LMFDB - Embedded newform 546.2.cg.b.145.2

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			145.2
Character	$\chi$	$=$	546.145
Dual form			546.2.cg.b.241.2

$q$-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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

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

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	−0.538393	−	0.842694i	$-0.680968\pi$
$5$	−1.30432	+	0.349490i	−0.583308	+	0.156297i	−0.0449150	+	0.998991i	$0.514302\pi$
$6$	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	0.150843	−	0.988558i	$-0.451801\pi$
$11$	2.57289	−	0.689405i	0.775757	−	0.207863i	0.624913	+	0.780694i	$0.285134\pi$
$12$	−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	0.384720	+	0.923033i	$0.374298\pi$
$19$	−1.78704	+	6.66931i	−0.409974	+	1.53004i	−0.794694	+	0.607011i	$0.792369\pi$
$20$	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	$-0.991288\pi$
$23$		−	0.262474i		−	0.0547296i	0.999626	−	0.0273648i	$-0.00871157\pi$
$24$	−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	0.996416	+	0.0845847i	$0.0269564\pi$
$29$	3.07741	+	5.33023i	0.571461	+	0.989799i	−0.424956	+	0.905214i	$0.639710\pi$
$30$	−1.16942	+	0.675164i	−0.213506	+	0.123267i
$31$	−0.112859	+	0.421196i	−0.0202701	+	0.0756491i	−0.975320	−	0.220796i	$-0.929135\pi$
$31$	−0.112859	+	0.421196i	−0.0202701	+	0.0756491i	0.955050	+	0.296445i	$0.0958012\pi$
$32$	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	0.848782	−	0.528743i	$-0.177336\pi$
$37$	1.94672	+	1.94672i	0.320039	+	0.320039i	−0.528743	+	0.848782i	$0.677336\pi$
$38$	−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	0.289483	+	0.957183i	$0.406517\pi$
$41$	−2.81615	+	10.5100i	−0.439808	+	1.64139i	−0.729291	+	0.684203i	$0.760150\pi$
$42$	−2.26541	−	1.36672i	−0.349560	−	0.210889i
$43$	6.74810	+	3.89602i	1.02908	+	0.594137i	0.916720	−	0.399531i	$-0.130827\pi$
$43$	6.74810	+	3.89602i	1.02908	+	0.594137i	0.112356	+	0.993668i	$0.464160\pi$
$44$	−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	−0.985457	−	0.169924i	$-0.945648\pi$
$47$	−1.48760	−	5.55179i	−0.216988	−	0.809812i	0.768469	−	0.639887i	$-0.221019\pi$
$48$	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	0.920018	−	0.391875i	$-0.128174\pi$
$53$	0.878238	+	1.52115i	0.120635	+	0.208946i	−0.799383	+	0.600822i	$0.794840\pi$
$54$	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	−0.981969	−	0.189042i	$-0.939462\pi$
$59$	−6.09059	+	6.09059i	−0.792927	+	0.792927i	0.189042	+	0.981969i	$0.439462\pi$
$60$	0.349490	−	1.30432i	0.0451190	−	0.168387i
$61$	−7.62133	+	4.40017i	−0.975811	+	0.563385i	−0.901003	−	0.433813i	$-0.857168\pi$
$61$	−7.62133	+	4.40017i	−0.975811	+	0.563385i	−0.0748080	+	0.997198i	$0.523834\pi$
$62$	−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	−0.911751	−	0.410743i	$-0.865269\pi$
$67$	−2.68089	−	10.0052i	−0.327523	−	1.22233i	0.584228	−	0.811589i	$-0.301397\pi$
$68$		−	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	0.999944	−	0.0105994i	$-0.00337396\pi$
$71$	1.08417	+	4.04618i	0.128667	+	0.480193i	−0.871276	+	0.490793i	$0.836707\pi$
$72$	−0.258819	+	0.965926i	−0.0305021	+	0.113835i
$73$	4.86981	+	1.30486i	0.569968	+	0.152723i	0.532282	−	0.846567i	$-0.321335\pi$
$73$	4.86981	+	1.30486i	0.569968	+	0.152723i	0.0376862	+	0.999290i	$0.488001\pi$
$74$	−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	−0.634522	−	0.772905i	$-0.718803\pi$
$79$	3.12948	−	5.42042i	0.352094	−	0.609845i	0.986616	+	0.163060i	$0.0521364\pi$
$80$	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	0.999723	+	0.0235188i	$0.00748696\pi$
$83$	9.32218	+	9.32218i	1.02324	+	1.02324i	0.0235188	+	0.999723i	$0.492513\pi$
$84$	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	−0.435268	−	0.900301i	$-0.643346\pi$
$89$	4.38711	−	4.38711i	0.465033	−	0.465033i	0.900301	+	0.435268i	$0.143346\pi$
$90$	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	−0.886757	+	0.462236i	$0.847047\pi$
$97$	−18.5733	+	4.97669i	−1.88583	+	0.505306i	−0.999072	+	0.0430700i	$0.986286\pi$
$98$	−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	−0.777601	−	0.628759i	$-0.783563\pi$
$101$	1.56497	−	2.71061i	0.155721	−	0.269716i	0.933321	+	0.359043i	$0.116897\pi$
$102$	5.06662	−	1.35760i	0.501671	−	0.134422i
$103$	5.32608	−	9.22505i	0.524795	−	0.908971i	−0.474789	−	0.880100i	$-0.657475\pi$
$103$	5.32608	−	9.22505i	0.524795	−	0.908971i	0.999583	−	0.0288710i	$-0.00919119\pi$
$104$	−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	−0.369970	−	0.929044i	$-0.620632\pi$
$109$	−12.0575	−	3.23079i	−1.15490	−	0.309453i	−0.784925	+	0.619590i	$0.787299\pi$
$110$	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	−0.867839	−	0.496845i	$-0.834492\pi$
$113$	−0.0386809	+	0.0669973i	−0.00363879	+	0.00630257i	0.864200	+	0.503148i	$0.167825\pi$
$114$			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	0.162197	−	0.986758i	$-0.448142\pi$
$127$	12.3722	−	7.14308i	1.09785	−	0.633846i	0.935656	+	0.352913i	$0.114809\pi$
$128$	−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	0.880262	−	0.474488i	$-0.157367\pi$
$131$	10.4094	+	6.00988i	0.909475	+	0.525086i	0.0292128	+	0.999573i	$0.490700\pi$
$132$	−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	0.603852	−	0.797096i	$-0.293632\pi$
$137$	−2.26186	−	2.26186i	−0.193244	−	0.193244i	−0.797096	+	0.603852i	$0.793632\pi$
$138$	−0.0679332	−	0.253530i	−0.00578286	−	0.0215819i
$139$	5.23898	+	3.02473i	0.444365	+	0.256554i	0.705447	−	0.708762i	$-0.250746\pi$
$139$	5.23898	+	3.02473i	0.444365	+	0.256554i	−0.261083	+	0.965316i	$0.584079\pi$
$140$	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	0.365893	−	0.930657i	$-0.380764\pi$
$149$	2.65415	+	0.711179i	0.217437	+	0.0582620i	−0.148456	+	0.988919i	$0.547430\pi$
$150$	−2.24621	+	2.24621i	−0.183402	+	0.183402i
$151$	3.25321	−	12.1411i	0.264742	−	0.988032i	−0.697665	−	0.716424i	$-0.745778\pi$
$151$	3.25321	−	12.1411i	0.264742	−	0.988032i	0.962408	−	0.271608i	$-0.0875556\pi$
$152$	−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	−0.671829	−	0.740706i	$-0.734491\pi$
$157$	−4.58939	+	2.64969i	−0.366273	+	0.211468i	0.305556	+	0.952174i	$0.401158\pi$
$158$	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	−0.00375811	+	0.999993i	$0.501196\pi$
$163$	−6.38996	+	23.8476i	−0.500500	+	1.86789i	−0.496742	+	0.867898i	$0.665470\pi$
$164$	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	−0.829796	−	0.558066i	$-0.811544\pi$
$167$	−23.6159	−	6.32787i	−1.82745	−	0.489665i	−0.997658	+	0.0684012i	$0.978210\pi$
$168$	−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	0.872380	−	0.488828i	$-0.162575\pi$
$173$	0.169053	+	0.292808i	0.0128528	+	0.0222618i	−0.859527	+	0.511090i	$0.829242\pi$
$174$	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	0.668822	−	0.743423i	$-0.266799\pi$
$179$	4.80858	+	2.77624i	0.359410	+	0.207506i	−0.309412	+	0.950928i	$0.600132\pi$
$180$	−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	0.999824	−	0.0187426i	$-0.00596631\pi$
$191$	6.68460	+	11.5781i	0.483681	+	0.837759i	−0.516144	+	0.856502i	$0.672633\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−9.13181	+	2.44686i	−0.657322	+	0.176129i	−0.572037	−	0.820228i	$-0.693847\pi$
$193$	−9.13181	+	2.44686i	−0.657322	+	0.176129i	−0.0852847	+	0.996357i	$0.527180\pi$
$194$	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	0.633115	−	0.774058i	$-0.281776\pi$
$197$	11.1496	+	2.98754i	0.794379	+	0.212853i	0.161265	+	0.986911i	$0.448443\pi$
$198$	−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	−0.937033	−	0.349241i	$-0.886439\pi$
$211$	−11.1990	−	19.3972i	−0.770968	−	1.33536i	0.166065	−	0.986115i	$-0.446894\pi$
$212$	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	0.631598	+	0.775296i	$0.282399\pi$
$223$	−4.52520	+	16.8883i	−0.303030	+	1.13092i	−0.934628	+	0.355627i	$0.884267\pi$
$224$	−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	−0.983068	−	0.183240i	$-0.941342\pi$
$227$	−17.5722	−	17.5722i	−1.16631	−	1.16631i	−0.183240	−	0.983068i	$-0.558658\pi$
$228$	−4.88227	−	4.88227i	−0.323336	−	0.323336i
$229$	0.302393	+	1.12855i	0.0199827	+	0.0745765i	0.975197	−	0.221338i	$-0.0710424\pi$
$229$	0.302393	+	1.12855i	0.0199827	+	0.0745765i	−0.955214	+	0.295914i	$0.904376\pi$
$230$	−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	0.133172	−	0.991093i	$-0.457484\pi$
$233$	−10.0524	−	5.80374i	−0.658553	−	0.380216i	−0.791725	+	0.610877i	$0.790817\pi$
$234$	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	−0.212325	+	0.977199i	$0.568103\pi$
$239$	−18.3896	+	18.3896i	−1.18952	+	1.18952i	−0.977199	+	0.212325i	$0.931897\pi$
$240$	−1.30432	−	0.349490i	−0.0841933	−	0.0225595i
$241$	−21.0520	+	21.0520i	−1.35608	+	1.35608i	−0.477390	+	0.878691i	$0.658417\pi$
$241$	−21.0520	+	21.0520i	−1.35608	+	1.35608i	−0.878691	+	0.477390i	$0.841583\pi$
$242$	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	−0.829291	−	0.558817i	$-0.811255\pi$
$251$	1.09799	−	1.90177i	0.0693042	−	0.120038i	0.898595	+	0.438779i	$0.144589\pi$
$252$	−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	0.179526	+	0.983753i	$0.442543\pi$
$263$	−12.3607	+	21.4093i	−0.762192	+	1.32016i	−0.941718	+	0.336402i	$0.890790\pi$
$264$	−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	$0.199453\pi$
$269$			19.2352i			1.17279i	−0.810025	+	0.586395i	$0.800547\pi$
$270$	−1.16942	−	0.675164i	−0.0711685	−	0.0410892i
$271$	0.615634	−	0.615634i	0.0373971	−	0.0373971i	−0.688161	−	0.725558i	$-0.741582\pi$
$271$	0.615634	−	0.615634i	0.0373971	−	0.0373971i	0.725558	+	0.688161i	$0.241582\pi$
$272$	−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	$0.219767\pi$
$277$			21.1989i			1.27372i	−0.770980	+	0.636859i	$0.780233\pi$
$278$	−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	0.960006	+	0.279980i	$0.0903278\pi$
$281$	20.7859	+	20.7859i	1.23999	+	1.23999i	0.279980	+	0.960006i	$0.409672\pi$
$282$	−2.87382	−	4.97760i	−0.171133	−	0.296412i
$283$	7.09128	−	12.2825i	0.421533	−	0.730116i	−0.574557	−	0.818465i	$-0.694826\pi$
$283$	7.09128	−	12.2825i	0.421533	−	0.730116i	0.996090	+	0.0883485i	$0.0281589\pi$
$284$	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	0.985977	−	0.166879i	$-0.0533689\pi$
$293$	0.832864	+	3.10829i	0.0486564	+	0.181588i	−0.937321	+	0.348467i	$0.886702\pi$
$294$	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	−0.871956	−	0.489584i	$-0.837149\pi$
$307$	−6.69970	+	6.69970i	−0.382372	+	0.382372i	0.489584	+	0.871956i	$0.337149\pi$
$308$	−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	−0.798780	−	0.601624i	$-0.794521\pi$
$311$	−16.2316	−	28.1140i	−0.920411	−	1.59420i	−0.121631	−	0.992575i	$-0.538813\pi$
$312$	2.18547	+	2.86771i	0.123728	+	0.162352i
$313$	17.6916	+	10.2143i	0.999989	+	0.577344i	0.908245	−	0.418438i	$-0.137422\pi$
$313$	17.6916	+	10.2143i	0.999989	+	0.577344i	0.0917443	+	0.995783i	$0.470756\pi$
$314$	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	0.987361	−	0.158486i	$-0.0506614\pi$
$317$	0.944317	+	3.52424i	0.0530381	+	0.197941i	−0.934323	+	0.356427i	$0.883995\pi$
$318$	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	0.198243	−	0.980153i	$-0.436477\pi$
$331$	−2.18594	−	0.585722i	−0.120150	−	0.0321942i	−0.318393	+	0.947959i	$0.603143\pi$
$332$	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	$-0.838371\pi$
$337$		−	17.8521i		−	0.972466i	0.873829	−	0.486233i	$-0.161629\pi$
$338$	−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	0.928131	−	0.372254i	$-0.121415\pi$
$349$	28.8777	+	7.73776i	1.54579	+	0.414193i	0.617658	+	0.786447i	$0.288082\pi$
$350$	−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	−0.871866	−	0.489744i	$-0.837090\pi$
$353$	−25.9664	+	6.95768i	−1.38205	+	0.370320i	−0.510187	+	0.860064i	$0.670424\pi$
$354$	−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	0.630059	−	0.776547i	$-0.283031\pi$
$359$	29.6332	−	7.94019i	1.56398	−	0.419067i	0.933921	+	0.357480i	$0.116364\pi$
$360$		−	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	0.800051	−	0.599931i	$-0.204805\pi$
$367$	13.0369	+	7.52686i	0.680521	+	0.392899i	−0.119530	+	0.992831i	$0.538139\pi$
$368$			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	0.694902	−	0.719104i	$-0.255448\pi$
$373$	−5.31715	−	9.20957i	−0.275311	−	0.476853i	−0.970214	+	0.242251i	$0.922114\pi$
$374$	−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	0.294498	−	0.955652i	$-0.404847\pi$
$379$	1.39615	+	0.374098i	0.0717156	+	0.0192161i	−0.222783	+	0.974868i	$0.571514\pi$
$380$	−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	−0.547935	−	0.836521i	$-0.684586\pi$
$383$	6.74887	−	25.1871i	0.344851	−	1.28700i	0.892786	−	0.450480i	$-0.148747\pi$
$384$	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	−0.368460	−	0.929643i	$-0.620115\pi$
$389$	4.97819	−	2.87416i	0.252404	−	0.145726i	0.620865	+	0.783918i	$0.286782\pi$
$390$	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	0.619524	−	0.784978i	$-0.287326\pi$
$397$	15.2138	+	4.07652i	0.763558	+	0.204595i	0.144034	+	0.989573i	$0.453993\pi$
$398$	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	0.958832	−	0.283975i	$-0.0916532\pi$
$401$	13.5140	+	13.5140i	0.674857	+	0.674857i	−0.283975	+	0.958832i	$0.591653\pi$
$402$	−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	0.320473	−	0.947258i	$-0.396158\pi$
$409$	−12.6759	−	12.6759i	−0.626784	−	0.626784i	−0.947258	+	0.320473i	$0.896158\pi$
$410$	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	−0.374345	−	0.927290i	$-0.622132\pi$
$419$	4.94418	−	2.85452i	0.241539	−	0.139452i	0.615884	+	0.787837i	$0.288799\pi$
$420$	−3.12779	+	1.72645i	−0.152620	+	0.0842424i
$421$	11.2327	−	11.2327i	0.547449	−	0.547449i	−0.378253	−	0.925702i	$-0.623475\pi$
$421$	11.2327	−	11.2327i	0.547449	−	0.547449i	0.925702	+	0.378253i	$0.123475\pi$
$422$	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	−0.982293	−	0.187349i	$-0.940011\pi$
$431$	−4.67687	−	17.4543i	−0.225277	−	0.840744i	0.757017	−	0.653395i	$-0.226656\pi$
$432$			1.00000i			0.0481125i
$433$	8.06894	−	13.9758i	0.387768	−	0.671635i	−0.604381	−	0.796696i	$-0.706579\pi$
$433$	8.06894	−	13.9758i	0.387768	−	0.671635i	0.992149	+	0.125061i	$0.0399127\pi$
$434$	−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	−0.845485	−	0.534000i	$-0.820688\pi$
$443$	0.835906	−	1.44783i	0.0397151	−	0.0687885i	0.885200	+	0.465211i	$0.154022\pi$
$444$	−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	−0.277538	−	0.960715i	$-0.589519\pi$
$449$	−0.795385	+	0.213123i	−0.0375366	+	0.0100579i	0.240002	+	0.970772i	$0.422852\pi$
$450$	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	−0.390292	−	0.920691i	$-0.627626\pi$
$457$	11.3386	−	11.3386i	0.530399	−	0.530399i	0.920691	+	0.390292i	$0.127626\pi$
$458$	−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	0.0993736	−	0.995050i	$-0.468316\pi$
$461$	14.6637	−	3.92914i	0.682959	−	0.182998i	0.583585	+	0.812052i	$0.301649\pi$
$462$	−6.77088	−	1.95463i	−0.315010	−	0.0909377i
$463$	−2.81768	−	2.81768i	−0.130948	−	0.130948i	0.638595	−	0.769543i	$-0.279516\pi$
$463$	−2.81768	−	2.81768i	−0.130948	−	0.130948i	−0.769543	+	0.638595i	$0.779516\pi$
$464$	−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	−0.914095	−	0.405500i	$-0.867098\pi$
$467$	−2.28797	+	3.96288i	−0.105875	+	0.183380i	0.808221	+	0.588880i	$0.200431\pi$
$468$	−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	−0.580314	−	0.814393i	$-0.697070\pi$
$479$	−10.6135	−	39.6102i	−0.484944	−	1.80983i	0.0953704	−	0.995442i	$-0.469596\pi$
$480$	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	−0.936937	−	0.349499i	$-0.886352\pi$
$487$	−12.9636	+	12.9636i	−0.587438	+	0.587438i	0.349499	+	0.936937i	$0.386352\pi$
$488$	−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	−0.886141	−	0.463415i	$-0.846624\pi$
$491$	−20.5605	+	11.8706i	−0.927883	+	0.535713i	−0.0417413	+	0.999128i	$0.513291\pi$
$492$	−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	0.808452	+	0.588562i	$0.200306\pi$
$499$	8.99324	+	33.5632i	0.402593	+	1.50250i	−0.405859	+	0.913935i	$0.633028\pi$
$500$	−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	0.753649	−	0.657277i	$-0.228292\pi$
$503$	12.5876	+	7.26748i	0.561256	+	0.324041i	−0.192394	+	0.981318i	$0.561625\pi$
$504$	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	0.999524	−	0.0308623i	$-0.00982535\pi$
$509$	21.8540	+	21.8540i	0.968661	+	0.968661i	−0.0308623	+	0.999524i	$0.509825\pi$
$510$	−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	0.686375	−	0.727247i	$-0.259201\pi$
$521$	37.8760	−	21.8677i	1.65938	−	0.958042i	0.973002	−	0.230795i	$-0.0741326\pi$
$522$	−1.59298	−	5.94510i	−0.0697230	−	0.260210i
$523$		−	14.3172i		−	0.626048i	−0.949745	−	0.313024i	$-0.898658\pi$
$523$		−	14.3172i		−	0.626048i	0.949745	−	0.313024i	$-0.101342\pi$
$524$	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	−0.532409	−	0.846487i	$-0.678713\pi$
$541$	−13.2636	+	3.55396i	−0.570246	+	0.152797i	−0.0378365	+	0.999284i	$0.512047\pi$
$542$			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	−0.475968	−	0.879463i	$-0.657902\pi$
$557$	−10.5835	+	2.83584i	−0.448437	+	0.120158i	0.0275312	+	0.999621i	$0.491235\pi$
$558$	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	$-0.935324\pi$
$569$		−	9.62692i		−	0.403581i	0.979429	−	0.201791i	$-0.0646761\pi$
$570$	−2.41308	−	9.00575i	−0.101073	−	0.377209i
$571$	9.45507	−	5.45889i	0.395682	−	0.228447i	−0.288937	−	0.957348i	$-0.593302\pi$
$571$	9.45507	−	5.45889i	0.395682	−	0.228447i	0.684619	+	0.728901i	$0.259968\pi$
$572$	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	−0.656110	−	0.754666i	$-0.727799\pi$
$577$	6.95237	−	25.9466i	0.289431	−	1.08017i	0.945540	−	0.325505i	$-0.105534\pi$
$578$	−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	−0.618269	−	0.785967i	$-0.712166\pi$
$587$	7.51437	−	28.0440i	0.310151	−	1.15750i	0.928420	−	0.371533i	$-0.121168\pi$
$588$	−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	0.926919	−	0.375262i	$-0.122447\pi$
$593$	−1.54505	−	5.76620i	−0.0634475	−	0.236789i	−0.990366	+	0.138473i	$0.955781\pi$
$594$	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	0.511742	−	0.859139i	$-0.329000\pi$
$599$	−11.9476	−	20.6938i	−0.488165	−	0.845527i	−0.999907	+	0.0136121i	$0.995667\pi$
$600$	2.24621	+	2.24621i	0.0917010	+	0.0917010i
$601$	31.4273	−	18.1445i	1.28194	−	0.740131i	0.304741	−	0.952435i	$-0.401430\pi$
$601$	31.4273	−	18.1445i	1.28194	−	0.740131i	0.977204	+	0.212304i	$0.0680967\pi$
$602$	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	−0.500791	−	0.865568i	$-0.666957\pi$
$607$	−0.0389874	+	0.0225094i	−0.00158245	+	0.000913628i	0.499209	+	0.866482i	$0.333624\pi$
$608$	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	0.996908	−	0.0785715i	$-0.0250359\pi$
$613$	2.33413	+	8.71109i	0.0942747	+	0.351838i	−0.902634	+	0.430409i	$0.858369\pi$
$614$		−	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	−0.697054	−	0.717019i	$-0.745506\pi$
$617$	−11.2249	−	41.8918i	−0.451897	−	1.68650i	0.245157	−	0.969483i	$-0.421161\pi$
$618$	2.75698	−	10.2892i	0.110902	−	0.413892i
$619$	19.8679	+	5.32358i	0.798557	+	0.213973i	0.634950	−	0.772553i	$-0.281021\pi$
$619$	19.8679	+	5.32358i	0.798557	+	0.213973i	0.163607	+	0.986526i	$0.447687\pi$
$620$	−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	−0.162746	−	0.986668i	$-0.552035\pi$
$631$	4.76385	−	1.27647i	0.189646	−	0.0508154i	0.352392	+	0.935853i	$0.385368\pi$
$632$	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	$0.304268\pi$
$641$			41.3607i			1.63365i	−0.576885	+	0.816825i	$0.695732\pi$
$642$	8.70769	−	2.33322i	0.343665	−	0.0920848i
$643$	−9.73707	+	2.60904i	−0.383992	+	0.102890i	−0.445651	−	0.895207i	$-0.647028\pi$
$643$	−9.73707	+	2.60904i	−0.383992	+	0.102890i	0.0616584	+	0.998097i	$0.480361\pi$
$644$	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	−0.654040	−	0.756460i	$-0.726927\pi$
$647$	8.34544	−	14.4547i	0.328093	−	0.568274i	0.982133	+	0.188186i	$0.0602607\pi$
$648$	−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	0.423585	+	0.905856i	$0.360772\pi$
$659$	−14.7018	+	25.4643i	−0.572702	+	0.991950i	−0.996287	+	0.0860931i	$0.972562\pi$
$660$		−	3.59681i		−	0.140006i
$661$	9.53644	+	35.5905i	0.370925	+	1.38431i	0.859209	+	0.511625i	$0.170956\pi$
$661$	9.53644	+	35.5905i	0.370925	+	1.38431i	−0.488284	+	0.872685i	$0.662377\pi$
$662$	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	−0.656790	−	0.754073i	$-0.728086\pi$
$673$	−8.61642	+	4.97469i	−0.332138	+	0.191760i	0.324652	+	0.945834i	$0.394753\pi$
$674$	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	0.487347	−	0.873208i	$-0.337965\pi$
$677$	−0.655682	−	0.378558i	−0.0251999	−	0.0145492i	−0.512547	+	0.858659i	$0.671298\pi$
$678$	−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	0.736884	−	0.676019i	$-0.236296\pi$
$683$	1.59067	+	1.59067i	0.0608652	+	0.0608652i	−0.676019	+	0.736884i	$0.736296\pi$
$684$	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	0.933325	−	0.359032i	$-0.116893\pi$
$691$	15.0964	+	15.0964i	0.574293	+	0.574293i	−0.359032	+	0.933325i	$0.616893\pi$
$692$	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	$0.0335241\pi$
$701$			5.56664i			0.210249i	−0.994459	+	0.105124i	$0.966476\pi$
$702$	−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	0.516215	+	0.856459i	$0.327340\pi$
$709$	−9.56097	+	35.6820i	−0.359070	+	1.34007i	−0.875285	+	0.483607i	$0.839326\pi$
$710$	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	0.999966	+	0.00824079i	$0.00262315\pi$
$719$	13.5980	+	23.5524i	0.507120	+	0.878357i	−0.492846	+	0.870116i	$0.664044\pi$
$720$	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	0.00538890	−	0.999985i	$-0.498285\pi$
$733$	13.8090	−	3.70012i	0.510049	−	0.136667i	0.504660	+	0.863318i	$0.331618\pi$
$734$	−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	−0.702069	−	0.712109i	$-0.747740\pi$
$739$	−25.9347	+	6.94919i	−0.954025	+	0.255630i	−0.251955	+	0.967739i	$0.581074\pi$
$740$	−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	0.178856	−	0.983875i	$-0.442760\pi$
$743$	−4.31189	−	1.15537i	−0.158188	−	0.0423863i	−0.337044	+	0.941489i	$0.609427\pi$
$744$	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	$-0.738120\pi$
$751$		−	40.1747i		−	1.46600i	0.680230	−	0.732999i	$-0.261880\pi$
$752$	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	−0.898560	−	0.438852i	$-0.855385\pi$
$757$	−22.8181	−	39.5220i	−0.829336	−	1.43645i	0.0692231	−	0.997601i	$-0.477948\pi$
$758$	−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	0.932579	−	0.360965i	$-0.117553\pi$
$761$	43.0272	+	11.5291i	1.55973	+	0.417930i	0.627155	+	0.778894i	$0.284219\pi$
$762$	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	−0.867894	−	0.496750i	$-0.834526\pi$
$769$	3.66323	−	13.6714i	0.132099	−	0.493002i	0.999993	+	0.00374840i	$0.00119316\pi$
$770$	−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	0.998160	−	0.0606384i	$-0.0193136\pi$
$773$	26.0658	+	26.0658i	0.937521	+	0.937521i	−0.0606384	+	0.998160i	$0.519314\pi$
$774$	−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	−0.562879	−	0.826539i	$-0.690306\pi$
$787$	7.39659	−	7.39659i	0.263660	−	0.263660i	0.826539	+	0.562879i	$0.190306\pi$
$788$	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	−0.639081	−	0.769139i	$-0.720685\pi$
$797$	9.78362	−	16.9457i	0.346554	−	0.600248i	0.985635	+	0.168891i	$0.0540185\pi$
$798$	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	−0.923022	−	0.384746i	$-0.874289\pi$
$809$	−3.64954	+	6.32120i	−0.128311	+	0.222241i	0.794711	+	0.606988i	$0.207622\pi$
$810$	0.675164	+	1.16942i	0.0237228	+	0.0410892i
$811$	13.4146	+	13.4146i	0.471049	+	0.471049i	0.902254	−	0.431205i	$-0.141911\pi$
$811$	13.4146	+	13.4146i	0.471049	+	0.471049i	−0.431205	+	0.902254i	$0.641911\pi$
$812$	−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	0.140443	−	0.990089i	$-0.455147\pi$
$821$	32.3932	−	32.3932i	1.13053	−	1.13053i	0.990089	−	0.140443i	$-0.0448528\pi$
$822$	−2.77021	−	1.59938i	−0.0966221	−	0.0557848i
$823$			45.2057i			1.57577i	0.615822	+	0.787885i	$0.288824\pi$
$823$			45.2057i			1.57577i	−0.615822	+	0.787885i	$0.711176\pi$
$824$	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	0.638497	−	0.769625i	$-0.279557\pi$
$827$	−3.77092	−	3.77092i	−0.131128	−	0.131128i	−0.769625	+	0.638497i	$0.779557\pi$
$828$	−0.131237	−	0.227309i	−0.00456080	−	0.00789954i
$829$	−19.9577	+	34.5677i	−0.693159	+	1.20059i	0.277638	+	0.960686i	$0.410448\pi$
$829$	−19.9577	+	34.5677i	−0.693159	+	1.20059i	−0.970797	+	0.239901i	$0.922885\pi$
$830$	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	−0.727882	−	0.685702i	$-0.759495\pi$
$839$	−12.7555	−	47.6042i	−0.440369	−	1.64348i	0.287514	−	0.957777i	$-0.407171\pi$
$840$	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	−0.702183	−	0.711997i	$-0.747791\pi$
$853$	0.286626	−	0.286626i	0.00981388	−	0.00981388i	0.711997	+	0.702183i	$0.247791\pi$
$854$	−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	0.521896	−	0.853009i	$-0.325225\pi$
$857$	−13.9868	−	24.2258i	−0.477780	−	0.827539i	−0.999676	+	0.0254706i	$0.991892\pi$
$858$	−5.87163	+	7.59998i	−0.200454	+	0.259459i
$859$	14.1312	+	8.15866i	0.482151	+	0.278370i	0.721312	−	0.692610i	$-0.243539\pi$
$859$	14.1312	+	8.15866i	0.482151	+	0.278370i	−0.239161	+	0.970980i	$0.576873\pi$
$860$	−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	0.998785	−	0.0492701i	$-0.0156895\pi$
$863$	3.20727	+	11.9697i	0.109177	+	0.407453i	−0.889609	+	0.456724i	$0.849023\pi$
$864$	−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	0.824712	−	0.565554i	$-0.191337\pi$
$877$	37.2000	+	9.96772i	1.25616	+	0.336586i	0.431444	+	0.902140i	$0.358004\pi$
$878$	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	0.965781	+	0.259360i	$0.0835116\pi$
$881$	20.9998	+	36.3728i	0.707503	+	1.22543i	−0.258278	+	0.966071i	$0.583155\pi$
$882$	2.07053	−	6.68677i	0.0697185	−	0.225155i
$883$			56.1761i			1.89048i	0.326383	+	0.945238i	$0.394170\pi$
$883$			56.1761i			1.89048i	−0.326383	+	0.945238i	$0.605830\pi$
$884$	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	$0.0728675\pi$
$887$			13.5169i			0.453852i	−0.973912	+	0.226926i	$0.927133\pi$
$888$	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	−0.435629	−	0.900127i	$-0.643474\pi$
$907$	−43.1561	−	24.9162i	−1.43298	−	0.827329i	−0.997347	+	0.0727979i	$0.976807\pi$
$908$	−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	0.892265	−	0.451511i	$-0.149115\pi$
$919$	1.67074	+	2.89380i	0.0551125	+	0.0954576i	−0.837153	+	0.546969i	$0.815782\pi$
$920$	−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	−0.873755	−	0.486366i	$-0.838322\pi$
$929$	3.84413	−	14.3465i	0.126122	−	0.470693i	0.999877	+	0.0156726i	$0.00498896\pi$
$930$	−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	$0.197774\pi$
$937$			35.6374i			1.16422i	−0.813108	+	0.582112i	$0.802226\pi$
$938$	−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	−0.650829	−	0.759225i	$-0.725578\pi$
$941$	8.97013	−	33.4770i	0.292418	−	1.09132i	0.943246	−	0.332093i	$-0.107755\pi$
$942$	−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	0.286678	−	0.958027i	$-0.407449\pi$
$947$	−20.6597	−	20.6597i	−0.671349	−	0.671349i	−0.958027	+	0.286678i	$0.907449\pi$
$948$	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	0.893700	−	0.448665i	$-0.148100\pi$
$953$	29.3888	+	16.9676i	0.951995	+	0.549635i	0.0582951	+	0.998299i	$0.481434\pi$
$954$	−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	−0.863901	−	0.503662i	$-0.831986\pi$
$967$	−11.2022	+	11.2022i	−0.360239	+	0.360239i	0.503662	+	0.863901i	$0.331986\pi$
$968$	−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	−0.380616	−	0.924733i	$-0.624288\pi$
$971$	7.16445	−	4.13639i	0.229918	−	0.132743i	0.610534	+	0.791990i	$0.290955\pi$
$972$	−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	0.942912	−	0.333042i	$-0.108075\pi$
$977$	−1.25636	−	4.68882i	−0.0401947	−	0.150008i	−0.983107	+	0.183033i	$0.941408\pi$
$978$			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	0.0396949	−	0.999212i	$-0.487361\pi$
$983$	−13.3417	−	3.57490i	−0.425534	−	0.114022i	−0.465229	+	0.885190i	$0.654028\pi$
$984$	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	−0.620465	−	0.784234i	$-0.713056\pi$
$991$	11.6141	−	20.1162i	0.368935	−	0.639014i	0.989399	+	0.145221i	$0.0463893\pi$
$992$	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	$-0.973603\pi$
$997$		−	5.23091i		−	0.165665i	0.996564	−	0.0828323i	$-0.0263966\pi$
$998$	−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.145.2	yes	40
7.3	odd	6		546.2.by.b.535.2	yes	40
13.7	odd	12		546.2.by.b.397.2	✓	40
91.59	even	12	inner	546.2.cg.b.241.2	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.b.397.2	✓	40	13.7	odd	12
546.2.by.b.535.2	yes	40	7.3	odd	6
546.2.cg.b.145.2	yes	40	1.1	even	1	trivial
546.2.cg.b.241.2	yes	40	91.59	even	12	inner

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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