LMFDB - Embedded newform 820.2.bk.c.267.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(43,820)] 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, 13])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.43"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.bk (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			267.19
Character	$\chi$	$=$	820.267
Dual form			820.2.bk.c.43.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.26252 - 0.637224i) q^{2} -1.94267i q^{3} +(1.18789 + 1.60901i) q^{4} +(-2.19825 - 0.409529i) q^{5} +(-1.23792 + 2.45265i) q^{6} +(1.22687 + 3.77593i) q^{7} +(-0.474434 - 2.78835i) q^{8} -0.773974 q^{9} +(2.51436 + 1.91781i) q^{10} +(0.621132 - 3.92167i) q^{11} +(3.12578 - 2.30768i) q^{12} +(-0.213440 + 0.656902i) q^{13} +(0.857164 - 5.54897i) q^{14} +(-0.795580 + 4.27047i) q^{15} +(-1.17782 + 3.82266i) q^{16} +(2.52712 - 1.83606i) q^{17} +(0.977154 + 0.493194i) q^{18} +(-7.31333 - 3.72633i) q^{19} +(-1.95234 - 4.02348i) q^{20} +(7.33540 - 2.38341i) q^{21} +(-3.28317 + 4.55537i) q^{22} +(-0.124519 + 0.0634454i) q^{23} +(-5.41685 + 0.921669i) q^{24} +(4.66457 + 1.80049i) q^{25} +(0.688065 - 0.693340i) q^{26} -4.32444i q^{27} +(-4.61812 + 6.45945i) q^{28} +(-7.09518 + 1.12377i) q^{29} +(3.72568 - 4.88457i) q^{30} +(-5.70984 - 7.85892i) q^{31} +(3.92291 - 4.07563i) q^{32} +(-7.61852 - 1.20666i) q^{33} +(-4.36052 + 0.707716i) q^{34} +(-1.15062 - 8.80287i) q^{35} +(-0.919397 - 1.24533i) q^{36} +(0.340997 + 2.15297i) q^{37} +(6.85869 + 9.36478i) q^{38} +(1.27615 + 0.414645i) q^{39} +(-0.0989891 + 6.32378i) q^{40} +(-6.12018 - 1.88239i) q^{41} +(-10.7798 - 1.66519i) q^{42} +(1.39075 + 2.72949i) q^{43} +(7.04785 - 3.65912i) q^{44} +(1.70138 + 0.316964i) q^{45} +(0.197636 - 0.000754621i) q^{46} +(-5.29255 - 1.71965i) q^{47} +(7.42617 + 2.28813i) q^{48} +(-7.08932 + 5.15070i) q^{49} +(-4.74178 - 5.24552i) q^{50} +(-3.56687 - 4.90937i) q^{51} +(-1.31051 + 0.436901i) q^{52} +(7.05059 + 5.12255i) q^{53} +(-2.75563 + 5.45967i) q^{54} +(-2.97144 + 8.36643i) q^{55} +(9.94656 - 5.21239i) q^{56} +(-7.23904 + 14.2074i) q^{57} +(9.67387 + 3.10245i) q^{58} +(3.88082 - 11.9439i) q^{59} +(-7.81629 + 3.79276i) q^{60} +(3.25904 - 1.05893i) q^{61} +(2.20087 + 13.5605i) q^{62} +(-0.949569 - 2.92247i) q^{63} +(-7.54983 + 2.64578i) q^{64} +(0.738215 - 1.35662i) q^{65} +(8.84960 + 6.37812i) q^{66} +(-0.542015 + 0.746020i) q^{67} +(5.95620 + 1.88512i) q^{68} +(0.123254 + 0.241899i) q^{69} +(-4.15672 + 11.8470i) q^{70} +(-2.55138 + 16.1088i) q^{71} +(0.367199 + 2.15811i) q^{72} +(-0.650616 - 0.650616i) q^{73} +(0.941409 - 2.93545i) q^{74} +(3.49776 - 9.06173i) q^{75} +(-2.69175 - 16.1937i) q^{76} +(15.5700 - 2.46605i) q^{77} +(-1.34693 - 1.33669i) q^{78} +(-4.91440 - 4.91440i) q^{79} +(4.15464 - 7.92079i) q^{80} -10.7229 q^{81} +(6.52732 + 6.27647i) q^{82} +(-2.84351 - 2.84351i) q^{83} +(12.5486 + 8.97148i) q^{84} +(-6.30716 + 3.00119i) q^{85} +(-0.0165416 - 4.33224i) q^{86} +(2.18311 + 13.7836i) q^{87} +(-11.2297 + 0.128638i) q^{88} +(5.28228 + 2.69145i) q^{89} +(-1.94605 - 1.48433i) q^{90} -2.74228 q^{91} +(-0.249999 - 0.124985i) q^{92} +(-15.2673 + 11.0923i) q^{93} +(5.58612 + 5.54363i) q^{94} +(14.5505 + 11.1864i) q^{95} +(-7.91761 - 7.62093i) q^{96} +(0.182409 + 0.132528i) q^{97} +(12.2325 - 1.98535i) q^{98} +(-0.480740 + 3.03527i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 960 q - 10 q^{2} - 20 q^{5} - 16 q^{6} - 22 q^{8} - 960 q^{9} + 20 q^{12} + 12 q^{13} + 8 q^{14} - 28 q^{16} - 52 q^{17} + 12 q^{18} + 14 q^{20} - 40 q^{21} + 18 q^{22} + 48 q^{24} - 4 q^{25} - 20 q^{26}+ \cdots + 42 q^{98}+O(q^{100}) $ 960 * q - 10 * q^2 - 20 * q^5 - 16 * q^6 - 22 * q^8 - 960 * q^9 + 20 * q^12 + 12 * q^13 + 8 * q^14 - 28 * q^16 - 52 * q^17 + 12 * q^18 + 14 * q^20 - 40 * q^21 + 18 * q^22 + 48 * q^24 - 4 * q^25 - 20 * q^26 - 2 * q^28 + 30 * q^30 + 16 * q^33 + 20 * q^34 - 100 * q^36 - 112 * q^37 - 36 * q^38 - 16 * q^40 - 24 * q^41 - 104 * q^42 + 20 * q^45 - 20 * q^46 + 12 * q^48 - 224 * q^49 + 12 * q^50 + 190 * q^52 + 12 * q^53 + 52 * q^54 + 96 * q^56 + 48 * q^57 - 10 * q^58 + 14 * q^60 - 40 * q^61 - 10 * q^62 + 120 * q^64 - 92 * q^65 - 12 * q^66 + 104 * q^69 - 120 * q^70 + 36 * q^72 + 72 * q^73 + 28 * q^74 - 40 * q^76 + 36 * q^77 + 16 * q^78 - 130 * q^80 + 592 * q^81 + 146 * q^82 + 92 * q^84 + 112 * q^85 - 12 * q^86 + 100 * q^88 - 136 * q^89 - 136 * q^90 + 160 * q^92 - 24 * q^93 + 32 * q^94 - 44 * q^96 - 72 * q^97 + 42 * q^98

Character values

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

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

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 $

$2$	−1.26252	−	0.637224i	−0.892733	−	0.450585i
$2$	−1.26252	−	0.637224i	−0.892733	−	0.450585i
$3$		−	1.94267i		−	1.12160i	−0.827951	−	0.560801i	$-0.810493\pi$
$3$		−	1.94267i		−	1.12160i	0.827951	−	0.560801i	$-0.189507\pi$
$4$	1.18789	+	1.60901i	0.593946	+	0.804505i
$5$	−2.19825	−	0.409529i	−0.983086	−	0.183147i
$5$	−2.19825	−	0.409529i	−0.983086	−	0.183147i
$6$	−1.23792	+	2.45265i	−0.505377	+	1.00129i
$7$	1.22687	+	3.77593i	0.463715	+	1.42717i	0.860591	+	0.509296i	$0.170094\pi$
$7$	1.22687	+	3.77593i	0.463715	+	1.42717i	−0.396876	+	0.917872i	$0.629906\pi$
$8$	−0.474434	−	2.78835i	−0.167738	−	0.985832i
$9$	−0.773974			−0.257991
$10$	2.51436	+	1.91781i	0.795110	+	0.606465i
$11$	0.621132	−	3.92167i	0.187278	−	1.18243i	−0.697558	−	0.716528i	$-0.745730\pi$
$11$	0.621132	−	3.92167i	0.187278	−	1.18243i	0.884837	−	0.465901i	$-0.154270\pi$
$12$	3.12578	−	2.30768i	0.902334	−	0.666171i
$13$	−0.213440	+	0.656902i	−0.0591977	+	0.182192i	−0.976283	−	0.216500i	$-0.930536\pi$
$13$	−0.213440	+	0.656902i	−0.0591977	+	0.182192i	0.917085	+	0.398692i	$0.130536\pi$
$14$	0.857164	−	5.54897i	0.229087	−	1.48302i
$15$	−0.795580	+	4.27047i	−0.205418	+	1.10263i
$16$	−1.17782	+	3.82266i	−0.294456	+	0.955665i
$17$	2.52712	−	1.83606i	0.612918	−	0.445311i	−0.237523	−	0.971382i	$-0.576335\pi$
$17$	2.52712	−	1.83606i	0.612918	−	0.445311i	0.850441	+	0.526071i	$0.176335\pi$
$18$	0.977154	+	0.493194i	0.230317	+	0.116247i
$19$	−7.31333	−	3.72633i	−1.67779	−	0.854879i	−0.991877	−	0.127199i	$-0.959401\pi$
$19$	−7.31333	−	3.72633i	−1.67779	−	0.854879i	−0.685917	−	0.727680i	$-0.740599\pi$
$20$	−1.95234	−	4.02348i	−0.436557	−	0.899676i
$21$	7.33540	−	2.38341i	1.60071	−	0.520104i
$22$	−3.28317	+	4.55537i	−0.699975	+	0.971209i
$23$	−0.124519	+	0.0634454i	−0.0259639	+	0.0132293i	−0.466924	−	0.884297i	$-0.654638\pi$
$23$	−0.124519	+	0.0634454i	−0.0259639	+	0.0132293i	0.440960	+	0.897527i	$0.354638\pi$
$24$	−5.41685	+	0.921669i	−1.10571	+	0.188135i
$25$	4.66457	+	1.80049i	0.932914	+	0.360098i
$26$	0.688065	−	0.693340i	0.134941	−	0.135975i
$27$		−	4.32444i		−	0.832239i
$28$	−4.61812	+	6.45945i	−0.872742	+	1.22072i
$29$	−7.09518	+	1.12377i	−1.31754	+	0.208678i	−0.775326	−	0.631561i	$-0.782415\pi$
$29$	−7.09518	+	1.12377i	−1.31754	+	0.208678i	−0.542216	+	0.840239i	$0.682415\pi$
$30$	3.72568	−	4.88457i	0.680212	−	0.891797i
$31$	−5.70984	−	7.85892i	−1.02552	−	1.41150i	−0.908262	−	0.418402i	$-0.862590\pi$
$31$	−5.70984	−	7.85892i	−1.02552	−	1.41150i	−0.117256	−	0.993102i	$-0.537410\pi$
$32$	3.92291	−	4.07563i	0.693479	−	0.720477i
$33$	−7.61852	−	1.20666i	−1.32621	−	0.210052i
$34$	−4.36052	+	0.707716i	−0.747823	+	0.121372i
$35$	−1.15062	−	8.80287i	−0.194490	−	1.48796i
$36$	−0.919397	−	1.24533i	−0.153233	−	0.207555i
$37$	0.340997	+	2.15297i	0.0560596	+	0.353946i	0.999734	+	0.0230703i	$0.00734415\pi$
$37$	0.340997	+	2.15297i	0.0560596	+	0.353946i	−0.943674	+	0.330876i	$0.892656\pi$
$38$	6.85869	+	9.36478i	1.11263	+	1.51917i
$39$	1.27615	+	0.414645i	0.204347	+	0.0663963i
$40$	−0.0989891	+	6.32378i	−0.0156516	+	0.999878i
$41$	−6.12018	−	1.88239i	−0.955812	−	0.293980i
$41$	−6.12018	−	1.88239i	−0.955812	−	0.293980i
$42$	−10.7798	−	1.66519i	−1.66336	−	0.256944i
$43$	1.39075	+	2.72949i	0.212087	+	0.416244i	0.972402	−	0.233310i	$-0.0749557\pi$
$43$	1.39075	+	2.72949i	0.212087	+	0.416244i	−0.760316	+	0.649554i	$0.774956\pi$
$44$	7.04785	−	3.65912i	1.06250	−	0.551633i
$45$	1.70138	+	0.316964i	0.253627	+	0.0472503i
$46$	0.197636		0.000754621i	0.0291398		0.000111263i
$47$	−5.29255	−	1.71965i	−0.771997	−	0.250837i	−0.103578	−	0.994621i	$-0.533029\pi$
$47$	−5.29255	−	1.71965i	−0.771997	−	0.250837i	−0.668420	+	0.743784i	$0.733029\pi$
$48$	7.42617	+	2.28813i	1.07188	+	0.330263i
$49$	−7.08932	+	5.15070i	−1.01276	+	0.735814i
$50$	−4.74178	−	5.24552i	−0.670589	−	0.741829i
$51$	−3.56687	−	4.90937i	−0.499462	−	0.687450i
$52$	−1.31051	+	0.436901i	−0.181734	+	0.0605873i
$53$	7.05059	+	5.12255i	0.968473	+	0.703637i	0.955103	−	0.296274i	$-0.0957440\pi$
$53$	7.05059	+	5.12255i	0.968473	+	0.703637i	0.0133701	+	0.999911i	$0.495744\pi$
$54$	−2.75563	+	5.45967i	−0.374994	+	0.742967i
$55$	−2.97144	+	8.36643i	−0.400669	+	1.12813i
$56$	9.94656	−	5.21239i	1.32917	−	0.696535i
$57$	−7.23904	+	14.2074i	−0.958834	+	1.88182i
$58$	9.67387	+	3.10245i	1.27024	+	0.407371i
$59$	3.88082	−	11.9439i	0.505240	−	1.55497i	−0.295128	−	0.955458i	$-0.595362\pi$
$59$	3.88082	−	11.9439i	0.505240	−	1.55497i	0.800367	−	0.599510i	$-0.204638\pi$
$60$	−7.81629	+	3.79276i	−1.00908	+	0.489644i
$61$	3.25904	−	1.05893i	0.417278	−	0.135582i	−0.0928507	−	0.995680i	$-0.529598\pi$
$61$	3.25904	−	1.05893i	0.417278	−	0.135582i	0.510128	+	0.860098i	$0.329598\pi$
$62$	2.20087	+	13.5605i	0.279511	+	1.72218i
$63$	−0.949569	−	2.92247i	−0.119634	−	0.368197i
$64$	−7.54983	+	2.64578i	−0.943728	+	0.330722i
$65$	0.738215	−	1.35662i	0.0915643	−	0.168268i
$66$	8.84960	+	6.37812i	1.08931	+	0.785093i
$67$	−0.542015	+	0.746020i	−0.0662177	+	0.0911408i	−0.840841	−	0.541282i	$-0.817939\pi$
$67$	−0.542015	+	0.746020i	−0.0662177	+	0.0911408i	0.774624	+	0.632422i	$0.217939\pi$
$68$	5.95620	+	1.88512i	0.722295	+	0.228605i
$69$	0.123254	+	0.241899i	0.0148380	+	0.0291212i
$70$	−4.15672	+	11.8470i	−0.496823	+	1.41598i
$71$	−2.55138	+	16.1088i	−0.302793	+	1.91176i	0.0972432	+	0.995261i	$0.468998\pi$
$71$	−2.55138	+	16.1088i	−0.302793	+	1.91176i	−0.400036	+	0.916499i	$0.631002\pi$
$72$	0.367199	+	2.15811i	0.0432748	+	0.254336i
$73$	−0.650616	−	0.650616i	−0.0761488	−	0.0761488i	0.668007	−	0.744155i	$-0.267148\pi$
$73$	−0.650616	−	0.650616i	−0.0761488	−	0.0761488i	−0.744155	+	0.668007i	$0.767148\pi$
$74$	0.941409	−	2.93545i	0.109437	−	0.341239i
$75$	3.49776	−	9.06173i	0.403887	−	1.04636i
$76$	−2.69175	−	16.1937i	−0.308765	−	1.85755i
$77$	15.5700	−	2.46605i	1.77437	−	0.281032i
$78$	−1.34693	−	1.33669i	−0.152510	−	0.151350i
$79$	−4.91440	−	4.91440i	−0.552914	−	0.552914i	0.374367	−	0.927281i	$-0.377860\pi$
$79$	−4.91440	−	4.91440i	−0.552914	−	0.552914i	−0.927281	+	0.374367i	$0.877860\pi$
$80$	4.15464	−	7.92079i	0.464503	−	0.885572i
$81$	−10.7229			−1.19143
$82$	6.52732	+	6.27647i	0.720822	+	0.693120i
$83$	−2.84351	−	2.84351i	−0.312116	−	0.312116i	0.533613	−	0.845729i	$-0.320834\pi$
$83$	−2.84351	−	2.84351i	−0.312116	−	0.312116i	−0.845729	+	0.533613i	$0.820834\pi$
$84$	12.5486	+	8.97148i	1.36916	+	0.978869i
$85$	−6.30716	+	3.00119i	−0.684108	+	0.325525i
$86$	−0.0165416	−	4.33224i	−0.00178372	−	0.467158i
$87$	2.18311	+	13.7836i	0.234054	+	1.47776i
$88$	−11.2297	+	0.128638i	−1.19709	+	0.0137129i
$89$	5.28228	+	2.69145i	0.559920	+	0.285294i	0.710958	−	0.703234i	$-0.248262\pi$
$89$	5.28228	+	2.69145i	0.559920	+	0.285294i	−0.151038	+	0.988528i	$0.548262\pi$
$90$	−1.94605	−	1.48433i	−0.205131	−	0.156463i
$91$	−2.74228			−0.287469
$92$	−0.249999	−	0.124985i	−0.0260642	−	0.0130306i
$93$	−15.2673	+	11.0923i	−1.58315	+	1.15022i
$94$	5.58612	+	5.54363i	0.576164	+	0.571781i
$95$	14.5505	+	11.1864i	1.49285	+	1.14770i
$96$	−7.91761	−	7.62093i	−0.808088	−	0.777808i
$97$	0.182409	+	0.132528i	0.0185208	+	0.0134561i	0.597007	−	0.802236i	$-0.296356\pi$
$97$	0.182409	+	0.132528i	0.0185208	+	0.0134561i	−0.578486	+	0.815692i	$0.696356\pi$
$98$	12.2325	−	1.98535i	1.23567	−	0.200551i
$99$	−0.480740	+	3.03527i	−0.0483162	+	0.305056i
$100$	2.64400	+	9.64413i	0.264400	+	0.964413i
$101$	−12.9732	−	6.61020i	−1.29089	−	0.657739i	−0.332470	−	0.943114i	$-0.607882\pi$
$101$	−12.9732	−	6.61020i	−1.29089	−	0.657739i	−0.958416	+	0.285374i	$0.907882\pi$
$102$	1.37486	+	8.47106i	0.136131	+	0.838759i
$103$	−4.68908	−	2.38921i	−0.462029	−	0.235415i	0.207451	−	0.978245i	$-0.433483\pi$
$103$	−4.68908	−	2.38921i	−0.462029	−	0.235415i	−0.669480	+	0.742830i	$0.733483\pi$
$104$	1.93294	+	0.283491i	0.189540	+	0.0277986i
$105$	−17.1011	+	2.23528i	−1.66890	+	0.218141i
$106$	−5.63727	−	10.9601i	−0.547540	−	1.06454i
$107$	−15.7769	−	8.03875i	−1.52521	−	0.777136i	−0.527826	−	0.849353i	$-0.676993\pi$
$107$	−15.7769	−	8.03875i	−1.52521	−	0.777136i	−0.997389	+	0.0722168i	$0.976993\pi$
$108$	6.95806	−	5.13697i	0.669540	−	0.494305i
$109$	−3.90272	−	3.90272i	−0.373813	−	0.373813i	0.495051	−	0.868864i	$-0.335149\pi$
$109$	−3.90272	−	3.90272i	−0.373813	−	0.373813i	−0.868864	+	0.495051i	$0.835149\pi$
$110$	9.08278	−	8.66928i	0.866009	−	0.826583i
$111$	4.18251	−	0.662445i	0.396987	−	0.0628765i
$112$	−15.8791	+	0.242540i	−1.50044	+	0.0229178i
$113$	0.930632	−	5.87578i	0.0875465	−	0.552747i	−0.904460	−	0.426559i	$-0.859726\pi$
$113$	0.930632	−	5.87578i	0.0875465	−	0.552747i	0.992006	−	0.126188i	$-0.0402743\pi$
$114$	18.1927	−	13.3242i	1.70390	−	1.24792i
$115$	0.299705	−	0.0884746i	0.0279477	−	0.00825030i
$116$	−10.2365	−	10.0813i	−0.950432	−	0.936026i
$117$	0.165197	−	0.508425i	0.0152725	−	0.0470039i
$118$	−12.5106	+	12.6065i	−1.15169	+	1.16052i
$119$	10.0333	+	7.28963i	0.919753	+	0.668239i
$120$	12.2850	+	0.192303i	1.12146	+	0.0175548i
$121$	−4.53209	−	1.47257i	−0.412009	−	0.133870i
$122$	−4.78936	−	0.739826i	−0.433609	−	0.0669807i
$123$	−3.65686	+	11.8895i	−0.329728	+	1.07204i
$124$	5.86241	−	18.5227i	0.526460	−	1.66339i
$125$	−9.51653	−	5.86820i	−0.851184	−	0.524868i
$126$	−0.663423	+	4.29475i	−0.0591024	+	0.382607i
$127$	5.73734	−	0.908705i	0.509106	−	0.0806345i	0.103403	−	0.994640i	$-0.467027\pi$
$127$	5.73734	−	0.908705i	0.509106	−	0.0806345i	0.405703	+	0.914005i	$0.367027\pi$
$128$	11.2177	+	1.47059i	0.991516	+	0.129983i
$129$	5.30251	−	2.70176i	0.466860	−	0.237877i
$130$	−1.79648	+	1.24235i	−0.157562	+	0.108961i
$131$	6.74020	−	4.89705i	0.588894	−	0.427857i	−0.253025	−	0.967460i	$-0.581426\pi$
$131$	6.74020	−	4.89705i	0.588894	−	0.427857i	0.841920	+	0.539603i	$0.181426\pi$
$132$	−7.10846	−	13.6917i	−0.618712	−	1.19171i
$133$	5.09782	−	32.1864i	0.442037	−	2.79091i
$134$	1.15968	−	0.596477i	0.100181	−	0.0515278i
$135$	−1.77098	+	9.50618i	−0.152422	+	0.818162i
$136$	−6.31855	−	6.17543i	−0.541811	−	0.529538i
$137$	−17.2573			−1.47439			−0.737193	−	0.675682i	$-0.763849\pi$
$137$	−17.2573			−1.47439			−0.737193	+	0.675682i	$0.763849\pi$
$138$	−0.00146598	−	0.383941i	−0.000124793	−	0.0326832i
$139$	−0.00890311	−	0.0274009i	−0.000755152	−	0.00232412i	0.950678	−	0.310179i	$-0.100389\pi$
$139$	−0.00890311	−	0.0274009i	−0.000755152	−	0.00232412i	−0.951433	+	0.307855i	$0.900389\pi$
$140$	12.7971	−	12.3082i	1.08155	−	1.04023i
$141$	−3.34072	+	10.2817i	−0.281340	+	0.865874i
$142$	13.4860	−	18.7118i	1.13172	−	1.57026i
$143$	2.44358	+	1.24507i	0.204342	+	0.104118i
$144$	0.911605	−	2.95864i	0.0759671	−	0.246553i
$145$	16.0572	+	0.435366i	1.33348	+	0.0361552i
$146$	0.406825	+	1.23600i	0.0336691	+	0.102292i
$147$	10.0061	+	13.7722i	0.825290	+	1.13591i
$148$	−3.05908	+	3.10616i	−0.251455	+	0.255325i
$149$	3.33284	+	21.0428i	0.273037	+	1.72389i	0.618784	+	0.785562i	$0.287626\pi$
$149$	3.33284	+	21.0428i	0.273037	+	1.72389i	−0.345746	+	0.938328i	$0.612374\pi$
$150$	−10.1903	+	9.21172i	−0.832037	+	0.752134i
$151$	−5.38367	−	10.5660i	−0.438117	−	0.859852i	−0.999479	−	0.0322819i	$-0.989723\pi$
$151$	−5.38367	−	10.5660i	−0.438117	−	0.859852i	0.561362	−	0.827570i	$-0.310277\pi$
$152$	−6.92063	+	22.1601i	−0.561337	+	1.79742i
$153$	−1.95593	+	1.42106i	−0.158127	+	0.114886i
$154$	−21.2288	−	6.80816i	−1.71067	−	0.548617i
$155$	9.33318	+	19.6142i	0.749659	+	1.57545i
$156$	0.848755	+	2.54588i	0.0679548	+	0.203834i
$157$	7.25577	−	2.35754i	0.579074	−	0.188152i	−0.00481187	−	0.999988i	$-0.501532\pi$
$157$	7.25577	−	2.35754i	0.579074	−	0.188152i	0.583886	+	0.811836i	$0.301532\pi$
$158$	3.07294	+	9.33609i	0.244470	+	0.742739i
$159$	9.95144	−	13.6970i	0.789201	−	1.08624i
$160$	−10.2926	+	7.35269i	−0.813702	+	0.581282i
$161$	−0.392334	−	0.392334i	−0.0309203	−	0.0309203i
$162$	13.5378	+	6.83288i	1.06363	+	0.536841i
$163$	−0.268366	−	0.268366i	−0.0210200	−	0.0210200i	0.696519	−	0.717539i	$-0.254731\pi$
$163$	−0.268366	−	0.268366i	−0.0210200	−	0.0210200i	−0.717539	+	0.696519i	$0.754731\pi$
$164$	−4.24134	−	12.0835i	−0.331193	−	0.943563i
$165$	16.2532	+	5.77253i	1.26531	+	0.449391i
$166$	1.77802	+	5.40193i	0.138001	+	0.419271i
$167$	13.8256			1.06986			0.534928	−	0.844898i	$-0.320339\pi$
$167$	13.8256			1.06986			0.534928	+	0.844898i	$0.320339\pi$
$168$	−10.1260	−	19.3229i	−0.781235	−	1.49079i
$169$	10.1313	+	7.36079i	0.779327	+	0.566215i
$170$	9.87532	+	0.230024i	0.757403	+	0.0176421i
$171$	5.66033	+	2.88408i	0.432856	+	0.220551i
$172$	−2.73972	+	5.48007i	−0.208902	+	0.417851i
$173$	−6.59554	−	6.59554i	−0.501450	−	0.501450i	0.410438	−	0.911888i	$-0.365376\pi$
$173$	−6.59554	−	6.59554i	−0.501450	−	0.501450i	−0.911888	+	0.410438i	$0.865376\pi$
$174$	6.02703	−	18.7932i	0.456908	−	1.42471i
$175$	−1.07568	+	19.8221i	−0.0813140	+	1.49841i
$176$	14.2596	+	6.99342i	1.07486	+	0.527149i
$177$	−23.2031	−	7.53916i	−1.74405	−	0.566678i
$178$	−4.95390	−	6.76399i	−0.371310	−	0.506983i
$179$	6.53662	−	1.03530i	0.488570	−	0.0773818i	0.0927106	−	0.995693i	$-0.470447\pi$
$179$	6.53662	−	1.03530i	0.488570	−	0.0773818i	0.395859	+	0.918311i	$0.370447\pi$
$180$	1.51106	+	3.11406i	0.112628	+	0.232109i
$181$	0.374492	−	2.36445i	0.0278358	−	0.175748i	−0.969854	−	0.243688i	$-0.921643\pi$
$181$	0.374492	−	2.36445i	0.0278358	−	0.175748i	0.997689	+	0.0679401i	$0.0216427\pi$
$182$	3.46217	+	1.74745i	0.256633	+	0.129529i
$183$	−2.05715	−	6.33125i	−0.152069	−	0.468019i
$184$	0.235984	+	0.317101i	0.0173970	+	0.0233770i
$185$	0.132108	−	4.87241i	0.00971278	−	0.358226i
$186$	26.3435	−	4.27557i	1.93160	−	0.313500i
$187$	−5.63076	−	11.0510i	−0.411762	−	0.808129i
$188$	−3.52004	−	10.5585i	−0.256725	−	0.770059i
$189$	16.3288	−	5.30554i	1.18774	−	0.385922i
$190$	−11.2420	−	23.3949i	−0.815577	−	1.69725i
$191$	−14.1579	−	14.1579i	−1.02443	−	1.02443i	−0.999694	−	0.0247385i	$-0.992125\pi$
$191$	−14.1579	−	14.1579i	−1.02443	−	1.02443i	−0.0247385	−	0.999694i	$-0.507875\pi$
$192$	5.13988	+	14.6668i	0.370939	+	1.05849i
$193$	6.99572	+	5.08269i	0.503563	+	0.365860i	0.810376	−	0.585910i	$-0.199263\pi$
$193$	6.99572	+	5.08269i	0.503563	+	0.365860i	−0.306813	+	0.951770i	$0.599263\pi$
$194$	−0.145844	−	0.283553i	−0.0104710	−	0.0203579i
$195$	−2.63547	−	1.43411i	−0.188730	−	0.102699i
$196$	−16.7089	−	5.28832i	−1.19349	−	0.377737i
$197$	2.87386	−	18.1448i	0.204754	−	1.29277i	−0.644428	−	0.764665i	$-0.722905\pi$
$197$	2.87386	−	18.1448i	0.204754	−	1.29277i	0.849182	−	0.528100i	$-0.177095\pi$
$198$	2.54109	−	3.52574i	0.180587	−	0.250563i
$199$	4.73631	+	9.29553i	0.335748	+	0.658943i	0.995727	−	0.0923411i	$-0.0294350\pi$
$199$	4.73631	+	9.29553i	0.335748	+	0.658943i	−0.659979	+	0.751284i	$0.729435\pi$
$200$	2.80737	−	13.8607i	0.198511	−	0.980099i
$201$	1.44927	+	1.05296i	0.102224	+	0.0742699i
$202$	12.1668	+	16.6123i	0.856050	+	1.16884i
$203$	−12.9482	−	25.4122i	−0.908783	−	1.78359i
$204$	3.66217	−	11.5709i	0.256404	−	0.810127i
$205$	12.6828	+	6.64434i	0.885803	+	0.464061i
$206$	4.39758	+	6.00440i	0.306394	+	0.418346i
$207$	0.0963741	−	0.0491050i	0.00669846	−	0.00341304i
$208$	−2.25972	−	1.58963i	−0.156683	−	0.110221i
$209$	−19.1560	+	26.3660i	−1.32505	+	1.82377i
$210$	23.0148	+	8.07514i	1.58817	+	0.557238i
$211$	21.2264	−	10.8154i	1.46128	−	0.744561i	0.470805	−	0.882237i	$-0.343963\pi$
$211$	21.2264	−	10.8154i	1.46128	−	0.744561i	0.990477	+	0.137677i	$0.0439635\pi$
$212$	0.133102	+	17.4295i	0.00914150	+	1.19706i
$213$	31.2941	+	4.95649i	2.14423	+	0.339613i
$214$	14.7962	+	20.2025i	1.01144	+	1.38101i
$215$	−1.93940	−	6.56965i	−0.132266	−	0.448046i
$216$	−12.0581	+	2.05166i	−0.820447	+	0.139598i
$217$	22.6695	−	31.2019i	1.53891	−	2.11812i
$218$	2.44034	+	7.41416i	0.165281	+	0.502150i
$219$	−1.26393	+	1.26393i	−0.0854087	+	0.0854087i
$220$	−16.9914	+	5.15734i	−1.14556	+	0.347708i
$221$	0.666723	+	2.05196i	0.0448487	+	0.138030i
$222$	−5.70262	−	1.82885i	−0.382735	−	0.122744i
$223$	−5.53669	+	2.82108i	−0.370764	+	0.188914i	−0.629438	−	0.777051i	$-0.716715\pi$
$223$	−5.53669	+	2.82108i	−0.370764	+	0.188914i	0.258673	+	0.965965i	$0.416715\pi$
$224$	20.2022	+	9.81236i	1.34982	+	0.655616i
$225$	−3.61026	−	1.39353i	−0.240684	−	0.0929021i
$226$	−4.91912	+	6.82525i	−0.327215	+	0.454009i
$227$	−11.5216	+	3.74360i	−0.764717	+	0.248472i	−0.665302	−	0.746574i	$-0.731697\pi$
$227$	−11.5216	+	3.74360i	−0.764717	+	0.248472i	−0.0994154	+	0.995046i	$0.531697\pi$
$228$	−31.4591	+	5.22919i	−2.08343	+	0.346312i
$229$	10.5315	+	1.66803i	0.695944	+	0.110227i	0.494377	−	0.869248i	$-0.335396\pi$
$229$	10.5315	+	1.66803i	0.695944	+	0.110227i	0.201568	+	0.979475i	$0.435396\pi$
$230$	−0.434761	−	0.0792786i	−0.0286673	−	0.00522748i
$231$	−4.79072	−	30.2474i	−0.315207	−	1.99014i
$232$	6.49965	+	19.2507i	0.426723	+	1.26387i
$233$	2.65980	−	8.18603i	0.174250	−	0.536285i	−0.825349	−	0.564623i	$-0.809022\pi$
$233$	2.65980	−	8.18603i	0.174250	−	0.536285i	0.999598	+	0.0283382i	$0.00902153\pi$
$234$	−0.532544	+	0.536627i	−0.0348135	+	0.0350804i
$235$	10.9301	+	5.94767i	0.713000	+	0.387983i
$236$	23.8279	−	7.94383i	1.55106	−	0.517099i
$237$	−9.54707	+	9.54707i	−0.620149	+	0.620149i
$238$	−8.02210	−	15.5967i	−0.519995	−	1.01099i
$239$	7.87540	−	15.4564i	0.509418	−	0.999788i	−0.482854	−	0.875701i	$-0.660400\pi$
$239$	7.87540	−	15.4564i	0.509418	−	0.999788i	0.992271	−	0.124087i	$-0.0396003\pi$
$240$	−15.3875	−	8.07110i	−0.993259	−	0.520987i
$241$	3.78517	−	5.20983i	0.243824	−	0.335595i	−0.669512	−	0.742801i	$-0.733497\pi$
$241$	3.78517	−	5.20983i	0.243824	−	0.335595i	0.913336	+	0.407206i	$0.133497\pi$
$242$	4.78349	+	4.74710i	0.307494	+	0.305155i
$243$			7.85773i			0.504074i
$244$	5.57521	+	3.98594i	0.356916	+	0.255174i
$245$	17.6934	−	8.41921i	1.13039	−	0.537884i
$246$	12.1931	−	12.6804i	0.777405	−	0.808476i
$247$	4.00880	−	4.00880i	0.255074	−	0.255074i
$248$	−19.2045	+	19.6496i	−1.21949	+	1.24775i
$249$	−5.52400	+	5.52400i	−0.350070	+	0.350070i
$250$	8.27541	+	13.4728i	0.523383	+	0.852098i
$251$	9.35884	+	6.79960i	0.590725	+	0.429187i	0.842575	−	0.538580i	$-0.181039\pi$
$251$	9.35884	+	6.79960i	0.590725	+	0.429187i	−0.251850	+	0.967766i	$0.581039\pi$
$252$	3.57430	−	4.99945i	0.225160	−	0.314935i
$253$	0.171470	+	0.527729i	0.0107802	+	0.0331780i
$254$	−7.82253	−	2.50871i	−0.490829	−	0.157411i
$255$	5.83033	+	12.2527i	0.365109	+	0.767297i
$256$	−13.2255	−	9.00485i	−0.826591	−	0.562803i
$257$	16.6138	+	22.8669i	1.03634	+	1.42640i	0.900079	+	0.435726i	$0.143508\pi$
$257$	16.6138	+	22.8669i	1.03634	+	1.42640i	0.136261	+	0.990673i	$0.456492\pi$
$258$	−8.41613	+	0.0321348i	−0.523965	+	0.00200063i
$259$	−7.71111	+	3.92901i	−0.479145	+	0.244137i
$260$	3.05974	−	0.423726i	0.189757	−	0.0262784i
$261$	5.49148	−	0.869766i	0.339914	−	0.0538371i
$262$	−11.6301	+	1.88758i	−0.718512	+	0.116615i
$263$	20.7327	−	15.0632i	1.27844	−	0.928838i	0.278931	−	0.960311i	$-0.410020\pi$
$263$	20.7327	−	15.0632i	1.27844	−	0.928838i	0.999505	+	0.0314733i	$0.0100199\pi$
$264$	0.249902	+	21.8156i	0.0153804	+	1.34266i
$265$	−13.4011	−	14.1481i	−0.823223	−	0.869108i
$266$	−26.9460	+	37.3874i	−1.65217	+	2.29237i
$267$	5.22861	−	10.2617i	0.319986	−	0.628008i
$268$	−1.84421	+	0.0140835i	−0.112653	+	0.000860286i
$269$	10.9748	+	3.56592i	0.669145	+	0.217418i	0.623837	−	0.781555i	$-0.285573\pi$
$269$	10.9748	+	3.56592i	0.669145	+	0.217418i	0.0453080	+	0.998973i	$0.485573\pi$
$270$	8.29346	−	10.8732i	0.504724	−	0.661721i
$271$	10.6949	−	3.47499i	0.649669	−	0.211090i	0.0344010	−	0.999408i	$-0.489048\pi$
$271$	10.6949	−	3.47499i	0.649669	−	0.211090i	0.615268	+	0.788318i	$0.289048\pi$
$272$	4.04214	+	11.8229i	0.245091	+	0.716869i
$273$			5.32735i			0.322426i
$274$	21.7876	+	10.9967i	1.31623	+	0.664337i
$275$	9.95825	−	17.1746i	0.600505	−	1.03567i
$276$	−0.242805	+	0.485666i	−0.0146152	+	0.0292336i
$277$	2.95449	+	0.467945i	0.177518	+	0.0281161i	0.244561	−	0.969634i	$-0.421356\pi$
$277$	2.95449	+	0.467945i	0.177518	+	0.0281161i	−0.0670425	+	0.997750i	$0.521356\pi$
$278$	−0.00622022	+	0.0402674i	−0.000373064	+	0.00241508i
$279$	4.41927	+	6.08260i	0.264574	+	0.364156i
$280$	−23.9996	+	7.38471i	−1.43425	+	0.441321i
$281$	0.578540	+	1.13545i	0.0345128	+	0.0677352i	0.907619	−	0.419795i	$-0.137898\pi$
$281$	0.578540	+	1.13545i	0.0345128	+	0.0677352i	−0.873106	+	0.487530i	$0.837898\pi$
$282$	10.7694	−	10.8520i	0.641311	−	0.646227i
$283$	1.51168	+	9.54435i	0.0898598	+	0.567352i	0.991004	+	0.133833i	$0.0427285\pi$
$283$	1.51168	+	9.54435i	0.0898598	+	0.567352i	−0.901144	+	0.433520i	$0.857271\pi$
$284$	−28.9499	+	15.0303i	−1.71786	+	0.891884i
$285$	21.7315	−	28.2668i	1.28726	−	1.67438i
$286$	−2.29167	−	3.12902i	−0.135509	−	0.185023i
$287$	−0.400928	−	25.4188i	−0.0236661	−	1.50043i
$288$	−3.03623	+	3.15443i	−0.178912	+	0.185877i
$289$	−2.23806	+	6.88804i	−0.131651	+	0.405179i
$290$	−19.9950	−	10.7817i	−1.17415	−	0.633121i
$291$	0.257458	−	0.354360i	0.0150924	−	0.0207729i
$292$	0.273986	−	1.81971i	0.0160338	−	0.106490i
$293$	−16.1499	−	5.24741i	−0.943486	−	0.306557i	−0.203420	−	0.979092i	$-0.565206\pi$
$293$	−16.1499	−	5.24741i	−0.943486	−	0.306557i	−0.740066	+	0.672534i	$0.765206\pi$
$294$	−3.85688	−	23.7638i	−0.224938	−	1.38593i
$295$	−13.4224	+	24.6664i	−0.781481	+	1.43613i
$296$	5.84146	−	1.97226i	0.339528	−	0.114635i
$297$	−16.9590	−	2.68605i	−0.984063	−	0.155860i
$298$	9.20117	−	28.6906i	0.533009	−	1.66200i
$299$	−0.0151001	−	0.0953383i	−0.000873262	−	0.00551356i
$300$	18.7354	−	5.13643i	1.08169	−	0.296552i
$301$	−8.60011	+	8.60011i	−0.495702	+	0.495702i
$302$	0.0640334	+	16.7704i	0.00368471	+	0.965028i
$303$	−12.8414	+	25.2028i	−0.737722	+	1.44786i
$304$	22.8583	−	23.5674i	1.31101	−	1.35168i
$305$	−7.59784	+	0.993110i	−0.435051	+	0.0568653i
$306$	3.37493	−	0.547753i	0.192932	−	0.0313130i
$307$	−12.0460	+	23.6416i	−0.687502	+	1.34930i	0.238263	+	0.971201i	$0.423422\pi$
$307$	−12.0460	+	23.6416i	−0.687502	+	1.34930i	−0.925765	+	0.378098i	$0.876578\pi$
$308$	22.4634	+	22.1229i	1.27997	+	1.26057i
$309$	−4.64144	+	9.10934i	−0.264042	+	0.518212i
$310$	0.715336	−	30.7105i	0.0406284	−	1.74424i
$311$	−5.68082	−	0.899754i	−0.322130	−	0.0510204i	−0.00672452	−	0.999977i	$-0.502140\pi$
$311$	−5.68082	−	0.899754i	−0.322130	−	0.0510204i	−0.315405	+	0.948957i	$0.602140\pi$
$312$	0.550730	−	3.75506i	0.0311789	−	0.212589i
$313$	4.83856	−	6.65971i	0.273492	−	0.376429i	−0.650073	−	0.759872i	$-0.725262\pi$
$313$	4.83856	−	6.65971i	0.273492	−	0.376429i	0.923565	+	0.383443i	$0.125262\pi$
$314$	−10.6628	−	1.64711i	−0.601737	−	0.0929520i
$315$	0.890549	+	6.81319i	0.0501768	+	0.383880i
$316$	2.06954	−	13.7451i	0.116421	−	0.773223i
$317$	−9.27438	−	12.7651i	−0.520901	−	0.716959i	0.464809	−	0.885411i	$-0.346123\pi$
$317$	−9.27438	−	12.7651i	−0.520901	−	0.716959i	−0.985710	+	0.168452i	$0.946123\pi$
$318$	−21.2919	+	10.9514i	−1.19399	+	0.614122i
$319$			28.5230i			1.59698i
$320$	17.6799	−	2.72420i	0.988336	−	0.152287i
$321$	−15.6167	+	30.6494i	−0.871637	+	1.71068i
$322$	0.245323	+	0.745333i	0.0136713	+	0.0415358i
$323$	−25.3235	+	4.01085i	−1.40904	+	0.223169i
$324$	−12.7376	−	17.2532i	−0.707646	−	0.958513i
$325$	−2.17835	+	2.67987i	−0.120833	+	0.148652i
$326$	0.167807	+	0.509825i	0.00929397	+	0.0282366i
$327$	−7.58171	+	7.58171i	−0.419269	+	0.419269i
$328$	−2.34514	+	17.9583i	−0.129489	+	0.991581i
$329$		−	22.0941i		−	1.21809i
$330$	−16.8416	−	17.6449i	−0.927098	−	0.971317i
$331$	5.00712	−	5.00712i	0.275216	−	0.275216i	−0.555980	−	0.831196i	$-0.687657\pi$
$331$	5.00712	−	5.00712i	0.275216	−	0.275216i	0.831196	+	0.555980i	$0.187657\pi$
$332$	1.19745	−	7.95301i	0.0657187	−	0.436478i
$333$	−0.263923	−	1.66634i	−0.0144629	−	0.0913150i
$334$	−17.4550	−	8.80999i	−0.955096	−	0.482061i
$335$	1.49700	−	1.41796i	0.0817898	−	0.0774717i
$336$	0.471175	+	30.8480i	0.0257047	+	1.68289i
$337$	−7.83011	+	7.83011i	−0.426533	+	0.426533i	−0.887446	−	0.460912i	$-0.847522\pi$
$337$	−7.83011	+	7.83011i	−0.426533	+	0.426533i	0.460912	+	0.887446i	$0.347522\pi$
$338$	−8.10040	−	15.7490i	−0.440604	−	0.856632i
$339$	−11.4147	−	1.80791i	−0.619962	−	0.0981924i
$340$	−12.3212	−	6.58320i	−0.668209	−	0.357024i
$341$	−34.3667	+	17.5107i	−1.86106	+	0.948258i
$342$	−5.30845	−	7.24809i	−0.287048	−	0.391932i
$343$	−5.66239	−	4.11397i	−0.305740	−	0.222133i
$344$	6.95097	−	5.17285i	0.374771	−	0.278902i
$345$	−0.171877	−	0.582229i	−0.00925355	−	0.0313461i
$346$	4.12414	+	12.5298i	0.221715	+	0.673607i
$347$	16.9483	−	5.50684i	0.909833	−	0.295623i	0.183543	−	0.983012i	$-0.441243\pi$
$347$	16.9483	−	5.50684i	0.909833	−	0.295623i	0.726289	+	0.687389i	$0.241243\pi$
$348$	−19.5847	+	19.8861i	−1.04985	+	1.06601i
$349$	−6.10125	−	18.7777i	−0.326592	−	1.00515i	−0.970717	−	0.240227i	$-0.922778\pi$
$349$	−6.10125	−	18.7777i	−0.326592	−	1.00515i	0.644124	−	0.764921i	$-0.277222\pi$
$350$	13.9892	−	24.3402i	0.747752	−	1.30104i
$351$	2.84073	+	0.923010i	0.151627	+	0.0492666i
$352$	−13.5466	−	17.9159i	−0.722039	−	0.954920i
$353$	17.2319	+	8.78012i	0.917164	+	0.467318i	0.847826	−	0.530275i	$-0.177911\pi$
$353$	17.2319	+	8.78012i	0.917164	+	0.467318i	0.0693381	+	0.997593i	$0.477911\pi$
$354$	24.4902	+	24.3039i	1.30164	+	1.29174i
$355$	12.2056	−	34.3662i	0.647804	−	1.82397i
$356$	1.94420	+	11.6964i	0.103042	+	0.619907i
$357$	14.1614	−	19.4914i	0.749499	−	1.03160i
$358$	−8.91230	−	2.85821i	−0.471030	−	0.151061i
$359$	−4.89342	+	3.55528i	−0.258265	+	0.187640i	−0.709382	−	0.704824i	$-0.751026\pi$
$359$	−4.89342	+	3.55528i	−0.258265	+	0.187640i	0.451117	+	0.892465i	$0.351026\pi$
$360$	0.0766149	−	4.89444i	0.00403796	−	0.257960i
$361$	28.4314	+	39.1325i	1.49639	+	2.05960i
$362$	−1.97948	+	2.74652i	−0.104039	+	0.144354i
$363$	−2.86071	+	8.80437i	−0.150149	+	0.462110i
$364$	−3.25754	−	4.41236i	−0.170741	−	0.231270i
$365$	1.16377	+	1.69666i	0.0609144	+	0.0888072i
$366$	−1.43724	+	9.30416i	−0.0751257	+	0.486336i
$367$	−27.3176	+	13.9190i	−1.42597	+	0.726566i	−0.985257	−	0.171083i	$-0.945273\pi$
$367$	−27.3176	+	13.9190i	−1.42597	+	0.726566i	−0.440710	+	0.897650i	$0.645273\pi$
$368$	−0.0958691	−	0.550720i	−0.00499752	−	0.0287082i
$369$	4.73686	+	1.45692i	0.246591	+	0.0758441i
$370$	−3.27160	+	6.06731i	−0.170082	+	0.315424i
$371$	−10.6922	+	32.9073i	−0.555113	+	1.70846i
$372$	−35.9836	−	11.3887i	−1.86566	−	0.590478i
$373$	0.815486	−	0.129160i	0.0422243	−	0.00668767i	−0.135287	−	0.990807i	$-0.543196\pi$
$373$	0.815486	−	0.129160i	0.0422243	−	0.00668767i	0.177511	+	0.984119i	$0.443196\pi$
$374$	0.0669724	+	17.5401i	0.00346306	+	0.906978i
$375$	−11.4000	+	18.4875i	−0.588693	+	0.954690i
$376$	−2.28404	+	15.5734i	−0.117790	+	0.803134i
$377$	0.776194	−	4.90070i	0.0399760	−	0.252399i
$378$	−23.9962	−	3.70676i	−1.23423	−	0.190655i
$379$	−14.5753	+	10.5896i	−0.748682	+	0.543949i	−0.895418	−	0.445226i	$-0.853123\pi$
$379$	−14.5753	+	10.5896i	−0.748682	+	0.543949i	0.146736	+	0.989176i	$0.453123\pi$
$380$	−0.714656	+	36.7001i	−0.0366611	+	1.88268i
$381$	−1.76532	−	11.1458i	−0.0904398	−	0.571015i
$382$	8.85285	+	26.8964i	0.452951	+	1.37614i
$383$	11.4803			0.586615			0.293307	−	0.956018i	$-0.405244\pi$
$383$	11.4803			0.586615			0.293307	+	0.956018i	$0.405244\pi$
$384$	2.85688	−	21.7924i	0.145789	−	1.11209i
$385$	−35.2367	−	0.955389i	−1.79583	−	0.0486912i
$386$	−5.59339	−	10.8748i	−0.284696	−	0.553513i
$387$	−1.07640	−	2.11255i	−0.0547165	−	0.107387i
$388$	0.00344354	+	0.450926i	0.000174819	+	0.0228923i
$389$	8.45433	+	26.0198i	0.428652	+	1.31925i	0.899454	+	0.437016i	$0.143965\pi$
$389$	8.45433	+	26.0198i	0.428652	+	1.31925i	−0.470802	+	0.882239i	$0.656035\pi$
$390$	2.41348	+	3.48997i	0.122211	+	0.176722i
$391$	−0.198184	+	0.388958i	−0.0100226	+	0.0196705i
$392$	17.7254	+	17.3239i	0.895266	+	0.874988i
$393$	−9.51335	−	13.0940i	−0.479885	−	0.660505i
$394$	−15.1906	+	21.0768i	−0.765291	+	1.06184i
$395$	8.79048	+	12.8157i	0.442297	+	0.644826i
$396$	−5.45485	+	2.83206i	−0.274116	+	0.142316i
$397$	21.1359	+	6.86748i	1.06078	+	0.344669i	0.786891	−	0.617092i	$-0.211689\pi$
$397$	21.1359	+	6.86748i	1.06078	+	0.344669i	0.273891	+	0.961761i	$0.411689\pi$
$398$	−0.0563338	−	14.7538i	−0.00282376	−	0.739543i
$399$	−62.5276	−	9.90340i	−3.13030	−	0.495790i
$400$	−12.3767	+	15.7104i	−0.618835	+	0.785521i
$401$		−	14.6549i		−	0.731829i	−0.930648	−	0.365915i	$-0.880756\pi$
$401$		−	14.6549i		−	0.731829i	0.930648	−	0.365915i	$-0.119244\pi$
$402$	−1.15876	−	2.25289i	−0.0577936	−	0.112364i
$403$	6.38125	−	2.07339i	0.317873	−	0.103283i
$404$	−4.77494	−	28.7263i	−0.237562	−	1.42919i
$405$	23.5715	+	4.39133i	1.17128	+	0.218207i
$406$	0.154006	+	40.3342i	0.00764318	+	2.00175i
$407$	8.65505			0.429015
$408$	−11.9968	+	12.2749i	−0.593931	+	0.607696i
$409$		−	26.8239i		−	1.32636i	−0.748462	−	0.663178i	$-0.769207\pi$
$409$		−	26.8239i		−	1.32636i	0.748462	−	0.663178i	$-0.230793\pi$
$410$	−11.7783	−	16.4703i	−0.581687	−	0.813413i
$411$			33.5252i			1.65368i
$412$	−1.72587	−	10.3829i	−0.0850273	−	0.511528i
$413$	49.8608			2.45349
$414$	−0.152965		0.000584057i	−0.00751780		2.87048e-5i
$415$	5.08623	+	7.41523i	0.249673	+	0.363999i
$416$	1.83998	+	3.44687i	0.0902126	+	0.168997i
$417$	−0.0532310	+	0.0172958i	−0.00260674	+	0.000846980i
$418$	40.9858	−	21.0808i	2.00468	−	1.03110i
$419$		−	1.28591i		−	0.0628209i	−0.999507	−	0.0314104i	$-0.990000\pi$
$419$		−	1.28591i		−	0.0628209i	0.999507	−	0.0314104i	$-0.00999990\pi$
$420$	−23.9108	−	24.8605i	−1.16673	−	1.21307i
$421$	−4.05236	−	0.641831i	−0.197500	−	0.0312809i	0.0569007	−	0.998380i	$-0.481878\pi$
$421$	−4.05236	−	0.641831i	−0.197500	−	0.0312809i	−0.254401	+	0.967099i	$0.581878\pi$
$422$	−33.6904	+	0.128638i	−1.64002	+	0.00626201i
$423$	4.09629	+	1.33097i	0.199169	+	0.0647138i
$424$	10.9385	−	22.0898i	0.531218	−	1.07278i
$425$	15.0938	−	4.01439i	0.732155	−	0.194726i
$426$	−36.3509	−	26.1990i	−1.76120	−	1.26934i
$427$	7.99687	+	11.0067i	0.386996	+	0.532654i
$428$	−5.80687	−	34.9344i	−0.280686	−	1.68862i
$429$	2.41876	−	4.74708i	0.116779	−	0.229191i
$430$	−1.73782	+	9.53011i	−0.0838049	+	0.459583i
$431$	−7.66730	−	23.5975i	−0.369321	−	1.13665i	−0.947231	−	0.320552i	$-0.896132\pi$
$431$	−7.66730	−	23.5975i	−0.369321	−	1.13665i	0.577910	−	0.816100i	$-0.303868\pi$
$432$	16.5309	+	5.09343i	0.795341	+	0.245058i
$433$	7.51169	+	14.7425i	0.360989	+	0.708480i	0.998056	−	0.0623284i	$-0.0198526\pi$
$433$	7.51169	+	14.7425i	0.360989	+	0.708480i	−0.637067	+	0.770808i	$0.719853\pi$
$434$	−48.5032	+	24.9473i	−2.32823	+	1.19751i
$435$	0.845774	−	31.1938i	0.0405518	−	1.49563i
$436$	1.64351	−	10.9155i	0.0787096	−	0.522759i
$437$	1.14706			0.0548715
$438$	2.40114	−	0.790327i	0.114731	−	0.0377633i
$439$	−1.24859	−	7.88329i	−0.0595919	−	0.376249i	−0.999403	−	0.0345537i	$-0.988999\pi$
$439$	−1.24859	−	7.88329i	−0.0595919	−	0.376249i	0.939811	−	0.341695i	$-0.111001\pi$
$440$	24.7383	+	4.31611i	1.17935	+	0.205762i
$441$	5.48695	−	3.98650i	0.261283	−	0.189833i
$442$	0.465811	−	3.01549i	0.0221564	−	0.143432i
$443$	−0.180655	+	1.14061i	−0.00858317	+	0.0541920i	−0.991608	−	0.129280i	$-0.958734\pi$
$443$	−0.180655	+	1.14061i	−0.00858317	+	0.0541920i	0.983025	+	0.183472i	$0.0587335\pi$
$444$	6.03426	+	5.94279i	0.286373	+	0.282032i
$445$	−10.5095	−	8.07972i	−0.498199	−	0.383016i
$446$	8.78782	−	0.0335540i	0.416115	−	0.00158883i
$447$	40.8792	−	6.47462i	1.93352	−	0.306239i
$448$	−19.2530	−	25.2616i	−0.909617	−	1.19350i
$449$	9.23950	−	28.4363i	0.436039	−	1.34199i	−0.455979	−	0.889990i	$-0.650711\pi$
$449$	9.23950	−	28.4363i	0.436039	−	1.34199i	0.892018	−	0.451999i	$-0.149289\pi$
$450$	3.67001	+	4.05990i	0.173006	+	0.191385i
$451$	−11.1835	+	22.8321i	−0.526613	+	1.07512i
$452$	10.5597	−	5.48240i	0.496686	−	0.257870i
$453$	−20.5263	+	10.4587i	−0.964412	+	0.491392i
$454$	16.9318	+	2.61549i	0.794647	+	0.122751i
$455$	6.02821	+	1.12304i	0.282607	+	0.0526491i
$456$	43.0497	+	13.4445i	2.01599	+	0.629597i
$457$	10.2196	−	31.4526i	0.478052	−	1.47129i	−0.363746	−	0.931498i	$-0.618502\pi$
$457$	10.2196	−	31.4526i	0.478052	−	1.47129i	0.841798	−	0.539793i	$-0.181498\pi$
$458$	−12.2333	−	8.81687i	−0.571626	−	0.411985i
$459$	−7.93994	−	10.9284i	−0.370605	−	0.510094i
$460$	0.498374	+	0.377130i	0.0232368	+	0.0175838i
$461$	13.3887	−	9.72749i	0.623576	−	0.453054i	−0.230593	−	0.973050i	$-0.574067\pi$
$461$	13.3887	−	9.72749i	0.623576	−	0.453054i	0.854169	+	0.519996i	$0.174067\pi$
$462$	−13.2260	+	41.2406i	−0.615330	+	1.91869i
$463$	1.28734	−	1.77187i	0.0598275	−	0.0823456i	−0.778055	−	0.628196i	$-0.783793\pi$
$463$	1.28734	−	1.77187i	0.0598275	−	0.0823456i	0.837882	+	0.545851i	$0.183793\pi$
$464$	4.06110	−	28.4461i	0.188532	−	1.32058i
$465$	38.1039	−	18.1313i	1.76703	−	0.840819i
$466$	−8.57438	+	8.64011i	−0.397200	+	0.400245i
$467$	−9.95198	−	5.07079i	−0.460523	−	0.234648i	0.208307	−	0.978063i	$-0.433205\pi$
$467$	−9.95198	−	5.07079i	−0.460523	−	0.234648i	−0.668830	+	0.743415i	$0.733205\pi$
$468$	1.01430	−	0.338150i	0.0468859	−	0.0156310i
$469$	−3.48190	−	1.13134i	−0.160779	−	0.0522404i
$470$	−10.0094	−	14.4739i	−0.461699	−	0.667633i
$471$	−4.57993	−	14.0956i	−0.211032	−	0.649490i
$472$	−35.1451	−	5.15449i	−1.61768	−	0.237255i
$473$	11.5680	−	3.75868i	0.531898	−	0.172824i
$474$	18.1370	−	5.96971i	0.833058	−	0.274198i
$475$	−27.4044	−	30.5493i	−1.25740	−	1.40170i
$476$	0.189411	+	24.8030i	0.00868162	+	1.13684i
$477$	−5.45697	−	3.96472i	−0.249858	−	0.181532i
$478$	−19.7920	+	14.4955i	−0.905264	+	0.663008i
$479$	−6.44214	+	3.28243i	−0.294349	+	0.149978i	−0.594929	−	0.803778i	$-0.702820\pi$
$479$	−6.44214	+	3.28243i	−0.294349	+	0.149978i	0.300580	+	0.953757i	$0.402820\pi$
$480$	14.2839	+	19.9952i	0.651967	+	0.912650i
$481$	−1.48707	−	0.235529i	−0.0678047	−	0.0107392i
$482$	−8.09866	+	4.16550i	−0.368884	+	0.189733i
$483$	−0.762176	+	0.762176i	−0.0346802	+	0.0346802i
$484$	−3.01426	−	9.04143i	−0.137012	−	0.410974i
$485$	−0.346705	−	0.366030i	−0.0157431	−	0.0166206i
$486$	5.00713	−	9.92051i	0.227128	−	0.450003i
$487$	1.39655	+	8.81749i	0.0632839	+	0.399559i	0.998915	+	0.0465784i	$0.0148317\pi$
$487$	1.39655	+	8.81749i	0.0632839	+	0.399559i	−0.935631	+	0.352980i	$0.885168\pi$
$488$	−4.49886	−	8.58497i	−0.203654	−	0.388623i
$489$	−0.521346	+	0.521346i	−0.0235761	+	0.0235761i
$490$	−27.7032	−	0.645286i	−1.25150	−	0.0291510i
$491$		−	4.41751i		−	0.199359i	−0.995020	−	0.0996797i	$-0.968218\pi$
$491$		−	4.41751i		−	0.199359i	0.995020	−	0.0996797i	$-0.0317818\pi$
$492$	−23.4743	+	8.23952i	−1.05830	+	0.371466i
$493$	−15.8671	+	15.8671i	−0.714619	+	0.714619i
$494$	−7.61567	+	2.50667i	−0.342645	+	0.112780i
$495$	2.29982	−	6.47540i	0.103369	−	0.291047i
$496$	36.7672	−	12.5703i	1.65089	−	0.564425i
$497$	−63.9559	+	10.1296i	−2.86881	+	0.454375i
$498$	10.4942	−	3.45412i	0.470255	−	0.154783i
$499$	−5.33681	+	10.4741i	−0.238908	+	0.468884i	−0.979064	−	0.203551i	$-0.934752\pi$
$499$	−5.33681	+	10.4741i	−0.238908	+	0.468884i	0.740156	+	0.672435i	$0.234752\pi$
$500$	−1.86262	−	22.2830i	−0.0832989	−	0.996525i
$501$		−	26.8586i		−	1.19995i
$502$	−7.48282	−	14.5483i	−0.333975	−	0.649321i
$503$	21.7247	+	29.9014i	0.968655	+	1.33324i	0.942723	+	0.333576i	$0.108255\pi$
$503$	21.7247	+	29.9014i	0.968655	+	1.33324i	0.0259317	+	0.999664i	$0.491745\pi$
$504$	−7.69838	+	4.03425i	−0.342913	+	0.179700i
$505$	25.8113	+	19.8438i	1.14859	+	0.883036i
$506$	0.119798	−	0.775531i	0.00532569	−	0.0344765i
$507$	14.2996	−	19.6817i	0.635067	−	0.874095i
$508$	8.27745	+	8.15199i	0.367253	+	0.361686i
$509$	29.9946	+	4.75068i	1.32949	+	0.210570i	0.780445	−	0.625225i	$-0.214993\pi$
$509$	29.9946	+	4.75068i	1.32949	+	0.210570i	0.549042	+	0.835795i	$0.314993\pi$
$510$	0.446862	−	19.1845i	0.0197874	−	0.849504i
$511$	1.65846	−	3.25490i	0.0733658	−	0.143988i
$512$	10.9593	+	19.7963i	0.484335	+	0.874883i
$513$	−16.1143	+	31.6261i	−0.711463	+	1.39632i
$514$	−6.40383	−	39.4565i	−0.282461	−	1.74035i
$515$	9.32930	+	7.17237i	0.411098	+	0.316053i
$516$	10.6460	+	5.32238i	0.468663	+	0.234305i
$517$	−10.0313	+	19.6875i	−0.441176	+	0.865856i
$518$	12.2391	−	0.0467317i	0.537753	−	0.00205327i
$519$	−12.8130	+	12.8130i	−0.562427	+	0.562427i
$520$	−4.13298	−	1.41478i	−0.181243	−	0.0620421i
$521$	−3.14372	−	19.8486i	−0.137729	−	0.869585i	−0.955704	−	0.294331i	$-0.904903\pi$
$521$	−3.14372	−	19.8486i	−0.137729	−	0.869585i	0.817975	−	0.575254i	$-0.195097\pi$
$522$	−7.48732	−	2.40121i	−0.327711	−	0.105098i
$523$	23.0315	+	3.64783i	1.00710	+	0.159508i	0.638125	−	0.769933i	$-0.279710\pi$
$523$	23.0315	+	3.64783i	1.00710	+	0.159508i	0.368971	+	0.929441i	$0.379710\pi$
$524$	15.8860	+	5.02789i	0.693984	+	0.219645i
$525$	38.5078	+	2.08970i	1.68062	+	0.0912020i
$526$	−35.7741	+	5.80616i	−1.55982	+	0.253161i
$527$	−28.8590	−	9.37684i	−1.25712	−	0.408462i
$528$	13.5859	−	27.7018i	0.591251	−	1.20557i
$529$	−13.5076	+	18.5916i	−0.587286	+	0.808330i
$530$	7.90363	+	26.4016i	0.343312	+	1.14681i
$531$	−3.00365	+	9.24429i	−0.130347	+	0.401168i
$532$	57.8439	−	30.0315i	2.50785	−	1.30203i
$533$	2.54284	−	3.61858i	0.110143	−	0.156738i
$534$	−13.1402	+	9.62380i	−0.568633	+	0.416463i
$535$	31.3895	+	24.1323i	1.35709	+	1.04333i
$536$	2.33732	+	1.15739i	0.100957	+	0.0499917i
$537$	−2.01125	−	12.6985i	−0.0867916	−	0.547981i
$538$	−11.5836	−	11.4954i	−0.499402	−	0.495603i
$539$	15.7959	+	31.0013i	0.680379	+	1.33532i
$540$	−17.3993	+	8.44279i	−0.748746	+	0.363320i
$541$	−25.4499	−	35.0287i	−1.09417	−	1.50600i	−0.842888	−	0.538089i	$-0.819146\pi$
$541$	−25.4499	−	35.0287i	−1.09417	−	1.50600i	−0.251287	−	0.967913i	$-0.580854\pi$
$542$	−15.7168	−	2.42782i	−0.675096	−	0.104284i
$543$	−4.59335	−	0.727515i	−0.197119	−	0.0312206i
$544$	2.43057	−	17.5023i	0.104210	−	0.750407i
$545$	6.98087	+	10.1774i	0.299028	+	0.435953i
$546$	3.39472	−	6.72587i	0.145280	−	0.287841i
$547$			0.0721726i			0.00308588i	0.999999	+	0.00154294i	$0.000491133\pi$
$547$			0.0721726i			0.00308588i	−0.999999	+	0.00154294i	$0.999509\pi$
$548$	−20.4998	−	27.7671i	−0.875706	−	1.18615i
$549$	−2.52241	+	0.819581i	−0.107654	+	0.0349789i
$550$	−23.5165	+	15.3376i	−1.00275	+	0.653995i
$551$	56.0770	+	18.2205i	2.38896	+	0.776220i
$552$	0.616023	−	0.458439i	0.0262197	−	0.0195125i
$553$	12.5271	−	24.5858i	0.532706	−	1.04550i
$554$	−3.43190	−	2.47346i	−0.145808	−	0.105087i
$555$	−9.46549	−	0.256643i	−0.401788	−	0.0108939i
$556$	0.0335125	−	0.0468746i	0.00142124	−	0.00198792i
$557$	−36.6840	+	26.6525i	−1.55435	+	1.12930i	−0.613898	+	0.789386i	$0.710399\pi$
$557$	−36.6840	+	26.6525i	−1.55435	+	1.12930i	−0.940455	+	0.339918i	$0.889601\pi$
$558$	−1.70342	−	10.4954i	−0.0721114	−	0.444307i
$559$	−2.08985	+	0.331000i	−0.0883913	+	0.0139998i
$560$	35.0056	+	5.96981i	1.47926	+	0.252270i
$561$	−21.4685	+	10.9387i	−0.906399	+	0.461833i
$562$	−0.00688117	−	1.80218i	−0.000290265	−	0.0760205i
$563$	−0.361905	−	0.498120i	−0.0152525	−	0.0209932i	0.801323	−	0.598232i	$-0.204130\pi$
$563$	−0.361905	−	0.498120i	−0.0152525	−	0.0209932i	−0.816575	+	0.577239i	$0.804130\pi$
$564$	−20.5117	+	6.83828i	−0.863700	+	0.287943i
$565$	−4.45206	+	12.5353i	−0.187300	+	0.527364i
$566$	4.17337	−	13.0132i	0.175420	−	0.546984i
$567$	−13.1556	−	40.4889i	−0.552485	−	1.70037i
$568$	46.1274	−	0.528398i	1.93546	−	0.0221711i
$569$	−9.87258	−	7.17285i	−0.413880	−	0.300701i	0.361291	−	0.932453i	$-0.382336\pi$
$569$	−9.87258	−	7.17285i	−0.413880	−	0.300701i	−0.775171	+	0.631752i	$0.782336\pi$
$570$	−45.4487	+	21.8394i	−1.90363	+	0.914753i
$571$	−12.8260	+	12.8260i	−0.536753	+	0.536753i	−0.922574	−	0.385821i	$-0.873918\pi$
$571$	−12.8260	+	12.8260i	−0.536753	+	0.536753i	0.385821	+	0.922574i	$0.373918\pi$
$572$	0.899386	+	5.41075i	0.0376052	+	0.226235i
$573$	−27.5042	+	27.5042i	−1.14901	+	1.14901i
$574$	−15.6913	+	32.3472i	−0.654943	+	1.35014i
$575$	−0.695059	+	0.0717511i	−0.0289860	+	0.00299223i
$576$	5.84336	−	2.04776i	0.243474	−	0.0853234i
$577$			2.49024i			0.103670i	0.998656	+	0.0518351i	$0.0165070\pi$
$577$			2.49024i			0.103670i	−0.998656	+	0.0518351i	$0.983493\pi$
$578$	7.21480	−	7.27011i	0.300096	−	0.302397i
$579$	9.87399	−	13.5904i	0.410349	−	0.564797i
$580$	18.3737	+	26.3533i	0.762926	+	1.09426i
$581$	7.24827	−	14.2255i	0.300709	−	0.590174i
$582$	−0.550851	+	0.283327i	−0.0228335	+	0.0117443i
$583$	24.4683	−	24.4683i	1.01337	−	1.01337i
$584$	−1.50547	+	2.12282i	−0.0622969	+	0.0878429i
$585$	−0.571359	+	1.04999i	−0.0236228	+	0.0434117i
$586$	17.0457	+	16.9160i	0.704151	+	0.698794i
$587$	−10.7588	+	33.1122i	−0.444063	+	1.36668i	0.439445	+	0.898269i	$0.355175\pi$
$587$	−10.7588	+	33.1122i	−0.444063	+	1.36668i	−0.883508	+	0.468416i	$0.844825\pi$
$588$	−10.2735	+	32.4599i	−0.423671	+	1.33862i
$589$	12.4730	+	78.7517i	0.513943	+	3.24491i
$590$	32.6640	−	22.5887i	1.34475	−	0.929960i
$591$	−35.2494	−	5.58296i	−1.44997	−	0.229652i
$592$	−8.63171	−	1.23231i	−0.354761	−	0.0506475i
$593$	9.90861	−	3.21950i	0.406898	−	0.132209i	−0.0984148	−	0.995145i	$-0.531377\pi$
$593$	9.90861	−	3.21950i	0.406898	−	0.132209i	0.505313	+	0.862936i	$0.331377\pi$
$594$	19.6994	+	14.1979i	0.808278	+	0.582546i
$595$	−19.0704	−	20.1333i	−0.781810	−	0.825386i
$596$	−29.8989	+	30.3591i	−1.22471	+	1.24356i
$597$	18.0582	−	9.20109i	0.739071	−	0.376576i
$598$	−0.0416877	+	0.129988i	−0.00170474	+	0.00531562i
$599$	−1.20763	−	3.71670i	−0.0493424	−	0.151860i	0.923349	−	0.383961i	$-0.125440\pi$
$599$	−1.20763	−	3.71670i	−0.0493424	−	0.151860i	−0.972692	+	0.232100i	$0.925440\pi$
$600$	−26.9268	−	5.45380i	−1.09928	−	0.222651i
$601$	−3.29591	+	3.29591i	−0.134443	+	0.134443i	−0.771126	−	0.636683i	$-0.780306\pi$
$601$	−3.29591	+	3.29591i	−0.134443	+	0.134443i	0.636683	+	0.771126i	$0.280306\pi$
$602$	16.3380	−	5.37758i	0.665886	−	0.219174i
$603$	0.419505	−	0.577400i	0.0170836	−	0.0235135i
$604$	10.6056	−	21.2137i	0.431538	−	0.863173i
$605$	9.35960	+	5.09309i	0.380522	+	0.207063i
$606$	32.2723	−	23.6360i	1.31097	−	0.960147i
$607$	34.0267	+	5.38929i	1.38110	+	0.218745i	0.802395	−	0.596793i	$-0.203559\pi$
$607$	34.0267	+	5.38929i	1.38110	+	0.218745i	0.578704	+	0.815538i	$0.303559\pi$
$608$	−43.8767	+	15.1884i	−1.77944	+	0.615971i
$609$	−49.3676	+	25.1540i	−2.00048	+	1.01929i
$610$	10.2252	+	3.58770i	0.414007	+	0.145262i
$611$	2.25929	−	3.10964i	0.0914010	−	0.125803i
$612$	−4.60994	−	1.45904i	−0.186346	−	0.0589780i
$613$	14.6327	−	7.45572i	0.591009	−	0.301134i	−0.132791	−	0.991144i	$-0.542394\pi$
$613$	14.6327	−	7.45572i	0.591009	−	0.301134i	0.723800	+	0.690010i	$0.242394\pi$
$614$	30.2733	−	22.1719i	1.22173	−	0.894786i
$615$	12.9078	−	24.6385i	0.520492	−	0.993519i
$616$	−14.2632	−	42.2447i	−0.574679	−	1.70209i
$617$	7.22811	+	14.1860i	0.290993	+	0.571106i	0.989506	−	0.144492i	$-0.0461547\pi$
$617$	7.22811	+	14.1860i	0.290993	+	0.571106i	−0.698513	+	0.715597i	$0.746155\pi$
$618$	11.6646	−	8.54305i	0.469218	−	0.343652i
$619$	12.5365	+	9.10827i	0.503883	+	0.366092i	0.810498	−	0.585741i	$-0.199197\pi$
$619$	12.5365	+	9.10827i	0.503883	+	0.366092i	−0.306615	+	0.951833i	$0.599197\pi$
$620$	−20.4726	+	38.3167i	−0.822200	+	1.53884i
$621$	0.274366	+	0.538473i	0.0110099	+	0.0216082i
$622$	6.59878	+	4.75591i	0.264587	+	0.190695i
$623$	−3.68206	+	23.2476i	−0.147519	+	0.931395i
$624$	−3.08812	+	4.38989i	−0.123624	+	0.175736i
$625$	18.5165	+	16.7970i	0.740659	+	0.671881i
$626$	−10.3525	+	5.32474i	−0.413768	+	0.212819i
$627$	51.2204	+	37.2138i	2.04555	+	1.48618i
$628$	12.4124	+	8.87410i	0.495308	+	0.354115i
$629$	4.81473	+	4.81473i	0.191976	+	0.191976i
$630$	3.21719	−	9.16924i	0.128176	−	0.365311i
$631$	7.87080	−	2.55738i	0.313332	−	0.101808i	−0.148130	−	0.988968i	$-0.547325\pi$
$631$	7.87080	−	2.55738i	0.313332	−	0.101808i	0.461461	+	0.887160i	$0.347325\pi$
$632$	−11.3715	+	16.0347i	−0.452335	+	0.637824i
$633$	−21.0107	−	41.2358i	−0.835101	−	1.63898i
$634$	3.57483	+	22.0260i	0.141975	+	0.874763i
$635$	−12.9842	−	0.352048i	−0.515263	−	0.0139706i
$636$	33.8598	−	0.258574i	1.34263	−	0.0102531i
$637$	−1.87035	−	5.75636i	−0.0741061	−	0.228075i
$638$	18.1755	−	36.0107i	0.719576	−	1.42568i
$639$	1.97470	−	12.4678i	0.0781179	−	0.493217i
$640$	−24.0571	−	7.82671i	−0.950939	−	0.309378i
$641$	−7.54825	+	1.19553i	−0.298138	+	0.0472204i	−0.303711	−	0.952764i	$-0.598226\pi$
$641$	−7.54825	+	1.19553i	−0.298138	+	0.0472204i	0.00557354	+	0.999984i	$0.498226\pi$
$642$	39.2468	−	28.7441i	1.54895	−	1.13444i
$643$	44.1321	+	14.3394i	1.74040	+	0.565491i	0.994887	−	0.100998i	$-0.0322037\pi$
$643$	44.1321	+	14.3394i	1.74040	+	0.565491i	0.745515	+	0.666489i	$0.232204\pi$
$644$	0.165219	−	1.09732i	0.00651053	−	0.0432405i
$645$	−12.7627	+	3.76761i	−0.502530	+	0.148349i
$646$	34.5271	+	11.0730i	1.35845	+	0.435660i
$647$	21.2820	+	21.2820i	0.836683	+	0.836683i	0.988421	−	0.151738i	$-0.0484869\pi$
$647$	21.2820	+	21.2820i	0.836683	+	0.836683i	−0.151738	+	0.988421i	$0.548487\pi$
$648$	5.08730	+	29.8992i	0.199848	+	1.17455i
$649$	−44.4297	−	22.6381i	−1.74402	−	0.888622i
$650$	4.45788	−	1.99528i	0.174853	−	0.0782613i
$651$	−60.6150	−	44.0394i	−2.37569	−	1.72604i
$652$	0.113013	−	0.750592i	0.00442595	−	0.0293955i
$653$	−6.58136			−0.257549			−0.128774	−	0.991674i	$-0.541104\pi$
$653$	−6.58136			−0.257549			−0.128774	+	0.991674i	$0.541104\pi$
$654$	14.4033	−	4.74078i	0.563212	−	0.185379i
$655$	−16.8221	+	8.00460i	−0.657294	+	0.312766i
$656$	14.4042	−	21.1782i	0.562391	−	0.826872i
$657$	0.503559	+	0.503559i	0.0196457	+	0.0196457i
$658$	−14.0789	+	27.8942i	−0.548852	+	1.08743i
$659$	−1.77429	−	1.77429i	−0.0691164	−	0.0691164i	0.671704	−	0.740820i	$-0.265563\pi$
$659$	−1.77429	−	1.77429i	−0.0691164	−	0.0691164i	−0.740820	+	0.671704i	$0.765563\pi$
$660$	10.0190	+	33.0087i	0.389990	+	1.28486i
$661$	15.7892	−	21.7320i	0.614128	−	0.845275i	−0.382781	−	0.923839i	$-0.625034\pi$
$661$	15.7892	−	21.7320i	0.614128	−	0.845275i	0.996909	+	0.0785643i	$0.0250336\pi$
$662$	−9.51222	+	3.13091i	−0.369703	+	0.121686i
$663$	3.98629	−	1.29522i	0.154815	−	0.0503024i
$664$	−6.57965	+	9.27776i	−0.255340	+	0.360047i
$665$	−24.3875	+	68.6659i	−0.945708	+	2.66275i
$666$	−0.728626	+	2.27196i	−0.0282337	+	0.0880367i
$667$	0.812184	−	0.590086i	0.0314479	−	0.0228482i
$668$	16.4233	+	22.2455i	0.635436	+	0.860704i
$669$	5.48044	+	10.7560i	0.211886	+	0.415850i
$670$	−2.79355	+	0.836279i	−0.107924	+	0.0323083i
$671$	−2.12847	−	13.4386i	−0.0821687	−	0.518793i
$672$	19.0622	−	39.2463i	0.735340	−	1.51396i
$673$	29.9211	+	41.1828i	1.15337	+	1.58748i	0.733160	+	0.680056i	$0.238044\pi$
$673$	29.9211	+	41.1828i	1.15337	+	1.58748i	0.420212	+	0.907426i	$0.361956\pi$
$674$	14.8752	−	4.89611i	0.572970	−	0.188591i
$675$	7.78611	−	20.1717i	0.299688	−	0.776407i
$676$	0.191260	+	25.0451i	0.00735614	+	0.963274i
$677$	5.21570	+	2.65753i	0.200455	+	0.102137i	0.551337	−	0.834283i	$-0.314118\pi$
$677$	5.21570	+	2.65753i	0.200455	+	0.102137i	−0.350881	+	0.936420i	$0.614118\pi$
$678$	13.2592	+	9.55624i	0.509217	+	0.367005i
$679$	−0.276623	+	0.851357i	−0.0106158	+	0.0326721i
$680$	11.3607	+	16.1627i	0.435663	+	0.619813i
$681$	7.27259	+	22.3827i	0.278686	+	0.857709i
$682$	54.5467	−	0.208273i	2.08870	−	0.00797517i
$683$	−36.8792			−1.41114			−0.705571	−	0.708639i	$-0.749309\pi$
$683$	−36.8792			−1.41114			−0.705571	+	0.708639i	$0.749309\pi$
$684$	2.08334	+	12.5335i	0.0796587	+	0.479230i
$685$	37.9357	+	7.06734i	1.44945	+	0.270029i
$686$	4.52734	+	8.80216i	0.172855	+	0.336068i
$687$	3.24044	−	20.4593i	0.123631	−	0.780572i
$688$	−12.0720	+	2.10149i	−0.460240	+	0.0801184i
$689$	−4.86990	+	3.53819i	−0.185528	+	0.134794i
$690$	−0.154012	+	0.844597i	−0.00586315	+	0.0321533i
$691$	−19.2704	+	9.81874i	−0.733079	+	0.373522i	−0.780336	−	0.625360i	$-0.784952\pi$
$691$	−19.2704	+	9.81874i	−0.733079	+	0.373522i	0.0472571	+	0.998883i	$0.484952\pi$
$692$	2.77750	−	18.4471i	0.105585	−	0.701253i
$693$	−12.0508	+	1.90866i	−0.457771	+	0.0725039i
$694$	−24.9066	−	3.84739i	−0.945441	−	0.146045i
$695$	0.00834974	+	0.0638801i	0.000316724	+	0.00242311i
$696$	37.3978	−	12.6267i	1.41756	−	0.478613i
$697$	−18.9226	+	6.48001i	−0.716746	+	0.245448i
$698$	−4.26268	+	27.5950i	−0.161345	+	1.04449i
$699$	−15.9028	−	5.16713i	−0.601498	−	0.195439i
$700$	−33.1717	+	21.8157i	−1.25377	+	0.824556i
$701$	−21.9708	−	15.9627i	−0.829825	−	0.602903i	0.0896849	−	0.995970i	$-0.471414\pi$
$701$	−21.9708	−	15.9627i	−0.829825	−	0.602903i	−0.919510	+	0.393067i	$0.871414\pi$
$702$	−2.99831	−	2.97550i	−0.113164	−	0.112303i
$703$	5.52885	−	17.0161i	0.208525	−	0.641773i
$704$	5.68643	+	31.2513i	0.214316	+	1.17783i
$705$	11.5544	−	21.2335i	0.435163	−	0.799702i
$706$	−16.1607	−	22.0656i	−0.608216	−	0.830451i
$707$	9.04312	−	57.0960i	0.340101	−	2.14732i
$708$	−15.4323	−	46.2898i	−0.579980	−	1.73968i
$709$	43.5546	−	6.89838i	1.63573	−	0.259074i	0.730161	−	0.683275i	$-0.239445\pi$
$709$	43.5546	−	6.89838i	1.63573	−	0.259074i	0.905568	+	0.424201i	$0.139445\pi$
$710$	−37.3087	+	35.6102i	−1.40017	+	1.33643i
$711$	3.80362	+	3.80362i	0.142647	+	0.142647i
$712$	4.99864	−	16.0058i	0.187332	−	0.599841i
$713$	1.20959	+	0.616319i	0.0452996	+	0.0230813i
$714$	−30.2993	+	15.5843i	−1.13392	+	0.583228i
$715$	−4.86170	−	3.73768i	−0.181817	−	0.139781i
$716$	9.43060	+	9.28766i	0.352438	+	0.347096i
$717$	−30.0266	−	15.2993i	−1.12136	−	0.571364i
$718$	8.44353	−	1.37039i	0.315110	−	0.0511426i
$719$	−42.0391	−	21.4200i	−1.56780	−	0.798832i	−0.568087	−	0.822969i	$-0.692316\pi$
$719$	−42.0391	−	21.4200i	−1.56780	−	0.798832i	−0.999709	+	0.0241372i	$0.992316\pi$
$720$	−3.21558	+	6.13049i	−0.119838	+	0.228470i
$721$	3.26856	−	20.6369i	0.121728	−	0.768558i
$722$	−10.9590	−	67.5225i	−0.407850	−	2.51293i
$723$	−10.1210	−	7.35333i	−0.376404	−	0.273473i
$724$	4.24928	−	2.20615i	0.157923	−	0.0819909i
$725$	−35.1193	−	7.53292i	−1.30430	−	0.279766i
$726$	9.22205	−	9.29274i	0.342262	−	0.344886i
$727$	−19.7578	+	14.3549i	−0.732775	+	0.532392i	−0.890440	−	0.455100i	$-0.849603\pi$
$727$	−19.7578	+	14.3549i	−0.732775	+	0.532392i	0.157665	+	0.987493i	$0.449603\pi$
$728$	1.30103	+	7.64645i	0.0482194	+	0.283396i
$729$	−16.9037			−0.626062
$730$	−0.388124	−	2.88364i	−0.0143651	−	0.106728i
$731$	8.52611	+	4.34427i	0.315350	+	0.160679i
$732$	7.74337	−	10.8308i	0.286203	−	0.400318i
$733$	−2.17911	−	13.7584i	−0.0804873	−	0.508177i	−0.994690	−	0.102919i	$-0.967182\pi$
$733$	−2.17911	−	13.7584i	−0.0804873	−	0.508177i	0.914202	−	0.405258i	$-0.132818\pi$
$734$	43.3584	−	0.165553i	1.60039	−	0.00611067i
$735$	−16.3558	−	34.3725i	−0.603292	−	1.26785i
$736$	−0.229895	+	0.756382i	−0.00847405	+	0.0278806i
$737$	2.58898	+	2.58898i	0.0953664	+	0.0953664i
$738$	−5.05198	−	4.85782i	−0.185966	−	0.178819i
$739$	−15.7354			−0.578835			−0.289418	−	0.957203i	$-0.593462\pi$
$739$	−15.7354			−0.578835			−0.289418	+	0.957203i	$0.593462\pi$
$740$	7.99668	−	5.57533i	0.293964	−	0.204953i
$741$	−7.78777	−	7.78777i	−0.286091	−	0.286091i
$742$	34.4684	−	34.7326i	1.26537	−	1.27507i
$743$	41.3351	−	6.54683i	1.51644	−	0.240180i	0.657968	−	0.753046i	$-0.271416\pi$
$743$	41.3351	−	6.54683i	1.51644	−	0.240180i	0.858469	+	0.512866i	$0.171416\pi$
$744$	38.1727	+	37.3081i	1.39948	+	1.36778i
$745$	1.29120	−	47.6220i	0.0473059	−	1.74474i
$746$	−1.11187	−	0.356580i	−0.0407084	−	0.0130553i
$747$	2.20080	+	2.20080i	0.0805231	+	0.0805231i
$748$	11.0924	−	22.1873i	0.405579	−	0.811250i
$749$	10.9975	−	69.4352i	0.401838	−	2.53711i
$750$	26.1733	−	16.0764i	0.955714	−	0.587027i
$751$	11.8872	+	23.3299i	0.433770	+	0.851321i	0.999640	+	0.0268269i	$0.00854030\pi$
$751$	11.8872	+	23.3299i	0.433770	+	0.851321i	−0.565870	+	0.824494i	$0.691460\pi$
$752$	12.8073	−	18.2062i	0.467036	−	0.663910i
$753$	13.2094	−	18.1812i	0.481377	−	0.662558i
$754$	−4.10280	+	5.69260i	−0.149415	+	0.207312i
$755$	7.50753	+	25.4315i	0.273227	+	0.925548i
$756$	27.9335	+	19.9708i	1.01593	+	0.726330i
$757$	10.3661	+	31.9034i	0.376761	+	1.15955i	0.942283	+	0.334817i	$0.108674\pi$
$757$	10.3661	+	31.9034i	0.376761	+	1.15955i	−0.565523	+	0.824733i	$0.691326\pi$
$758$	25.1494	−	4.08177i	0.913469	−	0.148257i
$759$	1.02520	−	0.333109i	0.0372126	−	0.0120911i
$760$	24.2884	−	45.8791i	0.881034	−	1.66421i
$761$	−1.41026	+	4.34035i	−0.0511221	+	0.157338i	−0.973358	−	0.229289i	$-0.926360\pi$
$761$	−1.41026	+	4.34035i	−0.0511221	+	0.157338i	0.922236	+	0.386627i	$0.126360\pi$
$762$	−4.87360	+	15.1966i	−0.176552	+	0.550515i
$763$	9.94826	−	19.5246i	0.360151	−	0.706837i
$764$	5.96216	−	39.5984i	0.215703	−	1.43262i
$765$	4.88158	−	2.32284i	0.176494	−	0.0839825i
$766$	−14.4940	−	7.31551i	−0.523691	−	0.264320i
$767$	7.01767	+	5.09864i	0.253393	+	0.184101i
$768$	−17.4935	+	25.6927i	−0.631241	+	0.927106i
$769$	−16.8620	−	23.2085i	−0.608058	−	0.836920i	0.388358	−	0.921509i	$-0.373042\pi$
$769$	−16.8620	−	23.2085i	−0.608058	−	0.836920i	−0.996416	+	0.0845885i	$0.973042\pi$
$770$	43.8780	+	23.6598i	1.58126	+	0.852641i
$771$	44.4229	−	32.2751i	1.59985	−	1.16236i
$772$	0.132066	+	17.2939i	0.00475317	+	0.622420i
$773$	−24.5241	−	7.96837i	−0.882071	−	0.286602i	−0.167254	−	0.985914i	$-0.553490\pi$
$773$	−24.5241	−	7.96837i	−0.882071	−	0.286602i	−0.714817	+	0.699312i	$0.753490\pi$
$774$	0.0128027	+	3.35304i	0.000460185	+	0.120523i
$775$	−12.4841	−	46.9390i	−0.448440	−	1.68610i
$776$	0.282993	−	0.571495i	0.0101589	−	0.0205155i
$777$	7.63277	+	14.9802i	0.273824	+	0.537410i
$778$	5.90668	−	38.2377i	0.211765	−	1.37089i
$779$	37.7445	+	36.5723i	1.35234	+	1.31034i
$780$	−0.823161	−	5.94407i	−0.0294739	−	0.212832i
$781$	61.5886	+	20.0114i	2.20381	+	0.716063i
$782$	0.498064	−	0.364778i	0.0178107	−	0.0130445i
$783$	4.85966	+	30.6827i	0.173670	+	1.09651i
$784$	−11.3394	−	33.1667i	−0.404978	−	1.18452i
$785$	−16.9155	+	2.21101i	−0.603739	+	0.0789144i
$786$	3.66695	+	22.5935i	0.130796	+	0.805884i
$787$	−11.2417	−	1.78050i	−0.400722	−	0.0634681i	−0.0471791	−	0.998886i	$-0.515023\pi$
$787$	−11.2417	−	1.78050i	−0.400722	−	0.0634681i	−0.353543	+	0.935418i	$0.615023\pi$
$788$	32.6090	−	16.9300i	1.16165	−	0.603107i
$789$	−29.2629	−	40.2769i	−1.04179	−	1.43390i
$790$	−2.93168	−	21.7815i	−0.104304	−	0.774950i
$791$	23.3283	−	3.69484i	0.829460	−	0.131373i
$792$	8.69149	−	0.0995625i	0.308839	−	0.00353780i
$793$			2.36689i			0.0840507i
$794$	−22.3083	−	22.1386i	−0.791693	−	0.785670i
$795$	−27.4850	+	26.0339i	−0.974793	+	0.923329i
$796$	−9.33037	+	18.6629i	−0.330706	+	0.661487i
$797$	17.4027	−	8.86711i	0.616434	−	0.314089i	−0.117746	−	0.993044i	$-0.537567\pi$
$797$	17.4027	−	8.86711i	0.616434	−	0.314089i	0.734180	+	0.678955i	$0.237567\pi$
$798$	72.6314	+	52.3473i	2.57112	+	1.85307i
$799$	−16.5323	+	5.37168i	−0.584872	+	0.190036i
$800$	25.6368	−	11.9479i	0.906399	−	0.422422i
$801$	−4.08834	−	2.08311i	−0.144454	−	0.0736032i
$802$	−9.33843	+	18.5020i	−0.329751	+	0.653329i
$803$	−2.95562	+	2.14738i	−0.104302	+	0.0757795i
$804$	0.0273596	+	3.58269i	0.000964898	+	0.126352i
$805$	0.701775	+	1.02312i	0.0247343	+	0.0360602i
$806$	−9.37765	−	1.44859i	−0.330314	−	0.0510245i
$807$	6.92742	−	21.3204i	0.243857	−	0.750514i
$808$	−12.2766	+	39.3101i	−0.431890	+	1.38292i
$809$	−4.94653	+	31.2312i	−0.173911	+	1.09803i	0.734087	+	0.679055i	$0.237610\pi$
$809$	−4.94653	+	31.2312i	−0.173911	+	1.09803i	−0.907998	+	0.418975i	$0.862390\pi$
$810$	−26.9612	−	20.5645i	−0.947319	−	0.722562i
$811$	12.6378			0.443772			0.221886	−	0.975073i	$-0.428779\pi$
$811$	12.6378			0.443772			0.221886	+	0.975073i	$0.428779\pi$
$812$	25.5075	−	51.0207i	0.895137	−	1.79048i
$813$	−6.75076	−	20.7767i	−0.236759	−	0.728671i
$814$	−10.9271	−	5.51520i	−0.382996	−	0.193308i
$815$	0.480030	+	0.699837i	0.0168147	+	0.0245142i
$816$	22.9680	−	7.85255i	0.804041	−	0.274894i
$817$		−	25.1441i		−	0.879680i
$818$	−17.0928	+	33.8656i	−0.597636	+	1.18408i
$819$	2.12245			0.0741645
$820$	4.37496	+	28.2995i	0.152780	+	0.988260i
$821$	3.00487			0.104871			0.0524353	−	0.998624i	$-0.483302\pi$
$821$	3.00487			0.104871			0.0524353	+	0.998624i	$0.483302\pi$
$822$	21.3630	−	42.3261i	0.745121	−	1.47629i
$823$		−	1.32646i		−	0.0462375i	−0.999733	−	0.0231187i	$-0.992640\pi$
$823$		−	1.32646i		−	0.0462375i	0.999733	−	0.0231187i	$-0.00735958\pi$
$824$	−4.43729	+	14.2083i	−0.154580	+	0.494971i
$825$	−33.3646	−	19.3456i	−1.16161	−	0.673528i
$826$	−62.9500	−	31.7725i	−2.19031	−	1.10551i
$827$	−3.31439	−	10.2006i	−0.115253	−	0.354711i	0.876747	−	0.480952i	$-0.159709\pi$
$827$	−3.31439	−	10.2006i	−0.115253	−	0.354711i	−0.992000	+	0.126241i	$0.959709\pi$
$828$	0.193493	+	0.0967353i	0.00672433	+	0.00336179i
$829$	−28.5887			−0.992928			−0.496464	−	0.868057i	$-0.665368\pi$
$829$	−28.5887			−0.992928			−0.496464	+	0.868057i	$0.665368\pi$
$830$	−1.69629	−	12.6029i	−0.0588791	−	0.437454i
$831$	0.909064	−	5.73960i	0.0315351	−	0.199105i
$832$	−0.126578	−	5.52421i	−0.00438831	−	0.191518i
$833$	−8.45860	+	26.0329i	−0.293073	+	0.901986i
$834$	0.0782263	+	0.0120838i	0.00270876	+	0.000418429i
$835$	−30.3920	−	5.66197i	−1.05176	−	0.195941i
$836$	−65.1783	+	0.497741i	−2.25424	+	0.0172147i
$837$	−33.9854	+	24.6919i	−1.17471	+	0.853475i
$838$	−0.819413	+	1.62348i	−0.0283062	+	0.0560823i
$839$	−24.0486	−	12.2534i	−0.830252	−	0.423034i	−0.0134196	−	0.999910i	$-0.504272\pi$
$839$	−24.0486	−	12.2534i	−0.830252	−	0.423034i	−0.816832	+	0.576876i	$0.804272\pi$
$840$	14.3461	+	46.6234i	0.494986	+	1.60866i
$841$	21.4981	−	6.98517i	0.741315	−	0.240868i
$842$	4.70718	+	3.39258i	0.162220	+	0.116916i
$843$	2.20581	−	1.12391i	0.0759720	−	0.0387096i
$844$	42.6166	+	21.3059i	1.46693	+	0.733380i
$845$	−19.2565	−	20.3299i	−0.662445	−	0.699369i
$846$	−4.32351	−	4.29062i	−0.148645	−	0.147515i
$847$		−	18.9195i		−	0.650083i
$848$	−27.8861	+	20.9185i	−0.957614	+	0.718346i
$849$	18.5415	−	2.93669i	0.636344	−	0.100787i
$850$	−21.6142	−	4.54988i	−0.741360	−	0.156060i
$851$	−0.179056	−	0.246450i	−0.00613798	−	0.00844820i
$852$	29.1989	+	56.2402i	1.00034	+	1.92676i
$853$	−39.7996	−	6.30363i	−1.36271	−	0.215832i	−0.568104	−	0.822957i	$-0.692323\pi$
$853$	−39.7996	−	6.30363i	−1.36271	−	0.215832i	−0.794607	+	0.607124i	$0.792323\pi$
$854$	−3.08242	−	18.9920i	−0.105478	−	0.649893i
$855$	−11.2617	−	8.65799i	−0.385141	−	0.296097i
$856$	−14.9298	+	47.8055i	−0.510289	+	1.63396i
$857$	−5.64875	−	35.6648i	−0.192958	−	1.21829i	−0.873957	−	0.486003i	$-0.838454\pi$
$857$	−5.64875	−	35.6648i	−0.192958	−	1.21829i	0.680999	−	0.732284i	$-0.261546\pi$
$858$	−6.07867	+	4.45197i	−0.207522	+	0.151988i
$859$	4.72695	+	1.53588i	0.161282	+	0.0524036i	0.388545	−	0.921430i	$-0.372978\pi$
$859$	4.72695	+	1.53588i	0.161282	+	0.0524036i	−0.227263	+	0.973833i	$0.572978\pi$
$860$	8.26683	−	10.9245i	0.281897	−	0.372524i
$861$	−49.3805	+	0.778872i	−1.68288	+	0.0265439i
$862$	−5.35681	+	34.6780i	−0.182454	+	1.18114i
$863$	−20.2514	−	39.7457i	−0.689367	−	1.35296i	−0.924570	−	0.381013i	$-0.875575\pi$
$863$	−20.2514	−	39.7457i	−0.689367	−	1.35296i	0.235202	−	0.971946i	$-0.424425\pi$
$864$	−17.6248	−	16.9644i	−0.599608	−	0.577140i
$865$	11.7976	+	17.1997i	0.401129	+	0.584807i
$866$	−0.0893442	−	23.3993i	−0.00303604	−	0.795140i
$867$	13.3812	+	4.34781i	0.454449	+	0.147659i
$868$	77.1330	−	0.589034i	2.61807	−	0.0199931i
$869$	−22.3252	+	16.2202i	−0.757330	+	0.550232i
$870$	−20.9452	+	38.8437i	−0.710110	+	1.31693i
$871$	−0.374374	−	0.515282i	−0.0126852	−	0.0174597i
$872$	−9.03059	+	12.7338i	−0.305814	+	0.431219i
$873$	−0.141179	−	0.102573i	−0.00477820	−	0.00347156i
$874$	−1.44819	−	0.730937i	−0.0489857	−	0.0247243i
$875$	10.4823	−	43.1333i	0.354367	−	1.45817i
$876$	−3.53510	−	0.532264i	−0.119440	−	0.0179835i
$877$	5.26635	−	10.3358i	0.177832	−	0.349015i	−0.784834	−	0.619706i	$-0.787252\pi$
$877$	5.26635	−	10.3358i	0.177832	−	0.349015i	0.962666	+	0.270691i	$0.0872520\pi$
$878$	−3.44705	+	10.7484i	−0.116332	+	0.362741i
$879$	−10.1940	+	31.3739i	−0.343835	+	1.05822i
$880$	−28.4822	−	21.2130i	−0.960134	−	0.715090i
$881$	40.0275	−	13.0057i	1.34856	−	0.438174i	0.456352	−	0.889799i	$-0.349156\pi$
$881$	40.0275	−	13.0057i	1.34856	−	0.438174i	0.892208	+	0.451626i	$0.149156\pi$
$882$	−9.46765	+	1.53661i	−0.318792	+	0.0517403i
$883$	−3.55226	−	10.9327i	−0.119543	−	0.367915i	0.873325	−	0.487139i	$-0.161959\pi$
$883$	−3.55226	−	10.9327i	−0.119543	−	0.367915i	−0.992867	+	0.119224i	$0.961959\pi$
$884$	−2.50963	+	3.51028i	−0.0844081	+	0.118063i
$885$	47.9187	+	26.0753i	1.61077	+	0.876511i
$886$	0.954903	−	1.32492i	0.0320806	−	0.0445116i
$887$	−6.30480	+	8.67781i	−0.211694	+	0.291372i	−0.901639	−	0.432490i	$-0.857635\pi$
$887$	−6.30480	+	8.67781i	−0.211694	+	0.291372i	0.689944	+	0.723863i	$0.257635\pi$
$888$	−3.83146	−	11.3480i	−0.128575	−	0.380815i
$889$	10.4702	+	20.5489i	0.351159	+	0.689189i
$890$	8.11984	+	16.8977i	0.272178	+	0.566412i
$891$	−6.66033	+	42.0517i	−0.223129	+	1.40878i
$892$	−11.1161	−	5.55744i	−0.372196	−	0.186077i
$893$	32.2982	+	32.2982i	1.08082	+	1.08082i
$894$	−55.7364	−	17.8749i	−1.86410	−	0.597825i
$895$	−14.7931	−	0.401092i	−0.494478	−	0.0134070i
$896$	8.20989	+	44.1616i	0.274273	+	1.47534i
$897$	−0.185211	+	0.0293346i	−0.00618402	+	0.000979452i
$898$	−29.7853	+	30.0136i	−0.993947	+	1.00157i
$899$	49.3440	+	49.3440i	1.64571	+	1.64571i
$900$	−2.04639	−	7.46430i	−0.0682129	−	0.248810i
$901$	27.2231			0.906932
$902$	28.6686	−	21.6995i	0.954559	−	0.722515i
$903$	16.7072	+	16.7072i	0.555980	+	0.555980i
$904$	−16.8253	+	0.192737i	−0.559600	+	0.00641032i
$905$	−1.79153	+	5.04427i	−0.0595526	+	0.167677i
$906$	32.5794	−	0.124396i	1.08238	−	0.00413278i
$907$	−6.35970	−	40.1535i	−0.211170	−	1.33328i	−0.834366	−	0.551211i	$-0.814166\pi$
$907$	−6.35970	−	40.1535i	−0.211170	−	1.33328i	0.623196	−	0.782066i	$-0.285834\pi$
$908$	−19.7099	−	14.0914i	−0.654098	−	0.467640i
$909$	10.0409	+	5.11612i	0.333037	+	0.169691i
$910$	−6.89508	−	5.25918i	−0.228570	−	0.174340i
$911$	−12.8587			−0.426028			−0.213014	−	0.977049i	$-0.568328\pi$
$911$	−12.8587			−0.426028			−0.213014	+	0.977049i	$0.568328\pi$
$912$	−45.7838	−	44.4062i	−1.51605	−	1.47044i
$913$	−12.9175	+	9.38512i	−0.427507	+	0.310602i
$914$	−32.9447	+	33.1973i	−1.08971	+	1.09807i
$915$	1.92929	+	14.7601i	0.0637803	+	0.487954i
$916$	9.82646	+	18.9268i	0.324675	+	0.625359i
$917$	26.7603	+	19.4425i	0.883703	+	0.642048i
$918$	3.06047	+	18.8568i	0.101011	+	0.622367i
$919$	7.54866	−	47.6604i	0.249007	−	1.57217i	−0.473491	−	0.880799i	$-0.657006\pi$
$919$	7.54866	−	47.6604i	0.249007	−	1.57217i	0.722498	−	0.691373i	$-0.242994\pi$
$920$	−0.388889	−	0.793709i	−0.0128213	−	0.0261678i
$921$	45.9279	+	23.4014i	1.51338	+	0.771104i
$922$	−23.1021	+	3.74949i	−0.760827	+	0.123483i
$923$	−10.0373	−	5.11427i	−0.330382	−	0.168338i
$924$	42.9776	−	43.6390i	1.41386	−	1.43562i
$925$	−2.28580	+	10.6566i	−0.0751565	+	0.350388i
$926$	−2.75436	+	1.41669i	−0.0905137	+	0.0465552i
$927$	3.62922	+	1.84918i	0.119199	+	0.0607351i
$928$	−23.2537	+	33.3258i	−0.763341	+	1.09397i
$929$	−11.0249	−	11.0249i	−0.361714	−	0.361714i	0.502730	−	0.864444i	$-0.332329\pi$
$929$	−11.0249	−	11.0249i	−0.361714	−	0.361714i	−0.864444	+	0.502730i	$0.832329\pi$
$930$	−59.6605	−	1.38966i	−1.95635	−	0.0455689i
$931$	71.0398	−	11.2516i	2.32823	−	0.368756i
$932$	16.3310	−	5.44448i	0.534939	−	0.178340i
$933$	−1.74793	+	11.0360i	−0.0572245	+	0.361302i
$934$	9.33330	+	12.7436i	0.305395	+	0.416983i
$935$	7.85210	+	26.5988i	0.256791	+	0.869873i
$936$	−1.49604	−	0.219414i	−0.0488997	−	0.00717178i
$937$	11.7731	−	36.2338i	0.384609	−	1.18371i	−0.552154	−	0.833742i	$-0.686194\pi$
$937$	11.7731	−	36.2338i	0.384609	−	1.18371i	0.936763	−	0.349964i	$-0.113806\pi$
$938$	3.67504	+	3.64709i	0.119994	+	0.119082i
$939$	−12.9376	−	9.39973i	−0.422203	−	0.306749i
$940$	3.41389	+	24.6518i	0.111349	+	0.804053i
$941$	−14.2604	−	4.63348i	−0.464875	−	0.151047i	0.0672083	−	0.997739i	$-0.478591\pi$
$941$	−14.2604	−	4.63348i	−0.464875	−	0.151047i	−0.532084	+	0.846692i	$0.678591\pi$
$942$	−3.19980	+	20.7143i	−0.104255	+	0.674910i
$943$	0.881505	−	0.153905i	0.0287058	−	0.00501184i
$944$	41.0867	+	28.9029i	1.33726	+	0.940710i
$945$	−38.0675	+	4.97578i	−1.23833	+	0.161862i
$946$	−16.9999	−	2.62602i	−0.552715	−	0.0853794i
$947$	−33.1994	+	5.25827i	−1.07884	+	0.170871i	−0.670462	−	0.741944i	$-0.733904\pi$
$947$	−33.1994	+	5.25827i	−1.07884	+	0.170871i	−0.408374	+	0.912815i	$0.633904\pi$
$948$	−26.7022	−	4.02044i	−0.867248	−	0.130578i
$949$	0.566258	−	0.288523i	0.0183815	−	0.00936586i
$950$	15.1317	+	56.0317i	0.490937	+	1.81791i
$951$	−24.7984	+	18.0171i	−0.804142	+	0.584244i
$952$	15.5659	−	31.4349i	0.504495	−	1.01881i
$953$	3.90712	−	24.6686i	0.126564	−	0.799094i	−0.839985	−	0.542610i	$-0.817436\pi$
$953$	3.90712	−	24.6686i	0.126564	−	0.799094i	0.966549	−	0.256483i	$-0.0825639\pi$
$954$	4.36310	+	8.48283i	0.141261	+	0.274642i
$955$	25.3245	+	36.9207i	0.819483	+	1.19473i
$956$	34.2246	−	5.68888i	1.10690	−	0.183991i
$957$	55.4108			1.79118
$958$	10.2249	−	0.0390413i	0.330353	−	0.00126137i
$959$	−21.1725	−	65.1622i	−0.683695	−	2.10420i
$960$	−5.29222	−	34.3462i	−0.170806	−	1.10852i
$961$	−19.5808	+	60.2636i	−0.631640	+	1.94399i
$962$	1.72737	+	1.24496i	0.0556926	+	0.0401390i
$963$	12.2109	+	6.22178i	0.393492	+	0.200494i
$964$	12.8790	−	0.0983521i	0.414806	−	0.00316771i
$965$	−13.2968	−	14.0379i	−0.428039	−	0.451897i
$966$	1.44794	−	0.476583i	0.0465866	−	0.0153338i
$967$	30.6467	+	42.1816i	0.985533	+	1.35647i	0.933795	+	0.357809i	$0.116476\pi$
$967$	30.6467	+	42.1816i	0.985533	+	1.35647i	0.0517377	+	0.998661i	$0.483524\pi$
$968$	−1.95586	+	13.3357i	−0.0628637	+	0.428626i
$969$	7.79176	+	49.1952i	0.250307	+	1.58038i
$970$	0.204478	+	0.683047i	0.00656539	+	0.0219313i
$971$	4.66908	+	9.16358i	0.149838	+	0.294073i	0.953709	−	0.300730i	$-0.0972302\pi$
$971$	4.66908	+	9.16358i	0.149838	+	0.294073i	−0.803872	+	0.594803i	$0.797230\pi$
$972$	−12.6432	+	9.33414i	−0.405530	+	0.299393i
$973$	0.0925411	−	0.0672351i	0.00296673	−	0.00215546i
$974$	3.85554	−	12.0221i	0.123540	−	0.385214i
$975$	5.20611	+	4.23183i	0.166729	+	0.135527i
$976$	0.209338	+	13.7054i	0.00670075	+	0.438700i
$977$	21.4928	−	6.98344i	0.687616	−	0.223420i	0.0556892	−	0.998448i	$-0.482264\pi$
$977$	21.4928	−	6.98344i	0.687616	−	0.223420i	0.631927	+	0.775028i	$0.282264\pi$
$978$	0.990422	−	0.325994i	0.0316702	−	0.0104241i
$979$	13.8360	−	19.0436i	0.442200	−	0.608637i
$980$	34.5645	+	18.4678i	1.10412	+	0.589932i
$981$	3.02060	+	3.02060i	0.0964405	+	0.0964405i
$982$	−2.81494	+	5.57718i	−0.0898284	+	0.177975i
$983$	−1.46022	−	1.46022i	−0.0465738	−	0.0465738i	0.683436	−	0.730010i	$-0.260485\pi$
$983$	−1.46022	−	1.46022i	−0.0465738	−	0.0465738i	−0.730010	+	0.683436i	$0.760485\pi$
$984$	34.8871	+	4.55584i	1.11216	+	0.145235i
$985$	−13.7483	+	38.7099i	−0.438056	+	1.23340i
$986$	30.1434	−	9.92158i	0.959960	−	0.315967i
$987$	−42.9216			−1.36621
$988$	11.2122	+	1.68817i	0.356708	+	0.0537080i
$989$	−0.346347	−	0.251636i	−0.0110132	−	0.00800156i
$990$	−7.02983	+	6.70979i	−0.223423	+	0.213251i
$991$	−49.7909	−	25.3697i	−1.58166	−	0.805896i	−0.581689	−	0.813411i	$-0.697608\pi$
$991$	−49.7909	−	25.3697i	−1.58166	−	0.805896i	−0.999972	+	0.00751489i	$0.997608\pi$
$992$	−54.4293	−	7.55865i	−1.72813	−	0.239987i
$993$	−9.72719	−	9.72719i	−0.308683	−	0.308683i
$994$	87.2001	+	27.9654i	2.76582	+	0.887008i
$995$	−6.60479	−	22.3735i	−0.209386	−	0.709288i
$996$	−15.4501	−	2.32626i	−0.489555	−	0.0737102i
$997$	−16.1288	−	5.24057i	−0.510804	−	0.165970i	0.0422637	−	0.999106i	$-0.486543\pi$
$997$	−16.1288	−	5.24057i	−0.510804	−	0.165970i	−0.553068	+	0.833136i	$0.686543\pi$
$998$	13.4121	−	9.82295i	0.424554	−	0.310940i
$999$	9.31039	−	1.47462i	0.294568	−	0.0466549i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.bk.c.267.19	yes	960
4.3	odd	2	inner	820.2.bk.c.267.68	yes	960
5.3	odd	4		820.2.bv.c.103.44	yes	960
20.3	even	4		820.2.bv.c.103.7	yes	960
41.2	even	20		820.2.bv.c.207.7	yes	960
164.43	odd	20		820.2.bv.c.207.44	yes	960
205.43	odd	20	inner	820.2.bk.c.43.68	yes	960
820.43	even	20	inner	820.2.bk.c.43.19	✓	960

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.bk.c.43.19	✓	960	820.43	even	20	inner
820.2.bk.c.43.68	yes	960	205.43	odd	20	inner
820.2.bk.c.267.19	yes	960	1.1	even	1	trivial
820.2.bk.c.267.68	yes	960	4.3	odd	2	inner
820.2.bv.c.103.7	yes	960	20.3	even	4
820.2.bv.c.103.44	yes	960	5.3	odd	4
820.2.bv.c.207.7	yes	960	41.2	even	20
820.2.bv.c.207.44	yes	960	164.43	odd	20

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.bk (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26252 - 0.637224i) q^{2} -1.94267i q^{3} +(1.18789 + 1.60901i) q^{4} +(-2.19825 - 0.409529i) q^{5} +(-1.23792 + 2.45265i) q^{6} +(1.22687 + 3.77593i) q^{7} +(-0.474434 - 2.78835i) q^{8} -0.773974 q^{9} +(2.51436 + 1.91781i) q^{10} +(0.621132 - 3.92167i) q^{11} +(3.12578 - 2.30768i) q^{12} +(-0.213440 + 0.656902i) q^{13} +(0.857164 - 5.54897i) q^{14} +(-0.795580 + 4.27047i) q^{15} +(-1.17782 + 3.82266i) q^{16} +(2.52712 - 1.83606i) q^{17} +(0.977154 + 0.493194i) q^{18} +(-7.31333 - 3.72633i) q^{19} +(-1.95234 - 4.02348i) q^{20} +(7.33540 - 2.38341i) q^{21} +(-3.28317 + 4.55537i) q^{22} +(-0.124519 + 0.0634454i) q^{23} +(-5.41685 + 0.921669i) q^{24} +(4.66457 + 1.80049i) q^{25} +(0.688065 - 0.693340i) q^{26} -4.32444i q^{27} +(-4.61812 + 6.45945i) q^{28} +(-7.09518 + 1.12377i) q^{29} +(3.72568 - 4.88457i) q^{30} +(-5.70984 - 7.85892i) q^{31} +(3.92291 - 4.07563i) q^{32} +(-7.61852 - 1.20666i) q^{33} +(-4.36052 + 0.707716i) q^{34} +(-1.15062 - 8.80287i) q^{35} +(-0.919397 - 1.24533i) q^{36} +(0.340997 + 2.15297i) q^{37} +(6.85869 + 9.36478i) q^{38} +(1.27615 + 0.414645i) q^{39} +(-0.0989891 + 6.32378i) q^{40} +(-6.12018 - 1.88239i) q^{41} +(-10.7798 - 1.66519i) q^{42} +(1.39075 + 2.72949i) q^{43} +(7.04785 - 3.65912i) q^{44} +(1.70138 + 0.316964i) q^{45} +(0.197636 - 0.000754621i) q^{46} +(-5.29255 - 1.71965i) q^{47} +(7.42617 + 2.28813i) q^{48} +(-7.08932 + 5.15070i) q^{49} +(-4.74178 - 5.24552i) q^{50} +(-3.56687 - 4.90937i) q^{51} +(-1.31051 + 0.436901i) q^{52} +(7.05059 + 5.12255i) q^{53} +(-2.75563 + 5.45967i) q^{54} +(-2.97144 + 8.36643i) q^{55} +(9.94656 - 5.21239i) q^{56} +(-7.23904 + 14.2074i) q^{57} +(9.67387 + 3.10245i) q^{58} +(3.88082 - 11.9439i) q^{59} +(-7.81629 + 3.79276i) q^{60} +(3.25904 - 1.05893i) q^{61} +(2.20087 + 13.5605i) q^{62} +(-0.949569 - 2.92247i) q^{63} +(-7.54983 + 2.64578i) q^{64} +(0.738215 - 1.35662i) q^{65} +(8.84960 + 6.37812i) q^{66} +(-0.542015 + 0.746020i) q^{67} +(5.95620 + 1.88512i) q^{68} +(0.123254 + 0.241899i) q^{69} +(-4.15672 + 11.8470i) q^{70} +(-2.55138 + 16.1088i) q^{71} +(0.367199 + 2.15811i) q^{72} +(-0.650616 - 0.650616i) q^{73} +(0.941409 - 2.93545i) q^{74} +(3.49776 - 9.06173i) q^{75} +(-2.69175 - 16.1937i) q^{76} +(15.5700 - 2.46605i) q^{77} +(-1.34693 - 1.33669i) q^{78} +(-4.91440 - 4.91440i) q^{79} +(4.15464 - 7.92079i) q^{80} -10.7229 q^{81} +(6.52732 + 6.27647i) q^{82} +(-2.84351 - 2.84351i) q^{83} +(12.5486 + 8.97148i) q^{84} +(-6.30716 + 3.00119i) q^{85} +(-0.0165416 - 4.33224i) q^{86} +(2.18311 + 13.7836i) q^{87} +(-11.2297 + 0.128638i) q^{88} +(5.28228 + 2.69145i) q^{89} +(-1.94605 - 1.48433i) q^{90} -2.74228 q^{91} +(-0.249999 - 0.124985i) q^{92} +(-15.2673 + 11.0923i) q^{93} +(5.58612 + 5.54363i) q^{94} +(14.5505 + 11.1864i) q^{95} +(-7.91761 - 7.62093i) q^{96} +(0.182409 + 0.132528i) q^{97} +(12.2325 - 1.98535i) q^{98} +(-0.480740 + 3.03527i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 960 q - 10 q^{2} - 20 q^{5} - 16 q^{6} - 22 q^{8} - 960 q^{9} + 20 q^{12} + 12 q^{13} + 8 q^{14} - 28 q^{16} - 52 q^{17} + 12 q^{18} + 14 q^{20} - 40 q^{21} + 18 q^{22} + 48 q^{24} - 4 q^{25} - 20 q^{26}+ \cdots + 42 q^{98}+O(q^{100}) \) 960 * q - 10 * q^2 - 20 * q^5 - 16 * q^6 - 22 * q^8 - 960 * q^9 + 20 * q^12 + 12 * q^13 + 8 * q^14 - 28 * q^16 - 52 * q^17 + 12 * q^18 + 14 * q^20 - 40 * q^21 + 18 * q^22 + 48 * q^24 - 4 * q^25 - 20 * q^26 - 2 * q^28 + 30 * q^30 + 16 * q^33 + 20 * q^34 - 100 * q^36 - 112 * q^37 - 36 * q^38 - 16 * q^40 - 24 * q^41 - 104 * q^42 + 20 * q^45 - 20 * q^46 + 12 * q^48 - 224 * q^49 + 12 * q^50 + 190 * q^52 + 12 * q^53 + 52 * q^54 + 96 * q^56 + 48 * q^57 - 10 * q^58 + 14 * q^60 - 40 * q^61 - 10 * q^62 + 120 * q^64 - 92 * q^65 - 12 * q^66 + 104 * q^69 - 120 * q^70 + 36 * q^72 + 72 * q^73 + 28 * q^74 - 40 * q^76 + 36 * q^77 + 16 * q^78 - 130 * q^80 + 592 * q^81 + 146 * q^82 + 92 * q^84 + 112 * q^85 - 12 * q^86 + 100 * q^88 - 136 * q^89 - 136 * q^90 + 160 * q^92 - 24 * q^93 + 32 * q^94 - 44 * q^96 - 72 * q^97 + 42 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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