LMFDB - Embedded newform 847.2.f.t.323.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [847,2,Mod(148,847)] 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("847.148"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(847, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.f (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,-2,1,-8,-1,-12,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 7 x^{10} - 15 x^{9} + 59 x^{8} + 118 x^{7} + 266 x^{6} + 324 x^{5} + 1036 x^{4} + \cdots + 16 $ x^12 - x^11 + 7x^10 - 15x^9 + 59x^8 + 118x^7 + 266x^6 + 324x^5 + 1036x^4 + 376x^3 + 136x^2 + 48x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			323.3
Root			$-0.965643 - 2.97194i$ of defining polynomial
Character	$\chi$	$=$	847.323
Dual form			847.2.f.t.729.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.71907 + 1.24898i) q^{2} +(-0.965643 + 2.97194i) q^{3} +(0.777220 + 2.39204i) q^{4} +(-0.392262 + 0.284995i) q^{5} +(-5.37189 + 3.90291i) q^{6} +(0.309017 + 0.951057i) q^{7} +(-0.338253 + 1.04104i) q^{8} +(-5.47293 - 3.97631i) q^{9} -1.03028 q^{10} -7.85952 q^{12} +(-4.53838 - 3.29733i) q^{13} +(-0.656626 + 2.02089i) q^{14} +(-0.468203 - 1.44098i) q^{15} +(2.18787 - 1.58958i) q^{16} +(-4.53838 + 3.29733i) q^{17} +(-4.44201 - 13.6711i) q^{18} +(-1.63162 + 5.02162i) q^{19} +(-0.986592 - 0.716801i) q^{20} -3.12489 q^{21} +2.48486 q^{23} +(-2.76727 - 2.01054i) q^{24} +(-1.47244 + 4.53170i) q^{25} +(-3.68350 - 11.3367i) q^{26} +(9.51801 - 6.91524i) q^{27} +(-2.03479 + 1.47836i) q^{28} +(1.63162 + 5.02162i) q^{29} +(0.994879 - 3.06192i) q^{30} +(5.76415 + 4.18790i) q^{31} +7.93567 q^{32} -11.9201 q^{34} +(-0.392262 - 0.284995i) q^{35} +(5.25783 - 16.1819i) q^{36} +(-0.0726471 - 0.223585i) q^{37} +(-9.07676 + 6.59465i) q^{38} +(14.1819 - 10.3038i) q^{39} +(-0.164006 - 0.504758i) q^{40} +(0.738629 - 2.27327i) q^{41} +(-5.37189 - 3.90291i) q^{42} +1.03028 q^{43} +3.28005 q^{45} +(4.27165 + 3.10353i) q^{46} +(-0.497439 + 1.53096i) q^{47} +(2.61144 + 8.03719i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(-8.19120 + 5.95126i) q^{50} +(-5.41701 - 16.6718i) q^{51} +(4.36001 - 13.4187i) q^{52} +(2.45154 + 1.78115i) q^{53} +24.9991 q^{54} -1.09461 q^{56} +(-13.3484 - 9.69819i) q^{57} +(-3.46701 + 10.6704i) q^{58} +(0.965643 + 2.97194i) q^{59} +(3.08299 - 2.23992i) q^{60} +(1.93375 - 1.40496i) q^{61} +(4.67838 + 14.3986i) q^{62} +(2.09047 - 6.43381i) q^{63} +(9.26621 + 6.73230i) q^{64} +2.71995 q^{65} +10.0147 q^{67} +(-11.4147 - 8.29323i) q^{68} +(-2.39949 + 7.38487i) q^{69} +(-0.318373 - 0.979851i) q^{70} +(-9.76907 + 7.09764i) q^{71} +(5.99072 - 4.35251i) q^{72} +(0.738629 + 2.27327i) q^{73} +(0.154367 - 0.475092i) q^{74} +(-12.0461 - 8.75200i) q^{75} -13.2800 q^{76} +37.2489 q^{78} +(-7.30565 - 5.30786i) q^{79} +(-0.405195 + 1.24706i) q^{80} +(5.08928 + 15.6632i) q^{81} +(4.10901 - 2.98537i) q^{82} +(2.60463 - 1.89237i) q^{83} +(-2.42872 - 7.47485i) q^{84} +(0.840512 - 2.58683i) q^{85} +(1.77112 + 1.28679i) q^{86} -16.4995 q^{87} -1.26537 q^{89} +(5.63863 + 4.09670i) q^{90} +(1.73351 - 5.33519i) q^{91} +(1.93129 + 5.94389i) q^{92} +(-18.0123 + 13.0867i) q^{93} +(-2.76727 + 2.01054i) q^{94} +(-0.791113 - 2.43479i) q^{95} +(-7.66302 + 23.5843i) q^{96} +(7.11545 + 5.16968i) q^{97} -2.12489 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} + q^{3} - 8 q^{4} - q^{5} - 12 q^{6} - 3 q^{7} - 6 q^{8} - 4 q^{9} - 16 q^{10} + 8 q^{12} - 8 q^{13} - 2 q^{14} + 5 q^{15} - 10 q^{16} - 8 q^{17} + 18 q^{18} + 14 q^{20} - 4 q^{21} + 28 q^{23}+ \cdots + 8 q^{98}+O(q^{100}) $ 12 * q - 2 * q^2 + q^3 - 8 * q^4 - q^5 - 12 * q^6 - 3 * q^7 - 6 * q^8 - 4 * q^9 - 16 * q^10 + 8 * q^12 - 8 * q^13 - 2 * q^14 + 5 * q^15 - 10 * q^16 - 8 * q^17 + 18 * q^18 + 14 * q^20 - 4 * q^21 + 28 * q^23 - 20 * q^24 - 2 * q^25 + 12 * q^26 + 19 * q^27 - 8 * q^28 + 8 * q^30 + 13 * q^31 + 136 * q^32 - 48 * q^34 - q^35 - 18 * q^36 + 17 * q^37 - 16 * q^38 + 20 * q^39 + 36 * q^40 - 16 * q^41 - 12 * q^42 + 16 * q^43 - 24 * q^45 - 4 * q^47 - 36 * q^48 - 3 * q^49 - 22 * q^50 + 20 * q^51 + 10 * q^53 + 32 * q^54 + 24 * q^56 - 16 * q^57 + 16 * q^58 - q^59 + 30 * q^60 + 16 * q^61 - 4 * q^62 - 4 * q^63 - 34 * q^64 + 96 * q^65 - 12 * q^67 + 7 * q^69 + 4 * q^70 - 5 * q^71 - 2 * q^72 - 16 * q^73 + 32 * q^74 - 20 * q^75 - 96 * q^76 + 112 * q^78 - 28 * q^79 + 56 * q^80 - 15 * q^81 - 28 * q^82 - 8 * q^83 - 2 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 84 * q^89 + 20 * q^90 - 8 * q^91 - 2 * q^92 - 17 * q^93 - 20 * q^94 - 24 * q^95 - 20 * q^96 + 11 * q^97 + 8 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	1.71907	+	1.24898i	1.21556	+	0.883160i	0.995724	−	0.0923762i	$-0.0294462\pi$
$2$	1.71907	+	1.24898i	1.21556	+	0.883160i	0.219841	+	0.975536i	$0.429446\pi$
$3$	−0.965643	+	2.97194i	−0.557514	+	1.71585i	0.131696	+	0.991290i	$0.457958\pi$
$3$	−0.965643	+	2.97194i	−0.557514	+	1.71585i	−0.689210	+	0.724562i	$0.742042\pi$
$4$	0.777220	+	2.39204i	0.388610	+	1.19602i
$5$	−0.392262	+	0.284995i	−0.175425	+	0.127454i	−0.672033	−	0.740521i	$-0.734579\pi$
$5$	−0.392262	+	0.284995i	−0.175425	+	0.127454i	0.496608	+	0.867975i	$0.334579\pi$
$6$	−5.37189	+	3.90291i	−2.19307	+	1.59336i
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$8$	−0.338253	+	1.04104i	−0.119590	+	0.368062i
$9$	−5.47293	−	3.97631i	−1.82431	−	1.32544i
$10$	−1.03028			−0.325802
$11$		0			0
$11$		0			0
$12$	−7.85952			−2.26885
$13$	−4.53838	−	3.29733i	−1.25872	−	0.914514i	−0.260026	−	0.965602i	$-0.583731\pi$
$13$	−4.53838	−	3.29733i	−1.25872	−	0.914514i	−0.998694	+	0.0510876i	$0.983731\pi$
$14$	−0.656626	+	2.02089i	−0.175491	+	0.540105i
$15$	−0.468203	−	1.44098i	−0.120890	−	0.372060i
$16$	2.18787	−	1.58958i	0.546968	−	0.397395i
$17$	−4.53838	+	3.29733i	−1.10072	+	0.799719i	−0.981177	−	0.193110i	$-0.938143\pi$
$17$	−4.53838	+	3.29733i	−1.10072	+	0.799719i	−0.119542	+	0.992829i	$0.538143\pi$
$18$	−4.44201	−	13.6711i	−1.04699	−	3.22231i
$19$	−1.63162	+	5.02162i	−0.374320	+	1.15204i	0.569616	+	0.821911i	$0.307092\pi$
$19$	−1.63162	+	5.02162i	−0.374320	+	1.15204i	−0.943936	+	0.330128i	$0.892908\pi$
$20$	−0.986592	−	0.716801i	−0.220609	−	0.160282i
$21$	−3.12489			−0.681906
$22$		0			0
$23$	2.48486			0.518130			0.259065	−	0.965860i	$-0.416586\pi$
$23$	2.48486			0.518130			0.259065	+	0.965860i	$0.416586\pi$
$24$	−2.76727	−	2.01054i	−0.564866	−	0.410399i
$25$	−1.47244	+	4.53170i	−0.294488	+	0.906340i
$26$	−3.68350	−	11.3367i	−0.722395	−	2.22330i
$27$	9.51801	−	6.91524i	1.83174	−	1.33084i
$28$	−2.03479	+	1.47836i	−0.384539	+	0.279384i
$29$	1.63162	+	5.02162i	0.302985	+	0.932492i	0.980421	+	0.196911i	$0.0630909\pi$
$29$	1.63162	+	5.02162i	0.302985	+	0.932492i	−0.677436	+	0.735581i	$0.736909\pi$
$30$	0.994879	−	3.06192i	0.181639	−	0.559028i
$31$	5.76415	+	4.18790i	1.03527	+	0.752170i	0.969357	−	0.245656i	$-0.0790033\pi$
$31$	5.76415	+	4.18790i	1.03527	+	0.752170i	0.0659154	+	0.997825i	$0.479003\pi$
$32$	7.93567			1.40284
$33$		0			0
$34$	−11.9201			−2.04428
$35$	−0.392262	−	0.284995i	−0.0663043	−	0.0481729i
$36$	5.25783	−	16.1819i	0.876304	−	2.69699i
$37$	−0.0726471	−	0.223585i	−0.0119431	−	0.0367571i	0.944907	−	0.327338i	$-0.106152\pi$
$37$	−0.0726471	−	0.223585i	−0.0119431	−	0.0367571i	−0.956850	+	0.290581i	$0.906152\pi$
$38$	−9.07676	+	6.59465i	−1.47245	+	1.06979i
$39$	14.1819	−	10.3038i	2.27092	−	1.64992i
$40$	−0.164006	−	0.504758i	−0.0259316	−	0.0798093i
$41$	0.738629	−	2.27327i	0.115354	−	0.355024i	−0.876666	−	0.481099i	$-0.840238\pi$
$41$	0.738629	−	2.27327i	0.115354	−	0.355024i	0.992021	+	0.126074i	$0.0402378\pi$
$42$	−5.37189	−	3.90291i	−0.828901	−	0.602232i
$43$	1.03028			0.157116			0.0785578	−	0.996910i	$-0.474968\pi$
$43$	1.03028			0.157116			0.0785578	+	0.996910i	$0.474968\pi$
$44$		0			0
$45$	3.28005			0.488961
$46$	4.27165	+	3.10353i	0.629820	+	0.457591i
$47$	−0.497439	+	1.53096i	−0.0725590	+	0.223314i	−0.980759	−	0.195223i	$-0.937457\pi$
$47$	−0.497439	+	1.53096i	−0.0725590	+	0.223314i	0.908200	+	0.418537i	$0.137457\pi$
$48$	2.61144	+	8.03719i	0.376929	+	1.16007i
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$	−8.19120	+	5.95126i	−1.15841	+	0.841635i
$51$	−5.41701	−	16.6718i	−0.758533	−	2.33453i
$52$	4.36001	−	13.4187i	0.604625	−	1.86084i
$53$	2.45154	+	1.78115i	0.336746	+	0.244660i	0.743287	−	0.668972i	$-0.233265\pi$
$53$	2.45154	+	1.78115i	0.336746	+	0.244660i	−0.406542	+	0.913632i	$0.633265\pi$
$54$	24.9991			3.40194
$55$		0			0
$56$	−1.09461			−0.146273
$57$	−13.3484	−	9.69819i	−1.76804	−	1.28456i
$58$	−3.46701	+	10.6704i	−0.455241	+	1.40109i
$59$	0.965643	+	2.97194i	0.125716	+	0.386914i	0.994031	−	0.109099i	$-0.0347967\pi$
$59$	0.965643	+	2.97194i	0.125716	+	0.386914i	−0.868315	+	0.496013i	$0.834797\pi$
$60$	3.08299	−	2.23992i	0.398012	−	0.289173i
$61$	1.93375	−	1.40496i	0.247592	−	0.179886i	−0.457067	−	0.889432i	$-0.651100\pi$
$61$	1.93375	−	1.40496i	0.247592	−	0.179886i	0.704659	+	0.709546i	$0.251100\pi$
$62$	4.67838	+	14.3986i	0.594155	+	1.82862i
$63$	2.09047	−	6.43381i	0.263375	−	0.810584i
$64$	9.26621	+	6.73230i	1.15828	+	0.841537i
$65$	2.71995			0.337369
$66$		0			0
$67$	10.0147			1.22349			0.611744	−	0.791056i	$-0.290468\pi$
$67$	10.0147			1.22349			0.611744	+	0.791056i	$0.290468\pi$
$68$	−11.4147	−	8.29323i	−1.38423	−	1.00570i
$69$	−2.39949	+	7.38487i	−0.288865	+	0.889034i
$70$	−0.318373	−	0.979851i	−0.0380528	−	0.117115i
$71$	−9.76907	+	7.09764i	−1.15938	+	0.842335i	−0.989699	−	0.143165i	$-0.954272\pi$
$71$	−9.76907	+	7.09764i	−1.15938	+	0.842335i	−0.169676	+	0.985500i	$0.554272\pi$
$72$	5.99072	−	4.35251i	0.706013	−	0.512948i
$73$	0.738629	+	2.27327i	0.0864499	+	0.266066i	0.984931	−	0.172946i	$-0.0553287\pi$
$73$	0.738629	+	2.27327i	0.0864499	+	0.266066i	−0.898481	+	0.439012i	$0.855329\pi$
$74$	0.154367	−	0.475092i	0.0179448	−	0.0552284i
$75$	−12.0461	−	8.75200i	−1.39096	−	1.01059i
$76$	−13.2800			−1.52333
$77$		0			0
$78$	37.2489			4.21760
$79$	−7.30565	−	5.30786i	−0.821949	−	0.597181i	0.0953208	−	0.995447i	$-0.469612\pi$
$79$	−7.30565	−	5.30786i	−0.821949	−	0.597181i	−0.917270	+	0.398265i	$0.869612\pi$
$80$	−0.405195	+	1.24706i	−0.0453022	+	0.139426i
$81$	5.08928	+	15.6632i	0.565476	+	1.74036i
$82$	4.10901	−	2.98537i	0.453764	−	0.329679i
$83$	2.60463	−	1.89237i	0.285895	−	0.207715i	−0.435590	−	0.900145i	$-0.643460\pi$
$83$	2.60463	−	1.89237i	0.285895	−	0.207715i	0.721484	+	0.692431i	$0.243460\pi$
$84$	−2.42872	−	7.47485i	−0.264996	−	0.815573i
$85$	0.840512	−	2.58683i	0.0911663	−	0.280581i
$86$	1.77112	+	1.28679i	0.190984	+	0.138758i
$87$	−16.4995			−1.76894
$88$		0			0
$89$	−1.26537			−0.134129			−0.0670643	−	0.997749i	$-0.521363\pi$
$89$	−1.26537			−0.134129			−0.0670643	+	0.997749i	$0.521363\pi$
$90$	5.63863	+	4.09670i	0.594363	+	0.431830i
$91$	1.73351	−	5.33519i	0.181721	−	0.559280i
$92$	1.93129	+	5.94389i	0.201350	+	0.619693i
$93$	−18.0123	+	13.0867i	−1.86779	+	1.35703i
$94$	−2.76727	+	2.01054i	−0.285422	+	0.207371i
$95$	−0.791113	−	2.43479i	−0.0811664	−	0.249805i
$96$	−7.66302	+	23.5843i	−0.782104	+	2.40707i
$97$	7.11545	+	5.16968i	0.722465	+	0.524901i	0.887171	−	0.461441i	$-0.152667\pi$
$97$	7.11545	+	5.16968i	0.722465	+	0.524901i	−0.164706	+	0.986343i	$0.552667\pi$
$98$	−2.12489			−0.214646
$99$		0			0
$100$	−11.9844			−1.19844
$101$	10.4771	+	7.61202i	1.04251	+	0.757425i	0.970773	−	0.239999i	$-0.0771472\pi$
$101$	10.4771	+	7.61202i	1.04251	+	0.757425i	0.0717324	+	0.997424i	$0.477147\pi$
$102$	11.5105	−	35.4258i	1.13971	−	3.50767i
$103$	3.76069	+	11.5742i	0.370552	+	1.14044i	0.946431	+	0.322906i	$0.104660\pi$
$103$	3.76069	+	11.5742i	0.370552	+	1.14044i	−0.575880	+	0.817535i	$0.695340\pi$
$104$	4.96775	−	3.60928i	0.487128	−	0.353919i
$105$	1.22577	−	0.890576i	0.119623	−	0.0869113i
$106$	1.98976	+	6.12384i	0.193262	+	0.594800i
$107$	3.26325	−	10.0432i	0.315470	−	0.970917i	−0.660090	−	0.751186i	$-0.729482\pi$
$107$	3.26325	−	10.0432i	0.315470	−	0.970917i	0.975560	−	0.219731i	$-0.0705180\pi$
$108$	23.9391	+	17.3928i	2.30354	+	1.67362i
$109$	−7.34060			−0.703102			−0.351551	−	0.936169i	$-0.614346\pi$
$109$	−7.34060			−0.703102			−0.351551	+	0.936169i	$0.614346\pi$
$110$		0			0
$111$	0.734633			0.0697283
$112$	2.18787	+	1.58958i	0.206734	+	0.150201i
$113$	4.25359	−	13.0912i	0.400144	−	1.23152i	−0.524738	−	0.851264i	$-0.675837\pi$
$113$	4.25359	−	13.0912i	0.400144	−	1.23152i	0.924882	−	0.380253i	$-0.124163\pi$
$114$	−10.8340	−	33.3437i	−1.01470	−	3.12292i
$115$	−0.974716	+	0.708172i	−0.0908927	+	0.0660374i
$116$	−10.7438	+	7.80582i	−0.997535	+	0.724752i
$117$	11.7270	+	36.0921i	1.08416	+	3.33671i
$118$	−2.05188	+	6.31504i	−0.188891	+	0.581346i
$119$	−4.53838	−	3.29733i	−0.416033	−	0.302265i
$120$	1.65848			0.151398
$121$		0			0
$122$	5.07901			0.459832
$123$	6.04276	+	4.39032i	0.544858	+	0.395862i
$124$	−5.53761	+	17.0430i	−0.497292	+	1.53051i
$125$	−1.46308	−	4.50290i	−0.130862	−	0.402752i
$126$	11.6293	−	8.44921i	1.03602	−	0.752716i
$127$	−2.07116	+	1.50479i	−0.183786	+	0.133528i	−0.675874	−	0.737017i	$-0.736234\pi$
$127$	−2.07116	+	1.50479i	−0.183786	+	0.133528i	0.492088	+	0.870545i	$0.336234\pi$
$128$	2.61626	+	8.05203i	0.231247	+	0.711705i
$129$	−0.994879	+	3.06192i	−0.0875942	+	0.269587i
$130$	4.67579	+	3.39716i	0.410094	+	0.297950i
$131$	−2.71995			−0.237643			−0.118822	−	0.992916i	$-0.537912\pi$
$131$	−2.71995			−0.237643			−0.118822	+	0.992916i	$0.537912\pi$
$132$		0			0
$133$	−5.28005			−0.457838
$134$	17.2159	+	12.5081i	1.48723	+	1.08054i
$135$	−1.76274	+	5.42517i	−0.151713	+	0.466924i
$136$	−1.89751	−	5.83995i	−0.162710	−	0.500771i
$137$	7.85099	−	5.70408i	0.670755	−	0.487332i	−0.199523	−	0.979893i	$-0.563939\pi$
$137$	7.85099	−	5.70408i	0.670755	−	0.487332i	0.870278	+	0.492561i	$0.163939\pi$
$138$	−13.3484	+	9.69819i	−1.13629	+	0.825565i
$139$	−6.09352	−	18.7539i	−0.516845	−	1.59069i	−0.779899	−	0.625905i	$-0.784730\pi$
$139$	−6.09352	−	18.7539i	−0.516845	−	1.59069i	0.263054	−	0.964781i	$-0.415270\pi$
$140$	0.376845	−	1.15981i	0.0318492	−	0.0980217i
$141$	−4.06958	−	2.95672i	−0.342720	−	0.249001i
$142$	−25.6585			−2.15321
$143$		0			0
$144$	−18.2947			−1.52456
$145$	−2.07116	−	1.50479i	−0.172000	−	0.124966i
$146$	−1.56950	+	4.83043i	−0.129893	+	0.399769i
$147$	−0.965643	−	2.97194i	−0.0796449	−	0.245122i
$148$	0.478361	−	0.347550i	0.0393210	−	0.0285684i
$149$	−8.54330	+	6.20707i	−0.699894	+	0.508503i	−0.879898	−	0.475163i	$-0.842389\pi$
$149$	−8.54330	+	6.20707i	−0.699894	+	0.508503i	0.180004	+	0.983666i	$0.442389\pi$
$150$	−9.77702	−	30.0906i	−0.798290	−	2.45689i
$151$	4.78027	−	14.7121i	0.389013	−	1.19726i	−0.544515	−	0.838751i	$-0.683286\pi$
$151$	4.78027	−	14.7121i	0.389013	−	1.19726i	0.933527	−	0.358506i	$-0.116714\pi$
$152$	−4.67579	−	3.39716i	−0.379256	−	0.275546i
$153$	37.9494			3.06803
$154$		0			0
$155$	−3.45459			−0.277479
$156$	35.6695	+	25.9154i	2.85584	+	2.07489i
$157$	2.81376	−	8.65985i	0.224562	−	0.691131i	−0.773774	−	0.633462i	$-0.781633\pi$
$157$	2.81376	−	8.65985i	0.224562	−	0.691131i	0.998336	−	0.0576691i	$-0.0183668\pi$
$158$	−5.92951	−	18.2492i	−0.471727	−	1.45183i
$159$	−7.66080	+	5.56589i	−0.607541	+	0.441404i
$160$	−3.11286	+	2.26162i	−0.246093	+	0.178797i
$161$	0.767865	+	2.36324i	0.0605162	+	0.186250i
$162$	−10.8141	+	33.2825i	−0.849639	+	2.61492i
$163$	10.7438	+	7.80582i	0.841518	+	0.611399i	0.922794	−	0.385293i	$-0.125900\pi$
$163$	10.7438	+	7.80582i	0.841518	+	0.611399i	−0.0812762	+	0.996692i	$0.525900\pi$
$164$	6.01182			0.469444
$165$		0			0
$166$	6.84106			0.530969
$167$	−8.13916	−	5.91344i	−0.629827	−	0.457596i	0.226513	−	0.974008i	$-0.427267\pi$
$167$	−8.13916	−	5.91344i	−0.629827	−	0.457596i	−0.856340	+	0.516412i	$0.827267\pi$
$168$	1.05700	−	3.25312i	0.0815494	−	0.250983i
$169$	5.70732	+	17.5653i	0.439024	+	1.35118i
$170$	4.67579	−	3.39716i	0.358616	−	0.260550i
$171$	28.8973	−	20.9951i	2.20983	−	1.60554i
$172$	0.800752	+	2.46446i	0.0610567	+	0.187913i
$173$	−2.52462	+	7.76998i	−0.191943	+	0.590741i	0.808055	+	0.589107i	$0.200520\pi$
$173$	−2.52462	+	7.76998i	−0.191943	+	0.590741i	−0.999999	+	0.00163416i	$0.999480\pi$
$174$	−28.3638	−	20.6075i	−2.15026	−	1.56225i
$175$	−4.76491			−0.360193
$176$		0			0
$177$	−9.76491			−0.733975
$178$	−2.17525	−	1.58041i	−0.163042	−	0.118457i
$179$	−3.78992	+	11.6642i	−0.283272	+	0.871822i	0.703639	+	0.710558i	$0.251557\pi$
$179$	−3.78992	+	11.6642i	−0.283272	+	0.871822i	−0.986911	+	0.161265i	$0.948443\pi$
$180$	2.54932	+	7.84600i	0.190015	+	0.584806i
$181$	5.69949	−	4.14092i	0.423640	−	0.307792i	−0.355461	−	0.934691i	$-0.615676\pi$
$181$	5.69949	−	4.14092i	0.423640	−	0.307792i	0.779101	+	0.626899i	$0.215676\pi$
$182$	9.64354	−	7.00644i	0.714827	−	0.519352i
$183$	2.30813	+	7.10369i	0.170622	+	0.525120i
$184$	−0.840512	+	2.58683i	−0.0619633	+	0.190704i
$185$	0.0922172	+	0.0669997i	0.00677994	+	0.00492592i
$186$	−47.3094			−3.46889
$187$		0			0
$188$	−4.04874			−0.295284
$189$	9.51801	+	6.91524i	0.692333	+	0.503010i
$190$	1.68102	−	5.17366i	0.121954	−	0.375337i
$191$	5.80803	+	17.8753i	0.420254	+	1.29341i	0.907466	+	0.420126i	$0.138014\pi$
$191$	5.80803	+	17.8753i	0.420254	+	1.29341i	−0.487211	+	0.873284i	$0.661986\pi$
$192$	−28.9559	+	21.0377i	−2.08971	+	1.51826i
$193$	−13.3484	+	9.69819i	−0.960840	+	0.698091i	−0.953346	−	0.301881i	$-0.902385\pi$
$193$	−13.3484	+	9.69819i	−0.960840	+	0.698091i	−0.00749397	+	0.999972i	$0.502385\pi$
$194$	5.77514	+	17.7741i	0.414631	+	1.27610i
$195$	−2.62650	+	8.08354i	−0.188088	+	0.578875i
$196$	−2.03479	−	1.47836i	−0.145342	−	0.105597i
$197$	24.4995			1.74552			0.872760	−	0.488149i	$-0.162328\pi$
$197$	24.4995			1.74552			0.872760	+	0.488149i	$0.162328\pi$
$198$		0			0
$199$	−15.3893			−1.09092			−0.545461	−	0.838136i	$-0.683645\pi$
$199$	−15.3893			−1.09092			−0.545461	+	0.838136i	$0.683645\pi$
$200$	−4.21960	−	3.06572i	−0.298371	−	0.216779i
$201$	−9.67060	+	29.7631i	−0.682112	+	2.09932i
$202$	8.50353	+	26.1712i	0.598306	+	1.84140i
$203$	−4.27165	+	3.10353i	−0.299811	+	0.217825i
$204$	35.6695	−	25.9154i	2.49736	−	1.81444i
$205$	0.358133	+	1.10222i	0.0250131	+	0.0769824i
$206$	−7.99103	+	24.5939i	−0.556761	+	1.71354i
$207$	−13.5995	−	9.88059i	−0.945228	−	0.686749i
$208$	−15.1708			−1.05190
$209$		0			0
$210$	3.21949			0.222166
$211$	11.6814	+	8.48703i	0.804180	+	0.584271i	0.912137	−	0.409885i	$-0.134431\pi$
$211$	11.6814	+	8.48703i	0.804180	+	0.584271i	−0.107957	+	0.994156i	$0.534431\pi$
$212$	−2.35519	+	7.24854i	−0.161755	+	0.497832i
$213$	−11.6604	−	35.8869i	−0.798955	−	2.45893i
$214$	18.1535	−	13.1893i	1.24095	−	0.901602i
$215$	−0.404138	+	0.293623i	−0.0275620	+	0.0200249i
$216$	3.97951	+	12.2477i	0.270772	+	0.833349i
$217$	−2.20171	+	6.77617i	−0.149462	+	0.459996i
$218$	−12.6190	−	9.16823i	−0.854666	−	0.620951i
$219$	−7.46927			−0.504726
$220$		0			0
$221$	31.4693			2.11685
$222$	1.26288	+	0.917539i	0.0847592	+	0.0615812i
$223$	5.33164	−	16.4091i	0.357033	−	1.09883i	−0.597788	−	0.801654i	$-0.703954\pi$
$223$	5.33164	−	16.4091i	0.357033	−	1.09883i	0.954821	−	0.297181i	$-0.0960464\pi$
$224$	2.45226	+	7.54727i	0.163848	+	0.504273i
$225$	26.0780	−	18.9468i	1.73853	−	1.26312i
$226$	23.6628	−	17.1920i	1.57403	−	1.14360i
$227$	3.31265	+	10.1953i	0.219868	+	0.676685i	0.998772	+	0.0495413i	$0.0157759\pi$
$227$	3.31265	+	10.1953i	0.219868	+	0.676685i	−0.778904	+	0.627143i	$0.784224\pi$
$228$	12.8238	−	39.4675i	0.849276	−	2.61380i
$229$	−4.41285	−	3.20613i	−0.291610	−	0.211867i	0.432356	−	0.901703i	$-0.357682\pi$
$229$	−4.41285	−	3.20613i	−0.291610	−	0.211867i	−0.723965	+	0.689836i	$0.757682\pi$
$230$	−2.56009			−0.168808
$231$		0			0
$232$	−5.77959			−0.379449
$233$	−24.0922	−	17.5040i	−1.57833	−	1.14673i	−0.918575	−	0.395246i	$-0.870659\pi$
$233$	−24.0922	−	17.5040i	−1.57833	−	1.14673i	−0.659757	−	0.751479i	$-0.729341\pi$
$234$	−24.9186	+	76.6915i	−1.62898	+	5.01348i
$235$	−0.241189	−	0.742305i	−0.0157335	−	0.0484226i
$236$	−6.35848	+	4.61971i	−0.413902	+	0.300717i
$237$	22.8293	−	16.5865i	1.48292	−	1.07741i
$238$	−3.68350	−	11.3367i	−0.238766	−	0.734847i
$239$	0.791113	−	2.43479i	0.0511728	−	0.157494i	−0.922204	−	0.386703i	$-0.873614\pi$
$239$	0.791113	−	2.43479i	0.0511728	−	0.157494i	0.973377	+	0.229209i	$0.0736139\pi$
$240$	−3.31493	−	2.40843i	−0.213978	−	0.155464i
$241$	27.3893			1.76430			0.882151	−	0.470966i	$-0.156095\pi$
$241$	27.3893			1.76430			0.882151	+	0.470966i	$0.156095\pi$
$242$		0			0
$243$	−16.1698			−1.03730
$244$	4.86366	+	3.53366i	0.311364	+	0.226219i
$245$	0.149831	−	0.461131i	0.00957232	−	0.0294606i
$246$	4.90451	+	15.0945i	0.312700	+	0.962392i
$247$	23.9629	−	17.4100i	1.52472	−	1.10777i
$248$	−6.30950	+	4.58412i	−0.400653	+	0.291092i
$249$	3.10888	+	9.56815i	0.197017	+	0.606357i
$250$	3.10888	−	9.56815i	0.196623	−	0.605143i
$251$	−7.96464	−	5.78665i	−0.502724	−	0.365250i	0.307333	−	0.951602i	$-0.400564\pi$
$251$	−7.96464	−	5.78665i	−0.502724	−	0.365250i	−0.810056	+	0.586352i	$0.800564\pi$
$252$	17.0147			1.07182
$253$		0			0
$254$	−5.43991			−0.341330
$255$	6.87627	+	4.99591i	0.430609	+	0.312856i
$256$	1.51950	−	4.67654i	0.0949688	−	0.292284i
$257$	−6.95274	−	21.3983i	−0.433700	−	1.33479i	−0.894413	−	0.447242i	$-0.852406\pi$
$257$	−6.95274	−	21.3983i	−0.433700	−	1.33479i	0.460713	−	0.887549i	$-0.347594\pi$
$258$	−5.53453	+	4.02107i	−0.344565	+	0.250341i
$259$	0.190193	−	0.138183i	0.0118180	−	0.00858628i
$260$	2.11400	+	6.50623i	0.131105	+	0.403499i
$261$	11.0378	−	33.9708i	0.683222	−	2.10274i
$262$	−4.67579	−	3.39716i	−0.288871	−	0.209877i
$263$	−16.0000			−0.986602			−0.493301	−	0.869859i	$-0.664210\pi$
$263$	−16.0000			−0.986602			−0.493301	+	0.869859i	$0.664210\pi$
$264$		0			0
$265$	−1.46927			−0.0902563
$266$	−9.07676	−	6.59465i	−0.556532	−	0.404344i
$267$	1.22189	−	3.76060i	0.0747786	−	0.230145i
$268$	7.78361	+	23.9555i	0.475460	+	1.46331i
$269$	−7.45873	+	5.41908i	−0.454767	+	0.330407i	−0.791475	−	0.611202i	$-0.790686\pi$
$269$	−7.45873	+	5.41908i	−0.454767	+	0.330407i	0.336708	+	0.941609i	$0.390686\pi$
$270$	−9.80618	+	7.12461i	−0.596785	+	0.433590i
$271$	3.26325	+	10.0432i	0.198228	+	0.610084i	0.999924	+	0.0123511i	$0.00393157\pi$
$271$	3.26325	+	10.0432i	0.198228	+	0.610084i	−0.801695	+	0.597733i	$0.796068\pi$
$272$	−4.68802	+	14.4282i	−0.284253	+	0.874841i
$273$	14.1819	+	10.3038i	0.858329	+	0.623612i
$274$	20.6206			1.24574
$275$		0			0
$276$	−19.5298			−1.17556
$277$	15.0154	+	10.9093i	0.902190	+	0.655479i	0.939028	−	0.343842i	$-0.111728\pi$
$277$	15.0154	+	10.9093i	0.902190	+	0.655479i	−0.0368377	+	0.999321i	$0.511728\pi$
$278$	12.9480	−	39.8499i	0.776571	−	2.39004i
$279$	−14.8944	−	45.8402i	−0.891703	−	2.74438i
$280$	0.429373	−	0.311958i	0.0256600	−	0.0186430i
$281$	−20.7581	+	15.0817i	−1.23833	+	0.899698i	−0.997486	−	0.0708669i	$-0.977423\pi$
$281$	−20.7581	+	15.0817i	−1.23833	+	0.899698i	−0.240842	+	0.970564i	$0.577423\pi$
$282$	−3.30301	−	10.1656i	−0.196691	−	0.605354i
$283$	9.35677	−	28.7972i	0.556202	−	1.71181i	−0.136546	−	0.990634i	$-0.543600\pi$
$283$	9.35677	−	28.7972i	0.556202	−	1.71181i	0.692748	−	0.721180i	$-0.256400\pi$
$284$	−24.5706	−	17.8516i	−1.45799	−	1.05929i
$285$	8.00000			0.473879
$286$		0			0
$287$	2.39025			0.141092
$288$	−43.4313	−	31.5547i	−2.55922	−	1.85938i
$289$	4.47125	−	13.7611i	0.263015	−	0.809476i
$290$	−1.68102	−	5.17366i	−0.0987131	−	0.303808i
$291$	−22.2350	+	16.1547i	−1.30344	+	0.947003i
$292$	−4.86366	+	3.53366i	−0.284624	+	0.206792i
$293$	0.942395	+	2.90039i	0.0550553	+	0.169443i	0.974803	−	0.223067i	$-0.0716069\pi$
$293$	0.942395	+	2.90039i	0.0550553	+	0.169443i	−0.919748	+	0.392510i	$0.871607\pi$
$294$	2.05188	−	6.31504i	0.119668	−	0.368300i
$295$	−1.22577	−	0.890576i	−0.0713672	−	0.0518513i
$296$	0.257333			0.0149572
$297$		0			0
$298$	−22.4390			−1.29986
$299$	−11.2773	−	8.19340i	−0.652180	−	0.473837i
$300$	11.5727	−	35.6170i	0.668147	−	2.05635i
$301$	0.318373	+	0.979851i	0.0183507	+	0.0564777i
$302$	26.5927	−	19.3207i	1.53024	−	1.11178i
$303$	−32.7396	+	23.7867i	−1.88084	+	1.36651i
$304$	4.41249	+	13.5803i	0.253074	+	0.778881i
$305$	−0.358133	+	1.10222i	−0.0205066	+	0.0631129i
$306$	65.2377	+	47.3979i	3.72939	+	2.70956i
$307$	3.71904			0.212257			0.106128	−	0.994352i	$-0.466155\pi$
$307$	3.71904			0.212257			0.106128	+	0.994352i	$0.466155\pi$
$308$		0			0
$309$	−38.0294			−2.16341
$310$	−5.93867	−	4.31470i	−0.337294	−	0.245058i
$311$	1.28855	−	3.96575i	0.0730671	−	0.224877i	−0.907853	−	0.419288i	$-0.862280\pi$
$311$	1.28855	−	3.96575i	0.0730671	−	0.224877i	0.980920	+	0.194411i	$0.0622796\pi$
$312$	5.92951	+	18.2492i	0.335692	+	1.03316i
$313$	9.46902	−	6.87965i	0.535221	−	0.388861i	−0.287086	−	0.957905i	$-0.592687\pi$
$313$	9.46902	−	6.87965i	0.535221	−	0.388861i	0.822307	+	0.569044i	$0.192687\pi$
$314$	15.6530	−	11.3726i	0.883349	−	0.641791i
$315$	1.01359	+	3.11951i	0.0571093	+	0.175764i
$316$	7.01851	−	21.6008i	0.394822	−	1.21514i
$317$	1.80823	+	1.31375i	0.101560	+	0.0737878i	0.637406	−	0.770528i	$-0.280007\pi$
$317$	1.80823	+	1.31375i	0.101560	+	0.0737878i	−0.535846	+	0.844316i	$0.680007\pi$
$318$	−20.1211			−1.12834
$319$		0			0
$320$	−5.55345			−0.310447
$321$	26.6968	+	19.3964i	1.49007	+	1.08260i
$322$	−1.63162	+	5.02162i	−0.0909269	+	0.279844i
$323$	−9.15300	−	28.1700i	−0.509287	−	1.56742i
$324$	−33.5115	+	24.3475i	−1.86175	+	1.35264i
$325$	21.6250	−	15.7115i	1.19954	−	0.871515i
$326$	8.72002	+	26.8375i	0.482957	+	1.48639i
$327$	7.08840	−	21.8158i	0.391989	−	1.20642i
$328$	2.11671	+	1.53788i	0.116876	+	0.0849151i
$329$	−1.60975			−0.0887482
$330$		0			0
$331$	22.3250			1.22709			0.613547	−	0.789659i	$-0.289742\pi$
$331$	22.3250			1.22709			0.613547	+	0.789659i	$0.289742\pi$
$332$	6.55099	+	4.75958i	0.359532	+	0.261216i
$333$	−0.491451	+	1.51253i	−0.0269314	+	0.0828862i
$334$	−6.60602	−	20.3312i	−0.361465	−	1.11248i
$335$	−3.92837	+	2.85413i	−0.214630	+	0.155938i
$336$	−6.83684	+	4.96726i	−0.372980	+	0.270986i
$337$	−4.10376	−	12.6301i	−0.223546	−	0.688004i	−0.998436	−	0.0559078i	$-0.982195\pi$
$337$	−4.10376	−	12.6301i	−0.223546	−	0.688004i	0.774890	−	0.632096i	$-0.217805\pi$
$338$	−12.1274	+	37.3243i	−0.659643	+	2.03017i
$339$	34.7989	+	25.2829i	1.89001	+	1.37318i
$340$	6.84106			0.371008
$341$		0			0
$342$	75.8989			4.10414
$343$	−0.809017	−	0.587785i	−0.0436828	−	0.0317374i
$344$	−0.348494	+	1.07255i	−0.0187895	+	0.0578282i
$345$	−1.16342	−	3.58064i	−0.0626365	−	0.192775i
$346$	−14.0445	+	10.2039i	−0.755038	+	0.548567i
$347$	14.5861	−	10.5974i	0.783021	−	0.568898i	−0.122863	−	0.992424i	$-0.539208\pi$
$347$	14.5861	−	10.5974i	0.783021	−	0.568898i	0.905884	+	0.423526i	$0.139208\pi$
$348$	−12.8238	−	39.4675i	−0.687427	−	2.11568i
$349$	−6.78275	+	20.8751i	−0.363072	+	1.11742i	0.588107	+	0.808783i	$0.299873\pi$
$349$	−6.78275	+	20.8751i	−0.363072	+	1.11742i	−0.951180	+	0.308638i	$0.900127\pi$
$350$	−8.19120	−	5.95126i	−0.437838	−	0.318108i
$351$	−65.9982			−3.52272
$352$		0			0
$353$	18.8557			1.00359			0.501795	−	0.864987i	$-0.332673\pi$
$353$	18.8557			1.00359			0.501795	+	0.864987i	$0.332673\pi$
$354$	−16.7865	−	12.1961i	−0.892195	−	0.648218i
$355$	1.80924	−	5.56827i	0.0960244	−	0.295533i
$356$	−0.983469	−	3.02681i	−0.0521238	−	0.160420i
$357$	14.1819	−	10.3038i	0.750587	−	0.545333i
$358$	−21.0834	+	15.3180i	−1.11429	+	0.809582i
$359$	0.472740	+	1.45494i	0.0249502	+	0.0767890i	0.962756	−	0.270371i	$-0.0871462\pi$
$359$	0.472740	+	1.45494i	0.0249502	+	0.0767890i	−0.937806	+	0.347160i	$0.887146\pi$
$360$	−1.10949	+	3.41464i	−0.0584750	+	0.179968i
$361$	−7.18318	−	5.21888i	−0.378062	−	0.274678i
$362$	14.9697			0.786791
$363$		0			0
$364$	14.1093			0.739528
$365$	−0.937604	−	0.681209i	−0.0490764	−	0.0356561i
$366$	−4.90451	+	15.0945i	−0.256363	+	0.789004i
$367$	4.52855	+	13.9375i	0.236389	+	0.727529i	0.996934	+	0.0782446i	$0.0249315\pi$
$367$	4.52855	+	13.9375i	0.236389	+	0.727529i	−0.760546	+	0.649284i	$0.775068\pi$
$368$	5.43656	−	3.94989i	0.283400	−	0.205902i
$369$	−13.0817	+	9.50439i	−0.681005	+	0.494779i
$370$	0.0748466	+	0.230354i	0.00389109	+	0.0119755i
$371$	−0.936407	+	2.88196i	−0.0486158	+	0.149624i
$372$	−45.3035	−	32.9149i	−2.34888	−	1.70656i
$373$	10.0606			0.520916			0.260458	−	0.965485i	$-0.416127\pi$
$373$	10.0606			0.520916			0.260458	+	0.965485i	$0.416127\pi$
$374$		0			0
$375$	14.7952			0.764020
$376$	−1.42552	−	1.03570i	−0.0735158	−	0.0534123i
$377$	9.15300	−	28.1700i	0.471403	−	1.45083i
$378$	7.72514	+	23.7755i	0.397338	+	1.22288i
$379$	14.4762	−	10.5176i	0.743593	−	0.540252i	−0.150241	−	0.988649i	$-0.548005\pi$
$379$	14.4762	−	10.5176i	0.743593	−	0.540252i	0.893834	+	0.448398i	$0.148005\pi$
$380$	5.20925	−	3.78474i	0.267229	−	0.194153i
$381$	−2.47214	−	7.60845i	−0.126651	−	0.389793i
$382$	−12.3414	+	37.9829i	−0.631441	+	1.94338i
$383$	15.3430	+	11.1474i	0.783992	+	0.569604i	0.906174	−	0.422904i	$-0.138989\pi$
$383$	15.3430	+	11.1474i	0.783992	+	0.569604i	−0.122182	+	0.992508i	$0.538989\pi$
$384$	−26.4565			−1.35010
$385$		0			0
$386$	−35.0596			−1.78449
$387$	−5.63863	−	4.09670i	−0.286627	−	0.208247i
$388$	−6.83580	+	21.0384i	−0.347035	+	1.06806i
$389$	10.5883	+	32.5874i	0.536848	+	1.65225i	0.739622	+	0.673023i	$0.235004\pi$
$389$	10.5883	+	32.5874i	0.536848	+	1.65225i	−0.202774	+	0.979226i	$0.564996\pi$
$390$	−14.6113	+	10.6157i	−0.739872	+	0.537548i
$391$	−11.2773	+	8.19340i	−0.570315	+	0.414358i
$392$	−0.338253	−	1.04104i	−0.0170844	−	0.0525802i
$393$	2.62650	−	8.08354i	0.132490	−	0.407761i
$394$	42.1164	+	30.5993i	2.12179	+	1.54157i
$395$	4.37844			0.220303
$396$		0			0
$397$	16.2791			0.817026			0.408513	−	0.912752i	$-0.366047\pi$
$397$	16.2791			0.817026			0.408513	+	0.912752i	$0.366047\pi$
$398$	−26.4553	−	19.2209i	−1.32609	−	0.963457i
$399$	5.09864	−	15.6920i	0.255251	−	0.785582i
$400$	3.98200	+	12.2553i	0.199100	+	0.612766i
$401$	−23.4118	+	17.0096i	−1.16913	+	0.849421i	−0.990904	−	0.134569i	$-0.957035\pi$
$401$	−23.4118	+	17.0096i	−1.16913	+	0.849421i	−0.178223	+	0.983990i	$0.557035\pi$
$402$	−53.7978	+	39.0864i	−2.68319	+	1.94945i
$403$	−12.3510	−	38.0126i	−0.615249	−	1.89354i
$404$	−10.0653	+	30.9777i	−0.500766	+	1.54120i
$405$	−6.46026	−	4.69365i	−0.321013	−	0.233230i
$406$	−11.2195			−0.556814
$407$		0			0
$408$	19.1883			0.949963
$409$	−12.5482	−	9.11681i	−0.620469	−	0.450797i	0.232616	−	0.972569i	$-0.425271\pi$
$409$	−12.5482	−	9.11681i	−0.620469	−	0.450797i	−0.853085	+	0.521771i	$0.825271\pi$
$410$	−0.760991	+	2.34209i	−0.0375827	+	0.115668i
$411$	9.37094	+	28.8408i	0.462234	+	1.42261i
$412$	−24.7631	+	17.9914i	−1.21999	+	0.886374i
$413$	−2.52809	+	1.83676i	−0.124399	+	0.0903811i
$414$	−11.0378	−	33.9708i	−0.542478	−	1.66957i
$415$	−0.482379	+	1.48461i	−0.0236790	+	0.0728766i
$416$	−36.0151	−	26.1665i	−1.76578	−	1.28292i
$417$	61.6197			3.01753
$418$		0			0
$419$	−12.9503			−0.632666			−0.316333	−	0.948648i	$-0.602452\pi$
$419$	−12.9503			−0.632666			−0.316333	+	0.948648i	$0.602452\pi$
$420$	3.08299	+	2.23992i	0.150434	+	0.109297i
$421$	−5.28136	+	16.2543i	−0.257398	+	0.792188i	0.735950	+	0.677036i	$0.236736\pi$
$421$	−5.28136	+	16.2543i	−0.257398	+	0.792188i	−0.993348	+	0.115153i	$0.963264\pi$
$422$	9.48101	+	29.1796i	0.461528	+	1.42044i
$423$	8.81003	−	6.40086i	0.428358	−	0.311220i
$424$	−2.68348	+	1.94967i	−0.130321	+	0.0946841i
$425$	−8.26000	−	25.4217i	−0.400669	−	1.23313i
$426$	24.7769	−	76.2555i	1.20045	−	3.69459i
$427$	1.93375	+	1.40496i	0.0935810	+	0.0679905i
$428$	26.5601			1.28383
$429$		0			0
$430$	−1.06147			−0.0511886
$431$	−15.6530	−	11.3726i	−0.753978	−	0.547797i	0.143079	−	0.989711i	$-0.454300\pi$
$431$	−15.6530	−	11.3726i	−0.753978	−	0.547797i	−0.897057	+	0.441914i	$0.854300\pi$
$432$	9.83184	−	30.2593i	0.473035	−	1.45585i
$433$	4.89034	+	15.0509i	0.235015	+	0.723300i	0.997119	+	0.0758469i	$0.0241660\pi$
$433$	4.89034	+	15.0509i	0.235015	+	0.723300i	−0.762105	+	0.647454i	$0.775834\pi$
$434$	−12.2482	+	8.89881i	−0.587931	+	0.427157i
$435$	6.47214	−	4.70228i	0.310315	−	0.225457i
$436$	−5.70526	−	17.5590i	−0.273233	−	0.840923i
$437$	−4.05436	+	12.4780i	−0.193946	+	0.596906i
$438$	−12.8402	−	9.32894i	−0.613527	−	0.445754i
$439$	−11.0596			−0.527848			−0.263924	−	0.964544i	$-0.585017\pi$
$439$	−11.0596			−0.527848			−0.263924	+	0.964544i	$0.585017\pi$
$440$		0			0
$441$	6.76491			0.322139
$442$	54.0978	+	39.3044i	2.57317	+	1.86952i
$443$	−10.7240	+	33.0049i	−0.509510	+	1.56811i	0.283543	+	0.958960i	$0.408490\pi$
$443$	−10.7240	+	33.0049i	−0.509510	+	1.56811i	−0.793053	+	0.609152i	$0.791510\pi$
$444$	0.570972	+	1.75727i	0.0270971	+	0.0833963i
$445$	0.496355	−	0.360623i	0.0235295	−	0.0170952i
$446$	29.6600	−	21.5493i	1.40444	−	1.02039i
$447$	−10.1973	−	31.3840i	−0.482315	−	1.48441i
$448$	−3.53938	+	10.8931i	−0.167220	+	0.514650i
$449$	29.3623	+	21.3330i	1.38569	+	1.00676i	0.996322	+	0.0856838i	$0.0273075\pi$
$449$	29.3623	+	21.3330i	1.38569	+	1.00676i	0.389371	+	0.921081i	$0.372693\pi$
$450$	68.4939			3.22883
$451$		0			0
$452$	34.6206			1.62842
$453$	39.1076	+	28.4134i	1.83744	+	1.33498i
$454$	−7.03900	+	21.6638i	−0.330356	+	1.01673i
$455$	0.840512	+	2.58683i	0.0394038	+	0.121272i
$456$	14.6113	−	10.6157i	0.684237	−	0.497127i
$457$	1.66702	−	1.21116i	0.0779800	−	0.0566558i	−0.548112	−	0.836405i	$-0.684653\pi$
$457$	1.66702	−	1.21116i	0.0779800	−	0.0566558i	0.626092	+	0.779749i	$0.284653\pi$
$458$	−3.58162	−	11.0231i	−0.167358	−	0.515075i
$459$	−20.3946	+	62.7680i	−0.951936	+	2.92976i
$460$	−2.45154	−	1.78115i	−0.114304	−	0.0830466i
$461$	−7.17076			−0.333975			−0.166988	−	0.985959i	$-0.553404\pi$
$461$	−7.17076			−0.333975			−0.166988	+	0.985959i	$0.553404\pi$
$462$		0			0
$463$	3.45459			0.160548			0.0802741	−	0.996773i	$-0.474420\pi$
$463$	3.45459			0.160548			0.0802741	+	0.996773i	$0.474420\pi$
$464$	11.5521	+	8.39306i	0.536291	+	0.389638i
$465$	3.33590	−	10.2668i	0.154698	−	0.476113i
$466$	−19.5540	−	60.1812i	−0.905824	−	2.78784i
$467$	10.9183	−	7.93261i	0.505239	−	0.367077i	−0.305776	−	0.952104i	$-0.598916\pi$
$467$	10.9183	−	7.93261i	0.505239	−	0.367077i	0.811014	+	0.585026i	$0.198916\pi$
$468$	−77.2191	+	56.1030i	−3.56945	+	2.59336i
$469$	3.09471	+	9.52453i	0.142900	+	0.439802i
$470$	0.512500	−	1.57731i	0.0236399	−	0.0727560i
$471$	23.0195	+	16.7246i	1.06068	+	0.770631i
$472$	−3.42053			−0.157443
$473$		0			0
$474$	59.9612			2.75411
$475$	−20.3540	−	14.7881i	−0.933906	−	0.678523i
$476$	4.36001	−	13.4187i	0.199841	−	0.615047i
$477$	−6.33471	−	19.4962i	−0.290046	−	0.892671i
$478$	4.40098	−	3.19750i	0.201296	−	0.146250i
$479$	−28.3638	+	20.6075i	−1.29598	+	0.941582i	−0.999908	−	0.0135841i	$-0.995676\pi$
$479$	−28.3638	+	20.6075i	−1.29598	+	0.941582i	−0.296069	+	0.955166i	$0.595676\pi$
$480$	−3.71551	−	11.4352i	−0.169589	−	0.521941i
$481$	−0.407532	+	1.25426i	−0.0185819	+	0.0571891i
$482$	47.0841	+	34.2086i	2.14462	+	1.55816i
$483$	−7.76491			−0.353316
$484$		0			0
$485$	−4.26445			−0.193639
$486$	−27.7971	−	20.1957i	−1.26090	−	0.916098i
$487$	9.16718	−	28.2137i	0.415404	−	1.27848i	−0.496484	−	0.868046i	$-0.665376\pi$
$487$	9.16718	−	28.2137i	0.415404	−	1.27848i	0.911889	−	0.410437i	$-0.134624\pi$
$488$	0.808510	+	2.48834i	0.0365995	+	0.112642i
$489$	−33.5731	+	24.3923i	−1.51823	+	1.10306i
$490$	0.833511	−	0.605581i	0.0376542	−	0.0273574i
$491$	7.88915	+	24.2803i	0.356032	+	1.09575i	0.955409	+	0.295287i	$0.0954153\pi$
$491$	7.88915	+	24.2803i	0.356032	+	1.09575i	−0.599376	+	0.800467i	$0.704585\pi$
$492$	−5.80527	+	17.8668i	−0.261722	+	0.805496i
$493$	−23.9629	−	17.4100i	−1.07923	−	0.784109i
$494$	62.9385			2.83174
$495$		0			0
$496$	19.2682			0.865169
$497$	−9.76907	−	7.09764i	−0.438203	−	0.318373i
$498$	−6.60602	+	20.3312i	−0.296023	+	0.911064i
$499$	−7.92891	−	24.4027i	−0.354947	−	1.09241i	−0.956040	−	0.293235i	$-0.905268\pi$
$499$	−7.92891	−	24.4027i	−0.354947	−	1.09241i	0.601094	−	0.799179i	$-0.294732\pi$
$500$	9.63398	−	6.99950i	0.430845	−	0.313027i
$501$	25.4339	−	18.4788i	1.13630	−	0.825573i
$502$	−6.46437	−	19.8953i	−0.288519	−	0.887971i
$503$	0.791113	−	2.43479i	0.0352740	−	0.108562i	−0.931869	−	0.362794i	$-0.881823\pi$
$503$	0.791113	−	2.43479i	0.0352740	−	0.108562i	0.967143	+	0.254232i	$0.0818228\pi$
$504$	5.99072	+	4.35251i	0.266848	+	0.193876i
$505$	−6.27913			−0.279418
$506$		0			0
$507$	−57.7143			−2.56318
$508$	−5.20925	−	3.78474i	−0.231123	−	0.167921i
$509$	4.15770	−	12.7961i	0.184287	−	0.567176i	−0.815649	−	0.578547i	$-0.803620\pi$
$509$	4.15770	−	12.7961i	0.184287	−	0.567176i	0.999935	+	0.0113716i	$0.00361976\pi$
$510$	5.58102	+	17.1766i	0.247132	+	0.760593i
$511$	−1.93375	+	1.40496i	−0.0855443	+	0.0621516i
$512$	22.1519	−	16.0943i	0.978987	−	0.711275i
$513$	19.1959	+	59.0789i	0.847520	+	2.60840i
$514$	14.7738	−	45.4690i	0.651643	−	2.00555i
$515$	−4.77376	−	3.46834i	−0.210357	−	0.152833i
$516$	−8.09747			−0.356471
$517$		0			0
$518$	0.499542			0.0219486
$519$	−20.6541	−	15.0061i	−0.906612	−	0.658693i
$520$	−0.920032	+	2.83157i	−0.0403461	+	0.124172i
$521$	−9.96062	−	30.6556i	−0.436383	−	1.34305i	−0.891663	−	0.452700i	$-0.850461\pi$
$521$	−9.96062	−	30.6556i	−0.436383	−	1.34305i	0.455280	−	0.890348i	$-0.349539\pi$
$522$	61.4035	−	44.6122i	2.68756	−	1.95262i
$523$	26.1634	−	19.0088i	1.14404	−	0.831196i	0.156366	−	0.987699i	$-0.450022\pi$
$523$	26.1634	−	19.0088i	1.14404	−	0.831196i	0.987678	+	0.156503i	$0.0500221\pi$
$524$	−2.11400	−	6.50623i	−0.0923507	−	0.284226i
$525$	4.60120	−	14.1610i	0.200813	−	0.618038i
$526$	−27.5051	−	19.9836i	−1.19928	−	0.871327i
$527$	−39.9688			−1.74107
$528$		0			0
$529$	−16.8255			−0.731542
$530$	−2.52577	−	1.83508i	−0.109712	−	0.0797107i
$531$	6.53248	−	20.1049i	0.283486	−	0.872479i
$532$	−4.10376	−	12.6301i	−0.177921	−	0.547583i
$533$	−10.8479	+	7.88144i	−0.469874	+	0.341383i
$534$	6.79742	−	4.93861i	0.294153	−	0.213715i
$535$	1.58223	+	4.86959i	0.0684056	+	0.210531i
$536$	−3.38749	+	10.4256i	−0.146317	+	0.450319i
$537$	−31.0056	−	22.5269i	−1.33799	−	0.972106i
$538$	−19.5904			−0.844601
$539$		0			0
$540$	−14.3472			−0.617407
$541$	19.0123	+	13.8132i	0.817401	+	0.593877i	0.915967	−	0.401254i	$-0.131425\pi$
$541$	19.0123	+	13.8132i	0.817401	+	0.593877i	−0.0985656	+	0.995131i	$0.531425\pi$
$542$	−6.93403	+	21.3407i	−0.297842	+	0.916664i
$543$	6.80291	+	20.9372i	0.291941	+	0.898501i
$544$	−36.0151	+	26.1665i	−1.54413	+	1.12188i
$545$	2.87943	−	2.09203i	0.123341	−	0.0896128i
$546$	11.5105	+	35.4258i	0.492605	+	1.51608i
$547$	−1.27349	+	3.91940i	−0.0544506	+	0.167582i	−0.974583	−	0.224025i	$-0.928080\pi$
$547$	−1.27349	+	3.91940i	−0.0544506	+	0.167582i	0.920133	+	0.391606i	$0.128080\pi$
$548$	19.7463	+	14.3465i	0.843521	+	0.612854i
$549$	−16.1698			−0.690112
$550$		0			0
$551$	−27.8789			−1.18768
$552$	−6.87627	−	4.99591i	−0.292674	−	0.212640i
$553$	2.79051	−	8.58830i	0.118665	−	0.365212i
$554$	12.1870	+	37.5078i	0.517777	+	1.59356i
$555$	−0.288168	+	0.209366i	−0.0122321	+	0.00888711i
$556$	40.1241	−	29.1519i	1.70164	−	1.23631i
$557$	−4.30753	−	13.2572i	−0.182516	−	0.561726i	0.817381	−	0.576098i	$-0.195425\pi$
$557$	−4.30753	−	13.2572i	−0.182516	−	0.561726i	−0.999897	+	0.0143718i	$0.995425\pi$
$558$	31.6488	−	97.4051i	1.33980	−	4.12349i
$559$	−4.67579	−	3.39716i	−0.197765	−	0.143684i
$560$	−1.31124			−0.0554100
$561$		0			0
$562$	−54.5213			−2.29984
$563$	−2.20049	−	1.59875i	−0.0927395	−	0.0673792i	0.540449	−	0.841377i	$-0.318254\pi$
$563$	−2.20049	−	1.59875i	−0.0927395	−	0.0673792i	−0.633189	+	0.773997i	$0.718254\pi$
$564$	3.90963	−	12.0326i	0.164625	−	0.506664i
$565$	2.06240	+	6.34743i	0.0867660	+	0.267038i
$566$	52.0519	−	37.8179i	2.18790	−	1.58961i
$567$	−13.3239	+	9.68039i	−0.559552	+	0.406538i
$568$	−4.08448	−	12.5707i	−0.171381	−	0.527457i
$569$	−8.56565	+	26.3624i	−0.359091	+	1.10517i	0.594508	+	0.804089i	$0.297347\pi$
$569$	−8.56565	+	26.3624i	−0.359091	+	1.10517i	−0.953599	+	0.301079i	$0.902653\pi$
$570$	13.7525	+	9.99181i	0.576031	+	0.418511i
$571$	38.1193			1.59524			0.797621	−	0.603159i	$-0.206092\pi$
$571$	38.1193			1.59524			0.797621	+	0.603159i	$0.206092\pi$
$572$		0			0
$573$	−58.7328			−2.45360
$574$	4.10901	+	2.98537i	0.171507	+	0.124607i
$575$	−3.65880	+	11.2606i	−0.152583	+	0.469601i
$576$	−23.9436	−	73.6907i	−0.997649	−	3.07045i
$577$	−18.7731	+	13.6394i	−0.781534	+	0.567818i	−0.905439	−	0.424476i	$-0.860458\pi$
$577$	−18.7731	+	13.6394i	−0.781534	+	0.567818i	0.123905	+	0.992294i	$0.460458\pi$
$578$	24.8737	−	18.0718i	1.03461	−	0.751687i
$579$	−15.9327	−	49.0357i	−0.662139	−	2.03785i
$580$	1.98976	−	6.12384i	0.0826202	−	0.254279i
$581$	2.60463	+	1.89237i	0.108058	+	0.0785088i
$582$	−58.4002			−2.42077
$583$		0			0
$584$	−2.61639			−0.108267
$585$	−14.8861	−	10.8154i	−0.615465	−	0.447161i
$586$	−2.00248	+	6.16300i	−0.0827217	+	0.254591i
$587$	−3.41453	−	10.5088i	−0.140933	−	0.433746i	0.855533	−	0.517749i	$-0.173230\pi$
$587$	−3.41453	−	10.5088i	−0.140933	−	0.433746i	−0.996466	+	0.0840022i	$0.973230\pi$
$588$	6.35848	−	4.61971i	0.262219	−	0.190514i
$589$	−30.4350	+	22.1123i	−1.25405	+	0.911122i
$590$	−0.994879	−	3.06192i	−0.0409585	−	0.126057i
$591$	−23.6578	+	72.8112i	−0.973152	+	2.99505i
$592$	−0.514349	−	0.373696i	−0.0211396	−	0.0153588i
$593$	−36.3884			−1.49429			−0.747147	−	0.664659i	$-0.768577\pi$
$593$	−36.3884			−1.49429			−0.747147	+	0.664659i	$0.768577\pi$
$594$		0			0
$595$	2.71995			0.111507
$596$	−21.4876	−	15.6116i	−0.880165	−	0.639477i
$597$	14.8606	−	45.7362i	0.608204	−	1.87186i
$598$	−9.15300	−	28.1700i	−0.374294	−	1.15196i
$599$	−23.9942	+	17.4328i	−0.980377	+	0.712286i	−0.957793	−	0.287459i	$-0.907189\pi$
$599$	−23.9942	+	17.4328i	−0.980377	+	0.712286i	−0.0225843	+	0.999745i	$0.507189\pi$
$600$	13.1858	−	9.58002i	0.538307	−	0.391103i
$601$	0.429895	+	1.32308i	0.0175358	+	0.0539696i	0.959442	−	0.281908i	$-0.0909672\pi$
$601$	0.429895	+	1.32308i	0.0175358	+	0.0539696i	−0.941906	+	0.335877i	$0.890967\pi$
$602$	−0.676506	+	2.08207i	−0.0275723	+	0.0848589i
$603$	−54.8096	−	39.8215i	−2.23202	−	1.62166i
$604$	38.9073			1.58312
$605$		0			0
$606$	−85.9906			−3.49313
$607$	−25.0298	−	18.1852i	−1.01593	−	0.738115i	−0.0504839	−	0.998725i	$-0.516076\pi$
$607$	−25.0298	−	18.1852i	−1.01593	−	0.738115i	−0.965444	+	0.260610i	$0.916076\pi$
$608$	−12.9480	+	39.8499i	−0.525112	+	1.61613i
$609$	−5.09864	−	15.6920i	−0.206607	−	0.635872i
$610$	−1.99230	+	1.44749i	−0.0806659	+	0.0586072i
$611$	7.30565	−	5.30786i	0.295555	−	0.214733i
$612$	29.4951	+	90.7765i	1.19227	+	3.66942i
$613$	2.52154	−	7.76049i	0.101844	−	0.313443i	−0.887133	−	0.461514i	$-0.847306\pi$
$613$	2.52154	−	7.76049i	0.101844	−	0.313443i	0.988977	+	0.148071i	$0.0473064\pi$
$614$	6.39328	+	4.64499i	0.258012	+	0.187456i
$615$	−3.62156			−0.146036
$616$		0			0
$617$	−27.5298			−1.10831			−0.554154	−	0.832414i	$-0.686958\pi$
$617$	−27.5298			−1.10831			−0.554154	+	0.832414i	$0.686958\pi$
$618$	−65.3751	−	47.4978i	−2.62977	−	1.91064i
$619$	6.17215	−	18.9959i	0.248080	−	0.763511i	−0.747035	−	0.664785i	$-0.768523\pi$
$619$	6.17215	−	18.9959i	0.248080	−	0.763511i	0.995115	−	0.0987261i	$-0.0314768\pi$
$620$	−2.68497	−	8.26350i	−0.107831	−	0.331870i
$621$	23.6509	−	17.1834i	0.949080	−	0.689547i
$622$	7.16824	−	5.20803i	0.287420	−	0.208823i
$623$	−0.391020	−	1.20344i	−0.0156659	−	0.0482146i
$624$	14.6495	−	45.0866i	0.586451	−	1.80491i
$625$	−17.4172	−	12.6544i	−0.696690	−	0.506175i
$626$	24.8704			0.994022
$627$		0			0
$628$	22.9016			0.913874
$629$	1.06693	+	0.775172i	0.0425414	+	0.0309081i
$630$	−2.15376	+	6.62860i	−0.0858080	+	0.264090i
$631$	−5.32565	−	16.3907i	−0.212011	−	0.652502i	−0.999352	−	0.0359852i	$-0.988543\pi$
$631$	−5.32565	−	16.3907i	−0.212011	−	0.652502i	0.787341	−	0.616517i	$-0.211457\pi$
$632$	7.99683	−	5.81004i	0.318097	−	0.231111i
$633$	−36.5030	+	26.5210i	−1.45086	+	1.05411i
$634$	1.46762	+	4.51686i	0.0582866	+	0.179388i
$635$	0.383580	−	1.18054i	0.0152219	−	0.0468483i
$636$	−19.2680	−	13.9990i	−0.764024	−	0.555096i
$637$	5.60975			0.222266
$638$		0			0
$639$	81.6878			3.23152
$640$	−3.32104	−	2.41288i	−0.131276	−	0.0953774i
$641$	−13.7250	+	42.2411i	−0.542103	+	1.66842i	0.185675	+	0.982611i	$0.440553\pi$
$641$	−13.7250	+	42.2411i	−0.542103	+	1.66842i	−0.727779	+	0.685812i	$0.759447\pi$
$642$	21.6680	+	66.6874i	0.855170	+	2.63194i
$643$	18.2301	−	13.2449i	0.718924	−	0.522329i	−0.167117	−	0.985937i	$-0.553446\pi$
$643$	18.2301	−	13.2449i	0.718924	−	0.522329i	0.886040	+	0.463609i	$0.153446\pi$
$644$	−5.05617	+	3.67352i	−0.199241	+	0.144757i
$645$	−0.482379	−	1.48461i	−0.0189936	−	0.0584564i
$646$	19.4491	−	59.8581i	0.765214	−	2.35509i
$647$	15.1899	+	11.0361i	0.597178	+	0.433876i	0.844876	−	0.534962i	$-0.179674\pi$
$647$	15.1899	+	11.0361i	0.597178	+	0.433876i	−0.247698	+	0.968837i	$0.579674\pi$
$648$	−18.0274			−0.708184
$649$		0			0
$650$	56.7980			2.22780
$651$	−18.0123	−	13.0867i	−0.705958	−	0.512909i
$652$	−10.3215	+	31.7664i	−0.404222	+	1.24407i
$653$	9.76883	+	30.0654i	0.382284	+	1.17655i	0.938431	+	0.345466i	$0.112279\pi$
$653$	9.76883	+	30.0654i	0.382284	+	1.17655i	−0.556147	+	0.831084i	$0.687721\pi$
$654$	39.4329	−	28.6497i	1.54195	−	1.12029i
$655$	1.06693	−	0.775172i	0.0416885	−	0.0302885i
$656$	−1.99752	−	6.14772i	−0.0779899	−	0.240028i
$657$	4.99676	−	15.3784i	0.194942	−	0.599970i
$658$	−2.76727	−	2.01054i	−0.107879	−	0.0783789i
$659$	19.8477			0.773157			0.386578	−	0.922257i	$-0.373657\pi$
$659$	19.8477			0.773157			0.386578	+	0.922257i	$0.373657\pi$
$660$		0			0
$661$	31.4234			1.22223			0.611114	−	0.791542i	$-0.290722\pi$
$661$	31.4234			1.22223			0.611114	+	0.791542i	$0.290722\pi$
$662$	38.3782	+	27.8834i	1.49161	+	1.08372i
$663$	−30.3881	+	93.5249i	−1.18017	+	3.63220i
$664$	1.08900	+	3.35161i	0.0422615	+	0.130068i
$665$	2.07116	−	1.50479i	0.0803161	−	0.0583531i
$666$	−2.73395	+	1.98633i	−0.105939	+	0.0769689i
$667$	4.05436	+	12.4780i	0.156985	+	0.483152i
$668$	7.81927	−	24.0652i	0.302536	−	0.931112i
$669$	43.6185	+	31.6907i	1.68639	+	1.22523i
$670$	−10.3179			−0.398615
$671$		0			0
$672$	−24.7980			−0.956606
$673$	15.5489	+	11.2969i	0.599366	+	0.435465i	0.845654	−	0.533732i	$-0.179211\pi$
$673$	15.5489	+	11.2969i	0.599366	+	0.435465i	−0.246288	+	0.969197i	$0.579211\pi$
$674$	8.72002	−	26.8375i	0.335883	−	1.03374i
$675$	17.3231	+	53.3150i	0.666766	+	2.05210i
$676$	−37.5811	+	27.3042i	−1.44543	+	1.05016i
$677$	−20.8167	+	15.1242i	−0.800051	+	0.581271i	−0.910929	−	0.412563i	$-0.864634\pi$
$677$	−20.8167	+	15.1242i	−0.800051	+	0.581271i	0.110878	+	0.993834i	$0.464634\pi$
$678$	28.2439	+	86.9259i	1.08470	+	3.33837i
$679$	−2.71786	+	8.36472i	−0.104302	+	0.321008i
$680$	2.40867	+	1.75000i	0.0923685	+	0.0671096i
$681$	−33.4986			−1.28367
$682$		0			0
$683$	−11.0596			−0.423185			−0.211593	−	0.977358i	$-0.567865\pi$
$683$	−11.0596			−0.423185			−0.211593	+	0.977358i	$0.567865\pi$
$684$	72.6807	+	52.8056i	2.77902	+	2.01907i
$685$	−1.45401	+	4.47498i	−0.0555548	+	0.170980i
$686$	−0.656626	−	2.02089i	−0.0250701	−	0.0771578i
$687$	13.7897	−	10.0188i	0.526108	−	0.382240i
$688$	2.25411	−	1.63771i	0.0859372	−	0.0624370i
$689$	−5.25301	−	16.1671i	−0.200124	−	0.615917i
$690$	2.47214	−	7.60845i	0.0941126	−	0.289649i
$691$	−36.4265	−	26.4654i	−1.38573	−	1.00679i	−0.996319	−	0.0857252i	$-0.972679\pi$
$691$	−36.4265	−	26.4654i	−1.38573	−	1.00679i	−0.389409	−	0.921065i	$-0.627321\pi$
$692$	−20.5483			−0.781128
$693$		0			0
$694$	38.3103			1.45424
$695$	7.73502	+	5.61982i	0.293406	+	0.213172i
$696$	5.58102	−	17.1766i	0.211548	−	0.651078i
$697$	4.14352	+	12.7524i	0.156947	+	0.483033i
$698$	−37.7326	+	27.4143i	−1.42820	+	1.03765i
$699$	75.2853	−	54.6980i	2.84755	−	2.06887i
$700$	−3.70338	−	11.3978i	−0.139975	−	0.430798i
$701$	14.4554	−	44.4892i	0.545973	−	1.68033i	−0.172692	−	0.984976i	$-0.555246\pi$
$701$	14.4554	−	44.4892i	0.545973	−	1.68033i	0.718665	−	0.695357i	$-0.244754\pi$
$702$	−113.455	−	82.4301i	−4.28210	−	3.11113i
$703$	1.24129			0.0468162
$704$		0			0
$705$	2.43899			0.0918577
$706$	32.4143	+	23.5504i	1.21993	+	0.886330i
$707$	−4.00188	+	12.3165i	−0.150506	+	0.463210i
$708$	−7.58949	−	23.3580i	−0.285230	−	0.877849i
$709$	7.39786	−	5.37486i	0.277833	−	0.201857i	−0.440139	−	0.897930i	$-0.645071\pi$
$709$	7.39786	−	5.37486i	0.277833	−	0.201857i	0.717972	+	0.696072i	$0.245071\pi$
$710$	10.0648	−	7.31253i	0.377727	−	0.274434i
$711$	18.8775	+	58.0991i	0.707963	+	2.17889i
$712$	0.428014	−	1.31729i	0.0160405	−	0.0493676i
$713$	14.3231	+	10.4064i	0.536405	+	0.389721i
$714$	37.2489			1.39400
$715$		0			0
$716$	−30.8468			−1.15280
$717$	6.47214	+	4.70228i	0.241706	+	0.175610i
$718$	−1.00452	+	3.09159i	−0.0374883	+	0.115377i
$719$	−9.41435	−	28.9744i	−0.351096	−	1.08056i	−0.958239	−	0.285970i	$-0.907684\pi$
$719$	−9.41435	−	28.9744i	−0.351096	−	1.08056i	0.607143	−	0.794593i	$-0.292316\pi$
$720$	7.17632	−	5.21390i	0.267446	−	0.194311i
$721$	−9.84561	+	7.15325i	−0.366670	+	0.266401i
$722$	−5.83011	−	17.9432i	−0.216974	−	0.667778i
$723$	−26.4483	+	81.3995i	−0.983623	+	3.02728i
$724$	14.3350	+	10.4150i	0.532756	+	0.387070i
$725$	−25.1589			−0.934380
$726$		0			0
$727$	−6.12580			−0.227193			−0.113597	−	0.993527i	$-0.536237\pi$
$727$	−6.12580			−0.227193			−0.113597	+	0.993527i	$0.536237\pi$
$728$	4.96775	+	3.60928i	0.184117	+	0.133769i
$729$	0.346440	−	1.06623i	0.0128311	−	0.0394901i
$730$	−0.760991	−	2.34209i	−0.0281656	−	0.0866847i
$731$	−4.67579	+	3.39716i	−0.172940	+	0.125648i
$732$	−15.1984	+	11.0423i	−0.561748	+	0.408134i
$733$	−13.0005	−	40.0115i	−0.480185	−	1.47786i	−0.838835	−	0.544385i	$-0.816763\pi$
$733$	−13.0005	−	40.0115i	−0.480185	−	1.47786i	0.358651	−	0.933472i	$-0.383237\pi$
$734$	−9.62265	+	29.6155i	−0.355179	+	1.09313i
$735$	1.22577	+	0.890576i	0.0452133	+	0.0328494i
$736$	19.7190			0.726853
$737$		0			0
$738$	−34.3591			−1.26477
$739$	23.3628	+	16.9741i	0.859414	+	0.624401i	0.927725	−	0.373263i	$-0.121761\pi$
$739$	23.3628	+	16.9741i	0.859414	+	0.624401i	−0.0683118	+	0.997664i	$0.521761\pi$
$740$	−0.0885928	+	0.272661i	−0.00325674	+	0.0100232i
$741$	28.6021	+	88.0281i	1.05072	+	3.23379i
$742$	−5.20925	+	3.78474i	−0.191238	+	0.138942i
$743$	11.8773	−	8.62939i	0.435737	−	0.316582i	−0.348202	−	0.937420i	$-0.613208\pi$
$743$	11.8773	−	8.62939i	0.435737	−	0.316582i	0.783939	+	0.620838i	$0.213208\pi$
$744$	−7.53101	−	23.1781i	−0.276100	−	0.849750i
$745$	1.58223	−	4.86959i	0.0579682	−	0.178408i
$746$	17.2948	+	12.5654i	0.633207	+	0.460052i
$747$	−21.7796			−0.796873
$748$		0			0
$749$	10.5601			0.385857
$750$	25.4339	+	18.4788i	0.928716	+	0.674752i
$751$	−2.04136	+	6.28265i	−0.0744901	+	0.229257i	−0.981368	−	0.192136i	$-0.938459\pi$
$751$	−2.04136	+	6.28265i	−0.0744901	+	0.229257i	0.906878	+	0.421393i	$0.138459\pi$
$752$	1.34525	+	4.14026i	0.0490563	+	0.150980i
$753$	24.8886	−	18.0826i	0.906991	−	0.658967i
$754$	50.9183	−	36.9943i	1.85434	−	1.34725i
$755$	2.31777	+	7.13336i	0.0843523	+	0.259610i
$756$	−9.14393	+	28.1421i	−0.332561	+	1.02352i
$757$	−2.02217	−	1.46919i	−0.0734971	−	0.0533988i	0.550430	−	0.834881i	$-0.314464\pi$
$757$	−2.02217	−	1.46919i	−0.0734971	−	0.0533988i	−0.623927	+	0.781483i	$0.714464\pi$
$758$	38.0218			1.38101
$759$		0			0
$760$	2.80230			0.101650
$761$	9.74763	+	7.08207i	0.353351	+	0.256725i	0.750274	−	0.661127i	$-0.229922\pi$
$761$	9.74763	+	7.08207i	0.353351	+	0.256725i	−0.396922	+	0.917852i	$0.629922\pi$
$762$	5.25301	−	16.1671i	0.190296	−	0.585672i
$763$	−2.26837	−	6.98132i	−0.0821205	−	0.252741i
$764$	−38.2442	+	27.7861i	−1.38363	+	1.00526i
$765$	−14.8861	+	10.8154i	−0.538208	+	0.391031i
$766$	12.4529	+	38.3262i	0.449942	+	1.38478i
$767$	5.41701	−	16.6718i	0.195597	−	0.601986i
$768$	12.4311	+	9.03173i	0.448569	+	0.325905i
$769$	0.489560			0.0176540			0.00882699	−	0.999961i	$-0.497190\pi$
$769$	0.489560			0.0176540			0.00882699	+	0.999961i	$0.497190\pi$
$770$		0			0
$771$	70.3085			2.53210
$772$	−33.5731	−	24.3923i	−1.20832	−	0.877897i
$773$	−14.4367	+	44.4316i	−0.519252	+	1.59809i	0.256159	+	0.966635i	$0.417543\pi$
$773$	−14.4367	+	44.4316i	−0.519252	+	1.59809i	−0.775410	+	0.631458i	$0.782457\pi$
$774$	−4.57650	−	14.0850i	−0.164499	−	0.506276i
$775$	−27.4657	+	19.9550i	−0.986596	+	0.716804i
$776$	−7.78864	+	5.65878i	−0.279596	+	0.203138i
$777$	0.227014	+	0.698677i	0.00814408	+	0.0250649i
$778$	−22.4989	+	69.2446i	−0.806625	+	2.48254i
$779$	10.2103	+	7.41823i	0.365823	+	0.265786i
$780$	−21.3775			−0.765438
$781$		0			0
$782$	−29.6197			−1.05920
$783$	50.2555	+	36.5128i	1.79599	+	1.30486i
$784$	−0.835692	+	2.57200i	−0.0298461	+	0.0918570i
$785$	1.36428	+	4.19883i	0.0486934	+	0.149863i
$786$	14.6113	−	10.6157i	0.521168	−	0.378650i
$787$	6.74694	−	4.90194i	0.240503	−	0.174735i	−0.461005	−	0.887398i	$-0.652511\pi$
$787$	6.74694	−	4.90194i	0.240503	−	0.174735i	0.701507	+	0.712662i	$0.252511\pi$
$788$	19.0415	+	58.6038i	0.678327	+	2.08768i
$789$	15.4503	−	47.5511i	0.550045	−	1.69286i
$790$	7.52683	+	5.46856i	0.267793	+	0.194563i
$791$	13.7649			0.489424
$792$		0			0
$793$	−13.4087			−0.476157
$794$	27.9849	+	20.3322i	0.993148	+	0.721564i
$795$	1.41879	−	4.36657i	0.0503191	−	0.154866i
$796$	−11.9609	−	36.8119i	−0.423943	−	1.30476i
$797$	25.4963	−	18.5241i	0.903125	−	0.656158i	−0.0361420	−	0.999347i	$-0.511507\pi$
$797$	25.4963	−	18.5241i	0.903125	−	0.656158i	0.939267	+	0.343188i	$0.111507\pi$
$798$	28.3638	−	20.6075i	1.00407	−	0.729499i
$799$	−2.79051	−	8.58830i	−0.0987211	−	0.303832i
$800$	−11.6848	+	35.9620i	−0.413119	+	1.27145i
$801$	6.92526	+	5.03150i	0.244692	+	0.177779i
$802$	−61.4911			−2.17132
$803$		0			0
$804$	−78.7106			−2.77591
$805$	−0.974716	−	0.708172i	−0.0343542	−	0.0249598i
$806$	26.2445	−	80.7724i	0.924425	−	2.84509i
$807$	−8.90274	−	27.3998i	−0.313391	−	0.964519i
$808$	−11.4683	+	8.33219i	−0.403453	+	0.293125i
$809$	−12.5401	+	9.11094i	−0.440888	+	0.320324i	−0.785988	−	0.618242i	$-0.787845\pi$
$809$	−12.5401	+	9.11094i	−0.440888	+	0.320324i	0.345100	+	0.938566i	$0.387845\pi$
$810$	−5.24337	−	16.1374i	−0.184233	−	0.567011i
$811$	−14.9378	+	45.9738i	−0.524537	+	1.61436i	0.240694	+	0.970601i	$0.422625\pi$
$811$	−14.9378	+	45.9738i	−0.524537	+	1.61436i	−0.765231	+	0.643756i	$0.777375\pi$
$812$	−10.7438	−	7.80582i	−0.377033	−	0.273930i
$813$	−32.9991			−1.15733
$814$		0			0
$815$	−6.43899			−0.225548
$816$	−38.3530	−	27.8651i	−1.34262	−	0.975472i
$817$	−1.68102	+	5.17366i	−0.0588116	+	0.181003i
$818$	−10.1846	−	31.3448i	−0.356095	−	1.09595i
$819$	−30.7017	+	22.3061i	−1.07281	+	0.779439i
$820$	−2.35820	+	1.71334i	−0.0823521	+	0.0598323i
$821$	−3.26325	−	10.0432i	−0.113888	−	0.350512i	0.877825	−	0.478981i	$-0.158994\pi$
$821$	−3.26325	−	10.0432i	−0.113888	−	0.350512i	−0.991714	+	0.128469i	$0.958994\pi$
$822$	−19.9122	+	61.2834i	−0.694517	+	2.13750i
$823$	−15.6335	−	11.3584i	−0.544950	−	0.395929i	0.280970	−	0.959717i	$-0.409344\pi$
$823$	−15.6335	−	11.3584i	−0.544950	−	0.395929i	−0.825920	+	0.563787i	$0.809344\pi$
$824$	−13.3212			−0.464067
$825$		0			0
$826$	−6.64002			−0.231036
$827$	0.429373	+	0.311958i	0.0149308	+	0.0108478i	0.595226	−	0.803559i	$-0.297063\pi$
$827$	0.429373	+	0.311958i	0.0149308	+	0.0108478i	−0.580295	+	0.814406i	$0.697063\pi$
$828$	13.0650	−	40.2098i	0.454039	−	1.39739i
$829$	−14.5842	−	44.8855i	−0.506530	−	1.55894i	−0.798184	−	0.602414i	$-0.794206\pi$
$829$	−14.5842	−	44.8855i	−0.506530	−	1.55894i	0.291654	−	0.956524i	$-0.405794\pi$
$830$	−2.68348	+	1.94967i	−0.0931451	+	0.0676739i
$831$	−46.9215	+	34.0905i	−1.62769	+	1.18259i
$832$	−19.8550	−	61.1075i	−0.688349	−	2.11852i
$833$	1.73351	−	5.33519i	0.0600625	−	0.184853i
$834$	105.929	+	76.9616i	3.66801	+	2.66496i
$835$	4.87798			0.168809
$836$		0			0
$837$	83.8236			2.89737
$838$	−22.2625	−	16.1747i	−0.769046	−	0.558745i
$839$	−11.7128	+	36.0484i	−0.404372	+	1.24453i	0.517046	+	0.855958i	$0.327032\pi$
$839$	−11.7128	+	36.0484i	−0.404372	+	1.24453i	−0.921418	+	0.388572i	$0.872968\pi$
$840$	0.512500	+	1.57731i	0.0176829	+	0.0544224i
$841$	0.906992	−	0.658969i	0.0312756	−	0.0227231i
$842$	−29.3803	+	21.3460i	−1.01251	+	0.735633i
$843$	−24.7769	−	76.2555i	−0.853363	−	2.62638i
$844$	−11.2223	+	34.5386i	−0.386287	+	1.18887i
$845$	−7.24478	−	5.26364i	−0.249228	−	0.181075i
$846$	23.1396			0.795555
$847$		0			0
$848$	8.19495			0.281416
$849$	76.5482	+	55.6155i	2.62713	+	1.90872i
$850$	17.5516	−	54.0182i	0.602014	−	1.85281i
$851$	−0.180518	−	0.555578i	−0.00618808	−	0.0190450i
$852$	76.7802	−	55.7841i	2.63045	−	1.91113i
$853$	5.07185	−	3.68491i	0.173657	−	0.126169i	−0.497562	−	0.867429i	$-0.665771\pi$
$853$	5.07185	−	3.68491i	0.173657	−	0.126169i	0.671219	+	0.741260i	$0.265771\pi$
$854$	1.56950	+	4.83043i	0.0537072	+	0.165294i
$855$	−5.35180	+	16.4712i	−0.183028	+	0.563302i
$856$	9.35157	+	6.79431i	0.319630	+	0.232225i
$857$	36.9503			1.26220			0.631100	−	0.775702i	$-0.282604\pi$
$857$	36.9503			1.26220			0.631100	+	0.775702i	$0.282604\pi$
$858$		0			0
$859$	8.90447			0.303817			0.151908	−	0.988395i	$-0.451458\pi$
$859$	8.90447			0.303817			0.151908	+	0.988395i	$0.451458\pi$
$860$	−1.01646	−	0.738503i	−0.0346611	−	0.0251827i
$861$	−2.30813	+	7.10369i	−0.0786609	+	0.242093i
$862$	−12.7045	−	39.1004i	−0.432717	−	1.33177i
$863$	34.0752	−	24.7571i	1.15993	−	0.842741i	0.170164	−	0.985416i	$-0.445570\pi$
$863$	34.0752	−	24.7571i	1.15993	−	0.842741i	0.989770	+	0.142675i	$0.0455703\pi$
$864$	75.5318	−	54.8770i	2.56964	−	1.86695i
$865$	−1.22409	−	3.76737i	−0.0416204	−	0.128094i
$866$	−10.3914	+	31.9815i	−0.353114	+	1.08677i
$867$	36.5795	+	26.5766i	1.24231	+	0.902588i
$868$	−17.9201			−0.608247
$869$		0			0
$870$	16.9991			0.576323
$871$	−45.4504	−	33.0217i	−1.54003	−	1.11890i
$872$	2.48298	−	7.64182i	0.0840843	−	0.258785i
$873$	−18.3861	−	56.5866i	−0.622275	−	1.91516i
$874$	−22.5545	+	16.3868i	−0.762917	+	0.554292i
$875$	3.83040	−	2.78295i	0.129491	−	0.0940808i
$876$	−5.80527	−	17.8668i	−0.196142	−	0.603662i
$877$	7.52138	−	23.1484i	0.253979	−	0.781666i	−0.740050	−	0.672551i	$-0.765198\pi$
$877$	7.52138	−	23.1484i	0.253979	−	0.781666i	0.994029	−	0.109115i	$-0.0348016\pi$
$878$	−19.0123	−	13.8132i	−0.641633	−	0.466174i
$879$	−9.52982			−0.321433
$880$		0			0
$881$	5.64380			0.190145			0.0950723	−	0.995470i	$-0.469692\pi$
$881$	5.64380			0.190145			0.0950723	+	0.995470i	$0.469692\pi$
$882$	11.6293	+	8.44921i	0.391580	+	0.284500i
$883$	4.69111	−	14.4377i	0.157868	−	0.485869i	−0.840572	−	0.541700i	$-0.817781\pi$
$883$	4.69111	−	14.4377i	0.157868	−	0.485869i	0.998440	+	0.0558313i	$0.0177809\pi$
$884$	24.4586	+	75.2757i	0.822630	+	2.53180i
$885$	3.83040	−	2.78295i	0.128757	−	0.0935478i
$886$	−59.6576	+	43.3438i	−2.00424	+	1.45616i
$887$	8.28704	+	25.5049i	0.278252	+	0.856370i	0.988341	+	0.152259i	$0.0486546\pi$
$887$	8.28704	+	25.5049i	0.278252	+	0.856370i	−0.710089	+	0.704112i	$0.751345\pi$
$888$	−0.248492	+	0.764779i	−0.00833883	+	0.0256643i
$889$	−2.07116	−	1.50479i	−0.0694645	−	0.0504689i
$890$	1.30368			0.0436994
$891$		0			0
$892$	43.3951			1.45297
$893$	−6.87627	−	4.99591i	−0.230106	−	0.167182i
$894$	21.6680	−	66.6874i	0.724688	−	2.23036i
$895$	−1.83759	−	5.65552i	−0.0614239	−	0.189043i
$896$	−6.84946	+	4.97643i	−0.228824	+	0.166251i
$897$	35.2401	−	25.6034i	1.17663	−	0.854874i
$898$	23.8314	+	73.3457i	0.795266	+	2.44758i
$899$	−11.6251	+	35.7785i	−0.387720	+	1.19328i
$900$	65.5898	+	47.6537i	2.18633	+	1.58846i
$901$	−16.9991			−0.566322
$902$		0			0
$903$	−3.21949			−0.107138
$904$	12.1896	+	8.85628i	0.405421	+	0.294555i
$905$	−1.05555	+	3.24865i	−0.0350877	+	0.107989i
$906$	31.7411	+	97.6890i	1.05453	+	3.24550i
$907$	−25.9674	+	18.8664i	−0.862233	+	0.626449i	−0.928492	−	0.371353i	$-0.878894\pi$
$907$	−25.9674	+	18.8664i	−0.862233	+	0.626449i	0.0662582	+	0.997803i	$0.478894\pi$
$908$	−21.8128	+	15.8480i	−0.723885	+	0.525933i
$909$	−27.0723	−	83.3201i	−0.897933	−	2.76355i
$910$	−1.78599	+	5.49672i	−0.0592050	+	0.182214i
$911$	−9.83753	−	7.14739i	−0.325932	−	0.236803i	0.412771	−	0.910835i	$-0.364561\pi$
$911$	−9.83753	−	7.14739i	−0.325932	−	0.236803i	−0.738703	+	0.674032i	$0.764561\pi$
$912$	−44.6206			−1.47754
$913$		0			0
$914$	4.37844			0.144826
$915$	−2.92991	−	2.12870i	−0.0968597	−	0.0703727i
$916$	4.23942	−	13.0476i	0.140074	−	0.431104i
$917$	−0.840512	−	2.58683i	−0.0277561	−	0.0854246i
$918$	−113.455	+	82.4301i	−3.74458	+	2.72060i
$919$	32.3607	−	23.5114i	1.06748	−	0.775570i	0.0920227	−	0.995757i	$-0.470667\pi$
$919$	32.3607	−	23.5114i	1.06748	−	0.775570i	0.975458	+	0.220187i	$0.0706668\pi$
$920$	−0.407532	−	1.25426i	−0.0134359	−	0.0413516i
$921$	−3.59126	+	11.0528i	−0.118336	+	0.364201i
$922$	−12.3270	−	8.95611i	−0.405969	−	0.294954i
$923$	67.7390			2.22966
$924$		0			0
$925$	1.12019			0.0368315
$926$	5.93867	+	4.31470i	0.195157	+	0.141790i
$927$	25.4407	−	78.2985i	0.835583	−	2.57166i
$928$	12.9480	+	39.8499i	0.425040	+	1.30814i
$929$	17.2963	−	12.5665i	0.567472	−	0.412292i	−0.266714	−	0.963776i	$-0.585938\pi$
$929$	17.2963	−	12.5665i	0.567472	−	0.412292i	0.834186	+	0.551483i	$0.185938\pi$
$930$	18.5577	−	13.4829i	0.608530	−	0.442123i
$931$	−1.63162	−	5.02162i	−0.0534743	−	0.164577i
$932$	23.1453	−	71.2339i	0.758150	−	2.33334i
$933$	10.5417	+	7.65900i	0.345120	+	0.250745i
$934$	28.6769			0.938338
$935$		0			0
$936$	−41.5398			−1.35777
$937$	25.4925	+	18.5214i	0.832803	+	0.605067i	0.920351	−	0.391093i	$-0.127903\pi$
$937$	25.4925	+	18.5214i	0.832803	+	0.605067i	−0.0875479	+	0.996160i	$0.527903\pi$
$938$	−6.57590	+	20.2385i	−0.214711	+	0.660811i
$939$	11.3022	+	34.7847i	0.368834	+	1.13516i
$940$	1.58816	−	1.15387i	0.0518002	−	0.0376350i
$941$	−34.5692	+	25.1160i	−1.12693	+	0.818759i	−0.985244	−	0.171153i	$-0.945251\pi$
$941$	−34.5692	+	25.1160i	−1.12693	+	0.818759i	−0.141681	+	0.989912i	$0.545251\pi$
$942$	18.6834	+	57.5016i	0.608738	+	1.87350i
$943$	1.83539	−	5.64875i	0.0597685	−	0.183949i
$944$	6.83684	+	4.96726i	0.222520	+	0.161670i
$945$	−5.70436			−0.185563
$946$		0			0
$947$	3.29473			0.107064			0.0535321	−	0.998566i	$-0.482952\pi$
$947$	3.29473			0.107064			0.0535321	+	0.998566i	$0.482952\pi$
$948$	57.4189	+	41.7172i	1.86488	+	1.35491i
$949$	4.14352	−	12.7524i	0.134504	−	0.413962i
$950$	−16.5200	−	50.8434i	−0.535980	−	1.64958i
$951$	−5.65050	+	4.10533i	−0.183230	+	0.133124i
$952$	4.96775	−	3.60928i	0.161006	−	0.116978i
$953$	11.9531	+	36.7880i	0.387200	+	1.19168i	0.934871	+	0.354987i	$0.115515\pi$
$953$	11.9531	+	36.7880i	0.387200	+	1.19168i	−0.547671	+	0.836694i	$0.684485\pi$
$954$	13.4605	−	41.4272i	0.435801	−	1.34126i
$955$	−7.37263	−	5.35653i	−0.238573	−	0.173333i
$956$	6.43899			0.208252
$957$		0			0
$958$	−74.4977			−2.40691
$959$	7.85099	+	5.70408i	0.253522	+	0.184194i
$960$	5.36265	−	16.5045i	0.173079	−	0.532681i
$961$	6.10741	+	18.7967i	0.197013	+	0.606344i
$962$	−2.26711	+	1.64715i	−0.0730946	+	0.0531063i
$963$	−57.7946	+	41.9902i	−1.86241	+	1.35312i
$964$	21.2876	+	65.5163i	0.685626	+	2.11014i
$965$	2.47214	−	7.60845i	0.0795809	−	0.244925i
$966$	−13.3484	−	9.69819i	−0.429478	−	0.312034i
$967$	−3.34816			−0.107670			−0.0538348	−	0.998550i	$-0.517144\pi$
$967$	−3.34816			−0.107670			−0.0538348	+	0.998550i	$0.517144\pi$
$968$		0			0
$969$	92.5583			2.97340
$970$	−7.33088	−	5.32620i	−0.235380	−	0.171014i
$971$	18.1434	−	55.8398i	0.582251	−	1.79198i	−0.0277898	−	0.999614i	$-0.508847\pi$
$971$	18.1434	−	55.8398i	0.582251	−	1.79198i	0.610041	−	0.792370i	$-0.291153\pi$
$972$	−12.5675	−	38.6789i	−0.403104	−	1.24063i
$973$	15.9530	−	11.5906i	0.511431	−	0.371576i
$974$	50.9972	−	37.0516i	1.63406	−	1.18721i
$975$	25.8116	+	79.4398i	0.826632	+	2.54411i
$976$	1.99752	−	6.14772i	0.0639389	−	0.196784i
$977$	−11.1360	−	8.09081i	−0.356274	−	0.258848i	0.395223	−	0.918585i	$-0.370667\pi$
$977$	−11.1360	−	8.09081i	−0.356274	−	0.258848i	−0.751496	+	0.659737i	$0.770667\pi$
$978$	−88.1798			−2.81968
$979$		0			0
$980$	1.21949			0.0389553
$981$	40.1746	+	29.1885i	1.28267	+	0.931918i
$982$	−16.7635	+	51.5929i	−0.534946	+	1.64639i
$983$	15.5169	+	47.7562i	0.494914	+	1.52319i	0.817091	+	0.576508i	$0.195585\pi$
$983$	15.5169	+	47.7562i	0.494914	+	1.52319i	−0.322178	+	0.946679i	$0.604415\pi$
$984$	−6.61446	+	4.80569i	−0.210861	+	0.153200i
$985$	−9.61023	+	6.98224i	−0.306207	+	0.222473i
$986$	−19.4491	−	59.8581i	−0.619385	−	1.90627i
$987$	1.55444	−	4.78408i	0.0494784	−	0.152279i
$988$	60.2699	+	43.7887i	1.91744	+	1.39310i
$989$	2.56009			0.0814062
$990$		0			0
$991$	−4.65940			−0.148011			−0.0740054	−	0.997258i	$-0.523578\pi$
$991$	−4.65940			−0.148011			−0.0740054	+	0.997258i	$0.523578\pi$
$992$	45.7424	+	33.2338i	1.45232	+	1.05517i
$993$	−21.5580	+	66.3486i	−0.684122	+	2.10551i
$994$	−7.92891	−	24.4027i	−0.251490	−	0.774006i
$995$	6.03664	−	4.38588i	0.191375	−	0.139042i
$996$	−20.4711	+	14.8731i	−0.648652	+	0.471273i
$997$	1.04736	+	3.22345i	0.0331703	+	0.102088i	0.966271	−	0.257528i	$-0.0829079\pi$
$997$	1.04736	+	3.22345i	0.0331703	+	0.102088i	−0.933101	+	0.359615i	$0.882908\pi$
$998$	16.8480	−	51.8529i	0.533315	−	1.64137i
$999$	−2.23760	−	1.62571i	−0.0707945	−	0.0514352i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.t.323.3		12
11.2	odd	10		847.2.f.u.148.3		12
11.3	even	5	inner	847.2.f.t.729.3		12
11.4	even	5	inner	847.2.f.t.372.1		12
11.5	even	5		847.2.a.j.1.1	yes	3
11.6	odd	10		847.2.a.i.1.3	✓	3
11.7	odd	10		847.2.f.u.372.3		12
11.8	odd	10		847.2.f.u.729.1		12
11.9	even	5	inner	847.2.f.t.148.1		12
11.10	odd	2		847.2.f.u.323.1		12
33.5	odd	10		7623.2.a.bz.1.3		3
33.17	even	10		7623.2.a.ce.1.1		3
77.6	even	10		5929.2.a.t.1.3		3
77.27	odd	10		5929.2.a.y.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
847.2.a.i.1.3	✓	3	11.6	odd	10
847.2.a.j.1.1	yes	3	11.5	even	5
847.2.f.t.148.1		12	11.9	even	5	inner
847.2.f.t.323.3		12	1.1	even	1	trivial
847.2.f.t.372.1		12	11.4	even	5	inner
847.2.f.t.729.3		12	11.3	even	5	inner
847.2.f.u.148.3		12	11.2	odd	10
847.2.f.u.323.1		12	11.10	odd	2
847.2.f.u.372.3		12	11.7	odd	10
847.2.f.u.729.1		12	11.8	odd	10
5929.2.a.t.1.3		3	77.6	even	10
5929.2.a.y.1.1		3	77.27	odd	10
7623.2.a.bz.1.3		3	33.5	odd	10
7623.2.a.ce.1.1		3	33.17	even	10

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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.f (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.71907 + 1.24898i) q^{2} +(-0.965643 + 2.97194i) q^{3} +(0.777220 + 2.39204i) q^{4} +(-0.392262 + 0.284995i) q^{5} +(-5.37189 + 3.90291i) q^{6} +(0.309017 + 0.951057i) q^{7} +(-0.338253 + 1.04104i) q^{8} +(-5.47293 - 3.97631i) q^{9} -1.03028 q^{10} -7.85952 q^{12} +(-4.53838 - 3.29733i) q^{13} +(-0.656626 + 2.02089i) q^{14} +(-0.468203 - 1.44098i) q^{15} +(2.18787 - 1.58958i) q^{16} +(-4.53838 + 3.29733i) q^{17} +(-4.44201 - 13.6711i) q^{18} +(-1.63162 + 5.02162i) q^{19} +(-0.986592 - 0.716801i) q^{20} -3.12489 q^{21} +2.48486 q^{23} +(-2.76727 - 2.01054i) q^{24} +(-1.47244 + 4.53170i) q^{25} +(-3.68350 - 11.3367i) q^{26} +(9.51801 - 6.91524i) q^{27} +(-2.03479 + 1.47836i) q^{28} +(1.63162 + 5.02162i) q^{29} +(0.994879 - 3.06192i) q^{30} +(5.76415 + 4.18790i) q^{31} +7.93567 q^{32} -11.9201 q^{34} +(-0.392262 - 0.284995i) q^{35} +(5.25783 - 16.1819i) q^{36} +(-0.0726471 - 0.223585i) q^{37} +(-9.07676 + 6.59465i) q^{38} +(14.1819 - 10.3038i) q^{39} +(-0.164006 - 0.504758i) q^{40} +(0.738629 - 2.27327i) q^{41} +(-5.37189 - 3.90291i) q^{42} +1.03028 q^{43} +3.28005 q^{45} +(4.27165 + 3.10353i) q^{46} +(-0.497439 + 1.53096i) q^{47} +(2.61144 + 8.03719i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(-8.19120 + 5.95126i) q^{50} +(-5.41701 - 16.6718i) q^{51} +(4.36001 - 13.4187i) q^{52} +(2.45154 + 1.78115i) q^{53} +24.9991 q^{54} -1.09461 q^{56} +(-13.3484 - 9.69819i) q^{57} +(-3.46701 + 10.6704i) q^{58} +(0.965643 + 2.97194i) q^{59} +(3.08299 - 2.23992i) q^{60} +(1.93375 - 1.40496i) q^{61} +(4.67838 + 14.3986i) q^{62} +(2.09047 - 6.43381i) q^{63} +(9.26621 + 6.73230i) q^{64} +2.71995 q^{65} +10.0147 q^{67} +(-11.4147 - 8.29323i) q^{68} +(-2.39949 + 7.38487i) q^{69} +(-0.318373 - 0.979851i) q^{70} +(-9.76907 + 7.09764i) q^{71} +(5.99072 - 4.35251i) q^{72} +(0.738629 + 2.27327i) q^{73} +(0.154367 - 0.475092i) q^{74} +(-12.0461 - 8.75200i) q^{75} -13.2800 q^{76} +37.2489 q^{78} +(-7.30565 - 5.30786i) q^{79} +(-0.405195 + 1.24706i) q^{80} +(5.08928 + 15.6632i) q^{81} +(4.10901 - 2.98537i) q^{82} +(2.60463 - 1.89237i) q^{83} +(-2.42872 - 7.47485i) q^{84} +(0.840512 - 2.58683i) q^{85} +(1.77112 + 1.28679i) q^{86} -16.4995 q^{87} -1.26537 q^{89} +(5.63863 + 4.09670i) q^{90} +(1.73351 - 5.33519i) q^{91} +(1.93129 + 5.94389i) q^{92} +(-18.0123 + 13.0867i) q^{93} +(-2.76727 + 2.01054i) q^{94} +(-0.791113 - 2.43479i) q^{95} +(-7.66302 + 23.5843i) q^{96} +(7.11545 + 5.16968i) q^{97} -2.12489 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} + q^{3} - 8 q^{4} - q^{5} - 12 q^{6} - 3 q^{7} - 6 q^{8} - 4 q^{9} - 16 q^{10} + 8 q^{12} - 8 q^{13} - 2 q^{14} + 5 q^{15} - 10 q^{16} - 8 q^{17} + 18 q^{18} + 14 q^{20} - 4 q^{21} + 28 q^{23}+ \cdots + 8 q^{98}+O(q^{100}) \) 12 * q - 2 * q^2 + q^3 - 8 * q^4 - q^5 - 12 * q^6 - 3 * q^7 - 6 * q^8 - 4 * q^9 - 16 * q^10 + 8 * q^12 - 8 * q^13 - 2 * q^14 + 5 * q^15 - 10 * q^16 - 8 * q^17 + 18 * q^18 + 14 * q^20 - 4 * q^21 + 28 * q^23 - 20 * q^24 - 2 * q^25 + 12 * q^26 + 19 * q^27 - 8 * q^28 + 8 * q^30 + 13 * q^31 + 136 * q^32 - 48 * q^34 - q^35 - 18 * q^36 + 17 * q^37 - 16 * q^38 + 20 * q^39 + 36 * q^40 - 16 * q^41 - 12 * q^42 + 16 * q^43 - 24 * q^45 - 4 * q^47 - 36 * q^48 - 3 * q^49 - 22 * q^50 + 20 * q^51 + 10 * q^53 + 32 * q^54 + 24 * q^56 - 16 * q^57 + 16 * q^58 - q^59 + 30 * q^60 + 16 * q^61 - 4 * q^62 - 4 * q^63 - 34 * q^64 + 96 * q^65 - 12 * q^67 + 7 * q^69 + 4 * q^70 - 5 * q^71 - 2 * q^72 - 16 * q^73 + 32 * q^74 - 20 * q^75 - 96 * q^76 + 112 * q^78 - 28 * q^79 + 56 * q^80 - 15 * q^81 - 28 * q^82 - 8 * q^83 - 2 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 84 * q^89 + 20 * q^90 - 8 * q^91 - 2 * q^92 - 17 * q^93 - 20 * q^94 - 24 * q^95 - 20 * q^96 + 11 * q^97 + 8 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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