LMFDB - Embedded newform 95.2.p.a.4.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [95,2,Mod(4,95)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(95, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("95.4"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 95 = 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	95.p (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.758578819202$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			4.7
Character	$\chi$	$=$	95.4
Dual form			95.2.p.a.24.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.795068 - 2.18443i) q^{2} +(1.13113 - 0.199449i) q^{3} +(-2.60752 - 2.18797i) q^{4} +(-0.914172 + 2.04066i) q^{5} +(0.463643 - 2.62945i) q^{6} +(0.124103 + 0.0716510i) q^{7} +(-2.82626 + 1.63174i) q^{8} +(-1.57940 + 0.574856i) q^{9} +(3.73085 + 3.61941i) q^{10} +(1.40779 + 2.43836i) q^{11} +(-3.38583 - 1.95481i) q^{12} +(-1.68258 - 0.296685i) q^{13} +(0.255187 - 0.214128i) q^{14} +(-0.627041 + 2.49058i) q^{15} +(0.135204 + 0.766781i) q^{16} +(1.21720 - 3.34424i) q^{17} +3.90715i q^{18} +(-2.82087 + 3.32305i) q^{19} +(6.84862 - 3.32088i) q^{20} +(0.154668 + 0.0562944i) q^{21} +(6.44571 - 1.13655i) q^{22} +(4.62417 - 5.51088i) q^{23} +(-2.87141 + 2.40940i) q^{24} +(-3.32858 - 3.73103i) q^{25} +(-1.98586 + 3.43960i) q^{26} +(-4.65595 + 2.68812i) q^{27} +(-0.166831 - 0.458365i) q^{28} +(7.11492 - 2.58962i) q^{29} +(4.94196 + 3.34991i) q^{30} +(-2.42343 + 4.19751i) q^{31} +(-4.64532 - 0.819095i) q^{32} +(2.07872 + 2.47732i) q^{33} +(-6.33750 - 5.31779i) q^{34} +(-0.259667 + 0.187751i) q^{35} +(5.37609 + 1.95674i) q^{36} +9.49127i q^{37} +(5.01619 + 8.80406i) q^{38} -1.96239 q^{39} +(-0.746138 - 7.25911i) q^{40} +(-0.0325278 - 0.184474i) q^{41} +(0.245943 - 0.293103i) q^{42} +(-7.06701 - 8.42213i) q^{43} +(1.66422 - 9.43825i) q^{44} +(0.270762 - 3.74854i) q^{45} +(-8.36160 - 14.4827i) q^{46} +(1.25532 + 3.44897i) q^{47} +(0.305867 + 0.840363i) q^{48} +(-3.48973 - 6.04439i) q^{49} +(-10.7966 + 4.30463i) q^{50} +(0.709811 - 4.02554i) q^{51} +(3.73823 + 4.45505i) q^{52} +(1.05624 - 1.25878i) q^{53} +(2.17020 + 12.3078i) q^{54} +(-6.26281 + 0.643732i) q^{55} -0.467663 q^{56} +(-2.52800 + 4.32142i) q^{57} -17.6010i q^{58} +(-5.04274 - 1.83541i) q^{59} +(7.08433 - 5.12229i) q^{60} +(7.74681 + 6.50035i) q^{61} +(7.24237 + 8.63112i) q^{62} +(-0.237198 - 0.0418244i) q^{63} +(-6.26121 + 10.8447i) q^{64} +(2.14360 - 3.16236i) q^{65} +(7.06425 - 2.57118i) q^{66} +(-2.05488 - 5.64572i) q^{67} +(-10.4910 + 6.05696i) q^{68} +(4.13141 - 7.15580i) q^{69} +(0.203676 + 0.716500i) q^{70} +(0.414414 - 0.347735i) q^{71} +(3.52578 - 4.20186i) q^{72} +(10.3084 - 1.81765i) q^{73} +(20.7330 + 7.54620i) q^{74} +(-4.50920 - 3.55640i) q^{75} +(14.6262 - 2.49294i) q^{76} +0.403477i q^{77} +(-1.56024 + 4.28672i) q^{78} +(2.01585 + 11.4325i) q^{79} +(-1.68834 - 0.425065i) q^{80} +(-0.867724 + 0.728107i) q^{81} +(-0.428833 - 0.0756149i) q^{82} +(6.57815 + 3.79789i) q^{83} +(-0.280128 - 0.485197i) q^{84} +(5.71172 + 5.54111i) q^{85} +(-24.0163 + 8.74123i) q^{86} +(7.53141 - 4.34826i) q^{87} +(-7.95753 - 4.59428i) q^{88} +(-0.251241 + 1.42486i) q^{89} +(-7.97315 - 3.57181i) q^{90} +(-0.187556 - 0.157378i) q^{91} +(-24.1152 + 4.25217i) q^{92} +(-1.90403 + 5.23127i) q^{93} +8.53210 q^{94} +(-4.20245 - 8.79428i) q^{95} -5.41783 q^{96} +(3.01050 - 8.27128i) q^{97} +(-15.9781 + 2.81738i) q^{98} +(-3.62516 - 3.04187i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 18 q^{4} - 6 q^{5} - 6 q^{6} - 12 q^{9} - 15 q^{10} - 12 q^{11} + 6 q^{14} + 3 q^{15} - 42 q^{16} + 12 q^{19} + 42 q^{20} - 54 q^{21} + 24 q^{24} + 12 q^{25} + 12 q^{26} + 18 q^{30} - 42 q^{31} - 36 q^{34}+ \cdots - 36 q^{99}+O(q^{100}) $ 48 * q - 18 * q^4 - 6 * q^5 - 6 * q^6 - 12 * q^9 - 15 * q^10 - 12 * q^11 + 6 * q^14 + 3 * q^15 - 42 * q^16 + 12 * q^19 + 42 * q^20 - 54 * q^21 + 24 * q^24 + 12 * q^25 + 12 * q^26 + 18 * q^30 - 42 * q^31 - 36 * q^34 + 6 * q^35 + 18 * q^36 - 48 * q^39 + 66 * q^40 + 6 * q^41 - 6 * q^44 - 9 * q^45 - 6 * q^46 + 12 * q^49 - 18 * q^50 + 108 * q^51 + 24 * q^54 + 36 * q^56 - 36 * q^59 - 114 * q^60 + 48 * q^61 - 18 * q^65 + 180 * q^66 + 66 * q^69 - 123 * q^70 - 24 * q^71 + 84 * q^74 + 72 * q^75 + 66 * q^76 + 48 * q^79 - 39 * q^80 - 78 * q^81 - 54 * q^84 - 84 * q^85 - 42 * q^86 - 12 * q^89 + 18 * q^90 - 30 * q^91 - 72 * q^94 - 63 * q^95 - 240 * q^96 - 36 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/95\mathbb{Z}\right)^\times$.

$n$	$21$	$77$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$-1$

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 $

$2$	0.795068	−	2.18443i	0.562198	−	1.54463i	−0.254209	−	0.967149i	$-0.581815\pi$
$2$	0.795068	−	2.18443i	0.562198	−	1.54463i	0.816407	−	0.577477i	$-0.195963\pi$
$3$	1.13113	−	0.199449i	0.653058	−	0.115152i	0.162704	−	0.986675i	$-0.447978\pi$
$3$	1.13113	−	0.199449i	0.653058	−	0.115152i	0.490354	+	0.871523i	$0.336867\pi$
$4$	−2.60752	−	2.18797i	−1.30376	−	1.09398i
$5$	−0.914172	+	2.04066i	−0.408830	+	0.912610i
$5$	−0.914172	+	2.04066i	−0.408830	+	0.912610i
$6$	0.463643	−	2.62945i	0.189282	−	1.07347i
$7$	0.124103	+	0.0716510i	0.0469066	+	0.0270816i	0.523270	−	0.852167i	$-0.324712\pi$
$7$	0.124103	+	0.0716510i	0.0469066	+	0.0270816i	−0.476363	+	0.879249i	$0.658045\pi$
$8$	−2.82626	+	1.63174i	−0.999232	+	0.576907i
$9$	−1.57940	+	0.574856i	−0.526468	+	0.191619i
$10$	3.73085	+	3.61941i	1.17980	+	1.14456i
$11$	1.40779	+	2.43836i	0.424463	+	0.735192i	0.996370	−	0.0851264i	$-0.0271294\pi$
$11$	1.40779	+	2.43836i	0.424463	+	0.735192i	−0.571907	+	0.820319i	$0.693796\pi$
$12$	−3.38583	−	1.95481i	−0.977405	−	0.564305i
$13$	−1.68258	−	0.296685i	−0.466665	−	0.0822856i	−0.0646286	−	0.997909i	$-0.520586\pi$
$13$	−1.68258	−	0.296685i	−0.466665	−	0.0822856i	−0.402036	+	0.915624i	$0.631697\pi$
$14$	0.255187	−	0.214128i	0.0682017	−	0.0572280i
$15$	−0.627041	+	2.49058i	−0.161901	+	0.643065i
$16$	0.135204	+	0.766781i	0.0338011	+	0.191695i
$17$	1.21720	−	3.34424i	0.295215	−	0.811097i	−0.700067	−	0.714077i	$-0.746847\pi$
$17$	1.21720	−	3.34424i	0.295215	−	0.811097i	0.995282	−	0.0970200i	$-0.0309311\pi$
$18$			3.90715i			0.920923i
$19$	−2.82087	+	3.32305i	−0.647153	+	0.762360i
$19$	−2.82087	+	3.32305i	−0.647153	+	0.762360i
$20$	6.84862	−	3.32088i	1.53140	−	0.742571i
$21$	0.154668	+	0.0562944i	0.0337512	+	0.0122844i
$22$	6.44571	−	1.13655i	1.37423	−	0.242314i
$23$	4.62417	−	5.51088i	0.964207	−	1.14910i	−0.0245699	−	0.999698i	$-0.507822\pi$
$23$	4.62417	−	5.51088i	0.964207	−	1.14910i	0.988777	−	0.149399i	$-0.0477339\pi$
$24$	−2.87141	+	2.40940i	−0.586125	+	0.491817i
$25$	−3.32858	−	3.73103i	−0.665716	−	0.746206i
$26$	−1.98586	+	3.43960i	−0.389459	+	0.674562i
$27$	−4.65595	+	2.68812i	−0.896038	+	0.517328i
$28$	−0.166831	−	0.458365i	−0.0315282	−	0.0866229i
$29$	7.11492	−	2.58962i	1.32121	−	0.480880i	0.417363	−	0.908740i	$-0.362954\pi$
$29$	7.11492	−	2.58962i	1.32121	−	0.480880i	0.903845	+	0.427860i	$0.140732\pi$
$30$	4.94196	+	3.34991i	0.902275	+	0.611607i
$31$	−2.42343	+	4.19751i	−0.435261	+	0.753894i	−0.997317	−	0.0732050i	$-0.976677\pi$
$31$	−2.42343	+	4.19751i	−0.435261	+	0.753894i	0.562056	+	0.827099i	$0.310011\pi$
$32$	−4.64532	−	0.819095i	−0.821184	−	0.144797i
$33$	2.07872	+	2.47732i	0.361858	+	0.431246i
$34$	−6.33750	−	5.31779i	−1.08687	−	0.911994i
$35$	−0.259667	+	0.187751i	−0.0438918	+	0.0317357i
$36$	5.37609	+	1.95674i	0.896015	+	0.326123i
$37$			9.49127i			1.56035i	0.625559	+	0.780177i	$0.284871\pi$
$37$			9.49127i			1.56035i	−0.625559	+	0.780177i	$0.715129\pi$
$38$	5.01619	+	8.80406i	0.813734	+	1.42821i
$39$	−1.96239			−0.314235
$40$	−0.746138	−	7.25911i	−0.117975	−	1.14777i
$41$	−0.0325278	−	0.184474i	−0.00507999	−	0.0288100i	0.982162	−	0.188035i	$-0.0602117\pi$
$41$	−0.0325278	−	0.184474i	−0.00507999	−	0.0288100i	−0.987242	+	0.159225i	$0.949101\pi$
$42$	0.245943	−	0.293103i	0.0379498	−	0.0452268i
$43$	−7.06701	−	8.42213i	−1.07771	−	1.28436i	−0.956499	−	0.291736i	$-0.905767\pi$
$43$	−7.06701	−	8.42213i	−1.07771	−	1.28436i	−0.121210	−	0.992627i	$-0.538677\pi$
$44$	1.66422	−	9.43825i	0.250890	−	1.42287i
$45$	0.270762	−	3.74854i	0.0403629	−	0.558799i
$46$	−8.36160	−	14.4827i	−1.23285	−	2.13536i
$47$	1.25532	+	3.44897i	0.183108	+	0.503084i	0.996954	−	0.0779967i	$-0.0248524\pi$
$47$	1.25532	+	3.44897i	0.183108	+	0.503084i	−0.813846	+	0.581080i	$0.802630\pi$
$48$	0.305867	+	0.840363i	0.0441481	+	0.121296i
$49$	−3.48973	−	6.04439i	−0.498533	−	0.863485i
$50$	−10.7966	+	4.30463i	−1.52687	+	0.608766i
$51$	0.709811	−	4.02554i	0.0993934	−	0.563688i
$52$	3.73823	+	4.45505i	0.518399	+	0.617804i
$53$	1.05624	−	1.25878i	0.145086	−	0.172907i	−0.688607	−	0.725134i	$-0.741778\pi$
$53$	1.05624	−	1.25878i	0.145086	−	0.172907i	0.833693	+	0.552228i	$0.186222\pi$
$54$	2.17020	+	12.3078i	0.295327	+	1.67489i
$55$	−6.26281	+	0.643732i	−0.844478	+	0.0868009i
$56$	−0.467663			−0.0624941
$57$	−2.52800	+	4.32142i	−0.334841	+	0.572386i
$58$		−	17.6010i		−	2.31112i
$59$	−5.04274	−	1.83541i	−0.656509	−	0.238950i	−0.00778043	−	0.999970i	$-0.502477\pi$
$59$	−5.04274	−	1.83541i	−0.656509	−	0.238950i	−0.648728	+	0.761020i	$0.724699\pi$
$60$	7.08433	−	5.12229i	0.914583	−	0.661285i
$61$	7.74681	+	6.50035i	0.991878	+	0.832284i	0.985839	−	0.167697i	$-0.0536331\pi$
$61$	7.74681	+	6.50035i	0.991878	+	0.832284i	0.00603938	+	0.999982i	$0.498078\pi$
$62$	7.24237	+	8.63112i	0.919782	+	1.09615i
$63$	−0.237198	−	0.0418244i	−0.0298841	−	0.00526938i
$64$	−6.26121	+	10.8447i	−0.782652	+	1.35559i
$65$	2.14360	−	3.16236i	0.265881	−	0.392242i
$66$	7.06425	−	2.57118i	0.869549	−	0.316490i
$67$	−2.05488	−	5.64572i	−0.251043	−	0.689735i	−0.999643	−	0.0267132i	$-0.991496\pi$
$67$	−2.05488	−	5.64572i	−0.251043	−	0.689735i	0.748600	−	0.663022i	$-0.230726\pi$
$68$	−10.4910	+	6.05696i	−1.27222	+	0.734514i
$69$	4.13141	−	7.15580i	0.497363	−	0.861457i
$70$	0.203676	+	0.716500i	0.0243440	+	0.0856381i
$71$	0.414414	−	0.347735i	0.0491819	−	0.0412685i	−0.617865	−	0.786284i	$-0.712002\pi$
$71$	0.414414	−	0.347735i	0.0491819	−	0.0412685i	0.667047	+	0.745015i	$0.267558\pi$
$72$	3.52578	−	4.20186i	0.415517	−	0.495194i
$73$	10.3084	−	1.81765i	1.20651	−	0.212740i	0.465997	−	0.884786i	$-0.345696\pi$
$73$	10.3084	−	1.81765i	1.20651	−	0.212740i	0.740509	+	0.672047i	$0.234585\pi$
$74$	20.7330	+	7.54620i	2.41016	+	0.877228i
$75$	−4.50920	−	3.55640i	−0.520678	−	0.410657i
$76$	14.6262	−	2.49294i	1.67774	−	0.285960i
$77$			0.403477i			0.0459805i
$78$	−1.56024	+	4.28672i	−0.176662	+	0.485375i
$79$	2.01585	+	11.4325i	0.226801	+	1.28625i	0.859212	+	0.511620i	$0.170954\pi$
$79$	2.01585	+	11.4325i	0.226801	+	1.28625i	−0.632411	+	0.774633i	$0.717935\pi$
$80$	−1.68834	−	0.425065i	−0.188762	−	0.0475237i
$81$	−0.867724	+	0.728107i	−0.0964137	+	0.0809007i
$82$	−0.428833	−	0.0756149i	−0.0473567	−	0.00835027i
$83$	6.57815	+	3.79789i	0.722045	+	0.416873i	0.815505	−	0.578750i	$-0.196459\pi$
$83$	6.57815	+	3.79789i	0.722045	+	0.416873i	−0.0934597	+	0.995623i	$0.529793\pi$
$84$	−0.280128	−	0.485197i	−0.0305645	−	0.0529393i
$85$	5.71172	+	5.54111i	0.619523	+	0.601017i
$86$	−24.0163	+	8.74123i	−2.58975	+	0.942591i
$87$	7.53141	−	4.34826i	0.807452	−	0.466182i
$88$	−7.95753	−	4.59428i	−0.848275	−	0.489752i
$89$	−0.251241	+	1.42486i	−0.0266315	+	0.151035i	−0.995224	−	0.0976195i	$-0.968877\pi$
$89$	−0.251241	+	1.42486i	−0.0266315	+	0.151035i	0.968592	+	0.248654i	$0.0799883\pi$
$90$	−7.97315	−	3.57181i	−0.840444	−	0.376501i
$91$	−0.187556	−	0.157378i	−0.0196612	−	0.0164977i
$92$	−24.1152	+	4.25217i	−2.51419	+	0.443319i
$93$	−1.90403	+	5.23127i	−0.197439	+	0.542458i
$94$	8.53210			0.880019
$95$	−4.20245	−	8.79428i	−0.431162	−	0.902274i
$96$	−5.41783			−0.552955
$97$	3.01050	−	8.27128i	0.305670	−	0.839822i	−0.687818	−	0.725883i	$-0.741431\pi$
$97$	3.01050	−	8.27128i	0.305670	−	0.839822i	0.993488	−	0.113938i	$-0.0363466\pi$
$98$	−15.9781	+	2.81738i	−1.61404	+	0.284598i
$99$	−3.62516	−	3.04187i	−0.364343	−	0.305720i
$100$	0.515958	+	17.0115i	0.0515958	+	1.70115i
$101$	−0.499751	+	2.83423i	−0.0497270	+	0.282016i	−0.999524	−	0.0308509i	$-0.990178\pi$
$101$	−0.499751	+	2.83423i	−0.0497270	+	0.282016i	0.949797	+	0.312867i	$0.101289\pi$
$102$	−8.22916	−	4.75111i	−0.814808	−	0.470430i
$103$	−1.03894	+	0.599832i	−0.102370	+	0.0591032i	−0.550311	−	0.834960i	$-0.685491\pi$
$103$	−1.03894	+	0.599832i	−0.102370	+	0.0591032i	0.447941	+	0.894063i	$0.352157\pi$
$104$	5.23952	−	1.90703i	0.513778	−	0.187000i
$105$	−0.256271	+	0.264161i	−0.0250094	+	0.0257795i
$106$	−1.90994	−	3.30811i	−0.185509	−	0.321312i
$107$	3.54668	+	2.04768i	0.342871	+	0.197957i	0.661541	−	0.749909i	$-0.269903\pi$
$107$	3.54668	+	2.04768i	0.342871	+	0.197957i	−0.318670	+	0.947866i	$0.603236\pi$
$108$	18.0220	+	3.17776i	1.73417	+	0.305780i
$109$	12.4054	−	10.4093i	1.18822	−	0.997034i	0.188331	−	0.982106i	$-0.439692\pi$
$109$	12.4054	−	10.4093i	1.18822	−	0.997034i	0.999889	−	0.0149287i	$-0.00475214\pi$
$110$	−3.57317	+	14.1925i	−0.340689	+	1.35320i
$111$	1.89302	+	10.7359i	0.179678	+	1.01900i
$112$	−0.0381614	+	0.104848i	−0.00360591	+	0.00990716i
$113$		−	3.11845i		−	0.293359i	−0.989184	−	0.146680i	$-0.953141\pi$
$113$		−	3.11845i		−	0.293359i	0.989184	−	0.146680i	$-0.0468586\pi$
$114$	7.42992	+	8.95806i	0.695876	+	0.838999i
$115$	7.01853	+	14.4743i	0.654481	+	1.34973i
$116$	−24.2183	−	8.81474i	−2.24861	−	0.818428i
$117$	2.82803	−	0.498658i	0.261451	−	0.0461009i
$118$	−8.01864	+	9.55625i	−0.738176	+	0.879724i
$119$	0.390677	−	0.327817i	0.0358133	−	0.0300509i
$120$	−2.29180	−	8.06218i	−0.209212	−	0.735973i
$121$	1.53628	−	2.66091i	0.139661	−	0.241901i
$122$	20.3588	−	11.7542i	1.84320	−	1.06417i
$123$	−0.0735863	−	0.202177i	−0.00663506	−	0.0182297i
$124$	15.5031	−	5.64268i	1.39222	−	0.506728i
$125$	10.6566	−	3.38169i	0.953160	−	0.302467i
$126$	−0.279951	+	0.484890i	−0.0249400	+	0.0431974i
$127$	−8.03622	−	1.41700i	−0.713099	−	0.125739i	−0.194682	−	0.980866i	$-0.562367\pi$
$127$	−8.03622	−	1.41700i	−0.713099	−	0.125739i	−0.518417	+	0.855128i	$0.673479\pi$
$128$	12.6475	+	15.0727i	1.11789	+	1.33225i
$129$	−9.67349	−	8.11702i	−0.851703	−	0.714664i
$130$	−5.20364	−	7.19685i	−0.456390	−	0.631205i
$131$	−2.46196	−	0.896079i	−0.215102	−	0.0782908i	0.232222	−	0.972663i	$-0.425401\pi$
$131$	−2.46196	−	0.896079i	−0.215102	−	0.0782908i	−0.447324	+	0.894372i	$0.647623\pi$
$132$		−	11.0078i		−	0.958108i
$133$	−0.588180	+	0.210283i	−0.0510017	+	0.0182338i
$134$	−13.9665			−1.20652
$135$	−1.22918	−	11.9586i	−0.105791	−	1.02923i
$136$	2.01680	+	11.4378i	0.172939	+	0.980786i
$137$	7.91946	−	9.43805i	0.676605	−	0.806347i	−0.313062	−	0.949733i	$-0.601355\pi$
$137$	7.91946	−	9.43805i	0.676605	−	0.806347i	0.989667	+	0.143386i	$0.0457991\pi$
$138$	−12.3466	−	14.7141i	−1.05101	−	1.25255i
$139$	−1.38116	+	7.83292i	−0.117148	+	0.664380i	0.868516	+	0.495661i	$0.165074\pi$
$139$	−1.38116	+	7.83292i	−0.117148	+	0.664380i	−0.985664	+	0.168719i	$0.946037\pi$
$140$	1.08788	+	0.0785791i	0.0919426	+	0.00664115i
$141$	2.10782	+	3.65086i	0.177511	+	0.307458i
$142$	−0.430115	−	1.18173i	−0.0360945	−	0.0991687i
$143$	−1.64529	−	4.52041i	−0.137586	−	0.378016i
$144$	−0.654330	−	1.13333i	−0.0545275	−	0.0944445i
$145$	−1.21974	+	16.8865i	−0.101293	+	1.40235i
$146$	4.22535	−	23.9631i	0.349692	−	1.98320i
$147$	−5.15289	−	6.14097i	−0.425003	−	0.506499i
$148$	20.7666	−	24.7487i	1.70700	−	2.03433i
$149$	0.728662	+	4.13245i	0.0596943	+	0.338543i	0.999998	−	0.00179219i	$-0.000570472\pi$
$149$	0.728662	+	4.13245i	0.0596943	+	0.338543i	−0.940304	+	0.340335i	$0.889459\pi$
$150$	−11.3538	+	7.02247i	−0.927036	+	0.573382i
$151$	−2.86140			−0.232857			−0.116429	−	0.993199i	$-0.537145\pi$
$151$	−2.86140			−0.232857			−0.116429	+	0.993199i	$0.537145\pi$
$152$	2.55015	−	13.9947i	0.206845	−	1.13512i
$153$			5.98161i			0.483585i
$154$	0.881369	+	0.320792i	0.0710227	+	0.0258502i
$155$	−6.35024	−	8.78264i	−0.510064	−	0.705439i
$156$	5.11698	+	4.29366i	0.409686	+	0.343768i
$157$	−7.40771	−	8.82817i	−0.591200	−	0.704565i	0.384636	−	0.923068i	$-0.374327\pi$
$157$	−7.40771	−	8.82817i	−0.591200	−	0.704565i	−0.975836	+	0.218504i	$0.929882\pi$
$158$	26.5762	+	4.68610i	2.11429	+	0.372806i
$159$	0.943685	−	1.63451i	0.0748391	−	0.129625i
$160$	5.91812	−	8.73072i	0.467868	−	0.690224i
$161$	0.968735	−	0.352591i	0.0763470	−	0.0277880i
$162$	0.900600	+	2.47438i	0.0707578	+	0.194405i
$163$	−16.3847	+	9.45974i	−1.28335	+	0.740944i	−0.977460	−	0.211122i	$-0.932288\pi$
$163$	−16.3847	+	9.45974i	−1.28335	+	0.740944i	−0.305892	+	0.952066i	$0.598955\pi$
$164$	−0.318807	+	0.552190i	−0.0248946	+	0.0431188i
$165$	−6.95567	+	1.97726i	−0.541498	+	0.153929i
$166$	13.5263	−	11.3499i	1.04985	−	0.880925i
$167$	−9.68614	+	11.5435i	−0.749536	+	0.893262i	−0.997138	−	0.0755996i	$-0.975913\pi$
$167$	−9.68614	+	11.5435i	−0.749536	+	0.893262i	0.247602	+	0.968862i	$0.420357\pi$
$168$	−0.528988	+	0.0932748i	−0.0408123	+	0.00719631i
$169$	−9.47294	−	3.44787i	−0.728688	−	0.265221i
$170$	16.6454	−	8.07129i	1.27664	−	0.619040i
$171$	2.54502	−	6.87003i	0.194623	−	0.525364i
$172$			37.4233i			2.85350i
$173$	−7.42012	+	20.3866i	−0.564141	+	1.54997i	0.249365	+	0.968410i	$0.419778\pi$
$173$	−7.42012	+	20.3866i	−0.564141	+	1.54997i	−0.813506	+	0.581556i	$0.802444\pi$
$174$	−3.51049	−	19.9090i	−0.266130	−	1.50930i
$175$	−0.145755	−	0.701529i	−0.0110181	−	0.0530306i
$176$	−1.67935	+	1.40914i	−0.126586	+	0.106218i
$177$	−6.07006	−	1.07032i	−0.456254	−	0.0804499i
$178$	2.91275	+	1.68168i	0.218320	+	0.126047i
$179$	11.4395	+	19.8138i	0.855028	+	1.48095i	0.876619	+	0.481185i	$0.159794\pi$
$179$	11.4395	+	19.8138i	0.855028	+	1.48095i	−0.0215906	+	0.999767i	$0.506873\pi$
$180$	−8.90770	+	9.18197i	−0.663941	+	0.684383i
$181$	10.8685	−	3.95580i	0.807847	−	0.294032i	0.0951131	−	0.995466i	$-0.469679\pi$
$181$	10.8685	−	3.95580i	0.807847	−	0.294032i	0.712734	+	0.701434i	$0.247457\pi$
$182$	−0.492903	+	0.284577i	−0.0365364	+	0.0210943i
$183$	10.0591	+	5.80765i	0.743593	+	0.429314i
$184$	−4.07678	+	23.1206i	−0.300544	+	1.70447i
$185$	−19.3684	−	8.67665i	−1.42400	−	0.637920i
$186$	9.91353	+	8.31844i	0.726895	+	0.609937i
$187$	9.86801	−	1.74000i	0.721620	−	0.127241i
$188$	4.27296	−	11.7399i	0.311637	−	0.856217i
$189$	−0.770425			−0.0560402
$190$	−22.5517	+	2.18791i	−1.63608	+	0.158728i
$191$	7.28958			0.527455			0.263728	−	0.964597i	$-0.415048\pi$
$191$	7.28958			0.527455			0.263728	+	0.964597i	$0.415048\pi$
$192$	−4.91928	+	13.5156i	−0.355018	+	0.975404i
$193$	−25.7884	+	4.54719i	−1.85629	+	0.327314i	−0.986198	−	0.165572i	$-0.947053\pi$
$193$	−25.7884	+	4.54719i	−1.85629	+	0.327314i	−0.870094	+	0.492887i	$0.835942\pi$
$194$	−15.6745	−	13.1525i	−1.12536	−	0.944292i
$195$	1.79397	−	4.00458i	0.128469	−	0.286774i
$196$	−4.12540	+	23.3963i	−0.294671	+	1.67116i
$197$	1.98164	+	1.14410i	0.141186	+	0.0815136i	0.568929	−	0.822387i	$-0.307358\pi$
$197$	1.98164	+	1.14410i	0.141186	+	0.0815136i	−0.427743	+	0.903900i	$0.640691\pi$
$198$	−9.52702	+	5.50043i	−0.677056	+	0.390898i
$199$	−11.5083	+	4.18868i	−0.815802	+	0.296928i	−0.716018	−	0.698081i	$-0.754037\pi$
$199$	−11.5083	+	4.18868i	−0.815802	+	0.296928i	−0.0997838	+	0.995009i	$0.531815\pi$
$200$	15.4955	+	5.11347i	1.09570	+	0.361577i
$201$	−3.45036	−	5.97621i	−0.243370	−	0.421529i
$202$	5.79384	+	3.34507i	0.407653	+	0.235359i
$203$	1.06853	+	0.188411i	0.0749964	+	0.0132239i
$204$	−10.6586	+	8.94362i	−0.746251	+	0.626179i
$205$	0.406185	+	0.102263i	0.0283692	+	0.00714237i
$206$	0.484264	+	2.74640i	0.0337403	+	0.191351i
$207$	−4.13548	+	11.3621i	−0.287435	+	0.789722i
$208$		−	1.33029i		−	0.0922388i
$209$	−12.0740	−	2.20015i	−0.835174	−	0.152188i
$210$	0.373289	+	0.769832i	0.0257594	+	0.0531234i
$211$	−2.82198	−	1.02712i	−0.194273	−	0.0707097i	0.243051	−	0.970013i	$-0.421852\pi$
$211$	−2.82198	−	1.02712i	−0.194273	−	0.0707097i	−0.437325	+	0.899304i	$0.644074\pi$
$212$	−5.50834	+	0.971270i	−0.378315	+	0.0667071i
$213$	0.399401	−	0.475987i	0.0273665	−	0.0326141i
$214$	7.29287	−	6.11944i	0.498530	−	0.418316i
$215$	23.6472	−	6.72207i	1.61272	−	0.458441i
$216$	8.77261	−	15.1946i	0.596900	−	1.03386i
$217$	−0.601511	+	0.347283i	−0.0408332	+	0.0235751i
$218$	−12.8754	−	35.3748i	−0.872031	−	2.39589i
$219$	11.2976	−	4.11199i	0.763421	−	0.277863i
$220$	17.7389	+	12.0243i	1.19595	+	0.810678i
$221$	−3.04023	+	5.26583i	−0.204508	+	0.354218i
$222$	24.9568	+	4.40056i	1.67499	+	0.295346i
$223$	−1.41004	−	1.68042i	−0.0944233	−	0.112529i	0.716764	−	0.697316i	$-0.245623\pi$
$223$	−1.41004	−	1.68042i	−0.0944233	−	0.112529i	−0.811187	+	0.584787i	$0.801178\pi$
$224$	−0.517810	−	0.434494i	−0.0345977	−	0.0290309i
$225$	7.40197	+	3.97934i	0.493464	+	0.265290i
$226$	−6.81204	−	2.47938i	−0.453130	−	0.164926i
$227$		−	6.44357i		−	0.427675i	−0.976869	−	0.213838i	$-0.931404\pi$
$227$		−	6.44357i		−	0.427675i	0.976869	−	0.213838i	$-0.0685963\pi$
$228$	16.0469	−	5.73702i	1.06273	−	0.379943i
$229$	1.54321			0.101978			0.0509892	−	0.998699i	$-0.483763\pi$
$229$	1.54321			0.101978			0.0509892	+	0.998699i	$0.483763\pi$
$230$	37.1982	−	3.82347i	2.45278	−	0.252112i
$231$	0.0804731	+	0.456385i	0.00529474	+	0.0300280i
$232$	−15.8830	+	18.9286i	−1.04277	+	1.24273i
$233$	−13.1522	−	15.6742i	−0.861629	−	1.02685i	−0.999338	−	0.0363763i	$-0.988419\pi$
$233$	−13.1522	−	15.6742i	−0.861629	−	1.02685i	0.137710	−	0.990473i	$-0.456026\pi$
$234$	1.15919	−	6.57410i	0.0757787	−	0.429762i
$235$	−8.18575	−	0.591268i	−0.533979	−	0.0385701i
$236$	9.13323	+	15.8192i	0.594522	+	1.02974i
$237$	4.56038	+	12.5295i	0.296229	+	0.813881i
$238$	−0.405479	−	1.11404i	−0.0262833	−	0.0722127i
$239$	3.12033	+	5.40457i	0.201837	+	0.349592i	0.949120	−	0.314913i	$-0.101975\pi$
$239$	3.12033	+	5.40457i	0.201837	+	0.349592i	−0.747283	+	0.664506i	$0.768642\pi$
$240$	−1.99451	−	0.144066i	−0.128745	−	0.00929943i
$241$	−4.56951	+	25.9150i	−0.294348	+	1.66933i	0.375491	+	0.926826i	$0.377474\pi$
$241$	−4.56951	+	25.9150i	−0.294348	+	1.66933i	−0.669839	+	0.742506i	$0.733637\pi$
$242$	−4.59113	−	5.47149i	−0.295129	−	0.351721i
$243$	9.53104	−	11.3586i	0.611416	−	0.728657i
$244$	−5.97741	−	33.8996i	−0.382664	−	2.17020i
$245$	15.5248	−	1.59574i	0.991841	−	0.101948i
$246$	−0.500147			−0.0318882
$247$	5.73226	−	4.75440i	0.364735	−	0.302515i
$248$		−	15.8176i		−	1.00442i
$249$	8.19822	+	2.98391i	0.519541	+	0.189098i
$250$	1.08570	−	25.9674i	0.0686654	−	1.64232i
$251$	−8.20154	−	6.88191i	−0.517677	−	0.434382i	0.346144	−	0.938181i	$-0.387491\pi$
$251$	−8.20154	−	6.88191i	−0.517677	−	0.434382i	−0.863821	+	0.503799i	$0.831935\pi$
$252$	0.526988	+	0.628040i	0.0331971	+	0.0395628i
$253$	19.9473	+	3.51725i	1.25408	+	0.221128i
$254$	−9.48469	+	16.4280i	−0.595122	+	1.03078i
$255$	7.56586	+	5.12852i	0.473792	+	0.321160i
$256$	19.4463	−	7.07788i	1.21540	−	0.442368i
$257$	4.62548	+	12.7084i	0.288529	+	0.792728i	0.996273	+	0.0862582i	$0.0274910\pi$
$257$	4.62548	+	12.7084i	0.288529	+	0.792728i	−0.707744	+	0.706469i	$0.750287\pi$
$258$	−25.4222	+	14.6775i	−1.58271	+	0.913781i
$259$	−0.680059	+	1.17790i	−0.0422568	+	0.0731910i
$260$	−12.5086	+	3.55577i	−0.775752	+	0.220520i
$261$	−9.74867	+	8.18011i	−0.603428	+	0.506336i
$262$	−3.91485	+	4.66553i	−0.241860	+	0.288238i
$263$	−6.44120	+	1.13576i	−0.397181	+	0.0700337i	−0.368671	−	0.929560i	$-0.620187\pi$
$263$	−6.44120	+	1.13576i	−0.397181	+	0.0700337i	−0.0285097	+	0.999594i	$0.509076\pi$
$264$	−9.91732	−	3.60961i	−0.610369	−	0.222156i
$265$	1.60315	+	3.30617i	0.0984810	+	0.203097i
$266$	−0.00829414	+	1.45203i	−0.000508546	+	0.0890295i
$267$			1.66181i			0.101701i
$268$	−6.99454	+	19.2173i	−0.427259	+	1.17389i
$269$	−2.50436	−	14.2029i	−0.152693	−	0.865968i	−0.960864	−	0.277020i	$-0.910653\pi$
$269$	−2.50436	−	14.2029i	−0.152693	−	0.865968i	0.808171	−	0.588948i	$-0.200458\pi$
$270$	−27.1001	−	6.82284i	−1.64926	−	0.415225i
$271$	−1.67326	+	1.40404i	−0.101644	+	0.0852891i	−0.692193	−	0.721712i	$-0.743355\pi$
$271$	−1.67326	+	1.40404i	−0.101644	+	0.0852891i	0.590550	+	0.807001i	$0.298911\pi$
$272$	2.72887	+	0.481173i	0.165462	+	0.0291754i
$273$	−0.243540	−	0.140608i	−0.0147397	−	0.00850996i
$274$	−14.3203	−	24.8034i	−0.865118	−	1.49843i
$275$	4.41165	−	13.3688i	0.266033	−	0.806166i
$276$	−26.4294	+	9.61951i	−1.59086	+	0.579026i
$277$	13.8344	−	7.98732i	0.831231	−	0.479911i	−0.0230432	−	0.999734i	$-0.507336\pi$
$277$	13.8344	−	7.98732i	0.831231	−	0.479911i	0.854274	+	0.519823i	$0.174002\pi$
$278$	16.0124	+	9.24475i	0.960358	+	0.554463i
$279$	1.41461	−	8.02267i	0.0846907	−	0.480305i
$280$	0.427525	−	0.954341i	0.0255495	−	0.0570328i
$281$	−10.9214	−	9.16416i	−0.651517	−	0.546688i	0.256014	−	0.966673i	$-0.417591\pi$
$281$	−10.9214	−	9.16416i	−0.651517	−	0.546688i	−0.907531	+	0.419985i	$0.862035\pi$
$282$	9.65092	−	1.70172i	0.574704	−	0.101336i
$283$	−2.41716	+	6.64111i	−0.143686	+	0.394773i	−0.990571	−	0.137003i	$-0.956253\pi$
$283$	−2.41716	+	6.64111i	−0.143686	+	0.394773i	0.846885	+	0.531776i	$0.178475\pi$
$284$	−1.84142			−0.109268
$285$	−6.50753	−	9.10930i	−0.385473	−	0.539589i
$286$	−11.1826			−0.661244
$287$	0.00918097	−	0.0252245i	0.000541936	−	0.00148896i
$288$	7.80769	−	1.37671i	0.460073	−	0.0811232i
$289$	3.32041	+	2.78616i	0.195318	+	0.163892i
$290$	35.9176	+	16.0903i	2.10915	+	0.944857i
$291$	1.75557	−	9.95634i	0.102913	−	0.583651i
$292$	−30.8563	−	17.8149i	−1.80573	−	1.04254i
$293$	0.845886	−	0.488373i	0.0494172	−	0.0285310i	−0.475088	−	0.879938i	$-0.657584\pi$
$293$	0.845886	−	0.488373i	0.0494172	−	0.0285310i	0.524505	+	0.851407i	$0.324250\pi$
$294$	−17.5114	+	6.37364i	−1.02129	+	0.371718i
$295$	8.35537	−	8.61263i	0.486469	−	0.501447i
$296$	−15.4873	−	26.8247i	−0.900179	−	1.55916i
$297$	−13.1092	−	7.56858i	−0.760671	−	0.439174i
$298$	9.60638	+	1.69386i	0.556483	+	0.0981230i
$299$	−9.41556	+	7.90059i	−0.544516	+	0.456903i
$300$	3.97655	+	19.1394i	0.229586	+	1.10501i
$301$	−0.273584	−	1.55157i	−0.0157691	−	0.0894312i
$302$	−2.27500	+	6.25052i	−0.130912	+	0.359677i
$303$			3.30555i			0.189899i
$304$	−2.92945	−	1.71370i	−0.168015	−	0.0982876i
$305$	−20.3469	+	9.86617i	−1.16506	+	0.564935i
$306$	13.0664	+	4.75579i	0.746958	+	0.271870i
$307$	28.0346	−	4.94325i	1.60002	−	0.282126i	0.698742	−	0.715374i	$-0.253744\pi$
$307$	28.0346	−	4.94325i	1.60002	−	0.282126i	0.901275	+	0.433248i	$0.142633\pi$
$308$	0.882796	−	1.05207i	0.0503020	−	0.0599475i
$309$	−1.05554	+	0.885703i	−0.0600475	+	0.0503859i
$310$	−24.2339	+	6.88887i	−1.37640	+	0.391262i
$311$	12.7730	−	22.1235i	0.724292	−	1.25451i	−0.234972	−	0.972002i	$-0.575500\pi$
$311$	12.7730	−	22.1235i	0.724292	−	1.25451i	0.959265	−	0.282509i	$-0.0911668\pi$
$312$	5.54623	−	3.20212i	0.313993	−	0.181284i
$313$	5.11365	+	14.0496i	0.289041	+	0.794133i	0.996201	+	0.0870798i	$0.0277535\pi$
$313$	5.11365	+	14.0496i	0.289041	+	0.794133i	−0.707161	+	0.707053i	$0.750024\pi$
$314$	−25.1742	+	9.16265i	−1.42066	+	0.517078i
$315$	0.302189	−	0.445806i	0.0170264	−	0.0251183i
$316$	19.7575	−	34.2210i	1.11145	−	1.92508i
$317$	−22.1977	−	3.91406i	−1.24675	−	0.219835i	−0.488943	−	0.872316i	$-0.662617\pi$
$317$	−22.1977	−	3.91406i	−1.24675	−	0.219835i	−0.757805	+	0.652481i	$0.773728\pi$
$318$	−2.82018	−	3.36096i	−0.158148	−	0.188473i
$319$	16.3307	+	13.7031i	0.914344	+	0.767226i
$320$	−16.4066	−	22.6910i	−0.917156	−	1.26846i
$321$	4.42017	+	1.60881i	0.246710	+	0.0897950i
$322$		−	2.39647i		−	0.133550i
$323$	7.67950	+	13.4785i	0.427299	+	0.749964i
$324$	3.85568			0.214204
$325$	4.49367	+	7.26531i	0.249264	+	0.403007i
$326$	7.63716	+	43.3125i	0.422983	+	2.39886i
$327$	11.9560	−	14.2486i	0.661166	−	0.787947i
$328$	0.392946	+	0.468295i	0.0216968	+	0.0258572i
$329$	−0.0913327	+	0.517973i	−0.00503533	+	0.0285568i
$330$	−1.21105	+	16.7662i	−0.0666660	+	0.922950i
$331$	5.43405	+	9.41205i	0.298682	+	0.517333i	0.975835	−	0.218510i	$-0.0701196\pi$
$331$	5.43405	+	9.41205i	0.298682	+	0.517333i	−0.677152	+	0.735843i	$0.736786\pi$
$332$	−8.84297	−	24.2959i	−0.485321	−	1.33341i
$333$	−5.45611	−	14.9905i	−0.298993	−	0.821476i
$334$	17.5148	+	30.3366i	0.958369	+	1.65994i
$335$	13.3995	+	0.967865i	0.732093	+	0.0528801i
$336$	−0.0222538	+	0.126207i	−0.00121404	+	0.00688518i
$337$	4.95529	+	5.90548i	0.269932	+	0.321692i	0.883934	−	0.467612i	$-0.154886\pi$
$337$	4.95529	+	5.90548i	0.269932	+	0.321692i	−0.614002	+	0.789305i	$0.710441\pi$
$338$	−15.0633	+	17.9517i	−0.819333	+	0.976443i
$339$	−0.621971	−	3.52737i	−0.0337808	−	0.191581i
$340$	−2.76964	−	26.9456i	−0.150205	−	1.46133i
$341$	−13.6467			−0.739010
$342$	−12.9836	−	11.0216i	−0.702075	−	0.595978i
$343$		−	2.00329i		−	0.108167i
$344$	33.7159	+	12.2716i	1.81784	+	0.661639i
$345$	10.8257	+	14.9724i	0.582838	+	0.806088i
$346$	38.6337	+	32.4175i	2.07696	+	1.74278i
$347$	13.0292	+	15.5276i	0.699445	+	0.833566i	0.992464	−	0.122540i	$-0.0391041\pi$
$347$	13.0292	+	15.5276i	0.699445	+	0.833566i	−0.293018	+	0.956107i	$0.594660\pi$
$348$	−29.1521	−	5.14031i	−1.56272	−	0.275549i
$349$	9.52515	−	16.4981i	0.509870	−	0.883120i	−0.490065	−	0.871686i	$-0.663027\pi$
$349$	9.52515	−	16.4981i	0.509870	−	0.883120i	0.999935	−	0.0114345i	$-0.00363978\pi$
$350$	−1.64833	−	0.239371i	−0.0881068	−	0.0127949i
$351$	8.63155	−	3.14163i	0.460718	−	0.167688i
$352$	−4.54237	−	12.4801i	−0.242109	−	0.665189i
$353$	15.7328	−	9.08336i	0.837375	−	0.483459i	−0.0189962	−	0.999820i	$-0.506047\pi$
$353$	15.7328	−	9.08336i	0.837375	−	0.483459i	0.856371	+	0.516361i	$0.172714\pi$
$354$	−7.16414	+	12.4087i	−0.380770	+	0.659513i
$355$	0.330762	+	1.16357i	0.0175550	+	0.0617557i
$356$	3.77266	−	3.16564i	0.199951	−	0.167778i
$357$	0.376524	−	0.448724i	0.0199278	−	0.0237490i
$358$	52.3771	−	9.23549i	2.76821	−	0.488111i
$359$	−15.1590	−	5.51741i	−0.800060	−	0.291198i	−0.0905485	−	0.995892i	$-0.528862\pi$
$359$	−15.1590	−	5.51741i	−0.800060	−	0.291198i	−0.709511	+	0.704694i	$0.751084\pi$
$360$	5.35139	+	11.0361i	0.282043	+	0.581656i
$361$	−3.08534	−	18.7478i	−0.162387	−	0.986727i
$362$		−	26.8866i		−	1.41313i
$363$	1.20701	−	3.31624i	0.0633518	−	0.174058i
$364$	0.144718	+	0.820735i	0.00758527	+	0.0430182i
$365$	−5.71445	+	22.6975i	−0.299108	+	1.18804i
$366$	20.6841	−	17.3560i	1.08118	−	0.907214i
$367$	−31.7715	−	5.60217i	−1.65846	−	0.292431i	−0.735555	−	0.677465i	$-0.763079\pi$
$367$	−31.7715	−	5.60217i	−1.65846	−	0.292431i	−0.922902	+	0.385034i	$0.874190\pi$
$368$	4.85084	+	2.80064i	0.252868	+	0.145993i
$369$	0.157421	+	0.272660i	0.00819499	+	0.0141941i
$370$	−34.3528	+	35.4105i	−1.78592	+	1.84090i
$371$	0.221276	−	0.0805379i	0.0114881	−	0.00418132i
$372$	16.4106	−	9.47469i	0.850853	−	0.491240i
$373$	−2.06146	−	1.19018i	−0.106738	−	0.0616253i	0.445681	−	0.895192i	$-0.352962\pi$
$373$	−2.06146	−	1.19018i	−0.106738	−	0.0616253i	−0.552419	+	0.833567i	$0.686295\pi$
$374$	4.04484	−	22.9394i	0.209153	−	1.18617i
$375$	11.3796	−	5.95058i	0.587639	−	0.307287i
$376$	−9.17568	−	7.69931i	−0.473199	−	0.397061i
$377$	−12.7398	+	2.24636i	−0.656131	+	0.115694i
$378$	−0.612540	+	1.68294i	−0.0315057	+	0.0865611i
$379$	−17.7215			−0.910291			−0.455145	−	0.890417i	$-0.650413\pi$
$379$	−17.7215			−0.910291			−0.455145	+	0.890417i	$0.650413\pi$
$380$	−8.28364	+	32.1261i	−0.424942	+	1.64803i
$381$	−9.37263			−0.480174
$382$	5.79571	−	15.9236i	0.296534	−	0.814722i
$383$	−10.5025	+	1.85188i	−0.536655	+	0.0946268i	−0.435406	−	0.900234i	$-0.643395\pi$
$383$	−10.5025	+	1.85188i	−0.536655	+	0.0946268i	−0.101249	+	0.994861i	$0.532284\pi$
$384$	17.3121	+	14.5266i	0.883457	+	0.741308i
$385$	−0.823360	−	0.368848i	−0.0419623	−	0.0187982i
$386$	−10.5705	+	59.9484i	−0.538025	+	3.05129i
$387$	16.0032	+	9.23943i	0.813486	+	0.469667i
$388$	−25.9472	+	14.9806i	−1.31727	+	0.760527i
$389$	21.3605	−	7.77458i	1.08302	−	0.394187i	0.261989	−	0.965071i	$-0.415622\pi$
$389$	21.3605	−	7.77458i	1.08302	−	0.394187i	0.821031	+	0.570884i	$0.193400\pi$
$390$	−7.32140	−	7.10271i	−0.370733	−	0.359660i
$391$	−12.8011	−	22.1722i	−0.647381	−	1.12130i
$392$	19.7257	+	11.3887i	0.996301	+	0.575214i
$393$	−2.96351	−	0.522548i	−0.149490	−	0.0263590i
$394$	4.07474	−	3.41911i	0.205282	−	0.172252i
$395$	−25.1726	−	6.33758i	−1.26657	−	0.318878i
$396$	2.79716	+	15.8635i	0.140563	+	0.797170i
$397$	6.99106	−	19.2078i	0.350871	−	0.964011i	−0.631220	−	0.775604i	$-0.717445\pi$
$397$	6.99106	−	19.2078i	0.350871	−	0.964011i	0.982091	−	0.188407i	$-0.0603323\pi$
$398$			28.4694i			1.42704i
$399$	−0.623367	+	0.355169i	−0.0312074	+	0.0177807i
$400$	2.41084	−	3.05674i	0.120542	−	0.152837i
$401$	−15.6902	−	5.71077i	−0.783531	−	0.285182i	−0.0808870	−	0.996723i	$-0.525775\pi$
$401$	−15.6902	−	5.71077i	−0.783531	−	0.285182i	−0.702644	+	0.711541i	$0.747998\pi$
$402$	−15.7979	+	2.78559i	−0.787927	+	0.138933i
$403$	5.32296	−	6.34366i	0.265156	−	0.316000i
$404$	7.50431	−	6.29686i	0.373353	−	0.313281i
$405$	−0.692568	−	2.43634i	−0.0344140	−	0.121063i
$406$	1.26113	−	2.18434i	0.0625888	−	0.108407i
$407$	−23.1431	+	13.3617i	−1.14716	+	0.662313i
$408$	4.56252	+	12.5354i	0.225878	+	0.620596i
$409$	−16.6181	+	6.04849i	−0.821712	+	0.299079i	−0.718453	−	0.695576i	$-0.755149\pi$
$409$	−16.6181	+	6.04849i	−0.821712	+	0.299079i	−0.103259	+	0.994655i	$0.532927\pi$
$410$	0.546332	−	0.805977i	0.0269814	−	0.0398044i
$411$	7.07553	−	12.2552i	0.349010	−	0.604504i
$412$	4.02147	+	0.709093i	0.198123	+	0.0349345i
$413$	−0.494312	−	0.589098i	−0.0243235	−	0.0289876i
$414$	21.5318	+	18.0673i	1.05823	+	0.887961i
$415$	−13.7638	+	9.95182i	−0.675637	+	0.488516i
$416$	7.57313	+	2.75639i	0.371303	+	0.135143i
$417$			9.13552i			0.447369i
$418$	−14.4057	+	24.6255i	−0.704606	+	1.20447i
$419$	37.9339			1.85319			0.926596	−	0.376059i	$-0.122721\pi$
$419$	37.9339			1.85319			0.926596	+	0.376059i	$0.122721\pi$
$420$	1.24621	−	0.128093i	0.0608086	−	0.00625030i
$421$	2.01122	+	11.4062i	0.0980211	+	0.555905i	0.993780	+	0.111364i	$0.0355221\pi$
$421$	2.01122	+	11.4062i	0.0980211	+	0.555905i	−0.895759	+	0.444541i	$0.853367\pi$
$422$	−4.48734	+	5.34780i	−0.218440	+	0.260327i
$423$	−3.96532	−	4.72568i	−0.192800	−	0.229770i
$424$	−0.931209	+	5.28115i	−0.0452235	+	0.256475i
$425$	−16.5290	+	6.59014i	−0.801774	+	0.319669i
$426$	−0.722211	−	1.25091i	−0.0349912	−	0.0606066i
$427$	0.495648	+	1.36178i	0.0239861	+	0.0659012i
$428$	−4.76779	−	13.0994i	−0.230460	−	0.633183i
$429$	−2.76263	−	4.78502i	−0.133381	−	0.231023i
$430$	4.11720	−	57.0001i	0.198549	−	2.74879i
$431$	5.52023	−	31.3068i	0.265900	−	1.50800i	−0.500559	−	0.865702i	$-0.666872\pi$
$431$	5.52023	−	31.3068i	0.265900	−	1.50800i	0.766459	−	0.642293i	$-0.222017\pi$
$432$	−2.69070	−	3.20665i	−0.129456	−	0.154280i
$433$	2.62802	−	3.13196i	0.126295	−	0.150512i	−0.699192	−	0.714934i	$-0.746457\pi$
$433$	2.62802	−	3.13196i	0.126295	−	0.150512i	0.825486	+	0.564422i	$0.190901\pi$
$434$	0.280373	+	1.59007i	0.0134583	+	0.0763260i
$435$	1.98831	+	19.3441i	0.0953322	+	0.927478i
$436$	−55.1226			−2.63989
$437$	5.26872	+	30.9119i	0.252037	+	1.47871i
$438$		−	27.9481i		−	1.33541i
$439$	−11.0468	−	4.02069i	−0.527233	−	0.191897i	0.0646692	−	0.997907i	$-0.479401\pi$
$439$	−11.0468	−	4.02069i	−0.527233	−	0.191897i	−0.591903	+	0.806009i	$0.701623\pi$
$440$	16.6499	−	12.0386i	0.793753	−	0.573919i
$441$	8.98635	+	7.54044i	0.427921	+	0.359069i
$442$	9.08566	+	10.8279i	0.432161	+	0.515029i
$443$	−7.76677	−	1.36949i	−0.369010	−	0.0650665i	−0.0139318	−	0.999903i	$-0.504435\pi$
$443$	−7.76677	−	1.36949i	−0.369010	−	0.0650665i	−0.355079	+	0.934836i	$0.615546\pi$
$444$	18.5536	−	32.1358i	0.880516	−	1.52510i
$445$	−2.67797	−	1.81526i	−0.126948	−	0.0860517i
$446$	−4.79184	+	1.74409i	−0.226900	+	0.0825850i
$447$	1.64842	+	4.52900i	0.0779677	+	0.214215i
$448$	−1.55407	+	0.897245i	−0.0734231	+	0.0423908i
$449$	−0.580397	+	1.00528i	−0.0273906	+	0.0474419i	−0.879396	−	0.476091i	$-0.842053\pi$
$449$	−0.580397	+	1.00528i	−0.0273906	+	0.0474419i	0.852005	+	0.523533i	$0.175386\pi$
$450$	14.5777	−	13.0052i	0.687198	−	0.613073i
$451$	0.404022	−	0.339015i	0.0190247	−	0.0159636i
$452$	−6.82307	+	8.13142i	−0.320930	+	0.382470i
$453$	−3.23661	+	0.570702i	−0.152069	+	0.0268139i
$454$	−14.0755	−	5.12308i	−0.660598	−	0.240438i
$455$	0.492615	−	0.238867i	0.0230941	−	0.0111983i
$456$	0.0933272	−	16.3385i	0.00437045	−	0.765119i
$457$		−	38.6888i		−	1.80978i	−0.425641	−	0.904892i	$-0.639951\pi$
$457$		−	38.6888i		−	1.80978i	0.425641	−	0.904892i	$-0.360049\pi$
$458$	1.22696	−	3.37105i	0.0573321	−	0.157519i
$459$	3.32246	+	18.8426i	0.155079	+	0.879497i
$460$	13.3683	−	53.0982i	0.623299	−	2.47572i
$461$	−18.7676	+	15.7479i	−0.874096	+	0.733453i	−0.964956	−	0.262410i	$-0.915483\pi$
$461$	−18.7676	+	15.7479i	−0.874096	+	0.733453i	0.0908609	+	0.995864i	$0.471038\pi$
$462$	1.06092	+	0.187070i	0.0493587	+	0.00870326i
$463$	28.1328	+	16.2425i	1.30744	+	0.754852i	0.981669	−	0.190596i	$-0.0610421\pi$
$463$	28.1328	+	16.2425i	1.30744	+	0.754852i	0.325773	+	0.945448i	$0.394375\pi$
$464$	2.94764	+	5.10546i	0.136841	+	0.237015i
$465$	−8.93464	−	8.66776i	−0.414334	−	0.401958i
$466$	−44.6960	+	16.2680i	−2.07050	+	0.753602i
$467$	−12.7323	+	7.35099i	−0.589180	+	0.340163i	−0.764773	−	0.644299i	$-0.777149\pi$
$467$	−12.7323	+	7.35099i	−0.589180	+	0.340163i	0.175593	+	0.984463i	$0.443816\pi$
$468$	−8.46518	−	4.88738i	−0.391303	−	0.225919i
$469$	0.149505	−	0.847887i	0.00690351	−	0.0391518i
$470$	−7.79981	+	17.4111i	−0.359779	+	0.803115i
$471$	−10.1399	−	8.50835i	−0.467220	−	0.392044i
$472$	17.2470	−	3.04111i	0.793856	−	0.139978i
$473$	10.5873	−	29.0885i	0.486806	−	1.33749i
$474$	30.9957			1.42368
$475$	21.7879	−	0.536276i	0.999697	−	0.0246060i
$476$	−1.73595			−0.0795672
$477$	−0.944615	+	2.59531i	−0.0432510	+	0.118831i
$478$	14.2868	−	2.51915i	0.653462	−	0.115223i
$479$	10.1268	+	8.49741i	0.462706	+	0.388256i	0.844125	−	0.536146i	$-0.180120\pi$
$479$	10.1268	+	8.49741i	0.462706	+	0.388256i	−0.381420	+	0.924402i	$0.624565\pi$
$480$	4.95283	−	11.0559i	0.226065	−	0.504632i
$481$	2.81592	−	15.9699i	0.128395	−	0.728162i
$482$	52.9765	+	30.5860i	2.41301	+	1.39315i
$483$	1.02544	−	0.592039i	0.0466592	−	0.0269387i
$484$	−9.82785	+	3.57705i	−0.446721	+	0.162593i
$485$	14.1268	+	13.7048i	0.641463	+	0.622302i
$486$	−17.2344	−	29.8508i	−0.781767	−	1.35406i
$487$	−8.36642	−	4.83036i	−0.379119	−	0.218884i	0.298316	−	0.954467i	$-0.403575\pi$
$487$	−8.36642	−	4.83036i	−0.379119	−	0.218884i	−0.677435	+	0.735583i	$0.736908\pi$
$488$	−32.5013	−	5.73086i	−1.47127	−	0.259424i
$489$	−16.6465	+	13.9681i	−0.752783	+	0.631660i
$490$	8.85747	−	35.1815i	0.400140	−	1.58934i
$491$	0.466479	+	2.64553i	0.0210519	+	0.119391i	0.993523	−	0.113633i	$-0.0362489\pi$
$491$	0.466479	+	2.64553i	0.0210519	+	0.119391i	−0.972471	+	0.233024i	$0.925138\pi$
$492$	−0.250479	+	0.688184i	−0.0112924	+	0.0310257i
$493$		−	26.9461i		−	1.21359i
$494$	−5.82813	−	16.3018i	−0.262220	−	0.733452i
$495$	9.52145	−	4.61693i	0.427957	−	0.207515i
$496$	−3.54623	−	1.29072i	−0.159230	−	0.0579551i
$497$	0.0763457	−	0.0134618i	0.00342457	−	0.000603844i
$498$	13.0363	−	15.5360i	0.584170	−	0.696187i
$499$	−1.80438	+	1.51406i	−0.0807753	+	0.0677786i	−0.682281	−	0.731090i	$-0.739012\pi$
$499$	−1.80438	+	1.51406i	−0.0807753	+	0.0677786i	0.601506	+	0.798868i	$0.294568\pi$
$500$	−35.1864	−	14.4986i	−1.57359	−	0.648397i
$501$	−8.65395	+	14.9891i	−0.386630	+	0.669663i
$502$	−21.5538	+	12.4441i	−0.961995	+	0.555408i
$503$	−4.69900	−	12.9104i	−0.209518	−	0.575646i	0.789769	−	0.613405i	$-0.210201\pi$
$503$	−4.69900	−	12.9104i	−0.209518	−	0.575646i	−0.999287	+	0.0377584i	$0.987978\pi$
$504$	0.738629	−	0.268839i	0.0329011	−	0.0119750i
$505$	−5.32683	−	3.61079i	−0.237041	−	0.160678i
$506$	23.5427	−	40.7771i	1.04660	−	1.81276i
$507$	−11.4028	−	2.01062i	−0.506416	−	0.0892948i
$508$	17.8542	+	21.2779i	0.792154	+	0.944052i
$509$	27.8684	+	23.3844i	1.23524	+	1.03649i	0.997881	+	0.0650727i	$0.0207279\pi$
$509$	27.8684	+	23.3844i	1.23524	+	1.03649i	0.237364	+	0.971421i	$0.423717\pi$
$510$	17.2183	−	12.4496i	0.762438	−	0.551277i
$511$	1.40954	+	0.513031i	0.0623544	+	0.0226952i
$512$		−	8.75464i		−	0.386904i
$513$	4.20111	−	23.0548i	0.185483	−	1.01789i
$514$	31.4382			1.38668
$515$	−0.274283	−	2.66847i	−0.0120863	−	0.117587i
$516$	7.46402	+	42.3306i	0.328585	+	1.86350i
$517$	−6.64259	+	7.91633i	−0.292141	+	0.348160i
$518$	2.03234	+	2.42205i	0.0892960	+	0.106419i
$519$	−4.32704	+	24.5398i	−0.189936	+	1.07718i
$520$	−0.898229	+	12.4354i	−0.0393899	+	0.545330i
$521$	−0.290212	−	0.502661i	−0.0127144	−	0.0220220i	0.859598	−	0.510971i	$-0.170714\pi$
$521$	−0.290212	−	0.502661i	−0.0127144	−	0.0220220i	−0.872313	+	0.488949i	$0.837381\pi$
$522$	10.1180	+	27.7990i	0.442854	+	1.21673i
$523$	6.58262	+	18.0856i	0.287838	+	0.790828i	0.996368	+	0.0851478i	$0.0271363\pi$
$523$	6.58262	+	18.0856i	0.287838	+	0.790828i	−0.708530	+	0.705680i	$0.750642\pi$
$524$	4.45901	+	7.72322i	0.194793	+	0.337391i
$525$	−0.304787	−	0.764450i	−0.0133020	−	0.0333633i
$526$	−2.64021	+	14.9734i	−0.115118	+	0.652869i
$527$	11.0876	+	13.2137i	0.482986	+	0.575600i
$528$	−1.61851	+	1.92886i	−0.0704366	+	0.0839431i
$529$	−4.99286	−	28.3159i	−0.217081	−	1.23113i
$530$	8.49673	−	0.873348i	0.369074	−	0.0379358i
$531$	9.01961			0.391418
$532$	1.99378	+	0.738602i	0.0864414	+	0.0320224i
$533$			0.320044i			0.0138626i
$534$	3.63011	+	1.32125i	0.157090	+	0.0571762i
$535$	−7.42089	+	5.36564i	−0.320833	+	0.231977i
$536$	15.0200	+	12.6032i	0.648763	+	0.544377i
$537$	16.8914	+	20.1304i	0.728918	+	0.868690i
$538$	−33.0165	−	5.82169i	−1.42344	−	0.250991i
$539$	9.82559	−	17.0184i	0.423218	−	0.733036i
$540$	−22.9599	+	33.8717i	−0.988039	+	1.45761i
$541$	29.9824	−	10.9127i	1.28904	−	0.469174i	0.395631	−	0.918410i	$-0.370526\pi$
$541$	29.9824	−	10.9127i	1.28904	−	0.469174i	0.893413	+	0.449236i	$0.148304\pi$
$542$	1.73666	+	4.77143i	0.0745959	+	0.204951i
$543$	11.5047	−	6.64223i	0.493713	−	0.285045i
$544$	−8.39355	+	14.5380i	−0.359870	+	0.623314i
$545$	9.90127	+	34.8311i	0.424124	+	1.49200i
$546$	−0.500778	+	0.420203i	−0.0214313	+	0.0179830i
$547$	2.20766	−	2.63099i	0.0943929	−	0.112493i	−0.716780	−	0.697299i	$-0.754385\pi$
$547$	2.20766	−	2.63099i	0.0943929	−	0.112493i	0.811173	+	0.584806i	$0.198829\pi$
$548$	−41.3003	+	7.28235i	−1.76426	+	0.311087i
$549$	−15.9721	−	5.81337i	−0.681673	−	0.248109i
$550$	−25.6956	−	20.2660i	−1.09566	−	0.864146i
$551$	−11.4649	+	30.9482i	−0.488419	+	1.31844i
$552$			26.9655i			1.14773i
$553$	−0.568974	+	1.56324i	−0.0241952	+	0.0664759i
$554$	−6.44843	−	36.5708i	−0.273967	−	1.55375i
$555$	−23.6388	−	5.95141i	−1.00341	−	0.252623i
$556$	20.7396	−	17.4026i	0.879554	−	0.738033i
$557$	6.72634	+	1.18604i	0.285004	+	0.0502539i	0.314323	−	0.949316i	$-0.398223\pi$
$557$	6.72634	+	1.18604i	0.285004	+	0.0502539i	−0.0293185	+	0.999570i	$0.509334\pi$
$558$	−16.4003	−	9.46870i	−0.694279	−	0.400842i
$559$	9.39211	+	16.2676i	0.397244	+	0.688047i
$560$	−0.179072	−	0.173723i	−0.00756717	−	0.00734114i
$561$	10.8150	−	3.93632i	0.456608	−	0.166192i
$562$	−28.7018	+	16.5710i	−1.21071	+	0.699004i
$563$	−10.8797	−	6.28141i	−0.458526	−	0.264730i	0.252898	−	0.967493i	$-0.418616\pi$
$563$	−10.8797	−	6.28141i	−0.458526	−	0.264730i	−0.711424	+	0.702763i	$0.751949\pi$
$564$	2.49177	−	14.1315i	0.104922	−	0.595045i
$565$	6.36369	+	2.85080i	0.267723	+	0.119934i
$566$	12.5852	+	10.5603i	0.528997	+	0.443881i
$567$	−0.159857	+	0.0281871i	−0.00671336	+	0.00118375i
$568$	−0.603827	+	1.65900i	−0.0253360	+	0.0696102i
$569$	−3.47978			−0.145880			−0.0729400	−	0.997336i	$-0.523238\pi$
$569$	−3.47978			−0.145880			−0.0729400	+	0.997336i	$0.523238\pi$
$570$	−25.0726	+	6.97273i	−1.05017	+	0.292055i
$571$	−0.621524			−0.0260100			−0.0130050	−	0.999915i	$-0.504140\pi$
$571$	−0.621524			−0.0260100			−0.0130050	+	0.999915i	$0.504140\pi$
$572$	−5.60037	+	15.3869i	−0.234163	+	0.643359i
$573$	8.24546	−	1.45390i	0.344459	−	0.0607374i
$574$	−0.0478017	−	0.0401104i	−0.00199521	−	0.00167418i
$575$	−35.9532	+	1.09045i	−1.49935	+	0.0454751i
$576$	3.65482	−	20.7275i	0.152284	−	0.863646i
$577$	−3.33567	−	1.92585i	−0.138866	−	0.0801742i	0.428958	−	0.903325i	$-0.358881\pi$
$577$	−3.33567	−	1.92585i	−0.138866	−	0.0801742i	−0.567823	+	0.823150i	$0.692214\pi$
$578$	8.72612	−	5.03803i	0.362959	−	0.209554i
$579$	−28.2631	+	10.2869i	−1.17458	+	0.427510i
$580$	40.1276	−	41.3631i	1.66621	−	1.71751i
$581$	0.544246	+	0.942662i	0.0225791	+	0.0391082i
$582$	−20.3531	−	11.7509i	−0.843665	−	0.487090i
$583$	4.55632	+	0.803402i	0.188704	+	0.0332735i
$584$	−26.1682	+	21.9577i	−1.08285	+	0.908618i
$585$	−1.56772	+	6.22690i	−0.0648171	+	0.257451i
$586$	−0.394279	−	2.23607i	−0.0162875	−	0.0923712i
$587$	13.8290	−	37.9949i	0.570784	−	1.56822i	−0.232485	−	0.972600i	$-0.574686\pi$
$587$	13.8290	−	37.9949i	0.570784	−	1.56822i	0.803269	−	0.595616i	$-0.203092\pi$
$588$			27.2871i			1.12530i
$589$	−7.11233	−	19.8938i	−0.293059	−	0.819710i
$590$	−12.1706	−	25.0994i	−0.501056	−	1.03332i
$591$	2.46968	+	0.898889i	0.101589	+	0.0369753i
$592$	−7.27772	+	1.28326i	−0.299113	+	0.0527416i
$593$	−3.77549	+	4.49946i	−0.155041	+	0.184771i	−0.837974	−	0.545711i	$-0.816260\pi$
$593$	−3.77549	+	4.49946i	−0.155041	+	0.184771i	0.682933	+	0.730481i	$0.260704\pi$
$594$	−26.9557	+	22.6185i	−1.10601	+	0.928050i
$595$	0.311816	+	1.09692i	0.0127832	+	0.0449693i
$596$	7.14166	−	12.3697i	0.292534	−	0.506684i
$597$	−12.1820	+	7.03326i	−0.498575	+	0.287852i
$598$	9.77229	+	26.8491i	0.399619	+	1.09794i
$599$	−12.5080	+	4.55254i	−0.511063	+	0.186012i	−0.584663	−	0.811276i	$-0.698773\pi$
$599$	−12.5080	+	4.55254i	−0.511063	+	0.186012i	0.0736001	+	0.997288i	$0.476551\pi$
$600$	18.5473	+	2.69344i	0.757189	+	0.109959i
$601$	−2.58008	+	4.46883i	−0.105244	+	0.182287i	−0.913838	−	0.406079i	$-0.866896\pi$
$601$	−2.58008	+	4.46883i	−0.105244	+	0.182287i	0.808594	+	0.588367i	$0.200229\pi$
$602$	−3.60682	−	0.635980i	−0.147003	−	0.0259206i
$603$	6.49095	+	7.73561i	0.264332	+	0.315019i
$604$	7.46114	+	6.26064i	0.303590	+	0.254742i
$605$	4.02559	+	5.56755i	0.163663	+	0.226353i
$606$	7.22076	+	2.62814i	0.293323	+	0.106761i
$607$			30.5069i			1.23824i	0.785297	+	0.619119i	$0.212510\pi$
$607$			30.5069i			1.23824i	−0.785297	+	0.619119i	$0.787490\pi$
$608$	15.8258	−	13.1261i	0.641819	−	0.532333i
$609$	1.24623			0.0504998
$610$	5.37478	+	52.2907i	0.217618	+	2.11719i
$611$	−1.08893	−	6.17561i	−0.0440533	−	0.249839i
$612$	13.0876	−	15.5972i	0.529034	−	0.630478i
$613$	29.2473	+	34.8556i	1.18129	+	1.40780i	0.892879	+	0.450297i	$0.148682\pi$
$613$	29.2473	+	34.8556i	1.18129	+	1.40780i	0.288409	+	0.957507i	$0.406874\pi$
$614$	11.4912	−	65.1698i	0.463747	−	2.63004i
$615$	0.479844	+	0.0346598i	0.0193492	+	0.00139762i
$616$	−0.658370	−	1.14033i	−0.0265265	−	0.0459452i
$617$	−0.849053	−	2.33275i	−0.0341816	−	0.0939131i	0.921428	−	0.388549i	$-0.127024\pi$
$617$	−0.849053	−	2.33275i	−0.0341816	−	0.0939131i	−0.955609	+	0.294636i	$0.904802\pi$
$618$	1.09553	+	3.00995i	0.0440687	+	0.121078i
$619$	11.7473	+	20.3469i	0.472162	+	0.817809i	0.999493	−	0.0318512i	$-0.0101403\pi$
$619$	11.7473	+	20.3469i	0.472162	+	0.817809i	−0.527330	+	0.849660i	$0.676807\pi$
$620$	−2.65776	+	36.7950i	−0.106738	+	1.47772i
$621$	−6.71606	+	38.0887i	−0.269506	+	1.52845i
$622$	−38.1719	−	45.4915i	−1.53056	−	1.82404i
$623$	−0.133272	+	0.158828i	−0.00533945	+	0.00636330i
$624$	−0.265324	−	1.50473i	−0.0106215	−	0.0602373i
$625$	−2.84114	+	24.8380i	−0.113646	+	0.993521i
$626$	34.7562			1.38914
$627$	−14.0961	−	0.0805182i	−0.562942	−	0.00321559i
$628$			39.2275i			1.56535i
$629$	31.7410	+	11.5528i	1.26560	+	0.460640i
$630$	−0.733571	−	1.01456i	−0.0292262	−	0.0404209i
$631$	−13.6507	−	11.4543i	−0.543426	−	0.455989i	0.329282	−	0.944232i	$-0.393193\pi$
$631$	−13.6507	−	11.4543i	−0.543426	−	0.455989i	−0.872708	+	0.488243i	$0.837638\pi$
$632$	−24.3521	−	29.0217i	−0.968675	−	1.15442i
$633$	−3.39689	−	0.598963i	−0.135014	−	0.0238066i
$634$	−26.1987	+	45.3774i	−1.04048	+	1.80217i
$635$	10.2381	−	15.1038i	0.406287	−	0.599376i
$636$	−6.03693	+	2.19726i	−0.239380	+	0.0871272i
$637$	4.07849	+	11.2056i	0.161596	+	0.443980i
$638$	42.9175	−	24.7784i	1.69912	−	0.980987i
$639$	−0.454629	+	0.787441i	−0.0179849	+	0.0311507i
$640$	−42.3201	+	12.0301i	−1.67285	+	0.475533i
$641$	28.6984	−	24.0808i	1.13352	−	0.951135i	0.134311	−	0.990939i	$-0.457118\pi$
$641$	28.6984	−	24.0808i	1.13352	−	0.951135i	0.999207	+	0.0398045i	$0.0126735\pi$
$642$	7.02867	−	8.37644i	0.277399	−	0.330592i
$643$	−19.5865	+	3.45362i	−0.772415	+	0.136198i	−0.545946	−	0.837821i	$-0.683829\pi$
$643$	−19.5865	+	3.45362i	−0.772415	+	0.136198i	−0.226469	+	0.974018i	$0.572718\pi$
$644$	−3.29745	−	1.20017i	−0.129938	−	0.0472935i
$645$	25.4073	−	12.3199i	1.00041	−	0.485097i
$646$	35.5486	−	6.05901i	1.39864	−	0.238389i
$647$		−	23.0645i		−	0.906759i	−0.891318	−	0.453380i	$-0.850218\pi$
$647$		−	23.0645i		−	0.906759i	0.891318	−	0.453380i	$-0.149782\pi$
$648$	1.26433	−	3.47371i	0.0496675	−	0.136460i
$649$	−2.62372	−	14.8799i	−0.102990	−	0.584086i
$650$	19.4433	−	4.03970i	0.762630	−	0.158450i
$651$	−0.611122	+	0.512793i	−0.0239518	+	0.0200979i
$652$	63.4211	+	11.1829i	2.48376	+	0.437954i
$653$	−23.3687	−	13.4919i	−0.914489	−	0.527981i	−0.0326165	−	0.999468i	$-0.510384\pi$
$653$	−23.3687	−	13.4919i	−0.914489	−	0.527981i	−0.881873	+	0.471487i	$0.843717\pi$
$654$	−21.6192	−	37.4455i	−0.845377	−	1.46424i
$655$	4.07924	−	4.20484i	0.159389	−	0.164297i
$656$	0.137054	−	0.0498834i	0.00535104	−	0.00194762i
$657$	−15.2362	+	8.79663i	−0.594421	+	0.343189i
$658$	1.05886	+	0.611334i	0.0412787	+	0.0238323i
$659$	−2.34217	+	13.2831i	−0.0912379	+	0.517436i	0.904598	+	0.426267i	$0.140171\pi$
$659$	−2.34217	+	13.2831i	−0.0912379	+	0.517436i	−0.995835	+	0.0911691i	$0.970940\pi$
$660$	22.4632	+	10.0630i	0.874379	+	0.391703i
$661$	−16.8359	−	14.1270i	−0.654842	−	0.549477i	0.253694	−	0.967284i	$-0.418354\pi$
$661$	−16.8359	−	14.1270i	−0.654842	−	0.549477i	−0.908536	+	0.417807i	$0.862799\pi$
$662$	24.8804	−	4.38709i	0.967005	−	0.170509i
$663$	−2.38863	+	6.56271i	−0.0927668	+	0.254875i
$664$	−24.7887			−0.961988
$665$	0.108582	−	1.39251i	0.00421062	−	0.0539992i
$666$	−37.0838			−1.43697
$667$	18.6296	−	51.1843i	0.721340	−	1.98186i
$668$	50.5136	−	8.90691i	1.95443	−	0.344619i
$669$	−1.93010	−	1.61954i	−0.0746219	−	0.0626152i
$670$	12.7678	−	28.5008i	0.493261	−	1.10108i
$671$	−4.94431	+	28.0406i	−0.190873	+	1.08250i
$672$	−0.672370	−	0.388193i	−0.0259372	−	0.0149749i
$673$	20.0916	−	11.5999i	0.774475	−	0.447143i	−0.0599940	−	0.998199i	$-0.519108\pi$
$673$	20.0916	−	11.5999i	0.774475	−	0.447143i	0.834468	+	0.551056i	$0.185775\pi$
$674$	16.8399	−	6.12923i	0.648649	−	0.236089i
$675$	25.5271	+	8.42389i	0.982540	+	0.324236i
$676$	17.1570	+	29.7169i	0.659886	+	1.14296i
$677$	−24.8804	−	14.3647i	−0.956232	−	0.552081i	−0.0612208	−	0.998124i	$-0.519499\pi$
$677$	−24.8804	−	14.3647i	−0.956232	−	0.552081i	−0.895011	+	0.446043i	$0.852833\pi$
$678$	−8.19981	−	1.44585i	−0.314912	−	0.0555275i
$679$	0.966259	−	0.810788i	0.0370816	−	0.0311152i
$680$	−25.1844	−	6.34055i	−0.965778	−	0.243149i
$681$	−1.28516	−	7.28852i	−0.0492475	−	0.279297i
$682$	−10.8500	+	29.8103i	−0.415470	+	1.14149i
$683$		−	24.0010i		−	0.918374i	−0.888340	−	0.459187i	$-0.848141\pi$
$683$		−	24.0010i		−	0.918374i	0.888340	−	0.459187i	$-0.151859\pi$
$684$	−21.6676	+	12.3453i	−0.828481	+	0.472035i
$685$	12.0201	+	24.7889i	0.459264	+	0.947136i
$686$	−4.37604	−	1.59275i	−0.167078	−	0.0608114i
$687$	1.74558	−	0.307792i	0.0665979	−	0.0117430i
$688$	5.50244	−	6.55756i	0.209779	−	0.250005i
$689$	−2.15068	+	1.80463i	−0.0819343	+	0.0687510i
$690$	41.3134	−	11.7440i	1.57278	−	0.447086i
$691$	−18.6933	+	32.3778i	−0.711128	+	1.23171i	0.253307	+	0.967386i	$0.418482\pi$
$691$	−18.6933	+	32.3778i	−0.711128	+	1.23171i	−0.964434	+	0.264323i	$0.914851\pi$
$692$	63.9534	−	36.9235i	2.43114	−	1.40362i
$693$	−0.231941	−	0.637253i	−0.00881072	−	0.0242073i
$694$	44.2781	−	16.1159i	1.68078	−	0.611752i
$695$	−14.7217	−	9.97911i	−0.558426	−	0.378529i
$696$	−14.1905	+	24.5786i	−0.537888	+	0.931649i
$697$	−0.656519	−	0.115762i	−0.0248674	−	0.00438480i
$698$	−28.4657	−	33.9241i	−1.07744	−	1.28405i
$699$	−18.0030	−	15.1063i	−0.680937	−	0.571374i
$700$	−1.15486	+	2.14816i	−0.0436497	+	0.0811927i
$701$	2.18595	+	0.795621i	0.0825622	+	0.0300502i	0.382971	−	0.923760i	$-0.374901\pi$
$701$	2.18595	+	0.795621i	0.0825622	+	0.0300502i	−0.300409	+	0.953811i	$0.597123\pi$
$702$		−	21.3528i		−	0.805911i
$703$	−31.5400	−	26.7737i	−1.18955	−	1.00979i
$704$	−35.2578			−1.32883
$705$	−9.37707	+	0.963836i	−0.353161	+	0.0363002i
$706$	−7.33330	−	41.5892i	−0.275992	−	1.56523i
$707$	−0.265096	+	0.315929i	−0.00996996	+	0.0118817i
$708$	13.4860	+	16.0720i	0.506834	+	0.604022i
$709$	4.22872	−	23.9823i	0.158813	−	0.900674i	−0.796403	−	0.604766i	$-0.793267\pi$
$709$	4.22872	−	23.9823i	0.158813	−	0.900674i	0.955216	−	0.295908i	$-0.0956222\pi$
$710$	2.80471	+	0.202588i	0.105259	+	0.00760300i
$711$	−9.75586	−	16.8976i	−0.365873	−	0.633711i
$712$	−1.61493	−	4.43697i	−0.0605219	−	0.166283i
$713$	11.9256	+	32.7652i	0.446616	+	1.22707i
$714$	−0.680844	−	1.17926i	−0.0254799	−	0.0441326i
$715$	10.7287	+	0.774949i	0.401230	+	0.0289814i
$716$	13.5232	−	76.6941i	0.505387	−	2.86619i
$717$	4.60743	+	5.49092i	0.172068	+	0.205062i
$718$	−24.1048	+	28.7270i	−0.899584	+	1.07208i
$719$	−2.96281	−	16.8029i	−0.110494	−	0.626644i	−0.988883	−	0.148697i	$-0.952492\pi$
$719$	−2.96281	−	16.8029i	−0.110494	−	0.626644i	0.878389	−	0.477947i	$-0.158619\pi$
$720$	2.91092	−	0.299203i	0.108483	−	0.0111506i
$721$	−0.171914			−0.00640242
$722$	−43.4064	−	8.16607i	−1.61542	−	0.303910i
$723$			30.2246i			1.12407i
$724$	−36.9949	−	13.4650i	−1.37491	−	0.500425i
$725$	−33.3445	−	17.9262i	−1.23838	−	0.665763i
$726$	−6.28445	−	5.27328i	−0.233238	−	0.195710i
$727$	−9.40083	−	11.2035i	−0.348657	−	0.415514i	0.563005	−	0.826453i	$-0.309645\pi$
$727$	−9.40083	−	11.2035i	−0.348657	−	0.415514i	−0.911663	+	0.410940i	$0.865201\pi$
$728$	0.786883	+	0.138749i	0.0291638	+	0.00514237i
$729$	10.2145	−	17.6920i	0.378314	−	0.655259i
$730$	45.0379	+	30.5289i	1.66693	+	1.12993i
$731$	−36.7676	+	13.3823i	−1.35990	+	0.494963i
$732$	−13.5224	−	37.1526i	−0.499804	−	1.37320i
$733$	−29.0344	+	16.7630i	−1.07241	+	0.619156i	−0.928839	−	0.370484i	$-0.879192\pi$
$733$	−29.0344	+	16.7630i	−1.07241	+	0.619156i	−0.143570	+	0.989640i	$0.545858\pi$
$734$	−37.4980	+	64.9485i	−1.38408	+	2.39729i
$735$	17.2423	−	4.90138i	0.635990	−	0.180790i
$736$	−25.9947	+	21.8121i	−0.958177	+	0.804006i
$737$	10.8735	−	12.9585i	0.400529	−	0.477332i
$738$	0.720768	−	0.127091i	0.0265318	−	0.00467828i
$739$	−14.2925	−	5.20205i	−0.525759	−	0.191361i	0.0654847	−	0.997854i	$-0.479141\pi$
$739$	−14.2925	−	5.20205i	−0.525759	−	0.191361i	−0.591244	+	0.806493i	$0.701363\pi$
$740$	31.5193	+	65.0021i	1.15867	+	2.38952i
$741$	5.53567	−	6.52114i	0.203358	−	0.239560i
$742$		−	0.547396i		−	0.0200955i
$743$	−2.27717	+	6.25647i	−0.0835412	+	0.229528i	−0.974429	−	0.224696i	$-0.927861\pi$
$743$	−2.27717	+	6.25647i	−0.0835412	+	0.229528i	0.890888	+	0.454224i	$0.150083\pi$
$744$	−3.15481	−	17.8918i	−0.115661	−	0.655945i
$745$	−9.09904	−	2.29082i	−0.333363	−	0.0839291i
$746$	−4.23887	+	3.55684i	−0.155196	+	0.130225i
$747$	−12.5728	−	2.21692i	−0.460014	−	0.0811129i
$748$	−29.5381	−	17.0538i	−1.08002	−	0.623549i
$749$	0.293437	+	0.508247i	0.0107219	+	0.0185709i
$750$	−3.95110	−	29.5890i	−0.144274	−	1.08044i
$751$	−7.34004	+	2.67155i	−0.267842	+	0.0974864i	−0.472450	−	0.881358i	$-0.656630\pi$
$751$	−7.34004	+	2.67155i	−0.267842	+	0.0974864i	0.204608	+	0.978844i	$0.434408\pi$
$752$	−2.47488	+	1.42887i	−0.0902496	+	0.0521056i
$753$	−10.6496	−	6.14855i	−0.388093	−	0.224066i
$754$	−5.22195	+	29.6151i	−0.190172	+	1.07852i
$755$	2.61581	−	5.83913i	0.0951990	−	0.212508i
$756$	2.00890	+	1.68567i	0.0730629	+	0.0613071i
$757$	18.1053	−	3.19246i	0.658049	−	0.116032i	0.165355	−	0.986234i	$-0.447123\pi$
$757$	18.1053	−	3.19246i	0.658049	−	0.116032i	0.492695	+	0.870202i	$0.336012\pi$
$758$	−14.0898	+	38.7113i	−0.511764	+	1.40606i
$759$	23.2645			0.844449
$760$	26.2272	+	17.9976i	0.951360	+	0.652841i
$761$	22.4779			0.814822			0.407411	−	0.913245i	$-0.366432\pi$
$761$	22.4779			0.814822			0.407411	+	0.913245i	$0.366432\pi$
$762$	−7.45188	+	20.4739i	−0.269953	+	0.741690i
$763$	2.28539	−	0.402976i	0.0827366	−	0.0145887i
$764$	−19.0077	−	15.9494i	−0.687675	−	0.577028i
$765$	−12.2064	−	5.46823i	−0.441325	−	0.197704i
$766$	−4.30493	+	24.4145i	−0.155543	+	0.882131i
$767$	7.94029	+	4.58433i	0.286707	+	0.165531i
$768$	20.5846	−	11.8846i	0.742784	−	0.428847i
$769$	5.18597	−	1.88754i	0.187011	−	0.0680664i	−0.246817	−	0.969062i	$-0.579385\pi$
$769$	5.18597	−	1.88754i	0.187011	−	0.0680664i	0.433828	+	0.900996i	$0.357162\pi$
$770$	−1.46035	+	1.50531i	−0.0526274	+	0.0542477i
$771$	7.76669	+	13.4523i	0.279710	+	0.484473i
$772$	77.1929	+	44.5673i	2.77823	+	1.60401i
$773$	32.6839	+	5.76305i	1.17556	+	0.207283i	0.727106	−	0.686525i	$-0.240865\pi$
$773$	32.6839	+	5.76305i	1.17556	+	0.207283i	0.448451	+	0.893807i	$0.351976\pi$
$774$	32.9065	−	27.6118i	1.18280	−	0.992487i
$775$	23.7276	−	4.92983i	0.852320	−	0.177085i
$776$	4.98813	+	28.2891i	0.179064	+	1.01552i
$777$	−0.534305	+	1.46799i	−0.0191681	+	0.0526639i
$778$		−	52.8418i		−	1.89447i
$779$	0.704774	+	0.412287i	0.0252512	+	0.0147717i
$780$	−13.4397	+	6.51687i	−0.481218	+	0.233341i
$781$	1.43131	+	0.520953i	0.0512162	+	0.0186412i
$782$	−58.6114	+	10.3348i	−2.09594	+	0.369571i
$783$	−26.1655	+	31.1829i	−0.935080	+	1.11439i
$784$	4.16290	−	3.49309i	0.148675	−	0.124753i
$785$	24.7872	−	7.04615i	0.884694	−	0.251488i
$786$	−3.49767	+	6.05813i	−0.124758	+	0.216086i
$787$	−42.1279	+	24.3225i	−1.50170	+	0.867005i	−0.501698	+	0.865043i	$0.667291\pi$
$787$	−42.1279	+	24.3225i	−1.50170	+	0.867005i	−0.999998	+	0.00196163i	$0.999376\pi$
$788$	−2.66390	−	7.31901i	−0.0948976	−	0.260729i
$789$	−7.05930	+	2.56938i	−0.251318	+	0.0914722i
$790$	−33.8579	+	49.9490i	−1.20461	+	1.77711i
$791$	0.223440	−	0.387010i	0.00794462	−	0.0137605i
$792$	15.2092	+	2.68179i	0.540435	+	0.0952932i
$793$	−11.1061	−	13.2357i	−0.394389	−	0.470015i
$794$	−36.3997	−	30.5430i	−1.29178	−	1.08393i
$795$	2.47279	+	3.41996i	0.0877008	+	0.121294i
$796$	39.1728	+	14.2577i	1.38844	+	0.505352i
$797$		−	1.06027i		−	0.0375567i	−0.999824	−	0.0187784i	$-0.994022\pi$
$797$		−	1.06027i		−	0.0375567i	0.999824	−	0.0187784i	$-0.00597769\pi$
$798$	0.280223	+	1.64409i	0.00991980	+	0.0582000i
$799$	13.0622			0.462106
$800$	12.4062	+	20.0582i	0.438627	+	0.709166i
$801$	−0.422277	−	2.39485i	−0.0149204	−	0.0846179i
$802$	−24.9496	+	29.7337i	−0.881000	+	1.04993i
$803$	18.9441	+	22.5767i	0.668522	+	0.796714i
$804$	−4.07886	+	23.1324i	−0.143850	+	0.815815i
$805$	−0.166074	+	2.29919i	−0.00585332	+	0.0810357i
$806$	−9.62517	−	16.6713i	−0.339032	−	0.587221i
$807$	−5.66551	−	15.5659i	−0.199435	−	0.547944i
$808$	−3.21230	−	8.82571i	−0.113008	−	0.310487i
$809$	−6.80960	−	11.7946i	−0.239413	−	0.414675i	0.721133	−	0.692797i	$-0.243622\pi$
$809$	−6.80960	−	11.7946i	−0.239413	−	0.414675i	−0.960546	+	0.278121i	$0.910288\pi$
$810$	−5.87266	−	0.424191i	−0.206344	−	0.0149045i
$811$	3.88880	−	22.0545i	0.136554	−	0.774438i	−0.837210	−	0.546881i	$-0.815815\pi$
$811$	3.88880	−	22.0545i	0.136554	−	0.774438i	0.973765	−	0.227557i	$-0.0730738\pi$
$812$	−2.37398	−	2.82920i	−0.0833105	−	0.0992856i
$813$	−1.61265	+	1.92188i	−0.0565580	+	0.0674032i
$814$	10.7873	+	61.1779i	0.378095	+	2.14429i
$815$	−4.32561	−	42.0835i	−0.151520	−	1.47412i
$816$	3.18268			0.111416
$817$	47.9223	+	0.273738i	1.67659	+	0.00957687i
$818$			41.1100i			1.43738i
$819$	0.386697	+	0.140746i	0.0135123	+	0.00491807i
$820$	−0.835387	−	1.15537i	−0.0291730	−	0.0403474i
$821$	−4.22809	−	3.54778i	−0.147561	−	0.123819i	0.566019	−	0.824392i	$-0.308483\pi$
$821$	−4.22809	−	3.54778i	−0.147561	−	0.123819i	−0.713580	+	0.700574i	$0.752927\pi$
$822$	−21.1451	−	25.1997i	−0.737519	−	0.878941i
$823$	22.0128	+	3.88144i	0.767317	+	0.135299i	0.543587	−	0.839353i	$-0.317066\pi$
$823$	22.0128	+	3.88144i	0.767317	+	0.135299i	0.223729	+	0.974651i	$0.428177\pi$
$824$	1.95754	−	3.39055i	0.0681941	−	0.118116i
$825$	2.32377	−	16.0017i	0.0809034	−	0.557107i
$826$	−1.67985	+	0.611417i	−0.0584496	+	0.0212739i
$827$	1.53460	+	4.21627i	0.0533632	+	0.146614i	0.963510	−	0.267671i	$-0.0862539\pi$
$827$	1.53460	+	4.21627i	0.0533632	+	0.146614i	−0.910147	+	0.414285i	$0.864032\pi$
$828$	35.6433	−	20.5787i	1.23869	−	0.715158i
$829$	13.5156	−	23.4097i	0.469416	−	0.813052i	−0.529973	−	0.848015i	$-0.677798\pi$
$829$	13.5156	−	23.4097i	0.469416	−	0.813052i	0.999389	+	0.0349625i	$0.0111312\pi$
$830$	10.7959	+	37.9784i	0.374733	+	1.31825i
$831$	14.0555	−	11.7940i	0.487579	−	0.409128i
$832$	13.7525	−	16.3896i	0.476782	−	0.568206i
$833$	−24.4616	+	4.31324i	−0.847544	+	0.149445i
$834$	19.9559	+	7.26336i	0.691017	+	0.251510i
$835$	−14.7015	−	30.3188i	−0.508767	−	1.04923i
$836$	26.6693	+	32.1544i	0.922375	+	1.11208i
$837$		−	26.0578i		−	0.900691i
$838$	30.1600	−	82.8640i	1.04186	−	2.86249i
$839$	1.75648	+	9.96148i	0.0606404	+	0.343909i	1.00000		0.000973662i	$0.000309926\pi$
$839$	1.75648	+	9.96148i	0.0606404	+	0.343909i	−0.939359	+	0.342935i	$0.888579\pi$
$840$	0.293244	−	1.16475i	0.0101179	−	0.0401878i
$841$	21.7007	−	18.2091i	0.748300	−	0.627898i
$842$	26.5152	+	4.67534i	0.913773	+	0.161123i
$843$	−14.1813	−	8.18759i	−0.488431	−	0.281996i
$844$	5.11107	+	8.85264i	0.175930	+	0.304720i
$845$	15.6958	−	16.1791i	0.539953	−	0.556578i
$846$	−13.4756	+	4.90473i	−0.463301	+	0.168628i
$847$	0.381314	−	0.220152i	0.0131021	−	0.00756450i
$848$	1.10802	+	0.639714i	0.0380495	+	0.0219679i
$849$	−1.40957	+	7.99405i	−0.0483762	+	0.274355i
$850$	1.25402	+	41.3461i	0.0430125	+	1.41816i
$851$	52.3052	+	43.8893i	1.79300	+	1.50450i
$852$	−2.08289	+	0.367270i	−0.0713586	+	0.0125825i
$853$	−9.44325	+	25.9451i	−0.323331	+	0.888344i	0.666425	+	0.745572i	$0.267824\pi$
$853$	−9.44325	+	25.9451i	−0.323331	+	0.888344i	−0.989756	+	0.142772i	$0.954399\pi$
$854$	3.36879			0.115278
$855$	11.6928	+	11.4739i	0.399885	+	0.392400i
$856$	−13.3651			−0.456810
$857$	−13.2079	+	36.2885i	−0.451175	+	1.23959i	0.480723	+	0.876872i	$0.340374\pi$
$857$	−13.2079	+	36.2885i	−0.451175	+	1.23959i	−0.931898	+	0.362720i	$0.881848\pi$
$858$	−12.6490	+	2.23036i	−0.431831	+	0.0761434i
$859$	−43.7965	−	36.7496i	−1.49432	−	1.25388i	−0.889009	−	0.457889i	$-0.848606\pi$
$859$	−43.7965	−	36.7496i	−1.49432	−	1.25388i	−0.605307	−	0.795992i	$-0.706950\pi$
$860$	−76.3681	−	34.2113i	−2.60413	−	1.16660i
$861$	0.00535387	−	0.0303633i	0.000182460	−	0.00103478i
$862$	−63.9986	−	36.9496i	−2.17980	−	1.25851i
$863$	24.6314	−	14.2209i	0.838463	−	0.484087i	−0.0182787	−	0.999833i	$-0.505819\pi$
$863$	24.6314	−	14.2209i	0.838463	−	0.484087i	0.856741	+	0.515746i	$0.172485\pi$
$864$	23.8302	−	8.67349i	0.810720	−	0.295078i
$865$	−34.8189	−	33.7788i	−1.18388	−	1.14851i
$866$	−4.75209	−	8.23085i	−0.161482	−	0.279696i
$867$	4.31151	+	2.48925i	0.146427	+	0.0845395i
$868$	2.32830	+	0.410541i	0.0790275	+	0.0139347i
$869$	−25.0385	+	21.0098i	−0.849374	+	0.712710i
$870$	43.8367	+	11.0365i	1.48620	+	0.374174i
$871$	1.78250	+	10.1091i	0.0603977	+	0.342532i
$872$	−18.0754	+	49.6618i	−0.612111	+	1.68176i
$873$			14.7943i			0.500711i
$874$	71.7138	+	13.0679i	2.42576	+	0.442028i
$875$	1.56483	+	0.343882i	0.0529008	+	0.0116253i
$876$	−38.4556	−	13.9967i	−1.29929	−	0.472905i
$877$	13.1274	−	2.31472i	0.443282	−	0.0781626i	0.0524480	−	0.998624i	$-0.483298\pi$
$877$	13.1274	−	2.31472i	0.443282	−	0.0781626i	0.390834	+	0.920461i	$0.372187\pi$
$878$	−17.5659	+	20.9342i	−0.592819	+	0.706494i
$879$	0.859402	−	0.721124i	0.0289869	−	0.0243229i
$880$	−1.34036	−	4.71517i	−0.0451836	−	0.158948i
$881$	14.0692	−	24.3686i	0.474004	−	0.820999i	−0.525553	−	0.850761i	$-0.676142\pi$
$881$	14.0692	−	24.3686i	0.474004	−	0.820999i	0.999557	+	0.0297621i	$0.00947498\pi$
$882$	23.6163	−	13.6349i	0.795203	−	0.459111i
$883$	−12.1840	−	33.4754i	−0.410026	−	1.12654i	−0.957177	−	0.289503i	$-0.906510\pi$
$883$	−12.1840	−	33.4754i	−0.410026	−	1.12654i	0.547151	−	0.837034i	$-0.315712\pi$
$884$	19.4489	−	7.07883i	0.654139	−	0.238087i
$885$	7.73323	−	11.4085i	0.259950	−	0.383492i
$886$	−9.16667	+	15.8771i	−0.307960	+	0.533403i
$887$	58.2732	+	10.2751i	1.95662	+	0.345005i	0.998224	+	0.0595725i	$0.0189738\pi$
$887$	58.2732	+	10.2751i	1.95662	+	0.345005i	0.958399	+	0.285433i	$0.0921374\pi$
$888$	−22.8683	−	27.2533i	−0.767409	−	0.914562i
$889$	−0.895791	−	0.751658i	−0.0300439	−	0.0252098i
$890$	−6.09449	+	4.40659i	−0.204288	+	0.147709i
$891$	−2.99695	−	1.09080i	−0.100402	−	0.0365432i
$892$			7.46685i			0.250009i
$893$	−15.0022	−	5.55760i	−0.502030	−	0.185978i
$894$	11.2039			0.374715
$895$	−50.8909	+	5.23089i	−1.70109	+	0.174849i
$896$	0.489620	+	2.77677i	0.0163570	+	0.0927654i
$897$	−9.07445	+	10.8145i	−0.302987	+	0.361086i
$898$	1.73450	+	2.06710i	0.0578811	+	0.0689800i
$899$	−6.37258	+	36.1407i	−0.212537	+	1.20536i
$900$	−10.5941	−	26.5715i	−0.353136	−	0.885716i
$901$	−2.92400	−	5.06452i	−0.0974126	−	0.168724i
$902$	−0.419329	−	1.15210i	−0.0139621	−	0.0383607i
$903$	−0.618918	−	1.70046i	−0.0205963	−	0.0565879i
$904$	5.08850	+	8.81354i	0.169241	+	0.293134i
$905$	−1.86322	+	25.7951i	−0.0619355	+	0.857459i
$906$	−1.32667	+	7.52390i	−0.0440755	+	0.249965i
$907$	29.7254	+	35.4253i	0.987016	+	1.17628i	0.984340	+	0.176283i	$0.0564074\pi$
$907$	29.7254	+	35.4253i	0.987016	+	1.17628i	0.00267604	+	0.999996i	$0.499148\pi$
$908$	−14.0983	+	16.8017i	−0.467870	+	0.557585i
$909$	−0.839964	−	4.76367i	−0.0278598	−	0.158001i
$910$	−0.130128	−	1.26600i	−0.00431369	−	0.0419675i
$911$	48.8276			1.61773			0.808866	−	0.587994i	$-0.200082\pi$
$911$	48.8276			1.61773			0.808866	+	0.587994i	$0.200082\pi$
$912$	−3.65538	−	1.35415i	−0.121042	−	0.0448402i
$913$			21.3865i			0.707790i
$914$	−84.5130	−	30.7602i	−2.79544	−	1.01746i
$915$	−21.0472	+	15.2181i	−0.695799	+	0.503094i
$916$	−4.02396	−	3.37650i	−0.132955	−	0.111563i
$917$	−0.241332	−	0.287608i	−0.00796948	−	0.00949766i
$918$	43.8019	+	7.72346i	1.44568	+	0.254912i
$919$	−4.80464	+	8.32189i	−0.158491	+	0.274514i	−0.934325	−	0.356423i	$-0.883996\pi$
$919$	−4.80464	+	8.32189i	−0.158491	+	0.274514i	0.775834	+	0.630937i	$0.217329\pi$
$920$	−43.4544	−	29.4555i	−1.43265	−	0.971120i
$921$	30.7248	−	11.1829i	1.01242	−	0.368490i
$922$	19.4787	+	53.5173i	0.641496	+	1.76250i
$923$	−0.800454	+	0.462142i	−0.0263473	+	0.0152116i
$924$	0.788722	−	1.36611i	0.0259470	−	0.0449416i
$925$	35.4122	−	31.5924i	1.16435	−	1.03875i
$926$	57.8481	−	48.5403i	1.90100	−	1.59513i
$927$	1.29609	−	1.54462i	0.0425691	−	0.0507318i
$928$	−35.1722	+	6.20181i	−1.15459	+	0.203585i
$929$	48.5984	+	17.6884i	1.59446	+	0.580337i	0.978284	−	0.207269i	$-0.0664577\pi$
$929$	48.5984	+	17.6884i	1.59446	+	0.580337i	0.616179	+	0.787606i	$0.288680\pi$
$930$	−26.0378	+	12.6256i	−0.853812	+	0.414011i
$931$	29.9299	+	5.45391i	0.980914	+	0.178745i
$932$			69.6473i			2.28137i
$933$	10.0355	−	27.5722i	0.328546	−	0.902672i
$934$	5.93470	+	33.6574i	0.194189	+	1.10130i
$935$	−5.47032	+	21.7279i	−0.178899	+	0.710578i
$936$	−7.17905	+	6.02394i	−0.234655	+	0.196899i
$937$	−11.3148	−	1.99511i	−0.369639	−	0.0651773i	−0.0142567	−	0.999898i	$-0.504538\pi$
$937$	−11.3148	−	1.99511i	−0.369639	−	0.0651773i	−0.355382	+	0.934721i	$0.615649\pi$
$938$	−1.73328	−	1.00071i	−0.0565937	−	0.0326744i
$939$	8.58639	+	14.8721i	0.280206	+	0.485331i
$940$	20.0508	+	19.4519i	0.653986	+	0.634451i
$941$	−24.8922	+	9.06002i	−0.811462	+	0.295348i	−0.714228	−	0.699913i	$-0.753222\pi$
$941$	−24.8922	+	9.06002i	−0.811462	+	0.295348i	−0.0972346	+	0.995261i	$0.531000\pi$
$942$	−26.6478	+	15.3851i	−0.868232	+	0.501274i
$943$	−1.16703	−	0.673785i	−0.0380037	−	0.0219414i
$944$	0.725556	−	4.11483i	0.0236148	−	0.133926i
$945$	0.704301	−	1.57217i	0.0229109	−	0.0511429i
$946$	−55.1241	−	46.2546i	−1.79224	−	1.50387i
$947$	−14.4785	+	2.55295i	−0.470487	+	0.0829596i	−0.403865	−	0.914819i	$-0.632333\pi$
$947$	−14.4785	+	2.55295i	−0.470487	+	0.0829596i	−0.0666224	+	0.997778i	$0.521222\pi$
$948$	15.5230	−	42.6490i	0.504162	−	1.38517i
$949$	−17.8840			−0.580539
$950$	16.1514	−	48.0205i	0.524021	−	1.55799i
$951$	−25.8892			−0.839513
$952$	−0.569241	+	1.56398i	−0.0184492	+	0.0506888i
$953$	5.76163	−	1.01593i	0.186637	−	0.0329092i	−0.0795481	−	0.996831i	$-0.525348\pi$
$953$	5.76163	−	1.01593i	0.186637	−	0.0329092i	0.266186	+	0.963922i	$0.414237\pi$
$954$	4.91824	+	4.12689i	0.159234	+	0.133613i
$955$	−6.66393	+	14.8755i	−0.215640	+	0.481361i
$956$	3.68871	−	20.9197i	0.119301	−	0.676591i
$957$	21.2052	+	12.2428i	0.685467	+	0.395755i
$958$	26.6135	−	15.3653i	0.859843	−	0.496431i
$959$	1.65908	−	0.603855i	0.0535744	−	0.0194995i
$960$	−23.0837	−	22.3942i	−0.745022	−	0.722768i
$961$	3.75397	+	6.50206i	0.121096	+	0.209744i
$962$	−32.6462	−	18.8483i	−1.05256	−	0.607693i
$963$	−6.77876	−	1.19528i	−0.218442	−	0.0385173i
$964$	68.6163	−	57.5759i	2.20998	−	1.85440i
$965$	14.2958	−	56.7823i	0.460198	−	1.82789i
$966$	−0.477973	−	2.71072i	−0.0153785	−	0.0872159i
$967$	−8.23258	+	22.6188i	−0.264742	+	0.727373i	0.734090	+	0.679052i	$0.237609\pi$
$967$	−8.23258	+	22.6188i	−0.264742	+	0.727373i	−0.998832	+	0.0483204i	$0.984613\pi$
$968$			10.0272i			0.322287i
$969$	11.3748	+	13.7143i	0.365411	+	0.440566i
$970$	41.1689	−	19.9627i	1.32185	−	0.640963i
$971$	−49.4859	−	18.0114i	−1.58808	−	0.578013i	−0.611137	−	0.791524i	$-0.709288\pi$
$971$	−49.4859	−	18.0114i	−1.58808	−	0.578013i	−0.976941	+	0.213511i	$0.931510\pi$
$972$	−49.7047	+	8.76428i	−1.59428	+	0.281114i
$973$	−0.732643	+	0.873130i	−0.0234875	+	0.0279913i
$974$	−17.2035	+	14.4354i	−0.551234	+	0.462540i
$975$	6.53198	+	7.32175i	0.209191	+	0.234484i
$976$	−3.93694	+	6.81899i	−0.126018	+	0.218270i
$977$	−5.63672	+	3.25436i	−0.180335	+	0.104116i	−0.587450	−	0.809261i	$-0.699868\pi$
$977$	−5.63672	+	3.25436i	−0.180335	+	0.104116i	0.407115	+	0.913377i	$0.366535\pi$
$978$	17.2772	+	47.4688i	0.552465	+	1.51789i
$979$	−3.82801	+	1.39328i	−0.122344	+	0.0445294i
$980$	−43.9725	−	29.8068i	−1.40465	−	0.952142i
$981$	−13.6092	+	23.5718i	−0.434509	+	0.752591i
$982$	6.14987	+	1.08439i	0.196250	+	0.0346042i
$983$	0.803066	+	0.957057i	0.0256138	+	0.0305254i	0.778699	−	0.627397i	$-0.215880\pi$
$983$	0.803066	+	0.957057i	0.0256138	+	0.0305254i	−0.753085	+	0.657923i	$0.771435\pi$
$984$	0.537873	+	0.451329i	0.0171468	+	0.0143879i
$985$	−4.14627	+	2.99794i	−0.132111	+	0.0955223i
$986$	−58.8619	−	21.4240i	−1.87454	−	0.682278i
$987$			0.604111i			0.0192291i
$988$	−25.3494	−	0.144799i	−0.806473	−	0.00460666i
$989$	−79.0924			−2.51499
$990$	−2.51516	−	24.4697i	−0.0799369	−	0.777699i
$991$	6.52844	+	37.0246i	0.207383	+	1.17613i	0.893646	+	0.448772i	$0.148139\pi$
$991$	6.52844	+	37.0246i	0.207383	+	1.17613i	−0.686264	+	0.727353i	$0.740750\pi$
$992$	14.6958	−	17.5137i	0.466591	−	0.556062i
$993$	8.02384	+	9.56244i	0.254629	+	0.303455i
$994$	0.0312936	−	0.177475i	0.000992573	−	0.00562916i
$995$	1.97291	−	27.3137i	0.0625454	−	0.865903i
$996$	−14.8483	−	25.7181i	−0.470487	−	0.814908i
$997$	−10.2369	−	28.1257i	−0.324207	−	0.890751i	−0.989547	−	0.144211i	$-0.953936\pi$
$997$	−10.2369	−	28.1257i	−0.324207	−	0.890751i	0.665340	−	0.746540i	$-0.268287\pi$
$998$	1.87275	+	5.14533i	0.0592808	+	0.162873i
$999$	−25.5136	−	44.1909i	−0.807215	−	1.39814i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	95.2.p.a.4.7	yes	48
3.2	odd	2		855.2.da.b.289.2		48
5.2	odd	4		475.2.l.f.251.7		48
5.3	odd	4		475.2.l.f.251.2		48
5.4	even	2	inner	95.2.p.a.4.2	✓	48
15.14	odd	2		855.2.da.b.289.7		48
19.5	even	9	inner	95.2.p.a.24.2	yes	48
19.9	even	9		1805.2.b.k.1084.22		24
19.10	odd	18		1805.2.b.l.1084.3		24
57.5	odd	18		855.2.da.b.784.7		48
95.9	even	18		1805.2.b.k.1084.3		24
95.24	even	18	inner	95.2.p.a.24.7	yes	48
95.28	odd	36		9025.2.a.cu.1.22		24
95.29	odd	18		1805.2.b.l.1084.22		24
95.43	odd	36		475.2.l.f.176.2		48
95.47	odd	36		9025.2.a.cu.1.3		24
95.48	even	36		9025.2.a.ct.1.3		24
95.62	odd	36		475.2.l.f.176.7		48
95.67	even	36		9025.2.a.ct.1.22		24
285.119	odd	18		855.2.da.b.784.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.p.a.4.2	✓	48	5.4	even	2	inner
95.2.p.a.4.7	yes	48	1.1	even	1	trivial
95.2.p.a.24.2	yes	48	19.5	even	9	inner
95.2.p.a.24.7	yes	48	95.24	even	18	inner
475.2.l.f.176.2		48	95.43	odd	36
475.2.l.f.176.7		48	95.62	odd	36
475.2.l.f.251.2		48	5.3	odd	4
475.2.l.f.251.7		48	5.2	odd	4
855.2.da.b.289.2		48	3.2	odd	2
855.2.da.b.289.7		48	15.14	odd	2
855.2.da.b.784.2		48	285.119	odd	18
855.2.da.b.784.7		48	57.5	odd	18
1805.2.b.k.1084.3		24	95.9	even	18
1805.2.b.k.1084.22		24	19.9	even	9
1805.2.b.l.1084.3		24	19.10	odd	18
1805.2.b.l.1084.22		24	95.29	odd	18
9025.2.a.ct.1.3		24	95.48	even	36
9025.2.a.ct.1.22		24	95.67	even	36
9025.2.a.cu.1.3		24	95.47	odd	36
9025.2.a.cu.1.22		24	95.28	odd	36

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	95.p (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.795068 - 2.18443i) q^{2} +(1.13113 - 0.199449i) q^{3} +(-2.60752 - 2.18797i) q^{4} +(-0.914172 + 2.04066i) q^{5} +(0.463643 - 2.62945i) q^{6} +(0.124103 + 0.0716510i) q^{7} +(-2.82626 + 1.63174i) q^{8} +(-1.57940 + 0.574856i) q^{9} +(3.73085 + 3.61941i) q^{10} +(1.40779 + 2.43836i) q^{11} +(-3.38583 - 1.95481i) q^{12} +(-1.68258 - 0.296685i) q^{13} +(0.255187 - 0.214128i) q^{14} +(-0.627041 + 2.49058i) q^{15} +(0.135204 + 0.766781i) q^{16} +(1.21720 - 3.34424i) q^{17} +3.90715i q^{18} +(-2.82087 + 3.32305i) q^{19} +(6.84862 - 3.32088i) q^{20} +(0.154668 + 0.0562944i) q^{21} +(6.44571 - 1.13655i) q^{22} +(4.62417 - 5.51088i) q^{23} +(-2.87141 + 2.40940i) q^{24} +(-3.32858 - 3.73103i) q^{25} +(-1.98586 + 3.43960i) q^{26} +(-4.65595 + 2.68812i) q^{27} +(-0.166831 - 0.458365i) q^{28} +(7.11492 - 2.58962i) q^{29} +(4.94196 + 3.34991i) q^{30} +(-2.42343 + 4.19751i) q^{31} +(-4.64532 - 0.819095i) q^{32} +(2.07872 + 2.47732i) q^{33} +(-6.33750 - 5.31779i) q^{34} +(-0.259667 + 0.187751i) q^{35} +(5.37609 + 1.95674i) q^{36} +9.49127i q^{37} +(5.01619 + 8.80406i) q^{38} -1.96239 q^{39} +(-0.746138 - 7.25911i) q^{40} +(-0.0325278 - 0.184474i) q^{41} +(0.245943 - 0.293103i) q^{42} +(-7.06701 - 8.42213i) q^{43} +(1.66422 - 9.43825i) q^{44} +(0.270762 - 3.74854i) q^{45} +(-8.36160 - 14.4827i) q^{46} +(1.25532 + 3.44897i) q^{47} +(0.305867 + 0.840363i) q^{48} +(-3.48973 - 6.04439i) q^{49} +(-10.7966 + 4.30463i) q^{50} +(0.709811 - 4.02554i) q^{51} +(3.73823 + 4.45505i) q^{52} +(1.05624 - 1.25878i) q^{53} +(2.17020 + 12.3078i) q^{54} +(-6.26281 + 0.643732i) q^{55} -0.467663 q^{56} +(-2.52800 + 4.32142i) q^{57} -17.6010i q^{58} +(-5.04274 - 1.83541i) q^{59} +(7.08433 - 5.12229i) q^{60} +(7.74681 + 6.50035i) q^{61} +(7.24237 + 8.63112i) q^{62} +(-0.237198 - 0.0418244i) q^{63} +(-6.26121 + 10.8447i) q^{64} +(2.14360 - 3.16236i) q^{65} +(7.06425 - 2.57118i) q^{66} +(-2.05488 - 5.64572i) q^{67} +(-10.4910 + 6.05696i) q^{68} +(4.13141 - 7.15580i) q^{69} +(0.203676 + 0.716500i) q^{70} +(0.414414 - 0.347735i) q^{71} +(3.52578 - 4.20186i) q^{72} +(10.3084 - 1.81765i) q^{73} +(20.7330 + 7.54620i) q^{74} +(-4.50920 - 3.55640i) q^{75} +(14.6262 - 2.49294i) q^{76} +0.403477i q^{77} +(-1.56024 + 4.28672i) q^{78} +(2.01585 + 11.4325i) q^{79} +(-1.68834 - 0.425065i) q^{80} +(-0.867724 + 0.728107i) q^{81} +(-0.428833 - 0.0756149i) q^{82} +(6.57815 + 3.79789i) q^{83} +(-0.280128 - 0.485197i) q^{84} +(5.71172 + 5.54111i) q^{85} +(-24.0163 + 8.74123i) q^{86} +(7.53141 - 4.34826i) q^{87} +(-7.95753 - 4.59428i) q^{88} +(-0.251241 + 1.42486i) q^{89} +(-7.97315 - 3.57181i) q^{90} +(-0.187556 - 0.157378i) q^{91} +(-24.1152 + 4.25217i) q^{92} +(-1.90403 + 5.23127i) q^{93} +8.53210 q^{94} +(-4.20245 - 8.79428i) q^{95} -5.41783 q^{96} +(3.01050 - 8.27128i) q^{97} +(-15.9781 + 2.81738i) q^{98} +(-3.62516 - 3.04187i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 18 q^{4} - 6 q^{5} - 6 q^{6} - 12 q^{9} - 15 q^{10} - 12 q^{11} + 6 q^{14} + 3 q^{15} - 42 q^{16} + 12 q^{19} + 42 q^{20} - 54 q^{21} + 24 q^{24} + 12 q^{25} + 12 q^{26} + 18 q^{30} - 42 q^{31} - 36 q^{34}+ \cdots - 36 q^{99}+O(q^{100}) \) 48 * q - 18 * q^4 - 6 * q^5 - 6 * q^6 - 12 * q^9 - 15 * q^10 - 12 * q^11 + 6 * q^14 + 3 * q^15 - 42 * q^16 + 12 * q^19 + 42 * q^20 - 54 * q^21 + 24 * q^24 + 12 * q^25 + 12 * q^26 + 18 * q^30 - 42 * q^31 - 36 * q^34 + 6 * q^35 + 18 * q^36 - 48 * q^39 + 66 * q^40 + 6 * q^41 - 6 * q^44 - 9 * q^45 - 6 * q^46 + 12 * q^49 - 18 * q^50 + 108 * q^51 + 24 * q^54 + 36 * q^56 - 36 * q^59 - 114 * q^60 + 48 * q^61 - 18 * q^65 + 180 * q^66 + 66 * q^69 - 123 * q^70 - 24 * q^71 + 84 * q^74 + 72 * q^75 + 66 * q^76 + 48 * q^79 - 39 * q^80 - 78 * q^81 - 54 * q^84 - 84 * q^85 - 42 * q^86 - 12 * q^89 + 18 * q^90 - 30 * q^91 - 72 * q^94 - 63 * q^95 - 240 * q^96 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more