LMFDB - Embedded newform 552.2.bb.a.469.31

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(13,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 0, 14]))

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

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

chi := DirichletCharacter("552.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.bb (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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$48$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			469.31
Character	$\chi$	$=$	552.469
Dual form			552.2.bb.a.133.31

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.744845 - 1.20217i) q^{2} +(0.755750 - 0.654861i) q^{3} +(-0.890411 - 1.79086i) q^{4} +(3.37124 - 0.484711i) q^{5} +(-0.224336 - 1.39631i) q^{6} +(-0.316431 + 0.692886i) q^{7} +(-2.81613 - 0.263488i) q^{8} +(0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(q+(0.744845 - 1.20217i) q^{2} +(0.755750 - 0.654861i) q^{3} +(-0.890411 - 1.79086i) q^{4} +(3.37124 - 0.484711i) q^{5} +(-0.224336 - 1.39631i) q^{6} +(-0.316431 + 0.692886i) q^{7} +(-2.81613 - 0.263488i) q^{8} +(0.142315 - 0.989821i) q^{9} +(1.92835 - 4.41383i) q^{10} +(0.0629377 - 0.214346i) q^{11} +(-1.84569 - 0.770344i) q^{12} +(2.05893 - 0.940282i) q^{13} +(0.597273 + 0.896496i) q^{14} +(2.23040 - 2.57401i) q^{15} +(-2.41434 + 3.18920i) q^{16} +(-2.82263 - 1.81399i) q^{17} +(-1.08393 - 0.908350i) q^{18} +(2.18696 + 3.40298i) q^{19} +(-3.86984 - 5.60582i) q^{20} +(0.214602 + 0.730867i) q^{21} +(-0.210801 - 0.235316i) q^{22} +(-3.23803 + 3.53767i) q^{23} +(-2.30084 + 1.64504i) q^{24} +(6.33286 - 1.85949i) q^{25} +(0.403208 - 3.17554i) q^{26} +(-0.540641 - 0.841254i) q^{27} +(1.52261 - 0.0502719i) q^{28} +(3.61990 - 5.63267i) q^{29} +(-1.43310 - 4.59855i) q^{30} +(-1.24806 + 1.44034i) q^{31} +(2.03564 + 5.27789i) q^{32} +(-0.0928018 - 0.203208i) q^{33} +(-4.28314 + 2.04213i) q^{34} +(-0.730914 + 2.48926i) q^{35} +(-1.89935 + 0.626483i) q^{36} +(-5.62168 - 0.808276i) q^{37} +(5.71989 - 0.0944007i) q^{38} +(0.940282 - 2.05893i) q^{39} +(-9.62156 + 0.476727i) q^{40} +(1.00369 + 6.98082i) q^{41} +(1.03847 + 0.286395i) q^{42} +(-5.19521 + 4.50167i) q^{43} +(-0.439904 + 0.0781438i) q^{44} -3.40591i q^{45} +(1.84104 + 6.52768i) q^{46} -0.215592 q^{47} +(0.263847 + 3.99129i) q^{48} +(4.20406 + 4.85175i) q^{49} +(2.48157 - 8.99819i) q^{50} +(-3.32111 + 0.477504i) q^{51} +(-3.51720 - 2.85001i) q^{52} +(-1.46597 - 0.669486i) q^{53} +(-1.41402 + 0.0233369i) q^{54} +(0.108282 - 0.753119i) q^{55} +(1.07368 - 1.86788i) q^{56} +(3.88127 + 1.13964i) q^{57} +(-4.07515 - 8.54719i) q^{58} +(0.724804 - 0.331007i) q^{59} +(-6.59566 - 1.70239i) q^{60} +(-11.2061 - 9.71014i) q^{61} +(0.801916 + 2.57321i) q^{62} +(0.640801 + 0.411818i) q^{63} +(7.86115 + 1.48403i) q^{64} +(6.48538 - 4.16790i) q^{65} +(-0.313412 - 0.0397949i) q^{66} +(0.207372 + 0.706243i) q^{67} +(-0.735302 + 6.67012i) q^{68} +(-0.130458 + 4.79406i) q^{69} +(2.44809 + 2.73280i) q^{70} +(7.00932 - 2.05812i) q^{71} +(-0.661583 + 2.74997i) q^{72} +(0.532000 - 0.341896i) q^{73} +(-5.15897 + 6.15616i) q^{74} +(3.56834 - 5.55245i) q^{75} +(4.14695 - 6.94658i) q^{76} +(0.128602 + 0.111434i) q^{77} +(-1.77481 - 2.66396i) q^{78} +(2.04670 + 4.48164i) q^{79} +(-6.59347 + 11.9218i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(9.13971 + 3.99303i) q^{82} +(7.36506 + 1.05894i) q^{83} +(1.11779 - 1.03509i) q^{84} +(-10.3950 - 4.74725i) q^{85} +(1.54214 + 9.59856i) q^{86} +(-0.952878 - 6.62741i) q^{87} +(-0.233718 + 0.587043i) q^{88} +(1.00957 + 1.16511i) q^{89} +(-4.09447 - 2.53687i) q^{90} +1.72414i q^{91} +(9.21865 + 2.64887i) q^{92} +1.90584i q^{93} +(-0.160583 + 0.259178i) q^{94} +(9.02223 + 10.4122i) q^{95} +(4.99472 + 2.65570i) q^{96} +(1.48334 + 10.3169i) q^{97} +(8.96398 - 1.44018i) q^{98} +(-0.203208 - 0.0928018i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9}+O(q^{10}) $ 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9	$ 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32} + 6 q^{34} - 22 q^{36} + 90 q^{38} - 74 q^{40} + 90 q^{42} - 130 q^{44} + 96 q^{46} - 88 q^{48} - 48 q^{49} + 142 q^{50} - 142 q^{52} + 18 q^{54} - 82 q^{56} + 22 q^{58} + 2 q^{60} - 40 q^{62} - 8 q^{63} + 16 q^{66} - 44 q^{68} + 16 q^{71} - 4 q^{72} + 10 q^{74} - 138 q^{76} - 40 q^{79} - 170 q^{80} - 48 q^{81} - 124 q^{82} - 8 q^{84} - 216 q^{86} - 108 q^{88} + 4 q^{90} - 198 q^{92} - 238 q^{94} + 80 q^{95} + 4 q^{96} - 132 q^{98}+O(q^{100}) $ 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{5}{11}\right)$	$1$	$-1$	$1$

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 $

$2$	0.744845	−	1.20217i	0.526685	−	0.850060i
$2$	0.744845	−	1.20217i	0.526685	−	0.850060i
$3$	0.755750	−	0.654861i	0.436332	−	0.378084i
$3$	0.755750	−	0.654861i	0.436332	−	0.378084i
$4$	−0.890411	−	1.79086i	−0.445206	−	0.895428i
$5$	3.37124	−	0.484711i	1.50766	−	0.216769i	0.661603	−	0.749854i	$-0.269876\pi$
$5$	3.37124	−	0.484711i	1.50766	−	0.216769i	0.846062	+	0.533085i	$0.178967\pi$
$6$	−0.224336	−	1.39631i	−0.0915846	−	0.570040i
$7$	−0.316431	+	0.692886i	−0.119600	+	0.261886i	−0.959958	−	0.280145i	$-0.909617\pi$
$7$	−0.316431	+	0.692886i	−0.119600	+	0.261886i	0.840358	+	0.542032i	$0.182345\pi$
$8$	−2.81613	−	0.263488i	−0.995651	−	0.0931571i
$9$	0.142315	−	0.989821i	0.0474383	−	0.329940i
$10$	1.92835	−	4.41383i	0.609797	−	1.39578i
$11$	0.0629377	−	0.214346i	0.0189764	−	0.0646278i	−0.949460	−	0.313887i	$-0.898369\pi$
$11$	0.0629377	−	0.214346i	0.0189764	−	0.0646278i	0.968437	+	0.249259i	$0.0801870\pi$
$12$	−1.84569	−	0.770344i	−0.532805	−	0.222379i
$13$	2.05893	−	0.940282i	0.571045	−	0.260787i	−0.108898	−	0.994053i	$-0.534732\pi$
$13$	2.05893	−	0.940282i	0.571045	−	0.260787i	0.679942	+	0.733266i	$0.262005\pi$
$14$	0.597273	+	0.896496i	0.159628	+	0.239599i
$15$	2.23040	−	2.57401i	0.575886	−	0.664607i
$16$	−2.41434	+	3.18920i	−0.603584	+	0.797299i
$17$	−2.82263	−	1.81399i	−0.684588	−	0.439958i	0.151570	−	0.988446i	$-0.451567\pi$
$17$	−2.82263	−	1.81399i	−0.684588	−	0.439958i	−0.836158	+	0.548489i	$0.815203\pi$
$18$	−1.08393	−	0.908350i	−0.255484	−	0.214100i
$19$	2.18696	+	3.40298i	0.501723	+	0.780696i	0.996070	−	0.0885685i	$-0.0282292\pi$
$19$	2.18696	+	3.40298i	0.501723	+	0.780696i	−0.494347	+	0.869265i	$0.664593\pi$
$20$	−3.86984	−	5.60582i	−0.865322	−	1.25350i
$21$	0.214602	+	0.730867i	0.0468300	+	0.159488i
$22$	−0.210801	−	0.235316i	−0.0449429	−	0.0501696i
$23$	−3.23803	+	3.53767i	−0.675177	+	0.737656i
$23$	−3.23803	+	3.53767i	−0.675177	+	0.737656i
$24$	−2.30084	+	1.64504i	−0.469656	+	0.335792i
$25$	6.33286	−	1.85949i	1.26657	−	0.371899i
$26$	0.403208	−	3.17554i	0.0790757	−	0.622775i
$27$	−0.540641	−	0.841254i	−0.104046	−	0.161899i
$28$	1.52261	−	0.0502719i	0.287747	−	0.00950050i
$29$	3.61990	−	5.63267i	0.672198	−	1.04596i	−0.322839	−	0.946454i	$-0.604637\pi$
$29$	3.61990	−	5.63267i	0.672198	−	1.04596i	0.995037	−	0.0995064i	$-0.0317264\pi$
$30$	−1.43310	−	4.59855i	−0.261646	−	0.839577i
$31$	−1.24806	+	1.44034i	−0.224158	+	0.258693i	−0.856678	−	0.515852i	$-0.827475\pi$
$31$	−1.24806	+	1.44034i	−0.224158	+	0.258693i	0.632519	+	0.774545i	$0.282021\pi$
$32$	2.03564	+	5.27789i	0.359854	+	0.933009i
$33$	−0.0928018	−	0.203208i	−0.0161547	−	0.0353739i
$34$	−4.28314	+	2.04213i	−0.734553	+	0.350222i
$35$	−0.730914	+	2.48926i	−0.123547	+	0.420763i
$36$	−1.89935	+	0.626483i	−0.316558	+	0.104414i
$37$	−5.62168	−	0.808276i	−0.924199	−	0.132880i	−0.336245	−	0.941774i	$-0.609157\pi$
$37$	−5.62168	−	0.808276i	−0.924199	−	0.132880i	−0.587954	+	0.808895i	$0.700066\pi$
$38$	5.71989	−	0.0944007i	0.927889	−	0.0153138i
$39$	0.940282	−	2.05893i	0.150566	−	0.329693i
$40$	−9.62156	+	0.476727i	−1.52130	+	0.0753772i
$41$	1.00369	+	6.98082i	0.156750	+	1.09022i	0.904572	+	0.426321i	$0.140191\pi$
$41$	1.00369	+	6.98082i	0.156750	+	1.09022i	−0.747822	+	0.663900i	$0.768900\pi$
$42$	1.03847	+	0.286395i	0.160239	+	0.0441918i
$43$	−5.19521	+	4.50167i	−0.792262	+	0.686499i	−0.953825	−	0.300363i	$-0.902892\pi$
$43$	−5.19521	+	4.50167i	−0.792262	+	0.686499i	0.161563	+	0.986862i	$0.448347\pi$
$44$	−0.439904	+	0.0781438i	−0.0663180	+	0.0117806i
$45$		−	3.40591i		−	0.507723i
$46$	1.84104	+	6.52768i	0.271447	+	0.962453i
$47$	−0.215592			−0.0314474			−0.0157237	−	0.999876i	$-0.505005\pi$
$47$	−0.215592			−0.0314474			−0.0157237	+	0.999876i	$0.505005\pi$
$48$	0.263847	+	3.99129i	0.0380831	+	0.576093i
$49$	4.20406	+	4.85175i	0.600580	+	0.693107i
$50$	2.48157	−	8.99819i	0.350948	−	1.27254i
$51$	−3.32111	+	0.477504i	−0.465049	+	0.0668639i
$52$	−3.51720	−	2.85001i	−0.487749	−	0.395225i
$53$	−1.46597	−	0.669486i	−0.201367	−	0.0919610i	0.312179	−	0.950023i	$-0.398941\pi$
$53$	−1.46597	−	0.669486i	−0.201367	−	0.0919610i	−0.513546	+	0.858062i	$0.671668\pi$
$54$	−1.41402	+	0.0233369i	−0.192424	+	0.00317575i
$55$	0.108282	−	0.753119i	0.0146008	−	0.101551i
$56$	1.07368	−	1.86788i	0.143476	−	0.249606i
$57$	3.88127	+	1.13964i	0.514087	+	0.150949i
$58$	−4.07515	−	8.54719i	−0.535093	−	1.12230i
$59$	0.724804	−	0.331007i	0.0943614	−	0.0430934i	−0.367675	−	0.929954i	$-0.619846\pi$
$59$	0.724804	−	0.331007i	0.0943614	−	0.0430934i	0.462037	+	0.886861i	$0.347119\pi$
$60$	−6.59566	−	1.70239i	−0.851496	−	0.219777i
$61$	−11.2061	−	9.71014i	−1.43479	−	1.24326i	−0.923361	−	0.383932i	$-0.874570\pi$
$61$	−11.2061	−	9.71014i	−1.43479	−	1.24326i	−0.511432	−	0.859324i	$-0.670885\pi$
$62$	0.801916	+	2.57321i	0.101843	+	0.326798i
$63$	0.640801	+	0.411818i	0.0807333	+	0.0518842i
$64$	7.86115	+	1.48403i	0.982644	+	0.185504i
$65$	6.48538	−	4.16790i	0.804413	−	0.516965i
$66$	−0.313412	−	0.0397949i	−0.0385784	−	0.00489842i
$67$	0.207372	+	0.706243i	0.0253345	+	0.0862813i	0.971190	−	0.238307i	$-0.0765924\pi$
$67$	0.207372	+	0.706243i	0.0253345	+	0.0862813i	−0.945855	+	0.324588i	$0.894774\pi$
$68$	−0.735302	+	6.67012i	−0.0891684	+	0.808871i
$69$	−0.130458	+	4.79406i	−0.0157052	+	0.577137i
$70$	2.44809	+	2.73280i	0.292603	+	0.326632i
$71$	7.00932	−	2.05812i	0.831854	−	0.244254i	0.162041	−	0.986784i	$-0.448192\pi$
$71$	7.00932	−	2.05812i	0.831854	−	0.244254i	0.669813	+	0.742530i	$0.266374\pi$
$72$	−0.661583	+	2.74997i	−0.0779683	+	0.324086i
$73$	0.532000	−	0.341896i	0.0622659	−	0.0400159i	−0.509137	−	0.860685i	$-0.670036\pi$
$73$	0.532000	−	0.341896i	0.0622659	−	0.0400159i	0.571403	+	0.820669i	$0.306399\pi$
$74$	−5.15897	+	6.15616i	−0.599718	+	0.715639i
$75$	3.56834	−	5.55245i	0.412037	−	0.641142i
$76$	4.14695	−	6.94658i	0.475688	−	0.796827i
$77$	0.128602	+	0.111434i	0.0146556	+	0.0126991i
$78$	−1.77481	−	2.66396i	−0.200958	−	0.301634i
$79$	2.04670	+	4.48164i	0.230271	+	0.504224i	0.989132	−	0.147029i	$-0.0469710\pi$
$79$	2.04670	+	4.48164i	0.230271	+	0.504224i	−0.758861	+	0.651253i	$0.774244\pi$
$80$	−6.59347	+	11.9218i	−0.737172	+	1.33290i
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$	9.13971	+	3.99303i	1.00931	+	0.440956i
$83$	7.36506	+	1.05894i	0.808421	+	0.116233i	0.534118	−	0.845410i	$-0.320644\pi$
$83$	7.36506	+	1.05894i	0.808421	+	0.116233i	0.274303	+	0.961643i	$0.411553\pi$
$84$	1.11779	−	1.03509i	0.121961	−	0.112938i
$85$	−10.3950	−	4.74725i	−1.12750	−	0.514911i
$86$	1.54214	+	9.59856i	0.166293	+	1.03504i
$87$	−0.952878	−	6.62741i	−0.102159	−	0.710533i
$88$	−0.233718	+	0.587043i	−0.0249145	+	0.0625790i
$89$	1.00957	+	1.16511i	0.107014	+	0.123501i	0.806730	−	0.590921i	$-0.201235\pi$
$89$	1.00957	+	1.16511i	0.107014	+	0.123501i	−0.699715	+	0.714422i	$0.746690\pi$
$90$	−4.09447	−	2.53687i	−0.431595	−	0.267410i
$91$			1.72414i			0.180739i
$92$	9.21865	+	2.64887i	0.961111	+	0.276164i
$93$			1.90584i			0.197627i
$94$	−0.160583	+	0.259178i	−0.0165629	+	0.0267322i
$95$	9.02223	+	10.4122i	0.925661	+	1.06827i
$96$	4.99472	+	2.65570i	0.509772	+	0.271047i
$97$	1.48334	+	10.3169i	0.150610	+	1.04752i	0.915200	+	0.403001i	$0.132033\pi$
$97$	1.48334	+	10.3169i	0.150610	+	1.04752i	−0.764589	+	0.644518i	$0.777058\pi$
$98$	8.96398	−	1.44018i	0.905499	−	0.145481i
$99$	−0.203208	−	0.0928018i	−0.0204231	−	0.00932693i
$100$	−8.96893	−	9.68552i	−0.896893	−	0.968552i
$101$	16.8327	+	2.42018i	1.67492	+	0.240816i	0.913322	−	0.407239i	$-0.133508\pi$
$101$	16.8327	+	2.42018i	1.67492	+	0.240816i	0.761594	+	0.648055i	$0.224417\pi$
$102$	−1.89968	+	4.34820i	−0.188096	+	0.430536i
$103$	−18.8505	−	5.53501i	−1.85740	−	0.545381i	−0.999502	−	0.0315531i	$-0.989955\pi$
$103$	−18.8505	−	5.53501i	−1.85740	−	0.545381i	−0.857894	−	0.513827i	$-0.828227\pi$
$104$	−6.04596	+	2.10545i	−0.592855	+	0.206456i
$105$	1.07773	+	2.35991i	0.105176	+	0.230303i
$106$	−1.89676	+	1.26368i	−0.184229	+	0.122739i
$107$	12.1279	+	10.5089i	1.17245	+	1.01593i	0.999519	+	0.0309966i	$0.00986809\pi$
$107$	12.1279	+	10.5089i	1.17245	+	1.01593i	0.172928	+	0.984935i	$0.444677\pi$
$108$	−1.02517	+	1.71727i	−0.0986472	+	0.165245i
$109$	1.37464	−	2.13899i	0.131667	−	0.204878i	−0.769160	−	0.639057i	$-0.779325\pi$
$109$	1.37464	−	2.13899i	0.131667	−	0.204878i	0.900827	+	0.434179i	$0.142961\pi$
$110$	−0.824722	−	0.691131i	−0.0786341	−	0.0658967i
$111$	−4.77789	+	3.07057i	−0.453498	+	0.291445i
$112$	−1.44578	−	2.68202i	−0.136614	−	0.253427i
$113$	4.52740	−	1.32937i	0.425902	−	0.125056i	−0.0617549	−	0.998091i	$-0.519670\pi$
$113$	4.52740	−	1.32937i	0.425902	−	0.125056i	0.487657	+	0.873035i	$0.337852\pi$
$114$	4.26099	−	3.81708i	0.399078	−	0.357502i
$115$	−9.20144	+	13.4959i	−0.858039	+	1.25850i
$116$	−13.3105	−	1.46732i	−1.23585	−	0.136238i
$117$	−0.637695	−	2.17179i	−0.0589549	−	0.200782i
$118$	0.141941	−	1.11788i	0.0130667	−	0.102910i
$119$	2.15006	−	1.38176i	0.197095	−	0.126666i
$120$	−6.95930	+	6.66107i	−0.635294	+	0.608070i
$121$	9.21181	+	5.92007i	0.837437	+	0.538188i
$122$	−20.0200	+	6.23905i	−1.81253	+	0.564857i
$123$	5.33000	+	4.61847i	0.480590	+	0.416434i
$124$	3.69073	+	0.952605i	0.331437	+	0.0855464i
$125$	4.95765	−	2.26408i	0.443426	−	0.202506i
$126$	0.972371	−	0.463609i	0.0866257	−	0.0413016i
$127$	1.91443	+	0.562127i	0.169878	+	0.0498807i	0.365565	−	0.930786i	$-0.380876\pi$
$127$	1.91443	+	0.562127i	0.169878	+	0.0498807i	−0.195687	+	0.980666i	$0.562694\pi$
$128$	7.63939	−	8.34504i	0.675233	−	0.737604i
$129$	−0.978307	+	6.80428i	−0.0861352	+	0.599083i
$130$	−0.179909	−	10.9010i	−0.0157790	−	0.956077i
$131$	−16.7105	−	7.63144i	−1.46001	−	0.666762i	−0.482158	−	0.876084i	$-0.660147\pi$
$131$	−16.7105	−	7.63144i	−1.46001	−	0.666762i	−0.977847	+	0.209322i	$0.932874\pi$
$132$	−0.281284	+	0.347133i	−0.0244826	+	0.0302140i
$133$	−3.04990	+	0.438509i	−0.264460	+	0.0380235i
$134$	1.00348	+	0.276746i	0.0866876	+	0.0239072i
$135$	−2.23040	−	2.57401i	−0.191962	−	0.221536i
$136$	7.47091	+	5.85216i	0.640626	+	0.501819i
$137$	7.41583			0.633577			0.316789	−	0.948496i	$-0.397395\pi$
$137$	7.41583			0.633577			0.316789	+	0.948496i	$0.397395\pi$
$138$	5.66609	+	3.72766i	0.482329	+	0.317320i
$139$			14.4647i			1.22688i	0.789741	+	0.613441i	$0.210215\pi$
$139$			14.4647i			1.22688i	−0.789741	+	0.613441i	$0.789785\pi$
$140$	5.10873	−	0.907507i	0.431767	−	0.0766983i
$141$	−0.162934	+	0.141183i	−0.0137215	+	0.0118898i
$142$	2.74665	−	9.95936i	0.230494	−	0.835771i
$143$	−0.0719615	−	0.500503i	−0.00601772	−	0.0418542i
$144$	2.81314	+	2.84363i	0.234428	+	0.236969i
$145$	9.47332	−	20.7437i	0.786717	−	1.72267i
$146$	−0.0147580	−	0.894213i	−0.00122138	−	0.0740056i
$147$	6.35444	+	0.913630i	0.524105	+	0.0753549i
$148$	3.55810	+	10.7873i	0.292474	+	0.886713i
$149$	4.88390	−	16.6330i	0.400105	−	1.36263i	−0.475547	−	0.879690i	$-0.657750\pi$
$149$	4.88390	−	16.6330i	0.400105	−	1.36263i	0.875652	−	0.482942i	$-0.160432\pi$
$150$	−4.01711	−	8.42546i	−0.327996	−	0.687936i
$151$	−6.90872	−	15.1280i	−0.562223	−	1.23110i	−0.950836	−	0.309696i	$-0.899773\pi$
$151$	−6.90872	−	15.1280i	−0.562223	−	1.23110i	0.388612	−	0.921401i	$-0.372955\pi$
$152$	−5.26211	−	10.1594i	−0.426814	−	0.824040i
$153$	−2.19723	+	2.53574i	−0.177636	+	0.205002i
$154$	0.229751	−	0.0715999i	0.0185139	−	0.00576968i
$155$	−3.50937	+	5.46068i	−0.281879	+	0.438613i
$156$	−4.52449	+	0.149384i	−0.362249	+	0.0119603i
$157$	5.73460	+	8.92321i	0.457671	+	0.712150i	0.991015	−	0.133748i	$-0.0427014\pi$
$157$	5.73460	+	8.92321i	0.457671	+	0.712150i	−0.533345	+	0.845898i	$0.679065\pi$
$158$	6.91215	+	0.877657i	0.549901	+	0.0698226i
$159$	−1.54633	+	0.454043i	−0.122632	+	0.0360079i
$160$	9.42090	+	16.8064i	0.744787	+	1.32866i
$161$	−1.42659	−	3.36302i	−0.112431	−	0.265043i
$162$	−1.05336	+	0.943624i	−0.0827600	+	0.0741381i
$163$	−4.72714	−	16.0992i	−0.370258	−	1.26098i	−0.908390	−	0.418124i	$-0.862688\pi$
$163$	−4.72714	−	16.0992i	−0.370258	−	1.26098i	0.538132	−	0.842861i	$-0.319130\pi$
$164$	11.6080	−	8.01327i	0.906429	−	0.625731i
$165$	−0.411354	−	0.640079i	−0.0320239	−	0.0498301i
$166$	6.75885	−	8.06529i	0.524589	−	0.625988i
$167$	−1.82379	−	1.17208i	−0.141129	−	0.0906983i	0.468171	−	0.883638i	$-0.344913\pi$
$167$	−1.82379	−	1.17208i	−0.141129	−	0.0906983i	−0.609300	+	0.792940i	$0.708550\pi$
$168$	−0.411771	−	2.11476i	−0.0317689	−	0.163157i
$169$	−5.15813	+	5.95279i	−0.396779	+	0.457907i
$170$	−13.4497	+	8.96059i	−1.03154	+	0.687246i
$171$	3.67957	−	1.68041i	0.281384	−	0.128504i
$172$	12.6877	+	5.29553i	0.967430	+	0.403781i
$173$	1.51653	−	5.16482i	0.115300	−	0.392674i	−0.881541	−	0.472108i	$-0.843493\pi$
$173$	1.51653	−	5.16482i	0.115300	−	0.392674i	0.996840	+	0.0794341i	$0.0253113\pi$
$174$	−8.67701	−	3.79088i	−0.657802	−	0.287386i
$175$	−0.715491	+	4.97635i	−0.0540861	+	0.376177i
$176$	0.531640	+	0.718225i	0.0400738	+	0.0541382i
$177$	0.331007	−	0.724804i	0.0248800	−	0.0544796i
$178$	2.15263	−	0.345848i	0.161346	−	0.0259224i
$179$	1.08488	−	0.155982i	0.0810878	−	0.0116587i	−0.101651	−	0.994820i	$-0.532413\pi$
$179$	1.08488	−	0.155982i	0.0810878	−	0.0116587i	0.182739	+	0.983161i	$0.441504\pi$
$180$	−6.09949	+	3.03266i	−0.454629	+	0.226041i
$181$	−16.2856	+	14.1115i	−1.21050	+	1.04890i	−0.213083	+	0.977034i	$0.568350\pi$
$181$	−16.2856	+	14.1115i	−1.21050	+	1.04890i	−0.997414	+	0.0718677i	$0.977104\pi$
$182$	2.07270	+	1.28422i	0.153639	+	0.0951925i
$183$	−14.8278			−1.09610
$184$	10.0508	−	9.10936i	0.740958	−	0.671551i
$185$	−19.3438			−1.42219
$186$	2.29114	+	1.41956i	0.167995	+	0.104087i
$187$	−0.566472	+	0.490851i	−0.0414246	+	0.0358946i
$188$	0.191966	+	0.386095i	0.0140006	+	0.0281589i
$189$	0.753968	−	0.108404i	0.0548431	−	0.00788525i
$190$	19.2374	−	3.09074i	1.39563	−	0.224226i
$191$	−2.54321	+	5.56886i	−0.184020	+	0.402948i	−0.979049	−	0.203623i	$-0.934728\pi$
$191$	−2.54321	+	5.56886i	−0.184020	+	0.402948i	0.795029	+	0.606571i	$0.207456\pi$
$192$	6.91289	−	4.02640i	0.498895	−	0.290580i
$193$	0.653478	−	4.54504i	0.0470384	−	0.327159i	−0.952692	−	0.303938i	$-0.901699\pi$
$193$	0.653478	−	4.54504i	0.0470384	−	0.327159i	0.999730	−	0.0232216i	$-0.00739233\pi$
$194$	13.5074	+	5.90124i	0.969778	+	0.423684i
$195$	2.17193	−	7.39692i	0.155535	−	0.529704i
$196$	4.94544	−	11.8489i	0.353246	−	0.846352i
$197$	6.73788	−	3.07708i	0.480054	−	0.219233i	−0.160665	−	0.987009i	$-0.551364\pi$
$197$	6.73788	−	3.07708i	0.480054	−	0.219233i	0.640719	+	0.767776i	$0.278637\pi$
$198$	−0.262921	+	0.175166i	−0.0186850	+	0.0124485i
$199$	3.50247	−	4.04207i	0.248283	−	0.286534i	−0.617904	−	0.786254i	$-0.712018\pi$
$199$	3.50247	−	4.04207i	0.248283	−	0.286534i	0.866188	+	0.499719i	$0.166563\pi$
$200$	−18.3241	+	3.56794i	−1.29571	+	0.252292i
$201$	0.619212	+	0.397943i	0.0436758	+	0.0280688i
$202$	15.4472	−	18.4330i	1.08686	−	1.29694i
$203$	2.75735	+	4.29053i	0.193528	+	0.301136i
$204$	3.81230	+	5.52246i	0.266914	+	0.386650i
$205$	6.76736	+	23.0475i	0.472653	+	1.60971i
$206$	−20.6947	+	18.5387i	−1.44187	+	1.29165i
$207$	3.04085	+	3.70854i	0.211353	+	0.257761i
$208$	−1.97220	+	8.83649i	−0.136748	+	0.612701i
$209$	0.867057	−	0.254591i	0.0599756	−	0.0176104i
$210$	3.63975	+	0.462150i	0.251166	+	0.0318914i
$211$	−12.4618	−	19.3910i	−0.857908	−	1.33493i	−0.941006	−	0.338390i	$-0.890118\pi$
$211$	−12.4618	−	19.3910i	−0.857908	−	1.33493i	0.0830977	−	0.996541i	$-0.473519\pi$
$212$	0.106363	+	3.22146i	0.00730501	+	0.221251i
$213$	3.94951	−	6.14556i	0.270616	−	0.421087i
$214$	21.6668	−	6.75226i	1.48111	−	0.461575i
$215$	−15.3323	+	17.6944i	−1.04565	+	1.20675i
$216$	1.30085	+	2.51153i	0.0885119	+	0.170888i
$217$	−0.603067	−	1.32053i	−0.0409389	−	0.0896436i
$218$	−1.54752	−	3.24577i	−0.104812	−	0.219831i
$219$	0.178165	−	0.606774i	0.0120393	−	0.0410020i
$220$	−1.44514	+	0.476668i	−0.0974316	+	0.0321370i
$221$	−7.51726	−	1.08082i	−0.505666	−	0.0727037i
$222$	0.132542	+	8.03092i	0.00889563	+	0.539000i
$223$	−4.38880	+	9.61014i	−0.293896	+	0.643543i	−0.997767	−	0.0667849i	$-0.978726\pi$
$223$	−4.38880	+	9.61014i	−0.293896	+	0.643543i	0.703871	+	0.710327i	$0.251453\pi$
$224$	−4.30112	−	0.259618i	−0.287381	−	0.0173465i
$225$	−0.939308	−	6.53303i	−0.0626205	−	0.435535i
$226$	1.77410	−	6.43287i	0.118011	−	0.427908i
$227$	−20.6762	+	17.9160i	−1.37233	+	1.18913i	−0.411687	+	0.911325i	$0.635060\pi$
$227$	−20.6762	+	17.9160i	−1.37233	+	1.18913i	−0.960639	+	0.277801i	$0.910394\pi$
$228$	−1.41499	−	7.96555i	−0.0937098	−	0.527531i
$229$		−	8.59511i		−	0.567981i	−0.958827	−	0.283990i	$-0.908342\pi$
$229$		−	8.59511i		−	0.567981i	0.958827	−	0.283990i	$-0.0916583\pi$
$230$	9.37064	+	21.1140i	0.617882	+	1.39222i
$231$	0.170165			0.0111960
$232$	−11.6782	+	14.9085i	−0.766713	+	0.978792i
$233$	−16.2256	−	18.7254i	−1.06298	−	1.22674i	−0.973002	−	0.230798i	$-0.925866\pi$
$233$	−16.2256	−	18.7254i	−1.06298	−	1.22674i	−0.0899759	−	0.995944i	$-0.528679\pi$
$234$	−3.08584	−	0.851031i	−0.201728	−	0.0556336i
$235$	−0.726814	+	0.104500i	−0.0474121	+	0.00681684i
$236$	−1.23816	−	1.00329i	−0.0805973	−	0.0653085i
$237$	4.48164	+	2.04670i	0.291114	+	0.132947i
$238$	−0.0596440	−	3.61392i	−0.00386614	−	0.234256i
$239$	−2.84454	+	19.7842i	−0.183998	+	1.27973i	0.663195	+	0.748447i	$0.269200\pi$
$239$	−2.84454	+	19.7842i	−0.183998	+	1.27973i	−0.847193	+	0.531286i	$0.821709\pi$
$240$	2.82412	+	13.3277i	0.182296	+	0.860300i
$241$	−20.5151	−	6.02378i	−1.32150	−	0.388026i	−0.456463	−	0.889742i	$-0.650884\pi$
$241$	−20.5151	−	6.02378i	−1.32150	−	0.388026i	−0.865032	+	0.501716i	$0.832702\pi$
$242$	13.9783	−	6.66460i	0.898558	−	0.428416i
$243$	−0.909632	+	0.415415i	−0.0583529	+	0.0266489i
$244$	−7.41143	+	28.7145i	−0.474468	+	1.83826i
$245$	16.5246	+	14.3186i	1.05572	+	0.914785i
$246$	9.52221	−	2.96751i	0.607114	−	0.189201i
$247$	7.70255	+	4.95013i	0.490102	+	0.314969i
$248$	3.89421	−	3.72733i	0.247283	−	0.236686i
$249$	6.25960	−	4.02280i	0.396686	−	0.254935i
$250$	0.970876	−	7.64632i	0.0614036	−	0.483596i
$251$	−1.23472	−	4.20508i	−0.0779350	−	0.265422i	0.911303	−	0.411736i	$-0.135077\pi$
$251$	−1.23472	−	4.20508i	−0.0779350	−	0.265422i	−0.989238	+	0.146314i	$0.953259\pi$
$252$	0.166930	−	1.51427i	0.0105156	−	0.0953901i
$253$	0.554493	+	0.916713i	0.0348607	+	0.0576333i
$254$	2.10172	−	1.88276i	0.131874	−	0.118135i
$255$	−10.9648	+	3.21956i	−0.686644	+	0.201617i
$256$	−4.34197	−	15.3996i	−0.271373	−	0.962474i
$257$	21.6364	−	13.9049i	1.34964	−	0.867363i	0.352002	−	0.935999i	$-0.385501\pi$
$257$	21.6364	−	13.9049i	1.34964	−	0.867363i	0.997642	+	0.0686362i	$0.0218648\pi$
$258$	7.45119	+	6.24422i	0.463891	+	0.388748i
$259$	2.33892	−	3.63942i	0.145333	−	0.226143i
$260$	−13.2388	−	7.90325i	−0.821034	−	0.490139i
$261$	−5.06017	−	4.38466i	−0.313217	−	0.271404i
$262$	−21.6210	+	14.4046i	−1.33575	+	0.889919i
$263$	−12.0085	−	26.2949i	−0.740474	−	1.62141i	−0.782773	−	0.622307i	$-0.786196\pi$
$263$	−12.0085	−	26.2949i	−0.740474	−	1.62141i	0.0422993	−	0.999105i	$-0.486532\pi$
$264$	0.207799	+	0.596710i	0.0127891	+	0.0367250i
$265$	−5.26665	−	1.54643i	−0.323528	−	0.0949963i
$266$	−1.74454	+	3.99311i	−0.106965	+	0.244833i
$267$	1.52597	+	0.219401i	0.0933875	+	0.0134271i
$268$	1.08013	−	1.00022i	0.0659797	−	0.0610981i
$269$	−21.3013	−	9.72799i	−1.29877	−	0.593126i	−0.358488	−	0.933534i	$-0.616707\pi$
$269$	−21.3013	−	9.72799i	−1.29877	−	0.593126i	−0.940278	+	0.340408i	$0.889435\pi$
$270$	−4.75569	+	0.764066i	−0.289422	+	0.0464996i
$271$	−4.50467	−	31.3306i	−0.273639	−	1.90320i	−0.409223	−	0.912435i	$-0.634200\pi$
$271$	−4.50467	−	31.3306i	−0.273639	−	1.90320i	0.135584	−	0.990766i	$-0.456709\pi$
$272$	12.6000	−	4.62233i	0.763984	−	0.280270i
$273$	1.12907	+	1.30302i	0.0683345	+	0.0788622i
$274$	5.52365	−	8.91507i	0.333696	−	0.538579i
$275$		−	1.47446i		−	0.0889130i
$276$	8.70163	−	4.03505i	0.523777	−	0.242882i
$277$			6.36756i			0.382590i	0.981533	+	0.191295i	$0.0612686\pi$
$277$			6.36756i			0.382590i	−0.981533	+	0.191295i	$0.938731\pi$
$278$	17.3890	+	10.7740i	1.04292	+	0.646180i
$279$	1.24806	+	1.44034i	0.0747195	+	0.0862309i
$280$	2.71424	−	6.81750i	0.162207	−	0.407424i
$281$	0.161438	+	1.12283i	0.00963060	+	0.0669823i	0.994070	−	0.108742i	$-0.0346823\pi$
$281$	0.161438	+	1.12283i	0.00963060	+	0.0669823i	−0.984439	+	0.175724i	$0.943773\pi$
$282$	0.0483651	+	0.301033i	0.00288010	+	0.0179263i
$283$	11.6093	+	5.30179i	0.690101	+	0.315159i	0.729418	−	0.684068i	$-0.239791\pi$
$283$	11.6093	+	5.30179i	0.690101	+	0.315159i	−0.0393170	+	0.999227i	$0.512518\pi$
$284$	−9.92698	−	10.7201i	−0.589058	−	0.636122i
$285$	13.6371	+	1.96072i	0.807791	+	0.116143i
$286$	−0.655289	−	0.286288i	−0.0387480	−	0.0169285i
$287$	−5.15451	−	1.51350i	−0.304261	−	0.0893392i
$288$	5.51387	−	1.26380i	0.324908	−	0.0744701i
$289$	−2.38540	−	5.22329i	−0.140317	−	0.307252i
$290$	−17.8812	−	26.8394i	−1.05002	−	1.57606i
$291$	7.87714	+	6.82558i	0.461766	+	0.400123i
$292$	−1.08599	−	0.648309i	−0.0635525	−	0.0379394i
$293$	11.8944	−	18.5080i	0.694878	−	1.08125i	−0.297101	−	0.954846i	$-0.596020\pi$
$293$	11.8944	−	18.5080i	0.694878	−	1.08125i	0.991979	−	0.126405i	$-0.0403440\pi$
$294$	5.83141	−	6.95858i	0.340095	−	0.405833i
$295$	2.28305	−	1.46722i	0.132924	−	0.0854251i
$296$	15.6184	+	3.75745i	0.907801	+	0.218398i
$297$	−0.214346	+	0.0629377i	−0.0124376	+	0.00365202i
$298$	−16.3579	−	18.2603i	−0.947590	−	1.05779i
$299$	−3.34047	+	10.3285i	−0.193184	+	0.597312i
$300$	−13.1209	−	1.44643i	−0.757538	−	0.0835095i
$301$	−1.47523	−	5.02416i	−0.0850306	−	0.289588i
$302$	−23.3323	−	2.96257i	−1.34262	−	0.170477i
$303$	14.3062	−	9.19402i	0.821868	−	0.528183i
$304$	−16.1328	−	1.24128i	−0.925280	−	0.0711922i
$305$	−42.4851	−	27.3035i	−2.43269	−	1.56339i
$306$	1.41179	+	4.53017i	0.0807064	+	0.258973i
$307$	−17.4304	−	15.1036i	−0.994807	−	0.862005i	−0.00437274	−	0.999990i	$-0.501392\pi$
$307$	−17.4304	−	15.1036i	−0.994807	−	0.862005i	−0.990434	+	0.137985i	$0.955937\pi$
$308$	0.0850542	−	0.329530i	0.00484642	−	0.0187767i
$309$	−17.8709	+	8.16138i	−1.01664	+	0.464284i
$310$	3.95072	+	8.28621i	0.224386	+	0.470625i
$311$	13.1060	+	3.84826i	0.743172	+	0.218215i	0.631333	−	0.775512i	$-0.282508\pi$
$311$	13.1060	+	3.84826i	0.743172	+	0.218215i	0.111838	+	0.993726i	$0.464326\pi$
$312$	−3.19046	+	5.55046i	−0.180624	+	0.314233i
$313$	−2.90038	+	20.1726i	−0.163939	+	1.14022i	0.727179	+	0.686448i	$0.240831\pi$
$313$	−2.90038	+	20.1726i	−0.163939	+	1.14022i	−0.891118	+	0.453772i	$0.850078\pi$
$314$	14.9986	−	0.247536i	0.846419	−	0.0139692i
$315$	2.35991	+	1.07773i	0.132966	+	0.0607234i
$316$	6.20357	−	7.65584i	0.348978	−	0.430675i
$317$	−15.8979	+	2.28577i	−0.892914	+	0.128382i	−0.573473	−	0.819224i	$-0.694404\pi$
$317$	−15.8979	+	2.28577i	−0.892914	+	0.128382i	−0.319441	+	0.947606i	$0.603495\pi$
$318$	−0.605939	+	2.19714i	−0.0339794	+	0.123209i
$319$	−0.979513	−	1.13042i	−0.0548422	−	0.0632913i
$320$	27.2212	+	1.19264i	1.52171	+	0.0666707i
$321$	16.0475			0.895684
$322$	−5.10550	−	0.789923i	−0.284518	−	0.0440207i
$323$		−	13.5725i		−	0.755192i
$324$	0.349801	+	1.96917i	0.0194334	+	0.109398i
$325$	11.2905	−	9.78324i	0.626282	−	0.542676i
$326$	−22.8749	−	6.30858i	−1.26692	−	0.349400i
$327$	−0.361853	−	2.51674i	−0.0200105	−	0.139176i
$328$	−0.987158	−	19.9233i	−0.0545067	−	1.10008i
$329$	0.0682201	−	0.149381i	0.00376109	−	0.00823565i
$330$	−1.07588	+	0.0177562i	−0.0592251	+	0.000977448i
$331$	6.76742	+	0.973008i	0.371971	+	0.0534814i	0.325766	−	0.945451i	$-0.394378\pi$
$331$	6.76742	+	0.973008i	0.371971	+	0.0534814i	0.0462055	+	0.998932i	$0.485287\pi$
$332$	−4.66153	−	14.1327i	−0.255835	−	0.775631i
$333$	−1.60010	+	5.44943i	−0.0876848	+	0.298627i
$334$	−2.76748	+	1.31948i	−0.151430	+	0.0721990i
$335$	1.04142	+	2.28040i	0.0568991	+	0.124592i
$336$	−2.84900	−	1.08015i	−0.155426	−	0.0589270i
$337$	−21.3225	+	24.6075i	−1.16151	+	1.34046i	−0.231542	+	0.972825i	$0.574377\pi$
$337$	−21.3225	+	24.6075i	−1.16151	+	1.34046i	−0.929971	+	0.367632i	$0.880169\pi$
$338$	3.31425	+	10.6348i	0.180271	+	0.578459i
$339$	2.55103	−	3.96949i	0.138553	−	0.215593i
$340$	0.754204	+	22.8430i	0.0409025	+	1.23884i
$341$	0.230181	+	0.358169i	0.0124650	+	0.0193959i
$342$	0.720585	−	5.67511i	0.0389648	−	0.306875i
$343$	−9.80807	+	2.87991i	−0.529586	+	0.155500i
$344$	15.8165	−	11.3084i	0.852769	−	0.609709i
$345$	1.88393	+	16.2252i	0.101427	+	0.873533i
$346$	−5.07940	−	5.67011i	−0.273070	−	0.304827i
$347$	−2.50931	−	8.54593i	−0.134707	−	0.458770i	0.864317	−	0.502948i	$-0.167751\pi$
$347$	−2.50931	−	8.54593i	−0.134707	−	0.458770i	−0.999024	+	0.0441783i	$0.985933\pi$
$348$	−11.0203	+	7.60759i	−0.590750	+	0.407810i
$349$	12.3374	+	19.1974i	0.660406	+	1.02761i	0.996319	+	0.0857189i	$0.0273187\pi$
$349$	12.3374	+	19.1974i	0.660406	+	1.02761i	−0.335913	+	0.941893i	$0.609045\pi$
$350$	5.44948	+	4.56675i	0.291287	+	0.244103i
$351$	−1.90416	−	1.22373i	−0.101636	−	0.0653177i
$352$	1.25942	−	0.104154i	0.0671271	−	0.00555141i
$353$	−17.1734	+	19.8192i	−0.914049	+	1.05487i	0.0842432	+	0.996445i	$0.473153\pi$
$353$	−17.1734	+	19.8192i	−0.914049	+	1.05487i	−0.998292	+	0.0584232i	$0.981393\pi$
$354$	−0.624786	−	0.937792i	−0.0332070	−	0.0498431i
$355$	22.6325	−	10.3359i	1.20121	−	0.548574i
$356$	1.18761	−	2.84542i	0.0629430	−	0.150807i
$357$	0.720046	−	2.45225i	0.0381089	−	0.129787i
$358$	0.620552	−	1.42039i	0.0327972	−	0.0750700i
$359$	1.18518	−	8.24311i	0.0625515	−	0.435055i	−0.934348	−	0.356363i	$-0.884017\pi$
$359$	1.18518	−	8.24311i	0.0625515	−	0.435055i	0.996899	−	0.0786918i	$-0.0250743\pi$
$360$	−0.897416	+	9.59147i	−0.0472980	+	0.505515i
$361$	1.09544	−	2.39867i	0.0576546	−	0.126246i
$362$	4.83419	+	30.0889i	0.254079	+	1.58144i
$363$	10.8386	−	1.55836i	0.568881	−	0.0817927i
$364$	3.08769	−	1.53519i	0.161839	−	0.0804660i
$365$	1.62778	−	1.41048i	0.0852020	−	0.0738279i
$366$	−11.0444	+	17.8255i	−0.577301	+	0.931753i
$367$	2.72151			0.142061			0.0710307	−	0.997474i	$-0.477371\pi$
$367$	2.72151			0.142061			0.0710307	+	0.997474i	$0.477371\pi$
$368$	−3.46465	−	18.8679i	−0.180607	−	0.983555i
$369$	7.05261			0.367144
$370$	−14.4082	+	23.2545i	−0.749044	+	1.20894i
$371$	0.927756	−	0.803905i	0.0481667	−	0.0417367i
$372$	3.41309	−	1.69698i	0.176961	−	0.0879845i
$373$	−25.8744	+	3.72018i	−1.33973	+	0.192624i	−0.774637	−	0.632406i	$-0.782067\pi$
$373$	−25.8744	+	3.72018i	−1.33973	+	0.192624i	−0.565090	+	0.825030i	$0.691158\pi$
$374$	0.168151	+	1.04660i	0.00869487	+	0.0541185i
$375$	2.26408	−	4.95765i	0.116917	−	0.256012i
$376$	0.607136	+	0.0568060i	0.0313106	+	0.00292955i
$377$	2.15682	−	15.0010i	0.111082	−	0.772591i
$378$	0.431270	−	0.987141i	0.0221821	−	0.0507730i
$379$	7.04063	−	23.9782i	0.361653	−	1.23168i	−0.554952	−	0.831882i	$-0.687263\pi$
$379$	7.04063	−	23.9782i	0.361653	−	1.23168i	0.916605	−	0.399794i	$-0.130918\pi$
$380$	10.6133	−	25.4287i	0.544450	−	1.30446i
$381$	1.81494	−	0.828856i	0.0929823	−	0.0424636i
$382$	4.80040	+	7.20530i	0.245610	+	0.368655i
$383$	9.24904	−	10.6740i	0.472604	−	0.545414i	−0.468530	−	0.883447i	$-0.655216\pi$
$383$	9.24904	−	10.6740i	0.472604	−	0.545414i	0.941134	+	0.338034i	$0.109762\pi$
$384$	0.308629	−	11.3095i	0.0157496	−	0.577135i
$385$	0.487562	+	0.313337i	0.0248485	+	0.0159691i
$386$	−4.97716	−	4.17094i	−0.253331	−	0.212295i
$387$	3.71650	+	5.78298i	0.188920	+	0.293966i
$388$	17.1552	−	11.8427i	0.870925	−	0.601222i
$389$	6.61877	+	22.5415i	0.335585	+	1.14290i	0.938554	+	0.345133i	$0.112166\pi$
$389$	6.61877	+	22.5415i	0.335585	+	1.14290i	−0.602969	+	0.797765i	$0.706016\pi$
$390$	−7.27458	−	8.12058i	−0.368362	−	0.411202i
$391$	15.5571	−	4.11177i	0.786755	−	0.207941i
$392$	−10.5608	−	14.7709i	−0.533401	−	0.746041i
$393$	−17.6265	+	5.17561i	−0.889139	+	0.261075i
$394$	1.31950	−	10.3920i	0.0664757	−	0.523542i
$395$	9.07221	+	14.1166i	0.456472	+	0.710285i
$396$	0.0147436	+	0.446547i	0.000740893	+	0.0224398i
$397$	4.64858	−	7.23333i	0.233305	−	0.363030i	−0.704785	−	0.709421i	$-0.748956\pi$
$397$	4.64858	−	7.23333i	0.233305	−	0.363030i	0.938090	+	0.346391i	$0.112593\pi$
$398$	−2.25044	−	7.22127i	−0.112804	−	0.361969i
$399$	−2.01780	+	2.32866i	−0.101016	+	0.116579i
$400$	−9.35935	+	24.6862i	−0.467967	+	1.23431i
$401$	−6.09554	−	13.3474i	−0.304397	−	0.666536i	0.694184	−	0.719798i	$-0.255765\pi$
$401$	−6.09554	−	13.3474i	−0.304397	−	0.666536i	−0.998581	+	0.0532619i	$0.983038\pi$
$402$	0.939611	−	0.447990i	0.0468636	−	0.0223437i
$403$	−1.21535	+	4.13909i	−0.0605407	+	0.206183i
$404$	−10.6538	−	32.2999i	−0.530048	−	1.60698i
$405$	−3.37124	−	0.484711i	−0.167518	−	0.0240855i
$406$	7.21173	−	0.119022i	0.357912	−	0.00590696i
$407$	−0.527067	+	1.15412i	−0.0261257	+	0.0572074i
$408$	9.47849	−	0.469639i	0.469255	−	0.0232506i
$409$	2.64975	+	18.4294i	0.131022	+	0.911276i	0.944226	+	0.329298i	$0.106812\pi$
$409$	2.64975	+	18.4294i	0.131022	+	0.911276i	−0.813205	+	0.581978i	$0.802279\pi$
$410$	32.7476	+	9.03134i	1.61729	+	0.446026i
$411$	5.60451	−	4.85634i	0.276450	−	0.239545i
$412$	6.87230	+	38.6870i	0.338574	+	1.90597i
$413$			0.606947i			0.0298659i
$414$	6.72324	−	0.893319i	0.330429	−	0.0439042i
$415$	25.3427			1.24402
$416$	9.15395	+	8.95274i	0.448809	+	0.438944i
$417$	9.47237	+	10.9317i	0.463864	+	0.535328i
$418$	0.339762	−	1.23198i	0.0166183	−	0.0602580i
$419$	20.2238	−	2.90775i	0.987999	−	0.142053i	0.370676	−	0.928762i	$-0.379126\pi$
$419$	20.2238	−	2.90775i	0.987999	−	0.142053i	0.617323	+	0.786709i	$0.288217\pi$
$420$	3.26663	−	4.03136i	0.159395	−	0.196710i
$421$	11.1554	+	5.09451i	0.543682	+	0.248291i	0.668272	−	0.743917i	$-0.267034\pi$
$421$	11.1554	+	5.09451i	0.543682	+	0.248291i	−0.124590	+	0.992208i	$0.539762\pi$
$422$	−32.5934	+	0.537919i	−1.58662	+	0.0261855i
$423$	−0.0306820	+	0.213398i	−0.00149181	+	0.0103758i
$424$	3.95196	+	2.27162i	0.191924	+	0.110320i
$425$	−21.2484	−	6.23909i	−1.03070	−	0.302641i
$426$	−4.44621	−	9.32546i	−0.215420	−	0.451820i
$427$	10.2740	−	4.69197i	0.497193	−	0.227060i
$428$	8.02108	−	31.0765i	0.387714	−	1.50214i
$429$	−0.382145	−	0.331130i	−0.0184501	−	0.0159871i
$430$	9.85145	+	31.6116i	0.475079	+	1.52445i
$431$	23.0426	+	14.8086i	1.10992	+	0.713305i	0.961277	−	0.275585i	$-0.0888716\pi$
$431$	23.0426	+	14.8086i	1.10992	+	0.713305i	0.148648	+	0.988890i	$0.452508\pi$
$432$	3.98821	+	0.306858i	0.191883	+	0.0147637i
$433$	−22.1536	+	14.2373i	−1.06463	+	0.684199i	−0.950958	−	0.309319i	$-0.899899\pi$
$433$	−22.1536	+	14.2373i	−1.06463	+	0.684199i	−0.113676	+	0.993518i	$0.536263\pi$
$434$	−2.03669	−	0.258605i	−0.0977644	−	0.0124134i
$435$	−6.42477	−	21.8807i	−0.308044	−	1.04910i
$436$	−5.05462	−	0.557212i	−0.242073	−	0.0266856i
$437$	−19.1201	−	3.28219i	−0.914637	−	0.157009i
$438$	−0.596738	−	0.666137i	−0.0285133	−	0.0318292i
$439$	15.3955	−	4.52054i	0.734789	−	0.215754i	0.107134	−	0.994245i	$-0.465833\pi$
$439$	15.3955	−	4.52054i	0.734789	−	0.215754i	0.627656	+	0.778491i	$0.284015\pi$
$440$	−0.503374	+	2.09235i	−0.0239974	+	0.0997488i
$441$	5.40066	−	3.47080i	0.257174	−	0.165276i
$442$	−6.89852	+	8.23196i	−0.328129	+	0.391554i
$443$	−12.2873	+	19.1194i	−0.583786	+	0.908389i	−1.00000		0.000878112i	$-0.999720\pi$
$443$	−12.2873	+	19.1194i	−0.583786	+	0.908389i	0.416214	+	0.909267i	$0.363357\pi$
$444$	9.75323	+	5.82246i	0.462868	+	0.276322i
$445$	3.96825	+	3.43850i	0.188113	+	0.163001i
$446$	8.28401	+	12.4341i	0.392259	+	0.588774i
$447$	−7.20132	−	15.7687i	−0.340611	−	0.745834i
$448$	−3.51577	+	4.97729i	−0.166105	+	0.235155i
$449$	32.6134	+	9.57615i	1.53912	+	0.451926i	0.937827	−	0.347102i	$-0.112834\pi$
$449$	32.6134	+	9.57615i	1.53912	+	0.451926i	0.601293	+	0.799029i	$0.294653\pi$
$450$	−8.55343	−	3.73689i	−0.403213	−	0.176159i
$451$	1.55948	+	0.224220i	0.0734332	+	0.0105581i
$452$	−6.41196	−	6.92425i	−0.301593	−	0.325689i
$453$	−15.1280	−	6.90872i	−0.710775	−	0.324600i
$454$	6.13748	+	38.2009i	0.288046	+	1.79285i
$455$	0.835710	+	5.81249i	0.0391787	+	0.272494i
$456$	−10.6299	−	4.23205i	−0.497789	−	0.198184i
$457$	6.59091	+	7.60631i	0.308310	+	0.355808i	0.888667	−	0.458554i	$-0.151632\pi$
$457$	6.59091	+	7.60631i	0.308310	+	0.355808i	−0.580357	+	0.814362i	$0.697087\pi$
$458$	−10.3328	−	6.40202i	−0.482818	−	0.299147i
$459$			3.35526i			0.156610i
$460$	32.3622	+	4.46159i	1.50890	+	0.208023i
$461$		−	36.5081i		−	1.70035i	−0.526500	−	0.850175i	$-0.676496\pi$
$461$		−	36.5081i		−	1.70035i	0.526500	−	0.850175i	$-0.323504\pi$
$462$	0.126747	−	0.204567i	0.00589679	−	0.00951731i
$463$	5.75206	+	6.63823i	0.267321	+	0.308505i	0.873501	−	0.486823i	$-0.161844\pi$
$463$	5.75206	+	6.63823i	0.267321	+	0.308505i	−0.606180	+	0.795328i	$0.707299\pi$
$464$	9.22405	+	25.1437i	0.428216	+	1.16727i
$465$	0.923783	+	6.42505i	0.0428394	+	0.297955i
$466$	−34.5967	+	5.55842i	−1.60266	+	0.257489i
$467$	−8.28381	−	3.78309i	−0.383329	−	0.175060i	0.214424	−	0.976741i	$-0.431212\pi$
$467$	−8.28381	−	3.78309i	−0.383329	−	0.175060i	−0.597753	+	0.801680i	$0.703940\pi$
$468$	−3.32155	+	3.07581i	−0.153539	+	0.142179i
$469$	−0.554965	−	0.0797919i	−0.0256259	−	0.00368445i
$470$	−0.415737	+	0.951588i	−0.0191765	+	0.0438935i
$471$	10.1774	+	2.98835i	0.468949	+	0.137696i
$472$	−2.12836	+	0.741180i	−0.0979655	+	0.0341156i
$473$	0.637942	+	1.39690i	0.0293326	+	0.0642295i
$474$	5.79860	−	3.86321i	0.266338	−	0.177443i
$475$	20.1775	+	17.4839i	0.925808	+	0.802217i
$476$	−4.38896	−	2.62011i	−0.201168	−	0.120093i
$477$	−0.871301	+	1.35577i	−0.0398942	+	0.0620765i
$478$	21.6652	+	18.1558i	0.990941	+	0.830425i
$479$	30.2459	−	19.4379i	1.38197	−	0.888139i	0.382612	−	0.923909i	$-0.375025\pi$
$479$	30.2459	−	19.4379i	1.38197	−	0.888139i	0.999360	+	0.0357697i	$0.0113883\pi$
$480$	18.1257	+	6.53202i	0.827319	+	0.298145i
$481$	−12.3347	+	3.62178i	−0.562412	+	0.165139i
$482$	−22.5222	+	20.1758i	−1.02586	+	0.918983i
$483$	−3.28046	−	1.60738i	−0.149266	−	0.0731383i
$484$	2.39970	−	21.7683i	0.109077	−	0.989469i
$485$	10.0014	+	34.0616i	0.454140	+	1.54666i
$486$	−0.178137	+	1.40295i	−0.00808045	+	0.0636391i
$487$	−23.5987	+	15.1660i	−1.06936	+	0.687237i	−0.952076	−	0.305862i	$-0.901056\pi$
$487$	−23.5987	+	15.1660i	−1.06936	+	0.687237i	−0.117285	+	0.993098i	$0.537419\pi$
$488$	28.9993	+	30.2977i	1.31274	+	1.37151i
$489$	−14.1153	−	9.07132i	−0.638314	−	0.410219i
$490$	29.5217	−	9.20015i	1.33365	−	0.415621i
$491$	−17.0940	−	14.8120i	−0.771441	−	0.668457i	0.177426	−	0.984134i	$-0.443223\pi$
$491$	−17.0940	−	14.8120i	−0.771441	−	0.668457i	−0.948867	+	0.315677i	$0.897768\pi$
$492$	3.52513	−	13.6576i	0.158925	−	0.615733i
$493$	−20.4352	+	9.33246i	−0.920357	+	0.420313i
$494$	11.6881	−	5.57267i	0.525872	−	0.250726i
$495$	−0.730044	−	0.214360i	−0.0328130	−	0.00963477i
$496$	−1.58029	−	7.45778i	−0.0709571	−	0.334864i
$497$	−0.791919	+	5.50792i	−0.0355224	+	0.247064i
$498$	−0.173645	−	10.5214i	−0.00778123	−	0.471477i
$499$	2.22543	+	1.01632i	0.0996240	+	0.0454967i	0.464604	−	0.885519i	$-0.346197\pi$
$499$	2.22543	+	1.01632i	0.0996240	+	0.0454967i	−0.364980	+	0.931015i	$0.618924\pi$
$500$	−8.46900	−	6.86248i	−0.378745	−	0.306899i
$501$	−2.14588	+	0.308531i	−0.0958708	+	0.0137841i
$502$	−5.97488	−	1.64779i	−0.266672	−	0.0735445i
$503$	−3.61376	−	4.17050i	−0.161130	−	0.185954i	0.669444	−	0.742863i	$-0.266533\pi$
$503$	−3.61376	−	4.17050i	−0.161130	−	0.185954i	−0.830573	+	0.556909i	$0.811987\pi$
$504$	−1.69607	−	1.32857i	−0.0755489	−	0.0591794i
$505$	57.9201			2.57741
$506$	1.51505	+	0.0162165i	0.0673524	+	0.000720914i
$507$			7.87668i			0.349815i
$508$	−0.697939	−	3.92899i	−0.0309661	−	0.174321i
$509$	−12.1911	+	10.5636i	−0.540361	+	0.468225i	−0.881763	−	0.471692i	$-0.843643\pi$
$509$	−12.1911	+	10.5636i	−0.540361	+	0.468225i	0.341403	+	0.939917i	$0.389098\pi$
$510$	−4.29664	+	15.5796i	−0.190259	+	0.689877i
$511$	0.0685538	+	0.476802i	0.00303264	+	0.0210925i
$512$	−21.7470	−	6.25054i	−0.961089	−	0.276237i
$513$	1.68041	−	3.67957i	0.0741917	−	0.162457i
$514$	−0.600209	−	36.3676i	−0.0264741	−	1.60411i
$515$	−66.2325	−	9.52279i	−2.91855	−	0.419624i
$516$	13.0566	−	4.30660i	0.574784	−	0.189587i
$517$	−0.0135689	+	0.0462114i	−0.000596760	+	0.00203238i
$518$	−2.63307	−	5.52258i	−0.115690	−	0.242648i
$519$	−2.23612	−	4.89643i	−0.0981549	−	0.214929i
$520$	−19.3619	+	10.0285i	−0.849074	+	0.439780i
$521$	−14.9498	+	17.2530i	−0.654961	+	0.755866i	−0.981945	−	0.189164i	$-0.939422\pi$
$521$	−14.9498	+	17.2530i	−0.654961	+	0.755866i	0.326984	+	0.945030i	$0.393968\pi$
$522$	−9.04014	+	2.81728i	−0.395676	+	0.123309i
$523$	10.1242	−	15.7536i	0.442700	−	0.688855i	−0.546164	−	0.837678i	$-0.683912\pi$
$523$	10.1242	−	15.7536i	0.442700	−	0.688855i	0.988864	+	0.148824i	$0.0475487\pi$
$524$	1.21242	+	36.7213i	0.0529649	+	1.60418i
$525$	2.71808	+	4.22942i	0.118627	+	0.184587i
$526$	−40.5553	−	5.14943i	−1.76829	−	0.224526i
$527$	6.13558	−	1.80157i	0.267270	−	0.0784776i
$528$	0.872124	+	0.194648i	0.0379543	+	0.00847096i
$529$	−2.03029	−	22.9102i	−0.0882733	−	0.996096i
$530$	−5.78190	+	5.17954i	−0.251150	+	0.224985i
$531$	−0.224487	−	0.764533i	−0.00974192	−	0.0331779i
$532$	3.50097	+	5.07147i	0.151786	+	0.219876i
$533$	8.63047	+	13.4293i	0.373827	+	0.581686i
$534$	1.40036	−	1.67105i	0.0605997	−	0.0723132i
$535$	45.9798	+	29.5494i	1.98788	+	1.27753i
$536$	−0.397899	−	2.04351i	−0.0171866	−	0.0882662i
$537$	0.717752	−	0.828330i	0.0309733	−	0.0357451i
$538$	−27.5609	+	18.3619i	−1.18823	+	0.791638i
$539$	1.30455	−	0.595767i	0.0561908	−	0.0256615i
$540$	−2.62372	+	6.28625i	−0.112907	+	0.270517i
$541$	−1.06686	+	3.63339i	−0.0458679	+	0.156212i	−0.979243	−	0.202692i	$-0.935031\pi$
$541$	−1.06686	+	3.63339i	−0.0458679	+	0.156212i	0.933375	+	0.358903i	$0.116849\pi$
$542$	−41.0199	−	17.9211i	−1.76196	−	0.769778i
$543$	−3.06673	+	21.3296i	−0.131606	+	0.915339i
$544$	3.82820	−	18.5902i	0.164133	−	0.797047i
$545$	3.59747	−	7.87735i	0.154099	−	0.337429i
$546$	2.40743	−	0.386786i	0.103028	−	0.0165529i
$547$	−5.89549	+	0.847643i	−0.252073	+	0.0362426i	−0.267193	−	0.963643i	$-0.586096\pi$
$547$	−5.89549	+	0.847643i	−0.252073	+	0.0362426i	0.0151200	+	0.999886i	$0.495187\pi$
$548$	−6.60314	−	13.2807i	−0.282072	−	0.567323i
$549$	−11.2061	+	9.71014i	−0.478265	+	0.414419i
$550$	−1.77254	−	1.09824i	−0.0755815	−	0.0468292i
$551$	27.0844			1.15383
$552$	1.63056	−	13.4663i	0.0694013	−	0.573164i
$553$	−3.75290			−0.159590
$554$	7.65487	+	4.74285i	0.325224	+	0.201504i
$555$	−14.6191	+	12.6675i	−0.620546	+	0.537706i
$556$	25.9042	−	12.8795i	1.09858	−	0.546214i
$557$	−37.9754	+	5.46004i	−1.60907	+	0.231349i	−0.887438	−	0.460927i	$-0.847517\pi$
$557$	−37.9754	+	5.46004i	−1.60907	+	0.231349i	−0.721632	+	0.692277i	$0.756608\pi$
$558$	2.66114	−	0.427548i	0.112655	−	0.0180996i
$559$	−6.46373	+	14.1536i	−0.273387	+	0.598633i
$560$	−6.17409	−	8.34095i	−0.260903	−	0.352469i
$561$	−0.106672	+	0.741921i	−0.00450370	+	0.0313239i
$562$	1.47007	+	0.642257i	0.0620113	+	0.0270920i
$563$	12.1606	−	41.4150i	0.512506	−	1.74544i	−0.142482	−	0.989797i	$-0.545508\pi$
$563$	12.1606	−	41.4150i	0.512506	−	1.74544i	0.654989	−	0.755639i	$-0.272673\pi$
$564$	0.397917	+	0.166080i	0.0167553	+	0.00699324i
$565$	14.6186	−	6.67610i	0.615010	−	0.280866i
$566$	15.0208	−	10.0073i	0.631370	−	0.420638i
$567$	0.498822	−	0.575671i	0.0209485	−	0.0241759i
$568$	−20.2814	+	3.94906i	−0.850990	+	0.165699i
$569$	20.4255	+	13.1267i	0.856282	+	0.550299i	0.893528	−	0.449007i	$-0.148222\pi$
$569$	20.4255	+	13.1267i	0.856282	+	0.550299i	−0.0372460	+	0.999306i	$0.511859\pi$
$570$	12.5146	−	14.9336i	0.524180	−	0.625501i
$571$	−2.42695	−	3.77641i	−0.101565	−	0.158038i	0.786752	−	0.617269i	$-0.211761\pi$
$571$	−2.42695	−	3.77641i	−0.101565	−	0.158038i	−0.888317	+	0.459232i	$0.848125\pi$
$572$	−0.832254	+	0.574526i	−0.0347983	+	0.0240222i
$573$	1.72479	+	5.87411i	0.0720543	+	0.245395i
$574$	−5.65880	+	5.06926i	−0.236194	+	0.211587i
$575$	−13.9277	+	28.4247i	−0.580826	+	1.18539i
$576$	2.58768	−	7.56993i	0.107820	−	0.315414i
$577$	36.7421	−	10.7885i	1.52960	−	0.449130i	0.594669	−	0.803971i	$-0.297283\pi$
$577$	36.7421	−	10.7885i	1.52960	−	0.449130i	0.934927	+	0.354841i	$0.115465\pi$
$578$	−8.05602	−	1.02290i	−0.335086	−	0.0425469i
$579$	−2.48250	−	3.86285i	−0.103169	−	0.160535i
$580$	−45.5841	+	1.50505i	−1.89278	+	0.0624936i
$581$	−3.06425	+	4.76807i	−0.127127	+	0.197813i
$582$	14.0727	−	4.38564i	0.583334	−	0.181791i
$583$	−0.235767	+	0.272089i	−0.00976446	+	0.0112688i
$584$	−1.58827	+	0.822647i	−0.0657229	+	0.0340414i
$585$	−3.20251	−	7.01253i	−0.132408	−	0.289932i
$586$	−13.3903	−	28.0847i	−0.553147	−	1.16017i
$587$	−4.56978	+	15.5632i	−0.188615	+	0.642363i	0.809833	+	0.586661i	$0.199558\pi$
$587$	−4.56978	+	15.5632i	−0.188615	+	0.642363i	−0.998447	+	0.0557022i	$0.982260\pi$
$588$	−4.02188	−	12.1934i	−0.165860	−	0.502847i
$589$	−7.63090	−	1.09716i	−0.314426	−	0.0452076i
$590$	−0.0633332	−	3.83746i	−0.00260738	−	0.157986i
$591$	3.07708	−	6.73788i	0.126574	−	0.277159i
$592$	16.1504	−	15.9772i	0.663777	−	0.656659i
$593$	−1.95000	−	13.5625i	−0.0800768	−	0.556947i	−0.989880	−	0.141907i	$-0.954677\pi$
$593$	−1.95000	−	13.5625i	−0.0800768	−	0.556947i	0.909803	−	0.415040i	$-0.136232\pi$
$594$	−0.0839931	+	0.304559i	−0.00344628	+	0.0124962i
$595$	6.57861	−	5.70040i	0.269697	−	0.233693i
$596$	−34.1361	+	6.06388i	−1.39827	+	0.248386i
$597$		−	5.34842i		−	0.218896i
$598$	9.92844	+	11.7089i	0.406004	+	0.478814i
$599$	35.9111			1.46729			0.733645	−	0.679533i	$-0.237818\pi$
$599$	35.9111			1.46729			0.733645	+	0.679533i	$0.237818\pi$
$600$	−11.5119	+	14.6962i	−0.469972	+	0.599970i
$601$	15.0845	+	17.4084i	0.615308	+	0.710104i	0.974809	−	0.223041i	$-0.0715984\pi$
$601$	15.0845	+	17.4084i	0.615308	+	0.710104i	−0.359501	+	0.933145i	$0.617053\pi$
$602$	−7.13869	−	1.96875i	−0.290951	−	0.0802403i
$603$	0.728567	−	0.104752i	0.0296695	−	0.00426583i
$604$	−20.9404	+	25.8426i	−0.852055	+	1.05152i
$605$	33.9247	+	15.4929i	1.37924	+	0.629876i
$606$	−0.396863	−	24.0465i	−0.0161214	−	0.976824i
$607$	2.45840	−	17.0985i	0.0997833	−	0.694008i	−0.877111	−	0.480287i	$-0.840533\pi$
$607$	2.45840	−	17.0985i	0.0997833	−	0.694008i	0.976895	−	0.213721i	$-0.0685583\pi$
$608$	−13.5087	+	18.4698i	−0.547849	+	0.749048i
$609$	4.89357	+	1.43688i	0.198297	+	0.0582253i
$610$	−64.4682	+	30.7373i	−2.61024	+	1.24452i
$611$	−0.443890	+	0.202718i	−0.0179579	+	0.00820108i
$612$	6.49759	+	1.67707i	0.262649	+	0.0677917i
$613$	9.97288	+	8.64155i	0.402801	+	0.349029i	0.832580	−	0.553905i	$-0.186863\pi$
$613$	9.97288	+	8.64155i	0.402801	+	0.349029i	−0.429779	+	0.902934i	$0.641409\pi$
$614$	−31.1400	+	9.70448i	−1.25671	+	0.391641i
$615$	20.2074	+	12.9865i	0.814839	+	0.523665i
$616$	−0.332798	−	0.347699i	−0.0134088	−	0.0140092i
$617$	16.8354	−	10.8194i	0.677766	−	0.435574i	−0.155952	−	0.987765i	$-0.549844\pi$
$617$	16.8354	−	10.8194i	0.677766	−	0.435574i	0.833718	+	0.552191i	$0.186208\pi$
$618$	−3.49973	+	27.5628i	−0.140780	+	1.10874i
$619$	4.14043	+	14.1010i	0.166418	+	0.566767i	0.999899	+	0.0142190i	$0.00452619\pi$
$619$	4.14043	+	14.1010i	0.166418	+	0.566767i	−0.833481	+	0.552548i	$0.813656\pi$
$620$	12.9041	+	1.42252i	0.518240	+	0.0571298i
$621$	4.72669	+	0.811395i	0.189676	+	0.0325602i
$622$	14.3882	−	12.8892i	0.576913	−	0.516810i
$623$	−1.12675	+	0.330842i	−0.0451421	+	0.0132549i
$624$	4.29618	+	7.96969i	0.171985	+	0.319043i
$625$	−12.1462	+	7.80592i	−0.485850	+	0.312237i
$626$	22.0905	+	18.5122i	0.882912	+	0.739895i
$627$	0.488556	−	0.760209i	0.0195111	−	0.0303598i
$628$	10.8740	−	18.2152i	0.433921	−	0.726864i
$629$	14.4017	+	12.4792i	0.574234	+	0.497576i
$630$	3.05338	−	2.03426i	0.121650	−	0.0810468i
$631$	2.76537	+	6.05531i	0.110088	+	0.241058i	0.956655	−	0.291223i	$-0.0940622\pi$
$631$	2.76537	+	6.05531i	0.110088	+	0.241058i	−0.846568	+	0.532281i	$0.821335\pi$
$632$	−4.58290	−	13.1601i	−0.182298	−	0.523483i
$633$	−22.1164	−	6.49397i	−0.879049	−	0.258112i
$634$	−9.09359	+	20.8145i	−0.361153	+	0.826648i
$635$	6.72647	+	0.967120i	0.266932	+	0.0383790i
$636$	2.18999	+	2.36497i	0.0868388	+	0.0937770i
$637$	13.2179	+	6.03640i	0.523711	+	0.239171i
$638$	−2.08854	+	0.335552i	−0.0826860	+	0.0132846i
$639$	−1.03964	−	7.23088i	−0.0411277	−	0.286049i
$640$	21.7093	−	31.8360i	0.858135	−	1.25843i
$641$	13.8366	+	15.9683i	0.546512	+	0.630709i	0.960067	−	0.279771i	$-0.0902584\pi$
$641$	13.8366	+	15.9683i	0.546512	+	0.630709i	−0.413555	+	0.910479i	$0.635713\pi$
$642$	11.9529	−	19.2918i	0.471743	−	0.761385i
$643$			3.49414i			0.137795i	0.997624	+	0.0688976i	$0.0219482\pi$
$643$			3.49414i			0.137795i	−0.997624	+	0.0688976i	$0.978052\pi$
$644$	−4.75243	+	5.54929i	−0.187272	+	0.218673i
$645$			23.4131i			0.921888i
$646$	−16.3164	−	10.1094i	−0.641959	−	0.397748i
$647$	22.7570	+	26.2630i	0.894671	+	1.03251i	0.999278	+	0.0379917i	$0.0120960\pi$
$647$	22.7570	+	26.2630i	0.894671	+	1.03251i	−0.104607	+	0.994514i	$0.533359\pi$
$648$	2.62782	+	1.04621i	0.103231	+	0.0410990i
$649$	−0.0253325	−	0.176192i	−0.000994390	−	0.00691613i
$650$	−3.35144	−	20.8600i	−0.131454	−	0.818197i
$651$	−1.32053	−	0.603067i	−0.0517557	−	0.0236361i
$652$	−24.6222	+	22.8005i	−0.964280	+	0.892937i
$653$	11.4702	+	1.64917i	0.448865	+	0.0645371i	0.363041	−	0.931773i	$-0.381738\pi$
$653$	11.4702	+	1.64917i	0.448865	+	0.0645371i	0.0858244	+	0.996310i	$0.472648\pi$
$654$	−3.29507	−	1.43958i	−0.128847	−	0.0562918i
$655$	−60.0342	−	17.6276i	−2.34573	−	0.688769i
$656$	−24.6865	−	13.6531i	−0.963844	−	0.533063i
$657$	−0.262704	−	0.575242i	−0.0102491	−	0.0224423i
$658$	−0.128768	−	0.193278i	−0.00501989	−	0.00753475i
$659$	−3.15276	−	2.73188i	−0.122814	−	0.106419i	0.591288	−	0.806460i	$-0.298620\pi$
$659$	−3.15276	−	2.73188i	−0.122814	−	0.106419i	−0.714102	+	0.700041i	$0.753165\pi$
$660$	−0.780016	+	1.30661i	−0.0303621	+	0.0508597i
$661$	−4.61213	+	7.17661i	−0.179391	+	0.279138i	−0.919291	−	0.393580i	$-0.871237\pi$
$661$	−4.61213	+	7.17661i	−0.179391	+	0.279138i	0.739900	+	0.672717i	$0.234873\pi$
$662$	6.21040	−	7.41083i	0.241374	−	0.288030i
$663$	−6.38895	+	4.10593i	−0.248126	+	0.159461i
$664$	−20.4619	−	4.92271i	−0.794077	−	0.191038i
$665$	−10.0694	+	2.95664i	−0.390474	+	0.114654i
$666$	5.35930	+	5.98257i	0.207669	+	0.231820i
$667$	8.20521	+	31.0448i	0.317707	+	1.20206i
$668$	−0.475102	+	4.30978i	−0.0183823	+	0.166750i
$669$	2.97647	+	10.1369i	0.115077	+	0.391916i
$670$	3.51712	+	0.446580i	0.135878	+	0.0172529i
$671$	−2.78662	+	1.79085i	−0.107576	+	0.0691350i
$672$	−3.42058	+	2.62043i	−0.131952	+	0.101085i
$673$	−31.9667	−	20.5437i	−1.23223	−	0.791903i	−0.247989	−	0.968763i	$-0.579770\pi$
$673$	−31.9667	−	20.5437i	−1.23223	−	0.791903i	−0.984236	+	0.176860i	$0.943406\pi$
$674$	13.7004	+	43.9621i	0.527718	+	1.69336i
$675$	−4.98811	−	4.32222i	−0.191992	−	0.166362i
$676$	15.2535	+	3.93703i	0.586671	+	0.151424i
$677$	21.7589	−	9.93696i	0.836263	−	0.381909i	0.0492060	−	0.998789i	$-0.484331\pi$
$677$	21.7589	−	9.93696i	0.836263	−	0.381909i	0.787057	+	0.616880i	$0.211604\pi$
$678$	−2.87186	−	6.02342i	−0.110293	−	0.231328i
$679$	−7.61779	−	2.23678i	−0.292344	−	0.0858399i
$680$	28.0229	+	16.1078i	1.07463	+	0.617707i
$681$	−3.89352	+	27.0800i	−0.149200	+	1.03771i
$682$	0.602028	−	0.00993584i	0.0230529	−	0.000380463i
$683$	36.5255	+	16.6806i	1.39761	+	0.638266i	0.964743	−	0.263192i	$-0.0847754\pi$
$683$	36.5255	+	16.6806i	1.39761	+	0.638266i	0.432865	+	0.901459i	$0.357503\pi$
$684$	−6.28570	−	5.09334i	−0.240340	−	0.194749i
$685$	25.0005	−	3.59454i	0.955222	−	0.137340i
$686$	−3.84336	+	13.9360i	−0.146740	+	0.532080i
$687$	−5.62860	−	6.49575i	−0.214744	−	0.247828i
$688$	−1.81375	−	27.4371i	−0.0691486	−	1.04603i
$689$	−3.64784			−0.138972
$690$	20.9086	+	9.82043i	0.795976	+	0.373857i
$691$		−	27.1206i		−	1.03172i	−0.856674	−	0.515858i	$-0.827473\pi$
$691$		−	27.1206i		−	1.03172i	0.856674	−	0.515858i	$-0.172527\pi$
$692$	−10.5998	+	1.88293i	−0.402943	+	0.0715782i
$693$	0.128602	−	0.111434i	0.00488519	−	0.00423304i
$694$	−12.1427	−	3.34878i	−0.460930	−	0.127118i
$695$	7.01121	+	48.7640i	0.265950	+	1.84973i
$696$	0.937183	+	18.9147i	0.0355238	+	0.716960i
$697$	9.83011	−	21.5249i	0.372342	−	0.815315i
$698$	32.2679	−	0.532548i	1.22136	−	0.0201572i
$699$	−24.5251	−	3.52617i	−0.927623	−	0.133372i
$700$	9.54901	−	3.14966i	0.360919	−	0.119046i
$701$	−8.65861	+	29.4885i	−0.327031	+	1.11377i	0.617835	+	0.786308i	$0.288010\pi$
$701$	−8.65861	+	29.4885i	−0.327031	+	1.11377i	−0.944866	+	0.327458i	$0.893808\pi$
$702$	−2.88943	+	1.37763i	−0.109054	+	0.0519952i
$703$	−9.54385	−	20.8981i	−0.359953	−	0.788187i
$704$	0.812859	−	1.59161i	0.0306358	−	0.0599859i
$705$	−0.480856	+	0.554938i	−0.0181101	+	0.0209002i
$706$	11.0344	+	35.4075i	0.415286	+	1.33258i
$707$	−7.00329	+	10.8973i	−0.263386	+	0.409836i
$708$	−1.59275	+	0.0525877i	−0.0598593	+	0.00197637i
$709$	−13.3492	−	20.7718i	−0.501340	−	0.780100i	0.494695	−	0.869067i	$-0.335280\pi$
$709$	−13.3492	−	20.7718i	−0.501340	−	0.780100i	−0.996035	+	0.0889670i	$0.971643\pi$
$710$	4.43221	−	34.9067i	0.166338	−	1.31003i
$711$	4.72730	−	1.38806i	0.177288	−	0.0520563i
$712$	−2.53609	−	3.54710i	−0.0950439	−	0.132933i
$713$	−1.05419	−	9.07910i	−0.0394797	−	0.340015i
$714$	−2.41169	−	2.69216i	−0.0902553	−	0.100752i
$715$	−0.485199	−	1.65244i	−0.0181454	−	0.0617976i
$716$	−1.24533	−	1.80398i	−0.0465403	−	0.0674179i
$717$	10.8061	+	16.8147i	0.403562	+	0.627955i
$718$	−9.02682	−	7.56463i	−0.336878	−	0.282309i
$719$	−5.15639	−	3.31381i	−0.192301	−	0.123584i	0.440947	−	0.897533i	$-0.354643\pi$
$719$	−5.15639	−	3.31381i	−0.192301	−	0.123584i	−0.633248	+	0.773949i	$0.718279\pi$
$720$	10.8621	+	8.22301i	0.404807	+	0.306453i
$721$	9.80001	−	11.3098i	0.364971	−	0.421199i
$722$	−2.06767	−	3.10354i	−0.0769508	−	0.115502i
$723$	−19.4490	+	8.88208i	−0.723317	+	0.330328i
$724$	39.7726	+	16.6001i	1.47814	+	0.616937i
$725$	12.4504	−	42.4021i	0.462395	−	1.57477i
$726$	6.19970	−	14.1906i	0.230092	−	0.526662i
$727$	−4.65575	+	32.3814i	−0.172672	+	1.20096i	0.700537	+	0.713616i	$0.252944\pi$
$727$	−4.65575	+	32.3814i	−0.172672	+	1.20096i	−0.873209	+	0.487345i	$0.837965\pi$
$728$	0.454290	−	4.85539i	0.0168371	−	0.179953i
$729$	−0.415415	+	0.909632i	−0.0153857	+	0.0336901i
$730$	−0.483188	−	3.00745i	−0.0178836	−	0.111311i
$731$	22.8301	−	3.28248i	0.844404	−	0.121407i
$732$	13.2028	+	26.5544i	0.487991	+	0.981481i
$733$	38.9227	−	33.7267i	1.43764	−	1.24573i	0.516622	−	0.856214i	$-0.327189\pi$
$733$	38.9227	−	33.7267i	1.43764	−	1.24573i	0.921022	−	0.389511i	$-0.127356\pi$
$734$	2.02710	−	3.27170i	0.0748216	−	0.120761i
$735$	21.8652			0.806509
$736$	−25.2629	−	9.88855i	−0.931205	−	0.364497i
$737$	0.164432			0.00605693
$738$	5.25310	−	8.47841i	0.193369	−	0.312095i
$739$	15.6972	−	13.6017i	0.577431	−	0.500347i	−0.316475	−	0.948601i	$-0.602499\pi$
$739$	15.6972	−	13.6017i	0.577431	−	0.500347i	0.893906	+	0.448254i	$0.147954\pi$
$740$	17.2240	+	34.6420i	0.633165	+	1.27347i
$741$	9.06285	−	1.30304i	0.332932	−	0.0478684i
$742$	−0.275394	−	1.71410i	−0.0101100	−	0.0629267i
$743$	−4.46652	+	9.78031i	−0.163861	+	0.358805i	−0.973695	−	0.227853i	$-0.926829\pi$
$743$	−4.46652	+	9.78031i	−0.163861	+	0.358805i	0.809835	+	0.586658i	$0.199557\pi$
$744$	0.502167	−	5.36710i	0.0184103	−	0.196767i
$745$	8.40259	−	58.4413i	0.307847	−	2.14112i
$746$	−14.8002	+	33.8763i	−0.541872	+	1.24030i
$747$	2.09632	−	7.13940i	0.0767002	−	0.261217i
$748$	1.38344	+	0.577411i	0.0505835	+	0.0211123i
$749$	−11.1191	+	5.07792i	−0.406283	+	0.185543i
$750$	−4.27353	−	6.41449i	−0.156047	−	0.234224i
$751$	9.70672	−	11.2022i	0.354203	−	0.408772i	−0.550486	−	0.834844i	$-0.685558\pi$
$751$	9.70672	−	11.2022i	0.354203	−	0.408772i	0.904689	+	0.426072i	$0.140103\pi$
$752$	0.520513	−	0.687567i	0.0189811	−	0.0250730i
$753$	−3.68688	−	2.36941i	−0.134357	−	0.0863463i
$754$	−16.4272	−	13.7663i	−0.598244	−	0.501338i
$755$	−30.6237	−	47.6513i	−1.11451	−	1.73421i
$756$	−0.865479	−	1.25373i	−0.0314772	−	0.0455975i
$757$	1.64724	+	5.60998i	0.0598699	+	0.203898i	0.983996	−	0.178189i	$-0.0570237\pi$
$757$	1.64724	+	5.60998i	0.0598699	+	0.203898i	−0.924126	+	0.382087i	$0.875206\pi$
$758$	−23.5816	−	26.3240i	−0.856522	−	0.956132i
$759$	1.01938	+	0.329690i	0.0370010	+	0.0119670i
$760$	−22.6643	−	31.6993i	−0.822119	−	1.14986i
$761$	1.06687	−	0.313262i	0.0386741	−	0.0113557i	−0.262338	−	0.964976i	$-0.584494\pi$
$761$	1.06687	−	0.313262i	0.0386741	−	0.0113557i	0.301012	+	0.953620i	$0.402675\pi$
$762$	0.355427	−	2.79923i	0.0128758	−	0.101406i
$763$	1.04710	+	1.62931i	0.0379075	+	0.0589851i
$764$	12.2375	−	0.404045i	0.442738	−	0.0146178i
$765$	−6.17829	+	9.61361i	−0.223377	+	0.347581i
$766$	−5.94278	−	19.0693i	−0.214721	−	0.689003i
$767$	1.18108	−	1.36304i	0.0426464	−	0.0492165i
$768$	−13.3660	−	8.79485i	−0.482305	−	0.317357i
$769$	12.7173	+	27.8470i	0.458597	+	1.00419i	0.987805	+	0.155695i	$0.0497618\pi$
$769$	12.7173	+	27.8470i	0.458597	+	1.00419i	−0.529208	+	0.848492i	$0.677511\pi$
$770$	0.739842	−	0.352744i	0.0266621	−	0.0127120i
$771$	7.24596	−	24.6775i	0.260957	−	0.888737i
$772$	−8.72138	+	2.87667i	−0.313889	+	0.103534i
$773$	−4.15568	−	0.597496i	−0.149469	−	0.0214905i	0.0671739	−	0.997741i	$-0.478602\pi$
$773$	−4.15568	−	0.597496i	−0.149469	−	0.0214905i	−0.216643	+	0.976251i	$0.569511\pi$
$774$	9.72033	−	0.160424i	0.349390	−	0.00576631i
$775$	−5.22549	+	11.4422i	−0.187705	+	0.411017i
$776$	−1.45891	−	29.4444i	−0.0523717	−	1.05699i
$777$	−0.615681	−	4.28216i	−0.0220874	−	0.153622i
$778$	32.0286	+	8.83303i	1.14828	+	0.316680i
$779$	−21.5605	+	18.6823i	−0.772486	+	0.669363i
$780$	−15.1807	+	2.69668i	−0.543557	+	0.0965567i
$781$		−	1.63196i		−	0.0583960i
$782$	6.64458	−	21.7648i	0.237610	−	0.778309i
$783$	−6.69557			−0.239280
$784$	−25.6232	+	1.69384i	−0.915114	+	0.0604944i
$785$	23.6579	+	27.3027i	0.844386	+	0.974474i
$786$	−6.90707	+	25.0450i	−0.246367	+	0.893327i
$787$	−5.65668	+	0.813308i	−0.201639	+	0.0289913i	−0.242394	−	0.970178i	$-0.577933\pi$
$787$	−5.65668	+	0.813308i	−0.201639	+	0.0289913i	0.0407552	+	0.999169i	$0.487024\pi$
$788$	−11.5101	−	9.32670i	−0.410030	−	0.332250i
$789$	−26.2949	−	12.0085i	−0.936123	−	0.427513i
$790$	23.7279	−	0.391604i	0.844202	−	0.0139327i
$791$	−0.511510	+	3.55763i	−0.0181872	+	0.126495i
$792$	0.547806	+	0.314884i	0.0194654	+	0.0111889i
$793$	−32.2028	−	9.45561i	−1.14356	−	0.335778i
$794$	−5.23320	−	10.9761i	−0.185719	−	0.389526i
$795$	−4.99296	+	2.28021i	−0.177082	+	0.0808707i
$796$	−10.3574	−	2.67332i	−0.367108	−	0.0947533i
$797$	−19.1815	−	16.6208i	−0.679443	−	0.588741i	0.245248	−	0.969460i	$-0.421131\pi$
$797$	−19.1815	−	16.6208i	−0.679443	−	0.588741i	−0.924690	+	0.380720i	$0.875676\pi$
$798$	1.29649	+	4.16022i	0.0458954	+	0.147270i
$799$	0.608537	+	0.391083i	0.0215285	+	0.0138355i
$800$	22.7056	+	29.6389i	0.802766	+	1.04789i
$801$	1.29692	−	0.833483i	0.0458246	−	0.0294497i
$802$	−20.5860	−	2.61387i	−0.726917	−	0.0922989i
$803$	−0.0398012	−	0.135550i	−0.00140455	−	0.00478347i
$804$	0.161306	−	1.46325i	0.00568883	−	0.0516050i
$805$	−6.43949	−	10.6461i	−0.226962	−	0.375224i
$806$	4.07063	+	4.54403i	0.143382	+	0.160057i
$807$	−22.4690	+	6.59748i	−0.790945	+	0.232242i
$808$	−46.7653	−	11.2507i	−1.64520	−	0.395799i
$809$	15.3467	−	9.86276i	0.539563	−	0.346756i	−0.242305	−	0.970200i	$-0.577903\pi$
$809$	15.3467	−	9.86276i	0.539563	−	0.346756i	0.781868	+	0.623444i	$0.214267\pi$
$810$	−3.09376	+	3.69176i	−0.108704	+	0.129715i
$811$	20.7209	−	32.2423i	0.727608	−	1.13218i	−0.258490	−	0.966014i	$-0.583225\pi$
$811$	20.7209	−	32.2423i	0.727608	−	1.13218i	0.986098	−	0.166166i	$-0.0531388\pi$
$812$	5.22854	−	8.75836i	0.183486	−	0.307358i
$813$	−23.9216	−	20.7282i	−0.838967	−	0.726969i
$814$	0.994856	+	1.49326i	0.0348697	+	0.0523387i
$815$	−23.7398	−	51.9829i	−0.831569	−	1.82088i
$816$	6.49543	−	11.7445i	0.227385	−	0.411141i
$817$	−26.6808	−	7.83419i	−0.933443	−	0.274084i
$818$	24.1289	+	10.5416i	0.843647	+	0.368579i
$819$	1.70659	+	0.245371i	0.0596331	+	0.00857394i
$820$	35.2491	−	32.6412i	1.23095	−	1.13988i
$821$	−1.27101	−	0.580452i	−0.0443587	−	0.0202579i	0.393112	−	0.919491i	$-0.371398\pi$
$821$	−1.27101	−	0.580452i	−0.0443587	−	0.0202579i	−0.437471	+	0.899233i	$0.644126\pi$
$822$	−1.66363	−	10.3548i	−0.0580259	−	0.361164i
$823$	−5.91879	−	41.1661i	−0.206316	−	1.43496i	−0.785045	−	0.619439i	$-0.787360\pi$
$823$	−5.91879	−	41.1661i	−0.206316	−	1.43496i	0.578729	−	0.815520i	$-0.303549\pi$
$824$	51.6270	+	20.5542i	1.79851	+	0.716038i
$825$	−0.965563	−	1.11432i	−0.0336166	−	0.0387956i
$826$	0.729652	+	0.452082i	0.0253878	+	0.0157299i
$827$		−	6.30096i		−	0.219106i	−0.993981	−	0.109553i	$-0.965058\pi$
$827$		−	6.30096i		−	0.219106i	0.993981	−	0.109553i	$-0.0349419\pi$
$828$	3.93386	−	8.74784i	0.136711	−	0.304009i
$829$		−	28.1673i		−	0.978290i	−0.872202	−	0.489145i	$-0.837309\pi$
$829$		−	28.1673i		−	0.978290i	0.872202	−	0.489145i	$-0.162691\pi$
$830$	18.8764	−	30.4661i	0.655209	−	1.05750i
$831$	4.16986	+	4.81228i	0.144651	+	0.166936i
$832$	17.5810	−	4.33618i	0.609510	−	0.150330i
$833$	−3.06547	−	21.3208i	−0.106212	−	0.738722i
$834$	20.1972	−	3.24495i	0.699371	−	0.112363i
$835$	−6.71656	−	3.06735i	−0.232436	−	0.106150i
$836$	−1.22797	−	1.32608i	−0.0424703	−	0.0458636i
$837$	1.88644	+	0.271230i	0.0652050	+	0.00937507i
$838$	11.5680	−	26.4783i	0.399611	−	0.914676i
$839$	−38.7966	−	11.3917i	−1.33941	−	0.393286i	−0.467950	−	0.883755i	$-0.655007\pi$
$839$	−38.7966	−	11.3917i	−1.33941	−	0.393286i	−0.871458	+	0.490470i	$0.836825\pi$
$840$	−2.41323	−	6.92977i	−0.0832643	−	0.239100i
$841$	−6.57627	−	14.4000i	−0.226768	−	0.496552i
$842$	14.4335	−	9.61605i	0.497412	−	0.331391i
$843$	0.857303	+	0.742857i	0.0295271	+	0.0255854i
$844$	−23.6303	+	39.5833i	−0.813390	+	1.36251i
$845$	−14.5039	+	22.5685i	−0.498949	+	0.776380i
$846$	0.233687	+	0.195833i	0.00803432	+	0.00673289i
$847$	−7.01683	+	4.50944i	−0.241101	+	0.154946i
$848$	5.67447	−	3.05891i	0.194862	−	0.105043i
$849$	12.2457	−	3.59565i	0.420270	−	0.123402i
$850$	−23.3272	+	20.8970i	−0.800117	+	0.716760i
$851$	21.0626	−	17.2705i	0.722017	−	0.592024i
$852$	−14.5225	−	1.60093i	−0.497533	−	0.0548470i
$853$	−4.89631	−	16.6753i	−0.167646	−	0.570951i	−0.999864	−	0.0165019i	$-0.994747\pi$
$853$	−4.89631	−	16.6753i	−0.167646	−	0.570951i	0.832217	−	0.554449i	$-0.187071\pi$
$854$	2.01199	−	15.8458i	0.0688490	−	0.542233i
$855$	11.5902	−	7.44858i	0.396377	−	0.254736i
$856$	−31.3847	−	32.7899i	−1.07271	−	1.12073i
$857$	−20.2076	−	12.9867i	−0.690279	−	0.443616i	0.147906	−	0.989001i	$-0.452747\pi$
$857$	−20.2076	−	12.9867i	−0.690279	−	0.443616i	−0.838185	+	0.545386i	$0.816383\pi$
$858$	−0.682713	+	0.212761i	−0.0233074	+	0.00726354i
$859$	31.5435	+	27.3326i	1.07625	+	0.932575i	0.997927	−	0.0643527i	$-0.0204983\pi$
$859$	31.5435	+	27.3326i	1.07625	+	0.932575i	0.0783222	+	0.996928i	$0.475044\pi$
$860$	45.3402	+	11.7026i	1.54609	+	0.399057i
$861$	−4.88665	+	2.23166i	−0.166537	+	0.0760548i
$862$	34.9656	−	16.6710i	1.19093	−	0.567816i
$863$	−37.4239	−	10.9887i	−1.27393	−	0.374058i	−0.426265	−	0.904598i	$-0.640171\pi$
$863$	−37.4239	−	10.9887i	−1.27393	−	0.374058i	−0.847660	+	0.530540i	$0.821989\pi$
$864$	3.33950	−	4.56594i	0.113612	−	0.155336i
$865$	2.60914	−	18.1469i	0.0887133	−	0.617014i
$866$	0.614555	+	37.2369i	0.0208834	+	1.26536i
$867$	−5.22329	−	2.38540i	−0.177392	−	0.0810123i
$868$	−1.82791	+	2.25582i	−0.0620432	+	0.0765676i
$869$	1.08944	−	0.156637i	0.0369566	−	0.00531356i
$870$	−31.0898	−	8.57412i	−1.05404	−	0.290690i
$871$	1.09103	+	1.25912i	0.0369682	+	0.0426636i
$872$	−4.43477	+	5.66146i	−0.150180	+	0.191721i
$873$	10.4230			0.352763
$874$	−18.1872	+	20.5408i	−0.615192	+	0.694802i
$875$			4.15151i			0.140347i
$876$	−1.24529	+	0.221211i	−0.0420743	+	0.00747401i
$877$	20.1513	−	17.4612i	0.680460	−	0.589622i	−0.244517	−	0.969645i	$-0.578629\pi$
$877$	20.1513	−	17.4612i	0.680460	−	0.589622i	0.924977	+	0.380023i	$0.124084\pi$
$878$	6.03285	−	21.8751i	0.203599	−	0.738249i
$879$	−3.13101	−	21.7766i	−0.105606	−	0.734507i
$880$	2.14042	+	2.16362i	0.0721534	+	0.0729355i
$881$	−3.07163	+	6.72593i	−0.103486	+	0.226602i	−0.954291	−	0.298879i	$-0.903387\pi$
$881$	−3.07163	+	6.72593i	−0.103486	+	0.226602i	0.850805	+	0.525481i	$0.176115\pi$
$882$	−0.149818	−	9.07770i	−0.00504463	−	0.305662i
$883$	−55.9951	−	8.05087i	−1.88438	−	0.270933i	−0.898577	−	0.438816i	$-0.855398\pi$
$883$	−55.9951	−	8.05087i	−1.88438	−	0.270933i	−0.985807	+	0.167883i	$0.946307\pi$
$884$	4.75786	+	14.4247i	0.160024	+	0.485155i
$885$	0.764583	−	2.60393i	0.0257012	−	0.0875302i
$886$	13.8326	+	29.0123i	0.464714	+	0.974688i
$887$	−13.9159	−	30.4715i	−0.467249	−	1.02313i	−0.985775	−	0.168070i	$-0.946246\pi$
$887$	−13.9159	−	30.4715i	−0.467249	−	1.02313i	0.518526	−	0.855062i	$-0.326481\pi$
$888$	14.2642	−	7.38819i	0.478676	−	0.247931i
$889$	−0.995273	+	1.14861i	−0.0333804	+	0.0385230i
$890$	7.08939	−	2.20934i	0.237637	−	0.0740573i
$891$	−0.120777	+	0.187932i	−0.00404617	+	0.00629596i
$892$	21.1182	−	0.697258i	0.707090	−	0.0233459i
$893$	−0.471492	−	0.733656i	−0.0157779	−	0.0245509i
$894$	−24.3205	−	3.08804i	−0.813398	−	0.103280i
$895$	3.58179	−	1.05171i	0.119726	−	0.0351547i
$896$	3.36483	+	7.93386i	0.112411	+	0.265052i
$897$	4.23916	+	9.99330i	0.141541	+	0.333666i
$898$	35.8040	−	32.0740i	1.19480	−	1.07032i
$899$	3.59510	+	12.2438i	0.119903	+	0.408353i
$900$	−10.8634	+	7.49925i	−0.362112	+	0.249975i
$901$	2.92345	+	4.54897i	0.0973941	+	0.151548i
$902$	1.43112	−	1.70775i	0.0476512	−	0.0568618i
$903$	−4.40503	−	2.83094i	−0.146590	−	0.0942077i
$904$	−13.1000	+	2.55075i	−0.435700	+	0.0848366i
$905$	−48.0626	+	55.4672i	−1.59765	+	1.84379i
$906$	−19.5734	+	13.0404i	−0.650284	+	0.433239i
$907$	10.9330	−	4.99296i	0.363026	−	0.165788i	−0.225547	−	0.974232i	$-0.572417\pi$
$907$	10.9330	−	4.99296i	0.363026	−	0.165788i	0.588573	+	0.808444i	$0.299690\pi$
$908$	50.4953	+	21.0754i	1.67574	+	0.699413i
$909$	4.79108	−	16.3169i	0.158910	−	0.541198i
$910$	7.61006	+	3.32474i	0.252271	+	0.110214i
$911$	−0.214833	+	1.49420i	−0.00711773	+	0.0495049i	−0.993071	−	0.117518i	$-0.962506\pi$
$911$	−0.214833	+	1.49420i	−0.00711773	+	0.0495049i	0.985953	+	0.167023i	$0.0534153\pi$
$912$	−13.0052	+	9.62665i	−0.430646	+	0.318770i
$913$	0.690519	−	1.51203i	0.0228529	−	0.0500408i
$914$	14.0533	−	2.25785i	0.464841	−	0.0746829i
$915$	−49.9881	+	7.18720i	−1.65255	+	0.237601i
$916$	−15.3926	+	7.65318i	−0.508586	+	0.252868i
$917$	10.5754	−	9.16367i	0.349232	−	0.302611i
$918$	4.03359	+	2.49915i	0.133128	+	0.0824843i
$919$	4.89083			0.161334			0.0806668	−	0.996741i	$-0.474295\pi$
$919$	4.89083			0.161334			0.0806668	+	0.996741i	$0.474295\pi$
$920$	29.4684	−	35.5816i	0.971545	−	1.17309i
$921$	−23.0638			−0.759977
$922$	−43.8888	−	27.1929i	−1.44540	−	0.895549i
$923$	12.4965	−	10.8283i	0.411327	−	0.356417i
$924$	−0.151517	−	0.304741i	−0.00498454	−	0.0100252i
$925$	−37.1043	+	5.33479i	−1.21998	+	0.175407i
$926$	12.2647	−	1.97048i	0.403042	−	0.0647541i
$927$	−8.16138	+	17.8709i	−0.268055	+	0.586958i
$928$	37.0974	+	7.63933i	1.21778	+	0.250773i
$929$	−4.48577	+	31.1992i	−0.147173	+	1.02361i	0.773644	+	0.633620i	$0.218432\pi$
$929$	−4.48577	+	31.1992i	−0.147173	+	1.02361i	−0.920818	+	0.389994i	$0.872477\pi$
$930$	8.41206	+	3.67513i	0.275842	+	0.120512i
$931$	−7.31626	+	24.9169i	−0.239781	+	0.816618i
$932$	−19.0870	+	45.7311i	−0.625216	+	1.49797i
$933$	12.4249	−	5.67427i	0.406773	−	0.185767i
$934$	−10.7181	+	7.14071i	−0.350706	+	0.233651i
$935$	−1.67179	+	1.92935i	−0.0546735	+	0.0630966i
$936$	1.22359	+	6.28406i	0.0399943	+	0.205401i
$937$	47.2121	+	30.3414i	1.54235	+	0.991209i	0.987205	+	0.159457i	$0.0509744\pi$
$937$	47.2121	+	30.3414i	1.54235	+	0.991209i	0.555147	+	0.831752i	$0.312662\pi$
$938$	−0.509286	+	0.607728i	−0.0166288	+	0.0198430i
$939$	11.0183	+	17.1447i	0.359567	+	0.559498i
$940$	0.834308	+	1.20857i	0.0272121	+	0.0394193i
$941$	−5.44512	−	18.5444i	−0.177506	−	0.604529i	−0.999392	−	0.0348769i	$-0.988896\pi$
$941$	−5.44512	−	18.5444i	−0.177506	−	0.604529i	0.821886	−	0.569652i	$-0.192922\pi$
$942$	11.1731	−	10.0091i	0.364038	−	0.326113i
$943$	−27.9459	−	19.0534i	−0.910042	−	0.620464i
$944$	−0.694273	+	3.11070i	−0.0225967	+	0.101245i
$945$	2.48926	−	0.730914i	0.0809758	−	0.0237766i
$946$	2.15447	+	0.273560i	0.0700480	+	0.00889421i
$947$	28.7876	+	44.7944i	0.935472	+	1.45562i	0.889634	+	0.456674i	$0.150959\pi$
$947$	28.7876	+	44.7944i	0.935472	+	1.45562i	0.0458378	+	0.998949i	$0.485404\pi$
$948$	−0.325163	−	9.84838i	−0.0105608	−	0.319860i
$949$	0.773873	−	1.20417i	0.0251210	−	0.0390890i
$950$	36.0477	−	11.2339i	1.16954	−	0.364477i
$951$	−10.5180	+	12.1384i	−0.341068	+	0.393614i
$952$	−6.41891	+	3.32469i	−0.208038	+	0.107754i
$953$	1.94229	+	4.25303i	0.0629170	+	0.137769i	0.938479	−	0.345338i	$-0.112236\pi$
$953$	1.94229	+	4.25303i	0.0629170	+	0.137769i	−0.875562	+	0.483107i	$0.839508\pi$
$954$	0.980879	+	2.05729i	0.0317571	+	0.0666072i
$955$	−5.87449	+	20.0067i	−0.190094	+	0.647401i
$956$	37.9634	−	12.5219i	1.22783	−	0.404987i
$957$	−1.48053	−	0.212869i	−0.0478588	−	0.00688106i
$958$	−0.839042	−	50.8389i	−0.0271082	−	1.64253i
$959$	−2.34660	+	5.13833i	−0.0757755	+	0.165925i
$960$	21.3534	−	16.9247i	0.689178	−	0.546243i
$961$	3.89484	+	27.0892i	0.125640	+	0.873845i
$962$	−4.83342	+	17.5260i	−0.155836	+	0.565061i
$963$	12.1279	−	10.5089i	0.390816	−	0.338644i
$964$	7.47916	+	42.1033i	0.240888	+	1.35606i
$965$		−	15.6392i		−	0.503443i
$966$	−4.37577	+	2.74641i	−0.140788	+	0.0883642i
$967$	−11.5838			−0.372509			−0.186254	−	0.982502i	$-0.559635\pi$
$967$	−11.5838			−0.372509			−0.186254	+	0.982502i	$0.559635\pi$
$968$	−24.3818	−	19.0989i	−0.783659	−	0.613861i
$969$	−8.88807	−	10.2574i	−0.285526	−	0.329515i
$970$	48.3973	+	13.3473i	1.55394	+	0.428556i
$971$	21.8814	−	3.14607i	0.702208	−	0.100962i	0.218043	−	0.975939i	$-0.430033\pi$
$971$	21.8814	−	3.14607i	0.702208	−	0.100962i	0.484165	+	0.874977i	$0.339123\pi$
$972$	1.55390	+	1.25913i	0.0498412	+	0.0403866i
$973$	−10.0224	−	4.57708i	−0.321304	−	0.146734i
$974$	0.654644	+	39.6659i	0.0209762	+	1.27098i
$975$	2.12610	−	14.7874i	0.0680897	−	0.473574i
$976$	58.0228	−	12.2949i	1.85727	−	0.393551i
$977$	−12.8994	−	3.78762i	−0.412690	−	0.121177i	0.0687957	−	0.997631i	$-0.478084\pi$
$977$	−12.8994	−	3.78762i	−0.412690	−	0.121177i	−0.481485	+	0.876454i	$0.659903\pi$
$978$	−21.4189	+	10.2122i	−0.684902	+	0.326549i
$979$	0.313276	−	0.143068i	0.0100124	−	0.00457249i
$980$	10.9290	−	42.3427i	0.349113	−	1.35259i
$981$	−1.92159	−	1.66506i	−0.0613515	−	0.0531614i
$982$	−30.5389	+	9.51716i	−0.974535	+	0.303705i
$983$	−0.272329	−	0.175015i	−0.00868595	−	0.00558212i	0.536291	−	0.844033i	$-0.319825\pi$
$983$	−0.272329	−	0.175015i	−0.00868595	−	0.00558212i	−0.544977	+	0.838451i	$0.683461\pi$
$984$	−13.7931	−	14.4106i	−0.439707	−	0.459393i
$985$	21.2235	−	13.6395i	0.676237	−	0.434591i
$986$	−4.00191	+	31.5178i	−0.127447	+	1.00373i
$987$	−0.0462665	−	0.157569i	−0.00147268	−	0.00501549i
$988$	2.00653	−	18.2018i	0.0638364	−	0.579077i
$989$	0.896798	−	32.9555i	0.0285165	−	1.04792i
$990$	−0.801466	+	0.717969i	−0.0254723	+	0.0228186i
$991$	24.0574	−	7.06390i	0.764209	−	0.224392i	0.123676	−	0.992323i	$-0.460532\pi$
$991$	24.0574	−	7.06390i	0.764209	−	0.224392i	0.640533	+	0.767931i	$0.278713\pi$
$992$	−10.1426	−	3.65512i	−0.322027	−	0.116050i
$993$	5.75166	−	3.69637i	0.182523	−	0.117301i
$994$	6.03158	+	5.05456i	0.191310	+	0.160321i
$995$	9.84843	−	15.3245i	0.312216	−	0.485818i
$996$	−12.7779	−	7.62810i	−0.404883	−	0.241706i
$997$	−7.94553	−	6.88484i	−0.251637	−	0.218045i	0.519903	−	0.854225i	$-0.325968\pi$
$997$	−7.94553	−	6.88484i	−0.251637	−	0.218045i	−0.771540	+	0.636180i	$0.780513\pi$
$998$	2.87939	−	1.91834i	0.0911454	−	0.0607239i
$999$	2.35935	+	5.16625i	0.0746464	+	0.163453i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.bb.a.469.31	yes	480
8.5	even	2	inner	552.2.bb.a.469.41	yes	480
23.18	even	11	inner	552.2.bb.a.133.41	yes	480
184.133	even	22	inner	552.2.bb.a.133.31	✓	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.bb.a.133.31	✓	480	184.133	even	22	inner
552.2.bb.a.133.41	yes	480	23.18	even	11	inner
552.2.bb.a.469.31	yes	480	1.1	even	1	trivial
552.2.bb.a.469.41	yes	480	8.5	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.bb (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.744845 - 1.20217i) q^{2} +(0.755750 - 0.654861i) q^{3} +(-0.890411 - 1.79086i) q^{4} +(3.37124 - 0.484711i) q^{5} +(-0.224336 - 1.39631i) q^{6} +(-0.316431 + 0.692886i) q^{7} +(-2.81613 - 0.263488i) q^{8} +(0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(q+(0.744845 - 1.20217i) q^{2} +(0.755750 - 0.654861i) q^{3} +(-0.890411 - 1.79086i) q^{4} +(3.37124 - 0.484711i) q^{5} +(-0.224336 - 1.39631i) q^{6} +(-0.316431 + 0.692886i) q^{7} +(-2.81613 - 0.263488i) q^{8} +(0.142315 - 0.989821i) q^{9} +(1.92835 - 4.41383i) q^{10} +(0.0629377 - 0.214346i) q^{11} +(-1.84569 - 0.770344i) q^{12} +(2.05893 - 0.940282i) q^{13} +(0.597273 + 0.896496i) q^{14} +(2.23040 - 2.57401i) q^{15} +(-2.41434 + 3.18920i) q^{16} +(-2.82263 - 1.81399i) q^{17} +(-1.08393 - 0.908350i) q^{18} +(2.18696 + 3.40298i) q^{19} +(-3.86984 - 5.60582i) q^{20} +(0.214602 + 0.730867i) q^{21} +(-0.210801 - 0.235316i) q^{22} +(-3.23803 + 3.53767i) q^{23} +(-2.30084 + 1.64504i) q^{24} +(6.33286 - 1.85949i) q^{25} +(0.403208 - 3.17554i) q^{26} +(-0.540641 - 0.841254i) q^{27} +(1.52261 - 0.0502719i) q^{28} +(3.61990 - 5.63267i) q^{29} +(-1.43310 - 4.59855i) q^{30} +(-1.24806 + 1.44034i) q^{31} +(2.03564 + 5.27789i) q^{32} +(-0.0928018 - 0.203208i) q^{33} +(-4.28314 + 2.04213i) q^{34} +(-0.730914 + 2.48926i) q^{35} +(-1.89935 + 0.626483i) q^{36} +(-5.62168 - 0.808276i) q^{37} +(5.71989 - 0.0944007i) q^{38} +(0.940282 - 2.05893i) q^{39} +(-9.62156 + 0.476727i) q^{40} +(1.00369 + 6.98082i) q^{41} +(1.03847 + 0.286395i) q^{42} +(-5.19521 + 4.50167i) q^{43} +(-0.439904 + 0.0781438i) q^{44} -3.40591i q^{45} +(1.84104 + 6.52768i) q^{46} -0.215592 q^{47} +(0.263847 + 3.99129i) q^{48} +(4.20406 + 4.85175i) q^{49} +(2.48157 - 8.99819i) q^{50} +(-3.32111 + 0.477504i) q^{51} +(-3.51720 - 2.85001i) q^{52} +(-1.46597 - 0.669486i) q^{53} +(-1.41402 + 0.0233369i) q^{54} +(0.108282 - 0.753119i) q^{55} +(1.07368 - 1.86788i) q^{56} +(3.88127 + 1.13964i) q^{57} +(-4.07515 - 8.54719i) q^{58} +(0.724804 - 0.331007i) q^{59} +(-6.59566 - 1.70239i) q^{60} +(-11.2061 - 9.71014i) q^{61} +(0.801916 + 2.57321i) q^{62} +(0.640801 + 0.411818i) q^{63} +(7.86115 + 1.48403i) q^{64} +(6.48538 - 4.16790i) q^{65} +(-0.313412 - 0.0397949i) q^{66} +(0.207372 + 0.706243i) q^{67} +(-0.735302 + 6.67012i) q^{68} +(-0.130458 + 4.79406i) q^{69} +(2.44809 + 2.73280i) q^{70} +(7.00932 - 2.05812i) q^{71} +(-0.661583 + 2.74997i) q^{72} +(0.532000 - 0.341896i) q^{73} +(-5.15897 + 6.15616i) q^{74} +(3.56834 - 5.55245i) q^{75} +(4.14695 - 6.94658i) q^{76} +(0.128602 + 0.111434i) q^{77} +(-1.77481 - 2.66396i) q^{78} +(2.04670 + 4.48164i) q^{79} +(-6.59347 + 11.9218i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(9.13971 + 3.99303i) q^{82} +(7.36506 + 1.05894i) q^{83} +(1.11779 - 1.03509i) q^{84} +(-10.3950 - 4.74725i) q^{85} +(1.54214 + 9.59856i) q^{86} +(-0.952878 - 6.62741i) q^{87} +(-0.233718 + 0.587043i) q^{88} +(1.00957 + 1.16511i) q^{89} +(-4.09447 - 2.53687i) q^{90} +1.72414i q^{91} +(9.21865 + 2.64887i) q^{92} +1.90584i q^{93} +(-0.160583 + 0.259178i) q^{94} +(9.02223 + 10.4122i) q^{95} +(4.99472 + 2.65570i) q^{96} +(1.48334 + 10.3169i) q^{97} +(8.96398 - 1.44018i) q^{98} +(-0.203208 - 0.0928018i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9}+O(q^{10}) \) 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9	\( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32} + 6 q^{34} - 22 q^{36} + 90 q^{38} - 74 q^{40} + 90 q^{42} - 130 q^{44} + 96 q^{46} - 88 q^{48} - 48 q^{49} + 142 q^{50} - 142 q^{52} + 18 q^{54} - 82 q^{56} + 22 q^{58} + 2 q^{60} - 40 q^{62} - 8 q^{63} + 16 q^{66} - 44 q^{68} + 16 q^{71} - 4 q^{72} + 10 q^{74} - 138 q^{76} - 40 q^{79} - 170 q^{80} - 48 q^{81} - 124 q^{82} - 8 q^{84} - 216 q^{86} - 108 q^{88} + 4 q^{90} - 198 q^{92} - 238 q^{94} + 80 q^{95} + 4 q^{96} - 132 q^{98}+O(q^{100}) \) 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Introduction

L-functions

Modular forms

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