LMFDB - Embedded newform 150.2.l.a.23.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,2,Mod(17,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 13]))

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

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

chi := DirichletCharacter("150.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	150.l (of order $20$, degree $8$, 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:	$1.19775603032$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			23.9
Character	$\chi$	$=$	150.23
Dual form			150.2.l.a.137.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.987688 + 0.156434i) q^{2} +(0.513483 - 1.65419i) q^{3} +(0.951057 + 0.309017i) q^{4} +(-0.545143 - 2.16860i) q^{5} +(0.765933 - 1.55349i) q^{6} +(-1.41702 + 1.41702i) q^{7} +(0.891007 + 0.453990i) q^{8} +(-2.47267 - 1.69880i) q^{9} +O(q^{10})$	\(q+(0.987688 + 0.156434i) q^{2} +(0.513483 - 1.65419i) q^{3} +(0.951057 + 0.309017i) q^{4} +(-0.545143 - 2.16860i) q^{5} +(0.765933 - 1.55349i) q^{6} +(-1.41702 + 1.41702i) q^{7} +(0.891007 + 0.453990i) q^{8} +(-2.47267 - 1.69880i) q^{9} +(-0.199188 - 2.22718i) q^{10} +(2.37267 + 3.26569i) q^{11} +(0.999524 - 1.41455i) q^{12} +(0.301677 + 1.90471i) q^{13} +(-1.62125 + 1.17790i) q^{14} +(-3.86719 - 0.211770i) q^{15} +(0.809017 + 0.587785i) q^{16} +(-1.78386 + 3.50102i) q^{17} +(-2.17648 - 2.06469i) q^{18} +(6.42284 - 2.08691i) q^{19} +(0.151672 - 2.23092i) q^{20} +(1.61640 + 3.07163i) q^{21} +(1.83259 + 3.59666i) q^{22} +(0.317431 - 2.00418i) q^{23} +(1.20850 - 1.24077i) q^{24} +(-4.40564 + 2.36439i) q^{25} +1.92846i q^{26} +(-4.07980 + 3.21796i) q^{27} +(-1.78555 + 0.909783i) q^{28} +(-1.79717 + 5.53113i) q^{29} +(-3.78645 - 0.814125i) q^{30} +(-2.88201 - 8.86991i) q^{31} +(0.707107 + 0.707107i) q^{32} +(6.62039 - 2.24795i) q^{33} +(-2.30957 + 3.17886i) q^{34} +(3.84543 + 2.30047i) q^{35} +(-1.82669 - 2.37975i) q^{36} +(-6.31949 + 1.00091i) q^{37} +(6.67023 - 1.05646i) q^{38} +(3.30566 + 0.479008i) q^{39} +(0.498797 - 2.17973i) q^{40} +(-0.756950 + 1.04185i) q^{41} +(1.11599 + 3.28668i) q^{42} +(-6.68950 - 6.68950i) q^{43} +(1.24738 + 3.83905i) q^{44} +(-2.33605 + 6.28831i) q^{45} +(0.627046 - 1.92985i) q^{46} +(1.18073 - 0.601612i) q^{47} +(1.38772 - 1.03645i) q^{48} +2.98411i q^{49} +(-4.72127 + 1.64609i) q^{50} +(4.87536 + 4.74855i) q^{51} +(-0.301677 + 1.90471i) q^{52} +(-4.96215 - 9.73877i) q^{53} +(-4.53297 + 2.54012i) q^{54} +(5.78854 - 6.92563i) q^{55} +(-1.90589 + 0.619261i) q^{56} +(-0.154113 - 11.6962i) q^{57} +(-2.64031 + 5.18189i) q^{58} +(3.81952 + 2.77504i) q^{59} +(-3.61247 - 1.39643i) q^{60} +(-0.433671 + 0.315081i) q^{61} +(-1.45897 - 9.21155i) q^{62} +(5.91105 - 1.09660i) q^{63} +(0.587785 + 0.809017i) q^{64} +(3.96610 - 1.69256i) q^{65} +(6.89054 - 1.18462i) q^{66} +(-1.35097 - 0.688356i) q^{67} +(-2.77842 + 2.77842i) q^{68} +(-3.15229 - 1.55420i) q^{69} +(3.43821 + 2.87370i) q^{70} +(-0.520251 - 0.169040i) q^{71} +(-1.43193 - 2.63621i) q^{72} +(7.37855 + 1.16865i) q^{73} -6.39826 q^{74} +(1.64893 + 8.50183i) q^{75} +6.75337 q^{76} +(-7.98967 - 1.26544i) q^{77} +(3.19003 + 0.990230i) q^{78} +(10.2088 + 3.31704i) q^{79} +(0.833640 - 2.07486i) q^{80} +(3.22819 + 8.40112i) q^{81} +(-0.910612 + 0.910612i) q^{82} +(3.00600 + 1.53163i) q^{83} +(0.588101 + 3.42079i) q^{84} +(8.56476 + 1.95991i) q^{85} +(-5.56067 - 7.65361i) q^{86} +(8.22670 + 5.81300i) q^{87} +(0.631467 + 3.98692i) q^{88} +(11.4865 - 8.34544i) q^{89} +(-3.29099 + 5.84546i) q^{90} +(-3.12650 - 2.27153i) q^{91} +(0.921220 - 1.80800i) q^{92} +(-16.1523 + 0.212830i) q^{93} +(1.26031 - 0.409498i) q^{94} +(-8.02703 - 12.7909i) q^{95} +(1.53277 - 0.806599i) q^{96} +(-4.82956 - 9.47854i) q^{97} +(-0.466817 + 2.94737i) q^{98} +(-0.319074 - 12.1057i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{3} + 4 q^{7}+O(q^{10}) $ 80 * q + 4 * q^3 + 4 * q^7	$ 80 q + 4 q^{3} + 4 q^{7} - 4 q^{10} - 4 q^{12} - 8 q^{15} + 20 q^{16} - 8 q^{18} - 40 q^{19} - 36 q^{22} - 104 q^{25} + 4 q^{27} - 16 q^{28} + 12 q^{30} + 4 q^{33} - 40 q^{34} - 24 q^{37} - 40 q^{39} - 8 q^{40} - 4 q^{42} - 24 q^{43} - 72 q^{45} - 4 q^{48} - 12 q^{55} - 64 q^{57} + 20 q^{58} + 24 q^{60} + 64 q^{63} + 96 q^{67} + 140 q^{69} + 76 q^{70} + 8 q^{72} + 100 q^{73} + 132 q^{75} + 100 q^{78} + 80 q^{79} - 40 q^{81} + 96 q^{82} + 60 q^{84} + 32 q^{85} + 80 q^{87} + 4 q^{88} + 52 q^{90} + 12 q^{93} - 32 q^{97}+O(q^{100}) $ 80 * q + 4 * q^3 + 4 * q^7 - 4 * q^10 - 4 * q^12 - 8 * q^15 + 20 * q^16 - 8 * q^18 - 40 * q^19 - 36 * q^22 - 104 * q^25 + 4 * q^27 - 16 * q^28 + 12 * q^30 + 4 * q^33 - 40 * q^34 - 24 * q^37 - 40 * q^39 - 8 * q^40 - 4 * q^42 - 24 * q^43 - 72 * q^45 - 4 * q^48 - 12 * q^55 - 64 * q^57 + 20 * q^58 + 24 * q^60 + 64 * q^63 + 96 * q^67 + 140 * q^69 + 76 * q^70 + 8 * q^72 + 100 * q^73 + 132 * q^75 + 100 * q^78 + 80 * q^79 - 40 * q^81 + 96 * q^82 + 60 * q^84 + 32 * q^85 + 80 * q^87 + 4 * q^88 + 52 * q^90 + 12 * q^93 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{11}{20}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.987688	+	0.156434i	0.698401	+	0.110616i
$2$	0.987688	+	0.156434i	0.698401	+	0.110616i
$3$	0.513483	−	1.65419i	0.296460	−	0.955045i
$3$	0.513483	−	1.65419i	0.296460	−	0.955045i
$4$	0.951057	+	0.309017i	0.475528	+	0.154508i
$5$	−0.545143	−	2.16860i	−0.243795	−	0.969827i
$5$	−0.545143	−	2.16860i	−0.243795	−	0.969827i
$6$	0.765933	−	1.55349i	0.312691	−	0.634212i
$7$	−1.41702	+	1.41702i	−0.535583	+	0.535583i	−0.922229	−	0.386645i	$-0.873634\pi$
$7$	−1.41702	+	1.41702i	−0.535583	+	0.535583i	0.386645	+	0.922229i	$0.373634\pi$
$8$	0.891007	+	0.453990i	0.315018	+	0.160510i
$9$	−2.47267	−	1.69880i	−0.824223	−	0.566265i
$10$	−0.199188	−	2.22718i	−0.0629888	−	0.704296i
$11$	2.37267	+	3.26569i	0.715386	+	0.984644i	0.999664	+	0.0259024i	$0.00824591\pi$
$11$	2.37267	+	3.26569i	0.715386	+	0.984644i	−0.284279	+	0.958742i	$0.591754\pi$
$12$	0.999524	−	1.41455i	0.288538	−	0.408345i
$13$	0.301677	+	1.90471i	0.0836701	+	0.528272i	0.993549	+	0.113399i	$0.0361740\pi$
$13$	0.301677	+	1.90471i	0.0836701	+	0.528272i	−0.909879	+	0.414873i	$0.863826\pi$
$14$	−1.62125	+	1.17790i	−0.433296	+	0.314808i
$15$	−3.86719	−	0.211770i	−0.998504	−	0.0546789i
$16$	0.809017	+	0.587785i	0.202254	+	0.146946i
$17$	−1.78386	+	3.50102i	−0.432649	+	0.849121i	0.567028	+	0.823699i	$0.308093\pi$
$17$	−1.78386	+	3.50102i	−0.432649	+	0.849121i	−0.999677	+	0.0254227i	$0.991907\pi$
$18$	−2.17648	−	2.06469i	−0.513001	−	0.486652i
$19$	6.42284	−	2.08691i	1.47350	−	0.478769i	0.541336	−	0.840806i	$-0.317919\pi$
$19$	6.42284	−	2.08691i	1.47350	−	0.478769i	0.932164	+	0.362037i	$0.117919\pi$
$20$	0.151672	−	2.23092i	0.0339148	−	0.498848i
$21$	1.61640	+	3.07163i	0.352727	+	0.670285i
$22$	1.83259	+	3.59666i	0.390709	+	0.766810i
$23$	0.317431	−	2.00418i	0.0661889	−	0.417900i	−0.932239	−	0.361844i	$-0.882147\pi$
$23$	0.317431	−	2.00418i	0.0661889	−	0.417900i	0.998428	−	0.0560564i	$-0.0178527\pi$
$24$	1.20850	−	1.24077i	0.246684	−	0.253272i
$25$	−4.40564	+	2.36439i	−0.881128	+	0.472879i
$26$			1.92846i			0.378201i
$27$	−4.07980	+	3.21796i	−0.785158	+	0.619296i
$28$	−1.78555	+	0.909783i	−0.337437	+	0.171933i
$29$	−1.79717	+	5.53113i	−0.333727	+	1.02710i	0.633619	+	0.773645i	$0.281569\pi$
$29$	−1.79717	+	5.53113i	−0.333727	+	1.02710i	−0.967346	+	0.253460i	$0.918431\pi$
$30$	−3.78645	−	0.814125i	−0.691308	−	0.148638i
$31$	−2.88201	−	8.86991i	−0.517624	−	1.59308i	−0.778457	−	0.627698i	$-0.783997\pi$
$31$	−2.88201	−	8.86991i	−0.517624	−	1.59308i	0.260833	−	0.965384i	$-0.416003\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	6.62039	−	2.24795i	1.15246	−	0.391319i
$34$	−2.30957	+	3.17886i	−0.396089	+	0.545169i
$35$	3.84543	+	2.30047i	0.649996	+	0.388850i
$36$	−1.82669	−	2.37975i	−0.304449	−	0.396625i
$37$	−6.31949	+	1.00091i	−1.03892	+	0.164548i	−0.652510	−	0.757780i	$-0.726284\pi$
$37$	−6.31949	+	1.00091i	−1.03892	+	0.164548i	−0.386407	+	0.922328i	$0.626284\pi$
$38$	6.67023	−	1.05646i	1.08205	−	0.171380i
$39$	3.30566	+	0.479008i	0.529329	+	0.0767027i
$40$	0.498797	−	2.17973i	0.0788667	−	0.344645i
$41$	−0.756950	+	1.04185i	−0.118216	+	0.162710i	−0.864024	−	0.503451i	$-0.832064\pi$
$41$	−0.756950	+	1.04185i	−0.118216	+	0.162710i	0.745808	+	0.666161i	$0.232064\pi$
$42$	1.11599	+	3.28668i	0.172201	+	0.507145i
$43$	−6.68950	−	6.68950i	−1.02014	−	1.02014i	−0.999793	−	0.0203466i	$-0.993523\pi$
$43$	−6.68950	−	6.68950i	−1.02014	−	1.02014i	−0.0203466	−	0.999793i	$-0.506477\pi$
$44$	1.24738	+	3.83905i	0.188050	+	0.578759i
$45$	−2.33605	+	6.28831i	−0.348237	+	0.937407i
$46$	0.627046	−	1.92985i	0.0924528	−	0.284541i
$47$	1.18073	−	0.601612i	0.172227	−	0.0877541i	−0.365752	−	0.930712i	$-0.619188\pi$
$47$	1.18073	−	0.601612i	0.172227	−	0.0877541i	0.537979	+	0.842958i	$0.319188\pi$
$48$	1.38772	−	1.03645i	0.200301	−	0.149598i
$49$			2.98411i			0.426301i
$50$	−4.72127	+	1.64609i	−0.667688	+	0.232792i
$51$	4.87536	+	4.74855i	0.682686	+	0.664930i
$52$	−0.301677	+	1.90471i	−0.0418351	+	0.264136i
$53$	−4.96215	−	9.73877i	−0.681604	−	1.33772i	−0.929459	−	0.368926i	$-0.879725\pi$
$53$	−4.96215	−	9.73877i	−0.681604	−	1.33772i	0.247854	−	0.968797i	$-0.420275\pi$
$54$	−4.53297	+	2.54012i	−0.616859	+	0.345666i
$55$	5.78854	−	6.92563i	0.780526	−	0.933852i
$56$	−1.90589	+	0.619261i	−0.254685	+	0.0827522i
$57$	−0.154113	−	11.6962i	−0.0204128	−	1.54920i
$58$	−2.64031	+	5.18189i	−0.346689	+	0.680416i
$59$	3.81952	+	2.77504i	0.497259	+	0.361280i	0.807969	−	0.589225i	$-0.200567\pi$
$59$	3.81952	+	2.77504i	0.497259	+	0.361280i	−0.310710	+	0.950505i	$0.600567\pi$
$60$	−3.61247	−	1.39643i	−0.466369	−	0.180279i
$61$	−0.433671	+	0.315081i	−0.0555259	+	0.0403419i	−0.615202	−	0.788370i	$-0.710926\pi$
$61$	−0.433671	+	0.315081i	−0.0555259	+	0.0403419i	0.559676	+	0.828711i	$0.310926\pi$
$62$	−1.45897	−	9.21155i	−0.185289	−	1.16987i
$63$	5.91105	−	1.09660i	0.744722	−	0.138158i
$64$	0.587785	+	0.809017i	0.0734732	+	0.101127i
$65$	3.96610	−	1.69256i	0.491934	−	0.209936i
$66$	6.89054	−	1.18462i	0.848167	−	0.145817i
$67$	−1.35097	−	0.688356i	−0.165048	−	0.0840960i	0.369515	−	0.929225i	$-0.379524\pi$
$67$	−1.35097	−	0.688356i	−0.165048	−	0.0840960i	−0.534563	+	0.845129i	$0.679524\pi$
$68$	−2.77842	+	2.77842i	−0.336933	+	0.336933i
$69$	−3.15229	−	1.55420i	−0.379491	−	0.187104i
$70$	3.43821	+	2.87370i	0.410945	+	0.343473i
$71$	−0.520251	−	0.169040i	−0.0617424	−	0.0200613i	0.277983	−	0.960586i	$-0.410334\pi$
$71$	−0.520251	−	0.169040i	−0.0617424	−	0.0200613i	−0.339725	+	0.940525i	$0.610334\pi$
$72$	−1.43193	−	2.63621i	−0.168754	−	0.310680i
$73$	7.37855	+	1.16865i	0.863594	+	0.136780i	0.572490	−	0.819912i	$-0.305977\pi$
$73$	7.37855	+	1.16865i	0.863594	+	0.136780i	0.291104	+	0.956691i	$0.405977\pi$
$74$	−6.39826			−0.743783
$75$	1.64893	+	8.50183i	0.190402	+	0.981706i
$76$	6.75337			0.774665
$77$	−7.98967	−	1.26544i	−0.910508	−	0.144210i
$78$	3.19003	+	0.990230i	0.361199	+	0.112121i
$79$	10.2088	+	3.31704i	1.14858	+	0.373196i	0.820607	−	0.571492i	$-0.193635\pi$
$79$	10.2088	+	3.31704i	1.14858	+	0.373196i	0.327971	+	0.944688i	$0.393635\pi$
$80$	0.833640	−	2.07486i	0.0932038	−	0.231976i
$81$	3.22819	+	8.40112i	0.358688	+	0.933458i
$82$	−0.910612	+	0.910612i	−0.100560	+	0.100560i
$83$	3.00600	+	1.53163i	0.329952	+	0.168119i	0.611116	−	0.791541i	$-0.290721\pi$
$83$	3.00600	+	1.53163i	0.329952	+	0.168119i	−0.281165	+	0.959659i	$0.590721\pi$
$84$	0.588101	+	3.42079i	0.0641671	+	0.373239i
$85$	8.56476	+	1.95991i	0.928978	+	0.212583i
$86$	−5.56067	−	7.65361i	−0.599623	−	0.825310i
$87$	8.22670	+	5.81300i	0.881995	+	0.623219i
$88$	0.631467	+	3.98692i	0.0673146	+	0.425007i
$89$	11.4865	−	8.34544i	1.21757	−	0.884615i	0.221672	−	0.975121i	$-0.428849\pi$
$89$	11.4865	−	8.34544i	1.21757	−	0.884615i	0.995896	+	0.0905063i	$0.0288485\pi$
$90$	−3.29099	+	5.84546i	−0.346901	+	0.616165i
$91$	−3.12650	−	2.27153i	−0.327746	−	0.238122i
$92$	0.921220	−	1.80800i	0.0960439	−	0.188497i
$93$	−16.1523	+	0.212830i	−1.67492	+	0.0220694i
$94$	1.26031	−	0.409498i	0.129991	−	0.0422365i
$95$	−8.02703	−	12.7909i	−0.823556	−	1.31232i
$96$	1.53277	−	0.806599i	0.156438	−	0.0823232i
$97$	−4.82956	−	9.47854i	−0.490367	−	0.962400i	−0.995076	−	0.0991108i	$-0.968400\pi$
$97$	−4.82956	−	9.47854i	−0.490367	−	0.962400i	0.504709	−	0.863290i	$-0.331600\pi$
$98$	−0.466817	+	2.94737i	−0.0471557	+	0.297729i
$99$	−0.319074	−	12.1057i	−0.0320681	−	1.21666i
$100$	−4.92065	+	0.887255i	−0.492065	+	0.0887255i
$101$		−	11.9603i		−	1.19010i	−0.803690	−	0.595048i	$-0.797133\pi$
$101$		−	11.9603i		−	1.19010i	0.803690	−	0.595048i	$-0.202867\pi$
$102$	4.07250	+	5.45276i	0.403237	+	0.539904i
$103$	2.58470	−	1.31697i	0.254678	−	0.129765i	−0.321991	−	0.946743i	$-0.604352\pi$
$103$	2.58470	−	1.31697i	0.254678	−	0.129765i	0.576669	+	0.816978i	$0.304352\pi$
$104$	−0.595926	+	1.83407i	−0.0584353	+	0.179845i
$105$	5.77997	−	5.17980i	0.564067	−	0.505497i
$106$	−3.37758	−	10.3951i	−0.328060	−	1.00966i
$107$	10.4011	+	10.4011i	1.00551	+	1.00551i	0.999985	+	0.00552544i	$0.00175881\pi$
$107$	10.4011	+	10.4011i	1.00551	+	1.00551i	0.00552544	+	0.999985i	$0.498241\pi$
$108$	−4.87452	+	1.79973i	−0.469051	+	0.173179i
$109$	−7.36263	+	10.1338i	−0.705212	+	0.970641i	0.294675	+	0.955598i	$0.404789\pi$
$109$	−7.36263	+	10.1338i	−0.705212	+	0.970641i	−0.999887	+	0.0150436i	$0.995211\pi$
$110$	6.80068	−	5.93484i	0.648419	−	0.565865i
$111$	−1.58926	+	10.9676i	−0.150846	+	1.04100i
$112$	−1.97930	+	0.313490i	−0.187026	+	0.0296220i
$113$	−14.3852	+	2.27840i	−1.35325	+	0.214333i	−0.790585	−	0.612353i	$-0.790223\pi$
$113$	−14.3852	+	2.27840i	−1.35325	+	0.214333i	−0.562663	+	0.826686i	$0.690223\pi$
$114$	1.67747	−	11.5763i	0.157109	−	1.08422i
$115$	−4.51931	+	0.404185i	−0.421428	+	0.0376904i
$116$	−3.41843	+	4.70506i	−0.317393	+	0.436854i
$117$	2.48977	−	5.22221i	0.230179	−	0.482794i
$118$	3.33838	+	3.33838i	0.307323	+	0.307323i
$119$	−2.43325	−	7.48877i	−0.223056	−	0.686495i
$120$	−3.34955	−	1.94436i	−0.305771	−	0.177495i
$121$	−1.63603	+	5.03519i	−0.148730	+	0.457744i
$122$	−0.477622	+	0.243360i	−0.0432418	+	0.0220328i
$123$	1.33474	+	1.78711i	0.120349	+	0.161138i
$124$		−	9.32637i		−	0.837533i
$125$	7.52912	+	8.26513i	0.673425	+	0.739255i
$126$	6.00982	−	0.158403i	0.535397	−	0.0141117i
$127$	0.572870	−	3.61696i	0.0508340	−	0.320953i	−0.949147	−	0.314832i	$-0.898052\pi$
$127$	0.572870	−	3.61696i	0.0508340	−	0.320953i	0.999981	−	0.00612070i	$-0.00194829\pi$
$128$	0.453990	+	0.891007i	0.0401275	+	0.0787546i
$129$	−14.5006	+	7.63074i	−1.27671	+	0.671849i
$130$	4.18205	−	1.05128i	0.366790	−	0.0922037i
$131$	−2.34952	+	0.763407i	−0.205279	+	0.0666992i	−0.409852	−	0.912152i	$-0.634420\pi$
$131$	−2.34952	+	0.763407i	−0.205279	+	0.0666992i	0.204573	+	0.978851i	$0.434420\pi$
$132$	6.99103	−	0.0921166i	0.608491	−	0.00801772i
$133$	−6.14410	+	12.0585i	−0.532761	+	1.04560i
$134$	−1.22666	−	0.891220i	−0.105967	−	0.0769897i
$135$	9.20253	+	7.09320i	0.792027	+	0.610485i
$136$	−3.17886	+	2.30957i	−0.272585	+	0.198044i
$137$	0.709676	+	4.48072i	0.0606317	+	0.382814i	0.999280	+	0.0379379i	$0.0120789\pi$
$137$	0.709676	+	4.48072i	0.0606317	+	0.382814i	−0.938648	+	0.344876i	$0.887921\pi$
$138$	−2.87035	−	2.02820i	−0.244341	−	0.172651i
$139$	3.37296	+	4.64248i	0.286091	+	0.393770i	0.927739	−	0.373228i	$-0.121749\pi$
$139$	3.37296	+	4.64248i	0.286091	+	0.393770i	−0.641649	+	0.766999i	$0.721749\pi$
$140$	2.94633	+	3.37618i	0.249011	+	0.285339i
$141$	−0.388893	−	2.26206i	−0.0327507	−	0.190500i
$142$	−0.487402	−	0.248344i	−0.0409019	−	0.0208405i
$143$	−5.50443	+	5.50443i	−0.460304	+	0.460304i
$144$	−1.00191	−	2.82775i	−0.0834921	−	0.235646i
$145$	12.9745	+	0.882088i	1.07747	+	0.0732534i
$146$	7.10489	+	2.30852i	0.588005	+	0.191054i
$147$	4.93627	+	1.53229i	0.407137	+	0.126381i
$148$	−6.31949	−	1.00091i	−0.519459	−	0.0822742i
$149$	−15.3490			−1.25744			−0.628720	−	0.777632i	$-0.716421\pi$
$149$	−15.3490			−1.25744			−0.628720	+	0.777632i	$0.716421\pi$
$150$	0.298648	+	8.65510i	0.0243845	+	0.706686i
$151$	−22.6955			−1.84694			−0.923468	−	0.383676i	$-0.874658\pi$
$151$	−22.6955			−1.84694			−0.923468	+	0.383676i	$0.874658\pi$
$152$	6.67023	+	1.05646i	0.541027	+	0.0856902i
$153$	10.3584	−	5.62645i	0.837427	−	0.454872i
$154$	−7.69335	−	2.49972i	−0.619948	−	0.201433i
$155$	−17.6642	+	11.0853i	−1.41882	+	0.890392i
$156$	2.99585	+	1.47707i	0.239860	+	0.118260i
$157$	0.431200	−	0.431200i	0.0344135	−	0.0344135i	−0.689691	−	0.724104i	$-0.742253\pi$
$157$	0.431200	−	0.431200i	0.0344135	−	0.0344135i	0.724104	+	0.689691i	$0.242253\pi$
$158$	9.56420	+	4.87320i	0.760887	+	0.387691i
$159$	−18.6577	+	3.20763i	−1.47965	+	0.254382i
$160$	1.14796	−	1.91891i	0.0907539	−	0.151703i
$161$	2.39016	+	3.28977i	0.188371	+	0.259270i
$162$	1.87422	+	8.80269i	0.147253	+	0.691604i
$163$	3.70877	+	23.4163i	0.290493	+	1.83410i	0.512049	+	0.858956i	$0.328886\pi$
$163$	3.70877	+	23.4163i	0.290493	+	1.83410i	−0.221556	+	0.975148i	$0.571114\pi$
$164$	−1.04185	+	0.756950i	−0.0813550	+	0.0591079i
$165$	−8.48397	−	13.1315i	−0.660476	−	1.02229i
$166$	2.72939	+	1.98302i	0.211842	+	0.153912i
$167$	−1.54555	+	3.03330i	−0.119598	+	0.234724i	−0.943042	−	0.332673i	$-0.892050\pi$
$167$	−1.54555	+	3.03330i	−0.119598	+	0.234724i	0.823444	+	0.567397i	$0.192050\pi$
$168$	0.0457310	+	3.47068i	0.00352823	+	0.267768i
$169$	8.82681	−	2.86800i	0.678986	−	0.220616i
$170$	8.15271	+	3.27561i	0.625285	+	0.251228i
$171$	−19.4268	−	5.75086i	−1.48560	−	0.439779i
$172$	−4.29493	−	8.42926i	−0.327485	−	0.642725i
$173$	0.203505	−	1.28488i	0.0154722	−	0.0976874i	−0.978744	−	0.205087i	$-0.934252\pi$
$173$	0.203505	−	1.28488i	0.0154722	−	0.0976874i	0.994216	+	0.107399i	$0.0342523\pi$
$174$	7.21606	+	7.02837i	0.547048	+	0.532820i
$175$	2.89248	−	9.59327i	0.218651	−	0.725183i
$176$			4.03662i			0.304272i
$177$	6.55170	−	4.89326i	0.492456	−	0.367800i
$178$	12.6506	−	6.44581i	0.948203	−	0.483134i
$179$	7.13852	−	21.9701i	0.533558	−	1.64212i	−0.213186	−	0.977012i	$-0.568384\pi$
$179$	7.13852	−	21.9701i	0.533558	−	1.64212i	0.746744	−	0.665112i	$-0.231616\pi$
$180$	−4.16491	+	5.25866i	−0.310434	+	0.391958i
$181$	5.01359	+	15.4302i	0.372657	+	1.14692i	0.945046	+	0.326938i	$0.106017\pi$
$181$	5.01359	+	15.4302i	0.372657	+	1.14692i	−0.572389	+	0.819983i	$0.693983\pi$
$182$	−2.73266	−	2.73266i	−0.202558	−	0.202558i
$183$	0.298519	+	0.879162i	0.0220672	+	0.0649895i
$184$	1.19271	−	1.64163i	0.0879279	−	0.121022i
$185$	5.61560	+	13.1588i	0.412867	+	0.967454i
$186$	−15.9868	−	2.31657i	−1.17221	−	0.169859i
$187$	−15.6658	+	2.48121i	−1.14559	+	0.181444i
$188$	1.30885	−	0.207301i	0.0954576	−	0.0151190i
$189$	1.22125	−	10.3411i	0.0888329	−	0.752202i
$190$	−5.92727	−	13.8891i	−0.430009	−	1.00762i
$191$	3.27557	−	4.50844i	0.237012	−	0.326219i	−0.673898	−	0.738825i	$-0.735381\pi$
$191$	3.27557	−	4.50844i	0.237012	−	0.326219i	0.910910	+	0.412606i	$0.135381\pi$
$192$	1.64008	−	0.556890i	0.118363	−	0.0401901i
$193$	−6.12138	−	6.12138i	−0.440626	−	0.440626i	0.451596	−	0.892222i	$-0.350855\pi$
$193$	−6.12138	−	6.12138i	−0.440626	−	0.440626i	−0.892222	+	0.451596i	$0.850855\pi$
$194$	−3.28733	−	10.1174i	−0.236016	−	0.726384i
$195$	−0.763280	−	7.42977i	−0.0546596	−	0.532057i
$196$	−0.922140	+	2.83806i	−0.0658671	+	0.202718i
$197$	15.7984	−	8.04970i	1.12559	−	0.573518i	0.210834	−	0.977522i	$-0.432382\pi$
$197$	15.7984	−	8.04970i	1.12559	−	0.573518i	0.914757	+	0.404004i	$0.132382\pi$
$198$	1.57860	−	12.0065i	0.112186	−	0.853267i
$199$		−	10.3594i		−	0.734359i	−0.930150	−	0.367180i	$-0.880323\pi$
$199$		−	10.3594i		−	0.734359i	0.930150	−	0.367180i	$-0.119677\pi$
$200$	−4.99886	+	0.106572i	−0.353473	+	0.00753580i
$201$	−1.83237	+	1.88130i	−0.129246	+	0.132697i
$202$	1.87101	−	11.8131i	0.131644	−	0.831165i
$203$	−5.29109	−	10.3843i	−0.371362	−	0.728838i
$204$	3.16936	+	6.02270i	0.221899	+	0.421674i
$205$	2.67201	+	1.07356i	0.186621	+	0.0749808i
$206$	2.75890	−	0.896420i	0.192221	−	0.0624565i
$207$	−4.18959	+	4.41642i	−0.291197	+	0.306963i
$208$	−0.875501	+	1.71827i	−0.0607050	+	0.119140i
$209$	22.0545	+	16.0235i	1.52554	+	1.10837i
$210$	6.51911	−	4.21184i	0.449861	−	0.290645i
$211$	17.8594	−	12.9756i	1.22949	−	0.893278i	0.232640	−	0.972563i	$-0.425264\pi$
$211$	17.8594	−	12.9756i	1.22949	−	0.893278i	0.996852	+	0.0792851i	$0.0252638\pi$
$212$	−1.70984	−	10.7955i	−0.117432	−	0.741439i
$213$	−0.546764	+	0.773793i	−0.0374636	+	0.0530194i
$214$	8.64594	+	11.9001i	0.591024	+	0.813475i
$215$	−10.8601	+	18.1536i	−0.740653	+	1.23806i
$216$	−5.09605	+	1.01503i	−0.346742	+	0.0690640i
$217$	16.6527	+	8.48497i	1.13046	+	0.575998i
$218$	−8.85726	+	8.85726i	−0.599889	+	0.599889i
$219$	5.72192	−	11.6054i	0.386652	−	0.784222i
$220$	7.64536	−	4.79791i	0.515450	−	0.323475i
$221$	−7.20658	−	2.34156i	−0.484767	−	0.157510i
$222$	−3.28540	+	10.5839i	−0.220502	+	0.710346i
$223$	14.8047	+	2.34483i	0.991395	+	0.157022i	0.631004	−	0.775780i	$-0.282643\pi$
$223$	14.8047	+	2.34483i	0.991395	+	0.157022i	0.360391	+	0.932801i	$0.382643\pi$
$224$	−2.00397			−0.133896
$225$	14.9103	+	1.63791i	0.994020	+	0.109194i
$226$	−14.5645			−0.968819
$227$	−3.77582	−	0.598031i	−0.250610	−	0.0396927i	0.0298656	−	0.999554i	$-0.490492\pi$
$227$	−3.77582	−	0.598031i	−0.250610	−	0.0396927i	−0.280475	+	0.959861i	$0.590492\pi$
$228$	3.46774	−	11.1713i	0.229657	−	0.739840i
$229$	−21.4172	−	6.95886i	−1.41529	−	0.459854i	−0.501185	−	0.865340i	$-0.667102\pi$
$229$	−21.4172	−	6.95886i	−1.41529	−	0.459854i	−0.914101	+	0.405486i	$0.867102\pi$
$230$	−4.52689	−	0.307767i	−0.298495	−	0.0202935i
$231$	−6.19584	+	12.5666i	−0.407656	+	0.826823i
$232$	−4.11237	+	4.11237i	−0.269990	+	0.269990i
$233$	15.3187	+	7.80526i	1.00356	+	0.511340i	0.876934	−	0.480611i	$-0.159585\pi$
$233$	15.3187	+	7.80526i	1.00356	+	0.511340i	0.126626	+	0.991950i	$0.459585\pi$
$234$	3.27605	−	4.76843i	0.214162	−	0.311722i
$235$	−1.94832	−	2.23256i	−0.127094	−	0.145636i
$236$	2.77504	+	3.81952i	0.180640	+	0.248630i
$237$	10.7290	−	15.1840i	0.696926	−	0.986307i
$238$	−1.23179	−	7.77722i	−0.0798451	−	0.504122i
$239$	−2.77696	+	2.01758i	−0.179626	+	0.130506i	−0.673965	−	0.738763i	$-0.735410\pi$
$239$	−2.77696	+	2.01758i	−0.179626	+	0.130506i	0.494339	+	0.869269i	$0.335410\pi$
$240$	−3.00415	−	2.44440i	−0.193917	−	0.157786i
$241$	−6.92845	−	5.03381i	−0.446300	−	0.324256i	0.341833	−	0.939761i	$-0.388952\pi$
$241$	−6.92845	−	5.03381i	−0.446300	−	0.324256i	−0.788133	+	0.615505i	$0.788952\pi$
$242$	−2.40357	+	4.71726i	−0.154507	+	0.303237i
$243$	15.5546	−	1.02620i	0.997831	−	0.0658306i
$244$	−0.509811	+	0.165648i	−0.0326373	+	0.0106045i
$245$	6.47133	−	1.62677i	0.413438	−	0.103930i
$246$	1.03874	+	1.97391i	0.0662276	+	0.125852i
$247$	5.91258	+	11.6041i	0.376209	+	0.738351i
$248$	1.45897	−	9.21155i	0.0926444	−	0.584934i
$249$	4.07714	−	4.18602i	0.258378	−	0.265278i
$250$	6.14348	+	9.34118i	0.388548	+	0.590788i
$251$		−	11.9423i		−	0.753789i	−0.926256	−	0.376894i	$-0.876992\pi$
$251$		−	11.9423i		−	0.753789i	0.926256	−	0.376894i	$-0.123008\pi$
$252$	5.96061	+	0.783690i	0.375483	+	0.0493678i
$253$	7.29820	−	3.71862i	0.458834	−	0.233787i
$254$	1.13163	−	3.48281i	0.0710050	−	0.218531i
$255$	7.63993	−	13.1613i	0.478431	−	0.824194i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	2.09358	+	2.09358i	0.130594	+	0.130594i	0.769382	−	0.638789i	$-0.220564\pi$
$257$	2.09358	+	2.09358i	0.130594	+	0.130594i	−0.638789	+	0.769382i	$0.720564\pi$
$258$	−15.5158	+	5.26839i	−0.965973	+	0.327996i
$259$	7.53654	−	10.3732i	0.468298	−	0.644556i
$260$	4.29501	−	0.384125i	0.266366	−	0.0238224i
$261$	13.8401	−	10.6236i	0.856679	−	0.657586i
$262$	−2.44002	+	0.386461i	−0.150745	+	0.0238757i
$263$	22.4419	−	3.55445i	1.38383	−	0.219177i	0.580279	−	0.814418i	$-0.302943\pi$
$263$	22.4419	−	3.55445i	1.38383	−	0.219177i	0.803547	+	0.595241i	$0.202943\pi$
$264$	6.91936	+	1.00265i	0.425857	+	0.0617091i
$265$	−18.4144	+	16.0699i	−1.13119	+	0.987169i
$266$	−7.95482	+	10.9489i	−0.487741	+	0.671318i
$267$	−7.90679	−	23.2861i	−0.483887	−	1.42509i
$268$	−1.07214	−	1.07214i	−0.0654913	−	0.0654913i
$269$	3.72777	+	11.4729i	0.227286	+	0.699515i	0.998051	+	0.0623960i	$0.0198742\pi$
$269$	3.72777	+	11.4729i	0.227286	+	0.699515i	−0.770765	+	0.637119i	$0.780126\pi$
$270$	7.97961	+	8.44546i	0.485623	+	0.513975i
$271$	2.54786	−	7.84151i	0.154772	−	0.476338i	−0.843366	−	0.537339i	$-0.819429\pi$
$271$	2.54786	−	7.84151i	0.154772	−	0.476338i	0.998138	+	0.0610015i	$0.0194294\pi$
$272$	−3.50102	+	1.78386i	−0.212280	+	0.108162i
$273$	−5.36295	+	4.00542i	−0.324580	+	0.242419i
$274$			4.53657i			0.274064i
$275$	−18.1745	−	8.77755i	−1.09596	−	0.529306i
$276$	−2.51773	−	2.45225i	−0.151550	−	0.147608i
$277$	1.31490	−	8.30193i	0.0790045	−	0.498815i	−0.916178	−	0.400772i	$-0.868742\pi$
$277$	1.31490	−	8.30193i	0.0790045	−	0.498815i	0.995182	−	0.0980425i	$-0.0312581\pi$
$278$	2.60519	+	5.11297i	0.156249	+	0.306656i
$279$	−7.94190	+	26.8283i	−0.475469	+	1.60617i
$280$	2.38191	+	3.79552i	0.142346	+	0.226826i
$281$	0.214763	−	0.0697807i	0.0128117	−	0.00416277i	−0.302604	−	0.953116i	$-0.597856\pi$
$281$	0.214763	−	0.0697807i	0.0128117	−	0.00416277i	0.315416	+	0.948954i	$0.397856\pi$
$282$	−0.0302405	−	2.29505i	−0.00180080	−	0.136668i
$283$	−10.2206	+	20.0591i	−0.607554	+	1.19239i	0.358374	+	0.933578i	$0.383331\pi$
$283$	−10.2206	+	20.0591i	−0.607554	+	1.19239i	−0.965927	+	0.258813i	$0.916669\pi$
$284$	−0.442552	−	0.321533i	−0.0262606	−	0.0190795i
$285$	−25.2803	+	6.71030i	−1.49747	+	0.397484i
$286$	−6.29775	+	4.57558i	−0.372394	+	0.270560i
$287$	−0.403712	−	2.54894i	−0.0238304	−	0.150459i
$288$	−0.547212	−	2.94967i	−0.0322448	−	0.173811i
$289$	0.917376	+	1.26266i	0.0539633	+	0.0742741i
$290$	12.6768	+	2.90089i	0.744406	+	0.170346i
$291$	−18.1592	+	3.12192i	−1.06451	+	0.183010i
$292$	6.65629	+	3.39155i	0.389530	+	0.198475i
$293$	−7.91375	+	7.91375i	−0.462326	+	0.462326i	−0.899417	−	0.437091i	$-0.856009\pi$
$293$	−7.91375	+	7.91375i	−0.462326	+	0.462326i	0.437091	+	0.899417i	$0.356009\pi$
$294$	4.63580	+	2.28563i	0.270365	+	0.133301i
$295$	3.93577	−	9.79580i	0.229149	−	0.570334i
$296$	−6.08511	−	1.97717i	−0.353690	−	0.114921i
$297$	−20.1889	−	5.68825i	−1.17148	−	0.330066i
$298$	−15.1600	−	2.40111i	−0.878197	−	0.139093i
$299$	3.91315			0.226303
$300$	−1.05899	+	8.59526i	−0.0611406	+	0.496248i
$301$	18.9583			1.09274
$302$	−22.4161	−	3.55036i	−1.28990	−	0.204300i
$303$	−19.7846	−	6.14143i	−1.13660	−	0.352816i
$304$	6.42284	+	2.08691i	0.368375	+	0.119692i
$305$	0.919696	+	0.768695i	0.0526617	+	0.0440153i
$306$	11.1110	−	3.93677i	0.635176	−	0.225050i
$307$	−7.00526	+	7.00526i	−0.399811	+	0.399811i	−0.878166	−	0.478355i	$-0.841233\pi$
$307$	−7.00526	+	7.00526i	−0.399811	+	0.399811i	0.478355	+	0.878166i	$0.341233\pi$
$308$	−7.20759	−	3.67245i	−0.410690	−	0.209257i
$309$	−0.851315	−	4.95182i	−0.0484296	−	0.281699i
$310$	−19.1808	+	8.18552i	−1.08940	+	0.464907i
$311$	7.14665	+	9.83652i	0.405249	+	0.557778i	0.962052	−	0.272867i	$-0.0879719\pi$
$311$	7.14665	+	9.83652i	0.405249	+	0.557778i	−0.556802	+	0.830645i	$0.687972\pi$
$312$	2.72790	+	1.92754i	0.154437	+	0.109125i
$313$	−3.84643	−	24.2854i	−0.217413	−	1.37269i	−0.818958	−	0.573853i	$-0.805448\pi$
$313$	−3.84643	−	24.2854i	−0.217413	−	1.37269i	0.601545	−	0.798839i	$-0.294552\pi$
$314$	0.493346	−	0.358437i	0.0278411	−	0.0202278i
$315$	−5.60044	−	12.2209i	−0.315549	−	0.688569i
$316$	8.68411	+	6.30938i	0.488519	+	0.354930i
$317$	−4.73623	+	9.29537i	−0.266013	+	0.522080i	−0.984917	−	0.173030i	$-0.944644\pi$
$317$	−4.73623	+	9.29537i	−0.266013	+	0.522080i	0.718904	+	0.695110i	$0.244644\pi$
$318$	−18.9298	+	0.249427i	−1.06153	+	0.0139872i
$319$	−22.3271	+	7.25450i	−1.25008	+	0.406174i
$320$	1.43401	−	1.71570i	0.0801634	−	0.0959106i
$321$	22.5461	−	11.8645i	1.25840	−	0.662215i
$322$	1.84610	+	3.62317i	0.102879	+	0.201911i
$323$	−4.15113	+	26.2092i	−0.230975	+	1.45832i
$324$	0.474104	+	8.98750i	0.0263391	+	0.499306i
$325$	−5.83257	−	7.67819i	−0.323533	−	0.425910i
$326$			23.7082i			1.31307i
$327$	12.9826	+	17.3827i	0.717939	+	0.961266i
$328$	−1.14744	+	0.584649i	−0.0633567	+	0.0322818i
$329$	−0.820621	+	2.52561i	−0.0452423	+	0.139242i
$330$	−6.32530	−	14.2970i	−0.348196	−	0.787026i
$331$	5.72324	+	17.6143i	0.314578	+	0.968170i	0.975928	+	0.218093i	$0.0699837\pi$
$331$	5.72324	+	17.6143i	0.314578	+	0.968170i	−0.661350	+	0.750077i	$0.730016\pi$
$332$	2.38558	+	2.38558i	0.130926	+	0.130926i
$333$	17.3263	+	8.26060i	0.949478	+	0.452678i
$334$	−2.00103	+	2.75418i	−0.109492	+	0.150702i
$335$	−0.756293	+	3.30497i	−0.0413207	+	0.180570i
$336$	−0.497765	+	3.43510i	−0.0271553	+	0.187400i
$337$	11.7295	−	1.85777i	0.638947	−	0.101199i	0.171448	−	0.985193i	$-0.445155\pi$
$337$	11.7295	−	1.85777i	0.638947	−	0.101199i	0.467498	+	0.883994i	$0.345155\pi$
$338$	9.16679	−	1.45188i	0.498608	−	0.0789717i
$339$	−3.61768	+	24.9658i	−0.196485	+	1.35595i
$340$	7.53992	+	4.51064i	0.408910	+	0.244624i
$341$	22.1284	−	30.4571i	1.19832	−	1.64934i
$342$	−18.2880	−	8.71907i	−0.988901	−	0.471473i
$343$	−14.1477	−	14.1477i	−0.763903	−	0.763903i
$344$	−2.92342	−	8.99736i	−0.157620	−	0.485105i
$345$	−1.65199	+	7.68332i	−0.0889402	+	0.413656i
$346$	0.401998	−	1.23722i	0.0216115	−	0.0665135i
$347$	−6.98295	+	3.55799i	−0.374864	+	0.191003i	−0.631264	−	0.775568i	$-0.717464\pi$
$347$	−6.98295	+	3.55799i	−0.374864	+	0.191003i	0.256400	+	0.966571i	$0.417464\pi$
$348$	6.02774	+	8.07068i	0.323121	+	0.432634i
$349$			9.37804i			0.501995i	0.967988	+	0.250997i	$0.0807586\pi$
$349$			9.37804i			0.501995i	−0.967988	+	0.250997i	$0.919241\pi$
$350$	4.35759	−	9.02268i	0.232923	−	0.482282i
$351$	−7.36006	−	6.80006i	−0.392851	−	0.362961i
$352$	−0.631467	+	3.98692i	−0.0336573	+	0.212504i
$353$	−6.61368	−	12.9801i	−0.352010	−	0.690859i	0.645317	−	0.763915i	$-0.276725\pi$
$353$	−6.61368	−	12.9801i	−0.352010	−	0.690859i	−0.997328	+	0.0730551i	$0.976725\pi$
$354$	7.23652	−	3.80811i	0.384616	−	0.202399i
$355$	−0.0829681	+	1.22037i	−0.00440349	+	0.0647703i
$356$	13.5032	−	4.38746i	0.715669	−	0.232535i
$357$	−13.6373	+	0.179690i	−0.721761	+	0.00951021i
$358$	10.4875	−	20.5829i	0.554283	−	1.08784i
$359$	9.55110	+	6.93928i	0.504088	+	0.366241i	0.810576	−	0.585633i	$-0.199154\pi$
$359$	9.55110	+	6.93928i	0.504088	+	0.366241i	−0.306488	+	0.951874i	$0.599154\pi$
$360$	−4.93627	+	4.54239i	−0.260164	+	0.239405i
$361$	21.5264	−	15.6398i	1.13297	−	0.823148i
$362$	2.53804	+	16.0246i	0.133397	+	0.842233i
$363$	7.48907	+	5.29179i	0.393074	+	0.277747i
$364$	−2.27153	−	3.12650i	−0.119061	−	0.163873i
$365$	−1.48804	−	16.6382i	−0.0778875	−	0.870883i
$366$	0.157313	+	0.915037i	0.00822287	+	0.0478297i
$367$	−2.40607	−	1.22595i	−0.125596	−	0.0639943i	0.390064	−	0.920788i	$-0.372453\pi$
$367$	−2.40607	−	1.22595i	−0.125596	−	0.0639943i	−0.515659	+	0.856794i	$0.672453\pi$
$368$	1.43483	−	1.43483i	0.0747959	−	0.0747959i
$369$	3.64158	−	1.29025i	0.189573	−	0.0671679i
$370$	3.48797	+	13.8753i	0.181331	+	0.721340i
$371$	20.8315	+	6.76857i	1.08152	+	0.351407i
$372$	−15.4276	−	4.78894i	−0.799882	−	0.248295i
$373$	−21.1854	−	3.35543i	−1.09694	−	0.173738i	−0.418370	−	0.908277i	$-0.637398\pi$
$373$	−21.1854	−	3.35543i	−1.09694	−	0.173738i	−0.678566	+	0.734539i	$0.737398\pi$
$374$	−15.8610			−0.820154
$375$	17.5381	−	8.21057i	0.905666	−	0.423992i
$376$	1.32516			0.0683401
$377$	−11.0774	−	1.75448i	−0.570514	−	0.0903605i
$378$	2.82391	−	10.0227i	0.145246	−	0.515512i
$379$	−10.0630	−	3.26966i	−0.516901	−	0.167951i	0.0389376	−	0.999242i	$-0.487603\pi$
$379$	−10.0630	−	3.26966i	−0.516901	−	0.167951i	−0.555838	+	0.831290i	$0.687603\pi$
$380$	−3.68156	−	14.6454i	−0.188860	−	0.751291i
$381$	−5.68896	−	2.80488i	−0.291454	−	0.143698i
$382$	3.94052	−	3.94052i	0.201614	−	0.201614i
$383$	−0.124163	−	0.0632642i	−0.00634444	−	0.00323265i	0.450815	−	0.892617i	$-0.351133\pi$
$383$	−0.124163	−	0.0632642i	−0.00634444	−	0.00323265i	−0.457160	+	0.889385i	$0.651133\pi$
$384$	1.70701	−	0.293468i	0.0871104	−	0.0149760i
$385$	1.61128	+	18.0162i	0.0821187	+	0.918192i
$386$	−5.08842	−	7.00360i	−0.258994	−	0.356474i
$387$	5.17684	+	27.9050i	0.263153	+	1.41849i
$388$	−1.66415	−	10.5070i	−0.0844846	−	0.533415i
$389$	−28.0002	+	20.3434i	−1.41967	+	1.03145i	−0.427842	+	0.903854i	$0.640726\pi$
$389$	−28.0002	+	20.3434i	−1.41967	+	1.03145i	−0.991826	+	0.127596i	$0.959274\pi$
$390$	0.408390	−	7.45770i	0.0206796	−	0.377635i
$391$	6.45042	+	4.68650i	0.326212	+	0.237007i
$392$	−1.35476	+	2.65886i	−0.0684255	+	0.134293i
$393$	0.0563759	+	4.27855i	0.00284379	+	0.215824i
$394$	16.8632	−	5.47918i	0.849555	−	0.276037i
$395$	1.62807	−	23.9470i	0.0819170	−	1.20490i
$396$	3.43740	−	11.6118i	0.172736	−	0.583513i
$397$	13.8341	+	27.1510i	0.694315	+	1.36267i	0.921331	+	0.388778i	$0.127103\pi$
$397$	13.8341	+	27.1510i	0.694315	+	1.36267i	−0.227017	+	0.973891i	$0.572897\pi$
$398$	1.62057	−	10.2319i	0.0812318	−	0.512877i
$399$	16.7921	+	16.3553i	0.840656	+	0.818790i
$400$	−4.95399	−	0.676734i	−0.247700	−	0.0338367i
$401$			0.718503i			0.0358803i	0.999839	+	0.0179402i	$0.00571084\pi$
$401$			0.718503i			0.0358803i	−0.999839	+	0.0179402i	$0.994289\pi$
$402$	−2.10411	+	1.57150i	−0.104944	+	0.0783791i
$403$	16.0252	−	8.16524i	0.798272	−	0.406740i
$404$	3.69594	−	11.3749i	0.183880	−	0.565925i
$405$	16.4588	−	11.5805i	0.817846	−	0.575438i
$406$	−3.60148	−	11.0842i	−0.178738	−	0.550100i
$407$	−18.2627	−	18.2627i	−0.905248	−	0.905248i
$408$	2.18818	+	6.44435i	0.108331	+	0.319043i
$409$	1.73765	−	2.39167i	0.0859211	−	0.118260i	−0.763893	−	0.645343i	$-0.776714\pi$
$409$	1.73765	−	2.39167i	0.0859211	−	0.118260i	0.849814	+	0.527083i	$0.176714\pi$
$410$	2.47117	+	1.47834i	0.122042	+	0.0730099i
$411$	7.77635	+	1.12684i	0.383579	+	0.0555828i
$412$	2.86516	−	0.453797i	0.141156	−	0.0223570i
$413$	−9.34463	+	1.48004i	−0.459819	+	0.0728282i
$414$	−4.82889	+	3.70665i	−0.237327	+	0.182172i
$415$	1.68280	−	7.35377i	0.0826053	−	0.360982i
$416$	−1.13352	+	1.56015i	−0.0555753	+	0.0764928i
$417$	9.41149	−	3.19567i	0.460883	−	0.156493i
$418$	19.2763	+	19.2763i	0.942835	+	0.942835i
$419$	0.976706	+	3.00599i	0.0477152	+	0.146852i	0.972075	−	0.234668i	$-0.0754005\pi$
$419$	0.976706	+	3.00599i	0.0477152	+	0.146852i	−0.924360	+	0.381521i	$0.875400\pi$
$420$	7.09772	−	3.14018i	0.346333	−	0.153225i
$421$	−3.57566	+	11.0047i	−0.174267	+	0.536338i	−0.999599	−	0.0283089i	$-0.990988\pi$
$421$	−3.57566	+	11.0047i	−0.174267	+	0.536338i	0.825332	+	0.564647i	$0.190988\pi$
$422$	19.6694	−	10.0220i	0.957489	−	0.487865i
$423$	−3.94157	−	0.518230i	−0.191646	−	0.0251972i
$424$		−	10.9301i		−	0.530812i
$425$	−0.418753	−	19.6420i	−0.0203125	−	0.952775i
$426$	−0.661080	+	0.678734i	−0.0320294	+	0.0328848i
$427$	0.168045	−	1.06100i	0.00813228	−	0.0513452i
$428$	6.67790	+	13.1061i	0.322789	+	0.633508i
$429$	6.27893	+	11.9318i	0.303149	+	0.576073i
$430$	−13.5662	+	16.2312i	−0.654223	+	0.782737i
$431$	−24.8006	+	8.05821i	−1.19460	+	0.388150i	−0.837773	−	0.546019i	$-0.816143\pi$
$431$	−24.8006	+	8.05821i	−1.19460	+	0.388150i	−0.356831	+	0.934169i	$0.616143\pi$
$432$	−5.19209	+	0.205335i	−0.249805	+	0.00987916i
$433$	6.52479	−	12.8056i	0.313561	−	0.615399i	−0.679409	−	0.733759i	$-0.737764\pi$
$433$	6.52479	−	12.8056i	0.313561	−	0.615399i	0.992971	+	0.118361i	$0.0377639\pi$
$434$	15.1203	+	10.9856i	0.725799	+	0.527324i
$435$	8.12133	−	21.0093i	0.389388	−	1.00732i
$436$	−10.1338	+	7.36263i	−0.485321	+	0.352606i
$437$	−2.14373	−	13.5350i	−0.102548	−	0.647466i
$438$	7.46697	−	10.5674i	0.356785	−	0.504932i
$439$	2.49050	+	3.42787i	0.118865	+	0.163604i	0.864303	−	0.502971i	$-0.167760\pi$
$439$	2.49050	+	3.42787i	0.118865	+	0.163604i	−0.745438	+	0.666575i	$0.767760\pi$
$440$	8.30180	−	3.54284i	0.395773	−	0.168898i
$441$	5.06939	−	7.37871i	0.241399	−	0.351367i
$442$	−6.75156	−	3.44009i	−0.321139	−	0.163628i
$443$	18.5118	−	18.5118i	0.879523	−	0.879523i	−0.113962	−	0.993485i	$-0.536354\pi$
$443$	18.5118	−	18.5118i	0.879523	−	0.879523i	0.993485	+	0.113962i	$0.0363542\pi$
$444$	−4.90064	+	9.93967i	−0.232574	+	0.471716i
$445$	−24.3597	−	20.3602i	−1.15476	−	0.965165i
$446$	14.2556	+	4.63193i	0.675022	+	0.219328i
$447$	−7.88146	+	25.3901i	−0.372780	+	1.20091i
$448$	−1.97930	−	0.313490i	−0.0935130	−	0.0148110i
$449$	−36.0779			−1.70262			−0.851311	−	0.524662i	$-0.824192\pi$
$449$	−36.0779			−1.70262			−0.851311	+	0.524662i	$0.824192\pi$
$450$	14.4705	+	3.95023i	0.682146	+	0.186216i
$451$	−5.19836			−0.244781
$452$	−14.3852	−	2.27840i	−0.676624	−	0.107167i
$453$	−11.6538	+	37.5426i	−0.547542	+	1.76391i
$454$	−3.63578	−	1.18134i	−0.170635	−	0.0554428i
$455$	−3.22166	+	8.01843i	−0.151034	+	0.375910i
$456$	5.17263	−	10.4913i	0.242231	−	0.491301i
$457$	12.7889	−	12.7889i	0.598241	−	0.598241i	−0.341604	−	0.939844i	$-0.610970\pi$
$457$	12.7889	−	12.7889i	0.598241	−	0.598241i	0.939844	+	0.341604i	$0.110970\pi$
$458$	−20.0649	−	10.2236i	−0.937570	−	0.477716i
$459$	−3.98834	−	20.0238i	−0.186160	−	0.934632i
$460$	−4.42302	−	1.01214i	−0.206224	−	0.0471913i
$461$	−10.1363	−	13.9514i	−0.472092	−	0.649779i	0.504869	−	0.863196i	$-0.331541\pi$
$461$	−10.1363	−	13.9514i	−0.472092	−	0.649779i	−0.976961	+	0.213417i	$0.931541\pi$
$462$	−8.08541	+	11.4427i	−0.376167	+	0.532361i
$463$	−0.946894	−	5.97845i	−0.0440059	−	0.277842i	0.955867	−	0.293800i	$-0.0949201\pi$
$463$	−0.946894	−	5.97845i	−0.0440059	−	0.277842i	−0.999873	+	0.0159582i	$0.994920\pi$
$464$	−4.70506	+	3.41843i	−0.218427	+	0.158696i
$465$	9.26688	+	34.9119i	0.429741	+	1.61900i
$466$	13.9091	+	10.1055i	0.644325	+	0.468130i
$467$	0.901038	−	1.76839i	0.0416951	−	0.0818311i	−0.869219	−	0.494427i	$-0.835378\pi$
$467$	0.901038	−	1.76839i	0.0416951	−	0.0818311i	0.910914	+	0.412596i	$0.135378\pi$
$468$	3.98166	−	4.19724i	0.184053	−	0.194017i
$469$	2.88977	−	0.938944i	0.133437	−	0.0433564i
$470$	−1.57508	−	2.50986i	−0.0726532	−	0.115771i
$471$	−0.491872	−	0.934700i	−0.0226643	−	0.0430687i
$472$	2.14337	+	4.20661i	0.0986568	+	0.193625i
$473$	5.97392	−	37.7178i	0.274681	−	1.73427i
$474$	12.9722	−	13.3187i	0.595835	−	0.611747i
$475$	−23.3624	+	24.3803i	−1.07194	+	1.11864i
$476$		−	7.87416i		−	0.360912i
$477$	−4.27442	+	32.5105i	−0.195712	+	1.48855i
$478$	−3.05839	+	1.55833i	−0.139887	+	0.0712762i
$479$	10.9260	−	33.6268i	0.499222	−	1.53645i	−0.311051	−	0.950393i	$-0.600681\pi$
$479$	10.9260	−	33.6268i	0.499222	−	1.53645i	0.810273	−	0.586053i	$-0.199319\pi$
$480$	−2.58477	−	2.88426i	−0.117978	−	0.131648i
$481$	−3.81289	−	11.7349i	−0.173853	−	0.535064i
$482$	−6.05568	−	6.05568i	−0.275829	−	0.275829i
$483$	6.66920	−	2.26453i	0.303459	−	0.103039i
$484$	−3.11192	+	4.28319i	−0.141451	+	0.194690i
$485$	−17.9224	+	15.6405i	−0.813812	+	0.710200i
$486$	15.5237	+	1.41972i	0.704168	+	0.0643998i
$487$	24.6253	−	3.90026i	1.11588	−	0.176738i	0.428855	−	0.903373i	$-0.358917\pi$
$487$	24.6253	−	3.90026i	1.11588	−	0.176738i	0.687023	+	0.726636i	$0.258917\pi$
$488$	−0.529448	+	0.0838563i	−0.0239670	+	0.00379599i
$489$	40.6393	+	5.88886i	1.83777	+	0.266303i
$490$	6.64614	−	0.594399i	0.300242	−	0.0268522i
$491$	−3.22682	+	4.44133i	−0.145624	+	0.200434i	−0.875598	−	0.483041i	$-0.839532\pi$
$491$	−3.22682	+	4.44133i	−0.145624	+	0.200434i	0.729974	+	0.683475i	$0.239532\pi$
$492$	0.717163	+	2.11210i	0.0323322	+	0.0952208i
$493$	−16.1587	−	16.1587i	−0.727750	−	0.727750i
$494$	4.02451	+	12.3862i	0.181071	+	0.557280i
$495$	−26.0784	+	7.29126i	−1.17214	+	0.327718i
$496$	2.88201	−	8.86991i	0.129406	−	0.398271i
$497$	0.976739	−	0.497673i	0.0438127	−	0.0223237i
$498$	4.68178	−	3.49668i	0.209796	−	0.156690i
$499$		−	0.383555i		−	0.0171703i	−0.999963	−	0.00858514i	$-0.997267\pi$
$499$		−	0.383555i		−	0.0171703i	0.999963	−	0.00858514i	$-0.00273277\pi$
$500$	4.60656	+	10.1872i	0.206012	+	0.455587i
$501$	4.22404	+	4.11417i	0.188716	+	0.183808i
$502$	1.86818	−	11.7952i	0.0833810	−	0.526447i
$503$	3.58816	+	7.04217i	0.159988	+	0.313995i	0.957060	−	0.289890i	$-0.0936187\pi$
$503$	3.58816	+	7.04217i	0.159988	+	0.313995i	−0.797072	+	0.603885i	$0.793619\pi$
$504$	5.76463	+	1.70649i	0.256777	+	0.0760129i
$505$	−25.9371	+	6.52009i	−1.15419	+	0.290140i
$506$	7.79006	−	2.53115i	0.346311	−	0.112523i
$507$	−0.211796	−	16.0739i	−0.00940619	−	0.713866i
$508$	1.66253	−	3.26290i	0.0737630	−	0.144768i
$509$	20.5303	+	14.9162i	0.909990	+	0.661147i	0.941012	−	0.338372i	$-0.109876\pi$
$509$	20.5303	+	14.9162i	0.909990	+	0.661147i	−0.0310220	+	0.999519i	$0.509876\pi$
$510$	9.60475	−	11.8041i	0.425305	−	0.522696i
$511$	−12.1116	+	8.79956i	−0.535784	+	0.389270i
$512$	0.156434	+	0.987688i	0.00691349	+	0.0436501i
$513$	−19.4883	+	29.1826i	−0.860430	+	1.28844i
$514$	1.74029	+	2.39531i	0.0767611	+	0.105653i
$515$	−4.26501	−	4.88724i	−0.187939	−	0.215357i
$516$	−16.1490	+	2.77632i	−0.710918	+	0.122221i
$517$	4.76616	+	2.42848i	0.209615	+	0.106804i
$518$	9.06647	−	9.06647i	0.398358	−	0.398358i
$519$	−2.02093	−	0.996397i	−0.0887090	−	0.0437370i
$520$	4.30223	+	0.292492i	0.188665	+	0.0128266i
$521$	−19.7375	−	6.41311i	−0.864716	−	0.280963i	−0.157119	−	0.987580i	$-0.550221\pi$
$521$	−19.7375	−	6.41311i	−0.864716	−	0.280963i	−0.707597	+	0.706616i	$0.750221\pi$
$522$	15.3316	−	8.32777i	0.671045	−	0.364496i
$523$	17.5234	+	2.77544i	0.766246	+	0.121361i	0.527309	−	0.849674i	$-0.323201\pi$
$523$	17.5234	+	2.77544i	0.766246	+	0.121361i	0.238937	+	0.971035i	$0.423201\pi$
$524$	−2.47044			−0.107922
$525$	−14.3838	−	9.71069i	−0.627761	−	0.423809i
$526$	22.7216			0.990710
$527$	36.1948	+	5.73269i	1.57667	+	0.249720i
$528$	6.67733	+	2.07274i	0.290593	+	0.0902043i
$529$	17.9583	+	5.83501i	0.780797	+	0.253696i
$530$	−20.7016	+	12.9914i	−0.899220	+	0.564313i
$531$	−4.73018	−	13.3504i	−0.205272	−	0.579356i
$532$	−9.56966	+	9.56966i	−0.414898	+	0.414898i
$533$	−2.21278	−	1.12747i	−0.0958463	−	0.0488361i
$534$	−4.16669	−	24.2363i	−0.180311	−	1.04881i
$535$	16.8857	−	28.2258i	0.730032	−	1.22031i
$536$	−0.891220	−	1.22666i	−0.0384948	−	0.0529836i
$537$	−32.6772	−	23.0897i	−1.41012	−	0.996396i
$538$	1.88712	+	11.9148i	0.0813595	+	0.513684i
$539$	−9.74519	+	7.08029i	−0.419755	+	0.304970i
$540$	6.56020	+	9.58977i	0.282306	+	0.412678i
$541$	10.0053	+	7.26924i	0.430160	+	0.312529i	0.781713	−	0.623639i	$-0.214346\pi$
$541$	10.0053	+	7.26924i	0.430160	+	0.312529i	−0.351553	+	0.936168i	$0.614346\pi$
$542$	3.74318	−	7.34640i	0.160783	−	0.315555i
$543$	28.0989	−	0.370243i	1.20584	−	0.0158886i
$544$	−3.73697	+	1.21422i	−0.160221	+	0.0520591i
$545$	25.9898	+	10.4422i	1.11328	+	0.447296i
$546$	−5.92351	+	3.11716i	−0.253503	+	0.133402i
$547$	−12.0831	−	23.7144i	−0.516636	−	1.01396i	−0.991030	−	0.133643i	$-0.957333\pi$
$547$	−12.0831	−	23.7144i	−0.516636	−	1.01396i	0.474393	−	0.880313i	$-0.342667\pi$
$548$	−0.709676	+	4.48072i	−0.0303159	+	0.191407i
$549$	1.60758	−	0.0423717i	0.0686100	−	0.00180838i
$550$	−16.5776	−	11.5126i	−0.706872	−	0.490899i
$551$			39.2761i			1.67322i
$552$	−2.10312	−	2.81592i	−0.0895147	−	0.119853i
$553$	−19.1664	+	9.76575i	−0.815036	+	0.415282i
$554$	2.59742	−	7.99403i	0.110354	−	0.339634i
$555$	24.6506	−	2.53242i	1.04636	−	0.107495i
$556$	1.77327	+	5.45757i	0.0752034	+	0.231452i
$557$	28.3195	+	28.3195i	1.19993	+	1.19993i	0.974186	+	0.225748i	$0.0724825\pi$
$557$	28.3195	+	28.3195i	1.19993	+	1.19993i	0.225748	+	0.974186i	$0.427517\pi$
$558$	−12.0410	+	25.2556i	−0.509736	+	1.06915i
$559$	10.7235	−	14.7597i	0.453556	−	0.624267i
$560$	1.75883	+	4.12140i	0.0743243	+	0.174161i
$561$	−3.93971	+	27.1881i	−0.166335	+	1.14788i
$562$	0.223035	−	0.0353253i	0.00940816	−	0.00149011i
$563$	−8.73181	+	1.38298i	−0.368002	+	0.0582858i	−0.337697	−	0.941255i	$-0.609648\pi$
$563$	−8.73181	+	1.38298i	−0.368002	+	0.0582858i	−0.0303051	+	0.999541i	$0.509648\pi$
$564$	0.329157	−	2.27153i	0.0138600	−	0.0956485i
$565$	12.7829	+	29.9537i	0.537782	+	1.26016i
$566$	−13.2327	+	18.2133i	−0.556214	+	0.765563i
$567$	−16.4790	−	7.33014i	−0.692051	−	0.307837i
$568$	−0.386804	−	0.386804i	−0.0162300	−	0.0162300i
$569$	7.02196	+	21.6114i	0.294376	+	0.905996i	0.983430	+	0.181286i	$0.0580261\pi$
$569$	7.02196	+	21.6114i	0.294376	+	0.905996i	−0.689054	+	0.724710i	$0.741974\pi$
$570$	−26.0188	+	2.67298i	−1.08981	+	0.111959i
$571$	−8.54837	+	26.3092i	−0.357738	+	1.10101i	0.596666	+	0.802489i	$0.296492\pi$
$571$	−8.54837	+	26.3092i	−0.357738	+	1.10101i	−0.954405	+	0.298516i	$0.903508\pi$
$572$	−6.93599	+	3.53406i	−0.290008	+	0.147767i
$573$	−5.77584	−	7.73341i	−0.241289	−	0.323068i
$574$		−	2.58071i		−	0.107717i
$575$	3.34018	+	9.58022i	0.139295	+	0.399523i
$576$	−0.0790447	−	2.99896i	−0.00329353	−	0.124957i
$577$	1.72432	−	10.8869i	0.0717842	−	0.453228i	−0.925448	−	0.378875i	$-0.876311\pi$
$577$	1.72432	−	10.8869i	0.0717842	−	0.453228i	0.997232	−	0.0743526i	$-0.0236890\pi$
$578$	0.708558	+	1.39062i	0.0294721	+	0.0578423i
$579$	−13.2691	+	6.98268i	−0.551446	+	0.290190i
$580$	12.0669	+	4.84826i	0.501051	+	0.201313i
$581$	−6.42992	+	2.08921i	−0.266758	+	0.0866750i
$582$	−18.4240	+	0.242762i	−0.763699	+	0.0100628i
$583$	20.0303	−	39.3117i	0.829572	−	1.62813i
$584$	6.04378	+	4.39106i	0.250093	+	0.181704i
$585$	−12.6822	−	2.55246i	−0.524343	−	0.105531i
$586$	−9.05430	+	6.57833i	−0.374030	+	0.271749i
$587$	−3.29168	−	20.7828i	−0.135862	−	0.857800i	−0.957635	−	0.287985i	$-0.907015\pi$
$587$	−3.29168	−	20.7828i	−0.135862	−	0.857800i	0.821773	−	0.569815i	$-0.192985\pi$
$588$	4.22117	+	2.98269i	0.174078	+	0.123004i
$589$	−37.0213	−	50.9555i	−1.52544	−	2.09958i
$590$	5.41972	−	9.05951i	0.223126	−	0.372974i
$591$	−5.20348	−	30.2669i	−0.214043	−	1.24502i
$592$	−5.70089	−	2.90475i	−0.234305	−	0.119385i
$593$	10.8276	−	10.8276i	0.444635	−	0.444635i	−0.448931	−	0.893566i	$-0.648195\pi$
$593$	10.8276	−	10.8276i	0.444635	−	0.444635i	0.893566	+	0.448931i	$0.148195\pi$
$594$	−19.0505	−	8.77645i	−0.781650	−	0.360102i
$595$	−14.9137	+	9.35920i	−0.611401	+	0.383690i
$596$	−14.5978	−	4.74310i	−0.597948	−	0.194285i
$597$	−17.1364	−	5.31939i	−0.701346	−	0.217708i
$598$	3.86497	+	0.612151i	0.158050	+	0.0250327i
$599$	20.9614			0.856459			0.428230	−	0.903670i	$-0.359137\pi$
$599$	20.9614			0.856459			0.428230	+	0.903670i	$0.359137\pi$
$600$	−2.39054	+	8.32378i	−0.0975935	+	0.339817i
$601$	−24.3199			−0.992029			−0.496015	−	0.868314i	$-0.665204\pi$
$601$	−24.3199			−0.992029			−0.496015	+	0.868314i	$0.665204\pi$
$602$	18.7249	+	2.96573i	0.763170	+	0.120874i
$603$	2.17114	+	3.99710i	0.0884156	+	0.162775i
$604$	−21.5847	−	7.01330i	−0.878270	−	0.285367i
$605$	11.8112	+	0.802997i	0.480192	+	0.0326465i
$606$	−18.5803	−	9.16081i	−0.754773	−	0.372133i
$607$	−12.8780	+	12.8780i	−0.522702	+	0.522702i	−0.918386	−	0.395685i	$-0.870507\pi$
$607$	−12.8780	+	12.8780i	−0.522702	+	0.522702i	0.395685	+	0.918386i	$0.370507\pi$
$608$	6.01730	+	3.06597i	0.244034	+	0.124341i
$609$	−19.8945	+	3.42026i	−0.806168	+	0.138596i
$610$	0.788123	+	0.903103i	0.0319102	+	0.0365656i
$611$	1.50210	+	2.06746i	0.0607683	+	0.0836404i
$612$	11.5901	−	2.15015i	0.468502	−	0.0869147i
$613$	1.91504	+	12.0911i	0.0773477	+	0.488354i	0.995704	+	0.0925984i	$0.0295173\pi$
$613$	1.91504	+	12.0911i	0.0773477	+	0.488354i	−0.918356	+	0.395756i	$0.870483\pi$
$614$	−8.01488	+	5.82315i	−0.323454	+	0.235003i
$615$	3.14790	−	3.86874i	0.126936	−	0.156003i
$616$	−6.54435	−	4.75475i	−0.263679	−	0.191574i
$617$	−11.6432	+	22.8510i	−0.468737	+	0.919948i	0.528728	+	0.848791i	$0.322669\pi$
$617$	−11.6432	+	22.8510i	−0.468737	+	0.919948i	−0.997465	+	0.0711569i	$0.977331\pi$
$618$	−0.0661986	−	5.02403i	−0.00266290	−	0.202096i
$619$	−28.2577	+	9.18149i	−1.13577	+	0.369035i	−0.815767	−	0.578380i	$-0.803685\pi$
$619$	−28.2577	+	9.18149i	−1.13577	+	0.369035i	−0.320006	+	0.947415i	$0.603685\pi$
$620$	−20.2252	+	5.08421i	−0.812262	+	0.204187i
$621$	5.15431	+	9.19813i	0.206835	+	0.369108i
$622$	5.51989	+	10.8334i	0.221328	+	0.434380i
$623$	−4.45096	+	28.1023i	−0.178324	+	1.12589i
$624$	2.39278	+	2.33054i	0.0957878	+	0.0932964i
$625$	13.8193	−	20.8333i	0.552772	−	0.833333i
$626$		−	24.5881i		−	0.982739i
$627$	37.8305	−	28.2544i	1.51080	−	1.12837i
$628$	0.543344	−	0.276848i	0.0216818	−	0.0110474i
$629$	7.76887	−	23.9101i	0.309765	−	0.953359i
$630$	−3.61973	−	12.9465i	−0.144213	−	0.515802i
$631$	−0.858936	−	2.64353i	−0.0341937	−	0.105237i	0.932503	−	0.361162i	$-0.117620\pi$
$631$	−0.858936	−	2.64353i	−0.0341937	−	0.105237i	−0.966697	+	0.255925i	$0.917620\pi$
$632$	7.59019	+	7.59019i	0.301922	+	0.301922i
$633$	−12.2936	−	36.2055i	−0.488626	−	1.43904i
$634$	−6.13203	+	8.44002i	−0.243534	+	0.335196i
$635$	−8.15602	+	0.729435i	−0.323662	+	0.0289468i
$636$	−18.7358	−	2.71492i	−0.742922	−	0.107654i
$637$	−5.68387	+	0.900236i	−0.225203	+	0.0356687i
$638$	−23.1870	+	3.67247i	−0.917984	+	0.145394i
$639$	0.999245	+	1.30178i	0.0395295	+	0.0514976i
$640$	1.68475	−	1.47025i	0.0665954	−	0.0581167i
$641$	−18.3443	+	25.2487i	−0.724554	+	0.997264i	0.274806	+	0.961500i	$0.411386\pi$
$641$	−18.3443	+	25.2487i	−0.724554	+	0.997264i	−0.999360	+	0.0357639i	$0.988614\pi$
$642$	24.1246	−	8.19149i	0.952120	−	0.323292i
$643$	23.9422	+	23.9422i	0.944188	+	0.944188i	0.998523	−	0.0543345i	$-0.0173037\pi$
$643$	23.9422	+	23.9422i	0.944188	+	0.944188i	−0.0543345	+	0.998523i	$0.517304\pi$
$644$	1.25658	+	3.86736i	0.0495162	+	0.152395i
$645$	24.4529	+	27.2862i	0.962833	+	1.07439i
$646$	−8.20005	+	25.2372i	−0.322627	+	0.992942i
$647$	0.500806	−	0.255174i	0.0196887	−	0.0100319i	−0.444118	−	0.895968i	$-0.646483\pi$
$647$	0.500806	−	0.255174i	0.0196887	−	0.0100319i	0.463807	+	0.885936i	$0.346483\pi$
$648$	−0.937689	+	8.95102i	−0.0368359	+	0.351629i
$649$			19.0576i			0.748078i
$650$	−4.55963	−	8.49608i	−0.178843	−	0.333244i
$651$	22.5866	−	23.1898i	0.885239	−	0.908879i
$652$	−3.70877	+	23.4163i	−0.145247	+	0.917052i
$653$	10.9835	+	21.5563i	0.429816	+	0.843562i	0.999761	+	0.0218786i	$0.00696474\pi$
$653$	10.9835	+	21.5563i	0.429816	+	0.843562i	−0.569944	+	0.821683i	$0.693035\pi$
$654$	10.1035	+	19.1996i	0.395078	+	0.750764i
$655$	2.93635	+	4.67901i	0.114733	+	0.182824i
$656$	−1.22477	+	0.397952i	−0.0478193	+	0.0155374i
$657$	−16.2594	−	15.4243i	−0.634341	−	0.601760i
$658$	−1.20561	+	2.36614i	−0.0469996	+	0.0922419i
$659$	−4.30697	−	3.12920i	−0.167776	−	0.121896i	0.500729	−	0.865604i	$-0.333065\pi$
$659$	−4.30697	−	3.12920i	−0.167776	−	0.121896i	−0.668505	+	0.743708i	$0.733065\pi$
$660$	−4.01087	−	15.1105i	−0.156123	−	0.588176i
$661$	−10.9702	+	7.97029i	−0.426690	+	0.310008i	−0.780324	−	0.625376i	$-0.784946\pi$
$661$	−10.9702	+	7.97029i	−0.426690	+	0.310008i	0.353634	+	0.935384i	$0.384946\pi$
$662$	2.89729	+	18.2928i	0.112606	+	0.710969i
$663$	−7.57384	+	10.7187i	−0.294144	+	0.416279i
$664$	1.98302	+	2.72939i	0.0769561	+	0.105921i
$665$	29.4994	+	6.75049i	1.14394	+	0.261773i
$666$	15.8208	+	10.8693i	0.613043	+	0.421178i
$667$	10.5149	+	5.35761i	0.407138	+	0.207447i
$668$	−2.40724	+	2.40724i	−0.0931391	+	0.0931391i
$669$	11.4807	−	23.2857i	0.443871	−	0.900276i
$670$	−1.26399	+	3.14597i	−0.0488323	+	0.121540i
$671$	−2.05791	−	0.668657i	−0.0794449	−	0.0258132i
$672$	−1.02900	+	3.31494i	−0.0396947	+	0.127877i
$673$	48.7489	+	7.72106i	1.87913	+	0.297625i	0.987800	−	0.155727i	$-0.0497721\pi$
$673$	48.7489	+	7.72106i	1.87913	+	0.297625i	0.891331	+	0.453353i	$0.149772\pi$
$674$	11.8757			0.457435
$675$	10.3656	−	23.8234i	0.398972	−	0.916963i
$676$	9.28106			0.356964
$677$	−3.02000	−	0.478321i	−0.116068	−	0.0183834i	0.0981301	−	0.995174i	$-0.468714\pi$
$677$	−3.02000	−	0.478321i	−0.116068	−	0.0183834i	−0.214198	+	0.976790i	$0.568714\pi$
$678$	−7.47865	+	24.0925i	−0.287216	+	0.925266i
$679$	20.2749	+	6.58771i	0.778078	+	0.252813i
$680$	6.74147	+	5.63461i	0.258524	+	0.216078i
$681$	−2.92807	+	5.93883i	−0.112204	+	0.227576i
$682$	26.6205	−	26.6205i	1.01935	−	1.01935i
$683$	−31.2546	−	15.9250i	−1.19592	−	0.609353i	−0.261391	−	0.965233i	$-0.584181\pi$
$683$	−31.2546	−	15.9250i	−1.19592	−	0.609353i	−0.934532	+	0.355880i	$0.884181\pi$
$684$	−16.6989	−	11.4726i	−0.638497	−	0.438666i
$685$	9.33000	−	3.98163i	0.356481	−	0.152130i
$686$	−11.7603	−	16.1867i	−0.449011	−	0.618011i
$687$	−22.5086	+	31.8547i	−0.858757	+	1.21533i
$688$	−1.47993	−	9.34391i	−0.0564218	−	0.356233i
$689$	17.0526	−	12.3894i	0.649652	−	0.472000i
$690$	−2.83359	+	7.33030i	−0.107873	+	0.279060i
$691$	−2.34860	−	1.70636i	−0.0893451	−	0.0649130i	0.542216	−	0.840239i	$-0.317585\pi$
$691$	−2.34860	−	1.70636i	−0.0893451	−	0.0649130i	−0.631561	+	0.775326i	$0.717585\pi$
$692$	0.590593	−	1.15910i	0.0224510	−	0.0440625i
$693$	17.6061	+	16.7018i	0.668800	+	0.634450i
$694$	−7.45357	+	2.42181i	−0.282934	+	0.0919307i
$695$	8.22893	−	9.84542i	0.312141	−	0.373458i
$696$	4.69100	+	8.91427i	0.177812	+	0.337894i
$697$	−2.29725	−	4.50861i	−0.0870146	−	0.170776i
$698$	−1.46705	+	9.26258i	−0.0555286	+	0.350594i
$699$	20.7773	−	21.3321i	0.785868	−	0.806854i
$700$	5.71540	−	8.22992i	0.216022	−	0.311062i
$701$		−	5.87338i		−	0.221834i	−0.993830	−	0.110917i	$-0.964621\pi$
$701$		−	5.87338i		−	0.221834i	0.993830	−	0.110917i	$-0.0353788\pi$
$702$	−6.20568	−	7.86771i	−0.234218	−	0.296948i
$703$	−38.5003	+	19.6169i	−1.45206	+	0.739864i
$704$	−1.24738	+	3.83905i	−0.0470126	+	0.144690i
$705$	−4.69351	+	2.07650i	−0.176768	+	0.0782056i
$706$	−4.50172	−	13.8549i	−0.169424	−	0.521435i
$707$	16.9480	+	16.9480i	0.637396	+	0.637396i
$708$	7.74314	−	2.62918i	0.291005	−	0.0988107i
$709$	10.1538	−	13.9755i	0.381335	−	0.524862i	−0.574603	−	0.818432i	$-0.694843\pi$
$709$	10.1538	−	13.9755i	0.381335	−	0.524862i	0.955938	+	0.293570i	$0.0948434\pi$
$710$	−0.272854	+	1.19236i	−0.0102400	+	0.0447486i
$711$	−19.6080	−	25.5446i	−0.735357	−	0.957996i
$712$	14.0233	−	2.22107i	0.525546	−	0.0832383i
$713$	−18.6917	+	2.96048i	−0.700011	+	0.110871i
$714$	−13.4975	−	1.95586i	−0.505130	−	0.0731962i
$715$	14.9376	+	8.93620i	0.558635	+	0.334195i
$716$	13.5783	−	18.6889i	0.507444	−	0.698437i
$717$	1.91153	+	5.62960i	0.0713874	+	0.210241i
$718$	8.34797	+	8.34797i	0.311544	+	0.311544i
$719$	−12.3239	−	37.9289i	−0.459602	−	1.41451i	−0.865646	−	0.500656i	$-0.833092\pi$
$719$	−12.3239	−	37.9289i	−0.459602	−	1.41451i	0.406044	−	0.913854i	$-0.366908\pi$
$720$	−5.58608	+	3.71426i	−0.208181	+	0.138422i
$721$	−1.79640	+	5.52874i	−0.0669013	+	0.205901i
$722$	23.7079	−	12.0798i	0.882318	−	0.449563i
$723$	−11.8845	+	8.87617i	−0.441989	+	0.330108i
$724$			16.2243i			0.602972i
$725$	−5.16007	−	28.6174i	−0.191640	−	1.06282i
$726$	6.56905	+	6.39818i	0.243800	+	0.237459i
$727$	3.26644	−	20.6235i	0.121146	−	0.764883i	−0.850068	−	0.526673i	$-0.823439\pi$
$727$	3.26644	−	20.6235i	0.121146	−	0.764883i	0.971214	−	0.238210i	$-0.0765608\pi$
$728$	−1.75448	−	3.44335i	−0.0650252	−	0.127619i
$729$	6.28953	−	26.2572i	0.232945	−	0.972490i
$730$	1.13307	−	16.6661i	0.0419367	−	0.616841i
$731$	35.3532	−	11.4869i	1.30758	−	0.424860i
$732$	0.0122327	+	0.928380i	0.000452134	+	0.0343139i
$733$	4.26895	−	8.37829i	0.157677	−	0.309459i	−0.798630	−	0.601822i	$-0.794442\pi$
$733$	4.26895	−	8.37829i	0.157677	−	0.309459i	0.956307	+	0.292363i	$0.0944416\pi$
$734$	−2.18467	−	1.58725i	−0.0806375	−	0.0585866i
$735$	0.631945	−	11.5401i	0.0233097	−	0.425663i
$736$	1.64163	−	1.19271i	0.0605112	−	0.0439639i
$737$	−0.957451	−	6.04511i	−0.0352682	−	0.222674i
$738$	3.79859	−	0.704700i	0.139828	−	0.0259404i
$739$	0.0758416	+	0.104387i	0.00278988	+	0.00383994i	0.810410	−	0.585864i	$-0.199245\pi$
$739$	0.0758416	+	0.104387i	0.00278988	+	0.00383994i	−0.807620	+	0.589704i	$0.799245\pi$
$740$	1.27446	+	14.2501i	0.0468500	+	0.523843i
$741$	22.2314	−	3.82201i	0.816689	−	0.140405i
$742$	19.5162	+	9.94400i	0.716462	+	0.365056i
$743$	−7.88637	+	7.88637i	−0.289323	+	0.289323i	−0.836812	−	0.547490i	$-0.815584\pi$
$743$	−7.88637	+	7.88637i	−0.289323	+	0.289323i	0.547490	+	0.836812i	$0.315584\pi$
$744$	−14.4885	−	7.14338i	−0.531173	−	0.261889i
$745$	8.36741	+	33.2858i	0.306558	+	1.21950i
$746$	−20.3996	−	6.62824i	−0.746883	−	0.242677i
$747$	−4.83092	−	8.89381i	−0.176754	−	0.325407i
$748$	−15.6658	−	2.48121i	−0.572797	−	0.0907221i
$749$	−29.4771			−1.07707
$750$	18.6066	−	5.36592i	0.679418	−	0.195936i
$751$	24.5205			0.894768			0.447384	−	0.894342i	$-0.352356\pi$
$751$	24.5205			0.894768			0.447384	+	0.894342i	$0.352356\pi$
$752$	1.30885	+	0.207301i	0.0477288	+	0.00755950i
$753$	−19.7547	−	6.13215i	−0.719902	−	0.223468i
$754$	−10.6665	−	3.46577i	−0.388452	−	0.126216i
$755$	12.3723	+	49.2175i	0.450275	+	1.79121i
$756$	4.35704	−	9.45755i	0.158464	−	0.343968i
$757$	13.4521	−	13.4521i	0.488924	−	0.488924i	−0.419042	−	0.907967i	$-0.637634\pi$
$757$	13.4521	−	13.4521i	0.488924	−	0.488924i	0.907967	+	0.419042i	$0.137634\pi$
$758$	−9.42760	−	4.80360i	−0.342426	−	0.174475i
$759$	−2.40379	−	13.9820i	−0.0872519	−	0.507516i
$760$	−1.34519	−	15.0410i	−0.0487952	−	0.545593i
$761$	9.74504	+	13.4129i	0.353258	+	0.486217i	0.948255	−	0.317510i	$-0.102847\pi$
$761$	9.74504	+	13.4129i	0.353258	+	0.486217i	−0.594997	+	0.803728i	$0.702847\pi$
$762$	−5.18014	−	3.66030i	−0.187657	−	0.132599i
$763$	−3.92679	−	24.7928i	−0.142159	−	0.897559i
$764$	4.50844	−	3.27557i	0.163109	−	0.118506i
$765$	−17.8483	−	19.3960i	−0.645307	−	0.701263i
$766$	−0.112738	−	0.0819087i	−0.00407338	−	0.00295948i
$767$	−4.13340	+	8.11226i	−0.149249	+	0.292917i
$768$	1.73190	−	0.0228202i	0.0624946	−	0.000823454i
$769$	−24.2927	+	7.89319i	−0.876018	+	0.284636i	−0.712303	−	0.701872i	$-0.752348\pi$
$769$	−24.2927	+	7.89319i	−0.876018	+	0.284636i	−0.163715	+	0.986508i	$0.552348\pi$
$770$	−1.22691	+	18.0465i	−0.0442149	+	0.650350i
$771$	4.53819	−	2.38815i	0.163439	−	0.0860072i
$772$	−3.93016	−	7.71338i	−0.141450	−	0.277611i
$773$	−1.33889	+	8.45340i	−0.0481564	+	0.304048i	−0.999997	−	0.00254649i	$-0.999189\pi$
$773$	−1.33889	+	8.45340i	−0.0481564	+	0.304048i	0.951840	+	0.306594i	$0.0991894\pi$
$774$	0.747794	+	28.3713i	0.0268789	+	1.01979i
$775$	33.6690	+	32.2634i	1.20943	+	1.15894i
$776$		−	10.6380i		−	0.381883i
$777$	−13.2892	−	17.7933i	−0.476749	−	0.638330i
$778$	−30.8379	+	15.7127i	−1.10559	+	0.563327i
$779$	−2.68752	+	8.27133i	−0.0962904	+	0.296351i
$780$	1.57000	−	7.30200i	0.0562151	−	0.261454i
$781$	−0.682349	−	2.10006i	−0.0244164	−	0.0751459i
$782$	5.63787	+	5.63787i	0.201610	+	0.201610i
$783$	−10.4668	−	28.3491i	−0.374054	−	1.01311i
$784$	−1.75401	+	2.41419i	−0.0626434	+	0.0862212i
$785$	−1.17017	−	0.700035i	−0.0417650	−	0.0249853i
$786$	−0.613631	+	4.23469i	−0.0218875	+	0.151047i
$787$	22.6192	−	3.58252i	0.806286	−	0.127703i	0.260333	−	0.965519i	$-0.416168\pi$
$787$	22.6192	−	3.58252i	0.806286	−	0.127703i	0.545953	+	0.837816i	$0.316168\pi$
$788$	17.5127	−	2.77374i	0.623864	−	0.0988103i
$789$	5.64382	−	38.9482i	0.200925	−	1.38659i
$790$	5.35416	−	23.3975i	0.190493	−	0.832446i
$791$	17.1556	−	23.6127i	0.609984	−	0.839571i
$792$	5.21156	−	10.9311i	0.185185	−	0.388419i
$793$	−0.730967	−	0.730967i	−0.0259574	−	0.0259574i
$794$	9.41645	+	28.9808i	0.334177	+	1.02849i
$795$	17.1272	+	38.7125i	0.607439	+	1.37299i
$796$	3.20123	−	9.85239i	0.113465	−	0.349209i
$797$	38.3454	−	19.5380i	1.35826	−	0.692070i	0.385250	−	0.922812i	$-0.374115\pi$
$797$	38.3454	−	19.5380i	1.35826	−	0.692070i	0.973015	+	0.230742i	$0.0741153\pi$
$798$	14.0268	+	18.7808i	0.496544	+	0.664834i
$799$			5.20694i			0.184208i
$800$	−4.78713	−	1.44338i	−0.169251	−	0.0510311i
$801$	−42.5795	+	1.12229i	−1.50447	+	0.0396540i
$802$	−0.112399	+	0.709657i	−0.00396893	+	0.0250589i
$803$	13.6904	+	26.8689i	0.483123	+	0.948183i
$804$	−2.32404	+	1.22299i	−0.0819627	+	0.0431316i
$805$	5.83121	−	6.97669i	0.205523	−	0.245896i
$806$	17.1052	−	5.55782i	0.602506	−	0.195766i
$807$	20.8925	−	0.275288i	0.735450	−	0.00969059i
$808$	5.42987	−	10.6567i	0.191022	−	0.374902i
$809$	−36.2976	−	26.3717i	−1.27616	−	0.927181i	−0.276726	−	0.960949i	$-0.589249\pi$
$809$	−36.2976	−	26.3717i	−1.27616	−	0.927181i	−0.999430	+	0.0337679i	$0.989249\pi$
$810$	18.0678	−	8.86316i	0.634837	−	0.311420i
$811$	−6.93867	+	5.04124i	−0.243650	+	0.177022i	−0.702908	−	0.711281i	$-0.748115\pi$
$811$	−6.93867	+	5.04124i	−0.243650	+	0.177022i	0.459258	+	0.888303i	$0.348115\pi$
$812$	−1.82319	−	11.5111i	−0.0639813	−	0.403962i
$813$	−11.6630	−	8.24112i	−0.409041	−	0.289029i
$814$	−15.1809	−	20.8948i	−0.532092	−	0.732361i
$815$	48.7587	−	20.8081i	1.70794	−	0.728874i
$816$	1.15312	+	6.70732i	0.0403673	+	0.234803i
$817$	−56.9260	−	29.0052i	−1.99159	−	1.01476i
$818$	2.09039	−	2.09039i	0.0730889	−	0.0730889i
$819$	3.87193	+	10.9280i	0.135296	+	0.381856i
$820$	2.20948	+	1.84671i	0.0771584	+	0.0644900i
$821$	−21.1200	−	6.86230i	−0.737093	−	0.239496i	−0.0836747	−	0.996493i	$-0.526666\pi$
$821$	−21.1200	−	6.86230i	−0.737093	−	0.239496i	−0.653418	+	0.756997i	$0.726666\pi$
$822$	7.50434	+	2.32945i	0.261744	+	0.0812490i
$823$	−0.969602	−	0.153570i	−0.0337982	−	0.00535311i	0.139512	−	0.990220i	$-0.455446\pi$
$823$	−0.969602	−	0.153570i	−0.0337982	−	0.00535311i	−0.173311	+	0.984867i	$0.555446\pi$
$824$	2.90088			0.101057
$825$	−23.8520	+	25.5569i	−0.830421	+	0.889777i
$826$	−9.46111			−0.329194
$827$	−56.0204	−	8.87275i	−1.94802	−	0.308536i	−0.948065	−	0.318078i	$-0.896963\pi$
$827$	−56.0204	−	8.87275i	−1.94802	−	0.308536i	−0.999954	+	0.00954211i	$0.996963\pi$
$828$	−5.34929	+	2.90561i	−0.185901	+	0.100977i
$829$	8.48021	+	2.75539i	0.294530	+	0.0956986i	0.452555	−	0.891737i	$-0.350513\pi$
$829$	8.48021	+	2.75539i	0.294530	+	0.0956986i	−0.158025	+	0.987435i	$0.550513\pi$
$830$	2.81246	−	6.99998i	0.0976220	−	0.242973i
$831$	−13.0578	−	6.43799i	−0.452969	−	0.223331i
$832$	−1.36362	+	1.36362i	−0.0472752	+	0.0472752i
$833$	−10.4474	−	5.32322i	−0.361981	−	0.184439i
$834$	9.79554	−	1.68405i	0.339192	−	0.0583137i
$835$	7.42056	+	1.69808i	0.256799	+	0.0587646i
$836$	16.0235	+	22.0545i	0.554184	+	0.762769i
$837$	40.3010	+	26.9133i	1.39301	+	0.930259i
$838$	0.494441	+	3.12177i	0.0170802	+	0.107840i
$839$	−24.2019	+	17.5837i	−0.835542	+	0.607057i	−0.921122	−	0.389275i	$-0.872726\pi$
$839$	−24.2019	+	17.5837i	−0.835542	+	0.607057i	0.0855799	+	0.996331i	$0.472726\pi$
$840$	7.50157	−	1.99119i	0.258829	−	0.0687025i
$841$	−3.90206	−	2.83501i	−0.134554	−	0.0977590i
$842$	−5.25316	+	10.3099i	−0.181036	+	0.355303i
$843$	−0.00515315	−	0.391089i	−0.000177484	−	0.0134698i
$844$	20.9950	−	6.82168i	0.722677	−	0.234812i
$845$	−11.0314	−	17.5783i	−0.379493	−	0.604713i
$846$	−3.81197	−	1.12845i	−0.131058	−	0.0387968i
$847$	−4.81667	−	9.45325i	−0.165503	−	0.324818i
$848$	1.70984	−	10.7955i	0.0587162	−	0.370720i
$849$	27.9334	+	27.2069i	0.958673	+	0.933738i
$850$	2.65908	−	19.4656i	0.0912057	−	0.667666i
$851$			12.9831i			0.445055i
$852$	−0.759118	+	0.566962i	−0.0260070	+	0.0194238i
$853$	13.8564	−	7.06020i	0.474435	−	0.241737i	−0.200388	−	0.979717i	$-0.564220\pi$
$853$	13.8564	−	7.06020i	0.474435	−	0.241737i	0.674823	+	0.737980i	$0.264220\pi$
$854$	0.331953	−	1.02165i	0.0113592	−	0.0349600i
$855$	−1.88092	+	45.2639i	−0.0643259	+	1.54799i
$856$	4.54544	+	13.9894i	0.155360	+	0.478149i
$857$	14.2259	+	14.2259i	0.485948	+	0.485948i	0.907025	−	0.421077i	$-0.138348\pi$
$857$	14.2259	+	14.2259i	0.485948	+	0.485948i	−0.421077	+	0.907025i	$0.638348\pi$
$858$	4.33508	+	12.7671i	0.147997	+	0.435863i
$859$	−0.328571	+	0.452239i	−0.0112107	+	0.0154302i	−0.814586	−	0.580043i	$-0.803036\pi$
$859$	−0.328571	+	0.452239i	−0.0112107	+	0.0154302i	0.803375	+	0.595474i	$0.203036\pi$
$860$	−15.9383	+	13.9091i	−0.543493	+	0.474297i
$861$	−4.42372	−	0.641022i	−0.150760	−	0.0218460i
$862$	−25.7559	+	4.07933i	−0.877248	+	0.138942i
$863$	−8.78203	+	1.39094i	−0.298944	+	0.0473480i	−0.304105	−	0.952639i	$-0.598357\pi$
$863$	−8.78203	+	1.39094i	−0.298944	+	0.0473480i	0.00516090	+	0.999987i	$0.498357\pi$
$864$	−5.16029	−	0.609416i	−0.175557	−	0.0207328i
$865$	−2.89732	+	0.259122i	−0.0985119	+	0.00881042i
$866$	8.44770	−	11.6273i	0.287064	−	0.395110i
$867$	2.55973	−	0.869157i	0.0869331	−	0.0295181i
$868$	13.2157	+	13.2157i	0.448569	+	0.448569i
$869$	13.3896	+	41.2090i	0.454212	+	1.39792i
$870$	11.3079	−	19.4802i	0.383375	−	0.660441i
$871$	0.903562	−	2.78088i	0.0306160	−	0.0942265i
$872$	−11.1608	+	5.68671i	−0.377952	+	0.192576i
$873$	−4.16020	+	31.6417i	−0.140801	+	1.07091i
$874$		−	13.7037i		−	0.463534i
$875$	−22.3808	−	1.04293i	−0.756608	−	0.0352575i
$876$	9.02815	−	9.26924i	0.305033	−	0.313179i
$877$	−5.62983	+	35.5453i	−0.190106	+	1.20028i	0.689396	+	0.724385i	$0.257876\pi$
$877$	−5.62983	+	35.5453i	−0.190106	+	1.20028i	−0.879502	+	0.475896i	$0.842124\pi$
$878$	1.92360	+	3.77527i	0.0649182	+	0.127409i
$879$	9.02724	+	17.1544i	0.304481	+	0.578604i
$880$	8.75381	−	2.20054i	0.295091	−	0.0741801i
$881$	−44.3078	+	14.3965i	−1.49277	+	0.485029i	−0.937899	−	0.346909i	$-0.887231\pi$
$881$	−44.3078	+	14.3965i	−1.49277	+	0.485029i	−0.554868	+	0.831938i	$0.687231\pi$
$882$	6.16126	−	6.49484i	0.207460	−	0.218693i
$883$	−18.6174	+	36.5387i	−0.626525	+	1.22962i	0.331640	+	0.943406i	$0.392398\pi$
$883$	−18.6174	+	36.5387i	−0.626525	+	1.22962i	−0.958164	+	0.286218i	$0.907602\pi$
$884$	−6.13028	−	4.45391i	−0.206184	−	0.149801i
$885$	−14.1831	−	11.5405i	−0.476761	−	0.387929i
$886$	21.1798	−	15.3880i	0.711549	−	0.516971i
$887$	−6.17999	−	39.0189i	−0.207504	−	1.31013i	−0.842954	−	0.537985i	$-0.819186\pi$
$887$	−6.17999	−	39.0189i	−0.207504	−	1.31013i	0.635451	−	0.772141i	$-0.280814\pi$
$888$	−6.39521	+	9.05066i	−0.214609	+	0.303720i
$889$	4.31353	+	5.93707i	0.144671	+	0.199123i
$890$	−20.8748	−	23.9202i	−0.699724	−	0.801807i
$891$	−19.7761	+	30.4753i	−0.662523	+	1.02096i
$892$	13.3555	+	6.80497i	0.447175	+	0.227847i
$893$	6.32813	−	6.32813i	0.211763	−	0.211763i
$894$	−11.7563	+	23.8446i	−0.393190	+	0.797483i
$895$	−51.5359	−	3.50373i	−1.72265	−	0.117117i
$896$	−1.90589	−	0.619261i	−0.0636712	−	0.0206880i
$897$	2.00934	−	6.47308i	0.0670898	−	0.216130i
$898$	−35.6337	−	5.64383i	−1.18911	−	0.188337i
$899$	54.2401			1.80901
$900$	13.6744	+	6.16528i	0.455813	+	0.205509i
$901$	42.9474			1.43079
$902$	−5.13436	−	0.813203i	−0.170956	−	0.0270767i
$903$	9.73478	−	31.3606i	0.323953	−	1.04362i
$904$	−13.8517	−	4.50069i	−0.460701	−	0.149691i
$905$	30.7289	−	19.2842i	1.02146	−	0.641027i
$906$	−17.3833	+	35.2574i	−0.577520	+	1.17135i
$907$	−25.5617	+	25.5617i	−0.848763	+	0.848763i	−0.989979	−	0.141216i	$-0.954899\pi$
$907$	−25.5617	+	25.5617i	−0.848763	+	0.848763i	0.141216	+	0.989979i	$0.454899\pi$
$908$	−3.40621	−	1.73555i	−0.113039	−	0.0575963i
$909$	−20.3181	+	29.5739i	−0.673910	+	0.980905i
$910$	−4.43635	+	7.41573i	−0.147064	+	0.245829i
$911$	−1.31952	−	1.81616i	−0.0437177	−	0.0601722i	0.786599	−	0.617465i	$-0.211840\pi$
$911$	−1.31952	−	1.81616i	−0.0437177	−	0.0601722i	−0.830316	+	0.557293i	$0.811840\pi$
$912$	6.75015	−	9.55298i	0.223520	−	0.316331i
$913$	2.13039	+	13.4507i	0.0705056	+	0.445155i
$914$	14.6321	−	10.6308i	0.483987	−	0.351637i
$915$	1.74381	−	1.12664i	0.0576487	−	0.0372455i
$916$	−18.2185	−	13.2365i	−0.601957	−	0.437347i
$917$	2.24756	−	4.41109i	0.0742210	−	0.145667i
$918$	−0.806817	−	20.4012i	−0.0266289	−	0.673340i
$919$	−17.3500	+	5.63735i	−0.572323	+	0.185959i	−0.580858	−	0.814005i	$-0.697283\pi$
$919$	−17.3500	+	5.63735i	−0.572323	+	0.185959i	0.00853567	+	0.999964i	$0.497283\pi$
$920$	−4.21023	−	1.69159i	−0.138807	−	0.0557701i
$921$	7.99093	+	15.1851i	0.263310	+	0.500366i
$922$	−7.82899	−	15.3653i	−0.257834	−	0.506028i
$923$	0.165025	−	1.04192i	0.00543185	−	0.0342953i
$924$	−9.77589	+	10.0370i	−0.321603	+	0.330192i
$925$	25.4748	−	19.3514i	0.837607	−	0.636270i
$926$		−	6.05297i		−	0.198913i
$927$	−8.62837	−	1.13444i	−0.283393	−	0.0372600i
$928$	−5.18189	+	2.64031i	−0.170104	+	0.0866723i
$929$	14.4639	−	44.5152i	0.474544	−	1.46050i	−0.372028	−	0.928221i	$-0.621338\pi$
$929$	14.4639	−	44.5152i	0.474544	−	1.46050i	0.846572	−	0.532274i	$-0.178662\pi$
$930$	3.69137	+	35.9318i	0.121045	+	1.17825i
$931$	6.22755	+	19.1664i	0.204100	+	0.628155i
$932$	12.1570	+	12.1570i	0.398215	+	0.398215i
$933$	19.9411	−	6.77101i	0.652843	−	0.221673i
$934$	1.16658	−	1.60566i	0.0381717	−	0.0525388i
$935$	13.9208	+	32.6201i	0.455260	+	1.06679i
$936$	4.58924	−	3.52269i	0.150004	−	0.115143i
$937$	−42.6595	+	6.75660i	−1.39362	+	0.220728i	−0.807679	−	0.589622i	$-0.799277\pi$
$937$	−42.6595	+	6.75660i	−1.39362	+	0.220728i	−0.585945	+	0.810351i	$0.699277\pi$
$938$	3.00108	−	0.475324i	0.0979886	−	0.0155199i
$939$	−42.1477	−	6.10743i	−1.37544	−	0.199309i
$940$	−1.16306	−	2.72536i	−0.0379349	−	0.0888914i
$941$	−15.3900	+	21.1825i	−0.501699	+	0.690529i	−0.982492	−	0.186305i	$-0.940349\pi$
$941$	−15.3900	+	21.1825i	−0.501699	+	0.690529i	0.480793	+	0.876834i	$0.340349\pi$
$942$	−0.339597	−	1.00014i	−0.0110647	−	0.0325863i
$943$	1.84778	+	1.84778i	0.0601720	+	0.0601720i
$944$	1.45893	+	4.49012i	0.0474840	+	0.146141i
$945$	−23.0914	+	2.98896i	−0.751162	+	0.0972309i
$946$	11.8007	−	36.3189i	0.383675	−	1.18083i
$947$	−38.1664	+	19.4468i	−1.24024	+	0.631935i	−0.946115	−	0.323831i	$-0.895029\pi$
$947$	−38.1664	+	19.4468i	−1.24024	+	0.631935i	−0.294127	+	0.955766i	$0.595029\pi$
$948$	14.8960	−	11.1254i	0.483801	−	0.361336i
$949$			14.4066i			0.467657i
$950$	−26.8887	+	20.4254i	−0.872385	+	0.662688i
$951$	12.9443	+	12.6076i	0.419748	+	0.408830i
$952$	1.23179	−	7.77722i	0.0399226	−	0.252061i
$953$	0.380531	+	0.746833i	0.0123266	+	0.0241923i	0.897088	−	0.441853i	$-0.145679\pi$
$953$	0.380531	+	0.746833i	0.0123266	+	0.0241923i	−0.884761	+	0.466045i	$0.845679\pi$
$954$	−9.30755	+	31.4415i	−0.301343	+	1.01796i
$955$	−11.5626	−	4.64565i	−0.374158	−	0.150330i
$956$	−3.26451	+	1.06070i	−0.105582	+	0.0343056i
$957$	0.535729	+	40.6582i	0.0173177	+	1.31429i
$958$	16.0519	−	31.5036i	0.518612	−	1.01783i
$959$	−7.35489	−	5.34364i	−0.237502	−	0.172555i
$960$	−2.10175	−	3.25310i	−0.0678337	−	0.104993i
$961$	−45.2897	+	32.9049i	−1.46096	+	1.06145i
$962$	−1.93021	−	12.1869i	−0.0622324	−	0.392920i
$963$	−8.04913	−	43.3877i	−0.259380	−	1.39815i
$964$	−5.03381	−	6.92845i	−0.162128	−	0.223150i
$965$	−9.93778	+	16.6118i	−0.319908	+	0.534754i
$966$	6.94134	−	1.19335i	0.223334	−	0.0383955i
$967$	23.5300	+	11.9891i	0.756674	+	0.385545i	0.789368	−	0.613921i	$-0.210409\pi$
$967$	23.5300	+	11.9891i	0.756674	+	0.385545i	−0.0326938	+	0.999465i	$0.510409\pi$
$968$	−3.74364	+	3.74364i	−0.120325	+	0.120325i
$969$	41.2234	+	20.3247i	1.32429	+	0.652925i
$970$	−20.1484	+	12.6443i	−0.646927	+	0.405984i
$971$	17.8859	+	5.81148i	0.573985	+	0.186499i	0.581604	−	0.813472i	$-0.302425\pi$
$971$	17.8859	+	5.81148i	0.573985	+	0.186499i	−0.00761891	+	0.999971i	$0.502425\pi$
$972$	15.1105	+	3.83068i	0.484668	+	0.122869i
$973$	−11.3580	−	1.79894i	−0.364122	−	0.0576713i
$974$	24.9322			0.798881
$975$	−15.6961	+	5.70554i	−0.502677	+	0.182723i
$976$	−0.536047			−0.0171585
$977$	−30.0169	−	4.75421i	−0.960326	−	0.152101i	−0.343459	−	0.939168i	$-0.611599\pi$
$977$	−30.0169	−	4.75421i	−0.960326	−	0.152101i	−0.616867	+	0.787067i	$0.711599\pi$
$978$	39.2177	+	12.1737i	1.25404	+	0.389273i
$979$	54.5073	+	17.7105i	1.74206	+	0.566030i
$980$	6.65730	+	0.452605i	0.212660	+	0.0144579i
$981$	35.4206	−	12.5499i	1.13089	−	0.400688i
$982$	−3.88187	+	3.88187i	−0.123875	+	0.123875i
$983$	2.70453	+	1.37803i	0.0862611	+	0.0439522i	0.496589	−	0.867986i	$-0.334586\pi$
$983$	2.70453	+	1.37803i	0.0862611	+	0.0439522i	−0.410328	+	0.911938i	$0.634586\pi$
$984$	0.377928	+	2.19829i	0.0120479	+	0.0700788i
$985$	−26.0690	−	29.8722i	−0.830627	−	0.951808i
$986$	−13.4320	−	18.4875i	−0.427761	−	0.588762i
$987$	3.75646	+	2.65432i	0.119569	+	0.0844880i
$988$	2.03734	+	12.8632i	0.0648163	+	0.409234i
$989$	−15.5304	+	11.2835i	−0.493839	+	0.358795i
$990$	−26.8979	+	3.12194i	−0.854872	+	0.0992217i
$991$	−13.3909	−	9.72904i	−0.425375	−	0.309053i	0.354422	−	0.935086i	$-0.384678\pi$
$991$	−13.3909	−	9.72904i	−0.425375	−	0.309053i	−0.779797	+	0.626032i	$0.784678\pi$
$992$	4.23408	−	8.30986i	0.134432	−	0.263838i
$993$	32.0762	−	0.422649i	1.01791	−	0.0134123i
$994$	1.04257	−	0.338750i	0.0330682	−	0.0107445i
$995$	−22.4654	+	5.64736i	−0.712201	+	0.179033i
$996$	5.17114	−	2.72124i	0.163854	−	0.0862257i
$997$	−10.0986	−	19.8197i	−0.319827	−	0.627697i	0.673988	−	0.738742i	$-0.264580\pi$
$997$	−10.0986	−	19.8197i	−0.319827	−	0.627697i	−0.993815	+	0.111046i	$0.964580\pi$
$998$	0.0600012	−	0.378833i	0.00189931	−	0.0119917i
$999$	22.5614	−	24.4193i	0.713810	−	0.772594i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.2.l.a.23.9	yes	80
3.2	odd	2	inner	150.2.l.a.23.5	✓	80
5.2	odd	4		750.2.l.c.407.2		80
5.3	odd	4		750.2.l.a.407.9		80
5.4	even	2		750.2.l.b.593.2		80
15.2	even	4		750.2.l.c.407.8		80
15.8	even	4		750.2.l.a.407.3		80
15.14	odd	2		750.2.l.b.593.6		80
25.9	even	10		750.2.l.a.293.3		80
25.12	odd	20	inner	150.2.l.a.137.5	yes	80
25.13	odd	20		750.2.l.b.707.6		80
25.16	even	5		750.2.l.c.293.8		80
75.38	even	20		750.2.l.b.707.2		80
75.41	odd	10		750.2.l.c.293.2		80
75.59	odd	10		750.2.l.a.293.9		80
75.62	even	20	inner	150.2.l.a.137.9	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.23.5	✓	80	3.2	odd	2	inner
150.2.l.a.23.9	yes	80	1.1	even	1	trivial
150.2.l.a.137.5	yes	80	25.12	odd	20	inner
150.2.l.a.137.9	yes	80	75.62	even	20	inner
750.2.l.a.293.3		80	25.9	even	10
750.2.l.a.293.9		80	75.59	odd	10
750.2.l.a.407.3		80	15.8	even	4
750.2.l.a.407.9		80	5.3	odd	4
750.2.l.b.593.2		80	5.4	even	2
750.2.l.b.593.6		80	15.14	odd	2
750.2.l.b.707.2		80	75.38	even	20
750.2.l.b.707.6		80	25.13	odd	20
750.2.l.c.293.2		80	75.41	odd	10
750.2.l.c.293.8		80	25.16	even	5
750.2.l.c.407.2		80	5.2	odd	4
750.2.l.c.407.8		80	15.2	even	4

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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	150.l (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.987688 + 0.156434i) q^{2} +(0.513483 - 1.65419i) q^{3} +(0.951057 + 0.309017i) q^{4} +(-0.545143 - 2.16860i) q^{5} +(0.765933 - 1.55349i) q^{6} +(-1.41702 + 1.41702i) q^{7} +(0.891007 + 0.453990i) q^{8} +(-2.47267 - 1.69880i) q^{9} +O(q^{10})\)	\(q+(0.987688 + 0.156434i) q^{2} +(0.513483 - 1.65419i) q^{3} +(0.951057 + 0.309017i) q^{4} +(-0.545143 - 2.16860i) q^{5} +(0.765933 - 1.55349i) q^{6} +(-1.41702 + 1.41702i) q^{7} +(0.891007 + 0.453990i) q^{8} +(-2.47267 - 1.69880i) q^{9} +(-0.199188 - 2.22718i) q^{10} +(2.37267 + 3.26569i) q^{11} +(0.999524 - 1.41455i) q^{12} +(0.301677 + 1.90471i) q^{13} +(-1.62125 + 1.17790i) q^{14} +(-3.86719 - 0.211770i) q^{15} +(0.809017 + 0.587785i) q^{16} +(-1.78386 + 3.50102i) q^{17} +(-2.17648 - 2.06469i) q^{18} +(6.42284 - 2.08691i) q^{19} +(0.151672 - 2.23092i) q^{20} +(1.61640 + 3.07163i) q^{21} +(1.83259 + 3.59666i) q^{22} +(0.317431 - 2.00418i) q^{23} +(1.20850 - 1.24077i) q^{24} +(-4.40564 + 2.36439i) q^{25} +1.92846i q^{26} +(-4.07980 + 3.21796i) q^{27} +(-1.78555 + 0.909783i) q^{28} +(-1.79717 + 5.53113i) q^{29} +(-3.78645 - 0.814125i) q^{30} +(-2.88201 - 8.86991i) q^{31} +(0.707107 + 0.707107i) q^{32} +(6.62039 - 2.24795i) q^{33} +(-2.30957 + 3.17886i) q^{34} +(3.84543 + 2.30047i) q^{35} +(-1.82669 - 2.37975i) q^{36} +(-6.31949 + 1.00091i) q^{37} +(6.67023 - 1.05646i) q^{38} +(3.30566 + 0.479008i) q^{39} +(0.498797 - 2.17973i) q^{40} +(-0.756950 + 1.04185i) q^{41} +(1.11599 + 3.28668i) q^{42} +(-6.68950 - 6.68950i) q^{43} +(1.24738 + 3.83905i) q^{44} +(-2.33605 + 6.28831i) q^{45} +(0.627046 - 1.92985i) q^{46} +(1.18073 - 0.601612i) q^{47} +(1.38772 - 1.03645i) q^{48} +2.98411i q^{49} +(-4.72127 + 1.64609i) q^{50} +(4.87536 + 4.74855i) q^{51} +(-0.301677 + 1.90471i) q^{52} +(-4.96215 - 9.73877i) q^{53} +(-4.53297 + 2.54012i) q^{54} +(5.78854 - 6.92563i) q^{55} +(-1.90589 + 0.619261i) q^{56} +(-0.154113 - 11.6962i) q^{57} +(-2.64031 + 5.18189i) q^{58} +(3.81952 + 2.77504i) q^{59} +(-3.61247 - 1.39643i) q^{60} +(-0.433671 + 0.315081i) q^{61} +(-1.45897 - 9.21155i) q^{62} +(5.91105 - 1.09660i) q^{63} +(0.587785 + 0.809017i) q^{64} +(3.96610 - 1.69256i) q^{65} +(6.89054 - 1.18462i) q^{66} +(-1.35097 - 0.688356i) q^{67} +(-2.77842 + 2.77842i) q^{68} +(-3.15229 - 1.55420i) q^{69} +(3.43821 + 2.87370i) q^{70} +(-0.520251 - 0.169040i) q^{71} +(-1.43193 - 2.63621i) q^{72} +(7.37855 + 1.16865i) q^{73} -6.39826 q^{74} +(1.64893 + 8.50183i) q^{75} +6.75337 q^{76} +(-7.98967 - 1.26544i) q^{77} +(3.19003 + 0.990230i) q^{78} +(10.2088 + 3.31704i) q^{79} +(0.833640 - 2.07486i) q^{80} +(3.22819 + 8.40112i) q^{81} +(-0.910612 + 0.910612i) q^{82} +(3.00600 + 1.53163i) q^{83} +(0.588101 + 3.42079i) q^{84} +(8.56476 + 1.95991i) q^{85} +(-5.56067 - 7.65361i) q^{86} +(8.22670 + 5.81300i) q^{87} +(0.631467 + 3.98692i) q^{88} +(11.4865 - 8.34544i) q^{89} +(-3.29099 + 5.84546i) q^{90} +(-3.12650 - 2.27153i) q^{91} +(0.921220 - 1.80800i) q^{92} +(-16.1523 + 0.212830i) q^{93} +(1.26031 - 0.409498i) q^{94} +(-8.02703 - 12.7909i) q^{95} +(1.53277 - 0.806599i) q^{96} +(-4.82956 - 9.47854i) q^{97} +(-0.466817 + 2.94737i) q^{98} +(-0.319074 - 12.1057i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{3} + 4 q^{7}+O(q^{10}) \) 80 * q + 4 * q^3 + 4 * q^7	\( 80 q + 4 q^{3} + 4 q^{7} - 4 q^{10} - 4 q^{12} - 8 q^{15} + 20 q^{16} - 8 q^{18} - 40 q^{19} - 36 q^{22} - 104 q^{25} + 4 q^{27} - 16 q^{28} + 12 q^{30} + 4 q^{33} - 40 q^{34} - 24 q^{37} - 40 q^{39} - 8 q^{40} - 4 q^{42} - 24 q^{43} - 72 q^{45} - 4 q^{48} - 12 q^{55} - 64 q^{57} + 20 q^{58} + 24 q^{60} + 64 q^{63} + 96 q^{67} + 140 q^{69} + 76 q^{70} + 8 q^{72} + 100 q^{73} + 132 q^{75} + 100 q^{78} + 80 q^{79} - 40 q^{81} + 96 q^{82} + 60 q^{84} + 32 q^{85} + 80 q^{87} + 4 q^{88} + 52 q^{90} + 12 q^{93} - 32 q^{97}+O(q^{100}) \) 80 * q + 4 * q^3 + 4 * q^7 - 4 * q^10 - 4 * q^12 - 8 * q^15 + 20 * q^16 - 8 * q^18 - 40 * q^19 - 36 * q^22 - 104 * q^25 + 4 * q^27 - 16 * q^28 + 12 * q^30 + 4 * q^33 - 40 * q^34 - 24 * q^37 - 40 * q^39 - 8 * q^40 - 4 * q^42 - 24 * q^43 - 72 * q^45 - 4 * q^48 - 12 * q^55 - 64 * q^57 + 20 * q^58 + 24 * q^60 + 64 * q^63 + 96 * q^67 + 140 * q^69 + 76 * q^70 + 8 * q^72 + 100 * q^73 + 132 * q^75 + 100 * q^78 + 80 * q^79 - 40 * q^81 + 96 * q^82 + 60 * q^84 + 32 * q^85 + 80 * q^87 + 4 * q^88 + 52 * q^90 + 12 * q^93 - 32 * q^97

Introduction

L-functions

Modular forms

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