LMFDB - Embedded newform 552.2.bb.a.13.7

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			13.7
Character	$\chi$	$=$	552.13
Dual form			552.2.bb.a.85.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30419 - 0.546886i) q^{2} +(-0.540641 + 0.841254i) q^{3} +(1.40183 + 1.42649i) q^{4} +(-0.190010 - 0.0867748i) q^{5} +(1.16517 - 0.801487i) q^{6} +(2.41838 + 0.710100i) q^{7} +(-1.04813 - 2.62706i) q^{8} +(-0.415415 - 0.909632i) q^{9} +O(q^{10})$	\(q+(-1.30419 - 0.546886i) q^{2} +(-0.540641 + 0.841254i) q^{3} +(1.40183 + 1.42649i) q^{4} +(-0.190010 - 0.0867748i) q^{5} +(1.16517 - 0.801487i) q^{6} +(2.41838 + 0.710100i) q^{7} +(-1.04813 - 2.62706i) q^{8} +(-0.415415 - 0.909632i) q^{9} +(0.200354 + 0.217085i) q^{10} +(-4.36540 - 3.78264i) q^{11} +(-1.95793 + 0.408077i) q^{12} +(-1.69874 - 5.78537i) q^{13} +(-2.76568 - 2.24868i) q^{14} +(0.175727 - 0.112933i) q^{15} +(-0.0697411 + 3.99939i) q^{16} +(0.569168 + 3.95865i) q^{17} +(0.0443154 + 1.41352i) q^{18} +(6.83272 + 0.982398i) q^{19} +(-0.142579 - 0.392691i) q^{20} +(-1.90485 + 1.65056i) q^{21} +(3.62464 + 7.32066i) q^{22} +(3.93147 - 2.74655i) q^{23} +(2.77668 + 0.538552i) q^{24} +(-3.24573 - 3.74577i) q^{25} +(-0.948460 + 8.47425i) q^{26} +(0.989821 + 0.142315i) q^{27} +(2.37721 + 4.44523i) q^{28} +(-0.673989 + 0.0969050i) q^{29} +(-0.290943 + 0.0511834i) q^{30} +(0.246501 - 0.158417i) q^{31} +(2.27817 - 5.17783i) q^{32} +(5.54227 - 1.62736i) q^{33} +(1.42263 - 5.47411i) q^{34} +(-0.397898 - 0.344780i) q^{35} +(0.715238 - 1.86774i) q^{36} +(-1.94862 + 0.889905i) q^{37} +(-8.37392 - 5.01796i) q^{38} +(5.78537 + 1.69874i) q^{39} +(-0.0288071 + 0.590119i) q^{40} +(4.71909 - 10.3334i) q^{41} +(3.38695 - 1.11091i) q^{42} +(3.10617 - 4.83330i) q^{43} +(-0.723657 - 11.5298i) q^{44} +0.208887i q^{45} +(-6.62944 + 1.43196i) q^{46} +3.14610 q^{47} +(-3.32680 - 2.22090i) q^{48} +(-0.544467 - 0.349908i) q^{49} +(2.18454 + 6.66025i) q^{50} +(-3.63794 - 1.66139i) q^{51} +(5.87142 - 10.5333i) q^{52} +(-0.724646 + 2.46792i) q^{53} +(-1.21309 - 0.726926i) q^{54} +(0.501233 + 1.09755i) q^{55} +(-0.669298 - 7.09749i) q^{56} +(-4.52050 + 5.21693i) q^{57} +(0.932007 + 0.242213i) q^{58} +(-2.17725 - 7.41504i) q^{59} +(0.407437 + 0.0923597i) q^{60} +(6.75974 + 10.5184i) q^{61} +(-0.408120 + 0.0717975i) q^{62} +(-0.358701 - 2.49482i) q^{63} +(-5.80285 + 5.50699i) q^{64} +(-0.179247 + 1.24669i) q^{65} +(-8.11816 - 0.908606i) q^{66} +(2.83098 - 2.45306i) q^{67} +(-4.84909 + 6.36127i) q^{68} +(0.185034 + 4.79226i) q^{69} +(0.330379 + 0.667264i) q^{70} +(7.73672 + 8.92865i) q^{71} +(-1.95425 + 2.04473i) q^{72} +(1.62593 - 11.3086i) q^{73} +(3.02805 - 0.0949329i) q^{74} +(4.90592 - 0.705364i) q^{75} +(8.17694 + 11.1240i) q^{76} +(-7.87113 - 12.2477i) q^{77} +(-6.61621 - 5.37942i) q^{78} +(-2.27930 + 0.669262i) q^{79} +(0.360298 - 0.753874i) q^{80} +(-0.654861 + 0.755750i) q^{81} +(-11.8058 + 10.8959i) q^{82} +(13.0165 - 5.94443i) q^{83} +(-5.02478 - 0.403438i) q^{84} +(0.235363 - 0.801573i) q^{85} +(-6.69431 + 4.60482i) q^{86} +(0.282864 - 0.619387i) q^{87} +(-5.36171 + 15.4328i) q^{88} +(-14.0921 - 9.05642i) q^{89} +(0.114237 - 0.272429i) q^{90} -15.1975i q^{91} +(9.42918 + 1.75800i) q^{92} +0.293016i q^{93} +(-4.10311 - 1.72056i) q^{94} +(-1.21304 - 0.779574i) q^{95} +(3.12420 + 4.71586i) q^{96} +(-2.56200 + 5.60999i) q^{97} +(0.518729 + 0.754108i) q^{98} +(-1.62736 + 5.54227i) 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 $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{7}{11}\right)$	$1$	$-1$	$1$

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 $

$2$	−1.30419	−	0.546886i	−0.922203	−	0.386707i
$2$	−1.30419	−	0.546886i	−0.922203	−	0.386707i
$3$	−0.540641	+	0.841254i	−0.312139	+	0.485698i
$3$	−0.540641	+	0.841254i	−0.312139	+	0.485698i
$4$	1.40183	+	1.42649i	0.700915	+	0.713244i
$5$	−0.190010	−	0.0867748i	−0.0849752	−	0.0388069i	0.372474	−	0.928043i	$-0.378510\pi$
$5$	−0.190010	−	0.0867748i	−0.0849752	−	0.0388069i	−0.457449	+	0.889236i	$0.651237\pi$
$6$	1.16517	−	0.801487i	0.475678	−	0.327206i
$7$	2.41838	+	0.710100i	0.914061	+	0.268392i	0.704749	−	0.709457i	$-0.251060\pi$
$7$	2.41838	+	0.710100i	0.914061	+	0.268392i	0.209312	+	0.977849i	$0.432878\pi$
$8$	−1.04813	−	2.62706i	−0.370569	−	0.928805i
$9$	−0.415415	−	0.909632i	−0.138472	−	0.303211i
$10$	0.200354	+	0.217085i	0.0633574	+	0.0686483i
$11$	−4.36540	−	3.78264i	−1.31622	−	1.14051i	−0.980060	−	0.198703i	$-0.936327\pi$
$11$	−4.36540	−	3.78264i	−1.31622	−	1.14051i	−0.336157	−	0.941806i	$-0.609127\pi$
$12$	−1.95793	+	0.408077i	−0.565204	+	0.117802i
$13$	−1.69874	−	5.78537i	−0.471145	−	1.60457i	−0.761845	−	0.647759i	$-0.775706\pi$
$13$	−1.69874	−	5.78537i	−0.471145	−	1.60457i	0.290700	−	0.956814i	$-0.406112\pi$
$14$	−2.76568	−	2.24868i	−0.739160	−	0.600986i
$15$	0.175727	−	0.112933i	0.0453725	−	0.0291591i
$16$	−0.0697411	+	3.99939i	−0.0174353	+	0.999848i
$17$	0.569168	+	3.95865i	0.138043	+	0.960114i	0.934638	+	0.355600i	$0.115723\pi$
$17$	0.569168	+	3.95865i	0.138043	+	0.960114i	−0.796595	+	0.604514i	$0.793367\pi$
$18$	0.0443154	+	1.41352i	0.0104452	+	0.333170i
$19$	6.83272	+	0.982398i	1.56753	+	0.225377i	0.870685	−	0.491840i	$-0.163676\pi$
$19$	6.83272	+	0.982398i	1.56753	+	0.225377i	0.696849	+	0.717218i	$0.254585\pi$
$20$	−0.142579	−	0.392691i	−0.0318816	−	0.0878084i
$21$	−1.90485	+	1.65056i	−0.415672	+	0.360182i
$22$	3.62464	+	7.32066i	0.772776	+	1.56077i
$23$	3.93147	−	2.74655i	0.819768	−	0.572696i
$23$	3.93147	−	2.74655i	0.819768	−	0.572696i
$24$	2.77668	+	0.538552i	0.566788	+	0.109932i
$25$	−3.24573	−	3.74577i	−0.649146	−	0.749154i
$26$	−0.948460	+	8.47425i	−0.186008	+	1.66194i
$27$	0.989821	+	0.142315i	0.190491	+	0.0273885i
$28$	2.37721	+	4.44523i	0.449250	+	0.840069i
$29$	−0.673989	+	0.0969050i	−0.125157	+	0.0179948i	−0.204608	−	0.978844i	$-0.565592\pi$
$29$	−0.673989	+	0.0969050i	−0.125157	+	0.0179948i	0.0794518	+	0.996839i	$0.474683\pi$
$30$	−0.290943	+	0.0511834i	−0.0531187	+	0.00934476i
$31$	0.246501	−	0.158417i	0.0442729	−	0.0284525i	−0.518317	−	0.855188i	$-0.673441\pi$
$31$	0.246501	−	0.158417i	0.0442729	−	0.0284525i	0.562590	+	0.826736i	$0.309805\pi$
$32$	2.27817	−	5.17783i	0.402727	−	0.915320i
$33$	5.54227	−	1.62736i	0.964786	−	0.283287i
$34$	1.42263	−	5.47411i	0.243979	−	0.938802i
$35$	−0.397898	−	0.344780i	−0.0672570	−	0.0582785i
$36$	0.715238	−	1.86774i	0.119206	−	0.311289i
$37$	−1.94862	+	0.889905i	−0.320351	+	0.146300i	−0.569100	−	0.822269i	$-0.692708\pi$
$37$	−1.94862	+	0.889905i	−0.320351	+	0.146300i	0.248748	+	0.968568i	$0.419981\pi$
$38$	−8.37392	−	5.01796i	−1.35843	−	0.814020i
$39$	5.78537	+	1.69874i	0.926401	+	0.272016i
$40$	−0.0288071	+	0.590119i	−0.00455480	+	0.0933060i
$41$	4.71909	−	10.3334i	0.736997	−	1.61380i	−0.0514343	−	0.998676i	$-0.516379\pi$
$41$	4.71909	−	10.3334i	0.736997	−	1.61380i	0.788432	−	0.615123i	$-0.210893\pi$
$42$	3.38695	−	1.11091i	0.522618	−	0.171417i
$43$	3.10617	−	4.83330i	0.473687	−	0.737071i	−0.519390	−	0.854537i	$-0.673841\pi$
$43$	3.10617	−	4.83330i	0.473687	−	0.737071i	0.993077	+	0.117466i	$0.0374771\pi$
$44$	−0.723657	−	11.5298i	−0.109095	−	1.73818i
$45$			0.208887i			0.0311390i
$46$	−6.62944	+	1.43196i	−0.977458	+	0.211131i
$47$	3.14610			0.458905			0.229453	−	0.973320i	$-0.426306\pi$
$47$	3.14610			0.458905			0.229453	+	0.973320i	$0.426306\pi$
$48$	−3.32680	−	2.22090i	−0.480182	−	0.320560i
$49$	−0.544467	−	0.349908i	−0.0777810	−	0.0499868i
$50$	2.18454	+	6.66025i	0.308941	+	0.941901i
$51$	−3.63794	−	1.66139i	−0.509414	−	0.232642i
$52$	5.87142	−	10.5333i	0.814220	−	1.46071i
$53$	−0.724646	+	2.46792i	−0.0995378	+	0.338995i	−0.994172	−	0.107804i	$-0.965618\pi$
$53$	−0.724646	+	2.46792i	−0.0995378	+	0.338995i	0.894634	+	0.446799i	$0.147436\pi$
$54$	−1.21309	−	0.726926i	−0.165080	−	0.0989220i
$55$	0.501233	+	1.09755i	0.0675862	+	0.147993i
$56$	−0.669298	−	7.09749i	−0.0894387	−	0.948442i
$57$	−4.52050	+	5.21693i	−0.598754	+	0.690999i
$58$	0.932007	+	0.242213i	0.122379	+	0.0318041i
$59$	−2.17725	−	7.41504i	−0.283454	−	0.965356i	−0.970973	−	0.239189i	$-0.923118\pi$
$59$	−2.17725	−	7.41504i	−0.283454	−	0.965356i	0.687519	−	0.726167i	$-0.258700\pi$
$60$	0.407437	+	0.0923597i	0.0525998	+	0.0119236i
$61$	6.75974	+	10.5184i	0.865496	+	1.34674i	0.937012	+	0.349298i	$0.113580\pi$
$61$	6.75974	+	10.5184i	0.865496	+	1.34674i	−0.0715158	+	0.997439i	$0.522784\pi$
$62$	−0.408120	+	0.0717975i	−0.0518313	+	0.00911830i
$63$	−0.358701	−	2.49482i	−0.0451921	−	0.314318i
$64$	−5.80285	+	5.50699i	−0.725357	+	0.688373i
$65$	−0.179247	+	1.24669i	−0.0222328	+	0.154632i
$66$	−8.11816	−	0.908606i	−0.999277	−	0.111842i
$67$	2.83098	−	2.45306i	0.345859	−	0.299689i	−0.464557	−	0.885543i	$-0.653786\pi$
$67$	2.83098	−	2.45306i	0.345859	−	0.299689i	0.810416	+	0.585854i	$0.199241\pi$
$68$	−4.84909	+	6.36127i	−0.588039	+	0.771417i
$69$	0.185034	+	4.79226i	0.0222754	+	0.576920i
$70$	0.330379	+	0.667264i	0.0394879	+	0.0797533i
$71$	7.73672	+	8.92865i	0.918180	+	1.05964i	0.998024	+	0.0628285i	$0.0200121\pi$
$71$	7.73672	+	8.92865i	0.918180	+	1.05964i	−0.0798447	+	0.996807i	$0.525442\pi$
$72$	−1.95425	+	2.04473i	−0.230310	+	0.240974i
$73$	1.62593	−	11.3086i	0.190300	−	1.32357i	−0.640912	−	0.767614i	$-0.721444\pi$
$73$	1.62593	−	11.3086i	0.190300	−	1.32357i	0.831213	−	0.555954i	$-0.187647\pi$
$74$	3.02805	−	0.0949329i	0.352004	−	0.0110357i
$75$	4.90592	−	0.705364i	0.566487	−	0.0814485i
$76$	8.17694	+	11.1240i	0.937960	+	1.27601i
$77$	−7.87113	−	12.2477i	−0.896999	−	1.39576i
$78$	−6.61621	−	5.37942i	−0.749139	−	0.609099i
$79$	−2.27930	+	0.669262i	−0.256441	+	0.0752978i	−0.407426	−	0.913238i	$-0.633574\pi$
$79$	−2.27930	+	0.669262i	−0.256441	+	0.0752978i	0.150985	+	0.988536i	$0.451755\pi$
$80$	0.360298	−	0.753874i	0.0402825	−	0.0842856i
$81$	−0.654861	+	0.755750i	−0.0727623	+	0.0839722i
$82$	−11.8058	+	10.8959i	−1.30373	+	1.20325i
$83$	13.0165	−	5.94443i	1.42874	−	0.652486i	0.457204	−	0.889362i	$-0.348851\pi$
$83$	13.0165	−	5.94443i	1.42874	−	0.652486i	0.971540	+	0.236876i	$0.0761235\pi$
$84$	−5.02478	−	0.403438i	−0.548248	−	0.0440187i
$85$	0.235363	−	0.801573i	0.0255287	−	0.0869428i
$86$	−6.69431	+	4.60482i	−0.721866	+	0.496551i
$87$	0.282864	−	0.619387i	0.0303263	−	0.0664052i
$88$	−5.36171	+	15.4328i	−0.571560	+	1.64515i
$89$	−14.0921	−	9.05642i	−1.49376	−	0.959979i	−0.995681	−	0.0928449i	$-0.970404\pi$
$89$	−14.0921	−	9.05642i	−1.49376	−	0.959979i	−0.498075	−	0.867134i	$-0.665960\pi$
$90$	0.114237	−	0.272429i	0.0120417	−	0.0287165i
$91$		−	15.1975i		−	1.59313i
$92$	9.42918	+	1.75800i	0.983060	+	0.183284i
$93$			0.293016i			0.0303844i
$94$	−4.10311	−	1.72056i	−0.423204	−	0.177462i
$95$	−1.21304	−	0.779574i	−0.124455	−	0.0799826i
$96$	3.12420	+	4.71586i	0.318862	+	0.481311i
$97$	−2.56200	+	5.60999i	−0.260131	+	0.569608i	−0.993962	−	0.109724i	$-0.965003\pi$
$97$	−2.56200	+	5.60999i	−0.260131	+	0.569608i	0.733831	+	0.679332i	$0.237731\pi$
$98$	0.518729	+	0.754108i	0.0523996	+	0.0761764i
$99$	−1.62736	+	5.54227i	−0.163556	+	0.557019i
$100$	0.793338	−	9.88094i	0.0793338	−	0.988094i
$101$	−11.3221	+	5.17063i	−1.12659	+	0.514497i	−0.889475	−	0.456984i	$-0.848930\pi$
$101$	−11.3221	+	5.17063i	−1.12659	+	0.514497i	−0.237117	+	0.971481i	$0.576202\pi$
$102$	3.83598	+	4.15632i	0.379819	+	0.411537i
$103$	7.58841	−	8.75749i	0.747708	−	0.862901i	−0.246636	−	0.969108i	$-0.579325\pi$
$103$	7.58841	−	8.75749i	0.747708	−	0.862901i	0.994344	+	0.106207i	$0.0338706\pi$
$104$	−13.4180	+	10.5265i	−1.31574	+	1.03221i
$105$	0.505167	−	0.148331i	0.0492993	−	0.0144756i
$106$	2.29475	−	2.82234i	0.222886	−	0.274130i
$107$	2.68053	+	4.17098i	0.259137	+	0.403224i	0.946306	−	0.323273i	$-0.104783\pi$
$107$	2.68053	+	4.17098i	0.259137	+	0.403224i	−0.687169	+	0.726497i	$0.741147\pi$
$108$	1.18455	+	1.61147i	0.113984	+	0.155064i
$109$	−9.47882	+	1.36285i	−0.907906	+	0.130537i	−0.580419	−	0.814318i	$-0.697111\pi$
$109$	−9.47882	+	1.36285i	−0.907906	+	0.130537i	−0.327488	+	0.944855i	$0.606202\pi$
$110$	−0.0534703	−	1.70553i	−0.00509819	−	0.162616i
$111$	0.304868	−	2.12040i	0.0289368	−	0.201260i
$112$	−3.00863	+	9.62252i	−0.284289	+	0.909242i
$113$	6.04769	+	6.97941i	0.568919	+	0.656567i	0.965185	−	0.261568i	$-0.0842397\pi$
$113$	6.04769	+	6.97941i	0.568919	+	0.656567i	−0.396266	+	0.918136i	$0.629694\pi$
$114$	8.74866	−	4.33168i	0.819387	−	0.405699i
$115$	−0.985351	+	0.180721i	−0.0918844	+	0.0168523i
$116$	−1.08305	−	0.825594i	−0.100559	−	0.0766545i
$117$	−4.55688	+	3.94856i	−0.421283	+	0.365044i
$118$	−1.21563	+	10.8613i	−0.111908	+	0.999867i
$119$	−1.43457	+	9.97767i	−0.131507	+	0.914652i
$120$	−0.480865	−	0.343276i	−0.0438968	−	0.0313367i
$121$	3.18288	+	22.1374i	0.289353	+	2.01249i
$122$	−3.06365	−	17.4148i	−0.277370	−	1.57666i
$123$	6.14164	+	9.55658i	0.553773	+	0.861688i
$124$	0.571532	+	0.129558i	0.0513251	+	0.0116346i
$125$	0.585935	+	1.99551i	0.0524076	+	0.178484i
$126$	−0.896568	+	3.44989i	−0.0798726	+	0.307341i
$127$	5.68698	−	6.56313i	0.504638	−	0.582383i	−0.445080	−	0.895491i	$-0.646825\pi$
$127$	5.68698	−	6.56313i	0.504638	−	0.582383i	0.949718	+	0.313108i	$0.101370\pi$
$128$	10.5797	−	4.00866i	0.935125	−	0.354319i
$129$	2.38671	+	5.22616i	0.210138	+	0.460138i
$130$	0.915568	−	1.52789i	0.0803006	−	0.134005i
$131$	−1.76611	+	6.01481i	−0.154306	+	0.525517i	−0.999966	−	0.00820412i	$-0.997389\pi$
$131$	−1.76611	+	6.01481i	−0.154306	+	0.525517i	0.845661	+	0.533721i	$0.179207\pi$
$132$	10.0907	+	5.62471i	0.878286	+	0.489568i
$133$	15.8265	+	7.22772i	1.37233	+	0.626723i
$134$	−5.03368	+	1.65103i	−0.434844	+	0.142628i
$135$	−0.175727	−	0.112933i	−0.0151242	−	0.00971971i
$136$	9.80304	−	5.64441i	0.840603	−	0.484004i
$137$	−0.313042			−0.0267450			−0.0133725	−	0.999911i	$-0.504257\pi$
$137$	−0.313042			−0.0267450			−0.0133725	+	0.999911i	$0.504257\pi$
$138$	2.37950	−	6.35122i	0.202557	−	0.540652i
$139$			5.60105i			0.475075i	0.971378	+	0.237538i	$0.0763403\pi$
$139$			5.60105i			0.475075i	−0.971378	+	0.237538i	$0.923660\pi$
$140$	−0.0659599	−	1.05092i	−0.00557463	−	0.0888190i
$141$	−1.70091	+	2.64667i	−0.143242	+	0.222889i
$142$	−5.20721	−	15.8758i	−0.436979	−	1.33227i
$143$	−14.4683	+	31.6812i	−1.20990	+	2.64931i
$144$	3.66695	−	1.59797i	0.305579	−	0.133164i
$145$	0.136474	+	0.0400723i	0.0113335	+	0.00332782i
$146$	−8.30502	+	13.8593i	−0.687329	+	1.14701i
$147$	0.588722	−	0.268860i	0.0485570	−	0.0221752i
$148$	−4.00108	−	1.53219i	−0.328887	−	0.125945i
$149$	−1.66760	−	1.44498i	−0.136615	−	0.118377i	0.583873	−	0.811845i	$-0.301537\pi$
$149$	−1.66760	−	1.44498i	−0.136615	−	0.118377i	−0.720488	+	0.693468i	$0.756082\pi$
$150$	−6.78401	−	1.76305i	−0.553912	−	0.143952i
$151$	−23.0454	+	6.76675i	−1.87541	+	0.550670i	−0.878007	+	0.478647i	$0.841127\pi$
$151$	−23.0454	+	6.76675i	−1.87541	+	0.550670i	−0.997403	+	0.0720229i	$0.977055\pi$
$152$	−4.58076	−	18.9796i	−0.371549	−	1.53945i
$153$	3.36447	−	2.16222i	0.272002	−	0.174805i
$154$	3.56735	+	20.2780i	0.287465	+	1.63405i
$155$	−0.0605843	+	0.00871070i	−0.00486625	+	0.000699661i
$156$	5.68688	+	10.6341i	0.455315	+	0.851410i
$157$	−18.5052	−	2.66065i	−1.47688	−	0.212343i	−0.643671	−	0.765303i	$-0.722589\pi$
$157$	−18.5052	−	2.66065i	−1.47688	−	0.212343i	−0.833208	+	0.552960i	$0.813498\pi$
$158$	3.33865	+	0.373670i	0.265609	+	0.0297276i
$159$	−1.68437	−	1.94387i	−0.133579	−	0.154159i
$160$	−0.882180	+	0.786154i	−0.0697425	+	0.0621509i
$161$	11.4581	−	3.85046i	0.903025	−	0.303459i
$162$	1.26737	−	0.627508i	0.0995742	−	0.0493017i
$163$	−1.36908	+	1.18632i	−0.107235	+	0.0929194i	−0.706828	−	0.707386i	$-0.749875\pi$
$163$	−1.36908	+	1.18632i	−0.107235	+	0.0929194i	0.599593	+	0.800305i	$0.295329\pi$
$164$	21.3558	−	7.75389i	1.66761	−	0.605477i
$165$	−1.19430	−	0.171715i	−0.0929763	−	0.0133680i
$166$	−20.2269	+	0.634137i	−1.56991	+	0.0492185i
$167$	−0.591885	−	4.11665i	−0.0458014	−	0.318556i	−0.999823	−	0.0188177i	$-0.994010\pi$
$167$	−0.591885	−	4.11665i	−0.0458014	−	0.318556i	0.954022	−	0.299738i	$-0.0968993\pi$
$168$	6.33264	+	3.27414i	0.488574	+	0.252606i
$169$	−19.6485	+	12.6273i	−1.51142	+	0.971333i
$170$	−0.745328	+	0.916688i	−0.0571640	+	0.0703068i
$171$	−1.94480	−	6.62337i	−0.148722	−	0.506502i
$172$	11.2490	−	2.34455i	0.857726	−	0.178770i
$173$	13.3481	+	11.5662i	1.01483	+	0.879359i	0.992726	−	0.120397i	$-0.0384166\pi$
$173$	13.3481	+	11.5662i	1.01483	+	0.879359i	0.0221086	+	0.999756i	$0.492962\pi$
$174$	−0.707644	+	0.653104i	−0.0536463	+	0.0495117i
$175$	−5.18953	−	11.3635i	−0.392291	−	0.858998i
$176$	15.4327	−	17.1951i	1.16328	−	1.29613i
$177$	7.41504	+	2.17725i	0.557348	+	0.163652i
$178$	13.4259	+	19.5181i	1.00632	+	1.46294i
$179$	−9.69685	−	4.42840i	−0.724777	−	0.330994i	0.0186370	−	0.999826i	$-0.494067\pi$
$179$	−9.69685	−	4.42840i	−0.724777	−	0.330994i	−0.743414	+	0.668832i	$0.766795\pi$
$180$	−0.297975	+	0.292824i	−0.0222097	+	0.0218258i
$181$	7.44916	−	11.5911i	0.553692	−	0.861561i	−0.445744	−	0.895161i	$-0.647061\pi$
$181$	7.44916	−	11.5911i	0.553692	−	0.861561i	0.999435	+	0.0335996i	$0.0106971\pi$
$182$	−8.31130	+	19.8204i	−0.616074	+	1.46919i
$183$	−12.5032			−0.924263
$184$	−11.3360	−	7.44945i	−0.835703	−	0.549181i
$185$	0.447479			0.0328993
$186$	0.160247	−	0.382149i	0.0117499	−	0.0280206i
$187$	12.4895	−	19.4340i	0.913323	−	1.42116i
$188$	4.41030	+	4.48787i	0.321654	+	0.327312i
$189$	2.29270	+	1.04704i	0.166770	+	0.0761612i
$190$	1.15570	+	1.68011i	0.0838432	+	0.121888i
$191$	14.1397	+	4.15180i	1.02311	+	0.300413i	0.749908	−	0.661542i	$-0.230098\pi$
$191$	14.1397	+	4.15180i	1.02311	+	0.300413i	0.273206	+	0.961956i	$0.411916\pi$
$192$	−1.49551	−	7.85897i	−0.107929	−	0.567172i
$193$	−7.89644	−	17.2908i	−0.568398	−	1.24462i	−0.947646	−	0.319324i	$-0.896544\pi$
$193$	−7.89644	−	17.2908i	−0.568398	−	1.24462i	0.379247	−	0.925295i	$-0.376183\pi$
$194$	6.40936	−	5.91538i	0.460165	−	0.424700i
$195$	−0.951872	−	0.824802i	−0.0681650	−	0.0590653i
$196$	−0.264111	−	1.26719i	−0.0188651	−	0.0905134i
$197$	5.86293	+	19.9673i	0.417716	+	1.42261i	0.852808	+	0.522225i	$0.174898\pi$
$197$	5.86293	+	19.9673i	0.417716	+	1.42261i	−0.435091	+	0.900386i	$0.643284\pi$
$198$	5.15338	−	6.33820i	0.366235	−	0.450436i
$199$	−13.8730	+	8.91566i	−0.983434	+	0.632014i	−0.930387	−	0.366578i	$-0.880529\pi$
$199$	−13.8730	+	8.91566i	−0.983434	+	0.632014i	−0.0530462	+	0.998592i	$0.516893\pi$
$200$	−6.43841	+	12.4528i	−0.455265	+	0.880544i
$201$	0.533101	+	3.70780i	0.0376020	+	0.261528i
$202$	17.5939	−	0.551590i	1.23791	−	0.0388097i
$203$	−1.69877	−	0.244247i	−0.119230	−	0.0171428i
$204$	−2.72982	−	7.51848i	−0.191126	−	0.526399i
$205$	−1.79335	+	1.55395i	−0.125253	+	0.108532i
$206$	−14.6861	+	7.27145i	−1.02323	+	0.506626i
$207$	−4.13154	−	2.43523i	−0.287162	−	0.169260i
$208$	23.2564	−	6.39044i	1.61254	−	0.443097i
$209$	−26.1115	−	30.1343i	−1.80617	−	2.08443i
$210$	−0.739955	−	0.0828177i	−0.0510617	−	0.00571497i
$211$	−2.81311	−	0.404463i	−0.193662	−	0.0278444i	0.0448011	−	0.998996i	$-0.485735\pi$
$211$	−2.81311	−	0.404463i	−0.193662	−	0.0278444i	−0.238463	+	0.971152i	$0.576644\pi$
$212$	−4.53629	+	2.42590i	−0.311554	+	0.166612i
$213$	−11.6940	+	1.68135i	−0.801263	+	0.115204i
$214$	−1.21487	−	6.90571i	−0.0830467	−	0.472064i
$215$	−1.00961	+	0.648839i	−0.0688550	+	0.0442504i
$216$	−0.663591	−	2.74948i	−0.0451516	−	0.187079i
$217$	0.708624	−	0.208071i	0.0481045	−	0.0141248i
$218$	13.1075	+	3.40642i	0.887753	+	0.230712i
$219$	8.63433	+	7.48169i	0.583454	+	0.505566i
$220$	−0.862994	+	2.25358i	−0.0581831	+	0.151936i
$221$	21.9354	−	10.0176i	1.47553	−	0.673854i
$222$	−1.55723	+	2.59868i	−0.104514	+	0.174412i
$223$	8.55889	+	2.51312i	0.573146	+	0.168291i	0.555446	−	0.831553i	$-0.312548\pi$
$223$	8.55889	+	2.51312i	0.573146	+	0.168291i	0.0176997	+	0.999843i	$0.494366\pi$
$224$	9.18625	−	10.9042i	0.613782	−	0.728569i
$225$	−2.05895	+	4.50847i	−0.137263	+	0.300565i
$226$	−4.07040	−	12.4099i	−0.270759	−	0.825493i
$227$	−2.26730	+	3.52799i	−0.150486	+	0.234161i	−0.908309	−	0.418299i	$-0.862626\pi$
$227$	−2.26730	+	3.52799i	−0.150486	+	0.234161i	0.757823	+	0.652460i	$0.226263\pi$
$228$	−13.7789	+	0.864816i	−0.912527	+	0.0572738i
$229$		−	3.13780i		−	0.207351i	−0.994611	−	0.103676i	$-0.966940\pi$
$229$		−	3.13780i		−	0.207351i	0.994611	−	0.103676i	$-0.0330604\pi$
$230$	1.38392	+	0.303181i	0.0912530	+	0.0199911i
$231$	14.5589			0.957905
$232$	0.961003	+	1.66904i	0.0630929	+	0.109578i
$233$	−5.10382	−	3.28003i	−0.334362	−	0.214882i	0.362676	−	0.931915i	$-0.381863\pi$
$233$	−5.10382	−	3.28003i	−0.334362	−	0.214882i	−0.697039	+	0.717034i	$0.745499\pi$
$234$	8.10245	−	2.65758i	0.529674	−	0.173731i
$235$	−0.597791	−	0.273002i	−0.0389956	−	0.0178087i
$236$	7.52533	−	13.5005i	0.489857	−	0.878805i
$237$	0.669262	−	2.27930i	0.0434732	−	0.148056i
$238$	7.32761	−	12.2282i	0.474979	−	0.792640i
$239$	0.205268	+	0.449474i	0.0132777	+	0.0290740i	0.916155	−	0.400825i	$-0.131276\pi$
$239$	0.205268	+	0.449474i	0.0132777	+	0.0290740i	−0.902877	+	0.429899i	$0.858549\pi$
$240$	0.439407	+	0.710677i	0.0283636	+	0.0458740i
$241$	10.9064	−	12.5866i	0.702541	−	0.810776i	−0.286552	−	0.958065i	$-0.592509\pi$
$241$	10.9064	−	12.5866i	0.702541	−	0.810776i	0.989094	+	0.147289i	$0.0470546\pi$
$242$	7.95557	−	30.6121i	0.511403	−	1.96782i
$243$	−0.281733	−	0.959493i	−0.0180732	−	0.0615515i
$244$	−5.52831	+	24.3876i	−0.353914	+	1.56126i
$245$	0.0730911	+	0.113732i	0.00466962	+	0.00726607i
$246$	−2.78351	−	15.8224i	−0.177470	−	1.00880i
$247$	−5.92348	−	41.1987i	−0.376902	−	2.62141i
$248$	−0.674534	−	0.481531i	−0.0428330	−	0.0305773i
$249$	−2.03647	+	14.1640i	−0.129056	+	0.897604i
$250$	0.327146	−	2.92297i	0.0206905	−	0.184865i
$251$	−16.8344	+	14.5871i	−1.06258	+	0.920727i	−0.997022	−	0.0771224i	$-0.975427\pi$
$251$	−16.8344	+	14.5871i	−1.06258	+	0.920727i	−0.0655535	+	0.997849i	$0.520881\pi$
$252$	3.05599	−	4.00900i	0.192510	−	0.252543i
$253$	−27.5516	−	2.88154i	−1.73216	−	0.181161i
$254$	−11.0062	+	5.44944i	−0.690590	+	0.341928i
$255$	0.547079	+	0.631363i	0.0342594	+	0.0395375i
$256$	−15.9903	−	0.557844i	−0.999392	−	0.0348653i
$257$	2.35328	−	16.3674i	0.146794	−	1.02097i	−0.774630	−	0.632414i	$-0.782064\pi$
$257$	2.35328	−	16.3674i	0.146794	−	1.02097i	0.921424	−	0.388559i	$-0.127027\pi$
$258$	−0.254608	−	8.12117i	−0.0158512	−	0.505602i
$259$	−5.34442	+	0.768412i	−0.332086	+	0.0477468i
$260$	−2.02966	+	1.49195i	−0.125874	+	0.0925269i
$261$	0.368133	+	0.572827i	0.0227869	+	0.0354571i
$262$	5.59276	−	6.87861i	0.345522	−	0.424962i
$263$	7.83744	−	2.30128i	0.483277	−	0.141903i	−0.0310135	−	0.999519i	$-0.509873\pi$
$263$	7.83744	−	2.30128i	0.483277	−	0.141903i	0.514291	+	0.857616i	$0.328055\pi$
$264$	−10.0842	−	12.8542i	−0.620638	−	0.791120i
$265$	0.351843	−	0.406049i	0.0216136	−	0.0249434i
$266$	−16.6881	−	18.0816i	−1.02321	−	1.10866i
$267$	15.2375	−	6.95873i	0.932519	−	0.425867i
$268$	7.46782	+	0.599589i	0.456169	+	0.0366257i
$269$	−4.28400	+	14.5900i	−0.261200	+	0.889566i	0.719573	+	0.694416i	$0.244337\pi$
$269$	−4.28400	+	14.5900i	−0.261200	+	0.889566i	−0.980773	+	0.195150i	$0.937481\pi$
$270$	0.167420	+	0.243389i	0.0101889	+	0.0148122i
$271$	−7.62800	+	16.7030i	−0.463368	+	1.01463i	0.523339	+	0.852125i	$0.324686\pi$
$271$	−7.62800	+	16.7030i	−0.463368	+	1.01463i	−0.986707	+	0.162510i	$0.948041\pi$
$272$	−15.8719	+	2.00024i	−0.962374	+	0.121283i
$273$	12.7849	+	8.21638i	0.773780	+	0.497278i
$274$	0.408266	+	0.171198i	0.0246643	+	0.0103425i
$275$			28.6292i			1.72641i
$276$	−6.57672	+	6.98189i	−0.395872	+	0.420260i
$277$		−	16.6080i		−	0.997878i	−0.866637	−	0.498939i	$-0.833723\pi$
$277$		−	16.6080i		−	0.997878i	0.866637	−	0.498939i	$-0.166277\pi$
$278$	3.06314	−	7.30485i	0.183715	−	0.438116i
$279$	−0.246501	−	0.158417i	−0.0147576	−	0.00948415i
$280$	−0.488710	+	1.40667i	−0.0292060	+	0.0840648i
$281$	−5.99935	+	13.1367i	−0.357891	+	0.783672i	0.641966	+	0.766733i	$0.278119\pi$
$281$	−5.99935	+	13.1367i	−0.357891	+	0.783672i	−0.999857	+	0.0169385i	$0.994608\pi$
$282$	3.66574	−	2.52155i	0.218291	−	0.150156i
$283$	1.63467	−	5.56718i	0.0971711	−	0.330935i	−0.896532	−	0.442979i	$-0.853922\pi$
$283$	1.63467	−	5.56718i	0.0971711	−	0.330935i	0.993703	+	0.112044i	$0.0357399\pi$
$284$	−1.89105	+	23.5528i	−0.112213	+	1.39760i
$285$	1.31164	−	0.599005i	0.0776947	−	0.0354820i
$286$	36.1954	−	33.4058i	2.14028	−	1.97533i
$287$	18.7502	−	21.6389i	1.10679	−	1.27731i
$288$	−5.65631	+	0.0786544i	−0.333301	+	0.00463476i
$289$	0.964427	−	0.283181i	0.0567310	−	0.0166577i
$290$	−0.156073	−	0.126898i	−0.00916492	−	0.00745168i
$291$	−3.33430	−	5.18828i	−0.195460	−	0.304142i
$292$	18.4108	−	13.5333i	1.07741	−	0.791979i
$293$	4.17079	−	0.599670i	0.243660	−	0.0350331i	−0.0194025	−	0.999812i	$-0.506176\pi$
$293$	4.17079	−	0.599670i	0.243660	−	0.0350331i	0.263063	+	0.964779i	$0.415267\pi$
$294$	−0.914842	+	0.0286813i	−0.0533547	+	0.00167273i
$295$	−0.229738	+	1.59786i	−0.0133759	+	0.0930312i
$296$	4.38024	+	4.18640i	0.254596	+	0.243330i
$297$	−3.78264	−	4.36540i	−0.219491	−	0.253306i
$298$	1.38463	+	2.79652i	0.0802092	+	0.161998i
$299$	−22.5684	−	18.0793i	−1.30516	−	1.04555i
$300$	7.88346	+	6.00944i	0.455152	+	0.346955i
$301$	10.9440	−	9.48305i	0.630803	−	0.546594i
$302$	33.7563	+	3.77809i	1.94246	+	0.217405i
$303$	1.77138	−	12.3202i	0.101763	−	0.707778i
$304$	−4.40551	+	27.2582i	−0.252674	+	1.56337i
$305$	−0.371691	−	2.58517i	−0.0212830	−	0.148026i
$306$	−5.57040	+	0.979959i	−0.318439	+	0.0560205i
$307$	15.9820	+	24.8685i	0.912142	+	1.41932i	0.907834	+	0.419330i	$0.137735\pi$
$307$	15.9820	+	24.8685i	0.912142	+	1.41932i	0.00430825	+	0.999991i	$0.498629\pi$
$308$	6.43724	−	28.3973i	0.366796	−	1.61809i
$309$	3.26467	+	11.1184i	0.185720	+	0.632505i
$310$	0.0837773	+	0.0217723i	0.00475823	+	0.00123658i
$311$	−17.3341	+	20.0047i	−0.982929	+	1.13436i	0.00799972	+	0.999968i	$0.497454\pi$
$311$	−17.3341	+	20.0047i	−0.982929	+	1.13436i	−0.990928	+	0.134392i	$0.957092\pi$
$312$	−1.60113	−	16.9790i	−0.0906462	−	0.961246i
$313$	−1.24374	−	2.72340i	−0.0703002	−	0.153936i	0.871220	−	0.490893i	$-0.163329\pi$
$313$	−1.24374	−	2.72340i	−0.0703002	−	0.153936i	−0.941520	+	0.336957i	$0.890602\pi$
$314$	22.6793	+	13.5903i	1.27987	+	0.766943i
$315$	−0.148331	+	0.505167i	−0.00835748	+	0.0284630i
$316$	−4.14988	−	2.31320i	−0.233449	−	0.130128i
$317$	4.70433	+	2.14839i	0.264221	+	0.120666i	0.543121	−	0.839654i	$-0.317242\pi$
$317$	4.70433	+	2.14839i	0.264221	+	0.120666i	−0.278900	+	0.960320i	$0.589970\pi$
$318$	1.13367	+	3.45634i	0.0635730	+	0.193822i
$319$	3.30879	+	2.12643i	0.185257	+	0.119057i
$320$	1.58047	−	0.542842i	0.0883509	−	0.0303458i
$321$	−4.95806			−0.276732
$322$	−17.0493	−	1.24454i	−0.950122	−	0.0693553i
$323$			27.6075i			1.53612i
$324$	−1.99607	+	0.125281i	−0.110893	+	0.00696008i
$325$	−16.1570	+	25.1408i	−0.896231	+	1.39456i
$326$	2.43432	−	0.798451i	0.134825	−	0.0442221i
$327$	3.97814	−	8.71090i	0.219991	−	0.481714i
$328$	−32.0925	−	1.56662i	−1.77201	−	0.0865021i
$329$	7.60845	+	2.23404i	0.419467	+	0.123167i
$330$	1.46369	+	0.877096i	0.0805735	+	0.0482825i
$331$	18.5154	−	8.45572i	1.01770	−	0.464768i	0.164514	−	0.986375i	$-0.447394\pi$
$331$	18.5154	−	8.45572i	1.01770	−	0.464768i	0.853186	+	0.521607i	$0.174667\pi$
$332$	26.7266	+	10.2348i	1.46681	+	0.561707i
$333$	1.61897	+	1.40285i	0.0887192	+	0.0768756i
$334$	−1.47941	+	5.69259i	−0.0809496	+	0.311485i
$335$	−0.750779	+	0.220449i	−0.0410194	+	0.0120444i
$336$	−6.46839	−	7.73334i	−0.352880	−	0.421888i
$337$	−17.0822	+	10.9781i	−0.930527	+	0.598013i	−0.915694	−	0.401877i	$-0.868358\pi$
$337$	−17.0822	+	10.9781i	−0.930527	+	0.598013i	−0.0148328	+	0.999890i	$0.504722\pi$
$338$	32.5311	−	5.72295i	1.76946	−	0.311288i
$339$	−9.14108	+	1.31429i	−0.496475	+	0.0713824i
$340$	1.47337	−	0.787927i	0.0799050	−	0.0427313i
$341$	−1.67531	−	0.240873i	−0.0907230	−	0.0130440i
$342$	−1.08584	+	9.70172i	−0.0587156	+	0.524609i
$343$	−12.6222	−	14.5668i	−0.681533	−	0.786531i
$344$	−15.9530	−	3.09417i	−0.860129	−	0.166827i
$345$	0.380689	−	0.926635i	0.0204956	−	0.0498883i
$346$	−11.0831	−	22.3844i	−0.595829	−	1.20339i
$347$	6.73110	−	5.83253i	0.361344	−	0.313107i	−0.455200	−	0.890389i	$-0.650432\pi$
$347$	6.73110	−	5.83253i	0.361344	−	0.313107i	0.816545	+	0.577282i	$0.195887\pi$
$348$	1.28008	−	0.464772i	0.0686193	−	0.0249144i
$349$	12.2865	+	1.76653i	0.657680	+	0.0945602i	0.463072	−	0.886321i	$-0.346747\pi$
$349$	12.2865	+	1.76653i	0.657680	+	0.0945602i	0.194609	+	0.980881i	$0.437656\pi$
$350$	0.553606	+	17.6582i	0.0295915	+	0.943872i
$351$	−0.858103	−	5.96824i	−0.0458022	−	0.318561i
$352$	−29.5310	+	13.9858i	−1.57401	+	0.745446i
$353$	4.05166	−	2.60384i	0.215648	−	0.138589i	−0.428358	−	0.903609i	$-0.640908\pi$
$353$	4.05166	−	2.60384i	0.215648	−	0.138589i	0.644006	+	0.765021i	$0.277271\pi$
$354$	−8.47992	−	6.89474i	−0.450703	−	0.366451i
$355$	−0.695274	−	2.36789i	−0.0369013	−	0.125674i
$356$	−6.83581	−	32.7977i	−0.362297	−	1.73828i
$357$	−7.61817	−	6.60118i	−0.403196	−	0.349371i
$358$	10.2247	+	11.0786i	0.540393	+	0.585520i
$359$	−0.655620	−	1.43561i	−0.0346023	−	0.0757685i	0.891542	−	0.452939i	$-0.149624\pi$
$359$	−0.655620	−	1.43561i	−0.0346023	−	0.0757685i	−0.926144	+	0.377170i	$0.876897\pi$
$360$	0.548758	−	0.218940i	0.0289221	−	0.0115392i
$361$	27.4907	+	8.07198i	1.44688	+	0.424841i
$362$	−16.0542	+	11.0432i	−0.843788	+	0.580417i
$363$	−20.3440	−	9.29078i	−1.06778	−	0.487640i
$364$	21.6790	−	21.3043i	1.13629	−	1.11665i
$365$	−1.29024	+	2.00765i	−0.0675343	+	0.105085i
$366$	16.3066	+	6.83783i	0.852358	+	0.357419i
$367$	8.96669			0.468057			0.234029	−	0.972230i	$-0.424809\pi$
$367$	8.96669			0.468057			0.234029	+	0.972230i	$0.424809\pi$
$368$	10.7104	+	15.9150i	0.558316	+	0.829629i
$369$	−11.3599			−0.591374
$370$	−0.583599	−	0.244720i	−0.0303398	−	0.0127224i
$371$	−3.50494	+	5.45379i	−0.181967	+	0.283147i
$372$	−0.417985	+	0.410759i	−0.0216715	+	0.0212969i
$373$	−3.15179	−	1.43937i	−0.163193	−	0.0745280i	0.332144	−	0.943229i	$-0.392228\pi$
$373$	−3.15179	−	1.43937i	−0.163193	−	0.0745280i	−0.495337	+	0.868701i	$0.664955\pi$
$374$	−26.9169	+	18.5154i	−1.39184	+	0.957407i
$375$	−1.99551	−	0.585935i	−0.103048	−	0.0302575i
$376$	−3.29751	−	8.26498i	−0.170056	−	0.426234i
$377$	1.70556	+	3.73466i	0.0878410	+	0.192345i
$378$	−2.41751	−	2.61939i	−0.124343	−	0.134727i
$379$	5.67753	+	4.91961i	0.291635	+	0.252703i	0.788373	−	0.615197i	$-0.210924\pi$
$379$	5.67753	+	4.91961i	0.291635	+	0.252703i	−0.496738	+	0.867900i	$0.665469\pi$
$380$	−0.588424	−	2.82322i	−0.0301855	−	0.144828i
$381$	2.44664	+	8.33249i	0.125345	+	0.426886i
$382$	−16.1703	−	13.1476i	−0.827347	−	0.672687i
$383$	−6.90273	+	4.43612i	−0.352713	+	0.226675i	−0.704984	−	0.709223i	$-0.749046\pi$
$383$	−6.90273	+	4.43612i	−0.352713	+	0.226675i	0.352271	+	0.935898i	$0.385410\pi$
$384$	−2.34753	+	11.0675i	−0.119797	+	0.564785i
$385$	0.432802	+	3.01021i	0.0220577	+	0.153414i
$386$	0.842373	+	26.8690i	0.0428757	+	1.36759i
$387$	−5.68687	−	0.817649i	−0.289080	−	0.0415634i
$388$	−11.5941	+	4.20960i	−0.588600	+	0.213710i
$389$	19.8326	−	17.1850i	1.00555	−	0.871314i	0.0138524	−	0.999904i	$-0.495590\pi$
$389$	19.8326	−	17.1850i	1.00555	−	0.871314i	0.991698	+	0.128590i	$0.0410450\pi$
$390$	0.790350	+	1.59627i	0.0400210	+	0.0808300i
$391$	13.1103	+	14.0001i	0.663017	+	0.708013i
$392$	−0.348556	+	1.79709i	−0.0176047	+	0.0907669i
$393$	−4.10515	−	4.73760i	−0.207078	−	0.238980i
$394$	3.27346	−	29.2475i	0.164915	−	1.47347i
$395$	0.491165	+	0.0706188i	0.0247132	+	0.00355322i
$396$	−10.1873	+	5.44792i	−0.511929	+	0.273768i
$397$	26.6381	−	3.82998i	1.33693	−	0.192221i	0.563505	−	0.826112i	$-0.309452\pi$
$397$	26.6381	−	3.82998i	1.33693	−	0.192221i	0.773422	+	0.633891i	$0.218543\pi$
$398$	22.9690	−	4.04075i	1.15133	−	0.202545i
$399$	−14.6368	+	9.40650i	−0.732757	+	0.470914i
$400$	15.2072	−	12.7197i	0.760359	−	0.635986i
$401$	8.00460	−	2.35036i	0.399731	−	0.117372i	−0.0756872	−	0.997132i	$-0.524115\pi$
$401$	8.00460	−	2.35036i	0.399731	−	0.117372i	0.475418	+	0.879760i	$0.342297\pi$
$402$	1.33248	−	5.12722i	0.0664579	−	0.255723i
$403$	−1.33524	−	1.15699i	−0.0665130	−	0.0576338i
$404$	−23.2475	−	8.90251i	−1.15661	−	0.442916i
$405$	0.190010	−	0.0867748i	0.00944168	−	0.00431187i
$406$	2.08195	+	1.24758i	0.103325	+	0.0619164i
$407$	11.8727	+	3.48614i	0.588508	+	0.172801i
$408$	−0.551542	+	11.2984i	−0.0273054	+	0.559356i
$409$	−6.73387	+	14.7451i	−0.332968	+	0.729099i	−0.999871	−	0.0160457i	$-0.994892\pi$
$409$	−6.73387	+	14.7451i	−0.332968	+	0.729099i	0.666903	+	0.745145i	$0.267620\pi$
$410$	3.18870	−	1.04588i	0.157479	−	0.0516526i
$411$	0.169243	−	0.263347i	0.00834815	−	0.0129900i
$412$	23.1301	−	1.45174i	1.13954	−	0.0715220i
$413$		−	19.4784i		−	0.958471i
$414$	4.05653	+	5.43549i	0.199367	+	0.267140i
$415$	−2.98909			−0.146729
$416$	−33.8257	−	4.38427i	−1.65844	−	0.214956i
$417$	−4.71191	−	3.02816i	−0.230743	−	0.148290i
$418$	17.5744	+	53.5809i	0.859591	+	2.62073i
$419$	10.9304	+	4.99177i	0.533987	+	0.243864i	0.664111	−	0.747634i	$-0.268810\pi$
$419$	10.9304	+	4.99177i	0.533987	+	0.243864i	−0.130124	+	0.991498i	$0.541538\pi$
$420$	0.919751	+	0.512681i	0.0448793	+	0.0250163i
$421$	6.74790	−	22.9812i	0.328872	−	1.12004i	−0.614670	−	0.788784i	$-0.710711\pi$
$421$	6.74790	−	22.9812i	0.328872	−	1.12004i	0.943542	−	0.331252i	$-0.107471\pi$
$422$	3.44763	+	2.06595i	0.167828	+	0.100569i
$423$	−1.30694	−	2.86179i	−0.0635454	−	0.139145i
$424$	7.24289	−	0.683009i	0.351746	−	0.0331698i
$425$	12.9808	−	14.9807i	0.629663	−	0.726670i
$426$	16.1708	+	4.20251i	0.783477	+	0.203612i
$427$	8.87852	+	30.2374i	0.429661	+	1.46329i
$428$	−2.19222	+	9.67076i	−0.105965	+	0.467454i
$429$	−18.8297	−	29.2996i	−0.909108	−	1.41460i
$430$	1.67157	−	0.294067i	0.0806103	−	0.0141812i
$431$	−1.39568	−	9.70715i	−0.0672274	−	0.467577i	−0.995429	−	0.0955002i	$-0.969555\pi$
$431$	−1.39568	−	9.70715i	−0.0672274	−	0.467577i	0.928202	−	0.372077i	$-0.121354\pi$
$432$	−0.638204	+	3.94876i	−0.0307056	+	0.189985i
$433$	−0.927383	+	6.45009i	−0.0445672	+	0.309972i	0.955329	+	0.295545i	$0.0955013\pi$
$433$	−0.927383	+	6.45009i	−0.0445672	+	0.309972i	−0.999896	+	0.0144264i	$0.995408\pi$
$434$	−1.03797	−	0.116173i	−0.0498243	−	0.00557647i
$435$	−0.107494	+	0.0931443i	−0.00515396	+	0.00446593i
$436$	−15.2318	−	11.6109i	−0.729470	−	0.556064i
$437$	29.5609	−	14.9042i	1.41409	−	0.712963i
$438$	−7.16919	−	14.4796i	−0.342557	−	0.691860i
$439$	−15.6599	−	18.0725i	−0.747405	−	0.862552i	0.246909	−	0.969039i	$-0.420585\pi$
$439$	−15.6599	−	18.0725i	−0.747405	−	0.862552i	−0.994314	+	0.106487i	$0.966040\pi$
$440$	2.35796	−	2.46714i	0.112411	−	0.117616i
$441$	−0.0921074	+	0.640621i	−0.00438607	+	0.0305058i
$442$	−34.0864	+	1.06865i	−1.62133	+	0.0508304i
$443$	5.03264	−	0.723584i	0.239108	−	0.0343785i	−0.0217190	−	0.999764i	$-0.506914\pi$
$443$	5.03264	−	0.723584i	0.239108	−	0.0343785i	0.260827	+	0.965386i	$0.416005\pi$
$444$	3.45211	−	2.53756i	0.163830	−	0.120427i
$445$	1.89177	+	2.94365i	0.0896784	+	0.139542i
$446$	−9.78804	−	7.95833i	−0.463477	−	0.376838i
$447$	2.11717	−	0.621656i	0.100139	−	0.0294033i
$448$	−17.9440	+	9.19737i	−0.847774	+	0.434535i
$449$	5.35031	−	6.17459i	0.252497	−	0.291397i	−0.615324	−	0.788274i	$-0.710975\pi$
$449$	5.35031	−	6.17459i	0.252497	−	0.291397i	0.867821	+	0.496878i	$0.165520\pi$
$450$	5.15088	−	4.75390i	0.242815	−	0.224101i
$451$	−59.6880	+	27.2586i	−2.81060	+	1.28356i
$452$	−1.47821	+	18.4109i	−0.0695290	+	0.865976i
$453$	6.76675	−	23.0454i	0.317930	−	1.08277i
$454$	4.88640	−	3.36122i	0.229330	−	0.157750i
$455$	−1.31876	+	2.88768i	−0.0618243	+	0.135376i
$456$	18.4432	+	6.40758i	0.863683	+	0.300063i
$457$	19.4119	+	12.4753i	0.908051	+	0.583569i	0.909168	−	0.416430i	$-0.136719\pi$
$457$	19.4119	+	12.4753i	0.908051	+	0.583569i	−0.00111654	+	0.999999i	$0.500355\pi$
$458$	−1.71602	+	4.09229i	−0.0801842	+	0.191220i
$459$			3.99936i			0.186674i
$460$	−1.63909	−	1.15225i	−0.0764230	−	0.0537240i
$461$			18.6881i			0.870391i	0.900336	+	0.435195i	$0.143321\pi$
$461$			18.6881i			0.870391i	−0.900336	+	0.435195i	$0.856679\pi$
$462$	−18.9876	−	7.96206i	−0.883382	−	0.370428i
$463$	30.2126	+	19.4164i	1.40410	+	0.902358i	0.999924	−	0.0123242i	$-0.00392302\pi$
$463$	30.2126	+	19.4164i	1.40410	+	0.902358i	0.404173	+	0.914683i	$0.367559\pi$
$464$	−0.340557	−	2.70231i	−0.0158099	−	0.125451i
$465$	0.0254264	−	0.0556761i	0.00117912	−	0.00258192i
$466$	4.86256	+	7.06899i	0.225254	+	0.327465i
$467$	1.04167	−	3.54761i	0.0482029	−	0.164164i	−0.931874	−	0.362782i	$-0.881827\pi$
$467$	1.04167	−	3.54761i	0.0482029	−	0.164164i	0.980077	+	0.198618i	$0.0636452\pi$
$468$	−12.0205	−	0.965127i	−0.555650	−	0.0446130i
$469$	8.58830	−	3.92214i	0.396571	−	0.181108i
$470$	0.630332	+	0.682970i	0.0290751	+	0.0315031i
$471$	12.2430	−	14.1291i	0.564126	−	0.651036i
$472$	−17.1977	+	13.4917i	−0.791588	+	0.621005i
$473$	−31.8423	+	9.34975i	−1.46411	+	0.429902i
$474$	−2.11936	+	2.60663i	−0.0973455	+	0.119726i
$475$	−18.4973	−	28.7824i	−0.848716	−	1.32063i
$476$	−16.2441	+	11.9406i	−0.744546	+	0.547297i
$477$	2.54593	−	0.366049i	0.116570	−	0.0167602i
$478$	−0.0218975	−	0.698458i	−0.00100157	−	0.0319467i
$479$	−5.37801	+	37.4049i	−0.245728	+	1.70907i	0.376649	+	0.926356i	$0.377076\pi$
$479$	−5.37801	+	37.4049i	−0.245728	+	1.70907i	−0.622377	+	0.782718i	$0.713833\pi$
$480$	−0.184412	−	1.16716i	−0.00841720	−	0.0532735i
$481$	8.45863	+	9.76178i	0.385680	+	0.445099i
$482$	−21.1075	+	10.4508i	−0.961418	+	0.476022i
$483$	−2.95550	+	11.7209i	−0.134480	+	0.533319i
$484$	−27.1169	+	35.5733i	−1.23259	+	1.61697i
$485$	0.973611	−	0.843639i	0.0442094	−	0.0383077i
$486$	−0.157300	+	1.40544i	−0.00713529	+	0.0637520i
$487$	−2.92088	+	20.3152i	−0.132358	+	0.920569i	0.810111	+	0.586276i	$0.199407\pi$
$487$	−2.92088	+	20.3152i	−0.132358	+	0.920569i	−0.942469	+	0.334293i	$0.891503\pi$
$488$	20.5472	−	28.7828i	0.930130	−	1.30294i
$489$	−0.257811	−	1.79311i	−0.0116586	−	0.0810875i
$490$	−0.0331263	−	0.188301i	−0.00149650	−	0.00850656i
$491$	−2.28446	−	3.55468i	−0.103096	−	0.160421i	0.785873	−	0.618388i	$-0.212214\pi$
$491$	−2.28446	−	3.55468i	−0.103096	−	0.160421i	−0.888969	+	0.457967i	$0.848578\pi$
$492$	−5.02281	+	22.1577i	−0.226446	+	0.998946i
$493$	−0.767226	−	2.61293i	−0.0345541	−	0.117681i
$494$	−14.8056	+	56.9704i	−0.666138	+	2.56322i
$495$	0.790144	−	0.911875i	0.0355143	−	0.0409857i
$496$	0.616379	+	0.996902i	0.0276762	+	0.0447622i
$497$	12.3701	+	27.0867i	0.554874	+	1.21500i
$498$	10.4020	−	17.3588i	0.466126	−	0.777866i
$499$	−4.17031	+	14.2028i	−0.186689	+	0.635803i	0.811954	+	0.583721i	$0.198404\pi$
$499$	−4.17031	+	14.2028i	−0.186689	+	0.635803i	−0.998643	+	0.0520817i	$0.983414\pi$
$500$	−2.02519	+	3.63320i	−0.0905693	+	0.162481i
$501$	3.78314	+	1.72770i	0.169018	+	0.0771881i
$502$	29.9327	−	9.81783i	1.33596	−	0.438191i
$503$	11.8887	+	7.64042i	0.530092	+	0.340669i	0.778153	−	0.628075i	$-0.216157\pi$
$503$	11.8887	+	7.64042i	0.530092	+	0.340669i	−0.248061	+	0.968744i	$0.579793\pi$
$504$	−6.17807	+	3.55722i	−0.275193	+	0.158451i
$505$	2.60000			0.115698
$506$	34.3567	+	18.8257i	1.52734	+	0.836904i
$507$		−	23.3562i		−	1.03729i
$508$	17.3344	−	1.08798i	0.769090	−	0.0482712i
$509$	8.86210	−	13.7897i	0.392806	−	0.611218i	−0.587377	−	0.809314i	$-0.699839\pi$
$509$	8.86210	−	13.7897i	0.392806	−	0.611218i	0.980183	+	0.198096i	$0.0634757\pi$
$510$	−0.368212	−	1.12261i	−0.0163047	−	0.0497100i
$511$	11.9623	−	26.1938i	0.529182	−	1.15875i
$512$	20.5493	+	9.47240i	0.908159	+	0.418625i
$513$	6.62337	+	1.94480i	0.292429	+	0.0858649i
$514$	−12.0203	+	20.0593i	−0.530191	+	0.884778i
$515$	−2.20180	+	1.00553i	−0.0970231	+	0.0443090i
$516$	−4.10930	+	10.7308i	−0.180902	+	0.472397i
$517$	−13.7340	−	11.9006i	−0.604019	−	0.523386i
$518$	7.39038	+	1.92064i	0.324715	+	0.0843879i
$519$	−16.9466	+	4.97597i	−0.743872	+	0.218421i
$520$	3.46299	−	0.835797i	0.151862	−	0.0366521i
$521$	3.96667	−	2.54922i	0.173783	−	0.111683i	−0.450858	−	0.892596i	$-0.648882\pi$
$521$	3.96667	−	2.54922i	0.173783	−	0.111683i	0.624641	+	0.780912i	$0.285245\pi$
$522$	−0.166845	−	0.948402i	−0.00730262	−	0.0415104i
$523$	−23.8003	+	3.42197i	−1.04071	+	0.149632i	−0.641419	−	0.767191i	$-0.721654\pi$
$523$	−23.8003	+	3.42197i	−1.04071	+	0.149632i	−0.399295	+	0.916823i	$0.630745\pi$
$524$	−11.0559	+	5.91242i	−0.482977	+	0.258285i
$525$	12.3652	+	1.77785i	0.539663	+	0.0775919i
$526$	−11.4801	−	1.28488i	−0.500554	−	0.0560233i
$527$	0.767416	+	0.885646i	0.0334292	+	0.0385793i
$528$	6.12192	+	22.2792i	0.266422	+	0.969578i
$529$	7.91290	−	21.5960i	0.344039	−	0.938955i
$530$	−0.680933	+	0.337147i	−0.0295779	+	0.0146447i
$531$	−5.84049	+	5.06082i	−0.253456	+	0.219621i
$532$	11.8758	+	32.7084i	0.514882	+	1.41809i
$533$	−67.7988	−	9.74799i	−2.93669	−	0.422232i
$534$	−23.6782	+	0.742340i	−1.02466	+	0.0321242i
$535$	−0.147392	−	1.02513i	−0.00637230	−	0.0443203i
$536$	−9.41156	−	4.86603i	−0.406517	−	0.210180i
$537$	8.96792	−	5.76333i	0.386994	−	0.248706i
$538$	13.5662	−	16.6853i	0.584881	−	0.719352i
$539$	1.05324	+	3.58701i	0.0453663	+	0.154503i
$540$	−0.0852419	−	0.408985i	−0.00366823	−	0.0175999i
$541$	14.6834	+	12.7232i	0.631288	+	0.547014i	0.910654	−	0.413171i	$-0.135579\pi$
$541$	14.6834	+	12.7232i	0.631288	+	0.547014i	−0.279366	+	0.960185i	$0.590124\pi$
$542$	19.0830	−	17.6123i	0.819686	−	0.756511i
$543$	5.72375	+	12.5333i	0.245630	+	0.537854i
$544$	21.7939	+	6.07141i	0.934405	+	0.260310i
$545$	1.91933	+	0.563567i	0.0822152	+	0.0241406i
$546$	−12.1806	−	17.7076i	−0.521281	−	0.757817i
$547$	−0.996632	−	0.455147i	−0.0426129	−	0.0194607i	0.393995	−	0.919113i	$-0.371093\pi$
$547$	−0.996632	−	0.455147i	−0.0426129	−	0.0194607i	−0.436607	+	0.899652i	$0.643820\pi$
$548$	−0.438831	−	0.446550i	−0.0187460	−	0.0190757i
$549$	6.75974	−	10.5184i	0.288499	−	0.448913i
$550$	15.6569	−	37.3380i	0.667613	−	1.59210i
$551$	−4.70038			−0.200243
$552$	12.3956	−	5.50900i	0.527592	−	0.234479i
$553$	−5.98744			−0.254612
$554$	−9.08269	+	21.6600i	−0.385886	+	0.920246i
$555$	−0.241926	+	0.376443i	−0.0102692	+	0.0159791i
$556$	−7.98984	+	7.85173i	−0.338845	+	0.332988i
$557$	3.16457	+	1.44521i	0.134087	+	0.0612356i	0.481329	−	0.876540i	$-0.340154\pi$
$557$	3.16457	+	1.44521i	0.134087	+	0.0612356i	−0.347242	+	0.937776i	$0.612882\pi$
$558$	0.234849	+	0.341414i	0.00994194	+	0.0144532i
$559$	−33.2390	−	9.75985i	−1.40586	−	0.412798i
$560$	1.40666	−	1.56730i	0.0594423	−	0.0662307i
$561$	9.59662	+	21.0137i	0.405170	+	0.887198i
$562$	15.0086	−	13.8519i	0.633099	−	0.584305i
$563$	16.2854	+	14.1113i	0.686346	+	0.594722i	0.926627	−	0.375981i	$-0.122694\pi$
$563$	16.2854	+	14.1113i	0.686346	+	0.594722i	−0.240281	+	0.970703i	$0.577240\pi$
$564$	−6.15983	+	1.28385i	−0.259375	+	0.0540598i
$565$	−0.543487	−	1.85095i	−0.0228647	−	0.0778699i
$566$	−5.17654	+	6.36669i	−0.217586	+	0.267612i
$567$	−2.12036	+	1.36267i	−0.0890467	+	0.0572268i
$568$	15.3470	−	29.6832i	0.643946	−	1.24548i
$569$	−0.432272	−	3.00652i	−0.0181218	−	0.126040i	0.978752	−	0.205046i	$-0.0657344\pi$
$569$	−0.432272	−	3.00652i	−0.0181218	−	0.126040i	−0.996874	+	0.0790062i	$0.974825\pi$
$570$	−2.03821	+	0.0639004i	−0.0853714	+	0.00267649i
$571$	10.0516	+	1.44520i	0.420645	+	0.0604796i	0.349388	−	0.936978i	$-0.386390\pi$
$571$	10.0516	+	1.44520i	0.420645	+	0.0604796i	0.0712576	+	0.997458i	$0.477299\pi$
$572$	−65.4749	+	23.7728i	−2.73764	+	0.993989i
$573$	−11.1372	+	9.65046i	−0.465264	+	0.403154i
$574$	−36.2879	+	17.9671i	−1.51463	+	0.749931i
$575$	−23.0484	−	5.81182i	−0.961187	−	0.242370i
$576$	7.41992	+	2.99078i	0.309163	+	0.124616i
$577$	−0.302321	−	0.348897i	−0.0125858	−	0.0145248i	0.749422	−	0.662093i	$-0.230332\pi$
$577$	−0.302321	−	0.348897i	−0.0125858	−	0.0145248i	−0.762008	+	0.647568i	$0.775786\pi$
$578$	−1.41267	−	0.158109i	−0.0587591	−	0.00657648i
$579$	18.8151	+	2.70520i	0.781928	+	0.112424i
$580$	0.134150	+	0.250853i	0.00557029	+	0.0104161i
$581$	35.6999	−	5.13287i	1.48108	−	0.212947i
$582$	1.51117	+	8.59000i	0.0626401	+	0.356067i
$583$	12.4986	−	8.03237i	0.517640	−	0.332667i
$584$	−31.4124	+	7.58143i	−1.29986	+	0.313722i
$585$	1.20849	−	0.354844i	0.0499648	−	0.0146710i
$586$	−5.76747	−	1.49887i	−0.238252	−	0.0619176i
$587$	−29.9501	−	25.9519i	−1.23617	−	1.07115i	−0.994918	−	0.100689i	$-0.967895\pi$
$587$	−29.9501	−	25.9519i	−1.23617	−	1.07115i	−0.241256	−	0.970462i	$-0.577559\pi$
$588$	1.20881	+	0.462909i	0.0498507	+	0.0190900i
$589$	1.83990	−	0.840255i	0.0758118	−	0.0346221i
$590$	1.17347	−	1.95828i	0.0483111	−	0.0806211i
$591$	−19.9673	−	5.86293i	−0.821345	−	0.241169i
$592$	−3.42318	−	7.85536i	−0.140692	−	0.322853i
$593$	−5.40534	+	11.8360i	−0.221971	+	0.486048i	−0.987552	−	0.157291i	$-0.949724\pi$
$593$	−5.40534	+	11.8360i	−0.221971	+	0.486048i	0.765582	+	0.643339i	$0.222451\pi$
$594$	2.54591	+	7.76199i	0.104460	+	0.318478i
$595$	1.13839	−	1.77138i	0.0466696	−	0.0726193i
$596$	−0.276439	−	4.40443i	−0.0113234	−	0.180412i
$597$		−	16.4909i		−	0.674928i
$598$	19.5461	+	35.9212i	0.799300	+	1.46893i
$599$	18.0460			0.737340			0.368670	−	0.929560i	$-0.379813\pi$
$599$	18.0460			0.737340			0.368670	+	0.929560i	$0.379813\pi$
$600$	−6.99506	−	12.1488i	−0.285572	−	0.495973i
$601$	−0.411046	−	0.264163i	−0.0167669	−	0.0107754i	0.532231	−	0.846599i	$-0.321354\pi$
$601$	−0.411046	−	0.264163i	−0.0167669	−	0.0107754i	−0.548997	+	0.835824i	$0.684990\pi$
$602$	−19.4593	+	6.38258i	−0.793100	+	0.260134i
$603$	−3.40741	−	1.55611i	−0.138761	−	0.0633698i
$604$	−41.9585	−	23.3882i	−1.70727	−	0.951653i
$605$	1.31619	−	4.48253i	0.0535107	−	0.182241i
$606$	−9.04797	+	15.0992i	−0.367549	+	0.613362i
$607$	3.73915	+	8.18759i	0.151767	+	0.332324i	0.970211	−	0.242263i	$-0.0778898\pi$
$607$	3.73915	+	8.18759i	0.151767	+	0.332324i	−0.818443	+	0.574587i	$0.805163\pi$
$608$	20.6528	−	33.1406i	0.837581	−	1.34403i
$609$	1.12390	−	1.29705i	0.0455427	−	0.0525591i
$610$	−0.929037	+	3.57483i	−0.0376156	+	0.144741i
$611$	−5.34440	−	18.2013i	−0.216211	−	0.736347i
$612$	7.80080	+	1.76832i	0.315329	+	0.0714802i
$613$	15.1375	+	23.5543i	0.611396	+	0.951351i	0.999557	+	0.0297591i	$0.00947402\pi$
$613$	15.1375	+	23.5543i	0.611396	+	0.951351i	−0.388161	+	0.921592i	$0.626890\pi$
$614$	−7.24337	−	41.1736i	−0.292319	−	1.66163i
$615$	−0.337705	−	2.34879i	−0.0136176	−	0.0947122i
$616$	−23.9255	+	33.5151i	−0.963986	+	1.35036i
$617$	6.03774	−	41.9934i	0.243070	−	1.69059i	−0.393462	−	0.919341i	$-0.628723\pi$
$617$	6.03774	−	41.9934i	0.243070	−	1.69059i	0.636532	−	0.771250i	$-0.280368\pi$
$618$	1.82277	−	16.2860i	0.0733225	−	0.655118i
$619$	13.1961	−	11.4345i	0.530395	−	0.459590i	−0.348021	−	0.937487i	$-0.613146\pi$
$619$	13.1961	−	11.4345i	0.530395	−	0.459590i	0.878416	+	0.477897i	$0.158601\pi$
$620$	−0.0973546	−	0.0742119i	−0.00390986	−	0.00298042i
$621$	4.28233	−	2.15909i	0.171844	−	0.0866413i
$622$	33.5473	−	16.6101i	1.34512	−	0.666004i
$623$	−27.6490	−	31.9086i	−1.10773	−	1.27839i
$624$	−7.19740	+	23.0195i	−0.288126	+	0.921517i
$625$	−3.46500	+	24.0996i	−0.138600	+	0.963983i
$626$	0.132679	+	4.23202i	0.00530291	+	0.169146i
$627$	39.4675	−	5.67457i	1.57618	−	0.226621i
$628$	−22.1458	−	30.1273i	−0.883714	−	1.20221i
$629$	−4.63192	−	7.20740i	−0.184687	−	0.287378i
$630$	0.469721	−	0.577715i	0.0187141	−	0.0230167i
$631$	38.7533	−	11.3790i	1.54274	−	0.452991i	0.603822	−	0.797119i	$-0.293644\pi$
$631$	38.7533	−	11.3790i	1.54274	−	0.452991i	0.938922	+	0.344129i	$0.111826\pi$
$632$	4.14718	+	5.28637i	0.164966	+	0.210280i
$633$	1.86114	−	2.14787i	0.0739735	−	0.0853700i
$634$	−4.96041	−	5.37465i	−0.197003	−	0.213455i
$635$	−1.65010	+	0.753575i	−0.0654821	+	0.0299047i
$636$	0.411703	−	5.12771i	0.0163251	−	0.203327i
$637$	−1.09944	+	3.74434i	−0.0435613	+	0.148356i
$638$	−3.15238	−	4.58280i	−0.124804	−	0.181435i
$639$	4.90784	−	10.7467i	0.194151	−	0.425131i
$640$	−2.35811	−	0.156366i	−0.0932124	−	0.00618092i
$641$	20.6635	+	13.2796i	0.816158	+	0.524513i	0.880852	−	0.473392i	$-0.156971\pi$
$641$	20.6635	+	13.2796i	0.816158	+	0.524513i	−0.0646939	+	0.997905i	$0.520607\pi$
$642$	6.46626	+	2.71149i	0.255203	+	0.107014i
$643$		−	11.8132i		−	0.465866i	−0.972493	−	0.232933i	$-0.925168\pi$
$643$		−	11.8132i		−	0.465866i	0.972493	−	0.232933i	$-0.0748323\pi$
$644$	21.5550	+	10.9472i	0.849385	+	0.431378i
$645$		−	1.20013i		−	0.0472550i
$646$	15.0982	−	36.0055i	0.594030	−	1.41662i
$647$	−15.6174	−	10.0367i	−0.613985	−	0.394584i	0.196364	−	0.980531i	$-0.437086\pi$
$647$	−15.6174	−	10.0367i	−0.613985	−	0.394584i	−0.810350	+	0.585947i	$0.800723\pi$
$648$	2.67178	+	0.928234i	0.104957	+	0.0364645i
$649$	−18.5438	+	40.6054i	−0.727910	+	1.59390i
$650$	34.8210	−	23.9524i	1.36579	−	0.939490i
$651$	−0.208071	+	0.708624i	−0.00815494	+	0.0277732i
$652$	−3.61149	−	0.289965i	−0.141437	−	0.0113559i
$653$	−9.25563	+	4.22690i	−0.362201	+	0.165411i	−0.588199	−	0.808716i	$-0.700163\pi$
$653$	−9.25563	+	4.22690i	−0.362201	+	0.165411i	0.225998	+	0.974128i	$0.427436\pi$
$654$	−9.95212	+	9.18510i	−0.389159	+	0.359166i
$655$	0.857513	−	0.989622i	0.0335058	−	0.0386677i
$656$	40.9980	+	19.5941i	1.60070	+	0.765022i
$657$	−10.9621	+	3.21876i	−0.427671	+	0.125576i
$658$	−8.70111	−	7.07458i	−0.339205	−	0.275796i
$659$	0.122174	+	0.190106i	0.00475921	+	0.00740547i	0.843625	−	0.536933i	$-0.180417\pi$
$659$	0.122174	+	0.190106i	0.00475921	+	0.00740547i	−0.838866	+	0.544338i	$0.816781\pi$
$660$	−1.42926	−	1.94437i	−0.0556339	−	0.0756846i
$661$	14.2576	−	2.04994i	0.554558	−	0.0797334i	0.140662	−	0.990058i	$-0.455077\pi$
$661$	14.2576	−	2.04994i	0.554558	−	0.0797334i	0.413896	+	0.910324i	$0.364168\pi$
$662$	−28.7720	+	0.902035i	−1.11826	+	0.0350586i
$663$	−3.43186	+	23.8691i	−0.133282	+	0.927000i
$664$	−29.2593	−	27.9645i	−1.13548	−	1.08523i
$665$	−2.38001	−	2.74668i	−0.0922930	−	0.106512i
$666$	−1.34425	−	2.71498i	−0.0520887	−	0.105203i
$667$	−2.38361	+	2.23213i	−0.0922939	+	0.0864283i
$668$	5.04263	−	6.61516i	0.195105	−	0.255948i
$669$	−6.74146	+	5.84150i	−0.260640	+	0.225846i
$670$	1.09972	+	0.123084i	0.0424859	+	0.00475513i
$671$	10.2782	−	71.4865i	0.396786	−	2.75970i
$672$	4.20676	+	13.6232i	0.162279	+	0.525528i
$673$	−1.01054	−	7.02849i	−0.0389536	−	0.270928i	0.961031	−	0.276440i	$-0.0891547\pi$
$673$	−1.01054	−	7.02849i	−0.0389536	−	0.270928i	−0.999985	+	0.00551154i	$0.998246\pi$
$674$	28.2822	−	4.97547i	1.08939	−	0.191648i
$675$	−2.67961	−	4.16956i	−0.103138	−	0.160486i
$676$	−45.5566	−	10.3270i	−1.75218	−	0.397192i
$677$	−6.29145	−	21.4267i	−0.241800	−	0.823495i	−0.987555	−	0.157275i	$-0.949729\pi$
$677$	−6.29145	−	21.4267i	−0.241800	−	0.823495i	0.745755	−	0.666220i	$-0.232089\pi$
$678$	12.6405	+	3.28505i	0.485455	+	0.126161i
$679$	−10.1795	+	11.7478i	−0.390654	+	0.450839i
$680$	−2.35247	+	0.221839i	−0.0902131	+	0.00850715i
$681$	−1.74214	−	3.81475i	−0.0667588	−	0.146181i
$682$	2.05319	+	1.23035i	0.0786208	+	0.0471124i
$683$	3.42492	−	11.6642i	0.131051	−	0.446318i	−0.867656	−	0.497166i	$-0.834374\pi$
$683$	3.42492	−	11.6642i	0.131051	−	0.446318i	0.998706	+	0.0508475i	$0.0161922\pi$
$684$	6.72189	−	12.0591i	0.257018	−	0.461090i
$685$	0.0594811	+	0.0271641i	0.00227266	+	0.00103789i
$686$	8.49537	+	25.9007i	0.324355	+	0.988895i
$687$	2.63968	+	1.69642i	0.100710	+	0.0647225i
$688$	19.1136	+	12.7599i	0.728700	+	0.486466i
$689$	15.5088			0.590839
$690$	−1.00326	+	1.00032i	−0.0381933	+	0.0380814i
$691$			11.4682i			0.436270i	0.975919	+	0.218135i	$0.0699974\pi$
$691$			11.4682i			0.436270i	−0.975919	+	0.218135i	$0.930003\pi$
$692$	2.21272	+	35.2547i	0.0841151	+	1.34018i
$693$	−7.87113	+	12.2477i	−0.299000	+	0.465252i
$694$	−11.9684	+	3.92559i	−0.454313	+	0.149013i
$695$	0.486030	−	1.06426i	0.0184362	−	0.0403696i
$696$	−1.92364	−	0.0939041i	−0.0729155	−	0.00355942i
$697$	43.5921	+	12.7998i	1.65117	+	0.484827i
$698$	−15.0578	−	9.02320i	−0.569948	−	0.341533i
$699$	5.51867	−	2.52029i	0.208735	−	0.0953262i
$700$	8.93504	−	23.3325i	0.337713	−	0.881885i
$701$	−9.31667	−	8.07294i	−0.351886	−	0.304911i	0.460924	−	0.887439i	$-0.347518\pi$
$701$	−9.31667	−	8.07294i	−0.351886	−	0.304911i	−0.812810	+	0.582529i	$0.802063\pi$
$702$	−2.14482	+	8.25301i	−0.0809509	+	0.311490i
$703$	−14.1886	+	4.16616i	−0.535134	+	0.157130i
$704$	46.1627	−	2.09009i	1.73982	−	0.0787731i
$705$	0.552854	−	0.355298i	0.0208217	−	0.0133813i
$706$	−6.70814	+	1.18011i	−0.252464	+	0.0444141i
$707$	−31.0528	+	4.46472i	−1.16786	+	0.167913i
$708$	7.28880	+	13.6296i	0.273930	+	0.512232i
$709$	−14.9934	−	2.15572i	−0.563088	−	0.0809598i	−0.145108	−	0.989416i	$-0.546353\pi$
$709$	−14.9934	−	2.15572i	−0.563088	−	0.0809598i	−0.417980	+	0.908456i	$0.637262\pi$
$710$	−0.388194	+	3.46841i	−0.0145687	+	0.130167i
$711$	1.55564	+	1.79530i	0.0583409	+	0.0673290i
$712$	−9.02143	+	46.5129i	−0.338093	+	1.74315i
$713$	0.534012	−	1.29984i	0.0199989	−	0.0486793i
$714$	6.32545	+	12.7755i	0.236724	+	0.478110i
$715$	5.49825	−	4.76426i	0.205623	−	0.178173i
$716$	−7.27628	−	20.0403i	−0.271927	−	0.748942i
$717$	−0.489097	−	0.0703216i	−0.0182657	−	0.00262621i
$718$	0.0699399	+	2.23086i	0.00261013	+	0.0832549i
$719$	3.62904	+	25.2405i	0.135340	+	0.941313i	0.938434	+	0.345460i	$0.112277\pi$
$719$	3.62904	+	25.2405i	0.135340	+	0.941313i	−0.803093	+	0.595853i	$0.796814\pi$
$720$	−0.835421	−	0.0145680i	−0.0311343	−	0.000542917i
$721$	24.5703	−	15.7904i	0.915047	−	0.588065i
$722$	−31.4386	−	25.5617i	−1.17002	−	0.951307i
$723$	4.69211	+	15.9799i	0.174502	+	0.594298i
$724$	26.9771	−	5.62264i	1.00259	−	0.208964i
$725$	2.55057	+	2.21008i	0.0947259	+	0.0820804i
$726$	21.4514	+	23.2428i	0.796138	+	0.862621i
$727$	10.8370	+	23.7298i	0.401924	+	0.880090i	0.997072	+	0.0764737i	$0.0243661\pi$
$727$	10.8370	+	23.7298i	0.401924	+	0.880090i	−0.595148	+	0.803616i	$0.702907\pi$
$728$	−39.9246	+	15.9289i	−1.47971	+	0.590365i
$729$	0.959493	+	0.281733i	0.0355368	+	0.0104345i
$730$	2.78068	−	1.91275i	0.102918	−	0.0707941i
$731$	20.9013	+	9.54529i	0.773061	+	0.353045i
$732$	−17.5274	−	17.8357i	−0.647830	−	0.659225i
$733$	−25.5647	+	39.7795i	−0.944255	+	1.46929i	−0.0622441	+	0.998061i	$0.519826\pi$
$733$	−25.5647	+	39.7795i	−0.944255	+	1.46929i	−0.882011	+	0.471229i	$0.843811\pi$
$734$	−11.6943	−	4.90376i	−0.431644	−	0.181001i
$735$	−0.135193			−0.00498669
$736$	−5.26464	−	26.6136i	−0.194057	−	0.980990i
$737$	−21.6374			−0.797024
$738$	14.8155	+	6.21259i	0.545367	+	0.228689i
$739$	3.49616	−	5.44013i	0.128608	−	0.200119i	−0.770978	−	0.636862i	$-0.780232\pi$
$739$	3.49616	−	5.44013i	0.128608	−	0.200119i	0.899586	+	0.436744i	$0.143868\pi$
$740$	0.627290	+	0.638324i	0.0230596	+	0.0234653i
$741$	37.8610	+	17.2905i	1.39086	+	0.635184i
$742$	7.55371	−	5.19598i	0.277305	−	0.190750i
$743$	21.9447	+	6.44355i	0.805074	+	0.236391i	0.658277	−	0.752776i	$-0.271286\pi$
$743$	21.9447	+	6.44355i	0.805074	+	0.236391i	0.146797	+	0.989167i	$0.453104\pi$
$744$	0.769771	−	0.307119i	0.0282212	−	0.0112595i
$745$	0.191473	+	0.419267i	0.00701501	+	0.0153607i
$746$	3.32336	+	3.60089i	0.121677	+	0.131838i
$747$	−10.8145	−	9.37080i	−0.395681	−	0.342860i
$748$	45.2306	−	9.42710i	1.65379	−	0.344689i
$749$	3.52072	+	11.9905i	0.128644	+	0.438122i
$750$	2.28209	+	1.85549i	0.0833300	+	0.0677528i
$751$	32.9771	−	21.1931i	1.20335	−	0.773346i	0.223818	−	0.974631i	$-0.428148\pi$
$751$	32.9771	−	21.1931i	1.20335	−	0.773346i	0.979533	+	0.201285i	$0.0645116\pi$
$752$	−0.219412	+	12.5825i	−0.00800114	+	0.458836i
$753$	−3.17007	−	22.0483i	−0.115524	−	0.803485i
$754$	−0.181945	−	5.80346i	−0.00662605	−	0.211350i
$755$	4.96605	+	0.714010i	0.180733	+	0.0259855i
$756$	1.72039	+	4.73829i	0.0625699	+	0.172330i
$757$	−20.6418	+	17.8862i	−0.750240	+	0.650087i	−0.943617	−	0.331038i	$-0.892601\pi$
$757$	−20.6418	+	17.8862i	−0.750240	+	0.650087i	0.193378	+	0.981124i	$0.438056\pi$
$758$	−4.71412	−	9.52107i	−0.171225	−	0.345821i
$759$	17.3196	−	21.6200i	0.628663	−	0.784758i
$760$	−0.776562	+	4.00382i	−0.0281689	+	0.145234i
$761$	−11.6373	−	13.4302i	−0.421852	−	0.486844i	0.504548	−	0.863384i	$-0.331659\pi$
$761$	−11.6373	−	13.4302i	−0.421852	−	0.486844i	−0.926400	+	0.376540i	$0.877114\pi$
$762$	1.36604	−	12.2052i	0.0494863	−	0.442147i
$763$	−23.8911	−	3.43503i	−0.864917	−	0.124356i
$764$	13.8990	+	25.9903i	0.502848	+	0.940295i
$765$	−0.826910	+	0.118892i	−0.0298970	+	0.00429854i
$766$	11.4285	−	2.01054i	0.412930	−	0.0726436i
$767$	−39.2002	+	25.1924i	−1.41544	+	0.909646i
$768$	9.11428	−	13.1503i	0.328883	−	0.474520i
$769$	−3.69461	+	1.08484i	−0.133231	+	0.0391202i	−0.347668	−	0.937618i	$-0.613026\pi$
$769$	−3.69461	+	1.08484i	−0.133231	+	0.0391202i	0.214437	+	0.976738i	$0.431208\pi$
$770$	1.08178	−	4.16258i	0.0389848	−	0.150009i
$771$	12.4969	+	10.8286i	0.450064	+	0.389983i
$772$	13.5957	−	35.5030i	0.489318	−	1.27778i
$773$	35.4864	−	16.2061i	1.27636	−	0.582894i	0.342158	−	0.939642i	$-0.388842\pi$
$773$	35.4864	−	16.2061i	1.27636	−	0.582894i	0.934200	+	0.356749i	$0.116115\pi$
$774$	6.96961	+	4.17644i	0.250518	+	0.150119i
$775$	−1.39347	−	0.409159i	−0.0500549	−	0.0146974i
$776$	17.4231	+	0.850520i	0.625452	+	0.0305319i
$777$	2.24298	−	4.91145i	0.0804666	−	0.176197i
$778$	−35.2637	+	11.5664i	−1.26426	+	0.414675i
$779$	42.3957	−	65.9690i	1.51898	−	2.36358i
$780$	−0.157793	−	2.51407i	−0.00564989	−	0.0900180i
$781$		−	68.2423i		−	2.44190i
$782$	−9.44190	−	25.4286i	−0.337642	−	0.909325i
$783$	−0.680920			−0.0243341
$784$	1.43739	−	2.15313i	0.0513353	−	0.0768976i
$785$	3.28531	+	2.11134i	0.117258	+	0.0753569i
$786$	2.76298	+	8.42379i	0.0985521	+	0.300467i
$787$	9.90130	+	4.52177i	0.352943	+	0.161184i	0.583994	−	0.811758i	$-0.301489\pi$
$787$	9.90130	+	4.52177i	0.352943	+	0.161184i	−0.231051	+	0.972942i	$0.574216\pi$
$788$	−20.2643	+	36.3542i	−0.721886	+	1.29506i
$789$	−2.30128	+	7.83744i	−0.0819277	+	0.279020i
$790$	−0.601952	−	0.360712i	−0.0214165	−	0.0128335i
$791$	9.66952	+	21.1733i	0.343809	+	0.752836i
$792$	16.2655	−	1.53385i	0.577971	−	0.0545030i
$793$	49.3696	−	56.9755i	1.75316	−	2.02326i
$794$	−36.8357	−	9.57298i	−1.30725	−	0.339732i
$795$	0.151369	+	0.515516i	0.00536851	+	0.0182835i
$796$	−32.1657	−	7.29149i	−1.14008	−	0.258440i
$797$	−4.64398	−	7.22618i	−0.164498	−	0.255964i	0.749212	−	0.662330i	$-0.230432\pi$
$797$	−4.64398	−	7.22618i	−0.164498	−	0.255964i	−0.913711	+	0.406366i	$0.866796\pi$
$798$	24.2335	−	4.26321i	0.857856	−	0.150916i
$799$	1.79066	+	12.4543i	0.0633489	+	0.440601i
$800$	−26.7893	+	8.27235i	−0.947145	+	0.292472i
$801$	−2.38395	+	16.5808i	−0.0842329	+	0.585853i
$802$	−11.7249	−	1.31228i	−0.414021	−	0.0463383i
$803$	−49.8741	+	43.2161i	−1.76002	+	1.52506i
$804$	−4.54181	+	5.95816i	−0.160177	+	0.210128i
$805$	−2.51128	−	0.262647i	−0.0885110	−	0.00925708i
$806$	1.10866	+	2.23916i	0.0390511	+	0.0788711i
$807$	−9.95776	−	11.4919i	−0.350530	−	0.404533i
$808$	25.4506	+	24.3243i	0.895348	+	0.855727i
$809$	0.995509	−	6.92392i	0.0350002	−	0.243432i	−0.964809	−	0.262951i	$-0.915304\pi$
$809$	0.995509	−	6.92392i	0.0350002	−	0.243432i	0.999809	+	0.0195188i	$0.00621341\pi$
$810$	−0.295266	+	0.00925691i	−0.0103746	+	0.000325255i
$811$	−12.3166	+	1.77086i	−0.432495	+	0.0621834i	−0.355125	−	0.934819i	$-0.615562\pi$
$811$	−12.3166	+	1.77086i	−0.432495	+	0.0621834i	−0.0773707	+	0.997002i	$0.524652\pi$
$812$	−2.03298	−	2.76567i	−0.0713435	−	0.0970561i
$813$	−9.92744	−	15.4474i	−0.348171	−	0.541764i
$814$	−13.5778	−	11.0396i	−0.475900	−	0.386938i
$815$	0.363082	−	0.106610i	0.0127182	−	0.00373440i
$816$	6.89828	−	14.4337i	0.241488	−	0.505280i
$817$	25.9718	−	29.9731i	0.908640	−	1.04863i
$818$	16.8462	−	15.5478i	0.589012	−	0.543616i
$819$	−13.8241	+	6.31326i	−0.483054	+	0.220603i
$820$	−4.73066	−	0.379823i	−0.165202	−	0.0132640i
$821$	1.59913	−	5.44614i	0.0558100	−	0.190072i	−0.926870	−	0.375383i	$-0.877511\pi$
$821$	1.59913	−	5.44614i	0.0558100	−	0.190072i	0.982680	+	0.185311i	$0.0593294\pi$
$822$	−0.364747	+	0.250899i	−0.0127220	+	0.00875110i
$823$	3.10014	−	6.78837i	0.108064	−	0.236628i	−0.847873	−	0.530200i	$-0.822117\pi$
$823$	3.10014	−	6.78837i	0.108064	−	0.236628i	0.955937	+	0.293572i	$0.0948441\pi$
$824$	−30.9600	−	10.7562i	−1.07854	−	0.374710i
$825$	−24.0844	−	15.4781i	−0.838512	−	0.538879i
$826$	−10.6525	+	25.4036i	−0.370647	+	0.883904i
$827$			1.48225i			0.0515429i	0.999668	+	0.0257715i	$0.00820422\pi$
$827$			1.48225i			0.0515429i	−0.999668	+	0.0257715i	$0.991796\pi$
$828$	−2.31789	−	9.30738i	−0.0805524	−	0.323454i
$829$			34.1951i			1.18764i	0.804597	+	0.593822i	$0.202382\pi$
$829$			34.1951i			1.18764i	−0.804597	+	0.593822i	$0.797618\pi$
$830$	3.89835	+	1.63469i	0.135314	+	0.0567410i
$831$	13.9715	+	8.97896i	0.484667	+	0.311477i
$832$	41.7175	+	24.2167i	1.44629	+	0.839564i
$833$	1.07527	−	2.35451i	0.0372558	−	0.0815789i
$834$	4.48917	+	6.52618i	0.155447	+	0.225983i
$835$	−0.244757	+	0.833566i	−0.00847017	+	0.0288467i
$836$	6.38231	−	79.4910i	0.220737	−	2.74925i
$837$	0.266537	−	0.121723i	0.00921287	−	0.00420738i
$838$	−11.5255	−	12.4879i	−0.398141	−	0.431388i
$839$	−12.3653	+	14.2703i	−0.426898	+	0.492666i	−0.927926	−	0.372765i	$-0.878410\pi$
$839$	−12.3653	+	14.2703i	−0.426898	+	0.492666i	0.501028	+	0.865431i	$0.332955\pi$
$840$	−0.919153	−	1.17163i	−0.0317138	−	0.0404252i
$841$	−27.3804	+	8.03962i	−0.944153	+	0.277228i
$842$	−21.3687	+	26.2816i	−0.736413	+	0.905723i
$843$	−7.80783	−	12.1492i	−0.268916	−	0.418442i
$844$	−3.36653	−	4.57985i	−0.115881	−	0.157645i
$845$	4.82915	−	0.694327i	0.166128	−	0.0238856i
$846$	0.139421	+	4.44707i	0.00479338	+	0.152893i
$847$	−8.02237	+	55.7968i	−0.275652	+	1.91720i
$848$	−9.81964	−	3.07026i	−0.337208	−	0.105433i
$849$	3.79964	+	4.38502i	0.130403	+	0.150493i
$850$	−25.1222	+	12.4386i	−0.861685	+	0.426642i
$851$	−5.21677	+	8.85062i	−0.178829	+	0.303396i
$852$	−18.7915	−	14.3245i	−0.643786	−	0.490748i
$853$	−21.1648	+	18.3394i	−0.724668	+	0.627928i	−0.937024	−	0.349264i	$-0.886432\pi$
$853$	−21.1648	+	18.3394i	−0.724668	+	0.627928i	0.212357	+	0.977192i	$0.431886\pi$
$854$	4.95716	−	44.2910i	0.169631	−	1.51561i
$855$	−0.205210	+	1.42727i	−0.00701803	+	0.0488115i
$856$	8.14787	−	11.4136i	0.278489	−	0.390110i
$857$	1.32436	+	9.21115i	0.0452394	+	0.314647i	0.999859	+	0.0168177i	$0.00535348\pi$
$857$	1.32436	+	9.21115i	0.0452394	+	0.314647i	−0.954619	+	0.297829i	$0.903737\pi$
$858$	8.53401	+	48.5101i	0.291346	+	1.65611i
$859$	12.9257	+	20.1128i	0.441019	+	0.686238i	0.988609	−	0.150508i	$-0.0480911\pi$
$859$	12.9257	+	20.1128i	0.441019	+	0.686238i	−0.547590	+	0.836747i	$0.684455\pi$
$860$	−2.34087	−	0.530639i	−0.0798229	−	0.0180947i
$861$	8.06668	+	27.4726i	0.274912	+	0.936264i
$862$	−3.48848	+	13.4233i	−0.118818	+	0.457198i
$863$	36.3504	−	41.9506i	1.23738	−	1.42801i	0.370998	−	0.928634i	$-0.379016\pi$
$863$	36.3504	−	41.9506i	1.23738	−	1.42801i	0.866383	−	0.499380i	$-0.166439\pi$
$864$	2.99186	−	4.80091i	0.101785	−	0.163330i
$865$	−1.53262	−	3.35596i	−0.0521106	−	0.114106i
$866$	4.73695	−	7.90498i	0.160968	−	0.268622i
$867$	−0.283181	+	0.964427i	−0.00961734	+	0.0327537i
$868$	1.29018	+	0.719164i	0.0437916	+	0.0244100i
$869$	12.4816	+	5.70016i	0.423410	+	0.193365i
$870$	0.191132	−	0.0626909i	0.00648000	−	0.00212542i
$871$	−19.0009	−	12.2112i	−0.643823	−	0.413760i
$872$	13.5153	+	23.4730i	0.457686	+	0.794895i
$873$	6.16732			0.208732
$874$	−46.7039	+	3.27146i	−1.57978	+	0.110659i
$875$			5.24197i			0.177211i
$876$	1.43132	+	22.8049i	0.0483599	+	0.770504i
$877$	−12.4730	+	19.4084i	−0.421185	+	0.655377i	−0.985401	−	0.170251i	$-0.945542\pi$
$877$	−12.4730	+	19.4084i	−0.421185	+	0.655377i	0.564216	+	0.825627i	$0.309179\pi$
$878$	10.5399	+	32.1341i	0.355704	+	1.08447i
$879$	−1.75043	+	3.83290i	−0.0590404	+	0.129281i
$880$	−4.42448	+	1.92808i	−0.149149	+	0.0649956i
$881$	24.5128	+	7.19759i	0.825856	+	0.242493i	0.667236	−	0.744847i	$-0.267477\pi$
$881$	24.5128	+	7.19759i	0.825856	+	0.242493i	0.158620	+	0.987340i	$0.449296\pi$
$882$	0.470473	−	0.785121i	0.0158416	−	0.0264364i
$883$	−14.9132	+	6.81063i	−0.501869	+	0.229196i	−0.650230	−	0.759737i	$-0.725327\pi$
$883$	−14.9132	+	6.81063i	−0.501869	+	0.229196i	0.148361	+	0.988933i	$0.452600\pi$
$884$	45.0396	+	17.2477i	1.51485	+	0.580102i
$885$	−1.22000	−	1.05714i	−0.0410099	−	0.0355353i
$886$	−6.95924	−	1.80859i	−0.233800	−	0.0607607i
$887$	1.01442	−	0.297862i	0.0340610	−	0.0100012i	−0.264658	−	0.964342i	$-0.585259\pi$
$887$	1.01442	−	0.297862i	0.0340610	−	0.0100012i	0.298719	+	0.954341i	$0.403441\pi$
$888$	−5.88996	+	1.42155i	−0.197654	+	0.0477041i
$889$	18.4137	−	11.8338i	0.617577	−	0.396893i
$890$	−0.857386	−	4.87366i	−0.0287397	−	0.163366i
$891$	5.71746	−	0.822046i	0.191542	−	0.0275396i
$892$	8.41318	+	15.7321i	0.281694	+	0.526751i
$893$	21.4964	+	3.09072i	0.719350	+	0.103427i
$894$	−3.10117	−	0.347091i	−0.103719	−	0.0116084i
$895$	1.45823	+	1.68288i	0.0487432	+	0.0562526i
$896$	28.4323	−	2.18180i	0.949857	−	0.0728888i
$897$	27.4107	−	9.21128i	0.915216	−	0.307556i
$898$	−10.3546	+	5.12683i	−0.345538	+	0.171085i
$899$	−0.150788	+	0.130658i	−0.00502905	+	0.00435770i
$900$	−9.31758	+	3.38304i	−0.310586	+	0.112768i
$901$	−10.1821	−	1.46396i	−0.339214	−	0.0487716i
$902$	92.7520	−	2.90788i	3.08830	−	0.0968218i
$903$	2.06086	+	14.3336i	0.0685813	+	0.476993i
$904$	11.9965	−	23.2029i	0.398999	−	0.771718i
$905$	−2.42123	+	1.55603i	−0.0804845	+	0.0517242i
$906$	−21.4284	+	26.3550i	−0.711910	+	0.875586i
$907$	7.08244	+	24.1206i	0.235169	+	0.800910i	0.989515	+	0.144433i	$0.0461359\pi$
$907$	7.08244	+	24.1206i	0.235169	+	0.800910i	−0.754346	+	0.656477i	$0.772046\pi$
$908$	−8.21101	+	1.71136i	−0.272492	+	0.0567936i
$909$	9.40674	+	8.15099i	0.312002	+	0.270351i
$910$	3.29914	−	3.04487i	0.109366	−	0.100937i
$911$	21.6016	+	47.3008i	0.715692	+	1.56715i	0.819845	+	0.572585i	$0.194059\pi$
$911$	21.6016	+	47.3008i	0.715692	+	1.56715i	−0.104154	+	0.994561i	$0.533213\pi$
$912$	−20.5493	−	18.4431i	−0.680455	−	0.610711i
$913$	−79.3077	−	23.2869i	−2.62470	−	0.770682i
$914$	−18.4943	−	26.8863i	−0.611737	−	0.889319i
$915$	2.37573	+	1.08496i	0.0785394	+	0.0358677i
$916$	4.47603	−	4.39866i	0.147892	−	0.145336i
$917$	−8.54224	+	13.2920i	−0.282089	+	0.438940i
$918$	2.18719	−	5.21593i	0.0721881	−	0.172151i
$919$	24.8732			0.820490			0.410245	−	0.911975i	$-0.365443\pi$
$919$	24.8732			0.820490			0.410245	+	0.911975i	$0.365443\pi$
$920$	1.50754	+	2.39915i	0.0497020	+	0.0790978i
$921$	−29.5613			−0.974076
$922$	10.2203	−	24.3728i	0.336586	−	0.802677i
$923$	38.5129	−	59.9272i	1.26767	−	1.97253i
$924$	20.4091	+	20.7681i	0.671410	+	0.683220i
$925$	9.65808	+	4.41070i	0.317556	+	0.145023i
$926$	−28.7844	−	41.8456i	−0.945914	−	1.37513i
$927$	−11.1184	−	3.26467i	−0.365177	−	0.107226i
$928$	−1.03370	+	3.71057i	−0.0339330	+	0.121805i
$929$	6.53377	+	14.3070i	0.214366	+	0.469396i	0.986016	−	0.166651i	$-0.0532954\pi$
$929$	6.53377	+	14.3070i	0.214366	+	0.469396i	−0.771650	+	0.636048i	$0.780568\pi$
$930$	−0.0636094	+	0.0587069i	−0.00208583	+	0.00192508i
$931$	−3.37644	−	2.92570i	−0.110658	−	0.0958861i
$932$	−2.47577	−	11.8786i	−0.0810966	−	0.389096i
$933$	−7.45745	−	25.3977i	−0.244146	−	0.831485i
$934$	−3.29868	+	4.05709i	−0.107936	+	0.132752i
$935$	−4.05952	+	2.60889i	−0.132760	+	0.0853199i
$936$	15.1493	+	7.83258i	0.495169	+	0.256016i
$937$	1.10766	+	7.70394i	0.0361857	+	0.251677i	0.999883	−	0.0153217i	$-0.00487724\pi$
$937$	1.10766	+	7.70394i	0.0361857	+	0.251677i	−0.963697	+	0.266998i	$0.913968\pi$
$938$	−13.3457	+	0.418404i	−0.435754	+	0.0136614i
$939$	2.96349	+	0.426085i	0.0967098	+	0.0139048i
$940$	−0.448567	−	1.23544i	−0.0146306	−	0.0402957i
$941$	−4.62640	+	4.00880i	−0.150816	+	0.130683i	−0.727001	−	0.686637i	$-0.759086\pi$
$941$	−4.62640	+	4.00880i	−0.150816	+	0.130683i	0.576185	+	0.817320i	$0.304541\pi$
$942$	−23.6942	+	11.7316i	−0.771999	+	0.382236i
$943$	−9.82816	−	53.5865i	−0.320049	−	1.74502i
$944$	29.8075	−	8.19055i	0.970151	−	0.266580i
$945$	−0.344780	−	0.397898i	−0.0112157	−	0.0129436i
$946$	46.6417	+	5.22026i	1.51645	+	0.169725i
$947$	−16.5999	−	2.38671i	−0.539424	−	0.0775575i	−0.132783	−	0.991145i	$-0.542391\pi$
$947$	−16.5999	−	2.38671i	−0.539424	−	0.0775575i	−0.406642	+	0.913588i	$0.633300\pi$
$948$	4.18958	−	2.24049i	0.136071	−	0.0727678i
$949$	−68.1863	+	9.80371i	−2.21342	+	0.318242i
$950$	8.38336	+	47.6537i	0.271992	+	1.54609i
$951$	−4.35069	+	2.79602i	−0.141081	+	0.0906672i
$952$	27.7155	−	6.68918i	0.898266	−	0.216798i
$953$	−21.7018	+	6.37224i	−0.702992	+	0.206417i	−0.613643	−	0.789583i	$-0.710297\pi$
$953$	−21.7018	+	6.37224i	−0.702992	+	0.206417i	−0.0893485	+	0.996000i	$0.528478\pi$
$954$	−3.52056	−	0.914935i	−0.113982	−	0.0296221i
$955$	−2.32642	−	2.01585i	−0.0752812	−	0.0652315i
$956$	−0.353419	+	0.922898i	−0.0114304	+	0.0298487i
$957$	−3.57773	+	1.63390i	−0.115652	+	0.0528164i
$958$	27.4702	−	45.8420i	0.887521	−	1.48109i
$959$	−0.757053	−	0.222291i	−0.0244465	−	0.00717814i
$960$	−0.397798	+	1.62306i	−0.0128389	+	0.0523840i
$961$	−12.8422	+	28.1205i	−0.414264	+	0.907113i
$962$	−5.69309	−	17.3571i	−0.183553	−	0.559617i
$963$	2.68053	−	4.17098i	0.0863788	−	0.134408i
$964$	33.2436	−	2.08650i	1.07070	−	0.0672016i
$965$			3.97064i			0.127819i
$966$	10.2645	−	13.6700i	0.330256	−	0.439824i
$967$	−36.6351			−1.17810			−0.589052	−	0.808095i	$-0.700499\pi$
$967$	−36.6351			−1.17810			−0.589052	+	0.808095i	$0.700499\pi$
$968$	54.8202	−	31.5645i	1.76199	−	1.01452i
$969$	−23.2249	−	14.9257i	−0.746092	−	0.479484i
$970$	−1.73115	+	0.567812i	−0.0555839	+	0.0182313i
$971$	17.3842	+	7.93909i	0.557885	+	0.254777i	0.674343	−	0.738418i	$-0.264427\pi$
$971$	17.3842	+	7.93909i	0.557885	+	0.254777i	−0.116458	+	0.993196i	$0.537154\pi$
$972$	0.973765	−	1.74694i	0.0312335	−	0.0560330i
$973$	−3.97731	+	13.5455i	−0.127507	+	0.434248i
$974$	14.9195	−	24.8975i	0.478051	−	0.797767i
$975$	−12.4147	−	27.1843i	−0.397587	−	0.870595i
$976$	−42.5385	+	26.3013i	−1.36162	+	0.841883i
$977$	−9.38645	+	10.8325i	−0.300299	+	0.346564i	−0.885765	−	0.464133i	$-0.846366\pi$
$977$	−9.38645	+	10.8325i	−0.300299	+	0.346564i	0.585466	+	0.810697i	$0.300911\pi$
$978$	−0.644395	+	2.47956i	−0.0206055	+	0.0792875i
$979$	27.2603	+	92.8401i	0.871243	+	2.96718i
$980$	−0.0597761	+	0.263697i	−0.00190948	+	0.00842348i
$981$	5.17734	+	8.05609i	0.165300	+	0.257211i
$982$	1.03536	+	5.88532i	0.0330397	+	0.187808i
$983$	−5.61170	−	39.0302i	−0.178985	−	1.24487i	−0.859117	−	0.511780i	$-0.828986\pi$
$983$	−5.61170	−	39.0302i	−0.178985	−	1.24487i	0.680131	−	0.733090i	$-0.261923\pi$
$984$	18.6684	−	26.1510i	0.595128	−	0.833662i
$985$	0.618641	−	4.30275i	0.0197116	−	0.137097i
$986$	−0.428367	+	3.82735i	−0.0136420	+	0.121888i
$987$	−5.99284	+	5.19282i	−0.190754	+	0.165289i
$988$	50.4657	−	66.2033i	1.60553	−	2.10621i
$989$	−1.06308	−	27.5332i	−0.0338041	−	0.875506i
$990$	−1.52919	+	0.757140i	−0.0486009	+	0.0240635i
$991$	−14.7563	−	17.0296i	−0.468748	−	0.540964i	0.471315	−	0.881965i	$-0.343780\pi$
$991$	−14.7563	−	17.0296i	−0.468748	−	0.540964i	−0.940063	+	0.341001i	$0.889234\pi$
$992$	−0.258684	−	1.63724i	−0.00821322	−	0.0519824i
$993$	−2.89680	+	20.1477i	−0.0919271	+	0.639367i
$994$	−1.31961	−	42.0913i	−0.0418555	−	1.33505i
$995$	3.40967	−	0.490237i	0.108094	−	0.0155416i
$996$	−23.0595	+	16.9505i	−0.730669	+	0.537096i
$997$	6.54173	+	10.1791i	0.207179	+	0.322376i	0.929256	−	0.369436i	$-0.120449\pi$
$997$	6.54173	+	10.1791i	0.207179	+	0.322376i	−0.722078	+	0.691812i	$0.756813\pi$
$998$	13.2062	−	16.2424i	0.418034	−	0.514145i
$999$	−2.05543	+	0.603530i	−0.0650310	+	0.0190948i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.bb.a.13.7	✓	480
8.5	even	2	inner	552.2.bb.a.13.20	yes	480
23.16	even	11	inner	552.2.bb.a.85.20	yes	480
184.85	even	22	inner	552.2.bb.a.85.7	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.bb.a.13.7	✓	480	1.1	even	1	trivial
552.2.bb.a.13.20	yes	480	8.5	even	2	inner
552.2.bb.a.85.7	yes	480	184.85	even	22	inner
552.2.bb.a.85.20	yes	480	23.16	even	11	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)

\(f(q)\)	\(=\)	\(q+(-1.30419 - 0.546886i) q^{2} +(-0.540641 + 0.841254i) q^{3} +(1.40183 + 1.42649i) q^{4} +(-0.190010 - 0.0867748i) q^{5} +(1.16517 - 0.801487i) q^{6} +(2.41838 + 0.710100i) q^{7} +(-1.04813 - 2.62706i) q^{8} +(-0.415415 - 0.909632i) q^{9} +O(q^{10})\)	\(q+(-1.30419 - 0.546886i) q^{2} +(-0.540641 + 0.841254i) q^{3} +(1.40183 + 1.42649i) q^{4} +(-0.190010 - 0.0867748i) q^{5} +(1.16517 - 0.801487i) q^{6} +(2.41838 + 0.710100i) q^{7} +(-1.04813 - 2.62706i) q^{8} +(-0.415415 - 0.909632i) q^{9} +(0.200354 + 0.217085i) q^{10} +(-4.36540 - 3.78264i) q^{11} +(-1.95793 + 0.408077i) q^{12} +(-1.69874 - 5.78537i) q^{13} +(-2.76568 - 2.24868i) q^{14} +(0.175727 - 0.112933i) q^{15} +(-0.0697411 + 3.99939i) q^{16} +(0.569168 + 3.95865i) q^{17} +(0.0443154 + 1.41352i) q^{18} +(6.83272 + 0.982398i) q^{19} +(-0.142579 - 0.392691i) q^{20} +(-1.90485 + 1.65056i) q^{21} +(3.62464 + 7.32066i) q^{22} +(3.93147 - 2.74655i) q^{23} +(2.77668 + 0.538552i) q^{24} +(-3.24573 - 3.74577i) q^{25} +(-0.948460 + 8.47425i) q^{26} +(0.989821 + 0.142315i) q^{27} +(2.37721 + 4.44523i) q^{28} +(-0.673989 + 0.0969050i) q^{29} +(-0.290943 + 0.0511834i) q^{30} +(0.246501 - 0.158417i) q^{31} +(2.27817 - 5.17783i) q^{32} +(5.54227 - 1.62736i) q^{33} +(1.42263 - 5.47411i) q^{34} +(-0.397898 - 0.344780i) q^{35} +(0.715238 - 1.86774i) q^{36} +(-1.94862 + 0.889905i) q^{37} +(-8.37392 - 5.01796i) q^{38} +(5.78537 + 1.69874i) q^{39} +(-0.0288071 + 0.590119i) q^{40} +(4.71909 - 10.3334i) q^{41} +(3.38695 - 1.11091i) q^{42} +(3.10617 - 4.83330i) q^{43} +(-0.723657 - 11.5298i) q^{44} +0.208887i q^{45} +(-6.62944 + 1.43196i) q^{46} +3.14610 q^{47} +(-3.32680 - 2.22090i) q^{48} +(-0.544467 - 0.349908i) q^{49} +(2.18454 + 6.66025i) q^{50} +(-3.63794 - 1.66139i) q^{51} +(5.87142 - 10.5333i) q^{52} +(-0.724646 + 2.46792i) q^{53} +(-1.21309 - 0.726926i) q^{54} +(0.501233 + 1.09755i) q^{55} +(-0.669298 - 7.09749i) q^{56} +(-4.52050 + 5.21693i) q^{57} +(0.932007 + 0.242213i) q^{58} +(-2.17725 - 7.41504i) q^{59} +(0.407437 + 0.0923597i) q^{60} +(6.75974 + 10.5184i) q^{61} +(-0.408120 + 0.0717975i) q^{62} +(-0.358701 - 2.49482i) q^{63} +(-5.80285 + 5.50699i) q^{64} +(-0.179247 + 1.24669i) q^{65} +(-8.11816 - 0.908606i) q^{66} +(2.83098 - 2.45306i) q^{67} +(-4.84909 + 6.36127i) q^{68} +(0.185034 + 4.79226i) q^{69} +(0.330379 + 0.667264i) q^{70} +(7.73672 + 8.92865i) q^{71} +(-1.95425 + 2.04473i) q^{72} +(1.62593 - 11.3086i) q^{73} +(3.02805 - 0.0949329i) q^{74} +(4.90592 - 0.705364i) q^{75} +(8.17694 + 11.1240i) q^{76} +(-7.87113 - 12.2477i) q^{77} +(-6.61621 - 5.37942i) q^{78} +(-2.27930 + 0.669262i) q^{79} +(0.360298 - 0.753874i) q^{80} +(-0.654861 + 0.755750i) q^{81} +(-11.8058 + 10.8959i) q^{82} +(13.0165 - 5.94443i) q^{83} +(-5.02478 - 0.403438i) q^{84} +(0.235363 - 0.801573i) q^{85} +(-6.69431 + 4.60482i) q^{86} +(0.282864 - 0.619387i) q^{87} +(-5.36171 + 15.4328i) q^{88} +(-14.0921 - 9.05642i) q^{89} +(0.114237 - 0.272429i) q^{90} -15.1975i q^{91} +(9.42918 + 1.75800i) q^{92} +0.293016i q^{93} +(-4.10311 - 1.72056i) q^{94} +(-1.21304 - 0.779574i) q^{95} +(3.12420 + 4.71586i) q^{96} +(-2.56200 + 5.60999i) q^{97} +(0.518729 + 0.754108i) q^{98} +(-1.62736 + 5.54227i) 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