LMFDB - Embedded newform 552.2.bb.a.469.39

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(13,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 0, 14]))

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

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

chi := DirichletCharacter("552.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.bb (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$48$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			469.39
Character	$\chi$	$=$	552.469
Dual form			552.2.bb.a.133.39

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.19448 - 0.757104i) q^{2} +(-0.755750 + 0.654861i) q^{3} +(0.853587 - 1.80870i) q^{4} +(-2.01890 + 0.290274i) q^{5} +(-0.406934 + 1.35440i) q^{6} +(0.214664 - 0.470048i) q^{7} +(-0.349776 - 2.80672i) q^{8} +(0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(q+(1.19448 - 0.757104i) q^{2} +(-0.755750 + 0.654861i) q^{3} +(0.853587 - 1.80870i) q^{4} +(-2.01890 + 0.290274i) q^{5} +(-0.406934 + 1.35440i) q^{6} +(0.214664 - 0.470048i) q^{7} +(-0.349776 - 2.80672i) q^{8} +(0.142315 - 0.989821i) q^{9} +(-2.19178 + 1.87525i) q^{10} +(0.754084 - 2.56817i) q^{11} +(0.539347 + 1.92590i) q^{12} +(5.11019 - 2.33374i) q^{13} +(-0.0994628 - 0.723988i) q^{14} +(1.33570 - 1.54147i) q^{15} +(-2.54278 - 3.08776i) q^{16} +(-3.23560 - 2.07940i) q^{17} +(-0.579405 - 1.29007i) q^{18} +(-0.853390 - 1.32790i) q^{19} +(-1.19829 + 3.89936i) q^{20} +(0.145584 + 0.495814i) q^{21} +(-1.04363 - 3.63856i) q^{22} +(-2.90764 - 3.81387i) q^{23} +(2.10235 + 1.89212i) q^{24} +(-0.805758 + 0.236592i) q^{25} +(4.33715 - 6.65657i) q^{26} +(0.540641 + 0.841254i) q^{27} +(-0.666941 - 0.789489i) q^{28} +(1.80210 - 2.80412i) q^{29} +(0.428411 - 2.85253i) q^{30} +(2.62274 - 3.02681i) q^{31} +(-5.37507 - 1.76314i) q^{32} +(1.11190 + 2.43472i) q^{33} +(-5.43920 - 0.0341182i) q^{34} +(-0.296942 + 1.01129i) q^{35} +(-1.66881 - 1.10230i) q^{36} +(6.67926 + 0.960332i) q^{37} +(-2.02472 - 0.940052i) q^{38} +(-2.33374 + 5.11019i) q^{39} +(1.52088 + 5.56495i) q^{40} +(0.979178 + 6.81033i) q^{41} +(0.549280 + 0.482019i) q^{42} +(-7.51004 + 6.50749i) q^{43} +(-4.00137 - 3.55607i) q^{44} +2.03966i q^{45} +(-6.36063 - 2.35422i) q^{46} +7.60726 q^{47} +(3.94376 + 0.668409i) q^{48} +(4.40916 + 5.08844i) q^{49} +(-0.783340 + 0.892648i) q^{50} +(3.80702 - 0.547367i) q^{51} +(0.140950 - 11.2348i) q^{52} +(1.29655 + 0.592116i) q^{53} +(1.28270 + 0.595543i) q^{54} +(-0.776947 + 5.40378i) q^{55} +(-1.39438 - 0.438089i) q^{56} +(1.51454 + 0.444709i) q^{57} +(0.0295683 - 4.71385i) q^{58} +(0.925840 - 0.422817i) q^{59} +(-1.64793 - 3.73165i) q^{60} +(4.46843 + 3.87191i) q^{61} +(0.841219 - 5.60117i) q^{62} +(-0.434714 - 0.279374i) q^{63} +(-7.75531 + 1.96345i) q^{64} +(-9.63954 + 6.19496i) q^{65} +(3.17148 + 2.06641i) q^{66} +(0.456590 + 1.55500i) q^{67} +(-6.52287 + 4.07728i) q^{68} +(4.69500 + 0.978231i) q^{69} +(0.410961 + 1.43279i) q^{70} +(-14.2043 + 4.17075i) q^{71} +(-2.82793 - 0.0532214i) q^{72} +(10.3050 - 6.62265i) q^{73} +(8.70534 - 3.90979i) q^{74} +(0.454016 - 0.706463i) q^{75} +(-3.13022 + 0.410046i) q^{76} +(-1.04529 - 0.905749i) q^{77} +(1.08132 + 7.87093i) q^{78} +(-3.77937 - 8.27566i) q^{79} +(6.02992 + 5.49579i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(6.32574 + 7.39350i) q^{82} +(-5.36142 - 0.770855i) q^{83} +(1.02105 + 0.159902i) q^{84} +(7.13596 + 3.25888i) q^{85} +(-4.04378 + 13.4590i) q^{86} +(0.474372 + 3.29933i) q^{87} +(-7.47189 - 1.21821i) q^{88} +(8.92759 + 10.3030i) q^{89} +(1.54424 + 2.43635i) q^{90} -2.90300i q^{91} +(-9.38007 + 2.00358i) q^{92} +4.00504i q^{93} +(9.08675 - 5.75948i) q^{94} +(2.10837 + 2.43319i) q^{95} +(5.21681 - 2.18743i) q^{96} +(-0.0860829 - 0.598720i) q^{97} +(9.11915 + 2.73987i) q^{98} +(-2.43472 - 1.11190i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9}+O(q^{10}) $ 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9	$ 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32} + 6 q^{34} - 22 q^{36} + 90 q^{38} - 74 q^{40} + 90 q^{42} - 130 q^{44} + 96 q^{46} - 88 q^{48} - 48 q^{49} + 142 q^{50} - 142 q^{52} + 18 q^{54} - 82 q^{56} + 22 q^{58} + 2 q^{60} - 40 q^{62} - 8 q^{63} + 16 q^{66} - 44 q^{68} + 16 q^{71} - 4 q^{72} + 10 q^{74} - 138 q^{76} - 40 q^{79} - 170 q^{80} - 48 q^{81} - 124 q^{82} - 8 q^{84} - 216 q^{86} - 108 q^{88} + 4 q^{90} - 198 q^{92} - 238 q^{94} + 80 q^{95} + 4 q^{96} - 132 q^{98}+O(q^{100}) $ 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{5}{11}\right)$	$1$	$-1$	$1$

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 $

$2$	1.19448	−	0.757104i	0.844628	−	0.535353i
$2$	1.19448	−	0.757104i	0.844628	−	0.535353i
$3$	−0.755750	+	0.654861i	−0.436332	+	0.378084i
$3$	−0.755750	+	0.654861i	−0.436332	+	0.378084i
$4$	0.853587	−	1.80870i	0.426793	−	0.904349i
$5$	−2.01890	+	0.290274i	−0.902881	+	0.129815i	−0.578092	−	0.815972i	$-0.696202\pi$
$5$	−2.01890	+	0.290274i	−0.902881	+	0.129815i	−0.324789	+	0.945787i	$0.605293\pi$
$6$	−0.406934	+	1.35440i	−0.166130	+	0.552932i
$7$	0.214664	−	0.470048i	0.0811353	−	0.177662i	−0.864717	−	0.502260i	$-0.832502\pi$
$7$	0.214664	−	0.470048i	0.0811353	−	0.177662i	0.945852	+	0.324599i	$0.105229\pi$
$8$	−0.349776	−	2.80672i	−0.123665	−	0.992324i
$9$	0.142315	−	0.989821i	0.0474383	−	0.329940i
$10$	−2.19178	+	1.87525i	−0.693102	+	0.593005i
$11$	0.754084	−	2.56817i	0.227365	−	0.774333i	−0.764229	−	0.644945i	$-0.776880\pi$
$11$	0.754084	−	2.56817i	0.227365	−	0.774333i	0.991594	−	0.129389i	$-0.0413015\pi$
$12$	0.539347	+	1.92590i	0.155696	+	0.555960i
$13$	5.11019	−	2.33374i	1.41731	−	0.647264i	0.448210	−	0.893928i	$-0.352062\pi$
$13$	5.11019	−	2.33374i	1.41731	−	0.647264i	0.969101	+	0.246664i	$0.0793344\pi$
$14$	−0.0994628	−	0.723988i	−0.0265825	−	0.193494i
$15$	1.33570	−	1.54147i	0.344875	−	0.398007i
$16$	−2.54278	−	3.08776i	−0.635695	−	0.771941i
$17$	−3.23560	−	2.07940i	−0.784749	−	0.504327i	0.0858577	−	0.996307i	$-0.472637\pi$
$17$	−3.23560	−	2.07940i	−0.784749	−	0.504327i	−0.870607	+	0.491980i	$0.836273\pi$
$18$	−0.579405	−	1.29007i	−0.136567	−	0.304073i
$19$	−0.853390	−	1.32790i	−0.195781	−	0.304641i	0.729458	−	0.684025i	$-0.239772\pi$
$19$	−0.853390	−	1.32790i	−0.195781	−	0.304641i	−0.925239	+	0.379384i	$0.876136\pi$
$20$	−1.19829	+	3.89936i	−0.267946	+	0.871923i
$21$	0.145584	+	0.495814i	0.0317690	+	0.108195i
$22$	−1.04363	−	3.63856i	−0.222503	−	0.775744i
$23$	−2.90764	−	3.81387i	−0.606285	−	0.795247i
$23$	−2.90764	−	3.81387i	−0.606285	−	0.795247i
$24$	2.10235	+	1.89212i	0.429141	+	0.386227i
$25$	−0.805758	+	0.236592i	−0.161152	+	0.0473184i
$26$	4.33715	−	6.65657i	0.850586	−	1.30546i
$27$	0.540641	+	0.841254i	0.104046	+	0.161899i
$28$	−0.666941	−	0.789489i	−0.126040	−	0.149199i
$29$	1.80210	−	2.80412i	0.334641	−	0.520712i	−0.632631	−	0.774453i	$-0.718025\pi$
$29$	1.80210	−	2.80412i	0.334641	−	0.520712i	0.967272	+	0.253742i	$0.0816614\pi$
$30$	0.428411	−	2.85253i	0.0782168	−	0.520798i
$31$	2.62274	−	3.02681i	0.471059	−	0.543631i	−0.469647	−	0.882854i	$-0.655619\pi$
$31$	2.62274	−	3.02681i	0.471059	−	0.543631i	0.940706	+	0.339223i	$0.110164\pi$
$32$	−5.37507	−	1.76314i	−0.950187	−	0.311682i
$33$	1.11190	+	2.43472i	0.193556	+	0.423830i
$34$	−5.43920	−	0.0341182i	−0.932814	−	0.00585122i
$35$	−0.296942	+	1.01129i	−0.0501924	+	0.170940i
$36$	−1.66881	−	1.10230i	−0.278135	−	0.183717i
$37$	6.67926	+	0.960332i	1.09806	+	0.157878i	0.667447	−	0.744658i	$-0.267387\pi$
$37$	6.67926	+	0.960332i	1.09806	+	0.157878i	0.430616	+	0.902535i	$0.358296\pi$
$38$	−2.02472	−	0.940052i	−0.328453	−	0.152497i
$39$	−2.33374	+	5.11019i	−0.373698	+	0.818285i
$40$	1.52088	+	5.56495i	0.240473	+	0.879897i
$41$	0.979178	+	6.81033i	0.152922	+	1.06360i	0.911289	+	0.411768i	$0.135088\pi$
$41$	0.979178	+	6.81033i	0.152922	+	1.06360i	−0.758367	+	0.651828i	$0.774002\pi$
$42$	0.549280	+	0.482019i	0.0847558	+	0.0743772i
$43$	−7.51004	+	6.50749i	−1.14527	+	0.992383i	−0.145275	+	0.989391i	$0.546407\pi$
$43$	−7.51004	+	6.50749i	−1.14527	+	0.992383i	−0.999996	+	0.00299165i	$0.999048\pi$
$44$	−4.00137	−	3.55607i	−0.603230	−	0.536098i
$45$			2.03966i			0.304055i
$46$	−6.36063	−	2.35422i	−0.937824	−	0.347111i
$47$	7.60726			1.10963			0.554816	−	0.831973i	$-0.312789\pi$
$47$	7.60726			1.10963			0.554816	+	0.831973i	$0.312789\pi$
$48$	3.94376	+	0.668409i	0.569232	+	0.0964766i
$49$	4.40916	+	5.08844i	0.629880	+	0.726920i
$50$	−0.783340	+	0.892648i	−0.110781	+	0.126239i
$51$	3.80702	−	0.547367i	0.533089	−	0.0766467i
$52$	0.140950	−	11.2348i	0.0195463	−	1.55799i
$53$	1.29655	+	0.592116i	0.178095	+	0.0813334i	0.502467	−	0.864596i	$-0.332426\pi$
$53$	1.29655	+	0.592116i	0.178095	+	0.0813334i	−0.324372	+	0.945930i	$0.605153\pi$
$54$	1.28270	+	0.595543i	0.174554	+	0.0810431i
$55$	−0.776947	+	5.40378i	−0.104763	+	0.728646i
$56$	−1.39438	−	0.438089i	−0.186331	−	0.0585421i
$57$	1.51454	+	0.444709i	0.200606	+	0.0589032i
$58$	0.0295683	−	4.71385i	0.00388251	−	0.618959i
$59$	0.925840	−	0.422817i	0.120534	−	0.0550461i	−0.354235	−	0.935156i	$-0.615259\pi$
$59$	0.925840	−	0.422817i	0.120534	−	0.0550461i	0.474769	+	0.880110i	$0.342531\pi$
$60$	−1.64793	−	3.73165i	−0.212747	−	0.481754i
$61$	4.46843	+	3.87191i	0.572124	+	0.495748i	0.892198	−	0.451645i	$-0.149162\pi$
$61$	4.46843	+	3.87191i	0.572124	+	0.495748i	−0.320074	+	0.947392i	$0.603708\pi$
$62$	0.841219	−	5.60117i	0.106835	−	0.711349i
$63$	−0.434714	−	0.279374i	−0.0547688	−	0.0351978i
$64$	−7.75531	+	1.96345i	−0.969414	+	0.245431i
$65$	−9.63954	+	6.19496i	−1.19564	+	0.768390i
$66$	3.17148	+	2.06641i	0.390382	+	0.254357i
$67$	0.456590	+	1.55500i	0.0557813	+	0.189974i	0.982670	−	0.185362i	$-0.0593457\pi$
$67$	0.456590	+	1.55500i	0.0557813	+	0.189974i	−0.926889	+	0.375336i	$0.877527\pi$
$68$	−6.52287	+	4.07728i	−0.791014	+	0.494443i
$69$	4.69500	+	0.978231i	0.565212	+	0.117765i
$70$	0.410961	+	1.43279i	0.0491192	+	0.171251i
$71$	−14.2043	+	4.17075i	−1.68574	+	0.494977i	−0.977489	−	0.210986i	$-0.932332\pi$
$71$	−14.2043	+	4.17075i	−1.68574	+	0.494977i	−0.708248	+	0.705963i	$0.750514\pi$
$72$	−2.82793	−	0.0532214i	−0.333274	−	0.00627220i
$73$	10.3050	−	6.62265i	1.20611	−	0.775123i	0.226111	−	0.974102i	$-0.427399\pi$
$73$	10.3050	−	6.62265i	1.20611	−	0.775123i	0.980004	+	0.198979i	$0.0637625\pi$
$74$	8.70534	−	3.90979i	1.01198	−	0.454504i
$75$	0.454016	−	0.706463i	0.0524253	−	0.0815753i
$76$	−3.13022	+	0.410046i	−0.359060	+	0.0470355i
$77$	−1.04529	−	0.905749i	−0.119122	−	0.103220i
$78$	1.08132	+	7.87093i	0.122436	+	0.891207i
$79$	−3.77937	−	8.27566i	−0.425212	−	0.931085i	−0.994079	−	0.108656i	$-0.965345\pi$
$79$	−3.77937	−	8.27566i	−0.425212	−	0.931085i	0.568867	−	0.822429i	$-0.307382\pi$
$80$	6.02992	+	5.49579i	0.674166	+	0.614448i
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$	6.32574	+	7.39350i	0.698562	+	0.816475i
$83$	−5.36142	−	0.770855i	−0.588492	−	0.0846124i	−0.158365	−	0.987381i	$-0.550622\pi$
$83$	−5.36142	−	0.770855i	−0.588492	−	0.0846124i	−0.430127	+	0.902768i	$0.641531\pi$
$84$	1.02105	+	0.159902i	0.111405	+	0.0174468i
$85$	7.13596	+	3.25888i	0.774004	+	0.353476i
$86$	−4.04378	+	13.4590i	−0.436053	+	1.45132i
$87$	0.474372	+	3.29933i	0.0508581	+	0.353726i
$88$	−7.47189	−	1.21821i	−0.796507	−	0.129862i
$89$	8.92759	+	10.3030i	0.946322	+	1.09211i	0.995635	+	0.0933307i	$0.0297514\pi$
$89$	8.92759	+	10.3030i	0.946322	+	1.09211i	−0.0493129	+	0.998783i	$0.515703\pi$
$90$	1.54424	+	2.43635i	0.162777	+	0.256813i
$91$		−	2.90300i		−	0.304318i
$92$	−9.38007	+	2.00358i	−0.977940	+	0.208887i
$93$			4.00504i			0.415303i
$94$	9.08675	−	5.75948i	0.937227	−	0.594046i
$95$	2.10837	+	2.43319i	0.216314	+	0.249640i
$96$	5.21681	−	2.18743i	0.532439	−	0.223254i
$97$	−0.0860829	−	0.598720i	−0.00874040	−	0.0607908i	0.984984	−	0.172643i	$-0.0552307\pi$
$97$	−0.0860829	−	0.598720i	−0.00874040	−	0.0607908i	−0.993725	+	0.111852i	$0.964322\pi$
$98$	9.11915	+	2.73987i	0.921174	+	0.276769i
$99$	−2.43472	−	1.11190i	−0.244698	−	0.111750i
$100$	−0.259861	+	1.65932i	−0.0259861	+	0.165932i
$101$	10.9578	+	1.57550i	1.09035	+	0.156768i	0.663956	−	0.747772i	$-0.268876\pi$
$101$	10.9578	+	1.57550i	1.09035	+	0.156768i	0.426389	+	0.904540i	$0.359785\pi$
$102$	4.13301	−	3.53613i	0.409229	−	0.350129i
$103$	−3.57440	−	1.04954i	−0.352197	−	0.103414i	0.100849	−	0.994902i	$-0.467844\pi$
$103$	−3.57440	−	1.04954i	−0.352197	−	0.103414i	−0.453045	+	0.891488i	$0.649662\pi$
$104$	−8.33758	−	13.5266i	−0.817567	−	1.32639i
$105$	−0.437842	−	0.958740i	−0.0427290	−	0.0935634i
$106$	1.99701	−	0.274352i	0.193966	−	0.0266475i
$107$	0.348630	+	0.302090i	0.0337033	+	0.0292041i	0.671550	−	0.740960i	$-0.265629\pi$
$107$	0.348630	+	0.302090i	0.0337033	+	0.0292041i	−0.637846	+	0.770164i	$0.720174\pi$
$108$	1.98306	−	0.259773i	0.190820	−	0.0249967i
$109$	2.26020	−	3.51695i	0.216488	−	0.336862i	−0.715976	−	0.698125i	$-0.754018\pi$
$109$	2.26020	−	3.51695i	0.216488	−	0.336862i	0.932464	+	0.361263i	$0.117654\pi$
$110$	3.16317	+	7.04296i	0.301597	+	0.671520i
$111$	−5.67673	+	3.64821i	−0.538811	+	0.346273i
$112$	−1.99724	+	0.532398i	−0.188721	+	0.0503068i
$113$	−11.5184	+	3.38210i	−1.08356	+	0.318162i	−0.774301	−	0.632817i	$-0.781899\pi$
$113$	−11.5184	+	3.38210i	−1.08356	+	0.318162i	−0.309257	+	0.950978i	$0.600080\pi$
$114$	2.14579	−	0.615466i	0.200971	−	0.0576437i
$115$	6.97731	+	6.85582i	0.650638	+	0.639308i
$116$	−3.53356	−	5.65301i	−0.328082	−	0.524869i
$117$	−1.58273	−	5.39030i	−0.146324	−	0.498333i
$118$	0.785785	−	1.20601i	0.0723374	−	0.111022i
$119$	−1.67198	+	1.07452i	−0.153270	+	0.0985009i
$120$	−4.79368	−	3.20975i	−0.437601	−	0.293008i
$121$	3.22692	+	2.07381i	0.293356	+	0.188529i
$122$	8.26891	+	1.24188i	0.748632	+	0.112434i
$123$	−5.19983	−	4.50568i	−0.468853	−	0.406264i
$124$	−3.23584	−	7.32740i	−0.290587	−	0.658020i
$125$	10.8348	−	4.94808i	0.969092	−	0.442570i
$126$	−0.730774	−	0.00458389i	−0.0651025	−	0.000408365i
$127$	14.4025	+	4.22896i	1.27802	+	0.375260i	0.849171	−	0.528118i	$-0.177102\pi$
$127$	14.4025	+	4.22896i	1.27802	+	0.375260i	0.428846	+	0.903378i	$0.358920\pi$
$128$	−7.77707	+	8.21688i	−0.687402	+	0.726277i
$129$	1.41421	−	9.83607i	0.124514	−	0.866017i
$130$	−6.82406	+	14.6979i	−0.598509	+	1.28909i
$131$	−17.5620	−	8.02030i	−1.53440	−	0.700737i	−0.544014	−	0.839076i	$-0.683096\pi$
$131$	−17.5620	−	8.02030i	−1.53440	−	0.700737i	−0.990385	+	0.138339i	$0.955824\pi$
$132$	5.35277	+	0.0671547i	0.465899	+	0.00584507i
$133$	−0.807370	+	0.116082i	−0.0700078	+	0.0100656i
$134$	1.72269	+	1.51174i	0.148818	+	0.130594i
$135$	−1.33570	−	1.54147i	−0.114958	−	0.132669i
$136$	−4.70454	+	9.80874i	−0.403411	+	0.841093i
$137$	−11.0872			−0.947242			−0.473621	−	0.880729i	$-0.657053\pi$
$137$	−11.0872			−0.947242			−0.473621	+	0.880729i	$0.657053\pi$
$138$	6.34873	−	2.38612i	0.540440	−	0.203120i
$139$			12.6389i			1.07202i	0.844211	+	0.536010i	$0.180069\pi$
$139$			12.6389i			1.07202i	−0.844211	+	0.536010i	$0.819931\pi$
$140$	1.57566	+	1.40031i	0.133167	+	0.118347i
$141$	−5.74918	+	4.98169i	−0.484168	+	0.419534i
$142$	−13.8091	+	15.7360i	−1.15883	+	1.32054i
$143$	−2.13995	−	14.8837i	−0.178952	−	1.24464i
$144$	−3.41821	+	2.07746i	−0.284851	+	0.173122i
$145$	−2.82429	+	6.18434i	−0.234545	+	0.513582i
$146$	7.29519	−	15.7127i	0.603754	−	1.30039i
$147$	−6.66444	−	0.958202i	−0.549674	−	0.0790312i
$148$	7.43828	−	11.2610i	0.611423	−	0.925651i
$149$	3.58066	−	12.1946i	0.293339	−	0.999022i	−0.672547	−	0.740055i	$-0.734800\pi$
$149$	3.58066	−	12.1946i	0.293339	−	0.999022i	0.965886	−	0.258967i	$-0.0833822\pi$
$150$	0.00744938	−	1.18760i	0.000608240	−	0.0969669i
$151$	2.85780	+	6.25771i	0.232565	+	0.509246i	0.989551	−	0.144185i	$-0.0460562\pi$
$151$	2.85780	+	6.25771i	0.232565	+	0.509246i	−0.756986	+	0.653431i	$0.773329\pi$
$152$	−3.42855	+	2.85969i	−0.278092	+	0.231952i
$153$	−2.51870	+	2.90674i	−0.203625	+	0.234996i
$154$	−1.93433	−	0.290510i	−0.155873	−	0.0234100i
$155$	−4.41646	+	6.87215i	−0.354739	+	0.551984i
$156$	7.25073	+	8.58303i	0.580523	+	0.687192i
$157$	7.88633	+	12.2714i	0.629398	+	0.979362i	0.998746	+	0.0500708i	$0.0159447\pi$
$157$	7.88633	+	12.2714i	0.629398	+	0.979362i	−0.369348	+	0.929291i	$0.620419\pi$
$158$	−10.7799	−	7.02378i	−0.857606	−	0.558782i
$159$	−1.36762	+	0.401571i	−0.108460	+	0.0318466i
$160$	11.3635	+	1.99936i	0.898366	+	0.158063i
$161$	−2.41687	+	0.548032i	−0.190476	+	0.0431910i
$162$	−1.35940	+	0.389911i	−0.106805	+	0.0306343i
$163$	−2.49635	−	8.50179i	−0.195529	−	0.665911i	−0.997635	−	0.0687298i	$-0.978105\pi$
$163$	−2.49635	−	8.50179i	−0.195529	−	0.665911i	0.802106	−	0.597182i	$-0.203713\pi$
$164$	13.1537	+	4.04217i	1.02713	+	0.315641i
$165$	−2.95155	−	4.59270i	−0.229778	−	0.357541i
$166$	−6.98775	+	3.13838i	−0.542354	+	0.243585i
$167$	14.3689	+	9.23435i	1.11190	+	0.714575i	0.961707	−	0.274081i	$-0.0883737\pi$
$167$	14.3689	+	9.23435i	1.11190	+	0.714575i	0.150194	+	0.988656i	$0.452010\pi$
$168$	1.34069	−	0.582037i	0.103436	−	0.0449051i
$169$	12.1545	−	14.0270i	0.934959	−	1.07900i
$170$	10.9911	−	1.50998i	0.842980	−	0.115810i
$171$	−1.43584	+	0.655724i	−0.109801	+	0.0501445i
$172$	5.35961	+	19.1381i	0.408666	+	1.45927i
$173$	1.79624	−	6.11742i	0.136565	−	0.465099i	−0.862603	−	0.505882i	$-0.831167\pi$
$173$	1.79624	−	6.11742i	0.136565	−	0.465099i	0.999168	+	0.0407831i	$0.0129853\pi$
$174$	3.06457	+	3.58185i	0.232324	+	0.271540i
$175$	−0.0617575	+	0.429533i	−0.00466843	+	0.0324696i
$176$	−9.84738	+	4.20186i	−0.742274	+	0.316727i
$177$	−0.422817	+	0.925840i	−0.0317809	+	0.0695904i
$178$	18.4643	+	5.54764i	1.38396	+	0.415814i
$179$	9.60657	−	1.38122i	0.718029	−	0.103237i	0.226391	−	0.974037i	$-0.427307\pi$
$179$	9.60657	−	1.38122i	0.718029	−	0.103237i	0.491638	+	0.870800i	$0.336398\pi$
$180$	3.68914	+	1.74103i	0.274972	+	0.129769i
$181$	−10.0306	+	8.69160i	−0.745571	+	0.646041i	−0.942435	−	0.334390i	$-0.891470\pi$
$181$	−10.0306	+	8.69160i	−0.745571	+	0.646041i	0.196864	+	0.980431i	$0.436924\pi$
$182$	−2.19788	−	3.46759i	−0.162917	−	0.257035i
$183$	−5.91258			−0.437070
$184$	−9.68743	+	9.49493i	−0.714167	+	0.699975i
$185$	−13.7635			−1.01191
$186$	3.03223	+	4.78396i	0.222334	+	0.350777i
$187$	−7.78016	+	6.74155i	−0.568942	+	0.492991i
$188$	6.49346	−	13.7592i	0.473584	−	1.00350i
$189$	0.511486	−	0.0735405i	0.0372051	−	0.00534929i
$190$	4.36059	+	1.31015i	0.316350	+	0.0950482i
$191$	8.37301	−	18.3343i	0.605850	−	1.32663i	−0.319527	−	0.947577i	$-0.603524\pi$
$191$	8.37301	−	18.3343i	0.605850	−	1.32663i	0.925377	−	0.379049i	$-0.123749\pi$
$192$	4.57529	−	6.56252i	0.330193	−	0.473609i
$193$	3.39679	−	23.6252i	0.244506	−	1.70058i	−0.384458	−	0.923142i	$-0.625612\pi$
$193$	3.39679	−	23.6252i	0.244506	−	1.70058i	0.628964	−	0.777434i	$-0.283479\pi$
$194$	−0.556118	−	0.649988i	−0.0399270	−	0.0466664i
$195$	3.22825	−	10.9944i	0.231179	−	0.787325i
$196$	12.9671	−	3.63141i	0.926218	−	0.259387i
$197$	−4.34657	+	1.98501i	−0.309681	+	0.141426i	−0.564193	−	0.825643i	$-0.690812\pi$
$197$	−4.34657	+	1.98501i	−0.309681	+	0.141426i	0.254512	+	0.967070i	$0.418085\pi$
$198$	−3.75005	+	0.515189i	−0.266505	+	0.0366129i
$199$	6.14112	−	7.08723i	0.435332	−	0.502400i	−0.495114	−	0.868828i	$-0.664874\pi$
$199$	6.14112	−	7.08723i	0.435332	−	0.502400i	0.930447	+	0.366427i	$0.119419\pi$
$200$	0.945881	+	2.17878i	0.0668839	+	0.154063i
$201$	−1.36338	−	0.876190i	−0.0961653	−	0.0618017i
$202$	14.2818	−	6.41431i	1.00486	−	0.451309i
$203$	−0.931225	−	1.44901i	−0.0653592	−	0.101701i
$204$	2.25960	−	7.35297i	0.158204	−	0.514811i
$205$	−3.95373	−	13.4652i	−0.276140	−	0.940448i
$206$	−5.06418	+	1.45254i	−0.352838	+	0.101203i
$207$	−4.18885	+	2.33528i	−0.291145	+	0.162313i
$208$	−20.2001	−	9.84485i	−1.40063	−	0.682617i
$209$	−4.05381	+	1.19031i	−0.280408	+	0.0823352i
$210$	−1.24886	−	0.813708i	−0.0861796	−	0.0561512i
$211$	1.44925	+	2.25508i	0.0997706	+	0.155246i	0.887550	−	0.460711i	$-0.152406\pi$
$211$	1.44925	+	2.25508i	0.0997706	+	0.155246i	−0.787779	+	0.615957i	$0.788769\pi$
$212$	2.17768	−	1.83965i	0.149564	−	0.126348i
$213$	8.00361	−	12.4539i	0.548399	−	0.853325i
$214$	0.645147	+	0.0968922i	0.0441013	+	0.00662342i
$215$	13.2731	−	15.3180i	0.905217	−	1.04468i
$216$	2.17206	−	1.81168i	0.147790	−	0.123269i
$217$	−0.859737	−	1.88256i	−0.0583628	−	0.127797i
$218$	0.0370848	−	5.91215i	0.00251170	−	0.400421i
$219$	−3.45112	+	11.7534i	−0.233205	+	0.794224i
$220$	9.11062	+	6.01786i	0.614238	+	0.405724i
$221$	−21.3873	−	3.07503i	−1.43867	−	0.206849i
$222$	−4.01869	+	8.65561i	−0.269717	+	0.580926i
$223$	2.65631	−	5.81651i	0.177880	−	0.389502i	−0.799600	−	0.600534i	$-0.794955\pi$
$223$	2.65631	−	5.81651i	0.177880	−	0.389502i	0.977479	+	0.211031i	$0.0676821\pi$
$224$	−1.98259	+	2.14806i	−0.132467	+	0.143523i
$225$	0.119512	+	0.831227i	0.00796749	+	0.0554151i
$226$	−11.1979	+	12.7605i	−0.744875	+	0.848815i
$227$	13.2020	−	11.4396i	0.876245	−	0.759270i	−0.0954690	−	0.995432i	$-0.530435\pi$
$227$	13.2020	−	11.4396i	0.876245	−	0.759270i	0.971714	+	0.236162i	$0.0758896\pi$
$228$	2.09714	−	2.35975i	0.138886	−	0.156278i
$229$			20.5469i			1.35778i	0.734240	+	0.678890i	$0.237539\pi$
$229$			20.5469i			1.35778i	−0.734240	+	0.678890i	$0.762461\pi$
$230$	13.5249	+	2.90662i	0.891803	+	0.191657i
$231$	1.38312			0.0910025
$232$	−8.50069	−	4.07716i	−0.558098	−	0.267679i
$233$	1.75321	+	2.02331i	0.114857	+	0.132552i	0.810266	−	0.586062i	$-0.199322\pi$
$233$	1.75321	+	2.02331i	0.114857	+	0.132552i	−0.695410	+	0.718614i	$0.744777\pi$
$234$	−5.97157	−	5.24033i	−0.390374	−	0.342571i
$235$	−15.3583	+	2.20819i	−1.00187	+	0.144047i
$236$	0.0255367	−	2.03548i	0.00166230	−	0.132498i
$237$	8.27566	+	3.77937i	0.537562	+	0.245496i
$238$	−1.18364	+	2.54936i	−0.0767237	+	0.165250i
$239$	−1.51784	+	10.5568i	−0.0981806	+	0.682861i	0.879980	+	0.475011i	$0.157556\pi$
$239$	−1.51784	+	10.5568i	−0.0981806	+	0.682861i	−0.978161	+	0.207850i	$0.933353\pi$
$240$	−8.15608	−	0.204681i	−0.526473	−	0.0132121i
$241$	11.4679	+	3.36729i	0.738714	+	0.216906i	0.629378	−	0.777099i	$-0.283310\pi$
$241$	11.4679	+	3.36729i	0.738714	+	0.216906i	0.109335	+	0.994005i	$0.465128\pi$
$242$	5.42460	+	0.0340266i	0.348706	+	0.00218731i
$243$	0.909632	−	0.415415i	0.0583529	−	0.0266489i
$244$	10.8173	−	4.77702i	0.692508	−	0.305817i
$245$	−10.3787	−	8.99320i	−0.663071	−	0.574555i
$246$	−9.62239	−	1.44515i	−0.613501	−	0.0921395i
$247$	−7.45997	−	4.79423i	−0.474666	−	0.305050i
$248$	−9.41277	−	6.30259i	−0.597711	−	0.400215i
$249$	4.55669	−	2.92841i	0.288769	−	0.185580i
$250$	9.19577	−	14.1135i	0.581592	−	0.892614i
$251$	4.73784	+	16.1356i	0.299050	+	1.01847i	0.962732	+	0.270455i	$0.0871743\pi$
$251$	4.73784	+	16.1356i	0.299050	+	1.01847i	−0.663683	+	0.748014i	$0.731008\pi$
$252$	−0.876369	+	0.547797i	−0.0552060	+	0.0345079i
$253$	−11.9873	+	4.59135i	−0.753634	+	0.288656i
$254$	20.4054	−	5.85278i	1.28035	−	0.367236i
$255$	−7.52711	+	2.21016i	−0.471366	+	0.138406i
$256$	−3.06855	+	15.7030i	−0.191785	+	0.981437i
$257$	−3.07254	+	1.97460i	−0.191660	+	0.123172i	−0.632952	−	0.774191i	$-0.718157\pi$
$257$	−3.07254	+	1.97460i	−0.191660	+	0.123172i	0.441292	+	0.897364i	$0.354520\pi$
$258$	−5.75767	−	12.8197i	−0.358457	−	0.798122i
$259$	1.88520	−	2.93342i	0.117140	−	0.182274i
$260$	2.97662	+	22.7230i	0.184602	+	1.40922i
$261$	−2.51911	−	2.18282i	−0.155929	−	0.135113i
$262$	−27.0497	+	3.71614i	−1.67114	+	0.229584i
$263$	−3.06878	−	6.71969i	−0.189229	−	0.414354i	0.791110	−	0.611674i	$-0.209503\pi$
$263$	−3.06878	−	6.71969i	−0.189229	−	0.414354i	−0.980339	+	0.197320i	$0.936776\pi$
$264$	6.44464	−	3.97239i	0.396640	−	0.244483i
$265$	−2.78949	−	0.819069i	−0.171357	−	0.0503150i
$266$	−0.876504	+	0.749921i	−0.0537419	+	0.0459806i
$267$	−13.4940	−	1.94015i	−0.825822	−	0.118735i
$268$	3.20227	+	0.501497i	0.195610	+	0.0306338i
$269$	−5.43388	−	2.48157i	−0.331310	−	0.151304i	0.242813	−	0.970073i	$-0.421930\pi$
$269$	−5.43388	−	2.48157i	−0.331310	−	0.151304i	−0.574123	+	0.818769i	$0.694657\pi$
$270$	−2.76252	−	0.830007i	−0.168122	−	0.0505126i
$271$	2.25768	+	15.7025i	0.137144	+	0.953859i	0.935916	+	0.352224i	$0.114575\pi$
$271$	2.25768	+	15.7025i	0.137144	+	0.953859i	−0.798772	+	0.601634i	$0.794516\pi$
$272$	1.80674	+	15.2782i	0.109550	+	0.926378i
$273$	1.90106	+	2.19394i	0.115058	+	0.132784i
$274$	−13.2435	+	8.39415i	−0.800068	+	0.507109i
$275$			2.24774i			0.135544i
$276$	5.77692	−	7.65684i	0.347730	−	0.460888i
$277$		−	18.8452i		−	1.13230i	−0.824303	−	0.566148i	$-0.808433\pi$
$277$		−	18.8452i		−	1.13230i	0.824303	−	0.566148i	$-0.191567\pi$
$278$	9.56899	+	15.0970i	0.573910	+	0.905459i
$279$	−2.62274	−	3.02681i	−0.157020	−	0.181210i
$280$	2.94228	+	0.479707i	0.175835	+	0.0286680i
$281$	2.41163	+	16.7733i	0.143866	+	1.00061i	0.926007	+	0.377507i	$0.123219\pi$
$281$	2.41163	+	16.7733i	0.143866	+	1.00061i	−0.782141	+	0.623101i	$0.785872\pi$
$282$	−3.09565	+	10.3033i	−0.184343	+	0.613552i
$283$	−12.3344	−	5.63292i	−0.733203	−	0.334842i	0.0135825	−	0.999908i	$-0.495676\pi$
$283$	−12.3344	−	5.63292i	−0.733203	−	0.334842i	−0.746785	+	0.665065i	$0.768404\pi$
$284$	−4.58095	+	29.2513i	−0.271830	+	1.73575i
$285$	−3.18680	−	0.458192i	−0.188769	−	0.0271410i
$286$	−13.8246	−	16.1582i	−0.817468	−	0.955452i
$287$	3.41138	+	1.00167i	0.201367	+	0.0591268i
$288$	−2.51014	+	5.06944i	−0.147912	+	0.298719i
$289$	−0.916817	−	2.00755i	−0.0539304	−	0.118091i
$290$	1.30861	+	9.52539i	0.0768445	+	0.559350i
$291$	0.457135	+	0.396110i	0.0267978	+	0.0232204i
$292$	−3.18212	−	24.2917i	−0.186220	−	1.42157i
$293$	−10.7413	+	16.7138i	−0.627515	+	0.976432i	0.371336	+	0.928499i	$0.378900\pi$
$293$	−10.7413	+	16.7138i	−0.627515	+	0.976432i	−0.998851	+	0.0479334i	$0.984736\pi$
$294$	−8.68603	+	3.90112i	−0.506580	+	0.227518i
$295$	−1.74645	+	1.12237i	−0.101682	+	0.0653471i
$296$	0.359135	−	19.0827i	0.0208743	−	1.10916i
$297$	2.56817	−	0.754084i	0.149021	−	0.0437564i
$298$	−4.95555	−	17.2772i	−0.287067	−	1.00084i
$299$	−23.7592	−	12.7039i	−1.37403	−	0.734686i
$300$	−0.890236	−	1.42421i	−0.0513978	−	0.0822266i
$301$	1.44670	+	4.92700i	0.0833864	+	0.283988i
$302$	8.15134	+	5.31109i	0.469057	+	0.305619i
$303$	−9.31311	+	5.98517i	−0.535024	+	0.343839i
$304$	−1.93026	+	6.01163i	−0.110708	+	0.344790i
$305$	−10.1452	−	6.51995i	−0.580915	−	0.373331i
$306$	−0.807849	+	5.37898i	−0.0461817	+	0.307496i
$307$	−18.5242	−	16.0513i	−1.05723	−	0.916095i	−0.0606031	−	0.998162i	$-0.519302\pi$
$307$	−18.5242	−	16.0513i	−1.05723	−	0.916095i	−0.996627	+	0.0820670i	$0.973848\pi$
$308$	−2.53047	+	1.11748i	−0.144187	+	0.0636743i
$309$	3.38866	−	1.54755i	0.192774	−	0.0880369i
$310$	−0.0724641	+	11.5524i	−0.00411569	+	0.656132i
$311$	10.6769	+	3.13501i	0.605430	+	0.177770i	0.570059	−	0.821604i	$-0.306920\pi$
$311$	10.6769	+	3.13501i	0.605430	+	0.177770i	0.0353712	+	0.999374i	$0.488739\pi$
$312$	15.1591	+	4.76274i	0.858217	+	0.269637i
$313$	3.94994	−	27.4725i	0.223264	−	1.55284i	−0.502308	−	0.864689i	$-0.667515\pi$
$313$	3.94994	−	27.4725i	0.223264	−	1.55284i	0.725572	−	0.688147i	$-0.241575\pi$
$314$	18.7108	+	8.68719i	1.05591	+	0.490247i
$315$	0.958740	+	0.437842i	0.0540189	+	0.0246696i
$316$	−18.1942	−	0.228261i	−1.02350	−	0.0128407i
$317$	−0.871027	+	0.125235i	−0.0489217	+	0.00703388i	−0.166732	−	0.986002i	$-0.553322\pi$
$317$	−0.871027	+	0.125235i	−0.0489217	+	0.00703388i	0.117811	+	0.993036i	$0.462412\pi$
$318$	−1.32957	+	1.51510i	−0.0745588	+	0.0849628i
$319$	−5.84253	−	6.74264i	−0.327119	−	0.377515i
$320$	15.0873	−	6.21517i	0.843405	−	0.347439i
$321$	−0.461304			−0.0257475
$322$	−2.47200	+	2.48444i	−0.137759	+	0.138452i
$323$			6.07110i			0.337805i
$324$	−1.32858	+	1.49495i	−0.0738100	+	0.0830528i
$325$	−3.56543	+	3.08946i	−0.197774	+	0.171372i
$326$	−9.41859	−	8.26526i	−0.521647	−	0.457770i
$327$	0.594962	+	4.13805i	0.0329014	+	0.228835i
$328$	18.7722	−	5.13037i	1.03652	−	0.283277i
$329$	1.63300	−	3.57578i	0.0900304	−	0.197139i
$330$	−7.00273	−	3.25128i	−0.385487	−	0.178977i
$331$	27.7790	+	3.99401i	1.52687	+	0.219531i	0.854017	−	0.520246i	$-0.174160\pi$
$331$	27.7790	+	3.99401i	1.52687	+	0.219531i	0.672853	+	0.739776i	$0.265069\pi$
$332$	−5.97068	+	9.03919i	−0.327684	+	0.496090i
$333$	1.90111	−	6.47460i	0.104180	−	0.354806i
$334$	24.1548	+	0.151515i	1.32169	+	0.00829052i
$335$	−1.37319	−	3.00686i	−0.0750253	−	0.164282i
$336$	1.16077	−	1.71027i	0.0633250	−	0.0933030i
$337$	−20.4827	+	23.6383i	−1.11576	+	1.28766i	−0.162102	+	0.986774i	$0.551827\pi$
$337$	−20.4827	+	23.6383i	−1.11576	+	1.28766i	−0.953660	+	0.300885i	$0.902718\pi$
$338$	3.89842	−	25.9572i	0.212046	−	1.41189i
$339$	6.49021	−	10.0990i	0.352500	−	0.548500i
$340$	11.9855	−	10.1251i	0.650005	−	0.549108i
$341$	−5.79560	−	9.01813i	−0.313849	−	0.488359i
$342$	−1.21863	+	1.87033i	−0.0658961	+	0.101136i
$343$	6.80900	−	1.99930i	0.367651	−	0.107952i
$344$	20.8915	+	18.8024i	1.12639	+	1.01376i
$345$	−9.76271	−	0.612113i	−0.525607	−	0.0329551i
$346$	−2.48595	−	8.66710i	−0.133645	−	0.465946i
$347$	6.96813	+	23.7313i	0.374069	+	1.27396i	0.904588	+	0.426288i	$0.140179\pi$
$347$	6.96813	+	23.7313i	0.374069	+	1.27396i	−0.530519	+	0.847673i	$0.678003\pi$
$348$	6.37242	+	1.95827i	0.341597	+	0.104974i
$349$	−2.57513	−	4.00697i	−0.137843	−	0.214488i	0.765468	−	0.643474i	$-0.222507\pi$
$349$	−2.57513	−	4.00697i	−0.137843	−	0.214488i	−0.903311	+	0.428986i	$0.858871\pi$
$350$	0.251433	+	0.559827i	0.0134396	+	0.0299240i
$351$	4.72605	+	3.03725i	0.252258	+	0.162116i
$352$	−8.58129	+	12.4746i	−0.457384	+	0.664896i
$353$	18.2894	−	21.1071i	0.973446	−	1.12342i	−0.0188865	−	0.999822i	$-0.506012\pi$
$353$	18.2894	−	21.1071i	0.973446	−	1.12342i	0.992333	−	0.123595i	$-0.0394424\pi$
$354$	0.195909	+	1.42602i	0.0104124	+	0.0757920i
$355$	27.4664	−	12.5435i	1.45776	−	0.665739i
$356$	26.2555	−	7.35282i	1.39154	−	0.389699i
$357$	0.559941	−	1.90698i	0.0296352	−	0.100928i
$358$	10.4292	−	8.92301i	0.551199	−	0.471596i
$359$	3.36682	−	23.4167i	0.177694	−	1.23589i	−0.684388	−	0.729118i	$-0.739930\pi$
$359$	3.36682	−	23.4167i	0.177694	−	1.23589i	0.862082	−	0.506769i	$-0.169160\pi$
$360$	5.72476	−	0.713426i	0.301721	−	0.0376008i
$361$	6.85784	−	15.0166i	0.360939	−	0.790346i
$362$	−5.40100	+	17.9762i	−0.283870	+	0.944809i
$363$	−3.79680	+	0.545898i	−0.199280	+	0.0286522i
$364$	−5.25066	−	2.47797i	−0.275209	−	0.129881i
$365$	−18.8825	+	16.3618i	−0.988355	+	0.856415i
$366$	−7.06248	+	4.47644i	−0.369162	+	0.233987i
$367$	−19.9636			−1.04209			−0.521046	−	0.853529i	$-0.674458\pi$
$367$	−19.9636			−1.04209			−0.521046	+	0.853529i	$0.674458\pi$
$368$	−4.38284	+	18.6759i	−0.228471	+	0.973551i
$369$	6.88037			0.358178
$370$	−16.4403	+	10.4204i	−0.854691	+	0.541732i
$371$	0.556646	−	0.482337i	0.0288996	−	0.0250417i
$372$	7.24391	+	3.41865i	0.375579	+	0.177249i
$373$	−30.0606	+	4.32206i	−1.55648	+	0.223788i	−0.866178	−	0.499735i	$-0.833431\pi$
$373$	−30.0606	+	4.32206i	−1.55648	+	0.223788i	−0.690300	+	0.723523i	$0.742522\pi$
$374$	−4.18923	+	13.9431i	−0.216620	+	0.720979i
$375$	−4.94808	+	10.8348i	−0.255518	+	0.559506i
$376$	−2.66084	−	21.3514i	−0.137222	−	1.10112i
$377$	2.66496	−	18.5352i	0.137252	−	0.954611i
$378$	0.555284	−	0.475091i	0.0285607	−	0.0244360i
$379$	7.14274	−	24.3259i	0.366898	−	1.24954i	−0.544761	−	0.838591i	$-0.683380\pi$
$379$	7.14274	−	24.3259i	0.366898	−	1.24954i	0.911659	−	0.410948i	$-0.134802\pi$
$380$	6.20057	−	1.73646i	0.318083	−	0.0890788i
$381$	−13.6541	+	6.23561i	−0.699520	+	0.319460i
$382$	−3.87957	−	28.2393i	−0.198496	−	1.44485i
$383$	9.29738	−	10.7297i	0.475074	−	0.548264i	−0.466742	−	0.884393i	$-0.654572\pi$
$383$	9.29738	−	10.7297i	0.475074	−	0.548264i	0.941816	+	0.336129i	$0.109118\pi$
$384$	0.496603	−	11.3028i	0.0253421	−	0.576794i
$385$	2.37326	+	1.52520i	0.120952	+	0.0777313i
$386$	−13.8293	−	30.7916i	−0.703893	−	1.56725i
$387$	5.37246	+	8.35971i	0.273098	+	0.424948i
$388$	−1.15638	−	0.355362i	−0.0587065	−	0.0180407i
$389$	5.93379	+	20.2086i	0.300855	+	1.02462i	0.961702	+	0.274098i	$0.0883793\pi$
$389$	5.93379	+	20.2086i	0.300855	+	1.02462i	−0.660846	+	0.750521i	$0.729803\pi$
$390$	−4.46781	−	15.5768i	−0.226236	−	0.788760i
$391$	1.47743	+	18.3863i	0.0747167	+	0.929836i
$392$	12.7396	−	14.1551i	0.643447	−	0.714939i
$393$	18.5247	−	5.43933i	0.934445	−	0.274378i
$394$	−3.68905	+	5.66188i	−0.185852	+	0.285241i
$395$	10.0324	+	15.6107i	0.504784	+	0.785460i
$396$	−4.08933	+	3.45456i	−0.205496	+	0.173598i
$397$	9.89176	−	15.3919i	0.496453	−	0.772496i	−0.499115	−	0.866536i	$-0.666342\pi$
$397$	9.89176	−	15.3919i	0.496453	−	0.772496i	0.995568	+	0.0940393i	$0.0299779\pi$
$398$	1.96970	−	13.1151i	0.0987323	−	0.657398i
$399$	0.534152	−	0.616444i	0.0267410	−	0.0308608i
$400$	2.77940	+	1.88639i	0.138970	+	0.0943194i
$401$	15.0980	+	33.0600i	0.753958	+	1.65094i	0.759120	+	0.650951i	$0.225630\pi$
$401$	15.0980	+	33.0600i	0.753958	+	1.65094i	−0.00516189	+	0.999987i	$0.501643\pi$
$402$	−2.29190	−	0.0143763i	−0.114310	−	0.000717024i
$403$	6.33892	−	21.5884i	0.315764	−	1.07539i
$404$	12.2031	−	18.4746i	0.607125	−	0.919145i
$405$	2.01890	+	0.290274i	0.100320	+	0.0144238i
$406$	−2.20939	−	1.02579i	−0.109650	−	0.0509092i
$407$	7.50302	−	16.4293i	0.371911	−	0.814371i
$408$	−2.86791	−	10.4938i	−0.141983	−	0.519519i
$409$	4.06636	+	28.2821i	0.201068	+	1.39846i	0.801122	+	0.598501i	$0.204237\pi$
$409$	4.06636	+	28.2821i	0.201068	+	1.39846i	−0.600054	+	0.799960i	$0.704854\pi$
$410$	−14.9172	−	13.0906i	−0.736708	−	0.646496i
$411$	8.37914	−	7.26056i	0.413312	−	0.358137i
$412$	−4.94937	+	5.56915i	−0.243838	+	0.274372i
$413$		−	0.525953i		−	0.0258805i
$414$	−3.23547	+	5.96085i	−0.159015	+	0.292960i
$415$	11.0479			0.542322
$416$	−31.5823	+	3.53407i	−1.54845	+	0.173272i
$417$	−8.27674	−	9.55187i	−0.405314	−	0.467757i
$418$	−3.94103	+	4.49096i	−0.192762	+	0.219660i
$419$	3.42952	−	0.493091i	0.167543	−	0.0240891i	−0.0580326	−	0.998315i	$-0.518483\pi$
$419$	3.42952	−	0.493091i	0.167543	−	0.0240891i	0.225576	+	0.974226i	$0.427574\pi$
$420$	−2.10781	−	0.0264441i	−0.102850	−	0.00129034i
$421$	16.3495	+	7.46657i	0.796826	+	0.363898i	0.771862	−	0.635790i	$-0.219326\pi$
$421$	16.3495	+	7.46657i	0.796826	+	0.363898i	0.0249641	+	0.999688i	$0.492053\pi$
$422$	3.43844	+	1.59642i	0.167381	+	0.0777127i
$423$	1.08263	−	7.52983i	0.0526391	−	0.366113i
$424$	1.20840	−	3.84617i	0.0586850	−	0.186786i
$425$	3.09908	+	0.909972i	0.150327	+	0.0441401i
$426$	0.131321	−	20.9355i	0.00636253	−	1.01433i
$427$	2.77920	−	1.26922i	0.134495	−	0.0614217i
$428$	0.843975	−	0.372707i	0.0407951	−	0.0180155i
$429$	11.3640	+	9.84697i	0.548659	+	0.475416i
$430$	4.25721	−	28.3462i	0.205301	−	1.36697i
$431$	3.74242	+	2.40511i	0.180266	+	0.115850i	0.627662	−	0.778486i	$-0.284012\pi$
$431$	3.74242	+	2.40511i	0.180266	+	0.115850i	−0.447396	+	0.894336i	$0.647648\pi$
$432$	1.22286	−	3.80849i	0.0588349	−	0.183236i
$433$	−3.14167	+	2.01903i	−0.150979	+	0.0970282i	−0.613949	−	0.789346i	$-0.710420\pi$
$433$	−3.14167	+	2.01903i	−0.150979	+	0.0970282i	0.462970	+	0.886374i	$0.346784\pi$
$434$	−2.45224	−	1.59778i	−0.117711	−	0.0766959i
$435$	−1.91542	−	6.52333i	−0.0918375	−	0.312770i
$436$	−4.43181	−	7.09004i	−0.212245	−	0.339552i
$437$	−2.58309	+	7.11578i	−0.123566	+	0.340394i
$438$	4.77626	+	16.6522i	0.228219	+	0.795671i
$439$	−27.0062	+	7.92972i	−1.28893	+	0.378465i	−0.853187	−	0.521605i	$-0.825334\pi$
$439$	−27.0062	+	7.92972i	−1.28893	+	0.378465i	−0.435746	+	0.900070i	$0.643515\pi$
$440$	15.4386	+	0.290554i	0.736008	+	0.0138516i
$441$	5.66414	−	3.64012i	0.269721	−	0.173339i
$442$	−27.8749	+	12.5193i	−1.32588	+	0.595484i
$443$	−4.29701	+	6.68627i	−0.204157	+	0.317674i	−0.928201	−	0.372079i	$-0.878645\pi$
$443$	−4.29701	+	6.68627i	−0.204157	+	0.317674i	0.724044	+	0.689754i	$0.242281\pi$
$444$	1.75293	+	13.3816i	0.0831905	+	0.635060i
$445$	−21.0146	−	18.2093i	−0.996188	−	0.863202i
$446$	−1.23078	−	8.95884i	−0.0582792	−	0.424213i
$447$	5.27969	+	11.5609i	0.249721	+	0.546812i
$448$	−0.741871	+	4.06685i	−0.0350501	+	0.192141i
$449$	−5.66006	−	1.66194i	−0.267115	−	0.0784319i	0.145433	−	0.989368i	$-0.453543\pi$
$449$	−5.66006	−	1.66194i	−0.267115	−	0.0784319i	−0.412547	+	0.910936i	$0.635361\pi$
$450$	0.772081	+	0.902404i	0.0363962	+	0.0425397i
$451$	18.2285	+	2.62086i	0.858346	+	0.123412i
$452$	−3.71474	+	23.7202i	−0.174727	+	1.11570i
$453$	−6.25771	−	2.85780i	−0.294013	−	0.134271i
$454$	7.10860	−	23.6596i	0.333623	−	1.11040i
$455$	0.842668	+	5.86088i	0.0395049	+	0.274762i
$456$	0.718422	−	4.40643i	0.0336432	−	0.206350i
$457$	0.232393	+	0.268195i	0.0108709	+	0.0125457i	0.761159	−	0.648565i	$-0.224631\pi$
$457$	0.232393	+	0.268195i	0.0108709	+	0.0125457i	−0.750288	+	0.661111i	$0.770085\pi$
$458$	15.5562	+	24.5430i	0.726892	+	1.14682i
$459$		−	3.84617i		−	0.179524i
$460$	18.3559	−	6.76782i	0.855846	−	0.315551i
$461$		−	9.49749i		−	0.442342i	−0.975235	−	0.221171i	$-0.929012\pi$
$461$		−	9.49749i		−	0.442342i	0.975235	−	0.221171i	$-0.0709879\pi$
$462$	1.65211	−	1.04716i	0.0768632	−	0.0487185i
$463$	−12.9762	−	14.9753i	−0.603054	−	0.695962i	0.369343	−	0.929293i	$-0.379583\pi$
$463$	−12.9762	−	14.9753i	−0.603054	−	0.695962i	−0.972397	+	0.233332i	$0.925037\pi$
$464$	−13.2408	+	1.56580i	−0.614688	+	0.0726906i
$465$	−1.16256	−	8.08579i	−0.0539125	−	0.374969i
$466$	3.62604	+	1.08945i	0.167973	+	0.0504679i
$467$	28.0694	+	12.8189i	1.29890	+	0.593187i	0.940313	−	0.340311i	$-0.110532\pi$
$467$	28.0694	+	12.8189i	1.29890	+	0.593187i	0.358584	+	0.933497i	$0.383260\pi$
$468$	−11.1004	−	1.73840i	−0.513117	−	0.0803576i
$469$	0.828940	+	0.119184i	0.0382769	+	0.00550338i
$470$	−16.6734	+	14.2655i	−0.769088	+	0.658018i
$471$	−13.9961	−	4.10963i	−0.644908	−	0.189362i
$472$	−1.51056	−	2.45068i	−0.0695294	−	0.112802i
$473$	11.0492	+	24.1943i	0.508041	+	1.11245i
$474$	12.7465	−	1.75114i	0.585467	−	0.0804325i
$475$	1.00180	+	0.868062i	0.0459656	+	0.0398294i
$476$	0.516296	+	3.94131i	0.0236644	+	0.180650i
$477$	0.770608	−	1.19909i	0.0352837	−	0.0549025i
$478$	6.17955	+	13.7591i	0.282646	+	0.629325i
$479$	−17.1188	+	11.0016i	−0.782177	+	0.502675i	−0.869755	−	0.493483i	$-0.835724\pi$
$479$	−17.1188	+	11.0016i	−0.782177	+	0.502675i	0.0875785	+	0.996158i	$0.472087\pi$
$480$	−9.89728	+	5.93052i	−0.451747	+	0.270690i
$481$	36.3734	−	10.6802i	1.65849	−	0.486975i
$482$	16.2476	−	4.66024i	0.740060	−	0.212268i
$483$	1.46766	−	1.99689i	0.0667810	−	0.0908615i
$484$	6.50536	−	4.06634i	0.295698	−	0.184834i
$485$	0.347586	+	1.18377i	0.0157831	+	0.0537522i
$486$	0.772029	−	1.18489i	0.0350199	−	0.0537478i
$487$	−20.0699	+	12.8982i	−0.909455	+	0.584471i	−0.909580	−	0.415529i	$-0.863597\pi$
$487$	−20.0699	+	12.8982i	−0.909455	+	0.584471i	0.000125165		1.00000i	$0.499960\pi$
$488$	9.30442	−	13.8959i	0.421191	−	0.629038i
$489$	7.45410	+	4.79046i	0.337086	+	0.216632i
$490$	−19.2060	−	2.88448i	−0.867638	−	0.130307i
$491$	15.4721	+	13.4066i	0.698244	+	0.605032i	0.929920	−	0.367761i	$-0.119875\pi$
$491$	15.4721	+	13.4066i	0.698244	+	0.605032i	−0.231676	+	0.972793i	$0.574421\pi$
$492$	−12.5879	+	5.55894i	−0.567508	+	0.250616i
$493$	−11.6617	+	5.32574i	−0.525218	+	0.239859i
$494$	−12.5405	−	0.0786625i	−0.564226	−	0.00353919i
$495$	5.23821	+	1.53808i	0.235440	+	0.0691314i
$496$	−16.0151	−	0.401908i	−0.719100	−	0.0180462i
$497$	−1.08869	+	7.57200i	−0.0488344	+	0.339651i
$498$	3.22579	−	6.94783i	0.144551	−	0.311340i
$499$	11.2018	+	5.11568i	0.501460	+	0.229009i	0.650053	−	0.759889i	$-0.274747\pi$
$499$	11.2018	+	5.11568i	0.501460	+	0.229009i	−0.148592	+	0.988899i	$0.547474\pi$
$500$	0.298847	−	23.8205i	0.0133648	−	1.06528i
$501$	−16.9065	+	2.43079i	−0.755328	+	0.108600i
$502$	17.8756	+	15.6867i	0.797827	+	0.700131i
$503$	22.4596	+	25.9197i	1.00142	+	1.15570i	0.987789	+	0.155796i	$0.0497944\pi$
$503$	22.4596	+	25.9197i	1.00142	+	1.15570i	0.0136335	+	0.999907i	$0.495660\pi$
$504$	−0.632070	+	1.31784i	−0.0281546	+	0.0587011i
$505$	−22.5801			−1.00480
$506$	−10.8425	+	14.5599i	−0.482008	+	0.647267i
$507$			18.5604i			0.824295i
$508$	19.9427	−	22.4400i	0.884815	−	0.995615i
$509$	3.19111	−	2.76511i	0.141443	−	0.122561i	−0.581265	−	0.813714i	$-0.697442\pi$
$509$	3.19111	−	2.76511i	0.141443	−	0.122561i	0.722709	+	0.691153i	$0.242897\pi$
$510$	−7.31770	+	8.33881i	−0.324033	+	0.369249i
$511$	−0.900845	−	6.26551i	−0.0398510	−	0.277170i
$512$	8.22346	+	21.0802i	0.363429	+	0.931622i
$513$	0.655724	−	1.43584i	0.0289509	−	0.0633937i
$514$	−2.17512	+	4.68486i	−0.0959406	+	0.206640i
$515$	7.52103	+	1.08136i	0.331416	+	0.0476504i
$516$	−16.5833	−	10.9538i	−0.730040	−	0.482215i
$517$	5.73651	−	19.5368i	0.252291	−	0.859225i
$518$	0.0309318	−	4.93122i	0.00135907	−	0.216665i
$519$	2.64855	+	5.79952i	0.116259	+	0.254571i
$520$	20.7592	+	24.8886i	0.910350	+	1.09144i
$521$	−5.54587	+	6.40028i	−0.242969	+	0.280401i	−0.864116	−	0.503293i	$-0.832122\pi$
$521$	−5.54587	+	6.40028i	−0.242969	+	0.280401i	0.621147	+	0.783694i	$0.286667\pi$
$522$	−4.66166	−	0.700118i	−0.204035	−	0.0306433i
$523$	−19.5121	+	30.3614i	−0.853205	+	1.32761i	0.0901840	+	0.995925i	$0.471254\pi$
$523$	−19.5121	+	30.3614i	−0.853205	+	1.32761i	−0.943389	+	0.331688i	$0.892382\pi$
$524$	−29.4970	+	24.9183i	−1.28858	+	1.08856i
$525$	−0.234611	−	0.365062i	−0.0102393	−	0.0159326i
$526$	−8.75311	−	5.70318i	−0.381654	−	0.248670i
$527$	−14.7801	+	4.33983i	−0.643831	+	0.189046i
$528$	4.69051	−	9.62422i	0.204128	−	0.418840i
$529$	−6.09123	+	22.1787i	−0.264836	+	0.964293i
$530$	−3.95212	+	1.13357i	−0.171669	+	0.0492391i
$531$	−0.286753	−	0.976590i	−0.0124440	−	0.0423804i
$532$	−0.479203	+	1.55937i	−0.0207761	+	0.0676075i
$533$	20.8974	+	32.5169i	0.905165	+	1.40846i
$534$	−17.5873	+	7.89891i	−0.761078	+	0.341819i
$535$	−0.791539	−	0.508691i	−0.0342212	−	0.0219926i
$536$	4.20475	−	1.82542i	0.181617	−	0.0788462i
$537$	−6.35566	+	7.33482i	−0.274267	+	0.316521i
$538$	−8.36950	+	1.14982i	−0.360835	+	0.0495721i
$539$	16.3929	−	7.48638i	0.706091	−	0.322461i
$540$	−3.92819	+	1.10009i	−0.169043	+	0.0473402i
$541$	−8.69532	+	29.6135i	−0.373841	+	1.27319i	0.530977	+	0.847386i	$0.321825\pi$
$541$	−8.69532	+	29.6135i	−0.373841	+	1.27319i	−0.904818	+	0.425799i	$0.859993\pi$
$542$	14.5852	+	17.0471i	0.626487	+	0.732235i
$543$	1.88886	−	13.1373i	0.0810589	−	0.563777i
$544$	13.7253	+	16.8817i	0.588468	+	0.723797i
$545$	−3.54225	+	7.75645i	−0.151733	+	0.332250i
$546$	3.93184	+	1.18133i	0.168267	+	0.0505563i
$547$	28.7038	−	4.12699i	1.22729	−	0.176457i	0.501978	−	0.864880i	$-0.332606\pi$
$547$	28.7038	−	4.12699i	1.22729	−	0.176457i	0.725310	+	0.688423i	$0.241697\pi$
$548$	−9.46388	+	20.0534i	−0.404277	+	0.856638i
$549$	4.46843	−	3.87191i	0.190708	−	0.165249i
$550$	1.70177	+	2.68488i	0.0725637	+	0.114484i
$551$	−5.26148			−0.224147
$552$	1.10342	−	13.5197i	0.0469645	−	0.575437i
$553$	−4.70125			−0.199918
$554$	−14.2678	−	22.5103i	−0.606179	−	0.956370i
$555$	10.4018	−	9.01319i	0.441531	−	0.382589i
$556$	22.8600	+	10.7884i	0.969481	+	0.457531i
$557$	45.5949	−	6.55556i	1.93192	−	0.277768i	0.934900	−	0.354911i	$-0.115489\pi$
$557$	45.5949	−	6.55556i	1.93192	−	0.277768i	0.997020	+	0.0771431i	$0.0245798\pi$
$558$	−5.42444	−	1.62979i	−0.229635	−	0.0689943i
$559$	−23.1909	+	50.7810i	−0.980871	+	2.14781i
$560$	3.87769	−	1.65461i	0.163862	−	0.0699199i
$561$	1.46508	−	10.1898i	0.0618557	−	0.430216i
$562$	15.5798	+	18.2095i	0.657192	+	0.768123i
$563$	5.05415	−	17.2128i	0.213007	−	0.725435i	−0.781789	−	0.623544i	$-0.785692\pi$
$563$	5.05415	−	17.2128i	0.213007	−	0.725435i	0.994796	−	0.101891i	$-0.0324894\pi$
$564$	4.10295	+	14.6508i	0.172766	+	0.616912i
$565$	22.2728	−	10.1716i	0.937022	−	0.427924i
$566$	−18.9979	+	2.60997i	−0.798543	+	0.109705i
$567$	−0.338396	+	0.390530i	−0.0142113	+	0.0164007i
$568$	16.6744	+	38.4085i	0.699644	+	1.61159i
$569$	−15.7142	−	10.0989i	−0.658774	−	0.423368i	0.168089	−	0.985772i	$-0.446240\pi$
$569$	−15.7142	−	10.0989i	−0.658774	−	0.423368i	−0.826863	+	0.562403i	$0.809877\pi$
$570$	−4.15348	+	1.86543i	−0.173970	+	0.0781344i
$571$	−2.95467	−	4.59755i	−0.123649	−	0.192402i	0.773910	−	0.633295i	$-0.218298\pi$
$571$	−2.95467	−	4.59755i	−0.123649	−	0.192402i	−0.897559	+	0.440893i	$0.854662\pi$
$572$	−28.7467	−	8.83399i	−1.20196	−	0.369368i
$573$	5.67854	+	19.3393i	0.237224	+	0.807912i
$574$	4.83321	−	1.38629i	0.201734	−	0.0578625i
$575$	3.24519	+	2.38513i	0.135334	+	0.0994669i
$576$	0.839764	+	7.95580i	0.0349902	+	0.331492i
$577$	−21.4206	+	6.28966i	−0.891752	+	0.261842i	−0.695341	−	0.718680i	$-0.744747\pi$
$577$	−21.4206	+	6.28966i	−0.891752	+	0.261842i	−0.196411	+	0.980522i	$0.562929\pi$
$578$	−2.61505	−	1.70386i	−0.108772	−	0.0708713i
$579$	12.9041	+	20.0791i	0.536275	+	0.834460i
$580$	8.77483	+	10.3872i	0.364355	+	0.431304i
$581$	−1.51324	+	2.35465i	−0.0627798	+	0.0976873i
$582$	0.845938	+	0.127048i	0.0350652	+	0.00526632i
$583$	2.49837	−	2.88327i	0.103472	−	0.119413i
$584$	−22.1924	−	26.6069i	−0.918327	−	1.10100i
$585$	4.76005	+	10.4231i	0.196804	+	0.430941i
$586$	−0.176241	+	28.0967i	−0.00728044	+	1.16066i
$587$	2.91461	−	9.92625i	0.120299	−	0.409700i	−0.877221	−	0.480087i	$-0.840605\pi$
$587$	2.91461	−	9.92625i	0.120299	−	0.409700i	0.997520	+	0.0703867i	$0.0224233\pi$
$588$	−7.42178	+	11.2361i	−0.306069	+	0.463367i
$589$	−6.25753	−	0.899697i	−0.257837	−	0.0370714i
$590$	−1.23635	+	2.66290i	−0.0508998	+	0.109630i
$591$	1.98501	−	4.34657i	0.0816525	−	0.178794i
$592$	−14.0186	−	23.0659i	−0.576161	−	0.948001i
$593$	1.45495	+	10.1194i	0.0597476	+	0.415554i	0.997642	+	0.0686329i	$0.0218637\pi$
$593$	1.45495	+	10.1194i	0.0597476	+	0.415554i	−0.937894	+	0.346921i	$0.887227\pi$
$594$	2.49672	−	2.84512i	0.102442	−	0.116737i
$595$	3.06366	−	2.65468i	0.125598	−	0.108831i
$596$	−19.0000	−	16.8855i	−0.778269	−	0.691657i
$597$			9.37775i			0.383806i
$598$	−37.9982	+	2.81357i	−1.55386	+	0.115055i
$599$	13.4538			0.549708			0.274854	−	0.961486i	$-0.411370\pi$
$599$	13.4538			0.549708			0.274854	+	0.961486i	$0.411370\pi$
$600$	−2.14165	−	1.02719i	−0.0874323	−	0.0419349i
$601$	−31.1854	−	35.9898i	−1.27208	−	1.46806i	−0.815929	−	0.578152i	$-0.803774\pi$
$601$	−31.1854	−	35.9898i	−1.27208	−	1.46806i	−0.456148	−	0.889904i	$-0.650771\pi$
$602$	5.45832	+	4.78993i	0.222464	+	0.195223i
$603$	1.60415	−	0.230643i	0.0653262	−	0.00939249i
$604$	13.7577	+	0.172601i	0.559793	+	0.00702305i
$605$	−7.11681	−	3.25014i	−0.289339	−	0.132137i
$606$	−6.59297	+	14.2002i	−0.267821	+	0.576843i
$607$	−4.77355	+	33.2008i	−0.193752	+	1.34758i	0.628214	+	0.778041i	$0.283786\pi$
$607$	−4.77355	+	33.2008i	−0.193752	+	1.34758i	−0.821966	+	0.569536i	$0.807123\pi$
$608$	2.24576	+	8.64220i	0.0910776	+	0.350488i
$609$	1.65268	+	0.485269i	0.0669698	+	0.0196641i
$610$	−17.0546	−	0.106978i	−0.690521	−	0.00433140i
$611$	38.8745	−	17.7534i	1.57269	−	0.718225i
$612$	3.10748	+	7.03673i	0.125613	+	0.284443i
$613$	−32.6987	−	28.3336i	−1.32069	−	1.14438i	−0.978840	−	0.204629i	$-0.934401\pi$
$613$	−32.6987	−	28.3336i	−1.32069	−	1.14438i	−0.341849	−	0.939755i	$-0.611053\pi$
$614$	−34.2793	−	5.14829i	−1.38340	−	0.207768i
$615$	11.8058	+	7.58715i	0.476057	+	0.305944i
$616$	−2.17656	+	3.25064i	−0.0876963	+	0.130972i
$617$	−14.9576	+	9.61265i	−0.602169	+	0.386991i	−0.805913	−	0.592033i	$-0.798325\pi$
$617$	−14.9576	+	9.61265i	−0.602169	+	0.386991i	0.203744	+	0.979024i	$0.434689\pi$
$618$	2.87604	−	4.41409i	0.115691	−	0.177561i
$619$	7.25273	+	24.7005i	0.291512	+	0.992798i	0.966862	+	0.255301i	$0.0821744\pi$
$619$	7.25273	+	24.7005i	0.291512	+	0.992798i	−0.675350	+	0.737497i	$0.736007\pi$
$620$	8.65980	+	13.8540i	0.347786	+	0.556391i
$621$	1.63644	−	4.50800i	0.0656682	−	0.180900i
$622$	15.1269	−	4.33878i	0.606533	−	0.173969i
$623$	6.75933	−	1.98472i	0.270807	−	0.0795160i
$624$	21.7132	−	5.78803i	0.869225	−	0.231706i
$625$	−16.9058	+	10.8647i	−0.676230	+	0.434587i
$626$	−16.0814	−	35.8060i	−0.642741	−	1.43109i
$627$	2.28418	−	3.55425i	0.0912214	−	0.141943i
$628$	28.9269	−	3.78931i	1.15431	−	0.151210i
$629$	−19.6145	−	16.9961i	−0.782082	−	0.677678i
$630$	1.47669	−	0.202871i	0.0588328	−	0.00808255i
$631$	7.33737	+	16.0666i	0.292096	+	0.639602i	0.997610	−	0.0690945i	$-0.0220110\pi$
$631$	7.33737	+	16.0666i	0.292096	+	0.639602i	−0.705514	+	0.708696i	$0.749284\pi$
$632$	−21.9055	+	13.5022i	−0.871354	+	0.537091i
$633$	−2.57203	−	0.755217i	−0.102229	−	0.0300172i
$634$	−0.945612	+	0.809049i	−0.0375551	+	0.0321314i
$635$	−30.3048	−	4.35718i	−1.20261	−	0.172909i
$636$	−0.441066	+	2.81639i	−0.0174894	+	0.111677i
$637$	34.4068	+	15.7130i	1.36325	+	0.622573i
$638$	−12.0837	−	3.63057i	−0.478398	−	0.143736i
$639$	2.10682	+	14.6533i	0.0833445	+	0.579674i
$640$	13.3160	−	18.8466i	0.526361	−	0.744976i
$641$	−23.6008	−	27.2368i	−0.932176	−	1.07579i	−0.996962	−	0.0778892i	$-0.975182\pi$
$641$	−23.6008	−	27.2368i	−0.932176	−	1.07579i	0.0647861	−	0.997899i	$-0.479363\pi$
$642$	−0.551020	+	0.349255i	−0.0217470	+	0.0137840i
$643$		−	4.28058i		−	0.168810i	−0.996432	−	0.0844049i	$-0.973101\pi$
$643$		−	4.28058i		−	0.168810i	0.996432	−	0.0844049i	$-0.0268989\pi$
$644$	−1.07178	+	4.83918i	−0.0422342	+	0.190690i
$645$			20.2686i			0.798074i
$646$	4.59645	+	7.25183i	0.180845	+	0.285320i
$647$	1.18773	+	1.37071i	0.0466945	+	0.0538883i	0.778616	−	0.627500i	$-0.215922\pi$
$647$	1.18773	+	1.37071i	0.0466945	+	0.0538883i	−0.731922	+	0.681389i	$0.761376\pi$
$648$	−0.455136	+	2.79157i	−0.0178794	+	0.109663i
$649$	−0.387706	−	2.69656i	−0.0152188	−	0.105849i
$650$	−1.91981	+	6.38971i	−0.0753010	+	0.250625i
$651$	1.88256	+	0.859737i	0.0737834	+	0.0336958i
$652$	−17.5080	−	2.74187i	−0.685667	−	0.107380i
$653$	−17.1590	−	2.46709i	−0.671484	−	0.0965448i	−0.201864	−	0.979414i	$-0.564700\pi$
$653$	−17.1590	−	2.46709i	−0.671484	−	0.0965448i	−0.469620	+	0.882869i	$0.655609\pi$
$654$	3.84361	+	4.49239i	0.150297	+	0.175666i
$655$	37.7841	+	11.0944i	1.47635	+	0.433494i
$656$	18.5389	−	20.3406i	0.723821	−	0.794169i
$657$	−5.08868	−	11.1427i	−0.198528	−	0.434717i
$658$	−0.756639	−	5.50756i	−0.0294968	−	0.214707i
$659$	24.7045	+	21.4065i	0.962350	+	0.833881i	0.986153	−	0.165836i	$-0.0530322\pi$
$659$	24.7045	+	21.4065i	0.962350	+	0.833881i	−0.0238037	+	0.999717i	$0.507578\pi$
$660$	−10.8262	+	1.41819i	−0.421410	+	0.0552030i
$661$	1.02006	−	1.58724i	0.0396757	−	0.0617365i	−0.820849	−	0.571145i	$-0.806499\pi$
$661$	1.02006	−	1.58724i	0.0396757	−	0.0617365i	0.860525	+	0.509408i	$0.170136\pi$
$662$	36.2054	−	16.2608i	1.40716	−	0.631993i
$663$	18.1772	−	11.6818i	0.705943	−	0.453682i
$664$	−0.288276	+	15.3176i	−0.0111873	+	0.594438i
$665$	1.59630	−	0.468717i	0.0619020	−	0.0181761i
$666$	−2.63109	−	9.17315i	−0.101953	−	0.355452i
$667$	−15.9344	+	1.28041i	−0.616982	+	0.0495775i
$668$	28.9673	−	18.1067i	1.12078	−	0.700571i
$669$	1.80150	+	6.13534i	0.0696500	+	0.237206i
$670$	−3.91676	−	2.55200i	−0.151318	−	0.0985925i
$671$	13.3133	−	8.55595i	0.513955	−	0.330299i
$672$	0.0916634	−	2.92172i	0.00353599	−	0.112708i
$673$	−19.4115	−	12.4750i	−0.748259	−	0.480877i	0.110104	−	0.993920i	$-0.464882\pi$
$673$	−19.4115	−	12.4750i	−0.748259	−	0.480877i	−0.858363	+	0.513043i	$0.828518\pi$
$674$	−6.56961	+	43.7431i	−0.253052	+	1.68492i
$675$	−0.634659	−	0.549935i	−0.0244280	−	0.0211670i
$676$	−14.9957	−	33.9570i	−0.576758	−	1.30604i
$677$	−3.67614	+	1.67884i	−0.141285	+	0.0645229i	−0.484803	−	0.874623i	$-0.661109\pi$
$677$	−3.67614	+	1.67884i	−0.141285	+	0.0645229i	0.343518	+	0.939146i	$0.388381\pi$
$678$	0.106490	−	16.9768i	0.00408971	−	0.651991i
$679$	−0.299906	−	0.0880604i	−0.0115093	−	0.00337945i
$680$	6.65077	−	21.1685i	0.255046	−	0.811775i
$681$	−2.48605	+	17.2909i	−0.0952658	+	0.662588i
$682$	−13.7504	−	6.38414i	−0.526531	−	0.244462i
$683$	−23.9588	−	10.9416i	−0.916760	−	0.418670i	−0.0995644	−	0.995031i	$-0.531745\pi$
$683$	−23.9588	−	10.9416i	−0.916760	−	0.418670i	−0.817195	+	0.576361i	$0.804472\pi$
$684$	−0.0396034	+	3.15671i	−0.00151428	+	0.120700i
$685$	22.3839	−	3.21833i	0.855247	−	0.122966i
$686$	6.61956	−	7.54325i	0.252736	−	0.288003i
$687$	−13.4554	−	15.5283i	−0.513355	−	0.592443i
$688$	39.1900	+	6.64213i	1.49410	+	0.253229i
$689$	8.00748			0.305061
$690$	−12.1248	+	6.66023i	−0.461585	+	0.253551i
$691$		−	23.8911i		−	0.908861i	−0.890782	−	0.454431i	$-0.849843\pi$
$691$		−	23.8911i		−	0.908861i	0.890782	−	0.454431i	$-0.150157\pi$
$692$	−9.53132	−	8.47060i	−0.362327	−	0.322004i
$693$	−1.04529	+	0.905749i	−0.0397073	+	0.0344066i
$694$	26.2904	+	23.0710i	0.997968	+	0.875764i
$695$	−3.66876	−	25.5168i	−0.139164	−	0.967907i
$696$	9.09437	−	2.48546i	0.344721	−	0.0942110i
$697$	10.9931	−	24.0716i	0.416395	−	0.911778i
$698$	−6.10964	−	2.83663i	−0.231253	−	0.107368i
$699$	−2.64998	−	0.381009i	−0.100231	−	0.0144111i
$700$	0.724179	+	0.478344i	0.0273714	+	0.0180797i
$701$	12.4878	−	42.5294i	0.471656	−	1.60631i	−0.289115	−	0.957294i	$-0.593361\pi$
$701$	12.4878	−	42.5294i	0.471656	−	1.60631i	0.760771	−	0.649020i	$-0.224821\pi$
$702$	7.94470	+	0.0498343i	0.299853	+	0.00188088i
$703$	−4.42479	−	9.68893i	−0.166884	−	0.365425i
$704$	−0.805688	+	21.3976i	−0.0303655	+	0.806452i
$705$	10.1610	−	11.7264i	0.382685	−	0.441641i
$706$	5.86614	−	39.0591i	0.220775	−	1.47001i
$707$	3.09281	−	4.81251i	0.116317	−	0.180993i
$708$	1.31365	+	1.55503i	0.0493702	+	0.0584417i
$709$	3.52862	+	5.49065i	0.132520	+	0.206206i	0.901172	−	0.433462i	$-0.142708\pi$
$709$	3.52862	+	5.49065i	0.132520	+	0.206206i	−0.768651	+	0.639668i	$0.779072\pi$
$710$	23.3115	−	35.7779i	0.874863	−	1.34272i
$711$	−8.72929	+	2.56315i	−0.327374	+	0.0961257i
$712$	25.7949	−	28.6609i	0.966705	−	1.07411i
$713$	−19.1699	−	1.20193i	−0.717917	−	0.0450128i
$714$	−0.774944	−	2.70179i	−0.0290015	−	0.101112i
$715$	8.64070	+	29.4275i	0.323144	+	1.10053i
$716$	5.70184	−	18.5544i	0.213088	−	0.693410i
$717$	−5.76612	−	8.97225i	−0.215340	−	0.335075i
$718$	−13.7073	−	30.5199i	−0.511551	−	1.13899i
$719$	16.1691	+	10.3913i	0.603006	+	0.387529i	0.806229	−	0.591604i	$-0.201505\pi$
$719$	16.1691	+	10.3913i	0.603006	+	0.387529i	−0.203222	+	0.979133i	$0.565141\pi$
$720$	6.29800	−	5.18641i	0.234712	−	0.193286i
$721$	−1.26063	+	1.45484i	−0.0469483	+	0.0541812i
$722$	−3.17752	−	23.1292i	−0.118255	−	0.860778i
$723$	−10.8720	+	4.96507i	−0.404333	+	0.184653i
$724$	7.15845	+	25.5614i	0.266042	+	0.949983i
$725$	−0.788622	+	2.68580i	−0.0292887	+	0.0997481i
$726$	−4.12192	+	3.52664i	−0.152979	+	0.130886i
$727$	3.70230	−	25.7501i	0.137311	−	0.955017i	−0.798370	−	0.602168i	$-0.794304\pi$
$727$	3.70230	−	25.7501i	0.137311	−	0.955017i	0.935680	−	0.352849i	$-0.114787\pi$
$728$	−8.14791	+	1.01540i	−0.301982	+	0.0376333i
$729$	−0.415415	+	0.909632i	−0.0153857	+	0.0336901i
$730$	−10.1673	+	33.8399i	−0.376308	+	1.25247i
$731$	37.8312	−	5.43930i	1.39924	−	0.201180i
$732$	−5.04690	+	10.6941i	−0.186539	+	0.395264i
$733$	−3.92773	+	3.40340i	−0.145074	+	0.125707i	−0.724374	−	0.689407i	$-0.757871\pi$
$733$	−3.92773	+	3.40340i	−0.145074	+	0.125707i	0.579300	+	0.815114i	$0.303326\pi$
$734$	−23.8462	+	15.1145i	−0.880180	+	0.557887i
$735$	13.7330			0.506549
$736$	8.90440	+	25.6264i	0.328220	+	0.944601i
$737$	4.33782			0.159786
$738$	8.21849	−	5.20915i	0.302527	−	0.191752i
$739$	−11.6762	+	10.1175i	−0.429517	+	0.372178i	−0.842623	−	0.538505i	$-0.818989\pi$
$739$	−11.6762	+	10.1175i	−0.429517	+	0.372178i	0.413106	+	0.910683i	$0.364444\pi$
$740$	−11.7484	+	24.8941i	−0.431878	+	0.915124i
$741$	8.77742	−	1.26200i	0.322447	−	0.0463608i
$742$	0.299726	−	0.997583i	0.0110033	−	0.0366224i
$743$	−15.8464	+	34.6988i	−0.581349	+	1.27298i	0.359182	+	0.933267i	$0.383056\pi$
$743$	−15.8464	+	34.6988i	−0.581349	+	1.27298i	−0.940531	+	0.339708i	$0.889672\pi$
$744$	11.2410	−	1.40087i	0.412116	−	0.0513583i
$745$	−3.68922	+	25.6591i	−0.135163	+	0.940077i
$746$	−32.6347	+	27.9216i	−1.19484	+	1.02228i
$747$	−1.52602	+	5.19714i	−0.0558341	+	0.190153i
$748$	5.55238	+	19.8265i	0.203015	+	0.724927i
$749$	0.216835	−	0.0990252i	0.00792298	−	0.00361830i
$750$	2.29265	+	16.6882i	0.0837159	+	0.609367i
$751$	17.1121	−	19.7484i	0.624430	−	0.720631i	−0.352112	−	0.935958i	$-0.614536\pi$
$751$	17.1121	−	19.7484i	0.624430	−	0.720631i	0.976542	+	0.215327i	$0.0690818\pi$
$752$	−19.3436	−	23.4894i	−0.705387	−	0.856570i
$753$	−14.1472	−	9.09184i	−0.515552	−	0.331325i
$754$	−10.8498	−	24.1577i	−0.395127	−	0.879770i
$755$	−7.58608	−	11.8042i	−0.276086	−	0.429598i
$756$	0.303585	−	0.987897i	0.0110413	−	0.0359295i
$757$	−14.3747	−	48.9556i	−0.522456	−	1.77932i	−0.620577	−	0.784146i	$-0.713101\pi$
$757$	−14.3747	−	48.9556i	−0.522456	−	1.77932i	0.0981211	−	0.995174i	$-0.468717\pi$
$758$	−9.88537	−	34.4648i	−0.359053	−	1.25182i
$759$	6.05269	−	11.3199i	0.219699	−	0.410887i
$760$	6.09181	−	6.76866i	0.220973	−	0.245525i
$761$	31.6116	−	9.28199i	1.14592	−	0.336472i	0.346973	−	0.937875i	$-0.387210\pi$
$761$	31.6116	−	9.28199i	1.14592	−	0.336472i	0.798946	+	0.601403i	$0.205392\pi$
$762$	−11.5886	+	17.7859i	−0.419810	+	0.644315i
$763$	−1.16795	−	1.81737i	−0.0422826	−	0.0657930i
$764$	−26.0142	−	30.7942i	−0.941161	−	1.11410i
$765$	4.24127	−	6.59954i	0.153343	−	0.238607i
$766$	2.98204	−	19.8556i	0.107746	−	0.717412i
$767$	3.74447	−	4.32135i	0.135205	−	0.156035i
$768$	−7.96421	−	13.8770i	−0.287384	−	0.500743i
$769$	16.2309	+	35.5406i	0.585300	+	1.28163i	0.938241	+	0.345982i	$0.112454\pi$
$769$	16.2309	+	35.5406i	0.585300	+	1.28163i	−0.352941	+	0.935645i	$0.614819\pi$
$770$	3.98955	+	0.0250251i	0.143773	+	0.000901841i
$771$	1.02898	−	3.50439i	0.0370579	−	0.126208i
$772$	−39.8313	−	26.3099i	−1.43356	−	0.946914i
$773$	−41.1105	−	5.91080i	−1.47864	−	0.212597i	−0.644694	−	0.764440i	$-0.723015\pi$
$773$	−41.1105	−	5.91080i	−1.47864	−	0.212597i	−0.833948	+	0.551844i	$0.813924\pi$
$774$	12.7465	+	5.91804i	0.458163	+	0.212719i
$775$	−1.39718	+	3.05939i	−0.0501881	+	0.109897i
$776$	−1.65033	+	0.451028i	−0.0592433	+	0.0161910i
$777$	0.496247	+	3.45147i	0.0178028	+	0.123821i
$778$	22.3879	+	19.6464i	0.802644	+	0.704358i
$779$	8.20783	−	7.11213i	0.294076	−	0.254818i
$780$	−17.1300	−	15.2236i	−0.613351	−	0.545092i
$781$			39.6241i			1.41786i
$782$	15.6851	+	20.8436i	0.560899	+	0.745366i
$783$	3.33326			0.119121
$784$	4.50038	−	26.5532i	0.160728	−	0.948329i
$785$	−19.4838	−	22.4855i	−0.695407	−	0.802542i
$786$	18.0093	−	20.5223i	0.642370	−	0.732006i
$787$	−46.3916	+	6.67011i	−1.65368	+	0.237764i	−0.905076	−	0.425251i	$-0.860186\pi$
$787$	−46.3916	+	6.67011i	−1.65368	+	0.237764i	−0.748607	+	0.663014i	$0.769277\pi$
$788$	−0.119888	+	9.55602i	−0.00427083	+	0.340419i
$789$	6.71969	+	3.06878i	0.239227	+	0.109251i
$790$	23.8025	+	11.0512i	0.846854	+	0.393183i
$791$	−0.882829	+	6.14021i	−0.0313898	+	0.218321i
$792$	−2.26917	+	7.22247i	−0.0806316	+	0.256639i
$793$	31.8706	+	9.35804i	1.13176	+	0.332314i
$794$	0.162301	−	25.8745i	0.00575986	−	0.918250i
$795$	2.64453	−	1.20772i	0.0937919	−	0.0428333i
$796$	−7.57668	−	17.1570i	−0.268548	−	0.608114i
$797$	2.32053	+	2.01075i	0.0821974	+	0.0712245i	0.694990	−	0.719019i	$-0.255409\pi$
$797$	2.32053	+	2.01075i	0.0821974	+	0.0712245i	−0.612793	+	0.790243i	$0.709954\pi$
$798$	0.171324	−	1.14074i	0.00606480	−	0.0403818i
$799$	−24.6141	−	15.8185i	−0.870783	−	0.559618i
$800$	4.74815	+	0.148964i	0.167872	+	0.00526668i
$801$	11.4686	−	7.37045i	0.405225	−	0.260422i
$802$	43.0642	+	28.0589i	1.52065	+	0.990794i
$803$	−9.23725	−	31.4592i	−0.325975	−	1.11017i
$804$	−2.74852	+	1.71803i	−0.0969330	+	0.0605904i
$805$	4.72034	−	1.80798i	0.166370	−	0.0637228i
$806$	−8.77290	−	30.5862i	−0.309012	−	1.07735i
$807$	5.73174	−	1.68299i	0.201767	−	0.0592441i
$808$	0.589188	−	31.3066i	0.0207276	−	1.10136i
$809$	4.45876	−	2.86547i	0.156762	−	0.100745i	−0.459908	−	0.887966i	$-0.652118\pi$
$809$	4.45876	−	2.86547i	0.156762	−	0.100745i	0.616670	+	0.787222i	$0.288481\pi$
$810$	2.63132	−	1.18179i	0.0924550	−	0.0415239i
$811$	−20.4690	+	31.8505i	−0.718765	+	1.11842i	0.269100	+	0.963112i	$0.413274\pi$
$811$	−20.4690	+	31.8505i	−0.718765	+	1.11842i	−0.987866	+	0.155309i	$0.950363\pi$
$812$	−3.41571	+	0.447445i	−0.119868	+	0.0157023i
$813$	−11.9892	−	10.3887i	−0.420479	−	0.364347i
$814$	−3.47646	−	25.3051i	−0.121850	−	0.886944i
$815$	7.50774	+	16.4397i	0.262985	+	0.575856i
$816$	−11.3705	−	10.3633i	−0.398049	−	0.362789i
$817$	15.0503	+	4.41917i	0.526543	+	0.154607i
$818$	26.2697	+	30.7039i	0.918499	+	1.07354i
$819$	−2.87346	−	0.413141i	−0.100407	−	0.0144363i
$820$	−27.7293	−	4.34259i	−0.968348	−	0.151650i
$821$	36.6190	+	16.7233i	1.27801	+	0.583648i	0.934654	−	0.355557i	$-0.115709\pi$
$821$	36.6190	+	16.7233i	1.27801	+	0.583648i	0.343356	+	0.939205i	$0.388436\pi$
$822$	4.51175	−	15.0165i	0.157365	−	0.523761i
$823$	−6.28217	−	43.6935i	−0.218983	−	1.52306i	−0.741805	−	0.670616i	$-0.766030\pi$
$823$	−6.28217	−	43.6935i	−0.218983	−	1.52306i	0.522822	−	0.852442i	$-0.324879\pi$
$824$	−1.69552	+	10.3994i	−0.0590662	+	0.362282i
$825$	−1.47195	−	1.69872i	−0.0512468	−	0.0591420i
$826$	−0.398201	−	0.628243i	−0.0138552	−	0.0218594i
$827$			45.9955i			1.59942i	0.600386	+	0.799710i	$0.295014\pi$
$827$			45.9955i			1.59942i	−0.600386	+	0.799710i	$0.704986\pi$
$828$	0.648260	+	9.56973i	0.0225286	+	0.332571i
$829$			7.92405i			0.275214i	0.990487	+	0.137607i	$0.0439411\pi$
$829$			7.92405i			0.275214i	−0.990487	+	0.137607i	$0.956059\pi$
$830$	13.1966	−	8.36444i	0.458060	−	0.290334i
$831$	12.3410	+	14.2422i	0.428103	+	0.494057i
$832$	−35.0489	+	28.1325i	−1.21510	+	0.975319i
$833$	−3.68541	−	25.6326i	−0.127692	−	0.888116i
$834$	−17.1182	−	5.14321i	−0.592755	−	0.178095i
$835$	−31.6900	−	14.4723i	−1.09668	−	0.500835i
$836$	−1.30737	+	8.34815i	−0.0452165	+	0.288727i
$837$	3.96428	+	0.569977i	0.137025	+	0.0197013i
$838$	3.72319	−	3.18550i	0.128616	−	0.110041i
$839$	2.17195	+	0.637742i	0.0749841	+	0.0220173i	0.319009	−	0.947752i	$-0.396650\pi$
$839$	2.17195	+	0.637742i	0.0749841	+	0.0220173i	−0.244025	+	0.969769i	$0.578468\pi$
$840$	−2.53776	+	1.56424i	−0.0875612	+	0.0539715i
$841$	7.43151	+	16.2727i	0.256259	+	0.561129i
$842$	25.1822	−	3.45957i	0.867836	−	0.119225i
$843$	−12.8067	−	11.0971i	−0.441087	−	0.382204i
$844$	5.31582	−	0.696352i	0.182978	−	0.0239694i
$845$	−20.4670	+	31.8473i	−0.704086	+	1.09558i
$846$	−4.40768	−	9.81392i	−0.151539	−	0.337410i
$847$	1.66750	−	1.07163i	0.0572958	−	0.0368218i
$848$	−1.46853	−	5.50907i	−0.0504297	−	0.189182i
$849$	13.0105	−	3.82022i	0.446519	−	0.131110i
$850$	4.39075	−	1.25938i	0.150601	−	0.0431963i
$851$	−15.7583	−	28.2661i	−0.540188	−	0.968950i
$852$	−15.6935	−	25.1066i	−0.537651	−	0.860137i
$853$	3.48871	+	11.8815i	0.119451	+	0.406813i	0.997410	−	0.0719225i	$-0.0229134\pi$
$853$	3.48871	+	11.8815i	0.119451	+	0.406813i	−0.877959	+	0.478736i	$0.841095\pi$
$854$	2.35878	−	3.62020i	0.0807157	−	0.123881i
$855$	2.70847	−	1.74063i	0.0926278	−	0.0595283i
$856$	0.725938	−	1.08417i	0.0248120	−	0.0370562i
$857$	35.8714	+	23.0531i	1.22534	+	0.787480i	0.983159	−	0.182750i	$-0.0585000\pi$
$857$	35.8714	+	23.0531i	1.22534	+	0.787480i	0.242184	+	0.970230i	$0.422136\pi$
$858$	21.0293	+	3.15832i	0.717929	+	0.107823i
$859$	−42.5127	−	36.8375i	−1.45052	−	1.25688i	−0.909395	−	0.415934i	$-0.863455\pi$
$859$	−42.5127	−	36.8375i	−1.45052	−	1.25688i	−0.541121	−	0.840945i	$-0.682000\pi$
$860$	−16.3758	−	37.0822i	−0.558411	−	1.26449i
$861$	−3.23410	+	1.47697i	−0.110218	+	0.0503349i
$862$	6.29118	+	0.0394624i	0.214278	+	0.00134409i
$863$	−39.0288	−	11.4599i	−1.32856	−	0.390099i	−0.460983	−	0.887409i	$-0.652503\pi$
$863$	−39.0288	−	11.4599i	−1.32856	−	0.390099i	−0.867573	+	0.497310i	$0.834321\pi$
$864$	−1.42274	−	5.47502i	−0.0484025	−	0.186264i
$865$	−1.85070	+	12.8719i	−0.0629256	+	0.437657i
$866$	−2.22406	+	4.79027i	−0.0755766	+	0.162780i
$867$	2.00755	+	0.916817i	0.0681800	+	0.0311367i
$868$	−4.13885	−	0.0519251i	−0.140482	−	0.00176245i
$869$	−24.1033	+	3.46553i	−0.817648	+	0.117560i
$870$	−7.22679	−	6.34185i	−0.245011	−	0.215009i
$871$	5.96224	+	6.88079i	0.202023	+	0.233147i
$872$	−10.6616	−	5.11361i	−0.361048	−	0.173169i
$873$	−0.604877			−0.0204720
$874$	2.30193	+	10.4554i	0.0778638	+	0.353658i
$875$		−	6.15504i		−	0.208078i
$876$	18.3126	+	16.2746i	0.618725	+	0.549868i
$877$	−21.3154	+	18.4699i	−0.719769	+	0.623684i	−0.935729	−	0.352719i	$-0.885257\pi$
$877$	−21.3154	+	18.4699i	−0.719769	+	0.623684i	0.215960	+	0.976402i	$0.430712\pi$
$878$	−26.2548	+	29.9184i	−0.886057	+	1.00970i
$879$	−2.82748	−	19.6655i	−0.0953684	−	0.663302i
$880$	18.6612	−	11.3416i	0.629069	−	0.382325i
$881$	4.36675	−	9.56184i	0.147119	−	0.322147i	−0.821698	−	0.569924i	$-0.806973\pi$
$881$	4.36675	−	9.56184i	0.147119	−	0.322147i	0.968817	+	0.247777i	$0.0797000\pi$
$882$	4.00978	−	8.63641i	0.135016	−	0.290803i
$883$	26.7644	+	3.84813i	0.900692	+	0.129500i	0.577078	−	0.816689i	$-0.304193\pi$
$883$	26.7644	+	3.84813i	0.900692	+	0.129500i	0.323614	+	0.946189i	$0.395102\pi$
$884$	−23.8177	+	36.0584i	−0.801077	+	1.21277i
$885$	0.584879	−	1.99191i	0.0196605	−	0.0669574i
$886$	−0.0705042	+	11.2399i	−0.00236863	+	0.377613i
$887$	−0.461541	−	1.01063i	−0.0154970	−	0.0339338i	0.901725	−	0.432310i	$-0.142301\pi$
$887$	−0.461541	−	1.01063i	−0.0154970	−	0.0339338i	−0.917222	+	0.398376i	$0.869574\pi$
$888$	12.2251	+	14.6569i	0.410247	+	0.491854i
$889$	5.07952	−	5.86207i	0.170361	−	0.196608i
$890$	−38.8879	−	5.84044i	−1.30353	−	0.195772i
$891$	−1.44708	+	2.25169i	−0.0484789	+	0.0754346i
$892$	−8.25292	−	9.76937i	−0.276328	−	0.327103i
$893$	−6.49196	−	10.1017i	−0.217245	−	0.338040i
$894$	15.0593	+	9.81205i	0.503659	+	0.328164i
$895$	−18.9938	+	5.57708i	−0.634893	+	0.186421i
$896$	2.19288	+	5.41947i	0.0732588	+	0.181052i
$897$	26.2753	−	5.95800i	0.877306	−	0.198932i
$898$	−8.01912	+	2.30009i	−0.267601	+	0.0767549i
$899$	−3.76109	−	12.8091i	−0.125439	−	0.427207i
$900$	1.60545	+	0.493362i	0.0535151	+	0.0164454i
$901$	−2.96389	−	4.61190i	−0.0987414	−	0.153645i
$902$	23.7579	−	10.6703i	0.791052	−	0.355282i
$903$	−4.31984	−	2.77620i	−0.143755	−	0.0923860i
$904$	13.5215	+	31.1459i	0.449717	+	1.03590i
$905$	17.7279	−	20.4591i	0.589296	−	0.680084i
$906$	−9.63840	+	1.32414i	−0.320214	+	0.0439916i
$907$	14.9283	−	6.81753i	0.495686	−	0.226372i	−0.151855	−	0.988403i	$-0.548525\pi$
$907$	14.9283	−	6.81753i	0.495686	−	0.226372i	0.647541	+	0.762031i	$0.275797\pi$
$908$	−9.42169	−	33.6430i	−0.312670	−	1.11648i
$909$	3.11892	−	10.6221i	0.103448	−	0.352312i
$910$	5.44385	+	6.36275i	0.180462	+	0.210923i
$911$	−0.0598575	+	0.416318i	−0.00198317	+	0.0137932i	−0.990789	−	0.135415i	$-0.956763\pi$
$911$	−0.0598575	+	0.416318i	−0.00198317	+	0.0137932i	0.988806	+	0.149208i	$0.0476724\pi$
$912$	−2.47798	−	5.80734i	−0.0820542	−	0.192300i
$913$	−6.02265	+	13.1878i	−0.199320	+	0.436451i
$914$	0.480641	+	0.144410i	0.0158982	+	0.00477665i
$915$	11.9369	−	1.71627i	0.394622	−	0.0567381i
$916$	37.1632	+	17.5386i	1.22791	+	0.579492i
$917$	−7.53985	+	6.53332i	−0.248988	+	0.215749i
$918$	−2.91195	−	4.59419i	−0.0961087	−	0.151631i
$919$	41.3907			1.36535			0.682676	−	0.730721i	$-0.260816\pi$
$919$	41.3907			1.36535			0.682676	+	0.730721i	$0.260816\pi$
$920$	16.8018	−	21.9813i	0.553940	−	0.724704i
$921$	24.5110			0.807664
$922$	−7.19058	−	11.3446i	−0.236809	−	0.373615i
$923$	−62.8530	+	54.4625i	−2.06883	+	1.79265i
$924$	1.18061	−	2.50164i	0.0388393	−	0.0822980i
$925$	−5.60907	+	0.806462i	−0.184425	+	0.0265163i
$926$	−26.8377	−	8.06346i	−0.881942	−	0.264982i
$927$	−1.54755	+	3.38866i	−0.0508281	+	0.111298i
$928$	−14.6304	+	11.8950i	−0.480268	+	0.390472i
$929$	−0.414287	+	2.88143i	−0.0135923	+	0.0945367i	−0.995488	−	0.0948841i	$-0.969752\pi$
$929$	−0.414287	+	2.88143i	−0.0135923	+	0.0945367i	0.981896	+	0.189421i	$0.0606610\pi$
$930$	−7.51044	−	8.77817i	−0.246277	−	0.287847i
$931$	2.99421	−	10.1974i	0.0981314	−	0.334205i
$932$	5.15608	−	1.44396i	0.168893	−	0.0472983i
$933$	−10.1220	+	4.62258i	−0.331381	+	0.151336i
$934$	43.2337	−	5.93952i	1.41465	−	0.194347i
$935$	13.7505	−	15.8689i	0.449689	−	0.518969i
$936$	−14.5754	+	6.32769i	−0.476413	+	0.206827i
$937$	−18.7784	−	12.0682i	−0.613465	−	0.394250i	0.196690	−	0.980466i	$-0.436981\pi$
$937$	−18.7784	−	12.0682i	−0.613465	−	0.394250i	−0.810155	+	0.586216i	$0.800617\pi$
$938$	1.08039	−	0.485231i	0.0352760	−	0.0158433i
$939$	15.0055	+	23.3490i	0.489685	+	0.761965i
$940$	−9.11570	+	29.6634i	−0.297321	+	0.967514i
$941$	−13.6050	−	46.3342i	−0.443509	−	1.51045i	−0.813582	−	0.581450i	$-0.802486\pi$
$941$	−13.6050	−	46.3342i	−0.443509	−	1.51045i	0.370073	−	0.929003i	$-0.379333\pi$
$942$	−19.8296	+	5.68763i	−0.646083	+	0.185313i
$943$	23.1266	−	23.5365i	0.753107	−	0.766453i
$944$	−3.65977	−	1.78364i	−0.119115	−	0.0580527i
$945$	−1.01129	+	0.296942i	−0.0328974	+	0.00965954i
$946$	31.5156	+	20.5343i	1.02466	+	0.667629i
$947$	−13.3870	−	20.8306i	−0.435020	−	0.676905i	0.552657	−	0.833409i	$-0.313614\pi$
$947$	−13.3870	−	20.8306i	−0.435020	−	0.676905i	−0.987677	+	0.156504i	$0.949978\pi$
$948$	13.8997	−	11.7422i	0.451442	−	0.381368i
$949$	37.2052	−	57.8923i	1.20773	−	1.87927i
$950$	1.85384	+	0.278422i	0.0601466	+	0.00903320i
$951$	0.576267	−	0.665047i	0.0186867	−	0.0215656i
$952$	3.60069	+	4.31694i	0.116699	+	0.139913i
$953$	−20.4280	−	44.7311i	−0.661728	−	1.44898i	−0.880903	−	0.473297i	$-0.843064\pi$
$953$	−20.4280	−	44.7311i	−0.661728	−	1.44898i	0.219175	−	0.975686i	$-0.429663\pi$
$954$	0.0126439	−	2.01572i	0.000409363	−	0.0652615i
$955$	−11.5823	+	39.4457i	−0.374795	+	1.27643i
$956$	17.7984	+	11.7564i	0.575642	+	0.380230i
$957$	8.83098	+	1.26970i	0.285465	+	0.0410437i
$958$	−12.1188	+	26.1019i	−0.391540	+	0.843314i
$959$	−2.38002	+	5.21151i	−0.0768548	+	0.168288i
$960$	−7.33213	+	14.5772i	−0.236644	+	0.470477i
$961$	2.12898	+	14.8074i	0.0686768	+	0.477657i
$962$	35.3615	−	40.2958i	1.14010	−	1.29919i
$963$	0.348630	−	0.302090i	0.0112344	−	0.00973470i
$964$	15.8793	−	17.8677i	0.511437	−	0.575481i
$965$			48.6829i			1.56716i
$966$	0.241250	−	3.49642i	0.00776208	−	0.112496i
$967$	−38.1596			−1.22713			−0.613566	−	0.789644i	$-0.710265\pi$
$967$	−38.1596			−1.22713			−0.613566	+	0.789644i	$0.710265\pi$
$968$	4.69191	−	9.78241i	0.150804	−	0.314419i
$969$	−3.97572	−	4.58823i	−0.127719	−	0.147395i
$970$	1.31142	+	1.15084i	0.0421073	+	0.0369511i
$971$	−46.3993	+	6.67121i	−1.48902	+	0.214089i	−0.838294	−	0.545219i	$-0.816447\pi$
$971$	−46.3993	+	6.67121i	−1.48902	+	0.214089i	−0.650731	+	0.759308i	$0.725537\pi$
$972$	0.0250896	−	1.99984i	0.000804750	−	0.0641450i
$973$	5.94091	+	2.71312i	0.190457	+	0.0869787i
$974$	−14.2080	+	30.6017i	−0.455253	+	0.980541i
$975$	0.671404	−	4.66972i	0.0215021	−	0.149551i
$976$	0.593331	−	23.6429i	0.0189920	−	0.756790i
$977$	35.0133	+	10.2808i	1.12017	+	0.328913i	0.788839	−	0.614600i	$-0.210683\pi$
$977$	35.0133	+	10.2808i	1.12017	+	0.328913i	0.331335	+	0.943513i	$0.392501\pi$
$978$	12.5307	+	0.0786006i	0.400687	+	0.00251337i
$979$	33.1920	−	15.1583i	1.06082	−	0.484461i
$980$	−25.1251	+	11.0955i	−0.802592	+	0.354432i
$981$	−3.15949	−	2.73771i	−0.100875	−	0.0874084i
$982$	28.6313	+	4.30004i	0.913663	+	0.137220i
$983$	−38.1383	−	24.5100i	−1.21642	−	0.781747i	−0.234700	−	0.972068i	$-0.575411\pi$
$983$	−38.1383	−	24.5100i	−1.21642	−	0.781747i	−0.981722	+	0.190321i	$0.939047\pi$
$984$	−10.8274	+	16.1704i	−0.345165	+	0.515495i
$985$	8.19911	−	5.26925i	0.261245	−	0.167892i
$986$	−9.89763	+	15.1907i	−0.315205	+	0.483769i
$987$	1.10749	+	3.77178i	0.0352520	+	0.120057i
$988$	−15.0390	+	9.40054i	−0.478456	+	0.299071i
$989$	46.6553	+	9.72089i	1.48355	+	0.309106i
$990$	7.42144	−	2.12866i	0.235869	−	0.0676532i
$991$	6.00886	−	1.76436i	0.190878	−	0.0560468i	−0.184897	−	0.982758i	$-0.559195\pi$
$991$	6.00886	−	1.76436i	0.190878	−	0.0560468i	0.375774	+	0.926711i	$0.377377\pi$
$992$	−19.4341	+	11.6450i	−0.617033	+	0.369730i
$993$	−23.6095	+	15.1729i	−0.749223	+	0.481497i
$994$	4.43237	+	9.86889i	0.140586	+	0.313022i
$995$	−10.3411	+	16.0910i	−0.327834	+	0.510120i
$996$	−1.40707	−	10.7413i	−0.0445848	−	0.340352i
$997$	13.7807	+	11.9411i	0.436441	+	0.378178i	0.845188	−	0.534470i	$-0.179489\pi$
$997$	13.7807	+	11.9411i	0.436441	+	0.378178i	−0.408747	+	0.912648i	$0.634034\pi$
$998$	17.2535	−	2.37031i	0.546149	−	0.0750308i
$999$	2.80320	+	6.13814i	0.0886892	+	0.194202i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.bb.a.469.39	yes	480
8.5	even	2	inner	552.2.bb.a.469.47	yes	480
23.18	even	11	inner	552.2.bb.a.133.47	yes	480
184.133	even	22	inner	552.2.bb.a.133.39	✓	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.bb.a.133.39	✓	480	184.133	even	22	inner
552.2.bb.a.133.47	yes	480	23.18	even	11	inner
552.2.bb.a.469.39	yes	480	1.1	even	1	trivial
552.2.bb.a.469.47	yes	480	8.5	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.bb (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.19448 - 0.757104i) q^{2} +(-0.755750 + 0.654861i) q^{3} +(0.853587 - 1.80870i) q^{4} +(-2.01890 + 0.290274i) q^{5} +(-0.406934 + 1.35440i) q^{6} +(0.214664 - 0.470048i) q^{7} +(-0.349776 - 2.80672i) q^{8} +(0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(q+(1.19448 - 0.757104i) q^{2} +(-0.755750 + 0.654861i) q^{3} +(0.853587 - 1.80870i) q^{4} +(-2.01890 + 0.290274i) q^{5} +(-0.406934 + 1.35440i) q^{6} +(0.214664 - 0.470048i) q^{7} +(-0.349776 - 2.80672i) q^{8} +(0.142315 - 0.989821i) q^{9} +(-2.19178 + 1.87525i) q^{10} +(0.754084 - 2.56817i) q^{11} +(0.539347 + 1.92590i) q^{12} +(5.11019 - 2.33374i) q^{13} +(-0.0994628 - 0.723988i) q^{14} +(1.33570 - 1.54147i) q^{15} +(-2.54278 - 3.08776i) q^{16} +(-3.23560 - 2.07940i) q^{17} +(-0.579405 - 1.29007i) q^{18} +(-0.853390 - 1.32790i) q^{19} +(-1.19829 + 3.89936i) q^{20} +(0.145584 + 0.495814i) q^{21} +(-1.04363 - 3.63856i) q^{22} +(-2.90764 - 3.81387i) q^{23} +(2.10235 + 1.89212i) q^{24} +(-0.805758 + 0.236592i) q^{25} +(4.33715 - 6.65657i) q^{26} +(0.540641 + 0.841254i) q^{27} +(-0.666941 - 0.789489i) q^{28} +(1.80210 - 2.80412i) q^{29} +(0.428411 - 2.85253i) q^{30} +(2.62274 - 3.02681i) q^{31} +(-5.37507 - 1.76314i) q^{32} +(1.11190 + 2.43472i) q^{33} +(-5.43920 - 0.0341182i) q^{34} +(-0.296942 + 1.01129i) q^{35} +(-1.66881 - 1.10230i) q^{36} +(6.67926 + 0.960332i) q^{37} +(-2.02472 - 0.940052i) q^{38} +(-2.33374 + 5.11019i) q^{39} +(1.52088 + 5.56495i) q^{40} +(0.979178 + 6.81033i) q^{41} +(0.549280 + 0.482019i) q^{42} +(-7.51004 + 6.50749i) q^{43} +(-4.00137 - 3.55607i) q^{44} +2.03966i q^{45} +(-6.36063 - 2.35422i) q^{46} +7.60726 q^{47} +(3.94376 + 0.668409i) q^{48} +(4.40916 + 5.08844i) q^{49} +(-0.783340 + 0.892648i) q^{50} +(3.80702 - 0.547367i) q^{51} +(0.140950 - 11.2348i) q^{52} +(1.29655 + 0.592116i) q^{53} +(1.28270 + 0.595543i) q^{54} +(-0.776947 + 5.40378i) q^{55} +(-1.39438 - 0.438089i) q^{56} +(1.51454 + 0.444709i) q^{57} +(0.0295683 - 4.71385i) q^{58} +(0.925840 - 0.422817i) q^{59} +(-1.64793 - 3.73165i) q^{60} +(4.46843 + 3.87191i) q^{61} +(0.841219 - 5.60117i) q^{62} +(-0.434714 - 0.279374i) q^{63} +(-7.75531 + 1.96345i) q^{64} +(-9.63954 + 6.19496i) q^{65} +(3.17148 + 2.06641i) q^{66} +(0.456590 + 1.55500i) q^{67} +(-6.52287 + 4.07728i) q^{68} +(4.69500 + 0.978231i) q^{69} +(0.410961 + 1.43279i) q^{70} +(-14.2043 + 4.17075i) q^{71} +(-2.82793 - 0.0532214i) q^{72} +(10.3050 - 6.62265i) q^{73} +(8.70534 - 3.90979i) q^{74} +(0.454016 - 0.706463i) q^{75} +(-3.13022 + 0.410046i) q^{76} +(-1.04529 - 0.905749i) q^{77} +(1.08132 + 7.87093i) q^{78} +(-3.77937 - 8.27566i) q^{79} +(6.02992 + 5.49579i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(6.32574 + 7.39350i) q^{82} +(-5.36142 - 0.770855i) q^{83} +(1.02105 + 0.159902i) q^{84} +(7.13596 + 3.25888i) q^{85} +(-4.04378 + 13.4590i) q^{86} +(0.474372 + 3.29933i) q^{87} +(-7.47189 - 1.21821i) q^{88} +(8.92759 + 10.3030i) q^{89} +(1.54424 + 2.43635i) q^{90} -2.90300i q^{91} +(-9.38007 + 2.00358i) q^{92} +4.00504i q^{93} +(9.08675 - 5.75948i) q^{94} +(2.10837 + 2.43319i) q^{95} +(5.21681 - 2.18743i) q^{96} +(-0.0860829 - 0.598720i) q^{97} +(9.11915 + 2.73987i) q^{98} +(-2.43472 - 1.11190i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9}+O(q^{10}) \) 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9	\( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32} + 6 q^{34} - 22 q^{36} + 90 q^{38} - 74 q^{40} + 90 q^{42} - 130 q^{44} + 96 q^{46} - 88 q^{48} - 48 q^{49} + 142 q^{50} - 142 q^{52} + 18 q^{54} - 82 q^{56} + 22 q^{58} + 2 q^{60} - 40 q^{62} - 8 q^{63} + 16 q^{66} - 44 q^{68} + 16 q^{71} - 4 q^{72} + 10 q^{74} - 138 q^{76} - 40 q^{79} - 170 q^{80} - 48 q^{81} - 124 q^{82} - 8 q^{84} - 216 q^{86} - 108 q^{88} + 4 q^{90} - 198 q^{92} - 238 q^{94} + 80 q^{95} + 4 q^{96} - 132 q^{98}+O(q^{100}) \) 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more