LMFDB - Embedded newform 820.2.bv.c.103.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(103,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([10, 15, 7])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.103"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.bv (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [960,-10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$960$
Relative dimension:	$120$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			103.17
Character	$\chi$	$=$	820.103
Dual form			820.2.bv.c.207.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.28771 - 0.584633i) q^{2} +0.0874408 q^{3} +(1.31641 + 1.50568i) q^{4} +(-0.437444 - 2.19286i) q^{5} +(-0.112599 - 0.0511208i) q^{6} +(-3.19012 + 1.03653i) q^{7} +(-0.814885 - 2.70850i) q^{8} -2.99235 q^{9} +(-0.718718 + 3.07952i) q^{10} +(0.441826 - 2.78958i) q^{11} +(0.115108 + 0.131658i) q^{12} +(-2.09602 - 0.681038i) q^{13} +(4.71394 + 0.530293i) q^{14} +(-0.0382504 - 0.191746i) q^{15} +(-0.534140 + 3.96418i) q^{16} +(0.954122 + 1.31324i) q^{17} +(3.85329 + 1.74943i) q^{18} +(4.39283 + 2.23826i) q^{19} +(2.72589 - 3.54535i) q^{20} +(-0.278946 + 0.0906351i) q^{21} +(-2.19983 + 3.33387i) q^{22} +(3.68299 + 7.22827i) q^{23} +(-0.0712542 - 0.236833i) q^{24} +(-4.61729 + 1.91851i) q^{25} +(2.30091 + 2.10238i) q^{26} -0.523976 q^{27} +(-5.76018 - 3.43879i) q^{28} +(6.02052 - 0.953557i) q^{29} +(-0.0628453 + 0.269276i) q^{30} +(4.48863 + 6.17807i) q^{31} +(3.00541 - 4.79244i) q^{32} +(0.0386336 - 0.243923i) q^{33} +(-0.460874 - 2.24888i) q^{34} +(3.66847 + 6.54206i) q^{35} +(-3.93916 - 4.50553i) q^{36} +(-6.99381 + 1.10771i) q^{37} +(-4.34814 - 5.45042i) q^{38} +(-0.183277 - 0.0595505i) q^{39} +(-5.58290 + 2.97175i) q^{40} +(-6.31926 + 1.03296i) q^{41} +(0.412191 + 0.0463692i) q^{42} +(-0.133674 + 0.0681104i) q^{43} +(4.78184 - 3.00698i) q^{44} +(1.30899 + 6.56182i) q^{45} +(-0.516743 - 11.4611i) q^{46} +(-2.35576 + 7.25028i) q^{47} +(-0.0467056 + 0.346631i) q^{48} +(3.43932 - 2.49881i) q^{49} +(7.06736 + 0.228932i) q^{50} +(0.0834292 + 0.114830i) q^{51} +(-1.73379 - 4.05246i) q^{52} +(1.53538 - 2.11326i) q^{53} +(0.674731 + 0.306334i) q^{54} +(-6.31044 + 0.251421i) q^{55} +(5.40702 + 7.79577i) q^{56} +(0.384112 + 0.195715i) q^{57} +(-8.31019 - 2.29189i) q^{58} +(0.934995 - 2.87762i) q^{59} +(0.238354 - 0.310008i) q^{60} +(5.95586 - 1.93517i) q^{61} +(-2.16816 - 10.5798i) q^{62} +(9.54596 - 3.10167i) q^{63} +(-6.67192 + 4.41423i) q^{64} +(-0.576531 + 4.89419i) q^{65} +(-0.192355 + 0.291516i) q^{66} +(-6.52642 - 4.74172i) q^{67} +(-0.721299 + 3.16536i) q^{68} +(0.322043 + 0.632046i) q^{69} +(-0.899226 - 10.5690i) q^{70} +(-2.11086 + 13.3274i) q^{71} +(2.43842 + 8.10479i) q^{72} +(-7.23913 + 7.23913i) q^{73} +(9.65362 + 2.66240i) q^{74} +(-0.403739 + 0.167756i) q^{75} +(2.41265 + 9.56065i) q^{76} +(1.48201 + 9.35705i) q^{77} +(0.201194 + 0.183834i) q^{78} +(4.92171 + 4.92171i) q^{79} +(8.92655 - 0.562808i) q^{80} +8.93125 q^{81} +(8.74129 + 2.36429i) q^{82} +(-2.96110 + 2.96110i) q^{83} +(-0.503674 - 0.300691i) q^{84} +(2.46237 - 2.66673i) q^{85} +(0.211954 - 0.00955625i) q^{86} +(0.526439 - 0.0833798i) q^{87} +(-7.91561 + 1.07650i) q^{88} +(-13.4242 - 6.84000i) q^{89} +(2.15066 - 9.21501i) q^{90} +7.39246 q^{91} +(-6.03514 + 15.0608i) q^{92} +(0.392489 + 0.540215i) q^{93} +(7.27229 - 7.95902i) q^{94} +(2.98657 - 10.6120i) q^{95} +(0.262795 - 0.419055i) q^{96} +(-5.19566 + 7.15121i) q^{97} +(-5.88975 + 1.20701i) q^{98} +(-1.32210 + 8.34741i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 960 q - 10 q^{2} - 20 q^{5} - 16 q^{6} + 2 q^{8} + 960 q^{9} - 60 q^{10} - 40 q^{12} - 20 q^{13} - 8 q^{14} - 28 q^{16} - 20 q^{17} - 48 q^{18} - 34 q^{20} - 40 q^{21} - 10 q^{22} - 48 q^{24} - 4 q^{25}+ \cdots - 38 q^{98}+O(q^{100}) $ 960 * q - 10 * q^2 - 20 * q^5 - 16 * q^6 + 2 * q^8 + 960 * q^9 - 60 * q^10 - 40 * q^12 - 20 * q^13 - 8 * q^14 - 28 * q^16 - 20 * q^17 - 48 * q^18 - 34 * q^20 - 40 * q^21 - 10 * q^22 - 48 * q^24 - 4 * q^25 - 20 * q^26 - 10 * q^28 - 10 * q^30 - 56 * q^33 - 20 * q^34 - 100 * q^36 + 88 * q^37 - 16 * q^40 - 24 * q^41 - 104 * q^42 - 100 * q^45 - 20 * q^46 - 40 * q^48 + 224 * q^49 - 12 * q^50 - 38 * q^52 - 20 * q^53 - 52 * q^54 + 96 * q^56 - 72 * q^57 - 38 * q^58 - 14 * q^60 - 40 * q^61 - 10 * q^62 - 120 * q^64 - 60 * q^65 - 12 * q^66 - 116 * q^68 - 104 * q^69 - 96 * q^70 - 24 * q^72 - 72 * q^73 - 28 * q^74 - 40 * q^76 - 76 * q^77 - 44 * q^78 - 90 * q^80 + 592 * q^81 - 130 * q^82 - 92 * q^84 - 64 * q^85 - 12 * q^86 - 104 * q^88 + 136 * q^89 - 364 * q^90 - 220 * q^92 - 32 * q^94 - 44 * q^96 + 80 * q^97 - 38 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$-1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.28771	−	0.584633i	−0.910550	−	0.413398i
$2$	−1.28771	−	0.584633i	−0.910550	−	0.413398i
$3$	0.0874408			0.0504840			0.0252420	−	0.999681i	$-0.491964\pi$
$3$	0.0874408			0.0504840			0.0252420	+	0.999681i	$0.491964\pi$
$4$	1.31641	+	1.50568i	0.658204	+	0.752840i
$5$	−0.437444	−	2.19286i	−0.195631	−	0.980678i
$5$	−0.437444	−	2.19286i	−0.195631	−	0.980678i
$6$	−0.112599	−	0.0511208i	−0.0459682	−	0.0208700i
$7$	−3.19012	+	1.03653i	−1.20575	+	0.391772i	−0.841873	−	0.539675i	$-0.818547\pi$
$7$	−3.19012	+	1.03653i	−1.20575	+	0.391772i	−0.363877	+	0.931447i	$0.618547\pi$
$8$	−0.814885	−	2.70850i	−0.288105	−	0.957599i
$9$	−2.99235			−0.997451
$10$	−0.718718	+	3.07952i	−0.227279	+	0.973830i
$11$	0.441826	−	2.78958i	0.133216	−	0.841090i	−0.827076	−	0.562091i	$-0.809997\pi$
$11$	0.441826	−	2.78958i	0.133216	−	0.841090i	0.960291	−	0.278999i	$-0.0900028\pi$
$12$	0.115108	+	0.131658i	0.0332287	+	0.0380063i
$13$	−2.09602	−	0.681038i	−0.581331	−	0.188886i	0.00356578	−	0.999994i	$-0.498865\pi$
$13$	−2.09602	−	0.681038i	−0.581331	−	0.188886i	−0.584897	+	0.811108i	$0.698865\pi$
$14$	4.71394	+	0.530293i	1.25985	+	0.141727i
$15$	−0.0382504	−	0.191746i	−0.00987622	−	0.0495085i
$16$	−0.534140	+	3.96418i	−0.133535	+	0.991044i
$17$	0.954122	+	1.31324i	0.231409	+	0.318507i	0.908892	−	0.417031i	$-0.136929\pi$
$17$	0.954122	+	1.31324i	0.231409	+	0.318507i	−0.677483	+	0.735538i	$0.736929\pi$
$18$	3.85329	+	1.74943i	0.908230	+	0.412345i
$19$	4.39283	+	2.23826i	1.00778	+	0.513491i	0.878310	−	0.478091i	$-0.158671\pi$
$19$	4.39283	+	2.23826i	1.00778	+	0.513491i	0.129474	+	0.991583i	$0.458671\pi$
$20$	2.72589	−	3.54535i	0.609528	−	0.792765i
$21$	−0.278946	+	0.0906351i	−0.0608711	+	0.0197782i
$22$	−2.19983	+	3.33387i	−0.469005	+	0.710784i
$23$	3.68299	+	7.22827i	0.767956	+	1.50720i	0.859352	+	0.511384i	$0.170867\pi$
$23$	3.68299	+	7.22827i	0.767956	+	1.50720i	−0.0913962	+	0.995815i	$0.529133\pi$
$24$	−0.0712542	−	0.236833i	−0.0145447	−	0.0483434i
$25$	−4.61729	+	1.91851i	−0.923457	+	0.383701i
$26$	2.30091	+	2.10238i	0.451246	+	0.412311i
$27$	−0.523976			−0.100839
$28$	−5.76018	−	3.43879i	−1.08857	−	0.649871i
$29$	6.02052	−	0.953557i	1.11798	−	0.177071i	0.430022	−	0.902818i	$-0.358506\pi$
$29$	6.02052	−	0.953557i	1.11798	−	0.177071i	0.687961	+	0.725747i	$0.258506\pi$
$30$	−0.0628453	+	0.269276i	−0.0114739	+	0.0491628i
$31$	4.48863	+	6.17807i	0.806182	+	1.10961i	0.991901	+	0.127012i	$0.0405386\pi$
$31$	4.48863	+	6.17807i	0.806182	+	1.10961i	−0.185719	+	0.982603i	$0.559461\pi$
$32$	3.00541	−	4.79244i	0.531286	−	0.847192i
$33$	0.0386336	−	0.243923i	0.00672525	−	0.0424615i
$34$	−0.460874	−	2.24888i	−0.0790392	−	0.385680i
$35$	3.66847	+	6.54206i	0.620084	+	1.10581i
$36$	−3.93916	−	4.50553i	−0.656526	−	0.750921i
$37$	−6.99381	+	1.10771i	−1.14978	+	0.182107i	−0.702092	−	0.712086i	$-0.747751\pi$
$37$	−6.99381	+	1.10771i	−1.14978	+	0.182107i	−0.447683	+	0.894192i	$0.647751\pi$
$38$	−4.34814	−	5.45042i	−0.705361	−	0.884176i
$39$	−0.183277	−	0.0595505i	−0.0293479	−	0.00953571i
$40$	−5.58290	+	2.97175i	−0.882733	+	0.469874i
$41$	−6.31926	+	1.03296i	−0.986902	+	0.161322i
$41$	−6.31926	+	1.03296i	−0.986902	+	0.161322i
$42$	0.412191	+	0.0463692i	0.0636024	+	0.00715493i
$43$	−0.133674	+	0.0681104i	−0.0203851	+	0.0103867i	−0.464153	−	0.885755i	$-0.653641\pi$
$43$	−0.133674	+	0.0681104i	−0.0203851	+	0.0103867i	0.443768	+	0.896142i	$0.353641\pi$
$44$	4.78184	−	3.00698i	0.720889	−	0.453319i
$45$	1.30899	+	6.56182i	0.195132	+	0.978178i
$46$	−0.516743	−	11.4611i	−0.0761896	−	1.68985i
$47$	−2.35576	+	7.25028i	−0.343623	+	1.05756i	0.618694	+	0.785632i	$0.287662\pi$
$47$	−2.35576	+	7.25028i	−0.343623	+	1.05756i	−0.962317	+	0.271930i	$0.912338\pi$
$48$	−0.0467056	+	0.346631i	−0.00674138	+	0.0500318i
$49$	3.43932	−	2.49881i	0.491332	−	0.356973i
$50$	7.06736	+	0.228932i	0.999476	+	0.0323759i
$51$	0.0834292	+	0.114830i	0.0116824	+	0.0160795i
$52$	−1.73379	−	4.05246i	−0.240434	−	0.561974i
$53$	1.53538	−	2.11326i	0.210900	−	0.290279i	−0.690441	−	0.723388i	$-0.742584\pi$
$53$	1.53538	−	2.11326i	0.210900	−	0.290279i	0.901341	+	0.433109i	$0.142584\pi$
$54$	0.674731	+	0.306334i	0.0918192	+	0.0416868i
$55$	−6.31044	+	0.251421i	−0.850899	+	0.0339016i
$56$	5.40702	+	7.79577i	0.722544	+	1.04175i
$57$	0.384112	+	0.195715i	0.0508769	+	0.0259231i
$58$	−8.31019	−	2.29189i	−1.09118	−	0.300940i
$59$	0.934995	−	2.87762i	0.121726	−	0.374634i	−0.871564	−	0.490281i	$-0.836894\pi$
$59$	0.934995	−	2.87762i	0.121726	−	0.374634i	0.993290	+	0.115647i	$0.0368941\pi$
$60$	0.238354	−	0.310008i	0.0307714	−	0.0400219i
$61$	5.95586	−	1.93517i	0.762569	−	0.247774i	0.0981882	−	0.995168i	$-0.468695\pi$
$61$	5.95586	−	1.93517i	0.762569	−	0.247774i	0.664381	+	0.747394i	$0.268695\pi$
$62$	−2.16816	−	10.5798i	−0.275357	−	1.34363i
$63$	9.54596	−	3.10167i	1.20268	−	0.390774i
$64$	−6.67192	+	4.41423i	−0.833991	+	0.551779i
$65$	−0.576531	+	4.89419i	−0.0715099	+	0.607050i
$66$	−0.192355	+	0.291516i	−0.0236772	+	0.0358832i
$67$	−6.52642	−	4.74172i	−0.797329	−	0.579294i	0.112800	−	0.993618i	$-0.464018\pi$
$67$	−6.52642	−	4.74172i	−0.797329	−	0.579294i	−0.910129	+	0.414324i	$0.864018\pi$
$68$	−0.721299	+	3.16536i	−0.0874704	+	0.383856i
$69$	0.322043	+	0.632046i	0.0387695	+	0.0760893i
$70$	−0.899226	−	10.5690i	−0.107478	−	1.26324i
$71$	−2.11086	+	13.3274i	−0.250513	+	1.58167i	0.466440	+	0.884553i	$0.345536\pi$
$71$	−2.11086	+	13.3274i	−0.250513	+	1.58167i	−0.716953	+	0.697122i	$0.754464\pi$
$72$	2.43842	+	8.10479i	0.287371	+	0.955158i
$73$	−7.23913	+	7.23913i	−0.847276	+	0.847276i	−0.989792	−	0.142516i	$-0.954481\pi$
$73$	−7.23913	+	7.23913i	−0.847276	+	0.847276i	0.142516	+	0.989792i	$0.454481\pi$
$74$	9.65362	+	2.66240i	1.12221	+	0.309498i
$75$	−0.403739	+	0.167756i	−0.0466198	+	0.0193708i
$76$	2.41265	+	9.56065i	0.276750	+	1.09668i
$77$	1.48201	+	9.35705i	0.168891	+	1.06633i
$78$	0.201194	+	0.183834i	0.0227807	+	0.0208151i
$79$	4.92171	+	4.92171i	0.553736	+	0.553736i	0.927517	−	0.373781i	$-0.121939\pi$
$79$	4.92171	+	4.92171i	0.553736	+	0.553736i	−0.373781	+	0.927517i	$0.621939\pi$
$80$	8.92655	−	0.562808i	0.998018	−	0.0629239i
$81$	8.93125			0.992361
$82$	8.74129	+	2.36429i	0.965314	+	0.261092i
$83$	−2.96110	+	2.96110i	−0.325023	+	0.325023i	−0.850690	−	0.525667i	$-0.823816\pi$
$83$	−2.96110	+	2.96110i	−0.325023	+	0.325023i	0.525667	+	0.850690i	$0.323816\pi$
$84$	−0.503674	−	0.300691i	−0.0549554	−	0.0328080i
$85$	2.46237	−	2.66673i	0.267082	−	0.289247i
$86$	0.211954	−	0.00955625i	0.0228555	−	0.00103048i
$87$	0.526439	−	0.0833798i	0.0564402	−	0.00893925i
$88$	−7.91561	+	1.07650i	−0.843807	+	0.114755i
$89$	−13.4242	−	6.84000i	−1.42297	−	0.725038i	−0.438194	−	0.898880i	$-0.644382\pi$
$89$	−13.4242	−	6.84000i	−1.42297	−	0.725038i	−0.984774	+	0.173842i	$0.944382\pi$
$90$	2.15066	−	9.21501i	0.226699	−	0.971348i
$91$	7.39246			0.774940
$92$	−6.03514	+	15.0608i	−0.629207	+	1.57019i
$93$	0.392489	+	0.540215i	0.0406993	+	0.0560177i
$94$	7.27229	−	7.95902i	0.750080	−	0.820910i
$95$	2.98657	−	10.6120i	0.306416	−	1.08877i
$96$	0.262795	−	0.419055i	0.0268214	−	0.0427696i
$97$	−5.19566	+	7.15121i	−0.527539	+	0.726095i	−0.986753	−	0.162231i	$-0.948131\pi$
$97$	−5.19566	+	7.15121i	−0.527539	+	0.726095i	0.459214	+	0.888326i	$0.348131\pi$
$98$	−5.88975	+	1.20701i	−0.594955	+	0.121927i
$99$	−1.32210	+	8.34741i	−0.132876	+	0.838946i
$100$	−8.96689	−	4.42661i	−0.896689	−	0.442661i
$101$	11.9849	+	6.10663i	1.19255	+	0.607632i	0.933620	−	0.358265i	$-0.116632\pi$
$101$	11.9849	+	6.10663i	1.19255	+	0.607632i	0.258926	+	0.965897i	$0.416632\pi$
$102$	−0.0402991	−	0.196644i	−0.00399021	−	0.0194707i
$103$	2.32395	−	4.56100i	0.228985	−	0.449409i	−0.747714	−	0.664021i	$-0.768849\pi$
$103$	2.32395	−	4.56100i	0.228985	−	0.449409i	0.976699	+	0.214612i	$0.0688486\pi$
$104$	−0.136575	+	6.23203i	−0.0133923	+	0.611101i
$105$	0.320774	+	0.572043i	0.0313043	+	0.0558257i
$106$	−3.21261	+	1.82364i	−0.312036	+	0.177128i
$107$	2.81393	−	5.52265i	0.272033	−	0.533894i	−0.714061	−	0.700083i	$-0.753146\pi$
$107$	2.81393	−	5.52265i	0.272033	−	0.533894i	0.986094	+	0.166189i	$0.0531462\pi$
$108$	−0.689766	−	0.788940i	−0.0663728	−	0.0759158i
$109$	−8.17576	−	8.17576i	−0.783095	−	0.783095i	0.197257	−	0.980352i	$-0.436797\pi$
$109$	−8.17576	−	8.17576i	−0.783095	−	0.783095i	−0.980352	+	0.197257i	$0.936797\pi$
$110$	8.27302	+	3.36553i	0.788801	+	0.320891i
$111$	−0.611544	+	0.0968591i	−0.0580452	+	0.00919346i
$112$	−2.40502	−	13.1998i	−0.227253	−	1.24727i
$113$	11.2793	+	1.78647i	1.06107	+	0.168057i	0.662486	−	0.749074i	$-0.269501\pi$
$113$	11.2793	+	1.78647i	1.06107	+	0.168057i	0.398585	+	0.917131i	$0.369501\pi$
$114$	−0.380205	−	0.476589i	−0.0356094	−	0.0446367i
$115$	14.2395	−	11.2382i	1.32784	−	1.04797i
$116$	9.36122	+	7.80971i	0.869167	+	0.725113i
$117$	6.27203	+	2.03791i	0.579849	+	0.188404i
$118$	−2.88636	+	3.15892i	−0.265711	+	0.290802i
$119$	−4.40497	−	3.20040i	−0.403803	−	0.293380i
$120$	−0.488173	+	0.259852i	−0.0445639	+	0.0237211i
$121$	2.87508	+	0.934169i	0.261370	+	0.0849244i
$122$	−8.80080	−	0.990042i	−0.796787	−	0.0896342i
$123$	−0.552561	+	0.0903230i	−0.0498227	+	0.00814415i
$124$	−3.39332	+	14.8913i	−0.304730	+	1.33728i
$125$	6.22682	+	9.28583i	0.556944	+	0.830550i
$126$	−14.1058	−	1.58682i	−1.25664	−	0.141366i
$127$	1.22502	+	7.73449i	0.108703	+	0.686325i	0.980509	+	0.196473i	$0.0629490\pi$
$127$	1.22502	+	7.73449i	0.108703	+	0.686325i	−0.871806	+	0.489851i	$0.837051\pi$
$128$	11.1722	−	1.78363i	0.987495	−	0.157652i
$129$	−0.0116886	+	0.00595563i	−0.00102912	+	0.000524364i
$130$	3.60372	−	5.96526i	0.316067	−	0.523188i
$131$	−8.10031	+	5.88522i	−0.707727	+	0.514194i	−0.882440	−	0.470425i	$-0.844100\pi$
$131$	−8.10031	+	5.88522i	−0.707727	+	0.514194i	0.174712	+	0.984620i	$0.444100\pi$
$132$	0.418127	−	0.262932i	0.0363933	−	0.0228853i
$133$	−16.3337	−	2.58700i	−1.41631	−	0.224321i
$134$	5.63199	+	9.92154i	0.486530	+	0.857091i
$135$	0.229210	+	1.14901i	0.0197273	+	0.0988908i
$136$	2.77940	−	3.65437i	0.238331	−	0.313360i
$137$		−	8.29161i		−	0.708400i	−0.935170	−	0.354200i	$-0.884753\pi$
$137$		−	8.29161i		−	0.708400i	0.935170	−	0.354200i	$-0.115247\pi$
$138$	−0.0451844	−	1.00217i	−0.00384635	−	0.0853104i
$139$	−1.00225	−	3.08462i	−0.0850100	−	0.261634i	0.899512	−	0.436897i	$-0.143922\pi$
$139$	−1.00225	−	3.08462i	−0.0850100	−	0.261634i	−0.984522	+	0.175263i	$0.943922\pi$
$140$	−5.02104	+	14.1356i	−0.424356	+	1.19467i
$141$	−0.205989	+	0.633970i	−0.0173474	+	0.0533899i
$142$	10.5098	−	15.9278i	0.881966	−	1.33663i
$143$	−2.82588	+	5.54611i	−0.236312	+	0.463789i
$144$	1.59834	−	11.8622i	0.133195	−	0.988518i
$145$	−4.72466	−	12.7851i	−0.392362	−	1.06174i
$146$	13.5542	−	5.08968i	1.12175	−	0.421225i
$147$	0.300737	−	0.218498i	0.0248044	−	0.0180214i
$148$	−10.8746	−	9.07224i	−0.893884	−	0.745733i
$149$	1.08523	+	6.85190i	0.0889059	+	0.561330i	0.991425	+	0.130679i	$0.0417158\pi$
$149$	1.08523	+	6.85190i	0.0889059	+	0.561330i	−0.902519	+	0.430650i	$0.858284\pi$
$150$	0.617976	+	0.0200180i	0.0504575	+	0.00163447i
$151$	6.43889	+	12.6370i	0.523989	+	1.02839i	0.989661	+	0.143429i	$0.0458129\pi$
$151$	6.43889	+	12.6370i	0.523989	+	1.02839i	−0.465671	+	0.884958i	$0.654187\pi$
$152$	2.48267	−	13.7219i	0.201371	−	1.11299i
$153$	−2.85507	−	3.92967i	−0.230819	−	0.317695i
$154$	3.56204	−	12.9156i	0.287037	−	1.04077i
$155$	11.5841	−	12.5455i	0.930460	−	1.00768i
$156$	−0.151604	−	0.354350i	−0.0121380	−	0.0283707i
$157$	−0.546971	−	1.68340i	−0.0436530	−	0.134350i	0.926855	−	0.375420i	$-0.122502\pi$
$157$	−0.546971	−	1.68340i	−0.0436530	−	0.134350i	−0.970508	+	0.241070i	$0.922502\pi$
$158$	−3.46035	−	9.21514i	−0.275291	−	0.733117i
$159$	0.134254	−	0.184785i	0.0106471	−	0.0146544i
$160$	−11.8239	−	4.49402i	−0.934759	−	0.355284i
$161$	−19.2415	−	19.2415i	−1.51644	−	1.51644i
$162$	−11.5009	−	5.22150i	−0.903594	−	0.410240i
$163$	−0.577449	+	0.577449i	−0.0452293	+	0.0452293i	−0.729360	−	0.684130i	$-0.760182\pi$
$163$	−0.577449	+	0.577449i	−0.0452293	+	0.0452293i	0.684130	+	0.729360i	$0.260182\pi$
$164$	−9.87403	−	8.15497i	−0.771032	−	0.636796i
$165$	−0.551790	+	0.0219844i	−0.0429568	+	0.00171149i
$166$	5.54420	−	2.08189i	0.430314	−	0.161586i
$167$		−	4.26749i		−	0.330228i	−0.986274	−	0.165114i	$-0.947201\pi$
$167$		−	4.26749i		−	0.330228i	0.986274	−	0.165114i	$-0.0527992\pi$
$168$	0.472794	+	0.681668i	0.0364769	+	0.0525918i
$169$	−6.58774	−	4.78627i	−0.506749	−	0.368175i
$170$	−4.72988	+	1.99439i	−0.362765	+	0.152963i
$171$	−13.1449	−	6.69766i	−1.00522	−	0.512183i
$172$	−0.278522	−	0.111609i	−0.0212371	−	0.00851014i
$173$	−1.36508	+	1.36508i	−0.103785	+	0.103785i	−0.757093	−	0.653307i	$-0.773381\pi$
$173$	−1.36508	+	1.36508i	−0.103785	+	0.103785i	0.653307	+	0.757093i	$0.273381\pi$
$174$	−0.726649	−	0.200405i	−0.0550871	−	0.0151926i
$175$	12.7411	−	10.9062i	0.963135	−	0.824433i
$176$	10.8224	+	3.24150i	0.815768	+	0.244338i
$177$	0.0817567	−	0.251621i	0.00614521	−	0.0189130i
$178$	13.2877	+	16.6562i	0.995954	+	1.24844i
$179$	−20.7975	+	3.29400i	−1.55448	+	0.246205i	−0.873767	−	0.486345i	$-0.838330\pi$
$179$	−20.7975	+	3.29400i	−1.55448	+	0.246205i	−0.680713	+	0.732550i	$0.738330\pi$
$180$	−8.15683	+	10.6089i	−0.607975	+	0.790744i
$181$	2.02554	−	12.7887i	0.150557	−	0.950580i	−0.790532	−	0.612421i	$-0.790196\pi$
$181$	2.02554	−	12.7887i	0.150557	−	0.950580i	0.941089	−	0.338159i	$-0.109804\pi$
$182$	−9.51936	−	4.32188i	−0.705622	−	0.320359i
$183$	0.520785	−	0.169213i	0.0384975	−	0.0125086i
$184$	16.5765	−	15.8656i	1.22204	−	1.16963i
$185$	5.48846	+	14.8519i	0.403519	+	1.09193i
$186$	−0.189586	−	0.925105i	−0.0139011	−	0.0678320i
$187$	4.08493	−	2.08138i	0.298720	−	0.152205i
$188$	−14.0177	+	5.99731i	−1.02235	+	0.437399i
$189$	1.67154	−	0.543118i	0.121587	−	0.0395060i
$190$	−10.0500	+	11.9191i	−0.729101	+	0.864704i
$191$	4.99906	+	4.99906i	0.361719	+	0.361719i	0.864446	−	0.502726i	$-0.167670\pi$
$191$	4.99906	+	4.99906i	0.361719	+	0.361719i	−0.502726	+	0.864446i	$0.667670\pi$
$192$	−0.583398	+	0.385984i	−0.0421031	+	0.0278560i
$193$	−12.0084	+	16.5281i	−0.864381	+	1.18972i	0.116126	+	0.993234i	$0.462952\pi$
$193$	−12.0084	+	16.5281i	−0.864381	+	1.18972i	−0.980507	+	0.196484i	$0.937048\pi$
$194$	10.8713	−	6.17115i	0.780517	−	0.443062i
$195$	−0.0504123	+	0.427952i	−0.00361010	+	0.0306463i
$196$	8.28996	+	1.88906i	0.592140	+	0.134933i
$197$	−21.4312	−	3.39437i	−1.52691	−	0.241839i	−0.664207	−	0.747548i	$-0.731231\pi$
$197$	−21.4312	−	3.39437i	−1.52691	−	0.241839i	−0.862704	+	0.505709i	$0.831231\pi$
$198$	6.58266	−	9.97612i	0.467809	−	0.708972i
$199$	−9.41458	−	18.4772i	−0.667382	−	1.30981i	−0.937836	−	0.347078i	$-0.887174\pi$
$199$	−9.41458	−	18.4772i	−0.667382	−	1.30981i	0.270454	−	0.962733i	$-0.412826\pi$
$200$	8.95883	+	10.9425i	0.633485	+	0.773755i
$201$	−0.570675	−	0.414620i	−0.0402523	−	0.0292450i
$202$	−11.8630	−	14.8704i	−0.834679	−	1.04628i
$203$	−18.2178	+	9.28242i	−1.27864	+	0.651498i
$204$	−0.0630709	+	0.276781i	−0.00441585	+	0.0193786i
$205$	5.02946	+	13.4054i	0.351273	+	0.936273i
$206$	−5.65909	+	4.51460i	−0.394287	+	0.314547i
$207$	−11.0208	−	21.6295i	−0.765999	−	1.50336i
$208$	3.81932	−	7.94522i	0.264822	−	0.550902i
$209$	8.18466	−	11.2652i	0.566145	−	0.779232i
$210$	−0.0786290	−	0.924162i	−0.00542592	−	0.0637732i
$211$	−8.74091	+	4.45372i	−0.601749	+	0.306607i	−0.728198	−	0.685367i	$-0.759642\pi$
$211$	−8.74091	+	4.45372i	−0.601749	+	0.306607i	0.126449	+	0.991973i	$0.459642\pi$
$212$	5.20308	−	0.470133i	0.357349	−	0.0322889i
$213$	−0.184575	+	1.16536i	−0.0126469	+	0.0798492i
$214$	−6.85226	+	5.46647i	−0.468411	+	0.373680i
$215$	0.207832	+	0.263335i	0.0141740	+	0.0179593i
$216$	0.426980	+	1.41919i	0.0290523	+	0.0965635i
$217$	−20.7230	−	15.0562i	−1.40677	−	1.02208i
$218$	5.74821	+	15.3078i	0.389318	+	1.03678i
$219$	−0.632995	+	0.632995i	−0.0427739	+	0.0427739i
$220$	−8.68567	−	9.17052i	−0.585588	−	0.618277i
$221$	−1.10549	−	3.40236i	−0.0743636	−	0.228868i
$222$	0.844120	+	0.232802i	0.0566536	+	0.0156247i
$223$	−8.02402	−	15.7480i	−0.537328	−	1.05457i	−0.986902	−	0.161323i	$-0.948424\pi$
$223$	−8.02402	−	15.7480i	−0.537328	−	1.05457i	0.449574	−	0.893243i	$-0.351576\pi$
$224$	−4.62008	+	18.4037i	−0.308692	+	1.22965i
$225$	13.8166	−	5.74085i	0.921104	−	0.382724i
$226$	−13.4801	−	8.89474i	−0.896684	−	0.591669i
$227$	−0.114809	−	0.353345i	−0.00762012	−	0.0234523i	0.947174	−	0.320720i	$-0.103925\pi$
$227$	−0.114809	−	0.353345i	−0.00762012	−	0.0234523i	−0.954794	+	0.297267i	$0.903925\pi$
$228$	0.210964	+	0.835990i	0.0139715	+	0.0553648i
$229$	18.0658	+	2.86135i	1.19382	+	0.189083i	0.721546	−	0.692366i	$-0.243432\pi$
$229$	18.0658	+	2.86135i	1.19382	+	0.189083i	0.472279	+	0.881449i	$0.343432\pi$
$230$	−24.9066	+	6.14675i	−1.64229	+	0.405304i
$231$	0.129588	+	0.818188i	0.00852628	+	0.0538328i
$232$	−7.48874	−	15.5295i	−0.491660	−	1.01956i
$233$	19.2371	+	6.25052i	1.26027	+	0.409485i	0.861589	−	0.507606i	$-0.169470\pi$
$233$	19.2371	+	6.25052i	1.26027	+	0.409485i	0.398677	+	0.917092i	$0.369470\pi$
$234$	−6.88514	−	6.29107i	−0.450096	−	0.411260i
$235$	16.9294	+	1.99426i	1.10435	+	0.130091i
$236$	5.56361	−	2.38032i	0.362160	−	0.154945i
$237$	0.430358	+	0.430358i	0.0279548	+	0.0279548i
$238$	3.80128	+	6.69649i	0.246400	+	0.434069i
$239$	−8.51644	+	16.7145i	−0.550883	+	1.08117i	0.432839	+	0.901471i	$0.357512\pi$
$239$	−8.51644	+	16.7145i	−0.550883	+	1.08117i	−0.983722	+	0.179697i	$0.942488\pi$
$240$	0.780544	−	0.0492124i	0.0503839	−	0.00317665i
$241$	−16.3073	+	22.4451i	−1.05045	+	1.44582i	−0.162028	+	0.986786i	$0.551803\pi$
$241$	−16.3073	+	22.4451i	−1.05045	+	1.44582i	−0.888420	+	0.459031i	$0.848197\pi$
$242$	−3.15613	−	2.88381i	−0.202883	−	0.185378i
$243$	2.35288			0.150938
$244$	10.7541	+	6.42013i	0.688460	+	0.411007i
$245$	−6.98406	−	6.44887i	−0.446196	−	0.412003i
$246$	0.764345	+	0.206735i	0.0487329	+	0.0131810i
$247$	−7.68311	−	7.68311i	−0.488865	−	0.488865i
$248$	13.0756	−	17.1919i	0.830300	−	1.09168i
$249$	−0.258921	+	0.258921i	−0.0164084	+	0.0164084i
$250$	−2.58956	−	15.5979i	−0.163778	−	0.986497i
$251$	−8.87634	−	6.44904i	−0.560270	−	0.407060i	0.271288	−	0.962498i	$-0.412550\pi$
$251$	−8.87634	−	6.44904i	−0.560270	−	0.407060i	−0.831558	+	0.555438i	$0.812550\pi$
$252$	17.2365	+	10.2901i	1.08580	+	0.648215i
$253$	21.7911	−	7.08035i	1.36999	−	0.445138i
$254$	2.94436	−	10.6760i	0.184746	−	0.669871i
$255$	0.215312	−	0.233181i	0.0134833	−	0.0146023i
$256$	−15.4294	−	4.23485i	−0.964337	−	0.264678i
$257$	9.75238	−	7.08552i	0.608337	−	0.441983i	−0.240491	−	0.970651i	$-0.577309\pi$
$257$	9.75238	−	7.08552i	0.608337	−	0.441983i	0.848828	+	0.528669i	$0.177309\pi$
$258$	0.0185334		0.000835606i	0.00115384		5.20226e-5i
$259$	21.1629	−	10.7830i	1.31500	−	0.670025i
$260$	−8.12804	+	5.57469i	−0.504080	+	0.345727i
$261$	−18.0155	+	2.85338i	−1.11513	+	0.176620i
$262$	13.8716	−	2.84276i	0.856988	−	0.175626i
$263$	−1.33587	−	1.83867i	−0.0823735	−	0.113377i	0.765842	−	0.643029i	$-0.222323\pi$
$263$	−1.33587	−	1.83867i	−0.0823735	−	0.113377i	−0.848215	+	0.529652i	$0.822323\pi$
$264$	−0.692147	+	0.0941302i	−0.0425987	+	0.00579331i
$265$	−5.30573	−	2.44243i	−0.325929	−	0.150037i
$266$	19.5206	+	12.8805i	1.19689	+	0.789754i
$267$	−1.17383	−	0.598095i	−0.0718370	−	0.0366028i
$268$	−1.45192	−	16.0687i	−0.0886901	−	0.981555i
$269$	14.7229	+	4.78375i	0.897669	+	0.291670i	0.721275	−	0.692649i	$-0.243557\pi$
$269$	14.7229	+	4.78375i	0.897669	+	0.291670i	0.176394	+	0.984320i	$0.443557\pi$
$270$	0.376591	−	1.61359i	0.0229186	−	0.0982003i
$271$	−9.41706	+	3.05979i	−0.572045	+	0.185869i	−0.580734	−	0.814093i	$-0.697234\pi$
$271$	−9.41706	+	3.05979i	−0.572045	+	0.185869i	0.00868853	+	0.999962i	$0.497234\pi$
$272$	−5.71554	+	3.08086i	−0.346555	+	0.186804i
$273$	0.646402			0.0391221
$274$	−4.84755	+	10.6772i	−0.292851	+	0.645034i
$275$	3.31179	+	13.7279i	0.199709	+	0.827826i
$276$	−0.527718	+	1.31692i	−0.0317649	+	0.0792695i
$277$	−4.35321	+	27.4851i	−0.261559	+	1.65142i	0.411190	+	0.911550i	$0.365113\pi$
$277$	−4.35321	+	27.4851i	−0.261559	+	1.65142i	−0.672750	+	0.739870i	$0.734887\pi$
$278$	−0.512756	+	4.55805i	−0.0307531	+	0.273374i
$279$	−13.4316	−	18.4870i	−0.804128	−	1.10679i
$280$	14.7298	−	15.2671i	0.880273	−	0.912381i
$281$	8.21034	+	16.1137i	0.489788	+	0.961263i	0.995151	+	0.0983562i	$0.0313584\pi$
$281$	8.21034	+	16.1137i	0.489788	+	0.961263i	−0.505363	+	0.862907i	$0.668642\pi$
$282$	0.635895	−	0.695943i	0.0378670	−	0.0414428i
$283$	11.2918	−	1.78844i	0.671225	−	0.106312i	0.188486	−	0.982076i	$-0.439642\pi$
$283$	11.2918	−	1.78844i	0.671225	−	0.106312i	0.482739	+	0.875764i	$0.339642\pi$
$284$	−22.8456	+	14.3661i	−1.35564	+	0.852469i
$285$	0.261148	−	0.927919i	0.0154691	−	0.0549652i
$286$	6.88137	−	5.48969i	0.406904	−	0.324612i
$287$	19.0885	−	9.84538i	1.12676	−	0.581154i
$288$	−8.99325	+	14.3407i	−0.529932	+	0.845033i
$289$	4.43905	−	13.6620i	0.261120	−	0.803646i
$290$	−1.39056	+	19.2257i	−0.0816565	+	1.12897i
$291$	−0.454312	+	0.625307i	−0.0266322	+	0.0366561i
$292$	−20.4295	−	1.37016i	−1.19554	−	0.0801826i
$293$	−3.92211	+	12.0710i	−0.229132	+	0.705197i	0.768714	+	0.639593i	$0.220897\pi$
$293$	−3.92211	+	12.0710i	−0.229132	+	0.705197i	−0.997846	+	0.0656033i	$0.979103\pi$
$294$	−0.515004	+	0.105542i	−0.0300357	+	0.00615534i
$295$	−6.71923	−	0.791518i	−0.391209	−	0.0460840i
$296$	8.69938	+	18.0401i	0.505641	+	1.04856i
$297$	−0.231506	+	1.46167i	−0.0134334	+	0.0848149i
$298$	2.60838	−	9.45775i	0.151099	−	0.547872i
$299$	−2.79689	−	17.6588i	−0.161748	−	1.02124i
$300$	−0.784072	−	0.387066i	−0.0452684	−	0.0223473i
$301$	0.355838	−	0.355838i	0.0205101	−	0.0205101i
$302$	−0.903410	−	20.0373i	−0.0519854	−	1.15301i
$303$	1.04797	+	0.533968i	0.0602044	+	0.0306757i
$304$	−11.2192	+	16.2184i	−0.643467	+	0.930189i
$305$	−6.84892	−	12.2138i	−0.392168	−	0.699362i
$306$	1.37910	+	6.72945i	0.0788377	+	0.384697i
$307$	6.53128	+	3.32785i	0.372760	+	0.189930i	0.630327	−	0.776330i	$-0.282921\pi$
$307$	6.53128	+	3.32785i	0.372760	+	0.189930i	−0.257567	+	0.966260i	$0.582921\pi$
$308$	−12.1378	+	14.5491i	−0.691614	+	0.829014i
$309$	0.203208	−	0.398818i	0.0115601	−	0.0226879i
$310$	−22.2516	+	9.38254i	−1.26380	+	0.532893i
$311$	−0.479154	−	0.0758905i	−0.0271703	−	0.00430335i	0.142835	−	0.989747i	$-0.454378\pi$
$311$	−0.479154	−	0.0758905i	−0.0271703	−	0.00430335i	−0.170005	+	0.985443i	$0.554378\pi$
$312$	−0.0119422	+	0.544934i	−0.000676097	+	0.0308508i
$313$	−0.0229018	−	0.0166392i	−0.00129449	−	0.000940501i	0.587138	−	0.809487i	$-0.300255\pi$
$313$	−0.0229018	−	0.0166392i	−0.00129449	−	0.000940501i	−0.588432	+	0.808546i	$0.700255\pi$
$314$	−0.279832	+	2.48752i	−0.0157918	+	0.140379i
$315$	−10.9774	−	19.5762i	−0.618504	−	1.10299i
$316$	−0.931539	+	13.8895i	−0.0524031	+	0.781345i
$317$	22.6714	−	16.4718i	1.27335	−	0.925146i	0.274024	−	0.961723i	$-0.411645\pi$
$317$	22.6714	−	16.4718i	1.27335	−	0.925146i	0.999331	+	0.0365769i	$0.0116454\pi$
$318$	−0.280913	+	0.159461i	−0.0157528	+	0.00894212i
$319$		−	17.2160i		−	0.963913i
$320$	12.5984	+	12.6996i	0.704271	+	0.709931i
$321$	0.246052	−	0.482905i	0.0137333	−	0.0269531i
$322$	13.5283	+	36.0267i	0.753902	+	2.00769i
$323$	1.25193	+	7.90439i	0.0696594	+	0.439812i
$324$	11.7572	+	13.4476i	0.653176	+	0.747088i
$325$	10.9845	−	0.876681i	0.609310	−	0.0486295i
$326$	1.08118	−	0.405992i	0.0598812	−	0.0224858i
$327$	−0.714894	−	0.714894i	−0.0395337	−	0.0395337i
$328$	7.94724	+	16.2739i	0.438813	+	0.898578i
$329$		−	25.5710i		−	1.40978i
$330$	0.723399	+	0.294285i	0.0398218	+	0.0161998i
$331$	−14.1122	+	14.1122i	−0.775675	+	0.775675i	−0.979092	−	0.203417i	$-0.934795\pi$
$331$	−14.1122	+	14.1122i	−0.775675	+	0.775675i	0.203417	+	0.979092i	$0.434795\pi$
$332$	−8.35648	−	0.560451i	−0.458622	−	0.0307588i
$333$	20.9280	−	3.31466i	1.14685	−	0.181642i
$334$	−2.49492	+	5.49530i	−0.136516	+	0.300689i
$335$	−7.54300	+	16.3858i	−0.412118	+	0.895251i
$336$	−0.210297	−	1.15420i	−0.0114727	−	0.0629670i
$337$	−15.5590	−	15.5590i	−0.847552	−	0.847552i	0.142275	−	0.989827i	$-0.454558\pi$
$337$	−15.5590	−	15.5590i	−0.847552	−	0.847552i	−0.989827	+	0.142275i	$0.954558\pi$
$338$	5.68490	+	10.0148i	0.309218	+	0.544731i
$339$	0.986274	+	0.156210i	0.0535670	+	0.00848419i
$340$	7.25672	+	0.197043i	0.393551	+	0.0106862i
$341$	19.2174	−	9.79177i	1.04068	−	0.530254i
$342$	13.0112	+	16.3096i	0.703564	+	0.881922i
$343$	5.41946	−	7.45925i	0.292623	−	0.402762i
$344$	0.293406	+	0.306554i	0.0158194	+	0.0165283i
$345$	1.24511	−	0.982681i	0.0670346	−	0.0529058i
$346$	2.55591	−	0.959762i	0.137407	−	0.0515971i
$347$	4.99525	+	15.3738i	0.268159	+	0.825309i	0.990949	+	0.134241i	$0.0428596\pi$
$347$	4.99525	+	15.3738i	0.268159	+	0.825309i	−0.722790	+	0.691068i	$0.757140\pi$
$348$	0.818552	+	0.682887i	0.0438790	+	0.0366066i
$349$	8.25397	+	25.4031i	0.441825	+	1.35980i	0.885928	+	0.463822i	$0.153522\pi$
$349$	8.25397	+	25.4031i	0.441825	+	1.35980i	−0.444103	+	0.895976i	$0.646478\pi$
$350$	−22.7830	+	6.59522i	−1.21780	+	0.352529i
$351$	1.09826	+	0.356847i	0.0586210	+	0.0190471i
$352$	−12.0410	−	10.5013i	−0.641789	−	0.559719i
$353$	6.67274	−	13.0960i	0.355154	−	0.697029i	−0.642442	−	0.766335i	$-0.722078\pi$
$353$	6.67274	−	13.0960i	0.355154	−	0.697029i	0.997595	+	0.0693059i	$0.0220785\pi$
$354$	−0.252385	+	0.276218i	−0.0134141	+	0.0146808i
$355$	30.1486	−	1.20118i	1.60012	−	0.0637521i
$356$	−7.37295	−	29.2168i	−0.390765	−	1.54849i
$357$	−0.385174	−	0.279845i	−0.0203856	−	0.0148110i
$358$	28.7070	+	7.91719i	1.51721	+	0.418437i
$359$	26.3433	−	19.1395i	1.39035	−	1.01015i	0.394518	−	0.918888i	$-0.370912\pi$
$359$	26.3433	−	19.1395i	1.39035	−	1.01015i	0.995827	−	0.0912570i	$-0.0290885\pi$
$360$	16.7060	−	8.89252i	0.880484	−	0.468677i
$361$	3.11921	+	4.29323i	0.164169	+	0.225959i
$362$	−10.0850	+	15.2840i	−0.530058	+	0.803311i
$363$	0.251399	+	0.0816844i	0.0131950	+	0.00428732i
$364$	9.73149	+	11.1307i	0.510069	+	0.583406i
$365$	19.0411	+	12.7077i	0.996658	+	0.665152i
$366$	−0.769549	−	0.0865700i	−0.0402249	−	0.00452509i
$367$	13.0154	+	25.5442i	0.679398	+	1.33339i	0.930806	+	0.365513i	$0.119106\pi$
$367$	13.0154	+	25.5442i	0.679398	+	1.33339i	−0.251408	+	0.967881i	$0.580894\pi$
$368$	−30.6214	+	10.7391i	−1.59625	+	0.559814i
$369$	18.9094	−	3.09099i	0.984387	−	0.160910i
$370$	1.61536	−	22.3337i	0.0839786	−	1.16107i
$371$	−2.70756	+	8.33302i	−0.140570	+	0.432629i
$372$	−0.296715	+	1.30211i	−0.0153840	+	0.0675111i
$373$	−1.68630	−	10.6469i	−0.0873131	−	0.551273i	−0.992104	−	0.125417i	$-0.959973\pi$
$373$	−1.68630	−	10.6469i	−0.0873131	−	0.551273i	0.904791	−	0.425856i	$-0.140027\pi$
$374$	−6.47706	+	0.292028i	−0.334921	+	0.0151004i
$375$	0.544478	+	0.811960i	0.0281167	+	0.0419294i
$376$	21.5570	+	0.472424i	1.11172	+	0.0243634i
$377$	−13.2685	−	2.10153i	−0.683365	−	0.108234i
$378$	−2.46999	−	0.277861i	−0.127043	−	0.0142916i
$379$	−25.7316	+	18.6951i	−1.32174	+	0.960301i	−0.321832	+	0.946797i	$0.604299\pi$
$379$	−25.7316	+	18.6951i	−1.32174	+	0.960301i	−0.999909	+	0.0135045i	$0.995701\pi$
$380$	19.9098	−	9.47286i	1.02135	−	0.485948i
$381$	0.107117	+	0.676310i	0.00548777	+	0.0346484i
$382$	−3.51473	−	9.35997i	−0.179829	−	0.478897i
$383$			12.0350i			0.614959i	0.951555	+	0.307480i	$0.0994856\pi$
$383$			12.0350i			0.614959i	−0.951555	+	0.307480i	$0.900514\pi$
$384$	0.976908	−	0.155962i	0.0498526	−	0.00795890i
$385$	19.8704	−	7.34303i	1.01269	−	0.374235i
$386$	25.1262	−	14.2629i	1.27889	−	0.725965i
$387$	0.400001	−	0.203810i	0.0203332	−	0.0103603i
$388$	−17.6070	+	1.59091i	−0.893861	+	0.0807664i
$389$	−6.55855	−	20.1851i	−0.332532	−	1.02343i	−0.967925	−	0.251238i	$-0.919162\pi$
$389$	−6.55855	−	20.1851i	−0.332532	−	1.02343i	0.635394	−	0.772188i	$-0.280838\pi$
$390$	0.315112	−	0.521607i	0.0159563	−	0.0264126i
$391$	−5.97841	+	11.7333i	−0.302341	+	0.593378i
$392$	−9.57069	−	7.27915i	−0.483393	−	0.367653i
$393$	−0.708297	+	0.514608i	−0.0357289	+	0.0259585i
$394$	25.6128	+	16.9004i	1.29035	+	0.851429i
$395$	8.63966	−	12.9456i	0.434708	−	0.651364i
$396$	−14.3089	+	8.99794i	−0.719052	+	0.452163i
$397$	−5.68490	+	17.4963i	−0.285317	+	0.878115i	0.700987	+	0.713174i	$0.252743\pi$
$397$	−5.68490	+	17.4963i	−0.285317	+	0.878115i	−0.986304	+	0.164941i	$0.947257\pi$
$398$	1.32092	+	29.2974i	0.0662115	+	1.46854i
$399$	−1.42823	−	0.226209i	−0.0715008	−	0.0113246i
$400$	−5.13902	−	19.3285i	−0.256951	−	0.966424i
$401$		−	18.9583i		−	0.946733i	−0.880866	−	0.473366i	$-0.843039\pi$
$401$		−	18.9583i		−	0.946733i	0.880866	−	0.473366i	$-0.156961\pi$
$402$	0.492465	+	0.867547i	0.0245619	+	0.0432693i
$403$	−5.20076	−	16.0063i	−0.259068	−	0.797330i
$404$	6.58244	+	26.0843i	0.327489	+	1.29774i
$405$	−3.90692	−	19.5850i	−0.194136	−	0.973186i
$406$	28.8861	−	1.30237i	1.43359	−	0.0646357i
$407$			19.9992i			0.991324i
$408$	0.243033	−	0.319541i	0.0120319	−	0.0158197i
$409$			0.258705i			0.0127922i	0.999980	+	0.00639608i	$0.00203595\pi$
$409$			0.258705i			0.0127922i	−0.999980	+	0.00639608i	$0.997964\pi$
$410$	1.36073	−	20.2027i	0.0672019	−	0.997739i
$411$		−	0.725025i		−	0.0357628i
$412$	9.92667	−	2.50502i	0.489052	−	0.123414i
$413$			10.1491i			0.499404i
$414$	1.54628	+	34.2958i	0.0759954	+	1.68555i
$415$	7.78860	+	5.19797i	0.382327	+	0.255158i
$416$	−9.56323	+	7.99826i	−0.468876	+	0.392147i
$417$	−0.0876377	−	0.269721i	−0.00429164	−	0.0132083i
$418$	−17.1255	+	9.72134i	−0.837636	+	0.475486i
$419$			16.3736i			0.799904i	0.916536	+	0.399952i	$0.130973\pi$
$419$			16.3736i			0.799904i	−0.916536	+	0.399952i	$0.869027\pi$
$420$	−0.439044	+	1.23602i	−0.0214232	+	0.0603118i
$421$	−29.1808	−	4.62178i	−1.42218	−	0.225252i	−0.602523	−	0.798101i	$-0.705838\pi$
$421$	−29.1808	−	4.62178i	−1.42218	−	0.225252i	−0.819661	+	0.572849i	$0.805838\pi$
$422$	13.8596	−	0.624880i	0.674674	−	0.0304187i
$423$	7.04926	−	21.6954i	0.342747	−	1.05487i
$424$	−6.97492	−	2.43650i	−0.338732	−	0.118327i
$425$	−6.92491	−	4.23310i	−0.335907	−	0.205335i
$426$	0.918988	−	1.39274i	0.0445251	−	0.0674785i
$427$	−16.9940	+	12.3469i	−0.822397	+	0.597507i
$428$	12.0196	−	3.03318i	0.580990	−	0.146614i
$429$	−0.247098	+	0.484956i	−0.0119300	+	0.0234139i
$430$	−0.113673	−	0.460605i	−0.00548181	−	0.0222123i
$431$	−3.61303	−	11.1197i	−0.174033	−	0.535619i	0.825555	−	0.564322i	$-0.190862\pi$
$431$	−3.61303	−	11.1197i	−0.174033	−	0.535619i	−0.999588	+	0.0287027i	$0.990862\pi$
$432$	0.279877	−	2.07713i	0.0134656	−	0.0999361i
$433$	−5.05567	+	2.57599i	−0.242960	+	0.123794i	−0.571231	−	0.820789i	$-0.693534\pi$
$433$	−5.05567	+	2.57599i	−0.242960	+	0.123794i	0.328271	+	0.944584i	$0.393534\pi$
$434$	17.8830	+	31.5034i	0.858410	+	1.51221i
$435$	−0.413128	−	1.11793i	−0.0198080	−	0.0536009i
$436$	1.54744	−	23.0727i	0.0741088	−	1.10498i
$437$			39.9960i			1.91327i
$438$	1.18519	−	0.445046i	0.0566304	−	0.0212651i
$439$	2.16546	+	13.6722i	0.103352	+	0.652538i	0.983919	+	0.178616i	$0.0571621\pi$
$439$	2.16546	+	13.6722i	0.103352	+	0.652538i	−0.880567	+	0.473922i	$0.842838\pi$
$440$	5.82325	+	16.8869i	0.277613	+	0.805053i
$441$	−10.2917	+	7.47734i	−0.490080	+	0.356064i
$442$	−0.565575	+	5.02757i	−0.0269016	+	0.239137i
$443$	−29.7904	−	4.71834i	−1.41539	−	0.224175i	−0.598569	−	0.801071i	$-0.704264\pi$
$443$	−29.7904	−	4.71834i	−1.41539	−	0.224175i	−0.816817	+	0.576896i	$0.804264\pi$
$444$	−0.950880	−	0.793283i	−0.0451268	−	0.0376476i
$445$	−9.12681	+	32.4296i	−0.432652	+	1.53731i
$446$	1.12581	+	24.9700i	0.0533088	+	1.18237i
$447$	0.0948938	+	0.599136i	0.00448832	+	0.0283381i
$448$	16.7087	−	20.9976i	0.789413	−	0.992042i
$449$	10.5273	−	32.3997i	0.496814	−	1.52904i	−0.317297	−	0.948326i	$-0.602775\pi$
$449$	10.5273	−	32.3997i	0.496814	−	1.52904i	0.814111	−	0.580709i	$-0.197225\pi$
$450$	−21.1480	−	0.685047i	−0.996928	−	0.0322934i
$451$	0.0895198	+	18.0845i	0.00421532	+	0.851564i
$452$	12.1584	+	19.3348i	0.571881	+	0.909432i
$453$	0.563021	+	1.10499i	0.0264531	+	0.0519170i
$454$	−0.0587365	+	0.522128i	−0.00275664	+	0.0245047i
$455$	−3.23379	−	16.2106i	−0.151602	−	0.759967i
$456$	0.217086	−	1.19985i	0.0101660	−	0.0561882i
$457$	19.9057	+	6.46776i	0.931151	+	0.302549i	0.735033	−	0.678031i	$-0.237167\pi$
$457$	19.9057	+	6.46776i	0.931151	+	0.302549i	0.196118	+	0.980580i	$0.437167\pi$
$458$	−21.5908	−	14.2465i	−1.00887	−	0.665695i
$459$	−0.499937	−	0.688105i	−0.0233351	−	0.0321180i
$460$	35.6662	+	6.64600i	1.66294	+	0.309871i
$461$	−26.6317	+	19.3491i	−1.24036	+	0.901176i	−0.997622	−	0.0689158i	$-0.978046\pi$
$461$	−26.6317	+	19.3491i	−1.24036	+	0.901176i	−0.242739	+	0.970092i	$0.578046\pi$
$462$	0.311467	−	1.12935i	0.0144908	−	0.0525422i
$463$	−4.96941	−	3.61048i	−0.230948	−	0.167793i	0.466293	−	0.884630i	$-0.345589\pi$
$463$	−4.96941	−	3.61048i	−0.230948	−	0.167793i	−0.697241	+	0.716837i	$0.745589\pi$
$464$	0.564265	+	24.3758i	0.0261953	+	1.13162i
$465$	1.01293	−	1.09699i	0.0469733	−	0.0508717i
$466$	−21.1176	−	19.2955i	−0.978255	−	0.893848i
$467$	4.17478	−	8.19346i	0.193186	−	0.379148i	−0.774013	−	0.633170i	$-0.781753\pi$
$467$	4.17478	−	8.19346i	0.193186	−	0.379148i	0.967199	+	0.254022i	$0.0817535\pi$
$468$	5.18812	+	12.1264i	0.239821	+	0.560542i
$469$	25.7350	+	8.36180i	1.18833	+	0.386112i
$470$	−20.6342	−	12.4655i	−0.951787	−	0.574991i
$471$	−0.0478276	−	0.147198i	−0.00220378	−	0.00678253i
$472$	−8.55594	−	0.187504i	−0.393819	−	0.00863056i
$473$	0.130939	+	0.402988i	0.00602057	+	0.0185294i
$474$	−0.302576	−	0.805779i	−0.0138978	−	0.0370107i
$475$	−24.5770	−	1.90700i	−1.12767	−	0.0874992i
$476$	−0.979965	−	10.8455i	−0.0449166	−	0.497103i
$477$	−4.59439	+	6.32363i	−0.210363	+	0.289539i
$478$	20.7386	−	16.5444i	0.948560	−	0.756724i
$479$	−23.1893	+	11.8155i	−1.05955	+	0.539865i	−0.894798	−	0.446471i	$-0.852681\pi$
$479$	−23.1893	+	11.8155i	−1.05955	+	0.539865i	−0.164747	+	0.986336i	$0.552681\pi$
$480$	−1.03389	−	0.392961i	−0.0471903	−	0.0179361i
$481$	15.4135	+	2.44127i	0.702797	+	0.111312i
$482$	34.1213	−	19.3691i	1.55418	−	0.882237i
$483$	−1.68249	−	1.68249i	−0.0765560	−	0.0765560i
$484$	2.37821	+	5.55869i	0.108101	+	0.252668i
$485$	17.9544	+	8.26510i	0.815268	+	0.375299i
$486$	−3.02984	−	1.37557i	−0.137436	−	0.0623973i
$487$	−38.7387	+	6.13561i	−1.75542	+	0.278031i	−0.949448	−	0.313924i	$-0.898356\pi$
$487$	−38.7387	+	6.13561i	−1.75542	+	0.278031i	−0.805971	+	0.591955i	$0.798356\pi$
$488$	−10.0948	−	14.5545i	−0.456968	−	0.658850i
$489$	−0.0504926	+	0.0504926i	−0.00228335	+	0.00228335i
$490$	5.22325	+	12.3874i	0.235962	+	0.559606i
$491$		−	9.05402i		−	0.408602i	−0.978908	−	0.204301i	$-0.934508\pi$
$491$		−	9.05402i		−	0.408602i	0.978908	−	0.204301i	$-0.0654921\pi$
$492$	−0.863393	−	0.713077i	−0.0389247	−	0.0321480i
$493$	6.99656	+	6.99656i	0.315109	+	0.315109i
$494$	5.40184	+	14.3854i	0.243040	+	0.647231i
$495$	18.8831	−	0.752340i	0.848731	−	0.0338152i
$496$	−26.8885	+	14.4938i	−1.20733	+	0.650790i
$497$	−7.08042	−	44.7040i	−0.317600	−	2.00525i
$498$	0.484789	−	0.182042i	0.0217239	−	0.00815749i
$499$	−3.93488	+	7.72264i	−0.176149	+	0.345713i	−0.962153	−	0.272509i	$-0.912147\pi$
$499$	−3.93488	+	7.72264i	−0.176149	+	0.345713i	0.786004	+	0.618222i	$0.212147\pi$
$500$	−5.78444	+	21.5995i	−0.258688	+	0.965961i
$501$		−	0.373153i		−	0.0166712i
$502$	7.65986	+	13.4939i	0.341876	+	0.602263i
$503$	−7.18103	+	5.21733i	−0.320186	+	0.232629i	−0.736255	−	0.676704i	$-0.763408\pi$
$503$	−7.18103	+	5.21733i	−0.320186	+	0.232629i	0.416069	+	0.909333i	$0.363408\pi$
$504$	−16.1797	−	23.3277i	−0.720702	−	1.03910i
$505$	8.14826	−	28.9526i	0.362593	−	1.28837i
$506$	−32.2001	−	3.62233i	−1.43147	−	0.161032i
$507$	−0.576037	−	0.418515i	−0.0255827	−	0.0185869i
$508$	−10.0330	+	12.0262i	−0.445144	+	0.533578i
$509$	9.61667	+	1.52313i	0.426251	+	0.0675116i	0.365875	−	0.930664i	$-0.380770\pi$
$509$	9.61667	+	1.52313i	0.426251	+	0.0675116i	0.0603765	+	0.998176i	$0.480770\pi$
$510$	−0.413585	+	0.174391i	−0.0183138	+	0.00772217i
$511$	15.5901	−	30.5973i	0.689665	−	1.35354i
$512$	17.3928	+	14.4738i	0.768660	+	0.639658i
$513$	−2.30174	−	1.17279i	−0.101624	−	0.0517801i
$514$	−16.7007	+	3.42255i	−0.736636	+	0.150962i
$515$	−11.0182	−	3.10091i	−0.485522	−	0.136643i
$516$	−0.0243542	−	0.00975921i	−0.00107213	−	0.000429625i
$517$	19.1844	+	9.77494i	0.843729	+	0.429901i
$518$	−33.5558	+	1.51292i	−1.47436	+	0.0664737i
$519$	−0.119364	+	0.119364i	−0.00523950	+	0.00523950i
$520$	13.7257	−	2.42667i	0.601913	−	0.106417i
$521$	−5.96773	−	37.6787i	−0.261451	−	1.65074i	−0.673216	−	0.739446i	$-0.735088\pi$
$521$	−5.96773	−	37.6787i	−0.261451	−	1.65074i	0.411766	−	0.911290i	$-0.364912\pi$
$522$	24.8670	+	6.85815i	1.08840	+	0.300173i
$523$	−6.40663	+	40.4499i	−0.280143	+	1.76875i	0.299711	+	0.954030i	$0.403110\pi$
$523$	−6.40663	+	40.4499i	−0.280143	+	1.76875i	−0.579854	+	0.814721i	$0.696890\pi$
$524$	−19.5246	−	4.44912i	−0.852935	−	0.194361i
$525$	1.11409	−	0.953649i	0.0486229	−	0.0416206i
$526$	0.645272	+	3.14868i	0.0281352	+	0.137289i
$527$	−3.83057	+	11.7893i	−0.166862	+	0.513549i
$528$	0.946318	+	0.283440i	0.0411832	+	0.0123351i
$529$	−25.1644	+	34.6359i	−1.09411	+	1.50591i
$530$	5.40433	+	6.24706i	0.234749	+	0.271355i
$531$	−2.79784	+	8.61085i	−0.121416	+	0.373679i
$532$	−17.6066	−	27.9988i	−0.763341	−	1.21390i
$533$	13.9488	+	2.13854i	0.604188	+	0.0926306i
$534$	1.16189	+	1.45643i	0.0502797	+	0.0630260i
$535$	−13.3413	−	3.75471i	−0.576796	−	0.162330i
$536$	−7.52467	+	21.5408i	−0.325016	+	0.930419i
$537$	−1.81855	+	0.288030i	−0.0784763	+	0.0124294i
$538$	−16.1621	−	14.7676i	−0.696797	−	0.636675i
$539$	−5.45106	−	10.6983i	−0.234794	−	0.460809i
$540$	−1.42830	+	1.85768i	−0.0614643	+	0.0799418i
$541$	−21.7339	−	29.9142i	−0.934415	−	1.28611i	−0.958112	−	0.286393i	$-0.907544\pi$
$541$	−21.7339	−	29.9142i	−0.934415	−	1.28611i	0.0236972	−	0.999719i	$-0.492456\pi$
$542$	13.9153	+	1.56540i	0.597714	+	0.0672396i
$543$	0.177115	−	1.11826i	0.00760072	−	0.0479891i
$544$	9.16114	−	0.625765i	0.392781	−	0.0268295i
$545$	−14.3519	+	21.5047i	−0.614766	+	0.921162i
$546$	−0.832381	−	0.377908i	−0.0356226	−	0.0161730i
$547$	23.2717			0.995025			0.497512	−	0.867457i	$-0.334247\pi$
$547$	23.2717			0.995025			0.497512	+	0.867457i	$0.334247\pi$
$548$	12.4845	−	10.9151i	0.533312	−	0.466272i
$549$	−17.8220	+	5.79073i	−0.760626	+	0.247142i
$550$	3.76117	−	19.6138i	0.160377	−	0.836336i
$551$	28.5814	+	9.28667i	1.21761	+	0.395625i
$552$	1.44947	−	1.38730i	0.0616934	−	0.0590473i
$553$	−20.8023	−	10.5993i	−0.884605	−	0.450729i
$554$	21.6744	−	32.8479i	0.920857	−	1.39557i
$555$	0.479915	+	1.29866i	0.0203712	+	0.0551251i
$556$	3.32507	−	5.56968i	0.141014	−	0.236207i
$557$	3.50229	+	4.82048i	0.148397	+	0.204250i	0.876744	−	0.480958i	$-0.159711\pi$
$557$	3.50229	+	4.82048i	0.148397	+	0.204250i	−0.728347	+	0.685209i	$0.759711\pi$
$558$	6.48791	+	31.6585i	0.274655	+	1.34021i
$559$	0.326569	−	0.0517235i	0.0138124	−	0.00218767i
$560$	−27.8934	+	11.0481i	−1.17871	+	0.466866i
$561$	0.357190	−	0.181997i	0.0150806	−	0.00768393i
$562$	−1.15195	−	25.5499i	−0.0485923	−	1.07776i
$563$	26.7630	−	19.4444i	1.12793	−	0.819486i	0.142534	−	0.989790i	$-0.454475\pi$
$563$	26.7630	−	19.4444i	1.12793	−	0.819486i	0.985392	+	0.170304i	$0.0544751\pi$
$564$	−1.22572	+	0.524409i	−0.0516122	+	0.0220816i
$565$	−1.01659	−	25.5155i	−0.0427683	−	1.07345i
$566$	−15.5861	−	4.29854i	−0.655133	−	0.180681i
$567$	−28.4917	+	9.25752i	−1.19654	+	0.388779i
$568$	37.8174	−	5.14307i	1.58678	−	0.215798i
$569$	1.59465	+	1.15858i	0.0668511	+	0.0485702i	0.620709	−	0.784041i	$-0.286845\pi$
$569$	1.59465	+	1.15858i	0.0668511	+	0.0485702i	−0.553858	+	0.832611i	$0.686845\pi$
$570$	−0.878776	+	1.04222i	−0.0368079	+	0.0436537i
$571$	−1.76942	+	1.76942i	−0.0740479	+	0.0740479i	−0.743161	−	0.669113i	$-0.766674\pi$
$571$	−1.76942	+	1.76942i	−0.0740479	+	0.0740479i	0.669113	+	0.743161i	$0.266674\pi$
$572$	−12.0707	+	3.04607i	−0.504701	+	0.127363i
$573$	0.437121	+	0.437121i	0.0182610	+	0.0182610i
$574$	−30.3364	+	1.51827i	−1.26622	+	0.0633713i
$575$	−30.8729	−	26.3092i	−1.28749	−	1.09717i
$576$	19.9648	−	13.2089i	0.831865	−	0.550372i
$577$	17.3765			0.723393			0.361696	−	0.932296i	$-0.382198\pi$
$577$	17.3765			0.723393			0.361696	+	0.932296i	$0.382198\pi$
$578$	−13.7035	+	14.9975i	−0.569989	+	0.623814i
$579$	−1.05002	+	1.44523i	−0.0436374	+	0.0600617i
$580$	13.0306	−	23.9442i	0.541066	−	0.994227i
$581$	6.37698	−	12.5155i	0.264562	−	0.519232i
$582$	0.950599	−	0.539610i	0.0394036	−	0.0223675i
$583$	−5.21675	−	5.21675i	−0.216056	−	0.216056i
$584$	25.5062	+	13.7081i	1.05546	+	0.567246i
$585$	1.72519	−	14.6452i	0.0713277	−	0.605503i
$586$	12.1077	−	13.2510i	0.500163	−	0.547394i
$587$	36.8064	+	11.9591i	1.51916	+	0.493606i	0.945538	−	0.325512i	$-0.105537\pi$
$587$	36.8064	+	11.9591i	1.51916	+	0.493606i	0.573625	+	0.819118i	$0.305537\pi$
$588$	0.724881	+	0.165181i	0.0298936	+	0.00681194i
$589$	5.88967	+	37.1859i	0.242680	+	1.53222i
$590$	8.18969	+	4.94753i	0.337164	+	0.203687i
$591$	−1.87396	−	0.296807i	−0.0770845	−	0.0122090i
$592$	−0.655485	−	28.3164i	−0.0269403	−	1.16380i
$593$	1.79779	+	5.53303i	0.0738265	+	0.227214i	0.981160	−	0.193197i	$-0.0618857\pi$
$593$	1.79779	+	5.53303i	0.0738265	+	0.227214i	−0.907334	+	0.420412i	$0.861886\pi$
$594$	1.15266	−	1.74687i	0.0472941	−	0.0716749i
$595$	−5.09111	+	11.0595i	−0.208715	+	0.453395i
$596$	−8.88816	+	10.6539i	−0.364073	+	0.436401i
$597$	−0.823218	−	1.61566i	−0.0336921	−	0.0661244i
$598$	−6.72236	+	24.3747i	−0.274898	+	0.996754i
$599$	9.54360	+	29.3722i	0.389941	+	1.20012i	0.932832	+	0.360312i	$0.117330\pi$
$599$	9.54360	+	29.3722i	0.389941	+	1.20012i	−0.542891	+	0.839803i	$0.682670\pi$
$600$	0.783367	+	0.956825i	0.0319808	+	0.0390622i
$601$	−14.9944	+	14.9944i	−0.611635	+	0.611635i	−0.943372	−	0.331737i	$-0.892365\pi$
$601$	−14.9944	+	14.9944i	−0.611635	+	0.611635i	0.331737	+	0.943372i	$0.392365\pi$
$602$	−0.666251	+	0.250182i	−0.0271544	+	0.0101967i
$603$	19.5294	+	14.1889i	0.795297	+	0.577817i
$604$	−10.5511	+	26.3304i	−0.429319	+	1.07137i
$605$	0.790819	−	6.71329i	0.0321514	−	0.272934i
$606$	−1.03731	−	1.30028i	−0.0421379	−	0.0528202i
$607$	−0.549594	+	3.47000i	−0.0223073	+	0.140843i	−0.996328	−	0.0856148i	$-0.972715\pi$
$607$	−0.549594	+	3.47000i	−0.0223073	+	0.140843i	0.974021	+	0.226458i	$0.0727145\pi$
$608$	23.9290	−	14.3255i	0.970447	−	0.580976i
$609$	−1.59298	+	0.811662i	−0.0645507	+	0.0328902i
$610$	1.67883	+	19.7320i	0.0679738	+	0.798926i
$611$	9.87542	−	13.5924i	0.399517	−	0.549888i
$612$	2.15838	−	9.47187i	0.0872474	−	0.382878i
$613$	−3.02985	−	5.94641i	−0.122374	−	0.240173i	0.821690	−	0.569935i	$-0.193032\pi$
$613$	−3.02985	−	5.94641i	−0.122374	−	0.240173i	−0.944064	+	0.329762i	$0.893032\pi$
$614$	−6.46483	−	8.10372i	−0.260899	−	0.327039i
$615$	0.439780	+	1.17218i	0.0177336	+	0.0472668i
$616$	24.1359	−	11.6389i	0.972462	−	0.468946i
$617$	−13.0408	+	6.64461i	−0.525002	+	0.267502i	−0.696342	−	0.717710i	$-0.745190\pi$
$617$	−13.0408	+	6.64461i	−0.525002	+	0.267502i	0.171340	+	0.985212i	$0.445190\pi$
$618$	−0.494835	+	0.394760i	−0.0199052	+	0.0158796i
$619$	−29.2174	−	21.2277i	−1.17434	−	0.853212i	−0.182822	−	0.983146i	$-0.558523\pi$
$619$	−29.2174	−	21.2277i	−1.17434	−	0.853212i	−0.991523	+	0.129934i	$0.958523\pi$
$620$	34.1390	+	0.926983i	1.37105	+	0.0372285i
$621$	−1.92980	−	3.78744i	−0.0774401	−	0.151985i
$622$	0.572644	+	0.377854i	0.0229609	+	0.0151506i
$623$	49.9148	+	7.90572i	1.99979	+	0.316736i
$624$	0.333964	−	0.694736i	0.0133693	−	0.0278117i
$625$	17.6387	−	17.7166i	0.705546	−	0.708664i
$626$	0.0197632	+	0.0348156i	0.000789896	+	0.00139151i
$627$	0.715673	−	0.985040i	0.0285812	−	0.0393387i
$628$	1.81463	−	3.03961i	0.0724116	−	0.121294i
$629$	−8.12764	−	8.12764i	−0.324070	−	0.324070i
$630$	2.69080	+	31.6262i	0.107204	+	1.26002i
$631$	−9.61993	+	3.12571i	−0.382964	+	0.124432i	−0.494171	−	0.869365i	$-0.664528\pi$
$631$	−9.61993	+	3.12571i	−0.382964	+	0.124432i	0.111207	+	0.993797i	$0.464528\pi$
$632$	9.31981	−	17.3411i	0.370722	−	0.689791i
$633$	−0.764312	+	0.389437i	−0.0303787	+	0.0154787i
$634$	−38.8242	+	7.95642i	−1.54191	+	0.315990i
$635$	16.4248	−	6.06971i	0.651798	−	0.240869i
$636$	0.454961	−	0.0411088i	0.0180404	−	0.00163007i
$637$	−8.91067	+	2.89525i	−0.353054	+	0.114714i
$638$	−10.0651	+	22.1693i	−0.398480	+	0.877692i
$639$	6.31643	−	39.8804i	0.249874	−	1.57764i
$640$	−8.79848	−	23.7189i	−0.347790	−	0.937572i
$641$	30.2858	−	4.79679i	1.19622	−	0.189462i	0.473618	−	0.880730i	$-0.342948\pi$
$641$	30.2858	−	4.79679i	1.19622	−	0.189462i	0.722598	+	0.691268i	$0.242948\pi$
$642$	−0.599167	+	0.477992i	−0.0236472	+	0.0188648i
$643$	10.2482	−	31.5408i	0.404151	−	1.24385i	−0.517451	−	0.855713i	$-0.673119\pi$
$643$	10.2482	−	31.5408i	0.404151	−	1.24385i	0.921602	−	0.388136i	$-0.126881\pi$
$644$	3.64186	−	54.3012i	0.143509	−	2.13977i
$645$	0.0181730	+	0.0230262i	0.000715560	+	0.000906655i
$646$	3.00904	−	10.9105i	0.118389	−	0.429268i
$647$	35.5349	−	35.5349i	1.39702	−	1.39702i	0.588581	−	0.808438i	$-0.299687\pi$
$647$	35.5349	−	35.5349i	1.39702	−	1.39702i	0.808438	−	0.588581i	$-0.200313\pi$
$648$	−7.27794	−	24.1903i	−0.285904	−	0.950283i
$649$	−7.61424	−	3.87965i	−0.298885	−	0.152290i
$650$	−14.6574	−	5.29299i	−0.574911	−	0.207608i
$651$	−1.81204	−	1.31652i	−0.0710193	−	0.0515986i
$652$	−1.62961	−	0.109294i	−0.0638205	−	0.00428030i
$653$			6.37159i			0.249339i	0.992198	+	0.124670i	$0.0397871\pi$
$653$			6.37159i			0.249339i	−0.992198	+	0.124670i	$0.960213\pi$
$654$	0.502628	+	1.33853i	0.0196543	+	0.0523406i
$655$	16.4489	+	15.1884i	0.642712	+	0.593460i
$656$	−0.719477	−	25.6024i	−0.0280908	−	0.999605i
$657$	21.6620	−	21.6620i	0.845117	−	0.845117i
$658$	−14.9497	+	32.9282i	−0.582799	+	1.28367i
$659$	−22.2224	−	22.2224i	−0.865664	−	0.865664i	0.126325	−	0.991989i	$-0.459682\pi$
$659$	−22.2224	−	22.2224i	−0.865664	−	0.865664i	−0.991989	+	0.126325i	$0.959682\pi$
$660$	−0.759482	−	0.801878i	−0.0295628	−	0.0312130i
$661$	−14.4899	+	19.9436i	−0.563591	+	0.775716i	−0.991777	−	0.127974i	$-0.959153\pi$
$661$	−14.4899	+	19.9436i	−0.563591	+	0.775716i	0.428187	+	0.903690i	$0.359153\pi$
$662$	26.4229	−	9.92198i	1.02695	−	0.385629i
$663$	−0.0966653	−	0.297505i	−0.00375417	−	0.0115541i
$664$	10.4331	+	5.60718i	0.404882	+	0.217601i
$665$	1.47213	+	36.9491i	0.0570867	+	1.43282i
$666$	−28.8871	−	7.96685i	−1.11935	−	0.308709i
$667$	29.0661	+	40.0060i	1.12544	+	1.54904i
$668$	6.42547	−	5.61776i	0.248609	−	0.217358i
$669$	−0.701627	−	1.37702i	−0.0271265	−	0.0532387i
$670$	19.2929	−	16.6903i	0.745349	−	0.644802i
$671$	−2.76687	−	17.4693i	−0.106814	−	0.674397i
$672$	−0.403984	+	1.60923i	−0.0155840	+	0.0620774i
$673$	−2.32076	+	1.68613i	−0.0894589	+	0.0649957i	−0.631616	−	0.775282i	$-0.717608\pi$
$673$	−2.32076	+	1.68613i	−0.0894589	+	0.0649957i	0.542157	+	0.840277i	$0.317608\pi$
$674$	10.9392	+	29.1318i	0.421362	+	1.12212i
$675$	2.41935	−	1.00525i	0.0931207	−	0.0386922i
$676$	−1.46556	−	16.2197i	−0.0563677	−	0.623835i
$677$	−8.40263	+	16.4911i	−0.322939	+	0.633804i	−0.994216	−	0.107403i	$-0.965746\pi$
$677$	−8.40263	+	16.4911i	−0.322939	+	0.633804i	0.671276	+	0.741207i	$0.265746\pi$
$678$	−1.17871	−	0.777763i	−0.0452681	−	0.0298698i
$679$	9.16229	−	28.1986i	0.351616	−	1.08216i
$680$	−9.22937	−	4.49625i	−0.353930	−	0.172423i
$681$	−0.0100390	−	0.0308968i	−0.000384694	−	0.00118397i
$682$	−30.4711	+	1.37384i	−1.16680	+	0.0526069i
$683$			7.24141i			0.277085i	0.990356	+	0.138543i	$0.0442418\pi$
$683$			7.24141i			0.277085i	−0.990356	+	0.138543i	$0.955758\pi$
$684$	−7.21952	−	28.6088i	−0.276045	−	1.09389i
$685$	−18.1824	+	3.62711i	−0.694712	+	0.138585i
$686$	−11.3396	+	6.43697i	−0.432949	+	0.245765i
$687$	1.57969	+	0.250199i	0.0602690	+	0.00954567i
$688$	−0.198601	−	0.566289i	−0.00757159	−	0.0215896i
$689$	−4.65739	+	3.38379i	−0.177432	+	0.128912i
$690$	−2.17786	+	0.537476i	−0.0829095	+	0.0204614i
$691$	30.7830	−	15.6847i	1.17104	−	0.596675i	0.243318	−	0.969946i	$-0.421764\pi$
$691$	30.7830	−	15.6847i	1.17104	−	0.596675i	0.927722	+	0.373272i	$0.121764\pi$
$692$	−3.85239	−	0.258371i	−0.146446	−	0.00982180i
$693$	−4.43470	−	27.9996i	−0.168460	−	1.06362i
$694$	2.55559	−	22.7174i	0.0970088	−	0.862342i
$695$	−6.32571	+	3.54715i	−0.239948	+	0.134551i
$696$	−0.654822	−	1.35792i	−0.0248209	−	0.0514716i
$697$	−7.38587	−	7.31310i	−0.279760	−	0.277004i
$698$	4.22276	−	37.5375i	0.159834	−	1.42081i
$699$	1.68211	+	0.546550i	0.0636232	+	0.0206724i
$700$	33.1937	+	4.82695i	1.25461	+	0.182441i
$701$	−30.4791	−	22.1444i	−1.15118	−	0.836382i	−0.162543	−	0.986701i	$-0.551970\pi$
$701$	−30.4791	−	22.1444i	−1.15118	−	0.836382i	−0.988637	+	0.150320i	$0.951970\pi$
$702$	−1.20562	−	1.10160i	−0.0455033	−	0.0415772i
$703$	−33.2019	−	10.7880i	−1.25223	−	0.406876i
$704$	9.36602	+	20.5622i	0.352995	+	0.774967i
$705$	1.48032	+	0.174380i	0.0557520	+	0.00656753i
$706$	−16.2489	+	12.9628i	−0.611536	+	0.487860i
$707$	−44.5630	−	7.05809i	−1.67597	−	0.265447i
$708$	0.486486	−	0.208137i	0.0182833	−	0.00782226i
$709$	10.8206	−	1.71381i	0.406375	−	0.0643635i	0.0500991	−	0.998744i	$-0.484046\pi$
$709$	10.8206	−	1.71381i	0.406375	−	0.0643635i	0.356276	+	0.934381i	$0.384046\pi$
$710$	−39.5250	−	16.0791i	−1.48335	−	0.603438i
$711$	−14.7275	−	14.7275i	−0.552324	−	0.552324i
$712$	−7.58690	+	41.9334i	−0.284331	+	1.57152i
$713$	−28.1252	+	55.1988i	−1.05330	+	2.06721i
$714$	0.332387	+	0.585546i	0.0124393	+	0.0219135i
$715$	13.3980	+	3.77066i	0.501058	+	0.141015i
$716$	−32.3377	−	26.9781i	−1.20852	−	1.00822i
$717$	−0.744684	+	1.46153i	−0.0278107	+	0.0545817i
$718$	−45.1122	+	9.24504i	−1.68357	+	0.345022i
$719$	−3.86089	−	1.96722i	−0.143987	−	0.0733651i	0.380513	−	0.924776i	$-0.375748\pi$
$719$	−3.86089	−	1.96722i	−0.143987	−	0.0733651i	−0.524500	+	0.851411i	$0.675748\pi$
$720$	−26.7114	+	1.68412i	−0.995475	+	0.0627635i
$721$	−2.68604	+	16.9590i	−0.100033	+	0.631585i
$722$	−1.50669	−	7.35204i	−0.0560730	−	0.273615i
$723$	−1.42593	+	1.96262i	−0.0530308	+	0.0729906i
$724$	21.9222	−	13.7854i	0.814732	−	0.512330i
$725$	−25.9691	+	15.9533i	−0.964467	+	0.592490i
$726$	−0.275974	−	0.252162i	−0.0102424	−	0.00935862i
$727$	28.6948	+	39.4950i	1.06423	+	1.46479i	0.875782	+	0.482708i	$0.160347\pi$
$727$	28.6948	+	39.4950i	1.06423	+	1.46479i	0.188451	+	0.982083i	$0.439653\pi$
$728$	−6.02400	−	20.0225i	−0.223264	−	0.742082i
$729$	−26.5880			−0.984741
$730$	−17.0902	−	27.4959i	−0.632535	−	1.01767i
$731$	−0.216987	−	0.110560i	−0.00802554	−	0.00408922i
$732$	0.940346	+	0.561381i	0.0347562	+	0.0207492i
$733$	33.5002	−	5.30591i	1.23736	−	0.195978i	0.496737	−	0.867901i	$-0.334531\pi$
$733$	33.5002	−	5.30591i	1.23736	−	0.195978i	0.740621	+	0.671923i	$0.234531\pi$
$734$	−1.82613	−	40.5028i	−0.0674037	−	1.49498i
$735$	−0.610692	−	0.563894i	−0.0225257	−	0.0207995i
$736$	45.7100	+	4.07339i	1.68489	+	0.150147i
$737$	−16.1110	+	16.1110i	−0.593455	+	0.593455i
$738$	−26.1570	−	7.07479i	−0.962854	−	0.260426i
$739$	24.6730			0.907612			0.453806	−	0.891101i	$-0.350066\pi$
$739$	24.6730			0.907612			0.453806	+	0.891101i	$0.350066\pi$
$740$	−15.1372	+	27.8150i	−0.556453	+	1.02250i
$741$	−0.671817	−	0.671817i	−0.0246798	−	0.0246798i
$742$	8.35832	−	9.14760i	0.306844	−	0.335819i
$743$	6.61151	+	41.7434i	0.242553	+	1.53142i	0.745150	+	0.666897i	$0.232378\pi$
$743$	6.61151	+	41.7434i	0.242553	+	1.53142i	−0.502597	+	0.864521i	$0.667622\pi$
$744$	1.14334	−	1.50327i	0.0419168	−	0.0551126i
$745$	14.5505	−	5.37709i	0.533091	−	0.197001i
$746$	−4.05304	+	14.6960i	−0.148392	+	0.538057i
$747$	8.86066	−	8.86066i	0.324195	−	0.324195i
$748$	8.51133	+	3.41066i	0.311205	+	0.124706i
$749$	−3.25236	+	20.5346i	−0.118839	+	0.750318i
$750$	−0.226433	−	1.36389i	−0.00826816	−	0.0498023i
$751$	17.1039	+	33.5683i	0.624129	+	1.22492i	0.959200	+	0.282730i	$0.0912400\pi$
$751$	17.1039	+	33.5683i	0.624129	+	1.22492i	−0.335070	+	0.942193i	$0.608760\pi$
$752$	−27.4831	−	13.2113i	−1.00220	−	0.481767i
$753$	−0.776154	−	0.563909i	−0.0282846	−	0.0205500i
$754$	15.8574	+	10.4634i	0.577494	+	0.381054i
$755$	24.8946	−	19.6476i	0.906008	−	0.715049i
$756$	3.01820	+	1.80185i	0.109771	+	0.0655325i
$757$	−19.8824	+	6.46020i	−0.722640	+	0.234800i	−0.647167	−	0.762348i	$-0.724047\pi$
$757$	−19.8824	+	6.46020i	−0.722640	+	0.234800i	−0.0754725	+	0.997148i	$0.524047\pi$
$758$	44.0646	−	9.03036i	1.60050	−	0.327997i
$759$	1.90543	−	0.619111i	0.0691627	−	0.0224723i
$760$	−31.1762	+	0.558409i	−1.13088	+	0.0202556i
$761$	−3.11611	+	9.59039i	−0.112959	+	0.347651i	−0.991516	−	0.129986i	$-0.958507\pi$
$761$	−3.11611	+	9.59039i	−0.112959	+	0.347651i	0.878557	+	0.477637i	$0.158507\pi$
$762$	0.257457	−	0.933517i	0.00932669	−	0.0338177i
$763$	34.5560	+	17.6072i	1.25101	+	0.637423i
$764$	−0.946178	+	14.1078i	−0.0342315	+	0.510401i
$765$	−7.36829	+	7.97979i	−0.266401	+	0.288510i
$766$	7.03606	−	15.4976i	0.254223	−	0.559952i
$767$	−3.91953	+	5.39478i	−0.141526	+	0.194794i
$768$	−1.34916	−	0.370299i	−0.0486835	−	0.0133620i
$769$	−22.7398	−	31.2986i	−0.820017	−	1.12866i	−0.989700	−	0.143157i	$-0.954274\pi$
$769$	−22.7398	−	31.2986i	−0.820017	−	1.12866i	0.169683	−	0.985499i	$-0.445726\pi$
$770$	−29.8804	−	2.16120i	−1.07681	−	0.0778841i
$771$	0.852756	−	0.619564i	0.0307113	−	0.0223130i
$772$	−40.6939	+	3.67697i	−1.46461	+	0.132337i
$773$	3.02323	−	9.30455i	0.108738	−	0.334662i	−0.881851	−	0.471527i	$-0.843703\pi$
$773$	3.02323	−	9.30455i	0.108738	−	0.334662i	0.990590	+	0.136866i	$0.0437029\pi$
$774$	−0.634240	+	0.0285957i	−0.0227973	+	0.00102785i
$775$	−32.5780	−	19.9145i	−1.17024	−	0.715348i
$776$	23.6029	+	8.24501i	0.847294	+	0.295979i
$777$	1.85050	−	0.942877i	0.0663863	−	0.0338255i
$778$	−3.35538	+	29.8270i	−0.120296	+	1.06935i
$779$	−30.0714	−	9.60649i	−1.07742	−	0.344188i
$780$	−0.710722	+	0.487455i	−0.0254479	+	0.0174537i
$781$	36.2453	+	11.7768i	1.29696	+	0.421407i
$782$	14.5581	−	11.6139i	0.520598	−	0.415313i
$783$	−3.15461	+	0.499641i	−0.112737	+	0.0178557i
$784$	8.06866	+	14.9688i	0.288166	+	0.534600i
$785$	−3.45220	+	1.93583i	−0.123214	+	0.0690926i
$786$	1.21294	−	0.248573i	0.0432642	−	0.00886632i
$787$	−2.86104	+	18.0639i	−0.101985	+	0.643909i	0.882749	+	0.469845i	$0.155690\pi$
$787$	−2.86104	+	18.0639i	−0.101985	+	0.643909i	−0.984734	+	0.174064i	$0.944310\pi$
$788$	−23.1014	−	36.7369i	−0.822953	−	1.30870i
$789$	−0.116810	−	0.160775i	−0.00415854	−	0.00572374i
$790$	−18.6938	+	11.6192i	−0.665096	+	0.413392i
$791$	−37.8341	+	5.99234i	−1.34523	+	0.213063i
$792$	23.6863	−	3.22127i	0.841656	−	0.114463i
$793$	−13.8015			−0.490106
$794$	17.5494	−	19.2066i	0.622806	−	0.681618i
$795$	−0.463938	−	0.213568i	−0.0164542	−	0.00757448i
$796$	15.4272	−	38.4988i	0.546804	−	1.36455i
$797$	−12.2391	−	24.0206i	−0.433532	−	0.850855i	−0.999648	−	0.0265293i	$-0.991554\pi$
$797$	−12.2391	−	24.0206i	−0.433532	−	0.850855i	0.566116	−	0.824326i	$-0.308446\pi$
$798$	1.70690	+	1.12628i	0.0604235	+	0.0398699i
$799$	−11.7690	+	3.82398i	−0.416358	+	0.135283i
$800$	−4.68249	+	27.8940i	−0.165551	+	0.986201i
$801$	40.1701	+	20.4677i	1.41934	+	0.723190i
$802$	−11.0837	+	24.4128i	−0.391377	+	0.862048i
$803$	16.9957	+	23.3926i	0.599765	+	0.825506i
$804$	−0.126957	−	1.40506i	−0.00447743	−	0.0495528i
$805$	−33.7769	+	50.6110i	−1.19048	+	1.78380i
$806$	−2.66072	+	23.6520i	−0.0937200	+	0.833107i
$807$	1.28738	+	0.418295i	0.0453179	+	0.0147247i
$808$	6.77345	−	37.4374i	0.238289	−	1.31704i
$809$	1.77460	−	11.2044i	0.0623917	−	0.393926i	−0.936654	−	0.350255i	$-0.886095\pi$
$809$	1.77460	−	11.2044i	0.0623917	−	0.393926i	0.999046	−	0.0436706i	$-0.0139052\pi$
$810$	−6.41905	+	27.5040i	−0.225542	+	0.966390i
$811$	17.1126			0.600906			0.300453	−	0.953797i	$-0.402862\pi$
$811$	17.1126			0.600906			0.300453	+	0.953797i	$0.402862\pi$
$812$	−37.9584	−	15.2107i	−1.33208	−	0.533790i
$813$	−0.823435	+	0.267550i	−0.0288791	+	0.00938339i
$814$	11.6922	−	25.7532i	0.409811	−	0.902650i
$815$	1.51887	+	1.01366i	0.0532036	+	0.0355071i
$816$	−0.499771	+	0.269392i	−0.0174955	+	0.00943062i
$817$	−0.739656			−0.0258773
$818$	0.151248	−	0.333138i	0.00528825	−	0.0116479i
$819$	−22.1209			−0.772965
$820$	−13.5634	+	25.2197i	−0.473654	+	0.880711i
$821$	−22.3091			−0.778592			−0.389296	−	0.921113i	$-0.627282\pi$
$821$	−22.3091			−0.778592			−0.389296	+	0.921113i	$0.627282\pi$
$822$	−0.423874	+	0.933624i	−0.0147843	+	0.0325639i
$823$	5.72441			0.199540			0.0997702	−	0.995011i	$-0.468189\pi$
$823$	5.72441			0.199540			0.0997702	+	0.995011i	$0.468189\pi$
$824$	−14.2472	−	2.57771i	−0.496325	−	0.0897989i
$825$	0.289586	+	1.20038i	0.0100821	+	0.0417919i
$826$	5.93349	−	13.0691i	0.206453	−	0.454732i
$827$	28.6665	−	9.31432i	0.996833	−	0.323891i	0.235234	−	0.971939i	$-0.424414\pi$
$827$	28.6665	−	9.31432i	0.996833	−	0.323891i	0.761599	+	0.648048i	$0.224414\pi$
$828$	18.0593	−	45.0671i	0.627604	−	1.56619i
$829$	−29.3125			−1.01807			−0.509033	−	0.860747i	$-0.669997\pi$
$829$	−29.3125			−1.01807			−0.509033	+	0.860747i	$0.669997\pi$
$830$	−6.99057	−	11.2470i	−0.242646	−	0.390388i
$831$	−0.380648	+	2.40332i	−0.0132045	+	0.0833702i
$832$	16.9907	−	4.70847i	0.589048	−	0.163237i
$833$	6.56307	+	2.13247i	0.227397	+	0.0738857i
$834$	−0.0448358	+	0.398559i	−0.00155254	+	0.0138010i
$835$	−9.35801	+	1.86679i	−0.323847	+	0.0646028i
$836$	27.7362	−	2.50615i	0.959275	−	0.0866770i
$837$	−2.35194	−	3.23716i	−0.0812948	−	0.111893i
$838$	9.57257	−	21.0845i	0.330679	−	0.728353i
$839$	22.6367	+	11.5340i	0.781507	+	0.398198i	0.798757	−	0.601654i	$-0.205491\pi$
$839$	22.6367	+	11.5340i	0.781507	+	0.398198i	−0.0172503	+	0.999851i	$0.505491\pi$
$840$	1.28798	−	1.33496i	0.0444396	−	0.0460606i
$841$	7.75681	−	2.52034i	0.267476	−	0.0869082i
$842$	34.8744	+	23.0116i	1.20185	+	0.793031i
$843$	0.717919	+	1.40899i	0.0247264	+	0.0485283i
$844$	−18.2125	−	7.29810i	−0.626899	−	0.251211i
$845$	−7.61387	+	16.5397i	−0.261925	+	0.568984i
$846$	−21.7613	+	23.8162i	−0.748168	+	0.818818i
$847$	−10.1401			−0.348419
$848$	7.55724	+	7.21528i	0.259517	+	0.247774i
$849$	0.987360	−	0.156382i	0.0338861	−	0.00536703i
$850$	6.44248	+	9.49955i	0.220975	+	0.325832i
$851$	−33.7650	−	46.4735i	−1.15745	−	1.59309i
$852$	−1.99764	+	1.25618i	−0.0684379	+	0.0430360i
$853$	4.90676	−	30.9801i	0.168004	−	1.06074i	−0.749207	−	0.662336i	$-0.769565\pi$
$853$	4.90676	−	30.9801i	0.168004	−	1.06074i	0.917211	−	0.398401i	$-0.130435\pi$
$854$	29.1018	−	5.96396i	0.995842	−	0.204082i
$855$	−8.93689	+	31.7548i	−0.305635	+	1.08599i
$856$	−17.2511	−	3.12120i	−0.589631	−	0.106680i
$857$	45.2910	−	7.17339i	1.54711	−	0.245038i	0.676289	−	0.736636i	$-0.263587\pi$
$857$	45.2910	−	7.17339i	1.54711	−	0.245038i	0.870822	+	0.491598i	$0.163587\pi$
$858$	0.601712	−	0.480023i	0.0205421	−	0.0163877i
$859$	−26.7360	−	8.68706i	−0.912222	−	0.296399i	−0.184950	−	0.982748i	$-0.559212\pi$
$859$	−26.7360	−	8.68706i	−0.912222	−	0.296399i	−0.727272	+	0.686349i	$0.759212\pi$
$860$	−0.122906	+	0.659584i	−0.00419107	+	0.0224916i
$861$	1.66911	−	0.860887i	0.0568831	−	0.0293390i
$862$	−1.84844	+	16.4313i	−0.0629580	+	0.559653i
$863$	0.315474	−	0.160742i	0.0107389	−	0.00547172i	−0.448613	−	0.893726i	$-0.648082\pi$
$863$	0.315474	−	0.160742i	0.0107389	−	0.00547172i	0.459352	+	0.888254i	$0.348082\pi$
$864$	−1.57476	+	2.51113i	−0.0535745	+	0.0854302i
$865$	3.59059	+	2.39629i	0.122084	+	0.0814764i
$866$	8.01626	−	0.361425i	0.272404	−	0.0122817i
$867$	0.388154	−	1.19461i	0.0131824	−	0.0405712i
$868$	−4.61021	−	51.0223i	−0.156481	−	1.73181i
$869$	15.9040	−	11.5550i	0.539508	−	0.391975i
$870$	−0.121592	+	1.68111i	−0.00412234	+	0.0569949i
$871$	10.4502	+	14.3835i	0.354092	+	0.487366i
$872$	−15.4817	+	28.8063i	−0.524277	+	0.975505i
$873$	15.5472	−	21.3989i	0.526194	−	0.724244i
$874$	23.3830	−	51.5034i	0.790942	−	1.74213i
$875$	−29.4893	−	23.1686i	−0.996922	−	0.783241i
$876$	−1.78637	−	0.119808i	−0.0603558	−	0.00404793i
$877$	39.4830	+	20.1176i	1.33324	+	0.679322i	0.967849	−	0.251530i	$-0.0809338\pi$
$877$	39.4830	+	20.1176i	1.33324	+	0.679322i	0.365395	+	0.930852i	$0.380934\pi$
$878$	5.20473	−	18.8719i	0.175651	−	0.636895i
$879$	−0.342953	+	1.05550i	−0.0115675	+	0.0356011i
$880$	2.37398	−	25.1500i	0.0800269	−	0.847806i
$881$	22.7112	−	7.37932i	0.765161	−	0.248616i	0.0996686	−	0.995021i	$-0.468222\pi$
$881$	22.7112	−	7.37932i	0.765161	−	0.248616i	0.665492	+	0.746405i	$0.268222\pi$
$882$	17.6242	−	3.61181i	0.593438	−	0.121616i
$883$	18.3014	−	5.94648i	0.615890	−	0.200115i	0.0155755	−	0.999879i	$-0.495042\pi$
$883$	18.3014	−	5.94648i	0.615890	−	0.200115i	0.600315	+	0.799764i	$0.295042\pi$
$884$	3.66758	−	6.14342i	0.123354	−	0.206625i
$885$	−0.587534	−	0.0692110i	−0.0197498	−	0.00232650i
$886$	35.6030	+	23.4923i	1.19611	+	0.789241i
$887$	−37.6615	−	27.3627i	−1.26455	−	0.918748i	−0.265577	−	0.964090i	$-0.585562\pi$
$887$	−37.6615	−	27.3627i	−1.26455	−	0.918748i	−0.998972	+	0.0453418i	$0.985562\pi$
$888$	0.760681	+	1.57744i	0.0255268	+	0.0529353i
$889$	−11.9250	−	23.4041i	−0.399952	−	0.784950i
$890$	30.7122	−	36.4242i	1.02947	−	1.22094i
$891$	3.94606	−	24.9144i	0.132198	−	0.834665i
$892$	13.1486	−	32.8124i	0.440248	−	1.09864i
$893$	−26.5764	+	26.5764i	−0.889346	+	0.889346i
$894$	0.228079	−	0.826993i	0.00762809	−	0.0276588i
$895$	16.3210	+	44.1652i	0.545552	+	1.47628i
$896$	−33.7919	+	17.2704i	−1.12891	+	0.576962i
$897$	−0.244562	−	1.54410i	−0.00816568	−	0.0515561i
$898$	−32.4981	+	35.5669i	−1.08447	+	1.18688i
$899$	32.9151	+	32.9151i	1.09778	+	1.09778i
$900$	26.8321	+	13.2460i	0.894404	+	0.441533i
$901$	4.24015			0.141260
$902$	10.4575	−	23.3399i	0.348197	−	0.777134i
$903$	0.0311147	−	0.0311147i	0.00103543	−	0.00103543i
$904$	−4.35271	−	32.0058i	−0.144769	−	1.06450i
$905$	−28.9300	+	1.15263i	−0.961666	+	0.0383148i
$906$	−0.0789949	−	1.75207i	−0.00262443	−	0.0582087i
$907$	−26.5832	+	4.21037i	−0.882682	+	0.139803i	−0.581289	−	0.813697i	$-0.697452\pi$
$907$	−26.5832	+	4.21037i	−0.882682	+	0.139803i	−0.301393	+	0.953500i	$0.597452\pi$
$908$	0.380889	−	0.638011i	0.0126402	−	0.0211731i
$909$	−35.8632	−	18.2732i	−1.18951	−	0.606084i
$910$	−5.31309	+	22.7652i	−0.176127	+	0.754660i
$911$	−15.4649			−0.512374			−0.256187	−	0.966627i	$-0.582466\pi$
$911$	−15.4649			−0.512374			−0.256187	+	0.966627i	$0.582466\pi$
$912$	−0.981018	+	1.41815i	−0.0324848	+	0.0469596i
$913$	6.95193	+	9.56852i	0.230075	+	0.316672i
$914$	−21.8516	−	19.9662i	−0.722787	−	0.660422i
$915$	−0.598875	−	1.06799i	−0.0197982	−	0.0353066i
$916$	19.4738	+	30.9681i	0.643431	+	1.02321i
$917$	19.7407	−	27.1708i	0.651896	−	0.897258i
$918$	0.241487	+	1.17836i	0.00797025	+	0.0388917i
$919$	−6.07542	+	38.3587i	−0.200409	+	1.26534i	0.658254	+	0.752796i	$0.271295\pi$
$919$	−6.07542	+	38.3587i	−0.200409	+	1.26534i	−0.858664	+	0.512540i	$0.828705\pi$
$920$	−42.0423	−	29.4098i	−1.38609	−	0.969612i
$921$	0.571100	+	0.290990i	0.0188184	+	0.00958844i
$922$	45.6061	−	9.34626i	1.50196	−	0.307803i
$923$	13.5009	−	26.4970i	0.444387	−	0.872158i
$924$	−1.06134	+	1.27219i	−0.0349154	+	0.0418519i
$925$	30.1673	−	18.5323i	0.991894	−	0.609338i
$926$	4.28836	+	7.55455i	0.140924	+	0.248258i
$927$	−6.95407	+	13.6481i	−0.228402	+	0.448264i
$928$	13.5243	−	31.7189i	0.443956	−	1.04122i
$929$	25.0345	+	25.0345i	0.821357	+	0.821357i	0.986303	−	0.164946i	$-0.0527450\pi$
$929$	25.0345	+	25.0345i	0.821357	+	0.821357i	−0.164946	+	0.986303i	$0.552745\pi$
$930$	−1.94569	+	0.820417i	−0.0638018	+	0.0269025i
$931$	20.7013	−	3.27877i	0.678459	−	0.107457i
$932$	15.9126	+	37.1932i	0.521235	+	1.21830i
$933$	−0.0418976	−	0.00663592i	−0.00137166	−	0.000217250i
$934$	−10.1661	+	8.11011i	−0.332644	+	0.265371i
$935$	−6.35110	−	8.04721i	−0.207703	−	0.263172i
$936$	0.408682	−	18.6484i	0.0133582	−	0.609543i
$937$	−40.4221	−	13.1339i	−1.32053	−	0.429067i	−0.437854	−	0.899046i	$-0.644261\pi$
$937$	−40.4221	−	13.1339i	−1.32053	−	0.429067i	−0.882677	+	0.469979i	$0.844261\pi$
$938$	−28.2507	−	25.8131i	−0.922417	−	0.842829i
$939$	−0.00200255	−	0.00145494i	−6.53509e−5	−	4.74802e-5i
$940$	19.2832	+	28.1155i	0.628950	+	0.917025i
$941$	41.0952	+	13.3526i	1.33966	+	0.435283i	0.889203	−	0.457512i	$-0.151259\pi$
$941$	41.0952	+	13.3526i	1.33966	+	0.435283i	0.450462	+	0.892796i	$0.351259\pi$
$942$	−0.0244687	+	0.217510i	−0.000797235	+	0.00708687i
$943$	−30.7403	−	41.8729i	−1.00104	−	1.36357i
$944$	10.9080	+	5.24354i	0.355024	+	0.170663i
$945$	−1.92219	−	3.42788i	−0.0625288	−	0.111509i
$946$	0.0669887	−	0.595484i	0.00217799	−	0.0193608i
$947$	0.186088	+	1.17492i	0.00604706	+	0.0381796i	0.990527	−	0.137315i	$-0.0438474\pi$
$947$	0.186088	+	1.17492i	0.00604706	+	0.0381796i	−0.984480	+	0.175495i	$0.943847\pi$
$948$	−0.0814545	+	1.21451i	−0.00264552	+	0.0394454i
$949$	20.1035	−	10.2432i	0.652586	−	0.332509i
$950$	30.5333	+	16.8242i	0.990630	+	0.545850i
$951$	1.98241	−	1.44030i	0.0642840	−	0.0467050i
$952$	−5.07873	+	14.5388i	−0.164603	+	0.471206i
$953$	−26.5127	−	4.19919i	−0.858829	−	0.136025i	−0.288539	−	0.957468i	$-0.593169\pi$
$953$	−26.5127	−	4.19919i	−0.858829	−	0.136025i	−0.570291	+	0.821443i	$0.693169\pi$
$954$	9.61326	−	5.45699i	0.311241	−	0.176677i
$955$	8.77544	−	13.1490i	0.283966	−	0.425493i
$956$	−36.3777	+	9.18001i	−1.17654	+	0.296903i
$957$		−	1.50538i		−	0.0486622i
$958$	36.7689	−	1.65778i	1.18795	−	0.0535605i
$959$	8.59452	+	26.4512i	0.277531	+	0.854154i
$960$	1.10161	+	1.11047i	0.0355544	+	0.0358401i
$961$	−8.44123	+	25.9794i	−0.272298	+	0.838046i
$962$	−18.4210	−	12.1549i	−0.593916	−	0.391890i
$963$	−8.42027	+	16.5257i	−0.271339	+	0.532534i
$964$	−55.2623	+	4.99332i	−1.77988	+	0.160824i
$965$	41.4968	+	19.1026i	1.33583	+	0.614933i
$966$	1.18292	+	3.15020i	0.0380600	+	0.101356i
$967$	18.7680	−	13.6358i	0.603538	−	0.438496i	−0.243595	−	0.969877i	$-0.578327\pi$
$967$	18.7680	−	13.6358i	0.603538	−	0.438496i	0.847133	+	0.531381i	$0.178327\pi$
$968$	0.187338	−	8.54838i	0.00602128	−	0.274755i
$969$	0.109470	+	0.691166i	0.00351668	+	0.0222035i
$970$	−18.2881	−	21.1398i	−0.587195	−	0.678759i
$971$	5.54027	+	10.8734i	0.177796	+	0.348944i	0.962655	−	0.270730i	$-0.0872650\pi$
$971$	5.54027	+	10.8734i	0.177796	+	0.348944i	−0.784860	+	0.619674i	$0.787265\pi$
$972$	3.09735	+	3.54269i	0.0993477	+	0.113632i
$973$	6.39460	+	8.80142i	0.205002	+	0.282160i
$974$	53.4714	+	14.7470i	1.71334	+	0.472526i
$975$	0.960493	−	0.0766577i	0.0307604	−	0.00245501i
$976$	4.49011	+	24.6437i	0.143725	+	0.788826i
$977$	2.12398	+	6.53693i	0.0679521	+	0.209135i	0.979267	−	0.202576i	$-0.0649313\pi$
$977$	2.12398	+	6.53693i	0.0679521	+	0.209135i	−0.911314	+	0.411711i	$0.864931\pi$
$978$	0.0945395	−	0.0355003i	0.00302304	−	0.00113517i
$979$	−25.0119	+	34.4259i	−0.799384	+	1.10026i
$980$	0.516050	−	19.0051i	0.0164846	−	0.607096i
$981$	24.4648	+	24.4648i	0.781099	+	0.781099i
$982$	−5.29328	+	11.6590i	−0.168915	+	0.372053i
$983$	31.3301	−	31.3301i	0.999274	−	0.999274i	−0.000726002	−	1.00000i	$-0.500231\pi$
$983$	31.3301	−	31.3301i	0.999274	−	0.999274i	1.00000		0.000726002i	$0.000231094\pi$
$984$	0.694913	+	1.42301i	0.0221530	+	0.0453638i
$985$	1.93157	+	48.4806i	0.0615448	+	1.54472i
$986$	−4.91914	−	13.1000i	−0.156657	−	0.417189i
$987$		−	2.23595i		−	0.0711711i
$988$	1.45419	−	21.6824i	0.0462640	−	0.689809i
$989$	−0.984641	−	0.715384i	−0.0313098	−	0.0227479i
$990$	−24.7558	−	10.0709i	−0.786791	−	0.320073i
$991$	21.6206	+	11.0162i	0.686800	+	0.349942i	0.762318	−	0.647202i	$-0.224061\pi$
$991$	21.6206	+	11.0162i	0.686800	+	0.349942i	−0.0755181	+	0.997144i	$0.524061\pi$
$992$	43.0982	−	2.94389i	1.36837	−	0.0934685i
$993$	−1.23398	+	1.23398i	−0.0391592	+	0.0391592i
$994$	−17.0179	+	61.7054i	−0.539775	+	1.95718i
$995$	−36.3995	+	28.7276i	−1.15394	+	0.910726i
$996$	−0.730697	−	0.0490063i	−0.0231530	−	0.00155282i
$997$	−8.31094	+	25.5784i	−0.263210	+	0.810077i	0.728890	+	0.684631i	$0.240036\pi$
$997$	−8.31094	+	25.5784i	−0.263210	+	0.810077i	−0.992100	+	0.125447i	$0.959964\pi$
$998$	9.58190	−	7.64407i	0.303310	−	0.241969i
$999$	3.66459	−	0.580414i	0.115942	−	0.0183635i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.bv.c.103.17	yes	960
4.3	odd	2	inner	820.2.bv.c.103.54	yes	960
5.2	odd	4		820.2.bk.c.267.78	yes	960
20.7	even	4		820.2.bk.c.267.8	yes	960
41.2	even	20		820.2.bk.c.43.8	✓	960
164.43	odd	20		820.2.bk.c.43.78	yes	960
205.2	odd	20	inner	820.2.bv.c.207.54	yes	960
820.207	even	20	inner	820.2.bv.c.207.17	yes	960

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.bk.c.43.8	✓	960	41.2	even	20
820.2.bk.c.43.78	yes	960	164.43	odd	20
820.2.bk.c.267.8	yes	960	20.7	even	4
820.2.bk.c.267.78	yes	960	5.2	odd	4
820.2.bv.c.103.17	yes	960	1.1	even	1	trivial
820.2.bv.c.103.54	yes	960	4.3	odd	2	inner
820.2.bv.c.207.17	yes	960	820.207	even	20	inner
820.2.bv.c.207.54	yes	960	205.2	odd	20	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.bv (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.28771 - 0.584633i) q^{2} +0.0874408 q^{3} +(1.31641 + 1.50568i) q^{4} +(-0.437444 - 2.19286i) q^{5} +(-0.112599 - 0.0511208i) q^{6} +(-3.19012 + 1.03653i) q^{7} +(-0.814885 - 2.70850i) q^{8} -2.99235 q^{9} +(-0.718718 + 3.07952i) q^{10} +(0.441826 - 2.78958i) q^{11} +(0.115108 + 0.131658i) q^{12} +(-2.09602 - 0.681038i) q^{13} +(4.71394 + 0.530293i) q^{14} +(-0.0382504 - 0.191746i) q^{15} +(-0.534140 + 3.96418i) q^{16} +(0.954122 + 1.31324i) q^{17} +(3.85329 + 1.74943i) q^{18} +(4.39283 + 2.23826i) q^{19} +(2.72589 - 3.54535i) q^{20} +(-0.278946 + 0.0906351i) q^{21} +(-2.19983 + 3.33387i) q^{22} +(3.68299 + 7.22827i) q^{23} +(-0.0712542 - 0.236833i) q^{24} +(-4.61729 + 1.91851i) q^{25} +(2.30091 + 2.10238i) q^{26} -0.523976 q^{27} +(-5.76018 - 3.43879i) q^{28} +(6.02052 - 0.953557i) q^{29} +(-0.0628453 + 0.269276i) q^{30} +(4.48863 + 6.17807i) q^{31} +(3.00541 - 4.79244i) q^{32} +(0.0386336 - 0.243923i) q^{33} +(-0.460874 - 2.24888i) q^{34} +(3.66847 + 6.54206i) q^{35} +(-3.93916 - 4.50553i) q^{36} +(-6.99381 + 1.10771i) q^{37} +(-4.34814 - 5.45042i) q^{38} +(-0.183277 - 0.0595505i) q^{39} +(-5.58290 + 2.97175i) q^{40} +(-6.31926 + 1.03296i) q^{41} +(0.412191 + 0.0463692i) q^{42} +(-0.133674 + 0.0681104i) q^{43} +(4.78184 - 3.00698i) q^{44} +(1.30899 + 6.56182i) q^{45} +(-0.516743 - 11.4611i) q^{46} +(-2.35576 + 7.25028i) q^{47} +(-0.0467056 + 0.346631i) q^{48} +(3.43932 - 2.49881i) q^{49} +(7.06736 + 0.228932i) q^{50} +(0.0834292 + 0.114830i) q^{51} +(-1.73379 - 4.05246i) q^{52} +(1.53538 - 2.11326i) q^{53} +(0.674731 + 0.306334i) q^{54} +(-6.31044 + 0.251421i) q^{55} +(5.40702 + 7.79577i) q^{56} +(0.384112 + 0.195715i) q^{57} +(-8.31019 - 2.29189i) q^{58} +(0.934995 - 2.87762i) q^{59} +(0.238354 - 0.310008i) q^{60} +(5.95586 - 1.93517i) q^{61} +(-2.16816 - 10.5798i) q^{62} +(9.54596 - 3.10167i) q^{63} +(-6.67192 + 4.41423i) q^{64} +(-0.576531 + 4.89419i) q^{65} +(-0.192355 + 0.291516i) q^{66} +(-6.52642 - 4.74172i) q^{67} +(-0.721299 + 3.16536i) q^{68} +(0.322043 + 0.632046i) q^{69} +(-0.899226 - 10.5690i) q^{70} +(-2.11086 + 13.3274i) q^{71} +(2.43842 + 8.10479i) q^{72} +(-7.23913 + 7.23913i) q^{73} +(9.65362 + 2.66240i) q^{74} +(-0.403739 + 0.167756i) q^{75} +(2.41265 + 9.56065i) q^{76} +(1.48201 + 9.35705i) q^{77} +(0.201194 + 0.183834i) q^{78} +(4.92171 + 4.92171i) q^{79} +(8.92655 - 0.562808i) q^{80} +8.93125 q^{81} +(8.74129 + 2.36429i) q^{82} +(-2.96110 + 2.96110i) q^{83} +(-0.503674 - 0.300691i) q^{84} +(2.46237 - 2.66673i) q^{85} +(0.211954 - 0.00955625i) q^{86} +(0.526439 - 0.0833798i) q^{87} +(-7.91561 + 1.07650i) q^{88} +(-13.4242 - 6.84000i) q^{89} +(2.15066 - 9.21501i) q^{90} +7.39246 q^{91} +(-6.03514 + 15.0608i) q^{92} +(0.392489 + 0.540215i) q^{93} +(7.27229 - 7.95902i) q^{94} +(2.98657 - 10.6120i) q^{95} +(0.262795 - 0.419055i) q^{96} +(-5.19566 + 7.15121i) q^{97} +(-5.88975 + 1.20701i) q^{98} +(-1.32210 + 8.34741i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 960 q - 10 q^{2} - 20 q^{5} - 16 q^{6} + 2 q^{8} + 960 q^{9} - 60 q^{10} - 40 q^{12} - 20 q^{13} - 8 q^{14} - 28 q^{16} - 20 q^{17} - 48 q^{18} - 34 q^{20} - 40 q^{21} - 10 q^{22} - 48 q^{24} - 4 q^{25}+ \cdots - 38 q^{98}+O(q^{100}) \) 960 * q - 10 * q^2 - 20 * q^5 - 16 * q^6 + 2 * q^8 + 960 * q^9 - 60 * q^10 - 40 * q^12 - 20 * q^13 - 8 * q^14 - 28 * q^16 - 20 * q^17 - 48 * q^18 - 34 * q^20 - 40 * q^21 - 10 * q^22 - 48 * q^24 - 4 * q^25 - 20 * q^26 - 10 * q^28 - 10 * q^30 - 56 * q^33 - 20 * q^34 - 100 * q^36 + 88 * q^37 - 16 * q^40 - 24 * q^41 - 104 * q^42 - 100 * q^45 - 20 * q^46 - 40 * q^48 + 224 * q^49 - 12 * q^50 - 38 * q^52 - 20 * q^53 - 52 * q^54 + 96 * q^56 - 72 * q^57 - 38 * q^58 - 14 * q^60 - 40 * q^61 - 10 * q^62 - 120 * q^64 - 60 * q^65 - 12 * q^66 - 116 * q^68 - 104 * q^69 - 96 * q^70 - 24 * q^72 - 72 * q^73 - 28 * q^74 - 40 * q^76 - 76 * q^77 - 44 * q^78 - 90 * q^80 + 592 * q^81 - 130 * q^82 - 92 * q^84 - 64 * q^85 - 12 * q^86 - 104 * q^88 + 136 * q^89 - 364 * q^90 - 220 * q^92 - 32 * q^94 - 44 * q^96 + 80 * q^97 - 38 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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