LMFDB - Embedded newform 690.2.n.a.89.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(89,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 5]))

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

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

chi := DirichletCharacter("690.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.n (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			89.18
Character	$\chi$	$=$	690.89
Dual form			690.2.n.a.659.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 - 0.989821i) q^{2} +(1.11013 - 1.32951i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(1.06732 - 1.96490i) q^{5} +(-1.47397 - 0.909626i) q^{6} +(0.483302 - 0.310599i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-0.535201 - 2.95187i) q^{9} +O(q^{10})$	\(q+(-0.142315 - 0.989821i) q^{2} +(1.11013 - 1.32951i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(1.06732 - 1.96490i) q^{5} +(-1.47397 - 0.909626i) q^{6} +(0.483302 - 0.310599i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-0.535201 - 2.95187i) q^{9} +(-2.09680 - 0.776821i) q^{10} +(0.617442 - 4.29440i) q^{11} +(-0.690600 + 1.58842i) q^{12} +(-1.02536 + 1.59549i) q^{13} +(-0.376219 - 0.434180i) q^{14} +(-1.42749 - 3.60032i) q^{15} +(0.841254 - 0.540641i) q^{16} +(-1.19284 + 4.06243i) q^{17} +(-2.84566 + 0.949849i) q^{18} +(0.213298 + 0.726425i) q^{19} +(-0.470509 + 2.18601i) q^{20} +(0.123585 - 0.987363i) q^{21} -4.33856 q^{22} +(4.22869 + 2.26235i) q^{23} +(1.67053 + 0.457515i) q^{24} +(-2.72166 - 4.19435i) q^{25} +(1.72517 + 0.787858i) q^{26} +(-4.51870 - 2.56542i) q^{27} +(-0.376219 + 0.434180i) q^{28} +(1.29159 - 4.39876i) q^{29} +(-3.36052 + 1.92534i) q^{30} +(1.13568 + 2.48679i) q^{31} +(-0.654861 - 0.755750i) q^{32} +(-5.02401 - 5.58826i) q^{33} +(4.19084 + 0.602551i) q^{34} +(-0.0944592 - 1.28115i) q^{35} +(1.34516 + 2.68152i) q^{36} +(-0.469465 - 0.541792i) q^{37} +(0.688676 - 0.314508i) q^{38} +(0.982932 + 3.13443i) q^{39} +(2.23072 + 0.154619i) q^{40} +(0.688519 + 0.596605i) q^{41} +(-0.994901 + 0.0181892i) q^{42} +(1.91710 - 4.19786i) q^{43} +(0.617442 + 4.29440i) q^{44} +(-6.37137 - 2.09897i) q^{45} +(1.63751 - 4.50761i) q^{46} -6.98212 q^{47} +(0.215117 - 1.71864i) q^{48} +(-2.77080 + 6.06720i) q^{49} +(-3.76432 + 3.29088i) q^{50} +(4.07683 + 6.09573i) q^{51} +(0.534322 - 1.81973i) q^{52} +(1.10788 + 1.72390i) q^{53} +(-1.89623 + 4.83780i) q^{54} +(-7.77906 - 5.79671i) q^{55} +(0.483302 + 0.310599i) q^{56} +(1.20258 + 0.522848i) q^{57} +(-4.53780 - 0.652438i) q^{58} +(-2.47824 + 3.85621i) q^{59} +(2.38399 + 3.05231i) q^{60} +(3.92849 - 1.79408i) q^{61} +(2.29985 - 1.47803i) q^{62} +(-1.17551 - 1.26041i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(2.04059 + 3.71761i) q^{65} +(-4.81639 + 5.76817i) q^{66} +(1.50369 + 10.4584i) q^{67} -4.23393i q^{68} +(7.70223 - 3.11058i) q^{69} +(-1.25467 + 0.275824i) q^{70} +(11.6770 - 1.67890i) q^{71} +(2.46279 - 1.71309i) q^{72} +(-1.52050 - 5.17834i) q^{73} +(-0.469465 + 0.541792i) q^{74} +(-8.59785 - 1.03781i) q^{75} +(-0.409315 - 0.636907i) q^{76} +(-1.03543 - 2.26727i) q^{77} +(2.96264 - 1.41900i) q^{78} +(-5.12499 + 7.97465i) q^{79} +(-0.164419 - 2.23001i) q^{80} +(-8.42712 + 3.15969i) q^{81} +(0.492546 - 0.766417i) q^{82} +(8.24830 - 7.14720i) q^{83} +(0.159593 + 0.982185i) q^{84} +(6.70912 + 6.67971i) q^{85} +(-4.42796 - 1.30017i) q^{86} +(-4.41436 - 6.60041i) q^{87} +(4.16282 - 1.22231i) q^{88} +(4.53438 - 9.92892i) q^{89} +(-1.17087 + 6.60523i) q^{90} +1.08958i q^{91} +(-4.69477 - 0.979347i) q^{92} +(4.56697 + 1.25077i) q^{93} +(0.993659 + 6.91105i) q^{94} +(1.65501 + 0.356219i) q^{95} +(-1.73176 + 0.0316608i) q^{96} +(-5.09324 + 5.87791i) q^{97} +(6.39977 + 1.87914i) q^{98} +(-13.0070 + 0.475758i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 24 q^{2} + 2 q^{3} - 24 q^{4} + 2 q^{6} - 24 q^{8} - 6 q^{9}+O(q^{10}) $ 240 * q - 24 * q^2 + 2 * q^3 - 24 * q^4 + 2 * q^6 - 24 * q^8 - 6 * q^9	$ 240 q - 24 q^{2} + 2 q^{3} - 24 q^{4} + 2 q^{6} - 24 q^{8} - 6 q^{9} - 9 q^{12} + 11 q^{15} - 24 q^{16} - 6 q^{18} - 4 q^{23} + 2 q^{24} - 12 q^{25} + 2 q^{27} + 22 q^{30} + 28 q^{31} - 24 q^{32} - 36 q^{35} - 6 q^{36} - 4 q^{46} + 104 q^{47} - 9 q^{48} + 70 q^{49} + 54 q^{50} - 9 q^{54} - 26 q^{55} - 44 q^{57} - 11 q^{60} + 44 q^{61} + 28 q^{62} - 121 q^{63} - 24 q^{64} + 44 q^{65} + 44 q^{66} - 102 q^{69} - 36 q^{70} + 16 q^{72} - 82 q^{75} + 8 q^{77} - 44 q^{79} + 74 q^{81} - 11 q^{84} + 22 q^{85} - 93 q^{87} - 4 q^{92} + 172 q^{93} + 16 q^{94} + 26 q^{95} + 2 q^{96} + 4 q^{98}+O(q^{100}) $ 240 * q - 24 * q^2 + 2 * q^3 - 24 * q^4 + 2 * q^6 - 24 * q^8 - 6 * q^9 - 9 * q^12 + 11 * q^15 - 24 * q^16 - 6 * q^18 - 4 * q^23 + 2 * q^24 - 12 * q^25 + 2 * q^27 + 22 * q^30 + 28 * q^31 - 24 * q^32 - 36 * q^35 - 6 * q^36 - 4 * q^46 + 104 * q^47 - 9 * q^48 + 70 * q^49 + 54 * q^50 - 9 * q^54 - 26 * q^55 - 44 * q^57 - 11 * q^60 + 44 * q^61 + 28 * q^62 - 121 * q^63 - 24 * q^64 + 44 * q^65 + 44 * q^66 - 102 * q^69 - 36 * q^70 + 16 * q^72 - 82 * q^75 + 8 * q^77 - 44 * q^79 + 74 * q^81 - 11 * q^84 + 22 * q^85 - 93 * q^87 - 4 * q^92 + 172 * q^93 + 16 * q^94 + 26 * q^95 + 2 * q^96 + 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{22}\right)$

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 $

$2$	−0.142315	−	0.989821i	−0.100632	−	0.699909i
$2$	−0.142315	−	0.989821i	−0.100632	−	0.699909i
$3$	1.11013	−	1.32951i	0.640937	−	0.767594i
$3$	1.11013	−	1.32951i	0.640937	−	0.767594i
$4$	−0.959493	+	0.281733i	−0.479746	+	0.140866i
$5$	1.06732	−	1.96490i	0.477319	−	0.878730i
$5$	1.06732	−	1.96490i	0.477319	−	0.878730i
$6$	−1.47397	−	0.909626i	−0.601745	−	0.371353i
$7$	0.483302	−	0.310599i	0.182671	−	0.117396i	−0.446109	−	0.894978i	$-0.647191\pi$
$7$	0.483302	−	0.310599i	0.182671	−	0.117396i	0.628780	+	0.777583i	$0.283554\pi$
$8$	0.415415	+	0.909632i	0.146871	+	0.321603i
$9$	−0.535201	−	2.95187i	−0.178400	−	0.983958i
$10$	−2.09680	−	0.776821i	−0.663065	−	0.245652i
$11$	0.617442	−	4.29440i	0.186166	−	1.29481i	−0.655658	−	0.755058i	$-0.727609\pi$
$11$	0.617442	−	4.29440i	0.186166	−	1.29481i	0.841824	−	0.539753i	$-0.181482\pi$
$12$	−0.690600	+	1.58842i	−0.199359	+	0.458537i
$13$	−1.02536	+	1.59549i	−0.284383	+	0.442508i	−0.953828	−	0.300353i	$-0.902895\pi$
$13$	−1.02536	+	1.59549i	−0.284383	+	0.442508i	0.669445	+	0.742861i	$0.266532\pi$
$14$	−0.376219	−	0.434180i	−0.100549	−	0.116039i
$15$	−1.42749	−	3.60032i	−0.368576	−	0.929598i
$16$	0.841254	−	0.540641i	0.210313	−	0.135160i
$17$	−1.19284	+	4.06243i	−0.289305	+	0.985283i	0.678713	+	0.734404i	$0.262538\pi$
$17$	−1.19284	+	4.06243i	−0.289305	+	0.985283i	−0.968018	+	0.250880i	$0.919280\pi$
$18$	−2.84566	+	0.949849i	−0.670729	+	0.223882i
$19$	0.213298	+	0.726425i	0.0489338	+	0.166653i	0.980335	−	0.197341i	$-0.0632308\pi$
$19$	0.213298	+	0.726425i	0.0489338	+	0.166653i	−0.931401	+	0.363995i	$0.881413\pi$
$20$	−0.470509	+	2.18601i	−0.105209	+	0.488806i
$21$	0.123585	−	0.987363i	0.0269685	−	0.215460i
$22$	−4.33856			−0.924985
$23$	4.22869	+	2.26235i	0.881742	+	0.471732i
$23$	4.22869	+	2.26235i	0.881742	+	0.471732i
$24$	1.67053	+	0.457515i	0.340996	+	0.0933899i
$25$	−2.72166	−	4.19435i	−0.544332	−	0.838870i
$26$	1.72517	+	0.787858i	0.338334	+	0.154512i
$27$	−4.51870	−	2.56542i	−0.869623	−	0.493716i
$28$	−0.376219	+	0.434180i	−0.0710987	+	0.0820523i
$29$	1.29159	−	4.39876i	0.239843	−	0.816830i	−0.748309	−	0.663350i	$-0.769134\pi$
$29$	1.29159	−	4.39876i	0.239843	−	0.816830i	0.988152	−	0.153480i	$-0.0490480\pi$
$30$	−3.36052	+	1.92534i	−0.613544	+	0.351517i
$31$	1.13568	+	2.48679i	0.203974	+	0.446640i	0.983780	−	0.179381i	$-0.0574095\pi$
$31$	1.13568	+	2.48679i	0.203974	+	0.446640i	−0.779806	+	0.626021i	$0.784682\pi$
$32$	−0.654861	−	0.755750i	−0.115764	−	0.133599i
$33$	−5.02401	−	5.58826i	−0.874568	−	0.972791i
$34$	4.19084	+	0.602551i	0.718722	+	0.103337i
$35$	−0.0944592	−	1.28115i	−0.0159665	−	0.216554i
$36$	1.34516	+	2.68152i	0.224193	+	0.446920i
$37$	−0.469465	−	0.541792i	−0.0771796	−	0.0890700i	0.715846	−	0.698258i	$-0.246041\pi$
$37$	−0.469465	−	0.541792i	−0.0771796	−	0.0890700i	−0.793026	+	0.609188i	$0.791496\pi$
$38$	0.688676	−	0.314508i	0.111718	−	0.0510199i
$39$	0.982932	+	3.13443i	0.157395	+	0.501910i
$40$	2.23072	+	0.154619i	0.352707	+	0.0244473i
$41$	0.688519	+	0.596605i	0.107529	+	0.0931741i	0.706966	−	0.707248i	$-0.250063\pi$
$41$	0.688519	+	0.596605i	0.107529	+	0.0931741i	−0.599437	+	0.800422i	$0.704609\pi$
$42$	−0.994901	+	0.0181892i	−0.153517	+	0.00280666i
$43$	1.91710	−	4.19786i	0.292355	−	0.640168i	−0.705278	−	0.708931i	$-0.749178\pi$
$43$	1.91710	−	4.19786i	0.292355	−	0.640168i	0.997633	+	0.0687629i	$0.0219052\pi$
$44$	0.617442	+	4.29440i	0.0930829	+	0.647405i
$45$	−6.37137	−	2.09897i	−0.949787	−	0.312897i
$46$	1.63751	−	4.50761i	0.241438	−	0.664611i
$47$	−6.98212			−1.01845			−0.509223	−	0.860634i	$-0.670067\pi$
$47$	−6.98212			−1.01845			−0.509223	+	0.860634i	$0.670067\pi$
$48$	0.215117	−	1.71864i	0.0310494	−	0.248064i
$49$	−2.77080	+	6.06720i	−0.395828	+	0.866742i
$50$	−3.76432	+	3.29088i	−0.532356	+	0.465400i
$51$	4.07683	+	6.09573i	0.570871	+	0.853573i
$52$	0.534322	−	1.81973i	0.0740971	−	0.252352i
$53$	1.10788	+	1.72390i	0.152180	+	0.236796i	0.908970	−	0.416862i	$-0.136870\pi$
$53$	1.10788	+	1.72390i	0.152180	+	0.236796i	−0.756790	+	0.653658i	$0.773234\pi$
$54$	−1.89623	+	4.83780i	−0.258045	+	0.658341i
$55$	−7.77906	−	5.79671i	−1.04893	−	0.781628i
$56$	0.483302	+	0.310599i	0.0645839	+	0.0415056i
$57$	1.20258	+	0.522848i	0.159286	+	0.0692530i
$58$	−4.53780	−	0.652438i	−0.595843	−	0.0856693i
$59$	−2.47824	+	3.85621i	−0.322639	+	0.502036i	−0.964250	−	0.264994i	$-0.914630\pi$
$59$	−2.47824	+	3.85621i	−0.322639	+	0.502036i	0.641611	+	0.767030i	$0.278266\pi$
$60$	2.38399	+	3.05231i	0.307772	+	0.394051i
$61$	3.92849	−	1.79408i	0.502991	−	0.229708i	−0.147726	−	0.989028i	$-0.547195\pi$
$61$	3.92849	−	1.79408i	0.502991	−	0.229708i	0.650718	+	0.759320i	$0.274468\pi$
$62$	2.29985	−	1.47803i	0.292082	−	0.187709i
$63$	−1.17551	−	1.26041i	−0.148101	−	0.158797i
$64$	−0.654861	+	0.755750i	−0.0818576	+	0.0944687i
$65$	2.04059	+	3.71761i	0.253104	+	0.461113i
$66$	−4.81639	+	5.76817i	−0.592857	+	0.710012i
$67$	1.50369	+	10.4584i	0.183705	+	1.27770i	0.847908	+	0.530144i	$0.177862\pi$
$67$	1.50369	+	10.4584i	0.183705	+	1.27770i	−0.664202	+	0.747553i	$0.731229\pi$
$68$		−	4.23393i		−	0.513439i
$69$	7.70223	−	3.11058i	0.927239	−	0.374469i
$70$	−1.25467	+	0.275824i	−0.149961	+	0.0329673i
$71$	11.6770	−	1.67890i	1.38580	−	0.199248i	0.591272	−	0.806472i	$-0.298626\pi$
$71$	11.6770	−	1.67890i	1.38580	−	0.199248i	0.794531	+	0.607224i	$0.207717\pi$
$72$	2.46279	−	1.71309i	0.290242	−	0.201889i
$73$	−1.52050	−	5.17834i	−0.177961	−	0.606079i	−0.999362	−	0.0357274i	$-0.988625\pi$
$73$	−1.52050	−	5.17834i	−0.177961	−	0.606079i	0.821401	−	0.570351i	$-0.193193\pi$
$74$	−0.469465	+	0.541792i	−0.0545742	+	0.0629820i
$75$	−8.59785	−	1.03781i	−0.992794	−	0.119836i
$76$	−0.409315	−	0.636907i	−0.0469517	−	0.0730582i
$77$	−1.03543	−	2.26727i	−0.117998	−	0.258379i
$78$	2.96264	−	1.41900i	0.335453	−	0.160670i
$79$	−5.12499	+	7.97465i	−0.576607	+	0.897218i	−0.999962	−	0.00874603i	$-0.997216\pi$
$79$	−5.12499	+	7.97465i	−0.576607	+	0.897218i	0.423355	+	0.905964i	$0.360852\pi$
$80$	−0.164419	−	2.23001i	−0.0183826	−	0.249323i
$81$	−8.42712	+	3.15969i	−0.936347	+	0.351077i
$82$	0.492546	−	0.766417i	0.0543926	−	0.0846366i
$83$	8.24830	−	7.14720i	0.905369	−	0.784507i	−0.0717007	−	0.997426i	$-0.522843\pi$
$83$	8.24830	−	7.14720i	0.905369	−	0.784507i	0.977070	+	0.212919i	$0.0682972\pi$
$84$	0.159593	+	0.982185i	0.0174130	+	0.107165i
$85$	6.70912	+	6.67971i	0.727707	+	0.724516i
$86$	−4.42796	−	1.30017i	−0.477480	−	0.140201i
$87$	−4.41436	−	6.60041i	−0.473270	−	0.707638i
$88$	4.16282	−	1.22231i	0.443758	−	0.130299i
$89$	4.53438	−	9.92892i	0.480644	−	1.05246i	−0.501642	−	0.865075i	$-0.667271\pi$
$89$	4.53438	−	9.92892i	0.480644	−	1.05246i	0.982286	−	0.187388i	$-0.0600021\pi$
$90$	−1.17087	+	6.60523i	−0.123421	+	0.696252i
$91$			1.08958i			0.114219i
$92$	−4.69477	−	0.979347i	−0.489464	−	0.102104i
$93$	4.56697	+	1.25077i	0.473573	+	0.129699i
$94$	0.993659	+	6.91105i	0.102488	+	0.712821i
$95$	1.65501	+	0.356219i	0.169800	+	0.0365473i
$96$	−1.73176	+	0.0316608i	−0.176747	+	0.00323137i
$97$	−5.09324	+	5.87791i	−0.517140	+	0.596812i	−0.952913	−	0.303245i	$-0.901930\pi$
$97$	−5.09324	+	5.87791i	−0.517140	+	0.596812i	0.435772	+	0.900057i	$0.356475\pi$
$98$	6.39977	+	1.87914i	0.646474	+	0.189822i
$99$	−13.0070	+	0.475758i	−1.30725	+	0.0478155i
$100$	3.79310	+	3.25767i	0.379310	+	0.325767i
$101$	10.8521	−	9.40339i	1.07982	−	0.935672i	0.0816842	−	0.996658i	$-0.473970\pi$
$101$	10.8521	−	9.40339i	1.07982	−	0.935672i	0.998139	+	0.0609865i	$0.0194247\pi$
$102$	5.45349	−	4.90285i	0.539976	−	0.485455i
$103$	−0.130735	+	0.909280i	−0.0128817	+	0.0895941i	−0.995248	−	0.0973720i	$-0.968956\pi$
$103$	−0.130735	+	0.909280i	−0.0128817	+	0.0895941i	0.982366	+	0.186966i	$0.0598654\pi$
$104$	−1.87725	−	0.269908i	−0.184080	−	0.0264667i
$105$	−1.80816	−	1.29666i	−0.176459	−	0.126541i
$106$	1.54869	−	1.34194i	0.150422	−	0.130341i
$107$	−10.6883	+	4.88119i	−1.03328	+	0.471882i	−0.858548	−	0.512734i	$-0.828633\pi$
$107$	−10.6883	+	4.88119i	−1.03328	+	0.471882i	−0.174731	+	0.984616i	$0.555906\pi$
$108$	5.05842	+	1.18844i	0.486747	+	0.114358i
$109$	−0.620718	+	2.11397i	−0.0594540	+	0.202482i	−0.983864	−	0.178919i	$-0.942740\pi$
$109$	−0.620718	+	2.11397i	−0.0594540	+	0.202482i	0.924410	+	0.381401i	$0.124558\pi$
$110$	−4.63063	+	8.52484i	−0.441513	+	0.812812i
$111$	−1.24149	+	0.0226974i	−0.117837	+	0.00215434i
$112$	0.238657	−	0.522586i	0.0225510	−	0.0493797i
$113$	17.1376	−	2.46401i	1.61217	−	0.231795i	0.723493	−	0.690332i	$-0.242536\pi$
$113$	17.1376	−	2.46401i	1.61217	−	0.231795i	0.888675	+	0.458538i	$0.151627\pi$
$114$	0.346382	−	1.26475i	0.0324416	−	0.118455i
$115$	8.95864	−	5.89430i	0.835398	−	0.549646i
$116$			4.58447i			0.425657i
$117$	5.25844	+	2.17282i	0.486143	+	0.200877i
$118$	4.16965	+	1.90422i	0.383848	+	0.175297i
$119$	0.685287	+	2.33387i	0.0628201	+	0.213946i
$120$	2.68196	−	2.79411i	0.244829	−	0.255067i
$121$	−7.50623	−	2.20403i	−0.682385	−	0.200366i
$122$	−2.33490	−	3.63318i	−0.211392	−	0.328932i
$123$	1.55754	−	0.253082i	0.140439	−	0.0228196i
$124$	−1.79028	−	2.06610i	−0.160772	−	0.185541i
$125$	−11.1464	+	0.871084i	−0.996960	+	0.0779121i
$126$	−1.08029	+	1.34292i	−0.0962400	+	0.119637i
$127$	16.3010	+	2.34373i	1.44648	+	0.207973i	0.820403	−	0.571786i	$-0.193749\pi$
$127$	16.3010	+	2.34373i	1.44648	+	0.207973i	0.626080	+	0.779759i	$0.284658\pi$
$128$	0.841254	+	0.540641i	0.0743570	+	0.0477863i
$129$	−3.45287	−	7.20900i	−0.304008	−	0.634717i
$130$	3.38937	−	2.54889i	0.297267	−	0.223552i
$131$	−2.50347	−	3.89548i	−0.218729	−	0.340349i	0.714497	−	0.699638i	$-0.246656\pi$
$131$	−2.50347	−	3.89548i	−0.218729	−	0.340349i	−0.933226	+	0.359289i	$0.883019\pi$
$132$	6.39490	+	3.94647i	0.556605	+	0.343496i
$133$	0.328714	+	0.284833i	0.0285032	+	0.0246981i
$134$	10.1380	−	2.97677i	0.875786	−	0.257154i
$135$	−9.86369	+	6.14066i	−0.848931	+	0.528504i
$136$	−4.19084	+	0.602551i	−0.359361	+	0.0516683i
$137$			8.34533i			0.712989i	0.934297	+	0.356495i	$0.116028\pi$
$137$			8.34533i			0.712989i	−0.934297	+	0.356495i	$0.883972\pi$
$138$	−4.17506	−	7.18115i	−0.355404	−	0.611300i
$139$	−2.74816			−0.233096			−0.116548	−	0.993185i	$-0.537183\pi$
$139$	−2.74816			−0.233096			−0.116548	+	0.993185i	$0.537183\pi$
$140$	0.451574	+	1.20264i	0.0381650	+	0.101642i
$141$	−7.75110	+	9.28281i	−0.652760	+	0.781754i
$142$	−3.32361	−	11.3192i	−0.278912	−	0.949886i
$143$	6.21856	+	5.38841i	0.520022	+	0.450602i
$144$	−2.04614	−	2.19392i	−0.170512	−	0.182827i
$145$	−7.26459	−	7.23274i	−0.603291	−	0.600646i
$146$	−4.90924	+	2.24198i	−0.406292	+	0.185547i
$147$	4.99045	+	10.4192i	0.411605	+	0.859362i
$148$	0.603089	+	0.387582i	0.0495736	+	0.0318590i
$149$	3.05802	−	21.2690i	0.250523	−	1.74242i	−0.344565	−	0.938762i	$-0.611974\pi$
$149$	3.05802	−	21.2690i	0.250523	−	1.74242i	0.595088	−	0.803661i	$-0.297117\pi$
$150$	0.196351	+	8.65803i	0.0160320	+	0.706925i
$151$	6.59432	+	4.23791i	0.536638	+	0.344876i	0.780723	−	0.624878i	$-0.214851\pi$
$151$	6.59432	+	4.23791i	0.536638	+	0.344876i	−0.244085	+	0.969754i	$0.578487\pi$
$152$	−0.572173	+	0.495790i	−0.0464093	+	0.0402139i
$153$	12.6302	+	1.34689i	1.02109	+	0.108889i
$154$	−2.09684	+	1.34755i	−0.168968	+	0.108589i
$155$	6.09842	+	0.422702i	0.489837	+	0.0339523i
$156$	−1.82619	−	2.73054i	−0.146212	−	0.218618i
$157$	1.67360	−	0.491414i	0.133568	−	0.0392191i	−0.214265	−	0.976776i	$-0.568736\pi$
$157$	1.67360	−	0.491414i	0.133568	−	0.0392191i	0.347833	+	0.937556i	$0.386918\pi$
$158$	8.62284	+	3.93792i	0.685996	+	0.313284i
$159$	3.52185	+	0.440818i	0.279301	+	0.0349592i
$160$	−2.18392	+	0.480110i	−0.172654	+	0.0379560i
$161$	2.74642	−	0.220031i	0.216448	−	0.0173408i
$162$	4.32684	+	7.89167i	0.339948	+	0.620028i
$163$	13.8447	−	1.99057i	1.08440	−	0.155913i	0.423136	−	0.906066i	$-0.360929\pi$
$163$	13.8447	−	1.99057i	1.08440	−	0.155913i	0.661264	+	0.750153i	$0.270020\pi$
$164$	−0.828712	−	0.378460i	−0.0647116	−	0.0295528i
$165$	−16.3426	+	3.90722i	−1.27227	+	0.304177i
$166$	−8.24830	−	7.14720i	−0.640193	−	0.554730i
$167$	4.63776	+	1.36177i	0.358880	+	0.105377i	0.456202	−	0.889876i	$-0.349209\pi$
$167$	4.63776	+	1.36177i	0.358880	+	0.105377i	−0.0973218	+	0.995253i	$0.531028\pi$
$168$	0.949476	−	0.297748i	0.0732536	−	0.0229718i
$169$	3.90618	+	8.55333i	0.300475	+	0.657949i
$170$	5.65691	−	7.59146i	0.433865	−	0.582238i
$171$	2.03016	−	1.01841i	0.155250	−	0.0778799i
$172$	−0.656769	+	4.56793i	−0.0500781	+	0.348301i
$173$	3.55519	−	24.7269i	0.270296	−	1.87995i	−0.175006	−	0.984567i	$-0.555994\pi$
$173$	3.55519	−	24.7269i	0.270296	−	1.87995i	0.445301	−	0.895381i	$-0.353097\pi$
$174$	−5.90500	+	5.30877i	−0.447657	+	0.402457i
$175$	−2.61815	−	1.18179i	−0.197913	−	0.0893350i
$176$	−1.80230	−	3.94650i	−0.135854	−	0.297478i
$177$	2.37570	+	7.57577i	0.178569	+	0.569429i
$178$	−10.4732	−	3.07520i	−0.784997	−	0.230496i
$179$	19.4179	+	16.8257i	1.45136	+	1.25761i	0.908561	+	0.417752i	$0.137182\pi$
$179$	19.4179	+	16.8257i	1.45136	+	1.25761i	0.542801	+	0.839861i	$0.317364\pi$
$180$	6.70463	+	0.218930i	0.499734	+	0.0163181i
$181$	−7.28066	−	3.32497i	−0.541167	−	0.247143i	0.126027	−	0.992027i	$-0.459777\pi$
$181$	−7.28066	−	3.32497i	−0.541167	−	0.247143i	−0.667194	+	0.744884i	$0.732505\pi$
$182$	1.07849	−	0.155063i	0.0799427	−	0.0114940i
$183$	1.97590	−	7.21464i	0.146063	−	0.533321i
$184$	−0.301243	+	4.78636i	−0.0222079	+	0.352855i
$185$	−1.56563	+	0.344187i	−0.115108	+	0.0253052i
$186$	0.588095	−	4.69849i	0.0431212	−	0.344510i
$187$	16.7092	+	7.63083i	1.22190	+	0.558022i
$188$	6.69930	−	1.96709i	0.488596	−	0.143465i
$189$	−2.98071	+	0.163630i	−0.216815	+	0.0119023i
$190$	0.117061	−	1.68886i	0.00849247	−	0.122523i
$191$	−7.47791	+	4.80576i	−0.541083	+	0.347733i	−0.782462	−	0.622698i	$-0.786037\pi$
$191$	−7.47791	+	4.80576i	−0.541083	+	0.347733i	0.241380	+	0.970431i	$0.422400\pi$
$192$	0.277794	+	1.70963i	0.0200480	+	0.123382i
$193$	−12.2701	+	10.6321i	−0.883223	+	0.765317i	−0.973039	−	0.230641i	$-0.925918\pi$
$193$	−12.2701	+	10.6321i	−0.883223	+	0.765317i	0.0898159	+	0.995958i	$0.471372\pi$
$194$	6.54293	+	4.20489i	0.469755	+	0.301893i
$195$	7.20794	+	1.41407i	0.516171	+	0.101264i
$196$	0.949232	−	6.60206i	0.0678023	−	0.471575i
$197$	−12.6059	−	8.10129i	−0.898130	−	0.577193i	0.00810523	−	0.999967i	$-0.497420\pi$
$197$	−12.6059	−	8.10129i	−0.898130	−	0.577193i	−0.906235	+	0.422774i	$0.861056\pi$
$198$	2.32200	+	12.8069i	0.165018	+	0.910146i
$199$	13.6835	−	6.24904i	0.969996	−	0.442982i	0.133556	−	0.991041i	$-0.457360\pi$
$199$	13.6835	−	6.24904i	0.969996	−	0.442982i	0.836440	+	0.548059i	$0.184633\pi$
$200$	2.68469	−	4.21811i	0.189837	−	0.298265i
$201$	15.5739	+	9.61106i	1.09850	+	0.677912i
$202$	−10.8521	−	9.40339i	−0.763550	−	0.661620i
$203$	−0.742023	−	2.52710i	−0.0520798	−	0.177368i
$204$	−5.62906	−	4.70023i	−0.394113	−	0.329082i
$205$	1.90714	−	0.716103i	0.133200	−	0.0500148i
$206$	0.918631			0.0640040
$207$	4.41496	−	13.6934i	0.306861	−	0.951754i
$208$			1.89656i			0.131503i
$209$	3.25126	−	0.467461i	0.224894	−	0.0323349i
$210$	−1.02614	+	1.97429i	−0.0708101	+	0.136239i
$211$	26.9399	−	7.91027i	1.85462	−	0.544566i	0.854955	−	0.518703i	$-0.173585\pi$
$211$	26.9399	−	7.91027i	1.85462	−	0.544566i	0.999665	−	0.0258630i	$-0.00823337\pi$
$212$	−1.54869	−	1.34194i	−0.106364	−	0.0921651i
$213$	10.7309	−	17.3885i	0.735270	−	1.19144i
$214$	6.35261	+	9.88486i	0.434256	+	0.675715i
$215$	−6.20222	−	8.24736i	−0.422988	−	0.562465i
$216$	0.456456	−	5.17606i	0.0310579	−	0.352187i
$217$	1.32127	+	0.849129i	0.0896937	+	0.0576426i
$218$	2.18079	+	0.313551i	0.147702	+	0.0212363i
$219$	−8.57262	−	3.72714i	−0.579284	−	0.251857i
$220$	9.09708	+	3.37028i	0.613325	+	0.227225i
$221$	−5.25846	−	6.06859i	−0.353722	−	0.408217i
$222$	0.199148	+	1.22562i	0.0133660	+	0.0822583i
$223$	2.67478	+	4.16204i	0.179117	+	0.278711i	0.919189	−	0.393816i	$-0.128845\pi$
$223$	2.67478	+	4.16204i	0.179117	+	0.278711i	−0.740073	+	0.672527i	$0.765209\pi$
$224$	−0.551231	−	0.161856i	−0.0368307	−	0.0108145i
$225$	−10.9246	+	10.2788i	−0.728303	+	0.685255i
$226$	−4.87786	−	16.6125i	−0.324471	−	1.10505i
$227$	−2.57634	−	1.17657i	−0.170998	−	0.0780920i	0.328077	−	0.944651i	$-0.393599\pi$
$227$	−2.57634	−	1.17657i	−0.170998	−	0.0780920i	−0.499075	+	0.866559i	$0.666327\pi$
$228$	−1.30117	−	0.162863i	−0.0861721	−	0.0107859i
$229$			19.8432i			1.31127i	0.755076	+	0.655637i	$0.227600\pi$
$229$			19.8432i			1.31127i	−0.755076	+	0.655637i	$0.772400\pi$
$230$	−7.10925	−	8.02861i	−0.468770	−	0.529391i
$231$	−4.16383	−	1.14036i	−0.273960	−	0.0750304i
$232$	4.53780	−	0.652438i	0.297921	−	0.0428346i
$233$	2.54537	−	5.57357i	0.166752	−	0.365137i	−0.807746	−	0.589530i	$-0.799313\pi$
$233$	2.54537	−	5.57357i	0.166752	−	0.365137i	0.974499	+	0.224394i	$0.0720401\pi$
$234$	1.40235	−	5.51414i	0.0916742	−	0.360471i
$235$	−7.45215	+	13.7192i	−0.486125	+	0.894940i
$236$	1.29143	−	4.39821i	0.0840650	−	0.286299i
$237$	4.91295	+	15.6667i	0.319130	+	1.01766i
$238$	2.21259	−	1.01046i	0.143421	−	0.0654982i
$239$	−15.4131	+	13.3555i	−0.996989	+	0.863896i	−0.990697	−	0.136084i	$-0.956548\pi$
$239$	−15.4131	+	13.3555i	−0.996989	+	0.863896i	−0.00629177	+	0.999980i	$0.502003\pi$
$240$	−3.14736	−	2.25702i	−0.203161	−	0.145690i
$241$	−10.5689	−	1.51958i	−0.680804	−	0.0978848i	−0.206768	−	0.978390i	$-0.566294\pi$
$241$	−10.5689	−	1.51958i	−0.680804	−	0.0978848i	−0.474036	+	0.880505i	$0.657203\pi$
$242$	−1.11335	+	7.74350i	−0.0715686	+	0.497771i
$243$	−5.15439	+	14.7116i	−0.330654	+	0.943752i
$244$	−3.26390	+	2.82819i	−0.208950	+	0.181056i
$245$	8.96411	+	11.9200i	0.572696	+	0.761539i
$246$	−0.472167	−	1.50567i	−0.0301043	−	0.0959981i
$247$	−1.37771	−	0.404531i	−0.0876614	−	0.0257397i
$248$	−1.79028	+	2.06610i	−0.113683	+	0.131197i
$249$	−0.345549	−	18.9006i	−0.0218982	−	1.19777i
$250$	2.44851	+	10.9089i	0.154857	+	0.689941i
$251$	4.38354	+	30.4882i	0.276686	+	1.92440i	0.370553	+	0.928811i	$0.379168\pi$
$251$	4.38354	+	30.4882i	0.276686	+	1.92440i	−0.0938662	+	0.995585i	$0.529923\pi$
$252$	1.48300	+	0.878177i	0.0934200	+	0.0553200i
$253$	12.3264	−	16.7628i	0.774954	−	1.05387i
$254$		−	16.4687i		−	1.03334i
$255$	16.3288	−	1.50448i	1.02255	−	0.0942142i
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	−8.37632	+	2.45951i	−0.522500	+	0.153420i	−0.532338	−	0.846532i	$-0.678687\pi$
$257$	−8.37632	+	2.45951i	−0.522500	+	0.153420i	0.00983804	+	0.999952i	$0.496868\pi$
$258$	−6.64422	+	4.44367i	−0.413651	+	0.276651i
$259$	−0.395173	−	0.116033i	−0.0245549	−	0.00720996i
$260$	−3.00530	−	2.99212i	−0.186381	−	0.185564i
$261$	−13.6759	−	1.45840i	−0.846515	−	0.0902726i
$262$	−3.49954	+	3.03237i	−0.216203	+	0.187341i
$263$	−14.4425	+	22.4730i	−0.890566	+	1.38575i	0.0318271	+	0.999493i	$0.489867\pi$
$263$	−14.4425	+	22.4730i	−0.890566	+	1.38575i	−0.922393	+	0.386254i	$0.873769\pi$
$264$	2.99621	−	6.89145i	0.184404	−	0.424139i
$265$	4.56976	−	0.336929i	0.280718	−	0.0206974i
$266$	0.235153	−	0.365904i	0.0144181	−	0.0224350i
$267$	−8.16683	−	17.0510i	−0.499802	−	1.04350i
$268$	−4.38925	−	9.61112i	−0.268116	−	0.587093i
$269$	1.65040	+	2.56807i	0.100627	+	0.156578i	0.887916	−	0.460006i	$-0.152153\pi$
$269$	1.65040	+	2.56807i	0.100627	+	0.156578i	−0.787289	+	0.616584i	$0.788516\pi$
$270$	7.48191	+	8.88938i	0.455334	+	0.540990i
$271$	−10.6069	+	12.2410i	−0.644321	+	0.743586i	−0.980133	−	0.198343i	$-0.936444\pi$
$271$	−10.6069	+	12.2410i	−0.644321	+	0.743586i	0.335811	+	0.941929i	$0.390990\pi$
$272$	1.19284	+	4.06243i	0.0723263	+	0.246321i
$273$	1.44860	+	1.20958i	0.0876735	+	0.0732069i
$274$	8.26038	−	1.18766i	0.499028	−	0.0717494i
$275$	−19.6927	+	9.09814i	−1.18751	+	0.548639i
$276$	−6.51388	+	5.15454i	−0.392090	+	0.310267i
$277$		−	21.8781i		−	1.31453i	−0.753661	−	0.657263i	$-0.771714\pi$
$277$		−	21.8781i		−	1.31453i	0.753661	−	0.657263i	$-0.228286\pi$
$278$	0.391104	+	2.72018i	0.0234568	+	0.163146i
$279$	6.73287	−	4.68331i	0.403086	−	0.280382i
$280$	1.12613	−	0.618131i	0.0672994	−	0.0369404i
$281$	−14.4695	+	16.6987i	−0.863181	+	0.996164i	0.136804	+	0.990598i	$0.456317\pi$
$281$	−14.4695	+	16.6987i	−0.863181	+	0.996164i	−0.999985	+	0.00556568i	$0.998228\pi$
$282$	10.2914	+	6.35112i	0.612845	+	0.378204i
$283$	−9.17567	+	5.89685i	−0.545437	+	0.350531i	−0.784162	−	0.620556i	$-0.786907\pi$
$283$	−9.17567	+	5.89685i	−0.545437	+	0.350531i	0.238725	+	0.971087i	$0.423271\pi$
$284$	−10.7310	+	4.90067i	−0.636767	+	0.290802i
$285$	2.31088	−	1.80490i	0.136885	−	0.106913i
$286$	4.44857	−	6.92211i	0.263050	−	0.409313i
$287$	0.518068	+	0.0744869i	0.0305806	+	0.00439682i
$288$	−1.88040	+	2.33754i	−0.110803	+	0.137741i
$289$	−0.779142	−	0.500724i	−0.0458319	−	0.0294544i
$290$	−6.12526	+	8.21997i	−0.359688	+	0.482693i
$291$	2.16057	+	13.2968i	0.126655	+	0.779472i
$292$	2.91781	+	4.54021i	0.170752	+	0.265696i
$293$	−1.07672	+	3.66698i	−0.0629028	+	0.214227i	−0.984947	−	0.172858i	$-0.944700\pi$
$293$	−1.07672	+	3.66698i	−0.0629028	+	0.214227i	0.922044	+	0.387085i	$0.126518\pi$
$294$	9.60294	−	6.42246i	0.560055	−	0.374566i
$295$	4.93200	+	8.98530i	0.287152	+	0.523144i
$296$	0.297808	−	0.652109i	0.0173097	−	0.0379030i
$297$	−13.8070	+	17.8211i	−0.801163	+	1.03408i
$298$	−21.4877			−1.24475
$299$	−7.94545	+	4.42710i	−0.459497	+	0.256026i
$300$	8.54196	−	1.42652i	0.493170	−	0.0823601i
$301$	−0.377315	−	2.62428i	−0.0217481	−	0.151261i
$302$	3.25631	−	7.13032i	0.187379	−	0.410304i
$303$	−0.454629	−	24.8670i	−0.0261178	−	1.42857i
$304$	0.572173	+	0.495790i	0.0328163	+	0.0284355i
$305$	0.667761	−	9.63394i	0.0382359	−	0.551638i
$306$	−0.464284	−	12.6933i	−0.0265414	−	0.725628i
$307$	−18.2286	+	8.32473i	−1.04036	+	0.475117i	−0.860968	−	0.508660i	$-0.830141\pi$
$307$	−18.2286	+	8.32473i	−1.04036	+	0.475117i	−0.179395	+	0.983777i	$0.557414\pi$
$308$	1.63225	+	1.88372i	0.0930060	+	0.107335i
$309$	1.06377	+	1.18324i	0.0605155	+	0.0673120i
$310$	−0.449496	−	6.09650i	−0.0255297	−	0.346258i
$311$	−30.1498	−	4.33488i	−1.70964	−	0.245809i	−0.783069	−	0.621935i	$-0.786347\pi$
$311$	−30.1498	−	4.33488i	−1.70964	−	0.245809i	−0.926568	+	0.376126i	$0.877256\pi$
$312$	−2.44285	+	2.19619i	−0.138299	+	0.124335i
$313$	−7.66085	−	8.84109i	−0.433017	−	0.499728i	0.496742	−	0.867898i	$-0.334530\pi$
$313$	−7.66085	−	8.84109i	−0.433017	−	0.499728i	−0.929758	+	0.368171i	$0.879984\pi$
$314$	−0.724591	−	1.58663i	−0.0408910	−	0.0895388i
$315$	−3.73123	+	0.964504i	−0.210231	+	0.0543436i
$316$	2.67068	−	9.09550i	0.150237	−	0.511662i
$317$	13.4695	−	15.5446i	0.756521	−	0.873072i	−0.238662	−	0.971103i	$-0.576709\pi$
$317$	13.4695	−	15.5446i	0.756521	−	0.873072i	0.995183	+	0.0980304i	$0.0312543\pi$
$318$	−0.0648795	−	3.54873i	−0.00363826	−	0.199003i
$319$	−18.0926	−	8.26260i	−1.01299	−	0.462617i
$320$	0.786027	+	2.09336i	0.0439402	+	0.117022i
$321$	−5.37587	+	19.6290i	−0.300052	+	1.09558i
$322$	−0.608647	−	2.68715i	−0.0339186	−	0.149749i
$323$	−3.20548			−0.178358
$324$	7.19557	−	5.40590i	0.399754	−	0.300328i
$325$	9.48269	−	0.0416694i	0.526005	−	0.00231140i
$326$	−3.94061	−	13.4205i	−0.218250	−	0.743292i
$327$	2.12147	+	3.17205i	0.117318	+	0.175415i
$328$	−0.256670	+	0.874138i	−0.0141722	+	0.0482662i
$329$	−3.37447	+	2.16864i	−0.186041	+	0.119561i
$330$	6.19325	+	15.6202i	0.340927	+	0.859863i
$331$	13.2938	+	15.3419i	0.730693	+	0.843265i	0.992550	−	0.121842i	$-0.0388801\pi$
$331$	13.2938	+	15.3419i	0.730693	+	0.843265i	−0.261856	+	0.965107i	$0.584335\pi$
$332$	−5.90059	+	9.18150i	−0.323837	+	0.503900i
$333$	−1.34804	+	1.67577i	−0.0738722	+	0.0918316i
$334$	0.687886	−	4.78435i	0.0376394	−	0.261788i
$335$	22.1546	+	8.20785i	1.21044	+	0.448443i
$336$	−0.429842	−	0.897437i	−0.0234498	−	0.0489592i
$337$	−7.95109	−	17.4105i	−0.433123	−	0.948408i	−0.992810	−	0.119703i	$-0.961806\pi$
$337$	−7.95109	−	17.4105i	−0.433123	−	0.948408i	0.559686	−	0.828705i	$-0.310922\pi$
$338$	7.91037	−	5.08368i	0.430267	−	0.276516i
$339$	15.7491	−	25.5200i	0.855373	−	1.38606i
$340$	−8.31925	−	4.51895i	−0.451175	−	0.245075i
$341$	11.3805	−	3.34161i	0.616288	−	0.180958i
$342$	−1.29697	−	1.86456i	−0.0701320	−	0.100824i
$343$	1.11766	+	7.77348i	0.0603478	+	0.419728i
$344$	4.61490			0.248819
$345$	2.10876	−	18.4541i	0.113532	−	0.993534i
$346$	−24.9811			−1.34299
$347$	−2.90162	−	20.1812i	−0.155767	−	1.08339i	−0.906325	−	0.422581i	$-0.861124\pi$
$347$	−2.90162	−	20.1812i	−0.155767	−	1.08339i	0.750558	−	0.660805i	$-0.229785\pi$
$348$	6.09510	+	5.08938i	0.326732	+	0.272819i
$349$	−9.06471	+	2.66164i	−0.485223	+	0.142474i	−0.515189	−	0.857077i	$-0.672278\pi$
$349$	−9.06471	+	2.66164i	−0.485223	+	0.142474i	0.0299660	+	0.999551i	$0.490460\pi$
$350$	−0.797161	+	2.75968i	−0.0426100	+	0.147511i
$351$	8.72637	−	4.57904i	0.465779	−	0.244411i
$352$	−3.64983	+	2.34560i	−0.194537	+	0.125021i
$353$	0.141241	+	0.309274i	0.00751748	+	0.0164610i	0.913354	−	0.407168i	$-0.133483\pi$
$353$	0.141241	+	0.309274i	0.00751748	+	0.0164610i	−0.905836	+	0.423629i	$0.860756\pi$
$354$	7.16056	−	3.42966i	0.380579	−	0.182285i
$355$	9.16420	−	24.7360i	0.486385	−	1.31285i
$356$	−1.55341	+	10.8042i	−0.0823306	+	0.572622i
$357$	3.86367	+	1.67982i	0.204487	+	0.0889053i
$358$	13.8910	−	21.6148i	0.734162	−	1.14238i
$359$	−19.9323	−	23.0031i	−1.05199	−	1.21406i	−0.976187	−	0.216933i	$-0.930395\pi$
$359$	−19.9323	−	23.0031i	−1.05199	−	1.21406i	−0.0757989	−	0.997123i	$-0.524151\pi$
$360$	−0.737467	−	6.66754i	−0.0388679	−	0.351410i
$361$	15.5016	−	9.96229i	0.815875	−	0.524331i
$362$	−2.25498	+	7.67974i	−0.118519	+	0.403638i
$363$	−11.2632	+	7.53285i	−0.591165	+	0.395372i
$364$	−0.306969	−	1.04544i	−0.0160896	−	0.0547960i
$365$	−11.7978	−	2.53931i	−0.617524	−	0.132914i
$366$	−7.42240	−	0.929039i	−0.387975	−	0.0485616i
$367$	−25.8828			−1.35107			−0.675537	−	0.737326i	$-0.736088\pi$
$367$	−25.8828			−1.35107			−0.675537	+	0.737326i	$0.736088\pi$
$368$	4.78051	−	0.382993i	0.249202	−	0.0199649i
$369$	1.39261	−	2.35173i	0.0724962	−	0.122426i
$370$	0.563497	+	1.50072i	0.0292948	+	0.0780185i
$371$	1.07088	+	0.489057i	0.0555976	+	0.0253906i
$372$	−4.73436	+	0.0865556i	−0.245465	+	0.00448770i
$373$	1.11913	−	1.29155i	0.0579465	−	0.0668738i	−0.726036	−	0.687656i	$-0.758640\pi$
$373$	1.11913	−	1.29155i	0.0579465	−	0.0668738i	0.783983	+	0.620783i	$0.213185\pi$
$374$	5.17519	−	17.6251i	0.267603	−	0.911372i
$375$	−11.2158	+	15.7862i	−0.579184	+	0.815197i
$376$	−2.90048	−	6.35116i	−0.149581	−	0.327536i
$377$	5.69382	+	6.57102i	0.293247	+	0.338425i
$378$	0.586164	+	2.92709i	0.0301490	+	0.150553i
$379$	−16.0166	−	2.30284i	−0.822716	−	0.118289i	−0.281915	−	0.959439i	$-0.590970\pi$
$379$	−16.0166	−	2.30284i	−0.822716	−	0.118289i	−0.540801	+	0.841151i	$0.681879\pi$
$380$	−1.68833	+	0.124481i	−0.0866094	+	0.00638572i
$381$	21.2124	−	19.0705i	1.08674	−	0.977013i
$382$	5.82106	+	6.71787i	0.297832	+	0.343716i
$383$	−24.9667	+	11.4019i	−1.27574	+	0.582611i	−0.934030	−	0.357194i	$-0.883734\pi$
$383$	−24.9667	+	11.4019i	−1.27574	+	0.582611i	−0.341711	+	0.939805i	$0.611006\pi$
$384$	1.65269	−	0.518272i	0.0843386	−	0.0264480i
$385$	−5.56009	−	0.385389i	−0.283368	−	0.0196412i
$386$	12.2701	+	10.6321i	0.624533	+	0.541161i
$387$	−13.4176	−	3.41233i	−0.682054	−	0.173459i
$388$	3.23093	−	7.07475i	0.164026	−	0.359166i
$389$	4.66718	+	32.4610i	0.236636	+	1.64584i	0.668365	+	0.743833i	$0.266994\pi$
$389$	4.66718	+	32.4610i	0.236636	+	1.64584i	−0.431730	+	0.902003i	$0.642097\pi$
$390$	0.373880	−	7.33581i	0.0189321	−	0.371463i
$391$	−14.2347	+	14.4801i	−0.719882	+	0.732291i
$392$	−6.66995			−0.336883
$393$	−7.95827	−	0.996111i	−0.401442	−	0.0502472i
$394$	−6.22483	+	13.6305i	−0.313602	+	0.686694i
$395$	10.1994	+	18.5816i	0.513186	+	0.934941i
$396$	12.3461	−	4.12098i	0.620414	−	0.207087i
$397$	4.05961	−	13.8257i	0.203746	−	0.693894i	−0.792696	−	0.609616i	$-0.791323\pi$
$397$	4.05961	−	13.8257i	0.203746	−	0.693894i	0.996442	−	0.0842780i	$-0.0268584\pi$
$398$	−8.13279	−	12.6549i	−0.407660	−	0.634331i
$399$	0.743606	−	0.120827i	0.0372268	−	0.00604891i
$400$	−4.55724	−	2.05707i	−0.227862	−	0.102853i
$401$	−19.4753	−	12.5160i	−0.972550	−	0.625020i	−0.0451061	−	0.998982i	$-0.514363\pi$
$401$	−19.4753	−	12.5160i	−0.972550	−	0.625020i	−0.927444	+	0.373962i	$0.877999\pi$
$402$	7.29684	−	16.7831i	0.363933	−	0.837067i
$403$	−5.13211	−	0.737886i	−0.255649	−	0.0367567i
$404$	−7.76326	+	12.0799i	−0.386237	+	0.600996i
$405$	−2.78595	+	19.9308i	−0.138435	+	0.990372i
$406$	−2.39578	+	1.09411i	−0.118900	+	0.0543000i
$407$	−2.61654	+	1.68155i	−0.129697	+	0.0833512i
$408$	−3.85129	+	6.24068i	−0.190667	+	0.308960i
$409$	14.8528	−	17.1410i	0.734422	−	0.847568i	−0.258540	−	0.966001i	$-0.583241\pi$
$409$	14.8528	−	17.1410i	0.734422	−	0.847568i	0.992962	+	0.118432i	$0.0377868\pi$
$410$	−0.980228	−	1.78581i	−0.0484100	−	0.0881951i
$411$	11.0952	+	9.26444i	0.547286	+	0.456981i
$412$	−0.130735	−	0.909280i	−0.00644084	−	0.0447970i
$413$			2.63346i			0.129584i
$414$	−14.1823	−	2.42126i	−0.697022	−	0.118998i
$415$	−5.23995	−	23.8354i	−0.257219	−	1.17004i
$416$	1.87725	−	0.269908i	0.0920399	−	0.0132333i
$417$	−3.05083	+	3.65371i	−0.149400	+	0.178923i
$418$	−0.925405	−	3.15164i	−0.0452631	−	0.154152i
$419$	−24.8634	+	28.6938i	−1.21465	+	1.40179i	−0.324650	+	0.945834i	$0.605246\pi$
$419$	−24.8634	+	28.6938i	−1.21465	+	1.40179i	−0.890005	+	0.455951i	$0.849299\pi$
$420$	2.10023	+	0.734720i	0.102481	+	0.0358507i
$421$	5.69135	+	8.85592i	0.277380	+	0.431611i	0.951792	−	0.306744i	$-0.0992394\pi$
$421$	5.69135	+	8.85592i	0.277380	+	0.431611i	−0.674413	+	0.738355i	$0.735603\pi$
$422$	−11.6637	−	25.5400i	−0.567780	−	1.24327i
$423$	3.73684	+	20.6103i	0.181691	+	1.00211i
$424$	−1.10788	+	1.72390i	−0.0538036	+	0.0837200i
$425$	20.2857	−	6.05338i	0.984002	−	0.293632i
$426$	−18.7387	−	8.14705i	−0.907891	−	0.394726i
$427$	1.34141	−	2.08727i	0.0649152	−	0.101010i
$428$	8.88017	−	7.69471i	0.429239	−	0.371938i
$429$	14.0674	−	2.28578i	0.679180	−	0.110359i
$430$	−7.28075	+	7.31281i	−0.351109	+	0.352655i
$431$	31.8931	+	9.36465i	1.53624	+	0.451080i	0.936952	−	0.349457i	$-0.113634\pi$
$431$	31.8931	+	9.36465i	1.53624	+	0.451080i	0.599284	+	0.800537i	$0.295452\pi$
$432$	−5.18834	+	0.284821i	−0.249624	+	0.0137034i
$433$	−36.5857	+	10.7425i	−1.75820	+	0.516253i	−0.991987	−	0.126340i	$-0.959677\pi$
$433$	−36.5857	+	10.7425i	−1.75820	+	0.516253i	−0.766208	+	0.642593i	$0.777859\pi$
$434$	0.652450	−	1.42867i	0.0313186	−	0.0685781i
$435$	−17.6807	+	1.62904i	−0.847724	+	0.0781065i
$436$		−	2.20322i		−	0.105515i
$437$	−0.741457	+	3.55438i	−0.0354687	+	0.170029i
$438$	−2.46919	+	9.01579i	−0.117982	+	0.430791i
$439$	−1.54789	−	10.7658i	−0.0738770	−	0.513826i	−0.992837	−	0.119475i	$-0.961879\pi$
$439$	−1.54789	−	10.7658i	−0.0738770	−	0.513826i	0.918960	−	0.394350i	$-0.129030\pi$
$440$	2.04133	−	9.48412i	0.0973166	−	0.452138i
$441$	19.3925	+	4.93187i	0.923454	+	0.234851i
$442$	−5.25846	+	6.06859i	−0.250119	+	0.288653i
$443$	−23.6937	−	6.95711i	−1.12572	−	0.330542i	−0.334698	−	0.942325i	$-0.608634\pi$
$443$	−23.6937	−	6.95711i	−1.12572	−	0.330542i	−0.791026	+	0.611783i	$0.790452\pi$
$444$	1.18480	−	0.371545i	0.0562283	−	0.0176328i
$445$	−14.6697	−	19.5069i	−0.695410	−	0.924717i
$446$	3.73902	−	3.23988i	0.177048	−	0.153413i
$447$	−24.8825	−	27.6771i	−1.17690	−	1.30908i
$448$	−0.0817602	+	0.568655i	−0.00386281	+	0.0268664i
$449$	−16.8672	−	2.42514i	−0.796013	−	0.114449i	−0.267704	−	0.963501i	$-0.586265\pi$
$449$	−16.8672	−	2.42514i	−0.796013	−	0.114449i	−0.528309	+	0.849052i	$0.677174\pi$
$450$	11.7289	+	9.35053i	0.552907	+	0.440788i
$451$	2.98718	−	2.58841i	0.140661	−	0.121883i
$452$	−15.7492	+	7.19241i	−0.740780	+	0.338303i
$453$	12.9549	−	4.06257i	0.608676	−	0.190876i
$454$	−0.797948	+	2.71756i	−0.0374495	+	0.127541i
$455$	2.14091	+	1.16293i	0.100367	+	0.0545188i
$456$	0.0239702	+	1.31110i	0.00112251	+	0.0613981i
$457$	−2.74112	+	6.00221i	−0.128224	+	0.280771i	−0.962846	−	0.270052i	$-0.912959\pi$
$457$	−2.74112	+	6.00221i	−0.128224	+	0.280771i	0.834622	+	0.550824i	$0.185686\pi$
$458$	19.6412	−	2.82398i	0.917773	−	0.131956i
$459$	15.8119	−	15.2967i	0.738036	−	0.713991i
$460$	−6.93514	+	8.17948i	−0.323352	+	0.381370i
$461$		−	19.2937i		−	0.898596i	−0.893382	−	0.449298i	$-0.851674\pi$
$461$		−	19.2937i		−	0.898596i	0.893382	−	0.449298i	$-0.148326\pi$
$462$	−0.536181	+	4.28373i	−0.0249454	+	0.199297i
$463$	34.3737	+	15.6979i	1.59748	+	0.729545i	0.997513	−	0.0704797i	$-0.0224530\pi$
$463$	34.3737	+	15.6979i	1.59748	+	0.729545i	0.599967	+	0.800025i	$0.295180\pi$
$464$	−1.29159	−	4.39876i	−0.0599607	−	0.204208i
$465$	7.33206	−	7.63866i	0.340016	−	0.354234i
$466$	−5.87908	−	1.72625i	−0.272343	−	0.0799672i
$467$	10.4129	+	16.2028i	0.481852	+	0.749776i	0.994030	−	0.109103i	$-0.0347978\pi$
$467$	10.4129	+	16.2028i	0.481852	+	0.749776i	−0.512179	+	0.858879i	$0.671161\pi$
$468$	−5.65759	−	0.603328i	−0.261522	−	0.0278888i
$469$	3.97511	+	4.58752i	0.183553	+	0.211832i
$470$	14.6401	+	5.42386i	0.675296	+	0.250184i
$471$	1.20458	−	2.77061i	0.0555043	−	0.127663i
$472$	−4.53723	−	0.652356i	−0.208843	−	0.0300271i
$473$	−16.8436	−	10.8247i	−0.774470	−	0.497721i
$474$	14.8080	−	7.09254i	0.680155	−	0.325771i
$475$	2.46636	−	2.87173i	0.113164	−	0.131764i
$476$	−1.31506	−	2.04627i	−0.0602755	−	0.0937905i
$477$	4.49580	−	4.19297i	0.205848	−	0.191983i
$478$	15.4131	+	13.3555i	0.704978	+	0.610867i
$479$	7.04036	−	2.06724i	0.321682	−	0.0944545i	−0.116905	−	0.993143i	$-0.537297\pi$
$479$	7.04036	−	2.06724i	0.321682	−	0.0944545i	0.438587	+	0.898689i	$0.355479\pi$
$480$	−1.78613	+	3.43653i	−0.0815254	+	0.156855i
$481$	1.34579	−	0.193495i	0.0613627	−	0.00882263i
$482$			10.6776i			0.486351i
$483$	2.75636	−	3.89565i	0.125419	−	0.177258i
$484$	7.82312			0.355597
$485$	6.11340	+	16.2813i	0.277595	+	0.739297i
$486$	15.2954	+	3.00824i	0.693815	+	0.136457i
$487$	0.132000	+	0.449551i	0.00598149	+	0.0203711i	0.962430	−	0.271531i	$-0.0875300\pi$
$487$	0.132000	+	0.449551i	0.00598149	+	0.0203711i	−0.956448	+	0.291902i	$0.905712\pi$
$488$	3.26390	+	2.82819i	0.147750	+	0.128026i
$489$	12.7230	−	20.6165i	0.575354	−	0.932310i
$490$	10.5229	−	10.5693i	0.475377	−	0.477470i
$491$	−6.87073	+	3.13776i	−0.310072	+	0.141605i	−0.564373	−	0.825520i	$-0.690882\pi$
$491$	−6.87073	+	3.13776i	−0.310072	+	0.141605i	0.254301	+	0.967125i	$0.418155\pi$
$492$	−1.42315	+	0.681641i	−0.0641606	+	0.0307307i
$493$	16.3290	+	10.4940i	0.735421	+	0.472626i
$494$	−0.204346	+	1.42125i	−0.00919394	+	0.0639453i
$495$	−12.9478	+	26.0652i	−0.581960	+	1.17154i
$496$	2.29985	+	1.47803i	0.103266	+	0.0663653i
$497$	5.12204	−	4.43828i	0.229755	−	0.199084i
$498$	−18.6590	+	3.03186i	−0.836130	+	0.135861i
$499$	−13.8982	+	8.93186i	−0.622171	+	0.399845i	−0.813404	−	0.581700i	$-0.802388\pi$
$499$	−13.8982	+	8.93186i	−0.622171	+	0.399845i	0.191233	+	0.981545i	$0.438751\pi$
$500$	10.4494	−	3.97609i	0.467313	−	0.177816i
$501$	6.95902	−	4.65420i	0.310906	−	0.207934i
$502$	29.5540	−	8.67784i	1.31906	−	0.387311i
$503$	23.3427	+	10.6603i	1.04080	+	0.475317i	0.861117	−	0.508407i	$-0.169765\pi$
$503$	23.3427	+	10.6603i	1.04080	+	0.475317i	0.179683	+	0.983725i	$0.442493\pi$
$504$	0.658186	−	1.59288i	0.0293179	−	0.0709525i
$505$	−6.89407	−	31.3597i	−0.306782	−	1.39549i
$506$	−18.3464	−	9.81533i	−0.815598	−	0.436345i
$507$	15.7081	+	4.30205i	0.697623	+	0.191061i
$508$	−16.3010	+	2.34373i	−0.723241	+	0.103986i
$509$	−29.4046	−	13.4286i	−1.30334	−	0.595214i	−0.361841	−	0.932240i	$-0.617852\pi$
$509$	−29.4046	−	13.4286i	−1.30334	−	0.595214i	−0.941495	+	0.337026i	$0.890579\pi$
$510$	−3.81300	−	15.9485i	−0.168842	−	0.706210i
$511$	−2.34325	−	2.03044i	−0.103659	−	0.0898212i
$512$	−0.959493	−	0.281733i	−0.0424040	−	0.0124509i
$513$	0.899760	−	3.82969i	0.0397254	−	0.169085i
$514$	3.62655	+	7.94103i	0.159960	+	0.350264i
$515$	1.64711	+	1.22737i	0.0725803	+	0.0540845i
$516$	5.34401	+	5.94420i	0.235257	+	0.261679i
$517$	−4.31105	+	29.9840i	−0.189600	+	1.31870i
$518$	−0.0586133	+	0.407664i	−0.00257532	+	0.0179117i
$519$	−28.9279	−	32.1768i	−1.26979	−	1.41241i
$520$	−2.53397	+	3.40054i	−0.111122	+	0.149123i
$521$	10.4930	+	22.9765i	0.459706	+	1.00662i	0.987554	+	0.157278i	$0.0502718\pi$
$521$	10.4930	+	22.9765i	0.459706	+	1.00662i	−0.527848	+	0.849339i	$0.677001\pi$
$522$	0.502724	+	13.7442i	0.0220036	+	0.601568i
$523$	12.4314	+	3.65020i	0.543588	+	0.159612i	0.541987	−	0.840387i	$-0.317672\pi$
$523$	12.4314	+	3.65020i	0.543588	+	0.159612i	0.00160124	+	0.999999i	$0.499490\pi$
$524$	3.49954	+	3.03237i	0.152878	+	0.132470i
$525$	−4.47770	+	2.16891i	−0.195423	+	0.0946589i
$526$	24.2997	+	11.0973i	1.05952	+	0.483865i
$527$	−11.4571	+	1.64728i	−0.499078	+	0.0717566i
$528$	−7.24771	−	1.98496i	−0.315416	−	0.0863842i
$529$	12.7636	+	19.1335i	0.554938	+	0.831892i
$530$	−0.983843	−	4.47529i	−0.0427354	−	0.194394i
$531$	12.7094	+	5.25160i	0.551542	+	0.227900i
$532$	−0.395646	−	0.180685i	−0.0171534	−	0.00783370i
$533$	−1.65785	+	0.486789i	−0.0718096	+	0.0210852i
$534$	−15.7151	+	10.5103i	−0.680061	+	0.454825i
$535$	−1.81679	+	26.2113i	−0.0785467	+	1.13321i
$536$	−8.88864	+	5.71238i	−0.383931	+	0.246737i
$537$	43.9265	−	7.13752i	1.89557	−	0.308007i
$538$	2.30705	−	1.99907i	0.0994642	−	0.0861862i
$539$	24.3442	+	15.6451i	1.04858	+	0.673880i
$540$	7.73411	−	8.67084i	0.332823	−	0.373134i
$541$	−6.07479	+	42.2511i	−0.261176	+	1.81652i	0.262876	+	0.964830i	$0.415329\pi$
$541$	−6.07479	+	42.2511i	−0.261176	+	1.81652i	−0.524051	+	0.851687i	$0.675580\pi$
$542$	13.6259	+	8.75683i	0.585282	+	0.376138i
$543$	−12.5031	+	5.98856i	−0.536559	+	0.256994i
$544$	3.85132	−	1.75884i	0.165124	−	0.0754096i
$545$	3.49124	+	3.47593i	0.149548	+	0.148893i
$546$	0.991107	−	1.60600i	0.0424155	−	0.0687305i
$547$	25.1502	+	21.7928i	1.07535	+	0.931792i	0.997872	−	0.0652022i	$-0.0207692\pi$
$547$	25.1502	+	21.7928i	1.07535	+	0.931792i	0.0774734	+	0.996994i	$0.475315\pi$
$548$	−2.35115	−	8.00728i	−0.100436	−	0.342054i
$549$	−7.39843	−	10.6362i	−0.315757	−	0.453942i
$550$	11.8081	+	18.1974i	0.503499	+	0.775942i
$551$	3.47087			0.147864
$552$	6.02910	+	5.71401i	0.256616	+	0.243205i
$553$			5.44598i			0.231587i
$554$	−21.6554	+	3.11357i	−0.920049	+	0.132283i
$555$	−1.28046	+	2.46362i	−0.0543527	+	0.104575i
$556$	2.63684	−	0.774245i	0.111827	−	0.0328353i
$557$	−17.4925	−	15.1573i	−0.741181	−	0.642237i	0.200133	−	0.979769i	$-0.435862\pi$
$557$	−17.4925	−	15.1573i	−0.741181	−	0.642237i	−0.941314	+	0.337532i	$0.890408\pi$
$558$	−5.59383	−	5.99783i	−0.236806	−	0.253909i
$559$	4.73192	+	7.36301i	0.200139	+	0.311422i
$560$	−0.772105	−	1.02670i	−0.0326274	−	0.0433861i
$561$	28.6947	−	13.7438i	1.21149	−	0.580264i
$562$	18.5880	+	11.9458i	0.784088	+	0.503903i
$563$	5.50318	+	0.791238i	0.231932	+	0.0333467i	0.257301	−	0.966331i	$-0.417167\pi$
$563$	5.50318	+	0.791238i	0.231932	+	0.0333467i	−0.0253690	+	0.999678i	$0.508076\pi$
$564$	4.82185	−	11.0905i	0.203037	−	0.466995i
$565$	13.4497	−	36.3035i	0.565834	−	1.52730i
$566$	7.14266	+	8.24307i	0.300228	+	0.346482i
$567$	−3.09145	+	4.14454i	−0.129829	+	0.174054i
$568$	6.37797	+	9.92432i	0.267614	+	0.416415i
$569$	−0.643026	−	0.188810i	−0.0269571	−	0.00791531i	0.268226	−	0.963356i	$-0.413563\pi$
$569$	−0.643026	−	0.188810i	−0.0269571	−	0.00791531i	−0.295183	+	0.955441i	$0.595381\pi$
$570$	−2.11540	−	2.03049i	−0.0886045	−	0.0850481i
$571$	1.67479	+	5.70380i	0.0700876	+	0.238696i	0.987085	−	0.160196i	$-0.0512127\pi$
$571$	1.67479	+	5.70380i	0.0700876	+	0.238696i	−0.916998	+	0.398893i	$0.869395\pi$
$572$	−7.48475	−	3.41817i	−0.312953	−	0.142921i
$573$	−1.91218	+	15.2770i	−0.0798823	+	0.638206i
$574$		−	0.523395i		−	0.0218461i
$575$	−2.01998	−	23.8939i	−0.0842391	−	0.996446i
$576$	2.58136	+	1.52859i	0.107557	+	0.0636912i
$577$	2.33005	−	0.335011i	0.0970015	−	0.0139467i	−0.0936432	−	0.995606i	$-0.529851\pi$
$577$	2.33005	−	0.335011i	0.0970015	−	0.0139467i	0.190645	+	0.981659i	$0.438942\pi$
$578$	−0.384744	+	0.842472i	−0.0160032	+	0.0350422i
$579$	0.514036	+	28.1164i	0.0213626	+	1.16848i
$580$	9.00802	+	4.89309i	0.374038	+	0.203174i
$581$	1.76651	−	6.01617i	0.0732871	−	0.249593i
$582$	12.8540	−	4.03091i	0.532815	−	0.167087i
$583$	8.08718	−	3.69329i	0.334937	−	0.152960i
$584$	4.07875	−	3.53425i	0.168780	−	0.146248i
$585$	9.88180	−	8.01323i	0.408562	−	0.331306i
$586$	3.78289	+	0.543897i	0.156270	+	0.0224682i
$587$	−0.0775637	+	0.539468i	−0.00320140	+	0.0222662i	−0.991360	−	0.131173i	$-0.958126\pi$
$587$	−0.0775637	+	0.539468i	−0.00320140	+	0.0222662i	0.988158	+	0.153439i	$0.0490348\pi$
$588$	−7.72373	−	8.59119i	−0.318521	−	0.354295i
$589$	−1.56423	+	1.35541i	−0.0644529	+	0.0558488i
$590$	8.19195	−	6.16055i	0.337257	−	0.253626i
$591$	−24.7650	+	7.76610i	−1.01869	+	0.319455i
$592$	−0.687854	−	0.201972i	−0.0282706	−	0.00830100i
$593$	−18.9862	+	21.9112i	−0.779670	+	0.899787i	−0.997086	−	0.0762921i	$-0.975692\pi$
$593$	−18.9862	+	21.9112i	−0.779670	+	0.899787i	0.217416	+	0.976079i	$0.430237\pi$
$594$	19.6046	+	11.1302i	0.804388	+	0.456679i
$595$	5.31725	+	1.14447i	0.217986	+	0.0469185i
$596$	3.05802	+	21.2690i	0.125261	+	0.871212i
$597$	6.88235	−	25.1296i	0.281676	−	1.02849i
$598$	5.51279	+	7.23454i	0.225435	+	0.295842i
$599$		−	41.0074i		−	1.67552i	−0.546041	−	0.837758i	$-0.683866\pi$
$599$		−	41.0074i		−	1.67552i	0.546041	−	0.837758i	$-0.316134\pi$
$600$	−2.62765	−	8.25200i	−0.107273	−	0.336886i
$601$	4.61828	−	10.1126i	0.188383	−	0.412502i	−0.791749	−	0.610847i	$-0.790829\pi$
$601$	4.61828	−	10.1126i	0.188383	−	0.412502i	0.980132	+	0.198344i	$0.0635564\pi$
$602$	−2.54387	+	0.746949i	−0.103681	+	0.0304434i
$603$	30.0671	−	10.0361i	1.22443	−	0.408700i
$604$	−7.52116	−	2.20841i	−0.306032	−	0.0898590i
$605$	−12.3422	+	12.3966i	−0.501783	+	0.503993i
$606$	−24.5492	+	3.98894i	−0.997242	+	0.162040i
$607$	8.31904	−	7.20849i	0.337659	−	0.292584i	−0.469482	−	0.882942i	$-0.655559\pi$
$607$	8.31904	−	7.20849i	0.337659	−	0.292584i	0.807141	+	0.590359i	$0.201014\pi$
$608$	0.409315	−	0.636907i	0.0165999	−	0.0258300i
$609$	−4.18355	−	1.81889i	−0.169526	−	0.0737053i
$610$	−9.63091	+	0.710088i	−0.389944	+	0.0287506i
$611$	7.15916	−	11.1399i	0.289629	−	0.450671i
$612$	−12.4980	+	2.26600i	−0.505203	+	0.0915978i
$613$	−1.45018	−	3.17544i	−0.0585721	−	0.128255i	0.878083	−	0.478509i	$-0.158823\pi$
$613$	−1.45018	−	3.17544i	−0.0585721	−	0.128255i	−0.936655	+	0.350254i	$0.886095\pi$
$614$	10.8342	+	16.8583i	0.437233	+	0.680347i
$615$	1.16511	−	3.33053i	0.0469819	−	0.134300i
$616$	1.63225	−	1.88372i	0.0657652	−	0.0758971i
$617$	11.5226	+	39.2424i	0.463883	+	1.57984i	0.776601	+	0.629993i	$0.216942\pi$
$617$	11.5226	+	39.2424i	0.463883	+	1.57984i	−0.312718	+	0.949846i	$0.601239\pi$
$618$	1.01980	−	1.22133i	0.0410225	−	0.0491291i
$619$	−16.3081	+	2.34475i	−0.655477	+	0.0942433i	−0.462026	−	0.886867i	$-0.652877\pi$
$619$	−16.3081	+	2.34475i	−0.655477	+	0.0942433i	−0.193451	+	0.981110i	$0.561968\pi$
$620$	−5.97048	+	1.31254i	−0.239780	+	0.0527130i
$621$	−13.3043	−	21.0712i	−0.533882	−	0.845559i
$622$			30.4598i			1.22133i
$623$	−0.892438	−	6.20704i	−0.0357548	−	0.248680i
$624$	2.52149	+	2.10543i	0.100941	+	0.0842848i
$625$	−10.1851	+	22.8312i	−0.407405	+	0.913248i
$626$	−7.66085	+	8.84109i	−0.306189	+	0.353361i
$627$	2.98784	−	4.84153i	0.119323	−	0.193352i
$628$	−1.46736	+	0.943017i	−0.0585541	+	0.0376305i
$629$	2.76098	−	1.26090i	0.110088	−	0.0502753i
$630$	1.48570	+	3.55599i	0.0591916	+	0.141674i
$631$	1.99723	−	3.10775i	0.0795086	−	0.123718i	−0.799222	−	0.601036i	$-0.794755\pi$
$631$	1.99723	−	3.10775i	0.0795086	−	0.123718i	0.878730	+	0.477318i	$0.158391\pi$
$632$	−9.38299	−	1.34907i	−0.373235	−	0.0536632i
$633$	19.3901	−	44.5984i	0.770689	−	1.77263i
$634$	−17.3033	−	11.1202i	−0.687202	−	0.441638i
$635$	22.0036	−	29.5284i	0.873186	−	1.17180i
$636$	−3.50338	+	0.569257i	−0.138918	+	0.0225725i
$637$	−6.83907	−	10.6418i	−0.270974	−	0.421644i
$638$	−5.60366	+	19.0843i	−0.221851	+	0.755555i
$639$	−11.2054	−	33.5704i	−0.443280	−	1.32803i
$640$	1.96019	−	1.07594i	0.0774833	−	0.0425304i
$641$	10.9234	−	23.9190i	0.431450	−	0.944743i	−0.561639	−	0.827382i	$-0.689829\pi$
$641$	10.9234	−	23.9190i	0.431450	−	0.944743i	0.993089	−	0.117361i	$-0.0374435\pi$
$642$	20.1943	+	2.52766i	0.797005	+	0.0997586i
$643$	−5.68433			−0.224168			−0.112084	−	0.993699i	$-0.535753\pi$
$643$	−5.68433			−0.224168			−0.112084	+	0.993699i	$0.535753\pi$
$644$	−2.57318	+	0.984873i	−0.101397	+	0.0388094i
$645$	−17.8503	−	0.909763i	−0.702853	−	0.0358219i
$646$	0.456187	+	3.17285i	0.0179484	+	0.124834i
$647$	13.7095	−	30.0195i	0.538974	−	1.18019i	−0.422769	−	0.906237i	$-0.638942\pi$
$647$	13.7095	−	30.0195i	0.538974	−	1.18019i	0.961744	−	0.273951i	$-0.0883307\pi$
$648$	−6.37491	−	6.35299i	−0.250430	−	0.249569i
$649$	15.0300	+	13.0235i	0.589978	+	0.511219i
$650$	−1.39077	−	9.38024i	−0.0545506	−	0.367923i
$651$	2.59571	−	0.813996i	0.101734	−	0.0319030i
$652$	−12.7231	+	5.81044i	−0.498274	+	0.227554i
$653$	−18.3593	−	21.1877i	−0.718453	−	0.829139i	0.272667	−	0.962108i	$-0.412094\pi$
$653$	−18.3593	−	21.1877i	−0.718453	−	0.829139i	−0.991120	+	0.132969i	$0.957549\pi$
$654$	2.83784	−	2.55130i	0.110968	−	0.0997639i
$655$	−10.3262	+	0.761353i	−0.403479	+	0.0297485i
$656$	0.901768	+	0.129655i	0.0352081	+	0.00506217i
$657$	−14.4720	+	7.25977i	−0.564608	+	0.283231i
$658$	2.62681	+	3.03150i	0.102404	+	0.118180i
$659$	12.2381	+	26.7977i	0.476729	+	1.04389i	0.983350	+	0.181722i	$0.0581670\pi$
$659$	12.2381	+	26.7977i	0.476729	+	1.04389i	−0.506621	+	0.862169i	$0.669106\pi$
$660$	14.5798	−	8.35320i	0.567518	−	0.325148i
$661$	3.70112	−	12.6048i	0.143957	−	0.490272i	−0.855672	−	0.517518i	$-0.826856\pi$
$661$	3.70112	−	12.6048i	0.143957	−	0.490272i	0.999629	+	0.0272470i	$0.00867405\pi$
$662$	13.2938	−	15.3419i	0.516678	−	0.596278i
$663$	−13.9059	+	0.254233i	−0.540059	+	0.00987359i
$664$	9.92779	+	4.53387i	0.385273	+	0.175948i
$665$	0.910511	−	0.341884i	0.0353081	−	0.0132577i
$666$	1.85056	+	1.09583i	0.0717077	+	0.0424627i
$667$	15.4133	−	15.6790i	0.596804	−	0.607092i
$668$	−4.83355			−0.187016
$669$	8.50286	+	1.06428i	0.328739	+	0.0411473i
$670$	4.97137	−	23.0972i	0.192061	−	0.892323i
$671$	−5.27889	−	17.9782i	−0.203789	−	0.694042i
$672$	−0.827130	+	0.553186i	−0.0319072	+	0.0213396i
$673$	1.70195	−	5.79630i	0.0656052	−	0.223431i	−0.920165	−	0.391532i	$-0.871945\pi$
$673$	1.70195	−	5.79630i	0.0656052	−	0.223431i	0.985770	+	0.168101i	$0.0537635\pi$
$674$	−16.1017	+	10.3479i	−0.620214	+	0.398587i
$675$	1.53808	+	25.9352i	0.0592008	+	0.998246i
$676$	−6.15770	−	7.10637i	−0.236835	−	0.273322i
$677$	20.1519	−	31.3569i	0.774500	−	1.20515i	−0.199788	−	0.979839i	$-0.564025\pi$
$677$	20.1519	−	31.3569i	0.774500	−	1.20515i	0.974288	−	0.225306i	$-0.0723382\pi$
$678$	−27.5016	−	11.9569i	−1.05619	−	0.459203i
$679$	−0.635898	+	4.42277i	−0.0244035	+	0.169730i
$680$	−3.28900	+	8.87768i	−0.126128	+	0.340444i
$681$	−4.42435	+	2.11912i	−0.169542	+	0.0812047i
$682$	−4.92721	−	10.7891i	−0.188673	−	0.413135i
$683$	−26.2398	+	16.8633i	−1.00404	+	0.645255i	−0.935843	−	0.352417i	$-0.885360\pi$
$683$	−26.2398	+	16.8633i	−1.00404	+	0.645255i	−0.0681933	+	0.997672i	$0.521723\pi$
$684$	−1.66100	+	1.54912i	−0.0635100	+	0.0592321i
$685$	16.3977	+	8.90712i	0.626525	+	0.340324i
$686$	7.53530	−	2.21256i	0.287699	−	0.0844760i
$687$	26.3817	+	22.0286i	1.00653	+	0.840443i
$688$	−0.656769	−	4.56793i	−0.0250391	−	0.174151i
$689$	−3.88643			−0.148061
$690$	−18.5664	+	0.538993i	−0.706809	+	0.0205191i
$691$	23.5950			0.897594			0.448797	−	0.893634i	$-0.351853\pi$
$691$	23.5950			0.897594			0.448797	+	0.893634i	$0.351853\pi$
$692$	3.55519	+	24.7269i	0.135148	+	0.939974i
$693$	−6.13853	+	4.26990i	−0.233184	+	0.162200i
$694$	−19.5629	+	5.74418i	−0.742596	+	0.218046i
$695$	−2.93316	+	5.39985i	−0.111261	+	0.204828i
$696$	4.17015	−	6.75736i	0.158069	−	0.256137i
$697$	−3.24496	+	2.08541i	−0.122911	+	0.0789904i
$698$	3.92459	+	8.59366i	0.148548	+	0.325275i
$699$	−4.58443	−	9.57151i	−0.173399	−	0.362028i
$700$	2.84504	+	0.396303i	0.107532	+	0.0149788i
$701$	2.27831	−	15.8460i	0.0860507	−	0.598496i	−0.900477	−	0.434903i	$-0.856783\pi$
$701$	2.27831	−	15.8460i	0.0860507	−	0.598496i	0.986528	−	0.163593i	$-0.0523083\pi$
$702$	−5.77432	−	7.98588i	−0.217938	−	0.301408i
$703$	0.293435	−	0.456594i	0.0110671	−	0.0172208i
$704$	2.84115	+	3.27887i	0.107080	+	0.123577i
$705$	9.96690	+	25.1378i	0.375375	+	0.946746i
$706$	0.286025	−	0.183817i	0.0107647	−	0.00691806i
$707$	2.32415	−	7.91532i	0.0874086	−	0.297686i
$708$	−4.41381	−	6.59958i	−0.165881	−	0.248027i
$709$	3.93294	+	13.3944i	0.147705	+	0.503036i	0.999793	−	0.0203625i	$-0.00648203\pi$
$709$	3.93294	+	13.3944i	0.147705	+	0.503036i	−0.852088	+	0.523399i	$0.824664\pi$
$710$	−25.7884	−	5.55062i	−0.967823	−	0.208311i
$711$	26.2831	+	10.8603i	0.985692	+	0.407293i
$712$	10.9153			0.409069
$713$	−0.823550	+	13.0851i	−0.0308422	+	0.490043i
$714$	1.11286	−	4.06341i	0.0416478	−	0.152069i
$715$	17.2249	−	6.46769i	0.644174	−	0.241878i
$716$	−23.3717	−	10.6735i	−0.873441	−	0.398887i
$717$	0.645704	+	35.3183i	0.0241143	+	1.31899i
$718$	−19.9323	+	23.0031i	−0.743866	+	0.858467i
$719$	11.4827	−	39.1066i	0.428234	−	1.45843i	−0.409479	−	0.912320i	$-0.634289\pi$
$719$	11.4827	−	39.1066i	0.428234	−	1.45843i	0.837713	−	0.546111i	$-0.183892\pi$
$720$	−6.49473	+	1.67885i	−0.242044	+	0.0625671i
$721$	0.219237	+	0.480063i	0.00816483	+	0.0178785i
$722$	−12.0670	−	13.9261i	−0.449087	−	0.518274i
$723$	−13.7532	+	12.3646i	−0.511488	+	0.459843i
$724$	7.92249	+	1.13908i	0.294437	+	0.0423337i
$725$	−21.9652	+	6.55455i	−0.815768	+	0.243430i
$726$	9.05910	+	10.0765i	0.336215	+	0.373975i
$727$	9.06946	+	10.4667i	0.336368	+	0.388189i	0.898584	−	0.438801i	$-0.144597\pi$
$727$	9.06946	+	10.4667i	0.336368	+	0.388189i	−0.562217	+	0.826990i	$0.690051\pi$
$728$	−0.991113	+	0.452626i	−0.0367331	+	0.0167754i
$729$	13.8372	+	23.1847i	0.512489	+	0.858694i
$730$	−0.834469	+	12.0391i	−0.0308851	+	0.445586i
$731$	14.7667	+	12.7954i	0.546167	+	0.473256i
$732$	0.136736	+	7.47907i	0.00505390	+	0.276434i
$733$	−0.916145	+	2.00608i	−0.0338386	+	0.0740962i	−0.925797	−	0.378022i	$-0.876604\pi$
$733$	−0.916145	+	2.00608i	−0.0338386	+	0.0740962i	0.891958	+	0.452118i	$0.149332\pi$
$734$	3.68351	+	25.6194i	0.135961	+	0.945629i
$735$	25.7991	+	1.31489i	0.951614	+	0.0485003i
$736$	−1.05943	−	4.67735i	−0.0390512	−	0.172409i
$737$	45.8410			1.68858
$738$	−2.52598	−	1.04375i	−0.0929825	−	0.0384209i
$739$	−8.91485	+	19.5208i	−0.327938	+	0.718084i	−0.999744	−	0.0226436i	$-0.992792\pi$
$739$	−8.91485	+	19.5208i	−0.327938	+	0.718084i	0.671806	+	0.740727i	$0.265519\pi$
$740$	1.40525	−	0.771336i	0.0516579	−	0.0283549i
$741$	−2.06727	+	1.38259i	−0.0759431	+	0.0507908i
$742$	0.331676	−	1.12958i	0.0121762	−	0.0414684i
$743$	−17.5658	−	27.3330i	−0.644428	−	1.00275i	−0.997737	−	0.0672427i	$-0.978580\pi$
$743$	−17.5658	−	27.3330i	−0.644428	−	1.00275i	0.353309	−	0.935507i	$-0.385057\pi$
$744$	0.759444	+	4.67385i	0.0278426	+	0.171352i
$745$	−38.5275	−	28.7095i	−1.41154	−	1.05183i
$746$	−1.43767	−	0.923935i	−0.0526369	−	0.0338277i
$747$	−25.5121	−	20.5228i	−0.933440	−	0.750889i
$748$	−18.1822	−	2.61421i	−0.664807	−	0.0955848i
$749$	−3.64959	+	5.67887i	−0.133353	+	0.207501i
$750$	17.2217	+	8.85507i	0.628848	+	0.323341i
$751$	−29.0480	+	13.2658i	−1.05998	+	0.484074i	−0.867608	−	0.497249i	$-0.834344\pi$
$751$	−29.0480	+	13.2658i	−1.05998	+	0.484074i	−0.192367	+	0.981323i	$0.561616\pi$
$752$	−5.87373	+	3.77482i	−0.214193	+	0.137653i
$753$	45.4007	+	28.0180i	1.65449	+	1.02103i
$754$	5.69382	−	6.57102i	0.207357	−	0.239302i
$755$	15.3653	−	8.43397i	0.559201	−	0.306944i
$756$	2.81387	−	0.996766i	0.102340	−	0.0362520i
$757$	−5.12196	−	35.6240i	−0.186161	−	1.29478i	−0.841835	−	0.539734i	$-0.818525\pi$
$757$	−5.12196	−	35.6240i	−0.186161	−	1.29478i	0.655674	−	0.755044i	$-0.272384\pi$
$758$			16.1813i			0.587730i
$759$	−8.60239	−	34.9971i	−0.312247	−	1.27031i
$760$	0.363488	+	1.65343i	0.0131851	+	0.0599761i
$761$	−19.8969	+	2.86075i	−0.721263	+	0.103702i	−0.493165	−	0.869936i	$-0.664160\pi$
$761$	−19.8969	+	2.86075i	−0.721263	+	0.103702i	−0.228099	+	0.973638i	$0.573251\pi$
$762$	−21.8953	−	18.2824i	−0.793182	−	0.662302i
$763$	0.356604	+	1.21448i	0.0129099	+	0.0439672i
$764$	5.82106	−	6.71787i	0.210599	−	0.243044i
$765$	16.1269	−	23.3795i	0.583070	−	0.845287i
$766$	14.8390	+	23.0900i	0.536155	+	0.834274i
$767$	−3.61146	−	7.90799i	−0.130402	−	0.285541i
$768$	−0.748199	−	1.56211i	−0.0269983	−	0.0563679i
$769$	−26.3684	+	41.0300i	−0.950869	+	1.47958i	−0.0749124	+	0.997190i	$0.523868\pi$
$769$	−26.3684	+	41.0300i	−0.950869	+	1.47958i	−0.875956	+	0.482390i	$0.839769\pi$
$770$	0.409817	+	5.55834i	0.0147688	+	0.200309i
$771$	−6.02890	+	13.8668i	−0.217125	+	0.499400i
$772$	8.77768	−	13.6583i	0.315916	−	0.491574i
$773$	−32.9457	+	28.5476i	−1.18498	+	1.02679i	−0.185954	+	0.982558i	$0.559538\pi$
$773$	−32.9457	+	28.5476i	−1.18498	+	1.02679i	−0.999021	+	0.0442290i	$0.985917\pi$
$774$	−1.46808	+	13.7666i	−0.0527690	+	0.494832i
$775$	7.33953	−	11.5316i	0.263644	−	0.414228i
$776$	−7.46255	−	2.19120i	−0.267890	−	0.0786596i
$777$	−0.592964	+	0.396575i	−0.0212724	+	0.0142270i
$778$	31.4664	−	9.23935i	1.12812	−	0.331247i
$779$	−0.286530	+	0.627412i	−0.0102660	+	0.0224794i
$780$	−7.31435	+	0.673921i	−0.261896	+	0.0241302i
$781$		−	51.1823i		−	1.83145i
$782$	16.3585	+	12.0291i	0.584980	+	0.430160i
$783$	−17.1210	+	16.5632i	−0.611855	+	0.591920i
$784$	0.949232	+	6.60206i	0.0339012	+	0.235788i
$785$	0.820688	−	3.81296i	0.0292916	−	0.136090i
$786$	0.146607	+	8.01903i	0.00522931	+	0.286029i
$787$	−1.46018	+	1.68513i	−0.0520497	+	0.0600686i	−0.781177	−	0.624309i	$-0.785381\pi$
$787$	−1.46018	+	1.68513i	−0.0520497	+	0.0600686i	0.729128	+	0.684378i	$0.239926\pi$
$788$	14.3776	+	4.22165i	0.512182	+	0.150390i
$789$	13.8450	+	44.1496i	0.492895	+	1.57177i
$790$	16.9409	−	12.7400i	0.602731	−	0.453269i
$791$	7.51730	−	6.51378i	0.267285	−	0.231603i
$792$	−5.83606	−	11.6339i	−0.207375	−	0.413394i
$793$	−1.16567	+	8.10741i	−0.0413942	+	0.287903i
$794$	−14.2628	−	2.05068i	−0.506167	−	0.0727758i
$795$	4.62510	−	6.44958i	0.164035	−	0.228743i
$796$	−11.3686	+	9.85099i	−0.402951	+	0.349159i
$797$	17.7550	−	8.10843i	0.628914	−	0.287215i	−0.0753460	−	0.997157i	$-0.524006\pi$
$797$	17.7550	−	8.10843i	0.628914	−	0.287215i	0.704260	+	0.709942i	$0.251279\pi$
$798$	−0.225423	−	0.718841i	−0.00797989	−	0.0254467i
$799$	8.32853	−	28.3644i	0.294642	−	1.00346i
$800$	−1.38757	+	4.80361i	−0.0490579	+	0.169833i
$801$	−31.7357	−	8.07096i	−1.12133	−	0.285174i
$802$	−9.61700	+	21.0583i	−0.339588	+	0.743594i
$803$	−23.1767	+	3.33231i	−0.817888	+	0.117595i
$804$	−17.6508	−	4.83408i	−0.622494	−	0.170485i
$805$	2.49896	−	5.63127i	0.0880769	−	0.198476i
$806$			5.18488i			0.182630i
$807$	5.24644	+	0.656681i	0.184684	+	0.0231163i
$808$	13.0617	+	5.96510i	0.459510	+	0.209851i
$809$	4.71888	+	16.0710i	0.165907	+	0.565027i	0.999912	+	0.0132704i	$0.00422424\pi$
$809$	4.71888	+	16.0710i	0.165907	+	0.565027i	−0.834005	+	0.551757i	$0.813958\pi$
$810$	20.1245	−	0.0788663i	0.707101	−	0.00277108i
$811$	4.67490	+	1.37267i	0.164158	+	0.0482011i	0.362779	−	0.931875i	$-0.381828\pi$
$811$	4.67490	+	1.37267i	0.164158	+	0.0482011i	−0.198621	+	0.980076i	$0.563646\pi$
$812$	1.42393	+	2.21568i	0.0499702	+	0.0777552i
$813$	4.49947	+	27.6911i	0.157803	+	0.971169i
$814$	2.03680	+	2.35060i	0.0713899	+	0.0823884i
$815$	10.8654	−	29.3280i	0.380600	−	1.02732i
$816$	6.72525	+	2.92395i	0.235431	+	0.102359i
$817$	3.45834	+	0.497235i	0.120992	+	0.0173960i
$818$	−19.0803	−	12.2622i	−0.667127	−	0.428737i
$819$	3.21629	−	0.583142i	0.112386	−	0.0203766i
$820$	−1.62814	+	1.22440i	−0.0568570	+	0.0427579i
$821$	19.9985	+	31.1183i	0.697954	+	1.08604i	0.991502	+	0.130093i	$0.0415277\pi$
$821$	19.9985	+	31.1183i	0.697954	+	1.08604i	−0.293548	+	0.955944i	$0.594836\pi$
$822$	7.59113	−	12.3007i	0.264771	−	0.429038i
$823$	12.4013	+	10.7458i	0.432281	+	0.374574i	0.843649	−	0.536896i	$-0.180403\pi$
$823$	12.4013	+	10.7458i	0.432281	+	0.374574i	−0.411367	+	0.911470i	$0.634949\pi$
$824$	−0.881420	+	0.258808i	−0.0307057	+	0.00901601i
$825$	−9.76546	+	36.2818i	−0.339990	+	1.26317i
$826$	2.60665	−	0.374780i	0.0906970	−	0.0130403i
$827$		−	20.8536i		−	0.725152i	−0.931954	−	0.362576i	$-0.881897\pi$
$827$		−	20.8536i		−	0.725152i	0.931954	−	0.362576i	$-0.118103\pi$
$828$	−0.378262	+	14.3825i	−0.0131455	+	0.499827i
$829$	45.9011			1.59421			0.797106	−	0.603840i	$-0.206363\pi$
$829$	45.9011			1.59421			0.797106	+	0.603840i	$0.206363\pi$
$830$	−22.8471	+	8.57875i	−0.793034	+	0.297773i
$831$	−29.0871	−	24.2876i	−1.00902	−	0.842528i
$832$	−0.534322	−	1.81973i	−0.0185243	−	0.0630879i
$833$	−21.3424	−	18.4933i	−0.739472	−	0.640756i
$834$	4.05069	+	2.49980i	0.140264	+	0.0865608i
$835$	7.62570	−	7.65928i	0.263898	−	0.265060i
$836$	−2.98786	+	1.36451i	−0.103337	+	0.0471926i
$837$	1.24788	−	14.1505i	0.0431330	−	0.489114i
$838$	31.9402	+	20.5267i	1.10336	+	0.709084i
$839$	5.15148	−	35.8293i	0.177849	−	1.23697i	−0.683879	−	0.729595i	$-0.739709\pi$
$839$	5.15148	−	35.8293i	0.177849	−	1.23697i	0.861728	−	0.507370i	$-0.169382\pi$
$840$	0.428348	−	2.18342i	0.0147794	−	0.0753350i
$841$	6.71543	+	4.31575i	0.231567	+	0.148819i
$842$	7.95581	−	6.89375i	0.274175	−	0.237574i
$843$	6.13803	+	37.7753i	0.211405	+	1.30105i
$844$	−23.6201	+	15.1797i	−0.813037	+	0.522507i
$845$	20.9756	+	1.45389i	0.721582	+	0.0500153i
$846$	19.8687	−	6.63196i	0.683102	−	0.228011i
$847$	−4.31235	+	1.26622i	−0.148174	+	0.0435078i
$848$	1.86402	+	0.851270i	0.0640108	+	0.0292327i
$849$	−2.34631	+	18.7455i	−0.0805251	+	0.643342i
$850$	−8.87872	−	19.2178i	−0.304538	−	0.659164i
$851$	−0.759500	−	3.35316i	−0.0260353	−	0.114945i
$852$	−5.39733	+	19.7074i	−0.184910	+	0.675163i
$853$	−21.9576	+	3.15703i	−0.751814	+	0.108095i	−0.507560	−	0.861617i	$-0.669452\pi$
$853$	−21.9576	+	3.15703i	−0.751814	+	0.108095i	−0.244255	+	0.969711i	$0.578543\pi$
$854$	−2.25692	−	1.03070i	−0.0772304	−	0.0352699i
$855$	0.165750	−	5.07603i	0.00566853	−	0.173596i
$856$	−8.88017	−	7.69471i	−0.303518	−	0.263000i
$857$	46.1218	+	13.5426i	1.57549	+	0.462606i	0.948594	−	0.316495i	$-0.102506\pi$
$857$	46.1218	+	13.5426i	1.57549	+	0.462606i	0.626898	+	0.779102i	$0.284324\pi$
$858$	−4.26451	−	13.5989i	−0.145588	−	0.464259i
$859$	−0.128080	−	0.280457i	−0.00437004	−	0.00956906i	0.907434	−	0.420194i	$-0.138038\pi$
$859$	−0.128080	−	0.280457i	−0.00437004	−	0.00956906i	−0.911804	+	0.410625i	$0.865311\pi$
$860$	8.27454	+	6.16592i	0.282159	+	0.210256i
$861$	0.674156	−	0.606087i	0.0229752	−	0.0206554i
$862$	4.73048	−	32.9012i	0.161121	−	1.12062i
$863$	−0.195700	+	1.36112i	−0.00666170	+	0.0463331i	−0.992881	−	0.119109i	$-0.961996\pi$
$863$	−0.195700	+	1.36112i	−0.00666170	+	0.0463331i	0.986219	+	0.165442i	$0.0529052\pi$
$864$	1.02030	+	5.09500i	0.0347113	+	0.173335i
$865$	−44.7913	−	33.3770i	−1.52295	−	1.13485i
$866$	15.8399	+	34.6845i	0.538260	+	1.17863i
$867$	−1.53067	+	0.480007i	−0.0519843	+	0.0163019i
$868$	−1.50698	−	0.442488i	−0.0511501	−	0.0150190i
$869$	31.0820	+	26.9327i	1.05438	+	0.913628i
$870$	4.12868	+	17.2689i	0.139975	+	0.585470i
$871$	−18.2280	−	8.32447i	−0.617634	−	0.282064i
$872$	−2.18079	+	0.313551i	−0.0738509	+	0.0106182i
$873$	20.0768	+	11.8887i	0.679496	+	0.402373i
$874$	3.62372	+	0.228069i	0.122574	+	0.00771454i
$875$	−5.11650	+	3.88305i	−0.172969	+	0.131271i
$876$	9.27542	+	1.16098i	0.313388	+	0.0392257i
$877$	−22.3934	−	10.2267i	−0.756172	−	0.345332i	−0.000255372	−	1.00000i	$-0.500081\pi$
$877$	−22.3934	−	10.2267i	−0.756172	−	0.345332i	−0.755917	+	0.654668i	$0.772809\pi$
$878$	−10.4360	+	3.06428i	−0.352197	+	0.103414i
$879$	3.67998	+	5.50236i	0.124123	+	0.185590i
$880$	−9.67810	−	0.670822i	−0.326249	−	0.0226134i
$881$	−28.3862	+	18.2427i	−0.956355	+	0.614612i	−0.922987	−	0.384831i	$-0.874260\pi$
$881$	−28.3862	+	18.2427i	−0.956355	+	0.614612i	−0.0333679	+	0.999443i	$0.510623\pi$
$882$	2.12183	−	19.8970i	0.0714456	−	0.669968i
$883$	0.965230	−	0.836377i	0.0324826	−	0.0281463i	−0.638468	−	0.769648i	$-0.720432\pi$
$883$	0.965230	−	0.836377i	0.0324826	−	0.0281463i	0.670951	+	0.741502i	$0.265886\pi$
$884$	6.75517	+	4.34129i	0.227201	+	0.146013i
$885$	17.4213	+	3.41774i	0.585609	+	0.114886i
$886$	−3.51433	+	24.4427i	−0.118066	+	0.821168i
$887$	38.0487	+	24.4524i	1.27755	+	0.821031i	0.990583	−	0.136910i	$-0.0437172\pi$
$887$	38.0487	+	24.4524i	1.27755	+	0.821031i	0.286965	+	0.957941i	$0.407354\pi$
$888$	−0.536379	−	1.11987i	−0.0179997	−	0.0375803i
$889$	8.60628	−	3.93036i	0.288645	−	0.131820i
$890$	−17.2207	+	17.2965i	−0.577238	+	0.579780i
$891$	8.36573	+	38.1404i	0.280263	+	1.27775i
$892$	−3.73902	−	3.23988i	−0.125192	−	0.108479i
$893$	−1.48927	−	5.07199i	−0.0498365	−	0.169728i
$894$	−23.8542	+	28.5681i	−0.797805	+	0.955462i
$895$	53.7859	−	20.1958i	1.79787	−	0.675072i
$896$	0.574502			0.0191928
$897$	−2.93465	+	15.4782i	−0.0979850	+	0.516803i
$898$			17.0407i			0.568654i
$899$	12.4056	−	1.78366i	0.413751	−	0.0594884i
$900$	7.58615	−	12.9403i	0.252872	−	0.431342i
$901$	−8.32474	+	2.44437i	−0.277337	+	0.0814336i
$902$	−2.98718	−	2.58841i	−0.0994623	−	0.0861846i
$903$	−3.90789	−	2.41166i	−0.130046	−	0.0802552i
$904$	9.36055	+	14.5653i	0.311327	+	0.484435i
$905$	−14.3040	+	10.7570i	−0.475481	+	0.357574i
$906$	−5.86490	−	12.2449i	−0.194848	−	0.406810i
$907$	1.28958	+	0.828764i	0.0428199	+	0.0275187i	0.561876	−	0.827222i	$-0.310080\pi$
$907$	1.28958	+	0.828764i	0.0428199	+	0.0275187i	−0.519056	+	0.854740i	$0.673716\pi$
$908$	2.80346	+	0.403077i	0.0930361	+	0.0133766i
$909$	−33.5657	−	27.0013i	−1.11330	−	0.895576i
$910$	0.846405	−	2.28462i	0.0280581	−	0.0757344i
$911$	−20.9992	−	24.2344i	−0.695736	−	0.802922i	0.292434	−	0.956286i	$-0.405535\pi$
$911$	−20.9992	−	24.2344i	−0.695736	−	0.802922i	−0.988170	+	0.153364i	$0.950989\pi$
$912$	1.29435	−	0.210316i	0.0428601	−	0.00696425i
$913$	−25.6001	−	39.8345i	−0.847239	−	1.31833i
$914$	6.33122	+	1.85901i	0.209418	+	0.0614907i
$915$	−12.0671	−	11.5828i	−0.398927	−	0.382914i
$916$	−5.59047	−	19.0394i	−0.184714	−	0.629079i
$917$	−2.41986	−	1.10511i	−0.0799109	−	0.0364941i
$918$	−17.3913	−	13.4740i	−0.573999	−	0.444709i
$919$			37.6970i			1.24351i	0.783212	+	0.621754i	$0.213580\pi$
$919$			37.6970i			1.24351i	−0.783212	+	0.621754i	$0.786420\pi$
$920$	9.08320	+	5.70049i	0.299464	+	0.187939i
$921$	−9.16840	+	33.4767i	−0.302109	+	1.10310i
$922$	−19.0973	+	2.74577i	−0.628936	+	0.0904273i
$923$	−9.29441	+	20.3519i	−0.305929	+	0.669892i
$924$	4.31644	−	0.0789150i	0.142000	−	0.00259611i
$925$	−0.994738	+	3.44367i	−0.0327068	+	0.113227i
$926$	10.6463	−	36.2579i	0.349858	−	1.19151i
$927$	2.75405	−	0.100735i	0.0904549	−	0.00330858i
$928$	−4.17018	+	1.90446i	−0.136893	+	0.0625169i
$929$	42.9138	−	37.1850i	1.40796	−	1.22000i	0.465772	−	0.884905i	$-0.345777\pi$
$929$	42.9138	−	37.1850i	1.40796	−	1.22000i	0.942184	−	0.335096i	$-0.108769\pi$
$930$	−8.60437	−	6.17033i	−0.282148	−	0.202333i
$931$	−4.99837	−	0.718657i	−0.163815	−	0.0235530i
$932$	−0.872003	+	6.06492i	−0.0285634	+	0.198663i
$933$	−39.2336	+	35.2722i	−1.28445	+	1.15476i
$934$	14.5560	−	12.6128i	0.476286	−	0.412704i
$935$	32.8278	−	24.6873i	1.07359	−	0.807363i
$936$	0.207973	+	5.68587i	0.00679780	+	0.185848i
$937$	−40.9032	−	12.0103i	−1.33625	−	0.392358i	−0.465918	−	0.884828i	$-0.654276\pi$
$937$	−40.9032	−	12.0103i	−1.33625	−	0.392358i	−0.870329	+	0.492470i	$0.836094\pi$
$938$	3.97511	−	4.58752i	0.129792	−	0.149788i
$939$	−20.2589	+	0.370382i	−0.661124	+	0.0120870i
$940$	3.28515	−	15.2630i	0.107150	−	0.497823i
$941$	0.546060	+	3.79793i	0.0178011	+	0.123809i	0.996784	−	0.0801317i	$-0.0255341\pi$
$941$	0.546060	+	3.79793i	0.0178011	+	0.123809i	−0.978983	+	0.203941i	$0.934625\pi$
$942$	−2.91384	−	0.798024i	−0.0949380	−	0.0260010i
$943$	1.56180	+	4.08053i	0.0508593	+	0.132880i
$944$			4.58389i			0.149193i
$945$	−2.85985	+	6.03145i	−0.0930311	+	0.196203i
$946$	−8.31745	+	18.2127i	−0.270424	+	0.592145i
$947$	−12.3754	+	3.63375i	−0.402146	+	0.118081i	−0.476550	−	0.879147i	$-0.658113\pi$
$947$	−12.3754	+	3.63375i	−0.402146	+	0.118081i	0.0744036	+	0.997228i	$0.476295\pi$
$948$	−9.12775	−	13.6479i	−0.296456	−	0.443264i
$949$	9.82102	+	2.88371i	0.318804	+	0.0936092i
$950$	−3.19350	−	2.03256i	−0.103611	−	0.0659451i
$951$	−5.71379	−	35.1644i	−0.185282	−	1.14029i
$952$	−1.83829	+	1.59288i	−0.0595792	+	0.0516257i
$953$	−25.7184	+	40.0186i	−0.833101	+	1.29633i	0.119723	+	0.992807i	$0.461799\pi$
$953$	−25.7184	+	40.0186i	−0.833101	+	1.29633i	−0.952824	+	0.303523i	$0.901837\pi$
$954$	−4.79011	−	3.85331i	−0.155085	−	0.124756i
$955$	1.46152	+	19.8226i	0.0472938	+	0.641445i
$956$	11.0261	−	17.1569i	0.356608	−	0.554893i
$957$	−31.0704	+	14.8817i	−1.00436	+	0.481057i
$958$	−3.04814	−	6.67450i	−0.0984810	−	0.215643i
$959$	2.59205	+	4.03331i	0.0837017	+	0.130242i
$960$	3.65574	+	1.27888i	0.117989	+	0.0412757i
$961$	15.4063	−	17.7799i	0.496978	−	0.573544i
$962$	−0.383052	−	1.30455i	−0.0123501	−	0.0420605i
$963$	20.1291	+	28.9381i	0.648650	+	0.932519i
$964$	10.5689	−	1.51958i	0.340402	−	0.0489424i
$965$	7.79492	+	35.4574i	0.250927	+	1.14142i
$966$	−4.24827	−	2.17389i	−0.136686	−	0.0699439i
$967$		−	37.1036i		−	1.19317i	−0.802550	−	0.596585i	$-0.796524\pi$
$967$		−	37.1036i		−	1.19317i	0.802550	−	0.596585i	$-0.203476\pi$
$968$	−1.11335	−	7.74350i	−0.0357843	−	0.248885i
$969$	−3.55851	+	4.26172i	−0.114316	+	0.136906i
$970$	15.2456	−	8.36825i	0.489506	−	0.268688i
$971$	−14.0560	+	16.2215i	−0.451079	+	0.520573i	−0.935052	−	0.354510i	$-0.884648\pi$
$971$	−14.0560	+	16.2215i	−0.451079	+	0.520573i	0.483973	+	0.875083i	$0.339193\pi$
$972$	0.800857	−	15.5679i	0.0256875	−	0.499340i
$973$	−1.32819	+	0.853576i	−0.0425798	+	0.0273644i
$974$	0.426189	−	0.194634i	0.0136560	−	0.00623648i
$975$	10.4717	−	12.6536i	0.335362	−	0.405240i
$976$	2.33490	−	3.63318i	0.0747383	−	0.116295i
$977$	4.82874	+	0.694268i	0.154485	+	0.0222116i	0.219123	−	0.975697i	$-0.429680\pi$
$977$	4.82874	+	0.694268i	0.154485	+	0.0222116i	−0.0646383	+	0.997909i	$0.520589\pi$
$978$	−22.2173	−	9.65947i	−0.710431	−	0.308876i
$979$	−39.8390	−	25.6030i	−1.27326	−	0.818275i
$980$	−11.9592	−	8.91165i	−0.382024	−	0.284672i
$981$	6.57239	+	0.700882i	0.209840	+	0.0223774i
$982$	4.08363	+	6.35425i	0.130314	+	0.202772i
$983$	−5.59955	+	19.0703i	−0.178598	+	0.608249i	0.820720	+	0.571330i	$0.193572\pi$
$983$	−5.59955	+	19.0703i	−0.178598	+	0.608249i	−0.999318	+	0.0369187i	$0.988246\pi$
$984$	0.877238	+	1.31166i	0.0279653	+	0.0418141i
$985$	−29.3727	+	16.1226i	−0.935892	+	0.513708i
$986$	8.06334	−	17.6562i	0.256789	−	0.562289i
$987$	−0.862886	+	6.89388i	−0.0274660	+	0.219435i
$988$	1.43587			0.0456811
$989$	17.6038	−	13.4143i	0.559769	−	0.426550i
$990$	27.6426	+	9.10653i	0.878539	+	0.289425i
$991$	−1.84800	−	12.8531i	−0.0587036	−	0.408293i	−0.997892	−	0.0648913i	$-0.979330\pi$
$991$	−1.84800	−	12.8531i	−0.0587036	−	0.408293i	0.939189	−	0.343402i	$-0.111579\pi$
$992$	1.13568	−	2.48679i	0.0360578	−	0.0789556i
$993$	35.1551	−	0.642721i	1.11561	−	0.0203961i
$994$	−5.12204	−	4.43828i	−0.162461	−	0.140774i
$995$	2.32591	−	33.5564i	0.0737362	−	1.06381i
$996$	5.65646	+	18.0376i	0.179232	+	0.571543i
$997$	−56.2702	+	25.6978i	−1.78210	+	0.813856i	−0.807506	+	0.589859i	$0.799183\pi$
$997$	−56.2702	+	25.6978i	−1.78210	+	0.813856i	−0.974590	+	0.223997i	$0.928089\pi$
$998$	10.8189	+	12.4856i	0.342465	+	0.395226i
$999$	0.731445	+	3.65257i	0.0231419	+	0.115562i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.n.a.89.18	yes	240
3.2	odd	2		690.2.n.b.89.11	yes	240
5.4	even	2		690.2.n.b.89.7	yes	240
15.14	odd	2	inner	690.2.n.a.89.14	✓	240
23.15	odd	22	inner	690.2.n.a.659.14	yes	240
69.38	even	22		690.2.n.b.659.7	yes	240
115.84	odd	22		690.2.n.b.659.11	yes	240
345.314	even	22	inner	690.2.n.a.659.18	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.n.a.89.14	✓	240	15.14	odd	2	inner
690.2.n.a.89.18	yes	240	1.1	even	1	trivial
690.2.n.a.659.14	yes	240	23.15	odd	22	inner
690.2.n.a.659.18	yes	240	345.314	even	22	inner
690.2.n.b.89.7	yes	240	5.4	even	2
690.2.n.b.89.11	yes	240	3.2	odd	2
690.2.n.b.659.7	yes	240	69.38	even	22
690.2.n.b.659.11	yes	240	115.84	odd	22

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.n (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.142315 - 0.989821i) q^{2} +(1.11013 - 1.32951i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(1.06732 - 1.96490i) q^{5} +(-1.47397 - 0.909626i) q^{6} +(0.483302 - 0.310599i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-0.535201 - 2.95187i) q^{9} +O(q^{10})\)	\(q+(-0.142315 - 0.989821i) q^{2} +(1.11013 - 1.32951i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(1.06732 - 1.96490i) q^{5} +(-1.47397 - 0.909626i) q^{6} +(0.483302 - 0.310599i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-0.535201 - 2.95187i) q^{9} +(-2.09680 - 0.776821i) q^{10} +(0.617442 - 4.29440i) q^{11} +(-0.690600 + 1.58842i) q^{12} +(-1.02536 + 1.59549i) q^{13} +(-0.376219 - 0.434180i) q^{14} +(-1.42749 - 3.60032i) q^{15} +(0.841254 - 0.540641i) q^{16} +(-1.19284 + 4.06243i) q^{17} +(-2.84566 + 0.949849i) q^{18} +(0.213298 + 0.726425i) q^{19} +(-0.470509 + 2.18601i) q^{20} +(0.123585 - 0.987363i) q^{21} -4.33856 q^{22} +(4.22869 + 2.26235i) q^{23} +(1.67053 + 0.457515i) q^{24} +(-2.72166 - 4.19435i) q^{25} +(1.72517 + 0.787858i) q^{26} +(-4.51870 - 2.56542i) q^{27} +(-0.376219 + 0.434180i) q^{28} +(1.29159 - 4.39876i) q^{29} +(-3.36052 + 1.92534i) q^{30} +(1.13568 + 2.48679i) q^{31} +(-0.654861 - 0.755750i) q^{32} +(-5.02401 - 5.58826i) q^{33} +(4.19084 + 0.602551i) q^{34} +(-0.0944592 - 1.28115i) q^{35} +(1.34516 + 2.68152i) q^{36} +(-0.469465 - 0.541792i) q^{37} +(0.688676 - 0.314508i) q^{38} +(0.982932 + 3.13443i) q^{39} +(2.23072 + 0.154619i) q^{40} +(0.688519 + 0.596605i) q^{41} +(-0.994901 + 0.0181892i) q^{42} +(1.91710 - 4.19786i) q^{43} +(0.617442 + 4.29440i) q^{44} +(-6.37137 - 2.09897i) q^{45} +(1.63751 - 4.50761i) q^{46} -6.98212 q^{47} +(0.215117 - 1.71864i) q^{48} +(-2.77080 + 6.06720i) q^{49} +(-3.76432 + 3.29088i) q^{50} +(4.07683 + 6.09573i) q^{51} +(0.534322 - 1.81973i) q^{52} +(1.10788 + 1.72390i) q^{53} +(-1.89623 + 4.83780i) q^{54} +(-7.77906 - 5.79671i) q^{55} +(0.483302 + 0.310599i) q^{56} +(1.20258 + 0.522848i) q^{57} +(-4.53780 - 0.652438i) q^{58} +(-2.47824 + 3.85621i) q^{59} +(2.38399 + 3.05231i) q^{60} +(3.92849 - 1.79408i) q^{61} +(2.29985 - 1.47803i) q^{62} +(-1.17551 - 1.26041i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(2.04059 + 3.71761i) q^{65} +(-4.81639 + 5.76817i) q^{66} +(1.50369 + 10.4584i) q^{67} -4.23393i q^{68} +(7.70223 - 3.11058i) q^{69} +(-1.25467 + 0.275824i) q^{70} +(11.6770 - 1.67890i) q^{71} +(2.46279 - 1.71309i) q^{72} +(-1.52050 - 5.17834i) q^{73} +(-0.469465 + 0.541792i) q^{74} +(-8.59785 - 1.03781i) q^{75} +(-0.409315 - 0.636907i) q^{76} +(-1.03543 - 2.26727i) q^{77} +(2.96264 - 1.41900i) q^{78} +(-5.12499 + 7.97465i) q^{79} +(-0.164419 - 2.23001i) q^{80} +(-8.42712 + 3.15969i) q^{81} +(0.492546 - 0.766417i) q^{82} +(8.24830 - 7.14720i) q^{83} +(0.159593 + 0.982185i) q^{84} +(6.70912 + 6.67971i) q^{85} +(-4.42796 - 1.30017i) q^{86} +(-4.41436 - 6.60041i) q^{87} +(4.16282 - 1.22231i) q^{88} +(4.53438 - 9.92892i) q^{89} +(-1.17087 + 6.60523i) q^{90} +1.08958i q^{91} +(-4.69477 - 0.979347i) q^{92} +(4.56697 + 1.25077i) q^{93} +(0.993659 + 6.91105i) q^{94} +(1.65501 + 0.356219i) q^{95} +(-1.73176 + 0.0316608i) q^{96} +(-5.09324 + 5.87791i) q^{97} +(6.39977 + 1.87914i) q^{98} +(-13.0070 + 0.475758i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 24 q^{2} + 2 q^{3} - 24 q^{4} + 2 q^{6} - 24 q^{8} - 6 q^{9}+O(q^{10}) \) 240 * q - 24 * q^2 + 2 * q^3 - 24 * q^4 + 2 * q^6 - 24 * q^8 - 6 * q^9	\( 240 q - 24 q^{2} + 2 q^{3} - 24 q^{4} + 2 q^{6} - 24 q^{8} - 6 q^{9} - 9 q^{12} + 11 q^{15} - 24 q^{16} - 6 q^{18} - 4 q^{23} + 2 q^{24} - 12 q^{25} + 2 q^{27} + 22 q^{30} + 28 q^{31} - 24 q^{32} - 36 q^{35} - 6 q^{36} - 4 q^{46} + 104 q^{47} - 9 q^{48} + 70 q^{49} + 54 q^{50} - 9 q^{54} - 26 q^{55} - 44 q^{57} - 11 q^{60} + 44 q^{61} + 28 q^{62} - 121 q^{63} - 24 q^{64} + 44 q^{65} + 44 q^{66} - 102 q^{69} - 36 q^{70} + 16 q^{72} - 82 q^{75} + 8 q^{77} - 44 q^{79} + 74 q^{81} - 11 q^{84} + 22 q^{85} - 93 q^{87} - 4 q^{92} + 172 q^{93} + 16 q^{94} + 26 q^{95} + 2 q^{96} + 4 q^{98}+O(q^{100}) \) 240 * q - 24 * q^2 + 2 * q^3 - 24 * q^4 + 2 * q^6 - 24 * q^8 - 6 * q^9 - 9 * q^12 + 11 * q^15 - 24 * q^16 - 6 * q^18 - 4 * q^23 + 2 * q^24 - 12 * q^25 + 2 * q^27 + 22 * q^30 + 28 * q^31 - 24 * q^32 - 36 * q^35 - 6 * q^36 - 4 * q^46 + 104 * q^47 - 9 * q^48 + 70 * q^49 + 54 * q^50 - 9 * q^54 - 26 * q^55 - 44 * q^57 - 11 * q^60 + 44 * q^61 + 28 * q^62 - 121 * q^63 - 24 * q^64 + 44 * q^65 + 44 * q^66 - 102 * q^69 - 36 * q^70 + 16 * q^72 - 82 * q^75 + 8 * q^77 - 44 * q^79 + 74 * q^81 - 11 * q^84 + 22 * q^85 - 93 * q^87 - 4 * q^92 + 172 * q^93 + 16 * q^94 + 26 * q^95 + 2 * q^96 + 4 * q^98

Introduction

L-functions

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