LMFDB - Embedded newform 250.2.g.a.11.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [250,2,Mod(11,250)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(250, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([38]))

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

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

chi := DirichletCharacter("250.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 250 = 2 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	250.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:	$1.99626005053$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$6$ over $\Q(\zeta_{25})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{25}]$

Embedding invariants

Embedding label			11.1
Character	$\chi$	$=$	250.11
Dual form			250.2.g.a.91.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.728969 + 0.684547i) q^{2} +(-1.16685 - 1.83867i) q^{3} +(0.0627905 - 0.998027i) q^{4} +(-2.20262 - 0.385324i) q^{5} +(2.10925 + 0.541564i) q^{6} +(-0.748412 + 2.30337i) q^{7} +(0.637424 + 0.770513i) q^{8} +(-0.741812 + 1.57643i) q^{9} +O(q^{10})$	\(q+(-0.728969 + 0.684547i) q^{2} +(-1.16685 - 1.83867i) q^{3} +(0.0627905 - 0.998027i) q^{4} +(-2.20262 - 0.385324i) q^{5} +(2.10925 + 0.541564i) q^{6} +(-0.748412 + 2.30337i) q^{7} +(0.637424 + 0.770513i) q^{8} +(-0.741812 + 1.57643i) q^{9} +(1.86941 - 1.22691i) q^{10} +(1.36747 - 1.28414i) q^{11} +(-1.90831 + 1.04910i) q^{12} +(-2.28731 + 4.86079i) q^{13} +(-1.03120 - 2.19141i) q^{14} +(1.86165 + 4.49950i) q^{15} +(-0.992115 - 0.125333i) q^{16} +(0.357109 + 5.67608i) q^{17} +(-0.538384 - 1.65697i) q^{18} +(-2.36094 + 3.72025i) q^{19} +(-0.522868 + 2.17408i) q^{20} +(5.10843 - 1.31162i) q^{21} +(-0.117789 + 1.87220i) q^{22} +(0.564019 - 2.95669i) q^{23} +(0.672937 - 2.07109i) q^{24} +(4.70305 + 1.69745i) q^{25} +(-1.66006 - 5.10914i) q^{26} +(-2.71737 + 0.343284i) q^{27} +(2.25184 + 0.891565i) q^{28} +(-7.02034 - 2.77955i) q^{29} +(-4.43720 - 2.00561i) q^{30} +(0.176682 + 2.80828i) q^{31} +(0.809017 - 0.587785i) q^{32} +(-3.95675 - 1.01592i) q^{33} +(-4.14587 - 3.89323i) q^{34} +(2.53601 - 4.78507i) q^{35} +(1.52674 + 0.839334i) q^{36} +(-7.34968 - 0.928480i) q^{37} +(-0.825633 - 4.32812i) q^{38} +(11.6063 - 1.46622i) q^{39} +(-1.10710 - 1.94276i) q^{40} +(-0.413845 - 2.16945i) q^{41} +(-2.82602 + 4.45309i) q^{42} +(1.74683 + 1.26915i) q^{43} +(-1.19574 - 1.44541i) q^{44} +(2.24137 - 3.18644i) q^{45} +(1.61284 + 2.54143i) q^{46} +(5.67779 - 6.86327i) q^{47} +(0.927207 + 1.97041i) q^{48} +(0.917704 + 0.666751i) q^{49} +(-4.59036 + 1.98208i) q^{50} +(10.0197 - 7.27976i) q^{51} +(4.70757 + 2.58801i) q^{52} +(-12.3820 + 3.17916i) q^{53} +(1.74589 - 2.11041i) q^{54} +(-3.50683 + 2.30155i) q^{55} +(-2.25184 + 0.891565i) q^{56} +9.59517 q^{57} +(7.02034 - 2.77955i) q^{58} +(8.84578 - 4.86301i) q^{59} +(4.60751 - 1.57545i) q^{60} +(-1.91400 + 10.0336i) q^{61} +(-2.05120 - 1.92620i) q^{62} +(-3.07593 - 2.88849i) q^{63} +(-0.187381 + 0.982287i) q^{64} +(6.91106 - 9.82510i) q^{65} +(3.57979 - 1.96801i) q^{66} +(2.26003 - 0.894809i) q^{67} +5.68730 q^{68} +(-6.09450 + 2.41298i) q^{69} +(1.42693 + 5.22419i) q^{70} +(-7.65261 + 9.25042i) q^{71} +(-1.68751 + 0.433279i) q^{72} +(-10.0616 - 5.53140i) q^{73} +(5.99327 - 4.35437i) q^{74} +(-2.36674 - 10.6280i) q^{75} +(3.56466 + 2.58988i) q^{76} +(1.93443 + 4.11087i) q^{77} +(-7.45696 + 9.01391i) q^{78} +(-1.92043 - 3.02611i) q^{79} +(2.13696 + 0.658347i) q^{80} +(7.13361 + 8.62306i) q^{81} +(1.78677 + 1.29816i) q^{82} +(1.51846 - 2.39272i) q^{83} +(-0.988272 - 5.18070i) q^{84} +(1.40056 - 12.6398i) q^{85} +(-2.14217 + 0.270620i) q^{86} +(3.08105 + 16.1514i) q^{87} +(1.86111 + 0.235113i) q^{88} +(1.04684 + 0.575507i) q^{89} +(0.547381 + 3.85713i) q^{90} +(-9.48436 - 8.90641i) q^{91} +(-2.91544 - 0.748559i) q^{92} +(4.95734 - 3.60172i) q^{93} +(0.559300 + 8.88982i) q^{94} +(6.63375 - 7.28455i) q^{95} +(-2.02475 - 0.801654i) q^{96} +(2.44253 + 0.967066i) q^{97} +(-1.12540 + 0.142171i) q^{98} +(1.00995 + 3.10832i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 5 q^{5} + 10 q^{7} + 10 q^{9}+O(q^{10}) $ 120 * q - 5 * q^5 + 10 * q^7 + 10 * q^9	$ 120 q - 5 q^{5} + 10 q^{7} + 10 q^{9} - 20 q^{10} + 20 q^{12} - 20 q^{14} - 10 q^{15} - 5 q^{17} + 25 q^{18} - 60 q^{19} + 5 q^{20} + 5 q^{21} - 10 q^{22} + 10 q^{23} - 5 q^{24} + 55 q^{25} + 5 q^{26} - 90 q^{27} - 5 q^{28} - 10 q^{29} - 10 q^{30} - 45 q^{31} + 30 q^{32} - 15 q^{33} - 10 q^{34} + 15 q^{35} + 10 q^{36} + 10 q^{37} + 10 q^{39} - 55 q^{41} - 5 q^{42} + 5 q^{43} - 40 q^{44} + 85 q^{45} - 20 q^{46} + 90 q^{47} - 5 q^{48} - 20 q^{49} - 30 q^{50} + 60 q^{51} + 5 q^{53} + 5 q^{54} - 15 q^{55} + 5 q^{56} - 120 q^{57} + 10 q^{58} - 75 q^{59} + 15 q^{60} - 85 q^{61} - 15 q^{62} - 45 q^{63} + 5 q^{65} - 15 q^{66} - 25 q^{67} - 70 q^{68} + 5 q^{69} - 65 q^{70} + 55 q^{71} + 5 q^{72} - 30 q^{73} - 70 q^{74} - 20 q^{75} - 5 q^{76} - 130 q^{77} + 60 q^{78} + 10 q^{79} + 5 q^{80} - 65 q^{81} + 80 q^{82} - 135 q^{83} + 20 q^{84} - 30 q^{85} + 10 q^{86} - 200 q^{87} - 80 q^{90} + 175 q^{91} - 5 q^{92} + 50 q^{93} + 35 q^{94} - 20 q^{95} - 15 q^{98} - 120 q^{99}+O(q^{100}) $ 120 * q - 5 * q^5 + 10 * q^7 + 10 * q^9 - 20 * q^10 + 20 * q^12 - 20 * q^14 - 10 * q^15 - 5 * q^17 + 25 * q^18 - 60 * q^19 + 5 * q^20 + 5 * q^21 - 10 * q^22 + 10 * q^23 - 5 * q^24 + 55 * q^25 + 5 * q^26 - 90 * q^27 - 5 * q^28 - 10 * q^29 - 10 * q^30 - 45 * q^31 + 30 * q^32 - 15 * q^33 - 10 * q^34 + 15 * q^35 + 10 * q^36 + 10 * q^37 + 10 * q^39 - 55 * q^41 - 5 * q^42 + 5 * q^43 - 40 * q^44 + 85 * q^45 - 20 * q^46 + 90 * q^47 - 5 * q^48 - 20 * q^49 - 30 * q^50 + 60 * q^51 + 5 * q^53 + 5 * q^54 - 15 * q^55 + 5 * q^56 - 120 * q^57 + 10 * q^58 - 75 * q^59 + 15 * q^60 - 85 * q^61 - 15 * q^62 - 45 * q^63 + 5 * q^65 - 15 * q^66 - 25 * q^67 - 70 * q^68 + 5 * q^69 - 65 * q^70 + 55 * q^71 + 5 * q^72 - 30 * q^73 - 70 * q^74 - 20 * q^75 - 5 * q^76 - 130 * q^77 + 60 * q^78 + 10 * q^79 + 5 * q^80 - 65 * q^81 + 80 * q^82 - 135 * q^83 + 20 * q^84 - 30 * q^85 + 10 * q^86 - 200 * q^87 - 80 * q^90 + 175 * q^91 - 5 * q^92 + 50 * q^93 + 35 * q^94 - 20 * q^95 - 15 * q^98 - 120 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/250\mathbb{Z}\right)^\times$.

$n$	$127$
$\chi(n)$	$e\left(\frac{19}{25}\right)$

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 $

$2$	−0.728969	+	0.684547i	−0.515459	+	0.484048i
$2$	−0.728969	+	0.684547i	−0.515459	+	0.484048i
$3$	−1.16685	−	1.83867i	−0.673683	−	1.06156i	−0.993473	−	0.114067i	$-0.963612\pi$
$3$	−1.16685	−	1.83867i	−0.673683	−	1.06156i	0.319790	−	0.947489i	$-0.396388\pi$
$4$	0.0627905	−	0.998027i	0.0313953	−	0.499013i
$5$	−2.20262	−	0.385324i	−0.985041	−	0.172322i
$5$	−2.20262	−	0.385324i	−0.985041	−	0.172322i
$6$	2.10925	+	0.541564i	0.861100	+	0.221093i
$7$	−0.748412	+	2.30337i	−0.282873	+	0.870594i	0.704155	+	0.710046i	$0.251326\pi$
$7$	−0.748412	+	2.30337i	−0.282873	+	0.870594i	−0.987028	+	0.160548i	$0.948674\pi$
$8$	0.637424	+	0.770513i	0.225363	+	0.272418i
$9$	−0.741812	+	1.57643i	−0.247271	+	0.525477i
$10$	1.86941	−	1.22691i	0.591160	−	0.387982i
$11$	1.36747	−	1.28414i	0.412308	−	0.387183i	−0.450448	−	0.892802i	$-0.648736\pi$
$11$	1.36747	−	1.28414i	0.412308	−	0.387183i	0.862757	+	0.505619i	$0.168736\pi$
$12$	−1.90831	+	1.04910i	−0.550881	+	0.302849i
$13$	−2.28731	+	4.86079i	−0.634387	+	1.34814i	0.286414	+	0.958106i	$0.407537\pi$
$13$	−2.28731	+	4.86079i	−0.634387	+	1.34814i	−0.920800	+	0.390034i	$0.872463\pi$
$14$	−1.03120	−	2.19141i	−0.275600	−	0.585679i
$15$	1.86165	+	4.49950i	0.480676	+	1.16177i
$16$	−0.992115	−	0.125333i	−0.248029	−	0.0313333i
$17$	0.357109	+	5.67608i	0.0866116	+	1.37665i	0.765985	+	0.642859i	$0.222252\pi$
$17$	0.357109	+	5.67608i	0.0866116	+	1.37665i	−0.679373	+	0.733793i	$0.737748\pi$
$18$	−0.538384	−	1.65697i	−0.126898	−	0.390553i
$19$	−2.36094	+	3.72025i	−0.541637	+	0.853483i	−0.999366	−	0.0356086i	$-0.988663\pi$
$19$	−2.36094	+	3.72025i	−0.541637	+	0.853483i	0.457729	+	0.889092i	$0.348663\pi$
$20$	−0.522868	+	2.17408i	−0.116917	+	0.486138i
$21$	5.10843	−	1.31162i	1.11475	−	0.286219i
$22$	−0.117789	+	1.87220i	−0.0251126	+	0.399154i
$23$	0.564019	−	2.95669i	0.117606	−	0.616513i	−0.873863	−	0.486172i	$-0.838393\pi$
$23$	0.564019	−	2.95669i	0.117606	−	0.616513i	0.991469	−	0.130341i	$-0.0416072\pi$
$24$	0.672937	−	2.07109i	0.137363	−	0.422759i
$25$	4.70305	+	1.69745i	0.940610	+	0.339489i
$26$	−1.66006	−	5.10914i	−0.325564	−	1.00198i
$27$	−2.71737	+	0.343284i	−0.522959	+	0.0660651i
$28$	2.25184	+	0.891565i	0.425557	+	0.168490i
$29$	−7.02034	−	2.77955i	−1.30365	−	0.516150i	−0.389310	−	0.921107i	$-0.627286\pi$
$29$	−7.02034	−	2.77955i	−1.30365	−	0.516150i	−0.914336	+	0.404957i	$0.867286\pi$
$30$	−4.43720	−	2.00561i	−0.810119	−	0.366172i
$31$	0.176682	+	2.80828i	0.0317331	+	0.504383i	0.981505	+	0.191439i	$0.0613153\pi$
$31$	0.176682	+	2.80828i	0.0317331	+	0.504383i	−0.949772	+	0.312944i	$0.898685\pi$
$32$	0.809017	−	0.587785i	0.143015	−	0.103907i
$33$	−3.95675	−	1.01592i	−0.688782	−	0.176849i
$34$	−4.14587	−	3.89323i	−0.711010	−	0.667683i
$35$	2.53601	−	4.78507i	0.428664	−	0.808825i
$36$	1.52674	+	0.839334i	0.254457	+	0.139889i
$37$	−7.34968	−	0.928480i	−1.20828	−	0.152641i	−0.504724	−	0.863281i	$-0.668406\pi$
$37$	−7.34968	−	0.928480i	−1.20828	−	0.152641i	−0.703556	+	0.710640i	$0.748406\pi$
$38$	−0.825633	−	4.32812i	−0.133935	−	0.702114i
$39$	11.6063	−	1.46622i	1.85850	−	0.234783i
$40$	−1.10710	−	1.94276i	−0.175048	−	0.307178i
$41$	−0.413845	−	2.16945i	−0.0646317	−	0.338811i	0.935253	−	0.353979i	$-0.115172\pi$
$41$	−0.413845	−	2.16945i	−0.0646317	−	0.338811i	−0.999885	+	0.0151681i	$0.995172\pi$
$42$	−2.82602	+	4.45309i	−0.436064	+	0.687127i
$43$	1.74683	+	1.26915i	0.266389	+	0.193543i	0.712959	−	0.701206i	$-0.247355\pi$
$43$	1.74683	+	1.26915i	0.266389	+	0.193543i	−0.446570	+	0.894749i	$0.647355\pi$
$44$	−1.19574	−	1.44541i	−0.180265	−	0.217903i
$45$	2.24137	−	3.18644i	0.334123	−	0.475006i
$46$	1.61284	+	2.54143i	0.237801	+	0.374714i
$47$	5.67779	−	6.86327i	0.828190	−	1.00111i	−0.171682	−	0.985152i	$-0.554920\pi$
$47$	5.67779	−	6.86327i	0.828190	−	1.00111i	0.999873	−	0.0159579i	$-0.00507977\pi$
$48$	0.927207	+	1.97041i	0.133831	+	0.284405i
$49$	0.917704	+	0.666751i	0.131101	+	0.0952501i
$50$	−4.59036	+	1.98208i	−0.649175	+	0.280308i
$51$	10.0197	−	7.27976i	1.40304	−	1.01937i
$52$	4.70757	+	2.58801i	0.652823	+	0.358893i
$53$	−12.3820	+	3.17916i	−1.70080	+	0.436691i	−0.969445	−	0.245307i	$-0.921111\pi$
$53$	−12.3820	+	3.17916i	−1.70080	+	0.436691i	−0.731354	+	0.681998i	$0.761111\pi$
$54$	1.74589	−	2.11041i	0.237585	−	0.287191i
$55$	−3.50683	+	2.30155i	−0.472861	+	0.310341i
$56$	−2.25184	+	0.891565i	−0.300914	+	0.119140i
$57$	9.59517			1.27091
$58$	7.02034	−	2.77955i	0.921816	−	0.364973i
$59$	8.84578	−	4.86301i	1.15162	−	0.633110i	0.212659	−	0.977126i	$-0.431788\pi$
$59$	8.84578	−	4.86301i	1.15162	−	0.633110i	0.938964	+	0.344017i	$0.111788\pi$
$60$	4.60751	−	1.57545i	0.594828	−	0.203390i
$61$	−1.91400	+	10.0336i	−0.245063	+	1.28467i	0.620635	+	0.784100i	$0.286875\pi$
$61$	−1.91400	+	10.0336i	−0.245063	+	1.28467i	−0.865698	+	0.500566i	$0.833125\pi$
$62$	−2.05120	−	1.92620i	−0.260502	−	0.244628i
$63$	−3.07593	−	2.88849i	−0.387531	−	0.363916i
$64$	−0.187381	+	0.982287i	−0.0234227	+	0.122786i
$65$	6.91106	−	9.82510i	0.857211	−	1.21865i
$66$	3.57979	−	1.96801i	0.440642	−	0.242245i
$67$	2.26003	−	0.894809i	0.276107	−	0.109318i	−0.225991	−	0.974129i	$-0.572562\pi$
$67$	2.26003	−	0.894809i	0.276107	−	0.109318i	0.502097	+	0.864811i	$0.332562\pi$
$68$	5.68730			0.689687
$69$	−6.09450	+	2.41298i	−0.733692	+	0.290489i
$70$	1.42693	+	5.22419i	0.170551	+	0.624410i
$71$	−7.65261	+	9.25042i	−0.908198	+	1.09782i	0.0866292	+	0.996241i	$0.472390\pi$
$71$	−7.65261	+	9.25042i	−0.908198	+	1.09782i	−0.994827	+	0.101582i	$0.967610\pi$
$72$	−1.68751	+	0.433279i	−0.198875	+	0.0510624i
$73$	−10.0616	−	5.53140i	−1.17762	−	0.647402i	−0.232012	−	0.972713i	$-0.574531\pi$
$73$	−10.0616	−	5.53140i	−1.17762	−	0.647402i	−0.945607	+	0.325311i	$0.894531\pi$
$74$	5.99327	−	4.35437i	0.696704	−	0.506185i
$75$	−2.36674	−	10.6280i	−0.273287	−	1.22722i
$76$	3.56466	+	2.58988i	0.408895	+	0.297079i
$77$	1.93443	+	4.11087i	0.220448	+	0.468477i
$78$	−7.45696	+	9.01391i	−0.844334	+	1.02062i
$79$	−1.92043	−	3.02611i	−0.216065	−	0.340464i	0.718956	−	0.695055i	$-0.244620\pi$
$79$	−1.92043	−	3.02611i	−0.216065	−	0.340464i	−0.935022	+	0.354591i	$0.884620\pi$
$80$	2.13696	+	0.658347i	0.238919	+	0.0736055i
$81$	7.13361	+	8.62306i	0.792624	+	0.958118i
$82$	1.78677	+	1.29816i	0.197316	+	0.143358i
$83$	1.51846	−	2.39272i	0.166673	−	0.262635i	−0.750717	−	0.660624i	$-0.770292\pi$
$83$	1.51846	−	2.39272i	0.166673	−	0.262635i	0.917390	+	0.397989i	$0.130292\pi$
$84$	−0.988272	−	5.18070i	−0.107829	−	0.565261i
$85$	1.40056	−	12.6398i	0.151912	−	1.37098i
$86$	−2.14217	+	0.270620i	−0.230997	+	0.0291817i
$87$	3.08105	+	16.1514i	0.330323	+	1.73161i
$88$	1.86111	+	0.235113i	0.198395	+	0.0250631i
$89$	1.04684	+	0.575507i	0.110965	+	0.0610036i	0.536270	−	0.844047i	$-0.319833\pi$
$89$	1.04684	+	0.575507i	0.110965	+	0.0610036i	−0.425305	+	0.905050i	$0.639833\pi$
$90$	0.547381	+	3.85713i	0.0576990	+	0.406578i
$91$	−9.48436	−	8.90641i	−0.994232	−	0.933646i
$92$	−2.91544	−	0.748559i	−0.303956	−	0.0780426i
$93$	4.95734	−	3.60172i	0.514052	−	0.373481i
$94$	0.559300	+	8.88982i	0.0576874	+	0.916915i
$95$	6.63375	−	7.28455i	0.680609	−	0.747379i
$96$	−2.02475	−	0.801654i	−0.206650	−	0.0818184i
$97$	2.44253	+	0.967066i	0.248001	+	0.0981907i	0.488837	−	0.872375i	$-0.337421\pi$
$97$	2.44253	+	0.967066i	0.248001	+	0.0981907i	−0.240835	+	0.970566i	$0.577421\pi$
$98$	−1.12540	+	0.142171i	−0.113683	+	0.0143614i
$99$	1.00995	+	3.10832i	0.101504	+	0.312398i
$100$	1.98940	−	4.58719i	0.198940	−	0.458719i
$101$	−1.84938	+	5.69180i	−0.184020	+	0.566355i	−0.999930	−	0.0118236i	$-0.996236\pi$
$101$	−1.84938	+	5.69180i	−0.184020	+	0.566355i	0.815910	+	0.578179i	$0.196236\pi$
$102$	−2.32073	+	12.1657i	−0.229787	+	1.20458i
$103$	−0.0870514	+	1.38364i	−0.00857743	+	0.136334i	0.991407	+	0.130811i	$0.0417581\pi$
$103$	−0.0870514	+	1.38364i	−0.00857743	+	0.136334i	−0.999985	+	0.00552327i	$0.998242\pi$
$104$	−5.20329	+	1.33598i	−0.510225	+	0.131003i
$105$	−11.7573	+	0.920598i	−1.14740	+	0.0898412i
$106$	6.84981	−	10.7936i	0.665312	−	1.04836i
$107$	−2.42848	−	7.47409i	−0.234770	−	0.722547i	−0.997152	−	0.0754200i	$-0.975970\pi$
$107$	−2.42848	−	7.47409i	−0.234770	−	0.722547i	0.762382	−	0.647127i	$-0.224030\pi$
$108$	0.171982	+	2.73357i	0.0165489	+	0.263038i
$109$	−6.67497	−	0.843244i	−0.639346	−	0.0807682i	−0.201024	−	0.979586i	$-0.564427\pi$
$109$	−6.67497	−	0.843244i	−0.639346	−	0.0807682i	−0.438322	+	0.898818i	$0.644427\pi$
$110$	0.980847	−	4.07835i	0.0935201	−	0.388855i
$111$	6.86883	+	14.5970i	0.651961	+	1.38549i
$112$	1.03120	−	2.19141i	0.0974392	−	0.207069i
$113$	−13.2372	+	7.27721i	−1.24525	+	0.684582i	−0.961629	−	0.274354i	$-0.911536\pi$
$113$	−13.2372	+	7.27721i	−1.24525	+	0.684582i	−0.283622	+	0.958936i	$0.591536\pi$
$114$	−6.99458	+	6.56835i	−0.655102	+	0.615182i
$115$	−2.38160	+	6.29513i	−0.222086	+	0.587024i
$116$	−3.21488	+	6.83196i	−0.298494	+	0.634332i
$117$	−5.96594	−	7.21159i	−0.551552	−	0.666711i
$118$	−3.11934	+	9.60033i	−0.287158	+	0.883782i
$119$	−13.3414	−	3.42549i	−1.22300	−	0.314014i
$120$	−2.28026	+	4.30251i	−0.208159	+	0.392764i
$121$	−0.469736	+	7.46624i	−0.0427033	+	0.678749i
$122$	−5.47320	−	8.62438i	−0.495520	−	0.780814i
$123$	−3.50600	+	3.29235i	−0.316125	+	0.296862i
$124$	2.81384			0.252690
$125$	−9.70495	−	5.55102i	−0.868038	−	0.496499i
$126$	4.21957			0.375909
$127$	8.69664	−	8.16669i	0.771702	−	0.724676i	−0.194938	−	0.980816i	$-0.562451\pi$
$127$	8.69664	−	8.16669i	0.771702	−	0.724676i	0.966640	+	0.256139i	$0.0824505\pi$
$128$	−0.535827	−	0.844328i	−0.0473608	−	0.0746288i
$129$	0.295243	−	4.69275i	0.0259947	−	0.413173i
$130$	1.68780	+	11.8931i	0.148030	+	1.04310i
$131$	−2.94334	−	0.755721i	−0.257161	−	0.0660277i	0.117908	−	0.993024i	$-0.462381\pi$
$131$	−2.94334	−	0.755721i	−0.257161	−	0.0660277i	−0.375069	+	0.926997i	$0.622381\pi$
$132$	−1.26236	+	3.88515i	−0.109875	+	0.338159i
$133$	−6.80217	−	8.22241i	−0.589823	−	0.712973i
$134$	−1.03495	+	2.19939i	−0.0894063	+	0.189998i
$135$	6.11761	+	0.290947i	0.526520	+	0.0250407i
$136$	−4.14587	+	3.89323i	−0.355505	+	0.333842i
$137$	5.26310	−	2.89341i	0.449657	−	0.247201i	−0.240800	−	0.970575i	$-0.577410\pi$
$137$	5.26310	−	2.89341i	0.449657	−	0.247201i	0.690457	+	0.723374i	$0.257410\pi$
$138$	2.79090	−	5.93096i	0.237577	−	0.504877i
$139$	7.33322	+	15.5839i	0.621996	+	1.32181i	0.928993	+	0.370098i	$0.120676\pi$
$139$	7.33322	+	15.5839i	0.621996	+	1.32181i	−0.306997	+	0.951711i	$0.599324\pi$
$140$	−4.61639	−	2.83146i	−0.390156	−	0.239302i
$141$	−19.2444	−	2.43113i	−1.62067	−	0.204738i
$142$	−0.753833	−	11.9818i	−0.0632603	−	1.00549i
$143$	3.11410	+	9.58423i	0.260414	+	0.801473i
$144$	0.933542	−	1.47103i	0.0777952	−	0.122586i
$145$	14.3921	+	8.82740i	1.19520	+	0.733076i
$146$	11.1211	−	2.85541i	0.920387	−	0.236315i
$147$	0.155107	−	2.46535i	0.0127930	−	0.203339i
$148$	−1.38814	+	7.27688i	−0.114104	+	0.598156i
$149$	4.33356	−	13.3373i	0.355019	−	1.09264i	−0.600980	−	0.799264i	$-0.705223\pi$
$149$	4.33356	−	13.3373i	0.355019	−	1.09264i	0.955999	−	0.293371i	$-0.0947773\pi$
$150$	9.00065	+	6.12735i	0.734900	+	0.500296i
$151$	−3.41216	−	10.5016i	−0.277678	−	0.854605i	−0.988498	−	0.151231i	$-0.951676\pi$
$151$	−3.41216	−	10.5016i	−0.277678	−	0.854605i	0.710820	−	0.703374i	$-0.248324\pi$
$152$	−4.37142	+	0.552239i	−0.354569	+	0.0447925i
$153$	−9.21286	−	3.64763i	−0.744816	−	0.294893i
$154$	−4.22422	−	1.67249i	−0.340397	−	0.134773i
$155$	0.692937	−	6.25366i	0.0556580	−	0.502306i
$156$	−0.734560	−	11.6755i	−0.0588119	−	0.934788i
$157$	13.5266	−	9.82765i	1.07954	−	0.784332i	0.101938	−	0.994791i	$-0.467496\pi$
$157$	13.5266	−	9.82765i	1.07954	−	0.784332i	0.977603	+	0.210459i	$0.0674958\pi$
$158$	3.47145	+	0.891317i	0.276174	+	0.0709094i
$159$	20.2934	+	19.0568i	1.60937	+	1.51130i
$160$	−2.00844	+	0.982932i	−0.158781	+	0.0777076i
$161$	6.38825	+	3.51197i	0.503465	+	0.276782i
$162$	−11.1031	−	1.40264i	−0.872340	−	0.110202i
$163$	0.448882	+	2.35312i	0.0351592	+	0.184311i	0.995534	−	0.0943994i	$-0.0300931\pi$
$163$	0.448882	+	2.35312i	0.0351592	+	0.184311i	−0.960375	+	0.278710i	$0.910093\pi$
$164$	−2.19115	+	0.276807i	−0.171100	+	0.0216150i
$165$	8.32375	+	3.76232i	0.648003	+	0.292896i
$166$	0.531015	+	2.78368i	0.0412147	+	0.216055i
$167$	−13.3243	+	20.9957i	−1.03106	+	1.62469i	−0.285353	+	0.958422i	$0.592111\pi$
$167$	−13.3243	+	20.9957i	−1.03106	+	1.62469i	−0.745709	+	0.666272i	$0.767889\pi$
$168$	4.26686	+	3.10005i	0.329195	+	0.239174i
$169$	−10.1089	−	12.2196i	−0.777611	−	0.939971i
$170$	7.63160	+	10.1728i	0.585317	+	0.780218i
$171$	−4.11334	−	6.48159i	−0.314555	−	0.495659i
$172$	1.37633	−	1.66369i	0.104944	−	0.126855i
$173$	9.87509	+	20.9856i	0.750789	+	1.59551i	0.802361	+	0.596839i	$0.203577\pi$
$173$	9.87509	+	20.9856i	0.750789	+	1.59551i	−0.0515720	+	0.998669i	$0.516423\pi$
$174$	−13.3024	−	9.66475i	−1.00845	−	0.732683i
$175$	−7.42967	+	9.56250i	−0.561630	+	0.722857i
$176$	−1.51763	+	1.10263i	−0.114396	+	0.0831136i
$177$	−19.2632	−	10.5900i	−1.44791	−	0.795995i
$178$	−1.15708	+	0.297087i	−0.0867266	+	0.0222676i
$179$	4.58951	−	5.54776i	0.343036	−	0.414659i	−0.570577	−	0.821244i	$-0.693280\pi$
$179$	4.58951	−	5.54776i	0.343036	−	0.414659i	0.913613	+	0.406585i	$0.133280\pi$
$180$	−3.03941	−	2.43702i	−0.226544	−	0.181645i
$181$	0.808260	−	0.320013i	0.0600775	−	0.0237864i	−0.337894	−	0.941184i	$-0.609714\pi$
$181$	0.808260	−	0.320013i	0.0600775	−	0.0237864i	0.397971	+	0.917398i	$0.369714\pi$
$182$	13.0107			0.964414
$183$	20.6817	−	8.18848i	1.52884	−	0.605310i
$184$	2.63769	−	1.45008i	0.194453	−	0.106901i
$185$	15.8308	+	4.87710i	1.16390	+	0.358571i
$186$	−1.14820	+	6.01907i	−0.0841900	+	0.441340i
$187$	7.77723	+	7.30331i	0.568727	+	0.534071i
$188$	−6.49321	−	6.09753i	−0.473566	−	0.444708i
$189$	1.24300	−	6.51605i	0.0904152	−	0.473973i
$190$	0.150823	+	9.85133i	0.0109419	+	0.714690i
$191$	−11.2945	+	6.20922i	−0.817243	+	0.449283i	−0.834794	−	0.550563i	$-0.814413\pi$
$191$	−11.2945	+	6.20922i	−0.817243	+	0.449283i	0.0175508	+	0.999846i	$0.494413\pi$
$192$	2.02475	−	0.801654i	0.146123	−	0.0578544i
$193$	23.4831			1.69035			0.845174	−	0.534491i	$-0.179497\pi$
$193$	23.4831			1.69035			0.845174	+	0.534491i	$0.179497\pi$
$194$	−2.44253	+	0.967066i	−0.175363	+	0.0694313i
$195$	−26.1293	−	1.24268i	−1.87116	−	0.0889902i
$196$	0.723058	−	0.874027i	0.0516470	−	0.0624305i
$197$	19.7021	−	5.05863i	1.40371	−	0.360412i	0.530473	−	0.847702i	$-0.322014\pi$
$197$	19.7021	−	5.05863i	1.40371	−	0.360412i	0.873240	+	0.487290i	$0.162014\pi$
$198$	−2.86402	−	1.57451i	−0.203537	−	0.111895i
$199$	−14.4228	+	10.4788i	−1.02241	+	0.742821i	−0.966775	−	0.255630i	$-0.917717\pi$
$199$	−14.4228	+	10.4788i	−1.02241	+	0.742821i	−0.0556312	+	0.998451i	$0.517717\pi$
$200$	1.68993	+	4.70575i	0.119496	+	0.332747i
$201$	−4.28238	−	3.11133i	−0.302056	−	0.219457i
$202$	−2.54817	−	5.41513i	−0.179288	−	0.381007i
$203$	11.6565	−	14.0902i	0.818123	−	0.988941i
$204$	−6.63625	−	10.4571i	−0.464631	−	0.732141i
$205$	0.0755996	+	4.93793i	0.00528010	+	0.344880i
$206$	−0.883711	−	1.06822i	−0.0615710	−	0.0744266i
$207$	4.24263	+	3.08245i	0.294883	+	0.214245i
$208$	2.87850	−	4.53578i	0.199588	−	0.314500i
$209$	1.54880	+	8.11912i	0.107133	+	0.561611i
$210$	7.94052	−	8.71952i	0.547948	−	0.601704i
$211$	11.6526	−	1.47206i	0.802197	−	0.101341i	0.286465	−	0.958091i	$-0.407520\pi$
$211$	11.6526	−	1.47206i	0.802197	−	0.101341i	0.515733	+	0.856750i	$0.327520\pi$
$212$	2.39541	+	12.5572i	0.164518	+	0.862432i
$213$	25.9379	+	3.27672i	1.77724	+	0.224517i
$214$	6.88665	+	3.78597i	0.470762	+	0.258803i
$215$	−3.35857	−	3.46854i	−0.229052	−	0.236553i
$216$	−1.99662	−	1.87496i	−0.135853	−	0.127575i
$217$	−6.60076	−	1.69479i	−0.448089	−	0.115050i
$218$	5.44308	−	3.95463i	0.368652	−	0.267841i
$219$	1.56999	+	24.9542i	0.106090	+	1.68625i
$220$	2.07682	+	3.64443i	0.140019	+	0.245707i
$221$	−28.4071	−	11.2471i	−1.91087	−	0.756565i
$222$	−14.9995	−	5.93873i	−1.00670	−	0.398581i
$223$	−3.13815	+	0.396441i	−0.210146	+	0.0265477i	−0.229702	−	0.973261i	$-0.573775\pi$
$223$	−3.13815	+	0.396441i	−0.210146	+	0.0265477i	0.0195552	+	0.999809i	$0.493775\pi$
$224$	0.748412	+	2.30337i	0.0500054	+	0.153901i
$225$	−6.16469	+	6.15485i	−0.410979	+	0.410323i
$226$	4.66791	−	14.3663i	0.310504	−	0.955635i
$227$	3.75316	−	19.6747i	0.249106	−	1.30586i	−0.609322	−	0.792923i	$-0.708558\pi$
$227$	3.75316	−	19.6747i	0.249106	−	1.30586i	0.858427	−	0.512935i	$-0.171442\pi$
$228$	0.602486	−	9.57624i	0.0399006	−	0.634202i
$229$	6.55969	−	1.68424i	0.433477	−	0.111298i	−0.0256453	−	0.999671i	$-0.508164\pi$
$229$	6.55969	−	1.68424i	0.433477	−	0.111298i	0.459122	+	0.888373i	$0.348164\pi$
$230$	−2.57320	−	6.21927i	−0.169672	−	0.410087i
$231$	5.30132	−	8.35355i	0.348802	−	0.549623i
$232$	−2.33325	−	7.18102i	−0.153186	−	0.471457i
$233$	−0.195349	−	3.10499i	−0.0127977	−	0.203414i	−0.999230	−	0.0392436i	$-0.987505\pi$
$233$	−0.195349	−	3.10499i	−0.0127977	−	0.203414i	0.986432	−	0.164171i	$-0.0524948\pi$
$234$	9.28565	+	1.17305i	0.607022	+	0.0766847i
$235$	−15.1506	+	12.9294i	−0.988315	+	0.843419i
$236$	−4.29798	−	9.13368i	−0.279775	−	0.594552i
$237$	−3.32316	+	7.06207i	−0.215862	+	0.458730i
$238$	12.0704	−	6.63575i	0.782406	−	0.430132i
$239$	8.81317	−	8.27612i	0.570076	−	0.535337i	−0.345008	−	0.938600i	$-0.612124\pi$
$239$	8.81317	−	8.27612i	0.570076	−	0.535337i	0.915084	+	0.403262i	$0.132124\pi$
$240$	−1.28303	−	4.69735i	−0.0828194	−	0.303212i
$241$	4.77024	−	10.1373i	0.307278	−	0.652999i	−0.690227	−	0.723593i	$-0.742489\pi$
$241$	4.77024	−	10.1373i	0.307278	−	0.652999i	0.997505	+	0.0705940i	$0.0224895\pi$
$242$	−4.76857	−	5.76421i	−0.306535	−	0.370537i
$243$	4.99188	−	15.3634i	0.320230	−	0.985565i
$244$	9.89358	+	2.54024i	0.633372	+	0.162622i
$245$	−1.76444	−	1.82221i	−0.112726	−	0.116417i
$246$	0.301993	−	4.80005i	0.0192544	−	0.306040i
$247$	−12.6831	−	19.9854i	−0.807008	−	1.27164i
$248$	−2.05120	+	1.92620i	−0.130251	+	0.122314i
$249$	−6.17124			−0.391086
$250$	10.8745	−	2.59698i	0.687767	−	0.164247i
$251$	−23.1068			−1.45849			−0.729243	−	0.684255i	$-0.760127\pi$
$251$	−23.1068			−1.45849			−0.729243	+	0.684255i	$0.760127\pi$
$252$	−3.07593	+	2.88849i	−0.193765	+	0.181958i
$253$	−3.02553	−	4.76748i	−0.190214	−	0.299729i
$254$	−0.749095	+	11.9065i	−0.0470024	+	0.747081i
$255$	−24.8747	+	12.1737i	−1.55772	+	0.762346i
$256$	0.968583	+	0.248690i	0.0605364	+	0.0155431i
$257$	−5.23443	+	16.1099i	−0.326515	+	1.00491i	0.644238	+	0.764825i	$0.277175\pi$
$257$	−5.23443	+	16.1099i	−0.326515	+	1.00491i	−0.970752	+	0.240083i	$0.922825\pi$
$258$	2.99718	+	3.62297i	0.186597	+	0.225556i
$259$	7.63923	−	16.2342i	0.474678	−	1.00874i
$260$	−9.37176	−	7.51434i	−0.581212	−	0.466020i
$261$	9.58955	−	9.00519i	0.593578	−	0.557407i
$262$	2.66293	−	1.46396i	0.164516	−	0.0904436i
$263$	6.08376	−	12.9286i	0.375141	−	0.797214i	−0.624725	−	0.780845i	$-0.714789\pi$
$263$	6.08376	−	12.9286i	0.375141	−	0.797214i	0.999866	−	0.0163698i	$-0.00521091\pi$
$264$	−1.73935	−	3.69630i	−0.107049	−	0.227492i
$265$	28.4978	−	2.23138i	1.75061	−	0.137073i
$266$	10.5872	+	1.33747i	0.649142	+	0.0820058i
$267$	−0.163347	−	2.59633i	−0.00999668	−	0.158893i
$268$	−0.751135	−	2.31176i	−0.0458829	−	0.141213i
$269$	1.50391	−	2.36979i	0.0916952	−	0.144489i	−0.795384	−	0.606106i	$-0.792731\pi$
$269$	1.50391	−	2.36979i	0.0916952	−	0.144489i	0.887079	+	0.461617i	$0.152731\pi$
$270$	−4.65872	+	3.97570i	−0.283520	+	0.241954i
$271$	27.3850	−	7.03128i	1.66352	−	0.427120i	0.704329	−	0.709874i	$-0.251248\pi$
$271$	27.3850	−	7.03128i	1.66352	−	0.427120i	0.959192	+	0.282754i	$0.0912481\pi$
$272$	0.357109	−	5.67608i	0.0216529	−	0.344163i
$273$	−5.30906	+	27.8311i	−0.321319	+	1.68441i
$274$	−1.85596	+	5.71205i	−0.112122	+	0.345077i
$275$	8.61105	−	3.71817i	0.519266	−	0.224214i
$276$	2.02555	+	6.23399i	0.121924	+	0.375242i
$277$	14.9933	−	1.89410i	0.900861	−	0.113805i	0.338759	−	0.940873i	$-0.389993\pi$
$277$	14.9933	−	1.89410i	0.900861	−	0.113805i	0.562102	+	0.827068i	$0.309993\pi$
$278$	−16.0136	−	6.34023i	−0.960432	−	0.380262i
$279$	−4.55813	−	1.80469i	−0.272888	−	0.108044i
$280$	5.30348	−	1.09609i	0.316943	−	0.0655039i
$281$	1.00048	+	15.9022i	0.0596836	+	0.948644i	0.907951	+	0.419076i	$0.137646\pi$
$281$	1.00048	+	15.9022i	0.0596836	+	0.948644i	−0.848268	+	0.529568i	$0.822354\pi$
$282$	15.6928	−	11.4015i	0.934493	−	0.678949i
$283$	−26.5903	−	6.82723i	−1.58063	−	0.405837i	−0.646542	−	0.762879i	$-0.723785\pi$
$283$	−26.5903	−	6.82723i	−1.58063	−	0.405837i	−0.934088	+	0.357042i	$0.883785\pi$
$284$	8.75165	+	8.21835i	0.519315	+	0.487669i
$285$	−21.1345	−	3.69725i	−1.25190	−	0.219006i
$286$	−8.83094	−	4.85485i	−0.522184	−	0.287073i
$287$	5.30678	+	0.670403i	0.313249	+	0.0395726i
$288$	0.326464	+	1.71139i	0.0192371	+	0.100844i
$289$	−15.2244	+	1.92329i	−0.895555	+	0.113135i
$290$	−16.5342	+	3.41718i	−0.970919	+	0.200664i
$291$	−1.07196	−	5.61943i	−0.0628396	−	0.329417i
$292$	−6.15226	+	9.69441i	−0.360034	+	0.567322i
$293$	22.9014	+	16.6388i	1.33791	+	0.972049i	0.999518	+	0.0310447i	$0.00988342\pi$
$293$	22.9014	+	16.6388i	1.33791	+	0.972049i	0.338393	+	0.941005i	$0.390117\pi$
$294$	1.57458	+	1.90334i	0.0918315	+	0.111005i
$295$	−21.3577	+	7.30285i	−1.24349	+	0.425189i
$296$	−3.96946	−	6.25486i	−0.230720	−	0.363556i
$297$	−3.27511	+	3.95893i	−0.190041	+	0.229720i
$298$	5.97100	+	12.6890i	0.345890	+	0.735055i
$299$	13.0818	+	9.50446i	0.756538	+	0.549657i
$300$	−10.7557	+	1.69473i	−0.620978	+	0.0978451i
$301$	−4.23067	+	3.07376i	−0.243852	+	0.177169i
$302$	9.67618	+	5.31952i	0.556801	+	0.306104i
$303$	12.6233	−	3.24111i	0.725188	−	0.186197i
$304$	2.80859	−	3.39501i	0.161084	−	0.194717i
$305$	8.08200	−	21.3626i	0.462774	−	1.22322i
$306$	9.21286	−	3.64763i	0.526664	−	0.208521i
$307$	−10.8109			−0.617013			−0.308506	−	0.951222i	$-0.599829\pi$
$307$	−10.8109			−0.617013			−0.308506	+	0.951222i	$0.599829\pi$
$308$	4.22422	−	1.67249i	0.240697	−	0.0952988i
$309$	2.64563	−	1.45445i	0.150505	−	0.0827408i
$310$	3.77579	+	5.03307i	0.214451	+	0.285859i
$311$	−3.53930	+	18.5537i	−0.200696	+	1.05208i	0.729211	+	0.684288i	$0.239887\pi$
$311$	−3.53930	+	18.5537i	−0.200696	+	1.05208i	−0.929907	+	0.367795i	$0.880113\pi$
$312$	8.52790	+	8.00823i	0.482797	+	0.453377i
$313$	−6.46206	−	6.06828i	−0.365257	−	0.342999i	0.480087	−	0.877221i	$-0.340605\pi$
$313$	−6.46206	−	6.06828i	−0.365257	−	0.342999i	−0.845345	+	0.534221i	$0.820605\pi$
$314$	−3.13298	+	16.4236i	−0.176804	+	0.926840i
$315$	5.66209	+	7.54748i	0.319023	+	0.425252i
$316$	−3.14073	+	1.72663i	−0.176680	+	0.0971305i
$317$	−31.3700	+	12.4203i	−1.76191	+	0.697591i	−0.763240	+	0.646115i	$0.776393\pi$
$317$	−31.3700	+	12.4203i	−1.76191	+	0.697591i	−0.998674	+	0.0514758i	$0.983607\pi$
$318$	−27.8385			−1.56111
$319$	−13.1695	+	5.21416i	−0.737348	+	0.291937i
$320$	0.791229	−	2.09140i	0.0442310	−	0.116913i
$321$	−10.9087	+	13.1863i	−0.608863	+	0.735989i
$322$	−7.06094	+	1.81294i	−0.393491	+	0.101031i
$323$	−21.9595	−	12.0724i	−1.22186	−	0.671724i
$324$	9.05397	−	6.57809i	0.502998	−	0.365449i
$325$	−19.0083	+	18.9779i	−1.05439	+	1.05271i
$326$	−1.93804	−	1.40807i	−0.107338	−	0.0779859i
$327$	6.23826	+	13.2570i	0.344977	+	0.733113i
$328$	1.40780	−	1.70173i	0.0777325	−	0.0939625i
$329$	11.5594	+	18.2146i	0.637288	+	1.00420i
$330$	−8.64324	+	2.95539i	−0.475794	+	0.162689i
$331$	16.2725	+	19.6701i	0.894418	+	1.08117i	0.996264	+	0.0863651i	$0.0275251\pi$
$331$	16.2725	+	19.6701i	0.894418	+	1.08117i	−0.101846	+	0.994800i	$0.532475\pi$
$332$	−2.29265	−	1.66571i	−0.125826	−	0.0914176i
$333$	6.91577	−	10.8975i	0.378982	−	0.597180i
$334$	−4.65956	−	24.4263i	−0.254960	−	1.33655i
$335$	−5.32278	+	1.10008i	−0.290814	+	0.0601037i
$336$	−5.23254	+	0.661023i	−0.285458	+	0.0360618i
$337$	0.801340	+	4.20077i	0.0436518	+	0.228831i	0.997427	−	0.0716905i	$-0.0228394\pi$
$337$	0.801340	+	4.20077i	0.0436518	+	0.228831i	−0.953775	+	0.300521i	$0.902839\pi$
$338$	15.7340	+	1.98767i	0.855817	+	0.108115i
$339$	28.8262	+	15.8474i	1.56563	+	0.860710i
$340$	−12.5270	−	2.19146i	−0.679370	−	0.118848i
$341$	3.84784	+	3.61336i	0.208372	+	0.195675i
$342$	7.43545	+	1.90910i	0.402063	+	0.103232i
$343$	−15.9382	+	11.5798i	−0.860580	+	0.625248i
$344$	0.135577	+	2.15494i	0.00730984	+	0.116187i
$345$	14.3536	−	2.96652i	0.772774	−	0.159712i
$346$	−21.5643	−	8.53790i	−1.15930	−	0.459001i
$347$	20.1969	+	7.99653i	1.08423	+	0.429276i	0.841190	−	0.540740i	$-0.181856\pi$
$347$	20.1969	+	7.99653i	1.08423	+	0.429276i	0.243039	+	0.970017i	$0.421856\pi$
$348$	16.3130	−	2.06081i	0.874468	−	0.110471i
$349$	−3.39333	−	10.4436i	−0.181641	−	0.559033i	0.818233	−	0.574886i	$-0.194954\pi$
$349$	−3.39333	−	10.4436i	−0.181641	−	0.559033i	−0.999874	+	0.0158529i	$0.994954\pi$
$350$	−1.12998	−	12.0567i	−0.0604002	−	0.644459i
$351$	4.54686	−	13.9938i	0.242693	−	0.746933i
$352$	0.351509	−	1.84267i	0.0187355	−	0.0982148i
$353$	0.0220916	−	0.351137i	0.00117582	−	0.0186891i	−0.997395	−	0.0721323i	$-0.977020\pi$
$353$	0.0220916	−	0.351137i	0.00117582	−	0.0186891i	0.998571	+	0.0534432i	$0.0170196\pi$
$354$	21.2916	−	5.46676i	1.13164	−	0.290555i
$355$	20.4202	−	17.4264i	1.08379	−	0.924897i
$356$	0.640103	−	1.00864i	0.0339254	−	0.0534578i
$357$	9.26913	+	28.5275i	0.490575	+	1.50983i
$358$	0.452097	+	7.18588i	0.0238941	+	0.379785i
$359$	5.00753	+	0.632598i	0.264287	+	0.0333873i	0.256360	−	0.966581i	$-0.417477\pi$
$359$	5.00753	+	0.632598i	0.264287	+	0.0333873i	0.00792717	+	0.999969i	$0.497477\pi$
$360$	3.88389	−	0.304109i	0.204699	−	0.0160280i
$361$	−0.176391	−	0.374850i	−0.00928375	−	0.0197290i
$362$	−0.370132	+	0.786571i	−0.0194537	+	0.0413413i
$363$	14.2760	−	7.84832i	0.749298	−	0.411930i
$364$	−9.48436	+	8.90641i	−0.497116	+	0.466823i
$365$	20.0304	+	16.0605i	1.04844	+	0.840647i
$366$	−9.47094	+	20.1268i	−0.495054	+	1.05204i
$367$	−19.5539	−	23.6366i	−1.02070	−	1.23382i	−0.971994	−	0.235007i	$-0.924489\pi$
$367$	−19.5539	−	23.6366i	−1.02070	−	1.23382i	−0.0487114	−	0.998813i	$-0.515511\pi$
$368$	−0.930144	+	2.86269i	−0.0484871	+	0.149228i
$369$	3.72698	+	0.956927i	0.194019	+	0.0498156i
$370$	−14.8787	+	7.28165i	−0.773509	+	0.378555i
$371$	1.94405	−	30.8997i	0.100930	−	1.60423i
$372$	−3.28334	−	5.17371i	−0.170233	−	0.268244i
$373$	4.43983	−	4.16928i	0.229886	−	0.215877i	−0.561041	−	0.827788i	$-0.689599\pi$
$373$	4.43983	−	4.16928i	0.229886	−	0.215877i	0.790927	+	0.611911i	$0.209599\pi$
$374$	−10.6688			−0.551671
$375$	1.11778	+	24.3214i	0.0577218	+	1.25595i
$376$	8.90740			0.459364
$377$	29.5685	−	27.7667i	1.52286	−	1.43006i
$378$	3.55443	+	5.60089i	0.182820	+	0.288079i
$379$	−0.281316	+	4.47139i	−0.0144502	+	0.229680i	0.984172	+	0.177213i	$0.0567082\pi$
$379$	−0.281316	+	4.47139i	−0.0144502	+	0.229680i	−0.998623	+	0.0524664i	$0.983292\pi$
$380$	−6.85364	−	7.07806i	−0.351584	−	0.363097i
$381$	−25.1635	−	6.46090i	−1.28917	−	0.331002i
$382$	3.98285	−	12.2580i	0.203780	−	0.627172i
$383$	−10.8144	−	13.0724i	−0.552592	−	0.667969i	0.418071	−	0.908414i	$-0.362706\pi$
$383$	−10.8144	−	13.0724i	−0.552592	−	0.667969i	−0.970663	+	0.240446i	$0.922706\pi$
$384$	−0.927207	+	1.97041i	−0.0473163	+	0.100552i
$385$	−2.67679	−	9.80005i	−0.136422	−	0.499457i
$386$	−17.1184	+	16.0753i	−0.871305	+	0.818210i
$387$	−3.29654	+	1.81229i	−0.167573	+	0.0921239i
$388$	1.11853	−	2.37699i	0.0567845	−	0.120673i
$389$	7.39956	+	15.7249i	0.375173	+	0.797283i	0.999865	+	0.0164119i	$0.00522430\pi$
$389$	7.39956	+	15.7249i	0.375173	+	0.797283i	−0.624693	+	0.780871i	$0.714776\pi$
$390$	19.8981	−	16.9809i	1.00758	−	0.859859i
$391$	16.9838	+	2.14556i	0.858910	+	0.108506i
$392$	0.0712261	+	1.13211i	0.00359746	+	0.0571800i
$393$	2.04493	+	6.29364i	0.103153	+	0.317472i
$394$	−10.8993	+	17.1746i	−0.549099	+	0.865242i
$395$	3.06394	+	7.40536i	0.154163	+	0.372604i
$396$	3.16560	−	0.812788i	0.159077	−	0.0408441i
$397$	0.352713	−	5.60621i	0.0177021	−	0.281367i	−0.979210	−	0.202847i	$-0.934980\pi$
$397$	0.352713	−	5.60621i	0.0177021	−	0.281367i	0.996913	−	0.0785202i	$-0.0250195\pi$
$398$	3.34055	−	17.5118i	0.167447	−	0.877787i
$399$	−7.18114	+	22.1013i	−0.359507	+	1.10645i
$400$	−4.45322	−	2.27351i	−0.222661	−	0.113675i
$401$	−5.20971	−	16.0338i	−0.260161	−	0.800692i	−0.992769	−	0.120041i	$-0.961697\pi$
$401$	−5.20971	−	16.0338i	−0.260161	−	0.800692i	0.732608	−	0.680650i	$-0.238303\pi$
$402$	5.25158	−	0.663428i	0.261925	−	0.0330888i
$403$	−14.0546	−	5.56461i	−0.700110	−	0.277193i
$404$	5.56444	+	2.20312i	0.276841	+	0.109609i
$405$	−12.3899	−	21.7421i	−0.615662	−	1.08037i
$406$	1.14824	+	18.2507i	0.0569861	+	0.905769i
$407$	−11.2428	+	8.16836i	−0.557284	+	0.404891i
$408$	11.9960	+	3.08004i	0.593889	+	0.152485i
$409$	−9.11719	−	8.56161i	−0.450816	−	0.423344i	0.425591	−	0.904916i	$-0.360066\pi$
$409$	−9.11719	−	8.56161i	−0.450816	−	0.423344i	−0.876407	+	0.481571i	$0.840066\pi$
$410$	−3.43536	−	3.54785i	−0.169660	−	0.175216i
$411$	−11.4613	−	6.30090i	−0.565344	−	0.310800i
$412$	1.37545	+	0.173759i	0.0677634	+	0.00856050i
$413$	4.58105	+	24.0147i	0.225419	+	1.18169i
$414$	−5.20282	+	0.657269i	−0.255705	+	0.0323030i
$415$	−4.26657	+	4.68514i	−0.209438	+	0.229985i
$416$	1.00662	+	5.27691i	0.0493538	+	0.258722i
$417$	20.0968	−	31.6675i	0.984144	−	1.55076i
$418$	−6.68695	−	4.85835i	−0.327069	−	0.237630i
$419$	−8.81412	−	10.6544i	−0.430598	−	0.520503i	0.509932	−	0.860215i	$-0.329671\pi$
$419$	−8.81412	−	10.6544i	−0.430598	−	0.520503i	−0.940530	+	0.339711i	$0.889671\pi$
$420$	0.180534	+	11.7919i	0.00880915	+	0.575387i
$421$	13.3383	+	21.0178i	0.650070	+	1.02435i	0.996279	+	0.0861890i	$0.0274689\pi$
$421$	13.3383	+	21.0178i	0.650070	+	1.02435i	−0.346209	+	0.938158i	$0.612531\pi$
$422$	−7.48668	+	9.04984i	−0.364446	+	0.440539i
$423$	6.60762	+	14.0419i	0.321273	+	0.682741i
$424$	−10.3422	−	7.51403i	−0.502260	−	0.364913i
$425$	−7.95534	+	27.3011i	−0.385891	+	1.32430i
$426$	−21.1510	+	15.3671i	−1.02477	+	0.744539i
$427$	−21.6786	−	11.9179i	−1.04910	−	0.576748i
$428$	−7.61182	+	1.95438i	−0.367931	+	0.0944687i
$429$	13.9885	−	16.9092i	0.675371	−	0.816384i
$430$	4.82267	+	0.229361i	0.232570	+	0.0110608i
$431$	16.7812	−	6.64415i	0.808322	−	0.320037i	0.0726347	−	0.997359i	$-0.476859\pi$
$431$	16.7812	−	6.64415i	0.808322	−	0.320037i	0.735687	+	0.677321i	$0.236859\pi$
$432$	2.73897			0.131779
$433$	−29.8499	+	11.8184i	−1.43450	+	0.567957i	−0.951495	−	0.307664i	$-0.900453\pi$
$433$	−29.8499	+	11.8184i	−1.43450	+	0.567957i	−0.483000	+	0.875620i	$0.660453\pi$
$434$	5.97191	−	3.28309i	0.286661	−	0.157593i
$435$	−0.562834	−	36.7626i	−0.0269858	−	1.76263i
$436$	−1.26070	+	6.60885i	−0.0603768	+	0.316506i
$437$	9.66801	+	9.07887i	0.462484	+	0.434301i
$438$	−18.2268	−	17.1161i	−0.870911	−	0.817840i
$439$	−1.62010	+	8.49288i	−0.0773233	+	0.405343i	0.922490	+	0.386021i	$0.126151\pi$
$439$	−1.62010	+	8.49288i	−0.0773233	+	0.405343i	−0.999813	+	0.0193220i	$0.993849\pi$
$440$	−4.00871	−	1.23499i	−0.191108	−	0.0588760i
$441$	−1.73185	+	0.952093i	−0.0824691	+	0.0453378i
$442$	28.4071	−	11.2471i	1.35119	−	0.534972i
$443$	−19.4181			−0.922583			−0.461291	−	0.887249i	$-0.652614\pi$
$443$	−19.4181			−0.922583			−0.461291	+	0.887249i	$0.652614\pi$
$444$	14.9995	−	5.93873i	0.711845	−	0.281839i
$445$	−2.08404	−	1.67100i	−0.0987928	−	0.0792128i
$446$	2.01623	−	2.43721i	0.0954714	−	0.115405i
$447$	−29.5795	+	7.59473i	−1.39906	+	0.359218i
$448$	−2.12234	−	1.16676i	−0.100271	−	0.0551245i
$449$	−11.5702	+	8.40622i	−0.546030	+	0.396714i	−0.826320	−	0.563201i	$-0.809570\pi$
$449$	−11.5702	+	8.40622i	−0.546030	+	0.396714i	0.280290	+	0.959916i	$0.409570\pi$
$450$	0.280578	−	8.70671i	0.0132266	−	0.410438i
$451$	−3.35180	−	2.43523i	−0.157830	−	0.114670i
$452$	6.43168	+	13.6680i	0.302521	+	0.642889i
$453$	−15.3274	+	18.5276i	−0.720143	+	0.870504i
$454$	10.7324	+	16.9115i	0.503694	+	0.793695i
$455$	17.4586	+	23.2720i	0.818470	+	1.09101i
$456$	6.11619	+	7.39321i	0.286417	+	0.346219i
$457$	−30.9103	−	22.4576i	−1.44592	−	1.05052i	−0.986763	−	0.162171i	$-0.948150\pi$
$457$	−30.9103	−	22.4576i	−1.44592	−	1.05052i	−0.459160	−	0.888354i	$-0.651850\pi$
$458$	−3.62887	+	5.71818i	−0.169566	+	0.267193i
$459$	−2.91891	−	15.3015i	−0.136243	−	0.714211i
$460$	6.13317	+	2.77218i	0.285960	+	0.129254i
$461$	−19.6480	+	2.48212i	−0.915099	+	0.115604i	−0.568758	−	0.822505i	$-0.692576\pi$
$461$	−19.6480	+	2.48212i	−0.915099	+	0.115604i	−0.346341	+	0.938109i	$0.612576\pi$
$462$	1.85390	+	9.71848i	0.0862512	+	0.452145i
$463$	18.4713	+	2.33347i	0.858436	+	0.108446i	0.542215	−	0.840240i	$-0.317586\pi$
$463$	18.4713	+	2.33347i	0.858436	+	0.108446i	0.316221	+	0.948685i	$0.397586\pi$
$464$	6.61662	+	3.63752i	0.307169	+	0.168867i
$465$	−12.3070	+	6.02302i	−0.570721	+	0.279311i
$466$	2.26791	+	2.12971i	0.105059	+	0.0986570i
$467$	39.5336	+	10.1505i	1.82940	+	0.469710i	0.996491	−	0.0837026i	$-0.0266746\pi$
$467$	39.5336	+	10.1505i	1.82940	+	0.469710i	0.832908	+	0.553412i	$0.186675\pi$
$468$	−7.57196	+	5.50135i	−0.350014	+	0.254300i
$469$	0.369648	+	5.87538i	0.0170687	+	0.271300i
$470$	2.19354	−	19.7964i	0.101180	−	0.913139i
$471$	−33.8534	−	13.4035i	−1.55988	−	0.617600i
$472$	9.38553	+	3.71599i	0.432004	+	0.171042i
$473$	4.01851	−	0.507655i	0.184771	−	0.0233420i
$474$	−2.41184	−	7.42288i	−0.110779	−	0.340944i
$475$	−17.4185	+	13.4889i	−0.799217	+	0.618915i
$476$	−4.25645	+	13.1000i	−0.195094	+	0.600437i
$477$	4.17340	−	21.8777i	0.191087	−	1.00171i
$478$	−0.759132	+	12.0661i	−0.0347219	+	0.551889i
$479$	−9.98079	+	2.56263i	−0.456034	+	0.117090i	−0.469718	−	0.882817i	$-0.655644\pi$
$479$	−9.98079	+	2.56263i	−0.456034	+	0.117090i	0.0136836	+	0.999906i	$0.495644\pi$
$480$	4.15085	+	2.54592i	0.189459	+	0.116205i
$481$	21.3242	−	33.6015i	0.972298	−	1.53210i
$482$	3.46208	+	10.6552i	0.157694	+	0.485331i
$483$	−0.996809	−	15.8438i	−0.0453564	−	0.720919i
$484$	7.42201	+	0.937618i	0.337364	+	0.0426190i
$485$	−5.00733	−	3.07124i	−0.227371	−	0.139458i
$486$	6.87807	+	14.6166i	0.311996	+	0.663024i
$487$	9.88741	−	21.0118i	0.448041	−	0.952136i	−0.545441	−	0.838149i	$-0.683638\pi$
$487$	9.88741	−	21.0118i	0.448041	−	0.952136i	0.993482	−	0.113987i	$-0.0363622\pi$
$488$	−8.95102	+	4.92087i	−0.405194	+	0.222757i
$489$	3.80283	−	3.57110i	0.171970	−	0.161491i
$490$	2.53361	+	0.120496i	0.114457	+	0.00544344i
$491$	−11.9944	+	25.4894i	−0.541300	+	1.15032i	0.427850	+	0.903850i	$0.359271\pi$
$491$	−11.9944	+	25.4894i	−0.541300	+	1.15032i	−0.969150	+	0.246472i	$0.920729\pi$
$492$	3.06571	+	3.70581i	0.138213	+	0.167071i
$493$	13.2699	−	40.8406i	0.597648	−	1.83937i
$494$	22.9265	+	5.88654i	1.03151	+	0.264848i
$495$	−1.02683	−	7.23560i	−0.0461526	−	0.325216i
$496$	0.176682	−	2.80828i	0.00793327	−	0.126096i
$497$	−15.5799	−	24.5500i	−0.698853	−	1.10122i
$498$	4.49864	−	4.22450i	0.201589	−	0.189305i
$499$	−30.6286			−1.37113			−0.685563	−	0.728013i	$-0.740444\pi$
$499$	−30.6286			−1.37113			−0.685563	+	0.728013i	$0.740444\pi$
$500$	−6.14945	+	9.33725i	−0.275012	+	0.417575i
$501$	54.1515			2.41931
$502$	16.8441	−	15.8177i	0.751789	−	0.705977i
$503$	3.96095	+	6.24146i	0.176610	+	0.278293i	0.921088	−	0.389354i	$-0.127302\pi$
$503$	3.96095	+	6.24146i	0.176610	+	0.278293i	−0.744478	+	0.667647i	$0.767302\pi$
$504$	0.264949	−	4.21124i	0.0118018	−	0.187584i
$505$	6.26666	−	11.8242i	0.278863	−	0.526172i
$506$	5.46908	+	1.40422i	0.243130	+	0.0624252i
$507$	−10.6722	+	32.8455i	−0.473967	+	1.45872i
$508$	−7.60451	−	9.19227i	−0.337395	−	0.407841i
$509$	−1.51836	+	3.22667i	−0.0673000	+	0.143020i	−0.935647	−	0.352938i	$-0.885183\pi$
$509$	−1.51836	+	3.22667i	−0.0673000	+	0.143020i	0.868347	+	0.495957i	$0.165183\pi$
$510$	9.79942	−	25.9021i	0.433926	−	1.14697i
$511$	20.2711	−	19.0358i	0.896740	−	0.842095i
$512$	−0.876307	+	0.481754i	−0.0387276	+	0.0212907i
$513$	5.13846	−	10.9198i	0.226868	−	0.482120i
$514$	−7.21226	−	15.3268i	−0.318119	−	0.676038i
$515$	0.724892	−	3.01409i	0.0319426	−	0.132817i
$516$	−4.66495	−	0.589320i	−0.205363	−	0.0259434i
$517$	−1.04919	−	16.6764i	−0.0461434	−	0.733428i
$518$	5.54431	+	17.0636i	0.243603	+	0.749732i
$519$	27.0628	−	42.6442i	1.18793	−	1.87187i
$520$	11.9756	−	0.937693i	0.525167	−	0.0411206i
$521$	3.74136	−	0.960617i	0.163912	−	0.0420854i	−0.165842	−	0.986152i	$-0.553034\pi$
$521$	3.74136	−	0.960617i	0.163912	−	0.0420854i	0.329754	+	0.944067i	$0.393034\pi$
$522$	−0.826006	+	13.1290i	−0.0361533	+	0.574641i
$523$	−0.686375	+	3.59811i	−0.0300131	+	0.157334i	−0.994139	−	0.108112i	$-0.965519\pi$
$523$	−0.686375	+	3.59811i	−0.0300131	+	0.157334i	0.964126	+	0.265447i	$0.0855194\pi$
$524$	−0.939044	+	2.89008i	−0.0410223	+	0.126254i
$525$	26.2516	+	2.50265i	1.14571	+	0.109225i
$526$	4.41540	+	13.5892i	0.192520	+	0.592517i
$527$	−15.8770	+	2.00573i	−0.691611	+	0.0873708i
$528$	3.79822	+	1.50382i	0.165296	+	0.0654455i
$529$	12.9609	+	5.13160i	0.563519	+	0.223113i
$530$	−19.2465	+	21.1347i	−0.836016	+	0.918034i
$531$	1.10429	+	17.5522i	0.0479222	+	0.761701i
$532$	−8.63329	+	6.27246i	−0.374301	+	0.271945i
$533$	11.4918	+	2.95060i	0.497766	+	0.127805i
$534$	1.89638	+	1.78082i	0.0820645	+	0.0770637i
$535$	2.46906	+	17.3983i	0.106747	+	0.752194i
$536$	2.13006	+	1.17101i	0.0920046	+	0.0505800i
$537$	−15.5558	−	1.96515i	−0.671281	−	0.0848025i
$538$	0.525926	+	2.75700i	0.0226743	+	0.118863i
$539$	2.11114	−	0.266699i	0.0909331	−	0.0114875i
$540$	0.674501	−	6.08727i	0.0290259	−	0.261955i
$541$	3.08866	+	16.1913i	0.132792	+	0.696119i	0.984951	+	0.172836i	$0.0552930\pi$
$541$	3.08866	+	16.1913i	0.132792	+	0.696119i	−0.852159	+	0.523283i	$0.824707\pi$
$542$	−15.1496	+	23.8719i	−0.650730	+	1.02539i
$543$	−1.53152	−	1.11271i	−0.0657237	−	0.0477511i
$544$	3.62522	+	4.38214i	0.155430	+	0.187883i
$545$	14.3775	+	4.42937i	0.615863	+	0.189733i
$546$	−15.1815	−	23.9223i	−0.649710	−	1.02378i
$547$	−27.3177	+	33.0214i	−1.16802	+	1.41189i	−0.275254	+	0.961372i	$0.588762\pi$
$547$	−27.3177	+	33.0214i	−1.16802	+	1.41189i	−0.892766	+	0.450521i	$0.851238\pi$
$548$	−2.55723	−	5.43439i	−0.109240	−	0.232146i
$549$	−14.3974	−	10.4603i	−0.614466	−	0.446435i
$550$	−3.73192	+	8.60510i	−0.159130	+	0.366923i
$551$	26.9152	−	19.5551i	1.14663	−	0.833074i
$552$	−5.74402	−	3.15780i	−0.244482	−	0.134405i
$553$	8.40755	−	2.15869i	0.357525	−	0.0917969i
$554$	−9.63306	+	11.6444i	−0.409269	+	0.494722i
$555$	−9.50483	−	34.7984i	−0.403458	−	1.47711i
$556$	16.0136	−	6.34023i	0.679128	−	0.268886i
$557$	2.33232			0.0988235			0.0494118	−	0.998778i	$-0.484265\pi$
$557$	2.33232			0.0988235			0.0494118	+	0.998778i	$0.484265\pi$
$558$	4.55813	−	1.80469i	0.192961	−	0.0763987i
$559$	−10.1646	+	5.58804i	−0.429917	+	0.236349i
$560$	−3.11574	+	4.42949i	−0.131664	+	0.187180i
$561$	4.35346	−	22.8216i	0.183803	−	0.963530i
$562$	−11.6151	−	10.9073i	−0.489954	−	0.460097i
$563$	−0.638087	−	0.599204i	−0.0268922	−	0.0252534i	0.670985	−	0.741471i	$-0.265872\pi$
$563$	−0.638087	−	0.599204i	−0.0268922	−	0.0252534i	−0.697877	+	0.716218i	$0.745872\pi$
$564$	−3.63470	+	19.0538i	−0.153049	+	0.802309i
$565$	31.9606	−	10.9283i	1.34459	−	0.459757i
$566$	24.0571	−	13.2255i	1.01119	−	0.555909i
$567$	−25.2010	+	9.97779i	−1.05834	+	0.419028i
$568$	−12.0055			−0.503741
$569$	−24.9985	+	9.89760i	−1.04799	+	0.414929i	−0.828091	−	0.560593i	$-0.810573\pi$
$569$	−24.9985	+	9.89760i	−1.04799	+	0.414929i	−0.219900	+	0.975522i	$0.570573\pi$
$570$	17.9373	−	11.7724i	0.751312	−	0.493090i
$571$	19.3198	−	23.3536i	0.808507	−	0.977317i	−0.191484	−	0.981496i	$-0.561330\pi$
$571$	19.3198	−	23.3536i	0.808507	−	0.977317i	0.999991	+	0.00417854i	$0.00133007\pi$
$572$	9.76085	−	2.50616i	0.408122	−	0.104788i
$573$	24.5957	+	13.5216i	1.02750	+	0.564874i
$574$	−4.32740	+	3.14404i	−0.180622	+	0.131230i
$575$	7.67143	−	12.9481i	0.319921	−	0.539972i
$576$	−1.40951	−	1.02407i	−0.0587295	−	0.0426694i
$577$	11.3364	+	24.0910i	0.471940	+	1.00292i	0.989129	+	0.147052i	$0.0469784\pi$
$577$	11.3364	+	24.0910i	0.471940	+	1.00292i	−0.517189	+	0.855871i	$0.673022\pi$
$578$	9.78155	−	11.8239i	0.406859	−	0.491808i
$579$	−27.4013	−	43.1776i	−1.13876	−	1.79440i
$580$	9.71367	−	13.8094i	0.403338	−	0.573405i
$581$	4.37489	+	5.28833i	0.181501	+	0.219397i
$582$	4.62819	+	3.36258i	0.191845	+	0.139383i
$583$	−12.8496	+	20.2477i	−0.532174	+	0.838573i
$584$	−2.15148	−	11.2784i	−0.0890287	−	0.466705i
$585$	10.3619	+	18.1832i	0.428411	+	0.751782i
$586$	−28.0844	+	3.54789i	−1.16016	+	0.146562i
$587$	−0.334285	−	1.75238i	−0.0137974	−	0.0723286i	0.974723	−	0.223419i	$-0.0717217\pi$
$587$	−0.334285	−	1.75238i	−0.0137974	−	0.0723286i	−0.988520	+	0.151090i	$0.951722\pi$
$588$	−2.45075	−	0.309602i	−0.101067	−	0.0127678i
$589$	−10.8646	−	5.97289i	−0.447670	−	0.246109i
$590$	10.5700	−	19.9439i	0.435158	−	0.821078i
$591$	−32.2905	−	30.3228i	−1.32826	−	1.24732i
$592$	7.17536	+	1.84232i	0.294905	+	0.0757188i
$593$	−7.39982	+	5.37628i	−0.303874	+	0.220777i	−0.729263	−	0.684233i	$-0.760137\pi$
$593$	−7.39982	+	5.37628i	−0.303874	+	0.220777i	0.425389	+	0.905010i	$0.360137\pi$
$594$	−0.322620	−	5.12790i	−0.0132373	−	0.210400i
$595$	28.0661	+	12.6858i	1.15060	+	0.520068i
$596$	−13.0389	−	5.16246i	−0.534094	−	0.211463i
$597$	36.0963	+	14.2915i	1.47732	+	0.584914i
$598$	−16.0424	+	2.02663i	−0.656024	+	0.0828752i
$599$	−8.11399	−	24.9723i	−0.331529	−	1.02034i	−0.968407	−	0.249376i	$-0.919775\pi$
$599$	−8.11399	−	24.9723i	−0.331529	−	1.02034i	0.636878	−	0.770964i	$-0.280225\pi$
$600$	6.68041	−	8.59815i	0.272727	−	0.351018i
$601$	−4.10327	+	12.6286i	−0.167376	+	0.515130i	−0.999204	−	0.0399039i	$-0.987295\pi$
$601$	−4.10327	+	12.6286i	−0.167376	+	0.515130i	0.831828	+	0.555034i	$0.187295\pi$
$602$	0.979891	−	5.13677i	0.0399374	−	0.209359i
$603$	−0.265913	+	4.22656i	−0.0108288	+	0.172119i
$604$	−10.6951	+	2.74603i	−0.435177	+	0.111734i
$605$	3.91157	−	16.2643i	0.159028	−	0.661236i
$606$	−6.98328	+	11.0039i	−0.283676	+	0.447003i
$607$	14.0504	+	43.2426i	0.570288	+	1.75516i	0.651692	+	0.758483i	$0.274059\pi$
$607$	14.0504	+	43.2426i	0.570288	+	1.75516i	−0.0814048	+	0.996681i	$0.525941\pi$
$608$	0.276665	+	4.39747i	0.0112203	+	0.178341i
$609$	−39.5086	−	4.99110i	−1.60097	−	0.202250i
$610$	8.73218	+	21.1052i	0.353555	+	0.854523i
$611$	20.3740	+	43.2970i	0.824244	+	1.75161i
$612$	−4.21891	+	8.96565i	−0.170539	+	0.362415i
$613$	7.30908	−	4.01820i	0.295211	−	0.162294i	−0.327265	−	0.944933i	$-0.606127\pi$
$613$	7.30908	−	4.01820i	0.295211	−	0.162294i	0.622476	+	0.782639i	$0.286127\pi$
$614$	7.88084	−	7.40060i	0.318045	−	0.298664i
$615$	8.99100	−	5.90085i	0.362552	−	0.237945i
$616$	−1.93443	+	4.11087i	−0.0779403	+	0.165632i
$617$	−14.3680	−	17.3679i	−0.578432	−	0.699204i	0.397420	−	0.917637i	$-0.369906\pi$
$617$	−14.3680	−	17.3679i	−0.578432	−	0.699204i	−0.975852	+	0.218433i	$0.929906\pi$
$618$	−0.932945	+	2.87131i	−0.0375286	+	0.115501i
$619$	2.96815	+	0.762090i	0.119300	+	0.0306310i	0.307868	−	0.951429i	$-0.400385\pi$
$619$	2.96815	+	0.762090i	0.119300	+	0.0306310i	−0.188568	+	0.982060i	$0.560385\pi$
$620$	−6.19781	−	1.08424i	−0.248910	−	0.0435441i
$621$	−0.517666	+	8.22806i	−0.0207732	+	0.330181i
$622$	−10.1208	−	15.9479i	−0.405808	−	0.639452i
$623$	−2.10908	+	1.98055i	−0.0844984	+	0.0793493i
$624$	−11.6986			−0.468318
$625$	19.2374	+	15.9663i	0.769494	+	0.638654i
$626$	8.86466			0.354303
$627$	13.1211	−	12.3216i	0.524007	−	0.492076i
$628$	−8.95892	−	14.1170i	−0.357500	−	0.563329i
$629$	2.64550	−	42.0489i	0.105483	−	1.67660i
$630$	−9.29409	−	1.62590i	−0.370285	−	0.0647775i
$631$	14.4338	+	3.70596i	0.574600	+	0.147532i	0.524798	−	0.851227i	$-0.324141\pi$
$631$	14.4338	+	3.70596i	0.574600	+	0.147532i	0.0498019	+	0.998759i	$0.484141\pi$
$632$	1.10753	−	3.40863i	0.0440553	−	0.135588i
$633$	−16.3035	−	19.7076i	−0.648006	−	0.783305i
$634$	14.3655	−	30.5282i	0.570526	−	1.21243i
$635$	−22.3022	+	14.6371i	−0.885036	+	0.580854i
$636$	20.2934	−	19.0568i	0.804686	−	0.755650i
$637$	−5.34001	+	2.93570i	−0.211579	+	0.116317i
$638$	6.03079	−	12.8161i	0.238761	−	0.507393i
$639$	−8.90585	−	18.9259i	−0.352310	−	0.748697i
$640$	0.854881	+	2.06620i	0.0337922	+	0.0816737i
$641$	29.1135	+	3.67789i	1.14991	+	0.145268i	0.677097	−	0.735894i	$-0.263238\pi$
$641$	29.1135	+	3.67789i	1.14991	+	0.145268i	0.472815	+	0.881161i	$0.343238\pi$
$642$	−1.07458	−	17.0799i	−0.0424102	−	0.674091i
$643$	−6.34234	−	19.5197i	−0.250117	−	0.769782i	−0.994753	−	0.102310i	$-0.967377\pi$
$643$	−6.34234	−	19.5197i	−0.250117	−	0.769782i	0.744635	−	0.667472i	$-0.232623\pi$
$644$	3.90616	−	6.15513i	0.153924	−	0.242546i
$645$	−2.45854	+	10.2226i	−0.0968048	+	0.402513i
$646$	24.2719	−	6.23197i	0.954966	−	0.245194i
$647$	−2.67778	+	42.5621i	−0.105274	+	1.67329i	0.491500	+	0.870878i	$0.336449\pi$
$647$	−2.67778	+	42.5621i	−0.105274	+	1.67329i	−0.596774	+	0.802409i	$0.703551\pi$
$648$	−2.09704	+	10.9931i	−0.0823797	+	0.431849i
$649$	5.85157	−	18.0093i	0.229694	−	0.706926i
$650$	0.865137	−	26.8464i	0.0339335	−	1.05300i
$651$	4.58597	+	14.1142i	0.179738	+	0.553178i
$652$	2.37667	−	0.300243i	0.0930774	−	0.0117584i
$653$	37.5189	+	14.8548i	1.46823	+	0.581313i	0.960023	−	0.279922i	$-0.0903085\pi$
$653$	37.5189	+	14.8548i	1.46823	+	0.581313i	0.508207	+	0.861235i	$0.330308\pi$
$654$	−13.6225	−	5.39354i	−0.532683	−	0.210904i
$655$	6.19186	+	2.79871i	0.241936	+	0.109355i
$656$	0.138677	+	2.20421i	0.00541444	+	0.0860600i
$657$	16.1837	−	11.7581i	0.631386	−	0.458728i
$658$	−20.8952	−	5.36497i	−0.814579	−	0.209148i
$659$	−8.51596	−	7.99702i	−0.331735	−	0.311520i	0.500724	−	0.865607i	$-0.333067\pi$
$659$	−8.51596	−	7.99702i	−0.331735	−	0.311520i	−0.832458	+	0.554088i	$0.813067\pi$
$660$	4.27755	−	8.07109i	0.166503	−	0.314167i
$661$	−29.1901	−	16.0474i	−1.13536	−	0.624172i	−0.200683	−	0.979656i	$-0.564316\pi$
$661$	−29.1901	−	16.0474i	−1.13536	−	0.624172i	−0.934682	+	0.355484i	$0.884316\pi$
$662$	−25.3272	−	3.19957i	−0.984371	−	0.124355i
$663$	12.4671	+	65.3549i	0.484183	+	2.53817i
$664$	2.81153	−	0.355178i	0.109108	−	0.0137836i
$665$	11.8143	+	20.7319i	0.458138	+	0.803947i
$666$	2.41848	+	12.6781i	0.0937142	+	0.491267i
$667$	−12.1779	+	19.1893i	−0.471530	+	0.743012i
$668$	20.1176	+	14.6163i	0.778374	+	0.565522i
$669$	4.39069	+	5.30743i	0.169754	+	0.205197i
$670$	3.12708	−	4.44561i	0.120810	−	0.171749i
$671$	10.2672	+	16.1785i	0.396360	+	0.624563i
$672$	3.36185	−	4.06378i	0.129686	−	0.156764i
$673$	5.55099	+	11.7964i	0.213975	+	0.454720i	0.982784	−	0.184759i	$-0.0591504\pi$
$673$	5.55099	+	11.7964i	0.213975	+	0.454720i	−0.768809	+	0.639478i	$0.779150\pi$
$674$	−3.45978	−	2.51368i	−0.133266	−	0.0968232i
$675$	−13.3627	−	2.99811i	−0.514329	−	0.115397i
$676$	−12.8303	+	9.32172i	−0.493471	+	0.358528i
$677$	15.1399	+	8.32321i	0.581872	+	0.319887i	0.745364	−	0.666658i	$-0.232276\pi$
$677$	15.1399	+	8.32321i	0.581872	+	0.319887i	−0.163492	+	0.986545i	$0.552276\pi$
$678$	−31.8617	+	8.18069i	−1.22364	+	0.314177i
$679$	−4.05553	+	4.90230i	−0.155637	+	0.188133i
$680$	10.6319	−	6.97779i	0.407715	−	0.267586i
$681$	−40.5547	+	16.0567i	−1.55406	+	0.615295i
$682$	−5.27848			−0.202123
$683$	−1.45759	+	0.577103i	−0.0557733	+	0.0220822i	−0.395846	−	0.918317i	$-0.629548\pi$
$683$	−1.45759	+	0.577103i	−0.0557733	+	0.0220822i	0.340072	+	0.940399i	$0.389548\pi$
$684$	−6.72708	+	3.69824i	−0.257216	+	0.141406i
$685$	−12.7075	+	4.34508i	−0.485529	+	0.166017i
$686$	3.69154	−	19.3517i	0.140944	−	0.738852i
$687$	−10.7510	−	10.0958i	−0.410175	−	0.385180i
$688$	−1.57399	−	1.47807i	−0.0600078	−	0.0563511i
$689$	12.8683	−	67.4580i	0.490244	−	2.56995i
$690$	−8.43263	+	11.9882i	−0.321025	+	0.456385i
$691$	−3.82903	+	2.10503i	−0.145663	+	0.0800789i	−0.552918	−	0.833235i	$-0.686486\pi$
$691$	−3.82903	+	2.10503i	−0.145663	+	0.0800789i	0.407255	+	0.913314i	$0.366486\pi$
$692$	21.5643	−	8.53790i	0.819751	−	0.324562i
$693$	−7.91548			−0.300684
$694$	−20.1969	+	7.99653i	−0.766665	+	0.303544i
$695$	−10.1474	−	37.1510i	−0.384914	−	1.40922i
$696$	−10.4809	+	12.6693i	−0.397279	+	0.480228i
$697$	12.1662	−	3.12375i	0.460827	−	0.118320i
$698$	9.62277	+	5.29016i	0.364227	+	0.200236i
$699$	−5.48109	+	3.98225i	−0.207314	+	0.150622i
$700$	9.07712	+	8.01544i	0.343083	+	0.302955i
$701$	−24.7871	−	18.0089i	−0.936194	−	0.680185i	0.0113073	−	0.999936i	$-0.496401\pi$
$701$	−24.7871	−	18.0089i	−0.936194	−	0.680185i	−0.947502	+	0.319751i	$0.896401\pi$
$702$	6.26489	+	13.3136i	0.236453	+	0.502488i
$703$	20.8063	−	25.1505i	0.784726	−	0.948570i
$704$	1.00516	+	1.58387i	0.0378833	+	0.0596945i
$705$	41.4513	+	12.7702i	1.56115	+	0.480954i
$706$	0.224265	+	0.271090i	0.00844034	+	0.0102026i
$707$	−11.7262	−	8.51962i	−0.441011	−	0.320413i
$708$	−11.7787	+	18.5602i	−0.442670	+	0.697536i
$709$	8.06741	+	42.2908i	0.302978	+	1.58827i	0.729625	+	0.683847i	$0.239695\pi$
$709$	8.06741	+	42.2908i	0.302978	+	1.58827i	−0.426647	+	0.904418i	$0.640305\pi$
$710$	−2.95649	+	26.6819i	−0.110955	+	1.00135i
$711$	6.19506	−	0.782618i	0.232333	−	0.0293505i
$712$	0.223847	+	1.17345i	0.00838903	+	0.0439768i
$713$	8.40288	+	1.06153i	0.314690	+	0.0397547i
$714$	−26.2853	−	14.4505i	−0.983703	−	0.540795i
$715$	−3.16614	−	22.3103i	−0.118407	−	0.834359i
$716$	−5.24864	−	4.92880i	−0.196151	−	0.184198i
$717$	−25.5007	−	6.54747i	−0.952341	−	0.244520i
$718$	−4.08338	+	2.96675i	−0.152390	+	0.110718i
$719$	0.665819	+	10.5829i	0.0248309	+	0.394675i	0.990738	+	0.135787i	$0.0433562\pi$
$719$	0.665819	+	10.5829i	0.0248309	+	0.394675i	−0.965907	+	0.258888i	$0.916644\pi$
$720$	−2.62306	+	2.88039i	−0.0977557	+	0.107346i
$721$	−3.12190	−	1.23605i	−0.116265	−	0.0460328i
$722$	0.385186	+	0.152506i	0.0143352	+	0.00567569i
$723$	−24.2052	+	3.05783i	−0.900202	+	0.113722i
$724$	−0.268630	−	0.826759i	−0.00998356	−	0.0307262i
$725$	−28.2989	−	24.9890i	−1.05099	−	0.928069i
$726$	−5.03424	+	15.4938i	−0.186838	+	0.575029i
$727$	−8.45615	+	44.3287i	−0.313621	+	1.64406i	0.380921	+	0.924608i	$0.375607\pi$
$727$	−8.45615	+	44.3287i	−0.313621	+	1.64406i	−0.694542	+	0.719452i	$0.744393\pi$
$728$	0.816946	−	12.9850i	0.0302780	−	0.481256i
$729$	−1.55389	+	0.398972i	−0.0575516	+	0.0147767i
$730$	−25.5958	+	2.00415i	−0.947341	+	0.0741769i
$731$	−6.57997	+	10.3684i	−0.243369	+	0.383488i
$732$	−6.87371	−	21.1551i	−0.254060	−	0.781915i
$733$	1.96806	+	31.2814i	0.0726920	+	1.15541i	0.850174	+	0.526501i	$0.176496\pi$
$733$	1.96806	+	31.2814i	0.0726920	+	1.15541i	−0.777483	+	0.628905i	$0.783504\pi$
$734$	30.4345	+	3.84478i	1.12336	+	0.141913i
$735$	−1.29160	+	5.37046i	−0.0476415	+	0.198093i
$736$	−1.28160	−	2.72354i	−0.0472404	−	0.100391i
$737$	1.94147	−	4.12583i	0.0715148	−	0.151977i
$738$	−3.37192	+	1.85373i	−0.124122	+	0.0682366i
$739$	−19.8253	+	18.6172i	−0.729284	+	0.684843i	−0.957392	−	0.288793i	$-0.906746\pi$
$739$	−19.8253	+	18.6172i	−0.729284	+	0.684843i	0.228108	+	0.973636i	$0.426746\pi$
$740$	5.86150	−	15.4933i	0.215473	−	0.569545i
$741$	−21.9472	+	46.6401i	−0.806249	+	1.71337i
$742$	19.7352	+	23.8557i	0.724501	+	0.875771i
$743$	−14.0754	+	43.3197i	−0.516377	+	1.58924i	0.264386	+	0.964417i	$0.414831\pi$
$743$	−14.0754	+	43.3197i	−0.516377	+	1.58924i	−0.780763	+	0.624828i	$0.785169\pi$
$744$	5.93510	+	1.52387i	0.217591	+	0.0558679i
$745$	−14.6844	+	27.7072i	−0.537994	+	1.01511i
$746$	−0.382430	+	6.07854i	−0.0140017	+	0.222551i
$747$	2.64554	+	4.16870i	0.0967952	+	0.152525i
$748$	7.77723	−	7.30331i	0.284364	−	0.267035i
$749$	19.0331			0.695455
$750$	−17.4640	−	16.9644i	−0.637694	−	0.619452i
$751$	45.7774			1.67044			0.835220	−	0.549916i	$-0.185340\pi$
$751$	45.7774			1.67044			0.835220	+	0.549916i	$0.185340\pi$
$752$	−6.49321	+	6.09753i	−0.236783	+	0.222354i
$753$	26.9622	+	42.4856i	0.982557	+	1.54826i
$754$	−2.54692	+	40.4821i	−0.0927533	+	1.47427i
$755$	3.46919	+	24.4457i	0.126257	+	0.889671i
$756$	−6.42514	−	1.64970i	−0.233680	−	0.0599989i
$757$	−2.26517	+	6.97147i	−0.0823290	+	0.253382i	−0.983745	−	0.179572i	$-0.942529\pi$
$757$	−2.26517	+	6.97147i	−0.0823290	+	0.253382i	0.901416	+	0.432954i	$0.142529\pi$
$758$	−2.85580	−	3.45207i	−0.103727	−	0.125385i
$759$	−5.23545	+	11.1259i	−0.190035	+	0.403844i
$760$	9.84136	+	0.468044i	0.356984	+	0.0169777i
$761$	18.2228	−	17.1123i	0.660576	−	0.620322i	−0.279962	−	0.960011i	$-0.590322\pi$
$761$	18.2228	−	17.1123i	0.660576	−	0.620322i	0.940538	+	0.339689i	$0.110322\pi$
$762$	22.7662	−	12.5158i	0.824733	−	0.453401i
$763$	6.93793	−	14.7439i	0.251170	−	0.533763i
$764$	5.48777	+	11.6621i	0.198541	+	0.421920i
$765$	18.8869	+	11.5843i	0.682857	+	0.418830i
$766$	16.8321	+	2.12638i	0.608167	+	0.0768294i
$767$	3.40499	+	54.1207i	0.122947	+	1.95418i
$768$	−0.672937	−	2.07109i	−0.0242825	−	0.0747339i
$769$	4.21365	−	6.63964i	0.151948	−	0.239432i	−0.759824	−	0.650129i	$-0.774715\pi$
$769$	4.21365	−	6.63964i	0.151948	−	0.239432i	0.911772	+	0.410698i	$0.134715\pi$
$770$	8.65989	+	5.31154i	0.312081	+	0.191415i
$771$	35.7286	−	9.17354i	1.28673	−	0.330377i
$772$	1.47451	−	23.4367i	0.0530689	−	0.843507i
$773$	3.11095	−	16.3082i	0.111893	−	0.586564i	−0.881536	−	0.472116i	$-0.843490\pi$
$773$	3.11095	−	16.3082i	0.111893	−	0.586564i	0.993429	−	0.114448i	$-0.0365098\pi$
$774$	1.16248	−	3.57774i	0.0417844	−	0.128599i
$775$	−3.93596	+	13.5074i	−0.141384	+	0.485200i
$776$	0.811790	+	2.49843i	0.0291416	+	0.0896885i
$777$	−38.7631	+	4.89692i	−1.39062	+	0.175676i
$778$	−16.1585	−	6.39759i	−0.579309	−	0.229365i
$779$	9.04795	+	3.58234i	0.324177	+	0.128351i
$780$	−2.88090	+	25.9997i	−0.103153	+	0.930939i
$781$	1.41412	+	22.4767i	0.0506010	+	0.804281i
$782$	−13.8494	+	10.0622i	−0.495254	+	0.359823i
$783$	20.0311	+	5.14311i	0.715852	+	0.183800i
$784$	−0.826902	−	0.776512i	−0.0295322	−	0.0277326i
$785$	−33.5808	+	16.4344i	−1.19855	+	0.586570i
$786$	−5.79898	−	3.18802i	−0.206843	−	0.113713i
$787$	46.8667	+	5.92064i	1.67062	+	0.211048i	0.902934	−	0.429780i	$-0.141409\pi$
$787$	46.8667	+	5.92064i	1.67062	+	0.211048i	0.767684	+	0.640828i	$0.221409\pi$
$788$	−3.81154	−	19.9808i	−0.135781	−	0.711787i
$789$	−30.8703	+	3.89983i	−1.09901	+	0.138838i
$790$	−7.30283	−	3.30087i	−0.259823	−	0.117440i
$791$	−6.85527	−	35.9366i	−0.243745	−	1.27776i
$792$	−1.75123	+	2.75950i	−0.0622273	+	0.0980545i
$793$	−44.3931	−	32.2535i	−1.57644	−	1.14535i
$794$	3.58060	+	4.32820i	0.127071	+	0.153602i
$795$	−37.3556	−	49.7944i	−1.32487	−	1.76602i
$796$	9.55249	+	15.0523i	0.338579	+	0.533515i
$797$	−12.0129	+	14.5211i	−0.425518	+	0.514363i	−0.939084	−	0.343687i	$-0.888324\pi$
$797$	−12.0129	+	14.5211i	−0.425518	+	0.514363i	0.513566	+	0.858050i	$0.328324\pi$
$798$	−9.89454	−	21.0270i	−0.350263	−	0.744346i
$799$	40.9840	+	29.7767i	1.44991	+	1.05342i
$800$	4.80258	−	1.39112i	0.169797	−	0.0491836i
$801$	−1.68381	+	1.22336i	−0.0594944	+	0.0432252i
$802$	14.7736	+	8.12187i	0.521675	+	0.286793i
$803$	−20.8620	+	5.35646i	−0.736205	+	0.189025i
$804$	−3.37409	+	4.07857i	−0.118995	+	0.143840i
$805$	−12.7176	−	10.1971i	−0.448238	−	0.359400i
$806$	14.0546	−	5.56461i	0.495052	−	0.196005i
$807$	−6.11210			−0.215156
$808$	−5.56444	+	2.20312i	−0.195756	+	0.0775054i
$809$	−7.82476	+	4.30170i	−0.275104	+	0.151240i	−0.613334	−	0.789824i	$-0.710172\pi$
$809$	−7.82476	+	4.30170i	−0.275104	+	0.151240i	0.338230	+	0.941064i	$0.390172\pi$
$810$	23.9153	+	7.36777i	0.840300	+	0.258877i
$811$	−2.05734	+	10.7850i	−0.0722430	+	0.378711i	0.927742	+	0.373222i	$0.121747\pi$
$811$	−2.05734	+	10.7850i	−0.0722430	+	0.378711i	−0.999985	+	0.00548878i	$0.998253\pi$
$812$	−13.3305	−	12.5182i	−0.467809	−	0.439302i
$813$	−44.8825	−	42.1475i	−1.57410	−	1.47818i
$814$	2.60401	−	13.6507i	0.0912705	−	0.478456i
$815$	−0.0820001	−	5.35600i	−0.00287234	−	0.187612i
$816$	−10.8531	+	5.96655i	−0.379935	+	0.208871i
$817$	−8.84570	+	3.50226i	−0.309472	+	0.122529i
$818$	12.5070			0.437296
$819$	21.0760	−	8.34457i	0.736454	−	0.291583i
$820$	4.93294	+	0.234605i	0.172266	+	0.00819276i
$821$	−35.7844	+	43.2559i	−1.24888	+	1.50964i	−0.469727	+	0.882812i	$0.655648\pi$
$821$	−35.7844	+	43.2559i	−1.24888	+	1.50964i	−0.779157	+	0.626829i	$0.784352\pi$
$822$	12.6682	−	3.25264i	0.441854	−	0.113449i
$823$	−48.1532	−	26.4725i	−1.67852	−	0.922772i	−0.977856	−	0.209277i	$-0.932889\pi$
$823$	−48.1532	−	26.4725i	−1.67852	−	0.922772i	−0.700660	−	0.713495i	$-0.747111\pi$
$824$	−1.12160	+	0.814892i	−0.0390729	+	0.0283881i
$825$	−16.8843	−	11.4943i	−0.587837	−	0.400180i
$826$	−19.7786	−	14.3700i	−0.688186	−	0.499997i
$827$	−12.2151	−	25.9585i	−0.424762	−	0.902666i	−0.996607	−	0.0823040i	$-0.973772\pi$
$827$	−12.2151	−	25.9585i	−0.424762	−	0.902666i	0.571845	−	0.820362i	$-0.306228\pi$
$828$	3.34276	−	4.04071i	0.116169	−	0.140424i
$829$	−12.1654	−	19.1696i	−0.422523	−	0.665789i	0.564671	−	0.825316i	$-0.309003\pi$
$829$	−12.1654	−	19.1696i	−0.422523	−	0.665789i	−0.987194	+	0.159527i	$0.949003\pi$
$830$	−0.0970037	−	6.33599i	−0.00336705	−	0.219925i
$831$	−20.9776	−	25.3576i	−0.727706	−	0.879645i
$832$	−4.34609	−	3.15762i	−0.150674	−	0.109471i
$833$	−3.45681	+	5.44707i	−0.119771	+	0.188730i
$834$	7.02795	+	36.8418i	0.243358	+	1.27573i
$835$	37.4384	−	41.1113i	1.29561	−	1.42271i
$836$	8.20035	−	1.03594i	0.283615	−	0.0358289i
$837$	−1.44415	−	7.57051i	−0.0499172	−	0.261675i
$838$	13.7187	+	1.73307i	0.473904	+	0.0598680i
$839$	−4.17113	−	2.29310i	−0.144004	−	0.0791666i	0.408123	−	0.912927i	$-0.366183\pi$
$839$	−4.17113	−	2.29310i	−0.144004	−	0.0791666i	−0.552127	+	0.833760i	$0.686183\pi$
$840$	−8.20373	−	8.47235i	−0.283055	−	0.292324i
$841$	20.4192	+	19.1749i	0.704112	+	0.661205i
$842$	−24.1109	−	6.19063i	−0.830917	−	0.213343i
$843$	28.0714	−	20.3951i	0.966830	−	0.702443i
$844$	−0.737487	−	11.7220i	−0.0253854	−	0.403489i
$845$	17.5576	+	30.8104i	0.604001	+	1.05991i
$846$	−14.4291	−	5.71288i	−0.496082	−	0.196413i
$847$	−16.8460	−	6.66980i	−0.578835	−	0.229177i
$848$	12.6828	−	1.60221i	0.435530	−	0.0550202i
$849$	18.4740	+	56.8571i	0.634026	+	1.95133i
$850$	−12.8897	−	25.3474i	−0.442112	−	0.869410i
$851$	−6.89059	+	21.2071i	−0.236206	+	0.726969i
$852$	4.89891	−	25.6810i	0.167834	−	0.879816i
$853$	1.22276	−	19.4352i	0.0418664	−	0.665448i	−0.919998	−	0.391922i	$-0.871810\pi$
$853$	1.22276	−	19.4352i	0.0418664	−	0.665448i	0.961865	−	0.273526i	$-0.0881898\pi$
$854$	23.9614	−	6.15224i	0.819941	−	0.210525i
$855$	6.56260	+	15.8614i	0.224436	+	0.542449i
$856$	4.21091	−	6.63534i	0.143926	−	0.226791i
$857$	−1.94716	−	5.99273i	−0.0665136	−	0.204708i	0.912276	−	0.409576i	$-0.134323\pi$
$857$	−1.94716	−	5.99273i	−0.0665136	−	0.204708i	−0.978790	+	0.204868i	$0.934323\pi$
$858$	1.37796	+	21.9021i	0.0470428	+	0.747724i
$859$	38.5254	+	4.86689i	1.31447	+	0.166056i	0.751121	−	0.660164i	$-0.229513\pi$
$859$	38.5254	+	4.86689i	1.31447	+	0.166056i	0.563347	+	0.826220i	$0.309513\pi$
$860$	−3.67258	+	3.13415i	−0.125234	+	0.106874i
$861$	−4.95959	−	10.5397i	−0.169022	−	0.359191i
$862$	−7.68474	+	16.3309i	−0.261743	+	0.556233i
$863$	−1.86930	+	1.02765i	−0.0636316	+	0.0349818i	−0.513252	−	0.858238i	$-0.671559\pi$
$863$	−1.86930	+	1.02765i	−0.0636316	+	0.0349818i	0.449620	+	0.893220i	$0.351559\pi$
$864$	−1.99662	+	1.87496i	−0.0679266	+	0.0637873i
$865$	−13.6648	−	50.0284i	−0.464616	−	1.70102i
$866$	13.6694	−	29.0489i	0.464505	−	0.987123i
$867$	21.3010	+	25.7485i	0.723419	+	0.874464i
$868$	−2.10591	+	6.48132i	−0.0714792	+	0.219990i
$869$	−6.51209	−	1.67202i	−0.220908	−	0.0567195i
$870$	25.5760	+	26.4135i	0.867108	+	0.895501i
$871$	−0.819919	+	13.0322i	−0.0277819	+	0.441581i
$872$	−3.60505	−	5.68065i	−0.122082	−	0.192371i
$873$	−3.33641	+	3.13310i	−0.112920	+	0.106039i
$874$	−13.2626			−0.448614
$875$	20.0494	−	18.1997i	0.677793	−	0.615262i
$876$	25.0036			0.844793
$877$	7.16793	−	6.73114i	0.242044	−	0.227294i	−0.554026	−	0.832500i	$-0.686909\pi$
$877$	7.16793	−	6.73114i	0.242044	−	0.227294i	0.796069	+	0.605205i	$0.206909\pi$
$878$	−4.63277	−	7.30008i	−0.156348	−	0.246366i
$879$	3.87070	−	61.5230i	0.130556	−	2.07512i
$880$	3.76764	−	1.84388i	0.127007	−	0.0621573i
$881$	−43.9956	−	11.2962i	−1.48225	−	0.380577i	−0.581010	−	0.813896i	$-0.697342\pi$
$881$	−43.9956	−	11.2962i	−1.48225	−	0.380577i	−0.901241	+	0.433319i	$0.857342\pi$
$882$	0.610713	−	1.87958i	0.0205638	−	0.0632888i
$883$	−5.80025	−	7.01130i	−0.195194	−	0.235949i	0.663831	−	0.747883i	$-0.268929\pi$
$883$	−5.80025	−	7.01130i	−0.195194	−	0.235949i	−0.859025	+	0.511934i	$0.828929\pi$
$884$	−13.0086	+	27.6448i	−0.437528	+	0.929795i
$885$	38.3488	+	30.7484i	1.28908	+	1.03359i
$886$	14.1552	−	13.2926i	0.475553	−	0.446574i
$887$	12.3328	−	6.78001i	0.414095	−	0.227651i	−0.261066	−	0.965321i	$-0.584074\pi$
$887$	12.3328	−	6.78001i	0.414095	−	0.227651i	0.675161	+	0.737670i	$0.264074\pi$
$888$	−6.86883	+	14.5970i	−0.230503	+	0.489844i
$889$	12.3023	+	26.1437i	0.412605	+	0.876830i
$890$	2.66307	−	0.208519i	0.0892664	−	0.00698956i
$891$	20.8282	+	2.63122i	0.697773	+	0.0881492i
$892$	0.198612	+	3.15685i	0.00665004	+	0.105699i
$893$	12.1281	+	37.3265i	0.405852	+	1.24908i
$894$	16.3636	−	25.7849i	0.547280	−	0.862376i
$895$	−12.2466	+	10.4511i	−0.409359	+	0.349343i
$896$	2.34582	−	0.602305i	0.0783684	−	0.0201216i
$897$	2.21103	−	35.1433i	0.0738242	−	1.17340i
$898$	2.67984	−	14.0482i	0.0894273	−	0.468795i
$899$	6.56540	−	20.2062i	0.218968	−	0.673915i
$900$	5.75562	+	6.53899i	0.191854	+	0.217966i
$901$	−22.4669	−	69.1460i	−0.748481	−	2.30359i
$902$	4.11039	−	0.519263i	0.136861	−	0.0172896i
$903$	10.5882	+	4.19216i	0.352353	+	0.139506i
$904$	−14.0449	−	5.56076i	−0.467126	−	0.184948i
$905$	−1.90360	+	0.393423i	−0.0632777	+	0.0130778i
$906$	−1.50985	−	23.9984i	−0.0501614	−	0.797293i
$907$	25.1494	−	18.2721i	0.835073	−	0.606716i	−0.0859170	−	0.996302i	$-0.527382\pi$
$907$	25.1494	−	18.2721i	0.835073	−	0.606716i	0.920990	+	0.389586i	$0.127382\pi$
$908$	−19.4002	−	4.98114i	−0.643820	−	0.165305i
$909$	−7.60084	−	7.13766i	−0.252104	−	0.236741i
$910$	−28.6575	−	5.01333i	−0.949987	−	0.166190i
$911$	2.22839	+	1.22507i	0.0738298	+	0.0405883i	0.518241	−	0.855235i	$-0.326587\pi$
$911$	2.22839	+	1.22507i	0.0738298	+	0.0405883i	−0.444411	+	0.895823i	$0.646587\pi$
$912$	−9.51951	−	1.20259i	−0.315222	−	0.0398219i
$913$	−0.996131	−	5.22190i	−0.0329671	−	0.172820i
$914$	37.9060	−	4.78864i	1.25382	−	0.158394i
$915$	−48.7092	+	10.0669i	−1.61028	+	0.332802i
$916$	−1.26903	−	6.65250i	−0.0419300	−	0.219805i
$917$	3.94354	−	6.21402i	0.130227	−	0.205205i
$918$	12.6024	+	9.15615i	0.415940	+	0.302198i
$919$	7.36956	+	8.90827i	0.243099	+	0.293857i	0.877924	−	0.478799i	$-0.158928\pi$
$919$	7.36956	+	8.90827i	0.243099	+	0.293857i	−0.634825	+	0.772656i	$0.718928\pi$
$920$	−6.36858	+	2.17761i	−0.209966	+	0.0717937i
$921$	12.6148	+	19.8777i	0.415671	+	0.654993i
$922$	12.6236	−	15.2594i	0.415738	−	0.502541i
$923$	−27.4604	−	58.3563i	−0.903870	−	1.92082i
$924$	−8.00419	−	5.81539i	−0.263319	−	0.191312i
$925$	−32.9899	−	16.8424i	−1.08470	−	0.553774i
$926$	−15.0624	+	10.9435i	−0.494981	+	0.359625i
$927$	−2.11664	−	1.16363i	−0.0695196	−	0.0382187i
$928$	−7.31336	+	1.87775i	−0.240073	+	0.0616402i
$929$	−15.8067	+	19.1070i	−0.518601	+	0.626881i	−0.963180	−	0.268859i	$-0.913354\pi$
$929$	−15.8067	+	19.1070i	−0.518601	+	0.626881i	0.444578	+	0.895740i	$0.353354\pi$
$930$	4.84834	−	12.8153i	0.158983	−	0.420230i
$931$	−4.64712	+	1.83993i	−0.152303	+	0.0603011i
$932$	−3.11112			−0.101908
$933$	38.2439	−	15.1418i	1.25205	−	0.495721i
$934$	−35.7673	+	19.6632i	−1.17034	+	0.643400i
$935$	−14.3161	−	19.0831i	−0.468187	−	0.624086i
$936$	1.75379	−	9.19368i	0.0573243	−	0.300505i
$937$	3.37260	+	3.16708i	0.110178	+	0.103464i	0.737679	−	0.675152i	$-0.235922\pi$
$937$	3.37260	+	3.16708i	0.110178	+	0.103464i	−0.627501	+	0.778616i	$0.715922\pi$
$938$	−4.29144	−	4.02993i	−0.140120	−	0.131582i
$939$	−3.61727	+	18.9624i	−0.118045	+	0.618814i
$940$	11.9525	+	15.9325i	0.389849	+	0.519662i
$941$	20.4461	−	11.2403i	0.666523	−	0.366424i	−0.112294	−	0.993675i	$-0.535820\pi$
$941$	20.4461	−	11.2403i	0.666523	−	0.366424i	0.778817	+	0.627251i	$0.215820\pi$
$942$	33.8534	−	13.4035i	1.10300	−	0.436709i
$943$	−6.64781			−0.216483
$944$	−9.38553	+	3.71599i	−0.305473	+	0.120945i
$945$	−5.24865	+	13.8734i	−0.170739	+	0.451302i
$946$	−2.58185	+	3.12092i	−0.0839432	+	0.101470i
$947$	7.55087	−	1.93873i	0.245370	−	0.0630004i	−0.124002	−	0.992282i	$-0.539573\pi$
$947$	7.55087	−	1.93873i	0.245370	−	0.0630004i	0.369372	+	0.929282i	$0.379573\pi$
$948$	6.83947	+	3.76003i	0.222136	+	0.122120i
$949$	49.9010	−	36.2552i	1.61985	−	1.17689i
$950$	3.46375	−	21.7568i	0.112379	−	0.705885i
$951$	59.4409	+	43.1864i	1.92750	+	1.40041i
$952$	−5.86475	−	12.4632i	−0.190078	−	0.403935i
$953$	5.71254	−	6.90528i	0.185047	−	0.223684i	−0.669829	−	0.742515i	$-0.733633\pi$
$953$	5.71254	−	6.90528i	0.185047	−	0.223684i	0.854877	+	0.518831i	$0.173633\pi$
$954$	11.9341	+	18.8051i	0.386379	+	0.608836i
$955$	27.2701	−	9.32447i	0.882439	−	0.301733i
$956$	−7.70640	−	9.31544i	−0.249243	−	0.301283i
$957$	24.9539	+	18.1301i	0.806646	+	0.586063i
$958$	5.52144	−	8.70040i	0.178390	−	0.281097i
$959$	2.72565	+	14.2884i	0.0880158	+	0.461395i
$960$	−4.76864	+	0.985553i	−0.153907	+	0.0318086i
$961$	22.9003	−	2.89298i	0.738720	−	0.0933220i
$962$	7.45717	+	39.0918i	0.240429	+	1.26037i
$963$	13.5839	+	1.71604i	0.437734	+	0.0552986i
$964$	−9.81774	−	5.39735i	−0.316208	−	0.173837i
$965$	−51.7242	−	9.04860i	−1.66506	−	0.291285i
$966$	11.5725	+	10.8673i	0.372339	+	0.349649i
$967$	22.8106	+	5.85678i	0.733541	+	0.188341i	0.596941	−	0.802285i	$-0.296383\pi$
$967$	22.8106	+	5.85678i	0.733541	+	0.188341i	0.136600	+	0.990626i	$0.456383\pi$
$968$	−6.05226	+	4.39722i	−0.194527	+	0.141332i
$969$	3.42652	+	54.4630i	0.110076	+	1.74960i
$970$	5.75260	−	1.18891i	0.184705	−	0.0381736i
$971$	18.1659	+	7.19237i	0.582970	+	0.230814i	0.641052	−	0.767498i	$-0.278498\pi$
$971$	18.1659	+	7.19237i	0.582970	+	0.230814i	−0.0580817	+	0.998312i	$0.518498\pi$
$972$	−15.0197	−	5.94671i	−0.481756	−	0.190741i
$973$	−41.3838	+	5.22799i	−1.32670	+	0.167602i
$974$	7.17597	+	22.0854i	0.229933	+	0.707660i
$975$	57.0740	+	12.8054i	1.82783	+	0.410101i
$976$	3.15645	−	9.71456i	0.101036	−	0.310955i
$977$	−2.02966	+	10.6399i	−0.0649346	+	0.340399i	−0.999897	−	0.0143475i	$-0.995433\pi$
$977$	−2.02966	+	10.6399i	−0.0649346	+	0.340399i	0.934962	+	0.354747i	$0.115433\pi$
$978$	−0.327561	+	5.20643i	−0.0104742	+	0.166483i
$979$	2.17056	−	0.557305i	0.0693714	−	0.0178115i
$980$	−1.92941	+	1.64654i	−0.0616326	+	0.0525967i
$981$	6.28089	−	9.89710i	0.200533	−	0.315990i
$982$	−8.70516	−	26.7917i	−0.277793	−	0.854958i
$983$	−1.90121	−	30.2188i	−0.0606391	−	0.963831i	−0.904285	−	0.426930i	$-0.859595\pi$
$983$	−1.90121	−	30.2188i	−0.0606391	−	0.963831i	0.843646	−	0.536901i	$-0.180405\pi$
$984$	−4.77161	−	0.602795i	−0.152113	−	0.0192164i
$985$	−45.3453	+	3.55054i	−1.44482	+	0.113130i
$986$	18.2840	+	38.8554i	0.582281	+	1.23741i
$987$	20.0026	−	42.5076i	0.636689	−	1.35303i
$988$	−20.7423	+	11.4032i	−0.659902	+	0.362784i
$989$	4.73772	−	4.44902i	0.150651	−	0.141470i
$990$	5.70164	+	4.57161i	0.181210	+	0.145295i
$991$	−18.2202	+	38.7199i	−0.578784	+	1.22998i	0.374309	+	0.927304i	$0.377880\pi$
$991$	−18.2202	+	38.7199i	−0.578784	+	1.22998i	−0.953094	+	0.302675i	$0.902120\pi$
$992$	1.79361	+	2.16810i	0.0569471	+	0.0688372i
$993$	17.1791	−	52.8718i	0.545162	−	1.67784i
$994$	28.1628	+	7.23099i	0.893271	+	0.229353i
$995$	35.8057	−	17.5233i	1.13512	−	0.555526i
$996$	−0.387495	+	6.15906i	−0.0122783	+	0.195157i
$997$	21.5698	+	33.9886i	0.683122	+	1.07643i	0.992111	+	0.125363i	$0.0400095\pi$
$997$	21.5698	+	33.9886i	0.683122	+	1.07643i	−0.308989	+	0.951066i	$0.599990\pi$
$998$	22.3273	−	20.9667i	0.706759	−	0.663690i
$999$	20.2906			0.641965

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	250.2.g.a.11.1	✓	120
125.91	even	25	inner	250.2.g.a.91.1	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
250.2.g.a.11.1	✓	120	1.1	even	1	trivial
250.2.g.a.91.1	yes	120	125.91	even	25	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 250 = 2 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	250.g (of order \(25\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.728969 + 0.684547i) q^{2} +(-1.16685 - 1.83867i) q^{3} +(0.0627905 - 0.998027i) q^{4} +(-2.20262 - 0.385324i) q^{5} +(2.10925 + 0.541564i) q^{6} +(-0.748412 + 2.30337i) q^{7} +(0.637424 + 0.770513i) q^{8} +(-0.741812 + 1.57643i) q^{9} +O(q^{10})\)	\(q+(-0.728969 + 0.684547i) q^{2} +(-1.16685 - 1.83867i) q^{3} +(0.0627905 - 0.998027i) q^{4} +(-2.20262 - 0.385324i) q^{5} +(2.10925 + 0.541564i) q^{6} +(-0.748412 + 2.30337i) q^{7} +(0.637424 + 0.770513i) q^{8} +(-0.741812 + 1.57643i) q^{9} +(1.86941 - 1.22691i) q^{10} +(1.36747 - 1.28414i) q^{11} +(-1.90831 + 1.04910i) q^{12} +(-2.28731 + 4.86079i) q^{13} +(-1.03120 - 2.19141i) q^{14} +(1.86165 + 4.49950i) q^{15} +(-0.992115 - 0.125333i) q^{16} +(0.357109 + 5.67608i) q^{17} +(-0.538384 - 1.65697i) q^{18} +(-2.36094 + 3.72025i) q^{19} +(-0.522868 + 2.17408i) q^{20} +(5.10843 - 1.31162i) q^{21} +(-0.117789 + 1.87220i) q^{22} +(0.564019 - 2.95669i) q^{23} +(0.672937 - 2.07109i) q^{24} +(4.70305 + 1.69745i) q^{25} +(-1.66006 - 5.10914i) q^{26} +(-2.71737 + 0.343284i) q^{27} +(2.25184 + 0.891565i) q^{28} +(-7.02034 - 2.77955i) q^{29} +(-4.43720 - 2.00561i) q^{30} +(0.176682 + 2.80828i) q^{31} +(0.809017 - 0.587785i) q^{32} +(-3.95675 - 1.01592i) q^{33} +(-4.14587 - 3.89323i) q^{34} +(2.53601 - 4.78507i) q^{35} +(1.52674 + 0.839334i) q^{36} +(-7.34968 - 0.928480i) q^{37} +(-0.825633 - 4.32812i) q^{38} +(11.6063 - 1.46622i) q^{39} +(-1.10710 - 1.94276i) q^{40} +(-0.413845 - 2.16945i) q^{41} +(-2.82602 + 4.45309i) q^{42} +(1.74683 + 1.26915i) q^{43} +(-1.19574 - 1.44541i) q^{44} +(2.24137 - 3.18644i) q^{45} +(1.61284 + 2.54143i) q^{46} +(5.67779 - 6.86327i) q^{47} +(0.927207 + 1.97041i) q^{48} +(0.917704 + 0.666751i) q^{49} +(-4.59036 + 1.98208i) q^{50} +(10.0197 - 7.27976i) q^{51} +(4.70757 + 2.58801i) q^{52} +(-12.3820 + 3.17916i) q^{53} +(1.74589 - 2.11041i) q^{54} +(-3.50683 + 2.30155i) q^{55} +(-2.25184 + 0.891565i) q^{56} +9.59517 q^{57} +(7.02034 - 2.77955i) q^{58} +(8.84578 - 4.86301i) q^{59} +(4.60751 - 1.57545i) q^{60} +(-1.91400 + 10.0336i) q^{61} +(-2.05120 - 1.92620i) q^{62} +(-3.07593 - 2.88849i) q^{63} +(-0.187381 + 0.982287i) q^{64} +(6.91106 - 9.82510i) q^{65} +(3.57979 - 1.96801i) q^{66} +(2.26003 - 0.894809i) q^{67} +5.68730 q^{68} +(-6.09450 + 2.41298i) q^{69} +(1.42693 + 5.22419i) q^{70} +(-7.65261 + 9.25042i) q^{71} +(-1.68751 + 0.433279i) q^{72} +(-10.0616 - 5.53140i) q^{73} +(5.99327 - 4.35437i) q^{74} +(-2.36674 - 10.6280i) q^{75} +(3.56466 + 2.58988i) q^{76} +(1.93443 + 4.11087i) q^{77} +(-7.45696 + 9.01391i) q^{78} +(-1.92043 - 3.02611i) q^{79} +(2.13696 + 0.658347i) q^{80} +(7.13361 + 8.62306i) q^{81} +(1.78677 + 1.29816i) q^{82} +(1.51846 - 2.39272i) q^{83} +(-0.988272 - 5.18070i) q^{84} +(1.40056 - 12.6398i) q^{85} +(-2.14217 + 0.270620i) q^{86} +(3.08105 + 16.1514i) q^{87} +(1.86111 + 0.235113i) q^{88} +(1.04684 + 0.575507i) q^{89} +(0.547381 + 3.85713i) q^{90} +(-9.48436 - 8.90641i) q^{91} +(-2.91544 - 0.748559i) q^{92} +(4.95734 - 3.60172i) q^{93} +(0.559300 + 8.88982i) q^{94} +(6.63375 - 7.28455i) q^{95} +(-2.02475 - 0.801654i) q^{96} +(2.44253 + 0.967066i) q^{97} +(-1.12540 + 0.142171i) q^{98} +(1.00995 + 3.10832i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 5 q^{5} + 10 q^{7} + 10 q^{9}+O(q^{10}) \) 120 * q - 5 * q^5 + 10 * q^7 + 10 * q^9	\( 120 q - 5 q^{5} + 10 q^{7} + 10 q^{9} - 20 q^{10} + 20 q^{12} - 20 q^{14} - 10 q^{15} - 5 q^{17} + 25 q^{18} - 60 q^{19} + 5 q^{20} + 5 q^{21} - 10 q^{22} + 10 q^{23} - 5 q^{24} + 55 q^{25} + 5 q^{26} - 90 q^{27} - 5 q^{28} - 10 q^{29} - 10 q^{30} - 45 q^{31} + 30 q^{32} - 15 q^{33} - 10 q^{34} + 15 q^{35} + 10 q^{36} + 10 q^{37} + 10 q^{39} - 55 q^{41} - 5 q^{42} + 5 q^{43} - 40 q^{44} + 85 q^{45} - 20 q^{46} + 90 q^{47} - 5 q^{48} - 20 q^{49} - 30 q^{50} + 60 q^{51} + 5 q^{53} + 5 q^{54} - 15 q^{55} + 5 q^{56} - 120 q^{57} + 10 q^{58} - 75 q^{59} + 15 q^{60} - 85 q^{61} - 15 q^{62} - 45 q^{63} + 5 q^{65} - 15 q^{66} - 25 q^{67} - 70 q^{68} + 5 q^{69} - 65 q^{70} + 55 q^{71} + 5 q^{72} - 30 q^{73} - 70 q^{74} - 20 q^{75} - 5 q^{76} - 130 q^{77} + 60 q^{78} + 10 q^{79} + 5 q^{80} - 65 q^{81} + 80 q^{82} - 135 q^{83} + 20 q^{84} - 30 q^{85} + 10 q^{86} - 200 q^{87} - 80 q^{90} + 175 q^{91} - 5 q^{92} + 50 q^{93} + 35 q^{94} - 20 q^{95} - 15 q^{98} - 120 q^{99}+O(q^{100}) \) 120 * q - 5 * q^5 + 10 * q^7 + 10 * q^9 - 20 * q^10 + 20 * q^12 - 20 * q^14 - 10 * q^15 - 5 * q^17 + 25 * q^18 - 60 * q^19 + 5 * q^20 + 5 * q^21 - 10 * q^22 + 10 * q^23 - 5 * q^24 + 55 * q^25 + 5 * q^26 - 90 * q^27 - 5 * q^28 - 10 * q^29 - 10 * q^30 - 45 * q^31 + 30 * q^32 - 15 * q^33 - 10 * q^34 + 15 * q^35 + 10 * q^36 + 10 * q^37 + 10 * q^39 - 55 * q^41 - 5 * q^42 + 5 * q^43 - 40 * q^44 + 85 * q^45 - 20 * q^46 + 90 * q^47 - 5 * q^48 - 20 * q^49 - 30 * q^50 + 60 * q^51 + 5 * q^53 + 5 * q^54 - 15 * q^55 + 5 * q^56 - 120 * q^57 + 10 * q^58 - 75 * q^59 + 15 * q^60 - 85 * q^61 - 15 * q^62 - 45 * q^63 + 5 * q^65 - 15 * q^66 - 25 * q^67 - 70 * q^68 + 5 * q^69 - 65 * q^70 + 55 * q^71 + 5 * q^72 - 30 * q^73 - 70 * q^74 - 20 * q^75 - 5 * q^76 - 130 * q^77 + 60 * q^78 + 10 * q^79 + 5 * q^80 - 65 * q^81 + 80 * q^82 - 135 * q^83 + 20 * q^84 - 30 * q^85 + 10 * q^86 - 200 * q^87 - 80 * q^90 + 175 * q^91 - 5 * q^92 + 50 * q^93 + 35 * q^94 - 20 * q^95 - 15 * q^98 - 120 * q^99

Introduction

L-functions

Modular forms

Varieties

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