LMFDB - Embedded newform 546.2.cg.b.241.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(145,546)]

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, 1]))

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

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

chi := DirichletCharacter("546.145");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			241.2
Character	$\chi$	$=$	546.241
Dual form			546.2.cg.b.145.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-0.866025 + 0.500000i) q^{3} +1.00000i q^{4} +(-1.30432 - 0.349490i) q^{5} +(0.965926 + 0.258819i) q^{6} +(-1.83449 + 1.90648i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.866025 + 0.500000i) q^{3} +1.00000i q^{4} +(-1.30432 - 0.349490i) q^{5} +(0.965926 + 0.258819i) q^{6} +(-1.83449 + 1.90648i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +(0.675164 + 1.16942i) q^{10} +(2.57289 + 0.689405i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-3.33563 - 1.36878i) q^{13} +(2.64526 - 0.0509058i) q^{14} +(1.30432 - 0.349490i) q^{15} -1.00000 q^{16} +5.24536 q^{17} +(-0.965926 + 0.258819i) q^{18} +(-1.78704 - 6.66931i) q^{19} +(0.349490 - 1.30432i) q^{20} +(0.635473 - 2.56830i) q^{21} +(-1.33183 - 2.30679i) q^{22} +0.262474i q^{23} +(-0.258819 + 0.965926i) q^{24} +(-2.75103 - 1.58831i) q^{25} +(1.39077 + 3.32652i) q^{26} +1.00000i q^{27} +(-1.90648 - 1.83449i) q^{28} +(3.07741 - 5.33023i) q^{29} +(-1.16942 - 0.675164i) q^{30} +(-0.112859 - 0.421196i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-2.57289 + 0.689405i) q^{33} +(-3.70903 - 3.70903i) q^{34} +(3.05905 - 1.84551i) q^{35} +(0.866025 + 0.500000i) q^{36} +(1.94672 - 1.94672i) q^{37} +(-3.45229 + 5.97954i) q^{38} +(3.57313 - 0.482416i) q^{39} +(-1.16942 + 0.675164i) q^{40} +(-2.81615 - 10.5100i) q^{41} +(-2.26541 + 1.36672i) q^{42} +(6.74810 - 3.89602i) q^{43} +(-0.689405 + 2.57289i) q^{44} +(-0.954826 + 0.954826i) q^{45} +(0.185597 - 0.185597i) q^{46} +(-1.48760 + 5.55179i) q^{47} +(0.866025 - 0.500000i) q^{48} +(-0.269318 - 6.99482i) q^{49} +(0.822169 + 3.06837i) q^{50} +(-4.54261 + 2.62268i) q^{51} +(1.36878 - 3.33563i) q^{52} +(0.878238 - 1.52115i) q^{53} +(0.707107 - 0.707107i) q^{54} +(-3.11493 - 1.79840i) q^{55} +(0.0509058 + 2.64526i) q^{56} +(4.88227 + 4.88227i) q^{57} +(-5.94510 + 1.59298i) q^{58} +(-6.09059 - 6.09059i) q^{59} +(0.349490 + 1.30432i) q^{60} +(-7.62133 - 4.40017i) q^{61} +(-0.218027 + 0.377634i) q^{62} +(0.733815 + 2.54195i) q^{63} -1.00000i q^{64} +(3.87234 + 2.95110i) q^{65} +(2.30679 + 1.33183i) q^{66} +(-2.68089 + 10.0052i) q^{67} +5.24536i q^{68} +(-0.131237 - 0.227309i) q^{69} +(-3.46805 - 0.858097i) q^{70} +(1.08417 - 4.04618i) q^{71} +(-0.258819 - 0.965926i) q^{72} +(4.86981 - 1.30486i) q^{73} -2.75308 q^{74} +3.17662 q^{75} +(6.66931 - 1.78704i) q^{76} +(-6.03427 + 3.64046i) q^{77} +(-2.86771 - 2.18547i) q^{78} +(3.12948 + 5.42042i) q^{79} +(1.30432 + 0.349490i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-5.44038 + 9.42301i) q^{82} +(9.32218 - 9.32218i) q^{83} +(2.56830 + 0.635473i) q^{84} +(-6.84160 - 1.83320i) q^{85} +(-7.52653 - 2.01673i) q^{86} +6.15482i q^{87} +(2.30679 - 1.33183i) q^{88} +(4.38711 + 4.38711i) q^{89} +1.35033 q^{90} +(8.72872 - 3.84830i) q^{91} -0.262474 q^{92} +(0.308337 + 0.308337i) q^{93} +(4.97760 - 2.87382i) q^{94} +9.32344i q^{95} +(-0.965926 - 0.258819i) q^{96} +(-18.5733 - 4.97669i) q^{97} +(-4.75565 + 5.13652i) q^{98} +(1.88349 - 1.88349i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{7} + 20 q^{9}+O(q^{10}) $ 40 * q + 4 * q^7 + 20 * q^9	$ 40 q + 4 q^{7} + 20 q^{9} + 8 q^{11} - 20 q^{12} + 4 q^{14} - 40 q^{16} + 16 q^{17} + 4 q^{19} + 4 q^{21} - 4 q^{22} - 24 q^{25} + 8 q^{26} - 4 q^{28} - 12 q^{29} - 8 q^{33} - 8 q^{34} - 32 q^{35} + 40 q^{37} + 8 q^{38} + 20 q^{39} + 20 q^{41} + 12 q^{42} - 24 q^{43} - 4 q^{44} + 32 q^{46} + 4 q^{47} + 32 q^{49} - 16 q^{50} + 24 q^{51} + 16 q^{52} - 4 q^{53} + 24 q^{55} + 12 q^{56} + 8 q^{57} + 12 q^{58} + 24 q^{59} + 60 q^{61} + 32 q^{62} - 4 q^{63} + 44 q^{65} - 12 q^{67} - 8 q^{69} - 24 q^{70} - 28 q^{71} + 60 q^{73} - 40 q^{74} - 72 q^{75} + 4 q^{76} - 12 q^{77} + 4 q^{78} - 20 q^{81} - 24 q^{82} + 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{89} - 16 q^{92} - 24 q^{93} - 48 q^{97} - 88 q^{98} + 4 q^{99}+O(q^{100}) $ 40 * q + 4 * q^7 + 20 * q^9 + 8 * q^11 - 20 * q^12 + 4 * q^14 - 40 * q^16 + 16 * q^17 + 4 * q^19 + 4 * q^21 - 4 * q^22 - 24 * q^25 + 8 * q^26 - 4 * q^28 - 12 * q^29 - 8 * q^33 - 8 * q^34 - 32 * q^35 + 40 * q^37 + 8 * q^38 + 20 * q^39 + 20 * q^41 + 12 * q^42 - 24 * q^43 - 4 * q^44 + 32 * q^46 + 4 * q^47 + 32 * q^49 - 16 * q^50 + 24 * q^51 + 16 * q^52 - 4 * q^53 + 24 * q^55 + 12 * q^56 + 8 * q^57 + 12 * q^58 + 24 * q^59 + 60 * q^61 + 32 * q^62 - 4 * q^63 + 44 * q^65 - 12 * q^67 - 8 * q^69 - 24 * q^70 - 28 * q^71 + 60 * q^73 - 40 * q^74 - 72 * q^75 + 4 * q^76 - 12 * q^77 + 4 * q^78 - 20 * q^81 - 24 * q^82 + 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^89 - 16 * q^92 - 24 * q^93 - 48 * q^97 - 88 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$			1.00000i			0.500000i
$5$	−1.30432	−	0.349490i	−0.583308	−	0.156297i	−0.0449150	−	0.998991i	$-0.514302\pi$
$5$	−1.30432	−	0.349490i	−0.583308	−	0.156297i	−0.538393	+	0.842694i	$0.680968\pi$
$6$	0.965926	+	0.258819i	0.394338	+	0.105662i
$7$	−1.83449	+	1.90648i	−0.693371	+	0.720581i
$7$	−1.83449	+	1.90648i	−0.693371	+	0.720581i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	0.675164	+	1.16942i	0.213506	+	0.369802i
$11$	2.57289	+	0.689405i	0.775757	+	0.207863i	0.624913	−	0.780694i	$-0.285134\pi$
$11$	2.57289	+	0.689405i	0.775757	+	0.207863i	0.150843	+	0.988558i	$0.451801\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	−3.33563	−	1.36878i	−0.925138	−	0.379632i
$13$	−3.33563	−	1.36878i	−0.925138	−	0.379632i
$14$	2.64526	−	0.0509058i	0.706976	−	0.0136051i
$15$	1.30432	−	0.349490i	0.336773	−	0.0902381i
$16$	−1.00000			−0.250000
$17$	5.24536			1.27219			0.636093	−	0.771613i	$-0.280550\pi$
$17$	5.24536			1.27219			0.636093	+	0.771613i	$0.280550\pi$
$18$	−0.965926	+	0.258819i	−0.227671	+	0.0610042i
$19$	−1.78704	−	6.66931i	−0.409974	−	1.53004i	−0.794694	−	0.607011i	$-0.792369\pi$
$19$	−1.78704	−	6.66931i	−0.409974	−	1.53004i	0.384720	−	0.923033i	$-0.374298\pi$
$20$	0.349490	−	1.30432i	0.0781485	−	0.291654i
$21$	0.635473	−	2.56830i	0.138672	−	0.560449i
$22$	−1.33183	−	2.30679i	−0.283947	−	0.491810i
$23$			0.262474i			0.0547296i	0.999626	+	0.0273648i	$0.00871157\pi$
$23$			0.262474i			0.0547296i	−0.999626	+	0.0273648i	$0.991288\pi$
$24$	−0.258819	+	0.965926i	−0.0528312	+	0.197169i
$25$	−2.75103	−	1.58831i	−0.550206	−	0.317662i
$26$	1.39077	+	3.32652i	0.272753	+	0.652385i
$27$			1.00000i			0.192450i
$28$	−1.90648	−	1.83449i	−0.360291	−	0.346685i
$29$	3.07741	−	5.33023i	0.571461	−	0.989799i	−0.424956	−	0.905214i	$-0.639710\pi$
$29$	3.07741	−	5.33023i	0.571461	−	0.989799i	0.996416	−	0.0845847i	$-0.0269564\pi$
$30$	−1.16942	−	0.675164i	−0.213506	−	0.123267i
$31$	−0.112859	−	0.421196i	−0.0202701	−	0.0756491i	0.955050	−	0.296445i	$-0.0958012\pi$
$31$	−0.112859	−	0.421196i	−0.0202701	−	0.0756491i	−0.975320	+	0.220796i	$0.929135\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	−2.57289	+	0.689405i	−0.447883	+	0.120010i
$34$	−3.70903	−	3.70903i	−0.636093	−	0.636093i
$35$	3.05905	−	1.84551i	0.517073	−	0.311949i
$36$	0.866025	+	0.500000i	0.144338	+	0.0833333i
$37$	1.94672	−	1.94672i	0.320039	−	0.320039i	−0.528743	−	0.848782i	$-0.677336\pi$
$37$	1.94672	−	1.94672i	0.320039	−	0.320039i	0.848782	+	0.528743i	$0.177336\pi$
$38$	−3.45229	+	5.97954i	−0.560035	+	0.970009i
$39$	3.57313	−	0.482416i	0.572159	−	0.0772484i
$40$	−1.16942	+	0.675164i	−0.184901	+	0.106753i
$41$	−2.81615	−	10.5100i	−0.439808	−	1.64139i	−0.729291	−	0.684203i	$-0.760150\pi$
$41$	−2.81615	−	10.5100i	−0.439808	−	1.64139i	0.289483	−	0.957183i	$-0.406517\pi$
$42$	−2.26541	+	1.36672i	−0.349560	+	0.210889i
$43$	6.74810	−	3.89602i	1.02908	−	0.594137i	0.112356	−	0.993668i	$-0.464160\pi$
$43$	6.74810	−	3.89602i	1.02908	−	0.594137i	0.916720	+	0.399531i	$0.130827\pi$
$44$	−0.689405	+	2.57289i	−0.103932	+	0.387878i
$45$	−0.954826	+	0.954826i	−0.142337	+	0.142337i
$46$	0.185597	−	0.185597i	0.0273648	−	0.0273648i
$47$	−1.48760	+	5.55179i	−0.216988	+	0.809812i	0.768469	+	0.639887i	$0.221019\pi$
$47$	−1.48760	+	5.55179i	−0.216988	+	0.809812i	−0.985457	+	0.169924i	$0.945648\pi$
$48$	0.866025	−	0.500000i	0.125000	−	0.0721688i
$49$	−0.269318	−	6.99482i	−0.0384740	−	0.999260i
$50$	0.822169	+	3.06837i	0.116272	+	0.433934i
$51$	−4.54261	+	2.62268i	−0.636093	+	0.367248i
$52$	1.36878	−	3.33563i	0.189816	−	0.462569i
$53$	0.878238	−	1.52115i	0.120635	−	0.208946i	−0.799383	−	0.600822i	$-0.794840\pi$
$53$	0.878238	−	1.52115i	0.120635	−	0.208946i	0.920018	+	0.391875i	$0.128174\pi$
$54$	0.707107	−	0.707107i	0.0962250	−	0.0962250i
$55$	−3.11493	−	1.79840i	−0.420017	−	0.242497i
$56$	0.0509058	+	2.64526i	0.00680257	+	0.353488i
$57$	4.88227	+	4.88227i	0.646673	+	0.646673i
$58$	−5.94510	+	1.59298i	−0.780630	+	0.209169i
$59$	−6.09059	−	6.09059i	−0.792927	−	0.792927i	0.189042	−	0.981969i	$-0.439462\pi$
$59$	−6.09059	−	6.09059i	−0.792927	−	0.792927i	−0.981969	+	0.189042i	$0.939462\pi$
$60$	0.349490	+	1.30432i	0.0451190	+	0.168387i
$61$	−7.62133	−	4.40017i	−0.975811	−	0.563385i	−0.0748080	−	0.997198i	$-0.523834\pi$
$61$	−7.62133	−	4.40017i	−0.975811	−	0.563385i	−0.901003	+	0.433813i	$0.857168\pi$
$62$	−0.218027	+	0.377634i	−0.0276895	+	0.0479596i
$63$	0.733815	+	2.54195i	0.0924520	+	0.320256i
$64$		−	1.00000i		−	0.125000i
$65$	3.87234	+	2.95110i	0.480305	+	0.366038i
$66$	2.30679	+	1.33183i	0.283947	+	0.163937i
$67$	−2.68089	+	10.0052i	−0.327523	+	1.22233i	0.584228	+	0.811589i	$0.301397\pi$
$67$	−2.68089	+	10.0052i	−0.327523	+	1.22233i	−0.911751	+	0.410743i	$0.865269\pi$
$68$			5.24536i			0.636093i
$69$	−0.131237	−	0.227309i	−0.0157991	−	0.0273648i
$70$	−3.46805	−	0.858097i	−0.414511	−	0.102562i
$71$	1.08417	−	4.04618i	0.128667	−	0.480193i	−0.871276	−	0.490793i	$-0.836707\pi$
$71$	1.08417	−	4.04618i	0.128667	−	0.480193i	0.999944	+	0.0105994i	$0.00337396\pi$
$72$	−0.258819	−	0.965926i	−0.0305021	−	0.113835i
$73$	4.86981	−	1.30486i	0.569968	−	0.152723i	0.0376862	−	0.999290i	$-0.488001\pi$
$73$	4.86981	−	1.30486i	0.569968	−	0.152723i	0.532282	+	0.846567i	$0.321335\pi$
$74$	−2.75308			−0.320039
$75$	3.17662			0.366804
$76$	6.66931	−	1.78704i	0.765022	−	0.204987i
$77$	−6.03427	+	3.64046i	−0.687669	+	0.414869i
$78$	−2.86771	−	2.18547i	−0.324704	−	0.247455i
$79$	3.12948	+	5.42042i	0.352094	+	0.609845i	0.986616	−	0.163060i	$-0.0521364\pi$
$79$	3.12948	+	5.42042i	0.352094	+	0.609845i	−0.634522	+	0.772905i	$0.718803\pi$
$80$	1.30432	+	0.349490i	0.145827	+	0.0390742i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−5.44038	+	9.42301i	−0.600789	+	1.04060i
$83$	9.32218	−	9.32218i	1.02324	−	1.02324i	0.0235188	−	0.999723i	$-0.492513\pi$
$83$	9.32218	−	9.32218i	1.02324	−	1.02324i	0.999723	−	0.0235188i	$-0.00748696\pi$
$84$	2.56830	+	0.635473i	0.280225	+	0.0693358i
$85$	−6.84160	−	1.83320i	−0.742076	−	0.198839i
$86$	−7.52653	−	2.01673i	−0.811606	−	0.217469i
$87$			6.15482i			0.659866i
$88$	2.30679	−	1.33183i	0.245905	−	0.141973i
$89$	4.38711	+	4.38711i	0.465033	+	0.465033i	0.900301	−	0.435268i	$-0.143346\pi$
$89$	4.38711	+	4.38711i	0.465033	+	0.465033i	−0.435268	+	0.900301i	$0.643346\pi$
$90$	1.35033			0.142337
$91$	8.72872	−	3.84830i	0.915019	−	0.403411i
$92$	−0.262474			−0.0273648
$93$	0.308337	+	0.308337i	0.0319731	+	0.0319731i
$94$	4.97760	−	2.87382i	0.513400	−	0.296412i
$95$			9.32344i			0.956565i
$96$	−0.965926	−	0.258819i	−0.0985844	−	0.0264156i
$97$	−18.5733	−	4.97669i	−1.88583	−	0.505306i	−0.999072	−	0.0430700i	$-0.986286\pi$
$97$	−18.5733	−	4.97669i	−1.88583	−	0.505306i	−0.886757	−	0.462236i	$-0.847047\pi$
$98$	−4.75565	+	5.13652i	−0.480393	+	0.518867i
$99$	1.88349	−	1.88349i	0.189298	−	0.189298i
$100$	1.58831	−	2.75103i	0.158831	−	0.275103i
$101$	1.56497	+	2.71061i	0.155721	+	0.269716i	0.933321	−	0.359043i	$-0.116897\pi$
$101$	1.56497	+	2.71061i	0.155721	+	0.269716i	−0.777601	+	0.628759i	$0.783563\pi$
$102$	5.06662	+	1.35760i	0.501671	+	0.134422i
$103$	5.32608	+	9.22505i	0.524795	+	0.908971i	0.999583	+	0.0288710i	$0.00919119\pi$
$103$	5.32608	+	9.22505i	0.524795	+	0.908971i	−0.474789	+	0.880100i	$0.657475\pi$
$104$	−3.32652	+	1.39077i	−0.326192	+	0.136376i
$105$	−1.72645	+	3.12779i	−0.168485	+	0.305241i
$106$	−1.69662	+	0.454609i	−0.164791	+	0.0441556i
$107$	9.01487			0.871500			0.435750	−	0.900068i	$-0.356483\pi$
$107$	9.01487			0.871500			0.435750	+	0.900068i	$0.356483\pi$
$108$	−1.00000			−0.0962250
$109$	−12.0575	+	3.23079i	−1.15490	+	0.309453i	−0.784925	−	0.619590i	$-0.787299\pi$
$109$	−12.0575	+	3.23079i	−1.15490	+	0.309453i	−0.369970	+	0.929044i	$0.620632\pi$
$110$	0.930922	+	3.47425i	0.0887600	+	0.331257i
$111$	−0.712550	+	2.65927i	−0.0676323	+	0.252407i
$112$	1.83449	−	1.90648i	0.173343	−	0.180145i
$113$	−0.0386809	−	0.0669973i	−0.00363879	−	0.00630257i	0.864200	−	0.503148i	$-0.167825\pi$
$113$	−0.0386809	−	0.0669973i	−0.00363879	−	0.00630257i	−0.867839	+	0.496845i	$0.834492\pi$
$114$		−	6.90457i		−	0.646673i
$115$	0.0917321	−	0.342349i	0.00855406	−	0.0319242i
$116$	5.33023	+	3.07741i	0.494899	+	0.285730i
$117$	−2.85322	+	2.20435i	−0.263780	+	0.203792i
$118$			8.61339i			0.792927i
$119$	−9.62253	+	10.0002i	−0.882096	+	0.916713i
$120$	0.675164	−	1.16942i	0.0616337	−	0.106753i
$121$	−3.38178	−	1.95247i	−0.307434	−	0.177497i
$122$	2.27770	+	8.50048i	0.206213	+	0.769598i
$123$	7.69386	+	7.69386i	0.693732	+	0.693732i
$124$	0.421196	−	0.112859i	0.0378246	−	0.0101351i
$125$	7.80724	+	7.80724i	0.698301	+	0.698301i
$126$	1.27855	−	2.31632i	0.113902	−	0.206354i
$127$	12.3722	+	7.14308i	1.09785	+	0.633846i	0.935656	−	0.352913i	$-0.114809\pi$
$127$	12.3722	+	7.14308i	1.09785	+	0.633846i	0.162197	+	0.986758i	$0.448142\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	−3.89602	+	6.74810i	−0.343025	+	0.594137i
$130$	−0.651419	−	4.82490i	−0.0571333	−	0.423172i
$131$	10.4094	−	6.00988i	0.909475	−	0.525086i	0.0292128	−	0.999573i	$-0.490700\pi$
$131$	10.4094	−	6.00988i	0.909475	−	0.525086i	0.880262	+	0.474488i	$0.157367\pi$
$132$	−0.689405	−	2.57289i	−0.0600050	−	0.223942i
$133$	15.9932	+	8.82781i	1.38678	+	0.765468i
$134$	8.97043	−	5.17908i	0.774928	−	0.447405i
$135$	0.349490	−	1.30432i	0.0300794	−	0.112258i
$136$	3.70903	−	3.70903i	0.318046	−	0.318046i
$137$	−2.26186	+	2.26186i	−0.193244	+	0.193244i	−0.797096	−	0.603852i	$-0.793632\pi$
$137$	−2.26186	+	2.26186i	−0.193244	+	0.193244i	0.603852	+	0.797096i	$0.293632\pi$
$138$	−0.0679332	+	0.253530i	−0.00578286	+	0.0215819i
$139$	5.23898	−	3.02473i	0.444365	−	0.256554i	−0.261083	−	0.965316i	$-0.584079\pi$
$139$	5.23898	−	3.02473i	0.444365	−	0.256554i	0.705447	+	0.708762i	$0.250746\pi$
$140$	1.84551	+	3.05905i	0.155974	+	0.258537i
$141$	−1.48760	−	5.55179i	−0.125278	−	0.467545i
$142$	−3.62770	+	2.09446i	−0.304430	+	0.175763i
$143$	−7.63858	−	5.82133i	−0.638770	−	0.486804i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−5.87678	+	5.87678i	−0.488040	+	0.488040i
$146$	−4.36615	−	2.52080i	−0.361345	−	0.208623i
$147$	3.73064	+	5.92303i	0.307698	+	0.488523i
$148$	1.94672	+	1.94672i	0.160020	+	0.160020i
$149$	2.65415	−	0.711179i	0.217437	−	0.0582620i	−0.148456	−	0.988919i	$-0.547430\pi$
$149$	2.65415	−	0.711179i	0.217437	−	0.0582620i	0.365893	+	0.930657i	$0.380764\pi$
$150$	−2.24621	−	2.24621i	−0.183402	−	0.183402i
$151$	3.25321	+	12.1411i	0.264742	+	0.988032i	0.962408	+	0.271608i	$0.0875556\pi$
$151$	3.25321	+	12.1411i	0.264742	+	0.988032i	−0.697665	+	0.716424i	$0.745778\pi$
$152$	−5.97954	−	3.45229i	−0.485004	−	0.280017i
$153$	2.62268	−	4.54261i	0.212031	−	0.367248i
$154$	6.84107	+	1.69268i	0.551269	+	0.136400i
$155$			0.588817i			0.0472949i
$156$	0.482416	+	3.57313i	0.0386242	+	0.286080i
$157$	−4.58939	−	2.64969i	−0.366273	−	0.211468i	0.305556	−	0.952174i	$-0.401158\pi$
$157$	−4.58939	−	2.64969i	−0.366273	−	0.211468i	−0.671829	+	0.740706i	$0.734491\pi$
$158$	1.61994	−	6.04569i	0.128875	−	0.480969i
$159$			1.75648i			0.139298i
$160$	−0.675164	−	1.16942i	−0.0533764	−	0.0924506i
$161$	−0.500401	−	0.481505i	−0.0394371	−	0.0379479i
$162$	−0.258819	+	0.965926i	−0.0203347	+	0.0758903i
$163$	−6.38996	−	23.8476i	−0.500500	−	1.86789i	−0.496742	−	0.867898i	$-0.665470\pi$
$163$	−6.38996	−	23.8476i	−0.500500	−	1.86789i	−0.00375811	−	0.999993i	$-0.501196\pi$
$164$	10.5100	−	2.81615i	0.820693	−	0.219904i
$165$	3.59681			0.280011
$166$	−13.1836			−1.02324
$167$	−23.6159	+	6.32787i	−1.82745	+	0.489665i	−0.997658	−	0.0684012i	$-0.978210\pi$
$167$	−23.6159	+	6.32787i	−1.82745	+	0.489665i	−0.829796	+	0.558066i	$0.811544\pi$
$168$	−1.36672	−	2.26541i	−0.105444	−	0.174780i
$169$	9.25287	+	9.13150i	0.711759	+	0.702423i
$170$	3.54147	+	6.13401i	0.271619	+	0.470457i
$171$	−6.66931	−	1.78704i	−0.510015	−	0.136658i
$172$	3.89602	+	6.74810i	0.297069	+	0.514538i
$173$	0.169053	−	0.292808i	0.0128528	−	0.0222618i	−0.859527	−	0.511090i	$-0.829242\pi$
$173$	0.169053	−	0.292808i	0.0128528	−	0.0222618i	0.872380	+	0.488828i	$0.162575\pi$
$174$	4.35211	−	4.35211i	0.329933	−	0.329933i
$175$	8.07480	−	2.33105i	0.610398	−	0.176211i
$176$	−2.57289	−	0.689405i	−0.193939	−	0.0519658i
$177$	8.31990	+	2.22931i	0.625362	+	0.167565i
$178$		−	6.20432i		−	0.465033i
$179$	4.80858	−	2.77624i	0.359410	−	0.207506i	−0.309412	−	0.950928i	$-0.600132\pi$
$179$	4.80858	−	2.77624i	0.359410	−	0.207506i	0.668822	+	0.743423i	$0.266799\pi$
$180$	−0.954826	−	0.954826i	−0.0711685	−	0.0711685i
$181$	−8.08476			−0.600935			−0.300468	−	0.953792i	$-0.597143\pi$
$181$	−8.08476			−0.600935			−0.300468	+	0.953792i	$0.597143\pi$
$182$	−8.89330	−	3.45098i	−0.659215	−	0.255804i
$183$	8.80035			0.650541
$184$	0.185597	+	0.185597i	0.0136824	+	0.0136824i
$185$	−3.21950	+	1.85878i	−0.236703	+	0.136660i
$186$		−	0.436055i		−	0.0319731i
$187$	13.4957	+	3.61617i	0.986906	+	0.264441i
$188$	−5.55179	−	1.48760i	−0.404906	−	0.108494i
$189$	−1.90648	−	1.83449i	−0.138676	−	0.133439i
$190$	6.59267	−	6.59267i	0.478282	−	0.478282i
$191$	6.68460	−	11.5781i	0.483681	−	0.837759i	−0.516144	−	0.856502i	$-0.672633\pi$
$191$	6.68460	−	11.5781i	0.483681	−	0.837759i	0.999824	+	0.0187426i	$0.00596631\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−9.13181	−	2.44686i	−0.657322	−	0.176129i	−0.0852847	−	0.996357i	$-0.527180\pi$
$193$	−9.13181	−	2.44686i	−0.657322	−	0.176129i	−0.572037	+	0.820228i	$0.693847\pi$
$194$	9.61423	+	16.6523i	0.690261	+	1.19557i
$195$	−4.82909	−	0.619553i	−0.345819	−	0.0443671i
$196$	6.99482	−	0.269318i	0.499630	−	0.0192370i
$197$	11.1496	−	2.98754i	0.794379	−	0.212853i	0.161265	−	0.986911i	$-0.448443\pi$
$197$	11.1496	−	2.98754i	0.794379	−	0.212853i	0.633115	+	0.774058i	$0.281776\pi$
$198$	−2.66366			−0.189298
$199$	−2.25391			−0.159775			−0.0798877	−	0.996804i	$-0.525456\pi$
$199$	−2.25391			−0.159775			−0.0798877	+	0.996804i	$0.525456\pi$
$200$	−3.06837	+	0.822169i	−0.216967	+	0.0581361i
$201$	−2.68089	−	10.0052i	−0.189095	−	0.705714i
$202$	0.810090	−	3.02330i	0.0569977	−	0.212718i
$203$	4.51650	+	15.6453i	0.316996	+	1.09808i
$204$	−2.62268	−	4.54261i	−0.183624	−	0.318046i
$205$			14.6926i			1.02617i
$206$	2.75698	−	10.2892i	0.192088	−	0.716883i
$207$	0.227309	+	0.131237i	0.0157991	+	0.00912160i
$208$	3.33563	+	1.36878i	0.231284	+	0.0949079i
$209$		−	18.3914i		−	1.27216i
$210$	3.43247	−	0.990891i	0.236863	−	0.0683780i
$211$	−11.1990	+	19.3972i	−0.770968	+	1.33536i	0.166065	+	0.986115i	$0.446894\pi$
$211$	−11.1990	+	19.3972i	−0.770968	+	1.33536i	−0.937033	+	0.349241i	$0.886439\pi$
$212$	1.52115	+	0.878238i	0.104473	+	0.0603176i
$213$	1.08417	+	4.04618i	0.0742861	+	0.277240i
$214$	−6.37447	−	6.37447i	−0.435750	−	0.435750i
$215$	−10.1633	+	2.72324i	−0.693130	+	0.185724i
$216$	0.707107	+	0.707107i	0.0481125	+	0.0481125i
$217$	1.01004	+	0.557515i	0.0685660	+	0.0378466i
$218$	10.8104	+	6.24140i	0.732174	+	0.422721i
$219$	−3.56495	+	3.56495i	−0.240897	+	0.240897i
$220$	1.79840	−	3.11493i	0.121248	−	0.210008i
$221$	−17.4966	−	7.17975i	−1.17695	−	0.482962i
$222$	2.38424	−	1.37654i	0.160020	−	0.0923874i
$223$	−4.52520	−	16.8883i	−0.303030	−	1.13092i	−0.934628	−	0.355627i	$-0.884267\pi$
$223$	−4.52520	−	16.8883i	−0.303030	−	1.13092i	0.631598	−	0.775296i	$-0.282399\pi$
$224$	−2.64526	+	0.0509058i	−0.176744	+	0.00340128i
$225$	−2.75103	+	1.58831i	−0.183402	+	0.105887i
$226$	−0.0200227	+	0.0747257i	−0.00133189	+	0.00497068i
$227$	−17.5722	+	17.5722i	−1.16631	+	1.16631i	−0.183240	+	0.983068i	$0.558658\pi$
$227$	−17.5722	+	17.5722i	−1.16631	+	1.16631i	−0.983068	+	0.183240i	$0.941342\pi$
$228$	−4.88227	+	4.88227i	−0.323336	+	0.323336i
$229$	0.302393	−	1.12855i	0.0199827	−	0.0745765i	−0.955214	−	0.295914i	$-0.904376\pi$
$229$	0.302393	−	1.12855i	0.0199827	−	0.0745765i	0.975197	+	0.221338i	$0.0710424\pi$
$230$	−0.306942	+	0.177213i	−0.0202391	+	0.0116851i
$231$	3.40560	−	6.16987i	0.224072	−	0.405948i
$232$	−1.59298	−	5.94510i	−0.104585	−	0.390315i
$233$	−10.0524	+	5.80374i	−0.658553	+	0.380216i	−0.791725	−	0.610877i	$-0.790817\pi$
$233$	−10.0524	+	5.80374i	−0.658553	+	0.380216i	0.133172	+	0.991093i	$0.457484\pi$
$234$	3.57624	+	0.458817i	0.233786	+	0.0299938i
$235$	3.88060	−	6.72139i	0.253142	−	0.438455i
$236$	6.09059	−	6.09059i	0.396464	−	0.396464i
$237$	−5.42042	−	3.12948i	−0.352094	−	0.203282i
$238$	13.8753	−	0.267019i	0.899404	−	0.0173083i
$239$	−18.3896	−	18.3896i	−1.18952	−	1.18952i	−0.977199	−	0.212325i	$-0.931897\pi$
$239$	−18.3896	−	18.3896i	−1.18952	−	1.18952i	−0.212325	−	0.977199i	$-0.568103\pi$
$240$	−1.30432	+	0.349490i	−0.0841933	+	0.0225595i
$241$	−21.0520	−	21.0520i	−1.35608	−	1.35608i	−0.878691	−	0.477390i	$-0.841583\pi$
$241$	−21.0520	−	21.0520i	−1.35608	−	1.35608i	−0.477390	−	0.878691i	$-0.658417\pi$
$242$	1.01067	+	3.77188i	0.0649685	+	0.242466i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	4.40017	−	7.62133i	0.281692	−	0.487905i
$245$	−2.09335	+	9.21758i	−0.133739	+	0.588889i
$246$		−	10.8808i		−	0.693732i
$247$	−3.16793	+	24.6924i	−0.201571	+	1.57114i
$248$	−0.377634	−	0.218027i	−0.0239798	−	0.0138447i
$249$	−3.41215	+	12.7343i	−0.216237	+	0.807006i
$250$		−	11.0411i		−	0.698301i
$251$	1.09799	+	1.90177i	0.0693042	+	0.120038i	0.898595	−	0.438779i	$-0.144589\pi$
$251$	1.09799	+	1.90177i	0.0693042	+	0.120038i	−0.829291	+	0.558817i	$0.811255\pi$
$252$	−2.54195	+	0.733815i	−0.160128	+	0.0462260i
$253$	−0.180951	+	0.675317i	−0.0113763	+	0.0424568i
$254$	−3.69753	−	13.7994i	−0.232004	−	0.865849i
$255$	6.84160	−	1.83320i	0.428438	−	0.114800i
$256$	1.00000			0.0625000
$257$	−9.37596			−0.584857			−0.292428	−	0.956287i	$-0.594463\pi$
$257$	−9.37596			−0.584857			−0.292428	+	0.956287i	$0.594463\pi$
$258$	7.52653	−	2.01673i	0.468581	−	0.125556i
$259$	0.140148	+	7.28262i	0.00870836	+	0.452520i
$260$	−2.95110	+	3.87234i	−0.183019	+	0.240152i
$261$	−3.07741	−	5.33023i	−0.190487	−	0.329933i
$262$	−11.6102	−	3.11094i	−0.717280	−	0.192195i
$263$	−12.3607	−	21.4093i	−0.762192	−	1.32016i	−0.941718	−	0.336402i	$-0.890790\pi$
$263$	−12.3607	−	21.4093i	−0.762192	−	1.32016i	0.179526	−	0.983753i	$-0.442543\pi$
$264$	−1.33183	+	2.30679i	−0.0819683	+	0.141973i
$265$	−1.67713	+	1.67713i	−0.103025	+	0.103025i
$266$	−5.06668	−	17.5511i	−0.310658	−	1.07613i
$267$	−5.99291	−	1.60580i	−0.366760	−	0.0982731i
$268$	−10.0052	−	2.68089i	−0.611166	−	0.163761i
$269$		−	19.2352i		−	1.17279i	−0.810025	−	0.586395i	$-0.800547\pi$
$269$		−	19.2352i		−	1.17279i	0.810025	−	0.586395i	$-0.199453\pi$
$270$	−1.16942	+	0.675164i	−0.0711685	+	0.0410892i
$271$	0.615634	+	0.615634i	0.0373971	+	0.0373971i	0.725558	−	0.688161i	$-0.241582\pi$
$271$	0.615634	+	0.615634i	0.0373971	+	0.0373971i	−0.688161	+	0.725558i	$0.741582\pi$
$272$	−5.24536			−0.318046
$273$	−5.63515	+	7.69708i	−0.341055	+	0.465849i
$274$	3.19876			0.193244
$275$	−5.98312	−	5.98312i	−0.360796	−	0.360796i
$276$	0.227309	−	0.131237i	0.0136824	−	0.00789954i
$277$		−	21.1989i		−	1.27372i	−0.770980	−	0.636859i	$-0.780233\pi$
$277$		−	21.1989i		−	1.27372i	0.770980	−	0.636859i	$-0.219767\pi$
$278$	−5.84333	−	1.56571i	−0.350459	−	0.0939053i
$279$	−0.421196	−	0.112859i	−0.0252164	−	0.00675671i
$280$	0.858097	−	3.46805i	0.0512811	−	0.207256i
$281$	20.7859	−	20.7859i	1.23999	−	1.23999i	0.279980	−	0.960006i	$-0.409672\pi$
$281$	20.7859	−	20.7859i	1.23999	−	1.23999i	0.960006	−	0.279980i	$-0.0903278\pi$
$282$	−2.87382	+	4.97760i	−0.171133	+	0.296412i
$283$	7.09128	+	12.2825i	0.421533	+	0.730116i	0.996090	−	0.0883485i	$-0.0281589\pi$
$283$	7.09128	+	12.2825i	0.421533	+	0.730116i	−0.574557	+	0.818465i	$0.694826\pi$
$284$	4.04618	+	1.08417i	0.240097	+	0.0643337i
$285$	−4.66172	−	8.07433i	−0.276136	−	0.478282i
$286$	1.28499	+	9.51759i	0.0759830	+	0.562787i
$287$	25.2033	+	13.9115i	1.48770	+	0.821172i
$288$	0.965926	−	0.258819i	0.0569177	−	0.0152511i
$289$	10.5137			0.618456
$290$	8.31102			0.488040
$291$	18.5733	−	4.97669i	1.08878	−	0.291739i
$292$	1.30486	+	4.86981i	0.0763613	+	0.284984i
$293$	0.832864	−	3.10829i	0.0486564	−	0.181588i	−0.937321	−	0.348467i	$-0.886702\pi$
$293$	0.832864	−	3.10829i	0.0486564	−	0.181588i	0.985977	+	0.166879i	$0.0533689\pi$
$294$	1.55025	−	6.82618i	0.0904125	−	0.398111i
$295$	5.81545	+	10.0727i	0.338589	+	0.586453i
$296$		−	2.75308i		−	0.160020i
$297$	−0.689405	+	2.57289i	−0.0400033	+	0.149294i
$298$	−2.37965	−	1.37389i	−0.137849	−	0.0795874i
$299$	0.359269	−	0.875516i	0.0207771	−	0.0506324i
$300$			3.17662i			0.183402i
$301$	−4.95163	+	20.0123i	−0.285407	+	1.15349i
$302$	6.28472	−	10.8855i	0.361645	−	0.626387i
$303$	−2.71061	−	1.56497i	−0.155721	−	0.0899053i
$304$	1.78704	+	6.66931i	0.102494	+	0.382511i
$305$	8.40280	+	8.40280i	0.481143	+	0.481143i
$306$	−5.06662	+	1.35760i	−0.289640	+	0.0776087i
$307$	−6.69970	−	6.69970i	−0.382372	−	0.382372i	0.489584	−	0.871956i	$-0.337149\pi$
$307$	−6.69970	−	6.69970i	−0.382372	−	0.382372i	−0.871956	+	0.489584i	$0.837149\pi$
$308$	−3.64046	−	6.03427i	−0.207435	−	0.343835i
$309$	−9.22505	−	5.32608i	−0.524795	−	0.302990i
$310$	0.416356	−	0.416356i	0.0236474	−	0.0236474i
$311$	−16.2316	+	28.1140i	−0.920411	+	1.59420i	−0.121631	+	0.992575i	$0.538813\pi$
$311$	−16.2316	+	28.1140i	−0.920411	+	1.59420i	−0.798780	+	0.601624i	$0.794521\pi$
$312$	2.18547	−	2.86771i	0.123728	−	0.162352i
$313$	17.6916	−	10.2143i	0.999989	−	0.577344i	0.0917443	−	0.995783i	$-0.470756\pi$
$313$	17.6916	−	10.2143i	0.999989	−	0.577344i	0.908245	+	0.418438i	$0.137422\pi$
$314$	1.37158	+	5.11880i	0.0774026	+	0.288871i
$315$	−0.0687394	−	3.57197i	−0.00387303	−	0.201258i
$316$	−5.42042	+	3.12948i	−0.304922	+	0.176047i
$317$	0.944317	−	3.52424i	0.0530381	−	0.197941i	−0.934323	−	0.356427i	$-0.883995\pi$
$317$	0.944317	−	3.52424i	0.0530381	−	0.197941i	0.987361	+	0.158486i	$0.0506614\pi$
$318$	1.24202	−	1.24202i	0.0696488	−	0.0696488i
$319$	11.5925	−	11.5925i	0.649057	−	0.649057i
$320$	−0.349490	+	1.30432i	−0.0195371	+	0.0729135i
$321$	−7.80711	+	4.50743i	−0.435750	+	0.251580i
$322$	0.0133614	+	0.694312i	0.000744603	+	0.0386925i
$323$	−9.37364	−	34.9829i	−0.521563	−	1.94650i
$324$	0.866025	−	0.500000i	0.0481125	−	0.0277778i
$325$	7.00237	+	9.06357i	0.388422	+	0.502756i
$326$	−12.3444	+	21.3812i	−0.683696	+	1.18420i
$327$	8.82668	−	8.82668i	0.488116	−	0.488116i
$328$	−9.42301	−	5.44038i	−0.520299	−	0.300395i
$329$	−7.85539	−	13.0208i	−0.433082	−	0.717858i
$330$	−2.54333	−	2.54333i	−0.140006	−	0.140006i
$331$	−2.18594	+	0.585722i	−0.120150	+	0.0321942i	−0.318393	−	0.947959i	$-0.603143\pi$
$331$	−2.18594	+	0.585722i	−0.120150	+	0.0321942i	0.198243	+	0.980153i	$0.436477\pi$
$332$	9.32218	+	9.32218i	0.511621	+	0.511621i
$333$	−0.712550	−	2.65927i	−0.0390475	−	0.145727i
$334$	21.1734	+	12.2245i	1.15856	+	0.668895i
$335$	6.99346	−	12.1130i	0.382093	−	0.661805i
$336$	−0.635473	+	2.56830i	−0.0346679	+	0.140112i
$337$			17.8521i			0.972466i	0.873829	+	0.486233i	$0.161629\pi$
$337$			17.8521i			0.972466i	−0.873829	+	0.486233i	$0.838371\pi$
$338$	−0.0858213	−	12.9997i	−0.00466806	−	0.707091i
$339$	0.0669973	+	0.0386809i	0.00363879	+	0.00210086i
$340$	1.83320	−	6.84160i	0.0994193	−	0.371038i
$341$		−	1.16150i		−	0.0628987i
$342$	3.45229	+	5.97954i	0.186678	+	0.323336i
$343$	13.8295	+	12.3184i	0.746724	+	0.665134i
$344$	2.01673	−	7.52653i	0.108735	−	0.405803i
$345$	0.0917321	+	0.342349i	0.00493869	+	0.0184314i
$346$	−0.326585	+	0.0875081i	−0.0175573	+	0.00470446i
$347$	15.6971			0.842664			0.421332	−	0.906906i	$-0.361563\pi$
$347$	15.6971			0.842664			0.421332	+	0.906906i	$0.361563\pi$
$348$	−6.15482			−0.329933
$349$	28.8777	−	7.73776i	1.54579	−	0.414193i	0.617658	−	0.786447i	$-0.288082\pi$
$349$	28.8777	−	7.73776i	1.54579	−	0.414193i	0.928131	+	0.372254i	$0.121415\pi$
$350$	−7.35805	−	4.06145i	−0.393304	−	0.217093i
$351$	1.36878	−	3.33563i	0.0730602	−	0.178043i
$352$	1.33183	+	2.30679i	0.0709867	+	0.122952i
$353$	−25.9664	−	6.95768i	−1.38205	−	0.370320i	−0.510187	−	0.860064i	$-0.670424\pi$
$353$	−25.9664	−	6.95768i	−1.38205	−	0.370320i	−0.871866	+	0.489744i	$0.837090\pi$
$354$	−4.30670	−	7.45942i	−0.228898	−	0.396464i
$355$	−2.82820	+	4.89859i	−0.150105	+	0.259990i
$356$	−4.38711	+	4.38711i	−0.232517	+	0.232517i
$357$	3.33328	−	13.4717i	0.176416	−	0.712996i
$358$	−5.36328	−	1.43709i	−0.283458	−	0.0759523i
$359$	29.6332	+	7.94019i	1.56398	+	0.419067i	0.933921	−	0.357480i	$-0.116364\pi$
$359$	29.6332	+	7.94019i	1.56398	+	0.419067i	0.630059	+	0.776547i	$0.283031\pi$
$360$			1.35033i			0.0711685i
$361$	−24.8317	+	14.3366i	−1.30693	+	0.754557i
$362$	5.71679	+	5.71679i	0.300468	+	0.300468i
$363$	3.90494			0.204956
$364$	3.84830	+	8.72872i	0.201706	+	0.457509i
$365$	−6.80781			−0.356337
$366$	−6.22279	−	6.22279i	−0.325270	−	0.325270i
$367$	13.0369	−	7.52686i	0.680521	−	0.392899i	−0.119530	−	0.992831i	$-0.538139\pi$
$367$	13.0369	−	7.52686i	0.680521	−	0.392899i	0.800051	+	0.599931i	$0.204805\pi$
$368$		−	0.262474i		−	0.0136824i
$369$	−10.5100	−	2.81615i	−0.547129	−	0.146603i
$370$	3.59089	+	0.962176i	0.186681	+	0.0500212i
$371$	1.28893	+	4.46487i	0.0669178	+	0.231805i
$372$	−0.308337	+	0.308337i	−0.0159865	+	0.0159865i
$373$	−5.31715	+	9.20957i	−0.275311	+	0.476853i	−0.970214	−	0.242251i	$-0.922114\pi$
$373$	−5.31715	+	9.20957i	−0.275311	+	0.476853i	0.694902	+	0.719104i	$0.255448\pi$
$374$	−6.98591	−	12.0999i	−0.361233	−	0.625674i
$375$	−10.6649	−	2.85765i	−0.550733	−	0.147568i
$376$	2.87382	+	4.97760i	0.148206	+	0.256700i
$377$	−17.5610	+	13.5674i	−0.904439	+	0.698756i
$378$	0.0509058	+	2.64526i	0.00261831	+	0.136058i
$379$	1.39615	−	0.374098i	0.0717156	−	0.0192161i	−0.222783	−	0.974868i	$-0.571514\pi$
$379$	1.39615	−	0.374098i	0.0717156	−	0.0192161i	0.294498	+	0.955652i	$0.404847\pi$
$380$	−9.32344			−0.478282
$381$	−14.2862			−0.731902
$382$	−12.9137	+	3.46020i	−0.660720	+	0.177039i
$383$	6.74887	+	25.1871i	0.344851	+	1.28700i	0.892786	+	0.450480i	$0.148747\pi$
$383$	6.74887	+	25.1871i	0.344851	+	1.28700i	−0.547935	+	0.836521i	$0.684586\pi$
$384$	0.258819	−	0.965926i	0.0132078	−	0.0492922i
$385$	9.14291	−	2.63939i	0.465966	−	0.134516i
$386$	4.72697	+	8.18735i	0.240596	+	0.416725i
$387$		−	7.79203i		−	0.396091i
$388$	4.97669	−	18.5733i	0.252653	−	0.942914i
$389$	4.97819	+	2.87416i	0.252404	+	0.145726i	0.620865	−	0.783918i	$-0.286782\pi$
$389$	4.97819	+	2.87416i	0.252404	+	0.145726i	−0.368460	+	0.929643i	$0.620115\pi$
$390$	2.97660	+	3.85278i	0.150726	+	0.195093i
$391$			1.37677i			0.0696262i
$392$	−5.13652	−	4.75565i	−0.259433	−	0.240196i
$393$	−6.00988	+	10.4094i	−0.303158	+	0.525086i
$394$	−9.99650	−	5.77148i	−0.503616	−	0.290763i
$395$	−2.18745	−	8.16367i	−0.110062	−	0.410759i
$396$	1.88349	+	1.88349i	0.0946489	+	0.0946489i
$397$	15.2138	−	4.07652i	0.763558	−	0.204595i	0.144034	−	0.989573i	$-0.453993\pi$
$397$	15.2138	−	4.07652i	0.763558	−	0.204595i	0.619524	+	0.784978i	$0.287326\pi$
$398$	1.59375	+	1.59375i	0.0798877	+	0.0798877i
$399$	−18.2644	+	0.351483i	−0.914364	+	0.0175961i
$400$	2.75103	+	1.58831i	0.137551	+	0.0794154i
$401$	13.5140	−	13.5140i	0.674857	−	0.674857i	−0.283975	−	0.958832i	$-0.591653\pi$
$401$	13.5140	−	13.5140i	0.674857	−	0.674857i	0.958832	+	0.283975i	$0.0916532\pi$
$402$	−5.17908	+	8.97043i	−0.258309	+	0.447405i
$403$	−0.200069	+	1.55944i	−0.00996615	+	0.0776810i
$404$	−2.71061	+	1.56497i	−0.134858	+	0.0778603i
$405$	0.349490	+	1.30432i	0.0173663	+	0.0648120i
$406$	7.86921	−	14.2565i	0.390543	−	0.707539i
$407$	6.35079	−	3.66663i	0.314797	−	0.181748i
$408$	−1.35760	+	5.06662i	−0.0672111	+	0.250835i
$409$	−12.6759	+	12.6759i	−0.626784	+	0.626784i	−0.947258	−	0.320473i	$-0.896158\pi$
$409$	−12.6759	+	12.6759i	−0.626784	+	0.626784i	0.320473	+	0.947258i	$0.396158\pi$
$410$	10.3892	−	10.3892i	0.513087	−	0.513087i
$411$	0.827900	−	3.08976i	0.0408373	−	0.152407i
$412$	−9.22505	+	5.32608i	−0.454485	+	0.262397i
$413$	22.7847	−	0.438471i	1.12116	−	0.0215758i
$414$	−0.0679332	−	0.253530i	−0.00333874	−	0.0124603i
$415$	−15.4171	+	8.90106i	−0.756795	+	0.436936i
$416$	−1.39077	−	3.32652i	−0.0681882	−	0.163096i
$417$	−3.02473	+	5.23898i	−0.148122	+	0.256554i
$418$	−13.0047	+	13.0047i	−0.636080	+	0.636080i
$419$	4.94418	+	2.85452i	0.241539	+	0.139452i	0.615884	−	0.787837i	$-0.288799\pi$
$419$	4.94418	+	2.85452i	0.241539	+	0.139452i	−0.374345	+	0.927290i	$0.622132\pi$
$420$	−3.12779	−	1.72645i	−0.152620	−	0.0842424i
$421$	11.2327	+	11.2327i	0.547449	+	0.547449i	0.925702	−	0.378253i	$-0.123475\pi$
$421$	11.2327	+	11.2327i	0.547449	+	0.547449i	−0.378253	+	0.925702i	$0.623475\pi$
$422$	21.6347	−	5.79701i	1.05316	−	0.282194i
$423$	4.06419	+	4.06419i	0.197608	+	0.197608i
$424$	−0.454609	−	1.69662i	−0.0220778	−	0.0823954i
$425$	−14.4301	−	8.33124i	−0.699964	−	0.404124i
$426$	2.09446	−	3.62770i	0.101477	−	0.175763i
$427$	22.3701	−	6.45783i	1.08256	−	0.312516i
$428$			9.01487i			0.435750i
$429$	9.52587	+	1.22213i	0.459913	+	0.0590050i
$430$	9.11215	+	5.26090i	0.439427	+	0.253703i
$431$	−4.67687	+	17.4543i	−0.225277	+	0.840744i	0.757017	+	0.653395i	$0.226656\pi$
$431$	−4.67687	+	17.4543i	−0.225277	+	0.840744i	−0.982293	+	0.187349i	$0.940011\pi$
$432$		−	1.00000i		−	0.0481125i
$433$	8.06894	+	13.9758i	0.387768	+	0.671635i	0.992149	−	0.125061i	$-0.0399127\pi$
$433$	8.06894	+	13.9758i	0.387768	+	0.671635i	−0.604381	+	0.796696i	$0.706579\pi$
$434$	−0.319983	−	1.10843i	−0.0153597	−	0.0532063i
$435$	2.15105	−	8.02783i	0.103135	−	0.384905i
$436$	−3.23079	−	12.0575i	−0.154727	−	0.577448i
$437$	1.75052	−	0.469050i	0.0837387	−	0.0224377i
$438$	5.04160			0.240897
$439$	−10.4334			−0.497957			−0.248979	−	0.968509i	$-0.580095\pi$
$439$	−10.4334			−0.497957			−0.248979	+	0.968509i	$0.580095\pi$
$440$	−3.47425	+	0.930922i	−0.165628	+	0.0443800i
$441$	−6.19235	−	3.26417i	−0.294874	−	0.155437i
$442$	7.29510	+	17.4488i	0.346992	+	0.829954i
$443$	0.835906	+	1.44783i	0.0397151	+	0.0687885i	0.885200	−	0.465211i	$-0.154022\pi$
$443$	0.835906	+	1.44783i	0.0397151	+	0.0687885i	−0.845485	+	0.534000i	$0.820688\pi$
$444$	−2.65927	−	0.712550i	−0.126204	−	0.0338161i
$445$	−4.18893	−	7.25544i	−0.198574	−	0.343941i
$446$	−8.74202	+	15.1416i	−0.413947	+	0.716977i
$447$	−1.94298	+	1.94298i	−0.0918996	+	0.0918996i
$448$	1.90648	+	1.83449i	0.0900726	+	0.0866713i
$449$	−0.795385	−	0.213123i	−0.0375366	−	0.0100579i	0.240002	−	0.970772i	$-0.422852\pi$
$449$	−0.795385	−	0.213123i	−0.0375366	−	0.0100579i	−0.277538	+	0.960715i	$0.589519\pi$
$450$	3.06837	+	0.822169i	0.144645	+	0.0387574i
$451$		−	28.9826i		−	1.36474i
$452$	0.0669973	−	0.0386809i	0.00315129	−	0.00181940i
$453$	−8.88793	−	8.88793i	−0.417592	−	0.417592i
$454$	24.8508			1.16631
$455$	−12.7300	+	1.96879i	−0.596790	+	0.0922983i
$456$	6.90457			0.323336
$457$	11.3386	+	11.3386i	0.530399	+	0.530399i	0.920691	−	0.390292i	$-0.127626\pi$
$457$	11.3386	+	11.3386i	0.530399	+	0.530399i	−0.390292	+	0.920691i	$0.627626\pi$
$458$	−1.01183	+	0.584179i	−0.0472796	+	0.0272969i
$459$			5.24536i			0.244832i
$460$	0.342349	+	0.0917321i	0.0159621	+	0.00427703i
$461$	14.6637	+	3.92914i	0.682959	+	0.182998i	0.583585	−	0.812052i	$-0.301649\pi$
$461$	14.6637	+	3.92914i	0.682959	+	0.182998i	0.0993736	+	0.995050i	$0.468316\pi$
$462$	−6.77088	+	1.95463i	−0.315010	+	0.0909377i
$463$	−2.81768	+	2.81768i	−0.130948	+	0.130948i	−0.769543	−	0.638595i	$-0.779516\pi$
$463$	−2.81768	+	2.81768i	−0.130948	+	0.130948i	0.638595	+	0.769543i	$0.279516\pi$
$464$	−3.07741	+	5.33023i	−0.142865	+	0.247450i
$465$	−0.294408	−	0.509930i	−0.0136529	−	0.0236474i
$466$	11.2120	+	3.00424i	0.519384	+	0.139169i
$467$	−2.28797	−	3.96288i	−0.105875	−	0.183380i	0.808221	−	0.588880i	$-0.200431\pi$
$467$	−2.28797	−	3.96288i	−0.105875	−	0.183380i	−0.914095	+	0.405500i	$0.867098\pi$
$468$	−2.20435	−	2.85322i	−0.101896	−	0.131890i
$469$	−14.1567	−	23.4655i	−0.653695	−	1.08354i
$470$	−7.49674	+	2.00874i	−0.345799	+	0.0926565i
$471$	5.29937			0.244182
$472$	−8.61339			−0.396464
$473$	20.0481	−	5.37187i	0.921811	−	0.246999i
$474$	1.61994	+	6.04569i	0.0744062	+	0.277688i
$475$	−5.67672	+	21.1858i	−0.260466	+	0.972072i
$476$	−10.0002	−	9.62253i	−0.458356	−	0.441048i
$477$	−0.878238	−	1.52115i	−0.0402117	−	0.0696488i
$478$			26.0068i			1.18952i
$479$	−10.6135	+	39.6102i	−0.484944	+	1.80983i	0.0953704	+	0.995442i	$0.469596\pi$
$479$	−10.6135	+	39.6102i	−0.484944	+	1.80983i	−0.580314	+	0.814393i	$0.697070\pi$
$480$	1.16942	+	0.675164i	0.0533764	+	0.0308169i
$481$	−9.15819	+	3.82891i	−0.417578	+	0.174583i
$482$			29.7721i			1.35608i
$483$	0.674112	+	0.166795i	0.0306732	+	0.00758944i
$484$	1.95247	−	3.38178i	0.0887486	−	0.153717i
$485$	22.4861	+	12.9824i	1.02104	+	0.589498i
$486$	−0.258819	−	0.965926i	−0.0117403	−	0.0438153i
$487$	−12.9636	−	12.9636i	−0.587438	−	0.587438i	0.349499	−	0.936937i	$-0.386352\pi$
$487$	−12.9636	−	12.9636i	−0.587438	−	0.587438i	−0.936937	+	0.349499i	$0.886352\pi$
$488$	−8.50048	+	2.27770i	−0.384799	+	0.103107i
$489$	17.4577	+	17.4577i	0.789464	+	0.789464i
$490$	7.99803	−	5.03759i	0.361314	−	0.227575i
$491$	−20.5605	−	11.8706i	−0.927883	−	0.535713i	−0.0417413	−	0.999128i	$-0.513291\pi$
$491$	−20.5605	−	11.8706i	−0.927883	−	0.535713i	−0.886141	+	0.463415i	$0.846624\pi$
$492$	−7.69386	+	7.69386i	−0.346866	+	0.346866i
$493$	16.1421	−	27.9590i	0.727004	−	1.25921i
$494$	19.7002	−	15.2201i	0.886356	−	0.684785i
$495$	−3.11493	+	1.79840i	−0.140006	+	0.0808322i
$496$	0.112859	+	0.421196i	0.00506753	+	0.0189123i
$497$	5.72506	+	9.48961i	0.256804	+	0.425667i
$498$	11.4173	−	6.59178i	0.511621	−	0.295385i
$499$	8.99324	−	33.5632i	0.402593	−	1.50250i	−0.405859	−	0.913935i	$-0.633028\pi$
$499$	8.99324	−	33.5632i	0.402593	−	1.50250i	0.808452	−	0.588562i	$-0.200306\pi$
$500$	−7.80724	+	7.80724i	−0.349151	+	0.349151i
$501$	17.2880	−	17.2880i	0.772373	−	0.772373i
$502$	0.568359	−	2.12114i	0.0253671	−	0.0946713i
$503$	12.5876	−	7.26748i	0.561256	−	0.324041i	−0.192394	−	0.981318i	$-0.561625\pi$
$503$	12.5876	−	7.26748i	0.561256	−	0.324041i	0.753649	+	0.657277i	$0.228292\pi$
$504$	2.31632	+	1.27855i	0.103177	+	0.0569509i
$505$	−1.09389	−	4.08244i	−0.0486773	−	0.181666i
$506$	0.605473	−	0.349570i	0.0269166	−	0.0155403i
$507$	−12.5790	−	3.28168i	−0.558652	−	0.145744i
$508$	−7.14308	+	12.3722i	−0.316923	+	0.548927i
$509$	21.8540	−	21.8540i	0.968661	−	0.968661i	−0.0308623	−	0.999524i	$-0.509825\pi$
$509$	21.8540	−	21.8540i	0.968661	−	0.968661i	0.999524	+	0.0308623i	$0.00982535\pi$
$510$	−6.13401	−	3.54147i	−0.271619	−	0.156819i
$511$	−6.44591	+	11.6779i	−0.285150	+	0.516602i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	6.66931	−	1.78704i	0.294457	−	0.0788995i
$514$	6.62981	+	6.62981i	0.292428	+	0.292428i
$515$	−3.72283	−	13.8938i	−0.164048	−	0.612234i
$516$	−6.74810	−	3.89602i	−0.297069	−	0.171513i
$517$	−7.65486	+	13.2586i	−0.336660	+	0.583113i
$518$	5.05049	−	5.24869i	0.221906	−	0.230614i
$519$			0.338105i			0.0148412i
$520$	4.82490	−	0.651419i	0.211586	−	0.0285666i
$521$	37.8760	+	21.8677i	1.65938	+	0.958042i	0.973002	+	0.230795i	$0.0741326\pi$
$521$	37.8760	+	21.8677i	1.65938	+	0.958042i	0.686375	+	0.727247i	$0.259201\pi$
$522$	−1.59298	+	5.94510i	−0.0697230	+	0.260210i
$523$			14.3172i			0.626048i	0.949745	+	0.313024i	$0.101342\pi$
$523$			14.3172i			0.626048i	−0.949745	+	0.313024i	$0.898658\pi$
$524$	6.00988	+	10.4094i	0.262543	+	0.454738i
$525$	−5.82746	+	6.05615i	−0.254331	+	0.264312i
$526$	−6.39836	+	23.8790i	−0.278982	+	1.04117i
$527$	−0.591987	−	2.20932i	−0.0257873	−	0.0962397i
$528$	2.57289	−	0.689405i	0.111971	−	0.0300025i
$529$	22.9311			0.997005
$530$	2.37182			0.103025
$531$	−8.31990	+	2.22931i	−0.361053	+	0.0967438i
$532$	−8.82781	+	15.9932i	−0.382734	+	0.693392i
$533$	−4.99227	+	38.9122i	−0.216239	+	1.68547i
$534$	3.10216	+	5.37310i	0.134244	+	0.232517i
$535$	−11.7582	−	3.15061i	−0.508353	−	0.136213i
$536$	5.17908	+	8.97043i	0.223702	+	0.387464i
$537$	−2.77624	+	4.80858i	−0.119803	+	0.207506i
$538$	−13.6013	+	13.6013i	−0.586395	+	0.586395i
$539$	4.12933	−	18.1826i	0.177863	−	0.783180i
$540$	1.30432	+	0.349490i	0.0561288	+	0.0150397i
$541$	−13.2636	−	3.55396i	−0.570246	−	0.152797i	−0.0378365	−	0.999284i	$-0.512047\pi$
$541$	−13.2636	−	3.55396i	−0.570246	−	0.152797i	−0.532409	+	0.846487i	$0.678713\pi$
$542$		−	0.870637i		−	0.0373971i
$543$	7.00160	−	4.04238i	0.300468	−	0.173475i
$544$	3.70903	+	3.70903i	0.159023	+	0.159023i
$545$	16.8559			0.722026
$546$	9.42731	−	1.45801i	0.403452	−	0.0623970i
$547$	−12.5282			−0.535667			−0.267833	−	0.963465i	$-0.586308\pi$
$547$	−12.5282			−0.535667			−0.267833	+	0.963465i	$0.586308\pi$
$548$	−2.26186	−	2.26186i	−0.0966221	−	0.0966221i
$549$	−7.62133	+	4.40017i	−0.325270	+	0.187795i
$550$			8.46141i			0.360796i
$551$	−41.0484	−	10.9989i	−1.74872	−	0.468568i
$552$	−0.253530	−	0.0679332i	−0.0107910	−	0.00289143i
$553$	−16.0749	−	3.97740i	−0.683574	−	0.169136i
$554$	−14.9899	+	14.9899i	−0.636859	+	0.636859i
$555$	1.85878	−	3.21950i	0.0789009	−	0.136660i
$556$	3.02473	+	5.23898i	0.128277	+	0.222182i
$557$	−10.5835	−	2.83584i	−0.448437	−	0.120158i	0.0275312	−	0.999621i	$-0.491235\pi$
$557$	−10.5835	−	2.83584i	−0.448437	−	0.120158i	−0.475968	+	0.879463i	$0.657902\pi$
$558$	0.218027	+	0.377634i	0.00922983	+	0.0159865i
$559$	−27.8420	+	3.75900i	−1.17759	+	0.158989i
$560$	−3.05905	+	1.84551i	−0.129268	+	0.0779872i
$561$	−13.4957	+	3.61617i	−0.569791	+	0.152675i
$562$	−29.3958			−1.23999
$563$	11.3695			0.479165			0.239583	−	0.970876i	$-0.422989\pi$
$563$	11.3695			0.479165			0.239583	+	0.970876i	$0.422989\pi$
$564$	5.55179	−	1.48760i	0.233773	−	0.0626392i
$565$	0.0270372	+	0.100904i	0.00113746	+	0.00424507i
$566$	3.67072	−	13.6993i	0.154292	−	0.575824i
$567$	2.56830	+	0.635473i	0.107859	+	0.0266874i
$568$	−2.09446	−	3.62770i	−0.0878814	−	0.152215i
$569$			9.62692i			0.403581i	0.979429	+	0.201791i	$0.0646761\pi$
$569$			9.62692i			0.403581i	−0.979429	+	0.201791i	$0.935324\pi$
$570$	−2.41308	+	9.00575i	−0.101073	+	0.377209i
$571$	9.45507	+	5.45889i	0.395682	+	0.228447i	0.684619	−	0.728901i	$-0.259968\pi$
$571$	9.45507	+	5.45889i	0.395682	+	0.228447i	−0.288937	+	0.957348i	$0.593302\pi$
$572$	5.82133	−	7.63858i	0.243402	−	0.319385i
$573$			13.3692i			0.558506i
$574$	−7.98446	−	27.6583i	−0.333265	−	1.15444i
$575$	0.416889	−	0.722073i	0.0173855	−	0.0301125i
$576$	−0.866025	−	0.500000i	−0.0360844	−	0.0208333i
$577$	6.95237	+	25.9466i	0.289431	+	1.08017i	0.945540	+	0.325505i	$0.105534\pi$
$577$	6.95237	+	25.9466i	0.289431	+	1.08017i	−0.656110	+	0.754666i	$0.727799\pi$
$578$	−7.43434	−	7.43434i	−0.309228	−	0.309228i
$579$	9.13181	−	2.44686i	0.379505	−	0.101688i
$580$	−5.87678	−	5.87678i	−0.244020	−	0.244020i
$581$	0.671119	+	34.8739i	0.0278427	+	1.44682i
$582$	−16.6523	−	9.61423i	−0.690261	−	0.398523i
$583$	3.30830	−	3.30830i	0.137016	−	0.137016i
$584$	2.52080	−	4.36615i	0.104311	−	0.180673i
$585$	4.49189	−	1.87800i	0.185717	−	0.0776457i
$586$	−2.78682	+	1.60897i	−0.115122	+	0.0664659i
$587$	7.51437	+	28.0440i	0.310151	+	1.15750i	0.928420	+	0.371533i	$0.121168\pi$
$587$	7.51437	+	28.0440i	0.310151	+	1.15750i	−0.618269	+	0.785967i	$0.712166\pi$
$588$	−5.92303	+	3.73064i	−0.244262	+	0.153849i
$589$	−2.60740	+	1.50539i	−0.107436	+	0.0620283i
$590$	3.01030	−	11.2346i	0.123932	−	0.462521i
$591$	−8.16211	+	8.16211i	−0.335744	+	0.335744i
$592$	−1.94672	+	1.94672i	−0.0800098	+	0.0800098i
$593$	−1.54505	+	5.76620i	−0.0634475	+	0.236789i	−0.990366	−	0.138473i	$-0.955781\pi$
$593$	−1.54505	+	5.76620i	−0.0634475	+	0.236789i	0.926919	+	0.375262i	$0.122447\pi$
$594$	2.30679	−	1.33183i	0.0946489	−	0.0546456i
$595$	16.0458	−	9.68038i	0.657813	−	0.396857i
$596$	0.711179	+	2.65415i	0.0291310	+	0.108718i
$597$	1.95194	−	1.12695i	0.0798877	−	0.0461232i
$598$	−0.873125	+	0.365041i	−0.0357047	+	0.0149277i
$599$	−11.9476	+	20.6938i	−0.488165	+	0.845527i	−0.999907	−	0.0136121i	$-0.995667\pi$
$599$	−11.9476	+	20.6938i	−0.488165	+	0.845527i	0.511742	+	0.859139i	$0.329000\pi$
$600$	2.24621	−	2.24621i	0.0917010	−	0.0917010i
$601$	31.4273	+	18.1445i	1.28194	+	0.740131i	0.977204	−	0.212304i	$-0.0680967\pi$
$601$	31.4273	+	18.1445i	1.28194	+	0.740131i	0.304741	+	0.952435i	$0.401430\pi$
$602$	17.6522	−	10.6495i	0.719448	−	0.434041i
$603$	7.32433	+	7.32433i	0.298270	+	0.298270i
$604$	−12.1411	+	3.25321i	−0.494016	+	0.132371i
$605$	3.72854	+	3.72854i	0.151587	+	0.151587i
$606$	0.810090	+	3.02330i	0.0329076	+	0.122813i
$607$	−0.0389874	−	0.0225094i	−0.00158245	−	0.000913628i	0.499209	−	0.866482i	$-0.333624\pi$
$607$	−0.0389874	−	0.0225094i	−0.00158245	−	0.000913628i	−0.500791	+	0.865568i	$0.666957\pi$
$608$	3.45229	−	5.97954i	0.140009	−	0.242502i
$609$	−11.7340	−	11.2909i	−0.475487	−	0.457532i
$610$		−	11.8834i		−	0.481143i
$611$	12.5613	−	16.4825i	0.508174	−	0.666812i
$612$	4.54261	+	2.62268i	0.183624	+	0.106015i
$613$	2.33413	−	8.71109i	0.0942747	−	0.351838i	−0.902634	−	0.430409i	$-0.858369\pi$
$613$	2.33413	−	8.71109i	0.0942747	−	0.351838i	0.996908	+	0.0785715i	$0.0250359\pi$
$614$			9.47481i			0.382372i
$615$	−7.34629	−	12.7242i	−0.296231	−	0.513087i
$616$	−1.69268	+	6.84107i	−0.0682001	+	0.275635i
$617$	−11.2249	+	41.8918i	−0.451897	+	1.68650i	0.245157	+	0.969483i	$0.421161\pi$
$617$	−11.2249	+	41.8918i	−0.451897	+	1.68650i	−0.697054	+	0.717019i	$0.745506\pi$
$618$	2.75698	+	10.2892i	0.110902	+	0.413892i
$619$	19.8679	−	5.32358i	0.798557	−	0.213973i	0.163607	−	0.986526i	$-0.447687\pi$
$619$	19.8679	−	5.32358i	0.798557	−	0.213973i	0.634950	+	0.772553i	$0.281021\pi$
$620$	−0.588817			−0.0236474
$621$	−0.262474			−0.0105327
$622$	31.3571	−	8.40211i	1.25731	−	0.336894i
$623$	−16.4120	+	0.315835i	−0.657534	+	0.0126537i
$624$	−3.57313	+	0.482416i	−0.143040	+	0.0193121i
$625$	0.486981	+	0.843477i	0.0194793	+	0.0337391i
$626$	−19.7324	−	5.28729i	−0.788667	−	0.211323i
$627$	9.19570	+	15.9274i	0.367241	+	0.636080i
$628$	2.64969	−	4.58939i	0.105734	−	0.183137i
$629$	10.2113	−	10.2113i	0.407149	−	0.407149i
$630$	−2.47716	+	2.57437i	−0.0986923	+	0.102565i
$631$	4.76385	+	1.27647i	0.189646	+	0.0508154i	0.352392	−	0.935853i	$-0.385368\pi$
$631$	4.76385	+	1.27647i	0.189646	+	0.0508154i	−0.162746	+	0.986668i	$0.552035\pi$
$632$	6.04569	+	1.61994i	0.240485	+	0.0644377i
$633$		−	22.3979i		−	0.890237i
$634$	−3.15975	+	1.82428i	−0.125490	+	0.0724514i
$635$	−13.6408	−	13.6408i	−0.541318	−	0.541318i
$636$	−1.75648			−0.0696488
$637$	−8.67603	+	23.7008i	−0.343757	+	0.939059i
$638$	−16.3943			−0.649057
$639$	−2.96201	−	2.96201i	−0.117175	−	0.117175i
$640$	1.16942	−	0.675164i	0.0462253	−	0.0266882i
$641$		−	41.3607i		−	1.63365i	−0.576885	−	0.816825i	$-0.695732\pi$
$641$		−	41.3607i		−	1.63365i	0.576885	−	0.816825i	$-0.304268\pi$
$642$	8.70769	+	2.33322i	0.343665	+	0.0920848i
$643$	−9.73707	−	2.60904i	−0.383992	−	0.102890i	0.0616584	−	0.998097i	$-0.480361\pi$
$643$	−9.73707	−	2.60904i	−0.383992	−	0.102890i	−0.445651	+	0.895207i	$0.647028\pi$
$644$	0.481505	−	0.500401i	0.0189739	−	0.0197185i
$645$	7.44004	−	7.44004i	0.292951	−	0.292951i
$646$	−18.1085	+	31.3648i	−0.712468	+	1.23403i
$647$	8.34544	+	14.4547i	0.328093	+	0.568274i	0.982133	−	0.188186i	$-0.0602607\pi$
$647$	8.34544	+	14.4547i	0.328093	+	0.568274i	−0.654040	+	0.756460i	$0.726927\pi$
$648$	−0.965926	−	0.258819i	−0.0379452	−	0.0101674i
$649$	−11.4716	−	19.8693i	−0.450298	−	0.779939i
$650$	1.45748	−	11.3603i	0.0571672	−	0.445589i
$651$	−1.15348	+	0.0221977i	−0.0452084	+	0.000869996i
$652$	23.8476	−	6.38996i	0.933946	−	0.250250i
$653$	−26.9629			−1.05514			−0.527571	−	0.849511i	$-0.676897\pi$
$653$	−26.9629			−1.05514			−0.527571	+	0.849511i	$0.676897\pi$
$654$	−12.4828			−0.488116
$655$	−15.6776	+	4.20079i	−0.612573	+	0.164139i
$656$	2.81615	+	10.5100i	0.109952	+	0.410347i
$657$	1.30486	−	4.86981i	0.0509075	−	0.189989i
$658$	−3.65247	+	14.7617i	−0.142388	+	0.575470i
$659$	−14.7018	−	25.4643i	−0.572702	−	0.991950i	−0.996287	−	0.0860931i	$-0.972562\pi$
$659$	−14.7018	−	25.4643i	−0.572702	−	0.991950i	0.423585	−	0.905856i	$-0.360772\pi$
$660$			3.59681i			0.140006i
$661$	9.53644	−	35.5905i	0.370925	−	1.38431i	−0.488284	−	0.872685i	$-0.662377\pi$
$661$	9.53644	−	35.5905i	0.370925	−	1.38431i	0.859209	−	0.511625i	$-0.170956\pi$
$662$	1.95986	+	1.13153i	0.0761723	+	0.0439781i
$663$	18.7423	−	2.53044i	0.727892	−	0.0982742i
$664$		−	13.1836i		−	0.511621i
$665$	−17.7749	−	17.1037i	−0.689282	−	0.663254i
$666$	−1.37654	+	2.38424i	−0.0533399	+	0.0923874i
$667$	1.39905	+	0.807740i	0.0541713	+	0.0312758i
$668$	−6.32787	−	23.6159i	−0.244832	−	0.913727i
$669$	12.3631	+	12.3631i	0.477985	+	0.477985i
$670$	−13.5103	+	3.62008i	−0.521949	+	0.139856i
$671$	−16.5754	−	16.5754i	−0.639885	−	0.639885i
$672$	2.26541	−	1.36672i	0.0873901	−	0.0527222i
$673$	−8.61642	−	4.97469i	−0.332138	−	0.191760i	0.324652	−	0.945834i	$-0.394753\pi$
$673$	−8.61642	−	4.97469i	−0.332138	−	0.191760i	−0.656790	+	0.754073i	$0.728086\pi$
$674$	12.6233	−	12.6233i	0.486233	−	0.486233i
$675$	1.58831	−	2.75103i	0.0611340	−	0.105887i
$676$	−9.13150	+	9.25287i	−0.351212	+	0.355880i
$677$	−0.655682	+	0.378558i	−0.0251999	+	0.0145492i	−0.512547	−	0.858659i	$-0.671298\pi$
$677$	−0.655682	+	0.378558i	−0.0251999	+	0.0145492i	0.487347	+	0.873208i	$0.337965\pi$
$678$	−0.0200227	−	0.0747257i	−0.000768967	−	0.00286982i
$679$	43.5603	−	26.2798i	1.67169	−	1.00853i
$680$	−6.13401	+	3.54147i	−0.235229	+	0.135809i
$681$	6.43187	−	24.0041i	0.246470	−	0.919838i
$682$	−0.821304	+	0.821304i	−0.0314494	+	0.0314494i
$683$	1.59067	−	1.59067i	0.0608652	−	0.0608652i	−0.676019	−	0.736884i	$-0.736296\pi$
$683$	1.59067	−	1.59067i	0.0608652	−	0.0608652i	0.736884	+	0.676019i	$0.236296\pi$
$684$	1.78704	−	6.66931i	0.0683290	−	0.255007i
$685$	3.74069	−	2.15969i	0.142924	−	0.0825174i
$686$	−1.06849	−	18.4894i	−0.0407953	−	0.705929i
$687$	0.302393	+	1.12855i	0.0115370	+	0.0430567i
$688$	−6.74810	+	3.89602i	−0.257269	+	0.148534i
$689$	−5.01160	+	3.87189i	−0.190927	+	0.147507i
$690$	0.177213	−	0.306942i	0.00674638	−	0.0116851i
$691$	15.0964	−	15.0964i	0.574293	−	0.574293i	−0.359032	−	0.933325i	$-0.616893\pi$
$691$	15.0964	−	15.0964i	0.574293	−	0.574293i	0.933325	+	0.359032i	$0.116893\pi$
$692$	0.292808	+	0.169053i	0.0111309	+	0.00642642i
$693$	0.135595	+	7.04607i	0.00515084	+	0.267658i
$694$	−11.0995	−	11.0995i	−0.421332	−	0.421332i
$695$	−7.89041	+	2.11423i	−0.299300	+	0.0801972i
$696$	4.35211	+	4.35211i	0.164966	+	0.164966i
$697$	−14.7717	−	55.1287i	−0.559518	−	2.08815i
$698$	−25.8910	−	14.9482i	−0.979991	−	0.565798i
$699$	5.80374	−	10.0524i	0.219518	−	0.380216i
$700$	2.33105	+	8.07480i	0.0881054	+	0.305199i
$701$		−	5.56664i		−	0.210249i	−0.994459	−	0.105124i	$-0.966476\pi$
$701$		−	5.56664i		−	0.210249i	0.994459	−	0.105124i	$-0.0335241\pi$
$702$	−3.32652	+	1.39077i	−0.125551	+	0.0524913i
$703$	−16.4622	−	9.50443i	−0.620882	−	0.358466i
$704$	0.689405	−	2.57289i	0.0259829	−	0.0969696i
$705$			7.76119i			0.292303i
$706$	13.4412	+	23.2809i	0.505866	+	0.876186i
$707$	−8.03864	−	1.98900i	−0.302324	−	0.0748039i
$708$	−2.22931	+	8.31990i	−0.0837826	+	0.312681i
$709$	−9.56097	−	35.6820i	−0.359070	−	1.34007i	−0.875285	−	0.483607i	$-0.839326\pi$
$709$	−9.56097	−	35.6820i	−0.359070	−	1.34007i	0.516215	−	0.856459i	$-0.327340\pi$
$710$	5.46367	−	1.46399i	0.205048	−	0.0549424i
$711$	6.25896			0.234729
$712$	6.20432			0.232517
$713$	0.110553	−	0.0296226i	0.00414024	−	0.00110938i
$714$	−11.8829	+	7.16891i	−0.444706	+	0.268290i
$715$	7.92862	+	10.2625i	0.296514	+	0.383794i
$716$	2.77624	+	4.80858i	0.103753	+	0.179705i
$717$	25.1206	+	6.73106i	0.938148	+	0.251376i
$718$	−15.3393	−	26.5684i	−0.572456	−	0.991524i
$719$	13.5980	−	23.5524i	0.507120	−	0.878357i	−0.492846	−	0.870116i	$-0.664044\pi$
$719$	13.5980	−	23.5524i	0.507120	−	0.878357i	0.999966	−	0.00824079i	$-0.00262315\pi$
$720$	0.954826	−	0.954826i	0.0355843	−	0.0355843i
$721$	−27.3580	−	6.76916i	−1.01886	−	0.252097i
$722$	27.6961	+	7.42116i	1.03074	+	0.276187i
$723$	28.7576	+	7.70558i	1.06951	+	0.286574i
$724$		−	8.08476i		−	0.300468i
$725$	−16.9321	+	9.77575i	−0.628842	+	0.363062i
$726$	−2.76121	−	2.76121i	−0.102478	−	0.102478i
$727$	−23.9303			−0.887524			−0.443762	−	0.896145i	$-0.646356\pi$
$727$	−23.9303			−0.887524			−0.443762	+	0.896145i	$0.646356\pi$
$728$	3.45098	−	8.89330i	0.127902	−	0.329607i
$729$	−1.00000			−0.0370370
$730$	4.81385	+	4.81385i	0.178169	+	0.178169i
$731$	35.3962	−	20.4360i	1.30917	−	0.755853i
$732$			8.80035i			0.325270i
$733$	13.8090	+	3.70012i	0.510049	+	0.136667i	0.504660	−	0.863318i	$-0.331618\pi$
$733$	13.8090	+	3.70012i	0.510049	+	0.136667i	0.00538890	+	0.999985i	$0.498285\pi$
$734$	−14.5408	−	3.89619i	−0.536710	−	0.143811i
$735$	−2.79590	−	9.02933i	−0.103128	−	0.333052i
$736$	−0.185597	+	0.185597i	−0.00684120	+	0.00684120i
$737$	−13.7953	+	23.8941i	−0.508156	+	0.880152i
$738$	5.44038	+	9.42301i	0.200263	+	0.346866i
$739$	−25.9347	−	6.94919i	−0.954025	−	0.255630i	−0.251955	−	0.967739i	$-0.581074\pi$
$739$	−25.9347	−	6.94919i	−0.954025	−	0.255630i	−0.702069	+	0.712109i	$0.747740\pi$
$740$	−1.85878	−	3.21950i	−0.0683302	−	0.118351i
$741$	−9.60269	−	22.9682i	−0.352764	−	0.843759i
$742$	2.24573	−	4.06855i	0.0824434	−	0.149361i
$743$	−4.31189	+	1.15537i	−0.158188	+	0.0423863i	−0.337044	−	0.941489i	$-0.609427\pi$
$743$	−4.31189	+	1.15537i	−0.158188	+	0.0423863i	0.178856	+	0.983875i	$0.442760\pi$
$744$	0.436055			0.0159865
$745$	−3.71041			−0.135939
$746$	10.2719	−	2.75236i	0.376082	−	0.100771i
$747$	−3.41215	−	12.7343i	−0.124844	−	0.465925i
$748$	−3.61617	+	13.4957i	−0.132220	+	0.493453i
$749$	−16.5377	+	17.1867i	−0.604273	+	0.627987i
$750$	5.52055	+	9.56188i	0.201582	+	0.349151i
$751$			40.1747i			1.46600i	0.680230	+	0.732999i	$0.261880\pi$
$751$			40.1747i			1.46600i	−0.680230	+	0.732999i	$0.738120\pi$
$752$	1.48760	−	5.55179i	0.0542471	−	0.202453i
$753$	−1.90177	−	1.09799i	−0.0693042	−	0.0400128i
$754$	22.0111	+	2.82393i	0.801597	+	0.102842i
$755$		−	16.9729i		−	0.617705i
$756$	1.83449	−	1.90648i	0.0667196	−	0.0693379i
$757$	−22.8181	+	39.5220i	−0.829336	+	1.43645i	0.0692231	+	0.997601i	$0.477948\pi$
$757$	−22.8181	+	39.5220i	−0.829336	+	1.43645i	−0.898560	+	0.438852i	$0.855385\pi$
$758$	−1.25176	−	0.722703i	−0.0454659	−	0.0262497i
$759$	−0.180951	−	0.675317i	−0.00656810	−	0.0245125i
$760$	6.59267	+	6.59267i	0.239141	+	0.239141i
$761$	43.0272	−	11.5291i	1.55973	−	0.417930i	0.627155	−	0.778894i	$-0.284219\pi$
$761$	43.0272	−	11.5291i	1.55973	−	0.417930i	0.932579	+	0.360965i	$0.117553\pi$
$762$	10.1018	+	10.1018i	0.365951	+	0.365951i
$763$	15.9598	−	28.9141i	0.577785	−	1.04676i
$764$	11.5781	+	6.68460i	0.418880	+	0.241840i
$765$	−5.00840	+	5.00840i	−0.181079	+	0.181079i
$766$	13.0378	−	22.5821i	0.471075	−	0.815926i
$767$	11.9793	+	28.6526i	0.432546	+	1.03459i
$768$	−0.866025	+	0.500000i	−0.0312500	+	0.0180422i
$769$	3.66323	+	13.6714i	0.132099	+	0.493002i	0.999993	−	0.00374840i	$-0.00119316\pi$
$769$	3.66323	+	13.6714i	0.132099	+	0.493002i	−0.867894	+	0.496750i	$0.834526\pi$
$770$	−8.33134	−	4.59868i	−0.300241	−	0.165725i
$771$	8.11982	−	4.68798i	0.292428	−	0.168834i
$772$	2.44686	−	9.13181i	0.0880644	−	0.328661i
$773$	26.0658	−	26.0658i	0.937521	−	0.937521i	−0.0606384	−	0.998160i	$-0.519314\pi$
$773$	26.0658	−	26.0658i	0.937521	−	0.937521i	0.998160	+	0.0606384i	$0.0193136\pi$
$774$	−5.50980	+	5.50980i	−0.198046	+	0.198046i
$775$	−0.358510	+	1.33798i	−0.0128781	+	0.0480616i
$776$	−16.6523	+	9.61423i	−0.597784	+	0.345131i
$777$	−3.76268	−	6.23686i	−0.134985	−	0.223746i
$778$	−1.48778	−	5.55245i	−0.0533393	−	0.199065i
$779$	−65.0619	+	37.5635i	−2.33108	+	1.34585i
$780$	0.619553	−	4.82909i	0.0221836	−	0.172909i
$781$	5.57891	−	9.66296i	0.199629	−	0.345768i
$782$	0.973522	−	0.973522i	0.0348131	−	0.0348131i
$783$	5.33023	+	3.07741i	0.190487	+	0.109978i
$784$	0.269318	+	6.99482i	0.00961850	+	0.249815i
$785$	5.05998	+	5.05998i	0.180598	+	0.180598i
$786$	11.6102	−	3.11094i	0.414122	−	0.110964i
$787$	7.39659	+	7.39659i	0.263660	+	0.263660i	0.826539	−	0.562879i	$-0.190306\pi$
$787$	7.39659	+	7.39659i	0.263660	+	0.263660i	−0.562879	+	0.826539i	$0.690306\pi$
$788$	2.98754	+	11.1496i	0.106427	+	0.397190i
$789$	21.4093	+	12.3607i	0.762192	+	0.440052i
$790$	−4.22582	+	7.31934i	−0.150348	+	0.260411i
$791$	0.198688	+	0.0491613i	0.00706455	+	0.00174797i
$792$		−	2.66366i		−	0.0946489i
$793$	19.3991	+	25.1093i	0.688881	+	0.891657i
$794$	−13.6403	−	7.87523i	−0.484076	−	0.279481i
$795$	0.613871	−	2.29100i	0.0217718	−	0.0812534i
$796$		−	2.25391i		−	0.0798877i
$797$	9.78362	+	16.9457i	0.346554	+	0.600248i	0.985635	−	0.168891i	$-0.0540185\pi$
$797$	9.78362	+	16.9457i	0.346554	+	0.600248i	−0.639081	+	0.769139i	$0.720685\pi$
$798$	13.1634	+	12.6663i	0.465980	+	0.448384i
$799$	−7.80298	+	29.1211i	−0.276050	+	1.03023i
$800$	−0.822169	−	3.06837i	−0.0290680	−	0.108483i
$801$	5.99291	−	1.60580i	0.211749	−	0.0567380i
$802$	−19.1117			−0.674857
$803$	13.4291			0.473902
$804$	10.0052	−	2.68089i	0.352857	−	0.0945477i
$805$	0.484399	+	0.802920i	0.0170728	+	0.0282992i
$806$	1.24416	−	0.961217i	0.0438236	−	0.0338574i
$807$	9.61759	+	16.6582i	0.338555	+	0.586395i
$808$	3.02330	+	0.810090i	0.106359	+	0.0284988i
$809$	−3.64954	−	6.32120i	−0.128311	−	0.222241i	0.794711	−	0.606988i	$-0.207622\pi$
$809$	−3.64954	−	6.32120i	−0.128311	−	0.222241i	−0.923022	+	0.384746i	$0.874289\pi$
$810$	0.675164	−	1.16942i	0.0237228	−	0.0410892i
$811$	13.4146	−	13.4146i	0.471049	−	0.471049i	−0.431205	−	0.902254i	$-0.641911\pi$
$811$	13.4146	−	13.4146i	0.471049	−	0.471049i	0.902254	+	0.431205i	$0.141911\pi$
$812$	−15.6453	+	4.51650i	−0.549041	+	0.158498i
$813$	−0.840971	−	0.225338i	−0.0294941	−	0.00790293i
$814$	−7.08339	−	1.89799i	−0.248273	−	0.0665244i
$815$			33.3381i			1.16778i
$816$	4.54261	−	2.62268i	0.159023	−	0.0918121i
$817$	−38.0428	−	38.0428i	−1.33095	−	1.33095i
$818$	17.9265			0.626784
$819$	1.03164	−	9.48344i	0.0360484	−	0.331378i
$820$	−14.6926			−0.513087
$821$	32.3932	+	32.3932i	1.13053	+	1.13053i	0.990089	+	0.140443i	$0.0448528\pi$
$821$	32.3932	+	32.3932i	1.13053	+	1.13053i	0.140443	+	0.990089i	$0.455147\pi$
$822$	−2.77021	+	1.59938i	−0.0966221	+	0.0557848i
$823$		−	45.2057i		−	1.57577i	−0.615822	−	0.787885i	$-0.711176\pi$
$823$		−	45.2057i		−	1.57577i	0.615822	−	0.787885i	$-0.288824\pi$
$824$	10.2892	+	2.75698i	0.358441	+	0.0960441i
$825$	8.17309	+	2.18997i	0.284551	+	0.0762451i
$826$	−16.4212	−	15.8012i	−0.571368	−	0.549793i
$827$	−3.77092	+	3.77092i	−0.131128	+	0.131128i	−0.769625	−	0.638497i	$-0.779557\pi$
$827$	−3.77092	+	3.77092i	−0.131128	+	0.131128i	0.638497	+	0.769625i	$0.279557\pi$
$828$	−0.131237	+	0.227309i	−0.00456080	+	0.00789954i
$829$	−19.9577	−	34.5677i	−0.693159	−	1.20059i	−0.970797	−	0.239901i	$-0.922885\pi$
$829$	−19.9577	−	34.5677i	−0.693159	−	1.20059i	0.277638	−	0.960686i	$-0.410448\pi$
$830$	17.1955	+	4.60753i	0.596865	+	0.159930i
$831$	10.5994	+	18.3588i	0.367691	+	0.636859i
$832$	−1.36878	+	3.33563i	−0.0474540	+	0.115642i
$833$	−1.41267	−	36.6903i	−0.0489461	−	1.27124i
$834$	5.84333	−	1.56571i	0.202338	−	0.0542163i
$835$	33.0142			1.14250
$836$	18.3914			0.636080
$837$	0.421196	−	0.112859i	0.0145587	−	0.00390099i
$838$	−1.47761	−	5.51451i	−0.0510431	−	0.190496i
$839$	−12.7555	+	47.6042i	−0.440369	+	1.64348i	0.287514	+	0.957777i	$0.407171\pi$
$839$	−12.7555	+	47.6042i	−0.440369	+	1.64348i	−0.727882	+	0.685702i	$0.759495\pi$
$840$	0.990891	+	3.43247i	0.0341890	+	0.118431i
$841$	−4.44090	−	7.69187i	−0.153135	−	0.265237i
$842$		−	15.8855i		−	0.547449i
$843$	−7.60818	+	28.3941i	−0.262040	+	0.977946i
$844$	−19.3972	−	11.1990i	−0.667678	−	0.385484i
$845$	−8.87730	−	15.1442i	−0.305388	−	0.520975i
$846$		−	5.74764i		−	0.197608i
$847$	9.92617	−	2.86550i	0.341067	−	0.0984599i
$848$	−0.878238	+	1.52115i	−0.0301588	+	0.0522366i
$849$	−12.2825	−	7.09128i	−0.421533	−	0.243372i
$850$	4.31257	+	16.0947i	0.147920	+	0.552044i
$851$	0.510964	+	0.510964i	0.0175156	+	0.0175156i
$852$	−4.04618	+	1.08417i	−0.138620	+	0.0371431i
$853$	0.286626	+	0.286626i	0.00981388	+	0.00981388i	0.711997	−	0.702183i	$-0.247791\pi$
$853$	0.286626	+	0.286626i	0.00981388	+	0.00981388i	−0.702183	+	0.711997i	$0.747791\pi$
$854$	−20.3844	−	11.2516i	−0.697540	−	0.385023i
$855$	8.07433	+	4.66172i	0.276136	+	0.159427i
$856$	6.37447	−	6.37447i	0.217875	−	0.217875i
$857$	−13.9868	+	24.2258i	−0.477780	+	0.827539i	−0.999676	−	0.0254706i	$-0.991892\pi$
$857$	−13.9868	+	24.2258i	−0.477780	+	0.827539i	0.521896	+	0.853009i	$0.325225\pi$
$858$	−5.87163	−	7.59998i	−0.200454	−	0.259459i
$859$	14.1312	−	8.15866i	0.482151	−	0.278370i	−0.239161	−	0.970980i	$-0.576873\pi$
$859$	14.1312	−	8.15866i	0.482151	−	0.278370i	0.721312	+	0.692610i	$0.243539\pi$
$860$	−2.72324	−	10.1633i	−0.0928618	−	0.346565i
$861$	−28.7824	+	0.553893i	−0.980903	+	0.0188766i
$862$	15.6491	−	9.03501i	0.533010	−	0.307734i
$863$	3.20727	−	11.9697i	0.109177	−	0.407453i	−0.889609	−	0.456724i	$-0.849023\pi$
$863$	3.20727	−	11.9697i	0.109177	−	0.407453i	0.998785	+	0.0492701i	$0.0156895\pi$
$864$	−0.707107	+	0.707107i	−0.0240563	+	0.0240563i
$865$	−0.322832	+	0.322832i	−0.0109766	+	0.0109766i
$866$	4.17679	−	15.5880i	0.141933	−	0.529702i
$867$	−9.10517	+	5.25687i	−0.309228	+	0.178533i
$868$	−0.557515	+	1.01004i	−0.0189233	+	0.0342830i
$869$	4.31496	+	16.1036i	0.146375	+	0.546279i
$870$	−7.19756	+	4.15551i	−0.244020	+	0.140885i
$871$	22.6374	−	29.7042i	0.767040	−	1.00649i
$872$	−6.24140	+	10.8104i	−0.211361	+	0.366087i
$873$	−13.5966	+	13.5966i	−0.460174	+	0.460174i
$874$	−1.56947	−	0.906135i	−0.0530882	−	0.0306505i
$875$	−29.2066	+	0.562056i	−0.987364	+	0.0190010i
$876$	−3.56495	−	3.56495i	−0.120448	−	0.120448i
$877$	37.2000	−	9.96772i	1.25616	−	0.336586i	0.431444	−	0.902140i	$-0.358004\pi$
$877$	37.2000	−	9.96772i	1.25616	−	0.336586i	0.824712	+	0.565554i	$0.191337\pi$
$878$	7.37750	+	7.37750i	0.248979	+	0.248979i
$879$	0.832864	+	3.10829i	0.0280918	+	0.104840i
$880$	3.11493	+	1.79840i	0.105004	+	0.0606242i
$881$	20.9998	−	36.3728i	0.707503	−	1.22543i	−0.258278	−	0.966071i	$-0.583155\pi$
$881$	20.9998	−	36.3728i	0.707503	−	1.22543i	0.965781	−	0.259360i	$-0.0835116\pi$
$882$	2.07053	+	6.68677i	0.0697185	+	0.225155i
$883$		−	56.1761i		−	1.89048i	−0.326383	−	0.945238i	$-0.605830\pi$
$883$		−	56.1761i		−	1.89048i	0.326383	−	0.945238i	$-0.394170\pi$
$884$	7.17975	−	17.4966i	0.241481	−	0.588473i
$885$	−10.0727	−	5.81545i	−0.338589	−	0.195484i
$886$	0.432697	−	1.61485i	0.0145367	−	0.0542518i
$887$		−	13.5169i		−	0.453852i	−0.973912	−	0.226926i	$-0.927133\pi$
$887$		−	13.5169i		−	0.453852i	0.973912	−	0.226926i	$-0.0728675\pi$
$888$	1.37654	+	2.38424i	0.0461937	+	0.0800098i
$889$	−36.3147	+	10.4834i	−1.21796	+	0.351602i
$890$	−2.16835	+	8.09239i	−0.0726832	+	0.271258i
$891$	−0.689405	−	2.57289i	−0.0230959	−	0.0861952i
$892$	16.8883	−	4.52520i	0.565462	−	0.151515i
$893$	39.6850			1.32801
$894$	2.74778			0.0918996
$895$	−7.24218	+	1.94054i	−0.242079	+	0.0648650i
$896$	−0.0509058	−	2.64526i	−0.00170064	−	0.0883720i
$897$	0.126622	+	0.937854i	0.00422777	+	0.0313140i
$898$	0.411722	+	0.713123i	0.0137393	+	0.0237972i
$899$	−2.59239	−	0.694628i	−0.0864610	−	0.0231671i
$900$	−1.58831	−	2.75103i	−0.0529436	−	0.0917010i
$901$	4.60667	−	7.97898i	0.153470	−	0.265818i
$902$	−20.4938	+	20.4938i	−0.682368	+	0.682368i
$903$	−5.71791	−	19.8070i	−0.190280	−	0.659135i
$904$	−0.0747257	−	0.0200227i	−0.00248534	−	0.000665945i
$905$	10.5451	+	2.82555i	0.350530	+	0.0939243i
$906$			12.5694i			0.417592i
$907$	−43.1561	+	24.9162i	−1.43298	+	0.827329i	−0.997347	−	0.0727979i	$-0.976807\pi$
$907$	−43.1561	+	24.9162i	−1.43298	+	0.827329i	−0.435629	+	0.900127i	$0.643474\pi$
$908$	−17.5722	−	17.5722i	−0.583154	−	0.583154i
$909$	3.12995			0.103814
$910$	10.3936	+	7.60930i	0.344544	+	0.252246i
$911$	−0.960415			−0.0318200			−0.0159100	−	0.999873i	$-0.505065\pi$
$911$	−0.960415			−0.0318200			−0.0159100	+	0.999873i	$0.505065\pi$
$912$	−4.88227	−	4.88227i	−0.161668	−	0.161668i
$913$	30.4117	−	17.5582i	1.00648	−	0.581092i
$914$		−	16.0352i		−	0.530399i
$915$	−11.4784	−	3.07564i	−0.379465	−	0.101677i
$916$	1.12855	+	0.302393i	0.0372882	+	0.00999135i
$917$	−7.63823	+	30.8704i	−0.252237	+	1.01943i
$918$	3.70903	−	3.70903i	0.122416	−	0.122416i
$919$	1.67074	−	2.89380i	0.0551125	−	0.0954576i	−0.837153	−	0.546969i	$-0.815782\pi$
$919$	1.67074	−	2.89380i	0.0551125	−	0.0954576i	0.892265	+	0.451511i	$0.149115\pi$
$920$	−0.177213	−	0.306942i	−0.00584253	−	0.0101196i
$921$	9.15196	+	2.45226i	0.301567	+	0.0808048i
$922$	−7.59051	−	13.1472i	−0.249980	−	0.432979i
$923$	−9.15473	+	12.0126i	−0.301332	+	0.395399i
$924$	6.16987	+	3.40560i	0.202974	+	0.112036i
$925$	−8.44749	+	2.26350i	−0.277752	+	0.0744233i
$926$	3.98479			0.130948
$927$	10.6522			0.349863
$928$	5.94510	−	1.59298i	0.195157	−	0.0522923i
$929$	3.84413	+	14.3465i	0.126122	+	0.470693i	0.999877	−	0.0156726i	$-0.00498896\pi$
$929$	3.84413	+	14.3465i	0.126122	+	0.470693i	−0.873755	+	0.486366i	$0.838322\pi$
$930$	−0.152397	+	0.568753i	−0.00499729	+	0.0186501i
$931$	−46.1693	+	14.2962i	−1.51314	+	0.468537i
$932$	−5.80374	−	10.0524i	−0.190108	−	0.329276i
$933$		−	32.4633i		−	1.06280i
$934$	−1.18434	+	4.42002i	−0.0387528	+	0.144627i
$935$	−16.3389	−	9.43327i	−0.534339	−	0.308501i
$936$	−0.458817	+	3.57624i	−0.0149969	+	0.116893i
$937$		−	35.6374i		−	1.16422i	−0.813108	−	0.582112i	$-0.802226\pi$
$937$		−	35.6374i		−	1.16422i	0.813108	−	0.582112i	$-0.197774\pi$
$938$	−6.58233	+	26.6029i	−0.214921	+	0.868615i
$939$	−10.2143	+	17.6916i	−0.333330	+	0.577344i
$940$	6.72139	+	3.88060i	0.219228	+	0.126571i
$941$	8.97013	+	33.4770i	0.292418	+	1.09132i	0.943246	+	0.332093i	$0.107755\pi$
$941$	8.97013	+	33.4770i	0.292418	+	1.09132i	−0.650829	+	0.759225i	$0.725578\pi$
$942$	−3.74722	−	3.74722i	−0.122091	−	0.122091i
$943$	2.75860	−	0.739165i	0.0898324	−	0.0240705i
$944$	6.09059	+	6.09059i	0.198232	+	0.198232i
$945$	1.84551	+	3.05905i	0.0600346	+	0.0995108i
$946$	−17.9746	−	10.3776i	−0.584405	−	0.337406i
$947$	−20.6597	+	20.6597i	−0.671349	+	0.671349i	−0.958027	−	0.286678i	$-0.907449\pi$
$947$	−20.6597	+	20.6597i	−0.671349	+	0.671349i	0.286678	+	0.958027i	$0.407449\pi$
$948$	3.12948	−	5.42042i	0.101641	−	0.176047i
$949$	−18.0300	−	2.31317i	−0.585277	−	0.0750887i
$950$	18.9947	−	10.9666i	0.616269	−	0.355803i
$951$	0.944317	+	3.52424i	0.0306216	+	0.114281i
$952$	0.267019	+	13.8753i	0.00865413	+	0.449702i
$953$	29.3888	−	16.9676i	0.951995	−	0.549635i	0.0582951	−	0.998299i	$-0.481434\pi$
$953$	29.3888	−	16.9676i	0.951995	−	0.549635i	0.893700	+	0.448665i	$0.148100\pi$
$954$	−0.454609	+	1.69662i	−0.0147185	+	0.0549303i
$955$	−12.7653	+	12.7653i	−0.413074	+	0.413074i
$956$	18.3896	−	18.3896i	0.594762	−	0.594762i
$957$	−4.24316	+	15.8357i	−0.137162	+	0.511895i
$958$	35.5135	−	20.5037i	1.14739	−	0.662445i
$959$	−0.162835	−	8.46155i	−0.00525822	−	0.273238i
$960$	−0.349490	−	1.30432i	−0.0112798	−	0.0420966i
$961$	26.6821	−	15.4049i	0.860713	−	0.496933i
$962$	9.18327	+	3.76837i	0.296080	+	0.121497i
$963$	4.50743	−	7.80711i	0.145250	−	0.251580i
$964$	21.0520	−	21.0520i	0.678041	−	0.678041i
$965$	11.0556	+	6.38296i	0.355893	+	0.205475i
$966$	−0.358727	−	0.594611i	−0.0115419	−	0.0191313i
$967$	−11.2022	−	11.2022i	−0.360239	−	0.360239i	0.503662	−	0.863901i	$-0.331986\pi$
$967$	−11.2022	−	11.2022i	−0.360239	−	0.360239i	−0.863901	+	0.503662i	$0.831986\pi$
$968$	−3.77188	+	1.01067i	−0.121233	+	0.0324843i
$969$	25.6092	+	25.6092i	0.822688	+	0.822688i
$970$	−6.72016	−	25.0800i	−0.215771	−	0.805270i
$971$	7.16445	+	4.13639i	0.229918	+	0.132743i	0.610534	−	0.791990i	$-0.290955\pi$
$971$	7.16445	+	4.13639i	0.229918	+	0.132743i	−0.380616	+	0.924733i	$0.624288\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	−3.84427	+	15.5368i	−0.123242	+	0.498088i
$974$			18.3333i			0.587438i
$975$	−10.5960	−	4.34809i	−0.339344	−	0.139250i
$976$	7.62133	+	4.40017i	0.243953	+	0.140846i
$977$	−1.25636	+	4.68882i	−0.0401947	+	0.150008i	−0.983107	−	0.183033i	$-0.941408\pi$
$977$	−1.25636	+	4.68882i	−0.0401947	+	0.150008i	0.942912	+	0.333042i	$0.108075\pi$
$978$		−	24.6889i		−	0.789464i
$979$	8.26308	+	14.3121i	0.264089	+	0.457416i
$980$	−9.21758	−	2.09335i	−0.294445	−	0.0668695i
$981$	−3.23079	+	12.0575i	−0.103151	+	0.384965i
$982$	6.14468	+	22.9323i	0.196085	+	0.731798i
$983$	−13.3417	+	3.57490i	−0.425534	+	0.114022i	−0.465229	−	0.885190i	$-0.654028\pi$
$983$	−13.3417	+	3.57490i	−0.425534	+	0.114022i	0.0396949	+	0.999212i	$0.487361\pi$
$984$	10.8808			0.346866
$985$	−15.5868			−0.496636
$986$	−31.1842	+	8.35577i	−0.993106	+	0.266102i
$987$	13.3133	+	7.34861i	0.423768	+	0.233909i
$988$	−24.6924	−	3.16793i	−0.785570	−	0.100785i
$989$	1.02260	+	1.77120i	0.0325169	+	0.0563209i
$990$	3.47425	+	0.930922i	0.110419	+	0.0295867i
$991$	11.6141	+	20.1162i	0.368935	+	0.639014i	0.989399	−	0.145221i	$-0.0463893\pi$
$991$	11.6141	+	20.1162i	0.368935	+	0.639014i	−0.620465	+	0.784234i	$0.713056\pi$
$992$	0.218027	−	0.377634i	0.00692237	−	0.0119899i
$993$	1.60022	−	1.60022i	0.0507815	−	0.0507815i
$994$	2.66194	−	10.7584i	0.0844316	−	0.341235i
$995$	2.93981	+	0.787719i	0.0931982	+	0.0249724i
$996$	−12.7343	−	3.41215i	−0.403503	−	0.108118i
$997$			5.23091i			0.165665i	0.996564	+	0.0828323i	$0.0263966\pi$
$997$			5.23091i			0.165665i	−0.996564	+	0.0828323i	$0.973603\pi$
$998$	−30.0920	+	17.3736i	−0.952545	+	0.549952i
$999$	1.94672	+	1.94672i	0.0615916	+	0.0615916i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.cg.b.241.2	yes	40
7.5	odd	6		546.2.by.b.397.2	✓	40
13.2	odd	12		546.2.by.b.535.2	yes	40
91.54	even	12	inner	546.2.cg.b.145.2	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.b.397.2	✓	40	7.5	odd	6
546.2.by.b.535.2	yes	40	13.2	odd	12
546.2.cg.b.145.2	yes	40	91.54	even	12	inner
546.2.cg.b.241.2	yes	40	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.cg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.866025 + 0.500000i) q^{3} +1.00000i q^{4} +(-1.30432 - 0.349490i) q^{5} +(0.965926 + 0.258819i) q^{6} +(-1.83449 + 1.90648i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.866025 + 0.500000i) q^{3} +1.00000i q^{4} +(-1.30432 - 0.349490i) q^{5} +(0.965926 + 0.258819i) q^{6} +(-1.83449 + 1.90648i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +(0.675164 + 1.16942i) q^{10} +(2.57289 + 0.689405i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-3.33563 - 1.36878i) q^{13} +(2.64526 - 0.0509058i) q^{14} +(1.30432 - 0.349490i) q^{15} -1.00000 q^{16} +5.24536 q^{17} +(-0.965926 + 0.258819i) q^{18} +(-1.78704 - 6.66931i) q^{19} +(0.349490 - 1.30432i) q^{20} +(0.635473 - 2.56830i) q^{21} +(-1.33183 - 2.30679i) q^{22} +0.262474i q^{23} +(-0.258819 + 0.965926i) q^{24} +(-2.75103 - 1.58831i) q^{25} +(1.39077 + 3.32652i) q^{26} +1.00000i q^{27} +(-1.90648 - 1.83449i) q^{28} +(3.07741 - 5.33023i) q^{29} +(-1.16942 - 0.675164i) q^{30} +(-0.112859 - 0.421196i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-2.57289 + 0.689405i) q^{33} +(-3.70903 - 3.70903i) q^{34} +(3.05905 - 1.84551i) q^{35} +(0.866025 + 0.500000i) q^{36} +(1.94672 - 1.94672i) q^{37} +(-3.45229 + 5.97954i) q^{38} +(3.57313 - 0.482416i) q^{39} +(-1.16942 + 0.675164i) q^{40} +(-2.81615 - 10.5100i) q^{41} +(-2.26541 + 1.36672i) q^{42} +(6.74810 - 3.89602i) q^{43} +(-0.689405 + 2.57289i) q^{44} +(-0.954826 + 0.954826i) q^{45} +(0.185597 - 0.185597i) q^{46} +(-1.48760 + 5.55179i) q^{47} +(0.866025 - 0.500000i) q^{48} +(-0.269318 - 6.99482i) q^{49} +(0.822169 + 3.06837i) q^{50} +(-4.54261 + 2.62268i) q^{51} +(1.36878 - 3.33563i) q^{52} +(0.878238 - 1.52115i) q^{53} +(0.707107 - 0.707107i) q^{54} +(-3.11493 - 1.79840i) q^{55} +(0.0509058 + 2.64526i) q^{56} +(4.88227 + 4.88227i) q^{57} +(-5.94510 + 1.59298i) q^{58} +(-6.09059 - 6.09059i) q^{59} +(0.349490 + 1.30432i) q^{60} +(-7.62133 - 4.40017i) q^{61} +(-0.218027 + 0.377634i) q^{62} +(0.733815 + 2.54195i) q^{63} -1.00000i q^{64} +(3.87234 + 2.95110i) q^{65} +(2.30679 + 1.33183i) q^{66} +(-2.68089 + 10.0052i) q^{67} +5.24536i q^{68} +(-0.131237 - 0.227309i) q^{69} +(-3.46805 - 0.858097i) q^{70} +(1.08417 - 4.04618i) q^{71} +(-0.258819 - 0.965926i) q^{72} +(4.86981 - 1.30486i) q^{73} -2.75308 q^{74} +3.17662 q^{75} +(6.66931 - 1.78704i) q^{76} +(-6.03427 + 3.64046i) q^{77} +(-2.86771 - 2.18547i) q^{78} +(3.12948 + 5.42042i) q^{79} +(1.30432 + 0.349490i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-5.44038 + 9.42301i) q^{82} +(9.32218 - 9.32218i) q^{83} +(2.56830 + 0.635473i) q^{84} +(-6.84160 - 1.83320i) q^{85} +(-7.52653 - 2.01673i) q^{86} +6.15482i q^{87} +(2.30679 - 1.33183i) q^{88} +(4.38711 + 4.38711i) q^{89} +1.35033 q^{90} +(8.72872 - 3.84830i) q^{91} -0.262474 q^{92} +(0.308337 + 0.308337i) q^{93} +(4.97760 - 2.87382i) q^{94} +9.32344i q^{95} +(-0.965926 - 0.258819i) q^{96} +(-18.5733 - 4.97669i) q^{97} +(-4.75565 + 5.13652i) q^{98} +(1.88349 - 1.88349i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{7} + 20 q^{9}+O(q^{10}) \) 40 * q + 4 * q^7 + 20 * q^9	\( 40 q + 4 q^{7} + 20 q^{9} + 8 q^{11} - 20 q^{12} + 4 q^{14} - 40 q^{16} + 16 q^{17} + 4 q^{19} + 4 q^{21} - 4 q^{22} - 24 q^{25} + 8 q^{26} - 4 q^{28} - 12 q^{29} - 8 q^{33} - 8 q^{34} - 32 q^{35} + 40 q^{37} + 8 q^{38} + 20 q^{39} + 20 q^{41} + 12 q^{42} - 24 q^{43} - 4 q^{44} + 32 q^{46} + 4 q^{47} + 32 q^{49} - 16 q^{50} + 24 q^{51} + 16 q^{52} - 4 q^{53} + 24 q^{55} + 12 q^{56} + 8 q^{57} + 12 q^{58} + 24 q^{59} + 60 q^{61} + 32 q^{62} - 4 q^{63} + 44 q^{65} - 12 q^{67} - 8 q^{69} - 24 q^{70} - 28 q^{71} + 60 q^{73} - 40 q^{74} - 72 q^{75} + 4 q^{76} - 12 q^{77} + 4 q^{78} - 20 q^{81} - 24 q^{82} + 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{89} - 16 q^{92} - 24 q^{93} - 48 q^{97} - 88 q^{98} + 4 q^{99}+O(q^{100}) \) 40 * q + 4 * q^7 + 20 * q^9 + 8 * q^11 - 20 * q^12 + 4 * q^14 - 40 * q^16 + 16 * q^17 + 4 * q^19 + 4 * q^21 - 4 * q^22 - 24 * q^25 + 8 * q^26 - 4 * q^28 - 12 * q^29 - 8 * q^33 - 8 * q^34 - 32 * q^35 + 40 * q^37 + 8 * q^38 + 20 * q^39 + 20 * q^41 + 12 * q^42 - 24 * q^43 - 4 * q^44 + 32 * q^46 + 4 * q^47 + 32 * q^49 - 16 * q^50 + 24 * q^51 + 16 * q^52 - 4 * q^53 + 24 * q^55 + 12 * q^56 + 8 * q^57 + 12 * q^58 + 24 * q^59 + 60 * q^61 + 32 * q^62 - 4 * q^63 + 44 * q^65 - 12 * q^67 - 8 * q^69 - 24 * q^70 - 28 * q^71 + 60 * q^73 - 40 * q^74 - 72 * q^75 + 4 * q^76 - 12 * q^77 + 4 * q^78 - 20 * q^81 - 24 * q^82 + 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^89 - 16 * q^92 - 24 * q^93 - 48 * q^97 - 88 * q^98 + 4 * q^99

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