LMFDB - Embedded newform 261.2.q.a.103.24

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [261,2,Mod(7,261)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(261, base_ring=CyclotomicField(42)) chi = DirichletCharacter(H, H._module([28, 18])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("261.7"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	261.q (of order $21$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.08409549276$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$28$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			103.24
Character	$\chi$	$=$	261.103
Dual form			261.2.q.a.223.24

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.144668 + 1.93046i) q^{2} +(-1.66251 + 0.485844i) q^{3} +(-1.72807 + 0.260465i) q^{4} +(3.35707 - 2.28881i) q^{5} +(-1.17841 - 3.13913i) q^{6} +(3.79717 + 0.572331i) q^{7} +(0.108732 + 0.476384i) q^{8} +(2.52791 - 1.61545i) q^{9} +(4.90411 + 6.14956i) q^{10} +(-1.24771 + 0.384867i) q^{11} +(2.74640 - 1.27260i) q^{12} +(-3.20912 - 2.97763i) q^{13} +(-0.555533 + 7.41307i) q^{14} +(-4.46917 + 5.43619i) q^{15} +(-4.24381 + 1.30904i) q^{16} +4.03457 q^{17} +(3.48425 + 4.64632i) q^{18} +(-2.46134 - 3.08642i) q^{19} +(-5.20510 + 4.82962i) q^{20} +(-6.59092 + 0.893322i) q^{21} +(-0.923471 - 2.35297i) q^{22} +(-0.504497 + 6.73204i) q^{23} +(-0.412216 - 0.739170i) q^{24} +(4.20455 - 10.7130i) q^{25} +(5.28392 - 6.62583i) q^{26} +(-3.41784 + 3.91387i) q^{27} -6.71085 q^{28} +(-1.66579 + 5.12105i) q^{29} +(-11.1409 - 7.84110i) q^{30} +(-3.72911 + 2.54246i) q^{31} +(-2.78395 - 7.09339i) q^{32} +(1.88735 - 1.24604i) q^{33} +(0.583672 + 7.78856i) q^{34} +(14.0573 - 6.76965i) q^{35} +(-3.94764 + 3.45003i) q^{36} +(-0.0121631 - 0.0532900i) q^{37} +(5.60212 - 5.19801i) q^{38} +(6.78187 + 3.39122i) q^{39} +(1.45537 + 1.35039i) q^{40} +(-1.95712 + 3.38984i) q^{41} +(-2.67801 - 12.5942i) q^{42} +(-3.94005 - 2.68628i) q^{43} +(2.05588 - 0.990060i) q^{44} +(4.78893 - 11.2091i) q^{45} -13.0689 q^{46} +(4.97035 - 1.53315i) q^{47} +(6.41940 - 4.23813i) q^{48} +(7.40193 + 2.28319i) q^{49} +(21.2893 + 6.56688i) q^{50} +(-6.70753 + 1.96017i) q^{51} +(6.32115 + 4.30968i) q^{52} +(-5.90857 - 2.84542i) q^{53} +(-8.05001 - 6.03177i) q^{54} +(-3.30775 + 4.14779i) q^{55} +(0.140223 + 1.87114i) q^{56} +(5.59152 + 3.93539i) q^{57} +(-10.1269 - 2.47488i) q^{58} +(5.54407 - 9.60261i) q^{59} +(6.30711 - 10.5582i) q^{60} +(-5.81559 - 0.876559i) q^{61} +(-5.44760 - 6.83107i) q^{62} +(10.5235 - 4.68732i) q^{63} +(5.28812 - 2.54662i) q^{64} +(-17.5885 - 2.65103i) q^{65} +(2.67846 + 3.46318i) q^{66} +(-1.39895 - 0.431518i) q^{67} +(-6.97202 + 1.05086i) q^{68} +(-2.43199 - 11.4372i) q^{69} +(15.1022 + 26.1577i) q^{70} +(-2.24473 + 9.83479i) q^{71} +(1.04444 + 1.02861i) q^{72} +(3.80506 - 1.83242i) q^{73} +(0.101114 - 0.0311896i) q^{74} +(-1.78528 + 19.8533i) q^{75} +(5.05726 + 4.69245i) q^{76} +(-4.95803 + 0.747303i) q^{77} +(-5.56548 + 13.5827i) q^{78} +(1.29710 - 1.20354i) q^{79} +(-11.2506 + 14.1078i) q^{80} +(3.78067 - 8.16741i) q^{81} +(-6.82706 - 3.28774i) q^{82} +(0.0584925 - 0.149036i) q^{83} +(11.1569 - 3.26042i) q^{84} +(13.5443 - 9.23437i) q^{85} +(4.61575 - 7.99472i) q^{86} +(0.281364 - 9.32313i) q^{87} +(-0.319010 - 0.552541i) q^{88} +(-3.79906 - 1.82953i) q^{89} +(22.3314 + 7.62322i) q^{90} +(-10.4814 - 13.1432i) q^{91} +(-0.881653 - 11.7648i) q^{92} +(4.96446 - 6.03865i) q^{93} +(3.67873 + 9.37324i) q^{94} +(-15.3271 - 4.72779i) q^{95} +(8.07464 + 10.4403i) q^{96} +(4.93043 - 12.5625i) q^{97} +(-3.33678 + 14.6194i) q^{98} +(-2.53236 + 2.98851i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 5 q^{2} - 10 q^{3} + 21 q^{4} - 9 q^{5} - 40 q^{6} - 5 q^{7} + 2 q^{8} - 6 q^{9} - 28 q^{10} - q^{11} - 22 q^{12} - 5 q^{13} - 9 q^{14} - 26 q^{15} + 21 q^{16} - 60 q^{17} - 90 q^{18} - 20 q^{19}+ \cdots + 196 q^{99}+O(q^{100}) $ 336 * q - 5 * q^2 - 10 * q^3 + 21 * q^4 - 9 * q^5 - 40 * q^6 - 5 * q^7 + 2 * q^8 - 6 * q^9 - 28 * q^10 - q^11 - 22 * q^12 - 5 * q^13 - 9 * q^14 - 26 * q^15 + 21 * q^16 - 60 * q^17 - 90 * q^18 - 20 * q^19 - 15 * q^20 - 2 * q^21 - 13 * q^22 - 32 * q^23 + 44 * q^24 + 15 * q^25 - 4 * q^26 - 43 * q^27 - 72 * q^28 - q^29 - 8 * q^30 - 5 * q^31 + 7 * q^32 - 37 * q^33 - 15 * q^34 + 16 * q^35 - 104 * q^36 - 20 * q^37 + 63 * q^38 + 38 * q^39 + 5 * q^40 - 20 * q^41 + 11 * q^42 - 5 * q^43 - 8 * q^44 + 30 * q^45 - 80 * q^46 + 5 * q^47 + 12 * q^48 - 19 * q^49 - 3 * q^50 - 62 * q^51 + q^52 - 4 * q^53 + 26 * q^54 - 100 * q^55 - 5 * q^56 - 50 * q^57 - 7 * q^58 + 154 * q^59 + 23 * q^60 + 7 * q^61 - 4 * q^62 - 144 * q^63 + 18 * q^64 - 65 * q^65 + 44 * q^66 - 5 * q^67 - 9 * q^68 + 22 * q^69 - 14 * q^70 + 18 * q^71 + 37 * q^72 - 20 * q^73 - 77 * q^74 + 16 * q^75 - 5 * q^76 + 39 * q^77 + 52 * q^78 - 5 * q^79 - 104 * q^80 + 54 * q^81 + 12 * q^82 - 23 * q^83 + 175 * q^84 - 42 * q^85 + 128 * q^86 + 42 * q^87 - 8 * q^88 + 34 * q^89 + 222 * q^90 + 12 * q^91 - 115 * q^92 + 64 * q^93 - 25 * q^94 + 89 * q^95 - 49 * q^96 + 55 * q^97 - 88 * q^98 + 196 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.144668	+	1.93046i	0.102295	+	1.36504i	0.778185	+	0.628035i	$0.216141\pi$
$2$	0.144668	+	1.93046i	0.102295	+	1.36504i	−0.675889	+	0.737003i	$0.736240\pi$
$3$	−1.66251	+	0.485844i	−0.959853	+	0.280502i
$3$	−1.66251	+	0.485844i	−0.959853	+	0.280502i
$4$	−1.72807	+	0.260465i	−0.864035	+	0.130232i
$5$	3.35707	−	2.28881i	1.50133	−	1.02359i	0.515299	−	0.857011i	$-0.327681\pi$
$5$	3.35707	−	2.28881i	1.50133	−	1.02359i	0.986028	−	0.166577i	$-0.0532714\pi$
$6$	−1.17841	−	3.13913i	−0.481085	−	1.28154i
$7$	3.79717	+	0.572331i	1.43520	+	0.216321i	0.820140	−	0.572163i	$-0.193896\pi$
$7$	3.79717	+	0.572331i	1.43520	+	0.216321i	0.615055	+	0.788484i	$0.289134\pi$
$8$	0.108732	+	0.476384i	0.0384424	+	0.168427i
$9$	2.52791	−	1.61545i	0.842637	−	0.538482i
$10$	4.90411	+	6.14956i	1.55082	+	1.94466i
$11$	−1.24771	+	0.384867i	−0.376198	+	0.116042i	−0.477087	−	0.878856i	$-0.658307\pi$
$11$	−1.24771	+	0.384867i	−0.376198	+	0.116042i	0.100889	+	0.994898i	$0.467831\pi$
$12$	2.74640	−	1.27260i	0.792816	−	0.367367i
$13$	−3.20912	−	2.97763i	−0.890049	−	0.825845i	0.0954658	−	0.995433i	$-0.469566\pi$
$13$	−3.20912	−	2.97763i	−0.890049	−	0.825845i	−0.985515	+	0.169588i	$0.945756\pi$
$14$	−0.555533	+	7.41307i	−0.148472	+	1.98123i
$15$	−4.46917	+	5.43619i	−1.15394	+	1.40362i
$16$	−4.24381	+	1.30904i	−1.06095	+	0.327260i
$17$	4.03457			0.978527			0.489263	−	0.872136i	$-0.337266\pi$
$17$	4.03457			0.978527			0.489263	+	0.872136i	$0.337266\pi$
$18$	3.48425	+	4.64632i	0.821246	+	1.09515i
$19$	−2.46134	−	3.08642i	−0.564669	−	0.708073i	0.414744	−	0.909938i	$-0.363871\pi$
$19$	−2.46134	−	3.08642i	−0.564669	−	0.708073i	−0.979413	+	0.201865i	$0.935300\pi$
$20$	−5.20510	+	4.82962i	−1.16389	+	1.07994i
$21$	−6.59092	+	0.893322i	−1.43826	+	0.194939i
$22$	−0.923471	−	2.35297i	−0.196885	−	0.501654i
$23$	−0.504497	+	6.73204i	−0.105195	+	1.40373i	0.655783	+	0.754950i	$0.272339\pi$
$23$	−0.504497	+	6.73204i	−0.105195	+	1.40373i	−0.760978	+	0.648778i	$0.775280\pi$
$24$	−0.412216	−	0.739170i	−0.0841433	−	0.150882i
$25$	4.20455	−	10.7130i	0.840911	−	2.14261i
$26$	5.28392	−	6.62583i	1.03626	−	1.29943i
$27$	−3.41784	+	3.91387i	−0.657763	+	0.753225i
$28$	−6.71085			−1.26823
$29$	−1.66579	+	5.12105i	−0.309329	+	0.950955i
$29$	−1.66579	+	5.12105i	−0.309329	+	0.950955i
$30$	−11.1409	−	7.84110i	−2.03404	−	1.43158i
$31$	−3.72911	+	2.54246i	−0.669768	+	0.456640i	−0.849859	−	0.527010i	$-0.823313\pi$
$31$	−3.72911	+	2.54246i	−0.669768	+	0.456640i	0.180091	+	0.983650i	$0.442361\pi$
$32$	−2.78395	−	7.09339i	−0.492137	−	1.25395i
$33$	1.88735	−	1.24604i	0.328545	−	0.216907i
$34$	0.583672	+	7.78856i	0.100099	+	1.33573i
$35$	14.0573	−	6.76965i	2.37612	−	1.14428i
$36$	−3.94764	+	3.45003i	−0.657940	+	0.575005i
$37$	−0.0121631	−	0.0532900i	−0.00199960	−	0.00876082i	0.973918	−	0.226899i	$-0.0728588\pi$
$37$	−0.0121631	−	0.0532900i	−0.00199960	−	0.00876082i	−0.975918	+	0.218138i	$0.930002\pi$
$38$	5.60212	−	5.19801i	0.908783	−	0.843228i
$39$	6.78187	+	3.39122i	1.08597	+	0.543030i
$40$	1.45537	+	1.35039i	0.230115	+	0.213515i
$41$	−1.95712	+	3.38984i	−0.305651	+	0.529403i	−0.977406	−	0.211370i	$-0.932207\pi$
$41$	−1.95712	+	3.38984i	−0.305651	+	0.529403i	0.671755	+	0.740773i	$0.265541\pi$
$42$	−2.67801	−	12.5942i	−0.413226	−	1.94333i
$43$	−3.94005	−	2.68628i	−0.600853	−	0.409654i	0.224336	−	0.974512i	$-0.427979\pi$
$43$	−3.94005	−	2.68628i	−0.600853	−	0.409654i	−0.825188	+	0.564857i	$0.808931\pi$
$44$	2.05588	−	0.990060i	0.309936	−	0.149257i
$45$	4.78893	−	11.2091i	0.713891	−	1.67095i
$46$	−13.0689			−1.92690
$47$	4.97035	−	1.53315i	0.725000	−	0.223633i	0.0897773	−	0.995962i	$-0.471384\pi$
$47$	4.97035	−	1.53315i	0.725000	−	0.223633i	0.635223	+	0.772329i	$0.280908\pi$
$48$	6.41940	−	4.23813i	0.926561	−	0.611721i
$49$	7.40193	+	2.28319i	1.05742	+	0.326170i
$50$	21.2893	+	6.56688i	3.01076	+	0.928697i
$51$	−6.70753	+	1.96017i	−0.939242	+	0.274479i
$52$	6.32115	+	4.30968i	0.876585	+	0.597646i
$53$	−5.90857	−	2.84542i	−0.811605	−	0.390848i	−0.0184209	−	0.999830i	$-0.505864\pi$
$53$	−5.90857	−	2.84542i	−0.811605	−	0.390848i	−0.793184	+	0.608982i	$0.791578\pi$
$54$	−8.05001	−	6.03177i	−1.09547	−	0.820820i
$55$	−3.30775	+	4.14779i	−0.446017	+	0.559288i
$56$	0.140223	+	1.87114i	0.0187381	+	0.250042i
$57$	5.59152	+	3.93539i	0.740616	+	0.521255i
$58$	−10.1269	−	2.47488i	−1.32973	−	0.324967i
$59$	5.54407	−	9.60261i	0.721776	−	1.25015i	−0.238511	−	0.971140i	$-0.576659\pi$
$59$	5.54407	−	9.60261i	0.721776	−	1.25015i	0.960287	−	0.279013i	$-0.0900074\pi$
$60$	6.30711	−	10.5582i	0.814244	−	1.36306i
$61$	−5.81559	−	0.876559i	−0.744610	−	0.112232i	−0.234230	−	0.972181i	$-0.575257\pi$
$61$	−5.81559	−	0.876559i	−0.744610	−	0.112232i	−0.510380	+	0.859949i	$0.670495\pi$
$62$	−5.44760	−	6.83107i	−0.691845	−	0.867547i
$63$	10.5235	−	4.68732i	1.32583	−	0.590546i
$64$	5.28812	−	2.54662i	0.661015	−	0.318328i
$65$	−17.5885	−	2.65103i	−2.18158	−	0.328820i
$66$	2.67846	+	3.46318i	0.329695	+	0.426288i
$67$	−1.39895	−	0.431518i	−0.170909	−	0.0527183i	0.208120	−	0.978103i	$-0.433266\pi$
$67$	−1.39895	−	0.431518i	−0.170909	−	0.0527183i	−0.379028	+	0.925385i	$0.623742\pi$
$68$	−6.97202	+	1.05086i	−0.845481	+	0.127436i
$69$	−2.43199	−	11.4372i	−0.292777	−	1.37688i
$70$	15.1022	+	26.1577i	1.80505	+	3.12644i
$71$	−2.24473	+	9.83479i	−0.266400	+	1.16717i	0.647768	+	0.761838i	$0.275703\pi$
$71$	−2.24473	+	9.83479i	−0.266400	+	1.16717i	−0.914168	+	0.405337i	$0.867154\pi$
$72$	1.04444	+	1.02861i	0.123088	+	0.121223i
$73$	3.80506	−	1.83242i	0.445349	−	0.214469i	−0.197749	−	0.980253i	$-0.563363\pi$
$73$	3.80506	−	1.83242i	0.445349	−	0.214469i	0.643098	+	0.765784i	$0.277649\pi$
$74$	0.101114	−	0.0311896i	0.0117543	−	0.00362572i
$75$	−1.78528	+	19.8533i	−0.206146	+	2.29247i
$76$	5.05726	+	4.69245i	0.580108	+	0.538261i
$77$	−4.95803	+	0.747303i	−0.565020	+	0.0851630i
$78$	−5.56548	+	13.5827i	−0.630167	+	1.53794i
$79$	1.29710	−	1.20354i	0.145936	−	0.135409i	−0.603827	−	0.797115i	$-0.706358\pi$
$79$	1.29710	−	1.20354i	0.145936	−	0.135409i	0.749763	+	0.661707i	$0.230168\pi$
$80$	−11.2506	+	14.1078i	−1.25786	+	1.57730i
$81$	3.78067	−	8.16741i	0.420075	−	0.907489i
$82$	−6.82706	−	3.28774i	−0.753923	−	0.363070i
$83$	0.0584925	−	0.149036i	0.00642038	−	0.0163589i	−0.927628	−	0.373506i	$-0.878155\pi$
$83$	0.0584925	−	0.149036i	0.00642038	−	0.0163589i	0.934048	+	0.357147i	$0.116251\pi$
$84$	11.1569	−	3.26042i	1.21732	−	0.355741i
$85$	13.5443	−	9.23437i	1.46909	−	1.00161i
$86$	4.61575	−	7.99472i	0.497730	−	0.862093i
$87$	0.281364	−	9.32313i	0.0301654	−	0.999545i
$88$	−0.319010	−	0.552541i	−0.0340066	−	0.0589011i
$89$	−3.79906	−	1.82953i	−0.402700	−	0.193930i	0.221560	−	0.975147i	$-0.428885\pi$
$89$	−3.79906	−	1.82953i	−0.402700	−	0.193930i	−0.624260	+	0.781217i	$0.714599\pi$
$90$	22.3314	+	7.62322i	2.35394	+	0.803558i
$91$	−10.4814	−	13.1432i	−1.09875	−	1.37779i
$92$	−0.881653	−	11.7648i	−0.0919186	−	1.22657i
$93$	4.96446	−	6.03865i	0.514791	−	0.626179i
$94$	3.67873	+	9.37324i	0.379432	+	0.966776i
$95$	−15.3271	−	4.72779i	−1.57253	−	0.485061i
$96$	8.07464	+	10.4403i	0.824114	+	1.06556i
$97$	4.93043	−	12.5625i	0.500610	−	1.27553i	−0.427766	−	0.903890i	$-0.640699\pi$
$97$	4.93043	−	12.5625i	0.500610	−	1.27553i	0.928376	−	0.371643i	$-0.121206\pi$
$98$	−3.33678	+	14.6194i	−0.337066	+	1.47678i
$99$	−2.53236	+	2.98851i	−0.254512	+	0.300357i
$100$	−4.47540	+	19.6080i	−0.447540	+	1.96080i
$101$	0.379136	+	0.258490i	0.0377254	+	0.0257207i	0.582036	−	0.813163i	$-0.302256\pi$
$101$	0.379136	+	0.258490i	0.0377254	+	0.0257207i	−0.544311	+	0.838884i	$0.683209\pi$
$102$	−4.75439	−	12.6650i	−0.470754	−	1.25402i
$103$	−5.47138	−	5.07670i	−0.539111	−	0.500222i	0.362963	−	0.931804i	$-0.381765\pi$
$103$	−5.47138	−	5.07670i	−0.539111	−	0.500222i	−0.902074	+	0.431582i	$0.857956\pi$
$104$	1.06956	−	1.85254i	0.104879	−	0.181656i
$105$	−20.0815	+	18.0843i	−1.95976	+	1.76485i
$106$	4.63818	−	11.8179i	0.450500	−	1.14785i
$107$	0.458441	+	2.00856i	0.0443192	+	0.194175i	0.992241	−	0.124327i	$-0.0396773\pi$
$107$	0.458441	+	2.00856i	0.0443192	+	0.194175i	−0.947922	+	0.318502i	$0.896820\pi$
$108$	4.88683	−	7.65367i	0.470236	−	0.736475i
$109$	−5.40439	+	6.77689i	−0.517647	+	0.649108i	−0.970107	−	0.242676i	$-0.921975\pi$
$109$	−5.40439	+	6.77689i	−0.517647	+	0.649108i	0.452461	+	0.891784i	$0.350546\pi$
$110$	−8.48565	−	5.78542i	−0.809075	−	0.551618i
$111$	0.0461119	+	0.0826860i	0.00437675	+	0.00784821i
$112$	−16.8637	+	2.54179i	−1.59347	+	0.240176i
$113$	−1.20409	−	3.06797i	−0.113271	−	0.288611i	0.862985	−	0.505230i	$-0.168592\pi$
$113$	−1.20409	−	3.06797i	−0.113271	−	0.288611i	−0.976256	+	0.216619i	$0.930497\pi$
$114$	−6.78818	+	11.3635i	−0.635772	+	1.06429i
$115$	13.7147	+	23.7546i	1.27891	+	2.21513i
$116$	1.54474	−	9.28341i	0.143426	−	0.861943i
$117$	−12.9226	−	2.34302i	−1.19469	−	0.216612i
$118$	19.3395	+	9.31339i	1.78034	+	0.857367i
$119$	15.3199	+	2.30911i	1.40438	+	0.211676i
$120$	−3.07566	−	1.53796i	−0.280768	−	0.140396i
$121$	−7.67998	+	5.23612i	−0.698180	+	0.476011i
$122$	0.850831	−	11.3536i	0.0770306	−	1.02790i
$123$	1.60681	−	6.58651i	0.144882	−	0.593885i
$124$	5.78194	−	5.36486i	0.519233	−	0.481778i
$125$	−5.88453	−	25.7818i	−0.526328	−	2.30599i
$126$	10.5711	+	19.6370i	0.941745	+	1.74940i
$127$	1.85976	−	8.14812i	0.165027	−	0.723029i	−0.822910	−	0.568171i	$-0.807651\pi$
$127$	1.85976	−	8.14812i	0.165027	−	0.723029i	0.987937	−	0.154857i	$-0.0494918\pi$
$128$	−1.93898	−	3.35840i	−0.171383	−	0.296844i
$129$	7.85551	+	2.55174i	0.691639	+	0.224668i
$130$	2.57322	−	34.3373i	0.225687	−	3.01158i
$131$	−0.963515	+	12.8572i	−0.0841827	+	1.12334i	0.781888	+	0.623419i	$0.214257\pi$
$131$	−0.963515	+	12.8572i	−0.0841827	+	1.12334i	−0.866071	+	0.499922i	$0.833362\pi$
$132$	−2.93692	+	2.64483i	−0.255626	+	0.230203i
$133$	−7.57966	−	13.1284i	−0.657240	−	1.13837i
$134$	0.630644	−	2.76303i	0.0544793	−	0.238690i
$135$	−2.51580	+	20.9619i	−0.216526	+	1.80412i
$136$	0.438685	+	1.92201i	0.0376170	+	0.164811i
$137$	−4.12187	+	3.82454i	−0.352155	+	0.326752i	−0.836338	−	0.548215i	$-0.815308\pi$
$137$	−4.12187	+	3.82454i	−0.352155	+	0.326752i	0.484182	+	0.874967i	$0.339117\pi$
$138$	21.7272	−	6.34944i	1.84954	−	0.540500i
$139$	−0.984730	+	13.1403i	−0.0835237	+	1.11455i	0.785198	+	0.619245i	$0.212561\pi$
$139$	−0.984730	+	13.1403i	−0.0835237	+	1.11455i	−0.868721	+	0.495301i	$0.835058\pi$
$140$	−22.5288	+	15.3599i	−1.90403	+	1.29815i
$141$	−7.51841	+	4.96370i	−0.633164	+	0.418019i
$142$	−19.3104	−	2.91057i	−1.62049	−	0.244250i
$143$	5.15003	+	2.48012i	0.430667	+	0.207398i
$144$	−8.61328	+	10.1648i	−0.717773	+	0.847064i
$145$	6.12896	+	21.0044i	0.508982	+	1.74432i
$146$	4.08788	+	7.08041i	0.338315	+	0.585979i
$147$	−13.4151	−	0.199660i	−1.10646	−	0.0164677i
$148$	0.0348988	+	0.0889207i	0.00286866	+	0.00730924i
$149$	12.1647	−	1.83353i	0.996569	−	0.150209i	0.369549	−	0.929211i	$-0.379512\pi$
$149$	12.1647	−	1.83353i	0.996569	−	0.150209i	0.627020	+	0.779003i	$0.284274\pi$
$150$	−38.5842	−	0.574260i	−3.15039	−	0.0468881i
$151$	11.7780	+	8.03009i	0.958478	+	0.653479i	0.938119	−	0.346313i	$-0.112567\pi$
$151$	11.7780	+	8.03009i	0.958478	+	0.653479i	0.0203594	+	0.999793i	$0.493519\pi$
$152$	1.20270	−	1.50813i	0.0975515	−	0.122326i
$153$	10.1990	−	6.51763i	0.824543	−	0.526919i
$154$	−2.15990	−	9.46314i	−0.174050	−	0.762562i
$155$	−6.69966	+	17.0705i	−0.538130	+	1.37113i
$156$	−12.6028	−	4.09382i	−1.00903	−	0.327768i
$157$	4.01648	−	6.95674i	0.320550	−	0.555209i	−0.660052	−	0.751220i	$-0.729466\pi$
$157$	4.01648	−	6.95674i	0.320550	−	0.555209i	0.980602	+	0.196012i	$0.0627990\pi$
$158$	2.51102	+	2.32989i	0.199766	+	0.185356i
$159$	11.2055	+	1.85991i	0.888656	+	0.147500i
$160$	−25.5813	−	17.4411i	−2.02238	−	1.37884i
$161$	−5.76862	+	25.2740i	−0.454631	+	1.99187i
$162$	16.3138	+	6.11686i	1.28173	+	0.480586i
$163$	−1.21278	+	5.31353i	−0.0949921	+	0.416187i	−0.999957	−	0.00929923i	$-0.997040\pi$
$163$	−1.21278	+	5.31353i	−0.0949921	+	0.416187i	0.904965	+	0.425487i	$0.139897\pi$
$164$	2.49911	−	6.36763i	0.195148	−	0.497229i
$165$	3.48401	−	8.50282i	0.271230	−	0.661943i
$166$	0.296170	+	0.0913564i	0.0229873	+	0.00709063i
$167$	−2.04241	−	5.20397i	−0.158046	−	0.402695i	0.829814	−	0.558040i	$-0.188446\pi$
$167$	−2.04241	−	5.20397i	−0.158046	−	0.402695i	−0.987860	+	0.155345i	$0.950351\pi$
$168$	−1.14221	−	3.04268i	−0.0881231	−	0.234748i
$169$	0.460689	+	6.14746i	0.0354376	+	0.472882i
$170$	19.7860	+	24.8108i	1.51751	+	1.90290i
$171$	−11.2080	−	3.82604i	−0.857095	−	0.292584i
$172$	7.50837	+	3.61584i	0.572508	+	0.275705i
$173$	8.22022	+	14.2378i	0.624971	+	1.08248i	0.988546	+	0.150917i	$0.0482227\pi$
$173$	8.22022	+	14.2378i	0.624971	+	1.08248i	−0.363575	+	0.931565i	$0.618444\pi$
$174$	18.0386	−	0.805596i	1.36750	−	0.0610721i
$175$	22.0968	−	38.2728i	1.67036	−	2.89315i
$176$	4.79122	−	3.26660i	0.361152	−	0.246229i
$177$	−4.55173	+	18.6580i	−0.342129	+	1.40242i
$178$	2.98223	−	7.59859i	0.223527	−	0.569539i
$179$	−9.74766	−	4.69422i	−0.728574	−	0.350863i	0.0325491	−	0.999470i	$-0.489637\pi$
$179$	−9.74766	−	4.69422i	−0.728574	−	0.350863i	−0.761123	+	0.648607i	$0.775352\pi$
$180$	−5.35603	+	20.6174i	−0.399215	+	1.53673i
$181$	−2.01346	+	2.52480i	−0.149659	+	0.187667i	−0.851010	−	0.525150i	$-0.824009\pi$
$181$	−2.01346	+	2.52480i	−0.149659	+	0.187667i	0.701351	+	0.712816i	$0.252581\pi$
$182$	23.8561	−	22.1352i	1.76833	−	1.64077i
$183$	10.0944	−	1.36818i	0.746198	−	0.101138i
$184$	−3.26189	+	0.491651i	−0.240470	+	0.0362450i
$185$	−0.162803	−	0.151059i	−0.0119695	−	0.0111061i
$186$	12.3755	+	8.71007i	0.907419	+	0.638654i
$187$	−5.03396	+	1.55277i	−0.368120	+	0.113550i
$188$	−8.18978	+	3.94399i	−0.597301	+	0.287645i
$189$	−15.2181	+	12.9055i	−1.10696	+	0.938737i
$190$	6.90944	−	30.2723i	0.501264	−	2.19618i
$191$	−7.35761	−	12.7438i	−0.532378	−	0.922106i	−0.999285	−	0.0377999i	$-0.987965\pi$
$191$	−7.35761	−	12.7438i	−0.532378	−	0.922106i	0.466907	−	0.884306i	$-0.345368\pi$
$192$	−7.55431	+	6.80300i	−0.545186	+	0.490964i
$193$	18.1392	−	2.73404i	1.30569	−	0.196801i	0.540902	−	0.841085i	$-0.318083\pi$
$193$	18.1392	−	2.73404i	1.30569	−	0.196801i	0.764786	+	0.644285i	$0.222845\pi$
$194$	24.9647	+	7.70059i	1.79236	+	0.552870i
$195$	30.5291	−	4.13786i	2.18623	−	0.296318i
$196$	−13.3857	−	2.01757i	−0.956124	−	0.144112i
$197$	6.23462	−	3.00243i	0.444198	−	0.213915i	−0.198395	−	0.980122i	$-0.563573\pi$
$197$	6.23462	−	3.00243i	0.444198	−	0.213915i	0.642593	+	0.766208i	$0.277859\pi$
$198$	−6.13554	−	4.45627i	−0.436034	−	0.316694i
$199$	−2.28709	−	2.86792i	−0.162127	−	0.203301i	0.694132	−	0.719848i	$-0.255789\pi$
$199$	−2.28709	−	2.86792i	−0.162127	−	0.203301i	−0.856259	+	0.516547i	$0.827217\pi$
$200$	5.56069	+	0.838139i	0.393200	+	0.0592654i
$201$	2.53542	+	0.0377353i	0.178835	+	0.00266165i
$202$	−0.444156	+	0.769300i	−0.0312507	+	0.0541278i
$203$	−9.25621	+	18.4921i	−0.649659	+	1.29789i
$204$	11.0805	−	5.13439i	0.775792	−	0.359479i
$205$	1.18850	+	15.8594i	0.0830083	+	1.10767i
$206$	9.00881	−	11.2967i	0.627674	−	0.787078i
$207$	9.59992	+	17.8330i	0.667241	+	1.23948i
$208$	17.5167	+	8.43560i	1.21457	+	0.584904i
$209$	4.25889	+	2.90366i	0.294593	+	0.200850i
$210$	−37.8161	−	36.1503i	−2.60956	−	2.49461i
$211$	14.1750	+	4.37240i	0.975846	+	0.301009i	0.741358	−	0.671110i	$-0.234182\pi$
$211$	14.1750	+	4.37240i	0.975846	+	0.301009i	0.234489	+	0.972119i	$0.424658\pi$
$212$	10.9516	+	3.37811i	0.752156	+	0.232009i
$213$	−1.04628	−	17.4411i	−0.0716899	−	1.19504i
$214$	−3.81112	+	1.17557i	−0.260523	+	0.0803606i
$215$	−19.3754			−1.32139
$216$	−2.23613	−	1.20264i	−0.152150	−	0.0818294i
$217$	−15.6152	+	7.51988i	−1.06003	+	0.510483i
$218$	−13.8643	−	9.45254i	−0.939011	−	0.640207i
$219$	−5.43570	+	4.89509i	−0.367311	+	0.330780i
$220$	4.63567	−	8.02922i	0.312537	−	0.541330i
$221$	−12.9474	−	12.0134i	−0.870937	−	0.808112i
$222$	−0.152951	+	0.100979i	−0.0102654	+	0.00677727i
$223$	−1.96637	+	1.82452i	−0.131678	+	0.122179i	−0.743263	−	0.669000i	$-0.766723\pi$
$223$	−1.96637	+	1.82452i	−0.131678	+	0.122179i	0.611585	+	0.791179i	$0.290532\pi$
$224$	−6.51136	−	28.5281i	−0.435059	−	1.90612i
$225$	−6.67757	−	33.8738i	−0.445171	−	2.25825i
$226$	5.74839	−	2.76828i	0.382377	−	0.184143i
$227$	−0.311561	−	4.15749i	−0.0206790	−	0.275943i	−0.997952	−	0.0639599i	$-0.979627\pi$
$227$	−0.311561	−	4.15749i	−0.0206790	−	0.275943i	0.977273	−	0.211983i	$-0.0679920\pi$
$228$	−10.6876	−	5.34423i	−0.707802	−	0.353931i
$229$	0.525784	+	1.33968i	0.0347448	+	0.0885283i	0.947193	−	0.320664i	$-0.103906\pi$
$229$	0.525784	+	1.33968i	0.0347448	+	0.0885283i	−0.912448	+	0.409192i	$0.865811\pi$
$230$	−43.8732	+	29.9122i	−2.89291	+	1.97235i
$231$	7.87972	−	3.65123i	0.518448	−	0.240233i
$232$	−2.62071	−	0.236734i	−0.172058	−	0.0155424i
$233$	−13.2578			−0.868545			−0.434272	−	0.900782i	$-0.642994\pi$
$233$	−13.2578			−0.868545			−0.434272	+	0.900782i	$0.642994\pi$
$234$	2.65362	−	25.2854i	0.173473	−	1.65296i
$235$	13.1767	−	16.5231i	0.859554	−	1.07785i
$236$	−7.07940	+	18.0380i	−0.460830	+	1.17417i
$237$	−1.57172	+	2.63109i	−0.102094	+	0.170908i
$238$	−2.24134	+	29.9085i	−0.145284	+	1.93868i
$239$	−9.18650	−	23.4068i	−0.594225	−	1.51406i	−0.838805	−	0.544432i	$-0.816745\pi$
$239$	−9.18650	−	23.4068i	−0.594225	−	1.51406i	0.244579	−	0.969629i	$-0.421350\pi$
$240$	11.8501	−	28.9205i	0.764921	−	1.86681i
$241$	1.93872	−	1.79887i	0.124884	−	0.115875i	−0.615259	−	0.788325i	$-0.710948\pi$
$241$	1.93872	−	1.79887i	0.124884	−	0.115875i	0.740143	+	0.672450i	$0.234758\pi$
$242$	−11.2191	−	14.0684i	−0.721194	−	0.904348i
$243$	−2.31734	+	15.4152i	−0.148658	+	0.988889i
$244$	10.2781			0.657985
$245$	30.0746	−	9.27678i	1.92139	−	0.592672i
$246$	12.9474	+	2.14903i	0.825497	+	0.137017i
$247$	−1.29148	+	17.2336i	−0.0821750	+	1.09655i
$248$	−1.61666	−	1.50004i	−0.102658	−	0.0952529i
$249$	−0.0248362	+	0.276193i	−0.00157393	+	0.0175031i
$250$	48.9193	−	15.0896i	3.09393	−	0.954351i
$251$	−2.53977	−	3.18478i	−0.160309	−	0.201021i	0.695189	−	0.718827i	$-0.255321\pi$
$251$	−2.53977	−	3.18478i	−0.160309	−	0.201021i	−0.855498	+	0.517805i	$0.826749\pi$
$252$	−16.9644	+	10.8410i	−1.06866	+	0.682919i
$253$	−1.96147	−	8.59378i	−0.123317	−	0.540286i
$254$	15.9986	+	2.41141i	1.00384	+	0.151305i
$255$	−18.0312	+	21.9327i	−1.12916	+	1.37348i
$256$	15.9017	−	10.8416i	0.993859	−	0.677602i
$257$	6.76589	−	1.01979i	0.422045	−	0.0636130i	0.0654135	−	0.997858i	$-0.479163\pi$
$257$	6.76589	−	1.01979i	0.422045	−	0.0636130i	0.356631	+	0.934245i	$0.383925\pi$
$258$	−3.78957	+	15.5339i	−0.235929	+	0.967097i
$259$	−0.0156858	−	0.209312i	−0.000974668	−	0.0130060i
$260$	31.0846			1.92778
$261$	4.06182	+	15.6365i	0.251420	+	0.967878i
$262$	−24.9597			−1.54201
$263$	0.902158	+	12.0385i	0.0556294	+	0.742323i	0.953371	+	0.301801i	$0.0975877\pi$
$263$	0.902158	+	12.0385i	0.0556294	+	0.742323i	−0.897742	+	0.440522i	$0.854793\pi$
$264$	0.798807	+	0.763619i	0.0491632	+	0.0469975i
$265$	−26.3481	+	3.97134i	−1.61855	+	0.243958i
$266$	24.2472	−	16.5314i	1.48669	−	1.01361i
$267$	7.20486	+	1.19587i	0.440930	+	0.0731862i
$268$	2.52987	+	0.381317i	0.154537	+	0.0232926i
$269$	5.36370	+	23.4999i	0.327031	+	1.43281i	0.824760	+	0.565482i	$0.191310\pi$
$269$	5.36370	+	23.4999i	0.327031	+	1.43281i	−0.497730	+	0.867332i	$0.665833\pi$
$270$	−40.8300	−	1.82413i	−2.48484	−	0.111013i
$271$	−15.1249	−	18.9661i	−0.918775	−	1.15211i	−0.987992	−	0.154506i	$-0.950621\pi$
$271$	−15.1249	−	18.9661i	−0.918775	−	1.15211i	0.0692168	−	0.997602i	$-0.477950\pi$
$272$	−17.1219	+	5.28142i	−1.03817	+	0.320233i
$273$	23.8110	+	16.7585i	1.44111	+	1.01427i
$274$	−7.97941	−	7.40381i	−0.482054	−	0.447280i
$275$	−1.12296	+	14.9849i	−0.0677173	+	0.903625i
$276$	7.18163	+	19.1309i	0.432284	+	1.15154i
$277$	8.57178	−	2.64404i	0.515028	−	0.158865i	−0.0263362	−	0.999653i	$-0.508384\pi$
$277$	8.57178	−	2.64404i	0.515028	−	0.158865i	0.541365	+	0.840788i	$0.317908\pi$
$278$	−25.5092			−1.52994
$279$	−5.31965	+	12.4513i	−0.318479	+	0.745440i
$280$	4.75343	+	5.96061i	0.284072	+	0.356215i
$281$	0.553979	−	0.514018i	0.0330476	−	0.0306637i	−0.663476	−	0.748197i	$-0.730920\pi$
$281$	0.553979	−	0.514018i	0.0330476	−	0.0306637i	0.696524	+	0.717534i	$0.254729\pi$
$282$	−10.6699	−	13.7959i	−0.635382	−	0.821532i
$283$	−8.46272	−	21.5627i	−0.503057	−	1.28177i	−0.926654	−	0.375916i	$-0.877328\pi$
$283$	−8.46272	−	21.5627i	−0.503057	−	1.28177i	0.423597	−	0.905851i	$-0.360767\pi$
$284$	1.31743	−	17.5799i	0.0781750	−	1.04317i
$285$	27.7785	+	0.413435i	1.64546	+	0.0244898i
$286$	−4.04273	+	10.3007i	−0.239051	+	0.609093i
$287$	−9.37164	+	11.7517i	−0.553190	+	0.693679i
$288$	−18.4966	−	13.4341i	−1.08992	−	0.791614i
$289$	−0.722244			−0.0424850
$290$	−39.6614	+	14.8703i	−2.32900	+	0.873216i
$291$	−2.09349	+	23.2808i	−0.122722	+	1.36475i
$292$	−6.09813	+	4.15763i	−0.356866	+	0.243307i
$293$	−5.86777	−	14.9508i	−0.342799	−	0.873436i	−0.993472	−	0.114079i	$-0.963608\pi$
$293$	−5.86777	−	14.9508i	−0.342799	−	0.873436i	0.650673	−	0.759358i	$-0.274487\pi$
$294$	−1.55529	−	25.9261i	−0.0907066	−	1.51204i
$295$	−3.36674	−	44.9260i	−0.196019	−	2.61569i
$296$	0.0240640	−	0.0115886i	0.00139869	−	0.000673574i
$297$	2.75814	−	6.19878i	0.160044	−	0.359690i
$298$	5.29938	+	23.2181i	0.306985	+	1.34499i
$299$	21.6645	−	20.1017i	1.25289	−	1.16251i
$300$	−2.08601	−	34.7729i	−0.120436	−	2.00762i
$301$	−13.4236	−	12.4553i	−0.773724	−	0.717911i
$302$	−13.7978	+	23.8986i	−0.793977	+	1.37521i
$303$	−0.755905	−	0.245543i	−0.0434256	−	0.0141061i
$304$	14.4857	+	9.87617i	0.830810	+	0.566437i
$305$	−21.5296	+	10.3681i	−1.23278	+	0.593677i
$306$	14.0575	+	18.7459i	0.803612	+	1.07163i
$307$	25.5077			1.45580			0.727900	−	0.685683i	$-0.240496\pi$
$307$	25.5077			1.45580			0.727900	+	0.685683i	$0.240496\pi$
$308$	8.37317	−	2.58278i	0.477106	−	0.147168i
$309$	11.5627	+	5.78185i	0.657781	+	0.328918i
$310$	−33.9230	−	10.4639i	−1.92670	−	0.594307i
$311$	2.62146	+	0.808612i	0.148649	+	0.0458522i	0.368187	−	0.929752i	$-0.379979\pi$
$311$	2.62146	+	0.808612i	0.148649	+	0.0458522i	−0.219538	+	0.975604i	$0.570455\pi$
$312$	−0.878120	+	3.59951i	−0.0497137	+	0.203782i
$313$	19.3494	+	13.1922i	1.09369	+	0.745667i	0.969131	−	0.246545i	$-0.0792954\pi$
$313$	19.3494	+	13.1922i	1.09369	+	0.745667i	0.124561	+	0.992212i	$0.460248\pi$
$314$	14.0107	+	6.74722i	0.790672	+	0.380767i
$315$	24.5997	−	39.8219i	1.38603	−	2.24371i
$316$	−1.92801	+	2.41765i	−0.108459	+	0.136003i
$317$	−1.94183	−	25.9119i	−0.109064	−	1.45536i	−0.736366	−	0.676583i	$-0.763460\pi$
$317$	−1.94183	−	25.9119i	−0.109064	−	1.45536i	0.627302	−	0.778776i	$-0.284159\pi$
$318$	−1.96939	+	21.9008i	−0.110438	+	1.22814i
$319$	0.107492	−	7.03068i	0.00601838	−	0.393642i
$320$	11.9238	−	20.6527i	0.666563	−	1.15452i
$321$	−1.73801	−	3.11653i	−0.0970064	−	0.173948i
$322$	−49.6248	−	7.47974i	−2.76548	−	0.416829i
$323$	−9.93043	−	12.4524i	−0.552544	−	0.692868i
$324$	−4.40595	+	15.0986i	−0.244775	+	0.838810i
$325$	−45.3923	+	21.8598i	−2.51791	+	1.21256i
$326$	−10.4330	−	1.57252i	−0.577829	−	0.0870937i
$327$	5.69237	−	13.8924i	0.314789	−	0.768250i
$328$	−1.82767	−	0.563760i	−0.100916	−	0.0311285i
$329$	19.7507	−	2.97694i	1.08889	−	0.164124i
$330$	16.9183	+	5.49565i	0.931324	+	0.302525i
$331$	−3.65144	−	6.32449i	−0.200702	−	0.347625i	0.748053	−	0.663639i	$-0.230989\pi$
$331$	−3.65144	−	6.32449i	−0.200702	−	0.347625i	−0.948755	+	0.316014i	$0.897655\pi$
$332$	−0.0622604	+	0.272781i	−0.00341698	+	0.0149708i
$333$	−0.116834	−	0.115064i	−0.00640248	−	0.00630544i
$334$	9.75056	−	4.69562i	0.533527	−	0.256933i
$335$	−5.68403	+	1.75329i	−0.310552	+	0.0957925i
$336$	26.8012	−	12.4189i	1.46212	−	0.677504i
$337$	14.2865	+	13.2560i	0.778237	+	0.722098i	0.965554	−	0.260201i	$-0.0837889\pi$
$337$	14.2865	+	13.2560i	0.778237	+	0.722098i	−0.187318	+	0.982299i	$0.559979\pi$
$338$	−11.8008	+	1.77868i	−0.641877	+	0.0967474i
$339$	3.49237	+	4.51555i	0.189680	+	0.245251i
$340$	−21.0003	+	19.4855i	−1.13890	+	1.05675i
$341$	3.67433	−	4.60746i	0.198976	−	0.249508i
$342$	5.76456	−	22.1900i	0.311712	−	1.19990i
$343$	2.58121	+	1.24304i	0.139372	+	0.0671181i
$344$	0.851295	−	2.16906i	0.0458988	−	0.116948i
$345$	−34.3420	−	32.8292i	−1.84891	−	1.76746i
$346$	−26.2963	+	17.9285i	−1.41370	+	0.963843i
$347$	15.3781	−	26.6357i	0.825542	−	1.42988i	−0.0759627	−	0.997111i	$-0.524203\pi$
$347$	15.3781	−	26.6357i	0.825542	−	1.42988i	0.901505	−	0.432770i	$-0.142464\pi$
$348$	1.94213	+	16.1843i	0.104109	+	0.867570i
$349$	16.4569	+	28.5041i	0.880916	+	1.52579i	0.850324	+	0.526260i	$0.176406\pi$
$349$	16.4569	+	28.5041i	0.880916	+	1.52579i	0.0305922	+	0.999532i	$0.490261\pi$
$350$	77.0806	+	37.1201i	4.12013	+	1.98415i
$351$	22.6223	−	2.38304i	1.20749	−	0.127197i
$352$	6.20356	+	7.77902i	0.330651	+	0.414623i
$353$	2.30553	+	30.7651i	0.122711	+	1.63746i	0.630648	+	0.776069i	$0.282789\pi$
$353$	2.30553	+	30.7651i	0.122711	+	1.63746i	−0.507937	+	0.861394i	$0.669592\pi$
$354$	−36.6770	−	6.08770i	−1.94936	−	0.323558i
$355$	14.9743	+	38.1538i	0.794752	+	2.02499i
$356$	7.04157	+	2.17204i	0.373202	+	0.115118i
$357$	−26.5915	+	3.60417i	−1.40737	+	0.190753i
$358$	7.65182	−	19.4965i	0.404411	−	1.03042i
$359$	−1.00719	+	4.41280i	−0.0531576	+	0.232899i	−0.994527	−	0.104479i	$-0.966683\pi$
$359$	−1.00719	+	4.41280i	−0.0531576	+	0.232899i	0.941370	+	0.337377i	$0.109540\pi$
$360$	5.86054	+	1.06259i	0.308877	+	0.0560033i
$361$	0.760099	−	3.33021i	0.0400052	−	0.175274i
$362$	−5.16529	−	3.52163i	−0.271482	−	0.185093i
$363$	10.2241	−	12.4364i	0.536628	−	0.652741i
$364$	21.5359	+	19.9824i	1.12879	+	1.04736i
$365$	8.57979	−	14.8606i	0.449087	−	0.777841i
$366$	4.10153	+	19.2888i	0.214391	+	1.00824i
$367$	−7.66012	+	19.5177i	−0.399855	+	1.01881i	0.579194	+	0.815189i	$0.303367\pi$
$367$	−7.66012	+	19.5177i	−0.399855	+	1.01881i	−0.979049	+	0.203624i	$0.934728\pi$
$368$	−6.67153	−	29.2299i	−0.347777	−	1.52371i
$369$	0.528661	+	11.7308i	0.0275210	+	0.610683i
$370$	0.268061	−	0.336137i	0.0139358	−	0.0174750i
$371$	−20.8073	−	14.1862i	−1.08026	−	0.736511i
$372$	−7.00608	+	11.7283i	−0.363248	+	0.608083i
$373$	−0.640711	+	0.0965717i	−0.0331748	+	0.00500029i	−0.165609	−	0.986192i	$-0.552959\pi$
$373$	−0.640711	+	0.0965717i	−0.0331748	+	0.00500029i	0.132434	+	0.991192i	$0.457721\pi$
$374$	−3.72581	−	9.49321i	−0.192657	−	0.490882i
$375$	22.3090	+	40.0037i	1.15203	+	2.06578i
$376$	1.27080	+	2.20109i	0.0655366	+	0.113513i
$377$	20.5943	−	11.4740i	1.06066	−	0.590939i
$378$	−27.1151	−	27.5109i	−1.39465	−	1.41501i
$379$	−26.2054	−	12.6199i	−1.34608	−	0.648238i	−0.384593	−	0.923086i	$-0.625658\pi$
$379$	−26.2054	−	12.6199i	−1.34608	−	0.648238i	−0.961488	+	0.274848i	$0.911373\pi$
$380$	27.7177	+	4.17777i	1.42189	+	0.214315i
$381$	0.866843	+	14.4499i	0.0444097	+	0.740292i
$382$	23.5369	−	16.0472i	1.20425	−	0.821044i
$383$	−1.14675	+	15.3023i	−0.0585962	+	0.781912i	0.888072	+	0.459704i	$0.152044\pi$
$383$	−1.14675	+	15.3023i	−0.0585962	+	0.781912i	−0.946669	+	0.322209i	$0.895575\pi$
$384$	4.85524	+	4.64136i	0.247768	+	0.236853i
$385$	−14.9340	+	13.8567i	−0.761108	+	0.706205i
$386$	7.90211	+	34.6214i	0.402207	+	1.76218i
$387$	−14.2997	−	0.425746i	−0.726892	−	0.0216419i
$388$	−5.24804	+	22.9931i	−0.266429	+	1.16730i
$389$	15.8577	+	27.4664i	0.804018	+	1.39260i	0.916952	+	0.398998i	$0.130642\pi$
$389$	15.8577	+	27.4664i	0.804018	+	1.39260i	−0.112934	+	0.993602i	$0.536025\pi$
$390$	12.4045	+	58.3364i	0.628128	+	2.95398i
$391$	−2.03543	+	27.1609i	−0.102936	+	1.37359i
$392$	−0.282853	+	3.77442i	−0.0142863	+	0.190637i
$393$	−4.64474	−	21.8434i	−0.234296	−	1.10186i
$394$	6.69801	+	11.6013i	0.337441	+	0.584465i
$395$	1.59980	−	7.00919i	0.0804947	−	0.352670i
$396$	3.59770	−	5.82395i	0.180791	−	0.292664i
$397$	7.02476	+	30.7775i	0.352563	+	1.54468i	0.771241	+	0.636543i	$0.219636\pi$
$397$	7.02476	+	30.7775i	0.352563	+	1.54468i	−0.418678	+	0.908135i	$0.637507\pi$
$398$	5.20552	−	4.83001i	0.260929	−	0.242107i
$399$	18.9796	+	18.1436i	0.950170	+	0.908314i
$400$	−3.81952	+	50.9679i	−0.190976	+	2.54840i
$401$	−5.19541	+	3.54217i	−0.259446	+	0.176888i	−0.686057	−	0.727548i	$-0.740660\pi$
$401$	−5.19541	+	3.54217i	−0.259446	+	0.176888i	0.426611	+	0.904435i	$0.359708\pi$
$402$	0.293947	+	4.89998i	0.0146607	+	0.244389i
$403$	19.5377	+	2.94483i	0.973240	+	0.146692i
$404$	−0.722500	−	0.347938i	−0.0359457	−	0.0173106i
$405$	−6.00166	−	36.0718i	−0.298225	−	1.79242i
$406$	−37.0373	−	15.1935i	−1.83813	−	0.754040i
$407$	0.0356855	+	0.0618091i	0.00176887	+	0.00306376i
$408$	−1.66312	−	2.98223i	−0.0823365	−	0.147642i
$409$	−4.60414	−	11.7312i	−0.227660	−	0.580068i	0.770707	−	0.637189i	$-0.219903\pi$
$409$	−4.60414	−	11.7312i	−0.227660	−	0.580068i	−0.998367	+	0.0571211i	$0.981808\pi$
$410$	−30.4439	+	4.58868i	−1.50352	+	0.226619i
$411$	4.99455	−	8.36094i	0.246363	−	0.412415i
$412$	10.7772	+	7.34779i	0.530956	+	0.362000i
$413$	26.5476	−	33.2897i	1.30632	−	1.63808i
$414$	−33.0370	+	21.1121i	−1.62368	+	1.03760i
$415$	−0.144753	−	0.634204i	−0.00710564	−	0.0311318i
$416$	−12.1874	+	31.0531i	−0.597538	+	1.52250i
$417$	−4.74701	−	22.3244i	−0.232462	−	1.09323i
$418$	−4.98926	+	8.64166i	−0.244033	+	0.422677i
$419$	10.8602	+	10.0768i	0.530557	+	0.492285i	0.899352	−	0.437226i	$-0.144039\pi$
$419$	10.8602	+	10.0768i	0.530557	+	0.492285i	−0.368795	+	0.929511i	$0.620230\pi$
$420$	29.9919	−	36.4815i	1.46346	−	1.78011i
$421$	−12.5174	−	8.53425i	−0.610063	−	0.415934i	0.218494	−	0.975838i	$-0.429886\pi$
$421$	−12.5174	−	8.53425i	−0.610063	−	0.415934i	−0.828557	+	0.559904i	$0.810838\pi$
$422$	−6.39007	+	27.9967i	−0.311064	+	1.36286i
$423$	10.0879	−	11.9050i	0.490490	−	0.578841i
$424$	0.713064	−	3.12414i	0.0346295	−	0.151722i
$425$	16.9636	−	43.2225i	0.822854	−	2.09660i
$426$	33.5178	−	4.54296i	1.62395	−	0.220107i
$427$	−21.5811	−	6.65689i	−1.04438	−	0.322149i
$428$	−1.31538	−	3.35153i	−0.0635812	−	0.162002i
$429$	−9.76695	−	1.62113i	−0.471553	−	0.0782690i
$430$	−2.80300	−	37.4034i	−0.135173	−	1.80375i
$431$	24.2562	+	30.4164i	1.16838	+	1.46511i	0.857371	+	0.514699i	$0.172096\pi$
$431$	24.2562	+	30.4164i	1.16838	+	1.46511i	0.311011	+	0.950406i	$0.399332\pi$
$432$	9.38122	−	21.0838i	0.451354	−	1.01439i
$433$	23.3421	+	11.2410i	1.12175	+	0.540206i	0.900432	−	0.434996i	$-0.143250\pi$
$433$	23.3421	+	11.2410i	1.12175	+	0.540206i	0.221317	+	0.975202i	$0.428965\pi$
$434$	−16.7758	−	29.0566i	−0.805265	−	1.39476i
$435$	−20.3943	−	31.9424i	−0.977834	−	1.53152i
$436$	7.57402	−	13.1186i	0.362730	−	0.628266i
$437$	22.0196	−	15.0127i	1.05334	−	0.718156i
$438$	−10.2361	−	9.78522i	−0.489101	−	0.467556i
$439$	−13.0311	+	33.2027i	−0.621941	+	1.58468i	0.177622	+	0.984099i	$0.443159\pi$
$439$	−13.0311	+	33.2027i	−0.621941	+	1.58468i	−0.799564	+	0.600581i	$0.794936\pi$
$440$	−2.33560	−	1.12477i	−0.111345	−	0.0536211i
$441$	22.3998	−	6.18570i	1.06666	−	0.294557i
$442$	21.3184	−	26.7324i	1.01401	−	1.27153i
$443$	−20.8680	+	19.3626i	−0.991467	+	0.919947i	−0.996792	−	0.0800391i	$-0.974495\pi$
$443$	−20.8680	+	19.3626i	−0.991467	+	0.919947i	0.00532497	+	0.999986i	$0.498305\pi$
$444$	−0.101221	−	0.130877i	−0.00480375	−	0.00621113i
$445$	−16.9412	+	2.55347i	−0.803088	+	0.121046i
$446$	−3.80663	−	3.53204i	−0.180249	−	0.167247i
$447$	−19.3331	+	8.95840i	−0.914426	+	0.423718i
$448$	21.5374	−	6.64341i	1.01755	−	0.313871i
$449$	−35.4096	+	17.0523i	−1.67108	+	0.804750i	−0.673215	+	0.739447i	$0.735087\pi$
$449$	−35.4096	+	17.0523i	−1.67108	+	0.804750i	−0.997865	+	0.0653032i	$0.979199\pi$
$450$	64.4259	−	17.7912i	3.03707	−	0.838685i
$451$	1.13728	−	4.98275i	0.0535525	−	0.234629i
$452$	2.87985	+	4.98805i	0.135457	+	0.234618i
$453$	−23.4824	−	7.62789i	−1.10330	−	0.358389i
$454$	7.98078	−	1.20291i	0.374557	−	0.0564553i
$455$	−65.2691	−	20.1329i	−3.05986	−	0.943843i
$456$	−1.26678	+	3.09162i	−0.0593225	+	0.144778i
$457$	−11.2599	−	1.69716i	−0.526717	−	0.0793899i	−0.119700	−	0.992810i	$-0.538193\pi$
$457$	−11.2599	−	1.69716i	−0.526717	−	0.0793899i	−0.407018	+	0.913420i	$0.633431\pi$
$458$	−2.51012	+	1.20881i	−0.117290	+	0.0564840i
$459$	−13.7895	+	15.7908i	−0.643639	+	0.737051i
$460$	−29.8873	−	37.4774i	−1.39350	−	1.74739i
$461$	25.6756	+	3.86997i	1.19583	+	0.180242i	0.716624	−	0.697460i	$-0.245687\pi$
$461$	25.6756	+	3.86997i	1.19583	+	0.180242i	0.479206	+	0.877702i	$0.340925\pi$
$462$	8.18848	+	14.6832i	0.380962	+	0.683126i
$463$	−0.164519	+	0.284956i	−0.00764587	+	0.0132430i	−0.869823	−	0.493364i	$-0.835767\pi$
$463$	−0.164519	+	0.284956i	−0.00764587	+	0.0132430i	0.862177	+	0.506607i	$0.169100\pi$
$464$	0.365610	−	23.9133i	0.0169730	−	1.11015i
$465$	2.84471	−	31.6349i	0.131920	−	1.46703i
$466$	−1.91797	−	25.5935i	−0.0888482	−	1.18560i
$467$	−25.6715	+	32.1910i	−1.18793	+	1.48962i	−0.356235	+	0.934396i	$0.615940\pi$
$467$	−25.6715	+	32.1910i	−1.18793	+	1.48962i	−0.831699	+	0.555226i	$0.812632\pi$
$468$	22.9414	+	0.683036i	1.06046	+	0.0315734i
$469$	−5.06507	−	2.43921i	−0.233883	−	0.112632i
$470$	33.8033	+	23.0467i	1.55923	+	1.06307i
$471$	−3.29756	+	13.5171i	−0.151944	+	0.622834i
$472$	5.17735	+	1.59700i	0.238307	+	0.0735079i
$473$	5.94990	+	1.83530i	0.273577	+	0.0843872i
$474$	−5.30658	−	2.65351i	−0.243739	−	0.121880i
$475$	−43.4137	+	13.3914i	−1.99196	+	0.614438i
$476$	−27.0754			−1.24100
$477$	−19.5330	+	2.35201i	−0.894353	+	0.107691i
$478$	43.8569	−	21.1203i	2.00597	−	0.966022i
$479$	−12.5834	−	8.57923i	−0.574951	−	0.391995i	0.240648	−	0.970612i	$-0.422640\pi$
$479$	−12.5834	−	8.57923i	−0.574951	−	0.391995i	−0.815599	+	0.578617i	$0.803592\pi$
$480$	51.0030	+	16.5675i	2.32796	+	0.756199i
$481$	−0.119645	+	0.207231i	−0.00545534	+	0.00944892i
$482$	3.75311	+	3.48238i	0.170949	+	0.158618i
$483$	−2.68879	−	44.8210i	−0.122344	−	2.03943i
$484$	11.9077	−	11.0487i	0.541259	−	0.502215i
$485$	−12.2015	−	53.4582i	−0.554041	−	2.42741i
$486$	−30.0937	−	2.24344i	−1.36508	−	0.101765i
$487$	26.8766	−	12.9431i	1.21789	−	0.586507i	0.289170	−	0.957278i	$-0.406621\pi$
$487$	26.8766	−	12.9431i	1.21789	−	0.586507i	0.928724	+	0.370771i	$0.120906\pi$
$488$	−0.214760	−	2.86577i	−0.00972171	−	0.129727i
$489$	−0.565283	−	9.42304i	−0.0255630	−	0.426124i
$490$	22.2592	+	56.7156i	1.00557	+	2.56215i
$491$	22.0105	−	15.0065i	0.993320	−	0.677234i	0.0464732	−	0.998920i	$-0.485202\pi$
$491$	22.0105	−	15.0065i	0.993320	−	0.677234i	0.946847	+	0.321686i	$0.104249\pi$
$492$	−1.06114	+	11.8005i	−0.0478397	+	0.532006i
$493$	−6.72073	+	20.6612i	−0.302687	+	0.930535i
$494$	−33.4556			−1.50524
$495$	−1.66118	+	15.8287i	−0.0746644	+	0.711449i
$496$	12.4974	−	15.6713i	0.561151	−	0.703661i
$497$	−14.1524	+	36.0596i	−0.634820	+	1.61750i
$498$	−0.536772	−	0.00798893i	−0.0240533	−	0.000357992i
$499$	−0.556062	+	7.42013i	−0.0248928	+	0.332171i	0.970829	+	0.239772i	$0.0770726\pi$
$499$	−0.556062	+	7.42013i	−0.0248928	+	0.332171i	−0.995722	+	0.0923991i	$0.970546\pi$
$500$	16.8841	+	43.0200i	0.755081	+	1.92391i
$501$	5.92385	+	7.65939i	0.264658	+	0.342196i
$502$	5.78065	−	5.36366i	0.258003	−	0.239392i
$503$	6.41354	+	8.04232i	0.285965	+	0.358589i	0.903978	−	0.427579i	$-0.140633\pi$
$503$	6.41354	+	8.04232i	0.285965	+	0.358589i	−0.618013	+	0.786168i	$0.712062\pi$
$504$	3.37720	+	4.50356i	0.150432	+	0.200605i
$505$	1.86442			0.0829656
$506$	16.3062	−	5.02978i	0.724897	−	0.223601i
$507$	−3.75261	−	9.99643i	−0.166659	−	0.443957i
$508$	−1.09149	+	14.5649i	−0.0484270	+	0.646214i
$509$	7.78175	+	7.22041i	0.344920	+	0.320039i	0.833541	−	0.552457i	$-0.186310\pi$
$509$	7.78175	+	7.22041i	0.344920	+	0.320039i	−0.488621	+	0.872496i	$0.662500\pi$
$510$	−44.9487	−	31.6355i	−1.99036	−	1.40084i
$511$	15.4972	−	4.78026i	0.685556	−	0.211466i
$512$	18.3940	+	23.0654i	0.812908	+	1.01935i
$513$	20.4923	+	0.915518i	0.904757	+	0.0404211i
$514$	2.94747	+	12.9137i	0.130007	+	0.569600i
$515$	−29.9874	−	4.51987i	−1.32140	−	0.199169i
$516$	−14.2395	−	2.36349i	−0.626860	−	0.104047i
$517$	−5.61148	+	3.82584i	−0.246793	+	0.168260i
$518$	0.401799	−	0.0605615i	0.0176540	−	0.00266092i
$519$	−20.5836	−	19.6769i	−0.903519	−	0.863718i
$520$	−0.649511	−	8.66712i	−0.0284829	−	0.380078i
$521$	−15.5623			−0.681795			−0.340897	−	0.940101i	$-0.610731\pi$
$521$	−15.5623			−0.681795			−0.340897	+	0.940101i	$0.610731\pi$
$522$	−29.5981	+	10.1033i	−1.29547	+	0.442208i
$523$	−1.40462			−0.0614198			−0.0307099	−	0.999528i	$-0.509777\pi$
$523$	−1.40462			−0.0614198			−0.0307099	+	0.999528i	$0.509777\pi$
$524$	−1.68383	−	22.4691i	−0.0735584	−	0.981568i
$525$	−18.1417	+	74.3647i	−0.791768	+	3.24554i
$526$	−23.1092	+	3.48315i	−1.00761	+	0.151873i
$527$	−15.0454	+	10.2578i	−0.655386	+	0.446835i
$528$	−6.37842	+	7.75855i	−0.277585	+	0.337648i
$529$	−22.3227	−	3.36461i	−0.970554	−	0.146287i
$530$	−11.4782	−	50.2894i	−0.498582	−	2.18443i
$531$	−1.49757	−	33.2307i	−0.0649891	−	1.44209i
$532$	16.5176	+	20.7125i	0.716131	+	0.897999i
$533$	16.3743	−	5.05080i	0.709250	−	0.218775i
$534$	−1.26627	+	14.0817i	−0.0547968	+	0.609373i
$535$	6.13624	+	5.69360i	0.265293	+	0.246156i
$536$	0.0534586	−	0.713356i	0.00230906	−	0.0308123i
$537$	18.4863	+	3.06838i	0.797742	+	0.132410i
$538$	−44.5896	+	13.7541i	−1.92239	+	0.592980i
$539$	−10.1142			−0.435648
$540$	−1.11236	−	36.8789i	−0.0478683	−	1.58702i
$541$	−25.0277	−	31.3837i	−1.07602	−	1.34929i	−0.933124	−	0.359555i	$-0.882928\pi$
$541$	−25.0277	−	31.3837i	−1.07602	−	1.34929i	−0.142901	−	0.989737i	$-0.545643\pi$
$542$	34.4251	−	31.9418i	1.47868	−	1.37202i
$543$	2.12075	−	5.17574i	0.0910099	−	0.222112i
$544$	−11.2320	−	28.6188i	−0.481570	−	1.22702i
$545$	−2.63189	+	35.1201i	−0.112738	+	1.50438i
$546$	−28.9069	+	48.3905i	−1.23710	+	2.07092i
$547$	−9.96498	+	25.3904i	−0.426072	+	1.08561i	0.543196	+	0.839606i	$0.317214\pi$
$547$	−9.96498	+	25.3904i	−0.426072	+	1.08561i	−0.969268	+	0.246008i	$0.920881\pi$
$548$	6.12673	−	7.68267i	0.261721	−	0.328188i
$549$	−16.1173	+	7.17890i	−0.687871	+	0.306388i
$550$	−29.0902			−1.24041
$551$	19.9058	−	7.46331i	0.848014	−	0.317948i
$552$	5.18408	−	2.40215i	0.220649	−	0.102242i
$553$	5.61415	−	3.82766i	0.238738	−	0.162769i
$554$	6.34427	+	16.1649i	0.269542	+	0.686782i
$555$	0.344054	+	0.172041i	0.0146043	+	0.00730274i
$556$	−1.72090	−	22.9638i	−0.0729825	−	0.973884i
$557$	31.1072	−	14.9804i	1.31805	−	0.634742i	0.363171	−	0.931722i	$-0.381694\pi$
$557$	31.1072	−	14.9804i	1.31805	−	0.634742i	0.954883	+	0.296981i	$0.0959797\pi$
$558$	−24.8063	−	8.46805i	−1.05013	−	0.358481i
$559$	4.64535	+	20.3526i	0.196477	+	0.860824i
$560$	−50.7948	+	47.1307i	−2.14647	+	1.99163i
$561$	7.61463	−	5.02723i	0.321490	−	0.212250i
$562$	1.07243	+	0.995071i	0.0452378	+	0.0419745i
$563$	−0.422003	+	0.730931i	−0.0177853	+	0.0308051i	−0.874781	−	0.484518i	$-0.838995\pi$
$563$	−0.422003	+	0.730931i	−0.0177853	+	0.0308051i	0.856996	+	0.515323i	$0.172328\pi$
$564$	11.6995	−	10.5359i	0.492636	−	0.443641i
$565$	−11.0642	−	7.54346i	−0.465476	−	0.317356i
$566$	40.4015	−	19.4563i	1.69820	−	0.817810i
$567$	19.0303	−	28.8492i	0.799198	−	1.21155i
$568$	−4.92921			−0.206825
$569$	33.2640	−	10.2606i	1.39450	−	0.430146i	0.495694	−	0.868497i	$-0.334914\pi$
$569$	33.2640	−	10.2606i	1.39450	−	0.430146i	0.898804	+	0.438352i	$0.144438\pi$
$570$	3.22053	+	53.6850i	0.134893	+	2.24862i
$571$	7.24566	+	2.23499i	0.303222	+	0.0935315i	0.442632	−	0.896703i	$-0.354045\pi$
$571$	7.24566	+	2.23499i	0.303222	+	0.0935315i	−0.139411	+	0.990235i	$0.544521\pi$
$572$	−9.54559	−	2.94443i	−0.399121	−	0.123113i
$573$	18.4236	+	17.6120i	0.769658	+	0.735754i
$574$	−24.0418	−	16.3914i	−1.00349	−	0.684166i
$575$	69.9994	+	33.7099i	2.91918	+	1.40580i
$576$	9.25396	−	14.9803i	0.385582	−	0.624179i
$577$	27.8052	−	34.8666i	1.15755	−	1.45152i	0.288025	−	0.957623i	$-0.407001\pi$
$577$	27.8052	−	34.8666i	1.15755	−	1.45152i	0.869522	−	0.493895i	$-0.164427\pi$
$578$	−0.104485	−	1.39426i	−0.00434602	−	0.0579936i
$579$	−28.8284	+	13.3582i	−1.19807	+	0.555148i
$580$	−16.0622	−	34.7007i	−0.666945	−	1.44087i
$581$	0.307404	−	0.532440i	0.0127533	−	0.0220893i
$582$	−45.2455	−	0.673401i	−1.87549	−	0.0279134i
$583$	8.46728	+	1.27624i	0.350679	+	0.0528563i
$584$	1.28667	+	1.61343i	0.0532427	+	0.0667642i
$585$	−48.7447	+	21.7116i	−2.01534	+	0.897665i
$586$	28.0130	−	13.4904i	1.15721	−	0.557282i
$587$	−29.5285	−	4.45071i	−1.21877	−	0.183700i	−0.492010	−	0.870590i	$-0.663738\pi$
$587$	−29.5285	−	4.45071i	−1.21877	−	0.183700i	−0.726762	+	0.686889i	$0.758976\pi$
$588$	23.2342	−	3.14913i	0.958163	−	0.129868i
$589$	17.0257	+	5.25173i	0.701532	+	0.216394i
$590$	86.2405	−	12.9987i	3.55047	−	0.535147i
$591$	−8.90643	+	8.02064i	−0.366362	+	0.329925i
$592$	0.121376	+	0.210230i	0.00498854	+	0.00864041i
$593$	7.15459	−	31.3463i	0.293804	−	1.28724i	−0.585382	−	0.810758i	$-0.699055\pi$
$593$	7.15459	−	31.3463i	0.293804	−	1.28724i	0.879185	−	0.476480i	$-0.158088\pi$
$594$	12.3655	+	4.42771i	0.507362	+	0.181671i
$595$	56.7153	−	27.3126i	2.32510	−	1.11971i
$596$	−20.5438	+	6.33693i	−0.841508	+	0.259571i
$597$	5.19567	+	3.65678i	0.212645	+	0.149662i
$598$	41.9396	+	38.9143i	1.71504	+	1.59132i
$599$	−15.5231	+	2.33973i	−0.634257	+	0.0955988i	−0.458298	−	0.888799i	$-0.651541\pi$
$599$	−15.5231	+	2.33973i	−0.634257	+	0.0955988i	−0.175959	+	0.984398i	$0.556303\pi$
$600$	−9.65193	+	1.30821i	−0.394038	+	0.0534074i
$601$	6.90192	−	6.40404i	0.281535	−	0.261226i	−0.526747	−	0.850022i	$-0.676588\pi$
$601$	6.90192	−	6.40404i	0.281535	−	0.261226i	0.808282	+	0.588796i	$0.200398\pi$
$602$	22.1024	−	27.7156i	0.900828	−	1.12960i
$603$	−4.23351	+	1.16908i	−0.172402	+	0.0476087i
$604$	−22.4447	−	10.8088i	−0.913263	−	0.439804i
$605$	−13.7977	+	35.1560i	−0.560957	+	1.42930i
$606$	0.364656	−	1.49476i	0.0148131	−	0.0607206i
$607$	14.2703	−	9.72930i	0.579212	−	0.394900i	−0.237976	−	0.971271i	$-0.576484\pi$
$607$	14.2703	−	9.72930i	0.579212	−	0.394900i	0.817188	+	0.576371i	$0.195532\pi$
$608$	−15.0409	+	26.0516i	−0.609990	+	1.05653i
$609$	6.40431	−	35.2405i	0.259516	−	1.42802i
$610$	−23.1298	−	40.0621i	−0.936500	−	1.62207i
$611$	−20.5156	−	9.87979i	−0.829972	−	0.399693i
$612$	−15.9270	+	13.9194i	−0.643812	+	0.562658i
$613$	5.87230	+	7.36363i	0.237180	+	0.297414i	0.886149	−	0.463401i	$-0.153371\pi$
$613$	5.87230	+	7.36363i	0.237180	+	0.297414i	−0.648969	+	0.760815i	$0.724800\pi$
$614$	3.69014	+	49.2415i	0.148922	+	1.98722i
$615$	−9.68109	−	25.7891i	−0.390379	−	1.03992i
$616$	−0.895098	−	2.28067i	−0.0360645	−	0.0918909i
$617$	31.6477	+	9.76201i	1.27409	+	0.393004i	0.856742	−	0.515744i	$-0.172485\pi$
$617$	31.6477	+	9.76201i	1.27409	+	0.393004i	0.417345	+	0.908748i	$0.362961\pi$
$618$	−9.48885	+	23.1578i	−0.381698	+	0.931543i
$619$	13.5595	−	34.5491i	0.545002	−	1.38864i	−0.347534	−	0.937668i	$-0.612981\pi$
$619$	13.5595	−	34.5491i	0.545002	−	1.38864i	0.892536	−	0.450976i	$-0.148924\pi$
$620$	7.13123	−	31.2440i	0.286397	−	1.25479i
$621$	−24.6241	−	24.9835i	−0.988129	−	1.00256i
$622$	−1.18175	+	5.17758i	−0.0473839	+	0.207602i
$623$	−13.3786	−	9.12136i	−0.536001	−	0.365440i
$624$	−33.2202	−	5.51393i	−1.32987	−	0.220734i
$625$	−36.5825	−	33.9436i	−1.46330	−	1.35775i
$626$	−22.6677	+	39.2616i	−0.905984	+	1.56921i
$627$	−8.49119	−	2.75822i	−0.339105	−	0.110153i
$628$	−5.12877	+	13.0679i	−0.204660	+	0.521465i
$629$	−0.0490728	−	0.215002i	−0.00195666	−	0.00857270i
$630$	80.4332	+	41.7276i	3.20454	+	1.66247i
$631$	12.1390	−	15.2218i	0.483244	−	0.605969i	−0.479114	−	0.877752i	$-0.659042\pi$
$631$	12.1390	−	15.2218i	0.483244	−	0.605969i	0.962358	+	0.271784i	$0.0876135\pi$
$632$	0.714383	+	0.487058i	0.0284166	+	0.0193741i
$633$	−25.6904	−	0.382358i	−1.02110	−	0.0151973i
$634$	49.7409	−	7.49724i	1.97546	−	0.297753i
$635$	−12.4062	−	31.6104i	−0.492324	−	1.25442i
$636$	−19.8484	−	0.295408i	−0.787039	−	0.0117137i
$637$	−16.9552	−	29.3672i	−0.671788	−	1.16357i
$638$	13.5880	−	0.809604i	0.537953	−	0.0320525i
$639$	10.2131	+	28.4877i	0.404024	+	1.12696i
$640$	−14.1960	−	6.83645i	−0.561147	−	0.270234i
$641$	−10.3094	−	1.55390i	−0.407198	−	0.0613752i	−0.0577503	−	0.998331i	$-0.518393\pi$
$641$	−10.3094	−	1.55390i	−0.407198	−	0.0613752i	−0.349448	+	0.936956i	$0.613631\pi$
$642$	5.76489	−	3.80602i	0.227522	−	0.150212i
$643$	26.3800	−	17.9856i	1.04033	−	0.709283i	0.0824890	−	0.996592i	$-0.473713\pi$
$643$	26.3800	−	17.9856i	1.04033	−	0.709283i	0.957838	+	0.287309i	$0.0927607\pi$
$644$	3.38560	−	45.1777i	0.133411	−	1.78025i
$645$	32.2120	−	9.41344i	1.26834	−	0.370654i
$646$	22.6021	−	20.9717i	0.889269	−	0.825121i
$647$	−4.74981	−	20.8103i	−0.186734	−	0.818136i	−0.978324	−	0.207082i	$-0.933603\pi$
$647$	−4.74981	−	20.8103i	−0.186734	−	0.818136i	0.791589	−	0.611053i	$-0.209254\pi$
$648$	4.30190	+	0.912999i	0.168995	+	0.0358660i
$649$	−3.22165	+	14.1150i	−0.126461	+	0.554061i
$650$	−48.7662	−	84.4655i	−1.91277	−	3.31301i
$651$	22.3070	−	20.0885i	0.874281	−	0.787329i
$652$	0.711779	−	9.49803i	0.0278754	−	0.371971i
$653$	−2.42020	+	32.2953i	−0.0947097	+	1.26381i	0.724079	+	0.689717i	$0.242265\pi$
$653$	−2.42020	+	32.2953i	−0.0947097	+	1.26381i	−0.818788	+	0.574096i	$0.805354\pi$
$654$	27.6421	+	8.97909i	1.08089	+	0.351110i
$655$	26.1932	+	45.3679i	1.02345	+	1.77267i
$656$	3.86821	−	16.9478i	0.151028	−	0.661699i
$657$	6.65868	−	10.7791i	0.259780	−	0.420531i
$658$	8.60415	+	37.6972i	0.335425	+	1.46959i
$659$	3.30841	−	3.06975i	0.128877	−	0.119581i	−0.613101	−	0.790004i	$-0.710078\pi$
$659$	3.30841	−	3.06975i	0.128877	−	0.119581i	0.741978	+	0.670424i	$0.233888\pi$
$660$	−3.80593	+	15.6009i	−0.148146	+	0.607265i
$661$	2.86306	−	38.2049i	0.111360	−	1.48600i	−0.609427	−	0.792842i	$-0.708600\pi$
$661$	2.86306	−	38.2049i	0.111360	−	1.48600i	0.720787	−	0.693156i	$-0.243781\pi$
$662$	11.6809	−	7.96390i	0.453991	−	0.309526i
$663$	27.3619	+	13.6821i	1.06265	+	0.531369i
$664$	0.0773586	+	0.0116599i	0.00300210	+	0.000452493i
$665$	−55.4938	−	26.7244i	−2.15196	−	1.03633i
$666$	0.205223	−	0.242189i	0.00795223	−	0.00938464i
$667$	−33.6347	−	13.7977i	−1.30234	−	0.534249i
$668$	4.88487	+	8.46085i	0.189001	+	0.327360i
$669$	2.38268	−	3.98865i	0.0921199	−	0.154210i
$670$	−4.20694	−	10.7191i	−0.162528	−	0.414116i
$671$	7.59352	−	1.14454i	0.293144	−	0.0441844i
$672$	24.6855	+	44.2649i	0.952262	+	1.70756i
$673$	13.8720	+	9.45775i	0.534725	+	0.364570i	0.800375	−	0.599500i	$-0.204634\pi$
$673$	13.8720	+	9.45775i	0.534725	+	0.364570i	−0.265649	+	0.964070i	$0.585586\pi$
$674$	−23.5233	+	29.4972i	−0.906082	+	1.13619i
$675$	27.5589	+	53.0715i	1.06074	+	2.04272i
$676$	−2.39730	−	10.5033i	−0.0922038	−	0.403971i
$677$	−1.15140	+	2.93373i	−0.0442521	+	0.112752i	−0.951291	−	0.308294i	$-0.900242\pi$
$677$	−1.15140	+	2.93373i	−0.0442521	+	0.112752i	0.907039	+	0.421047i	$0.138337\pi$
$678$	−8.21184	+	7.39513i	−0.315374	+	0.284008i
$679$	25.9116	−	44.8803i	0.994397	−	1.72235i
$680$	5.87181	+	5.44824i	0.225174	+	0.208930i
$681$	2.53787	+	6.76052i	0.0972513	+	0.259064i
$682$	9.42606	+	6.42658i	0.360942	+	0.246086i
$683$	−1.52220	+	6.66921i	−0.0582455	+	0.255190i	−0.995665	−	0.0930118i	$-0.970351\pi$
$683$	−1.52220	+	6.66921i	−0.0582455	+	0.255190i	0.937419	+	0.348202i	$0.113208\pi$
$684$	20.3647	+	3.69238i	0.778664	+	0.141182i
$685$	−5.08377	+	22.2734i	−0.194241	+	0.851024i
$686$	−2.02622	+	5.16274i	−0.0773616	+	0.197114i
$687$	−1.52500	−	1.97178i	−0.0581823	−	0.0752282i
$688$	20.2373	+	6.24237i	0.771539	+	0.237988i
$689$	10.4887	+	26.7248i	0.399588	+	1.01813i
$690$	58.4071	−	71.0450i	2.22352	−	2.70464i
$691$	−2.71851	−	36.2759i	−0.103417	−	1.38000i	−0.771649	−	0.636049i	$-0.780568\pi$
$691$	−2.71851	−	36.2759i	−0.103417	−	1.38000i	0.668232	−	0.743953i	$-0.267051\pi$
$692$	−17.9136	−	22.4629i	−0.680971	−	0.853911i
$693$	−11.3262	+	9.89854i	−0.430248	+	0.376014i
$694$	53.6438	+	25.8335i	2.03629	+	0.980626i
$695$	26.7699	+	46.3668i	1.01544	+	1.75879i
$696$	4.47199	−	0.879682i	0.169510	−	0.0333443i
$697$	−7.89615	+	13.6765i	−0.299088	+	0.518035i
$698$	−52.6452	+	35.8929i	−1.99265	+	1.35857i
$699$	22.0412	−	6.44120i	0.833676	−	0.243629i
$700$	−28.2161	+	71.8935i	−1.06647	+	2.71732i
$701$	31.3828	+	15.1131i	1.18531	+	0.570816i	0.919454	−	0.393197i	$-0.128631\pi$
$701$	31.3828	+	15.1131i	1.18531	+	0.570816i	0.265857	+	0.964013i	$0.414345\pi$
$702$	7.87306	+	43.3266i	0.297150	+	1.63526i
$703$	−0.134538	+	0.168705i	−0.00507418	+	0.00636282i
$704$	−5.61791	+	5.21266i	−0.211733	+	0.196460i
$705$	−13.8789	+	33.8717i	−0.522708	+	1.27568i
$706$	−59.0572	+	8.90144i	−2.22265	+	0.335010i
$707$	1.29170	+	1.19852i	0.0485794	+	0.0450751i
$708$	3.00595	−	33.4279i	0.112970	−	1.25630i
$709$	−27.2850	+	8.41631i	−1.02471	+	0.316081i	−0.761160	−	0.648565i	$-0.775370\pi$
$709$	−27.2850	+	8.41631i	−1.02471	+	0.316081i	−0.263550	+	0.964646i	$0.584893\pi$
$710$	−71.4880	+	34.4268i	−2.68290	+	1.29201i
$711$	1.33472	−	5.13784i	0.0500558	−	0.192684i
$712$	0.458482	−	2.00874i	0.0171823	−	0.0752807i
$713$	−15.2346	−	26.3872i	−0.570542	−	0.988208i
$714$	−10.8046	−	50.8123i	−0.404353	−	1.90160i
$715$	22.9655	−	3.46150i	0.858863	−	0.129453i
$716$	18.0673	+	5.57303i	0.675207	+	0.208274i
$717$	26.6448	+	34.4510i	0.995067	+	1.28660i
$718$	−8.66443	−	1.30595i	−0.323353	−	0.0487377i
$719$	−3.82445	+	1.84176i	−0.142628	+	0.0686859i	−0.503836	−	0.863799i	$-0.668079\pi$
$719$	−3.82445	+	1.84176i	−0.142628	+	0.0686859i	0.361209	+	0.932485i	$0.382364\pi$
$720$	−5.65014	+	53.8380i	−0.210568	+	2.00642i
$721$	−17.8702	−	22.4085i	−0.665521	−	0.834537i
$722$	6.53878	+	0.985563i	0.243348	+	0.0366789i
$723$	−2.34918	+	3.93256i	−0.0873670	+	0.146254i
$724$	2.82177	−	4.88746i	0.104870	−	0.181641i
$725$	47.8581	+	39.3774i	1.77740	+	1.46244i
$726$	25.4870	+	17.9381i	0.945912	+	0.665745i
$727$	−0.762053	−	10.1689i	−0.0282630	−	0.377144i	−0.993343	−	0.115190i	$-0.963252\pi$
$727$	−0.762053	−	10.1689i	−0.0282630	−	0.377144i	0.965080	−	0.261954i	$-0.0843667\pi$
$728$	5.12157	−	6.42225i	0.189818	−	0.238024i
$729$	−3.63679	−	26.7539i	−0.134696	−	0.990887i
$730$	29.9290	+	14.4131i	1.10772	+	0.533451i
$731$	−15.8964	−	10.8380i	−0.587951	−	0.400858i
$732$	−17.0874	+	4.99353i	−0.631569	+	0.184566i
$733$	−32.3592	−	9.98148i	−1.19521	−	0.368674i	−0.367605	−	0.929982i	$-0.619822\pi$
$733$	−32.3592	−	9.98148i	−1.19521	−	0.368674i	−0.827607	+	0.561308i	$0.810299\pi$
$734$	−38.7861	−	11.9639i	−1.43162	−	0.441597i
$735$	−45.4924	+	30.0343i	−1.67801	+	1.10783i
$736$	49.1575	−	15.1631i	1.81197	−	0.558918i
$737$	1.91155			0.0704130
$738$	−22.5694	+	2.71763i	−0.830790	+	0.100037i
$739$	−25.2646	+	12.1668i	−0.929373	+	0.447562i	−0.836408	−	0.548107i	$-0.815349\pi$
$739$	−25.2646	+	12.1668i	−0.929373	+	0.447562i	−0.0929646	+	0.995669i	$0.529634\pi$
$740$	0.320680	+	0.218636i	0.0117884	+	0.00803723i
$741$	−6.22574	−	29.2786i	−0.228708	−	1.07558i
$742$	24.3757	−	42.2199i	0.894860	−	1.54994i
$743$	9.51422	+	8.82791i	0.349043	+	0.323864i	0.835137	−	0.550042i	$-0.185388\pi$
$743$	9.51422	+	8.82791i	0.349043	+	0.323864i	−0.486094	+	0.873906i	$0.661579\pi$
$744$	3.41651	+	1.70840i	0.125255	+	0.0626330i
$745$	36.6411	−	33.9979i	1.34242	−	1.24559i
$746$	−0.279118	−	1.22289i	−0.0102192	−	0.0447733i
$747$	−0.0928963	−	0.471242i	−0.00339890	−	0.0172419i
$748$	8.29460	−	3.99447i	0.303280	−	0.146052i
$749$	0.591216	+	7.88923i	0.0216026	+	0.288266i
$750$	−73.9979	+	48.8539i	−2.70202	+	1.78389i
$751$	0.739430	+	1.88404i	0.0269822	+	0.0687495i	0.943730	−	0.330717i	$-0.107291\pi$
$751$	0.739430	+	1.88404i	0.0269822	+	0.0687495i	−0.916748	+	0.399467i	$0.869195\pi$
$752$	−19.0862	+	13.0128i	−0.696004	+	0.474527i
$753$	5.76972	+	4.06080i	0.210260	+	0.147984i
$754$	25.1293	+	38.0964i	0.915156	+	1.38739i
$755$	57.9189			2.10788
$756$	22.9366	−	26.2654i	0.834195	−	0.955263i
$757$	−18.7005	+	23.4497i	−0.679681	+	0.852293i	−0.995325	−	0.0965848i	$-0.969208\pi$
$757$	−18.7005	+	23.4497i	−0.679681	+	0.852293i	0.315644	+	0.948878i	$0.397780\pi$
$758$	20.5710	−	52.4140i	0.747172	−	1.90376i
$759$	7.43622	+	13.3343i	0.269918	+	0.484005i
$760$	0.585702	−	7.81565i	0.0212457	−	0.283504i
$761$	−5.25467	−	13.3887i	−0.190481	−	0.485339i	0.803446	−	0.595378i	$-0.202998\pi$
$761$	−5.25467	−	13.3887i	−0.190481	−	0.485339i	−0.993927	+	0.110039i	$0.964902\pi$
$762$	−27.7695	+	3.76384i	−1.00598	+	0.136350i
$763$	−24.4000	+	22.6399i	−0.883340	+	0.819619i
$764$	16.0338	+	20.1057i	0.580081	+	0.727399i
$765$	19.3213	−	45.2238i	0.698562	−	1.63507i
$766$	−29.7064			−1.07333
$767$	−46.3846	+	14.3077i	−1.67485	+	0.516623i
$768$	−21.1695	+	25.7501i	−0.763890	+	0.929178i
$769$	−2.93696	+	39.1911i	−0.105910	+	1.41327i	0.650668	+	0.759362i	$0.274489\pi$
$769$	−2.93696	+	39.1911i	−0.105910	+	1.41327i	−0.756578	+	0.653904i	$0.773130\pi$
$770$	−28.9103	−	26.8248i	−1.04185	−	0.966700i
$771$	−10.7529	+	4.98259i	−0.387257	+	0.179444i
$772$	−30.6337	+	9.44924i	−1.10253	+	0.340085i
$773$	8.51439	+	10.6767i	0.306241	+	0.384014i	0.911008	−	0.412388i	$-0.135305\pi$
$773$	8.51439	+	10.6767i	0.306241	+	0.384014i	−0.604767	+	0.796402i	$0.706734\pi$
$774$	−1.24681	−	27.6664i	−0.0448158	−	0.994450i
$775$	11.5582	+	50.6400i	0.415185	+	1.81904i
$776$	6.52069	+	0.982836i	0.234079	+	0.0352818i
$777$	0.127771	+	0.340364i	0.00458376	+	0.0122105i
$778$	−50.7285	+	34.5861i	−1.81871	+	1.23997i
$779$	15.2796	−	2.30303i	0.547448	−	0.0825145i
$780$	−51.6786	+	15.1023i	−1.85039	+	0.540747i
$781$	−0.984322	−	13.1349i	−0.0352218	−	0.470002i
$782$	−52.7274			−1.88553
$783$	−14.3497	−	24.0226i	−0.512818	−	0.858497i
$784$	−34.4011			−1.22861
$785$	−2.43908	−	32.5472i	−0.0870544	−	1.16166i
$786$	41.4958	−	12.1265i	1.48011	−	0.432538i
$787$	−7.78992	+	1.17414i	−0.277681	+	0.0418536i	−0.286406	−	0.958108i	$-0.592461\pi$
$787$	−7.78992	+	1.17414i	−0.277681	+	0.0418536i	0.00872555	+	0.999962i	$0.497223\pi$
$788$	−9.99183	+	6.81231i	−0.355944	+	0.242679i
$789$	−7.34866	−	19.5758i	−0.261619	−	0.696917i
$790$	13.7624	+	2.07434i	0.489643	+	0.0738018i
$791$	−2.81624	−	12.3388i	−0.100134	−	0.438716i
$792$	−1.69903	−	0.881432i	−0.0603723	−	0.0313203i
$793$	16.0529	+	20.1296i	0.570054	+	0.714825i
$794$	−58.3983	+	18.0135i	−2.07248	+	0.639275i
$795$	41.8747	−	19.4035i	1.48514	−	0.688171i
$796$	4.69923	+	4.36025i	0.166560	+	0.154545i
$797$	2.74024	−	36.5659i	0.0970642	−	1.29523i	−0.709761	−	0.704442i	$-0.751197\pi$
$797$	2.74024	−	36.5659i	0.0970642	−	1.29523i	0.806826	−	0.590790i	$-0.201184\pi$
$798$	−32.2796	+	39.2641i	−1.14268	+	1.38993i
$799$	20.0532	−	6.18560i	0.709432	−	0.218831i
$800$	−87.6969			−3.10055
$801$	−12.5592	+	1.51228i	−0.443757	+	0.0534338i
$802$	−7.58961	−	9.51707i	−0.267998	−	0.336059i
$803$	−4.04236	+	3.75077i	−0.142652	+	0.132362i
$804$	−4.39121	+	0.595178i	−0.154866	+	0.0209903i
$805$	38.4817	+	98.0497i	1.35630	+	3.45580i
$806$	−2.85839	+	38.1426i	−0.100683	+	1.34352i
$807$	−20.3345	−	36.4630i	−0.715809	−	1.28356i
$808$	−0.0819167	+	0.208720i	−0.00288182	+	0.00734276i
$809$	−14.8021	+	18.5612i	−0.520413	+	0.652577i	−0.970697	−	0.240308i	$-0.922751\pi$
$809$	−14.8021	+	18.5612i	−0.520413	+	0.652577i	0.450284	+	0.892886i	$0.351323\pi$
$810$	68.7668	−	16.8044i	2.41622	−	0.590445i
$811$	−14.8118			−0.520113			−0.260056	−	0.965593i	$-0.583741\pi$
$811$	−14.8118			−0.520113			−0.260056	+	0.965593i	$0.583741\pi$
$812$	11.1788	−	34.3666i	0.392300	−	1.20603i
$813$	34.3600	+	24.1830i	1.20506	+	0.848136i
$814$	−0.114157	+	0.0778311i	−0.00400121	+	0.00272798i
$815$	8.09028	+	20.6137i	0.283390	+	0.722066i
$816$	25.8995	−	17.0990i	0.906665	−	0.598585i
$817$	1.40680	+	18.7725i	0.0492179	+	0.656767i
$818$	21.9804	−	10.5852i	0.768527	−	0.370103i
$819$	−47.7282	−	16.2928i	−1.66776	−	0.569318i
$820$	−6.18462	−	27.0966i	−0.215976	−	0.946254i
$821$	−23.2725	+	21.5937i	−0.812217	+	0.753627i	−0.972365	−	0.233466i	$-0.924993\pi$
$821$	−23.2725	+	21.5937i	−0.812217	+	0.753627i	0.160148	+	0.987093i	$0.448803\pi$
$822$	16.8630	+	8.43220i	0.588164	+	0.294107i
$823$	−11.6566	−	10.8158i	−0.406325	−	0.377015i	0.450366	−	0.892844i	$-0.351293\pi$
$823$	−11.6566	−	10.8158i	−0.406325	−	0.377015i	−0.856691	+	0.515829i	$0.827484\pi$
$824$	1.82355	−	3.15848i	0.0635263	−	0.110031i
$825$	−5.41339	−	25.4582i	−0.188470	−	0.886342i
$826$	68.1049	+	46.4331i	2.36967	+	1.61561i
$827$	12.4052	−	5.97404i	0.431372	−	0.207738i	−0.205581	−	0.978640i	$-0.565909\pi$
$827$	12.4052	−	5.97404i	0.431372	−	0.207738i	0.636954	+	0.770902i	$0.280194\pi$
$828$	−21.2342	−	28.3162i	−0.737939	−	0.984056i
$829$	−0.0933682			−0.00324281			−0.00162140	−	0.999999i	$-0.500516\pi$
$829$	−0.0933682			−0.00324281			−0.00162140	+	0.999999i	$0.500516\pi$
$830$	1.20336	−	0.371188i	0.0417693	−	0.0128841i
$831$	−12.9661	+	8.56031i	−0.449790	+	0.296954i
$832$	−24.5531	−	7.57362i	−0.851225	−	0.262568i
$833$	29.8636	+	9.21170i	1.03471	+	0.319166i
$834$	42.4095	−	12.3935i	1.46852	−	0.429152i
$835$	−18.7674	−	12.7954i	−0.649473	−	0.442803i
$836$	−8.11595	−	3.90844i	−0.280696	−	0.135176i
$837$	2.79461	−	23.2850i	0.0965958	−	0.804847i
$838$	−17.8817	+	22.4230i	−0.617714	+	0.774589i
$839$	2.65473	+	35.4250i	0.0916516	+	1.22301i	0.833531	+	0.552472i	$0.186316\pi$
$839$	2.65473	+	35.4250i	0.0916516	+	1.22301i	−0.741880	+	0.670533i	$0.766065\pi$
$840$	−10.7986	−	7.60018i	−0.372586	−	0.262231i
$841$	−23.4503	−	17.0611i	−0.808631	−	0.588316i
$842$	14.6641	−	25.3990i	0.505359	−	0.875308i
$843$	−0.671266	+	1.12371i	−0.0231196	+	0.0387026i
$844$	−25.6342	−	3.86374i	−0.882366	−	0.132995i
$845$	15.6169	+	19.5830i	0.537239	+	0.673677i
$846$	24.4415	+	17.7519i	0.840315	+	0.610325i
$847$	−32.1590	+	15.4869i	−1.10500	+	0.532138i
$848$	28.7996	+	4.34084i	0.988983	+	0.149065i
$849$	24.5455	+	31.7367i	0.842399	+	1.08920i
$850$	85.8932	+	26.4945i	2.94611	+	0.908755i
$851$	0.364886	−	0.0549978i	0.0125081	−	0.00188530i
$852$	6.35083	+	29.8669i	0.217576	+	1.02322i
$853$	20.3518	+	35.2504i	0.696834	+	1.20695i	0.969559	+	0.244859i	$0.0787418\pi$
$853$	20.3518	+	35.2504i	0.696834	+	1.20695i	−0.272725	+	0.962092i	$0.587925\pi$
$854$	9.72874	−	42.6244i	0.332911	−	1.45858i
$855$	−46.3830	+	12.8087i	−1.58627	+	0.438047i
$856$	−0.907000	+	0.436788i	−0.0310006	+	0.0149291i
$857$	35.3600	−	10.9071i	1.20787	−	0.372580i	0.375514	−	0.926817i	$-0.377466\pi$
$857$	35.3600	−	10.9071i	1.20787	−	0.372580i	0.832359	+	0.554237i	$0.186990\pi$
$858$	1.71656	−	19.0892i	0.0586025	−	0.651695i
$859$	−3.81584	−	3.54059i	−0.130195	−	0.120803i	0.612388	−	0.790557i	$-0.290209\pi$
$859$	−3.81584	−	3.54059i	−0.130195	−	0.120803i	−0.742583	+	0.669754i	$0.766400\pi$
$860$	33.4821	−	5.04661i	1.14173	−	0.172088i
$861$	9.87101	−	24.0905i	0.336403	−	0.821001i
$862$	−55.2084	+	51.2259i	−1.88040	+	1.74476i
$863$	−5.00214	+	6.27249i	−0.170275	+	0.213518i	−0.859646	−	0.510891i	$-0.829316\pi$
$863$	−5.00214	+	6.27249i	−0.170275	+	0.213518i	0.689371	+	0.724409i	$0.257887\pi$
$864$	37.2777	+	13.3480i	1.26821	+	0.454109i
$865$	60.1835	+	28.9829i	2.04630	+	0.985447i
$866$	−18.3233	+	46.6871i	−0.622652	+	1.58649i
$867$	1.20074	−	0.350898i	0.0407793	−	0.0119171i
$868$	25.0255	−	17.0621i	0.849420	−	0.579125i
$869$	−1.15521	+	2.00087i	−0.0391877	+	0.0678750i
$870$	58.7130	−	43.9914i	1.99056	−	1.49145i
$871$	3.20449	+	5.55033i	0.108580	+	0.188066i
$872$	−3.81603	−	1.83770i	−0.129227	−	0.0622325i
$873$	−7.83040	−	39.7218i	−0.265019	−	1.34438i
$874$	32.1669	+	40.3361i	1.08806	+	1.36439i
$875$	−7.58882	−	101.266i	−0.256549	−	3.42341i
$876$	8.11827	−	9.87487i	0.274291	−	0.333641i
$877$	5.42554	+	13.8240i	0.183207	+	0.466805i	0.992741	−	0.120268i	$-0.0383755\pi$
$877$	5.42554	+	13.8240i	0.183207	+	0.466805i	−0.809534	+	0.587073i	$0.800280\pi$
$878$	−65.9816	−	20.3526i	−2.22677	−	0.686868i
$879$	17.0190	+	22.0052i	0.574037	+	0.742215i
$880$	8.60783	−	21.9324i	0.290170	−	0.739341i
$881$	−2.95418	+	12.9431i	−0.0995289	+	0.436064i	0.900470	+	0.434917i	$0.143222\pi$
$881$	−2.95418	+	12.9431i	−0.0995289	+	0.436064i	−0.999999	+	0.00114731i	$0.999635\pi$
$882$	15.1817	+	42.3469i	0.511196	+	1.42590i
$883$	12.4995	−	54.7638i	0.420641	−	1.84295i	−0.108064	−	0.994144i	$-0.534465\pi$
$883$	12.4995	−	54.7638i	0.420641	−	1.84295i	0.528705	−	0.848806i	$-0.322678\pi$
$884$	25.5031	+	17.3877i	0.857762	+	0.584812i
$885$	27.4242	+	73.0544i	0.921856	+	2.45570i
$886$	−40.3976	−	37.4835i	−1.35719	−	1.25928i
$887$	6.08658	−	10.5423i	0.204367	−	0.353975i	−0.745564	−	0.666434i	$-0.767820\pi$
$887$	6.08658	−	10.5423i	0.204367	−	0.353975i	0.949931	+	0.312460i	$0.101153\pi$
$888$	−0.0343765	+	0.0309576i	−0.00115360	+	0.00103887i
$889$	11.7252	−	29.8754i	0.393252	−	1.00199i
$890$	−7.38020	−	32.3348i	−0.247385	−	1.08386i
$891$	−1.57381	+	11.6456i	−0.0527247	+	0.390142i
$892$	2.92280	−	3.66507i	0.0978626	−	0.122716i
$893$	−16.9656	−	11.5670i	−0.567734	−	0.387074i
$894$	−20.0907	−	36.0258i	−0.671933	−	1.20488i
$895$	−43.4678	+	6.55171i	−1.45297	+	0.219000i
$896$	−5.44050	−	13.8622i	−0.181754	−	0.463103i
$897$	−26.2512	+	43.9450i	−0.876504	+	1.46728i
$898$	−38.0414	−	65.8897i	−1.26946	−	2.19877i
$899$	−6.80819	−	23.3322i	−0.227066	−	0.778171i
$900$	20.3622	+	56.7970i	0.678741	+	1.89323i
$901$	−23.8386	−	11.4800i	−0.794177	−	0.382456i
$902$	9.78351	+	1.47463i	0.325755	+	0.0490997i
$903$	28.3683	+	14.1853i	0.944037	+	0.472058i
$904$	1.33061	−	0.907196i	0.0442555	−	0.0301729i
$905$	−0.980535	+	13.0843i	−0.0325941	+	0.434938i
$906$	11.3281	−	46.4353i	0.376353	−	1.54271i
$907$	15.1926	−	14.0967i	0.504463	−	0.468073i	−0.386409	−	0.922327i	$-0.626285\pi$
$907$	15.1926	−	14.0967i	0.504463	−	0.468073i	0.890872	+	0.454255i	$0.150094\pi$
$908$	1.62128	+	7.10329i	0.0538040	+	0.235731i
$909$	1.37600	+	0.0409678i	0.0456390	+	0.00135882i
$910$	29.4233	−	128.912i	0.975371	−	4.27338i
$911$	−19.2506	−	33.3430i	−0.637801	−	1.10470i	−0.985914	−	0.167251i	$-0.946511\pi$
$911$	−19.2506	−	33.3430i	−0.637801	−	1.10470i	0.348113	−	0.937452i	$-0.386822\pi$
$912$	−28.8809	−	9.38150i	−0.956343	−	0.310652i
$913$	−0.0156223	+	0.208466i	−0.000517024	+	0.00689921i
$914$	1.64735	−	21.9823i	0.0544894	−	0.727111i
$915$	30.7560	−	27.6972i	1.01676	−	0.915641i
$916$	−1.25753	−	2.17811i	−0.0415500	−	0.0719666i
$917$	−11.0172	+	48.2696i	−0.363821	+	1.59400i
$918$	−32.4783	−	24.3356i	−1.07194	−	0.803195i
$919$	−2.44444	−	10.7098i	−0.0806345	−	0.353283i	0.918475	−	0.395479i	$-0.129422\pi$
$919$	−2.44444	−	10.7098i	−0.0806345	−	0.353283i	−0.999109	+	0.0421966i	$0.986564\pi$
$920$	−9.82511	+	9.11637i	−0.323924	+	0.300558i
$921$	−42.4069	+	12.3928i	−1.39736	+	0.408355i
$922$	−3.75638	+	50.1254i	−0.123710	+	1.65079i
$923$	36.4879	−	24.8770i	1.20101	−	0.818838i
$924$	−12.6657	+	8.36197i	−0.416671	+	0.275088i
$925$	−0.622037	−	0.0937570i	−0.0204525	−	0.00308271i
$926$	−0.573896	−	0.276374i	−0.0188594	−	0.00908220i
$927$	−22.0323	−	3.99473i	−0.723635	−	0.131204i
$928$	40.9631	−	2.44068i	1.34468	−	0.0801192i
$929$	−16.5839	−	28.7241i	−0.544100	−	0.942409i	−0.998663	−	0.0516942i	$-0.983538\pi$
$929$	−16.5839	−	28.7241i	−0.544100	−	0.942409i	0.454563	−	0.890715i	$-0.349795\pi$
$930$	61.4813	+	0.915043i	2.01605	+	0.0300054i
$931$	−11.1717	−	28.4651i	−0.366139	−	0.932907i
$932$	22.9103	−	3.45318i	0.750453	−	0.113113i
$933$	−4.75107	−	0.0707114i	−0.155543	−	0.00231499i
$934$	−65.8572	−	44.9007i	−2.15491	−	1.46919i
$935$	−13.3454	+	16.7346i	−0.436440	+	0.547278i
$936$	−0.288912	−	6.41087i	−0.00944338	−	0.209546i
$937$	11.3869	+	49.8894i	0.371995	+	1.62981i	0.721171	+	0.692758i	$0.243604\pi$
$937$	11.3869	+	49.8894i	0.371995	+	1.62981i	−0.349176	+	0.937057i	$0.613538\pi$
$938$	3.97603	−	10.1308i	0.129822	−	0.330781i
$939$	−38.5780	−	12.5314i	−1.25895	−	0.408948i
$940$	−18.4666	+	31.9851i	−0.602314	+	1.04324i
$941$	−37.7434	−	35.0207i	−1.23040	−	1.14164i	−0.985061	−	0.172206i	$-0.944911\pi$
$941$	−37.7434	−	35.0207i	−1.23040	−	1.14164i	−0.245338	−	0.969438i	$-0.578899\pi$
$942$	−26.5712	−	4.41032i	−0.865735	−	0.143696i
$943$	−21.8331	−	14.8856i	−0.710985	−	0.484741i
$944$	−10.9577	+	48.0090i	−0.356644	+	1.56256i
$945$	−21.5501	+	78.1561i	−0.701024	+	2.54242i
$946$	−2.68221	+	11.7515i	−0.0872061	+	0.382075i
$947$	−4.98203	+	12.6940i	−0.161894	+	0.412499i	−0.988684	−	0.150011i	$-0.952069\pi$
$947$	−4.98203	+	12.6940i	−0.161894	+	0.412499i	0.826790	+	0.562510i	$0.190164\pi$
$948$	2.03074	−	4.95608i	0.0659555	−	0.160966i
$949$	−17.6672	−	5.44960i	−0.573500	−	0.176901i
$950$	−32.1320	−	81.8709i	−1.04250	−	2.65624i
$951$	15.8175	+	42.1356i	0.512917	+	1.36634i
$952$	0.565739	+	7.54926i	0.0183357	+	0.244673i
$953$	32.2960	+	40.4979i	1.04617	+	1.31186i	0.948548	+	0.316633i	$0.102552\pi$
$953$	32.2960	+	40.4979i	1.04617	+	1.31186i	0.0976225	+	0.995224i	$0.468876\pi$
$954$	−7.36624	−	37.3673i	−0.238491	−	1.20981i
$955$	−53.8681	−	25.9415i	−1.74313	−	0.839447i
$956$	21.9716	+	38.0559i	0.710611	+	1.23081i
$957$	3.23710	+	11.7408i	0.104641	+	0.379527i
$958$	14.7414	−	25.5329i	0.476274	−	0.824930i
$959$	−17.8404	+	12.1634i	−0.576095	+	0.392775i
$960$	−9.78957	+	40.1285i	−0.315957	+	1.29514i
$961$	−3.88343	+	9.89483i	−0.125272	+	0.319188i
$962$	−0.417359	−	0.200989i	−0.0134562	−	0.00648016i
$963$	4.40362	+	4.33688i	0.141905	+	0.139754i
$964$	−2.88170	+	3.61354i	−0.0928134	+	0.116384i
$965$	54.6368	−	50.6956i	1.75882	−	1.63195i
$966$	86.1360	−	11.6747i	2.77138	−	0.375628i
$967$	37.9809	−	5.72469i	1.22138	−	0.184094i	0.493469	−	0.869763i	$-0.335729\pi$
$967$	37.9809	−	5.72469i	1.22138	−	0.184094i	0.727913	+	0.685670i	$0.240491\pi$
$968$	−3.32946	−	3.08929i	−0.107013	−	0.0992935i
$969$	22.5594	+	15.8776i	0.724712	+	0.510062i
$970$	101.433	−	31.2881i	3.25683	−	1.00460i
$971$	37.2753	−	17.9508i	1.19622	−	0.576070i	0.273625	−	0.961836i	$-0.411777\pi$
$971$	37.2753	−	17.9508i	1.19622	−	0.576070i	0.922596	+	0.385766i	$0.126063\pi$
$972$	−0.0105964	−	27.2422i	−0.000339881	−	0.873794i
$973$	−11.2598	+	49.3324i	−0.360972	+	1.58152i
$974$	28.8742	+	50.0116i	0.925190	+	1.60248i
$975$	64.8450	−	58.3958i	2.07670	−	1.87016i
$976$	25.8277	−	3.89290i	0.826724	−	0.124609i
$977$	−8.96648	−	2.76579i	−0.286863	−	0.0884856i	0.147984	−	0.988990i	$-0.452721\pi$
$977$	−8.96648	−	2.76579i	−0.286863	−	0.0884856i	−0.434847	+	0.900504i	$0.643198\pi$
$978$	18.1090	−	2.45446i	0.579061	−	0.0784850i
$979$	5.44424	+	0.820587i	0.173999	+	0.0262261i
$980$	−49.5547	+	23.8643i	−1.58297	+	0.762316i
$981$	−2.71412	+	25.8619i	−0.0866553	+	0.825706i
$982$	32.1536	+	40.3193i	1.02606	+	1.28664i
$983$	11.8394	+	1.78451i	0.377619	+	0.0569170i	0.335110	−	0.942179i	$-0.391227\pi$
$983$	11.8394	+	1.78451i	0.377619	+	0.0569170i	0.0425096	+	0.999096i	$0.486465\pi$
$984$	3.31242	+	0.0492997i	0.105596	+	0.00157162i
$985$	14.0580	−	24.3492i	0.447927	−	0.775832i
$986$	−40.8579	−	9.98506i	−1.30118	−	0.317989i
$987$	−31.3896	+	14.5450i	−0.999141	+	0.462972i
$988$	−2.25698	−	30.1173i	−0.0718040	−	0.958158i
$989$	20.0719	−	25.1694i	0.638250	−	0.800340i
$990$	−30.7970	−	0.916924i	−0.978793	−	0.0291417i
$991$	−36.5422	−	17.5978i	−1.16080	−	0.559013i	−0.248541	−	0.968621i	$-0.579951\pi$
$991$	−36.5422	−	17.5978i	−1.16080	−	0.559013i	−0.912261	+	0.409608i	$0.865665\pi$
$992$	28.4163	+	19.3739i	0.902220	+	0.615123i
$993$	9.14329	+	8.74052i	0.290154	+	0.277372i
$994$	−71.6589	−	22.1039i	−2.27288	−	0.701092i
$995$	−14.2420	−	4.39308i	−0.451503	−	0.139270i
$996$	−0.0290199	−	0.483750i	−0.000919532	−	0.0153282i
$997$	30.5528	−	9.42430i	0.967618	−	0.298471i	0.229625	−	0.973279i	$-0.426250\pi$
$997$	30.5528	−	9.42430i	0.967618	−	0.298471i	0.737993	+	0.674809i	$0.235774\pi$
$998$	−14.4047			−0.455972
$999$	0.250142	+	0.134532i	0.00791413	+	0.00425639i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.2.q.a.103.24	yes	336
3.2	odd	2		783.2.u.a.712.5		336
9.2	odd	6		783.2.u.a.451.5		336
9.7	even	3	inner	261.2.q.a.16.24	✓	336
29.20	even	7	inner	261.2.q.a.49.24	yes	336
87.20	odd	14		783.2.u.a.658.5		336
261.20	odd	42		783.2.u.a.397.5		336
261.223	even	21	inner	261.2.q.a.223.24	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
261.2.q.a.16.24	✓	336	9.7	even	3	inner
261.2.q.a.49.24	yes	336	29.20	even	7	inner
261.2.q.a.103.24	yes	336	1.1	even	1	trivial
261.2.q.a.223.24	yes	336	261.223	even	21	inner
783.2.u.a.397.5		336	261.20	odd	42
783.2.u.a.451.5		336	9.2	odd	6
783.2.u.a.658.5		336	87.20	odd	14
783.2.u.a.712.5		336	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	261.q (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.144668 + 1.93046i) q^{2} +(-1.66251 + 0.485844i) q^{3} +(-1.72807 + 0.260465i) q^{4} +(3.35707 - 2.28881i) q^{5} +(-1.17841 - 3.13913i) q^{6} +(3.79717 + 0.572331i) q^{7} +(0.108732 + 0.476384i) q^{8} +(2.52791 - 1.61545i) q^{9} +(4.90411 + 6.14956i) q^{10} +(-1.24771 + 0.384867i) q^{11} +(2.74640 - 1.27260i) q^{12} +(-3.20912 - 2.97763i) q^{13} +(-0.555533 + 7.41307i) q^{14} +(-4.46917 + 5.43619i) q^{15} +(-4.24381 + 1.30904i) q^{16} +4.03457 q^{17} +(3.48425 + 4.64632i) q^{18} +(-2.46134 - 3.08642i) q^{19} +(-5.20510 + 4.82962i) q^{20} +(-6.59092 + 0.893322i) q^{21} +(-0.923471 - 2.35297i) q^{22} +(-0.504497 + 6.73204i) q^{23} +(-0.412216 - 0.739170i) q^{24} +(4.20455 - 10.7130i) q^{25} +(5.28392 - 6.62583i) q^{26} +(-3.41784 + 3.91387i) q^{27} -6.71085 q^{28} +(-1.66579 + 5.12105i) q^{29} +(-11.1409 - 7.84110i) q^{30} +(-3.72911 + 2.54246i) q^{31} +(-2.78395 - 7.09339i) q^{32} +(1.88735 - 1.24604i) q^{33} +(0.583672 + 7.78856i) q^{34} +(14.0573 - 6.76965i) q^{35} +(-3.94764 + 3.45003i) q^{36} +(-0.0121631 - 0.0532900i) q^{37} +(5.60212 - 5.19801i) q^{38} +(6.78187 + 3.39122i) q^{39} +(1.45537 + 1.35039i) q^{40} +(-1.95712 + 3.38984i) q^{41} +(-2.67801 - 12.5942i) q^{42} +(-3.94005 - 2.68628i) q^{43} +(2.05588 - 0.990060i) q^{44} +(4.78893 - 11.2091i) q^{45} -13.0689 q^{46} +(4.97035 - 1.53315i) q^{47} +(6.41940 - 4.23813i) q^{48} +(7.40193 + 2.28319i) q^{49} +(21.2893 + 6.56688i) q^{50} +(-6.70753 + 1.96017i) q^{51} +(6.32115 + 4.30968i) q^{52} +(-5.90857 - 2.84542i) q^{53} +(-8.05001 - 6.03177i) q^{54} +(-3.30775 + 4.14779i) q^{55} +(0.140223 + 1.87114i) q^{56} +(5.59152 + 3.93539i) q^{57} +(-10.1269 - 2.47488i) q^{58} +(5.54407 - 9.60261i) q^{59} +(6.30711 - 10.5582i) q^{60} +(-5.81559 - 0.876559i) q^{61} +(-5.44760 - 6.83107i) q^{62} +(10.5235 - 4.68732i) q^{63} +(5.28812 - 2.54662i) q^{64} +(-17.5885 - 2.65103i) q^{65} +(2.67846 + 3.46318i) q^{66} +(-1.39895 - 0.431518i) q^{67} +(-6.97202 + 1.05086i) q^{68} +(-2.43199 - 11.4372i) q^{69} +(15.1022 + 26.1577i) q^{70} +(-2.24473 + 9.83479i) q^{71} +(1.04444 + 1.02861i) q^{72} +(3.80506 - 1.83242i) q^{73} +(0.101114 - 0.0311896i) q^{74} +(-1.78528 + 19.8533i) q^{75} +(5.05726 + 4.69245i) q^{76} +(-4.95803 + 0.747303i) q^{77} +(-5.56548 + 13.5827i) q^{78} +(1.29710 - 1.20354i) q^{79} +(-11.2506 + 14.1078i) q^{80} +(3.78067 - 8.16741i) q^{81} +(-6.82706 - 3.28774i) q^{82} +(0.0584925 - 0.149036i) q^{83} +(11.1569 - 3.26042i) q^{84} +(13.5443 - 9.23437i) q^{85} +(4.61575 - 7.99472i) q^{86} +(0.281364 - 9.32313i) q^{87} +(-0.319010 - 0.552541i) q^{88} +(-3.79906 - 1.82953i) q^{89} +(22.3314 + 7.62322i) q^{90} +(-10.4814 - 13.1432i) q^{91} +(-0.881653 - 11.7648i) q^{92} +(4.96446 - 6.03865i) q^{93} +(3.67873 + 9.37324i) q^{94} +(-15.3271 - 4.72779i) q^{95} +(8.07464 + 10.4403i) q^{96} +(4.93043 - 12.5625i) q^{97} +(-3.33678 + 14.6194i) q^{98} +(-2.53236 + 2.98851i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 5 q^{2} - 10 q^{3} + 21 q^{4} - 9 q^{5} - 40 q^{6} - 5 q^{7} + 2 q^{8} - 6 q^{9} - 28 q^{10} - q^{11} - 22 q^{12} - 5 q^{13} - 9 q^{14} - 26 q^{15} + 21 q^{16} - 60 q^{17} - 90 q^{18} - 20 q^{19}+ \cdots + 196 q^{99}+O(q^{100}) \) 336 * q - 5 * q^2 - 10 * q^3 + 21 * q^4 - 9 * q^5 - 40 * q^6 - 5 * q^7 + 2 * q^8 - 6 * q^9 - 28 * q^10 - q^11 - 22 * q^12 - 5 * q^13 - 9 * q^14 - 26 * q^15 + 21 * q^16 - 60 * q^17 - 90 * q^18 - 20 * q^19 - 15 * q^20 - 2 * q^21 - 13 * q^22 - 32 * q^23 + 44 * q^24 + 15 * q^25 - 4 * q^26 - 43 * q^27 - 72 * q^28 - q^29 - 8 * q^30 - 5 * q^31 + 7 * q^32 - 37 * q^33 - 15 * q^34 + 16 * q^35 - 104 * q^36 - 20 * q^37 + 63 * q^38 + 38 * q^39 + 5 * q^40 - 20 * q^41 + 11 * q^42 - 5 * q^43 - 8 * q^44 + 30 * q^45 - 80 * q^46 + 5 * q^47 + 12 * q^48 - 19 * q^49 - 3 * q^50 - 62 * q^51 + q^52 - 4 * q^53 + 26 * q^54 - 100 * q^55 - 5 * q^56 - 50 * q^57 - 7 * q^58 + 154 * q^59 + 23 * q^60 + 7 * q^61 - 4 * q^62 - 144 * q^63 + 18 * q^64 - 65 * q^65 + 44 * q^66 - 5 * q^67 - 9 * q^68 + 22 * q^69 - 14 * q^70 + 18 * q^71 + 37 * q^72 - 20 * q^73 - 77 * q^74 + 16 * q^75 - 5 * q^76 + 39 * q^77 + 52 * q^78 - 5 * q^79 - 104 * q^80 + 54 * q^81 + 12 * q^82 - 23 * q^83 + 175 * q^84 - 42 * q^85 + 128 * q^86 + 42 * q^87 - 8 * q^88 + 34 * q^89 + 222 * q^90 + 12 * q^91 - 115 * q^92 + 64 * q^93 - 25 * q^94 + 89 * q^95 - 49 * q^96 + 55 * q^97 - 88 * q^98 + 196 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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