LMFDB - Embedded newform 552.2.bb.a.85.12

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			85.12
Character	$\chi$	$=$	552.85
Dual form			552.2.bb.a.13.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.08248 - 0.910071i) q^{2} +(0.540641 + 0.841254i) q^{3} +(0.343541 + 1.97027i) q^{4} +(-2.04961 + 0.936025i) q^{5} +(0.180366 - 1.40266i) q^{6} +(3.54305 - 1.04033i) q^{7} +(1.42121 - 2.44544i) q^{8} +(-0.415415 + 0.909632i) q^{9} +O(q^{10})$	\(q+(-1.08248 - 0.910071i) q^{2} +(0.540641 + 0.841254i) q^{3} +(0.343541 + 1.97027i) q^{4} +(-2.04961 + 0.936025i) q^{5} +(0.180366 - 1.40266i) q^{6} +(3.54305 - 1.04033i) q^{7} +(1.42121 - 2.44544i) q^{8} +(-0.415415 + 0.909632i) q^{9} +(3.07052 + 0.852058i) q^{10} +(2.25379 - 1.95292i) q^{11} +(-1.47177 + 1.35422i) q^{12} +(-1.41971 + 4.83508i) q^{13} +(-4.78207 - 2.09828i) q^{14} +(-1.89554 - 1.21819i) q^{15} +(-3.76396 + 1.35374i) q^{16} +(0.385395 - 2.68048i) q^{17} +(1.27751 - 0.606604i) q^{18} +(0.208985 - 0.0300475i) q^{19} +(-2.54835 - 3.71673i) q^{20} +(2.79070 + 2.41816i) q^{21} +(-4.21699 + 0.0628947i) q^{22} +(2.30498 + 4.20560i) q^{23} +(2.82560 - 0.126503i) q^{24} +(0.0504502 - 0.0582227i) q^{25} +(5.93707 - 3.94186i) q^{26} +(-0.989821 + 0.142315i) q^{27} +(3.26693 + 6.62338i) q^{28} +(-1.25460 - 0.180384i) q^{29} +(0.943250 + 3.04374i) q^{30} +(7.50991 + 4.82632i) q^{31} +(5.30642 + 1.96007i) q^{32} +(2.86140 + 0.840182i) q^{33} +(-2.85661 + 2.55084i) q^{34} +(-6.28809 + 5.44866i) q^{35} +(-1.93494 - 0.505986i) q^{36} +(8.01424 + 3.65998i) q^{37} +(-0.253568 - 0.157665i) q^{38} +(-4.83508 + 1.41971i) q^{39} +(-0.623940 + 6.34248i) q^{40} +(2.68265 + 5.87419i) q^{41} +(-0.820194 - 5.15735i) q^{42} +(-1.18566 - 1.84492i) q^{43} +(4.62207 + 3.76968i) q^{44} -2.25323i q^{45} +(1.33229 - 6.65019i) q^{46} -7.74290 q^{47} +(-3.17379 - 2.43456i) q^{48} +(5.58214 - 3.58742i) q^{49} +(-0.107598 + 0.0171118i) q^{50} +(2.46333 - 1.12496i) q^{51} +(-10.0142 - 1.13616i) q^{52} +(1.35011 + 4.59806i) q^{53} +(1.20098 + 0.746754i) q^{54} +(-2.79141 + 6.11234i) q^{55} +(2.49136 - 10.1428i) q^{56} +(0.138263 + 0.159564i) q^{57} +(1.19392 + 1.33704i) q^{58} +(0.831099 - 2.83046i) q^{59} +(1.74897 - 4.15322i) q^{60} +(2.51896 - 3.91958i) q^{61} +(-3.73705 - 12.0590i) q^{62} +(-0.525516 + 3.65504i) q^{63} +(-3.96031 - 6.95097i) q^{64} +(-1.61591 - 11.2389i) q^{65} +(-2.33279 - 3.51356i) q^{66} +(9.06703 + 7.85662i) q^{67} +(5.41368 - 0.161521i) q^{68} +(-2.29181 + 4.21279i) q^{69} +(11.7654 - 0.175476i) q^{70} +(-9.89160 + 11.4155i) q^{71} +(1.63405 + 2.30865i) q^{72} +(-2.26270 - 15.7374i) q^{73} +(-5.34444 - 11.2554i) q^{74} +(0.0762555 + 0.0109639i) q^{75} +(0.130997 + 0.401435i) q^{76} +(5.95362 - 9.26401i) q^{77} +(6.52593 + 2.86346i) q^{78} +(2.60042 + 0.763551i) q^{79} +(6.44751 - 6.29780i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(2.44200 - 8.80012i) q^{82} +(1.34692 + 0.615119i) q^{83} +(-3.80571 + 6.32918i) q^{84} +(1.71909 + 5.85468i) q^{85} +(-0.395553 + 3.07613i) q^{86} +(-0.526538 - 1.15296i) q^{87} +(-1.57263 - 8.28703i) q^{88} +(6.87125 - 4.41588i) q^{89} +(-2.05060 + 2.43908i) q^{90} +18.6079i q^{91} +(-7.49432 + 5.98624i) q^{92} +8.92704i q^{93} +(8.38156 + 7.04659i) q^{94} +(-0.400212 + 0.257201i) q^{95} +(1.21995 + 5.52374i) q^{96} +(-3.69982 - 8.10148i) q^{97} +(-9.30739 - 1.19682i) q^{98} +(0.840182 + 2.86140i) 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 $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{4}{11}\right)$	$1$	$-1$	$1$

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 $

$2$	−1.08248	−	0.910071i	−0.765431	−	0.643517i
$2$	−1.08248	−	0.910071i	−0.765431	−	0.643517i
$3$	0.540641	+	0.841254i	0.312139	+	0.485698i
$3$	0.540641	+	0.841254i	0.312139	+	0.485698i
$4$	0.343541	+	1.97027i	0.171770	+	0.985137i
$5$	−2.04961	+	0.936025i	−0.916613	+	0.418603i	−0.817141	−	0.576437i	$-0.804443\pi$
$5$	−2.04961	+	0.936025i	−0.916613	+	0.418603i	−0.0994716	+	0.995040i	$0.531715\pi$
$6$	0.180366	−	1.40266i	0.0736340	−	0.572635i
$7$	3.54305	−	1.04033i	1.33915	−	0.393209i	0.467782	−	0.883844i	$-0.345053\pi$
$7$	3.54305	−	1.04033i	1.33915	−	0.393209i	0.871365	+	0.490635i	$0.163235\pi$
$8$	1.42121	−	2.44544i	0.502474	−	0.864592i
$9$	−0.415415	+	0.909632i	−0.138472	+	0.303211i
$10$	3.07052	+	0.852058i	0.970983	+	0.269444i
$11$	2.25379	−	1.95292i	0.679545	−	0.588829i	−0.245175	−	0.969479i	$-0.578845\pi$
$11$	2.25379	−	1.95292i	0.679545	−	0.588829i	0.924719	+	0.380650i	$0.124300\pi$
$12$	−1.47177	+	1.35422i	−0.424863	+	0.390928i
$13$	−1.41971	+	4.83508i	−0.393756	+	1.34101i	0.489453	+	0.872030i	$0.337196\pi$
$13$	−1.41971	+	4.83508i	−0.393756	+	1.34101i	−0.883209	+	0.468980i	$0.844622\pi$
$14$	−4.78207	−	2.09828i	−1.27806	−	0.560790i
$15$	−1.89554	−	1.21819i	−0.489425	−	0.314535i
$16$	−3.76396	+	1.35374i	−0.940990	+	0.338435i
$17$	0.385395	−	2.68048i	0.0934721	−	0.650113i	−0.888189	−	0.459478i	$-0.848036\pi$
$17$	0.385395	−	2.68048i	0.0934721	−	0.650113i	0.981661	−	0.190634i	$-0.0610545\pi$
$18$	1.27751	−	0.606604i	0.301112	−	0.142978i
$19$	0.208985	−	0.0300475i	0.0479444	−	0.00689336i	−0.118301	−	0.992978i	$-0.537745\pi$
$19$	0.208985	−	0.0300475i	0.0479444	−	0.00689336i	0.166245	+	0.986084i	$0.446836\pi$
$20$	−2.54835	−	3.71673i	−0.569828	−	0.831086i
$21$	2.79070	+	2.41816i	0.608981	+	0.527685i
$22$	−4.21699	+	0.0628947i	−0.899066	+	0.0134092i
$23$	2.30498	+	4.20560i	0.480622	+	0.876928i
$23$	2.30498	+	4.20560i	0.480622	+	0.876928i
$24$	2.82560	−	0.126503i	0.576773	−	0.0258223i
$25$	0.0504502	−	0.0582227i	0.0100900	−	0.0116445i
$26$	5.93707	−	3.94186i	1.16436	−	0.773062i
$27$	−0.989821	+	0.142315i	−0.190491	+	0.0273885i
$28$	3.26693	+	6.62338i	0.617391	+	1.25170i
$29$	−1.25460	−	0.180384i	−0.232973	−	0.0334964i	0.0248395	−	0.999691i	$-0.492093\pi$
$29$	−1.25460	−	0.180384i	−0.232973	−	0.0334964i	−0.257812	+	0.966195i	$0.583002\pi$
$30$	0.943250	+	3.04374i	0.172213	+	0.555709i
$31$	7.50991	+	4.82632i	1.34882	+	0.866833i	0.997585	−	0.0694545i	$-0.0221259\pi$
$31$	7.50991	+	4.82632i	1.34882	+	0.866833i	0.351234	+	0.936288i	$0.385762\pi$
$32$	5.30642	+	1.96007i	0.938052	+	0.346495i
$33$	2.86140	+	0.840182i	0.498105	+	0.146257i
$34$	−2.85661	+	2.55084i	−0.489905	+	0.437466i
$35$	−6.28809	+	5.44866i	−1.06288	+	0.920992i
$36$	−1.93494	−	0.505986i	−0.322489	−	0.0843309i
$37$	8.01424	+	3.65998i	1.31753	+	0.601697i	0.945227	−	0.326413i	$-0.105840\pi$
$37$	8.01424	+	3.65998i	1.31753	+	0.601697i	0.372306	+	0.928110i	$0.378567\pi$
$38$	−0.253568	−	0.157665i	−0.0411341	−	0.0255767i
$39$	−4.83508	+	1.41971i	−0.774232	+	0.227335i
$40$	−0.623940	+	6.34248i	−0.0986536	+	1.00283i
$41$	2.68265	+	5.87419i	0.418960	+	0.917395i	0.994991	+	0.0999666i	$0.0318736\pi$
$41$	2.68265	+	5.87419i	0.418960	+	0.917395i	−0.576031	+	0.817428i	$0.695399\pi$
$42$	−0.820194	−	5.15735i	−0.126559	−	0.795797i
$43$	−1.18566	−	1.84492i	−0.180811	−	0.281347i	0.739003	−	0.673702i	$-0.235297\pi$
$43$	−1.18566	−	1.84492i	−0.180811	−	0.281347i	−0.919814	+	0.392355i	$0.871661\pi$
$44$	4.62207	+	3.76968i	0.696803	+	0.568301i
$45$		−	2.25323i		−	0.335892i
$46$	1.33229	−	6.65019i	0.196435	−	0.980517i
$47$	−7.74290			−1.12942			−0.564709	−	0.825290i	$-0.691011\pi$
$47$	−7.74290			−1.12942			−0.564709	+	0.825290i	$0.691011\pi$
$48$	−3.17379	−	2.43456i	−0.458097	−	0.351398i
$49$	5.58214	−	3.58742i	0.797449	−	0.512489i
$50$	−0.107598	+	0.0171118i	−0.0152167	+	0.00241997i
$51$	2.46333	−	1.12496i	0.344935	−	0.157526i
$52$	−10.0142	−	1.13616i	−1.38871	−	0.157558i
$53$	1.35011	+	4.59806i	0.185452	+	0.631593i	0.998761	+	0.0497604i	$0.0158458\pi$
$53$	1.35011	+	4.59806i	0.185452	+	0.631593i	−0.813309	+	0.581832i	$0.802336\pi$
$54$	1.20098	+	0.746754i	0.163433	+	0.101620i
$55$	−2.79141	+	6.11234i	−0.376394	+	0.824187i
$56$	2.49136	−	10.1428i	0.332922	−	1.35539i
$57$	0.138263	+	0.159564i	0.0183134	+	0.0211348i
$58$	1.19392	+	1.33704i	0.156769	+	0.175561i
$59$	0.831099	−	2.83046i	0.108200	−	0.368495i	−0.887537	−	0.460737i	$-0.847585\pi$
$59$	0.831099	−	2.83046i	0.108200	−	0.368495i	0.995737	+	0.0922420i	$0.0294033\pi$
$60$	1.74897	−	4.15322i	0.225791	−	0.536179i
$61$	2.51896	−	3.91958i	0.322520	−	0.501851i	−0.641700	−	0.766956i	$-0.721770\pi$
$61$	2.51896	−	3.91958i	0.322520	−	0.501851i	0.964219	+	0.265105i	$0.0854067\pi$
$62$	−3.73705	−	12.0590i	−0.474606	−	1.53149i
$63$	−0.525516	+	3.65504i	−0.0662088	+	0.460492i
$64$	−3.96031	−	6.95097i	−0.495039	−	0.868871i
$65$	−1.61591	−	11.2389i	−0.200429	−	1.39401i
$66$	−2.33279	−	3.51356i	−0.287147	−	0.432489i
$67$	9.06703	+	7.85662i	1.10771	+	0.959839i	0.999412	−	0.0342787i	$-0.0109134\pi$
$67$	9.06703	+	7.85662i	1.10771	+	0.959839i	0.108301	+	0.994118i	$0.465459\pi$
$68$	5.41368	−	0.161521i	0.656506	−	0.0195874i
$69$	−2.29181	+	4.21279i	−0.275901	+	0.507161i
$70$	11.7654	−	0.175476i	1.40624	−	0.0209734i
$71$	−9.89160	+	11.4155i	−1.17392	+	1.35477i	−0.251839	+	0.967769i	$0.581035\pi$
$71$	−9.89160	+	11.4155i	−1.17392	+	1.35477i	−0.922078	+	0.387004i	$0.873510\pi$
$72$	1.63405	+	2.30865i	0.192575	+	0.272077i
$73$	−2.26270	−	15.7374i	−0.264829	−	1.84192i	−0.495148	−	0.868809i	$-0.664886\pi$
$73$	−2.26270	−	15.7374i	−0.264829	−	1.84192i	0.230319	−	0.973115i	$-0.426023\pi$
$74$	−5.34444	−	11.2554i	−0.621279	−	1.30841i
$75$	0.0762555	+	0.0109639i	0.00880522	+	0.00126600i
$76$	0.130997	+	0.401435i	0.0150263	+	0.0460477i
$77$	5.95362	−	9.26401i	0.678477	−	1.05573i
$78$	6.52593	+	2.86346i	0.738916	+	0.324222i
$79$	2.60042	+	0.763551i	0.292570	+	0.0859062i	0.424724	−	0.905323i	$-0.360371\pi$
$79$	2.60042	+	0.763551i	0.292570	+	0.0859062i	−0.132154	+	0.991229i	$0.542189\pi$
$80$	6.44751	−	6.29780i	0.720854	−	0.704115i
$81$	−0.654861	−	0.755750i	−0.0727623	−	0.0839722i
$82$	2.44200	−	8.80012i	0.269674	−	0.971811i
$83$	1.34692	+	0.615119i	0.147844	+	0.0675180i	0.487963	−	0.872864i	$-0.337740\pi$
$83$	1.34692	+	0.615119i	0.147844	+	0.0675180i	−0.340119	+	0.940382i	$0.610467\pi$
$84$	−3.80571	+	6.32918i	−0.415237	+	0.690571i
$85$	1.71909	+	5.85468i	0.186461	+	0.635029i
$86$	−0.395553	+	3.07613i	−0.0426536	+	0.331707i
$87$	−0.526538	−	1.15296i	−0.0564508	−	0.123610i
$88$	−1.57263	−	8.28703i	−0.167643	−	0.883400i
$89$	6.87125	−	4.41588i	0.728351	−	0.468083i	−0.123182	−	0.992384i	$-0.539310\pi$
$89$	6.87125	−	4.41588i	0.728351	−	0.468083i	0.851533	+	0.524301i	$0.175673\pi$
$90$	−2.05060	+	2.43908i	−0.216152	+	0.257102i
$91$			18.6079i			1.95064i
$92$	−7.49432	+	5.98624i	−0.781337	+	0.624109i
$93$			8.92704i			0.925691i
$94$	8.38156	+	7.04659i	0.864492	+	0.726800i
$95$	−0.400212	+	0.257201i	−0.0410609	+	0.0263882i
$96$	1.21995	+	5.52374i	0.124511	+	0.563764i
$97$	−3.69982	−	8.10148i	−0.375660	−	0.822580i	−0.999169	−	0.0407642i	$-0.987021\pi$
$97$	−3.69982	−	8.10148i	−0.375660	−	0.822580i	0.623509	−	0.781816i	$-0.285707\pi$
$98$	−9.30739	−	1.19682i	−0.940188	−	0.120897i
$99$	0.840182	+	2.86140i	0.0844415	+	0.287581i
$100$	0.132046	+	0.0793989i	0.0132046	+	0.00793989i
$101$	6.45872	+	2.94960i	0.642667	+	0.293496i	0.709965	−	0.704237i	$-0.248711\pi$
$101$	6.45872	+	2.94960i	0.642667	+	0.293496i	−0.0672984	+	0.997733i	$0.521438\pi$
$102$	−3.69031	−	1.02405i	−0.365395	−	0.101396i
$103$	−10.1383	−	11.7002i	−0.998957	−	1.15286i	−0.988239	−	0.152915i	$-0.951134\pi$
$103$	−10.1383	−	11.7002i	−0.998957	−	1.15286i	−0.0107178	−	0.999943i	$-0.503412\pi$
$104$	9.80617	+	10.3435i	0.961574	+	1.01426i
$105$	−7.98330	−	2.34411i	−0.779091	−	0.228762i
$106$	2.72309	−	6.20603i	0.264490	−	0.602783i
$107$	4.66567	−	7.25992i	0.451047	−	0.701843i	−0.539043	−	0.842278i	$-0.681214\pi$
$107$	4.66567	−	7.25992i	0.451047	−	0.701843i	0.990090	+	0.140435i	$0.0448503\pi$
$108$	−0.620443	−	1.90133i	−0.0597022	−	0.182955i
$109$	−17.8497	−	2.56640i	−1.70969	−	0.245817i	−0.783103	−	0.621892i	$-0.786364\pi$
$109$	−17.8497	−	2.56640i	−1.70969	−	0.245817i	−0.926589	+	0.376076i	$0.877273\pi$
$110$	8.58432	−	4.07612i	0.818483	−	0.388643i
$111$	1.25385	+	8.72074i	0.119011	+	0.827736i
$112$	−11.9276	+	8.71214i	−1.12705	+	0.823220i
$113$	−2.94496	+	3.39867i	−0.277039	+	0.319720i	−0.877168	−	0.480183i	$-0.840570\pi$
$113$	−2.94496	+	3.39867i	−0.277039	+	0.319720i	0.600130	+	0.799903i	$0.295116\pi$
$114$	−0.00445282	−	0.298555i	−0.000417045	−	0.0279622i
$115$	−8.66086	−	6.46231i	−0.807629	−	0.602613i
$116$	−0.0756000	−	2.53387i	−0.00701928	−	0.235264i
$117$	−3.80837	−	3.29997i	−0.352084	−	0.305083i
$118$	−3.47557	+	2.30757i	−0.319953	+	0.212429i
$119$	−1.42312	−	9.89803i	−0.130457	−	0.907351i
$120$	−5.67296	+	2.90411i	−0.517868	+	0.265108i
$121$	−0.299786	+	2.08506i	−0.0272533	+	0.189551i
$122$	−6.29383	+	1.95045i	−0.569817	+	0.176585i
$123$	−3.49133	+	5.43262i	−0.314803	+	0.489843i
$124$	−6.92922	+	16.4546i	−0.622262	+	1.47767i
$125$	3.12513	−	10.6432i	0.279520	−	0.951959i
$126$	3.89521	−	3.47827i	0.347013	−	0.309869i
$127$	0.785003	+	0.905942i	0.0696578	+	0.0803893i	0.789509	−	0.613739i	$-0.210335\pi$
$127$	0.785003	+	0.905942i	0.0696578	+	0.0803893i	−0.719851	+	0.694129i	$0.755790\pi$
$128$	−2.03890	+	11.1285i	−0.180215	+	0.983627i
$129$	0.911030	−	1.99488i	0.0802117	−	0.175639i
$130$	−8.47900	+	13.6365i	−0.743658	+	1.19600i
$131$	0.552936	+	1.88313i	0.0483102	+	0.164529i	0.980115	−	0.198430i	$-0.0635844\pi$
$131$	0.552936	+	1.88313i	0.0483102	+	0.164529i	−0.931805	+	0.362960i	$0.881766\pi$
$132$	−0.672382	+	5.92637i	−0.0585233	+	0.515825i
$133$	0.709184	−	0.323874i	0.0614941	−	0.0280834i
$134$	−2.66482	−	16.7563i	−0.230205	−	1.44752i
$135$	1.89554	−	1.21819i	0.163142	−	0.104845i
$136$	−6.00722	−	4.75199i	−0.515115	−	0.407480i
$137$	−8.50993			−0.727053			−0.363526	−	0.931584i	$-0.618427\pi$
$137$	−8.50993			−0.727053			−0.363526	+	0.931584i	$0.618427\pi$
$138$	6.31478	−	2.47457i	0.537550	−	0.210650i
$139$		−	19.7006i		−	1.67099i	−0.549501	−	0.835493i	$-0.685182\pi$
$139$		−	19.7006i		−	1.67099i	0.549501	−	0.835493i	$-0.314818\pi$
$140$	−12.8956	−	10.5174i	−1.08987	−	0.888884i
$141$	−4.18613	−	6.51374i	−0.352535	−	0.548556i
$142$	21.0964	−	3.35505i	1.77037	−	0.281549i
$143$	6.24281	+	13.6698i	0.522050	+	1.14313i
$144$	0.332200	−	3.98618i	0.0276833	−	0.332182i
$145$	2.74028	−	0.804618i	0.227568	−	0.0668199i
$146$	−11.8728	+	19.0947i	−0.982602	+	1.58029i
$147$	6.03587	+	2.75649i	0.497830	+	0.227351i
$148$	−4.45795	+	17.0476i	−0.366441	+	1.40130i
$149$	8.48173	−	7.34946i	0.694850	−	0.602091i	−0.234137	−	0.972204i	$-0.575226\pi$
$149$	8.48173	−	7.34946i	0.694850	−	0.602091i	0.928987	+	0.370113i	$0.120681\pi$
$150$	−0.0725674	−	0.0812661i	−0.00592510	−	0.00663535i
$151$	−3.79293	−	1.11371i	−0.308664	−	0.0906320i	0.123732	−	0.992316i	$-0.460514\pi$
$151$	−3.79293	−	1.11371i	−0.308664	−	0.0906320i	−0.432396	+	0.901684i	$0.642332\pi$
$152$	0.223533	−	0.553763i	0.0181309	−	0.0449161i
$153$	2.27815	+	1.46408i	0.184178	+	0.118364i
$154$	−14.8756	+	4.60992i	−1.19871	+	0.371478i
$155$	−19.9099	−	2.86262i	−1.59920	−	0.229931i
$156$	−4.45826	−	9.03870i	−0.356946	−	0.723675i
$157$	−13.3923	+	1.92553i	−1.06883	+	0.153674i	−0.654203	−	0.756319i	$-0.726996\pi$
$157$	−13.3923	+	1.92553i	−1.06883	+	0.153674i	−0.414623	+	0.909993i	$0.636087\pi$
$158$	−2.12002	−	3.19309i	−0.168660	−	0.254029i
$159$	−3.13821	+	3.62169i	−0.248876	+	0.287219i
$160$	−12.7108	+	0.949568i	−1.00487	+	0.0750700i
$161$	12.5419	+	12.5027i	0.988440	+	0.985350i
$162$	0.0210900	+	1.41406i	0.00165699	+	0.111099i
$163$	8.11964	+	7.03571i	0.635979	+	0.551079i	0.912061	−	0.410055i	$-0.134491\pi$
$163$	8.11964	+	7.03571i	0.635979	+	0.551079i	−0.276082	+	0.961134i	$0.589036\pi$
$164$	−10.6522	+	7.30359i	−0.831794	+	0.570314i
$165$	−6.65118	+	0.956295i	−0.517793	+	0.0744475i
$166$	−0.898219	−	1.89165i	−0.0697153	−	0.146821i
$167$	1.36676	−	9.50600i	0.105763	−	0.735596i	−0.866070	−	0.499923i	$-0.833362\pi$
$167$	1.36676	−	9.50600i	0.105763	−	0.735596i	0.971832	−	0.235673i	$-0.0757294\pi$
$168$	9.87963	−	3.38777i	0.762230	−	0.261372i
$169$	−10.4261	−	6.70045i	−0.802008	−	0.515420i
$170$	3.46729	−	7.90209i	0.265929	−	0.606063i
$171$	−0.0594833	+	0.202581i	−0.00454880	+	0.0154918i
$172$	3.22767	−	2.96987i	0.246108	−	0.226451i
$173$	16.2696	−	14.0976i	1.23695	−	1.07182i	0.242124	−	0.970245i	$-0.422156\pi$
$173$	16.2696	−	14.0976i	1.23695	−	1.07182i	0.994827	−	0.101579i	$-0.0323895\pi$
$174$	−0.479304	+	1.72724i	−0.0363360	+	0.130942i
$175$	0.118177	−	0.258771i	0.00893332	−	0.0195612i
$176$	−5.83944	+	10.4018i	−0.440164	+	0.784063i
$177$	2.83046	−	0.831099i	0.212751	−	0.0624692i
$178$	−11.4568	−	1.47320i	−0.858722	−	0.110421i
$179$	−20.6597	+	9.43497i	−1.54418	+	0.705203i	−0.991730	−	0.128344i	$-0.959034\pi$
$179$	−20.6597	+	9.43497i	−1.54418	+	0.705203i	−0.552449	+	0.833547i	$0.686307\pi$
$180$	4.43948	−	0.774076i	0.330899	−	0.0576962i
$181$	−2.63125	−	4.09430i	−0.195579	−	0.304327i	0.729588	−	0.683887i	$-0.239712\pi$
$181$	−2.63125	−	4.09430i	−0.195579	−	0.304327i	−0.925167	+	0.379560i	$0.876075\pi$
$182$	16.9345	−	20.1427i	1.25527	−	1.49308i
$183$	4.65921			0.344419
$184$	13.5604	+	0.340358i	0.999685	+	0.0250915i
$185$	−19.8519			−1.45954
$186$	8.12424	−	9.66338i	0.595698	−	0.708553i
$187$	−4.36618	−	6.79390i	−0.319286	−	0.496819i
$188$	−2.66000	−	15.2556i	−0.194001	−	1.11263i
$189$	−3.35893	+	1.53397i	−0.244326	+	0.111580i
$190$	0.667294	+	0.0858059i	0.0484106	+	0.00622502i
$191$	−1.93310	+	0.567610i	−0.139874	+	0.0410708i	−0.350920	−	0.936405i	$-0.614131\pi$
$191$	−1.93310	+	0.567610i	−0.139874	+	0.0410708i	0.211046	+	0.977476i	$0.432313\pi$
$192$	3.70642	−	7.08960i	0.267488	−	0.511648i
$193$	6.06200	−	13.2739i	0.436352	−	0.955478i	−0.555902	−	0.831248i	$-0.687627\pi$
$193$	6.06200	−	13.2739i	0.436352	−	0.955478i	0.992254	−	0.124229i	$-0.0396459\pi$
$194$	−3.36793	+	12.1368i	−0.241803	+	0.871373i
$195$	8.58114	−	7.43560i	0.614508	−	0.532474i
$196$	8.98590	+	9.76592i	0.641850	+	0.697566i
$197$	−0.719709	+	2.45110i	−0.0512772	+	0.174634i	−0.981150	−	0.193247i	$-0.938098\pi$
$197$	−0.719709	+	2.45110i	−0.0512772	+	0.174634i	0.929873	+	0.367881i	$0.119916\pi$
$198$	1.69459	−	3.86204i	0.120429	−	0.274463i
$199$	−1.56789	−	1.00762i	−0.111145	−	0.0714283i	0.483888	−	0.875130i	$-0.339224\pi$
$199$	−1.56789	−	1.00762i	−0.111145	−	0.0714283i	−0.595032	+	0.803702i	$0.702861\pi$
$200$	−0.0706793	−	0.206120i	−0.00499778	−	0.0145749i
$201$	−1.70741	+	11.8753i	−0.120431	+	0.837618i
$202$	−4.30711	−	9.07079i	−0.303047	−	0.638218i
$203$	−4.63276	+	0.666090i	−0.325156	+	0.0467504i
$204$	3.06274	+	4.46696i	0.214435	+	0.312749i
$205$	−10.9968	−	9.52877i	−0.768049	−	0.665518i
$206$	0.326508	+	21.8919i	0.0227489	+	1.52528i
$207$	−4.78307	+	0.349618i	−0.332446	+	0.0243001i
$208$	−1.20172	−	20.1209i	−0.0833241	−	1.39514i
$209$	0.412328	−	0.475852i	0.0285213	−	0.0329154i
$210$	6.50849	+	9.80283i	0.449128	+	0.676460i
$211$	6.27233	−	0.901825i	0.431805	−	0.0620842i	0.0770143	−	0.997030i	$-0.475461\pi$
$211$	6.27233	−	0.901825i	0.431805	−	0.0620842i	0.354791	+	0.934946i	$0.384552\pi$
$212$	−8.59563	+	4.23972i	−0.590350	+	0.291185i
$213$	−14.9512	−	2.14965i	−1.02444	−	0.147292i
$214$	−11.6576	+	3.61265i	−0.796894	+	0.246956i
$215$	4.15702	+	2.67156i	0.283507	+	0.182199i
$216$	−1.05872	+	2.62280i	−0.0720371	+	0.178459i
$217$	31.6290	+	9.28710i	2.14711	+	0.630450i
$218$	16.9864	+	19.0226i	1.15046	+	1.28837i
$219$	12.0158	−	10.4118i	0.811955	−	0.703563i
$220$	−13.0019	−	3.40001i	−0.876591	−	0.229228i
$221$	12.4132	+	5.66892i	0.835002	+	0.381333i
$222$	6.57922	−	10.5812i	0.441568	−	0.710161i
$223$	18.7183	−	5.49620i	1.25347	−	0.368052i	0.413411	−	0.910545i	$-0.364337\pi$
$223$	18.7183	−	5.49620i	1.25347	−	0.368052i	0.840061	+	0.542492i	$0.182519\pi$
$224$	20.8401	+	1.42418i	1.39243	+	0.0951568i
$225$	0.0320034	+	0.0700777i	0.00213356	+	0.00467185i
$226$	6.28090	−	0.998876i	0.417799	−	0.0664442i
$227$	−3.03396	−	4.72094i	−0.201371	−	0.313340i	0.725851	−	0.687852i	$-0.241446\pi$
$227$	−3.03396	−	4.72094i	−0.201371	−	0.313340i	−0.927222	+	0.374513i	$0.877810\pi$
$228$	−0.266886	+	0.327233i	−0.0176750	+	0.0216716i
$229$			14.9339i			0.986857i	0.869786	+	0.493429i	$0.164257\pi$
$229$			14.9339i			0.986857i	−0.869786	+	0.493429i	$0.835743\pi$
$230$	3.49408	+	14.8773i	0.230393	+	0.980983i
$231$	11.0121			0.724546
$232$	−2.22417	+	2.81167i	−0.146024	+	0.184595i
$233$	12.1086	−	7.78170i	0.793259	−	0.509796i	−0.0801510	−	0.996783i	$-0.525540\pi$
$233$	12.1086	−	7.78170i	0.793259	−	0.509796i	0.873410	+	0.486986i	$0.161904\pi$
$234$	1.11929	+	7.03806i	0.0731703	+	0.460092i
$235$	15.8699	−	7.24754i	1.03524	−	0.472778i
$236$	5.86231	+	0.665113i	0.381604	+	0.0432951i
$237$	0.763551	+	2.60042i	0.0495980	+	0.168915i
$238$	−7.46740	+	12.0096i	−0.484040	+	0.778466i
$239$	−11.3927	+	24.9466i	−0.736933	+	1.61366i	0.0516014	+	0.998668i	$0.483567\pi$
$239$	−11.3927	+	24.9466i	−0.736933	+	1.61366i	−0.788534	+	0.614991i	$0.789160\pi$
$240$	8.78383	+	2.01914i	0.566994	+	0.130335i
$241$	8.18095	+	9.44132i	0.526981	+	0.608169i	0.955365	−	0.295428i	$-0.0954623\pi$
$241$	8.18095	+	9.44132i	0.526981	+	0.608169i	−0.428384	+	0.903597i	$0.640917\pi$
$242$	2.22207	−	1.98422i	0.142840	−	0.127550i
$243$	0.281733	−	0.959493i	0.0180732	−	0.0615515i
$244$	8.58801	+	3.61651i	0.549791	+	0.231523i
$245$	−8.08329	+	12.5778i	−0.516422	+	0.803569i
$246$	8.72338	−	2.70336i	0.556182	−	0.172360i
$247$	−0.151415	+	1.05312i	−0.00963432	+	0.0670082i
$248$	22.4756	−	11.5058i	1.42720	−	0.730617i
$249$	0.210730	+	1.46566i	0.0133545	+	0.0928825i
$250$	−13.0690	+	8.67703i	−0.826556	+	0.548783i
$251$	−2.98029	−	2.58244i	−0.188114	−	0.163002i	0.555712	−	0.831375i	$-0.312446\pi$
$251$	−2.98029	−	2.58244i	−0.188114	−	0.163002i	−0.743827	+	0.668373i	$0.766991\pi$
$252$	−7.38197	+	0.220247i	−0.465021	+	0.0138742i
$253$	13.4082	+	4.97710i	0.842964	+	0.312907i
$254$	−0.0252813	−	1.69508i	−0.00158629	−	0.106359i
$255$	−3.99586	+	4.61147i	−0.250231	+	0.288781i
$256$	12.3348	−	10.1908i	0.770924	−	0.636928i
$257$	−2.10570	−	14.6455i	−0.131350	−	0.913559i	−0.943797	−	0.330525i	$-0.892774\pi$
$257$	−2.10570	−	14.6455i	−0.131350	−	0.913559i	0.812447	−	0.583035i	$-0.198135\pi$
$258$	−2.80165	+	1.33032i	−0.174423	+	0.0828221i
$259$	32.2025	+	4.63002i	2.00096	+	0.287695i
$260$	21.5886	−	7.04481i	1.33887	−	0.436900i
$261$	0.685261	−	1.06629i	0.0424166	−	0.0660015i
$262$	1.11523	−	2.54166i	0.0688994	−	0.157025i
$263$	22.7382	+	6.67655i	1.40210	+	0.411694i	0.893404	−	0.449253i	$-0.148310\pi$
$263$	22.7382	+	6.67655i	1.40210	+	0.411694i	0.508695	+	0.860947i	$0.330128\pi$
$264$	6.12126	−	5.80329i	0.376738	−	0.357168i
$265$	−7.07111	−	8.16049i	−0.434375	−	0.501295i
$266$	−1.06243	−	0.294820i	−0.0651417	−	0.0180766i
$267$	7.42976	+	3.39306i	0.454694	+	0.207652i
$268$	−12.3648	+	20.5636i	−0.755301	+	1.25612i
$269$	1.37834	+	4.69419i	0.0840388	+	0.286210i	0.990781	−	0.135476i	$-0.0432565\pi$
$269$	1.37834	+	4.69419i	0.0840388	+	0.286210i	−0.906742	+	0.421686i	$0.861438\pi$
$270$	−3.16052	−	0.406405i	−0.192343	−	0.0247330i
$271$	−12.9654	−	28.3902i	−0.787590	−	1.72458i	−0.683425	−	0.730021i	$-0.739510\pi$
$271$	−12.9654	−	28.3902i	−0.787590	−	1.72458i	−0.104165	−	0.994560i	$-0.533217\pi$
$272$	2.17806	+	10.6110i	0.132065	+	0.643384i
$273$	−15.6540	+	10.0602i	−0.947421	+	0.608870i
$274$	9.21186	+	7.74464i	0.556509	+	0.467871i
$275$		−	0.229747i		−	0.0138543i
$276$	−9.08769	−	3.06822i	−0.547014	−	0.184685i
$277$		−	30.0507i		−	1.80557i	−0.430091	−	0.902786i	$-0.641519\pi$
$277$		−	30.0507i		−	1.80557i	0.430091	−	0.902786i	$-0.358481\pi$
$278$	−17.9290	+	21.3256i	−1.07531	+	1.27903i
$279$	−7.50991	+	4.82632i	−0.449606	+	0.288944i
$280$	4.38764	+	23.1208i	0.262212	+	1.38173i
$281$	6.32815	+	13.8567i	0.377506	+	0.826622i	0.999064	+	0.0432542i	$0.0137725\pi$
$281$	6.32815	+	13.8567i	0.377506	+	0.826622i	−0.621559	+	0.783368i	$0.713500\pi$
$282$	−1.39655	+	10.8607i	−0.0831636	+	0.646745i
$283$	−4.68166	−	15.9443i	−0.278296	−	0.947788i	−0.973445	−	0.228922i	$-0.926480\pi$
$283$	−4.68166	−	15.9443i	−0.278296	−	0.947788i	0.695149	−	0.718866i	$-0.255338\pi$
$284$	−25.8899	−	15.5675i	−1.53628	−	0.923759i
$285$	−0.432742	−	0.197627i	−0.0256334	−	0.0117064i
$286$	5.68280	−	20.4788i	0.336031	−	1.21094i
$287$	15.6159	+	18.0217i	0.921777	+	1.06379i
$288$	−3.98731	+	4.01265i	−0.234954	+	0.236448i
$289$	9.27492	+	2.72336i	0.545584	+	0.160198i
$290$	−3.69856	−	1.62286i	−0.217187	−	0.0952977i
$291$	4.81512	−	7.49248i	0.282267	−	0.439217i
$292$	30.2297	−	9.86458i	1.76906	−	0.577281i
$293$	−31.5248	−	4.53258i	−1.84170	−	0.264796i	−0.868653	−	0.495420i	$-0.835014\pi$
$293$	−31.5248	−	4.53258i	−1.84170	−	0.264796i	−0.973043	+	0.230624i	$0.925923\pi$
$294$	−4.02513	−	8.47692i	−0.234750	−	0.494384i
$295$	0.945957	+	6.57927i	0.0550757	+	0.383060i
$296$	20.3402	−	14.3967i	1.18225	−	0.836791i
$297$	−1.95292	+	2.25379i	−0.113320	+	0.130778i
$298$	−15.8699	+	0.236692i	−0.919316	+	0.0137112i
$299$	−23.6068	+	5.17406i	−1.36522	+	0.299223i
$300$	0.00459503	+	0.154011i	0.000265294	+	0.00889181i
$301$	−6.12017	−	5.30316i	−0.352761	−	0.305669i
$302$	3.09223	+	4.65740i	0.177938	+	0.268004i
$303$	1.01049	+	7.02810i	0.0580510	+	0.403754i
$304$	−0.745934	+	0.396008i	−0.0427822	+	0.0227126i
$305$	−1.49406	+	10.3914i	−0.0855496	+	0.595011i
$306$	−1.13365	−	3.65813i	−0.0648063	−	0.209121i
$307$	−0.456124	+	0.709743i	−0.0260324	+	0.0405072i	−0.854026	−	0.520231i	$-0.825846\pi$
$307$	−0.456124	+	0.709743i	−0.0260324	+	0.0405072i	0.827993	+	0.560738i	$0.189482\pi$
$308$	20.2979	+	8.54769i	1.15658	+	0.487050i
$309$	4.36168	−	14.8545i	0.248127	−	0.845043i
$310$	18.9470	+	21.2182i	1.07612	+	1.20511i
$311$	−14.4322	−	16.6556i	−0.818373	−	0.944453i	0.180864	−	0.983508i	$-0.442111\pi$
$311$	−14.4322	−	16.6556i	−0.818373	−	0.944453i	−0.999237	+	0.0390551i	$0.987565\pi$
$312$	−3.39987	+	13.8416i	−0.192480	+	0.783625i
$313$	7.20180	−	15.7697i	0.407070	−	0.891358i	−0.589434	−	0.807816i	$-0.700649\pi$
$313$	7.20180	−	15.7697i	0.407070	−	0.891358i	0.996504	−	0.0835423i	$-0.0266234\pi$
$314$	16.2494	+	10.1036i	0.917005	+	0.570181i
$315$	−2.34411	−	7.98330i	−0.132076	−	0.449808i
$316$	−0.611055	+	5.38584i	−0.0343745	+	0.302977i
$317$	16.1806	−	7.38943i	0.908793	−	0.415032i	0.0945257	−	0.995522i	$-0.469867\pi$
$317$	16.1806	−	7.38943i	0.908793	−	0.415032i	0.814267	+	0.580491i	$0.197139\pi$
$318$	6.69306	−	1.06442i	0.375328	−	0.0596899i
$319$	−3.17988	+	2.04358i	−0.178039	+	0.114419i
$320$	14.6234	+	10.5398i	0.817471	+	0.589193i
$321$	8.62988			0.481673
$322$	−2.19805	−	24.9480i	−0.122493	−	1.39030i
$323$		−	0.571760i		−	0.0318136i
$324$	1.26406	−	1.54989i	0.0702257	−	0.0861048i
$325$	0.209887	+	0.326590i	0.0116424	+	0.0181159i
$326$	−2.38638	−	15.0055i	−0.132169	−	0.831077i
$327$	−7.49129	−	16.4036i	−0.414269	−	0.907123i
$328$	18.1776	+	1.78822i	1.00369	+	0.0987377i
$329$	−27.4335	+	8.05520i	−1.51246	+	0.444097i
$330$	8.07009	+	5.01787i	0.444244	+	0.276225i
$331$	−16.5740	−	7.56908i	−0.910988	−	0.416034i	−0.0959130	−	0.995390i	$-0.530577\pi$
$331$	−16.5740	−	7.56908i	−0.910988	−	0.416034i	−0.815075	+	0.579355i	$0.803304\pi$
$332$	−0.749229	+	2.86512i	−0.0411193	+	0.157244i
$333$	−6.65847	+	5.76960i	−0.364882	+	0.316172i
$334$	−10.1306	+	9.04624i	−0.554323	+	0.494988i
$335$	−25.9379	−	7.61604i	−1.41714	−	0.416109i
$336$	−13.7776	−	5.32396i	−0.751632	−	0.290446i
$337$	6.02405	+	3.87142i	0.328151	+	0.210890i	0.694334	−	0.719653i	$-0.255699\pi$
$337$	6.02405	+	3.87142i	0.328151	+	0.210890i	−0.366183	+	0.930543i	$0.619335\pi$
$338$	5.18820	+	16.7416i	0.282201	+	0.910625i
$339$	−4.45131	−	0.640001i	−0.241762	−	0.0347601i
$340$	−10.9447	+	5.39840i	−0.593562	+	0.292769i
$341$	26.3512	−	3.78873i	1.42700	−	0.205171i
$342$	0.248753	−	0.165157i	0.0134510	−	0.00893067i
$343$	−0.881408	+	1.01720i	−0.0475916	+	0.0549236i
$344$	−6.19670	+	0.277428i	−0.334104	+	0.0149579i
$345$	0.754026	−	10.7798i	0.0405954	−	0.580363i
$346$	−30.4414	+	0.454020i	−1.63654	+	0.0244083i
$347$	−7.45661	−	6.46119i	−0.400292	−	0.346855i	0.431333	−	0.902193i	$-0.358043\pi$
$347$	−7.45661	−	6.46119i	−0.400292	−	0.346855i	−0.831625	+	0.555338i	$0.812589\pi$
$348$	2.09075	−	1.43351i	0.112076	−	0.0768443i
$349$	−16.0875	+	2.31304i	−0.861145	+	0.123814i	−0.558717	−	0.829358i	$-0.688706\pi$
$349$	−16.0875	+	2.31304i	−0.861145	+	0.123814i	−0.302428	+	0.953172i	$0.597797\pi$
$350$	−0.363424	+	0.172566i	−0.0194258	+	0.00922404i
$351$	0.717153	−	4.98791i	0.0382788	−	0.266235i
$352$	15.7875	−	5.94545i	0.841474	−	0.316893i
$353$	6.65839	+	4.27909i	0.354391	+	0.227753i	0.705707	−	0.708504i	$-0.250629\pi$
$353$	6.65839	+	4.27909i	0.354391	+	0.227753i	−0.351316	+	0.936257i	$0.614266\pi$
$354$	−3.82029	−	1.67627i	−0.203046	−	0.0890929i
$355$	9.58871	−	32.6561i	0.508916	−	1.73321i
$356$	11.0611	+	12.0212i	0.586235	+	0.637123i
$357$	7.55735	−	6.54848i	0.399978	−	0.346582i
$358$	30.9503	+	8.58860i	1.63577	+	0.453922i
$359$	10.3008	−	22.5555i	0.543653	−	1.19043i	−0.416030	−	0.909351i	$-0.636579\pi$
$359$	10.3008	−	22.5555i	0.543653	−	1.19043i	0.959683	−	0.281084i	$-0.0906938\pi$
$360$	−5.51013	−	3.20232i	−0.290409	−	0.168777i
$361$	−18.1876	+	5.34036i	−0.957242	+	0.281072i
$362$	−0.877823	+	6.82664i	−0.0461374	+	0.358800i
$363$	−1.91614	+	0.875072i	−0.100571	+	0.0459294i
$364$	−36.6627	+	6.39257i	−1.92165	+	0.335062i
$365$	19.3682	+	30.1376i	1.01378	+	1.57747i
$366$	−5.04352	−	4.24022i	−0.263629	−	0.221640i
$367$	21.1541			1.10423			0.552117	−	0.833767i	$-0.313820\pi$
$367$	21.1541			1.10423			0.552117	+	0.833767i	$0.313820\pi$
$368$	−14.3691	−	12.7094i	−0.749044	−	0.662521i
$369$	−6.45777			−0.336178
$370$	21.4894	+	18.0666i	1.11718	+	0.939240i
$371$	9.56704	+	14.8866i	0.496696	+	0.772874i
$372$	−17.5887	+	3.06681i	−0.911933	+	0.159006i
$373$	−8.98707	+	4.10426i	−0.465333	+	0.212510i	−0.634263	−	0.773118i	$-0.718696\pi$
$373$	−8.98707	+	4.10426i	−0.465333	+	0.212510i	0.168930	+	0.985628i	$0.445969\pi$
$374$	−1.45662	+	11.3278i	−0.0753201	+	0.585748i
$375$	10.6432	−	3.12513i	0.549614	−	0.161381i
$376$	−11.0043	+	18.9348i	−0.567503	+	0.976485i
$377$	2.65333	−	5.80998i	0.136653	−	0.299229i
$378$	5.03201	+	1.39637i	0.258819	+	0.0718214i
$379$	−25.1717	+	21.8114i	−1.29298	+	1.12038i	−0.307330	+	0.951603i	$0.599435\pi$
$379$	−25.1717	+	21.8114i	−1.29298	+	1.12038i	−0.985655	+	0.168774i	$0.946019\pi$
$380$	−0.644245	−	0.700168i	−0.0330491	−	0.0359179i
$381$	−0.337722	+	1.15018i	−0.0173020	+	0.0589253i
$382$	2.60911	+	1.14483i	0.133494	+	0.0585747i
$383$	0.684470	+	0.439882i	0.0349748	+	0.0224769i	0.558011	−	0.829833i	$-0.311565\pi$
$383$	0.684470	+	0.439882i	0.0349748	+	0.0224769i	−0.523037	+	0.852310i	$0.675201\pi$
$384$	−10.4642	+	4.30127i	−0.533998	+	0.219498i
$385$	−3.53124	+	24.5603i	−0.179969	+	1.25171i
$386$	−18.6422	+	8.85195i	−0.948864	+	0.450552i
$387$	2.17074	−	0.312105i	0.110345	−	0.0158652i
$388$	14.6911	−	10.0729i	0.745827	−	0.511372i
$389$	4.01106	+	3.47560i	0.203369	+	0.176220i	0.750591	−	0.660768i	$-0.229769\pi$
$389$	4.01106	+	3.47560i	0.203369	+	0.176220i	−0.547222	+	0.836988i	$0.684315\pi$
$390$	−16.0559	+	0.239466i	−0.813020	+	0.0121258i
$391$	12.1614	−	4.55765i	0.615027	−	0.230490i
$392$	−0.839409	−	18.7493i	−0.0423966	−	0.946981i
$393$	−1.28525	+	1.48325i	−0.0648321	+	0.0748203i
$394$	3.00975	−	1.99829i	0.151629	−	0.100673i
$395$	−6.04454	+	0.869073i	−0.304134	+	0.0437278i
$396$	−5.34910	+	2.63840i	−0.268802	+	0.132584i
$397$	17.0090	+	2.44553i	0.853657	+	0.122737i	0.555232	−	0.831696i	$-0.312629\pi$
$397$	17.0090	+	2.44553i	0.853657	+	0.122737i	0.298425	+	0.954433i	$0.403539\pi$
$398$	0.780206	+	2.51762i	0.0391082	+	0.126197i
$399$	0.655874	+	0.421505i	0.0328348	+	0.0211016i
$400$	−0.111074	+	0.287444i	−0.00555371	+	0.0143722i
$401$	0.982046	+	0.288355i	0.0490410	+	0.0143997i	0.306161	−	0.951980i	$-0.400955\pi$
$401$	0.982046	+	0.288355i	0.0490410	+	0.0143997i	−0.257120	+	0.966379i	$0.582774\pi$
$402$	12.6556	−	11.3009i	0.631204	−	0.563639i
$403$	−33.9975	+	29.4590i	−1.69354	+	1.46746i
$404$	−3.59268	+	13.7388i	−0.178743	+	0.683529i
$405$	2.04961	+	0.936025i	0.101846	+	0.0465115i
$406$	5.62108	+	3.49511i	0.278969	+	0.173459i
$407$	25.2101	−	7.40236i	1.24962	−	0.366921i
$408$	0.749883	−	7.62272i	0.0371247	−	0.377381i
$409$	0.765633	+	1.67650i	0.0378581	+	0.0828977i	0.927616	−	0.373535i	$-0.121854\pi$
$409$	0.765633	+	1.67650i	0.0378581	+	0.0828977i	−0.889758	+	0.456432i	$0.849127\pi$
$410$	3.23198	+	20.3226i	0.159616	+	1.00366i
$411$	−4.60082	−	7.15901i	−0.226942	−	0.353128i
$412$	19.5697	−	23.9948i	0.964132	−	1.18214i
$413$		−	10.8931i		−	0.536014i
$414$	5.49577	+	3.97448i	0.270102	+	0.195335i
$415$	−3.33643			−0.163779
$416$	−17.0107	+	22.8742i	−0.834016	+	1.12150i
$417$	16.5732	−	10.6510i	0.811595	−	0.521580i
$418$	−0.879398	+	0.139854i	−0.0430128	+	0.00684049i
$419$	−20.4854	+	9.35535i	−1.00078	+	0.457039i	−0.847300	−	0.531114i	$-0.821774\pi$
$419$	−20.4854	+	9.35535i	−1.00078	+	0.457039i	−0.153475	+	0.988153i	$0.549046\pi$
$420$	1.87595	−	16.5346i	0.0915368	−	0.806806i
$421$	−6.39531	−	21.7804i	−0.311688	−	1.06151i	−0.955171	−	0.296053i	$-0.904329\pi$
$421$	−6.39531	−	21.7804i	−0.311688	−	1.06151i	0.643483	−	0.765460i	$-0.277489\pi$
$422$	−7.61042	−	4.73205i	−0.370469	−	0.230353i
$423$	3.21652	−	7.04319i	0.156392	−	0.342451i
$424$	13.1631	+	3.23321i	0.639255	+	0.157018i
$425$	−0.136622	−	0.157670i	−0.00662712	−	0.00764810i
$426$	14.2280	+	15.9336i	0.689351	+	0.771984i
$427$	4.84714	−	16.5078i	0.234569	−	0.798870i
$428$	15.9069	+	6.69856i	0.768888	+	0.323787i
$429$	−8.12469	+	12.6423i	−0.392264	+	0.610374i
$430$	−2.06860	−	6.67510i	−0.0997569	−	0.321902i
$431$	4.39529	−	30.5699i	0.211713	−	1.47250i	−0.555719	−	0.831370i	$-0.687557\pi$
$431$	4.39529	−	30.5699i	0.211713	−	1.47250i	0.767433	−	0.641130i	$-0.221534\pi$
$432$	3.53299	−	1.87563i	0.169981	−	0.0902412i
$433$	2.56768	+	17.8586i	0.123395	+	0.858229i	0.953665	+	0.300869i	$0.0972767\pi$
$433$	2.56768	+	17.8586i	0.123395	+	0.858229i	−0.830271	+	0.557360i	$0.811814\pi$
$434$	−25.7859	−	38.8377i	−1.23776	−	1.86427i
$435$	2.15839	+	1.87026i	0.103487	+	0.0896720i
$436$	−1.07559	−	36.0505i	−0.0515116	−	1.72650i
$437$	0.608074	+	0.809647i	0.0290881	+	0.0387307i
$438$	−22.4824	+	0.335316i	−1.07425	+	0.0160220i
$439$	−15.8078	+	18.2432i	−0.754466	+	0.870700i	−0.994993	−	0.0999420i	$-0.968134\pi$
$439$	−15.8078	+	18.2432i	−0.754466	+	0.870700i	0.240527	+	0.970642i	$0.422680\pi$
$440$	10.9801	+	15.5131i	0.523458	+	0.739560i
$441$	0.944331	+	6.56796i	0.0449681	+	0.312760i
$442$	−8.27796	−	17.4334i	−0.393742	−	0.829222i
$443$	4.71201	+	0.677484i	0.223874	+	0.0321883i	0.253339	−	0.967378i	$-0.418471\pi$
$443$	4.71201	+	0.677484i	0.223874	+	0.0321883i	−0.0294648	+	0.999566i	$0.509380\pi$
$444$	−16.7515	+	5.46637i	−0.794991	+	0.259422i
$445$	−9.95000	+	15.4825i	−0.471675	+	0.733941i
$446$	−25.2642	−	11.0855i	−1.19629	−	0.524912i
$447$	10.7683	+	3.16187i	0.509324	+	0.149551i
$448$	−21.2629	−	20.5076i	−1.00458	−	0.968892i
$449$	−8.42199	−	9.71950i	−0.397458	−	0.458692i	0.521380	−	0.853324i	$-0.325417\pi$
$449$	−8.42199	−	9.71950i	−0.397458	−	0.458692i	−0.918839	+	0.394633i	$0.870872\pi$
$450$	0.0291325	−	0.104983i	0.00137332	−	0.00494896i
$451$	17.5180	+	8.00020i	0.824890	+	0.376715i
$452$	−7.70802	−	4.63480i	−0.362555	−	0.218003i
$453$	−1.11371	−	3.79293i	−0.0523264	−	0.178207i
$454$	−1.01218	+	7.87146i	−0.0475038	+	0.369426i
$455$	−17.4175	−	38.1389i	−0.816543	−	1.78798i
$456$	0.586706	−	0.111339i	0.0274750	−	0.00521394i
$457$	−18.5504	+	11.9216i	−0.867752	+	0.557670i	−0.897064	−	0.441900i	$-0.854305\pi$
$457$	−18.5504	+	11.9216i	−0.867752	+	0.557670i	0.0293123	+	0.999570i	$0.490668\pi$
$458$	13.5909	−	16.1657i	0.635060	−	0.755371i
$459$			2.70805i			0.126401i
$460$	9.75716	−	19.2843i	0.454930	−	0.899137i
$461$			4.98610i			0.232226i	0.993236	+	0.116113i	$0.0370434\pi$
$461$			4.98610i			0.232226i	−0.993236	+	0.116113i	$0.962957\pi$
$462$	−11.9205	−	10.0218i	−0.554590	−	0.466258i
$463$	−6.78229	+	4.35871i	−0.315200	+	0.202567i	−0.688669	−	0.725076i	$-0.741805\pi$
$463$	−6.78229	+	4.35871i	−0.315200	+	0.202567i	0.373469	+	0.927643i	$0.378168\pi$
$464$	4.96645	−	1.01944i	0.230561	−	0.0473263i
$465$	−8.35594	−	18.2969i	−0.387497	−	0.848501i
$466$	−20.1892	−	2.59609i	−0.935248	−	0.120262i
$467$	11.9809	+	40.8031i	0.554409	+	1.88814i	0.448540	+	0.893763i	$0.351944\pi$
$467$	11.9809	+	40.8031i	0.554409	+	1.88814i	0.105869	+	0.994380i	$0.466238\pi$
$468$	5.19352	−	8.63722i	0.240071	−	0.399255i
$469$	40.2985	+	18.4037i	1.86081	+	0.849803i
$470$	−23.7747	−	6.59740i	−1.09664	−	0.304315i
$471$	−8.86031	−	10.2253i	−0.408261	−	0.471159i
$472$	−5.74055	−	6.05509i	−0.264230	−	0.278708i
$473$	−6.27521	−	1.84257i	−0.288535	−	0.0847214i
$474$	1.54003	−	3.50979i	0.0707360	−	0.161210i
$475$	0.00879389	−	0.0136836i	0.000403491	−	0.000627844i
$476$	19.0129	−	6.20432i	0.871456	−	0.284374i
$477$	−4.74340	−	0.681998i	−0.217185	−	0.0312266i
$478$	35.0356	−	16.6361i	1.60249	−	0.760915i
$479$	1.69123	+	11.7628i	0.0772745	+	0.537456i	0.991282	+	0.131758i	$0.0420623\pi$
$479$	1.69123	+	11.7628i	0.0772745	+	0.537456i	−0.914007	+	0.405697i	$0.867029\pi$
$480$	−7.67079	−	10.1796i	−0.350122	−	0.464633i
$481$	−29.0742	+	33.5534i	−1.32567	+	1.52990i
$482$	−0.263471	−	17.6653i	−0.0120008	−	0.804633i
$483$	−3.73728	+	17.3104i	−0.170052	+	0.787650i
$484$	−4.21113	+	0.125642i	−0.191415	+	0.00571101i
$485$	15.1664	+	13.1417i	0.688670	+	0.596736i
$486$	−1.17818	+	0.782239i	−0.0534432	+	0.0354831i
$487$	3.42009	+	23.7872i	0.154979	+	1.07790i	0.907717	+	0.419583i	$0.137824\pi$
$487$	3.42009	+	23.7872i	0.154979	+	1.07790i	−0.752738	+	0.658320i	$0.771267\pi$
$488$	−6.00510	−	11.7305i	−0.271838	−	0.531015i
$489$	−1.52901	+	10.6345i	−0.0691440	+	0.480907i
$490$	20.1968	−	6.25894i	0.912396	−	0.282750i
$491$	−14.8349	+	23.0835i	−0.669488	+	1.04174i	0.325862	+	0.945418i	$0.394346\pi$
$491$	−14.8349	+	23.0835i	−0.669488	+	1.04174i	−0.995350	+	0.0963266i	$0.969291\pi$
$492$	−11.9032	−	5.01255i	−0.536636	−	0.225983i
$493$	−0.967032	+	3.29341i	−0.0435529	+	0.148328i
$494$	1.12232	−	1.00218i	0.0504954	−	0.0450903i
$495$	−4.40038	−	5.07831i	−0.197783	−	0.228253i
$496$	−34.8006	−	7.99963i	−1.56259	−	0.359194i
$497$	−23.1705	+	50.7363i	−1.03934	+	2.27584i
$498$	1.10574	−	1.77833i	0.0495496	−	0.0796890i
$499$	−1.33643	−	4.55146i	−0.0598268	−	0.203752i	0.924156	−	0.382016i	$-0.124770\pi$
$499$	−1.33643	−	4.55146i	−0.0598268	−	0.203752i	−0.983983	+	0.178264i	$0.942952\pi$
$500$	22.0437	+	2.50098i	0.985824	+	0.111847i
$501$	8.73588	−	3.98954i	0.390290	−	0.178240i
$502$	0.875915	+	5.50773i	0.0390940	+	0.245822i
$503$	−10.2482	+	6.58609i	−0.456943	+	0.293659i	−0.748792	−	0.662805i	$-0.769366\pi$
$503$	−10.2482	+	6.58609i	−0.456943	+	0.293659i	0.291849	+	0.956464i	$0.405729\pi$
$504$	8.19130	+	6.47971i	0.364870	+	0.288629i
$505$	−15.9988			−0.711935
$506$	−9.98461	−	17.5900i	−0.443870	−	0.781971i
$507$		−	12.3935i		−	0.550416i
$508$	−1.51527	+	1.85790i	−0.0672294	+	0.0824310i
$509$	−6.00693	−	9.34697i	−0.266252	−	0.414297i	0.682225	−	0.731143i	$-0.261013\pi$
$509$	−6.00693	−	9.34697i	−0.266252	−	0.414297i	−0.948477	+	0.316846i	$0.897376\pi$
$510$	8.52222	−	1.35532i	0.377370	−	0.0600147i
$511$	−24.3890	−	53.4045i	−1.07891	−	2.36247i
$512$	−22.6266	−	0.194107i	−0.999963	−	0.00857838i
$513$	−0.202581	+	0.0594833i	−0.00894419	+	0.00262625i
$514$	−11.0490	+	17.7698i	−0.487352	+	0.783793i
$515$	31.7313	+	14.4912i	1.39825	+	0.638558i
$516$	4.24343	+	1.10966i	0.186807	+	0.0488499i
$517$	−17.4509	+	15.1213i	−0.767489	+	0.665033i
$518$	−30.6450	−	34.3185i	−1.34646	−	1.50787i
$519$	20.6557	+	6.06506i	0.906684	+	0.266226i
$520$	−29.7806	−	12.0213i	−1.30596	−	0.527167i
$521$	17.7133	+	11.3837i	0.776035	+	0.498727i	0.867715	−	0.497061i	$-0.165588\pi$
$521$	17.7133	+	11.3837i	0.776035	+	0.498727i	−0.0916808	+	0.995788i	$0.529224\pi$
$522$	−1.71218	+	0.530602i	−0.0749402	+	0.0232238i
$523$	18.5017	+	2.66014i	0.809023	+	0.116320i	0.534400	−	0.845232i	$-0.320538\pi$
$523$	18.5017	+	2.66014i	0.809023	+	0.116320i	0.274624	+	0.961552i	$0.411447\pi$
$524$	−3.52032	+	1.73637i	−0.153786	+	0.0758535i
$525$	0.281583	−	0.0404855i	0.0122893	−	0.00176693i
$526$	−18.5376	−	27.9207i	−0.808279	−	1.21740i
$527$	15.8312	−	18.2701i	0.689616	−	0.795859i
$528$	−11.9076	+	0.711176i	−0.518210	+	0.0309500i
$529$	−12.3741	+	19.3877i	−0.538005	+	0.842942i
$530$	0.227728	+	15.2688i	0.00989186	+	0.663235i
$531$	2.22943	+	1.93181i	0.0967490	+	0.0838335i
$532$	0.881754	+	1.28602i	0.0382289	+	0.0557562i
$533$	−32.2108	+	4.63121i	−1.39520	+	0.200600i
$534$	−4.95467	−	10.4345i	−0.214409	−	0.451546i
$535$	−2.76733	+	19.2472i	−0.119642	+	0.832128i
$536$	32.0990	−	11.0069i	1.38647	−	0.475426i
$537$	−19.1067	−	12.2791i	−0.824514	−	0.529883i
$538$	2.78002	−	6.33577i	0.119855	−	0.273155i
$539$	5.57503	−	18.9868i	0.240134	−	0.817820i
$540$	3.05136	+	3.31623i	0.131310	+	0.142708i
$541$	−4.70932	+	4.08065i	−0.202470	+	0.175441i	−0.750194	−	0.661218i	$-0.770040\pi$
$541$	−4.70932	+	4.08065i	−0.202470	+	0.175441i	0.547724	+	0.836659i	$0.315494\pi$
$542$	−11.8023	+	42.5313i	−0.506952	+	1.82688i
$543$	2.02179	−	4.42709i	0.0867631	−	0.189985i
$544$	7.29900	−	13.4684i	0.312942	−	0.577452i
$545$	38.9871	−	11.4477i	1.67003	−	0.490364i
$546$	26.1006	+	3.35623i	1.11700	+	0.143633i
$547$	−6.36652	+	2.90749i	−0.272213	+	0.124315i	−0.546845	−	0.837234i	$-0.684171\pi$
$547$	−6.36652	+	2.90749i	−0.272213	+	0.124315i	0.274632	+	0.961549i	$0.411444\pi$
$548$	−2.92351	−	16.7669i	−0.124886	−	0.716246i
$549$	2.51896	+	3.91958i	0.107507	+	0.167284i
$550$	−0.209086	+	0.248698i	−0.00891548	+	0.0106045i
$551$	−0.267612			−0.0114006
$552$	7.04497	+	11.5917i	0.299854	+	0.493377i
$553$	10.0078			0.425573
$554$	−27.3483	+	32.5294i	−1.16192	+	1.38204i
$555$	−10.7327	−	16.7005i	−0.455580	−	0.708896i
$556$	38.8157	−	6.76798i	1.64615	−	0.287026i
$557$	−6.13447	+	2.80152i	−0.259926	+	0.118704i	−0.541116	−	0.840948i	$-0.681998\pi$
$557$	−6.13447	+	2.80152i	−0.259926	+	0.118704i	0.281190	+	0.959652i	$0.409271\pi$
$558$	12.5216	+	1.61013i	0.530084	+	0.0681624i
$559$	10.6036	−	3.11350i	0.448485	−	0.131687i
$560$	16.2920	−	29.0210i	0.688465	−	1.22636i
$561$	3.35486	−	7.34612i	0.141642	−	0.310154i
$562$	5.76048	−	20.7587i	0.242991	−	0.875654i
$563$	10.7805	−	9.34135i	0.454344	−	0.393691i	−0.397404	−	0.917644i	$-0.630089\pi$
$563$	10.7805	−	9.34135i	0.454344	−	0.393691i	0.851747	+	0.523953i	$0.175543\pi$
$564$	11.3957	−	10.4856i	0.479847	−	0.441521i
$565$	2.85478	−	9.72250i	0.120102	−	0.409028i
$566$	−9.44259	+	21.5200i	−0.396902	+	0.904555i
$567$	−3.10644	−	1.99639i	−0.130458	−	0.0838403i
$568$	13.8579	+	40.4132i	0.581463	+	1.69570i
$569$	−5.99943	+	41.7269i	−0.251509	+	1.74928i	0.337655	+	0.941270i	$0.390366\pi$
$569$	−5.99943	+	41.7269i	−0.251509	+	1.74928i	−0.589164	+	0.808014i	$0.700543\pi$
$570$	0.288582	+	0.607753i	0.0120874	+	0.0254560i
$571$	30.4480	−	4.37776i	1.27421	−	0.183203i	0.528188	−	0.849127i	$-0.322872\pi$
$571$	30.4480	−	4.37776i	1.27421	−	0.183203i	0.746020	+	0.665924i	$0.231962\pi$
$572$	−24.7887	+	16.9962i	−1.03647	+	0.710647i
$573$	−1.52262	−	1.31935i	−0.0636082	−	0.0551168i
$574$	−0.502916	−	33.7198i	−0.0209913	−	1.40744i
$575$	0.361148	+	0.0779711i	0.0150609	+	0.00325162i
$576$	7.96799	−	0.714891i	0.332000	−	0.0297871i
$577$	−7.08329	+	8.17455i	−0.294881	+	0.340311i	−0.883786	−	0.467891i	$-0.845014\pi$
$577$	−7.08329	+	8.17455i	−0.294881	+	0.340311i	0.588905	+	0.808202i	$0.299559\pi$
$578$	−7.56150	−	11.3888i	−0.314517	−	0.473713i
$579$	14.4441	−	2.07675i	0.600276	−	0.0863067i
$580$	2.52672	+	5.12268i	0.104916	+	0.212708i
$581$	5.41214	+	0.778149i	0.224533	+	0.0322830i
$582$	−12.0310	+	3.72838i	−0.498700	+	0.154546i
$583$	12.0225	+	7.72642i	0.497923	+	0.319996i
$584$	−41.7006	−	16.8329i	−1.72558	−	0.696551i
$585$	10.8945	+	3.19892i	0.450434	+	0.132259i
$586$	30.0001	+	33.5962i	1.23929	+	1.38785i
$587$	20.5766	−	17.8298i	0.849289	−	0.735913i	−0.117067	−	0.993124i	$-0.537349\pi$
$587$	20.5766	−	17.8298i	0.849289	−	0.735913i	0.966355	+	0.257211i	$0.0828037\pi$
$588$	−3.35747	+	12.8393i	−0.138460	+	0.529483i
$589$	1.71448	+	0.782975i	0.0706437	+	0.0322619i
$590$	4.96362	−	7.98284i	0.204349	−	0.328648i
$591$	−2.45110	+	0.719709i	−0.100825	+	0.0296049i
$592$	−35.1199	−	2.92682i	−1.44342	−	0.120292i
$593$	−17.8842	−	39.1610i	−0.734417	−	1.60815i	−0.792526	−	0.609838i	$-0.791234\pi$
$593$	−17.8842	−	39.1610i	−0.734417	−	1.60815i	0.0581094	−	0.998310i	$-0.481493\pi$
$594$	4.16512	−	0.662395i	0.170897	−	0.0271784i
$595$	12.1816	+	18.9550i	0.499399	+	0.777080i
$596$	17.3943	+	14.1865i	0.712497	+	0.581101i
$597$		−	1.86375i		−	0.0762783i
$598$	30.2627	+	15.8830i	1.23753	+	0.649505i
$599$	−5.97461			−0.244116			−0.122058	−	0.992523i	$-0.538949\pi$
$599$	−5.97461			−0.244116			−0.122058	+	0.992523i	$0.538949\pi$
$600$	0.135187	−	0.170896i	0.00551897	−	0.00697679i
$601$	21.9797	−	14.1255i	0.896571	−	0.576191i	−0.00920026	−	0.999958i	$-0.502929\pi$
$601$	21.9797	−	14.1255i	0.896571	−	0.576191i	0.905772	+	0.423766i	$0.139292\pi$
$602$	1.79873	+	11.3104i	0.0733109	+	0.460977i
$603$	−10.9132	+	4.98390i	−0.444421	+	0.202960i
$604$	0.891277	−	7.85572i	0.0362655	−	0.319645i
$605$	−1.33722	−	4.55416i	−0.0543658	−	0.185153i
$606$	5.30223	−	8.52741i	0.215388	−	0.346402i
$607$	−0.375766	+	0.822812i	−0.0152519	+	0.0333969i	−0.917105	−	0.398647i	$-0.869480\pi$
$607$	−0.375766	+	0.822812i	−0.0152519	+	0.0333969i	0.901853	+	0.432043i	$0.142207\pi$
$608$	1.16786	+	0.250180i	0.0473629	+	0.0101461i
$609$	−3.06501	−	3.53721i	−0.124201	−	0.143335i
$610$	11.0742	−	9.88884i	0.448382	−	0.400387i
$611$	10.9926	−	37.4375i	0.444715	−	1.51456i
$612$	−2.10200	+	4.99156i	−0.0849683	+	0.201772i
$613$	11.4209	−	17.7713i	0.461286	−	0.717775i	−0.530216	−	0.847862i	$-0.677889\pi$
$613$	11.4209	−	17.7713i	0.461286	−	0.717775i	0.991503	+	0.130087i	$0.0415257\pi$
$614$	1.13966	−	0.353180i	0.0459931	−	0.0142532i
$615$	2.07080	−	14.4027i	0.0835027	−	0.580774i
$616$	−14.1932	−	27.7253i	−0.571860	−	1.11708i
$617$	−6.88248	−	47.8687i	−0.277078	−	1.92712i	−0.365026	−	0.930997i	$-0.618940\pi$
$617$	−6.88248	−	47.8687i	−0.277078	−	1.92712i	0.0879474	−	0.996125i	$-0.471969\pi$
$618$	−18.2401	+	12.1103i	−0.733725	+	0.487149i
$619$	−1.20992	−	1.04840i	−0.0486308	−	0.0421388i	0.630206	−	0.776428i	$-0.282970\pi$
$619$	−1.20992	−	1.04840i	−0.0486308	−	0.0421388i	−0.678837	+	0.734289i	$0.737516\pi$
$620$	−1.19974	−	40.2114i	−0.0481827	−	1.61493i
$621$	−2.88004	−	3.83476i	−0.115572	−	0.153884i
$622$	0.464794	+	31.1637i	0.0186365	+	1.24955i
$623$	19.7512	−	22.7941i	0.791315	−	0.913226i
$624$	16.2771	−	11.8892i	0.651606	−	0.475947i
$625$	3.61185	+	25.1209i	0.144474	+	1.00484i
$626$	−22.1474	+	10.5163i	−0.885189	+	0.420317i
$627$	0.623234	+	0.0896075i	0.0248896	+	0.00357858i
$628$	−8.39464	−	25.7251i	−0.334983	−	1.02654i
$629$	12.8992	−	20.0715i	0.514324	−	0.800303i
$630$	−4.72791	+	10.7751i	−0.188365	+	0.429290i
$631$	7.75957	+	2.27842i	0.308904	+	0.0907023i	0.432510	−	0.901629i	$-0.357628\pi$
$631$	7.75957	+	2.27842i	0.308904	+	0.0907023i	−0.123607	+	0.992331i	$0.539446\pi$
$632$	5.56296	−	5.27398i	0.221283	−	0.209788i
$633$	4.14974	+	4.78905i	0.164937	+	0.190348i
$634$	−24.2401	−	6.72656i	−0.962699	−	0.267146i
$635$	−2.45693	−	1.12204i	−0.0975004	−	0.0445270i
$636$	−8.21382	−	4.93894i	−0.325699	−	0.195842i
$637$	9.42047	+	32.0832i	0.373253	+	1.27118i
$638$	5.30197	+	0.681770i	0.209907	+	0.0269915i
$639$	−6.27480	−	13.7399i	−0.248227	−	0.543542i
$640$	−6.23758	−	24.7175i	−0.246562	−	0.977044i
$641$	24.1109	−	15.4951i	0.952322	−	0.612020i	0.0304588	−	0.999536i	$-0.490303\pi$
$641$	24.1109	−	15.4951i	0.952322	−	0.612020i	0.921863	+	0.387516i	$0.126667\pi$
$642$	−9.34171	−	7.85381i	−0.368688	−	0.309965i
$643$		−	0.0544138i		−	0.00214587i	−0.999999	−	0.00107294i	$-0.999658\pi$
$643$		−	0.0544138i		−	0.00214587i	0.999999	−	0.00107294i	$-0.000341526\pi$
$644$	−20.3251	+	29.0062i	−0.800920	+	1.14300i
$645$			4.94146i			0.194570i
$646$	−0.520343	+	0.618921i	−0.0204726	+	0.0243511i
$647$	−27.3843	+	17.5988i	−1.07659	+	0.691880i	−0.953766	−	0.300549i	$-0.902830\pi$
$647$	−27.3843	+	17.5988i	−1.07659	+	0.691880i	−0.122820	+	0.992429i	$0.539194\pi$
$648$	−2.77883	+	0.527339i	−0.109163	+	0.0207159i
$649$	−3.65455	−	8.00236i	−0.143454	−	0.314120i
$650$	0.0700213	−	0.544540i	0.00274646	−	0.0213586i
$651$	9.28710	+	31.6290i	0.363990	+	1.23964i
$652$	−11.0728	+	18.4150i	−0.433646	+	0.721186i
$653$	15.9162	+	7.26870i	0.622850	+	0.284446i	0.701735	−	0.712438i	$-0.252409\pi$
$653$	15.9162	+	7.26870i	0.622850	+	0.284446i	−0.0788855	+	0.996884i	$0.525136\pi$
$654$	−6.81928	+	24.5743i	−0.266655	+	0.960930i
$655$	−2.89596	−	3.34211i	−0.113154	−	0.130587i
$656$	−18.0495	−	18.4786i	−0.704716	−	0.721468i
$657$	15.2552	+	4.47933i	0.595162	+	0.174755i
$658$	37.0271	+	16.2468i	1.44347	+	0.633366i
$659$	−24.1148	+	37.5234i	−0.939381	+	1.46171i	−0.0530829	+	0.998590i	$0.516905\pi$
$659$	−24.1148	+	37.5234i	−0.939381	+	1.46171i	−0.886298	+	0.463115i	$0.846732\pi$
$660$	−4.16911	−	12.7761i	−0.162283	−	0.497310i
$661$	8.75569	+	1.25888i	0.340557	+	0.0489647i	0.310472	−	0.950583i	$-0.399513\pi$
$661$	8.75569	+	1.25888i	0.340557	+	0.0489647i	0.0300853	+	0.999547i	$0.490422\pi$
$662$	11.0527	+	23.2769i	0.429573	+	0.904682i
$663$	1.94208	+	13.5075i	0.0754243	+	0.524587i
$664$	3.41850	−	2.41960i	0.132663	−	0.0938986i
$665$	−1.15040	+	1.32763i	−0.0446105	+	0.0514832i
$666$	12.4584	−	0.185812i	0.482754	−	0.00720008i
$667$	−2.13320	−	5.69211i	−0.0825980	−	0.220399i
$668$	19.1990	−	0.572816i	0.742830	−	0.0221629i
$669$	14.7436	+	12.7754i	0.570020	+	0.493925i
$670$	21.1462	+	31.8495i	0.816948	+	1.23045i
$671$	−1.97742	−	13.7533i	−0.0763375	−	0.530939i
$672$	10.0689	+	18.3017i	0.388416	+	0.706005i
$673$	5.94638	−	41.3580i	0.229216	−	1.59423i	−0.472207	−	0.881488i	$-0.656543\pi$
$673$	5.94638	−	41.3580i	0.229216	−	1.59423i	0.701423	−	0.712745i	$-0.252548\pi$
$674$	−2.99767	−	9.67307i	−0.115466	−	0.372593i
$675$	−0.0416508	+	0.0648099i	−0.00160314	+	0.00249453i
$676$	9.61993	−	22.8442i	0.369997	−	0.878622i
$677$	−3.98473	+	13.5707i	−0.153146	+	0.521566i	−0.999946	−	0.0103441i	$-0.996707\pi$
$677$	−3.98473	+	13.5707i	−0.153146	+	0.521566i	0.846801	+	0.531910i	$0.178526\pi$
$678$	4.23602	+	4.74380i	0.162683	+	0.182184i
$679$	−21.5369	−	24.8549i	−0.826510	−	0.953844i
$680$	16.7604	+	4.11682i	0.642733	+	0.157873i
$681$	2.33122	−	5.10467i	0.0893327	−	0.195611i
$682$	−31.9728	−	19.8802i	−1.22430	−	0.761254i
$683$	−8.70812	−	29.6571i	−0.333207	−	1.13480i	−0.940351	−	0.340206i	$-0.889503\pi$
$683$	−8.70812	−	29.6571i	−0.333207	−	1.13480i	0.607144	−	0.794592i	$-0.292315\pi$
$684$	−0.419576	−	0.0476033i	−0.0160429	−	0.00182016i
$685$	17.4420	−	7.96551i	0.666426	−	0.304346i
$686$	1.87983	−	0.298957i	0.0717723	−	0.0114142i
$687$	−12.5632	+	8.07385i	−0.479314	+	0.308037i
$688$	6.96030	+	5.33913i	0.265359	+	0.203552i
$689$	−24.1488			−0.919994
$690$	−10.6266	+	10.9827i	−0.404547	+	0.418104i
$691$			25.9008i			0.985313i	0.870224	+	0.492656i	$0.163974\pi$
$691$			25.9008i			0.985313i	−0.870224	+	0.492656i	$0.836026\pi$
$692$	33.3655	+	27.2124i	1.26837	+	1.03446i
$693$	5.95362	+	9.26401i	0.226159	+	0.351911i
$694$	2.19152	+	13.7802i	0.0831888	+	0.523088i
$695$	18.4403	+	40.3786i	0.699480	+	1.53165i
$696$	−3.56780	−	0.350982i	−0.135237	−	0.0133039i
$697$	16.7796	−	4.92692i	0.635571	−	0.186620i
$698$	19.5195	+	12.1370i	0.738824	+	0.459391i
$699$	13.0928	+	5.97927i	0.495214	+	0.226157i
$700$	0.550448	+	0.143942i	0.0208050	+	0.00544050i
$701$	−32.5863	+	28.2362i	−1.23077	+	1.06647i	−0.235247	+	0.971936i	$0.575590\pi$
$701$	−32.5863	+	28.2362i	−1.23077	+	1.06647i	−0.995522	+	0.0945313i	$0.969865\pi$
$702$	−5.31566	+	4.74667i	−0.200627	+	0.179151i
$703$	1.78483	+	0.524073i	0.0673161	+	0.0197658i
$704$	−22.5004	−	7.93186i	−0.848017	−	0.298943i
$705$	14.6769	+	9.43230i	0.552766	+	0.355241i
$706$	−3.31333	−	10.6917i	−0.124699	−	0.402386i
$707$	25.9521	+	3.73136i	0.976031	+	0.140332i
$708$	2.60987	+	5.29127i	0.0980850	+	0.198858i
$709$	−37.4679	+	5.38707i	−1.40714	+	0.202316i	−0.803671	−	0.595074i	$-0.797123\pi$
$709$	−37.4679	+	5.38707i	−1.40714	+	0.202316i	−0.603465	+	0.797390i	$0.706214\pi$
$710$	−40.0990	+	26.6233i	−1.50489	+	0.999156i
$711$	−1.77480	+	2.04823i	−0.0665603	+	0.0768146i
$712$	−1.03326	−	23.0791i	−0.0387230	−	0.864926i
$713$	−2.98737	+	42.7082i	−0.111878	+	1.59944i
$714$	−14.1403	+	0.210896i	−0.529187	+	0.00789260i
$715$	−25.5906	−	22.1744i	−0.957036	−	0.829276i
$716$	−25.6869	−	37.4640i	−0.959966	−	1.40009i
$717$	−27.1457	+	3.90297i	−1.01378	+	0.145759i
$718$	−31.6775	+	15.0415i	−1.18219	+	0.561346i
$719$	1.92573	−	13.3937i	0.0718174	−	0.499501i	−0.921886	−	0.387461i	$-0.873352\pi$
$719$	1.92573	−	13.3937i	0.0718174	−	0.499501i	0.993704	−	0.112040i	$-0.0357386\pi$
$720$	3.05029	+	8.48106i	0.113677	+	0.316070i
$721$	−48.0927	−	30.9073i	−1.79107	−	1.15105i
$722$	24.5479	+	10.7712i	0.913577	+	0.400861i
$723$	−3.51959	+	11.9866i	−0.130895	+	0.445787i
$724$	7.16295	−	6.59084i	0.266209	−	0.244947i
$725$	−0.0737971	+	0.0639456i	−0.00274076	+	0.00237488i
$726$	2.87057	+	0.796573i	0.106537	+	0.0295636i
$727$	3.91823	−	8.57972i	0.145319	−	0.318204i	−0.822950	−	0.568113i	$-0.807673\pi$
$727$	3.91823	−	8.57972i	0.145319	−	0.318204i	0.968269	+	0.249909i	$0.0804007\pi$
$728$	45.5044	+	26.4458i	1.68651	+	0.980145i
$729$	0.959493	−	0.281733i	0.0355368	−	0.0104345i
$730$	6.46154	−	50.2499i	0.239152	−	1.85983i
$731$	−5.40222	+	2.46711i	−0.199808	+	0.0912494i
$732$	1.60063	+	9.17993i	0.0591610	+	0.339300i
$733$	15.5514	+	24.1985i	0.574406	+	0.893793i	0.999938	−	0.0111506i	$-0.00354941\pi$
$733$	15.5514	+	24.1985i	0.574406	+	0.893793i	−0.425532	+	0.904943i	$0.639913\pi$
$734$	−22.8989	−	19.2517i	−0.845215	−	0.710594i
$735$	−14.9513			−0.551487
$736$	3.98795	+	26.8346i	0.146998	+	0.989137i
$737$	35.7786			1.31792
$738$	6.99043	+	5.87703i	0.257321	+	0.216336i
$739$	26.7781	+	41.6676i	0.985050	+	1.53277i	0.839459	+	0.543423i	$0.182872\pi$
$739$	26.7781	+	41.6676i	0.985050	+	1.53277i	0.145591	+	0.989345i	$0.453492\pi$
$740$	−6.81994	−	39.1137i	−0.250706	−	1.43785i
$741$	−0.967799	+	0.441979i	−0.0355530	+	0.0162365i
$742$	3.19171	−	24.8212i	0.117171	−	0.911215i
$743$	−6.82530	+	2.00409i	−0.250396	+	0.0735229i	−0.404522	−	0.914528i	$-0.632562\pi$
$743$	−6.82530	+	2.00409i	−0.250396	+	0.0735229i	0.154126	+	0.988051i	$0.450744\pi$
$744$	21.8305	+	12.6872i	0.800345	+	0.465136i
$745$	−10.5049	+	23.0026i	−0.384871	+	0.842751i
$746$	13.4635	+	3.73608i	0.492935	+	0.136788i
$747$	−1.11906	+	0.969674i	−0.0409444	+	0.0354785i
$748$	11.8859	−	10.9365i	0.434591	−	0.399880i
$749$	8.97796	−	30.5761i	0.328047	−	1.11723i
$750$	−14.3652	−	6.30319i	−0.524543	−	0.230160i
$751$	23.1362	+	14.8687i	0.844252	+	0.542568i	0.889777	−	0.456395i	$-0.150860\pi$
$751$	23.1362	+	14.8687i	0.844252	+	0.542568i	−0.0455249	+	0.998963i	$0.514496\pi$
$752$	29.1439	−	10.4819i	1.06277	−	0.382234i
$753$	0.561218	−	3.90336i	0.0204519	−	0.142246i
$754$	−8.15968	+	3.87449i	−0.297158	+	0.141101i
$755$	8.81648	−	1.26762i	0.320865	−	0.0461334i
$756$	−4.17628	−	6.09104i	−0.151890	−	0.221529i
$757$	−28.1014	−	24.3500i	−1.02136	−	0.885015i	−0.0279495	−	0.999609i	$-0.508898\pi$
$757$	−28.1014	−	24.3500i	−1.02136	−	0.885015i	−0.993412	+	0.114594i	$0.963443\pi$
$758$	47.0979	−	0.702445i	1.71067	−	0.0255140i
$759$	3.06200	+	13.9705i	0.111144	+	0.507097i
$760$	0.0601815	+	1.34423i	0.00218301	+	0.0487603i
$761$	−12.0057	+	13.8553i	−0.435206	+	0.502255i	−0.930409	−	0.366523i	$-0.880548\pi$
$761$	−12.0057	+	13.8553i	−0.435206	+	0.502255i	0.495203	+	0.868777i	$0.335094\pi$
$762$	1.41232	−	0.937695i	0.0511630	−	0.0339691i
$763$	−65.9123	+	9.47676i	−2.38619	+	0.343082i
$764$	−1.78245	−	3.61374i	−0.0644866	−	0.130741i
$765$	−6.03974	−	0.868384i	−0.218367	−	0.0313965i
$766$	−0.340603	−	1.09908i	−0.0123065	−	0.0397114i
$767$	12.5056	+	8.03686i	0.451551	+	0.290194i
$768$	15.2418	+	4.86709i	0.549990	+	0.175626i
$769$	−21.0989	−	6.19519i	−0.760845	−	0.223404i	−0.121780	−	0.992557i	$-0.538860\pi$
$769$	−21.0989	−	6.19519i	−0.760845	−	0.223404i	−0.639065	+	0.769153i	$0.720678\pi$
$770$	26.1742	−	23.3725i	0.943251	−	0.842285i
$771$	11.1821	−	9.68937i	0.402714	−	0.348954i
$772$	28.2358	+	7.38366i	1.01623	+	0.265744i
$773$	−18.4186	−	8.41150i	−0.662471	−	0.302540i	0.0556583	−	0.998450i	$-0.482274\pi$
$773$	−18.4186	−	8.41150i	−0.662471	−	0.302540i	−0.718130	+	0.695909i	$0.755002\pi$
$774$	−2.63382	−	1.63768i	−0.0946709	−	0.0588651i
$775$	0.659878	−	0.193758i	0.0237035	−	0.00695998i
$776$	−25.0699	−	2.46624i	−0.899956	−	0.0885330i
$777$	13.5150	+	29.5936i	0.484846	+	1.06167i
$778$	−1.17886	−	7.41263i	−0.0422641	−	0.265756i
$779$	0.737138	+	1.14701i	0.0264107	+	0.0410959i
$780$	17.5981	+	14.3528i	0.630114	+	0.513911i
$781$			45.0458i			1.61186i
$782$	−17.3123	−	6.13412i	−0.619085	−	0.219356i
$783$	1.26750			0.0452967
$784$	−16.1545	+	21.0597i	−0.576947	+	0.752132i
$785$	25.6467	−	16.4822i	0.915371	−	0.588273i
$786$	2.74113	−	0.435932i	0.0977727	−	0.0155492i
$787$	30.1144	−	13.7528i	1.07346	−	0.490234i	0.201341	−	0.979521i	$-0.435470\pi$
$787$	30.1144	−	13.7528i	1.07346	−	0.490234i	0.872123	+	0.489287i	$0.162743\pi$
$788$	−5.07660	−	0.575969i	−0.180846	−	0.0205181i
$789$	6.67655	+	22.7382i	0.237691	+	0.809502i
$790$	7.33403	+	4.56020i	0.260933	+	0.162245i
$791$	−6.89840	+	15.1054i	−0.245279	+	0.537086i
$792$	8.19144	+	2.01204i	0.291070	+	0.0714948i
$793$	15.3753	+	17.7440i	0.545992	+	0.630109i
$794$	−16.1864	−	18.1266i	−0.574433	−	0.643291i
$795$	3.04211	−	10.3605i	0.107893	−	0.367449i
$796$	1.44665	−	3.43533i	0.0512753	−	0.121762i
$797$	24.0592	−	37.4369i	0.852222	−	1.32608i	−0.0916564	−	0.995791i	$-0.529216\pi$
$797$	24.0592	−	37.4369i	0.852222	−	1.32608i	0.943879	−	0.330293i	$-0.107148\pi$
$798$	−0.326374	−	1.05316i	−0.0115535	−	0.0372816i
$799$	−2.98408	+	20.7547i	−0.105569	+	0.734249i
$800$	0.381831	−	0.210068i	0.0134998	−	0.00742703i
$801$	1.16241	+	8.08473i	0.0410717	+	0.285660i
$802$	−0.800625	−	1.20587i	−0.0282710	−	0.0425808i
$803$	−35.8336	−	31.0500i	−1.26454	−	1.09573i
$804$	−23.9841	+	0.715585i	−0.845855	+	0.0252367i
$805$	−37.4088	−	13.8861i	−1.31849	−	0.489421i
$806$	63.6115	−	0.948739i	2.24062	−	0.0334179i
$807$	−3.20382	+	3.69741i	−0.112780	+	0.130155i
$808$	16.3923	−	11.6024i	0.576678	−	0.408170i
$809$	−3.00160	−	20.8766i	−0.105531	−	0.733982i	−0.972039	−	0.234820i	$-0.924550\pi$
$809$	−3.00160	−	20.8766i	−0.105531	−	0.733982i	0.866508	−	0.499163i	$-0.166359\pi$
$810$	−1.36682	−	2.87852i	−0.0480251	−	0.101141i
$811$	13.0024	+	1.86946i	0.456575	+	0.0656456i	0.366766	−	0.930313i	$-0.380465\pi$
$811$	13.0024	+	1.86946i	0.456575	+	0.0656456i	0.0898094	+	0.995959i	$0.471374\pi$
$812$	−2.90392	−	8.89898i	−0.101908	−	0.312293i
$813$	16.8737	−	26.2561i	0.591788	−	0.920840i
$814$	−34.0262	−	14.9301i	−1.19262	−	0.523299i
$815$	−23.2277	−	6.82026i	−0.813630	−	0.238903i
$816$	−7.74895	+	7.56902i	−0.271268	+	0.264969i
$817$	−0.303219	−	0.349934i	−0.0106083	−	0.0122426i
$818$	0.696951	−	2.51157i	0.0243683	−	0.0878149i
$819$	−16.9263	−	7.73000i	−0.591454	−	0.270108i
$820$	14.9964	−	24.9402i	0.523698	−	0.870949i
$821$	−6.13759	−	20.9027i	−0.214203	−	0.729509i	−0.994559	−	0.104174i	$-0.966780\pi$
$821$	−6.13759	−	20.9027i	−0.214203	−	0.729509i	0.780356	−	0.625336i	$-0.215038\pi$
$822$	−1.53490	+	11.9366i	−0.0535358	+	0.416336i
$823$	11.6716	+	25.5572i	0.406845	+	0.890867i	0.996530	+	0.0832332i	$0.0265246\pi$
$823$	11.6716	+	25.5572i	0.406845	+	0.890867i	−0.589685	+	0.807633i	$0.700748\pi$
$824$	−43.0208	+	8.16407i	−1.49870	+	0.284409i
$825$	0.193276	−	0.124211i	0.00672900	−	0.00432446i
$826$	−9.91349	+	11.7916i	−0.344935	+	0.410282i
$827$			35.6399i			1.23932i	0.784870	+	0.619661i	$0.212730\pi$
$827$			35.6399i			1.23932i	−0.784870	+	0.619661i	$0.787270\pi$
$828$	−2.33202	−	9.30385i	−0.0810434	−	0.323331i
$829$		−	18.1449i		−	0.630199i	−0.949059	−	0.315099i	$-0.897962\pi$
$829$		−	18.1449i		−	0.630199i	0.949059	−	0.315099i	$-0.102038\pi$
$830$	3.61163	+	3.03639i	0.125362	+	0.105395i
$831$	25.2803	−	16.2466i	0.876962	−	0.563589i
$832$	39.2309	−	9.28008i	1.36009	−	0.321729i
$833$	−7.46470	−	16.3454i	−0.258636	−	0.566335i
$834$	−27.6334	−	3.55332i	−0.956866	−	0.123041i
$835$	6.09654	+	20.7629i	0.210979	+	0.718530i
$836$	1.07921	+	0.648925i	0.0373253	+	0.0224435i
$837$	−8.12032	−	3.70843i	−0.280679	−	0.128182i
$838$	30.6891	+	8.51612i	1.06014	+	0.294185i
$839$	35.9853	+	41.5293i	1.24235	+	1.43375i	0.860441	+	0.509550i	$0.170188\pi$
$839$	35.9853	+	41.5293i	1.24235	+	1.43375i	0.381910	+	0.924200i	$0.375266\pi$
$840$	−17.0783	+	16.1912i	−0.589259	+	0.558649i
$841$	−26.2838	−	7.71763i	−0.906339	−	0.266125i
$842$	−12.8989	+	29.3972i	−0.444526	+	1.01309i
$843$	−8.23575	+	12.8151i	−0.283654	+	0.441375i
$844$	3.93164	+	12.0484i	0.135333	+	0.414723i
$845$	27.6412	+	3.97421i	0.950888	+	0.136717i
$846$	−9.89163	+	4.69687i	−0.340081	+	0.161482i
$847$	1.10700	+	7.69935i	0.0380369	+	0.264553i
$848$	−11.3064	−	15.4792i	−0.388262	−	0.531559i
$849$	10.8821	−	12.5586i	0.373472	−	0.431009i
$850$	0.00439995	+	0.295010i	0.000150917	+	0.0101188i
$851$	3.08028	+	42.1409i	0.105591	+	1.44457i
$852$	−0.900932	−	30.1964i	−0.0308654	−	1.03451i
$853$	−35.1773	−	30.4813i	−1.20445	−	1.04366i	−0.997870	−	0.0652289i	$-0.979222\pi$
$853$	−35.1773	−	30.4813i	−1.20445	−	1.04366i	−0.206577	−	0.978430i	$-0.566232\pi$
$854$	−20.2702	+	13.4582i	−0.693634	+	0.460531i
$855$	−0.0677038	−	0.470891i	−0.00231542	−	0.0161041i
$856$	−11.1228	−	21.7275i	−0.380168	−	0.742630i
$857$	1.11664	−	7.76639i	0.0381436	−	0.265295i	−0.961821	−	0.273678i	$-0.911760\pi$
$857$	1.11664	−	7.76639i	0.0381436	−	0.265295i	0.999965	+	0.00838378i	$0.00266867\pi$
$858$	20.3002	−	6.29100i	0.693038	−	0.214771i
$859$	7.64079	−	11.8893i	0.260700	−	0.405658i	−0.686086	−	0.727521i	$-0.740673\pi$
$859$	7.64079	−	11.8893i	0.260700	−	0.405658i	0.946786	+	0.321863i	$0.104309\pi$
$860$	−3.83559	+	9.10826i	−0.130793	+	0.310589i
$861$	−6.71823	+	22.8802i	−0.228957	+	0.779755i
$862$	−32.5786	+	29.0914i	−1.10963	+	0.990856i
$863$	8.79734	+	10.1527i	0.299465	+	0.345601i	0.885462	−	0.464712i	$-0.153842\pi$
$863$	8.79734	+	10.1527i	0.299465	+	0.345601i	−0.585997	+	0.810313i	$0.699297\pi$
$864$	−5.53136	−	1.18494i	−0.188181	−	0.0403124i
$865$	−20.1505	+	44.1234i	−0.685137	+	1.50024i
$866$	13.4731	−	21.6684i	0.457835	−	0.736322i
$867$	2.72336	+	9.27492i	0.0924902	+	0.314993i
$868$	−7.43229	+	65.5082i	−0.252268	+	2.22349i
$869$	7.35196	−	3.35753i	0.249398	−	0.113896i
$870$	−0.634357	−	3.98882i	−0.0215067	−	0.135234i
$871$	−50.8599	+	32.6857i	−1.72332	+	1.10751i
$872$	−31.6442	+	40.0029i	−1.07161	+	1.35467i
$873$	8.90633			0.301433
$874$	0.0786063	−	1.42982i	0.00265890	−	0.0483644i
$875$		−	40.9607i		−	1.38472i
$876$	24.6420	+	20.0976i	0.832576	+	0.679036i
$877$	−1.16391	−	1.81107i	−0.0393023	−	0.0611556i	0.821046	−	0.570861i	$-0.193391\pi$
$877$	−1.16391	−	1.81107i	−0.0393023	−	0.0611556i	−0.860349	+	0.509706i	$0.829754\pi$
$878$	33.7143	−	5.36172i	1.13780	−	0.180949i
$879$	−13.2305	−	28.9708i	−0.446255	−	0.977161i
$880$	2.23224	−	26.7854i	0.0752489	−	0.902937i
$881$	40.0834	−	11.7695i	1.35044	−	0.396526i	0.475059	−	0.879954i	$-0.342427\pi$
$881$	40.0834	−	11.7695i	1.35044	−	0.396526i	0.875384	+	0.483428i	$0.160609\pi$
$882$	4.95509	−	7.96912i	0.166847	−	0.268334i
$883$	−17.8380	−	8.14634i	−0.600297	−	0.274146i	0.0920004	−	0.995759i	$-0.470674\pi$
$883$	−17.8380	−	8.14634i	−0.600297	−	0.274146i	−0.692297	+	0.721613i	$0.743401\pi$
$884$	−6.90488	+	26.4049i	−0.232236	+	0.888093i
$885$	−5.02341	+	4.35281i	−0.168860	+	0.146318i
$886$	−4.48411	−	5.02163i	−0.150647	−	0.168705i
$887$	−8.26450	−	2.42668i	−0.277495	−	0.0814798i	0.140024	−	0.990148i	$-0.455282\pi$
$887$	−8.26450	−	2.42668i	−0.277495	−	0.0814798i	−0.417519	+	0.908668i	$0.637100\pi$
$888$	23.1080	+	9.32781i	0.775454	+	0.313021i
$889$	3.72379	+	2.39313i	0.124892	+	0.0802631i
$890$	24.8609	−	7.70434i	0.833339	−	0.258250i
$891$	−2.95184	−	0.424411i	−0.0988905	−	0.0142183i
$892$	17.2595	+	34.9921i	0.577892	+	1.17162i
$893$	−1.61815	+	0.232655i	−0.0541492	+	0.00778549i
$894$	−8.77901	−	13.2226i	−0.293614	−	0.442230i
$895$	33.5129	−	38.6760i	1.12021	−	1.29280i
$896$	4.35339	+	41.5499i	0.145437	+	1.38808i
$897$	−17.1155	−	17.0620i	−0.571470	−	0.569683i
$898$	0.271234	+	18.1858i	0.00905118	+	0.606868i
$899$	−8.55132	−	7.40976i	−0.285202	−	0.247129i
$900$	−0.127078	+	0.0871301i	−0.00423593	+	0.00290434i
$901$	12.8454	−	1.84688i	0.427941	−	0.0615286i
$902$	−11.6822	−	24.6027i	−0.388974	−	0.819181i
$903$	1.15249	−	8.01572i	0.0383524	−	0.266747i
$904$	4.12581	+	12.0319i	0.137222	+	0.400176i
$905$	9.22540	+	5.92880i	0.306663	+	0.197080i
$906$	−2.24627	+	5.11934i	−0.0746273	+	0.170079i
$907$	3.87970	−	13.2130i	0.128823	−	0.438732i	−0.869668	−	0.493636i	$-0.835667\pi$
$907$	3.87970	−	13.2130i	0.128823	−	0.438732i	0.998492	+	0.0549048i	$0.0174855\pi$
$908$	8.25925	−	7.59958i	0.274093	−	0.252201i
$909$	−5.36610	+	4.64975i	−0.177982	+	0.154223i
$910$	−15.8550	+	57.1359i	−0.525589	+	1.89404i
$911$	16.8390	−	36.8723i	0.557901	−	1.22163i	−0.395092	−	0.918642i	$-0.629287\pi$
$911$	16.8390	−	36.8723i	0.557901	−	1.22163i	0.952993	−	0.302992i	$-0.0979856\pi$
$912$	−0.736426	−	0.413421i	−0.0243855	−	0.0136897i
$913$	4.23697	−	1.24409i	0.140223	−	0.0411732i
$914$	30.9301	+	3.97723i	1.02308	+	0.131555i
$915$	−9.54957	+	4.36114i	−0.315699	+	0.144175i
$916$	−29.4238	+	5.13039i	−0.972189	+	0.169513i
$917$	3.91816	+	6.09677i	0.129389	+	0.201333i
$918$	2.46452	−	2.93142i	0.0813411	−	0.0967511i
$919$	15.8630			0.523271			0.261635	−	0.965167i	$-0.415738\pi$
$919$	15.8630			0.523271			0.261635	+	0.965167i	$0.415738\pi$
$920$	−28.1121	+	11.9953i	−0.926828	+	0.395472i
$921$	−0.843674			−0.0278000
$922$	4.53770	−	5.39737i	0.149441	−	0.177753i
$923$	−41.1517	−	64.0334i	−1.35453	−	2.10768i
$924$	3.78312	+	21.6969i	0.124456	+	0.713777i
$925$	0.617414	−	0.281964i	0.0203005	−	0.00927091i
$926$	11.3085	+	1.45413i	0.371619	+	0.0477857i
$927$	14.8545	−	4.36168i	0.487886	−	0.143256i
$928$	−6.30386	−	3.41629i	−0.206934	−	0.112145i
$929$	−17.2924	+	37.8652i	−0.567347	+	1.24232i	0.380851	+	0.924636i	$0.375631\pi$
$929$	−17.2924	+	37.8652i	−0.567347	+	1.24232i	−0.948198	+	0.317680i	$0.897096\pi$
$930$	−7.60636	+	27.4106i	−0.249422	+	0.898830i
$931$	1.05879	−	0.917446i	0.0347004	−	0.0300681i
$932$	19.4919	+	21.1839i	0.638478	+	0.693900i
$933$	6.20897	−	21.1458i	0.203273	−	0.692283i
$934$	24.1646	−	55.0721i	0.790691	−	1.80202i
$935$	15.3082	+	9.83800i	0.500632	+	0.321737i
$936$	−13.4824	+	4.62317i	−0.440685	+	0.151113i
$937$	2.83694	−	19.7313i	0.0926788	−	0.644595i	−0.889540	−	0.456857i	$-0.848975\pi$
$937$	2.83694	−	19.7313i	0.0926788	−	0.644595i	0.982219	−	0.187738i	$-0.0601157\pi$
$938$	−26.8737	−	56.5961i	−0.877459	−	1.84793i
$939$	17.1599	−	2.46723i	0.559993	−	0.0805149i
$940$	19.7316	+	28.7782i	0.643574	+	0.938643i
$941$	−14.4329	−	12.5062i	−0.470498	−	0.407689i	0.387077	−	0.922047i	$-0.373485\pi$
$941$	−14.4329	−	12.5062i	−0.470498	−	0.407689i	−0.857575	+	0.514358i	$0.828030\pi$
$942$	0.285350	+	19.1323i	0.00929719	+	0.623363i
$943$	−18.5210	+	24.8221i	−0.603127	+	0.808318i
$944$	0.703488	+	11.7788i	0.0228966	+	0.383369i
$945$	5.44866	−	6.28809i	0.177245	−	0.204552i
$946$	5.11595	+	7.70544i	0.166334	+	0.250525i
$947$	26.2077	−	3.76810i	0.851636	−	0.122447i	0.297346	−	0.954770i	$-0.403899\pi$
$947$	26.2077	−	3.76810i	0.851636	−	0.122447i	0.554291	+	0.832323i	$0.312990\pi$
$948$	−4.86122	+	2.39775i	−0.157885	+	0.0778754i
$949$	79.3039	+	11.4022i	2.57431	+	0.370131i
$950$	−0.0219722	+	0.00680916i	−0.000712874	+	0.000220918i
$951$	14.9643	+	9.61695i	0.485250	+	0.311851i
$952$	−26.2275	−	10.5870i	−0.850040	−	0.343128i
$953$	14.8763	+	4.36808i	0.481891	+	0.141496i	0.513651	−	0.857999i	$-0.328293\pi$
$953$	14.8763	+	4.36808i	0.481891	+	0.141496i	−0.0317591	+	0.999496i	$0.510111\pi$
$954$	4.51399	+	5.05509i	0.146146	+	0.163664i
$955$	3.43080	−	2.97281i	0.111018	−	0.0961978i
$956$	−53.0654	−	13.8766i	−1.71626	−	0.448801i
$957$	−3.43835	−	1.57024i	−0.111146	−	0.0507586i
$958$	8.87425	−	14.2722i	0.286714	−	0.461113i
$959$	−30.1511	+	8.85317i	−0.973630	+	0.285884i
$960$	−0.960662	+	18.0002i	−0.0310052	+	0.580954i
$961$	20.2274	+	44.2919i	0.652498	+	1.42877i
$962$	62.0083	−	9.86142i	1.99923	−	0.317945i
$963$	4.66567	+	7.25992i	0.150349	+	0.233948i
$964$	−15.7915	+	19.3622i	−0.508610	+	0.623614i
$965$			32.8805i			1.05846i
$966$	19.7992	−	15.3370i	0.637029	−	0.493460i
$967$	−30.7063			−0.987449			−0.493724	−	0.869618i	$-0.664365\pi$
$967$	−30.7063			−0.987449			−0.493724	+	0.869618i	$0.664365\pi$
$968$	4.67282	+	3.69642i	0.150190	+	0.118807i
$969$	0.480995	−	0.309117i	0.0154518	−	0.00993027i
$970$	−4.45743	−	28.0282i	−0.143120	−	0.899931i
$971$	−3.40387	+	1.55450i	−0.109235	+	0.0498862i	−0.469283	−	0.883048i	$-0.655488\pi$
$971$	−3.40387	+	1.55450i	−0.109235	+	0.0498862i	0.360048	+	0.932934i	$0.382760\pi$
$972$	1.98725	+	0.225465i	0.0637411	+	0.00723180i
$973$	−20.4952	−	69.8004i	−0.657047	−	2.23770i
$974$	17.9459	−	28.8618i	0.575023	−	0.924792i
$975$	−0.161272	+	0.353136i	−0.00516483	+	0.0113094i
$976$	−4.17518	+	18.1632i	−0.133644	+	0.581389i
$977$	−33.5484	−	38.7169i	−1.07331	−	1.23866i	−0.969766	−	0.244037i	$-0.921528\pi$
$977$	−33.5484	−	38.7169i	−1.07331	−	1.23866i	−0.103541	−	0.994625i	$-0.533017\pi$
$978$	11.3332	−	10.1201i	0.362397	−	0.323606i
$979$	6.86250	−	23.3715i	0.219326	−	0.746957i
$980$	−27.5587	−	11.6053i	−0.880331	−	0.370717i
$981$	9.74952	−	15.1705i	0.311278	−	0.484358i
$982$	37.0661	−	11.4867i	1.18283	−	0.366556i
$983$	2.52719	−	17.5770i	0.0806049	−	0.560619i	−0.908999	−	0.416799i	$-0.863152\pi$
$983$	2.52719	−	17.5770i	0.0806049	−	0.560619i	0.989604	−	0.143821i	$-0.0459389\pi$
$984$	8.32320	+	16.2587i	0.265334	+	0.518310i
$985$	−0.819173	−	5.69747i	−0.0261010	−	0.181537i
$986$	4.04403	−	2.68499i	0.128788	−	0.0855075i
$987$	−21.6081	−	18.7235i	−0.687794	−	0.595977i
$988$	−2.12694	+	0.0634591i	−0.0676671	+	0.00201890i
$989$	5.02607	−	9.23890i	0.159820	−	0.293780i
$990$	0.141716	+	9.50185i	0.00450403	+	0.301989i
$991$	−29.7034	+	34.2796i	−0.943561	+	1.08893i	0.0523540	+	0.998629i	$0.483328\pi$
$991$	−29.7034	+	34.2796i	−0.943561	+	1.08893i	−0.995915	+	0.0902986i	$0.971218\pi$
$992$	30.3908	+	40.3305i	0.964909	+	1.28049i
$993$	−2.59305	−	18.0351i	−0.0822880	−	0.572326i
$994$	71.2554	−	33.8344i	2.26008	−	1.07316i
$995$	4.15671	+	0.597645i	0.131777	+	0.0189466i
$996$	−2.81536	+	0.918711i	−0.0892081	+	0.0291105i
$997$	−23.7249	+	36.9167i	−0.751375	+	1.16916i	0.229269	+	0.973363i	$0.426366\pi$
$997$	−23.7249	+	36.9167i	−0.751375	+	1.16916i	−0.980644	+	0.195799i	$0.937270\pi$
$998$	−2.69549	+	6.14313i	−0.0853243	+	0.194457i
$999$	−8.45354	−	2.48218i	−0.267458	−	0.0785328i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.bb.a.85.12	yes	480
8.5	even	2	inner	552.2.bb.a.85.38	yes	480
23.13	even	11	inner	552.2.bb.a.13.38	yes	480
184.13	even	22	inner	552.2.bb.a.13.12	✓	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.bb.a.13.12	✓	480	184.13	even	22	inner
552.2.bb.a.13.38	yes	480	23.13	even	11	inner
552.2.bb.a.85.12	yes	480	1.1	even	1	trivial
552.2.bb.a.85.38	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)

\(f(q)\)	\(=\)	\(q+(-1.08248 - 0.910071i) q^{2} +(0.540641 + 0.841254i) q^{3} +(0.343541 + 1.97027i) q^{4} +(-2.04961 + 0.936025i) q^{5} +(0.180366 - 1.40266i) q^{6} +(3.54305 - 1.04033i) q^{7} +(1.42121 - 2.44544i) q^{8} +(-0.415415 + 0.909632i) q^{9} +O(q^{10})\)	\(q+(-1.08248 - 0.910071i) q^{2} +(0.540641 + 0.841254i) q^{3} +(0.343541 + 1.97027i) q^{4} +(-2.04961 + 0.936025i) q^{5} +(0.180366 - 1.40266i) q^{6} +(3.54305 - 1.04033i) q^{7} +(1.42121 - 2.44544i) q^{8} +(-0.415415 + 0.909632i) q^{9} +(3.07052 + 0.852058i) q^{10} +(2.25379 - 1.95292i) q^{11} +(-1.47177 + 1.35422i) q^{12} +(-1.41971 + 4.83508i) q^{13} +(-4.78207 - 2.09828i) q^{14} +(-1.89554 - 1.21819i) q^{15} +(-3.76396 + 1.35374i) q^{16} +(0.385395 - 2.68048i) q^{17} +(1.27751 - 0.606604i) q^{18} +(0.208985 - 0.0300475i) q^{19} +(-2.54835 - 3.71673i) q^{20} +(2.79070 + 2.41816i) q^{21} +(-4.21699 + 0.0628947i) q^{22} +(2.30498 + 4.20560i) q^{23} +(2.82560 - 0.126503i) q^{24} +(0.0504502 - 0.0582227i) q^{25} +(5.93707 - 3.94186i) q^{26} +(-0.989821 + 0.142315i) q^{27} +(3.26693 + 6.62338i) q^{28} +(-1.25460 - 0.180384i) q^{29} +(0.943250 + 3.04374i) q^{30} +(7.50991 + 4.82632i) q^{31} +(5.30642 + 1.96007i) q^{32} +(2.86140 + 0.840182i) q^{33} +(-2.85661 + 2.55084i) q^{34} +(-6.28809 + 5.44866i) q^{35} +(-1.93494 - 0.505986i) q^{36} +(8.01424 + 3.65998i) q^{37} +(-0.253568 - 0.157665i) q^{38} +(-4.83508 + 1.41971i) q^{39} +(-0.623940 + 6.34248i) q^{40} +(2.68265 + 5.87419i) q^{41} +(-0.820194 - 5.15735i) q^{42} +(-1.18566 - 1.84492i) q^{43} +(4.62207 + 3.76968i) q^{44} -2.25323i q^{45} +(1.33229 - 6.65019i) q^{46} -7.74290 q^{47} +(-3.17379 - 2.43456i) q^{48} +(5.58214 - 3.58742i) q^{49} +(-0.107598 + 0.0171118i) q^{50} +(2.46333 - 1.12496i) q^{51} +(-10.0142 - 1.13616i) q^{52} +(1.35011 + 4.59806i) q^{53} +(1.20098 + 0.746754i) q^{54} +(-2.79141 + 6.11234i) q^{55} +(2.49136 - 10.1428i) q^{56} +(0.138263 + 0.159564i) q^{57} +(1.19392 + 1.33704i) q^{58} +(0.831099 - 2.83046i) q^{59} +(1.74897 - 4.15322i) q^{60} +(2.51896 - 3.91958i) q^{61} +(-3.73705 - 12.0590i) q^{62} +(-0.525516 + 3.65504i) q^{63} +(-3.96031 - 6.95097i) q^{64} +(-1.61591 - 11.2389i) q^{65} +(-2.33279 - 3.51356i) q^{66} +(9.06703 + 7.85662i) q^{67} +(5.41368 - 0.161521i) q^{68} +(-2.29181 + 4.21279i) q^{69} +(11.7654 - 0.175476i) q^{70} +(-9.89160 + 11.4155i) q^{71} +(1.63405 + 2.30865i) q^{72} +(-2.26270 - 15.7374i) q^{73} +(-5.34444 - 11.2554i) q^{74} +(0.0762555 + 0.0109639i) q^{75} +(0.130997 + 0.401435i) q^{76} +(5.95362 - 9.26401i) q^{77} +(6.52593 + 2.86346i) q^{78} +(2.60042 + 0.763551i) q^{79} +(6.44751 - 6.29780i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(2.44200 - 8.80012i) q^{82} +(1.34692 + 0.615119i) q^{83} +(-3.80571 + 6.32918i) q^{84} +(1.71909 + 5.85468i) q^{85} +(-0.395553 + 3.07613i) q^{86} +(-0.526538 - 1.15296i) q^{87} +(-1.57263 - 8.28703i) q^{88} +(6.87125 - 4.41588i) q^{89} +(-2.05060 + 2.43908i) q^{90} +18.6079i q^{91} +(-7.49432 + 5.98624i) q^{92} +8.92704i q^{93} +(8.38156 + 7.04659i) q^{94} +(-0.400212 + 0.257201i) q^{95} +(1.21995 + 5.52374i) q^{96} +(-3.69982 - 8.10148i) q^{97} +(-9.30739 - 1.19682i) q^{98} +(0.840182 + 2.86140i) 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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