LMFDB - Embedded newform 552.2.x.a.35.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(35,552)]

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([11, 11, 11, 20]))

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

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

chi := DirichletCharacter("552.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.x (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:	$920$
Relative dimension:	$92$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			35.9
Character	$\chi$	$=$	552.35
Dual form			552.2.x.a.347.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33559 + 0.464960i) q^{2} +(1.06576 + 1.36534i) q^{3} +(1.56763 - 1.24199i) q^{4} +(3.82579 - 1.12335i) q^{5} +(-2.05825 - 1.32801i) q^{6} +(2.32451 - 2.01420i) q^{7} +(-1.51623 + 2.38768i) q^{8} +(-0.728327 + 2.91025i) q^{9} +O(q^{10})$	\(q+(-1.33559 + 0.464960i) q^{2} +(1.06576 + 1.36534i) q^{3} +(1.56763 - 1.24199i) q^{4} +(3.82579 - 1.12335i) q^{5} +(-2.05825 - 1.32801i) q^{6} +(2.32451 - 2.01420i) q^{7} +(-1.51623 + 2.38768i) q^{8} +(-0.728327 + 2.91025i) q^{9} +(-4.58739 + 3.27918i) q^{10} +(-1.21838 + 1.89584i) q^{11} +(3.36646 + 0.816684i) q^{12} +(1.25284 + 1.08559i) q^{13} +(-2.16809 + 3.77096i) q^{14} +(5.61112 + 4.02630i) q^{15} +(0.914898 - 3.89396i) q^{16} +(-3.48116 + 1.58979i) q^{17} +(-0.380397 - 4.22555i) q^{18} +(1.94850 - 4.26662i) q^{19} +(4.60220 - 6.51261i) q^{20} +(5.22745 + 1.02711i) q^{21} +(0.745774 - 3.09856i) q^{22} +(-2.11886 - 4.30238i) q^{23} +(-4.87595 + 0.474508i) q^{24} +(9.16847 - 5.89222i) q^{25} +(-2.17804 - 0.867390i) q^{26} +(-4.74971 + 2.10720i) q^{27} +(1.14234 - 6.04455i) q^{28} +(1.00325 + 2.19681i) q^{29} +(-9.36625 - 2.76856i) q^{30} +(-7.35171 + 1.05702i) q^{31} +(0.588604 + 5.62615i) q^{32} +(-3.88696 + 0.356991i) q^{33} +(3.91022 - 3.74191i) q^{34} +(6.63044 - 10.3172i) q^{35} +(2.47277 + 5.46676i) q^{36} +(2.02365 - 6.89193i) q^{37} +(-0.618600 + 6.60444i) q^{38} +(-0.146984 + 2.86753i) q^{39} +(-3.11858 + 10.8380i) q^{40} +(1.78280 + 6.07166i) q^{41} +(-7.45931 + 1.05875i) q^{42} +(-0.371563 + 2.58428i) q^{43} +(0.444655 + 4.48518i) q^{44} +(0.482808 + 11.9522i) q^{45} +(4.83036 + 4.76105i) q^{46} -2.63889 q^{47} +(6.29166 - 2.90087i) q^{48} +(0.350149 - 2.43534i) q^{49} +(-9.50571 + 12.1326i) q^{50} +(-5.88067 - 3.05864i) q^{51} +(3.31228 + 0.145781i) q^{52} +(3.99275 + 4.60788i) q^{53} +(5.36392 - 5.02278i) q^{54} +(-2.53157 + 8.62173i) q^{55} +(1.28477 + 8.60421i) q^{56} +(7.90203 - 1.88680i) q^{57} +(-2.36137 - 2.46758i) q^{58} +(-10.1358 - 8.78269i) q^{59} +(13.7968 - 0.657259i) q^{60} +(-7.11683 + 1.02325i) q^{61} +(9.32744 - 4.83000i) q^{62} +(4.16882 + 8.23191i) q^{63} +(-3.40207 - 7.24058i) q^{64} +(6.01260 + 2.74586i) q^{65} +(5.02542 - 2.28408i) q^{66} +(-3.13450 + 2.01442i) q^{67} +(-3.48264 + 6.81577i) q^{68} +(3.61604 - 7.47825i) q^{69} +(-4.05851 + 16.8624i) q^{70} +(11.4169 - 7.33718i) q^{71} +(-5.84444 - 6.15163i) q^{72} +(-3.99111 + 8.73930i) q^{73} +(0.501689 + 10.1457i) q^{74} +(17.8163 + 6.23845i) q^{75} +(-2.24460 - 9.10848i) q^{76} +(0.986457 + 6.86096i) q^{77} +(-1.13698 - 3.89820i) q^{78} +(4.00403 + 3.46951i) q^{79} +(-0.874092 - 15.9252i) q^{80} +(-7.93908 - 4.23923i) q^{81} +(-5.20417 - 7.28034i) q^{82} +(-2.55196 + 8.69119i) q^{83} +(9.47034 - 4.88233i) q^{84} +(-11.5323 + 9.99277i) q^{85} +(-0.705327 - 3.62431i) q^{86} +(-1.93019 + 3.71105i) q^{87} +(-2.67931 - 5.78363i) q^{88} +(1.56952 + 0.225662i) q^{89} +(-6.20211 - 15.7388i) q^{90} +5.09884 q^{91} +(-8.66510 - 4.11291i) q^{92} +(-9.27833 - 8.91109i) q^{93} +(3.52449 - 1.22698i) q^{94} +(2.66163 - 18.5120i) q^{95} +(-7.05432 + 6.79975i) q^{96} +(11.4356 - 3.35780i) q^{97} +(0.664677 + 3.41543i) q^{98} +(-4.62997 - 4.92657i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 920 q - 18 q^{3} - 14 q^{4} - 16 q^{6} - 18 q^{9}+O(q^{10}) $ 920 * q - 18 * q^3 - 14 * q^4 - 16 * q^6 - 18 * q^9	$ 920 q - 18 q^{3} - 14 q^{4} - 16 q^{6} - 18 q^{9} - 14 q^{10} - 6 q^{12} - 30 q^{16} - 16 q^{18} - 52 q^{19} - 32 q^{22} - 26 q^{24} - 112 q^{25} - 30 q^{27} - 34 q^{28} + 11 q^{30} - 30 q^{33} - 88 q^{34} - 18 q^{36} + 124 q^{40} - 3 q^{42} - 36 q^{43} - 110 q^{46} + 32 q^{49} - 30 q^{51} + 90 q^{52} - 39 q^{54} - 6 q^{57} - 68 q^{58} + 13 q^{60} + 28 q^{64} - 46 q^{66} - 100 q^{67} - 92 q^{70} + 29 q^{72} - 36 q^{73} + 14 q^{75} - 50 q^{76} - 86 q^{78} - 2 q^{81} - 12 q^{82} - 151 q^{84} - 42 q^{88} - 196 q^{90} - 136 q^{91} - 68 q^{94} - 175 q^{96} - 36 q^{97} - 54 q^{99}+O(q^{100}) $ 920 * q - 18 * q^3 - 14 * q^4 - 16 * q^6 - 18 * q^9 - 14 * q^10 - 6 * q^12 - 30 * q^16 - 16 * q^18 - 52 * q^19 - 32 * q^22 - 26 * q^24 - 112 * q^25 - 30 * q^27 - 34 * q^28 + 11 * q^30 - 30 * q^33 - 88 * q^34 - 18 * q^36 + 124 * q^40 - 3 * q^42 - 36 * q^43 - 110 * q^46 + 32 * q^49 - 30 * q^51 + 90 * q^52 - 39 * q^54 - 6 * q^57 - 68 * q^58 + 13 * q^60 + 28 * q^64 - 46 * q^66 - 100 * q^67 - 92 * q^70 + 29 * q^72 - 36 * q^73 + 14 * q^75 - 50 * q^76 - 86 * q^78 - 2 * q^81 - 12 * q^82 - 151 * q^84 - 42 * q^88 - 196 * q^90 - 136 * q^91 - 68 * q^94 - 175 * q^96 - 36 * q^97 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{10}{11}\right)$	$-1$	$-1$	$-1$

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 $

$2$	−1.33559	+	0.464960i	−0.944408	+	0.328776i
$2$	−1.33559	+	0.464960i	−0.944408	+	0.328776i
$3$	1.06576	+	1.36534i	0.615315	+	0.788282i
$3$	1.06576	+	1.36534i	0.615315	+	0.788282i
$4$	1.56763	−	1.24199i	0.783813	−	0.620997i
$5$	3.82579	−	1.12335i	1.71094	−	0.502379i	0.727890	−	0.685693i	$-0.240501\pi$
$5$	3.82579	−	1.12335i	1.71094	−	0.502379i	0.983054	+	0.183315i	$0.0586827\pi$
$6$	−2.05825	−	1.32801i	−0.840276	−	0.542159i
$7$	2.32451	−	2.01420i	0.878584	−	0.761297i	−0.0935770	−	0.995612i	$-0.529830\pi$
$7$	2.32451	−	2.01420i	0.878584	−	0.761297i	0.972161	+	0.234315i	$0.0752847\pi$
$8$	−1.51623	+	2.38768i	−0.536070	+	0.844174i
$9$	−0.728327	+	2.91025i	−0.242776	+	0.970082i
$10$	−4.58739	+	3.27918i	−1.45066	+	1.03697i
$11$	−1.21838	+	1.89584i	−0.367355	+	0.571616i	−0.974893	−	0.222675i	$-0.928521\pi$
$11$	−1.21838	+	1.89584i	−0.367355	+	0.571616i	0.607538	+	0.794291i	$0.292157\pi$
$12$	3.36646	+	0.816684i	0.971812	+	0.235756i
$13$	1.25284	+	1.08559i	0.347475	+	0.301089i	0.811059	−	0.584964i	$-0.198891\pi$
$13$	1.25284	+	1.08559i	0.347475	+	0.301089i	−0.463584	+	0.886053i	$0.653437\pi$
$14$	−2.16809	+	3.77096i	−0.579445	+	1.00783i
$15$	5.61112	+	4.02630i	1.44879	+	1.03959i
$16$	0.914898	−	3.89396i	0.228724	−	0.973491i
$17$	−3.48116	+	1.58979i	−0.844304	+	0.385581i	−0.790122	−	0.612950i	$-0.789983\pi$
$17$	−3.48116	+	1.58979i	−0.844304	+	0.385581i	−0.0541827	+	0.998531i	$0.517255\pi$
$18$	−0.380397	−	4.22555i	−0.0896605	−	0.995972i
$19$	1.94850	−	4.26662i	0.447016	−	0.978829i	−0.543241	−	0.839577i	$-0.682803\pi$
$19$	1.94850	−	4.26662i	0.447016	−	0.978829i	0.990257	−	0.139252i	$-0.0444699\pi$
$20$	4.60220	−	6.51261i	1.02908	−	1.45626i
$21$	5.22745	+	1.02711i	1.14072	+	0.224134i
$22$	0.745774	−	3.09856i	0.159000	−	0.660616i
$23$	−2.11886	−	4.30238i	−0.441812	−	0.897108i
$23$	−2.11886	−	4.30238i	−0.441812	−	0.897108i
$24$	−4.87595	+	0.474508i	−0.995298	+	0.0968585i
$25$	9.16847	−	5.89222i	1.83369	−	1.17844i
$26$	−2.17804	−	0.867390i	−0.427149	−	0.170109i
$27$	−4.74971	+	2.10720i	−0.914082	+	0.405530i
$28$	1.14234	−	6.04455i	0.215881	−	1.14231i
$29$	1.00325	+	2.19681i	0.186299	+	0.407938i	0.979618	−	0.200868i	$-0.0643761\pi$
$29$	1.00325	+	2.19681i	0.186299	+	0.407938i	−0.793319	+	0.608806i	$0.791649\pi$
$30$	−9.36625	−	2.76856i	−1.71003	−	0.505467i
$31$	−7.35171	+	1.05702i	−1.32041	+	0.189846i	−0.766237	−	0.642558i	$-0.777873\pi$
$31$	−7.35171	+	1.05702i	−1.32041	+	0.189846i	−0.554170	+	0.832404i	$0.686964\pi$
$32$	0.588604	+	5.62615i	0.104051	+	0.994572i
$33$	−3.88696	+	0.356991i	−0.676633	+	0.0621442i
$34$	3.91022	−	3.74191i	0.670598	−	0.641733i
$35$	6.63044	−	10.3172i	1.12075	−	1.74392i
$36$	2.47277	+	5.46676i	0.412128	+	0.911126i
$37$	2.02365	−	6.89193i	0.332687	−	1.13303i	−0.608053	−	0.793896i	$-0.708049\pi$
$37$	2.02365	−	6.89193i	0.332687	−	1.13303i	0.940740	−	0.339130i	$-0.110133\pi$
$38$	−0.618600	+	6.60444i	−0.100350	+	1.07138i
$39$	−0.146984	+	2.86753i	−0.0235363	+	0.459173i
$40$	−3.11858	+	10.8380i	−0.493091	+	1.71364i
$41$	1.78280	+	6.07166i	0.278426	+	0.948233i	0.973384	+	0.229182i	$0.0736051\pi$
$41$	1.78280	+	6.07166i	0.278426	+	0.948233i	−0.694957	+	0.719051i	$0.744577\pi$
$42$	−7.45931	+	1.05875i	−1.15100	+	0.163368i
$43$	−0.371563	+	2.58428i	−0.0566628	+	0.394099i	0.941678	+	0.336516i	$0.109248\pi$
$43$	−0.371563	+	2.58428i	−0.0566628	+	0.394099i	−0.998341	+	0.0575830i	$0.981661\pi$
$44$	0.444655	+	4.48518i	0.0670343	+	0.676166i
$45$	0.482808	+	11.9522i	0.0719727	+	1.78172i
$46$	4.83036	+	4.76105i	0.712198	+	0.701978i
$47$	−2.63889			−0.384922			−0.192461	−	0.981305i	$-0.561647\pi$
$47$	−2.63889			−0.384922			−0.192461	+	0.981305i	$0.561647\pi$
$48$	6.29166	−	2.90087i	0.908123	−	0.418704i
$49$	0.350149	−	2.43534i	0.0500212	−	0.347905i
$50$	−9.50571	+	12.1326i	−1.34431	+	1.71581i
$51$	−5.88067	−	3.05864i	−0.823459	−	0.428296i
$52$	3.31228	+	0.145781i	0.459331	+	0.0202161i
$53$	3.99275	+	4.60788i	0.548447	+	0.632941i	0.960521	−	0.278209i	$-0.0897408\pi$
$53$	3.99275	+	4.60788i	0.548447	+	0.632941i	−0.412074	+	0.911151i	$0.635195\pi$
$54$	5.36392	−	5.02278i	0.729937	−	0.683514i
$55$	−2.53157	+	8.62173i	−0.341357	+	1.16255i
$56$	1.28477	+	8.60421i	0.171685	+	1.14979i
$57$	7.90203	−	1.88680i	1.04665	−	0.249913i
$58$	−2.36137	−	2.46758i	−0.310063	−	0.324009i
$59$	−10.1358	−	8.78269i	−1.31956	−	1.14341i	−0.979151	−	0.203133i	$-0.934888\pi$
$59$	−10.1358	−	8.78269i	−1.31956	−	1.14341i	−0.340413	−	0.940276i	$-0.610567\pi$
$60$	13.7968	−	0.657259i	1.78116	−	0.0848518i
$61$	−7.11683	+	1.02325i	−0.911217	+	0.131013i	−0.581951	−	0.813224i	$-0.697710\pi$
$61$	−7.11683	+	1.02325i	−0.911217	+	0.131013i	−0.329266	+	0.944237i	$0.606801\pi$
$62$	9.32744	−	4.83000i	1.18459	−	0.613410i
$63$	4.16882	+	8.23191i	0.525222	+	1.03712i
$64$	−3.40207	−	7.24058i	−0.425258	−	0.905072i
$65$	6.01260	+	2.74586i	0.745771	+	0.340582i
$66$	5.02542	−	2.28408i	0.618586	−	0.281150i
$67$	−3.13450	+	2.01442i	−0.382940	+	0.246100i	−0.717921	−	0.696124i	$-0.754906\pi$
$67$	−3.13450	+	2.01442i	−0.382940	+	0.246100i	0.334982	+	0.942225i	$0.391270\pi$
$68$	−3.48264	+	6.81577i	−0.422332	+	0.826534i
$69$	3.61604	−	7.47825i	0.435320	−	0.900276i
$70$	−4.05851	+	16.8624i	−0.485085	+	2.01545i
$71$	11.4169	−	7.33718i	1.35493	−	0.870763i	0.356943	−	0.934126i	$-0.383819\pi$
$71$	11.4169	−	7.33718i	1.35493	−	0.870763i	0.997991	+	0.0633632i	$0.0201827\pi$
$72$	−5.84444	−	6.15163i	−0.688773	−	0.724977i
$73$	−3.99111	+	8.73930i	−0.467124	+	1.02286i	0.518682	+	0.854967i	$0.326423\pi$
$73$	−3.99111	+	8.73930i	−0.467124	+	1.02286i	−0.985806	+	0.167891i	$0.946304\pi$
$74$	0.501689	+	10.1457i	0.0583201	+	1.17942i
$75$	17.8163	+	6.23845i	2.05724	+	0.720354i
$76$	−2.24460	−	9.10848i	−0.257473	−	1.04481i
$77$	0.986457	+	6.86096i	0.112417	+	0.781879i
$78$	−1.13698	−	3.89820i	−0.128737	−	0.441384i
$79$	4.00403	+	3.46951i	0.450488	+	0.390350i	0.850344	−	0.526228i	$-0.176394\pi$
$79$	4.00403	+	3.46951i	0.450488	+	0.390350i	−0.399855	+	0.916578i	$0.630940\pi$
$80$	−0.874092	−	15.9252i	−0.0977264	−	1.78050i
$81$	−7.93908	−	4.23923i	−0.882120	−	0.471025i
$82$	−5.20417	−	7.28034i	−0.574704	−	0.803979i
$83$	−2.55196	+	8.69119i	−0.280114	+	0.953982i	0.692473	+	0.721444i	$0.256521\pi$
$83$	−2.55196	+	8.69119i	−0.280114	+	0.953982i	−0.972587	+	0.232538i	$0.925297\pi$
$84$	9.47034	−	4.88233i	1.03330	−	0.532706i
$85$	−11.5323	+	9.99277i	−1.25085	+	1.08387i
$86$	−0.705327	−	3.62431i	−0.0760574	−	0.390819i
$87$	−1.93019	+	3.71105i	−0.206938	+	0.397867i
$88$	−2.67931	−	5.78363i	−0.285615	−	0.616538i
$89$	1.56952	+	0.225662i	0.166368	+	0.0239201i	0.224996	−	0.974360i	$-0.427763\pi$
$89$	1.56952	+	0.225662i	0.166368	+	0.0239201i	−0.0586272	+	0.998280i	$0.518672\pi$
$90$	−6.20211	−	15.7388i	−0.653759	−	1.65901i
$91$	5.09884			0.534504
$92$	−8.66510	−	4.11291i	−0.903399	−	0.428800i
$93$	−9.27833	−	8.91109i	−0.962118	−	0.924037i
$94$	3.52449	−	1.22698i	0.363523	−	0.126553i
$95$	2.66163	−	18.5120i	0.273077	−	1.89929i
$96$	−7.05432	+	6.79975i	−0.719978	+	0.693996i
$97$	11.4356	−	3.35780i	1.16111	−	0.340933i	0.356246	−	0.934392i	$-0.384057\pi$
$97$	11.4356	−	3.35780i	1.16111	−	0.340933i	0.804864	+	0.593460i	$0.202238\pi$
$98$	0.664677	+	3.41543i	0.0671425	+	0.345010i
$99$	−4.62997	−	4.92657i	−0.465329	−	0.495139i
$100$	7.05462	−	20.6240i	0.705462	−	2.06240i
$101$	−17.2004	−	5.05050i	−1.71151	−	0.502544i	−0.728334	−	0.685222i	$-0.759705\pi$
$101$	−17.2004	−	5.05050i	−1.71151	−	0.502544i	−0.983173	+	0.182678i	$0.941523\pi$
$102$	9.27634	+	1.35083i	0.918495	+	0.133753i
$103$	−6.29903	+	9.80148i	−0.620662	+	0.965768i	0.378531	+	0.925589i	$0.376429\pi$
$103$	−6.29903	+	9.80148i	−0.620662	+	0.965768i	−0.999192	+	0.0401797i	$0.987207\pi$
$104$	−4.49165	+	1.34537i	−0.440442	+	0.131925i
$105$	21.1529	−	1.94275i	2.06431	−	0.189593i
$106$	−7.47518	−	4.29779i	−0.726053	−	0.417439i
$107$	−13.3733	+	1.92280i	−1.29285	+	0.185884i	−0.754199	−	0.656646i	$-0.771975\pi$
$107$	−13.3733	+	1.92280i	−1.29285	+	0.185884i	−0.538650	+	0.842530i	$0.681066\pi$
$108$	−4.82863	+	9.20241i	−0.464636	+	0.885502i
$109$	14.7742	−	6.74714i	1.41511	−	0.646259i	0.446485	−	0.894791i	$-0.352675\pi$
$109$	14.7742	−	6.74714i	1.41511	−	0.646259i	0.968624	+	0.248532i	$0.0799482\pi$
$110$	−0.627607	−	12.6922i	−0.0598400	−	1.21016i
$111$	11.5666	−	4.58213i	1.09785	−	0.434917i
$112$	−5.71654	−	10.8944i	−0.540163	−	1.02942i
$113$	5.73433	+	8.92279i	0.539440	+	0.839386i	0.998806	−	0.0488618i	$-0.0155594\pi$
$113$	5.73433	+	8.92279i	0.539440	+	0.839386i	−0.459365	+	0.888248i	$0.651923\pi$
$114$	−9.67661	+	6.19413i	−0.906298	+	0.580133i
$115$	−12.9394	−	14.0798i	−1.20660	−	1.31294i
$116$	4.30115	+	2.19775i	0.399352	+	0.204056i
$117$	−4.07182	+	2.85541i	−0.376440	+	0.263982i
$118$	17.6209	+	7.01739i	1.62213	+	0.646003i
$119$	−4.88983	+	10.7072i	−0.448250	+	0.981531i
$120$	−18.1213	+	7.29277i	−1.65424	+	0.665736i
$121$	2.45982	+	5.38626i	0.223620	+	0.489660i
$122$	9.02943	−	4.67568i	0.817486	−	0.423316i
$123$	−6.38987	+	8.90504i	−0.576155	+	0.802940i
$124$	−10.2119	+	10.7878i	−0.917058	+	0.968773i
$125$	15.4019	−	17.7748i	1.37759	−	1.58983i
$126$	−9.39536	−	9.05616i	−0.837005	−	0.806787i
$127$	1.00467	−	1.56330i	0.0891500	−	0.138720i	−0.793814	−	0.608160i	$-0.791908\pi$
$127$	1.00467	−	1.56330i	0.0891500	−	0.138720i	0.882964	+	0.469440i	$0.155544\pi$
$128$	7.91036	+	8.08865i	0.699183	+	0.714942i
$129$	−3.92442	+	2.24690i	−0.345526	+	0.197828i
$130$	−9.30711	−	0.871743i	−0.816288	−	0.0764569i
$131$	10.8411	−	9.39390i	0.947194	−	0.820748i	−0.0367317	−	0.999325i	$-0.511695\pi$
$131$	10.8411	−	9.39390i	0.947194	−	0.820748i	0.983926	+	0.178577i	$0.0571493\pi$
$132$	−5.64992	+	5.38722i	−0.491762	+	0.468897i
$133$	−4.06452	−	13.8425i	−0.352439	−	1.20030i
$134$	3.24979	−	4.14786i	0.280739	−	0.358321i
$135$	−15.8043	+	13.3973i	−1.36021	+	1.15305i
$136$	1.48233	−	10.7224i	0.127109	−	0.919438i
$137$		−	7.24379i		−	0.618878i	−0.950919	−	0.309439i	$-0.899859\pi$
$137$		−	7.24379i		−	0.618878i	0.950919	−	0.309439i	$-0.100141\pi$
$138$	−1.35248	+	11.6692i	−0.115131	+	0.993350i
$139$	−11.3848			−0.965643			−0.482822	−	0.875719i	$-0.660388\pi$
$139$	−11.3848			−0.965643			−0.482822	+	0.875719i	$0.660388\pi$
$140$	−2.41982	−	24.4084i	−0.204512	−	2.06289i
$141$	−2.81241	−	3.60299i	−0.236848	−	0.303427i
$142$	−11.8368	+	15.1079i	−0.993324	+	1.26783i
$143$	−3.58454	+	1.05251i	−0.299754	+	0.0880157i
$144$	10.6661	+	5.49866i	0.888838	+	0.458222i
$145$	6.30603	+	7.27754i	0.523687	+	0.604367i
$146$	1.26708	−	13.5279i	0.104864	−	1.11957i
$147$	3.69825	−	2.11740i	0.305026	−	0.174640i
$148$	−5.38741	−	13.3173i	−0.442842	−	1.09468i
$149$	−2.57299	−	1.65356i	−0.210788	−	0.135465i	0.430987	−	0.902358i	$-0.358165\pi$
$149$	−2.57299	−	1.65356i	−0.210788	−	0.135465i	−0.641775	+	0.766893i	$0.721802\pi$
$150$	−26.6959	−	0.0481954i	−2.17971	−	0.00393514i
$151$	5.00142	+	4.33375i	0.407010	+	0.352676i	0.834177	−	0.551497i	$-0.185943\pi$
$151$	5.00142	+	4.33375i	0.407010	+	0.352676i	−0.427167	+	0.904173i	$0.640488\pi$
$152$	7.23295	+	11.1216i	0.586670	+	0.902080i
$153$	−2.09126	−	11.2889i	−0.169069	−	0.912654i
$154$	−4.50757	−	8.70480i	−0.363231	−	0.701452i
$155$	−26.9387	+	12.3025i	−2.16377	+	0.988160i
$156$	3.33104	+	4.67777i	0.266697	+	0.374521i
$157$	7.55834	+	3.45178i	0.603221	+	0.275482i	0.693525	−	0.720432i	$-0.256057\pi$
$157$	7.55834	+	3.45178i	0.603221	+	0.275482i	−0.0903040	+	0.995914i	$0.528784\pi$
$158$	−6.96094	−	2.77215i	−0.553783	−	0.220540i
$159$	−2.03604	+	10.3624i	−0.161469	+	0.821789i
$160$	8.57202	+	20.8632i	0.677678	+	1.64938i
$161$	−13.5912	−	5.73313i	−1.07113	−	0.451834i
$162$	12.5745	+	1.97054i	0.987943	+	0.154820i
$163$	−6.83157	+	4.39039i	−0.535090	+	0.343882i	−0.780116	−	0.625635i	$-0.784840\pi$
$163$	−6.83157	+	4.39039i	−0.535090	+	0.343882i	0.245026	+	0.969517i	$0.421204\pi$
$164$	10.3357	+	7.30385i	0.807085	+	0.570335i
$165$	−14.4697	+	5.73220i	−1.12646	+	0.446251i
$166$	−0.632663	−	12.7945i	−0.0491042	−	0.993043i
$167$	1.26611	+	2.77239i	0.0979745	+	0.214534i	0.952272	−	0.305249i	$-0.0987398\pi$
$167$	1.26611	+	2.77239i	0.0979745	+	0.214534i	−0.854298	+	0.519784i	$0.826013\pi$
$168$	−10.3784	+	10.9241i	−0.800715	+	0.842816i
$169$	−1.45900	−	10.1475i	−0.112230	−	0.780580i
$170$	10.7562	−	18.7083i	0.824963	−	1.43486i
$171$	10.9978	+	8.77811i	0.841020	+	0.671279i
$172$	2.62719	+	4.51266i	0.200321	+	0.344087i
$173$	−4.22360	−	2.71434i	−0.321114	−	0.206368i	0.370146	−	0.928974i	$-0.379308\pi$
$173$	−4.22360	−	2.71434i	−0.321114	−	0.206368i	−0.691260	+	0.722606i	$0.742944\pi$
$174$	0.852456	−	5.85392i	0.0646245	−	0.443784i
$175$	9.44412	−	32.1637i	0.713908	−	2.43135i
$176$	6.26762	+	6.47882i	0.472440	+	0.488360i
$177$	1.18914	−	23.1990i	0.0893811	−	1.74374i
$178$	−2.20116	+	0.428368i	−0.164984	+	0.0321075i
$179$	−5.42015	−	18.4593i	−0.405121	−	1.37972i	−0.869436	−	0.494045i	$-0.835518\pi$
$179$	−5.42015	−	18.4593i	−0.405121	−	1.37972i	0.464315	−	0.885670i	$-0.346301\pi$
$180$	15.6014	+	18.1369i	1.16286	+	1.35184i
$181$	−14.3997	−	2.07036i	−1.07032	−	0.153889i	−0.415440	−	0.909621i	$-0.636372\pi$
$181$	−14.3997	−	2.07036i	−1.07032	−	0.153889i	−0.654881	+	0.755732i	$0.727281\pi$
$182$	−6.80999	+	2.37076i	−0.504790	+	0.175732i
$183$	−8.98189	−	8.62639i	−0.663960	−	0.637681i
$184$	13.4854	+	1.46425i	0.994157	+	0.107946i
$185$		−	28.6403i		−	2.10568i
$186$	16.5354	+	7.58756i	1.21243	+	0.556347i
$187$	1.22739	−	8.53666i	0.0897554	−	0.624263i
$188$	−4.13679	+	3.27749i	−0.301707	+	0.239035i
$189$	−6.79644	+	14.4651i	−0.494368	+	1.05218i
$190$	5.05249	+	25.9621i	0.366546	+	1.88349i
$191$	−2.86267	−	3.30370i	−0.207135	−	0.239047i	0.642671	−	0.766143i	$-0.277826\pi$
$191$	−2.86267	−	3.30370i	−0.207135	−	0.239047i	−0.849806	+	0.527096i	$0.823281\pi$
$192$	6.26010	−	12.3617i	0.451784	−	0.892127i
$193$	−3.37248	−	0.990249i	−0.242756	−	0.0712797i	0.158091	−	0.987425i	$-0.449466\pi$
$193$	−3.37248	−	0.990249i	−0.242756	−	0.0712797i	−0.400847	+	0.916145i	$0.631284\pi$
$194$	−13.7121	+	9.80175i	−0.984471	+	0.703724i
$195$	2.65892	+	11.1357i	0.190409	+	0.797443i
$196$	−2.47577	−	4.25258i	−0.176841	−	0.303756i
$197$	13.2152	−	15.2512i	0.941547	−	1.08660i	−0.0545657	−	0.998510i	$-0.517377\pi$
$197$	13.2152	−	15.2512i	0.941547	−	1.08660i	0.996112	−	0.0880925i	$-0.0280771\pi$
$198$	8.47442	+	4.42716i	0.602251	+	0.314624i
$199$	0.380498	−	0.0547074i	0.0269728	−	0.00387810i	−0.128815	−	0.991669i	$-0.541117\pi$
$199$	0.380498	−	0.0547074i	0.0269728	−	0.00387810i	0.155788	+	0.987791i	$0.450208\pi$
$200$	0.167205	+	30.8254i	0.0118232	+	2.17968i
$201$	−6.09098	−	2.13279i	−0.429625	−	0.150435i
$202$	25.3211	−	1.25208i	1.78159	−	0.0880962i
$203$	6.75690	+	3.08577i	0.474242	+	0.216579i
$204$	−13.0175	+	2.50896i	−0.911408	+	0.175662i
$205$	13.6412	+	21.2262i	0.952744	+	1.48250i
$206$	3.85566	−	16.0196i	0.268636	−	1.11614i
$207$	14.0642	−	3.03285i	0.977530	−	0.210798i
$208$	5.37347	−	3.88531i	0.372583	−	0.269398i
$209$	5.71479	+	8.89239i	0.395301	+	0.615100i
$210$	−27.3484	+	12.4300i	−1.88722	+	0.857750i
$211$	−5.02990	+	11.0139i	−0.346272	+	0.758231i	0.653726	+	0.756731i	$0.273205\pi$
$211$	−5.02990	+	11.0139i	−0.346272	+	0.758231i	−0.999999	+	0.00149983i	$0.999523\pi$
$212$	11.9821	+	2.26445i	0.822934	+	0.155523i
$213$	22.1854	+	7.76831i	1.52012	+	0.532276i
$214$	16.9673	−	8.78613i	1.15986	−	0.600608i
$215$	1.48153	+	10.3043i	0.101040	+	0.702747i
$216$	2.17035	−	14.5358i	0.147674	−	0.989036i
$217$	−14.9601	+	17.2649i	−1.01556	+	1.17202i
$218$	−16.5952	+	15.8808i	−1.12397	+	1.07559i
$219$	−16.1857	+	3.86473i	−1.09373	+	0.261155i
$220$	6.73960	+	16.6598i	0.454384	+	1.12321i
$221$	−6.08719	−	1.78736i	−0.409469	−	0.120231i
$222$	−13.3177	+	11.4979i	−0.893829	+	0.771686i
$223$	5.85736	−	5.07543i	0.392238	−	0.339876i	−0.436308	−	0.899797i	$-0.643714\pi$
$223$	5.85736	−	5.07543i	0.392238	−	0.339876i	0.828546	+	0.559922i	$0.189169\pi$
$224$	12.7004	+	11.8925i	0.848583	+	0.794601i
$225$	10.4702	+	30.9740i	0.698011	+	2.06493i
$226$	−11.8075	−	9.25100i	−0.785422	−	0.615367i
$227$	22.4398	+	3.22636i	1.48938	+	0.214141i	0.838443	−	0.544989i	$-0.183466\pi$
$227$	22.4398	+	3.22636i	1.48938	+	0.214141i	0.650939	+	0.759130i	$0.274375\pi$
$228$	10.0440	−	12.7721i	0.665181	−	0.845851i
$229$		−	9.81023i		−	0.648278i	−0.946009	−	0.324139i	$-0.894925\pi$
$229$		−	9.81023i		−	0.648278i	0.946009	−	0.324139i	$-0.105075\pi$
$230$	23.8283	+	12.7886i	1.57119	+	0.843253i
$231$	−8.31625	+	8.65896i	−0.547169	+	0.569718i
$232$	−6.76646	−	0.935438i	−0.444240	−	0.0614145i
$233$	−5.87094	−	0.844114i	−0.384618	−	0.0552997i	−0.0527061	−	0.998610i	$-0.516785\pi$
$233$	−5.87094	−	0.844114i	−0.384618	−	0.0552997i	−0.331912	+	0.943310i	$0.607694\pi$
$234$	4.11065	−	5.70689i	0.268721	−	0.373071i
$235$	−10.0958	+	2.96441i	−0.658580	+	0.193377i
$236$	−26.7971	−	1.17940i	−1.74434	−	0.0767723i
$237$	−0.469756	+	9.16452i	−0.0305140	+	0.595300i
$238$	1.55240	−	16.5741i	0.100627	−	1.07434i
$239$	−20.1334	−	5.91169i	−1.30232	−	0.382396i	−0.444238	−	0.895909i	$-0.646526\pi$
$239$	−20.1334	−	5.91169i	−1.30232	−	0.382396i	−0.858082	+	0.513513i	$0.828344\pi$
$240$	20.8119	−	18.1659i	1.34340	−	1.17260i
$241$	12.3208	+	7.91810i	0.793653	+	0.510050i	0.873539	−	0.486754i	$-0.161819\pi$
$241$	12.3208	+	7.91810i	0.793653	+	0.510050i	−0.0798862	+	0.996804i	$0.525456\pi$
$242$	−5.78972	−	6.05014i	−0.372177	−	0.388918i
$243$	−2.67312	−	15.3576i	−0.171481	−	0.985187i
$244$	−9.88566	+	10.4431i	−0.632864	+	0.668553i
$245$	−1.39615	−	9.71043i	−0.0891967	−	0.620376i
$246$	4.39379	−	14.8645i	0.280138	−	0.947729i
$247$	7.07296	−	3.23011i	0.450042	−	0.205527i
$248$	8.62310	−	19.1563i	0.547567	−	1.21642i
$249$	−14.5862	+	5.77838i	−0.924365	+	0.366190i
$250$	−12.3062	+	30.9012i	−0.778312	+	1.95436i
$251$	−3.77295	−	5.87082i	−0.238146	−	0.370563i	0.701523	−	0.712647i	$-0.252504\pi$
$251$	−3.77295	−	5.87082i	−0.238146	−	0.370563i	−0.939669	+	0.342084i	$0.888867\pi$
$252$	16.7591	+	7.72690i	1.05573	+	0.486749i
$253$	10.7382	+	1.22493i	0.675103	+	0.0770104i
$254$	−0.614961	+	2.55506i	−0.0385861	+	0.160319i
$255$	−25.9342	−	5.09566i	−1.62406	−	0.319102i
$256$	−14.3259	−	7.12516i	−0.895370	−	0.445322i
$257$	24.8514	+	11.3493i	1.55019	+	0.707948i	0.992516	−	0.122113i	$-0.0389671\pi$
$257$	24.8514	+	11.3493i	1.55019	+	0.707948i	0.557673	+	0.830061i	$0.311694\pi$
$258$	4.19672	−	4.82564i	0.261276	−	0.300431i
$259$	−9.17774	−	20.0964i	−0.570277	−	1.24873i
$260$	12.8359	−	3.16314i	0.796046	−	0.196169i
$261$	−7.12397	+	1.31971i	−0.440963	+	0.0816880i
$262$	−10.1116	+	17.5871i	−0.624695	+	1.08654i
$263$	−1.74672	+	2.01582i	−0.107707	+	0.124301i	−0.807043	−	0.590492i	$-0.798934\pi$
$263$	−1.74672	+	2.01582i	−0.107707	+	0.124301i	0.699336	+	0.714793i	$0.253479\pi$
$264$	5.04116	−	9.82212i	0.310262	−	0.604510i
$265$	20.4517	+	13.1435i	1.25634	+	0.807400i
$266$	11.8647	+	16.5981i	0.727474	+	1.01770i
$267$	1.36461	+	2.38343i	0.0835130	+	0.145863i
$268$	−2.41182	+	7.05088i	−0.147325	+	0.430701i
$269$	−12.2649	−	14.1545i	−0.747806	−	0.863014i	0.246548	−	0.969131i	$-0.420704\pi$
$269$	−12.2649	−	14.1545i	−0.747806	−	0.863014i	−0.994354	+	0.106117i	$0.966158\pi$
$270$	14.8789	−	25.2417i	0.905500	−	1.53616i
$271$	−1.29514	−	4.41083i	−0.0786740	−	0.267939i	0.910757	−	0.412942i	$-0.135499\pi$
$271$	−1.29514	−	4.41083i	−0.0786740	−	0.267939i	−0.989431	+	0.145003i	$0.953681\pi$
$272$	3.00569	+	15.0100i	0.182247	+	0.910114i
$273$	5.43412	+	6.96168i	0.328888	+	0.421340i
$274$	3.36807	+	9.67476i	0.203472	+	0.584474i
$275$			24.5609i			1.48108i
$276$	−3.61935	−	16.2142i	−0.217859	−	0.975980i
$277$		−	0.774779i		−	0.0465520i	−0.999729	−	0.0232760i	$-0.992590\pi$
$277$		−	0.774779i		−	0.0465520i	0.999729	−	0.0232760i	$-0.00740965\pi$
$278$	15.2054	−	5.29346i	0.911961	−	0.317480i
$279$	2.27827	−	22.1652i	0.136397	−	1.32699i
$280$	14.5808	+	31.4746i	0.871371	+	1.88097i
$281$	3.24912	+	11.0655i	0.193826	+	0.660111i	0.997851	+	0.0655164i	$0.0208695\pi$
$281$	3.24912	+	11.0655i	0.193826	+	0.660111i	−0.804025	+	0.594595i	$0.797312\pi$
$282$	5.43149	+	3.50448i	0.323441	+	0.208689i
$283$	5.48030	+	6.32461i	0.325770	+	0.375959i	0.894883	−	0.446301i	$-0.147259\pi$
$283$	5.48030	+	6.32461i	0.325770	+	0.375959i	−0.569113	+	0.822259i	$0.692713\pi$
$284$	8.78464	−	25.6816i	0.521272	−	1.52393i
$285$	28.1119	−	16.0953i	1.66521	−	0.953402i
$286$	4.29811	−	3.07240i	0.254153	−	0.181675i
$287$	16.3737	+	10.5227i	0.966508	+	0.621137i
$288$	−16.8022	−	2.38470i	−0.990078	−	0.140520i
$289$	−1.54162	+	1.77913i	−0.0906838	+	0.104655i
$290$	−11.8061	−	6.78780i	−0.693276	−	0.398593i
$291$	16.7721	+	12.0349i	0.983199	+	0.705501i
$292$	4.59761	+	18.6569i	0.269055	+	1.09181i
$293$	7.68930	+	16.8372i	0.449214	+	0.983641i	0.989815	+	0.142362i	$0.0454696\pi$
$293$	7.68930	+	16.8372i	0.449214	+	0.983641i	−0.540601	+	0.841279i	$0.681803\pi$
$294$	−3.95485	+	4.54753i	−0.230652	+	0.265217i
$295$	−48.6434	−	22.2147i	−2.83213	−	1.29339i
$296$	13.3874	+	15.2816i	0.778128	+	0.888226i
$297$	1.79205	−	11.5720i	0.103985	−	0.671477i
$298$	4.20532	+	1.01215i	0.243607	+	0.0586324i
$299$	2.01604	−	7.69040i	0.116590	−	0.444747i
$300$	35.6773	−	12.3482i	2.05983	−	0.712921i
$301$	4.34156	+	6.75559i	0.250243	+	0.389386i
$302$	−8.69489	−	3.46268i	−0.500335	−	0.199255i
$303$	−11.4358	−	28.8671i	−0.656969	−	1.65837i
$304$	−14.8314	−	11.4909i	−0.850638	−	0.659049i
$305$	−26.0780	+	11.9094i	−1.49322	+	0.681932i
$306$	8.04196	+	14.1051i	0.459729	+	0.806332i
$307$	−0.415204	−	2.88780i	−0.0236969	−	0.164816i	0.974537	−	0.224229i	$-0.0719862\pi$
$307$	−0.415204	−	2.88780i	−0.0236969	−	0.164816i	−0.998233	+	0.0594129i	$0.981077\pi$
$308$	10.0677	+	9.53024i	0.573659	+	0.543036i
$309$	−20.0956	+	1.84565i	−1.14320	+	0.104995i
$310$	30.2590	−	28.9565i	1.71860	−	1.64462i
$311$	5.97665	+	3.84096i	0.338905	+	0.217801i	0.699012	−	0.715110i	$-0.253623\pi$
$311$	5.97665	+	3.84096i	0.338905	+	0.217801i	−0.360107	+	0.932911i	$0.617260\pi$
$312$	−6.62390	−	4.69880i	−0.375004	−	0.266017i
$313$	−15.9455	−	4.68203i	−0.901295	−	0.264644i	−0.201922	−	0.979402i	$-0.564719\pi$
$313$	−15.9455	−	4.68203i	−0.901295	−	0.264644i	−0.699372	+	0.714758i	$0.746537\pi$
$314$	−11.6998	−	1.09585i	−0.660259	−	0.0618426i
$315$	25.1964	+	26.8105i	1.41965	+	1.51060i
$316$	10.5859	+	0.465909i	0.595505	+	0.0262094i
$317$	−6.23158	+	1.82976i	−0.350000	+	0.102769i	−0.452007	−	0.892014i	$-0.649292\pi$
$317$	−6.23158	+	1.82976i	−0.350000	+	0.102769i	0.102007	+	0.994784i	$0.467474\pi$
$318$	−2.09875	−	14.7866i	−0.117692	−	0.829191i
$319$	−5.38714	−	0.774554i	−0.301622	−	0.0433667i
$320$	−21.1493	−	23.8792i	−1.18228	−	1.33489i
$321$	−16.8780	−	16.2100i	−0.942038	−	0.904752i
$322$	20.8180	+	1.33779i	1.16014	+	0.0745523i
$323$			17.9505i			0.998791i
$324$	−17.7106	+	3.21478i	−0.983922	+	0.178599i
$325$	17.8832	+	2.57121i	0.991979	+	0.142625i
$326$	7.08286	−	9.04018i	0.392283	−	0.500689i
$327$	24.9578	+	12.9810i	1.38017	+	0.717852i
$328$	−17.2003	−	4.94929i	−0.949730	−	0.273279i
$329$	−6.13414	+	5.31526i	−0.338186	+	0.293040i
$330$	16.6604	−	14.3837i	0.917123	−	0.791797i
$331$	26.7245	+	7.84703i	1.46891	+	0.431312i	0.915746	−	0.401758i	$-0.131601\pi$
$331$	26.7245	+	7.84703i	1.46891	+	0.431312i	0.553167	+	0.833070i	$0.313419\pi$
$332$	6.79389	+	16.7940i	0.372863	+	0.921693i
$333$	18.5833	+	10.9089i	1.01836	+	0.597805i
$334$	−2.98006	−	3.11410i	−0.163062	−	0.170396i
$335$	−9.72902	+	11.2279i	−0.531553	+	0.613445i
$336$	8.78211	−	19.4158i	0.479104	−	1.05922i
$337$	0.789635	+	5.49203i	0.0430142	+	0.299170i	0.999960	+	0.00890467i	$0.00283448\pi$
$337$	0.789635	+	5.49203i	0.0430142	+	0.299170i	−0.956946	+	0.290265i	$0.906256\pi$
$338$	6.66682	+	12.8746i	0.362627	+	0.700287i
$339$	−6.07128	+	17.3389i	−0.329747	+	0.941717i
$340$	−5.66731	+	29.9879i	−0.307353	+	1.62632i
$341$	6.95325	−	15.2255i	0.376539	−	0.824506i
$342$	−18.7700	−	6.61048i	−1.01497	−	0.357454i
$343$	7.54888	+	11.7463i	0.407601	+	0.634240i
$344$	−5.60706	−	4.80554i	−0.302312	−	0.259098i
$345$	5.43349	−	32.6723i	0.292529	−	1.75902i
$346$	6.90308	+	1.66146i	0.371112	+	0.0893206i
$347$	1.13953	+	1.77314i	0.0611731	+	0.0951872i	0.870493	−	0.492181i	$-0.163800\pi$
$347$	1.13953	+	1.77314i	0.0611731	+	0.0951872i	−0.809320	+	0.587369i	$0.800164\pi$
$348$	1.58330	+	8.21482i	0.0848738	+	0.440361i
$349$	−18.3213	−	8.36707i	−0.980718	−	0.447879i	−0.140472	−	0.990085i	$-0.544862\pi$
$349$	−18.3213	−	8.36707i	−0.980718	−	0.447879i	−0.840246	+	0.542206i	$0.817589\pi$
$350$	2.34131	+	47.3488i	0.125148	+	2.53090i
$351$	−8.23817	−	2.51626i	−0.439721	−	0.134308i
$352$	−11.3834	−	5.73889i	−0.606737	−	0.305884i
$353$	−20.4191	+	2.93582i	−1.08680	+	0.156258i	−0.662350	−	0.749194i	$-0.730441\pi$
$353$	−20.4191	+	2.93582i	−1.08680	+	0.156258i	−0.424448	+	0.905452i	$0.639532\pi$
$354$	9.19840	+	31.5374i	0.488889	+	1.67619i
$355$	35.4363	−	40.8957i	1.88076	−	2.17052i
$356$	2.74068	−	1.59558i	0.145256	−	0.0845654i
$357$	−19.8304	+	4.73501i	−1.04954	+	0.250603i
$358$	15.8220	+	22.1340i	0.836217	+	1.16982i
$359$	−0.906077	−	0.266048i	−0.0478209	−	0.0140415i	0.257735	−	0.966216i	$-0.417024\pi$
$359$	−0.906077	−	0.266048i	−0.0478209	−	0.0140415i	−0.305556	+	0.952174i	$0.598842\pi$
$360$	−29.2700	−	16.9695i	−1.54267	−	0.894370i
$361$	−1.96503	−	2.26776i	−0.103422	−	0.119356i
$362$	20.1948	−	3.93011i	1.06141	−	0.206562i
$363$	−4.73253	+	9.09894i	−0.248393	+	0.477571i
$364$	7.99308	−	6.33274i	0.418951	−	0.331926i
$365$	−5.45181	+	37.9182i	−0.285361	+	1.98473i
$366$	16.0071	+	7.34514i	0.836704	+	0.383937i
$367$			5.45537i			0.284768i	0.989811	+	0.142384i	$0.0454768\pi$
$367$			5.45537i			0.284768i	−0.989811	+	0.142384i	$0.954523\pi$
$368$	−18.6918	+	4.31451i	−0.974380	+	0.224910i
$369$	−18.9685	+	0.766232i	−0.987460	+	0.0398884i
$370$	13.3166	+	38.2519i	0.692297	+	1.98862i
$371$	18.5624	+	2.66887i	0.963713	+	0.138561i
$372$	−25.6125	−	2.44562i	−1.32794	−	0.126800i
$373$	−8.22690	−	28.0183i	−0.425973	−	1.45073i	−0.841057	−	0.540947i	$-0.818066\pi$
$373$	−8.22690	−	28.0183i	−0.425973	−	1.45073i	0.415084	−	0.909783i	$-0.363752\pi$
$374$	2.32991	+	11.9722i	0.120477	+	0.619068i
$375$	40.6834	+	2.08536i	2.10088	+	0.107687i
$376$	4.00118	−	6.30084i	0.206345	−	0.324941i
$377$	−1.12793	+	3.84138i	−0.0580913	+	0.197841i
$378$	2.35161	−	22.4796i	0.120954	−	1.15622i
$379$	−13.9558	−	8.96883i	−0.716860	−	0.460698i	0.130683	−	0.991424i	$-0.458283\pi$
$379$	−13.9558	−	8.96883i	−0.716860	−	0.460698i	−0.847543	+	0.530726i	$0.821919\pi$
$380$	−18.8194	−	32.3257i	−0.965415	−	1.65827i
$381$	3.20517	−	0.294373i	0.164206	−	0.0150812i
$382$	5.35945	+	3.08137i	0.274213	+	0.157657i
$383$	−3.01714	−	20.9846i	−0.154168	−	1.07226i	−0.909135	−	0.416502i	$-0.863256\pi$
$383$	−3.01714	−	20.9846i	−0.154168	−	1.07226i	0.754967	−	0.655763i	$-0.227653\pi$
$384$	−2.61327	+	19.4209i	−0.133358	+	0.991068i
$385$	11.4813	+	25.1404i	0.585139	+	1.28128i
$386$	4.96469	−	0.245495i	0.252696	−	0.0124954i
$387$	−7.25027	−	2.96354i	−0.368552	−	0.150645i
$388$	13.7564	−	19.4667i	0.698374	−	0.988273i
$389$	3.65245	−	2.34729i	0.185187	−	0.119012i	−0.444763	−	0.895648i	$-0.646712\pi$
$389$	3.65245	−	2.34729i	0.185187	−	0.119012i	0.629949	+	0.776636i	$0.283076\pi$
$390$	−8.72888	−	13.6365i	−0.442004	−	0.690510i
$391$	14.2159	+	11.6087i	0.718931	+	0.587078i
$392$	5.28391	+	4.52859i	0.266878	+	0.228728i
$393$	24.3799	+	4.79027i	1.22980	+	0.241637i
$394$	−10.5590	+	26.5140i	−0.531955	+	1.33575i
$395$	19.2160	+	8.77567i	0.966864	+	0.441552i
$396$	−13.3768	−	1.97262i	−0.672211	−	0.0991280i
$397$	16.3826	−	7.48170i	0.822221	−	0.375496i	0.0405430	−	0.999178i	$-0.487091\pi$
$397$	16.3826	−	7.48170i	0.822221	−	0.375496i	0.781678	+	0.623682i	$0.214364\pi$
$398$	−0.482755	+	0.249983i	−0.0241983	+	0.0125305i
$399$	14.5680	−	20.3022i	0.729311	−	1.01638i
$400$	−14.5559	−	41.0925i	−0.727794	−	2.05462i
$401$	−24.1825	−	20.9542i	−1.20761	−	1.04640i	−0.997638	−	0.0686973i	$-0.978116\pi$
$401$	−24.1825	−	20.9542i	−1.20761	−	1.04640i	−0.209977	−	0.977706i	$-0.567339\pi$
$402$	9.12674	+	0.0164769i	0.455201	+	0.000821794i
$403$	−10.3580	−	6.65669i	−0.515969	−	0.331593i
$404$	−33.2365	+	13.4456i	−1.65358	+	0.668941i
$405$	−35.1354	−	7.30000i	−1.74589	−	0.362740i
$406$	−10.4592	−	0.979656i	−0.519083	−	0.0486195i
$407$	10.6004	+	12.2335i	0.525442	+	0.606392i
$408$	16.2196	−	9.40357i	0.802988	−	0.465546i
$409$	−32.5679	+	9.56281i	−1.61038	+	0.472850i	−0.958410	−	0.285394i	$-0.907875\pi$
$409$	−32.5679	+	9.56281i	−1.61038	+	0.472850i	−0.651970	+	0.758245i	$0.726057\pi$
$410$	−28.0884	−	22.0069i	−1.38719	−	1.08684i
$411$	9.89026	−	7.72011i	0.487850	−	0.380805i
$412$	2.29887	+	23.1884i	0.113257	+	1.14241i
$413$	−41.2508			−2.02982
$414$	−17.3739	+	10.5899i	−0.853881	+	0.520468i
$415$			36.1174i			1.77293i
$416$	−5.37027	+	7.68764i	−0.263299	+	0.376918i
$417$	−12.1334	−	15.5441i	−0.594175	−	0.761199i
$418$	−11.7672	−	9.21948i	−0.575555	−	0.450940i
$419$	−10.4104	−	35.4546i	−0.508582	−	1.73207i	−0.667340	−	0.744753i	$-0.732567\pi$
$419$	−10.4104	−	35.4546i	−0.508582	−	1.73207i	0.158758	−	0.987317i	$-0.449251\pi$
$420$	30.7469	−	29.3173i	1.50030	−	1.43054i
$421$	−19.6321	+	17.0113i	−0.956808	+	0.829079i	−0.985355	−	0.170513i	$-0.945457\pi$
$421$	−19.6321	+	17.0113i	−0.956808	+	0.829079i	0.0285471	+	0.999592i	$0.490912\pi$
$422$	1.59687	−	17.0489i	0.0777343	−	0.829925i
$423$	1.92198	−	7.67983i	0.0934497	−	0.373406i
$424$	−17.0561	+	2.54680i	−0.828318	+	0.123684i
$425$	−22.5495	+	35.0877i	−1.09381	+	1.70200i
$426$	−33.2426	−	0.0600144i	−1.61061	−	0.00290771i
$427$	−14.4822	+	16.7133i	−0.700840	+	0.808813i
$428$	−18.5763	+	19.6238i	−0.897918	+	0.948554i
$429$	−5.25729	−	3.77240i	−0.253824	−	0.182133i
$430$	−6.76981	−	13.0735i	−0.326469	−	0.630460i
$431$	−3.36041	−	7.35826i	−0.161865	−	0.354435i	0.811269	−	0.584672i	$-0.198777\pi$
$431$	−3.36041	−	7.35826i	−0.161865	−	0.354435i	−0.973134	+	0.230237i	$0.926050\pi$
$432$	3.85985	+	20.4231i	0.185707	+	0.982605i
$433$	9.25671	−	20.2694i	0.444849	−	0.974084i	−0.545834	−	0.837894i	$-0.683787\pi$
$433$	9.25671	−	20.2694i	0.444849	−	0.974084i	0.990683	−	0.136190i	$-0.0434858\pi$
$434$	11.9532	−	30.0147i	0.573771	−	1.44075i
$435$	−3.21566	+	16.3660i	−0.154179	+	0.784689i
$436$	14.7805	−	28.9264i	0.707855	−	1.38532i
$437$	−22.4852	+	0.657169i	−1.07561	+	0.0314367i
$438$	19.8206	−	12.6874i	0.947064	−	0.606228i
$439$	0.185395	+	0.288480i	0.00884843	+	0.0137684i	0.845650	−	0.533739i	$-0.179213\pi$
$439$	0.185395	+	0.288480i	0.00884843	+	0.0137684i	−0.836801	+	0.547507i	$0.815577\pi$
$440$	−16.7475	−	19.1172i	−0.798407	−	0.911375i
$441$	6.83241	+	2.79274i	0.325353	+	0.132988i
$442$	8.96107	−	0.443109i	0.426235	−	0.0210765i
$443$	19.7722	−	9.02968i	0.939407	−	0.429013i	0.113956	−	0.993486i	$-0.463648\pi$
$443$	19.7722	−	9.02968i	0.939407	−	0.429013i	0.825452	+	0.564473i	$0.190921\pi$
$444$	12.4411	−	21.5487i	0.590427	−	1.02266i
$445$	6.25813	−	0.899784i	0.296664	−	0.0426538i
$446$	−5.46318	+	9.50215i	−0.258689	+	0.449940i
$447$	−0.484503	−	5.27532i	−0.0229162	−	0.249514i
$448$	−22.4921	−	9.97837i	−1.06265	−	0.471434i
$449$	7.10643	−	11.0578i	0.335373	−	0.521851i	−0.632079	−	0.774904i	$-0.717798\pi$
$449$	7.10643	−	11.0578i	0.335373	−	0.521851i	0.967452	+	0.253053i	$0.0814346\pi$
$450$	−28.3855	−	36.5005i	−1.33811	−	1.72065i
$451$	−13.6830	−	4.01769i	−0.644306	−	0.189185i
$452$	20.0713	+	6.86559i	0.944077	+	0.322930i
$453$	−0.586771	+	11.4474i	−0.0275689	+	0.537845i
$454$	−31.4706	+	6.12450i	−1.47699	+	0.287437i
$455$	19.5071	−	5.72780i	0.914507	−	0.268523i
$456$	−7.47623	+	21.7284i	−0.350107	+	1.01752i
$457$	−4.57898	+	31.8475i	−0.214196	+	1.48976i	0.544744	+	0.838603i	$0.316627\pi$
$457$	−4.57898	+	31.8475i	−0.214196	+	1.48976i	−0.758939	+	0.651161i	$0.774282\pi$
$458$	4.56136	+	13.1025i	0.213138	+	0.612239i
$459$	13.1845	−	14.8865i	0.615398	−	0.694843i
$460$	−37.7711	−	6.00115i	−1.76109	−	0.279805i
$461$	23.3189			1.08607			0.543034	−	0.839711i	$-0.317276\pi$
$461$	23.3189			1.08607			0.543034	+	0.839711i	$0.317276\pi$
$462$	7.08106	−	15.4316i	0.329441	−	0.717942i
$463$	12.9049	+	1.85545i	0.599743	+	0.0862300i	0.435498	−	0.900190i	$-0.356572\pi$
$463$	12.9049	+	1.85545i	0.599743	+	0.0862300i	0.164245	+	0.986420i	$0.447481\pi$
$464$	9.47219	−	1.89677i	0.439735	−	0.0880551i
$465$	−45.5072	−	23.6691i	−2.11035	−	1.09763i
$466$	8.23368	−	1.60236i	0.381418	−	0.0742277i
$467$	0.286485	−	0.248241i	0.0132570	−	0.0114872i	−0.648207	−	0.761464i	$-0.724481\pi$
$467$	0.286485	−	0.248241i	0.0132570	−	0.0114872i	0.661464	+	0.749977i	$0.269935\pi$
$468$	−2.83668	+	9.53338i	−0.131126	+	0.440681i
$469$	−3.22873	+	10.9961i	−0.149089	+	0.507751i
$470$	12.1056	−	8.65340i	0.558391	−	0.399152i
$471$	3.34248	+	13.9985i	0.154014	+	0.645016i
$472$	36.3385	−	10.8844i	1.67261	−	0.500994i
$473$	−4.44666	−	3.85305i	−0.204458	−	0.177164i
$474$	−3.63373	−	12.4585i	−0.166903	−	0.572238i
$475$	−7.27509	−	50.5993i	−0.333804	−	2.32166i
$476$	5.63291	+	22.8581i	0.258184	+	1.04770i
$477$	−16.3181	+	8.26385i	−0.747155	+	0.378376i
$478$	29.6387	−	1.46558i	1.35564	−	0.0670342i
$479$	−10.6807	+	23.3875i	−0.488014	+	1.06860i	0.492167	+	0.870501i	$0.336205\pi$
$479$	−10.6807	+	23.3875i	−0.488014	+	1.06860i	−0.980181	+	0.198102i	$0.936522\pi$
$480$	−19.3498	+	33.9389i	−0.883194	+	1.54909i
$481$	10.0171	−	6.43762i	0.456742	−	0.293530i
$482$	−20.1372	−	4.84669i	−0.917224	−	0.220761i
$483$	−6.65718	−	24.6667i	−0.302912	−	1.12238i
$484$	10.5458	+	5.38855i	0.479354	+	0.244934i
$485$	39.9782	−	25.6924i	1.81532	−	1.16663i
$486$	10.7108	+	19.2686i	0.485854	+	0.874040i
$487$	29.9224	+	13.6651i	1.35592	+	0.619226i	0.954922	−	0.296856i	$-0.0959380\pi$
$487$	29.9224	+	13.6651i	1.35592	+	0.619226i	0.400993	+	0.916081i	$0.368665\pi$
$488$	8.34760	−	18.5442i	0.377878	−	0.839458i
$489$	−13.2752	−	4.64837i	−0.600324	−	0.210206i
$490$	6.37964	+	12.3200i	0.288203	+	0.556563i
$491$	6.32572	−	0.909501i	0.285476	−	0.0410452i	0.00191045	−	0.999998i	$-0.499392\pi$
$491$	6.32572	−	0.909501i	0.285476	−	0.0410452i	0.283565	+	0.958953i	$0.408483\pi$
$492$	1.04309	+	21.8959i	0.0470262	+	0.987145i
$493$	−6.98495	−	6.05249i	−0.314586	−	0.272591i
$494$	−7.94473	+	7.60276i	−0.357451	+	0.342064i
$495$	−23.2476	−	13.6469i	−1.04490	−	0.613384i
$496$	−2.61008	+	29.5944i	−0.117196	+	1.32883i
$497$	11.7601	−	40.0513i	0.527513	−	1.79655i
$498$	16.7946	−	14.4996i	0.752583	−	0.649742i
$499$	10.1616	+	11.7272i	0.454897	+	0.524979i	0.936149	−	0.351603i	$-0.114363\pi$
$499$	10.1616	+	11.7272i	0.454897	+	0.524979i	−0.481252	+	0.876582i	$0.659818\pi$
$500$	2.06828	−	46.9934i	0.0924962	−	2.10161i
$501$	−2.43591	+	4.68337i	−0.108828	+	0.209238i
$502$	7.76882	+	6.08676i	0.346739	+	0.271666i
$503$	−1.67372	+	11.6410i	−0.0746277	+	0.519047i	0.917879	+	0.396859i	$0.129900\pi$
$503$	−1.67372	+	11.6410i	−0.0746277	+	0.519047i	−0.992507	+	0.122187i	$0.961009\pi$
$504$	−25.9761	−	2.52768i	−1.15707	−	0.112592i
$505$	−71.4787			−3.18076
$506$	−14.9114	+	3.35681i	−0.662892	+	0.149228i
$507$	12.2999	−	12.8068i	0.546260	−	0.568771i
$508$	−0.366661	−	3.69846i	−0.0162679	−	0.164092i
$509$	−0.613024	+	4.26368i	−0.0271718	+	0.188984i	−0.998887	−	0.0471728i	$-0.984979\pi$
$509$	−0.613024	+	4.26368i	−0.0271718	+	0.188984i	0.971715	+	0.236157i	$0.0758880\pi$
$510$	37.0068	−	5.25260i	1.63869	−	0.232589i
$511$	8.32535	+	28.3535i	0.368292	+	1.25429i
$512$	22.4465	+	2.85535i	0.992006	+	0.126190i
$513$	−0.264198	+	24.3711i	−0.0116646	+	1.07601i
$514$	−38.4684	−	3.60311i	−1.69677	−	0.158926i
$515$	−13.0882	+	44.5744i	−0.576736	+	1.96418i
$516$	−3.36139	+	8.39641i	−0.147977	+	0.369631i
$517$	3.21517	−	5.00290i	0.141403	−	0.220027i
$518$	21.6018	+	22.5734i	0.949127	+	0.991819i
$519$	−0.795317	−	8.65950i	−0.0349105	−	0.380110i
$520$	−15.6728	+	10.1928i	−0.687296	+	0.446985i
$521$	13.2782	−	1.90911i	0.581727	−	0.0836398i	0.154832	−	0.987941i	$-0.450516\pi$
$521$	13.2782	−	1.90911i	0.581727	−	0.0836398i	0.426895	+	0.904301i	$0.359607\pi$
$522$	8.90112	−	5.07495i	0.389592	−	0.222125i
$523$	14.8032	+	32.4145i	0.647298	+	1.41739i	0.893899	+	0.448268i	$0.147959\pi$
$523$	14.8032	+	32.4145i	0.647298	+	1.41739i	−0.246601	+	0.969117i	$0.579314\pi$
$524$	5.32766	−	28.1907i	0.232740	−	1.23152i
$525$	53.9796	−	21.3842i	2.35586	−	0.933283i
$526$	1.39563	−	3.50447i	0.0608525	−	0.152802i
$527$	23.9120	−	15.3673i	1.04162	−	0.669411i
$528$	−2.16606	+	15.4623i	−0.0942657	+	0.672910i
$529$	−14.0209	+	18.2322i	−0.609604	+	0.792706i
$530$	−33.4264	−	8.04519i	−1.45195	−	0.349461i
$531$	32.9420	−	23.1009i	1.42956	−	1.00249i
$532$	−23.5639	−	16.6517i	−1.02163	−	0.721944i
$533$	−4.35778	+	9.54220i	−0.188756	+	0.413319i
$534$	−2.93077	−	2.54880i	−0.126827	−	0.110298i
$535$	−49.0036	+	22.3792i	−2.11861	+	0.967537i
$536$	−0.0571636	−	10.5385i	−0.00246909	−	0.455195i
$537$	19.4268	−	27.0735i	0.838328	−	1.16831i
$538$	22.9622	+	13.2020i	0.989972	+	0.569177i
$539$	4.19038	+	3.63099i	0.180493	+	0.156398i
$540$	−8.13578	+	40.6307i	−0.350108	+	1.74847i
$541$	−1.99488	+	3.10409i	−0.0857664	+	0.133455i	−0.881486	−	0.472210i	$-0.843456\pi$
$541$	−1.99488	+	3.10409i	−0.0857664	+	0.133455i	0.795720	+	0.605665i	$0.207093\pi$
$542$	3.78064	+	5.28890i	0.162392	+	0.227178i
$543$	−12.5198	−	21.8670i	−0.537276	−	0.938404i
$544$	−10.9934	−	18.6497i	−0.471339	−	0.799601i
$545$	48.9434	−	42.4097i	2.09651	−	1.81663i
$546$	−10.4947	−	6.77133i	−0.449131	−	0.289786i
$547$	21.4889	−	6.30972i	0.918800	−	0.269784i	0.212060	−	0.977257i	$-0.431983\pi$
$547$	21.4889	−	6.30972i	0.918800	−	0.269784i	0.706741	+	0.707473i	$0.250165\pi$
$548$	−8.99674	−	11.3555i	−0.384322	−	0.485085i
$549$	2.20549	−	21.4570i	0.0941278	−	0.915762i
$550$	−11.4198	−	32.8034i	−0.486942	−	1.39874i
$551$	11.3278			0.482581
$552$	12.3729	+	19.9727i	0.526627	+	0.850096i
$553$	16.2957			0.692964
$554$	0.360241	+	1.03479i	0.0153052	+	0.0439641i
$555$	39.1039	−	30.5236i	1.65987	−	1.29566i
$556$	−17.8471	+	14.1398i	−0.756884	+	0.599662i
$557$	−14.7839	+	4.34096i	−0.626416	+	0.183932i	−0.579507	−	0.814967i	$-0.696755\pi$
$557$	−14.7839	+	4.34096i	−0.626416	+	0.183932i	−0.0469082	+	0.998899i	$0.514937\pi$
$558$	7.26305	+	30.6630i	0.307469	+	1.29807i
$559$	−3.27098	+	2.83432i	−0.138348	+	0.119879i
$560$	−34.1085	−	35.2578i	−1.44135	−	1.48992i
$561$	12.9636	−	7.42220i	0.547323	−	0.313365i
$562$	−9.48451	−	13.2683i	−0.400080	−	0.559689i
$563$	1.68607	−	2.62358i	0.0710595	−	0.110571i	−0.803905	−	0.594757i	$-0.797248\pi$
$563$	1.68607	−	2.62358i	0.0710595	−	0.110571i	0.874965	+	0.484187i	$0.160884\pi$
$564$	−8.88371	−	2.15514i	−0.374072	−	0.0907477i
$565$	31.9618	+	27.6950i	1.34464	+	1.16514i
$566$	−10.2601	−	5.89899i	−0.431266	−	0.247953i
$567$	−26.9932	+	6.13677i	−1.13361	+	0.257720i
$568$	0.208209	+	38.3848i	0.00873625	+	1.61059i
$569$	24.7688	−	11.3115i	1.03836	−	0.474205i	0.178077	−	0.984017i	$-0.443012\pi$
$569$	24.7688	−	11.3115i	1.03836	−	0.474205i	0.860286	+	0.509812i	$0.170285\pi$
$570$	−30.0625	+	34.5677i	−1.25918	+	1.44788i
$571$	17.3199	−	37.9253i	0.724815	−	1.58712i	−0.0822150	−	0.996615i	$-0.526199\pi$
$571$	17.3199	−	37.9253i	0.724815	−	1.58712i	0.807030	−	0.590510i	$-0.201073\pi$
$572$	−4.31199	+	6.10192i	−0.180293	+	0.255134i
$573$	1.45977	−	7.42946i	0.0609829	−	0.310370i
$574$	−26.7613	−	6.44100i	−1.11699	−	0.268842i
$575$	−44.7772	−	26.9615i	−1.86734	−	1.12437i
$576$	23.5497	−	4.62735i	0.981237	−	0.192806i
$577$	36.8829	−	23.7032i	1.53546	−	0.986778i	0.546686	−	0.837338i	$-0.315889\pi$
$577$	36.8829	−	23.7032i	1.53546	−	0.986778i	0.988771	−	0.149440i	$-0.0477470\pi$
$578$	1.23176	−	3.09299i	0.0512345	−	0.128651i
$579$	−2.24221	−	5.65995i	−0.0931830	−	0.235220i
$580$	18.9242	+	3.57641i	0.785783	+	0.148502i
$581$	11.5737	+	25.3430i	0.480160	+	1.05140i
$582$	−27.9965	−	8.27544i	−1.16049	−	0.343028i
$583$	−13.6005	+	1.95545i	−0.563274	+	0.0809866i
$584$	−14.8152	−	22.7803i	−0.613059	−	0.942657i
$585$	−12.3703	+	15.4983i	−0.511448	+	0.640774i
$586$	−18.0984	−	18.9125i	−0.747638	−	0.781267i
$587$	−12.1582	+	18.9186i	−0.501824	+	0.780853i	−0.996079	−	0.0884635i	$-0.971804\pi$
$587$	−12.1582	+	18.9186i	−0.501824	+	0.780853i	0.494256	+	0.869317i	$0.335441\pi$
$588$	3.16766	−	7.91250i	0.130632	−	0.326306i
$589$	−9.81492	+	33.4266i	−0.404417	+	1.37732i
$590$	75.2967	+	7.05261i	3.09992	+	0.290351i
$591$	34.9073	+	1.78928i	1.43590	+	0.0736013i
$592$	−24.9855	−	14.1854i	−1.02690	−	0.583018i
$593$	1.26638	+	4.31289i	0.0520039	+	0.177109i	0.981400	−	0.191976i	$-0.0614894\pi$
$593$	1.26638	+	4.31289i	0.0520039	+	0.177109i	−0.929396	+	0.369085i	$0.879671\pi$
$594$	2.98708	+	16.2888i	0.122561	+	0.668336i
$595$	−6.67946	+	46.4567i	−0.273831	+	1.90454i
$596$	−6.08721	+	0.603478i	−0.249342	+	0.0247194i
$597$	0.480213	+	0.461206i	0.0196538	+	0.0188759i
$598$	0.883115	+	11.2086i	0.0361133	+	0.458355i
$599$	43.1008			1.76105			0.880526	−	0.473998i	$-0.157189\pi$
$599$	43.1008			1.76105			0.880526	+	0.473998i	$0.157189\pi$
$600$	−41.9091	+	33.0806i	−1.71093	+	1.35051i
$601$	−6.33091	+	44.0325i	−0.258243	+	1.79612i	0.287091	+	0.957903i	$0.407312\pi$
$601$	−6.33091	+	44.0325i	−0.258243	+	1.79612i	−0.545335	+	0.838218i	$0.683597\pi$
$602$	−8.93964	−	7.00408i	−0.364352	−	0.285465i
$603$	−3.57952	−	10.5893i	−0.145769	−	0.431230i
$604$	13.2229	+	0.581966i	0.538030	+	0.0236799i
$605$	15.4614	+	17.8434i	0.628597	+	0.725439i
$606$	28.6956	+	33.2376i	1.16568	+	1.35018i
$607$	6.85722	−	23.3536i	0.278326	−	0.947892i	−0.695104	−	0.718909i	$-0.744642\pi$
$607$	6.85722	−	23.3536i	0.278326	−	0.947892i	0.973430	−	0.228983i	$-0.0735400\pi$
$608$	25.1515	+	8.45120i	1.02003	+	0.342741i
$609$	2.98807	+	12.5142i	0.121083	+	0.507100i
$610$	29.2923	−	28.0314i	1.18601	−	1.13496i
$611$	−3.30611	−	2.86476i	−0.133751	−	0.115896i
$612$	−17.2991	−	15.0994i	−0.699274	−	0.610359i
$613$	−5.22311	+	0.750969i	−0.210959	+	0.0303314i	−0.246984	−	0.969020i	$-0.579440\pi$
$613$	−5.22311	+	0.750969i	−0.210959	+	0.0303314i	0.0360249	+	0.999351i	$0.488530\pi$
$614$	1.89726	+	3.66388i	0.0765670	+	0.147862i
$615$	−14.4428	+	41.2469i	−0.582389	+	1.66323i
$616$	−17.8775	−	8.04747i	−0.720305	−	0.324242i
$617$	19.3350	+	8.83000i	0.778398	+	0.355482i	0.764669	−	0.644423i	$-0.222903\pi$
$617$	19.3350	+	8.83000i	0.778398	+	0.355482i	0.0137288	+	0.999906i	$0.495630\pi$
$618$	25.9814	−	11.8087i	1.04513	−	0.475015i
$619$	−18.9822	+	12.1991i	−0.762960	+	0.490325i	−0.863339	−	0.504625i	$-0.831631\pi$
$619$	−18.9822	+	12.1991i	−0.762960	+	0.490325i	0.100379	+	0.994949i	$0.467994\pi$
$620$	−26.9502	+	52.7434i	−1.08234	+	2.11823i
$621$	19.1299	+	15.9702i	0.767656	+	0.640862i
$622$	−9.76827	−	2.35106i	−0.391672	−	0.0942691i
$623$	4.10289	−	2.63677i	0.164379	−	0.105640i
$624$	11.0316	+	3.19585i	0.441617	+	0.127936i
$625$	16.3201	−	35.7360i	0.652803	−	1.42944i
$626$	23.4737	−	1.16073i	0.938198	−	0.0463922i
$627$	−6.05060	+	17.2798i	−0.241638	+	0.690088i
$628$	16.1357	−	3.97632i	0.643886	−	0.158673i
$629$	3.91207	+	27.2091i	0.155985	+	1.08490i
$630$	−46.1179	−	24.0927i	−1.83738	−	0.959874i
$631$	−12.6572	−	10.9675i	−0.503874	−	0.436609i	0.365465	−	0.930825i	$-0.380910\pi$
$631$	−12.6572	−	10.9675i	−0.503874	−	0.436609i	−0.869339	+	0.494216i	$0.835455\pi$
$632$	−14.3551	+	4.29976i	−0.571017	+	0.171035i
$633$	−20.3985	+	4.87063i	−0.810766	+	0.193590i
$634$	7.47210	−	5.34125i	0.296755	−	0.212128i
$635$	2.08752	−	7.10944i	0.0828407	−	0.282129i
$636$	9.67825	+	18.7731i	0.383767	+	0.744400i
$637$	3.08246	−	2.67097i	0.122132	−	0.105828i
$638$	7.55517	−	1.47031i	0.299112	−	0.0582102i
$639$	13.0378	+	38.5698i	0.515767	+	1.52580i
$640$	39.3498	+	22.0593i	1.55544	+	0.871972i
$641$	−39.7181	−	5.71060i	−1.56877	−	0.225555i	−0.697582	−	0.716504i	$-0.745741\pi$
$641$	−39.7181	−	5.71060i	−1.56877	−	0.225555i	−0.871188	+	0.490949i	$0.836650\pi$
$642$	30.0791	+	13.8024i	1.18713	+	0.544736i
$643$	0.857195			0.0338045			0.0169022	−	0.999857i	$-0.494620\pi$
$643$	0.857195			0.0338045			0.0169022	+	0.999857i	$0.494620\pi$
$644$	−28.4264	+	7.89276i	−1.12016	+	0.311018i
$645$	−12.4900	+	13.0047i	−0.491791	+	0.512058i
$646$	−8.34624	−	23.9745i	−0.328378	−	0.943266i
$647$	−4.15845	+	28.9227i	−0.163486	+	1.13707i	0.728514	+	0.685031i	$0.240212\pi$
$647$	−4.15845	+	28.9227i	−0.163486	+	1.13707i	−0.891999	+	0.452037i	$0.850698\pi$
$648$	22.1594	−	12.5283i	0.870505	−	0.492160i
$649$	28.9997	−	8.51509i	1.13834	−	0.334247i
$650$	−25.0802	+	4.88085i	−0.983725	+	0.191443i
$651$	−39.5164	−	2.02553i	−1.54877	−	0.0793869i
$652$	−5.25651	+	15.3673i	−0.205861	+	0.601828i
$653$	−0.265257	−	0.0778866i	−0.0103803	−	0.00304794i	0.276538	−	0.961003i	$-0.410813\pi$
$653$	−0.265257	−	0.0778866i	−0.0103803	−	0.00304794i	−0.286919	+	0.957955i	$0.592631\pi$
$654$	−39.3692	−	5.73300i	−1.53946	−	0.224178i
$655$	30.9232	−	48.1175i	1.20827	−	1.88011i
$656$	25.2739	−	1.38721i	0.986780	−	0.0541616i
$657$	−22.5267	−	17.9802i	−0.878850	−	0.701474i
$658$	5.72134	−	9.95116i	0.223041	−	0.387937i
$659$	39.3122	−	5.65223i	1.53138	−	0.220180i	0.675505	−	0.737356i	$-0.263926\pi$
$659$	39.3122	−	5.65223i	1.53138	−	0.220180i	0.855879	+	0.517176i	$0.173017\pi$
$660$	−15.5636	+	26.9572i	−0.605814	+	1.04931i
$661$	32.8351	−	14.9953i	1.27714	−	0.583250i	0.342724	−	0.939436i	$-0.388651\pi$
$661$	32.8351	−	14.9953i	1.27714	−	0.583250i	0.934415	+	0.356187i	$0.115923\pi$
$662$	−39.3417	+	1.94538i	−1.52906	+	0.0756092i
$663$	−4.04710	−	10.2160i	−0.157176	−	0.396757i
$664$	−16.8824	−	19.2712i	−0.655165	−	0.747866i
$665$	−31.1000	−	48.3925i	−1.20601	−	1.87658i
$666$	−29.8920	−	5.92938i	−1.15829	−	0.229759i
$667$	7.32578	−	8.97110i	0.283655	−	0.347362i
$668$	5.42808	+	2.77357i	0.210019	+	0.107313i
$669$	13.1722	+	2.58814i	0.509267	+	0.100063i
$670$	7.77351	−	19.5195i	0.300317	−	0.754104i
$671$	6.73109	−	14.7390i	0.259851	−	0.568994i
$672$	−2.70179	+	30.0149i	−0.104224	+	1.15785i
$673$	8.21626	+	17.9911i	0.316713	+	0.693506i	0.999304	−	0.0372951i	$-0.0118741\pi$
$673$	8.21626	+	17.9911i	0.316713	+	0.693506i	−0.682591	+	0.730801i	$0.739147\pi$
$674$	−3.60820	−	6.96798i	−0.138983	−	0.268397i
$675$	−31.1315	+	47.3061i	−1.19825	+	1.82081i
$676$	−14.8903	−	14.0955i	−0.572706	−	0.542133i
$677$	2.64054	−	3.04735i	0.101484	−	0.117119i	−0.702735	−	0.711451i	$-0.748038\pi$
$677$	2.64054	−	3.04735i	0.101484	−	0.117119i	0.804220	+	0.594332i	$0.202584\pi$
$678$	0.0469039	−	25.9806i	0.00180133	−	0.997778i
$679$	19.8189	−	30.8389i	0.760581	−	1.18349i
$680$	−6.37395	−	42.6868i	−0.244430	−	1.63696i
$681$	19.5103	+	34.0766i	0.747635	+	1.30582i
$682$	−2.20748	+	23.5681i	−0.0845289	+	0.902467i
$683$	−15.0703	+	13.0585i	−0.576649	+	0.499669i	−0.893655	−	0.448754i	$-0.851868\pi$
$683$	−15.0703	+	13.0585i	−0.576649	+	0.499669i	0.317006	+	0.948423i	$0.397322\pi$
$684$	28.1427	+	0.101615i	1.07606	+	0.00388535i
$685$	−8.13733	−	27.7132i	−0.310911	−	1.05887i
$686$	−15.5438	−	12.1784i	−0.593465	−	0.464972i
$687$	13.3943	−	10.4553i	0.511026	−	0.398895i
$688$	9.72314	+	3.81120i	0.370691	+	0.145301i
$689$			10.1074i			0.385063i
$690$	7.93436	+	46.1633i	0.302056	+	1.75741i
$691$	26.1693			0.995526			0.497763	−	0.867313i	$-0.334155\pi$
$691$	26.1693			0.995526			0.497763	+	0.867313i	$0.334155\pi$
$692$	−9.99222	+	0.990617i	−0.379847	+	0.0376576i
$693$	−20.6856	−	2.12619i	−0.785779	−	0.0807673i
$694$	−2.34639	−	1.83836i	−0.0890677	−	0.0697833i
$695$	−43.5557	+	12.7891i	−1.65216	+	0.485119i
$696$	−5.93421	−	10.2355i	−0.224935	−	0.387975i
$697$	−15.8589	−	18.3021i	−0.600697	−	0.693241i
$698$	28.3602	+	2.65634i	1.07345	+	0.100544i
$699$	−5.10449	−	8.91547i	−0.193069	−	0.337214i
$700$	−25.1423	−	62.1502i	−0.950290	−	2.34906i
$701$	−8.62312	−	5.54174i	−0.325691	−	0.209309i	0.367570	−	0.929996i	$-0.380190\pi$
$701$	−8.62312	−	5.54174i	−0.325691	−	0.209309i	−0.693260	+	0.720687i	$0.743826\pi$
$702$	12.1728	−	0.469711i	0.459434	−	0.0177281i
$703$	−25.4621	−	22.0631i	−0.960323	−	0.832125i
$704$	17.8719	+	2.37201i	0.673574	+	0.0893984i
$705$	−14.8071	−	10.6250i	−0.557669	−	0.400159i
$706$	25.9066	−	13.4151i	0.975007	−	0.504885i
$707$	−50.1554	+	22.9052i	−1.88629	+	0.861439i
$708$	−26.9489	−	37.8443i	−1.01280	−	1.42227i
$709$	42.3742	+	19.3517i	1.59140	+	0.726767i	0.997000	−	0.0774042i	$-0.0246632\pi$
$709$	42.3742	+	19.3517i	1.59140	+	0.726767i	0.594398	+	0.804171i	$0.297390\pi$
$710$	−28.3137	+	71.0965i	−1.06259	+	2.66820i
$711$	−13.0134	+	9.12577i	−0.488040	+	0.342243i
$712$	−2.91856	+	3.40535i	−0.109378	+	0.127621i
$713$	20.1249	+	29.3902i	0.753684	+	1.10067i
$714$	24.2838	−	15.5444i	0.908800	−	0.581735i
$715$	−12.5313	+	8.05340i	−0.468645	+	0.301180i
$716$	−31.4232	−	22.2055i	−1.17434	−	0.829859i
$717$	−13.3858	−	33.7894i	−0.499901	−	1.26189i
$718$	1.33385	−	0.0659566i	0.0497790	−	0.00246148i
$719$	−2.07317	−	4.53961i	−0.0773162	−	0.169299i	0.867027	−	0.498262i	$-0.166028\pi$
$719$	−2.07317	−	4.53961i	−0.0773162	−	0.169299i	−0.944343	+	0.328963i	$0.893301\pi$
$720$	46.9830	+	9.05497i	1.75095	+	0.337459i
$721$	5.09999	+	35.4712i	0.189933	+	1.32102i
$722$	3.67890	+	2.11515i	0.136914	+	0.0787178i
$723$	2.32004	+	25.2609i	0.0862834	+	0.939463i
$724$	−25.1447	+	14.6388i	−0.934496	+	0.544046i
$725$	22.1424	+	14.2301i	0.822348	+	0.528491i
$726$	2.09009	−	14.3529i	0.0775707	−	0.532687i
$727$	1.35861	−	4.62701i	0.0503882	−	0.171606i	−0.930455	−	0.366407i	$-0.880588\pi$
$727$	1.35861	−	4.62701i	0.0503882	−	0.171606i	0.980843	+	0.194801i	$0.0624060\pi$
$728$	−7.73104	+	12.1744i	−0.286531	+	0.451214i
$729$	18.1194	−	20.0171i	0.671091	−	0.741375i
$730$	−10.3490	−	53.1781i	−0.383034	−	1.96821i
$731$	−2.81499	−	9.58698i	−0.104116	−	0.354587i
$732$	−24.7942	−	2.36749i	−0.916419	−	0.0875049i
$733$	−5.21681	−	0.750064i	−0.192687	−	0.0277042i	0.0452955	−	0.998974i	$-0.485577\pi$
$733$	−5.21681	−	0.750064i	−0.192687	−	0.0277042i	−0.237983	+	0.971269i	$0.576486\pi$
$734$	−2.53653	−	7.28616i	−0.0936249	−	0.268937i
$735$	11.7701	−	12.2552i	0.434147	−	0.452039i
$736$	22.9586	−	14.4534i	0.846267	−	0.532759i
$737$		−	8.39681i		−	0.309301i
$738$	24.9779	−	9.84295i	0.919450	−	0.362324i
$739$	−3.77390	+	26.2480i	−0.138825	+	0.965549i	0.794691	+	0.607014i	$0.207633\pi$
$739$	−3.77390	+	26.2480i	−0.138825	+	0.965549i	−0.933516	+	0.358535i	$0.883276\pi$
$740$	−35.5712	−	44.8973i	−1.30762	−	1.65046i
$741$	11.9483	+	6.21451i	0.438931	+	0.228296i
$742$	−26.0328	+	5.06624i	−0.955694	+	0.185988i
$743$	−4.61367	−	5.32446i	−0.169259	−	0.195336i	0.664782	−	0.747037i	$-0.268524\pi$
$743$	−4.61367	−	5.32446i	−0.169259	−	0.195336i	−0.834042	+	0.551701i	$0.813979\pi$
$744$	35.3450	−	8.64240i	1.29581	−	0.316846i
$745$	−11.7013	−	3.43580i	−0.428701	−	0.125878i
$746$	24.0152	+	33.5959i	0.879258	+	1.23003i
$747$	−23.4348	−	13.7569i	−0.857436	−	0.503338i
$748$	−8.67841	−	14.9067i	−0.317314	−	0.545043i
$749$	−27.2136	+	31.4062i	−0.994364	+	1.14756i
$750$	−55.3062	+	16.1310i	−2.01950	+	0.589019i
$751$	16.4788	−	2.36930i	0.601322	−	0.0864570i	0.165070	−	0.986282i	$-0.447215\pi$
$751$	16.4788	−	2.36930i	0.601322	−	0.0864570i	0.436251	+	0.899825i	$0.356306\pi$
$752$	−2.41432	+	10.2757i	−0.0880410	+	0.374718i
$753$	3.99464	−	11.4082i	0.145573	−	0.415739i
$754$	−0.279628	−	5.65496i	−0.0101834	−	0.205942i
$755$	24.0027	+	10.9617i	0.873548	+	0.398936i
$756$	7.31129	+	31.1170i	0.265909	+	1.13171i
$757$	4.94505	+	7.69465i	0.179731	+	0.279667i	0.919416	−	0.393286i	$-0.128662\pi$
$757$	4.94505	+	7.69465i	0.179731	+	0.279667i	−0.739685	+	0.672953i	$0.765026\pi$
$758$	22.8094	+	5.48985i	0.828474	+	0.199400i
$759$	9.77182	+	15.9668i	0.354695	+	0.579557i
$760$	40.1652	+	34.4237i	1.45695	+	1.24868i
$761$	1.09737	+	1.70754i	0.0397795	+	0.0618982i	0.860574	−	0.509326i	$-0.170105\pi$
$761$	1.09737	+	1.70754i	0.0397795	+	0.0618982i	−0.820794	+	0.571224i	$0.806469\pi$
$762$	−4.14393	+	1.88344i	−0.150119	+	0.0682297i
$763$	20.7527	−	45.4420i	0.751297	−	1.64511i
$764$	−8.59077	−	1.62354i	−0.310803	−	0.0587375i
$765$	−20.6822	−	40.8398i	−0.747765	−	1.47656i
$766$	13.7867	+	26.6241i	0.498133	+	0.961968i
$767$	−3.16407	−	22.0066i	−0.114248	−	0.794612i
$768$	−5.53965	−	27.1535i	−0.199895	−	0.979817i
$769$	2.18016	−	2.51604i	0.0786186	−	0.0907307i	−0.715077	−	0.699045i	$-0.753609\pi$
$769$	2.18016	−	2.51604i	0.0786186	−	0.0907307i	0.793696	+	0.608315i	$0.208154\pi$
$770$	−27.0236	−	28.2391i	−0.973863	−	1.01767i
$771$	10.9899	+	46.0263i	0.395792	+	1.65760i
$772$	−6.51666	+	2.63626i	−0.234540	+	0.0948811i
$773$	33.9782	+	9.97690i	1.22211	+	0.358844i	0.828267	−	0.560333i	$-0.189327\pi$
$773$	33.9782	+	9.97690i	1.22211	+	0.358844i	0.393844	+	0.919177i	$0.371145\pi$
$774$	11.0613	+	0.587007i	0.397592	+	0.0210995i
$775$	−61.1758	+	53.0091i	−2.19750	+	1.90414i
$776$	−9.32170	+	32.3958i	−0.334629	+	1.16294i
$777$	17.6573	−	33.9487i	0.633453	−	1.21790i
$778$	−3.78680	+	4.83326i	−0.135763	+	0.173281i
$779$	29.3792	+	4.22409i	1.05262	+	0.151344i
$780$	17.9987	+	14.1542i	0.644455	+	0.506802i
$781$			30.5840i			1.09438i
$782$	−24.3843	−	8.89469i	−0.871981	−	0.318073i
$783$	−9.39427	−	8.32018i	−0.335724	−	0.297339i
$784$	−9.16277	−	3.59155i	−0.327242	−	0.128270i
$785$	32.7942	+	4.71509i	1.17047	+	0.168289i
$786$	−34.7889	+	4.93781i	−1.24088	+	0.176126i
$787$	−14.4092	+	4.23092i	−0.513632	+	0.150816i	−0.528269	−	0.849077i	$-0.677159\pi$
$787$	−14.4092	+	4.23092i	−0.513632	+	0.150816i	0.0146372	+	0.999893i	$0.495341\pi$
$788$	1.77463	−	40.3214i	0.0632186	−	1.43639i
$789$	−4.61387	−	0.236498i	−0.164258	−	0.00841955i
$790$	−29.7452	−	2.78606i	−1.05829	−	0.0991235i
$791$	31.3018	+	9.19105i	1.11297	+	0.326796i
$792$	18.7832	−	3.58506i	0.667433	−	0.127390i
$793$	−10.0271	−	6.44401i	−0.356072	−	0.228833i
$794$	−18.4019	+	17.6098i	−0.653058	+	0.624948i
$795$	3.85112	+	41.9314i	0.136585	+	1.48715i
$796$	0.528532	−	0.558337i	0.0187333	−	0.0197897i
$797$	5.56462	+	38.7028i	0.197109	+	1.37092i	0.812620	+	0.582794i	$0.198040\pi$
$797$	5.56462	+	38.7028i	0.197109	+	1.37092i	−0.615511	+	0.788128i	$0.711050\pi$
$798$	−10.0172	+	33.8890i	−0.354605	+	1.19966i
$799$	9.18639	−	4.19528i	0.324991	−	0.148418i
$800$	38.5471	+	48.1150i	1.36285	+	1.70112i
$801$	−1.79985	+	4.40332i	−0.0635947	+	0.155584i
$802$	42.0408	+	16.7425i	1.48451	+	0.591197i
$803$	−11.7056	−	18.2143i	−0.413082	−	0.642767i
$804$	−12.1973	+	4.22156i	−0.430165	+	0.148883i
$805$	−58.4373	−	6.66607i	−2.05964	−	0.234948i
$806$	16.9292	+	4.07458i	0.596305	+	0.143521i
$807$	6.25431	−	31.8311i	0.220162	−	1.12051i
$808$	38.1389	−	33.4114i	1.34172	−	1.17541i
$809$	22.3560	+	10.2097i	0.785996	+	0.358952i	0.767642	−	0.640879i	$-0.221430\pi$
$809$	22.3560	+	10.2097i	0.785996	+	0.358952i	0.0183543	+	0.999832i	$0.494157\pi$
$810$	50.3208	−	6.58670i	1.76809	−	0.231433i
$811$	−13.8461	−	30.3188i	−0.486204	−	1.06464i	−0.980711	−	0.195464i	$-0.937379\pi$
$811$	−13.8461	−	30.3188i	−0.486204	−	1.06464i	0.494507	−	0.869174i	$-0.335349\pi$
$812$	14.4248	−	3.55470i	0.506211	−	0.124746i
$813$	4.64200	−	6.46918i	0.162802	−	0.226884i
$814$	−19.8459	−	11.4102i	−0.695598	−	0.399929i
$815$	−21.2042	+	24.4710i	−0.742751	+	0.857180i
$816$	−17.2905	+	20.1008i	−0.605288	+	0.703668i
$817$	10.3021	+	6.62078i	0.360426	+	0.231632i
$818$	39.0512	−	27.9148i	1.36539	−	0.976018i
$819$	−3.71363	+	14.8389i	−0.129765	+	0.518513i
$820$	47.7471	+	16.3323i	1.66740	+	0.570350i
$821$	−1.45507	−	1.67924i	−0.0507823	−	0.0586059i	0.729790	−	0.683671i	$-0.239618\pi$
$821$	−1.45507	−	1.67924i	−0.0507823	−	0.0586059i	−0.780572	+	0.625065i	$0.785072\pi$
$822$	−9.61983	+	14.9095i	−0.335530	+	0.520029i
$823$	11.6074	+	39.5312i	0.404608	+	1.37797i	0.870082	+	0.492908i	$0.164066\pi$
$823$	11.6074	+	39.5312i	0.404608	+	1.37797i	−0.465473	+	0.885062i	$0.654116\pi$
$824$	−13.8520	−	29.9014i	−0.482558	−	1.04167i
$825$	−33.5340	+	26.1759i	−1.16750	+	0.911328i
$826$	55.0944	−	19.1800i	1.91698	−	0.667357i
$827$			10.5263i			0.366035i	0.983110	+	0.183018i	$0.0585865\pi$
$827$			10.5263i			0.366035i	−0.983110	+	0.183018i	$0.941413\pi$
$828$	18.2806	−	22.2220i	0.635295	−	0.772269i
$829$			30.6511i			1.06456i	0.846570	+	0.532278i	$0.178664\pi$
$829$			30.6511i			1.06456i	−0.846570	+	0.532278i	$0.821336\pi$
$830$	−16.7931	−	48.2382i	−0.582898	−	1.67437i
$831$	1.05784	−	0.825726i	0.0366961	−	0.0286441i
$832$	3.59806	−	12.7645i	0.124740	−	0.442531i
$833$	2.65275	+	9.03445i	0.0919125	+	0.313025i
$834$	23.4327	+	15.1191i	0.811407	+	0.523532i
$835$	7.95824	+	9.18430i	0.275406	+	0.317836i
$836$	20.0030	+	6.84219i	0.691817	+	0.236642i
$837$	32.6911	−	20.5120i	1.12997	−	0.708999i
$838$	30.3890	+	42.5125i	1.04977	+	1.46857i
$839$	−17.0321	−	10.9459i	−0.588013	−	0.377893i	0.212542	−	0.977152i	$-0.431826\pi$
$839$	−17.0321	−	10.9459i	−0.588013	−	0.377893i	−0.800555	+	0.599259i	$0.795462\pi$
$840$	−27.4341	+	53.4521i	−0.946566	+	1.84427i
$841$	15.1715	−	17.5088i	0.523155	−	0.603753i
$842$	18.3109	−	31.8483i	0.631036	−	1.09756i
$843$	−11.6454	+	16.2293i	−0.401090	+	0.558966i
$844$	5.79426	+	23.5128i	0.199447	+	0.809345i
$845$	−16.9811	−	37.1834i	−0.584167	−	1.27915i
$846$	1.00383	+	11.1508i	0.0345123	+	0.383372i
$847$	16.5669	+	7.56586i	0.569246	+	0.259966i
$848$	21.5959	−	11.3319i	0.741606	−	0.389139i
$849$	−2.79460	+	14.2230i	−0.0959103	+	0.488132i
$850$	13.8026	−	57.3475i	0.473426	−	1.96700i
$851$	−33.9395	+	5.89649i	−1.16343	+	0.202129i
$852$	44.4266	−	15.3763i	1.52203	−	0.526784i
$853$	−26.1260	−	40.6528i	−0.894537	−	1.39193i	−0.919860	−	0.392248i	$-0.871698\pi$
$853$	−26.1260	−	40.6528i	−0.894537	−	1.39193i	0.0253225	−	0.999679i	$-0.491939\pi$
$854$	11.5713	−	29.0558i	0.395961	−	0.994269i
$855$	51.9361	+	21.2288i	1.77618	+	0.726010i
$856$	15.6861	−	34.8467i	0.536139	−	1.19104i
$857$	31.7785	−	14.5128i	1.08553	−	0.495747i	0.209408	−	0.977828i	$-0.432846\pi$
$857$	31.7785	−	14.5128i	1.08553	−	0.495747i	0.876126	+	0.482082i	$0.160119\pi$
$858$	8.77561	+	2.59397i	0.299595	+	0.0885567i
$859$	1.90612	+	13.2574i	0.0650361	+	0.452336i	0.996154	+	0.0876180i	$0.0279255\pi$
$859$	1.90612	+	13.2574i	0.0650361	+	0.452336i	−0.931118	+	0.364718i	$0.881165\pi$
$860$	15.1204	+	14.3132i	0.515600	+	0.488077i
$861$	3.08321	+	33.5704i	0.105076	+	1.14408i
$862$	7.90943	+	8.26520i	0.269396	+	0.281514i
$863$	10.2943	+	6.61572i	0.350421	+	0.225202i	0.703995	−	0.710205i	$-0.251398\pi$
$863$	10.2943	+	6.61572i	0.350421	+	0.225202i	−0.353575	+	0.935406i	$0.615034\pi$
$864$	−14.6511	−	25.4823i	−0.498440	−	0.866924i
$865$	−19.2078	−	5.63991i	−0.653084	−	0.191763i
$866$	−2.93877	+	31.3757i	−0.0998636	+	1.06619i
$867$	−4.07212	−	0.208729i	−0.138296	−	0.00708881i
$868$	−2.00895	+	45.6453i	−0.0681881	+	1.54930i
$869$	−11.4560	+	3.36380i	−0.388620	+	0.114109i
$870$	−3.31470	−	23.3535i	−0.112379	−	0.791757i
$871$	−6.11386	−	0.879040i	−0.207160	−	0.0297851i
$872$	−6.29107	+	45.5063i	−0.213043	+	1.54104i
$873$	1.44315	+	35.7260i	0.0488433	+	1.20914i
$874$	29.7255	−	11.3324i	1.00548	−	0.383325i
$875$		−	72.3404i		−	2.44555i
$876$	−20.5731	+	26.1610i	−0.695102	+	0.883899i
$877$	−16.6457	−	2.39329i	−0.562085	−	0.0808156i	−0.144585	−	0.989492i	$-0.546185\pi$
$877$	−16.6457	−	2.39329i	−0.562085	−	0.0808156i	−0.417500	+	0.908677i	$0.637094\pi$
$878$	−0.381744	−	0.299092i	−0.0128832	−	0.0100939i
$879$	−14.7937	+	28.4429i	−0.498978	+	0.959355i
$880$	31.2566	+	17.7458i	1.05366	+	0.598212i
$881$	−2.43491	+	2.10986i	−0.0820343	+	0.0710831i	−0.694913	−	0.719094i	$-0.744557\pi$
$881$	−2.43491	+	2.10986i	−0.0820343	+	0.0710831i	0.612878	+	0.790177i	$0.290012\pi$
$882$	−10.4238	−	0.553176i	−0.350989	−	0.0186264i
$883$	9.22924	+	2.70995i	0.310588	+	0.0911970i	0.433312	−	0.901244i	$-0.357345\pi$
$883$	9.22924	+	2.70995i	0.310588	+	0.0911970i	−0.122724	+	0.992441i	$0.539163\pi$
$884$	−11.7623	+	4.75835i	−0.395610	+	0.160041i
$885$	−21.5113	−	90.0903i	−0.723094	−	3.02835i
$886$	−22.2093	+	21.2533i	−0.746135	+	0.714018i
$887$	−7.03837	+	8.12271i	−0.236325	+	0.272734i	−0.861507	−	0.507745i	$-0.830479\pi$
$887$	−7.03837	+	8.12271i	−0.236325	+	0.272734i	0.625182	+	0.780479i	$0.285025\pi$
$888$	−6.59695	+	34.5649i	−0.221379	+	1.15992i
$889$	−0.813427	−	5.65751i	−0.0272815	−	0.189747i
$890$	−7.93996	+	4.11152i	−0.266148	+	0.137819i
$891$	17.7097	−	9.88620i	0.593297	−	0.331200i
$892$	2.87848	−	15.2312i	0.0963788	−	0.509977i
$893$	−5.14188	+	11.2591i	−0.172066	+	0.376773i
$894$	3.09991	+	6.82041i	0.103676	+	0.228109i
$895$	−41.4727	−	64.5328i	−1.38628	−	2.15709i
$896$	34.6799	+	2.86911i	1.15857	+	0.0958504i
$897$	12.6486	−	5.44350i	0.422326	−	0.181753i
$898$	−4.34987	+	18.0730i	−0.145157	+	0.603103i
$899$	−9.69769	−	15.0899i	−0.323436	−	0.503276i
$900$	54.8828	+	35.5517i	1.82943	+	1.18506i
$901$	−21.2250	−	9.69311i	−0.707106	−	0.322924i
$902$	20.1430	−	0.996034i	0.670688	−	0.0331643i
$903$	−4.59667	+	13.1275i	−0.152967	+	0.436857i
$904$	−29.9994	+	0.162724i	−0.997765	+	0.00541214i
$905$	−57.4159	+	8.25517i	−1.90857	+	0.274411i
$906$	−4.53888	−	15.5619i	−0.150794	−	0.517009i
$907$	−18.0891	+	20.8759i	−0.600637	+	0.693172i	−0.971910	−	0.235351i	$-0.924376\pi$
$907$	−18.0891	+	20.8759i	−0.600637	+	0.693172i	0.371273	+	0.928524i	$0.378921\pi$
$908$	39.1843	−	22.8124i	1.30038	−	0.757056i
$909$	27.2258	−	46.3791i	0.903021	−	1.53830i
$910$	−23.3904	+	16.7200i	−0.775384	+	0.554264i
$911$	35.0232	+	10.2837i	1.16037	+	0.340716i	0.804577	−	0.593849i	$-0.202392\pi$
$911$	35.0232	+	10.2837i	1.16037	+	0.340716i	0.355794	+	0.934564i	$0.384210\pi$
$912$	−0.117601	−	32.4964i	−0.00389415	−	1.07606i
$913$	−13.3678	−	15.4273i	−0.442410	−	0.510568i
$914$	−8.69215	−	44.6644i	−0.287511	−	1.47737i
$915$	−44.0533	−	22.9129i	−1.45636	−	0.757478i
$916$	−12.1843	−	15.3788i	−0.402579	−	0.508128i
$917$	6.27916	−	43.6725i	0.207356	−	1.44219i
$918$	−10.6875	+	26.0126i	−0.352739	+	0.858544i
$919$		−	18.0771i		−	0.596308i	−0.954518	−	0.298154i	$-0.903629\pi$
$919$		−	18.0771i		−	0.596308i	0.954518	−	0.298154i	$-0.0963708\pi$
$920$	53.2372	−	9.54693i	1.75518	−	0.314753i
$921$	3.50034	−	3.64459i	0.115340	−	0.120093i
$922$	−31.1445	+	10.8423i	−1.02569	+	0.357073i
$923$	22.2687	+	3.20175i	0.732983	+	0.105387i
$924$	−2.28237	+	23.9027i	−0.0750844	+	0.786342i
$925$	−22.0549	−	75.1123i	−0.725162	−	2.46968i
$926$	−18.0984	+	3.52214i	−0.594752	+	0.115745i
$927$	−23.9370	−	25.4704i	−0.786193	−	0.836558i
$928$	−11.7691	+	6.93750i	−0.386339	+	0.227734i
$929$	−4.58664	+	15.6206i	−0.150483	+	0.512497i	−0.999884	−	0.0152511i	$-0.995145\pi$
$929$	−4.58664	+	15.6206i	−0.150483	+	0.512497i	0.849401	+	0.527748i	$0.176963\pi$
$930$	71.7844	+	10.4533i	2.35390	+	0.342779i
$931$	−9.70839	−	6.23920i	−0.318180	−	0.204482i
$932$	−10.2518	+	5.96842i	−0.335810	+	0.195502i
$933$	1.12542	+	12.2537i	0.0368446	+	0.401168i
$934$	−0.267206	+	0.464753i	−0.00874325	+	0.0152072i
$935$	−4.89396	−	34.0383i	−0.160050	−	1.11317i
$936$	−0.643979	−	14.0517i	−0.0210491	−	0.459293i
$937$	−0.407378	−	0.892034i	−0.0133085	−	0.0291415i	0.902861	−	0.429932i	$-0.141463\pi$
$937$	−0.407378	−	0.892034i	−0.0133085	−	0.0291415i	−0.916170	+	0.400791i	$0.868735\pi$
$938$	−0.800443	−	16.1875i	−0.0261354	−	0.528541i
$939$	−10.6015	−	26.7610i	−0.345966	−	0.873313i
$940$	−12.1447	+	17.1861i	−0.396117	+	0.560547i
$941$	9.62330	−	6.18452i	0.313711	−	0.201610i	−0.374305	−	0.927306i	$-0.622119\pi$
$941$	9.62330	−	6.18452i	0.313711	−	0.201610i	0.688015	+	0.725696i	$0.258482\pi$
$942$	−10.9729	−	17.1422i	−0.357517	−	0.558522i
$943$	22.3451	−	20.5352i	0.727655	−	0.668719i
$944$	−43.4727	+	31.4330i	−1.41491	+	1.02306i
$945$	−9.75235	+	62.9752i	−0.317244	+	2.04858i
$946$	7.73045	+	3.07860i	0.251338	+	0.100094i
$947$	−5.09254	−	2.32569i	−0.165485	−	0.0755747i	0.330950	−	0.943648i	$-0.392631\pi$
$947$	−5.09254	−	2.32569i	−0.165485	−	0.0755747i	−0.496436	+	0.868074i	$0.665358\pi$
$948$	10.6459	+	14.9500i	0.345762	+	0.485553i
$949$	−14.4875	+	6.61623i	−0.470285	+	0.214772i
$950$	33.2432	+	64.1976i	1.07855	+	2.08284i
$951$	−9.13959	−	6.55817i	−0.296372	−	0.212663i
$952$	−18.1514	−	27.9101i	−0.588290	−	0.904570i
$953$	−3.57130	−	3.09455i	−0.115686	−	0.100242i	0.595097	−	0.803654i	$-0.297114\pi$
$953$	−3.57130	−	3.09455i	−0.115686	−	0.100242i	−0.710783	+	0.703412i	$0.751659\pi$
$954$	17.9520	−	18.6244i	0.581218	−	0.602988i
$955$	−14.6632	−	9.42346i	−0.474490	−	0.304936i
$956$	−38.9039	+	15.7382i	−1.25824	+	0.509011i
$957$	−4.68384	−	8.18078i	−0.151407	−	0.264447i
$958$	3.39086	−	36.2023i	0.109554	−	1.16964i
$959$	−14.5905	−	16.8383i	−0.471150	−	0.543736i
$960$	10.0633	−	54.3255i	0.324791	−	1.75335i
$961$	23.1861	−	6.80806i	0.747940	−	0.219615i
$962$	−10.3856	+	13.2556i	−0.334845	+	0.427378i
$963$	4.14436	−	40.3201i	0.133550	−	1.29930i
$964$	29.1486	−	2.88976i	0.938814	−	0.0930729i
$965$	−14.0148			−0.451152
$966$	20.3603	+	29.8494i	0.655083	+	0.960390i
$967$			28.7120i			0.923316i	0.887058	+	0.461658i	$0.152745\pi$
$967$			28.7120i			0.923316i	−0.887058	+	0.461658i	$0.847255\pi$
$968$	−16.5904	−	2.29355i	−0.533234	−	0.0737176i
$969$	−24.5086	+	19.1308i	−0.787328	+	0.614570i
$970$	−41.4487	+	52.9029i	−1.33084	+	1.69861i
$971$	−5.68544	−	19.3628i	−0.182454	−	0.621383i	−0.999025	−	0.0441377i	$-0.985946\pi$
$971$	−5.68544	−	19.3628i	−0.182454	−	0.621383i	0.816571	−	0.577245i	$-0.195872\pi$
$972$	−23.2645	−	20.7549i	−0.746208	−	0.665713i
$973$	−26.4641	+	22.9312i	−0.848399	+	0.735142i
$974$	−46.3180	−	4.33833i	−1.48412	−	0.139009i
$975$	15.5485	+	27.1569i	0.497951	+	0.869718i
$976$	−2.52669	+	28.6489i	−0.0808773	+	0.917028i
$977$	−23.8587	+	37.1249i	−0.763309	+	1.18773i	0.214190	+	0.976792i	$0.431289\pi$
$977$	−23.8587	+	37.1249i	−0.763309	+	1.18773i	−0.977499	+	0.210940i	$0.932348\pi$
$978$	19.8916	+	0.0359111i	0.636062	+	0.00114831i
$979$	−2.34008	+	2.70060i	−0.0747894	+	0.0863115i
$980$	−14.2489	−	13.4883i	−0.455166	−	0.430868i
$981$	8.87541	+	47.9106i	0.283370	+	1.52967i
$982$	−8.02571	+	4.15593i	−0.256111	+	0.132621i
$983$	20.4318	+	44.7394i	0.651673	+	1.42697i	0.890082	+	0.455800i	$0.150647\pi$
$983$	20.4318	+	44.7394i	0.651673	+	1.42697i	−0.238409	+	0.971165i	$0.576626\pi$
$984$	−11.5739	−	28.7591i	−0.368962	−	0.916807i
$985$	33.4262	−	73.1932i	1.06505	−	2.33213i
$986$	12.1432	+	4.83596i	0.386719	+	0.154008i
$987$	−13.7947	−	2.71044i	−0.439089	−	0.0862741i
$988$	7.07597	−	13.8482i	0.225117	−	0.440569i
$989$	11.9058	−	3.87711i	0.378583	−	0.123285i
$990$	37.3946	+	7.41760i	1.18848	+	0.235747i
$991$	11.6075	+	18.0616i	0.368723	+	0.573745i	0.975191	−	0.221363i	$-0.0710506\pi$
$991$	11.6075	+	18.0616i	0.368723	+	0.573745i	−0.606468	+	0.795108i	$0.707414\pi$
$992$	−10.2742	−	40.7397i	−0.326206	−	1.29349i
$993$	17.7679	+	44.8512i	0.563849	+	1.42331i
$994$	2.91548	+	58.9602i	0.0924733	+	1.87011i
$995$	1.39425	−	0.636733i	0.0442007	−	0.0201858i
$996$	−15.6890	+	27.1744i	−0.497126	+	0.861052i
$997$	29.1782	−	4.19519i	0.924083	−	0.132863i	0.336183	−	0.941797i	$-0.390864\pi$
$997$	29.1782	−	4.19519i	0.924083	−	0.132863i	0.587900	+	0.808934i	$0.299955\pi$
$998$	−19.0245	−	10.9380i	−0.602209	−	0.346235i
$999$	4.91089	+	36.9989i	0.155374	+	1.17059i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.x.a.35.9	✓	920
3.2	odd	2	inner	552.2.x.a.35.84	yes	920
8.3	odd	2	inner	552.2.x.a.35.69	yes	920
23.2	even	11	inner	552.2.x.a.347.24	yes	920
24.11	even	2	inner	552.2.x.a.35.24	yes	920
69.2	odd	22	inner	552.2.x.a.347.69	yes	920
184.163	odd	22	inner	552.2.x.a.347.84	yes	920
552.347	even	22	inner	552.2.x.a.347.9	yes	920

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.x.a.35.9	✓	920	1.1	even	1	trivial
552.2.x.a.35.24	yes	920	24.11	even	2	inner
552.2.x.a.35.69	yes	920	8.3	odd	2	inner
552.2.x.a.35.84	yes	920	3.2	odd	2	inner
552.2.x.a.347.9	yes	920	552.347	even	22	inner
552.2.x.a.347.24	yes	920	23.2	even	11	inner
552.2.x.a.347.69	yes	920	69.2	odd	22	inner
552.2.x.a.347.84	yes	920	184.163	odd	22	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.x (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33559 + 0.464960i) q^{2} +(1.06576 + 1.36534i) q^{3} +(1.56763 - 1.24199i) q^{4} +(3.82579 - 1.12335i) q^{5} +(-2.05825 - 1.32801i) q^{6} +(2.32451 - 2.01420i) q^{7} +(-1.51623 + 2.38768i) q^{8} +(-0.728327 + 2.91025i) q^{9} +O(q^{10})\)	\(q+(-1.33559 + 0.464960i) q^{2} +(1.06576 + 1.36534i) q^{3} +(1.56763 - 1.24199i) q^{4} +(3.82579 - 1.12335i) q^{5} +(-2.05825 - 1.32801i) q^{6} +(2.32451 - 2.01420i) q^{7} +(-1.51623 + 2.38768i) q^{8} +(-0.728327 + 2.91025i) q^{9} +(-4.58739 + 3.27918i) q^{10} +(-1.21838 + 1.89584i) q^{11} +(3.36646 + 0.816684i) q^{12} +(1.25284 + 1.08559i) q^{13} +(-2.16809 + 3.77096i) q^{14} +(5.61112 + 4.02630i) q^{15} +(0.914898 - 3.89396i) q^{16} +(-3.48116 + 1.58979i) q^{17} +(-0.380397 - 4.22555i) q^{18} +(1.94850 - 4.26662i) q^{19} +(4.60220 - 6.51261i) q^{20} +(5.22745 + 1.02711i) q^{21} +(0.745774 - 3.09856i) q^{22} +(-2.11886 - 4.30238i) q^{23} +(-4.87595 + 0.474508i) q^{24} +(9.16847 - 5.89222i) q^{25} +(-2.17804 - 0.867390i) q^{26} +(-4.74971 + 2.10720i) q^{27} +(1.14234 - 6.04455i) q^{28} +(1.00325 + 2.19681i) q^{29} +(-9.36625 - 2.76856i) q^{30} +(-7.35171 + 1.05702i) q^{31} +(0.588604 + 5.62615i) q^{32} +(-3.88696 + 0.356991i) q^{33} +(3.91022 - 3.74191i) q^{34} +(6.63044 - 10.3172i) q^{35} +(2.47277 + 5.46676i) q^{36} +(2.02365 - 6.89193i) q^{37} +(-0.618600 + 6.60444i) q^{38} +(-0.146984 + 2.86753i) q^{39} +(-3.11858 + 10.8380i) q^{40} +(1.78280 + 6.07166i) q^{41} +(-7.45931 + 1.05875i) q^{42} +(-0.371563 + 2.58428i) q^{43} +(0.444655 + 4.48518i) q^{44} +(0.482808 + 11.9522i) q^{45} +(4.83036 + 4.76105i) q^{46} -2.63889 q^{47} +(6.29166 - 2.90087i) q^{48} +(0.350149 - 2.43534i) q^{49} +(-9.50571 + 12.1326i) q^{50} +(-5.88067 - 3.05864i) q^{51} +(3.31228 + 0.145781i) q^{52} +(3.99275 + 4.60788i) q^{53} +(5.36392 - 5.02278i) q^{54} +(-2.53157 + 8.62173i) q^{55} +(1.28477 + 8.60421i) q^{56} +(7.90203 - 1.88680i) q^{57} +(-2.36137 - 2.46758i) q^{58} +(-10.1358 - 8.78269i) q^{59} +(13.7968 - 0.657259i) q^{60} +(-7.11683 + 1.02325i) q^{61} +(9.32744 - 4.83000i) q^{62} +(4.16882 + 8.23191i) q^{63} +(-3.40207 - 7.24058i) q^{64} +(6.01260 + 2.74586i) q^{65} +(5.02542 - 2.28408i) q^{66} +(-3.13450 + 2.01442i) q^{67} +(-3.48264 + 6.81577i) q^{68} +(3.61604 - 7.47825i) q^{69} +(-4.05851 + 16.8624i) q^{70} +(11.4169 - 7.33718i) q^{71} +(-5.84444 - 6.15163i) q^{72} +(-3.99111 + 8.73930i) q^{73} +(0.501689 + 10.1457i) q^{74} +(17.8163 + 6.23845i) q^{75} +(-2.24460 - 9.10848i) q^{76} +(0.986457 + 6.86096i) q^{77} +(-1.13698 - 3.89820i) q^{78} +(4.00403 + 3.46951i) q^{79} +(-0.874092 - 15.9252i) q^{80} +(-7.93908 - 4.23923i) q^{81} +(-5.20417 - 7.28034i) q^{82} +(-2.55196 + 8.69119i) q^{83} +(9.47034 - 4.88233i) q^{84} +(-11.5323 + 9.99277i) q^{85} +(-0.705327 - 3.62431i) q^{86} +(-1.93019 + 3.71105i) q^{87} +(-2.67931 - 5.78363i) q^{88} +(1.56952 + 0.225662i) q^{89} +(-6.20211 - 15.7388i) q^{90} +5.09884 q^{91} +(-8.66510 - 4.11291i) q^{92} +(-9.27833 - 8.91109i) q^{93} +(3.52449 - 1.22698i) q^{94} +(2.66163 - 18.5120i) q^{95} +(-7.05432 + 6.79975i) q^{96} +(11.4356 - 3.35780i) q^{97} +(0.664677 + 3.41543i) q^{98} +(-4.62997 - 4.92657i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 920 q - 18 q^{3} - 14 q^{4} - 16 q^{6} - 18 q^{9}+O(q^{10}) \) 920 * q - 18 * q^3 - 14 * q^4 - 16 * q^6 - 18 * q^9	\( 920 q - 18 q^{3} - 14 q^{4} - 16 q^{6} - 18 q^{9} - 14 q^{10} - 6 q^{12} - 30 q^{16} - 16 q^{18} - 52 q^{19} - 32 q^{22} - 26 q^{24} - 112 q^{25} - 30 q^{27} - 34 q^{28} + 11 q^{30} - 30 q^{33} - 88 q^{34} - 18 q^{36} + 124 q^{40} - 3 q^{42} - 36 q^{43} - 110 q^{46} + 32 q^{49} - 30 q^{51} + 90 q^{52} - 39 q^{54} - 6 q^{57} - 68 q^{58} + 13 q^{60} + 28 q^{64} - 46 q^{66} - 100 q^{67} - 92 q^{70} + 29 q^{72} - 36 q^{73} + 14 q^{75} - 50 q^{76} - 86 q^{78} - 2 q^{81} - 12 q^{82} - 151 q^{84} - 42 q^{88} - 196 q^{90} - 136 q^{91} - 68 q^{94} - 175 q^{96} - 36 q^{97} - 54 q^{99}+O(q^{100}) \) 920 * q - 18 * q^3 - 14 * q^4 - 16 * q^6 - 18 * q^9 - 14 * q^10 - 6 * q^12 - 30 * q^16 - 16 * q^18 - 52 * q^19 - 32 * q^22 - 26 * q^24 - 112 * q^25 - 30 * q^27 - 34 * q^28 + 11 * q^30 - 30 * q^33 - 88 * q^34 - 18 * q^36 + 124 * q^40 - 3 * q^42 - 36 * q^43 - 110 * q^46 + 32 * q^49 - 30 * q^51 + 90 * q^52 - 39 * q^54 - 6 * q^57 - 68 * q^58 + 13 * q^60 + 28 * q^64 - 46 * q^66 - 100 * q^67 - 92 * q^70 + 29 * q^72 - 36 * q^73 + 14 * q^75 - 50 * q^76 - 86 * q^78 - 2 * q^81 - 12 * q^82 - 151 * q^84 - 42 * q^88 - 196 * q^90 - 136 * q^91 - 68 * q^94 - 175 * q^96 - 36 * q^97 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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