LMFDB - Embedded newform 630.2.cg.a.157.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [630,2,Mod(157,630)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(630, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([4, 3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("630.157"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.cg (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			157.9
Character	$\chi$	$=$	630.157
Dual form			630.2.cg.a.313.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.965926 + 0.258819i) q^{2} +(-0.798392 + 1.53707i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-1.46535 - 1.68900i) q^{5} +(0.373365 - 1.69133i) q^{6} +(-1.21582 - 2.34985i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.72514 - 2.45436i) q^{9} +(1.85257 + 1.25219i) q^{10} +0.949211 q^{11} +(0.0771054 + 1.73033i) q^{12} +(0.0652359 - 0.0174799i) q^{13} +(1.78258 + 1.95510i) q^{14} +(3.76604 - 0.903859i) q^{15} +(0.500000 - 0.866025i) q^{16} +(1.72170 + 6.42548i) q^{17} +(2.30159 + 1.92423i) q^{18} +(2.50146 + 4.33266i) q^{19} +(-2.11354 - 0.730044i) q^{20} +(4.58257 + 0.00729502i) q^{21} +(-0.916867 + 0.245674i) q^{22} +(-5.21266 + 5.21266i) q^{23} +(-0.522321 - 1.65142i) q^{24} +(-0.705473 + 4.94998i) q^{25} +(-0.0584889 + 0.0337686i) q^{26} +(5.14985 - 0.692115i) q^{27} +(-2.22786 - 1.42711i) q^{28} +(-5.14160 + 2.96850i) q^{29} +(-3.40378 + 1.84778i) q^{30} +(9.47045 - 5.46777i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-0.757842 + 1.45900i) q^{33} +(-3.32607 - 5.76092i) q^{34} +(-2.18729 + 5.49689i) q^{35} +(-2.72120 - 1.26297i) q^{36} +(0.254710 - 0.950590i) q^{37} +(-3.53760 - 3.53760i) q^{38} +(-0.0252160 + 0.114228i) q^{39} +(2.23047 + 0.158145i) q^{40} +(-0.0900541 - 0.0519927i) q^{41} +(-4.42831 + 1.17901i) q^{42} +(-1.30034 - 0.348425i) q^{43} +(0.822041 - 0.474605i) q^{44} +(-1.61748 + 6.51028i) q^{45} +(3.68591 - 6.38418i) q^{46} +(-0.817097 - 3.04945i) q^{47} +(0.931942 + 1.45996i) q^{48} +(-4.04354 + 5.71400i) q^{49} +(-0.599714 - 4.96390i) q^{50} +(-11.2510 - 2.48368i) q^{51} +(0.0477560 - 0.0477560i) q^{52} +(3.33476 + 12.4455i) q^{53} +(-4.79524 + 2.00141i) q^{54} +(-1.39093 - 1.60322i) q^{55} +(2.52131 + 0.801874i) q^{56} +(-8.65673 + 0.385753i) q^{57} +(4.19810 - 4.19810i) q^{58} +(-3.34785 - 5.79864i) q^{59} +(2.80955 - 2.66578i) q^{60} +(4.21118 + 2.43133i) q^{61} +(-7.73259 + 7.73259i) q^{62} +(-3.66990 + 7.03789i) q^{63} -1.00000i q^{64} +(-0.125117 - 0.0845695i) q^{65} +(0.354402 - 1.60543i) q^{66} +(-3.55288 + 13.2595i) q^{67} +(4.70378 + 4.70378i) q^{68} +(-3.85046 - 12.1739i) q^{69} +(0.690057 - 5.87570i) q^{70} +6.67608 q^{71} +(2.95535 + 0.515636i) q^{72} +(-7.73892 + 2.07364i) q^{73} +0.984123i q^{74} +(-7.04520 - 5.03638i) q^{75} +(4.33266 + 2.50146i) q^{76} +(-1.15407 - 2.23050i) q^{77} +(-0.00520748 - 0.116862i) q^{78} +(12.2952 + 7.09862i) q^{79} +(-2.19540 + 0.424532i) q^{80} +(-3.04777 + 8.46824i) q^{81} +(0.100442 + 0.0269134i) q^{82} +(0.749023 - 2.79539i) q^{83} +(3.97227 - 2.28497i) q^{84} +(8.32976 - 12.3236i) q^{85} +1.34621 q^{86} +(-0.457775 - 10.2730i) q^{87} +(-0.671193 + 0.671193i) q^{88} +(-1.58328 - 2.74232i) q^{89} +(-0.122616 - 6.70708i) q^{90} +(-0.120390 - 0.132042i) q^{91} +(-1.90797 + 7.12063i) q^{92} +(0.843188 + 18.9221i) q^{93} +(1.57851 + 2.73406i) q^{94} +(3.65235 - 10.5739i) q^{95} +(-1.27805 - 1.16901i) q^{96} +(14.3486 + 3.84470i) q^{97} +(2.42687 - 6.56584i) q^{98} +(-1.63752 - 2.32971i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 16 q^{11} - 12 q^{15} + 96 q^{16} + 36 q^{17} + 16 q^{18} + 12 q^{21} - 16 q^{23} - 36 q^{27} + 12 q^{30} - 60 q^{33} + 48 q^{35} - 16 q^{36} + 12 q^{41} + 4 q^{42} - 36 q^{45} + 12 q^{46} - 16 q^{50}+ \cdots - 48 q^{98}+O(q^{100}) $ 192 * q - 16 * q^11 - 12 * q^15 + 96 * q^16 + 36 * q^17 + 16 * q^18 + 12 * q^21 - 16 * q^23 - 36 * q^27 + 12 * q^30 - 60 * q^33 + 48 * q^35 - 16 * q^36 + 12 * q^41 + 4 * q^42 - 36 * q^45 + 12 * q^46 - 16 * q^50 + 24 * q^51 - 40 * q^53 + 8 * q^56 - 32 * q^57 + 24 * q^58 + 8 * q^60 + 36 * q^61 - 108 * q^63 - 8 * q^65 + 16 * q^71 - 8 * q^72 + 80 * q^77 - 16 * q^78 + 4 * q^81 - 168 * q^83 - 16 * q^86 + 36 * q^90 + 8 * q^92 - 60 * q^93 + 64 * q^95 - 12 * q^96 - 48 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$3$	−0.798392	+	1.53707i	−0.460952	+	0.887425i
$3$	−0.798392	+	1.53707i	−0.460952	+	0.887425i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−1.46535	−	1.68900i	−0.655326	−	0.755346i
$5$	−1.46535	−	1.68900i	−0.655326	−	0.755346i
$6$	0.373365	−	1.69133i	0.152426	−	0.690483i
$7$	−1.21582	−	2.34985i	−0.459538	−	0.888158i
$7$	−1.21582	−	2.34985i	−0.459538	−	0.888158i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−1.72514	−	2.45436i	−0.575047	−	0.818120i
$10$	1.85257	+	1.25219i	0.585834	+	0.395978i
$11$	0.949211			0.286198			0.143099	−	0.989708i	$-0.454293\pi$
$11$	0.949211			0.286198			0.143099	+	0.989708i	$0.454293\pi$
$12$	0.0771054	+	1.73033i	0.0222584	+	0.499504i
$13$	0.0652359	−	0.0174799i	0.0180932	−	0.00484806i	−0.249761	−	0.968307i	$-0.580352\pi$
$13$	0.0652359	−	0.0174799i	0.0180932	−	0.00484806i	0.267854	+	0.963459i	$0.413685\pi$
$14$	1.78258	+	1.95510i	0.476415	+	0.522522i
$15$	3.76604	−	0.903859i	0.972387	−	0.233375i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	1.72170	+	6.42548i	0.417574	+	1.55841i	0.779624	+	0.626248i	$0.215410\pi$
$17$	1.72170	+	6.42548i	0.417574	+	1.55841i	−0.362050	+	0.932159i	$0.617923\pi$
$18$	2.30159	+	1.92423i	0.542491	+	0.453546i
$19$	2.50146	+	4.33266i	0.573875	+	0.993981i	0.996163	+	0.0875188i	$0.0278938\pi$
$19$	2.50146	+	4.33266i	0.573875	+	0.993981i	−0.422288	+	0.906462i	$0.638773\pi$
$20$	−2.11354	−	0.730044i	−0.472601	−	0.163243i
$21$	4.58257	+	0.00729502i	0.999999	+	0.00159190i
$22$	−0.916867	+	0.245674i	−0.195477	+	0.0523778i
$23$	−5.21266	+	5.21266i	−1.08692	+	1.08692i	−0.0910706	+	0.995844i	$0.529029\pi$
$23$	−5.21266	+	5.21266i	−1.08692	+	1.08692i	−0.995844	+	0.0910706i	$0.970971\pi$
$24$	−0.522321	−	1.65142i	−0.106618	−	0.337094i
$25$	−0.705473	+	4.94998i	−0.141095	+	0.989996i
$26$	−0.0584889	+	0.0337686i	−0.0114706	+	0.00662257i
$27$	5.14985	−	0.692115i	0.991090	−	0.133198i
$28$	−2.22786	−	1.42711i	−0.421025	−	0.269699i
$29$	−5.14160	+	2.96850i	−0.954771	+	0.551237i	−0.894560	−	0.446949i	$-0.852511\pi$
$29$	−5.14160	+	2.96850i	−0.954771	+	0.551237i	−0.0602110	+	0.998186i	$0.519177\pi$
$30$	−3.40378	+	1.84778i	−0.621442	+	0.337357i
$31$	9.47045	−	5.46777i	1.70094	−	0.982040i	0.756134	−	0.654417i	$-0.227086\pi$
$31$	9.47045	−	5.46777i	1.70094	−	0.982040i	0.944809	−	0.327623i	$-0.106248\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$	−0.757842	+	1.45900i	−0.131923	+	0.253979i
$34$	−3.32607	−	5.76092i	−0.570417	−	0.987990i
$35$	−2.18729	+	5.49689i	−0.369719	+	0.929144i
$36$	−2.72120	−	1.26297i	−0.453533	−	0.210495i
$37$	0.254710	−	0.950590i	0.0418740	−	0.156276i	−0.941823	−	0.336109i	$-0.890889\pi$
$37$	0.254710	−	0.950590i	0.0418740	−	0.156276i	0.983697	+	0.179833i	$0.0575557\pi$
$38$	−3.53760	−	3.53760i	−0.573875	−	0.573875i
$39$	−0.0252160	+	0.114228i	−0.00403780	+	0.0182911i
$40$	2.23047	+	0.158145i	0.352668	+	0.0250049i
$41$	−0.0900541	−	0.0519927i	−0.0140641	−	0.00811990i	0.492951	−	0.870057i	$-0.335918\pi$
$41$	−0.0900541	−	0.0519927i	−0.0140641	−	0.00811990i	−0.507016	+	0.861937i	$0.669251\pi$
$42$	−4.42831	+	1.17901i	−0.683303	+	0.181925i
$43$	−1.30034	−	0.348425i	−0.198300	−	0.0531343i	0.158302	−	0.987391i	$-0.449398\pi$
$43$	−1.30034	−	0.348425i	−0.198300	−	0.0531343i	−0.356602	+	0.934256i	$0.616065\pi$
$44$	0.822041	−	0.474605i	0.123927	−	0.0715495i
$45$	−1.61748	+	6.51028i	−0.241120	+	0.970495i
$46$	3.68591	−	6.38418i	0.543458	−	0.941296i
$47$	−0.817097	−	3.04945i	−0.119186	−	0.444808i	0.880380	−	0.474269i	$-0.157288\pi$
$47$	−0.817097	−	3.04945i	−0.119186	−	0.444808i	−0.999566	+	0.0294612i	$0.990621\pi$
$48$	0.931942	+	1.45996i	0.134514	+	0.210727i
$49$	−4.04354	+	5.71400i	−0.577649	+	0.816285i
$50$	−0.599714	−	4.96390i	−0.0848124	−	0.702002i
$51$	−11.2510	−	2.48368i	−1.57545	−	0.347785i
$52$	0.0477560	−	0.0477560i	0.00662257	−	0.00662257i
$53$	3.33476	+	12.4455i	0.458064	+	1.70952i	0.678920	+	0.734212i	$0.262448\pi$
$53$	3.33476	+	12.4455i	0.458064	+	1.70952i	−0.220856	+	0.975307i	$0.570885\pi$
$54$	−4.79524	+	2.00141i	−0.652550	+	0.272358i
$55$	−1.39093	−	1.60322i	−0.187553	−	0.216178i
$56$	2.52131	+	0.801874i	0.336924	+	0.107155i
$57$	−8.65673	+	0.385753i	−1.14661	+	0.0510942i
$58$	4.19810	−	4.19810i	0.551237	−	0.551237i
$59$	−3.34785	−	5.79864i	−0.435852	−	0.754919i	0.561512	−	0.827468i	$-0.310220\pi$
$59$	−3.34785	−	5.79864i	−0.435852	−	0.754919i	−0.997365	+	0.0725498i	$0.976886\pi$
$60$	2.80955	−	2.66578i	0.362712	−	0.344151i
$61$	4.21118	+	2.43133i	0.539187	+	0.311300i	0.744749	−	0.667344i	$-0.232569\pi$
$61$	4.21118	+	2.43133i	0.539187	+	0.311300i	−0.205563	+	0.978644i	$0.565902\pi$
$62$	−7.73259	+	7.73259i	−0.982040	+	0.982040i
$63$	−3.66990	+	7.03789i	−0.462364	+	0.886690i
$64$		−	1.00000i		−	0.125000i
$65$	−0.125117	−	0.0845695i	−0.0155189	−	0.0104896i
$66$	0.354402	−	1.60543i	0.0436239	−	0.197615i
$67$	−3.55288	+	13.2595i	−0.434053	+	1.61991i	0.309270	+	0.950974i	$0.399915\pi$
$67$	−3.55288	+	13.2595i	−0.434053	+	1.61991i	−0.743323	+	0.668933i	$0.766751\pi$
$68$	4.70378	+	4.70378i	0.570417	+	0.570417i
$69$	−3.85046	−	12.1739i	−0.463541	−	1.46557i
$70$	0.690057	−	5.87570i	0.0824775	−	0.702280i
$71$	6.67608			0.792305			0.396153	−	0.918185i	$-0.370345\pi$
$71$	6.67608			0.792305			0.396153	+	0.918185i	$0.370345\pi$
$72$	2.95535	+	0.515636i	0.348292	+	0.0607683i
$73$	−7.73892	+	2.07364i	−0.905772	+	0.242701i	−0.681494	−	0.731824i	$-0.738669\pi$
$73$	−7.73892	+	2.07364i	−0.905772	+	0.242701i	−0.224279	+	0.974525i	$0.572003\pi$
$74$			0.984123i			0.114402i
$75$	−7.04520	−	5.03638i	−0.813510	−	0.581551i
$76$	4.33266	+	2.50146i	0.496990	+	0.286937i
$77$	−1.15407	−	2.23050i	−0.131519	−	0.254189i
$78$	−0.00520748	−	0.116862i	−0.000589631	−	0.0132320i
$79$	12.2952	+	7.09862i	1.38332	+	0.798658i	0.992551	−	0.121833i	$-0.0388772\pi$
$79$	12.2952	+	7.09862i	1.38332	+	0.798658i	0.390765	+	0.920491i	$0.372211\pi$
$80$	−2.19540	+	0.424532i	−0.245453	+	0.0474641i
$81$	−3.04777	+	8.46824i	−0.338641	+	0.940916i
$82$	0.100442	+	0.0269134i	0.0110920	+	0.00297209i
$83$	0.749023	−	2.79539i	0.0822159	−	0.306834i	−0.912556	−	0.408951i	$-0.865895\pi$
$83$	0.749023	−	2.79539i	0.0822159	−	0.306834i	0.994772	+	0.102117i	$0.0325615\pi$
$84$	3.97227	−	2.28497i	0.433410	−	0.249310i
$85$	8.32976	−	12.3236i	0.903489	−	1.33668i
$86$	1.34621			0.145166
$87$	−0.457775	−	10.2730i	−0.0490786	−	1.10138i
$88$	−0.671193	+	0.671193i	−0.0715495	+	0.0715495i
$89$	−1.58328	−	2.74232i	−0.167827	−	0.290685i	0.769829	−	0.638251i	$-0.220342\pi$
$89$	−1.58328	−	2.74232i	−0.167827	−	0.290685i	−0.937656	+	0.347566i	$0.887008\pi$
$90$	−0.122616	−	6.70708i	−0.0129249	−	0.706989i
$91$	−0.120390	−	0.132042i	−0.0126204	−	0.0138417i
$92$	−1.90797	+	7.12063i	−0.198919	+	0.742377i
$93$	0.843188	+	18.9221i	0.0874346	+	1.96213i
$94$	1.57851	+	2.73406i	0.162811	+	0.281997i
$95$	3.65235	−	10.5739i	0.374724	−	1.08486i
$96$	−1.27805	−	1.16901i	−0.130441	−	0.119311i
$97$	14.3486	+	3.84470i	1.45688	+	0.390371i	0.898412	−	0.439153i	$-0.144722\pi$
$97$	14.3486	+	3.84470i	1.45688	+	0.390371i	0.558471	+	0.829524i	$0.311388\pi$
$98$	2.42687	−	6.56584i	0.245151	−	0.663250i
$99$	−1.63752	−	2.32971i	−0.164577	−	0.234144i
$100$	1.86403	+	4.63955i	0.186403	+	0.463955i
$101$			17.2359i			1.71504i	0.514453	+	0.857518i	$0.327995\pi$
$101$			17.2359i			1.71504i	−0.514453	+	0.857518i	$0.672005\pi$
$102$	11.5104	−	0.512916i	1.13970	−	0.0507863i
$103$	−1.02784	−	1.02784i	−0.101276	−	0.101276i	0.654653	−	0.755929i	$-0.272815\pi$
$103$	−1.02784	−	1.02784i	−0.101276	−	0.101276i	−0.755929	+	0.654653i	$0.772815\pi$
$104$	−0.0337686	+	0.0584889i	−0.00331128	+	0.00573531i
$105$	−6.70277	−	7.75067i	−0.654123	−	0.756388i
$106$	−6.44226	−	11.1583i	−0.625727	−	1.08379i
$107$	−0.106682	+	0.398142i	−0.0103133	+	0.0384898i	−0.970891	−	0.239523i	$-0.923009\pi$
$107$	−0.106682	+	0.398142i	−0.0103133	+	0.0384898i	0.960577	+	0.278013i	$0.0896757\pi$
$108$	4.11385	−	3.17432i	0.395855	−	0.305449i
$109$	−6.00268	−	3.46565i	−0.574952	−	0.331949i	0.184173	−	0.982894i	$-0.441039\pi$
$109$	−6.00268	−	3.46565i	−0.574952	−	0.331949i	−0.759125	+	0.650945i	$0.774373\pi$
$110$	1.75848	+	1.18859i	0.167664	+	0.113328i
$111$	1.25776	+	1.15045i	0.119381	+	0.109196i
$112$	−2.64294	−	0.121988i	−0.249734	−	0.0115268i
$113$	1.44237	+	5.38302i	0.135687	+	0.506392i	0.999994	+	0.00342680i	$0.00109079\pi$
$113$	1.44237	+	5.38302i	0.135687	+	0.506392i	−0.864307	+	0.502965i	$0.832243\pi$
$114$	8.26192	−	2.61314i	0.773800	−	0.244743i
$115$	16.4426	+	1.16581i	1.53328	+	0.108713i
$116$	−2.96850	+	5.14160i	−0.275619	+	0.477385i
$117$	−0.155443	−	0.129957i	−0.0143707	−	0.0120145i
$118$	4.73457	+	4.73457i	0.435852	+	0.435852i
$119$	13.0056	−	11.8580i	1.19222	−	1.08702i
$120$	−2.02387	+	3.30212i	−0.184753	+	0.301441i
$121$	−10.0990			−0.918091
$122$	−4.69696	−	1.25855i	−0.425243	−	0.113944i
$123$	0.151815	−	0.0969084i	0.0136887	−	0.00873794i
$124$	5.46777	−	9.47045i	0.491020	−	0.850471i
$125$	9.39431	−	6.06193i	0.840252	−	0.542195i
$126$	1.72331	−	7.74792i	0.153525	−	0.690239i
$127$	−12.8755	−	12.8755i	−1.14252	−	1.14252i	−0.987988	−	0.154529i	$-0.950614\pi$
$127$	−12.8755	−	12.8755i	−1.14252	−	1.14252i	−0.154529	−	0.987988i	$-0.549386\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$	1.57373	−	1.72053i	0.138559	−	0.151484i
$130$	0.142742	+	0.0493051i	0.0125193	+	0.00432434i
$131$		−	1.78715i		−	0.156144i	−0.996948	−	0.0780719i	$-0.975124\pi$
$131$		−	1.78715i		−	0.156144i	0.996948	−	0.0780719i	$-0.0248764\pi$
$132$	0.0731893	+	1.64245i	0.00637031	+	0.142957i
$133$	7.13974	−	11.1458i	0.619094	−	0.966464i
$134$		−	13.7273i		−	1.18585i
$135$	−8.71534	−	7.68393i	−0.750097	−	0.661327i
$136$	−5.76092	−	3.32607i	−0.493995	−	0.285208i
$137$	−0.469103	−	0.469103i	−0.0400782	−	0.0400782i	0.686784	−	0.726862i	$-0.259022\pi$
$137$	−0.469103	−	0.469103i	−0.0400782	−	0.0400782i	−0.726862	+	0.686784i	$0.759022\pi$
$138$	6.87011	+	10.7626i	0.584822	+	0.916170i
$139$	0.677966	−	1.17427i	0.0575043	−	0.0996004i	−0.835840	−	0.548973i	$-0.815019\pi$
$139$	0.677966	−	1.17427i	0.0575043	−	0.0996004i	0.893345	+	0.449372i	$0.148352\pi$
$140$	0.854199	+	5.85409i	0.0721930	+	0.494761i
$141$	5.33956	+	1.17872i	0.449672	+	0.0992662i
$142$	−6.44860	+	1.72790i	−0.541155	+	0.145002i
$143$	0.0619226	−	0.0165921i	0.00517823	−	0.00138750i
$144$	−2.98811	+	0.266836i	−0.249009	+	0.0222363i
$145$	12.5481	+	4.33427i	1.04206	+	0.359942i
$146$	6.93853	−	4.00596i	0.574237	−	0.331536i
$147$	−5.55446	−	10.7772i	−0.458124	−	0.888888i
$148$	−0.254710	−	0.950590i	−0.0209370	−	0.0781380i
$149$			8.19330i			0.671221i	0.942001	+	0.335611i	$0.108943\pi$
$149$			8.19330i			0.671221i	−0.942001	+	0.335611i	$0.891057\pi$
$150$	8.10865	+	3.04134i	0.662069	+	0.248324i
$151$	−6.61808			−0.538572			−0.269286	−	0.963060i	$-0.586788\pi$
$151$	−6.61808			−0.538572			−0.269286	+	0.963060i	$0.586788\pi$
$152$	−4.83246	−	1.29485i	−0.391964	−	0.105026i
$153$	12.8003	−	15.3105i	1.03484	−	1.23778i
$154$	1.69204	+	1.85580i	0.136349	+	0.149545i
$155$	−23.1126	−	7.98342i	−1.85645	−	0.641243i
$156$	0.0352761	+	0.111532i	0.00282435	+	0.00892972i
$157$	0.777762	+	0.208401i	0.0620722	+	0.0166322i	0.289721	−	0.957111i	$-0.406437\pi$
$157$	0.777762	+	0.208401i	0.0620722	+	0.0166322i	−0.227649	+	0.973743i	$0.573104\pi$
$158$	−13.7135	−	3.67452i	−1.09099	−	0.292329i
$159$	−21.7920	−	4.81063i	−1.72822	−	0.381508i
$160$	2.01071	−	0.978277i	0.158961	−	0.0773396i
$161$	18.5866	+	5.91127i	1.46483	+	0.465873i
$162$	0.752181	−	8.96851i	0.0590969	−	0.704633i
$163$	15.0992	+	4.04583i	1.18266	+	0.316894i	0.795982	−	0.605320i	$-0.206955\pi$
$163$	15.0992	+	4.04583i	1.18266	+	0.316894i	0.386681	+	0.922214i	$0.373622\pi$
$164$	−0.103985			−0.00811990
$165$	3.57476	−	0.857953i	0.278295	−	0.0667915i
$166$			2.89400i			0.224618i
$167$	−3.65013	−	13.6225i	−0.282456	−	1.05414i	−0.950679	−	0.310178i	$-0.899611\pi$
$167$	−3.65013	−	13.6225i	−0.282456	−	1.05414i	0.668223	−	0.743961i	$-0.267055\pi$
$168$	−3.24552	+	3.23521i	−0.250398	+	0.249602i
$169$	−11.2544	+	6.49772i	−0.865722	+	0.499825i
$170$	−4.85636	+	14.0595i	−0.372465	+	1.07832i
$171$	6.31853	−	13.6139i	0.483190	−	1.04108i
$172$	−1.30034	+	0.348425i	−0.0991499	+	0.0265671i
$173$	8.12848	−	2.17802i	0.617997	−	0.165592i	0.0637798	−	0.997964i	$-0.479684\pi$
$173$	8.12848	−	2.17802i	0.617997	−	0.165592i	0.554217	+	0.832372i	$0.313018\pi$
$174$	3.10102	+	9.80448i	0.235088	+	0.743275i
$175$	12.4894	−	4.36055i	0.944111	−	0.329627i
$176$	0.474605	−	0.822041i	0.0357747	−	0.0619637i
$177$	11.5858	−	0.516274i	0.870841	−	0.0388055i
$178$	2.23909	+	2.23909i	0.167827	+	0.167827i
$179$	0.617119	+	0.356294i	0.0461256	+	0.0266306i	0.522885	−	0.852403i	$-0.324856\pi$
$179$	0.617119	+	0.356294i	0.0461256	+	0.0266306i	−0.476760	+	0.879034i	$0.658189\pi$
$180$	1.85436	+	6.44681i	0.138216	+	0.480517i
$181$			5.47375i			0.406861i	0.979089	+	0.203430i	$0.0652090\pi$
$181$			5.47375i			0.406861i	−0.979089	+	0.203430i	$0.934791\pi$
$182$	0.150463	+	0.0963832i	0.0111531	+	0.00714440i
$183$	−7.09928	+	4.53171i	−0.524794	+	0.334994i
$184$		−	7.37182i		−	0.543458i
$185$	−1.97879	+	0.962745i	−0.145484	+	0.0707824i
$186$	−5.71186	−	18.0591i	−0.418814	−	1.32416i
$187$	1.63426	+	6.09913i	0.119509	+	0.446013i
$188$	−2.23235	−	2.23235i	−0.162811	−	0.162811i
$189$	−7.88768	−	11.2599i	−0.573744	−	0.819035i
$190$	−0.791186	+	11.1589i	−0.0573987	+	0.809549i
$191$	10.0613	−	17.4267i	0.728011	−	1.26095i	−0.229711	−	0.973259i	$-0.573778\pi$
$191$	10.0613	−	17.4267i	0.728011	−	1.26095i	0.957722	−	0.287694i	$-0.0928886\pi$
$192$	1.53707	+	0.798392i	0.110928	+	0.0576190i
$193$	−17.3540	−	4.64998i	−1.24916	−	0.334713i	−0.427151	−	0.904180i	$-0.640483\pi$
$193$	−17.3540	−	4.64998i	−1.24916	−	0.334713i	−0.822014	+	0.569468i	$0.807149\pi$
$194$	−14.8548			−1.06651
$195$	0.229882	−	0.124794i	0.0164622	−	0.00893669i
$196$	−0.644813	+	6.97024i	−0.0460581	+	0.497874i
$197$	0.963967	+	0.963967i	0.0686798	+	0.0686798i	0.740612	−	0.671933i	$-0.234536\pi$
$197$	0.963967	+	0.963967i	0.0686798	+	0.0686798i	−0.671933	+	0.740612i	$0.734536\pi$
$198$	2.18470	+	1.82650i	0.155260	+	0.129804i
$199$	−10.0879	+	17.4728i	−0.715114	+	1.23861i	0.247802	+	0.968811i	$0.420292\pi$
$199$	−10.0879	+	17.4728i	−0.715114	+	1.23861i	−0.962916	+	0.269803i	$0.913041\pi$
$200$	−3.00132	−	3.99901i	−0.212225	−	0.282773i
$201$	−17.5442	−	16.0473i	−1.23747	−	1.13189i
$202$	−4.46098	−	16.6486i	−0.313874	−	1.17139i
$203$	13.2268	+	8.47278i	0.928339	+	0.594673i
$204$	−10.9855	+	3.47456i	−0.769137	+	0.243268i
$205$	0.0441451	+	0.228290i	0.00308323	+	0.0159444i
$206$	1.25884	+	0.726789i	0.0877073	+	0.0506378i
$207$	21.7863	+	3.80117i	1.51425	+	0.264200i
$208$	0.0174799	−	0.0652359i	0.00121201	−	0.00452330i
$209$	2.37442	+	4.11261i	0.164242	+	0.284475i
$210$	8.48040	+	5.75177i	0.585203	+	0.396910i
$211$	−5.28894	+	9.16071i	−0.364106	+	0.630650i	−0.988632	−	0.150354i	$-0.951959\pi$
$211$	−5.28894	+	9.16071i	−0.364106	+	0.630650i	0.624527	+	0.781004i	$0.285292\pi$
$212$	9.11073	+	9.11073i	0.625727	+	0.625727i
$213$	−5.33013	+	10.2616i	−0.365214	+	0.703112i
$214$		−	0.412187i		−	0.0281765i
$215$	1.31697	+	2.70684i	0.0898164	+	0.184605i
$216$	−3.15210	+	4.13089i	−0.214473	+	0.281072i
$217$	−24.3628	−	15.6062i	−1.65385	−	1.05942i
$218$	6.69512	+	1.79395i	0.453450	+	0.121502i
$219$	2.99137	−	13.5508i	0.202138	−	0.915679i
$220$	−2.00619	−	0.692965i	−0.135257	−	0.0467197i
$221$	0.224634	+	0.389077i	0.0151105	+	0.0261721i
$222$	−1.51266	−	0.785715i	−0.101523	−	0.0527338i
$223$	4.88469	−	18.2299i	0.327103	−	1.22077i	−0.585078	−	0.810977i	$-0.698936\pi$
$223$	4.88469	−	18.2299i	0.327103	−	1.22077i	0.912181	−	0.409788i	$-0.134397\pi$
$224$	2.58445	−	0.566211i	0.172681	−	0.0378316i
$225$	13.3661	−	6.80793i	0.891072	−	0.453862i
$226$	−2.78645	−	4.82628i	−0.185352	−	0.321039i
$227$	−12.6778	+	12.6778i	−0.841456	+	0.841456i	−0.989048	−	0.147592i	$-0.952848\pi$
$227$	−12.6778	+	12.6778i	−0.841456	+	0.841456i	0.147592	+	0.989048i	$0.452848\pi$
$228$	−7.30407	+	4.66244i	−0.483724	+	0.308777i
$229$	13.4647			0.889772			0.444886	−	0.895587i	$-0.353244\pi$
$229$	13.4647			0.889772			0.444886	+	0.895587i	$0.353244\pi$
$230$	−16.1841	+	3.12957i	−1.06715	+	0.206358i
$231$	4.34983	+	0.00692452i	0.286197	+	0.000455600i
$232$	1.53661	−	5.73471i	0.100883	−	0.376502i
$233$	8.01817	+	2.14846i	0.525288	+	0.140750i	0.511711	−	0.859157i	$-0.329012\pi$
$233$	8.01817	+	2.14846i	0.525288	+	0.140750i	0.0135764	+	0.999908i	$0.495678\pi$
$234$	0.183782	+	0.0852973i	0.0120142	+	0.00557606i
$235$	−3.95319	+	5.84860i	−0.257878	+	0.381521i
$236$	−5.79864	−	3.34785i	−0.377459	−	0.217926i
$237$	−20.7274	+	13.2310i	−1.34639	+	0.859447i
$238$	−9.49336	+	14.8200i	−0.615363	+	0.960639i
$239$	−18.0561	−	10.4247i	−1.16795	−	0.674316i	−0.214753	−	0.976668i	$-0.568895\pi$
$239$	−18.0561	−	10.4247i	−1.16795	−	0.674316i	−0.953196	+	0.302352i	$0.902228\pi$
$240$	1.10025	−	3.71341i	0.0710211	−	0.239700i
$241$			0.0775126i			0.00499302i	0.999997	+	0.00249651i	$0.000794665\pi$
$241$			0.0775126i			0.00499302i	−0.999997	+	0.00249651i	$0.999205\pi$
$242$	9.75488	−	2.61381i	0.627068	−	0.168022i
$243$	−10.5829	−	11.4456i	−0.678895	−	0.734235i
$244$	4.86265			0.311300
$245$	15.5762	−	1.54347i	0.995126	−	0.0986085i
$246$	−0.121560	+	0.132899i	−0.00775038	+	0.00847332i
$247$	0.238920	+	0.238920i	0.0152021	+	0.0152021i
$248$	−2.83032	+	10.5629i	−0.179726	+	0.670746i
$249$	3.69869	+	3.38311i	0.234395	+	0.214396i
$250$	−7.50526	+	8.28680i	−0.474674	+	0.524103i
$251$			19.8619i			1.25367i	0.779151	+	0.626837i	$0.215651\pi$
$251$			19.8619i			1.25367i	−0.779151	+	0.626837i	$0.784349\pi$
$252$	0.340718	+	7.92994i	0.0214632	+	0.499539i
$253$	−4.94792	+	4.94792i	−0.311073	+	0.311073i
$254$	15.7692	+	9.10437i	0.989449	+	0.571259i
$255$	12.2917	+	22.6424i	0.769737	+	1.41792i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	7.37198	−	7.37198i	0.459852	−	0.459852i	−0.438755	−	0.898607i	$-0.644580\pi$
$257$	7.37198	−	7.37198i	0.459852	−	0.459852i	0.898607	+	0.438755i	$0.144580\pi$
$258$	−1.07480	+	2.06921i	−0.0669143	+	0.128824i
$259$	−2.54342	+	0.557221i	−0.158040	+	0.0346241i
$260$	−0.150640	−	0.0106806i	−0.00934227	−	0.000662385i
$261$	16.1558	+	7.49825i	1.00002	+	0.464130i
$262$	0.462548	+	1.72625i	0.0285763	+	0.106648i
$263$	11.4097	−	11.4097i	0.703550	−	0.703550i	−0.261620	−	0.965171i	$-0.584257\pi$
$263$	11.4097	−	11.4097i	0.703550	−	0.703550i	0.965171	+	0.261620i	$0.0842569\pi$
$264$	−0.495793	−	1.56754i	−0.0305140	−	0.0964756i
$265$	16.1339	−	23.8695i	0.991096	−	1.46629i
$266$	−4.01172	+	12.6139i	−0.245974	+	0.773409i
$267$	5.47919	−	0.244158i	0.335321	−	0.0149423i
$268$	3.55288	+	13.2595i	0.217026	+	0.809954i
$269$	0.238038	−	0.412294i	0.0145135	−	0.0251380i	−0.858677	−	0.512516i	$-0.828713\pi$
$269$	0.238038	−	0.412294i	0.0145135	−	0.0251380i	0.873191	+	0.487378i	$0.162047\pi$
$270$	10.4071	+	5.16641i	0.633357	+	0.314418i
$271$	−0.956150	+	0.552033i	−0.0580820	+	0.0335336i	−0.528760	−	0.848772i	$-0.677343\pi$
$271$	−0.956150	+	0.552033i	−0.0580820	+	0.0335336i	0.470678	+	0.882305i	$0.344009\pi$
$272$	6.42548	+	1.72170i	0.389602	+	0.104393i
$273$	0.299076	−	0.0796270i	0.0181009	−	0.00481925i
$274$	0.574532	+	0.331706i	0.0347087	+	0.0200391i
$275$	−0.669643	+	4.69858i	−0.0403810	+	0.283335i
$276$	−9.42157	−	8.61772i	−0.567112	−	0.518726i
$277$	10.4770	+	10.4770i	0.629502	+	0.629502i	0.947943	−	0.318441i	$-0.103159\pi$
$277$	10.4770	+	10.4770i	0.629502	+	0.629502i	−0.318441	+	0.947943i	$0.603159\pi$
$278$	−0.350941	+	1.30973i	−0.0210480	+	0.0785524i
$279$	−29.7577	−	13.8112i	−1.78155	−	0.826856i
$280$	−2.34024	−	5.43353i	−0.139856	−	0.324716i
$281$	5.64007	+	9.76888i	0.336458	+	0.582763i	0.983764	−	0.179468i	$-0.0574376\pi$
$281$	5.64007	+	9.76888i	0.336458	+	0.582763i	−0.647306	+	0.762231i	$0.724104\pi$
$282$	−5.46270	+	0.243423i	−0.325299	+	0.0144956i
$283$	−1.61883	+	6.04156i	−0.0962295	+	0.359133i	−0.997203	−	0.0747407i	$-0.976187\pi$
$283$	−1.61883	+	6.04156i	−0.0962295	+	0.359133i	0.900973	+	0.433874i	$0.142854\pi$
$284$	5.78166	−	3.33804i	0.343078	−	0.198076i
$285$	13.3367	+	14.0560i	0.789999	+	0.832605i
$286$	−0.0555183	+	0.0320535i	−0.00328287	+	0.00189536i
$287$	−0.0126850	+	0.274827i	−0.000748770	+	0.0162225i
$288$	2.81723	−	1.03112i	0.166007	−	0.0607595i
$289$	−23.6001	+	13.6255i	−1.38824	+	0.801500i
$290$	−13.2423	−	0.938905i	−0.777615	−	0.0551344i
$291$	−17.3654	+	18.9852i	−1.01798	+	1.11293i
$292$	−5.66528	+	5.66528i	−0.331536	+	0.331536i
$293$	−1.48555	+	0.398051i	−0.0867865	+	0.0232544i	−0.301951	−	0.953323i	$-0.597638\pi$
$293$	−1.48555	+	0.398051i	−0.0867865	+	0.0232544i	0.215164	+	0.976578i	$0.430971\pi$
$294$	8.15454	+	8.97238i	0.475582	+	0.523280i
$295$	−4.88815	+	14.1516i	−0.284599	+	0.823937i
$296$	0.492061	+	0.852275i	0.0286005	+	0.0495375i
$297$	4.88830	−	0.656963i	0.283648	−	0.0381209i
$298$	−2.12058	−	7.91412i	−0.122842	−	0.458453i
$299$	−0.248936	+	0.431170i	−0.0143963	+	0.0249352i
$300$	−8.61951	−	0.839034i	−0.497648	−	0.0484416i
$301$	0.762239	+	3.47922i	0.0439347	+	0.200539i
$302$	6.39258	−	1.71289i	0.367851	−	0.0985655i
$303$	−26.4927	−	13.7610i	−1.52197	−	0.790549i
$304$	5.00293			0.286937
$305$	−2.06435	−	10.6755i	−0.118204	−	0.611275i
$306$	−8.40144	+	18.1018i	−0.480279	+	1.03481i
$307$	1.25068	−	1.25068i	0.0713800	−	0.0713800i	−0.670516	−	0.741895i	$-0.733927\pi$
$307$	1.25068	−	1.25068i	0.0713800	−	0.0713800i	0.741895	+	0.670516i	$0.233927\pi$
$308$	−2.11471	−	1.35463i	−0.120497	−	0.0771873i
$309$	2.40047	−	0.759235i	0.136558	−	0.0431914i
$310$	24.3914	+	1.72940i	1.38534	+	0.0982231i
$311$	−9.33899	+	5.39187i	−0.529566	+	0.305745i	−0.740840	−	0.671682i	$-0.765572\pi$
$311$	−9.33899	+	5.39187i	−0.529566	+	0.305745i	0.211274	+	0.977427i	$0.432239\pi$
$312$	−0.0629408	−	0.0986016i	−0.00356332	−	0.00558222i
$313$	4.25643	−	1.14051i	0.240587	−	0.0644652i	−0.136510	−	0.990639i	$-0.543589\pi$
$313$	4.25643	−	1.14051i	0.240587	−	0.0644652i	0.377098	+	0.926173i	$0.376922\pi$
$314$	−0.805198			−0.0454400
$315$	17.2647	−	4.11452i	0.972757	−	0.231827i
$316$	14.1972			0.798658
$317$	−0.388715	+	0.104156i	−0.0218324	+	0.00584998i	−0.269719	−	0.962939i	$-0.586931\pi$
$317$	−0.388715	+	0.104156i	−0.0218324	+	0.00584998i	0.247886	+	0.968789i	$0.420264\pi$
$318$	22.2945	−	0.993466i	1.25021	−	0.0557108i
$319$	−4.88046	+	2.81774i	−0.273253	+	0.157763i
$320$	−1.68900	+	1.46535i	−0.0944182	+	0.0819158i
$321$	−0.526796	−	0.481850i	−0.0294029	−	0.0268942i
$322$	−19.4833	−	0.899272i	−1.08576	−	0.0501145i
$323$	−23.5326	+	23.5326i	−1.30939	+	1.30939i
$324$	1.59467	+	8.85760i	0.0885928	+	0.492089i
$325$	0.0405030	+	0.335248i	0.00224670	+	0.0185962i
$326$	−15.6319			−0.865769
$327$	10.1194	−	6.45956i	0.559605	−	0.357215i
$328$	0.100442	−	0.0269134i	0.00554600	−	0.00148605i
$329$	−6.17228	+	5.62764i	−0.340289	+	0.310262i
$330$	−3.23090	+	1.75394i	−0.177855	+	0.0965510i
$331$	−7.67752	+	13.2979i	−0.421995	+	0.730916i	−0.996135	−	0.0878411i	$-0.972003\pi$
$331$	−7.67752	+	13.2979i	−0.421995	+	0.730916i	0.574140	+	0.818757i	$0.305337\pi$
$332$	−0.749023	−	2.79539i	−0.0411080	−	0.153417i
$333$	−2.77250	+	1.01475i	−0.151932	+	0.0556081i
$334$	7.05151	+	12.2136i	0.385842	+	0.668297i
$335$	27.6016	−	13.4291i	1.50804	−	0.733708i
$336$	2.29760	−	3.96497i	0.125344	−	0.216307i
$337$	−17.7272	+	4.75000i	−0.965664	+	0.258749i	−0.706996	−	0.707217i	$-0.749950\pi$
$337$	−17.7272	+	4.75000i	−0.965664	+	0.258749i	−0.258668	+	0.965966i	$0.583284\pi$
$338$	9.18916	−	9.18916i	0.499825	−	0.499825i
$339$	−9.42563	−	2.08073i	−0.511930	−	0.113010i
$340$	1.05200	−	14.8374i	0.0570527	−	0.804671i
$341$	8.98945	−	5.19006i	0.486806	−	0.281058i
$342$	−2.57969	+	14.7854i	−0.139494	+	0.799504i
$343$	18.3432	+	2.55448i	0.990442	+	0.137929i
$344$	1.16585	−	0.673105i	0.0628585	−	0.0362914i
$345$	−14.9196	+	24.3426i	−0.803243	+	1.31056i
$346$	−7.28779	+	4.20761i	−0.391794	+	0.226203i
$347$	5.03743	−	18.8000i	0.270424	−	1.00923i	−0.688423	−	0.725310i	$-0.741697\pi$
$347$	5.03743	−	18.8000i	0.270424	−	1.00923i	0.958846	−	0.283925i	$-0.0916367\pi$
$348$	−5.53294	−	8.66779i	−0.296597	−	0.464642i
$349$	7.18672	+	12.4478i	0.384696	+	0.666313i	0.991727	−	0.128365i	$-0.0409729\pi$
$349$	7.18672	+	12.4478i	0.384696	+	0.666313i	−0.607031	+	0.794678i	$0.707640\pi$
$350$	−10.9353	+	7.44447i	−0.584514	+	0.397924i
$351$	0.323857	−	0.135170i	0.0172862	−	0.00721483i
$352$	−0.245674	+	0.916867i	−0.0130945	+	0.0488692i
$353$	−15.4093	−	15.4093i	−0.820156	−	0.820156i	0.165974	−	0.986130i	$-0.446923\pi$
$353$	−15.4093	−	15.4093i	−0.820156	−	0.820156i	−0.986130	+	0.165974i	$0.946923\pi$
$354$	−11.0574	+	3.49730i	−0.587693	+	0.185880i
$355$	−9.78283	−	11.2759i	−0.519219	−	0.598465i
$356$	−2.74232	−	1.58328i	−0.145342	−	0.0839135i
$357$	7.84294	+	29.4578i	0.415093	+	1.55907i
$358$	−0.688307	−	0.184431i	−0.0363781	−	0.00974749i
$359$	27.2802	−	15.7502i	1.43979	−	0.831265i	0.441958	−	0.897036i	$-0.354284\pi$
$359$	27.2802	−	15.7502i	1.43979	−	0.831265i	0.997835	+	0.0657705i	$0.0209505\pi$
$360$	−3.45973	−	5.74720i	−0.182344	−	0.302904i
$361$	−3.01463	+	5.22150i	−0.158665	+	0.274816i
$362$	−1.41671	−	5.28723i	−0.0744606	−	0.277891i
$363$	8.06296	−	15.5228i	0.423195	−	0.814737i
$364$	−0.170282	−	0.0541563i	−0.00892521	−	0.00283856i
$365$	14.8426	+	10.0325i	0.776900	+	0.525123i
$366$	5.68449	−	6.21473i	0.297133	−	0.324849i
$367$	−6.70157	+	6.70157i	−0.349819	+	0.349819i	−0.860042	−	0.510223i	$-0.829563\pi$
$367$	−6.70157	+	6.70157i	−0.349819	+	0.349819i	0.510223	+	0.860042i	$0.329563\pi$
$368$	1.90797	+	7.12063i	0.0994596	+	0.371188i
$369$	0.0277471	+	0.310720i	0.00144446	+	0.0161754i
$370$	1.66219	−	1.44209i	0.0864130	−	0.0749706i
$371$	25.1905	−	22.9677i	1.30782	−	1.19242i
$372$	10.1913	+	15.9654i	0.528393	+	0.827770i
$373$	−0.704523	+	0.704523i	−0.0364788	+	0.0364788i	−0.725111	−	0.688632i	$-0.758212\pi$
$373$	−0.704523	+	0.704523i	−0.0364788	+	0.0364788i	0.688632	+	0.725111i	$0.258212\pi$
$374$	−3.15714	−	5.46833i	−0.163252	−	0.282761i
$375$	1.81724	+	19.2795i	0.0938421	+	0.995587i
$376$	2.73406	+	1.57851i	0.140998	+	0.0814054i
$377$	−0.283528	+	0.283528i	−0.0146024	+	0.0146024i
$378$	10.5332	+	8.83471i	0.541768	+	0.454409i
$379$			5.43571i			0.279214i	0.990207	+	0.139607i	$0.0445839\pi$
$379$			5.43571i			0.279214i	−0.990207	+	0.139607i	$0.955416\pi$
$380$	−2.12390	−	10.9834i	−0.108954	−	0.563437i
$381$	30.0702	−	9.51081i	1.54054	−	0.487254i
$382$	−5.20812	+	19.4370i	−0.266471	+	0.994482i
$383$	−26.4371	−	26.4371i	−1.35087	−	1.35087i	−0.884688	−	0.466184i	$-0.845628\pi$
$383$	−26.4371	−	26.4371i	−1.35087	−	1.35087i	−0.466184	−	0.884688i	$-0.654372\pi$
$384$	−1.69133	−	0.373365i	−0.0863103	−	0.0190532i
$385$	−2.07620	+	5.21771i	−0.105813	+	0.265919i
$386$	17.9661			0.914452
$387$	1.38811	+	3.79258i	0.0705615	+	0.192788i
$388$	14.3486	−	3.84470i	0.728442	−	0.195185i
$389$		−	36.6195i		−	1.85668i	−0.371728	−	0.928342i	$-0.621235\pi$
$389$		−	36.6195i		−	1.85668i	0.371728	−	0.928342i	$-0.378765\pi$
$390$	−0.189749	+	0.180040i	−0.00960834	+	0.00911666i
$391$	−42.4685	−	24.5192i	−2.14772	−	1.23999i
$392$	−1.18119	−	6.89962i	−0.0596591	−	0.348484i
$393$	2.74696	+	1.42684i	0.138566	+	0.0719747i
$394$	−1.18061	−	0.681628i	−0.0594785	−	0.0343399i
$395$	−6.02718	−	31.1686i	−0.303260	−	1.56826i
$396$	−2.58299	−	1.19882i	−0.129800	−	0.0602431i
$397$	13.2028	+	3.53768i	0.662630	+	0.177551i	0.574432	−	0.818552i	$-0.305223\pi$
$397$	13.2028	+	3.53768i	0.662630	+	0.177551i	0.0881971	+	0.996103i	$0.471889\pi$
$398$	5.22189	−	19.4884i	0.261750	−	0.976864i
$399$	11.4315	+	19.8730i	0.572292	+	0.994893i
$400$	3.93407	+	3.08595i	0.196704	+	0.154297i
$401$	−29.5025			−1.47328			−0.736642	−	0.676283i	$-0.763590\pi$
$401$	−29.5025			−1.47328			−0.736642	+	0.676283i	$0.763590\pi$
$402$	21.0997	+	10.9597i	1.05236	+	0.546622i
$403$	0.522237	−	0.522237i	0.0260145	−	0.0260145i
$404$	8.61795	+	14.9267i	0.428759	+	0.742633i
$405$	18.7690	−	7.26127i	0.932637	−	0.360815i
$406$	−14.9690	−	4.76073i	−0.742900	−	0.236271i
$407$	0.241773	−	0.902310i	0.0119843	−	0.0447258i
$408$	9.71186	−	6.19941i	0.480809	−	0.306917i
$409$	13.5211	+	23.4193i	0.668576	+	1.15801i	0.978302	+	0.207182i	$0.0664292\pi$
$409$	13.5211	+	23.4193i	0.668576	+	1.15801i	−0.309726	+	0.950826i	$0.600237\pi$
$410$	−0.101727	−	0.209085i	−0.00502392	−	0.0103260i
$411$	1.09557	−	0.346514i	0.0540405	−	0.0170923i
$412$	−1.40405	−	0.376214i	−0.0691726	−	0.0185347i
$413$	−9.55551	+	14.9170i	−0.470196	+	0.734020i
$414$	−22.0278	+	1.96707i	−1.08261	+	0.0966761i
$415$	−5.81901	+	2.83114i	−0.285644	+	0.138975i
$416$			0.0675372i			0.00331128i
$417$	1.26365	+	1.97961i	0.0618812	+	0.0969418i
$418$	−3.35793	−	3.35793i	−0.164242	−	0.164242i
$419$	−13.0427	+	22.5907i	−0.637178	+	1.10363i	0.348871	+	0.937171i	$0.386565\pi$
$419$	−13.0427	+	22.5907i	−0.637178	+	1.10363i	−0.986049	+	0.166455i	$0.946768\pi$
$420$	−9.68010	−	3.36089i	−0.472341	−	0.163995i
$421$	−5.88770	−	10.1978i	−0.286949	−	0.497010i	0.686131	−	0.727478i	$-0.259308\pi$
$421$	−5.88770	−	10.1978i	−0.286949	−	0.497010i	−0.973080	+	0.230468i	$0.925974\pi$
$422$	2.73776	−	10.2174i	0.133272	−	0.497378i
$423$	−6.07483	+	7.26618i	−0.295369	+	0.353294i
$424$	−11.1583	−	6.44226i	−0.541896	−	0.312864i
$425$	−33.0206	+	3.98939i	−1.60173	+	0.193514i
$426$	2.49262	−	11.2915i	0.120768	−	0.547073i
$427$	0.593185	−	12.8517i	0.0287062	−	0.621937i
$428$	0.106682	+	0.398142i	0.00515666	+	0.0192449i
$429$	−0.0239353	+	0.108426i	−0.00115561	+	0.00523487i
$430$	−1.97267	−	2.27375i	−0.0951308	−	0.109650i
$431$	−4.43300	+	7.67819i	−0.213530	+	0.369845i	−0.952817	−	0.303546i	$-0.901830\pi$
$431$	−4.43300	+	7.67819i	−0.213530	+	0.369845i	0.739287	+	0.673391i	$0.235163\pi$
$432$	1.97554	−	4.80596i	0.0950481	−	0.231227i
$433$	−1.01195	−	1.01195i	−0.0486312	−	0.0486312i	0.682373	−	0.731004i	$-0.260948\pi$
$433$	−1.01195	−	1.01195i	−0.0486312	−	0.0486312i	−0.731004	+	0.682373i	$0.760948\pi$
$434$	27.5719	+	8.76892i	1.32349	+	0.420921i
$435$	−16.6803	+	15.8268i	−0.799761	+	0.758836i
$436$	−6.93129			−0.331949
$437$	−35.6240	−	9.54541i	−1.70413	−	0.456619i
$438$	0.617762	+	13.8633i	0.0295178	+	0.662414i
$439$	−12.4811	+	21.6178i	−0.595689	+	1.03176i	0.397761	+	0.917489i	$0.369787\pi$
$439$	−12.4811	+	21.6178i	−0.595689	+	1.03176i	−0.993449	+	0.114274i	$0.963546\pi$
$440$	2.11719	+	0.150113i	0.100933	+	0.00715634i
$441$	20.9999	+	0.0668599i	0.999995	+	0.00318380i
$442$	−0.317680	−	0.317680i	−0.0151105	−	0.0151105i
$443$	0.304843	+	1.13769i	0.0144835	+	0.0540532i	0.972789	−	0.231691i	$-0.0744259\pi$
$443$	0.304843	+	1.13769i	0.0144835	+	0.0540532i	−0.958306	+	0.285744i	$0.907759\pi$
$444$	1.66448	+	0.367437i	0.0789926	+	0.0174378i
$445$	−2.31172	+	6.69263i	−0.109586	+	0.317261i
$446$			18.8730i			0.893662i
$447$	−12.5936	−	6.54146i	−0.595659	−	0.309401i
$448$	−2.34985	+	1.21582i	−0.111020	+	0.0574423i
$449$			1.31043i			0.0618428i	0.999522	+	0.0309214i	$0.00984415\pi$
$449$			1.31043i			0.0618428i	−0.999522	+	0.0309214i	$0.990156\pi$
$450$	−11.1486	+	10.0354i	−0.525551	+	0.473071i
$451$	−0.0854803	−	0.0493521i	−0.00402511	−	0.00232390i
$452$	3.94064	+	3.94064i	0.185352	+	0.185352i
$453$	5.28382	−	10.1724i	0.248256	−	0.477942i
$454$	8.96457	−	15.5271i	0.420728	−	0.728722i
$455$	−0.0466045	+	0.396828i	−0.00218485	+	0.0186036i
$456$	5.84847	−	6.39400i	0.273879	−	0.299427i
$457$	−36.8591	+	9.87636i	−1.72419	+	0.461996i	−0.978832	−	0.204664i	$-0.934390\pi$
$457$	−36.8591	+	9.87636i	−1.72419	+	0.461996i	−0.745362	+	0.666660i	$0.767723\pi$
$458$	−13.0059	+	3.48492i	−0.607726	+	0.162840i
$459$	13.3137	+	31.8986i	0.621429	+	1.48890i
$460$	14.8226	−	7.21168i	0.691108	−	0.336246i
$461$	−9.52104	+	5.49697i	−0.443439	+	0.256020i	−0.705055	−	0.709152i	$-0.749078\pi$
$461$	−9.52104	+	5.49697i	−0.443439	+	0.256020i	0.261616	+	0.965172i	$0.415744\pi$
$462$	−4.20340	+	1.11913i	−0.195560	+	0.0520666i
$463$	0.0395902	+	0.147753i	0.00183991	+	0.00686665i	0.966840	−	0.255384i	$-0.0822019\pi$
$463$	0.0395902	+	0.147753i	0.00183991	+	0.00686665i	−0.965000	+	0.262251i	$0.915535\pi$
$464$			5.93701i			0.275619i
$465$	30.7240	−	29.1518i	1.42479	−	1.35188i
$466$	−8.30102			−0.384537
$467$	12.8753	+	3.44992i	0.595796	+	0.159643i	0.544101	−	0.839020i	$-0.316871\pi$
$467$	12.8753	+	3.44992i	0.595796	+	0.159643i	0.0516954	+	0.998663i	$0.483537\pi$
$468$	−0.199596	−	0.0348246i	−0.00922634	−	0.00160977i
$469$	35.4775	−	7.77253i	1.63820	−	0.358902i
$470$	2.30476	−	6.67248i	0.106311	−	0.307778i
$471$	−0.941284	+	1.02909i	−0.0433721	+	0.0474178i
$472$	6.46754	+	1.73297i	0.297693	+	0.0797665i
$473$	−1.23430	−	0.330729i	−0.0567530	−	0.0152069i
$474$	16.5967	−	18.1448i	0.762312	−	0.833419i
$475$	−23.2113	+	9.32562i	−1.06501	+	0.427889i
$476$	5.33418	−	16.7721i	0.244492	−	0.768748i
$477$	24.7928	−	29.6549i	1.13518	−	1.35781i
$478$	20.1389	+	5.39621i	0.921133	+	0.246817i
$479$	15.1285			0.691239			0.345619	−	0.938375i	$-0.387669\pi$
$479$	15.1285			0.691239			0.345619	+	0.938375i	$0.387669\pi$
$480$	−0.101662	+	3.87165i	−0.00464021	+	0.176716i
$481$		−	0.0664649i		−	0.00303054i
$482$	−0.0200617	−	0.0748714i	−0.000913787	−	0.00341030i
$483$	−23.9254	+	23.8494i	−1.08864	+	1.08518i
$484$	−8.74599	+	5.04950i	−0.397545	+	0.229523i
$485$	−14.5321	−	29.8688i	−0.659869	−	1.35627i
$486$	13.1847	+	8.31654i	0.598068	+	0.377246i
$487$	−9.29104	+	2.48953i	−0.421017	+	0.112811i	−0.463107	−	0.886303i	$-0.653265\pi$
$487$	−9.29104	+	2.48953i	−0.421017	+	0.112811i	0.0420893	+	0.999114i	$0.486599\pi$
$488$	−4.69696	+	1.25855i	−0.212622	+	0.0569718i
$489$	−18.2738	+	19.9784i	−0.826370	+	0.903452i
$490$	−14.6460	+	5.52229i	−0.661637	+	0.249472i
$491$	6.91875	−	11.9836i	0.312239	−	0.540814i	−0.666608	−	0.745409i	$-0.732254\pi$
$491$	6.91875	−	11.9836i	0.312239	−	0.540814i	0.978847	+	0.204595i	$0.0655877\pi$
$492$	0.0830211	−	0.159833i	0.00374288	−	0.00720581i
$493$	−27.9263	−	27.9263i	−1.25774	−	1.25774i
$494$	−0.292616	−	0.168942i	−0.0131654	−	0.00760105i
$495$	−1.53533	+	6.17963i	−0.0690081	+	0.277754i
$496$		−	10.9355i		−	0.491020i
$497$	−8.11694	−	15.6878i	−0.364095	−	0.703692i
$498$	−4.44827	−	2.31055i	−0.199332	−	0.103538i
$499$		−	0.123932i		−	0.00554798i	−0.999996	−	0.00277399i	$-0.999117\pi$
$499$		−	0.123932i		−	0.00554798i	0.999996	−	0.00277399i	$-0.000882989\pi$
$500$	5.10475	−	9.94694i	0.228291	−	0.444841i
$501$	23.8529	+	5.26558i	1.06567	+	0.235249i
$502$	−5.14064	−	19.1851i	−0.229438	−	0.856275i
$503$	7.49110	+	7.49110i	0.334012	+	0.334012i	0.854108	−	0.520096i	$-0.174104\pi$
$503$	7.49110	+	7.49110i	0.334012	+	0.334012i	−0.520096	+	0.854108i	$0.674104\pi$
$504$	−2.38153	−	7.57155i	−0.106082	−	0.337264i
$505$	29.1115	−	25.2567i	1.29545	−	1.12391i
$506$	3.49870	−	6.05993i	0.155536	−	0.269397i
$507$	−1.00202	−	22.4864i	−0.0445012	−	0.998658i
$508$	−17.5883	−	4.71277i	−0.780354	−	0.209095i
$509$	27.8631			1.23501			0.617505	−	0.786567i	$-0.288144\pi$
$509$	27.8631			1.23501			0.617505	+	0.786567i	$0.288144\pi$
$510$	−17.7332	−	18.6896i	−0.785238	−	0.827588i
$511$	14.2819	+	15.6641i	0.631794	+	0.692938i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	15.8809	+	20.5813i	0.701157	+	0.908685i
$514$	−5.21278	+	9.02880i	−0.229926	+	0.398243i
$515$	−0.229876	+	3.24216i	−0.0101295	+	0.142867i
$516$	0.502628	−	2.27689i	0.0221270	−	0.100234i
$517$	−0.775597	−	2.89457i	−0.0341107	−	0.127303i
$518$	2.31254	−	1.19652i	0.101607	−	0.0525721i
$519$	−3.14195	+	14.2329i	−0.137916	+	0.624756i
$520$	0.148271	−	0.0286717i	0.00650211	−	0.00125734i
$521$	8.62034	+	4.97695i	0.377664	+	0.218044i	0.676801	−	0.736166i	$-0.263366\pi$
$521$	8.62034	+	4.97695i	0.377664	+	0.218044i	−0.299138	+	0.954210i	$0.596699\pi$
$522$	−17.5460	−	3.06133i	−0.767966	−	0.133991i
$523$	8.75707	−	32.6818i	0.382920	−	1.42908i	−0.458500	−	0.888694i	$-0.651613\pi$
$523$	8.75707	−	32.6818i	0.382920	−	1.42908i	0.841420	−	0.540382i	$-0.181720\pi$
$524$	−0.893574	−	1.54771i	−0.0390359	−	0.0676122i
$525$	−3.26899	+	22.6785i	−0.142670	+	0.989770i
$526$	−8.06785	+	13.9739i	−0.351775	+	0.609292i
$527$	51.4383	+	51.4383i	2.24069	+	2.24069i
$528$	0.884610	+	1.38581i	0.0384977	+	0.0603096i
$529$		−	31.3437i		−	1.36277i
$530$	−9.40626	+	27.2319i	−0.408582	+	1.18288i
$531$	−8.45644	+	18.2203i	−0.366978	+	0.790693i
$532$	0.610296	−	13.2224i	0.0264597	−	0.573265i
$533$	−0.00678359	−	0.00181766i	−0.000293830	−	7.87315e-5i
$534$	−5.22930	+	1.65396i	−0.226294	+	0.0715738i
$535$	0.828790	−	0.403233i	0.0358317	−	0.0174333i
$536$	−6.86363	−	11.8882i	−0.296464	−	0.513490i
$537$	−1.04035	+	0.664090i	−0.0448944	+	0.0286576i
$538$	−0.123218	+	0.459855i	−0.00531229	+	0.0198257i
$539$	−3.83818	+	5.42379i	−0.165322	+	0.233619i
$540$	−11.3897	−	2.29681i	−0.490134	−	0.0988388i
$541$	−11.5659	−	20.0327i	−0.497255	−	0.861271i	0.502740	−	0.864438i	$-0.332325\pi$
$541$	−11.5659	−	20.0327i	−0.497255	−	0.861271i	−0.999995	+	0.00316662i	$0.998992\pi$
$542$	0.780693	−	0.780693i	0.0335336	−	0.0335336i
$543$	−8.41351	−	4.37019i	−0.361058	−	0.187543i
$544$	−6.65214			−0.285208
$545$	2.94255	+	15.2169i	0.126045	+	0.651822i
$546$	−0.268276	+	0.154320i	−0.0114811	+	0.00660430i
$547$	−1.73195	+	6.46372i	−0.0740528	+	0.276369i	−0.993017	−	0.117972i	$-0.962361\pi$
$547$	−1.73195	+	6.46372i	−0.0740528	+	0.276369i	0.918964	+	0.394341i	$0.129027\pi$
$548$	−0.640807	−	0.171704i	−0.0273739	−	0.00733482i
$549$	−1.29753	−	14.5301i	−0.0553773	−	0.620131i
$550$	−0.569255	−	4.71179i	−0.0242731	−	0.200911i
$551$	−25.7230	−	14.8512i	−1.09584	−	0.632682i
$552$	11.3310	+	5.88560i	0.482278	+	0.250508i
$553$	1.73189	−	37.5224i	0.0736476	−	1.59562i
$554$	−12.8317	−	7.40836i	−0.545165	−	0.314751i
$555$	0.100048	−	3.81018i	0.00424679	−	0.161733i
$556$		−	1.35593i		−	0.0575043i
$557$	−39.6965	+	10.6367i	−1.68200	+	0.450689i	−0.968305	−	0.249771i	$-0.919645\pi$
$557$	−39.6965	+	10.6367i	−1.68200	+	0.450689i	−0.713691	+	0.700461i	$0.752978\pi$
$558$	32.3184	+	5.63875i	1.36815	+	0.238707i
$559$	−0.0909192			−0.00384547
$560$	3.66680	+	4.64269i	0.154951	+	0.196189i
$561$	−10.6795	−	2.35754i	−0.450891	−	0.0995352i
$562$	−7.97626	−	7.97626i	−0.336458	−	0.336458i
$563$	7.69205	−	28.7071i	0.324181	−	1.20986i	−0.590951	−	0.806708i	$-0.701247\pi$
$563$	7.69205	−	28.7071i	0.324181	−	1.20986i	0.915132	−	0.403154i	$-0.132086\pi$
$564$	5.21356	−	1.64898i	0.219530	−	0.0694345i
$565$	6.97835	−	10.3242i	0.293581	−	0.434343i
$566$		−	6.25468i		−	0.262904i
$567$	23.6046	−	3.13410i	0.991300	−	0.131620i
$568$	−4.72070	+	4.72070i	−0.198076	+	0.198076i
$569$	13.8748	+	8.01064i	0.581664	+	0.335824i	0.761794	−	0.647819i	$-0.224319\pi$
$569$	13.8748	+	8.01064i	0.581664	+	0.335824i	−0.180131	+	0.983643i	$0.557652\pi$
$570$	−16.5202	−	10.1253i	−0.691957	−	0.424100i
$571$	12.9389	+	22.4108i	0.541474	+	0.937861i	0.998820	+	0.0485719i	$0.0154670\pi$
$571$	12.9389	+	22.4108i	0.541474	+	0.937861i	−0.457345	+	0.889289i	$0.651200\pi$
$572$	0.0453305	−	0.0453305i	0.00189536	−	0.00189536i
$573$	18.7531	+	29.3782i	0.783423	+	1.22729i
$574$	−0.0588778	−	0.268746i	−0.00245751	−	0.0112172i
$575$	−22.1252	−	29.4800i	−0.922684	−	1.22940i
$576$	−2.45436	+	1.72514i	−0.102265	+	0.0718809i
$577$	−0.200134	−	0.746909i	−0.00833168	−	0.0310942i	0.961635	−	0.274333i	$-0.0884569\pi$
$577$	−0.200134	−	0.746909i	−0.00833168	−	0.0310942i	−0.969967	+	0.243238i	$0.921790\pi$
$578$	19.2694	−	19.2694i	0.801500	−	0.801500i
$579$	21.0026	−	22.9617i	0.872837	−	0.954254i
$580$	13.0341	−	2.52045i	0.541211	−	0.104656i
$581$	−7.47942	+	1.63862i	−0.310299	+	0.0679813i
$582$	11.8599	−	22.8328i	0.491611	−	0.946450i
$583$	3.16539	+	11.8134i	0.131097	+	0.489261i
$584$	4.00596	−	6.93853i	0.165768	−	0.287118i
$585$	0.00828115	+	0.452978i	0.000342384	+	0.0187283i
$586$	1.33190	−	0.768975i	0.0550204	−	0.0317661i
$587$	28.3596	+	7.59893i	1.17053	+	0.313642i	0.791162	−	0.611606i	$-0.209476\pi$
$587$	28.3596	+	7.59893i	1.17053	+	0.313642i	0.379364	+	0.925248i	$0.376143\pi$
$588$	−10.1989	−	6.55610i	−0.420596	−	0.270369i
$589$	47.3799	+	27.3548i	1.95226	+	1.12714i
$590$	1.05889	−	14.9345i	0.0435937	−	0.614845i
$591$	−2.25130	+	0.712057i	−0.0926063	+	0.0292901i
$592$	−0.695880	−	0.695880i	−0.0286005	−	0.0286005i
$593$	7.39790	−	27.6093i	0.303795	−	1.13378i	−0.630182	−	0.776447i	$-0.717020\pi$
$593$	7.39790	−	27.6093i	0.303795	−	1.13378i	0.933977	−	0.357332i	$-0.116314\pi$
$594$	−4.55170	+	1.89976i	−0.186758	+	0.0779482i
$595$	−39.0860	−	4.59036i	−1.60237	−	0.188186i
$596$	4.09665	+	7.09561i	0.167805	+	0.290647i
$597$	−18.8027	−	29.4559i	−0.769544	−	1.20555i
$598$	0.128859	−	0.480907i	0.00526942	−	0.0196658i
$599$	23.9890	−	13.8501i	0.980164	−	0.565898i	0.0778442	−	0.996966i	$-0.475196\pi$
$599$	23.9890	−	13.8501i	0.980164	−	0.565898i	0.902320	+	0.431068i	$0.141863\pi$
$600$	8.54297	−	1.42045i	0.348765	−	0.0579896i
$601$	19.6062	−	11.3196i	0.799752	−	0.461737i	−0.0436324	−	0.999048i	$-0.513893\pi$
$601$	19.6062	−	11.3196i	0.799752	−	0.461737i	0.843384	+	0.537311i	$0.180560\pi$
$602$	−1.63675	−	3.16338i	−0.0667091	−	0.128930i
$603$	38.6728	−	14.1545i	1.57488	−	0.576416i
$604$	−5.73143	+	3.30904i	−0.233208	+	0.134643i
$605$	14.7986	+	17.0573i	0.601649	+	0.693476i
$606$	29.1516	+	6.43529i	1.18420	+	0.261416i
$607$	18.8480	−	18.8480i	0.765015	−	0.765015i	−0.212209	−	0.977224i	$-0.568066\pi$
$607$	18.8480	−	18.8480i	0.765015	−	0.765015i	0.977224	+	0.212209i	$0.0680658\pi$
$608$	−4.83246	+	1.29485i	−0.195982	+	0.0525132i
$609$	−23.5834	+	13.5659i	−0.955647	+	0.549716i
$610$	4.75702	+	9.77741i	0.192606	+	0.395876i
$611$	−0.106608	−	0.184651i	−0.00431290	−	0.00747017i
$612$	3.43008	−	19.6594i	0.138653	−	0.794686i
$613$	5.64441	+	21.0652i	0.227975	+	0.850816i	0.981191	+	0.193042i	$0.0618352\pi$
$613$	5.64441	+	21.0652i	0.227975	+	0.850816i	−0.753215	+	0.657774i	$0.771498\pi$
$614$	−0.884363	+	1.53176i	−0.0356900	+	0.0618169i
$615$	−0.386141	−	0.114410i	−0.0155707	−	0.00461348i
$616$	2.39325	+	0.761147i	0.0964269	+	0.0306675i
$617$	−30.5170	+	8.17701i	−1.22857	+	0.329194i	−0.814022	−	0.580834i	$-0.802727\pi$
$617$	−30.5170	+	8.17701i	−1.22857	+	0.329194i	−0.414547	+	0.910028i	$0.636060\pi$
$618$	−2.12217	+	1.35465i	−0.0853661	+	0.0544921i
$619$	38.4481			1.54536			0.772679	−	0.634796i	$-0.218916\pi$
$619$	38.4481			1.54536			0.772679	+	0.634796i	$0.218916\pi$
$620$	−24.0078	+	4.64248i	−0.964178	+	0.186447i
$621$	−23.2367	+	30.4522i	−0.932456	+	1.22200i
$622$	7.62526	−	7.62526i	0.305745	−	0.305745i
$623$	−4.51903	+	7.05463i	−0.181051	+	0.282638i
$624$	0.0863161	+	0.0789516i	0.00345541	+	0.00316059i
$625$	−24.0046	−	6.98416i	−0.960185	−	0.279366i
$626$	−3.81621	+	2.20329i	−0.152526	+	0.0880611i
$627$	−8.21706	+	0.366161i	−0.328158	+	0.0146230i
$628$	0.777762	−	0.208401i	0.0310361	−	0.00831609i
$629$	6.54653			0.261027
$630$	−15.6115	+	8.44276i	−0.621978	+	0.336368i
$631$	25.9982			1.03497			0.517487	−	0.855691i	$-0.326868\pi$
$631$	25.9982			1.03497			0.517487	+	0.855691i	$0.326868\pi$
$632$	−13.7135	+	3.67452i	−0.545493	+	0.146164i
$633$	−9.85797	−	15.4433i	−0.391819	−	0.613816i
$634$	0.348512	−	0.201214i	0.0138412	−	0.00799121i
$635$	−2.87961	+	40.6140i	−0.114274	+	1.61172i
$636$	−21.2777	+	6.72986i	−0.843716	+	0.266856i
$637$	−0.163904	+	0.443439i	−0.00649412	+	0.0175697i
$638$	3.98488	−	3.98488i	0.157763	−	0.157763i
$639$	−11.5172	−	16.3855i	−0.455613	−	0.648201i
$640$	1.25219	−	1.85257i	0.0494972	−	0.0732293i
$641$	24.0889			0.951455			0.475728	−	0.879593i	$-0.342185\pi$
$641$	24.0889			0.951455			0.475728	+	0.879593i	$0.342185\pi$
$642$	0.633558	+	0.329086i	0.0250045	+	0.0129880i
$643$	10.9319	−	2.92920i	0.431112	−	0.115516i	−0.0367360	−	0.999325i	$-0.511696\pi$
$643$	10.9319	−	2.92920i	0.431112	−	0.115516i	0.467848	+	0.883809i	$0.345029\pi$
$644$	19.0521	−	4.17401i	0.750759	−	0.164479i
$645$	−5.21205	−	0.136858i	−0.205224	−	0.00538878i
$646$	16.6401	−	28.8215i	0.654696	−	1.13397i
$647$	3.12094	+	11.6475i	0.122697	+	0.457911i	0.999747	−	0.0224877i	$-0.00715866\pi$
$647$	3.12094	+	11.6475i	0.122697	+	0.457911i	−0.877050	+	0.480399i	$0.840492\pi$
$648$	−3.83285	−	8.14305i	−0.150569	−	0.319889i
$649$	−3.17781	−	5.50413i	−0.124740	−	0.216056i
$650$	−0.125892	−	0.313342i	−0.00493787	−	0.0122903i
$651$	43.4389	−	24.9873i	1.70250	−	0.979331i
$652$	15.0992	−	4.04583i	0.591331	−	0.158447i
$653$	1.82318	−	1.82318i	0.0713466	−	0.0713466i	−0.670533	−	0.741880i	$-0.733935\pi$
$653$	1.82318	−	1.82318i	0.0713466	−	0.0713466i	0.741880	+	0.670533i	$0.233935\pi$
$654$	−8.10274	+	8.85856i	−0.316842	+	0.346397i
$655$	−3.01850	+	2.61880i	−0.117943	+	0.102325i
$656$	−0.0900541	+	0.0519927i	−0.00351602	+	0.00202998i
$657$	18.4402	+	15.4168i	0.719420	+	0.601466i
$658$	4.50543	−	7.03339i	0.175640	−	0.274190i
$659$	−21.8907	+	12.6386i	−0.852742	+	0.492331i	−0.861575	−	0.507630i	$-0.830522\pi$
$659$	−21.8907	+	12.6386i	−0.852742	+	0.492331i	0.00883313	+	0.999961i	$0.497188\pi$
$660$	2.66686	−	2.53039i	0.103807	−	0.0984953i
$661$	−26.2910	+	15.1791i	−1.02260	+	0.590399i	−0.914856	−	0.403779i	$-0.867696\pi$
$661$	−26.2910	+	15.1791i	−1.02260	+	0.590399i	−0.107745	+	0.994179i	$0.534363\pi$
$662$	3.97418	−	14.8318i	0.154461	−	0.576455i
$663$	−0.777382	+	0.0346409i	−0.0301910	+	0.00134534i
$664$	1.44700	+	2.50628i	0.0561545	+	0.0972625i
$665$	−29.2876	+	4.27349i	−1.13572	+	0.165719i
$666$	2.41539	−	1.69775i	0.0935946	−	0.0657865i
$667$	11.3276	−	42.2752i	0.438607	−	1.63690i
$668$	−9.97235	−	9.97235i	−0.385842	−	0.385842i
$669$	24.1207	+	22.0627i	0.932559	+	0.852993i
$670$	−23.1854	+	20.1153i	−0.895730	+	0.777122i
$671$	3.99730	+	2.30784i	0.154314	+	0.0890933i
$672$	−1.19310	+	4.42453i	−0.0460249	+	0.170680i
$673$	−18.4173	−	4.93490i	−0.709935	−	0.190226i	−0.114258	−	0.993451i	$-0.536449\pi$
$673$	−18.4173	−	4.93490i	−0.709935	−	0.190226i	−0.595676	+	0.803225i	$0.703116\pi$
$674$	15.8938	−	9.17629i	0.612206	−	0.353458i
$675$	−0.207127	+	25.9799i	−0.00797234	+	0.999968i
$676$	−6.49772	+	11.2544i	−0.249912	+	0.432861i
$677$	7.92581	+	29.5795i	0.304614	+	1.13683i	0.933277	+	0.359156i	$0.116935\pi$
$677$	7.92581	+	29.5795i	0.304614	+	1.13683i	−0.628664	+	0.777677i	$0.716398\pi$
$678$	9.64299	−	0.429701i	0.370337	−	0.0165026i
$679$	−8.41096	−	38.3916i	−0.322783	−	1.47333i
$680$	2.82405	+	14.6041i	0.108297	+	0.560042i
$681$	−9.36477	−	29.6085i	−0.358859	−	1.13460i
$682$	−7.33986	+	7.33986i	−0.281058	+	0.281058i
$683$	−2.45012	−	9.14397i	−0.0937512	−	0.349884i	0.903076	−	0.429481i	$-0.141303\pi$
$683$	−2.45012	−	9.14397i	−0.0937512	−	0.349884i	−0.996827	+	0.0795966i	$0.974637\pi$
$684$	−1.33496	−	14.9493i	−0.0510435	−	0.571600i
$685$	−0.104915	+	1.47972i	−0.00400860	+	0.0565372i
$686$	−18.3794	+	2.28014i	−0.701727	+	0.0870561i
$687$	−10.7501	+	20.6961i	−0.410142	+	0.789606i
$688$	−0.951914	+	0.951914i	−0.0362914	+	0.0362914i
$689$	0.435092	+	0.753601i	0.0165757	+	0.0287099i
$690$	8.11087	−	27.3746i	0.308776	−	1.04213i
$691$	−6.89925	−	3.98329i	−0.262460	−	0.151531i	0.362996	−	0.931791i	$-0.381754\pi$
$691$	−6.89925	−	3.98329i	−0.262460	−	0.151531i	−0.625456	+	0.780259i	$0.715087\pi$
$692$	5.95046	−	5.95046i	0.226203	−	0.226203i
$693$	−3.48351	+	6.68044i	−0.132328	+	0.253769i
$694$			19.4631i			0.738811i
$695$	−2.97681	+	0.575636i	−0.112917	+	0.0218351i
$696$	7.58780	+	6.94041i	0.287615	+	0.263076i
$697$	0.179032	−	0.668156i	0.00678132	−	0.0253082i
$698$	−10.1636	−	10.1636i	−0.384696	−	0.384696i
$699$	−9.70397	+	10.6091i	−0.367038	+	0.401274i
$700$	8.63588	−	10.0211i	0.326405	−	0.378760i
$701$	−23.0164			−0.869317			−0.434658	−	0.900595i	$-0.643131\pi$
$701$	−23.0164			−0.869317			−0.434658	+	0.900595i	$0.643131\pi$
$702$	−0.277838	+	0.214384i	−0.0104863	+	0.00809142i
$703$	4.75573	−	1.27429i	0.179366	−	0.0480609i
$704$		−	0.949211i		−	0.0357747i
$705$	−5.83349	−	10.7458i	−0.219702	−	0.404710i
$706$	18.8725	+	10.8960i	0.710276	+	0.410078i
$707$	40.5017	−	20.9558i	1.52322	−	0.788125i
$708$	9.77544	−	6.24000i	0.367384	−	0.234513i
$709$	−8.91099	−	5.14476i	−0.334659	−	0.193216i	0.323248	−	0.946314i	$-0.395225\pi$
$709$	−8.91099	−	5.14476i	−0.334659	−	0.193216i	−0.657908	+	0.753098i	$0.728558\pi$
$710$	12.3679	+	8.35974i	0.464160	+	0.313735i
$711$	−3.78834	−	42.4229i	−0.142074	−	1.59098i
$712$	3.05866	+	0.819564i	0.114628	+	0.0307145i
$713$	−20.8646	+	77.8678i	−0.781386	+	2.91617i
$714$	−15.1999	−	26.4241i	−0.568843	−	0.988897i
$715$	−0.118763	−	0.0802743i	−0.00444148	−	0.00300209i
$716$	0.712587			0.0266306
$717$	30.4392	−	19.4304i	1.13677	−	0.725641i
$718$	−22.2742	+	22.2742i	−0.831265	+	0.831265i
$719$	−25.4609	−	44.0996i	−0.949533	−	1.64464i	−0.746410	−	0.665486i	$-0.768224\pi$
$719$	−25.4609	−	44.0996i	−0.949533	−	1.64464i	−0.203123	−	0.979153i	$-0.565109\pi$
$720$	4.82933	+	4.65592i	0.179978	+	0.173516i
$721$	−1.16559	+	3.66492i	−0.0434087	+	0.136489i
$722$	1.56049	−	5.82382i	0.0580754	−	0.216740i
$723$	−0.119142	−	0.0618854i	−0.00443093	−	0.00230154i
$724$	2.73687	+	4.74041i	0.101715	+	0.176176i
$725$	−11.0668	−	27.5450i	−0.411010	−	1.02300i
$726$	−3.77061	+	17.0807i	−0.139941	+	0.633926i
$727$	11.6602	+	3.12434i	0.432453	+	0.115875i	0.468478	−	0.883475i	$-0.344803\pi$
$727$	11.6602	+	3.12434i	0.432453	+	0.115875i	−0.0360243	+	0.999351i	$0.511469\pi$
$728$	0.178497	+	0.00823872i	0.00661552	+	0.000305347i
$729$	26.0420	−	7.12858i	0.964517	−	0.264021i
$730$	−16.9335	−	5.84905i	−0.626736	−	0.216483i
$731$		−	8.95518i		−	0.331219i
$732$	−3.88230	+	7.47422i	−0.143494	+	0.276255i
$733$	11.3561	+	11.3561i	0.419448	+	0.419448i	0.885014	−	0.465565i	$-0.154149\pi$
$733$	11.3561	+	11.3561i	0.419448	+	0.419448i	−0.465565	+	0.885014i	$0.654149\pi$
$734$	4.73873	−	8.20772i	0.174910	−	0.302952i
$735$	−10.0635	+	25.1739i	−0.371197	+	0.928554i
$736$	−3.68591	−	6.38418i	−0.135864	−	0.235324i
$737$	−3.37243	+	12.5861i	−0.124225	+	0.463614i
$738$	−0.107222	−	0.292951i	−0.00394689	−	0.0107837i
$739$	−26.5149	−	15.3084i	−0.975367	−	0.563129i	−0.0744990	−	0.997221i	$-0.523736\pi$
$739$	−26.5149	−	15.3084i	−0.975367	−	0.563129i	−0.900868	+	0.434093i	$0.857069\pi$
$740$	−1.23231	+	1.82316i	−0.0453006	+	0.0670206i
$741$	−0.557987	+	0.176484i	−0.0204982	+	0.00648330i
$742$	−18.3877	+	28.7049i	−0.675032	+	1.05379i
$743$	6.00190	+	22.3994i	0.220188	+	0.821754i	0.984275	+	0.176641i	$0.0565232\pi$
$743$	6.00190	+	22.3994i	0.220188	+	0.821754i	−0.764087	+	0.645113i	$0.776810\pi$
$744$	−13.9762	−	12.7837i	−0.512392	−	0.468674i
$745$	13.8385	−	12.0061i	0.507004	−	0.439869i
$746$	0.498173	−	0.862861i	0.0182394	−	0.0315916i
$747$	−8.15307	+	2.98407i	−0.298305	+	0.109182i
$748$	4.46488	+	4.46488i	0.163252	+	0.163252i
$749$	1.06528	−	0.233385i	0.0389244	−	0.00852769i
$750$	−6.74521	−	18.1522i	−0.246300	−	0.662824i
$751$	−2.51606			−0.0918125			−0.0459062	−	0.998946i	$-0.514618\pi$
$751$	−2.51606			−0.0918125			−0.0459062	+	0.998946i	$0.514618\pi$
$752$	−3.04945	−	0.817097i	−0.111202	−	0.0297965i
$753$	−30.5291	−	15.8576i	−1.11254	−	0.577883i
$754$	0.200484	−	0.347249i	0.00730121	−	0.0126461i
$755$	9.69784	+	11.1780i	0.352940	+	0.406808i
$756$	−12.4609	−	5.80749i	−0.453197	−	0.211216i
$757$	−32.7287	−	32.7287i	−1.18954	−	1.18954i	−0.977194	−	0.212350i	$-0.931888\pi$
$757$	−32.7287	−	32.7287i	−1.18954	−	1.18954i	−0.212350	−	0.977194i	$-0.568112\pi$
$758$	−1.40686	−	5.25049i	−0.0510996	−	0.190706i
$759$	−3.65490	−	11.5556i	−0.132664	−	0.419443i
$760$	4.89425	+	10.0595i	0.177533	+	0.364895i
$761$			30.0142i			1.08801i	0.839081	+	0.544007i	$0.183093\pi$
$761$			30.0142i			1.08801i	−0.839081	+	0.544007i	$0.816907\pi$
$762$	−26.5840	+	16.9695i	−0.963038	+	0.614740i
$763$	−0.845534	+	18.3190i	−0.0306104	+	0.663191i
$764$		−	20.1226i		−	0.728011i
$765$	−44.6165	+	0.815660i	−1.61311	+	0.0294903i
$766$	32.3787	+	18.6938i	1.16989	+	0.675436i
$767$	−0.319760	−	0.319760i	−0.0115458	−	0.0115458i
$768$	1.73033	−	0.0771054i	0.0624380	−	0.00278230i
$769$	−22.1913	+	38.4365i	−0.800240	+	1.38606i	0.119217	+	0.992868i	$0.461961\pi$
$769$	−22.1913	+	38.4365i	−0.800240	+	1.38606i	−0.919458	+	0.393189i	$0.871372\pi$
$770$	0.655009	−	5.57728i	0.0236049	−	0.200991i
$771$	5.44549	+	17.2169i	0.196115	+	0.620053i
$772$	−17.3540	+	4.64998i	−0.624582	+	0.167356i
$773$	9.11974	−	2.44363i	0.328014	−	0.0878911i	−0.0910539	−	0.995846i	$-0.529024\pi$
$773$	9.11974	−	2.44363i	0.328014	−	0.0878911i	0.419068	+	0.907955i	$0.362357\pi$
$774$	−2.32240	−	3.30408i	−0.0834770	−	0.118763i
$775$	20.3842	+	50.7359i	0.732222	+	1.82249i
$776$	−12.8646	+	7.42740i	−0.461813	+	0.266628i
$777$	1.17416	−	4.35429i	0.0421227	−	0.156209i
$778$	9.47783	+	35.3717i	0.339797	+	1.26814i
$779$		−	0.520232i		−	0.0186392i
$780$	0.136686	−	0.223016i	0.00489415	−	0.00798524i
$781$	6.33701			0.226756
$782$	47.3674	+	12.6921i	1.69386	+	0.453867i
$783$	−24.4239	+	18.8459i	−0.872840	+	0.673498i
$784$	2.92669	+	6.35881i	0.104525	+	0.227100i
$785$	−0.787707	−	1.61902i	−0.0281145	−	0.0577855i
$786$	−3.02266	−	0.667259i	−0.107815	−	0.0238003i
$787$	27.4777	+	7.36262i	0.979473	+	0.262449i	0.712823	−	0.701344i	$-0.247416\pi$
$787$	27.4777	+	7.36262i	0.979473	+	0.262449i	0.266650	+	0.963793i	$0.414083\pi$
$788$	1.31680	+	0.352836i	0.0469092	+	0.0125693i
$789$	8.42803	+	26.6468i	0.300046	+	0.948651i
$790$	13.8888	+	28.5466i	0.494143	+	1.01564i
$791$	10.8956	−	9.93416i	0.387402	−	0.353218i
$792$	2.80525	+	0.489447i	0.0996804	+	0.0173917i
$793$	0.317220	+	0.0849988i	0.0112648	+	0.00301840i
$794$	−13.6685			−0.485078
$795$	23.8078	+	43.8560i	0.844375	+	1.55541i
$796$			20.1758i			0.715114i
$797$	3.92713	+	14.6563i	0.139106	+	0.519151i	0.999947	+	0.0102773i	$0.00327141\pi$
$797$	3.92713	+	14.6563i	0.139106	+	0.519151i	−0.860841	+	0.508874i	$0.830062\pi$
$798$	−16.1855	−	16.2371i	−0.572961	−	0.574788i
$799$	18.1874	−	10.5005i	0.643422	−	0.371480i
$800$	−4.59872	−	1.96258i	−0.162589	−	0.0693878i
$801$	−3.99926	+	8.61682i	−0.141307	+	0.304460i
$802$	28.4972	−	7.63581i	1.00627	−	0.269630i
$803$	−7.34587	+	1.96832i	−0.259230	+	0.0694605i
$804$	−23.2173	−	5.12528i	−0.818812	−	0.180755i
$805$	−17.2518	−	40.0550i	−0.608047	−	1.41175i
$806$	−0.369278	+	0.639607i	−0.0130072	+	0.0225292i
$807$	0.443676	+	0.695053i	0.0156181	+	0.0244670i
$808$	−12.1876	−	12.1876i	−0.428759	−	0.428759i
$809$	0.524603	+	0.302880i	0.0184441	+	0.0106487i	0.509194	−	0.860652i	$-0.329944\pi$
$809$	0.524603	+	0.302880i	0.0184441	+	0.0106487i	−0.490750	+	0.871301i	$0.663277\pi$
$810$	−16.2501	+	11.8716i	−0.570969	+	0.417126i
$811$			47.4663i			1.66677i	0.552694	+	0.833384i	$0.313600\pi$
$811$			47.4663i			1.66677i	−0.552694	+	0.833384i	$0.686400\pi$
$812$	15.6911	+	0.724243i	0.550651	+	0.0254159i
$813$	−0.0851295	−	1.91040i	−0.00298562	−	0.0670008i
$814$			0.934140i			0.0327416i
$815$	−15.2923	−	31.4312i	−0.535666	−	1.10099i
$816$	−7.77641	+	8.50179i	−0.272229	+	0.297622i
$817$	−1.74314	−	6.50550i	−0.0609849	−	0.227599i
$818$	−19.1217	−	19.1217i	−0.668576	−	0.668576i
$819$	−0.116388	+	0.523272i	−0.00406691	+	0.0182846i
$820$	0.152376	+	0.175632i	0.00532119	+	0.00613333i
$821$	−23.7133	+	41.0726i	−0.827599	+	1.43344i	0.0723175	+	0.997382i	$0.476961\pi$
$821$	−23.7133	+	41.0726i	−0.827599	+	1.43344i	−0.899917	+	0.436062i	$0.856373\pi$
$822$	−0.968555	+	0.618262i	−0.0337822	+	0.0215643i
$823$	20.2612	+	5.42896i	0.706260	+	0.189242i	0.594033	−	0.804441i	$-0.297535\pi$
$823$	20.2612	+	5.42896i	0.706260	+	0.189242i	0.112227	+	0.993683i	$0.464202\pi$
$824$	1.45358			0.0506378
$825$	−6.68738	−	4.78059i	−0.232825	−	0.166439i
$826$	5.36910	−	16.8819i	0.186815	−	0.587397i
$827$	29.9746	+	29.9746i	1.04232	+	1.04232i	0.999064	+	0.0432550i	$0.0137728\pi$
$827$	29.9746	+	29.9746i	1.04232	+	1.04232i	0.0432550	+	0.999064i	$0.486227\pi$
$828$	20.7681	−	7.60125i	0.721741	−	0.264162i
$829$	−24.3544	+	42.1831i	−0.845864	+	1.46508i	0.0390039	+	0.999239i	$0.487582\pi$
$829$	−24.3544	+	42.1831i	−0.845864	+	1.46508i	−0.884868	+	0.465841i	$0.845752\pi$
$830$	4.88798	−	4.24074i	0.169664	−	0.147198i
$831$	−24.4686	+	7.73909i	−0.848806	+	0.268466i
$832$	−0.0174799	−	0.0652359i	−0.000606007	−	0.00226165i
$833$	−43.6769	−	16.1439i	−1.51332	−	0.559353i
$834$	−1.73295	−	1.58510i	−0.0600072	−	0.0548874i
$835$	−17.6597	+	26.1268i	−0.611139	+	0.904157i
$836$	4.11261	+	2.37442i	0.142238	+	0.0821209i
$837$	44.9871	−	34.7128i	1.55498	−	1.19985i
$838$	6.75141	−	25.1966i	0.233224	−	0.870402i
$839$	−12.3589	−	21.4062i	−0.426676	−	0.739024i	0.569899	−	0.821714i	$-0.306982\pi$
$839$	−12.3589	−	21.4062i	−0.426676	−	0.739024i	−0.996575	+	0.0826901i	$0.973649\pi$
$840$	10.2201	+	0.740980i	0.352628	+	0.0255662i
$841$	3.12401	−	5.41095i	0.107725	−	0.186585i
$842$	8.32646	+	8.32646i	0.286949	+	0.286949i
$843$	−19.5184	+	0.869759i	−0.672249	+	0.0299561i
$844$			10.5779i			0.364106i
$845$	27.4663	+	9.48724i	0.944871	+	0.326371i
$846$	3.98721	−	8.59087i	0.137083	−	0.295360i
$847$	12.2786	+	23.7311i	0.421898	+	0.815410i
$848$	12.4455	+	3.33476i	0.427380	+	0.114516i
$849$	−7.99381	−	7.31178i	−0.274347	−	0.250940i
$850$	30.8629	−	12.3998i	1.05859	−	0.425310i
$851$	3.62739	+	6.28282i	0.124345	+	0.215372i
$852$	0.514762	+	11.5519i	0.0176355	+	0.395760i
$853$	12.5499	−	46.8370i	0.429702	−	1.60367i	−0.323734	−	0.946148i	$-0.604938\pi$
$853$	12.5499	−	46.8370i	0.429702	−	1.60367i	0.753436	−	0.657522i	$-0.228395\pi$
$854$	2.75329	+	12.5673i	0.0942157	+	0.430044i
$855$	−32.2529	+	9.27722i	−1.10303	+	0.317274i
$856$	−0.206093	−	0.356964i	−0.00704412	−	0.0122008i
$857$	−21.5142	+	21.5142i	−0.734910	+	0.734910i	−0.971588	−	0.236678i	$-0.923941\pi$
$857$	−21.5142	+	21.5142i	−0.734910	+	0.734910i	0.236678	+	0.971588i	$0.423941\pi$
$858$	−0.00494300	−	0.110927i	−0.000168751	−	0.00378697i
$859$	39.4018			1.34437			0.672186	−	0.740383i	$-0.265356\pi$
$859$	39.4018			1.34437			0.672186	+	0.740383i	$0.265356\pi$
$860$	2.49395	+	1.68571i	0.0850429	+	0.0574823i
$861$	−0.412300	−	0.238917i	−0.0140511	−	0.00814228i
$862$	2.29469	−	8.56391i	0.0781575	−	0.291688i
$863$	−3.75076	−	1.00501i	−0.127677	−	0.0342111i	0.194414	−	0.980919i	$-0.437719\pi$
$863$	−3.75076	−	1.00501i	−0.127677	−	0.0342111i	−0.322092	+	0.946708i	$0.604386\pi$
$864$	−0.664348	+	5.15351i	−0.0226016	+	0.175326i
$865$	−15.5898	−	10.5375i	−0.530069	−	0.358285i
$866$	1.23938	+	0.715556i	0.0421159	+	0.0243156i
$867$	−2.10120	−	47.1533i	−0.0713605	−	1.60141i
$868$	−28.9019	−	1.33400i	−0.980995	−	0.0452790i
$869$	11.6707	+	6.73809i	0.395902	+	0.228574i
$870$	12.0157	−	19.6047i	0.407370	−	0.664661i
$871$			0.927100i			0.0314136i
$872$	6.69512	−	1.79395i	0.226725	−	0.0607508i
$873$	−15.3171	−	41.8494i	−0.518406	−	1.41639i
$874$	36.8807			1.24751
$875$	−25.6664	−	14.7049i	−0.867683	−	0.497117i
$876$	−4.18480	−	13.2310i	−0.141391	−	0.447035i
$877$	37.5598	+	37.5598i	1.26830	+	1.26830i	0.946964	+	0.321339i	$0.104133\pi$
$877$	37.5598	+	37.5598i	1.26830	+	1.26830i	0.321339	+	0.946964i	$0.395867\pi$
$878$	6.46067	−	24.1116i	0.218037	−	0.813726i
$879$	0.574217	−	2.60118i	0.0193679	−	0.0877357i
$880$	−2.08390	+	0.402970i	−0.0702481	+	0.0135841i
$881$		−	7.61093i		−	0.256419i	−0.991747	−	0.128209i	$-0.959077\pi$
$881$		−	7.61093i		−	0.256419i	0.991747	−	0.128209i	$-0.0409229\pi$
$882$	−20.3016	+	5.37059i	−0.683592	+	0.180837i
$883$	17.5939	−	17.5939i	0.592083	−	0.592083i	−0.346111	−	0.938194i	$-0.612498\pi$
$883$	17.5939	−	17.5939i	0.592083	−	0.592083i	0.938194	+	0.346111i	$0.112498\pi$
$884$	0.389077	+	0.224634i	0.0130861	+	0.00755524i
$885$	−17.8493	−	18.8119i	−0.599996	−	0.632356i
$886$	−0.588911	−	1.02002i	−0.0197848	−	0.0342684i
$887$	−37.9792	+	37.9792i	−1.27522	+	1.27522i	−0.331903	+	0.943314i	$0.607691\pi$
$887$	−37.9792	+	37.9792i	−1.27522	+	1.27522i	−0.943314	+	0.331903i	$0.892309\pi$
$888$	−1.70286	+	0.0758812i	−0.0571443	+	0.00254641i
$889$	−14.6011	+	45.9098i	−0.489705	+	1.53977i
$890$	0.500773	−	7.06290i	0.0167860	−	0.236749i
$891$	−2.89298	+	8.03815i	−0.0969184	+	0.269288i
$892$	−4.88469	−	18.2299i	−0.163552	−	0.610383i
$893$	11.1683	−	11.1683i	0.373732	−	0.373732i
$894$	13.8576	+	3.05909i	0.463467	+	0.102311i
$895$	−0.302516	−	1.56441i	−0.0101120	−	0.0522926i
$896$	1.95510	−	1.78258i	0.0653152	−	0.0595518i
$897$	−0.463988	−	0.726873i	−0.0154921	−	0.0242696i
$898$	−0.339163	−	1.26577i	−0.0113180	−	0.0422394i
$899$	−32.4622	+	56.2261i	−1.08267	+	1.87525i
$900$	8.17140	−	12.5789i	0.272380	−	0.419296i
$901$	−74.2267	+	42.8548i	−2.47285	+	1.42770i
$902$	0.0953409	+	0.0255465i	0.00317450	+	0.000850606i
$903$	−5.95635	−	1.60617i	−0.198215	−	0.0534499i
$904$	−4.82628	−	2.78645i	−0.160520	−	0.0926761i
$905$	9.24519	−	8.02098i	0.307320	−	0.266626i
$906$	−2.47096	+	11.1934i	−0.0820922	+	0.371875i
$907$	−3.55043	−	3.55043i	−0.117890	−	0.117890i	0.645701	−	0.763591i	$-0.276565\pi$
$907$	−3.55043	−	3.55043i	−0.117890	−	0.117890i	−0.763591	+	0.645701i	$0.776565\pi$
$908$	−4.64040	+	17.3182i	−0.153997	+	0.574725i
$909$	42.3031	−	29.7344i	1.40311	−	0.986227i
$910$	−0.0576902	−	0.395369i	−0.00191241	−	0.0131063i
$911$	20.7781	+	35.9888i	0.688410	+	1.19236i	0.972352	+	0.233519i	$0.0750242\pi$
$911$	20.7781	+	35.9888i	0.688410	+	1.19236i	−0.283943	+	0.958841i	$0.591642\pi$
$912$	−3.99429	+	7.68983i	−0.132264	+	0.254636i
$913$	0.710981	−	2.65342i	0.0235300	−	0.0878153i
$914$	33.0469	−	19.0797i	1.09310	−	0.631099i
$915$	18.0570	+	5.35016i	0.596948	+	0.176871i
$916$	11.6608	−	6.73235i	0.385283	−	0.222443i
$917$	−4.19952	+	2.17286i	−0.138680	+	0.0717540i
$918$	−21.1160	−	27.3659i	−0.696932	−	0.903209i
$919$	−15.7157	+	9.07349i	−0.518415	+	0.299307i	−0.736286	−	0.676671i	$-0.763422\pi$
$919$	−15.7157	+	9.07349i	−0.518415	+	0.299307i	0.217871	+	0.975978i	$0.430089\pi$
$920$	−12.4510	+	10.8023i	−0.410498	+	0.356142i
$921$	0.923843	+	2.92091i	0.0304417	+	0.0962471i
$922$	7.77390	−	7.77390i	0.256020	−	0.256020i
$923$	0.435520	−	0.116697i	0.0143353	−	0.00384114i
$924$	3.77052	−	2.16892i	0.124041	−	0.0713521i
$925$	4.52571	+	1.93142i	0.148804	+	0.0635048i
$926$	−0.0764824	−	0.132471i	−0.00251337	−	0.00435328i
$927$	−0.749517	+	4.29584i	−0.0246174	+	0.141094i
$928$	−1.53661	−	5.73471i	−0.0504417	−	0.188251i
$929$	26.2464	−	45.4602i	0.861118	−	1.49150i	−0.00973296	−	0.999953i	$-0.503098\pi$
$929$	26.2464	−	45.4602i	0.861118	−	1.49150i	0.870851	−	0.491547i	$-0.163569\pi$
$930$	−22.1321	+	36.1104i	−0.725739	+	1.18411i
$931$	−34.8716	−	3.22595i	−1.14287	−	0.105726i
$932$	8.01817	−	2.14846i	0.262644	−	0.0703752i
$933$	−0.831485	−	18.6595i	−0.0272216	−	0.610884i
$934$	−13.3295			−0.436153
$935$	7.90670	−	11.6977i	0.258577	−	0.382554i
$936$	0.201809	−	0.0180214i	0.00659632	−	0.000589047i
$937$	37.2574	−	37.2574i	1.21715	−	1.21715i	0.248520	−	0.968627i	$-0.420056\pi$
$937$	37.2574	−	37.2574i	1.21715	−	1.21715i	0.968627	−	0.248520i	$-0.0799442\pi$
$938$	−32.2569	+	16.6899i	−1.05323	+	0.544946i
$939$	−1.64526	+	7.45298i	−0.0536911	+	0.243219i
$940$	−0.499266	+	7.04163i	−0.0162843	+	0.229673i
$941$	9.21795	−	5.32198i	0.300497	−	0.173492i	−0.342169	−	0.939638i	$-0.611162\pi$
$941$	9.21795	−	5.32198i	0.300497	−	0.173492i	0.642666	+	0.766147i	$0.277828\pi$
$942$	0.642864	−	1.23764i	0.0209456	−	0.0403246i
$943$	0.740442	−	0.198401i	0.0241121	−	0.00646082i
$944$	−6.69569			−0.217926
$945$	−7.45972	+	29.8220i	−0.242665	+	0.970110i
$946$	1.27784			0.0415461
$947$	−52.2197	+	13.9922i	−1.69691	+	0.454686i	−0.972159	−	0.234324i	$-0.924712\pi$
$947$	−52.2197	+	13.9922i	−1.69691	+	0.454686i	−0.724752	+	0.689010i	$0.758046\pi$
$948$	−11.3350	+	21.8221i	−0.368142	+	0.708749i
$949$	−0.468609	+	0.270551i	−0.0152117	+	0.00878247i
$950$	20.0067	−	15.0154i	0.649105	−	0.487163i
$951$	0.150252	−	0.680638i	0.00487227	−	0.0220712i
$952$	−0.811481	+	17.5812i	−0.0263002	+	0.569810i
$953$	10.0648	−	10.0648i	0.326031	−	0.326031i	−0.525044	−	0.851075i	$-0.675951\pi$
$953$	10.0648	−	10.0648i	0.326031	−	0.326031i	0.851075	+	0.525044i	$0.175951\pi$
$954$	−16.2727	+	35.0613i	−0.526849	+	1.13515i
$955$	−44.1772	+	8.54270i	−1.42954	+	0.276435i
$956$	−20.8493			−0.674316
$957$	−0.434525	−	9.75124i	−0.0140462	−	0.315213i
$958$	−14.6130	+	3.91554i	−0.472125	+	0.126505i
$959$	−0.531973	+	1.67267i	−0.0171783	+	0.0540132i
$960$	−0.903859	−	3.76604i	−0.0291719	−	0.121548i
$961$	44.2929	−	76.7176i	1.42880	−	2.47476i
$962$	0.0172024	+	0.0642002i	0.000554627	+	0.00206990i
$963$	1.16122	−	0.425015i	0.0374199	−	0.0136959i
$964$	0.0387563	+	0.0671278i	0.00124826	+	0.00216204i
$965$	17.5759	+	36.1248i	0.565787	+	1.16290i
$966$	16.9375	−	29.2291i	0.544955	−	0.940430i
$967$	48.4289	−	12.9765i	1.55737	−	0.417296i	0.625540	−	0.780192i	$-0.284879\pi$
$967$	48.4289	−	12.9765i	1.55737	−	0.417296i	0.931830	+	0.362896i	$0.118212\pi$
$968$	7.14107	−	7.14107i	0.229523	−	0.229523i
$969$	−17.3829	−	54.9595i	−0.558421	−	1.76555i
$970$	21.7675	+	25.0898i	0.698914	+	0.805586i
$971$	38.8956	−	22.4564i	1.24822	−	0.720659i	0.277465	−	0.960736i	$-0.410506\pi$
$971$	38.8956	−	22.4564i	1.24822	−	0.720659i	0.970754	+	0.240077i	$0.0771725\pi$
$972$	−14.8879	−	4.62072i	−0.477529	−	0.148210i
$973$	−3.58364	−	0.165407i	−0.114886	−	0.00530271i
$974$	8.33012	−	4.80940i	0.266914	−	0.154103i
$975$	−0.547636	−	0.205403i	−0.0175384	−	0.00657818i
$976$	4.21118	−	2.43133i	0.134797	−	0.0778249i
$977$	5.90176	−	22.0257i	0.188814	−	0.704664i	−0.804968	−	0.593319i	$-0.797817\pi$
$977$	5.90176	−	22.0257i	0.188814	−	0.704664i	0.993782	−	0.111345i	$-0.0355159\pi$
$978$	12.4804	−	24.0272i	0.399078	−	0.768306i
$979$	−1.50286	−	2.60304i	−0.0480317	−	0.0831934i
$980$	12.7176	−	9.12478i	0.406250	−	0.291480i
$981$	1.84952	+	20.7115i	0.0590506	+	0.661266i
$982$	−3.58141	+	13.3660i	−0.114287	+	0.426526i
$983$	1.06552	+	1.06552i	0.0339850	+	0.0339850i	0.723895	−	0.689910i	$-0.242350\pi$
$983$	1.06552	+	1.06552i	0.0339850	+	0.0339850i	−0.689910	+	0.723895i	$0.742350\pi$
$984$	−0.0388246	+	0.175874i	−0.00123768	+	0.00560665i
$985$	0.215592	−	3.04070i	0.00686932	−	0.0968847i
$986$	34.2026	+	19.7469i	1.08923	+	0.628870i
$987$	−3.72216	−	13.9803i	−0.118478	−	0.444997i
$988$	0.326370	+	0.0874507i	0.0103832	+	0.00278218i
$989$	8.59445	−	4.96201i	0.273288	−	0.157783i
$990$	−0.116389	−	6.36644i	−0.00369907	−	0.202339i
$991$	9.82208	−	17.0123i	0.312009	−	0.540415i	−0.666788	−	0.745247i	$-0.732332\pi$
$991$	9.82208	−	17.0123i	0.312009	−	0.540415i	0.978797	+	0.204832i	$0.0656648\pi$
$992$	2.83032	+	10.5629i	0.0898629	+	0.335373i
$993$	−14.3100	−	22.4177i	−0.454114	−	0.711406i
$994$	11.9007	+	13.0524i	0.377466	+	0.413997i
$995$	44.2940	−	8.56529i	1.40421	−	0.271538i
$996$	4.89471	+	1.08052i	0.155095	+	0.0342376i
$997$	−27.2396	+	27.2396i	−0.862686	+	0.862686i	−0.991649	−	0.128963i	$-0.958835\pi$
$997$	−27.2396	+	27.2396i	−0.862686	+	0.862686i	0.128963	+	0.991649i	$0.458835\pi$
$998$	0.0320761	+	0.119709i	0.00101535	+	0.00378934i
$999$	0.653800	−	5.07168i	0.0206853	−	0.160461i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.cg.a.157.9	yes	192
5.3	odd	4	inner	630.2.cg.a.283.28	yes	192
7.5	odd	6		630.2.bw.a.607.41	yes	192
9.7	even	3		630.2.bw.a.367.29	yes	192
35.33	even	12		630.2.bw.a.103.29	✓	192
45.43	odd	12		630.2.bw.a.493.41	yes	192
63.61	odd	6	inner	630.2.cg.a.187.28	yes	192
315.313	even	12	inner	630.2.cg.a.313.9	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bw.a.103.29	✓	192	35.33	even	12
630.2.bw.a.367.29	yes	192	9.7	even	3
630.2.bw.a.493.41	yes	192	45.43	odd	12
630.2.bw.a.607.41	yes	192	7.5	odd	6
630.2.cg.a.157.9	yes	192	1.1	even	1	trivial
630.2.cg.a.187.28	yes	192	63.61	odd	6	inner
630.2.cg.a.283.28	yes	192	5.3	odd	4	inner
630.2.cg.a.313.9	yes	192	315.313	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.cg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(-0.798392 + 1.53707i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-1.46535 - 1.68900i) q^{5} +(0.373365 - 1.69133i) q^{6} +(-1.21582 - 2.34985i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.72514 - 2.45436i) q^{9} +(1.85257 + 1.25219i) q^{10} +0.949211 q^{11} +(0.0771054 + 1.73033i) q^{12} +(0.0652359 - 0.0174799i) q^{13} +(1.78258 + 1.95510i) q^{14} +(3.76604 - 0.903859i) q^{15} +(0.500000 - 0.866025i) q^{16} +(1.72170 + 6.42548i) q^{17} +(2.30159 + 1.92423i) q^{18} +(2.50146 + 4.33266i) q^{19} +(-2.11354 - 0.730044i) q^{20} +(4.58257 + 0.00729502i) q^{21} +(-0.916867 + 0.245674i) q^{22} +(-5.21266 + 5.21266i) q^{23} +(-0.522321 - 1.65142i) q^{24} +(-0.705473 + 4.94998i) q^{25} +(-0.0584889 + 0.0337686i) q^{26} +(5.14985 - 0.692115i) q^{27} +(-2.22786 - 1.42711i) q^{28} +(-5.14160 + 2.96850i) q^{29} +(-3.40378 + 1.84778i) q^{30} +(9.47045 - 5.46777i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-0.757842 + 1.45900i) q^{33} +(-3.32607 - 5.76092i) q^{34} +(-2.18729 + 5.49689i) q^{35} +(-2.72120 - 1.26297i) q^{36} +(0.254710 - 0.950590i) q^{37} +(-3.53760 - 3.53760i) q^{38} +(-0.0252160 + 0.114228i) q^{39} +(2.23047 + 0.158145i) q^{40} +(-0.0900541 - 0.0519927i) q^{41} +(-4.42831 + 1.17901i) q^{42} +(-1.30034 - 0.348425i) q^{43} +(0.822041 - 0.474605i) q^{44} +(-1.61748 + 6.51028i) q^{45} +(3.68591 - 6.38418i) q^{46} +(-0.817097 - 3.04945i) q^{47} +(0.931942 + 1.45996i) q^{48} +(-4.04354 + 5.71400i) q^{49} +(-0.599714 - 4.96390i) q^{50} +(-11.2510 - 2.48368i) q^{51} +(0.0477560 - 0.0477560i) q^{52} +(3.33476 + 12.4455i) q^{53} +(-4.79524 + 2.00141i) q^{54} +(-1.39093 - 1.60322i) q^{55} +(2.52131 + 0.801874i) q^{56} +(-8.65673 + 0.385753i) q^{57} +(4.19810 - 4.19810i) q^{58} +(-3.34785 - 5.79864i) q^{59} +(2.80955 - 2.66578i) q^{60} +(4.21118 + 2.43133i) q^{61} +(-7.73259 + 7.73259i) q^{62} +(-3.66990 + 7.03789i) q^{63} -1.00000i q^{64} +(-0.125117 - 0.0845695i) q^{65} +(0.354402 - 1.60543i) q^{66} +(-3.55288 + 13.2595i) q^{67} +(4.70378 + 4.70378i) q^{68} +(-3.85046 - 12.1739i) q^{69} +(0.690057 - 5.87570i) q^{70} +6.67608 q^{71} +(2.95535 + 0.515636i) q^{72} +(-7.73892 + 2.07364i) q^{73} +0.984123i q^{74} +(-7.04520 - 5.03638i) q^{75} +(4.33266 + 2.50146i) q^{76} +(-1.15407 - 2.23050i) q^{77} +(-0.00520748 - 0.116862i) q^{78} +(12.2952 + 7.09862i) q^{79} +(-2.19540 + 0.424532i) q^{80} +(-3.04777 + 8.46824i) q^{81} +(0.100442 + 0.0269134i) q^{82} +(0.749023 - 2.79539i) q^{83} +(3.97227 - 2.28497i) q^{84} +(8.32976 - 12.3236i) q^{85} +1.34621 q^{86} +(-0.457775 - 10.2730i) q^{87} +(-0.671193 + 0.671193i) q^{88} +(-1.58328 - 2.74232i) q^{89} +(-0.122616 - 6.70708i) q^{90} +(-0.120390 - 0.132042i) q^{91} +(-1.90797 + 7.12063i) q^{92} +(0.843188 + 18.9221i) q^{93} +(1.57851 + 2.73406i) q^{94} +(3.65235 - 10.5739i) q^{95} +(-1.27805 - 1.16901i) q^{96} +(14.3486 + 3.84470i) q^{97} +(2.42687 - 6.56584i) q^{98} +(-1.63752 - 2.32971i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 16 q^{11} - 12 q^{15} + 96 q^{16} + 36 q^{17} + 16 q^{18} + 12 q^{21} - 16 q^{23} - 36 q^{27} + 12 q^{30} - 60 q^{33} + 48 q^{35} - 16 q^{36} + 12 q^{41} + 4 q^{42} - 36 q^{45} + 12 q^{46} - 16 q^{50}+ \cdots - 48 q^{98}+O(q^{100}) \) 192 * q - 16 * q^11 - 12 * q^15 + 96 * q^16 + 36 * q^17 + 16 * q^18 + 12 * q^21 - 16 * q^23 - 36 * q^27 + 12 * q^30 - 60 * q^33 + 48 * q^35 - 16 * q^36 + 12 * q^41 + 4 * q^42 - 36 * q^45 + 12 * q^46 - 16 * q^50 + 24 * q^51 - 40 * q^53 + 8 * q^56 - 32 * q^57 + 24 * q^58 + 8 * q^60 + 36 * q^61 - 108 * q^63 - 8 * q^65 + 16 * q^71 - 8 * q^72 + 80 * q^77 - 16 * q^78 + 4 * q^81 - 168 * q^83 - 16 * q^86 + 36 * q^90 + 8 * q^92 - 60 * q^93 + 64 * q^95 - 12 * q^96 - 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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