LMFDB - Embedded newform 690.2.n.a.659.14

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			659.14
Character	$\chi$	$=$	690.659
Dual form			690.2.n.a.89.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 + 0.989821i) q^{2} +(0.277794 + 1.70963i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(-1.79300 - 1.33609i) q^{5} +(-1.73176 + 0.0316608i) q^{6} +(-0.483302 - 0.310599i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-2.84566 + 0.949849i) q^{9} +O(q^{10})$	\(q+(-0.142315 + 0.989821i) q^{2} +(0.277794 + 1.70963i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(-1.79300 - 1.33609i) q^{5} +(-1.73176 + 0.0316608i) q^{6} +(-0.483302 - 0.310599i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-2.84566 + 0.949849i) q^{9} +(1.57766 - 1.58461i) q^{10} +(-0.617442 - 4.29440i) q^{11} +(0.215117 - 1.71864i) q^{12} +(1.02536 + 1.59549i) q^{13} +(0.376219 - 0.434180i) q^{14} +(1.78613 - 3.43653i) q^{15} +(0.841254 + 0.540641i) q^{16} +(-1.19284 - 4.06243i) q^{17} +(-0.535201 - 2.95187i) q^{18} +(0.213298 - 0.726425i) q^{19} +(1.34396 + 1.78712i) q^{20} +(0.396751 - 0.912550i) q^{21} +4.33856 q^{22} +(4.22869 - 2.26235i) q^{23} +(1.67053 + 0.457515i) q^{24} +(1.42973 + 4.79123i) q^{25} +(-1.72517 + 0.787858i) q^{26} +(-2.41440 - 4.60116i) q^{27} +(0.376219 + 0.434180i) q^{28} +(-1.29159 - 4.39876i) q^{29} +(3.14736 + 2.25702i) q^{30} +(1.13568 - 2.48679i) q^{31} +(-0.654861 + 0.755750i) q^{32} +(7.17031 - 2.24856i) q^{33} +(4.19084 - 0.602551i) q^{34} +(0.451574 + 1.20264i) q^{35} +(2.99800 - 0.109658i) q^{36} +(0.469465 - 0.541792i) q^{37} +(0.688676 + 0.314508i) q^{38} +(-2.44285 + 2.19619i) q^{39} +(-1.96019 + 1.07594i) q^{40} +(-0.688519 + 0.596605i) q^{41} +(0.846798 + 0.522582i) 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} +(-0.690600 + 1.58842i) q^{48} +(-2.77080 - 6.06720i) q^{49} +(-4.94593 + 0.733315i) q^{50} +(6.61388 - 3.16782i) q^{51} +(-0.534322 - 1.81973i) q^{52} +(1.10788 - 1.72390i) q^{53} +(4.89793 - 1.73501i) q^{54} +(-4.63063 + 8.52484i) q^{55} +(-0.483302 + 0.310599i) q^{56} +(1.30117 + 0.162863i) q^{57} +(4.53780 - 0.652438i) q^{58} +(2.47824 + 3.85621i) q^{59} +(-2.68196 + 2.79411i) q^{60} +(3.92849 + 1.79408i) q^{61} +(2.29985 + 1.47803i) q^{62} +(1.67034 + 0.424797i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(0.293243 - 4.23068i) q^{65} +(1.20523 + 7.41733i) q^{66} +(-1.50369 + 10.4584i) q^{67} +4.23393i q^{68} +(5.04248 + 6.60102i) q^{69} +(-1.25467 + 0.275824i) q^{70} +(-11.6770 - 1.67890i) q^{71} +(-0.318117 + 2.98309i) q^{72} +(1.52050 - 5.17834i) q^{73} +(0.469465 + 0.541792i) q^{74} +(-7.79405 + 3.77528i) q^{75} +(-0.409315 + 0.636907i) q^{76} +(-1.03543 + 2.26727i) q^{77} +(-1.82619 - 2.73054i) q^{78} +(-5.12499 - 7.97465i) q^{79} +(-0.786027 - 2.09336i) q^{80} +(7.19557 - 5.40590i) q^{81} +(-0.492546 - 0.766417i) q^{82} +(8.24830 + 7.14720i) q^{83} +(-0.637775 + 0.763807i) q^{84} +(-3.28900 + 8.87768i) q^{85} +(4.42796 - 1.30017i) q^{86} +(7.16146 - 3.43010i) q^{87} +(-4.16282 - 1.22231i) q^{88} +(-4.53438 - 9.92892i) q^{89} +(-2.98435 + 6.00780i) q^{90} -1.08958i q^{91} +(-4.69477 + 0.979347i) q^{92} +(4.56697 + 1.25077i) q^{93} +(0.993659 - 6.91105i) q^{94} +(-1.35301 + 1.01750i) q^{95} +(-1.47397 - 0.909626i) q^{96} +(5.09324 + 5.87791i) q^{97} +(6.39977 - 1.87914i) q^{98} +(5.83606 + 11.6339i) 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 $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{17}{22}\right)$

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
$3$	0.277794	+	1.70963i	0.160384	+	0.987055i
$3$	0.277794	+	1.70963i	0.160384	+	0.987055i
$4$	−0.959493	−	0.281733i	−0.479746	−	0.140866i
$5$	−1.79300	−	1.33609i	−0.801856	−	0.597517i
$5$	−1.79300	−	1.33609i	−0.801856	−	0.597517i
$6$	−1.73176	+	0.0316608i	−0.706989	+	0.0129255i
$7$	−0.483302	−	0.310599i	−0.182671	−	0.117396i	0.446109	−	0.894978i	$-0.352809\pi$
$7$	−0.483302	−	0.310599i	−0.182671	−	0.117396i	−0.628780	+	0.777583i	$0.716446\pi$
$8$	0.415415	−	0.909632i	0.146871	−	0.321603i
$9$	−2.84566	+	0.949849i	−0.948554	+	0.316616i
$10$	1.57766	−	1.58461i	0.498900	−	0.501097i
$11$	−0.617442	−	4.29440i	−0.186166	−	1.29481i	−0.841824	−	0.539753i	$-0.818518\pi$
$11$	−0.617442	−	4.29440i	−0.186166	−	1.29481i	0.655658	−	0.755058i	$-0.272391\pi$
$12$	0.215117	−	1.71864i	0.0620989	−	0.496129i
$13$	1.02536	+	1.59549i	0.284383	+	0.442508i	0.953828	−	0.300353i	$-0.0971046\pi$
$13$	1.02536	+	1.59549i	0.284383	+	0.442508i	−0.669445	+	0.742861i	$0.733468\pi$
$14$	0.376219	−	0.434180i	0.100549	−	0.116039i
$15$	1.78613	−	3.43653i	0.461177	−	0.887308i
$16$	0.841254	+	0.540641i	0.210313	+	0.135160i
$17$	−1.19284	−	4.06243i	−0.289305	−	0.985283i	−0.968018	−	0.250880i	$-0.919280\pi$
$17$	−1.19284	−	4.06243i	−0.289305	−	0.985283i	0.678713	−	0.734404i	$-0.262538\pi$
$18$	−0.535201	−	2.95187i	−0.126148	−	0.695763i
$19$	0.213298	−	0.726425i	0.0489338	−	0.166653i	−0.931401	−	0.363995i	$-0.881413\pi$
$19$	0.213298	−	0.726425i	0.0489338	−	0.166653i	0.980335	+	0.197341i	$0.0632308\pi$
$20$	1.34396	+	1.78712i	0.300518	+	0.399611i
$21$	0.396751	−	0.912550i	0.0865782	−	0.199135i
$22$	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
$25$	1.42973	+	4.79123i	0.285946	+	0.958246i
$26$	−1.72517	+	0.787858i	−0.338334	+	0.154512i
$27$	−2.41440	−	4.60116i	−0.464651	−	0.885494i
$28$	0.376219	+	0.434180i	0.0710987	+	0.0820523i
$29$	−1.29159	−	4.39876i	−0.239843	−	0.816830i	−0.988152	−	0.153480i	$-0.950952\pi$
$29$	−1.29159	−	4.39876i	−0.239843	−	0.816830i	0.748309	−	0.663350i	$-0.230866\pi$
$30$	3.14736	+	2.25702i	0.574626	+	0.412074i
$31$	1.13568	−	2.48679i	0.203974	−	0.446640i	−0.779806	−	0.626021i	$-0.784682\pi$
$31$	1.13568	−	2.48679i	0.203974	−	0.446640i	0.983780	+	0.179381i	$0.0574095\pi$
$32$	−0.654861	+	0.755750i	−0.115764	+	0.133599i
$33$	7.17031	−	2.24856i	1.24819	−	0.391423i
$34$	4.19084	−	0.602551i	0.718722	−	0.103337i
$35$	0.451574	+	1.20264i	0.0763300	+	0.203283i
$36$	2.99800	−	0.109658i	0.499666	−	0.0182763i
$37$	0.469465	−	0.541792i	0.0771796	−	0.0890700i	−0.715846	−	0.698258i	$-0.753959\pi$
$37$	0.469465	−	0.541792i	0.0771796	−	0.0890700i	0.793026	+	0.609188i	$0.208504\pi$
$38$	0.688676	+	0.314508i	0.111718	+	0.0510199i
$39$	−2.44285	+	2.19619i	−0.391169	+	0.351673i
$40$	−1.96019	+	1.07594i	−0.309933	+	0.170121i
$41$	−0.688519	+	0.596605i	−0.107529	+	0.0931741i	−0.706966	−	0.707248i	$-0.749937\pi$
$41$	−0.688519	+	0.596605i	−0.107529	+	0.0931741i	0.599437	+	0.800422i	$0.295391\pi$
$42$	0.846798	+	0.522582i	0.130664	+	0.0806362i
$43$	−1.91710	−	4.19786i	−0.292355	−	0.640168i	0.705278	−	0.708931i	$-0.250822\pi$
$43$	−1.91710	−	4.19786i	−0.292355	−	0.640168i	−0.997633	+	0.0687629i	$0.978095\pi$
$44$	−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	$0.670067\pi$
$48$	−0.690600	+	1.58842i	−0.0996795	+	0.229268i
$49$	−2.77080	−	6.06720i	−0.395828	−	0.866742i
$50$	−4.94593	+	0.733315i	−0.699460	+	0.103706i
$51$	6.61388	−	3.16782i	0.926128	−	0.443584i
$52$	−0.534322	−	1.81973i	−0.0740971	−	0.252352i
$53$	1.10788	−	1.72390i	0.152180	−	0.236796i	−0.756790	−	0.653658i	$-0.773234\pi$
$53$	1.10788	−	1.72390i	0.152180	−	0.236796i	0.908970	+	0.416862i	$0.136870\pi$
$54$	4.89793	−	1.73501i	0.666524	−	0.236105i
$55$	−4.63063	+	8.52484i	−0.624394	+	1.14949i
$56$	−0.483302	+	0.310599i	−0.0645839	+	0.0415056i
$57$	1.30117	+	0.162863i	0.172344	+	0.0215718i
$58$	4.53780	−	0.652438i	0.595843	−	0.0856693i
$59$	2.47824	+	3.85621i	0.322639	+	0.502036i	0.964250	−	0.264994i	$-0.0853699\pi$
$59$	2.47824	+	3.85621i	0.322639	+	0.502036i	−0.641611	+	0.767030i	$0.721734\pi$
$60$	−2.68196	+	2.79411i	−0.346240	+	0.360719i
$61$	3.92849	+	1.79408i	0.502991	+	0.229708i	0.650718	−	0.759320i	$-0.274468\pi$
$61$	3.92849	+	1.79408i	0.502991	+	0.229708i	−0.147726	+	0.989028i	$0.547195\pi$
$62$	2.29985	+	1.47803i	0.292082	+	0.187709i
$63$	1.67034	+	0.424797i	0.210443	+	0.0535193i
$64$	−0.654861	−	0.755750i	−0.0818576	−	0.0944687i
$65$	0.293243	−	4.23068i	0.0363723	−	0.524751i
$66$	1.20523	+	7.41733i	0.148353	+	0.913010i
$67$	−1.50369	+	10.4584i	−0.183705	+	1.27770i	0.664202	+	0.747553i	$0.268771\pi$
$67$	−1.50369	+	10.4584i	−0.183705	+	1.27770i	−0.847908	+	0.530144i	$0.822138\pi$
$68$			4.23393i			0.513439i
$69$	5.04248	+	6.60102i	0.607043	+	0.794669i
$70$	−1.25467	+	0.275824i	−0.149961	+	0.0329673i
$71$	−11.6770	−	1.67890i	−1.38580	−	0.199248i	−0.591272	−	0.806472i	$-0.701374\pi$
$71$	−11.6770	−	1.67890i	−1.38580	−	0.199248i	−0.794531	+	0.607224i	$0.792283\pi$
$72$	−0.318117	+	2.98309i	−0.0374905	+	0.351560i
$73$	1.52050	−	5.17834i	0.177961	−	0.606079i	−0.821401	−	0.570351i	$-0.806807\pi$
$73$	1.52050	−	5.17834i	0.177961	−	0.606079i	0.999362	−	0.0357274i	$-0.0113748\pi$
$74$	0.469465	+	0.541792i	0.0545742	+	0.0629820i
$75$	−7.79405	+	3.77528i	−0.899980	+	0.435932i
$76$	−0.409315	+	0.636907i	−0.0469517	+	0.0730582i
$77$	−1.03543	+	2.26727i	−0.117998	+	0.258379i
$78$	−1.82619	−	2.73054i	−0.206775	−	0.309172i
$79$	−5.12499	−	7.97465i	−0.576607	−	0.897218i	0.423355	−	0.905964i	$-0.360852\pi$
$79$	−5.12499	−	7.97465i	−0.576607	−	0.897218i	−0.999962	+	0.00874603i	$0.997216\pi$
$80$	−0.786027	−	2.09336i	−0.0878805	−	0.234045i
$81$	7.19557	−	5.40590i	0.799508	−	0.600655i
$82$	−0.492546	−	0.766417i	−0.0543926	−	0.0846366i
$83$	8.24830	+	7.14720i	0.905369	+	0.784507i	0.977070	−	0.212919i	$-0.0682972\pi$
$83$	8.24830	+	7.14720i	0.905369	+	0.784507i	−0.0717007	+	0.997426i	$0.522843\pi$
$84$	−0.637775	+	0.763807i	−0.0695869	+	0.0833382i
$85$	−3.28900	+	8.87768i	−0.356743	+	0.962920i
$86$	4.42796	−	1.30017i	0.477480	−	0.140201i
$87$	7.16146	−	3.43010i	0.767789	−	0.367745i
$88$	−4.16282	−	1.22231i	−0.443758	−	0.130299i
$89$	−4.53438	−	9.92892i	−0.480644	−	1.05246i	−0.982286	−	0.187388i	$-0.939998\pi$
$89$	−4.53438	−	9.92892i	−0.480644	−	1.05246i	0.501642	−	0.865075i	$-0.332729\pi$
$90$	−2.98435	+	6.00780i	−0.314578	+	0.633278i
$91$		−	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
$95$	−1.35301	+	1.01750i	−0.138816	+	0.104393i
$96$	−1.47397	−	0.909626i	−0.150436	−	0.0928383i
$97$	5.09324	+	5.87791i	0.517140	+	0.596812i	0.952913	−	0.303245i	$-0.0980701\pi$
$97$	5.09324	+	5.87791i	0.517140	+	0.596812i	−0.435772	+	0.900057i	$0.643525\pi$
$98$	6.39977	−	1.87914i	0.646474	−	0.189822i
$99$	5.83606	+	11.6339i	0.586546	+	1.16925i
$100$	−0.0219711	−	4.99995i	−0.00219711	−	0.499995i
$101$	−10.8521	−	9.40339i	−1.07982	−	0.935672i	−0.0816842	−	0.996658i	$-0.526030\pi$
$101$	−10.8521	−	9.40339i	−1.07982	−	0.935672i	−0.998139	+	0.0609865i	$0.980575\pi$
$102$	2.19433	+	6.99739i	0.217271	+	0.692845i
$103$	0.130735	+	0.909280i	0.0128817	+	0.0895941i	0.995248	−	0.0973720i	$-0.0310437\pi$
$103$	0.130735	+	0.909280i	0.0128817	+	0.0895941i	−0.982366	+	0.186966i	$0.940135\pi$
$104$	1.87725	−	0.269908i	0.184080	−	0.0264667i
$105$	−1.93062	+	1.10611i	−0.188410	+	0.107945i
$106$	1.54869	+	1.34194i	0.150422	+	0.130341i
$107$	−10.6883	−	4.88119i	−1.03328	−	0.471882i	−0.174731	−	0.984616i	$-0.555906\pi$
$107$	−10.6883	−	4.88119i	−1.03328	−	0.471882i	−0.858548	+	0.512734i	$0.828633\pi$
$108$	1.02030	+	5.09500i	0.0981783	+	0.490266i
$109$	−0.620718	−	2.11397i	−0.0594540	−	0.202482i	0.924410	−	0.381401i	$-0.124558\pi$
$109$	−0.620718	−	2.11397i	−0.0594540	−	0.202482i	−0.983864	+	0.178919i	$0.942740\pi$
$110$	−7.77906	−	5.79671i	−0.741704	−	0.552694i
$111$	1.05668	+	0.652105i	0.100295	+	0.0618950i
$112$	−0.238657	−	0.522586i	−0.0225510	−	0.0493797i
$113$	17.1376	+	2.46401i	1.61217	+	0.231795i	0.888675	−	0.458538i	$-0.151627\pi$
$113$	17.1376	+	2.46401i	1.61217	+	0.231795i	0.723493	+	0.690332i	$0.242536\pi$
$114$	−0.346382	+	1.26475i	−0.0324416	+	0.118455i
$115$	−10.6048	−	1.59351i	−0.988898	−	0.148595i
$116$			4.58447i			0.425657i
$117$	−4.43329	−	3.56628i	−0.409857	−	0.329702i
$118$	−4.16965	+	1.90422i	−0.383848	+	0.175297i
$119$	−0.685287	+	2.33387i	−0.0628201	+	0.213946i
$120$	−2.38399	−	3.05231i	−0.217628	−	0.278636i
$121$	−7.50623	+	2.20403i	−0.682385	+	0.200366i
$122$	−2.33490	+	3.63318i	−0.211392	+	0.328932i
$123$	−1.21124	−	1.01138i	−0.109214	−	0.0911930i
$124$	−1.79028	+	2.06610i	−0.160772	+	0.185541i
$125$	3.83800	−	10.5009i	0.343281	−	0.939233i
$126$	−0.658186	+	1.59288i	−0.0586359	+	0.141905i
$127$	−16.3010	+	2.34373i	−1.44648	+	0.207973i	−0.820403	−	0.571786i	$-0.806251\pi$
$127$	−16.3010	+	2.34373i	−1.44648	+	0.207973i	−0.626080	+	0.779759i	$0.715342\pi$
$128$	0.841254	−	0.540641i	0.0743570	−	0.0477863i
$129$	6.64422	−	4.44367i	0.584991	−	0.391243i
$130$	4.14589	+	0.892347i	0.363618	+	0.0782640i
$131$	2.50347	−	3.89548i	0.218729	−	0.340349i	−0.714497	−	0.699638i	$-0.753344\pi$
$131$	2.50347	−	3.89548i	0.218729	−	0.340349i	0.933226	+	0.359289i	$0.116981\pi$
$132$	−7.51335	+	0.137362i	−0.653954	+	0.0119559i
$133$	−0.328714	+	0.284833i	−0.0285032	+	0.0246981i
$134$	−10.1380	−	2.97677i	−0.875786	−	0.257154i
$135$	−1.81854	+	11.4758i	−0.156515	+	0.987676i
$136$	−4.19084	−	0.602551i	−0.359361	−	0.0516683i
$137$		−	8.34533i		−	0.712989i	−0.934297	−	0.356495i	$-0.883972\pi$
$137$		−	8.34533i		−	0.712989i	0.934297	−	0.356495i	$-0.116028\pi$
$138$	−7.25145	+	4.05173i	−0.617284	+	0.344906i
$139$	−2.74816			−0.233096			−0.116548	−	0.993185i	$-0.537183\pi$
$139$	−2.74816			−0.233096			−0.116548	+	0.993185i	$0.537183\pi$
$140$	−0.0944592	−	1.28115i	−0.00798326	−	0.108277i
$141$	−1.93959	−	11.9368i	−0.163343	−	1.00526i
$142$	3.32361	−	11.3192i	0.278912	−	0.949886i
$143$	6.21856	−	5.38841i	0.520022	−	0.450602i
$144$	−2.90745	−	0.739417i	−0.242287	−	0.0616181i
$145$	−3.56131	+	9.61269i	−0.295751	+	0.798290i
$146$	4.90924	+	2.24198i	0.406292	+	0.185547i
$147$	9.60294	−	6.42246i	0.792038	−	0.529716i
$148$	−0.603089	+	0.387582i	−0.0495736	+	0.0318590i
$149$	−3.05802	−	21.2690i	−0.250523	−	1.74242i	−0.595088	−	0.803661i	$-0.702883\pi$
$149$	−3.05802	−	21.2690i	−0.250523	−	1.74242i	0.344565	−	0.938762i	$-0.388026\pi$
$150$	−2.62765	−	8.25200i	−0.214546	−	0.673773i
$151$	6.59432	−	4.23791i	0.536638	−	0.344876i	−0.244085	−	0.969754i	$-0.578487\pi$
$151$	6.59432	−	4.23791i	0.536638	−	0.344876i	0.780723	+	0.624878i	$0.214851\pi$
$152$	−0.572173	−	0.495790i	−0.0464093	−	0.0402139i
$153$	7.25310	+	10.4273i	0.586378	+	0.842995i
$154$	−2.09684	−	1.34755i	−0.168968	−	0.108589i
$155$	−5.35885	+	2.94146i	−0.430433	+	0.236263i
$156$	2.96264	−	1.41900i	0.237201	−	0.113611i
$157$	−1.67360	−	0.491414i	−0.133568	−	0.0392191i	0.214265	−	0.976776i	$-0.431264\pi$
$157$	−1.67360	−	0.491414i	−0.133568	−	0.0392191i	−0.347833	+	0.937556i	$0.613082\pi$
$158$	8.62284	−	3.93792i	0.685996	−	0.313284i
$159$	3.25499	+	1.41518i	0.258138	+	0.112231i
$160$	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	$-0.639071\pi$
$163$	−13.8447	−	1.99057i	−1.08440	−	0.155913i	−0.661264	+	0.750153i	$0.729980\pi$
$164$	0.828712	−	0.378460i	0.0647116	−	0.0295528i
$165$	−15.8607	−	5.54851i	−1.23475	−	0.431951i
$166$	−8.24830	+	7.14720i	−0.640193	+	0.554730i
$167$	4.63776	−	1.36177i	0.358880	−	0.105377i	−0.0973218	−	0.995253i	$-0.531028\pi$
$167$	4.63776	−	1.36177i	0.358880	−	0.105377i	0.456202	+	0.889876i	$0.349209\pi$
$168$	−0.665268	−	0.739984i	−0.0513265	−	0.0570910i
$169$	3.90618	−	8.55333i	0.300475	−	0.657949i
$170$	−8.31925	−	4.51895i	−0.638057	−	0.346588i
$171$	0.0830213	+	2.26976i	0.00634880	+	0.173573i
$172$	0.656769	+	4.56793i	0.0500781	+	0.348301i
$173$	3.55519	+	24.7269i	0.270296	+	1.87995i	0.445301	+	0.895381i	$0.353097\pi$
$173$	3.55519	+	24.7269i	0.270296	+	1.87995i	−0.175006	+	0.984567i	$0.555994\pi$
$174$	2.37600	+	7.57672i	0.180124	+	0.574390i
$175$	0.797161	−	2.75968i	0.0602597	−	0.208612i
$176$	1.80230	−	3.94650i	0.135854	−	0.297478i
$177$	−5.90426	+	5.30810i	−0.443791	+	0.398981i
$178$	10.4732	−	3.07520i	0.784997	−	0.230496i
$179$	−19.4179	+	16.8257i	−1.45136	+	1.25761i	−0.542801	+	0.839861i	$0.682636\pi$
$179$	−19.4179	+	16.8257i	−1.45136	+	1.25761i	−0.908561	+	0.417752i	$0.862818\pi$
$180$	−5.52193	−	3.80897i	−0.411580	−	0.283904i
$181$	−7.28066	+	3.32497i	−0.541167	+	0.247143i	−0.667194	−	0.744884i	$-0.732505\pi$
$181$	−7.28066	+	3.32497i	−0.541167	+	0.247143i	0.126027	+	0.992027i	$0.459777\pi$
$182$	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
$186$	−1.88799	+	4.34248i	−0.138434	+	0.318406i
$187$	−16.7092	+	7.63083i	−1.22190	+	0.558022i
$188$	6.69930	+	1.96709i	0.488596	+	0.143465i
$189$	−0.262235	+	2.97366i	−0.0190748	+	0.216302i
$190$	−0.814589	−	1.48405i	−0.0590965	−	0.107664i
$191$	7.47791	+	4.80576i	0.541083	+	0.347733i	0.782462	−	0.622698i	$-0.213963\pi$
$191$	7.47791	+	4.80576i	0.541083	+	0.347733i	−0.241380	+	0.970431i	$0.577600\pi$
$192$	1.11013	−	1.32951i	0.0801171	−	0.0959492i
$193$	12.2701	+	10.6321i	0.883223	+	0.765317i	0.973039	−	0.230641i	$-0.0740824\pi$
$193$	12.2701	+	10.6321i	0.883223	+	0.765317i	−0.0898159	+	0.995958i	$0.528628\pi$
$194$	−6.54293	+	4.20489i	−0.469755	+	0.301893i
$195$	7.31435	−	0.673921i	0.523792	−	0.0482605i
$196$	0.949232	+	6.60206i	0.0678023	+	0.471575i
$197$	−12.6059	+	8.10129i	−0.898130	+	0.577193i	−0.906235	−	0.422774i	$-0.861056\pi$
$197$	−12.6059	+	8.10129i	−0.898130	+	0.577193i	0.00810523	+	0.999967i	$0.497420\pi$
$198$	−12.3461	+	4.12098i	−0.877398	+	0.292865i
$199$	13.6835	+	6.24904i	0.969996	+	0.442982i	0.836440	−	0.548059i	$-0.184633\pi$
$199$	13.6835	+	6.24904i	0.969996	+	0.442982i	0.133556	+	0.991041i	$0.457360\pi$
$200$	4.95219	+	0.689820i	0.350172	+	0.0487776i
$201$	−18.2977	+	0.334527i	−1.29062	+	0.0235957i
$202$	10.8521	−	9.40339i	0.763550	−	0.661620i
$203$	−0.742023	+	2.52710i	−0.0520798	+	0.177368i
$204$	−7.23845	+	1.17616i	−0.506793	+	0.0823477i
$205$	2.03164	−	0.149793i	0.141896	−	0.0104620i
$206$	−0.918631			−0.0640040
$207$	−9.88452	+	10.4545i	−0.687022	+	0.726637i
$208$			1.89656i			0.131503i
$209$	−3.25126	−	0.467461i	−0.224894	−	0.0323349i
$210$	−0.820095	−	2.06839i	−0.0565920	−	0.142732i
$211$	26.9399	+	7.91027i	1.85462	+	0.544566i	0.999665	+	0.0258630i	$0.00823337\pi$
$211$	26.9399	+	7.91027i	1.85462	+	0.544566i	0.854955	+	0.518703i	$0.173585\pi$
$212$	−1.54869	+	1.34194i	−0.106364	+	0.0921651i
$213$	−0.373505	−	20.4297i	−0.0255921	−	1.39982i
$214$	6.35261	−	9.88486i	0.434256	−	0.675715i
$215$	−2.17135	+	10.0882i	−0.148085	+	0.688009i
$216$	−5.18834	+	0.284821i	−0.353022	+	0.0193796i
$217$	−1.32127	+	0.849129i	−0.0896937	+	0.0576426i
$218$	2.18079	−	0.313551i	0.147702	−	0.0212363i
$219$	9.27542	+	1.16098i	0.626775	+	0.0784515i
$220$	6.84478	−	6.87492i	0.461475	−	0.463507i
$221$	5.25846	−	6.06859i	0.353722	−	0.408217i
$222$	−0.795848	+	0.953117i	−0.0534138	+	0.0639690i
$223$	−2.67478	+	4.16204i	−0.179117	+	0.278711i	−0.919189	−	0.393816i	$-0.871155\pi$
$223$	−2.67478	+	4.16204i	−0.179117	+	0.278711i	0.740073	+	0.672527i	$0.234791\pi$
$224$	0.551231	−	0.161856i	0.0368307	−	0.0108145i
$225$	−8.61947	−	12.2762i	−0.574631	−	0.818412i
$226$	−4.87786	+	16.6125i	−0.324471	+	1.10505i
$227$	−2.57634	+	1.17657i	−0.170998	+	0.0780920i	−0.499075	−	0.866559i	$-0.666327\pi$
$227$	−2.57634	+	1.17657i	−0.170998	+	0.0780920i	0.328077	+	0.944651i	$0.393599\pi$
$228$	−1.20258	−	0.522848i	−0.0796428	−	0.0346265i
$229$		−	19.8432i		−	1.31127i	−0.755076	−	0.655637i	$-0.772400\pi$
$229$		−	19.8432i		−	1.31127i	0.755076	−	0.655637i	$-0.227600\pi$
$230$	3.08650	−	10.2700i	0.203518	−	0.677186i
$231$	−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	0.974499	−	0.224394i	$-0.0720401\pi$
$233$	2.54537	+	5.57357i	0.166752	+	0.365137i	−0.807746	+	0.589530i	$0.799313\pi$
$234$	4.16090	−	3.88063i	0.272007	−	0.253685i
$235$	12.5190	+	9.32874i	0.816648	+	0.608540i
$236$	−1.29143	−	4.39821i	−0.0840650	−	0.286299i
$237$	12.2100	−	10.9771i	0.793124	−	0.713042i
$238$	−2.21259	−	1.01046i	−0.143421	−	0.0654982i
$239$	15.4131	+	13.3555i	0.996989	+	0.863896i	0.990697	−	0.136084i	$-0.0434518\pi$
$239$	15.4131	+	13.3555i	0.996989	+	0.863896i	0.00629177	+	0.999980i	$0.497997\pi$
$240$	3.36052	−	1.92534i	0.216920	−	0.124280i
$241$	−10.5689	+	1.51958i	−0.680804	+	0.0978848i	−0.474036	−	0.880505i	$-0.657203\pi$
$241$	−10.5689	+	1.51958i	−0.680804	+	0.0978848i	−0.206768	+	0.978390i	$0.566294\pi$
$242$	−1.11335	−	7.74350i	−0.0715686	−	0.497771i
$243$	11.2410	+	10.8000i	0.721108	+	0.692823i
$244$	−3.26390	−	2.82819i	−0.208950	−	0.181056i
$245$	−3.13827	+	14.5805i	−0.200497	+	0.931517i
$246$	1.17346	−	1.05498i	0.0748172	−	0.0672629i
$247$	1.37771	−	0.404531i	0.0876614	−	0.0257397i
$248$	−1.79028	−	2.06610i	−0.113683	−	0.131197i
$249$	−9.92772	+	16.0870i	−0.629144	+	1.01947i
$250$	9.84785	+	5.29337i	0.622833	+	0.334782i
$251$	−4.38354	+	30.4882i	−0.276686	+	1.92440i	0.0938662	+	0.995585i	$0.470077\pi$
$251$	−4.38354	+	30.4882i	−0.276686	+	1.92440i	−0.370553	+	0.928811i	$0.620832\pi$
$252$	−1.48300	−	0.878177i	−0.0934200	−	0.0553200i
$253$	−12.3264	−	16.7628i	−0.774954	−	1.05387i
$254$		−	16.4687i		−	1.03334i
$255$	−16.0912	−	3.15681i	−1.00767	−	0.197687i
$256$	0.415415	+	0.909632i	0.0259634	+	0.0568520i
$257$	−8.37632	−	2.45951i	−0.522500	−	0.153420i	0.00983804	−	0.999952i	$-0.496868\pi$
$257$	−8.37632	−	2.45951i	−0.522500	−	0.153420i	−0.532338	+	0.846532i	$0.678687\pi$
$258$	3.45287	+	7.20900i	0.214966	+	0.448812i
$259$	−0.395173	+	0.116033i	−0.0245549	+	0.00720996i
$260$	−1.47328	+	3.97669i	−0.0913692	+	0.246624i
$261$	7.85360	+	11.2906i	0.486126	+	0.698869i
$262$	3.49954	+	3.03237i	0.216203	+	0.187341i
$263$	−14.4425	−	22.4730i	−0.890566	−	1.38575i	−0.922393	−	0.386254i	$-0.873769\pi$
$263$	−14.4425	−	22.4730i	−0.890566	−	1.38575i	0.0318271	−	0.999493i	$-0.489867\pi$
$264$	0.933298	−	7.45643i	0.0574405	−	0.458911i
$265$	−4.28973	+	1.61073i	−0.263516	+	0.0989464i
$266$	−0.235153	−	0.365904i	−0.0144181	−	0.0224350i
$267$	15.7151	−	10.5103i	0.961751	−	0.643220i
$268$	4.38925	−	9.61112i	0.268116	−	0.587093i
$269$	−1.65040	+	2.56807i	−0.100627	+	0.156578i	−0.887916	−	0.460006i	$-0.847847\pi$
$269$	−1.65040	+	2.56807i	−0.100627	+	0.156578i	0.787289	+	0.616584i	$0.211484\pi$
$270$	−11.1001	−	3.43320i	−0.675533	−	0.208938i
$271$	−10.6069	−	12.2410i	−0.644321	−	0.743586i	0.335811	−	0.941929i	$-0.390990\pi$
$271$	−10.6069	−	12.2410i	−0.644321	−	0.743586i	−0.980133	+	0.198343i	$0.936444\pi$
$272$	1.19284	−	4.06243i	0.0723263	−	0.246321i
$273$	1.86277	−	0.302678i	0.112740	−	0.0183189i
$274$	8.26038	+	1.18766i	0.499028	+	0.0717494i
$275$	19.6927	−	9.09814i	1.18751	−	0.548639i
$276$	−2.97850	−	7.75426i	−0.179285	−	0.466752i
$277$		−	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
$279$	−0.869682	+	8.15528i	−0.0520665	+	0.488244i
$280$	1.28155	+	0.0888287i	0.0765873	+	0.00530853i
$281$	14.4695	+	16.6987i	0.863181	+	0.996164i	0.999985	+	0.00556568i	$0.00177162\pi$
$281$	14.4695	+	16.6987i	0.863181	+	0.996164i	−0.136804	+	0.990598i	$0.543683\pi$
$282$	12.0914	−	0.221060i	0.720030	−	0.0131639i
$283$	9.17567	+	5.89685i	0.545437	+	0.350531i	0.784162	−	0.620556i	$-0.213093\pi$
$283$	9.17567	+	5.89685i	0.545437	+	0.350531i	−0.238725	+	0.971087i	$0.576729\pi$
$284$	10.7310	+	4.90067i	0.636767	+	0.290802i
$285$	−2.11540	−	2.03049i	−0.125306	−	0.120276i
$286$	4.44857	+	6.92211i	0.263050	+	0.409313i
$287$	0.518068	−	0.0744869i	0.0305806	−	0.00439682i
$288$	1.14566	−	2.77263i	0.0675089	−	0.163379i
$289$	−0.779142	+	0.500724i	−0.0458319	+	0.0294544i
$290$	−9.00802	−	4.89309i	−0.528969	−	0.287332i
$291$	−8.63418	+	10.3404i	−0.506145	+	0.606165i
$292$	−2.91781	+	4.54021i	−0.170752	+	0.265696i
$293$	−1.07672	−	3.66698i	−0.0629028	−	0.214227i	0.922044	−	0.387085i	$-0.126518\pi$
$293$	−1.07672	−	3.66698i	−0.0629028	−	0.214227i	−0.984947	+	0.172858i	$0.944700\pi$
$294$	4.99045	+	10.4192i	0.291049	+	0.607661i
$295$	0.708754	−	10.2254i	0.0412653	−	0.595343i
$296$	−0.297808	−	0.652109i	−0.0173097	−	0.0379030i
$297$	−18.2685	+	13.2093i	−1.06005	+	0.766484i
$298$	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
$303$	13.0617	−	21.1652i	0.750372	−	1.21591i
$304$	0.572173	−	0.495790i	0.0328163	−	0.0284355i
$305$	−4.64674	−	8.46560i	−0.266072	−	0.484739i
$306$	−11.3534	+	5.69532i	−0.649029	+	0.325580i
$307$	18.2286	+	8.32473i	1.04036	+	0.475117i	0.860968	−	0.508660i	$-0.169859\pi$
$307$	18.2286	+	8.32473i	1.04036	+	0.475117i	0.179395	+	0.983777i	$0.442586\pi$
$308$	1.63225	−	1.88372i	0.0930060	−	0.107335i
$309$	−1.51821	+	0.476101i	−0.0863682	+	0.0270844i
$310$	−2.14887	−	5.72291i	−0.122048	−	0.325040i
$311$	30.1498	−	4.33488i	1.70964	−	0.245809i	0.783069	−	0.621935i	$-0.213653\pi$
$311$	30.1498	−	4.33488i	1.70964	−	0.245809i	0.926568	+	0.376126i	$0.122744\pi$
$312$	0.982932	+	3.13443i	0.0556476	+	0.177452i
$313$	7.66085	−	8.84109i	0.433017	−	0.499728i	−0.496742	−	0.867898i	$-0.665470\pi$
$313$	7.66085	−	8.84109i	0.433017	−	0.499728i	0.929758	+	0.368171i	$0.120016\pi$
$314$	0.724591	−	1.58663i	0.0408910	−	0.0895388i
$315$	−2.42735	−	2.99338i	−0.136766	−	0.168658i
$316$	2.67068	+	9.09550i	0.150237	+	0.511662i
$317$	13.4695	+	15.5446i	0.756521	+	0.873072i	0.995183	−	0.0980304i	$-0.0312543\pi$
$317$	13.4695	+	15.5446i	0.756521	+	0.873072i	−0.238662	+	0.971103i	$0.576709\pi$
$318$	−1.86401	+	3.02046i	−0.104528	+	0.169379i
$319$	−18.0926	+	8.26260i	−1.01299	+	0.462617i
$320$	0.164419	+	2.23001i	0.00919132	+	0.124662i
$321$	5.37587	−	19.6290i	0.300052	−	1.09558i
$322$	0.608647	−	2.68715i	0.0339186	−	0.149749i
$323$	−3.20548			−0.178358
$324$	−8.42712	+	3.15969i	−0.468173	+	0.175538i
$325$	−6.17835	+	7.19383i	−0.342713	+	0.399042i
$326$	3.94061	−	13.4205i	0.218250	−	0.743292i
$327$	3.44168	−	1.64845i	0.190325	−	0.0911593i
$328$	0.256670	+	0.874138i	0.0141722	+	0.0482662i
$329$	3.37447	+	2.16864i	0.186041	+	0.119561i
$330$	7.74924	−	14.9096i	0.426582	−	0.820746i
$331$	13.2938	−	15.3419i	0.730693	−	0.843265i	−0.261856	−	0.965107i	$-0.584335\pi$
$331$	13.2938	−	15.3419i	0.730693	−	0.843265i	0.992550	+	0.121842i	$0.0388801\pi$
$332$	−5.90059	−	9.18150i	−0.323837	−	0.503900i
$333$	−0.821318	+	1.98768i	−0.0450080	+	0.108924i
$334$	0.687886	+	4.78435i	0.0376394	+	0.261788i
$335$	16.6695	−	16.7429i	0.910751	−	0.914762i
$336$	0.827130	−	0.553186i	0.0451236	−	0.0301788i
$337$	7.95109	−	17.4105i	0.433123	−	0.948408i	−0.559686	−	0.828705i	$-0.689078\pi$
$337$	7.95109	−	17.4105i	0.433123	−	0.948408i	0.992810	−	0.119703i	$-0.0381943\pi$
$338$	7.91037	+	5.08368i	0.430267	+	0.276516i
$339$	0.548169	+	29.9834i	0.0297725	+	1.62847i
$340$	5.65691	−	7.59146i	0.306789	−	0.411705i
$341$	−11.3805	−	3.34161i	−0.616288	−	0.180958i
$342$	−2.25847	−	0.240844i	−0.122124	−	0.0130234i
$343$	−1.11766	+	7.77348i	−0.0603478	+	0.419728i
$344$	−4.61490			−0.248819
$345$	−0.221632	−	18.5729i	−0.0119323	−	0.999929i
$346$	−24.9811			−1.34299
$347$	−2.90162	+	20.1812i	−0.155767	+	1.08339i	0.750558	+	0.660805i	$0.229785\pi$
$347$	−2.90162	+	20.1812i	−0.155767	+	1.08339i	−0.906325	+	0.422581i	$0.861124\pi$
$348$	−7.83774	+	1.27354i	−0.420147	+	0.0682688i
$349$	−9.06471	−	2.66164i	−0.485223	−	0.142474i	0.0299660	−	0.999551i	$-0.490460\pi$
$349$	−9.06471	−	2.66164i	−0.485223	−	0.142474i	−0.515189	+	0.857077i	$0.672278\pi$
$350$	2.61815	+	1.18179i	0.139946	+	0.0631694i
$351$	4.86547	−	8.56996i	0.259700	−	0.457431i
$352$	3.64983	+	2.34560i	0.194537	+	0.125021i
$353$	0.141241	−	0.309274i	0.00751748	−	0.0164610i	−0.905836	−	0.423629i	$-0.860756\pi$
$353$	0.141241	−	0.309274i	0.00751748	−	0.0164610i	0.913354	+	0.407168i	$0.133483\pi$
$354$	−4.41381	−	6.59958i	−0.234591	−	0.350764i
$355$	18.6937	+	18.6118i	0.992160	+	0.987810i
$356$	1.55341	+	10.8042i	0.0823306	+	0.572622i
$357$	−4.18042	−	0.523251i	−0.221252	−	0.0276934i
$358$	−13.8910	−	21.6148i	−0.734162	−	1.14238i
$359$	19.9323	−	23.0031i	1.05199	−	1.21406i	0.0757989	−	0.997123i	$-0.475849\pi$
$359$	19.9323	−	23.0031i	1.05199	−	1.21406i	0.976187	−	0.216933i	$-0.0696052\pi$
$360$	4.55606	−	4.92365i	0.240125	−	0.259499i
$361$	15.5016	+	9.96229i	0.815875	+	0.524331i
$362$	−2.25498	−	7.67974i	−0.118519	−	0.403638i
$363$	−5.85326	−	12.2206i	−0.307216	−	0.641415i
$364$	−0.306969	+	1.04544i	−0.0160896	+	0.0547960i
$365$	−9.64499	+	7.25327i	−0.504842	+	0.379653i
$366$	−6.86000	−	2.98254i	−0.358578	−	0.155900i
$367$	25.8828			1.35107			0.675537	−	0.737326i	$-0.263912\pi$
$367$	25.8828			1.35107			0.675537	+	0.737326i	$0.263912\pi$
$368$	4.78051	+	0.382993i	0.249202	+	0.0199649i
$369$	1.39261	−	2.35173i	0.0724962	−	0.122426i
$370$	−0.117871	−	1.59868i	−0.00612782	−	0.0831115i
$371$	−1.07088	+	0.489057i	−0.0555976	+	0.0253906i
$372$	−4.02959	−	2.48677i	−0.208925	−	0.128933i
$373$	−1.11913	−	1.29155i	−0.0579465	−	0.0668738i	0.726036	−	0.687656i	$-0.241360\pi$
$373$	−1.11913	−	1.29155i	−0.0579465	−	0.0668738i	−0.783983	+	0.620783i	$0.786815\pi$
$374$	−5.17519	−	17.6251i	−0.267603	−	0.911372i
$375$	19.0189	+	3.64445i	0.982131	+	0.188199i
$376$	−2.90048	+	6.35116i	−0.149581	+	0.327536i
$377$	5.69382	−	6.57102i	0.293247	−	0.338425i
$378$	−2.90607	−	0.682762i	−0.149472	−	0.0351175i
$379$	−16.0166	+	2.30284i	−0.822716	+	0.118289i	−0.540801	−	0.841151i	$-0.681879\pi$
$379$	−16.0166	+	2.30284i	−0.822716	+	0.118289i	−0.281915	+	0.959439i	$0.590970\pi$
$380$	1.58487	−	0.595095i	0.0813021	−	0.0305277i
$381$	−8.53524	−	27.2176i	−0.437274	−	1.39440i
$382$	−5.82106	+	6.71787i	−0.297832	+	0.343716i
$383$	−24.9667	−	11.4019i	−1.27574	−	0.582611i	−0.341711	−	0.939805i	$-0.611006\pi$
$383$	−24.9667	−	11.4019i	−1.27574	−	0.582611i	−0.934030	+	0.357194i	$0.883734\pi$
$384$	1.15799	+	1.28804i	0.0590934	+	0.0657302i
$385$	4.88580	−	2.68180i	0.249004	−	0.136677i
$386$	−12.2701	+	10.6321i	−0.624533	+	0.541161i
$387$	9.44275	+	10.1247i	0.480002	+	0.514669i
$388$	−3.23093	−	7.07475i	−0.164026	−	0.359166i
$389$	−4.66718	+	32.4610i	−0.236636	+	1.64584i	0.431730	+	0.902003i	$0.357903\pi$
$389$	−4.66718	+	32.4610i	−0.236636	+	1.64584i	−0.668365	+	0.743833i	$0.733006\pi$
$390$	−0.373880	+	7.33581i	−0.0189321	+	0.371463i
$391$	−14.2347	−	14.4801i	−0.719882	−	0.732291i
$392$	−6.66995			−0.336883
$393$	7.35527	+	3.19786i	0.371024	+	0.161311i
$394$	−6.22483	−	13.6305i	−0.313602	−	0.686694i
$395$	−1.46570	+	21.1460i	−0.0737475	+	1.06397i
$396$	−2.32200	−	12.8069i	−0.116685	−	0.643570i
$397$	−4.05961	−	13.8257i	−0.203746	−	0.693894i	−0.996442	−	0.0842780i	$-0.973142\pi$
$397$	−4.05961	−	13.8257i	−0.203746	−	0.693894i	0.792696	−	0.609616i	$-0.208677\pi$
$398$	−8.13279	+	12.6549i	−0.407660	+	0.634331i
$399$	−0.578273	−	0.482855i	−0.0289499	−	0.0241730i
$400$	−1.38757	+	4.80361i	−0.0693784	+	0.240180i
$401$	19.4753	−	12.5160i	0.972550	−	0.625020i	0.0451061	−	0.998982i	$-0.485637\pi$
$401$	19.4753	−	12.5160i	0.972550	−	0.625020i	0.927444	+	0.373962i	$0.122001\pi$
$402$	2.27291	−	18.1591i	0.113363	−	0.905692i
$403$	5.13211	−	0.737886i	0.255649	−	0.0367567i
$404$	7.76326	+	12.0799i	0.386237	+	0.600996i
$405$	−20.1245	+	0.0788663i	−0.999992	+	0.00391890i
$406$	−2.39578	−	1.09411i	−0.118900	−	0.0543000i
$407$	−2.61654	−	1.68155i	−0.129697	−	0.0833512i
$408$	−0.134050	−	7.33216i	−0.00663645	−	0.362996i
$409$	14.8528	+	17.1410i	0.734422	+	0.847568i	0.992962	−	0.118432i	$-0.0377868\pi$
$409$	14.8528	+	17.1410i	0.734422	+	0.847568i	−0.258540	+	0.966001i	$0.583241\pi$
$410$	−0.140864	+	2.03227i	−0.00695677	+	0.100367i
$411$	14.2674	−	2.31828i	0.703759	−	0.114352i
$412$	0.130735	−	0.909280i	0.00644084	−	0.0447970i
$413$		−	2.63346i		−	0.129584i
$414$	−8.94136	−	11.2717i	−0.439444	−	0.553976i
$415$	−5.23995	−	23.8354i	−0.257219	−	1.17004i
$416$	−1.87725	−	0.269908i	−0.0920399	−	0.0132333i
$417$	−0.763421	−	4.69833i	−0.0373849	−	0.230078i
$418$	0.925405	−	3.15164i	0.0452631	−	0.154152i
$419$	24.8634	+	28.6938i	1.21465	+	1.40179i	0.890005	+	0.455951i	$0.150701\pi$
$419$	24.8634	+	28.6938i	1.21465	+	1.40179i	0.324650	+	0.945834i	$0.394754\pi$
$420$	2.16405	−	0.517385i	0.105595	−	0.0252458i
$421$	5.69135	−	8.85592i	0.277380	−	0.431611i	−0.674413	−	0.738355i	$-0.735603\pi$
$421$	5.69135	−	8.85592i	0.277380	−	0.431611i	0.951792	+	0.306744i	$0.0992394\pi$
$422$	−11.6637	+	25.5400i	−0.567780	+	1.24327i
$423$	19.8687	−	6.63196i	0.966052	−	0.322457i
$424$	−1.10788	−	1.72390i	−0.0538036	−	0.0837200i
$425$	17.7586	−	11.5233i	0.861418	−	0.558963i
$426$	20.2749	+	2.53774i	0.982322	+	0.122954i
$427$	−1.34141	−	2.08727i	−0.0649152	−	0.101010i
$428$	8.88017	+	7.69471i	0.429239	+	0.371938i
$429$	10.9397	+	9.13456i	0.528172	+	0.441021i
$430$	−9.67650	−	3.58495i	−0.466642	−	0.172882i
$431$	−31.8931	+	9.36465i	−1.53624	+	0.451080i	−0.936952	−	0.349457i	$-0.886366\pi$
$431$	−31.8931	+	9.36465i	−1.53624	+	0.451080i	−0.599284	+	0.800537i	$0.704548\pi$
$432$	0.456456	−	5.17606i	0.0219613	−	0.249034i
$433$	36.5857	+	10.7425i	1.75820	+	0.516253i	0.991987	−	0.126340i	$-0.0403230\pi$
$433$	36.5857	+	10.7425i	1.75820	+	0.516253i	0.766208	+	0.642593i	$0.222141\pi$
$434$	−0.652450	−	1.42867i	−0.0313186	−	0.0685781i
$435$	−17.4234	−	3.41817i	−0.835390	−	0.163889i
$436$			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	0.918960	+	0.394350i	$0.129030\pi$
$439$	−1.54789	+	10.7658i	−0.0738770	+	0.513826i	−0.992837	+	0.119475i	$0.961879\pi$
$440$	5.83083	+	7.75351i	0.277974	+	0.369634i
$441$	13.6477	+	14.6333i	0.649889	+	0.696826i
$442$	5.25846	+	6.06859i	0.250119	+	0.288653i
$443$	−23.6937	+	6.95711i	−1.12572	+	0.330542i	−0.791026	−	0.611783i	$-0.790452\pi$
$443$	−23.6937	+	6.95711i	−1.12572	+	0.330542i	−0.334698	+	0.942325i	$0.608634\pi$
$444$	−0.830155	−	0.923390i	−0.0393974	−	0.0438221i
$445$	−5.13575	+	23.8609i	−0.243458	+	1.13112i
$446$	−3.73902	−	3.23988i	−0.177048	−	0.153413i
$447$	35.5126	−	11.1365i	1.67969	−	0.526737i
$448$	0.0817602	+	0.568655i	0.00386281	+	0.0268664i
$449$	16.8672	−	2.42514i	0.796013	−	0.114449i	0.267704	−	0.963501i	$-0.413735\pi$
$449$	16.8672	−	2.42514i	0.796013	−	0.114449i	0.528309	+	0.849052i	$0.322826\pi$
$450$	13.3779	−	6.78465i	0.630641	−	0.319832i
$451$	2.98718	+	2.58841i	0.140661	+	0.121883i
$452$	−15.7492	−	7.19241i	−0.740780	−	0.338303i
$453$	9.07712	+	10.0966i	0.426480	+	0.474378i
$454$	−0.797948	−	2.71756i	−0.0374495	−	0.127541i
$455$	−1.45577	+	1.95362i	−0.0682476	+	0.0915869i
$456$	0.688671	−	1.11593i	0.0322500	−	0.0522582i
$457$	2.74112	+	6.00221i	0.128224	+	0.280771i	0.962846	−	0.270052i	$-0.0870410\pi$
$457$	2.74112	+	6.00221i	0.128224	+	0.280771i	−0.834622	+	0.550824i	$0.814314\pi$
$458$	19.6412	+	2.82398i	0.917773	+	0.131956i
$459$	−15.8119	+	15.2967i	−0.738036	+	0.713991i
$460$	9.72624	+	4.51666i	0.453488	+	0.210590i
$461$		−	19.2937i		−	0.898596i	−0.893382	−	0.449298i	$-0.851674\pi$
$461$		−	19.2937i		−	0.898596i	0.893382	−	0.449298i	$-0.148326\pi$
$462$	1.72133	−	3.95915i	0.0800835	−	0.184196i
$463$	−34.3737	+	15.6979i	−1.59748	+	0.729545i	−0.997513	−	0.0704797i	$-0.977547\pi$
$463$	−34.3737	+	15.6979i	−1.59748	+	0.729545i	−0.599967	+	0.800025i	$0.704820\pi$
$464$	1.29159	−	4.39876i	0.0599607	−	0.204208i
$465$	−6.51745	−	8.34452i	−0.302240	−	0.386968i
$466$	−5.87908	+	1.72625i	−0.272343	+	0.0799672i
$467$	10.4129	−	16.2028i	0.481852	−	0.749776i	−0.512179	−	0.858879i	$-0.671161\pi$
$467$	10.4129	−	16.2028i	0.481852	−	0.749776i	0.994030	+	0.109103i	$0.0347978\pi$
$468$	3.24897	+	4.67082i	0.150184	+	0.215909i
$469$	3.97511	−	4.58752i	0.183553	−	0.211832i
$470$	−11.0154	+	11.0639i	−0.508103	+	0.510341i
$471$	0.375219	−	2.99775i	0.0172892	−	0.138129i
$472$	4.53723	−	0.652356i	0.208843	−	0.0300271i
$473$	−16.8436	+	10.8247i	−0.774470	+	0.497721i
$474$	9.12775	+	13.6479i	0.419252	+	0.626870i
$475$	3.78543	−	0.0166341i	0.173687	−	0.000763226i
$476$	1.31506	−	2.04627i	0.0602755	−	0.0937905i
$477$	−1.51522	+	5.95796i	−0.0693770	+	0.272796i
$478$	−15.4131	+	13.3555i	−0.704978	+	0.610867i
$479$	−7.04036	−	2.06724i	−0.321682	−	0.0944545i	0.116905	−	0.993143i	$-0.462703\pi$
$479$	−7.04036	−	2.06724i	−0.321682	−	0.0944545i	−0.438587	+	0.898689i	$0.644521\pi$
$480$	1.42749	+	3.60032i	0.0651556	+	0.164331i
$481$	1.34579	+	0.193495i	0.0613627	+	0.00882263i
$482$		−	10.6776i		−	0.486351i
$483$	−0.386767	−	4.75647i	−0.0175985	−	0.216427i
$484$	7.82312			0.355597
$485$	−1.27879	−	17.3442i	−0.0580667	−	0.787557i
$486$	−12.2899	+	9.58954i	−0.557479	+	0.434990i
$487$	−0.132000	+	0.449551i	−0.00598149	+	0.0203711i	−0.962430	−	0.271531i	$-0.912470\pi$
$487$	−0.132000	+	0.449551i	−0.00598149	+	0.0203711i	0.956448	+	0.291902i	$0.0942882\pi$
$488$	3.26390	−	2.82819i	0.147750	−	0.128026i
$489$	−0.442842	−	24.2223i	−0.0200260	−	1.09537i
$490$	−13.9855	−	5.18135i	−0.631801	−	0.234070i
$491$	6.87073	+	3.13776i	0.310072	+	0.141605i	0.564373	−	0.825520i	$-0.309118\pi$
$491$	6.87073	+	3.13776i	0.310072	+	0.141605i	−0.254301	+	0.967125i	$0.581845\pi$
$492$	0.877238	+	1.31166i	0.0395489	+	0.0591341i
$493$	−16.3290	+	10.4940i	−0.735421	+	0.472626i
$494$	0.204346	+	1.42125i	0.00919394	+	0.0639453i
$495$	5.07989	−	28.6572i	0.228324	−	1.28805i
$496$	2.29985	−	1.47803i	0.103266	−	0.0663653i
$497$	5.12204	+	4.43828i	0.229755	+	0.199084i
$498$	−14.5104	−	12.1161i	−0.650226	−	0.542935i
$499$	−13.8982	−	8.93186i	−0.622171	−	0.399845i	0.191233	−	0.981545i	$-0.438751\pi$
$499$	−13.8982	−	8.93186i	−0.622171	−	0.399845i	−0.813404	+	0.581700i	$0.802388\pi$
$500$	−6.64099	+	8.99429i	−0.296994	+	0.402237i
$501$	3.61646	+	7.55055i	0.161571	+	0.337334i
$502$	−29.5540	−	8.67784i	−1.31906	−	0.387311i
$503$	23.3427	−	10.6603i	1.04080	−	0.475317i	0.179683	−	0.983725i	$-0.442493\pi$
$503$	23.3427	−	10.6603i	1.04080	−	0.475317i	0.861117	+	0.508407i	$0.169765\pi$
$504$	1.08029	−	1.34292i	0.0481200	−	0.0598186i
$505$	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	$-0.382148\pi$
$509$	29.4046	−	13.4286i	1.30334	−	0.595214i	0.941495	+	0.337026i	$0.109421\pi$
$510$	5.41470	−	15.4782i	0.239767	−	0.685385i
$511$	−2.34325	+	2.03044i	−0.103659	+	0.0898212i
$512$	−0.959493	+	0.281733i	−0.0424040	+	0.0124509i
$513$	−3.85739	+	0.772461i	−0.170308	+	0.0341050i
$514$	3.62655	−	7.94103i	0.159960	−	0.350264i
$515$	0.980472	−	1.80502i	0.0432048	−	0.0795386i
$516$	−7.62701	+	2.39177i	−0.335761	+	0.105292i
$517$	4.31105	+	29.9840i	0.189600	+	1.31870i
$518$	−0.0586133	−	0.407664i	−0.00257532	−	0.0179117i
$519$	−41.2861	+	12.9470i	−1.81226	+	0.568311i
$520$	−3.72654	−	2.02423i	−0.163420	−	0.0887684i
$521$	−10.4930	+	22.9765i	−0.459706	+	1.00662i	0.527848	+	0.849339i	$0.322999\pi$
$521$	−10.4930	+	22.9765i	−0.459706	+	1.00662i	−0.987554	+	0.157278i	$0.949728\pi$
$522$	−12.2933	+	6.16685i	−0.538065	+	0.269916i
$523$	−12.4314	+	3.65020i	−0.543588	+	0.159612i	−0.541987	−	0.840387i	$-0.682328\pi$
$523$	−12.4314	+	3.65020i	−0.543588	+	0.159612i	−0.00160124	+	0.999999i	$0.500510\pi$
$524$	−3.49954	+	3.03237i	−0.152878	+	0.132470i
$525$	4.93948	+	0.596226i	0.215577	+	0.0260214i
$526$	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
$531$	−10.7150	−	8.61953i	−0.464994	−	0.374056i
$532$	0.395646	−	0.180685i	0.0171534	−	0.00783370i
$533$	−1.65785	−	0.486789i	−0.0718096	−	0.0210852i
$534$	8.16683	+	17.0510i	0.353413	+	0.737867i
$535$	12.6425	+	23.0325i	0.546583	+	0.995784i
$536$	8.88864	+	5.71238i	0.383931	+	0.246737i
$537$	−34.1599	−	28.5233i	−1.47411	−	1.23087i
$538$	−2.30705	−	1.99907i	−0.0994642	−	0.0861862i
$539$	−24.3442	+	15.6451i	−1.04858	+	0.673880i
$540$	4.97797	−	10.4986i	0.214218	−	0.451786i
$541$	−6.07479	−	42.2511i	−0.261176	−	1.81652i	−0.524051	−	0.851687i	$-0.675580\pi$
$541$	−6.07479	−	42.2511i	−0.261176	−	1.81652i	0.262876	−	0.964830i	$-0.415329\pi$
$542$	13.6259	−	8.75683i	0.585282	−	0.376138i
$543$	−7.70698	−	11.5236i	−0.330738	−	0.494524i
$544$	3.85132	+	1.75884i	0.165124	+	0.0754096i
$545$	−1.71151	+	4.61970i	−0.0733128	+	0.197886i
$546$	0.0344969	+	1.88689i	0.00147633	+	0.0807513i
$547$	−25.1502	+	21.7928i	−1.07535	+	0.931792i	−0.997872	−	0.0652022i	$-0.979231\pi$
$547$	−25.1502	+	21.7928i	−1.07535	+	0.931792i	−0.0774734	+	0.996994i	$0.524685\pi$
$548$	−2.35115	+	8.00728i	−0.100436	+	0.342054i
$549$	−12.8832	−	1.37387i	−0.549844	−	0.0586355i
$550$	6.20297	+	20.7870i	0.264496	+	0.886363i
$551$	−3.47087			−0.147864
$552$	8.09922	−	1.84464i	0.344726	−	0.0785129i
$553$			5.44598i			0.231587i
$554$	21.6554	+	3.11357i	0.920049	+	0.132283i
$555$	−1.02336	−	2.58104i	−0.0434391	−	0.109559i
$556$	2.63684	+	0.774245i	0.111827	+	0.0328353i
$557$	−17.4925	+	15.1573i	−0.741181	+	0.642237i	−0.941314	−	0.337532i	$-0.890408\pi$
$557$	−17.4925	+	15.1573i	−0.741181	+	0.642237i	0.200133	+	0.979769i	$0.435862\pi$
$558$	−7.94850	−	2.02145i	−0.336487	−	0.0855747i
$559$	4.73192	−	7.36301i	0.200139	−	0.311422i
$560$	−0.270308	+	1.25587i	−0.0114226	+	0.0530700i
$561$	−17.6876	−	26.4467i	−0.746771	−	1.11658i
$562$	−18.5880	+	11.9458i	−0.784088	+	0.503903i
$563$	5.50318	−	0.791238i	0.231932	−	0.0333467i	−0.0253690	−	0.999678i	$-0.508076\pi$
$563$	5.50318	−	0.791238i	0.231932	−	0.0333467i	0.257301	+	0.966331i	$0.417167\pi$
$564$	−1.50197	+	11.9998i	−0.0632444	+	0.505281i
$565$	−27.4356	−	27.3153i	−1.15422	−	1.14916i
$566$	−7.14266	+	8.24307i	−0.300228	+	0.346482i
$567$	−5.15670	+	0.377740i	−0.216561	+	0.0158636i
$568$	−6.37797	+	9.92432i	−0.267614	+	0.416415i
$569$	0.643026	−	0.188810i	0.0269571	−	0.00791531i	−0.268226	−	0.963356i	$-0.586437\pi$
$569$	0.643026	−	0.188810i	0.0269571	−	0.00791531i	0.295183	+	0.955441i	$0.404619\pi$
$570$	2.31088	−	1.80490i	0.0967921	−	0.0755991i
$571$	1.67479	−	5.70380i	0.0700876	−	0.238696i	−0.916998	−	0.398893i	$-0.869395\pi$
$571$	1.67479	−	5.70380i	0.0700876	−	0.238696i	0.987085	+	0.160196i	$0.0512127\pi$
$572$	−7.48475	+	3.41817i	−0.312953	+	0.142921i
$573$	−6.13875	+	14.1195i	−0.256450	+	0.589849i
$574$			0.523395i			0.0218461i
$575$	16.8853	+	17.0261i	0.704166	+	0.710036i
$576$	2.58136	+	1.52859i	0.107557	+	0.0636912i
$577$	−2.33005	−	0.335011i	−0.0970015	−	0.0139467i	0.0936432	−	0.995606i	$-0.470149\pi$
$577$	−2.33005	−	0.335011i	−0.0970015	−	0.0139467i	−0.190645	+	0.981659i	$0.561058\pi$
$578$	−0.384744	−	0.842472i	−0.0160032	−	0.0350422i
$579$	−14.7684	+	23.9309i	−0.613755	+	0.994534i
$580$	6.12526	−	8.21997i	0.254338	−	0.341316i
$581$	−1.76651	−	6.01617i	−0.0732871	−	0.249593i
$582$	−9.00638	−	10.0179i	−0.373326	−	0.415255i
$583$	−8.08718	−	3.69329i	−0.334937	−	0.152960i
$584$	−4.07875	−	3.53425i	−0.168780	−	0.146248i
$585$	3.18404	+	12.3176i	0.131644	+	0.509271i
$586$	3.78289	−	0.543897i	0.156270	−	0.0224682i
$587$	−0.0775637	−	0.539468i	−0.00320140	−	0.0222662i	0.988158	−	0.153439i	$-0.0490348\pi$
$587$	−0.0775637	−	0.539468i	−0.00320140	−	0.0222662i	−0.991360	+	0.131173i	$0.958126\pi$
$588$	−11.0234	+	3.45685i	−0.454596	+	0.142558i
$589$	−1.56423	−	1.35541i	−0.0644529	−	0.0558488i
$590$	10.0204	+	2.15676i	0.412534	+	0.0887924i
$591$	−17.3520	−	19.3008i	−0.713767	−	0.793930i
$592$	0.687854	−	0.201972i	0.0282706	−	0.00830100i
$593$	−18.9862	−	21.9112i	−0.779670	−	0.899787i	0.217416	−	0.976079i	$-0.430237\pi$
$593$	−18.9862	−	21.9112i	−0.779670	−	0.899787i	−0.997086	+	0.0762921i	$0.975692\pi$
$594$	−10.4750	−	19.9624i	−0.429795	−	0.819068i
$595$	4.34699	−	3.26904i	0.178209	−	0.134018i
$596$	−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	$-0.316134\pi$
$600$	0.196351	+	8.65803i	0.00801601	+	0.353463i
$601$	4.61828	+	10.1126i	0.188383	+	0.412502i	0.980132	−	0.198344i	$-0.0635564\pi$
$601$	4.61828	+	10.1126i	0.188383	+	0.412502i	−0.791749	+	0.610847i	$0.790829\pi$
$602$	−2.54387	−	0.746949i	−0.103681	−	0.0304434i
$603$	−5.65491	−	31.1893i	−0.230286	−	1.27013i
$604$	−7.52116	+	2.20841i	−0.306032	+	0.0898590i
$605$	16.4035	+	6.07716i	0.666897	+	0.247072i
$606$	19.0909	+	15.9408i	0.775516	+	0.647552i
$607$	−8.31904	−	7.20849i	−0.337659	−	0.292584i	0.469482	−	0.882942i	$-0.344441\pi$
$607$	−8.31904	−	7.20849i	−0.337659	−	0.292584i	−0.807141	+	0.590359i	$0.798986\pi$
$608$	0.409315	+	0.636907i	0.0165999	+	0.0258300i
$609$	−4.52653	−	0.566572i	−0.183424	−	0.0229586i
$610$	9.04074	−	3.39467i	0.366049	−	0.137446i
$611$	−7.15916	−	11.1399i	−0.289629	−	0.450671i
$612$	−4.02159	−	12.0483i	−0.162563	−	0.487025i
$613$	1.45018	−	3.17544i	0.0585721	−	0.128255i	−0.878083	−	0.478509i	$-0.841177\pi$
$613$	1.45018	−	3.17544i	0.0585721	−	0.128255i	0.936655	+	0.350254i	$0.113905\pi$
$614$	−10.8342	+	16.8583i	−0.437233	+	0.680347i
$615$	0.820466	+	3.43173i	0.0330844	+	0.138381i
$616$	1.63225	+	1.88372i	0.0657652	+	0.0758971i
$617$	11.5226	−	39.2424i	0.463883	−	1.57984i	−0.312718	−	0.949846i	$-0.601239\pi$
$617$	11.5226	−	39.2424i	0.463883	−	1.57984i	0.776601	−	0.629993i	$-0.216942\pi$
$618$	−0.255190	−	1.57052i	−0.0102652	−	0.0631755i
$619$	−16.3081	−	2.34475i	−0.655477	−	0.0942433i	−0.193451	−	0.981110i	$-0.561968\pi$
$619$	−16.3081	−	2.34475i	−0.655477	−	0.0942433i	−0.462026	+	0.886867i	$0.652877\pi$
$620$	5.97048	−	1.31254i	0.239780	−	0.0527130i
$621$	−20.6191	−	13.9947i	−0.827418	−	0.561587i
$622$			30.4598i			1.22133i
$623$	−0.892438	+	6.20704i	−0.0357548	+	0.248680i
$624$	−3.24241	+	0.526852i	−0.129800	+	0.0210910i
$625$	−20.9117	+	13.7003i	−0.836470	+	0.548013i
$626$	7.66085	+	8.84109i	0.306189	+	0.353361i
$627$	−0.103996	−	5.68831i	−0.00415321	−	0.227169i
$628$	1.46736	+	0.943017i	0.0585541	+	0.0376305i
$629$	−2.76098	−	1.26090i	−0.110088	−	0.0502753i
$630$	3.30836	−	1.97664i	0.131808	−	0.0787514i
$631$	1.99723	+	3.10775i	0.0795086	+	0.123718i	0.878730	−	0.477318i	$-0.158391\pi$
$631$	1.99723	+	3.10775i	0.0795086	+	0.123718i	−0.799222	+	0.601036i	$0.794755\pi$
$632$	−9.38299	+	1.34907i	−0.373235	+	0.0536632i
$633$	−6.03989	+	48.2547i	−0.240064	+	1.91795i
$634$	−17.3033	+	11.1202i	−0.687202	+	0.441638i
$635$	32.3593	+	17.5773i	1.28414	+	0.697534i
$636$	−2.72444	−	2.27489i	−0.108031	−	0.0902054i
$637$	6.83907	−	10.6418i	0.270974	−	0.421644i
$638$	−5.60366	−	19.0843i	−0.221851	−	0.755555i
$639$	34.8234	−	6.31380i	1.37759	−	0.249770i
$640$	−2.23072	−	0.154619i	−0.0881768	−	0.00611183i
$641$	−10.9234	−	23.9190i	−0.431450	−	0.944743i	−0.993089	−	0.117361i	$-0.962556\pi$
$641$	−10.9234	−	23.9190i	−0.431450	−	0.944743i	0.561639	−	0.827382i	$-0.310171\pi$
$642$	18.6642	+	8.11466i	0.736615	+	0.320260i
$643$	5.68433			0.224168			0.112084	−	0.993699i	$-0.464247\pi$
$643$	5.68433			0.224168			0.112084	+	0.993699i	$0.464247\pi$
$644$	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	0.961744	+	0.273951i	$0.0883307\pi$
$647$	13.7095	+	30.0195i	0.538974	+	1.18019i	−0.422769	+	0.906237i	$0.638942\pi$
$648$	−1.92823	−	8.79101i	−0.0757479	−	0.345344i
$649$	15.0300	−	13.0235i	0.589978	−	0.511219i
$650$	−6.24134	−	7.13925i	−0.244805	−	0.280025i
$651$	−1.81874	−	2.02300i	−0.0712819	−	0.0792876i
$652$	12.7231	+	5.81044i	0.498274	+	0.227554i
$653$	−18.3593	+	21.1877i	−0.718453	+	0.829139i	−0.991120	−	0.132969i	$-0.957549\pi$
$653$	−18.3593	+	21.1877i	−0.718453	+	0.829139i	0.272667	+	0.962108i	$0.412094\pi$
$654$	1.14187	+	3.64124i	0.0446505	+	0.142384i
$655$	−9.69344	+	3.63974i	−0.378754	+	0.142217i
$656$	−0.901768	+	0.129655i	−0.0352081	+	0.00506217i
$657$	0.591819	+	16.1800i	0.0230891	+	0.631244i
$658$	−2.62681	+	3.03150i	−0.102404	+	0.118180i
$659$	−12.2381	+	26.7977i	−0.476729	+	1.04389i	0.506621	+	0.862169i	$0.330894\pi$
$659$	−12.2381	+	26.7977i	−0.476729	+	1.04389i	−0.983350	+	0.181722i	$0.941833\pi$
$660$	13.6550	+	9.79222i	0.531520	+	0.381162i
$661$	3.70112	+	12.6048i	0.143957	+	0.490272i	0.999629	−	0.0272470i	$-0.00867405\pi$
$661$	3.70112	+	12.6048i	0.143957	+	0.490272i	−0.855672	+	0.517518i	$0.826856\pi$
$662$	13.2938	+	15.3419i	0.516678	+	0.596278i
$663$	11.8358	+	7.30420i	0.459664	+	0.283672i
$664$	9.92779	−	4.53387i	0.385273	−	0.175948i
$665$	0.969948	−	0.0715144i	0.0376130	−	0.00277321i
$666$	−1.85056	−	1.09583i	−0.0717077	−	0.0424627i
$667$	−15.4133	−	15.6790i	−0.596804	−	0.607092i
$668$	−4.83355			−0.187016
$669$	−7.85859	−	3.41670i	−0.303831	−	0.132097i
$670$	14.2002	+	18.8826i	0.548600	+	0.729497i
$671$	5.27889	−	17.9782i	0.203789	−	0.694042i
$672$	0.429842	+	0.897437i	0.0165815	+	0.0346194i
$673$	−1.70195	−	5.79630i	−0.0656052	−	0.223431i	0.920165	−	0.391532i	$-0.128055\pi$
$673$	−1.70195	−	5.79630i	−0.0656052	−	0.223431i	−0.985770	+	0.168101i	$0.946237\pi$
$674$	16.1017	+	10.3479i	0.620214	+	0.398587i
$675$	18.5933	−	18.1463i	0.715656	−	0.698453i
$676$	−6.15770	+	7.10637i	−0.236835	+	0.273322i
$677$	20.1519	+	31.3569i	0.774500	+	1.20515i	0.974288	+	0.225306i	$0.0723382\pi$
$677$	20.1519	+	31.3569i	0.774500	+	1.20515i	−0.199788	+	0.979839i	$0.564025\pi$
$678$	−29.7562	−	3.72449i	−1.14278	−	0.143038i
$679$	−0.635898	−	4.42277i	−0.0244035	−	0.169730i
$680$	6.70912	+	6.67971i	0.257283	+	0.256155i
$681$	−2.72720	−	4.07774i	−0.104506	−	0.156259i
$682$	4.92721	−	10.7891i	0.188673	−	0.413135i
$683$	−26.2398	−	16.8633i	−1.00404	−	0.645255i	−0.0681933	−	0.997672i	$-0.521723\pi$
$683$	−26.2398	−	16.8633i	−1.00404	−	0.645255i	−0.935843	+	0.352417i	$0.885360\pi$
$684$	0.559807	−	2.20121i	0.0214048	−	0.0841653i
$685$	−11.1501	+	14.9632i	−0.426023	+	0.571715i
$686$	−7.53530	−	2.21256i	−0.287699	−	0.0844760i
$687$	33.9245	−	5.51231i	1.29430	−	0.210308i
$688$	0.656769	−	4.56793i	0.0250391	−	0.174151i
$689$	3.88643			0.148061
$690$	18.4153	+	2.42382i	0.701060	+	0.0922731i
$691$	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
$693$	0.792912	−	7.43538i	0.0301202	−	0.282447i
$694$	−19.5629	−	5.74418i	−0.742596	−	0.218046i
$695$	4.92746	+	3.67178i	0.186909	+	0.139279i
$696$	−0.145148	−	7.93920i	−0.00550182	−	0.300935i
$697$	3.24496	+	2.08541i	0.122911	+	0.0789904i
$698$	3.92459	−	8.59366i	0.148548	−	0.325275i
$699$	−8.82165	+	5.89993i	−0.333666	+	0.223156i
$700$	−1.54236	+	2.42331i	−0.0582958	+	0.0915925i
$701$	−2.27831	−	15.8460i	−0.0860507	−	0.598496i	−0.986528	−	0.163593i	$-0.947692\pi$
$701$	−2.27831	−	15.8460i	−0.0860507	−	0.598496i	0.900477	−	0.434903i	$-0.143217\pi$
$702$	7.79031	+	6.03558i	0.294026	+	0.227798i
$703$	−0.293435	−	0.456594i	−0.0110671	−	0.0172208i
$704$	−2.84115	+	3.27887i	−0.107080	+	0.123577i
$705$	−12.4710	+	23.9943i	−0.469684	+	0.903676i
$706$	0.286025	+	0.183817i	0.0107647	+	0.00691806i
$707$	2.32415	+	7.91532i	0.0874086	+	0.297686i
$708$	7.16056	−	3.42966i	0.269110	−	0.128895i
$709$	3.93294	−	13.3944i	0.147705	−	0.503036i	−0.852088	−	0.523399i	$-0.824664\pi$
$709$	3.93294	−	13.3944i	0.147705	−	0.503036i	0.999793	+	0.0203625i	$0.00648203\pi$
$710$	−21.0827	+	15.8547i	−0.791220	+	0.595017i
$711$	22.1587	+	17.8252i	0.831016	+	0.668496i
$712$	−10.9153			−0.409069
$713$	−0.823550	−	13.0851i	−0.0308422	−	0.490043i
$714$	1.11286	−	4.06341i	0.0416478	−	0.152069i
$715$	−18.3493	+	1.35290i	−0.686225	+	0.0505954i
$716$	23.3717	−	10.6735i	0.873441	−	0.398887i
$717$	−18.5513	+	30.0607i	−0.692811	+	1.12264i
$718$	19.9323	+	23.0031i	0.743866	+	0.858467i
$719$	−11.4827	−	39.1066i	−0.428234	−	1.45843i	−0.837713	−	0.546111i	$-0.816108\pi$
$719$	−11.4827	−	39.1066i	−0.428234	−	1.45843i	0.409479	−	0.912320i	$-0.365711\pi$
$720$	4.22514	+	5.21039i	0.157462	+	0.194180i
$721$	0.219237	−	0.480063i	0.00816483	−	0.0178785i
$722$	−12.0670	+	13.9261i	−0.449087	+	0.518274i
$723$	−5.53390	−	17.6468i	−0.205808	−	0.656291i
$724$	7.92249	−	1.13908i	0.294437	−	0.0423337i
$725$	19.2289	−	12.4774i	0.714142	−	0.463398i
$726$	12.9292	−	4.05451i	0.479848	−	0.150477i
$727$	−9.06946	+	10.4667i	−0.336368	+	0.388189i	−0.898584	−	0.438801i	$-0.855403\pi$
$727$	−9.06946	+	10.4667i	−0.336368	+	0.388189i	0.562217	+	0.826990i	$0.309949\pi$
$728$	−0.991113	−	0.452626i	−0.0367331	−	0.0167754i
$729$	−15.3414	+	22.2181i	−0.568199	+	0.822891i
$730$	−5.80681	−	10.5791i	−0.214920	−	0.391549i
$731$	−14.7667	+	12.7954i	−0.546167	+	0.473256i
$732$	3.92846	−	6.36572i	0.145200	−	0.235284i
$733$	0.916145	+	2.00608i	0.0338386	+	0.0740962i	0.925797	−	0.378022i	$-0.123396\pi$
$733$	0.916145	+	2.00608i	0.0338386	+	0.0740962i	−0.891958	+	0.452118i	$0.850668\pi$
$734$	−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
$738$	2.12960	+	1.71312i	0.0783917	+	0.0630607i
$739$	−8.91485	−	19.5208i	−0.327938	−	0.718084i	0.671806	−	0.740727i	$-0.265519\pi$
$739$	−8.91485	−	19.5208i	−0.327938	−	0.718084i	−0.999744	+	0.0226436i	$0.992792\pi$
$740$	1.59918	+	0.110845i	0.0587872	+	0.00407474i
$741$	1.07432	+	2.24299i	0.0394660	+	0.0823983i
$742$	−0.331676	−	1.12958i	−0.0121762	−	0.0414684i
$743$	−17.5658	+	27.3330i	−0.644428	+	1.00275i	0.353309	+	0.935507i	$0.385057\pi$
$743$	−17.5658	+	27.3330i	−0.644428	+	1.00275i	−0.997737	+	0.0672427i	$0.978580\pi$
$744$	3.03493	−	3.63467i	0.111266	−	0.133254i
$745$	−22.9342	+	42.2212i	−0.840245	+	1.54686i
$746$	1.43767	−	0.923935i	0.0526369	−	0.0338277i
$747$	−30.2606	−	12.5039i	−1.10718	−	0.457492i
$748$	18.1822	−	2.61421i	0.664807	−	0.0955848i
$749$	3.64959	+	5.67887i	0.133353	+	0.207501i
$750$	−6.31403	+	18.3066i	−0.230556	+	0.668464i
$751$	−29.0480	−	13.2658i	−1.05998	−	0.484074i	−0.192367	−	0.981323i	$-0.561616\pi$
$751$	−29.0480	−	13.2658i	−1.05998	−	0.484074i	−0.867608	+	0.497249i	$0.834344\pi$
$752$	−5.87373	−	3.77482i	−0.214193	−	0.137653i
$753$	−53.3412	+	0.975207i	−1.94386	+	0.0355385i
$754$	5.69382	+	6.57102i	0.207357	+	0.239302i
$755$	−17.4859	−	1.21201i	−0.636376	−	0.0441094i
$756$	1.08939	−	2.77933i	0.0396207	−	0.101083i
$757$	5.12196	−	35.6240i	0.186161	−	1.29478i	−0.655674	−	0.755044i	$-0.727616\pi$
$757$	5.12196	−	35.6240i	0.186161	−	1.29478i	0.841835	−	0.539734i	$-0.181475\pi$
$758$		−	16.1813i		−	0.587730i
$759$	25.2340	−	25.7302i	0.915936	−	0.933946i
$760$	0.363488	+	1.65343i	0.0131851	+	0.0599761i
$761$	19.8969	+	2.86075i	0.721263	+	0.103702i	0.493165	−	0.869936i	$-0.335840\pi$
$761$	19.8969	+	2.86075i	0.721263	+	0.103702i	0.228099	+	0.973638i	$0.426749\pi$
$762$	28.1553	−	4.57489i	1.01996	−	0.165731i
$763$	−0.356604	+	1.21448i	−0.0129099	+	0.0439672i
$764$	−5.82106	−	6.71787i	−0.210599	−	0.243044i
$765$	0.926933	−	28.3869i	0.0335133	−	1.02633i
$766$	14.8390	−	23.0900i	0.536155	−	0.834274i
$767$	−3.61146	+	7.90799i	−0.130402	+	0.285541i
$768$	−1.43973	+	0.962896i	−0.0519519	+	0.0347455i
$769$	−26.3684	−	41.0300i	−0.950869	−	1.47958i	−0.875956	−	0.482390i	$-0.839769\pi$
$769$	−26.3684	−	41.0300i	−0.950869	−	1.47958i	−0.0749124	−	0.997190i	$-0.523868\pi$
$770$	1.95918	+	5.21773i	0.0706040	+	0.188034i
$771$	1.87796	−	15.0036i	0.0676330	−	0.540343i
$772$	−8.77768	−	13.6583i	−0.315916	−	0.491574i
$773$	−32.9457	−	28.5476i	−1.18498	−	1.02679i	−0.999021	−	0.0442290i	$-0.985917\pi$
$773$	−32.9457	−	28.5476i	−1.18498	−	1.02679i	−0.185954	−	0.982558i	$-0.559538\pi$
$774$	−11.3655	+	7.90573i	−0.408525	+	0.284166i
$775$	13.5385	+	1.88586i	0.486317	+	0.0677420i
$776$	7.46255	−	2.19120i	0.267890	−	0.0786596i
$777$	−0.308151	−	0.643367i	−0.0110548	−	0.0230806i
$778$	−31.4664	−	9.23935i	−1.12812	−	0.331247i
$779$	0.286530	+	0.627412i	0.0102660	+	0.0224794i
$780$	−7.20794	−	1.41407i	−0.258086	−	0.0506318i
$781$			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
$785$	2.34420	+	3.11719i	0.0836682	+	0.111257i
$786$	−4.21208	+	6.82530i	−0.150240	+	0.243450i
$787$	1.46018	+	1.68513i	0.0520497	+	0.0600686i	0.781177	−	0.624309i	$-0.214619\pi$
$787$	1.46018	+	1.68513i	0.0520497	+	0.0600686i	−0.729128	+	0.684378i	$0.760074\pi$
$788$	14.3776	−	4.22165i	0.512182	−	0.150390i
$789$	34.4085	−	30.9343i	1.22498	−	1.10129i
$790$	−20.7222	−	4.46018i	−0.737263	−	0.158686i
$791$	−7.51730	−	6.51378i	−0.267285	−	0.231603i
$792$	13.0070	−	0.475758i	0.462183	−	0.0169053i
$793$	1.16567	+	8.10741i	0.0413942	+	0.287903i
$794$	14.2628	−	2.05068i	0.506167	−	0.0727758i
$795$	−3.94541	−	6.88639i	−0.139929	−	0.244235i
$796$	−11.3686	−	9.85099i	−0.402951	−	0.349159i
$797$	17.7550	+	8.10843i	0.628914	+	0.287215i	0.704260	−	0.709942i	$-0.251279\pi$
$797$	17.7550	+	8.10843i	0.628914	+	0.287215i	−0.0753460	+	0.997157i	$0.524006\pi$
$798$	0.560237	−	0.503670i	0.0198322	−	0.0178297i
$799$	8.32853	+	28.3644i	0.294642	+	1.00346i
$800$	−4.55724	−	2.05707i	−0.161123	−	0.0727284i
$801$	22.3343	+	23.9474i	0.789143	+	0.846138i
$802$	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
$805$	4.63036	+	4.06397i	0.163199	+	0.143236i
$806$			5.18488i			0.182630i
$807$	−4.84892	−	2.10817i	−0.170690	−	0.0742112i
$808$	−13.0617	+	5.96510i	−0.459510	+	0.209851i
$809$	−4.71888	+	16.0710i	−0.165907	+	0.565027i	0.834005	+	0.551757i	$0.186042\pi$
$809$	−4.71888	+	16.0710i	−0.165907	+	0.565027i	−0.999912	+	0.0132704i	$0.995776\pi$
$810$	2.78595	−	19.9308i	0.0978881	−	0.700298i
$811$	4.67490	−	1.37267i	0.164158	−	0.0482011i	−0.198621	−	0.980076i	$-0.563646\pi$
$811$	4.67490	−	1.37267i	0.164158	−	0.0482011i	0.362779	+	0.931875i	$0.381828\pi$
$812$	1.42393	−	2.21568i	0.0499702	−	0.0777552i
$813$	17.9810	−	21.5343i	0.630621	−	0.755240i
$814$	2.03680	−	2.35060i	0.0713899	−	0.0823884i
$815$	22.1640	+	22.0668i	0.776372	+	0.772968i
$816$	7.27660	+	0.910789i	0.254732	+	0.0318840i
$817$	−3.45834	+	0.497235i	−0.120992	+	0.0173960i
$818$	−19.0803	+	12.2622i	−0.667127	+	0.428737i
$819$	1.03493	+	3.10056i	0.0361635	+	0.108342i
$820$	−1.99154	−	0.428653i	−0.0695477	−	0.0149692i
$821$	−19.9985	+	31.1183i	−0.697954	+	1.08604i	0.293548	+	0.955944i	$0.405164\pi$
$821$	−19.9985	+	31.1183i	−0.697954	+	1.08604i	−0.991502	+	0.130093i	$0.958472\pi$
$822$	0.264220	+	14.4521i	0.00921573	+	0.504075i
$823$	−12.4013	+	10.7458i	−0.432281	+	0.374574i	−0.843649	−	0.536896i	$-0.819597\pi$
$823$	−12.4013	+	10.7458i	−0.432281	+	0.374574i	0.411367	+	0.911470i	$0.365051\pi$
$824$	0.881420	+	0.258808i	0.0307057	+	0.00901601i
$825$	21.0250	+	31.1398i	0.731995	+	1.08415i
$826$	2.60665	+	0.374780i	0.0906970	+	0.0130403i
$827$			20.8536i			0.725152i	0.931954	+	0.362576i	$0.118103\pi$
$827$			20.8536i			0.725152i	−0.931954	+	0.362576i	$0.881897\pi$
$828$	12.4295	−	7.24621i	0.431955	−	0.251823i
$829$	45.9011			1.59421			0.797106	−	0.603840i	$-0.206363\pi$
$829$	45.9011			1.59421			0.797106	+	0.603840i	$0.206363\pi$
$830$	24.3385	−	1.79448i	0.844803	−	0.0622874i
$831$	37.4034	−	6.07760i	1.29751	−	0.210829i
$832$	0.534322	−	1.81973i	0.0185243	−	0.0630879i
$833$	−21.3424	+	18.4933i	−0.739472	+	0.640756i
$834$	4.75915	−	0.0870089i	0.164796	−	0.00301287i
$835$	−10.1350	−	3.75480i	−0.350735	−	0.129940i
$836$	2.98786	+	1.36451i	0.103337	+	0.0471926i
$837$	−14.1841	+	0.778654i	−0.490274	+	0.0269142i
$838$	−31.9402	+	20.5267i	−1.10336	+	0.709084i
$839$	−5.15148	−	35.8293i	−0.177849	−	1.23697i	−0.861728	−	0.507370i	$-0.830618\pi$
$839$	−5.15148	−	35.8293i	−0.177849	−	1.23697i	0.683879	−	0.729595i	$-0.260291\pi$
$840$	0.204143	+	2.21565i	0.00704360	+	0.0764473i
$841$	6.71543	−	4.31575i	0.231567	−	0.148819i
$842$	7.95581	+	6.89375i	0.274175	+	0.237574i
$843$	−24.5291	+	29.3764i	−0.844827	+	1.01178i
$844$	−23.6201	−	15.1797i	−0.813037	−	0.522507i
$845$	−18.4318	+	10.1172i	−0.634074	+	0.348041i
$846$	3.73684	+	20.6103i	0.128475	+	0.708598i
$847$	4.31235	+	1.26622i	0.148174	+	0.0435078i
$848$	1.86402	−	0.851270i	0.0640108	−	0.0292327i
$849$	−7.53247	+	17.3251i	−0.258514	+	0.594596i
$850$	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	$-0.330548\pi$
$853$	21.9576	+	3.15703i	0.751814	+	0.108095i	0.244255	+	0.969711i	$0.421457\pi$
$854$	2.25692	−	1.03070i	0.0772304	−	0.0352699i
$855$	2.88375	−	4.18062i	0.0986220	−	0.142974i
$856$	−8.88017	+	7.69471i	−0.303518	+	0.263000i
$857$	46.1218	−	13.5426i	1.57549	−	0.462606i	0.626898	−	0.779102i	$-0.284324\pi$
$857$	46.1218	−	13.5426i	1.57549	−	0.462606i	0.948594	+	0.316495i	$0.102506\pi$
$858$	−10.5985	+	9.52833i	−0.361825	+	0.325292i
$859$	−0.128080	+	0.280457i	−0.00437004	+	0.00956906i	−0.911804	−	0.410625i	$-0.865311\pi$
$859$	−0.128080	+	0.280457i	−0.00437004	+	0.00956906i	0.907434	+	0.420194i	$0.138038\pi$
$860$	4.92557	−	9.06782i	0.167961	−	0.309210i
$861$	0.271261	+	0.865012i	0.00924455	+	0.0294795i
$862$	−4.73048	−	32.9012i	−0.161121	−	1.12062i
$863$	−0.195700	−	1.36112i	−0.00666170	−	0.0463331i	0.986219	−	0.165442i	$-0.0529052\pi$
$863$	−0.195700	−	1.36112i	−0.00666170	−	0.0463331i	−0.992881	+	0.119109i	$0.961996\pi$
$864$	5.05842	+	1.18844i	0.172091	+	0.0404316i
$865$	26.6628	−	49.0854i	0.906563	−	1.66895i
$866$	−15.8399	+	34.6845i	−0.538260	+	1.17863i
$867$	−1.07249	−	1.19295i	−0.0364238	−	0.0405146i
$868$	1.50698	−	0.442488i	0.0511501	−	0.0150190i
$869$	−31.0820	+	26.9327i	−1.05438	+	0.913628i
$870$	5.86299	−	16.7596i	0.198774	−	0.568205i
$871$	−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
$876$	−8.57262	−	3.72714i	−0.289642	−	0.125928i
$877$	22.3934	−	10.2267i	0.756172	−	0.345332i	0.000255372	−	1.00000i	$-0.499919\pi$
$877$	22.3934	−	10.2267i	0.756172	−	0.345332i	0.755917	+	0.654668i	$0.227191\pi$
$878$	−10.4360	−	3.06428i	−0.352197	−	0.103414i
$879$	5.97007	−	2.85946i	0.201365	−	0.0964472i
$880$	−8.50441	+	4.66804i	−0.286684	+	0.157360i
$881$	28.3862	+	18.2427i	0.956355	+	0.614612i	0.922987	−	0.384831i	$-0.125740\pi$
$881$	28.3862	+	18.2427i	0.956355	+	0.614612i	0.0333679	+	0.999443i	$0.489377\pi$
$882$	−16.4267	+	11.4262i	−0.553115	+	0.384741i
$883$	−0.965230	−	0.836377i	−0.0324826	−	0.0281463i	0.638468	−	0.769648i	$-0.279568\pi$
$883$	−0.965230	−	0.836377i	−0.0324826	−	0.0281463i	−0.670951	+	0.741502i	$0.734114\pi$
$884$	−6.75517	+	4.34129i	−0.227201	+	0.146013i
$885$	17.6785	−	1.62884i	0.594255	−	0.0547527i
$886$	−3.51433	−	24.4427i	−0.118066	−	0.821168i
$887$	38.0487	−	24.4524i	1.27755	−	0.821031i	0.286965	−	0.957941i	$-0.407354\pi$
$887$	38.0487	−	24.4524i	1.27755	−	0.821031i	0.990583	+	0.136910i	$0.0437172\pi$
$888$	1.03213	−	0.690293i	0.0346362	−	0.0231647i
$889$	8.60628	+	3.93036i	0.288645	+	0.131820i
$890$	−22.8872	−	8.47924i	−0.767180	−	0.284225i
$891$	−27.6579	−	27.5629i	−0.926576	−	0.923391i
$892$	3.73902	−	3.23988i	0.125192	−	0.108479i
$893$	−1.48927	+	5.07199i	−0.0498365	+	0.169728i
$894$	5.96915	+	36.7360i	0.199638	+	1.22864i
$895$	57.2971	−	4.22452i	1.91523	−	0.141210i
$896$	−0.574502			−0.0191928
$897$	−5.36149	+	14.8136i	−0.179015	+	0.494611i
$898$			17.0407i			0.568654i
$899$	−12.4056	−	1.78366i	−0.413751	−	0.0594884i
$900$	4.81172	+	14.2073i	0.160391	+	0.473577i
$901$	−8.32474	−	2.44437i	−0.277337	−	0.0814336i
$902$	−2.98718	+	2.58841i	−0.0994623	+	0.0861846i
$903$	−4.59137	+	0.0839414i	−0.152791	+	0.00279340i
$904$	9.36055	−	14.5653i	0.311327	−	0.484435i
$905$	17.4967	+	3.76593i	0.581610	+	0.125184i
$906$	−11.2856	+	7.54783i	−0.374939	+	0.250760i
$907$	−1.28958	+	0.828764i	−0.0428199	+	0.0275187i	−0.561876	−	0.827222i	$-0.689920\pi$
$907$	−1.28958	+	0.828764i	−0.0428199	+	0.0275187i	0.519056	+	0.854740i	$0.326284\pi$
$908$	2.80346	−	0.403077i	0.0930361	−	0.0133766i
$909$	39.8132	+	16.4510i	1.32052	+	0.545645i
$910$	−1.72655	−	1.71898i	−0.0572347	−	0.0569837i
$911$	20.9992	−	24.2344i	0.695736	−	0.802922i	−0.292434	−	0.956286i	$-0.594465\pi$
$911$	20.9992	−	24.2344i	0.695736	−	0.802922i	0.988170	+	0.153364i	$0.0490107\pi$
$912$	1.00656	+	0.840475i	0.0333307	+	0.0278309i
$913$	25.6001	−	39.8345i	0.847239	−	1.31833i
$914$	−6.33122	+	1.85901i	−0.209418	+	0.0614907i
$915$	13.1822	−	10.2959i	0.435790	−	0.340372i
$916$	−5.59047	+	19.0394i	−0.184714	+	0.629079i
$917$	−2.41986	+	1.10511i	−0.0799109	+	0.0364941i
$918$	−12.8908	−	17.8279i	−0.425459	−	0.588409i
$919$		−	37.6970i		−	1.24351i	−0.783212	−	0.621754i	$-0.786420\pi$
$919$		−	37.6970i		−	1.24351i	0.783212	−	0.621754i	$-0.213580\pi$
$920$	−5.85488	+	8.98445i	−0.193030	+	0.296209i
$921$	−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
$924$	3.67388	+	2.26726i	0.120862	+	0.0745872i
$925$	3.26706	+	1.47470i	0.107420	+	0.0484878i
$926$	−10.6463	−	36.2579i	−0.349858	−	1.19151i
$927$	−1.23571	−	2.46333i	−0.0405859	−	0.0809062i
$928$	4.17018	+	1.90446i	0.136893	+	0.0625169i
$929$	−42.9138	−	37.1850i	−1.40796	−	1.22000i	−0.942184	−	0.335096i	$-0.891231\pi$
$929$	−42.9138	−	37.1850i	−1.40796	−	1.22000i	−0.465772	−	0.884905i	$-0.654223\pi$
$930$	9.18712	−	5.26356i	0.301257	−	0.172599i
$931$	−4.99837	+	0.718657i	−0.163815	+	0.0235530i
$932$	−0.872003	−	6.06492i	−0.0285634	−	0.198663i
$933$	15.7865	+	50.3407i	0.516826	+	1.64808i
$934$	14.5560	+	12.6128i	0.476286	+	0.412704i
$935$	40.1551	+	8.64285i	1.31321	+	0.282652i
$936$	−5.08565	+	2.55117i	−0.166230	+	0.0833877i
$937$	40.9032	−	12.0103i	1.33625	−	0.392358i	0.465918	−	0.884828i	$-0.345724\pi$
$937$	40.9032	−	12.0103i	1.33625	−	0.392358i	0.870329	+	0.492470i	$0.163906\pi$
$938$	3.97511	+	4.58752i	0.129792	+	0.149788i
$939$	17.2431	+	10.6412i	0.562708	+	0.347262i
$940$	−9.38366	−	12.4779i	−0.306061	−	0.406983i
$941$	−0.546060	+	3.79793i	−0.0178011	+	0.123809i	−0.996784	−	0.0801317i	$-0.974466\pi$
$941$	−0.546060	+	3.79793i	−0.0178011	+	0.123809i	0.978983	+	0.203941i	$0.0653750\pi$
$942$	2.91384	+	0.798024i	0.0949380	+	0.0260010i
$943$	−1.56180	+	4.08053i	−0.0508593	+	0.132880i
$944$			4.58389i			0.149193i
$945$	4.44327	−	4.98142i	0.144539	−	0.162046i
$946$	−8.31745	−	18.2127i	−0.270424	−	0.592145i
$947$	−12.3754	−	3.63375i	−0.402146	−	0.118081i	0.0744036	−	0.997228i	$-0.476295\pi$
$947$	−12.3754	−	3.63375i	−0.402146	−	0.118081i	−0.476550	+	0.879147i	$0.658113\pi$
$948$	−14.8080	+	7.09254i	−0.480942	+	0.230355i
$949$	9.82102	−	2.88371i	0.318804	−	0.0936092i
$950$	−0.522258	+	3.74926i	−0.0169443	+	0.121642i
$951$	−22.8338	+	27.3460i	−0.740436	+	0.886755i
$952$	1.83829	+	1.59288i	0.0595792	+	0.0516257i
$953$	−25.7184	−	40.0186i	−0.833101	−	1.29633i	−0.952824	−	0.303523i	$-0.901837\pi$
$953$	−25.7184	−	40.0186i	−0.833101	−	1.29633i	0.119723	−	0.992807i	$-0.461799\pi$
$954$	−5.68168	−	2.34770i	−0.183951	−	0.0760096i
$955$	−6.98700	−	18.6079i	−0.226094	−	0.602138i
$956$	−11.0261	−	17.1569i	−0.356608	−	0.554893i
$957$	−19.1520	−	28.6363i	−0.619096	−	0.925680i
$958$	3.04814	−	6.67450i	0.0984810	−	0.215643i
$959$	−2.59205	+	4.03331i	−0.0837017	+	0.130242i
$960$	−3.76682	+	0.900580i	−0.121574	+	0.0290661i
$961$	15.4063	+	17.7799i	0.496978	+	0.573544i
$962$	−0.383052	+	1.30455i	−0.0123501	+	0.0420605i
$963$	35.0517	+	3.73793i	1.12953	+	0.120453i
$964$	10.5689	+	1.51958i	0.340402	+	0.0489424i
$965$	−7.79492	−	35.4574i	−0.250927	−	1.14142i
$966$	4.76310	+	0.294087i	0.153250	+	0.00946208i
$967$		−	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
$969$	−0.890462	−	5.48018i	−0.0286058	−	0.176049i
$970$	17.3496	+	1.20256i	0.557062	+	0.0386119i
$971$	14.0560	+	16.2215i	0.451079	+	0.520573i	0.935052	−	0.354510i	$-0.115352\pi$
$971$	14.0560	+	16.2215i	0.451079	+	0.520573i	−0.483973	+	0.875083i	$0.660807\pi$
$972$	−7.74290	−	13.5295i	−0.248354	−	0.433959i
$973$	1.32819	+	0.853576i	0.0425798	+	0.0273644i
$974$	−0.426189	−	0.194634i	−0.0136560	−	0.00623648i
$975$	−14.0151	−	8.56429i	−0.448842	−	0.274277i
$976$	2.33490	+	3.63318i	0.0747383	+	0.116295i
$977$	4.82874	−	0.694268i	0.154485	−	0.0222116i	−0.0646383	−	0.997909i	$-0.520589\pi$
$977$	4.82874	−	0.694268i	0.154485	−	0.0222116i	0.219123	+	0.975697i	$0.429680\pi$
$978$	24.0387	+	3.00885i	0.768674	+	0.0962125i
$979$	−39.8390	+	25.6030i	−1.27326	+	0.818275i
$980$	7.11896	−	13.1058i	0.227407	−	0.418649i
$981$	3.77431	+	5.42606i	0.120504	+	0.173241i
$982$	−4.08363	+	6.35425i	−0.130314	+	0.202772i
$983$	−5.59955	−	19.0703i	−0.178598	−	0.608249i	−0.999318	−	0.0369187i	$-0.988246\pi$
$983$	−5.59955	−	19.0703i	−0.178598	−	0.608249i	0.820720	−	0.571330i	$-0.193572\pi$
$984$	−1.42315	+	0.681641i	−0.0453684	+	0.0217299i
$985$	33.4264	+	2.31690i	1.06505	+	0.0738225i
$986$	−8.06334	−	17.6562i	−0.256789	−	0.562289i
$987$	−2.77016	+	6.37153i	−0.0881753	+	0.202808i
$988$	−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	0.939189	+	0.343402i	$0.111579\pi$
$991$	−1.84800	+	12.8531i	−0.0587036	+	0.408293i	−0.997892	+	0.0648913i	$0.979330\pi$
$992$	1.13568	+	2.48679i	0.0360578	+	0.0789556i
$993$	29.9218	+	18.4656i	0.949540	+	0.585988i
$994$	−5.12204	+	4.43828i	−0.162461	+	0.140774i
$995$	−16.1853	−	29.4869i	−0.513108	−	0.934798i
$996$	14.0578	−	12.6384i	0.445439	−	0.400463i
$997$	56.2702	+	25.6978i	1.78210	+	0.813856i	0.974590	+	0.223997i	$0.0719107\pi$
$997$	56.2702	+	25.6978i	1.78210	+	0.813856i	0.807506	+	0.589859i	$0.200817\pi$
$998$	10.8189	−	12.4856i	0.342465	−	0.395226i
$999$	−3.62634	−	0.851985i	−0.114732	−	0.0269556i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.n.a.89.14	✓	240	345.89	even	22	inner
690.2.n.a.89.18	yes	240	23.20	odd	22	inner
690.2.n.a.659.14	yes	240	1.1	even	1	trivial
690.2.n.a.659.18	yes	240	15.14	odd	2	inner
690.2.n.b.89.7	yes	240	115.89	odd	22
690.2.n.b.89.11	yes	240	69.20	even	22
690.2.n.b.659.7	yes	240	3.2	odd	2
690.2.n.b.659.11	yes	240	5.4	even	2

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)

\(f(q)\)	\(=\)	\(q+(-0.142315 + 0.989821i) q^{2} +(0.277794 + 1.70963i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(-1.79300 - 1.33609i) q^{5} +(-1.73176 + 0.0316608i) q^{6} +(-0.483302 - 0.310599i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-2.84566 + 0.949849i) q^{9} +O(q^{10})\)	\(q+(-0.142315 + 0.989821i) q^{2} +(0.277794 + 1.70963i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(-1.79300 - 1.33609i) q^{5} +(-1.73176 + 0.0316608i) q^{6} +(-0.483302 - 0.310599i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-2.84566 + 0.949849i) q^{9} +(1.57766 - 1.58461i) q^{10} +(-0.617442 - 4.29440i) q^{11} +(0.215117 - 1.71864i) q^{12} +(1.02536 + 1.59549i) q^{13} +(0.376219 - 0.434180i) q^{14} +(1.78613 - 3.43653i) q^{15} +(0.841254 + 0.540641i) q^{16} +(-1.19284 - 4.06243i) q^{17} +(-0.535201 - 2.95187i) q^{18} +(0.213298 - 0.726425i) q^{19} +(1.34396 + 1.78712i) q^{20} +(0.396751 - 0.912550i) q^{21} +4.33856 q^{22} +(4.22869 - 2.26235i) q^{23} +(1.67053 + 0.457515i) q^{24} +(1.42973 + 4.79123i) q^{25} +(-1.72517 + 0.787858i) q^{26} +(-2.41440 - 4.60116i) q^{27} +(0.376219 + 0.434180i) q^{28} +(-1.29159 - 4.39876i) q^{29} +(3.14736 + 2.25702i) q^{30} +(1.13568 - 2.48679i) q^{31} +(-0.654861 + 0.755750i) q^{32} +(7.17031 - 2.24856i) q^{33} +(4.19084 - 0.602551i) q^{34} +(0.451574 + 1.20264i) q^{35} +(2.99800 - 0.109658i) q^{36} +(0.469465 - 0.541792i) q^{37} +(0.688676 + 0.314508i) q^{38} +(-2.44285 + 2.19619i) q^{39} +(-1.96019 + 1.07594i) q^{40} +(-0.688519 + 0.596605i) q^{41} +(0.846798 + 0.522582i) 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} +(-0.690600 + 1.58842i) q^{48} +(-2.77080 - 6.06720i) q^{49} +(-4.94593 + 0.733315i) q^{50} +(6.61388 - 3.16782i) q^{51} +(-0.534322 - 1.81973i) q^{52} +(1.10788 - 1.72390i) q^{53} +(4.89793 - 1.73501i) q^{54} +(-4.63063 + 8.52484i) q^{55} +(-0.483302 + 0.310599i) q^{56} +(1.30117 + 0.162863i) q^{57} +(4.53780 - 0.652438i) q^{58} +(2.47824 + 3.85621i) q^{59} +(-2.68196 + 2.79411i) q^{60} +(3.92849 + 1.79408i) q^{61} +(2.29985 + 1.47803i) q^{62} +(1.67034 + 0.424797i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(0.293243 - 4.23068i) q^{65} +(1.20523 + 7.41733i) q^{66} +(-1.50369 + 10.4584i) q^{67} +4.23393i q^{68} +(5.04248 + 6.60102i) q^{69} +(-1.25467 + 0.275824i) q^{70} +(-11.6770 - 1.67890i) q^{71} +(-0.318117 + 2.98309i) q^{72} +(1.52050 - 5.17834i) q^{73} +(0.469465 + 0.541792i) q^{74} +(-7.79405 + 3.77528i) q^{75} +(-0.409315 + 0.636907i) q^{76} +(-1.03543 + 2.26727i) q^{77} +(-1.82619 - 2.73054i) q^{78} +(-5.12499 - 7.97465i) q^{79} +(-0.786027 - 2.09336i) q^{80} +(7.19557 - 5.40590i) q^{81} +(-0.492546 - 0.766417i) q^{82} +(8.24830 + 7.14720i) q^{83} +(-0.637775 + 0.763807i) q^{84} +(-3.28900 + 8.87768i) q^{85} +(4.42796 - 1.30017i) q^{86} +(7.16146 - 3.43010i) q^{87} +(-4.16282 - 1.22231i) q^{88} +(-4.53438 - 9.92892i) q^{89} +(-2.98435 + 6.00780i) q^{90} -1.08958i q^{91} +(-4.69477 + 0.979347i) q^{92} +(4.56697 + 1.25077i) q^{93} +(0.993659 - 6.91105i) q^{94} +(-1.35301 + 1.01750i) q^{95} +(-1.47397 - 0.909626i) q^{96} +(5.09324 + 5.87791i) q^{97} +(6.39977 - 1.87914i) q^{98} +(5.83606 + 11.6339i) 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

Modular forms

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