LMFDB - Embedded newform 156.2.w.c.67.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [156,2,Mod(7,156)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(156, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 11]))

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

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

chi := DirichletCharacter("156.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 156 = 2^{2} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	156.w (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:	$1.24566627153$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			67.4
Character	$\chi$	$=$	156.67
Dual form			156.2.w.c.7.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.101912 - 1.41054i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-1.97923 + 0.287501i) q^{4} +(2.43250 - 2.43250i) q^{5} +(-0.793527 - 1.17060i) q^{6} +(0.522652 + 1.95057i) q^{7} +(0.607239 + 2.76247i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.101912 - 1.41054i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-1.97923 + 0.287501i) q^{4} +(2.43250 - 2.43250i) q^{5} +(-0.793527 - 1.17060i) q^{6} +(0.522652 + 1.95057i) q^{7} +(0.607239 + 2.76247i) q^{8} +(0.500000 - 0.866025i) q^{9} +(-3.67903 - 3.18323i) q^{10} +(-3.03280 - 0.812637i) q^{11} +(-1.57031 + 1.23860i) q^{12} +(-3.44947 - 1.04938i) q^{13} +(2.69808 - 0.936007i) q^{14} +(0.890356 - 3.32285i) q^{15} +(3.83469 - 1.13806i) q^{16} +(4.36889 + 2.52238i) q^{17} +(-1.27252 - 0.617010i) q^{18} +(-2.75142 + 0.737240i) q^{19} +(-4.11512 + 5.51381i) q^{20} +(1.42791 + 1.42791i) q^{21} +(-0.837175 + 4.36070i) q^{22} +(2.20812 + 3.82458i) q^{23} +(1.90712 + 2.08875i) q^{24} -6.83408i q^{25} +(-1.12864 + 4.97254i) q^{26} -1.00000i q^{27} +(-1.59524 - 3.71035i) q^{28} +(0.754985 + 1.30767i) q^{29} +(-4.77774 - 0.917241i) q^{30} +(2.38964 + 2.38964i) q^{31} +(-1.99608 - 5.29298i) q^{32} +(-3.03280 + 0.812637i) q^{33} +(3.11267 - 6.41954i) q^{34} +(6.01610 + 3.47339i) q^{35} +(-0.740630 + 1.85781i) q^{36} +(-1.91258 + 7.13784i) q^{37} +(1.32031 + 3.80584i) q^{38} +(-3.51201 + 0.815946i) q^{39} +(8.19681 + 5.24260i) q^{40} +(3.46845 + 0.929369i) q^{41} +(1.86860 - 2.15965i) q^{42} +(-2.78445 + 4.82280i) q^{43} +(6.23624 + 0.736458i) q^{44} +(-0.890356 - 3.32285i) q^{45} +(5.16968 - 3.50441i) q^{46} +(8.53489 - 8.53489i) q^{47} +(2.75190 - 2.90293i) q^{48} +(2.53064 - 1.46106i) q^{49} +(-9.63972 + 0.696476i) q^{50} +5.04476 q^{51} +(7.12897 + 1.08523i) q^{52} -9.42530 q^{53} +(-1.41054 + 0.101912i) q^{54} +(-9.35402 + 5.40054i) q^{55} +(-5.07101 + 2.62827i) q^{56} +(-2.01418 + 2.01418i) q^{57} +(1.76758 - 1.19820i) q^{58} +(-2.67214 - 9.97257i) q^{59} +(-0.806892 + 6.83266i) q^{60} +(-5.34563 + 9.25891i) q^{61} +(3.12714 - 3.61420i) q^{62} +(1.95057 + 0.522652i) q^{63} +(-7.26252 + 3.35496i) q^{64} +(-10.9434 + 5.83821i) q^{65} +(1.45533 + 4.19506i) q^{66} +(3.40389 - 12.7035i) q^{67} +(-9.37222 - 3.73630i) q^{68} +(3.82458 + 2.20812i) q^{69} +(4.28624 - 8.83990i) q^{70} +(-10.4866 + 2.80989i) q^{71} +(2.69599 + 0.855353i) q^{72} +(-5.57628 - 5.57628i) q^{73} +(10.2631 + 1.97033i) q^{74} +(-3.41704 - 5.91849i) q^{75} +(5.23372 - 2.25020i) q^{76} -6.34041i q^{77} +(1.50884 + 4.87067i) q^{78} +11.8580i q^{79} +(6.55953 - 12.0962i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.957432 - 4.98709i) q^{82} +(-8.12570 - 8.12570i) q^{83} +(-3.23669 - 2.41564i) q^{84} +(16.7630 - 4.49163i) q^{85} +(7.08651 + 3.43606i) q^{86} +(1.30767 + 0.754985i) q^{87} +(0.403254 - 8.87150i) q^{88} +(-0.935561 + 3.49156i) q^{89} +(-4.59627 + 1.59452i) q^{90} +(0.244006 - 7.27687i) q^{91} +(-5.46995 - 6.93488i) q^{92} +(3.26430 + 0.874668i) q^{93} +(-12.9086 - 11.1690i) q^{94} +(-4.89948 + 8.48614i) q^{95} +(-4.37515 - 3.58582i) q^{96} +(-1.02076 - 3.80953i) q^{97} +(-2.31879 - 3.42066i) q^{98} +(-2.22016 + 2.22016i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{2} + 4 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{8} + 12 q^{9}+O(q^{10}) $ 24 * q - 4 * q^2 + 4 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 - 4 * q^8 + 12 * q^9	\( 24 q - 4 q^{2} + 4 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{8} + 12 q^{9} + 12 q^{10} + 4 q^{11} - 4 q^{12} - 22 q^{14} - 4 q^{15} + 12 q^{16} - 2 q^{18} - 22 q^{19} - 4 q^{20} + 10 q^{21} - 34 q^{22} + 2 q^{24} - 4 q^{26} - 14 q^{28} + 8 q^{29} - 16 q^{30} - 2 q^{31} - 34 q^{32} + 4 q^{33} + 20 q^{34} + 24 q^{35} - 4 q^{36} - 12 q^{37} - 12 q^{38} - 6 q^{39} + 28 q^{40} - 36 q^{41} + 6 q^{42} + 10 q^{43} + 20 q^{44} + 4 q^{45} - 2 q^{46} + 20 q^{47} + 32 q^{48} - 54 q^{49} - 24 q^{50} + 36 q^{51} + 4 q^{52} - 36 q^{53} - 4 q^{54} - 24 q^{55} + 70 q^{56} - 32 q^{57} + 48 q^{58} - 36 q^{59} - 28 q^{60} - 2 q^{61} + 64 q^{62} + 8 q^{63} - 8 q^{64} + 16 q^{65} + 20 q^{66} - 16 q^{67} - 10 q^{68} + 12 q^{69} + 36 q^{71} - 2 q^{72} - 40 q^{73} - 30 q^{74} - 8 q^{75} + 58 q^{76} + 24 q^{78} - 48 q^{80} - 12 q^{81} - 30 q^{82} - 24 q^{83} - 26 q^{84} + 18 q^{85} + 30 q^{86} + 6 q^{87} - 78 q^{88} + 66 q^{89} + 12 q^{90} + 42 q^{91} + 36 q^{92} - 10 q^{93} + 6 q^{94} - 28 q^{95} + 8 q^{96} + 4 q^{97} + 44 q^{98} - 4 q^{99}+O(q^{100}) \) 24 * q - 4 * q^2 + 4 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 - 4 * q^8 + 12 * q^9 + 12 * q^10 + 4 * q^11 - 4 * q^12 - 22 * q^14 - 4 * q^15 + 12 * q^16 - 2 * q^18 - 22 * q^19 - 4 * q^20 + 10 * q^21 - 34 * q^22 + 2 * q^24 - 4 * q^26 - 14 * q^28 + 8 * q^29 - 16 * q^30 - 2 * q^31 - 34 * q^32 + 4 * q^33 + 20 * q^34 + 24 * q^35 - 4 * q^36 - 12 * q^37 - 12 * q^38 - 6 * q^39 + 28 * q^40 - 36 * q^41 + 6 * q^42 + 10 * q^43 + 20 * q^44 + 4 * q^45 - 2 * q^46 + 20 * q^47 + 32 * q^48 - 54 * q^49 - 24 * q^50 + 36 * q^51 + 4 * q^52 - 36 * q^53 - 4 * q^54 - 24 * q^55 + 70 * q^56 - 32 * q^57 + 48 * q^58 - 36 * q^59 - 28 * q^60 - 2 * q^61 + 64 * q^62 + 8 * q^63 - 8 * q^64 + 16 * q^65 + 20 * q^66 - 16 * q^67 - 10 * q^68 + 12 * q^69 + 36 * q^71 - 2 * q^72 - 40 * q^73 - 30 * q^74 - 8 * q^75 + 58 * q^76 + 24 * q^78 - 48 * q^80 - 12 * q^81 - 30 * q^82 - 24 * q^83 - 26 * q^84 + 18 * q^85 + 30 * q^86 + 6 * q^87 - 78 * q^88 + 66 * q^89 + 12 * q^90 + 42 * q^91 + 36 * q^92 - 10 * q^93 + 6 * q^94 - 28 * q^95 + 8 * q^96 + 4 * q^97 + 44 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/156\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{12}\right)$

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 $

$2$	−0.101912	−	1.41054i	−0.0720627	−	0.997400i
$2$	−0.101912	−	1.41054i	−0.0720627	−	0.997400i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	−1.97923	+	0.287501i	−0.989614	+	0.143751i
$5$	2.43250	−	2.43250i	1.08785	−	1.08785i	0.0920955	−	0.995750i	$-0.470643\pi$
$5$	2.43250	−	2.43250i	1.08785	−	1.08785i	0.995750	−	0.0920955i	$-0.0293565\pi$
$6$	−0.793527	−	1.17060i	−0.323956	−	0.477897i
$7$	0.522652	+	1.95057i	0.197544	+	0.737245i	0.991594	+	0.129391i	$0.0413024\pi$
$7$	0.522652	+	1.95057i	0.197544	+	0.737245i	−0.794050	+	0.607853i	$0.792031\pi$
$8$	0.607239	+	2.76247i	0.214691	+	0.976682i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−3.67903	−	3.18323i	−1.16341	−	1.00662i
$11$	−3.03280	−	0.812637i	−0.914424	−	0.245019i	−0.229224	−	0.973374i	$-0.573619\pi$
$11$	−3.03280	−	0.812637i	−0.914424	−	0.245019i	−0.685200	+	0.728355i	$0.740285\pi$
$12$	−1.57031	+	1.23860i	−0.453310	+	0.357552i
$13$	−3.44947	−	1.04938i	−0.956709	−	0.291045i
$13$	−3.44947	−	1.04938i	−0.956709	−	0.291045i
$14$	2.69808	−	0.936007i	0.721092	−	0.250158i
$15$	0.890356	−	3.32285i	0.229889	−	0.857957i
$16$	3.83469	−	1.13806i	0.958671	−	0.284515i
$17$	4.36889	+	2.52238i	1.05961	+	0.611767i	0.925325	−	0.379175i	$-0.123792\pi$
$17$	4.36889	+	2.52238i	1.05961	+	0.611767i	0.134287	+	0.990942i	$0.457126\pi$
$18$	−1.27252	−	0.617010i	−0.299935	−	0.145431i
$19$	−2.75142	+	0.737240i	−0.631218	+	0.169134i	−0.560222	−	0.828342i	$-0.689284\pi$
$19$	−2.75142	+	0.737240i	−0.631218	+	0.169134i	−0.0709957	+	0.997477i	$0.522618\pi$
$20$	−4.11512	+	5.51381i	−0.920169	+	1.23293i
$21$	1.42791	+	1.42791i	0.311596	+	0.311596i
$22$	−0.837175	+	4.36070i	−0.178486	+	0.929703i
$23$	2.20812	+	3.82458i	0.460425	+	0.797480i	0.998982	−	0.0451091i	$-0.0143635\pi$
$23$	2.20812	+	3.82458i	0.460425	+	0.797480i	−0.538557	+	0.842589i	$0.681030\pi$
$24$	1.90712	+	2.08875i	0.389289	+	0.426365i
$25$		−	6.83408i		−	1.36682i
$26$	−1.12864	+	4.97254i	−0.221345	+	0.975196i
$27$		−	1.00000i		−	0.192450i
$28$	−1.59524	−	3.71035i	−0.301472	−	0.701190i
$29$	0.754985	+	1.30767i	0.140197	+	0.242829i	0.927571	−	0.373648i	$-0.121893\pi$
$29$	0.754985	+	1.30767i	0.140197	+	0.242829i	−0.787374	+	0.616476i	$0.788560\pi$
$30$	−4.77774	−	0.917241i	−0.872293	−	0.167464i
$31$	2.38964	+	2.38964i	0.429191	+	0.429191i	0.888353	−	0.459161i	$-0.151850\pi$
$31$	2.38964	+	2.38964i	0.429191	+	0.429191i	−0.459161	+	0.888353i	$0.651850\pi$
$32$	−1.99608	−	5.29298i	−0.352860	−	0.935676i
$33$	−3.03280	+	0.812637i	−0.527943	+	0.141462i
$34$	3.11267	−	6.41954i	0.533818	−	1.10094i
$35$	6.01610	+	3.47339i	1.01691	+	0.587111i
$36$	−0.740630	+	1.85781i	−0.123438	+	0.309635i
$37$	−1.91258	+	7.13784i	−0.314426	+	1.17345i	0.610097	+	0.792327i	$0.291131\pi$
$37$	−1.91258	+	7.13784i	−0.314426	+	1.17345i	−0.924523	+	0.381127i	$0.875536\pi$
$38$	1.32031	+	3.80584i	0.214182	+	0.617389i
$39$	−3.51201	+	0.815946i	−0.562372	+	0.130656i
$40$	8.19681	+	5.24260i	1.29603	+	0.828928i
$41$	3.46845	+	0.929369i	0.541681	+	0.145143i	0.519277	−	0.854606i	$-0.326201\pi$
$41$	3.46845	+	0.929369i	0.541681	+	0.145143i	0.0224041	+	0.999749i	$0.492868\pi$
$42$	1.86860	−	2.15965i	0.288332	−	0.333241i
$43$	−2.78445	+	4.82280i	−0.424624	+	0.735470i	−0.996385	−	0.0849496i	$-0.972927\pi$
$43$	−2.78445	+	4.82280i	−0.424624	+	0.735470i	0.571761	+	0.820420i	$0.306260\pi$
$44$	6.23624	+	0.736458i	0.940149	+	0.111025i
$45$	−0.890356	−	3.32285i	−0.132726	−	0.495342i
$46$	5.16968	−	3.50441i	0.762227	−	0.516697i
$47$	8.53489	−	8.53489i	1.24494	−	1.24494i	0.287017	−	0.957926i	$-0.407336\pi$
$47$	8.53489	−	8.53489i	1.24494	−	1.24494i	0.957926	−	0.287017i	$-0.0926635\pi$
$48$	2.75190	−	2.90293i	0.397203	−	0.419002i
$49$	2.53064	−	1.46106i	0.361520	−	0.208723i
$50$	−9.63972	+	0.696476i	−1.36326	+	0.0984965i
$51$	5.04476			0.706408
$52$	7.12897	+	1.08523i	0.988611	+	0.150494i
$53$	−9.42530			−1.29466			−0.647332	−	0.762208i	$-0.724115\pi$
$53$	−9.42530			−1.29466			−0.647332	+	0.762208i	$0.724115\pi$
$54$	−1.41054	+	0.101912i	−0.191950	+	0.0138685i
$55$	−9.35402	+	5.40054i	−1.26130	+	0.728209i
$56$	−5.07101	+	2.62827i	−0.677642	+	0.351218i
$57$	−2.01418	+	2.01418i	−0.266784	+	0.266784i
$58$	1.76758	−	1.19820i	0.232094	−	0.157332i
$59$	−2.67214	−	9.97257i	−0.347883	−	1.29832i	−0.889208	−	0.457504i	$-0.848744\pi$
$59$	−2.67214	−	9.97257i	−0.347883	−	1.29832i	0.541325	−	0.840814i	$-0.317923\pi$
$60$	−0.806892	+	6.83266i	−0.104169	+	0.882093i
$61$	−5.34563	+	9.25891i	−0.684438	+	1.18548i	0.289175	+	0.957276i	$0.406619\pi$
$61$	−5.34563	+	9.25891i	−0.684438	+	1.18548i	−0.973613	+	0.228206i	$0.926714\pi$
$62$	3.12714	−	3.61420i	0.397147	−	0.459004i
$63$	1.95057	+	0.522652i	0.245748	+	0.0658480i
$64$	−7.26252	+	3.35496i	−0.907815	+	0.419370i
$65$	−10.9434	+	5.83821i	−1.35736	+	0.724141i
$66$	1.45533	+	4.19506i	0.179139	+	0.516376i
$67$	3.40389	−	12.7035i	0.415852	−	1.55198i	−0.367271	−	0.930114i	$-0.619708\pi$
$67$	3.40389	−	12.7035i	0.415852	−	1.55198i	0.783123	−	0.621867i	$-0.213625\pi$
$68$	−9.37222	−	3.73630i	−1.13655	−	0.453093i
$69$	3.82458	+	2.20812i	0.460425	+	0.265827i
$70$	4.28624	−	8.83990i	0.512303	−	1.05657i
$71$	−10.4866	+	2.80989i	−1.24454	+	0.333472i	−0.820223	−	0.572044i	$-0.806151\pi$
$71$	−10.4866	+	2.80989i	−1.24454	+	0.333472i	−0.424312	+	0.905516i	$0.639484\pi$
$72$	2.69599	+	0.855353i	0.317726	+	0.100804i
$73$	−5.57628	−	5.57628i	−0.652654	−	0.652654i	0.300977	−	0.953631i	$-0.402687\pi$
$73$	−5.57628	−	5.57628i	−0.652654	−	0.652654i	−0.953631	+	0.300977i	$0.902687\pi$
$74$	10.2631	+	1.97033i	1.19306	+	0.229046i
$75$	−3.41704	−	5.91849i	−0.394566	−	0.683408i
$76$	5.23372	−	2.25020i	0.600349	−	0.258116i
$77$		−	6.34041i		−	0.722556i
$78$	1.50884	+	4.87067i	0.170842	+	0.551495i
$79$			11.8580i			1.33413i	0.745002	+	0.667063i	$0.232449\pi$
$79$			11.8580i			1.33413i	−0.745002	+	0.667063i	$0.767551\pi$
$80$	6.55953	−	12.0962i	0.733378	−	1.35240i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	0.957432	−	4.98709i	0.105731	−	0.550732i
$83$	−8.12570	−	8.12570i	−0.891911	−	0.891911i	0.102792	−	0.994703i	$-0.467223\pi$
$83$	−8.12570	−	8.12570i	−0.891911	−	0.891911i	−0.994703	+	0.102792i	$0.967223\pi$
$84$	−3.23669	−	2.41564i	−0.353152	−	0.263568i
$85$	16.7630	−	4.49163i	1.81820	−	0.487186i
$86$	7.08651	+	3.43606i	0.764158	+	0.370520i
$87$	1.30767	+	0.754985i	0.140197	+	0.0809428i
$88$	0.403254	−	8.87150i	0.0429870	−	0.945705i
$89$	−0.935561	+	3.49156i	−0.0991693	+	0.370105i	−0.997619	−	0.0689726i	$-0.978028\pi$
$89$	−0.935561	+	3.49156i	−0.0991693	+	0.370105i	0.898449	+	0.439077i	$0.144695\pi$
$90$	−4.59627	+	1.59452i	−0.484489	+	0.168077i
$91$	0.244006	−	7.27687i	0.0255788	−	0.762823i
$92$	−5.46995	−	6.93488i	−0.570282	−	0.723011i
$93$	3.26430	+	0.874668i	0.338493	+	0.0906988i
$94$	−12.9086	−	11.1690i	−1.33142	−	1.15199i
$95$	−4.89948	+	8.48614i	−0.502676	+	0.870660i
$96$	−4.37515	−	3.58582i	−0.446537	−	0.365976i
$97$	−1.02076	−	3.80953i	−0.103642	−	0.386799i	0.894545	−	0.446978i	$-0.147500\pi$
$97$	−1.02076	−	3.80953i	−0.103642	−	0.386799i	−0.998188	+	0.0601786i	$0.980833\pi$
$98$	−2.31879	−	3.42066i	−0.234233	−	0.345539i
$99$	−2.22016	+	2.22016i	−0.223135	+	0.223135i
$100$	1.96481	+	13.5262i	0.196481	+	1.35262i
$101$	7.49876	−	4.32941i	0.746155	−	0.430793i	−0.0781480	−	0.996942i	$-0.524901\pi$
$101$	7.49876	−	4.32941i	0.746155	−	0.430793i	0.824303	+	0.566149i	$0.191567\pi$
$102$	−0.514122	−	7.11582i	−0.0509057	−	0.704571i
$103$	−6.54115			−0.644519			−0.322260	−	0.946651i	$-0.604442\pi$
$103$	−6.54115			−0.644519			−0.322260	+	0.946651i	$0.604442\pi$
$104$	0.804227	−	10.1663i	0.0788609	−	0.996886i
$105$	6.94679			0.677937
$106$	0.960552	+	13.2947i	0.0932971	+	1.29130i
$107$	9.57744	−	5.52954i	0.925886	−	0.534561i	0.0403782	−	0.999184i	$-0.487144\pi$
$107$	9.57744	−	5.52954i	0.925886	−	0.534561i	0.885508	+	0.464624i	$0.153810\pi$
$108$	0.287501	+	1.97923i	0.0276648	+	0.190451i
$109$	−11.7400	+	11.7400i	−1.12449	+	1.12449i	−0.133427	+	0.991059i	$0.542598\pi$
$109$	−11.7400	+	11.7400i	−1.12449	+	1.12449i	−0.991059	+	0.133427i	$0.957402\pi$
$110$	8.57095	+	12.6438i	0.817208	+	1.20554i
$111$	1.91258	+	7.13784i	0.181534	+	0.677494i
$112$	4.22407	+	6.88500i	0.399137	+	0.650571i
$113$	−0.0930531	+	0.161173i	−0.00875370	+	0.0151619i	−0.870369	−	0.492400i	$-0.836120\pi$
$113$	−0.0930531	+	0.161173i	−0.00875370	+	0.0151619i	0.861615	+	0.507562i	$0.169453\pi$
$114$	3.04634	+	2.63580i	0.285316	+	0.246865i
$115$	14.6745	+	3.93203i	1.36841	+	0.366664i
$116$	−1.87024	−	2.37112i	−0.173648	−	0.220153i
$117$	−2.63352	+	2.46264i	−0.243469	+	0.227671i
$118$	−13.7943	+	4.78548i	−1.26987	+	0.440539i
$119$	−2.63666	+	9.84014i	−0.241702	+	0.902044i
$120$	9.71995	+	0.441820i	0.887306	+	0.0403325i
$121$	−0.988771	−	0.570867i	−0.0898883	−	0.0518970i
$122$	13.6048	+	6.59662i	1.23172	+	0.597230i
$123$	3.46845	−	0.929369i	0.312740	−	0.0837984i
$124$	−5.41666	−	4.04261i	−0.486430	−	0.363037i
$125$	−4.46140	−	4.46140i	−0.399040	−	0.399040i
$126$	0.538434	−	2.80461i	0.0479675	−	0.249854i
$127$	−1.57616	−	2.72999i	−0.139861	−	0.242247i	0.787583	−	0.616209i	$-0.211332\pi$
$127$	−1.57616	−	2.72999i	−0.139861	−	0.242247i	−0.927444	+	0.373962i	$0.877999\pi$
$128$	5.47243	+	9.90214i	0.483699	+	0.875234i
$129$			5.56889i			0.490314i
$130$	9.35027	+	14.8411i	0.820073	+	1.30165i
$131$		−	5.79804i		−	0.506577i	−0.967391	−	0.253289i	$-0.918488\pi$
$131$		−	5.79804i		−	0.506577i	0.967391	−	0.253289i	$-0.0815122\pi$
$132$	5.76897	−	2.48033i	0.502125	−	0.215885i
$133$	−2.87607	−	4.98150i	−0.249387	−	0.431951i
$134$	−18.2657	−	3.50668i	−1.57791	−	0.302931i
$135$	−2.43250	−	2.43250i	−0.209356	−	0.209356i
$136$	−4.31505	+	13.6006i	−0.370013	+	1.16624i
$137$	2.43946	−	0.653650i	0.208417	−	0.0558451i	−0.153100	−	0.988211i	$-0.548926\pi$
$137$	2.43946	−	0.653650i	0.208417	−	0.0558451i	0.361517	+	0.932366i	$0.382259\pi$
$138$	2.72487	−	5.61975i	0.231956	−	0.478385i
$139$	5.84911	+	3.37699i	0.496115	+	0.286432i	0.727108	−	0.686523i	$-0.240864\pi$
$139$	5.84911	+	3.37699i	0.496115	+	0.286432i	−0.230993	+	0.972956i	$0.574197\pi$
$140$	−12.9058	−	5.14500i	−1.09074	−	0.434832i
$141$	3.12399	−	11.6589i	0.263087	−	0.981855i
$142$	5.03216	+	14.5054i	0.422290	+	1.21727i
$143$	9.60878	+	5.98571i	0.803527	+	0.500550i
$144$	0.931753	−	3.88997i	0.0776460	−	0.324164i
$145$	5.01741	+	1.34441i	0.416673	+	0.111647i
$146$	−7.29726	+	8.43384i	−0.603926	+	0.697990i
$147$	1.46106	−	2.53064i	0.120507	−	0.208723i
$148$	1.73329	−	14.6773i	0.142476	−	1.20647i
$149$	−4.10065	−	15.3038i	−0.335938	−	1.25374i	−0.902848	−	0.429959i	$-0.858528\pi$
$149$	−4.10065	−	15.3038i	−0.335938	−	1.25374i	0.566910	−	0.823780i	$-0.308139\pi$
$150$	−8.00001	+	5.42303i	−0.653198	+	0.442788i
$151$	−1.14553	+	1.14553i	−0.0932221	+	0.0932221i	−0.752180	−	0.658958i	$-0.770998\pi$
$151$	−1.14553	+	1.14553i	−0.0932221	+	0.0932221i	0.658958	+	0.752180i	$0.270998\pi$
$152$	−3.70737	−	7.15303i	−0.300708	−	0.580188i
$153$	4.36889	−	2.52238i	0.353204	−	0.203922i
$154$	−8.94338	+	0.646164i	−0.720678	+	0.0520694i
$155$	11.6256			0.933788
$156$	6.71649	−	2.62465i	0.537749	−	0.210140i
$157$	10.5308			0.840453			0.420227	−	0.907419i	$-0.361951\pi$
$157$	10.5308			0.840453			0.420227	+	0.907419i	$0.361951\pi$
$158$	16.7261	−	1.20847i	1.33066	−	0.0961407i
$159$	−8.16255	+	4.71265i	−0.647332	+	0.373738i
$160$	−17.7306	−	8.01971i	−1.40173	−	0.634014i
$161$	−6.30602	+	6.30602i	−0.496984	+	0.496984i
$162$	−1.17060	+	0.793527i	−0.0919714	+	0.0623454i
$163$	0.235636	+	0.879405i	0.0184564	+	0.0688803i	0.974540	−	0.224214i	$-0.0719816\pi$
$163$	0.235636	+	0.879405i	0.0184564	+	0.0688803i	−0.956083	+	0.293095i	$0.905315\pi$
$164$	−7.13205	−	0.842248i	−0.556920	−	0.0657685i
$165$	−5.40054	+	9.35402i	−0.420432	+	0.728209i
$166$	−10.6335	+	12.2897i	−0.825319	+	0.953866i
$167$	−3.20374	−	0.858441i	−0.247913	−	0.0664281i	0.132722	−	0.991153i	$-0.457628\pi$
$167$	−3.20374	−	0.858441i	−0.247913	−	0.0664281i	−0.380636	+	0.924725i	$0.624295\pi$
$168$	−3.07749	+	4.81166i	−0.237433	+	0.371227i
$169$	10.7976	+	7.23958i	0.830586	+	0.556890i
$170$	−8.04396	−	23.1871i	−0.616944	−	1.77837i
$171$	−0.737240	+	2.75142i	−0.0563781	+	0.210406i
$172$	4.12449	−	10.3460i	0.314489	−	0.788872i
$173$	9.39229	+	5.42264i	0.714083	+	0.412276i	0.812571	−	0.582862i	$-0.198067\pi$
$173$	9.39229	+	5.42264i	0.714083	+	0.412276i	−0.0984883	+	0.995138i	$0.531401\pi$
$174$	0.931666	−	1.92146i	0.0706294	−	0.145666i
$175$	13.3303	−	3.57185i	1.00768	−	0.270006i
$176$	−12.5547	+	0.335309i	−0.946344	+	0.0252749i
$177$	−7.30042	−	7.30042i	−0.548734	−	0.548734i
$178$	5.02032	+	0.963811i	0.376289	+	0.0722407i
$179$	5.05705	+	8.75907i	0.377982	+	0.654683i	0.990768	−	0.135565i	$-0.0432849\pi$
$179$	5.05705	+	8.75907i	0.377982	+	0.654683i	−0.612787	+	0.790248i	$0.709952\pi$
$180$	2.71754	+	6.32070i	0.202554	+	0.471117i
$181$		−	2.36850i		−	0.176049i	−0.996118	−	0.0880245i	$-0.971945\pi$
$181$		−	2.36850i		−	0.176049i	0.996118	−	0.0880245i	$-0.0280554\pi$
$182$	−10.2892	+	0.397421i	−0.762683	+	0.0294588i
$183$			10.6913i			0.790321i
$184$	−9.22445	+	8.42231i	−0.680035	+	0.620901i
$185$	12.7104	+	22.0151i	0.934490	+	1.61858i
$186$	0.901079	−	4.69356i	0.0660703	−	0.344149i
$187$	−11.2002	−	11.2002i	−0.819040	−	0.819040i
$188$	−14.4387	+	19.3463i	−1.05305	+	1.41097i
$189$	1.95057	−	0.522652i	0.141883	−	0.0380174i
$190$	12.4693	+	6.04605i	0.904621	+	0.438627i
$191$	−10.4930	−	6.05814i	−0.759247	−	0.438351i	0.0697785	−	0.997563i	$-0.477771\pi$
$191$	−10.4930	−	6.05814i	−0.759247	−	0.438351i	−0.829025	+	0.559211i	$0.811104\pi$
$192$	−4.61205	+	6.53674i	−0.332846	+	0.471749i
$193$	3.74847	−	13.9895i	0.269821	−	1.00698i	−0.689413	−	0.724369i	$-0.742131\pi$
$193$	3.74847	−	13.9895i	0.269821	−	1.00698i	0.959233	−	0.282615i	$-0.0912020\pi$
$194$	−5.26945	+	1.82806i	−0.378325	+	0.131247i
$195$	−6.55817	+	10.5277i	−0.469641	+	0.753908i
$196$	−4.58865	+	3.61934i	−0.327761	+	0.258524i
$197$	6.26356	+	1.67831i	0.446260	+	0.119575i	0.474949	−	0.880013i	$-0.342467\pi$
$197$	6.26356	+	1.67831i	0.446260	+	0.119575i	−0.0286889	+	0.999588i	$0.509133\pi$
$198$	3.35789	+	2.90536i	0.238635	+	0.206475i
$199$	2.58783	−	4.48225i	0.183446	−	0.317738i	−0.759606	−	0.650384i	$-0.774608\pi$
$199$	2.58783	−	4.48225i	0.183446	−	0.317738i	0.943052	+	0.332646i	$0.107941\pi$
$200$	18.8790	−	4.14992i	1.33494	−	0.293444i
$201$	−3.40389	−	12.7035i	−0.240092	−	0.896036i
$202$	−6.87101	−	10.1361i	−0.483443	−	0.713171i
$203$	−2.15610	+	2.15610i	−0.151329	+	0.151329i
$204$	−9.98473	+	1.45038i	−0.699071	+	0.101547i
$205$	10.6977	−	6.17631i	0.747159	−	0.431372i
$206$	0.666623	+	9.22654i	0.0464458	+	0.642843i
$207$	4.41625			0.306950
$208$	−14.4219	−	0.0983251i	−0.999977	−	0.00681762i
$209$	8.94361			0.618642
$210$	−0.707962	−	9.79870i	−0.0488540	−	0.676175i
$211$	−4.89625	+	2.82685i	−0.337072	+	0.194608i	−0.658976	−	0.752164i	$-0.729010\pi$
$211$	−4.89625	+	2.82685i	−0.337072	+	0.194608i	0.321905	+	0.946772i	$0.395677\pi$
$212$	18.6548	−	2.70979i	1.28122	−	0.186109i
$213$	−7.67675	+	7.67675i	−0.526003	+	0.526003i
$214$	−8.77568	−	12.9458i	−0.599893	−	0.884957i
$215$	4.95830	+	18.5046i	0.338153	+	1.26200i
$216$	2.76247	−	0.607239i	0.187963	−	0.0413174i
$217$	−3.41219	+	5.91009i	−0.231635	+	0.401203i
$218$	17.7561	+	15.3632i	1.20260	+	1.04053i
$219$	−7.61734	−	2.04106i	−0.514732	−	0.137922i
$220$	16.9611	−	13.3782i	1.14351	−	0.901958i
$221$	−12.4234	−	13.2855i	−0.835689	−	0.893678i
$222$	9.87327	−	3.42519i	0.662651	−	0.229884i
$223$	4.96434	−	18.5272i	0.332436	−	1.24067i	−0.574185	−	0.818725i	$-0.694681\pi$
$223$	4.96434	−	18.5272i	0.332436	−	1.24067i	0.906622	−	0.421944i	$-0.138652\pi$
$224$	9.28106	−	6.65987i	0.620117	−	0.444982i
$225$	−5.91849	−	3.41704i	−0.394566	−	0.227803i
$226$	0.236823	+	0.114829i	0.0157533	+	0.00763834i
$227$	−15.7357	+	4.21636i	−1.04441	+	0.279849i	−0.739941	−	0.672672i	$-0.765146\pi$
$227$	−15.7357	+	4.21636i	−1.04441	+	0.279849i	−0.304471	+	0.952522i	$0.598480\pi$
$228$	3.40744	−	4.56559i	0.225663	−	0.302364i
$229$	2.75212	+	2.75212i	0.181865	+	0.181865i	0.792168	−	0.610303i	$-0.208952\pi$
$229$	2.75212	+	2.75212i	0.181865	+	0.181865i	−0.610303	+	0.792168i	$0.708952\pi$
$230$	4.05076	−	21.0997i	0.267099	−	1.39127i
$231$	−3.17020	−	5.49095i	−0.208584	−	0.361278i
$232$	−3.15395	+	2.87969i	−0.207067	+	0.189061i
$233$		−	24.7212i		−	1.61954i	−0.586747	−	0.809771i	$-0.699592\pi$
$233$		−	24.7212i		−	1.61954i	0.586747	−	0.809771i	$-0.300408\pi$
$234$	3.74203	+	3.46370i	0.244624	+	0.226429i
$235$		−	41.5222i		−	2.70861i
$236$	8.15590	+	18.9697i	0.530904	+	1.23482i
$237$	5.92898	+	10.2693i	0.385129	+	0.667063i
$238$	14.1486	+	2.71627i	0.917117	+	0.176070i
$239$	−3.51448	−	3.51448i	−0.227333	−	0.227333i	0.584245	−	0.811577i	$-0.301391\pi$
$239$	−3.51448	−	3.51448i	−0.227333	−	0.227333i	−0.811577	+	0.584245i	$0.801391\pi$
$240$	−0.367377	−	13.7554i	−0.0237141	−	0.887906i
$241$	−1.53556	+	0.411451i	−0.0989139	+	0.0265039i	−0.307937	−	0.951407i	$-0.599638\pi$
$241$	−1.53556	+	0.411451i	−0.0989139	+	0.0265039i	0.209023	+	0.977911i	$0.432972\pi$
$242$	−0.704462	+	1.45288i	−0.0452845	+	0.0933944i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	7.91828	−	19.8624i	0.506916	−	1.27156i
$245$	2.60173	−	9.70980i	0.166219	−	0.620336i
$246$	−1.66439	−	4.79766i	−0.106117	−	0.305888i
$247$	10.2646	+	0.344189i	0.653118	+	0.0219002i
$248$	−5.15023	+	8.05239i	−0.327040	+	0.511327i
$249$	−11.0999	−	2.97421i	−0.703428	−	0.188483i
$250$	−5.83830	+	6.74764i	−0.369246	+	0.426758i
$251$	−2.23278	+	3.86728i	−0.140932	+	0.244101i	−0.927848	−	0.372959i	$-0.878343\pi$
$251$	−2.23278	+	3.86728i	−0.140932	+	0.244101i	0.786916	+	0.617060i	$0.211676\pi$
$252$	−4.01088	−	0.473658i	−0.252662	−	0.0298376i
$253$	−3.58880	−	13.3936i	−0.225626	−	0.842048i
$254$	−3.69012	+	2.50145i	−0.231538	+	0.156955i
$255$	12.2714	−	12.2714i	0.768463	−	0.768463i
$256$	13.4096	−	8.72822i	0.838102	−	0.545514i
$257$	−7.11888	+	4.11009i	−0.444063	+	0.256380i	−0.705320	−	0.708889i	$-0.749197\pi$
$257$	−7.11888	+	4.11009i	−0.444063	+	0.256380i	0.261256	+	0.965269i	$0.415863\pi$
$258$	7.85513	−	0.567537i	0.489039	−	0.0353333i
$259$	−14.9224			−0.927235
$260$	19.9810	−	14.7014i	1.23917	−	0.911742i
$261$	1.50997			0.0934648
$262$	−8.17835	+	0.590890i	−0.505260	+	0.0365053i
$263$	−8.54118	+	4.93125i	−0.526672	+	0.304074i	−0.739660	−	0.672981i	$-0.765014\pi$
$263$	−8.54118	+	4.93125i	−0.526672	+	0.304074i	0.212988	+	0.977055i	$0.431680\pi$
$264$	−4.08652	−	7.88457i	−0.251508	−	0.485262i
$265$	−22.9270	+	22.9270i	−1.40840	+	1.40840i
$266$	−6.73348	+	4.56448i	−0.412856	+	0.279866i
$267$	0.935561	+	3.49156i	0.0572554	+	0.213680i
$268$	−3.08481	+	26.1218i	−0.188435	+	1.59564i
$269$	−8.08746	+	14.0079i	−0.493101	+	0.854076i	−0.999968	−	0.00794803i	$-0.997470\pi$
$269$	−8.08746	+	14.0079i	−0.493101	+	0.854076i	0.506867	+	0.862024i	$0.330803\pi$
$270$	−3.18323	+	3.67903i	−0.193725	+	0.223898i
$271$	19.1734	+	5.13750i	1.16470	+	0.312081i	0.788842	−	0.614596i	$-0.210681\pi$
$271$	19.1734	+	5.13750i	1.16470	+	0.312081i	0.375860	+	0.926677i	$0.377347\pi$
$272$	19.6240	+	4.70047i	1.18988	+	0.285008i
$273$	−3.42712	−	6.42395i	−0.207419	−	0.388795i
$274$	−1.17061	−	3.37433i	−0.0707190	−	0.203851i
$275$	−5.55363	+	20.7264i	−0.334896	+	1.24985i
$276$	−8.20456	−	3.27081i	−0.493856	−	0.196879i
$277$	10.8424	+	6.25985i	0.651455	+	0.376118i	0.789013	−	0.614376i	$-0.210592\pi$
$277$	10.8424	+	6.25985i	0.651455	+	0.376118i	−0.137558	+	0.990494i	$0.543925\pi$
$278$	4.16727	−	8.59455i	0.249936	−	0.515467i
$279$	3.26430	−	0.874668i	0.195429	−	0.0523650i
$280$	−5.94196	+	18.7285i	−0.355100	+	1.11924i
$281$	1.53313	+	1.53313i	0.0914590	+	0.0914590i	0.751356	−	0.659897i	$-0.229400\pi$
$281$	1.53313	+	1.53313i	0.0914590	+	0.0914590i	−0.659897	+	0.751356i	$0.729400\pi$
$282$	−16.7637	−	3.21832i	−0.998261	−	0.191648i
$283$	13.4494	+	23.2951i	0.799484	+	1.38475i	0.919952	+	0.392030i	$0.128227\pi$
$283$	13.4494	+	23.2951i	0.799484	+	1.38475i	−0.120468	+	0.992717i	$0.538440\pi$
$284$	19.9476	−	8.57633i	1.18367	−	0.508912i
$285$			9.79896i			0.580440i
$286$	7.46382	−	14.1636i	0.441345	−	0.837509i
$287$			7.25118i			0.428024i
$288$	−5.58190	−	0.917837i	−0.328916	−	0.0540840i
$289$	4.22481	+	7.31759i	0.248518	+	0.430446i
$290$	1.38501	−	7.21425i	0.0813303	−	0.423635i
$291$	−2.78877	−	2.78877i	−0.163480	−	0.163480i
$292$	12.6399	+	9.43354i	0.739696	+	0.552056i
$293$	−12.8858	+	3.45273i	−0.752794	+	0.201711i	−0.614757	−	0.788716i	$-0.710746\pi$
$293$	−12.8858	+	3.45273i	−0.752794	+	0.201711i	−0.138037	+	0.990427i	$0.544079\pi$
$294$	−3.71846	−	1.80298i	−0.216865	−	0.105152i
$295$	−30.7582	−	17.7583i	−1.79081	−	1.03393i
$296$	−20.8795	−	0.949076i	−1.21360	−	0.0551639i
$297$	−0.812637	+	3.03280i	−0.0471540	+	0.175981i
$298$	−21.1687	+	7.34376i	−1.22627	+	0.425413i
$299$	−3.60342	−	15.5099i	−0.208391	−	0.896961i
$300$	8.46468	+	10.7316i	0.488708	+	0.619591i
$301$	−10.8625	−	2.91060i	−0.626104	−	0.167764i
$302$	1.73256	+	1.49907i	0.0996975	+	0.0862619i
$303$	4.32941	−	7.49876i	0.248718	−	0.430793i
$304$	−9.71179	+	5.95836i	−0.557009	+	0.341736i
$305$	9.51903	+	35.5255i	0.545058	+	2.03418i
$306$	−4.00315	−	5.90542i	−0.228845	−	0.337590i
$307$	−7.67194	+	7.67194i	−0.437861	+	0.437861i	−0.891292	−	0.453431i	$-0.850200\pi$
$307$	−7.67194	+	7.67194i	−0.437861	+	0.437861i	0.453431	+	0.891292i	$0.350200\pi$
$308$	1.82288	+	12.5491i	0.103868	+	0.715052i
$309$	−5.66481	+	3.27058i	−0.322260	+	0.186057i
$310$	−1.18479	−	16.3983i	−0.0672913	−	0.931360i
$311$	19.1881			1.08806			0.544030	−	0.839066i	$-0.316898\pi$
$311$	19.1881			1.08806			0.544030	+	0.839066i	$0.316898\pi$
$312$	−4.38666	−	9.20637i	−0.248346	−	0.521208i
$313$	−19.3943			−1.09623			−0.548114	−	0.836403i	$-0.684654\pi$
$313$	−19.3943			−1.09623			−0.548114	+	0.836403i	$0.684654\pi$
$314$	−1.07322	−	14.8541i	−0.0605653	−	0.838268i
$315$	6.01610	−	3.47339i	0.338969	−	0.195704i
$316$	−3.40918	−	23.4696i	−0.191782	−	1.32027i
$317$	7.38597	−	7.38597i	0.414837	−	0.414837i	−0.468582	−	0.883420i	$-0.655235\pi$
$317$	7.38597	−	7.38597i	0.414837	−	0.414837i	0.883420	+	0.468582i	$0.155235\pi$
$318$	7.47923	+	11.0333i	0.419414	+	0.618717i
$319$	−1.22706	−	4.57944i	−0.0687020	−	0.256399i
$320$	−9.50513	+	25.8270i	−0.531353	+	1.44377i
$321$	5.52954	−	9.57744i	0.308629	−	0.534561i
$322$	9.53753	+	8.25221i	0.531506	+	0.459878i
$323$	−13.8802	−	3.71920i	−0.772317	−	0.206942i
$324$	1.23860	+	1.57031i	0.0688110	+	0.0872395i
$325$	−7.17153	+	23.5739i	−0.397805	+	1.30765i
$326$	1.21642	−	0.421995i	0.0673712	−	0.0233721i
$327$	−4.29713	+	16.0371i	−0.237632	+	0.886854i
$328$	−0.461179	+	10.1459i	−0.0254644	+	0.560211i
$329$	21.1087	+	12.1871i	1.16376	+	0.671896i
$330$	13.7446	+	6.66438i	0.756613	+	0.366862i
$331$	31.5577	−	8.45586i	1.73457	−	0.464776i	0.753341	−	0.657630i	$-0.228441\pi$
$331$	31.5577	−	8.45586i	1.73457	−	0.464776i	0.981228	+	0.192854i	$0.0617743\pi$
$332$	18.4188	+	13.7465i	1.01086	+	0.754435i
$333$	5.22526	+	5.22526i	0.286343	+	0.286343i
$334$	−0.884362	+	4.60648i	−0.0483901	+	0.252056i
$335$	−22.6213	−	39.1812i	−1.23593	−	2.14070i
$336$	7.10065	+	3.85054i	0.387372	+	0.210064i
$337$		−	25.6259i		−	1.39593i	−0.716132	−	0.697965i	$-0.754089\pi$
$337$		−	25.6259i		−	1.39593i	0.716132	−	0.697965i	$-0.245911\pi$
$338$	9.11128	−	15.9682i	0.495588	−	0.868558i
$339$			0.186106i			0.0101079i
$340$	−31.8864	+	13.7094i	−1.72929	+	0.743494i
$341$	−5.30539	−	9.18920i	−0.287303	−	0.497623i
$342$	3.95611	+	0.759501i	0.213922	+	0.0410691i
$343$	14.1679	+	14.1679i	0.764997	+	0.764997i
$344$	−15.0137	−	4.76337i	−0.809484	−	0.256824i
$345$	14.6745	−	3.93203i	0.790050	−	0.211693i
$346$	6.69165	−	13.8008i	0.359745	−	0.741936i
$347$	22.7500	+	13.1347i	1.22128	+	0.705107i	0.965191	−	0.261545i	$-0.0842321\pi$
$347$	22.7500	+	13.1347i	1.22128	+	0.705107i	0.256091	+	0.966653i	$0.417565\pi$
$348$	−2.80524	−	1.11833i	−0.150377	−	0.0599487i
$349$	−3.84773	+	14.3599i	−0.205964	+	0.768669i	0.783189	+	0.621784i	$0.213592\pi$
$349$	−3.84773	+	14.3599i	−0.205964	+	0.768669i	−0.989153	+	0.146886i	$0.953075\pi$
$350$	−6.39675	−	18.4389i	−0.341921	−	0.985601i
$351$	−1.04938	+	3.44947i	−0.0560116	+	0.184119i
$352$	1.75244	+	17.6747i	0.0934053	+	0.942062i
$353$	−18.2819	−	4.89863i	−0.973049	−	0.260728i	−0.262935	−	0.964814i	$-0.584690\pi$
$353$	−18.2819	−	4.89863i	−0.973049	−	0.260728i	−0.710115	+	0.704086i	$0.751357\pi$
$354$	−9.55352	+	11.0415i	−0.507764	+	0.586850i
$355$	−18.6737	+	32.3438i	−0.991096	+	1.71663i
$356$	0.847859	−	7.17957i	0.0449365	−	0.380516i
$357$	2.63666	+	9.84014i	0.139547	+	0.520795i
$358$	11.8396	−	8.02581i	0.625743	−	0.424177i
$359$	−1.83173	+	1.83173i	−0.0966748	+	0.0966748i	−0.753790	−	0.657115i	$-0.771776\pi$
$359$	−1.83173	+	1.83173i	−0.0966748	+	0.0966748i	0.657115	+	0.753790i	$0.271776\pi$
$360$	8.63863	−	4.47735i	0.455296	−	0.235977i
$361$	−9.42771	+	5.44309i	−0.496196	+	0.286479i
$362$	−3.34085	+	0.241378i	−0.175591	+	0.0126866i
$363$	−1.14173			−0.0599255
$364$	1.60917	+	14.4727i	0.0843432	+	0.758577i
$365$	−27.1286			−1.41997
$366$	15.0804	−	1.08957i	0.788267	−	0.0569527i
$367$	11.6551	−	6.72908i	0.608391	−	0.351255i	−0.163944	−	0.986470i	$-0.552422\pi$
$367$	11.6551	−	6.72908i	0.608391	−	0.351255i	0.772336	+	0.635215i	$0.219088\pi$
$368$	12.8201	+	12.1531i	0.668292	+	0.633523i
$369$	2.53908	−	2.53908i	0.132179	−	0.132179i
$370$	29.7578	−	20.1721i	1.54703	−	1.04870i
$371$	−4.92616	−	18.3847i	−0.255753	−	0.954484i
$372$	−6.71227	−	0.792675i	−0.348015	−	0.0410983i
$373$	12.6383	−	21.8902i	0.654386	−	1.13343i	−0.327661	−	0.944795i	$-0.606261\pi$
$373$	12.6383	−	21.8902i	0.654386	−	1.13343i	0.982047	−	0.188634i	$-0.0604061\pi$
$374$	−14.6569	+	16.9397i	−0.757888	+	0.875933i
$375$	−6.09439	−	1.63299i	−0.314713	−	0.0843270i
$376$	28.7601	+	18.3947i	1.48319	+	0.948634i
$377$	−1.23205	−	5.30303i	−0.0634540	−	0.273120i
$378$	−0.936007	−	2.69808i	−0.0481430	−	0.138774i
$379$	−4.25905	+	15.8950i	−0.218773	+	0.816470i	0.766032	+	0.642803i	$0.222228\pi$
$379$	−4.25905	+	15.8950i	−0.218773	+	0.816470i	−0.984804	+	0.173668i	$0.944438\pi$
$380$	7.25740	−	18.2046i	0.372297	−	0.933877i
$381$	−2.72999	−	1.57616i	−0.139861	−	0.0807490i
$382$	−7.47586	+	15.4182i	−0.382498	+	0.788862i
$383$	31.7746	−	8.51399i	1.62361	−	0.435045i	0.671550	−	0.740960i	$-0.265629\pi$
$383$	31.7746	−	8.51399i	1.62361	−	0.435045i	0.952059	+	0.305915i	$0.0989624\pi$
$384$	9.69034	+	5.83929i	0.494508	+	0.297985i
$385$	−15.4230	−	15.4230i	−0.786030	−	0.786030i
$386$	−20.1147	−	3.86165i	−1.02381	−	0.196553i
$387$	2.78445	+	4.82280i	0.141541	+	0.245157i
$388$	3.11556	+	7.24645i	0.158169	+	0.367883i
$389$		−	9.38923i		−	0.476053i	−0.971259	−	0.238026i	$-0.923500\pi$
$389$		−	9.38923i		−	0.476053i	0.971259	−	0.238026i	$-0.0765005\pi$
$390$	15.5181	+	8.17764i	0.785791	+	0.414091i
$391$			22.2789i			1.12669i
$392$	5.57285	+	6.10360i	0.281472	+	0.308279i
$393$	−2.89902	−	5.02125i	−0.146236	−	0.253289i
$394$	1.72899	−	9.00602i	0.0871054	−	0.453717i
$395$	28.8445	+	28.8445i	1.45132	+	1.45132i
$396$	3.75591	−	5.03251i	0.188742	−	0.252893i
$397$	−2.97217	+	0.796390i	−0.149169	+	0.0399697i	−0.332631	−	0.943057i	$-0.607936\pi$
$397$	−2.97217	+	0.796390i	−0.149169	+	0.0399697i	0.183462	+	0.983027i	$0.441270\pi$
$398$	−6.58611	−	3.19343i	−0.330132	−	0.160072i
$399$	−4.98150	−	2.87607i	−0.249387	−	0.143984i
$400$	−7.77761	−	26.2066i	−0.388880	−	1.31033i
$401$	−6.70305	+	25.0161i	−0.334735	+	1.24925i	0.569422	+	0.822045i	$0.307167\pi$
$401$	−6.70305	+	25.0161i	−0.334735	+	1.24925i	−0.904157	+	0.427201i	$0.859500\pi$
$402$	−17.5719	+	6.09596i	−0.876405	+	0.304039i
$403$	−5.73534	−	10.7506i	−0.285698	−	0.535525i
$404$	−13.5970	+	10.7248i	−0.676478	+	0.533579i
$405$	−3.32285	−	0.890356i	−0.165114	−	0.0442421i
$406$	3.26100	+	2.82153i	0.161841	+	0.140030i
$407$	11.6009	−	20.0934i	0.575037	−	0.995994i
$408$	3.06337	+	13.9360i	0.151660	+	0.689936i
$409$	2.60033	+	9.70457i	0.128578	+	0.479860i	0.999942	−	0.0107773i	$-0.00343059\pi$
$409$	2.60033	+	9.70457i	0.128578	+	0.479860i	−0.871364	+	0.490638i	$0.836764\pi$
$410$	−9.80214	−	14.4600i	−0.484093	−	0.714130i
$411$	1.78581	−	1.78581i	0.0880873	−	0.0880873i
$412$	12.9464	−	1.88059i	0.637825	−	0.0926501i
$413$	18.0555	−	10.4244i	0.888455	−	0.512950i
$414$	−0.450069	−	6.22928i	−0.0221197	−	0.306152i
$415$	−39.5315			−1.94052
$416$	1.33107	+	20.3526i	0.0652612	+	0.997868i
$417$	6.75398			0.330744
$418$	−0.911462	−	12.6153i	−0.0445810	−	0.617034i
$419$	−15.8667	+	9.16063i	−0.775138	+	0.447526i	−0.834704	−	0.550698i	$-0.814361\pi$
$419$	−15.8667	+	9.16063i	−0.775138	+	0.447526i	0.0595665	+	0.998224i	$0.481028\pi$
$420$	−13.7493	+	1.99721i	−0.670896	+	0.0974540i
$421$	21.1501	−	21.1501i	1.03080	−	1.03080i	0.0312847	−	0.999511i	$-0.490040\pi$
$421$	21.1501	−	21.1501i	1.03080	−	1.03080i	0.999511	−	0.0312847i	$-0.00995985\pi$
$422$	4.48636	+	6.61825i	0.218393	+	0.322171i
$423$	−3.12399	−	11.6589i	−0.151893	−	0.566874i
$424$	−5.72341	−	26.0371i	−0.277953	−	1.26448i
$425$	17.2382	−	29.8574i	0.836174	−	1.44830i
$426$	11.6107	+	10.0460i	0.562540	+	0.486730i
$427$	−20.8540	−	5.58782i	−1.00920	−	0.270413i
$428$	−17.3662	+	13.6977i	−0.839427	+	0.662106i
$429$	11.3143	+	0.379389i	0.546260	+	0.0183171i
$430$	25.5961	−	8.87970i	1.23435	−	0.428217i
$431$	−0.744066	+	2.77689i	−0.0358404	+	0.133758i	−0.981528	−	0.191319i	$-0.938724\pi$
$431$	−0.744066	+	2.77689i	−0.0358404	+	0.133758i	0.945688	+	0.325077i	$0.105390\pi$
$432$	−1.13806	−	3.83469i	−0.0547550	−	0.184496i
$433$	8.70510	+	5.02589i	0.418340	+	0.241529i	0.694367	−	0.719621i	$-0.255684\pi$
$433$	8.70510	+	5.02589i	0.418340	+	0.241529i	−0.276027	+	0.961150i	$0.589018\pi$
$434$	8.68415	+	4.21072i	0.416852	+	0.202121i
$435$	5.01741	−	1.34441i	0.240566	−	0.0644595i
$436$	19.8608	−	26.6113i	0.951161	−	1.27445i
$437$	−8.89510	−	8.89510i	−0.425510	−	0.425510i
$438$	−2.10269	+	10.9526i	−0.100471	+	0.523333i
$439$	15.2395	+	26.3956i	0.727343	+	1.25979i	0.958002	+	0.286760i	$0.0925784\pi$
$439$	15.2395	+	26.3956i	0.727343	+	1.25979i	−0.230659	+	0.973035i	$0.574088\pi$
$440$	−20.5990	−	22.5608i	−0.982018	−	1.07554i
$441$		−	2.92213i		−	0.139149i
$442$	−17.4736	+	18.8776i	−0.831132	+	0.897917i
$443$		−	30.5518i		−	1.45156i	−0.687928	−	0.725779i	$-0.741479\pi$
$443$		−	30.5518i		−	1.45156i	0.687928	−	0.725779i	$-0.258521\pi$
$444$	−5.83757	−	13.5775i	−0.277039	−	0.644362i
$445$	6.21746	+	10.7690i	0.294736	+	0.510498i
$446$	−26.6392	−	5.11424i	−1.26140	−	0.242166i
$447$	−11.2032	−	11.2032i	−0.529892	−	0.529892i
$448$	−10.3398	−	12.4125i	−0.488512	−	0.586438i
$449$	18.1610	−	4.86623i	0.857071	−	0.229651i	0.196582	−	0.980487i	$-0.437016\pi$
$449$	18.1610	−	4.86623i	0.857071	−	0.229651i	0.660489	+	0.750836i	$0.270349\pi$
$450$	−4.21670	+	8.69648i	−0.198777	+	0.409956i
$451$	−9.76389	−	5.63718i	−0.459763	−	0.265445i
$452$	0.137836	−	0.345750i	0.00648326	−	0.0162627i
$453$	−0.419294	+	1.56483i	−0.0197001	+	0.0735219i
$454$	7.55098	+	21.7660i	0.354385	+	1.02153i
$455$	−17.1074	−	18.2945i	−0.802008	−	0.857659i
$456$	−6.78719	−	4.34102i	−0.317840	−	0.203287i
$457$	25.6364	+	6.86925i	1.19922	+	0.321330i	0.802524	−	0.596620i	$-0.203490\pi$
$457$	25.6364	+	6.86925i	1.19922	+	0.321330i	0.396696	+	0.917950i	$0.370157\pi$
$458$	3.60149	−	4.16244i	0.168287	−	0.194498i
$459$	2.52238	−	4.36889i	0.117735	−	0.203922i
$460$	−30.1747	−	3.56343i	−1.40690	−	0.166146i
$461$	7.53177	+	28.1089i	0.350789	+	1.30916i	0.885701	+	0.464256i	$0.153678\pi$
$461$	7.53177	+	28.1089i	0.350789	+	1.30916i	−0.534912	+	0.844908i	$0.679655\pi$
$462$	−7.42211	+	5.03128i	−0.345308	+	0.234076i
$463$	−8.96109	+	8.96109i	−0.416457	+	0.416457i	−0.883981	−	0.467523i	$-0.845146\pi$
$463$	−8.96109	+	8.96109i	−0.416457	+	0.416457i	0.467523	+	0.883981i	$0.345146\pi$
$464$	4.38334	+	4.15529i	0.203491	+	0.192905i
$465$	10.0680	−	5.81278i	0.466894	−	0.269561i
$466$	−34.8702	+	2.51939i	−1.61533	+	0.116709i
$467$	34.4552			1.59440			0.797199	−	0.603716i	$-0.206314\pi$
$467$	34.4552			1.59440			0.797199	+	0.603716i	$0.206314\pi$
$468$	4.50432	−	5.63126i	0.208212	−	0.260305i
$469$	26.5581			1.22634
$470$	−58.5686	+	4.23161i	−2.70157	+	0.195190i
$471$	9.11998	−	5.26542i	0.420227	−	0.242618i
$472$	25.9263	−	13.4374i	1.19336	−	0.618509i
$473$	12.3639	−	12.3639i	0.568491	−	0.568491i
$474$	13.8810	−	9.40961i	0.637575	−	0.432198i
$475$	5.03836	+	18.8034i	0.231176	+	0.862759i
$476$	2.38949	−	20.2339i	0.109522	−	0.927420i
$477$	−4.71265	+	8.16255i	−0.215777	+	0.373738i
$478$	−4.59913	+	5.31546i	−0.210359	+	0.243124i
$479$	−12.6178	−	3.38094i	−0.576523	−	0.154479i	−0.0412366	−	0.999149i	$-0.513130\pi$
$479$	−12.6178	−	3.38094i	−0.576523	−	0.154479i	−0.535287	+	0.844670i	$0.679796\pi$
$480$	−19.3650	+	1.92004i	−0.883888	+	0.0876373i
$481$	14.0877	−	22.6147i	0.642342	−	1.03114i
$482$	0.736859	+	2.12403i	0.0335630	+	0.0967468i
$483$	−2.30816	+	8.61418i	−0.105025	+	0.391959i
$484$	2.12113	+	0.845603i	0.0964150	+	0.0384365i
$485$	−11.7497	−	6.78367i	−0.533525	−	0.308031i
$486$	−0.617010	+	1.27252i	−0.0279881	+	0.0577225i
$487$	−38.0822	+	10.2041i	−1.72567	+	0.462391i	−0.979178	−	0.203005i	$-0.934929\pi$
$487$	−38.0822	+	10.2041i	−1.72567	+	0.462391i	−0.746490	+	0.665396i	$0.768263\pi$
$488$	−28.8236	−	9.14481i	−1.30478	−	0.413966i
$489$	0.643769	+	0.643769i	0.0291122	+	0.0291122i
$490$	−13.9612	−	2.68029i	−0.630702	−	0.121083i
$491$	−4.78634	−	8.29019i	−0.216005	−	0.374131i	0.737578	−	0.675262i	$-0.235969\pi$
$491$	−4.78634	−	8.29019i	−0.216005	−	0.374131i	−0.953583	+	0.301131i	$0.902636\pi$
$492$	−6.59766	+	2.83662i	−0.297446	+	0.127885i
$493$			7.61744i			0.343072i
$494$	−0.560591	−	14.5136i	−0.0252222	−	0.652998i
$495$			10.8011i			0.485473i
$496$	11.8831	+	6.44395i	0.533565	+	0.289342i
$497$	−10.9617	−	18.9863i	−0.491701	−	0.851651i
$498$	−3.06402	+	15.9599i	−0.137302	+	0.715182i
$499$	11.9591	+	11.9591i	0.535364	+	0.535364i	0.922164	−	0.386800i	$-0.126420\pi$
$499$	11.9591	+	11.9591i	0.535364	+	0.535364i	−0.386800	+	0.922164i	$0.626420\pi$
$500$	10.1128	+	7.54747i	0.452258	+	0.337533i
$501$	−3.20374	+	0.858441i	−0.143133	+	0.0383523i
$502$	5.68249	+	2.75529i	0.253622	+	0.122975i
$503$	−2.86295	−	1.65293i	−0.127653	−	0.0737004i	0.434814	−	0.900520i	$-0.356814\pi$
$503$	−2.86295	−	1.65293i	−0.127653	−	0.0737004i	−0.562467	+	0.826820i	$0.690148\pi$
$504$	−0.259355	+	5.70576i	−0.0115526	+	0.254155i
$505$	7.70943	−	28.7720i	0.343065	−	1.28034i
$506$	−18.5264	+	6.42711i	−0.823600	+	0.285720i
$507$	12.9708	+	0.870847i	0.576053	+	0.0386757i
$508$	3.90445	+	4.95012i	0.173232	+	0.219626i
$509$	15.4031	+	4.12724i	0.682729	+	0.182937i	0.583482	−	0.812126i	$-0.301690\pi$
$509$	15.4031	+	4.12724i	0.682729	+	0.182937i	0.0992468	+	0.995063i	$0.468357\pi$
$510$	−18.5598	−	16.0586i	−0.821842	−	0.711087i
$511$	7.96245	−	13.7914i	0.352238	−	0.610094i
$512$	−13.6781	−	18.0253i	−0.604491	−	0.796612i
$513$	0.737240	+	2.75142i	0.0325499	+	0.121478i
$514$	6.52293	+	9.62257i	0.287714	+	0.424433i
$515$	−15.9113	+	15.9113i	−0.701137	+	0.701137i
$516$	−1.60106	−	11.0221i	−0.0704829	−	0.485221i
$517$	−32.8204	+	18.9489i	−1.44344	+	0.833370i
$518$	1.52078	+	21.0487i	0.0668191	+	0.924825i
$519$	10.8453			0.476055
$520$	−22.7732	−	26.6857i	−0.998669	−	1.17025i
$521$	−26.0583			−1.14163			−0.570817	−	0.821077i	$-0.693374\pi$
$521$	−26.0583			−1.14163			−0.570817	+	0.821077i	$0.693374\pi$
$522$	−0.153884	−	2.12987i	−0.00673532	−	0.0932218i
$523$	21.4072	−	12.3595i	0.936073	−	0.540442i	0.0473459	−	0.998879i	$-0.484924\pi$
$523$	21.4072	−	12.3595i	0.936073	−	0.540442i	0.888727	+	0.458437i	$0.151590\pi$
$524$	1.66694	+	11.4756i	0.0728208	+	0.501316i
$525$	9.75848	−	9.75848i	0.425895	−	0.425895i
$526$	7.82616	+	11.5451i	0.341237	+	0.503390i
$527$	4.41249	+	16.4676i	0.192211	+	0.717342i
$528$	−10.7050	+	6.56772i	−0.465876	+	0.285823i
$529$	1.74839	−	3.02830i	0.0760168	−	0.131665i
$530$	34.6759	+	30.0029i	1.50623	+	1.30324i
$531$	−9.97257	−	2.67214i	−0.432772	−	0.115961i
$532$	7.12458	+	9.03264i	0.308890	+	0.391615i
$533$	−10.9890	−	6.84554i	−0.475988	−	0.296513i
$534$	4.82963	−	1.67548i	0.208999	−	0.0725049i
$535$	9.84651	−	36.7477i	0.425702	−	1.58874i
$536$	37.1601	+	1.68911i	1.60507	+	0.0729584i
$537$	8.75907	+	5.05705i	0.377982	+	0.218228i
$538$	20.5829	+	9.98008i	0.887390	+	0.430272i
$539$	−8.86224	+	2.37463i	−0.381724	+	0.102283i
$540$	5.51381	+	4.11512i	0.237277	+	0.177087i
$541$	−13.1019	−	13.1019i	−0.563296	−	0.563296i	0.366946	−	0.930242i	$-0.380403\pi$
$541$	−13.1019	−	13.1019i	−0.563296	−	0.563296i	−0.930242	+	0.366946i	$0.880403\pi$
$542$	5.29263	−	27.5684i	0.227338	−	1.18416i
$543$	−1.18425	−	2.05118i	−0.0508209	−	0.0880245i
$544$	4.63027	−	28.1593i	0.198521	−	1.20732i
$545$			57.1149i			2.44653i
$546$	−8.71196	+	5.48875i	−0.372837	+	0.234897i
$547$			29.8165i			1.27486i	0.770508	+	0.637430i	$0.220002\pi$
$547$			29.8165i			1.27486i	−0.770508	+	0.637430i	$0.779998\pi$
$548$	−4.64031	+	1.99507i	−0.198224	+	0.0852251i
$549$	5.34563	+	9.25891i	0.228146	+	0.395161i
$550$	29.8014	+	5.72132i	1.27073	+	0.243958i
$551$	−3.04134	−	3.04134i	−0.129566	−	0.129566i
$552$	−3.77745	+	11.9062i	−0.160779	+	0.506760i
$553$	−23.1297	+	6.19760i	−0.983577	+	0.263549i
$554$	7.72477	−	15.9315i	0.328194	−	0.676865i
$555$	22.0151	+	12.7104i	0.934490	+	0.539528i
$556$	−12.5476	−	5.00220i	−0.532138	−	0.212141i
$557$	3.65965	−	13.6580i	0.155064	−	0.578708i	−0.844036	−	0.536287i	$-0.819826\pi$
$557$	3.65965	−	13.6580i	0.155064	−	0.578708i	0.999100	−	0.0424205i	$-0.0135069\pi$
$558$	−1.56642	−	4.51528i	−0.0663120	−	0.191147i
$559$	14.6658	−	13.7142i	0.620297	−	0.580047i
$560$	27.0228	+	6.47269i	1.14192	+	0.273521i
$561$	−15.2998	−	4.09956i	−0.645956	−	0.173084i
$562$	2.00630	−	2.31878i	0.0846305	−	0.0978120i
$563$	1.56760	−	2.71516i	0.0660663	−	0.114430i	−0.831100	−	0.556123i	$-0.812288\pi$
$563$	1.56760	−	2.71516i	0.0660663	−	0.114430i	0.897167	+	0.441692i	$0.145622\pi$
$564$	−2.83114	+	23.9737i	−0.119212	+	1.00948i
$565$	0.165701	+	0.618404i	0.00697108	+	0.0260164i
$566$	31.4879	−	21.3449i	1.32353	−	0.897194i
$567$	1.42791	−	1.42791i	0.0599667	−	0.0599667i
$568$	−14.1301	−	27.2628i	−0.592887	−	1.14392i
$569$	0.448262	−	0.258804i	0.0187921	−	0.0108496i	−0.490575	−	0.871399i	$-0.663213\pi$
$569$	0.448262	−	0.258804i	0.0187921	−	0.0108496i	0.509367	+	0.860550i	$0.329880\pi$
$570$	13.8218	−	0.998632i	0.578931	−	0.0418281i
$571$	7.16694			0.299927			0.149964	−	0.988692i	$-0.452084\pi$
$571$	7.16694			0.299927			0.149964	+	0.988692i	$0.452084\pi$
$572$	−20.7389	−	9.08455i	−0.867136	−	0.379844i
$573$	−12.1163			−0.506165
$574$	10.2281	−	0.738983i	0.426911	−	0.0308445i
$575$	26.1375	−	15.0905i	1.09001	−	0.629317i
$576$	−0.725780	+	7.96701i	−0.0302408	+	0.331959i
$577$	5.49183	−	5.49183i	0.228628	−	0.228628i	−0.583492	−	0.812119i	$-0.698314\pi$
$577$	5.49183	−	5.49183i	0.228628	−	0.228628i	0.812119	+	0.583492i	$0.198314\pi$
$578$	9.89117	−	6.70500i	0.411418	−	0.278891i
$579$	−3.74847	−	13.9895i	−0.155781	−	0.581382i
$580$	−10.3171	−	1.21838i	−0.428395	−	0.0505906i
$581$	11.6028	−	20.0966i	0.481365	−	0.833749i
$582$	−3.64945	+	4.21787i	−0.151275	+	0.174836i
$583$	28.5851	+	7.65935i	1.18387	+	0.317218i
$584$	12.0182	−	18.7905i	0.497317	−	0.777555i
$585$	−0.415673	+	12.3964i	−0.0171860	+	0.512527i
$586$	6.18342	+	17.8240i	0.255435	+	0.736301i
$587$	0.876019	−	3.26935i	0.0361572	−	0.134940i	−0.945488	−	0.325657i	$-0.894415\pi$
$587$	0.876019	−	3.26935i	0.0361572	−	0.134940i	0.981645	+	0.190717i	$0.0610812\pi$
$588$	−2.16422	+	5.42877i	−0.0892508	+	0.223879i
$589$	−8.33662	−	4.81315i	−0.343504	−	0.198322i
$590$	−21.9140	+	45.1954i	−0.902187	+	1.86066i
$591$	6.26356	−	1.67831i	0.257648	−	0.0690366i
$592$	0.789165	+	29.5480i	0.0324345	+	1.21442i
$593$	10.3636	+	10.3636i	0.425580	+	0.425580i	0.887120	−	0.461539i	$-0.152703\pi$
$593$	10.3636	+	10.3636i	0.425580	+	0.425580i	−0.461539	+	0.887120i	$0.652703\pi$
$594$	4.36070	+	0.837175i	0.178922	+	0.0343497i
$595$	17.5224	+	30.3498i	0.718350	+	1.24422i
$596$	12.5160	+	29.1108i	0.512675	+	1.19243i
$597$		−	5.17566i		−	0.211826i
$598$	−21.5101	+	6.66340i	−0.879612	+	0.272487i
$599$			21.1463i			0.864013i	0.901871	+	0.432006i	$0.142194\pi$
$599$			21.1463i			0.864013i	−0.901871	+	0.432006i	$0.857806\pi$
$600$	14.2747	−	13.0334i	0.582763	−	0.532087i
$601$	0.614650	+	1.06461i	0.0250721	+	0.0434262i	0.878289	−	0.478130i	$-0.158685\pi$
$601$	0.614650	+	1.06461i	0.0250721	+	0.0434262i	−0.853217	+	0.521556i	$0.825352\pi$
$602$	−2.99848	+	15.6186i	−0.122209	+	0.636565i
$603$	−9.29961	−	9.29961i	−0.378710	−	0.378710i
$604$	1.93793	−	2.59661i	0.0788531	−	0.105655i
$605$	−3.79382	+	1.01655i	−0.154241	+	0.0413286i
$606$	−11.0185	−	5.34258i	−0.447596	−	0.217028i
$607$	−20.4982	−	11.8346i	−0.831997	−	0.480354i	0.0225391	−	0.999746i	$-0.492825\pi$
$607$	−20.4982	−	11.8346i	−0.831997	−	0.480354i	−0.854536	+	0.519392i	$0.826158\pi$
$608$	9.39424	+	13.0916i	0.380987	+	0.530935i
$609$	−0.789189	+	2.94529i	−0.0319796	+	0.119349i
$610$	49.1399	−	17.0474i	1.98962	−	0.690230i
$611$	−38.3971	+	20.4845i	−1.55338	+	0.828714i
$612$	−7.92184	+	6.24843i	−0.320222	+	0.252578i
$613$	−13.4044	−	3.59169i	−0.541397	−	0.145067i	−0.0222510	−	0.999752i	$-0.507083\pi$
$613$	−13.4044	−	3.59169i	−0.541397	−	0.145067i	−0.519146	+	0.854686i	$0.673750\pi$
$614$	11.6034	+	10.0397i	0.468276	+	0.405169i
$615$	6.17631	−	10.6977i	0.249053	−	0.431372i
$616$	17.5152	−	3.85014i	0.705708	−	0.155127i
$617$	−3.66004	−	13.6595i	−0.147348	−	0.549909i	−0.999640	−	0.0268429i	$-0.991455\pi$
$617$	−3.66004	−	13.6595i	−0.147348	−	0.549909i	0.852292	−	0.523066i	$-0.175212\pi$
$618$	5.19058	+	7.65711i	0.208796	+	0.308014i
$619$	−13.8278	+	13.8278i	−0.555786	+	0.555786i	−0.928105	−	0.372319i	$-0.878563\pi$
$619$	−13.8278	+	13.8278i	−0.555786	+	0.555786i	0.372319	+	0.928105i	$0.378563\pi$
$620$	−23.0097	+	3.34237i	−0.924090	+	0.134233i
$621$	3.82458	−	2.20812i	0.153475	−	0.0886089i
$622$	−1.95550	−	27.0656i	−0.0784086	−	1.08523i
$623$	−7.29949			−0.292448
$624$	−12.5389	+	7.12578i	−0.501956	+	0.285260i
$625$	12.4657			0.498629
$626$	1.97651	+	27.3563i	0.0789972	+	1.09338i
$627$	7.74539	−	4.47180i	0.309321	−	0.178587i
$628$	−20.8429	+	3.02763i	−0.831724	+	0.120816i
$629$	−26.3602	+	26.3602i	−1.05105	+	1.05105i
$630$	−5.51246	−	8.13194i	−0.219622	−	0.323984i
$631$	1.92781	+	7.19467i	0.0767448	+	0.286415i	0.993623	−	0.112751i	$-0.0359662\pi$
$631$	1.92781	+	7.19467i	0.0767448	+	0.286415i	−0.916879	+	0.399166i	$0.869300\pi$
$632$	−32.7573	+	7.20061i	−1.30302	+	0.286425i
$633$	−2.82685	+	4.89625i	−0.112357	+	0.194608i
$634$	−11.1709	−	9.66546i	−0.443653	−	0.383864i
$635$	−10.4747	−	2.80668i	−0.415675	−	0.111380i
$636$	14.8007	−	11.6742i	0.586884	−	0.462910i
$637$	−10.2626	+	2.38430i	−0.406617	+	0.0944693i
$638$	−6.33441	+	2.19751i	−0.250782	+	0.0870002i
$639$	−2.80989	+	10.4866i	−0.111157	+	0.414845i
$640$	37.3986	+	10.7753i	1.47831	+	0.425929i
$641$	4.06149	+	2.34490i	0.160419	+	0.0926182i	0.578061	−	0.815994i	$-0.303810\pi$
$641$	4.06149	+	2.34490i	0.160419	+	0.0926182i	−0.417641	+	0.908612i	$0.637143\pi$
$642$	−14.0729	−	6.82356i	−0.555412	−	0.269304i
$643$	−46.3492	+	12.4192i	−1.82783	+	0.489767i	−0.997699	−	0.0677966i	$-0.978403\pi$
$643$	−46.3492	+	12.4192i	−1.82783	+	0.489767i	−0.830135	+	0.557563i	$0.811736\pi$
$644$	10.6681	−	14.2940i	0.420380	−	0.563264i
$645$	13.5463	+	13.5463i	0.533386	+	0.533386i
$646$	−3.83150	+	19.9576i	−0.150748	+	0.785222i
$647$	0.623804	+	1.08046i	0.0245243	+	0.0424772i	0.878027	−	0.478611i	$-0.158860\pi$
$647$	0.623804	+	1.08046i	0.0245243	+	0.0424772i	−0.853503	+	0.521088i	$0.825526\pi$
$648$	2.08875	−	1.90712i	0.0820540	−	0.0749188i
$649$			32.4163i			1.27245i
$650$	33.9828	+	7.71323i	1.33291	+	0.302538i
$651$			6.82439i			0.267469i
$652$	−0.719207	−	1.67280i	−0.0281663	−	0.0655118i
$653$	−4.89288	−	8.47472i	−0.191473	−	0.331641i	0.754265	−	0.656570i	$-0.227993\pi$
$653$	−4.89288	−	8.47472i	−0.191473	−	0.331641i	−0.945739	+	0.324928i	$0.894660\pi$
$654$	23.0588	+	4.42688i	0.901672	+	0.173105i
$655$	−14.1037	−	14.1037i	−0.551078	−	0.551078i
$656$	14.3581	−	0.383475i	0.560590	−	0.0149722i
$657$	−7.61734	+	2.04106i	−0.297181	+	0.0796294i
$658$	15.0391	−	31.0165i	0.586285	−	1.20915i
$659$	4.64491	+	2.68174i	0.180940	+	0.104466i	0.587734	−	0.809054i	$-0.300020\pi$
$659$	4.64491	+	2.68174i	0.180940	+	0.104466i	−0.406794	+	0.913520i	$0.633353\pi$
$660$	7.99961	−	20.0664i	0.311385	−	0.781083i
$661$	−11.2518	+	41.9923i	−0.437645	+	1.63331i	0.297012	+	0.954874i	$0.404010\pi$
$661$	−11.2518	+	41.9923i	−0.437645	+	1.63331i	−0.734657	+	0.678439i	$0.762657\pi$
$662$	−15.1434	−	43.6516i	−0.588566	−	1.69657i
$663$	−17.4017	−	5.29385i	−0.675827	−	0.205596i
$664$	17.5128	−	27.3813i	0.679628	−	1.06260i
$665$	−19.1135	−	5.12145i	−0.741190	−	0.198601i
$666$	6.83791	−	7.90294i	0.264964	−	0.306233i
$667$	−3.33420	+	5.77500i	−0.129101	+	0.223609i
$668$	6.58774	+	0.777969i	0.254887	+	0.0301005i
$669$	−4.96434	−	18.5272i	−0.191932	−	0.716301i
$670$	−52.9612	+	35.9012i	−2.04607	+	1.38698i
$671$	23.7364	−	23.7364i	0.916333	−	0.916333i
$672$	4.70769	−	10.4081i	0.181603	−	0.401503i
$673$	−28.1647	+	16.2609i	−1.08567	+	0.626811i	−0.932420	−	0.361376i	$-0.882307\pi$
$673$	−28.1647	+	16.2609i	−1.08567	+	0.626811i	−0.153249	+	0.988188i	$0.548974\pi$
$674$	−36.1462	+	2.61159i	−1.39230	+	0.100595i
$675$	−6.83408			−0.263044
$676$	−23.4523	−	11.2244i	−0.902013	−	0.431709i
$677$	40.6992			1.56420			0.782099	−	0.623154i	$-0.214149\pi$
$677$	40.6992			1.56420			0.782099	+	0.623154i	$0.214149\pi$
$678$	0.262510	−	0.0189665i	0.0100816	−	0.000728403i
$679$	6.89723	−	3.98212i	0.264691	−	0.152820i
$680$	22.5872	+	43.5799i	0.866178	+	1.67121i
$681$	−11.5193	+	11.5193i	−0.441420	+	0.441420i
$682$	−12.4210	+	8.41994i	−0.475626	+	0.322416i
$683$	−0.00355298	−	0.0132599i	−0.000135951	−	0.000507376i	0.965858	−	0.259073i	$-0.0834169\pi$
$683$	−0.00355298	−	0.0132599i	−0.000135951	−	0.000507376i	−0.965994	+	0.258565i	$0.916750\pi$
$684$	0.668129	−	5.65764i	0.0255466	−	0.216325i
$685$	4.34397	−	7.52397i	0.165974	−	0.287476i
$686$	18.5405	−	21.4283i	0.707880	−	0.818136i
$687$	3.75947	+	1.00735i	0.143433	+	0.0384326i
$688$	−5.18883	+	21.6628i	−0.197822	+	0.825887i
$689$	32.5122	+	9.89069i	1.23862	+	0.376805i
$690$	−7.04178	−	20.2982i	−0.268076	−	0.772741i
$691$	3.39966	−	12.6877i	0.129329	−	0.482663i	−0.870628	−	0.491942i	$-0.836287\pi$
$691$	3.39966	−	12.6877i	0.129329	−	0.482663i	0.999957	+	0.00927954i	$0.00295381\pi$
$692$	−20.1485	−	8.03235i	−0.765931	−	0.305344i
$693$	−5.49095	−	3.17020i	−0.208584	−	0.120426i
$694$	16.2085	−	33.4282i	0.615265	−	1.26892i
$695$	22.4425	−	6.01344i	0.851291	−	0.228103i
$696$	−1.29156	+	4.07086i	−0.0489563	+	0.154306i
$697$	12.8091	+	12.8091i	0.485178	+	0.485178i
$698$	20.6473	+	3.96392i	0.781513	+	0.150036i
$699$	−12.3606	−	21.4092i	−0.467521	−	0.809771i
$700$	−25.3568	+	10.9020i	−0.958398	+	0.412057i
$701$			2.79710i			0.105645i	0.998604	+	0.0528226i	$0.0168218\pi$
$701$			2.79710i			0.105645i	−0.998604	+	0.0528226i	$0.983178\pi$
$702$	4.97254	+	1.12864i	0.187676	+	0.0425978i
$703$		−	21.0492i		−	0.793886i
$704$	24.7522	−	4.27314i	0.932882	−	0.161050i
$705$	−20.7611	−	35.9593i	−0.781908	−	1.35431i
$706$	−5.04655	+	26.2866i	−0.189929	+	0.989308i
$707$	12.3641	+	12.3641i	0.464998	+	0.464998i
$708$	16.5481	+	12.3503i	0.621915	+	0.464153i
$709$	−33.4954	+	8.97506i	−1.25795	+	0.337065i	−0.825401	−	0.564547i	$-0.809051\pi$
$709$	−33.4954	+	8.97506i	−1.25795	+	0.337065i	−0.432544	+	0.901613i	$0.642384\pi$
$710$	47.5251	+	23.0437i	1.78359	+	0.864814i
$711$	10.2693	+	5.92898i	0.385129	+	0.222354i
$712$	−10.2135	−	0.464252i	−0.382765	−	0.0173986i
$713$	−3.86275	+	14.4160i	−0.144661	+	0.539882i
$714$	13.6112	−	4.72193i	0.509385	−	0.176714i
$715$	37.9336	−	8.81310i	1.41863	−	0.329591i
$716$	−12.5273	−	15.8823i	−0.468167	−	0.593549i
$717$	−4.80086	−	1.28639i	−0.179292	−	0.0480410i
$718$	2.77039	+	2.39704i	0.103390	+	0.0894568i
$719$	6.03295	−	10.4494i	0.224991	−	0.389696i	−0.731326	−	0.682028i	$-0.761098\pi$
$719$	6.03295	−	10.4494i	0.224991	−	0.389696i	0.956317	+	0.292332i	$0.0944314\pi$
$720$	−7.19585	−	11.7288i	−0.268173	−	0.437107i
$721$	−3.41875	−	12.7590i	−0.127321	−	0.475168i
$722$	8.63848	+	12.7434i	0.321491	+	0.474261i
$723$	−1.12411	+	1.12411i	−0.0418059	+	0.0418059i
$724$	0.680946	+	4.68779i	0.0253072	+	0.174220i
$725$	8.93674	−	5.15963i	0.331902	−	0.191624i
$726$	0.116357	+	1.61046i	0.00431840	+	0.0597697i
$727$	−43.6647			−1.61943			−0.809716	−	0.586822i	$-0.800379\pi$
$727$	−43.6647			−1.61943			−0.809716	+	0.586822i	$0.800379\pi$
$728$	20.2503	−	3.74473i	0.750527	−	0.138789i
$729$	−1.00000			−0.0370370
$730$	2.76473	+	38.2659i	0.102327	+	1.41628i
$731$	−24.3299	+	14.0469i	−0.899873	+	0.519542i
$732$	−3.07376	−	21.1605i	−0.113609	−	0.782113i
$733$	13.0136	−	13.0136i	0.480668	−	0.480668i	−0.424677	−	0.905345i	$-0.639612\pi$
$733$	13.0136	−	13.0136i	0.480668	−	0.480668i	0.905345	+	0.424677i	$0.139612\pi$
$734$	−10.6794	−	15.7542i	−0.394184	−	0.581497i
$735$	−2.60173	−	9.70980i	−0.0959664	−	0.358151i
$736$	15.8359	−	19.3217i	0.583717	−	0.712208i
$737$	−20.6467	+	35.7611i	−0.760530	+	1.31728i
$738$	−3.84023	−	3.32271i	−0.141361	−	0.122311i
$739$	5.62559	+	1.50737i	0.206941	+	0.0554496i	0.360800	−	0.932643i	$-0.382504\pi$
$739$	5.62559	+	1.50737i	0.206941	+	0.0554496i	−0.153860	+	0.988093i	$0.549170\pi$
$740$	−31.4862	−	39.9187i	−1.15746	−	1.46744i
$741$	9.06146	−	4.83420i	0.332881	−	0.177589i
$742$	−25.4302	+	8.82215i	−0.933573	+	0.323871i
$743$	3.66380	−	13.6735i	0.134412	−	0.501632i	−0.865588	−	0.500757i	$-0.833055\pi$
$743$	3.66380	−	13.6735i	0.134412	−	0.501632i	1.00000		0.000874528i	$-0.000278371\pi$
$744$	−0.434035	+	9.54869i	−0.0159125	+	0.350072i
$745$	−47.2013	−	27.2517i	−1.72932	−	0.998425i
$746$	−32.1649	−	15.5959i	−1.17764	−	0.571007i
$747$	−11.0999	+	2.97421i	−0.406125	+	0.108821i
$748$	25.3878	+	18.9477i	0.928271	+	0.692796i
$749$	15.7914	+	15.7914i	0.577005	+	0.577005i
$750$	−1.68229	+	8.76278i	−0.0614287	+	0.319971i
$751$	−10.3870	−	17.9907i	−0.379026	−	0.656492i	0.611895	−	0.790939i	$-0.290407\pi$
$751$	−10.3870	−	17.9907i	−0.379026	−	0.656492i	−0.990921	+	0.134447i	$0.957074\pi$
$752$	23.0154	−	42.4419i	0.839285	−	1.54770i
$753$			4.46555i			0.162734i
$754$	−7.35456	+	2.27830i	−0.267837	+	0.0829708i
$755$			5.57301i			0.202822i
$756$	−3.71035	+	1.59524i	−0.134944	+	0.0580183i
$757$	−9.51286	−	16.4767i	−0.345751	−	0.598858i	0.639739	−	0.768592i	$-0.279042\pi$
$757$	−9.51286	−	16.4767i	−0.345751	−	0.598858i	−0.985490	+	0.169734i	$0.945709\pi$
$758$	22.8545	+	4.38765i	0.830113	+	0.159367i
$759$	−9.80479	−	9.80479i	−0.355891	−	0.355891i
$760$	−26.4179	−	8.38156i	−0.958278	−	0.304031i
$761$	−18.6674	+	5.00191i	−0.676692	+	0.181319i	−0.580767	−	0.814070i	$-0.697247\pi$
$761$	−18.6674	+	5.00191i	−0.676692	+	0.181319i	−0.0959246	+	0.995389i	$0.530581\pi$
$762$	−1.94501	+	4.01137i	−0.0704603	+	0.145317i
$763$	−29.0355	−	16.7637i	−1.05116	−	0.606885i
$764$	22.5098	+	8.97368i	0.814375	+	0.324656i
$765$	4.49163	−	16.7630i	0.162395	−	0.606068i
$766$	−15.2475	−	43.9516i	−0.550915	−	1.58804i
$767$	−1.24752	+	37.2041i	−0.0450453	+	1.34336i
$768$	7.24897	−	14.2637i	0.261575	−	0.514696i
$769$	−11.5636	−	3.09846i	−0.416995	−	0.111733i	0.0442202	−	0.999022i	$-0.485920\pi$
$769$	−11.5636	−	3.09846i	−0.416995	−	0.111733i	−0.461215	+	0.887288i	$0.652586\pi$
$770$	−20.1829	+	23.3265i	−0.727343	+	0.840630i
$771$	−4.11009	+	7.11888i	−0.148021	+	0.256380i
$772$	−3.39708	+	28.7660i	−0.122263	+	1.03531i
$773$	−3.48923	−	13.0220i	−0.125499	−	0.468368i	0.874358	−	0.485281i	$-0.161283\pi$
$773$	−3.48923	−	13.0220i	−0.125499	−	0.468368i	−0.999857	+	0.0169134i	$0.994616\pi$
$774$	6.51897	−	4.41907i	0.234320	−	0.158840i
$775$	16.3310	−	16.3310i	0.586626	−	0.586626i
$776$	9.90388	−	5.13312i	0.355528	−	0.184268i
$777$	−12.9232	+	7.46122i	−0.463618	+	0.267670i
$778$	−13.2438	+	0.956876i	−0.474815	+	0.0343057i
$779$	−10.2283			−0.366468
$780$	9.95338	−	22.7223i	0.356388	−	0.813589i
$781$	34.0873			1.21974
$782$	31.4252	−	2.27049i	1.12376	−	0.0811925i
$783$	1.30767	−	0.754985i	0.0467324	−	0.0269809i
$784$	8.04142	−	8.48274i	0.287193	−	0.302955i
$785$	25.6163	−	25.6163i	0.914283	−	0.914283i
$786$	−6.78721	+	4.60090i	−0.242092	+	0.164109i
$787$	−8.82086	−	32.9199i	−0.314430	−	1.17347i	−0.924519	−	0.381135i	$-0.875533\pi$
$787$	−8.82086	−	32.9199i	−0.314430	−	1.17347i	0.610090	−	0.792332i	$-0.291133\pi$
$788$	−12.8795	−	1.52099i	−0.458814	−	0.0541829i
$789$	−4.93125	+	8.54118i	−0.175557	+	0.304074i
$790$	37.7466	−	43.6258i	1.34296	−	1.55214i
$791$	−0.363012	−	0.0972689i	−0.0129072	−	0.00345848i
$792$	−7.48132	−	4.78498i	−0.265837	−	0.170027i
$793$	28.1557	−	26.3287i	0.999837	−	0.934960i
$794$	1.42624	+	4.11119i	0.0506153	+	0.145901i
$795$	−8.39187	+	31.3189i	−0.297629	+	1.11077i
$796$	−3.83325	+	9.61540i	−0.135866	+	0.340809i
$797$	−40.3734	−	23.3096i	−1.43010	−	0.825668i	−0.432971	−	0.901408i	$-0.642535\pi$
$797$	−40.3734	−	23.3096i	−1.43010	−	0.825668i	−0.997128	+	0.0757404i	$0.975868\pi$
$798$	−3.54913	+	7.31969i	−0.125638	+	0.259114i
$799$	58.8163	−	15.7598i	2.08077	−	0.557541i
$800$	−36.1727	+	13.6414i	−1.27890	+	0.482295i
$801$	2.55600	+	2.55600i	0.0903118	+	0.0903118i
$802$	35.9693	+	6.90546i	1.27012	+	0.243840i
$803$	12.3803	+	21.4433i	0.436890	+	0.756716i
$804$	10.3894	+	24.1645i	0.366405	+	0.852217i
$805$			30.6787i			1.08128i
$806$	−14.5796	+	9.18552i	−0.513545	+	0.323546i
$807$			16.1749i			0.569384i
$808$	16.5134	+	18.0862i	0.580940	+	0.636269i
$809$	−3.07980	−	5.33436i	−0.108280	−	0.187546i	0.806794	−	0.590833i	$-0.201201\pi$
$809$	−3.07980	−	5.33436i	−0.108280	−	0.187546i	−0.915073	+	0.403287i	$0.867868\pi$
$810$	−0.917241	+	4.77774i	−0.0322285	+	0.167873i
$811$	31.5037	+	31.5037i	1.10625	+	1.10625i	0.993640	+	0.112607i	$0.0359199\pi$
$811$	31.5037	+	31.5037i	1.10625	+	1.10625i	0.112607	+	0.993640i	$0.464080\pi$
$812$	3.64754	−	4.88731i	0.128004	−	0.171511i
$813$	19.1734	−	5.13750i	0.672441	−	0.180180i
$814$	−29.5248	−	14.3158i	−1.03484	−	0.501768i
$815$	2.71233	+	1.56597i	0.0950089	+	0.0548534i
$816$	19.3451	−	5.74125i	0.677213	−	0.200984i
$817$	4.10561	−	15.3223i	0.143637	−	0.536061i
$818$	13.4237	−	4.65688i	0.469347	−	0.162824i
$819$	−6.17995	−	3.84975i	−0.215945	−	0.134521i
$820$	−19.3975	+	15.2999i	−0.677389	+	0.534297i
$821$	14.7969	+	3.96481i	0.516415	+	0.138373i	0.507608	−	0.861588i	$-0.330530\pi$
$821$	14.7969	+	3.96481i	0.516415	+	0.138373i	0.00880716	+	0.999961i	$0.497197\pi$
$822$	−2.70094	−	2.33695i	−0.0942061	−	0.0815105i
$823$	13.7097	−	23.7459i	0.477889	−	0.827728i	−0.521789	−	0.853074i	$-0.674735\pi$
$823$	13.7097	−	23.7459i	0.477889	−	0.827728i	0.999679	+	0.0253458i	$0.00806869\pi$
$824$	−3.97204	−	18.0698i	−0.138373	−	0.629490i
$825$	5.55363	+	20.7264i	0.193352	+	0.721601i
$826$	−16.5440	−	24.4056i	−0.575641	−	0.849181i
$827$	1.87844	−	1.87844i	0.0653199	−	0.0653199i	−0.673692	−	0.739012i	$-0.735293\pi$
$827$	1.87844	−	1.87844i	0.0653199	−	0.0653199i	0.739012	+	0.673692i	$0.235293\pi$
$828$	−8.74076	+	1.26968i	−0.303762	+	0.0441243i
$829$	11.0370	−	6.37221i	0.383330	−	0.221316i	−0.295936	−	0.955208i	$-0.595632\pi$
$829$	11.0370	−	6.37221i	0.383330	−	0.221316i	0.679266	+	0.733892i	$0.262298\pi$
$830$	4.02873	+	55.7606i	0.139839	+	1.93548i
$831$	12.5197			0.434303
$832$	28.5724	−	3.95170i	0.990571	−	0.137001i
$833$	14.7414			0.510761
$834$	−0.688312	−	9.52673i	−0.0238343	−	0.329884i
$835$	−9.88125	+	5.70494i	−0.341955	+	0.197428i
$836$	−17.7014	+	2.57130i	−0.612217	+	0.0889303i
$837$	2.38964	−	2.38964i	0.0825979	−	0.0825979i
$838$	14.5384	+	21.4470i	0.502221	+	0.740873i
$839$	−5.89000	−	21.9818i	−0.203345	−	0.758895i	−0.989948	−	0.141435i	$-0.954828\pi$
$839$	−5.89000	−	21.9818i	−0.203345	−	0.758895i	0.786602	−	0.617460i	$-0.211838\pi$
$840$	4.21836	+	19.1903i	0.145547	+	0.662129i
$841$	13.3600	−	23.1402i	0.460690	−	0.797938i
$842$	−31.9885	−	27.6776i	−1.10240	−	0.953833i
$843$	2.09430	+	0.561166i	0.0721315	+	0.0193276i
$844$	8.87807	−	7.00266i	0.305596	−	0.241042i
$845$	43.8754	−	8.65493i	1.50936	−	0.297739i
$846$	−16.1269	+	5.59468i	−0.554455	+	0.192349i
$847$	0.596731	−	2.22703i	0.0205039	−	0.0765216i
$848$	−36.1431	+	10.7266i	−1.24116	+	0.368352i
$849$	23.2951	+	13.4494i	0.799484	+	0.461582i
$850$	−43.8717	−	21.2722i	−1.50479	−	0.729631i
$851$	−31.5225	+	8.44642i	−1.08058	+	0.289539i
$852$	12.9870	−	17.4011i	0.444926	−	0.596153i
$853$	37.7776	+	37.7776i	1.29348	+	1.29348i	0.932620	+	0.360861i	$0.117517\pi$
$853$	37.7776	+	37.7776i	1.29348	+	1.29348i	0.360861	+	0.932620i	$0.382483\pi$
$854$	−5.75655	+	29.9848i	−0.196985	+	1.02606i
$855$	4.89948	+	8.48614i	0.167559	+	0.290220i
$856$	21.0910	+	23.0997i	0.720876	+	0.789531i
$857$			10.8981i			0.372271i	0.982524	+	0.186136i	$0.0595964\pi$
$857$			10.8981i			0.372271i	−0.982524	+	0.186136i	$0.940404\pi$
$858$	−0.617922	−	15.9979i	−0.0210955	−	0.546160i
$859$		−	47.3383i		−	1.61516i	−0.589757	−	0.807581i	$-0.700776\pi$
$859$		−	47.3383i		−	1.61516i	0.589757	−	0.807581i	$-0.299224\pi$
$860$	−15.1337	−	35.1993i	−0.516055	−	1.20029i
$861$	3.62559	+	6.27971i	0.123560	+	0.214012i
$862$	3.99274	+	0.766534i	0.135993	+	0.0261083i
$863$	−3.35974	−	3.35974i	−0.114367	−	0.114367i	0.647607	−	0.761974i	$-0.275770\pi$
$863$	−3.35974	−	3.35974i	−0.114367	−	0.114367i	−0.761974	+	0.647607i	$0.775770\pi$
$864$	−5.29298	+	1.99608i	−0.180071	+	0.0679080i
$865$	36.0373	−	9.65616i	1.22530	−	0.328319i
$866$	6.20205	−	12.7911i	0.210754	−	0.434658i
$867$	7.31759	+	4.22481i	0.248518	+	0.143482i
$868$	5.05435	−	12.6784i	0.171556	−	0.430334i
$869$	9.63622	−	35.9629i	0.326886	−	1.21996i
$870$	−2.40767	−	6.94022i	−0.0816278	−	0.235296i
$871$	−25.0724	+	40.2483i	−0.849545	+	1.36376i
$872$	−39.5603	−	25.3024i	−1.33968	−	0.856847i
$873$	−3.80953	−	1.02076i	−0.128933	−	0.0345475i
$874$	−11.6403	+	13.4534i	−0.393741	+	0.455067i
$875$	6.37049	−	11.0340i	0.215362	−	0.373018i
$876$	15.6633	+	1.84973i	0.529213	+	0.0624965i
$877$	0.279520	+	1.04318i	0.00943872	+	0.0352258i	0.970485	−	0.241163i	$-0.0775289\pi$
$877$	0.279520	+	1.04318i	0.00943872	+	0.0352258i	−0.961046	+	0.276389i	$0.910862\pi$
$878$	35.6789	−	24.1859i	1.20411	−	0.816236i
$879$	−9.43303	+	9.43303i	−0.318168	+	0.318168i
$880$	−29.7236	+	31.3548i	−1.00198	+	1.05697i
$881$	−24.7951	+	14.3154i	−0.835367	+	0.482299i	−0.855687	−	0.517494i	$-0.826865\pi$
$881$	−24.7951	+	14.3154i	−0.835367	+	0.482299i	0.0203197	+	0.999794i	$0.493532\pi$
$882$	−4.12177	+	0.297800i	−0.138787	+	0.0100275i
$883$	23.0468			0.775585			0.387793	−	0.921747i	$-0.373238\pi$
$883$	23.0468			0.775585			0.387793	+	0.921747i	$0.373238\pi$
$884$	28.4084	+	22.7232i	0.955476	+	0.764265i
$885$	−35.5165			−1.19387
$886$	−43.0944	+	3.11359i	−1.44778	+	0.104603i
$887$	−50.4640	+	29.1354i	−1.69441	+	0.978271i	−0.743541	+	0.668690i	$0.766855\pi$
$887$	−50.4640	+	29.1354i	−1.69441	+	0.978271i	−0.950873	+	0.309581i	$0.899811\pi$
$888$	−18.5567	+	9.61782i	−0.622722	+	0.322753i
$889$	4.50123	−	4.50123i	0.150967	−	0.150967i
$890$	14.5564	−	9.86745i	0.487931	−	0.330758i
$891$	0.812637	+	3.03280i	0.0272244	+	0.101603i
$892$	−4.49897	+	38.0967i	−0.150637	+	1.27557i
$893$	−17.1908	+	29.7753i	−0.575268	+	0.996393i
$894$	−14.6608	+	16.9442i	−0.490329	+	0.566700i
$895$	33.6077	+	9.00514i	1.12338	+	0.301009i
$896$	−16.4546	+	15.8497i	−0.549710	+	0.529502i
$897$	−10.8756	−	11.6303i	−0.363126	−	0.388323i
$898$	−8.71482	−	25.1208i	−0.290817	−	0.838293i
$899$	−1.32072	+	4.92900i	−0.0440485	+	0.164391i
$900$	12.6964	+	5.06153i	0.423215	+	0.168718i
$901$	−41.1781	−	23.7742i	−1.37184	−	0.792033i
$902$	−6.95640	+	14.3468i	−0.231623	+	0.477697i
$903$	−10.8625	+	2.91060i	−0.361481	+	0.0968586i
$904$	−0.501741	−	0.159186i	−0.0166877	−	0.00529446i
$905$	−5.76136	−	5.76136i	−0.191514	−	0.191514i
$906$	2.24998	+	0.431955i	0.0747504	+	0.0143507i
$907$	−11.5231	−	19.9586i	−0.382618	−	0.662713i	0.608818	−	0.793310i	$-0.291644\pi$
$907$	−11.5231	−	19.9586i	−0.382618	−	0.662713i	−0.991436	+	0.130597i	$0.958311\pi$
$908$	29.9322	−	12.8692i	0.993336	−	0.427078i
$909$		−	8.65883i		−	0.287195i
$910$	−24.0616	+	25.9951i	−0.797635	+	0.861728i
$911$			4.09749i			0.135756i	0.997694	+	0.0678780i	$0.0216229\pi$
$911$			4.09749i			0.135756i	−0.997694	+	0.0678780i	$0.978377\pi$
$912$	−5.43148	+	10.0160i	−0.179854	+	0.331663i
$913$	18.0404	+	31.2469i	0.597050	+	1.03412i
$914$	7.07667	−	36.8611i	0.234075	−	1.21926i
$915$	26.0065	+	26.0065i	0.859748	+	0.859748i
$916$	−6.23831	−	4.65583i	−0.206120	−	0.153833i
$917$	11.3095	−	3.03036i	0.373471	−	0.100071i
$918$	−6.41954	−	3.11267i	−0.211877	−	0.102733i
$919$	44.2356	+	25.5394i	1.45920	+	0.842468i	0.998972	−	0.0453333i	$-0.0144350\pi$
$919$	44.2356	+	25.5394i	1.45920	+	0.842468i	0.460226	+	0.887802i	$0.347768\pi$
$920$	−1.95119	+	42.9257i	−0.0643287	+	1.41522i
$921$	−2.80813	+	10.4801i	−0.0925309	+	0.345330i
$922$	38.8811	−	13.4885i	1.28048	−	0.444219i
$923$	39.1219	+	1.31183i	1.28771	+	0.0431793i
$924$	7.85321	+	9.95641i	0.258352	+	0.327542i
$925$	48.7806	+	13.0707i	1.60390	+	0.429763i
$926$	13.5532	+	11.7267i	0.445385	+	0.385363i
$927$	−3.27058	+	5.66481i	−0.107420	+	0.186057i
$928$	5.41448	−	6.60634i	0.177739	−	0.216864i
$929$	−8.01716	−	29.9205i	−0.263035	−	0.981658i	−0.963442	−	0.267915i	$-0.913665\pi$
$929$	−8.01716	−	29.9205i	−0.263035	−	0.981658i	0.700408	−	0.713743i	$-0.253001\pi$
$930$	−9.22520	−	13.6089i	−0.302506	−	0.446255i
$931$	−5.88568	+	5.88568i	−0.192895	+	0.192895i
$932$	7.10739	+	48.9289i	0.232810	+	1.60272i
$933$	16.6174	−	9.59407i	0.544030	−	0.314096i
$934$	−3.51141	−	48.6004i	−0.114897	−	1.59025i
$935$	−54.4889			−1.78198
$936$	−8.40214	−	5.77962i	−0.274633	−	0.188913i
$937$	−24.0978			−0.787241			−0.393620	−	0.919273i	$-0.628778\pi$
$937$	−24.0978			−0.787241			−0.393620	+	0.919273i	$0.628778\pi$
$938$	−2.70659	−	37.4612i	−0.0883733	−	1.22315i
$939$	−16.7959	+	9.69713i	−0.548114	+	0.316454i
$940$	11.9377	+	82.1819i	0.389365	+	2.68048i
$941$	4.58652	−	4.58652i	0.149516	−	0.149516i	−0.628386	−	0.777902i	$-0.716284\pi$
$941$	4.58652	−	4.58652i	0.149516	−	0.149516i	0.777902	+	0.628386i	$0.216284\pi$
$942$	−8.35651	−	12.3275i	−0.272270	−	0.401650i
$943$	4.10432	+	15.3175i	0.133655	+	0.498808i
$944$	−21.5962	−	35.2006i	−0.702897	−	1.14568i
$945$	3.47339	−	6.01610i	0.112990	−	0.195704i
$946$	−18.6997	−	16.1797i	−0.607980	−	0.526046i
$947$	32.6504	+	8.74864i	1.06099	+	0.284293i	0.746788	−	0.665062i	$-0.231595\pi$
$947$	32.6504	+	8.74864i	1.06099	+	0.284293i	0.314206	+	0.949355i	$0.398262\pi$
$948$	−14.6872	−	18.6207i	−0.477020	−	0.604772i
$949$	13.3836	+	25.0868i	0.434449	+	0.814352i
$950$	26.0094	−	9.02308i	0.843857	−	0.292747i
$951$	2.70345	−	10.0894i	0.0876654	−	0.327172i
$952$	−28.7842	−	1.30838i	−0.932901	−	0.0424050i
$953$	−12.8262	−	7.40518i	−0.415480	−	0.239877i	0.277662	−	0.960679i	$-0.410441\pi$
$953$	−12.8262	−	7.40518i	−0.415480	−	0.239877i	−0.693141	+	0.720802i	$0.743774\pi$
$954$	11.9939	+	5.81550i	0.388315	+	0.188284i
$955$	−40.2606	+	10.7878i	−1.30280	+	0.349085i
$956$	7.96637	+	5.94553i	0.257651	+	0.192292i
$957$	−3.35238	−	3.35238i	−0.108367	−	0.108367i
$958$	−3.48303	+	18.1425i	−0.112531	+	0.586157i
$959$	2.54997	+	4.41669i	0.0823430	+	0.142622i
$960$	4.68181	+	27.1194i	0.151105	+	0.875275i
$961$		−	19.5793i		−	0.631589i
$962$	−33.3346	−	17.5664i	−1.07475	−	0.566365i
$963$		−	11.0591i		−	0.356374i
$964$	2.92092	−	1.25583i	0.0940766	−	0.0404476i
$965$	−24.9112	−	43.1475i	−0.801920	−	1.38897i
$966$	12.3858	+	2.37786i	0.398508	+	0.0765063i
$967$	−31.1966	−	31.1966i	−1.00321	−	1.00321i	−0.999995	−	0.00322011i	$-0.998975\pi$
$967$	−31.1966	−	31.1966i	−1.00321	−	1.00321i	−0.00322011	−	0.999995i	$-0.501025\pi$
$968$	0.976586	−	3.07811i	0.0313887	−	0.0989341i
$969$	−13.8802	+	3.71920i	−0.445898	+	0.119478i
$970$	−8.37118	+	17.2647i	−0.268783	+	0.554335i
$971$	21.6403	+	12.4941i	0.694472	+	0.400953i	0.805285	−	0.592888i	$-0.202012\pi$
$971$	21.6403	+	12.4941i	0.694472	+	0.400953i	−0.110813	+	0.993841i	$0.535346\pi$
$972$	1.85781	+	0.740630i	0.0595894	+	0.0237557i
$973$	−3.52998	+	13.1741i	−0.113166	+	0.422341i
$974$	18.2743	+	52.6764i	0.585546	+	1.68786i
$975$	5.57624	+	24.0014i	0.178583	+	0.768659i
$976$	−9.96162	+	41.5887i	−0.318864	+	1.33122i
$977$	−24.6129	−	6.59500i	−0.787436	−	0.210993i	−0.157375	−	0.987539i	$-0.550303\pi$
$977$	−24.6129	−	6.59500i	−0.787436	−	0.210993i	−0.630060	+	0.776546i	$0.716970\pi$
$978$	0.842452	−	0.973668i	0.0269387	−	0.0311345i
$979$	5.67474	−	9.82894i	0.181366	−	0.314134i
$980$	−2.35784	+	19.9659i	−0.0753185	+	0.637788i
$981$	4.29713	+	16.0371i	0.137197	+	0.512025i
$982$	−11.2058	+	7.59618i	−0.357592	+	0.242404i
$983$	−17.6105	+	17.6105i	−0.561689	+	0.561689i	−0.929787	−	0.368098i	$-0.880009\pi$
$983$	−17.6105	+	17.6105i	−0.561689	+	0.561689i	0.368098	+	0.929787i	$0.380009\pi$
$984$	4.67353	+	9.01716i	0.148987	+	0.287456i
$985$	19.3186	−	11.1536i	0.615541	−	0.355383i
$986$	10.7447	−	0.776309i	0.342180	−	0.0247227i
$987$	24.3742			0.775839
$988$	−20.4148	+	2.26985i	−0.649483	+	0.0722134i
$989$	−24.5936			−0.782031
$990$	15.2353	−	1.10076i	0.484211	−	0.0349845i
$991$	6.69986	−	3.86817i	0.212828	−	0.122876i	−0.389797	−	0.920901i	$-0.627455\pi$
$991$	6.69986	−	3.86817i	0.212828	−	0.122876i	0.602625	+	0.798024i	$0.294121\pi$
$992$	7.87840	−	17.4182i	0.250140	−	0.553029i
$993$	23.1018	−	23.1018i	0.733115	−	0.733115i
$994$	−25.6637	+	17.3969i	−0.814004	+	0.551795i
$995$	−4.60818	−	17.1979i	−0.146089	−	0.545212i
$996$	22.8243	+	2.69540i	0.723217	+	0.0854071i
$997$	−0.336148	+	0.582225i	−0.0106459	+	0.0184393i	−0.871299	−	0.490752i	$-0.836722\pi$
$997$	−0.336148	+	0.582225i	−0.0106459	+	0.0184393i	0.860653	+	0.509191i	$0.170055\pi$
$998$	15.6500	−	18.0876i	0.495392	−	0.572552i
$999$	7.13784	+	1.91258i	0.225831	+	0.0605113i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	156.2.w.c.67.4	yes	24
3.2	odd	2		468.2.cb.h.379.3		24
4.3	odd	2		156.2.w.d.67.3	yes	24
12.11	even	2		468.2.cb.g.379.4		24
13.7	odd	12		156.2.w.d.7.3	yes	24
39.20	even	12		468.2.cb.g.163.4		24
52.7	even	12	inner	156.2.w.c.7.4	✓	24
156.59	odd	12		468.2.cb.h.163.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.2.w.c.7.4	✓	24	52.7	even	12	inner
156.2.w.c.67.4	yes	24	1.1	even	1	trivial
156.2.w.d.7.3	yes	24	13.7	odd	12
156.2.w.d.67.3	yes	24	4.3	odd	2
468.2.cb.g.163.4		24	39.20	even	12
468.2.cb.g.379.4		24	12.11	even	2
468.2.cb.h.163.3		24	156.59	odd	12
468.2.cb.h.379.3		24	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	156.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.101912 - 1.41054i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-1.97923 + 0.287501i) q^{4} +(2.43250 - 2.43250i) q^{5} +(-0.793527 - 1.17060i) q^{6} +(0.522652 + 1.95057i) q^{7} +(0.607239 + 2.76247i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.101912 - 1.41054i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-1.97923 + 0.287501i) q^{4} +(2.43250 - 2.43250i) q^{5} +(-0.793527 - 1.17060i) q^{6} +(0.522652 + 1.95057i) q^{7} +(0.607239 + 2.76247i) q^{8} +(0.500000 - 0.866025i) q^{9} +(-3.67903 - 3.18323i) q^{10} +(-3.03280 - 0.812637i) q^{11} +(-1.57031 + 1.23860i) q^{12} +(-3.44947 - 1.04938i) q^{13} +(2.69808 - 0.936007i) q^{14} +(0.890356 - 3.32285i) q^{15} +(3.83469 - 1.13806i) q^{16} +(4.36889 + 2.52238i) q^{17} +(-1.27252 - 0.617010i) q^{18} +(-2.75142 + 0.737240i) q^{19} +(-4.11512 + 5.51381i) q^{20} +(1.42791 + 1.42791i) q^{21} +(-0.837175 + 4.36070i) q^{22} +(2.20812 + 3.82458i) q^{23} +(1.90712 + 2.08875i) q^{24} -6.83408i q^{25} +(-1.12864 + 4.97254i) q^{26} -1.00000i q^{27} +(-1.59524 - 3.71035i) q^{28} +(0.754985 + 1.30767i) q^{29} +(-4.77774 - 0.917241i) q^{30} +(2.38964 + 2.38964i) q^{31} +(-1.99608 - 5.29298i) q^{32} +(-3.03280 + 0.812637i) q^{33} +(3.11267 - 6.41954i) q^{34} +(6.01610 + 3.47339i) q^{35} +(-0.740630 + 1.85781i) q^{36} +(-1.91258 + 7.13784i) q^{37} +(1.32031 + 3.80584i) q^{38} +(-3.51201 + 0.815946i) q^{39} +(8.19681 + 5.24260i) q^{40} +(3.46845 + 0.929369i) q^{41} +(1.86860 - 2.15965i) q^{42} +(-2.78445 + 4.82280i) q^{43} +(6.23624 + 0.736458i) q^{44} +(-0.890356 - 3.32285i) q^{45} +(5.16968 - 3.50441i) q^{46} +(8.53489 - 8.53489i) q^{47} +(2.75190 - 2.90293i) q^{48} +(2.53064 - 1.46106i) q^{49} +(-9.63972 + 0.696476i) q^{50} +5.04476 q^{51} +(7.12897 + 1.08523i) q^{52} -9.42530 q^{53} +(-1.41054 + 0.101912i) q^{54} +(-9.35402 + 5.40054i) q^{55} +(-5.07101 + 2.62827i) q^{56} +(-2.01418 + 2.01418i) q^{57} +(1.76758 - 1.19820i) q^{58} +(-2.67214 - 9.97257i) q^{59} +(-0.806892 + 6.83266i) q^{60} +(-5.34563 + 9.25891i) q^{61} +(3.12714 - 3.61420i) q^{62} +(1.95057 + 0.522652i) q^{63} +(-7.26252 + 3.35496i) q^{64} +(-10.9434 + 5.83821i) q^{65} +(1.45533 + 4.19506i) q^{66} +(3.40389 - 12.7035i) q^{67} +(-9.37222 - 3.73630i) q^{68} +(3.82458 + 2.20812i) q^{69} +(4.28624 - 8.83990i) q^{70} +(-10.4866 + 2.80989i) q^{71} +(2.69599 + 0.855353i) q^{72} +(-5.57628 - 5.57628i) q^{73} +(10.2631 + 1.97033i) q^{74} +(-3.41704 - 5.91849i) q^{75} +(5.23372 - 2.25020i) q^{76} -6.34041i q^{77} +(1.50884 + 4.87067i) q^{78} +11.8580i q^{79} +(6.55953 - 12.0962i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.957432 - 4.98709i) q^{82} +(-8.12570 - 8.12570i) q^{83} +(-3.23669 - 2.41564i) q^{84} +(16.7630 - 4.49163i) q^{85} +(7.08651 + 3.43606i) q^{86} +(1.30767 + 0.754985i) q^{87} +(0.403254 - 8.87150i) q^{88} +(-0.935561 + 3.49156i) q^{89} +(-4.59627 + 1.59452i) q^{90} +(0.244006 - 7.27687i) q^{91} +(-5.46995 - 6.93488i) q^{92} +(3.26430 + 0.874668i) q^{93} +(-12.9086 - 11.1690i) q^{94} +(-4.89948 + 8.48614i) q^{95} +(-4.37515 - 3.58582i) q^{96} +(-1.02076 - 3.80953i) q^{97} +(-2.31879 - 3.42066i) q^{98} +(-2.22016 + 2.22016i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{2} + 4 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{8} + 12 q^{9}+O(q^{10}) \) 24 * q - 4 * q^2 + 4 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 - 4 * q^8 + 12 * q^9	\( 24 q - 4 q^{2} + 4 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{8} + 12 q^{9} + 12 q^{10} + 4 q^{11} - 4 q^{12} - 22 q^{14} - 4 q^{15} + 12 q^{16} - 2 q^{18} - 22 q^{19} - 4 q^{20} + 10 q^{21} - 34 q^{22} + 2 q^{24} - 4 q^{26} - 14 q^{28} + 8 q^{29} - 16 q^{30} - 2 q^{31} - 34 q^{32} + 4 q^{33} + 20 q^{34} + 24 q^{35} - 4 q^{36} - 12 q^{37} - 12 q^{38} - 6 q^{39} + 28 q^{40} - 36 q^{41} + 6 q^{42} + 10 q^{43} + 20 q^{44} + 4 q^{45} - 2 q^{46} + 20 q^{47} + 32 q^{48} - 54 q^{49} - 24 q^{50} + 36 q^{51} + 4 q^{52} - 36 q^{53} - 4 q^{54} - 24 q^{55} + 70 q^{56} - 32 q^{57} + 48 q^{58} - 36 q^{59} - 28 q^{60} - 2 q^{61} + 64 q^{62} + 8 q^{63} - 8 q^{64} + 16 q^{65} + 20 q^{66} - 16 q^{67} - 10 q^{68} + 12 q^{69} + 36 q^{71} - 2 q^{72} - 40 q^{73} - 30 q^{74} - 8 q^{75} + 58 q^{76} + 24 q^{78} - 48 q^{80} - 12 q^{81} - 30 q^{82} - 24 q^{83} - 26 q^{84} + 18 q^{85} + 30 q^{86} + 6 q^{87} - 78 q^{88} + 66 q^{89} + 12 q^{90} + 42 q^{91} + 36 q^{92} - 10 q^{93} + 6 q^{94} - 28 q^{95} + 8 q^{96} + 4 q^{97} + 44 q^{98} - 4 q^{99}+O(q^{100}) \) 24 * q - 4 * q^2 + 4 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 - 4 * q^8 + 12 * q^9 + 12 * q^10 + 4 * q^11 - 4 * q^12 - 22 * q^14 - 4 * q^15 + 12 * q^16 - 2 * q^18 - 22 * q^19 - 4 * q^20 + 10 * q^21 - 34 * q^22 + 2 * q^24 - 4 * q^26 - 14 * q^28 + 8 * q^29 - 16 * q^30 - 2 * q^31 - 34 * q^32 + 4 * q^33 + 20 * q^34 + 24 * q^35 - 4 * q^36 - 12 * q^37 - 12 * q^38 - 6 * q^39 + 28 * q^40 - 36 * q^41 + 6 * q^42 + 10 * q^43 + 20 * q^44 + 4 * q^45 - 2 * q^46 + 20 * q^47 + 32 * q^48 - 54 * q^49 - 24 * q^50 + 36 * q^51 + 4 * q^52 - 36 * q^53 - 4 * q^54 - 24 * q^55 + 70 * q^56 - 32 * q^57 + 48 * q^58 - 36 * q^59 - 28 * q^60 - 2 * q^61 + 64 * q^62 + 8 * q^63 - 8 * q^64 + 16 * q^65 + 20 * q^66 - 16 * q^67 - 10 * q^68 + 12 * q^69 + 36 * q^71 - 2 * q^72 - 40 * q^73 - 30 * q^74 - 8 * q^75 + 58 * q^76 + 24 * q^78 - 48 * q^80 - 12 * q^81 - 30 * q^82 - 24 * q^83 - 26 * q^84 + 18 * q^85 + 30 * q^86 + 6 * q^87 - 78 * q^88 + 66 * q^89 + 12 * q^90 + 42 * q^91 + 36 * q^92 - 10 * q^93 + 6 * q^94 - 28 * q^95 + 8 * q^96 + 4 * q^97 + 44 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

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