LMFDB - Embedded newform 357.2.bj.a.26.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [357,2,Mod(26,357)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("357.26"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(357, base_ring=CyclotomicField(24)) chi = DirichletCharacter(H, H._module([12, 20, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 357 = 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	357.bj (of order $24$, degree $8$, 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:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$352$
Relative dimension:	$44$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			26.5
Character	$\chi$	$=$	357.26
Dual form			357.2.bj.a.206.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.24242 + 0.600854i) q^{2} +(-0.427208 + 1.67854i) q^{3} +(2.93536 - 1.69473i) q^{4} +(1.99584 + 2.60102i) q^{5} +(-0.0505770 - 4.02067i) q^{6} +(-2.05255 + 1.66944i) q^{7} +(-2.28089 + 2.28089i) q^{8} +(-2.63499 - 1.43417i) q^{9} +(-6.03833 - 4.63338i) q^{10} +(-2.64319 + 3.44467i) q^{11} +(1.59066 + 5.65112i) q^{12} +6.05584 q^{13} +(3.59959 - 4.97687i) q^{14} +(-5.21856 + 2.23891i) q^{15} +(0.354763 - 0.614468i) q^{16} +(2.50438 + 3.27538i) q^{17} +(6.77047 + 1.63277i) q^{18} +(1.63061 - 0.436922i) q^{19} +(10.2665 + 4.25254i) q^{20} +(-1.92536 - 4.15849i) q^{21} +(3.85739 - 9.31255i) q^{22} +(-3.08232 - 0.405795i) q^{23} +(-2.85415 - 4.80298i) q^{24} +(-1.48787 + 5.55280i) q^{25} +(-13.5797 + 3.63868i) q^{26} +(3.53300 - 3.81024i) q^{27} +(-3.19572 + 8.37893i) q^{28} +(-3.74955 - 1.55311i) q^{29} +(10.3569 - 8.15616i) q^{30} +(-4.59660 + 0.605153i) q^{31} +(1.24341 - 4.64045i) q^{32} +(-4.65282 - 5.90828i) q^{33} +(-7.58389 - 5.83999i) q^{34} +(-8.43881 - 2.00680i) q^{35} +(-10.1652 + 0.255781i) q^{36} +(3.59304 - 2.75704i) q^{37} +(-3.39399 + 1.95952i) q^{38} +(-2.58711 + 10.1650i) q^{39} +(-10.4849 - 1.38037i) q^{40} +(-2.69251 - 6.50029i) q^{41} +(6.81609 + 8.16820i) q^{42} +(-0.352360 - 0.352360i) q^{43} +(-1.92092 + 14.5908i) q^{44} +(-1.52868 - 9.71603i) q^{45} +(7.15567 - 0.942062i) q^{46} +(2.35770 + 1.36122i) q^{47} +(0.879851 + 0.857990i) q^{48} +(1.42593 - 6.85323i) q^{49} -13.3457i q^{50} +(-6.56774 + 2.80443i) q^{51} +(17.7761 - 10.2630i) q^{52} +(-0.663905 + 2.47773i) q^{53} +(-5.63307 + 10.6670i) q^{54} -14.2350 q^{55} +(0.873831 - 8.48945i) q^{56} +(0.0367780 + 2.92371i) q^{57} +(9.34125 + 1.22980i) q^{58} +(0.475797 - 1.77570i) q^{59} +(-11.5240 + 15.4161i) q^{60} +(-0.571080 + 4.33778i) q^{61} +(9.94388 - 4.11889i) q^{62} +(7.80271 - 1.45524i) q^{63} +12.5720i q^{64} +(12.0865 + 15.7514i) q^{65} +(13.9836 + 10.4532i) q^{66} +(-4.43728 - 7.68559i) q^{67} +(12.9021 + 5.37016i) q^{68} +(1.99794 - 5.00044i) q^{69} +(20.1291 - 0.570403i) q^{70} +(2.82463 - 6.81926i) q^{71} +(9.28130 - 2.73892i) q^{72} +(1.74091 + 13.2235i) q^{73} +(-6.40052 + 8.34132i) q^{74} +(-8.68497 - 4.86965i) q^{75} +(4.04597 - 4.04597i) q^{76} +(-0.325396 - 11.4830i) q^{77} +(-0.306287 - 24.3486i) q^{78} +(-1.34133 + 10.1884i) q^{79} +(2.30630 - 0.303630i) q^{80} +(4.88630 + 7.55805i) q^{81} +(9.94345 + 12.9586i) q^{82} +(4.48292 - 4.48292i) q^{83} +(-12.6991 - 8.94369i) q^{84} +(-3.52100 + 13.0511i) q^{85} +(1.00185 + 0.578421i) q^{86} +(4.20880 - 5.63026i) q^{87} +(-1.82809 - 13.8857i) q^{88} +(-8.31631 - 4.80142i) q^{89} +(9.26586 + 20.8689i) q^{90} +(-12.4299 + 10.1099i) q^{91} +(-9.73543 + 4.03255i) q^{92} +(0.947931 - 7.97409i) q^{93} +(-6.10483 - 1.63579i) q^{94} +(4.39088 + 3.36924i) q^{95} +(7.25798 + 4.06954i) q^{96} +(-7.65695 - 3.17161i) q^{97} +(0.920256 + 16.2246i) q^{98} +(11.9050 - 5.28587i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 352 q - 12 q^{3} - 16 q^{7} - 4 q^{9} - 24 q^{10} - 12 q^{12} - 24 q^{15} + 112 q^{16} - 24 q^{18} - 24 q^{19} - 80 q^{22} - 60 q^{24} - 8 q^{25} - 72 q^{28} - 24 q^{31} + 24 q^{33} - 64 q^{36} - 40 q^{37}+ \cdots + 256 q^{99}+O(q^{100}) $ 352 * q - 12 * q^3 - 16 * q^7 - 4 * q^9 - 24 * q^10 - 12 * q^12 - 24 * q^15 + 112 * q^16 - 24 * q^18 - 24 * q^19 - 80 * q^22 - 60 * q^24 - 8 * q^25 - 72 * q^28 - 24 * q^31 + 24 * q^33 - 64 * q^36 - 40 * q^37 - 24 * q^39 - 24 * q^40 + 68 * q^42 - 48 * q^45 - 40 * q^46 + 48 * q^49 - 20 * q^51 - 240 * q^52 - 16 * q^57 - 8 * q^58 + 44 * q^60 - 24 * q^61 + 88 * q^63 - 12 * q^66 - 16 * q^67 + 64 * q^70 - 120 * q^73 - 156 * q^75 - 176 * q^78 - 24 * q^79 + 120 * q^82 - 104 * q^84 + 112 * q^85 + 132 * q^87 - 24 * q^88 - 96 * q^91 - 8 * q^93 - 120 * q^94 + 60 * q^96 + 256 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$.

$n$	$52$	$190$	$239$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{8}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.24242	+	0.600854i	−1.58563	+	0.424868i	−0.940663	−	0.339343i	$-0.889795\pi$
$2$	−2.24242	+	0.600854i	−1.58563	+	0.424868i	−0.644966	+	0.764211i	$0.723128\pi$
$3$	−0.427208	+	1.67854i	−0.246649	+	0.969105i
$3$	−0.427208	+	1.67854i	−0.246649	+	0.969105i
$4$	2.93536	−	1.69473i	1.46768	−	0.847365i
$5$	1.99584	+	2.60102i	0.892565	+	1.16321i	0.985859	+	0.167575i	$0.0535935\pi$
$5$	1.99584	+	2.60102i	0.892565	+	1.16321i	−0.0932945	+	0.995639i	$0.529740\pi$
$6$	−0.0505770	−	4.02067i	−0.0206480	−	1.64143i
$7$	−2.05255	+	1.66944i	−0.775791	+	0.630990i
$7$	−2.05255	+	1.66944i	−0.775791	+	0.630990i
$8$	−2.28089	+	2.28089i	−0.806416	+	0.806416i
$9$	−2.63499	−	1.43417i	−0.878329	−	0.478057i
$10$	−6.03833	−	4.63338i	−1.90949	−	1.46520i
$11$	−2.64319	+	3.44467i	−0.796951	+	1.03861i	0.201303	+	0.979529i	$0.435482\pi$
$11$	−2.64319	+	3.44467i	−0.796951	+	1.03861i	−0.998253	+	0.0590773i	$0.981184\pi$
$12$	1.59066	+	5.65112i	0.459184	+	1.63134i
$13$	6.05584			1.67959			0.839794	−	0.542904i	$-0.182675\pi$
$13$	6.05584			1.67959			0.839794	+	0.542904i	$0.182675\pi$
$14$	3.59959	−	4.97687i	0.962030	−	1.33012i
$15$	−5.21856	+	2.23891i	−1.34743	+	0.578084i
$16$	0.354763	−	0.614468i	0.0886909	−	0.153617i
$17$	2.50438	+	3.27538i	0.607401	+	0.794395i
$17$	2.50438	+	3.27538i	0.607401	+	0.794395i
$18$	6.77047	+	1.63277i	1.59581	+	0.384848i
$19$	1.63061	−	0.436922i	0.374089	−	0.100237i	−0.0668759	−	0.997761i	$-0.521303\pi$
$19$	1.63061	−	0.436922i	0.374089	−	0.100237i	0.440964	+	0.897525i	$0.354636\pi$
$20$	10.2665	+	4.25254i	2.29567	+	0.950896i
$21$	−1.92536	−	4.15849i	−0.420147	−	0.907456i
$22$	3.85739	−	9.31255i	0.822397	−	1.98544i
$23$	−3.08232	−	0.405795i	−0.642708	−	0.0846142i	−0.197875	−	0.980227i	$-0.563404\pi$
$23$	−3.08232	−	0.405795i	−0.642708	−	0.0846142i	−0.444834	+	0.895613i	$0.646737\pi$
$24$	−2.85415	−	4.80298i	−0.582600	−	0.980404i
$25$	−1.48787	+	5.55280i	−0.297574	+	1.11056i
$26$	−13.5797	+	3.63868i	−2.66320	+	0.713603i
$27$	3.53300	−	3.81024i	0.679927	−	0.733280i
$28$	−3.19572	+	8.37893i	−0.603935	+	1.58347i
$29$	−3.74955	−	1.55311i	−0.696274	−	0.288406i	0.00633755	−	0.999980i	$-0.497983\pi$
$29$	−3.74955	−	1.55311i	−0.696274	−	0.288406i	−0.702611	+	0.711574i	$0.747983\pi$
$30$	10.3569	−	8.15616i	1.89091	−	1.48910i
$31$	−4.59660	+	0.605153i	−0.825573	+	0.108689i	−0.531462	−	0.847082i	$-0.678357\pi$
$31$	−4.59660	+	0.605153i	−0.825573	+	0.108689i	−0.294111	+	0.955771i	$0.595024\pi$
$32$	1.24341	−	4.64045i	0.219805	−	0.820324i
$33$	−4.65282	−	5.90828i	−0.809951	−	1.02850i
$34$	−7.58389	−	5.83999i	−1.30063	−	1.00155i
$35$	−8.43881	−	2.00680i	−1.42642	−	0.339212i
$36$	−10.1652	+	0.255781i	−1.69419	+	0.0426301i
$37$	3.59304	−	2.75704i	0.590692	−	0.453254i	−0.269659	−	0.962956i	$-0.586911\pi$
$37$	3.59304	−	2.75704i	0.590692	−	0.453254i	0.860351	+	0.509702i	$0.170244\pi$
$38$	−3.39399	+	1.95952i	−0.550578	+	0.317876i
$39$	−2.58711	+	10.1650i	−0.414269	+	1.62770i
$40$	−10.4849	−	1.38037i	−1.65781	−	0.218255i
$41$	−2.69251	−	6.50029i	−0.420499	−	1.01517i	−0.982201	−	0.187834i	$-0.939853\pi$
$41$	−2.69251	−	6.50029i	−0.420499	−	1.01517i	0.561702	−	0.827340i	$-0.310147\pi$
$42$	6.81609	+	8.16820i	1.05175	+	1.26038i
$43$	−0.352360	−	0.352360i	−0.0537343	−	0.0537343i	0.679729	−	0.733463i	$-0.262097\pi$
$43$	−0.352360	−	0.352360i	−0.0537343	−	0.0537343i	−0.733463	+	0.679729i	$0.762097\pi$
$44$	−1.92092	+	14.5908i	−0.289589	+	2.19965i
$45$	−1.52868	−	9.71603i	−0.227883	−	1.44838i
$46$	7.15567	−	0.942062i	1.05505	−	0.138900i
$47$	2.35770	+	1.36122i	0.343905	+	0.198554i	0.661998	−	0.749506i	$-0.269709\pi$
$47$	2.35770	+	1.36122i	0.343905	+	0.198554i	−0.318092	+	0.948060i	$0.603042\pi$
$48$	0.879851	+	0.857990i	0.126996	+	0.123840i
$49$	1.42593	−	6.85323i	0.203704	−	0.979032i
$50$		−	13.3457i		−	1.88737i
$51$	−6.56774	+	2.80443i	−0.919667	+	0.392699i
$52$	17.7761	−	10.2630i	2.46510	−	1.42323i
$53$	−0.663905	+	2.47773i	−0.0911944	+	0.340342i	−0.996415	−	0.0845998i	$-0.973039\pi$
$53$	−0.663905	+	2.47773i	−0.0911944	+	0.340342i	0.905221	+	0.424942i	$0.139705\pi$
$54$	−5.63307	+	10.6670i	−0.766564	+	1.45159i
$55$	−14.2350			−1.91945
$56$	0.873831	−	8.48945i	0.116771	−	1.13445i
$57$	0.0367780	+	2.92371i	0.00487137	+	0.387254i
$58$	9.34125	+	1.22980i	1.22657	+	0.161480i
$59$	0.475797	−	1.77570i	0.0619435	−	0.231176i	−0.928013	−	0.372547i	$-0.878484\pi$
$59$	0.475797	−	1.77570i	0.0619435	−	0.231176i	0.989957	+	0.141371i	$0.0451511\pi$
$60$	−11.5240	+	15.4161i	−1.48774	+	1.99020i
$61$	−0.571080	+	4.33778i	−0.0731193	+	0.555396i	0.915200	+	0.403000i	$0.132032\pi$
$61$	−0.571080	+	4.33778i	−0.0731193	+	0.555396i	−0.988319	+	0.152397i	$0.951301\pi$
$62$	9.94388	−	4.11889i	1.26287	−	0.523099i
$63$	7.80271	−	1.45524i	0.983049	−	0.183343i
$64$			12.5720i			1.57150i
$65$	12.0865	+	15.7514i	1.49914	+	1.95372i
$66$	13.9836	+	10.4532i	1.72126	+	1.28670i
$67$	−4.43728	−	7.68559i	−0.542100	−	0.938944i	−0.998783	−	0.0493151i	$-0.984296\pi$
$67$	−4.43728	−	7.68559i	−0.542100	−	0.938944i	0.456684	−	0.889629i	$-0.349037\pi$
$68$	12.9021	+	5.37016i	1.56461	+	0.651227i
$69$	1.99794	−	5.00044i	0.240523	−	0.601982i
$70$	20.1291	−	0.570403i	2.40589	−	0.0681762i
$71$	2.82463	−	6.81926i	0.335222	−	0.809298i	−0.662939	−	0.748674i	$-0.730691\pi$
$71$	2.82463	−	6.81926i	0.335222	−	0.809298i	0.998161	−	0.0606238i	$-0.0193090\pi$
$72$	9.28130	−	2.73892i	1.09381	−	0.322785i
$73$	1.74091	+	13.2235i	0.203758	+	1.54769i	0.721656	+	0.692252i	$0.243381\pi$
$73$	1.74091	+	13.2235i	0.203758	+	1.54769i	−0.517898	+	0.855442i	$0.673285\pi$
$74$	−6.40052	+	8.34132i	−0.744045	+	0.969659i
$75$	−8.68497	−	4.86965i	−1.00285	−	0.562299i
$76$	4.04597	−	4.04597i	0.464105	−	0.464105i
$77$	−0.325396	−	11.4830i	−0.0370823	−	1.30861i
$78$	−0.306287	−	24.3486i	−0.0346801	−	2.75693i
$79$	−1.34133	+	10.1884i	−0.150911	+	1.14628i	0.733538	+	0.679648i	$0.237868\pi$
$79$	−1.34133	+	10.1884i	−0.150911	+	1.14628i	−0.884449	+	0.466636i	$0.845466\pi$
$80$	2.30630	−	0.303630i	0.257852	−	0.0339468i
$81$	4.88630	+	7.55805i	0.542922	+	0.839783i
$82$	9.94345	+	12.9586i	1.09807	+	1.43103i
$83$	4.48292	−	4.48292i	0.492065	−	0.492065i	−0.416892	−	0.908956i	$-0.636881\pi$
$83$	4.48292	−	4.48292i	0.492065	−	0.492065i	0.908956	+	0.416892i	$0.136881\pi$
$84$	−12.6991	−	8.94369i	−1.38559	−	0.975837i
$85$	−3.52100	+	13.0511i	−0.381906	+	1.41559i
$86$	1.00185	+	0.578421i	0.108033	+	0.0623727i
$87$	4.20880	−	5.63026i	0.451231	−	0.603627i
$88$	−1.82809	−	13.8857i	−0.194875	−	1.48022i
$89$	−8.31631	−	4.80142i	−0.881527	−	0.508950i	−0.0103654	−	0.999946i	$-0.503299\pi$
$89$	−8.31631	−	4.80142i	−0.881527	−	0.508950i	−0.871162	+	0.490996i	$0.836633\pi$
$90$	9.26586	+	20.8689i	0.976708	+	2.19977i
$91$	−12.4299	+	10.1099i	−1.30301	+	1.05980i
$92$	−9.73543	+	4.03255i	−1.01499	+	0.420422i
$93$	0.947931	−	7.97409i	0.0982959	−	0.826875i
$94$	−6.10483	−	1.63579i	−0.629665	−	0.168718i
$95$	4.39088	+	3.36924i	0.450495	+	0.345677i
$96$	7.25798	+	4.06954i	0.740765	+	0.415346i
$97$	−7.65695	−	3.17161i	−0.777446	−	0.322029i	−0.0415615	−	0.999136i	$-0.513233\pi$
$97$	−7.65695	−	3.17161i	−0.777446	−	0.322029i	−0.735884	+	0.677107i	$0.763233\pi$
$98$	0.920256	+	16.2246i	0.0929599	+	1.63893i
$99$	11.9050	−	5.28587i	1.19650	−	0.531250i
$100$	5.04308	+	18.8210i	0.504308	+	1.88210i
$101$	3.03851	+	5.26286i	0.302343	+	0.523674i	0.976666	−	0.214763i	$-0.0688978\pi$
$101$	3.03851	+	5.26286i	0.302343	+	0.523674i	−0.674323	+	0.738437i	$0.735564\pi$
$102$	13.0426	−	10.2350i	1.29141	−	1.01341i
$103$	13.4724	+	7.77829i	1.32747	+	0.766418i	0.984909	−	0.173076i	$-0.0553705\pi$
$103$	13.4724	+	7.77829i	1.32747	+	0.766418i	0.342566	+	0.939494i	$0.388704\pi$
$104$	−13.8127	+	13.8127i	−1.35445	+	1.35445i
$105$	6.97363	−	13.3076i	0.680557	−	1.29868i
$106$		−	5.95501i		−	0.578402i
$107$	6.51353	−	4.99801i	0.629687	−	0.483175i	−0.243928	−	0.969793i	$-0.578436\pi$
$107$	6.51353	−	4.99801i	0.629687	−	0.483175i	0.873615	+	0.486618i	$0.161770\pi$
$108$	3.91331	−	17.1719i	0.376558	−	1.65237i
$109$	7.50998	−	9.78720i	0.719326	−	0.937444i	−0.280422	−	0.959877i	$-0.590475\pi$
$109$	7.50998	−	9.78720i	0.719326	−	0.937444i	0.999748	+	0.0224328i	$0.00714118\pi$
$110$	31.9209	−	8.55317i	3.04354	−	0.815513i
$111$	3.09282	+	7.20889i	0.293557	+	0.684237i
$112$	0.297649	+	1.85348i	0.0281252	+	0.175138i
$113$	5.43146	+	13.1127i	0.510948	+	1.23354i	0.943333	+	0.331849i	$0.107672\pi$
$113$	5.43146	+	13.1127i	0.510948	+	1.23354i	−0.432384	+	0.901689i	$0.642328\pi$
$114$	−1.83919	−	6.53407i	−0.172256	−	0.611972i
$115$	−5.09632	−	8.82709i	−0.475235	−	0.823130i
$116$	−13.6384	+	1.79553i	−1.26629	+	0.166711i
$117$	−15.9571	−	8.68512i	−1.47523	−	0.802940i
$118$			4.26774i			0.392878i
$119$	−10.6084	−	2.54196i	−0.972472	−	0.233021i
$120$	6.79625	−	17.0097i	0.620410	−	1.55276i
$121$	−2.03229	−	7.58461i	−0.184754	−	0.689510i
$122$	−1.32577	−	10.0703i	−0.120030	−	0.911718i
$123$	12.0612	−	1.74250i	1.08753	−	0.157116i
$124$	−12.4671	+	9.56633i	−1.11958	+	0.859082i
$125$	−2.26774	+	0.939328i	−0.202833	+	0.0840160i
$126$	−16.6225	+	7.95155i	−1.48085	+	0.708381i
$127$	5.92862	+	5.92862i	0.526080	+	0.526080i	0.919401	−	0.393321i	$-0.128674\pi$
$127$	5.92862	+	5.92862i	0.526080	+	0.526080i	−0.393321	+	0.919401i	$0.628674\pi$
$128$	−5.06712	−	18.9107i	−0.447874	−	1.67149i
$129$	0.741980	−	0.440918i	0.0653277	−	0.0388207i
$130$	−36.5672	−	28.0590i	−3.20716	−	2.46094i
$131$	10.4790	+	13.6566i	0.915559	+	1.19318i	0.980742	+	0.195306i	$0.0625700\pi$
$131$	10.4790	+	13.6566i	0.915559	+	1.19318i	−0.0651836	+	0.997873i	$0.520763\pi$
$132$	−23.6706	−	9.45766i	−2.06026	−	0.823184i
$133$	−2.61750	+	3.61902i	−0.226966	+	0.313809i
$134$	14.5681	+	14.5681i	1.25850	+	1.25850i
$135$	16.9618	+	1.58482i	1.45984	+	0.136399i
$136$	−13.1830	−	1.75856i	−1.13043	−	0.150795i
$137$	−3.56656	+	2.05915i	−0.304711	+	0.175925i	−0.644557	−	0.764556i	$-0.722958\pi$
$137$	−3.56656	+	2.05915i	−0.304711	+	0.175925i	0.339846	+	0.940481i	$0.389625\pi$
$138$	−1.47568	+	12.4135i	−0.125618	+	1.05671i
$139$	−3.87600	+	9.35749i	−0.328758	+	0.793692i	0.669927	+	0.742427i	$0.266325\pi$
$139$	−3.87600	+	9.35749i	−0.328758	+	0.793692i	−0.998685	+	0.0512650i	$0.983675\pi$
$140$	−28.1719	+	8.41082i	−2.38096	+	0.710844i
$141$	−3.29208	+	3.37596i	−0.277243	+	0.284307i
$142$	−2.23662	+	16.9888i	−0.187693	+	1.42567i
$143$	−16.0067	+	20.8604i	−1.33855	+	1.74443i
$144$	−1.81605	+	1.11032i	−0.151337	+	0.0925270i
$145$	−3.44380	−	12.8524i	−0.285992	−	1.06734i
$146$	−11.8492	−	28.6066i	−0.980650	−	2.36750i
$147$	10.8942	+	5.32124i	0.898542	+	0.438888i
$148$	5.87443	−	14.1821i	0.482875	−	1.16576i
$149$	−5.68748	+	9.85101i	−0.465937	+	0.807026i	−0.999243	−	0.0388958i	$-0.987616\pi$
$149$	−5.68748	+	9.85101i	−0.465937	+	0.807026i	0.533306	+	0.845922i	$0.320949\pi$
$150$	22.4013	+	5.70140i	1.82906	+	0.465517i
$151$	−11.6591	−	3.12403i	−0.948800	−	0.254230i	−0.248947	−	0.968517i	$-0.580085\pi$
$151$	−11.6591	−	3.12403i	−0.948800	−	0.254230i	−0.699853	+	0.714287i	$0.746751\pi$
$152$	−2.72268	+	4.71582i	−0.220839	+	0.382504i
$153$	−1.90155	−	12.2223i	−0.153731	−	0.988113i
$154$	7.62928	+	25.5542i	0.614785	+	2.05921i
$155$	−10.7481	−	10.7481i	−0.863306	−	0.863306i
$156$	9.63280	+	34.2223i	0.771241	+	2.73998i
$157$	2.28539	+	3.95840i	0.182394	+	0.315915i	0.942695	−	0.333655i	$-0.108282\pi$
$157$	2.28539	+	3.95840i	0.182394	+	0.315915i	−0.760302	+	0.649570i	$0.774949\pi$
$158$	−3.11392	−	23.6526i	−0.247730	−	1.88170i
$159$	−3.87534	−	2.17290i	−0.307334	−	0.172322i
$160$	14.5516	−	6.02745i	1.15040	−	0.476512i
$161$	7.00407	−	4.31284i	0.551998	−	0.339899i
$162$	−15.4984	−	14.0123i	−1.21767	−	1.10091i
$163$	−7.17831	−	0.945042i	−0.562249	−	0.0740214i	−0.155955	−	0.987764i	$-0.549846\pi$
$163$	−7.17831	−	0.945042i	−0.562249	−	0.0740214i	−0.406293	+	0.913743i	$0.633179\pi$
$164$	−18.9197	−	14.5176i	−1.47738	−	1.13363i
$165$	6.08132	−	23.8940i	0.473430	−	1.86015i
$166$	−7.35900	+	12.7462i	−0.571169	+	0.989294i
$167$	11.4430	+	4.73983i	0.885483	+	0.366779i	0.778621	−	0.627495i	$-0.215920\pi$
$167$	11.4430	+	4.73983i	0.885483	+	0.366779i	0.106862	+	0.994274i	$0.465920\pi$
$168$	13.8766	+	5.09352i	1.07060	+	0.392974i
$169$	23.6732			1.82102
$170$	0.0537695	−	31.3815i	0.00412394	−	2.40685i
$171$	−4.92327	−	1.18730i	−0.376492	−	0.0907950i
$172$	−1.63146	−	0.437148i	−0.124397	−	0.0333322i
$173$	−13.2680	+	10.1809i	−1.00875	+	0.774039i	−0.974274	−	0.225366i	$-0.927642\pi$
$173$	−13.2680	+	10.1809i	−1.00875	+	0.774039i	−0.0344735	+	0.999406i	$0.510975\pi$
$174$	−6.05493	+	15.1543i	−0.459023	+	1.14884i
$175$	−6.21615	−	13.8813i	−0.469897	−	1.04933i
$176$	1.17893	+	2.84620i	0.0888654	+	0.214540i
$177$	2.77731	+	1.55724i	0.208756	+	0.117049i
$178$	21.5336	+	5.76991i	1.61401	+	0.432473i
$179$	3.45895	+	0.926822i	0.258534	+	0.0692739i	0.385758	−	0.922600i	$-0.373940\pi$
$179$	3.45895	+	0.926822i	0.258534	+	0.0692739i	−0.127224	+	0.991874i	$0.540607\pi$
$180$	−20.9533	−	25.9293i	−1.56177	−	1.93266i
$181$	6.32178	+	15.2621i	0.469894	+	1.13442i	0.964209	+	0.265142i	$0.0854188\pi$
$181$	6.32178	+	15.2621i	0.469894	+	1.13442i	−0.494315	+	0.869283i	$0.664581\pi$
$182$	21.7985	−	30.1391i	1.61581	−	2.23406i
$183$	−7.03717	−	2.81172i	−0.520202	−	0.207848i
$184$	7.95601	−	6.10486i	0.586525	−	0.450056i
$185$	14.3422	+	3.84299i	1.05446	+	0.282542i
$186$	2.66561	+	18.4508i	0.195452	+	1.35288i
$187$	−17.9021	−	0.0306737i	−1.30913	−	0.00224309i
$188$	9.22758			0.672991
$189$	−0.890701	+	13.7188i	−0.0647889	+	0.997899i
$190$	−11.8706	−	4.91697i	−0.861185	−	0.356714i
$191$	5.57549	−	9.65703i	0.403428	−	0.698758i	−0.590709	−	0.806885i	$-0.701152\pi$
$191$	5.57549	−	9.65703i	0.403428	−	0.698758i	0.994137	+	0.108127i	$0.0344852\pi$
$192$	−21.1026	−	5.37086i	−1.52295	−	0.387608i
$193$	9.99782	+	7.67160i	0.719659	+	0.552214i	0.902375	−	0.430952i	$-0.141822\pi$
$193$	9.99782	+	7.67160i	0.719659	+	0.552214i	−0.182716	+	0.983166i	$0.558489\pi$
$194$	19.0758	+	2.51137i	1.36956	+	0.180306i
$195$	−31.6028	+	13.5585i	−2.26312	+	0.970943i
$196$	−7.42875	−	22.5333i	−0.530625	−	1.60952i
$197$	−10.4641	+	4.33435i	−0.745533	+	0.308810i	−0.722917	−	0.690934i	$-0.757199\pi$
$197$	−10.4641	+	4.33435i	−0.745533	+	0.308810i	−0.0226155	+	0.999744i	$0.507199\pi$
$198$	−23.5200	+	19.0063i	−1.67149	+	1.35072i
$199$	−0.381996	−	2.90155i	−0.0270790	−	0.205685i	0.972557	−	0.232665i	$-0.0747445\pi$
$199$	−0.381996	−	2.90155i	−0.0270790	−	0.205685i	−0.999636	+	0.0269793i	$0.991411\pi$
$200$	−9.27167	−	16.0590i	−0.655606	−	1.13554i
$201$	14.7962	−	4.16479i	1.04364	−	0.293762i
$202$	−9.97582	−	9.97582i	−0.701896	−	0.701896i
$203$	10.2890	−	3.07181i	0.722144	−	0.215599i
$204$	−14.5259	+	19.3626i	−1.01702	+	1.35565i
$205$	11.5336	−	19.9768i	0.805541	−	1.39524i
$206$	−34.8844	−	9.34724i	−2.43051	−	0.651253i
$207$	7.53989	+	5.48984i	0.524059	+	0.381570i
$208$	2.14839	−	3.72112i	0.148964	−	0.258014i
$209$	−2.80497	+	6.77179i	−0.194024	+	0.468414i
$210$	−7.64189	+	34.0312i	−0.527341	+	2.34838i
$211$	−2.74793	−	6.63409i	−0.189175	−	0.456710i	0.800626	−	0.599165i	$-0.204500\pi$
$211$	−2.74793	−	6.63409i	−0.189175	−	0.456710i	−0.989801	+	0.142455i	$0.954500\pi$
$212$	2.25028	+	8.39816i	0.154550	+	0.576788i
$213$	10.2397	+	7.65450i	0.701612	+	0.524478i
$214$	−11.6030	+	15.1213i	−0.793163	+	1.03367i
$215$	0.213244	−	1.61975i	0.0145431	−	0.110466i
$216$	0.632340	+	16.7491i	0.0430253	+	1.13963i
$217$	8.42448	−	8.91585i	0.571891	−	0.605248i
$218$	−10.9598	+	26.4594i	−0.742294	+	1.79206i
$219$	−22.9399	−	2.72701i	−1.55013	−	0.184274i
$220$	−41.7849	+	24.1245i	−2.81714	+	1.62648i
$221$	15.1661	+	19.8352i	1.02018	+	1.33426i
$222$	−11.2669	−	14.3070i	−0.756183	−	0.960223i
$223$	4.18923	+	4.18923i	0.280531	+	0.280531i	0.833321	−	0.552790i	$-0.186437\pi$
$223$	4.18923	+	4.18923i	0.280531	+	0.280531i	−0.552790	+	0.833321i	$0.686437\pi$
$224$	5.19481	+	11.6006i	0.347093	+	0.775095i
$225$	11.8842	−	12.4977i	0.792279	−	0.833180i
$226$	−20.0584	−	26.1406i	−1.33427	−	1.73885i
$227$	8.66682	+	6.65029i	0.575237	+	0.441395i	0.854966	−	0.518684i	$-0.173578\pi$
$227$	8.66682	+	6.65029i	0.575237	+	0.441395i	−0.279729	+	0.960079i	$0.590245\pi$
$228$	5.06285	+	8.51980i	0.335296	+	0.564238i
$229$	−6.42179	−	23.9664i	−0.424364	−	1.58375i	−0.765308	−	0.643664i	$-0.777413\pi$
$229$	−6.42179	−	23.9664i	−0.424364	−	1.58375i	0.340945	−	0.940083i	$-0.389253\pi$
$230$	16.7319	+	16.7319i	1.10327	+	1.10327i
$231$	19.4137	+	4.35945i	1.27733	+	0.286830i
$232$	12.0948	−	5.00982i	0.794062	−	0.328911i
$233$	−9.14357	+	7.01611i	−0.599015	+	0.459641i	−0.863221	−	0.504826i	$-0.831557\pi$
$233$	−9.14357	+	7.01611i	−0.599015	+	0.459641i	0.264206	+	0.964466i	$0.414890\pi$
$234$	41.0009	+	9.88781i	2.68031	+	0.646386i
$235$	1.16502	+	8.84919i	0.0759974	+	0.577258i
$236$	−1.61270	−	6.01866i	−0.104978	−	0.391782i
$237$	−16.5286	−	6.60404i	−1.07365	−	0.428978i
$238$	25.3158	−	0.673970i	1.64098	−	0.0436870i
$239$			12.4669i			0.806415i	0.915109	+	0.403207i	$0.132105\pi$
$239$			12.4669i			0.806415i	−0.915109	+	0.403207i	$0.867895\pi$
$240$	−0.475615	+	4.00092i	−0.0307008	+	0.258258i
$241$	4.34813	−	0.572442i	0.280088	−	0.0368742i	0.0108263	−	0.999941i	$-0.496554\pi$
$241$	4.34813	−	0.572442i	0.280088	−	0.0368742i	0.269261	+	0.963067i	$0.413220\pi$
$242$	9.11449	+	15.7868i	0.585902	+	1.01481i
$243$	−14.7739	+	4.97299i	−0.947749	+	0.319017i
$244$	5.67505	+	13.7008i	0.363308	+	0.877103i
$245$	20.6713	−	9.96904i	1.32064	−	0.636898i
$246$	−25.9994	+	11.1545i	−1.65766	+	0.711182i
$247$	9.87474	−	2.64593i	0.628315	−	0.168356i
$248$	9.10404	−	11.8646i	0.578107	−	0.753404i
$249$	5.60962	+	9.43990i	0.355495	+	0.598229i
$250$	4.52082	−	3.46894i	0.285922	−	0.219395i
$251$		−	22.2851i		−	1.40662i	−0.710882	−	0.703311i	$-0.751704\pi$
$251$		−	22.2851i		−	1.40662i	0.710882	−	0.703311i	$-0.248296\pi$
$252$	20.4375	−	17.4952i	1.28744	−	1.10209i
$253$	9.54498	−	9.54498i	0.600088	−	0.600088i
$254$	−16.8567	−	9.73221i	−1.05768	−	0.610653i
$255$	−20.4025	−	11.4857i	−1.27766	−	0.719260i
$256$	10.1532	+	17.5859i	0.634575	+	1.09912i
$257$	−2.45989	−	9.18042i	−0.153443	−	0.572659i	−0.999234	−	0.0391431i	$-0.987537\pi$
$257$	−2.45989	−	9.18042i	−0.153443	−	0.572659i	0.845790	−	0.533516i	$-0.179129\pi$
$258$	−1.39890	+	1.43454i	−0.0870919	+	0.0893109i
$259$	−2.77219	+	11.6573i	−0.172255	+	0.724351i
$260$	62.1725	+	25.7527i	3.85578	+	1.59711i
$261$	7.65258	+	9.46993i	0.473683	+	0.586174i
$262$	−31.7040	−	24.3273i	−1.95868	−	1.50295i
$263$	6.96322	+	1.86579i	0.429370	+	0.115049i	0.467031	−	0.884241i	$-0.345324\pi$
$263$	6.96322	+	1.86579i	0.429370	+	0.115049i	−0.0376602	+	0.999291i	$0.511990\pi$
$264$	24.0887	+	2.86358i	1.48256	+	0.176241i
$265$	−7.76968	+	3.21831i	−0.477287	+	0.197699i
$266$	3.69503	−	9.68809i	0.226557	−	0.594015i
$267$	11.6122	−	11.9080i	0.710653	−	0.728760i
$268$	−26.0500	−	15.0400i	−1.59126	−	0.918713i
$269$	−4.06924	−	30.9090i	−0.248106	−	1.88455i	−0.432400	−	0.901682i	$-0.642333\pi$
$269$	−4.06924	−	30.9090i	−0.248106	−	1.88455i	0.184294	−	0.982871i	$-0.441000\pi$
$270$	−38.9877	+	6.63775i	−2.37272	+	0.403960i
$271$	3.54136	+	2.04460i	0.215122	+	0.124201i	0.603690	−	0.797219i	$-0.293697\pi$
$271$	3.54136	+	2.04460i	0.215122	+	0.124201i	−0.388567	+	0.921420i	$0.627030\pi$
$272$	2.90108	−	0.376878i	0.175904	−	0.0228516i
$273$	−11.6597	−	25.1831i	−0.705674	−	1.52415i
$274$	6.76046	−	6.76046i	0.408414	−	0.408414i
$275$	−15.1948	−	19.8023i	−0.916284	−	1.19412i
$276$	−2.60973	−	18.0640i	−0.157087	−	1.08733i
$277$	16.2160	−	2.13487i	0.974324	−	0.128272i	0.373480	−	0.927638i	$-0.378165\pi$
$277$	16.2160	−	2.13487i	0.974324	−	0.128272i	0.600844	+	0.799366i	$0.294831\pi$
$278$	3.06912	−	23.3123i	0.184074	−	1.39818i
$279$	12.9799	+	4.99774i	0.777084	+	0.299207i
$280$	23.8253	−	14.6707i	1.42383	−	0.876742i
$281$	16.8446	−	16.8446i	1.00487	−	1.00487i	0.00487886	−	0.999988i	$-0.498447\pi$
$281$	16.8446	−	16.8446i	1.00487	−	1.00487i	0.999988	−	0.00487886i	$-0.00155299\pi$
$282$	5.35377	−	9.54838i	0.318812	−	0.568598i
$283$	−3.98320	+	5.19100i	−0.236777	+	0.308573i	−0.896595	−	0.442852i	$-0.853967\pi$
$283$	−3.98320	+	5.19100i	−0.236777	+	0.308573i	0.659818	+	0.751425i	$0.270633\pi$
$284$	−3.26551	−	24.8040i	−0.193772	−	1.47185i
$285$	−7.53123	+	5.93090i	−0.446111	+	0.351316i
$286$	23.3597	−	56.3954i	1.38129	−	3.33473i
$287$	16.3784	+	8.84719i	0.966784	+	0.522233i
$288$	−9.93156	+	10.4443i	−0.585223	+	0.615434i
$289$	−4.45617	+	16.4056i	−0.262128	+	0.965033i
$290$	15.4449	+	26.7513i	0.906954	+	1.57089i
$291$	8.59479	−	11.4976i	0.503836	−	0.673998i
$292$	27.5205	+	35.8654i	1.61051	+	2.09886i
$293$			20.2740i			1.18442i	0.805784	+	0.592210i	$0.201744\pi$
$293$			20.2740i			1.18442i	−0.805784	+	0.592210i	$0.798256\pi$
$294$	−27.6267	−	5.38659i	−1.61122	−	0.314152i
$295$	5.56825	−	2.30644i	0.324196	−	0.134286i
$296$	−1.90683	+	14.4838i	−0.110832	+	0.841855i
$297$	3.78661	+	22.2412i	0.219722	+	1.29056i
$298$	6.83470	−	25.5074i	0.395923	−	1.47761i
$299$	−18.6661	−	2.45743i	−1.07949	−	0.142117i
$300$	−33.7463	+	0.424502i	−1.94834	+	0.0245087i
$301$	1.31148	+	0.134992i	0.0755924	+	0.00778083i
$302$	28.0215			1.61246
$303$	−10.1320	+	2.85192i	−0.582068	+	0.163839i
$304$	0.310008	−	1.15696i	0.0177802	−	0.0663565i
$305$	−12.4225	+	7.17211i	−0.711308	+	0.410674i
$306$	11.6079	+	26.2649i	0.663578	+	1.50146i
$307$			3.45754i			0.197332i	0.995121	+	0.0986661i	$0.0314576\pi$
$307$			3.45754i			0.197332i	−0.995121	+	0.0986661i	$0.968542\pi$
$308$	−20.4157	−	33.1553i	−1.16330	−	1.88920i
$309$	−18.8117	+	19.2910i	−1.07016	+	1.09743i
$310$	30.5597	+	17.6436i	1.73567	+	1.00209i
$311$	0.235966	−	0.0310655i	0.0133804	−	0.00176156i	−0.123833	−	0.992303i	$-0.539519\pi$
$311$	0.235966	−	0.0310655i	0.0133804	−	0.00176156i	0.137213	+	0.990542i	$0.456185\pi$
$312$	−17.2843	−	29.0861i	−0.978529	−	1.64668i
$313$	4.57644	−	34.7615i	0.258676	−	1.96484i	−0.00414391	−	0.999991i	$-0.501319\pi$
$313$	4.57644	−	34.7615i	0.258676	−	1.96484i	0.262820	−	0.964845i	$-0.415348\pi$
$314$	−7.50321	−	7.50321i	−0.423431	−	0.423431i
$315$	19.3580	+	17.3906i	1.09070	+	0.979850i
$316$	13.3293	+	32.1798i	0.749832	+	1.81026i
$317$	12.9767	+	1.70842i	0.728845	+	0.0959542i	0.485811	−	0.874064i	$-0.338524\pi$
$317$	12.9767	+	1.70842i	0.728845	+	0.0959542i	0.243033	+	0.970018i	$0.421858\pi$
$318$	9.99572	+	2.54403i	0.560532	+	0.142662i
$319$	15.2607	−	8.81078i	0.854436	−	0.493309i
$320$	−32.7000	+	25.0916i	−1.82799	+	1.40266i
$321$	5.60671	+	13.0684i	0.312936	+	0.729407i
$322$	−13.1147	+	13.8796i	−0.730852	+	0.773480i
$323$	5.51476	+	4.24666i	0.306849	+	0.236290i
$324$	27.1519	+	13.9046i	1.50844	+	0.772479i
$325$	−9.01031	+	33.6269i	−0.499802	+	1.86529i
$326$	16.6646	−	2.19394i	0.922967	−	0.121511i
$327$	13.2199	+	16.7870i	0.731061	+	0.928322i
$328$	20.9677	+	8.68512i	1.15775	+	0.479556i
$329$	−7.11176	+	1.14207i	−0.392084	+	0.0629643i
$330$	0.719966	+	57.2344i	0.0396328	+	3.15065i
$331$	−6.62945	+	1.77636i	−0.364388	+	0.0976374i	−0.436367	−	0.899769i	$-0.643735\pi$
$331$	−6.62945	+	1.77636i	−0.364388	+	0.0976374i	0.0719794	+	0.997406i	$0.477068\pi$
$332$	5.56164	−	20.7563i	0.305235	−	1.13915i
$333$	−13.4217	+	2.11172i	−0.735503	+	0.115721i
$334$	−28.5078	−	3.75313i	−1.55988	−	0.205362i
$335$	11.1343	−	26.8806i	0.608333	−	1.46865i
$336$	−3.23830	−	0.292209i	−0.176664	−	0.0159413i
$337$	10.4657	+	4.33505i	0.570105	+	0.236145i	0.649065	−	0.760733i	$-0.275160\pi$
$337$	10.4657	+	4.33505i	0.570105	+	0.236145i	−0.0789606	+	0.996878i	$0.525160\pi$
$338$	−53.0853	+	14.2242i	−2.88746	+	0.773693i
$339$	−24.3305	+	3.51506i	−1.32145	+	0.190912i
$340$	11.7826	+	44.2767i	0.639003	+	2.40124i
$341$	10.0651	−	17.4333i	0.545056	−	0.944065i
$342$	11.7534	−	0.295745i	0.635552	−	0.0159920i
$343$	8.51427	+	16.4471i	0.459727	+	0.888060i
$344$	1.60739			0.0866645
$345$	16.9938	−	4.78337i	0.914916	−	0.257528i
$346$	23.6352	−	30.8020i	1.27063	−	1.65592i
$347$	0.483477	+	0.370985i	0.0259544	+	0.0199155i	0.621657	−	0.783289i	$-0.286460\pi$
$347$	0.483477	+	0.370985i	0.0259544	+	0.0199155i	−0.595703	+	0.803205i	$0.703126\pi$
$348$	2.81257	−	23.6596i	0.150770	−	1.26829i
$349$	5.44602	−	5.44602i	0.291519	−	0.291519i	−0.546161	−	0.837680i	$-0.683911\pi$
$349$	5.44602	−	5.44602i	0.291519	−	0.291519i	0.837680	+	0.546161i	$0.183911\pi$
$350$	22.2799	+	27.3927i	1.19091	+	1.46420i
$351$	21.3953	−	23.0742i	1.14200	−	1.23161i
$352$	12.6983	+	16.5487i	0.676819	+	0.882048i
$353$	−4.13845	+	2.38933i	−0.220267	+	0.127171i	−0.606074	−	0.795408i	$-0.707257\pi$
$353$	−4.13845	+	2.38933i	−0.220267	+	0.127171i	0.385807	+	0.922580i	$0.373923\pi$
$354$	−7.16357	−	1.82322i	−0.380740	−	0.0969028i
$355$	23.3746	−	6.26320i	1.24059	−	0.332416i
$356$	−32.5485			−1.72507
$357$	8.79878	−	16.7207i	0.465681	−	0.884953i
$358$	−8.31329			−0.439371
$359$	−9.33068	+	2.50015i	−0.492455	+	0.131953i	−0.496496	−	0.868039i	$-0.665380\pi$
$359$	−9.33068	+	2.50015i	−0.492455	+	0.131953i	0.00404135	+	0.999992i	$0.498714\pi$
$360$	25.6480	+	18.6744i	1.35177	+	0.984229i
$361$	−13.9865	+	8.07510i	−0.736131	+	0.425005i
$362$	−23.3464	−	30.4256i	−1.22706	−	1.59913i
$363$	13.5993	−	0.171069i	0.713777	−	0.00897877i
$364$	−19.3528	+	50.7415i	−1.01436	+	2.65958i
$365$	−30.9201	+	30.9201i	−1.61843	+	1.61843i
$366$	17.4697	+	2.07673i	0.913156	+	0.108553i
$367$	−19.1453	−	14.6907i	−0.999377	−	0.766849i	−0.0268497	−	0.999639i	$-0.508548\pi$
$367$	−19.1453	−	14.6907i	−0.999377	−	0.766849i	−0.972527	+	0.232791i	$0.925214\pi$
$368$	−1.34284	+	1.75003i	−0.0700005	+	0.0912265i
$369$	−2.22781	+	20.9897i	−0.115975	+	1.09268i
$370$	−34.4704			−1.79203
$371$	−2.77372	−	6.19401i	−0.144004	−	0.321577i
$372$	−10.7314	−	25.0133i	−0.556398	−	1.29688i
$373$	1.60982	−	2.78829i	0.0833533	−	0.144372i	−0.821335	−	0.570446i	$-0.806770\pi$
$373$	1.60982	−	2.78829i	0.0833533	−	0.144372i	0.904688	+	0.426074i	$0.140104\pi$
$374$	40.1625	−	10.6878i	2.07675	−	0.552652i
$375$	−0.607901	−	4.20777i	−0.0313919	−	0.217289i
$376$	−8.48243	+	2.27286i	−0.437448	+	0.117214i
$377$	−22.7067	−	9.40542i	−1.16945	−	0.484404i
$378$	−6.24570	−	31.2986i	−0.321244	−	1.60982i
$379$	−10.3189	+	24.9121i	−0.530048	+	1.27965i	0.401443	+	0.915884i	$0.368509\pi$
$379$	−10.3189	+	24.9121i	−0.530048	+	1.27965i	−0.931491	+	0.363764i	$0.881491\pi$
$380$	18.5988	+	2.44858i	0.954097	+	0.125609i
$381$	−12.4842	+	7.41866i	−0.639584	+	0.380070i
$382$	−6.70011	+	25.0051i	−0.342807	+	1.27937i
$383$	−27.3182	+	7.31990i	−1.39590	+	0.374029i	−0.876869	−	0.480729i	$-0.840372\pi$
$383$	−27.3182	+	7.31990i	−1.39590	+	0.374029i	−0.519027	+	0.854758i	$0.673705\pi$
$384$	33.9071	−	0.426526i	1.73032	−	0.0217661i
$385$	29.2181	−	23.7645i	1.48909	−	1.21115i
$386$	−27.0288	−	11.1957i	−1.37573	−	0.569846i
$387$	0.423118	+	1.43381i	0.0215083	+	0.0728845i
$388$	−27.8509	+	3.66665i	−1.41392	+	0.186146i
$389$	3.26530	−	12.1863i	0.165557	−	0.617869i	−0.832411	−	0.554159i	$-0.813040\pi$
$389$	3.26530	−	12.1863i	0.165557	−	0.617869i	0.997968	−	0.0637100i	$-0.0202933\pi$
$390$	62.7199	−	49.3924i	3.17595	−	2.50108i
$391$	−6.39017	−	11.1120i	−0.323165	−	0.561959i
$392$	12.3791	+	18.8838i	0.625237	+	0.953778i
$393$	−27.3998	+	11.7553i	−1.38214	+	0.592976i
$394$	20.8605	−	16.0068i	1.05094	−	0.806411i
$395$	−29.1773	+	16.8455i	−1.46807	+	0.847591i
$396$	25.9874	−	35.6917i	1.30591	−	1.79358i
$397$	2.83855	+	0.373702i	0.142463	+	0.0187556i	0.201420	−	0.979505i	$-0.435444\pi$
$397$	2.83855	+	0.373702i	0.142463	+	0.0187556i	−0.0589575	+	0.998260i	$0.518778\pi$
$398$	2.60000	+	6.27696i	0.130326	+	0.314636i
$399$	−4.95644	−	5.93966i	−0.248133	−	0.297355i
$400$	2.88418	+	2.88418i	0.144209	+	0.144209i
$401$	3.41063	−	25.9063i	0.170319	−	1.29370i	−0.666205	−	0.745769i	$-0.732082\pi$
$401$	3.41063	−	25.9063i	0.170319	−	1.29370i	0.836523	−	0.547931i	$-0.184584\pi$
$402$	−30.6768	+	18.2296i	−1.53002	+	0.909208i
$403$	−27.8363	+	3.66471i	−1.38662	+	0.182552i
$404$	17.8383	+	10.2989i	0.887486	+	0.512390i
$405$	−9.90640	+	27.7940i	−0.492253	+	1.38110i
$406$	−21.2265	+	13.0704i	−1.05345	+	0.648675i
$407$			19.6642i			0.974718i
$408$	8.58369	−	21.3769i	0.424956	−	1.05831i
$409$	−8.93049	+	5.15602i	−0.441584	+	0.254949i	−0.704269	−	0.709933i	$-0.748725\pi$
$409$	−8.93049	+	5.15602i	−0.441584	+	0.254949i	0.262685	+	0.964882i	$0.415392\pi$
$410$	−13.8600	+	51.7263i	−0.684497	+	2.55458i
$411$	−1.93270	−	6.86629i	−0.0953333	−	0.338689i
$412$	52.7285			2.59774
$413$	1.98783	+	4.43903i	0.0978146	+	0.218430i
$414$	−20.2062	−	7.78015i	−0.993079	−	0.382373i
$415$	20.6074	+	2.71301i	1.01158	+	0.133176i
$416$	7.52987	−	28.1018i	0.369182	−	1.37781i
$417$	−14.0511	−	10.5036i	−0.688083	−	0.514364i
$418$	2.22105	−	16.8706i	0.108635	−	0.825166i
$419$	−13.7261	+	5.68555i	−0.670566	+	0.277757i	−0.691877	−	0.722016i	$-0.743216\pi$
$419$	−13.7261	+	5.68555i	−0.670566	+	0.277757i	0.0213112	+	0.999773i	$0.493216\pi$
$420$	−2.08261	−	50.8809i	−0.101621	−	2.48273i
$421$			27.5348i			1.34196i	0.741474	+	0.670982i	$0.234127\pi$
$421$			27.5348i			1.34196i	−0.741474	+	0.670982i	$0.765873\pi$
$422$	10.1481	+	13.2253i	0.494003	+	0.643798i
$423$	−4.26028	−	6.96813i	−0.207142	−	0.338802i
$424$	−4.13713	−	7.16572i	−0.200917	−	0.347998i
$425$	−21.9137	+	9.03300i	−1.06297	+	0.438165i
$426$	−27.5609	−	11.0120i	−1.33533	−	0.533534i
$427$	−6.06950	−	9.85691i	−0.293724	−	0.477009i
$428$	10.6493	−	25.7096i	0.514752	−	1.24272i
$429$	−28.1767	−	35.7796i	−1.36039	−	1.72746i
$430$	0.495050	+	3.76028i	0.0238734	+	0.181337i
$431$	11.6923	−	15.2378i	0.563201	−	0.733977i	−0.421769	−	0.906703i	$-0.638591\pi$
$431$	11.6923	−	15.2378i	0.563201	−	0.733977i	0.984970	+	0.172726i	$0.0552575\pi$
$432$	−1.08789	−	3.52265i	−0.0523411	−	0.169484i
$433$	−15.5659	+	15.5659i	−0.748048	+	0.748048i	−0.974112	−	0.226064i	$-0.927414\pi$
$433$	−15.5659	+	15.5659i	−0.748048	+	0.748048i	0.226064	+	0.974112i	$0.427414\pi$
$434$	−13.5341	+	25.0549i	−0.649656	+	1.20268i
$435$	23.0445	−	0.289883i	1.10490	−	0.0138988i
$436$	5.45783	−	41.4564i	0.261383	−	1.98540i
$437$	−5.20338	+	0.685038i	−0.248911	+	0.0327698i
$438$	53.0794	−	7.66843i	2.53623	−	0.366412i
$439$	1.38174	+	1.80072i	0.0659470	+	0.0859438i	0.825162	−	0.564896i	$-0.191084\pi$
$439$	1.38174	+	1.80072i	0.0659470	+	0.0859438i	−0.759215	+	0.650840i	$0.774417\pi$
$440$	32.4685	−	32.4685i	1.54788	−	1.54788i
$441$	−13.5860	+	16.0131i	−0.646953	+	0.762530i
$442$	−45.9268	−	35.3661i	−2.18452	−	1.68219i
$443$	19.4116	+	11.2073i	0.922271	+	0.532474i	0.884359	−	0.466808i	$-0.154596\pi$
$443$	19.4116	+	11.2073i	0.922271	+	0.532474i	0.0379123	+	0.999281i	$0.487929\pi$
$444$	21.2957	+	15.9192i	1.01065	+	0.755491i
$445$	−4.10937	−	31.2138i	−0.194803	−	1.47967i
$446$	−11.9111	−	6.87688i	−0.564007	−	0.325630i
$447$	−14.1056	−	13.7551i	−0.667170	−	0.650594i
$448$	−20.9882	−	25.8046i	−0.991599	−	1.21915i
$449$	28.2774	−	11.7129i	1.33449	−	0.552766i	0.402560	−	0.915393i	$-0.368120\pi$
$449$	28.2774	−	11.7129i	1.33449	−	0.552766i	0.931934	+	0.362628i	$0.118120\pi$
$450$	−19.1400	+	35.1657i	−0.902270	+	1.65773i
$451$	29.5081	+	7.90668i	1.38948	+	0.372311i
$452$	38.1658	+	29.2856i	1.79517	+	1.37748i
$453$	10.2247	−	18.2356i	0.480396	−	0.856781i
$454$	−23.4305	−	9.70523i	−1.09965	−	0.455489i
$455$	−51.1041	−	12.1529i	−2.39580	−	0.569736i
$456$	−6.75254	−	6.58476i	−0.316217	−	0.308360i
$457$	−1.13176	−	4.22380i	−0.0529416	−	0.197581i	0.934390	−	0.356252i	$-0.115946\pi$
$457$	−1.13176	−	4.22380i	−0.0529416	−	0.197581i	−0.987331	+	0.158671i	$0.949279\pi$
$458$	28.8007	+	49.8842i	1.34577	+	2.33094i
$459$	21.3279	+	2.02963i	0.995503	+	0.0947351i
$460$	−29.9191	−	17.2738i	−1.39498	−	0.805395i
$461$	−3.58489	+	3.58489i	−0.166965	+	0.166965i	−0.785644	−	0.618679i	$-0.787668\pi$
$461$	−3.58489	+	3.58489i	−0.166965	+	0.166965i	0.618679	+	0.785644i	$0.287668\pi$
$462$	−46.1530	+	1.88909i	−2.14723	+	0.0878883i
$463$		−	17.1459i		−	0.796836i	−0.917204	−	0.398418i	$-0.869559\pi$
$463$		−	17.1459i		−	0.796836i	0.917204	−	0.398418i	$-0.130441\pi$
$464$	−2.28454	+	1.75299i	−0.106057	+	0.0813805i
$465$	22.6327	−	13.4494i	1.04957	−	0.623700i
$466$	16.2880	−	21.2270i	0.754529	−	0.983322i
$467$	10.2418	−	2.74427i	0.473932	−	0.126990i	−0.0139438	−	0.999903i	$-0.504439\pi$
$467$	10.2418	−	2.74427i	0.473932	−	0.126990i	0.487876	+	0.872913i	$0.337772\pi$
$468$	−61.5587	+	1.54897i	−2.84555	+	0.0716011i
$469$	21.9384	+	8.36729i	1.01302	+	0.386366i
$470$	−7.92953	−	19.1436i	−0.365762	−	0.883027i
$471$	−7.62067	+	2.14504i	−0.351142	+	0.0988385i
$472$	2.96493	+	5.13541i	0.136472	+	0.236377i
$473$	2.14511	−	0.282410i	0.0986325	−	0.0129852i
$474$	41.0321	+	4.87774i	1.88467	+	0.224042i
$475$			9.70456i			0.445276i
$476$	−35.4475	+	10.5168i	−1.62473	+	0.482038i
$477$	5.30287	−	5.57662i	0.242802	−	0.255336i
$478$	−7.49077	−	27.9559i	−0.342620	−	1.27867i
$479$	−2.67996	−	20.3563i	−0.122450	−	0.930102i	−0.936834	−	0.349775i	$-0.886258\pi$
$479$	−2.67996	−	20.3563i	−0.122450	−	0.930102i	0.814383	−	0.580327i	$-0.197075\pi$
$480$	3.90076	+	27.0003i	0.178045	+	1.23239i
$481$	21.7589	−	16.6962i	0.992120	−	0.761281i
$482$	−9.40637	+	3.89624i	−0.428448	+	0.177469i
$483$	4.24707	+	13.5991i	0.193248	+	0.618780i
$484$	−18.8194	−	18.8194i	−0.855426	−	0.855426i
$485$	−7.03258	−	26.2459i	−0.319333	−	1.19177i
$486$	30.1413	−	20.0285i	1.36724	−	0.908511i
$487$	−5.86216	−	4.49819i	−0.265640	−	0.203833i	0.467350	−	0.884073i	$-0.345209\pi$
$487$	−5.86216	−	4.49819i	−0.265640	−	0.203833i	−0.732990	+	0.680240i	$0.761876\pi$
$488$	−8.59143	−	11.1966i	−0.388916	−	0.506845i
$489$	4.65292	−	11.6453i	0.210413	−	0.526620i
$490$	−40.3638	+	34.7752i	−1.82345	+	1.57098i
$491$	12.9606	+	12.9606i	0.584903	+	0.584903i	0.936247	−	0.351343i	$-0.114275\pi$
$491$	12.9606	+	12.9606i	0.584903	+	0.584903i	−0.351343	+	0.936247i	$0.614275\pi$
$492$	32.4510	−	25.5554i	1.46301	−	1.15213i
$493$	−4.30326	−	16.1708i	−0.193809	−	0.728295i
$494$	−20.5535	+	11.8666i	−0.924745	+	0.533902i
$495$	37.5091	+	20.4155i	1.68591	+	0.917608i
$496$	−1.25886	+	3.03915i	−0.0565243	+	0.136462i
$497$	5.58666	+	18.7124i	0.250596	+	0.839368i
$498$	−18.2511	−	17.7976i	−0.817851	−	0.797531i
$499$	−3.96850	+	30.1437i	−0.177654	+	1.34942i	0.637623	+	0.770348i	$0.279918\pi$
$499$	−3.96850	+	30.1437i	−0.177654	+	1.34942i	−0.815277	+	0.579071i	$0.803416\pi$
$500$	−5.06472	+	6.60047i	−0.226501	+	0.295182i
$501$	−12.8445	+	17.1826i	−0.573851	+	0.767660i
$502$	13.3901	+	49.9725i	0.597629	+	2.23038i
$503$	11.0148	+	26.5921i	0.491126	+	1.18568i	0.954148	+	0.299336i	$0.0967651\pi$
$503$	11.0148	+	26.5921i	0.491126	+	1.18568i	−0.463022	+	0.886347i	$0.653235\pi$
$504$	−14.4779	+	21.1164i	−0.644895	+	0.940598i
$505$	−7.62445	+	18.4070i	−0.339283	+	0.819103i
$506$	−15.6687	+	27.1390i	−0.696558	+	1.20647i
$507$	−10.1134	+	39.7365i	−0.449152	+	1.76476i
$508$	27.4501	+	7.35522i	1.21790	+	0.326335i
$509$	16.5651	−	28.6915i	0.734233	−	1.27173i	−0.220826	−	0.975313i	$-0.570875\pi$
$509$	16.5651	−	28.6915i	0.734233	−	1.27173i	0.955059	−	0.296416i	$-0.0957913\pi$
$510$	52.6522	+	13.4967i	2.33148	+	0.597644i
$511$	−25.6492	−	24.2356i	−1.13465	−	1.07212i
$512$	−5.64700	−	5.64700i	−0.249564	−	0.249564i
$513$	4.09619	−	7.75667i	0.180851	−	0.342465i
$514$	11.0322	+	19.1083i	0.486609	+	0.842831i
$515$	6.65717	+	50.5662i	0.293350	+	2.22821i
$516$	1.43074	−	2.55171i	0.0629849	−	0.112333i
$517$	−10.9208	+	4.52353i	−0.480295	+	0.198945i
$518$	−0.787952	−	27.8063i	−0.0346206	−	1.22174i
$519$	−11.4208	−	26.6202i	−0.501319	−	1.16850i
$520$	−63.4951	−	8.35929i	−2.78444	−	0.366579i
$521$	−6.24984	−	4.79567i	−0.273810	−	0.210102i	0.462724	−	0.886503i	$-0.346872\pi$
$521$	−6.24984	−	4.79567i	−0.273810	−	0.210102i	−0.736534	+	0.676401i	$0.763539\pi$
$522$	−22.8503	−	16.6375i	−1.00013	−	0.728202i
$523$	10.8618	−	18.8132i	0.474954	−	0.822645i	−0.524635	−	0.851328i	$-0.675798\pi$
$523$	10.8618	−	18.8132i	0.474954	−	0.822645i	0.999589	+	0.0286830i	$0.00913135\pi$
$524$	53.9040	+	22.3278i	2.35481	+	0.975393i
$525$	25.9559	−	4.50384i	1.13281	−	0.196564i
$526$	−16.7355			−0.729703
$527$	−13.4937	−	13.5400i	−0.587796	−	0.589813i
$528$	−5.28110	+	0.762966i	−0.229830	+	0.0332038i
$529$	−12.8803	−	3.45126i	−0.560011	−	0.150055i
$530$	15.4891	−	11.8852i	0.672805	−	0.516261i
$531$	−3.80038	+	3.99657i	−0.164922	+	0.173436i
$532$	−1.55005	+	15.0591i	−0.0672033	+	0.652894i
$533$	−16.3054	−	39.3647i	−0.706265	−	1.70508i
$534$	−18.8843	+	33.6800i	−0.817206	+	1.45748i
$535$	25.9999	+	6.96664i	1.12407	+	0.301194i
$536$	27.6509	+	7.40904i	1.19434	+	0.320022i
$537$	−3.03340	+	5.41003i	−0.130901	+	0.233460i
$538$	27.6967	+	66.8658i	1.19409	+	2.88279i
$539$	19.8381	+	23.0262i	0.854487	+	0.991809i
$540$	52.4748	−	24.0937i	2.25816	−	1.03683i
$541$	8.13479	−	6.24205i	0.349742	−	0.268367i	−0.418918	−	0.908024i	$-0.637591\pi$
$541$	8.13479	−	6.24205i	0.349742	−	0.268367i	0.768660	+	0.639658i	$0.220924\pi$
$542$	−9.16971	−	2.45702i	−0.393873	−	0.105538i
$543$	−28.3188	+	4.09124i	−1.21528	+	0.175572i
$544$	18.3132	−	7.54883i	0.785171	−	0.323653i
$545$	40.4454			1.73249
$546$	41.2772	+	49.4654i	1.76650	+	2.11692i
$547$	−20.5912	−	8.52917i	−0.880418	−	0.364681i	−0.103759	−	0.994602i	$-0.533087\pi$
$547$	−20.5912	−	8.52917i	−0.880418	−	0.364681i	−0.776659	+	0.629921i	$0.783087\pi$
$548$	−6.97942	+	12.0887i	−0.298146	+	0.516404i
$549$	7.72592	−	10.6110i	0.329734	−	0.452865i
$550$	45.9715	+	35.2752i	1.96023	+	1.50414i
$551$	−6.79266	−	0.894270i	−0.289377	−	0.0380972i
$552$	6.84837	+	15.9625i	0.291486	+	0.679410i
$553$	−14.2558	−	23.1515i	−0.606218	−	0.984501i
$554$	−35.0803	+	14.5307i	−1.49042	+	0.617351i
$555$	−12.5777	+	22.4322i	−0.533895	+	0.952196i
$556$	4.48097	+	34.0364i	0.190036	+	1.44346i
$557$	−19.8629	−	34.4036i	−0.841619	−	1.45773i	−0.888525	−	0.458828i	$-0.848269\pi$
$557$	−19.8629	−	34.4036i	−0.841619	−	1.45773i	0.0469059	−	0.998899i	$-0.485064\pi$
$558$	−32.1092	−	3.40802i	−1.35929	−	0.144273i
$559$	−2.13384	−	2.13384i	−0.0902516	−	0.0902516i
$560$	−4.22690	+	4.47344i	−0.178619	+	0.189037i
$561$	7.69942	−	30.0363i	0.325070	−	1.26813i
$562$	−27.6515	+	47.8939i	−1.16641	+	2.02028i
$563$	17.5266	+	4.69623i	0.738656	+	0.197922i	0.608481	−	0.793569i	$-0.291779\pi$
$563$	17.5266	+	4.69623i	0.738656	+	0.197922i	0.130175	+	0.991491i	$0.458446\pi$
$564$	−3.94210	+	15.4889i	−0.165992	+	0.652199i
$565$	−23.2661	+	40.2981i	−0.978814	+	1.69536i
$566$	5.81296	−	14.0337i	0.244337	−	0.589881i
$567$	−22.6471	−	7.35588i	−0.951089	−	0.308918i
$568$	9.11131	+	21.9967i	0.382302	+	0.922959i
$569$	5.76958	+	21.5323i	0.241873	+	0.902683i	0.974929	+	0.222515i	$0.0714266\pi$
$569$	5.76958	+	21.5323i	0.241873	+	0.902683i	−0.733056	+	0.680168i	$0.761907\pi$
$570$	13.3246	−	17.8247i	0.558104	−	0.746595i
$571$	3.16932	−	4.13034i	0.132632	−	0.172849i	−0.722316	−	0.691563i	$-0.756922\pi$
$571$	3.16932	−	4.13034i	0.132632	−	0.172849i	0.854948	+	0.518714i	$0.173589\pi$
$572$	−11.6328	+	88.3598i	−0.486391	+	3.69451i
$573$	13.8278	+	13.4842i	0.577665	+	0.563312i
$574$	−42.0430	−	9.99809i	−1.75484	−	0.417312i
$575$	6.83939	−	16.5118i	0.285222	−	0.688588i
$576$	18.0304	−	33.1270i	0.751266	−	1.38029i
$577$	−12.4312	+	7.17716i	−0.517518	+	0.298789i	−0.735919	−	0.677070i	$-0.763249\pi$
$577$	−12.4312	+	7.17716i	−0.517518	+	0.298789i	0.218401	+	0.975859i	$0.429916\pi$
$578$	0.135242	−	39.4656i	0.00562534	−	1.64155i
$579$	−17.1482	+	13.5044i	−0.712656	+	0.561222i
$580$	−31.8902	−	31.8902i	−1.32417	−	1.32417i
$581$	−1.71745	+	16.6854i	−0.0712518	+	0.692227i
$582$	−12.3648	+	30.9465i	−0.512536	+	1.28277i
$583$	−6.78012	−	8.83603i	−0.280804	−	0.365951i
$584$	−34.1322	−	26.1905i	−1.41240	−	1.08377i
$585$	−9.25747	−	58.8388i	−0.382749	−	2.43268i
$586$	−12.1817	−	45.4628i	−0.503222	−	1.87805i
$587$	22.7221	+	22.7221i	0.937841	+	0.937841i	0.998178	−	0.0603370i	$-0.0192175\pi$
$587$	22.7221	+	22.7221i	0.937841	+	0.937841i	−0.0603370	+	0.998178i	$0.519218\pi$
$588$	40.9966	−	2.84306i	1.69067	−	0.117246i
$589$	−7.23087	+	2.99512i	−0.297943	+	0.123412i
$590$	−11.1005	+	8.51771i	−0.457000	+	0.350669i
$591$	−2.80505	−	19.4160i	−0.115384	−	0.798667i
$592$	−0.419432	−	3.18591i	−0.0172386	−	0.130940i
$593$	6.39678	+	23.8731i	0.262684	+	0.980352i	0.963652	+	0.267159i	$0.0860849\pi$
$593$	6.39678	+	23.8731i	0.262684	+	0.980352i	−0.700968	+	0.713193i	$0.747248\pi$
$594$	−21.8549	−	47.5988i	−0.896716	−	1.95300i
$595$	−14.5610	−	32.6661i	−0.596941	−	1.33918i
$596$			38.5550i			1.57928i
$597$	5.03356	+	0.598371i	0.206010	+	0.0244897i
$598$	43.3336	−	5.70498i	1.77204	−	0.233294i
$599$	−5.81744	−	10.0761i	−0.237694	−	0.411699i	0.722358	−	0.691519i	$-0.243058\pi$
$599$	−5.81744	−	10.0761i	−0.237694	−	0.411699i	−0.960052	+	0.279821i	$0.909725\pi$
$600$	30.9166	−	8.70231i	1.26216	−	0.355271i
$601$	−0.744998	−	1.79858i	−0.0303891	−	0.0733658i	0.907956	−	0.419065i	$-0.137642\pi$
$601$	−0.744998	−	1.79858i	−0.0303891	−	0.0733658i	−0.938346	+	0.345699i	$0.887642\pi$
$602$	−3.02200	+	0.485299i	−0.123167	+	0.0197793i
$603$	0.669705	+	26.6152i	0.0272725	+	1.08386i
$604$	−39.5179	+	10.5888i	−1.60796	+	0.430852i
$605$	15.6716	−	20.4237i	0.637143	−	0.830341i
$606$	21.0066	−	12.4831i	0.853333	−	0.507089i
$607$	23.5081	−	18.0384i	0.954164	−	0.732156i	−0.00931008	−	0.999957i	$-0.502964\pi$
$607$	23.5081	−	18.0384i	0.954164	−	0.732156i	0.963474	+	0.267801i	$0.0862969\pi$
$608$		−	8.11006i		−	0.328906i
$609$	0.760610	+	18.5827i	0.0308215	+	0.753011i
$610$	23.5469	−	23.5469i	0.953388	−	0.953388i
$611$	14.2778	+	8.24332i	0.577620	+	0.333489i
$612$	−26.2952	−	32.6542i	−1.06292	−	1.31997i
$613$	−21.9366	−	37.9953i	−0.886011	−	1.53462i	−0.844550	−	0.535476i	$-0.820132\pi$
$613$	−21.9366	−	37.9953i	−0.886011	−	1.53462i	−0.0414608	−	0.999140i	$-0.513201\pi$
$614$	−2.07748	−	7.75324i	−0.0838401	−	0.312895i
$615$	28.6045	+	27.8938i	1.15345	+	1.12479i
$616$	26.9336	+	25.4493i	1.08519	+	1.02538i
$617$	−7.61949	−	3.15610i	−0.306749	−	0.127060i	0.223999	−	0.974589i	$-0.428089\pi$
$617$	−7.61949	−	3.15610i	−0.306749	−	0.127060i	−0.530748	+	0.847530i	$0.678089\pi$
$618$	30.5926	−	54.5615i	1.23061	−	2.19479i
$619$	33.9988	+	26.0882i	1.36653	+	1.04857i	0.992641	+	0.121098i	$0.0386417\pi$
$619$	33.9988	+	26.0882i	1.36653	+	1.04857i	0.373886	+	0.927475i	$0.378025\pi$
$620$	−49.7645	−	13.3344i	−1.99859	−	0.535521i
$621$	−12.4360	+	10.3107i	−0.499040	+	0.413754i
$622$	−0.510468	+	0.211443i	−0.0204679	+	0.00847808i
$623$	25.0853	−	4.02842i	1.00502	−	0.161395i
$624$	5.32824	+	5.19586i	0.213300	+	0.208001i
$625$	17.9233	+	10.3480i	0.716932	+	0.413921i
$626$	10.6243	+	80.6996i	0.424632	+	3.22540i
$627$	−10.1684	−	7.60121i	−0.406087	−	0.303563i
$628$	13.4169	+	7.74623i	0.535391	+	0.309108i
$629$	18.0287	+	4.86389i	0.718850	+	0.193936i
$630$	−53.8580	−	27.3656i	−2.14576	−	1.09027i
$631$	33.5772	−	33.5772i	1.33669	−	1.33669i	0.437438	−	0.899248i	$-0.355886\pi$
$631$	33.5772	−	33.5772i	1.33669	−	1.33669i	0.899248	−	0.437438i	$-0.144114\pi$
$632$	−20.1792	−	26.2980i	−0.802685	−	1.04608i
$633$	12.3095	−	1.77837i	0.489260	−	0.0706838i
$634$	−30.1257	+	3.96613i	−1.19645	+	0.157515i
$635$	−3.58793	+	27.2530i	−0.142383	+	1.08150i
$636$	−15.0580	+	0.189418i	−0.597088	+	0.00751091i
$637$	8.63521	−	41.5021i	0.342140	−	1.64437i
$638$	−28.9269	+	28.9269i	−1.14523	+	1.14523i
$639$	−17.2229	+	13.9177i	−0.681326	+	0.550574i
$640$	39.0742	−	50.9224i	1.54454	−	2.01289i
$641$	4.59875	+	34.9309i	0.181640	+	1.37969i	0.802913	+	0.596096i	$0.203282\pi$
$641$	4.59875	+	34.9309i	0.181640	+	1.37969i	−0.621274	+	0.783593i	$0.713385\pi$
$642$	−20.4248	−	25.9360i	−0.806102	−	1.02361i
$643$	1.55428	−	3.75236i	0.0612948	−	0.147979i	−0.890265	−	0.455444i	$-0.849481\pi$
$643$	1.55428	−	3.75236i	0.0612948	−	0.147979i	0.951559	+	0.307465i	$0.0994807\pi$
$644$	13.2504	−	24.5297i	0.522138	−	0.966608i
$645$	2.62771	+	1.04991i	0.103466	+	0.0413401i
$646$	−14.9180	−	6.20921i	−0.586941	−	0.244298i
$647$	−15.8636	−	27.4766i	−0.623662	−	1.08021i	−0.988798	−	0.149261i	$-0.952311\pi$
$647$	−15.8636	−	27.4766i	−0.623662	−	1.08021i	0.365135	−	0.930954i	$-0.381023\pi$
$648$	−28.3842	−	6.09396i	−1.11504	−	0.239393i
$649$	4.85907	+	6.33246i	0.190735	+	0.248571i
$650$		−	80.8195i		−	3.17000i
$651$	11.3666	+	17.9497i	0.445492	+	0.703506i
$652$	−22.6725	+	9.39126i	−0.887924	+	0.367790i
$653$	−3.55135	+	26.9752i	−0.138975	+	1.05562i	0.769785	+	0.638303i	$0.220363\pi$
$653$	−3.55135	+	26.9752i	−0.138975	+	1.05562i	−0.908760	+	0.417318i	$0.862970\pi$
$654$	−39.7310	−	29.7002i	−1.55360	−	1.16137i
$655$	−14.6066	+	54.5125i	−0.570726	+	2.12998i
$656$	−4.94942	−	0.651604i	−0.193242	−	0.0254409i
$657$	14.3775	−	37.3405i	0.560920	−	1.45679i
$658$	15.2613	−	6.83413i	0.594949	−	0.266422i
$659$	−2.40981			−0.0938730			−0.0469365	−	0.998898i	$-0.514946\pi$
$659$	−2.40981			−0.0938730			−0.0469365	+	0.998898i	$0.514946\pi$
$660$	−22.6431	−	80.4438i	−0.881382	−	3.13127i
$661$	−2.25710	+	8.42362i	−0.0877911	+	0.327641i	−0.995828	−	0.0912491i	$-0.970914\pi$
$661$	−2.25710	+	8.42362i	−0.0877911	+	0.327641i	0.908037	+	0.418890i	$0.137581\pi$
$662$	13.7987	−	7.96667i	0.536301	−	0.309633i
$663$	−39.7732	+	16.9832i	−1.54466	+	0.659572i
$664$			20.4501i			0.793618i
$665$	−14.6373	+	0.414779i	−0.567609	+	0.0160844i
$666$	28.8282	−	12.7998i	1.11707	−	0.495983i
$667$	10.9271	+	6.30874i	0.423098	+	0.244276i
$668$	41.6219	−	5.47963i	1.61040	−	0.212013i
$669$	−8.82145	+	5.24211i	−0.341057	+	0.202672i
$670$	−8.81647	+	66.9677i	−0.340610	+	2.58719i
$671$	−13.4327	−	13.4327i	−0.518566	−	0.518566i
$672$	−21.6912	+	3.76383i	−0.836758	+	0.145193i
$673$	10.7813	+	26.0283i	0.415588	+	1.00332i	0.983611	+	0.180305i	$0.0577085\pi$
$673$	10.7813	+	26.0283i	0.415588	+	1.00332i	−0.568023	+	0.823013i	$0.692291\pi$
$674$	−26.0733	−	3.43261i	−1.00431	−	0.132219i
$675$	15.9008	+	25.2872i	0.612024	+	0.973305i
$676$	69.4895	−	40.1198i	2.67267	−	1.54307i
$677$	17.1652	−	13.1713i	0.659712	−	0.506215i	−0.223793	−	0.974637i	$-0.571844\pi$
$677$	17.1652	−	13.1713i	0.659712	−	0.506215i	0.883505	+	0.468422i	$0.155177\pi$
$678$	52.4472	−	22.5013i	2.01422	−	0.864158i
$679$	21.0111	−	6.27293i	0.806332	−	0.240733i
$680$	−21.7370	−	37.7990i	−0.833577	−	1.44953i
$681$	−14.8653	+	11.7065i	−0.569640	+	0.448596i
$682$	−12.0953	+	45.1403i	−0.463154	+	1.72851i
$683$	36.1706	−	4.76194i	1.38403	−	0.182211i	0.598543	−	0.801091i	$-0.295747\pi$
$683$	36.1706	−	4.76194i	1.38403	−	0.182211i	0.785485	+	0.618880i	$0.212413\pi$
$684$	−16.4637	+	4.85846i	−0.629506	+	0.185768i
$685$	−12.4742	−	5.16697i	−0.476613	−	0.197420i
$686$	−28.9748	−	31.7654i	−1.10626	−	1.21281i
$687$	42.9721	−	0.540556i	1.63949	−	0.0206235i
$688$	−0.341518	+	0.0915095i	−0.0130203	+	0.00348877i
$689$	−4.02051	+	15.0047i	−0.153169	+	0.571635i
$690$	−35.2331	+	20.9371i	−1.34130	+	0.797062i
$691$	16.6619	+	2.19358i	0.633850	+	0.0834479i	0.440603	−	0.897702i	$-0.354765\pi$
$691$	16.6619	+	2.19358i	0.633850	+	0.0834479i	0.193247	+	0.981150i	$0.438098\pi$
$692$	−21.6925	+	52.3703i	−0.824624	+	1.99082i
$693$	−15.6112	+	30.7242i	−0.593020	+	1.16712i
$694$	−1.30706	−	0.541404i	−0.0496155	−	0.0205514i
$695$	−32.0749	+	8.59445i	−1.21667	+	0.326006i
$696$	3.24219	+	22.4418i	0.122895	+	0.850655i
$697$	14.5478	−	25.0982i	0.551038	−	0.950660i
$698$	−8.93998	+	15.4845i	−0.338383	+	0.586097i
$699$	−7.87060	−	18.3452i	−0.297693	−	0.693878i
$700$	−41.7718	−	30.2120i	−1.57882	−	1.14191i
$701$	21.7381			0.821038			0.410519	−	0.911852i	$-0.365348\pi$
$701$	21.7381			0.821038			0.410519	+	0.911852i	$0.365348\pi$
$702$	−34.1130	+	64.5974i	−1.28751	+	2.43807i
$703$	4.65425	−	6.06554i	0.175539	−	0.228766i
$704$	−43.3063	−	33.2301i	−1.63217	−	1.25241i
$705$	−15.3514	−	1.82492i	−0.578168	−	0.0687305i
$706$	7.84449	−	7.84449i	0.295231	−	0.295231i
$707$	−15.0227	−	5.72967i	−0.564988	−	0.215486i
$708$	10.7915	−	0.135749i	0.405570	−	0.00510176i
$709$	−23.6414	−	30.8100i	−0.887870	−	1.15709i	−0.986791	−	0.162000i	$-0.948206\pi$
$709$	−23.6414	−	30.8100i	−0.887870	−	1.15709i	0.0989207	−	0.995095i	$-0.468461\pi$
$710$	−48.6523	+	28.0894i	−1.82589	+	1.05418i
$711$	18.1463	−	24.9226i	0.680539	−	0.934670i
$712$	29.9201	−	8.01707i	1.12130	−	0.300452i
$713$	14.4137			0.539799
$714$	−9.68386	+	42.7815i	−0.362409	+	1.60106i
$715$	−86.2051			−3.22389
$716$	11.7240	−	3.14143i	0.438145	−	0.117401i
$717$	−20.9261	−	5.32595i	−0.781500	−	0.198901i
$718$	19.4211	−	11.2128i	0.724788	−	0.418456i
$719$	−11.5601	−	15.0654i	−0.431118	−	0.561844i	0.526393	−	0.850241i	$-0.323544\pi$
$719$	−11.5601	−	15.0654i	−0.431118	−	0.561844i	−0.957511	+	0.288398i	$0.906877\pi$
$720$	−6.51251	−	2.50757i	−0.242707	−	0.0934515i
$721$	−40.6382	+	6.52604i	−1.51345	+	0.243042i
$722$	26.5116	−	26.5116i	0.986659	−	0.986659i
$723$	−0.896691	+	7.54306i	−0.0333483	+	0.280529i
$724$	44.4219	+	34.0861i	1.65093	+	1.26680i
$725$	14.2030	−	18.5097i	0.527485	−	0.687432i
$726$	−30.3925	+	8.55479i	−1.12797	+	0.317498i
$727$	12.9677			0.480946			0.240473	−	0.970656i	$-0.422698\pi$
$727$	12.9677			0.480946			0.240473	+	0.970656i	$0.422698\pi$
$728$	5.29178	−	51.4108i	0.196126	−	1.90541i
$729$	−2.03580	−	26.9231i	−0.0753998	−	0.997153i
$730$	50.7573	−	87.9142i	1.87861	−	3.25385i
$731$	0.271668	−	2.03655i	0.0100480	−	0.0753246i
$732$	−25.4217	+	3.67270i	−0.939614	+	0.135747i
$733$	−23.1497	+	6.20295i	−0.855054	+	0.229111i	−0.659614	−	0.751605i	$-0.729280\pi$
$733$	−23.1497	+	6.20295i	−0.855054	+	0.229111i	−0.195440	+	0.980716i	$0.562614\pi$
$734$	51.7587	+	21.4392i	1.91045	+	0.791334i
$735$	7.90245	+	38.9565i	0.291486	+	1.43693i
$736$	−5.71565	+	13.7988i	−0.210682	+	0.508630i
$737$	38.2029	+	5.02950i	1.40722	+	0.185264i
$738$	−7.61605	−	48.4062i	−0.280351	−	1.78186i
$739$	−7.19495	+	26.8519i	−0.264670	+	0.987764i	0.697781	+	0.716311i	$0.254171\pi$
$739$	−7.19495	+	26.8519i	−0.264670	+	0.987764i	−0.962452	+	0.271453i	$0.912496\pi$
$740$	48.6125	−	13.0257i	1.78703	−	0.478833i
$741$	0.222722	+	17.7055i	0.00818189	+	0.650428i
$742$	9.94154	+	12.2230i	0.364965	+	0.448719i
$743$	11.9538	+	4.95141i	0.438541	+	0.181649i	0.591020	−	0.806657i	$-0.298726\pi$
$743$	11.9538	+	4.95141i	0.438541	+	0.181649i	−0.152479	+	0.988307i	$0.548726\pi$
$744$	16.0259	+	20.3501i	0.587538	+	0.746073i
$745$	−36.9740	+	4.86772i	−1.35462	+	0.178339i
$746$	−1.93453	+	7.21977i	−0.0708282	+	0.264335i
$747$	−18.2417	+	5.38315i	−0.667429	+	0.196959i
$748$	−52.6012	+	30.2492i	−1.92329	+	1.10602i
$749$	−5.02547	+	21.1326i	−0.183627	+	0.772169i
$750$	3.89143	+	9.07033i	0.142095	+	0.331202i
$751$	−28.7790	+	22.0829i	−1.05016	+	0.805816i	−0.981430	−	0.191819i	$-0.938561\pi$
$751$	−28.7790	+	22.0829i	−1.05016	+	0.805816i	−0.0687296	+	0.997635i	$0.521895\pi$
$752$	1.67285	−	0.965820i	0.0610025	−	0.0352198i
$753$	37.4064	+	9.52038i	1.36316	+	0.346942i
$754$	56.5691	+	7.44747i	2.06013	+	0.271221i
$755$	−15.1439	−	36.5605i	−0.551142	−	1.33057i
$756$	20.6352	+	41.7792i	0.750496	+	1.51950i
$757$	27.8665	+	27.8665i	1.01282	+	1.01282i	0.999917	+	0.0129068i	$0.00410847\pi$
$757$	27.8665	+	27.8665i	1.01282	+	1.01282i	0.0129068	+	0.999917i	$0.495892\pi$
$758$	8.17081	−	62.0635i	0.296777	−	2.25425i
$759$	11.9439	+	20.0993i	0.433537	+	0.729559i
$760$	−17.7000	+	2.33025i	−0.642046	+	0.0845270i
$761$	17.6224	+	10.1743i	0.638811	+	0.368818i	0.784156	−	0.620563i	$-0.213096\pi$
$761$	17.6224	+	10.1743i	0.638811	+	0.368818i	−0.145345	+	0.989381i	$0.546429\pi$
$762$	23.5372	−	24.1369i	0.852663	−	0.874388i
$763$	0.924535	+	32.6262i	0.0334704	+	1.18115i
$764$		−	37.7958i		−	1.36740i
$765$	27.9953	−	29.3396i	1.01217	−	1.06078i
$766$	56.8607	−	32.8285i	2.05446	−	1.18614i
$767$	2.88135	−	10.7534i	0.104040	−	0.388281i
$768$	−33.8561	+	9.52971i	−1.22168	+	0.343874i
$769$	2.72364			0.0982168			0.0491084	−	0.998793i	$-0.484362\pi$
$769$	2.72364			0.0982168			0.0491084	+	0.998793i	$0.484362\pi$
$770$	−51.2402	+	70.8459i	−1.84657	+	2.55311i
$771$	16.4606	−	0.207062i	0.592813	−	0.00745714i
$772$	42.3485	+	5.57529i	1.52416	+	0.200659i
$773$	−5.71014	+	21.3105i	−0.205379	+	0.766486i	0.783954	+	0.620819i	$0.213200\pi$
$773$	−5.71014	+	21.3105i	−0.205379	+	0.766486i	−0.989334	+	0.145668i	$0.953467\pi$
$774$	−1.81032	−	2.96096i	−0.0650705	−	0.106430i
$775$	3.47884	−	26.4244i	0.124963	−	0.949192i
$776$	24.6988	−	10.2306i	0.886634	−	0.367256i
$777$	−18.3830	−	9.63333i	−0.659486	−	0.345594i
$778$			29.2887i			1.05005i
$779$	−7.23056	−	9.42304i	−0.259062	−	0.337616i
$780$	−69.7875	+	93.3572i	−2.49879	+	3.34272i
$781$	16.0241	+	27.7545i	0.573386	+	0.993134i
$782$	21.0061	+	21.0782i	0.751178	+	0.753756i
$783$	−19.1649	+	8.79951i	−0.684897	+	0.314469i
$784$	−3.70522	−	3.30746i	−0.132329	−	0.118124i
$785$	−5.73465	+	13.8447i	−0.204678	+	0.494137i
$786$	54.3786	−	42.8236i	1.93962	−	1.52747i
$787$	−7.30623	−	55.4963i	−0.260439	−	1.97823i	−0.198141	−	0.980173i	$-0.563490\pi$
$787$	−7.30623	−	55.4963i	−0.260439	−	1.97823i	−0.0622979	−	0.998058i	$-0.519843\pi$
$788$	−23.3702	+	30.4566i	−0.832529	+	1.08497i
$789$	−6.10655	+	10.8910i	−0.217399	+	0.387728i
$790$	55.3060	−	55.3060i	1.96770	−	1.96770i
$791$	−33.0392	−	17.8470i	−1.17474	−	0.634565i
$792$	−15.0975	+	39.2105i	−0.536467	+	1.39328i
$793$	−3.45837	+	26.2689i	−0.122810	+	0.932837i
$794$	−6.58975	+	0.867558i	−0.233862	+	0.0307885i
$795$	−2.08278	−	14.4166i	−0.0738686	−	0.511304i
$796$	−6.03864	−	7.86971i	−0.214034	−	0.278935i
$797$	−34.3837	+	34.3837i	−1.21793	+	1.21793i	−0.249577	+	0.968355i	$0.580292\pi$
$797$	−34.3837	+	34.3837i	−1.21793	+	1.21793i	−0.968355	+	0.249577i	$0.919708\pi$
$798$	14.6833	+	10.3411i	0.519783	+	0.366071i
$799$	1.44607	+	11.1313i	0.0511583	+	0.393799i
$800$	23.9175	+	13.8088i	0.845611	+	0.488214i
$801$	15.0273	+	24.5787i	0.530963	+	0.868446i
$802$	7.91786	+	60.1421i	0.279589	+	2.12369i
$803$	−50.1521	−	28.9553i	−1.76983	−	1.02181i
$804$	36.3740	−	37.3008i	1.28281	−	1.31550i
$805$	25.1968	+	9.61004i	0.888070	+	0.338709i
$806$	60.2186	−	24.9433i	2.12111	−	0.878592i
$807$	53.6203	+	6.37419i	1.88752	+	0.224382i
$808$	−18.9345	−	5.07349i	−0.666114	−	0.178485i
$809$	−7.98774	−	6.12921i	−0.280834	−	0.215492i	0.458733	−	0.888574i	$-0.348303\pi$
$809$	−7.98774	−	6.12921i	−0.280834	−	0.215492i	−0.739568	+	0.673082i	$0.764970\pi$
$810$	5.51416	−	68.2781i	0.193748	−	2.39905i
$811$	10.2360	+	4.23990i	0.359435	+	0.148883i	0.555091	−	0.831790i	$-0.312684\pi$
$811$	10.2360	+	4.23990i	0.359435	+	0.148883i	−0.195656	+	0.980673i	$0.562684\pi$
$812$	24.9960	−	26.4539i	0.877186	−	0.928350i
$813$	−4.94485	+	5.07084i	−0.173423	+	0.177842i
$814$	−11.8153	−	44.0953i	−0.414126	−	1.54554i
$815$	−11.8686	−	20.5571i	−0.415741	−	0.720084i
$816$	−0.606760	+	5.03058i	−0.0212408	+	0.176105i
$817$	−0.728516	−	0.420609i	−0.0254876	−	0.0147152i
$818$	16.9279	−	16.9279i	0.591869	−	0.591869i
$819$	47.2520	−	8.81273i	1.65112	−	0.307942i
$820$		−	78.1854i		−	2.73035i
$821$	−4.60703	+	3.53510i	−0.160786	+	0.123376i	−0.686021	−	0.727582i	$-0.740644\pi$
$821$	−4.60703	+	3.53510i	−0.160786	+	0.123376i	0.525235	+	0.850957i	$0.323978\pi$
$822$	8.45957	+	14.2358i	0.295061	+	0.496531i
$823$	16.2129	−	21.1290i	0.565145	−	0.736512i	−0.420134	−	0.907462i	$-0.638017\pi$
$823$	16.2129	−	21.1290i	0.565145	−	0.736512i	0.985280	+	0.170950i	$0.0546837\pi$
$824$	−48.4705	+	12.9876i	−1.68855	+	0.452445i
$825$	39.7303	−	17.0454i	1.38323	−	0.593446i
$826$	−7.12475	−	8.75976i	−0.247902	−	0.304791i
$827$	2.14757	+	5.18469i	0.0746783	+	0.180289i	0.956810	−	0.290713i	$-0.0938924\pi$
$827$	2.14757	+	5.18469i	0.0746783	+	0.180289i	−0.882132	+	0.471002i	$0.843892\pi$
$828$	31.4361	+	3.33658i	1.09248	+	0.115954i
$829$	−12.9064	−	22.3546i	−0.448259	−	0.776408i	0.550013	−	0.835156i	$-0.314623\pi$
$829$	−12.9064	−	22.3546i	−0.448259	−	0.776408i	−0.998273	+	0.0587477i	$0.981289\pi$
$830$	−47.8404	+	6.29831i	−1.66057	+	0.218618i
$831$	−3.34413	+	28.1312i	−0.116007	+	0.975860i
$832$			76.1340i			2.63947i
$833$	26.0180	−	12.4926i	0.901469	−	0.432844i
$834$	37.8195	+	15.1109i	1.30958	+	0.523246i
$835$	10.5099	+	39.2233i	0.363709	+	1.35738i
$836$	3.24277	+	24.6313i	0.112154	+	0.851891i
$837$	−13.9340	+	19.6521i	−0.481630	+	0.679277i
$838$	27.3635	−	20.9968i	0.945258	−	0.725322i
$839$	−25.3104	+	10.4839i	−0.873812	+	0.361945i	−0.774094	−	0.633071i	$-0.781794\pi$
$839$	−25.3104	+	10.4839i	−0.873812	+	0.361945i	−0.0997181	+	0.995016i	$0.531794\pi$
$840$	14.4470	+	46.2591i	0.498468	+	1.59609i
$841$	−8.85914	−	8.85914i	−0.305488	−	0.305488i
$842$	−16.5444	−	61.7445i	−0.570157	−	2.12786i
$843$	21.0782	+	35.4706i	0.725972	+	1.22167i
$844$	−19.3092	−	14.8164i	−0.664649	−	0.510003i
$845$	47.2479	+	61.5747i	1.62538	+	2.11823i
$846$	13.7402	+	13.0657i	0.472396	+	0.449206i
$847$	16.8334	+	12.1750i	0.578404	+	0.418338i
$848$	1.28696	+	1.28696i	0.0441942	+	0.0441942i
$849$	−7.01165	−	8.90359i	−0.240639	−	0.305571i
$850$	43.7122	−	33.4227i	1.49932	−	1.14639i
$851$	−12.1937	+	7.04003i	−0.417995	+	0.241329i
$852$	43.0295	+	5.11519i	1.47417	+	0.175244i
$853$	17.5869	−	42.4587i	0.602166	−	1.45376i	−0.269181	−	0.963089i	$-0.586753\pi$
$853$	17.5869	−	42.4587i	0.602166	−	1.45376i	0.871347	−	0.490667i	$-0.163247\pi$
$854$	19.5329	+	18.4564i	0.668403	+	0.631565i
$855$	−6.73784	−	15.1752i	−0.230429	−	0.518980i
$856$	−3.45674	+	26.2565i	−0.118149	+	0.897430i
$857$	6.00285	−	7.82307i	0.205053	−	0.267231i	−0.679494	−	0.733681i	$-0.737801\pi$
$857$	6.00285	−	7.82307i	0.205053	−	0.267231i	0.884547	+	0.466450i	$0.154467\pi$
$858$	84.6823	+	63.3028i	2.89101	+	2.16112i
$859$	−12.7447	−	47.5637i	−0.434842	−	1.62285i	−0.741444	−	0.671015i	$-0.765859\pi$
$859$	−12.7447	−	47.5637i	−0.434842	−	1.62285i	0.306601	−	0.951838i	$-0.400808\pi$
$860$	−2.11909	−	5.11593i	−0.0722603	−	0.174452i
$861$	−21.8473	+	23.7121i	−0.744555	+	0.808107i
$862$	−17.0635	+	41.1948i	−0.581184	+	1.40310i
$863$	13.3392	−	23.1042i	0.454072	−	0.786476i	−0.544562	−	0.838720i	$-0.683304\pi$
$863$	13.3392	−	23.1042i	0.454072	−	0.786476i	0.998634	+	0.0522447i	$0.0166376\pi$
$864$	−13.2883	−	21.1324i	−0.452076	−	0.718938i
$865$	−52.9615	−	14.1910i	−1.80075	−	0.482508i
$866$	25.5524	−	44.2580i	0.868305	−	1.50395i
$867$	−25.6337	−	14.4884i	−0.870565	−	0.492054i
$868$	9.61890	−	40.4485i	0.326487	−	1.37291i
$869$	−31.5503	−	31.5503i	−1.07027	−	1.07027i
$870$	−51.5013	+	14.4964i	−1.74606	+	0.491475i
$871$	−26.8715	−	46.5427i	−0.910505	−	1.57704i
$872$	5.19408	+	39.4530i	0.175894	+	1.33605i
$873$	15.6273	+	19.3385i	0.528905	+	0.654510i
$874$	11.2565	−	4.66261i	0.380758	−	0.157715i
$875$	3.08649	−	5.71387i	0.104343	−	0.193164i
$876$	−71.9584	+	30.8722i	−2.43125	+	1.04307i
$877$	−7.01190	−	0.923134i	−0.236775	−	0.0311720i	0.0112047	−	0.999937i	$-0.496433\pi$
$877$	−7.01190	−	0.923134i	−0.236775	−	0.0311720i	−0.247980	+	0.968765i	$0.579767\pi$
$878$	−4.18041	−	3.20774i	−0.141082	−	0.108256i
$879$	−34.0307	−	8.66123i	−1.14783	−	0.292136i
$880$	−5.05007	+	8.74697i	−0.170238	+	0.294860i
$881$	17.0036	+	7.04310i	0.572864	+	0.237288i	0.650259	−	0.759712i	$-0.274660\pi$
$881$	17.0036	+	7.04310i	0.572864	+	0.237288i	−0.0773949	+	0.997001i	$0.524660\pi$
$882$	20.8440	−	44.0713i	0.701853	−	1.48396i
$883$	48.8058			1.64244			0.821222	−	0.570608i	$-0.193292\pi$
$883$	48.8058			1.64244			0.821222	+	0.570608i	$0.193292\pi$
$884$	78.1333	+	32.5208i	2.62791	+	1.09379i
$885$	1.49265	+	10.3319i	0.0501750	+	0.347301i
$886$	−50.2628	−	13.4679i	−1.68861	−	0.452462i
$887$	43.1834	−	33.1358i	1.44996	−	1.11259i	0.477740	−	0.878501i	$-0.341456\pi$
$887$	43.1834	−	33.1358i	1.44996	−	1.11259i	0.972215	−	0.234089i	$-0.0752107\pi$
$888$	−23.4971	−	9.38830i	−0.788509	−	0.315051i
$889$	−22.0663	−	2.27131i	−0.740079	−	0.0761773i
$890$	27.9698	+	67.5252i	0.937551	+	2.26345i
$891$	−38.9504	−	3.14564i	−1.30489	−	0.105383i
$892$	19.3965	+	5.19728i	0.649443	+	0.174018i
$893$	4.43924	+	1.18949i	0.148553	+	0.0398048i
$894$	39.8954	+	22.3693i	1.33430	+	0.748141i
$895$	4.49280	+	10.8466i	0.150178	+	0.362561i
$896$	41.9709	+	30.3560i	1.40215	+	1.01412i
$897$	12.0992	−	30.2819i	0.403980	−	1.01108i
$898$	−56.3721	+	43.2558i	−1.88116	+	1.44346i
$899$	18.1750	+	4.86998i	0.606171	+	0.162423i
$900$	13.7041	−	56.8258i	0.456805	−	1.89419i
$901$	−9.77816	+	4.03063i	−0.325758	+	0.134280i
$902$	−70.9203			−2.36139
$903$	−0.786865	+	2.14370i	−0.0261852	+	0.0713379i
$904$	−42.2972	−	17.5201i	−1.40678	−	0.582708i
$905$	−27.0799	+	46.9038i	−0.900167	+	1.55913i
$906$	−11.9710	+	47.0353i	−0.397711	+	1.56264i
$907$	22.3220	+	17.1283i	0.741189	+	0.568735i	0.908856	−	0.417109i	$-0.136957\pi$
$907$	22.3220	+	17.1283i	0.741189	+	0.568735i	−0.167667	+	0.985844i	$0.553623\pi$
$908$	36.7107	+	4.83305i	1.21829	+	0.160391i
$909$	−0.458594	−	18.2253i	−0.0152106	−	0.604495i
$910$	121.899	−	3.45427i	4.04091	−	0.114508i
$911$	−21.0149	+	8.70467i	−0.696256	+	0.288399i	−0.702604	−	0.711581i	$-0.747979\pi$
$911$	−21.0149	+	8.70467i	−0.696256	+	0.288399i	0.00634789	+	0.999980i	$0.497979\pi$
$912$	1.80957	+	1.01462i	0.0599209	+	0.0335976i
$913$	3.59298	+	27.2914i	0.118910	+	0.903213i
$914$	5.07577	+	8.79149i	0.167892	+	0.290797i
$915$	−6.73169	−	23.9156i	−0.222543	−	0.790624i
$916$	−59.4669	−	59.4669i	−1.96484	−	1.96484i
$917$	−44.3076	−	10.5366i	−1.46317	−	0.347950i
$918$	−49.0456	+	8.26369i	−1.61875	+	0.272742i
$919$	16.3285	−	28.2818i	0.538627	−	0.932930i	−0.460351	−	0.887737i	$-0.652276\pi$
$919$	16.3285	−	28.2818i	0.538627	−	0.932930i	0.998978	−	0.0451927i	$-0.0143902\pi$
$920$	31.7578	+	8.50947i	1.04702	+	0.280549i
$921$	−5.80361	−	1.47709i	−0.191236	−	0.0486718i
$922$	5.88482	−	10.1928i	0.193806	−	0.335682i
$923$	17.1055	−	41.2964i	0.563035	−	1.35929i
$924$	64.3742	−	20.1044i	2.11776	−	0.661387i
$925$	9.96331	+	24.0536i	0.327592	+	0.790876i
$926$	10.3022	+	38.4482i	0.338550	+	1.26349i
$927$	−24.3442	−	39.8174i	−0.799567	−	1.30778i
$928$	−11.8694	+	15.4684i	−0.389631	+	0.507777i
$929$	−4.32600	+	32.8592i	−0.141931	+	1.07808i	0.761141	+	0.648587i	$0.224640\pi$
$929$	−4.32600	+	32.8592i	−0.141931	+	1.07808i	−0.903072	+	0.429489i	$0.858694\pi$
$930$	−42.6709	+	43.7581i	−1.39923	+	1.43488i
$931$	−0.669181	−	11.7980i	−0.0219315	−	0.386663i
$932$	−14.9493	+	36.0907i	−0.489679	+	1.18219i
$933$	−0.0486619	+	0.409349i	−0.00159312	+	0.0134015i
$934$	−21.3174	+	12.3076i	−0.697526	+	0.402717i
$935$	−35.6499	−	46.6251i	−1.16588	−	1.52480i
$936$	56.2061	−	16.5865i	1.83715	−	0.542147i
$937$	−22.5472	−	22.5472i	−0.736585	−	0.736585i	0.235330	−	0.971916i	$-0.424383\pi$
$937$	−22.5472	−	22.5472i	−0.736585	−	0.736585i	−0.971916	+	0.235330i	$0.924383\pi$
$938$	−54.2225	−	5.58120i	−1.77043	−	0.182233i
$939$	56.3934	+	22.5321i	1.84033	+	0.735309i
$940$	18.4167	+	24.0012i	0.600688	+	0.782832i
$941$	−7.99902	−	6.13787i	−0.260761	−	0.200089i	0.470104	−	0.882611i	$-0.344216\pi$
$941$	−7.99902	−	6.13787i	−0.260761	−	0.200089i	−0.730865	+	0.682522i	$0.760883\pi$
$942$	15.7999	−	9.38900i	0.514787	−	0.305910i
$943$	5.66138	+	21.1286i	0.184360	+	0.688041i
$944$	−0.922315	−	0.922315i	−0.0300188	−	0.0300188i
$945$	−37.4607	+	25.0638i	−1.21860	+	0.815326i
$946$	−4.64055	+	1.92218i	−0.150877	+	0.0624955i
$947$	−20.6198	+	15.8221i	−0.670054	+	0.514151i	−0.886845	−	0.462068i	$-0.847108\pi$
$947$	−20.6198	+	15.8221i	−0.670054	+	0.514151i	0.216791	+	0.976218i	$0.430441\pi$
$948$	−59.7094	+	8.62628i	−1.93927	+	0.280169i
$949$	10.5427	+	80.0795i	0.342229	+	2.59949i
$950$	−5.83103	−	21.7617i	−0.189183	−	0.706042i
$951$	−8.41141	+	21.0521i	−0.272759	+	0.682660i
$952$	29.9946	−	18.3987i	0.972129	−	0.596305i
$953$			18.6720i			0.604845i	0.953174	+	0.302422i	$0.0977953\pi$
$953$			18.6720i			0.604845i	−0.953174	+	0.302422i	$0.902205\pi$
$954$	−8.54051	+	15.6914i	−0.276509	+	0.508027i
$955$	36.2459	−	4.77187i	1.17289	−	0.154414i
$956$	21.1280	+	36.5947i	0.683328	+	1.18356i
$957$	8.26973	+	29.3797i	0.267322	+	0.949712i
$958$	18.2407	+	44.0370i	0.589331	+	1.42277i
$959$	3.88290	−	10.1807i	0.125386	−	0.328751i
$960$	−28.1475	−	65.6076i	−0.908458	−	2.11748i
$961$	−9.18122	+	2.46010i	−0.296169	+	0.0793581i
$962$	−38.7606	+	50.5137i	−1.24969	+	1.62863i
$963$	−24.3311	+	3.82815i	−0.784057	+	0.123361i
$964$	11.7932	−	9.04923i	0.379833	−	0.291456i
$965$			41.3158i			1.33000i
$966$	−17.6948	−	27.9430i	−0.569320	−	0.899050i
$967$	24.7983	−	24.7983i	0.797461	−	0.797461i	−0.185234	−	0.982695i	$-0.559304\pi$
$967$	24.7983	−	24.7983i	0.797461	−	0.797461i	0.982695	+	0.185234i	$0.0593042\pi$
$968$	21.9351	+	12.6642i	0.705021	+	0.407044i
$969$	−9.48413	+	7.44253i	−0.304674	+	0.239089i
$970$	31.5399	+	54.6288i	1.01269	+	1.75402i
$971$	−7.14530	−	26.6666i	−0.229304	−	0.855772i	−0.980634	−	0.195847i	$-0.937254\pi$
$971$	−7.14530	−	26.6666i	−0.229304	−	0.855772i	0.751331	−	0.659926i	$-0.229412\pi$
$972$	−34.9390	+	39.6354i	−1.12067	+	1.27130i
$973$	−7.66609	−	25.6775i	−0.245764	−	0.823182i
$974$	15.8482	+	6.56453i	0.507808	+	0.210341i
$975$	−52.5948	−	29.4899i	−1.68438	−	0.944431i
$976$	2.46283	+	1.88980i	0.0788333	+	0.0604909i
$977$	43.0895	+	11.5458i	1.37856	+	0.369383i	0.870596	−	0.491998i	$-0.163733\pi$
$977$	43.0895	+	11.5458i	1.37856	+	0.369383i	0.507959	+	0.861381i	$0.330400\pi$
$978$	−3.43665	+	28.9094i	−0.109892	+	0.924422i
$979$	38.5209	−	15.9559i	1.23113	−	0.509952i
$980$	43.7830	−	64.2951i	1.39860	−	2.05383i
$981$	−33.8252	+	15.0185i	−1.07996	+	0.479505i
$982$	−36.8505	−	21.2756i	−1.17595	−	0.678933i
$983$	−6.90443	−	52.4443i	−0.220217	−	1.67271i	−0.642527	−	0.766263i	$-0.722114\pi$
$983$	−6.90443	−	52.4443i	−0.220217	−	1.67271i	0.422310	−	0.906452i	$-0.361219\pi$
$984$	−23.5359	+	31.4848i	−0.750298	+	1.00370i
$985$	−32.1583	−	18.5666i	−1.02465	−	0.591581i
$986$	19.3660	+	33.6760i	0.616738	+	1.07246i
$987$	1.12120	−	12.4253i	0.0356881	−	0.395501i
$988$	24.5018	−	24.5018i	0.779506	−	0.779506i
$989$	0.943100	+	1.22907i	0.0299888	+	0.0390822i
$990$	−96.3778	−	23.2425i	−3.06309	−	0.738696i
$991$	−31.7914	+	4.18542i	−1.00989	+	0.132954i	−0.617273	−	0.786749i	$-0.711763\pi$
$991$	−31.7914	+	4.18542i	−1.00989	+	0.132954i	−0.392614	+	0.919703i	$0.628429\pi$
$992$	−2.90725	+	22.0827i	−0.0923051	+	0.701127i
$993$	−0.149525	−	11.8867i	−0.00474504	−	0.377212i
$994$	−23.7711	−	38.6043i	−0.753972	−	1.22446i
$995$	6.78460	−	6.78460i	0.215086	−	0.215086i
$996$	32.4643	+	18.2027i	1.02867	+	0.576775i
$997$	3.36249	−	4.38208i	0.106491	−	0.138782i	−0.737067	−	0.675819i	$-0.763790\pi$
$997$	3.36249	−	4.38208i	0.106491	−	0.138782i	0.843558	+	0.537038i	$0.180457\pi$
$998$	−9.21295	−	69.9793i	−0.291631	−	2.21516i
$999$	2.18926	−	23.4310i	0.0692651	−	0.741322i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.bj.a.26.5	✓	352
3.2	odd	2	inner	357.2.bj.a.26.40	yes	352
7.3	odd	6	inner	357.2.bj.a.332.40	yes	352
17.2	even	8	inner	357.2.bj.a.257.5	yes	352
21.17	even	6	inner	357.2.bj.a.332.5	yes	352
51.2	odd	8	inner	357.2.bj.a.257.40	yes	352
119.87	odd	24	inner	357.2.bj.a.206.40	yes	352
357.206	even	24	inner	357.2.bj.a.206.5	yes	352

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.bj.a.26.5	✓	352	1.1	even	1	trivial
357.2.bj.a.26.40	yes	352	3.2	odd	2	inner
357.2.bj.a.206.5	yes	352	357.206	even	24	inner
357.2.bj.a.206.40	yes	352	119.87	odd	24	inner
357.2.bj.a.257.5	yes	352	17.2	even	8	inner
357.2.bj.a.257.40	yes	352	51.2	odd	8	inner
357.2.bj.a.332.5	yes	352	21.17	even	6	inner
357.2.bj.a.332.40	yes	352	7.3	odd	6	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:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	357.bj (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.24242 + 0.600854i) q^{2} +(-0.427208 + 1.67854i) q^{3} +(2.93536 - 1.69473i) q^{4} +(1.99584 + 2.60102i) q^{5} +(-0.0505770 - 4.02067i) q^{6} +(-2.05255 + 1.66944i) q^{7} +(-2.28089 + 2.28089i) q^{8} +(-2.63499 - 1.43417i) q^{9} +(-6.03833 - 4.63338i) q^{10} +(-2.64319 + 3.44467i) q^{11} +(1.59066 + 5.65112i) q^{12} +6.05584 q^{13} +(3.59959 - 4.97687i) q^{14} +(-5.21856 + 2.23891i) q^{15} +(0.354763 - 0.614468i) q^{16} +(2.50438 + 3.27538i) q^{17} +(6.77047 + 1.63277i) q^{18} +(1.63061 - 0.436922i) q^{19} +(10.2665 + 4.25254i) q^{20} +(-1.92536 - 4.15849i) q^{21} +(3.85739 - 9.31255i) q^{22} +(-3.08232 - 0.405795i) q^{23} +(-2.85415 - 4.80298i) q^{24} +(-1.48787 + 5.55280i) q^{25} +(-13.5797 + 3.63868i) q^{26} +(3.53300 - 3.81024i) q^{27} +(-3.19572 + 8.37893i) q^{28} +(-3.74955 - 1.55311i) q^{29} +(10.3569 - 8.15616i) q^{30} +(-4.59660 + 0.605153i) q^{31} +(1.24341 - 4.64045i) q^{32} +(-4.65282 - 5.90828i) q^{33} +(-7.58389 - 5.83999i) q^{34} +(-8.43881 - 2.00680i) q^{35} +(-10.1652 + 0.255781i) q^{36} +(3.59304 - 2.75704i) q^{37} +(-3.39399 + 1.95952i) q^{38} +(-2.58711 + 10.1650i) q^{39} +(-10.4849 - 1.38037i) q^{40} +(-2.69251 - 6.50029i) q^{41} +(6.81609 + 8.16820i) q^{42} +(-0.352360 - 0.352360i) q^{43} +(-1.92092 + 14.5908i) q^{44} +(-1.52868 - 9.71603i) q^{45} +(7.15567 - 0.942062i) q^{46} +(2.35770 + 1.36122i) q^{47} +(0.879851 + 0.857990i) q^{48} +(1.42593 - 6.85323i) q^{49} -13.3457i q^{50} +(-6.56774 + 2.80443i) q^{51} +(17.7761 - 10.2630i) q^{52} +(-0.663905 + 2.47773i) q^{53} +(-5.63307 + 10.6670i) q^{54} -14.2350 q^{55} +(0.873831 - 8.48945i) q^{56} +(0.0367780 + 2.92371i) q^{57} +(9.34125 + 1.22980i) q^{58} +(0.475797 - 1.77570i) q^{59} +(-11.5240 + 15.4161i) q^{60} +(-0.571080 + 4.33778i) q^{61} +(9.94388 - 4.11889i) q^{62} +(7.80271 - 1.45524i) q^{63} +12.5720i q^{64} +(12.0865 + 15.7514i) q^{65} +(13.9836 + 10.4532i) q^{66} +(-4.43728 - 7.68559i) q^{67} +(12.9021 + 5.37016i) q^{68} +(1.99794 - 5.00044i) q^{69} +(20.1291 - 0.570403i) q^{70} +(2.82463 - 6.81926i) q^{71} +(9.28130 - 2.73892i) q^{72} +(1.74091 + 13.2235i) q^{73} +(-6.40052 + 8.34132i) q^{74} +(-8.68497 - 4.86965i) q^{75} +(4.04597 - 4.04597i) q^{76} +(-0.325396 - 11.4830i) q^{77} +(-0.306287 - 24.3486i) q^{78} +(-1.34133 + 10.1884i) q^{79} +(2.30630 - 0.303630i) q^{80} +(4.88630 + 7.55805i) q^{81} +(9.94345 + 12.9586i) q^{82} +(4.48292 - 4.48292i) q^{83} +(-12.6991 - 8.94369i) q^{84} +(-3.52100 + 13.0511i) q^{85} +(1.00185 + 0.578421i) q^{86} +(4.20880 - 5.63026i) q^{87} +(-1.82809 - 13.8857i) q^{88} +(-8.31631 - 4.80142i) q^{89} +(9.26586 + 20.8689i) q^{90} +(-12.4299 + 10.1099i) q^{91} +(-9.73543 + 4.03255i) q^{92} +(0.947931 - 7.97409i) q^{93} +(-6.10483 - 1.63579i) q^{94} +(4.39088 + 3.36924i) q^{95} +(7.25798 + 4.06954i) q^{96} +(-7.65695 - 3.17161i) q^{97} +(0.920256 + 16.2246i) q^{98} +(11.9050 - 5.28587i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 352 q - 12 q^{3} - 16 q^{7} - 4 q^{9} - 24 q^{10} - 12 q^{12} - 24 q^{15} + 112 q^{16} - 24 q^{18} - 24 q^{19} - 80 q^{22} - 60 q^{24} - 8 q^{25} - 72 q^{28} - 24 q^{31} + 24 q^{33} - 64 q^{36} - 40 q^{37}+ \cdots + 256 q^{99}+O(q^{100}) \) 352 * q - 12 * q^3 - 16 * q^7 - 4 * q^9 - 24 * q^10 - 12 * q^12 - 24 * q^15 + 112 * q^16 - 24 * q^18 - 24 * q^19 - 80 * q^22 - 60 * q^24 - 8 * q^25 - 72 * q^28 - 24 * q^31 + 24 * q^33 - 64 * q^36 - 40 * q^37 - 24 * q^39 - 24 * q^40 + 68 * q^42 - 48 * q^45 - 40 * q^46 + 48 * q^49 - 20 * q^51 - 240 * q^52 - 16 * q^57 - 8 * q^58 + 44 * q^60 - 24 * q^61 + 88 * q^63 - 12 * q^66 - 16 * q^67 + 64 * q^70 - 120 * q^73 - 156 * q^75 - 176 * q^78 - 24 * q^79 + 120 * q^82 - 104 * q^84 + 112 * q^85 + 132 * q^87 - 24 * q^88 - 96 * q^91 - 8 * q^93 - 120 * q^94 + 60 * q^96 + 256 * q^99

Introduction

L-functions

Modular forms

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