LMFDB - Embedded newform 483.2.q.f.400.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(64,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("483.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.q (of order $11$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$8$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			400.4
Character	$\chi$	$=$	483.400
Dual form			483.2.q.f.64.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.545660 + 0.160220i) q^{2} +(-0.654861 - 0.755750i) q^{3} +(-1.41043 + 0.906430i) q^{4} +(-0.339288 - 2.35980i) q^{5} +(0.478418 + 0.307461i) q^{6} +(-0.415415 + 0.909632i) q^{7} +(1.36922 - 1.58017i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})$	\(q+(-0.545660 + 0.160220i) q^{2} +(-0.654861 - 0.755750i) q^{3} +(-1.41043 + 0.906430i) q^{4} +(-0.339288 - 2.35980i) q^{5} +(0.478418 + 0.307461i) q^{6} +(-0.415415 + 0.909632i) q^{7} +(1.36922 - 1.58017i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(0.563223 + 1.23329i) q^{10} +(-4.74934 - 1.39453i) q^{11} +(1.60867 + 0.472348i) q^{12} +(2.17141 + 4.75473i) q^{13} +(0.0809340 - 0.562908i) q^{14} +(-1.56123 + 1.80175i) q^{15} +(0.899001 - 1.96854i) q^{16} +(2.04310 + 1.31302i) q^{17} +(-0.0809340 - 0.562908i) q^{18} +(-0.689053 + 0.442827i) q^{19} +(2.61753 + 3.02079i) q^{20} +(0.959493 - 0.281733i) q^{21} +2.81496 q^{22} +(2.01324 + 4.35280i) q^{23} -2.09086 q^{24} +(-0.656061 + 0.192637i) q^{25} +(-1.94666 - 2.24656i) q^{26} +(0.841254 - 0.540641i) q^{27} +(-0.238603 - 1.65952i) q^{28} +(1.50603 + 0.967864i) q^{29} +(0.563223 - 1.23329i) q^{30} +(-6.14851 + 7.09576i) q^{31} +(-0.770270 + 5.35735i) q^{32} +(2.05624 + 4.50254i) q^{33} +(-1.32521 - 0.389118i) q^{34} +(2.28749 + 0.671668i) q^{35} +(-0.696478 - 1.52507i) q^{36} +(-1.31701 + 9.16000i) q^{37} +(0.305039 - 0.352034i) q^{38} +(2.17141 - 4.75473i) q^{39} +(-4.19343 - 2.69496i) q^{40} +(1.17064 + 8.14197i) q^{41} +(-0.478418 + 0.307461i) q^{42} +(-1.32052 - 1.52396i) q^{43} +(7.96267 - 2.33805i) q^{44} +2.38406 q^{45} +(-1.79595 - 2.05259i) q^{46} -1.45235 q^{47} +(-2.07644 + 0.609698i) q^{48} +(-0.654861 - 0.755750i) q^{49} +(0.327122 - 0.210229i) q^{50} +(-0.345632 - 2.40392i) q^{51} +(-7.37246 - 4.73800i) q^{52} +(1.66340 - 3.64233i) q^{53} +(-0.372417 + 0.429792i) q^{54} +(-1.67942 + 11.6806i) q^{55} +(0.868575 + 1.90191i) q^{56} +(0.785900 + 0.230761i) q^{57} +(-0.976850 - 0.286829i) q^{58} +(-3.61224 - 7.90970i) q^{59} +(0.568844 - 3.95640i) q^{60} +(-2.09391 + 2.41650i) q^{61} +(2.21811 - 4.85699i) q^{62} +(-0.841254 - 0.540641i) q^{63} +(0.177918 + 1.23744i) q^{64} +(10.4835 - 6.73732i) q^{65} +(-1.84341 - 2.12741i) q^{66} +(9.40036 - 2.76019i) q^{67} -4.07182 q^{68} +(1.97123 - 4.37198i) q^{69} -1.35581 q^{70} +(2.93278 - 0.861143i) q^{71} +(1.36922 + 1.58017i) q^{72} +(-10.1096 + 6.49705i) q^{73} +(-0.748979 - 5.20926i) q^{74} +(0.575214 + 0.369668i) q^{75} +(0.570471 - 1.24916i) q^{76} +(3.24146 - 3.74084i) q^{77} +(-0.423050 + 2.94237i) q^{78} +(-0.292683 - 0.640887i) q^{79} +(-4.95037 - 1.45356i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(-1.94328 - 4.25519i) q^{82} +(0.992741 - 6.90467i) q^{83} +(-1.09793 + 1.26708i) q^{84} +(2.40527 - 5.26680i) q^{85} +(0.964727 + 0.619993i) q^{86} +(-0.254774 - 1.77199i) q^{87} +(-8.70650 + 5.59533i) q^{88} +(2.45113 + 2.82876i) q^{89} +(-1.30089 + 0.381975i) q^{90} -5.22710 q^{91} +(-6.78505 - 4.31446i) q^{92} +9.38904 q^{93} +(0.792489 - 0.232696i) q^{94} +(1.27877 + 1.47578i) q^{95} +(4.55323 - 2.92619i) q^{96} +(-1.89424 - 13.1747i) q^{97} +(0.478418 + 0.307461i) q^{98} +(2.05624 - 4.50254i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + q^{2} - 8 q^{3} - 9 q^{4} + 13 q^{5} + q^{6} + 8 q^{7} - 25 q^{8} - 8 q^{9}+O(q^{10}) $ 80 * q + q^2 - 8 * q^3 - 9 * q^4 + 13 * q^5 + q^6 + 8 * q^7 - 25 * q^8 - 8 * q^9	\( 80 q + q^{2} - 8 q^{3} - 9 q^{4} + 13 q^{5} + q^{6} + 8 q^{7} - 25 q^{8} - 8 q^{9} + 4 q^{10} + q^{11} - 9 q^{12} - 26 q^{13} - q^{14} + 2 q^{15} - 3 q^{16} - 23 q^{17} + q^{18} + 10 q^{19} + 63 q^{20} + 8 q^{21} - 9 q^{23} + 30 q^{24} - 29 q^{25} - 12 q^{26} - 8 q^{27} + 20 q^{28} + 13 q^{29} + 4 q^{30} - 27 q^{31} + 71 q^{32} + q^{33} - 45 q^{34} - 2 q^{35} - 9 q^{36} + 60 q^{37} - 2 q^{38} - 26 q^{39} + 7 q^{40} - 26 q^{41} - q^{42} + 5 q^{43} - 33 q^{44} - 20 q^{45} - 41 q^{46} + 34 q^{47} - 58 q^{48} - 8 q^{49} - 75 q^{50} - q^{51} + 108 q^{52} - 39 q^{53} - 10 q^{54} + 51 q^{55} + 3 q^{56} + 10 q^{57} + 47 q^{58} - 66 q^{59} + 19 q^{60} + 3 q^{61} + 103 q^{62} + 8 q^{63} - 25 q^{64} + 39 q^{65} - 33 q^{66} + 33 q^{67} - 88 q^{68} + 13 q^{69} + 18 q^{70} - 12 q^{71} - 25 q^{72} - 98 q^{73} + 123 q^{74} + 4 q^{75} - 41 q^{76} - 12 q^{77} + 10 q^{78} - 34 q^{79} + 163 q^{80} - 8 q^{81} + 48 q^{82} + 26 q^{83} + 9 q^{84} + 35 q^{85} + 4 q^{86} + 2 q^{87} + 178 q^{88} - 63 q^{89} + 4 q^{90} - 62 q^{91} - 39 q^{92} + 138 q^{93} - 28 q^{94} - 80 q^{95} - 17 q^{96} - 44 q^{97} + q^{98} + q^{99}+O(q^{100}) \) 80 * q + q^2 - 8 * q^3 - 9 * q^4 + 13 * q^5 + q^6 + 8 * q^7 - 25 * q^8 - 8 * q^9 + 4 * q^10 + q^11 - 9 * q^12 - 26 * q^13 - q^14 + 2 * q^15 - 3 * q^16 - 23 * q^17 + q^18 + 10 * q^19 + 63 * q^20 + 8 * q^21 - 9 * q^23 + 30 * q^24 - 29 * q^25 - 12 * q^26 - 8 * q^27 + 20 * q^28 + 13 * q^29 + 4 * q^30 - 27 * q^31 + 71 * q^32 + q^33 - 45 * q^34 - 2 * q^35 - 9 * q^36 + 60 * q^37 - 2 * q^38 - 26 * q^39 + 7 * q^40 - 26 * q^41 - q^42 + 5 * q^43 - 33 * q^44 - 20 * q^45 - 41 * q^46 + 34 * q^47 - 58 * q^48 - 8 * q^49 - 75 * q^50 - q^51 + 108 * q^52 - 39 * q^53 - 10 * q^54 + 51 * q^55 + 3 * q^56 + 10 * q^57 + 47 * q^58 - 66 * q^59 + 19 * q^60 + 3 * q^61 + 103 * q^62 + 8 * q^63 - 25 * q^64 + 39 * q^65 - 33 * q^66 + 33 * q^67 - 88 * q^68 + 13 * q^69 + 18 * q^70 - 12 * q^71 - 25 * q^72 - 98 * q^73 + 123 * q^74 + 4 * q^75 - 41 * q^76 - 12 * q^77 + 10 * q^78 - 34 * q^79 + 163 * q^80 - 8 * q^81 + 48 * q^82 + 26 * q^83 + 9 * q^84 + 35 * q^85 + 4 * q^86 + 2 * q^87 + 178 * q^88 - 63 * q^89 + 4 * q^90 - 62 * q^91 - 39 * q^92 + 138 * q^93 - 28 * q^94 - 80 * q^95 - 17 * q^96 - 44 * q^97 + q^98 + q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{11}\right)$

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 $

$2$	−0.545660	+	0.160220i	−0.385840	+	0.113293i	−0.468899	−	0.883252i	$-0.655349\pi$
$2$	−0.545660	+	0.160220i	−0.385840	+	0.113293i	0.0830589	+	0.996545i	$0.473531\pi$
$3$	−0.654861	−	0.755750i	−0.378084	−	0.436332i
$3$	−0.654861	−	0.755750i	−0.378084	−	0.436332i
$4$	−1.41043	+	0.906430i	−0.705216	+	0.453215i
$5$	−0.339288	−	2.35980i	−0.151734	−	1.05533i	−0.913312	−	0.407260i	$-0.866484\pi$
$5$	−0.339288	−	2.35980i	−0.151734	−	1.05533i	0.761578	−	0.648073i	$-0.224425\pi$
$6$	0.478418	+	0.307461i	0.195313	+	0.125520i
$7$	−0.415415	+	0.909632i	−0.157012	+	0.343809i
$7$	−0.415415	+	0.909632i	−0.157012	+	0.343809i
$8$	1.36922	−	1.58017i	0.484093	−	0.558673i
$9$	−0.142315	+	0.989821i	−0.0474383	+	0.329940i
$10$	0.563223	+	1.23329i	0.178107	+	0.390000i
$11$	−4.74934	−	1.39453i	−1.43198	−	0.420467i	−0.528440	−	0.848971i	$-0.677223\pi$
$11$	−4.74934	−	1.39453i	−1.43198	−	0.420467i	−0.903540	+	0.428503i	$0.859041\pi$
$12$	1.60867	+	0.472348i	0.464383	+	0.136355i
$13$	2.17141	+	4.75473i	0.602242	+	1.31873i	0.927756	+	0.373188i	$0.121735\pi$
$13$	2.17141	+	4.75473i	0.602242	+	1.31873i	−0.325514	+	0.945537i	$0.605537\pi$
$14$	0.0809340	−	0.562908i	0.0216305	−	0.150444i
$15$	−1.56123	+	1.80175i	−0.403108	+	0.465211i
$16$	0.899001	−	1.96854i	0.224750	−	0.492134i
$17$	2.04310	+	1.31302i	0.495525	+	0.318455i	0.764424	−	0.644714i	$-0.223023\pi$
$17$	2.04310	+	1.31302i	0.495525	+	0.318455i	−0.268899	+	0.963168i	$0.586660\pi$
$18$	−0.0809340	−	0.562908i	−0.0190763	−	0.132679i
$19$	−0.689053	+	0.442827i	−0.158080	+	0.101592i	−0.617289	−	0.786736i	$-0.711769\pi$
$19$	−0.689053	+	0.442827i	−0.158080	+	0.101592i	0.459209	+	0.888328i	$0.348133\pi$
$20$	2.61753	+	3.02079i	0.585298	+	0.675470i
$21$	0.959493	−	0.281733i	0.209379	−	0.0614791i
$22$	2.81496			0.600152
$23$	2.01324	+	4.35280i	0.419790	+	0.907621i
$23$	2.01324	+	4.35280i	0.419790	+	0.907621i
$24$	−2.09086			−0.426795
$25$	−0.656061	+	0.192637i	−0.131212	+	0.0385274i
$26$	−1.94666	−	2.24656i	−0.381771	−	0.440588i
$27$	0.841254	−	0.540641i	0.161899	−	0.104046i
$28$	−0.238603	−	1.65952i	−0.0450917	−	0.313620i
$29$	1.50603	+	0.967864i	0.279662	+	0.179728i	0.672951	−	0.739687i	$-0.265026\pi$
$29$	1.50603	+	0.967864i	0.279662	+	0.179728i	−0.393289	+	0.919415i	$0.628663\pi$
$30$	0.563223	−	1.23329i	0.102830	−	0.225166i
$31$	−6.14851	+	7.09576i	−1.10431	+	1.27444i	−0.145815	+	0.989312i	$0.546580\pi$
$31$	−6.14851	+	7.09576i	−1.10431	+	1.27444i	−0.958491	+	0.285124i	$0.907965\pi$
$32$	−0.770270	+	5.35735i	−0.136166	+	0.947054i
$33$	2.05624	+	4.50254i	0.357945	+	0.783791i
$34$	−1.32521	−	0.389118i	−0.227272	−	0.0667331i
$35$	2.28749	+	0.671668i	0.386657	+	0.113533i
$36$	−0.696478	−	1.52507i	−0.116080	−	0.254179i
$37$	−1.31701	+	9.16000i	−0.216515	+	1.50589i	0.534251	+	0.845326i	$0.320594\pi$
$37$	−1.31701	+	9.16000i	−0.216515	+	1.50589i	−0.750766	+	0.660569i	$0.770315\pi$
$38$	0.305039	−	0.352034i	0.0494839	−	0.0571074i
$39$	2.17141	−	4.75473i	0.347704	−	0.761367i
$40$	−4.19343	−	2.69496i	−0.663040	−	0.426110i
$41$	1.17064	+	8.14197i	0.182823	+	1.27156i	0.850048	+	0.526706i	$0.176573\pi$
$41$	1.17064	+	8.14197i	0.182823	+	1.27156i	−0.667224	+	0.744857i	$0.732518\pi$
$42$	−0.478418	+	0.307461i	−0.0738215	+	0.0474422i
$43$	−1.32052	−	1.52396i	−0.201378	−	0.232402i	0.646074	−	0.763275i	$-0.276410\pi$
$43$	−1.32052	−	1.52396i	−0.201378	−	0.232402i	−0.847452	+	0.530872i	$0.821864\pi$
$44$	7.96267	−	2.33805i	1.20042	−	0.352475i
$45$	2.38406			0.355395
$46$	−1.79595	−	2.05259i	−0.264799	−	0.302637i
$47$	−1.45235			−0.211847			−0.105923	−	0.994374i	$-0.533780\pi$
$47$	−1.45235			−0.211847			−0.105923	+	0.994374i	$0.533780\pi$
$48$	−2.07644	+	0.609698i	−0.299709	+	0.0880024i
$49$	−0.654861	−	0.755750i	−0.0935515	−	0.107964i
$50$	0.327122	−	0.210229i	0.0462621	−	0.0297308i
$51$	−0.345632	−	2.40392i	−0.0483981	−	0.336616i
$52$	−7.37246	−	4.73800i	−1.02238	−	0.657042i
$53$	1.66340	−	3.64233i	0.228485	−	0.500313i	−0.760316	−	0.649554i	$-0.774956\pi$
$53$	1.66340	−	3.64233i	0.228485	−	0.500313i	0.988801	+	0.149241i	$0.0476830\pi$
$54$	−0.372417	+	0.429792i	−0.0506795	+	0.0584873i
$55$	−1.67942	+	11.6806i	−0.226453	+	1.57502i
$56$	0.868575	+	1.90191i	0.116068	+	0.254154i
$57$	0.785900	+	0.230761i	0.104095	+	0.0305651i
$58$	−0.976850	−	0.286829i	−0.128267	−	0.0376625i
$59$	−3.61224	−	7.90970i	−0.470273	−	1.02976i	−0.985024	−	0.172415i	$-0.944843\pi$
$59$	−3.61224	−	7.90970i	−0.470273	−	1.02976i	0.514751	−	0.857340i	$-0.327884\pi$
$60$	0.568844	−	3.95640i	0.0734375	−	0.510769i
$61$	−2.09391	+	2.41650i	−0.268097	+	0.309401i	−0.873795	−	0.486294i	$-0.838349\pi$
$61$	−2.09391	+	2.41650i	−0.268097	+	0.309401i	0.605698	+	0.795695i	$0.292894\pi$
$62$	2.21811	−	4.85699i	0.281701	−	0.616839i
$63$	−0.841254	−	0.540641i	−0.105988	−	0.0681143i
$64$	0.177918	+	1.23744i	0.0222397	+	0.154681i
$65$	10.4835	−	6.73732i	1.30031	−	0.835661i
$66$	−1.84341	−	2.12741i	−0.226908	−	0.261865i
$67$	9.40036	−	2.76019i	1.14844	−	0.337211i	0.348507	−	0.937306i	$-0.386689\pi$
$67$	9.40036	−	2.76019i	1.14844	−	0.337211i	0.799929	+	0.600095i	$0.204870\pi$
$68$	−4.07182			−0.493781
$69$	1.97123	−	4.37198i	0.237308	−	0.526325i
$70$	−1.35581			−0.162050
$71$	2.93278	−	0.861143i	0.348057	−	0.102199i	−0.103031	−	0.994678i	$-0.532854\pi$
$71$	2.93278	−	0.861143i	0.348057	−	0.102199i	0.451088	+	0.892479i	$0.351036\pi$
$72$	1.36922	+	1.58017i	0.161364	+	0.186224i
$73$	−10.1096	+	6.49705i	−1.18324	+	0.760422i	−0.975979	−	0.217864i	$-0.930091\pi$
$73$	−10.1096	+	6.49705i	−1.18324	+	0.760422i	−0.207261	+	0.978286i	$0.566455\pi$
$74$	−0.748979	−	5.20926i	−0.0870670	−	0.605564i
$75$	0.575214	+	0.369668i	0.0664200	+	0.0426855i
$76$	0.570471	−	1.24916i	0.0654375	−	0.143288i
$77$	3.24146	−	3.74084i	0.369399	−	0.426309i
$78$	−0.423050	+	2.94237i	−0.0479009	+	0.333158i
$79$	−0.292683	−	0.640887i	−0.0329294	−	0.0721054i	0.892453	−	0.451141i	$-0.148983\pi$
$79$	−0.292683	−	0.640887i	−0.0329294	−	0.0721054i	−0.925382	+	0.379036i	$0.876256\pi$
$80$	−4.95037	−	1.45356i	−0.553468	−	0.162513i
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$	−1.94328	−	4.25519i	−0.214600	−	0.469907i
$83$	0.992741	−	6.90467i	0.108967	−	0.757886i	−0.859928	−	0.510415i	$-0.829492\pi$
$83$	0.992741	−	6.90467i	0.108967	−	0.757886i	0.968896	−	0.247470i	$-0.0795992\pi$
$84$	−1.09793	+	1.26708i	−0.119794	+	0.138250i
$85$	2.40527	−	5.26680i	0.260888	−	0.571265i
$86$	0.964727	+	0.619993i	0.104029	+	0.0668555i
$87$	−0.254774	−	1.77199i	−0.0273147	−	0.189978i
$88$	−8.70650	+	5.59533i	−0.928116	+	0.596464i
$89$	2.45113	+	2.82876i	0.259820	+	0.299848i	0.870639	−	0.491922i	$-0.163705\pi$
$89$	2.45113	+	2.82876i	0.259820	+	0.299848i	−0.610820	+	0.791770i	$0.709160\pi$
$90$	−1.30089	+	0.381975i	−0.137126	+	0.0402637i
$91$	−5.22710			−0.547948
$92$	−6.78505	−	4.31446i	−0.707390	−	0.449814i
$93$	9.38904			0.973598
$94$	0.792489	−	0.232696i	0.0817390	−	0.0240007i
$95$	1.27877	+	1.47578i	0.131199	+	0.151412i
$96$	4.55323	−	2.92619i	0.464713	−	0.298653i
$97$	−1.89424	−	13.1747i	−0.192331	−	1.33769i	−0.825818	−	0.563937i	$-0.809286\pi$
$97$	−1.89424	−	13.1747i	−0.192331	−	1.33769i	0.633487	−	0.773753i	$-0.281623\pi$
$98$	0.478418	+	0.307461i	0.0483275	+	0.0310582i
$99$	2.05624	−	4.50254i	0.206660	−	0.452522i
$100$	0.750718	−	0.866375i	0.0750718	−	0.0866375i
$101$	−1.40712	+	9.78670i	−0.140013	+	0.973813i	0.791776	+	0.610812i	$0.209157\pi$
$101$	−1.40712	+	9.78670i	−0.140013	+	0.973813i	−0.931789	+	0.363001i	$0.881752\pi$
$102$	0.573755	+	1.25635i	0.0568102	+	0.124397i
$103$	1.45897	+	0.428393i	0.143757	+	0.0422108i	0.352819	−	0.935691i	$-0.385223\pi$
$103$	1.45897	+	0.428393i	0.143757	+	0.0422108i	−0.209062	+	0.977902i	$0.567041\pi$
$104$	10.4864	+	3.07909i	1.02828	+	0.301930i
$105$	−0.990376	−	2.16862i	−0.0966508	−	0.211636i
$106$	−0.324074	+	2.25399i	−0.0314769	+	0.218926i
$107$	−9.09638	+	10.4978i	−0.879380	+	1.01486i	0.120375	+	0.992728i	$0.461590\pi$
$107$	−9.09638	+	10.4978i	−0.879380	+	1.01486i	−0.999755	+	0.0221300i	$0.992955\pi$
$108$	−0.696478	+	1.52507i	−0.0670186	+	0.146750i
$109$	−2.44573	−	1.57178i	−0.234259	−	0.150549i	0.418245	−	0.908334i	$-0.362645\pi$
$109$	−2.44573	−	1.57178i	−0.234259	−	0.150549i	−0.652504	+	0.757785i	$0.726282\pi$
$110$	−0.955081	−	6.64274i	−0.0910634	−	0.633360i
$111$	7.78512	−	5.00320i	0.738931	−	0.474882i
$112$	1.41719	+	1.63552i	0.133911	+	0.154542i
$113$	7.81444	−	2.29453i	0.735121	−	0.215851i	0.107319	−	0.994225i	$-0.465773\pi$
$113$	7.81444	−	2.29453i	0.735121	−	0.215851i	0.627801	+	0.778374i	$0.283955\pi$
$114$	−0.465807			−0.0436269
$115$	9.58865	−	6.22770i	0.894146	−	0.580736i
$116$	−3.00145			−0.278678
$117$	−5.01536	+	1.47264i	−0.463670	+	0.136146i
$118$	3.23835	+	3.73726i	0.298114	+	0.344042i
$119$	−2.04310	+	1.31302i	−0.187291	+	0.120365i
$120$	0.709403	+	4.93401i	0.0647594	+	0.450411i
$121$	11.3577	+	7.29918i	1.03252	+	0.663562i
$122$	0.755390	−	1.65407i	0.0683898	−	0.149753i
$123$	5.38669	−	6.21657i	0.485701	−	0.560529i
$124$	2.24025	−	15.5813i	0.201180	−	1.39924i
$125$	−4.27470	−	9.36029i	−0.382341	−	0.837210i
$126$	0.545660	+	0.160220i	0.0486113	+	0.0142736i
$127$	−16.4138	−	4.81953i	−1.45649	−	0.427664i	−0.544807	−	0.838561i	$-0.683397\pi$
$127$	−16.4138	−	4.81953i	−1.45649	−	0.427664i	−0.911682	+	0.410898i	$0.865215\pi$
$128$	−4.79216	−	10.4934i	−0.423571	−	0.927492i
$129$	−0.286977	+	1.99597i	−0.0252669	+	0.175735i
$130$	−4.64096	+	5.35595i	−0.407039	+	0.469748i
$131$	−6.44759	+	14.1182i	−0.563328	+	1.23352i	0.386946	+	0.922102i	$0.373530\pi$
$131$	−6.44759	+	14.1182i	−0.563328	+	1.23352i	−0.950274	+	0.311414i	$0.899197\pi$
$132$	−6.98142	−	4.48669i	−0.607655	−	0.390516i
$133$	−0.116567	−	0.810742i	−0.0101076	−	0.0703002i
$134$	−4.68716	+	3.01226i	−0.404909	+	0.260219i
$135$	−1.56123	−	1.80175i	−0.134369	−	0.155070i
$136$	4.87226	−	1.43062i	0.417793	−	0.122675i
$137$	−15.9687			−1.36430			−0.682151	−	0.731211i	$-0.738955\pi$
$137$	−15.9687			−1.36430			−0.682151	+	0.731211i	$0.738955\pi$
$138$	−0.375141	+	2.70145i	−0.0319342	+	0.229963i
$139$	9.13217			0.774581			0.387290	−	0.921958i	$-0.373411\pi$
$139$	9.13217			0.774581			0.387290	+	0.921958i	$0.373411\pi$
$140$	−3.83517	+	1.12611i	−0.324131	+	0.0951735i
$141$	0.951086	+	1.09761i	0.0800959	+	0.0924356i
$142$	−1.46233	+	0.939783i	−0.122716	+	0.0788649i
$143$	−3.68216	−	25.6100i	−0.307917	−	2.14161i
$144$	1.82056	+	1.17000i	0.151713	+	0.0975002i
$145$	1.77299	−	3.88230i	0.147239	−	0.322408i
$146$	4.47545	−	5.16495i	0.370391	−	0.427454i
$147$	−0.142315	+	0.989821i	−0.0117379	+	0.0816391i
$148$	−6.44535	−	14.1133i	−0.529804	−	1.16011i
$149$	7.27805	+	2.13703i	0.596241	+	0.175072i	0.565909	−	0.824468i	$-0.308525\pi$
$149$	7.27805	+	2.13703i	0.596241	+	0.175072i	0.0303321	+	0.999540i	$0.490343\pi$
$150$	−0.373100	−	0.109552i	−0.0304635	−	0.00894488i
$151$	2.72358	+	5.96381i	0.221642	+	0.485328i	0.987488	−	0.157696i	$-0.0504066\pi$
$151$	2.72358	+	5.96381i	0.221642	+	0.485328i	−0.765846	+	0.643024i	$0.777679\pi$
$152$	−0.243726	+	1.69515i	−0.0197688	+	0.137495i
$153$	−1.59042	+	1.83544i	−0.128578	+	0.148387i
$154$	−1.16938	+	2.56058i	−0.0942311	+	0.206337i
$155$	18.8307	+	12.1017i	1.51252	+	0.972035i
$156$	1.24720	+	8.67446i	0.0998559	+	0.694513i
$157$	−7.56302	+	4.86046i	−0.603595	+	0.387907i	−0.806450	−	0.591302i	$-0.798614\pi$
$157$	−7.56302	+	4.86046i	−0.603595	+	0.387907i	0.202855	+	0.979209i	$0.434978\pi$
$158$	0.262389	+	0.302813i	0.0208745	+	0.0240905i
$159$	−3.84198	+	1.12811i	−0.304689	+	0.0894648i
$160$	12.9036			1.02012
$161$	−4.79578	+	0.0230938i	−0.377960	+	0.00182005i
$162$	0.568697			0.0446810
$163$	9.22177	−	2.70776i	0.722305	−	0.212088i	0.100139	−	0.994973i	$-0.468071\pi$
$163$	9.22177	−	2.70776i	0.722305	−	0.212088i	0.622166	+	0.782886i	$0.286253\pi$
$164$	−9.03124	−	10.4226i	−0.705221	−	0.813868i
$165$	9.92742	−	6.37997i	0.772849	−	0.496680i
$166$	0.564568	+	3.92666i	0.0438190	+	0.304768i
$167$	5.20345	+	3.34405i	0.402655	+	0.258771i	0.726258	−	0.687422i	$-0.241258\pi$
$167$	5.20345	+	3.34405i	0.402655	+	0.258771i	−0.323603	+	0.946193i	$0.604894\pi$
$168$	0.868575	−	1.90191i	0.0670120	−	0.146736i
$169$	−9.37926	+	10.8242i	−0.721481	+	0.832634i
$170$	−0.468610	+	3.25926i	−0.0359408	+	0.249974i
$171$	−0.340258	−	0.745060i	−0.0260202	−	0.0569762i
$172$	3.24388	+	0.952488i	0.247343	+	0.0726265i
$173$	−9.09274	−	2.66987i	−0.691308	−	0.202986i	−0.0828378	−	0.996563i	$-0.526398\pi$
$173$	−9.09274	−	2.66987i	−0.691308	−	0.202986i	−0.608470	+	0.793577i	$0.708217\pi$
$174$	0.422930	+	0.926087i	0.0320622	+	0.0702065i
$175$	0.0973090	−	0.676799i	0.00735587	−	0.0511612i
$176$	−7.01485	+	8.09557i	−0.528764	+	0.610227i
$177$	−3.61224	+	7.90970i	−0.271512	+	0.594529i
$178$	−1.79071	−	1.15082i	−0.134219	−	0.0862576i
$179$	−2.60165	−	18.0949i	−0.194456	−	1.35247i	−0.820035	−	0.572313i	$-0.806046\pi$
$179$	−2.60165	−	18.0949i	−0.194456	−	1.35247i	0.625579	−	0.780161i	$-0.284863\pi$
$180$	−3.36256	+	2.16099i	−0.250630	+	0.161070i
$181$	14.8554	+	17.1440i	1.10419	+	1.27430i	0.958537	+	0.284967i	$0.0919828\pi$
$181$	14.8554	+	17.1440i	1.10419	+	1.27430i	0.145653	+	0.989336i	$0.453472\pi$
$182$	2.85222	−	0.837487i	0.211421	−	0.0620787i
$183$	3.19749			0.236365
$184$	9.63473	+	2.77869i	0.710282	+	0.204848i
$185$	22.0626			1.62207
$186$	−5.12323	+	1.50431i	−0.375653	+	0.110302i
$187$	−7.87234	−	9.08517i	−0.575683	−	0.664373i
$188$	2.04844	−	1.31645i	0.149398	−	0.0960121i
$189$	0.142315	+	0.989821i	0.0103519	+	0.0719989i
$190$	−0.934224	−	0.600389i	−0.0677757	−	0.0435568i
$191$	−3.34329	+	7.32078i	−0.241912	+	0.529713i	−0.991175	−	0.132559i	$-0.957681\pi$
$191$	−3.34329	+	7.32078i	−0.241912	+	0.529713i	0.749263	+	0.662272i	$0.230408\pi$
$192$	0.818687	−	0.944815i	0.0590836	−	0.0681862i
$193$	−2.39554	+	16.6613i	−0.172434	+	1.19931i	0.701286	+	0.712880i	$0.252610\pi$
$193$	−2.39554	+	16.6613i	−0.172434	+	1.19931i	−0.873721	+	0.486428i	$0.838300\pi$
$194$	3.14447	+	6.88543i	0.225760	+	0.494345i
$195$	−11.9569	−	3.51087i	−0.856254	−	0.251419i
$196$	1.60867	+	0.472348i	0.114905	+	0.0337392i
$197$	−0.0164543	−	0.0360298i	−0.00117232	−	0.00256702i	0.909045	−	0.416698i	$-0.136813\pi$
$197$	−0.0164543	−	0.0360298i	−0.00117232	−	0.00256702i	−0.910217	+	0.414131i	$0.864086\pi$
$198$	−0.400611	+	2.78631i	−0.0284702	+	0.198014i
$199$	−7.21043	+	8.32128i	−0.511134	+	0.589880i	−0.951389	−	0.307993i	$-0.900343\pi$
$199$	−7.21043	+	8.32128i	−0.511134	+	0.589880i	0.440255	+	0.897873i	$0.354888\pi$
$200$	−0.593895	+	1.30045i	−0.0419947	+	0.0919557i
$201$	−8.24194	−	5.29677i	−0.581342	−	0.373605i
$202$	−0.800222	−	5.56566i	−0.0563034	−	0.391599i
$203$	−1.50603	+	0.967864i	−0.105702	+	0.0679308i
$204$	2.66648	+	3.07728i	0.186691	+	0.215452i
$205$	18.8162	−	5.52494i	1.31418	−	0.385879i
$206$	−0.864741			−0.0602493
$207$	−4.59501	+	1.37328i	−0.319375	+	0.0954499i
$208$	11.3120			0.784344
$209$	3.89009	−	1.14223i	0.269083	−	0.0790099i
$210$	0.887866	+	1.02465i	0.0612686	+	0.0707077i
$211$	19.3934	−	12.4634i	1.33510	−	0.858015i	0.338543	−	0.940951i	$-0.390066\pi$
$211$	19.3934	−	12.4634i	1.33510	−	0.858015i	0.996555	+	0.0829357i	$0.0264296\pi$
$212$	0.955409	+	6.64502i	0.0656178	+	0.456382i
$213$	−2.57137	−	1.65252i	−0.176188	−	0.113229i
$214$	3.28157	−	7.18565i	0.224324	−	0.491201i
$215$	−3.14821	+	3.63323i	−0.214706	+	0.247784i
$216$	0.297561	−	2.06958i	0.0202464	−	0.140817i
$217$	−3.90035	−	8.54057i	−0.264773	−	0.579772i
$218$	1.58637	+	0.465801i	0.107443	+	0.0315480i
$219$	11.5305	+	3.38567i	0.779161	+	0.228782i
$220$	−8.21896	−	17.9970i	−0.554122	−	1.21336i
$221$	−1.80665	+	12.5655i	−0.121528	+	0.845249i
$222$	−3.44642	+	3.97738i	−0.231309	+	0.266944i
$223$	−10.7330	+	23.5020i	−0.718735	+	1.57381i	0.0969342	+	0.995291i	$0.469096\pi$
$223$	−10.7330	+	23.5020i	−0.718735	+	1.57381i	−0.815669	+	0.578519i	$0.803631\pi$
$224$	−4.55323	−	2.92619i	−0.304226	−	0.195514i
$225$	−0.0973090	−	0.676799i	−0.00648726	−	0.0451199i
$226$	−3.89640	+	2.50406i	−0.259185	+	0.166568i
$227$	−15.0179	−	17.3315i	−0.996771	−	1.15034i	−0.988630	−	0.150368i	$-0.951954\pi$
$227$	−15.0179	−	17.3315i	−0.996771	−	1.15034i	−0.00814114	−	0.999967i	$-0.502591\pi$
$228$	−1.31763	+	0.386891i	−0.0872621	+	0.0256225i
$229$	−14.9561			−0.988327			−0.494164	−	0.869369i	$-0.664526\pi$
$229$	−14.9561			−0.988327			−0.494164	+	0.869369i	$0.664526\pi$
$230$	−4.23434	+	4.93451i	−0.279204	+	0.325372i
$231$	−4.94985			−0.325676
$232$	3.59147	−	1.05455i	0.235792	−	0.0692347i
$233$	12.5518	+	14.4856i	0.822299	+	0.948984i	0.999380	−	0.0352127i	$-0.0112109\pi$
$233$	12.5518	+	14.4856i	0.822299	+	0.948984i	−0.177081	+	0.984196i	$0.556665\pi$
$234$	2.50074	−	1.60713i	0.163478	−	0.105061i
$235$	0.492764	+	3.42725i	0.0321444	+	0.223569i
$236$	12.2644	+	7.88186i	0.798345	+	0.513065i
$237$	−0.292683	+	0.640887i	−0.0190118	+	0.0416301i
$238$	0.904467	−	1.04381i	0.0586279	−	0.0676602i
$239$	−2.64093	+	18.3681i	−0.170828	+	1.18813i	0.706313	+	0.707900i	$0.250357\pi$
$239$	−2.64093	+	18.3681i	−0.170828	+	1.18813i	−0.877140	+	0.480234i	$0.840552\pi$
$240$	2.14327	+	4.69312i	0.138348	+	0.302939i
$241$	21.4460	+	6.29710i	1.38146	+	0.405632i	0.886275	−	0.463159i	$-0.153284\pi$
$241$	21.4460	+	6.29710i	1.38146	+	0.405632i	0.495180	+	0.868790i	$0.335102\pi$
$242$	−7.36695	−	2.16313i	−0.473565	−	0.139051i
$243$	0.415415	+	0.909632i	0.0266489	+	0.0583529i
$244$	0.762929	−	5.30629i	0.0488415	−	0.339700i
$245$	−1.56123	+	1.80175i	−0.0997433	+	0.115110i
$246$	−1.94328	+	4.25519i	−0.123899	+	0.271301i
$247$	−3.60175	−	2.31470i	−0.229174	−	0.147281i
$248$	2.79381	+	19.4314i	0.177407	+	1.23389i
$249$	−5.86831	+	3.77133i	−0.371889	+	0.238998i
$250$	3.83224	+	4.42265i	0.242372	+	0.279713i
$251$	−28.2004	+	8.28037i	−1.77999	+	0.522652i	−0.995266	−	0.0971921i	$-0.969014\pi$
$251$	−28.2004	+	8.28037i	−1.77999	+	0.522652i	−0.784725	+	0.619844i	$0.787196\pi$
$252$	1.67658			0.105615
$253$	−3.49147	−	23.4805i	−0.219507	−	1.47620i
$254$	9.72854			0.610423
$255$	−5.55550	+	1.63124i	−0.347899	+	0.102152i
$256$	2.65877	+	3.06839i	0.166173	+	0.191774i
$257$	−4.68591	+	3.01145i	−0.292299	+	0.187849i	−0.678569	−	0.734537i	$-0.737400\pi$
$257$	−4.68591	+	3.01145i	−0.292299	+	0.187849i	0.386270	+	0.922386i	$0.373763\pi$
$258$	−0.163203	−	1.13510i	−0.0101606	−	0.0706683i
$259$	−7.78512	−	5.00320i	−0.483744	−	0.310883i
$260$	−8.67932	+	19.0051i	−0.538269	+	1.17864i
$261$	−1.17234	+	1.35296i	−0.0725662	+	0.0837458i
$262$	1.25616	−	8.73680i	0.0776060	−	0.539761i
$263$	0.418048	+	0.915398i	0.0257780	+	0.0564459i	0.922083	−	0.386992i	$-0.126486\pi$
$263$	0.418048	+	0.915398i	0.0257780	+	0.0564459i	−0.896305	+	0.443438i	$0.853759\pi$
$264$	9.93021	+	2.91577i	0.611162	+	0.179453i
$265$	−9.15953	−	2.68948i	−0.562666	−	0.165214i
$266$	0.193503	+	0.423713i	0.0118645	+	0.0259795i
$267$	0.532682	−	3.70488i	0.0325996	−	0.226735i
$268$	−10.7566	+	12.4138i	−0.657067	+	0.758295i
$269$	4.75213	−	10.4057i	0.289743	−	0.634448i	−0.707654	−	0.706559i	$-0.750246\pi$
$269$	4.75213	−	10.4057i	0.289743	−	0.634448i	0.997397	+	0.0721112i	$0.0229736\pi$
$270$	1.14058	+	0.733006i	0.0694134	+	0.0446093i
$271$	0.822432	+	5.72014i	0.0499592	+	0.347474i	0.999434	+	0.0336315i	$0.0107073\pi$
$271$	0.822432	+	5.72014i	0.0499592	+	0.347474i	−0.949475	+	0.313842i	$0.898384\pi$
$272$	4.42148	−	2.84152i	0.268092	−	0.172292i
$273$	3.42302	+	3.95037i	0.207171	+	0.239088i
$274$	8.71351	−	2.55852i	0.526402	−	0.154566i
$275$	3.38450			0.204093
$276$	1.18261	+	7.95317i	0.0711848	+	0.478725i
$277$	29.4125			1.76723			0.883614	−	0.468217i	$-0.155103\pi$
$277$	29.4125			1.76723			0.883614	+	0.468217i	$0.155103\pi$
$278$	−4.98306	+	1.46316i	−0.298864	+	0.0877545i
$279$	−6.14851	−	7.09576i	−0.368102	−	0.424812i
$280$	4.19343	−	2.69496i	0.250606	−	0.161054i
$281$	1.76735	+	12.2922i	0.105432	+	0.733293i	0.972127	+	0.234455i	$0.0753305\pi$
$281$	1.76735	+	12.2922i	0.105432	+	0.733293i	−0.866695	+	0.498838i	$0.833760\pi$
$282$	−0.694830	−	0.446540i	−0.0413765	−	0.0265911i
$283$	−11.3336	+	24.8172i	−0.673714	+	1.47523i	0.195454	+	0.980713i	$0.437382\pi$
$283$	−11.3336	+	24.8172i	−0.673714	+	1.47523i	−0.869169	+	0.494516i	$0.835345\pi$
$284$	−3.35593	+	3.87295i	−0.199138	+	0.229817i
$285$	0.277903	−	1.93286i	0.0164616	−	0.114493i
$286$	6.11244	+	13.3844i	0.361436	+	0.791435i
$287$	−7.89250	−	2.31745i	−0.465880	−	0.136795i
$288$	−5.19320	−	1.52486i	−0.306012	−	0.0898533i
$289$	−4.61181	−	10.0985i	−0.271283	−	0.594027i
$290$	−0.345425	+	2.40249i	−0.0202841	+	0.141079i
$291$	−8.71633	+	10.0592i	−0.510960	+	0.589679i
$292$	8.36980	−	18.3273i	0.489805	−	1.07252i
$293$	−2.44262	−	1.56978i	−0.142700	−	0.0917074i	0.467343	−	0.884076i	$-0.345211\pi$
$293$	−2.44262	−	1.56978i	−0.142700	−	0.0917074i	−0.610043	+	0.792369i	$0.708848\pi$
$294$	−0.0809340	−	0.562908i	−0.00472016	−	0.0328295i
$295$	−17.4397	+	11.2078i	−1.01538	+	0.652544i
$296$	12.6711	+	14.6232i	0.736490	+	0.849955i
$297$	−4.74934	+	1.39453i	−0.275585	+	0.0809190i
$298$	−4.31374			−0.249888
$299$	−16.3248	+	19.0242i	−0.944088	+	1.10020i
$300$	−1.14638			−0.0661862
$301$	1.93481	−	0.568112i	0.111521	−	0.0327454i
$302$	−2.44168	−	2.81784i	−0.140503	−	0.162149i
$303$	8.31776	−	5.34550i	0.477843	−	0.307091i
$304$	0.252263	+	1.75453i	0.0144683	+	0.100629i
$305$	6.41288	+	4.12131i	0.367201	+	0.235985i
$306$	0.573755	−	1.25635i	0.0327994	−	0.0718206i
$307$	−17.8698	+	20.6228i	−1.01988	+	1.17700i	−0.0357860	+	0.999359i	$0.511393\pi$
$307$	−17.8698	+	20.6228i	−1.01988	+	1.17700i	−0.984095	+	0.177645i	$0.943152\pi$
$308$	−1.18105	+	8.21436i	−0.0672964	+	0.468057i
$309$	−0.631666	−	1.38316i	−0.0359342	−	0.0786850i
$310$	−12.2141	−	3.58638i	−0.693714	−	0.203693i
$311$	−15.8394	−	4.65088i	−0.898172	−	0.263727i	−0.200117	−	0.979772i	$-0.564132\pi$
$311$	−15.8394	−	4.65088i	−0.898172	−	0.263727i	−0.698054	+	0.716045i	$0.745951\pi$
$312$	−4.54012	−	9.94149i	−0.257034	−	0.562826i
$313$	3.37200	−	23.4528i	0.190597	−	1.32563i	−0.639836	−	0.768511i	$-0.720998\pi$
$313$	3.37200	−	23.4528i	0.190597	−	1.32563i	0.830433	−	0.557119i	$-0.188093\pi$
$314$	3.34810	−	3.86391i	0.188944	−	0.218053i
$315$	−0.990376	+	2.16862i	−0.0558014	+	0.122188i
$316$	0.993729	+	0.638631i	0.0559016	+	0.0359258i
$317$	−3.26993	−	22.7429i	−0.183657	−	1.27737i	−0.848024	−	0.529959i	$-0.822207\pi$
$317$	−3.26993	−	22.7429i	−0.183657	−	1.27737i	0.664366	−	0.747407i	$-0.268702\pi$
$318$	1.91567	−	1.23113i	0.107426	−	0.0690382i
$319$	−5.80292	−	6.69692i	−0.324901	−	0.374956i
$320$	2.85975	−	0.839699i	0.159865	−	0.0469406i
$321$	13.8906			0.775295
$322$	2.61316	−	0.780982i	0.145626	−	0.0435224i
$323$	−1.98925			−0.110685
$324$	1.60867	−	0.472348i	0.0893706	−	0.0262416i
$325$	−2.34052	−	2.70110i	−0.129829	−	0.149830i
$326$	−4.59812	+	2.95503i	−0.254666	+	0.163664i
$327$	0.413745	+	2.87766i	0.0228801	+	0.159135i
$328$	14.4685	+	9.29837i	0.798892	+	0.513417i
$329$	0.603327	−	1.32110i	0.0332625	−	0.0728347i
$330$	−4.39480	+	5.07187i	−0.241926	+	0.279197i
$331$	1.86692	−	12.9847i	0.102615	−	0.713703i	−0.871950	−	0.489596i	$-0.837144\pi$
$331$	1.86692	−	12.9847i	0.102615	−	0.713703i	0.974565	−	0.224107i	$-0.0719465\pi$
$332$	4.85840	+	10.6384i	0.266639	+	0.583859i
$333$	−8.87934	−	2.60721i	−0.486585	−	0.142874i
$334$	−3.37510	−	0.991020i	−0.184677	−	0.0542262i
$335$	−9.70292	−	21.2464i	−0.530127	−	1.16082i
$336$	0.307984	−	2.14208i	0.0168019	−	0.116860i
$337$	11.2688	−	13.0048i	0.613848	−	0.708418i	−0.360679	−	0.932690i	$-0.617455\pi$
$337$	11.2688	−	13.0048i	0.613848	−	0.708418i	0.974527	+	0.224272i	$0.0720003\pi$
$338$	3.38363	−	7.40911i	0.184045	−	0.403002i
$339$	−6.85146	−	4.40316i	−0.372120	−	0.239147i
$340$	1.38152	+	9.60867i	0.0749234	+	0.521103i
$341$	39.0967	−	25.1259i	2.11720	−	1.36064i
$342$	0.305039	+	0.352034i	0.0164946	+	0.0190358i
$343$	0.959493	−	0.281733i	0.0518078	−	0.0152121i
$344$	−4.21621			−0.227323
$345$	−10.9858	−	3.16834i	−0.591456	−	0.170578i
$346$	5.38931			0.289731
$347$	27.0326	−	7.93749i	1.45119	−	0.426107i	0.541252	−	0.840860i	$-0.317950\pi$
$347$	27.0326	−	7.93749i	1.45119	−	0.426107i	0.909934	+	0.414754i	$0.136132\pi$
$348$	1.96553	+	2.26834i	0.105364	+	0.121596i
$349$	15.9490	−	10.2498i	0.853733	−	0.548661i	−0.0390041	−	0.999239i	$-0.512419\pi$
$349$	15.9490	−	10.2498i	0.853733	−	0.548661i	0.892737	+	0.450578i	$0.148782\pi$
$350$	0.0553393	+	0.384893i	0.00295801	+	0.0205734i
$351$	4.39731	+	2.82598i	0.234711	+	0.150840i
$352$	11.1293	−	24.3697i	0.593192	−	1.29891i
$353$	−0.112896	+	0.130289i	−0.00600883	+	0.00693456i	−0.758746	−	0.651387i	$-0.774188\pi$
$353$	−0.112896	+	0.130289i	−0.00600883	+	0.00693456i	0.752737	+	0.658321i	$0.228733\pi$
$354$	0.703761	−	4.89476i	0.0374045	−	0.260154i
$355$	−3.02718	−	6.62860i	−0.160666	−	0.351810i
$356$	−6.02123	−	1.76799i	−0.319124	−	0.0937034i
$357$	2.33026	+	0.684227i	0.123331	+	0.0362131i
$358$	4.31878	+	9.45682i	0.228255	+	0.499808i
$359$	1.67464	−	11.6474i	0.0883842	−	0.614726i	−0.896698	−	0.442642i	$-0.854041\pi$
$359$	1.67464	−	11.6474i	0.0883842	−	0.614726i	0.985082	−	0.172083i	$-0.0550498\pi$
$360$	3.26431	−	3.76722i	0.172044	−	0.198550i
$361$	−7.61419	+	16.6727i	−0.400747	+	0.877513i
$362$	−10.8528	−	6.97467i	−0.570410	−	0.366580i
$363$	−1.92139	−	13.3636i	−0.100847	−	0.701405i
$364$	7.37246	−	4.73800i	0.386422	−	0.248338i
$365$	18.7618	+	21.6523i	0.982037	+	1.13333i
$366$	−1.74474	+	0.512302i	−0.0911991	+	0.0267785i
$367$	30.4506			1.58951			0.794753	−	0.606933i	$-0.207600\pi$
$367$	30.4506			1.58951			0.794753	+	0.606933i	$0.207600\pi$
$368$	10.3786	−	0.0499773i	0.541019	−	0.00260525i
$369$	−8.22570			−0.428213
$370$	−12.0387	+	3.53488i	−0.625861	+	0.183769i
$371$	2.62218	+	3.02616i	0.136137	+	0.157110i
$372$	−13.2426	+	8.51050i	−0.686597	+	0.441249i
$373$	−4.04456	−	28.1306i	−0.209420	−	1.45654i	−0.775057	−	0.631891i	$-0.782279\pi$
$373$	−4.04456	−	28.1306i	−0.209420	−	1.45654i	0.565638	−	0.824654i	$-0.308630\pi$
$374$	5.75125	+	3.69611i	0.297390	+	0.191121i
$375$	−4.27470	+	9.36029i	−0.220745	+	0.483363i
$376$	−1.98859	+	2.29495i	−0.102554	+	0.118353i
$377$	−1.33173	+	9.26239i	−0.0685876	+	0.477037i
$378$	−0.236245	−	0.517305i	−0.0121511	−	0.0266073i
$379$	28.3406	+	8.32156i	1.45576	+	0.427450i	0.911442	−	0.411429i	$-0.134970\pi$
$379$	28.3406	+	8.32156i	1.45576	+	0.427450i	0.544318	+	0.838879i	$0.316788\pi$
$380$	−3.14131	−	0.922372i	−0.161146	−	0.0473167i
$381$	7.10640	+	15.5608i	0.364072	+	0.797206i
$382$	0.651362	−	4.53032i	0.0333266	−	0.231792i
$383$	7.31367	−	8.44043i	0.373711	−	0.431286i	−0.537475	−	0.843279i	$-0.680622\pi$
$383$	7.31367	−	8.44043i	0.373711	−	0.431286i	0.911187	+	0.411994i	$0.135167\pi$
$384$	−4.79216	+	10.4934i	−0.244549	+	0.535488i
$385$	−9.92742	−	6.37997i	−0.505948	−	0.325153i
$386$	−1.36233	−	9.47523i	−0.0693409	−	0.482277i
$387$	1.69638	−	1.09020i	0.0862320	−	0.0554179i
$388$	14.6137	+	16.8651i	0.741896	+	0.856193i
$389$	27.0917	−	7.95484i	1.37360	−	0.403326i	0.490065	−	0.871686i	$-0.336973\pi$
$389$	27.0917	−	7.95484i	1.37360	−	0.403326i	0.883538	+	0.468360i	$0.155155\pi$
$390$	7.08694			0.358861
$391$	−1.60206	+	11.5366i	−0.0810195	+	0.583433i
$392$	−2.09086			−0.105604
$393$	14.8921	−	4.37272i	0.751209	−	0.220575i
$394$	0.0147511	+	0.0170237i	0.000743152	+	0.000857643i
$395$	−1.41306	+	0.908118i	−0.0710987	+	0.0456924i
$396$	1.18105	+	8.21436i	0.0593498	+	0.412787i
$397$	5.38312	+	3.45952i	0.270171	+	0.173628i	0.668711	−	0.743523i	$-0.266847\pi$
$397$	5.38312	+	3.45952i	0.270171	+	0.173628i	−0.398540	+	0.917151i	$0.630483\pi$
$398$	2.60121	−	5.69585i	0.130387	−	0.285507i
$399$	−0.536383	+	0.619019i	−0.0268527	+	0.0309897i
$400$	−0.210587	+	1.46466i	−0.0105293	+	0.0732331i
$401$	10.7251	+	23.4846i	0.535584	+	1.17277i	0.963195	+	0.268803i	$0.0866281\pi$
$401$	10.7251	+	23.4846i	0.535584	+	1.17277i	−0.427611	+	0.903963i	$0.640645\pi$
$402$	5.34595	+	1.56971i	0.266632	+	0.0782901i
$403$	−47.0894	−	13.8267i	−2.34569	−	0.688757i
$404$	−6.88632	−	15.0789i	−0.342607	−	0.750205i
$405$	−0.339288	+	2.35980i	−0.0168593	+	0.117259i
$406$	0.666707	−	0.769421i	0.0330881	−	0.0381857i
$407$	19.0289	−	41.6674i	0.943225	−	2.06537i
$408$	−4.27184	−	2.74535i	−0.211488	−	0.135915i
$409$	3.24560	+	22.5737i	0.160485	+	1.11620i	0.897722	+	0.440562i	$0.145221\pi$
$409$	3.24560	+	22.5737i	0.160485	+	1.11620i	−0.737238	+	0.675634i	$0.763870\pi$
$410$	−9.38206	+	6.02948i	−0.463347	+	0.297775i
$411$	10.4573	+	12.0684i	0.515821	+	0.595289i
$412$	−2.44609	+	0.718237i	−0.120510	+	0.0353850i
$413$	8.69549			0.427877
$414$	2.28729	−	1.48556i	0.112414	−	0.0730113i
$415$	−16.6304			−0.816356
$416$	−27.1453	+	7.97059i	−1.33091	+	0.390790i
$417$	−5.98030	−	6.90163i	−0.292857	−	0.337974i
$418$	−1.93966	+	1.24654i	−0.0948717	+	0.0609704i
$419$	−2.63137	−	18.3016i	−0.128551	−	0.894091i	−0.947393	−	0.320072i	$-0.896293\pi$
$419$	−2.63137	−	18.3016i	−0.128551	−	0.894091i	0.818842	−	0.574019i	$-0.194616\pi$
$420$	3.36256	+	2.16099i	0.164076	+	0.105445i
$421$	10.3420	−	22.6458i	0.504038	−	1.10369i	−0.471098	−	0.882081i	$-0.656142\pi$
$421$	10.3420	−	22.6458i	0.504038	−	1.10369i	0.975136	−	0.221608i	$-0.0711306\pi$
$422$	−8.58533	+	9.90800i	−0.417927	+	0.482314i
$423$	0.206691	−	1.43757i	0.0100496	−	0.0698968i
$424$	−3.47793	−	7.61561i	−0.168903	−	0.369847i
$425$	−1.59334	−	0.467846i	−0.0772882	−	0.0226939i
$426$	1.66786	+	0.489729i	0.0808083	+	0.0237275i
$427$	−1.32828	−	2.90853i	−0.0642801	−	0.140754i
$428$	3.31432	−	23.0516i	0.160204	−	1.11424i
$429$	−16.9434	+	19.5537i	−0.818036	+	0.944064i
$430$	1.13574	−	2.48692i	0.0547701	−	0.119930i
$431$	−19.1652	−	12.3167i	−0.923155	−	0.593276i	−0.00958376	−	0.999954i	$-0.503051\pi$
$431$	−19.1652	−	12.3167i	−0.923155	−	0.593276i	−0.913571	+	0.406678i	$0.866687\pi$
$432$	−0.307984	−	2.14208i	−0.0148179	−	0.103061i
$433$	5.90615	−	3.79565i	0.283832	−	0.182407i	−0.390977	−	0.920401i	$-0.627863\pi$
$433$	5.90615	−	3.79565i	0.283832	−	0.182407i	0.674808	+	0.737993i	$0.264226\pi$
$434$	3.49664	+	4.03534i	0.167844	+	0.193702i
$435$	−4.09511	+	1.20243i	−0.196345	+	0.0576522i
$436$	4.87425			0.233434
$437$	−3.31477	−	2.10779i	−0.158567	−	0.100829i
$438$	−6.83420			−0.326551
$439$	−19.8940	+	5.84141i	−0.949489	+	0.278795i	−0.719574	−	0.694416i	$-0.755663\pi$
$439$	−19.8940	+	5.84141i	−0.949489	+	0.278795i	−0.229915	+	0.973211i	$0.573845\pi$
$440$	16.1578	+	18.6472i	0.770295	+	0.888968i
$441$	0.841254	−	0.540641i	0.0400597	−	0.0257448i
$442$	−1.02744	−	7.14597i	−0.0488701	−	0.339899i
$443$	−31.6818	−	20.3606i	−1.50525	−	0.967363i	−0.994170	−	0.107828i	$-0.965611\pi$
$443$	−31.6818	−	20.3606i	−1.50525	−	0.967363i	−0.511076	−	0.859535i	$-0.670753\pi$
$444$	−6.44535	+	14.1133i	−0.305883	+	0.669789i
$445$	5.84366	−	6.74394i	0.277016	−	0.319693i
$446$	2.09108	−	14.5438i	0.0990153	−	0.688667i
$447$	−3.15105	−	6.89984i	−0.149040	−	0.326351i
$448$	−1.19953	−	0.352213i	−0.0566724	−	0.0166405i
$449$	−24.8095	−	7.28472i	−1.17083	−	0.343787i	−0.362199	−	0.932101i	$-0.617974\pi$
$449$	−24.8095	−	7.28472i	−1.17083	−	0.343787i	−0.808633	+	0.588313i	$0.799792\pi$
$450$	0.161535	+	0.353711i	0.00761481	+	0.0166741i
$451$	5.79448	−	40.3015i	0.272852	−	1.89772i
$452$	−8.94191	+	10.3195i	−0.420592	+	0.485389i
$453$	2.72358	−	5.96381i	0.127965	−	0.280204i
$454$	10.9715	+	7.05097i	0.514919	+	0.330918i
$455$	1.77349	+	12.3349i	0.0831424	+	0.578268i
$456$	1.44071	−	0.925891i	0.0674676	−	0.0433588i
$457$	−16.9932	−	19.6112i	−0.794908	−	0.917373i	0.203182	−	0.979141i	$-0.434872\pi$
$457$	−16.9932	−	19.6112i	−0.794908	−	0.917373i	−0.998091	+	0.0617678i	$0.980326\pi$
$458$	8.16095	−	2.39627i	0.381336	−	0.111970i
$459$	2.42864			0.113359
$460$	−7.87917	+	17.4752i	−0.367368	+	0.814785i
$461$	−7.18402			−0.334593			−0.167297	−	0.985907i	$-0.553504\pi$
$461$	−7.18402			−0.334593			−0.167297	+	0.985907i	$0.553504\pi$
$462$	2.70093	−	0.793066i	0.125659	−	0.0368968i
$463$	−0.899195	−	1.03773i	−0.0417891	−	0.0482272i	0.734470	−	0.678641i	$-0.237431\pi$
$463$	−0.899195	−	1.03773i	−0.0417891	−	0.0482272i	−0.776259	+	0.630414i	$0.782885\pi$
$464$	3.25920	−	2.09456i	0.151304	−	0.0972374i
$465$	−3.18558	−	22.1562i	−0.147728	−	1.02747i
$466$	−9.16994	−	5.89316i	−0.424789	−	0.272995i
$467$	6.60449	−	14.4618i	0.305619	−	0.669213i	−0.693044	−	0.720895i	$-0.743731\pi$
$467$	6.60449	−	14.4618i	0.305619	−	0.669213i	0.998664	+	0.0516819i	$0.0164582\pi$
$468$	5.73898	−	6.62314i	0.265284	−	0.306155i
$469$	−1.39429	+	9.69749i	−0.0643823	+	0.447788i
$470$	−0.817997	−	1.79116i	−0.0377314	−	0.0826202i
$471$	8.62602	+	2.53283i	0.397466	+	0.116707i
$472$	−17.4446	−	5.12220i	−0.802953	−	0.235768i
$473$	4.14640	+	9.07934i	0.190652	+	0.417469i
$474$	0.0570225	−	0.396600i	0.00261913	−	0.0182165i
$475$	0.366756	−	0.423259i	0.0168279	−	0.0194205i
$476$	1.69150	−	3.70386i	0.0775296	−	0.169766i
$477$	3.36853	+	2.16482i	0.154234	+	0.0991205i
$478$	−1.50189	−	10.4459i	−0.0686949	−	0.477783i
$479$	−7.29700	+	4.68950i	−0.333408	+	0.214269i	−0.696624	−	0.717437i	$-0.745315\pi$
$479$	−7.29700	+	4.68950i	−0.333408	+	0.214269i	0.363215	+	0.931705i	$0.381679\pi$
$480$	−8.45006	−	9.75189i	−0.385691	−	0.445111i
$481$	−46.4131	+	13.6281i	−2.11626	+	0.621389i
$482$	−12.7111			−0.578976
$483$	3.15802	+	3.60928i	0.143695	+	0.164228i
$484$	−22.6355			−1.02889
$485$	−30.4470	+	8.94004i	−1.38253	+	0.405946i
$486$	−0.372417	−	0.429792i	−0.0168932	−	0.0194958i
$487$	23.2073	−	14.9144i	1.05162	−	0.675836i	0.103787	−	0.994600i	$-0.466904\pi$
$487$	23.2073	−	14.9144i	1.05162	−	0.675836i	0.947834	+	0.318763i	$0.103268\pi$
$488$	0.951445	+	6.61745i	0.0430699	+	0.299558i
$489$	−8.08536	−	5.19615i	−0.365633	−	0.234978i
$490$	0.563223	−	1.23329i	0.0254438	−	0.0557142i
$491$	−13.4924	+	15.5711i	−0.608904	+	0.702712i	−0.973560	−	0.228430i	$-0.926641\pi$
$491$	−13.4924	+	15.5711i	−0.608904	+	0.702712i	0.364657	+	0.931142i	$0.381186\pi$
$492$	−1.96268	+	13.6507i	−0.0884842	+	0.615421i
$493$	1.80614	+	3.95489i	0.0813444	+	0.178119i
$494$	2.33619	+	0.685968i	0.105110	+	0.0308632i
$495$	−11.3227	−	3.32465i	−0.508919	−	0.149432i
$496$	8.44075	+	18.4827i	0.379001	+	0.829896i
$497$	−0.434999	+	3.02549i	−0.0195124	+	0.135712i
$498$	2.59786	−	2.99809i	0.116413	−	0.134348i
$499$	−1.42823	+	3.12740i	−0.0639365	+	0.140001i	−0.938903	−	0.344182i	$-0.888156\pi$
$499$	−1.42823	+	3.12740i	−0.0639365	+	0.140001i	0.874966	+	0.484184i	$0.160883\pi$
$500$	14.5136	+	9.32734i	0.649069	+	0.417131i
$501$	−0.880268	−	6.12240i	−0.0393275	−	0.273528i
$502$	14.0611	−	9.03654i	0.627579	−	0.403321i
$503$	3.39590	+	3.91908i	0.151416	+	0.174743i	0.826390	−	0.563098i	$-0.190391\pi$
$503$	3.39590	+	3.91908i	0.151416	+	0.174743i	−0.674974	+	0.737841i	$0.735845\pi$
$504$	−2.00617	+	0.589064i	−0.0893618	+	0.0262390i
$505$	23.5720			1.04894
$506$	5.66720	+	12.2530i	0.251938	+	0.544710i
$507$	14.3225			0.636086
$508$	27.5191	−	8.08034i	1.22096	−	0.358507i
$509$	−15.7456	−	18.1714i	−0.697912	−	0.805434i	0.290557	−	0.956858i	$-0.406160\pi$
$509$	−15.7456	−	18.1714i	−0.697912	−	0.805434i	−0.988469	+	0.151424i	$0.951614\pi$
$510$	2.77006	−	1.78021i	0.122660	−	0.0788289i
$511$	−1.71024	−	11.8950i	−0.0756566	−	0.526204i
$512$	17.4667	+	11.2252i	0.771928	+	0.496088i
$513$	−0.340258	+	0.745060i	−0.0150227	+	0.0328952i
$514$	2.07442	−	2.39401i	0.0914987	−	0.105595i
$515$	0.515909	−	3.58823i	0.0227337	−	0.158116i
$516$	−1.40444	−	3.07530i	−0.0618272	−	0.135383i
$517$	6.89770	+	2.02535i	0.303360	+	0.0890747i
$518$	5.04965	+	1.48271i	0.221869	+	0.0651466i
$519$	3.93673	+	8.62023i	0.172803	+	0.378386i
$520$	3.70812	−	25.7905i	0.162612	−	1.13099i
$521$	8.67545	−	10.0120i	0.380078	−	0.438634i	−0.533188	−	0.845997i	$-0.679006\pi$
$521$	8.67545	−	10.0120i	0.380078	−	0.438634i	0.913266	+	0.407363i	$0.133552\pi$
$522$	0.422930	−	0.926087i	0.0185111	−	0.0405337i
$523$	28.5328	+	18.3369i	1.24765	+	0.801819i	0.986545	−	0.163491i	$-0.0522753\pi$
$523$	28.5328	+	18.3369i	1.24765	+	0.801819i	0.261109	+	0.965309i	$0.415912\pi$
$524$	−3.70331	−	25.7571i	−0.161780	−	1.12520i
$525$	−0.575214	+	0.369668i	−0.0251044	+	0.0161336i
$526$	−0.374778	−	0.432517i	−0.0163411	−	0.0188586i
$527$	−21.8789	+	6.42423i	−0.953061	+	0.279844i
$528$	10.7120			0.466179
$529$	−14.8937	+	17.5265i	−0.647552	+	0.762021i
$530$	5.42890			0.235817
$531$	8.34327	−	2.44980i	0.362067	−	0.106312i
$532$	0.899291	+	1.03784i	0.0389892	+	0.0449959i
$533$	−36.1710	+	23.2457i	−1.56674	+	1.00688i
$534$	0.302934	+	2.10696i	0.0131093	+	0.0911769i
$535$	27.8589	+	17.9038i	1.20445	+	0.774050i
$536$	8.50961	−	18.6335i	0.367559	−	0.804843i
$537$	−11.9715	+	13.8158i	−0.516607	+	0.596197i
$538$	−0.925843	+	6.43938i	−0.0399159	+	0.277621i
$539$	2.05624	+	4.50254i	0.0885685	+	0.193938i
$540$	3.83517	+	1.12611i	0.165040	+	0.0484600i
$541$	6.59325	+	1.93595i	0.283466	+	0.0832331i	0.420375	−	0.907351i	$-0.361899\pi$
$541$	6.59325	+	1.93595i	0.283466	+	0.0832331i	−0.136909	+	0.990584i	$0.543717\pi$
$542$	−1.36525	−	2.98948i	−0.0586426	−	0.128409i
$543$	3.22838	−	22.4539i	0.138543	−	0.963587i
$544$	−8.60806	+	9.93423i	−0.369068	+	0.425927i
$545$	−2.87927	+	6.30472i	−0.123334	+	0.270065i
$546$	−2.50074	−	1.60713i	−0.107022	−	0.0687786i
$547$	6.12548	+	42.6036i	0.261906	+	1.82160i	0.518497	+	0.855079i	$0.326492\pi$
$547$	6.12548	+	42.6036i	0.261906	+	1.82160i	−0.256591	+	0.966520i	$0.582599\pi$
$548$	22.5228	−	14.4745i	0.962128	−	0.618322i
$549$	−2.09391	−	2.41650i	−0.0893658	−	0.103134i
$550$	−1.84679	+	0.542265i	−0.0787472	+	0.0231223i
$551$	−1.46633			−0.0624677
$552$	−4.20941	−	9.10109i	−0.179165	−	0.387368i
$553$	0.704556			0.0299608
$554$	−16.0493	+	4.71249i	−0.681867	+	0.200214i
$555$	−14.4479	−	16.6738i	−0.613280	−	0.707763i
$556$	−12.8803	+	8.27767i	−0.546247	+	0.351051i
$557$	−1.96543	−	13.6699i	−0.0832781	−	0.579212i	−0.988146	−	0.153519i	$-0.950939\pi$
$557$	−1.96543	−	13.6699i	−0.0832781	−	0.579212i	0.904868	−	0.425693i	$-0.139970\pi$
$558$	4.49188	+	2.88676i	0.190157	+	0.122206i
$559$	4.37864	−	9.58789i	0.185197	−	0.405525i
$560$	3.37866	−	3.89918i	0.142774	−	0.164771i
$561$	−1.71082	+	11.8990i	−0.0722310	+	0.502378i
$562$	−2.93384	−	6.42421i	−0.123757	−	0.270989i
$563$	−7.91936	−	2.32533i	−0.333761	−	0.0980012i	0.110558	−	0.993870i	$-0.464736\pi$
$563$	−7.91936	−	2.32533i	−0.333761	−	0.0980012i	−0.444319	+	0.895869i	$0.646554\pi$
$564$	−2.33635	−	0.686014i	−0.0983781	−	0.0288864i
$565$	−8.06596	−	17.6620i	−0.339337	−	0.743045i
$566$	2.20809	−	15.3576i	0.0928131	−	0.645530i
$567$	0.654861	−	0.755750i	0.0275016	−	0.0317385i
$568$	2.65488	−	5.81339i	0.111396	−	0.243924i
$569$	10.2244	+	6.57085i	0.428631	+	0.275464i	0.737118	−	0.675764i	$-0.236186\pi$
$569$	10.2244	+	6.57085i	0.428631	+	0.275464i	−0.308487	+	0.951229i	$0.599823\pi$
$570$	0.158043	+	1.09921i	0.00661968	+	0.0460409i
$571$	7.96320	−	5.11764i	0.333250	−	0.214167i	−0.363305	−	0.931670i	$-0.618352\pi$
$571$	7.96320	−	5.11764i	0.333250	−	0.214167i	0.696555	+	0.717504i	$0.254715\pi$
$572$	28.4071	+	32.7835i	1.18776	+	1.37075i
$573$	7.72207	−	2.26740i	0.322594	−	0.0947222i
$574$	4.67793			0.195253
$575$	−2.15932	−	2.46788i	−0.0900499	−	0.102918i
$576$	−1.25017			−0.0520904
$577$	18.9872	−	5.57515i	0.790448	−	0.232096i	0.138502	−	0.990362i	$-0.455771\pi$
$577$	18.9872	−	5.57515i	0.790448	−	0.232096i	0.651946	+	0.758266i	$0.273953\pi$
$578$	4.13446	+	4.77143i	0.171971	+	0.198465i
$579$	14.1605	−	9.10042i	0.588491	−	0.378200i
$580$	1.01835	+	7.08281i	0.0422849	+	0.294098i
$581$	5.86831	+	3.77133i	0.243458	+	0.156461i
$582$	3.14447	−	6.88543i	0.130342	−	0.285410i
$583$	−12.9794	+	14.9790i	−0.537552	+	0.620368i
$584$	−3.57588	+	24.8708i	−0.147971	+	1.02916i
$585$	5.17679	+	11.3356i	0.214034	+	0.468669i
$586$	1.58435	+	0.465208i	0.0654490	+	0.0192176i
$587$	−29.0148	−	8.51950i	−1.19757	−	0.351638i	−0.378645	−	0.925542i	$-0.623610\pi$
$587$	−29.0148	−	8.51950i	−1.19757	−	0.351638i	−0.818922	+	0.573904i	$0.805428\pi$
$588$	−0.696478	−	1.52507i	−0.0287223	−	0.0628930i
$589$	1.09445	−	7.61209i	0.0450961	−	0.313651i
$590$	7.72043	−	8.90985i	0.317845	−	0.366813i
$591$	−0.0164543	+	0.0360298i	−0.000676838	+	0.00148207i
$592$	16.8478	+	10.8274i	0.692441	+	0.445005i
$593$	−1.54779	−	10.7651i	−0.0635602	−	0.442071i	−0.996606	−	0.0823144i	$-0.973769\pi$
$593$	−1.54779	−	10.7651i	−0.0635602	−	0.442071i	0.933046	−	0.359757i	$-0.117140\pi$
$594$	2.36810	−	1.52188i	0.0971641	−	0.0624436i
$595$	3.79167	+	4.37582i	0.155443	+	0.179391i
$596$	−12.2023	+	3.58291i	−0.499824	+	0.146762i
$597$	11.0106			0.450635
$598$	5.85974	−	12.9963i	0.239623	−	0.531458i
$599$	45.0289			1.83983			0.919916	−	0.392116i	$-0.128257\pi$
$599$	45.0289			1.83983			0.919916	+	0.392116i	$0.128257\pi$
$600$	1.37173	−	0.402777i	0.0560008	−	0.0164433i
$601$	−6.56340	−	7.57457i	−0.267727	−	0.308973i	0.605928	−	0.795519i	$-0.292802\pi$
$601$	−6.56340	−	7.57457i	−0.267727	−	0.308973i	−0.873655	+	0.486546i	$0.838256\pi$
$602$	−0.964727	+	0.619993i	−0.0393194	+	0.0252690i
$603$	1.39429	+	9.69749i	0.0567798	+	0.394912i
$604$	−9.24721	−	5.94282i	−0.376264	−	0.241810i
$605$	13.3710	−	29.2785i	0.543610	−	1.19034i
$606$	−3.68221	+	4.24950i	−0.149580	+	0.172624i
$607$	−1.02917	+	7.15804i	−0.0417728	+	0.290536i	0.958217	+	0.286042i	$0.0923396\pi$
$607$	−1.02917	+	7.15804i	−0.0417728	+	0.290536i	−0.999990	+	0.00449414i	$0.998569\pi$
$608$	−1.84162	−	4.03259i	−0.0746877	−	0.163543i
$609$	1.71770	+	0.504362i	0.0696047	+	0.0204378i
$610$	−4.15957	−	1.22136i	−0.168416	−	0.0494515i
$611$	−3.15365	−	6.90553i	−0.127583	−	0.279368i
$612$	0.579481	−	4.03038i	0.0234241	−	0.162918i
$613$	−7.72330	+	8.91317i	−0.311941	+	0.359999i	−0.889972	−	0.456016i	$-0.849276\pi$
$613$	−7.72330	+	8.91317i	−0.311941	+	0.359999i	0.578030	+	0.816015i	$0.303821\pi$
$614$	6.44662	−	14.1161i	0.260165	−	0.569681i
$615$	−16.4975	−	10.6023i	−0.665243	−	0.427525i
$616$	−1.47288	−	10.2441i	−0.0593440	−	0.412746i
$617$	6.86910	−	4.41450i	0.276540	−	0.177721i	−0.395018	−	0.918673i	$-0.629262\pi$
$617$	6.86910	−	4.41450i	0.276540	−	0.177721i	0.671558	+	0.740952i	$0.265625\pi$
$618$	0.566285	+	0.653528i	0.0227793	+	0.0262887i
$619$	−3.23866	+	0.950955i	−0.130173	+	0.0382221i	−0.346170	−	0.938172i	$-0.612518\pi$
$619$	−3.23866	+	0.950955i	−0.130173	+	0.0382221i	0.215997	+	0.976394i	$0.430700\pi$
$620$	−37.5288			−1.50719
$621$	4.04695	+	2.57336i	0.162398	+	0.103266i
$622$	9.38811			0.376429
$623$	−3.59137	+	1.05452i	−0.143885	+	0.0422485i
$624$	−7.40777	−	8.54902i	−0.296548	−	0.342235i
$625$	−23.5141	+	15.1116i	−0.940564	+	0.604464i
$626$	1.91765	+	13.3375i	0.0766445	+	0.533075i
$627$	−3.41071	−	2.19193i	−0.136210	−	0.0875372i
$628$	6.26147	−	13.7107i	0.249860	−	0.547116i
$629$	−14.7181	+	16.9856i	−0.586848	+	0.677259i
$630$	0.192952	−	1.34201i	0.00768738	−	0.0534669i
$631$	−13.0161	−	28.5013i	−0.518164	−	1.13462i	−0.970130	−	0.242585i	$-0.922005\pi$
$631$	−13.0161	−	28.5013i	−0.518164	−	1.13462i	0.451967	−	0.892035i	$-0.350723\pi$
$632$	−1.41346	−	0.415028i	−0.0562243	−	0.0165089i
$633$	−22.1192	−	6.49478i	−0.879159	−	0.258144i
$634$	5.42814	+	11.8860i	0.215579	+	0.472052i
$635$	−5.80410	+	40.3684i	−0.230329	+	1.60197i
$636$	4.39631	−	5.07361i	0.174325	−	0.201182i
$637$	2.17141	−	4.75473i	0.0860345	−	0.188389i
$638$	4.23940	+	2.72450i	0.167840	+	0.107864i
$639$	0.434999	+	3.02549i	0.0172083	+	0.119686i
$640$	−23.1363	+	14.8688i	−0.914543	+	0.587741i
$641$	32.6010	+	37.6236i	1.28766	+	1.48604i	0.781950	+	0.623342i	$0.214225\pi$
$641$	32.6010	+	37.6236i	1.28766	+	1.48604i	0.505714	+	0.862701i	$0.331229\pi$
$642$	−7.57952	+	2.22555i	−0.299140	+	0.0878354i
$643$	−20.5529			−0.810526			−0.405263	−	0.914200i	$-0.632820\pi$
$643$	−20.5529			−0.810526			−0.405263	+	0.914200i	$0.632820\pi$
$644$	6.74318	−	4.37961i	0.265719	−	0.172581i
$645$	4.80745			0.189293
$646$	1.08545	−	0.318718i	0.0427066	−	0.0125398i
$647$	28.3461	+	32.7131i	1.11440	+	1.28608i	0.954256	+	0.298991i	$0.0966500\pi$
$647$	28.3461	+	32.7131i	1.11440	+	1.28608i	0.160143	+	0.987094i	$0.448805\pi$
$648$	−1.75894	+	1.13040i	−0.0690979	+	0.0444065i
$649$	6.12542	+	42.6033i	0.240444	+	1.67232i
$650$	1.70990	+	1.09889i	0.0670678	+	0.0431018i
$651$	−3.90035	+	8.54057i	−0.152867	+	0.334731i
$652$	−10.5523	+	12.1780i	−0.413260	+	0.476927i
$653$	−3.69386	+	25.6914i	−0.144552	+	1.00538i	0.780396	+	0.625286i	$0.215018\pi$
$653$	−3.69386	+	25.6914i	−0.144552	+	1.00538i	−0.924948	+	0.380095i	$0.875891\pi$
$654$	−0.686824	−	1.50393i	−0.0268569	−	0.0588085i
$655$	35.5038	+	10.4249i	1.38725	+	0.407333i
$656$	17.0802	+	5.01519i	0.666869	+	0.195810i
$657$	−4.99217	−	10.9313i	−0.194763	−	0.426472i
$658$	−0.117544	+	0.817539i	−0.00458235	+	0.0318710i
$659$	26.5680	−	30.6611i	1.03494	−	1.19439i	0.0543120	−	0.998524i	$-0.482703\pi$
$659$	26.5680	−	30.6611i	1.03494	−	1.19439i	0.980631	−	0.195864i	$-0.0627511\pi$
$660$	−8.21896	+	17.9970i	−0.319923	+	0.700533i
$661$	−6.94246	−	4.46165i	−0.270031	−	0.173538i	0.398617	−	0.917117i	$-0.369490\pi$
$661$	−6.94246	−	4.46165i	−0.270031	−	0.173538i	−0.668648	+	0.743579i	$0.733127\pi$
$662$	1.06171	+	7.38435i	0.0412645	+	0.287001i
$663$	10.6795	−	6.86329i	0.414757	−	0.266548i
$664$	−9.55124	−	11.0227i	−0.370660	−	0.427765i
$665$	−1.87364	+	0.550149i	−0.0726565	+	0.0213339i
$666$	5.26283			0.203931
$667$	−1.18092	+	8.50397i	−0.0457254	+	0.329275i
$668$	−10.3703			−0.401238
$669$	24.7902	−	7.27907i	0.958446	−	0.281425i
$670$	8.69861	+	10.0387i	0.336057	+	0.387830i
$671$	13.3146	−	8.55675i	0.514003	−	0.330330i
$672$	0.770270	+	5.35735i	0.0297138	+	0.206664i
$673$	−23.3467	−	15.0040i	−0.899951	−	0.578363i	0.00682489	−	0.999977i	$-0.497828\pi$
$673$	−23.3467	−	15.0040i	−0.899951	−	0.578363i	−0.906776	+	0.421613i	$0.861464\pi$
$674$	−4.06527	+	8.90170i	−0.156588	+	0.342881i
$675$	−0.447766	+	0.516750i	−0.0172345	+	0.0198897i
$676$	3.41739	−	23.7685i	0.131438	−	0.914173i
$677$	1.81407	+	3.97226i	0.0697204	+	0.152666i	0.941284	−	0.337617i	$-0.109621\pi$
$677$	1.81407	+	3.97226i	0.0697204	+	0.152666i	−0.871563	+	0.490283i	$0.836893\pi$
$678$	4.44405	+	1.30489i	0.170673	+	0.0501140i
$679$	12.7710	+	3.74992i	0.490108	+	0.143909i
$680$	−5.02908	−	11.0121i	−0.192856	−	0.422297i
$681$	−3.26370	+	22.6995i	−0.125065	+	0.869847i
$682$	−17.3078	+	19.9743i	−0.662751	+	0.764855i
$683$	10.4330	−	22.8452i	0.399209	−	0.874147i	−0.598140	−	0.801391i	$-0.704093\pi$
$683$	10.4330	−	22.8452i	0.399209	−	0.874147i	0.997350	−	0.0727555i	$-0.0231793\pi$
$684$	1.15526	+	0.742438i	0.0441723	+	0.0283878i
$685$	5.41800	+	37.6830i	0.207011	+	1.43979i
$686$	−0.478418	+	0.307461i	−0.0182661	+	0.0117389i
$687$	9.79417	+	11.3031i	0.373671	+	0.431239i
$688$	−4.18713	+	1.22945i	−0.159633	+	0.0468725i
$689$	20.9302			0.797379
$690$	6.50215	−	0.0313108i	0.247533	−	0.00119198i
$691$	5.57171			0.211958			0.105979	−	0.994368i	$-0.466202\pi$
$691$	5.57171			0.211958			0.105979	+	0.994368i	$0.466202\pi$
$692$	15.2447	−	4.47626i	0.579518	−	0.170162i
$693$	3.24146	+	3.74084i	0.123133	+	0.142103i
$694$	−13.4789	+	8.66235i	−0.511651	+	0.328818i
$695$	−3.09843	−	21.5501i	−0.117530	−	0.817441i
$696$	−3.14889	−	2.02367i	−0.119358	−	0.0767070i
$697$	−8.29886	+	18.1720i	−0.314342	+	0.688312i
$698$	−7.06053	+	8.14829i	−0.267245	+	0.308417i
$699$	2.72778	−	18.9721i	0.103174	−	0.717591i
$700$	0.476223	+	1.04278i	0.0179995	+	0.0394135i
$701$	40.9358	+	12.0198i	1.54612	+	0.453983i	0.939940	−	0.341341i	$-0.110881\pi$
$701$	40.9358	+	12.0198i	1.54612	+	0.453983i	0.606185	+	0.795324i	$0.292699\pi$
$702$	−2.85222	−	0.837487i	−0.107650	−	0.0316089i
$703$	−3.14881	−	6.89493i	−0.118760	−	0.260047i
$704$	0.880665	−	6.12516i	0.0331913	−	0.230851i
$705$	2.26745	−	2.61678i	0.0853971	−	0.0985535i
$706$	0.0407278	−	0.0891815i	0.00153281	−	0.00335639i
$707$	−8.31776	−	5.34550i	−0.312822	−	0.201038i
$708$	−2.07477	−	14.4303i	−0.0779746	−	0.542325i
$709$	−3.76355	+	2.41869i	−0.141343	+	0.0908357i	−0.609401	−	0.792862i	$-0.708590\pi$
$709$	−3.76355	+	2.41869i	−0.141343	+	0.0908357i	0.468058	+	0.883698i	$0.344954\pi$
$710$	2.71385	+	3.13195i	0.101849	+	0.117540i
$711$	0.676017	−	0.198496i	0.0253526	−	0.00744420i
$712$	7.82606			0.293294
$713$	−43.2649	−	12.4777i	−1.62028	−	0.467295i
$714$	−1.38116			−0.0516886
$715$	−59.1850	+	17.3783i	−2.21339	+	0.649911i
$716$	20.0712	+	23.1634i	0.750095	+	0.865656i
$717$	15.6111	−	10.0327i	0.583008	−	0.374677i
$718$	0.952363	+	6.62383i	0.0355419	+	0.247199i
$719$	8.02548	+	5.15766i	0.299300	+	0.192348i	0.681668	−	0.731662i	$-0.261255\pi$
$719$	8.02548	+	5.15766i	0.299300	+	0.192348i	−0.382368	+	0.924010i	$0.624891\pi$
$720$	2.14327	−	4.69312i	0.0798751	−	0.174902i
$721$	−0.995759	+	1.14917i	−0.0370840	+	0.0427972i
$722$	1.48345	−	10.3176i	0.0552082	−	0.383981i
$723$	−9.28508	−	20.3315i	−0.345316	−	0.756136i
$724$	−36.4923	−	10.7151i	−1.35623	−	0.398224i
$725$	−1.17449	−	0.344862i	−0.0436195	−	0.0128079i
$726$	3.18954	+	6.98412i	0.118375	+	0.259205i
$727$	−1.89261	+	13.1634i	−0.0701931	+	0.488204i	0.924154	+	0.382021i	$0.124772\pi$
$727$	−1.89261	+	13.1634i	−0.0701931	+	0.488204i	−0.994347	+	0.106182i	$0.966137\pi$
$728$	−7.15706	+	8.25968i	−0.265258	+	0.306124i
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$	−13.7067	−	8.80876i	−0.507307	−	0.326027i
$731$	−0.696964	−	4.84749i	−0.0257782	−	0.179291i
$732$	−4.50984	+	2.89830i	−0.166688	+	0.107124i
$733$	10.9431	+	12.6290i	0.404191	+	0.466462i	0.920956	−	0.389665i	$-0.127409\pi$
$733$	10.9431	+	12.6290i	0.404191	+	0.466462i	−0.516765	+	0.856127i	$0.672864\pi$
$734$	−16.6157	+	4.87880i	−0.613295	+	0.180080i
$735$	2.38406			0.0879375
$736$	−24.8702	+	7.43282i	−0.916728	+	0.273977i
$737$	−48.4947			−1.78632
$738$	4.48844	−	1.31792i	0.165222	−	0.0485135i
$739$	3.38119	+	3.90210i	0.124379	+	0.143541i	0.814524	−	0.580130i	$-0.196998\pi$
$739$	3.38119	+	3.90210i	0.124379	+	0.143541i	−0.690144	+	0.723672i	$0.742453\pi$
$740$	−31.1178	+	19.9982i	−1.14391	+	0.735148i
$741$	0.609307	+	4.23782i	0.0223835	+	0.155680i
$742$	−1.91567	−	1.23113i	−0.0703266	−	0.0451961i
$743$	−1.89603	+	4.15172i	−0.0695585	+	0.152312i	−0.941218	−	0.337801i	$-0.890317\pi$
$743$	−1.89603	+	4.15172i	−0.0695585	+	0.152312i	0.871659	+	0.490112i	$0.163044\pi$
$744$	12.8557	−	14.8362i	0.471312	−	0.543923i
$745$	2.57360	−	17.8998i	0.0942895	−	0.655798i
$746$	6.71404	+	14.7017i	0.245819	+	0.538268i
$747$	6.69310	+	1.96527i	0.244888	+	0.0719056i
$748$	19.3385	+	5.67829i	0.707085	+	0.207619i
$749$	−5.77034	−	12.6353i	−0.210844	−	0.461683i
$750$	0.832826	−	5.79243i	0.0304105	−	0.211510i
$751$	−17.0564	+	19.6841i	−0.622396	+	0.718283i	−0.976160	−	0.217052i	$-0.930356\pi$
$751$	−17.0564	+	19.6841i	−0.622396	+	0.718283i	0.353764	+	0.935335i	$0.384901\pi$
$752$	−1.30566	+	2.85900i	−0.0476126	+	0.104257i
$753$	24.7252	+	15.8899i	0.901036	+	0.579061i
$754$	−0.757350	−	5.26749i	−0.0275811	−	0.191831i
$755$	13.1493	−	8.45055i	0.478553	−	0.307547i
$756$	−1.09793	−	1.26708i	−0.0399313	−	0.0460832i
$757$	15.0549	−	4.42052i	0.547180	−	0.160667i	0.00355354	−	0.999994i	$-0.498869\pi$
$757$	15.0549	−	4.42052i	0.547180	−	0.160667i	0.543627	+	0.839327i	$0.317051\pi$
$758$	−16.7976			−0.610118
$759$	−15.4589	+	18.0151i	−0.561123	+	0.653907i
$760$	4.08290			0.148102
$761$	−9.87988	+	2.90099i	−0.358145	+	0.105161i	−0.455855	−	0.890054i	$-0.650666\pi$
$761$	−9.87988	+	2.90099i	−0.358145	+	0.105161i	0.0977098	+	0.995215i	$0.468848\pi$
$762$	−6.37084	−	7.35234i	−0.230791	−	0.266347i
$763$	2.44573	−	1.57178i	0.0885415	−	0.0569022i
$764$	−1.92029	−	13.3559i	−0.0694737	−	0.483200i
$765$	4.87089	+	3.13033i	0.176107	+	0.113177i
$766$	−2.63845	+	5.77741i	−0.0953312	+	0.208746i
$767$	29.7648	−	34.3505i	1.07475	−	1.24032i
$768$	0.577806	−	4.01873i	0.0208498	−	0.145014i
$769$	−0.634291	−	1.38890i	−0.0228731	−	0.0500851i	0.897851	−	0.440300i	$-0.145128\pi$
$769$	−0.634291	−	1.38890i	−0.0228731	−	0.0500851i	−0.920724	+	0.390215i	$0.872401\pi$
$770$	6.43920	+	1.89072i	0.232053	+	0.0681368i
$771$	5.34452	+	1.56929i	0.192478	+	0.0565167i
$772$	−11.7236	−	25.6710i	−0.421941	−	0.923921i
$773$	−5.18544	+	36.0655i	−0.186507	+	1.29719i	0.654458	+	0.756098i	$0.272897\pi$
$773$	−5.18544	+	36.0655i	−0.186507	+	1.29719i	−0.840965	+	0.541089i	$0.818012\pi$
$774$	−0.750977	+	0.866674i	−0.0269933	+	0.0311519i
$775$	2.66689	−	5.83968i	0.0957977	−	0.209768i
$776$	−23.4119	−	15.0459i	−0.840438	−	0.540117i
$777$	1.31701	+	9.16000i	0.0472474	+	0.328613i
$778$	−13.5083	+	8.68128i	−0.484297	+	0.311239i
$779$	−4.41212	−	5.09186i	−0.158081	−	0.182435i
$780$	20.0468	−	5.88628i	0.717791	−	0.210762i
$781$	−15.1297			−0.541383
$782$	−0.974227	−	6.55177i	−0.0348383	−	0.234291i
$783$	1.79022			0.0639771
$784$	−2.07644	+	0.609698i	−0.0741586	+	0.0217749i
$785$	14.0357	+	16.1981i	0.500957	+	0.578135i
$786$	−7.42545	+	4.77204i	−0.264857	+	0.170213i
$787$	0.365115	+	2.53943i	0.0130149	+	0.0905209i	0.995294	−	0.0969056i	$-0.0308945\pi$
$787$	0.365115	+	2.53943i	0.0130149	+	0.0905209i	−0.982279	+	0.187426i	$0.939985\pi$
$788$	0.0558661	+	0.0359030i	0.00199015	+	0.00127899i
$789$	0.418048	−	0.915398i	0.0148829	−	0.0325890i
$790$	0.625551	−	0.721925i	0.0222561	−	0.0256849i
$791$	−1.15906	+	8.06145i	−0.0412115	+	0.286632i
$792$	−4.29931	−	9.41418i	−0.152769	−	0.334518i
$793$	−16.0365	−	4.70875i	−0.569474	−	0.167213i
$794$	−3.49164	−	1.02524i	−0.123914	−	0.0363843i
$795$	3.96564	+	8.68355i	0.140647	+	0.307974i
$796$	2.62717	−	18.2724i	0.0931175	−	0.647647i
$797$	18.5225	−	21.3761i	0.656101	−	0.757181i	−0.326034	−	0.945358i	$-0.605712\pi$
$797$	18.5225	−	21.3761i	0.656101	−	0.757181i	0.982135	+	0.188177i	$0.0602579\pi$
$798$	0.193503	−	0.423713i	0.00684995	−	0.0149993i
$799$	−2.96730	−	1.90697i	−0.104975	−	0.0674636i
$800$	−0.526679	−	3.66313i	−0.0186209	−	0.129511i
$801$	−3.14880	+	2.02361i	−0.111257	+	0.0715007i
$802$	−9.61496	−	11.0963i	−0.339516	−	0.391822i
$803$	57.0743	−	16.7585i	2.01411	−	0.591396i
$804$	16.4258			0.579295
$805$	1.68164	+	11.3092i	0.0592702	+	0.398598i
$806$	27.9101			0.983093
$807$	−10.9761	+	3.22288i	−0.386377	+	0.113451i
$808$	13.5380	+	15.6237i	0.476264	+	0.549638i
$809$	−43.1053	+	27.7021i	−1.51550	+	0.973954i	−0.522920	+	0.852382i	$0.675157\pi$
$809$	−43.1053	+	27.7021i	−1.51550	+	0.973954i	−0.992583	+	0.121572i	$0.961206\pi$
$810$	−0.192952	−	1.34201i	−0.00677963	−	0.0471534i
$811$	30.7518	+	19.7630i	1.07984	+	0.693973i	0.954521	−	0.298143i	$-0.0963672\pi$
$811$	30.7518	+	19.7630i	1.07984	+	0.693973i	0.125322	+	0.992116i	$0.460004\pi$
$812$	1.24685	−	2.73021i	0.0437558	−	0.0958117i
$813$	3.78442	−	4.36745i	0.132725	−	0.153173i
$814$	−3.70733	+	25.7850i	−0.129942	+	0.903765i
$815$	−9.51859	−	20.8428i	−0.333422	−	0.730092i
$816$	−5.04293	−	1.48074i	−0.176538	−	0.0518362i
$817$	1.58476	+	0.465329i	0.0554439	+	0.0162798i
$818$	−5.38775	−	11.7975i	−0.188378	−	0.412491i
$819$	0.743893	−	5.17389i	0.0259937	−	0.180790i
$820$	−21.5310	+	24.8481i	−0.751896	+	0.867735i
$821$	−3.81874	+	8.36187i	−0.133275	+	0.291831i	−0.964490	−	0.264120i	$-0.914919\pi$
$821$	−3.81874	+	8.36187i	−0.133275	+	0.291831i	0.831215	+	0.555951i	$0.187646\pi$
$822$	−7.63973	−	4.90976i	−0.266466	−	0.171248i
$823$	3.36010	+	23.3700i	0.117126	+	0.814627i	0.960695	+	0.277607i	$0.0895412\pi$
$823$	3.36010	+	23.3700i	0.117126	+	0.814627i	−0.843569	+	0.537021i	$0.819550\pi$
$824$	2.67459	−	1.71886i	0.0931738	−	0.0598792i
$825$	−2.21637	−	2.55783i	−0.0771643	−	0.0890523i
$826$	−4.74479	+	1.39320i	−0.165092	+	0.0484755i
$827$	−6.54789			−0.227693			−0.113846	−	0.993498i	$-0.536317\pi$
$827$	−6.54789			−0.227693			−0.113846	+	0.993498i	$0.536317\pi$
$828$	5.23616	−	6.10198i	0.181969	−	0.212058i
$829$	19.9754			0.693774			0.346887	−	0.937907i	$-0.387239\pi$
$829$	19.9754			0.693774			0.346887	+	0.937907i	$0.387239\pi$
$830$	9.07457	−	2.66453i	0.314983	−	0.0924873i
$831$	−19.2611	−	22.2285i	−0.668160	−	0.771098i
$832$	−5.49739	+	3.53296i	−0.190588	+	0.122483i
$833$	−0.345632	−	2.40392i	−0.0119754	−	0.0832909i
$834$	4.36899	+	2.80778i	0.151286	+	0.0972256i
$835$	6.12582	−	13.4137i	0.211993	−	0.464200i
$836$	−4.45135	+	5.13713i	−0.153953	+	0.177671i
$837$	−1.33620	+	9.29347i	−0.0461858	+	0.321229i
$838$	4.36812	+	9.56485i	0.150894	+	0.330412i
$839$	33.3048	+	9.77918i	1.14981	+	0.337615i	0.800465	−	0.599379i	$-0.204586\pi$
$839$	33.3048	+	9.77918i	1.14981	+	0.337615i	0.349345	+	0.936994i	$0.386404\pi$
$840$	−4.78283	−	1.40436i	−0.165023	−	0.0484552i
$841$	−10.7157	−	23.4641i	−0.369506	−	0.809106i
$842$	−2.01490	+	14.0139i	−0.0694380	+	0.482952i
$843$	8.13247	−	9.38537i	0.280097	−	0.323249i
$844$	−16.0559	+	35.1575i	−0.552667	+	1.21017i
$845$	28.7253	+	18.4606i	0.988180	+	0.635065i
$846$	0.117544	+	0.817539i	0.00404126	+	0.0281076i
$847$	−11.3577	+	7.29918i	−0.390257	+	0.250803i
$848$	−5.67467	−	6.54892i	−0.194869	−	0.224891i
$849$	26.1775	−	7.68642i	0.898410	−	0.263797i
$850$	0.944380			0.0323920
$851$	−42.5231	+	12.7086i	−1.45767	+	0.435647i
$852$	5.12464			0.175567
$853$	−22.5154	+	6.61111i	−0.770912	+	0.226360i	−0.643455	−	0.765484i	$-0.722500\pi$
$853$	−22.5154	+	6.61111i	−0.770912	+	0.226360i	−0.127457	+	0.991844i	$0.540681\pi$
$854$	1.19080	+	1.37425i	0.0407483	+	0.0470260i
$855$	−1.64275	+	1.05573i	−0.0561807	+	0.0361052i
$856$	4.13328	+	28.7476i	0.141273	+	0.982572i
$857$	−30.9974	−	19.9208i	−1.05885	−	0.680482i	−0.109272	−	0.994012i	$-0.534852\pi$
$857$	−30.9974	−	19.9208i	−1.05885	−	0.680482i	−0.949578	+	0.313530i	$0.898488\pi$
$858$	6.11244	−	13.3844i	0.208675	−	0.456935i
$859$	24.4180	−	28.1798i	0.833130	−	0.961483i	−0.166569	−	0.986030i	$-0.553269\pi$
$859$	24.4180	−	28.1798i	0.833130	−	0.961483i	0.999699	+	0.0245464i	$0.00781415\pi$
$860$	1.14707	−	7.97806i	0.0391148	−	0.272049i
$861$	3.41708	+	7.48236i	0.116454	+	0.254998i
$862$	12.4311	+	3.65009i	0.423404	+	0.124323i
$863$	−49.7726	−	14.6146i	−1.69428	−	0.497485i	−0.714851	−	0.699276i	$-0.753506\pi$
$863$	−49.7726	−	14.6146i	−1.69428	−	0.497485i	−0.979429	+	0.201791i	$0.935324\pi$
$864$	2.24841	+	4.92333i	0.0764924	+	0.167495i
$865$	−3.21530	+	22.3629i	−0.109323	+	0.760360i
$866$	−2.61461	+	3.01742i	−0.0888481	+	0.102536i
$867$	−4.61181	+	10.0985i	−0.156625	+	0.342962i
$868$	13.2426	+	8.51050i	0.449483	+	0.288865i
$869$	0.496315	+	3.45195i	0.0168363	+	0.117099i
$870$	2.04188	−	1.31224i	0.0692263	−	0.0444891i
$871$	33.5360	+	38.7027i	1.13633	+	1.31139i
$872$	−5.83243	+	1.71256i	−0.197511	+	0.0579944i
$873$	13.3102			0.450482
$874$	2.14645	+	0.619043i	0.0726047	+	0.0209394i
$875$	10.2902			0.347872
$876$	−19.3319	+	5.67636i	−0.653164	+	0.191786i
$877$	−10.4452	−	12.0544i	−0.352710	−	0.407050i	0.551474	−	0.834192i	$-0.314066\pi$
$877$	−10.4452	−	12.0544i	−0.352710	−	0.407050i	−0.904184	+	0.427143i	$0.859520\pi$
$878$	9.91946	−	6.37485i	0.334765	−	0.215141i
$879$	0.413218	+	2.87400i	0.0139375	+	0.0969375i
$880$	21.4840	+	13.8069i	0.724224	+	0.465431i
$881$	0.276123	−	0.604625i	0.00930282	−	0.0203703i	−0.904924	−	0.425574i	$-0.860072\pi$
$881$	0.276123	−	0.604625i	0.00930282	−	0.0203703i	0.914226	+	0.405204i	$0.132799\pi$
$882$	−0.372417	+	0.429792i	−0.0125399	+	0.0144719i
$883$	6.98758	−	48.5997i	0.235151	−	1.63551i	−0.440119	−	0.897940i	$-0.645064\pi$
$883$	6.98758	−	48.5997i	0.235151	−	1.63551i	0.675270	−	0.737571i	$-0.264027\pi$
$884$	−8.84161	−	19.3604i	−0.297375	−	0.651161i
$885$	19.8909	+	5.84049i	0.668624	+	0.196326i
$886$	20.5497	+	6.03393i	0.690380	+	0.202714i
$887$	−3.70818	−	8.11979i	−0.124509	−	0.272636i	0.837105	−	0.547042i	$-0.184246\pi$
$887$	−3.70818	−	8.11979i	−0.124509	−	0.272636i	−0.961614	+	0.274406i	$0.911519\pi$
$888$	2.75368	−	19.1523i	0.0924076	−	0.642709i
$889$	11.2025	−	12.9284i	0.375721	−	0.433605i
$890$	−2.10814	+	4.61617i	−0.0706649	+	0.154734i
$891$	4.16408	+	2.67609i	0.139502	+	0.0896523i
$892$	−6.16474	−	42.8767i	−0.206411	−	1.43562i
$893$	1.00075	−	0.643140i	0.0334887	−	0.0215219i
$894$	2.82490	+	3.26011i	0.0944788	+	0.109034i
$895$	−41.8175	+	12.2787i	−1.39781	+	0.410433i
$896$	11.5358			0.385386
$897$	25.0680	−	0.120713i	0.836995	−	0.00403050i
$898$	14.7047			0.490703
$899$	−16.1276	+	4.73548i	−0.537884	+	0.157937i
$900$	0.750718	+	0.866375i	0.0250239	+	0.0288792i
$901$	8.18095	−	5.25758i	0.272547	−	0.175155i
$902$	3.29530	+	22.9193i	0.109722	+	0.763130i
$903$	−1.69638	−	1.09020i	−0.0564521	−	0.0362796i
$904$	7.07397	−	15.4898i	0.235277	−	0.515184i
$905$	35.4161	−	40.8724i	1.17727	−	1.35864i
$906$	−0.530627	+	3.69059i	−0.0176289	+	0.122612i
$907$	3.61369	+	7.91288i	0.119991	+	0.262743i	0.960091	−	0.279688i	$-0.0902312\pi$
$907$	3.61369	+	7.91288i	0.119991	+	0.262743i	−0.840100	+	0.542431i	$0.817504\pi$
$908$	36.8915	+	10.8323i	1.22429	+	0.359483i
$909$	−9.48683	−	2.78559i	−0.314658	−	0.0923920i
$910$	−2.94402	−	6.44651i	−0.0975934	−	0.213700i
$911$	0.428902	−	2.98308i	0.0142102	−	0.0988339i	−0.981482	−	0.191554i	$-0.938647\pi$
$911$	0.428902	−	2.98308i	0.0142102	−	0.0988339i	0.995692	+	0.0927204i	$0.0295563\pi$
$912$	1.16079	−	1.33962i	0.0384375	−	0.0443592i
$913$	−14.3436	+	31.4082i	−0.474706	+	1.03946i
$914$	12.4146	+	7.97840i	0.410639	+	0.263902i
$915$	−1.08487	−	7.54542i	−0.0358646	−	0.249444i
$916$	21.0946	−	13.5567i	0.696984	−	0.447925i
$917$	−10.1640	−	11.7299i	−0.335644	−	0.387354i
$918$	−1.32521	+	0.389118i	−0.0437386	+	0.0128428i
$919$	−0.905908			−0.0298832			−0.0149416	−	0.999888i	$-0.504756\pi$
$919$	−0.905908			−0.0298832			−0.0149416	+	0.999888i	$0.504756\pi$
$920$	3.28819	−	23.6788i	0.108409	−	0.780666i
$921$	27.2879			0.899166
$922$	3.92004	−	1.15103i	0.129100	−	0.0379070i
$923$	10.4628	+	12.0747i	0.344387	+	0.397444i
$924$	6.98142	−	4.48669i	0.229672	−	0.147601i
$925$	−0.900516	−	6.26323i	−0.0296088	−	0.205934i
$926$	0.656920	+	0.422177i	0.0215877	+	0.0138736i
$927$	−0.631666	+	1.38316i	−0.0207466	+	0.0454288i
$928$	−6.34523	+	7.32279i	−0.208293	+	0.240382i
$929$	−1.25809	+	8.75019i	−0.0412765	+	0.287084i	0.958720	+	0.284353i	$0.0917787\pi$
$929$	−1.25809	+	8.75019i	−0.0412765	+	0.287084i	−0.999996	+	0.00273181i	$0.999130\pi$
$930$	5.28812	+	11.5794i	0.173404	+	0.379703i
$931$	0.785900	+	0.230761i	0.0257568	+	0.00756289i
$932$	−30.8337	−	9.05360i	−1.00999	−	0.296560i
$933$	6.85772	+	15.0163i	0.224512	+	0.491612i
$934$	−1.28673	+	8.94942i	−0.0421032	+	0.292834i
$935$	−18.7682	+	21.6596i	−0.613785	+	0.708345i
$936$	−4.54012	+	9.94149i	−0.148399	+	0.324948i
$937$	−45.6696	−	29.3500i	−1.49196	−	0.958824i	−0.995893	−	0.0905396i	$-0.971141\pi$
$937$	−45.6696	−	29.3500i	−1.49196	−	0.958824i	−0.496067	−	0.868284i	$-0.665223\pi$
$938$	−0.792927	−	5.51493i	−0.0258900	−	0.180069i
$939$	−19.9326	+	12.8099i	−0.650477	+	0.418036i
$940$	−3.80157	−	4.38725i	−0.123994	−	0.143096i
$941$	55.5197	−	16.3021i	1.80989	−	0.531432i	0.811307	−	0.584620i	$-0.198756\pi$
$941$	55.5197	−	16.3021i	1.80989	−	0.531432i	0.998585	+	0.0531881i	$0.0169383\pi$
$942$	−5.11269			−0.166580
$943$	−33.0836	+	21.4873i	−1.07735	+	0.699724i
$944$	−18.8179			−0.612472
$945$	2.28749	−	0.671668i	0.0744121	−	0.0218494i
$946$	−3.71722	−	4.28990i	−0.120857	−	0.139477i
$947$	5.78625	−	3.71860i	0.188028	−	0.120838i	−0.443240	−	0.896403i	$-0.646171\pi$
$947$	5.78625	−	3.71860i	0.188028	−	0.120838i	0.631268	+	0.775565i	$0.282535\pi$
$948$	−0.168109	−	1.16922i	−0.00545993	−	0.0379746i
$949$	−52.8439	−	33.9607i	−1.71538	−	1.10241i
$950$	−0.132310	+	0.289717i	−0.00429269	+	0.00939968i
$951$	−15.0466	+	17.3646i	−0.487918	+	0.563087i
$952$	−0.722668	+	5.02626i	−0.0234218	+	0.162902i
$953$	−17.7510	−	38.8693i	−0.575011	−	1.25910i	−0.944086	−	0.329699i	$-0.893053\pi$
$953$	−17.7510	−	38.8693i	−0.575011	−	1.25910i	0.369075	−	0.929400i	$-0.379675\pi$
$954$	−2.18492	−	0.641551i	−0.0707395	−	0.0207710i
$955$	18.4099	+	5.40563i	0.595730	+	0.174922i
$956$	−12.9245	−	28.3008i	−0.418009	−	0.915313i
$957$	−1.26109	+	8.77110i	−0.0407654	+	0.283529i
$958$	3.23033	−	3.72800i	0.104367	−	0.120446i
$959$	6.63365	−	14.5257i	0.214212	−	0.469059i
$960$	−2.50734	−	1.61137i	−0.0809241	−	0.0520068i
$961$	−8.13386	−	56.5723i	−0.262383	−	1.82491i
$962$	23.1423	−	14.8727i	0.746138	−	0.479514i
$963$	−9.09638	−	10.4978i	−0.293127	−	0.338286i
$964$	−35.9559	+	10.5576i	−1.15806	+	0.340038i
$965$	40.1301			1.29183
$966$	−2.30149	−	1.46346i	−0.0740491	−	0.0470862i
$967$	27.8417			0.895330			0.447665	−	0.894201i	$-0.352256\pi$
$967$	27.8417			0.895330			0.447665	+	0.894201i	$0.352256\pi$
$968$	27.0852	−	7.95293i	0.870551	−	0.255617i
$969$	1.30268	+	1.50337i	0.0418481	+	0.0482953i
$970$	15.1813	−	9.75645i	0.487443	−	0.313261i
$971$	8.05664	+	56.0351i	0.258550	+	1.79825i	0.543180	+	0.839616i	$0.317220\pi$
$971$	8.05664	+	56.0351i	0.258550	+	1.79825i	−0.284631	+	0.958637i	$0.591871\pi$
$972$	−1.41043	−	0.906430i	−0.0452396	−	0.0290738i
$973$	−3.79364	+	8.30691i	−0.121619	+	0.266307i
$974$	−10.2737	+	11.8565i	−0.329190	+	0.379906i
$975$	−0.508643	+	3.53769i	−0.0162896	+	0.113297i
$976$	2.87454	+	6.29437i	0.0920118	+	0.201478i
$977$	−46.8181	−	13.7470i	−1.49784	−	0.439806i	−0.572808	−	0.819689i	$-0.694146\pi$
$977$	−46.8181	−	13.7470i	−1.49784	−	0.439806i	−0.925035	+	0.379883i	$0.875964\pi$
$978$	5.24439	+	1.53989i	0.167697	+	0.0492403i
$979$	−7.69647	−	16.8529i	−0.245980	−	0.538622i
$980$	0.568844	−	3.95640i	0.0181711	−	0.126383i
$981$	1.90384	−	2.19715i	0.0607851	−	0.0701497i
$982$	4.86747	−	10.6583i	0.155327	−	0.340119i
$983$	17.1100	+	10.9960i	0.545725	+	0.350716i	0.784274	−	0.620414i	$-0.213035\pi$
$983$	17.1100	+	10.9960i	0.545725	+	0.350716i	−0.238549	+	0.971130i	$0.576672\pi$
$984$	−2.44764	−	17.0237i	−0.0780280	−	0.542697i
$985$	−0.0794403	+	0.0510532i	−0.00253118	+	0.00162669i
$986$	−1.61919	−	1.86865i	−0.0515656	−	0.0595099i
$987$	−1.39352	+	0.409174i	−0.0443562	+	0.0130241i
$988$	7.17813			0.228367
$989$	3.97498	−	8.81608i	0.126397	−	0.280335i
$990$	6.71104			0.213291
$991$	23.5183	−	6.90559i	0.747083	−	0.219363i	0.114036	−	0.993477i	$-0.463622\pi$
$991$	23.5183	−	6.90559i	0.747083	−	0.219363i	0.633047	+	0.774113i	$0.281804\pi$
$992$	−33.2784	−	38.4054i	−1.05659	−	1.21937i
$993$	−11.0357	+	7.09224i	−0.350209	+	0.225065i
$994$	−0.247383	−	1.72058i	−0.00784650	−	0.0545736i
$995$	22.0830	+	14.1919i	0.700077	+	0.449912i
$996$	4.85840	−	10.6384i	0.153944	−	0.337091i
$997$	4.57334	−	5.27792i	0.144839	−	0.167153i	−0.678694	−	0.734421i	$-0.737454\pi$
$997$	4.57334	−	5.27792i	0.144839	−	0.167153i	0.823534	+	0.567267i	$0.191999\pi$
$998$	0.278258	−	1.93533i	0.00880811	−	0.0612617i
$999$	3.84433	+	8.41791i	0.121629	+	0.266331i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.q.f.400.4	yes	80
23.18	even	11	inner	483.2.q.f.64.4	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.q.f.64.4	✓	80	23.18	even	11	inner
483.2.q.f.400.4	yes	80	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.545660 + 0.160220i) q^{2} +(-0.654861 - 0.755750i) q^{3} +(-1.41043 + 0.906430i) q^{4} +(-0.339288 - 2.35980i) q^{5} +(0.478418 + 0.307461i) q^{6} +(-0.415415 + 0.909632i) q^{7} +(1.36922 - 1.58017i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})\)	\(q+(-0.545660 + 0.160220i) q^{2} +(-0.654861 - 0.755750i) q^{3} +(-1.41043 + 0.906430i) q^{4} +(-0.339288 - 2.35980i) q^{5} +(0.478418 + 0.307461i) q^{6} +(-0.415415 + 0.909632i) q^{7} +(1.36922 - 1.58017i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(0.563223 + 1.23329i) q^{10} +(-4.74934 - 1.39453i) q^{11} +(1.60867 + 0.472348i) q^{12} +(2.17141 + 4.75473i) q^{13} +(0.0809340 - 0.562908i) q^{14} +(-1.56123 + 1.80175i) q^{15} +(0.899001 - 1.96854i) q^{16} +(2.04310 + 1.31302i) q^{17} +(-0.0809340 - 0.562908i) q^{18} +(-0.689053 + 0.442827i) q^{19} +(2.61753 + 3.02079i) q^{20} +(0.959493 - 0.281733i) q^{21} +2.81496 q^{22} +(2.01324 + 4.35280i) q^{23} -2.09086 q^{24} +(-0.656061 + 0.192637i) q^{25} +(-1.94666 - 2.24656i) q^{26} +(0.841254 - 0.540641i) q^{27} +(-0.238603 - 1.65952i) q^{28} +(1.50603 + 0.967864i) q^{29} +(0.563223 - 1.23329i) q^{30} +(-6.14851 + 7.09576i) q^{31} +(-0.770270 + 5.35735i) q^{32} +(2.05624 + 4.50254i) q^{33} +(-1.32521 - 0.389118i) q^{34} +(2.28749 + 0.671668i) q^{35} +(-0.696478 - 1.52507i) q^{36} +(-1.31701 + 9.16000i) q^{37} +(0.305039 - 0.352034i) q^{38} +(2.17141 - 4.75473i) q^{39} +(-4.19343 - 2.69496i) q^{40} +(1.17064 + 8.14197i) q^{41} +(-0.478418 + 0.307461i) q^{42} +(-1.32052 - 1.52396i) q^{43} +(7.96267 - 2.33805i) q^{44} +2.38406 q^{45} +(-1.79595 - 2.05259i) q^{46} -1.45235 q^{47} +(-2.07644 + 0.609698i) q^{48} +(-0.654861 - 0.755750i) q^{49} +(0.327122 - 0.210229i) q^{50} +(-0.345632 - 2.40392i) q^{51} +(-7.37246 - 4.73800i) q^{52} +(1.66340 - 3.64233i) q^{53} +(-0.372417 + 0.429792i) q^{54} +(-1.67942 + 11.6806i) q^{55} +(0.868575 + 1.90191i) q^{56} +(0.785900 + 0.230761i) q^{57} +(-0.976850 - 0.286829i) q^{58} +(-3.61224 - 7.90970i) q^{59} +(0.568844 - 3.95640i) q^{60} +(-2.09391 + 2.41650i) q^{61} +(2.21811 - 4.85699i) q^{62} +(-0.841254 - 0.540641i) q^{63} +(0.177918 + 1.23744i) q^{64} +(10.4835 - 6.73732i) q^{65} +(-1.84341 - 2.12741i) q^{66} +(9.40036 - 2.76019i) q^{67} -4.07182 q^{68} +(1.97123 - 4.37198i) q^{69} -1.35581 q^{70} +(2.93278 - 0.861143i) q^{71} +(1.36922 + 1.58017i) q^{72} +(-10.1096 + 6.49705i) q^{73} +(-0.748979 - 5.20926i) q^{74} +(0.575214 + 0.369668i) q^{75} +(0.570471 - 1.24916i) q^{76} +(3.24146 - 3.74084i) q^{77} +(-0.423050 + 2.94237i) q^{78} +(-0.292683 - 0.640887i) q^{79} +(-4.95037 - 1.45356i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(-1.94328 - 4.25519i) q^{82} +(0.992741 - 6.90467i) q^{83} +(-1.09793 + 1.26708i) q^{84} +(2.40527 - 5.26680i) q^{85} +(0.964727 + 0.619993i) q^{86} +(-0.254774 - 1.77199i) q^{87} +(-8.70650 + 5.59533i) q^{88} +(2.45113 + 2.82876i) q^{89} +(-1.30089 + 0.381975i) q^{90} -5.22710 q^{91} +(-6.78505 - 4.31446i) q^{92} +9.38904 q^{93} +(0.792489 - 0.232696i) q^{94} +(1.27877 + 1.47578i) q^{95} +(4.55323 - 2.92619i) q^{96} +(-1.89424 - 13.1747i) q^{97} +(0.478418 + 0.307461i) q^{98} +(2.05624 - 4.50254i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + q^{2} - 8 q^{3} - 9 q^{4} + 13 q^{5} + q^{6} + 8 q^{7} - 25 q^{8} - 8 q^{9}+O(q^{10}) \) 80 * q + q^2 - 8 * q^3 - 9 * q^4 + 13 * q^5 + q^6 + 8 * q^7 - 25 * q^8 - 8 * q^9	\( 80 q + q^{2} - 8 q^{3} - 9 q^{4} + 13 q^{5} + q^{6} + 8 q^{7} - 25 q^{8} - 8 q^{9} + 4 q^{10} + q^{11} - 9 q^{12} - 26 q^{13} - q^{14} + 2 q^{15} - 3 q^{16} - 23 q^{17} + q^{18} + 10 q^{19} + 63 q^{20} + 8 q^{21} - 9 q^{23} + 30 q^{24} - 29 q^{25} - 12 q^{26} - 8 q^{27} + 20 q^{28} + 13 q^{29} + 4 q^{30} - 27 q^{31} + 71 q^{32} + q^{33} - 45 q^{34} - 2 q^{35} - 9 q^{36} + 60 q^{37} - 2 q^{38} - 26 q^{39} + 7 q^{40} - 26 q^{41} - q^{42} + 5 q^{43} - 33 q^{44} - 20 q^{45} - 41 q^{46} + 34 q^{47} - 58 q^{48} - 8 q^{49} - 75 q^{50} - q^{51} + 108 q^{52} - 39 q^{53} - 10 q^{54} + 51 q^{55} + 3 q^{56} + 10 q^{57} + 47 q^{58} - 66 q^{59} + 19 q^{60} + 3 q^{61} + 103 q^{62} + 8 q^{63} - 25 q^{64} + 39 q^{65} - 33 q^{66} + 33 q^{67} - 88 q^{68} + 13 q^{69} + 18 q^{70} - 12 q^{71} - 25 q^{72} - 98 q^{73} + 123 q^{74} + 4 q^{75} - 41 q^{76} - 12 q^{77} + 10 q^{78} - 34 q^{79} + 163 q^{80} - 8 q^{81} + 48 q^{82} + 26 q^{83} + 9 q^{84} + 35 q^{85} + 4 q^{86} + 2 q^{87} + 178 q^{88} - 63 q^{89} + 4 q^{90} - 62 q^{91} - 39 q^{92} + 138 q^{93} - 28 q^{94} - 80 q^{95} - 17 q^{96} - 44 q^{97} + q^{98} + q^{99}+O(q^{100}) \) 80 * q + q^2 - 8 * q^3 - 9 * q^4 + 13 * q^5 + q^6 + 8 * q^7 - 25 * q^8 - 8 * q^9 + 4 * q^10 + q^11 - 9 * q^12 - 26 * q^13 - q^14 + 2 * q^15 - 3 * q^16 - 23 * q^17 + q^18 + 10 * q^19 + 63 * q^20 + 8 * q^21 - 9 * q^23 + 30 * q^24 - 29 * q^25 - 12 * q^26 - 8 * q^27 + 20 * q^28 + 13 * q^29 + 4 * q^30 - 27 * q^31 + 71 * q^32 + q^33 - 45 * q^34 - 2 * q^35 - 9 * q^36 + 60 * q^37 - 2 * q^38 - 26 * q^39 + 7 * q^40 - 26 * q^41 - q^42 + 5 * q^43 - 33 * q^44 - 20 * q^45 - 41 * q^46 + 34 * q^47 - 58 * q^48 - 8 * q^49 - 75 * q^50 - q^51 + 108 * q^52 - 39 * q^53 - 10 * q^54 + 51 * q^55 + 3 * q^56 + 10 * q^57 + 47 * q^58 - 66 * q^59 + 19 * q^60 + 3 * q^61 + 103 * q^62 + 8 * q^63 - 25 * q^64 + 39 * q^65 - 33 * q^66 + 33 * q^67 - 88 * q^68 + 13 * q^69 + 18 * q^70 - 12 * q^71 - 25 * q^72 - 98 * q^73 + 123 * q^74 + 4 * q^75 - 41 * q^76 - 12 * q^77 + 10 * q^78 - 34 * q^79 + 163 * q^80 - 8 * q^81 + 48 * q^82 + 26 * q^83 + 9 * q^84 + 35 * q^85 + 4 * q^86 + 2 * q^87 + 178 * q^88 - 63 * q^89 + 4 * q^90 - 62 * q^91 - 39 * q^92 + 138 * q^93 - 28 * q^94 - 80 * q^95 - 17 * q^96 - 44 * q^97 + q^98 + q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more