LMFDB - Embedded newform 409.2.g.a.192.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [409,2,Mod(49,409)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(409, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([7])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("409.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 409 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	409.g (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.26588144267$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			192.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	409.192
Dual form			409.2.g.a.49.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.50000 - 0.866025i) q^{2} +(-2.36603 + 1.36603i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.73205 q^{5} +4.73205 q^{6} +(-1.00000 + 3.73205i) q^{7} +1.73205i q^{8} +(2.23205 - 3.86603i) q^{9} +(2.59808 + 1.50000i) q^{10} +(-3.00000 + 3.00000i) q^{11} +(-2.36603 - 1.36603i) q^{12} +(1.36603 - 1.36603i) q^{13} +(4.73205 - 4.73205i) q^{14} +(4.09808 - 2.36603i) q^{15} +(2.50000 - 4.33013i) q^{16} +(-3.23205 + 5.59808i) q^{17} +(-6.69615 + 3.86603i) q^{18} +(0.732051 - 0.732051i) q^{19} +(-0.866025 - 1.50000i) q^{20} +(-2.73205 - 10.1962i) q^{21} +(7.09808 - 1.90192i) q^{22} +(4.09808 + 2.36603i) q^{23} +(-2.36603 - 4.09808i) q^{24} -2.00000 q^{25} +(-3.23205 + 0.866025i) q^{26} +4.00000i q^{27} +(-3.73205 + 1.00000i) q^{28} +(-7.09808 - 1.90192i) q^{29} -8.19615 q^{30} +(-2.26795 - 2.26795i) q^{31} +(-4.50000 + 2.59808i) q^{32} +(3.00000 - 11.1962i) q^{33} +(9.69615 - 5.59808i) q^{34} +(1.73205 - 6.46410i) q^{35} +4.46410 q^{36} +(-2.90192 - 10.8301i) q^{37} +(-1.73205 + 0.464102i) q^{38} +(-1.36603 + 5.09808i) q^{39} -3.00000i q^{40} +(2.19615 - 1.26795i) q^{41} +(-4.73205 + 17.6603i) q^{42} +(2.00000 + 2.00000i) q^{43} +(-4.09808 - 1.09808i) q^{44} +(-3.86603 + 6.69615i) q^{45} +(-4.09808 - 7.09808i) q^{46} +(3.00000 + 0.803848i) q^{47} +13.6603i q^{48} +(-6.86603 - 3.96410i) q^{49} +(3.00000 + 1.73205i) q^{50} -17.6603i q^{51} +(1.86603 + 0.500000i) q^{52} +(-0.464102 - 0.803848i) q^{53} +(3.46410 - 6.00000i) q^{54} +(5.19615 - 5.19615i) q^{55} +(-6.46410 - 1.73205i) q^{56} +(-0.732051 + 2.73205i) q^{57} +(9.00000 + 9.00000i) q^{58} +(4.26795 - 4.26795i) q^{59} +(4.09808 + 2.36603i) q^{60} +(7.36603 + 7.36603i) q^{61} +(1.43782 + 5.36603i) q^{62} +(12.1962 + 12.1962i) q^{63} -1.00000 q^{64} +(-2.36603 + 2.36603i) q^{65} +(-14.1962 + 14.1962i) q^{66} +(-1.80385 + 6.73205i) q^{67} -6.46410 q^{68} -12.9282 q^{69} +(-8.19615 + 8.19615i) q^{70} +(-3.00000 + 5.19615i) q^{71} +(6.69615 + 3.86603i) q^{72} +(14.5622 + 3.90192i) q^{73} +(-5.02628 + 18.7583i) q^{74} +(4.73205 - 2.73205i) q^{75} +(1.00000 + 0.267949i) q^{76} +(-8.19615 - 14.1962i) q^{77} +(6.46410 - 6.46410i) q^{78} +(5.00000 - 5.00000i) q^{79} +(-4.33013 + 7.50000i) q^{80} +(1.23205 + 2.13397i) q^{81} -4.39230 q^{82} -1.26795 q^{83} +(7.46410 - 7.46410i) q^{84} +(5.59808 - 9.69615i) q^{85} +(-1.26795 - 4.73205i) q^{86} +(19.3923 - 5.19615i) q^{87} +(-5.19615 - 5.19615i) q^{88} -12.9282 q^{89} +(11.5981 - 6.69615i) q^{90} +(3.73205 + 6.46410i) q^{91} +4.73205i q^{92} +(8.46410 + 2.26795i) q^{93} +(-3.80385 - 3.80385i) q^{94} +(-1.26795 + 1.26795i) q^{95} +(7.09808 - 12.2942i) q^{96} +(-14.7942 - 3.96410i) q^{97} +(6.86603 + 11.8923i) q^{98} +(4.90192 + 18.2942i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{2} - 6 q^{3} + 2 q^{4} + 12 q^{6} - 4 q^{7} + 2 q^{9} - 12 q^{11} - 6 q^{12} + 2 q^{13} + 12 q^{14} + 6 q^{15} + 10 q^{16} - 6 q^{17} - 6 q^{18} - 4 q^{19} - 4 q^{21} + 18 q^{22} + 6 q^{23} - 6 q^{24}+ \cdots + 30 q^{99}+O(q^{100}) $ 4 * q - 6 * q^2 - 6 * q^3 + 2 * q^4 + 12 * q^6 - 4 * q^7 + 2 * q^9 - 12 * q^11 - 6 * q^12 + 2 * q^13 + 12 * q^14 + 6 * q^15 + 10 * q^16 - 6 * q^17 - 6 * q^18 - 4 * q^19 - 4 * q^21 + 18 * q^22 + 6 * q^23 - 6 * q^24 - 8 * q^25 - 6 * q^26 - 8 * q^28 - 18 * q^29 - 12 * q^30 - 16 * q^31 - 18 * q^32 + 12 * q^33 + 18 * q^34 + 4 * q^36 - 22 * q^37 - 2 * q^39 - 12 * q^41 - 12 * q^42 + 8 * q^43 - 6 * q^44 - 12 * q^45 - 6 * q^46 + 12 * q^47 - 24 * q^49 + 12 * q^50 + 4 * q^52 + 12 * q^53 - 12 * q^56 + 4 * q^57 + 36 * q^58 + 24 * q^59 + 6 * q^60 + 26 * q^61 + 30 * q^62 + 28 * q^63 - 4 * q^64 - 6 * q^65 - 36 * q^66 - 28 * q^67 - 12 * q^68 - 24 * q^69 - 12 * q^70 - 12 * q^71 + 6 * q^72 + 34 * q^73 + 18 * q^74 + 12 * q^75 + 4 * q^76 - 12 * q^77 + 12 * q^78 + 20 * q^79 - 2 * q^81 + 24 * q^82 - 12 * q^83 + 16 * q^84 + 12 * q^85 - 12 * q^86 + 36 * q^87 - 24 * q^89 + 36 * q^90 + 8 * q^91 + 20 * q^93 - 36 * q^94 - 12 * q^95 + 18 * q^96 - 28 * q^97 + 24 * q^98 + 30 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/409\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{5}{12}\right)$

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 $

$2$	−1.50000	−	0.866025i	−1.06066	−	0.612372i	−0.135045	−	0.990839i	$-0.543118\pi$
$2$	−1.50000	−	0.866025i	−1.06066	−	0.612372i	−0.925615	+	0.378467i	$0.876451\pi$
$3$	−2.36603	+	1.36603i	−1.36603	+	0.788675i	−0.990418	−	0.138104i	$-0.955899\pi$
$3$	−2.36603	+	1.36603i	−1.36603	+	0.788675i	−0.375608	+	0.926779i	$0.622566\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.73205			−0.774597			−0.387298	−	0.921954i	$-0.626592\pi$
$5$	−1.73205			−0.774597			−0.387298	+	0.921954i	$0.626592\pi$
$6$	4.73205			1.93185
$7$	−1.00000	+	3.73205i	−0.377964	+	1.41058i	0.471000	+	0.882133i	$0.343893\pi$
$7$	−1.00000	+	3.73205i	−0.377964	+	1.41058i	−0.848965	+	0.528450i	$0.822774\pi$
$8$			1.73205i			0.612372i
$9$	2.23205	−	3.86603i	0.744017	−	1.28868i
$10$	2.59808	+	1.50000i	0.821584	+	0.474342i
$11$	−3.00000	+	3.00000i	−0.904534	+	0.904534i	−0.995824	−	0.0912903i	$-0.970901\pi$
$11$	−3.00000	+	3.00000i	−0.904534	+	0.904534i	0.0912903	+	0.995824i	$0.470901\pi$
$12$	−2.36603	−	1.36603i	−0.683013	−	0.394338i
$13$	1.36603	−	1.36603i	0.378867	−	0.378867i	−0.491826	−	0.870693i	$-0.663670\pi$
$13$	1.36603	−	1.36603i	0.378867	−	0.378867i	0.870693	+	0.491826i	$0.163670\pi$
$14$	4.73205	−	4.73205i	1.26469	−	1.26469i
$15$	4.09808	−	2.36603i	1.05812	−	0.610905i
$16$	2.50000	−	4.33013i	0.625000	−	1.08253i
$17$	−3.23205	+	5.59808i	−0.783887	+	1.35773i	0.145774	+	0.989318i	$0.453433\pi$
$17$	−3.23205	+	5.59808i	−0.783887	+	1.35773i	−0.929661	+	0.368415i	$0.879901\pi$
$18$	−6.69615	+	3.86603i	−1.57830	+	0.911231i
$19$	0.732051	−	0.732051i	0.167944	−	0.167944i	−0.618131	−	0.786075i	$-0.712110\pi$
$19$	0.732051	−	0.732051i	0.167944	−	0.167944i	0.786075	+	0.618131i	$0.212110\pi$
$20$	−0.866025	−	1.50000i	−0.193649	−	0.335410i
$21$	−2.73205	−	10.1962i	−0.596182	−	2.22498i
$22$	7.09808	−	1.90192i	1.51331	−	0.405492i
$23$	4.09808	+	2.36603i	0.854508	+	0.493350i	0.862169	−	0.506620i	$-0.169105\pi$
$23$	4.09808	+	2.36603i	0.854508	+	0.493350i	−0.00766135	+	0.999971i	$0.502439\pi$
$24$	−2.36603	−	4.09808i	−0.482963	−	0.836516i
$25$	−2.00000			−0.400000
$26$	−3.23205	+	0.866025i	−0.633857	+	0.169842i
$27$			4.00000i			0.769800i
$28$	−3.73205	+	1.00000i	−0.705291	+	0.188982i
$29$	−7.09808	−	1.90192i	−1.31808	−	0.353178i	−0.469822	−	0.882761i	$-0.655682\pi$
$29$	−7.09808	−	1.90192i	−1.31808	−	0.353178i	−0.848258	+	0.529583i	$0.822348\pi$
$30$	−8.19615			−1.49641
$31$	−2.26795	−	2.26795i	−0.407336	−	0.407336i	0.473473	−	0.880808i	$-0.343000\pi$
$31$	−2.26795	−	2.26795i	−0.407336	−	0.407336i	−0.880808	+	0.473473i	$0.843000\pi$
$32$	−4.50000	+	2.59808i	−0.795495	+	0.459279i
$33$	3.00000	−	11.1962i	0.522233	−	1.94900i
$34$	9.69615	−	5.59808i	1.66288	−	0.960062i
$35$	1.73205	−	6.46410i	0.292770	−	1.09263i
$36$	4.46410			0.744017
$37$	−2.90192	−	10.8301i	−0.477073	−	1.78046i	−0.613372	−	0.789794i	$-0.710187\pi$
$37$	−2.90192	−	10.8301i	−0.477073	−	1.78046i	0.136299	−	0.990668i	$-0.456479\pi$
$38$	−1.73205	+	0.464102i	−0.280976	+	0.0752872i
$39$	−1.36603	+	5.09808i	−0.218739	+	0.816346i
$40$		−	3.00000i		−	0.474342i
$41$	2.19615	−	1.26795i	0.342981	−	0.198020i	−0.318608	−	0.947886i	$-0.603215\pi$
$41$	2.19615	−	1.26795i	0.342981	−	0.198020i	0.661590	+	0.749866i	$0.269882\pi$
$42$	−4.73205	+	17.6603i	−0.730171	+	2.72504i
$43$	2.00000	+	2.00000i	0.304997	+	0.304997i	0.842965	−	0.537968i	$-0.180808\pi$
$43$	2.00000	+	2.00000i	0.304997	+	0.304997i	−0.537968	+	0.842965i	$0.680808\pi$
$44$	−4.09808	−	1.09808i	−0.617808	−	0.165541i
$45$	−3.86603	+	6.69615i	−0.576313	+	0.998203i
$46$	−4.09808	−	7.09808i	−0.604228	−	1.04655i
$47$	3.00000	+	0.803848i	0.437595	+	0.117253i	0.470889	−	0.882192i	$-0.343933\pi$
$47$	3.00000	+	0.803848i	0.437595	+	0.117253i	−0.0332942	+	0.999446i	$0.510600\pi$
$48$			13.6603i			1.97169i
$49$	−6.86603	−	3.96410i	−0.980861	−	0.566300i
$50$	3.00000	+	1.73205i	0.424264	+	0.244949i
$51$		−	17.6603i		−	2.47293i
$52$	1.86603	+	0.500000i	0.258771	+	0.0693375i
$53$	−0.464102	−	0.803848i	−0.0637493	−	0.110417i	0.832389	−	0.554191i	$-0.186972\pi$
$53$	−0.464102	−	0.803848i	−0.0637493	−	0.110417i	−0.896138	+	0.443774i	$0.853639\pi$
$54$	3.46410	−	6.00000i	0.471405	−	0.816497i
$55$	5.19615	−	5.19615i	0.700649	−	0.700649i
$56$	−6.46410	−	1.73205i	−0.863802	−	0.231455i
$57$	−0.732051	+	2.73205i	−0.0969625	+	0.361869i
$58$	9.00000	+	9.00000i	1.18176	+	1.18176i
$59$	4.26795	−	4.26795i	0.555640	−	0.555640i	−0.372423	−	0.928063i	$-0.621473\pi$
$59$	4.26795	−	4.26795i	0.555640	−	0.555640i	0.928063	+	0.372423i	$0.121473\pi$
$60$	4.09808	+	2.36603i	0.529059	+	0.305453i
$61$	7.36603	+	7.36603i	0.943123	+	0.943123i	0.998467	−	0.0553444i	$-0.0176257\pi$
$61$	7.36603	+	7.36603i	0.943123	+	0.943123i	−0.0553444	+	0.998467i	$0.517626\pi$
$62$	1.43782	+	5.36603i	0.182604	+	0.681486i
$63$	12.1962	+	12.1962i	1.53657	+	1.53657i
$64$	−1.00000			−0.125000
$65$	−2.36603	+	2.36603i	−0.293469	+	0.293469i
$66$	−14.1962	+	14.1962i	−1.74743	+	1.74743i
$67$	−1.80385	+	6.73205i	−0.220375	+	0.822451i	0.763830	+	0.645418i	$0.223317\pi$
$67$	−1.80385	+	6.73205i	−0.220375	+	0.822451i	−0.984205	+	0.177033i	$0.943350\pi$
$68$	−6.46410			−0.783887
$69$	−12.9282			−1.55637
$70$	−8.19615	+	8.19615i	−0.979628	+	0.979628i
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	−0.987294	−	0.158901i	$-0.949205\pi$
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	0.631260	+	0.775571i	$0.282538\pi$
$72$	6.69615	+	3.86603i	0.789149	+	0.455615i
$73$	14.5622	+	3.90192i	1.70437	+	0.456686i	0.974035	−	0.226399i	$-0.0726953\pi$
$73$	14.5622	+	3.90192i	1.70437	+	0.456686i	0.730339	+	0.683085i	$0.239362\pi$
$74$	−5.02628	+	18.7583i	−0.584293	+	2.18061i
$75$	4.73205	−	2.73205i	0.546410	−	0.315470i
$76$	1.00000	+	0.267949i	0.114708	+	0.0307359i
$77$	−8.19615	−	14.1962i	−0.934038	−	1.61780i
$78$	6.46410	−	6.46410i	0.731915	−	0.731915i
$79$	5.00000	−	5.00000i	0.562544	−	0.562544i	−0.367485	−	0.930029i	$-0.619781\pi$
$79$	5.00000	−	5.00000i	0.562544	−	0.562544i	0.930029	+	0.367485i	$0.119781\pi$
$80$	−4.33013	+	7.50000i	−0.484123	+	0.838525i
$81$	1.23205	+	2.13397i	0.136895	+	0.237108i
$82$	−4.39230			−0.485049
$83$	−1.26795			−0.139176			−0.0695878	−	0.997576i	$-0.522168\pi$
$83$	−1.26795			−0.139176			−0.0695878	+	0.997576i	$0.522168\pi$
$84$	7.46410	−	7.46410i	0.814400	−	0.814400i
$85$	5.59808	−	9.69615i	0.607197	−	1.05170i
$86$	−1.26795	−	4.73205i	−0.136726	−	0.510270i
$87$	19.3923	−	5.19615i	2.07907	−	0.557086i
$88$	−5.19615	−	5.19615i	−0.553912	−	0.553912i
$89$	−12.9282			−1.37039			−0.685193	−	0.728361i	$-0.740282\pi$
$89$	−12.9282			−1.37039			−0.685193	+	0.728361i	$0.740282\pi$
$90$	11.5981	−	6.69615i	1.22254	−	0.705836i
$91$	3.73205	+	6.46410i	0.391225	+	0.677622i
$92$			4.73205i			0.493350i
$93$	8.46410	+	2.26795i	0.877686	+	0.235175i
$94$	−3.80385	−	3.80385i	−0.392337	−	0.392337i
$95$	−1.26795	+	1.26795i	−0.130089	+	0.130089i
$96$	7.09808	−	12.2942i	0.724444	−	1.25477i
$97$	−14.7942	−	3.96410i	−1.50213	−	0.402494i	−0.588315	−	0.808632i	$-0.700208\pi$
$97$	−14.7942	−	3.96410i	−1.50213	−	0.402494i	−0.913812	+	0.406138i	$0.866875\pi$
$98$	6.86603	+	11.8923i	0.693573	+	1.20130i
$99$	4.90192	+	18.2942i	0.492662	+	1.83864i
$100$	−1.00000	−	1.73205i	−0.100000	−	0.173205i
$101$	8.19615	−	14.1962i	0.815548	−	1.41257i	−0.0933864	−	0.995630i	$-0.529769\pi$
$101$	8.19615	−	14.1962i	0.815548	−	1.41257i	0.908934	−	0.416940i	$-0.136897\pi$
$102$	−15.2942	+	26.4904i	−1.51435	+	2.62294i
$103$			1.80385i			0.177738i	0.996043	+	0.0888692i	$0.0283253\pi$
$103$			1.80385i			0.177738i	−0.996043	+	0.0888692i	$0.971675\pi$
$104$	2.36603	+	2.36603i	0.232008	+	0.232008i
$105$	4.73205	+	17.6603i	0.461801	+	1.72346i
$106$			1.60770i			0.156153i
$107$	−0.464102	−	1.73205i	−0.0448664	−	0.167444i	0.939857	−	0.341567i	$-0.110958\pi$
$107$	−0.464102	−	1.73205i	−0.0448664	−	0.167444i	−0.984724	+	0.174123i	$0.944291\pi$
$108$	−3.46410	+	2.00000i	−0.333333	+	0.192450i
$109$	13.1603	+	7.59808i	1.26052	+	0.727764i	0.973176	−	0.230063i	$-0.0738931\pi$
$109$	13.1603	+	7.59808i	1.26052	+	0.727764i	0.287348	+	0.957826i	$0.407226\pi$
$110$	−12.2942	+	3.29423i	−1.17221	+	0.314092i
$111$	21.6603	+	21.6603i	2.05590	+	2.05590i
$112$	13.6603	+	13.6603i	1.29077	+	1.29077i
$113$	1.09808	−	0.294229i	0.103298	−	0.0276787i	−0.206800	−	0.978383i	$-0.566305\pi$
$113$	1.09808	−	0.294229i	0.103298	−	0.0276787i	0.310098	+	0.950705i	$0.399638\pi$
$114$	3.46410	−	3.46410i	0.324443	−	0.324443i
$115$	−7.09808	−	4.09808i	−0.661899	−	0.382148i
$116$	−1.90192	−	7.09808i	−0.176589	−	0.659040i
$117$	−2.23205	−	8.33013i	−0.206353	−	0.770121i
$118$	−10.0981	+	2.70577i	−0.929603	+	0.249086i
$119$	−17.6603	−	17.6603i	−1.61891	−	1.61891i
$120$	4.09808	+	7.09808i	0.374101	+	0.647963i
$121$		−	7.00000i		−	0.636364i
$122$	−4.66987	−	17.4282i	−0.422790	−	1.57788i
$123$	−3.46410	+	6.00000i	−0.312348	+	0.541002i
$124$	0.830127	−	3.09808i	0.0745476	−	0.278215i
$125$	12.1244			1.08444
$126$	−7.73205	−	28.8564i	−0.688826	−	2.57073i
$127$	1.00000	+	0.267949i	0.0887357	+	0.0237766i	0.302914	−	0.953018i	$-0.402041\pi$
$127$	1.00000	+	0.267949i	0.0887357	+	0.0237766i	−0.214178	+	0.976795i	$0.568707\pi$
$128$	10.5000	+	6.06218i	0.928078	+	0.535826i
$129$	−7.46410	−	2.00000i	−0.657178	−	0.176090i
$130$	5.59808	−	1.50000i	0.490984	−	0.131559i
$131$	7.90192	−	4.56218i	0.690394	−	0.398599i	−0.113365	−	0.993553i	$-0.536163\pi$
$131$	7.90192	−	4.56218i	0.690394	−	0.398599i	0.803760	+	0.594954i	$0.202830\pi$
$132$	11.1962	−	3.00000i	0.974500	−	0.261116i
$133$	2.00000	+	3.46410i	0.173422	+	0.300376i
$134$	8.53590	−	8.53590i	0.737389	−	0.737389i
$135$		−	6.92820i		−	0.596285i
$136$	−9.69615	−	5.59808i	−0.831438	−	0.480031i
$137$	−4.79423	−	8.30385i	−0.409599	−	0.709446i	0.585246	−	0.810856i	$-0.300998\pi$
$137$	−4.79423	−	8.30385i	−0.409599	−	0.709446i	−0.994845	+	0.101410i	$0.967665\pi$
$138$	19.3923	+	11.1962i	1.65078	+	0.953080i
$139$	1.09808	−	1.90192i	0.0931376	−	0.161319i	−0.815692	−	0.578486i	$-0.803644\pi$
$139$	1.09808	−	1.90192i	0.0931376	−	0.161319i	0.908830	+	0.417167i	$0.136977\pi$
$140$	6.46410	−	1.73205i	0.546316	−	0.146385i
$141$	−8.19615	+	2.19615i	−0.690241	+	0.184949i
$142$	9.00000	−	5.19615i	0.755263	−	0.436051i
$143$			8.19615i			0.685397i
$144$	−11.1603	−	19.3301i	−0.930021	−	1.61084i
$145$	12.2942	+	3.29423i	1.02098	+	0.273571i
$146$	−18.4641	−	18.4641i	−1.52810	−	1.52810i
$147$	21.6603			1.78651
$148$	7.92820	−	7.92820i	0.651694	−	0.651694i
$149$	−13.3301	−	3.57180i	−1.09205	−	0.292613i	−0.332525	−	0.943095i	$-0.607900\pi$
$149$	−13.3301	−	3.57180i	−1.09205	−	0.292613i	−0.759522	+	0.650482i	$0.774567\pi$
$150$	−9.46410			−0.772741
$151$	−15.3923	−	15.3923i	−1.25261	−	1.25261i	−0.954547	−	0.298061i	$-0.903660\pi$
$151$	−15.3923	−	15.3923i	−1.25261	−	1.25261i	−0.298061	−	0.954547i	$-0.596340\pi$
$152$	1.26795	+	1.26795i	0.102844	+	0.102844i
$153$	14.4282	+	24.9904i	1.16645	+	2.02035i
$154$			28.3923i			2.28792i
$155$	3.92820	+	3.92820i	0.315521	+	0.315521i
$156$	−5.09808	+	1.36603i	−0.408173	+	0.109370i
$157$	5.06218	−	18.8923i	0.404006	−	1.50777i	−0.401876	−	0.915694i	$-0.631642\pi$
$157$	5.06218	−	18.8923i	0.404006	−	1.50777i	0.805882	−	0.592076i	$-0.201692\pi$
$158$	−11.8301	+	3.16987i	−0.941154	+	0.252182i
$159$	2.19615	+	1.26795i	0.174166	+	0.100555i
$160$	7.79423	−	4.50000i	0.616188	−	0.355756i
$161$	−12.9282	+	12.9282i	−1.01889	+	1.01889i
$162$		−	4.26795i		−	0.335322i
$163$	−21.1244	+	12.1962i	−1.65459	+	0.955276i	−0.679436	+	0.733734i	$0.737776\pi$
$163$	−21.1244	+	12.1962i	−1.65459	+	0.955276i	−0.975151	+	0.221542i	$0.928891\pi$
$164$	2.19615	+	1.26795i	0.171491	+	0.0990102i
$165$	−5.19615	+	19.3923i	−0.404520	+	1.50969i
$166$	1.90192	+	1.09808i	0.147618	+	0.0852272i
$167$	−2.36603	+	4.09808i	−0.183089	+	0.317119i	−0.942931	−	0.332989i	$-0.891943\pi$
$167$	−2.36603	+	4.09808i	−0.183089	+	0.317119i	0.759842	+	0.650108i	$0.225276\pi$
$168$	17.6603	−	4.73205i	1.36252	−	0.365086i
$169$			9.26795i			0.712919i
$170$	−16.7942	+	9.69615i	−1.28806	+	0.743661i
$171$	−1.19615	−	4.46410i	−0.0914721	−	0.341378i
$172$	−0.732051	+	2.73205i	−0.0558184	+	0.208317i
$173$	−18.7583	−	5.02628i	−1.42617	−	0.382141i	−0.538501	−	0.842625i	$-0.681009\pi$
$173$	−18.7583	−	5.02628i	−1.42617	−	0.382141i	−0.887668	+	0.460484i	$0.847676\pi$
$174$	−33.5885	−	9.00000i	−2.54633	−	0.682288i
$175$	2.00000	−	7.46410i	0.151186	−	0.564233i
$176$	5.49038	+	20.4904i	0.413853	+	1.54452i
$177$	−4.26795	+	15.9282i	−0.320799	+	1.19724i
$178$	19.3923	+	11.1962i	1.45351	+	0.839187i
$179$	−7.09808	−	12.2942i	−0.530535	−	0.918914i	−0.999365	−	0.0356254i	$-0.988658\pi$
$179$	−7.09808	−	12.2942i	−0.530535	−	0.918914i	0.468830	−	0.883288i	$-0.344676\pi$
$180$	−7.73205			−0.576313
$181$	−7.69615	+	2.06218i	−0.572051	+	0.153280i	−0.533237	−	0.845966i	$-0.679025\pi$
$181$	−7.69615	+	2.06218i	−0.572051	+	0.153280i	−0.0388137	+	0.999246i	$0.512358\pi$
$182$		−	12.9282i		−	0.958302i
$183$	−27.4904	−	7.36603i	−2.03215	−	0.544512i
$184$	−4.09808	+	7.09808i	−0.302114	+	0.523277i
$185$	5.02628	+	18.7583i	0.369539	+	1.37914i
$186$	−10.7321	−	10.7321i	−0.786912	−	0.786912i
$187$	−7.09808	−	26.4904i	−0.519063	−	1.93717i
$188$	0.803848	+	3.00000i	0.0586266	+	0.218797i
$189$	−14.9282	−	4.00000i	−1.08587	−	0.290957i
$190$	3.00000	−	0.803848i	0.217643	−	0.0583172i
$191$	−1.09808	−	1.90192i	−0.0794540	−	0.137618i	0.823560	−	0.567228i	$-0.191984\pi$
$191$	−1.09808	−	1.90192i	−0.0794540	−	0.137618i	−0.903014	+	0.429610i	$0.858651\pi$
$192$	2.36603	−	1.36603i	0.170753	−	0.0985844i
$193$	0.803848			0.0578622			0.0289311	−	0.999581i	$-0.490790\pi$
$193$	0.803848			0.0578622			0.0289311	+	0.999581i	$0.490790\pi$
$194$	18.7583	+	18.7583i	1.34677	+	1.34677i
$195$	2.36603	−	8.83013i	0.169435	−	0.632339i
$196$		−	7.92820i		−	0.566300i
$197$	−3.46410	+	6.00000i	−0.246807	+	0.427482i	−0.962638	−	0.270791i	$-0.912715\pi$
$197$	−3.46410	+	6.00000i	−0.246807	+	0.427482i	0.715831	+	0.698273i	$0.246048\pi$
$198$	8.49038	−	31.6865i	0.603385	−	2.25186i
$199$	−6.36603	+	23.7583i	−0.451276	+	1.68418i	0.247537	+	0.968878i	$0.420379\pi$
$199$	−6.36603	+	23.7583i	−0.451276	+	1.68418i	−0.698812	+	0.715305i	$0.746288\pi$
$200$		−	3.46410i		−	0.244949i
$201$	−4.92820	−	18.3923i	−0.347609	−	1.29729i
$202$	−24.5885	+	14.1962i	−1.73004	+	0.998838i
$203$	14.1962	−	24.5885i	0.996375	−	1.72577i
$204$	15.2942	−	8.83013i	1.07081	−	0.618233i
$205$	−3.80385	+	2.19615i	−0.265672	+	0.153386i
$206$	1.56218	−	2.70577i	0.108842	−	0.188520i
$207$	18.2942	−	10.5622i	1.27154	−	0.734122i
$208$	−2.50000	−	9.33013i	−0.173344	−	0.646928i
$209$			4.39230i			0.303822i
$210$	8.19615	−	30.5885i	0.565588	−	2.11080i
$211$	6.66025	−	24.8564i	0.458511	−	1.71119i	−0.219045	−	0.975715i	$-0.570294\pi$
$211$	6.66025	−	24.8564i	0.458511	−	1.71119i	0.677556	−	0.735471i	$-0.263039\pi$
$212$	0.464102	−	0.803848i	0.0318746	−	0.0552085i
$213$		−	16.3923i		−	1.12318i
$214$	−0.803848	+	3.00000i	−0.0549499	+	0.205076i
$215$	−3.46410	−	3.46410i	−0.236250	−	0.236250i
$216$	−6.92820			−0.471405
$217$	10.7321	−	6.19615i	0.728539	−	0.420622i
$218$	−13.1603	−	22.7942i	−0.891325	−	1.54382i
$219$	−39.7846	+	10.6603i	−2.68839	+	0.720353i
$220$	7.09808	+	1.90192i	0.478552	+	0.128228i
$221$	3.23205	+	12.0622i	0.217411	+	0.811390i
$222$	−13.7321	−	51.2487i	−0.921635	−	3.43959i
$223$	18.3205	+	18.3205i	1.22683	+	1.22683i	0.965156	+	0.261676i	$0.0842753\pi$
$223$	18.3205	+	18.3205i	1.22683	+	1.22683i	0.261676	+	0.965156i	$0.415725\pi$
$224$	−5.19615	−	19.3923i	−0.347183	−	1.29570i
$225$	−4.46410	+	7.73205i	−0.297607	+	0.515470i
$226$	−1.90192	−	0.509619i	−0.126514	−	0.0338993i
$227$			27.1244i			1.80031i	0.435573	+	0.900153i	$0.356546\pi$
$227$			27.1244i			1.80031i	−0.435573	+	0.900153i	$0.643454\pi$
$228$	−2.73205	+	0.732051i	−0.180934	+	0.0484812i
$229$	6.46410			0.427160			0.213580	−	0.976926i	$-0.431488\pi$
$229$	6.46410			0.427160			0.213580	+	0.976926i	$0.431488\pi$
$230$	7.09808	+	12.2942i	0.468033	+	0.810657i
$231$	38.7846	+	22.3923i	2.55184	+	1.47331i
$232$	3.29423	−	12.2942i	0.216277	−	0.807156i
$233$	4.37564	+	16.3301i	0.286658	+	1.06982i	0.947619	+	0.319402i	$0.103482\pi$
$233$	4.37564	+	16.3301i	0.286658	+	1.06982i	−0.660961	+	0.750420i	$0.729851\pi$
$234$	−3.86603	+	14.4282i	−0.252730	+	0.943201i
$235$	−5.19615	−	1.39230i	−0.338960	−	0.0908240i
$236$	5.83013	+	1.56218i	0.379509	+	0.101689i
$237$	−5.00000	+	18.6603i	−0.324785	+	1.21211i
$238$	11.1962	+	41.7846i	0.725739	+	2.70849i
$239$	−5.70577	+	3.29423i	−0.369076	+	0.213086i	−0.673055	−	0.739593i	$-0.735018\pi$
$239$	−5.70577	+	3.29423i	−0.369076	+	0.213086i	0.303979	+	0.952679i	$0.401685\pi$
$240$		−	23.6603i		−	1.52726i
$241$	15.4282	−	4.13397i	0.993818	−	0.266293i	0.274965	−	0.961454i	$-0.411334\pi$
$241$	15.4282	−	4.13397i	0.993818	−	0.266293i	0.718853	+	0.695162i	$0.244667\pi$
$242$	−6.06218	+	10.5000i	−0.389692	+	0.674966i
$243$	−16.2224	−	9.36603i	−1.04067	−	0.600831i
$244$	−2.69615	+	10.0622i	−0.172603	+	0.644165i
$245$	11.8923	+	6.86603i	0.759771	+	0.438654i
$246$	10.3923	−	6.00000i	0.662589	−	0.382546i
$247$		−	2.00000i		−	0.127257i
$248$	3.92820	−	3.92820i	0.249441	−	0.249441i
$249$	3.00000	−	1.73205i	0.190117	−	0.109764i
$250$	−18.1865	−	10.5000i	−1.15022	−	0.664078i
$251$	24.7583	−	6.63397i	1.56273	−	0.418733i	0.629205	−	0.777240i	$-0.283381\pi$
$251$	24.7583	−	6.63397i	1.56273	−	0.418733i	0.933527	+	0.358507i	$0.116714\pi$
$252$	−4.46410	+	16.6603i	−0.281212	+	1.04950i
$253$	−19.3923	+	5.19615i	−1.21918	+	0.326679i
$254$	−1.26795	−	1.26795i	−0.0795582	−	0.0795582i
$255$			30.5885i			1.91552i
$256$	−9.50000	−	16.4545i	−0.593750	−	1.02841i
$257$	−13.9019	−	13.9019i	−0.867178	−	0.867178i	0.124981	−	0.992159i	$-0.460113\pi$
$257$	−13.9019	−	13.9019i	−0.867178	−	0.867178i	−0.992159	+	0.124981i	$0.960113\pi$
$258$	9.46410	+	9.46410i	0.589209	+	0.589209i
$259$	43.3205			2.69181
$260$	−3.23205	−	0.866025i	−0.200443	−	0.0537086i
$261$	−23.1962	+	23.1962i	−1.43581	+	1.43581i
$262$	−15.8038			−0.976365
$263$	−10.3923	−	10.3923i	−0.640817	−	0.640817i	0.309939	−	0.950756i	$-0.399691\pi$
$263$	−10.3923	−	10.3923i	−0.640817	−	0.640817i	−0.950756	+	0.309939i	$0.899691\pi$
$264$	19.3923	+	5.19615i	1.19351	+	0.319801i
$265$	0.803848	+	1.39230i	0.0493800	+	0.0855286i
$266$		−	6.92820i		−	0.424795i
$267$	30.5885	−	17.6603i	1.87198	−	1.08079i
$268$	−6.73205	+	1.80385i	−0.411225	+	0.110188i
$269$	14.2583	−	3.82051i	0.869346	−	0.232940i	0.203541	−	0.979066i	$-0.434755\pi$
$269$	14.2583	−	3.82051i	0.869346	−	0.232940i	0.665805	+	0.746126i	$0.268088\pi$
$270$	−6.00000	+	10.3923i	−0.365148	+	0.632456i
$271$	−17.3205	−	10.0000i	−1.05215	−	0.607457i	−0.128897	−	0.991658i	$-0.541144\pi$
$271$	−17.3205	−	10.0000i	−1.05215	−	0.607457i	−0.923249	+	0.384201i	$0.874477\pi$
$272$	16.1603	+	27.9904i	0.979859	+	1.69717i
$273$	−17.6603	−	10.1962i	−1.06885	−	0.617099i
$274$			16.6077i			1.00331i
$275$	6.00000	−	6.00000i	0.361814	−	0.361814i
$276$	−6.46410	−	11.1962i	−0.389093	−	0.673929i
$277$	−3.83013	+	1.02628i	−0.230130	+	0.0616632i	−0.372041	−	0.928216i	$-0.621342\pi$
$277$	−3.83013	+	1.02628i	−0.230130	+	0.0616632i	0.141911	+	0.989879i	$0.454675\pi$
$278$	−3.29423	+	1.90192i	−0.197575	+	0.114070i
$279$	−13.8301	+	3.70577i	−0.827988	+	0.221859i
$280$	11.1962	+	3.00000i	0.669098	+	0.179284i
$281$	−0.401924	−	0.232051i	−0.0239768	−	0.0138430i	0.487964	−	0.872864i	$-0.337740\pi$
$281$	−0.401924	−	0.232051i	−0.0239768	−	0.0138430i	−0.511940	+	0.859021i	$0.671073\pi$
$282$	14.1962	+	3.80385i	0.845369	+	0.226516i
$283$	2.29423	+	8.56218i	0.136378	+	0.508969i	0.999988	+	0.00480938i	$0.00153088\pi$
$283$	2.29423	+	8.56218i	0.136378	+	0.508969i	−0.863611	+	0.504159i	$0.831802\pi$
$284$	−6.00000			−0.356034
$285$	1.26795	−	4.73205i	0.0751068	−	0.280302i
$286$	7.09808	−	12.2942i	0.419718	−	0.726973i
$287$	2.53590	+	9.46410i	0.149689	+	0.558648i
$288$			23.1962i			1.36685i
$289$	−12.3923	−	21.4641i	−0.728959	−	1.26259i
$290$	−15.5885	−	15.5885i	−0.915386	−	0.915386i
$291$	40.4186	−	10.8301i	2.36938	−	0.634873i
$292$	3.90192	+	14.5622i	0.228343	+	0.852187i
$293$	−3.06218	−	11.4282i	−0.178894	−	0.667643i	−0.995855	−	0.0909500i	$-0.971010\pi$
$293$	−3.06218	−	11.4282i	−0.178894	−	0.667643i	0.816961	−	0.576693i	$-0.195657\pi$
$294$	−32.4904	−	18.7583i	−1.89488	−	1.09401i
$295$	−7.39230	+	7.39230i	−0.430397	+	0.430397i
$296$	18.7583	−	5.02628i	1.09031	−	0.292147i
$297$	−12.0000	−	12.0000i	−0.696311	−	0.696311i
$298$	16.9019	+	16.9019i	0.979102	+	0.979102i
$299$	8.83013	−	2.36603i	0.510659	−	0.136831i
$300$	4.73205	+	2.73205i	0.273205	+	0.157735i
$301$	−9.46410	+	5.46410i	−0.545502	+	0.314946i
$302$	9.75833	+	36.4186i	0.561529	+	2.09565i
$303$			44.7846i			2.57281i
$304$	−1.33975	−	5.00000i	−0.0768397	−	0.286770i
$305$	−12.7583	−	12.7583i	−0.730540	−	0.730540i
$306$		−	49.9808i		−	2.85721i
$307$	−5.09808	+	8.83013i	−0.290963	+	0.503962i	−0.974038	−	0.226386i	$-0.927309\pi$
$307$	−5.09808	+	8.83013i	−0.290963	+	0.503962i	0.683075	+	0.730348i	$0.260642\pi$
$308$	8.19615	−	14.1962i	0.467019	−	0.808901i
$309$	−2.46410	−	4.26795i	−0.140178	−	0.242795i
$310$	−2.49038	−	9.29423i	−0.141444	−	0.527877i
$311$	0.928203	+	1.60770i	0.0526336	+	0.0911640i	0.891142	−	0.453725i	$-0.149905\pi$
$311$	0.928203	+	1.60770i	0.0526336	+	0.0911640i	−0.838508	+	0.544889i	$0.816572\pi$
$312$	−8.83013	−	2.36603i	−0.499908	−	0.133950i
$313$	1.00000	−	1.73205i	0.0565233	−	0.0979013i	−0.836379	−	0.548151i	$-0.815332\pi$
$313$	1.00000	−	1.73205i	0.0565233	−	0.0979013i	0.892903	+	0.450250i	$0.148665\pi$
$314$	−23.9545	+	23.9545i	−1.35183	+	1.35183i
$315$	−21.1244	−	21.1244i	−1.19022	−	1.19022i
$316$	6.83013	+	1.83013i	0.384225	+	0.102953i
$317$		−	17.1962i		−	0.965832i	−0.875667	−	0.482916i	$-0.839578\pi$
$317$		−	17.1962i		−	0.965832i	0.875667	−	0.482916i	$-0.160422\pi$
$318$	−2.19615	−	3.80385i	−0.123154	−	0.213309i
$319$	27.0000	−	15.5885i	1.51171	−	0.872786i
$320$	1.73205			0.0968246
$321$	3.46410	+	3.46410i	0.193347	+	0.193347i
$322$	30.5885	−	8.19615i	1.70463	−	0.456754i
$323$	1.73205	+	6.46410i	0.0963739	+	0.359672i
$324$	−1.23205	+	2.13397i	−0.0684473	+	0.118554i
$325$	−2.73205	+	2.73205i	−0.151547	+	0.151547i
$326$	42.2487			2.33994
$327$	−41.5167			−2.29588
$328$	2.19615	+	3.80385i	0.121262	+	0.210032i
$329$	−6.00000	+	10.3923i	−0.330791	+	0.572946i
$330$	24.5885	−	24.5885i	1.35355	−	1.35355i
$331$	−4.80385	+	4.80385i	−0.264043	+	0.264043i	−0.826694	−	0.562651i	$-0.809781\pi$
$331$	−4.80385	+	4.80385i	−0.264043	+	0.264043i	0.562651	+	0.826694i	$0.309781\pi$
$332$	−0.633975	−	1.09808i	−0.0347939	−	0.0602648i
$333$	−48.3468	−	12.9545i	−2.64939	−	0.709901i
$334$	7.09808	−	4.09808i	0.388389	−	0.224237i
$335$	3.12436	−	11.6603i	0.170702	−	0.637068i
$336$	−50.9808	−	13.6603i	−2.78123	−	0.745228i
$337$	−3.58846	−	2.07180i	−0.195476	−	0.112858i	0.399068	−	0.916921i	$-0.369334\pi$
$337$	−3.58846	−	2.07180i	−0.195476	−	0.112858i	−0.594543	+	0.804064i	$0.702667\pi$
$338$	8.02628	−	13.9019i	0.436572	−	0.756165i
$339$	−2.19615	+	2.19615i	−0.119279	+	0.119279i
$340$	11.1962			0.607197
$341$	13.6077			0.736898
$342$	−2.07180	+	7.73205i	−0.112030	+	0.418101i
$343$	2.53590	−	2.53590i	0.136926	−	0.136926i
$344$	−3.46410	+	3.46410i	−0.186772	+	0.186772i
$345$	22.3923			1.20556
$346$	23.7846	+	23.7846i	1.27867	+	1.27867i
$347$	−3.80385	−	14.1962i	−0.204201	−	0.762089i	−0.989692	−	0.143215i	$-0.954256\pi$
$347$	−3.80385	−	14.1962i	−0.204201	−	0.762089i	0.785490	−	0.618874i	$-0.212411\pi$
$348$	14.1962	+	14.1962i	0.760994	+	0.760994i
$349$	−0.696152	−	0.401924i	−0.0372642	−	0.0215145i	0.481252	−	0.876582i	$-0.340182\pi$
$349$	−0.696152	−	0.401924i	−0.0372642	−	0.0215145i	−0.518516	+	0.855068i	$0.673515\pi$
$350$	−9.46410	+	9.46410i	−0.505878	+	0.505878i
$351$	5.46410	+	5.46410i	0.291652	+	0.291652i
$352$	5.70577	−	21.2942i	0.304119	−	1.13499i
$353$	14.4282	+	3.86603i	0.767936	+	0.205768i	0.621459	−	0.783446i	$-0.286540\pi$
$353$	14.4282	+	3.86603i	0.767936	+	0.205768i	0.146476	+	0.989214i	$0.453207\pi$
$354$	20.1962	−	20.1962i	1.07341	−	1.07341i
$355$	5.19615	−	9.00000i	0.275783	−	0.477670i
$356$	−6.46410	−	11.1962i	−0.342597	−	0.593395i
$357$	65.9090	+	17.6603i	3.48827	+	0.934680i
$358$			24.5885i			1.29954i
$359$	13.3923	+	7.73205i	0.706819	+	0.408082i	0.809882	−	0.586593i	$-0.199531\pi$
$359$	13.3923	+	7.73205i	0.706819	+	0.408082i	−0.103063	+	0.994675i	$0.532864\pi$
$360$	−11.5981	−	6.69615i	−0.611272	−	0.352918i
$361$			17.9282i			0.943590i
$362$	13.3301	+	3.57180i	0.700616	+	0.187729i
$363$	9.56218	+	16.5622i	0.501884	+	0.869289i
$364$	−3.73205	+	6.46410i	−0.195613	+	0.338811i
$365$	−25.2224	−	6.75833i	−1.32020	−	0.353747i
$366$	34.8564	+	34.8564i	1.82197	+	1.82197i
$367$	−3.19615	+	11.9282i	−0.166838	+	0.622647i	0.830961	+	0.556331i	$0.187791\pi$
$367$	−3.19615	+	11.9282i	−0.166838	+	0.622647i	−0.997799	+	0.0663163i	$0.978875\pi$
$368$	20.4904	−	11.8301i	1.06813	−	0.616688i
$369$		−	11.3205i		−	0.589322i
$370$	8.70577	−	32.4904i	0.452592	−	1.68909i
$371$	3.46410	−	0.928203i	0.179847	−	0.0481899i
$372$	2.26795	+	8.46410i	0.117588	+	0.438843i
$373$	−37.0526			−1.91851			−0.959254	−	0.282544i	$-0.908822\pi$
$373$	−37.0526			−1.91851			−0.959254	+	0.282544i	$0.908822\pi$
$374$	−12.2942	+	45.8827i	−0.635719	+	2.37254i
$375$	−28.6865	+	16.5622i	−1.48137	+	0.855267i
$376$	−1.39230	+	5.19615i	−0.0718026	+	0.267971i
$377$	−12.2942	+	7.09808i	−0.633185	+	0.365570i
$378$	18.9282	+	18.9282i	0.973562	+	0.973562i
$379$	−13.8038			−0.709056			−0.354528	−	0.935045i	$-0.615358\pi$
$379$	−13.8038			−0.709056			−0.354528	+	0.935045i	$0.615358\pi$
$380$	−1.73205	−	0.464102i	−0.0888523	−	0.0238079i
$381$	−2.73205	+	0.732051i	−0.139967	+	0.0375041i
$382$			3.80385i			0.194622i
$383$	16.3923	−	4.39230i	0.837608	−	0.224436i	0.185578	−	0.982630i	$-0.440584\pi$
$383$	16.3923	−	4.39230i	0.837608	−	0.224436i	0.652030	+	0.758193i	$0.273918\pi$
$384$	−33.1244			−1.69037
$385$	14.1962	+	24.5885i	0.723503	+	1.25314i
$386$	−1.20577	−	0.696152i	−0.0613721	−	0.0354332i
$387$	12.1962	−	3.26795i	0.619965	−	0.166119i
$388$	−3.96410	−	14.7942i	−0.201247	−	0.751063i
$389$	1.66987	+	2.89230i	0.0846659	+	0.146646i	0.905249	−	0.424882i	$-0.139684\pi$
$389$	1.66987	+	2.89230i	0.0846659	+	0.146646i	−0.820583	+	0.571528i	$0.806351\pi$
$390$	−11.1962	+	11.1962i	−0.566939	+	0.566939i
$391$	−26.4904	+	15.2942i	−1.33968	+	0.773462i
$392$	6.86603	−	11.8923i	0.346787	−	0.600652i
$393$	−12.4641	+	21.5885i	−0.628731	+	1.08899i
$394$	10.3923	−	6.00000i	0.523557	−	0.302276i
$395$	−8.66025	+	8.66025i	−0.435745	+	0.435745i
$396$	−13.3923	+	13.3923i	−0.672989	+	0.672989i
$397$	−14.5981	−	8.42820i	−0.732656	−	0.422999i	0.0867368	−	0.996231i	$-0.472356\pi$
$397$	−14.5981	−	8.42820i	−0.732656	−	0.422999i	−0.819393	+	0.573232i	$0.805689\pi$
$398$	30.1244	−	30.1244i	1.51000	−	1.51000i
$399$	−9.46410	−	5.46410i	−0.473798	−	0.273547i
$400$	−5.00000	+	8.66025i	−0.250000	+	0.433013i
$401$			0.803848i			0.0401422i	0.999799	+	0.0200711i	$0.00638926\pi$
$401$			0.803848i			0.0401422i	−0.999799	+	0.0200711i	$0.993611\pi$
$402$	−8.53590	+	31.8564i	−0.425732	+	1.58885i
$403$	−6.19615			−0.308652
$404$	16.3923			0.815548
$405$	−2.13397	−	3.69615i	−0.106038	−	0.183663i
$406$	−42.5885	+	24.5885i	−2.11363	+	1.22030i
$407$	41.1962	+	23.7846i	2.04202	+	1.17896i
$408$	30.5885			1.51435
$409$	−3.00000	−	20.0000i	−0.148340	−	0.988936i
$409$	−3.00000	−	20.0000i	−0.148340	−	0.988936i
$410$	7.60770			0.375717
$411$	22.6865	+	13.0981i	1.11904	+	0.646080i
$412$	−1.56218	+	0.901924i	−0.0769630	+	0.0444346i
$413$	11.6603	+	20.1962i	0.573764	+	0.993788i
$414$	−36.5885			−1.79822
$415$	2.19615			0.107805
$416$	−2.59808	+	9.69615i	−0.127381	+	0.475393i
$417$			6.00000i			0.293821i
$418$	3.80385	−	6.58846i	0.186052	−	0.322252i
$419$	4.39230	+	2.53590i	0.214578	+	0.123887i	0.603437	−	0.797410i	$-0.293797\pi$
$419$	4.39230	+	2.53590i	0.214578	+	0.123887i	−0.388859	+	0.921297i	$0.627131\pi$
$420$	−12.9282	+	12.9282i	−0.630832	+	0.630832i
$421$	−14.7224	−	8.50000i	−0.717527	−	0.414265i	0.0963145	−	0.995351i	$-0.469295\pi$
$421$	−14.7224	−	8.50000i	−0.717527	−	0.414265i	−0.813842	+	0.581086i	$0.802628\pi$
$422$	−31.5167	+	31.5167i	−1.53421	+	1.53421i
$423$	9.80385	−	9.80385i	0.476679	−	0.476679i
$424$	1.39230	−	0.803848i	0.0676163	−	0.0390383i
$425$	6.46410	−	11.1962i	0.313555	−	0.543093i
$426$	−14.1962	+	24.5885i	−0.687806	+	1.19131i
$427$	−34.8564	+	20.1244i	−1.68682	+	0.973886i
$428$	1.26795	−	1.26795i	0.0612886	−	0.0612886i
$429$	−11.1962	−	19.3923i	−0.540555	−	0.936269i
$430$	2.19615	+	8.19615i	0.105908	+	0.395254i
$431$	−34.0526	+	9.12436i	−1.64025	+	0.439505i	−0.956861	−	0.290546i	$-0.906163\pi$
$431$	−34.0526	+	9.12436i	−1.64025	+	0.439505i	−0.683393	+	0.730051i	$0.739496\pi$
$432$	17.3205	+	10.0000i	0.833333	+	0.481125i
$433$	−2.13397	−	3.69615i	−0.102552	−	0.177626i	0.810183	−	0.586177i	$-0.199368\pi$
$433$	−2.13397	−	3.69615i	−0.102552	−	0.177626i	−0.912736	+	0.408551i	$0.866034\pi$
$434$	−21.4641			−1.03031
$435$	−33.5885	+	9.00000i	−1.61044	+	0.431517i
$436$			15.1962i			0.727764i
$437$	4.73205	−	1.26795i	0.226365	−	0.0606542i
$438$	68.9090	+	18.4641i	3.29260	+	0.882249i
$439$	32.9808			1.57409			0.787043	−	0.616898i	$-0.211611\pi$
$439$	32.9808			1.57409			0.787043	+	0.616898i	$0.211611\pi$
$440$	9.00000	+	9.00000i	0.429058	+	0.429058i
$441$	−30.6506	+	17.6962i	−1.45955	+	0.842674i
$442$	5.59808	−	20.8923i	0.266273	−	0.993746i
$443$	0.294229	−	0.169873i	0.0139792	−	0.00807091i	−0.492994	−	0.870033i	$-0.664098\pi$
$443$	0.294229	−	0.169873i	0.0139792	−	0.00807091i	0.506973	+	0.861962i	$0.330764\pi$
$444$	−7.92820	+	29.5885i	−0.376256	+	1.40421i
$445$	22.3923			1.06150
$446$	−11.6147	−	43.3468i	−0.549974	−	2.05253i
$447$	36.4186	−	9.75833i	1.72254	−	0.461553i
$448$	1.00000	−	3.73205i	0.0472456	−	0.176323i
$449$		−	26.6603i		−	1.25818i	−0.777334	−	0.629088i	$-0.783429\pi$
$449$		−	26.6603i		−	1.25818i	0.777334	−	0.629088i	$-0.216571\pi$
$450$	13.3923	−	7.73205i	0.631319	−	0.364492i
$451$	−2.78461	+	10.3923i	−0.131122	+	0.489355i
$452$	0.803848	+	0.803848i	0.0378098	+	0.0378098i
$453$	57.4449	+	15.3923i	2.69900	+	0.723194i
$454$	23.4904	−	40.6865i	1.10246	−	1.90951i
$455$	−6.46410	−	11.1962i	−0.303042	−	0.524884i
$456$	−4.73205	−	1.26795i	−0.221599	−	0.0593772i
$457$			10.8038i			0.505383i	0.967547	+	0.252691i	$0.0813157\pi$
$457$			10.8038i			0.505383i	−0.967547	+	0.252691i	$0.918684\pi$
$458$	−9.69615	−	5.59808i	−0.453071	−	0.261581i
$459$	−22.3923	−	12.9282i	−1.04518	−	0.603437i
$460$		−	8.19615i		−	0.382148i
$461$	8.83013	+	2.36603i	0.411260	+	0.110197i	0.458516	−	0.888686i	$-0.348381\pi$
$461$	8.83013	+	2.36603i	0.411260	+	0.110197i	−0.0472563	+	0.998883i	$0.515048\pi$
$462$	−38.7846	−	67.1769i	−1.80442	−	3.12535i
$463$	−2.80385	+	4.85641i	−0.130306	+	0.225696i	−0.923794	−	0.382889i	$-0.874929\pi$
$463$	−2.80385	+	4.85641i	−0.130306	+	0.225696i	0.793489	+	0.608585i	$0.208263\pi$
$464$	−25.9808	+	25.9808i	−1.20613	+	1.20613i
$465$	−14.6603	−	3.92820i	−0.679853	−	0.182166i
$466$	7.57884	−	28.2846i	0.351083	−	1.31026i
$467$	−8.53590	−	8.53590i	−0.394994	−	0.394994i	0.481469	−	0.876463i	$-0.340103\pi$
$467$	−8.53590	−	8.53590i	−0.394994	−	0.394994i	−0.876463	+	0.481469i	$0.840103\pi$
$468$	6.09808	−	6.09808i	0.281884	−	0.281884i
$469$	−23.3205	−	13.4641i	−1.07684	−	0.621714i
$470$	6.58846	+	6.58846i	0.303903	+	0.303903i
$471$	13.8301	+	51.6147i	0.637259	+	2.37828i
$472$	7.39230	+	7.39230i	0.340258	+	0.340258i
$473$	−12.0000			−0.551761
$474$	23.6603	−	23.6603i	1.08675	−	1.08675i
$475$	−1.46410	+	1.46410i	−0.0671776	+	0.0671776i
$476$	6.46410	−	24.1244i	0.296282	−	1.10574i
$477$	−4.14359			−0.189722
$478$	11.4115			0.521952
$479$	12.5885	−	12.5885i	0.575181	−	0.575181i	−0.358390	−	0.933572i	$-0.616674\pi$
$479$	12.5885	−	12.5885i	0.575181	−	0.575181i	0.933572	+	0.358390i	$0.116674\pi$
$480$	−12.2942	+	21.2942i	−0.561152	+	0.971944i
$481$	−18.7583	−	10.8301i	−0.855306	−	0.493811i
$482$	−26.7224	−	7.16025i	−1.21717	−	0.326141i
$483$	12.9282	−	48.2487i	0.588254	−	2.19539i
$484$	6.06218	−	3.50000i	0.275554	−	0.159091i
$485$	25.6244	+	6.86603i	1.16354	+	0.311770i
$486$	16.2224	+	28.0981i	0.735864	+	1.27455i
$487$	−3.26795	+	3.26795i	−0.148085	+	0.148085i	−0.777262	−	0.629177i	$-0.783392\pi$
$487$	−3.26795	+	3.26795i	−0.148085	+	0.148085i	0.629177	+	0.777262i	$0.283392\pi$
$488$	−12.7583	+	12.7583i	−0.577542	+	0.577542i
$489$	33.3205	−	57.7128i	1.50681	−	2.60986i
$490$	−11.8923	−	20.5981i	−0.537240	−	0.930526i
$491$	−32.1962			−1.45299			−0.726496	−	0.687171i	$-0.758852\pi$
$491$	−32.1962			−1.45299			−0.726496	+	0.687171i	$0.758852\pi$
$492$	−6.92820			−0.312348
$493$	33.5885	−	33.5885i	1.51275	−	1.51275i
$494$	−1.73205	+	3.00000i	−0.0779287	+	0.134976i
$495$	−8.49038	−	31.6865i	−0.381614	−	1.42420i
$496$	−15.4904	+	4.15064i	−0.695539	+	0.186369i
$497$	−16.3923	−	16.3923i	−0.735295	−	0.735295i
$498$	−6.00000			−0.268866
$499$	−32.0263	+	18.4904i	−1.43369	+	0.827743i	−0.997400	−	0.0720615i	$-0.977042\pi$
$499$	−32.0263	+	18.4904i	−1.43369	+	0.827743i	−0.436293	+	0.899805i	$0.643709\pi$
$500$	6.06218	+	10.5000i	0.271109	+	0.469574i
$501$		−	12.9282i		−	0.577590i
$502$	−42.8827	−	11.4904i	−1.91395	−	0.512841i
$503$	3.33975	+	3.33975i	0.148912	+	0.148912i	0.777632	−	0.628720i	$-0.216421\pi$
$503$	3.33975	+	3.33975i	0.148912	+	0.148912i	−0.628720	+	0.777632i	$0.716421\pi$
$504$	−21.1244	+	21.1244i	−0.940954	+	0.940954i
$505$	−14.1962	+	24.5885i	−0.631720	+	1.09417i
$506$	33.5885	+	9.00000i	1.49319	+	0.400099i
$507$	−12.6603	−	21.9282i	−0.562262	−	0.973866i
$508$	0.267949	+	1.00000i	0.0118883	+	0.0443678i
$509$	−12.3564	−	21.4019i	−0.547688	−	0.948624i	−0.998432	−	0.0559705i	$-0.982175\pi$
$509$	−12.3564	−	21.4019i	−0.547688	−	0.948624i	0.450744	−	0.892653i	$-0.351159\pi$
$510$	26.4904	−	45.8827i	1.17301	−	2.03172i
$511$	−29.1244	+	50.4449i	−1.28839	+	2.23155i
$512$			8.66025i			0.382733i
$513$	2.92820	+	2.92820i	0.129283	+	0.129283i
$514$	8.81347	+	32.8923i	0.388745	+	1.45082i
$515$		−	3.12436i		−	0.137676i
$516$	−2.00000	−	7.46410i	−0.0880451	−	0.328589i
$517$	−11.4115	+	6.58846i	−0.501879	+	0.289760i
$518$	−64.9808	−	37.5167i	−2.85509	−	1.64839i
$519$	51.2487	−	13.7321i	2.24957	−	0.602770i
$520$	−4.09808	−	4.09808i	−0.179713	−	0.179713i
$521$	−9.33975	−	9.33975i	−0.409182	−	0.409182i	0.472271	−	0.881453i	$-0.343434\pi$
$521$	−9.33975	−	9.33975i	−0.409182	−	0.409182i	−0.881453	+	0.472271i	$0.843434\pi$
$522$	54.8827	−	14.7058i	2.40215	−	0.643654i
$523$	−4.00000	+	4.00000i	−0.174908	+	0.174908i	−0.789132	−	0.614224i	$-0.789469\pi$
$523$	−4.00000	+	4.00000i	−0.174908	+	0.174908i	0.614224	+	0.789132i	$0.289469\pi$
$524$	7.90192	+	4.56218i	0.345197	+	0.199300i
$525$	5.46410	+	20.3923i	0.238473	+	0.889993i
$526$	6.58846	+	24.5885i	0.287270	+	1.07211i
$527$	20.0263	−	5.36603i	0.872358	−	0.233748i
$528$	−40.9808	−	40.9808i	−1.78346	−	1.78346i
$529$	−0.303848	−	0.526279i	−0.0132108	−	0.0228817i
$530$		−	2.78461i		−	0.120956i
$531$	−6.97372	−	26.0263i	−0.302634	−	1.12944i
$532$	−2.00000	+	3.46410i	−0.0867110	+	0.150188i
$533$	1.26795	−	4.73205i	0.0549210	−	0.204968i
$534$	−61.1769			−2.64738
$535$	0.803848	+	3.00000i	0.0347534	+	0.129701i
$536$	−11.6603	−	3.12436i	−0.503646	−	0.134952i
$537$	33.5885	+	19.3923i	1.44945	+	0.836840i
$538$	−24.6962	−	6.61731i	−1.06473	−	0.285293i
$539$	32.4904	−	8.70577i	1.39946	−	0.374984i
$540$	6.00000	−	3.46410i	0.258199	−	0.149071i
$541$	35.4545	−	9.50000i	1.52431	−	0.408437i	0.603150	−	0.797628i	$-0.293912\pi$
$541$	35.4545	−	9.50000i	1.52431	−	0.408437i	0.921157	+	0.389191i	$0.127245\pi$
$542$	17.3205	+	30.0000i	0.743980	+	1.28861i
$543$	15.3923	−	15.3923i	0.660547	−	0.660547i
$544$		−	33.5885i		−	1.44009i
$545$	−22.7942	−	13.1603i	−0.976397	−	0.563723i
$546$	17.6603	+	30.5885i	0.755789	+	1.30907i
$547$	1.39230	+	0.803848i	0.0595307	+	0.0343700i	0.529470	−	0.848329i	$-0.322391\pi$
$547$	1.39230	+	0.803848i	0.0595307	+	0.0343700i	−0.469939	+	0.882699i	$0.655724\pi$
$548$	4.79423	−	8.30385i	0.204799	−	0.354723i
$549$	44.9186	−	12.0359i	1.91708	−	0.513680i
$550$	−14.1962	+	3.80385i	−0.605326	+	0.162197i
$551$	−6.58846	+	3.80385i	−0.280678	+	0.162049i
$552$		−	22.3923i		−	0.953080i
$553$	13.6603	+	23.6603i	0.580893	+	1.00614i
$554$	6.63397	+	1.77757i	0.281851	+	0.0755216i
$555$	−37.5167	−	37.5167i	−1.59249	−	1.59249i
$556$	2.19615			0.0931376
$557$	−28.0981	+	28.0981i	−1.19055	+	1.19055i	−0.213642	+	0.976912i	$0.568532\pi$
$557$	−28.0981	+	28.0981i	−1.19055	+	1.19055i	−0.976912	+	0.213642i	$0.931468\pi$
$558$	23.9545	+	6.41858i	1.01407	+	0.271720i
$559$	5.46410			0.231107
$560$	−23.6603	−	23.6603i	−0.999828	−	0.999828i
$561$	52.9808	+	52.9808i	2.23685	+	2.23685i
$562$	0.401924	+	0.696152i	0.0169541	+	0.0293654i
$563$		−	7.26795i		−	0.306308i	−0.988202	−	0.153154i	$-0.951057\pi$
$563$		−	7.26795i		−	0.306308i	0.988202	−	0.153154i	$-0.0489430\pi$
$564$	−6.00000	−	6.00000i	−0.252646	−	0.252646i
$565$	−1.90192	+	0.509619i	−0.0800145	+	0.0214398i
$566$	3.97372	−	14.8301i	0.167028	−	0.623357i
$567$	−9.19615	+	2.46410i	−0.386202	+	0.103483i
$568$	−9.00000	−	5.19615i	−0.377632	−	0.218026i
$569$	−3.00000	+	1.73205i	−0.125767	+	0.0726113i	−0.561563	−	0.827434i	$-0.689800\pi$
$569$	−3.00000	+	1.73205i	−0.125767	+	0.0726113i	0.435797	+	0.900045i	$0.356467\pi$
$570$	−6.00000	+	6.00000i	−0.251312	+	0.251312i
$571$		−	4.58846i		−	0.192021i	−0.995380	−	0.0960105i	$-0.969392\pi$
$571$		−	4.58846i		−	0.192021i	0.995380	−	0.0960105i	$-0.0306082\pi$
$572$	−7.09808	+	4.09808i	−0.296785	+	0.171349i
$573$	5.19615	+	3.00000i	0.217072	+	0.125327i
$574$	4.39230	−	16.3923i	0.183331	−	0.684202i
$575$	−8.19615	−	4.73205i	−0.341803	−	0.197340i
$576$	−2.23205	+	3.86603i	−0.0930021	+	0.161084i
$577$	18.8923	−	5.06218i	0.786497	−	0.210741i	0.156850	−	0.987622i	$-0.449866\pi$
$577$	18.8923	−	5.06218i	0.786497	−	0.210741i	0.629647	+	0.776881i	$0.283199\pi$
$578$			42.9282i			1.78558i
$579$	−1.90192	+	1.09808i	−0.0790413	+	0.0456345i
$580$	3.29423	+	12.2942i	0.136785	+	0.510490i
$581$	1.26795	−	4.73205i	0.0526034	−	0.196319i
$582$	−70.0070	−	18.7583i	−2.90189	−	0.777558i
$583$	3.80385	+	1.01924i	0.157539	+	0.0422125i
$584$	−6.75833	+	25.2224i	−0.279662	+	1.04371i
$585$	3.86603	+	14.4282i	0.159840	+	0.596533i
$586$	−5.30385	+	19.7942i	−0.219100	+	0.817692i
$587$	−35.4904	−	20.4904i	−1.46484	−	0.845729i	−0.465616	−	0.884987i	$-0.654167\pi$
$587$	−35.4904	−	20.4904i	−1.46484	−	0.845729i	−0.999229	+	0.0392585i	$0.987500\pi$
$588$	10.8301	+	18.7583i	0.446627	+	0.773581i
$589$	−3.32051			−0.136819
$590$	17.4904	−	4.68653i	0.720068	−	0.192942i
$591$		−	18.9282i		−	0.778602i
$592$	−54.1506	−	14.5096i	−2.22558	−	0.596342i
$593$	7.16025	−	12.4019i	0.294036	−	0.509286i	−0.680724	−	0.732540i	$-0.738335\pi$
$593$	7.16025	−	12.4019i	0.294036	−	0.509286i	0.974760	+	0.223254i	$0.0716680\pi$
$594$	7.60770	+	28.3923i	0.312148	+	1.16495i
$595$	30.5885	+	30.5885i	1.25400	+	1.25400i
$596$	−3.57180	−	13.3301i	−0.146306	−	0.546023i
$597$	−17.3923	−	64.9090i	−0.711820	−	2.65655i
$598$	−15.2942	−	4.09808i	−0.625428	−	0.167583i
$599$	37.0526	−	9.92820i	1.51393	−	0.405655i	0.596189	−	0.802844i	$-0.296681\pi$
$599$	37.0526	−	9.92820i	1.51393	−	0.405655i	0.917737	+	0.397188i	$0.130014\pi$
$600$	4.73205	+	8.19615i	0.193185	+	0.334607i
$601$	9.86603	−	5.69615i	0.402444	−	0.232351i	−0.285094	−	0.958499i	$-0.592025\pi$
$601$	9.86603	−	5.69615i	0.402444	−	0.232351i	0.687538	+	0.726149i	$0.258692\pi$
$602$	18.9282			0.771456
$603$	22.0000	+	22.0000i	0.895909	+	0.895909i
$604$	5.63397	−	21.0263i	0.229243	−	0.855547i
$605$			12.1244i			0.492925i
$606$	38.7846	−	67.1769i	1.57552	−	2.72888i
$607$	2.04552	−	7.63397i	0.0830250	−	0.309853i	−0.911908	−	0.410395i	$-0.865391\pi$
$607$	2.04552	−	7.63397i	0.0830250	−	0.309853i	0.994933	+	0.100541i	$0.0320575\pi$
$608$	−1.39230	+	5.19615i	−0.0564654	+	0.210732i
$609$			77.5692i			3.14326i
$610$	8.08846	+	30.1865i	0.327492	+	1.22222i
$611$	5.19615	−	3.00000i	0.210214	−	0.121367i
$612$	−14.4282	+	24.9904i	−0.583226	+	1.01018i
$613$	0.696152	−	0.401924i	0.0281173	−	0.0162335i	−0.485875	−	0.874028i	$-0.661499\pi$
$613$	0.696152	−	0.401924i	0.0281173	−	0.0162335i	0.513993	+	0.857795i	$0.328166\pi$
$614$	15.2942	−	8.83013i	0.617225	−	0.356355i
$615$	6.00000	−	10.3923i	0.241943	−	0.419058i
$616$	24.5885	−	14.1962i	0.990697	−	0.571979i
$617$	9.18653	+	34.2846i	0.369836	+	1.38025i	0.860745	+	0.509036i	$0.169998\pi$
$617$	9.18653	+	34.2846i	0.369836	+	1.38025i	−0.490909	+	0.871211i	$0.663335\pi$
$618$			8.53590i			0.343364i
$619$	1.36603	−	5.09808i	0.0549052	−	0.204909i	−0.933024	−	0.359813i	$-0.882840\pi$
$619$	1.36603	−	5.09808i	0.0549052	−	0.204909i	0.987929	+	0.154905i	$0.0495070\pi$
$620$	−1.43782	+	5.36603i	−0.0577443	+	0.215505i
$621$	−9.46410	+	16.3923i	−0.379781	+	0.657801i
$622$		−	3.21539i		−	0.128925i
$623$	12.9282	−	48.2487i	0.517958	−	1.93304i
$624$	18.6603	+	18.6603i	0.747008	+	0.747008i
$625$	−11.0000			−0.440000
$626$	−3.00000	+	1.73205i	−0.119904	+	0.0692267i
$627$	−6.00000	−	10.3923i	−0.239617	−	0.415029i
$628$	18.8923	−	5.06218i	0.753885	−	0.202003i
$629$	70.0070	+	18.7583i	2.79136	+	0.747944i
$630$	13.3923	+	49.9808i	0.533562	+	1.99128i
$631$	−2.67949	−	10.0000i	−0.106669	−	0.398094i	0.891860	−	0.452311i	$-0.149400\pi$
$631$	−2.67949	−	10.0000i	−0.106669	−	0.398094i	−0.998529	+	0.0542173i	$0.982734\pi$
$632$	8.66025	+	8.66025i	0.344486	+	0.344486i
$633$	18.1962	+	67.9090i	0.723232	+	2.69914i
$634$	−14.8923	+	25.7942i	−0.591449	+	1.02442i
$635$	−1.73205	−	0.464102i	−0.0687343	−	0.0184173i
$636$			2.53590i			0.100555i
$637$	−14.7942	+	3.96410i	−0.586169	+	0.157063i
$638$	−54.0000			−2.13788
$639$	13.3923	+	23.1962i	0.529791	+	0.917626i
$640$	−18.1865	−	10.5000i	−0.718886	−	0.415049i
$641$	7.31347	−	27.2942i	0.288865	−	1.07806i	−0.657104	−	0.753800i	$-0.728219\pi$
$641$	7.31347	−	27.2942i	0.288865	−	1.07806i	0.945969	−	0.324258i	$-0.105114\pi$
$642$	−2.19615	−	8.19615i	−0.0866752	−	0.323476i
$643$	10.3397	−	38.5885i	0.407760	−	1.52178i	−0.391149	−	0.920328i	$-0.627922\pi$
$643$	10.3397	−	38.5885i	0.407760	−	1.52178i	0.798908	−	0.601453i	$-0.205411\pi$
$644$	−17.6603	−	4.73205i	−0.695911	−	0.186469i
$645$	12.9282	+	3.46410i	0.509048	+	0.136399i
$646$	3.00000	−	11.1962i	0.118033	−	0.440507i
$647$	−0.588457	−	2.19615i	−0.0231346	−	0.0863397i	0.953393	−	0.301730i	$-0.0975642\pi$
$647$	−0.588457	−	2.19615i	−0.0231346	−	0.0863397i	−0.976528	+	0.215391i	$0.930898\pi$
$648$	−3.69615	+	2.13397i	−0.145199	+	0.0838304i
$649$			25.6077i			1.00519i
$650$	6.46410	−	1.73205i	0.253543	−	0.0679366i
$651$	−16.9282	+	29.3205i	−0.663469	+	1.14916i
$652$	−21.1244	−	12.1962i	−0.827294	−	0.477638i
$653$	−5.70577	+	21.2942i	−0.223284	+	0.833308i	0.759801	+	0.650156i	$0.225297\pi$
$653$	−5.70577	+	21.2942i	−0.223284	+	0.833308i	−0.983085	+	0.183151i	$0.941370\pi$
$654$	62.2750	+	35.9545i	2.43514	+	1.40593i
$655$	−13.6865	+	7.90192i	−0.534777	+	0.308754i
$656$		−	12.6795i		−	0.495051i
$657$	47.5885	−	47.5885i	1.85660	−	1.85660i
$658$	18.0000	−	10.3923i	0.701713	−	0.405134i
$659$	−4.31347	−	2.49038i	−0.168029	−	0.0970115i	0.413627	−	0.910446i	$-0.364262\pi$
$659$	−4.31347	−	2.49038i	−0.168029	−	0.0970115i	−0.581656	+	0.813435i	$0.697595\pi$
$660$	−19.3923	+	5.19615i	−0.754844	+	0.202260i
$661$	−5.62436	+	20.9904i	−0.218762	+	0.816431i	0.766046	+	0.642786i	$0.222221\pi$
$661$	−5.62436	+	20.9904i	−0.218762	+	0.816431i	−0.984808	+	0.173646i	$0.944445\pi$
$662$	11.3660	−	3.04552i	0.441753	−	0.118367i
$663$	−24.1244	−	24.1244i	−0.936912	−	0.936912i
$664$		−	2.19615i		−	0.0852272i
$665$	−3.46410	−	6.00000i	−0.134332	−	0.232670i
$666$	61.3013	+	61.3013i	2.37538	+	2.37538i
$667$	−24.5885	−	24.5885i	−0.952069	−	0.952069i
$668$	−4.73205			−0.183089
$669$	−68.3731	−	18.3205i	−2.64346	−	0.708312i
$670$	−14.7846	+	14.7846i	−0.571179	+	0.571179i
$671$	−44.1962			−1.70617
$672$	38.7846	+	38.7846i	1.49615	+	1.49615i
$673$	−5.06218	−	1.35641i	−0.195133	−	0.0522856i	0.159929	−	0.987129i	$-0.448873\pi$
$673$	−5.06218	−	1.35641i	−0.195133	−	0.0522856i	−0.355062	+	0.934843i	$0.615540\pi$
$674$	3.58846	+	6.21539i	0.138222	+	0.239408i
$675$		−	8.00000i		−	0.307920i
$676$	−8.02628	+	4.63397i	−0.308703	+	0.178230i
$677$	46.1147	−	12.3564i	1.77233	−	0.474895i	0.783182	−	0.621793i	$-0.213595\pi$
$677$	46.1147	−	12.3564i	1.77233	−	0.474895i	0.989152	+	0.146898i	$0.0469288\pi$
$678$	5.19615	−	1.39230i	0.199557	−	0.0534711i
$679$	29.5885	−	51.2487i	1.13550	−	1.96675i
$680$	16.7942	+	9.69615i	0.644029	+	0.371830i
$681$	−37.0526	−	64.1769i	−1.41986	−	2.45926i
$682$	−20.4115	−	11.7846i	−0.781598	−	0.451256i
$683$			10.9808i			0.420167i	0.977683	+	0.210084i	$0.0673736\pi$
$683$			10.9808i			0.420167i	−0.977683	+	0.210084i	$0.932626\pi$
$684$	3.26795	−	3.26795i	0.124953	−	0.124953i
$685$	8.30385	+	14.3827i	0.317274	+	0.549534i
$686$	−6.00000	+	1.60770i	−0.229081	+	0.0613821i
$687$	−15.2942	+	8.83013i	−0.583511	+	0.336890i
$688$	13.6603	−	3.66025i	0.520792	−	0.139546i
$689$	−1.73205	−	0.464102i	−0.0659859	−	0.0176809i
$690$	−33.5885	−	19.3923i	−1.27869	−	0.738252i
$691$	−13.7583	−	3.68653i	−0.523392	−	0.140242i	−0.0125566	−	0.999921i	$-0.503997\pi$
$691$	−13.7583	−	3.68653i	−0.523392	−	0.140242i	−0.510835	+	0.859679i	$0.670664\pi$
$692$	−5.02628	−	18.7583i	−0.191070	−	0.713085i
$693$	−73.1769			−2.77976
$694$	−6.58846	+	24.5885i	−0.250094	+	0.933365i
$695$	−1.90192	+	3.29423i	−0.0721441	+	0.124957i
$696$	9.00000	+	33.5885i	0.341144	+	1.27317i
$697$			16.3923i			0.620903i
$698$	0.696152	+	1.20577i	0.0263498	+	0.0456391i
$699$	−32.6603	−	32.6603i	−1.23532	−	1.23532i
$700$	7.46410	−	2.00000i	0.282117	−	0.0755929i
$701$	1.22243	+	4.56218i	0.0461706	+	0.172311i	0.985161	−	0.171632i	$-0.0549040\pi$
$701$	1.22243	+	4.56218i	0.0461706	+	0.172311i	−0.938991	+	0.343943i	$0.888237\pi$
$702$	−3.46410	−	12.9282i	−0.130744	−	0.487944i
$703$	−10.0526	−	5.80385i	−0.379139	−	0.218896i
$704$	3.00000	−	3.00000i	0.113067	−	0.113067i
$705$	14.1962	−	3.80385i	0.534658	−	0.143261i
$706$	−18.2942	−	18.2942i	−0.688512	−	0.688512i
$707$	44.7846	+	44.7846i	1.68430	+	1.68430i
$708$	−15.9282	+	4.26795i	−0.598619	+	0.160399i
$709$	30.3109	+	17.5000i	1.13835	+	0.657226i	0.946021	−	0.324104i	$-0.105063\pi$
$709$	30.3109	+	17.5000i	1.13835	+	0.657226i	0.192328	+	0.981331i	$0.438396\pi$
$710$	−15.5885	+	9.00000i	−0.585024	+	0.337764i
$711$	−8.16987	−	30.4904i	−0.306394	−	1.14348i
$712$		−	22.3923i		−	0.839187i
$713$	−3.92820	−	14.6603i	−0.147112	−	0.549031i
$714$	−83.5692	−	83.5692i	−3.12750	−	3.12750i
$715$		−	14.1962i		−	0.530906i
$716$	7.09808	−	12.2942i	0.265268	−	0.459457i
$717$	9.00000	−	15.5885i	0.336111	−	0.582162i
$718$	−13.3923	−	23.1962i	−0.499796	−	0.865673i
$719$	3.63397	+	13.5622i	0.135524	+	0.505784i	0.999995	+	0.00310086i	$0.000987037\pi$
$719$	3.63397	+	13.5622i	0.135524	+	0.505784i	−0.864471	+	0.502683i	$0.832346\pi$
$720$	19.3301	+	33.4808i	0.720391	+	1.24775i
$721$	−6.73205	−	1.80385i	−0.250715	−	0.0671788i
$722$	15.5263	−	26.8923i	0.577828	−	1.00083i
$723$	−30.8564	+	30.8564i	−1.14756	+	1.14756i
$724$	−5.63397	−	5.63397i	−0.209385	−	0.209385i
$725$	14.1962	+	3.80385i	0.527232	+	0.141271i
$726$		−	33.1244i		−	1.22936i
$727$	−16.5885	−	28.7321i	−0.615232	−	1.06561i	−0.990344	−	0.138633i	$-0.955729\pi$
$727$	−16.5885	−	28.7321i	−0.615232	−	1.06561i	0.375112	−	0.926980i	$-0.377604\pi$
$728$	−11.1962	+	6.46410i	−0.414957	+	0.239576i
$729$	43.7846			1.62165
$730$	31.9808	+	31.9808i	1.18366	+	1.18366i
$731$	−17.6603	+	4.73205i	−0.653188	+	0.175021i
$732$	−7.36603	−	27.4904i	−0.272256	−	1.01607i
$733$	−4.96410	+	8.59808i	−0.183353	+	0.317577i	−0.943020	−	0.332735i	$-0.892029\pi$
$733$	−4.96410	+	8.59808i	−0.183353	+	0.317577i	0.759667	+	0.650312i	$0.225362\pi$
$734$	15.1244	−	15.1244i	0.558250	−	0.558250i
$735$	−37.5167			−1.38382
$736$	−24.5885			−0.906343
$737$	−14.7846	−	25.6077i	−0.544598	−	0.943272i
$738$	−9.80385	+	16.9808i	−0.360885	+	0.625070i
$739$	−31.2487	+	31.2487i	−1.14950	+	1.14950i	−0.162852	+	0.986651i	$0.552069\pi$
$739$	−31.2487	+	31.2487i	−1.14950	+	1.14950i	−0.986651	+	0.162852i	$0.947931\pi$
$740$	−13.7321	+	13.7321i	−0.504800	+	0.504800i
$741$	2.73205	+	4.73205i	0.100364	+	0.173836i
$742$	−6.00000	−	1.60770i	−0.220267	−	0.0590203i
$743$	−4.90192	+	2.83013i	−0.179834	+	0.103827i	−0.587215	−	0.809431i	$-0.699776\pi$
$743$	−4.90192	+	2.83013i	−0.179834	+	0.103827i	0.407381	+	0.913258i	$0.366442\pi$
$744$	−3.92820	+	14.6603i	−0.144015	+	0.537471i
$745$	23.0885	+	6.18653i	0.845896	+	0.226657i
$746$	55.5788	+	32.0885i	2.03489	+	1.17484i
$747$	−2.83013	+	4.90192i	−0.103549	+	0.179352i
$748$	19.3923	−	19.3923i	0.709053	−	0.709053i
$749$	6.92820			0.253151
$750$	57.3731			2.09497
$751$	−5.16987	+	19.2942i	−0.188651	+	0.704056i	0.805168	+	0.593047i	$0.202075\pi$
$751$	−5.16987	+	19.2942i	−0.188651	+	0.704056i	−0.993819	+	0.111010i	$0.964592\pi$
$752$	10.9808	−	10.9808i	0.400427	−	0.400427i
$753$	−49.5167	+	49.5167i	−1.80449	+	1.80449i
$754$	24.5885			0.895459
$755$	26.6603	+	26.6603i	0.970266	+	0.970266i
$756$	−4.00000	−	14.9282i	−0.145479	−	0.542934i
$757$	−33.3468	−	33.3468i	−1.21201	−	1.21201i	−0.970365	−	0.241645i	$-0.922313\pi$
$757$	−33.3468	−	33.3468i	−1.21201	−	1.21201i	−0.241645	−	0.970365i	$-0.577687\pi$
$758$	20.7058	+	11.9545i	0.752067	+	0.434206i
$759$	38.7846	−	38.7846i	1.40779	−	1.40779i
$760$	−2.19615	−	2.19615i	−0.0796628	−	0.0796628i
$761$	8.24167	−	30.7583i	0.298760	−	1.11499i	−0.639425	−	0.768854i	$-0.720827\pi$
$761$	8.24167	−	30.7583i	0.298760	−	1.11499i	0.938185	−	0.346135i	$-0.112506\pi$
$762$	4.73205	+	1.26795i	0.171424	+	0.0459330i
$763$	−41.5167	+	41.5167i	−1.50300	+	1.50300i
$764$	1.09808	−	1.90192i	0.0397270	−	0.0688092i
$765$	−24.9904	−	43.2846i	−0.903529	−	1.56496i
$766$	−28.3923	−	7.60770i	−1.02586	−	0.274877i
$767$		−	11.6603i		−	0.421027i
$768$	44.9545	+	25.9545i	1.62216	+	0.936552i
$769$	1.79423	+	1.03590i	0.0647015	+	0.0373555i	0.532002	−	0.846743i	$-0.321440\pi$
$769$	1.79423	+	1.03590i	0.0647015	+	0.0373555i	−0.467300	+	0.884099i	$0.654773\pi$
$770$		−	49.1769i		−	1.77221i
$771$	51.8827	+	13.9019i	1.86851	+	0.500666i
$772$	0.401924	+	0.696152i	0.0144656	+	0.0250551i
$773$	−25.2846	+	43.7942i	−0.909424	+	1.57517i	−0.0945584	+	0.995519i	$0.530144\pi$
$773$	−25.2846	+	43.7942i	−0.909424	+	1.57517i	−0.814866	+	0.579650i	$0.803189\pi$
$774$	−21.1244	−	5.66025i	−0.759299	−	0.203454i
$775$	4.53590	+	4.53590i	0.162934	+	0.162934i
$776$	6.86603	−	25.6244i	0.246476	−	0.919861i
$777$	−102.497	+	59.1769i	−3.67707	+	2.12296i
$778$		−	5.78461i		−	0.207388i
$779$	0.679492	−	2.53590i	0.0243453	−	0.0908580i
$780$	8.83013	−	2.36603i	0.316169	−	0.0847173i
$781$	−6.58846	−	24.5885i	−0.235754	−	0.879844i
$782$	52.9808			1.89459
$783$	7.60770	−	28.3923i	0.271877	−	1.01466i
$784$	−34.3301	+	19.8205i	−1.22608	+	0.707875i
$785$	−8.76795	+	32.7224i	−0.312942	+	1.16791i
$786$	37.3923	−	21.5885i	1.33374	−	0.770035i
$787$	−35.2679	−	35.2679i	−1.25717	−	1.25717i	−0.952440	−	0.304727i	$-0.901435\pi$
$787$	−35.2679	−	35.2679i	−1.25717	−	1.25717i	−0.304727	−	0.952440i	$-0.598565\pi$
$788$	−6.92820			−0.246807
$789$	38.7846	+	10.3923i	1.38077	+	0.369976i
$790$	20.4904	−	5.49038i	0.729015	−	0.195339i
$791$			4.39230i			0.156172i
$792$	−31.6865	+	8.49038i	−1.12593	+	0.301693i
$793$	20.1244			0.714637
$794$	14.5981	+	25.2846i	0.518066	+	0.897317i
$795$	−3.80385	−	2.19615i	−0.134909	−	0.0778895i
$796$	−23.7583	+	6.36603i	−0.842092	+	0.225638i
$797$	−9.74167	−	36.3564i	−0.345068	−	1.28781i	−0.892533	−	0.450982i	$-0.851074\pi$
$797$	−9.74167	−	36.3564i	−0.345068	−	1.28781i	0.547466	−	0.836828i	$-0.315593\pi$
$798$	9.46410	+	16.3923i	0.335026	+	0.580281i
$799$	−14.1962	+	14.1962i	−0.502224	+	0.502224i
$800$	9.00000	−	5.19615i	0.318198	−	0.183712i
$801$	−28.8564	+	49.9808i	−1.01959	+	1.76598i
$802$	0.696152	−	1.20577i	0.0245820	−	0.0425773i
$803$	−55.3923	+	31.9808i	−1.95475	+	1.12858i
$804$	13.4641	−	13.4641i	0.474842	−	0.474842i
$805$	22.3923	−	22.3923i	0.789225	−	0.789225i
$806$	9.29423	+	5.36603i	0.327375	+	0.189010i
$807$	−28.5167	+	28.5167i	−1.00383	+	1.00383i
$808$	24.5885	+	14.1962i	0.865019	+	0.499419i
$809$	4.73205	−	8.19615i	0.166370	−	0.288161i	−0.770771	−	0.637112i	$-0.780129\pi$
$809$	4.73205	−	8.19615i	0.166370	−	0.288161i	0.937141	+	0.348951i	$0.113462\pi$
$810$			7.39230i			0.259739i
$811$	−12.1506	+	45.3468i	−0.426667	+	1.59234i	0.333590	+	0.942718i	$0.391740\pi$
$811$	−12.1506	+	45.3468i	−0.426667	+	1.59234i	−0.760257	+	0.649623i	$0.774927\pi$
$812$	28.3923			0.996375
$813$	54.6410			1.91634
$814$	−41.1962	−	71.3538i	−1.44392	−	2.50095i
$815$	36.5885	−	21.1244i	1.28164	−	0.739954i
$816$	−76.4711	−	44.1506i	−2.67703	−	1.54558i
$817$	2.92820			0.102445
$818$	−12.8205	+	32.5981i	−0.448259	+	1.13977i
$819$	33.3205			1.16431
$820$	−3.80385	−	2.19615i	−0.132836	−	0.0766930i
$821$	−17.8923	+	10.3301i	−0.624446	+	0.360524i	−0.778598	−	0.627523i	$-0.784069\pi$
$821$	−17.8923	+	10.3301i	−0.624446	+	0.360524i	0.154152	+	0.988047i	$0.450735\pi$
$822$	−22.6865	−	39.2942i	−0.791284	−	1.37054i
$823$	3.12436			0.108908			0.0544541	−	0.998516i	$-0.482658\pi$
$823$	3.12436			0.108908			0.0544541	+	0.998516i	$0.482658\pi$
$824$	−3.12436			−0.108842
$825$	−6.00000	+	22.3923i	−0.208893	+	0.779600i
$826$		−	40.3923i		−	1.40543i
$827$	−23.8301	+	41.2750i	−0.828655	+	1.43527i	0.0704391	+	0.997516i	$0.477560\pi$
$827$	−23.8301	+	41.2750i	−0.828655	+	1.43527i	−0.899094	+	0.437756i	$0.855773\pi$
$828$	18.2942	+	10.5622i	0.635768	+	0.367061i
$829$	−14.9737	+	14.9737i	−0.520059	+	0.520059i	−0.917589	−	0.397530i	$-0.869867\pi$
$829$	−14.9737	+	14.9737i	−0.520059	+	0.520059i	0.397530	+	0.917589i	$0.369867\pi$
$830$	−3.29423	−	1.90192i	−0.114344	−	0.0660167i
$831$	7.66025	−	7.66025i	0.265731	−	0.265731i
$832$	−1.36603	+	1.36603i	−0.0473584	+	0.0473584i
$833$	44.3827	−	25.6244i	1.53777	−	0.887831i
$834$	5.19615	−	9.00000i	0.179928	−	0.311645i
$835$	4.09808	−	7.09808i	0.141820	−	0.245639i
$836$	−3.80385	+	2.19615i	−0.131559	+	0.0759555i
$837$	9.07180	−	9.07180i	0.313567	−	0.313567i
$838$	−4.39230	−	7.60770i	−0.151730	−	0.262803i
$839$	8.83013	+	32.9545i	0.304850	+	1.13772i	0.933075	+	0.359683i	$0.117115\pi$
$839$	8.83013	+	32.9545i	0.304850	+	1.13772i	−0.628225	+	0.778032i	$0.716218\pi$
$840$	−30.5885	+	8.19615i	−1.05540	+	0.282794i
$841$	21.6506	+	12.5000i	0.746574	+	0.431034i
$842$	14.7224	+	25.5000i	0.507369	+	0.878788i
$843$	1.26795			0.0436705
$844$	24.8564	−	6.66025i	0.855593	−	0.229255i
$845$		−	16.0526i		−	0.552225i
$846$	−23.1962	+	6.21539i	−0.797500	+	0.213690i
$847$	26.1244	+	7.00000i	0.897643	+	0.240523i
$848$	−4.64102			−0.159373
$849$	−17.1244	−	17.1244i	−0.587706	−	0.587706i
$850$	−19.3923	+	11.1962i	−0.665151	+	0.384025i
$851$	13.7321	−	51.2487i	0.470729	−	1.75678i
$852$	14.1962	−	8.19615i	0.486352	−	0.280796i
$853$	8.86603	−	33.0885i	0.303567	−	1.13293i	−0.630605	−	0.776104i	$-0.717193\pi$
$853$	8.86603	−	33.0885i	0.303567	−	1.13293i	0.934172	−	0.356823i	$-0.116140\pi$
$854$	69.7128			2.38552
$855$	2.07180	+	7.73205i	0.0708540	+	0.264431i
$856$	3.00000	−	0.803848i	0.102538	−	0.0274749i
$857$	0.107695	−	0.401924i	0.00367880	−	0.0137295i	−0.964062	−	0.265677i	$-0.914404\pi$
$857$	0.107695	−	0.401924i	0.00367880	−	0.0137295i	0.967741	+	0.251948i	$0.0810711\pi$
$858$			38.7846i			1.32408i
$859$	−12.8038	+	7.39230i	−0.436862	+	0.252222i	−0.702265	−	0.711915i	$-0.747828\pi$
$859$	−12.8038	+	7.39230i	−0.436862	+	0.252222i	0.265404	+	0.964137i	$0.414495\pi$
$860$	1.26795	−	4.73205i	0.0432367	−	0.161362i
$861$	−18.9282	−	18.9282i	−0.645071	−	0.645071i
$862$	58.9808	+	15.8038i	2.00889	+	0.538281i
$863$	6.80385	−	11.7846i	0.231606	−	0.401153i	−0.726675	−	0.686981i	$-0.758935\pi$
$863$	6.80385	−	11.7846i	0.231606	−	0.401153i	0.958281	+	0.285828i	$0.0922688\pi$
$864$	−10.3923	−	18.0000i	−0.353553	−	0.612372i
$865$	32.4904	+	8.70577i	1.10471	+	0.296005i
$866$			7.39230i			0.251201i
$867$	58.6410	+	33.8564i	1.99155	+	1.14982i
$868$	10.7321	+	6.19615i	0.364270	+	0.210311i
$869$			30.0000i			1.01768i
$870$	58.1769	+	15.5885i	1.97238	+	0.528498i
$871$	6.73205	+	11.6603i	0.228107	+	0.395093i
$872$	−13.1603	+	22.7942i	−0.445662	+	0.771910i
$873$	−48.3468	+	48.3468i	−1.63629	+	1.63629i
$874$	−8.19615	−	2.19615i	−0.277239	−	0.0742860i
$875$	−12.1244	+	45.2487i	−0.409878	+	1.52969i
$876$	−29.1244	−	29.1244i	−0.984021	−	0.984021i
$877$	28.6603	−	28.6603i	0.967788	−	0.967788i	−0.0317091	−	0.999497i	$-0.510095\pi$
$877$	28.6603	−	28.6603i	0.967788	−	0.967788i	0.999497	+	0.0317091i	$0.0100950\pi$
$878$	−49.4711	−	28.5622i	−1.66957	−	0.963927i
$879$	22.8564	+	22.8564i	0.770927	+	0.770927i
$880$	−9.50962	−	35.4904i	−0.320569	−	1.19638i
$881$	26.0263	+	26.0263i	0.876848	+	0.876848i	0.993207	−	0.116360i	$-0.0371225\pi$
$881$	26.0263	+	26.0263i	0.876848	+	0.876848i	−0.116360	+	0.993207i	$0.537122\pi$
$882$	61.3013			2.06412
$883$	25.2487	−	25.2487i	0.849687	−	0.849687i	−0.140407	−	0.990094i	$-0.544841\pi$
$883$	25.2487	−	25.2487i	0.849687	−	0.849687i	0.990094	+	0.140407i	$0.0448411\pi$
$884$	−8.83013	+	8.83013i	−0.296989	+	0.296989i
$885$	7.39230	−	27.5885i	0.248490	−	0.927376i
$886$	−0.588457			−0.0197696
$887$	−38.7846			−1.30226			−0.651130	−	0.758966i	$-0.725705\pi$
$887$	−38.7846			−1.30226			−0.651130	+	0.758966i	$0.725705\pi$
$888$	−37.5167	+	37.5167i	−1.25898	+	1.25898i
$889$	−2.00000	+	3.46410i	−0.0670778	+	0.116182i
$890$	−33.5885	−	19.3923i	−1.12589	−	0.650032i
$891$	−10.0981	−	2.70577i	−0.338298	−	0.0906468i
$892$	−6.70577	+	25.0263i	−0.224526	+	0.837942i
$893$	2.78461	−	1.60770i	0.0931834	−	0.0537995i
$894$	−63.0788	−	16.9019i	−2.10967	−	0.565285i
$895$	12.2942	+	21.2942i	0.410951	+	0.711788i
$896$	−33.1244	+	33.1244i	−1.10661	+	1.10661i
$897$	−17.6603	+	17.6603i	−0.589659	+	0.589659i
$898$	−23.0885	+	39.9904i	−0.770472	+	1.33450i
$899$	11.7846	+	20.4115i	0.393039	+	0.680763i
$900$	−8.92820			−0.297607
$901$	6.00000			0.199889
$902$	13.1769	−	13.1769i	0.438743	−	0.438743i
$903$	14.9282	−	25.8564i	0.496779	−	0.860447i
$904$	0.509619	+	1.90192i	0.0169497	+	0.0632570i
$905$	13.3301	−	3.57180i	0.443108	−	0.118731i
$906$	−72.8372	−	72.8372i	−2.41985	−	2.41985i
$907$	18.9808			0.630246			0.315123	−	0.949051i	$-0.397954\pi$
$907$	18.9808			0.630246			0.315123	+	0.949051i	$0.397954\pi$
$908$	−23.4904	+	13.5622i	−0.779556	+	0.450077i
$909$	−36.5885	−	63.3731i	−1.21356	−	2.10195i
$910$			22.3923i			0.742298i
$911$	−2.36603	−	0.633975i	−0.0783899	−	0.0210045i	0.219411	−	0.975633i	$-0.429586\pi$
$911$	−2.36603	−	0.633975i	−0.0783899	−	0.0210045i	−0.297801	+	0.954628i	$0.596253\pi$
$912$	10.0000	+	10.0000i	0.331133	+	0.331133i
$913$	3.80385	−	3.80385i	0.125889	−	0.125889i
$914$	9.35641	−	16.2058i	0.309482	−	0.536039i
$915$	47.6147	+	12.7583i	1.57409	+	0.421777i
$916$	3.23205	+	5.59808i	0.106790	+	0.184966i
$917$	9.12436	+	34.0526i	0.301313	+	1.12451i
$918$	22.3923	+	38.7846i	0.739056	+	1.28008i
$919$	23.8301	−	41.2750i	0.786083	−	1.36154i	−0.142266	−	0.989828i	$-0.545439\pi$
$919$	23.8301	−	41.2750i	0.786083	−	1.36154i	0.928350	−	0.371708i	$-0.121228\pi$
$920$	7.09808	−	12.2942i	0.234017	−	0.405329i
$921$		−	27.8564i		−	0.917900i
$922$	−11.1962	−	11.1962i	−0.368726	−	0.368726i
$923$	3.00000	+	11.1962i	0.0987462	+	0.368526i
$924$			44.7846i			1.47331i
$925$	5.80385	+	21.6603i	0.190829	+	0.712185i
$926$	8.41154	−	4.85641i	0.276420	−	0.159591i
$927$	6.97372	+	4.02628i	0.229047	+	0.132240i
$928$	36.8827	−	9.88269i	1.21073	−	0.324415i
$929$	−30.0788	−	30.0788i	−0.986855	−	0.986855i	0.0130600	−	0.999915i	$-0.495843\pi$
$929$	−30.0788	−	30.0788i	−0.986855	−	0.986855i	−0.999915	+	0.0130600i	$0.995843\pi$
$930$	18.5885	+	18.5885i	0.609540	+	0.609540i
$931$	−7.92820	+	2.12436i	−0.259836	+	0.0696229i
$932$	−11.9545	+	11.9545i	−0.391582	+	0.391582i
$933$	−4.39230	−	2.53590i	−0.143798	−	0.0830216i
$934$	5.41154	+	20.1962i	0.177071	+	0.660838i
$935$	12.2942	+	45.8827i	0.402064	+	1.50052i
$936$	14.4282	−	3.86603i	0.471601	−	0.126365i
$937$	−34.6147	−	34.6147i	−1.13081	−	1.13081i	−0.990042	−	0.140772i	$-0.955042\pi$
$937$	−34.6147	−	34.6147i	−1.13081	−	1.13081i	−0.140772	−	0.990042i	$-0.544958\pi$
$938$	23.3205	+	40.3923i	0.761442	+	1.31886i
$939$			5.46410i			0.178314i
$940$	−1.39230	−	5.19615i	−0.0454120	−	0.169480i
$941$	11.7846	−	20.4115i	0.384167	−	0.665397i	−0.607486	−	0.794330i	$-0.707822\pi$
$941$	11.7846	−	20.4115i	0.384167	−	0.665397i	0.991653	+	0.128933i	$0.0411553\pi$
$942$	23.9545	−	89.3993i	0.780479	−	2.91279i
$943$	12.0000			0.390774
$944$	−7.81089	−	29.1506i	−0.254223	−	0.948772i
$945$	25.8564	+	6.92820i	0.841109	+	0.225374i
$946$	18.0000	+	10.3923i	0.585230	+	0.337883i
$947$	−25.8564	−	6.92820i	−0.840220	−	0.225136i	−0.187053	−	0.982350i	$-0.559894\pi$
$947$	−25.8564	−	6.92820i	−0.840220	−	0.225136i	−0.653167	+	0.757213i	$0.726560\pi$
$948$	−18.6603	+	5.00000i	−0.606057	+	0.162392i
$949$	25.2224	−	14.5622i	0.818755	−	0.472708i
$950$	3.46410	−	0.928203i	0.112390	−	0.0301149i
$951$	23.4904	+	40.6865i	0.761728	+	1.31935i
$952$	30.5885	−	30.5885i	0.991378	−	0.991378i
$953$		−	59.1051i		−	1.91460i	−0.289092	−	0.957301i	$-0.593353\pi$
$953$		−	59.1051i		−	1.91460i	0.289092	−	0.957301i	$-0.406647\pi$
$954$	6.21539	+	3.58846i	0.201231	+	0.116181i
$955$	1.90192	+	3.29423i	0.0615448	+	0.106599i
$956$	−5.70577	−	3.29423i	−0.184538	−	0.106543i
$957$	−42.5885	+	73.7654i	−1.37669	+	2.38450i
$958$	−29.7846	+	7.98076i	−0.962297	+	0.257847i
$959$	35.7846	−	9.58846i	1.15555	−	0.309627i
$960$	−4.09808	+	2.36603i	−0.132265	+	0.0763631i
$961$		−	20.7128i		−	0.668155i
$962$	18.7583	+	32.4904i	0.604793	+	1.04753i
$963$	−7.73205	−	2.07180i	−0.249162	−	0.0667627i
$964$	11.2942	+	11.2942i	0.363763	+	0.363763i
$965$	−1.39230			−0.0448199
$966$	−61.1769	+	61.1769i	−1.96833	+	1.96833i
$967$	−31.1506	−	8.34679i	−1.00174	−	0.268415i	−0.279564	−	0.960127i	$-0.590190\pi$
$967$	−31.1506	−	8.34679i	−1.00174	−	0.268415i	−0.722173	+	0.691712i	$0.756857\pi$
$968$	12.1244			0.389692
$969$	−12.9282	−	12.9282i	−0.415314	−	0.415314i
$970$	−32.4904	−	32.4904i	−1.04320	−	1.04320i
$971$	−21.8827	−	37.9019i	−0.702249	−	1.21633i	−0.967675	−	0.252200i	$-0.918846\pi$
$971$	−21.8827	−	37.9019i	−0.702249	−	1.21633i	0.265426	−	0.964131i	$-0.414487\pi$
$972$		−	18.7321i		−	0.600831i
$973$	6.00000	+	6.00000i	0.192351	+	0.192351i
$974$	7.73205	−	2.07180i	0.247751	−	0.0663847i
$975$	2.73205	−	10.1962i	0.0874957	−	0.326538i
$976$	50.3109	−	13.4808i	1.61041	−	0.431509i
$977$	−16.2058	−	9.35641i	−0.518469	−	0.299338i	0.217839	−	0.975985i	$-0.430099\pi$
$977$	−16.2058	−	9.35641i	−0.518469	−	0.299338i	−0.736308	+	0.676647i	$0.763432\pi$
$978$	−99.9615	+	57.7128i	−3.19642	+	1.84545i
$979$	38.7846	−	38.7846i	1.23956	−	1.23956i
$980$			13.7321i			0.438654i
$981$	58.7487	−	33.9186i	1.87570	−	1.08294i
$982$	48.2942	+	27.8827i	1.54113	+	0.889772i
$983$	−1.94744	+	7.26795i	−0.0621137	+	0.231812i	−0.990003	−	0.141043i	$-0.954954\pi$
$983$	−1.94744	+	7.26795i	−0.0621137	+	0.231812i	0.927890	+	0.372855i	$0.121621\pi$
$984$	−10.3923	−	6.00000i	−0.331295	−	0.191273i
$985$	6.00000	−	10.3923i	0.191176	−	0.331126i
$986$	−79.4711	+	21.2942i	−2.53088	+	0.678146i
$987$		−	32.7846i		−	1.04355i
$988$	1.73205	−	1.00000i	0.0551039	−	0.0318142i
$989$	3.46410	+	12.9282i	0.110152	+	0.411093i
$990$	−14.7058	+	54.8827i	−0.467380	+	1.74429i
$991$	−18.9545	−	5.07884i	−0.602109	−	0.161335i	−0.0551275	−	0.998479i	$-0.517557\pi$
$991$	−18.9545	−	5.07884i	−0.602109	−	0.161335i	−0.546981	+	0.837145i	$0.684223\pi$
$992$	16.0981	+	4.31347i	0.511114	+	0.136953i
$993$	4.80385	−	17.9282i	0.152445	−	0.568934i
$994$	10.3923	+	38.7846i	0.329624	+	1.23017i
$995$	11.0263	−	41.1506i	0.349557	−	1.30456i
$996$	3.00000	+	1.73205i	0.0950586	+	0.0548821i
$997$	12.9282	+	22.3923i	0.409440	+	0.709171i	0.994827	−	0.101583i	$-0.0323907\pi$
$997$	12.9282	+	22.3923i	0.409440	+	0.709171i	−0.585387	+	0.810754i	$0.699057\pi$
$998$	64.0526			2.02755
$999$	43.3205	−	11.6077i	1.37060	−	0.367251i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	409.2.g.a.192.1	yes	4
409.49	even	12	inner	409.2.g.a.49.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
409.2.g.a.49.1	✓	4	409.49	even	12	inner
409.2.g.a.192.1	yes	4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 409 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	409.g (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 - 0.866025i) q^{2} +(-2.36603 + 1.36603i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.73205 q^{5} +4.73205 q^{6} +(-1.00000 + 3.73205i) q^{7} +1.73205i q^{8} +(2.23205 - 3.86603i) q^{9} +(2.59808 + 1.50000i) q^{10} +(-3.00000 + 3.00000i) q^{11} +(-2.36603 - 1.36603i) q^{12} +(1.36603 - 1.36603i) q^{13} +(4.73205 - 4.73205i) q^{14} +(4.09808 - 2.36603i) q^{15} +(2.50000 - 4.33013i) q^{16} +(-3.23205 + 5.59808i) q^{17} +(-6.69615 + 3.86603i) q^{18} +(0.732051 - 0.732051i) q^{19} +(-0.866025 - 1.50000i) q^{20} +(-2.73205 - 10.1962i) q^{21} +(7.09808 - 1.90192i) q^{22} +(4.09808 + 2.36603i) q^{23} +(-2.36603 - 4.09808i) q^{24} -2.00000 q^{25} +(-3.23205 + 0.866025i) q^{26} +4.00000i q^{27} +(-3.73205 + 1.00000i) q^{28} +(-7.09808 - 1.90192i) q^{29} -8.19615 q^{30} +(-2.26795 - 2.26795i) q^{31} +(-4.50000 + 2.59808i) q^{32} +(3.00000 - 11.1962i) q^{33} +(9.69615 - 5.59808i) q^{34} +(1.73205 - 6.46410i) q^{35} +4.46410 q^{36} +(-2.90192 - 10.8301i) q^{37} +(-1.73205 + 0.464102i) q^{38} +(-1.36603 + 5.09808i) q^{39} -3.00000i q^{40} +(2.19615 - 1.26795i) q^{41} +(-4.73205 + 17.6603i) q^{42} +(2.00000 + 2.00000i) q^{43} +(-4.09808 - 1.09808i) q^{44} +(-3.86603 + 6.69615i) q^{45} +(-4.09808 - 7.09808i) q^{46} +(3.00000 + 0.803848i) q^{47} +13.6603i q^{48} +(-6.86603 - 3.96410i) q^{49} +(3.00000 + 1.73205i) q^{50} -17.6603i q^{51} +(1.86603 + 0.500000i) q^{52} +(-0.464102 - 0.803848i) q^{53} +(3.46410 - 6.00000i) q^{54} +(5.19615 - 5.19615i) q^{55} +(-6.46410 - 1.73205i) q^{56} +(-0.732051 + 2.73205i) q^{57} +(9.00000 + 9.00000i) q^{58} +(4.26795 - 4.26795i) q^{59} +(4.09808 + 2.36603i) q^{60} +(7.36603 + 7.36603i) q^{61} +(1.43782 + 5.36603i) q^{62} +(12.1962 + 12.1962i) q^{63} -1.00000 q^{64} +(-2.36603 + 2.36603i) q^{65} +(-14.1962 + 14.1962i) q^{66} +(-1.80385 + 6.73205i) q^{67} -6.46410 q^{68} -12.9282 q^{69} +(-8.19615 + 8.19615i) q^{70} +(-3.00000 + 5.19615i) q^{71} +(6.69615 + 3.86603i) q^{72} +(14.5622 + 3.90192i) q^{73} +(-5.02628 + 18.7583i) q^{74} +(4.73205 - 2.73205i) q^{75} +(1.00000 + 0.267949i) q^{76} +(-8.19615 - 14.1962i) q^{77} +(6.46410 - 6.46410i) q^{78} +(5.00000 - 5.00000i) q^{79} +(-4.33013 + 7.50000i) q^{80} +(1.23205 + 2.13397i) q^{81} -4.39230 q^{82} -1.26795 q^{83} +(7.46410 - 7.46410i) q^{84} +(5.59808 - 9.69615i) q^{85} +(-1.26795 - 4.73205i) q^{86} +(19.3923 - 5.19615i) q^{87} +(-5.19615 - 5.19615i) q^{88} -12.9282 q^{89} +(11.5981 - 6.69615i) q^{90} +(3.73205 + 6.46410i) q^{91} +4.73205i q^{92} +(8.46410 + 2.26795i) q^{93} +(-3.80385 - 3.80385i) q^{94} +(-1.26795 + 1.26795i) q^{95} +(7.09808 - 12.2942i) q^{96} +(-14.7942 - 3.96410i) q^{97} +(6.86603 + 11.8923i) q^{98} +(4.90192 + 18.2942i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{2} - 6 q^{3} + 2 q^{4} + 12 q^{6} - 4 q^{7} + 2 q^{9} - 12 q^{11} - 6 q^{12} + 2 q^{13} + 12 q^{14} + 6 q^{15} + 10 q^{16} - 6 q^{17} - 6 q^{18} - 4 q^{19} - 4 q^{21} + 18 q^{22} + 6 q^{23} - 6 q^{24}+ \cdots + 30 q^{99}+O(q^{100}) \) 4 * q - 6 * q^2 - 6 * q^3 + 2 * q^4 + 12 * q^6 - 4 * q^7 + 2 * q^9 - 12 * q^11 - 6 * q^12 + 2 * q^13 + 12 * q^14 + 6 * q^15 + 10 * q^16 - 6 * q^17 - 6 * q^18 - 4 * q^19 - 4 * q^21 + 18 * q^22 + 6 * q^23 - 6 * q^24 - 8 * q^25 - 6 * q^26 - 8 * q^28 - 18 * q^29 - 12 * q^30 - 16 * q^31 - 18 * q^32 + 12 * q^33 + 18 * q^34 + 4 * q^36 - 22 * q^37 - 2 * q^39 - 12 * q^41 - 12 * q^42 + 8 * q^43 - 6 * q^44 - 12 * q^45 - 6 * q^46 + 12 * q^47 - 24 * q^49 + 12 * q^50 + 4 * q^52 + 12 * q^53 - 12 * q^56 + 4 * q^57 + 36 * q^58 + 24 * q^59 + 6 * q^60 + 26 * q^61 + 30 * q^62 + 28 * q^63 - 4 * q^64 - 6 * q^65 - 36 * q^66 - 28 * q^67 - 12 * q^68 - 24 * q^69 - 12 * q^70 - 12 * q^71 + 6 * q^72 + 34 * q^73 + 18 * q^74 + 12 * q^75 + 4 * q^76 - 12 * q^77 + 12 * q^78 + 20 * q^79 - 2 * q^81 + 24 * q^82 - 12 * q^83 + 16 * q^84 + 12 * q^85 - 12 * q^86 + 36 * q^87 - 24 * q^89 + 36 * q^90 + 8 * q^91 + 20 * q^93 - 36 * q^94 - 12 * q^95 + 18 * q^96 - 28 * q^97 + 24 * q^98 + 30 * q^99

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