0.739428i	$0.264904\pi$
$830$	−2.44331	+	2.44331i	−0.0848084	+	0.0848084i
$831$	−9.34767	+	16.1906i	−0.324267	+	0.561647i
$832$	2.31893	+	2.76090i	0.0803943	+	0.0957170i
$833$	11.9025	+	30.3789i	0.412396	+	1.05257i
$834$	−16.7223	+	4.48072i	−0.579045	+	0.155155i
$835$	3.28453	+	5.68897i	0.113666	+	0.196875i
$836$	−0.0679100	+	0.117624i	−0.00234872	+	0.00406810i
$837$	0.500334	−	1.86727i	0.0172941	−	0.0645424i
$838$	−14.1954	+	14.1954i	−0.490373	+	0.490373i
$839$	−1.52601	+	5.69516i	−0.0526838	+	0.196619i	−0.987252	−	0.159166i	$-0.949120\pi$
$839$	−1.52601	+	5.69516i	−0.0526838	+	0.196619i	0.934568	+	0.355784i	$0.115786\pi$
$840$	0.127950	−	1.70074i	0.00441469	−	0.0586812i
$841$	−17.4963	−	30.3045i	−0.603321	−	1.04498i
$842$	−7.17467	+	4.14230i	−0.247255	+	0.142753i
$843$	18.8108	+	18.8108i	0.647879	+	0.647879i
$844$	−18.7132	+	10.8041i	−0.644135	+	0.371892i
$845$	−8.34769	+	0.738392i	−0.287169	+	0.0254015i
$846$			4.15130i			0.142725i
$847$	−12.5765	−	26.1349i	−0.432135	−	0.898005i
$848$	6.01682	−	10.4214i	0.206618	−	0.357873i
$849$			14.6008i			0.501099i
$850$	−20.6402	−	5.53053i	−0.707954	−	0.189696i
$851$	65.2137	−	17.4740i	2.23550	−	0.598999i
$852$	6.40191	+	6.40191i	0.219326	+	0.219326i
$853$	−32.7838	−	32.7838i	−1.12250	−	1.12250i	−0.991365	−	0.131130i	$-0.958139\pi$
$853$	−32.7838	−	32.7838i	−1.12250	−	1.12250i	−0.131130	−	0.991365i	$-0.541861\pi$
$854$	10.6108	−	2.00447i	0.363093	−	0.0685917i
$855$	0.390433	+	0.225417i	0.0133525	+	0.00770909i
$856$	−8.03782	−	2.15373i	−0.274727	−	0.0736129i
$857$	−1.36374	−	2.36206i	−0.0465844	−	0.0806865i	0.841793	−	0.539800i	$-0.181500\pi$
$857$	−1.36374	−	2.36206i	−0.0465844	−	0.0806865i	−0.888377	+	0.459114i	$0.848167\pi$
$858$	−0.239174	+	0.658106i	−0.00816526	+	0.0224674i
$859$	16.6381	+	9.60599i	0.567683	+	0.327752i	0.756223	−	0.654313i	$-0.227042\pi$
$859$	16.6381	+	9.60599i	0.567683	+	0.327752i	−0.188540	+	0.982065i	$0.560376\pi$
$860$	1.10847	+	4.13685i	0.0377984	+	0.141065i
$861$	−24.4115	+	20.9955i	−0.831942	+	0.715523i
$862$	−17.1324	+	9.89142i	−0.583533	+	0.336903i
$863$	6.91673	−	1.85333i	0.235448	−	0.0630881i	−0.139166	−	0.990269i	$-0.544442\pi$
$863$	6.91673	−	1.85333i	0.235448	−	0.0630881i	0.374614	+	0.927181i	$0.377775\pi$
$864$	−0.258819	−	0.965926i	−0.00880520	−	0.0328615i
$865$	−1.63728	−	6.11041i	−0.0556692	−	0.207760i
$866$	3.00509	−	0.805211i	0.102117	−	0.0273622i
$867$	−4.09234	+	2.36272i	−0.138983	+	0.0802421i
$868$	−4.82711	−	1.69065i	−0.163843	−	0.0573845i
$869$	−0.699558	−	2.61079i	−0.0237309	−	0.0885649i
$870$	4.46592	+	2.57840i	0.151409	+	0.0874159i
$871$	1.01759	+	0.0885362i	0.0344797	+	0.00299993i
$872$	0.171090	+	0.296336i	0.00579383	+	0.0100352i
$873$	6.54551	+	1.75386i	0.221532	+	0.0593593i
$874$	−3.56147	−	2.05621i	−0.120468	−	0.0695524i
$875$	15.4278	+	5.40347i	0.521556	+	0.182670i
$876$	−0.625566	−	0.625566i	−0.0211359	−	0.0211359i
$877$	−2.07925	−	2.07925i	−0.0702113	−	0.0702113i	0.671129	−	0.741340i	$-0.265810\pi$
$877$	−2.07925	−	2.07925i	−0.0702113	−	0.0702113i	−0.741340	+	0.671129i	$0.765810\pi$
$878$	−23.3589	+	6.25901i	−0.788326	+	0.211231i
$879$	26.9170	+	7.21239i	0.907888	+	0.243268i
$880$		−	0.125192i		−	0.00422023i
$881$	29.3876	−	50.9008i	0.990093	−	1.71489i	0.373447	−	0.927652i	$-0.378176\pi$
$881$	29.3876	−	50.9008i	0.990093	−	1.71489i	0.616647	−	0.787240i	$-0.288491\pi$
$882$	−4.15347	−	5.63460i	−0.139855	−	0.189727i
$883$		−	36.4558i		−	1.22684i	−0.789759	−	0.613418i	$-0.789794\pi$
$883$		−	36.4558i		−	1.22684i	0.789759	−	0.613418i	$-0.210206\pi$
$884$	−5.74031	+	15.7949i	−0.193067	+	0.531241i
$885$	2.14943	−	1.24097i	0.0722523	−	0.0417149i
$886$	−5.01195	−	5.01195i	−0.168380	−	0.168380i
$887$	−27.1801	+	15.6924i	−0.912618	+	0.526900i	−0.881272	−	0.472608i	$-0.843312\pi$
$887$	−27.1801	+	15.6924i	−0.912618	+	0.526900i	−0.0313453	+	0.999509i	$0.509979\pi$
$888$	5.74074	+	9.94325i	0.192647	+	0.333674i
$889$	−54.8588	−	4.12712i	−1.83990	−	0.138419i
$890$	−0.904921	+	3.37721i	−0.0303330	+	0.113204i
$891$	0.137324	−	0.137324i	0.00460054	−	0.00460054i
$892$	3.24031	−	12.0930i	0.108493	−	0.404903i
$893$	−1.45163	+	2.51429i	−0.0485768	+	0.0841375i
$894$	0.930324	+	1.61137i	0.0311147	+	0.0538922i
$895$	−2.84255	+	0.761659i	−0.0950160	+	0.0254595i
$896$	−2.59977	+	0.491121i	−0.0868522	+	0.0164072i
$897$	−19.9265	−	7.24183i	−0.665326	−	0.241798i
$898$	−2.79628	+	4.84331i	−0.0933132	+	0.161623i
$899$	10.9349	−	10.9349i	0.364699	−	0.364699i
$900$	4.58444			0.152815
$901$	56.0894			1.86861
$902$	−1.67121	+	1.67121i	−0.0556453	+	0.0556453i
$903$	14.5204	+	9.90604i	0.483210	+	0.329653i
$904$	9.26914	+	2.48366i	0.308287	+	0.0826053i
$905$	−2.16808	−	8.09140i	−0.0720695	−	0.268967i
$906$	−17.0674	−	9.85385i	−0.567026	−	0.327372i
$907$			49.9716i			1.65928i	0.558298	+	0.829641i	$0.311455\pi$
$907$			49.9716i			1.65928i	−0.558298	+	0.829641i	$0.688545\pi$
$908$	−6.32296	+	23.5976i	−0.209835	+	0.783114i
$909$	−13.0803			−0.433845
$910$	2.52813	−	5.60573i	0.0838066	−	0.185828i
$911$	14.0084			0.464120			0.232060	−	0.972702i	$-0.425453\pi$
$911$	14.0084			0.464120			0.232060	+	0.972702i	$0.425453\pi$
$912$	0.181008	−	0.675530i	0.00599376	−	0.0223690i
$913$			1.04098i			0.0344513i
$914$	14.9170	+	8.61235i	0.493411	+	0.284871i
$915$	−0.680963	−	2.54139i	−0.0225119	−	0.0840157i
$916$	18.3106	+	4.90630i	0.604998	+	0.162109i
$917$	−19.4829	−	1.46573i	−0.643381	−	0.0484027i
$918$	3.29586	−	3.29586i	0.108780	−	0.108780i
$919$	25.5741			0.843613			0.421806	−	0.906686i	$-0.361396\pi$
$919$	25.5741			0.843613			0.421806	+	0.906686i	$0.361396\pi$
$920$	3.79064			0.124974
$921$	1.42316	−	1.42316i	0.0468948	−	0.0468948i
$922$	−1.03510	+	1.79285i	−0.0340893	+	0.0590445i
$923$	13.8099	+	29.5784i	0.454559	+	0.973586i
$924$	−0.335046	−	0.389559i	−0.0110222	−	0.0128156i
$925$	−50.8426	+	13.6232i	−1.67170	+	0.447929i
$926$	0.246449	+	0.426861i	0.00809880	+	0.0140275i
$927$	−6.00747	+	10.4052i	−0.197311	+	0.341753i
$928$	2.07043	−	7.72696i	0.0679653	−	0.253650i
$929$	−24.2450	+	24.2450i	−0.795454	+	0.795454i	−0.982375	−	0.186921i	$-0.940149\pi$
$929$	−24.2450	+	24.2450i	−0.795454	+	0.795454i	0.186921	+	0.982375i	$0.440149\pi$
$930$	−0.322534	+	1.20371i	−0.0105763	+	0.0394713i
$931$	−0.545298	−	4.86506i	−0.0178714	−	0.159446i
$932$	−1.89226	−	3.27750i	−0.0619832	−	0.107358i
$933$	−9.53988	+	5.50785i	−0.312322	+	0.180319i
$934$	−11.6419	−	11.6419i	−0.380936	−	0.380936i
$935$	0.505351	−	0.291764i	0.0165267	−	0.00954171i
$936$	0.312523	−	3.59198i	0.0102151	−	0.117408i
$937$		−	32.4063i		−	1.05867i	−0.848414	−	0.529333i	$-0.822442\pi$
$937$		−	32.4063i		−	1.05867i	0.848414	−	0.529333i	$-0.177558\pi$
$938$	−0.422404	+	0.619167i	−0.0137920	+	0.0202165i
$939$	−2.92435	+	5.06512i	−0.0954326	+	0.165294i
$940$		−	2.67608i		−	0.0872841i
$941$	−21.1998	−	5.68046i	−0.691093	−	0.185178i	−0.103855	−	0.994592i	$-0.533118\pi$
$941$	−21.1998	−	5.68046i	−0.691093	−	0.185178i	−0.587238	+	0.809415i	$0.699785\pi$
$942$	−6.87130	+	1.84116i	−0.223879	+	0.0599882i
$943$	−50.6018	−	50.6018i	−1.64782	−	1.64782i
$944$	−2.72247	−	2.72247i	−0.0886087	−	0.0886087i
$945$	−1.29308	+	1.11213i	−0.0420639	+	0.0361777i
$946$	1.11739	+	0.645125i	0.0363295	+	0.0209748i
$947$	−33.5477	−	8.98909i	−1.09016	−	0.292106i	−0.331405	−	0.943488i	$-0.607523\pi$
$947$	−33.5477	−	8.98909i	−1.09016	−	0.292106i	−0.758750	+	0.651382i	$0.774189\pi$
$948$	6.95881	+	12.0530i	0.226012	+	0.391464i
$949$	−1.34944	−	2.89027i	−0.0438047	−	0.0938221i
$950$	2.77663	+	1.60309i	0.0900858	+	0.0520111i
$951$	−4.74204	−	17.6975i	−0.153771	−	0.573882i
$952$	−8.04129	−	9.34964i	−0.260620	−	0.303023i
$953$	−20.1372	+	11.6262i	−0.652308	+	0.376610i	−0.789340	−	0.613957i	$-0.789577\pi$
$953$	−20.1372	+	11.6262i	−0.652308	+	0.376610i	0.137032	+	0.990567i	$0.456244\pi$
$954$	−11.6236	+	3.11453i	−0.376328	+	0.100837i
$955$	−0.155748	−	0.581259i	−0.00503989	−	0.0188091i
$956$	−4.15714	−	15.5147i	−0.134451	−	0.501780i
$957$	1.50062	−	0.402091i	0.0485082	−	0.0129977i
$958$	11.7482	−	6.78280i	0.379566	−	0.219142i
$959$	−27.5348	−	32.0148i	−0.889144	−	1.03381i
$960$	0.166844	+	0.622671i	0.00538488	+	0.0200966i
$961$	−23.6104	−	13.6315i	−0.761626	−	0.439725i
$962$	7.20806	+	40.7647i	0.232397	+	1.31431i
$963$	4.16068	+	7.20651i	0.134076	+	0.232227i
$964$	24.8332	+	6.65403i	0.799823	+	0.214312i
$965$	−1.25904	−	0.726907i	−0.0405299	−	0.0233999i
$966$	11.7953	−	10.1447i	0.379507	−	0.326400i
$967$	36.7896	+	36.7896i	1.18307	+	1.18307i	0.978944	+	0.204130i	$0.0654366\pi$
$967$	36.7896	+	36.7896i	1.18307	+	1.18307i	0.204130	+	0.978944i	$0.434563\pi$
$968$	7.75151	+	7.75151i	0.249143	+	0.249143i
$969$	3.14868	−	0.843687i	0.101150	−	0.0271031i
$970$	−4.21948	−	1.13061i	−0.135479	−	0.0363016i
$971$		−	34.3030i		−	1.10083i	−0.834890	−	0.550417i	$-0.814469\pi$
$971$		−	34.3030i		−	1.10083i	0.834890	−	0.550417i	$-0.185531\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	25.8131	−	37.8373i	0.827530	−	1.21301i
$974$		−	20.3897i		−	0.653329i
$975$	15.5353	+	5.64596i	0.497528	+	0.180815i
$976$	−3.53462	+	2.04071i	−0.113140	+	0.0653217i
$977$	−8.93059	−	8.93059i	−0.285715	−	0.285715i	0.549668	−	0.835383i	$-0.314754\pi$
$977$	−8.93059	−	8.93059i	−0.285715	−	0.285715i	−0.835383	+	0.549668i	$0.814754\pi$
$978$	11.6731	−	6.73947i	0.373265	−	0.215504i
$979$	0.526662	+	0.912205i	0.0168322	+	0.0291542i
$980$	2.67748	+	3.63227i	0.0855289	+	0.116029i
$981$	0.0885625	−	0.330520i	0.00282758	−	0.0105527i
$982$	0.503329	−	0.503329i	0.0160619	−	0.0160619i
$983$	0.255889	−	0.954990i	0.00816159	−	0.0304595i	−0.961725	−	0.274017i	$-0.911648\pi$
$983$	0.255889	−	0.954990i	0.00816159	−	0.0304595i	0.969887	+	0.243557i	$0.0783143\pi$
$984$	6.08491	−	10.5394i	0.193980	−	0.335983i
$985$	6.40265	+	11.0897i	0.204005	+	0.353348i
$986$	36.0158	−	9.65040i	1.14698	−	0.307331i
$987$	−7.16186	−	8.32712i	−0.227964	−	0.265055i
$988$	1.44533	−	2.06625i	0.0459820	−	0.0657361i
$989$	−19.5334	+	33.8329i	−0.621127	+	1.07582i
$990$	−0.0885244	+	0.0885244i	−0.00281349	+	0.00281349i
$991$	−45.6086			−1.44880			−0.724402	−	0.689377i	$-0.757884\pi$
$991$	−45.6086			−1.44880			−0.724402	+	0.689377i	$0.757884\pi$
$992$	1.93314			0.0613774
$993$	11.5985	−	11.5985i	0.368067	−	0.368067i
$994$	−23.8863	−	1.79700i	−0.757626	−	0.0569975i
$995$	3.23229	+	0.866089i	0.102470	+	0.0274569i
$996$	−1.38731	−	5.17752i	−0.0439587	−	0.164056i
$997$	28.8090	+	16.6329i	0.912389	+	0.526768i	0.881199	−	0.472745i	$-0.156737\pi$
$997$	28.8090	+	16.6329i	0.912389	+	0.526768i	0.0311900	+	0.999513i	$0.490070\pi$
$998$			10.4790i			0.331708i
$999$	2.97162	−	11.0903i	0.0940180	−	0.350880i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.by.a.397.2	✓	32
7.3	odd	6		546.2.cg.a.241.2	yes	32
13.2	odd	12		546.2.cg.a.145.2	yes	32
91.80	even	12	inner	546.2.by.a.535.2	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.a.397.2	✓	32	1.1	even	1	trivial
546.2.by.a.535.2	yes	32	91.80	even	12	inner
546.2.cg.a.145.2	yes	32	13.2	odd	12
546.2.cg.a.241.2	yes	32	7.3	odd	6

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.by (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} -1.00000i q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.166844 - 0.622671i) q^{5} +(0.965926 + 0.258819i) q^{6} +(-2.38407 + 1.14726i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} -1.00000i q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.166844 - 0.622671i) q^{5} +(0.965926 + 0.258819i) q^{6} +(-2.38407 + 1.14726i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +0.644637 q^{10} +(0.137324 - 0.137324i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-2.76090 + 2.31893i) q^{13} +(-0.491121 - 2.59977i) q^{14} +(-0.622671 + 0.166844i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-2.33053 + 4.03659i) q^{17} +(0.258819 - 0.965926i) q^{18} +(0.494522 - 0.494522i) q^{19} +(-0.166844 + 0.622671i) q^{20} +(1.14726 + 2.38407i) q^{21} +(0.0971030 + 0.168187i) q^{22} +(-5.09246 + 2.94013i) q^{23} +(-0.707107 - 0.707107i) q^{24} +(3.97024 - 2.29222i) q^{25} +(-1.52534 - 3.26701i) q^{26} +1.00000i q^{27} +(2.63830 + 0.198484i) q^{28} +(-3.99977 + 6.92780i) q^{29} -0.644637i q^{30} +(-1.86727 - 0.500334i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-0.137324 - 0.137324i) q^{33} +(-3.29586 - 3.29586i) q^{34} +(1.11213 + 1.29308i) q^{35} +(0.866025 + 0.500000i) q^{36} +(-11.0903 - 2.97162i) q^{37} +(0.349680 + 0.605664i) q^{38} +(2.31893 + 2.76090i) q^{39} +(-0.558272 - 0.322318i) q^{40} +(3.14978 + 11.7551i) q^{41} +(-2.59977 + 0.491121i) q^{42} +(5.75363 - 3.32186i) q^{43} +(-0.187589 + 0.0502642i) q^{44} +(0.166844 + 0.622671i) q^{45} +(-1.52193 - 5.67990i) q^{46} +(-4.00985 + 1.07444i) q^{47} +(0.866025 - 0.500000i) q^{48} +(4.36761 - 5.47028i) q^{49} +(1.18654 + 4.42823i) q^{50} +(4.03659 + 2.33053i) q^{51} +(3.55047 - 0.627799i) q^{52} +(-6.01682 - 10.4214i) q^{53} +(-0.965926 - 0.258819i) q^{54} +(-0.108420 - 0.0625962i) q^{55} +(-0.874562 + 2.49703i) q^{56} +(-0.494522 - 0.494522i) q^{57} +(-5.65653 - 5.65653i) q^{58} +(-3.71896 + 0.996492i) q^{59} +(0.622671 + 0.166844i) q^{60} +4.08143i q^{61} +(0.966572 - 1.67415i) q^{62} +(2.38407 - 1.14726i) q^{63} -1.00000i q^{64} +(1.90457 + 1.33223i) q^{65} +(0.168187 - 0.0971030i) q^{66} +(-0.200320 - 0.200320i) q^{67} +(4.03659 - 2.33053i) q^{68} +(2.94013 + 5.09246i) q^{69} +(-1.53686 + 0.739564i) q^{70} +(2.34326 - 8.74517i) q^{71} +(-0.707107 + 0.707107i) q^{72} +(-0.228973 + 0.854539i) q^{73} +(5.74074 - 9.94325i) q^{74} +(-2.29222 - 3.97024i) q^{75} +(-0.675530 + 0.181008i) q^{76} +(-0.169845 + 0.484938i) q^{77} +(-3.26701 + 1.52534i) q^{78} +(6.95881 - 12.0530i) q^{79} +(0.455827 - 0.455827i) q^{80} +1.00000 q^{81} -12.1698 q^{82} +(-3.79021 + 3.79021i) q^{83} +(0.198484 - 2.63830i) q^{84} +(2.90231 + 0.777670i) q^{85} +(1.71952 + 6.41734i) q^{86} +(6.92780 + 3.99977i) q^{87} -0.194206i q^{88} +(-1.40377 + 5.23893i) q^{89} -0.644637 q^{90} +(3.92179 - 8.69595i) q^{91} +5.88027 q^{92} +(-0.500334 + 1.86727i) q^{93} -4.15130i q^{94} +(-0.390433 - 0.225417i) q^{95} +(0.258819 + 0.965926i) q^{96} +(-6.54551 - 1.75386i) q^{97} +(4.15347 + 5.63460i) q^{98} +(-0.137324 + 0.137324i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{7} - 32 q^{9}+O(q^{10}) \) 32 * q + 8 * q^7 - 32 * q^9	\( 32 q + 8 q^{7} - 32 q^{9} - 4 q^{11} - 16 q^{12} + 4 q^{14} + 16 q^{16} - 8 q^{17} - 12 q^{19} - 8 q^{21} - 4 q^{22} - 24 q^{23} - 24 q^{25} + 8 q^{26} - 4 q^{28} - 12 q^{29} - 28 q^{31} + 4 q^{33} - 8 q^{34} - 44 q^{35} - 36 q^{37} + 8 q^{38} - 20 q^{39} - 28 q^{41} + 12 q^{42} + 84 q^{43} + 8 q^{44} - 4 q^{46} + 16 q^{47} + 24 q^{49} - 16 q^{50} + 8 q^{52} - 4 q^{53} + 48 q^{55} + 12 q^{56} + 12 q^{57} + 24 q^{58} + 12 q^{59} - 40 q^{62} - 8 q^{63} - 4 q^{65} + 8 q^{67} - 8 q^{69} + 60 q^{70} + 20 q^{71} + 4 q^{73} + 20 q^{74} + 8 q^{75} + 36 q^{76} - 12 q^{77} - 20 q^{78} + 32 q^{81} - 48 q^{82} + 12 q^{83} - 16 q^{84} - 4 q^{85} + 52 q^{86} - 36 q^{87} - 36 q^{89} - 16 q^{92} + 4 q^{93} - 48 q^{95} + 76 q^{97} + 8 q^{98} + 4 q^{99}+O(q^{100}) \) 32 * q + 8 * q^7 - 32 * q^9 - 4 * q^11 - 16 * q^12 + 4 * q^14 + 16 * q^16 - 8 * q^17 - 12 * q^19 - 8 * q^21 - 4 * q^22 - 24 * q^23 - 24 * q^25 + 8 * q^26 - 4 * q^28 - 12 * q^29 - 28 * q^31 + 4 * q^33 - 8 * q^34 - 44 * q^35 - 36 * q^37 + 8 * q^38 - 20 * q^39 - 28 * q^41 + 12 * q^42 + 84 * q^43 + 8 * q^44 - 4 * q^46 + 16 * q^47 + 24 * q^49 - 16 * q^50 + 8 * q^52 - 4 * q^53 + 48 * q^55 + 12 * q^56 + 12 * q^57 + 24 * q^58 + 12 * q^59 - 40 * q^62 - 8 * q^63 - 4 * q^65 + 8 * q^67 - 8 * q^69 + 60 * q^70 + 20 * q^71 + 4 * q^73 + 20 * q^74 + 8 * q^75 + 36 * q^76 - 12 * q^77 - 20 * q^78 + 32 * q^81 - 48 * q^82 + 12 * q^83 - 16 * q^84 - 4 * q^85 + 52 * q^86 - 36 * q^87 - 36 * q^89 - 16 * q^92 + 4 * q^93 - 48 * q^95 + 76 * q^97 + 8 * q^98 + 4 * q^99

Introduction

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