LMFDB - Embedded newform 820.2.bv.c.103.54

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			103.54
Character	$\chi$	$=$	820.103
Dual form			820.2.bv.c.207.54

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.283920 + 1.38542i) q^{2} -0.0874408 q^{3} +(-1.83878 - 0.786698i) q^{4} +(-0.437444 - 2.19286i) q^{5} +(0.0248262 - 0.121142i) q^{6} +(3.19012 - 1.03653i) q^{7} +(1.61197 - 2.32412i) q^{8} -2.99235 q^{9} +(3.16223 + 0.0165545i) q^{10} +(-0.441826 + 2.78958i) q^{11} +(0.160784 + 0.0687895i) q^{12} +(-2.09602 - 0.681038i) q^{13} +(0.530293 + 4.71394i) q^{14} +(0.0382504 + 0.191746i) q^{15} +(2.76221 + 2.89313i) q^{16} +(0.954122 + 1.31324i) q^{17} +(0.849590 - 4.14567i) q^{18} +(-4.39283 - 2.23826i) q^{19} +(-0.920757 + 4.37632i) q^{20} +(-0.278946 + 0.0906351i) q^{21} +(-3.73930 - 1.40413i) q^{22} +(-3.68299 - 7.22827i) q^{23} +(-0.140952 + 0.203223i) q^{24} +(-4.61729 + 1.91851i) q^{25} +(1.53863 - 2.71051i) q^{26} +0.523976 q^{27} +(-6.68135 - 0.603705i) q^{28} +(6.02052 - 0.953557i) q^{29} +(-0.276508 - 0.00144754i) q^{30} +(-4.48863 - 6.17807i) q^{31} +(-4.79244 + 3.00541i) q^{32} +(0.0386336 - 0.243923i) q^{33} +(-2.09028 + 0.949006i) q^{34} +(-3.66847 - 6.54206i) q^{35} +(5.50228 + 2.35408i) q^{36} +(-6.99381 + 1.10771i) q^{37} +(4.34814 - 5.45042i) q^{38} +(0.183277 + 0.0595505i) q^{39} +(-5.80163 - 2.51816i) q^{40} +(-6.31926 + 1.03296i) q^{41} +(-0.0463692 - 0.412191i) q^{42} +(0.133674 - 0.0681104i) q^{43} +(3.00698 - 4.78184i) q^{44} +(1.30899 + 6.56182i) q^{45} +(11.0599 - 3.05023i) q^{46} +(2.35576 - 7.25028i) q^{47} +(-0.241530 - 0.252977i) q^{48} +(3.43932 - 2.49881i) q^{49} +(-1.34700 - 6.94158i) q^{50} +(-0.0834292 - 0.114830i) q^{51} +(3.31834 + 2.90121i) q^{52} +(1.53538 - 2.11326i) q^{53} +(-0.148767 + 0.725927i) q^{54} +(6.31044 - 0.251421i) q^{55} +(2.73336 - 9.08508i) q^{56} +(0.384112 + 0.195715i) q^{57} +(-0.388271 + 8.61169i) q^{58} +(-0.934995 + 2.87762i) q^{59} +(0.0805117 - 0.382669i) q^{60} +(5.95586 - 1.93517i) q^{61} +(9.83364 - 4.46456i) q^{62} +(-9.54596 + 3.10167i) q^{63} +(-2.80308 - 7.49285i) q^{64} +(-0.576531 + 4.89419i) q^{65} +(0.326967 + 0.122778i) q^{66} +(6.52642 + 4.74172i) q^{67} +(-0.721299 - 3.16536i) q^{68} +(0.322043 + 0.632046i) q^{69} +(10.1051 - 3.22494i) q^{70} +(2.11086 - 13.3274i) q^{71} +(-4.82360 + 6.95459i) q^{72} +(-7.23913 + 7.23913i) q^{73} +(0.451040 - 10.0039i) q^{74} +(0.403739 - 0.167756i) q^{75} +(6.31660 + 7.57149i) q^{76} +(1.48201 + 9.35705i) q^{77} +(-0.134539 + 0.237009i) q^{78} +(-4.92171 - 4.92171i) q^{79} +(5.13591 - 7.32273i) q^{80} +8.93125 q^{81} +(0.363078 - 9.04810i) q^{82} +(2.96110 - 2.96110i) q^{83} +(0.584223 + 0.0527885i) q^{84} +(2.46237 - 2.66673i) q^{85} +(0.0564087 + 0.204533i) q^{86} +(-0.526439 + 0.0833798i) q^{87} +(5.77111 + 5.52359i) q^{88} +(-13.4242 - 6.84000i) q^{89} +(-9.46252 - 0.0495370i) q^{90} -7.39246 q^{91} +(1.08573 + 16.1886i) q^{92} +(0.392489 + 0.540215i) q^{93} +(9.37583 + 5.32222i) q^{94} +(-2.98657 + 10.6120i) q^{95} +(0.419055 - 0.262795i) q^{96} +(-5.19566 + 7.15121i) q^{97} +(2.48541 + 5.47437i) 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 $

$2$	−0.283920	+	1.38542i	−0.200762	+	0.979640i
$2$	−0.283920	+	1.38542i	−0.200762	+	0.979640i
$3$	−0.0874408			−0.0504840			−0.0252420	−	0.999681i	$-0.508036\pi$
$3$	−0.0874408			−0.0504840			−0.0252420	+	0.999681i	$0.508036\pi$
$4$	−1.83878	−	0.786698i	−0.919389	−	0.393349i
$5$	−0.437444	−	2.19286i	−0.195631	−	0.980678i
$5$	−0.437444	−	2.19286i	−0.195631	−	0.980678i
$6$	0.0248262	−	0.121142i	0.0101353	−	0.0494561i
$7$	3.19012	−	1.03653i	1.20575	−	0.391772i	0.363877	−	0.931447i	$-0.381453\pi$
$7$	3.19012	−	1.03653i	1.20575	−	0.391772i	0.841873	+	0.539675i	$0.181453\pi$
$8$	1.61197	−	2.32412i	0.569919	−	0.821701i
$9$	−2.99235			−0.997451
$10$	3.16223	+	0.0165545i	0.999986	+	0.00523500i
$11$	−0.441826	+	2.78958i	−0.133216	+	0.841090i	0.827076	+	0.562091i	$0.190003\pi$
$11$	−0.441826	+	2.78958i	−0.133216	+	0.841090i	−0.960291	+	0.278999i	$0.909997\pi$
$12$	0.160784	+	0.0687895i	0.0464144	+	0.0198578i
$13$	−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	$0.698865\pi$
$14$	0.530293	+	4.71394i	0.141727	+	1.25985i
$15$	0.0382504	+	0.191746i	0.00987622	+	0.0495085i
$16$	2.76221	+	2.89313i	0.690553	+	0.723282i
$17$	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	$0.736929\pi$
$18$	0.849590	−	4.14567i	0.200250	−	0.977143i
$19$	−4.39283	−	2.23826i	−1.00778	−	0.513491i	−0.129474	−	0.991583i	$-0.541329\pi$
$19$	−4.39283	−	2.23826i	−1.00778	−	0.513491i	−0.878310	+	0.478091i	$0.841329\pi$
$20$	−0.920757	+	4.37632i	−0.205888	+	0.978576i
$21$	−0.278946	+	0.0906351i	−0.0608711	+	0.0197782i
$22$	−3.73930	−	1.40413i	−0.797221	−	0.299362i
$23$	−3.68299	−	7.22827i	−0.767956	−	1.50720i	−0.859352	−	0.511384i	$-0.829133\pi$
$23$	−3.68299	−	7.22827i	−0.767956	−	1.50720i	0.0913962	−	0.995815i	$-0.470867\pi$
$24$	−0.140952	+	0.203223i	−0.0287718	+	0.0414827i
$25$	−4.61729	+	1.91851i	−0.923457	+	0.383701i
$26$	1.53863	−	2.71051i	0.301749	−	0.531574i
$27$	0.523976			0.100839
$28$	−6.68135	−	0.603705i	−1.26266	−	0.114090i
$29$	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	$0.258506\pi$
$30$	−0.276508	−	0.00144754i	−0.0504833	−	0.000264284i
$31$	−4.48863	−	6.17807i	−0.806182	−	1.10961i	−0.991901	−	0.127012i	$-0.959461\pi$
$31$	−4.48863	−	6.17807i	−0.806182	−	1.10961i	0.185719	−	0.982603i	$-0.440539\pi$
$32$	−4.79244	+	3.00541i	−0.847192	+	0.531286i
$33$	0.0386336	−	0.243923i	0.00672525	−	0.0424615i
$34$	−2.09028	+	0.949006i	−0.358480	+	0.162753i
$35$	−3.66847	−	6.54206i	−0.620084	−	1.10581i
$36$	5.50228	+	2.35408i	0.917046	+	0.392346i
$37$	−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
$40$	−5.80163	−	2.51816i	−0.917317	−	0.398157i
$41$	−6.31926	+	1.03296i	−0.986902	+	0.161322i
$41$	−6.31926	+	1.03296i	−0.986902	+	0.161322i
$42$	−0.0463692	−	0.412191i	−0.00715493	−	0.0636024i
$43$	0.133674	−	0.0681104i	0.0203851	−	0.0103867i	−0.443768	−	0.896142i	$-0.646359\pi$
$43$	0.133674	−	0.0681104i	0.0203851	−	0.0103867i	0.464153	+	0.885755i	$0.346359\pi$
$44$	3.00698	−	4.78184i	0.453319	−	0.720889i
$45$	1.30899	+	6.56182i	0.195132	+	0.978178i
$46$	11.0599	−	3.05023i	1.63069	−	0.449732i
$47$	2.35576	−	7.25028i	0.343623	−	1.05756i	−0.618694	−	0.785632i	$-0.712338\pi$
$47$	2.35576	−	7.25028i	0.343623	−	1.05756i	0.962317	−	0.271930i	$-0.0876619\pi$
$48$	−0.241530	−	0.252977i	−0.0348619	−	0.0365141i
$49$	3.43932	−	2.49881i	0.491332	−	0.356973i
$50$	−1.34700	−	6.94158i	−0.190494	−	0.981688i
$51$	−0.0834292	−	0.114830i	−0.0116824	−	0.0160795i
$52$	3.31834	+	2.90121i	0.460171	+	0.402326i
$53$	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	$0.142584\pi$
$54$	−0.148767	+	0.725927i	−0.0202447	+	0.0987862i
$55$	6.31044	−	0.251421i	0.850899	−	0.0339016i
$56$	2.73336	−	9.08508i	0.365260	−	1.21404i
$57$	0.384112	+	0.195715i	0.0508769	+	0.0259231i
$58$	−0.388271	+	8.61169i	−0.0509825	+	1.13077i
$59$	−0.934995	+	2.87762i	−0.121726	+	0.374634i	−0.993290	−	0.115647i	$-0.963106\pi$
$59$	−0.934995	+	2.87762i	−0.121726	+	0.374634i	0.871564	+	0.490281i	$0.163106\pi$
$60$	0.0805117	−	0.382669i	0.0103940	−	0.0494024i
$61$	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	$0.268695\pi$
$62$	9.83364	−	4.46456i	1.24887	−	0.567000i
$63$	−9.54596	+	3.10167i	−1.20268	+	0.390774i
$64$	−2.80308	−	7.49285i	−0.350385	−	0.936606i
$65$	−0.576531	+	4.89419i	−0.0715099	+	0.607050i
$66$	0.326967	+	0.122778i	0.0402469	+	0.0151130i
$67$	6.52642	+	4.74172i	0.797329	+	0.579294i	0.910129	−	0.414324i	$-0.135982\pi$
$67$	6.52642	+	4.74172i	0.797329	+	0.579294i	−0.112800	+	0.993618i	$0.535982\pi$
$68$	−0.721299	−	3.16536i	−0.0874704	−	0.383856i
$69$	0.322043	+	0.632046i	0.0387695	+	0.0760893i
$70$	10.1051	−	3.22494i	1.20778	−	0.385455i
$71$	2.11086	−	13.3274i	0.250513	−	1.58167i	−0.466440	−	0.884553i	$-0.654464\pi$
$71$	2.11086	−	13.3274i	0.250513	−	1.58167i	0.716953	−	0.697122i	$-0.245536\pi$
$72$	−4.82360	+	6.95459i	−0.568466	+	0.819607i
$73$	−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	$0.454481\pi$
$74$	0.451040	−	10.0039i	0.0524323	−	1.16293i
$75$	0.403739	−	0.167756i	0.0466198	−	0.0193708i
$76$	6.31660	+	7.57149i	0.724564	+	0.868509i
$77$	1.48201	+	9.35705i	0.168891	+	1.06633i
$78$	−0.134539	+	0.237009i	−0.0152335	+	0.0268360i
$79$	−4.92171	−	4.92171i	−0.553736	−	0.553736i	0.373781	−	0.927517i	$-0.378061\pi$
$79$	−4.92171	−	4.92171i	−0.553736	−	0.553736i	−0.927517	+	0.373781i	$0.878061\pi$
$80$	5.13591	−	7.32273i	0.574213	−	0.818706i
$81$	8.93125			0.992361
$82$	0.363078	−	9.04810i	0.0400952	−	0.999196i
$83$	2.96110	−	2.96110i	0.325023	−	0.325023i	−0.525667	−	0.850690i	$-0.676184\pi$
$83$	2.96110	−	2.96110i	0.325023	−	0.325023i	0.850690	+	0.525667i	$0.176184\pi$
$84$	0.584223	+	0.0527885i	0.0637439	+	0.00575969i
$85$	2.46237	−	2.66673i	0.267082	−	0.289247i
$86$	0.0564087	+	0.204533i	0.00608271	+	0.0220553i
$87$	−0.526439	+	0.0833798i	−0.0564402	+	0.00893925i
$88$	5.77111	+	5.52359i	0.615202	+	0.588816i
$89$	−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	$0.944382\pi$
$90$	−9.46252	−	0.0495370i	−0.997438	−	0.00522166i
$91$	−7.39246			−0.774940
$92$	1.08573	+	16.1886i	0.113196	+	1.68778i
$93$	0.392489	+	0.540215i	0.0406993	+	0.0560177i
$94$	9.37583	+	5.32222i	0.967043	+	0.548945i
$95$	−2.98657	+	10.6120i	−0.306416	+	1.08877i
$96$	0.419055	−	0.262795i	0.0427696	−	0.0268214i
$97$	−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	$0.348131\pi$
$98$	2.48541	+	5.47437i	0.251065	+	0.552995i
$99$	1.32210	−	8.34741i	0.132876	−	0.838946i
$100$	9.99945	+	0.104699i	0.999945	+	0.0104699i
$101$	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	$0.416632\pi$
$102$	0.182776	−	0.0829818i	0.0180975	−	0.00821642i
$103$	−2.32395	+	4.56100i	−0.228985	+	0.449409i	−0.976699	−	0.214612i	$-0.931151\pi$
$103$	−2.32395	+	4.56100i	−0.228985	+	0.449409i	0.747714	+	0.664021i	$0.231151\pi$
$104$	−4.96154	+	3.77359i	−0.486519	+	0.370031i
$105$	0.320774	+	0.572043i	0.0313043	+	0.0558257i
$106$	2.49183	+	2.72714i	0.242028	+	0.264883i
$107$	−2.81393	+	5.52265i	−0.272033	+	0.533894i	−0.986094	−	0.166189i	$-0.946854\pi$
$107$	−2.81393	+	5.52265i	−0.272033	+	0.533894i	0.714061	+	0.700083i	$0.246854\pi$
$108$	−0.963476	−	0.412211i	−0.0927105	−	0.0396650i
$109$	−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	$0.936797\pi$
$110$	−1.44334	+	8.81399i	−0.137617	+	0.840381i
$111$	0.611544	−	0.0968591i	0.0580452	−	0.00919346i
$112$	11.8106	+	6.36629i	1.11600	+	0.601558i
$113$	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
$116$	−11.8206	−	2.98295i	−1.09751	−	0.276960i
$117$	6.27203	+	2.03791i	0.579849	+	0.188404i
$118$	−3.72125	−	2.11238i	−0.342569	−	0.194460i
$119$	4.40497	+	3.20040i	0.403803	+	0.293380i
$120$	0.507299	+	0.220190i	0.0463098	+	0.0201005i
$121$	2.87508	+	0.934169i	0.261370	+	0.0849244i
$122$	0.990042	+	8.80080i	0.0896342	+	0.796787i
$123$	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
$126$	−1.58682	−	14.1058i	−0.141366	−	1.25664i
$127$	−1.22502	−	7.73449i	−0.108703	−	0.686325i	−0.980509	−	0.196473i	$-0.937051\pi$
$127$	−1.22502	−	7.73449i	−0.108703	−	0.686325i	0.871806	−	0.489851i	$-0.162949\pi$
$128$	11.1766	−	1.75608i	0.987880	−	0.155217i
$129$	−0.0116886	+	0.00595563i	−0.00102912	+	0.000524364i
$130$	−6.61683	−	2.18830i	−0.580334	−	0.191927i
$131$	8.10031	−	5.88522i	0.707727	−	0.514194i	−0.174712	−	0.984620i	$-0.555900\pi$
$131$	8.10031	−	5.88522i	0.707727	−	0.514194i	0.882440	+	0.470425i	$0.155900\pi$
$132$	−0.262932	+	0.418127i	−0.0228853	+	0.0363933i
$133$	−16.3337	−	2.58700i	−1.41631	−	0.224321i
$134$	−8.42226	+	7.69557i	−0.727573	+	0.664796i
$135$	−0.229210	−	1.14901i	−0.0197273	−	0.0988908i
$136$	4.59014	−	0.100593i	0.393601	−	0.00862579i
$137$		−	8.29161i		−	0.708400i	−0.935170	−	0.354200i	$-0.884753\pi$
$137$		−	8.29161i		−	0.708400i	0.935170	−	0.354200i	$-0.115247\pi$
$138$	−0.967083	+	0.266715i	−0.0823236	+	0.0227043i
$139$	1.00225	+	3.08462i	0.0850100	+	0.261634i	0.984522	−	0.175263i	$-0.0560775\pi$
$139$	1.00225	+	3.08462i	0.0850100	+	0.261634i	−0.899512	+	0.436897i	$0.856078\pi$
$140$	1.59887	+	14.9154i	0.135129	+	1.26058i
$141$	−0.205989	+	0.633970i	−0.0173474	+	0.0533899i
$142$	17.8648	+	6.70835i	1.49918	+	0.562952i
$143$	2.82588	−	5.54611i	0.236312	−	0.463789i
$144$	−8.26552	−	8.65726i	−0.688793	−	0.721438i
$145$	−4.72466	−	12.7851i	−0.392362	−	1.06174i
$146$	−7.97390	−	12.0846i	−0.659925	−	1.00013i
$147$	−0.300737	+	0.218498i	−0.0248044	+	0.0180214i
$148$	13.7315	+	3.46518i	1.12872	+	0.284836i
$149$	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	$0.858284\pi$
$150$	0.117783	+	0.606978i	0.00961690	+	0.0495595i
$151$	−6.43889	−	12.6370i	−0.523989	−	1.02839i	−0.989661	−	0.143429i	$-0.954187\pi$
$151$	−6.43889	−	12.6370i	−0.523989	−	1.02839i	0.465671	−	0.884958i	$-0.345813\pi$
$152$	−12.2831	+	6.60145i	−0.996291	+	0.535448i
$153$	−2.85507	−	3.92967i	−0.230819	−	0.317695i
$154$	−13.3842	−	0.603448i	−1.07853	−	0.0486272i
$155$	−11.5841	+	12.5455i	−0.930460	+	1.00768i
$156$	−0.290158	−	0.253684i	−0.0232313	−	0.0203110i
$157$	−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	$0.922502\pi$
$158$	8.21601	−	5.42126i	0.653631	−	0.431293i
$159$	−0.134254	+	0.184785i	−0.0106471	+	0.0146544i
$160$	8.68687	+	9.19447i	0.686757	+	0.726887i
$161$	−19.2415	−	19.2415i	−1.51644	−	1.51644i
$162$	−2.53576	+	12.3735i	−0.199228	+	0.972156i
$163$	0.577449	−	0.577449i	0.0452293	−	0.0452293i	−0.684130	−	0.729360i	$-0.739818\pi$
$163$	0.577449	−	0.577449i	0.0452293	−	0.0452293i	0.729360	+	0.684130i	$0.239818\pi$
$164$	12.4323	+	3.07196i	0.970803	+	0.239879i
$165$	−0.551790	+	0.0219844i	−0.0429568	+	0.00171149i
$166$	3.26165	+	4.94308i	0.253153	+	0.383658i
$167$			4.26749i			0.330228i	0.986274	+	0.165114i	$0.0527992\pi$
$167$			4.26749i			0.330228i	−0.986274	+	0.165114i	$0.947201\pi$
$168$	−0.239007	+	0.794406i	−0.0184398	+	0.0612898i
$169$	−6.58774	−	4.78627i	−0.506749	−	0.368175i
$170$	2.99542	+	4.16856i	0.229738	+	0.319714i
$171$	13.1449	+	6.69766i	1.00522	+	0.512183i
$172$	−0.299380	+	0.0200787i	−0.0228275	+	0.00153099i
$173$	−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	$0.273381\pi$
$174$	0.0339507	−	0.753013i	0.00257380	−	0.0570858i
$175$	−12.7411	+	10.9062i	−0.963135	+	0.824433i
$176$	−9.29102	+	6.42716i	−0.700337	+	0.484465i
$177$	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	0.680713	−	0.732550i	$-0.261670\pi$
$179$	20.7975	−	3.29400i	1.55448	−	0.246205i	0.873767	+	0.486345i	$0.161670\pi$
$180$	2.75523	−	13.0955i	0.205363	−	0.976082i
$181$	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	$-0.109804\pi$
$182$	2.09887	−	10.2417i	0.155579	−	0.759163i
$183$	−0.520785	+	0.169213i	−0.0384975	+	0.0125086i
$184$	−22.7363	−	3.09207i	−1.67614	−	0.227950i
$185$	5.48846	+	14.8519i	0.403519	+	1.09193i
$186$	−0.859861	+	0.390385i	−0.0630481	+	0.0286244i
$187$	−4.08493	+	2.08138i	−0.298720	+	0.152205i
$188$	−10.0355	+	11.4784i	−0.731914	+	0.837147i
$189$	1.67154	−	0.543118i	0.121587	−	0.0395060i
$190$	−13.8541	−	7.15061i	−1.00508	−	0.518760i
$191$	−4.99906	−	4.99906i	−0.361719	−	0.361719i	0.502726	−	0.864446i	$-0.332330\pi$
$191$	−4.99906	−	4.99906i	−0.361719	−	0.361719i	−0.864446	+	0.502726i	$0.832330\pi$
$192$	0.245104	+	0.655180i	0.0176888	+	0.0472836i
$193$	−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	$0.937048\pi$
$194$	−8.43227	−	9.22854i	−0.605402	−	0.662570i
$195$	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	$0.831231\pi$
$198$	11.1893	+	4.20166i	0.795189	+	0.298599i
$199$	9.41458	+	18.4772i	0.667382	+	1.30981i	0.937836	+	0.347078i	$0.112826\pi$
$199$	9.41458	+	18.4772i	0.667382	+	1.30981i	−0.270454	+	0.962733i	$0.587174\pi$
$200$	−2.98410	+	13.8237i	−0.211008	+	0.977484i
$201$	−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
$210$	−0.883594	+	0.281992i	−0.0609738	+	0.0194593i
$211$	8.74091	−	4.45372i	0.601749	−	0.306607i	−0.126449	−	0.991973i	$-0.540358\pi$
$211$	8.74091	−	4.45372i	0.601749	−	0.306607i	0.728198	+	0.685367i	$0.240358\pi$
$212$	−4.48572	+	2.67795i	−0.308080	+	0.183922i
$213$	−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
$216$	0.844636	−	1.21778i	0.0574702	−	0.0828597i
$217$	−20.7230	−	15.0562i	−1.40677	−	1.02208i
$218$	13.6481	−	9.00559i	0.924367	−	0.609936i
$219$	0.632995	−	0.632995i	0.0427739	−	0.0427739i
$220$	−11.8013	−	4.50210i	−0.795643	−	0.303532i
$221$	−1.10549	−	3.40236i	−0.0743636	−	0.228868i
$222$	−0.0394393	+	0.874746i	−0.00264699	+	0.0587091i
$223$	8.02402	+	15.7480i	0.537328	+	1.05457i	0.986902	+	0.161323i	$0.0515760\pi$
$223$	8.02402	+	15.7480i	0.537328	+	1.05457i	−0.449574	+	0.893243i	$0.648424\pi$
$224$	−12.1733	+	14.5551i	−0.813360	+	0.972505i
$225$	13.8166	−	5.74085i	0.921104	−	0.382724i
$226$	−5.67745	+	15.1194i	−0.377658	+	1.00573i
$227$	0.114809	+	0.353345i	0.00762012	+	0.0234523i	0.954794	−	0.297267i	$-0.0960753\pi$
$227$	0.114809	+	0.353345i	0.00762012	+	0.0234523i	−0.947174	+	0.320720i	$0.896075\pi$
$228$	−0.552329	−	0.662057i	−0.0365789	−	0.0438458i
$229$	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	$0.343432\pi$
$230$	−11.5268	−	22.9185i	−0.760055	−	1.51120i
$231$	−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	$0.369470\pi$
$234$	−4.60411	+	8.11079i	−0.300980	+	0.530219i
$235$	−16.9294	−	1.99426i	−1.10435	−	0.130091i
$236$	3.98306	−	4.55574i	0.259275	−	0.296554i
$237$	0.430358	+	0.430358i	0.0279548	+	0.0279548i
$238$	−5.68456	+	5.19408i	−0.368475	+	0.336682i
$239$	8.51644	−	16.7145i	0.550883	−	1.08117i	−0.432839	−	0.901471i	$-0.642488\pi$
$239$	8.51644	−	16.7145i	0.550883	−	1.08117i	0.983722	−	0.179697i	$-0.0575118\pi$
$240$	−0.449088	+	0.640305i	−0.0289885	+	0.0413315i
$241$	−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	$0.848197\pi$
$242$	−2.11051	+	3.71796i	−0.135669	+	0.238999i
$243$	−2.35288			−0.150938
$244$	−12.4739	−	1.12710i	−0.798559	−	0.0721552i
$245$	−6.98406	−	6.44887i	−0.446196	−	0.412003i
$246$	−0.0317478	+	0.791173i	−0.00202417	+	0.0504434i
$247$	7.68311	+	7.68311i	0.488865	+	0.488865i
$248$	−21.5941	+	0.473237i	−1.37123	+	0.0300506i
$249$	−0.258921	+	0.258921i	−0.0164084	+	0.0164084i
$250$	−14.6327	+	5.99033i	−0.925453	+	0.378862i
$251$	8.87634	+	6.44904i	0.560270	+	0.407060i	0.831558	−	0.555438i	$-0.187450\pi$
$251$	8.87634	+	6.44904i	0.560270	+	0.407060i	−0.271288	+	0.962498i	$0.587450\pi$
$252$	19.9930	+	1.80650i	1.25944	+	0.113799i
$253$	21.7911	−	7.08035i	1.36999	−	0.445138i
$254$	11.0633	+	0.498807i	0.694175	+	0.0312979i
$255$	−0.215312	+	0.233181i	−0.0134833	+	0.0146023i
$256$	−0.740359	+	15.9829i	−0.0462724	+	0.998929i
$257$	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	$0.177309\pi$
$258$	−0.00493242	−	0.0178845i	−0.000307079	−	0.00111344i
$259$	−21.1629	+	10.7830i	−1.31500	+	0.670025i
$260$	4.91037	−	8.54578i	0.304528	−	0.529987i
$261$	−18.0155	+	2.85338i	−1.11513	+	0.176620i
$262$	5.85366	+	12.8933i	0.361640	+	0.796549i
$263$	1.33587	+	1.83867i	0.0823735	+	0.113377i	0.848215	−	0.529652i	$-0.177677\pi$
$263$	1.33587	+	1.83867i	0.0823735	+	0.113377i	−0.765842	+	0.643029i	$0.777677\pi$
$264$	−0.504630	−	0.482987i	−0.0310579	−	0.0297258i
$265$	−5.30573	−	2.44243i	−0.325929	−	0.150037i
$266$	8.22153	−	21.8945i	0.504094	−	1.34244i
$267$	1.17383	+	0.598095i	0.0718370	+	0.0366028i
$268$	−8.27034	−	13.8533i	−0.505192	−	0.846225i
$269$	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	$0.443557\pi$
$270$	1.65694	+	0.00867418i	0.100838	+	0.000527894i
$271$	9.41706	−	3.05979i	0.572045	−	0.185869i	−0.00868853	−	0.999962i	$-0.502766\pi$
$271$	9.41706	−	3.05979i	0.572045	−	0.185869i	0.580734	+	0.814093i	$0.302766\pi$
$272$	−1.16387	+	6.38783i	−0.0705700	+	0.387319i
$273$	0.646402			0.0391221
$274$	11.4874	+	2.35416i	0.693977	+	0.142220i
$275$	−3.31179	−	13.7279i	−0.199709	−	0.827826i
$276$	−0.0949374	−	1.41554i	−0.00571456	−	0.0852057i
$277$	−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	$0.734887\pi$
$278$	−4.55805	+	0.512756i	−0.273374	+	0.0307531i
$279$	13.4316	+	18.4870i	0.804128	+	1.10679i
$280$	−21.1180	−	2.01966i	−1.26204	−	0.120698i
$281$	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	$0.668642\pi$
$282$	−0.819830	−	0.465379i	−0.0488202	−	0.0277129i
$283$	−11.2918	+	1.78844i	−0.671225	+	0.106312i	−0.482739	−	0.875764i	$-0.660358\pi$
$283$	−11.2918	+	1.78844i	−0.671225	+	0.106312i	−0.188486	+	0.982076i	$0.560358\pi$
$284$	−14.3661	+	22.8456i	−0.852469	+	1.35564i
$285$	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
$288$	14.3407	−	8.99325i	0.845033	−	0.529932i
$289$	4.43905	−	13.6620i	0.261120	−	0.803646i
$290$	19.0541	−	2.91571i	1.11889	−	0.171216i
$291$	0.454312	−	0.625307i	0.0266322	−	0.0366561i
$292$	19.0062	−	7.61615i	1.11225	−	0.445702i
$293$	−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	$0.979103\pi$
$294$	−0.217327	−	0.478683i	−0.0126747	−	0.0279174i
$295$	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
$298$	−9.80088	−	0.441888i	−0.567750	−	0.0255979i
$299$	2.79689	+	17.6588i	0.161748	+	1.02124i
$300$	−0.874360	−	0.00915493i	−0.0504812	−	0.000528560i
$301$	0.355838	−	0.355838i	0.0205101	−	0.0205101i
$302$	19.3357	−	5.33266i	1.11265	−	0.306860i
$303$	−1.04797	−	0.533968i	−0.0602044	−	0.0306757i
$304$	−5.65836	−	18.8915i	−0.324529	−	1.08350i
$305$	−6.84892	−	12.2138i	−0.392168	−	0.699362i
$306$	6.25486	−	2.83976i	0.357566	−	0.162338i
$307$	−6.53128	−	3.32785i	−0.372760	−	0.189930i	0.257567	−	0.966260i	$-0.417079\pi$
$307$	−6.53128	−	3.32785i	−0.372760	−	0.189930i	−0.630327	+	0.776330i	$0.717079\pi$
$308$	4.63608	−	18.3714i	0.264165	−	1.04681i
$309$	0.203208	−	0.398818i	0.0115601	−	0.0226879i
$310$	−14.0918	−	19.6108i	−0.800362	−	1.11382i
$311$	0.479154	+	0.0758905i	0.0271703	+	0.00430335i	0.170005	−	0.985443i	$-0.445622\pi$
$311$	0.479154	+	0.0758905i	0.0271703	+	0.00430335i	−0.142835	+	0.989747i	$0.545622\pi$
$312$	0.433841	−	0.329965i	0.0245614	−	0.0186806i
$313$	−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	$0.700255\pi$
$314$	2.48752	−	0.279832i	0.140379	−	0.0157918i
$315$	10.9774	+	19.5762i	0.618504	+	1.10299i
$316$	5.17804	+	12.9218i	0.291287	+	0.726910i
$317$	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	$0.0116454\pi$
$318$	−0.217888	−	0.238463i	−0.0122185	−	0.0133723i
$319$			17.2160i			0.963913i
$320$	−15.2046	+	9.42447i	−0.849962	+	0.526844i
$321$	0.246052	−	0.482905i	0.0137333	−	0.0269531i
$322$	32.1206	−	21.1945i	1.79001	−	1.18112i
$323$	−1.25193	−	7.90439i	−0.0696594	−	0.439812i
$324$	−16.4226	−	7.02619i	−0.912366	−	0.390344i
$325$	10.9845	−	0.876681i	0.609310	−	0.0486295i
$326$	0.636060	+	0.963958i	0.0352281	+	0.0533887i
$327$	0.714894	+	0.714894i	0.0395337	+	0.0395337i
$328$	−7.78574	+	16.3518i	−0.429896	+	0.902879i
$329$		−	25.5710i		−	1.40978i
$330$	0.126207	−	0.770702i	0.00694744	−	0.0424258i
$331$	14.1122	−	14.1122i	0.775675	−	0.775675i	−0.203417	−	0.979092i	$-0.565205\pi$
$331$	14.1122	−	14.1122i	0.775675	−	0.775675i	0.979092	+	0.203417i	$0.0652046\pi$
$332$	−7.77430	+	3.11532i	−0.426670	+	0.170975i
$333$	20.9280	−	3.31466i	1.14685	−	0.181642i
$334$	−5.91227	−	1.21163i	−0.323505	−	0.0662973i
$335$	7.54300	−	16.3858i	0.412118	−	0.895251i
$336$	−1.03273	−	0.556673i	−0.0563399	−	0.0303690i
$337$	−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	$0.954558\pi$
$338$	8.50139	−	7.76787i	0.462415	−	0.422516i
$339$	−0.986274	−	0.156210i	−0.0535670	−	0.00848419i
$340$	−6.62566	+	2.96637i	−0.359327	+	0.160874i
$341$	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
$344$	0.0571824	−	0.420467i	0.00308307	−	0.0226701i
$345$	1.24511	−	0.982681i	0.0670346	−	0.0529058i
$346$	−1.50364	−	2.27879i	−0.0808362	−	0.122509i
$347$	−4.99525	−	15.3738i	−0.268159	−	0.825309i	−0.990949	−	0.134241i	$-0.957140\pi$
$347$	−4.99525	−	15.3738i	−0.268159	−	0.825309i	0.722790	−	0.691068i	$-0.242860\pi$
$348$	1.03360	+	0.260832i	0.0554068	+	0.0139820i
$349$	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	$0.646478\pi$
$350$	−11.4923	−	20.7483i	−0.614287	−	1.10904i
$351$	−1.09826	−	0.356847i	−0.0586210	−	0.0190471i
$352$	−6.26640	−	14.6968i	−0.334000	−	0.783341i
$353$	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	$0.0220785\pi$
$354$	0.325389	+	0.184708i	0.0172942	+	0.00981710i
$355$	−30.1486	+	1.20118i	−1.60012	+	0.0637521i
$356$	19.3032	+	23.1381i	1.02307	+	1.22632i
$357$	−0.385174	−	0.279845i	−0.0203856	−	0.0148110i
$358$	−1.34126	+	29.7485i	−0.0708877	+	1.57226i
$359$	−26.3433	+	19.1395i	−1.39035	+	1.01015i	−0.394518	+	0.918888i	$0.629088\pi$
$359$	−26.3433	+	19.1395i	−1.39035	+	1.01015i	−0.995827	+	0.0912570i	$0.970912\pi$
$360$	17.3605	+	7.53524i	0.914980	+	0.397142i
$361$	3.11921	+	4.29323i	0.164169	+	0.225959i
$362$	17.1427	+	6.43721i	0.901000	+	0.338332i
$363$	−0.251399	−	0.0816844i	−0.0131950	−	0.00428732i
$364$	13.5931	+	5.81563i	0.712472	+	0.304822i
$365$	19.0411	+	12.7077i	0.996658	+	0.665152i
$366$	−0.0865700	−	0.769549i	−0.00452509	−	0.0402249i
$367$	−13.0154	−	25.5442i	−0.679398	−	1.33339i	−0.930806	−	0.365513i	$-0.880894\pi$
$367$	−13.0154	−	25.5442i	−0.679398	−	1.33339i	0.251408	−	0.967881i	$-0.419106\pi$
$368$	10.7391	−	30.6214i	0.559814	−	1.59625i
$369$	18.9094	−	3.09099i	0.984387	−	0.160910i
$370$	−22.1344	+	3.38706i	−1.15071	+	0.176085i
$371$	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	$-0.140027\pi$
$374$	−1.72379	−	6.25030i	−0.0891349	−	0.323195i
$375$	−0.544478	−	0.811960i	−0.0281167	−	0.0419294i
$376$	−13.0531	−	17.1623i	−0.673163	−	0.885079i
$377$	−13.2685	−	2.10153i	−0.683365	−	0.108234i
$378$	0.277861	+	2.46999i	0.0142916	+	0.127043i
$379$	25.7316	−	18.6951i	1.32174	−	0.960301i	0.321832	−	0.946797i	$-0.395701\pi$
$379$	25.7316	−	18.6951i	1.32174	−	0.960301i	0.999909	−	0.0135045i	$-0.00429876\pi$
$380$	13.8401	−	17.1635i	0.709980	−	0.880471i
$381$	0.107117	+	0.676310i	0.00548777	+	0.0346484i
$382$	8.34513	−	5.50646i	0.426974	−	0.281735i
$383$		−	12.0350i		−	0.614959i	−0.951555	−	0.307480i	$-0.900514\pi$
$383$		−	12.0350i		−	0.614959i	0.951555	−	0.307480i	$-0.0994856\pi$
$384$	−0.977290	+	0.153553i	−0.0498721	+	0.00783595i
$385$	19.8704	−	7.34303i	1.01269	−	0.374235i
$386$	−19.4889	−	21.3293i	−0.991961	−	1.08563i
$387$	−0.400001	+	0.203810i	−0.0203332	+	0.0103603i
$388$	15.1795	−	9.06207i	0.770622	−	0.460057i
$389$	−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	$-0.280838\pi$
$390$	0.578581	+	0.191347i	0.0292976	+	0.00968921i
$391$	5.97841	−	11.7333i	0.302341	−	0.593378i
$392$	−0.263450	−	12.0214i	−0.0133062	−	0.607174i
$393$	−0.708297	+	0.514608i	−0.0357289	+	0.0259585i
$394$	10.7874	−	28.7275i	0.543461	−	1.44727i
$395$	−8.63966	+	12.9456i	−0.434708	+	0.651364i
$396$	−8.99794	+	14.3089i	−0.452163	+	0.719052i
$397$	−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	$0.947257\pi$
$398$	−28.2716	+	7.79711i	−1.41713	+	0.390834i
$399$	1.42823	+	0.226209i	0.0715008	+	0.0113246i
$400$	−18.3044	−	8.05906i	−0.915221	−	0.402953i
$401$		−	18.9583i		−	0.946733i	−0.880866	−	0.473366i	$-0.843039\pi$
$401$		−	18.9583i		−	0.946733i	0.880866	−	0.473366i	$-0.156961\pi$
$402$	0.736449	−	0.672906i	0.0367307	−	0.0335615i
$403$	5.20076	+	16.0063i	0.259068	+	0.797330i
$404$	−17.2336	−	20.6573i	−0.857402	−	1.02774i
$405$	−3.90692	−	19.5850i	−0.194136	−	0.973186i
$406$	7.68766	+	27.8747i	0.381532	+	1.38340i
$407$		−	19.9992i		−	0.991324i
$408$	−0.401365	+	0.00879595i	−0.0198706	+	0.000435464i
$409$			0.258705i			0.0127922i	0.999980	+	0.00639608i	$0.00203595\pi$
$409$			0.258705i			0.0127922i	−0.999980	+	0.00639608i	$0.997964\pi$
$410$	−20.0001	+	3.16186i	−0.987733	+	0.156153i
$411$			0.725025i			0.0357628i
$412$	7.86135	−	6.55843i	0.387301	−	0.323111i
$413$			10.1491i			0.499404i
$414$	−33.0950	+	9.12738i	−1.62653	+	0.448586i
$415$	−7.78860	−	5.19797i	−0.382327	−	0.255158i
$416$	12.0918	−	3.03556i	0.592852	−	0.148830i
$417$	−0.0876377	−	0.269721i	−0.00429164	−	0.0132083i
$418$	13.2833	+	14.5376i	0.649706	+	0.711058i
$419$		−	16.3736i		−	0.799904i	−0.916536	−	0.399952i	$-0.869027\pi$
$419$		−	16.3736i		−	0.799904i	0.916536	−	0.399952i	$-0.130973\pi$
$420$	−0.139807	−	1.30421i	−0.00682187	−	0.0636390i
$421$	−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	$0.805838\pi$
$422$	3.68855	+	13.3743i	0.179556	+	0.651053i
$423$	−7.04926	+	21.6954i	−0.342747	+	1.05487i
$424$	−2.43650	−	6.97492i	−0.118327	−	0.338732i
$425$	−6.92491	−	4.23310i	−0.335907	−	0.205335i
$426$	−1.56211	−	0.586584i	−0.0756845	−	0.0284201i
$427$	16.9940	−	12.3469i	0.822397	−	0.597507i
$428$	9.51885	−	7.94121i	0.460111	−	0.383853i
$429$	−0.247098	+	0.484956i	−0.0119300	+	0.0234139i
$430$	0.423837	−	0.213168i	0.0204392	−	0.0102799i
$431$	3.61303	+	11.1197i	0.174033	+	0.535619i	0.999588	−	0.0287027i	$-0.00913761\pi$
$431$	3.61303	+	11.1197i	0.174033	+	0.535619i	−0.825555	+	0.564322i	$0.809138\pi$
$432$	1.44733	+	1.51593i	0.0696349	+	0.0729352i
$433$	−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	$0.393534\pi$
$434$	26.7428	−	24.4353i	1.28370	−	1.17293i
$435$	0.413128	+	1.11793i	0.0198080	+	0.0536009i
$436$	8.60155	+	21.4653i	0.411940	+	1.02800i
$437$			39.9960i			1.91327i
$438$	0.697244	+	1.05668i	0.0333156	+	0.0504903i
$439$	−2.16546	−	13.6722i	−0.103352	−	0.652538i	−0.983919	−	0.178616i	$-0.942838\pi$
$439$	−2.16546	−	13.6722i	−0.103352	−	0.652538i	0.880567	−	0.473922i	$-0.157162\pi$
$440$	9.58793	−	15.0715i	0.457086	−	0.718506i
$441$	−10.2917	+	7.47734i	−0.490080	+	0.356064i
$442$	5.02757	−	0.565575i	0.239137	−	0.0269016i
$443$	29.7904	+	4.71834i	1.41539	+	0.224175i	0.816817	−	0.576896i	$-0.195736\pi$
$443$	29.7904	+	4.71834i	1.41539	+	0.224175i	0.598569	+	0.801071i	$0.295736\pi$
$444$	−1.20069	−	0.302998i	−0.0569824	−	0.0143797i
$445$	−9.12681	+	32.4296i	−0.432652	+	1.53731i
$446$	−24.0958	+	6.64546i	−1.14097	+	0.314671i
$447$	−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	$-0.197225\pi$
$450$	4.03069	+	20.7717i	0.190009	+	0.979186i
$451$	−0.0895198	−	18.0845i	−0.00421532	−	0.851564i
$452$	−19.3348	−	12.1584i	−0.909432	−	0.571881i
$453$	0.563021	+	1.10499i	0.0264531	+	0.0519170i
$454$	−0.522128	+	0.0587365i	−0.0245047	+	0.00275664i
$455$	3.23379	+	16.2106i	0.151602	+	0.759967i
$456$	1.07404	−	0.577236i	0.0502967	−	0.0270316i
$457$	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	$0.437167\pi$
$458$	−9.09343	+	24.2164i	−0.424908	+	1.13156i
$459$	0.499937	+	0.688105i	0.0233351	+	0.0321180i
$460$	35.0244	−	9.46246i	1.63302	−	0.441190i
$461$	−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	$0.578046\pi$
$462$	1.17033	+	0.0527660i	0.0544485	+	0.00245490i
$463$	4.96941	+	3.61048i	0.230948	+	0.167793i	0.697241	−	0.716837i	$-0.254411\pi$
$463$	4.96941	+	3.61048i	0.230948	+	0.167793i	−0.466293	+	0.884630i	$0.654411\pi$
$464$	19.3887	+	14.7842i	0.900099	+	0.686340i
$465$	1.01293	−	1.09699i	0.0469733	−	0.0508717i
$466$	−14.1214	+	24.8768i	−0.654162	+	1.15240i
$467$	−4.17478	+	8.19346i	−0.193186	+	0.379148i	−0.967199	−	0.254022i	$-0.918247\pi$
$467$	−4.17478	+	8.19346i	−0.193186	+	0.379148i	0.774013	+	0.633170i	$0.218247\pi$
$468$	−9.92966	−	8.68145i	−0.458999	−	0.401300i
$469$	25.7350	+	8.36180i	1.18833	+	0.386112i
$470$	7.56948	−	22.8881i	0.349154	−	1.05575i
$471$	0.0478276	+	0.147198i	0.00220378	+	0.00678253i
$472$	5.18075	+	6.81169i	0.238463	+	0.313533i
$473$	0.130939	+	0.402988i	0.00602057	+	0.0185294i
$474$	−0.718414	+	0.474039i	−0.0329979	+	0.0217734i
$475$	24.5770	+	1.90700i	1.12767	+	0.0874992i
$476$	−5.58202	−	9.35021i	−0.255851	−	0.428566i
$477$	−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	0.164747	−	0.986336i	$-0.447319\pi$
$479$	23.1893	−	11.8155i	1.05955	−	0.539865i	0.894798	+	0.446471i	$0.147319\pi$
$480$	−0.759587	−	0.803972i	−0.0346702	−	0.0366961i
$481$	15.4135	+	2.44127i	0.702797	+	0.111312i
$482$	−26.4659	−	28.9651i	−1.20549	−	1.31933i
$483$	1.68249	+	1.68249i	0.0765560	+	0.0765560i
$484$	−4.55172	−	3.97955i	−0.206896	−	0.180888i
$485$	17.9544	+	8.26510i	0.815268	+	0.375299i
$486$	0.668031	−	3.25973i	0.0303025	−	0.147864i
$487$	38.7387	−	6.13561i	1.75542	−	0.278031i	0.805971	−	0.591955i	$-0.201644\pi$
$487$	38.7387	−	6.13561i	1.75542	−	0.278031i	0.949448	+	0.313924i	$0.101644\pi$
$488$	5.10310	−	16.9616i	0.231007	−	0.767815i
$489$	−0.0504926	+	0.0504926i	−0.00228335	+	0.00228335i
$490$	10.9173	−	7.84490i	0.493194	−	0.354396i
$491$			9.05402i			0.408602i	0.978908	+	0.204301i	$0.0654921\pi$
$491$			9.05402i			0.408602i	−0.978908	+	0.204301i	$0.934508\pi$
$492$	−1.08709	−	0.268614i	−0.0490100	−	0.0121101i
$493$	6.99656	+	6.99656i	0.315109	+	0.315109i
$494$	−12.8257	+	8.46294i	−0.577057	+	0.380766i
$495$	−18.8831	+	0.752340i	−0.848731	+	0.0338152i
$496$	5.47539	−	30.0513i	0.245852	−	1.34934i
$497$	−7.08042	−	44.7040i	−0.317600	−	2.00525i
$498$	−0.285201	−	0.432227i	−0.0127802	−	0.0193686i
$499$	3.93488	−	7.72264i	0.176149	−	0.345713i	−0.786004	−	0.618222i	$-0.787853\pi$
$499$	3.93488	−	7.72264i	0.176149	−	0.345713i	0.962153	+	0.272509i	$0.0878534\pi$
$500$	−4.14461	−	21.9732i	−0.185353	−	0.982672i
$501$		−	0.373153i		−	0.0166712i
$502$	−11.4548	+	10.4665i	−0.511253	+	0.467141i
$503$	7.18103	−	5.21733i	0.320186	−	0.232629i	−0.416069	−	0.909333i	$-0.636592\pi$
$503$	7.18103	−	5.21733i	0.320186	−	0.232629i	0.736255	+	0.676704i	$0.236592\pi$
$504$	−8.17917	+	27.1858i	−0.364329	+	1.21095i
$505$	8.14826	−	28.9526i	0.362593	−	1.28837i
$506$	3.62233	+	32.2001i	0.161032	+	1.43147i
$507$	0.576037	+	0.418515i	0.0255827	+	0.0185869i
$508$	−3.83216	+	15.1857i	−0.170025	+	0.673758i
$509$	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	$0.480770\pi$
$510$	−0.261922	−	0.364502i	−0.0115981	−	0.0161404i
$511$	−15.5901	+	30.5973i	−0.689665	+	1.35354i
$512$	−21.9328	−	5.56357i	−0.969301	−	0.245877i
$513$	−2.30174	−	1.17279i	−0.101624	−	0.0517801i
$514$	7.04753	+	15.5229i	0.310853	+	0.684685i
$515$	11.0182	+	3.10091i	0.485522	+	0.136643i
$516$	0.0261780	−	0.00175570i	0.00115242	−	7.72904e-5i
$517$	19.1844	+	9.77494i	0.843729	+	0.429901i
$518$	−8.93045	−	32.3810i	−0.392382	−	1.42274i
$519$	0.119364	−	0.119364i	0.00523950	−	0.00523950i
$520$	10.4454	+	9.22924i	0.458059	+	0.404729i
$521$	−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	$-0.364912\pi$
$522$	1.16185	−	25.7692i	0.0508526	−	1.12789i
$523$	6.40663	−	40.4499i	0.280143	−	1.76875i	−0.299711	−	0.954030i	$-0.596890\pi$
$523$	6.40663	−	40.4499i	0.280143	−	1.76875i	0.579854	−	0.814721i	$-0.303110\pi$
$524$	−19.5246	+	4.44912i	−0.852935	+	0.194361i
$525$	1.11409	−	0.953649i	0.0486229	−	0.0416206i
$526$	−2.92661	+	1.32871i	−0.127606	+	0.0579345i
$527$	3.83057	−	11.7893i	0.166862	−	0.513549i
$528$	0.812414	−	0.561995i	0.0353558	−	0.0244577i
$529$	−25.1644	+	34.6359i	−1.09411	+	1.50591i
$530$	4.89020	−	6.65722i	0.212417	−	0.289171i
$531$	2.79784	−	8.61085i	0.121416	−	0.373679i
$532$	27.9988	+	17.6066i	1.21390	+	0.763341i
$533$	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
$536$	21.5408	−	7.52467i	0.930419	−	0.325016i
$537$	−1.81855	+	0.288030i	−0.0784763	+	0.0124294i
$538$	−10.8076	+	19.0392i	−0.465950	+	0.820836i
$539$	5.45106	+	10.6983i	0.234794	+	0.460809i
$540$	−0.482455	+	2.29309i	−0.0207616	+	0.0986788i
$541$	−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	$-0.492456\pi$
$542$	1.56540	+	13.9153i	0.0672396	+	0.597714i
$543$	−0.177115	+	1.11826i	−0.00760072	+	0.0479891i
$544$	−8.51939	−	3.42609i	−0.365266	−	0.146892i
$545$	−14.3519	+	21.5047i	−0.614766	+	0.921162i
$546$	−0.183527	+	0.895539i	−0.00785422	+	0.0383255i
$547$	−23.2717			−0.995025			−0.497512	−	0.867457i	$-0.665753\pi$
$547$	−23.2717			−0.995025			−0.497512	+	0.867457i	$0.665753\pi$
$548$	−6.52299	+	15.2464i	−0.278648	+	0.651296i
$549$	−17.8220	+	5.79073i	−0.760626	+	0.247142i
$550$	19.9592	−	0.690585i	0.851065	−	0.0294467i
$551$	−28.5814	−	9.28667i	−1.21761	−	0.395625i
$552$	1.98808	+	0.270373i	0.0846181	+	0.0115078i
$553$	−20.8023	−	10.5993i	−0.884605	−	0.450729i
$554$	−36.8425	−	13.8346i	−1.56529	−	0.587776i
$555$	−0.479915	−	1.29866i	−0.0203712	−	0.0551251i
$556$	0.583740	−	6.46040i	0.0247561	−	0.273982i
$557$	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	$0.759711\pi$
$558$	−29.4257	+	13.3596i	−1.24569	+	0.565555i
$559$	−0.326569	+	0.0517235i	−0.0138124	+	0.00218767i
$560$	8.79392	−	28.6839i	0.371611	−	1.21212i
$561$	0.357190	−	0.181997i	0.0150806	−	0.00768393i
$562$	−24.6553	+	6.79977i	−1.04002	+	0.286831i
$563$	−26.7630	+	19.4444i	−1.12793	+	0.819486i	−0.985392	−	0.170304i	$-0.945525\pi$
$563$	−26.7630	+	19.4444i	−1.12793	+	0.819486i	−0.142534	+	0.989790i	$0.545525\pi$
$564$	0.877511	−	1.00368i	0.0369499	−	0.0422625i
$565$	−1.01659	−	25.5155i	−0.0427683	−	1.07345i
$566$	0.728220	−	16.1516i	0.0306094	−	0.678902i
$567$	28.4917	−	9.25752i	1.19654	−	0.388779i
$568$	−27.5719	−	26.3894i	−1.15689	−	1.10727i
$569$	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	$0.686845\pi$
$570$	1.21141	+	0.625255i	0.0507405	+	0.0261891i
$571$	1.76942	−	1.76942i	0.0740479	−	0.0740479i	−0.669113	−	0.743161i	$-0.733326\pi$
$571$	1.76942	−	1.76942i	0.0740479	−	0.0740479i	0.743161	+	0.669113i	$0.233326\pi$
$572$	−9.55929	+	7.97495i	−0.399694	+	0.333450i
$573$	0.437121	+	0.437121i	0.0182610	+	0.0182610i
$574$	−8.22038	−	29.2408i	−0.343112	−	1.22049i
$575$	30.8729	+	26.3092i	1.28749	+	1.09717i
$576$	8.38781	+	22.4212i	0.349492	+	0.934219i
$577$	17.3765			0.723393			0.361696	−	0.932296i	$-0.382198\pi$
$577$	17.3765			0.723393			0.361696	+	0.932296i	$0.382198\pi$
$578$	17.6673	+	10.0289i	0.734861	+	0.417146i
$579$	1.05002	−	1.44523i	0.0436374	−	0.0600617i
$580$	−1.37037	+	27.2258i	−0.0569014	+	1.13049i
$581$	6.37698	−	12.5155i	0.264562	−	0.519232i
$582$	0.737325	+	0.806951i	0.0305631	+	0.0334492i
$583$	5.21675	+	5.21675i	0.216056	+	0.216056i
$584$	5.15533	+	28.4939i	0.213329	+	1.17909i
$585$	1.72519	−	14.6452i	0.0713277	−	0.605503i
$586$	−15.6099	−	8.86098i	−0.644838	−	0.366044i
$587$	−36.8064	−	11.9591i	−1.51916	−	0.493606i	−0.573625	−	0.819118i	$-0.694463\pi$
$587$	−36.8064	−	11.9591i	−1.51916	−	0.493606i	−0.945538	+	0.325512i	$0.894463\pi$
$588$	0.724881	−	0.165181i	0.0298936	−	0.00681194i
$589$	5.88967	+	37.1859i	0.242680	+	1.53222i
$590$	−3.00431	+	9.08423i	−0.123686	+	0.373992i
$591$	1.87396	+	0.296807i	0.0770845	+	0.0122090i
$592$	−22.5231	−	17.1742i	−0.925695	−	0.705857i
$593$	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	$0.861886\pi$
$594$	−1.95930	−	0.735732i	−0.0803911	−	0.0301875i
$595$	5.09111	−	11.0595i	0.208715	−	0.453395i
$596$	3.39487	−	13.4529i	0.139059	−	0.551052i
$597$	−0.823218	−	1.61566i	−0.0336921	−	0.0661244i
$598$	−25.2590	−	1.13884i	−1.03292	−	0.0465707i
$599$	−9.54360	−	29.3722i	−0.389941	−	1.20012i	−0.932832	−	0.360312i	$-0.882670\pi$
$599$	−9.54360	−	29.3722i	−0.389941	−	1.20012i	0.542891	−	0.839803i	$-0.317330\pi$
$600$	0.260932	−	1.20876i	0.0106525	−	0.0493473i
$601$	−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	$0.392365\pi$
$602$	0.391955	+	0.594014i	0.0159749	+	0.0242102i
$603$	−19.5294	−	14.1889i	−0.795297	−	0.577817i
$604$	1.89817	+	28.3022i	0.0772353	+	1.15160i
$605$	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	−0.974021	−	0.226458i	$-0.927285\pi$
$607$	0.549594	−	3.47000i	0.0223073	−	0.140843i	0.996328	+	0.0856148i	$0.0272855\pi$
$608$	27.7793	−	2.47552i	1.12660	−	0.100395i
$609$	−1.59298	+	0.811662i	−0.0645507	+	0.0328902i
$610$	18.8658	−	6.02088i	0.763856	−	0.243778i
$611$	−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	0.991523	−	0.129934i	$-0.0414767\pi$
$619$	29.2174	+	21.2277i	1.17434	+	0.853212i	0.182822	+	0.983146i	$0.441477\pi$
$620$	31.1702	−	13.9552i	1.25182	−	0.560454i
$621$	−1.92980	−	3.78744i	−0.0774401	−	0.151985i
$622$	−0.241182	+	0.642282i	−0.00967050	+	0.0257532i
$623$	−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
$626$	0.0295545	−	0.0270045i	0.00118124	−	0.00107932i
$627$	−0.715673	+	0.985040i	−0.0285812	+	0.0393387i
$628$	−0.318571	+	3.52571i	−0.0127124	+	0.140691i
$629$	−8.12764	−	8.12764i	−0.324070	−	0.324070i
$630$	−30.2379	+	9.65018i	−1.20471	+	0.384472i
$631$	9.61993	−	3.12571i	0.382964	−	0.124432i	−0.111207	−	0.993797i	$-0.535472\pi$
$631$	9.61993	−	3.12571i	0.382964	−	0.124432i	0.494171	+	0.869365i	$0.335472\pi$
$632$	−19.3723	+	3.50499i	−0.770589	+	0.139421i
$633$	−0.764312	+	0.389437i	−0.0303787	+	0.0154787i
$634$	16.3834	+	36.0861i	0.650669	+	1.43316i
$635$	−16.4248	+	6.06971i	−0.651798	+	0.240869i
$636$	0.392234	−	0.234162i	0.0155531	−	0.00928512i
$637$	−8.91067	+	2.89525i	−0.353054	+	0.114714i
$638$	−23.8515	−	4.88798i	−0.944288	−	0.193517i
$639$	−6.31643	+	39.8804i	−0.249874	+	1.57764i
$640$	−8.73996	−	23.7405i	−0.345477	−	0.938427i
$641$	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	$0.326881\pi$
$643$	−10.2482	+	31.5408i	−0.404151	+	1.24385i	−0.921602	+	0.388136i	$0.873119\pi$
$644$	20.2436	+	50.5181i	0.797710	+	1.99069i
$645$	0.0181730	+	0.0230262i	0.000715560	+	0.000906655i
$646$	11.3064	+	0.509764i	0.444842	+	0.0200564i
$647$	−35.5349	+	35.5349i	−1.39702	+	1.39702i	−0.588581	+	0.808438i	$0.700313\pi$
$647$	−35.5349	+	35.5349i	−1.39702	+	1.39702i	−0.808438	+	0.588581i	$0.799687\pi$
$648$	14.3969	−	20.7573i	0.565565	−	0.815424i
$649$	−7.61424	−	3.87965i	−0.298885	−	0.152290i
$650$	−1.90415	+	15.4670i	−0.0746868	+	0.606667i
$651$	1.81204	+	1.31652i	0.0710193	+	0.0515986i
$652$	−1.51608	+	0.607523i	−0.0593742	+	0.0237924i
$653$			6.37159i			0.249339i	0.992198	+	0.124670i	$0.0397871\pi$
$653$			6.37159i			0.249339i	−0.992198	+	0.124670i	$0.960213\pi$
$654$	−1.19340	+	0.787456i	−0.0466657	+	0.0307920i
$655$	−16.4489	−	15.1884i	−0.642712	−	0.593460i
$656$	−20.4436	−	15.4291i	−0.798189	−	0.602407i
$657$	21.6620	−	21.6620i	0.845117	−	0.845117i
$658$	35.4266	+	7.26014i	1.38107	+	0.283030i
$659$	22.2224	+	22.2224i	0.865664	+	0.865664i	0.991989	−	0.126325i	$-0.0403183\pi$
$659$	22.2224	+	22.2224i	0.865664	+	0.865664i	−0.126325	+	0.991989i	$0.540318\pi$
$660$	1.03191	+	0.393667i	0.0401672	+	0.0153235i
$661$	−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	$0.359153\pi$
$662$	15.5446	+	23.5580i	0.604157	+	0.915609i
$663$	0.0966653	+	0.297505i	0.00375417	+	0.0115541i
$664$	−2.10874	−	11.6552i	−0.0818350	−	0.452308i
$665$	1.47213	+	36.9491i	0.0570867	+	1.43282i
$666$	−1.34967	+	29.9351i	−0.0522987	+	1.15996i
$667$	−29.0661	−	40.0060i	−1.12544	−	1.54904i
$668$	3.35722	−	7.84697i	0.129895	−	0.303608i
$669$	−0.701627	−	1.37702i	−0.0271265	−	0.0532387i
$670$	20.5596	+	15.1025i	0.794286	+	0.583460i
$671$	2.76687	+	17.4693i	0.106814	+	0.674397i
$672$	1.06444	−	1.27271i	0.0410616	−	0.0490959i
$673$	−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	$0.317608\pi$
$674$	25.9732	−	17.1382i	1.00045	−	0.660140i
$675$	−2.41935	+	1.00525i	−0.0931207	+	0.0386922i
$676$	8.34804	+	13.9835i	0.321079	+	0.537825i
$677$	−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	$0.265746\pi$
$678$	0.496440	−	1.32205i	0.0190657	−	0.0507731i
$679$	−9.16229	+	28.1986i	−0.351616	+	1.08216i
$680$	−2.22852	−	10.0215i	−0.0854597	−	0.384309i
$681$	−0.0100390	−	0.0308968i	−0.000384694	−	0.00118397i
$682$	8.10949	+	29.4043i	0.310529	+	1.12595i
$683$		−	7.24141i		−	0.277085i	−0.990356	−	0.138543i	$-0.955758\pi$
$683$		−	7.24141i		−	0.277085i	0.990356	−	0.138543i	$-0.0442418\pi$
$684$	−18.9015	−	22.6566i	−0.722717	−	0.866296i
$685$	−18.1824	+	3.62711i	−0.694712	+	0.138585i
$686$	−8.79550	−	9.62606i	−0.335814	−	0.367525i
$687$	−1.57969	−	0.250199i	−0.0602690	−	0.00954567i
$688$	0.566289	+	0.198601i	0.0215896	+	0.00757159i
$689$	−4.65739	+	3.38379i	−0.177432	+	0.128912i
$690$	1.00791	+	2.00401i	0.0383706	+	0.0762913i
$691$	−30.7830	+	15.6847i	−1.17104	+	0.596675i	−0.927722	−	0.373272i	$-0.878236\pi$
$691$	−30.7830	+	15.6847i	−1.17104	+	0.596675i	−0.243318	+	0.969946i	$0.578236\pi$
$692$	3.58400	−	1.43618i	0.136243	−	0.0545953i
$693$	−4.43470	−	27.9996i	−0.168460	−	1.06362i
$694$	22.7174	−	2.55559i	0.862342	−	0.0970088i
$695$	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
$698$	−37.5375	+	4.22276i	−1.42081	+	0.159834i
$699$	−1.68211	−	0.546550i	−0.0636232	−	0.0206724i
$700$	32.0079	−	10.0307i	1.20979	−	0.379127i
$701$	−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	$0.951970\pi$
$702$	0.806203	−	1.42024i	0.0304282	−	0.0536035i
$703$	33.2019	+	10.7880i	1.25223	+	0.406876i
$704$	22.1404	−	4.50889i	0.834446	−	0.169935i
$705$	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
$708$	−0.348282	+	0.398358i	−0.0130892	+	0.0149712i
$709$	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	$0.384046\pi$
$710$	6.89565	−	42.1095i	0.258789	−	1.58034i
$711$	14.7275	+	14.7275i	0.552324	+	0.552324i
$712$	−37.5365	+	20.1737i	−1.40674	+	0.756041i
$713$	−28.1252	+	55.1988i	−1.05330	+	2.06721i
$714$	0.497062	−	0.454174i	0.0186021	−	0.0169970i
$715$	−13.3980	−	3.77066i	−0.501058	−	0.141015i
$716$	−40.8334	−	10.3044i	−1.52602	−	0.385094i
$717$	−0.744684	+	1.46153i	−0.0278107	+	0.0545817i
$718$	−19.0369	−	41.9306i	−0.710450	−	1.56484i
$719$	3.86089	+	1.96722i	0.143987	+	0.0733651i	0.524500	−	0.851411i	$-0.324252\pi$
$719$	3.86089	+	1.96722i	0.143987	+	0.0733651i	−0.380513	+	0.924776i	$0.624252\pi$
$720$	−15.3685	+	21.9122i	−0.572749	+	0.816620i
$721$	−2.68604	+	16.9590i	−0.100033	+	0.631585i
$722$	−6.83353	+	3.10249i	−0.254318	+	0.115463i
$723$	1.42593	−	1.96262i	0.0530308	−	0.0729906i
$724$	−13.7854	+	21.9222i	−0.512330	+	0.814732i
$725$	−25.9691	+	15.9533i	−0.964467	+	0.592490i
$726$	0.184544	−	0.325101i	0.00684909	−	0.0120656i
$727$	−28.6948	−	39.4950i	−1.06423	−	1.46479i	−0.875782	−	0.482708i	$-0.839653\pi$
$727$	−28.6948	−	39.4950i	−1.06423	−	1.46479i	−0.188451	−	0.982083i	$-0.560347\pi$
$728$	−11.9164	+	17.1810i	−0.441653	+	0.636769i
$729$	−26.5880			−0.984741
$730$	−23.0117	+	22.7720i	−0.851700	+	0.842829i
$731$	0.216987	+	0.110560i	0.00802554	+	0.00408922i
$732$	1.09073	+	0.0985546i	0.0403144	+	0.00364268i
$733$	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	$0.234531\pi$
$734$	39.0847	−	10.7793i	1.44264	−	0.397871i
$735$	0.610692	+	0.563894i	0.0225257	+	0.0207995i
$736$	39.3744	+	23.5722i	1.45136	+	0.868883i
$737$	−16.1110	+	16.1110i	−0.593455	+	0.593455i
$738$	−1.08646	+	27.0751i	−0.0399930	+	0.996649i
$739$	−24.6730			−0.907612			−0.453806	−	0.891101i	$-0.649934\pi$
$739$	−24.6730			−0.907612			−0.453806	+	0.891101i	$0.649934\pi$
$740$	1.59190	−	31.6271i	0.0585195	−	1.16264i
$741$	−0.671817	−	0.671817i	−0.0246798	−	0.0246798i
$742$	10.7760	+	6.11702i	0.395599	+	0.224563i
$743$	−6.61151	−	41.7434i	−0.242553	−	1.53142i	−0.745150	−	0.666897i	$-0.767622\pi$
$743$	−6.61151	−	41.7434i	−0.242553	−	1.53142i	0.502597	−	0.864521i	$-0.332378\pi$
$744$	1.88821	−	0.0413802i	0.0692251	−	0.00151707i
$745$	14.5505	−	5.37709i	0.533091	−	0.197001i
$746$	15.2291	+	0.686630i	0.557579	+	0.0251393i
$747$	−8.86066	+	8.86066i	−0.324195	+	0.324195i
$748$	9.14871	−	0.613584i	0.334510	−	0.0224349i
$749$	−3.25236	+	20.5346i	−0.118839	+	0.750318i
$750$	1.27949	−	0.523799i	0.0467205	−	0.0191264i
$751$	−17.1039	−	33.5683i	−0.624129	−	1.22492i	−0.959200	−	0.282730i	$-0.908760\pi$
$751$	−17.1039	−	33.5683i	−0.624129	−	1.22492i	0.335070	−	0.942193i	$-0.391240\pi$
$752$	27.4831	−	13.2113i	1.00220	−	0.481767i
$753$	−0.776154	−	0.563909i	−0.0282846	−	0.0205500i
$754$	6.67871	−	17.7858i	0.243224	−	0.647722i
$755$	−24.8946	+	19.6476i	−0.906008	+	0.715049i
$756$	−3.50087	−	0.316327i	−0.127325	−	0.0115047i
$757$	−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	$0.524047\pi$
$758$	18.5948	+	40.9569i	0.675394	+	1.48762i
$759$	−1.90543	+	0.619111i	−0.0691627	+	0.0224723i
$760$	19.8492	+	24.0474i	0.720008	+	0.872290i
$761$	−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	$0.158507\pi$
$762$	−0.967386	−	0.0436161i	−0.0350447	−	0.00158004i
$763$	−34.5560	−	17.6072i	−1.25101	−	0.637423i
$764$	5.25941	+	13.1249i	0.190279	+	0.474842i
$765$	−7.36829	+	7.97979i	−0.266401	+	0.288510i
$766$	16.6735	+	3.41698i	0.602439	+	0.123460i
$767$	3.91953	−	5.39478i	0.141526	−	0.194794i
$768$	0.0647376	−	1.39755i	0.00233602	−	0.0504299i
$769$	−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	$-0.445726\pi$
$770$	4.53156	+	29.6137i	0.163306	+	1.06720i
$771$	−0.852756	+	0.619564i	−0.0307113	+	0.0223130i
$772$	35.0833	−	20.9445i	1.26268	−	0.753811i
$773$	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	$0.0437029\pi$
$774$	−0.168795	−	0.612035i	−0.00606721	−	0.0219991i
$775$	32.5780	+	19.9145i	1.17024	+	0.715348i
$776$	8.24501	+	23.6029i	0.295979	+	0.847294i
$777$	1.85050	−	0.942877i	0.0663863	−	0.0338255i
$778$	29.8270	−	3.35538i	1.06935	−	0.120296i
$779$	30.0714	+	9.60649i	1.07742	+	0.344188i
$780$	−0.429366	+	0.747250i	−0.0153738	+	0.0267558i
$781$	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
$784$	16.7295	+	3.04814i	0.597483	+	0.108862i
$785$	−3.45220	+	1.93583i	−0.123214	+	0.0690926i
$786$	−0.511849	−	1.12740i	−0.0182570	−	0.0402129i
$787$	2.86104	−	18.0639i	0.101985	−	0.643909i	−0.882749	−	0.469845i	$-0.844310\pi$
$787$	2.86104	−	18.0639i	0.101985	−	0.643909i	0.984734	−	0.174064i	$-0.0556901\pi$
$788$	36.7369	+	23.1014i	1.30870	+	0.822953i
$789$	−0.116810	−	0.160775i	−0.00415854	−	0.00572374i
$790$	−15.4821	−	15.6451i	−0.550829	−	0.556627i
$791$	37.8341	−	5.99234i	1.34523	−	0.213063i
$792$	−17.2692	−	16.5285i	−0.613635	−	0.587316i
$793$	−13.8015			−0.490106
$794$	−22.6257	−	12.8435i	−0.802956	−	0.455800i
$795$	0.463938	+	0.213568i	0.0164542	+	0.00757448i
$796$	−2.77539	−	41.3818i	−0.0983711	−	1.46674i
$797$	−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	$-0.308446\pi$
$798$	−0.718897	+	1.91447i	−0.0254487	+	0.0677715i
$799$	11.7690	−	3.82398i	0.416358	−	0.135283i
$800$	16.3622	−	23.0712i	0.578491	−	0.815689i
$801$	40.1701	+	20.4677i	1.41934	+	0.723190i
$802$	26.2652	+	5.38265i	0.927457	+	0.190068i
$803$	−16.9957	−	23.3926i	−0.599765	−	0.825506i
$804$	0.723165	+	1.21134i	0.0255041	+	0.0427208i
$805$	−33.7769	+	50.6110i	−1.19048	+	1.78380i
$806$	−23.6520	+	2.66072i	−0.833107	+	0.0937200i
$807$	−1.28738	−	0.418295i	−0.0453179	−	0.0147247i
$808$	33.5120	−	18.0107i	1.17895	−	0.633615i
$809$	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	$-0.0139052\pi$
$810$	28.2427	+	0.147853i	0.992347	+	0.00519501i
$811$	−17.1126			−0.600906			−0.300453	−	0.953797i	$-0.597138\pi$
$811$	−17.1126			−0.600906			−0.300453	+	0.953797i	$0.597138\pi$
$812$	−40.8009	+	2.73643i	−1.43183	+	0.0960299i
$813$	−0.823435	+	0.267550i	−0.0288791	+	0.00938339i
$814$	27.7073	+	5.67818i	0.971141	+	0.199020i
$815$	−1.51887	−	1.01366i	−0.0532036	−	0.0355071i
$816$	0.101770	−	0.558557i	0.00356265	−	0.0195534i
$817$	−0.739656			−0.0258773
$818$	−0.358416	−	0.0734517i	−0.0125317	−	0.00256818i
$819$	22.1209			0.772965
$820$	1.29792	−	28.6062i	0.0453255	−	0.998972i
$821$	−22.3091			−0.778592			−0.389296	−	0.921113i	$-0.627282\pi$
$821$	−22.3091			−0.778592			−0.389296	+	0.921113i	$0.627282\pi$
$822$	−1.00446	−	0.205849i	−0.0350347	−	0.00717982i
$823$	−5.72441			−0.199540			−0.0997702	−	0.995011i	$-0.531811\pi$
$823$	−5.72441			−0.199540			−0.0997702	+	0.995011i	$0.531811\pi$
$824$	6.85418	+	12.7534i	0.238777	+	0.444284i
$825$	0.289586	+	1.20038i	0.0100821	+	0.0417919i
$826$	−14.0608	−	2.88153i	−0.489236	−	0.100261i
$827$	−28.6665	+	9.31432i	−0.996833	+	0.323891i	−0.761599	−	0.648048i	$-0.775586\pi$
$827$	−28.6665	+	9.31432i	−0.996833	+	0.323891i	−0.235234	+	0.971939i	$0.575586\pi$
$828$	−3.24890	−	48.4420i	−0.112907	−	1.68348i
$829$	−29.3125			−1.01807			−0.509033	−	0.860747i	$-0.669997\pi$
$829$	−29.3125			−1.01807			−0.509033	+	0.860747i	$0.669997\pi$
$830$	9.41271	−	9.31467i	0.326720	−	0.323317i
$831$	0.380648	−	2.40332i	0.0132045	−	0.0833702i
$832$	0.772401	+	17.6141i	0.0267782	+	0.610661i
$833$	6.56307	+	2.13247i	0.227397	+	0.0738857i
$834$	0.398559	−	0.0448358i	0.0138010	−	0.00155254i
$835$	9.35801	−	1.86679i	0.323847	−	0.0646028i
$836$	−23.9121	+	14.2754i	−0.827018	+	0.493725i
$837$	−2.35194	−	3.23716i	−0.0812948	−	0.111893i
$838$	22.6844	+	4.64881i	0.783618	+	0.160590i
$839$	−22.6367	−	11.5340i	−0.781507	−	0.398198i	0.0172503	−	0.999851i	$-0.494509\pi$
$839$	−22.6367	−	11.5340i	−0.781507	−	0.398198i	−0.798757	+	0.601654i	$0.794509\pi$
$840$	1.84658	+	0.176601i	0.0637129	+	0.00609332i
$841$	7.75681	−	2.52034i	0.267476	−	0.0869082i
$842$	14.6881	−	39.1154i	0.506186	−	1.34801i
$843$	−0.717919	−	1.40899i	−0.0247264	−	0.0485283i
$844$	−19.5763	+	1.31294i	−0.673845	+	0.0451934i
$845$	−7.61387	+	16.5397i	−0.261925	+	0.568984i
$846$	−28.0558	−	15.9260i	−0.964579	−	0.547546i
$847$	10.1401			0.348419
$848$	10.3550	−	1.39525i	0.355591	−	0.0479130i
$849$	0.987360	−	0.156382i	0.0338861	−	0.00536703i
$850$	7.83074	−	8.39205i	0.268592	−	0.287845i
$851$	33.7650	+	46.4735i	1.15745	+	1.59309i
$852$	1.25618	−	1.99764i	0.0430360	−	0.0684379i
$853$	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	$-0.130435\pi$
$854$	12.2807	+	27.0494i	0.420235	+	0.925610i
$855$	8.93689	−	31.7548i	0.305635	−	1.08599i
$856$	8.29932	+	15.4423i	0.283665	+	0.527806i
$857$	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	0.727272	−	0.686349i	$-0.240788\pi$
$859$	26.7360	+	8.68706i	0.912222	+	0.296399i	0.184950	+	0.982748i	$0.440788\pi$
$860$	0.174992	+	0.647715i	0.00596717	+	0.0220869i
$861$	1.66911	−	0.860887i	0.0568831	−	0.0293390i
$862$	−16.4313	+	1.84844i	−0.559653	+	0.0629580i
$863$	−0.315474	+	0.160742i	−0.0107389	+	0.00547172i	−0.459352	−	0.888254i	$-0.651918\pi$
$863$	−0.315474	+	0.160742i	−0.0107389	+	0.00547172i	0.448613	+	0.893726i	$0.351918\pi$
$864$	−2.51113	+	1.57476i	−0.0854302	+	0.0535745i
$865$	3.59059	+	2.39629i	0.122084	+	0.0814764i
$866$	−2.13342	−	7.73560i	−0.0724967	−	0.262866i
$867$	−0.388154	+	1.19461i	−0.0131824	+	0.0405712i
$868$	26.2604	+	43.9877i	0.891336	+	1.49304i
$869$	15.9040	−	11.5550i	0.539508	−	0.391975i
$870$	−1.66610	+	0.254952i	−0.0564862	+	0.00864367i
$871$	−10.4502	−	14.3835i	−0.354092	−	0.487366i
$872$	−32.1806	+	5.82235i	−1.08977	+	0.197170i
$873$	15.5472	−	21.3989i	0.526194	−	0.724244i
$874$	−55.4113	−	11.3557i	−1.87431	−	0.384112i
$875$	29.4893	+	23.1686i	0.996922	+	0.783241i
$876$	−1.66191	+	0.665962i	−0.0561509	+	0.0225008i
$877$	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	$0.380934\pi$
$878$	19.5566	+	0.881738i	0.660002	+	0.0297572i
$879$	0.342953	−	1.05550i	0.0115675	−	0.0356011i
$880$	18.1582	+	17.5624i	0.612112	+	0.592029i
$881$	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	$0.268222\pi$
$882$	−7.43724	−	16.3813i	−0.250425	−	0.551586i
$883$	−18.3014	+	5.94648i	−0.615890	+	0.200115i	−0.600315	−	0.799764i	$-0.704958\pi$
$883$	−18.3014	+	5.94648i	−0.615890	+	0.200115i	−0.0155755	+	0.999879i	$0.504958\pi$
$884$	−0.643871	+	7.12588i	−0.0216557	+	0.239669i
$885$	−0.587534	−	0.0692110i	−0.0197498	−	0.00232650i
$886$	−14.9950	+	39.9326i	−0.503767	+	1.34156i
$887$	37.6615	+	27.3627i	1.26455	+	0.918748i	0.998972	−	0.0453418i	$-0.0144377\pi$
$887$	37.6615	+	27.3627i	1.26455	+	0.918748i	0.265577	+	0.964090i	$0.414438\pi$
$888$	0.760681	−	1.57744i	0.0255268	−	0.0529353i
$889$	−11.9250	−	23.4041i	−0.399952	−	0.784950i
$890$	−42.3374	−	21.8519i	−1.41915	−	0.732477i
$891$	−3.94606	+	24.9144i	−0.132198	+	0.834665i
$892$	−2.36546	−	35.2696i	−0.0792014	−	1.18091i
$893$	−26.5764	+	26.5764i	−0.889346	+	0.889346i
$894$	0.856997	+	0.0386390i	0.0286623	+	0.00129228i
$895$	−16.3210	−	44.1652i	−0.545552	−	1.47628i
$896$	33.8344	−	17.1870i	1.13033	−	0.574176i
$897$	−0.244562	−	1.54410i	−0.00816568	−	0.0515561i
$898$	41.8983	+	23.7837i	1.39816	+	0.793671i
$899$	−32.9151	−	32.9151i	−1.09778	−	1.09778i
$900$	−29.9219	−	0.313295i	−0.997397	−	0.0104432i
$901$	4.24015			0.141260
$902$	25.0800	+	5.01052i	0.835072	+	0.166832i
$903$	−0.0311147	+	0.0311147i	−0.00103543	+	0.00103543i
$904$	22.3340	−	23.3348i	0.742817	−	0.776104i
$905$	−28.9300	+	1.15263i	−0.961666	+	0.0383148i
$906$	−1.69073	+	0.466292i	−0.0561708	+	0.0154915i
$907$	26.5832	−	4.21037i	0.882682	−	0.139803i	0.301393	−	0.953500i	$-0.402548\pi$
$907$	26.5832	−	4.21037i	0.882682	−	0.139803i	0.581289	+	0.813697i	$0.302548\pi$
$908$	0.0668679	−	0.740043i	0.00221909	−	0.0245592i
$909$	−35.8632	−	18.2732i	−1.18951	−	0.606084i
$910$	−23.3767	−	0.122379i	−0.774930	−	0.00405681i
$911$	15.4649			0.512374			0.256187	−	0.966627i	$-0.417534\pi$
$911$	15.4649			0.512374			0.256187	+	0.966627i	$0.417534\pi$
$912$	0.494772	+	1.65189i	0.0163835	+	0.0546996i
$913$	6.95193	+	9.56852i	0.230075	+	0.316672i
$914$	−14.6122	+	25.7415i	−0.483329	+	0.851452i
$915$	0.598875	+	1.06799i	0.0197982	+	0.0353066i
$916$	−30.9681	−	19.4738i	−1.02321	−	0.643431i
$917$	19.7407	−	27.1708i	0.651896	−	0.897258i
$918$	−1.09526	+	0.497256i	−0.0361488	+	0.0164119i
$919$	6.07542	−	38.3587i	0.200409	−	1.26534i	−0.658254	−	0.752796i	$-0.728705\pi$
$919$	6.07542	−	38.3587i	0.200409	−	1.26534i	0.858664	−	0.512540i	$-0.171295\pi$
$920$	3.16535	+	51.2101i	0.104359	+	1.68835i
$921$	0.571100	+	0.290990i	0.0188184	+	0.00958844i
$922$	−19.2453	−	42.3897i	−0.633810	−	1.39603i
$923$	−13.5009	+	26.4970i	−0.444387	+	0.872158i
$924$	−0.405383	+	1.60641i	−0.0133361	+	0.0528471i
$925$	30.1673	−	18.5323i	0.991894	−	0.609338i
$926$	−6.41295	+	5.85963i	−0.210743	+	0.192559i
$927$	6.95407	−	13.6481i	0.228402	−	0.448264i
$928$	−25.9872	+	22.6640i	−0.853072	+	0.743982i
$929$	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	$0.552745\pi$
$930$	1.23220	+	1.71479i	0.0404055	+	0.0562300i
$931$	−20.7013	+	3.27877i	−0.678459	+	0.107457i
$932$	−30.4555	−	26.6271i	−0.997604	−	0.872200i
$933$	−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
$936$	14.8467	−	11.2919i	0.485279	−	0.369088i
$937$	−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	$0.844261\pi$
$938$	−18.8913	+	33.2797i	−0.616823	+	1.08662i
$939$	0.00200255	+	0.00145494i	6.53509e−5	+	4.74802e-5i
$940$	29.5605	+	16.9853i	0.964156	+	0.554000i
$941$	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	$0.351259\pi$
$942$	−0.217510	+	0.0244687i	−0.00708687	+	0.000797235i
$943$	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
$946$	−0.595484	+	0.0669887i	−0.0193608	+	0.00217799i
$947$	−0.186088	−	1.17492i	−0.00604706	−	0.0381796i	0.984480	−	0.175495i	$-0.0561526\pi$
$947$	−0.186088	−	1.17492i	−0.00604706	−	0.0381796i	−0.990527	+	0.137315i	$0.956153\pi$
$948$	−0.452771	−	1.12990i	−0.0147053	−	0.0366973i
$949$	20.1035	−	10.2432i	0.652586	−	0.332509i
$950$	−9.61992	+	33.5081i	−0.312111	+	1.08715i
$951$	−1.98241	+	1.44030i	−0.0642840	+	0.0467050i
$952$	14.5388	−	5.07873i	0.471206	−	0.164603i
$953$	−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	$0.693169\pi$
$954$	−7.45645	−	8.16056i	−0.241411	−	0.264208i
$955$	−8.77544	+	13.1490i	−0.283966	+	0.425493i
$956$	−28.8091	+	24.0343i	−0.931752	+	0.777325i
$957$		−	1.50538i		−	0.0486622i
$958$	9.78556	+	35.4816i	0.316157	+	1.14636i
$959$	−8.59452	−	26.4512i	−0.277531	−	0.854154i
$960$	1.32950	−	0.824083i	0.0429094	−	0.0265972i
$961$	−8.44123	+	25.9794i	−0.272298	+	0.838046i
$962$	−7.75840	+	20.6611i	−0.250141	+	0.666141i
$963$	8.42027	−	16.5257i	0.271339	−	0.532534i
$964$	47.6431	−	28.4427i	1.53448	−	0.916077i
$965$	41.4968	+	19.1026i	1.33583	+	0.614933i
$966$	−2.80865	+	1.85326i	−0.0903668	+	0.0596278i
$967$	−18.7680	+	13.6358i	−0.603538	+	0.438496i	−0.847133	−	0.531381i	$-0.821673\pi$
$967$	−18.7680	+	13.6358i	−0.603538	+	0.438496i	0.243595	+	0.969877i	$0.421673\pi$
$968$	6.80567	−	5.17617i	0.218742	−	0.166368i
$969$	0.109470	+	0.691166i	0.00351668	+	0.0222035i
$970$	−16.5483	+	22.5278i	−0.531333	+	0.723323i
$971$	−5.54027	−	10.8734i	−0.177796	−	0.348944i	0.784860	−	0.619674i	$-0.212735\pi$
$971$	−5.54027	−	10.8734i	−0.177796	−	0.348944i	−0.962655	+	0.270730i	$0.912735\pi$
$972$	4.32643	+	1.85101i	0.138770	+	0.0593711i
$973$	6.39460	+	8.80142i	0.205002	+	0.282160i
$974$	−2.49831	+	55.4114i	−0.0800510	+	1.77550i
$975$	−0.960493	+	0.0766577i	−0.0307604	+	0.00245501i
$976$	22.0500	+	11.8857i	0.705805	+	0.380451i
$977$	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	$0.864931\pi$
$978$	−0.0556175	−	0.0842893i	−0.00177845	−	0.00269527i
$979$	25.0119	−	34.4259i	0.799384	−	1.10026i
$980$	7.76884	+	17.3524i	0.248166	+	0.554302i
$981$	24.4648	+	24.4648i	0.781099	+	0.781099i
$982$	−12.5436	−	2.57062i	−0.400283	−	0.0820317i
$983$	−31.3301	+	31.3301i	−0.999274	+	0.999274i	−1.00000		0.000726002i	$-0.999769\pi$
$983$	−31.3301	+	31.3301i	−0.999274	+	0.999274i	0.000726002		1.00000i	$0.499769\pi$
$984$	0.680791	−	1.42982i	0.0217028	−	0.0455809i
$985$	1.93157	+	48.4806i	0.0615448	+	1.54472i
$986$	−11.6796	+	7.70671i	−0.371956	+	0.245432i
$987$			2.23595i			0.0711711i
$988$	−8.08325	−	20.1718i	−0.257162	−	0.641751i
$989$	−0.984641	−	0.715384i	−0.0313098	−	0.0227479i
$990$	4.31898	−	26.3746i	0.137266	−	0.838239i
$991$	−21.6206	−	11.0162i	−0.686800	−	0.349942i	0.0755181	−	0.997144i	$-0.475939\pi$
$991$	−21.6206	−	11.0162i	−0.686800	−	0.349942i	−0.762318	+	0.647202i	$0.775939\pi$
$992$	40.0792	+	16.1179i	1.27251	+	0.511744i
$993$	−1.23398	+	1.23398i	−0.0391592	+	0.0391592i
$994$	63.9441	+	2.88302i	2.02818	+	0.0914438i
$995$	36.3995	−	28.7276i	1.15394	−	0.910726i
$996$	0.679791	−	0.272406i	0.0215400	−	0.00863150i
$997$	−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.103.54	yes	960
4.3	odd	2	inner	820.2.bv.c.103.17	yes	960
5.2	odd	4		820.2.bk.c.267.8	yes	960
20.7	even	4		820.2.bk.c.267.78	yes	960
41.2	even	20		820.2.bk.c.43.78	yes	960
164.43	odd	20		820.2.bk.c.43.8	✓	960
205.2	odd	20	inner	820.2.bv.c.207.17	yes	960
820.207	even	20	inner	820.2.bv.c.207.54	yes	960

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.bk.c.43.8	✓	960	164.43	odd	20
820.2.bk.c.43.78	yes	960	41.2	even	20
820.2.bk.c.267.8	yes	960	5.2	odd	4
820.2.bk.c.267.78	yes	960	20.7	even	4
820.2.bv.c.103.17	yes	960	4.3	odd	2	inner
820.2.bv.c.103.54	yes	960	1.1	even	1	trivial
820.2.bv.c.207.17	yes	960	205.2	odd	20	inner
820.2.bv.c.207.54	yes	960	820.207	even	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+(-0.283920 + 1.38542i) q^{2} -0.0874408 q^{3} +(-1.83878 - 0.786698i) q^{4} +(-0.437444 - 2.19286i) q^{5} +(0.0248262 - 0.121142i) q^{6} +(3.19012 - 1.03653i) q^{7} +(1.61197 - 2.32412i) q^{8} -2.99235 q^{9} +(3.16223 + 0.0165545i) q^{10} +(-0.441826 + 2.78958i) q^{11} +(0.160784 + 0.0687895i) q^{12} +(-2.09602 - 0.681038i) q^{13} +(0.530293 + 4.71394i) q^{14} +(0.0382504 + 0.191746i) q^{15} +(2.76221 + 2.89313i) q^{16} +(0.954122 + 1.31324i) q^{17} +(0.849590 - 4.14567i) q^{18} +(-4.39283 - 2.23826i) q^{19} +(-0.920757 + 4.37632i) q^{20} +(-0.278946 + 0.0906351i) q^{21} +(-3.73930 - 1.40413i) q^{22} +(-3.68299 - 7.22827i) q^{23} +(-0.140952 + 0.203223i) q^{24} +(-4.61729 + 1.91851i) q^{25} +(1.53863 - 2.71051i) q^{26} +0.523976 q^{27} +(-6.68135 - 0.603705i) q^{28} +(6.02052 - 0.953557i) q^{29} +(-0.276508 - 0.00144754i) q^{30} +(-4.48863 - 6.17807i) q^{31} +(-4.79244 + 3.00541i) q^{32} +(0.0386336 - 0.243923i) q^{33} +(-2.09028 + 0.949006i) q^{34} +(-3.66847 - 6.54206i) q^{35} +(5.50228 + 2.35408i) q^{36} +(-6.99381 + 1.10771i) q^{37} +(4.34814 - 5.45042i) q^{38} +(0.183277 + 0.0595505i) q^{39} +(-5.80163 - 2.51816i) q^{40} +(-6.31926 + 1.03296i) q^{41} +(-0.0463692 - 0.412191i) q^{42} +(0.133674 - 0.0681104i) q^{43} +(3.00698 - 4.78184i) q^{44} +(1.30899 + 6.56182i) q^{45} +(11.0599 - 3.05023i) q^{46} +(2.35576 - 7.25028i) q^{47} +(-0.241530 - 0.252977i) q^{48} +(3.43932 - 2.49881i) q^{49} +(-1.34700 - 6.94158i) q^{50} +(-0.0834292 - 0.114830i) q^{51} +(3.31834 + 2.90121i) q^{52} +(1.53538 - 2.11326i) q^{53} +(-0.148767 + 0.725927i) q^{54} +(6.31044 - 0.251421i) q^{55} +(2.73336 - 9.08508i) q^{56} +(0.384112 + 0.195715i) q^{57} +(-0.388271 + 8.61169i) q^{58} +(-0.934995 + 2.87762i) q^{59} +(0.0805117 - 0.382669i) q^{60} +(5.95586 - 1.93517i) q^{61} +(9.83364 - 4.46456i) q^{62} +(-9.54596 + 3.10167i) q^{63} +(-2.80308 - 7.49285i) q^{64} +(-0.576531 + 4.89419i) q^{65} +(0.326967 + 0.122778i) q^{66} +(6.52642 + 4.74172i) q^{67} +(-0.721299 - 3.16536i) q^{68} +(0.322043 + 0.632046i) q^{69} +(10.1051 - 3.22494i) q^{70} +(2.11086 - 13.3274i) q^{71} +(-4.82360 + 6.95459i) q^{72} +(-7.23913 + 7.23913i) q^{73} +(0.451040 - 10.0039i) q^{74} +(0.403739 - 0.167756i) q^{75} +(6.31660 + 7.57149i) q^{76} +(1.48201 + 9.35705i) q^{77} +(-0.134539 + 0.237009i) q^{78} +(-4.92171 - 4.92171i) q^{79} +(5.13591 - 7.32273i) q^{80} +8.93125 q^{81} +(0.363078 - 9.04810i) q^{82} +(2.96110 - 2.96110i) q^{83} +(0.584223 + 0.0527885i) q^{84} +(2.46237 - 2.66673i) q^{85} +(0.0564087 + 0.204533i) q^{86} +(-0.526439 + 0.0833798i) q^{87} +(5.77111 + 5.52359i) q^{88} +(-13.4242 - 6.84000i) q^{89} +(-9.46252 - 0.0495370i) q^{90} -7.39246 q^{91} +(1.08573 + 16.1886i) q^{92} +(0.392489 + 0.540215i) q^{93} +(9.37583 + 5.32222i) q^{94} +(-2.98657 + 10.6120i) q^{95} +(0.419055 - 0.262795i) q^{96} +(-5.19566 + 7.15121i) q^{97} +(2.48541 + 5.47437i) 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

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