LMFDB - Embedded newform 950.2.u.g.549.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(99,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 2]))

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

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

chi := DirichletCharacter("950.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.u (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			549.3
Character	$\chi$	$=$	950.549
Dual form			950.2.u.g.199.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.984808 - 0.173648i) q^{2} +(2.20410 - 2.62675i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-2.62675 + 2.20410i) q^{6} +(1.61687 - 0.933500i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-1.52078 - 8.62480i) q^{9} +O(q^{10})$	\(q+(-0.984808 - 0.173648i) q^{2} +(2.20410 - 2.62675i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-2.62675 + 2.20410i) q^{6} +(1.61687 - 0.933500i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-1.52078 - 8.62480i) q^{9} +(1.80254 - 3.12210i) q^{11} +(2.96958 - 1.71449i) q^{12} +(1.82353 + 2.17319i) q^{13} +(-1.75441 + 0.638551i) q^{14} +(0.766044 + 0.642788i) q^{16} +(5.89781 + 1.03994i) q^{17} +8.75785i q^{18} +(-4.32047 + 0.577506i) q^{19} +(1.11168 - 6.30463i) q^{21} +(-2.31731 + 2.76166i) q^{22} +(-1.74011 + 4.78092i) q^{23} +(-3.22218 + 1.17278i) q^{24} +(-1.41845 - 2.45683i) q^{26} +(-17.0984 - 9.87176i) q^{27} +(1.83864 - 0.324201i) q^{28} +(-0.204642 - 1.16058i) q^{29} +(2.59932 + 4.50215i) q^{31} +(-0.642788 - 0.766044i) q^{32} +(-4.22797 - 11.6162i) q^{33} +(-5.62762 - 2.04829i) q^{34} +(1.52078 - 8.62480i) q^{36} +3.35231i q^{37} +(4.35512 + 0.181510i) q^{38} +9.72766 q^{39} +(-2.85406 - 2.39484i) q^{41} +(-2.18958 + 6.01581i) q^{42} +(0.229755 + 0.631247i) q^{43} +(2.76166 - 2.31731i) q^{44} +(2.54388 - 4.40612i) q^{46} +(6.22647 - 1.09789i) q^{47} +(3.37688 - 0.595435i) q^{48} +(-1.75716 + 3.04348i) q^{49} +(15.7310 - 13.1999i) q^{51} +(0.970278 + 2.66582i) q^{52} +(-0.876116 + 2.40711i) q^{53} +(15.1244 + 12.6909i) q^{54} -1.86700 q^{56} +(-8.00580 + 12.6217i) q^{57} +1.17848i q^{58} +(0.827999 - 4.69581i) q^{59} +(-7.73966 - 2.81701i) q^{61} +(-1.77804 - 4.88512i) q^{62} +(-10.5102 - 12.5255i) q^{63} +(0.500000 + 0.866025i) q^{64} +(2.14660 + 12.1739i) q^{66} +(-7.84286 + 1.38291i) q^{67} +(5.18644 + 2.99439i) q^{68} +(8.72288 + 15.1085i) q^{69} +(1.81077 - 0.659065i) q^{71} +(-2.99536 + 8.22969i) q^{72} +(-3.22165 + 3.83942i) q^{73} +(0.582122 - 3.30138i) q^{74} +(-4.25744 - 0.935010i) q^{76} -6.73070i q^{77} +(-9.57988 - 1.68919i) q^{78} +(0.460535 + 0.386434i) q^{79} +(-38.9281 + 14.1687i) q^{81} +(2.39484 + 2.85406i) q^{82} +(1.64789 - 0.951408i) q^{83} +(3.20094 - 5.54420i) q^{84} +(-0.116650 - 0.661553i) q^{86} +(-3.49960 - 2.02049i) q^{87} +(-3.12210 + 1.80254i) q^{88} +(-0.755257 + 0.633736i) q^{89} +(4.97708 + 1.81151i) q^{91} +(-3.27034 + 3.89744i) q^{92} +(17.5552 + 3.09545i) q^{93} -6.32252 q^{94} -3.42897 q^{96} +(-0.184712 - 0.0325697i) q^{97} +(2.25896 - 2.69212i) q^{98} +(-29.6688 - 10.7985i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 36 q^{9}+O(q^{10}) $ 36 * q + 36 * q^9	$ 36 q + 36 q^{9} - 24 q^{11} - 12 q^{14} + 24 q^{21} - 18 q^{26} + 12 q^{29} - 12 q^{31} - 36 q^{34} - 36 q^{36} - 96 q^{39} - 42 q^{41} - 6 q^{44} + 36 q^{46} + 78 q^{49} + 84 q^{51} + 108 q^{54} + 60 q^{59} + 96 q^{61} + 18 q^{64} + 48 q^{66} + 60 q^{69} + 60 q^{71} + 6 q^{74} - 42 q^{76} - 60 q^{79} + 36 q^{81} - 12 q^{84} + 72 q^{86} - 60 q^{89} - 120 q^{91} - 12 q^{94} - 342 q^{99}+O(q^{100}) $ 36 * q + 36 * q^9 - 24 * q^11 - 12 * q^14 + 24 * q^21 - 18 * q^26 + 12 * q^29 - 12 * q^31 - 36 * q^34 - 36 * q^36 - 96 * q^39 - 42 * q^41 - 6 * q^44 + 36 * q^46 + 78 * q^49 + 84 * q^51 + 108 * q^54 + 60 * q^59 + 96 * q^61 + 18 * q^64 + 48 * q^66 + 60 * q^69 + 60 * q^71 + 6 * q^74 - 42 * q^76 - 60 * q^79 + 36 * q^81 - 12 * q^84 + 72 * q^86 - 60 * q^89 - 120 * q^91 - 12 * q^94 - 342 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{5}{9}\right)$

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 $

$2$	−0.984808	−	0.173648i	−0.696364	−	0.122788i
$2$	−0.984808	−	0.173648i	−0.696364	−	0.122788i
$3$	2.20410	−	2.62675i	1.27254	−	1.51655i	0.527450	−	0.849586i	$-0.323148\pi$
$3$	2.20410	−	2.62675i	1.27254	−	1.51655i	0.745088	−	0.666966i	$-0.232407\pi$
$4$	0.939693	+	0.342020i	0.469846	+	0.171010i
$5$		0			0
$5$		0			0
$6$	−2.62675	+	2.20410i	−1.07236	+	0.899820i
$7$	1.61687	−	0.933500i	0.611119	−	0.352830i	−0.162284	−	0.986744i	$-0.551886\pi$
$7$	1.61687	−	0.933500i	0.611119	−	0.352830i	0.773403	+	0.633914i	$0.218553\pi$
$8$	−0.866025	−	0.500000i	−0.306186	−	0.176777i
$9$	−1.52078	−	8.62480i	−0.506928	−	2.87493i
$10$		0			0
$11$	1.80254	−	3.12210i	0.543488	−	0.941348i	−0.455213	−	0.890383i	$-0.650437\pi$
$11$	1.80254	−	3.12210i	0.543488	−	0.941348i	0.998700	−	0.0509654i	$-0.0162298\pi$
$12$	2.96958	−	1.71449i	0.857243	−	0.494930i
$13$	1.82353	+	2.17319i	0.505755	+	0.602736i	0.957151	−	0.289588i	$-0.0935183\pi$
$13$	1.82353	+	2.17319i	0.505755	+	0.602736i	−0.451396	+	0.892324i	$0.649074\pi$
$14$	−1.75441	+	0.638551i	−0.468885	+	0.170660i
$15$		0			0
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	5.89781	+	1.03994i	1.43043	+	0.252223i	0.834586	−	0.550878i	$-0.185707\pi$
$17$	5.89781	+	1.03994i	1.43043	+	0.252223i	0.595842	+	0.803101i	$0.296818\pi$
$18$			8.75785i			2.06425i
$19$	−4.32047	+	0.577506i	−0.991184	+	0.132489i
$19$	−4.32047	+	0.577506i	−0.991184	+	0.132489i
$20$		0			0
$21$	1.11168	−	6.30463i	0.242588	−	1.37578i
$22$	−2.31731	+	2.76166i	−0.494051	+	0.588787i
$23$	−1.74011	+	4.78092i	−0.362839	+	0.996892i	0.615182	+	0.788385i	$0.289082\pi$
$23$	−1.74011	+	4.78092i	−0.362839	+	0.996892i	−0.978021	+	0.208507i	$0.933140\pi$
$24$	−3.22218	+	1.17278i	−0.657725	+	0.239392i
$25$		0			0
$26$	−1.41845	−	2.45683i	−0.278181	−	0.481824i
$27$	−17.0984	−	9.87176i	−3.29059	−	1.89982i
$28$	1.83864	−	0.324201i	0.347469	−	0.0612682i
$29$	−0.204642	−	1.16058i	−0.0380010	−	0.215514i	0.959894	−	0.280363i	$-0.0904547\pi$
$29$	−0.204642	−	1.16058i	−0.0380010	−	0.215514i	−0.997895	+	0.0648484i	$0.979344\pi$
$30$		0			0
$31$	2.59932	+	4.50215i	0.466851	+	0.808610i	0.999283	−	0.0378630i	$-0.0120550\pi$
$31$	2.59932	+	4.50215i	0.466851	+	0.808610i	−0.532432	+	0.846473i	$0.678722\pi$
$32$	−0.642788	−	0.766044i	−0.113630	−	0.135419i
$33$	−4.22797	−	11.6162i	−0.735995	−	2.02213i
$34$	−5.62762	−	2.04829i	−0.965129	−	0.351278i
$35$		0			0
$36$	1.52078	−	8.62480i	0.253464	−	1.43747i
$37$			3.35231i			0.551116i	0.961285	+	0.275558i	$0.0888625\pi$
$37$			3.35231i			0.551116i	−0.961285	+	0.275558i	$0.911137\pi$
$38$	4.35512	+	0.181510i	0.706493	+	0.0294447i
$39$	9.72766			1.55767
$40$		0			0
$41$	−2.85406	−	2.39484i	−0.445730	−	0.374012i	0.392119	−	0.919915i	$-0.371742\pi$
$41$	−2.85406	−	2.39484i	−0.445730	−	0.374012i	−0.837848	+	0.545903i	$0.816187\pi$
$42$	−2.18958	+	6.01581i	−0.337859	+	0.928259i
$43$	0.229755	+	0.631247i	0.0350373	+	0.0962642i	0.955978	−	0.293439i	$-0.0947998\pi$
$43$	0.229755	+	0.631247i	0.0350373	+	0.0962642i	−0.920940	+	0.389703i	$0.872578\pi$
$44$	2.76166	−	2.31731i	0.416336	−	0.349347i
$45$		0			0
$46$	2.54388	−	4.40612i	0.375074	−	0.649647i
$47$	6.22647	−	1.09789i	0.908223	−	0.160144i	0.300027	−	0.953931i	$-0.403004\pi$
$47$	6.22647	−	1.09789i	0.908223	−	0.160144i	0.608197	+	0.793786i	$0.291893\pi$
$48$	3.37688	−	0.595435i	0.487410	−	0.0859436i
$49$	−1.75716	+	3.04348i	−0.251022	+	0.434783i
$50$		0			0
$51$	15.7310	−	13.1999i	2.20278	−	1.84836i
$52$	0.970278	+	2.66582i	0.134553	+	0.369682i
$53$	−0.876116	+	2.40711i	−0.120344	+	0.330642i	−0.985208	−	0.171365i	$-0.945182\pi$
$53$	−0.876116	+	2.40711i	−0.120344	+	0.330642i	0.864864	+	0.502006i	$0.167405\pi$
$54$	15.1244	+	12.6909i	2.05817	+	1.72701i
$55$		0			0
$56$	−1.86700			−0.249488
$57$	−8.00580	+	12.6217i	−1.06039	+	1.67178i
$58$			1.17848i			0.154743i
$59$	0.827999	−	4.69581i	0.107796	−	0.611343i	−0.882270	−	0.470743i	$-0.843986\pi$
$59$	0.827999	−	4.69581i	0.107796	−	0.611343i	0.990067	−	0.140600i	$-0.0449031\pi$
$60$		0			0
$61$	−7.73966	−	2.81701i	−0.990962	−	0.360681i	−0.204869	−	0.978789i	$-0.565677\pi$
$61$	−7.73966	−	2.81701i	−0.990962	−	0.360681i	−0.786093	+	0.618109i	$0.787899\pi$
$62$	−1.77804	−	4.88512i	−0.225811	−	0.620411i
$63$	−10.5102	−	12.5255i	−1.32416	−	1.57807i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$		0			0
$66$	2.14660	+	12.1739i	0.264228	+	1.49851i
$67$	−7.84286	+	1.38291i	−0.958158	+	0.168949i	−0.630795	−	0.775949i	$-0.717271\pi$
$67$	−7.84286	+	1.38291i	−0.958158	+	0.168949i	−0.327363	+	0.944899i	$0.606160\pi$
$68$	5.18644	+	2.99439i	0.628949	+	0.363124i
$69$	8.72288	+	15.1085i	1.05011	+	1.81885i
$70$		0			0
$71$	1.81077	−	0.659065i	0.214898	−	0.0782166i	−0.232328	−	0.972638i	$-0.574634\pi$
$71$	1.81077	−	0.659065i	0.214898	−	0.0782166i	0.447226	+	0.894421i	$0.352412\pi$
$72$	−2.99536	+	8.22969i	−0.353007	+	0.969878i
$73$	−3.22165	+	3.83942i	−0.377066	+	0.449370i	−0.920886	−	0.389832i	$-0.872533\pi$
$73$	−3.22165	+	3.83942i	−0.377066	+	0.449370i	0.543820	+	0.839202i	$0.316978\pi$
$74$	0.582122	−	3.30138i	0.0676703	−	0.383777i
$75$		0			0
$76$	−4.25744	−	0.935010i	−0.488361	−	0.107253i
$77$		−	6.73070i		−	0.767034i
$78$	−9.57988	−	1.68919i	−1.08471	−	0.191263i
$79$	0.460535	+	0.386434i	0.0518142	+	0.0434773i	0.668327	−	0.743868i	$-0.267011\pi$
$79$	0.460535	+	0.386434i	0.0518142	+	0.0434773i	−0.616513	+	0.787345i	$0.711455\pi$
$80$		0			0
$81$	−38.9281	+	14.1687i	−4.32534	+	1.57430i
$82$	2.39484	+	2.85406i	0.264466	+	0.315179i
$83$	1.64789	−	0.951408i	0.180879	−	0.104431i	−0.406827	−	0.913505i	$-0.633365\pi$
$83$	1.64789	−	0.951408i	0.180879	−	0.104431i	0.587706	+	0.809075i	$0.300031\pi$
$84$	3.20094	−	5.54420i	0.349252	−	0.604922i
$85$		0			0
$86$	−0.116650	−	0.661553i	−0.0125787	−	0.0713371i
$87$	−3.49960	−	2.02049i	−0.375196	−	0.216620i
$88$	−3.12210	+	1.80254i	−0.332817	+	0.192152i
$89$	−0.755257	+	0.633736i	−0.0800571	+	0.0671759i	−0.681938	−	0.731410i	$-0.738863\pi$
$89$	−0.755257	+	0.633736i	−0.0800571	+	0.0671759i	0.601881	+	0.798586i	$0.294418\pi$
$90$		0			0
$91$	4.97708	+	1.81151i	0.521740	+	0.189898i
$92$	−3.27034	+	3.89744i	−0.340957	+	0.406337i
$93$	17.5552	+	3.09545i	1.82039	+	0.320983i
$94$	−6.32252			−0.652118
$95$		0			0
$96$	−3.42897			−0.349968
$97$	−0.184712	−	0.0325697i	−0.0187547	−	0.00330695i	0.164263	−	0.986417i	$-0.447475\pi$
$97$	−0.184712	−	0.0325697i	−0.0187547	−	0.00330695i	−0.183018	+	0.983110i	$0.558587\pi$
$98$	2.25896	−	2.69212i	0.228189	−	0.271945i
$99$	−29.6688	−	10.7985i	−2.98182	−	1.08529i
$100$		0			0
$101$	−1.50168	+	1.26006i	−0.149423	+	0.125380i	−0.714435	−	0.699702i	$-0.753316\pi$
$101$	−1.50168	+	1.26006i	−0.149423	+	0.125380i	0.565012	+	0.825083i	$0.308872\pi$
$102$	−17.7842	+	10.2677i	−1.76090	+	1.01665i
$103$	15.1589	+	8.75199i	1.49365	+	0.862359i	0.999973	−	0.00728653i	$-0.00231940\pi$
$103$	15.1589	+	8.75199i	1.49365	+	0.862359i	0.493676	+	0.869646i	$0.335653\pi$
$104$	−0.492623	−	2.79380i	−0.0483057	−	0.273955i
$105$		0			0
$106$	1.28080	−	2.21840i	0.124402	−	0.215470i
$107$	9.17096	−	5.29485i	0.886590	−	0.511873i	0.0137643	−	0.999905i	$-0.495619\pi$
$107$	9.17096	−	5.29485i	0.886590	−	0.511873i	0.872826	+	0.488032i	$0.162285\pi$
$108$	−12.6909	−	15.1244i	−1.22118	−	1.45535i
$109$	−13.0386	+	4.74565i	−1.24887	+	0.454551i	−0.880019	−	0.474939i	$-0.842470\pi$
$109$	−13.0386	+	4.74565i	−1.24887	+	0.454551i	−0.368849	+	0.929489i	$0.620248\pi$
$110$		0			0
$111$	8.80565	+	7.38882i	0.835796	+	0.701316i
$112$	1.83864	+	0.324201i	0.173735	+	0.0306341i
$113$			15.9357i			1.49911i	0.661944	+	0.749553i	$0.269732\pi$
$113$			15.9357i			1.49911i	−0.661944	+	0.749553i	$0.730268\pi$
$114$	10.0759	−	11.0397i	0.943694	−	1.03396i
$115$		0			0
$116$	0.204642	−	1.16058i	0.0190005	−	0.107757i
$117$	15.9702	−	19.0325i	1.47644	−	1.75956i
$118$	−1.63084	+	4.48069i	−0.150131	+	0.412481i
$119$	10.5068	−	3.82415i	0.963154	−	0.350559i
$120$		0			0
$121$	−0.998331	−	1.72916i	−0.0907574	−	0.157196i
$122$	7.13291	+	4.11819i	0.645783	+	0.372843i
$123$	−12.5813	+	2.21842i	−1.13442	+	0.200028i
$124$	0.902733	+	5.11966i	0.0810679	+	0.459759i
$125$		0			0
$126$	8.17545	+	14.1603i	0.728327	+	1.26150i
$127$	−10.8078	−	12.8803i	−0.959041	−	1.14294i	−0.989663	−	0.143409i	$-0.954193\pi$
$127$	−10.8078	−	12.8803i	−0.959041	−	1.14294i	0.0306225	−	0.999531i	$-0.490251\pi$
$128$	−0.342020	−	0.939693i	−0.0302306	−	0.0830579i
$129$	2.16453	+	0.787824i	0.190576	+	0.0693640i
$130$		0			0
$131$	1.13110	−	6.41481i	0.0988249	−	0.560464i	−0.894683	−	0.446702i	$-0.852599\pi$
$131$	1.13110	−	6.41481i	0.0988249	−	0.560464i	0.993508	−	0.113763i	$-0.0362903\pi$
$132$		−	12.3617i		−	1.07595i
$133$	−6.44654	+	4.96691i	−0.558986	+	0.430686i
$134$	7.96385			0.687972
$135$		0			0
$136$	−4.58768	−	3.84952i	−0.393390	−	0.330094i
$137$	6.92459	−	19.0252i	0.591608	−	1.62543i	−0.175914	−	0.984406i	$-0.556288\pi$
$137$	6.92459	−	19.0252i	0.591608	−	1.62543i	0.767521	−	0.641023i	$-0.221490\pi$
$138$	−5.96680	−	16.3937i	−0.507928	−	1.39552i
$139$	−3.05535	+	2.56374i	−0.259151	+	0.217454i	−0.763101	−	0.646279i	$-0.776324\pi$
$139$	−3.05535	+	2.56374i	−0.259151	+	0.217454i	0.503950	+	0.863733i	$0.331880\pi$
$140$		0			0
$141$	10.8399	−	18.7752i	0.912882	−	1.58116i
$142$	−1.89770	+	0.334616i	−0.159252	+	0.0280803i
$143$	10.0719	−	1.77595i	0.842256	−	0.148512i
$144$	4.37893	−	7.58452i	0.364910	−	0.632043i
$145$		0			0
$146$	3.83942	−	3.22165i	0.317753	−	0.266626i
$147$	4.12151	+	11.3237i	0.339936	+	0.933967i
$148$	−1.14656	+	3.15014i	−0.0942463	+	0.258940i
$149$	−4.31479	−	3.62054i	−0.353481	−	0.296606i	0.448705	−	0.893680i	$-0.351885\pi$
$149$	−4.31479	−	3.62054i	−0.353481	−	0.296606i	−0.802186	+	0.597074i	$0.796330\pi$
$150$		0			0
$151$	−1.23848			−0.100786			−0.0503932	−	0.998729i	$-0.516047\pi$
$151$	−1.23848			−0.100786			−0.0503932	+	0.998729i	$0.516047\pi$
$152$	4.03039	+	1.66010i	0.326908	+	0.134652i
$153$		−	52.4489i		−	4.24024i
$154$	−1.16877	+	6.62844i	−0.0941825	+	0.534135i
$155$		0			0
$156$	9.14101	+	3.32706i	0.731867	+	0.266378i
$157$	7.35594	+	20.2103i	0.587068	+	1.61296i	0.775837	+	0.630934i	$0.217328\pi$
$157$	7.35594	+	20.2103i	0.587068	+	1.61296i	−0.188769	+	0.982021i	$0.560450\pi$
$158$	−0.386434	−	0.460535i	−0.0307431	−	0.0366382i
$159$	4.39181	+	7.60685i	0.348294	+	0.603262i
$160$		0			0
$161$	1.64946	+	9.35452i	0.129995	+	0.737240i
$162$	40.7970	−	7.19362i	3.20532	−	0.565184i
$163$	15.6067	+	9.01050i	1.22241	+	0.705757i	0.965431	−	0.260660i	$-0.0839403\pi$
$163$	15.6067	+	9.01050i	1.22241	+	0.705757i	0.256977	+	0.966418i	$0.417274\pi$
$164$	−1.86286	−	3.22656i	−0.145465	−	0.251952i
$165$		0			0
$166$	−1.78806	+	0.650801i	−0.138781	+	0.0505120i
$167$	−3.73105	+	10.2510i	−0.288717	+	0.793244i	0.707530	+	0.706684i	$0.249810\pi$
$167$	−3.73105	+	10.2510i	−0.288717	+	0.793244i	−0.996247	+	0.0865598i	$0.972413\pi$
$168$	−4.11506	+	4.90413i	−0.317483	+	0.378362i
$169$	0.859902	−	4.87675i	0.0661463	−	0.375134i
$170$		0			0
$171$	11.5514	+	36.3850i	0.883357	+	2.78243i
$172$			0.671759i			0.0512211i
$173$	−0.143686	−	0.0253357i	−0.0109242	−	0.00192623i	0.168183	−	0.985756i	$-0.446210\pi$
$173$	−0.143686	−	0.0253357i	−0.0109242	−	0.00192623i	−0.179108	+	0.983829i	$0.557321\pi$
$174$	3.09558	+	2.59750i	0.234675	+	0.196916i
$175$		0			0
$176$	3.38767	−	1.23301i	0.255356	−	0.0929418i
$177$	−10.5097	−	12.5250i	−0.789958	−	0.941436i
$178$	0.853830	−	0.492959i	0.0639973	−	0.0369488i
$179$	2.84974	−	4.93590i	0.213000	−	0.368927i	−0.739652	−	0.672989i	$-0.765010\pi$
$179$	2.84974	−	4.93590i	0.213000	−	0.368927i	0.952652	+	0.304063i	$0.0983433\pi$
$180$		0			0
$181$	−3.21271	−	18.2202i	−0.238799	−	1.35430i	−0.834464	−	0.551063i	$-0.814223\pi$
$181$	−3.21271	−	18.2202i	−0.238799	−	1.35430i	0.595665	−	0.803233i	$-0.296889\pi$
$182$	−4.58690	−	2.64825i	−0.340004	−	0.196301i
$183$	−24.4586	+	14.1212i	−1.80803	+	1.04387i
$184$	3.89744	−	3.27034i	0.287323	−	0.241093i
$185$		0			0
$186$	−16.7509	−	6.09684i	−1.22824	−	0.447042i
$187$	13.8779	−	16.5390i	1.01485	−	1.20945i
$188$	6.22647	+	1.09789i	0.454112	+	0.0800721i
$189$	−36.8611			−2.68125
$190$		0			0
$191$	18.8820			1.36626			0.683128	−	0.730298i	$-0.260619\pi$
$191$	18.8820			1.36626			0.683128	+	0.730298i	$0.260619\pi$
$192$	3.37688	+	0.595435i	0.243705	+	0.0429718i
$193$	3.13916	−	3.74110i	0.225961	−	0.269290i	−0.641138	−	0.767426i	$-0.721537\pi$
$193$	3.13916	−	3.74110i	0.225961	−	0.269290i	0.867099	+	0.498135i	$0.165982\pi$
$194$	0.176250	+	0.0641498i	0.0126540	+	0.00460568i
$195$		0			0
$196$	−2.69212	+	2.25896i	−0.192294	+	0.161354i
$197$	−3.04622	+	1.75874i	−0.217034	+	0.125305i	−0.604576	−	0.796547i	$-0.706658\pi$
$197$	−3.04622	+	1.75874i	−0.217034	+	0.125305i	0.387542	+	0.921852i	$0.373324\pi$
$198$	27.3429	+	15.7864i	1.94317	+	1.12189i
$199$	0.145954	+	0.827747i	0.0103464	+	0.0586774i	0.989544	−	0.144232i	$-0.0460713\pi$
$199$	0.145954	+	0.827747i	0.0103464	+	0.0586774i	−0.979197	+	0.202910i	$0.934960\pi$
$200$		0			0
$201$	−13.6539	+	23.6493i	−0.963073	+	1.66809i
$202$	1.69767	−	0.980151i	0.119448	−	0.0689632i
$203$	−1.41428	−	1.68547i	−0.0992630	−	0.118297i
$204$	19.2970	−	7.02352i	1.35106	−	0.491745i
$205$		0			0
$206$	−13.4088	−	11.2513i	−0.934237	−	0.783918i
$207$	43.8809	+	7.73738i	3.04993	+	0.537785i
$208$			2.83690i			0.196704i
$209$	−5.98481	+	14.5299i	−0.413978	+	1.00506i
$210$		0			0
$211$	−4.75961	+	26.9931i	−0.327665	+	1.85828i	0.162579	+	0.986695i	$0.448019\pi$
$211$	−4.75961	+	26.9931i	−0.327665	+	1.85828i	−0.490244	+	0.871585i	$0.663092\pi$
$212$	−1.64656	+	1.96229i	−0.113086	+	0.134771i
$213$	2.25991	−	6.20906i	0.154847	−	0.425438i
$214$	−9.95107	+	3.62189i	−0.680241	+	0.247588i
$215$		0			0
$216$	9.87176	+	17.0984i	0.671688	+	1.16340i
$217$	8.40551	+	4.85292i	0.570603	+	0.329438i
$218$	13.6646	−	2.40943i	0.925480	−	0.163187i
$219$	2.98432	+	16.9249i	0.201662	+	1.14368i
$220$		0			0
$221$	8.49481	+	14.7134i	0.571423	+	0.989733i
$222$	−7.38882	−	8.80565i	−0.495905	−	0.590997i
$223$	−3.91105	−	10.7455i	−0.261903	−	0.719574i	−0.999039	−	0.0438288i	$-0.986044\pi$
$223$	−3.91105	−	10.7455i	−0.261903	−	0.719574i	0.737136	−	0.675745i	$-0.236178\pi$
$224$	−1.75441	−	0.638551i	−0.117221	−	0.0426650i
$225$		0			0
$226$	2.76721	−	15.6936i	0.184072	−	1.04392i
$227$			15.6154i			1.03643i	0.855251	+	0.518214i	$0.173403\pi$
$227$			15.6154i			1.03643i	−0.855251	+	0.518214i	$0.826597\pi$
$228$	−11.8399	+	9.12234i	−0.784113	+	0.604142i
$229$	−5.50003			−0.363452			−0.181726	−	0.983349i	$-0.558168\pi$
$229$	−5.50003			−0.363452			−0.181726	+	0.983349i	$0.558168\pi$
$230$		0			0
$231$	−17.6798	−	14.8351i	−1.16325	−	0.976080i
$232$	−0.403065	+	1.10741i	−0.0264625	+	0.0727052i
$233$	−3.87461	−	10.6454i	−0.253834	−	0.697404i	−0.999516	−	0.0311019i	$-0.990098\pi$
$233$	−3.87461	−	10.6454i	−0.253834	−	0.697404i	0.745682	−	0.666302i	$-0.232124\pi$
$234$	−19.0325	+	15.9702i	−1.24419	+	1.04400i
$235$		0			0
$236$	2.38413	−	4.12943i	0.155193	−	0.268803i
$237$	2.03013	−	0.357967i	0.131871	−	0.0232524i
$238$	−11.0112	+	1.94157i	−0.713750	+	0.125853i
$239$	0.741670	−	1.28461i	0.0479747	−	0.0830946i	−0.841041	−	0.540972i	$-0.818057\pi$
$239$	0.741670	−	1.28461i	0.0479747	−	0.0830946i	0.889016	+	0.457877i	$0.151390\pi$
$240$		0			0
$241$	−6.44943	+	5.41172i	−0.415444	+	0.348599i	−0.826427	−	0.563044i	$-0.809630\pi$
$241$	−6.44943	+	5.41172i	−0.415444	+	0.348599i	0.410983	+	0.911643i	$0.365186\pi$
$242$	0.682899	+	1.87625i	0.0438984	+	0.120610i
$243$	−28.3259	+	77.8248i	−1.81711	+	4.99247i
$244$	−6.30943	−	5.29424i	−0.403920	−	0.338929i
$245$		0			0
$246$	12.7754			0.814528
$247$	−9.13353	−	8.33613i	−0.581153	−	0.530415i
$248$		−	5.19863i		−	0.330114i
$249$	1.13300	−	6.42558i	0.0718011	−	0.407204i
$250$		0			0
$251$	−10.4219	−	3.79327i	−0.657826	−	0.239429i	−0.00852858	−	0.999964i	$-0.502715\pi$
$251$	−10.4219	−	3.79327i	−0.657826	−	0.239429i	−0.649298	+	0.760535i	$0.724937\pi$
$252$	−5.59234	−	15.3648i	−0.352284	−	0.967893i
$253$	11.7899	+	14.0506i	0.741223	+	0.883356i
$254$	8.40701	+	14.5614i	0.527503	+	0.913661i
$255$		0			0
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−11.3101	+	1.99428i	−0.705506	+	0.124400i	−0.514879	−	0.857263i	$-0.672163\pi$
$257$	−11.3101	+	1.99428i	−0.705506	+	0.124400i	−0.190627	+	0.981663i	$0.561052\pi$
$258$	−1.99484	−	1.15172i	−0.124193	−	0.0717030i
$259$	3.12938	+	5.42024i	0.194450	+	0.336797i
$260$		0			0
$261$	−9.69856	+	3.52999i	−0.600326	+	0.218501i
$262$	−2.22784	+	6.12094i	−0.137636	+	0.378153i
$263$	20.4010	−	24.3129i	1.25798	−	1.49920i	0.471113	−	0.882073i	$-0.343852\pi$
$263$	20.4010	−	24.3129i	1.25798	−	1.49920i	0.786864	−	0.617126i	$-0.211703\pi$
$264$	−2.14660	+	12.1739i	−0.132114	+	0.749255i
$265$		0			0
$266$	7.21109	−	3.77202i	0.442141	−	0.231278i
$267$			3.38069i			0.206895i
$268$	−7.84286	−	1.38291i	−0.479079	−	0.0844746i
$269$	17.8932	+	15.0142i	1.09097	+	0.915431i	0.996785	−	0.0801240i	$-0.0255316\pi$
$269$	17.8932	+	15.0142i	1.09097	+	0.915431i	0.0941831	+	0.995555i	$0.469976\pi$
$270$		0			0
$271$	20.7560	−	7.55458i	1.26084	−	0.458908i	0.376788	−	0.926299i	$-0.377028\pi$
$271$	20.7560	−	7.55458i	1.26084	−	0.458908i	0.884050	+	0.467392i	$0.154806\pi$
$272$	3.84952	+	4.58768i	0.233411	+	0.278169i
$273$	15.7284	−	9.08077i	0.951924	−	0.549593i
$274$	−10.1231	+	17.5337i	−0.611557	+	1.05925i
$275$		0			0
$276$	3.02943	+	17.1807i	0.182350	+	1.03416i
$277$	17.1581	+	9.90622i	1.03093	+	0.595207i	0.917251	−	0.398310i	$-0.130403\pi$
$277$	17.1581	+	9.90622i	1.03093	+	0.595207i	0.113679	+	0.993518i	$0.463737\pi$
$278$	3.45412	−	1.99424i	0.207164	−	0.119606i
$279$	34.8771	−	29.2654i	2.08804	−	1.75207i
$280$		0			0
$281$	19.8856	+	7.23776i	1.18627	+	0.431769i	0.858414	−	0.512958i	$-0.171450\pi$
$281$	19.8856	+	7.23776i	1.18627	+	0.431769i	0.327860	+	0.944726i	$0.393672\pi$
$282$	−13.9355	+	16.6076i	−0.829845	+	0.988971i
$283$	18.3665	+	3.23851i	1.09178	+	0.192510i	0.690418	−	0.723411i	$-0.257427\pi$
$283$	18.3665	+	3.23851i	1.09178	+	0.192510i	0.401359	+	0.915921i	$0.368538\pi$
$284$	1.92698			0.114345
$285$		0			0
$286$	−10.2273			−0.604752
$287$	−6.85023	−	1.20788i	−0.404356	−	0.0712989i
$288$	−5.62944	+	6.70890i	−0.331718	+	0.395326i
$289$	17.7279	+	6.45241i	1.04282	+	0.379554i
$290$		0			0
$291$	−0.492676	+	0.413404i	−0.0288812	+	0.0242342i
$292$	−4.34052	+	2.50600i	−0.254010	+	0.146653i
$293$	−25.7475	−	14.8653i	−1.50419	−	0.868442i	−0.999988	−	0.00485332i	$-0.998455\pi$
$293$	−25.7475	−	14.8653i	−1.50419	−	0.868442i	−0.504197	−	0.863589i	$-0.668212\pi$
$294$	−2.09254	−	11.8674i	−0.122040	−	0.692121i
$295$		0			0
$296$	1.67615	−	2.90318i	0.0974244	−	0.168744i
$297$	−61.6412	+	35.5886i	−3.57678	+	2.06506i
$298$	3.62054	+	4.31479i	0.209732	+	0.249949i
$299$	−13.5630	+	4.93654i	−0.784370	+	0.285487i
$300$		0			0
$301$	0.960753	+	0.806167i	0.0553769	+	0.0464667i
$302$	1.21967	+	0.215061i	0.0701841	+	0.0123753i
$303$			6.72182i			0.386159i
$304$	−3.68089	−	2.33475i	−0.211113	−	0.133907i
$305$		0			0
$306$	−9.10766	+	51.6521i	−0.520650	+	2.95275i
$307$	3.31770	−	3.95389i	0.189351	−	0.225660i	−0.663014	−	0.748607i	$-0.730723\pi$
$307$	3.31770	−	3.95389i	0.189351	−	0.225660i	0.852365	+	0.522947i	$0.175167\pi$
$308$	2.30203	−	6.32479i	0.131171	−	0.360388i
$309$	56.4010	−	20.5283i	3.20854	−	1.16781i
$310$		0			0
$311$	13.0187	+	22.5490i	0.738223	+	1.27864i	0.953295	+	0.302041i	$0.0976680\pi$
$311$	13.0187	+	22.5490i	0.738223	+	1.27864i	−0.215072	+	0.976598i	$0.568999\pi$
$312$	−8.42440	−	4.86383i	−0.476938	−	0.275360i
$313$	−0.272916	+	0.0481224i	−0.0154261	+	0.00272004i	−0.181356	−	0.983418i	$-0.558049\pi$
$313$	−0.272916	+	0.0481224i	−0.0154261	+	0.00272004i	0.165930	+	0.986138i	$0.446937\pi$
$314$	−3.73471	−	21.1806i	−0.210762	−	1.19529i
$315$		0			0
$316$	0.300593	+	0.520642i	0.0169097	+	0.0292884i
$317$	16.0233	+	19.0958i	0.899958	+	1.07253i	0.997012	+	0.0772492i	$0.0246137\pi$
$317$	16.0233	+	19.0958i	0.899958	+	1.07253i	−0.0970537	+	0.995279i	$0.530942\pi$
$318$	−3.00418	−	8.25391i	−0.168466	−	0.462856i
$319$	−3.99232	−	1.45309i	−0.223527	−	0.0813572i
$320$		0			0
$321$	6.30548	−	35.7602i	0.351938	−	1.99594i
$322$		−	9.49883i		−	0.529349i
$323$	−26.0819	−	1.08702i	−1.45123	−	0.0604835i
$324$	−41.4264			−2.30147
$325$		0			0
$326$	−13.8049	−	11.5837i	−0.764582	−	0.641561i
$327$	−16.2727	+	44.7089i	−0.899882	+	2.47241i
$328$	1.27427	+	3.50103i	0.0703598	+	0.193312i
$329$	9.04250	−	7.58755i	0.498529	−	0.418315i
$330$		0			0
$331$	5.34847	−	9.26381i	0.293978	−	0.509185i	−0.680768	−	0.732499i	$-0.738354\pi$
$331$	5.34847	−	9.26381i	0.293978	−	0.509185i	0.974747	+	0.223313i	$0.0716873\pi$
$332$	1.87391	−	0.330420i	0.102844	−	0.0181342i
$333$	28.9130	−	5.09814i	1.58442	−	0.279376i
$334$	5.45442	−	9.44734i	0.298453	−	0.516935i
$335$		0			0
$336$	4.90413	−	4.11506i	0.267542	−	0.224495i
$337$	1.55890	+	4.28303i	0.0849184	+	0.233312i	0.974883	−	0.222719i	$-0.0714931\pi$
$337$	1.55890	+	4.28303i	0.0849184	+	0.233312i	−0.889964	+	0.456030i	$0.849271\pi$
$338$	−1.69368	+	4.65334i	−0.0921238	+	0.253108i
$339$	41.8591	+	35.1239i	2.27347	+	1.90767i
$340$		0			0
$341$	18.7415			1.01491
$342$	−5.05771	−	37.8381i	−0.273490	−	2.04605i
$343$			19.6302i			1.05993i
$344$	0.116650	−	0.661553i	0.00628933	−	0.0356686i
$345$		0			0
$346$	0.137103	+	0.0499015i	0.00737072	+	0.00268272i
$347$	−7.14578	−	19.6329i	−0.383606	−	1.05395i	−0.969826	−	0.243796i	$-0.921607\pi$
$347$	−7.14578	−	19.6329i	−0.383606	−	1.05395i	0.586221	−	0.810151i	$-0.300615\pi$
$348$	−2.59750	−	3.09558i	−0.139240	−	0.165940i
$349$	−5.64218	−	9.77255i	−0.302019	−	0.523112i	0.674574	−	0.738207i	$-0.264327\pi$
$349$	−5.64218	−	9.77255i	−0.302019	−	0.523112i	−0.976593	+	0.215095i	$0.930994\pi$
$350$		0			0
$351$	−9.72611	−	55.1595i	−0.519141	−	2.94420i
$352$	−3.55032	+	0.626017i	−0.189233	+	0.0333668i
$353$	−7.11512	−	4.10792i	−0.378700	−	0.218642i	0.298553	−	0.954393i	$-0.403496\pi$
$353$	−7.11512	−	4.10792i	−0.378700	−	0.218642i	−0.677252	+	0.735751i	$0.736829\pi$
$354$	8.17511	+	14.1597i	0.434502	+	0.752580i
$355$		0			0
$356$	−0.926460	+	0.337204i	−0.0491023	+	0.0178718i
$357$	13.1129	−	36.0274i	0.694009	−	1.90677i
$358$	−3.66356	+	4.36606i	−0.193625	+	0.230753i
$359$	1.86656	−	10.5858i	0.0985131	−	0.558696i	−0.895101	−	0.445864i	$-0.852897\pi$
$359$	1.86656	−	10.5858i	0.0985131	−	0.558696i	0.993614	−	0.112832i	$-0.0359922\pi$
$360$		0			0
$361$	18.3330	−	4.99020i	0.964893	−	0.262642i
$362$			18.5013i			0.972405i
$363$	−6.74248	−	1.18888i	−0.353889	−	0.0624001i
$364$	4.05735	+	3.40452i	0.212663	+	0.178446i
$365$		0			0
$366$	26.5391	−	9.65944i	1.38722	−	0.504907i
$367$	−9.60825	−	11.4507i	−0.501547	−	0.597720i	0.454568	−	0.890712i	$-0.349794\pi$
$367$	−9.60825	−	11.4507i	−0.501547	−	0.597720i	−0.956115	+	0.292992i	$0.905349\pi$
$368$	−4.40612	+	2.54388i	−0.229685	+	0.132609i
$369$	−16.3146	+	28.2578i	−0.849306	+	1.47104i
$370$		0			0
$371$	0.830471	+	4.70983i	0.0431159	+	0.244522i
$372$	15.4377	+	8.91299i	0.800410	+	0.462117i
$373$	−7.55370	+	4.36113i	−0.391116	+	0.225811i	−0.682644	−	0.730752i	$-0.739170\pi$
$373$	−7.55370	+	4.36113i	−0.391116	+	0.225811i	0.291528	+	0.956562i	$0.405836\pi$
$374$	−16.5390	+	13.8779i	−0.855211	+	0.717607i
$375$		0			0
$376$	−5.94122	−	2.16243i	−0.306395	−	0.111519i
$377$	2.14900	−	2.56107i	0.110679	−	0.131902i
$378$	36.3011	+	6.40087i	1.86713	+	0.329225i
$379$	−15.9169			−0.817597			−0.408799	−	0.912625i	$-0.634052\pi$
$379$	−15.9169			−0.817597			−0.408799	+	0.912625i	$0.634052\pi$
$380$		0			0
$381$	−57.6548			−2.95375
$382$	−18.5952	−	3.27883i	−0.951412	−	0.167760i
$383$	−1.12094	+	1.33589i	−0.0572776	+	0.0682607i	−0.793923	−	0.608019i	$-0.791964\pi$
$383$	−1.12094	+	1.33589i	−0.0572776	+	0.0682607i	0.736645	+	0.676280i	$0.236409\pi$
$384$	−3.22218	−	1.17278i	−0.164431	−	0.0598481i
$385$		0			0
$386$	−3.74110	+	3.13916i	−0.190417	+	0.159779i
$387$	5.09497	−	2.94158i	0.258992	−	0.149529i
$388$	−0.162433	−	0.0937807i	−0.00824628	−	0.00476099i
$389$	−5.63929	−	31.9820i	−0.285924	−	1.62155i	−0.701968	−	0.712209i	$-0.747695\pi$
$389$	−5.63929	−	31.9820i	−0.285924	−	1.62155i	0.416044	−	0.909344i	$-0.363416\pi$
$390$		0			0
$391$	−15.2347	+	26.3873i	−0.770454	+	1.33447i
$392$	3.04348	−	1.75716i	0.153719	−	0.0887498i
$393$	−14.3570	−	17.1100i	−0.724214	−	0.863085i
$394$	3.30534	−	1.20305i	0.166521	−	0.0606086i
$395$		0			0
$396$	−24.1862	−	20.2946i	−1.21540	−	1.01984i
$397$	−4.04292	−	0.712877i	−0.202909	−	0.0357783i	0.0712700	−	0.997457i	$-0.477295\pi$
$397$	−4.04292	−	0.712877i	−0.202909	−	0.0357783i	−0.274179	+	0.961679i	$0.588406\pi$
$398$		−	0.840516i		−	0.0421313i
$399$	−1.16200	+	27.8810i	−0.0581730	+	1.39580i
$400$		0			0
$401$	5.41766	−	30.7251i	0.270545	−	1.53434i	−0.482221	−	0.876049i	$-0.660170\pi$
$401$	5.41766	−	30.7251i	0.270545	−	1.53434i	0.752766	−	0.658288i	$-0.228719\pi$
$402$	17.5531	−	20.9190i	0.875471	−	1.04335i
$403$	−5.04412	+	13.8586i	−0.251266	+	0.690347i
$404$	−1.84208	+	0.670463i	−0.0916470	+	0.0333568i
$405$		0			0
$406$	1.10011	+	1.90545i	0.0545978	+	0.0945661i
$407$	10.4662	+	6.04268i	0.518792	+	0.299524i
$408$	−20.2234	+	3.56593i	−1.00121	+	0.176540i
$409$	−1.52348	−	8.64010i	−0.0753313	−	0.427225i	−0.999027	−	0.0440987i	$-0.985958\pi$
$409$	−1.52348	−	8.64010i	−0.0753313	−	0.427225i	0.923696	−	0.383127i	$-0.125153\pi$
$410$		0			0
$411$	−34.7117	−	60.1225i	−1.71220	−	2.96562i
$412$	11.2513	+	13.4088i	0.554314	+	0.660605i
$413$	−3.04478	−	8.36545i	−0.149824	−	0.411637i
$414$	−41.8706	−	15.2397i	−2.05783	−	0.748988i
$415$		0			0
$416$	0.492623	−	2.79380i	0.0241528	−	0.136978i
$417$			13.6764i			0.669734i
$418$	8.41698	−	13.2699i	0.411688	−	0.649053i
$419$	6.13252			0.299593			0.149797	−	0.988717i	$-0.452138\pi$
$419$	6.13252			0.299593			0.149797	+	0.988717i	$0.452138\pi$
$420$		0			0
$421$	−2.93864	−	2.46581i	−0.143220	−	0.120176i	0.568363	−	0.822778i	$-0.307577\pi$
$421$	−2.93864	−	2.46581i	−0.143220	−	0.120176i	−0.711583	+	0.702602i	$0.752021\pi$
$422$	9.37460	−	25.7565i	0.456348	−	1.25381i
$423$	−18.9382	−	52.0324i	−0.920808	−	2.52990i
$424$	1.96229	−	1.64656i	0.0952974	−	0.0799640i
$425$		0			0
$426$	−3.30377	+	5.72230i	−0.160068	+	0.277247i
$427$	−15.1437	+	2.67024i	−0.732855	+	0.129222i
$428$	10.4288	−	1.83888i	0.504096	−	0.0888858i
$429$	17.5345	−	30.3707i	0.846576	−	1.46631i
$430$		0			0
$431$	−19.5996	+	16.4460i	−0.944081	+	0.792178i	−0.978291	−	0.207237i	$-0.933553\pi$
$431$	−19.5996	+	16.4460i	−0.944081	+	0.792178i	0.0342100	+	0.999415i	$0.489108\pi$
$432$	−6.75268	−	18.5528i	−0.324888	−	0.892624i
$433$	−9.73513	+	26.7471i	−0.467841	+	1.28538i	0.451624	+	0.892208i	$0.350845\pi$
$433$	−9.73513	+	26.7471i	−0.467841	+	1.28538i	−0.919464	+	0.393173i	$0.871377\pi$
$434$	−7.43511	−	6.23880i	−0.356897	−	0.299472i
$435$		0			0
$436$	−13.8754			−0.664509
$437$	4.75710	−	21.6608i	0.227563	−	1.03618i
$438$		−	17.1860i		−	0.821180i
$439$	−6.61684	+	37.5260i	−0.315805	+	1.79102i	0.251866	+	0.967762i	$0.418956\pi$
$439$	−6.61684	+	37.5260i	−0.315805	+	1.79102i	−0.567671	+	0.823256i	$0.692155\pi$
$440$		0			0
$441$	28.9217	+	10.5266i	1.37722	+	0.501268i
$442$	−5.81079	−	15.9650i	−0.276391	−	0.759379i
$443$	−14.6417	−	17.4493i	−0.695649	−	0.829042i	0.296377	−	0.955071i	$-0.404221\pi$
$443$	−14.6417	−	17.4493i	−0.695649	−	0.829042i	−0.992027	+	0.126029i	$0.959777\pi$
$444$	5.74748	+	9.95493i	0.272763	+	0.472440i
$445$		0			0
$446$	1.98569	+	11.2614i	0.0940253	+	0.533244i
$447$	−19.0205	+	3.35382i	−0.899637	+	0.158630i
$448$	1.61687	+	0.933500i	0.0763899	+	0.0441037i
$449$	−15.5911	−	27.0045i	−0.735787	−	1.27442i	−0.954377	−	0.298604i	$-0.903479\pi$
$449$	−15.5911	−	27.0045i	−0.735787	−	1.27442i	0.218590	−	0.975817i	$-0.429854\pi$
$450$		0			0
$451$	−12.6215	+	4.59385i	−0.594324	+	0.216316i
$452$	−5.45034	+	14.9747i	−0.256362	+	0.704350i
$453$	−2.72975	+	3.25318i	−0.128255	+	0.152848i
$454$	2.71158	−	15.3781i	0.127261	−	0.721731i
$455$		0			0
$456$	13.2441	−	6.92778i	0.620210	−	0.324423i
$457$		−	13.0810i		−	0.611902i	−0.952047	−	0.305951i	$-0.901026\pi$
$457$		−	13.0810i		−	0.611902i	0.952047	−	0.305951i	$-0.0989744\pi$
$458$	5.41647	+	0.955070i	0.253095	+	0.0446275i
$459$	−90.5769	−	76.0030i	−4.22777	−	3.54752i
$460$		0			0
$461$	−17.1219	+	6.23187i	−0.797448	+	0.290247i	−0.708429	−	0.705783i	$-0.750596\pi$
$461$	−17.1219	+	6.23187i	−0.797448	+	0.290247i	−0.0890194	+	0.996030i	$0.528373\pi$
$462$	14.8351	+	17.6798i	0.690193	+	0.822540i
$463$	19.9255	−	11.5040i	0.926017	−	0.534636i	0.0404670	−	0.999181i	$-0.487115\pi$
$463$	19.9255	−	11.5040i	0.926017	−	0.534636i	0.885550	+	0.464545i	$0.153782\pi$
$464$	0.589242	−	1.02060i	0.0273549	−	0.0473800i
$465$		0			0
$466$	1.96719	+	11.1565i	0.0911284	+	0.516815i
$467$	21.6966	+	12.5265i	1.00400	+	0.579658i	0.909429	−	0.415860i	$-0.136519\pi$
$467$	21.6966	+	12.5265i	1.00400	+	0.579658i	0.0945691	+	0.995518i	$0.469853\pi$
$468$	21.5166	−	12.4226i	0.994603	−	0.574234i
$469$	−11.3899	+	9.55729i	−0.525938	+	0.441315i
$470$		0			0
$471$	69.3005	+	25.2233i	3.19320	+	1.16223i
$472$	−3.06497	+	3.65269i	−0.141077	+	0.168129i
$473$	2.38496	+	0.420532i	0.109660	+	0.0193361i
$474$	−2.06145			−0.0946854
$475$		0			0
$476$	11.1811			0.512483
$477$	22.0932	+	3.89563i	1.01158	+	0.178369i
$478$	−0.953473	+	1.13631i	−0.0436108	+	0.0519734i
$479$	20.3567	+	7.40924i	0.930122	+	0.338537i	0.762258	−	0.647274i	$-0.224091\pi$
$479$	20.3567	+	7.40924i	0.930122	+	0.338537i	0.167864	+	0.985810i	$0.446313\pi$
$480$		0			0
$481$	−7.28521	+	6.11302i	−0.332177	+	0.278730i
$482$	7.29118	−	4.20957i	0.332104	−	0.191741i
$483$	28.2075	+	16.2856i	1.28349	+	0.741021i
$484$	−0.346717	−	1.96633i	−0.0157598	−	0.0893785i
$485$		0			0
$486$	41.4097	−	71.7238i	1.87838	−	3.25346i
$487$	−2.87982	+	1.66266i	−0.130497	+	0.0753425i	−0.563827	−	0.825893i	$-0.690672\pi$
$487$	−2.87982	+	1.66266i	−0.130497	+	0.0753425i	0.433330	+	0.901235i	$0.357338\pi$
$488$	5.29424	+	6.30943i	0.239659	+	0.285614i
$489$	58.0669	−	21.1346i	2.62588	−	0.955741i
$490$		0			0
$491$	−3.86014	−	3.23904i	−0.174206	−	0.146176i	0.551516	−	0.834164i	$-0.314050\pi$
$491$	−3.86014	−	3.23904i	−0.174206	−	0.146176i	−0.725722	+	0.687988i	$0.758494\pi$
$492$	−12.5813	−	2.21842i	−0.567208	−	0.100014i
$493$		−	7.05769i		−	0.317862i
$494$	7.54722	+	9.79551i	0.339565	+	0.440721i
$495$		0			0
$496$	−0.902733	+	5.11966i	−0.0405339	+	0.229879i
$497$	2.31253	−	2.75597i	0.103731	−	0.123622i
$498$	−2.23158	+	6.13121i	−0.0999995	+	0.274746i
$499$	−9.62114	+	3.50181i	−0.430701	+	0.156762i	−0.548268	−	0.836302i	$-0.684713\pi$
$499$	−9.62114	+	3.50181i	−0.430701	+	0.156762i	0.117567	+	0.993065i	$0.462491\pi$
$500$		0			0
$501$	18.7031	+	32.3947i	0.835592	+	1.44729i
$502$	9.60490	+	5.54539i	0.428688	+	0.247503i
$503$	6.60132	−	1.16399i	0.294338	−	0.0518998i	−0.0245291	−	0.999699i	$-0.507809\pi$
$503$	6.60132	−	1.16399i	0.294338	−	0.0518998i	0.318867	+	0.947799i	$0.396698\pi$
$504$	2.83930	+	16.1025i	0.126473	+	0.717262i
$505$		0			0
$506$	−9.17090	−	15.8845i	−0.407696	−	0.706151i
$507$	−10.9147	−	13.0076i	−0.484737	−	0.577687i
$508$	−5.75073	−	15.8000i	−0.255148	−	0.701012i
$509$	22.6049	+	8.22751i	1.00195	+	0.364678i	0.790334	−	0.612676i	$-0.209907\pi$
$509$	22.6049	+	8.22751i	1.00195	+	0.364678i	0.211611	+	0.977354i	$0.432129\pi$
$510$		0			0
$511$	−1.62490	+	9.21525i	−0.0718812	+	0.407659i
$512$		−	1.00000i		−	0.0441942i
$513$	79.5741	+	32.7762i	3.51328	+	1.44711i
$514$	11.4846			0.506564
$515$		0			0
$516$	1.76454	+	1.48062i	0.0776795	+	0.0651808i
$517$	7.79575	−	21.4186i	0.342857	−	0.941991i
$518$	−2.14062	−	5.88130i	−0.0940534	−	0.258410i
$519$	−0.383248	+	0.321583i	−0.0168227	+	0.0141159i
$520$		0			0
$521$	−13.2375	+	22.9280i	−0.579945	+	1.00449i	0.415540	+	0.909575i	$0.363593\pi$
$521$	−13.2375	+	22.9280i	−0.579945	+	1.00449i	−0.995485	+	0.0949192i	$0.969741\pi$
$522$	10.1642	−	1.79222i	0.444874	−	0.0784434i
$523$	−15.3861	+	2.71298i	−0.672787	+	0.118631i	−0.499597	−	0.866258i	$-0.666519\pi$
$523$	−15.3861	+	2.71298i	−0.672787	+	0.118631i	−0.173190	+	0.984888i	$0.555407\pi$
$524$	3.25688	−	5.64108i	0.142278	−	0.246432i
$525$		0			0
$526$	−24.3129	+	20.4010i	−1.06009	+	0.889524i
$527$	10.6483	+	29.2559i	0.463847	+	1.27441i
$528$	4.22797	−	11.6162i	0.183999	−	0.505532i
$529$	−2.21022	−	1.85459i	−0.0960963	−	0.0806344i
$530$		0			0
$531$	−41.7597			−1.81222
$532$	−7.75655	+	2.46253i	−0.336289	+	0.106764i
$533$		−	10.5695i		−	0.457816i
$534$	0.587050	−	3.32933i	0.0254041	−	0.144074i
$535$		0			0
$536$	7.48357	+	2.72380i	0.323241	+	0.117650i
$537$	−6.68423	−	18.3648i	−0.288446	−	0.792498i
$538$	−15.0142	−	17.8932i	−0.647307	−	0.771431i
$539$	6.33470	+	10.9720i	0.272855	+	0.472599i
$540$		0			0
$541$	−2.57421	−	14.5991i	−0.110674	−	0.627664i	−0.988801	−	0.149237i	$-0.952318\pi$
$541$	−2.57421	−	14.5991i	−0.110674	−	0.627664i	0.878127	−	0.478427i	$-0.158793\pi$
$542$	−21.7525	+	3.83556i	−0.934351	+	0.164751i
$543$	−54.9409	−	31.7202i	−2.35774	−	1.36124i
$544$	−2.99439	−	5.18644i	−0.128384	−	0.222367i
$545$		0			0
$546$	−17.0663	+	6.21161i	−0.730369	+	0.265833i
$547$	−6.62897	+	18.2130i	−0.283434	+	0.778730i	0.713512	+	0.700643i	$0.247103\pi$
$547$	−6.62897	+	18.2130i	−0.283434	+	0.778730i	−0.996947	+	0.0780869i	$0.975119\pi$
$548$	13.0140	−	15.5095i	0.555929	−	0.662531i
$549$	−12.5258	+	71.0371i	−0.534586	+	3.03179i
$550$		0			0
$551$	1.55439	+	4.89607i	0.0662193	+	0.208580i
$552$		−	17.4458i		−	0.742541i
$553$	1.10536	+	0.194905i	0.0470047	+	0.00828820i
$554$	−15.1772	−	12.7352i	−0.644818	−	0.541067i
$555$		0			0
$556$	−3.74794	+	1.36414i	−0.158948	+	0.0578523i
$557$	−24.5056	−	29.2047i	−1.03834	−	1.23744i	−0.970842	−	0.239721i	$-0.922944\pi$
$557$	−24.5056	−	29.2047i	−1.03834	−	1.23744i	−0.0674946	−	0.997720i	$-0.521501\pi$
$558$	−39.4292	+	22.7644i	−1.66917	+	0.963695i
$559$	−0.952858	+	1.65040i	−0.0403016	+	0.0698044i
$560$		0			0
$561$	−12.8555	−	72.9072i	−0.542760	−	3.07814i
$562$	−18.3267	−	10.5809i	−0.773063	−	0.446328i
$563$	−10.6774	+	6.16458i	−0.449998	+	0.259806i	−0.707829	−	0.706384i	$-0.750325\pi$
$563$	−10.6774	+	6.16458i	−0.449998	+	0.259806i	0.257832	+	0.966190i	$0.416992\pi$
$564$	16.6076	−	13.9355i	0.699308	−	0.586789i
$565$		0			0
$566$	−17.5251	−	6.37863i	−0.736636	−	0.268114i
$567$	−49.7152	+	59.2482i	−2.08784	+	2.48819i
$568$	−1.89770	−	0.334616i	−0.0796258	−	0.0140402i
$569$	3.18778			0.133639			0.0668194	−	0.997765i	$-0.478715\pi$
$569$	3.18778			0.133639			0.0668194	+	0.997765i	$0.478715\pi$
$570$		0			0
$571$	3.67370			0.153740			0.0768698	−	0.997041i	$-0.475507\pi$
$571$	3.67370			0.153740			0.0768698	+	0.997041i	$0.475507\pi$
$572$	10.0719	+	1.77595i	0.421128	+	0.0742562i
$573$	41.6179	−	49.5983i	1.73861	−	2.07200i
$574$	6.53641	+	2.37906i	0.272825	+	0.0993001i
$575$		0			0
$576$	6.70890	−	5.62944i	0.279538	−	0.234560i
$577$	−1.86286	+	1.07552i	−0.0775519	+	0.0447746i	−0.538274	−	0.842770i	$-0.680924\pi$
$577$	−1.86286	+	1.07552i	−0.0775519	+	0.0447746i	0.460723	+	0.887544i	$0.347590\pi$
$578$	−16.3381	−	9.43280i	−0.679575	−	0.392353i
$579$	−2.90790	−	16.4915i	−0.120848	−	0.685364i
$580$		0			0
$581$	1.77628	−	3.07660i	0.0736924	−	0.127639i
$582$	0.556978	−	0.321571i	0.0230875	−	0.0133296i
$583$	5.93599	+	7.07424i	0.245844	+	0.292985i
$584$	4.70974	−	1.71421i	0.194891	−	0.0709344i
$585$		0			0
$586$	22.7750	+	19.1105i	0.940827	+	0.789447i
$587$	−28.0908	−	4.95317i	−1.15943	−	0.204439i	−0.439342	−	0.898320i	$-0.644788\pi$
$587$	−28.0908	−	4.95317i	−1.15943	−	0.204439i	−0.720090	+	0.693880i	$0.755900\pi$
$588$			12.0505i			0.496953i
$589$	−13.8303	−	17.9503i	−0.569868	−	0.739629i
$590$		0			0
$591$	−2.09442	+	11.8781i	−0.0861531	+	0.488599i
$592$	−2.15482	+	2.56801i	−0.0885626	+	0.105545i
$593$	−3.45151	+	9.48294i	−0.141737	+	0.389418i	−0.990167	−	0.139889i	$-0.955326\pi$
$593$	−3.45151	+	9.48294i	−0.141737	+	0.389418i	0.848431	+	0.529306i	$0.177548\pi$
$594$	66.8846	−	24.3440i	2.74431	−	0.998847i
$595$		0			0
$596$	−2.81628	−	4.87794i	−0.115359	−	0.199808i
$597$	2.49598	+	1.44105i	0.102154	+	0.0589784i
$598$	14.2142	−	2.50635i	0.581261	−	0.102492i
$599$	−0.479831	−	2.72126i	−0.0196054	−	0.111188i	0.973435	−	0.228965i	$-0.0735341\pi$
$599$	−0.479831	−	2.72126i	−0.0196054	−	0.111188i	−0.993040	+	0.117778i	$0.962423\pi$
$600$		0			0
$601$	−8.51074	−	14.7410i	−0.347160	−	0.601299i	0.638583	−	0.769553i	$-0.279521\pi$
$601$	−8.51074	−	14.7410i	−0.347160	−	0.601299i	−0.985744	+	0.168253i	$0.946187\pi$
$602$	−0.806167	−	0.960753i	−0.0328569	−	0.0391574i
$603$	23.8546	+	65.5400i	0.971435	+	2.66900i
$604$	−1.16380	−	0.423587i	−0.0473542	−	0.0172355i
$605$		0			0
$606$	1.16723	−	6.61970i	0.0474156	−	0.268907i
$607$		−	45.0807i		−	1.82977i	−0.403717	−	0.914884i	$-0.632282\pi$
$607$		−	45.0807i		−	1.82977i	0.403717	−	0.914884i	$-0.367718\pi$
$608$	3.21954	+	2.93846i	0.130570	+	0.119170i
$609$	−7.54452			−0.305720
$610$		0			0
$611$	13.7401	+	11.5293i	0.555863	+	0.466425i
$612$	17.9386	−	49.2859i	0.725124	−	1.99226i
$613$	−0.420147	−	1.15435i	−0.0169696	−	0.0466236i	0.930919	−	0.365227i	$-0.119009\pi$
$613$	−0.420147	−	1.15435i	−0.0169696	−	0.0466236i	−0.947888	+	0.318603i	$0.896786\pi$
$614$	−3.95389	+	3.31770i	−0.159566	+	0.133892i
$615$		0			0
$616$	−3.36535	+	5.82896i	−0.135594	+	0.234855i
$617$	−23.3588	+	4.11879i	−0.940392	+	0.165816i	−0.622773	−	0.782402i	$-0.713994\pi$
$617$	−23.3588	+	4.11879i	−0.940392	+	0.165816i	−0.317618	+	0.948219i	$0.602883\pi$
$618$	−59.1088	+	10.4225i	−2.37771	+	0.419254i
$619$	6.32545	−	10.9560i	0.254241	−	0.440359i	−0.710448	−	0.703750i	$-0.751508\pi$
$619$	6.32545	−	10.9560i	0.254241	−	0.440359i	0.964689	+	0.263391i	$0.0848410\pi$
$620$		0			0
$621$	76.9493	−	64.5681i	3.08787	−	2.59103i
$622$	−8.90531	−	24.4672i	−0.357071	−	0.981043i
$623$	−0.629559	+	1.72970i	−0.0252228	+	0.0692990i
$624$	7.45182	+	6.25282i	0.298312	+	0.250313i
$625$		0			0
$626$	0.277126			0.0110762
$627$	24.9753	+	47.7460i	0.997416	+	1.90679i
$628$			21.5073i			0.858235i
$629$	−3.48620	+	19.7712i	−0.139004	+	0.788331i
$630$		0			0
$631$	−35.9350	−	13.0793i	−1.43055	−	0.520677i	−0.493460	−	0.869769i	$-0.664268\pi$
$631$	−35.9350	−	13.0793i	−1.43055	−	0.520677i	−0.937089	+	0.349091i	$0.886490\pi$
$632$	−0.205617	−	0.564929i	−0.00817902	−	0.0224717i
$633$	60.4133	+	71.9978i	2.40121	+	2.86165i
$634$	−12.4639	−	21.5881i	−0.495005	−	0.857374i
$635$		0			0
$636$	1.52526	+	8.65019i	0.0604805	+	0.343002i
$637$	−9.81830	+	1.73123i	−0.389015	+	0.0685939i
$638$	3.67934	+	2.12427i	0.145667	+	0.0841006i
$639$	−8.43809	−	14.6152i	−0.333806	−	0.578168i
$640$		0			0
$641$	−9.64318	+	3.50983i	−0.380883	+	0.138630i	−0.525364	−	0.850878i	$-0.676071\pi$
$641$	−9.64318	+	3.50983i	−0.380883	+	0.138630i	0.144481	+	0.989508i	$0.453849\pi$
$642$	−12.4194	+	34.1219i	−0.490154	+	1.34669i
$643$	−9.36407	+	11.1597i	−0.369283	+	0.440094i	−0.918401	−	0.395650i	$-0.870519\pi$
$643$	−9.36407	+	11.1597i	−0.369283	+	0.440094i	0.549118	+	0.835745i	$0.314964\pi$
$644$	−1.64946	+	9.35452i	−0.0649976	+	0.368620i
$645$		0			0
$646$	25.4969	+	5.59958i	1.00316	+	0.220313i
$647$			4.44223i			0.174642i	0.996180	+	0.0873211i	$0.0278306\pi$
$647$			4.44223i			0.174642i	−0.996180	+	0.0873211i	$0.972169\pi$
$648$	40.7970	+	7.19362i	1.60266	+	0.282592i
$649$	−13.1683	−	11.0495i	−0.516900	−	0.433731i
$650$		0			0
$651$	31.2740	−	11.3828i	1.22572	−	0.446127i
$652$	11.5837	+	13.8049i	0.453652	+	0.540641i
$653$	−16.8427	+	9.72417i	−0.659108	+	0.380536i	−0.791937	−	0.610603i	$-0.790927\pi$
$653$	−16.8427	+	9.72417i	−0.659108	+	0.380536i	0.132829	+	0.991139i	$0.457594\pi$
$654$	23.7891	−	41.2039i	0.930227	−	1.61120i
$655$		0			0
$656$	−0.646964	−	3.66911i	−0.0252597	−	0.143255i
$657$	38.0137	+	21.9472i	1.48305	+	0.856242i
$658$	−10.2227	+	5.90207i	−0.398522	+	0.230087i
$659$	−9.54535	+	8.00950i	−0.371834	+	0.312006i	−0.809487	−	0.587138i	$-0.800254\pi$
$659$	−9.54535	+	8.00950i	−0.371834	+	0.312006i	0.437652	+	0.899144i	$0.355810\pi$
$660$		0			0
$661$	−7.75350	−	2.82204i	−0.301576	−	0.109765i	0.186800	−	0.982398i	$-0.440188\pi$
$661$	−7.75350	−	2.82204i	−0.301576	−	0.109765i	−0.488376	+	0.872633i	$0.662411\pi$
$662$	−6.87585	+	8.19432i	−0.267238	+	0.318481i
$663$	57.3719	+	10.1162i	2.22814	+	0.392881i
$664$	−1.90282			−0.0738436
$665$		0			0
$666$	−29.3590			−1.13764
$667$	5.90475	+	1.04117i	0.228633	+	0.0403141i
$668$	−7.01207	+	8.35666i	−0.271305	+	0.323329i
$669$	−36.8461	−	13.4109i	−1.42455	−	0.518495i
$670$		0			0
$671$	−22.7461	+	19.0862i	−0.878102	+	0.736815i
$672$	−5.54420	+	3.20094i	−0.213872	+	0.123479i
$673$	−1.06793	−	0.616571i	−0.0411658	−	0.0237671i	0.479276	−	0.877664i	$-0.340899\pi$
$673$	−1.06793	−	0.616571i	−0.0411658	−	0.0237671i	−0.520442	+	0.853897i	$0.674233\pi$
$674$	−0.791472	−	4.48866i	−0.0304864	−	0.172897i
$675$		0			0
$676$	2.47599	−	4.28854i	0.0952303	−	0.164944i
$677$	−15.4608	+	8.92630i	−0.594207	+	0.343065i	−0.766759	−	0.641935i	$-0.778132\pi$
$677$	−15.4608	+	8.92630i	−0.594207	+	0.343065i	0.172552	+	0.985000i	$0.444799\pi$
$678$	−35.1239	−	41.8591i	−1.34893	−	1.60759i
$679$	−0.329059	+	0.119768i	−0.0126281	+	0.00459626i
$680$		0			0
$681$	41.0176	+	34.4178i	1.57180	+	1.31889i
$682$	−18.4568	−	3.25443i	−0.706748	−	0.124619i
$683$		−	27.7712i		−	1.06264i	−0.847173	−	0.531318i	$-0.821697\pi$
$683$		−	27.7712i		−	1.06264i	0.847173	−	0.531318i	$-0.178303\pi$
$684$	−1.58963	+	38.1415i	−0.0607812	+	1.45838i
$685$		0			0
$686$	3.40875	−	19.3320i	0.130147	−	0.738099i
$687$	−12.1226	+	14.4472i	−0.462507	+	0.551194i
$688$	−0.229755	+	0.631247i	−0.00875933	+	0.0240661i
$689$	−6.82874	+	2.48546i	−0.260154	+	0.0946884i
$690$		0			0
$691$	−21.3398	−	36.9617i	−0.811805	−	1.40609i	−0.911600	−	0.411079i	$-0.865152\pi$
$691$	−21.3398	−	36.9617i	−0.811805	−	1.40609i	0.0997945	−	0.995008i	$-0.468181\pi$
$692$	−0.126355	−	0.0729511i	−0.00480330	−	0.00277319i
$693$	−58.0509	+	10.2359i	−2.20517	+	0.388831i
$694$	3.62801	+	20.5755i	0.137717	+	0.781033i
$695$		0			0
$696$	2.02049	+	3.49960i	0.0765866	+	0.132652i
$697$	−14.3422	−	17.0924i	−0.543250	−	0.647420i
$698$	3.85948	+	10.6038i	0.146083	+	0.401361i
$699$	−36.5028	−	13.2859i	−1.38066	−	0.502520i
$700$		0			0
$701$	−6.91944	+	39.2421i	−0.261344	+	1.48215i	0.517905	+	0.855438i	$0.326712\pi$
$701$	−6.91944	+	39.2421i	−0.261344	+	1.48215i	−0.779249	+	0.626715i	$0.784399\pi$
$702$			56.0104i			2.11398i
$703$	−1.93598	−	14.4835i	−0.0730168	−	0.546257i
$704$	3.60509			0.135872
$705$		0			0
$706$	6.29370	+	5.28104i	0.236866	+	0.198754i
$707$	−1.25175	+	3.43916i	−0.0470770	+	0.129343i
$708$	−5.59210	−	15.3642i	−0.210164	−	0.577421i
$709$	−36.8093	+	30.8866i	−1.38240	+	1.15997i	−0.414086	+	0.910238i	$0.635899\pi$
$709$	−36.8093	+	30.8866i	−1.38240	+	1.15997i	−0.968314	+	0.249734i	$0.919657\pi$
$710$		0			0
$711$	2.63255	−	4.55970i	0.0987282	−	0.171002i
$712$	0.970940	−	0.171203i	0.0363875	−	0.00641610i
$713$	−26.0475	+	4.59288i	−0.975488	+	0.172005i
$714$	−19.1698	+	33.2030i	−0.717411	+	1.24259i
$715$		0			0
$716$	4.36606	−	3.66356i	0.163167	−	0.136914i
$717$	−1.73963	−	4.77959i	−0.0649676	−	0.178497i
$718$	−3.67640	+	10.1008i	−0.137202	+	0.376960i
$719$	23.2680	+	19.5242i	0.867749	+	0.728128i	0.963623	−	0.267266i	$-0.0861201\pi$
$719$	23.2680	+	19.5242i	0.867749	+	0.728128i	−0.0958738	+	0.995393i	$0.530565\pi$
$720$		0			0
$721$	32.6799			1.21706
$722$	−18.9210	+	1.73090i	−0.704166	+	0.0644175i
$723$			28.8690i			1.07365i
$724$	3.21271	−	18.2202i	0.119399	−	0.677148i
$725$		0			0
$726$	6.43360	+	2.34164i	0.238773	+	0.0869064i
$727$	10.4545	+	28.7236i	0.387737	+	1.06530i	0.968018	+	0.250883i	$0.0807208\pi$
$727$	10.4545	+	28.7236i	0.387737	+	1.06530i	−0.580280	+	0.814417i	$0.697057\pi$
$728$	−3.40452	−	4.05735i	−0.126180	−	0.150376i
$729$	79.8532	+	138.310i	2.95753	+	5.12259i
$730$		0			0
$731$	0.698590	+	3.96190i	0.0258383	+	0.146536i
$732$	−27.8132	+	4.90422i	−1.02801	+	0.181265i
$733$	−38.1050	−	21.9999i	−1.40744	−	0.812586i	−0.412299	−	0.911049i	$-0.635274\pi$
$733$	−38.1050	−	21.9999i	−1.40744	−	0.812586i	−0.995141	+	0.0984629i	$0.968607\pi$
$734$	7.47389	+	12.9452i	0.275866	+	0.477815i
$735$		0			0
$736$	4.78092	−	1.74011i	0.176227	−	0.0641415i
$737$	−9.81953	+	26.9789i	−0.361707	+	0.993782i
$738$	20.9737	−	24.9955i	0.772052	−	0.920096i
$739$	−5.08815	+	28.8563i	−0.187171	+	1.06150i	0.735964	+	0.677020i	$0.236729\pi$
$739$	−5.08815	+	28.8563i	−0.187171	+	1.06150i	−0.923135	+	0.384476i	$0.874382\pi$
$740$		0			0
$741$	−42.0281	+	5.61779i	−1.54394	+	0.206375i
$742$		−	4.78249i		−	0.175571i
$743$	−12.9235	−	2.27875i	−0.474116	−	0.0835994i	−0.0685156	−	0.997650i	$-0.521826\pi$
$743$	−12.9235	−	2.27875i	−0.474116	−	0.0835994i	−0.405600	+	0.914051i	$0.632937\pi$
$744$	−13.6555	−	11.4583i	−0.500635	−	0.420082i
$745$		0			0
$746$	8.19625	−	2.98319i	0.300086	−	0.109222i
$747$	−10.7118	−	12.7658i	−0.391924	−	0.467076i
$748$	18.6976	−	10.7951i	0.683651	−	0.394706i
$749$	9.88549	−	17.1222i	0.361208	−	0.625631i
$750$		0			0
$751$	3.47466	+	19.7058i	0.126792	+	0.719074i	0.980227	+	0.197875i	$0.0634040\pi$
$751$	3.47466	+	19.7058i	0.126792	+	0.719074i	−0.853435	+	0.521199i	$0.825485\pi$
$752$	5.47546	+	3.16126i	0.199670	+	0.115279i
$753$	−32.9349	+	19.0150i	−1.20022	+	0.692945i
$754$	−2.56107	+	2.14900i	−0.0932688	+	0.0782618i
$755$		0			0
$756$	−34.6381	−	12.6072i	−1.25978	−	0.458521i
$757$	23.4542	−	27.9516i	0.852458	−	1.01592i	−0.147183	−	0.989109i	$-0.547021\pi$
$757$	23.4542	−	27.9516i	0.852458	−	1.01592i	0.999641	−	0.0268104i	$-0.00853505\pi$
$758$	15.6751	+	2.76394i	0.569345	+	0.100391i
$759$	62.8935			2.28289
$760$		0			0
$761$	3.91470			0.141908			0.0709540	−	0.997480i	$-0.477396\pi$
$761$	3.91470			0.141908			0.0709540	+	0.997480i	$0.477396\pi$
$762$	56.7789	+	10.0117i	2.05688	+	0.362684i
$763$	−16.6516	+	19.8446i	−0.602828	+	0.718422i
$764$	17.7433	+	6.45804i	0.641931	+	0.233644i
$765$		0			0
$766$	1.33589	−	1.12094i	0.0482676	−	0.0405013i
$767$	11.7148	−	6.76354i	0.422997	−	0.244217i
$768$	2.96958	+	1.71449i	0.107155	+	0.0618662i
$769$	3.94857	+	22.3935i	0.142389	+	0.807530i	0.969426	+	0.245382i	$0.0789135\pi$
$769$	3.94857	+	22.3935i	0.142389	+	0.807530i	−0.827037	+	0.562147i	$0.809975\pi$
$770$		0			0
$771$	−19.6902	+	34.1044i	−0.709125	+	1.22824i
$772$	4.22937	−	2.44183i	0.152218	−	0.0878834i
$773$	−14.0531	−	16.7478i	−0.505454	−	0.602377i	0.451623	−	0.892209i	$-0.350845\pi$
$773$	−14.0531	−	16.7478i	−0.505454	−	0.602377i	−0.957078	+	0.289832i	$0.906401\pi$
$774$	−5.52837	+	2.01216i	−0.198713	+	0.0723256i
$775$		0			0
$776$	0.143680	+	0.120562i	0.00515782	+	0.00432793i
$777$	21.1350	+	3.72668i	0.758216	+	0.133694i
$778$			32.4754i			1.16430i
$779$	13.7139	+	8.69862i	0.491353	+	0.311660i
$780$		0			0
$781$	1.20632	−	6.84138i	0.0431655	−	0.244804i
$782$	19.5854	−	23.3410i	0.700373	−	0.834672i
$783$	−7.95792	+	21.8642i	−0.284393	+	0.781363i
$784$	−3.30237	+	1.20197i	−0.117942	+	0.0429273i
$785$		0			0
$786$	11.1678	+	19.3431i	0.398341	+	0.689946i
$787$	26.0977	+	15.0675i	0.930282	+	0.537098i	0.886901	−	0.461960i	$-0.152854\pi$
$787$	26.0977	+	15.0675i	0.930282	+	0.537098i	0.0433810	+	0.999059i	$0.486187\pi$
$788$	−3.46403	+	0.610802i	−0.123401	+	0.0217589i
$789$	−18.8981	−	107.176i	−0.672789	−	3.81558i
$790$		0			0
$791$	14.8760	+	25.7660i	0.528929	+	0.916133i
$792$	20.2946	+	24.1862i	0.721138	+	0.859419i
$793$	−7.99158	−	21.9567i	−0.283789	−	0.779704i
$794$	3.85771	+	1.40409i	0.136905	+	0.0498294i
$795$		0			0
$796$	−0.145954	+	0.827747i	−0.00517321	+	0.0293387i
$797$		−	19.4641i		−	0.689456i	−0.938703	−	0.344728i	$-0.887971\pi$
$797$		−	19.4641i		−	0.689456i	0.938703	−	0.344728i	$-0.112029\pi$
$798$	5.98583	−	27.2556i	0.211896	−	0.964839i
$799$	37.8642			1.33954
$800$		0			0
$801$	6.61443	+	5.55016i	0.233709	+	0.196105i
$802$	−10.6707	+	29.3175i	−0.376796	+	1.03524i
$803$	6.17987	+	16.9790i	0.218083	+	0.599177i
$804$	−20.9190	+	17.5531i	−0.737757	+	0.619051i
$805$		0			0
$806$	7.37401	−	12.7722i	0.259739	−	0.449880i
$807$	78.8769	−	13.9081i	2.77660	−	0.489589i
$808$	1.93052	−	0.340403i	0.0679155	−	0.0119753i
$809$	−20.1616	+	34.9209i	−0.708844	+	1.22775i	0.256443	+	0.966559i	$0.417450\pi$
$809$	−20.1616	+	34.9209i	−0.708844	+	1.22775i	−0.965286	+	0.261194i	$0.915884\pi$
$810$		0			0
$811$	−14.7737	+	12.3966i	−0.518775	+	0.435304i	−0.864204	−	0.503141i	$-0.832178\pi$
$811$	−14.7737	+	12.3966i	−0.518775	+	0.435304i	0.345430	+	0.938445i	$0.387733\pi$
$812$	−0.752523	−	2.06754i	−0.0264084	−	0.0725564i
$813$	25.9044	−	71.1718i	0.908508	−	2.49611i
$814$	−9.25792	−	7.76832i	−0.324490	−	0.272279i
$815$		0			0
$816$	20.5354			0.718883
$817$	−1.35720	−	2.59460i	−0.0474824	−	0.0907736i
$818$			8.77338i			0.306754i
$819$	8.05483	−	45.6812i	0.281459	−	1.59623i
$820$		0			0
$821$	−39.3911	−	14.3372i	−1.37476	−	0.500372i	−0.454175	−	0.890913i	$-0.650066\pi$
$821$	−39.3911	−	14.3372i	−1.37476	−	0.500372i	−0.920586	+	0.390541i	$0.872288\pi$
$822$	23.7442	+	65.2367i	0.828175	+	2.27539i
$823$	−15.3785	−	18.3273i	−0.536059	−	0.638851i	0.428240	−	0.903665i	$-0.359134\pi$
$823$	−15.3785	−	18.3273i	−0.536059	−	0.638851i	−0.964299	+	0.264814i	$0.914689\pi$
$824$	−8.75199	−	15.1589i	−0.304890	−	0.528085i
$825$		0			0
$826$	1.54587	+	8.76708i	0.0537878	+	0.305046i
$827$	−24.2286	+	4.27216i	−0.842511	+	0.148557i	−0.578215	−	0.815884i	$-0.696251\pi$
$827$	−24.2286	+	4.27216i	−0.842511	+	0.148557i	−0.264296	+	0.964442i	$0.585139\pi$
$828$	38.5882	+	22.2789i	1.34103	+	0.774245i
$829$	−17.5981	−	30.4809i	−0.611209	−	1.05865i	−0.991037	−	0.133588i	$-0.957350\pi$
$829$	−17.5981	−	30.4809i	−0.611209	−	1.05865i	0.379828	−	0.925057i	$-0.375983\pi$
$830$		0			0
$831$	63.8393	−	23.2356i	2.21456	−	0.806034i
$832$	−0.970278	+	2.66582i	−0.0336383	+	0.0924206i
$833$	−13.5284	+	16.1225i	−0.468732	+	0.558613i
$834$	2.37487	−	13.4686i	0.0822352	−	0.466379i
$835$		0			0
$836$	−10.5934	+	11.6067i	−0.366381	+	0.401427i
$837$		−	102.639i		−	3.54773i
$838$	−6.03935	−	1.06490i	−0.208626	−	0.0367864i
$839$	18.3065	+	15.3610i	0.632010	+	0.530319i	0.901553	−	0.432669i	$-0.142428\pi$
$839$	18.3065	+	15.3610i	0.632010	+	0.530319i	−0.269543	+	0.962988i	$0.586873\pi$
$840$		0			0
$841$	25.9460	−	9.44358i	0.894690	−	0.325641i
$842$	2.46581	+	2.93864i	0.0849774	+	0.101272i
$843$	62.8416	−	36.2816i	2.16438	−	1.24960i
$844$	−13.7047	+	23.7373i	−0.471737	+	0.817072i
$845$		0			0
$846$	9.61519	+	54.5305i	0.330577	+	1.87480i
$847$	−3.22834	−	1.86388i	−0.110927	−	0.0640438i
$848$	−2.21840	+	1.28080i	−0.0761803	+	0.0439827i
$849$	48.9884	−	41.1062i	1.68128	−	1.41076i
$850$		0			0
$851$	−16.0271	−	5.83339i	−0.549403	−	0.199966i
$852$	4.24725	−	5.06168i	0.145508	−	0.173410i
$853$	−25.7222	−	4.53551i	−0.880710	−	0.155293i	−0.285034	−	0.958517i	$-0.592005\pi$
$853$	−25.7222	−	4.53551i	−0.880710	−	0.155293i	−0.595676	+	0.803225i	$0.703116\pi$
$854$	15.3773			0.526201
$855$		0			0
$856$	−10.5897			−0.361949
$857$	−48.4238	−	8.53842i	−1.65412	−	0.291667i	−0.732795	−	0.680449i	$-0.761785\pi$
$857$	−48.4238	−	8.53842i	−1.65412	−	0.291667i	−0.921329	+	0.388783i	$0.872896\pi$
$858$	−22.5420	+	26.8645i	−0.769570	+	0.917138i
$859$	−13.6388	−	4.96410i	−0.465348	−	0.169373i	0.0986958	−	0.995118i	$-0.468533\pi$
$859$	−13.6388	−	4.96410i	−0.465348	−	0.169373i	−0.564044	+	0.825745i	$0.690755\pi$
$860$		0			0
$861$	−18.2714	+	15.3315i	−0.622688	+	0.522497i
$862$	22.1577	−	12.7927i	0.754694	−	0.435723i
$863$	−9.44276	−	5.45178i	−0.321435	−	0.185581i	0.330597	−	0.943772i	$-0.392750\pi$
$863$	−9.44276	−	5.45178i	−0.321435	−	0.185581i	−0.652032	+	0.758191i	$0.726083\pi$
$864$	3.42843	+	19.4436i	0.116637	+	0.661484i
$865$		0			0
$866$	14.2318	−	24.6502i	0.483617	−	0.837649i
$867$	56.0228	−	32.3448i	1.90264	−	1.09849i
$868$	6.23880	+	7.43511i	0.211759	+	0.252364i
$869$	2.03662	−	0.741269i	0.0690876	−	0.0251458i
$870$		0			0
$871$	−17.3070	−	14.5223i	−0.586425	−	0.492069i
$872$	13.6646	+	2.40943i	0.462740	+	0.0815936i
$873$			1.64263i			0.0555948i
$874$	−8.44619	+	20.5056i	−0.285696	+	0.693614i
$875$		0			0
$876$	−2.98432	+	16.9249i	−0.100831	+	0.571840i
$877$	−7.23032	+	8.61676i	−0.244150	+	0.290967i	−0.874178	−	0.485606i	$-0.838599\pi$
$877$	−7.23032	+	8.61676i	−0.244150	+	0.290967i	0.630028	+	0.776573i	$0.283044\pi$
$878$	13.0326	−	35.8069i	0.439830	−	1.20842i
$879$	−95.7975	+	34.8675i	−3.23117	+	1.17605i
$880$		0			0
$881$	4.90996	+	8.50431i	0.165421	+	0.286517i	0.936805	−	0.349853i	$-0.113768\pi$
$881$	4.90996	+	8.50431i	0.165421	+	0.286517i	−0.771384	+	0.636370i	$0.780435\pi$
$882$	−26.6544	−	15.3889i	−0.897500	−	0.518172i
$883$	29.9898	−	5.28801i	1.00924	−	0.177956i	0.355499	−	0.934677i	$-0.384311\pi$
$883$	29.9898	−	5.28801i	1.00924	−	0.177956i	0.653738	+	0.756721i	$0.273200\pi$
$884$	2.95022	+	16.7315i	0.0992265	+	0.562742i
$885$		0			0
$886$	11.3892	+	19.7267i	0.382629	+	0.662733i
$887$	7.91266	+	9.42994i	0.265681	+	0.316627i	0.882348	−	0.470598i	$-0.155962\pi$
$887$	7.91266	+	9.42994i	0.265681	+	0.316627i	−0.616667	+	0.787224i	$0.711517\pi$
$888$	−3.93151	−	10.8017i	−0.131933	−	0.362482i
$889$	−29.4986	−	10.7366i	−0.989352	−	0.360095i
$890$		0			0
$891$	−25.9336	+	147.077i	−0.868810	+	4.92726i
$892$		−	11.4351i		−	0.382877i
$893$	−26.2672	+	8.33924i	−0.879000	+	0.279062i
$894$	19.3139			0.645953
$895$		0			0
$896$	−1.43020	−	1.20008i	−0.0477798	−	0.0400920i
$897$	−16.9272	+	46.5072i	−0.565184	+	1.55283i
$898$	10.6649	+	29.3016i	0.355893	+	0.977807i
$899$	4.69318	−	3.93804i	0.156526	−	0.131341i
$900$		0			0
$901$	−7.67042	+	13.2856i	−0.255539	+	0.442606i
$902$	13.2275	−	2.33236i	0.440427	−	0.0776591i
$903$	4.23519	−	0.746778i	0.140938	−	0.0248512i
$904$	7.96786	−	13.8007i	0.265007	−	0.459006i
$905$		0			0
$906$	3.25318	−	2.72975i	0.108080	−	0.0906897i
$907$	13.9606	+	38.3564i	0.463554	+	1.27360i	0.922795	+	0.385292i	$0.125899\pi$
$907$	13.9606	+	38.3564i	0.463554	+	1.27360i	−0.459241	+	0.888312i	$0.651879\pi$
$908$	−5.34077	+	14.6736i	−0.177240	+	0.486962i
$909$	13.1515	+	11.0354i	0.436207	+	0.366021i
$910$		0			0
$911$	1.58058			0.0523671			0.0261836	−	0.999657i	$-0.491665\pi$
$911$	1.58058			0.0523671			0.0261836	+	0.999657i	$0.491665\pi$
$912$	−14.2458	+	4.52273i	−0.471727	+	0.149763i
$913$		−	6.85982i		−	0.227027i
$914$	−2.27149	+	12.8822i	−0.0751341	+	0.426107i
$915$		0			0
$916$	−5.16834	−	1.88112i	−0.170767	−	0.0621540i
$917$	−4.15937	−	11.4278i	−0.137355	−	0.377379i
$918$	76.0030	+	90.5769i	2.50847	+	2.98948i
$919$	−23.8891	−	41.3772i	−0.788029	−	1.36491i	−0.927172	−	0.374635i	$-0.877768\pi$
$919$	−23.8891	−	41.3772i	−0.788029	−	1.36491i	0.139143	−	0.990272i	$-0.455565\pi$
$920$		0			0
$921$	−3.07330	−	17.4295i	−0.101269	−	0.574322i
$922$	17.9440	−	3.16401i	0.590953	−	0.104201i
$923$	4.73425	+	2.73332i	0.155830	+	0.0899684i
$924$	−11.5397	−	19.9873i	−0.379628	−	0.657535i
$925$		0			0
$926$	−21.6204	+	7.86919i	−0.710492	+	0.258598i
$927$	52.4307	−	144.052i	1.72205	−	4.73130i
$928$	−0.757515	+	0.902771i	−0.0248666	+	0.0296349i
$929$	8.32760	−	47.2282i	0.273220	−	1.54951i	−0.471341	−	0.881951i	$-0.656230\pi$
$929$	8.32760	−	47.2282i	0.273220	−	1.54951i	0.744561	−	0.667555i	$-0.232659\pi$
$930$		0			0
$931$	5.83411	−	14.1641i	0.191205	−	0.464208i
$932$		−	11.3286i		−	0.371081i
$933$	87.9251	+	15.5036i	2.87854	+	0.507564i
$934$	−19.1917	−	16.1038i	−0.627973	−	0.526932i
$935$		0			0
$936$	−23.3468	+	8.49755i	−0.763115	+	0.277751i
$937$	24.4752	+	29.1684i	0.799570	+	0.952890i	0.999638	−	0.0268915i	$-0.00856087\pi$
$937$	24.4752	+	29.1684i	0.799570	+	0.952890i	−0.200068	+	0.979782i	$0.564116\pi$
$938$	12.8765	−	7.43425i	0.420433	−	0.242737i
$939$	−0.475128	+	0.822946i	−0.0155052	+	0.0268558i
$940$		0			0
$941$	−6.81969	−	38.6764i	−0.222315	−	1.26081i	−0.867751	−	0.496999i	$-0.834435\pi$
$941$	−6.81969	−	38.6764i	−0.222315	−	1.26081i	0.645436	−	0.763815i	$-0.276676\pi$
$942$	−63.8676	−	36.8740i	−2.08092	−	1.20142i
$943$	16.4160	−	9.47776i	0.534577	−	0.308638i
$944$	3.65269	−	3.06497i	0.118885	−	0.0997564i
$945$		0			0
$946$	−2.27570	−	0.828287i	−0.0739894	−	0.0269299i
$947$	4.60297	−	5.48561i	0.149577	−	0.178258i	−0.686053	−	0.727551i	$-0.740658\pi$
$947$	4.60297	−	5.48561i	0.149577	−	0.178258i	0.835630	+	0.549293i	$0.185103\pi$
$948$	2.03013	+	0.357967i	0.0659355	+	0.0116262i
$949$	−14.2186			−0.461555
$950$		0			0
$951$	85.4768			2.77178
$952$	−11.0112	−	1.94157i	−0.356875	−	0.0629267i
$953$	−21.3618	+	25.4580i	−0.691977	+	0.824667i	−0.991593	−	0.129393i	$-0.958697\pi$
$953$	−21.3618	+	25.4580i	−0.691977	+	0.824667i	0.299616	+	0.954060i	$0.403141\pi$
$954$	−21.0811	−	7.67290i	−0.682526	−	0.248419i
$955$		0			0
$956$	1.13631	−	0.953473i	0.0367507	−	0.0308375i
$957$	−12.6164	+	7.28406i	−0.407829	+	0.235460i
$958$	−18.7608	−	10.8316i	−0.606135	−	0.349952i
$959$	−6.56382	−	37.2253i	−0.211957	−	1.20207i
$960$		0			0
$961$	1.98710	−	3.44176i	0.0641000	−	0.111024i
$962$	8.23605	−	4.75508i	0.265541	−	0.153310i
$963$	−59.6141	−	71.0453i	−1.92104	−	2.28940i
$964$	−7.91140	+	2.87951i	−0.254809	+	0.0927429i
$965$		0			0
$966$	−24.9510	−	20.9364i	−0.802786	−	0.673617i
$967$	−24.8420	−	4.38031i	−0.798864	−	0.140861i	−0.240708	−	0.970597i	$-0.577380\pi$
$967$	−24.8420	−	4.38031i	−0.798864	−	0.140861i	−0.558156	+	0.829736i	$0.688491\pi$
$968$			1.99666i			0.0641751i
$969$	−60.3424	+	66.1146i	−1.93848	+	2.12391i
$970$		0			0
$971$	7.59334	−	43.0640i	0.243682	−	1.38199i	−0.579852	−	0.814722i	$-0.696890\pi$
$971$	7.59334	−	43.0640i	0.243682	−	1.38199i	0.823534	−	0.567267i	$-0.191999\pi$
$972$	−53.2353	+	63.4434i	−1.70752	+	2.03495i
$973$	−2.54684	+	6.99739i	−0.0816481	+	0.224326i
$974$	3.12479	−	1.13733i	0.100125	−	0.0364424i
$975$		0			0
$976$	−4.11819	−	7.13291i	−0.131820	−	0.228319i
$977$	0.00414279	+	0.00239184i	0.000132539	+	7.65217e-5i	0.500066	−	0.865987i	$-0.333309\pi$
$977$	0.00414279	+	0.00239184i	0.000132539	+	7.65217e-5i	−0.499934	+	0.866064i	$0.666642\pi$
$978$	−60.8548	+	10.7303i	−1.94592	+	0.343118i
$979$	0.617201	+	3.50032i	0.0197258	+	0.111871i
$980$		0			0
$981$	60.7591	+	105.238i	1.93989	+	3.35999i
$982$	3.23904	+	3.86014i	0.103362	+	0.123182i
$983$	12.6492	+	34.7535i	0.403448	+	1.10846i	0.960571	+	0.278034i	$0.0896829\pi$
$983$	12.6492	+	34.7535i	0.403448	+	1.10846i	−0.557123	+	0.830430i	$0.688095\pi$
$984$	12.0049	+	4.36943i	0.382703	+	0.139292i
$985$		0			0
$986$	−1.22556	+	6.95047i	−0.0390296	+	0.221348i
$987$		−	40.4761i		−	1.28837i
$988$	−5.73159	−	10.9573i	−0.182346	−	0.348597i
$989$	−3.41774			−0.108678
$990$		0			0
$991$	−4.48081	−	3.75985i	−0.142338	−	0.119435i	0.568839	−	0.822449i	$-0.307393\pi$
$991$	−4.48081	−	3.75985i	−0.142338	−	0.119435i	−0.711176	+	0.703014i	$0.751837\pi$
$992$	1.77804	−	4.88512i	0.0564528	−	0.155103i
$993$	−12.5451	−	34.4674i	−0.398107	−	1.09379i
$994$	−2.75597	+	2.31253i	−0.0874141	+	0.0733491i
$995$		0			0
$996$	3.26235	−	5.65056i	0.103372	−	0.179045i
$997$	57.0588	−	10.0610i	1.80707	−	0.318635i	0.834458	−	0.551072i	$-0.185781\pi$
$997$	57.0588	−	10.0610i	1.80707	−	0.318635i	0.972612	+	0.232437i	$0.0746698\pi$
$998$	10.0831	−	1.77791i	0.319174	−	0.0562789i
$999$	33.0931	−	57.3190i	1.04702	−	1.81349i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.u.g.549.3		36
5.2	odd	4		950.2.l.i.701.1		18
5.3	odd	4		190.2.k.d.131.3	✓	18
5.4	even	2	inner	950.2.u.g.549.4		36
19.9	even	9	inner	950.2.u.g.199.4		36
95.3	even	36		3610.2.a.bj.1.1		9
95.9	even	18	inner	950.2.u.g.199.3		36
95.28	odd	36		190.2.k.d.161.3	yes	18
95.47	odd	36		950.2.l.i.351.1		18
95.73	odd	36		3610.2.a.bi.1.9		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.d.131.3	✓	18	5.3	odd	4
190.2.k.d.161.3	yes	18	95.28	odd	36
950.2.l.i.351.1		18	95.47	odd	36
950.2.l.i.701.1		18	5.2	odd	4
950.2.u.g.199.3		36	95.9	even	18	inner
950.2.u.g.199.4		36	19.9	even	9	inner
950.2.u.g.549.3		36	1.1	even	1	trivial
950.2.u.g.549.4		36	5.4	even	2	inner
3610.2.a.bi.1.9		9	95.73	odd	36
3610.2.a.bj.1.1		9	95.3	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.984808 - 0.173648i) q^{2} +(2.20410 - 2.62675i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-2.62675 + 2.20410i) q^{6} +(1.61687 - 0.933500i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-1.52078 - 8.62480i) q^{9} +O(q^{10})\)	\(q+(-0.984808 - 0.173648i) q^{2} +(2.20410 - 2.62675i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-2.62675 + 2.20410i) q^{6} +(1.61687 - 0.933500i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-1.52078 - 8.62480i) q^{9} +(1.80254 - 3.12210i) q^{11} +(2.96958 - 1.71449i) q^{12} +(1.82353 + 2.17319i) q^{13} +(-1.75441 + 0.638551i) q^{14} +(0.766044 + 0.642788i) q^{16} +(5.89781 + 1.03994i) q^{17} +8.75785i q^{18} +(-4.32047 + 0.577506i) q^{19} +(1.11168 - 6.30463i) q^{21} +(-2.31731 + 2.76166i) q^{22} +(-1.74011 + 4.78092i) q^{23} +(-3.22218 + 1.17278i) q^{24} +(-1.41845 - 2.45683i) q^{26} +(-17.0984 - 9.87176i) q^{27} +(1.83864 - 0.324201i) q^{28} +(-0.204642 - 1.16058i) q^{29} +(2.59932 + 4.50215i) q^{31} +(-0.642788 - 0.766044i) q^{32} +(-4.22797 - 11.6162i) q^{33} +(-5.62762 - 2.04829i) q^{34} +(1.52078 - 8.62480i) q^{36} +3.35231i q^{37} +(4.35512 + 0.181510i) q^{38} +9.72766 q^{39} +(-2.85406 - 2.39484i) q^{41} +(-2.18958 + 6.01581i) q^{42} +(0.229755 + 0.631247i) q^{43} +(2.76166 - 2.31731i) q^{44} +(2.54388 - 4.40612i) q^{46} +(6.22647 - 1.09789i) q^{47} +(3.37688 - 0.595435i) q^{48} +(-1.75716 + 3.04348i) q^{49} +(15.7310 - 13.1999i) q^{51} +(0.970278 + 2.66582i) q^{52} +(-0.876116 + 2.40711i) q^{53} +(15.1244 + 12.6909i) q^{54} -1.86700 q^{56} +(-8.00580 + 12.6217i) q^{57} +1.17848i q^{58} +(0.827999 - 4.69581i) q^{59} +(-7.73966 - 2.81701i) q^{61} +(-1.77804 - 4.88512i) q^{62} +(-10.5102 - 12.5255i) q^{63} +(0.500000 + 0.866025i) q^{64} +(2.14660 + 12.1739i) q^{66} +(-7.84286 + 1.38291i) q^{67} +(5.18644 + 2.99439i) q^{68} +(8.72288 + 15.1085i) q^{69} +(1.81077 - 0.659065i) q^{71} +(-2.99536 + 8.22969i) q^{72} +(-3.22165 + 3.83942i) q^{73} +(0.582122 - 3.30138i) q^{74} +(-4.25744 - 0.935010i) q^{76} -6.73070i q^{77} +(-9.57988 - 1.68919i) q^{78} +(0.460535 + 0.386434i) q^{79} +(-38.9281 + 14.1687i) q^{81} +(2.39484 + 2.85406i) q^{82} +(1.64789 - 0.951408i) q^{83} +(3.20094 - 5.54420i) q^{84} +(-0.116650 - 0.661553i) q^{86} +(-3.49960 - 2.02049i) q^{87} +(-3.12210 + 1.80254i) q^{88} +(-0.755257 + 0.633736i) q^{89} +(4.97708 + 1.81151i) q^{91} +(-3.27034 + 3.89744i) q^{92} +(17.5552 + 3.09545i) q^{93} -6.32252 q^{94} -3.42897 q^{96} +(-0.184712 - 0.0325697i) q^{97} +(2.25896 - 2.69212i) q^{98} +(-29.6688 - 10.7985i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 36 q^{9}+O(q^{10}) \) 36 * q + 36 * q^9	\( 36 q + 36 q^{9} - 24 q^{11} - 12 q^{14} + 24 q^{21} - 18 q^{26} + 12 q^{29} - 12 q^{31} - 36 q^{34} - 36 q^{36} - 96 q^{39} - 42 q^{41} - 6 q^{44} + 36 q^{46} + 78 q^{49} + 84 q^{51} + 108 q^{54} + 60 q^{59} + 96 q^{61} + 18 q^{64} + 48 q^{66} + 60 q^{69} + 60 q^{71} + 6 q^{74} - 42 q^{76} - 60 q^{79} + 36 q^{81} - 12 q^{84} + 72 q^{86} - 60 q^{89} - 120 q^{91} - 12 q^{94} - 342 q^{99}+O(q^{100}) \) 36 * q + 36 * q^9 - 24 * q^11 - 12 * q^14 + 24 * q^21 - 18 * q^26 + 12 * q^29 - 12 * q^31 - 36 * q^34 - 36 * q^36 - 96 * q^39 - 42 * q^41 - 6 * q^44 + 36 * q^46 + 78 * q^49 + 84 * q^51 + 108 * q^54 + 60 * q^59 + 96 * q^61 + 18 * q^64 + 48 * q^66 + 60 * q^69 + 60 * q^71 + 6 * q^74 - 42 * q^76 - 60 * q^79 + 36 * q^81 - 12 * q^84 + 72 * q^86 - 60 * q^89 - 120 * q^91 - 12 * q^94 - 342 * q^99

Introduction

L-functions

Modular forms

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