LMFDB - Embedded newform 71.2.g.a.12.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [71,2,Mod(2,71)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(71, base_ring=CyclotomicField(70))

chi = DirichletCharacter(H, H._module([6]))

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

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

chi := DirichletCharacter("71.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	71.g (of order $35$, degree $24$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.566937854351$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$5$ over $\Q(\zeta_{35})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{35}]$

Embedding invariants

Embedding label			12.4
Character	$\chi$	$=$	71.12
Dual form			71.2.g.a.6.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0749867 + 0.0784299i) q^{2} +(1.72079 + 0.645822i) q^{3} +(0.0892014 - 1.98622i) q^{4} +(-1.81548 - 1.31902i) q^{5} +(0.0783843 + 0.183389i) q^{6} +(-0.608682 + 4.49347i) q^{7} +(0.325899 - 0.284729i) q^{8} +(0.284802 + 0.248824i) q^{9} +O(q^{10})$	\(q+(0.0749867 + 0.0784299i) q^{2} +(1.72079 + 0.645822i) q^{3} +(0.0892014 - 1.98622i) q^{4} +(-1.81548 - 1.31902i) q^{5} +(0.0783843 + 0.183389i) q^{6} +(-0.608682 + 4.49347i) q^{7} +(0.325899 - 0.284729i) q^{8} +(0.284802 + 0.248824i) q^{9} +(-0.0326858 - 0.241297i) q^{10} +(-2.41871 + 1.44511i) q^{11} +(1.43624 - 3.36026i) q^{12} +(2.26569 + 1.35368i) q^{13} +(-0.398066 + 0.289212i) q^{14} +(-2.27219 - 3.44222i) q^{15} +(-3.91367 - 0.352237i) q^{16} +(2.02728 - 6.23933i) q^{17} +(0.00184111 + 0.0409955i) q^{18} +(-1.83875 + 2.78559i) q^{19} +(-2.78181 + 3.48828i) q^{20} +(-3.94939 + 7.33920i) q^{21} +(-0.294711 - 0.0813351i) q^{22} +(0.664870 + 0.320185i) q^{23} +(0.744686 - 0.279485i) q^{24} +(0.0110529 + 0.0340172i) q^{25} +(0.0637269 + 0.279206i) q^{26} +(-2.28350 - 4.24346i) q^{27} +(8.87075 + 1.60980i) q^{28} +(1.70914 - 0.471693i) q^{29} +(0.0995892 - 0.436329i) q^{30} +(6.55948 - 0.590364i) q^{31} +(-0.805490 - 1.01005i) q^{32} +(-5.09537 + 0.924673i) q^{33} +(0.641369 - 0.308867i) q^{34} +(7.03203 - 7.35493i) q^{35} +(0.519626 - 0.543486i) q^{36} +(1.96340 - 0.945524i) q^{37} +(-0.356355 + 0.0646690i) q^{38} +(3.02452 + 3.79263i) q^{39} +(-0.967225 + 0.0870518i) q^{40} +(-0.206484 + 0.904666i) q^{41} +(-0.871765 + 0.240592i) q^{42} +(9.88571 + 1.79399i) q^{43} +(2.65456 + 4.93301i) q^{44} +(-0.188847 - 0.827395i) q^{45} +(0.0247444 + 0.0761553i) q^{46} +(-11.8783 + 4.45800i) q^{47} +(-6.50711 - 3.13366i) q^{48} +(-13.0731 - 3.60794i) q^{49} +(-0.00183915 + 0.00341771i) q^{50} +(7.51801 - 9.42728i) q^{51} +(2.89082 - 4.37941i) q^{52} +(0.533306 + 11.8750i) q^{53} +(0.161582 - 0.497298i) q^{54} +(6.29725 + 0.566762i) q^{55} +(1.08105 + 1.63773i) q^{56} +(-4.96309 + 3.60590i) q^{57} +(0.165158 + 0.0986771i) q^{58} +(1.24743 - 2.91850i) q^{59} +(-7.03971 + 4.20603i) q^{60} +(-0.355480 - 2.62426i) q^{61} +(0.538176 + 0.470190i) q^{62} +(-1.29144 + 1.12830i) q^{63} +(-1.03612 + 7.64895i) q^{64} +(-2.32776 - 5.44607i) q^{65} +(-0.454607 - 0.330291i) q^{66} +(0.0241967 - 0.538781i) q^{67} +(-12.2119 - 4.58319i) q^{68} +(0.937317 + 0.980356i) q^{69} +1.10416 q^{70} +(5.65214 - 6.24927i) q^{71} +0.163664 q^{72} +(-3.71196 - 3.88240i) q^{73} +(0.221386 + 0.0830876i) q^{74} +(-0.00294945 + 0.0656745i) q^{75} +(5.36878 + 3.90065i) q^{76} +(-5.02135 - 11.7480i) q^{77} +(-0.0706568 + 0.521610i) q^{78} +(-6.98479 + 6.10243i) q^{79} +(6.64057 + 5.80169i) q^{80} +(-1.34120 - 9.90111i) q^{81} +(-0.0864365 + 0.0516434i) q^{82} +(-0.514996 + 1.20489i) q^{83} +(14.2250 + 8.49905i) q^{84} +(-11.9103 + 8.65333i) q^{85} +(0.600594 + 0.909861i) q^{86} +(3.24569 + 0.292118i) q^{87} +(-0.376789 + 1.15964i) q^{88} +(-0.0743855 - 1.65632i) q^{89} +(0.0507315 - 0.0768549i) q^{90} +(-7.46183 + 9.35683i) q^{91} +(0.695266 - 1.29202i) q^{92} +(11.6687 + 3.22036i) q^{93} +(-1.24035 - 0.597323i) q^{94} +(7.01246 - 2.63182i) q^{95} +(-0.733761 - 2.25829i) q^{96} +(-2.13103 - 9.33664i) q^{97} +(-0.697336 - 1.29587i) q^{98} +(-1.04843 - 0.190263i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9}+O(q^{10}) $ 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9	\( 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9} - 8 q^{10} - 27 q^{11} + 3 q^{12} - 31 q^{13} + 2 q^{14} + 12 q^{15} + 30 q^{16} + 9 q^{17} + 27 q^{18} - 31 q^{19} + 72 q^{20} - 32 q^{21} - 24 q^{22} - 6 q^{23} - 47 q^{24} - 42 q^{25} + 77 q^{26} - 2 q^{27} - 18 q^{28} + q^{29} + 15 q^{30} + 15 q^{31} - 10 q^{32} - 24 q^{33} + 20 q^{34} + 74 q^{35} + 8 q^{36} - 22 q^{37} - 39 q^{38} + 86 q^{39} - 30 q^{40} + 39 q^{41} - 34 q^{42} + 33 q^{43} - 23 q^{44} + 121 q^{45} + 124 q^{46} + 6 q^{47} + 131 q^{48} - 22 q^{49} - 15 q^{50} + 29 q^{51} + 83 q^{52} - 30 q^{53} - 25 q^{54} + 32 q^{55} + 11 q^{56} - 10 q^{57} + 12 q^{58} - 80 q^{59} + 80 q^{60} - 12 q^{61} - 68 q^{62} - 79 q^{63} - 117 q^{64} - 89 q^{65} - 39 q^{66} - 74 q^{67} - 67 q^{68} - 95 q^{69} - 64 q^{70} - 115 q^{71} - 144 q^{72} - 14 q^{73} - 70 q^{74} - 13 q^{75} + 8 q^{76} + 47 q^{77} - 218 q^{78} - 25 q^{79} - 103 q^{80} - 28 q^{81} - 88 q^{82} - 20 q^{83} - 142 q^{84} + 22 q^{85} + 159 q^{86} - 105 q^{87} + 43 q^{88} + 33 q^{89} + 33 q^{90} + 60 q^{91} - 2 q^{92} + 63 q^{93} + 174 q^{94} + 20 q^{95} - 30 q^{96} + 121 q^{97} + 128 q^{98} - 2 q^{99}+O(q^{100}) \) 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9 - 8 * q^10 - 27 * q^11 + 3 * q^12 - 31 * q^13 + 2 * q^14 + 12 * q^15 + 30 * q^16 + 9 * q^17 + 27 * q^18 - 31 * q^19 + 72 * q^20 - 32 * q^21 - 24 * q^22 - 6 * q^23 - 47 * q^24 - 42 * q^25 + 77 * q^26 - 2 * q^27 - 18 * q^28 + q^29 + 15 * q^30 + 15 * q^31 - 10 * q^32 - 24 * q^33 + 20 * q^34 + 74 * q^35 + 8 * q^36 - 22 * q^37 - 39 * q^38 + 86 * q^39 - 30 * q^40 + 39 * q^41 - 34 * q^42 + 33 * q^43 - 23 * q^44 + 121 * q^45 + 124 * q^46 + 6 * q^47 + 131 * q^48 - 22 * q^49 - 15 * q^50 + 29 * q^51 + 83 * q^52 - 30 * q^53 - 25 * q^54 + 32 * q^55 + 11 * q^56 - 10 * q^57 + 12 * q^58 - 80 * q^59 + 80 * q^60 - 12 * q^61 - 68 * q^62 - 79 * q^63 - 117 * q^64 - 89 * q^65 - 39 * q^66 - 74 * q^67 - 67 * q^68 - 95 * q^69 - 64 * q^70 - 115 * q^71 - 144 * q^72 - 14 * q^73 - 70 * q^74 - 13 * q^75 + 8 * q^76 + 47 * q^77 - 218 * q^78 - 25 * q^79 - 103 * q^80 - 28 * q^81 - 88 * q^82 - 20 * q^83 - 142 * q^84 + 22 * q^85 + 159 * q^86 - 105 * q^87 + 43 * q^88 + 33 * q^89 + 33 * q^90 + 60 * q^91 - 2 * q^92 + 63 * q^93 + 174 * q^94 + 20 * q^95 - 30 * q^96 + 121 * q^97 + 128 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/71\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$e\left(\frac{19}{35}\right)$

Coefficient data

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

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

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

$2$	0.0749867	+	0.0784299i	0.0530236	+	0.0554583i	0.748775	−	0.662825i	$-0.230643\pi$
$2$	0.0749867	+	0.0784299i	0.0530236	+	0.0554583i	−0.695751	+	0.718283i	$0.744928\pi$
$3$	1.72079	+	0.645822i	0.993496	+	0.372865i	0.794585	−	0.607152i	$-0.207688\pi$
$3$	1.72079	+	0.645822i	0.993496	+	0.372865i	0.198910	+	0.980018i	$0.436260\pi$
$4$	0.0892014	−	1.98622i	0.0446007	−	0.993112i
$5$	−1.81548	−	1.31902i	−0.811906	−	0.589884i	0.102477	−	0.994735i	$-0.467323\pi$
$5$	−1.81548	−	1.31902i	−0.811906	−	0.589884i	−0.914382	+	0.404851i	$0.867323\pi$
$6$	0.0783843	+	0.183389i	0.0320002	+	0.0748683i
$7$	−0.608682	+	4.49347i	−0.230060	+	1.69837i	0.395718	+	0.918372i	$0.370496\pi$
$7$	−0.608682	+	4.49347i	−0.230060	+	1.69837i	−0.625778	+	0.780001i	$0.715218\pi$
$8$	0.325899	−	0.284729i	0.115223	−	0.100667i
$9$	0.284802	+	0.248824i	0.0949341	+	0.0829414i
$10$	−0.0326858	−	0.241297i	−0.0103362	−	0.0763047i
$11$	−2.41871	+	1.44511i	−0.729269	+	0.435718i	−0.828965	−	0.559300i	$-0.811070\pi$
$11$	−2.41871	+	1.44511i	−0.729269	+	0.435718i	0.0996964	+	0.995018i	$0.468213\pi$
$12$	1.43624	−	3.36026i	0.414608	−	0.970022i
$13$	2.26569	+	1.35368i	0.628388	+	0.375444i	0.791505	−	0.611162i	$-0.209298\pi$
$13$	2.26569	+	1.35368i	0.628388	+	0.375444i	−0.163117	+	0.986607i	$0.552155\pi$
$14$	−0.398066	+	0.289212i	−0.106388	+	0.0772951i
$15$	−2.27219	−	3.44222i	−0.586678	−	0.888779i
$16$	−3.91367	−	0.352237i	−0.978419	−	0.0880593i
$17$	2.02728	−	6.23933i	0.491688	−	1.51326i	−0.330368	−	0.943852i	$-0.607173\pi$
$17$	2.02728	−	6.23933i	0.491688	−	1.51326i	0.822056	−	0.569407i	$-0.192827\pi$
$18$	0.00184111	+	0.0409955i	0.000433954	+	0.00966274i
$19$	−1.83875	+	2.78559i	−0.421838	+	0.639058i	−0.981902	−	0.189392i	$-0.939348\pi$
$19$	−1.83875	+	2.78559i	−0.421838	+	0.639058i	0.560063	+	0.828450i	$0.310777\pi$
$20$	−2.78181	+	3.48828i	−0.622032	+	0.780004i
$21$	−3.94939	+	7.33920i	−0.861828	+	1.60155i
$22$	−0.294711	−	0.0813351i	−0.0628326	−	0.0173407i
$23$	0.664870	+	0.320185i	0.138635	+	0.0667631i	0.501915	−	0.864917i	$-0.332629\pi$
$23$	0.664870	+	0.320185i	0.138635	+	0.0667631i	−0.363280	+	0.931680i	$0.618343\pi$
$24$	0.744686	−	0.279485i	0.152008	−	0.0570497i
$25$	0.0110529	+	0.0340172i	0.00221057	+	0.00680345i
$26$	0.0637269	+	0.279206i	0.0124979	+	0.0547568i
$27$	−2.28350	−	4.24346i	−0.439460	−	0.816654i
$28$	8.87075	+	1.60980i	1.67641	+	0.304224i
$29$	1.70914	−	0.471693i	0.317379	−	0.0875911i	−0.103718	−	0.994607i	$-0.533074\pi$
$29$	1.70914	−	0.471693i	0.317379	−	0.0875911i	0.421097	+	0.907016i	$0.361645\pi$
$30$	0.0995892	−	0.436329i	0.0181824	−	0.0796624i
$31$	6.55948	−	0.590364i	1.17812	−	0.106032i	0.516778	−	0.856120i	$-0.327131\pi$
$31$	6.55948	−	0.590364i	1.17812	−	0.106032i	0.661339	+	0.750087i	$0.269988\pi$
$32$	−0.805490	−	1.01005i	−0.142392	−	0.178554i
$33$	−5.09537	+	0.924673i	−0.886990	+	0.160965i
$34$	0.641369	−	0.308867i	0.109994	−	0.0529703i
$35$	7.03203	−	7.35493i	1.18863	−	1.24321i
$36$	0.519626	−	0.543486i	0.0866043	−	0.0905810i
$37$	1.96340	−	0.945524i	0.322781	−	0.155443i	−0.265475	−	0.964118i	$-0.585529\pi$
$37$	1.96340	−	0.945524i	0.322781	−	0.155443i	0.588256	+	0.808675i	$0.299815\pi$
$38$	−0.356355	+	0.0646690i	−0.0578085	+	0.0104907i
$39$	3.02452	+	3.79263i	0.484311	+	0.607307i
$40$	−0.967225	+	0.0870518i	−0.152932	+	0.0137641i
$41$	−0.206484	+	0.904666i	−0.0322474	+	0.141285i	−0.988489	−	0.151293i	$-0.951656\pi$
$41$	−0.206484	+	0.904666i	−0.0322474	+	0.141285i	0.956241	+	0.292579i	$0.0945133\pi$
$42$	−0.871765	+	0.240592i	−0.134516	+	0.0371241i
$43$	9.88571	+	1.79399i	1.50756	+	0.273581i	0.868543	−	0.495614i	$-0.165057\pi$
$43$	9.88571	+	1.79399i	1.50756	+	0.273581i	0.639014	+	0.769195i	$0.279343\pi$
$44$	2.65456	+	4.93301i	0.400191	+	0.743679i
$45$	−0.188847	−	0.827395i	−0.0281517	−	0.123341i
$46$	0.0247444	+	0.0761553i	0.00364836	+	0.0112285i
$47$	−11.8783	+	4.45800i	−1.73263	+	0.650266i	−0.999553	−	0.0298840i	$-0.990486\pi$
$47$	−11.8783	+	4.45800i	−1.73263	+	0.650266i	−0.733073	+	0.680150i	$0.761915\pi$
$48$	−6.50711	−	3.13366i	−0.939221	−	0.452305i
$49$	−13.0731	−	3.60794i	−1.86758	−	0.515420i
$50$	−0.00183915	+	0.00341771i	−0.000260095	+	0.000483338i
$51$	7.51801	−	9.42728i	1.05273	−	1.32008i
$52$	2.89082	−	4.37941i	0.400885	−	0.607315i
$53$	0.533306	+	11.8750i	0.0732552	+	1.63115i	0.613534	+	0.789668i	$0.289747\pi$
$53$	0.533306	+	11.8750i	0.0732552	+	1.63115i	−0.540279	+	0.841486i	$0.681681\pi$
$54$	0.161582	−	0.497298i	0.0219885	−	0.0676737i
$55$	6.29725	+	0.566762i	0.849120	+	0.0764222i
$56$	1.08105	+	1.63773i	0.144462	+	0.218850i
$57$	−4.96309	+	3.60590i	−0.657377	+	0.477613i
$58$	0.165158	+	0.0986771i	0.0216863	+	0.0129569i
$59$	1.24743	−	2.91850i	0.162401	−	0.379956i	−0.818488	−	0.574524i	$-0.805187\pi$
$59$	1.24743	−	2.91850i	0.162401	−	0.379956i	0.980889	+	0.194567i	$0.0623302\pi$
$60$	−7.03971	+	4.20603i	−0.908823	+	0.542996i
$61$	−0.355480	−	2.62426i	−0.0455146	−	0.336002i	−0.999362	−	0.0357109i	$-0.988630\pi$
$61$	−0.355480	−	2.62426i	−0.0455146	−	0.336002i	0.953848	−	0.300291i	$-0.0970838\pi$
$62$	0.538176	+	0.470190i	0.0683484	+	0.0597142i
$63$	−1.29144	+	1.12830i	−0.162706	+	0.142152i
$64$	−1.03612	+	7.64895i	−0.129515	+	0.956118i
$65$	−2.32776	−	5.44607i	−0.288723	−	0.675501i
$66$	−0.454607	−	0.330291i	−0.0559582	−	0.0406560i
$67$	0.0241967	−	0.538781i	0.00295610	−	0.0658226i	−0.996973	−	0.0777518i	$-0.975226\pi$
$67$	0.0241967	−	0.538781i	0.00295610	−	0.0658226i	0.999929	+	0.0119292i	$0.00379726\pi$
$68$	−12.2119	−	4.58319i	−1.48091	−	0.555793i
$69$	0.937317	+	0.980356i	0.112840	+	0.118021i
$70$	1.10416			0.131972
$71$	5.65214	−	6.24927i	0.670785	−	0.741652i
$71$	5.65214	−	6.24927i	0.670785	−	0.741652i
$72$	0.163664			0.0192880
$73$	−3.71196	−	3.88240i	−0.434452	−	0.454401i	0.468932	−	0.883234i	$-0.344639\pi$
$73$	−3.71196	−	3.88240i	−0.434452	−	0.454401i	−0.903383	+	0.428834i	$0.858925\pi$
$74$	0.221386	+	0.0830876i	0.0257356	+	0.00965874i
$75$	−0.00294945	+	0.0656745i	−0.000340573	+	0.00758344i
$76$	5.36878	+	3.90065i	0.615842	+	0.447435i
$77$	−5.02135	−	11.7480i	−0.572236	−	1.33881i
$78$	−0.0706568	+	0.521610i	−0.00800031	+	0.0590607i
$79$	−6.98479	+	6.10243i	−0.785850	+	0.686577i	−0.954206	−	0.299150i	$-0.903297\pi$
$79$	−6.98479	+	6.10243i	−0.785850	+	0.686577i	0.168356	+	0.985726i	$0.446154\pi$
$80$	6.64057	+	5.80169i	0.742439	+	0.648649i
$81$	−1.34120	−	9.90111i	−0.149022	−	1.10012i
$82$	−0.0864365	+	0.0516434i	−0.00954531	+	0.00570306i
$83$	−0.514996	+	1.20489i	−0.0565281	+	0.132254i	−0.945411	−	0.325880i	$-0.894339\pi$
$83$	−0.514996	+	1.20489i	−0.0565281	+	0.132254i	0.888883	+	0.458134i	$0.151482\pi$
$84$	14.2250	+	8.49905i	1.55208	+	0.927322i
$85$	−11.9103	+	8.65333i	−1.29185	+	0.938585i
$86$	0.600594	+	0.909861i	0.0647637	+	0.0981128i
$87$	3.24569	+	0.292118i	0.347975	+	0.0313183i
$88$	−0.376789	+	1.15964i	−0.0401659	+	0.123618i
$89$	−0.0743855	−	1.65632i	−0.00788485	−	0.175570i	−0.999071	−	0.0430936i	$-0.986279\pi$
$89$	−0.0743855	−	1.65632i	−0.00788485	−	0.175570i	0.991186	−	0.132476i	$-0.0422928\pi$
$90$	0.0507315	−	0.0768549i	0.00534757	−	0.00810122i
$91$	−7.46183	+	9.35683i	−0.782212	+	0.980863i
$92$	0.695266	−	1.29202i	0.0724865	−	0.134702i
$93$	11.6687	+	3.22036i	1.20999	+	0.333936i
$94$	−1.24035	−	0.597323i	−0.127933	−	0.0616092i
$95$	7.01246	−	2.63182i	0.719463	−	0.270019i
$96$	−0.733761	−	2.25829i	−0.0748892	−	0.230485i
$97$	−2.13103	−	9.33664i	−0.216373	−	0.947992i	−0.960133	−	0.279545i	$-0.909816\pi$
$97$	−2.13103	−	9.33664i	−0.216373	−	0.947992i	0.743760	−	0.668447i	$-0.233041\pi$
$98$	−0.697336	−	1.29587i	−0.0704415	−	0.130902i
$99$	−1.04843	−	0.190263i	−0.105372	−	0.0191221i
$100$	0.0685518	−	0.0189191i	0.00685518	−	0.00189191i
$101$	−2.25570	+	9.88288i	−0.224451	+	0.983383i	0.729632	+	0.683840i	$0.239691\pi$
$101$	−2.25570	+	9.88288i	−0.224451	+	0.983383i	−0.954083	+	0.299543i	$0.903166\pi$
$102$	1.30313	−	0.117284i	0.129029	−	0.0116128i
$103$	−2.49242	−	3.12540i	−0.245585	−	0.307954i	0.643726	−	0.765256i	$-0.277387\pi$
$103$	−2.49242	−	3.12540i	−0.245585	−	0.307954i	−0.889312	+	0.457301i	$0.848816\pi$
$104$	1.12382	−	0.203943i	0.110199	−	0.0199982i
$105$	16.8506	−	8.11481i	1.64445	−	0.791925i
$106$	−0.891363	+	0.932293i	−0.0865768	+	0.0905523i
$107$	2.83348	−	2.96359i	0.273923	−	0.286501i	−0.571496	−	0.820605i	$-0.693637\pi$
$107$	2.83348	−	2.96359i	0.273923	−	0.286501i	0.845419	+	0.534104i	$0.179351\pi$
$108$	−8.63215	+	4.15702i	−0.830629	+	0.400010i
$109$	2.11258	−	0.383376i	0.202348	−	0.0367208i	−0.0764364	−	0.997074i	$-0.524354\pi$
$109$	2.11258	−	0.383376i	0.202348	−	0.0367208i	0.278784	+	0.960354i	$0.410068\pi$
$110$	0.427758	+	0.536392i	0.0407852	+	0.0511430i
$111$	3.98923	−	0.359037i	0.378641	−	0.0340783i
$112$	3.96495	−	17.3716i	0.374653	−	1.64146i
$113$	0.958947	−	0.264653i	0.0902102	−	0.0248964i	−0.220640	−	0.975355i	$-0.570815\pi$
$113$	0.958947	−	0.264653i	0.0902102	−	0.0248964i	0.310851	+	0.950459i	$0.399386\pi$
$114$	−0.654976	−	0.118861i	−0.0613441	−	0.0111323i
$115$	−0.784726	−	1.45826i	−0.0731761	−	0.135984i
$116$	−0.784430	−	3.43681i	−0.0728325	−	0.319100i
$117$	0.308443	+	0.949290i	0.0285156	+	0.0877619i
$118$	0.322438	−	0.121013i	0.0296828	−	0.0111402i
$119$	26.8023	+	12.9073i	2.45696	+	1.18321i
$120$	−1.72061	−	0.474857i	−0.157069	−	0.0433483i
$121$	−1.45074	+	2.69593i	−0.131886	+	0.245084i
$122$	0.179164	−	0.224665i	0.0162208	−	0.0203402i
$123$	−0.939568	+	1.42338i	−0.0847180	+	0.128342i
$124$	−0.587480	−	13.0813i	−0.0527572	−	1.17473i
$125$	−3.44245	+	10.5948i	−0.307902	+	0.947624i
$126$	−0.185333	−	0.0166803i	−0.0165108	−	0.00148600i
$127$	−3.21718	−	4.87382i	−0.285478	−	0.432481i	0.663333	−	0.748324i	$-0.269141\pi$
$127$	−3.21718	−	4.87382i	−0.285478	−	0.432481i	−0.948811	+	0.315843i	$0.897713\pi$
$128$	−2.76795	+	2.01103i	−0.244654	+	0.177752i
$129$	15.8526	+	9.47148i	1.39574	+	0.833917i
$130$	0.252584	−	0.590949i	0.0221530	−	0.0518296i
$131$	−5.15864	+	3.08214i	−0.450713	+	0.269288i	−0.720267	−	0.693697i	$-0.755981\pi$
$131$	−5.15864	+	3.08214i	−0.450713	+	0.269288i	0.269554	+	0.962985i	$0.413124\pi$
$132$	1.38209	+	10.2030i	0.120296	+	0.888059i
$133$	−11.3978	−	9.95792i	−0.988311	−	0.863461i
$134$	0.0440710	−	0.0385037i	0.00380715	−	0.00332621i
$135$	−1.45157	+	10.7159i	−0.124931	+	0.922276i
$136$	−1.11583	−	2.61062i	−0.0956817	−	0.223858i
$137$	14.2388	+	10.3451i	1.21650	+	0.883842i	0.995805	−	0.0914999i	$-0.0291661\pi$
$137$	14.2388	+	10.3451i	1.21650	+	0.883842i	0.220699	+	0.975342i	$0.429166\pi$
$138$	−0.00660301	+	0.147027i	−0.000562085	+	0.0125158i
$139$	−5.37448	−	2.01707i	−0.455857	−	0.171086i	0.112874	−	0.993609i	$-0.463994\pi$
$139$	−5.37448	−	2.01707i	−0.455857	−	0.171086i	−0.568731	+	0.822523i	$0.692566\pi$
$140$	−13.9813	−	14.6233i	−1.18163	−	1.23589i
$141$	−23.3191			−1.96382
$142$	0.913965	−	0.0253151i	0.0766982	−	0.00212439i
$143$	−7.43627			−0.621852
$144$	−1.02698	−	1.07414i	−0.0855815	−	0.0895113i
$145$	−3.72507	−	1.39804i	−0.309351	−	0.116101i
$146$	0.0261492	−	0.582257i	0.00216412	−	0.0481879i
$147$	−20.1659	−	14.6514i	−1.66325	−	1.20842i
$148$	−1.70288	−	3.98409i	−0.139976	−	0.327491i
$149$	−1.76867	+	13.0568i	−0.144895	+	1.06966i	0.761783	+	0.647833i	$0.224324\pi$
$149$	−1.76867	+	13.0568i	−0.144895	+	1.06966i	−0.906678	+	0.421824i	$0.861390\pi$
$150$	−0.00537202	+	0.00469339i	−0.000438623	+	0.000383214i
$151$	2.42987	+	2.12291i	0.197740	+	0.172760i	0.751114	−	0.660173i	$-0.229517\pi$
$151$	2.42987	+	2.12291i	0.197740	+	0.172760i	−0.553374	+	0.832933i	$0.686660\pi$
$152$	0.193892	+	1.43137i	0.0157267	+	0.116099i
$153$	2.12987	−	1.27254i	0.172190	−	0.102879i
$154$	0.544863	−	1.27477i	0.0439063	−	0.102724i
$155$	−12.6873	−	7.58029i	−1.01907	−	0.608864i
$156$	7.80280	−	5.66907i	0.624724	−	0.453889i
$157$	10.7727	+	16.3200i	0.859757	+	1.30248i	0.951799	+	0.306721i	$0.0992318\pi$
$157$	10.7727	+	16.3200i	0.859757	+	1.30248i	−0.0920426	+	0.995755i	$0.529340\pi$
$158$	−1.00238	−	0.0902157i	−0.0797450	−	0.00717718i
$159$	−6.75141	+	20.7787i	−0.535422	+	1.64786i
$160$	0.130068	+	2.89618i	0.0102828	+	0.228963i
$161$	−1.84344	+	2.79269i	−0.145283	+	0.220094i
$162$	0.675972	−	0.847641i	0.0531093	−	0.0665970i
$163$	0.371550	−	0.690456i	0.0291020	−	0.0540807i	−0.865629	−	0.500686i	$-0.833081\pi$
$163$	0.371550	−	0.690456i	0.0291020	−	0.0540807i	0.894731	+	0.446605i	$0.147367\pi$
$164$	1.77845	+	0.490821i	0.138874	+	0.0383267i
$165$	10.4702	+	5.04217i	0.815102	+	0.392533i
$166$	−0.133117	+	0.0499598i	−0.0103319	+	0.00387763i
$167$	−7.17698	−	22.0885i	−0.555371	−	1.70926i	−0.694961	−	0.719047i	$-0.744578\pi$
$167$	−7.17698	−	22.0885i	−0.555371	−	1.70926i	0.139590	−	0.990209i	$-0.455422\pi$
$168$	0.802583	+	3.51634i	0.0619206	+	0.271292i
$169$	−2.85942	−	5.31370i	−0.219955	−	0.408746i
$170$	−1.57179	−	0.285238i	−0.120551	−	0.0218768i
$171$	−1.21680	+	0.335816i	−0.0930512	+	0.0256805i
$172$	4.44509	−	19.4752i	0.338935	−	1.48497i
$173$	18.3253	−	1.64931i	1.39325	−	0.125394i	0.632558	−	0.774513i	$-0.282005\pi$
$173$	18.3253	−	1.64931i	1.39325	−	0.125394i	0.760687	+	0.649118i	$0.224862\pi$
$174$	0.220473	+	0.276464i	0.0167140	+	0.0209587i
$175$	−0.159583	+	0.0289601i	−0.0120634	+	0.00218918i
$176$	9.97507	−	4.80374i	0.751899	−	0.362096i
$177$	4.03138	−	4.21650i	0.303017	−	0.316931i
$178$	0.124327	−	0.130036i	0.00931873	−	0.00974662i
$179$	−13.3731	+	6.44014i	−0.999551	+	0.481358i	−0.860786	−	0.508967i	$-0.830028\pi$
$179$	−13.3731	+	6.44014i	−0.999551	+	0.481358i	−0.138765	+	0.990325i	$0.544313\pi$
$180$	−1.66024	+	0.301288i	−0.123747	+	0.0224567i
$181$	−11.4096	−	14.3072i	−0.848071	−	1.06345i	−0.997211	−	0.0746316i	$-0.976222\pi$
$181$	−11.4096	−	14.3072i	−0.848071	−	1.06345i	0.149140	−	0.988816i	$-0.452350\pi$
$182$	−1.29339	+	0.116408i	−0.0958727	+	0.00862870i
$183$	1.08310	−	4.74536i	0.0800649	−	0.350787i
$184$	0.307846	−	0.0849602i	0.0226947	−	0.00626335i
$185$	−4.81167	−	0.873190i	−0.353761	−	0.0641982i
$186$	0.622426	+	1.15666i	0.0456385	+	0.0848105i
$187$	4.11313	+	18.0208i	0.300782	+	1.31781i
$188$	7.79502	+	23.9906i	0.568510	+	1.74969i
$189$	20.4578	−	7.67794i	1.48809	−	0.558488i
$190$	0.732254	+	0.352635i	0.0531233	+	0.0255828i
$191$	20.5577	+	5.67357i	1.48750	+	0.410525i	0.912994	−	0.407972i	$-0.133764\pi$
$191$	20.5577	+	5.67357i	1.48750	+	0.410525i	0.574510	+	0.818497i	$0.305193\pi$
$192$	−6.72279	+	12.4930i	−0.485176	+	0.901608i
$193$	6.48386	−	8.13051i	0.466719	−	0.585247i	−0.491646	−	0.870795i	$-0.663604\pi$
$193$	6.48386	−	8.13051i	0.466719	−	0.585247i	0.958364	+	0.285549i	$0.0921758\pi$
$194$	0.572473	−	0.867260i	0.0411012	−	0.0622656i
$195$	−0.488389	−	10.8748i	−0.0349743	−	0.778763i
$196$	−8.33231	+	25.6442i	−0.595165	+	1.83173i
$197$	−10.1966	−	0.917715i	−0.726481	−	0.0653845i	−0.279775	−	0.960066i	$-0.590260\pi$
$197$	−10.1966	−	0.917715i	−0.726481	−	0.0653845i	−0.446705	+	0.894681i	$0.647403\pi$
$198$	−0.0636963	−	0.0964958i	−0.00452670	−	0.00685766i
$199$	−3.76812	+	2.73770i	−0.267115	+	0.194070i	−0.713278	−	0.700881i	$-0.752790\pi$
$199$	−3.76812	+	2.73770i	−0.267115	+	0.194070i	0.446163	+	0.894952i	$0.352790\pi$
$200$	0.0132878	+	0.00793910i	0.000939590	+	0.000561379i
$201$	0.389594	−	0.911500i	0.0274798	−	0.0642923i
$202$	−0.944261	+	0.564170i	−0.0664380	+	0.0396948i
$203$	1.07922	+	7.96709i	0.0757461	+	0.559180i
$204$	−18.0541	−	15.7734i	−1.26404	−	1.10436i
$205$	1.56814	−	1.37004i	0.109524	−	0.0956880i
$206$	0.0582262	−	0.429843i	0.00405681	−	0.0299486i
$207$	0.109687	+	0.256625i	0.00762376	+	0.0178367i
$208$	−8.39034	−	6.09594i	−0.581765	−	0.422677i
$209$	0.421918	−	9.39474i	0.0291847	−	0.649848i
$210$	1.90001	+	0.713087i	0.131113	+	0.0492077i
$211$	15.2966	+	15.9989i	1.05306	+	1.10141i	0.994669	+	0.103119i	$0.0328822\pi$
$211$	15.2966	+	15.9989i	1.05306	+	1.10141i	0.0583894	+	0.998294i	$0.481403\pi$
$212$	23.6339			1.62319
$213$	13.7620	−	7.10337i	0.942959	−	0.486715i
$214$	0.444907			0.0304132
$215$	−15.5810	−	16.2964i	−1.06261	−	1.11141i
$216$	−1.95243	−	0.732758i	−0.132846	−	0.0498579i
$217$	−1.33985	+	29.8342i	−0.0909552	+	2.02528i
$218$	0.188483	+	0.136941i	0.0127657	+	0.00927482i
$219$	−3.88014	−	9.07804i	−0.262196	−	0.613437i
$220$	1.68744	−	12.4572i	0.113767	−	0.839863i
$221$	13.0393	−	11.3921i	0.877116	−	0.766313i
$222$	0.327298	+	0.285952i	0.0219668	+	0.0191918i
$223$	−1.54549	−	11.4093i	−0.103494	−	0.764023i	−0.966104	−	0.258154i	$-0.916886\pi$
$223$	−1.54549	−	11.4093i	−0.103494	−	0.764023i	0.862610	−	0.505870i	$-0.168828\pi$
$224$	5.02893	−	3.00465i	0.336009	−	0.200756i
$225$	−0.00531643	+	0.0124384i	−0.000354429	+	0.000829227i
$226$	0.0926650	+	0.0553647i	0.00616398	+	0.00368281i
$227$	−14.6999	+	10.6801i	−0.975668	+	0.708865i	−0.956736	−	0.290956i	$-0.906027\pi$
$227$	−14.6999	+	10.6801i	−0.975668	+	0.708865i	−0.0189320	+	0.999821i	$0.506027\pi$
$228$	6.71940	+	10.1795i	0.445003	+	0.674151i
$229$	−3.03842	−	0.273462i	−0.200784	−	0.0180709i	−0.0112093	−	0.999937i	$-0.503568\pi$
$229$	−3.03842	−	0.273462i	−0.200784	−	0.0180709i	−0.189575	+	0.981866i	$0.560711\pi$
$230$	0.0555276	−	0.170896i	0.00366138	−	0.0112686i
$231$	−1.05353	−	23.4587i	−0.0693174	−	1.54347i
$232$	0.422702	−	0.640366i	0.0277517	−	0.0420421i
$233$	10.4964	−	13.1620i	0.687640	−	0.862273i	−0.308393	−	0.951259i	$-0.599791\pi$
$233$	10.4964	−	13.1620i	0.687640	−	0.862273i	0.996033	+	0.0889859i	$0.0283626\pi$
$234$	−0.0513236	+	0.0953753i	−0.00335513	+	0.00623488i
$235$	27.4449	+	7.57432i	1.79031	+	0.494094i
$236$	−5.68552	−	2.73800i	−0.370096	−	0.178229i
$237$	−15.9604	+	5.99004i	−1.03674	+	0.389095i
$238$	0.997496	+	3.06998i	0.0646581	+	0.198997i
$239$	0.595198	+	2.60773i	0.0385002	+	0.168680i	0.990523	−	0.137347i	$-0.0438574\pi$
$239$	0.595198	+	2.60773i	0.0385002	+	0.168680i	−0.952023	+	0.306027i	$0.901000\pi$
$240$	7.68014	+	14.2721i	0.495751	+	0.921260i
$241$	1.66978	+	0.303021i	0.107560	+	0.0195193i	0.232070	−	0.972699i	$-0.425450\pi$
$241$	1.66978	+	0.303021i	0.107560	+	0.0195193i	−0.124510	+	0.992218i	$0.539736\pi$
$242$	−0.320228	+	0.0883773i	−0.0205850	+	0.00568111i
$243$	0.869554	−	3.80976i	0.0557819	−	0.244397i
$244$	−5.24408	+	0.471975i	−0.335718	+	0.0302151i
$245$	18.9749	+	23.7938i	1.21226	+	1.52013i
$246$	−0.182091	+	0.0330447i	−0.0116097	+	0.00210685i
$247$	−7.93684	+	3.82218i	−0.505009	+	0.243200i
$248$	1.96963	−	2.06007i	0.125072	−	0.130815i
$249$	−1.66434	+	1.74077i	−0.105473	+	0.110317i
$250$	−1.08908	+	0.524475i	−0.0688797	+	0.0331707i
$251$	−19.6332	+	3.56291i	−1.23924	+	0.224889i	−0.758324	−	0.651878i	$-0.773981\pi$
$251$	−19.6332	+	3.56291i	−1.23924	+	0.224889i	−0.480916	+	0.876767i	$0.659696\pi$
$252$	2.12585	+	2.66573i	0.133916	+	0.167925i
$253$	−2.07083	+	0.186378i	−0.130192	+	0.0117175i
$254$	0.141008	−	0.617795i	0.00884760	−	0.0387639i
$255$	−26.0835	+	7.19860i	−1.63341	+	0.450794i
$256$	14.8242	+	2.69020i	0.926515	+	0.168138i
$257$	−5.55904	−	10.3304i	−0.346763	−	0.644394i	0.646153	−	0.763208i	$-0.276377\pi$
$257$	−5.55904	−	10.3304i	−0.346763	−	0.644394i	−0.992917	+	0.118814i	$0.962091\pi$
$258$	0.445885	+	1.95355i	0.0277596	+	0.121623i
$259$	3.05360	+	9.39801i	0.189741	+	0.583964i
$260$	−11.0247	+	4.13766i	−0.683726	+	0.256607i
$261$	0.604136	+	0.290936i	0.0373951	+	0.0180085i
$262$	−0.628562	−	0.173472i	−0.0388327	−	0.0107171i
$263$	5.59711	−	10.4012i	0.345133	−	0.641364i	−0.647563	−	0.762012i	$-0.724212\pi$
$263$	5.59711	−	10.4012i	0.345133	−	0.641364i	0.992695	+	0.120648i	$0.0384973\pi$
$264$	−1.39729	+	1.75215i	−0.0859974	+	0.107837i
$265$	14.6951	−	22.2622i	0.902715	−	1.36756i
$266$	−0.0736811	−	1.64064i	−0.00451768	−	0.100594i
$267$	0.941687	−	2.89821i	0.0576303	−	0.177368i
$268$	−1.06798	−	0.0961201i	−0.0652374	−	0.00587147i
$269$	−8.60324	−	13.0333i	−0.524549	−	0.794657i	0.471648	−	0.881787i	$-0.343659\pi$
$269$	−8.60324	−	13.0333i	−0.524549	−	0.794657i	−0.996197	+	0.0871294i	$0.972231\pi$
$270$	−0.949294	+	0.689702i	−0.0577722	+	0.0419740i
$271$	−25.0155	−	14.9461i	−1.51959	−	0.907910i	−0.998520	−	0.0543941i	$-0.982677\pi$
$271$	−25.0155	−	14.9461i	−1.51959	−	0.907910i	−0.521066	−	0.853516i	$-0.674466\pi$
$272$	−10.1318	+	23.7046i	−0.614333	+	1.43730i
$273$	−18.8830	+	11.2821i	−1.14285	+	0.682823i
$274$	0.256356	+	1.89249i	0.0154870	+	0.114330i
$275$	−0.0758924	−	0.0663052i	−0.00457649	−	0.00399835i
$276$	2.03082	−	1.77427i	0.122241	−	0.106799i
$277$	1.13282	−	8.36282i	0.0680646	−	0.502473i	−0.924540	−	0.381084i	$-0.875551\pi$
$277$	1.13282	−	8.36282i	0.0680646	−	0.502473i	0.992605	−	0.121389i	$-0.0387348\pi$
$278$	−0.244815	−	0.572773i	−0.0146830	−	0.0343527i
$279$	2.01505	+	1.46402i	0.120638	+	0.0876486i
$280$	0.197568	−	4.39919i	0.0118069	−	0.262902i
$281$	10.1220	+	3.79886i	0.603829	+	0.226621i	0.634518	−	0.772908i	$-0.281199\pi$
$281$	10.1220	+	3.79886i	0.603829	+	0.226621i	−0.0306888	+	0.999529i	$0.509770\pi$
$282$	−1.74862	−	1.82891i	−0.104129	−	0.108910i
$283$	−0.567291			−0.0337220			−0.0168610	−	0.999858i	$-0.505367\pi$
$283$	−0.567291			−0.0337220			−0.0168610	+	0.999858i	$0.505367\pi$
$284$	−11.9083	−	11.7839i	−0.706625	−	0.699243i
$285$	13.7666			0.815464
$286$	−0.557621	−	0.583226i	−0.0329728	−	0.0344869i
$287$	−3.93941	−	1.47849i	−0.232536	−	0.0872722i
$288$	0.0219202	−	0.488091i	0.00129166	−	0.0287610i
$289$	−21.0661	−	15.3054i	−1.23918	−	0.900317i
$290$	−0.169683	−	0.396992i	−0.00996410	−	0.0233122i
$291$	2.36276	−	17.4426i	0.138508	−	1.02250i
$292$	−8.04243	+	7.02646i	−0.470648	+	0.411192i
$293$	−6.10105	−	5.33032i	−0.356427	−	0.311401i	0.461037	−	0.887381i	$-0.347478\pi$
$293$	−6.10105	−	5.33032i	−0.356427	−	0.311401i	−0.817464	+	0.575980i	$0.804621\pi$
$294$	−0.363066	−	2.68026i	−0.0211745	−	0.156316i
$295$	−6.11423	+	3.65308i	−0.355984	+	0.212691i
$296$	0.370651	−	0.867182i	0.0215437	−	0.0504039i
$297$	11.6554	+	6.96378i	0.676315	+	0.404080i
$298$	−1.15667	+	0.840372i	−0.0670042	+	0.0486814i
$299$	1.07296	+	1.62546i	0.0620508	+	0.0940029i
$300$	0.130181	+	0.0117165i	0.00751602	+	0.000676454i
$301$	−14.0785	+	43.3292i	−0.811472	+	2.49745i
$302$	0.0157079	+	0.349764i	0.000903889	+	0.0201267i
$303$	−10.2642	+	15.5495i	−0.589660	+	0.893297i
$304$	8.17746	−	10.2542i	0.469010	−	0.588119i
$305$	−2.81609	+	5.23317i	−0.161249	+	0.299650i
$306$	0.259517	+	0.0716222i	0.0148356	+	0.00409437i
$307$	23.9806	+	11.5484i	1.36864	+	0.659105i	0.966546	−	0.256492i	$-0.0825666\pi$
$307$	23.9806	+	11.5484i	1.36864	+	0.659105i	0.402099	+	0.915596i	$0.368281\pi$
$308$	−23.7821	+	8.92558i	−1.35511	+	0.508582i
$309$	−2.27047	−	6.98779i	−0.129163	−	0.397522i
$310$	−0.356855	−	1.56348i	−0.0202680	−	0.0887999i
$311$	5.20985	+	9.68152i	0.295423	+	0.548988i	0.984432	−	0.175764i	$-0.0562397\pi$
$311$	5.20985	+	9.68152i	0.295423	+	0.548988i	−0.689009	+	0.724753i	$0.741954\pi$
$312$	2.06556	+	0.374844i	0.116939	+	0.0212213i
$313$	26.7146	−	7.37276i	1.51000	−	0.416733i	0.589594	−	0.807700i	$-0.299288\pi$
$313$	26.7146	−	7.37276i	1.51000	−	0.416733i	0.920405	+	0.390967i	$0.127859\pi$
$314$	−0.472164	+	2.06868i	−0.0266457	+	0.116743i
$315$	3.83282	−	0.344960i	0.215955	−	0.0194363i
$316$	11.4977	+	14.4177i	0.646798	+	0.811059i
$317$	4.07514	−	0.739528i	0.228882	−	0.0415360i	−0.0629038	−	0.998020i	$-0.520036\pi$
$317$	4.07514	−	0.739528i	0.228882	−	0.0415360i	0.291786	+	0.956484i	$0.405750\pi$
$318$	−2.13594	+	1.02861i	−0.119778	+	0.0576818i
$319$	−3.45227	+	3.61079i	−0.193290	+	0.202165i
$320$	11.9702	−	12.5198i	0.669153	−	0.699879i
$321$	6.78976	−	3.26977i	0.378967	−	0.182501i
$322$	−0.357263	+	0.0648337i	−0.0199095	+	0.00361304i
$323$	13.6525	+	17.1197i	0.759648	+	0.952568i
$324$	−19.7855	+	1.78072i	−1.09919	+	0.0989291i
$325$	−0.0210063	+	0.0920344i	−0.00116522	+	0.00510515i
$326$	0.0820137	−	0.0226343i	0.00454232	−	0.00125360i
$327$	3.88288	+	0.704639i	0.214724	+	0.0389666i
$328$	0.190292	+	0.353622i	0.0105071	+	0.0195255i
$329$	−12.8018	−	56.0883i	−0.705785	−	3.09225i
$330$	0.389667	+	1.19927i	0.0214505	+	0.0660177i
$331$	5.80707	−	2.17943i	0.319185	−	0.119792i	−0.186640	−	0.982428i	$-0.559760\pi$
$331$	5.80707	−	2.17943i	0.319185	−	0.119792i	0.505825	+	0.862636i	$0.331188\pi$
$332$	2.34725	+	1.13038i	0.128822	+	0.0620374i
$333$	0.794450	+	0.219254i	0.0435356	+	0.0120151i
$334$	1.19422	−	2.21923i	0.0653448	−	0.121431i
$335$	−0.754592	+	0.946228i	−0.0412278	+	0.0516980i
$336$	18.0418	−	27.3321i	0.984260	−	1.49109i
$337$	0.0843841	+	1.87896i	0.00459670	+	0.102353i	0.999980	+	0.00637077i	$0.00202789\pi$
$337$	0.0843841	+	1.87896i	0.00459670	+	0.102353i	−0.995383	+	0.0959826i	$0.969401\pi$
$338$	0.202334	−	0.622721i	0.0110055	−	0.0338715i
$339$	1.82106	+	0.163898i	0.0989064	+	0.00890174i
$340$	16.1250	+	24.4284i	0.874502	+	1.32481i
$341$	−15.0123	+	10.9071i	−0.812964	+	0.590653i
$342$	−0.117582	−	0.0702520i	−0.00635811	−	0.00379879i
$343$	11.6943	−	27.3601i	0.631432	−	1.47731i
$344$	3.73254	−	2.23009i	0.201245	−	0.120238i
$345$	−0.408566	−	3.01615i	−0.0219964	−	0.162384i
$346$	1.50351	+	1.31357i	0.0808290	+	0.0706182i
$347$	19.6070	−	17.1301i	1.05256	−	0.919593i	0.0556725	−	0.998449i	$-0.482270\pi$
$347$	19.6070	−	17.1301i	1.05256	−	0.919593i	0.996886	+	0.0788565i	$0.0251269\pi$
$348$	0.869731	−	6.42061i	0.0466225	−	0.344181i
$349$	−0.146075	−	0.341759i	−0.00781921	−	0.0182940i	0.915573	−	0.402153i	$-0.131738\pi$
$349$	−0.146075	−	0.341759i	−0.00781921	−	0.0182940i	−0.923392	+	0.383859i	$0.874595\pi$
$350$	−0.0142380	−	0.0103445i	−0.000761050	−	0.000552936i
$351$	0.570604	−	12.7055i	0.0304566	−	0.678169i
$352$	3.40789	+	1.27900i	0.181641	+	0.0681710i
$353$	7.48214	+	7.82571i	0.398234	+	0.416520i	0.891259	−	0.453495i	$-0.149823\pi$
$353$	7.48214	+	7.82571i	0.398234	+	0.416520i	−0.493024	+	0.870015i	$0.664109\pi$
$354$	0.633000			0.0336436
$355$	−18.5042	+	3.89011i	−0.982103	+	0.206466i
$356$	−3.29646			−0.174712
$357$	37.7852	+	39.5202i	1.99980	+	2.09163i
$358$	−1.50790	−	0.565925i	−0.0796951	−	0.0299101i
$359$	−0.408043	+	9.08578i	−0.0215357	+	0.479529i	0.959026	+	0.283318i	$0.0914352\pi$
$359$	−0.408043	+	9.08578i	−0.0215357	+	0.479529i	−0.980562	+	0.196211i	$0.937136\pi$
$360$	−0.297129	−	0.215877i	−0.0156600	−	0.0113777i
$361$	3.08898	+	7.22702i	0.162578	+	0.380369i
$362$	0.266544	−	1.96771i	0.0140093	−	0.103420i
$363$	−4.23750	+	3.70220i	−0.222411	+	0.194315i
$364$	17.9192	+	15.6555i	0.939219	+	0.820571i
$365$	1.61800	+	11.9446i	0.0846900	+	0.625206i
$366$	0.453397	−	0.270892i	0.0236994	−	0.0141597i
$367$	8.23973	−	19.2778i	0.430110	−	1.00629i	−0.554604	−	0.832115i	$-0.687130\pi$
$367$	8.23973	−	19.2778i	0.430110	−	1.00629i	0.984714	−	0.174179i	$-0.0557270\pi$
$368$	−2.48930	−	1.48729i	−0.129764	−	0.0775304i
$369$	−0.283910	+	0.206273i	−0.0147798	+	0.0107381i
$370$	−0.292327	−	0.442857i	−0.0151974	−	0.0230230i
$371$	−53.6845	−	4.83170i	−2.78716	−	0.250849i
$372$	7.43723	−	22.8894i	0.385602	−	1.18676i
$373$	−0.600344	−	13.3677i	−0.0310846	−	0.692153i	−0.952675	−	0.303990i	$-0.901681\pi$
$373$	−0.600344	−	13.3677i	−0.0310846	−	0.692153i	0.921591	−	0.388163i	$-0.126890\pi$
$374$	−1.10494	+	1.67391i	−0.0571350	+	0.0865559i
$375$	−12.7660	+	16.0081i	−0.659235	+	0.826655i
$376$	−2.60180	+	4.83495i	−0.134177	+	0.249344i
$377$	4.51090	+	1.24493i	0.232323	+	0.0641171i
$378$	2.13624	+	1.02876i	0.109876	+	0.0529137i
$379$	24.5242	−	9.20410i	1.25973	−	0.472783i	0.369895	−	0.929074i	$-0.379394\pi$
$379$	24.5242	−	9.20410i	1.25973	−	0.472783i	0.889831	+	0.456291i	$0.150822\pi$
$380$	−4.60186	−	14.1631i	−0.236070	−	0.726550i
$381$	−2.38846	−	10.4645i	−0.122364	−	0.536113i
$382$	1.09658	+	2.03778i	0.0561058	+	0.104262i
$383$	−14.8879	−	2.70176i	−0.760736	−	0.138053i	−0.215693	−	0.976461i	$-0.569201\pi$
$383$	−14.8879	−	2.70176i	−0.760736	−	0.138053i	−0.545043	+	0.838408i	$0.683487\pi$
$384$	−6.06181	+	1.67295i	−0.309341	+	0.0853726i
$385$	−6.37975	+	27.9515i	−0.325142	+	1.42454i
$386$	1.12388	−	0.101151i	0.0572039	−	0.00514844i
$387$	2.36908	+	2.97074i	0.120427	+	0.151011i
$388$	−18.7347	+	3.39985i	−0.951112	+	0.172601i
$389$	−17.1868	+	8.27675i	−0.871408	+	0.419648i	−0.815479	−	0.578787i	$-0.803526\pi$
$389$	−17.1868	+	8.27675i	−0.871408	+	0.419648i	−0.0559288	+	0.998435i	$0.517812\pi$
$390$	0.816289	−	0.853772i	0.0413344	−	0.0432324i
$391$	3.34562	−	3.49924i	0.169195	−	0.176964i
$392$	−5.28778	+	2.54646i	−0.267073	+	0.128616i
$393$	−10.8674	+	1.97215i	−0.548189	+	0.0994817i
$394$	−0.692636	−	0.868538i	−0.0348945	−	0.0437563i
$395$	20.7299	−	1.86573i	1.04304	−	0.0938750i
$396$	−0.471426	+	2.06545i	−0.0236901	+	0.103793i
$397$	−8.21355	+	2.26680i	−0.412226	+	0.113767i	−0.465998	−	0.884786i	$-0.654304\pi$
$397$	−8.21355	+	2.26680i	−0.412226	+	0.113767i	0.0537711	+	0.998553i	$0.482876\pi$
$398$	−0.497276	−	0.0902424i	−0.0249262	−	0.00452344i
$399$	−13.1820	−	24.4964i	−0.659928	−	1.22635i
$400$	−0.0312752	−	0.137026i	−0.00156376	−	0.00685128i
$401$	7.44847	+	22.9240i	0.371959	+	1.14477i	0.945507	+	0.325600i	$0.105566\pi$
$401$	7.44847	+	22.9240i	0.371959	+	1.14477i	−0.573549	+	0.819172i	$0.694434\pi$
$402$	0.100703	−	0.0377946i	0.00502262	−	0.00188502i
$403$	15.6609	+	7.54188i	0.780124	+	0.375688i
$404$	19.4284	+	5.36190i	0.966599	+	0.266764i
$405$	−10.6249	+	19.7443i	−0.527953	+	0.981102i
$406$	−0.543931	+	0.682068i	−0.0269949	+	0.0338505i
$407$	−3.38251	+	5.12428i	−0.167665	+	0.254001i
$408$	−0.234113	−	5.21294i	−0.0115903	−	0.258079i
$409$	9.22903	−	28.4040i	0.456346	−	1.40449i	−0.413201	−	0.910640i	$-0.635589\pi$
$409$	9.22903	−	28.4040i	0.456346	−	1.40449i	0.869547	−	0.493849i	$-0.164411\pi$
$410$	0.225042	+	0.0202541i	0.0111140	+	0.00100028i
$411$	17.8209	+	26.9974i	0.879038	+	1.33169i
$412$	−6.43006	+	4.67171i	−0.316786	+	0.230159i
$413$	12.3549	+	7.38172i	0.607946	+	0.363231i
$414$	−0.0119020	+	0.0278462i	−0.000584953	+	0.00136857i
$415$	2.52424	−	1.50816i	0.123910	−	0.0740328i
$416$	−0.457695	−	3.37884i	−0.0224403	−	0.165661i
$417$	−7.94565	−	6.94190i	−0.389100	−	0.339947i
$418$	0.768467	−	0.671389i	0.0375869	−	0.0328387i
$419$	1.95979	−	14.4677i	0.0957418	−	0.706795i	−0.877922	−	0.478804i	$-0.841070\pi$
$419$	1.95979	−	14.4677i	0.0957418	−	0.706795i	0.973663	−	0.227990i	$-0.0732154\pi$
$420$	−14.6147	−	34.1929i	−0.713126	−	1.66844i
$421$	−19.3790	−	14.0797i	−0.944474	−	0.686201i	0.00501943	−	0.999987i	$-0.498402\pi$
$421$	−19.3790	−	14.0797i	−0.944474	−	0.686201i	−0.949493	+	0.313787i	$0.898402\pi$
$422$	−0.107758	+	2.39942i	−0.00524557	+	0.116802i
$423$	−4.49222	−	1.68596i	−0.218419	−	0.0819742i
$424$	3.55496	+	3.71819i	0.172644	+	0.180571i
$425$	0.234652			0.0113823
$426$	1.58909	+	0.546696i	0.0769915	+	0.0264875i
$427$	12.0084			0.581128
$428$	−5.63359	−	5.89228i	−0.272310	−	0.284814i
$429$	−12.7962	−	4.80250i	−0.617807	−	0.231867i
$430$	0.109761	−	2.44403i	0.00529316	−	0.117861i
$431$	−10.0370	−	7.29234i	−0.483468	−	0.351260i	0.319199	−	0.947688i	$-0.396586\pi$
$431$	−10.0370	−	7.29234i	−0.483468	−	0.351260i	−0.802667	+	0.596428i	$0.796586\pi$
$432$	7.44218	+	17.4118i	0.358062	+	0.837728i
$433$	−2.48404	+	18.3379i	−0.119375	+	0.881263i	0.827908	+	0.560864i	$0.189531\pi$
$433$	−2.48404	+	18.3379i	−0.119375	+	0.881263i	−0.947283	+	0.320399i	$0.896183\pi$
$434$	−2.44036	+	2.13208i	−0.117141	+	0.102343i
$435$	−5.50717	−	4.81147i	−0.264048	−	0.230692i
$436$	−0.573026	−	4.23025i	−0.0274430	−	0.202592i
$437$	−2.11443	+	1.26332i	−0.101147	+	0.0604326i
$438$	0.421031	−	0.985051i	0.0201176	−	0.0470676i
$439$	21.7322	+	12.9844i	1.03722	+	0.619712i	0.927335	−	0.374232i	$-0.122094\pi$
$439$	21.7322	+	12.9844i	1.03722	+	0.619712i	0.109888	+	0.993944i	$0.464951\pi$
$440$	2.21364	−	1.60830i	0.105531	−	0.0766728i
$441$	−2.82550	−	4.28045i	−0.134548	−	0.203831i
$442$	1.87125	+	0.168415i	0.0890063	+	0.00801071i
$443$	3.22006	−	9.91032i	0.152990	−	0.470854i	−0.844962	−	0.534826i	$-0.820377\pi$
$443$	3.22006	−	9.91032i	0.152990	−	0.470854i	0.997952	+	0.0639726i	$0.0203770\pi$
$444$	−0.357283	−	7.95553i	−0.0169559	−	0.377553i
$445$	−2.04968	+	3.10513i	−0.0971640	+	0.147197i
$446$	0.778939	−	0.976759i	0.0368838	−	0.0462509i
$447$	−11.4759	+	21.3258i	−0.542790	+	1.00867i
$448$	−33.7397	−	9.31156i	−1.59405	−	0.439930i
$449$	−12.4264	−	5.98423i	−0.586438	−	0.282413i	0.117044	−	0.993127i	$-0.462658\pi$
$449$	−12.4264	−	5.98423i	−0.586438	−	0.282413i	−0.703482	+	0.710713i	$0.748372\pi$
$450$	−0.00137420		0.000515748i	−6.47806e−5		2.43126e-5i
$451$	−0.807919	−	2.48652i	−0.0380434	−	0.117086i
$452$	−0.440120	−	1.92829i	−0.0207015	−	0.0906992i
$453$	2.81026	+	5.22233i	0.132037	+	0.245367i
$454$	−1.93994	−	0.352047i	−0.0910459	−	0.0165224i
$455$	25.8886	−	7.14481i	1.21368	−	0.334954i
$456$	−0.590761	+	2.58829i	−0.0276649	+	0.121208i
$457$	−28.8681	+	2.59818i	−1.35039	+	0.121538i	−0.741093	−	0.671402i	$-0.765692\pi$
$457$	−28.8681	+	2.59818i	−1.35039	+	0.121538i	−0.609300	+	0.792940i	$0.708550\pi$
$458$	−0.206393	−	0.258809i	−0.00964412	−	0.0120933i
$459$	−31.1056	+	5.64484i	−1.45189	+	0.263479i
$460$	−2.96644	+	1.42856i	−0.138311	+	0.0666070i
$461$	17.5170	−	18.3213i	0.815848	−	0.853310i	−0.175513	−	0.984477i	$-0.556158\pi$
$461$	17.5170	−	18.3213i	0.815848	−	0.853310i	0.991360	+	0.131167i	$0.0418725\pi$
$462$	1.76087	−	1.84172i	0.0819229	−	0.0856846i
$463$	2.46087	−	1.18509i	0.114366	−	0.0550760i	−0.375826	−	0.926690i	$-0.622641\pi$
$463$	2.46087	−	1.18509i	0.114366	−	0.0550760i	0.490192	+	0.871614i	$0.336927\pi$
$464$	−6.85516	+	1.24403i	−0.318243	+	0.0577526i
$465$	−16.9366	−	21.2378i	−0.785414	−	0.984878i
$466$	1.81938	−	0.163748i	0.0842814	−	0.00758546i
$467$	−2.71962	+	11.9154i	−0.125849	+	0.551380i	0.872211	+	0.489129i	$0.162685\pi$
$467$	−2.71962	+	11.9154i	−0.125849	+	0.551380i	−0.998060	+	0.0622515i	$0.980172\pi$
$468$	1.91302	−	0.527959i	0.0884292	−	0.0244049i
$469$	2.40627	+	0.436674i	0.111111	+	0.0201637i
$470$	1.46395	+	2.72048i	0.0675270	+	0.125486i
$471$	7.99775	+	35.0404i	0.368517	+	1.61458i
$472$	−0.424447	−	1.30631i	−0.0195368	−	0.0601280i
$473$	−26.5032	+	9.94682i	−1.21862	+	0.457355i
$474$	−1.66662	−	0.802600i	−0.0765502	−	0.0368646i
$475$	−0.115081	−	0.0317605i	−0.00528030	−	0.00145727i
$476$	28.0276	−	52.0840i	1.28464	−	2.38727i
$477$	−2.80290	+	3.51472i	−0.128336	+	0.160928i
$478$	−0.159892	+	0.242227i	−0.00731331	+	0.0110792i
$479$	1.27611	+	28.4147i	0.0583068	+	1.29830i	0.788489	+	0.615049i	$0.210864\pi$
$479$	1.27611	+	28.4147i	0.0583068	+	1.29830i	−0.730182	+	0.683252i	$0.760565\pi$
$480$	−1.64660	+	5.06771i	−0.0751566	+	0.231308i
$481$	5.72839	+	0.515564i	0.261192	+	0.0235077i
$482$	0.101446	+	0.153683i	0.00462072	+	0.00700009i
$483$	−4.97573	+	3.61508i	−0.226404	+	0.164492i
$484$	5.22531	+	3.12198i	0.237514	+	0.141908i
$485$	−8.44639	+	19.7613i	−0.383531	+	0.897315i
$486$	0.364004	−	0.217483i	0.0165116	−	0.00986521i
$487$	3.48538	+	25.7301i	0.157937	+	1.16594i	0.880297	+	0.474423i	$0.157343\pi$
$487$	3.48538	+	25.7301i	0.157937	+	1.16594i	−0.722359	+	0.691518i	$0.756942\pi$
$488$	−0.863054	−	0.754027i	−0.0390686	−	0.0341332i
$489$	1.08527	−	0.948171i	0.0490776	−	0.0428778i
$490$	−0.443279	+	3.27242i	−0.0200253	+	0.147833i
$491$	11.6442	+	27.2430i	0.525497	+	1.22946i	0.946589	+	0.322443i	$0.104504\pi$
$491$	11.6442	+	27.2430i	0.525497	+	1.22946i	−0.421092	+	0.907018i	$0.638353\pi$
$492$	2.74335	+	1.99316i	0.123680	+	0.0898586i
$493$	0.521861	−	11.6201i	0.0235034	−	0.523345i
$494$	−0.894931	−	0.335873i	−0.0402648	−	0.0151116i
$495$	1.65245	+	1.72832i	0.0742719	+	0.0776824i
$496$	−25.8796			−1.16203
$497$	24.6406	+	29.2015i	1.10528	+	1.30987i
$498$	−0.261332			−0.0117106
$499$	0.756628	+	0.791370i	0.0338713	+	0.0354266i	0.739513	−	0.673142i	$-0.235056\pi$
$499$	0.756628	+	0.791370i	0.0338713	+	0.0354266i	−0.705642	+	0.708568i	$0.749341\pi$
$500$	20.7365	+	7.78254i	0.927364	+	0.348046i
$501$	1.91517	−	42.6446i	0.0855635	−	1.90522i
$502$	−1.75167	−	1.27266i	−0.0781809	−	0.0568018i
$503$	−0.584834	−	1.36829i	−0.0260765	−	0.0610089i	0.905983	−	0.423313i	$-0.139133\pi$
$503$	−0.584834	−	1.36829i	−0.0260765	−	0.0610089i	−0.932060	+	0.362304i	$0.881990\pi$
$504$	−0.0996195	+	0.735421i	−0.00443741	+	0.0327583i
$505$	17.1309	−	14.9668i	0.762315	−	0.666014i
$506$	−0.169902	−	0.148439i	−0.00755309	−	0.00659893i
$507$	−1.48875	−	10.9904i	−0.0661178	−	0.488101i
$508$	−9.96747	+	5.95529i	−0.442235	+	0.264223i
$509$	2.04492	−	4.78433i	0.0906395	−	0.212062i	−0.868074	−	0.496434i	$-0.834642\pi$
$509$	2.04492	−	4.78433i	0.0906395	−	0.212062i	0.958714	+	0.284373i	$0.0917853\pi$
$510$	−2.52050	−	1.50593i	−0.111610	−	0.0666837i
$511$	19.7049	−	14.3164i	0.871692	−	0.633321i
$512$	4.67027	+	7.07516i	0.206399	+	0.312681i
$513$	16.0193	+	1.44177i	0.707270	+	0.0636555i
$514$	0.393360	−	1.21064i	0.0173504	−	0.0533990i
$515$	0.402467	+	8.96163i	0.0177348	+	0.394897i
$516$	20.2265	−	30.6419i	0.890424	−	1.34893i
$517$	22.2878	−	27.9481i	0.980218	−	1.22916i
$518$	−0.508106	+	0.944219i	−0.0223249	+	0.0414866i
$519$	32.5990	+	8.99676i	1.43094	+	0.394914i
$520$	−2.30927	−	1.11209i	−0.101268	−	0.0487682i
$521$	4.09105	−	1.53540i	0.179232	−	0.0672669i	−0.260145	−	0.965569i	$-0.583770\pi$
$521$	4.09105	−	1.53540i	0.179232	−	0.0672669i	0.439377	+	0.898303i	$0.355199\pi$
$522$	0.0224840	+	0.0691987i	0.000984099	+	0.00302874i
$523$	−1.44113	−	6.31402i	−0.0630164	−	0.276093i	0.933597	−	0.358325i	$-0.116652\pi$
$523$	−1.44113	−	6.31402i	−0.0630164	−	0.276093i	−0.996613	+	0.0822325i	$0.973795\pi$
$524$	5.66167	+	10.5211i	0.247331	+	0.459618i
$525$	−0.293311	−	0.0532282i	−0.0128012	−	0.00232307i
$526$	1.23547	−	0.340969i	0.0538692	−	0.0148669i
$527$	9.61443	−	42.1236i	0.418811	−	1.83493i
$528$	20.2673	−	1.82409i	0.882022	−	0.0793834i
$529$	−14.0007	−	17.5564i	−0.608727	−	0.763320i
$530$	2.84796	−	0.516829i	0.123708	−	0.0224496i
$531$	1.08146	−	0.520806i	0.0469315	−	0.0226010i
$532$	−20.7953	+	21.7502i	−0.901593	+	0.942992i
$533$	−1.69246	+	1.77018i	−0.0733086	+	0.0766748i
$534$	0.297921	−	0.143471i	0.0128923	−	0.00620860i
$535$	−9.05314	+	1.64290i	−0.391401	+	0.0710289i
$536$	−0.145521	−	0.182478i	−0.00628555	−	0.00788183i
$537$	−27.1714	+	2.44547i	−1.17253	+	0.105530i
$538$	0.377076	−	1.65208i	0.0162569	−	0.0712262i
$539$	36.8339	−	10.1655i	1.58655	−	0.437859i
$540$	21.1547	+	3.83900i	0.910352	+	0.165204i
$541$	11.5822	+	21.5233i	0.497956	+	0.925357i	0.998229	+	0.0594896i	$0.0189473\pi$
$541$	11.5822	+	21.5233i	0.497956	+	0.925357i	−0.500273	+	0.865868i	$0.666767\pi$
$542$	−0.703612	−	3.08272i	−0.0302227	−	0.132414i
$543$	−10.3936	−	31.9883i	−0.446033	−	1.37275i
$544$	−7.93500	+	2.97806i	−0.340210	+	0.127683i
$545$	−4.34101	−	2.09052i	−0.185948	−	0.0895481i
$546$	−2.30083	−	0.634989i	−0.0984665	−	0.0271750i
$547$	−15.1900	+	28.2277i	−0.649477	+	1.20693i	0.316571	+	0.948569i	$0.397468\pi$
$547$	−15.1900	+	28.2277i	−0.649477	+	1.20693i	−0.966048	+	0.258362i	$0.916817\pi$
$548$	21.8178	−	27.3587i	0.932011	−	1.16870i
$549$	0.551738	−	0.835848i	0.0235476	−	0.0356731i
$550$	−0.000490608	−	0.0109242i	−2.09196e−5	−	0.000465811i
$551$	−1.82874	+	5.62829i	−0.0779070	+	0.239773i
$552$	0.584606	+	0.0526155i	0.0248825	+	0.00223947i
$553$	−23.1696	−	35.1004i	−0.985270	−	1.49262i
$554$	0.740842	−	0.538253i	0.0314753	−	0.0228682i
$555$	−7.71593	−	4.61005i	−0.327523	−	0.195686i
$556$	−4.48577	+	10.4950i	−0.190239	+	0.445086i
$557$	−8.96812	+	5.35820i	−0.379991	+	0.227034i	−0.690175	−	0.723642i	$-0.742467\pi$
$557$	−8.96812	+	5.35820i	−0.379991	+	0.227034i	0.310184	+	0.950677i	$0.399609\pi$
$558$	0.0362790	+	0.267822i	0.00153581	+	0.0113378i
$559$	19.9694	+	17.4468i	0.844616	+	0.737919i
$560$	−30.1118	+	26.3078i	−1.27245	+	1.11171i
$561$	−4.56040	+	33.6662i	−0.192540	+	1.42139i
$562$	0.461073	+	1.07873i	0.0194492	+	0.0455036i
$563$	−0.311257	−	0.226141i	−0.0131179	−	0.00953073i	0.581207	−	0.813756i	$-0.302581\pi$
$563$	−0.311257	−	0.226141i	−0.0131179	−	0.00953073i	−0.594325	+	0.804225i	$0.702581\pi$
$564$	−2.08009	+	46.3169i	−0.0875877	+	1.95029i
$565$	−2.09003	−	0.784401i	−0.0879281	−	0.0330000i
$566$	−0.0425393	−	0.0444926i	−0.00178806	−	0.00187016i
$567$	45.3067			1.90270
$568$	0.0626760	−	3.64596i	0.00262983	−	0.152981i
$569$	−6.76014			−0.283400			−0.141700	−	0.989910i	$-0.545257\pi$
$569$	−6.76014			−0.283400			−0.141700	+	0.989910i	$0.545257\pi$
$570$	1.03231	+	1.07971i	0.0432388	+	0.0452243i
$571$	−29.6667	−	11.1341i	−1.24151	−	0.465948i	−0.357722	−	0.933828i	$-0.616447\pi$
$571$	−29.6667	−	11.1341i	−1.24151	−	0.465948i	−0.883792	+	0.467880i	$0.845018\pi$
$572$	−0.663325	+	14.7701i	−0.0277350	+	0.617568i
$573$	31.7113	+	23.0396i	1.32476	+	0.962494i
$574$	−0.179446	−	0.419834i	−0.00748992	−	0.0175235i
$575$	−0.00354307	+	0.0261560i	−0.000147756	+	0.00109078i
$576$	−2.19833	+	1.92063i	−0.0915972	+	0.0800261i
$577$	11.4067	+	9.96574i	0.474867	+	0.414879i	0.861815	−	0.507222i	$-0.169328\pi$
$577$	11.4067	+	9.96574i	0.474867	+	0.414879i	−0.386948	+	0.922102i	$0.626471\pi$
$578$	−0.379274	−	2.79991i	−0.0157757	−	0.116461i
$579$	16.4082	−	9.80344i	0.681901	−	0.407417i
$580$	−3.10911	+	7.27412i	−0.129099	+	0.302042i
$581$	−5.10068	−	3.04752i	−0.211612	−	0.126432i
$582$	1.54520	−	1.12265i	0.0640505	−	0.0465354i
$583$	−18.4506	−	27.9515i	−0.764146	−	1.15763i
$584$	−2.31515	−	0.208368i	−0.0958018	−	0.00862232i
$585$	0.692162	−	2.13026i	0.0286174	−	0.0880753i
$586$	−0.0394404	−	0.878208i	−0.00162927	−	0.0362784i
$587$	12.3878	−	18.7666i	0.511297	−	0.774582i	−0.483620	−	0.875278i	$-0.660678\pi$
$587$	12.3878	−	18.7666i	0.511297	−	0.774582i	0.994917	+	0.100696i	$0.0321069\pi$
$588$	−30.8997	+	38.7470i	−1.27428	+	1.59790i
$589$	−10.4167	+	19.3575i	−0.429214	+	0.797613i
$590$	−0.744997	−	0.205606i	−0.0306711	−	0.00846467i
$591$	−16.9536	−	8.16440i	−0.697376	−	0.335839i
$592$	−8.01716	+	3.00889i	−0.329503	+	0.123665i
$593$	−2.92295	−	8.99591i	−0.120031	−	0.369418i	0.872932	−	0.487842i	$-0.162216\pi$
$593$	−2.92295	−	8.99591i	−0.120031	−	0.369418i	−0.992963	+	0.118424i	$0.962216\pi$
$594$	0.327832	+	1.43632i	0.0134511	+	0.0589331i
$595$	−31.6339	−	58.7857i	−1.29686	−	2.40998i
$596$	25.7760	+	4.67766i	1.05583	+	0.191604i
$597$	−8.25219	+	2.27746i	−0.337740	+	0.0932102i
$598$	−0.0470273	+	0.206040i	−0.00192309	+	0.00842560i
$599$	−18.1630	+	1.63470i	−0.742122	+	0.0667922i	−0.454247	−	0.890876i	$-0.650092\pi$
$599$	−18.1630	+	1.63470i	−0.742122	+	0.0667922i	−0.287875	+	0.957668i	$0.592949\pi$
$600$	0.0177382	+	0.0222430i	0.000724160	+	0.000908068i
$601$	18.3991	−	3.33894i	0.750515	−	0.136198i	0.210197	−	0.977659i	$-0.432590\pi$
$601$	18.3991	−	3.33894i	0.750515	−	0.136198i	0.540318	+	0.841461i	$0.318304\pi$
$602$	−4.45401	+	2.14494i	−0.181532	+	0.0874211i
$603$	0.140953	−	0.147425i	0.00574006	−	0.00600363i
$604$	4.43332	−	4.63689i	0.180389	−	0.188672i
$605$	6.18977	−	2.98084i	0.251650	−	0.121188i
$606$	−1.98922	+	0.360991i	−0.0808067	+	0.0146643i
$607$	−12.3695	−	15.5109i	−0.502063	−	0.629567i	0.464631	−	0.885505i	$-0.346187\pi$
$607$	−12.3695	−	15.5109i	−0.502063	−	0.629567i	−0.966693	+	0.255938i	$0.917616\pi$
$608$	4.29468	−	0.386529i	0.174172	−	0.0156758i
$609$	−3.28822	+	14.4066i	−0.133245	+	0.583786i
$610$	−0.621606	+	0.171552i	−0.0251681	+	0.00694595i
$611$	−32.9472	−	5.97903i	−1.33290	−	0.241886i
$612$	−2.33756	−	4.34391i	−0.0944902	−	0.175592i
$613$	2.69501	+	11.8076i	0.108850	+	0.476905i	0.999743	+	0.0226898i	$0.00722299\pi$
$613$	2.69501	+	11.8076i	0.108850	+	0.476905i	−0.890892	+	0.454215i	$0.849920\pi$
$614$	0.892482	+	2.74678i	0.0360176	+	0.110851i
$615$	3.58324	−	1.34481i	0.144490	−	0.0542280i
$616$	−4.98146	−	2.39894i	−0.200709	−	0.0966562i
$617$	−29.8854	−	8.24784i	−1.20314	−	0.332046i	−0.393695	−	0.919241i	$-0.628803\pi$
$617$	−29.8854	−	8.24784i	−1.20314	−	0.332046i	−0.809445	+	0.587195i	$0.800232\pi$
$618$	0.377797	−	0.702064i	0.0151972	−	0.0282412i
$619$	−1.82736	+	2.29143i	−0.0734477	+	0.0921005i	−0.817198	−	0.576357i	$-0.804474\pi$
$619$	−1.82736	+	2.29143i	−0.0734477	+	0.0921005i	0.743750	+	0.668458i	$0.233045\pi$
$620$	−16.1879	+	24.5236i	−0.650121	+	0.984891i
$621$	−0.159543	−	3.55249i	−0.00640222	−	0.142557i
$622$	−0.368652	+	1.13459i	−0.0147816	+	0.0454930i
$623$	7.48792	+	0.673925i	0.299997	+	0.0270002i
$624$	−10.5011	−	15.9085i	−0.420380	−	0.636848i
$625$	20.3691	−	14.7990i	0.814763	−	0.591960i
$626$	2.58148	+	1.54237i	0.103177	+	0.0616453i
$627$	6.79336	−	15.8938i	0.271300	−	0.634739i
$628$	33.3761	−	19.9413i	1.33185	−	0.795743i
$629$	−1.91907	−	14.1671i	−0.0765183	−	0.564881i
$630$	0.314466	+	0.274741i	0.0125286	+	0.0109459i
$631$	−12.9227	+	11.2902i	−0.514443	+	0.449456i	−0.875591	−	0.483053i	$-0.839528\pi$
$631$	−12.9227	+	11.2902i	−0.514443	+	0.449456i	0.361148	+	0.932509i	$0.382385\pi$
$632$	−0.538795	+	3.97755i	−0.0214321	+	0.158218i
$633$	15.9896	+	37.4096i	0.635531	+	1.48690i
$634$	0.363582	+	0.264158i	0.0144397	+	0.0104910i
$635$	−0.587954	+	13.0918i	−0.0233323	+	0.519533i
$636$	40.6689	+	15.2633i	1.61263	+	0.605230i
$637$	−24.7355	−	25.8713i	−0.980054	−	1.02506i
$638$	−0.542068			−0.0214607
$639$	3.16471	−	0.373417i	0.125194	−	0.0147721i
$640$	7.67773			0.303489
$641$	−26.8914	−	28.1262i	−1.06215	−	1.11092i	−0.993564	−	0.113274i	$-0.963866\pi$
$641$	−26.8914	−	28.1262i	−1.06215	−	1.11092i	−0.0685842	−	0.997645i	$-0.521848\pi$
$642$	0.765589	+	0.287331i	0.0302154	+	0.0113400i
$643$	−0.620804	+	13.8233i	−0.0244821	+	0.545137i	0.948849	+	0.315731i	$0.102250\pi$
$643$	−0.620804	+	13.8233i	−0.0244821	+	0.545137i	−0.973331	+	0.229406i	$0.926322\pi$
$644$	5.38246	+	3.91059i	0.212099	+	0.154099i
$645$	−16.2869	−	38.1051i	−0.641297	−	1.50039i
$646$	−0.318941	+	2.35452i	−0.0125486	+	0.0926374i
$647$	−19.0816	+	16.6711i	−0.750177	+	0.655410i	−0.945608	−	0.325308i	$-0.894532\pi$
$647$	−19.0816	+	16.6711i	−0.750177	+	0.655410i	0.195431	+	0.980717i	$0.437389\pi$
$648$	−3.25623	−	2.84488i	−0.127917	−	0.111758i
$649$	1.20040	+	8.86168i	0.0471197	+	0.347851i
$650$	−0.00879344	+	0.00525384i	−0.000344907	+	0.000206072i
$651$	−21.5732	+	50.4729i	−0.845519	+	1.97819i
$652$	−1.33826	−	0.799571i	−0.0524102	−	0.0313136i
$653$	−16.6612	+	12.1051i	−0.652003	+	0.473708i	−0.863953	−	0.503572i	$-0.832019\pi$
$653$	−16.6612	+	12.1051i	−0.652003	+	0.473708i	0.211950	+	0.977281i	$0.432019\pi$
$654$	0.235900	+	0.357373i	0.00922441	+	0.0139744i
$655$	13.4308	+	1.20879i	0.524785	+	0.0472315i
$656$	1.12677	−	3.46784i	0.0439929	−	0.135396i
$657$	−0.0911379	−	2.02934i	−0.00355563	−	0.0791722i
$658$	3.43904	−	5.20992i	0.134068	−	0.203104i
$659$	−3.21265	+	4.02853i	−0.125147	+	0.156929i	−0.840458	−	0.541877i	$-0.817714\pi$
$659$	−3.21265	+	4.02853i	−0.125147	+	0.156929i	0.715311	+	0.698807i	$0.246285\pi$
$660$	10.9488	−	20.3464i	0.426183	−	0.791981i
$661$	−40.6015	−	11.2053i	−1.57921	−	0.435835i	−0.637005	−	0.770860i	$-0.719827\pi$
$661$	−40.6015	−	11.2053i	−1.57921	−	0.435835i	−0.942209	+	0.335024i	$0.891255\pi$
$662$	0.606385	+	0.292020i	0.0235678	+	0.0113497i
$663$	29.7950	−	11.1823i	1.15714	−	0.434283i
$664$	0.175232	+	0.539307i	0.00680030	+	0.0209292i
$665$	7.55765	+	33.1122i	0.293073	+	1.28404i
$666$	0.0423771	+	0.0787498i	0.00164208	+	0.00305149i
$667$	1.28739	+	0.233626i	0.0498477	+	0.00904603i
$668$	−44.5128	+	12.2848i	−1.72225	+	0.475312i
$669$	4.70891	−	20.6311i	0.182057	−	0.797643i
$670$	−0.130797	+	0.0117719i	−0.00505313	+	0.000454790i
$671$	4.65216	+	5.83362i	0.179594	+	0.225204i
$672$	10.5942	−	1.92256i	0.408679	−	0.0741643i
$673$	42.2937	−	20.3676i	1.63030	−	0.785113i	0.630343	−	0.776317i	$-0.282914\pi$
$673$	42.2937	−	20.3676i	1.63030	−	0.785113i	0.999961	−	0.00879593i	$-0.00279987\pi$
$674$	−0.141039	+	0.147515i	−0.00543261	+	0.00568207i
$675$	0.119111	−	0.124581i	0.00458460	−	0.00479512i
$676$	−10.8093	+	5.20546i	−0.415740	+	0.200210i
$677$	46.8876	−	8.50884i	1.80204	−	0.327021i	0.829276	−	0.558839i	$-0.188753\pi$
$677$	46.8876	−	8.50884i	1.80204	−	0.327021i	0.972759	+	0.231818i	$0.0744673\pi$
$678$	0.123701	+	0.155116i	0.00475070	+	0.00595719i
$679$	43.2510	−	3.89266i	1.65982	−	0.149387i
$680$	−1.41769	+	6.21131i	−0.0543660	+	0.238193i
$681$	−32.1929	+	8.88467i	−1.23363	+	0.340461i
$682$	−1.98117	−	0.359529i	−0.0758629	−	0.0137671i
$683$	14.4591	+	26.8695i	0.553261	+	1.02813i	0.991602	+	0.129323i	$0.0412805\pi$
$683$	14.4591	+	26.8695i	0.553261	+	1.02813i	−0.438341	+	0.898809i	$0.644434\pi$
$684$	0.558466	+	2.44680i	0.0213535	+	0.0935557i
$685$	−12.2048	−	37.5626i	−0.466322	−	1.43519i
$686$	3.02277	−	1.13446i	0.115410	−	0.0433140i
$687$	−5.05185	−	2.43284i	−0.192740	−	0.0928188i
$688$	−38.0575	−	10.5032i	−1.45093	−	0.400431i
$689$	−14.8667	+	27.6269i	−0.566375	+	1.05250i
$690$	0.205920	−	0.258215i	0.00783923	−	0.00983008i
$691$	−2.10158	+	3.18376i	−0.0799480	+	0.121116i	−0.872347	−	0.488887i	$-0.837403\pi$
$691$	−2.10158	+	3.18376i	−0.0799480	+	0.121116i	0.792399	+	0.610003i	$0.208832\pi$
$692$	−1.64125	−	36.5452i	−0.0623909	−	1.38924i
$693$	1.49310	−	4.59530i	0.0567183	−	0.174561i
$694$	2.81378	+	0.253244i	0.106810	+	0.00961303i
$695$	7.09667	+	10.7510i	0.269192	+	0.407808i
$696$	1.14094	−	0.828942i	0.0432473	−	0.0314210i
$697$	5.22591	+	3.12234i	0.197945	+	0.118267i
$698$	0.0158505	−	0.0370840i	0.000599949	−	0.00140365i
$699$	26.5623	−	15.8702i	1.00468	−	0.600268i
$700$	0.0432861	+	0.319551i	0.00163606	+	0.0120779i
$701$	29.4967	+	25.7705i	1.11408	+	0.973339i	0.999798	−	0.0201098i	$-0.00640158\pi$
$701$	29.4967	+	25.7705i	1.11408	+	0.973339i	0.114278	+	0.993449i	$0.463544\pi$
$702$	1.03928	−	0.907990i	0.0392250	−	0.0342699i
$703$	−0.976364	+	7.20781i	−0.0368243	+	0.271848i
$704$	−8.54751	−	19.9979i	−0.322147	−	0.753699i
$705$	42.3352	+	30.7583i	1.59444	+	1.15843i
$706$	−0.0527086	+	1.17365i	−0.00198371	+	0.0441708i
$707$	−43.0354	−	16.1515i	−1.61851	−	0.607439i
$708$	−8.01530	−	8.38335i	−0.301233	−	0.315065i
$709$	−20.8986			−0.784863			−0.392432	−	0.919781i	$-0.628366\pi$
$709$	−20.8986			−0.784863			−0.392432	+	0.919781i	$0.628366\pi$
$710$	−1.69267	−	1.15958i	−0.0635248	−	0.0435182i
$711$	−3.50772			−0.131550
$712$	−0.495845	−	0.518614i	−0.0185826	−	0.0194359i
$713$	4.55023	+	1.70773i	0.170407	+	0.0639549i
$714$	−0.266181	+	5.92698i	−0.00996156	+	0.221811i
$715$	13.5004	+	9.80859i	0.504885	+	0.366820i
$716$	11.5987	+	27.1364i	0.433462	+	1.01413i
$717$	−0.659922	+	4.87174i	−0.0246452	+	0.181939i
$718$	−0.743194	+	0.649309i	−0.0277358	+	0.0242320i
$719$	−11.0736	−	9.67470i	−0.412975	−	0.360805i	0.426235	−	0.904612i	$-0.359840\pi$
$719$	−11.0736	−	9.67470i	−0.412975	−	0.360805i	−0.839210	+	0.543807i	$0.816982\pi$
$720$	0.447648	+	3.30467i	0.0166829	+	0.123158i
$721$	15.5610	−	9.29725i	0.579521	−	0.346248i
$722$	−0.335182	+	0.784198i	−0.0124742	+	0.0291848i
$723$	2.67764	+	1.59982i	0.0995825	+	0.0594978i
$724$	−29.4351	+	21.3859i	−1.09395	+	0.794799i
$725$	0.0349366	+	0.0529266i	0.00129751	+	0.00196565i
$726$	−0.608119	−	0.0547317i	−0.0225694	−	0.00203128i
$727$	0.387562	−	1.19279i	0.0143739	−	0.0442382i	−0.943612	−	0.331053i	$-0.892596\pi$
$727$	0.387562	−	1.19279i	0.0143739	−	0.0442382i	0.957986	+	0.286814i	$0.0925963\pi$
$728$	0.232364	+	5.17398i	0.00861197	+	0.191760i
$729$	−12.5562	+	19.0218i	−0.465044	+	0.704511i
$730$	−0.815482	+	1.02258i	−0.0301823	+	0.0378475i
$731$	31.2344	−	58.0433i	1.15525	−	2.14681i
$732$	−9.32874	−	2.57457i	−0.344800	−	0.0951588i
$733$	4.18316	+	2.01450i	0.154508	+	0.0744073i	0.509540	−	0.860447i	$-0.329816\pi$
$733$	4.18316	+	2.01450i	0.154508	+	0.0744073i	−0.355032	+	0.934854i	$0.615530\pi$
$734$	2.12983	−	0.799337i	0.0786133	−	0.0295041i
$735$	17.2852	+	53.1984i	0.637574	+	1.96225i
$736$	−0.212143	−	0.929459i	−0.00781969	−	0.0342603i
$737$	0.720075	+	1.33812i	0.0265243	+	0.0492904i
$738$	−0.0374674	−	0.00679934i	−0.00137920	−	0.000250287i
$739$	−24.9425	+	6.88370i	−0.917526	+	0.253221i	−0.692740	−	0.721187i	$-0.743597\pi$
$739$	−24.9425	+	6.88370i	−0.917526	+	0.253221i	−0.224785	+	0.974408i	$0.572168\pi$
$740$	−2.16356	+	9.47917i	−0.0795340	+	0.348461i
$741$	−16.1260	+	1.45137i	−0.592405	+	0.0533174i
$742$	−3.64668	−	4.57279i	−0.133874	−	0.167872i
$743$	41.2507	−	7.48589i	1.51334	−	0.274631i	0.642534	−	0.766257i	$-0.277883\pi$
$743$	41.2507	−	7.48589i	1.51334	−	0.274631i	0.870806	+	0.491627i	$0.163598\pi$
$744$	4.71975	−	2.27291i	0.173035	−	0.0833290i
$745$	20.4332	−	21.3714i	0.748614	−	0.782989i
$746$	1.00341	−	1.04948i	0.0367374	−	0.0384243i
$747$	−0.446479	+	0.215013i	−0.0163358	+	0.00786691i
$748$	36.1602	−	6.56211i	1.32215	−	0.239934i
$749$	11.5921	+	14.5360i	0.423566	+	0.531135i
$750$	−2.21280	+	0.199155i	−0.0807999	+	0.00727213i
$751$	−2.96036	+	12.9702i	−0.108025	+	0.473289i	0.891759	+	0.452511i	$0.149472\pi$
$751$	−2.96036	+	12.9702i	−0.108025	+	0.473289i	−0.999784	+	0.0207785i	$0.993386\pi$
$752$	48.0580	−	13.2632i	1.75250	−	0.483658i
$753$	−36.0856	−	6.54857i	−1.31503	−	0.238643i
$754$	0.240618	+	0.447142i	0.00876278	+	0.0162840i
$755$	−1.61120	−	7.05913i	−0.0586376	−	0.256908i
$756$	−13.4252	−	41.3186i	−0.488271	−	1.50274i
$757$	5.79987	−	2.17673i	0.210800	−	0.0791146i	−0.243741	−	0.969840i	$-0.578375\pi$
$757$	5.79987	−	2.17673i	0.210800	−	0.0791146i	0.454541	+	0.890726i	$0.349803\pi$
$758$	2.56087	+	1.23325i	0.0930149	+	0.0447936i
$759$	−3.68382	−	1.01667i	−0.133714	−	0.0369028i
$760$	1.53600	−	2.85436i	0.0557164	−	0.103538i
$761$	8.36161	−	10.4851i	0.303108	−	0.380086i	−0.606829	−	0.794833i	$-0.707559\pi$
$761$	8.36161	−	10.4851i	0.303108	−	0.380086i	0.909937	+	0.414747i	$0.136130\pi$
$762$	0.641629	−	0.972026i	0.0232438	−	0.0352128i
$763$	0.436802	+	9.72616i	0.0158133	+	0.352111i
$764$	13.1028	−	40.3261i	0.474041	−	1.45895i
$765$	−5.54523	−	0.499080i	−0.200488	−	0.0180443i
$766$	−0.904496	−	1.37025i	−0.0326808	−	0.0495092i
$767$	6.77700	−	4.92378i	0.244703	−	0.177787i
$768$	23.7719	+	14.2031i	0.857796	+	0.512509i
$769$	−4.75037	+	11.1140i	−0.171303	+	0.400782i	−0.983078	−	0.183187i	$-0.941359\pi$
$769$	−4.75037	+	11.1140i	−0.171303	+	0.400782i	0.811775	+	0.583970i	$0.198501\pi$
$770$	−2.67063	+	1.59563i	−0.0962429	+	0.0575025i
$771$	−2.89430	−	21.3666i	−0.104236	−	0.769499i
$772$	−15.5706	−	13.6037i	−0.560399	−	0.489606i
$773$	−0.600625	+	0.524751i	−0.0216030	+	0.0188740i	−0.668673	−	0.743557i	$-0.733137\pi$
$773$	−0.600625	+	0.524751i	−0.0216030	+	0.0188740i	0.647070	+	0.762431i	$0.275994\pi$
$774$	−0.0553450	+	0.408573i	−0.00198933	+	0.0146859i
$775$	0.0925836	+	0.216610i	0.00332570	+	0.00778086i
$776$	−3.35291	−	2.43603i	−0.120363	−	0.0874485i
$777$	−0.814850	+	18.1440i	−0.0292326	+	0.650914i
$778$	−1.93793	−	0.727317i	−0.0694781	−	0.0260756i
$779$	−2.14036	−	2.23864i	−0.0766862	−	0.0802075i
$780$	−21.6434			−0.774958
$781$	−4.63999	+	23.2832i	−0.166032	+	0.833137i
$782$	0.525322			0.0187855
$783$	−5.90443	−	6.17555i	−0.211007	−	0.220696i
$784$	49.8929	+	18.7251i	1.78189	+	0.668754i
$785$	1.96877	−	43.8380i	0.0702683	−	1.56464i
$786$	−0.969588	−	0.704447i	−0.0345841	−	0.0251268i
$787$	−6.20899	−	14.5267i	−0.221327	−	0.517820i	0.771661	−	0.636034i	$-0.219426\pi$
$787$	−6.20899	−	14.5267i	−0.221327	−	0.517820i	−0.992988	+	0.118214i	$0.962283\pi$
$788$	−2.73234	+	20.1710i	−0.0973356	+	0.718560i
$789$	16.3487	−	14.2835i	0.582030	−	0.508504i
$790$	1.70080	+	1.48594i	0.0605117	+	0.0528675i
$791$	0.605515	+	4.47009i	0.0215296	+	0.158938i
$792$	−0.395857	+	0.236513i	−0.0140662	+	0.00840414i
$793$	2.74701	−	6.42696i	0.0975493	−	0.228228i
$794$	−0.793692	−	0.474209i	−0.0281671	−	0.0168290i
$795$	39.6646	−	28.8180i	1.40676	−	1.02207i
$796$	5.10156	+	7.72854i	0.180820	+	0.273931i
$797$	3.27859	+	0.295078i	0.116133	+	0.0104522i	0.147554	−	0.989054i	$-0.452860\pi$
$797$	3.27859	+	0.295078i	0.116133	+	0.0104522i	−0.0314201	+	0.999506i	$0.510003\pi$
$798$	0.932769	−	2.87077i	0.0330197	−	0.101624i
$799$	3.73428	+	83.1502i	0.132109	+	2.94164i
$800$	0.0254562	−	0.0385645i	0.000900013	−	0.00136346i
$801$	0.390948	−	0.490233i	0.0138135	−	0.0173215i
$802$	−1.23939	+	2.30318i	−0.0437645	+	0.0813281i
$803$	14.5887	+	4.02621i	0.514823	+	0.142082i
$804$	−1.77569	−	0.855128i	−0.0626238	−	0.0301580i
$805$	7.03032	−	2.63852i	0.247786	−	0.0929958i
$806$	0.582848	+	1.79382i	0.0205300	+	0.0631847i
$807$	−6.38711	−	27.9838i	−0.224837	−	0.985075i
$808$	2.07881	+	3.86308i	0.0731324	+	0.135903i
$809$	−11.8171	−	2.14449i	−0.415469	−	0.0753964i	−0.0332023	−	0.999449i	$-0.510571\pi$
$809$	−11.8171	−	2.14449i	−0.415469	−	0.0753964i	−0.382266	+	0.924052i	$0.624856\pi$
$810$	−2.34527	+	0.647252i	−0.0824043	+	0.0227421i
$811$	−8.21220	+	35.9800i	−0.288369	+	1.26343i	0.598393	+	0.801203i	$0.295806\pi$
$811$	−8.21220	+	35.9800i	−0.288369	+	1.26343i	−0.886762	+	0.462226i	$0.847051\pi$
$812$	15.9207	−	1.43289i	0.558706	−	0.0502845i
$813$	−33.3939	−	41.8746i	−1.17117	−	1.46861i
$814$	−0.655540	+	0.118963i	−0.0229767	+	0.00416965i
$815$	−1.58527	+	0.763423i	−0.0555294	+	0.0267416i
$816$	−32.7437	+	34.2472i	−1.14626	+	1.19889i
$817$	−23.1747	+	24.2388i	−0.810780	+	0.848009i
$818$	2.91978	−	1.40609i	0.102088	−	0.0491629i
$819$	−4.45335	+	0.808165i	−0.155613	+	0.0282396i
$820$	−2.58133	−	3.23689i	−0.0901440	−	0.113037i
$821$	10.6352	−	0.957190i	0.371173	−	0.0334061i	0.0975170	−	0.995234i	$-0.468910\pi$
$821$	10.6352	−	0.957190i	0.371173	−	0.0334061i	0.273656	+	0.961828i	$0.411767\pi$
$822$	−0.781080	+	3.42214i	−0.0272433	+	0.119361i
$823$	5.54551	−	1.53046i	0.193304	−	0.0533486i	−0.168044	−	0.985779i	$-0.553745\pi$
$823$	5.54551	−	1.53046i	0.193304	−	0.0533486i	0.361348	+	0.932431i	$0.382317\pi$
$824$	−1.70217	−	0.308898i	−0.0592978	−	0.0107610i
$825$	−0.0877732	−	0.163110i	−0.00305587	−	0.00567876i
$826$	0.347507	+	1.52253i	0.0120913	+	0.0529754i
$827$	2.15366	+	6.62827i	0.0748900	+	0.230488i	0.981493	−	0.191496i	$-0.0613339\pi$
$827$	2.15366	+	6.62827i	0.0748900	+	0.230488i	−0.906603	+	0.421984i	$0.861334\pi$
$828$	0.519499	−	0.194971i	0.0180538	−	0.00677572i
$829$	−33.1269	−	15.9531i	−1.15054	−	0.554073i	−0.241347	−	0.970439i	$-0.577589\pi$
$829$	−33.1269	−	15.9531i	−1.15054	−	0.554073i	−0.909197	+	0.416366i	$0.863304\pi$
$830$	0.307570	+	0.0848838i	0.0106759	+	0.00294636i
$831$	7.35023	−	13.6590i	0.254977	−	0.473826i
$832$	−12.7018	+	15.9275i	−0.440355	+	0.552188i
$833$	−49.0139	+	74.2529i	−1.69823	+	2.57271i
$834$	−0.0513648	−	1.14373i	−0.00177862	−	0.0396040i
$835$	−16.1055	+	49.5677i	−0.557354	+	1.71536i
$836$	−18.6224	−	1.67605i	−0.644070	−	0.0579673i
$837$	−17.4838	−	26.4868i	−0.604327	−	0.915517i
$838$	1.28166	−	0.931181i	0.0442742	−	0.0321671i
$839$	−25.2573	−	15.0905i	−0.871979	−	0.520983i	0.00583605	−	0.999983i	$-0.498142\pi$
$839$	−25.2573	−	15.0905i	−0.871979	−	0.520983i	−0.877815	+	0.479000i	$0.840999\pi$
$840$	3.18106	−	7.44246i	0.109757	−	0.256789i
$841$	−22.1963	+	13.2617i	−0.765391	+	0.457300i
$842$	−0.348899	−	2.57568i	−0.0120239	−	0.0887638i
$843$	14.9644	+	13.0740i	0.515403	+	0.450294i
$844$	33.1420	−	28.9553i	1.14079	−	0.996681i
$845$	−1.81766	+	13.4185i	−0.0625295	+	0.461611i
$846$	−0.204627	−	0.478749i	−0.00703523	−	0.0164597i
$847$	−11.2310	−	8.15983i	−0.385903	−	0.280375i
$848$	2.09562	−	46.6627i	0.0719640	−	1.60240i
$849$	−0.976187	−	0.366369i	−0.0335026	−	0.0125738i
$850$	0.0175958	+	0.0184037i	0.000603530	+	0.000631243i
$851$	1.60815			0.0551266
$852$	−12.8813	−	27.9681i	−0.441306	−	0.958171i
$853$	−30.1061			−1.03081			−0.515407	−	0.856946i	$-0.672359\pi$
$853$	−30.1061			−1.03081			−0.515407	+	0.856946i	$0.672359\pi$
$854$	0.900471	+	0.941819i	0.0308135	+	0.0322284i
$855$	2.65202	+	0.995322i	0.0906973	+	0.0340393i
$856$	0.0796077	−	1.77260i	0.00272093	−	0.0605863i
$857$	37.0695	+	26.9325i	1.26627	+	0.919998i	0.999047	−	0.0436375i	$-0.0138947\pi$
$857$	37.0695	+	26.9325i	1.26627	+	0.919998i	0.267221	+	0.963635i	$0.413895\pi$
$858$	−0.582886	−	1.36373i	−0.0198994	−	0.0465570i
$859$	2.37019	−	17.4975i	0.0808699	−	0.597005i	−0.904487	−	0.426501i	$-0.859746\pi$
$859$	2.37019	−	17.4975i	0.0808699	−	0.597005i	0.985357	−	0.170504i	$-0.0545397\pi$
$860$	−33.7581	+	29.4936i	−1.15114	+	1.00572i
$861$	−5.82404	−	5.08831i	−0.198483	−	0.173409i
$862$	−0.180707	−	1.33403i	−0.00615491	−	0.0454374i
$863$	−23.6012	+	14.1011i	−0.803394	+	0.480006i	−0.854979	−	0.518663i	$-0.826430\pi$
$863$	−23.6012	+	14.1011i	−0.803394	+	0.480006i	0.0515847	+	0.998669i	$0.483573\pi$
$864$	−2.44678	+	5.72452i	−0.0832410	+	0.194752i
$865$	−35.4446	−	21.1772i	−1.20515	−	0.720045i
$866$	−1.62451	+	1.18028i	−0.0552031	+	0.0401074i
$867$	−26.3656	−	39.9422i	−0.895423	−	1.35651i
$868$	59.1378	+	5.32250i	2.00727	+	0.180657i
$869$	8.07549	−	24.8538i	0.273942	−	0.843108i
$870$	−0.0356012	−	0.792723i	−0.00120699	−	0.0268758i
$871$	0.784162	−	1.18795i	0.0265703	−	0.0402523i
$872$	0.579327	−	0.726454i	0.0196185	−	0.0246008i
$873$	1.71626	−	3.18935i	0.0580866	−	0.107943i
$874$	−0.257636	−	0.0711030i	−0.00871467	−	0.00240510i
$875$	−45.5119	−	21.9174i	−1.53858	−	0.740943i
$876$	−18.3771	+	6.89705i	−0.620906	+	0.233030i
$877$	8.85426	+	27.2506i	0.298987	+	0.920188i	0.981853	+	0.189644i	$0.0607334\pi$
$877$	8.85426	+	27.2506i	0.298987	+	0.920188i	−0.682866	+	0.730544i	$0.739267\pi$
$878$	0.611262	+	2.67812i	0.0206291	+	0.0903820i
$879$	−7.05615	−	13.1125i	−0.237998	−	0.442275i
$880$	−24.4457	−	4.43625i	−0.824065	−	0.149546i
$881$	20.7311	−	5.72141i	0.698447	−	0.192759i	0.101259	−	0.994860i	$-0.467713\pi$
$881$	20.7311	−	5.72141i	0.698447	−	0.192759i	0.597189	+	0.802101i	$0.296284\pi$
$882$	0.123840	−	0.542580i	0.00416992	−	0.0182696i
$883$	31.2200	−	2.80985i	1.05064	−	0.0945589i	0.449161	−	0.893451i	$-0.351723\pi$
$883$	31.2200	−	2.80985i	1.05064	−	0.0945589i	0.601474	+	0.798892i	$0.294580\pi$
$884$	−21.4641	−	26.9151i	−0.721914	−	0.905252i
$885$	−12.8805	+	2.33747i	−0.432974	+	0.0785732i
$886$	1.01873	−	0.490593i	0.0342248	−	0.0164818i
$887$	−15.2547	+	15.9552i	−0.512203	+	0.535723i	−0.927431	−	0.373995i	$-0.877988\pi$
$887$	−15.2547	+	15.9552i	−0.512203	+	0.535723i	0.415227	+	0.909718i	$0.363702\pi$
$888$	1.19786	−	1.25286i	0.0401974	−	0.0420432i
$889$	23.8586	−	11.4897i	0.800192	−	0.385352i
$890$	−0.397234	+	0.0720873i	−0.0133153	+	0.00241637i
$891$	17.5522	+	22.0098i	0.588021	+	0.737354i
$892$	−22.7993	+	2.05197i	−0.763377	+	0.0687051i
$893$	9.42307	−	41.2852i	0.315331	−	1.38156i
$894$	−2.53312	+	0.699095i	−0.0847200	+	0.0233812i
$895$	32.7732	+	5.94745i	1.09549	+	0.198801i
$896$	−7.35172	−	13.6618i	−0.245604	−	0.456408i
$897$	0.796572	+	3.49001i	0.0265968	+	0.116528i
$898$	−0.462471	−	1.42334i	−0.0154329	−	0.0474974i
$899$	10.9326	−	4.10307i	0.364622	−	0.136845i
$900$	0.0242312	+	0.0116691i	0.000807708	+	0.000388971i
$901$	75.1731	+	20.7465i	2.50438	+	0.691164i
$902$	0.134434	−	0.249821i	0.00447617	−	0.00831813i
$903$	−52.2090	+	65.4680i	−1.73741	+	2.17864i
$904$	0.237165	−	0.359290i	0.00788800	−	0.0119498i
$905$	1.84239	+	41.0240i	0.0612431	+	1.36368i
$906$	−0.198855	+	0.612013i	−0.00660652	+	0.0203328i
$907$	23.8774	+	2.14900i	0.792835	+	0.0713565i	0.478651	−	0.878005i	$-0.341126\pi$
$907$	23.8774	+	2.14900i	0.792835	+	0.0713565i	0.314185	+	0.949362i	$0.398269\pi$
$908$	19.9019	+	30.1500i	0.660466	+	1.00056i
$909$	−3.10153	+	2.25339i	−0.102871	+	0.0747404i
$910$	2.50167	+	1.49468i	0.0829295	+	0.0495481i
$911$	9.74569	−	22.8012i	0.322889	−	0.755437i	−0.676923	−	0.736054i	$-0.736687\pi$
$911$	9.74569	−	22.8012i	0.322889	−	0.755437i	0.999812	−	0.0193828i	$-0.00617013\pi$
$912$	20.6940	−	12.3641i	0.685248	−	0.409417i
$913$	−0.495579	−	3.65851i	−0.0164013	−	0.121079i
$914$	−2.36850	−	2.06930i	−0.0783430	−	0.0684462i
$915$	−8.22557	+	7.18647i	−0.271929	+	0.237577i
$916$	−0.814189	+	6.01058i	−0.0269015	+	0.198595i
$917$	−10.7096	−	25.0563i	−0.353661	−	0.827431i
$918$	−2.77523	−	2.01632i	−0.0915963	−	0.0665486i
$919$	−0.0663029	+	1.47635i	−0.00218713	+	0.0487003i	−0.999790	−	0.0205014i	$-0.993474\pi$
$919$	−0.0663029	+	1.47635i	−0.00218713	+	0.0487003i	0.997603	+	0.0692016i	$0.0220452\pi$
$920$	−0.670952	−	0.251812i	−0.0221206	−	0.00830201i
$921$	33.8072	+	35.3596i	1.11399	+	1.16514i
$922$	2.75048			0.0905823
$923$	21.2655	−	6.50767i	0.699963	−	0.214202i
$924$	−46.6883			−1.53593
$925$	0.0538653	+	0.0563387i	0.00177108	+	0.00185240i
$926$	0.277479	+	0.104140i	0.00911854	+	0.00342225i
$927$	0.0678274	−	1.51029i	0.00222774	−	0.0496046i
$928$	−1.85313	−	1.34638i	−0.0608319	−	0.0441970i
$929$	21.3324	+	49.9096i	0.699893	+	1.63748i	0.768510	+	0.639838i	$0.220998\pi$
$929$	21.3324	+	49.9096i	0.699893	+	1.63748i	−0.0686170	+	0.997643i	$0.521859\pi$
$930$	0.395661	−	2.92088i	0.0129742	−	0.0957795i
$931$	34.0883	−	29.7821i	1.11720	−	0.976069i
$932$	−25.2064	−	22.0222i	−0.825664	−	0.721361i
$933$	2.71250	+	20.0244i	0.0888031	+	0.655571i
$934$	−1.13846	+	0.680199i	−0.0372516	+	0.0222568i
$935$	16.3025	−	38.1416i	0.533149	−	1.24736i
$936$	0.370812	+	0.221550i	0.0121204	+	0.00724158i
$937$	22.1111	−	16.0647i	0.722339	−	0.524810i	−0.164791	−	0.986328i	$-0.552695\pi$
$937$	22.1111	−	16.0647i	0.722339	−	0.524810i	0.887131	+	0.461518i	$0.152695\pi$
$938$	0.146190	+	0.221468i	0.00477327	+	0.00723120i
$939$	50.7316	+	4.56593i	1.65556	+	0.149003i
$940$	17.4924	−	53.8361i	0.570540	−	1.75594i
$941$	−0.606954	−	13.5149i	−0.0197861	−	0.440573i	−0.984296	−	0.176526i	$-0.943514\pi$
$941$	−0.606954	−	13.5149i	−0.0197861	−	0.440573i	0.964510	−	0.264047i	$-0.0850573\pi$
$942$	−2.14849	+	3.25483i	−0.0700017	+	0.106048i
$943$	−0.426945	+	0.535373i	−0.0139033	+	0.0174341i
$944$	−5.91003	+	10.9827i	−0.192355	+	0.357455i
$945$	−47.2680	−	13.0451i	−1.53763	−	0.424358i
$946$	−2.76752	−	1.33277i	−0.0899797	−	0.0433319i
$947$	0.437909	−	0.164350i	0.0142301	−	0.00534066i	−0.344250	−	0.938878i	$-0.611867\pi$
$947$	0.437909	−	0.164350i	0.0142301	−	0.00534066i	0.358480	+	0.933538i	$0.383295\pi$
$948$	10.4739	+	32.2352i	0.340175	+	1.04695i
$949$	−3.15458	−	13.8211i	−0.102402	−	0.448652i
$950$	−0.00613861	−	0.0114074i	−0.000199163	−	0.000370106i
$951$	7.49004	+	1.35924i	0.242881	+	0.0440764i
$952$	12.4099	−	3.42492i	0.402208	−	0.111002i
$953$	−11.3475	+	49.7166i	−0.367581	+	1.61048i	0.365822	+	0.930685i	$0.380788\pi$
$953$	−11.3475	+	49.7166i	−0.367581	+	1.61048i	−0.733403	+	0.679794i	$0.762069\pi$
$954$	−0.485839	+	0.0437263i	−0.0157296	+	0.00141569i
$955$	−29.8385	−	37.4163i	−0.965551	−	1.21076i
$956$	5.23264	−	0.949583i	0.169236	−	0.0307117i
$957$	−8.27254	+	3.98384i	−0.267413	+	0.128779i
$958$	−2.13287	+	2.23081i	−0.0689100	+	0.0720742i
$959$	−55.1524	+	57.6849i	−1.78096	+	1.86274i
$960$	28.6837	−	13.8133i	0.925761	−	0.445823i
$961$	12.1764	−	2.20969i	0.392787	−	0.0712803i
$962$	0.389117	+	0.487938i	0.0125456	+	0.0157317i
$963$	1.54439	−	0.138998i	0.0497674	−	0.00447915i
$964$	0.750814	−	3.28953i	0.0241821	−	0.105949i
$965$	−22.4956	+	6.20839i	−0.724159	+	0.199855i
$966$	−0.656644	−	0.119163i	−0.0211272	−	0.00383402i
$967$	10.5936	+	19.6863i	0.340668	+	0.633068i	0.992073	−	0.125663i	$-0.0401057\pi$
$967$	10.5936	+	19.6863i	0.340668	+	0.633068i	−0.651405	+	0.758730i	$0.725820\pi$
$968$	0.294815	+	1.29167i	0.00947571	+	0.0415158i
$969$	12.4368	+	38.2765i	0.399527	+	1.22962i
$970$	−2.18324	+	0.819385i	−0.0700998	+	0.0263089i
$971$	−21.6696	−	10.4355i	−0.695410	−	0.334892i	0.0525659	−	0.998617i	$-0.483260\pi$
$971$	−21.6696	−	10.4355i	−0.695410	−	0.334892i	−0.747976	+	0.663725i	$0.768974\pi$
$972$	−7.48948	−	2.06696i	−0.240225	−	0.0662979i
$973$	12.3350	−	22.9223i	0.395443	−	0.734855i
$974$	−1.75665	+	2.20277i	−0.0562867	+	0.0705813i
$975$	−0.0955851	+	0.144805i	−0.00306117	+	0.00463748i
$976$	0.466872	+	10.3957i	0.0149442	+	0.332759i
$977$	10.3349	−	31.8076i	0.330643	−	1.01761i	−0.638186	−	0.769883i	$-0.720315\pi$
$977$	10.3349	−	31.8076i	0.330643	−	1.01761i	0.968829	−	0.247732i	$-0.0796853\pi$
$978$	0.155746	+	0.0140174i	0.00498020	+	0.000448226i
$979$	2.57349	+	3.89867i	0.0822491	+	0.124602i
$980$	48.9523	−	35.5659i	1.56372	−	1.13611i
$981$	0.697060	+	0.416474i	0.0222554	+	0.0132970i
$982$	−1.26351	+	2.95612i	−0.0403201	+	0.0943337i
$983$	−38.1048	+	22.7666i	−1.21536	+	0.726141i	−0.969956	−	0.243281i	$-0.921776\pi$
$983$	−38.1048	+	22.7666i	−1.21536	+	0.726141i	−0.245400	+	0.969422i	$0.578919\pi$
$984$	0.0990751	+	0.731402i	0.00315840	+	0.0233162i
$985$	17.3013	+	15.1157i	0.551265	+	0.481625i
$986$	0.950499	−	0.830426i	0.0302701	−	0.0264462i
$987$	14.1939	−	104.784i	0.451797	−	3.33530i
$988$	6.88373	+	16.1053i	0.219001	+	0.512377i
$989$	5.99830	+	4.35802i	0.190735	+	0.138577i
$990$	−0.0116408	+	0.259202i	−0.000369969	+	0.00823799i
$991$	−19.2507	−	7.22492i	−0.611520	−	0.229507i	0.0263483	−	0.999653i	$-0.491612\pi$
$991$	−19.2507	−	7.22492i	−0.611520	−	0.229507i	−0.637868	+	0.770146i	$0.720184\pi$
$992$	−5.87989	−	6.14988i	−0.186687	−	0.195259i
$993$	11.4002			0.361776
$994$	−0.442561	+	4.12228i	−0.0140372	+	0.130751i
$995$	10.4520			0.331351
$996$	3.30909	+	3.46104i	0.104853	+	0.109667i
$997$	15.4909	+	5.81382i	0.490601	+	0.184126i	0.584400	−	0.811465i	$-0.301330\pi$
$997$	15.4909	+	5.81382i	0.490601	+	0.184126i	−0.0937993	+	0.995591i	$0.529901\pi$
$998$	−0.00533013	+	0.118684i	−0.000168722	+	0.00375689i
$999$	−8.49572	−	6.17250i	−0.268793	−	0.195289i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	71.2.g.a.12.4	yes	120
3.2	odd	2		639.2.v.a.154.2		120
71.6	even	35	inner	71.2.g.a.6.4	✓	120
71.19	even	35		5041.2.a.s.1.32		60
71.52	odd	70		5041.2.a.t.1.32		60
213.77	odd	70		639.2.v.a.361.2		120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
71.2.g.a.6.4	✓	120	71.6	even	35	inner
71.2.g.a.12.4	yes	120	1.1	even	1	trivial
639.2.v.a.154.2		120	3.2	odd	2
639.2.v.a.361.2		120	213.77	odd	70
5041.2.a.s.1.32		60	71.19	even	35
5041.2.a.t.1.32		60	71.52	odd	70

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	71.g (of order \(35\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0749867 + 0.0784299i) q^{2} +(1.72079 + 0.645822i) q^{3} +(0.0892014 - 1.98622i) q^{4} +(-1.81548 - 1.31902i) q^{5} +(0.0783843 + 0.183389i) q^{6} +(-0.608682 + 4.49347i) q^{7} +(0.325899 - 0.284729i) q^{8} +(0.284802 + 0.248824i) q^{9} +O(q^{10})\)	\(q+(0.0749867 + 0.0784299i) q^{2} +(1.72079 + 0.645822i) q^{3} +(0.0892014 - 1.98622i) q^{4} +(-1.81548 - 1.31902i) q^{5} +(0.0783843 + 0.183389i) q^{6} +(-0.608682 + 4.49347i) q^{7} +(0.325899 - 0.284729i) q^{8} +(0.284802 + 0.248824i) q^{9} +(-0.0326858 - 0.241297i) q^{10} +(-2.41871 + 1.44511i) q^{11} +(1.43624 - 3.36026i) q^{12} +(2.26569 + 1.35368i) q^{13} +(-0.398066 + 0.289212i) q^{14} +(-2.27219 - 3.44222i) q^{15} +(-3.91367 - 0.352237i) q^{16} +(2.02728 - 6.23933i) q^{17} +(0.00184111 + 0.0409955i) q^{18} +(-1.83875 + 2.78559i) q^{19} +(-2.78181 + 3.48828i) q^{20} +(-3.94939 + 7.33920i) q^{21} +(-0.294711 - 0.0813351i) q^{22} +(0.664870 + 0.320185i) q^{23} +(0.744686 - 0.279485i) q^{24} +(0.0110529 + 0.0340172i) q^{25} +(0.0637269 + 0.279206i) q^{26} +(-2.28350 - 4.24346i) q^{27} +(8.87075 + 1.60980i) q^{28} +(1.70914 - 0.471693i) q^{29} +(0.0995892 - 0.436329i) q^{30} +(6.55948 - 0.590364i) q^{31} +(-0.805490 - 1.01005i) q^{32} +(-5.09537 + 0.924673i) q^{33} +(0.641369 - 0.308867i) q^{34} +(7.03203 - 7.35493i) q^{35} +(0.519626 - 0.543486i) q^{36} +(1.96340 - 0.945524i) q^{37} +(-0.356355 + 0.0646690i) q^{38} +(3.02452 + 3.79263i) q^{39} +(-0.967225 + 0.0870518i) q^{40} +(-0.206484 + 0.904666i) q^{41} +(-0.871765 + 0.240592i) q^{42} +(9.88571 + 1.79399i) q^{43} +(2.65456 + 4.93301i) q^{44} +(-0.188847 - 0.827395i) q^{45} +(0.0247444 + 0.0761553i) q^{46} +(-11.8783 + 4.45800i) q^{47} +(-6.50711 - 3.13366i) q^{48} +(-13.0731 - 3.60794i) q^{49} +(-0.00183915 + 0.00341771i) q^{50} +(7.51801 - 9.42728i) q^{51} +(2.89082 - 4.37941i) q^{52} +(0.533306 + 11.8750i) q^{53} +(0.161582 - 0.497298i) q^{54} +(6.29725 + 0.566762i) q^{55} +(1.08105 + 1.63773i) q^{56} +(-4.96309 + 3.60590i) q^{57} +(0.165158 + 0.0986771i) q^{58} +(1.24743 - 2.91850i) q^{59} +(-7.03971 + 4.20603i) q^{60} +(-0.355480 - 2.62426i) q^{61} +(0.538176 + 0.470190i) q^{62} +(-1.29144 + 1.12830i) q^{63} +(-1.03612 + 7.64895i) q^{64} +(-2.32776 - 5.44607i) q^{65} +(-0.454607 - 0.330291i) q^{66} +(0.0241967 - 0.538781i) q^{67} +(-12.2119 - 4.58319i) q^{68} +(0.937317 + 0.980356i) q^{69} +1.10416 q^{70} +(5.65214 - 6.24927i) q^{71} +0.163664 q^{72} +(-3.71196 - 3.88240i) q^{73} +(0.221386 + 0.0830876i) q^{74} +(-0.00294945 + 0.0656745i) q^{75} +(5.36878 + 3.90065i) q^{76} +(-5.02135 - 11.7480i) q^{77} +(-0.0706568 + 0.521610i) q^{78} +(-6.98479 + 6.10243i) q^{79} +(6.64057 + 5.80169i) q^{80} +(-1.34120 - 9.90111i) q^{81} +(-0.0864365 + 0.0516434i) q^{82} +(-0.514996 + 1.20489i) q^{83} +(14.2250 + 8.49905i) q^{84} +(-11.9103 + 8.65333i) q^{85} +(0.600594 + 0.909861i) q^{86} +(3.24569 + 0.292118i) q^{87} +(-0.376789 + 1.15964i) q^{88} +(-0.0743855 - 1.65632i) q^{89} +(0.0507315 - 0.0768549i) q^{90} +(-7.46183 + 9.35683i) q^{91} +(0.695266 - 1.29202i) q^{92} +(11.6687 + 3.22036i) q^{93} +(-1.24035 - 0.597323i) q^{94} +(7.01246 - 2.63182i) q^{95} +(-0.733761 - 2.25829i) q^{96} +(-2.13103 - 9.33664i) q^{97} +(-0.697336 - 1.29587i) q^{98} +(-1.04843 - 0.190263i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9}+O(q^{10}) \) 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9	\( 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9} - 8 q^{10} - 27 q^{11} + 3 q^{12} - 31 q^{13} + 2 q^{14} + 12 q^{15} + 30 q^{16} + 9 q^{17} + 27 q^{18} - 31 q^{19} + 72 q^{20} - 32 q^{21} - 24 q^{22} - 6 q^{23} - 47 q^{24} - 42 q^{25} + 77 q^{26} - 2 q^{27} - 18 q^{28} + q^{29} + 15 q^{30} + 15 q^{31} - 10 q^{32} - 24 q^{33} + 20 q^{34} + 74 q^{35} + 8 q^{36} - 22 q^{37} - 39 q^{38} + 86 q^{39} - 30 q^{40} + 39 q^{41} - 34 q^{42} + 33 q^{43} - 23 q^{44} + 121 q^{45} + 124 q^{46} + 6 q^{47} + 131 q^{48} - 22 q^{49} - 15 q^{50} + 29 q^{51} + 83 q^{52} - 30 q^{53} - 25 q^{54} + 32 q^{55} + 11 q^{56} - 10 q^{57} + 12 q^{58} - 80 q^{59} + 80 q^{60} - 12 q^{61} - 68 q^{62} - 79 q^{63} - 117 q^{64} - 89 q^{65} - 39 q^{66} - 74 q^{67} - 67 q^{68} - 95 q^{69} - 64 q^{70} - 115 q^{71} - 144 q^{72} - 14 q^{73} - 70 q^{74} - 13 q^{75} + 8 q^{76} + 47 q^{77} - 218 q^{78} - 25 q^{79} - 103 q^{80} - 28 q^{81} - 88 q^{82} - 20 q^{83} - 142 q^{84} + 22 q^{85} + 159 q^{86} - 105 q^{87} + 43 q^{88} + 33 q^{89} + 33 q^{90} + 60 q^{91} - 2 q^{92} + 63 q^{93} + 174 q^{94} + 20 q^{95} - 30 q^{96} + 121 q^{97} + 128 q^{98} - 2 q^{99}+O(q^{100}) \) 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9 - 8 * q^10 - 27 * q^11 + 3 * q^12 - 31 * q^13 + 2 * q^14 + 12 * q^15 + 30 * q^16 + 9 * q^17 + 27 * q^18 - 31 * q^19 + 72 * q^20 - 32 * q^21 - 24 * q^22 - 6 * q^23 - 47 * q^24 - 42 * q^25 + 77 * q^26 - 2 * q^27 - 18 * q^28 + q^29 + 15 * q^30 + 15 * q^31 - 10 * q^32 - 24 * q^33 + 20 * q^34 + 74 * q^35 + 8 * q^36 - 22 * q^37 - 39 * q^38 + 86 * q^39 - 30 * q^40 + 39 * q^41 - 34 * q^42 + 33 * q^43 - 23 * q^44 + 121 * q^45 + 124 * q^46 + 6 * q^47 + 131 * q^48 - 22 * q^49 - 15 * q^50 + 29 * q^51 + 83 * q^52 - 30 * q^53 - 25 * q^54 + 32 * q^55 + 11 * q^56 - 10 * q^57 + 12 * q^58 - 80 * q^59 + 80 * q^60 - 12 * q^61 - 68 * q^62 - 79 * q^63 - 117 * q^64 - 89 * q^65 - 39 * q^66 - 74 * q^67 - 67 * q^68 - 95 * q^69 - 64 * q^70 - 115 * q^71 - 144 * q^72 - 14 * q^73 - 70 * q^74 - 13 * q^75 + 8 * q^76 + 47 * q^77 - 218 * q^78 - 25 * q^79 - 103 * q^80 - 28 * q^81 - 88 * q^82 - 20 * q^83 - 142 * q^84 + 22 * q^85 + 159 * q^86 - 105 * q^87 + 43 * q^88 + 33 * q^89 + 33 * q^90 + 60 * q^91 - 2 * q^92 + 63 * q^93 + 174 * q^94 + 20 * q^95 - 30 * q^96 + 121 * q^97 + 128 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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