LMFDB - Embedded newform 125.2.g.a.11.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [125,2,Mod(6,125)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(125, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("125.6");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 125 = 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	125.g (of order $25$, degree $20$, 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:	$0.998130025266$
Analytic rank:	$0$
Dimension:	$220$
Relative dimension:	$11$ over $\Q(\zeta_{25})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{25}]$

Embedding invariants

Embedding label			11.7
Character	$\chi$	$=$	125.11
Dual form			125.2.g.a.91.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.436521 - 0.409921i) q^{2} +(1.22515 + 1.93053i) q^{3} +(-0.103065 + 1.63818i) q^{4} +(-1.37573 - 1.76278i) q^{5} +(1.32617 + 0.340503i) q^{6} +(0.159126 - 0.489740i) q^{7} +(1.38994 + 1.68015i) q^{8} +(-0.948615 + 2.01591i) q^{9} +O(q^{10})$	\(q+(0.436521 - 0.409921i) q^{2} +(1.22515 + 1.93053i) q^{3} +(-0.103065 + 1.63818i) q^{4} +(-1.37573 - 1.76278i) q^{5} +(1.32617 + 0.340503i) q^{6} +(0.159126 - 0.489740i) q^{7} +(1.38994 + 1.68015i) q^{8} +(-0.948615 + 2.01591i) q^{9} +(-1.32313 - 0.205550i) q^{10} +(0.488159 - 0.458412i) q^{11} +(-3.28882 + 1.80804i) q^{12} +(0.0974761 - 0.207147i) q^{13} +(-0.131293 - 0.279011i) q^{14} +(1.71762 - 4.81555i) q^{15} +(-1.96148 - 0.247792i) q^{16} +(-0.226633 - 3.60222i) q^{17} +(0.412273 + 1.26884i) q^{18} +(0.478528 - 0.754039i) q^{19} +(3.02952 - 2.07200i) q^{20} +(1.14041 - 0.292808i) q^{21} +(0.0251793 - 0.400214i) q^{22} +(1.47421 - 7.72809i) q^{23} +(-1.54069 + 4.74175i) q^{24} +(-1.21475 + 4.85019i) q^{25} +(-0.0423636 - 0.130382i) q^{26} +(1.75135 - 0.221247i) q^{27} +(0.785879 + 0.311152i) q^{28} +(-4.83511 - 1.91435i) q^{29} +(-1.22422 - 2.80618i) q^{30} +(0.338845 + 5.38579i) q^{31} +(-4.48601 + 3.25928i) q^{32} +(1.48305 + 0.380782i) q^{33} +(-1.57556 - 1.47955i) q^{34} +(-1.08222 + 0.393244i) q^{35} +(-3.20464 - 1.76177i) q^{36} +(-11.2304 - 1.41873i) q^{37} +(-0.100209 - 0.525313i) q^{38} +(0.519327 - 0.0656063i) q^{39} +(1.04955 - 4.76157i) q^{40} +(2.27631 + 11.9328i) q^{41} +(0.377786 - 0.595296i) q^{42} +(-1.81640 - 1.31969i) q^{43} +(0.700647 + 0.846937i) q^{44} +(4.85863 - 1.10114i) q^{45} +(-2.52438 - 3.97779i) q^{46} +(0.532079 - 0.643173i) q^{47} +(-1.92474 - 4.09028i) q^{48} +(5.44859 + 3.95864i) q^{49} +(1.45793 + 2.61517i) q^{50} +(6.67654 - 4.85079i) q^{51} +(0.329297 + 0.181033i) q^{52} +(10.1404 - 2.60362i) q^{53} +(0.673808 - 0.814494i) q^{54} +(-1.47965 - 0.229866i) q^{55} +(1.04401 - 0.413353i) q^{56} +2.04197 q^{57} +(-2.89536 + 1.14635i) q^{58} +(-5.28955 + 2.90796i) q^{59} +(7.71169 + 3.31008i) q^{60} +(-1.99636 + 10.4653i) q^{61} +(2.35566 + 2.21211i) q^{62} +(0.836322 + 0.785359i) q^{63} +(0.118737 - 0.622443i) q^{64} +(-0.499254 + 0.113149i) q^{65} +(0.803473 - 0.441713i) q^{66} +(4.36929 - 1.72992i) q^{67} +5.92443 q^{68} +(16.7255 - 6.62208i) q^{69} +(-0.311211 + 0.615282i) q^{70} +(0.203437 - 0.245913i) q^{71} +(-4.70554 + 1.20818i) q^{72} +(-7.96721 - 4.38001i) q^{73} +(-5.48390 + 3.98428i) q^{74} +(-10.8517 + 3.59711i) q^{75} +(1.18593 + 0.861627i) q^{76} +(-0.146824 - 0.312017i) q^{77} +(0.199804 - 0.241522i) q^{78} +(-6.06918 - 9.56349i) q^{79} +(2.26166 + 3.79854i) q^{80} +(6.83324 + 8.25997i) q^{81} +(5.88517 + 4.27582i) q^{82} +(-3.91097 + 6.16271i) q^{83} +(0.362134 + 1.89837i) q^{84} +(-6.03812 + 5.35517i) q^{85} +(-1.33387 + 0.168507i) q^{86} +(-2.22802 - 11.6797i) q^{87} +(1.44871 + 0.183015i) q^{88} +(-5.66187 - 3.11264i) q^{89} +(1.66951 - 2.47233i) q^{90} +(-0.0859372 - 0.0807004i) q^{91} +(12.5080 + 3.21152i) q^{92} +(-9.98230 + 7.25257i) q^{93} +(-0.0313862 - 0.498869i) q^{94} +(-1.98752 + 0.193815i) q^{95} +(-11.7882 - 4.66727i) q^{96} +(5.01593 + 1.98595i) q^{97} +(4.00116 - 0.505463i) q^{98} +(0.461042 + 1.41894i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 220 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 15 q^{5} - 20 q^{6} - 15 q^{7} - 5 q^{8} - 20 q^{9}+O(q^{10}) $ 220 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 15 * q^5 - 20 * q^6 - 15 * q^7 - 5 * q^8 - 20 * q^9	\( 220 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 15 q^{5} - 20 q^{6} - 15 q^{7} - 5 q^{8} - 20 q^{9} - 20 q^{10} - 15 q^{11} - 100 q^{12} - 20 q^{13} - 10 q^{14} - 15 q^{17} + 10 q^{18} - 10 q^{19} + 5 q^{20} - 5 q^{21} + 25 q^{22} - 90 q^{23} + 15 q^{24} - 45 q^{25} + 15 q^{26} + 10 q^{27} + 30 q^{28} - 10 q^{29} + 40 q^{30} - 10 q^{31} + 20 q^{32} + 15 q^{33} + 5 q^{34} + 10 q^{35} - 210 q^{36} + 20 q^{37} + 30 q^{38} + 45 q^{40} - 5 q^{41} + 70 q^{42} + 25 q^{43} + 15 q^{44} - 100 q^{45} - 100 q^{47} + 105 q^{48} - 20 q^{49} + 60 q^{50} + 25 q^{51} + 85 q^{52} + 20 q^{53} + 60 q^{54} + 15 q^{55} - 105 q^{56} + 40 q^{57} - 225 q^{58} + 5 q^{59} - 35 q^{60} + 65 q^{62} + 85 q^{63} + 45 q^{64} + 45 q^{65} + 55 q^{66} - 105 q^{67} + 80 q^{68} + 40 q^{69} + 95 q^{70} - 85 q^{71} + 160 q^{72} + 40 q^{73} + 35 q^{74} + 55 q^{75} + 35 q^{76} + 75 q^{77} - 10 q^{78} - 330 q^{80} + 55 q^{81} - 95 q^{82} + 50 q^{83} + 115 q^{84} + 85 q^{85} + 40 q^{86} + 95 q^{87} + 165 q^{88} + 55 q^{89} + 170 q^{90} - 105 q^{91} + 155 q^{92} - 185 q^{93} + 60 q^{94} + 30 q^{95} + 135 q^{96} + 65 q^{97} + 135 q^{98} + 45 q^{99}+O(q^{100}) \) 220 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 15 * q^5 - 20 * q^6 - 15 * q^7 - 5 * q^8 - 20 * q^9 - 20 * q^10 - 15 * q^11 - 100 * q^12 - 20 * q^13 - 10 * q^14 - 15 * q^17 + 10 * q^18 - 10 * q^19 + 5 * q^20 - 5 * q^21 + 25 * q^22 - 90 * q^23 + 15 * q^24 - 45 * q^25 + 15 * q^26 + 10 * q^27 + 30 * q^28 - 10 * q^29 + 40 * q^30 - 10 * q^31 + 20 * q^32 + 15 * q^33 + 5 * q^34 + 10 * q^35 - 210 * q^36 + 20 * q^37 + 30 * q^38 + 45 * q^40 - 5 * q^41 + 70 * q^42 + 25 * q^43 + 15 * q^44 - 100 * q^45 - 100 * q^47 + 105 * q^48 - 20 * q^49 + 60 * q^50 + 25 * q^51 + 85 * q^52 + 20 * q^53 + 60 * q^54 + 15 * q^55 - 105 * q^56 + 40 * q^57 - 225 * q^58 + 5 * q^59 - 35 * q^60 + 65 * q^62 + 85 * q^63 + 45 * q^64 + 45 * q^65 + 55 * q^66 - 105 * q^67 + 80 * q^68 + 40 * q^69 + 95 * q^70 - 85 * q^71 + 160 * q^72 + 40 * q^73 + 35 * q^74 + 55 * q^75 + 35 * q^76 + 75 * q^77 - 10 * q^78 - 330 * q^80 + 55 * q^81 - 95 * q^82 + 50 * q^83 + 115 * q^84 + 85 * q^85 + 40 * q^86 + 95 * q^87 + 165 * q^88 + 55 * q^89 + 170 * q^90 - 105 * q^91 + 155 * q^92 - 185 * q^93 + 60 * q^94 + 30 * q^95 + 135 * q^96 + 65 * q^97 + 135 * q^98 + 45 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/125\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{19}{25}\right)$

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 $

$2$	0.436521	−	0.409921i	0.308667	−	0.289858i	−0.514696	−	0.857373i	$-0.672095\pi$
$2$	0.436521	−	0.409921i	0.308667	−	0.289858i	0.823363	+	0.567515i	$0.192095\pi$
$3$	1.22515	+	1.93053i	0.707342	+	1.11459i	0.987950	+	0.154770i	$0.0494638\pi$
$3$	1.22515	+	1.93053i	0.707342	+	1.11459i	−0.280608	+	0.959822i	$0.590536\pi$
$4$	−0.103065	+	1.63818i	−0.0515326	+	0.819088i
$5$	−1.37573	−	1.76278i	−0.615244	−	0.788337i
$5$	−1.37573	−	1.76278i	−0.615244	−	0.788337i
$6$	1.32617	+	0.340503i	0.541407	+	0.139010i
$7$	0.159126	−	0.489740i	0.0601440	−	0.185104i	−0.916470	−	0.400102i	$-0.868975\pi$
$7$	0.159126	−	0.489740i	0.0601440	−	0.185104i	0.976614	+	0.214998i	$0.0689745\pi$
$8$	1.38994	+	1.68015i	0.491417	+	0.594021i
$9$	−0.948615	+	2.01591i	−0.316205	+	0.671970i
$10$	−1.32313	−	0.205550i	−0.418411	−	0.0650007i
$11$	0.488159	−	0.458412i	0.147186	−	0.138217i	−0.607457	−	0.794353i	$-0.707810\pi$
$11$	0.488159	−	0.458412i	0.147186	−	0.138217i	0.754643	+	0.656136i	$0.227810\pi$
$12$	−3.28882	+	1.80804i	−0.949400	+	0.521937i
$13$	0.0974761	−	0.207147i	0.0270350	−	0.0574523i	−0.890853	−	0.454291i	$-0.849893\pi$
$13$	0.0974761	−	0.207147i	0.0270350	−	0.0574523i	0.917888	+	0.396839i	$0.129893\pi$
$14$	−0.131293	−	0.279011i	−0.0350894	−	0.0745688i
$15$	1.71762	−	4.81555i	0.443487	−	1.24337i
$16$	−1.96148	−	0.247792i	−0.490370	−	0.0619481i
$17$	−0.226633	−	3.60222i	−0.0549665	−	0.873667i	−0.924831	−	0.380377i	$-0.875794\pi$
$17$	−0.226633	−	3.60222i	−0.0549665	−	0.873667i	0.869865	−	0.493290i	$-0.164206\pi$
$18$	0.412273	+	1.26884i	0.0971736	+	0.299070i
$19$	0.478528	−	0.754039i	0.109782	−	0.172988i	−0.784995	−	0.619502i	$-0.787335\pi$
$19$	0.478528	−	0.754039i	0.109782	−	0.172988i	0.894777	+	0.446514i	$0.147335\pi$
$20$	3.02952	−	2.07200i	0.677422	−	0.463313i
$21$	1.14041	−	0.292808i	0.248858	−	0.0638959i
$22$	0.0251793	−	0.400214i	0.00536824	−	0.0853258i
$23$	1.47421	−	7.72809i	0.307394	−	1.61142i	−0.408193	−	0.912896i	$-0.633841\pi$
$23$	1.47421	−	7.72809i	0.307394	−	1.61142i	0.715588	−	0.698523i	$-0.246159\pi$
$24$	−1.54069	+	4.74175i	−0.314492	+	0.967906i
$25$	−1.21475	+	4.85019i	−0.242951	+	0.970039i
$26$	−0.0423636	−	0.130382i	−0.00830818	−	0.0255699i
$27$	1.75135	−	0.221247i	0.337047	−	0.0425790i
$28$	0.785879	+	0.311152i	0.148517	+	0.0588021i
$29$	−4.83511	−	1.91435i	−0.897857	−	0.355487i	−0.126557	−	0.991959i	$-0.540393\pi$
$29$	−4.83511	−	1.91435i	−0.897857	−	0.355487i	−0.771299	+	0.636473i	$0.780393\pi$
$30$	−1.22422	−	2.80618i	−0.223511	−	0.512336i
$31$	0.338845	+	5.38579i	0.0608584	+	0.967317i	0.903431	+	0.428734i	$0.141040\pi$
$31$	0.338845	+	5.38579i	0.0608584	+	0.967317i	−0.842572	+	0.538583i	$0.818960\pi$
$32$	−4.48601	+	3.25928i	−0.793022	+	0.576164i
$33$	1.48305	+	0.380782i	0.258166	+	0.0662857i
$34$	−1.57556	−	1.47955i	−0.270206	−	0.253740i
$35$	−1.08222	+	0.393244i	−0.182928	+	0.0664704i
$36$	−3.20464	−	1.76177i	−0.534107	−	0.293628i
$37$	−11.2304	−	1.41873i	−1.84627	−	0.233239i	−0.877219	−	0.480090i	$-0.840604\pi$
$37$	−11.2304	−	1.41873i	−1.84627	−	0.233239i	−0.969053	+	0.246851i	$0.920604\pi$
$38$	−0.100209	−	0.525313i	−0.0162560	−	0.0852170i
$39$	0.519327	−	0.0656063i	0.0831589	−	0.0105054i
$40$	1.04955	−	4.76157i	0.165948	−	0.752870i
$41$	2.27631	+	11.9328i	0.355499	+	1.86359i	0.488626	+	0.872494i	$0.337498\pi$
$41$	2.27631	+	11.9328i	0.355499	+	1.86359i	−0.133126	+	0.991099i	$0.542502\pi$
$42$	0.377786	−	0.595296i	0.0582937	−	0.0918561i
$43$	−1.81640	−	1.31969i	−0.276999	−	0.201251i	0.440609	−	0.897699i	$-0.354763\pi$
$43$	−1.81640	−	1.31969i	−0.276999	−	0.201251i	−0.717607	+	0.696448i	$0.754763\pi$
$44$	0.700647	+	0.846937i	0.105627	+	0.127681i
$45$	4.85863	−	1.10114i	0.724282	−	0.164149i
$46$	−2.52438	−	3.97779i	−0.372200	−	0.586493i
$47$	0.532079	−	0.643173i	0.0776116	−	0.0938164i	−0.730278	−	0.683150i	$-0.760610\pi$
$47$	0.532079	−	0.643173i	0.0776116	−	0.0938164i	0.807890	+	0.589333i	$0.200610\pi$
$48$	−1.92474	−	4.09028i	−0.277812	−	0.590381i
$49$	5.44859	+	3.95864i	0.778371	+	0.565519i
$50$	1.45793	+	2.61517i	0.206182	+	0.369840i
$51$	6.67654	−	4.85079i	0.934903	−	0.679247i
$52$	0.329297	+	0.181033i	0.0456653	+	0.0251047i
$53$	10.1404	−	2.60362i	1.39289	−	0.357634i	0.523614	−	0.851956i	$-0.324584\pi$
$53$	10.1404	−	2.60362i	1.39289	−	0.357634i	0.869279	+	0.494322i	$0.164584\pi$
$54$	0.673808	−	0.814494i	0.0916936	−	0.110839i
$55$	−1.47965	−	0.229866i	−0.199516	−	0.0309951i
$56$	1.04401	−	0.413353i	0.139512	−	0.0552366i
$57$	2.04197			0.270465
$58$	−2.89536	+	1.14635i	−0.380179	+	0.150524i
$59$	−5.28955	+	2.90796i	−0.688641	+	0.378584i	−0.787327	−	0.616535i	$-0.788536\pi$
$59$	−5.28955	+	2.90796i	−0.688641	+	0.378584i	0.0986866	+	0.995119i	$0.468536\pi$
$60$	7.71169	+	3.31008i	0.995575	+	0.427329i
$61$	−1.99636	+	10.4653i	−0.255608	+	1.33994i	0.590545	+	0.807005i	$0.298913\pi$
$61$	−1.99636	+	10.4653i	−0.255608	+	1.33994i	−0.846153	+	0.532940i	$0.821087\pi$
$62$	2.35566	+	2.21211i	0.299169	+	0.280939i
$63$	0.836322	+	0.785359i	0.105367	+	0.0989459i
$64$	0.118737	−	0.622443i	0.0148422	−	0.0778053i
$65$	−0.499254	+	0.113149i	−0.0619249	+	0.0140345i
$66$	0.803473	−	0.441713i	0.0989007	−	0.0543711i
$67$	4.36929	−	1.72992i	0.533794	−	0.211344i	−0.0857350	−	0.996318i	$-0.527324\pi$
$67$	4.36929	−	1.72992i	0.533794	−	0.211344i	0.619528	+	0.784974i	$0.287324\pi$
$68$	5.92443			0.718442
$69$	16.7255	−	6.62208i	2.01351	−	0.797204i
$70$	−0.311211	+	0.615282i	−0.0371968	+	0.0735403i
$71$	0.203437	−	0.245913i	0.0241435	−	0.0291845i	−0.758303	−	0.651902i	$-0.773971\pi$
$71$	0.203437	−	0.245913i	0.0241435	−	0.0291845i	0.782447	+	0.622717i	$0.213971\pi$
$72$	−4.70554	+	1.20818i	−0.554553	+	0.142385i
$73$	−7.96721	−	4.38001i	−0.932492	−	0.512642i	−0.0583411	−	0.998297i	$-0.518581\pi$
$73$	−7.96721	−	4.38001i	−0.932492	−	0.512642i	−0.874150	+	0.485655i	$0.838581\pi$
$74$	−5.48390	+	3.98428i	−0.637490	+	0.463164i
$75$	−10.8517	+	3.59711i	−1.25305	+	0.415358i
$76$	1.18593	+	0.861627i	0.136035	+	0.0988354i
$77$	−0.146824	−	0.312017i	−0.0167321	−	0.0355576i
$78$	0.199804	−	0.241522i	0.0226234	−	0.0273469i
$79$	−6.06918	−	9.56349i	−0.682836	−	1.07598i	−0.992154	−	0.125019i	$-0.960101\pi$
$79$	−6.06918	−	9.56349i	−0.682836	−	1.07598i	0.309319	−	0.950958i	$-0.399899\pi$
$80$	2.26166	+	3.79854i	0.252861	+	0.424690i
$81$	6.83324	+	8.25997i	0.759249	+	0.917774i
$82$	5.88517	+	4.27582i	0.649908	+	0.472186i
$83$	−3.91097	+	6.16271i	−0.429285	+	0.676445i	−0.988267	−	0.152735i	$-0.951192\pi$
$83$	−3.91097	+	6.16271i	−0.429285	+	0.676445i	0.558982	+	0.829180i	$0.311192\pi$
$84$	0.362134	+	1.89837i	0.0395121	+	0.207129i
$85$	−6.03812	+	5.35517i	−0.654926	+	0.580850i
$86$	−1.33387	+	0.168507i	−0.143835	+	0.0181706i
$87$	−2.22802	−	11.6797i	−0.238869	−	1.25220i
$88$	1.44871	+	0.183015i	0.154433	+	0.0195094i
$89$	−5.66187	−	3.11264i	−0.600157	−	0.329939i	0.152549	−	0.988296i	$-0.451252\pi$
$89$	−5.66187	−	3.11264i	−0.600157	−	0.329939i	−0.752706	+	0.658357i	$0.771252\pi$
$90$	1.66951	−	2.47233i	0.175982	−	0.260606i
$91$	−0.0859372	−	0.0807004i	−0.00900867	−	0.00845970i
$92$	12.5080	+	3.21152i	1.30405	+	0.334824i
$93$	−9.98230	+	7.25257i	−1.03512	+	0.752056i
$94$	−0.0313862	−	0.498869i	−0.00323724	−	0.0514544i
$95$	−1.98752	+	0.193815i	−0.203916	+	0.0198850i
$96$	−11.7882	−	4.66727i	−1.20313	−	0.476352i
$97$	5.01593	+	1.98595i	0.509291	+	0.201643i	0.608695	−	0.793405i	$-0.291693\pi$
$97$	5.01593	+	1.98595i	0.509291	+	0.201643i	−0.0994036	+	0.995047i	$0.531693\pi$
$98$	4.00116	−	0.505463i	0.404178	−	0.0510595i
$99$	0.461042	+	1.41894i	0.0463365	+	0.142609i
$100$	−7.82027	−	2.48987i	−0.782027	−	0.248987i
$101$	4.99747	−	15.3806i	0.497267	−	1.53043i	−0.316127	−	0.948717i	$-0.602383\pi$
$101$	4.99747	−	15.3806i	0.497267	−	1.53043i	0.813394	−	0.581713i	$-0.197617\pi$
$102$	0.926013	−	4.85433i	0.0916889	−	0.480650i
$103$	−0.645944	+	10.2670i	−0.0636468	+	1.01164i	0.828528	+	0.559947i	$0.189179\pi$
$103$	−0.645944	+	10.2670i	−0.0636468	+	1.01164i	−0.892175	+	0.451690i	$0.850821\pi$
$104$	0.483523	−	0.124148i	0.0474133	−	0.0121737i
$105$	−2.08505	−	1.60747i	−0.203480	−	0.156873i
$106$	3.35923	−	5.29330i	0.326277	−	0.514131i
$107$	1.57150	+	4.83658i	0.151923	+	0.467570i	0.997836	−	0.0657502i	$-0.0209440\pi$
$107$	1.57150	+	4.83658i	0.151923	+	0.467570i	−0.845913	+	0.533320i	$0.820944\pi$
$108$	0.181938	+	2.89182i	0.0175070	+	0.278265i
$109$	8.64295	+	1.09186i	0.827844	+	0.104581i	0.527826	−	0.849352i	$-0.323007\pi$
$109$	8.64295	+	1.09186i	0.827844	+	0.104581i	0.300018	+	0.953934i	$0.403007\pi$
$110$	−0.740126	+	0.506199i	−0.0705683	+	0.0482642i
$111$	−11.0201	−	23.4189i	−1.04598	−	2.22282i
$112$	−0.433476	+	0.921184i	−0.0409596	+	0.0870437i
$113$	4.48721	−	2.46687i	0.422121	−	0.232063i	−0.256511	−	0.966541i	$-0.582573\pi$
$113$	4.48721	−	2.46687i	0.422121	−	0.232063i	0.678632	+	0.734478i	$0.262573\pi$
$114$	0.891362	−	0.837044i	0.0834837	−	0.0783964i
$115$	−15.6510	+	8.03303i	−1.45946	+	0.749084i
$116$	3.63438	−	7.72345i	0.337443	−	0.717104i
$117$	0.325123	+	0.393006i	0.0300576	+	0.0363334i
$118$	−1.11697	+	3.43768i	−0.102825	+	0.316464i
$119$	−1.80021	−	0.462217i	−0.165025	−	0.0423713i
$120$	10.4782	−	3.80747i	0.956525	−	0.347572i
$121$	−0.662538	+	10.5307i	−0.0602307	+	0.957340i
$122$	3.41849	+	5.38668i	0.309496	+	0.487687i
$123$	−20.2479	+	19.0140i	−1.82569	+	1.71443i
$124$	−8.85779			−0.795453
$125$	10.2210	−	4.53120i	0.914191	−	0.405283i
$126$	0.687007			0.0612035
$127$	10.4538	−	9.81673i	0.927621	−	0.871094i	−0.0643025	−	0.997930i	$-0.520482\pi$
$127$	10.4538	−	9.81673i	0.927621	−	0.871094i	0.991924	+	0.126836i	$0.0404823\pi$
$128$	−6.14566	−	9.68401i	−0.543204	−	0.855953i
$129$	0.322340	−	5.12345i	0.0283805	−	0.451094i
$130$	−0.171553	+	0.254047i	−0.0150462	+	0.0222814i
$131$	−17.2729	−	4.43492i	−1.50914	−	0.387481i	−0.598648	−	0.801012i	$-0.704295\pi$
$131$	−17.2729	−	4.43492i	−1.50914	−	0.387481i	−0.910490	+	0.413532i	$0.864295\pi$
$132$	−0.776639	+	2.39025i	−0.0675977	+	0.208044i
$133$	−0.293137	−	0.354341i	−0.0254182	−	0.0307253i
$134$	1.19816	−	2.54621i	0.103505	−	0.219959i
$135$	−2.79939	−	2.78286i	−0.240933	−	0.239510i
$136$	5.73725	−	5.38764i	0.491965	−	0.461986i
$137$	−2.97143	+	1.63356i	−0.253866	+	0.139564i	−0.603606	−	0.797283i	$-0.706270\pi$
$137$	−2.97143	+	1.63356i	−0.253866	+	0.139564i	0.349740	+	0.936847i	$0.386270\pi$
$138$	4.58649	−	9.74679i	0.390428	−	0.829702i
$139$	−0.937759	−	1.99284i	−0.0795397	−	0.169030i	0.861101	−	0.508433i	$-0.169775\pi$
$139$	−0.937759	−	1.99284i	−0.0795397	−	0.169030i	−0.940641	+	0.339403i	$0.889775\pi$
$140$	−0.532664	−	1.81339i	−0.0450184	−	0.153259i
$141$	1.89354	+	0.239210i	0.159465	+	0.0201451i
$142$	−0.0120003	−	0.190739i	−0.00100704	−	0.0160065i
$143$	−0.0473749	−	0.145805i	−0.00396169	−	0.0121928i
$144$	2.36021	−	3.71910i	0.196685	−	0.309925i
$145$	3.27721	+	11.1568i	0.272157	+	0.926524i
$146$	−5.27332	+	1.35396i	−0.436423	+	0.112054i
$147$	−0.966911	+	15.3686i	−0.0797495	+	1.26758i
$148$	3.48160	−	18.2512i	0.286186	−	1.50024i
$149$	0.806014	−	2.48066i	0.0660313	−	0.203223i	−0.912597	−	0.408860i	$-0.865926\pi$
$149$	0.806014	−	2.48066i	0.0660313	−	0.203223i	0.978628	+	0.205637i	$0.0659265\pi$
$150$	−3.26247	+	6.01856i	−0.266380	+	0.491413i
$151$	−0.728090	−	2.24083i	−0.0592511	−	0.182356i	0.917050	−	0.398772i	$-0.130563\pi$
$151$	−0.728090	−	2.24083i	−0.0592511	−	0.182356i	−0.976301	+	0.216416i	$0.930563\pi$
$152$	1.93202	−	0.244071i	0.156707	−	0.0197967i
$153$	7.47674	+	2.96025i	0.604459	+	0.239322i
$154$	−0.191994	−	0.0760157i	−0.0154713	−	0.00612552i
$155$	9.02778	−	8.00668i	0.725129	−	0.643112i
$156$	0.0539500	+	0.857511i	0.00431946	+	0.0686558i
$157$	0.491964	−	0.357433i	0.0392630	−	0.0285263i	−0.567981	−	0.823042i	$-0.692275\pi$
$157$	0.491964	−	0.357433i	0.0392630	−	0.0285263i	0.607244	+	0.794516i	$0.292275\pi$
$158$	−6.56960	−	1.68679i	−0.522649	−	0.134194i
$159$	17.4499	+	16.3866i	1.38387	+	1.29954i
$160$	11.9169	+	3.42396i	0.942114	+	0.270687i
$161$	−3.55017	−	1.95172i	−0.279792	−	0.153817i
$162$	6.36879	+	0.804565i	0.500379	+	0.0632126i
$163$	−1.36637	−	7.16277i	−0.107022	−	0.561031i	−0.994893	−	0.100938i	$-0.967816\pi$
$163$	−1.36637	−	7.16277i	−0.107022	−	0.561031i	0.887870	−	0.460094i	$-0.152184\pi$
$164$	−19.7826	+	2.49913i	−1.54477	+	0.195149i
$165$	−1.36904	−	3.13813i	−0.106579	−	0.244303i
$166$	0.818999	+	4.29334i	0.0635667	+	0.333228i
$167$	−6.19385	+	9.75994i	−0.479294	+	0.755247i	−0.994823	−	0.101626i	$-0.967596\pi$
$167$	−6.19385	+	9.75994i	−0.479294	+	0.755247i	0.515529	+	0.856872i	$0.327596\pi$
$168$	2.07706	+	1.50907i	0.160249	+	0.116428i
$169$	8.25310	+	9.97629i	0.634854	+	0.767407i
$170$	−0.440572	+	4.81280i	−0.0337904	+	0.369125i
$171$	1.06614	+	1.67996i	0.0815295	+	0.128470i
$172$	2.34910	−	2.83957i	0.179117	−	0.216515i
$173$	3.75381	+	7.97725i	0.285397	+	0.606499i	0.995196	−	0.0979051i	$-0.0312142\pi$
$173$	3.75381	+	7.97725i	0.285397	+	0.606499i	−0.709799	+	0.704404i	$0.751214\pi$
$174$	−5.76033	−	4.18513i	−0.436690	−	0.317274i
$175$	2.18203	+	1.36671i	0.164946	+	0.103313i
$176$	−1.07111	+	0.778203i	−0.0807376	+	0.0586593i
$177$	−12.0944	−	6.64896i	−0.909071	−	0.499766i
$178$	−3.74746	+	0.962185i	−0.280884	+	0.0721188i
$179$	8.64542	−	10.4505i	0.646189	−	0.781108i	−0.341103	−	0.940026i	$-0.610800\pi$
$179$	8.64542	−	10.4505i	0.646189	−	0.781108i	0.987292	+	0.158918i	$0.0508004\pi$
$180$	1.30311	+	8.07278i	0.0971282	+	0.601709i
$181$	−20.8248	+	8.24512i	−1.54789	+	0.612855i	−0.977952	−	0.208829i	$-0.933035\pi$
$181$	−20.8248	+	8.24512i	−1.54789	+	0.612855i	−0.569943	+	0.821684i	$0.693035\pi$
$182$	−0.0705942			−0.00523279
$183$	−22.6494	+	8.96755i	−1.67429	+	0.662900i
$184$	15.0334	−	8.26467i	1.10828	−	0.609280i
$185$	12.9491	+	21.7485i	0.952037	+	1.59898i
$186$	−1.38451	+	7.25786i	−0.101517	+	0.532172i
$187$	−1.76194	−	1.65457i	−0.128845	−	0.120994i
$188$	0.998790	+	0.937927i	0.0728443	+	0.0684053i
$189$	0.170332	−	0.892912i	0.0123898	−	0.0649498i
$190$	−0.788148	+	0.899332i	−0.0571783	+	0.0652444i
$191$	17.4878	−	9.61402i	1.26538	−	0.695646i	0.299363	−	0.954139i	$-0.403226\pi$
$191$	17.4878	−	9.61402i	1.26538	−	0.695646i	0.966013	+	0.258493i	$0.0832259\pi$
$192$	1.34712	−	0.533361i	0.0972198	−	0.0384920i
$193$	7.84327			0.564571			0.282286	−	0.959330i	$-0.408907\pi$
$193$	7.84327			0.564571			0.282286	+	0.959330i	$0.408907\pi$
$194$	3.00364	−	1.18923i	0.215649	−	0.0853815i
$195$	−0.830101	−	0.825201i	−0.0594448	−	0.0590939i
$196$	−7.04650	+	8.51775i	−0.503321	+	0.608411i
$197$	−16.2646	+	4.17605i	−1.15881	+	0.297531i	−0.778691	−	0.627408i	$-0.784116\pi$
$197$	−16.2646	+	4.17605i	−1.15881	+	0.297531i	−0.380116	+	0.924939i	$0.624116\pi$
$198$	0.782909	+	0.430408i	0.0556389	+	0.0305877i
$199$	18.7103	−	13.5938i	1.32634	−	0.963639i	0.326506	−	0.945195i	$-0.394129\pi$
$199$	18.7103	−	13.5938i	1.32634	−	0.963639i	0.999830	−	0.0184443i	$-0.00587132\pi$
$200$	−9.83746	+	4.70050i	−0.695613	+	0.332376i
$201$	8.69272	+	6.31563i	0.613137	+	0.445470i
$202$	−4.12334	−	8.76254i	−0.290117	−	0.616530i
$203$	−1.70693	+	2.06332i	−0.119803	+	0.144817i
$204$	7.25833	+	11.4373i	0.508185	+	0.800771i
$205$	17.9033	−	20.4289i	1.25042	−	1.42682i
$206$	3.92668	+	4.74655i	0.273585	+	0.330708i
$207$	14.1807	+	10.3029i	0.985625	+	0.716098i
$208$	−0.242527	+	0.382161i	−0.0168162	+	0.0264981i
$209$	−0.112063	−	0.587454i	−0.00775155	−	0.0406351i
$210$	−1.56910	+	0.153012i	−0.108278	+	0.0105588i
$211$	14.2667	−	1.80230i	0.982161	−	0.124076i	0.382178	−	0.924089i	$-0.375174\pi$
$211$	14.2667	−	1.80230i	0.982161	−	0.124076i	0.599983	+	0.800013i	$0.295174\pi$
$212$	3.22005	+	16.8801i	0.221154	+	1.15933i
$213$	0.723983	+	0.0914603i	0.0496065	+	0.00626676i
$214$	2.66861	+	1.46708i	0.182422	+	0.100288i
$215$	0.172549	+	5.01745i	0.0117678	+	0.342187i
$216$	2.80599	+	2.63500i	0.190924	+	0.179289i
$217$	2.69156	+	0.691074i	0.182715	+	0.0469132i
$218$	4.22041	−	3.06630i	0.285842	−	0.207676i
$219$	−1.30530	−	20.7471i	−0.0882039	−	1.40196i
$220$	0.529061	−	2.40024i	0.0356693	−	0.161824i
$221$	−0.768281	−	0.304184i	−0.0516802	−	0.0204616i
$222$	−14.4104	−	5.70548i	−0.967162	−	0.382927i
$223$	15.7529	−	1.99005i	1.05489	−	0.133264i	0.421293	−	0.906925i	$-0.361577\pi$
$223$	15.7529	−	1.99005i	1.05489	−	0.133264i	0.633600	+	0.773661i	$0.281577\pi$
$224$	0.882357	+	2.71562i	0.0589549	+	0.181445i
$225$	−8.62522	−	7.04980i	−0.575015	−	0.469987i
$226$	0.947544	−	2.91624i	0.0630297	−	0.193986i
$227$	2.07222	−	10.8630i	0.137538	−	0.721001i	−0.844975	−	0.534806i	$-0.820385\pi$
$227$	2.07222	−	10.8630i	0.137538	−	0.721001i	0.982513	−	0.186194i	$-0.0596154\pi$
$228$	−0.210456	+	3.34510i	−0.0139378	+	0.221534i
$229$	6.04551	−	1.55222i	0.399499	−	0.102574i	−0.0435946	−	0.999049i	$-0.513881\pi$
$229$	6.04551	−	1.55222i	0.399499	−	0.102574i	0.443093	+	0.896475i	$0.353881\pi$
$230$	−3.53909	+	9.92226i	−0.233361	+	0.654255i
$231$	0.422476	−	0.665716i	0.0277969	−	0.0438009i
$232$	−3.50410	−	10.7845i	−0.230055	−	0.708038i
$233$	−1.16297	−	18.4849i	−0.0761886	−	1.21098i	−0.831465	−	0.555577i	$-0.812497\pi$
$233$	−1.16297	−	18.4849i	−0.0761886	−	1.21098i	0.755276	−	0.655406i	$-0.227503\pi$
$234$	0.303024	+	0.0382809i	0.0198093	+	0.00250250i
$235$	−1.86576	−	0.0531056i	−0.121709	−	0.00346423i
$236$	−4.21857	−	8.96492i	−0.274606	−	0.583567i
$237$	11.0270	−	23.4335i	0.716278	−	1.52217i
$238$	−0.975304	+	0.536178i	−0.0632196	+	0.0347553i
$239$	−15.4508	+	14.5093i	−0.999431	+	0.938528i	−0.998109	−	0.0614709i	$-0.980421\pi$
$239$	−15.4508	+	14.5093i	−0.999431	+	0.938528i	−0.00132220	+	0.999999i	$0.500421\pi$
$240$	−4.56233	+	9.01999i	−0.294497	+	0.582238i
$241$	0.799410	−	1.69883i	0.0514945	−	0.109431i	−0.877424	−	0.479716i	$-0.840740\pi$
$241$	0.799410	−	1.69883i	0.0514945	−	0.109431i	0.928918	+	0.370284i	$0.120740\pi$
$242$	4.02756	+	4.86848i	0.258901	+	0.312958i
$243$	−5.93787	+	18.2749i	−0.380915	+	1.17234i
$244$	−16.9382	−	4.34900i	−1.08436	−	0.278416i
$245$	−0.517590	−	15.0506i	−0.0330676	−	0.961551i
$246$	−1.04439	+	16.6000i	−0.0665876	+	1.05838i
$247$	−0.109552	−	0.172626i	−0.00697063	−	0.0109840i
$248$	−8.57794	+	8.05522i	−0.544700	+	0.511507i
$249$	−16.6888			−1.05761
$250$	2.60424	−	6.16775i	0.164706	−	0.390083i
$251$	−24.0113			−1.51558			−0.757790	−	0.652498i	$-0.773721\pi$
$251$	−24.0113			−1.51558			−0.757790	+	0.652498i	$0.773721\pi$
$252$	−1.37275	+	1.28910i	−0.0864752	+	0.0812056i
$253$	−2.82300	−	4.44834i	−0.177481	−	0.279665i
$254$	0.539206	−	8.57043i	0.0338328	−	0.537756i
$255$	−17.7360	−	5.09588i	−1.11067	−	0.319117i
$256$	−5.42487	−	1.39287i	−0.339054	−	0.0870543i
$257$	−1.23068	+	3.78765i	−0.0767679	+	0.236267i	−0.982075	−	0.188490i	$-0.939641\pi$
$257$	−1.23068	+	3.78765i	−0.0767679	+	0.236267i	0.905307	+	0.424757i	$0.139641\pi$
$258$	−1.95950	−	2.36863i	−0.121993	−	0.147464i
$259$	−2.48187	+	5.27424i	−0.154216	+	0.327725i
$260$	−0.133903	−	0.829528i	−0.00830430	−	0.0514451i
$261$	8.44582	−	7.93115i	0.522783	−	0.490926i
$262$	−9.35794	+	5.14457i	−0.578136	+	0.317833i
$263$	9.28467	−	19.7309i	0.572518	−	1.21666i	−0.383551	−	0.923520i	$-0.625299\pi$
$263$	9.28467	−	19.7309i	0.572518	−	1.21666i	0.956069	−	0.293142i	$-0.0947009\pi$
$264$	1.42158	+	3.02100i	0.0874919	+	0.185930i
$265$	−18.5400	−	14.2934i	−1.13890	−	0.878037i
$266$	−0.273212	−	0.0345147i	−0.0167517	−	0.00211624i
$267$	−0.927606	−	14.7439i	−0.0567686	−	0.902310i
$268$	2.38360	+	7.33595i	0.145601	+	0.448115i
$269$	−14.5393	+	22.9102i	−0.886474	+	1.39686i	0.0311950	+	0.999513i	$0.490069\pi$
$269$	−14.5393	+	22.9102i	−0.886474	+	1.39686i	−0.917669	+	0.397346i	$0.869931\pi$
$270$	−2.36274	−	0.0672513i	−0.143792	−	0.00409278i
$271$	27.6823	−	7.10761i	1.68158	−	0.431757i	0.717327	−	0.696736i	$-0.245365\pi$
$271$	27.6823	−	7.10761i	1.68158	−	0.431757i	0.964254	+	0.264980i	$0.0853652\pi$
$272$	−0.448068	+	7.12184i	−0.0271681	+	0.431825i
$273$	0.0505085	−	0.264775i	0.00305691	−	0.0160249i
$274$	−0.627463	+	1.93113i	−0.0379065	+	0.116664i
$275$	1.63039	+	2.92453i	0.0983165	+	0.176356i
$276$	9.12431	+	28.0817i	0.549219	+	1.69032i
$277$	−25.8497	+	3.26557i	−1.55316	+	0.196209i	−0.854577	−	0.519324i	$-0.826184\pi$
$277$	−25.8497	+	3.26557i	−1.55316	+	0.196209i	−0.698579	+	0.715533i	$0.746184\pi$
$278$	−1.22626	−	0.485510i	−0.0735461	−	0.0291190i
$279$	−11.1787	−	4.42596i	−0.669252	−	0.264975i
$280$	−2.16492	−	1.27169i	−0.129379	−	0.0759983i
$281$	0.0750852	+	1.19344i	0.00447921	+	0.0711949i	0.999631	−	0.0271531i	$-0.00864416\pi$
$281$	0.0750852	+	1.19344i	0.00447921	+	0.0711949i	−0.995152	+	0.0983480i	$0.968644\pi$
$282$	0.924629	−	0.671782i	0.0550608	−	0.0400040i
$283$	−4.35779	−	1.11889i	−0.259044	−	0.0665111i	0.116934	−	0.993140i	$-0.462693\pi$
$283$	−4.35779	−	1.11889i	−0.259044	−	0.0665111i	−0.375978	+	0.926628i	$0.622693\pi$
$284$	0.381881	+	0.358610i	0.0226604	+	0.0212796i
$285$	−2.80919	−	3.59953i	−0.166402	−	0.213218i
$286$	−0.0804487	−	0.0442271i	−0.00475703	−	0.00261520i
$287$	6.20620	+	0.784025i	0.366340	+	0.0462795i
$288$	−2.31491	−	12.1352i	−0.136408	−	0.715073i
$289$	3.94131	−	0.497903i	0.231842	−	0.0292884i
$290$	6.00399	+	3.52680i	0.352566	+	0.207101i
$291$	2.31135	+	12.1165i	0.135494	+	0.710282i
$292$	7.99637	−	12.6003i	0.467952	−	0.737374i
$293$	2.63496	+	1.91441i	0.153936	+	0.111841i	0.662087	−	0.749427i	$-0.269671\pi$
$293$	2.63496	+	1.91441i	0.153936	+	0.111841i	−0.508151	+	0.861268i	$0.669671\pi$
$294$	5.87784	+	7.10509i	0.342803	+	0.414377i
$295$	12.4030	+	5.32374i	0.722133	+	0.309960i
$296$	−13.2259	−	20.8407i	−0.768741	−	1.21134i
$297$	0.753516	−	0.910844i	0.0437234	−	0.0528525i
$298$	−0.665031	−	1.41326i	−0.0385242	−	0.0818681i
$299$	−1.45715	−	1.05868i	−0.0842693	−	0.0612252i
$300$	−4.77426	−	18.1477i	−0.275642	−	1.04776i
$301$	−0.935344	+	0.679567i	−0.0539123	+	0.0391696i
$302$	−1.23639	−	0.679711i	−0.0711462	−	0.0391130i
$303$	35.8154	−	9.19584i	2.05754	−	0.528287i
$304$	−1.12547	+	1.36046i	−0.0645499	+	0.0780275i
$305$	21.1944	−	10.8783i	1.21359	−	0.622887i
$306$	4.47723	−	1.77266i	0.255946	−	0.101336i
$307$	16.5590			0.945074			0.472537	−	0.881311i	$-0.343338\pi$
$307$	16.5590			0.945074			0.472537	+	0.881311i	$0.343338\pi$
$308$	0.526270	−	0.208365i	0.0299870	−	0.0118727i
$309$	−20.6121	+	11.3316i	−1.17258	+	0.644633i
$310$	0.658713	−	7.19577i	0.0374124	−	0.408692i
$311$	−0.193441	+	1.01405i	−0.0109690	+	0.0575017i	−0.987351	−	0.158550i	$-0.949318\pi$
$311$	−0.193441	+	1.01405i	−0.0109690	+	0.0575017i	0.976382	+	0.216052i	$0.0693180\pi$
$312$	0.832060	+	0.781357i	0.0471061	+	0.0442356i
$313$	20.7565	+	19.4917i	1.17323	+	1.10173i	0.993001	+	0.118109i	$0.0376832\pi$
$313$	20.7565	+	19.4917i	1.17323	+	1.10173i	0.180227	+	0.983625i	$0.442317\pi$
$314$	0.0682337	−	0.357694i	0.00385065	−	0.0201858i
$315$	0.233861	−	2.55469i	0.0131765	−	0.143940i
$316$	16.2922	−	8.95671i	0.916508	−	0.503854i
$317$	−11.3136	+	4.47938i	−0.635436	+	0.251587i	−0.663683	−	0.748014i	$-0.731008\pi$
$317$	−11.3136	+	4.47938i	−0.635436	+	0.251587i	0.0282468	+	0.999601i	$0.491008\pi$
$318$	14.3345			0.803836
$319$	−3.23787	+	1.28196i	−0.181286	+	0.0717761i
$320$	−1.26058	+	0.647004i	−0.0704684	+	0.0361686i
$321$	−7.41185	+	8.95939i	−0.413689	+	0.500064i
$322$	−2.34978	+	0.603320i	−0.130948	+	0.0336217i
$323$	−2.82467	−	1.55287i	−0.157169	−	0.0864042i
$324$	−14.2355	+	10.3427i	−0.790864	+	0.574596i
$325$	0.886294	+	0.724411i	0.0491628	+	0.0401831i
$326$	−3.53262	−	2.56660i	−0.195654	−	0.142151i
$327$	8.48106	+	18.0232i	0.469004	+	0.996684i
$328$	−16.8849	+	20.4104i	−0.932315	+	1.12698i
$329$	−0.230320	−	0.362926i	−0.0126979	−	0.0200087i
$330$	−1.88400	−	0.808666i	−0.103711	−	0.0445156i
$331$	5.67872	+	6.86440i	0.312131	+	0.377301i	0.903127	−	0.429373i	$-0.141265\pi$
$331$	5.67872	+	6.86440i	0.312131	+	0.377301i	−0.590996	+	0.806674i	$0.701265\pi$
$332$	−9.69251	−	7.04202i	−0.531946	−	0.386481i
$333$	13.5134	−	21.2937i	0.740530	−	1.16689i
$334$	1.29706	+	6.79941i	0.0709718	+	0.372047i
$335$	−9.06041	−	5.32217i	−0.495023	−	0.290781i
$336$	−2.30945	+	0.291751i	−0.125991	+	0.0159163i
$337$	−1.59630	−	8.36812i	−0.0869562	−	0.455840i	−0.998957	−	0.0456528i	$-0.985463\pi$
$337$	−1.59630	−	8.36812i	−0.0869562	−	0.455840i	0.912001	−	0.410188i	$-0.134537\pi$
$338$	7.69214	+	0.971744i	0.418398	+	0.0528559i
$339$	10.2599	+	5.64042i	0.557240	+	0.306345i
$340$	−8.15039	−	10.4434i	−0.442017	−	0.566375i
$341$	2.63432	+	2.47379i	0.142657	+	0.133963i
$342$	1.15404	+	0.296308i	0.0624035	+	0.0160225i
$343$	5.72190	−	4.15720i	0.308953	−	0.224468i
$344$	−0.307408	−	4.88611i	−0.0165743	−	0.263441i
$345$	−34.6829	−	20.3731i	−1.86726	−	1.09685i
$346$	4.90866	+	1.94348i	0.263891	+	0.104482i
$347$	6.18984	+	2.45073i	0.332288	+	0.131562i	0.528344	−	0.849031i	$-0.322813\pi$
$347$	6.18984	+	2.45073i	0.332288	+	0.131562i	−0.196056	+	0.980593i	$0.562813\pi$
$348$	19.3630	−	2.44612i	1.03797	−	0.131126i
$349$	7.79782	+	23.9992i	0.417408	+	1.28465i	0.910080	+	0.414433i	$0.136020\pi$
$349$	7.79782	+	23.9992i	0.417408	+	1.28465i	−0.492672	+	0.870215i	$0.663980\pi$
$350$	1.51275	−	0.297865i	0.0808597	−	0.0159215i
$351$	0.124884	−	0.384353i	0.00666581	−	0.0205153i
$352$	−0.695796	+	3.64749i	−0.0370861	+	0.194412i
$353$	0.741228	−	11.7815i	0.0394516	−	0.627065i	−0.927773	−	0.373144i	$-0.878280\pi$
$353$	0.741228	−	11.7815i	0.0394516	−	0.627065i	0.967225	−	0.253921i	$-0.0817203\pi$
$354$	−8.00501	+	2.05534i	−0.425462	+	0.109240i
$355$	−0.713362	−	0.0203046i	−0.0378613	−	0.00107765i
$356$	5.68259	−	8.95433i	0.301177	−	0.474578i
$357$	−1.31321	−	4.04166i	−0.0695027	−	0.213907i
$358$	−0.509975	−	8.10581i	−0.0269530	−	0.428406i
$359$	−5.40518	−	0.682834i	−0.285275	−	0.0360386i	−0.0186062	−	0.999827i	$-0.505923\pi$
$359$	−5.40518	−	0.682834i	−0.285275	−	0.0360386i	−0.266669	+	0.963788i	$0.585923\pi$
$360$	8.60327	+	6.63268i	0.453432	+	0.349573i
$361$	7.75022	+	16.4701i	0.407906	+	0.866845i
$362$	−5.71062	+	12.1357i	−0.300144	+	0.637838i
$363$	−21.1416	+	11.6227i	−1.10965	+	0.610034i
$364$	0.141059	−	0.132463i	0.00739348	−	0.00694294i
$365$	3.23973	+	20.0701i	0.169575	+	1.05052i
$366$	−6.21098	+	13.1990i	−0.324653	+	0.689923i
$367$	9.79933	+	11.8454i	0.511521	+	0.618323i	0.961530	−	0.274702i	$-0.0885791\pi$
$367$	9.79933	+	11.8454i	0.511521	+	0.618323i	−0.450009	+	0.893024i	$0.648579\pi$
$368$	−4.80660	+	14.7932i	−0.250561	+	0.771148i
$369$	−26.2148	−	6.73082i	−1.36469	−	0.350393i
$370$	14.5677	+	4.18559i	0.757341	+	0.217599i
$371$	0.338510	−	5.38047i	0.0175746	−	0.279340i
$372$	−10.8521	−	17.1002i	−0.562658	−	0.886607i
$373$	−11.9240	+	11.1973i	−0.617399	+	0.579776i	−0.928836	−	0.370491i	$-0.879190\pi$
$373$	−11.9240	+	11.1973i	−0.617399	+	0.579776i	0.311437	+	0.950267i	$0.399190\pi$
$374$	−1.44736			−0.0748414
$375$	21.2699	+	14.1805i	1.09837	+	0.732277i
$376$	1.82018			0.0938686
$377$	−0.867860	+	0.814975i	−0.0446971	+	0.0419733i
$378$	−0.291670	−	0.459598i	−0.0150019	−	0.0236392i
$379$	−1.03567	+	16.4615i	−0.0531988	+	0.845571i	0.877452	+	0.479664i	$0.159241\pi$
$379$	−1.03567	+	16.4615i	−0.0531988	+	0.845571i	−0.930651	+	0.365907i	$0.880759\pi$
$380$	−0.112657	−	3.27589i	−0.00577921	−	0.168050i
$381$	31.7590	+	8.15432i	1.62706	+	0.417758i
$382$	3.69283	−	11.3654i	0.188942	−	0.581502i
$383$	16.9350	+	20.4709i	0.865337	+	1.04601i	0.998491	+	0.0549177i	$0.0174896\pi$
$383$	16.9350	+	20.4709i	0.865337	+	1.04601i	−0.133154	+	0.991095i	$0.542510\pi$
$384$	11.1659	−	23.7288i	0.569808	−	1.21090i
$385$	−0.348026	+	0.688067i	−0.0177370	+	0.0350671i
$386$	3.42376	−	3.21512i	0.174265	−	0.163645i
$387$	4.38345	−	2.40982i	0.222823	−	0.122498i
$388$	−3.77030	+	8.01230i	−0.191408	+	0.406763i
$389$	−3.78705	−	8.04789i	−0.192011	−	0.408044i	0.785520	−	0.618837i	$-0.212396\pi$
$389$	−3.78705	−	8.04789i	−0.192011	−	0.408044i	−0.977531	+	0.210792i	$0.932396\pi$
$390$	−0.700624	−	0.0199420i	−0.0354775	−	0.00100980i
$391$	−28.1724	−	3.55900i	−1.42474	−	0.179986i
$392$	0.922121	+	14.6567i	0.0465741	+	0.740274i
$393$	−12.6001	−	38.7793i	−0.635593	−	1.95616i
$394$	−5.38801	+	8.49014i	−0.271444	+	0.427727i
$395$	−8.50876	+	23.8553i	−0.428122	+	1.20029i
$396$	−2.37199	+	0.609024i	−0.119197	+	0.0306046i
$397$	−0.139842	+	2.22272i	−0.00701847	+	0.111555i	−0.999976	−	0.00691472i	$-0.997799\pi$
$397$	−0.139842	+	2.22272i	−0.00701847	+	0.111555i	0.992958	+	0.118470i	$0.0377990\pi$
$398$	2.59505	−	13.6037i	0.130078	−	0.681893i
$399$	0.324930	−	1.00003i	0.0162668	−	0.0500642i
$400$	3.58455	−	9.21254i	0.179228	−	0.460627i
$401$	−1.80319	−	5.54966i	−0.0900471	−	0.277137i	0.895884	−	0.444288i	$-0.146543\pi$
$401$	−1.80319	−	5.54966i	−0.0900471	−	0.277137i	−0.985931	+	0.167151i	$0.946543\pi$
$402$	6.38346	−	0.806419i	0.318378	−	0.0402205i
$403$	1.14868	+	0.454795i	0.0572199	+	0.0226550i
$404$	24.6811	+	9.77194i	1.22793	+	0.486172i
$405$	5.15980	−	23.4089i	0.256393	−	1.16320i
$406$	0.100688	+	1.60039i	0.00499706	+	0.0794259i
$407$	−6.13261	+	4.45560i	−0.303982	+	0.220856i
$408$	17.4300	+	4.47527i	0.862914	+	0.221559i
$409$	−7.89045	−	7.40963i	−0.390158	−	0.366382i	0.464501	−	0.885573i	$-0.346234\pi$
$409$	−7.89045	−	7.40963i	−0.390158	−	0.366382i	−0.854659	+	0.519190i	$0.826234\pi$
$410$	−0.559062	−	16.2566i	−0.0276101	−	0.802856i
$411$	−6.79409	−	3.73508i	−0.335128	−	0.184238i
$412$	−16.7526	−	2.11634i	−0.825339	−	0.104265i
$413$	0.582436	+	3.05324i	0.0286598	+	0.150240i
$414$	10.4135	−	1.31553i	0.511797	−	0.0646550i
$415$	16.2439	−	1.58403i	0.797382	−	0.0777571i
$416$	0.237872	+	1.24697i	0.0116626	+	0.0611376i
$417$	2.69834	−	4.25191i	0.132138	−	0.208217i
$418$	−0.289728	−	0.210499i	−0.0141710	−	0.0102959i
$419$	1.25191	+	1.51330i	0.0611599	+	0.0739296i	0.800206	−	0.599725i	$-0.204723\pi$
$419$	1.25191	+	1.51330i	0.0611599	+	0.0739296i	−0.739046	+	0.673655i	$0.764723\pi$
$420$	2.84821	−	3.25000i	0.138978	−	0.158584i
$421$	−2.21243	−	3.48623i	−0.107827	−	0.169908i	0.786130	−	0.618062i	$-0.212082\pi$
$421$	−2.21243	−	3.48623i	−0.107827	−	0.169908i	−0.893957	+	0.448153i	$0.852082\pi$
$422$	5.48892	−	6.63497i	0.267196	−	0.322985i
$423$	0.791840	+	1.68275i	0.0385006	+	0.0818179i
$424$	18.4690	+	13.4185i	0.896933	+	0.651660i
$425$	17.7468	+	3.27660i	0.860845	+	0.158938i
$426$	0.353525	−	0.256851i	0.0171284	−	0.0124445i
$427$	4.80760	+	2.64300i	0.232656	+	0.127904i
$428$	−8.08514	+	2.07591i	−0.390810	+	0.100343i
$429$	0.223440	−	0.270092i	0.0107878	−	0.0130402i
$430$	2.13208	+	2.11949i	0.102818	+	0.102211i
$431$	−3.12691	+	1.23803i	−0.150618	+	0.0596339i	−0.442224	−	0.896905i	$-0.645810\pi$
$431$	−3.12691	+	1.23803i	−0.150618	+	0.0596339i	0.291606	+	0.956539i	$0.405810\pi$
$432$	−3.49006			−0.167915
$433$	−0.378133	+	0.149713i	−0.0181719	+	0.00719476i	−0.377193	−	0.926135i	$-0.623111\pi$
$433$	−0.378133	+	0.149713i	−0.0181719	+	0.00719476i	0.359021	+	0.933329i	$0.383111\pi$
$434$	1.45821	−	0.801656i	0.0699962	−	0.0384807i
$435$	−17.5235	+	19.9956i	−0.840189	+	0.958714i
$436$	−2.67944	+	14.0461i	−0.128322	+	0.672688i
$437$	−5.12183	−	4.80972i	−0.245010	−	0.230080i
$438$	−9.07447	−	8.52150i	−0.433595	−	0.407173i
$439$	5.07313	−	26.5943i	0.242127	−	1.26928i	−0.628685	−	0.777660i	$-0.716406\pi$
$439$	5.07313	−	26.5943i	0.242127	−	1.26928i	0.870812	−	0.491616i	$-0.163594\pi$
$440$	−1.67042	−	2.80553i	−0.0796339	−	0.133748i
$441$	−13.1489	+	7.22865i	−0.626137	+	0.344222i
$442$	−0.460063	+	0.182152i	−0.0218829	+	0.00866407i
$443$	4.90029			0.232820			0.116410	−	0.993201i	$-0.462861\pi$
$443$	4.90029			0.232820			0.116410	+	0.993201i	$0.462861\pi$
$444$	39.5000	−	15.6392i	1.87459	−	0.742202i
$445$	2.30230	+	14.2627i	0.109139	+	0.676119i
$446$	6.06071	−	7.32615i	0.286983	−	0.346903i
$447$	5.77648	−	1.48315i	0.273218	−	0.0701505i
$448$	−0.285941	−	0.157197i	−0.0135094	−	0.00742687i
$449$	−11.1326	+	8.08832i	−0.525380	+	0.381711i	−0.818627	−	0.574326i	$-0.805264\pi$
$449$	−11.1326	+	8.08832i	−0.525380	+	0.381711i	0.293247	+	0.956037i	$0.405264\pi$
$450$	−6.65495	+	0.458268i	−0.313717	+	0.0216030i
$451$	6.58135	+	4.78163i	0.309904	+	0.225158i
$452$	3.57868	+	7.60509i	0.168327	+	0.357713i
$453$	3.43397	−	4.15096i	0.161342	−	0.195029i
$454$	−3.54839	−	5.59137i	−0.166534	−	0.262416i
$455$	−0.0240306	+	0.262510i	−0.00112657	+	0.0123066i
$456$	2.83820	+	3.43080i	0.132911	+	0.160662i
$457$	−23.0989	−	16.7824i	−1.08052	−	0.785046i	−0.102749	−	0.994707i	$-0.532764\pi$
$457$	−23.0989	−	16.7824i	−1.08052	−	0.785046i	−0.977774	+	0.209661i	$0.932764\pi$
$458$	2.00271	−	3.15576i	0.0935803	−	0.147459i
$459$	−1.19389	−	6.25861i	−0.0557262	−	0.292127i
$460$	−11.5464	−	26.4670i	−0.538356	−	1.23403i
$461$	−10.0045	+	1.26386i	−0.465956	+	0.0588639i	−0.354807	−	0.934940i	$-0.615453\pi$
$461$	−10.0045	+	1.26386i	−0.465956	+	0.0588639i	−0.111150	+	0.993804i	$0.535453\pi$
$462$	−0.0884710	−	0.463781i	−0.00411604	−	0.0215770i
$463$	−35.8057	−	4.52331i	−1.66403	−	0.210216i	−0.763747	−	0.645516i	$-0.776642\pi$
$463$	−35.8057	−	4.52331i	−1.66403	−	0.210216i	−0.900286	+	0.435300i	$0.856642\pi$
$464$	9.00959	+	4.95306i	0.418260	+	0.229940i
$465$	26.5176	+	7.61901i	1.22972	+	0.353323i
$466$	−8.08499	−	7.59231i	−0.374530	−	0.351707i
$467$	−26.3517	−	6.76597i	−1.21941	−	0.313092i	−0.416470	−	0.909149i	$-0.636733\pi$
$467$	−26.3517	−	6.76597i	−1.21941	−	0.313092i	−0.802942	+	0.596057i	$0.796733\pi$
$468$	−0.677321	+	0.492103i	−0.0313092	+	0.0227475i
$469$	−0.151945	−	2.41509i	−0.00701615	−	0.111519i
$470$	−0.836215	+	0.741634i	−0.0385717	+	0.0342090i
$471$	1.29277	+	0.511843i	0.0595676	+	0.0235845i
$472$	−12.2379	−	4.84534i	−0.563296	−	0.223025i
$473$	−1.49166	+	0.188440i	−0.0685865	+	0.00866449i
$474$	−4.79237	−	14.7494i	−0.220121	−	0.677462i
$475$	3.07594	+	3.23692i	0.141134	+	0.148520i
$476$	0.942731	−	2.90143i	0.0432100	−	0.132987i
$477$	−4.37069	+	22.9120i	−0.200120	+	1.04907i
$478$	−0.796955	+	12.6672i	−0.0364519	+	0.579386i
$479$	13.0395	−	3.34797i	0.595789	−	0.152973i	0.0612589	−	0.998122i	$-0.480488\pi$
$479$	13.0395	−	3.34797i	0.595789	−	0.152973i	0.534530	+	0.845149i	$0.320488\pi$
$480$	7.98997	+	27.2008i	0.364690	+	1.24154i
$481$	−1.38859	+	2.18806i	−0.0633141	+	0.0997670i
$482$	−0.347428	−	1.06927i	−0.0158249	−	0.0487040i
$483$	−0.581638	−	9.24487i	−0.0264654	−	0.420656i
$484$	−17.1829	−	2.17071i	−0.781041	−	0.0986685i
$485$	−3.39977	−	11.5741i	−0.154376	−	0.525552i
$486$	4.89925	+	10.4114i	0.222235	+	0.472273i
$487$	−6.91119	+	14.6870i	−0.313176	+	0.665533i	−0.998003	−	0.0631731i	$-0.979878\pi$
$487$	−6.91119	+	14.6870i	−0.313176	+	0.665533i	0.684826	+	0.728706i	$0.259878\pi$
$488$	−20.3580	+	11.1919i	−0.921565	+	0.506635i
$489$	12.1539	−	11.4133i	0.549620	−	0.516128i
$490$	−6.39551	−	6.35776i	−0.288920	−	0.287214i
$491$	−1.93495	+	4.11198i	−0.0873231	+	0.185571i	−0.943719	−	0.330749i	$-0.892699\pi$
$491$	−1.93495	+	4.11198i	−0.0873231	+	0.185571i	0.856396	+	0.516320i	$0.172699\pi$
$492$	−29.0614	−	35.1292i	−1.31019	−	1.58375i
$493$	−5.80013	+	17.8510i	−0.261225	+	0.803968i
$494$	−0.118585	−	0.0304475i	−0.00533539	−	0.00136990i
$495$	1.86701	−	2.76479i	0.0839158	−	0.124268i
$496$	0.669920	−	10.6481i	0.0300803	−	0.478113i
$497$	−0.0880611	−	0.138762i	−0.00395008	−	0.00622433i
$498$	−7.28504	+	6.84110i	−0.326450	+	0.306557i
$499$	39.4353			1.76537			0.882684	−	0.469966i	$-0.155734\pi$
$499$	39.4353			1.76537			0.882684	+	0.469966i	$0.155734\pi$
$500$	6.36947	+	17.2107i	0.284852	+	0.769688i
$501$	−26.4303			−1.18082
$502$	−10.4814	+	9.84274i	−0.467810	+	0.439303i
$503$	−15.9573	−	25.1446i	−0.711500	−	1.12114i	−0.987136	−	0.159882i	$-0.948888\pi$
$503$	−15.9573	−	25.1446i	−0.711500	−	1.12114i	0.275636	−	0.961262i	$-0.411112\pi$
$504$	−0.157082	+	2.49674i	−0.00699697	+	0.111214i
$505$	−33.9877	+	12.3501i	−1.51243	+	0.549573i
$506$	−3.05577	−	0.784588i	−0.135845	−	0.0348792i
$507$	−9.14823	+	28.1554i	−0.406287	+	1.25042i
$508$	15.0041	+	18.1369i	0.665700	+	0.804693i
$509$	−2.49644	+	5.30519i	−0.110653	+	0.235149i	−0.952482	−	0.304595i	$-0.901479\pi$
$509$	−2.49644	+	5.30519i	−0.110653	+	0.235149i	0.841829	+	0.539744i	$0.181479\pi$
$510$	−9.83103	+	5.04588i	−0.435325	+	0.223435i
$511$	−3.41286	+	3.20489i	−0.150976	+	0.141776i
$512$	17.1625	−	9.43518i	0.758484	−	0.416980i
$513$	0.671241	−	1.42646i	0.0296360	−	0.0629797i
$514$	1.01542	+	2.15787i	0.0447882	+	0.0951797i
$515$	18.9870	−	12.9859i	0.836669	−	0.572228i
$516$	8.35988	+	1.05610i	0.368023	+	0.0464922i
$517$	−0.0350990	−	0.557882i	−0.00154365	−	0.0245356i
$518$	1.07863	+	3.31969i	0.0473923	+	0.145859i
$519$	−10.8013	+	17.0202i	−0.474127	+	0.747104i
$520$	−0.884040	−	0.681549i	−0.0387677	−	0.0298879i
$521$	8.55368	−	2.19621i	0.374743	−	0.0962177i	−0.0566206	−	0.998396i	$-0.518033\pi$
$521$	8.55368	−	2.19621i	0.374743	−	0.0962177i	0.431364	+	0.902178i	$0.358033\pi$
$522$	0.435636	−	6.92423i	0.0190673	−	0.303065i
$523$	3.72133	−	19.5079i	0.162722	−	0.853020i	−0.803499	−	0.595306i	$-0.797031\pi$
$523$	3.72133	−	19.5079i	0.162722	−	0.853020i	0.966221	−	0.257714i	$-0.0829691\pi$
$524$	9.04541	−	27.8389i	0.395150	−	1.21615i
$525$	0.0348558	+	5.88691i	0.00152123	+	0.256926i
$526$	−4.03516	−	12.4190i	−0.175942	−	0.541492i
$527$	19.3240	−	2.44119i	0.841768	−	0.106340i
$528$	−2.81461	−	1.11438i	−0.122490	−	0.0484974i
$529$	−36.1652	−	14.3188i	−1.57240	−	0.622558i
$530$	−13.9523	+	1.36056i	−0.606048	+	0.0590991i
$531$	−0.844427	−	13.4218i	−0.0366450	−	0.582456i
$532$	0.610685	−	0.443689i	0.0264766	−	0.0192364i
$533$	2.69373	+	0.691633i	0.116679	+	0.0299580i
$534$	−6.44874	−	6.05577i	−0.279064	−	0.262059i
$535$	6.36385	−	9.42402i	0.275133	−	0.407436i
$536$	8.97956	+	4.93655i	0.387858	+	0.213227i
$537$	30.7670	+	3.88678i	1.32769	+	0.167727i
$538$	3.04467	+	15.9607i	0.131265	+	0.688116i
$539$	4.47447	−	0.565257i	0.192729	−	0.0243473i
$540$	4.84733	−	4.29907i	0.208596	−	0.185002i
$541$	−5.96247	−	31.2564i	−0.256347	−	1.34382i	−0.844712	−	0.535221i	$-0.820228\pi$
$541$	−5.96247	−	31.2564i	−0.256347	−	1.34382i	0.588366	−	0.808595i	$-0.299772\pi$
$542$	9.17037	−	14.4502i	0.393901	−	0.620689i
$543$	−41.4310	−	30.1014i	−1.77797	−	1.29177i
$544$	12.7573	+	15.4210i	0.546966	+	0.661168i
$545$	−9.96563	−	16.7377i	−0.426881	−	0.716963i
$546$	−0.0864887	−	0.136284i	−0.00370137	−	0.00583243i
$547$	22.8008	−	27.5614i	0.974891	−	1.17844i	−0.00905236	−	0.999959i	$-0.502881\pi$
$547$	22.8008	−	27.5614i	0.974891	−	1.17844i	0.983943	−	0.178482i	$-0.0571185\pi$
$548$	−2.36980	−	5.03609i	−0.101233	−	0.215131i
$549$	−19.2033	−	13.9520i	−0.819578	−	0.595458i
$550$	1.91053	+	0.608285i	0.0814651	+	0.0259374i
$551$	−3.75723	+	2.72979i	−0.160063	+	0.116293i
$552$	34.3734	+	18.8969i	1.46303	+	0.804307i
$553$	−5.64939	+	1.45052i	−0.240236	+	0.0616822i
$554$	−9.94530	+	12.0218i	−0.422536	+	0.510758i
$555$	−26.1216	+	51.6439i	−1.10880	+	2.19216i
$556$	3.36127	−	1.33082i	0.142550	−	0.0564394i
$557$	−13.0718			−0.553870			−0.276935	−	0.960889i	$-0.589319\pi$
$557$	−13.0718			−0.553870			−0.276935	+	0.960889i	$0.589319\pi$
$558$	−6.69404	+	2.65036i	−0.283381	+	0.112199i
$559$	−0.450427	+	0.247624i	−0.0190510	+	0.0104734i
$560$	2.22018	−	0.503176i	0.0938199	−	0.0212631i
$561$	1.03555	−	5.42857i	0.0437212	−	0.229194i
$562$	0.521994	+	0.490185i	0.0220190	+	0.0206772i
$563$	27.6175	+	25.9345i	1.16394	+	1.09301i	0.994203	+	0.107521i	$0.0342914\pi$
$563$	27.6175	+	25.9345i	1.16394	+	1.09301i	0.169736	+	0.985490i	$0.445709\pi$
$564$	−0.587026	+	3.07730i	−0.0247183	+	0.129578i
$565$	−10.5217	−	4.51622i	−0.442652	−	0.189999i
$566$	−2.36093	+	1.29793i	−0.0992371	+	0.0545561i
$567$	5.13258	−	2.03213i	0.215548	−	0.0853416i
$568$	0.695933			0.0292007
$569$	14.2810	−	5.65423i	0.598689	−	0.237038i	−0.0491794	−	0.998790i	$-0.515661\pi$
$569$	14.2810	−	5.65423i	0.598689	−	0.237038i	0.647869	+	0.761752i	$0.275661\pi$
$570$	−2.70179	−	0.419726i	−0.113166	−	0.0175804i
$571$	5.45866	−	6.59838i	0.228438	−	0.276134i	−0.643823	−	0.765174i	$-0.722653\pi$
$571$	5.45866	−	6.59838i	0.228438	−	0.276134i	0.872261	+	0.489040i	$0.162653\pi$
$572$	0.243737	−	0.0625810i	0.0101912	−	0.00261664i
$573$	39.9854	+	21.9822i	1.67042	+	0.918319i
$574$	3.03052	−	2.20181i	0.126492	−	0.0919016i
$575$	35.6919	+	16.5379i	1.48846	+	0.689680i
$576$	1.14215	+	0.829822i	0.0475897	+	0.0345759i
$577$	2.77622	+	5.89977i	0.115576	+	0.245610i	0.954242	−	0.299034i	$-0.0966645\pi$
$577$	2.77622	+	5.89977i	0.115576	+	0.245610i	−0.838667	+	0.544645i	$0.816664\pi$
$578$	1.51637	−	1.83297i	0.0630725	−	0.0762416i
$579$	9.60920	+	15.1417i	0.399345	+	0.629267i
$580$	−18.6146	+	4.21876i	−0.772930	+	0.175174i
$581$	2.39579	+	2.89601i	0.0993940	+	0.120147i
$582$	5.97576	+	4.34165i	0.247703	+	0.179967i
$583$	3.75661	−	5.91947i	0.155583	−	0.245159i
$584$	−3.71487	−	19.4740i	−0.153722	−	0.805840i
$585$	0.245501	−	1.11379i	0.0101502	−	0.0460494i
$586$	1.93497	−	0.244444i	0.0799330	−	0.0100979i
$587$	2.50545	+	13.1341i	0.103411	+	0.542100i	0.995856	+	0.0909439i	$0.0289884\pi$
$587$	2.50545	+	13.1341i	0.103411	+	0.542100i	−0.892445	+	0.451157i	$0.851012\pi$
$588$	−25.0768	−	3.16794i	−1.03415	−	0.130644i
$589$	4.22324	+	2.32175i	0.174016	+	0.0956660i
$590$	7.59651	−	2.76034i	0.312743	−	0.113641i
$591$	−27.9886	−	26.2831i	−1.15130	−	1.08114i
$592$	21.6767	+	5.56563i	0.890907	+	0.228746i
$593$	22.6055	−	16.4239i	0.928297	−	0.674447i	−0.0172785	−	0.999851i	$-0.505500\pi$
$593$	22.6055	−	16.4239i	0.928297	−	0.674447i	0.945575	+	0.325404i	$0.105500\pi$
$594$	−0.0444482	−	0.706485i	−0.00182373	−	0.0289874i
$595$	1.66182	+	3.80926i	0.0681279	+	0.156164i
$596$	3.98068	+	1.57606i	0.163055	+	0.0645580i
$597$	49.1662	+	19.4663i	2.01224	+	0.796702i
$598$	−1.07005	+	0.135179i	−0.0437578	+	0.00552789i
$599$	3.71749	+	11.4412i	0.151892	+	0.467477i	0.997833	−	0.0658008i	$-0.0209602\pi$
$599$	3.71749	+	11.4412i	0.151892	+	0.467477i	−0.845940	+	0.533277i	$0.820960\pi$
$600$	−21.1269	−	13.2327i	−0.862500	−	0.540223i
$601$	6.30287	−	19.3982i	0.257099	−	0.791270i	−0.736310	−	0.676645i	$-0.763433\pi$
$601$	6.30287	−	19.3982i	0.257099	−	0.791270i	0.993409	−	0.114625i	$-0.0365667\pi$
$602$	−0.129729	+	0.680062i	−0.00528735	+	0.0277173i
$603$	−0.657403	+	10.4491i	−0.0267715	+	0.425521i
$604$	3.74591	−	0.961787i	0.152419	−	0.0391345i
$605$	19.4748	−	13.3195i	0.791763	−	0.541515i
$606$	11.8646	−	18.6957i	0.481968	−	0.759460i
$607$	14.1542	+	43.5622i	0.574502	+	1.76814i	0.637867	+	0.770146i	$0.279817\pi$
$607$	14.1542	+	43.5622i	0.574502	+	1.76814i	−0.0633650	+	0.997990i	$0.520183\pi$
$608$	0.310942	+	4.94228i	0.0126104	+	0.200436i
$609$	−6.07455	−	0.767394i	−0.246153	−	0.0310964i
$610$	4.79260	−	13.4366i	0.194047	−	0.544033i
$611$	−0.0813665	−	0.172913i	−0.00329173	−	0.00699529i
$612$	−5.62000	+	11.9431i	−0.227175	+	0.482772i
$613$	−28.9095	+	15.8931i	−1.16764	+	0.641918i	−0.943088	−	0.332543i	$-0.892093\pi$
$613$	−28.9095	+	15.8931i	−1.16764	+	0.641918i	−0.224557	+	0.974461i	$0.572093\pi$
$614$	7.22837	−	6.78789i	0.291713	−	0.273937i
$615$	61.3729	+	9.53435i	2.47479	+	0.384462i
$616$	0.320157	−	0.680369i	0.0128995	−	0.0274128i
$617$	9.92258	+	11.9943i	0.399468	+	0.482874i	0.931444	−	0.363886i	$-0.118550\pi$
$617$	9.92258	+	11.9943i	0.399468	+	0.482874i	−0.531975	+	0.846760i	$0.678550\pi$
$618$	−4.35257	+	13.3958i	−0.175086	+	0.538859i
$619$	−36.5698	−	9.38954i	−1.46987	−	0.377397i	−0.572947	−	0.819592i	$-0.694200\pi$
$619$	−36.5698	−	9.38954i	−1.46987	−	0.377397i	−0.896919	+	0.442195i	$0.854200\pi$
$620$	12.1859	+	15.6143i	0.489398	+	0.627085i
$621$	0.872045	−	13.8608i	0.0349939	−	0.556213i
$622$	0.331241	+	0.521952i	0.0132815	+	0.0209284i
$623$	−2.42533	+	2.27754i	−0.0971690	+	0.0912477i
$624$	−1.03491			−0.0414294
$625$	−22.0487	−	11.7836i	−0.881950	−	0.471343i
$626$	17.0507			0.681483
$627$	0.996805	−	0.936062i	0.0398086	−	0.0373827i
$628$	0.534833	+	0.842763i	0.0213422	+	0.0336299i
$629$	−2.56541	+	40.7761i	−0.102290	+	1.62585i
$630$	−0.945134	−	1.21104i	−0.0376550	−	0.0482490i
$631$	−33.7042	−	8.65376i	−1.34174	−	0.344501i	−0.491493	−	0.870881i	$-0.663549\pi$
$631$	−33.7042	−	8.65376i	−1.34174	−	0.344501i	−0.850249	+	0.526380i	$0.823549\pi$
$632$	7.63228	−	23.4898i	0.303596	−	0.934372i
$633$	20.9583	+	25.3342i	0.833018	+	1.00695i
$634$	−3.10245	+	6.59303i	−0.123214	+	0.261843i
$635$	−31.6862	−	4.92249i	−1.25743	−	0.195343i
$636$	−28.6425	+	26.8971i	−1.13575	+	1.06654i
$637$	1.35113	−	0.742789i	0.0535336	−	0.0294304i
$638$	−0.887895	+	1.88687i	−0.0351521	+	0.0747020i
$639$	0.302755	+	0.643386i	0.0119768	+	0.0254520i
$640$	−8.61598	+	24.1560i	−0.340577	+	0.954848i
$641$	−11.8649	−	1.49889i	−0.468636	−	0.0592025i	−0.112530	−	0.993648i	$-0.535896\pi$
$641$	−11.8649	−	1.49889i	−0.468636	−	0.0592025i	−0.356105	+	0.934446i	$0.615896\pi$
$642$	0.437209	+	6.94923i	0.0172553	+	0.274264i
$643$	−8.06131	−	24.8102i	−0.317907	−	0.978417i	−0.974541	−	0.224208i	$-0.928020\pi$
$643$	−8.06131	−	24.8102i	−0.317907	−	0.978417i	0.656634	−	0.754209i	$-0.271980\pi$
$644$	3.56316	−	5.61464i	0.140408	−	0.221248i
$645$	−9.47494	+	6.48025i	−0.373075	+	0.255160i
$646$	−1.86958	+	0.480027i	−0.0735577	+	0.0188864i
$647$	1.76145	−	27.9975i	0.0692499	−	1.10070i	−0.797946	−	0.602729i	$-0.794080\pi$
$647$	1.76145	−	27.9975i	0.0692499	−	1.10070i	0.867196	−	0.497967i	$-0.165920\pi$
$648$	−4.38017	+	22.9617i	−0.172069	+	0.902020i
$649$	−1.24910	+	3.84434i	−0.0490315	+	0.150904i
$650$	0.683837	−	0.0470899i	0.0268223	−	0.00184702i
$651$	1.96343	+	6.04281i	0.0769527	+	0.236836i
$652$	11.8747	−	1.50012i	0.465049	−	0.0587493i
$653$	0.725457	+	0.287229i	0.0283893	+	0.0112401i	0.382276	−	0.924048i	$-0.375140\pi$
$653$	0.725457	+	0.287229i	0.0283893	+	0.0112401i	−0.353887	+	0.935288i	$0.615140\pi$
$654$	11.0902	+	4.39094i	0.433663	+	0.171699i
$655$	15.9450	+	36.5494i	0.623022	+	1.42810i
$656$	−1.50807	−	23.9700i	−0.0588800	−	0.935872i
$657$	16.3875	−	11.9062i	0.639338	−	0.464506i
$658$	−0.249310	−	0.0640120i	−0.00971913	−	0.00249545i
$659$	−9.75561	−	9.16113i	−0.380025	−	0.356867i	0.470871	−	0.882202i	$-0.343940\pi$
$659$	−9.75561	−	9.16113i	−0.380025	−	0.356867i	−0.850895	+	0.525335i	$0.823940\pi$
$660$	5.28191	−	1.91929i	0.205598	−	0.0747082i
$661$	20.4866	+	11.2626i	0.796838	+	0.438065i	0.827501	−	0.561465i	$-0.189762\pi$
$661$	20.4866	+	11.2626i	0.796838	+	0.438065i	−0.0306632	+	0.999530i	$0.509762\pi$
$662$	5.29274	+	0.668629i	0.205708	+	0.0259870i
$663$	−0.354025	−	1.85586i	−0.0137492	−	0.0720758i
$664$	−15.7903	+	1.99477i	−0.612781	+	0.0774122i
$665$	−0.221348	+	1.00421i	−0.00858352	+	0.0389416i
$666$	−2.82985	−	14.8346i	−0.109654	−	0.574829i
$667$	−21.9223	+	34.5440i	−0.848834	+	1.33755i
$668$	−15.3501	−	11.1525i	−0.593914	−	0.431504i
$669$	23.1416	+	27.9734i	0.894705	+	1.08151i
$670$	−6.13673	+	1.39081i	−0.237083	+	0.0537317i
$671$	3.82288	+	6.02389i	0.147581	+	0.232550i
$672$	−4.16156	+	5.03046i	−0.160536	+	0.194054i
$673$	−13.9306	−	29.6041i	−0.536986	−	1.14115i	−0.970742	−	0.240123i	$-0.922812\pi$
$673$	−13.9306	−	29.6041i	−0.536986	−	1.14115i	0.433757	−	0.901030i	$-0.357188\pi$
$674$	−4.12709	−	2.99850i	−0.158969	−	0.115498i
$675$	−1.05437	+	8.76314i	−0.0405827	+	0.337294i
$676$	−17.1935	+	12.4918i	−0.661289	+	0.480455i
$677$	−14.6073	−	8.03041i	−0.561403	−	0.308634i	0.175668	−	0.984450i	$-0.443792\pi$
$677$	−14.6073	−	8.03041i	−0.561403	−	0.308634i	−0.737071	+	0.675816i	$0.763792\pi$
$678$	6.79078	−	1.74358i	0.260798	−	0.0669617i
$679$	1.77076	−	2.14049i	0.0679557	−	0.0821443i
$680$	−17.3901	−	2.70157i	−0.666879	−	0.103600i
$681$	23.5101	−	9.30831i	0.900909	−	0.356695i
$682$	2.16400			0.0828638
$683$	−44.7883	+	17.7329i	−1.71378	+	0.678532i	−0.999767	−	0.0216027i	$-0.993123\pi$
$683$	−44.7883	+	17.7329i	−1.71378	+	0.678532i	−0.714010	+	0.700135i	$0.753123\pi$
$684$	−2.86195	+	1.57337i	−0.109429	+	0.0601594i
$685$	6.96747	+	2.99064i	0.266213	+	0.114266i
$686$	0.793607	−	4.16023i	0.0303001	−	0.158838i
$687$	10.4033	+	9.76934i	0.396910	+	0.372724i
$688$	3.23582	+	3.03864i	0.123365	+	0.115847i
$689$	0.449116	−	2.35435i	0.0171100	−	0.0896935i
$690$	−23.4912	+	5.32396i	−0.894293	+	0.202680i
$691$	−29.0557	+	15.9735i	−1.10533	+	0.607662i	−0.926529	−	0.376223i	$-0.877223\pi$
$691$	−29.0557	+	15.9735i	−1.10533	+	0.607662i	−0.178804	+	0.983885i	$0.557223\pi$
$692$	−13.4550	+	5.32722i	−0.511483	+	0.202511i
$693$	0.768276			0.0291844
$694$	3.70660	−	1.46755i	0.140701	−	0.0557074i
$695$	−2.22283	+	4.39466i	−0.0843167	+	0.166699i
$696$	16.5268	−	19.9774i	0.626446	−	0.757243i
$697$	42.4688	−	10.9041i	1.60862	−	0.413023i
$698$	13.2417	+	7.27968i	0.501205	+	0.275540i
$699$	34.2608	−	24.8919i	1.29586	−	0.941499i
$700$	−2.46380	+	3.43369i	−0.0931227	+	0.129781i
$701$	−6.11792	−	4.44493i	−0.231070	−	0.167883i	0.466225	−	0.884666i	$-0.345614\pi$
$701$	−6.11792	−	4.44493i	−0.231070	−	0.167883i	−0.697296	+	0.716783i	$0.745614\pi$
$702$	−0.103040	−	0.218971i	−0.00388899	−	0.00826453i
$703$	−6.44386	+	7.78929i	−0.243035	+	0.293779i
$704$	−0.227373	−	0.358282i	−0.00856943	−	0.0135033i
$705$	−2.18332	−	3.66698i	−0.0822287	−	0.138106i
$706$	−4.50591	−	5.44671i	−0.169582	−	0.204990i
$707$	−6.73728	−	4.89492i	−0.253381	−	0.184092i
$708$	12.1387	−	19.1275i	0.456199	−	0.718855i
$709$	−4.26369	−	22.3510i	−0.160126	−	0.839411i	−0.968171	−	0.250290i	$-0.919474\pi$
$709$	−4.26369	−	22.3510i	−0.160126	−	0.839411i	0.808045	−	0.589121i	$-0.200526\pi$
$710$	−0.319721	+	0.283558i	−0.0119989	+	0.0106418i
$711$	25.0365	−	3.16284i	0.938940	−	0.118616i
$712$	−2.63996	−	13.8391i	−0.0989365	−	0.518643i
$713$	42.1214	+	5.32117i	1.57746	+	0.199279i
$714$	−2.23001	−	1.22596i	−0.0834559	−	0.0458802i
$715$	−0.191847	+	0.284099i	−0.00717466	+	0.0106247i
$716$	16.2287	+	15.2398i	0.606496	+	0.569538i
$717$	−46.9403	−	12.0522i	−1.75302	−	0.450098i
$718$	−2.63939	+	1.91763i	−0.0985010	+	0.0715652i
$719$	−2.50517	−	39.8185i	−0.0934269	−	1.48498i	−0.713622	−	0.700531i	$-0.752947\pi$
$719$	−2.50517	−	39.8185i	−0.0934269	−	1.48498i	0.620195	−	0.784447i	$-0.287053\pi$
$720$	−9.80295	+	0.955940i	−0.365335	+	0.0356258i
$721$	4.92537	+	1.95009i	0.183430	+	0.0726252i
$722$	10.1346	+	4.01255i	0.377169	+	0.149332i
$723$	4.25905	−	0.538043i	0.158396	−	0.0200100i
$724$	−11.3606	−	34.9644i	−0.422215	−	1.29944i
$725$	15.1584	−	21.1257i	0.562971	−	0.784590i
$726$	−4.46438	+	13.7400i	−0.165689	+	0.509938i
$727$	−1.90288	+	9.97523i	−0.0705738	+	0.369961i	0.929426	+	0.369009i	$0.120303\pi$
$727$	−1.90288	+	9.97523i	−0.0705738	+	0.369961i	−1.00000		0.000951549i	$0.999697\pi$
$728$	0.0161411	−	0.256556i	0.000598229	−	0.00950858i
$729$	−11.4052	+	2.92835i	−0.422414	+	0.108457i
$730$	9.64136	+	7.43300i	0.356843	+	0.275108i
$731$	−4.34217	+	6.84217i	−0.160601	+	0.253067i
$732$	−12.3560	−	38.0280i	−0.456693	−	1.40556i
$733$	−0.786746	−	12.5050i	−0.0290591	−	0.461881i	−0.985469	−	0.169854i	$-0.945670\pi$
$733$	−0.786746	−	12.5050i	−0.0290591	−	0.461881i	0.956410	−	0.292027i	$-0.0943297\pi$
$734$	9.13328	+	1.15380i	0.337115	+	0.0425876i
$735$	28.4216	−	19.4386i	1.04835	−	0.717002i
$736$	18.5747	+	39.4732i	0.684671	+	1.45500i
$737$	1.33989	−	2.84741i	0.0493555	−	0.104886i
$738$	−14.2024	+	7.80785i	−0.522799	+	0.287411i
$739$	14.9918	−	14.0783i	0.551483	−	0.517877i	−0.357943	−	0.933744i	$-0.616522\pi$
$739$	14.9918	−	14.0783i	0.551483	−	0.517877i	0.909426	+	0.415867i	$0.136522\pi$
$740$	−36.9625	+	18.9714i	−1.35877	+	0.697402i
$741$	0.199043	−	0.422987i	0.00731202	−	0.0155388i
$742$	−2.05780	−	2.48745i	−0.0755442	−	0.0913172i
$743$	11.0187	−	33.9122i	0.404239	−	1.24412i	−0.517291	−	0.855810i	$-0.673059\pi$
$743$	11.0187	−	33.9122i	0.404239	−	1.24412i	0.921529	−	0.388309i	$-0.126941\pi$
$744$	−26.0601	−	6.69111i	−0.955411	−	0.245308i
$745$	−5.48170	+	1.99188i	−0.200834	+	0.0729770i
$746$	−0.615038	+	9.77575i	−0.0225181	+	0.357916i
$747$	−8.71346	−	13.7302i	−0.318809	−	0.502362i
$748$	2.89207	−	2.71583i	0.105744	−	0.0993006i
$749$	2.61873			0.0956865
$750$	15.0976	−	2.52888i	0.551288	−	0.0923415i
$751$	11.4975			0.419549			0.209774	−	0.977750i	$-0.432727\pi$
$751$	11.4975			0.419549			0.209774	+	0.977750i	$0.432727\pi$
$752$	−1.20303	+	1.12972i	−0.0438701	+	0.0411968i
$753$	−29.4175	−	46.3546i	−1.07203	−	1.68925i
$754$	−0.0447643	+	0.711508i	−0.00163022	+	0.0259116i
$755$	−2.94843	+	4.36623i	−0.107304	+	0.158903i
$756$	1.44519	+	0.371062i	0.0525611	+	0.0134954i
$757$	6.33823	−	19.5071i	0.230367	−	0.708997i	−0.767335	−	0.641246i	$-0.778418\pi$
$757$	6.33823	−	19.5071i	0.230367	−	0.708997i	0.997702	−	0.0677505i	$-0.0215822\pi$
$758$	6.29582	+	7.61034i	0.228675	+	0.276420i
$759$	5.12905	−	10.8998i	0.186173	−	0.395637i
$760$	−3.08817	−	3.06994i	−0.112020	−	0.111358i
$761$	−17.4811	+	16.4158i	−0.633689	+	0.595073i	−0.933348	−	0.358973i	$-0.883127\pi$
$761$	−17.4811	+	16.4158i	−0.633689	+	0.595073i	0.299659	+	0.954046i	$0.403127\pi$
$762$	17.2061	−	9.45913i	0.623311	−	0.342668i
$763$	1.91005	−	4.05905i	0.0691483	−	0.146948i
$764$	13.9471	+	29.6390i	0.504587	+	1.07230i
$765$	−5.06769	−	17.2523i	−0.183223	−	0.623759i
$766$	15.7839	+	1.99397i	0.570296	+	0.0720452i
$767$	0.0867701	+	1.37917i	0.00313309	+	0.0497990i
$768$	−3.95731	−	12.1794i	−0.142797	−	0.439485i
$769$	−26.5376	+	41.8165i	−0.956969	+	1.50794i	−0.0984617	+	0.995141i	$0.531392\pi$
$769$	−26.5376	+	41.8165i	−0.956969	+	1.50794i	−0.858507	+	0.512801i	$0.828608\pi$
$770$	0.130132	+	0.443019i	0.00468964	+	0.0159653i
$771$	−8.81996	+	2.26458i	−0.317643	+	0.0815568i
$772$	−0.808369	+	12.8487i	−0.0290938	+	0.462433i
$773$	−7.01875	+	36.7936i	−0.252447	+	1.32337i	0.599765	+	0.800177i	$0.295261\pi$
$773$	−7.01875	+	36.7936i	−0.252447	+	1.32337i	−0.852212	+	0.523197i	$0.824739\pi$
$774$	0.925633	−	2.84881i	0.0332712	−	0.102398i
$775$	−26.5337	−	4.89895i	−0.953120	−	0.175975i
$776$	3.63515	+	11.1878i	0.130494	+	0.401620i
$777$	−13.2227	+	1.67042i	−0.474363	+	0.0599260i
$778$	−4.95213	−	1.96069i	−0.177542	−	0.0702940i
$779$	10.0871	+	3.99376i	0.361407	+	0.143091i
$780$	1.43738	−	1.27480i	0.0514664	−	0.0456452i
$781$	−0.0134199	−	0.213302i	−0.000480200	−	0.00763256i
$782$	−13.7568	+	9.99487i	−0.491941	+	0.357416i
$783$	−8.89150	−	2.28295i	−0.317756	−	0.0815860i
$784$	−9.70638	−	9.11490i	−0.346656	−	0.325532i
$785$	−1.30688	−	0.375493i	−0.0466446	−	0.0134019i
$786$	−21.3967	−	11.7629i	−0.763194	−	0.419569i
$787$	−22.9067	−	2.89379i	−0.816535	−	0.103152i	−0.294038	−	0.955794i	$-0.594999\pi$
$787$	−22.9067	−	2.89379i	−0.816535	−	0.103152i	−0.522497	+	0.852641i	$0.674999\pi$
$788$	−5.16478	−	27.0747i	−0.183988	−	0.964497i
$789$	49.4663	−	6.24905i	1.76105	−	0.222472i
$790$	6.06455	+	13.9013i	0.215767	+	0.494586i
$791$	−0.494090	−	2.59011i	−0.0175678	−	0.0920937i
$792$	−1.74321	+	2.74686i	−0.0619422	+	0.0976054i
$793$	1.97326	+	1.43366i	0.0700725	+	0.0509107i
$794$	0.850097	+	1.02759i	0.0301688	+	0.0364678i
$795$	4.87952	−	53.3037i	0.173059	−	1.89049i
$796$	20.3407	+	32.0517i	0.720955	+	1.13604i
$797$	−13.4398	+	16.2459i	−0.476061	+	0.575459i	−0.952805	−	0.303583i	$-0.901817\pi$
$797$	−13.4398	+	16.2459i	−0.476061	+	0.575459i	0.476744	+	0.879042i	$0.341817\pi$
$798$	−0.268095	−	0.569731i	−0.00949046	−	0.0201683i
$799$	−2.43744	−	1.77090i	−0.0862303	−	0.0626500i
$800$	−10.3587	−	25.7172i	−0.366236	−	0.909242i
$801$	11.6457	−	8.46112i	0.411482	−	0.298959i
$802$	−3.06205	−	1.68338i	−0.108125	−	0.0594421i
$803$	−5.89712	+	1.51412i	−0.208105	+	0.0534323i
$804$	−11.2420	+	13.5893i	−0.396476	+	0.479257i
$805$	1.44361	+	8.94318i	0.0508807	+	0.315206i
$806$	0.687854	−	0.272341i	0.0242286	−	0.00959279i
$807$	−62.0417			−2.18397
$808$	32.7879	−	12.9816i	1.15347	−	0.456692i
$809$	−19.2374	+	10.5758i	−0.676349	+	0.371826i	−0.782610	−	0.622512i	$-0.786112\pi$
$809$	−19.2374	+	10.5758i	−0.676349	+	0.371826i	0.106261	+	0.994338i	$0.466112\pi$
$810$	−7.34344	−	12.3336i	−0.258022	−	0.433359i
$811$	5.64408	−	29.5873i	0.198190	−	1.03895i	−0.734592	−	0.678510i	$-0.762626\pi$
$811$	5.64408	−	29.5873i	0.198190	−	1.03895i	0.932782	−	0.360441i	$-0.117374\pi$
$812$	−3.20415	−	3.00890i	−0.112444	−	0.105592i
$813$	47.6365	+	44.7337i	1.67069	+	1.56888i
$814$	−0.850571	+	4.45885i	−0.0298125	+	0.156283i
$815$	−10.7466	+	12.2626i	−0.376437	+	0.429541i
$816$	−14.2979	+	7.86033i	−0.500526	+	0.275166i
$817$	−1.86430	+	0.738128i	−0.0652236	+	0.0258238i
$818$	−6.48171			−0.226628
$819$	0.244206	−	0.0966881i	0.00853325	−	0.00337855i
$820$	31.6209	+	31.4342i	1.10425	+	1.09773i
$821$	−3.00960	+	3.63798i	−0.105036	+	0.126967i	−0.820411	−	0.571774i	$-0.806256\pi$
$821$	−3.00960	+	3.63798i	−0.105036	+	0.126967i	0.715376	+	0.698740i	$0.246256\pi$
$822$	−4.49685	+	1.15460i	−0.156846	+	0.0402711i
$823$	7.51852	+	4.13334i	0.262079	+	0.144079i	0.607376	−	0.794414i	$-0.292222\pi$
$823$	7.51852	+	4.13334i	0.262079	+	0.144079i	−0.345297	+	0.938493i	$0.612222\pi$
$824$	−18.1479	+	13.1852i	−0.632210	+	0.459328i
$825$	−3.64841	+	6.73052i	−0.127021	+	0.234327i
$826$	1.50583	+	1.09405i	0.0523945	+	0.0380669i
$827$	−19.4474	−	41.3279i	−0.676253	−	1.43711i	−0.888026	−	0.459793i	$-0.847924\pi$
$827$	−19.4474	−	41.3279i	−0.676253	−	1.43711i	0.211773	−	0.977319i	$-0.432076\pi$
$828$	−18.3394	+	22.1686i	−0.637339	+	0.770411i
$829$	−7.32652	−	11.5448i	−0.254461	−	0.400966i	0.692950	−	0.720985i	$-0.256311\pi$
$829$	−7.32652	−	11.5448i	−0.254461	−	0.400966i	−0.947411	+	0.320020i	$0.896311\pi$
$830$	6.44148	−	7.35018i	0.223587	−	0.255128i
$831$	−37.9741	−	45.9028i	−1.31731	−	1.59235i
$832$	−0.117363	−	0.0852694i	−0.00406884	−	0.00295618i
$833$	13.0251	−	20.5242i	0.451291	−	0.711121i
$834$	−0.565061	−	2.96215i	−0.0195665	−	0.102571i
$835$	25.7256	−	2.50865i	0.890272	−	0.0868153i
$836$	0.973903	−	0.123033i	0.0336831	−	0.00425517i
$837$	1.78503	+	9.35744i	0.0616995	+	0.323440i
$838$	1.16682	+	0.147404i	0.0403071	+	0.00509197i
$839$	4.20237	+	2.31027i	0.145082	+	0.0797595i	0.552641	−	0.833419i	$-0.313620\pi$
$839$	4.20237	+	2.31027i	0.145082	+	0.0797595i	−0.407559	+	0.913179i	$0.633620\pi$
$840$	−0.197311	−	5.73746i	−0.00680787	−	0.197961i
$841$	−1.42660	−	1.33966i	−0.0491930	−	0.0461953i
$842$	−2.39485	−	0.614893i	−0.0825320	−	0.0211906i
$843$	−2.21199	+	1.60711i	−0.0761850	+	0.0553517i
$844$	1.48209	+	23.5571i	0.0510156	+	0.810870i
$845$	6.23194	−	28.2730i	0.214385	−	0.972621i
$846$	1.03545	+	0.409963i	0.0355994	+	0.0140948i
$847$	5.05189	+	2.00019i	0.173585	+	0.0687272i
$848$	−20.5354	+	2.59422i	−0.705187	+	0.0890858i
$849$	−3.17890	−	9.78366i	−0.109100	−	0.335774i
$850$	9.08999	−	5.84447i	0.311784	−	0.200464i
$851$	−27.5202	+	84.6983i	−0.943379	+	2.90342i
$852$	−0.224445	+	1.17658i	−0.00768937	+	0.0403091i
$853$	−0.337406	+	5.36291i	−0.0115526	+	0.183623i	0.988018	+	0.154336i	$0.0493237\pi$
$853$	−0.337406	+	5.36291i	−0.0115526	+	0.183623i	−0.999571	+	0.0292870i	$0.990676\pi$
$854$	3.18204	−	0.817010i	0.108887	−	0.0279575i
$855$	1.49468	−	4.19053i	0.0511171	−	0.143313i
$856$	−5.94188	+	9.36290i	−0.203089	+	0.320017i
$857$	−7.85132	−	24.1639i	−0.268196	−	0.825422i	−0.990940	−	0.134306i	$-0.957119\pi$
$857$	−7.85132	−	24.1639i	−0.268196	−	0.825422i	0.722744	−	0.691116i	$-0.242881\pi$
$858$	−0.0131802	−	0.209494i	−0.000449965	−	0.00715200i
$859$	40.3000	+	5.09107i	1.37502	+	0.173705i	0.777869	−	0.628426i	$-0.216301\pi$
$859$	40.3000	+	5.09107i	1.37502	+	0.173705i	0.597148	+	0.802131i	$0.296301\pi$
$860$	−8.23724	−	0.234458i	−0.280888	−	0.00799496i
$861$	6.08995	+	12.9418i	0.207545	+	0.441056i
$862$	−0.857469	+	1.82221i	−0.0292055	+	0.0620649i
$863$	8.65047	−	4.75563i	0.294465	−	0.161884i	−0.327673	−	0.944791i	$-0.606264\pi$
$863$	8.65047	−	4.75563i	0.294465	−	0.161884i	0.622138	+	0.782908i	$0.286264\pi$
$864$	−7.13547	+	6.70065i	−0.242754	+	0.227961i
$865$	8.89789	−	17.5916i	0.302537	−	0.598134i
$866$	−0.103692	+	0.220358i	−0.00352361	+	0.00748805i
$867$	5.78993	+	6.99882i	0.196636	+	0.237692i
$868$	−1.40951	+	4.33801i	−0.0478418	+	0.147242i
$869$	−7.34675	−	1.88632i	−0.249221	−	0.0639892i
$870$	0.547203	+	15.9118i	0.0185519	+	0.539459i
$871$	0.0675522	−	1.07371i	0.00228892	−	0.0363813i
$872$	10.1787	+	16.0390i	0.344693	+	0.543150i
$873$	−8.76169	+	8.22777i	−0.296538	+	0.278468i
$874$	−4.20739			−0.142317
$875$	−0.592686	−	5.72665i	−0.0200365	−	0.193596i
$876$	34.1220			1.15287
$877$	−32.8417	+	30.8404i	−1.10899	+	1.04141i	−0.110115	+	0.993919i	$0.535122\pi$
$877$	−32.8417	+	30.8404i	−1.10899	+	1.04141i	−0.998872	+	0.0474890i	$0.984878\pi$
$878$	−8.68702	−	13.6886i	−0.293173	−	0.461966i
$879$	−0.467602	+	7.43232i	−0.0157718	+	0.250686i
$880$	2.84535	+	0.817523i	0.0959166	+	0.0275587i
$881$	47.6892	+	12.2445i	1.60669	+	0.412528i	0.942276	−	0.334838i	$-0.108681\pi$
$881$	47.6892	+	12.2445i	1.60669	+	0.412528i	0.664413	+	0.747365i	$0.268681\pi$
$882$	−2.77659	+	8.54546i	−0.0934926	+	0.287741i
$883$	−10.6560	−	12.8809i	−0.358604	−	0.433478i	0.560100	−	0.828425i	$-0.310763\pi$
$883$	−10.6560	−	12.8809i	−0.358604	−	0.433478i	−0.918704	+	0.394948i	$0.870763\pi$
$884$	0.577490	−	1.22723i	0.0194231	−	0.0412762i
$885$	4.91798	+	30.4669i	0.165316	+	1.02413i
$886$	2.13908	−	2.00873i	0.0718638	−	0.0674846i
$887$	9.86752	−	5.42471i	0.331319	−	0.182144i	−0.307408	−	0.951578i	$-0.599462\pi$
$887$	9.86752	−	5.42471i	0.331319	−	0.182144i	0.638727	+	0.769434i	$0.279462\pi$
$888$	24.0299	−	51.0661i	0.806390	−	1.71367i
$889$	−3.14418	−	6.68172i	−0.105452	−	0.224098i
$890$	6.85160	+	5.28223i	0.229666	+	0.177061i
$891$	7.12218	+	0.899741i	0.238602	+	0.0301425i
$892$	1.63648	+	26.0111i	0.0547934	+	0.870917i
$893$	−0.230363	−	0.708984i	−0.00770880	−	0.0237252i
$894$	1.91358	−	3.01532i	0.0639998	−	0.100848i
$895$	−30.3156	−	0.862880i	−1.01334	−	0.0288429i
$896$	−5.72058	+	1.46879i	−0.191111	+	0.0490690i
$897$	0.258587	−	4.11013i	0.00863397	−	0.137233i
$898$	−1.54405	+	8.09421i	−0.0515257	+	0.270107i
$899$	8.67196	−	26.6895i	0.289226	−	0.890146i
$900$	12.4378	−	13.4030i	0.414592	−	0.446768i
$901$	−11.6769	−	35.9379i	−0.389015	−	1.19727i
$902$	4.83299	−	0.610549i	0.160921	−	0.0203290i
$903$	−2.45786	−	0.973137i	−0.0817926	−	0.0323840i
$904$	10.3816	+	4.11038i	0.345288	+	0.136709i
$905$	43.1835	+	25.3664i	1.43547	+	0.843208i
$906$	−0.202562	−	3.21964i	−0.00672969	−	0.106965i
$907$	28.6470	−	20.8133i	0.951208	−	0.691093i	0.000115950	−	1.00000i	$-0.499963\pi$
$907$	28.6470	−	20.8133i	0.951208	−	0.691093i	0.951092	+	0.308907i	$0.0999631\pi$
$908$	17.5819	+	4.51426i	0.583475	+	0.149811i
$909$	26.2653	+	24.6647i	0.871164	+	0.818078i
$910$	0.0971184	+	0.124442i	0.00321944	+	0.00412520i
$911$	11.0816	+	6.09216i	0.367150	+	0.201842i	0.654639	−	0.755942i	$-0.272821\pi$
$911$	11.0816	+	6.09216i	0.367150	+	0.201842i	−0.287489	+	0.957784i	$0.592821\pi$
$912$	−4.00527	−	0.505983i	−0.132628	−	0.0167548i
$913$	0.915882	+	4.80122i	0.0303113	+	0.158897i
$914$	−16.9626	+	2.14288i	−0.561074	+	0.0708801i
$915$	46.9672	+	27.5890i	1.55269	+	0.912064i
$916$	1.91973	+	10.0636i	0.0634297	+	0.332510i
$917$	−4.92052	+	7.75350i	−0.162490	+	0.256043i
$918$	−3.08669	−	2.24261i	−0.101876	−	0.0740173i
$919$	1.44365	+	1.74507i	0.0476215	+	0.0575645i	0.793786	−	0.608197i	$-0.208107\pi$
$919$	1.44365	+	1.74507i	0.0476215	+	0.0575645i	−0.746165	+	0.665761i	$0.768107\pi$
$920$	−35.2506	−	15.1305i	−1.16218	−	0.498839i
$921$	20.2873	+	31.9677i	0.668491	+	1.05337i
$922$	−3.84910	+	4.65276i	−0.126763	+	0.153230i
$923$	−0.0311099	−	0.0661119i	−0.00102399	−	0.00217610i
$924$	1.04702	+	0.760702i	0.0344443	+	0.0250253i
$925$	20.5234	−	52.7464i	0.674804	−	1.73429i
$926$	−17.4842	+	12.7030i	−0.574565	+	0.417446i
$927$	−20.0846	−	11.0416i	−0.659664	−	0.362653i
$928$	27.9298	−	7.17114i	0.916839	−	0.235404i
$929$	−5.44214	+	6.57842i	−0.178551	+	0.215831i	−0.852194	−	0.523226i	$-0.824728\pi$
$929$	−5.44214	+	6.57842i	−0.178551	+	0.215831i	0.673643	+	0.739057i	$0.264728\pi$
$930$	14.6987	−	7.54424i	0.481989	−	0.247385i
$931$	5.59227	−	2.21414i	0.183279	−	0.0725654i
$932$	30.4013			0.995828
$933$	−2.19466	+	0.868927i	−0.0718499	+	0.0284474i
$934$	−14.2766	+	7.84863i	−0.467145	+	0.256815i
$935$	−0.492690	+	5.38213i	−0.0161127	+	0.176014i
$936$	−0.208407	+	1.09251i	−0.00681199	+	0.0357097i
$937$	25.2569	+	23.7179i	0.825109	+	0.774829i	0.976926	−	0.213580i	$-0.0685124\pi$
$937$	25.2569	+	23.7179i	0.825109	+	0.774829i	−0.151817	+	0.988409i	$0.548512\pi$
$938$	−1.05632	−	0.991953i	−0.0344902	−	0.0323884i
$939$	−12.1994	+	63.9514i	−0.398112	+	2.08697i
$940$	0.279292	−	3.05097i	0.00910949	−	0.0995118i
$941$	−7.21837	+	3.96833i	−0.235312	+	0.129364i	−0.595048	−	0.803690i	$-0.702867\pi$
$941$	−7.21837	+	3.96833i	−0.235312	+	0.129364i	0.359736	+	0.933054i	$0.382867\pi$
$942$	0.774136	−	0.306502i	0.0252227	−	0.00998637i
$943$	95.5736			3.11231
$944$	11.0959	−	4.39318i	0.361141	−	0.142986i
$945$	−1.80833	+	0.928145i	−0.0588251	+	0.0301926i
$946$	−0.573895	+	0.693720i	−0.0186589	+	0.0225548i
$947$	−16.9440	+	4.35047i	−0.550605	+	0.141371i	−0.513735	−	0.857949i	$-0.671739\pi$
$947$	−16.9440	+	4.35047i	−0.550605	+	0.141371i	−0.0368699	+	0.999320i	$0.511739\pi$
$948$	37.2516	+	20.4793i	1.20988	+	0.665136i
$949$	−1.68392	+	1.22344i	−0.0546623	+	0.0397145i
$950$	2.66960	+	0.152094i	0.0866132	+	0.00493457i
$951$	−22.5085	−	16.3534i	−0.729888	−	0.530295i
$952$	−1.72559	−	3.66707i	−0.0559268	−	0.118851i
$953$	−29.2542	+	35.3623i	−0.947637	+	1.14550i	0.0415947	+	0.999135i	$0.486756\pi$
$953$	−29.2542	+	35.3623i	−0.947637	+	1.14550i	−0.989231	+	0.146361i	$0.953244\pi$
$954$	7.48420	+	11.7932i	0.242310	+	0.381819i
$955$	−41.0058	−	17.6009i	−1.32692	−	0.569551i
$956$	−22.1763	−	26.8066i	−0.717233	−	0.866986i
$957$	−6.44175	−	4.68020i	−0.208232	−	0.151289i
$958$	4.31961	−	6.80662i	0.139560	−	0.219912i
$959$	0.327186	+	1.71517i	0.0105654	+	0.0553857i
$960$	−2.79346	−	1.64090i	−0.0901585	−	0.0529600i
$961$	1.86361	−	0.235429i	0.0601166	−	0.00759449i
$962$	0.290785	+	1.52435i	0.00937527	+	0.0491469i
$963$	−11.2409	−	1.42005i	−0.362232	−	0.0457605i
$964$	2.70059	+	1.48466i	0.0869803	+	0.0478178i
$965$	−10.7902	−	13.8259i	−0.347349	−	0.445072i
$966$	−4.04356	−	3.79716i	−0.130099	−	0.122172i
$967$	12.6814	+	3.25602i	0.407805	+	0.104707i	0.447020	−	0.894524i	$-0.352485\pi$
$967$	12.6814	+	3.25602i	0.407805	+	0.104707i	−0.0392141	+	0.999231i	$0.512485\pi$
$968$	−18.6141	+	13.5239i	−0.598278	+	0.434675i
$969$	−0.462776	−	7.35561i	−0.0148665	−	0.236296i
$970$	−6.22853	−	3.65870i	−0.199986	−	0.117474i
$971$	53.0231	+	20.9933i	1.70159	+	0.673708i	0.999272	−	0.0381547i	$-0.0121480\pi$
$971$	53.0231	+	20.9933i	1.70159	+	0.673708i	0.702319	+	0.711862i	$0.252148\pi$
$972$	−29.3255	−	11.6108i	−0.940616	−	0.372416i
$973$	−1.12520	+	0.142145i	−0.0360721	+	0.00455697i
$974$	3.00364	+	9.24425i	0.0962428	+	0.296205i
$975$	−0.312652	+	2.59853i	−0.0100129	+	0.0832196i
$976$	6.50904	−	20.0328i	0.208349	−	0.641234i
$977$	1.82512	−	9.56763i	0.0583908	−	0.306095i	−0.941096	−	0.338141i	$-0.890202\pi$
$977$	1.82512	−	9.56763i	0.0583908	−	0.306095i	0.999486	+	0.0320452i	$0.0102020\pi$
$978$	0.626901	−	9.96431i	0.0200461	−	0.318623i
$979$	−4.19077	+	1.07601i	−0.133937	+	0.0343893i
$980$	24.7089	+	0.703296i	0.789298	+	0.0224660i
$981$	−10.3999	+	16.3876i	−0.332044	+	0.523217i
$982$	0.840939	+	2.58814i	0.0268354	+	0.0825910i
$983$	−0.604303	−	9.60511i	−0.0192743	−	0.306356i	−0.995839	−	0.0911312i	$-0.970952\pi$
$983$	−0.604303	−	9.60511i	−0.0192743	−	0.306356i	0.976565	−	0.215224i	$-0.0690483\pi$
$984$	−60.0895	−	7.59107i	−1.91558	−	0.241995i
$985$	29.7371	+	22.9258i	0.947503	+	0.730476i
$986$	4.78560	+	10.1699i	0.152405	+	0.323876i
$987$	0.418463	−	0.889279i	0.0133198	−	0.0283060i
$988$	0.294083	−	0.161674i	0.00935604	−	0.00514352i
$989$	−12.8765	+	12.0918i	−0.409448	+	0.384497i
$990$	−0.318356	−	1.97222i	−0.0101180	−	0.0626811i
$991$	14.9784	−	31.8307i	0.475804	−	1.01114i	−0.512507	−	0.858683i	$-0.671283\pi$
$991$	14.9784	−	31.8307i	0.475804	−	1.01114i	0.988311	−	0.152452i	$-0.0487169\pi$
$992$	−19.0739	−	23.0563i	−0.605596	−	0.732039i
$993$	−6.29463	+	19.3729i	−0.199754	+	0.614780i
$994$	−0.0953221	−	0.0244745i	−0.00302343	−	0.000776285i
$995$	−49.7030	−	14.2806i	−1.57569	−	0.452727i
$996$	1.72004	−	27.3392i	0.0545015	−	0.866277i
$997$	−22.1493	−	34.9018i	−0.701477	−	1.10535i	−0.989048	−	0.147591i	$-0.952848\pi$
$997$	−22.1493	−	34.9018i	−0.701477	−	1.10535i	0.287572	−	0.957759i	$-0.407152\pi$
$998$	17.2144	−	16.1654i	0.544911	−	0.511706i
$999$	−19.9823			−0.632212

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	125.2.g.a.11.7	✓	220
5.2	odd	4		625.2.h.b.199.13		440
5.3	odd	4		625.2.h.b.199.10		440
5.4	even	2		625.2.g.a.426.5		220
125.34	even	50		625.2.g.a.201.5		220
125.62	odd	100		625.2.h.b.424.10		440
125.63	odd	100		625.2.h.b.424.13		440
125.91	even	25	inner	125.2.g.a.91.7	yes	220

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
125.2.g.a.11.7	✓	220	1.1	even	1	trivial
125.2.g.a.91.7	yes	220	125.91	even	25	inner
625.2.g.a.201.5		220	125.34	even	50
625.2.g.a.426.5		220	5.4	even	2
625.2.h.b.199.10		440	5.3	odd	4
625.2.h.b.199.13		440	5.2	odd	4
625.2.h.b.424.10		440	125.62	odd	100
625.2.h.b.424.13		440	125.63	odd	100

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:	\( N \)	\(=\)	\( 125 = 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	125.g (of order \(25\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.436521 - 0.409921i) q^{2} +(1.22515 + 1.93053i) q^{3} +(-0.103065 + 1.63818i) q^{4} +(-1.37573 - 1.76278i) q^{5} +(1.32617 + 0.340503i) q^{6} +(0.159126 - 0.489740i) q^{7} +(1.38994 + 1.68015i) q^{8} +(-0.948615 + 2.01591i) q^{9} +O(q^{10})\)	\(q+(0.436521 - 0.409921i) q^{2} +(1.22515 + 1.93053i) q^{3} +(-0.103065 + 1.63818i) q^{4} +(-1.37573 - 1.76278i) q^{5} +(1.32617 + 0.340503i) q^{6} +(0.159126 - 0.489740i) q^{7} +(1.38994 + 1.68015i) q^{8} +(-0.948615 + 2.01591i) q^{9} +(-1.32313 - 0.205550i) q^{10} +(0.488159 - 0.458412i) q^{11} +(-3.28882 + 1.80804i) q^{12} +(0.0974761 - 0.207147i) q^{13} +(-0.131293 - 0.279011i) q^{14} +(1.71762 - 4.81555i) q^{15} +(-1.96148 - 0.247792i) q^{16} +(-0.226633 - 3.60222i) q^{17} +(0.412273 + 1.26884i) q^{18} +(0.478528 - 0.754039i) q^{19} +(3.02952 - 2.07200i) q^{20} +(1.14041 - 0.292808i) q^{21} +(0.0251793 - 0.400214i) q^{22} +(1.47421 - 7.72809i) q^{23} +(-1.54069 + 4.74175i) q^{24} +(-1.21475 + 4.85019i) q^{25} +(-0.0423636 - 0.130382i) q^{26} +(1.75135 - 0.221247i) q^{27} +(0.785879 + 0.311152i) q^{28} +(-4.83511 - 1.91435i) q^{29} +(-1.22422 - 2.80618i) q^{30} +(0.338845 + 5.38579i) q^{31} +(-4.48601 + 3.25928i) q^{32} +(1.48305 + 0.380782i) q^{33} +(-1.57556 - 1.47955i) q^{34} +(-1.08222 + 0.393244i) q^{35} +(-3.20464 - 1.76177i) q^{36} +(-11.2304 - 1.41873i) q^{37} +(-0.100209 - 0.525313i) q^{38} +(0.519327 - 0.0656063i) q^{39} +(1.04955 - 4.76157i) q^{40} +(2.27631 + 11.9328i) q^{41} +(0.377786 - 0.595296i) q^{42} +(-1.81640 - 1.31969i) q^{43} +(0.700647 + 0.846937i) q^{44} +(4.85863 - 1.10114i) q^{45} +(-2.52438 - 3.97779i) q^{46} +(0.532079 - 0.643173i) q^{47} +(-1.92474 - 4.09028i) q^{48} +(5.44859 + 3.95864i) q^{49} +(1.45793 + 2.61517i) q^{50} +(6.67654 - 4.85079i) q^{51} +(0.329297 + 0.181033i) q^{52} +(10.1404 - 2.60362i) q^{53} +(0.673808 - 0.814494i) q^{54} +(-1.47965 - 0.229866i) q^{55} +(1.04401 - 0.413353i) q^{56} +2.04197 q^{57} +(-2.89536 + 1.14635i) q^{58} +(-5.28955 + 2.90796i) q^{59} +(7.71169 + 3.31008i) q^{60} +(-1.99636 + 10.4653i) q^{61} +(2.35566 + 2.21211i) q^{62} +(0.836322 + 0.785359i) q^{63} +(0.118737 - 0.622443i) q^{64} +(-0.499254 + 0.113149i) q^{65} +(0.803473 - 0.441713i) q^{66} +(4.36929 - 1.72992i) q^{67} +5.92443 q^{68} +(16.7255 - 6.62208i) q^{69} +(-0.311211 + 0.615282i) q^{70} +(0.203437 - 0.245913i) q^{71} +(-4.70554 + 1.20818i) q^{72} +(-7.96721 - 4.38001i) q^{73} +(-5.48390 + 3.98428i) q^{74} +(-10.8517 + 3.59711i) q^{75} +(1.18593 + 0.861627i) q^{76} +(-0.146824 - 0.312017i) q^{77} +(0.199804 - 0.241522i) q^{78} +(-6.06918 - 9.56349i) q^{79} +(2.26166 + 3.79854i) q^{80} +(6.83324 + 8.25997i) q^{81} +(5.88517 + 4.27582i) q^{82} +(-3.91097 + 6.16271i) q^{83} +(0.362134 + 1.89837i) q^{84} +(-6.03812 + 5.35517i) q^{85} +(-1.33387 + 0.168507i) q^{86} +(-2.22802 - 11.6797i) q^{87} +(1.44871 + 0.183015i) q^{88} +(-5.66187 - 3.11264i) q^{89} +(1.66951 - 2.47233i) q^{90} +(-0.0859372 - 0.0807004i) q^{91} +(12.5080 + 3.21152i) q^{92} +(-9.98230 + 7.25257i) q^{93} +(-0.0313862 - 0.498869i) q^{94} +(-1.98752 + 0.193815i) q^{95} +(-11.7882 - 4.66727i) q^{96} +(5.01593 + 1.98595i) q^{97} +(4.00116 - 0.505463i) q^{98} +(0.461042 + 1.41894i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 220 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 15 q^{5} - 20 q^{6} - 15 q^{7} - 5 q^{8} - 20 q^{9}+O(q^{10}) \) 220 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 15 * q^5 - 20 * q^6 - 15 * q^7 - 5 * q^8 - 20 * q^9	\( 220 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 15 q^{5} - 20 q^{6} - 15 q^{7} - 5 q^{8} - 20 q^{9} - 20 q^{10} - 15 q^{11} - 100 q^{12} - 20 q^{13} - 10 q^{14} - 15 q^{17} + 10 q^{18} - 10 q^{19} + 5 q^{20} - 5 q^{21} + 25 q^{22} - 90 q^{23} + 15 q^{24} - 45 q^{25} + 15 q^{26} + 10 q^{27} + 30 q^{28} - 10 q^{29} + 40 q^{30} - 10 q^{31} + 20 q^{32} + 15 q^{33} + 5 q^{34} + 10 q^{35} - 210 q^{36} + 20 q^{37} + 30 q^{38} + 45 q^{40} - 5 q^{41} + 70 q^{42} + 25 q^{43} + 15 q^{44} - 100 q^{45} - 100 q^{47} + 105 q^{48} - 20 q^{49} + 60 q^{50} + 25 q^{51} + 85 q^{52} + 20 q^{53} + 60 q^{54} + 15 q^{55} - 105 q^{56} + 40 q^{57} - 225 q^{58} + 5 q^{59} - 35 q^{60} + 65 q^{62} + 85 q^{63} + 45 q^{64} + 45 q^{65} + 55 q^{66} - 105 q^{67} + 80 q^{68} + 40 q^{69} + 95 q^{70} - 85 q^{71} + 160 q^{72} + 40 q^{73} + 35 q^{74} + 55 q^{75} + 35 q^{76} + 75 q^{77} - 10 q^{78} - 330 q^{80} + 55 q^{81} - 95 q^{82} + 50 q^{83} + 115 q^{84} + 85 q^{85} + 40 q^{86} + 95 q^{87} + 165 q^{88} + 55 q^{89} + 170 q^{90} - 105 q^{91} + 155 q^{92} - 185 q^{93} + 60 q^{94} + 30 q^{95} + 135 q^{96} + 65 q^{97} + 135 q^{98} + 45 q^{99}+O(q^{100}) \) 220 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 15 * q^5 - 20 * q^6 - 15 * q^7 - 5 * q^8 - 20 * q^9 - 20 * q^10 - 15 * q^11 - 100 * q^12 - 20 * q^13 - 10 * q^14 - 15 * q^17 + 10 * q^18 - 10 * q^19 + 5 * q^20 - 5 * q^21 + 25 * q^22 - 90 * q^23 + 15 * q^24 - 45 * q^25 + 15 * q^26 + 10 * q^27 + 30 * q^28 - 10 * q^29 + 40 * q^30 - 10 * q^31 + 20 * q^32 + 15 * q^33 + 5 * q^34 + 10 * q^35 - 210 * q^36 + 20 * q^37 + 30 * q^38 + 45 * q^40 - 5 * q^41 + 70 * q^42 + 25 * q^43 + 15 * q^44 - 100 * q^45 - 100 * q^47 + 105 * q^48 - 20 * q^49 + 60 * q^50 + 25 * q^51 + 85 * q^52 + 20 * q^53 + 60 * q^54 + 15 * q^55 - 105 * q^56 + 40 * q^57 - 225 * q^58 + 5 * q^59 - 35 * q^60 + 65 * q^62 + 85 * q^63 + 45 * q^64 + 45 * q^65 + 55 * q^66 - 105 * q^67 + 80 * q^68 + 40 * q^69 + 95 * q^70 - 85 * q^71 + 160 * q^72 + 40 * q^73 + 35 * q^74 + 55 * q^75 + 35 * q^76 + 75 * q^77 - 10 * q^78 - 330 * q^80 + 55 * q^81 - 95 * q^82 + 50 * q^83 + 115 * q^84 + 85 * q^85 + 40 * q^86 + 95 * q^87 + 165 * q^88 + 55 * q^89 + 170 * q^90 - 105 * q^91 + 155 * q^92 - 185 * q^93 + 60 * q^94 + 30 * q^95 + 135 * q^96 + 65 * q^97 + 135 * q^98 + 45 * q^99

Introduction

L-functions

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