LMFDB - Embedded newform 475.2.l.f.176.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [475,2,Mod(101,475)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(475, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 14])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("475.101"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.l (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			176.7
Character	$\chi$	$=$	475.176
Dual form			475.2.l.f.251.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

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

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{8}{9}\right)$

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 $

$2$	2.18443	−	0.795068i	1.54463	−	0.562198i	0.577477	−	0.816407i	$-0.304037\pi$
$2$	2.18443	−	0.795068i	1.54463	−	0.562198i	0.967149	+	0.254209i	$0.0818151\pi$
$3$	−0.199449	+	1.13113i	−0.115152	+	0.653058i	0.871523	+	0.490354i	$0.163133\pi$
$3$	−0.199449	+	1.13113i	−0.115152	+	0.653058i	−0.986675	+	0.162704i	$0.947978\pi$
$4$	2.60752	−	2.18797i	1.30376	−	1.09398i
$5$		0			0
$5$		0			0
$6$	0.463643	+	2.62945i	0.189282	+	1.07347i
$7$	−0.0716510	−	0.124103i	−0.0270816	−	0.0469066i	0.852167	−	0.523270i	$-0.175288\pi$
$7$	−0.0716510	−	0.124103i	−0.0270816	−	0.0469066i	−0.879249	+	0.476363i	$0.841955\pi$
$8$	1.63174	−	2.82626i	0.576907	−	0.999232i
$9$	1.57940	+	0.574856i	0.526468	+	0.191619i
$10$		0			0
$11$	1.40779	−	2.43836i	0.424463	−	0.735192i	−0.571907	−	0.820319i	$-0.693796\pi$
$11$	1.40779	−	2.43836i	0.424463	−	0.735192i	0.996370	+	0.0851264i	$0.0271294\pi$
$12$	1.95481	+	3.38583i	0.564305	+	0.977405i
$13$	−0.296685	−	1.68258i	−0.0822856	−	0.466665i	−0.997909	−	0.0646286i	$-0.979414\pi$
$13$	−0.296685	−	1.68258i	−0.0822856	−	0.466665i	0.915624	−	0.402036i	$-0.131697\pi$
$14$	−0.255187	−	0.214128i	−0.0682017	−	0.0572280i
$15$		0			0
$16$	0.135204	−	0.766781i	0.0338011	−	0.191695i
$17$	3.34424	−	1.21720i	0.811097	−	0.295215i	0.0970200	−	0.995282i	$-0.469069\pi$
$17$	3.34424	−	1.21720i	0.811097	−	0.295215i	0.714077	+	0.700067i	$0.246847\pi$
$18$	3.90715			0.920923
$19$	2.82087	+	3.32305i	0.647153	+	0.762360i
$19$	2.82087	+	3.32305i	0.647153	+	0.762360i
$20$		0			0
$21$	0.154668	−	0.0562944i	0.0337512	−	0.0122844i
$22$	1.13655	−	6.44571i	0.242314	−	1.37423i
$23$	−5.51088	+	4.62417i	−1.14910	+	0.964207i	−0.999698	−	0.0245699i	$-0.992178\pi$
$23$	−5.51088	+	4.62417i	−1.14910	+	0.964207i	−0.149399	+	0.988777i	$0.547734\pi$
$24$	2.87141	+	2.40940i	0.586125	+	0.491817i
$25$		0			0
$26$	−1.98586	−	3.43960i	−0.389459	−	0.674562i
$27$	−2.68812	+	4.65595i	−0.517328	+	0.896038i
$28$	−0.458365	−	0.166831i	−0.0866229	−	0.0315282i
$29$	−7.11492	−	2.58962i	−1.32121	−	0.480880i	−0.417363	−	0.908740i	$-0.637046\pi$
$29$	−7.11492	−	2.58962i	−1.32121	−	0.480880i	−0.903845	+	0.427860i	$0.859268\pi$
$30$		0			0
$31$	−2.42343	−	4.19751i	−0.435261	−	0.753894i	0.562056	−	0.827099i	$-0.310011\pi$
$31$	−2.42343	−	4.19751i	−0.435261	−	0.753894i	−0.997317	+	0.0732050i	$0.976677\pi$
$32$	0.819095	+	4.64532i	0.144797	+	0.821184i
$33$	2.47732	+	2.07872i	0.431246	+	0.361858i
$34$	6.33750	−	5.31779i	1.08687	−	0.911994i
$35$		0			0
$36$	5.37609	−	1.95674i	0.896015	−	0.326123i
$37$	−9.49127			−1.56035			−0.780177	−	0.625559i	$-0.784871\pi$
$37$	−9.49127			−1.56035			−0.780177	+	0.625559i	$0.784871\pi$
$38$	8.80406	+	5.01619i	1.42821	+	0.813734i
$39$	1.96239			0.314235
$40$		0			0
$41$	−0.0325278	+	0.184474i	−0.00507999	+	0.0288100i	−0.987242	−	0.159225i	$-0.949101\pi$
$41$	−0.0325278	+	0.184474i	−0.00507999	+	0.0288100i	0.982162	+	0.188035i	$0.0602117\pi$
$42$	0.293103	−	0.245943i	0.0452268	−	0.0379498i
$43$	−8.42213	−	7.06701i	−1.28436	−	1.07771i	−0.992627	−	0.121210i	$-0.961323\pi$
$43$	−8.42213	−	7.06701i	−1.28436	−	1.07771i	−0.291736	−	0.956499i	$-0.594233\pi$
$44$	−1.66422	−	9.43825i	−0.250890	−	1.42287i
$45$		0			0
$46$	−8.36160	+	14.4827i	−1.23285	+	2.13536i
$47$	−3.44897	−	1.25532i	−0.503084	−	0.183108i	0.0779967	−	0.996954i	$-0.475148\pi$
$47$	−3.44897	−	1.25532i	−0.503084	−	0.183108i	−0.581080	+	0.813846i	$0.697370\pi$
$48$	0.840363	+	0.305867i	0.121296	+	0.0441481i
$49$	3.48973	−	6.04439i	0.498533	−	0.863485i
$50$		0			0
$51$	0.709811	+	4.02554i	0.0993934	+	0.563688i
$52$	−4.45505	−	3.73823i	−0.617804	−	0.518399i
$53$	−1.25878	+	1.05624i	−0.172907	+	0.145086i	−0.725134	−	0.688607i	$-0.758222\pi$
$53$	−1.25878	+	1.05624i	−0.172907	+	0.145086i	0.552228	+	0.833693i	$0.313778\pi$
$54$	−2.17020	+	12.3078i	−0.295327	+	1.67489i
$55$		0			0
$56$	−0.467663			−0.0624941
$57$	−4.32142	+	2.52800i	−0.572386	+	0.334841i
$58$	−17.6010			−2.31112
$59$	5.04274	−	1.83541i	0.656509	−	0.238950i	0.00778043	−	0.999970i	$-0.497523\pi$
$59$	5.04274	−	1.83541i	0.656509	−	0.238950i	0.648728	+	0.761020i	$0.275301\pi$
$60$		0			0
$61$	7.74681	−	6.50035i	0.991878	−	0.832284i	0.00603938	−	0.999982i	$-0.498078\pi$
$61$	7.74681	−	6.50035i	0.991878	−	0.832284i	0.985839	+	0.167697i	$0.0536331\pi$
$62$	−8.63112	−	7.24237i	−1.09615	−	0.919782i
$63$	−0.0418244	−	0.237198i	−0.00526938	−	0.0298841i
$64$	6.26121	+	10.8447i	0.782652	+	1.35559i
$65$		0			0
$66$	7.06425	+	2.57118i	0.869549	+	0.316490i
$67$	5.64572	+	2.05488i	0.689735	+	0.251043i	0.663022	−	0.748600i	$-0.269274\pi$
$67$	5.64572	+	2.05488i	0.689735	+	0.251043i	0.0267132	+	0.999643i	$0.491496\pi$
$68$	6.05696	−	10.4910i	0.734514	−	1.27222i
$69$	−4.13141	−	7.15580i	−0.497363	−	0.861457i
$70$		0			0
$71$	0.414414	+	0.347735i	0.0491819	+	0.0412685i	0.667047	−	0.745015i	$-0.267558\pi$
$71$	0.414414	+	0.347735i	0.0491819	+	0.0412685i	−0.617865	+	0.786284i	$0.712002\pi$
$72$	4.20186	−	3.52578i	0.495194	−	0.415517i
$73$	−1.81765	+	10.3084i	−0.212740	+	1.20651i	0.672047	+	0.740509i	$0.265415\pi$
$73$	−1.81765	+	10.3084i	−0.212740	+	1.20651i	−0.884786	+	0.465997i	$0.845696\pi$
$74$	−20.7330	+	7.54620i	−2.41016	+	0.877228i
$75$		0			0
$76$	14.6262	+	2.49294i	1.67774	+	0.285960i
$77$	−0.403477			−0.0459805
$78$	4.28672	−	1.56024i	0.485375	−	0.176662i
$79$	−2.01585	+	11.4325i	−0.226801	+	1.28625i	0.632411	+	0.774633i	$0.282065\pi$
$79$	−2.01585	+	11.4325i	−0.226801	+	1.28625i	−0.859212	+	0.511620i	$0.829046\pi$
$80$		0			0
$81$	−0.867724	−	0.728107i	−0.0964137	−	0.0809007i
$82$	0.0756149	+	0.428833i	0.00835027	+	0.0473567i
$83$	3.79789	+	6.57815i	0.416873	+	0.722045i	0.995623	−	0.0934597i	$-0.0297926\pi$
$83$	3.79789	+	6.57815i	0.416873	+	0.722045i	−0.578750	+	0.815505i	$0.696459\pi$
$84$	0.280128	−	0.485197i	0.0305645	−	0.0529393i
$85$		0			0
$86$	−24.0163	−	8.74123i	−2.58975	−	0.942591i
$87$	4.34826	−	7.53141i	0.466182	−	0.807452i
$88$	−4.59428	−	7.95753i	−0.489752	−	0.848275i
$89$	0.251241	+	1.42486i	0.0266315	+	0.151035i	0.995224	−	0.0976195i	$-0.0311228\pi$
$89$	0.251241	+	1.42486i	0.0266315	+	0.151035i	−0.968592	+	0.248654i	$0.920012\pi$
$90$		0			0
$91$	−0.187556	+	0.157378i	−0.0196612	+	0.0164977i
$92$	−4.25217	+	24.1152i	−0.443319	+	2.51419i
$93$	5.23127	−	1.90403i	0.542458	−	0.197439i
$94$	−8.53210			−0.880019
$95$		0			0
$96$	−5.41783			−0.552955
$97$	8.27128	−	3.01050i	0.839822	−	0.305670i	0.113938	−	0.993488i	$-0.463653\pi$
$97$	8.27128	−	3.01050i	0.839822	−	0.305670i	0.725883	+	0.687818i	$0.241431\pi$
$98$	2.81738	−	15.9781i	0.284598	−	1.61404i
$99$	3.62516	−	3.04187i	0.364343	−	0.305720i
$100$		0			0
$101$	−0.499751	−	2.83423i	−0.0497270	−	0.282016i	0.949797	−	0.312867i	$-0.101289\pi$
$101$	−0.499751	−	2.83423i	−0.0497270	−	0.282016i	−0.999524	+	0.0308509i	$0.990178\pi$
$102$	4.75111	+	8.22916i	0.470430	+	0.814808i
$103$	0.599832	−	1.03894i	0.0591032	−	0.102370i	−0.834960	−	0.550311i	$-0.814509\pi$
$103$	0.599832	−	1.03894i	0.0591032	−	0.102370i	0.894063	+	0.447941i	$0.147843\pi$
$104$	−5.23952	−	1.90703i	−0.513778	−	0.187000i
$105$		0			0
$106$	−1.90994	+	3.30811i	−0.185509	+	0.321312i
$107$	−2.04768	−	3.54668i	−0.197957	−	0.342871i	0.749909	−	0.661541i	$-0.230097\pi$
$107$	−2.04768	−	3.54668i	−0.197957	−	0.342871i	−0.947866	+	0.318670i	$0.896764\pi$
$108$	3.17776	+	18.0220i	0.305780	+	1.73417i
$109$	−12.4054	−	10.4093i	−1.18822	−	0.997034i	−0.999889	−	0.0149287i	$-0.995248\pi$
$109$	−12.4054	−	10.4093i	−1.18822	−	0.997034i	−0.188331	−	0.982106i	$-0.560308\pi$
$110$		0			0
$111$	1.89302	−	10.7359i	0.179678	−	1.01900i
$112$	−0.104848	+	0.0381614i	−0.00990716	+	0.00360591i
$113$	−3.11845			−0.293359			−0.146680	−	0.989184i	$-0.546859\pi$
$113$	−3.11845			−0.293359			−0.146680	+	0.989184i	$0.546859\pi$
$114$	−7.42992	+	8.95806i	−0.695876	+	0.838999i
$115$		0			0
$116$	−24.2183	+	8.81474i	−2.24861	+	0.818428i
$117$	0.498658	−	2.82803i	0.0461009	−	0.261451i
$118$	9.55625	−	8.01864i	0.879724	−	0.738176i
$119$	−0.390677	−	0.327817i	−0.0358133	−	0.0300509i
$120$		0			0
$121$	1.53628	+	2.66091i	0.139661	+	0.241901i
$122$	11.7542	−	20.3588i	1.06417	−	1.84320i
$123$	−0.202177	−	0.0735863i	−0.0182297	−	0.00663506i
$124$	−15.5031	−	5.64268i	−1.39222	−	0.506728i
$125$		0			0
$126$	−0.279951	−	0.484890i	−0.0249400	−	0.0431974i
$127$	1.41700	+	8.03622i	0.125739	+	0.713099i	0.980866	+	0.194682i	$0.0623675\pi$
$127$	1.41700	+	8.03622i	0.125739	+	0.713099i	−0.855128	+	0.518417i	$0.826521\pi$
$128$	15.0727	+	12.6475i	1.33225	+	1.11789i
$129$	9.67349	−	8.11702i	0.851703	−	0.714664i
$130$		0			0
$131$	−2.46196	+	0.896079i	−0.215102	+	0.0782908i	−0.447324	−	0.894372i	$-0.647623\pi$
$131$	−2.46196	+	0.896079i	−0.215102	+	0.0782908i	0.232222	+	0.972663i	$0.425401\pi$
$132$	11.0078			0.958108
$133$	0.210283	−	0.588180i	0.0182338	−	0.0510017i
$134$	13.9665			1.20652
$135$		0			0
$136$	2.01680	−	11.4378i	0.172939	−	0.980786i
$137$	9.43805	−	7.91946i	0.806347	−	0.676605i	−0.143386	−	0.989667i	$-0.545799\pi$
$137$	9.43805	−	7.91946i	0.806347	−	0.676605i	0.949733	+	0.313062i	$0.101355\pi$
$138$	−14.7141	−	12.3466i	−1.25255	−	1.05101i
$139$	1.38116	+	7.83292i	0.117148	+	0.664380i	0.985664	+	0.168719i	$0.0539630\pi$
$139$	1.38116	+	7.83292i	0.117148	+	0.664380i	−0.868516	+	0.495661i	$0.834926\pi$
$140$		0			0
$141$	2.10782	−	3.65086i	0.177511	−	0.307458i
$142$	1.18173	+	0.430115i	0.0991687	+	0.0360945i
$143$	−4.52041	−	1.64529i	−0.378016	−	0.137586i
$144$	0.654330	−	1.13333i	0.0545275	−	0.0944445i
$145$		0			0
$146$	4.22535	+	23.9631i	0.349692	+	1.98320i
$147$	6.14097	+	5.15289i	0.506499	+	0.425003i
$148$	−24.7487	+	20.7666i	−2.03433	+	1.70700i
$149$	−0.728662	+	4.13245i	−0.0596943	+	0.338543i	−0.999998	−	0.00179219i	$-0.999430\pi$
$149$	−0.728662	+	4.13245i	−0.0596943	+	0.338543i	0.940304	+	0.340335i	$0.110541\pi$
$150$		0			0
$151$	−2.86140			−0.232857			−0.116429	−	0.993199i	$-0.537145\pi$
$151$	−2.86140			−0.232857			−0.116429	+	0.993199i	$0.537145\pi$
$152$	13.9947	−	2.55015i	1.13512	−	0.206845i
$153$	5.98161			0.483585
$154$	−0.881369	+	0.320792i	−0.0710227	+	0.0258502i
$155$		0			0
$156$	5.11698	−	4.29366i	0.409686	−	0.343768i
$157$	8.82817	+	7.40771i	0.704565	+	0.591200i	0.923068	−	0.384636i	$-0.125673\pi$
$157$	8.82817	+	7.40771i	0.704565	+	0.591200i	−0.218504	+	0.975836i	$0.570118\pi$
$158$	4.68610	+	26.5762i	0.372806	+	2.11429i
$159$	−0.943685	−	1.63451i	−0.0748391	−	0.129625i
$160$		0			0
$161$	0.968735	+	0.352591i	0.0763470	+	0.0277880i
$162$	−2.47438	−	0.900600i	−0.194405	−	0.0707578i
$163$	9.45974	−	16.3847i	0.740944	−	1.28335i	−0.211122	−	0.977460i	$-0.567712\pi$
$163$	9.45974	−	16.3847i	0.740944	−	1.28335i	0.952066	−	0.305892i	$-0.0989548\pi$
$164$	0.318807	+	0.552190i	0.0248946	+	0.0431188i
$165$		0			0
$166$	13.5263	+	11.3499i	1.04985	+	0.880925i
$167$	−11.5435	+	9.68614i	−0.893262	+	0.749536i	−0.968862	−	0.247602i	$-0.920357\pi$
$167$	−11.5435	+	9.68614i	−0.893262	+	0.749536i	0.0755996	+	0.997138i	$0.475913\pi$
$168$	0.0932748	−	0.528988i	0.00719631	−	0.0408123i
$169$	9.47294	−	3.44787i	0.728688	−	0.265221i
$170$		0			0
$171$	2.54502	+	6.87003i	0.194623	+	0.525364i
$172$	−37.4233			−2.85350
$173$	20.3866	−	7.42012i	1.54997	−	0.564141i	0.581556	−	0.813506i	$-0.302444\pi$
$173$	20.3866	−	7.42012i	1.54997	−	0.564141i	0.968410	+	0.249365i	$0.0802219\pi$
$174$	3.51049	−	19.9090i	0.266130	−	1.50930i
$175$		0			0
$176$	−1.67935	−	1.40914i	−0.126586	−	0.106218i
$177$	1.07032	+	6.07006i	0.0804499	+	0.456254i
$178$	1.68168	+	2.91275i	0.126047	+	0.218320i
$179$	−11.4395	+	19.8138i	−0.855028	+	1.48095i	0.0215906	+	0.999767i	$0.493127\pi$
$179$	−11.4395	+	19.8138i	−0.855028	+	1.48095i	−0.876619	+	0.481185i	$0.840206\pi$
$180$		0			0
$181$	10.8685	+	3.95580i	0.807847	+	0.294032i	0.712734	−	0.701434i	$-0.247457\pi$
$181$	10.8685	+	3.95580i	0.807847	+	0.294032i	0.0951131	+	0.995466i	$0.469679\pi$
$182$	−0.284577	+	0.492903i	−0.0210943	+	0.0365364i
$183$	5.80765	+	10.0591i	0.429314	+	0.743593i
$184$	4.07678	+	23.1206i	0.300544	+	1.70447i
$185$		0			0
$186$	9.91353	−	8.31844i	0.726895	−	0.609937i
$187$	1.74000	−	9.86801i	0.127241	−	0.721620i
$188$	−11.7399	+	4.27296i	−0.856217	+	0.311637i
$189$	0.770425			0.0560402
$190$		0			0
$191$	7.28958			0.527455			0.263728	−	0.964597i	$-0.415048\pi$
$191$	7.28958			0.527455			0.263728	+	0.964597i	$0.415048\pi$
$192$	−13.5156	+	4.91928i	−0.975404	+	0.355018i
$193$	4.54719	−	25.7884i	0.327314	−	1.85629i	−0.165572	−	0.986198i	$-0.552947\pi$
$193$	4.54719	−	25.7884i	0.327314	−	1.85629i	0.492887	−	0.870094i	$-0.335942\pi$
$194$	15.6745	−	13.1525i	1.12536	−	0.944292i
$195$		0			0
$196$	−4.12540	−	23.3963i	−0.294671	−	1.67116i
$197$	−1.14410	−	1.98164i	−0.0815136	−	0.141186i	0.822387	−	0.568929i	$-0.192642\pi$
$197$	−1.14410	−	1.98164i	−0.0815136	−	0.141186i	−0.903900	+	0.427743i	$0.859309\pi$
$198$	5.50043	−	9.52702i	0.390898	−	0.677056i
$199$	11.5083	+	4.18868i	0.815802	+	0.296928i	0.716018	−	0.698081i	$-0.245963\pi$
$199$	11.5083	+	4.18868i	0.815802	+	0.296928i	0.0997838	+	0.995009i	$0.468185\pi$
$200$		0			0
$201$	−3.45036	+	5.97621i	−0.243370	+	0.421529i
$202$	−3.34507	−	5.79384i	−0.235359	−	0.407653i
$203$	0.188411	+	1.06853i	0.0132239	+	0.0749964i
$204$	10.6586	+	8.94362i	0.746251	+	0.626179i
$205$		0			0
$206$	0.484264	−	2.74640i	0.0337403	−	0.191351i
$207$	−11.3621	+	4.13548i	−0.789722	+	0.287435i
$208$	−1.33029			−0.0922388
$209$	12.0740	−	2.20015i	0.835174	−	0.152188i
$210$		0			0
$211$	−2.82198	+	1.02712i	−0.194273	+	0.0707097i	−0.437325	−	0.899304i	$-0.644074\pi$
$211$	−2.82198	+	1.02712i	−0.194273	+	0.0707097i	0.243051	+	0.970013i	$0.421852\pi$
$212$	−0.971270	+	5.50834i	−0.0667071	+	0.378315i
$213$	−0.475987	+	0.399401i	−0.0326141	+	0.0273665i
$214$	−7.29287	−	6.11944i	−0.498530	−	0.418316i
$215$		0			0
$216$	8.77261	+	15.1946i	0.596900	+	1.03386i
$217$	−0.347283	+	0.601511i	−0.0235751	+	0.0408332i
$218$	−35.3748	−	12.8754i	−2.39589	−	0.872031i
$219$	−11.2976	−	4.11199i	−0.763421	−	0.277863i
$220$		0			0
$221$	−3.04023	−	5.26583i	−0.204508	−	0.354218i
$222$	−4.40056	−	24.9568i	−0.295346	−	1.67499i
$223$	−1.68042	−	1.41004i	−0.112529	−	0.0944233i	0.584787	−	0.811187i	$-0.301178\pi$
$223$	−1.68042	−	1.41004i	−0.112529	−	0.0944233i	−0.697316	+	0.716764i	$0.745623\pi$
$224$	0.517810	−	0.434494i	0.0345977	−	0.0290309i
$225$		0			0
$226$	−6.81204	+	2.47938i	−0.453130	+	0.164926i
$227$	6.44357			0.427675			0.213838	−	0.976869i	$-0.431404\pi$
$227$	6.44357			0.427675			0.213838	+	0.976869i	$0.431404\pi$
$228$	−5.73702	+	16.0469i	−0.379943	+	1.06273i
$229$	−1.54321			−0.101978			−0.0509892	−	0.998699i	$-0.516237\pi$
$229$	−1.54321			−0.101978			−0.0509892	+	0.998699i	$0.516237\pi$
$230$		0			0
$231$	0.0804731	−	0.456385i	0.00529474	−	0.0300280i
$232$	−18.9286	+	15.8830i	−1.24273	+	1.04277i
$233$	−15.6742	−	13.1522i	−1.02685	−	0.861629i	−0.0363763	−	0.999338i	$-0.511581\pi$
$233$	−15.6742	−	13.1522i	−1.02685	−	0.861629i	−0.990473	+	0.137710i	$0.956026\pi$
$234$	−1.15919	−	6.57410i	−0.0757787	−	0.429762i
$235$		0			0
$236$	9.13323	−	15.8192i	0.594522	−	1.02974i
$237$	−12.5295	−	4.56038i	−0.813881	−	0.296229i
$238$	−1.11404	−	0.405479i	−0.0722127	−	0.0262833i
$239$	−3.12033	+	5.40457i	−0.201837	+	0.349592i	−0.949120	−	0.314913i	$-0.898025\pi$
$239$	−3.12033	+	5.40457i	−0.201837	+	0.349592i	0.747283	+	0.664506i	$0.231358\pi$
$240$		0			0
$241$	−4.56951	−	25.9150i	−0.294348	−	1.66933i	−0.669839	−	0.742506i	$-0.733637\pi$
$241$	−4.56951	−	25.9150i	−0.294348	−	1.66933i	0.375491	−	0.926826i	$-0.377474\pi$
$242$	5.47149	+	4.59113i	0.351721	+	0.295129i
$243$	−11.3586	+	9.53104i	−0.728657	+	0.611416i
$244$	5.97741	−	33.8996i	0.382664	−	2.17020i
$245$		0			0
$246$	−0.500147			−0.0318882
$247$	4.75440	−	5.73226i	0.302515	−	0.364735i
$248$	−15.8176			−1.00442
$249$	−8.19822	+	2.98391i	−0.519541	+	0.189098i
$250$		0			0
$251$	−8.20154	+	6.88191i	−0.517677	+	0.434382i	−0.863821	−	0.503799i	$-0.831935\pi$
$251$	−8.20154	+	6.88191i	−0.517677	+	0.434382i	0.346144	+	0.938181i	$0.387491\pi$
$252$	−0.628040	−	0.526988i	−0.0395628	−	0.0331971i
$253$	3.51725	+	19.9473i	0.221128	+	1.25408i
$254$	9.48469	+	16.4280i	0.595122	+	1.03078i
$255$		0			0
$256$	19.4463	+	7.07788i	1.21540	+	0.442368i
$257$	−12.7084	−	4.62548i	−0.792728	−	0.288529i	−0.0862582	−	0.996273i	$-0.527491\pi$
$257$	−12.7084	−	4.62548i	−0.792728	−	0.288529i	−0.706469	+	0.707744i	$0.749713\pi$
$258$	14.6775	−	25.4222i	0.913781	−	1.58271i
$259$	0.680059	+	1.17790i	0.0422568	+	0.0731910i
$260$		0			0
$261$	−9.74867	−	8.18011i	−0.603428	−	0.506336i
$262$	−4.66553	+	3.91485i	−0.288238	+	0.241860i
$263$	1.13576	−	6.44120i	0.0700337	−	0.397181i	−0.929560	−	0.368671i	$-0.879813\pi$
$263$	1.13576	−	6.44120i	0.0700337	−	0.397181i	0.999594	−	0.0285097i	$-0.00907614\pi$
$264$	9.91732	−	3.60961i	0.610369	−	0.222156i
$265$		0			0
$266$	−0.00829414	−	1.45203i	−0.000508546	−	0.0890295i
$267$	−1.66181			−0.101701
$268$	19.2173	−	6.99454i	1.17389	−	0.427259i
$269$	2.50436	−	14.2029i	0.152693	−	0.865968i	−0.808171	−	0.588948i	$-0.799542\pi$
$269$	2.50436	−	14.2029i	0.152693	−	0.865968i	0.960864	−	0.277020i	$-0.0893467\pi$
$270$		0			0
$271$	−1.67326	−	1.40404i	−0.101644	−	0.0852891i	0.590550	−	0.807001i	$-0.298911\pi$
$271$	−1.67326	−	1.40404i	−0.101644	−	0.0852891i	−0.692193	+	0.721712i	$0.743355\pi$
$272$	−0.481173	−	2.72887i	−0.0291754	−	0.165462i
$273$	−0.140608	−	0.243540i	−0.00850996	−	0.0147397i
$274$	14.3203	−	24.8034i	0.865118	−	1.49843i
$275$		0			0
$276$	−26.4294	−	9.61951i	−1.59086	−	0.579026i
$277$	7.98732	−	13.8344i	0.479911	−	0.831231i	−0.519823	−	0.854274i	$-0.674002\pi$
$277$	7.98732	−	13.8344i	0.479911	−	0.831231i	0.999734	+	0.0230432i	$0.00733551\pi$
$278$	9.24475	+	16.0124i	0.554463	+	0.960358i
$279$	−1.41461	−	8.02267i	−0.0846907	−	0.480305i
$280$		0			0
$281$	−10.9214	+	9.16416i	−0.651517	+	0.546688i	−0.907531	−	0.419985i	$-0.862035\pi$
$281$	−10.9214	+	9.16416i	−0.651517	+	0.546688i	0.256014	+	0.966673i	$0.417591\pi$
$282$	1.70172	−	9.65092i	0.101336	−	0.574704i
$283$	6.64111	−	2.41716i	0.394773	−	0.143686i	−0.137003	−	0.990571i	$-0.543747\pi$
$283$	6.64111	−	2.41716i	0.394773	−	0.143686i	0.531776	+	0.846885i	$0.321525\pi$
$284$	1.84142			0.109268
$285$		0			0
$286$	−11.1826			−0.661244
$287$	0.0252245	−	0.00918097i	0.00148896	−	0.000541936i
$288$	−1.37671	+	7.80769i	−0.0811232	+	0.460073i
$289$	−3.32041	+	2.78616i	−0.195318	+	0.163892i
$290$		0			0
$291$	1.75557	+	9.95634i	0.102913	+	0.583651i
$292$	17.8149	+	30.8563i	1.04254	+	1.80573i
$293$	−0.488373	+	0.845886i	−0.0285310	+	0.0494172i	−0.879938	−	0.475088i	$-0.842416\pi$
$293$	−0.488373	+	0.845886i	−0.0285310	+	0.0494172i	0.851407	+	0.524505i	$0.175750\pi$
$294$	17.5114	+	6.37364i	1.02129	+	0.371718i
$295$		0			0
$296$	−15.4873	+	26.8247i	−0.900179	+	1.55916i
$297$	7.56858	+	13.1092i	0.439174	+	0.760671i
$298$	1.69386	+	9.60638i	0.0981230	+	0.556483i
$299$	9.41556	+	7.90059i	0.544516	+	0.456903i
$300$		0			0
$301$	−0.273584	+	1.55157i	−0.0157691	+	0.0894312i
$302$	−6.25052	+	2.27500i	−0.359677	+	0.130912i
$303$	3.30555			0.189899
$304$	2.92945	−	1.71370i	0.168015	−	0.0982876i
$305$		0			0
$306$	13.0664	−	4.75579i	0.746958	−	0.271870i
$307$	4.94325	−	28.0346i	0.282126	−	1.60002i	−0.433248	−	0.901275i	$-0.642633\pi$
$307$	4.94325	−	28.0346i	0.282126	−	1.60002i	0.715374	−	0.698742i	$-0.246256\pi$
$308$	−1.05207	+	0.882796i	−0.0599475	+	0.0503020i
$309$	1.05554	+	0.885703i	0.0600475	+	0.0503859i
$310$		0			0
$311$	12.7730	+	22.1235i	0.724292	+	1.25451i	0.959265	+	0.282509i	$0.0911668\pi$
$311$	12.7730	+	22.1235i	0.724292	+	1.25451i	−0.234972	+	0.972002i	$0.575500\pi$
$312$	3.20212	−	5.54623i	0.181284	−	0.313993i
$313$	14.0496	+	5.11365i	0.794133	+	0.289041i	0.707053	−	0.707161i	$-0.250024\pi$
$313$	14.0496	+	5.11365i	0.794133	+	0.289041i	0.0870798	+	0.996201i	$0.472246\pi$
$314$	25.1742	+	9.16265i	1.42066	+	0.517078i
$315$		0			0
$316$	19.7575	+	34.2210i	1.11145	+	1.92508i
$317$	3.91406	+	22.1977i	0.219835	+	1.24675i	0.872316	+	0.488943i	$0.162617\pi$
$317$	3.91406	+	22.1977i	0.219835	+	1.24675i	−0.652481	+	0.757805i	$0.726272\pi$
$318$	−3.36096	−	2.82018i	−0.188473	−	0.158148i
$319$	−16.3307	+	13.7031i	−0.914344	+	0.767226i
$320$		0			0
$321$	4.42017	−	1.60881i	0.246710	−	0.0897950i
$322$	2.39647			0.133550
$323$	13.4785	+	7.67950i	0.749964	+	0.427299i
$324$	−3.85568			−0.214204
$325$		0			0
$326$	7.63716	−	43.3125i	0.422983	−	2.39886i
$327$	14.2486	−	11.9560i	0.787947	−	0.661166i
$328$	0.468295	+	0.392946i	0.0258572	+	0.0216968i
$329$	0.0913327	+	0.517973i	0.00503533	+	0.0285568i
$330$		0			0
$331$	5.43405	−	9.41205i	0.298682	−	0.517333i	−0.677152	−	0.735843i	$-0.736786\pi$
$331$	5.43405	−	9.41205i	0.298682	−	0.517333i	0.975835	+	0.218510i	$0.0701196\pi$
$332$	24.2959	+	8.84297i	1.33341	+	0.485321i
$333$	−14.9905	−	5.45611i	−0.821476	−	0.298993i
$334$	−17.5148	+	30.3366i	−0.958369	+	1.65994i
$335$		0			0
$336$	−0.0222538	−	0.126207i	−0.00121404	−	0.00688518i
$337$	−5.90548	−	4.95529i	−0.321692	−	0.269932i	0.467612	−	0.883934i	$-0.345114\pi$
$337$	−5.90548	−	4.95529i	−0.321692	−	0.269932i	−0.789305	+	0.614002i	$0.789559\pi$
$338$	17.9517	−	15.0633i	0.976443	−	0.819333i
$339$	0.621971	−	3.52737i	0.0337808	−	0.191581i
$340$		0			0
$341$	−13.6467			−0.739010
$342$	11.0216	+	12.9836i	0.595978	+	0.702075i
$343$	−2.00329			−0.108167
$344$	−33.7159	+	12.2716i	−1.81784	+	0.661639i
$345$		0			0
$346$	38.6337	−	32.4175i	2.07696	−	1.74278i
$347$	−15.5276	−	13.0292i	−0.833566	−	0.699445i	0.122540	−	0.992464i	$-0.460896\pi$
$347$	−15.5276	−	13.0292i	−0.833566	−	0.699445i	−0.956107	+	0.293018i	$0.905340\pi$
$348$	−5.14031	−	29.1521i	−0.275549	−	1.56272i
$349$	−9.52515	−	16.4981i	−0.509870	−	0.883120i	−0.999935	−	0.0114345i	$-0.996360\pi$
$349$	−9.52515	−	16.4981i	−0.509870	−	0.883120i	0.490065	−	0.871686i	$-0.336973\pi$
$350$		0			0
$351$	8.63155	+	3.14163i	0.460718	+	0.167688i
$352$	12.4801	+	4.54237i	0.665189	+	0.242109i
$353$	−9.08336	+	15.7328i	−0.483459	+	0.837375i	−0.999820	−	0.0189962i	$-0.993953\pi$
$353$	−9.08336	+	15.7328i	−0.483459	+	0.837375i	0.516361	+	0.856371i	$0.327286\pi$
$354$	7.16414	+	12.4087i	0.380770	+	0.659513i
$355$		0			0
$356$	3.77266	+	3.16564i	0.199951	+	0.167778i
$357$	0.448724	−	0.376524i	0.0237490	−	0.0199278i
$358$	−9.23549	+	52.3771i	−0.488111	+	2.76821i
$359$	15.1590	−	5.51741i	0.800060	−	0.291198i	0.0905485	−	0.995892i	$-0.471138\pi$
$359$	15.1590	−	5.51741i	0.800060	−	0.291198i	0.709511	+	0.704694i	$0.248916\pi$
$360$		0			0
$361$	−3.08534	+	18.7478i	−0.162387	+	0.986727i
$362$	26.8866			1.41313
$363$	−3.31624	+	1.20701i	−0.174058	+	0.0633518i
$364$	−0.144718	+	0.820735i	−0.00758527	+	0.0430182i
$365$		0			0
$366$	20.6841	+	17.3560i	1.08118	+	0.907214i
$367$	5.60217	+	31.7715i	0.292431	+	1.65846i	0.677465	+	0.735555i	$0.263079\pi$
$367$	5.60217	+	31.7715i	0.292431	+	1.65846i	−0.385034	+	0.922902i	$0.625810\pi$
$368$	2.80064	+	4.85084i	0.145993	+	0.252868i
$369$	−0.157421	+	0.272660i	−0.00819499	+	0.0141941i
$370$		0			0
$371$	0.221276	+	0.0805379i	0.0114881	+	0.00418132i
$372$	9.47469	−	16.4106i	0.491240	−	0.850853i
$373$	−1.19018	−	2.06146i	−0.0616253	−	0.106738i	0.833567	−	0.552419i	$-0.186295\pi$
$373$	−1.19018	−	2.06146i	−0.0616253	−	0.106738i	−0.895192	+	0.445681i	$0.852962\pi$
$374$	−4.04484	−	22.9394i	−0.209153	−	1.18617i
$375$		0			0
$376$	−9.17568	+	7.69931i	−0.473199	+	0.397061i
$377$	−2.24636	+	12.7398i	−0.115694	+	0.656131i
$378$	1.68294	−	0.612540i	0.0865611	−	0.0315057i
$379$	17.7215			0.910291			0.455145	−	0.890417i	$-0.349587\pi$
$379$	17.7215			0.910291			0.455145	+	0.890417i	$0.349587\pi$
$380$		0			0
$381$	−9.37263			−0.480174
$382$	15.9236	−	5.79571i	0.814722	−	0.296534i
$383$	1.85188	−	10.5025i	0.0946268	−	0.536655i	−0.900234	−	0.435406i	$-0.856605\pi$
$383$	1.85188	−	10.5025i	0.0946268	−	0.536655i	0.994861	−	0.101249i	$-0.0322840\pi$
$384$	−17.3121	+	14.5266i	−0.883457	+	0.741308i
$385$		0			0
$386$	−10.5705	−	59.9484i	−0.538025	−	3.05129i
$387$	−9.23943	−	16.0032i	−0.469667	−	0.813486i
$388$	14.9806	−	25.9472i	0.760527	−	1.31727i
$389$	−21.3605	−	7.77458i	−1.08302	−	0.394187i	−0.261989	−	0.965071i	$-0.584378\pi$
$389$	−21.3605	−	7.77458i	−1.08302	−	0.394187i	−0.821031	+	0.570884i	$0.806600\pi$
$390$		0			0
$391$	−12.8011	+	22.1722i	−0.647381	+	1.12130i
$392$	−11.3887	−	19.7257i	−0.575214	−	0.996301i
$393$	−0.522548	−	2.96351i	−0.0263590	−	0.149490i
$394$	−4.07474	−	3.41911i	−0.205282	−	0.172252i
$395$		0			0
$396$	2.79716	−	15.8635i	0.140563	−	0.797170i
$397$	19.2078	−	6.99106i	0.964011	−	0.350871i	0.188407	−	0.982091i	$-0.439668\pi$
$397$	19.2078	−	6.99106i	0.964011	−	0.350871i	0.775604	+	0.631220i	$0.217445\pi$
$398$	28.4694			1.42704
$399$	0.623367	+	0.355169i	0.0312074	+	0.0177807i
$400$		0			0
$401$	−15.6902	+	5.71077i	−0.783531	+	0.285182i	−0.702644	−	0.711541i	$-0.747998\pi$
$401$	−15.6902	+	5.71077i	−0.783531	+	0.285182i	−0.0808870	+	0.996723i	$0.525775\pi$
$402$	−2.78559	+	15.7979i	−0.138933	+	0.787927i
$403$	−6.34366	+	5.32296i	−0.316000	+	0.265156i
$404$	−7.50431	−	6.29686i	−0.373353	−	0.313281i
$405$		0			0
$406$	1.26113	+	2.18434i	0.0625888	+	0.108407i
$407$	−13.3617	+	23.1431i	−0.662313	+	1.14716i
$408$	12.5354	+	4.56252i	0.620596	+	0.225878i
$409$	16.6181	+	6.04849i	0.821712	+	0.299079i	0.718453	−	0.695576i	$-0.244851\pi$
$409$	16.6181	+	6.04849i	0.821712	+	0.299079i	0.103259	+	0.994655i	$0.467073\pi$
$410$		0			0
$411$	7.07553	+	12.2552i	0.349010	+	0.604504i
$412$	−0.709093	−	4.02147i	−0.0349345	−	0.198123i
$413$	−0.589098	−	0.494312i	−0.0289876	−	0.0243235i
$414$	−21.5318	+	18.0673i	−1.05823	+	0.887961i
$415$		0			0
$416$	7.57313	−	2.75639i	0.371303	−	0.135143i
$417$	−9.13552			−0.447369
$418$	24.6255	−	14.4057i	1.20447	−	0.704606i
$419$	−37.9339			−1.85319			−0.926596	−	0.376059i	$-0.877279\pi$
$419$	−37.9339			−1.85319			−0.926596	+	0.376059i	$0.877279\pi$
$420$		0			0
$421$	2.01122	−	11.4062i	0.0980211	−	0.555905i	−0.895759	−	0.444541i	$-0.853367\pi$
$421$	2.01122	−	11.4062i	0.0980211	−	0.555905i	0.993780	−	0.111364i	$-0.0355221\pi$
$422$	−5.34780	+	4.48734i	−0.260327	+	0.218440i
$423$	−4.72568	−	3.96532i	−0.229770	−	0.192800i
$424$	0.931209	+	5.28115i	0.0452235	+	0.256475i
$425$		0			0
$426$	−0.722211	+	1.25091i	−0.0349912	+	0.0606066i
$427$	−1.36178	−	0.495648i	−0.0659012	−	0.0239861i
$428$	−13.0994	−	4.76779i	−0.633183	−	0.230460i
$429$	2.76263	−	4.78502i	0.133381	−	0.231023i
$430$		0			0
$431$	5.52023	+	31.3068i	0.265900	+	1.50800i	0.766459	+	0.642293i	$0.222017\pi$
$431$	5.52023	+	31.3068i	0.265900	+	1.50800i	−0.500559	+	0.865702i	$0.666872\pi$
$432$	3.20665	+	2.69070i	0.154280	+	0.129456i
$433$	−3.13196	+	2.62802i	−0.150512	+	0.126295i	−0.714934	−	0.699192i	$-0.753543\pi$
$433$	−3.13196	+	2.62802i	−0.150512	+	0.126295i	0.564422	+	0.825486i	$0.309099\pi$
$434$	−0.280373	+	1.59007i	−0.0134583	+	0.0763260i
$435$		0			0
$436$	−55.1226			−2.63989
$437$	−30.9119	−	5.26872i	−1.47871	−	0.252037i
$438$	−27.9481			−1.33541
$439$	11.0468	−	4.02069i	0.527233	−	0.191897i	−0.0646692	−	0.997907i	$-0.520599\pi$
$439$	11.0468	−	4.02069i	0.527233	−	0.191897i	0.591903	+	0.806009i	$0.298377\pi$
$440$		0			0
$441$	8.98635	−	7.54044i	0.427921	−	0.359069i
$442$	−10.8279	−	9.08566i	−0.515029	−	0.432161i
$443$	−1.36949	−	7.76677i	−0.0650665	−	0.369010i	−0.999903	−	0.0139318i	$-0.995565\pi$
$443$	−1.36949	−	7.76677i	−0.0650665	−	0.369010i	0.934836	−	0.355079i	$-0.115546\pi$
$444$	−18.5536	−	32.1358i	−0.880516	−	1.52510i
$445$		0			0
$446$	−4.79184	−	1.74409i	−0.226900	−	0.0825850i
$447$	−4.52900	−	1.64842i	−0.214215	−	0.0779677i
$448$	0.897245	−	1.55407i	0.0423908	−	0.0734231i
$449$	0.580397	+	1.00528i	0.0273906	+	0.0474419i	0.879396	−	0.476091i	$-0.157947\pi$
$449$	0.580397	+	1.00528i	0.0273906	+	0.0474419i	−0.852005	+	0.523533i	$0.824614\pi$
$450$		0			0
$451$	0.404022	+	0.339015i	0.0190247	+	0.0159636i
$452$	−8.13142	+	6.82307i	−0.382470	+	0.320930i
$453$	0.570702	−	3.23661i	0.0268139	−	0.152069i
$454$	14.0755	−	5.12308i	0.660598	−	0.240438i
$455$		0			0
$456$	0.0933272	+	16.3385i	0.00437045	+	0.765119i
$457$	38.6888			1.80978			0.904892	−	0.425641i	$-0.139951\pi$
$457$	38.6888			1.80978			0.904892	+	0.425641i	$0.139951\pi$
$458$	−3.37105	+	1.22696i	−0.157519	+	0.0573321i
$459$	−3.32246	+	18.8426i	−0.155079	+	0.879497i
$460$		0			0
$461$	−18.7676	−	15.7479i	−0.874096	−	0.733453i	0.0908609	−	0.995864i	$-0.471038\pi$
$461$	−18.7676	−	15.7479i	−0.874096	−	0.733453i	−0.964956	+	0.262410i	$0.915483\pi$
$462$	−0.187070	−	1.06092i	−0.00870326	−	0.0493587i
$463$	16.2425	+	28.1328i	0.754852	+	1.30744i	0.945448	+	0.325773i	$0.105625\pi$
$463$	16.2425	+	28.1328i	0.754852	+	1.30744i	−0.190596	+	0.981669i	$0.561042\pi$
$464$	−2.94764	+	5.10546i	−0.136841	+	0.237015i
$465$		0			0
$466$	−44.6960	−	16.2680i	−2.07050	−	0.753602i
$467$	−7.35099	+	12.7323i	−0.340163	+	0.589180i	−0.984463	−	0.175593i	$-0.943816\pi$
$467$	−7.35099	+	12.7323i	−0.340163	+	0.589180i	0.644299	+	0.764773i	$0.277149\pi$
$468$	−4.88738	−	8.46518i	−0.225919	−	0.391303i
$469$	−0.149505	−	0.847887i	−0.00690351	−	0.0391518i
$470$		0			0
$471$	−10.1399	+	8.50835i	−0.467220	+	0.392044i
$472$	3.04111	−	17.2470i	0.139978	−	0.793856i
$473$	−29.0885	+	10.5873i	−1.33749	+	0.486806i
$474$	−30.9957			−1.42368
$475$		0			0
$476$	−1.73595			−0.0795672
$477$	−2.59531	+	0.944615i	−0.118831	+	0.0432510i
$478$	−2.51915	+	14.2868i	−0.115223	+	0.653462i
$479$	−10.1268	+	8.49741i	−0.462706	+	0.388256i	−0.844125	−	0.536146i	$-0.819880\pi$
$479$	−10.1268	+	8.49741i	−0.462706	+	0.388256i	0.381420	+	0.924402i	$0.375435\pi$
$480$		0			0
$481$	2.81592	+	15.9699i	0.128395	+	0.728162i
$482$	−30.5860	−	52.9765i	−1.39315	−	2.41301i
$483$	−0.592039	+	1.02544i	−0.0269387	+	0.0466592i
$484$	9.82785	+	3.57705i	0.446721	+	0.162593i
$485$		0			0
$486$	−17.2344	+	29.8508i	−0.781767	+	1.35406i
$487$	4.83036	+	8.36642i	0.218884	+	0.379119i	0.954467	−	0.298316i	$-0.0964249\pi$
$487$	4.83036	+	8.36642i	0.218884	+	0.379119i	−0.735583	+	0.677435i	$0.763092\pi$
$488$	−5.73086	−	32.5013i	−0.259424	−	1.47127i
$489$	16.6465	+	13.9681i	0.752783	+	0.631660i
$490$		0			0
$491$	0.466479	−	2.64553i	0.0210519	−	0.119391i	−0.972471	−	0.233024i	$-0.925138\pi$
$491$	0.466479	−	2.64553i	0.0210519	−	0.119391i	0.993523	+	0.113633i	$0.0362489\pi$
$492$	−0.688184	+	0.250479i	−0.0310257	+	0.0112924i
$493$	−26.9461			−1.21359
$494$	5.82813	−	16.3018i	0.262220	−	0.733452i
$495$		0			0
$496$	−3.54623	+	1.29072i	−0.159230	+	0.0579551i
$497$	0.0134618	−	0.0763457i	0.000603844	−	0.00342457i
$498$	−15.5360	+	13.0363i	−0.696187	+	0.584170i
$499$	1.80438	+	1.51406i	0.0807753	+	0.0677786i	0.682281	−	0.731090i	$-0.260988\pi$
$499$	1.80438	+	1.51406i	0.0807753	+	0.0677786i	−0.601506	+	0.798868i	$0.705432\pi$
$500$		0			0
$501$	−8.65395	−	14.9891i	−0.386630	−	0.669663i
$502$	−12.4441	+	21.5538i	−0.555408	+	0.961995i
$503$	−12.9104	−	4.69900i	−0.575646	−	0.209518i	0.0377584	−	0.999287i	$-0.487978\pi$
$503$	−12.9104	−	4.69900i	−0.575646	−	0.209518i	−0.613405	+	0.789769i	$0.710201\pi$
$504$	−0.738629	−	0.268839i	−0.0329011	−	0.0119750i
$505$		0			0
$506$	23.5427	+	40.7771i	1.04660	+	1.81276i
$507$	2.01062	+	11.4028i	0.0892948	+	0.506416i
$508$	21.2779	+	17.8542i	0.944052	+	0.792154i
$509$	−27.8684	+	23.3844i	−1.23524	+	1.03649i	−0.237364	+	0.971421i	$0.576283\pi$
$509$	−27.8684	+	23.3844i	−1.23524	+	1.03649i	−0.997881	+	0.0650727i	$0.979272\pi$
$510$		0			0
$511$	1.40954	−	0.513031i	0.0623544	−	0.0226952i
$512$	8.75464			0.386904
$513$	−23.0548	+	4.20111i	−1.01789	+	0.185483i
$514$	−31.4382			−1.38668
$515$		0			0
$516$	7.46402	−	42.3306i	0.328585	−	1.86350i
$517$	−7.91633	+	6.64259i	−0.348160	+	0.292141i
$518$	2.42205	+	2.03234i	0.106419	+	0.0892960i
$519$	4.32704	+	24.5398i	0.189936	+	1.07718i
$520$		0			0
$521$	−0.290212	+	0.502661i	−0.0127144	+	0.0220220i	−0.872313	−	0.488949i	$-0.837381\pi$
$521$	−0.290212	+	0.502661i	−0.0127144	+	0.0220220i	0.859598	+	0.510971i	$0.170714\pi$
$522$	−27.7990	−	10.1180i	−1.21673	−	0.442854i
$523$	18.0856	+	6.58262i	0.790828	+	0.287838i	0.705680	−	0.708530i	$-0.250642\pi$
$523$	18.0856	+	6.58262i	0.790828	+	0.287838i	0.0851478	+	0.996368i	$0.472864\pi$
$524$	−4.45901	+	7.72322i	−0.194793	+	0.337391i
$525$		0			0
$526$	−2.64021	−	14.9734i	−0.115118	−	0.652869i
$527$	−13.2137	−	11.0876i	−0.575600	−	0.482986i
$528$	1.92886	−	1.61851i	0.0839431	−	0.0704366i
$529$	4.99286	−	28.3159i	0.217081	−	1.23113i
$530$		0			0
$531$	9.01961			0.391418
$532$	−0.738602	−	1.99378i	−0.0320224	−	0.0864414i
$533$	0.320044			0.0138626
$534$	−3.63011	+	1.32125i	−0.157090	+	0.0571762i
$535$		0			0
$536$	15.0200	−	12.6032i	0.648763	−	0.544377i
$537$	−20.1304	−	16.8914i	−0.868690	−	0.728918i
$538$	−5.82169	−	33.0165i	−0.250991	−	1.42344i
$539$	−9.82559	−	17.0184i	−0.423218	−	0.733036i
$540$		0			0
$541$	29.9824	+	10.9127i	1.28904	+	0.469174i	0.893413	−	0.449236i	$-0.148304\pi$
$541$	29.9824	+	10.9127i	1.28904	+	0.469174i	0.395631	+	0.918410i	$0.370526\pi$
$542$	−4.77143	−	1.73666i	−0.204951	−	0.0745959i
$543$	−6.64223	+	11.5047i	−0.285045	+	0.493713i
$544$	8.39355	+	14.5380i	0.359870	+	0.623314i
$545$		0			0
$546$	−0.500778	−	0.420203i	−0.0214313	−	0.0179830i
$547$	2.63099	−	2.20766i	0.112493	−	0.0943929i	−0.584806	−	0.811173i	$-0.698829\pi$
$547$	2.63099	−	2.20766i	0.112493	−	0.0943929i	0.697299	+	0.716780i	$0.254385\pi$
$548$	7.28235	−	41.3003i	0.311087	−	1.76426i
$549$	15.9721	−	5.81337i	0.681673	−	0.248109i
$550$		0			0
$551$	−11.4649	−	30.9482i	−0.488419	−	1.31844i
$552$	−26.9655			−1.14773
$553$	1.56324	−	0.568974i	0.0664759	−	0.0241952i
$554$	6.44843	−	36.5708i	0.273967	−	1.55375i
$555$		0			0
$556$	20.7396	+	17.4026i	0.879554	+	0.738033i
$557$	−1.18604	−	6.72634i	−0.0502539	−	0.285004i	0.949316	−	0.314323i	$-0.101777\pi$
$557$	−1.18604	−	6.72634i	−0.0502539	−	0.285004i	−0.999570	+	0.0293185i	$0.990666\pi$
$558$	−9.46870	−	16.4003i	−0.400842	−	0.694279i
$559$	−9.39211	+	16.2676i	−0.397244	+	0.688047i
$560$		0			0
$561$	10.8150	+	3.93632i	0.456608	+	0.166192i
$562$	−16.5710	+	28.7018i	−0.699004	+	1.21071i
$563$	−6.28141	−	10.8797i	−0.264730	−	0.458526i	0.702763	−	0.711424i	$-0.251949\pi$
$563$	−6.28141	−	10.8797i	−0.264730	−	0.458526i	−0.967493	+	0.252898i	$0.918616\pi$
$564$	−2.49177	−	14.1315i	−0.104922	−	0.595045i
$565$		0			0
$566$	12.5852	−	10.5603i	0.528997	−	0.443881i
$567$	−0.0281871	+	0.159857i	−0.00118375	+	0.00671336i
$568$	1.65900	−	0.603827i	0.0696102	−	0.0253360i
$569$	3.47978			0.145880			0.0729400	−	0.997336i	$-0.476762\pi$
$569$	3.47978			0.145880			0.0729400	+	0.997336i	$0.476762\pi$
$570$		0			0
$571$	−0.621524			−0.0260100			−0.0130050	−	0.999915i	$-0.504140\pi$
$571$	−0.621524			−0.0260100			−0.0130050	+	0.999915i	$0.504140\pi$
$572$	−15.3869	+	5.60037i	−0.643359	+	0.234163i
$573$	−1.45390	+	8.24546i	−0.0607374	+	0.344459i
$574$	0.0478017	−	0.0401104i	0.00199521	−	0.00167418i
$575$		0			0
$576$	3.65482	+	20.7275i	0.152284	+	0.863646i
$577$	1.92585	+	3.33567i	0.0801742	+	0.138866i	0.903325	−	0.428958i	$-0.141119\pi$
$577$	1.92585	+	3.33567i	0.0801742	+	0.138866i	−0.823150	+	0.567823i	$0.807786\pi$
$578$	−5.03803	+	8.72612i	−0.209554	+	0.362959i
$579$	28.2631	+	10.2869i	1.17458	+	0.427510i
$580$		0			0
$581$	0.544246	−	0.942662i	0.0225791	−	0.0391082i
$582$	11.7509	+	20.3531i	0.487090	+	0.843665i
$583$	0.803402	+	4.55632i	0.0332735	+	0.188704i
$584$	26.1682	+	21.9577i	1.08285	+	0.908618i
$585$		0			0
$586$	−0.394279	+	2.23607i	−0.0162875	+	0.0923712i
$587$	37.9949	−	13.8290i	1.56822	−	0.570784i	0.595616	−	0.803269i	$-0.296908\pi$
$587$	37.9949	−	13.8290i	1.56822	−	0.570784i	0.972600	+	0.232485i	$0.0746856\pi$
$588$	27.2871			1.12530
$589$	7.11233	−	19.8938i	0.293059	−	0.819710i
$590$		0			0
$591$	2.46968	−	0.898889i	0.101589	−	0.0369753i
$592$	−1.28326	+	7.27772i	−0.0527416	+	0.299113i
$593$	4.49946	−	3.77549i	0.184771	−	0.155041i	−0.545711	−	0.837974i	$-0.683740\pi$
$593$	4.49946	−	3.77549i	0.184771	−	0.155041i	0.730481	+	0.682933i	$0.239296\pi$
$594$	26.9557	+	22.6185i	1.10601	+	0.928050i
$595$		0			0
$596$	7.14166	+	12.3697i	0.292534	+	0.506684i
$597$	−7.03326	+	12.1820i	−0.287852	+	0.498575i
$598$	26.8491	+	9.77229i	1.09794	+	0.399619i
$599$	12.5080	+	4.55254i	0.511063	+	0.186012i	0.584663	−	0.811276i	$-0.301227\pi$
$599$	12.5080	+	4.55254i	0.511063	+	0.186012i	−0.0736001	+	0.997288i	$0.523449\pi$
$600$		0			0
$601$	−2.58008	−	4.46883i	−0.105244	−	0.182287i	0.808594	−	0.588367i	$-0.200229\pi$
$601$	−2.58008	−	4.46883i	−0.105244	−	0.182287i	−0.913838	+	0.406079i	$0.866896\pi$
$602$	0.635980	+	3.60682i	0.0259206	+	0.147003i
$603$	7.73561	+	6.49095i	0.315019	+	0.264332i
$604$	−7.46114	+	6.26064i	−0.303590	+	0.254742i
$605$		0			0
$606$	7.22076	−	2.62814i	0.293323	−	0.106761i
$607$	−30.5069			−1.23824			−0.619119	−	0.785297i	$-0.712510\pi$
$607$	−30.5069			−1.23824			−0.619119	+	0.785297i	$0.712510\pi$
$608$	−13.1261	+	15.8258i	−0.532333	+	0.641819i
$609$	−1.24623			−0.0504998
$610$		0			0
$611$	−1.08893	+	6.17561i	−0.0440533	+	0.249839i
$612$	15.5972	−	13.0876i	0.630478	−	0.529034i
$613$	34.8556	+	29.2473i	1.40780	+	1.18129i	0.957507	+	0.288409i	$0.0931263\pi$
$613$	34.8556	+	29.2473i	1.40780	+	1.18129i	0.450297	+	0.892879i	$0.351318\pi$
$614$	−11.4912	−	65.1698i	−0.463747	−	2.63004i
$615$		0			0
$616$	−0.658370	+	1.14033i	−0.0265265	+	0.0459452i
$617$	2.33275	+	0.849053i	0.0939131	+	0.0341816i	0.388549	−	0.921428i	$-0.372976\pi$
$617$	2.33275	+	0.849053i	0.0939131	+	0.0341816i	−0.294636	+	0.955609i	$0.595198\pi$
$618$	3.00995	+	1.09553i	0.121078	+	0.0440687i
$619$	−11.7473	+	20.3469i	−0.472162	+	0.817809i	−0.999493	−	0.0318512i	$-0.989860\pi$
$619$	−11.7473	+	20.3469i	−0.472162	+	0.817809i	0.527330	+	0.849660i	$0.323193\pi$
$620$		0			0
$621$	−6.71606	−	38.0887i	−0.269506	−	1.52845i
$622$	45.4915	+	38.1719i	1.82404	+	1.53056i
$623$	0.158828	−	0.133272i	0.00636330	−	0.00533945i
$624$	0.265324	−	1.50473i	0.0106215	−	0.0602373i
$625$		0			0
$626$	34.7562			1.38914
$627$	0.0805182	+	14.0961i	0.00321559	+	0.562942i
$628$	39.2275			1.56535
$629$	−31.7410	+	11.5528i	−1.26560	+	0.460640i
$630$		0			0
$631$	−13.6507	+	11.4543i	−0.543426	+	0.455989i	−0.872708	−	0.488243i	$-0.837638\pi$
$631$	−13.6507	+	11.4543i	−0.543426	+	0.455989i	0.329282	+	0.944232i	$0.393193\pi$
$632$	29.0217	+	24.3521i	1.15442	+	0.968675i
$633$	−0.598963	−	3.39689i	−0.0238066	−	0.135014i
$634$	26.1987	+	45.3774i	1.04048	+	1.80217i
$635$		0			0
$636$	−6.03693	−	2.19726i	−0.239380	−	0.0871272i
$637$	−11.2056	−	4.07849i	−0.443980	−	0.161596i
$638$	−24.7784	+	42.9175i	−0.980987	+	1.69912i
$639$	0.454629	+	0.787441i	0.0179849	+	0.0311507i
$640$		0			0
$641$	28.6984	+	24.0808i	1.13352	+	0.951135i	0.999207	−	0.0398045i	$-0.0126735\pi$
$641$	28.6984	+	24.0808i	1.13352	+	0.951135i	0.134311	+	0.990939i	$0.457118\pi$
$642$	8.37644	−	7.02867i	0.330592	−	0.277399i
$643$	3.45362	−	19.5865i	0.136198	−	0.772415i	−0.837821	−	0.545946i	$-0.816171\pi$
$643$	3.45362	−	19.5865i	0.136198	−	0.772415i	0.974018	−	0.226469i	$-0.0727184\pi$
$644$	3.29745	−	1.20017i	0.129938	−	0.0472935i
$645$		0			0
$646$	35.5486	+	6.05901i	1.39864	+	0.238389i
$647$	23.0645			0.906759			0.453380	−	0.891318i	$-0.350218\pi$
$647$	23.0645			0.906759			0.453380	+	0.891318i	$0.350218\pi$
$648$	−3.47371	+	1.26433i	−0.136460	+	0.0496675i
$649$	2.62372	−	14.8799i	0.102990	−	0.584086i
$650$		0			0
$651$	−0.611122	−	0.512793i	−0.0239518	−	0.0200979i
$652$	−11.1829	−	63.4211i	−0.437954	−	2.48376i
$653$	−13.4919	−	23.3687i	−0.527981	−	0.914489i	−0.999468	−	0.0326165i	$-0.989616\pi$
$653$	−13.4919	−	23.3687i	−0.527981	−	0.914489i	0.471487	−	0.881873i	$-0.343717\pi$
$654$	21.6192	−	37.4455i	0.845377	−	1.46424i
$655$		0			0
$656$	0.137054	+	0.0498834i	0.00535104	+	0.00194762i
$657$	−8.79663	+	15.2362i	−0.343189	+	0.594421i
$658$	0.611334	+	1.05886i	0.0238323	+	0.0412787i
$659$	2.34217	+	13.2831i	0.0912379	+	0.517436i	0.995835	+	0.0911691i	$0.0290604\pi$
$659$	2.34217	+	13.2831i	0.0912379	+	0.517436i	−0.904598	+	0.426267i	$0.859829\pi$
$660$		0			0
$661$	−16.8359	+	14.1270i	−0.654842	+	0.549477i	−0.908536	−	0.417807i	$-0.862799\pi$
$661$	−16.8359	+	14.1270i	−0.654842	+	0.549477i	0.253694	+	0.967284i	$0.418354\pi$
$662$	4.38709	−	24.8804i	0.170509	−	0.967005i
$663$	6.56271	−	2.38863i	0.254875	−	0.0927668i
$664$	24.7887			0.961988
$665$		0			0
$666$	−37.0838			−1.43697
$667$	51.1843	−	18.6296i	1.98186	−	0.721340i
$668$	−8.90691	+	50.5136i	−0.344619	+	1.95443i
$669$	1.93010	−	1.61954i	0.0746219	−	0.0626152i
$670$		0			0
$671$	−4.94431	−	28.0406i	−0.190873	−	1.08250i
$672$	0.388193	+	0.672370i	0.0149749	+	0.0259372i
$673$	−11.5999	+	20.0916i	−0.447143	+	0.774475i	−0.998199	−	0.0599940i	$-0.980892\pi$
$673$	−11.5999	+	20.0916i	−0.447143	+	0.774475i	0.551056	+	0.834468i	$0.314225\pi$
$674$	−16.8399	−	6.12923i	−0.648649	−	0.236089i
$675$		0			0
$676$	17.1570	−	29.7169i	0.659886	−	1.14296i
$677$	14.3647	+	24.8804i	0.552081	+	0.956232i	0.998124	+	0.0612208i	$0.0194994\pi$
$677$	14.3647	+	24.8804i	0.552081	+	0.956232i	−0.446043	+	0.895011i	$0.647167\pi$
$678$	−1.44585	−	8.19981i	−0.0555275	−	0.314912i
$679$	−0.966259	−	0.810788i	−0.0370816	−	0.0311152i
$680$		0			0
$681$	−1.28516	+	7.28852i	−0.0492475	+	0.279297i
$682$	−29.8103	+	10.8500i	−1.14149	+	0.415470i
$683$	−24.0010			−0.918374			−0.459187	−	0.888340i	$-0.651859\pi$
$683$	−24.0010			−0.918374			−0.459187	+	0.888340i	$0.651859\pi$
$684$	21.6676	+	12.3453i	0.828481	+	0.472035i
$685$		0			0
$686$	−4.37604	+	1.59275i	−0.167078	+	0.0608114i
$687$	0.307792	−	1.74558i	0.0117430	−	0.0665979i
$688$	−6.55756	+	5.50244i	−0.250005	+	0.209779i
$689$	2.15068	+	1.80463i	0.0819343	+	0.0687510i
$690$		0			0
$691$	−18.6933	−	32.3778i	−0.711128	−	1.23171i	−0.964434	−	0.264323i	$-0.914851\pi$
$691$	−18.6933	−	32.3778i	−0.711128	−	1.23171i	0.253307	−	0.967386i	$-0.418482\pi$
$692$	36.9235	−	63.9534i	1.40362	−	2.43114i
$693$	−0.637253	−	0.231941i	−0.0242073	−	0.00881072i
$694$	−44.2781	−	16.1159i	−1.68078	−	0.611752i
$695$		0			0
$696$	−14.1905	−	24.5786i	−0.537888	−	0.931649i
$697$	0.115762	+	0.656519i	0.00438480	+	0.0248674i
$698$	−33.9241	−	28.4657i	−1.28405	−	1.07744i
$699$	18.0030	−	15.1063i	0.680937	−	0.571374i
$700$		0			0
$701$	2.18595	−	0.795621i	0.0825622	−	0.0300502i	−0.300409	−	0.953811i	$-0.597123\pi$
$701$	2.18595	−	0.795621i	0.0825622	−	0.0300502i	0.382971	+	0.923760i	$0.374901\pi$
$702$	21.3528			0.805911
$703$	−26.7737	−	31.5400i	−1.00979	−	1.18955i
$704$	35.2578			1.32883
$705$		0			0
$706$	−7.33330	+	41.5892i	−0.275992	+	1.56523i
$707$	−0.315929	+	0.265096i	−0.0118817	+	0.00996996i
$708$	16.0720	+	13.4860i	0.604022	+	0.506834i
$709$	−4.22872	−	23.9823i	−0.158813	−	0.900674i	−0.955216	−	0.295908i	$-0.904378\pi$
$709$	−4.22872	−	23.9823i	−0.158813	−	0.900674i	0.796403	−	0.604766i	$-0.206733\pi$
$710$		0			0
$711$	−9.75586	+	16.8976i	−0.365873	+	0.633711i
$712$	4.43697	+	1.61493i	0.166283	+	0.0605219i
$713$	32.7652	+	11.9256i	1.22707	+	0.446616i
$714$	0.680844	−	1.17926i	0.0254799	−	0.0441326i
$715$		0			0
$716$	13.5232	+	76.6941i	0.505387	+	2.86619i
$717$	−5.49092	−	4.60743i	−0.205062	−	0.172068i
$718$	28.7270	−	24.1048i	1.07208	−	0.899584i
$719$	2.96281	−	16.8029i	0.110494	−	0.626644i	−0.878389	−	0.477947i	$-0.841381\pi$
$719$	2.96281	−	16.8029i	0.110494	−	0.626644i	0.988883	−	0.148697i	$-0.0475078\pi$
$720$		0			0
$721$	−0.171914			−0.00640242
$722$	8.16607	+	43.4064i	0.303910	+	1.61542i
$723$	30.2246			1.12407
$724$	36.9949	−	13.4650i	1.37491	−	0.500425i
$725$		0			0
$726$	−6.28445	+	5.27328i	−0.233238	+	0.195710i
$727$	11.2035	+	9.40083i	0.415514	+	0.348657i	0.826453	−	0.563005i	$-0.190355\pi$
$727$	11.2035	+	9.40083i	0.415514	+	0.348657i	−0.410940	+	0.911663i	$0.634799\pi$
$728$	0.138749	+	0.786883i	0.00514237	+	0.0291638i
$729$	−10.2145	−	17.6920i	−0.378314	−	0.655259i
$730$		0			0
$731$	−36.7676	−	13.3823i	−1.35990	−	0.494963i
$732$	37.1526	+	13.5224i	1.37320	+	0.499804i
$733$	16.7630	−	29.0344i	0.619156	−	1.07241i	−0.370484	−	0.928839i	$-0.620808\pi$
$733$	16.7630	−	29.0344i	0.619156	−	1.07241i	0.989640	−	0.143570i	$-0.0458584\pi$
$734$	37.4980	+	64.9485i	1.38408	+	2.39729i
$735$		0			0
$736$	−25.9947	−	21.8121i	−0.958177	−	0.804006i
$737$	12.9585	−	10.8735i	0.477332	−	0.400529i
$738$	−0.127091	+	0.720768i	−0.00467828	+	0.0265318i
$739$	14.2925	−	5.20205i	0.525759	−	0.191361i	−0.0654847	−	0.997854i	$-0.520859\pi$
$739$	14.2925	−	5.20205i	0.525759	−	0.191361i	0.591244	+	0.806493i	$0.298637\pi$
$740$		0			0
$741$	5.53567	+	6.52114i	0.203358	+	0.239560i
$742$	0.547396			0.0200955
$743$	6.25647	−	2.27717i	0.229528	−	0.0835412i	−0.224696	−	0.974429i	$-0.572139\pi$
$743$	6.25647	−	2.27717i	0.229528	−	0.0835412i	0.454224	+	0.890888i	$0.349917\pi$
$744$	3.15481	−	17.8918i	0.115661	−	0.655945i
$745$		0			0
$746$	−4.23887	−	3.55684i	−0.155196	−	0.130225i
$747$	2.21692	+	12.5728i	0.0811129	+	0.460014i
$748$	−17.0538	−	29.5381i	−0.623549	−	1.08002i
$749$	−0.293437	+	0.508247i	−0.0107219	+	0.0185709i
$750$		0			0
$751$	−7.34004	−	2.67155i	−0.267842	−	0.0974864i	0.204608	−	0.978844i	$-0.434408\pi$
$751$	−7.34004	−	2.67155i	−0.267842	−	0.0974864i	−0.472450	+	0.881358i	$0.656630\pi$
$752$	−1.42887	+	2.47488i	−0.0521056	+	0.0902496i
$753$	−6.14855	−	10.6496i	−0.224066	−	0.388093i
$754$	5.22195	+	29.6151i	0.190172	+	1.07852i
$755$		0			0
$756$	2.00890	−	1.68567i	0.0730629	−	0.0613071i
$757$	3.19246	−	18.1053i	0.116032	−	0.658049i	−0.870202	−	0.492695i	$-0.836012\pi$
$757$	3.19246	−	18.1053i	0.116032	−	0.658049i	0.986234	−	0.165355i	$-0.0528769\pi$
$758$	38.7113	−	14.0898i	1.40606	−	0.511764i
$759$	−23.2645			−0.844449
$760$		0			0
$761$	22.4779			0.814822			0.407411	−	0.913245i	$-0.366432\pi$
$761$	22.4779			0.814822			0.407411	+	0.913245i	$0.366432\pi$
$762$	−20.4739	+	7.45188i	−0.741690	+	0.269953i
$763$	−0.402976	+	2.28539i	−0.0145887	+	0.0827366i
$764$	19.0077	−	15.9494i	0.687675	−	0.577028i
$765$		0			0
$766$	−4.30493	−	24.4145i	−0.155543	−	0.882131i
$767$	−4.58433	−	7.94029i	−0.165531	−	0.286707i
$768$	−11.8846	+	20.5846i	−0.428847	+	0.742784i
$769$	−5.18597	−	1.88754i	−0.187011	−	0.0680664i	0.246817	−	0.969062i	$-0.420615\pi$
$769$	−5.18597	−	1.88754i	−0.187011	−	0.0680664i	−0.433828	+	0.900996i	$0.642838\pi$
$770$		0			0
$771$	7.76669	−	13.4523i	0.279710	−	0.484473i
$772$	−44.5673	−	77.1929i	−1.60401	−	2.77823i
$773$	5.76305	+	32.6839i	0.207283	+	1.17556i	0.893807	+	0.448451i	$0.148024\pi$
$773$	5.76305	+	32.6839i	0.207283	+	1.17556i	−0.686525	+	0.727106i	$0.740865\pi$
$774$	−32.9065	−	27.6118i	−1.18280	−	0.992487i
$775$		0			0
$776$	4.98813	−	28.2891i	0.179064	−	1.01552i
$777$	−1.46799	+	0.534305i	−0.0526639	+	0.0191681i
$778$	−52.8418			−1.89447
$779$	−0.704774	+	0.412287i	−0.0252512	+	0.0147717i
$780$		0			0
$781$	1.43131	−	0.520953i	0.0512162	−	0.0186412i
$782$	−10.3348	+	58.6114i	−0.369571	+	2.09594i
$783$	31.1829	−	26.1655i	1.11439	−	0.935080i
$784$	−4.16290	−	3.49309i	−0.148675	−	0.124753i
$785$		0			0
$786$	−3.49767	−	6.05813i	−0.124758	−	0.216086i
$787$	−24.3225	+	42.1279i	−0.867005	+	1.50170i	−0.00196163	+	0.999998i	$0.500624\pi$
$787$	−24.3225	+	42.1279i	−0.867005	+	1.50170i	−0.865043	+	0.501698i	$0.832709\pi$
$788$	−7.31901	−	2.66390i	−0.260729	−	0.0948976i
$789$	7.05930	+	2.56938i	0.251318	+	0.0914722i
$790$		0			0
$791$	0.223440	+	0.387010i	0.00794462	+	0.0137605i
$792$	−2.68179	−	15.2092i	−0.0952932	−	0.540435i
$793$	−13.2357	−	11.1061i	−0.470015	−	0.394389i
$794$	36.3997	−	30.5430i	1.29178	−	1.08393i
$795$		0			0
$796$	39.1728	−	14.2577i	1.38844	−	0.505352i
$797$	1.06027			0.0375567			0.0187784	−	0.999824i	$-0.494022\pi$
$797$	1.06027			0.0375567			0.0187784	+	0.999824i	$0.494022\pi$
$798$	1.64409	+	0.280223i	0.0582000	+	0.00991980i
$799$	−13.0622			−0.462106
$800$		0			0
$801$	−0.422277	+	2.39485i	−0.0149204	+	0.0846179i
$802$	−29.7337	+	24.9496i	−1.04993	+	0.881000i
$803$	22.5767	+	18.9441i	0.796714	+	0.668522i
$804$	4.07886	+	23.1324i	0.143850	+	0.815815i
$805$		0			0
$806$	−9.62517	+	16.6713i	−0.339032	+	0.587221i
$807$	15.5659	+	5.66551i	0.547944	+	0.199435i
$808$	−8.82571	−	3.21230i	−0.310487	−	0.113008i
$809$	6.80960	−	11.7946i	0.239413	−	0.414675i	−0.721133	−	0.692797i	$-0.756378\pi$
$809$	6.80960	−	11.7946i	0.239413	−	0.414675i	0.960546	+	0.278121i	$0.0897117\pi$
$810$		0			0
$811$	3.88880	+	22.0545i	0.136554	+	0.774438i	0.973765	+	0.227557i	$0.0730738\pi$
$811$	3.88880	+	22.0545i	0.136554	+	0.774438i	−0.837210	+	0.546881i	$0.815815\pi$
$812$	2.82920	+	2.37398i	0.0992856	+	0.0833105i
$813$	1.92188	−	1.61265i	0.0674032	−	0.0565580i
$814$	−10.7873	+	61.1779i	−0.378095	+	2.14429i
$815$		0			0
$816$	3.18268			0.111416
$817$	−0.273738	−	47.9223i	−0.00957687	−	1.67659i
$818$	41.1100			1.43738
$819$	−0.386697	+	0.140746i	−0.0135123	+	0.00491807i
$820$		0			0
$821$	−4.22809	+	3.54778i	−0.147561	+	0.123819i	−0.713580	−	0.700574i	$-0.752927\pi$
$821$	−4.22809	+	3.54778i	−0.147561	+	0.123819i	0.566019	+	0.824392i	$0.308483\pi$
$822$	25.1997	+	21.1451i	0.878941	+	0.737519i
$823$	3.88144	+	22.0128i	0.135299	+	0.767317i	0.974651	+	0.223729i	$0.0718232\pi$
$823$	3.88144	+	22.0128i	0.135299	+	0.767317i	−0.839353	+	0.543587i	$0.817066\pi$
$824$	−1.95754	−	3.39055i	−0.0681941	−	0.118116i
$825$		0			0
$826$	−1.67985	−	0.611417i	−0.0584496	−	0.0212739i
$827$	−4.21627	−	1.53460i	−0.146614	−	0.0533632i	0.267671	−	0.963510i	$-0.413746\pi$
$827$	−4.21627	−	1.53460i	−0.146614	−	0.0533632i	−0.414285	+	0.910147i	$0.635968\pi$
$828$	−20.5787	+	35.6433i	−0.715158	+	1.23869i
$829$	−13.5156	−	23.4097i	−0.469416	−	0.813052i	0.529973	−	0.848015i	$-0.322202\pi$
$829$	−13.5156	−	23.4097i	−0.469416	−	0.813052i	−0.999389	+	0.0349625i	$0.988869\pi$
$830$		0			0
$831$	14.0555	+	11.7940i	0.487579	+	0.409128i
$832$	16.3896	−	13.7525i	0.568206	−	0.476782i
$833$	4.31324	−	24.4616i	0.149445	−	0.847544i
$834$	−19.9559	+	7.26336i	−0.691017	+	0.251510i
$835$		0			0
$836$	26.6693	−	32.1544i	0.922375	−	1.11208i
$837$	26.0578			0.900691
$838$	−82.8640	+	30.1600i	−2.86249	+	1.04186i
$839$	−1.75648	+	9.96148i	−0.0606404	+	0.343909i	0.939359	+	0.342935i	$0.111421\pi$
$839$	−1.75648	+	9.96148i	−0.0606404	+	0.343909i	−1.00000		0.000973662i	$0.999690\pi$
$840$		0			0
$841$	21.7007	+	18.2091i	0.748300	+	0.627898i
$842$	−4.67534	−	26.5152i	−0.161123	−	0.913773i
$843$	−8.18759	−	14.1813i	−0.281996	−	0.488431i
$844$	−5.11107	+	8.85264i	−0.175930	+	0.304720i
$845$		0			0
$846$	−13.4756	−	4.90473i	−0.463301	−	0.168628i
$847$	0.220152	−	0.381314i	0.00756450	−	0.0131021i
$848$	0.639714	+	1.10802i	0.0219679	+	0.0380495i
$849$	1.40957	+	7.99405i	0.0483762	+	0.274355i
$850$		0			0
$851$	52.3052	−	43.8893i	1.79300	−	1.50450i
$852$	−0.367270	+	2.08289i	−0.0125825	+	0.0713586i
$853$	25.9451	−	9.44325i	0.888344	−	0.323331i	0.142772	−	0.989756i	$-0.454399\pi$
$853$	25.9451	−	9.44325i	0.888344	−	0.323331i	0.745572	+	0.666425i	$0.232176\pi$
$854$	−3.36879			−0.115278
$855$		0			0
$856$	−13.3651			−0.456810
$857$	−36.2885	+	13.2079i	−1.23959	+	0.451175i	−0.876872	−	0.480723i	$-0.840374\pi$
$857$	−36.2885	+	13.2079i	−1.23959	+	0.451175i	−0.362720	+	0.931898i	$0.618152\pi$
$858$	2.23036	−	12.6490i	0.0761434	−	0.431831i
$859$	43.7965	−	36.7496i	1.49432	−	1.25388i	0.605307	−	0.795992i	$-0.293050\pi$
$859$	43.7965	−	36.7496i	1.49432	−	1.25388i	0.889009	−	0.457889i	$-0.151394\pi$
$860$		0			0
$861$	0.00535387	+	0.0303633i	0.000182460	+	0.00103478i
$862$	36.9496	+	63.9986i	1.25851	+	2.17980i
$863$	−14.2209	+	24.6314i	−0.484087	+	0.838463i	−0.999833	−	0.0182787i	$-0.994181\pi$
$863$	−14.2209	+	24.6314i	−0.484087	+	0.838463i	0.515746	+	0.856741i	$0.327515\pi$
$864$	−23.8302	−	8.67349i	−0.810720	−	0.295078i
$865$		0			0
$866$	−4.75209	+	8.23085i	−0.161482	+	0.279696i
$867$	−2.48925	−	4.31151i	−0.0845395	−	0.146427i
$868$	0.410541	+	2.32830i	0.0139347	+	0.0790275i
$869$	25.0385	+	21.0098i	0.849374	+	0.712710i
$870$		0			0
$871$	1.78250	−	10.1091i	0.0603977	−	0.342532i
$872$	−49.6618	+	18.0754i	−1.68176	+	0.612111i
$873$	14.7943			0.500711
$874$	−71.7138	+	13.0679i	−2.42576	+	0.442028i
$875$		0			0
$876$	−38.4556	+	13.9967i	−1.29929	+	0.472905i
$877$	2.31472	−	13.1274i	0.0781626	−	0.443282i	−0.920461	−	0.390834i	$-0.872187\pi$
$877$	2.31472	−	13.1274i	0.0781626	−	0.443282i	0.998624	−	0.0524480i	$-0.0167024\pi$
$878$	20.9342	−	17.5659i	0.706494	−	0.592819i
$879$	−0.859402	−	0.721124i	−0.0289869	−	0.0243229i
$880$		0			0
$881$	14.0692	+	24.3686i	0.474004	+	0.820999i	0.999557	−	0.0297621i	$-0.00947498\pi$
$881$	14.0692	+	24.3686i	0.474004	+	0.820999i	−0.525553	+	0.850761i	$0.676142\pi$
$882$	13.6349	−	23.6163i	0.459111	−	0.795203i
$883$	−33.4754	−	12.1840i	−1.12654	−	0.410026i	−0.289503	−	0.957177i	$-0.593490\pi$
$883$	−33.4754	−	12.1840i	−1.12654	−	0.410026i	−0.837034	+	0.547151i	$0.815712\pi$
$884$	−19.4489	−	7.07883i	−0.654139	−	0.238087i
$885$		0			0
$886$	−9.16667	−	15.8771i	−0.307960	−	0.533403i
$887$	−10.2751	−	58.2732i	−0.345005	−	1.95662i	−0.285433	−	0.958399i	$-0.592137\pi$
$887$	−10.2751	−	58.2732i	−0.345005	−	1.95662i	−0.0595725	−	0.998224i	$-0.518974\pi$
$888$	−27.2533	−	22.8683i	−0.914562	−	0.767409i
$889$	0.895791	−	0.751658i	0.0300439	−	0.0252098i
$890$		0			0
$891$	−2.99695	+	1.09080i	−0.100402	+	0.0365432i
$892$	−7.46685			−0.250009
$893$	−5.55760	−	15.0022i	−0.185978	−	0.502030i
$894$	−11.2039			−0.374715
$895$		0			0
$896$	0.489620	−	2.77677i	0.0163570	−	0.0927654i
$897$	−10.8145	+	9.07445i	−0.361086	+	0.302987i
$898$	2.06710	+	1.73450i	0.0689800	+	0.0578811i
$899$	6.37258	+	36.1407i	0.212537	+	1.20536i
$900$		0			0
$901$	−2.92400	+	5.06452i	−0.0974126	+	0.168724i
$902$	1.15210	+	0.419329i	0.0383607	+	0.0139621i
$903$	−1.70046	−	0.618918i	−0.0565879	−	0.0205963i
$904$	−5.08850	+	8.81354i	−0.169241	+	0.293134i
$905$		0			0
$906$	−1.32667	−	7.52390i	−0.0440755	−	0.249965i
$907$	−35.4253	−	29.7254i	−1.17628	−	0.987016i	−0.999996	−	0.00267604i	$-0.999148\pi$
$907$	−35.4253	−	29.7254i	−1.17628	−	0.987016i	−0.176283	−	0.984340i	$-0.556407\pi$
$908$	16.8017	−	14.0983i	0.557585	−	0.467870i
$909$	0.839964	−	4.76367i	0.0278598	−	0.158001i
$910$		0			0
$911$	48.8276			1.61773			0.808866	−	0.587994i	$-0.200082\pi$
$911$	48.8276			1.61773			0.808866	+	0.587994i	$0.200082\pi$
$912$	1.35415	+	3.65538i	0.0448402	+	0.121042i
$913$	21.3865			0.707790
$914$	84.5130	−	30.7602i	2.79544	−	1.01746i
$915$		0			0
$916$	−4.02396	+	3.37650i	−0.132955	+	0.111563i
$917$	0.287608	+	0.241332i	0.00949766	+	0.00796948i
$918$	7.72346	+	43.8019i	0.254912	+	1.44568i
$919$	4.80464	+	8.32189i	0.158491	+	0.274514i	0.934325	−	0.356423i	$-0.116004\pi$
$919$	4.80464	+	8.32189i	0.158491	+	0.274514i	−0.775834	+	0.630937i	$0.782671\pi$
$920$		0			0
$921$	30.7248	+	11.1829i	1.01242	+	0.368490i
$922$	−53.5173	−	19.4787i	−1.76250	−	0.641496i
$923$	0.462142	−	0.800454i	0.0152116	−	0.0263473i
$924$	−0.788722	−	1.36611i	−0.0259470	−	0.0449416i
$925$		0			0
$926$	57.8481	+	48.5403i	1.90100	+	1.59513i
$927$	1.54462	−	1.29609i	0.0507318	−	0.0425691i
$928$	6.20181	−	35.1722i	0.203585	−	1.15459i
$929$	−48.5984	+	17.6884i	−1.59446	+	0.580337i	−0.978284	−	0.207269i	$-0.933542\pi$
$929$	−48.5984	+	17.6884i	−1.59446	+	0.580337i	−0.616179	+	0.787606i	$0.711320\pi$
$930$		0			0
$931$	29.9299	−	5.45391i	0.980914	−	0.178745i
$932$	−69.6473			−2.28137
$933$	−27.5722	+	10.0355i	−0.902672	+	0.328546i
$934$	−5.93470	+	33.6574i	−0.194189	+	1.10130i
$935$		0			0
$936$	−7.17905	−	6.02394i	−0.234655	−	0.196899i
$937$	1.99511	+	11.3148i	0.0651773	+	0.369639i	0.999898	+	0.0142567i	$0.00453821\pi$
$937$	1.99511	+	11.3148i	0.0651773	+	0.369639i	−0.934721	+	0.355382i	$0.884351\pi$
$938$	−1.00071	−	1.73328i	−0.0326744	−	0.0565937i
$939$	−8.58639	+	14.8721i	−0.280206	+	0.485331i
$940$		0			0
$941$	−24.8922	−	9.06002i	−0.811462	−	0.295348i	−0.0972346	−	0.995261i	$-0.531000\pi$
$941$	−24.8922	−	9.06002i	−0.811462	−	0.295348i	−0.714228	+	0.699913i	$0.753222\pi$
$942$	−15.3851	+	26.6478i	−0.501274	+	0.868232i
$943$	−0.673785	−	1.16703i	−0.0219414	−	0.0380037i
$944$	−0.725556	−	4.11483i	−0.0236148	−	0.133926i
$945$		0			0
$946$	−55.1241	+	46.2546i	−1.79224	+	1.50387i
$947$	−2.55295	+	14.4785i	−0.0829596	+	0.470487i	0.914819	+	0.403865i	$0.132333\pi$
$947$	−2.55295	+	14.4785i	−0.0829596	+	0.470487i	−0.997778	+	0.0666224i	$0.978778\pi$
$948$	−42.6490	+	15.5230i	−1.38517	+	0.504162i
$949$	17.8840			0.580539
$950$		0			0
$951$	−25.8892			−0.839513
$952$	−1.56398	+	0.569241i	−0.0506888	+	0.0184492i
$953$	−1.01593	+	5.76163i	−0.0329092	+	0.186637i	−0.996831	−	0.0795481i	$-0.974652\pi$
$953$	−1.01593	+	5.76163i	−0.0329092	+	0.186637i	0.963922	+	0.266186i	$0.0857634\pi$
$954$	−4.91824	+	4.12689i	−0.159234	+	0.133613i
$955$		0			0
$956$	3.68871	+	20.9197i	0.119301	+	0.676591i
$957$	−12.2428	−	21.2052i	−0.395755	−	0.685467i
$958$	−15.3653	+	26.6135i	−0.496431	+	0.859843i
$959$	−1.65908	−	0.603855i	−0.0535744	−	0.0194995i
$960$		0			0
$961$	3.75397	−	6.50206i	0.121096	−	0.209744i
$962$	18.8483	+	32.6462i	0.607693	+	1.05256i
$963$	−1.19528	−	6.77876i	−0.0385173	−	0.218442i
$964$	−68.6163	−	57.5759i	−2.20998	−	1.85440i
$965$		0			0
$966$	−0.477973	+	2.71072i	−0.0153785	+	0.0872159i
$967$	−22.6188	+	8.23258i	−0.727373	+	0.264742i	−0.679052	−	0.734090i	$-0.737609\pi$
$967$	−22.6188	+	8.23258i	−0.727373	+	0.264742i	−0.0483204	+	0.998832i	$0.515387\pi$
$968$	10.0272			0.322287
$969$	−11.3748	+	13.7143i	−0.365411	+	0.440566i
$970$		0			0
$971$	−49.4859	+	18.0114i	−1.58808	+	0.578013i	−0.976941	−	0.213511i	$-0.931510\pi$
$971$	−49.4859	+	18.0114i	−1.58808	+	0.578013i	−0.611137	+	0.791524i	$0.709288\pi$
$972$	−8.76428	+	49.7047i	−0.281114	+	1.59428i
$973$	0.873130	−	0.732643i	0.0279913	−	0.0234875i
$974$	17.2035	+	14.4354i	0.551234	+	0.462540i
$975$		0			0
$976$	−3.93694	−	6.81899i	−0.126018	−	0.218270i
$977$	−3.25436	+	5.63672i	−0.104116	+	0.180335i	−0.913377	−	0.407115i	$-0.866535\pi$
$977$	−3.25436	+	5.63672i	−0.104116	+	0.180335i	0.809261	+	0.587450i	$0.199868\pi$
$978$	47.4688	+	17.2772i	1.51789	+	0.552465i
$979$	3.82801	+	1.39328i	0.122344	+	0.0445294i
$980$		0			0
$981$	−13.6092	−	23.5718i	−0.434509	−	0.752591i
$982$	−1.08439	−	6.14987i	−0.0346042	−	0.196250i
$983$	0.957057	+	0.803066i	0.0305254	+	0.0256138i	0.657923	−	0.753085i	$-0.271435\pi$
$983$	0.957057	+	0.803066i	0.0305254	+	0.0256138i	−0.627397	+	0.778699i	$0.715880\pi$
$984$	−0.537873	+	0.451329i	−0.0171468	+	0.0143879i
$985$		0			0
$986$	−58.8619	+	21.4240i	−1.87454	+	0.682278i
$987$	−0.604111			−0.0192291
$988$	−0.144799	−	25.3494i	−0.00460666	−	0.806473i
$989$	79.0924			2.51499
$990$		0			0
$991$	6.52844	−	37.0246i	0.207383	−	1.17613i	−0.686264	−	0.727353i	$-0.740750\pi$
$991$	6.52844	−	37.0246i	0.207383	−	1.17613i	0.893646	−	0.448772i	$-0.148139\pi$
$992$	17.5137	−	14.6958i	0.556062	−	0.466591i
$993$	9.56244	+	8.02384i	0.303455	+	0.254629i
$994$	−0.0312936	−	0.177475i	−0.000992573	−	0.00562916i
$995$		0			0
$996$	−14.8483	+	25.7181i	−0.470487	+	0.814908i
$997$	28.1257	+	10.2369i	0.890751	+	0.324207i	0.746540	−	0.665340i	$-0.231713\pi$
$997$	28.1257	+	10.2369i	0.890751	+	0.324207i	0.144211	+	0.989547i	$0.453936\pi$
$998$	5.14533	+	1.87275i	0.162873	+	0.0592808i
$999$	25.5136	−	44.1909i	0.807215	−	1.39814i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.l.f.176.7		48
5.2	odd	4		95.2.p.a.24.7	yes	48
5.3	odd	4		95.2.p.a.24.2	yes	48
5.4	even	2	inner	475.2.l.f.176.2		48
15.2	even	4		855.2.da.b.784.2		48
15.8	even	4		855.2.da.b.784.7		48
19.2	odd	18		9025.2.a.ct.1.22		24
19.4	even	9	inner	475.2.l.f.251.7		48
19.17	even	9		9025.2.a.cu.1.3		24
95.2	even	36		1805.2.b.l.1084.22		24
95.4	even	18	inner	475.2.l.f.251.2		48
95.17	odd	36		1805.2.b.k.1084.3		24
95.23	odd	36		95.2.p.a.4.7	yes	48
95.42	odd	36		95.2.p.a.4.2	✓	48
95.59	odd	18		9025.2.a.ct.1.3		24
95.74	even	18		9025.2.a.cu.1.22		24
95.78	even	36		1805.2.b.l.1084.3		24
95.93	odd	36		1805.2.b.k.1084.22		24
285.23	even	36		855.2.da.b.289.2		48
285.137	even	36		855.2.da.b.289.7		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.p.a.4.2	✓	48	95.42	odd	36
95.2.p.a.4.7	yes	48	95.23	odd	36
95.2.p.a.24.2	yes	48	5.3	odd	4
95.2.p.a.24.7	yes	48	5.2	odd	4
475.2.l.f.176.2		48	5.4	even	2	inner
475.2.l.f.176.7		48	1.1	even	1	trivial
475.2.l.f.251.2		48	95.4	even	18	inner
475.2.l.f.251.7		48	19.4	even	9	inner
855.2.da.b.289.2		48	285.23	even	36
855.2.da.b.289.7		48	285.137	even	36
855.2.da.b.784.2		48	15.2	even	4
855.2.da.b.784.7		48	15.8	even	4
1805.2.b.k.1084.3		24	95.17	odd	36
1805.2.b.k.1084.22		24	95.93	odd	36
1805.2.b.l.1084.3		24	95.78	even	36
1805.2.b.l.1084.22		24	95.2	even	36
9025.2.a.ct.1.3		24	95.59	odd	18
9025.2.a.ct.1.22		24	19.2	odd	18
9025.2.a.cu.1.3		24	19.17	even	9
9025.2.a.cu.1.22		24	95.74	even	18

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.l (of order \(9\), degree \(6\), minimal)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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