LMFDB - Embedded newform 287.2.u.a.8.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,2,Mod(8,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 19]))

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

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

chi := DirichletCharacter("287.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	287.u (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:	$2.29170653801$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$20$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			8.9
Character	$\chi$	$=$	287.8
Dual form			287.2.u.a.36.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.158161 + 0.217690i) q^{2} +(1.91716 + 1.91716i) q^{3} +(0.595660 + 1.83325i) q^{4} +(-0.605064 + 0.196597i) q^{5} +(-0.720570 + 0.114127i) q^{6} +(-0.987688 - 0.156434i) q^{7} +(-1.00511 - 0.326581i) q^{8} +4.35104i q^{9} +O(q^{10})$	\(q+(-0.158161 + 0.217690i) q^{2} +(1.91716 + 1.91716i) q^{3} +(0.595660 + 1.83325i) q^{4} +(-0.605064 + 0.196597i) q^{5} +(-0.720570 + 0.114127i) q^{6} +(-0.987688 - 0.156434i) q^{7} +(-1.00511 - 0.326581i) q^{8} +4.35104i q^{9} +(0.0529004 - 0.162811i) q^{10} +(2.68882 - 1.37002i) q^{11} +(-2.37267 + 4.65663i) q^{12} +(-0.581417 - 3.67092i) q^{13} +(0.190268 - 0.190268i) q^{14} +(-1.53692 - 0.783099i) q^{15} +(-2.88885 + 2.09887i) q^{16} +(1.39744 + 2.74264i) q^{17} +(-0.947180 - 0.688167i) q^{18} +(0.914872 - 5.77628i) q^{19} +(-0.720825 - 0.992131i) q^{20} +(-1.59365 - 2.19347i) q^{21} +(-0.127027 + 0.802014i) q^{22} +(0.215841 + 0.156818i) q^{23} +(-1.30086 - 2.55308i) q^{24} +(-3.71763 + 2.70102i) q^{25} +(0.891082 + 0.454029i) q^{26} +(-2.59017 + 2.59017i) q^{27} +(-0.301542 - 1.90386i) q^{28} +(3.58495 - 7.03586i) q^{29} +(0.413554 - 0.210716i) q^{30} +(-1.10272 + 3.39382i) q^{31} -3.07451i q^{32} +(7.78146 + 2.52835i) q^{33} +(-0.818068 - 0.129569i) q^{34} +(0.628370 - 0.0995240i) q^{35} +(-7.97656 + 2.59174i) q^{36} +(2.04273 + 6.28686i) q^{37} +(1.11274 + 1.11274i) q^{38} +(5.92309 - 8.15243i) q^{39} +0.672363 q^{40} +(2.45151 + 5.91524i) q^{41} +0.729552 q^{42} +(-4.21761 + 5.80504i) q^{43} +(4.11321 + 4.11321i) q^{44} +(-0.855403 - 2.63266i) q^{45} +(-0.0682756 + 0.0221841i) q^{46} +(11.9608 - 1.89441i) q^{47} +(-9.56229 - 1.51452i) q^{48} +(0.951057 + 0.309017i) q^{49} -1.23649i q^{50} +(-2.57896 + 7.93722i) q^{51} +(6.38340 - 3.25250i) q^{52} +(1.65831 - 3.25462i) q^{53} +(-0.154191 - 0.973521i) q^{54} +(-1.35756 + 1.35756i) q^{55} +(0.941650 + 0.479795i) q^{56} +(12.8280 - 9.32011i) q^{57} +(0.964639 + 1.89321i) q^{58} +(-1.86823 - 1.35735i) q^{59} +(0.520137 - 3.28402i) q^{60} +(-6.89983 - 9.49681i) q^{61} +(-0.564395 - 0.776824i) q^{62} +(0.680653 - 4.29747i) q^{63} +(-5.10841 - 3.71148i) q^{64} +(1.07349 + 2.10684i) q^{65} +(-1.78112 + 1.29406i) q^{66} +(-7.49995 - 3.82142i) q^{67} +(-4.19555 + 4.19555i) q^{68} +(0.113158 + 0.714450i) q^{69} +(-0.0777184 + 0.152531i) q^{70} +(-3.74649 + 1.90893i) q^{71} +(1.42097 - 4.37329i) q^{72} -5.65198i q^{73} +(-1.69167 - 0.549657i) q^{74} +(-12.3056 - 1.94902i) q^{75} +(11.1343 - 1.76350i) q^{76} +(-2.87003 + 0.932530i) q^{77} +(0.837903 + 2.57880i) q^{78} +(-4.66363 - 4.66363i) q^{79} +(1.33531 - 1.83789i) q^{80} +3.12156 q^{81} +(-1.67543 - 0.401892i) q^{82} +4.44944 q^{83} +(3.07191 - 4.22813i) q^{84} +(-1.38474 - 1.38474i) q^{85} +(-0.596639 - 1.83627i) q^{86} +(20.3618 - 6.61597i) q^{87} +(-3.14999 + 0.498909i) q^{88} +(-1.48345 - 0.234955i) q^{89} +(0.708397 + 0.230172i) q^{90} +3.71668i q^{91} +(-0.158919 + 0.489102i) q^{92} +(-8.62062 + 4.39242i) q^{93} +(-1.47935 + 2.90338i) q^{94} +(0.582044 + 3.67488i) q^{95} +(5.89435 - 5.89435i) q^{96} +(4.52332 + 2.30475i) q^{97} +(-0.217690 + 0.158161i) q^{98} +(5.96102 + 11.6992i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 4 q^{3} + 36 q^{4} - 28 q^{6}+O(q^{10}) $ 160 * q - 4 * q^3 + 36 * q^4 - 28 * q^6	$ 160 q - 4 q^{3} + 36 q^{4} - 28 q^{6} - 48 q^{10} + 8 q^{11} - 16 q^{12} - 16 q^{13} - 32 q^{15} - 28 q^{16} - 20 q^{17} + 12 q^{18} - 40 q^{19} - 4 q^{22} - 36 q^{23} - 108 q^{24} + 40 q^{25} + 20 q^{26} + 20 q^{27} + 12 q^{29} - 4 q^{30} + 20 q^{31} - 32 q^{34} - 4 q^{35} + 140 q^{36} - 44 q^{38} + 80 q^{39} - 64 q^{40} + 4 q^{41} - 72 q^{42} - 8 q^{44} + 8 q^{45} + 40 q^{46} - 56 q^{47} + 120 q^{48} + 24 q^{51} + 16 q^{52} + 12 q^{53} - 52 q^{54} - 72 q^{55} + 48 q^{57} + 36 q^{58} - 48 q^{59} - 52 q^{60} + 8 q^{63} - 96 q^{64} - 96 q^{65} + 24 q^{66} + 20 q^{67} - 80 q^{68} - 68 q^{69} + 8 q^{70} + 60 q^{71} + 100 q^{72} - 40 q^{74} - 120 q^{75} + 4 q^{76} - 12 q^{78} + 12 q^{79} + 200 q^{80} - 56 q^{81} - 68 q^{82} - 40 q^{83} + 132 q^{85} + 80 q^{86} - 16 q^{88} + 8 q^{89} + 140 q^{92} + 64 q^{93} + 128 q^{94} - 68 q^{96} + 4 q^{98} + 96 q^{99}+O(q^{100}) $ 160 * q - 4 * q^3 + 36 * q^4 - 28 * q^6 - 48 * q^10 + 8 * q^11 - 16 * q^12 - 16 * q^13 - 32 * q^15 - 28 * q^16 - 20 * q^17 + 12 * q^18 - 40 * q^19 - 4 * q^22 - 36 * q^23 - 108 * q^24 + 40 * q^25 + 20 * q^26 + 20 * q^27 + 12 * q^29 - 4 * q^30 + 20 * q^31 - 32 * q^34 - 4 * q^35 + 140 * q^36 - 44 * q^38 + 80 * q^39 - 64 * q^40 + 4 * q^41 - 72 * q^42 - 8 * q^44 + 8 * q^45 + 40 * q^46 - 56 * q^47 + 120 * q^48 + 24 * q^51 + 16 * q^52 + 12 * q^53 - 52 * q^54 - 72 * q^55 + 48 * q^57 + 36 * q^58 - 48 * q^59 - 52 * q^60 + 8 * q^63 - 96 * q^64 - 96 * q^65 + 24 * q^66 + 20 * q^67 - 80 * q^68 - 68 * q^69 + 8 * q^70 + 60 * q^71 + 100 * q^72 - 40 * q^74 - 120 * q^75 + 4 * q^76 - 12 * q^78 + 12 * q^79 + 200 * q^80 - 56 * q^81 - 68 * q^82 - 40 * q^83 + 132 * q^85 + 80 * q^86 - 16 * q^88 + 8 * q^89 + 140 * q^92 + 64 * q^93 + 128 * q^94 - 68 * q^96 + 4 * q^98 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$1$	$e\left(\frac{19}{20}\right)$

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 $

$2$	−0.158161	+	0.217690i	−0.111837	+	0.153930i	−0.861266	−	0.508154i	$-0.830328\pi$
$2$	−0.158161	+	0.217690i	−0.111837	+	0.153930i	0.749429	+	0.662085i	$0.230328\pi$
$3$	1.91716	+	1.91716i	1.10688	+	1.10688i	0.993559	+	0.113317i	$0.0361475\pi$
$3$	1.91716	+	1.91716i	1.10688	+	1.10688i	0.113317	+	0.993559i	$0.463853\pi$
$4$	0.595660	+	1.83325i	0.297830	+	0.916626i
$5$	−0.605064	+	0.196597i	−0.270593	+	0.0879210i	−0.441171	−	0.897423i	$-0.645437\pi$
$5$	−0.605064	+	0.196597i	−0.270593	+	0.0879210i	0.170578	+	0.985344i	$0.445437\pi$
$6$	−0.720570	+	0.114127i	−0.294171	+	0.0465922i
$7$	−0.987688	−	0.156434i	−0.373311	−	0.0591267i
$7$	−0.987688	−	0.156434i	−0.373311	−	0.0591267i
$8$	−1.00511	−	0.326581i	−0.355361	−	0.115464i
$9$			4.35104i			1.45035i
$10$	0.0529004	−	0.162811i	0.0167286	−	0.0514853i
$11$	2.68882	−	1.37002i	0.810709	−	0.413077i	0.00106580	−	0.999999i	$-0.499661\pi$
$11$	2.68882	−	1.37002i	0.810709	−	0.413077i	0.809643	+	0.586923i	$0.199661\pi$
$12$	−2.37267	+	4.65663i	−0.684931	+	1.34425i
$13$	−0.581417	−	3.67092i	−0.161256	−	1.01813i	−0.927021	−	0.375010i	$-0.877639\pi$
$13$	−0.581417	−	3.67092i	−0.161256	−	1.01813i	0.765765	−	0.643120i	$-0.222361\pi$
$14$	0.190268	−	0.190268i	0.0508514	−	0.0508514i
$15$	−1.53692	−	0.783099i	−0.396830	−	0.202195i
$16$	−2.88885	+	2.09887i	−0.722213	+	0.524718i
$17$	1.39744	+	2.74264i	0.338930	+	0.665187i	0.996069	−	0.0885821i	$-0.0282336\pi$
$17$	1.39744	+	2.74264i	0.338930	+	0.665187i	−0.657139	+	0.753769i	$0.728234\pi$
$18$	−0.947180	−	0.688167i	−0.223253	−	0.162202i
$19$	0.914872	−	5.77628i	0.209886	−	1.32517i	−0.627525	−	0.778596i	$-0.715932\pi$
$19$	0.914872	−	5.77628i	0.209886	−	1.32517i	0.837412	−	0.546573i	$-0.184068\pi$
$20$	−0.720825	−	0.992131i	−0.161181	−	0.221847i
$21$	−1.59365	−	2.19347i	−0.347763	−	0.478655i
$22$	−0.127027	+	0.802014i	−0.0270822	+	0.170990i
$23$	0.215841	+	0.156818i	0.0450061	+	0.0326988i	0.610061	−	0.792355i	$-0.291145\pi$
$23$	0.215841	+	0.156818i	0.0450061	+	0.0326988i	−0.565055	+	0.825053i	$0.691145\pi$
$24$	−1.30086	−	2.55308i	−0.265536	−	0.521145i
$25$	−3.71763	+	2.70102i	−0.743527	+	0.540204i
$26$	0.891082	+	0.454029i	0.174756	+	0.0890424i
$27$	−2.59017	+	2.59017i	−0.498479	+	0.498479i
$28$	−0.301542	−	1.90386i	−0.0569862	−	0.359796i
$29$	3.58495	−	7.03586i	0.665709	−	1.30653i	−0.273066	−	0.961995i	$-0.588038\pi$
$29$	3.58495	−	7.03586i	0.665709	−	1.30653i	0.938775	−	0.344531i	$-0.111962\pi$
$30$	0.413554	−	0.210716i	0.0755043	−	0.0384714i
$31$	−1.10272	+	3.39382i	−0.198054	+	0.609549i	0.801873	+	0.597495i	$0.203837\pi$
$31$	−1.10272	+	3.39382i	−0.198054	+	0.609549i	−0.999927	+	0.0120543i	$0.996163\pi$
$32$		−	3.07451i		−	0.543502i
$33$	7.78146	+	2.52835i	1.35458	+	0.440129i
$34$	−0.818068	−	0.129569i	−0.140297	−	0.0222209i
$35$	0.628370	−	0.0995240i	0.106214	−	0.0168226i
$36$	−7.97656	+	2.59174i	−1.32943	+	0.431957i
$37$	2.04273	+	6.28686i	0.335822	+	1.03355i	0.966316	+	0.257360i	$0.0828525\pi$
$37$	2.04273	+	6.28686i	0.335822	+	1.03355i	−0.630494	+	0.776194i	$0.717148\pi$
$38$	1.11274	+	1.11274i	0.180511	+	0.180511i
$39$	5.92309	−	8.15243i	0.948453	−	1.30543i
$40$	0.672363			0.106310
$41$	2.45151	+	5.91524i	0.382862	+	0.923806i
$41$	2.45151	+	5.91524i	0.382862	+	0.923806i
$42$	0.729552			0.112572
$43$	−4.21761	+	5.80504i	−0.643180	+	0.885261i	−0.998780	−	0.0493771i	$-0.984276\pi$
$43$	−4.21761	+	5.80504i	−0.643180	+	0.885261i	0.355600	+	0.934638i	$0.384276\pi$
$44$	4.11321	+	4.11321i	0.620090	+	0.620090i
$45$	−0.855403	−	2.63266i	−0.127516	−	0.392454i
$46$	−0.0682756	+	0.0221841i	−0.0100667	+	0.00327086i
$47$	11.9608	−	1.89441i	1.74467	−	0.276328i	0.798968	−	0.601374i	$-0.205380\pi$
$47$	11.9608	−	1.89441i	1.74467	−	0.276328i	0.945698	+	0.325046i	$0.105380\pi$
$48$	−9.56229	−	1.51452i	−1.38020	−	0.218602i
$49$	0.951057	+	0.309017i	0.135865	+	0.0441453i
$50$		−	1.23649i		−	0.174866i
$51$	−2.57896	+	7.93722i	−0.361126	+	1.11143i
$52$	6.38340	−	3.25250i	0.885218	−	0.451041i
$53$	1.65831	−	3.25462i	0.227786	−	0.447056i	−0.748619	−	0.663000i	$-0.769283\pi$
$53$	1.65831	−	3.25462i	0.227786	−	0.447056i	0.976406	+	0.215944i	$0.0692829\pi$
$54$	−0.154191	−	0.973521i	−0.0209827	−	0.132479i
$55$	−1.35756	+	1.35756i	−0.183054	+	0.183054i
$56$	0.941650	+	0.479795i	0.125833	+	0.0641152i
$57$	12.8280	−	9.32011i	1.69912	−	1.23448i
$58$	0.964639	+	1.89321i	0.126663	+	0.248591i
$59$	−1.86823	−	1.35735i	−0.243223	−	0.176712i	0.459495	−	0.888180i	$-0.348030\pi$
$59$	−1.86823	−	1.35735i	−0.243223	−	0.176712i	−0.702718	+	0.711469i	$0.748030\pi$
$60$	0.520137	−	3.28402i	0.0671495	−	0.423965i
$61$	−6.89983	−	9.49681i	−0.883433	−	1.21594i	−0.975458	−	0.220185i	$-0.929334\pi$
$61$	−6.89983	−	9.49681i	−0.883433	−	1.21594i	0.0920249	−	0.995757i	$-0.470666\pi$
$62$	−0.564395	−	0.776824i	−0.0716783	−	0.0986567i
$63$	0.680653	−	4.29747i	0.0857542	−	0.541431i
$64$	−5.10841	−	3.71148i	−0.638552	−	0.463935i
$65$	1.07349	+	2.10684i	0.133150	+	0.261321i
$66$	−1.78112	+	1.29406i	−0.219241	+	0.159288i
$67$	−7.49995	−	3.82142i	−0.916265	−	0.466860i	−0.0687515	−	0.997634i	$-0.521902\pi$
$67$	−7.49995	−	3.82142i	−0.916265	−	0.466860i	−0.847514	+	0.530773i	$0.821902\pi$
$68$	−4.19555	+	4.19555i	−0.508785	+	0.508785i
$69$	0.113158	+	0.714450i	0.0136226	+	0.0860096i
$70$	−0.0777184	+	0.152531i	−0.00928912	+	0.0182309i
$71$	−3.74649	+	1.90893i	−0.444627	+	0.226549i	−0.661945	−	0.749552i	$-0.730269\pi$
$71$	−3.74649	+	1.90893i	−0.444627	+	0.226549i	0.217319	+	0.976101i	$0.430269\pi$
$72$	1.42097	−	4.37329i	0.167463	−	0.515397i
$73$		−	5.65198i		−	0.661514i	−0.943716	−	0.330757i	$-0.892696\pi$
$73$		−	5.65198i		−	0.661514i	0.943716	−	0.330757i	$-0.107304\pi$
$74$	−1.69167	−	0.549657i	−0.196653	−	0.0638963i
$75$	−12.3056	−	1.94902i	−1.42093	−	0.225053i
$76$	11.1343	−	1.76350i	1.27720	−	0.202288i
$77$	−2.87003	+	0.932530i	−0.327070	+	0.106272i
$78$	0.837903	+	2.57880i	0.0948738	+	0.291991i
$79$	−4.66363	−	4.66363i	−0.524700	−	0.524700i	0.394287	−	0.918987i	$-0.370991\pi$
$79$	−4.66363	−	4.66363i	−0.524700	−	0.524700i	−0.918987	+	0.394287i	$0.870991\pi$
$80$	1.33531	−	1.83789i	0.149292	−	0.205483i
$81$	3.12156			0.346839
$82$	−1.67543	−	0.401892i	−0.185020	−	0.0443816i
$83$	4.44944			0.488389			0.244195	−	0.969726i	$-0.421476\pi$
$83$	4.44944			0.488389			0.244195	+	0.969726i	$0.421476\pi$
$84$	3.07191	−	4.22813i	0.335173	−	0.461327i
$85$	−1.38474	−	1.38474i	−0.150196	−	0.150196i
$86$	−0.596639	−	1.83627i	−0.0643373	−	0.198010i
$87$	20.3618	−	6.61597i	2.18302	−	0.709306i
$88$	−3.14999	+	0.498909i	−0.335790	+	0.0531839i
$89$	−1.48345	−	0.234955i	−0.157245	−	0.0249052i	0.0773155	−	0.997007i	$-0.475365\pi$
$89$	−1.48345	−	0.234955i	−0.157245	−	0.0249052i	−0.234561	+	0.972102i	$0.575365\pi$
$90$	0.708397	+	0.230172i	0.0746716	+	0.0242623i
$91$			3.71668i			0.389614i
$92$	−0.158919	+	0.489102i	−0.0165684	+	0.0509924i
$93$	−8.62062	+	4.39242i	−0.893917	+	0.455473i
$94$	−1.47935	+	2.90338i	−0.152583	+	0.299461i
$95$	0.582044	+	3.67488i	0.0597164	+	0.377035i
$96$	5.89435	−	5.89435i	0.601589	−	0.601589i
$97$	4.52332	+	2.30475i	0.459274	+	0.234012i	0.668291	−	0.743900i	$-0.267026\pi$
$97$	4.52332	+	2.30475i	0.459274	+	0.234012i	−0.209017	+	0.977912i	$0.567026\pi$
$98$	−0.217690	+	0.158161i	−0.0219901	+	0.0159767i
$99$	5.96102	+	11.6992i	0.599105	+	1.17581i
$100$	−7.16609	−	5.20647i	−0.716609	−	0.520647i
$101$	2.16808	−	13.6887i	0.215732	−	1.36208i	−0.607474	−	0.794339i	$-0.707817\pi$
$101$	2.16808	−	13.6887i	0.215732	−	1.36208i	0.823207	−	0.567742i	$-0.192183\pi$
$102$	−1.31997	−	1.81678i	−0.130696	−	0.179888i
$103$	−8.80985	−	12.1257i	−0.868061	−	1.19478i	−0.979587	−	0.201021i	$-0.935574\pi$
$103$	−8.80985	−	12.1257i	−0.868061	−	1.19478i	0.111526	−	0.993761i	$-0.464426\pi$
$104$	−0.614463	+	3.87957i	−0.0602531	+	0.380423i
$105$	1.39549	+	1.01388i	0.136186	+	0.0989450i
$106$	0.446218	+	0.875753i	0.0433406	+	0.0850606i
$107$	−15.8798	+	11.5374i	−1.53516	+	1.11536i	−0.581882	+	0.813273i	$0.697683\pi$
$107$	−15.8798	+	11.5374i	−1.53516	+	1.11536i	−0.953280	+	0.302087i	$0.902317\pi$
$108$	−6.29130	−	3.20558i	−0.605381	−	0.308457i
$109$	6.27980	−	6.27980i	0.601496	−	0.601496i	−0.339214	−	0.940709i	$-0.610161\pi$
$109$	6.27980	−	6.27980i	0.601496	−	0.601496i	0.940709	+	0.339214i	$0.110161\pi$
$110$	−0.0808146	−	0.510243i	−0.00770537	−	0.0486498i
$111$	−8.13671	+	15.9692i	−0.772303	+	1.51573i
$112$	3.18162	−	1.62112i	0.300635	−	0.153181i
$113$	−0.684567	+	2.10688i	−0.0643987	+	0.198199i	−0.978079	−	0.208235i	$-0.933228\pi$
$113$	−0.684567	+	2.10688i	−0.0643987	+	0.198199i	0.913680	+	0.406434i	$0.133228\pi$
$114$			4.26662i			0.399606i
$115$	−0.161428	−	0.0524511i	−0.0150532	−	0.00489109i
$116$	15.0339	+	2.38114i	1.39586	+	0.221083i
$117$	15.9723	−	2.52977i	1.47664	−	0.233877i
$118$	0.590964	−	0.192016i	0.0544027	−	0.0176765i
$119$	−0.951196	−	2.92748i	−0.0871960	−	0.268362i
$120$	1.28903	+	1.28903i	0.117672	+	0.117672i
$121$	−1.11286	+	1.53172i	−0.101169	+	0.139247i
$122$	3.15865			0.285971
$123$	−6.64054	+	16.0404i	−0.598758	+	1.44632i
$124$	−6.87858			−0.617715
$125$	3.58815	−	4.93866i	0.320933	−	0.441727i
$126$	0.827866	+	0.827866i	0.0737522	+	0.0737522i
$127$	5.29701	+	16.3025i	0.470034	+	1.44662i	0.852540	+	0.522662i	$0.175061\pi$
$127$	5.29701	+	16.3025i	0.470034	+	1.44662i	−0.382506	+	0.923953i	$0.624939\pi$
$128$	7.46398	−	2.42519i	0.659729	−	0.214359i
$129$	−19.2151	+	3.04337i	−1.69179	+	0.267954i
$130$	−0.628423	−	0.0995324i	−0.0551163	−	0.00872957i
$131$	−1.10692	−	0.359661i	−0.0967122	−	0.0314237i	0.260261	−	0.965538i	$-0.416191\pi$
$131$	−1.10692	−	0.359661i	−0.0967122	−	0.0314237i	−0.356973	+	0.934115i	$0.616191\pi$
$132$			15.7714i			1.37273i
$133$	−1.80722	+	5.56204i	−0.156706	+	0.482290i
$134$	2.01809	−	1.02827i	0.174336	−	0.0888288i
$135$	1.05800	−	2.07644i	0.0910581	−	0.178712i
$136$	−0.508895	−	3.21304i	−0.0436374	−	0.275516i
$137$	−9.38952	+	9.38952i	−0.802201	+	0.802201i	−0.983439	−	0.181238i	$-0.941989\pi$
$137$	−9.38952	+	9.38952i	−0.802201	+	0.802201i	0.181238	+	0.983439i	$0.441989\pi$
$138$	−0.173426	−	0.0883650i	−0.0147630	−	0.00752213i
$139$	1.41084	−	1.02504i	0.119666	−	0.0869425i	−0.526342	−	0.850273i	$-0.676437\pi$
$139$	1.41084	−	1.02504i	0.119666	−	0.0869425i	0.646009	+	0.763330i	$0.276437\pi$
$140$	0.556747	+	1.09268i	0.0470537	+	0.0923481i
$141$	26.5628	+	19.2990i	2.23699	+	1.62527i
$142$	0.176994	−	1.11749i	0.0148530	−	0.0937781i
$143$	−6.59256	−	9.07388i	−0.551297	−	0.758796i
$144$	−9.13229	−	12.5695i	−0.761024	−	1.04746i
$145$	−0.785894	+	4.96194i	−0.0652650	+	0.412067i
$146$	1.23038	+	0.893924i	0.101827	+	0.0739817i
$147$	1.23090	+	2.41577i	0.101523	+	0.199249i
$148$	−10.3086	+	7.48967i	−0.847365	+	0.615647i
$149$	−0.922519	−	0.470047i	−0.0755757	−	0.0385078i	0.415794	−	0.909459i	$-0.363504\pi$
$149$	−0.922519	−	0.470047i	−0.0755757	−	0.0385078i	−0.491370	+	0.870951i	$0.663504\pi$
$150$	2.37055	−	2.37055i	0.193555	−	0.193555i
$151$	0.522366	+	3.29809i	0.0425095	+	0.268394i	0.999784	−	0.0207866i	$-0.00661704\pi$
$151$	0.522366	+	3.29809i	0.0425095	+	0.268394i	−0.957274	+	0.289181i	$0.906617\pi$
$152$	−2.80597	+	5.50703i	−0.227594	+	0.446679i
$153$	−11.9333	+	6.08034i	−0.964753	+	0.491566i
$154$	0.250925	−	0.772269i	0.0202201	−	0.0622312i
$155$		−	2.27027i		−	0.182353i
$156$	18.4736	+	6.00244i	1.47907	+	0.480580i
$157$	−6.63979	−	1.05164i	−0.529913	−	0.0839300i	−0.114256	−	0.993451i	$-0.536448\pi$
$157$	−6.63979	−	1.05164i	−0.529913	−	0.0839300i	−0.415657	+	0.909521i	$0.636448\pi$
$158$	1.75283	−	0.277622i	0.139448	−	0.0220864i
$159$	9.41889	−	3.06038i	0.746966	−	0.242704i
$160$	0.604441	+	1.86028i	0.0477852	+	0.147068i
$161$	−0.188652	−	0.188652i	−0.0148679	−	0.0148679i
$162$	−0.493709	+	0.679533i	−0.0387895	+	0.0533891i
$163$	−4.64585			−0.363891			−0.181946	−	0.983309i	$-0.558239\pi$
$163$	−4.64585			−0.363891			−0.181946	+	0.983309i	$0.558239\pi$
$164$	−9.38387	+	8.01771i	−0.732757	+	0.626078i
$165$	−5.20535			−0.405236
$166$	−0.703729	+	0.968600i	−0.0546200	+	0.0751780i
$167$	−6.04072	−	6.04072i	−0.467445	−	0.467445i	0.433641	−	0.901086i	$-0.357229\pi$
$167$	−6.04072	−	6.04072i	−0.467445	−	0.467445i	−0.901086	+	0.433641i	$0.857229\pi$
$168$	0.885453	+	2.72514i	0.0683142	+	0.210249i
$169$	−0.773873	+	0.251446i	−0.0595287	+	0.0193420i
$170$	0.520456	−	0.0824322i	0.0399172	−	0.00632226i
$171$	25.1328	+	3.98065i	1.92196	+	0.304408i
$172$	−13.1544	−	4.27412i	−1.00301	−	0.325898i
$173$			0.635912i			0.0483475i	0.999708	+	0.0241738i	$0.00769550\pi$
$173$			0.635912i			0.0483475i	−0.999708	+	0.0241738i	$0.992305\pi$
$174$	−1.78023	+	5.47897i	−0.134959	+	0.415360i
$175$	4.09439	−	2.08620i	0.309507	−	0.157702i
$176$	−4.89209	+	9.60127i	−0.368755	+	0.723723i
$177$	−0.979445	−	6.18397i	−0.0736196	−	0.464816i
$178$	0.285771	−	0.285771i	0.0214195	−	0.0214195i
$179$	19.7575	+	10.0669i	1.47674	+	0.752439i	0.992471	−	0.122479i	$-0.0390843\pi$
$179$	19.7575	+	10.0669i	1.47674	+	0.752439i	0.484273	+	0.874917i	$0.339084\pi$
$180$	4.31680	−	3.13634i	0.321755	−	0.233769i
$181$	−9.37076	−	18.3912i	−0.696523	−	1.36700i	−0.919854	−	0.392261i	$-0.871693\pi$
$181$	−9.37076	−	18.3912i	−0.696523	−	1.36700i	0.223331	−	0.974743i	$-0.428307\pi$
$182$	−0.809085	−	0.587835i	−0.0599734	−	0.0435732i
$183$	4.97883	−	31.4351i	0.368045	−	2.32375i
$184$	−0.165731	−	0.228109i	−0.0122179	−	0.0168165i
$185$	−2.47196	−	3.40236i	−0.181742	−	0.250147i
$186$	0.407260	−	2.57134i	0.0298618	−	0.188540i
$187$	7.51494	+	5.45992i	0.549547	+	0.399269i
$188$	10.5975	+	20.7988i	0.772903	+	1.51691i
$189$	2.96347	−	2.15309i	0.215561	−	0.156614i
$190$	−0.892043	−	0.454519i	−0.0647156	−	0.0329743i
$191$	−14.6230	+	14.6230i	−1.05808	+	1.05808i	−0.0598766	+	0.998206i	$0.519071\pi$
$191$	−14.6230	+	14.6230i	−1.05808	+	1.05808i	−0.998206	+	0.0598766i	$0.980929\pi$
$192$	−2.67815	−	16.9092i	−0.193279	−	1.22032i
$193$	−0.247927	+	0.486583i	−0.0178462	+	0.0350250i	−0.899757	−	0.436390i	$-0.856257\pi$
$193$	−0.247927	+	0.486583i	−0.0178462	+	0.0350250i	0.881911	+	0.471415i	$0.156257\pi$
$194$	−1.21714	+	0.620162i	−0.0873853	+	0.0445251i
$195$	−1.98110	+	6.09721i	−0.141870	+	0.436630i
$196$			1.92760i			0.137685i
$197$	−6.35392	−	2.06451i	−0.452698	−	0.147090i	0.0737888	−	0.997274i	$-0.476491\pi$
$197$	−6.35392	−	2.06451i	−0.452698	−	0.147090i	−0.526487	+	0.850183i	$0.676491\pi$
$198$	−3.48960	−	0.552698i	−0.247995	−	0.0392785i
$199$	−9.90055	+	1.56809i	−0.701831	+	0.111159i	−0.497144	−	0.867668i	$-0.665618\pi$
$199$	−9.90055	+	1.56809i	−0.701831	+	0.111159i	−0.204688	+	0.978827i	$0.565618\pi$
$200$	4.61874	−	1.50072i	0.326594	−	0.106117i
$201$	−7.05236	−	21.7049i	−0.497435	−	1.53095i
$202$	2.63700	+	2.63700i	0.185539	+	0.185539i
$203$	−4.64147	+	6.38843i	−0.325767	+	0.448380i
$204$	−16.0871			−1.12632
$205$	−2.64624	−	3.09714i	−0.184822	−	0.216314i
$206$	4.03303			0.280995
$207$	−0.682322	+	0.939135i	−0.0474246	+	0.0652744i
$208$	9.38442	+	9.38442i	0.650693	+	0.650693i
$209$	−5.45369	−	16.7847i	−0.377240	−	1.16103i
$210$	−0.441426	+	0.143428i	−0.0304613	+	0.00989747i
$211$	−18.0566	+	2.85988i	−1.24307	+	0.196882i	−0.743111	−	0.669169i	$-0.766650\pi$
$211$	−18.0566	+	2.85988i	−1.24307	+	0.196882i	−0.499956	+	0.866051i	$0.666650\pi$
$212$	6.95432	+	1.10146i	0.477625	+	0.0756483i
$213$	−10.8424	−	3.52290i	−0.742908	−	0.241385i
$214$		−	5.28166i		−	0.361047i
$215$	1.41067	−	4.34160i	0.0962069	−	0.296094i
$216$	3.44932	−	1.75751i	0.234696	−	0.119584i
$217$	1.62006	−	3.17954i	0.109977	−	0.215841i
$218$	0.373831	+	2.36027i	0.0253190	+	0.159858i
$219$	10.8358	−	10.8358i	0.732214	−	0.732214i
$220$	−3.29741	−	1.68011i	−0.222311	−	0.113273i
$221$	9.25551	−	6.72452i	0.622593	−	0.452340i
$222$	−2.18943	−	4.29699i	−0.146945	−	0.288395i
$223$	16.0321	+	11.6480i	1.07359	+	0.780008i	0.976554	−	0.215272i	$-0.0690640\pi$
$223$	16.0321	+	11.6480i	1.07359	+	0.780008i	0.0970355	+	0.995281i	$0.469064\pi$
$224$	−0.480960	+	3.03666i	−0.0321355	+	0.202895i
$225$	−11.7522	−	16.1756i	−0.783483	−	1.07837i
$226$	−0.350376	−	0.482251i	−0.0233067	−	0.0320789i
$227$	−0.242594	+	1.53168i	−0.0161015	+	0.101661i	−0.994430	−	0.105397i	$-0.966389\pi$
$227$	−0.242594	+	1.53168i	−0.0161015	+	0.101661i	0.978329	+	0.207058i	$0.0663888\pi$
$228$	24.7273	+	17.9654i	1.63760	+	1.18979i
$229$	0.727772	+	1.42833i	0.0480925	+	0.0943869i	0.913802	−	0.406160i	$-0.133132\pi$
$229$	0.727772	+	1.42833i	0.0480925	+	0.0943869i	−0.865710	+	0.500547i	$0.833132\pi$
$230$	0.0369498	−	0.0268456i	0.00243640	−	0.00177015i
$231$	−7.29014	−	3.71451i	−0.479656	−	0.244397i
$232$	−5.90106	+	5.90106i	−0.387423	+	0.387423i
$233$	−0.276074	−	1.74306i	−0.0180862	−	0.114192i	0.976994	−	0.213269i	$-0.0684110\pi$
$233$	−0.276074	−	1.74306i	−0.0180862	−	0.114192i	−0.995080	+	0.0990770i	$0.968411\pi$
$234$	−1.97550	+	3.87713i	−0.129142	+	0.253456i
$235$	−6.86463	+	3.49770i	−0.447799	+	0.228165i
$236$	1.37553	−	4.23346i	0.0895397	−	0.275575i
$237$		−	17.8819i		−	1.16155i
$238$	0.787727	+	0.255948i	0.0510607	+	0.0165906i
$239$	15.2554	+	2.41622i	0.986790	+	0.156292i	0.628912	−	0.777476i	$-0.283500\pi$
$239$	15.2554	+	2.41622i	0.986790	+	0.156292i	0.357878	+	0.933768i	$0.383500\pi$
$240$	6.08355	−	0.963540i	0.392692	−	0.0621962i
$241$	10.6417	−	3.45769i	0.685491	−	0.222729i	0.0544931	−	0.998514i	$-0.482646\pi$
$241$	10.6417	−	3.45769i	0.685491	−	0.222729i	0.630998	+	0.775785i	$0.282646\pi$
$242$	−0.157429	−	0.484517i	−0.0101199	−	0.0311459i
$243$	13.7551	+	13.7551i	0.882387	+	0.882387i
$244$	13.3001	−	18.3060i	0.851451	−	1.17192i
$245$	−0.636202			−0.0406455
$246$	−2.44157	−	3.98256i	−0.155669	−	0.253919i
$247$	−21.7362			−1.38304
$248$	2.21672	−	3.05105i	0.140762	−	0.193742i
$249$	8.53031	+	8.53031i	0.540586	+	0.540586i
$250$	0.507593	+	1.56221i	0.0321030	+	0.0988028i
$251$	27.9096	−	9.06836i	1.76164	−	0.572390i	0.764268	−	0.644899i	$-0.223101\pi$
$251$	27.9096	−	9.06836i	1.76164	−	0.572390i	0.997368	+	0.0725093i	$0.0231007\pi$
$252$	8.28379	−	1.31202i	0.521830	−	0.0826497i
$253$	0.795202	+	0.125948i	0.0499939	+	0.00791826i
$254$	−4.38669	−	1.42532i	−0.275245	−	0.0894326i
$255$		−	5.30954i		−	0.332497i
$256$	3.24991	−	10.0022i	0.203119	−	0.625137i
$257$	−9.69242	+	4.93853i	−0.604596	+	0.308057i	−0.729361	−	0.684129i	$-0.760182\pi$
$257$	−9.69242	+	4.93853i	−0.604596	+	0.308057i	0.124765	+	0.992186i	$0.460182\pi$
$258$	2.37657	−	4.66428i	0.147959	−	0.290386i
$259$	−1.03409	−	6.52901i	−0.0642555	−	0.405693i
$260$	−3.22293	+	3.22293i	−0.199878	+	0.199878i
$261$	30.6133	+	15.5983i	1.89492	+	0.965509i
$262$	0.253367	−	0.184082i	0.0156531	−	0.0113726i
$263$	−9.43493	−	18.5171i	−0.581783	−	1.14181i	−0.974966	−	0.222353i	$-0.928626\pi$
$263$	−9.43493	−	18.5171i	−0.581783	−	1.14181i	0.393184	−	0.919460i	$-0.371374\pi$
$264$	−6.99554	−	5.08255i	−0.430545	−	0.312810i
$265$	−0.363535	+	2.29527i	−0.0223318	+	0.140997i
$266$	−0.924972	−	1.27311i	−0.0567137	−	0.0780597i
$267$	−2.39356	−	3.29446i	−0.146484	−	0.201618i
$268$	2.53820	−	16.0256i	0.155045	−	0.978918i
$269$	−15.5016	−	11.2626i	−0.945151	−	0.686693i	0.00450390	−	0.999990i	$-0.498566\pi$
$269$	−15.5016	−	11.2626i	−0.945151	−	0.686693i	−0.949655	+	0.313297i	$0.898566\pi$
$270$	0.284687	+	0.558729i	0.0173255	+	0.0340032i
$271$	−21.1000	+	15.3300i	−1.28173	+	0.931234i	−0.999604	−	0.0281428i	$-0.991041\pi$
$271$	−21.1000	+	15.3300i	−1.28173	+	0.931234i	−0.282129	+	0.959376i	$0.591041\pi$
$272$	−9.79346	−	4.99002i	−0.593816	−	0.302564i
$273$	−7.12549	+	7.12549i	−0.431254	+	0.431254i
$274$	−0.558950	−	3.52907i	−0.0337674	−	0.213199i
$275$	−6.29558	+	12.3558i	−0.379638	+	0.745081i
$276$	−1.24236	+	0.633016i	−0.0747815	+	0.0381031i
$277$	−6.37921	+	19.6332i	−0.383289	+	1.17964i	0.554424	+	0.832234i	$0.312939\pi$
$277$	−6.37921	+	19.6332i	−0.383289	+	1.17964i	−0.937714	+	0.347409i	$0.887061\pi$
$278$			0.469248i			0.0281436i
$279$	−14.7667	−	4.79798i	−0.884058	−	0.287248i
$280$	−0.664085	−	0.105181i	−0.0396867	−	0.00628575i
$281$	−15.9733	+	2.52992i	−0.952886	+	0.150922i	−0.613474	−	0.789715i	$-0.710228\pi$
$281$	−15.9733	+	2.52992i	−0.952886	+	0.150922i	−0.339413	+	0.940638i	$0.610228\pi$
$282$	−8.40241	+	2.73011i	−0.500356	+	0.162576i
$283$	6.09046	+	18.7445i	0.362041	+	1.11425i	0.951814	+	0.306677i	$0.0992172\pi$
$283$	6.09046	+	18.7445i	0.362041	+	1.11425i	−0.589773	+	0.807569i	$0.700783\pi$
$284$	−5.73119	−	5.73119i	−0.340084	−	0.340084i
$285$	−5.92948	+	8.16123i	−0.351232	+	0.483429i
$286$	3.01798			0.178457
$287$	−1.49598	−	6.22592i	−0.0883050	−	0.367504i
$288$	13.3773			0.788267
$289$	4.42314	−	6.08792i	0.260184	−	0.358113i
$290$	−0.955869	−	0.955869i	−0.0561306	−	0.0561306i
$291$	4.25338	+	13.0905i	0.249337	+	0.767381i
$292$	10.3615	−	3.36666i	0.606361	−	0.197019i
$293$	−8.57511	+	1.35816i	−0.500963	+	0.0793447i	−0.401802	−	0.915727i	$-0.631616\pi$
$293$	−8.57511	+	1.35816i	−0.500963	+	0.0793447i	−0.0991612	+	0.995071i	$0.531616\pi$
$294$	−0.720570	−	0.114127i	−0.0420245	−	0.00665603i
$295$	1.39725	+	0.453995i	0.0813511	+	0.0264326i
$296$		−	6.98612i		−	0.406060i
$297$	−3.41591	+	10.5131i	−0.198211	+	0.610031i
$298$	0.248232	−	0.126480i	0.0143797	−	0.00732681i
$299$	0.450172	−	0.883513i	0.0260341	−	0.0510949i
$300$	−3.75692	−	23.7202i	−0.216906	−	1.36949i
$301$	5.07379	−	5.07379i	0.292449	−	0.292449i
$302$	−0.800580	−	0.407916i	−0.0460682	−	0.0234729i
$303$	30.4002	−	22.0870i	1.74644	−	1.26887i
$304$	9.48075	+	18.6070i	0.543758	+	1.06719i
$305$	6.04189	+	4.38969i	0.345958	+	0.251353i
$306$	0.563761	−	3.55945i	0.0322281	−	0.203480i
$307$	18.8747	+	25.9788i	1.07724	+	1.48269i	0.862527	+	0.506011i	$0.168881\pi$
$307$	18.8747	+	25.9788i	1.07724	+	1.48269i	0.214710	+	0.976678i	$0.431119\pi$
$308$	−3.41913	−	4.70602i	−0.194823	−	0.268151i
$309$	6.35707	−	40.1369i	0.361641	−	2.28331i
$310$	0.494217	+	0.359070i	0.0280696	+	0.0203938i
$311$	12.1436	+	23.8332i	0.688601	+	1.35146i	0.925062	+	0.379815i	$0.124013\pi$
$311$	12.1436	+	23.8332i	0.688601	+	1.35146i	−0.236461	+	0.971641i	$0.575987\pi$
$312$	−8.61580	+	6.25974i	−0.487774	+	0.354388i
$313$	−10.7454	−	5.47506i	−0.607366	−	0.309469i	0.123124	−	0.992391i	$-0.460709\pi$
$313$	−10.7454	−	5.47506i	−0.607366	−	0.309469i	−0.730491	+	0.682923i	$0.760709\pi$
$314$	1.27909	−	1.27909i	0.0721832	−	0.0721832i
$315$	0.433033	+	2.73406i	0.0243986	+	0.154047i
$316$	5.77168	−	11.3276i	0.324682	−	0.637225i
$317$	1.94523	−	0.991144i	0.109255	−	0.0556682i	−0.398509	−	0.917164i	$-0.630472\pi$
$317$	1.94523	−	0.991144i	0.109255	−	0.0556682i	0.507764	+	0.861496i	$0.330472\pi$
$318$	−0.823488	+	2.53444i	−0.0461789	+	0.142124i
$319$		−	23.8296i		−	1.33420i
$320$	3.82058	+	1.24138i	0.213577	+	0.0693954i
$321$	−52.5633	−	8.32521i	−2.93380	−	0.464668i
$322$	0.0709053	−	0.0112303i	0.00395140	−	0.000625840i
$323$	17.1207	−	5.56286i	0.952622	−	0.309526i
$324$	1.85939	+	5.72260i	0.103299	+	0.317922i
$325$	12.0767	+	12.0767i	0.669896	+	0.669896i
$326$	0.734794	−	1.01136i	0.0406965	−	0.0560139i
$327$	24.0788			1.33156
$328$	−0.532240	−	6.74610i	−0.0293881	−	0.372491i
$329$	−12.1099			−0.667641
$330$	0.823285	−	1.13316i	0.0453204	−	0.0623781i
$331$	−2.75088	−	2.75088i	−0.151202	−	0.151202i	0.627453	−	0.778655i	$-0.284098\pi$
$331$	−2.75088	−	2.75088i	−0.151202	−	0.151202i	−0.778655	+	0.627453i	$0.784098\pi$
$332$	2.65035	+	8.15695i	0.145457	+	0.447671i
$333$	−27.3544	+	8.88799i	−1.49901	+	0.487059i
$334$	2.27041	−	0.359598i	0.124232	−	0.0196763i
$335$	5.28924	+	0.837733i	0.288982	+	0.0457702i
$336$	9.20764	+	2.99174i	0.502318	+	0.163213i
$337$			26.1747i			1.42583i	0.701252	+	0.712914i	$0.252625\pi$
$337$			26.1747i			1.42583i	−0.701252	+	0.712914i	$0.747375\pi$
$338$	0.0676593	−	0.208234i	0.00368018	−	0.0113264i
$339$	−5.35167	+	2.72681i	−0.290663	+	0.148100i
$340$	1.71374	−	3.36341i	0.0929407	−	0.182406i
$341$	1.68460	+	10.6361i	0.0912260	+	0.575978i
$342$	−4.84159	+	4.84159i	−0.261803	+	0.261803i
$343$	−0.891007	−	0.453990i	−0.0481098	−	0.0245132i
$344$	6.13499	−	4.45733i	0.330777	−	0.240323i
$345$	−0.208927	−	0.410041i	−0.0112482	−	0.0220759i
$346$	−0.138432	−	0.100577i	−0.00744215	−	0.00540704i
$347$	2.68343	−	16.9425i	0.144054	−	0.909522i	−0.804740	−	0.593627i	$-0.797695\pi$
$347$	2.68343	−	16.9425i	0.144054	−	0.909522i	0.948794	−	0.315895i	$-0.102305\pi$
$348$	24.2575	+	33.3875i	1.30034	+	1.78976i
$349$	−14.0920	−	19.3960i	−0.754328	−	1.03824i	−0.997665	−	0.0683019i	$-0.978242\pi$
$349$	−14.0920	−	19.3960i	−0.754328	−	1.03824i	0.243336	−	0.969942i	$-0.421758\pi$
$350$	−0.193430	+	1.22127i	−0.0103392	+	0.0652794i
$351$	11.0143	+	8.00234i	0.587899	+	0.427134i
$352$	−4.21215	−	8.26680i	−0.224508	−	0.440622i
$353$	24.8546	−	18.0580i	1.32288	−	0.961128i	0.322987	−	0.946403i	$-0.395313\pi$
$353$	24.8546	−	18.0580i	1.32288	−	0.961128i	0.999892	−	0.0147244i	$-0.00468709\pi$
$354$	1.50110	+	0.764850i	0.0797827	+	0.0406513i
$355$	1.89158	−	1.89158i	0.100395	−	0.100395i
$356$	−0.452898	−	2.85949i	−0.0240035	−	0.151552i
$357$	3.78886	−	7.43606i	0.200528	−	0.393558i
$358$	−5.31635	+	2.70881i	−0.280978	+	0.143165i
$359$	5.80133	−	17.8547i	0.306183	−	0.942333i	−0.673051	−	0.739596i	$-0.735016\pi$
$359$	5.80133	−	17.8547i	0.306183	−	0.942333i	0.979233	−	0.202737i	$-0.0649836\pi$
$360$			2.92548i			0.154186i
$361$	−14.4583	−	4.69779i	−0.760964	−	0.247252i
$362$	5.48567	+	0.868845i	0.288320	+	0.0456655i
$363$	−5.07009	+	0.803023i	−0.266111	+	0.0421478i
$364$	−6.81361	+	2.21388i	−0.357130	+	0.116039i
$365$	1.11116	+	3.41981i	0.0581609	+	0.179001i
$366$	6.05566	+	6.05566i	0.316534	+	0.316534i
$367$	−7.46862	+	10.2797i	−0.389859	+	0.536595i	−0.958163	−	0.286224i	$-0.907600\pi$
$367$	−7.46862	+	10.2797i	−0.389859	+	0.536595i	0.568304	+	0.822819i	$0.307600\pi$
$368$	−0.952675			−0.0496616
$369$	−25.7375	+	10.6666i	−1.33984	+	0.555283i
$370$	1.13163			0.0588307
$371$	−2.14703	+	2.95513i	−0.111468	+	0.153423i
$372$	−13.1874	−	13.1874i	−0.683734	−	0.683734i
$373$	7.35078	+	22.6234i	0.380609	+	1.17139i	0.939616	+	0.342231i	$0.111183\pi$
$373$	7.35078	+	22.6234i	0.380609	+	1.17139i	−0.559007	+	0.829163i	$0.688817\pi$
$374$	−2.37715	+	0.772382i	−0.122919	+	0.0399389i
$375$	16.3473	−	2.58916i	0.844170	−	0.133703i
$376$	−12.6407	−	2.00208i	−0.651892	−	0.103250i
$377$	−27.9124	−	9.06930i	−1.43756	−	0.467093i
$378$			0.985656i			0.0506967i
$379$	4.11548	−	12.6661i	0.211398	−	0.650616i	−0.787992	−	0.615686i	$-0.788879\pi$
$379$	4.11548	−	12.6661i	0.211398	−	0.650616i	0.999390	−	0.0349303i	$-0.0111209\pi$
$380$	−6.39028	+	3.25601i	−0.327815	+	0.167030i
$381$	−21.0994	+	41.4099i	−1.08095	+	2.12149i
$382$	−0.870493	−	5.49608i	−0.0445383	−	0.281204i
$383$	−12.7666	+	12.7666i	−0.652344	+	0.652344i	−0.953557	−	0.301213i	$-0.902608\pi$
$383$	−12.7666	+	12.7666i	−0.652344	+	0.652344i	0.301213	+	0.953557i	$0.402608\pi$
$384$	18.9592	+	9.66018i	0.967506	+	0.492969i
$385$	1.55322	−	1.12848i	0.0791595	−	0.0575127i
$386$	−0.0667122	−	0.130930i	−0.00339556	−	0.00666416i
$387$	−25.2580	−	18.3510i	−1.28394	−	0.932834i
$388$	−1.53082	+	9.66524i	−0.0777158	+	0.490678i
$389$	−19.0490	−	26.2186i	−0.965820	−	1.32934i	−0.944130	−	0.329573i	$-0.893095\pi$
$389$	−19.0490	−	26.2186i	−0.965820	−	1.32934i	−0.0216901	−	0.999765i	$-0.506905\pi$
$390$	−1.01397	−	1.39561i	−0.0513444	−	0.0706694i
$391$	−0.128469	+	0.811119i	−0.00649694	+	0.0410201i
$392$	−0.855000	−	0.621194i	−0.0431840	−	0.0313750i
$393$	−1.43262	−	2.81168i	−0.0722662	−	0.141830i
$394$	1.45437	−	1.05666i	0.0732700	−	0.0532338i
$395$	3.73866	+	1.90494i	0.188112	+	0.0958479i
$396$	−17.8968	+	17.8968i	−0.899347	+	0.899347i
$397$	0.811657	+	5.12460i	0.0407359	+	0.257196i	0.999649	−	0.0265047i	$-0.00843770\pi$
$397$	0.811657	+	5.12460i	0.0407359	+	0.257196i	−0.958913	+	0.283701i	$0.908438\pi$
$398$	1.22453	−	2.40327i	0.0613799	−	0.120465i
$399$	−14.1281	+	7.19862i	−0.707289	+	0.360382i
$400$	5.07059	−	15.6057i	0.253530	−	0.780284i
$401$		−	33.8002i		−	1.68790i	−0.536420	−	0.843951i	$-0.680224\pi$
$401$		−	33.8002i		−	1.68790i	0.536420	−	0.843951i	$-0.319776\pi$
$402$	5.84037	+	1.89765i	0.291291	+	0.0946462i
$403$	13.0996	+	2.07477i	0.652538	+	0.103352i
$404$	26.3864	−	4.17919i	1.31277	−	0.207923i
$405$	−1.88874	+	0.613689i	−0.0938523	+	0.0304945i
$406$	−0.656599	−	2.02081i	−0.0325865	−	0.100291i
$407$	14.1056	+	14.1056i	0.699191	+	0.699191i
$408$	5.18429	−	7.13556i	0.256661	−	0.353263i
$409$	2.87560			0.142189			0.0710945	−	0.997470i	$-0.477351\pi$
$409$	2.87560			0.142189			0.0710945	+	0.997470i	$0.477351\pi$
$410$	1.09275	−	0.0862137i	0.0539671	−	0.00425779i
$411$	−36.0025			−1.77587
$412$	16.9818	−	23.3735i	0.836635	−	1.15153i
$413$	1.63289	+	1.63289i	0.0803495	+	0.0803495i
$414$	−0.0965238	−	0.297070i	−0.00474389	−	0.0146002i
$415$	−2.69220	+	0.874748i	−0.132155	+	0.0429397i
$416$	−11.2863	+	1.78757i	−0.553356	+	0.0876430i
$417$	4.66998	+	0.739653i	0.228690	+	0.0362210i
$418$	4.51644	+	1.46748i	0.220906	+	0.0717768i
$419$			20.9657i			1.02424i	0.858913	+	0.512121i	$0.171140\pi$
$419$			20.9657i			1.02424i	−0.858913	+	0.512121i	$0.828860\pi$
$420$	−1.02747	+	3.16222i	−0.0501353	+	0.154300i
$421$	28.6024	−	14.5736i	1.39399	−	0.710276i	0.414182	−	0.910194i	$-0.364068\pi$
$421$	28.6024	−	14.5736i	1.39399	−	0.710276i	0.979813	+	0.199918i	$0.0640677\pi$
$422$	2.23328	−	4.38307i	0.108715	−	0.213364i
$423$	8.24265	+	52.0421i	0.400771	+	2.53037i
$424$	−2.72968	+	2.72968i	−0.132565	+	0.132565i
$425$	−12.6031	−	6.42160i	−0.611340	−	0.311493i
$426$	2.48175	−	1.80310i	0.120241	−	0.0873603i
$427$	5.32926	+	10.4593i	0.257901	+	0.506159i
$428$	−30.6099	−	22.2394i	−1.47959	−	1.07498i
$429$	4.75710	−	30.0351i	0.229675	−	1.45011i
$430$	0.722010	+	0.993762i	0.0348184	+	0.0479235i
$431$	23.0855	+	31.7744i	1.11199	+	1.53052i	0.818453	+	0.574573i	$0.194832\pi$
$431$	23.0855	+	31.7744i	1.11199	+	1.53052i	0.293535	+	0.955948i	$0.405168\pi$
$432$	2.04618	−	12.9191i	0.0984468	−	0.621569i
$433$	23.5752	+	17.1284i	1.13295	+	0.823139i	0.986122	−	0.166023i	$-0.0530925\pi$
$433$	23.5752	+	17.1284i	1.13295	+	0.823139i	0.146831	+	0.989162i	$0.453093\pi$
$434$	0.435925	+	0.855551i	0.0209251	+	0.0410677i
$435$	−11.0195	+	8.00617i	−0.528347	+	0.383866i
$436$	15.2531	+	7.77183i	0.730490	+	0.372203i
$437$	1.10329	−	1.10329i	0.0527776	−	0.0527776i
$438$	0.645043	+	4.07264i	0.0308214	+	0.194598i
$439$	−3.41003	+	6.69256i	−0.162752	+	0.319419i	−0.957952	−	0.286929i	$-0.907366\pi$
$439$	−3.41003	+	6.69256i	−0.162752	+	0.319419i	0.795200	+	0.606347i	$0.207366\pi$
$440$	1.80786	−	0.921151i	0.0861864	−	0.0439141i
$441$	−1.34455	+	4.13809i	−0.0640260	+	0.197052i
$442$			3.07839i			0.146424i
$443$	33.5893	+	10.9138i	1.59588	+	0.518532i	0.966083	−	0.258232i	$-0.0831397\pi$
$443$	33.5893	+	10.9138i	1.59588	+	0.518532i	0.629793	+	0.776763i	$0.283140\pi$
$444$	−34.1223	−	5.40444i	−1.61937	−	0.256483i
$445$	0.943772	−	0.149479i	0.0447391	−	0.00708598i
$446$	−5.07132	+	1.64777i	−0.240134	+	0.0780243i
$447$	−0.867464	−	2.66978i	−0.0410296	−	0.126276i
$448$	4.46492	+	4.46492i	0.210947	+	0.210947i
$449$	−5.66955	+	7.80346i	−0.267562	+	0.368268i	−0.921565	−	0.388224i	$-0.873089\pi$
$449$	−5.66955	+	7.80346i	−0.267562	+	0.368268i	0.654002	+	0.756492i	$0.273089\pi$
$450$	5.38002			0.253617
$451$	14.6957	+	12.5464i	0.691992	+	0.590786i
$452$	−4.27021			−0.200854
$453$	−5.32152	+	7.32444i	−0.250027	+	0.344132i
$454$	−0.295063	−	0.295063i	−0.0138480	−	0.0138480i
$455$	−0.730689	−	2.24883i	−0.0342552	−	0.105427i
$456$	−15.9374	+	5.17837i	−0.746337	+	0.242500i
$457$	14.9766	−	2.37207i	0.700578	−	0.110961i	0.204023	−	0.978966i	$-0.434598\pi$
$457$	14.9766	−	2.37207i	0.700578	−	0.110961i	0.496555	+	0.868005i	$0.334598\pi$
$458$	−0.426040	−	0.0674781i	−0.0199075	−	0.00315304i
$459$	−10.7235	−	3.48428i	−0.500531	−	0.162632i
$460$		−	0.327181i		−	0.0152549i
$461$	0.462408	−	1.42315i	0.0215365	−	0.0662825i	−0.939711	−	0.341971i	$-0.888906\pi$
$461$	0.462408	−	1.42315i	0.0215365	−	0.0662825i	0.961247	+	0.275688i	$0.0889057\pi$
$462$	1.96163	−	0.999501i	0.0912634	−	0.0465010i
$463$	−8.87517	+	17.4185i	−0.412464	+	0.809506i	0.587536	+	0.809198i	$0.300098\pi$
$463$	−8.87517	+	17.4185i	−0.412464	+	0.809506i	−1.00000		0.000308182i	$0.999902\pi$
$464$	4.41099	+	27.8499i	0.204775	+	1.29290i
$465$	4.35249	−	4.35249i	0.201842	−	0.201842i
$466$	0.423112	+	0.215586i	0.0196003	+	0.00998684i
$467$	−11.8892	+	8.63802i	−0.550167	+	0.399720i	−0.827847	−	0.560954i	$-0.810435\pi$
$467$	−11.8892	+	8.63802i	−0.550167	+	0.399720i	0.277680	+	0.960674i	$0.410435\pi$
$468$	14.1518	+	27.7744i	0.654166	+	1.28387i
$469$	6.80982	+	4.94762i	0.314448	+	0.228460i
$470$	0.324303	−	2.04757i	0.0149590	−	0.0944472i
$471$	−10.7134	−	14.7457i	−0.493648	−	0.679448i
$472$	1.43450	+	1.97442i	0.0660282	+	0.0908800i
$473$	−3.38735	+	21.3869i	−0.155751	+	0.983371i
$474$	3.89272	+	2.82823i	0.178799	+	0.129905i
$475$	12.2007	+	23.9452i	0.559805	+	1.09868i
$476$	4.80022	−	3.48756i	0.220018	−	0.159852i
$477$	14.1610	+	7.21538i	0.648386	+	0.330369i
$478$	−2.93880	+	2.93880i	−0.134418	+	0.134418i
$479$	−5.44356	−	34.3693i	−0.248723	−	1.57037i	−0.723536	−	0.690287i	$-0.757484\pi$
$479$	−5.44356	−	34.3693i	−0.248723	−	1.57037i	0.474813	−	0.880087i	$-0.342516\pi$
$480$	−2.40765	+	4.72527i	−0.109894	+	0.215678i
$481$	21.8909	−	11.1540i	0.998139	−	0.508577i
$482$	−0.930396	+	2.86346i	−0.0423784	+	0.130427i
$483$		−	0.723355i		−	0.0329138i
$484$	−3.47091	−	1.12777i	−0.157769	−	0.0512621i
$485$	−3.19001	−	0.505248i	−0.144851	−	0.0229421i
$486$	−5.16986	+	0.818826i	−0.234510	+	0.0371427i
$487$	−18.1145	+	5.88575i	−0.820845	+	0.266709i	−0.689184	−	0.724586i	$-0.742031\pi$
$487$	−18.1145	+	5.88575i	−0.820845	+	0.266709i	−0.131661	+	0.991295i	$0.542031\pi$
$488$	3.83364	+	11.7987i	0.173541	+	0.534103i
$489$	−8.90687	−	8.90687i	−0.402782	−	0.402782i
$490$	0.100623	−	0.138495i	0.00454567	−	0.00625657i
$491$	−43.3468			−1.95621			−0.978107	−	0.208103i	$-0.933271\pi$
$491$	−43.3468			−1.95621			−0.978107	+	0.208103i	$0.933271\pi$
$492$	−33.3617	−	2.61914i	−1.50406	−	0.118080i
$493$	24.3066			1.09471
$494$	3.43782	−	4.73176i	0.154675	−	0.212892i
$495$	−5.90682	−	5.90682i	−0.265492	−	0.265492i
$496$	−3.93761	−	12.1187i	−0.176804	−	0.544147i
$497$	3.99899	−	1.29935i	0.179379	−	0.0582838i
$498$	−3.20613	+	0.507801i	−0.143670	+	0.0227551i
$499$	−20.0141	−	3.16992i	−0.895952	−	0.141905i	−0.308558	−	0.951206i	$-0.599846\pi$
$499$	−20.0141	−	3.16992i	−0.895952	−	0.141905i	−0.587395	+	0.809301i	$0.699846\pi$
$500$	11.1911	+	3.63622i	0.500482	+	0.162617i
$501$		−	23.1621i		−	1.03481i
$502$	−2.44012	+	7.50991i	−0.108908	+	0.335184i
$503$	34.1982	−	17.4248i	1.52482	−	0.776935i	0.527462	−	0.849578i	$-0.323144\pi$
$503$	34.1982	−	17.4248i	1.52482	−	0.776935i	0.997358	+	0.0726438i	$0.0231436\pi$
$504$	−2.08761	+	4.09716i	−0.0929894	+	0.182502i
$505$	1.37934	+	8.70881i	0.0613798	+	0.387537i
$506$	−0.153188	+	0.153188i	−0.00681003	+	0.00681003i
$507$	−1.96571	−	1.00158i	−0.0873001	−	0.0444816i
$508$	−26.7314	+	19.4215i	−1.18602	+	0.861691i
$509$	10.2317	+	20.0809i	0.453513	+	0.890070i	0.998661	+	0.0517301i	$0.0164736\pi$
$509$	10.2317	+	20.0809i	0.453513	+	0.890070i	−0.545148	+	0.838340i	$0.683526\pi$
$510$	1.15584	+	0.839765i	0.0511813	+	0.0371854i
$511$	−0.884164	+	5.58239i	−0.0391131	+	0.246950i
$512$	10.8894	+	14.9879i	0.481246	+	0.662378i
$513$	12.5919	+	17.3312i	0.555945	+	0.765192i
$514$	0.457894	−	2.89103i	0.0201969	−	0.127518i
$515$	7.71441	+	5.60485i	0.339938	+	0.246979i
$516$	−17.0249	−	33.4133i	−0.749480	−	1.47094i
$517$	29.5651	−	21.4803i	1.30027	−	0.944702i
$518$	1.58486	+	0.807525i	0.0696347	+	0.0354806i
$519$	−1.21915	+	1.21915i	−0.0535147	+	0.0535147i
$520$	−0.390923	−	2.46819i	−0.0171431	−	0.108237i
$521$	−5.37178	+	10.5427i	−0.235342	+	0.461885i	−0.978228	−	0.207533i	$-0.933457\pi$
$521$	−5.37178	+	10.5427i	−0.235342	+	0.461885i	0.742886	+	0.669418i	$0.233457\pi$
$522$	−8.23744	+	4.19719i	−0.360543	+	0.183706i
$523$	2.47759	−	7.62525i	0.108338	−	0.333429i	−0.882162	−	0.470947i	$-0.843912\pi$
$523$	2.47759	−	7.62525i	0.108338	−	0.333429i	0.990499	+	0.137518i	$0.0439124\pi$
$524$		−	2.24350i		−	0.0980078i
$525$	11.8492	+	3.85004i	0.517142	+	0.168030i
$526$	5.52323	+	0.874794i	0.240824	+	0.0381428i
$527$	−10.8490	+	1.71832i	−0.472591	+	0.0748510i
$528$	−27.7862	+	9.02828i	−1.20924	+	0.392905i
$529$	−7.08540	−	21.8066i	−0.308061	−	0.948113i
$530$	−0.442161	−	0.442161i	−0.0192063	−	0.0192063i
$531$	5.90589	−	8.12876i	0.256294	−	0.352758i
$532$	−11.2731			−0.488752
$533$	20.2890	−	12.4385i	0.878815	−	0.538772i
$534$	1.09574			0.0474174
$535$	7.34011	−	10.1028i	0.317340	−	0.436782i
$536$	6.29030	+	6.29030i	0.271700	+	0.271700i
$537$	18.5784	+	57.1783i	0.801716	+	2.46743i
$538$	4.90352	−	1.59325i	0.211406	−	0.0686899i
$539$	2.98058	−	0.472077i	0.128383	−	0.0203338i
$540$	4.43685	+	0.702728i	0.190932	+	0.0302406i
$541$	17.9139	+	5.82056i	0.770177	+	0.250246i	0.667641	−	0.744484i	$-0.267304\pi$
$541$	17.9139	+	5.82056i	0.770177	+	0.250246i	0.102536	+	0.994729i	$0.467304\pi$
$542$		−	7.01789i		−	0.301444i
$543$	17.2936	−	53.2242i	0.742139	−	2.28407i
$544$	8.43227	−	4.29646i	0.361531	−	0.184209i
$545$	−2.56509	+	5.03427i	−0.109876	+	0.215645i
$546$	−0.424174	−	2.67813i	−0.0181530	−	0.114613i
$547$	28.6326	−	28.6326i	1.22424	−	1.22424i	0.258131	−	0.966110i	$-0.416894\pi$
$547$	28.6326	−	28.6326i	1.22424	−	1.22424i	0.966110	−	0.258131i	$-0.0831065\pi$
$548$	−22.8063	−	11.6204i	−0.974238	−	0.496399i
$549$	41.3210	−	30.0215i	1.76354	−	1.28129i
$550$	−1.69402	−	3.32469i	−0.0722331	−	0.141765i
$551$	−37.3613	−	27.1446i	−1.59165	−	1.15640i
$552$	0.119589	−	0.755058i	0.00509006	−	0.0321374i
$553$	3.87666	+	5.33577i	0.164852	+	0.226900i
$554$	−3.26501	−	4.49390i	−0.138717	−	0.190928i
$555$	1.78373	−	11.2620i	0.0757152	−	0.478047i
$556$	2.71953	+	1.97586i	0.115334	+	0.0837950i
$557$	0.0741602	+	0.145548i	0.00314227	+	0.00616705i	0.892572	−	0.450904i	$-0.148898\pi$
$557$	0.0741602	+	0.145548i	0.00314227	+	0.00616705i	−0.889430	+	0.457071i	$0.848898\pi$
$558$	3.37999	−	2.45571i	0.143087	−	0.103958i
$559$	23.7620	+	12.1074i	1.00503	+	0.512087i
$560$	−1.60638	+	1.60638i	−0.0678819	+	0.0678819i
$561$	3.93981	+	24.8750i	0.166339	+	1.05022i
$562$	1.97562	−	3.87737i	0.0833364	−	0.163557i
$563$	−21.9187	+	11.1681i	−0.923762	+	0.470680i	−0.850111	−	0.526604i	$-0.823465\pi$
$563$	−21.9187	+	11.1681i	−0.923762	+	0.470680i	−0.0736515	+	0.997284i	$0.523465\pi$
$564$	−19.5575	+	60.1919i	−0.823521	+	2.53454i
$565$		−	1.40938i		−	0.0592932i
$566$	−5.04378	−	1.63882i	−0.212006	−	0.0688849i
$567$	−3.08312	−	0.488319i	−0.129479	−	0.0205075i
$568$	4.38907	−	0.695160i	0.184161	−	0.0291683i
$569$	6.07185	−	1.97286i	0.254545	−	0.0827067i	−0.178965	−	0.983855i	$-0.557275\pi$
$569$	6.07185	−	1.97286i	0.254545	−	0.0827067i	0.433510	+	0.901149i	$0.357275\pi$
$570$	−0.838807	−	2.58158i	−0.0351337	−	0.108131i
$571$	20.8449	+	20.8449i	0.872333	+	0.872333i	0.992726	−	0.120393i	$-0.0384155\pi$
$571$	20.8449	+	20.8449i	0.872333	+	0.872333i	−0.120393	+	0.992726i	$0.538415\pi$
$572$	12.7078	−	17.4908i	0.531339	−	0.731326i
$573$	−56.0694			−2.34233
$574$	1.59193	+	0.659039i	0.0664458	+	0.0275077i
$575$	−1.22599			−0.0511272
$576$	16.1488	−	22.2269i	0.672867	−	0.926122i
$577$	−21.5104	−	21.5104i	−0.895491	−	0.895491i	0.0995421	−	0.995033i	$-0.468262\pi$
$577$	−21.5104	−	21.5104i	−0.895491	−	0.895491i	−0.995033	+	0.0995421i	$0.968262\pi$
$578$	0.625714	+	1.92575i	0.0260263	+	0.0801006i
$579$	−1.40818	+	0.457544i	−0.0585218	+	0.0190149i
$580$	−9.56462	+	1.51489i	−0.397149	+	0.0629022i
$581$	−4.39466	−	0.696046i	−0.182321	−	0.0288768i
$582$	−3.52241	−	1.14450i	−0.146008	−	0.0474410i
$583$		−	11.0230i		−	0.456525i
$584$	−1.84583	+	5.68087i	−0.0763809	+	0.235076i
$585$	−9.16694	+	4.67079i	−0.379006	+	0.193113i
$586$	1.06059	−	2.08153i	0.0438126	−	0.0859871i
$587$	−1.81395	−	11.4528i	−0.0748698	−	0.472710i	−0.996426	−	0.0844655i	$-0.973082\pi$
$587$	−1.81395	−	11.4528i	−0.0748698	−	0.472710i	0.921557	−	0.388244i	$-0.126918\pi$
$588$	−3.69552	+	3.69552i	−0.152401	+	0.152401i
$589$	18.5948	+	9.47454i	0.766186	+	0.390391i
$590$	−0.319821	+	0.232364i	−0.0131668	+	0.00956627i
$591$	−8.22349	−	16.1395i	−0.338269	−	0.663891i
$592$	−19.0965	−	13.8744i	−0.784860	−	0.570234i
$593$	0.767805	−	4.84773i	0.0315300	−	0.199072i	−0.966895	−	0.255174i	$-0.917867\pi$
$593$	0.767805	−	4.84773i	0.0315300	−	0.199072i	0.998425	+	0.0561019i	$0.0178672\pi$
$594$	−1.74833	−	2.40637i	−0.0717350	−	0.0987348i
$595$	1.15107	+	1.58431i	0.0471892	+	0.0649504i
$596$	0.312207	−	1.97120i	0.0127885	−	0.0807435i
$597$	−21.9873	−	15.9747i	−0.899879	−	0.653801i
$598$	0.121132	+	0.237736i	0.00495348	+	0.00972174i
$599$	−15.6277	+	11.3542i	−0.638532	+	0.463920i	−0.859345	−	0.511396i	$-0.829129\pi$
$599$	−15.6277	+	11.3542i	−0.638532	+	0.463920i	0.220814	+	0.975316i	$0.429129\pi$
$600$	11.7320	+	5.97776i	0.478958	+	0.244041i
$601$	14.5888	−	14.5888i	0.595089	−	0.595089i	−0.343912	−	0.939002i	$-0.611752\pi$
$601$	14.5888	−	14.5888i	0.595089	−	0.595089i	0.939002	+	0.343912i	$0.111752\pi$
$602$	0.302038	+	1.90699i	0.0123102	+	0.0777233i
$603$	16.6272	−	32.6326i	0.677110	−	1.32890i
$604$	−5.73507	+	2.92217i	−0.233357	+	0.118901i
$605$	0.372219	−	1.14557i	0.0151329	−	0.0465741i
$606$			10.1111i			0.410737i
$607$	−35.4381	−	11.5145i	−1.43839	−	0.467361i	−0.516994	−	0.855989i	$-0.672949\pi$
$607$	−35.4381	−	11.5145i	−1.43839	−	0.467361i	−0.921395	+	0.388628i	$0.872949\pi$
$608$	−17.7592	−	2.81279i	−0.720232	−	0.114074i
$609$	−21.1461	+	3.34922i	−0.856884	+	0.135717i
$610$	−1.91119	+	0.620982i	−0.0773817	+	0.0251428i
$611$	−13.9084	−	42.8058i	−0.562675	−	1.73174i
$612$	−18.2550	−	18.2550i	−0.737915	−	0.737915i
$613$	24.0298	−	33.0742i	0.970556	−	1.33586i	0.0287897	−	0.999585i	$-0.490835\pi$
$613$	24.0298	−	33.0742i	0.970556	−	1.33586i	0.941766	−	0.336270i	$-0.109165\pi$
$614$	−8.64059			−0.348706
$615$	0.864447	−	11.0110i	0.0348579	−	0.444007i
$616$	3.18925			0.128499
$617$	4.53280	−	6.23886i	0.182484	−	0.251167i	−0.707969	−	0.706244i	$-0.750388\pi$
$617$	4.53280	−	6.23886i	0.182484	−	0.251167i	0.890452	+	0.455077i	$0.150388\pi$
$618$	7.73199	+	7.73199i	0.311026	+	0.311026i
$619$	−10.1996	−	31.3911i	−0.409955	−	1.26171i	−0.916686	−	0.399609i	$-0.869146\pi$
$619$	−10.1996	−	31.3911i	−0.409955	−	1.26171i	0.506730	−	0.862105i	$-0.330854\pi$
$620$	4.16199	−	1.35231i	0.167149	−	0.0543101i
$621$	−0.965252	+	0.152881i	−0.0387342	+	0.00613490i
$622$	−7.10891	−	1.12594i	−0.285041	−	0.0451461i
$623$	1.42843	+	0.464124i	0.0572288	+	0.0185948i
$624$			35.9830i			1.44047i
$625$	5.89991	−	18.1581i	0.235997	−	0.726323i
$626$	2.89138	−	1.47323i	0.115563	−	0.0588821i
$627$	21.7235	−	42.6348i	0.867553	−	1.70267i
$628$	−2.02714	−	12.7988i	−0.0808915	−	0.510729i
$629$	−14.3880	+	14.3880i	−0.573687	+	0.573687i
$630$	−0.663668	−	0.338156i	−0.0264412	−	0.0134725i
$631$	−7.52216	+	5.46517i	−0.299452	+	0.217565i	−0.727357	−	0.686259i	$-0.759252\pi$
$631$	−7.52216	+	5.46517i	−0.299452	+	0.217565i	0.427905	+	0.903824i	$0.359252\pi$
$632$	3.16442	+	6.21053i	0.125874	+	0.247042i
$633$	−40.1003	−	29.1346i	−1.59384	−	1.15800i
$634$	−0.0918976	+	0.580219i	−0.00364972	+	0.0230434i
$635$	−6.41007	−	8.82270i	−0.254376	−	0.350118i
$636$	11.2209	+	15.4443i	0.444938	+	0.612405i
$637$	0.581417	−	3.67092i	0.0230366	−	0.145447i
$638$	5.18748	+	3.76892i	0.205374	+	0.149213i
$639$	−8.30585	−	16.3011i	−0.328574	−	0.644863i
$640$	−4.03940	+	2.93480i	−0.159671	+	0.116008i
$641$	37.5936	+	19.1549i	1.48486	+	0.756574i	0.993441	−	0.114350i	$-0.0364785\pi$
$641$	37.5936	+	19.1549i	1.48486	+	0.756574i	0.491419	+	0.870924i	$0.336479\pi$
$642$	10.1258	−	10.1258i	0.399634	−	0.399634i
$643$	5.39542	+	34.0653i	0.212774	+	1.34340i	0.830503	+	0.557014i	$0.188053\pi$
$643$	5.39542	+	34.0653i	0.212774	+	1.34340i	−0.617729	+	0.786391i	$0.711947\pi$
$644$	0.233475	−	0.458220i	0.00920019	−	0.0180564i
$645$	11.0280	−	5.61907i	0.434229	−	0.221251i
$646$	−1.49686	+	4.60685i	−0.0588930	+	0.181254i
$647$			24.7751i			0.974009i	0.873400	+	0.487004i	$0.161910\pi$
$647$			24.7751i			0.974009i	−0.873400	+	0.487004i	$0.838090\pi$
$648$	−3.13752	−	1.01944i	−0.123253	−	0.0400474i
$649$	−6.88293	−	1.09015i	−0.270179	−	0.0427921i
$650$	−4.53906	+	0.718916i	−0.178036	+	0.0281982i
$651$	9.20161	−	2.98978i	0.360640	−	0.117179i
$652$	−2.76735	−	8.51702i	−0.108378	−	0.333552i
$653$	11.1314	+	11.1314i	0.435603	+	0.435603i	0.890529	−	0.454926i	$-0.150334\pi$
$653$	11.1314	+	11.1314i	0.435603	+	0.435603i	−0.454926	+	0.890529i	$0.650334\pi$
$654$	−3.80834	+	5.24173i	−0.148918	+	0.204968i
$655$	0.740467			0.0289324
$656$	−19.4974	−	11.9428i	−0.761246	−	0.466290i
$657$	24.5920			0.959425
$658$	1.91532	−	2.63621i	0.0746670	−	0.102770i
$659$	7.73285	+	7.73285i	0.301229	+	0.301229i	0.841495	−	0.540265i	$-0.181676\pi$
$659$	7.73285	+	7.73285i	0.301229	+	0.301229i	−0.540265	+	0.841495i	$0.681676\pi$
$660$	−3.10062	−	9.54272i	−0.120691	−	0.371450i
$661$	45.2316	−	14.6966i	1.75931	−	0.571633i	0.762179	−	0.647367i	$-0.224130\pi$
$661$	45.2316	−	14.6966i	1.75931	−	0.571633i	0.997128	+	0.0757334i	$0.0241298\pi$
$662$	1.03392	−	0.163757i	0.0401845	−	0.00636461i
$663$	30.6363	+	4.85232i	1.18982	+	0.188449i
$664$	−4.47219	−	1.45310i	−0.173555	−	0.0563913i
$665$		−	3.72069i		−	0.144282i
$666$	2.39158	−	7.36053i	0.0926719	−	0.285215i
$667$	1.87713	−	0.956446i	0.0726828	−	0.0370337i
$668$	7.47595	−	14.6724i	0.289253	−	0.567691i
$669$	8.40504	+	53.0674i	0.324958	+	2.05170i
$670$	−1.01892	+	1.01892i	−0.0393643	+	0.0393643i
$671$	−31.5632	−	16.0823i	−1.21848	−	0.620849i
$672$	−6.74386	+	4.89970i	−0.260150	+	0.189010i
$673$	10.7043	+	21.0084i	0.412620	+	0.809813i	1.00000		0.000501150i	$0.000159521\pi$
$673$	10.7043	+	21.0084i	0.412620	+	0.809813i	−0.587380	+	0.809311i	$0.699840\pi$
$674$	−5.69798	−	4.13983i	−0.219478	−	0.159460i
$675$	2.63321	−	16.6254i	0.101352	−	0.639912i
$676$	−0.921930	−	1.26893i	−0.0354588	−	0.0488049i
$677$	17.1946	+	23.6663i	0.660841	+	0.909569i	0.999509	−	0.0313365i	$-0.00997637\pi$
$677$	17.1946	+	23.6663i	0.660841	+	0.909569i	−0.338668	+	0.940906i	$0.609976\pi$
$678$	0.252826	−	1.59628i	0.00970974	−	0.0613049i
$679$	−4.10709	−	2.98398i	−0.157616	−	0.114515i
$680$	0.939589	+	1.84405i	0.0360316	+	0.0707160i
$681$	−3.40157	+	2.47139i	−0.130348	+	0.0947037i
$682$	−2.58182	−	1.31550i	−0.0988630	−	0.0503732i
$683$	8.60066	−	8.60066i	0.329095	−	0.329095i	−0.523147	−	0.852242i	$-0.675242\pi$
$683$	8.60066	−	8.60066i	0.329095	−	0.329095i	0.852242	+	0.523147i	$0.175242\pi$
$684$	7.67308	+	48.4459i	0.293388	+	1.85238i
$685$	3.83531	−	7.52722i	0.146540	−	0.287600i
$686$	0.239752	−	0.122160i	0.00915378	−	0.00466408i
$687$	−1.34309	+	4.13361i	−0.0512421	+	0.157707i
$688$		−	25.6221i		−	0.976835i
$689$	−12.9116	−	4.19523i	−0.491893	−	0.159826i
$690$	0.122306	+	0.0193714i	0.00465612	+	0.000737457i
$691$	−11.3393	+	1.79597i	−0.431367	+	0.0683218i	−0.368343	−	0.929690i	$-0.620075\pi$
$691$	−11.3393	+	1.79597i	−0.431367	+	0.0683218i	−0.0630245	+	0.998012i	$0.520075\pi$
$692$	−1.16579	+	0.378788i	−0.0443166	+	0.0143993i
$693$	−4.05748	−	12.4876i	−0.154131	−	0.474366i
$694$	3.26381	+	3.26381i	0.123893	+	0.123893i
$695$	−0.652131	+	0.897581i	−0.0247367	+	0.0340472i
$696$	−22.6266			−0.857659
$697$	−12.7975	+	14.9898i	−0.484741	+	0.567780i
$698$	6.45114			0.244179
$699$	2.81246	−	3.87101i	0.106377	−	0.146415i
$700$	6.26340	+	6.26340i	0.236734	+	0.236734i
$701$	2.21924	+	6.83012i	0.0838196	+	0.257970i	0.984179	−	0.177177i	$-0.0566964\pi$
$701$	2.21924	+	6.83012i	0.0838196	+	0.257970i	−0.900359	+	0.435147i	$0.856696\pi$
$702$	−3.48407	+	1.13204i	−0.131498	+	0.0427262i
$703$	38.1835	−	6.04767i	1.44012	−	0.228092i
$704$	−18.8204	−	2.98086i	−0.709320	−	0.112345i
$705$	−19.8663	−	6.45496i	−0.748208	−	0.243108i
$706$			8.26669i			0.311121i
$707$	−4.28278	+	13.1811i	−0.161071	+	0.495724i
$708$	10.7534	−	5.47911i	0.404136	−	0.205918i
$709$	0.163004	−	0.319913i	0.00612174	−	0.0120146i	−0.887925	−	0.459987i	$-0.847854\pi$
$709$	0.163004	−	0.319913i	0.00612174	−	0.0120146i	0.894047	+	0.447973i	$0.147854\pi$
$710$	0.112604	+	0.710953i	0.00422595	+	0.0266816i
$711$	20.2917	−	20.2917i	0.760997	−	0.760997i
$712$	1.41430	+	0.720622i	0.0530031	+	0.0270064i
$713$	−0.770226	+	0.559602i	−0.0288452	+	0.0209572i
$714$	1.01951	+	2.00090i	0.0381541	+	0.0748817i
$715$	5.77282	+	4.19420i	0.215891	+	0.156854i
$716$	−6.68651	+	42.2169i	−0.249886	+	1.57772i
$717$	24.6148	+	33.8794i	0.919258	+	1.26525i
$718$	2.96924	+	4.08681i	0.110811	+	0.152519i
$719$	4.34994	−	27.4644i	0.162225	−	1.02425i	−0.763432	−	0.645888i	$-0.776487\pi$
$719$	4.34994	−	27.4644i	0.162225	−	1.02425i	0.925657	−	0.378363i	$-0.123513\pi$
$720$	7.99676	+	5.80998i	0.298021	+	0.216525i
$721$	6.80451	+	13.3546i	0.253413	+	0.497351i
$722$	3.30941	−	2.40443i	0.123164	−	0.0894835i
$723$	27.0308	+	13.7729i	1.00529	+	0.512219i
$724$	28.1338	−	28.1338i	1.04559	−	1.04559i
$725$	5.67646	+	35.8398i	0.210818	+	1.33106i
$726$	0.627082	−	1.23072i	0.0232732	−	0.0456762i
$727$	−6.68766	+	3.40753i	−0.248032	+	0.126378i	−0.573587	−	0.819144i	$-0.694449\pi$
$727$	−6.68766	+	3.40753i	−0.248032	+	0.126378i	0.325556	+	0.945523i	$0.394449\pi$
$728$	1.21380	−	3.73568i	0.0449863	−	0.138454i
$729$			43.3767i			1.60655i
$730$	−0.920203	−	0.298992i	−0.0340582	−	0.0110662i
$731$	−21.8150	−	3.45516i	−0.806857	−	0.127794i
$732$	60.5941	−	9.59716i	2.23962	−	0.354721i
$733$	−21.2139	+	6.89281i	−0.783553	+	0.254592i	−0.673356	−	0.739318i	$-0.735148\pi$
$733$	−21.2139	+	6.89281i	−0.783553	+	0.254592i	−0.110196	+	0.993910i	$0.535148\pi$
$734$	−1.05654	−	3.25170i	−0.0389976	−	0.120022i
$735$	−1.21970	−	1.21970i	−0.0449895	−	0.0449895i
$736$	0.482139	−	0.663607i	0.0177719	−	0.0244609i
$737$	−25.4014			−0.935674
$738$	1.74865	−	7.28985i	0.0643687	−	0.268343i
$739$	−39.8638			−1.46641			−0.733206	−	0.680006i	$-0.761977\pi$
$739$	−39.8638			−1.46641			−0.733206	+	0.680006i	$0.761977\pi$
$740$	4.76494	−	6.55838i	0.175163	−	0.241091i
$741$	−41.6718	−	41.6718i	−1.53085	−	1.53085i
$742$	−0.303727	−	0.934775i	−0.0111502	−	0.0343167i
$743$	0.129918	−	0.0422129i	0.00476623	−	0.00154864i	−0.306633	−	0.951828i	$-0.599202\pi$
$743$	0.129918	−	0.0422129i	0.00476623	−	0.00154864i	0.311399	+	0.950279i	$0.399202\pi$
$744$	10.0992	−	1.59955i	0.370254	−	0.0586424i
$745$	0.650593	+	0.103044i	0.0238359	+	0.00377524i
$746$	−6.08751	−	1.97795i	−0.222879	−	0.0724179i
$747$			19.3597i			0.708334i
$748$	−5.53307	+	17.0290i	−0.202309	+	0.622643i
$749$	17.4892	−	8.91118i	0.639041	−	0.325607i
$750$	−2.02187	+	3.96815i	−0.0738284	+	0.144896i
$751$	6.77534	+	42.7778i	0.247236	+	1.56098i	0.728895	+	0.684626i	$0.240034\pi$
$751$	6.77534	+	42.7778i	0.247236	+	1.56098i	−0.481659	+	0.876359i	$0.659966\pi$
$752$	−30.5769	+	30.5769i	−1.11503	+	1.11503i
$753$	70.8928	+	36.1217i	2.58348	+	1.31635i
$754$	6.38897	−	4.64186i	0.232673	−	0.169046i
$755$	−0.964460	−	1.89286i	−0.0351003	−	0.0688882i
$756$	5.71238	+	4.15029i	0.207757	+	0.150945i
$757$	−0.949008	+	5.99180i	−0.0344923	+	0.217776i	−0.998914	−	0.0465931i	$-0.985164\pi$
$757$	−0.949008	+	5.99180i	−0.0344923	+	0.217776i	0.964422	+	0.264369i	$0.0851636\pi$
$758$	2.10639	+	2.89919i	0.0765075	+	0.105303i
$759$	1.28307	+	1.76600i	0.0465725	+	0.0641016i
$760$	0.615126	−	3.88375i	0.0223130	−	0.140879i
$761$	28.3516	+	20.5986i	1.02774	+	0.746699i	0.967856	−	0.251506i	$-0.0809259\pi$
$761$	28.3516	+	20.5986i	1.02774	+	0.746699i	0.0598872	+	0.998205i	$0.480926\pi$
$762$	−5.67743	−	11.1426i	−0.205671	−	0.403653i
$763$	−7.18486	+	5.22011i	−0.260109	+	0.188981i
$764$	−35.5180	−	18.0973i	−1.28499	−	0.654738i
$765$	6.02506	−	6.02506i	0.217836	−	0.217836i
$766$	−0.759985	−	4.79836i	−0.0274594	−	0.173372i
$767$	−3.89650	+	7.64731i	−0.140694	+	0.276128i
$768$	25.4065	−	12.9452i	0.916776	−	0.467121i
$769$	−1.14882	+	3.53570i	−0.0414274	+	0.127500i	−0.969631	−	0.244572i	$-0.921353\pi$
$769$	−1.14882	+	3.53570i	−0.0414274	+	0.127500i	0.928204	+	0.372072i	$0.121353\pi$
$770$			0.516603i			0.0186171i
$771$	−28.0499	−	9.11398i	−1.01019	−	0.328232i
$772$	−1.03971	−	0.164674i	−0.0374200	−	0.00592675i
$773$	−25.6362	+	4.06038i	−0.922070	+	0.146042i	−0.599382	−	0.800463i	$-0.704587\pi$
$773$	−25.6362	+	4.06038i	−0.922070	+	0.146042i	−0.322689	+	0.946505i	$0.604587\pi$
$774$	7.98968	−	2.59600i	0.287183	−	0.0933114i
$775$	−5.06727	−	15.5955i	−0.182022	−	0.560206i
$776$	−3.79376	−	3.79376i	−0.136188	−	0.136188i
$777$	10.5347	−	14.4997i	0.377929	−	0.520175i
$778$	8.72035			0.312640
$779$	36.4109	−	8.74892i	1.30456	−	0.313463i
$780$	−12.3578			−0.442480
$781$	−7.45835	+	10.2655i	−0.266881	+	0.367330i
$782$	−0.156254	−	0.156254i	−0.00558764	−	0.00558764i
$783$	8.93845	+	27.5097i	0.319434	+	0.983117i
$784$	−3.39605	+	1.10344i	−0.121287	+	0.0394087i
$785$	4.22425	−	0.669055i	0.150770	−	0.0238796i
$786$	0.838661	+	0.132831i	0.0299141	+	0.00473792i
$787$	−7.75605	−	2.52009i	−0.276473	−	0.0898316i	0.167499	−	0.985872i	$-0.446431\pi$
$787$	−7.75605	−	2.52009i	−0.276473	−	0.0898316i	−0.443972	+	0.896041i	$0.646431\pi$
$788$		−	12.8781i		−	0.458763i
$789$	17.4120	−	53.5886i	0.619884	−	1.90781i
$790$	−1.00600	+	0.512582i	−0.0357918	+	0.0182368i
$791$	1.00573	−	1.97385i	0.0357596	−	0.0701821i
$792$	−2.17077	−	13.7057i	−0.0771351	−	0.487012i
$793$	−30.8503	+	30.8503i	−1.09553	+	1.09553i
$794$	−1.24395	−	0.633824i	−0.0441461	−	0.0224936i
$795$	−5.09737	+	3.70346i	−0.180785	+	0.131348i
$796$	−8.77207	−	17.2162i	−0.310918	−	0.610210i
$797$	26.1714	+	19.0146i	0.927037	+	0.673532i	0.945266	−	0.326302i	$-0.105803\pi$
$797$	26.1714	+	19.0146i	0.927037	+	0.673532i	−0.0182285	+	0.999834i	$0.505803\pi$
$798$	0.667447	−	4.21409i	0.0236274	−	0.149177i
$799$	21.9103	+	30.1569i	0.775129	+	1.06687i
$800$	8.30431	+	11.4299i	0.293602	+	0.404108i
$801$	1.02230	−	6.45454i	0.0361211	−	0.228060i
$802$	7.35799	+	5.34589i	0.259820	+	0.188770i
$803$	−7.74332	−	15.1971i	−0.273256	−	0.536295i
$804$	35.5898	−	25.8575i	1.25516	−	0.911924i
$805$	0.151235	+	0.0770583i	0.00533035	+	0.00271595i
$806$	−2.52351	+	2.52351i	−0.0888868	+	0.0888868i
$807$	−8.12693	−	51.3114i	−0.286082	−	1.80625i
$808$	−6.64965	+	13.0507i	−0.233934	+	0.459121i
$809$	−16.5566	+	8.43601i	−0.582099	+	0.296594i	−0.720136	−	0.693833i	$-0.755921\pi$
$809$	−16.5566	+	8.43601i	−0.582099	+	0.296594i	0.138037	+	0.990427i	$0.455921\pi$
$810$	0.165132	−	0.508223i	0.00580213	−	0.0178571i
$811$			33.4236i			1.17366i	0.809710	+	0.586830i	$0.199624\pi$
$811$			33.4236i			1.17366i	−0.809710	+	0.586830i	$0.800376\pi$
$812$	−14.4763	−	4.70365i	−0.508020	−	0.165066i
$813$	−69.8424	−	11.0619i	−2.44948	−	0.387959i
$814$	−5.30163	+	0.839696i	−0.185822	+	0.0294313i
$815$	2.81104	−	0.913362i	0.0984664	−	0.0319937i
$816$	−9.20899	−	28.3424i	−0.322379	−	0.992181i
$817$	29.6730	+	29.6730i	1.03813	+	1.03813i
$818$	−0.454808	+	0.625990i	−0.0159020	+	0.0218872i
$819$	−16.1714			−0.565075
$820$	4.10158	−	6.69607i	0.143233	−	0.233837i
$821$	30.0960			1.05036			0.525178	−	0.850992i	$-0.323999\pi$
$821$	30.0960			1.05036			0.525178	+	0.850992i	$0.323999\pi$
$822$	5.69421	−	7.83741i	0.198608	−	0.273361i
$823$	6.74574	+	6.74574i	0.235142	+	0.235142i	0.814835	−	0.579693i	$-0.196828\pi$
$823$	6.74574	+	6.74574i	0.235142	+	0.235142i	−0.579693	+	0.814835i	$0.696828\pi$
$824$	4.89487	+	15.0648i	0.170521	+	0.524809i
$825$	−35.7577	+	11.6184i	−1.24492	+	0.404500i
$826$	−0.613726	+	0.0972047i	−0.0213543	+	0.00338218i
$827$	−33.1387	−	5.24865i	−1.15234	−	0.182514i	−0.449114	−	0.893475i	$-0.648260\pi$
$827$	−33.1387	−	5.24865i	−1.15234	−	0.182514i	−0.703231	+	0.710961i	$0.748260\pi$
$828$	−2.12810	−	0.691463i	−0.0739567	−	0.0240300i
$829$			19.7421i			0.685673i	0.939395	+	0.342837i	$0.111388\pi$
$829$			19.7421i			0.685673i	−0.939395	+	0.342837i	$0.888612\pi$
$830$	0.235377	−	0.724417i	0.00817006	−	0.0251449i
$831$	−49.8700	+	25.4101i	−1.72997	+	0.881465i
$832$	−10.6544	+	20.9105i	−0.369376	+	0.724941i
$833$	0.481526	+	3.04024i	0.0166839	+	0.105338i
$834$	−0.899626	+	0.899626i	−0.0311515	+	0.0311515i
$835$	4.84261	+	2.46743i	0.167585	+	0.0853891i
$836$	27.5221	−	19.9960i	0.951873	−	0.691576i
$837$	−5.93435	−	11.6468i	−0.205121	−	0.402573i
$838$	−4.56404	−	3.31597i	−0.157662	−	0.114548i
$839$	0.653084	−	4.12341i	0.0225470	−	0.142356i	−0.973847	−	0.227206i	$-0.927041\pi$
$839$	0.653084	−	4.12341i	0.0225470	−	0.142356i	0.996394	+	0.0848497i	$0.0270410\pi$
$840$	−1.07151	−	1.47481i	−0.0369707	−	0.0508857i
$841$	−19.6057	−	26.9849i	−0.676059	−	0.930515i
$842$	−1.35125	+	8.53145i	−0.0465671	+	0.294013i
$843$	−35.4737	−	25.7732i	−1.22178	−	0.887675i
$844$	−15.9985	−	31.3988i	−0.550690	−	1.08079i
$845$	0.418809	−	0.304283i	0.0144075	−	0.0104676i
$846$	−12.6327	−	6.43670i	−0.434322	−	0.221298i
$847$	1.33877	−	1.33877i	0.0460007	−	0.0460007i
$848$	2.04042	+	12.8827i	0.0700682	+	0.442393i
$849$	−24.2599	+	47.6128i	−0.832598	+	1.63407i
$850$	3.39124	−	1.72792i	0.116319	−	0.0592673i
$851$	−0.544988	+	1.67730i	−0.0186820	+	0.0574972i
$852$		−	21.9753i		−	0.752861i
$853$	12.8750	+	4.18333i	0.440830	+	0.143234i	0.521019	−	0.853545i	$-0.325552\pi$
$853$	12.8750	+	4.18333i	0.440830	+	0.143234i	−0.0801883	+	0.996780i	$0.525552\pi$
$854$	−3.11976	−	0.494122i	−0.106756	−	0.0169085i
$855$	−15.9896	+	2.53250i	−0.546831	+	0.0866096i
$856$	19.7289	−	6.41031i	0.674321	−	0.219100i
$857$	−6.87089	−	21.1464i	−0.234705	−	0.722348i	−0.997160	−	0.0753071i	$-0.976006\pi$
$857$	−6.87089	−	21.1464i	−0.234705	−	0.722348i	0.762455	−	0.647041i	$-0.223994\pi$
$858$	5.78597	+	5.78597i	0.197530	+	0.197530i
$859$	−13.3477	+	18.3715i	−0.455417	+	0.626827i	−0.973550	−	0.228472i	$-0.926627\pi$
$859$	−13.3477	+	18.3715i	−0.455417	+	0.626827i	0.518134	+	0.855300i	$0.326627\pi$
$860$	8.79952			0.300061
$861$	9.06807	−	14.8042i	0.309039	−	0.504524i
$862$	−10.5682			−0.359955
$863$	−22.2455	+	30.6183i	−0.757245	+	1.04226i	0.240194	+	0.970725i	$0.422789\pi$
$863$	−22.2455	+	30.6183i	−0.757245	+	1.04226i	−0.997438	+	0.0715327i	$0.977211\pi$
$864$	7.96352	+	7.96352i	0.270924	+	0.270924i
$865$	−0.125019	−	0.384768i	−0.00425076	−	0.0130825i
$866$	−7.45738	+	2.42305i	−0.253412	+	0.0823386i
$867$	20.1514	−	3.19167i	0.684379	−	0.108395i
$868$	6.79390	+	1.07605i	0.230600	+	0.0365234i
$869$	−18.9289	−	6.15038i	−0.642120	−	0.208637i
$870$		−	3.66512i		−	0.124259i
$871$	−9.66752	+	29.7536i	−0.327571	+	1.00816i
$872$	−8.36277	+	4.26104i	−0.283199	+	0.144297i
$873$	−10.0281	+	19.6812i	−0.339398	+	0.666107i
$874$	0.0656779	+	0.414674i	0.00222159	+	0.0140266i
$875$	−4.31655	+	4.31655i	−0.145926	+	0.145926i
$876$	26.3191	+	13.4103i	0.889241	+	0.453091i
$877$	−38.7462	+	28.1508i	−1.30837	+	0.950583i	−1.00000		0.000684397i	$-0.999782\pi$
$877$	−38.7462	+	28.1508i	−1.30837	+	0.950583i	−0.308366	+	0.951268i	$0.599782\pi$
$878$	−0.917572	−	1.80084i	−0.0309665	−	0.0607753i
$879$	−19.0437	−	13.8361i	−0.642329	−	0.466679i
$880$	1.07245	−	6.77116i	0.0361522	−	0.228256i
$881$	−5.89699	−	8.11651i	−0.198675	−	0.273452i	0.698043	−	0.716056i	$-0.254055\pi$
$881$	−5.89699	−	8.11651i	−0.198675	−	0.273452i	−0.896717	+	0.442604i	$0.854055\pi$
$882$	−0.688167	−	0.947180i	−0.0231718	−	0.0318932i
$883$	2.70156	−	17.0570i	0.0909146	−	0.574012i	−0.899612	−	0.436690i	$-0.856151\pi$
$883$	2.70156	−	17.0570i	0.0909146	−	0.574012i	0.990526	−	0.137322i	$-0.0438494\pi$
$884$	17.8409	+	12.9622i	0.600054	+	0.435964i
$885$	1.80838	+	3.54914i	0.0607880	+	0.119303i
$886$	−7.68837	+	5.58592i	−0.258296	+	0.187663i
$887$	45.6984	+	23.2845i	1.53440	+	0.781817i	0.998065	−	0.0621859i	$-0.0198072\pi$
$887$	45.6984	+	23.2845i	1.53440	+	0.781817i	0.536338	+	0.844003i	$0.319807\pi$
$888$	13.3936	−	13.3936i	0.449458	−	0.449458i
$889$	−2.68152	−	16.9305i	−0.0899353	−	0.567829i
$890$	−0.116728	+	0.229092i	−0.00391274	+	0.00767918i
$891$	8.39329	−	4.27660i	0.281186	−	0.143271i
$892$	−11.8041	+	36.3292i	−0.395229	+	1.21639i
$893$		−	70.8222i		−	2.36997i
$894$	0.718385	+	0.233417i	0.0240264	+	0.00780664i
$895$	−13.9337	−	2.20688i	−0.465752	−	0.0737678i
$896$	−7.75147	+	1.22771i	−0.258958	+	0.0410150i
$897$	2.55690	−	0.830786i	0.0853723	−	0.0277391i
$898$	−0.802036	−	2.46841i	−0.0267643	−	0.0823720i
$899$	19.9253	+	19.9253i	0.664545	+	0.664545i
$900$	22.6536	−	31.1800i	0.755119	−	1.03933i
$901$	11.2436			0.374580
$902$	−5.05551	+	1.21475i	−0.168330	+	0.0404469i
$903$	19.4546			0.647409
$904$	1.37613	−	1.89409i	0.0457696	−	0.0629964i
$905$	9.28556	+	9.28556i	0.308663	+	0.308663i
$906$	−0.752802	−	2.31689i	−0.0250102	−	0.0769734i
$907$	−35.8621	+	11.6523i	−1.19078	+	0.386908i	−0.836362	−	0.548178i	$-0.815322\pi$
$907$	−35.8621	+	11.6523i	−1.19078	+	0.386908i	−0.354420	+	0.935086i	$0.615322\pi$
$908$	−2.95246	+	0.467623i	−0.0979807	+	0.0155186i
$909$	59.5603	+	9.43343i	1.97549	+	0.312887i
$910$	0.605115	+	0.196614i	0.0200594	+	0.00651769i
$911$		−	15.7731i		−	0.522588i	−0.965259	−	0.261294i	$-0.915851\pi$
$911$		−	15.7731i		−	0.522588i	0.965259	−	0.261294i	$-0.0841492\pi$
$912$	−17.4966	+	53.8489i	−0.579369	+	1.78311i
$913$	11.9637	−	6.09582i	0.395942	−	0.201742i
$914$	−1.85235	+	3.63544i	−0.0612703	+	0.120250i
$915$	3.16754	+	19.9991i	0.104716	+	0.661148i
$916$	−2.18499	+	2.18499i	−0.0721941	+	0.0721941i
$917$	1.03703	+	0.528393i	0.0342457	+	0.0174491i
$918$	2.45454	−	1.78333i	0.0810120	−	0.0588586i
$919$	−19.9122	−	39.0800i	−0.656844	−	1.28913i	−0.943588	−	0.331122i	$-0.892573\pi$
$919$	−19.9122	−	39.0800i	−0.656844	−	1.28913i	0.286744	−	0.958007i	$-0.407427\pi$
$920$	0.145124	+	0.105439i	0.00478459	+	0.00347621i
$921$	−13.6197	+	85.9916i	−0.448785	+	2.83352i
$922$	0.236670	+	0.325748i	0.00779431	+	0.0107280i
$923$	9.18581	+	12.6432i	0.302355	+	0.416156i
$924$	2.46719	−	15.5772i	0.0811647	−	0.512454i
$925$	−24.5750	−	17.8548i	−0.808022	−	0.587063i
$926$	−2.38813	−	4.68697i	−0.0784789	−	0.154023i
$927$	52.7595	−	38.3320i	1.73285	−	1.25899i
$928$	−21.6318	−	11.0220i	−0.710100	−	0.361814i
$929$	26.7594	−	26.7594i	0.877947	−	0.877947i	−0.115375	−	0.993322i	$-0.536807\pi$
$929$	26.7594	−	26.7594i	0.877947	−	0.877947i	0.993322	+	0.115375i	$0.0368070\pi$
$930$	0.259100	+	1.63589i	0.00849621	+	0.0536430i
$931$	2.65506	−	5.21085i	0.0870162	−	0.170779i
$932$	3.03102	−	1.54438i	0.0992845	−	0.0505880i
$933$	−22.4108	+	68.9735i	−0.733698	+	2.25809i
$934$		−	3.95437i		−	0.129391i
$935$	−5.62043	−	1.82619i	−0.183808	−	0.0597227i
$936$	−16.8802	−	2.67356i	−0.551746	−	0.0873879i
$937$	−55.3805	+	8.77141i	−1.80920	+	0.286549i	−0.967403	−	0.253242i	$-0.918503\pi$
$937$	−55.3805	+	8.77141i	−1.80920	+	0.286549i	−0.841799	+	0.539791i	$0.818503\pi$
$938$	−2.15410	+	0.699909i	−0.0703338	+	0.0228529i
$939$	−10.1041	−	31.0973i	−0.329736	−	1.01482i
$940$	−10.5012	−	10.5012i	−0.342510	−	0.342510i
$941$	−0.744350	+	1.02451i	−0.0242651	+	0.0333980i	−0.820977	−	0.570961i	$-0.806571\pi$
$941$	−0.744350	+	1.02451i	−0.0242651	+	0.0333980i	0.796712	+	0.604359i	$0.206571\pi$
$942$	4.90445			0.159796
$943$	−0.398479	+	1.66120i	−0.0129762	+	0.0540960i
$944$	8.24595			0.268383
$945$	−1.36980	+	1.88537i	−0.0445596	+	0.0613311i
$946$	−4.11998	−	4.11998i	−0.133952	−	0.133952i
$947$	4.75068	+	14.6211i	0.154376	+	0.475121i	0.998097	−	0.0616609i	$-0.0196397\pi$
$947$	4.75068	+	14.6211i	0.154376	+	0.475121i	−0.843721	+	0.536782i	$0.819640\pi$
$948$	32.7821	−	10.6515i	1.06471	−	0.345946i
$949$	−20.7480	+	3.28615i	−0.673507	+	0.106673i
$950$	−7.14231	−	1.13123i	−0.231727	−	0.0367020i
$951$	5.62951	+	1.82914i	0.182550	+	0.0593139i
$952$			3.25309i			0.105433i
$953$	−7.65242	+	23.5517i	−0.247886	+	0.762915i	0.747262	+	0.664529i	$0.231368\pi$
$953$	−7.65242	+	23.5517i	−0.247886	+	0.762915i	−0.995148	+	0.0983856i	$0.968632\pi$
$954$	−3.81044	+	1.94151i	−0.123367	+	0.0628589i
$955$	5.97301	−	11.7227i	0.193282	−	0.379337i
$956$	4.65749	+	29.4063i	0.150634	+	0.951066i
$957$	45.6853	−	45.6853i	1.47680	−	1.47680i
$958$	8.34283	+	4.25089i	0.269545	+	0.137340i
$959$	10.7428	−	7.80508i	0.346902	−	0.252039i
$960$	4.94475	+	9.70463i	0.159591	+	0.313215i
$961$	14.7775	+	10.7365i	0.476693	+	0.346337i
$962$	−1.03418	+	6.52957i	−0.0333434	+	0.210522i
$963$	−50.1996	−	69.0939i	−1.61766	−	2.22652i
$964$	12.6776	+	17.4493i	0.408319	+	0.562003i
$965$	0.0543506	−	0.343156i	0.00174961	−	0.0110466i
$966$	0.157468	+	0.114407i	0.00506643	+	0.00368098i
$967$	19.9112	+	39.0778i	0.640299	+	1.25666i	0.951889	+	0.306442i	$0.0991385\pi$
$967$	19.9112	+	39.0778i	0.640299	+	1.25666i	−0.311590	+	0.950217i	$0.600862\pi$
$968$	1.61878	−	1.17611i	0.0520295	−	0.0378016i
$969$	43.4882	+	22.1583i	1.39704	+	0.711828i
$970$	0.614524	−	0.614524i	0.0197312	−	0.0197312i
$971$	−3.34162	−	21.0981i	−0.107238	−	0.677071i	−0.981478	−	0.191577i	$-0.938640\pi$
$971$	−3.34162	−	21.0981i	−0.107238	−	0.677071i	0.874240	−	0.485494i	$-0.161360\pi$
$972$	−17.0232	+	33.4098i	−0.546018	+	1.07162i
$973$	−1.55382	+	0.791713i	−0.0498133	+	0.0253811i
$974$	1.58374	−	4.87425i	0.0507463	−	0.156181i
$975$			46.3061i			1.48298i
$976$	39.8652	+	12.9530i	1.27605	+	0.414615i
$977$	60.4418	+	9.57305i	1.93371	+	0.306269i	0.998815	−	0.0486673i	$-0.0154974\pi$
$977$	60.4418	+	9.57305i	1.93371	+	0.306269i	0.934891	+	0.354936i	$0.115497\pi$
$978$	3.34766	−	0.530218i	0.107046	−	0.0169545i
$979$	−4.31061	+	1.40060i	−0.137768	+	0.0447634i
$980$	−0.378960	−	1.16632i	−0.0121054	−	0.0372567i
$981$	27.3237	+	27.3237i	0.872378	+	0.872378i
$982$	6.85579	−	9.43618i	0.218777	−	0.301121i
$983$	−41.3356			−1.31840			−0.659200	−	0.751968i	$-0.729105\pi$
$983$	−41.3356			−1.31840			−0.659200	+	0.751968i	$0.729105\pi$
$984$	11.9130	−	13.9538i	0.379773	−	0.444830i
$985$	4.25041			0.135429
$986$	−3.84436	+	5.29131i	−0.122429	+	0.168510i
$987$	−23.2167	−	23.2167i	−0.738996	−	0.738996i
$988$	−12.9474	−	39.8479i	−0.411911	−	1.26773i
$989$	−1.82067	+	0.591572i	−0.0578940	+	0.0188109i
$990$	2.22009	−	0.351628i	0.0705591	−	0.0111755i
$991$	−5.21803	−	0.826455i	−0.165756	−	0.0262532i	0.0730047	−	0.997332i	$-0.476741\pi$
$991$	−5.21803	−	0.826455i	−0.165756	−	0.0262532i	−0.238761	+	0.971078i	$0.576741\pi$
$992$	10.4344	+	3.39033i	0.331291	+	0.107643i
$993$		−	10.5478i		−	0.334723i
$994$	−0.349629	+	1.07605i	−0.0110896	+	0.0341302i
$995$	5.68219	−	2.89522i	0.180137	−	0.0917846i
$996$	−10.5570	+	20.7194i	−0.334513	+	0.656518i
$997$	0.659591	+	4.16449i	0.0208894	+	0.131891i	0.995929	−	0.0901400i	$-0.0287315\pi$
$997$	0.659591	+	4.16449i	0.0208894	+	0.131891i	−0.975040	+	0.222031i	$0.928731\pi$
$998$	3.85551	−	3.85551i	0.122044	−	0.122044i
$999$	−21.5751	−	10.9930i	−0.682605	−	0.347805i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.u.a.8.9	✓	160
41.36	even	20	inner	287.2.u.a.36.9	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.u.a.8.9	✓	160	1.1	even	1	trivial
287.2.u.a.36.9	yes	160	41.36	even	20	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:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.u (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.158161 + 0.217690i) q^{2} +(1.91716 + 1.91716i) q^{3} +(0.595660 + 1.83325i) q^{4} +(-0.605064 + 0.196597i) q^{5} +(-0.720570 + 0.114127i) q^{6} +(-0.987688 - 0.156434i) q^{7} +(-1.00511 - 0.326581i) q^{8} +4.35104i q^{9} +O(q^{10})\)	\(q+(-0.158161 + 0.217690i) q^{2} +(1.91716 + 1.91716i) q^{3} +(0.595660 + 1.83325i) q^{4} +(-0.605064 + 0.196597i) q^{5} +(-0.720570 + 0.114127i) q^{6} +(-0.987688 - 0.156434i) q^{7} +(-1.00511 - 0.326581i) q^{8} +4.35104i q^{9} +(0.0529004 - 0.162811i) q^{10} +(2.68882 - 1.37002i) q^{11} +(-2.37267 + 4.65663i) q^{12} +(-0.581417 - 3.67092i) q^{13} +(0.190268 - 0.190268i) q^{14} +(-1.53692 - 0.783099i) q^{15} +(-2.88885 + 2.09887i) q^{16} +(1.39744 + 2.74264i) q^{17} +(-0.947180 - 0.688167i) q^{18} +(0.914872 - 5.77628i) q^{19} +(-0.720825 - 0.992131i) q^{20} +(-1.59365 - 2.19347i) q^{21} +(-0.127027 + 0.802014i) q^{22} +(0.215841 + 0.156818i) q^{23} +(-1.30086 - 2.55308i) q^{24} +(-3.71763 + 2.70102i) q^{25} +(0.891082 + 0.454029i) q^{26} +(-2.59017 + 2.59017i) q^{27} +(-0.301542 - 1.90386i) q^{28} +(3.58495 - 7.03586i) q^{29} +(0.413554 - 0.210716i) q^{30} +(-1.10272 + 3.39382i) q^{31} -3.07451i q^{32} +(7.78146 + 2.52835i) q^{33} +(-0.818068 - 0.129569i) q^{34} +(0.628370 - 0.0995240i) q^{35} +(-7.97656 + 2.59174i) q^{36} +(2.04273 + 6.28686i) q^{37} +(1.11274 + 1.11274i) q^{38} +(5.92309 - 8.15243i) q^{39} +0.672363 q^{40} +(2.45151 + 5.91524i) q^{41} +0.729552 q^{42} +(-4.21761 + 5.80504i) q^{43} +(4.11321 + 4.11321i) q^{44} +(-0.855403 - 2.63266i) q^{45} +(-0.0682756 + 0.0221841i) q^{46} +(11.9608 - 1.89441i) q^{47} +(-9.56229 - 1.51452i) q^{48} +(0.951057 + 0.309017i) q^{49} -1.23649i q^{50} +(-2.57896 + 7.93722i) q^{51} +(6.38340 - 3.25250i) q^{52} +(1.65831 - 3.25462i) q^{53} +(-0.154191 - 0.973521i) q^{54} +(-1.35756 + 1.35756i) q^{55} +(0.941650 + 0.479795i) q^{56} +(12.8280 - 9.32011i) q^{57} +(0.964639 + 1.89321i) q^{58} +(-1.86823 - 1.35735i) q^{59} +(0.520137 - 3.28402i) q^{60} +(-6.89983 - 9.49681i) q^{61} +(-0.564395 - 0.776824i) q^{62} +(0.680653 - 4.29747i) q^{63} +(-5.10841 - 3.71148i) q^{64} +(1.07349 + 2.10684i) q^{65} +(-1.78112 + 1.29406i) q^{66} +(-7.49995 - 3.82142i) q^{67} +(-4.19555 + 4.19555i) q^{68} +(0.113158 + 0.714450i) q^{69} +(-0.0777184 + 0.152531i) q^{70} +(-3.74649 + 1.90893i) q^{71} +(1.42097 - 4.37329i) q^{72} -5.65198i q^{73} +(-1.69167 - 0.549657i) q^{74} +(-12.3056 - 1.94902i) q^{75} +(11.1343 - 1.76350i) q^{76} +(-2.87003 + 0.932530i) q^{77} +(0.837903 + 2.57880i) q^{78} +(-4.66363 - 4.66363i) q^{79} +(1.33531 - 1.83789i) q^{80} +3.12156 q^{81} +(-1.67543 - 0.401892i) q^{82} +4.44944 q^{83} +(3.07191 - 4.22813i) q^{84} +(-1.38474 - 1.38474i) q^{85} +(-0.596639 - 1.83627i) q^{86} +(20.3618 - 6.61597i) q^{87} +(-3.14999 + 0.498909i) q^{88} +(-1.48345 - 0.234955i) q^{89} +(0.708397 + 0.230172i) q^{90} +3.71668i q^{91} +(-0.158919 + 0.489102i) q^{92} +(-8.62062 + 4.39242i) q^{93} +(-1.47935 + 2.90338i) q^{94} +(0.582044 + 3.67488i) q^{95} +(5.89435 - 5.89435i) q^{96} +(4.52332 + 2.30475i) q^{97} +(-0.217690 + 0.158161i) q^{98} +(5.96102 + 11.6992i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 4 q^{3} + 36 q^{4} - 28 q^{6}+O(q^{10}) \) 160 * q - 4 * q^3 + 36 * q^4 - 28 * q^6	\( 160 q - 4 q^{3} + 36 q^{4} - 28 q^{6} - 48 q^{10} + 8 q^{11} - 16 q^{12} - 16 q^{13} - 32 q^{15} - 28 q^{16} - 20 q^{17} + 12 q^{18} - 40 q^{19} - 4 q^{22} - 36 q^{23} - 108 q^{24} + 40 q^{25} + 20 q^{26} + 20 q^{27} + 12 q^{29} - 4 q^{30} + 20 q^{31} - 32 q^{34} - 4 q^{35} + 140 q^{36} - 44 q^{38} + 80 q^{39} - 64 q^{40} + 4 q^{41} - 72 q^{42} - 8 q^{44} + 8 q^{45} + 40 q^{46} - 56 q^{47} + 120 q^{48} + 24 q^{51} + 16 q^{52} + 12 q^{53} - 52 q^{54} - 72 q^{55} + 48 q^{57} + 36 q^{58} - 48 q^{59} - 52 q^{60} + 8 q^{63} - 96 q^{64} - 96 q^{65} + 24 q^{66} + 20 q^{67} - 80 q^{68} - 68 q^{69} + 8 q^{70} + 60 q^{71} + 100 q^{72} - 40 q^{74} - 120 q^{75} + 4 q^{76} - 12 q^{78} + 12 q^{79} + 200 q^{80} - 56 q^{81} - 68 q^{82} - 40 q^{83} + 132 q^{85} + 80 q^{86} - 16 q^{88} + 8 q^{89} + 140 q^{92} + 64 q^{93} + 128 q^{94} - 68 q^{96} + 4 q^{98} + 96 q^{99}+O(q^{100}) \) 160 * q - 4 * q^3 + 36 * q^4 - 28 * q^6 - 48 * q^10 + 8 * q^11 - 16 * q^12 - 16 * q^13 - 32 * q^15 - 28 * q^16 - 20 * q^17 + 12 * q^18 - 40 * q^19 - 4 * q^22 - 36 * q^23 - 108 * q^24 + 40 * q^25 + 20 * q^26 + 20 * q^27 + 12 * q^29 - 4 * q^30 + 20 * q^31 - 32 * q^34 - 4 * q^35 + 140 * q^36 - 44 * q^38 + 80 * q^39 - 64 * q^40 + 4 * q^41 - 72 * q^42 - 8 * q^44 + 8 * q^45 + 40 * q^46 - 56 * q^47 + 120 * q^48 + 24 * q^51 + 16 * q^52 + 12 * q^53 - 52 * q^54 - 72 * q^55 + 48 * q^57 + 36 * q^58 - 48 * q^59 - 52 * q^60 + 8 * q^63 - 96 * q^64 - 96 * q^65 + 24 * q^66 + 20 * q^67 - 80 * q^68 - 68 * q^69 + 8 * q^70 + 60 * q^71 + 100 * q^72 - 40 * q^74 - 120 * q^75 + 4 * q^76 - 12 * q^78 + 12 * q^79 + 200 * q^80 - 56 * q^81 - 68 * q^82 - 40 * q^83 + 132 * q^85 + 80 * q^86 - 16 * q^88 + 8 * q^89 + 140 * q^92 + 64 * q^93 + 128 * q^94 - 68 * q^96 + 4 * q^98 + 96 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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