LMFDB - Embedded newform 125.2.g.a.6.8

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			6.8
Character	$\chi$	$=$	125.6
Dual form			125.2.g.a.21.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.784012 + 0.201300i) q^{2} +(-0.488943 + 2.56313i) q^{3} +(-1.17846 - 0.647864i) q^{4} +(1.66759 + 1.48968i) q^{5} +(-0.899294 + 1.91110i) q^{6} +(-0.523443 + 0.380304i) q^{7} +(-1.97363 - 1.85336i) q^{8} +(-3.54123 - 1.40207i) q^{9} +O(q^{10})$	\(q+(0.784012 + 0.201300i) q^{2} +(-0.488943 + 2.56313i) q^{3} +(-1.17846 - 0.647864i) q^{4} +(1.66759 + 1.48968i) q^{5} +(-0.899294 + 1.91110i) q^{6} +(-0.523443 + 0.380304i) q^{7} +(-1.97363 - 1.85336i) q^{8} +(-3.54123 - 1.40207i) q^{9} +(1.00754 + 1.50361i) q^{10} +(-0.370305 - 0.0950783i) q^{11} +(2.23676 - 2.70378i) q^{12} +(6.01342 + 2.38088i) q^{13} +(-0.486940 + 0.192793i) q^{14} +(-4.63359 + 3.54588i) q^{15} +(0.266898 + 0.420564i) q^{16} +(3.20004 - 1.75924i) q^{17} +(-2.49413 - 1.81209i) q^{18} +(-1.14413 - 5.99774i) q^{19} +(-1.00008 - 2.83590i) q^{20} +(-0.718833 - 1.52760i) q^{21} +(-0.271185 - 0.149085i) q^{22} +(-0.378229 - 6.01178i) q^{23} +(5.71539 - 4.15247i) q^{24} +(0.561715 + 4.96835i) q^{25} +(4.23532 + 3.07714i) q^{26} +(1.13067 - 1.78165i) q^{27} +(0.863242 - 0.109053i) q^{28} +(-3.96750 + 0.501211i) q^{29} +(-4.34658 + 1.84727i) q^{30} +(0.629836 - 0.346255i) q^{31} +(1.79787 + 5.53328i) q^{32} +(0.424756 - 0.902652i) q^{33} +(2.86300 - 0.735094i) q^{34} +(-1.43942 - 0.145571i) q^{35} +(3.26485 + 3.94652i) q^{36} +(-1.63319 - 2.57349i) q^{37} +(0.310334 - 4.93261i) q^{38} +(-9.04272 + 14.2491i) q^{39} +(-0.530292 - 6.03071i) q^{40} +(-0.0888833 + 1.41276i) q^{41} +(-0.256068 - 1.34236i) q^{42} +(3.04645 - 9.37601i) q^{43} +(0.374793 + 0.351954i) q^{44} +(-3.81668 - 7.61337i) q^{45} +(0.913635 - 4.78944i) q^{46} +(-9.49196 + 8.91355i) q^{47} +(-1.20846 + 0.478462i) q^{48} +(-2.03376 + 6.25926i) q^{49} +(-0.559737 + 4.00832i) q^{50} +(2.94451 + 9.06227i) q^{51} +(-5.54409 - 6.70166i) q^{52} +(1.11564 + 2.37085i) q^{53} +(1.24511 - 1.16923i) q^{54} +(-0.475882 - 0.710188i) q^{55} +(1.73792 + 0.219550i) q^{56} +15.9324 q^{57} +(-3.21146 - 0.405701i) q^{58} +(1.48994 - 1.80103i) q^{59} +(7.75775 - 1.17674i) q^{60} +(-0.689122 - 10.9533i) q^{61} +(0.563500 - 0.144682i) q^{62} +(2.38684 - 0.612837i) q^{63} +(0.233151 + 3.70582i) q^{64} +(6.48118 + 12.9284i) q^{65} +(0.514718 - 0.622187i) q^{66} +(-0.529604 - 0.0669046i) q^{67} -4.91087 q^{68} +(15.5939 + 1.96997i) q^{69} +(-1.09922 - 0.403884i) q^{70} +(-5.36705 + 5.04000i) q^{71} +(4.39052 + 9.33033i) q^{72} +(-1.88247 - 2.27552i) q^{73} +(-0.762395 - 2.34641i) q^{74} +(-13.0092 - 0.989489i) q^{75} +(-2.53741 + 7.80934i) q^{76} +(0.229992 - 0.0910604i) q^{77} +(-9.95794 + 9.35112i) q^{78} +(0.744146 - 3.90095i) q^{79} +(-0.181429 + 1.09892i) q^{80} +(-4.31547 - 4.05249i) q^{81} +(-0.354074 + 1.08973i) q^{82} +(1.60386 + 8.40773i) q^{83} +(-0.142560 + 2.26592i) q^{84} +(7.95705 + 1.83334i) q^{85} +(4.27585 - 6.73765i) q^{86} +(0.655210 - 10.4143i) q^{87} +(0.554631 + 0.873958i) q^{88} +(-5.03780 - 6.08965i) q^{89} +(-1.45975 - 6.73727i) q^{90} +(-4.05314 + 1.04067i) q^{91} +(-3.44909 + 7.32969i) q^{92} +(0.579543 + 1.78365i) q^{93} +(-9.23611 + 5.07759i) q^{94} +(7.02677 - 11.7062i) q^{95} +(-15.0616 + 1.90272i) q^{96} +(3.72521 - 0.470603i) q^{97} +(-2.85448 + 4.49794i) q^{98} +(1.17803 + 0.855889i) 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 $\left(\mathbb{Z}/125\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.784012	+	0.201300i	0.554380	+	0.142341i	0.515479	−	0.856902i	$-0.327614\pi$
$2$	0.784012	+	0.201300i	0.554380	+	0.142341i	0.0389014	+	0.999243i	$0.487614\pi$
$3$	−0.488943	+	2.56313i	−0.282291	+	1.47982i	0.504935	+	0.863158i	$0.331517\pi$
$3$	−0.488943	+	2.56313i	−0.282291	+	1.47982i	−0.787226	+	0.616665i	$0.788483\pi$
$4$	−1.17846	−	0.647864i	−0.589230	−	0.323932i
$5$	1.66759	+	1.48968i	0.745769	+	0.666205i
$5$	1.66759	+	1.48968i	0.745769	+	0.666205i
$6$	−0.899294	+	1.91110i	−0.367135	+	0.780202i
$7$	−0.523443	+	0.380304i	−0.197843	+	0.143741i	−0.682296	−	0.731076i	$-0.739019\pi$
$7$	−0.523443	+	0.380304i	−0.197843	+	0.143741i	0.484453	+	0.874817i	$0.339019\pi$
$8$	−1.97363	−	1.85336i	−0.697783	−	0.655261i
$9$	−3.54123	−	1.40207i	−1.18041	−	0.467357i
$10$	1.00754	+	1.50361i	0.318612	+	0.475484i
$11$	−0.370305	−	0.0950783i	−0.111651	−	0.0286672i	0.192451	−	0.981307i	$-0.438356\pi$
$11$	−0.370305	−	0.0950783i	−0.111651	−	0.0286672i	−0.304102	+	0.952639i	$0.598356\pi$
$12$	2.23676	−	2.70378i	0.645697	−	0.780513i
$13$	6.01342	+	2.38088i	1.66782	+	0.660338i	0.996713	−	0.0810190i	$-0.0258174\pi$
$13$	6.01342	+	2.38088i	1.66782	+	0.660338i	0.671111	+	0.741357i	$0.265817\pi$
$14$	−0.486940	+	0.192793i	−0.130140	+	0.0515262i
$15$	−4.63359	+	3.54588i	−1.19639	+	0.915542i
$16$	0.266898	+	0.420564i	0.0667246	+	0.105141i
$17$	3.20004	−	1.75924i	0.776124	−	0.426678i	−0.0438794	−	0.999037i	$-0.513972\pi$
$17$	3.20004	−	1.75924i	0.776124	−	0.426678i	0.820003	+	0.572359i	$0.193972\pi$
$18$	−2.49413	−	1.81209i	−0.587871	−	0.427114i
$19$	−1.14413	−	5.99774i	−0.262482	−	1.37598i	−0.832355	−	0.554244i	$-0.813008\pi$
$19$	−1.14413	−	5.99774i	−0.262482	−	1.37598i	0.569873	−	0.821733i	$-0.306992\pi$
$20$	−1.00008	−	2.83590i	−0.223625	−	0.634126i
$21$	−0.718833	−	1.52760i	−0.156862	−	0.333349i
$22$	−0.271185	−	0.149085i	−0.0578167	−	0.0317850i
$23$	−0.378229	−	6.01178i	−0.0788662	−	1.25354i	−0.816102	−	0.577908i	$-0.803869\pi$
$23$	−0.378229	−	6.01178i	−0.0788662	−	1.25354i	0.737236	−	0.675635i	$-0.236131\pi$
$24$	5.71539	−	4.15247i	1.16665	−	0.847620i
$25$	0.561715	+	4.96835i	0.112343	+	0.993669i
$26$	4.23532	+	3.07714i	0.830615	+	0.603477i
$27$	1.13067	−	1.78165i	0.217598	−	0.342879i
$28$	0.863242	−	0.109053i	0.163137	−	0.0206090i
$29$	−3.96750	+	0.501211i	−0.736746	+	0.0930726i	−0.484746	−	0.874655i	$-0.661088\pi$
$29$	−3.96750	+	0.501211i	−0.736746	+	0.0930726i	−0.251999	+	0.967727i	$0.581088\pi$
$30$	−4.34658	+	1.84727i	−0.793573	+	0.337264i
$31$	0.629836	−	0.346255i	0.113122	−	0.0621893i	−0.424188	−	0.905574i	$-0.639440\pi$
$31$	0.629836	−	0.346255i	0.113122	−	0.0621893i	0.537310	+	0.843385i	$0.319440\pi$
$32$	1.79787	+	5.53328i	0.317822	+	0.978155i
$33$	0.424756	−	0.902652i	0.0739405	−	0.157132i
$34$	2.86300	−	0.735094i	0.491001	−	0.126068i
$35$	−1.43942	−	0.145571i	−0.243306	−	0.0246060i
$36$	3.26485	+	3.94652i	0.544141	+	0.657753i
$37$	−1.63319	−	2.57349i	−0.268495	−	0.423080i	0.683151	−	0.730277i	$-0.260609\pi$
$37$	−1.63319	−	2.57349i	−0.268495	−	0.423080i	−0.951646	+	0.307197i	$0.900609\pi$
$38$	0.310334	−	4.93261i	0.0503428	−	0.800175i
$39$	−9.04272	+	14.2491i	−1.44799	+	2.28167i
$40$	−0.530292	−	6.03071i	−0.0838465	−	0.953540i
$41$	−0.0888833	+	1.41276i	−0.0138812	+	0.220636i	0.984970	+	0.172724i	$0.0552568\pi$
$41$	−0.0888833	+	1.41276i	−0.0138812	+	0.220636i	−0.998852	+	0.0479122i	$0.984743\pi$
$42$	−0.256068	−	1.34236i	−0.0395121	−	0.207130i
$43$	3.04645	−	9.37601i	0.464579	−	1.42983i	−0.394931	−	0.918711i	$-0.629232\pi$
$43$	3.04645	−	9.37601i	0.464579	−	1.42983i	0.859511	−	0.511118i	$-0.170768\pi$
$44$	0.374793	+	0.351954i	0.0565021	+	0.0530590i
$45$	−3.81668	−	7.61337i	−0.568957	−	1.13493i
$46$	0.913635	−	4.78944i	0.134708	−	0.706165i
$47$	−9.49196	+	8.91355i	−1.38455	+	1.30017i	−0.477817	+	0.878460i	$0.658572\pi$
$47$	−9.49196	+	8.91355i	−1.38455	+	1.30017i	−0.906729	+	0.421715i	$0.861428\pi$
$48$	−1.20846	+	0.478462i	−0.174426	+	0.0690601i
$49$	−2.03376	+	6.25926i	−0.290537	+	0.894180i
$50$	−0.559737	+	4.00832i	−0.0791588	+	0.566861i
$51$	2.94451	+	9.06227i	0.412314	+	1.26897i
$52$	−5.54409	−	6.70166i	−0.768827	−	0.929353i
$53$	1.11564	+	2.37085i	0.153245	+	0.325661i	0.966677	−	0.255998i	$-0.0824039\pi$
$53$	1.11564	+	2.37085i	0.153245	+	0.325661i	−0.813433	+	0.581659i	$0.802404\pi$
$54$	1.24511	−	1.16923i	0.169438	−	0.159113i
$55$	−0.475882	−	0.710188i	−0.0641679	−	0.0957617i
$56$	1.73792	+	0.219550i	0.232239	+	0.0293387i
$57$	15.9324			2.11030
$58$	−3.21146	−	0.405701i	−0.421685	−	0.0532712i
$59$	1.48994	−	1.80103i	0.193974	−	0.234474i	−0.664555	−	0.747239i	$-0.731379\pi$
$59$	1.48994	−	1.80103i	0.193974	−	0.234474i	0.858529	+	0.512765i	$0.171379\pi$
$60$	7.75775	−	1.17674i	1.00152	−	0.151917i
$61$	−0.689122	−	10.9533i	−0.0882330	−	1.40242i	−0.754299	−	0.656531i	$-0.772023\pi$
$61$	−0.689122	−	10.9533i	−0.0882330	−	1.40242i	0.666066	−	0.745893i	$-0.267977\pi$
$62$	0.563500	−	0.144682i	0.0715646	−	0.0183747i
$63$	2.38684	−	0.612837i	0.300714	−	0.0772102i
$64$	0.233151	+	3.70582i	0.0291438	+	0.463228i
$65$	6.48118	+	12.9284i	0.803891	+	1.60357i
$66$	0.514718	−	0.622187i	0.0633573	−	0.0765859i
$67$	−0.529604	−	0.0669046i	−0.0647015	−	0.00817369i	0.0929159	−	0.995674i	$-0.470381\pi$
$67$	−0.529604	−	0.0669046i	−0.0647015	−	0.00817369i	−0.157617	+	0.987500i	$0.550381\pi$
$68$	−4.91087			−0.595530
$69$	15.5939	+	1.96997i	1.87728	+	0.237156i
$70$	−1.09922	−	0.403884i	−0.131382	−	0.0482734i
$71$	−5.36705	+	5.04000i	−0.636952	+	0.598138i	−0.934238	−	0.356651i	$-0.883919\pi$
$71$	−5.36705	+	5.04000i	−0.636952	+	0.598138i	0.297286	+	0.954789i	$0.403919\pi$
$72$	4.39052	+	9.33033i	0.517428	+	1.09959i
$73$	−1.88247	−	2.27552i	−0.220327	−	0.266329i	0.648756	−	0.760997i	$-0.275290\pi$
$73$	−1.88247	−	2.27552i	−0.220327	−	0.266329i	−0.869082	+	0.494668i	$0.835290\pi$
$74$	−0.762395	−	2.34641i	−0.0886266	−	0.272765i
$75$	−13.0092	−	0.989489i	−1.50217	−	0.114256i
$76$	−2.53741	+	7.80934i	−0.291061	+	0.895793i
$77$	0.229992	−	0.0910604i	0.0262101	−	0.0103773i
$78$	−9.95794	+	9.35112i	−1.12751	+	1.05881i
$79$	0.744146	−	3.90095i	0.0837230	−	0.438891i	−0.915600	−	0.402091i	$-0.868283\pi$
$79$	0.744146	−	3.90095i	0.0837230	−	0.438891i	0.999323	−	0.0368002i	$-0.0117165\pi$
$80$	−0.181429	+	1.09892i	−0.0202844	+	0.122863i
$81$	−4.31547	−	4.05249i	−0.479496	−	0.450277i
$82$	−0.354074	+	1.08973i	−0.0391009	+	0.120340i
$83$	1.60386	+	8.40773i	0.176046	+	0.922868i	0.955184	+	0.296014i	$0.0956576\pi$
$83$	1.60386	+	8.40773i	0.176046	+	0.922868i	−0.779137	+	0.626854i	$0.784342\pi$
$84$	−0.142560	+	2.26592i	−0.0155545	+	0.247232i
$85$	7.95705	+	1.83334i	0.863063	+	0.198854i
$86$	4.27585	−	6.73765i	0.461076	−	0.726540i
$87$	0.655210	−	10.4143i	0.0702459	−	1.11653i
$88$	0.554631	+	0.873958i	0.0591238	+	0.0931643i
$89$	−5.03780	−	6.08965i	−0.534006	−	0.645502i	0.432656	−	0.901559i	$-0.357576\pi$
$89$	−5.03780	−	6.08965i	−0.534006	−	0.645502i	−0.966662	+	0.256057i	$0.917576\pi$
$90$	−1.45975	−	6.73727i	−0.153871	−	0.710171i
$91$	−4.05314	+	1.04067i	−0.424885	+	0.109092i
$92$	−3.44909	+	7.32969i	−0.359592	+	0.764173i
$93$	0.579543	+	1.78365i	0.0600958	+	0.184956i
$94$	−9.23611	+	5.07759i	−0.952632	+	0.523714i
$95$	7.02677	−	11.7062i	0.720931	−	1.20103i
$96$	−15.0616	+	1.90272i	−1.53721	+	0.194195i
$97$	3.72521	−	0.470603i	0.378237	−	0.0477825i	0.0660837	−	0.997814i	$-0.478950\pi$
$97$	3.72521	−	0.470603i	0.378237	−	0.0477825i	0.312154	+	0.950032i	$0.398950\pi$
$98$	−2.85448	+	4.49794i	−0.288346	+	0.454360i
$99$	1.17803	+	0.855889i	0.118396	+	0.0860200i
$100$	2.55686	−	6.21892i	0.255686	−	0.621892i
$101$	2.40915	−	1.75035i	0.239719	−	0.174166i	−0.461439	−	0.887172i	$-0.652667\pi$
$101$	2.40915	−	1.75035i	0.239719	−	0.174166i	0.701158	+	0.713006i	$0.252667\pi$
$102$	0.484296	+	7.69766i	0.0479524	+	0.762182i
$103$	14.9624	+	8.22563i	1.47429	+	0.810496i	0.997644	−	0.0686017i	$-0.0218538\pi$
$103$	14.9624	+	8.22563i	1.47429	+	0.810496i	0.476642	+	0.879097i	$0.341854\pi$
$104$	−7.45562	−	15.8440i	−0.731084	−	1.55363i
$105$	1.07691	−	3.61824i	0.105096	−	0.353104i
$106$	0.397420	+	2.08335i	0.0386009	+	0.202353i
$107$	−2.47680	−	1.79950i	−0.239441	−	0.173964i	0.461593	−	0.887092i	$-0.347278\pi$
$107$	−2.47680	−	1.79950i	−0.239441	−	0.173964i	−0.701034	+	0.713128i	$0.747278\pi$
$108$	−2.48672	+	1.36709i	−0.239285	+	0.131548i
$109$	−6.34317	−	9.99524i	−0.607566	−	0.957371i	−0.999304	−	0.0372940i	$-0.988126\pi$
$109$	−6.34317	−	9.99524i	−0.607566	−	0.957371i	0.391738	−	0.920077i	$-0.371874\pi$
$110$	−0.230136	−	0.652591i	−0.0219426	−	0.0622221i
$111$	7.39473	−	2.92778i	0.701877	−	0.277893i
$112$	−0.299648	−	0.118639i	−0.0283141	−	0.0112103i
$113$	−2.46034	+	2.97404i	−0.231449	+	0.279774i	−0.873433	−	0.486944i	$-0.838112\pi$
$113$	−2.46034	+	2.97404i	−0.231449	+	0.279774i	0.641984	+	0.766718i	$0.278112\pi$
$114$	12.4912	+	3.20719i	1.16991	+	0.300381i
$115$	8.32489	−	10.5886i	0.776300	−	0.987395i
$116$	5.00025	+	1.97974i	0.464262	+	0.183814i
$117$	−17.9567	−	16.8625i	−1.66010	−	1.55894i
$118$	1.53068	−	1.11210i	0.140910	−	0.102377i
$119$	−1.00599	+	2.13785i	−0.0922193	+	0.195976i
$120$	15.7168	+	1.58947i	1.43474	+	0.145098i
$121$	−9.51129	−	5.22887i	−0.864662	−	0.475352i
$122$	1.66462	−	8.72622i	0.150707	−	0.790035i
$123$	−3.57762	−	0.918577i	−0.322583	−	0.0828253i
$124$	−0.966564			−0.0868000
$125$	−6.46453	+	9.12194i	−0.578205	+	0.815891i
$126$	1.99468			0.177700
$127$	14.3367	+	3.68105i	1.27218	+	0.326640i	0.823635	−	0.567121i	$-0.191943\pi$
$127$	14.3367	+	3.68105i	1.27218	+	0.326640i	0.448544	+	0.893761i	$0.351943\pi$
$128$	1.61719	−	8.47762i	0.142941	−	0.749323i
$129$	22.5424	+	12.3928i	1.98475	+	1.09112i
$130$	2.47883	+	11.4407i	0.217408	+	1.00341i
$131$	−0.428267	+	0.910113i	−0.0374178	+	0.0795169i	−0.922662	−	0.385610i	$-0.873991\pi$
$131$	−0.428267	+	0.910113i	−0.0374178	+	0.0795169i	0.885244	+	0.465127i	$0.153991\pi$
$132$	−1.08535	+	0.788556i	−0.0944680	+	0.0686350i
$133$	2.87985	+	2.70436i	0.249715	+	0.234498i
$134$	−0.401748	−	0.159063i	−0.0347057	−	0.0137410i
$135$	4.53959	−	1.28673i	0.390706	−	0.110744i
$136$	−9.57618	−	2.45875i	−0.821151	−	0.210836i
$137$	−1.06064	+	1.28210i	−0.0906169	+	0.109537i	−0.813873	−	0.581043i	$-0.802645\pi$
$137$	−1.06064	+	1.28210i	−0.0906169	+	0.109537i	0.723256	+	0.690580i	$0.242645\pi$
$138$	11.8292	+	4.68353i	1.00697	+	0.398688i
$139$	−0.0583355	+	0.0230967i	−0.00494796	+	0.00195903i	−0.370597	−	0.928794i	$-0.620847\pi$
$139$	−0.0583355	+	0.0230967i	−0.00494796	+	0.00195903i	0.365649	+	0.930753i	$0.380847\pi$
$140$	1.60199	+	1.10410i	0.135393	+	0.0933133i
$141$	−18.2055	−	28.6873i	−1.53318	−	2.41591i
$142$	−5.22238	+	2.87103i	−0.438253	+	0.240931i
$143$	−2.00043	−	1.45340i	−0.167285	−	0.121539i
$144$	−0.355486	−	1.86353i	−0.0296239	−	0.155294i
$145$	−7.36280	−	5.07448i	−0.611447	−	0.421413i
$146$	−1.01782	−	2.16297i	−0.0842352	−	0.179009i
$147$	−15.0489	−	8.27320i	−1.24121	−	0.682362i
$148$	0.257374	+	4.09085i	0.0211560	+	0.336266i
$149$	14.1000	−	10.2443i	1.15512	−	0.839243i	0.165965	−	0.986132i	$-0.446926\pi$
$149$	14.1000	−	10.2443i	1.15512	−	0.839243i	0.989153	+	0.146889i	$0.0469260\pi$
$150$	−10.0001	−	3.39451i	−0.816508	−	0.277161i
$151$	−6.26136	−	4.54915i	−0.509543	−	0.370204i	0.303107	−	0.952956i	$-0.401976\pi$
$151$	−6.26136	−	4.54915i	−0.509543	−	0.370204i	−0.812650	+	0.582752i	$0.801976\pi$
$152$	−8.85788	+	13.9578i	−0.718469	+	1.13213i
$153$	−13.7986	+	1.74317i	−1.11555	+	0.140927i
$154$	0.198647	−	0.0250950i	0.0160074	−	0.00202221i
$155$	1.56612	+	0.360841i	0.125794	+	0.0289835i
$156$	19.8879	−	10.9335i	1.59231	−	0.875380i
$157$	−4.51835	−	13.9060i	−0.360603	−	1.10982i	−0.952689	−	0.303948i	$-0.901695\pi$
$157$	−4.51835	−	13.9060i	−0.360603	−	1.10982i	0.592085	−	0.805875i	$-0.298305\pi$
$158$	1.36868	−	2.90859i	0.108886	−	0.231395i
$159$	−6.62227	+	1.70031i	−0.525180	+	0.134843i
$160$	−5.24470	+	11.9055i	−0.414630	+	0.941212i
$161$	2.48428	+	3.00298i	0.195789	+	0.236668i
$162$	−2.56761	−	4.04591i	−0.201731	−	0.317876i
$163$	−0.756394	+	12.0225i	−0.0592453	+	0.941677i	0.850359	+	0.526202i	$0.176385\pi$
$163$	−0.756394	+	12.0225i	−0.0592453	+	0.941677i	−0.909605	+	0.415475i	$0.863615\pi$
$164$	1.02002	−	1.60730i	0.0796503	−	0.125509i
$165$	2.05298	−	0.872504i	0.159824	−	0.0679244i
$166$	−0.435031	+	6.91461i	−0.0337649	+	0.536678i
$167$	0.458047	+	2.40117i	0.0354448	+	0.185808i	0.995606	−	0.0936373i	$-0.0298494\pi$
$167$	0.458047	+	2.40117i	0.0354448	+	0.185808i	−0.960162	+	0.279445i	$0.909849\pi$
$168$	−1.41248	+	4.34716i	−0.108975	+	0.335391i
$169$	21.0161	+	19.7354i	1.61662	+	1.51811i
$170$	5.86937	+	3.03912i	0.450160	+	0.233090i
$171$	−4.35763	+	22.8435i	−0.333237	+	1.74689i
$172$	−9.66451	+	9.07558i	−0.736912	+	0.692006i
$173$	−23.5272	+	9.31508i	−1.78874	+	0.708212i	−0.793749	+	0.608246i	$0.791874\pi$
$173$	−23.5272	+	9.31508i	−1.78874	+	0.708212i	−0.994991	+	0.0999666i	$0.968126\pi$
$174$	2.61008	−	8.03301i	0.197870	−	0.608981i
$175$	−2.18351	−	2.38702i	−0.165058	−	0.180442i
$176$	−0.0588474	−	0.181114i	−0.00443579	−	0.0136519i
$177$	3.88777	+	4.69951i	0.292223	+	0.353237i
$178$	−2.72385	−	5.78847i	−0.204161	−	0.433864i
$179$	−13.2681	+	12.4596i	−0.991705	+	0.931273i	−0.997637	−	0.0687098i	$-0.978112\pi$
$179$	−13.2681	+	12.4596i	−0.991705	+	0.931273i	0.00593206	+	0.999982i	$0.498112\pi$
$180$	−0.434622	+	11.4448i	−0.0323948	+	0.853041i
$181$	17.0174	+	2.14980i	1.26489	+	0.159793i	0.729013	−	0.684500i	$-0.239979\pi$
$181$	17.0174	+	2.14980i	1.26489	+	0.159793i	0.535881	+	0.844293i	$0.319979\pi$
$182$	−3.38720			−0.251076
$183$	28.4116	+	3.58922i	2.10025	+	0.265323i
$184$	−10.3955	+	12.5660i	−0.766367	+	0.926378i
$185$	1.11019	−	6.72446i	0.0816227	−	0.494392i
$186$	0.0953198	+	1.51506i	0.00698918	+	0.111090i
$187$	−1.35226	+	0.347201i	−0.0988868	+	0.0253898i
$188$	16.9607	−	4.35476i	1.23698	−	0.317604i
$189$	0.0857271	+	1.36259i	0.00623573	+	0.0991140i
$190$	7.86552	−	7.76328i	0.570625	−	0.563208i
$191$	11.1953	−	13.5328i	0.810064	−	0.979199i	−0.189933	−	0.981797i	$-0.560827\pi$
$191$	11.1953	−	13.5328i	0.810064	−	0.979199i	0.999997	+	0.00259790i	$0.000826938\pi$
$192$	−9.61249	−	1.21434i	−0.693722	−	0.0876375i
$193$	10.0389			0.722617			0.361309	−	0.932446i	$-0.382330\pi$
$193$	10.0389			0.722617			0.361309	+	0.932446i	$0.382330\pi$
$194$	3.01534	+	0.380926i	0.216489	+	0.0273489i
$195$	−36.3061	+	10.2908i	−2.59993	+	0.736942i
$196$	6.45185	−	6.05869i	0.460847	−	0.432764i
$197$	7.83814	+	16.6569i	0.558445	+	1.18676i	0.962315	+	0.271939i	$0.0876648\pi$
$197$	7.83814	+	16.6569i	0.558445	+	1.18676i	−0.403870	+	0.914816i	$0.632335\pi$
$198$	0.751299	+	0.908164i	0.0533925	+	0.0645404i
$199$	5.34423	+	16.4478i	0.378842	+	1.16596i	0.940850	+	0.338824i	$0.110029\pi$
$199$	5.34423	+	16.4478i	0.378842	+	1.16596i	−0.562008	+	0.827132i	$0.689971\pi$
$200$	8.09952	−	10.8467i	0.572722	−	0.766979i
$201$	0.430431	−	1.32473i	0.0303603	−	0.0934393i
$202$	2.24115	−	0.887333i	0.157687	−	0.0624325i
$203$	1.88615	−	1.77121i	0.132381	−	0.124314i
$204$	2.40113	−	12.5872i	0.168113	−	0.881279i
$205$	−2.25278	+	2.22350i	−0.157341	+	0.155296i
$206$	10.0749	+	9.46092i	0.701948	+	0.659173i
$207$	−7.08955	+	21.8194i	−0.492758	+	1.51655i
$208$	0.603658	+	3.16449i	0.0418561	+	0.219418i
$209$	−0.146577	+	2.32978i	−0.0101390	+	0.161154i
$210$	1.57266	−	2.61996i	0.108524	−	0.180794i
$211$	−7.11331	+	11.2088i	−0.489700	+	0.771644i	−0.995870	−	0.0907895i	$-0.971061\pi$
$211$	−7.11331	+	11.2088i	−0.489700	+	0.771644i	0.506170	+	0.862434i	$0.331061\pi$
$212$	0.221254	−	3.51673i	0.0151958	−	0.241530i
$213$	−10.2940	−	16.2207i	−0.705332	−	1.11142i
$214$	−1.57960	−	1.90941i	−0.107979	−	0.130524i
$215$	19.0475	−	11.0971i	1.29903	−	0.756817i
$216$	−5.53357	+	1.42078i	−0.376512	+	0.0966718i
$217$	−0.198001	+	0.420774i	−0.0134412	+	0.0285640i
$218$	−2.96108	−	9.11327i	−0.200550	−	0.617228i
$219$	6.75286	−	3.71242i	0.456316	−	0.250862i
$220$	0.100703	+	1.14524i	0.00678937	+	0.0772117i
$221$	23.4317	−	2.96012i	1.57619	−	0.199119i
$222$	6.38692	−	0.806855i	0.428662	−	0.0541526i
$223$	1.39794	−	2.20281i	0.0936133	−	0.147511i	−0.794294	−	0.607534i	$-0.792159\pi$
$223$	1.39794	−	2.20281i	0.0936133	−	0.147511i	0.887907	+	0.460023i	$0.152159\pi$
$224$	−3.04541	−	2.21262i	−0.203480	−	0.147837i
$225$	4.97682	−	18.3816i	0.331788	−	1.22544i
$226$	−2.52761	+	1.83641i	−0.168134	+	0.122156i
$227$	1.30311	+	20.7123i	0.0864902	+	1.37472i	0.766841	+	0.641837i	$0.221827\pi$
$227$	1.30311	+	20.7123i	0.0864902	+	1.37472i	−0.680351	+	0.732886i	$0.738173\pi$
$228$	−18.7757	−	10.3220i	−1.24345	−	0.683593i
$229$	−9.56403	−	20.3246i	−0.632009	−	1.34309i	−0.922421	−	0.386186i	$-0.873792\pi$
$229$	−9.56403	−	20.3246i	−0.632009	−	1.34309i	0.290412	−	0.956902i	$-0.406208\pi$
$230$	8.65830	−	6.62581i	0.570911	−	0.436893i
$231$	0.120946	+	0.634023i	0.00795769	+	0.0417157i
$232$	8.75928	+	6.36399i	0.575075	+	0.417817i
$233$	−13.5327	+	7.43965i	−0.886555	+	0.487388i	−0.858849	−	0.512228i	$-0.828820\pi$
$233$	−13.5327	+	7.43965i	−0.886555	+	0.487388i	−0.0277059	+	0.999616i	$0.508820\pi$
$234$	−10.6839	−	16.8351i	−0.698426	−	1.10054i
$235$	−29.1070	+	0.724170i	−1.89873	+	0.0472397i
$236$	−2.92266	+	1.15716i	−0.190249	+	0.0753249i
$237$	9.63479	+	3.81468i	0.625847	+	0.247790i
$238$	−1.21906	+	1.47359i	−0.0790199	+	0.0955186i
$239$	4.80175	+	1.23288i	0.310599	+	0.0797483i	0.400772	−	0.916178i	$-0.368742\pi$
$239$	4.80175	+	1.23288i	0.310599	+	0.0797483i	−0.0901728	+	0.995926i	$0.528742\pi$
$240$	−2.72797	−	1.00234i	−0.176090	−	0.0647004i
$241$	−5.25502	−	2.08061i	−0.338506	−	0.134024i	0.192721	−	0.981254i	$-0.438269\pi$
$241$	−5.25502	−	2.08061i	−0.338506	−	0.134024i	−0.531227	+	0.847230i	$0.678269\pi$
$242$	−6.40439	−	6.01412i	−0.411690	−	0.386602i
$243$	17.6185	−	12.8006i	1.13023	−	0.821158i
$244$	−6.28414	+	13.3545i	−0.402301	+	0.854932i
$245$	−12.7158	+	7.40824i	−0.812380	+	0.473295i
$246$	−2.61999	−	1.44035i	−0.167044	−	0.0918334i
$247$	7.39978	−	38.7910i	0.470837	−	2.46821i
$248$	−1.88480	−	0.483934i	−0.119685	−	0.0307298i
$249$	−22.3343			−1.41538
$250$	−6.90451	+	5.85040i	−0.436680	+	0.370012i
$251$	−23.0280			−1.45351			−0.726756	−	0.686896i	$-0.758973\pi$
$251$	−23.0280			−1.45351			−0.726756	+	0.686896i	$0.758973\pi$
$252$	−3.20984	−	0.824146i	−0.202201	−	0.0519163i
$253$	−0.431529	+	2.26216i	−0.0271300	+	0.142221i
$254$	10.4992	+	5.77197i	0.658776	+	0.362165i
$255$	−8.58964	+	19.4985i	−0.537904	+	1.22105i
$256$	6.13641	−	13.0405i	0.383526	−	0.815033i
$257$	10.1228	−	7.35467i	0.631445	−	0.458772i	−0.225455	−	0.974253i	$-0.572387\pi$
$257$	10.1228	−	7.35467i	0.631445	−	0.458772i	0.856901	+	0.515482i	$0.172387\pi$
$258$	15.1788	+	14.2539i	0.944992	+	0.887407i
$259$	1.83359	+	0.725970i	0.113934	+	0.0451096i
$260$	0.738039	−	19.4345i	0.0457713	−	1.20528i
$261$	14.7525	+	3.78781i	0.913159	+	0.234459i
$262$	−0.518972	+	0.627329i	−0.0320622	+	0.0387565i
$263$	−14.2037	−	5.62364i	−0.875837	−	0.346769i	−0.113182	−	0.993574i	$-0.536104\pi$
$263$	−14.2037	−	5.62364i	−0.875837	−	0.346769i	−0.762655	+	0.646806i	$0.776104\pi$
$264$	−2.51125	+	0.994274i	−0.154557	+	0.0611933i
$265$	−1.67138	+	5.61555i	−0.102672	+	0.344960i
$266$	1.71345	+	2.69996i	0.105058	+	0.165545i
$267$	18.0717	−	9.93503i	1.10597	−	0.608014i
$268$	0.580773	+	0.421956i	0.0354763	+	0.0257751i
$269$	−0.0509368	−	0.267020i	−0.00310567	−	0.0162805i	0.980701	−	0.195515i	$-0.0626379\pi$
$269$	−0.0509368	−	0.267020i	−0.00310567	−	0.0162805i	−0.983806	+	0.179235i	$0.942638\pi$
$270$	3.81811	−	0.0949929i	0.232363	−	0.00578109i
$271$	10.4917	+	22.2959i	0.637323	+	1.35438i	0.918766	+	0.394802i	$0.129187\pi$
$271$	10.4917	+	22.2959i	0.637323	+	1.35438i	−0.281443	+	0.959578i	$0.590813\pi$
$272$	1.59396	+	0.876286i	0.0966479	+	0.0531326i
$273$	−0.685615	−	10.8975i	−0.0414953	−	0.659549i
$274$	−1.08964	+	0.791672i	−0.0658277	+	0.0478266i
$275$	0.264376	−	1.89321i	0.0159425	−	0.114165i
$276$	−17.1005	−	12.4243i	−1.02933	−	0.747852i
$277$	−4.14874	+	6.53736i	−0.249274	+	0.392792i	−0.945806	−	0.324733i	$-0.894725\pi$
$277$	−4.14874	+	6.53736i	−0.249274	+	0.392792i	0.696532	+	0.717526i	$0.254725\pi$
$278$	−0.0503851	+	0.00636512i	−0.00302190	+	0.000381754i
$279$	−2.71587	+	0.343094i	−0.162595	+	0.0205405i
$280$	2.57108	+	2.95506i	0.153651	+	0.176599i
$281$	−17.8871	+	9.83349i	−1.06705	+	0.586617i	−0.915700	−	0.401863i	$-0.868363\pi$
$281$	−17.8871	+	9.83349i	−1.06705	+	0.586617i	−0.151352	+	0.988480i	$0.548363\pi$
$282$	−8.49859	−	26.1560i	−0.506084	−	1.55757i
$283$	1.35590	−	2.88144i	0.0806001	−	0.171284i	−0.860465	−	0.509510i	$-0.829827\pi$
$283$	1.35590	−	2.88144i	0.0806001	−	0.171284i	0.941065	+	0.338226i	$0.109827\pi$
$284$	9.59010	−	2.46232i	0.569067	−	0.146112i
$285$	26.5687	+	23.7341i	1.57379	+	1.40589i
$286$	−1.27579	−	1.54217i	−0.0754393	−	0.0911904i
$287$	−0.490752	−	0.773301i	−0.0289682	−	0.0456465i
$288$	1.39138	−	22.1154i	0.0819879	−	1.30316i
$289$	−1.96372	+	3.09432i	−0.115513	+	0.182019i
$290$	−4.75103	−	5.46058i	−0.278990	−	0.320656i
$291$	−0.615197	+	9.77828i	−0.0360635	+	0.573213i
$292$	0.744193	+	3.90119i	0.0435506	+	0.228300i
$293$	−1.26632	+	3.89735i	−0.0739795	+	0.227685i	−0.981208	−	0.192952i	$-0.938194\pi$
$293$	−1.26632	+	3.89735i	−0.0739795	+	0.227685i	0.907229	+	0.420638i	$0.138194\pi$
$294$	−10.1331	−	9.51563i	−0.590975	−	0.554963i
$295$	5.16757	−	0.783846i	0.300867	−	0.0456373i
$296$	−1.54630	+	8.10601i	−0.0898771	+	0.471152i
$297$	−0.588091	+	0.552254i	−0.0341245	+	0.0320450i
$298$	13.1167	−	5.19329i	0.759833	−	0.300839i
$299$	12.0389	−	37.0519i	0.696227	−	2.14277i
$300$	14.6897	+	9.59424i	0.848111	+	0.553924i
$301$	1.97109	+	6.06638i	0.113612	+	0.349661i
$302$	−3.99324	−	4.82700i	−0.229785	−	0.277763i
$303$	3.30843	+	7.03078i	0.190065	+	0.403908i
$304$	2.21707	−	2.08197i	0.127158	−	0.119409i
$305$	15.1677	−	19.2922i	0.868500	−	1.10467i
$306$	−11.1692	−	1.41100i	−0.638501	−	0.0806614i
$307$	14.1579			0.808032			0.404016	−	0.914752i	$-0.367614\pi$
$307$	14.1579			0.808032			0.404016	+	0.914752i	$0.367614\pi$
$308$	−0.330032	−	0.0416927i	−0.0188053	−	0.00237566i
$309$	−28.3991	+	34.3286i	−1.61557	+	1.95289i
$310$	1.15522	+	0.598163i	0.0656119	+	0.0339734i
$311$	−1.02064	−	16.2226i	−0.0578752	−	0.919901i	−0.914659	−	0.404225i	$-0.867541\pi$
$311$	−1.02064	−	16.2226i	−0.0578752	−	0.919901i	0.856784	−	0.515675i	$-0.172459\pi$
$312$	44.2556	−	11.3629i	2.50548	−	0.643298i
$313$	−29.2406	+	7.50771i	−1.65278	+	0.424361i	−0.956104	−	0.293027i	$-0.905337\pi$
$313$	−29.2406	+	7.50771i	−1.65278	+	0.424361i	−0.696673	+	0.717389i	$0.745337\pi$
$314$	−0.743151	−	11.8120i	−0.0419384	−	0.666592i
$315$	4.89321	+	2.53367i	0.275701	+	0.142756i
$316$	−3.40423	+	4.11501i	−0.191503	+	0.231488i
$317$	4.63307	+	0.585293i	0.260219	+	0.0328733i	0.254360	−	0.967110i	$-0.418135\pi$
$317$	4.63307	+	0.585293i	0.260219	+	0.0328733i	0.00585885	+	0.999983i	$0.498135\pi$
$318$	−5.53421			−0.310343
$319$	1.51684	+	0.191621i	0.0849267	+	0.0107287i
$320$	−5.13169	+	6.52711i	−0.286870	+	0.364877i
$321$	5.82335	−	5.46849i	0.325028	−	0.305221i
$322$	1.34321	+	2.85446i	0.0748540	+	0.159073i
$323$	−14.2127	−	17.1802i	−0.790816	−	0.955933i
$324$	2.46014	+	7.57154i	0.136675	+	0.420641i
$325$	−8.45122	+	31.2142i	−0.468789	+	1.73145i
$326$	−3.01316	+	9.27354i	−0.166883	+	0.513614i
$327$	28.7205	−	11.3713i	1.58825	−	0.628832i
$328$	2.79377	−	2.62353i	0.154260	−	0.144860i
$329$	1.57865	−	8.27556i	0.0870337	−	0.456246i
$330$	1.78520	−	0.270789i	0.0982718	−	0.0149064i
$331$	4.84397	+	4.54879i	0.266249	+	0.250024i	0.806160	−	0.591698i	$-0.201542\pi$
$331$	4.84397	+	4.54879i	0.266249	+	0.250024i	−0.539911	+	0.841722i	$0.681542\pi$
$332$	3.55698	−	10.9473i	0.195215	−	0.600809i
$333$	2.17527	+	11.4032i	0.119204	+	0.624890i
$334$	−0.124241	+	1.97475i	−0.00679815	+	0.108053i
$335$	−0.783497	−	0.900510i	−0.0428070	−	0.0492001i
$336$	0.450598	−	0.710029i	0.0245821	−	0.0387352i
$337$	−1.12979	+	17.9575i	−0.0615434	+	0.978205i	0.839192	+	0.543836i	$0.183029\pi$
$337$	−1.12979	+	17.9575i	−0.0615434	+	0.978205i	−0.900735	+	0.434369i	$0.856971\pi$
$338$	12.5041	+	19.7033i	0.680134	+	1.07172i
$339$	−6.41987	−	7.76029i	−0.348680	−	0.421481i
$340$	−8.18931	−	7.31561i	−0.444128	−	0.396745i
$341$	−0.266153	+	0.0683365i	−0.0144130	+	0.00370063i
$342$	−8.01484	+	17.0324i	−0.433393	+	0.921007i
$343$	−2.71543	−	8.35722i	−0.146619	−	0.451247i
$344$	−23.3897	+	12.8586i	−1.26109	+	0.693289i
$345$	23.0696	+	26.5150i	1.24203	+	1.42752i
$346$	−20.3207	+	2.56710i	−1.09245	+	0.138008i
$347$	−9.30862	+	1.17595i	−0.499713	+	0.0631284i	−0.371150	−	0.928573i	$-0.621036\pi$
$347$	−9.30862	+	1.17595i	−0.499713	+	0.0631284i	−0.128563	+	0.991701i	$0.541036\pi$
$348$	−7.51917	+	11.8483i	−0.403070	+	0.635136i
$349$	−8.33548	−	6.05608i	−0.446188	−	0.324175i	0.341901	−	0.939736i	$-0.388929\pi$
$349$	−8.33548	−	6.05608i	−0.446188	−	0.324175i	−0.788089	+	0.615561i	$0.788929\pi$
$350$	−1.23139	−	2.31099i	−0.0658204	−	0.123528i
$351$	11.0411	−	8.02184i	0.589331	−	0.428174i
$352$	−0.139667	−	2.21994i	−0.00744427	−	0.118323i
$353$	−3.47818	−	1.91214i	−0.185125	−	0.101773i	0.386496	−	0.922291i	$-0.373685\pi$
$353$	−3.47818	−	1.91214i	−0.185125	−	0.101773i	−0.571621	+	0.820518i	$0.693685\pi$
$354$	2.10205	+	4.46708i	0.111723	+	0.237423i
$355$	−16.4580	+	0.409468i	−0.873501	+	0.0217323i
$356$	1.99158	+	10.4402i	0.105553	+	0.553331i
$357$	−4.98770	−	3.62378i	−0.263977	−	0.191791i
$358$	−12.9105	+	7.09759i	−0.682339	+	0.375119i
$359$	−3.66038	−	5.76784i	−0.193188	−	0.304415i	0.733902	−	0.679256i	$-0.237697\pi$
$359$	−3.66038	−	5.76784i	−0.193188	−	0.304415i	−0.927089	+	0.374841i	$0.877697\pi$
$360$	−6.57761	+	22.0996i	−0.346670	+	1.16475i
$361$	−16.9981	+	6.73003i	−0.894638	+	0.354212i
$362$	12.9091	+	5.11107i	0.678487	+	0.268632i
$363$	18.0527	−	21.8220i	0.947523	−	1.14536i
$364$	5.45068	+	1.39950i	0.285693	+	0.0733536i
$365$	0.250598	−	6.59891i	0.0131169	−	0.345403i
$366$	21.5525	+	8.53324i	1.12657	+	0.446040i
$367$	6.01214	+	5.64577i	0.313831	+	0.294707i	0.825415	−	0.564526i	$-0.190941\pi$
$367$	6.01214	+	5.64577i	0.313831	+	0.294707i	−0.511584	+	0.859233i	$0.670941\pi$
$368$	2.42739	−	1.76360i	0.126537	−	0.0919342i
$369$	2.29554	−	4.87828i	0.119501	−	0.253953i
$370$	2.22404	−	5.04858i	0.115622	−	0.262463i
$371$	−1.48561	−	0.816723i	−0.0771293	−	0.0424022i
$372$	0.472594	−	2.47743i	0.0245029	−	0.128449i
$373$	23.8457	+	6.12253i	1.23468	+	0.317012i	0.808972	−	0.587847i	$-0.200024\pi$
$373$	23.8457	+	6.12253i	1.23468	+	0.317012i	0.425710	+	0.904860i	$0.360024\pi$
$374$	−1.13008			−0.0584349
$375$	−20.2199	−	21.0295i	−1.04415	−	1.08596i
$376$	35.2536			1.81807
$377$	−25.0516	−	6.43215i	−1.29022	−	0.331272i
$378$	−0.207079	+	1.08555i	−0.0106510	+	0.0558344i
$379$	−10.1742	−	5.59331i	−0.522613	−	0.287309i	0.198530	−	0.980095i	$-0.436383\pi$
$379$	−10.1742	−	5.59331i	−0.522613	−	0.287309i	−0.721144	+	0.692786i	$0.756383\pi$
$380$	−15.8648	+	9.24286i	−0.813846	+	0.474149i
$381$	−16.4448	+	34.9470i	−0.842494	+	1.79039i
$382$	11.5014	−	8.35626i	0.588463	−	0.427543i
$383$	−13.6174	−	12.7876i	−0.695815	−	0.653413i	0.253647	−	0.967297i	$-0.418370\pi$
$383$	−13.6174	−	12.7876i	−0.695815	−	0.653413i	−0.949462	+	0.313883i	$0.898370\pi$
$384$	20.9385	+	8.29014i	1.06851	+	0.423055i
$385$	0.519184	+	0.190763i	0.0264601	+	0.00972220i
$386$	7.87063	+	2.02083i	0.400605	+	0.102858i
$387$	−23.9340	+	28.9313i	−1.21663	+	1.47066i
$388$	−4.69490	−	1.85884i	−0.238347	−	0.0943684i
$389$	13.7322	−	5.43697i	0.696250	−	0.275665i	0.00677810	−	0.999977i	$-0.497842\pi$
$389$	13.7322	−	5.43697i	0.696250	−	0.275665i	0.689472	+	0.724312i	$0.257842\pi$
$390$	−30.5359	+	0.759721i	−1.54625	+	0.0384699i
$391$	−11.7865	−	18.5725i	−0.596069	−	0.939254i
$392$	15.6145	−	8.58417i	0.788653	−	0.433566i
$393$	−2.12334	−	1.54269i	−0.107108	−	0.0778186i
$394$	2.79216	+	14.6370i	0.140667	+	0.737403i
$395$	7.05210	−	5.39665i	0.354829	−	0.271535i
$396$	−0.833762	−	1.77183i	−0.0418981	−	0.0890380i
$397$	−18.6038	−	10.2275i	−0.933699	−	0.513305i	−0.0591533	−	0.998249i	$-0.518840\pi$
$397$	−18.6038	−	10.2275i	−0.933699	−	0.513305i	−0.874545	+	0.484944i	$0.838840\pi$
$398$	0.878986	+	13.9711i	0.0440596	+	0.700307i
$399$	−8.33970	+	6.05914i	−0.417507	+	0.303337i
$400$	−1.93959	+	1.56228i	−0.0969795	+	0.0781141i
$401$	17.7613	+	12.9043i	0.886958	+	0.644412i	0.935083	−	0.354429i	$-0.115325\pi$
$401$	17.7613	+	12.9043i	0.886958	+	0.644412i	−0.0481253	+	0.998841i	$0.515325\pi$
$402$	0.604131	−	0.951959i	0.0301313	−	0.0474794i
$403$	4.61186	−	0.582614i	0.229733	−	0.0290221i
$404$	−3.97308	+	0.501916i	−0.197668	+	0.0249713i
$405$	−1.15952	−	13.1866i	−0.0576170	−	0.655245i
$406$	1.83530	−	1.00897i	0.0910846	−	0.0500742i
$407$	0.360096	+	1.10826i	0.0178493	+	0.0549344i
$408$	10.9843	−	23.3428i	0.543803	−	1.15564i
$409$	19.5982	−	5.03197i	0.969070	−	0.248815i	0.269199	−	0.963085i	$-0.413241\pi$
$409$	19.5982	−	5.03197i	0.969070	−	0.248815i	0.699871	+	0.714270i	$0.253241\pi$
$410$	−2.21379	+	1.28976i	−0.109331	+	0.0636968i
$411$	−2.76759	−	3.34544i	−0.136515	−	0.165018i
$412$	−12.3035	−	19.3872i	−0.606149	−	0.955137i
$413$	−0.0949613	+	1.50937i	−0.00467274	+	0.0742711i
$414$	−9.95053	+	15.6795i	−0.489042	+	0.770607i
$415$	−9.85023	+	16.4099i	−0.483529	+	0.805529i
$416$	−2.36273	+	37.5545i	−0.115842	+	1.84126i
$417$	−0.0306770	−	0.160814i	−0.00150226	−	0.00787511i
$418$	−0.583903	+	1.79707i	−0.0285596	+	0.0878975i
$419$	−13.5564	−	12.7303i	−0.662274	−	0.621917i	0.278707	−	0.960376i	$-0.410094\pi$
$419$	−13.5564	−	12.7303i	−0.662274	−	0.621917i	−0.940981	+	0.338459i	$0.890094\pi$
$420$	−3.61322	+	3.56626i	−0.176307	+	0.174016i
$421$	3.44497	−	18.0591i	0.167897	−	0.880149i	−0.794244	−	0.607599i	$-0.792133\pi$
$421$	3.44497	−	18.0591i	0.167897	−	0.880149i	0.962142	−	0.272550i	$-0.0878671\pi$
$422$	−7.83325	+	7.35591i	−0.381316	+	0.358080i
$423$	46.1106	−	18.2565i	2.24198	−	0.887661i
$424$	2.19218	−	6.74685i	0.106462	−	0.327656i
$425$	10.5380	+	14.9107i	0.511169	+	0.723276i
$426$	−4.80537	−	14.7894i	−0.232821	−	0.716549i
$427$	4.52629	+	5.47134i	0.219042	+	0.264777i
$428$	1.75298	+	3.72526i	0.0847333	+	0.180067i
$429$	4.70335	−	4.41674i	0.227080	−	0.213242i
$430$	17.1673	−	4.86601i	0.827881	−	0.234660i
$431$	14.9116	+	1.88377i	0.718265	+	0.0907380i	0.475966	−	0.879464i	$-0.342098\pi$
$431$	14.9116	+	1.88377i	0.718265	+	0.0907380i	0.242299	+	0.970202i	$0.422098\pi$
$432$	1.05107			0.0505699
$433$	−1.05936	−	0.133828i	−0.0509094	−	0.00643135i	0.0998373	−	0.995004i	$-0.468168\pi$
$433$	−1.05936	−	0.133828i	−0.0509094	−	0.00643135i	−0.150747	+	0.988572i	$0.548168\pi$
$434$	−0.239937	+	0.290034i	−0.0115173	+	0.0139221i
$435$	16.6065	−	16.3907i	0.796222	−	0.785872i
$436$	0.999621	+	15.8885i	0.0478731	+	0.760922i
$437$	−35.6244	+	9.14678i	−1.70414	+	0.437550i
$438$	6.04163	−	1.55123i	0.288680	−	0.0741205i
$439$	−1.49275	−	23.7266i	−0.0712450	−	1.13241i	−0.857493	−	0.514496i	$-0.827979\pi$
$439$	−1.49275	−	23.7266i	−0.0712450	−	1.13241i	0.786248	−	0.617911i	$-0.212021\pi$
$440$	−0.377020	+	2.28363i	−0.0179737	+	0.108868i
$441$	15.9779	−	19.3140i	0.760854	−	0.919714i
$442$	18.9666	+	2.39604i	0.902150	+	0.113968i
$443$	−16.0523			−0.762669			−0.381335	−	0.924437i	$-0.624535\pi$
$443$	−16.0523			−0.762669			−0.381335	+	0.924437i	$0.624535\pi$
$444$	−10.6112	−	1.34051i	−0.503586	−	0.0636176i
$445$	0.670640	−	17.6597i	0.0317914	−	0.837152i
$446$	1.53943	−	1.44562i	0.0728941	−	0.0684522i
$447$	19.3632	+	41.1490i	0.915850	+	1.94628i
$448$	−1.53138	−	1.85112i	−0.0723508	−	0.0874571i
$449$	12.4842	+	38.4225i	0.589167	+	1.81327i	0.581851	+	0.813295i	$0.302329\pi$
$449$	12.4842	+	38.4225i	0.589167	+	1.81327i	0.00731540	+	0.999973i	$0.497671\pi$
$450$	7.60210	−	13.4096i	0.358366	−	0.632133i
$451$	0.167237	−	0.514701i	0.00787487	−	0.0242363i
$452$	4.82618	−	1.91082i	0.227005	−	0.0898774i
$453$	14.7215	−	13.8244i	0.691676	−	0.649527i
$454$	−3.14773	+	16.5010i	−0.147730	+	0.774430i
$455$	−8.30924	−	4.30247i	−0.389543	−	0.201703i
$456$	−31.4446	−	29.5284i	−1.47253	−	1.38280i
$457$	−0.561976	+	1.72959i	−0.0262881	+	0.0809066i	−0.963340	−	0.268284i	$-0.913543\pi$
$457$	−0.561976	+	1.72959i	−0.0262881	+	0.0809066i	0.937052	+	0.349191i	$0.113543\pi$
$458$	−3.40697	−	17.8600i	−0.159197	−	0.834542i
$459$	0.483844	−	7.69048i	0.0225839	−	0.358961i
$460$	−16.6705	+	7.08488i	−0.777268	+	0.330334i
$461$	16.6138	−	26.1792i	0.773784	−	1.21929i	−0.197251	−	0.980353i	$-0.563202\pi$
$461$	16.6138	−	26.1792i	0.773784	−	1.21929i	0.971035	−	0.238936i	$-0.0767985\pi$
$462$	−0.0328055	+	0.521428i	−0.00152625	+	0.0242590i
$463$	−6.69442	−	10.5487i	−0.311116	−	0.490241i	0.652406	−	0.757870i	$-0.273760\pi$
$463$	−6.69442	−	10.5487i	−0.311116	−	0.490241i	−0.963522	+	0.267629i	$0.913760\pi$
$464$	−1.26971	−	1.53482i	−0.0589448	−	0.0712520i
$465$	−1.69062	+	3.83773i	−0.0784008	+	0.177970i
$466$	−12.1074	+	3.10865i	−0.560864	+	0.144005i
$467$	1.54999	−	3.29390i	0.0717251	−	0.152424i	−0.865749	−	0.500478i	$-0.833158\pi$
$467$	1.54999	−	3.29390i	0.0717251	−	0.152424i	0.937474	+	0.348054i	$0.113158\pi$
$468$	10.2367	+	31.5053i	0.473191	+	1.45633i
$469$	0.302662	−	0.166390i	0.0139756	−	0.00768316i
$470$	−22.9660	−	5.29149i	−1.05934	−	0.244078i
$471$	37.8522	−	4.78184i	1.74414	−	0.220336i
$472$	−6.27855	+	0.793165i	−0.288993	+	0.0365084i
$473$	−2.01957	+	3.18234i	−0.0928601	+	0.146324i
$474$	6.78589	+	4.93024i	0.311686	+	0.226453i
$475$	29.1562	−	9.05346i	1.33778	−	0.415401i
$476$	2.57056	−	1.86762i	0.117821	−	0.0856022i
$477$	−0.626625	−	9.95992i	−0.0286912	−	0.456033i
$478$	3.51645	+	1.93318i	0.160839	+	0.0884217i
$479$	10.6916	+	22.7207i	0.488510	+	1.03814i	0.985389	+	0.170317i	$0.0544791\pi$
$479$	10.6916	+	22.7207i	0.488510	+	1.03814i	−0.496880	+	0.867820i	$0.665521\pi$
$480$	−27.9510	−	19.2639i	−1.27578	−	0.879274i
$481$	−3.69387	−	19.3639i	−0.168426	−	0.882920i
$482$	−3.70117	−	2.68906i	−0.168584	−	0.122483i
$483$	−8.91170	+	4.89925i	−0.405496	+	0.222923i
$484$	7.82108	+	12.3240i	0.355504	+	0.560184i
$485$	6.91317	+	4.76459i	0.313911	+	0.216349i
$486$	16.3899	−	6.48921i	0.743460	−	0.294357i
$487$	−5.24912	−	2.07827i	−0.237860	−	0.0941755i	0.246171	−	0.969227i	$-0.420828\pi$
$487$	−5.24912	−	2.07827i	−0.237860	−	0.0941755i	−0.484031	+	0.875051i	$0.660828\pi$
$488$	−18.9403	+	22.8949i	−0.857387	+	1.03640i
$489$	−30.4454	−	7.81706i	−1.37679	−	0.353500i
$490$	−11.4606	+	3.24846i	−0.517736	+	0.146751i
$491$	18.3466	+	7.26393i	0.827970	+	0.327817i	0.743606	−	0.668618i	$-0.233114\pi$
$491$	18.3466	+	7.26393i	0.827970	+	0.327817i	0.0843646	+	0.996435i	$0.473114\pi$
$492$	3.62097	+	3.40032i	0.163246	+	0.153298i
$493$	−11.8144	+	8.58366i	−0.532094	+	0.386589i
$494$	13.6101	−	28.9230i	0.612349	−	1.30131i
$495$	0.689472	+	3.18216i	0.0309895	+	0.143027i
$496$	0.313725	+	0.172472i	0.0140867	+	0.00774421i
$497$	0.892617	−	4.67926i	0.0400393	−	0.209894i
$498$	−17.5103	−	4.49589i	−0.784657	−	0.201466i
$499$	22.3477			1.00042			0.500210	−	0.865904i	$-0.333256\pi$
$499$	22.3477			1.00042			0.500210	+	0.865904i	$0.333256\pi$
$500$	13.5280	−	6.56171i	0.604989	−	0.293449i
$501$	−6.37846			−0.284969
$502$	−18.0542	−	4.63553i	−0.805798	−	0.206894i
$503$	−2.72429	+	14.2812i	−0.121470	+	0.636768i	0.868523	+	0.495649i	$0.165070\pi$
$503$	−2.72429	+	14.2812i	−0.121470	+	0.636768i	−0.989993	+	0.141119i	$0.954930\pi$
$504$	−5.84655	−	3.21417i	−0.260426	−	0.143170i
$505$	6.62493	+	0.669992i	0.294806	+	0.0298143i
$506$	−0.793696	+	1.68669i	−0.0352841	+	0.0749825i
$507$	−60.8600	+	44.2174i	−2.70289	+	1.96376i
$508$	−14.5104	−	13.6262i	−0.643797	−	0.604566i
$509$	8.68523	+	3.43873i	0.384966	+	0.152419i	0.552633	−	0.833425i	$-0.313623\pi$
$509$	8.68523	+	3.43873i	0.384966	+	0.152419i	−0.167667	+	0.985844i	$0.553623\pi$
$510$	−10.6594	+	13.5580i	−0.472008	+	0.600358i
$511$	1.85075	+	0.475193i	0.0818725	+	0.0210213i
$512$	−3.56649	+	4.31115i	−0.157618	+	0.190528i
$513$	−11.9795	−	4.74303i	−0.528909	−	0.209410i
$514$	9.41692	−	3.72842i	0.415362	−	0.164454i
$515$	12.6976	+	36.0061i	0.559521	+	1.58662i
$516$	−18.5365	−	29.2088i	−0.816023	−	1.28585i
$517$	4.36241	−	2.39826i	0.191859	−	0.105475i
$518$	1.29142	+	0.938271i	0.0567417	+	0.0412252i
$519$	−12.3723	−	64.8577i	−0.543083	−	2.84694i
$520$	11.1696	−	37.5278i	0.489817	−	1.64570i
$521$	−8.28676	−	17.6103i	−0.363049	−	0.771519i	−1.00000		0.000614502i	$-0.999804\pi$
$521$	−8.28676	−	17.6103i	−0.363049	−	0.771519i	0.636950	−	0.770905i	$-0.280196\pi$
$522$	10.8037	+	5.93937i	0.472864	+	0.259959i
$523$	−0.217281	−	3.45358i	−0.00950104	−	0.151015i	−0.999917	−	0.0128968i	$-0.995895\pi$
$523$	−0.217281	−	3.45358i	−0.00950104	−	0.151015i	0.990416	−	0.138118i	$-0.0441053\pi$
$524$	1.09432	−	0.795073i	0.0478058	−	0.0347329i
$525$	7.18586	−	4.42949i	0.313616	−	0.193319i
$526$	−10.0038	−	7.26820i	−0.436187	−	0.316909i
$527$	1.40636	−	2.21606i	0.0612618	−	0.0965332i
$528$	0.492990	−	0.0622791i	0.0214546	−	0.00271035i
$529$	−13.1798	+	1.66500i	−0.573035	+	0.0723912i
$530$	−2.44079	+	4.06620i	−0.106021	+	0.176625i
$531$	−7.80140	+	4.28885i	−0.338552	+	0.186120i
$532$	−1.64173	−	5.05273i	−0.0711781	−	0.219064i
$533$	−3.89811	+	8.28390i	−0.168846	+	0.358815i
$534$	16.1684	−	4.15134i	0.699674	−	0.179646i
$535$	−1.44961	−	6.69045i	−0.0626720	−	0.289254i
$536$	0.921243	+	1.11359i	0.0397916	+	0.0480998i
$537$	−25.4481	−	40.0999i	−1.09817	−	1.73044i
$538$	0.0138161	−	0.219600i	0.000595653	−	0.00946764i
$539$	1.34823	−	2.12447i	0.0580724	−	0.0915075i
$540$	−6.18336	−	1.42468i	−0.266089	−	0.0613083i
$541$	−1.76979	+	28.1301i	−0.0760894	+	1.20941i	0.755927	+	0.654656i	$0.227186\pi$
$541$	−1.76979	+	28.1301i	−0.0760894	+	1.20941i	−0.832016	+	0.554751i	$0.812814\pi$
$542$	3.73742	+	19.5922i	0.160536	+	0.841558i
$543$	−13.8307	+	42.5667i	−0.593534	+	1.82671i
$544$	15.4876	+	14.5438i	0.664026	+	0.623562i
$545$	4.31188	−	26.1173i	0.184701	−	1.11874i
$546$	1.65615	−	8.68182i	0.0708765	−	0.371548i
$547$	26.0668	−	24.4784i	1.11454	−	1.04662i	0.115963	−	0.993254i	$-0.463005\pi$
$547$	26.0668	−	24.4784i	1.11454	−	1.04662i	0.998575	−	0.0533673i	$-0.0169954\pi$
$548$	2.08055	−	0.823749i	0.0888767	−	0.0351888i
$549$	−12.9169	+	39.7543i	−0.551282	+	1.69667i
$550$	0.588377	−	1.43108i	0.0250885	−	0.0610216i
$551$	7.54547	+	23.2226i	0.321448	+	0.989314i
$552$	−27.1255	−	32.7891i	−1.15454	−	1.39560i
$553$	1.09403	+	2.32493i	0.0465228	+	0.0988659i
$554$	−4.56863	+	4.29023i	−0.194103	+	0.182274i
$555$	16.6928	+	6.13343i	0.708571	+	0.260350i
$556$	0.0837096	+	0.0105750i	0.00355008	+	0.000448479i
$557$	22.1092			0.936797			0.468398	−	0.883517i	$-0.344831\pi$
$557$	22.1092			0.936797			0.468398	+	0.883517i	$0.344831\pi$
$558$	−2.19834	−	0.277715i	−0.0930630	−	0.0117566i
$559$	40.6428	−	49.1287i	1.71901	−	2.07792i
$560$	−0.322956	−	0.644221i	−0.0136474	−	0.0272233i
$561$	−0.228743	−	3.63577i	−0.00965755	−	0.153502i
$562$	−16.0031	+	4.10891i	−0.675052	+	0.173324i
$563$	21.6483	−	5.55833i	0.912366	−	0.234256i	0.236803	−	0.971558i	$-0.423901\pi$
$563$	21.6483	−	5.55833i	0.912366	−	0.234256i	0.675563	+	0.737302i	$0.263901\pi$
$564$	2.86901	+	45.6016i	0.120807	+	1.92017i
$565$	−8.53319	+	1.29436i	−0.358994	+	0.0544543i
$566$	1.64308	−	1.98614i	0.0690637	−	0.0834837i
$567$	3.80008	+	0.480062i	0.159588	+	0.0201607i
$568$	19.9335			0.836391
$569$	−13.8899	−	1.75470i	−0.582295	−	0.0735610i	−0.171333	−	0.985213i	$-0.554807\pi$
$569$	−13.8899	−	1.75470i	−0.582295	−	0.0735610i	−0.410963	+	0.911652i	$0.634807\pi$
$570$	16.0525	+	23.9561i	0.672365	+	1.00341i
$571$	24.8898	−	23.3730i	1.04160	−	0.978131i	0.0418244	−	0.999125i	$-0.486683\pi$
$571$	24.8898	−	23.3730i	1.04160	−	0.978131i	0.999780	+	0.0209937i	$0.00668298\pi$
$572$	1.41583	+	3.00878i	0.0591987	+	0.125804i
$573$	29.2124	+	35.3118i	1.22037	+	1.47517i
$574$	−0.229090	−	0.705066i	−0.00956202	−	0.0294289i
$575$	29.6562	−	5.25608i	1.23675	−	0.219194i
$576$	4.37019	−	13.4501i	0.182091	−	0.560419i
$577$	34.1312	−	13.5135i	1.42090	−	0.562574i	0.472976	−	0.881075i	$-0.343180\pi$
$577$	34.1312	−	13.5135i	1.42090	−	0.562574i	0.947922	+	0.318502i	$0.103180\pi$
$578$	−2.16246	+	2.03069i	−0.0899467	+	0.0844655i
$579$	−4.90846	+	25.7310i	−0.203988	+	1.06935i
$580$	5.38920	+	10.7502i	0.223774	+	0.446377i
$581$	−4.03702	−	3.79101i	−0.167484	−	0.157278i
$582$	−2.45069	+	7.54245i	−0.101584	+	0.312644i
$583$	−0.187710	−	0.984011i	−0.00777416	−	0.0407536i
$584$	−0.502054	+	7.97992i	−0.0207751	+	0.330211i
$585$	−4.82478	−	54.8695i	−0.199480	−	2.26857i
$586$	−1.77735	+	2.80065i	−0.0734216	+	0.115694i
$587$	0.282538	−	4.49081i	0.0116616	−	0.185355i	−0.987884	−	0.155197i	$-0.950399\pi$
$587$	0.282538	−	4.49081i	0.0116616	−	0.185355i	0.999545	−	0.0301585i	$-0.00960122\pi$
$588$	12.3746	+	19.4993i	0.510321	+	0.804137i
$589$	−2.79737	−	3.38143i	−0.115263	−	0.139330i
$590$	4.20922	+	0.425687i	0.173291	+	0.0175253i
$591$	−46.5262	+	11.9459i	−1.91383	+	0.491388i
$592$	0.646425	−	1.37372i	0.0265679	−	0.0564597i
$593$	5.16751	+	15.9040i	0.212204	+	0.653097i	0.999340	+	0.0363178i	$0.0115629\pi$
$593$	5.16751	+	15.9040i	0.212204	+	0.653097i	−0.787136	+	0.616779i	$0.788437\pi$
$594$	−0.572239	+	0.314591i	−0.0234792	+	0.0129078i
$595$	−4.86229	+	2.06644i	−0.199334	+	0.0847159i
$596$	−23.2532	+	2.93756i	−0.952489	+	0.120327i
$597$	−44.7709	+	5.65588i	−1.83235	+	0.231480i
$598$	16.8972	−	26.6257i	0.690977	−	1.08881i
$599$	3.79459	+	2.75693i	0.155043	+	0.112645i	0.662602	−	0.748972i	$-0.269452\pi$
$599$	3.79459	+	2.75693i	0.155043	+	0.112645i	−0.507559	+	0.861617i	$0.669452\pi$
$600$	23.8413	+	26.0635i	0.973319	+	1.06404i
$601$	2.83842	−	2.06223i	0.115781	−	0.0841201i	−0.528388	−	0.849003i	$-0.677203\pi$
$601$	2.83842	−	2.06223i	0.115781	−	0.0841201i	0.644169	+	0.764883i	$0.277203\pi$
$602$	0.324193	+	5.15290i	0.0132131	+	0.210016i
$603$	1.78164	+	0.979467i	0.0725542	+	0.0398870i
$604$	4.43154	+	9.41751i	0.180317	+	0.383193i
$605$	−8.07159	−	22.8884i	−0.328157	−	0.930545i
$606$	1.17855	+	6.17820i	0.0478755	+	0.250972i
$607$	12.4234	+	9.02610i	0.504249	+	0.366358i	0.810637	−	0.585548i	$-0.199121\pi$
$607$	12.4234	+	9.02610i	0.504249	+	0.366358i	−0.306389	+	0.951906i	$0.599121\pi$
$608$	31.1302	−	17.1140i	1.26250	−	0.694063i
$609$	3.61762	+	5.70045i	0.146593	+	0.230994i
$610$	15.7752	−	12.0720i	0.638718	−	0.488782i
$611$	−78.3013	+	31.0017i	−3.16773	+	1.25419i
$612$	17.3905	+	6.88539i	0.702969	+	0.278325i
$613$	−5.28338	+	6.38651i	−0.213394	+	0.257949i	−0.866339	−	0.499456i	$-0.833533\pi$
$613$	−5.28338	+	6.38651i	−0.213394	+	0.257949i	0.652945	+	0.757405i	$0.273533\pi$
$614$	11.0999	+	2.84998i	0.447957	+	0.115016i
$615$	−4.59762	−	6.86132i	−0.185394	−	0.276675i
$616$	−0.622687	−	0.246539i	−0.0250888	−	0.00993335i
$617$	−15.0434	−	14.1267i	−0.605626	−	0.568721i	0.319878	−	0.947459i	$-0.396358\pi$
$617$	−15.0434	−	14.1267i	−0.605626	−	0.568721i	−0.925504	+	0.378738i	$0.876358\pi$
$618$	−29.1756	+	21.1973i	−1.17361	+	0.852680i
$619$	−2.08971	+	4.44085i	−0.0839923	+	0.178493i	−0.942411	−	0.334457i	$-0.891447\pi$
$619$	−2.08971	+	4.44085i	−0.0839923	+	0.178493i	0.858419	+	0.512950i	$0.171447\pi$
$620$	−1.61183	−	1.43987i	−0.0647327	−	0.0578265i
$621$	−11.1386	−	6.12348i	−0.446975	−	0.245727i
$622$	2.46542	−	12.9242i	0.0988543	−	0.518212i
$623$	4.95292	+	1.27169i	0.198434	+	0.0509493i
$624$	−8.40613			−0.336515
$625$	−24.3690	+	5.58159i	−0.974758	+	0.223264i
$626$	−24.4363			−0.976670
$627$	−5.89985	−	1.51482i	−0.235617	−	0.0604963i
$628$	−3.68453	+	19.3150i	−0.147029	+	0.770753i
$629$	−9.75366	−	5.36212i	−0.388904	−	0.213802i
$630$	3.32630	+	2.97143i	0.132523	+	0.118385i
$631$	−2.28055	+	4.84641i	−0.0907872	+	0.192933i	−0.945064	−	0.326886i	$-0.894001\pi$
$631$	−2.28055	+	4.84641i	−0.0907872	+	0.192933i	0.854276	+	0.519819i	$0.174001\pi$
$632$	−8.69853	+	6.31985i	−0.346009	+	0.251390i
$633$	−25.2515	−	23.7128i	−1.00366	−	0.942498i
$634$	3.51456	+	1.39151i	0.139581	+	0.0552641i
$635$	18.4242	+	27.4956i	0.731142	+	1.09113i
$636$	8.90566	+	2.28658i	0.353132	+	0.0906689i
$637$	−27.1324	+	32.7974i	−1.07503	+	1.29948i
$638$	1.15065	+	0.455573i	0.0455545	+	0.0180363i
$639$	26.0724	−	10.3228i	1.03141	−	0.408363i
$640$	15.3257	−	11.7281i	0.605803	−	0.463594i
$641$	19.2339	+	30.3077i	0.759692	+	1.19708i	0.975361	+	0.220616i	$0.0708067\pi$
$641$	19.2339	+	30.3077i	0.759692	+	1.19708i	−0.215669	+	0.976466i	$0.569193\pi$
$642$	5.66638	−	3.11512i	0.223634	−	0.122944i
$643$	−28.2259	−	20.5073i	−1.11312	−	0.808729i	−0.129968	−	0.991518i	$-0.541487\pi$
$643$	−28.2259	−	20.5073i	−1.11312	−	0.808729i	−0.983152	+	0.182790i	$0.941487\pi$
$644$	−0.982105	−	5.14837i	−0.0387004	−	0.202874i
$645$	19.1302	+	54.2470i	0.753251	+	2.13597i
$646$	−7.68455	−	16.3305i	−0.302345	−	0.642515i
$647$	24.2908	+	13.3540i	0.954970	+	0.524999i	0.881441	−	0.472294i	$-0.156574\pi$
$647$	24.2908	+	13.3540i	0.954970	+	0.524999i	0.0735290	+	0.997293i	$0.476574\pi$
$648$	1.00640	+	15.9962i	0.0395350	+	0.628391i
$649$	−0.722972	+	0.525270i	−0.0283791	+	0.0206187i
$650$	−12.9093	+	22.7710i	−0.506343	+	0.893153i
$651$	−0.981686	−	0.713236i	−0.0384753	−	0.0279539i
$652$	8.68035	−	13.6780i	0.339949	−	0.535673i
$653$	26.7520	−	3.37957i	1.04689	−	0.132253i	0.416974	−	0.908918i	$-0.363091\pi$
$653$	26.7520	−	3.37957i	1.04689	−	0.132253i	0.629913	+	0.776666i	$0.283091\pi$
$654$	24.8063	−	3.13376i	0.970002	−	0.122540i
$655$	−2.06995	+	0.879716i	−0.0808796	+	0.0343733i
$656$	−0.617879	+	0.339682i	−0.0241241	+	0.0132623i
$657$	3.47582	+	10.6975i	0.135605	+	0.417349i
$658$	2.90355	−	6.17035i	0.113192	−	0.240545i
$659$	−17.9921	+	4.61958i	−0.700871	+	0.179953i	−0.582278	−	0.812990i	$-0.697838\pi$
$659$	−17.9921	+	4.61958i	−0.700871	+	0.179953i	−0.118593	+	0.992943i	$0.537838\pi$
$660$	−2.98462	−	0.301841i	−0.116176	−	0.0117491i
$661$	6.91570	+	8.35965i	0.268990	+	0.325153i	0.887661	−	0.460497i	$-0.152329\pi$
$661$	6.91570	+	8.35965i	0.268990	+	0.325153i	−0.618672	+	0.785650i	$0.712329\pi$
$662$	2.88206	+	4.54140i	0.112014	+	0.176506i
$663$	−3.86962	+	61.5058i	−0.150284	+	2.38869i
$664$	12.4171	−	19.5662i	0.481878	−	0.759318i
$665$	0.773784	+	8.79981i	0.0300061	+	0.341242i
$666$	−0.590021	+	9.37811i	−0.0228628	+	0.363394i
$667$	4.51379	+	23.6621i	0.174775	+	0.916202i
$668$	1.01584	−	3.12644i	0.0393041	−	0.120965i
$669$	4.96256	+	4.66016i	0.191864	+	0.180172i
$670$	−0.432998	−	0.863728i	−0.0167282	−	0.0333687i
$671$	−0.786234	+	4.12158i	−0.0303522	+	0.159112i
$672$	7.16026	−	6.72393i	0.276213	−	0.259381i
$673$	−25.9856	+	10.2884i	−1.00167	+	0.396590i	−0.810989	−	0.585061i	$-0.801070\pi$
$673$	−25.9856	+	10.2884i	−1.00167	+	0.396590i	−0.190684	+	0.981652i	$0.561070\pi$
$674$	−4.50060	+	13.8514i	−0.173357	+	0.533537i
$675$	9.48699	+	4.61679i	0.365154	+	0.177700i
$676$	−11.9807	−	36.8729i	−0.460798	−	1.41819i
$677$	−18.8713	−	22.8114i	−0.725281	−	0.876714i	0.271026	−	0.962572i	$-0.412637\pi$
$677$	−18.8713	−	22.8114i	−0.725281	−	0.876714i	−0.996307	+	0.0858577i	$0.972637\pi$
$678$	−3.47111	−	7.37648i	−0.133307	−	0.283292i
$679$	−1.77096	+	1.66304i	−0.0679632	+	0.0638217i
$680$	−12.3064	−	18.3656i	−0.471929	−	0.704289i
$681$	−53.7254	−	6.78709i	−2.05876	−	0.260082i
$682$	−0.222423			−0.00851703
$683$	−28.6318	−	3.61704i	−1.09557	−	0.138402i	−0.443287	−	0.896380i	$-0.646188\pi$
$683$	−28.6318	−	3.61704i	−1.09557	−	0.138402i	−0.652281	+	0.757978i	$0.726188\pi$
$684$	19.9348	−	24.0970i	0.762226	−	0.921373i
$685$	−3.67863	+	0.557996i	−0.140553	+	0.0213199i
$686$	−0.446617	−	7.09877i	−0.0170519	−	0.271032i
$687$	56.7708	−	14.5763i	2.16594	−	0.556119i
$688$	4.75631	−	1.22121i	0.181333	−	0.0465583i
$689$	1.06408	+	16.9131i	0.0405383	+	0.644338i
$690$	12.7494	+	25.4320i	0.485360	+	0.968179i
$691$	8.59487	−	10.3894i	0.326964	−	0.395232i	−0.581258	−	0.813719i	$-0.697439\pi$
$691$	8.59487	−	10.3894i	0.326964	−	0.395232i	0.908223	+	0.418487i	$0.137439\pi$
$692$	33.7608	+	4.26498i	1.28339	+	0.162130i
$693$	−0.942129			−0.0357885
$694$	−7.53479	−	0.951865i	−0.286017	−	0.0361323i
$695$	−0.131686	−	0.0483854i	−0.00499515	−	0.00183536i
$696$	−20.5945	+	19.3395i	−0.780633	+	0.733063i
$697$	2.20095	+	4.67725i	0.0833668	+	0.177164i
$698$	−5.31603	−	6.42597i	−0.201215	−	0.243227i
$699$	−12.4521	−	38.3235i	−0.470981	−	1.44953i
$700$	1.02671	+	4.22763i	0.0388059	+	0.159789i
$701$	9.54262	−	29.3692i	0.360420	−	1.10926i	−0.592380	−	0.805659i	$-0.701812\pi$
$701$	9.54262	−	29.3692i	0.360420	−	1.10926i	0.952800	−	0.303600i	$-0.0981885\pi$
$702$	10.2712	−	4.06664i	0.387660	−	0.153485i
$703$	−13.5666	+	12.7399i	−0.511673	+	0.480493i
$704$	0.266006	−	1.39445i	0.0100255	−	0.0525555i
$705$	12.3755	−	74.9591i	0.466089	−	2.82312i
$706$	−2.34202	−	2.19930i	−0.0881429	−	0.0827717i
$707$	−0.595388	+	1.83242i	−0.0223919	+	0.0689151i
$708$	−1.53694	−	8.05694i	−0.0577619	−	0.302798i
$709$	0.0367345	−	0.583878i	0.00137959	−	0.0219280i	−0.997277	−	0.0737507i	$-0.976503\pi$
$709$	0.0367345	−	0.583878i	0.00137959	−	0.0219280i	0.998656	+	0.0518227i	$0.0165031\pi$
$710$	−12.9857	−	2.99197i	−0.487345	−	0.112287i
$711$	−8.10460	+	12.7708i	−0.303946	+	0.478943i
$712$	−1.34358	+	21.3556i	−0.0503527	+	0.800333i
$713$	−2.31983	−	3.65547i	−0.0868785	−	0.136899i
$714$	−3.18095	−	3.84511i	−0.119044	−	0.143899i
$715$	−1.17080	−	5.40368i	−0.0437856	−	0.202086i
$716$	23.7081	−	6.08719i	0.886012	−	0.227489i
$717$	−5.50780	+	11.7047i	−0.205693	+	0.437119i
$718$	−1.70872	−	5.25889i	−0.0637687	−	0.196260i
$719$	−9.66359	+	5.31260i	−0.360391	+	0.198127i	−0.651654	−	0.758516i	$-0.725925\pi$
$719$	−9.66359	+	5.31260i	−0.360391	+	0.198127i	0.291263	+	0.956643i	$0.405925\pi$
$720$	2.18325	−	3.63716i	0.0813648	−	0.135549i
$721$	−10.9602	+	1.38459i	−0.408179	+	0.0515649i
$722$	−14.6815	+	1.85470i	−0.546388	+	0.0690249i
$723$	7.90228	−	12.4520i	0.293889	−	0.463095i
$724$	−18.6616	−	13.5584i	−0.693552	−	0.503895i
$725$	−4.71879	−	19.4304i	−0.175252	−	0.721625i
$726$	18.5463	−	13.4747i	0.688319	−	0.500093i
$727$	−0.0450499	−	0.716047i	−0.00167081	−	0.0265567i	0.997103	−	0.0760633i	$-0.0242351\pi$
$727$	−0.0450499	−	0.716047i	−0.00167081	−	0.0265567i	−0.998774	+	0.0495066i	$0.984235\pi$
$728$	9.92813	+	5.45803i	0.367961	+	0.202288i
$729$	16.6333	+	35.3476i	0.616049	+	1.30917i
$730$	1.52483	−	5.12318i	0.0564366	−	0.189617i
$731$	−6.74586	−	35.3630i	−0.249505	−	1.30795i
$732$	−31.1566	−	22.6366i	−1.15158	−	0.836673i
$733$	−16.1152	+	8.85941i	−0.595228	+	0.327230i	−0.750733	−	0.660606i	$-0.770300\pi$
$733$	−16.1152	+	8.85941i	−0.595228	+	0.327230i	0.155505	+	0.987835i	$0.450300\pi$
$734$	3.57709	+	5.63660i	0.132033	+	0.208051i
$735$	−12.7710	−	36.2143i	−0.471065	−	1.33579i
$736$	32.5849	−	12.9013i	1.20109	−	0.475547i
$737$	0.189754	+	0.0751290i	0.00698969	+	0.00276741i
$738$	2.78173	−	3.36254i	0.102397	−	0.123777i
$739$	12.0460	+	3.09289i	0.443119	+	0.113774i	0.463656	−	0.886015i	$-0.346537\pi$
$739$	12.0460	+	3.09289i	0.443119	+	0.113774i	−0.0205364	+	0.999789i	$0.506537\pi$
$740$	−5.66485	+	7.20526i	−0.208244	+	0.264871i
$741$	95.8082	+	37.9331i	3.51960	+	1.39351i
$742$	−1.00033	−	0.939375i	−0.0367234	−	0.0344855i
$743$	−14.9651	+	10.8728i	−0.549018	+	0.398885i	−0.827423	−	0.561579i	$-0.810194\pi$
$743$	−14.9651	+	10.8728i	−0.549018	+	0.398885i	0.278405	+	0.960464i	$0.410194\pi$
$744$	2.16194	−	4.59436i	0.0792606	−	0.168437i
$745$	38.7737	+	3.92126i	1.42056	+	0.143664i
$746$	17.4628	+	9.60027i	0.639359	+	0.351491i
$747$	6.10860	−	32.0224i	0.223502	−	1.17164i
$748$	1.81852	+	0.466917i	0.0664917	+	0.0170722i
$749$	1.98082			0.0723775
$750$	−11.6194	−	20.5577i	−0.424281	−	0.750660i
$751$	4.10129			0.149658			0.0748291	−	0.997196i	$-0.476159\pi$
$751$	4.10129			0.149658			0.0748291	+	0.997196i	$0.476159\pi$
$752$	−6.28211	−	1.61297i	−0.229085	−	0.0588190i
$753$	11.2593	−	59.0236i	0.410314	−	2.15094i
$754$	−18.3459	−	10.0858i	−0.668119	−	0.367302i
$755$	−3.66462	−	16.9135i	−0.133369	−	0.615547i
$756$	0.781749	−	1.66130i	0.0284319	−	0.0604209i
$757$	−26.2863	+	19.0981i	−0.955392	+	0.694133i	−0.952076	−	0.305861i	$-0.901056\pi$
$757$	−26.2863	+	19.0981i	−0.955392	+	0.694133i	−0.00331614	+	0.999995i	$0.501056\pi$
$758$	−6.85076	−	6.43329i	−0.248831	−	0.233668i
$759$	−5.58720	−	2.21213i	−0.202803	−	0.0802952i
$760$	−35.5639	+	10.0805i	−1.29004	+	0.365657i
$761$	5.36021	+	1.37627i	0.194307	+	0.0498896i	0.344589	−	0.938754i	$-0.388018\pi$
$761$	5.36021	+	1.37627i	0.194307	+	0.0498896i	−0.150282	+	0.988643i	$0.548018\pi$
$762$	−19.9278	+	24.0885i	−0.721907	+	0.872636i
$763$	7.12152	+	2.81961i	0.257816	+	0.102077i
$764$	−21.9606	+	8.69484i	−0.794508	+	0.314568i
$765$	−25.6073	−	17.6486i	−0.925832	−	0.638088i
$766$	−8.10204	−	12.7668i	−0.292738	−	0.461282i
$767$	13.2477	−	7.28298i	0.478346	−	0.262973i
$768$	30.4242	+	22.1045i	1.09784	+	0.797626i
$769$	7.56667	+	39.6659i	0.272861	+	1.43039i	0.809770	+	0.586747i	$0.199592\pi$
$769$	7.56667	+	39.6659i	0.272861	+	1.43039i	−0.536909	+	0.843640i	$0.680408\pi$
$770$	0.368646	+	0.254072i	0.0132851	+	0.00915613i
$771$	13.9015	+	29.5421i	0.500649	+	1.06393i
$772$	−11.8305	−	6.50386i	−0.425788	−	0.234079i
$773$	−1.32345	−	21.0356i	−0.0476011	−	0.756597i	−0.947352	−	0.320194i	$-0.896252\pi$
$773$	−1.32345	−	21.0356i	−0.0476011	−	0.756597i	0.899751	−	0.436404i	$-0.143748\pi$
$774$	−24.5884	+	17.8645i	−0.883812	+	0.642127i
$775$	2.07411	+	2.93475i	0.0745041	+	0.105419i
$776$	−8.22437	−	5.97535i	−0.295238	−	0.214503i
$777$	−2.75727	+	4.34477i	−0.0989167	+	0.155868i
$778$	11.8607	−	1.49835i	0.425226	−	0.0537185i
$779$	8.57506	−	1.08328i	0.307233	−	0.0388126i
$780$	49.4523	+	11.3941i	1.77068	+	0.407973i
$781$	2.46664	−	1.35605i	0.0882634	−	0.0485232i
$782$	−5.50210	−	16.9337i	−0.196755	−	0.605548i
$783$	−3.59295	+	7.63541i	−0.128402	+	0.272867i
$784$	−3.17523	+	0.815260i	−0.113401	+	0.0291164i
$785$	13.1808	−	29.9205i	0.470442	−	1.06791i
$786$	−1.35418	−	1.63692i	−0.0483019	−	0.0583869i
$787$	11.1926	+	17.6367i	0.398974	+	0.628682i	0.983119	−	0.182967i	$-0.0585702\pi$
$787$	11.1926	+	17.6367i	0.398974	+	0.628682i	−0.584145	+	0.811649i	$0.698570\pi$
$788$	1.55447	−	24.7076i	0.0553756	−	0.880170i
$789$	21.3589	−	33.6562i	0.760397	−	1.19819i
$790$	6.61527	−	2.81145i	0.235361	−	0.100027i
$791$	0.156809	−	2.49241i	0.00557550	−	0.0886200i
$792$	−0.738722	−	3.87252i	−0.0262493	−	0.137604i
$793$	21.9345	−	67.5074i	0.778917	−	2.39726i
$794$	−12.5268	−	11.7635i	−0.444560	−	0.417469i
$795$	−13.5762	−	7.02963i	−0.481496	−	0.249315i
$796$	4.35800	−	22.8455i	0.154465	−	0.809736i
$797$	39.6611	−	37.2442i	1.40487	−	1.31926i	0.519419	−	0.854520i	$-0.326149\pi$
$797$	39.6611	−	37.2442i	1.40487	−	1.31926i	0.885448	−	0.464738i	$-0.153851\pi$
$798$	−7.75813	+	3.07166i	−0.274635	+	0.108736i
$799$	−14.6936	+	45.2223i	−0.519823	+	1.59985i
$800$	−26.4814	+	12.0406i	−0.936258	+	0.425699i
$801$	9.30186	+	28.6282i	0.328665	+	1.01153i
$802$	11.3274	+	13.6925i	0.399986	+	0.483499i
$803$	0.480737	+	1.02162i	0.0169649	+	0.0360521i
$804$	−1.36549	+	1.28228i	−0.0481572	+	0.0452226i
$805$	−0.330712	+	8.70853i	−0.0116561	+	0.306935i
$806$	3.73304	+	0.471592i	0.131491	+	0.0166111i
$807$	0.709311			0.0249689
$808$	−7.99879	−	1.01048i	−0.281396	−	0.0355486i
$809$	−11.4513	+	13.8422i	−0.402606	+	0.486667i	−0.932384	−	0.361469i	$-0.882275\pi$
$809$	−11.4513	+	13.8422i	−0.402606	+	0.486667i	0.529778	+	0.848136i	$0.322275\pi$
$810$	1.74538	−	10.5718i	0.0613263	−	0.371456i
$811$	2.08961	+	33.2135i	0.0733763	+	1.16628i	0.846629	+	0.532184i	$0.178629\pi$
$811$	2.08961	+	33.2135i	0.0733763	+	1.16628i	−0.773252	+	0.634099i	$0.781371\pi$
$812$	−3.37025	+	0.865333i	−0.118273	+	0.0303672i
$813$	−62.2771	+	15.9900i	−2.18415	+	0.560795i
$814$	0.0592264	+	0.941376i	0.00207588	+	0.0329952i
$815$	−19.1711	+	18.9219i	−0.671533	+	0.662804i
$816$	−3.02539	+	3.65706i	−0.105910	+	0.128023i
$817$	−59.7204	−	7.54445i	−2.08935	−	0.263947i
$818$	16.3782			0.572649
$819$	15.8122	+	1.99754i	0.552523	+	0.0697998i
$820$	4.09533	−	1.16081i	0.143015	−	0.0405372i
$821$	11.2680	−	10.5814i	0.393257	−	0.369293i	−0.462545	−	0.886596i	$-0.653064\pi$
$821$	11.2680	−	10.5814i	0.393257	−	0.369293i	0.855803	+	0.517302i	$0.173064\pi$
$822$	−1.49638	−	3.17998i	−0.0521923	−	0.110914i
$823$	17.8581	+	21.5867i	0.622493	+	0.752465i	0.983660	−	0.180036i	$-0.0576216\pi$
$823$	17.8581	+	21.5867i	0.622493	+	0.752465i	−0.361167	+	0.932501i	$0.617622\pi$
$824$	−14.2851	−	43.9650i	−0.497645	−	1.53159i
$825$	4.72328	+	1.60330i	0.164444	+	0.0558198i
$826$	−0.378286	+	1.16425i	−0.0131623	+	0.0405093i
$827$	−23.1969	+	9.18432i	−0.806636	+	0.319370i	−0.735005	−	0.678061i	$-0.762820\pi$
$827$	−23.1969	+	9.18432i	−0.806636	+	0.319370i	−0.0716310	+	0.997431i	$0.522820\pi$
$828$	22.4908	−	21.1202i	0.781608	−	0.733979i
$829$	4.36653	−	22.8901i	0.151656	−	0.795007i	−0.822437	−	0.568857i	$-0.807386\pi$
$829$	4.36653	−	22.8901i	0.151656	−	0.795007i	0.974092	−	0.226150i	$-0.0726141\pi$
$830$	−11.0260	+	10.8827i	−0.382718	+	0.377744i
$831$	−14.7276	−	13.8301i	−0.510895	−	0.479762i
$832$	−7.42110	+	22.8398i	−0.257280	+	0.791827i
$833$	4.50342	+	23.6077i	0.156034	+	0.817960i
$834$	0.00832082	−	0.132256i	0.000288126	−	0.00457964i
$835$	−2.81313	+	4.68651i	−0.0973525	+	0.162183i
$836$	1.68212	−	2.65059i	0.0581772	−	0.0916726i
$837$	0.0952309	−	1.51365i	0.00329166	−	0.0523194i
$838$	−8.06577	−	12.7096i	−0.278628	−	0.439047i
$839$	10.0685	+	12.1708i	0.347604	+	0.420181i	0.915120	−	0.403181i	$-0.132096\pi$
$839$	10.0685	+	12.1708i	0.347604	+	0.420181i	−0.567516	+	0.823362i	$0.692096\pi$
$840$	−8.83131	+	5.14515i	−0.304709	+	0.177524i
$841$	−12.5991	+	3.23490i	−0.434452	+	0.111548i
$842$	6.33620	−	13.4651i	0.218360	−	0.464038i
$843$	−16.4587	−	50.6548i	−0.566869	−	1.74464i
$844$	15.6445	−	8.60065i	0.538507	−	0.296047i
$845$	5.64679	+	64.2177i	0.194255	+	2.20916i
$846$	39.8263	−	5.03123i	1.36926	−	0.172977i
$847$	6.96718	−	0.880159i	0.239395	−	0.0302426i
$848$	−0.699333	+	1.10197i	−0.0240152	+	0.0378419i
$849$	6.72254	+	4.88421i	0.230717	+	0.167626i
$850$	5.26040	+	13.8115i	0.180430	+	0.473730i
$851$	−14.8536	+	10.7917i	−0.509174	+	0.369936i
$852$	1.62223	+	25.7846i	0.0555766	+	0.883365i
$853$	6.60242	+	3.62971i	0.226063	+	0.124279i	0.590761	−	0.806847i	$-0.298828\pi$
$853$	6.60242	+	3.62971i	0.226063	+	0.124279i	−0.364698	+	0.931126i	$0.618828\pi$
$854$	2.44728	+	5.20074i	0.0837443	+	0.177966i
$855$	−41.2963	+	31.6022i	−1.41230	+	1.08077i
$856$	1.55316	+	8.14193i	0.0530858	+	0.278285i
$857$	−5.18779	−	3.76915i	−0.177212	−	0.128752i	0.495643	−	0.868526i	$-0.334932\pi$
$857$	−5.18779	−	3.76915i	−0.177212	−	0.128752i	−0.672855	+	0.739774i	$0.734932\pi$
$858$	4.57657	−	2.51599i	0.156241	−	0.0858945i
$859$	18.8986	+	29.7795i	0.644812	+	1.01606i	0.996791	+	0.0800535i	$0.0255091\pi$
$859$	18.8986	+	29.7795i	0.644812	+	1.01606i	−0.351978	+	0.936008i	$0.614491\pi$
$860$	−29.6361	+	0.737334i	−1.01058	+	0.0251429i
$861$	2.22202	−	0.879760i	0.0757262	−	0.0299821i
$862$	11.3116	+	4.47860i	0.385276	+	0.152542i
$863$	20.8089	−	25.1536i	0.708343	−	0.856239i	−0.286456	−	0.958093i	$-0.592477\pi$
$863$	20.8089	−	25.1536i	0.708343	−	0.856239i	0.994799	+	0.101854i	$0.0324774\pi$
$864$	11.8912	+	3.05314i	0.404547	+	0.103870i
$865$	−53.1102	−	19.5142i	−1.80580	−	0.663504i
$866$	−0.803608	−	0.318171i	−0.0273077	−	0.0108119i
$867$	−6.97100	−	6.54620i	−0.236748	−	0.222321i
$868$	0.505941	−	0.367588i	0.0171728	−	0.0124767i
$869$	−0.646457	+	1.37379i	−0.0219296	+	0.0466027i
$870$	16.3192	−	9.50758i	0.553271	−	0.322337i
$871$	−3.02544	−	1.66325i	−0.102513	−	0.0563571i
$872$	−6.00572	+	31.4831i	−0.203379	+	1.06615i
$873$	−13.8516	−	3.55649i	−0.468806	−	0.120369i
$874$	−29.7712			−1.00702
$875$	−0.0852950	−	7.23330i	−0.00288350	−	0.244530i
$876$	−10.3631			−0.350138
$877$	3.80086	+	0.975894i	0.128346	+	0.0329536i	0.312316	−	0.949978i	$-0.398895\pi$
$877$	3.80086	+	0.975894i	0.128346	+	0.0329536i	−0.183971	+	0.982932i	$0.558895\pi$
$878$	3.60582	−	18.9024i	0.121691	−	0.637925i
$879$	−9.37024	−	5.15133i	−0.316050	−	0.173750i
$880$	0.171668	−	0.389687i	0.00578692	−	0.0131363i
$881$	9.80316	−	20.8328i	0.330277	−	0.701874i	−0.668861	−	0.743387i	$-0.733218\pi$
$881$	9.80316	−	20.8328i	0.330277	−	0.701874i	0.999138	+	0.0415135i	$0.0132180\pi$
$882$	16.4148	−	11.9260i	0.552715	−	0.401571i
$883$	3.84719	+	3.61276i	0.129468	+	0.121579i	0.746577	−	0.665299i	$-0.231696\pi$
$883$	3.84719	+	3.61276i	0.129468	+	0.121579i	−0.617108	+	0.786878i	$0.711696\pi$
$884$	−29.5311	−	11.6922i	−0.993239	−	0.393251i
$885$	−0.517547	+	13.6284i	−0.0173972	+	0.458113i
$886$	−12.5852	−	3.23133i	−0.422809	−	0.108559i
$887$	5.87579	−	7.10261i	0.197290	−	0.238482i	−0.662586	−	0.748986i	$-0.730541\pi$
$887$	5.87579	−	7.10261i	0.197290	−	0.238482i	0.859876	+	0.510504i	$0.170541\pi$
$888$	−20.0207	−	7.92675i	−0.671850	−	0.266004i
$889$	−8.90437	+	3.52549i	−0.298643	+	0.118241i
$890$	4.08070	−	13.7104i	0.136785	−	0.459575i
$891$	1.21274	+	1.91097i	0.0406282	+	0.0640198i
$892$	−3.07454	+	1.69024i	−0.102943	+	0.0565936i
$893$	64.3212	+	46.7321i	2.15243	+	1.56383i
$894$	6.89772	+	36.1591i	0.230694	+	1.20934i
$895$	−40.6865	+	1.01226i	−1.36000	+	0.0338362i
$896$	2.37756	+	5.05258i	0.0794288	+	0.168795i
$897$	89.0824	+	48.9735i	2.97437	+	1.63518i
$898$	2.05333	+	32.6367i	0.0685205	+	1.08910i
$899$	−2.32533	+	1.68945i	−0.0775539	+	0.0563462i
$900$	−17.7738	+	18.4377i	−0.592459	+	0.614590i
$901$	7.74097	+	5.62414i	0.257889	+	0.187367i
$902$	0.234725	−	0.369867i	0.00781548	−	0.0123152i
$903$	−16.5127	+	2.08603i	−0.549507	+	0.0694189i
$904$	10.3677	−	1.30975i	0.344826	−	0.0435617i
$905$	25.1756	+	28.9355i	0.836864	+	0.961847i
$906$	14.3247	−	7.87506i	0.475905	−	0.261631i
$907$	1.22187	+	3.76051i	0.0405714	+	0.124866i	0.969291	−	0.245918i	$-0.0790892\pi$
$907$	1.22187	+	3.76051i	0.0405714	+	0.124866i	−0.928719	+	0.370783i	$0.879089\pi$
$908$	11.8831	−	25.2529i	0.394354	−	0.838045i
$909$	−10.9855	+	2.82059i	−0.364365	+	0.0935530i
$910$	−5.64846	−	5.04584i	−0.187245	−	0.167268i
$911$	8.09385	+	9.78378i	0.268161	+	0.324151i	0.887355	−	0.461087i	$-0.152540\pi$
$911$	8.09385	+	9.78378i	0.268161	+	0.324151i	−0.619194	+	0.785238i	$0.712540\pi$
$912$	4.25233	+	6.70060i	0.140809	+	0.221879i
$913$	0.205474	−	3.26592i	0.00680020	−	0.108086i
$914$	−0.788762	+	1.24289i	−0.0260899	+	0.0411111i
$915$	42.0321	+	48.3095i	1.38954	+	1.59706i
$916$	−1.89675	+	30.1479i	−0.0626703	+	0.996116i
$917$	−0.121946	−	0.639263i	−0.00402701	−	0.0211103i
$918$	1.92743	−	5.93203i	0.0636148	−	0.195786i
$919$	−36.1633	−	33.9596i	−1.19292	−	1.12022i	−0.990006	−	0.141025i	$-0.954960\pi$
$919$	−36.1633	−	33.9596i	−1.19292	−	1.12022i	−0.202910	−	0.979197i	$-0.565040\pi$
$920$	−36.0548	+	5.46899i	−1.18869	+	0.180307i
$921$	−6.92238	+	36.2884i	−0.228100	+	1.19574i
$922$	18.2953	−	17.1805i	0.602525	−	0.565808i
$923$	−44.2740	+	17.5293i	−1.45730	+	0.576985i
$924$	0.268230	−	0.825528i	0.00882413	−	0.0271579i
$925$	11.8686	−	9.55982i	0.390238	−	0.314325i
$926$	−3.12505	−	9.61791i	−0.102695	−	0.316064i
$927$	−41.4522	−	50.1072i	−1.36147	−	1.64573i
$928$	−9.90639	−	21.0522i	−0.325193	−	0.691071i
$929$	−2.28208	+	2.14301i	−0.0748725	+	0.0703099i	−0.721080	−	0.692852i	$-0.756354\pi$
$929$	−2.28208	+	2.14301i	−0.0748725	+	0.0703099i	0.646208	+	0.763162i	$0.276354\pi$
$930$	−2.09800	+	2.66850i	−0.0687963	+	0.0875036i
$931$	39.8683	+	5.03654i	1.30663	+	0.165066i
$932$	20.7676			0.680266
$933$	42.0797	+	5.31590i	1.37763	+	0.174035i
$934$	1.87827	−	2.27044i	0.0614590	−	0.0742912i
$935$	−2.77223	−	1.43544i	−0.0906616	−	0.0469439i
$936$	4.18764	+	66.5606i	0.136877	+	2.17560i
$937$	20.7839	−	5.33639i	0.678979	−	0.174332i	0.106576	−	0.994305i	$-0.466011\pi$
$937$	20.7839	−	5.33639i	0.678979	−	0.174332i	0.572403	+	0.819972i	$0.306011\pi$
$938$	0.270784	−	0.0695256i	0.00884143	−	0.00227009i
$939$	−4.94624	−	78.6183i	−0.161415	−	2.56561i
$940$	34.7706	+	18.0040i	1.13409	+	0.587226i
$941$	32.1242	−	38.8315i	1.04722	−	1.26587i	0.0841974	−	0.996449i	$-0.473167\pi$
$941$	32.1242	−	38.8315i	1.04722	−	1.26587i	0.963022	−	0.269422i	$-0.0868326\pi$
$942$	30.6391	+	3.87062i	0.998277	+	0.126112i
$943$	8.52681			0.277671
$944$	1.15511	+	0.145925i	0.0375957	+	0.00474944i
$945$	−1.88687	+	2.39995i	−0.0613798	+	0.0780705i
$946$	−2.22397	+	2.08845i	−0.0723076	+	0.0679014i
$947$	−23.3940	−	49.7149i	−0.760204	−	1.61552i	−0.787826	−	0.615898i	$-0.788793\pi$
$947$	−23.3940	−	49.7149i	−0.760204	−	1.61552i	0.0276221	−	0.999618i	$-0.491207\pi$
$948$	−8.88283	−	10.7375i	−0.288501	−	0.348737i
$949$	−5.90236	−	18.1656i	−0.191599	−	0.589680i
$950$	24.6813	−	1.22888i	0.800766	−	0.0398701i
$951$	−3.76549	+	11.5890i	−0.122104	+	0.375798i
$952$	5.94765	−	2.35484i	0.192765	−	0.0763209i
$953$	22.9637	−	21.5643i	0.743866	−	0.698537i	−0.216808	−	0.976214i	$-0.569565\pi$
$953$	22.9637	−	21.5643i	0.743866	−	0.698537i	0.960674	+	0.277677i	$0.0895646\pi$
$954$	1.51365	−	7.93483i	0.0490062	−	0.256900i
$955$	38.8287	−	5.88976i	1.25647	−	0.190588i
$956$	−4.85993	−	4.56378i	−0.157181	−	0.147603i
$957$	−1.23280	+	3.79416i	−0.0398507	+	0.122648i
$958$	3.80863	+	19.9655i	0.123051	+	0.645057i
$959$	0.0676000	−	1.07447i	0.00218292	−	0.0346965i
$960$	−14.2207	−	16.3445i	−0.458972	−	0.527518i
$961$	−16.3338	+	25.7380i	−0.526898	+	0.830258i
$962$	1.00192	−	15.9251i	0.0323033	−	0.513447i
$963$	6.24787	+	9.84507i	0.201335	+	0.317253i
$964$	4.84488	+	5.85646i	0.156043	+	0.188624i
$965$	16.7408	+	14.9548i	0.538906	+	0.481411i
$966$	−7.97309	+	2.04714i	−0.256530	+	0.0658657i
$967$	−21.1176	+	44.8772i	−0.679097	+	1.44315i	0.206381	+	0.978472i	$0.433831\pi$
$967$	−21.1176	+	44.8772i	−0.679097	+	1.44315i	−0.885478	+	0.464682i	$0.846169\pi$
$968$	9.08075	+	27.9477i	0.291866	+	0.898273i
$969$	50.9843	−	28.0288i	1.63785	−	0.900416i
$970$	4.46089	+	5.12711i	0.143231	+	0.164622i
$971$	−11.3774	+	1.43730i	−0.365117	+	0.0461250i	−0.305752	−	0.952111i	$-0.598908\pi$
$971$	−11.3774	+	1.43730i	−0.365117	+	0.0461250i	−0.0593655	+	0.998236i	$0.518908\pi$
$972$	−29.0558	+	3.67060i	−0.931964	+	0.117734i
$973$	0.0217516	−	0.0342750i	0.000697323	−	0.00109881i
$974$	−3.69701	−	2.68604i	−0.118460	−	0.0860662i
$975$	−75.8737	−	36.9235i	−2.42990	−	1.18250i
$976$	4.42264	−	3.21323i	0.141565	−	0.102853i
$977$	1.13969	+	18.1149i	0.0364620	+	0.579546i	0.973264	+	0.229688i	$0.0737705\pi$
$977$	1.13969	+	18.1149i	0.0364620	+	0.579546i	−0.936802	+	0.349859i	$0.886230\pi$
$978$	−22.2960	−	12.2573i	−0.712948	−	0.391946i
$979$	1.28653	+	2.73402i	0.0411177	+	0.0873795i
$980$	19.7846	−	0.492231i	0.631995	−	0.0157237i
$981$	8.44858	+	44.2890i	0.269742	+	1.41404i
$982$	12.9217	+	9.38818i	0.412349	+	0.299589i
$983$	38.3546	−	21.0856i	1.22332	−	0.672527i	0.266678	−	0.963786i	$-0.414074\pi$
$983$	38.3546	−	21.0856i	1.22332	−	0.672527i	0.956644	+	0.291259i	$0.0940740\pi$
$984$	5.35844	+	8.44355i	0.170821	+	0.269171i
$985$	−11.7426	+	39.4532i	−0.374151	+	1.25708i
$986$	−10.9905	+	4.35145i	−0.350009	+	0.138578i
$987$	20.4394	+	8.09255i	0.650595	+	0.257589i
$988$	−33.8516	+	40.9196i	−1.07696	+	1.30183i
$989$	−57.5188	−	14.7683i	−1.82899	−	0.469605i
$990$	−0.100014	+	2.63364i	−0.00317866	+	0.0837025i
$991$	−29.9351	−	11.8522i	−0.950921	−	0.376496i	−0.159109	−	0.987261i	$-0.550862\pi$
$991$	−29.9351	−	11.8522i	−0.950921	−	0.376496i	−0.791812	+	0.610765i	$0.790862\pi$
$992$	3.04829	+	2.86254i	0.0967834	+	0.0908857i
$993$	−14.0276	+	10.1916i	−0.445151	+	0.323421i
$994$	1.64176	−	3.48891i	0.0520734	−	0.110662i
$995$	−15.5900	+	35.3894i	−0.494236	+	1.12192i
$996$	26.3201	+	14.4696i	0.833983	+	0.458486i
$997$	−1.20347	+	6.30879i	−0.0381142	+	0.199801i	−0.996251	−	0.0865090i	$-0.972429\pi$
$997$	−1.20347	+	6.30879i	−0.0381142	+	0.199801i	0.958137	+	0.286310i	$0.0924289\pi$
$998$	17.5209	+	4.49859i	0.554613	+	0.142400i
$999$	−6.43168			−0.203489

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	125.2.g.a.6.8	✓	220
5.2	odd	4		625.2.h.b.349.10		440
5.3	odd	4		625.2.h.b.349.13		440
5.4	even	2		625.2.g.a.276.4		220
125.21	even	25	inner	125.2.g.a.21.8	yes	220
125.53	odd	100		625.2.h.b.274.10		440
125.72	odd	100		625.2.h.b.274.13		440
125.104	even	50		625.2.g.a.351.4		220

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
125.2.g.a.6.8	✓	220	1.1	even	1	trivial
125.2.g.a.21.8	yes	220	125.21	even	25	inner
625.2.g.a.276.4		220	5.4	even	2
625.2.g.a.351.4		220	125.104	even	50
625.2.h.b.274.10		440	125.53	odd	100
625.2.h.b.274.13		440	125.72	odd	100
625.2.h.b.349.10		440	5.2	odd	4
625.2.h.b.349.13		440	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.784012 + 0.201300i) q^{2} +(-0.488943 + 2.56313i) q^{3} +(-1.17846 - 0.647864i) q^{4} +(1.66759 + 1.48968i) q^{5} +(-0.899294 + 1.91110i) q^{6} +(-0.523443 + 0.380304i) q^{7} +(-1.97363 - 1.85336i) q^{8} +(-3.54123 - 1.40207i) q^{9} +O(q^{10})\)	\(q+(0.784012 + 0.201300i) q^{2} +(-0.488943 + 2.56313i) q^{3} +(-1.17846 - 0.647864i) q^{4} +(1.66759 + 1.48968i) q^{5} +(-0.899294 + 1.91110i) q^{6} +(-0.523443 + 0.380304i) q^{7} +(-1.97363 - 1.85336i) q^{8} +(-3.54123 - 1.40207i) q^{9} +(1.00754 + 1.50361i) q^{10} +(-0.370305 - 0.0950783i) q^{11} +(2.23676 - 2.70378i) q^{12} +(6.01342 + 2.38088i) q^{13} +(-0.486940 + 0.192793i) q^{14} +(-4.63359 + 3.54588i) q^{15} +(0.266898 + 0.420564i) q^{16} +(3.20004 - 1.75924i) q^{17} +(-2.49413 - 1.81209i) q^{18} +(-1.14413 - 5.99774i) q^{19} +(-1.00008 - 2.83590i) q^{20} +(-0.718833 - 1.52760i) q^{21} +(-0.271185 - 0.149085i) q^{22} +(-0.378229 - 6.01178i) q^{23} +(5.71539 - 4.15247i) q^{24} +(0.561715 + 4.96835i) q^{25} +(4.23532 + 3.07714i) q^{26} +(1.13067 - 1.78165i) q^{27} +(0.863242 - 0.109053i) q^{28} +(-3.96750 + 0.501211i) q^{29} +(-4.34658 + 1.84727i) q^{30} +(0.629836 - 0.346255i) q^{31} +(1.79787 + 5.53328i) q^{32} +(0.424756 - 0.902652i) q^{33} +(2.86300 - 0.735094i) q^{34} +(-1.43942 - 0.145571i) q^{35} +(3.26485 + 3.94652i) q^{36} +(-1.63319 - 2.57349i) q^{37} +(0.310334 - 4.93261i) q^{38} +(-9.04272 + 14.2491i) q^{39} +(-0.530292 - 6.03071i) q^{40} +(-0.0888833 + 1.41276i) q^{41} +(-0.256068 - 1.34236i) q^{42} +(3.04645 - 9.37601i) q^{43} +(0.374793 + 0.351954i) q^{44} +(-3.81668 - 7.61337i) q^{45} +(0.913635 - 4.78944i) q^{46} +(-9.49196 + 8.91355i) q^{47} +(-1.20846 + 0.478462i) q^{48} +(-2.03376 + 6.25926i) q^{49} +(-0.559737 + 4.00832i) q^{50} +(2.94451 + 9.06227i) q^{51} +(-5.54409 - 6.70166i) q^{52} +(1.11564 + 2.37085i) q^{53} +(1.24511 - 1.16923i) q^{54} +(-0.475882 - 0.710188i) q^{55} +(1.73792 + 0.219550i) q^{56} +15.9324 q^{57} +(-3.21146 - 0.405701i) q^{58} +(1.48994 - 1.80103i) q^{59} +(7.75775 - 1.17674i) q^{60} +(-0.689122 - 10.9533i) q^{61} +(0.563500 - 0.144682i) q^{62} +(2.38684 - 0.612837i) q^{63} +(0.233151 + 3.70582i) q^{64} +(6.48118 + 12.9284i) q^{65} +(0.514718 - 0.622187i) q^{66} +(-0.529604 - 0.0669046i) q^{67} -4.91087 q^{68} +(15.5939 + 1.96997i) q^{69} +(-1.09922 - 0.403884i) q^{70} +(-5.36705 + 5.04000i) q^{71} +(4.39052 + 9.33033i) q^{72} +(-1.88247 - 2.27552i) q^{73} +(-0.762395 - 2.34641i) q^{74} +(-13.0092 - 0.989489i) q^{75} +(-2.53741 + 7.80934i) q^{76} +(0.229992 - 0.0910604i) q^{77} +(-9.95794 + 9.35112i) q^{78} +(0.744146 - 3.90095i) q^{79} +(-0.181429 + 1.09892i) q^{80} +(-4.31547 - 4.05249i) q^{81} +(-0.354074 + 1.08973i) q^{82} +(1.60386 + 8.40773i) q^{83} +(-0.142560 + 2.26592i) q^{84} +(7.95705 + 1.83334i) q^{85} +(4.27585 - 6.73765i) q^{86} +(0.655210 - 10.4143i) q^{87} +(0.554631 + 0.873958i) q^{88} +(-5.03780 - 6.08965i) q^{89} +(-1.45975 - 6.73727i) q^{90} +(-4.05314 + 1.04067i) q^{91} +(-3.44909 + 7.32969i) q^{92} +(0.579543 + 1.78365i) q^{93} +(-9.23611 + 5.07759i) q^{94} +(7.02677 - 11.7062i) q^{95} +(-15.0616 + 1.90272i) q^{96} +(3.72521 - 0.470603i) q^{97} +(-2.85448 + 4.49794i) q^{98} +(1.17803 + 0.855889i) 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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