LMFDB - Embedded newform 430.2.q.d.81.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(31,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 34]))

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

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

chi := DirichletCharacter("430.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.q (of order $21$, degree $12$, 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:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$5$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			81.4
Character	$\chi$	$=$	430.81
Dual form			430.2.q.d.361.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.222521 - 0.974928i) q^{2} +(2.08443 + 0.642961i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(-0.365341 - 0.930874i) q^{5} +(1.09067 - 1.88910i) q^{6} +(1.63836 + 2.83771i) q^{7} +(-0.623490 + 0.781831i) q^{8} +(1.45273 + 0.990455i) q^{9} +O(q^{10})$	\(q+(0.222521 - 0.974928i) q^{2} +(2.08443 + 0.642961i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(-0.365341 - 0.930874i) q^{5} +(1.09067 - 1.88910i) q^{6} +(1.63836 + 2.83771i) q^{7} +(-0.623490 + 0.781831i) q^{8} +(1.45273 + 0.990455i) q^{9} +(-0.988831 + 0.149042i) q^{10} +(0.302240 - 0.145551i) q^{11} +(-1.59904 - 1.48369i) q^{12} +(5.82532 + 0.878026i) q^{13} +(3.13114 - 0.965827i) q^{14} +(-0.163012 - 2.17524i) q^{15} +(0.623490 + 0.781831i) q^{16} +(2.66758 - 6.79687i) q^{17} +(1.28889 - 1.19591i) q^{18} +(-4.54331 + 3.09757i) q^{19} +(-0.0747301 + 0.997204i) q^{20} +(1.59050 + 6.96841i) q^{21} +(-0.0746471 - 0.327050i) q^{22} +(0.0128722 - 0.171767i) q^{23} +(-1.80231 + 1.22879i) q^{24} +(-0.733052 + 0.680173i) q^{25} +(2.15227 - 5.48389i) q^{26} +(-1.68884 - 2.11774i) q^{27} +(-0.244869 - 3.26755i) q^{28} +(1.36445 - 0.420878i) q^{29} +(-2.15698 - 0.325112i) q^{30} +(-7.27478 - 6.75001i) q^{31} +(0.900969 - 0.433884i) q^{32} +(0.723582 - 0.109062i) q^{33} +(-6.03287 - 4.11314i) q^{34} +(2.04300 - 2.56184i) q^{35} +(-0.879123 - 1.52269i) q^{36} +(-3.60587 + 6.24555i) q^{37} +(2.00893 + 5.11867i) q^{38} +(11.5779 + 5.57564i) q^{39} +(0.955573 + 0.294755i) q^{40} +(-2.66341 + 11.6692i) q^{41} +7.14762 q^{42} +(2.79807 + 5.93050i) q^{43} -0.335461 q^{44} +(0.391247 - 1.71416i) q^{45} +(-0.164596 - 0.0507712i) q^{46} +(-9.61165 - 4.62873i) q^{47} +(0.796933 + 2.03055i) q^{48} +(-1.86841 + 3.23619i) q^{49} +(0.500000 + 0.866025i) q^{50} +(9.93050 - 12.4525i) q^{51} +(-4.86747 - 3.31859i) q^{52} +(4.47053 - 0.673824i) q^{53} +(-2.44044 + 1.17526i) q^{54} +(-0.245910 - 0.228172i) q^{55} +(-3.24011 - 0.488368i) q^{56} +(-11.4618 + 3.53551i) q^{57} +(-0.106706 - 1.42390i) q^{58} +(-3.61455 - 4.53251i) q^{59} +(-0.796933 + 2.03055i) q^{60} +(7.98969 - 7.41335i) q^{61} +(-8.19956 + 5.59037i) q^{62} +(-0.430540 + 5.74515i) q^{63} +(-0.222521 - 0.974928i) q^{64} +(-1.31090 - 5.74342i) q^{65} +(0.0546841 - 0.729709i) q^{66} +(-12.1603 + 8.29074i) q^{67} +(-5.35246 + 4.96635i) q^{68} +(0.137271 - 0.349760i) q^{69} +(-2.04300 - 2.56184i) q^{70} +(0.105258 + 1.40456i) q^{71} +(-1.68013 + 0.518252i) q^{72} +(3.51601 + 0.529954i) q^{73} +(5.28658 + 4.90523i) q^{74} +(-1.96532 + 0.946448i) q^{75} +(5.43737 - 0.819551i) q^{76} +(0.908209 + 0.619206i) q^{77} +(8.01218 - 10.0470i) q^{78} +(-2.85473 - 4.94453i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-4.08572 - 10.4102i) q^{81} +(10.7839 + 5.19326i) q^{82} +(-5.58127 - 1.72159i) q^{83} +(1.59050 - 6.96841i) q^{84} -7.30161 q^{85} +(6.40444 - 1.40825i) q^{86} +3.11471 q^{87} +(-0.0746471 + 0.327050i) q^{88} +(3.29612 + 1.01672i) q^{89} +(-1.58413 - 0.762874i) q^{90} +(7.05236 + 17.9691i) q^{91} +(-0.0861244 + 0.149172i) q^{92} +(-10.8238 - 18.7473i) q^{93} +(-6.65147 + 8.34068i) q^{94} +(4.54331 + 3.09757i) q^{95} +(2.15698 - 0.325112i) q^{96} +(2.99123 - 1.44050i) q^{97} +(2.73929 + 2.54169i) q^{98} +(0.583235 + 0.0879086i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 10 q^{2} - q^{3} - 10 q^{4} - 5 q^{5} - 6 q^{6} + q^{7} + 10 q^{8} + 8 q^{9}+O(q^{10}) $ 60 * q + 10 * q^2 - q^3 - 10 * q^4 - 5 * q^5 - 6 * q^6 + q^7 + 10 * q^8 + 8 * q^9	\( 60 q + 10 q^{2} - q^{3} - 10 q^{4} - 5 q^{5} - 6 q^{6} + q^{7} + 10 q^{8} + 8 q^{9} + 5 q^{10} + 3 q^{11} - q^{12} + 13 q^{13} - 15 q^{14} + q^{15} - 10 q^{16} + 38 q^{17} + 6 q^{18} + 17 q^{19} - 5 q^{20} + 4 q^{21} + 11 q^{22} - 8 q^{23} + q^{24} + 5 q^{25} + 29 q^{26} - 16 q^{27} - 6 q^{28} - 41 q^{29} - q^{30} + 15 q^{31} + 10 q^{32} + 63 q^{33} - 10 q^{34} + 2 q^{35} - 48 q^{36} + 7 q^{37} + 25 q^{38} - 64 q^{39} + 5 q^{40} - 22 q^{41} - 60 q^{42} + 6 q^{43} - 4 q^{44} + 30 q^{45} - 20 q^{46} - 13 q^{47} - q^{48} - 93 q^{49} + 30 q^{50} + 18 q^{51} - 15 q^{52} + 71 q^{53} - 5 q^{54} - 16 q^{55} - q^{56} - 94 q^{57} - 22 q^{58} + 20 q^{59} + q^{60} + 91 q^{61} + 69 q^{62} - 50 q^{63} - 10 q^{64} + 5 q^{65} + 14 q^{66} - 26 q^{67} - 18 q^{68} - 94 q^{69} - 2 q^{70} + 20 q^{71} - 36 q^{72} - 56 q^{73} - 7 q^{74} + 2 q^{75} + 38 q^{76} + 41 q^{77} - 13 q^{78} - 46 q^{79} + 30 q^{80} + 39 q^{81} + 8 q^{82} - 115 q^{83} + 4 q^{84} + 6 q^{85} + 29 q^{86} + 20 q^{87} + 11 q^{88} + 30 q^{89} - 16 q^{90} - 53 q^{91} - 8 q^{92} + 16 q^{93} + 41 q^{94} - 17 q^{95} + q^{96} + 113 q^{97} + 2 q^{98} + 139 q^{99}+O(q^{100}) \) 60 * q + 10 * q^2 - q^3 - 10 * q^4 - 5 * q^5 - 6 * q^6 + q^7 + 10 * q^8 + 8 * q^9 + 5 * q^10 + 3 * q^11 - q^12 + 13 * q^13 - 15 * q^14 + q^15 - 10 * q^16 + 38 * q^17 + 6 * q^18 + 17 * q^19 - 5 * q^20 + 4 * q^21 + 11 * q^22 - 8 * q^23 + q^24 + 5 * q^25 + 29 * q^26 - 16 * q^27 - 6 * q^28 - 41 * q^29 - q^30 + 15 * q^31 + 10 * q^32 + 63 * q^33 - 10 * q^34 + 2 * q^35 - 48 * q^36 + 7 * q^37 + 25 * q^38 - 64 * q^39 + 5 * q^40 - 22 * q^41 - 60 * q^42 + 6 * q^43 - 4 * q^44 + 30 * q^45 - 20 * q^46 - 13 * q^47 - q^48 - 93 * q^49 + 30 * q^50 + 18 * q^51 - 15 * q^52 + 71 * q^53 - 5 * q^54 - 16 * q^55 - q^56 - 94 * q^57 - 22 * q^58 + 20 * q^59 + q^60 + 91 * q^61 + 69 * q^62 - 50 * q^63 - 10 * q^64 + 5 * q^65 + 14 * q^66 - 26 * q^67 - 18 * q^68 - 94 * q^69 - 2 * q^70 + 20 * q^71 - 36 * q^72 - 56 * q^73 - 7 * q^74 + 2 * q^75 + 38 * q^76 + 41 * q^77 - 13 * q^78 - 46 * q^79 + 30 * q^80 + 39 * q^81 + 8 * q^82 - 115 * q^83 + 4 * q^84 + 6 * q^85 + 29 * q^86 + 20 * q^87 + 11 * q^88 + 30 * q^89 - 16 * q^90 - 53 * q^91 - 8 * q^92 + 16 * q^93 + 41 * q^94 - 17 * q^95 + q^96 + 113 * q^97 + 2 * q^98 + 139 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$1$	$e\left(\frac{2}{21}\right)$

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 $

$2$	0.222521	−	0.974928i	0.157346	−	0.689378i
$2$	0.222521	−	0.974928i	0.157346	−	0.689378i
$3$	2.08443	+	0.642961i	1.20345	+	0.371214i	0.830700	−	0.556720i	$-0.187940\pi$
$3$	2.08443	+	0.642961i	1.20345	+	0.371214i	0.372746	+	0.927934i	$0.378416\pi$
$4$	−0.900969	−	0.433884i	−0.450484	−	0.216942i
$5$	−0.365341	−	0.930874i	−0.163385	−	0.416299i
$5$	−0.365341	−	0.930874i	−0.163385	−	0.416299i
$6$	1.09067	−	1.88910i	0.445264	−	0.771220i
$7$	1.63836	+	2.83771i	0.619240	+	1.07256i	0.989625	+	0.143677i	$0.0458925\pi$
$7$	1.63836	+	2.83771i	0.619240	+	1.07256i	−0.370385	+	0.928878i	$0.620774\pi$
$8$	−0.623490	+	0.781831i	−0.220437	+	0.276419i
$9$	1.45273	+	0.990455i	0.484244	+	0.330152i
$10$	−0.988831	+	0.149042i	−0.312696	+	0.0471313i
$11$	0.302240	−	0.145551i	0.0911288	−	0.0438853i	−0.387764	−	0.921759i	$-0.626752\pi$
$11$	0.302240	−	0.145551i	0.0911288	−	0.0438853i	0.478893	+	0.877873i	$0.341038\pi$
$12$	−1.59904	−	1.48369i	−0.461602	−	0.428304i
$13$	5.82532	+	0.878026i	1.61565	+	0.243521i	0.893781	−	0.448505i	$-0.148043\pi$
$13$	5.82532	+	0.878026i	1.61565	+	0.243521i	0.721873	+	0.692025i	$0.243281\pi$
$14$	3.13114	−	0.965827i	0.836831	−	0.258128i
$15$	−0.163012	−	2.17524i	−0.0420895	−	0.561645i
$16$	0.623490	+	0.781831i	0.155872	+	0.195458i
$17$	2.66758	−	6.79687i	0.646982	−	1.64848i	−0.109119	−	0.994029i	$-0.534803\pi$
$17$	2.66758	−	6.79687i	0.646982	−	1.64848i	0.756101	−	0.654455i	$-0.227102\pi$
$18$	1.28889	−	1.19591i	0.303793	−	0.281879i
$19$	−4.54331	+	3.09757i	−1.04231	+	0.710632i	−0.958280	−	0.285831i	$-0.907730\pi$
$19$	−4.54331	+	3.09757i	−1.04231	+	0.710632i	−0.0840263	+	0.996464i	$0.526778\pi$
$20$	−0.0747301	+	0.997204i	−0.0167102	+	0.222982i
$21$	1.59050	+	6.96841i	0.347074	+	1.52063i
$22$	−0.0746471	−	0.327050i	−0.0159148	−	0.0697274i
$23$	0.0128722	−	0.171767i	0.00268403	−	0.0358159i	−0.995701	−	0.0926260i	$-0.970474\pi$
$23$	0.0128722	−	0.171767i	0.00268403	−	0.0358159i	0.998385	+	0.0568101i	$0.0180930\pi$
$24$	−1.80231	+	1.22879i	−0.367895	+	0.250826i
$25$	−0.733052	+	0.680173i	−0.146610	+	0.136035i
$26$	2.15227	−	5.48389i	0.422095	−	1.07548i
$27$	−1.68884	−	2.11774i	−0.325017	−	0.407559i
$28$	−0.244869	−	3.26755i	−0.0462759	−	0.617508i
$29$	1.36445	−	0.420878i	0.253372	−	0.0781550i	−0.165467	−	0.986215i	$-0.552913\pi$
$29$	1.36445	−	0.420878i	0.253372	−	0.0781550i	0.418839	+	0.908060i	$0.362437\pi$
$30$	−2.15698	−	0.325112i	−0.393808	−	0.0593570i
$31$	−7.27478	−	6.75001i	−1.30659	−	1.21234i	−0.961831	−	0.273646i	$-0.911770\pi$
$31$	−7.27478	−	6.75001i	−1.30659	−	1.21234i	−0.344758	−	0.938692i	$-0.612039\pi$
$32$	0.900969	−	0.433884i	0.159270	−	0.0767005i
$33$	0.723582	−	0.109062i	0.125959	−	0.0189853i
$34$	−6.03287	−	4.11314i	−1.03463	−	0.705398i
$35$	2.04300	−	2.56184i	0.345329	−	0.433029i
$36$	−0.879123	−	1.52269i	−0.146521	−	0.253781i
$37$	−3.60587	+	6.24555i	−0.592802	+	1.02676i	0.401051	+	0.916056i	$0.368645\pi$
$37$	−3.60587	+	6.24555i	−0.592802	+	1.02676i	−0.993853	+	0.110707i	$0.964688\pi$
$38$	2.00893	+	5.11867i	0.325892	+	0.830358i
$39$	11.5779	+	5.57564i	1.85395	+	0.892817i
$40$	0.955573	+	0.294755i	0.151089	+	0.0466049i
$41$	−2.66341	+	11.6692i	−0.415955	+	1.82242i	0.138699	+	0.990335i	$0.455708\pi$
$41$	−2.66341	+	11.6692i	−0.415955	+	1.82242i	−0.554653	+	0.832082i	$0.687149\pi$
$42$	7.14762			1.10290
$43$	2.79807	+	5.93050i	0.426701	+	0.904393i
$43$	2.79807	+	5.93050i	0.426701	+	0.904393i
$44$	−0.335461			−0.0505727
$45$	0.391247	−	1.71416i	0.0583236	−	0.255532i
$46$	−0.164596	−	0.0507712i	−0.0242684	−	0.00748581i
$47$	−9.61165	−	4.62873i	−1.40200	−	0.675169i	−0.428437	−	0.903572i	$-0.640935\pi$
$47$	−9.61165	−	4.62873i	−1.40200	−	0.675169i	−0.973567	+	0.228403i	$0.926650\pi$
$48$	0.796933	+	2.03055i	0.115027	+	0.293085i
$49$	−1.86841	+	3.23619i	−0.266916	+	0.462313i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	9.93050	−	12.4525i	1.39055	−	1.74369i
$52$	−4.86747	−	3.31859i	−0.674997	−	0.460205i
$53$	4.47053	−	0.673824i	0.614074	−	0.0925568i	0.165362	−	0.986233i	$-0.447121\pi$
$53$	4.47053	−	0.673824i	0.614074	−	0.0925568i	0.448713	+	0.893676i	$0.351883\pi$
$54$	−2.44044	+	1.17526i	−0.332102	+	0.159932i
$55$	−0.245910	−	0.228172i	−0.0331586	−	0.0307666i
$56$	−3.24011	−	0.488368i	−0.432978	−	0.0652610i
$57$	−11.4618	+	3.53551i	−1.51816	+	0.468289i
$58$	−0.106706	−	1.42390i	−0.0140112	−	0.186967i
$59$	−3.61455	−	4.53251i	−0.470575	−	0.590082i	0.488737	−	0.872431i	$-0.337458\pi$
$59$	−3.61455	−	4.53251i	−0.470575	−	0.590082i	−0.959312	+	0.282349i	$0.908886\pi$
$60$	−0.796933	+	2.03055i	−0.102884	+	0.262143i
$61$	7.98969	−	7.41335i	1.02298	−	0.949183i	0.0242527	−	0.999706i	$-0.492279\pi$
$61$	7.98969	−	7.41335i	1.02298	−	0.949183i	0.998723	+	0.0505233i	$0.0160889\pi$
$62$	−8.19956	+	5.59037i	−1.04135	+	0.709977i
$63$	−0.430540	+	5.74515i	−0.0542429	+	0.723821i
$64$	−0.222521	−	0.974928i	−0.0278151	−	0.121866i
$65$	−1.31090	−	5.74342i	−0.162597	−	0.712383i
$66$	0.0546841	−	0.729709i	0.00673115	−	0.0898209i
$67$	−12.1603	+	8.29074i	−1.48561	+	1.01287i	−0.496128	+	0.868249i	$0.665245\pi$
$67$	−12.1603	+	8.29074i	−1.48561	+	1.01287i	−0.989486	+	0.144626i	$0.953802\pi$
$68$	−5.35246	+	4.96635i	−0.649081	+	0.602259i
$69$	0.137271	−	0.349760i	0.0165255	−	0.0421062i
$70$	−2.04300	−	2.56184i	−0.244185	−	0.306198i
$71$	0.105258	+	1.40456i	0.0124918	+	0.166691i	0.999961	+	0.00887697i	$0.00282567\pi$
$71$	0.105258	+	1.40456i	0.0124918	+	0.166691i	−0.987469	+	0.157814i	$0.949555\pi$
$72$	−1.68013	+	0.518252i	−0.198005	+	0.0610766i
$73$	3.51601	+	0.529954i	0.411518	+	0.0620264i	0.351539	−	0.936173i	$-0.385658\pi$
$73$	3.51601	+	0.529954i	0.411518	+	0.0620264i	0.0599792	+	0.998200i	$0.480897\pi$
$74$	5.28658	+	4.90523i	0.614553	+	0.570222i
$75$	−1.96532	+	0.946448i	−0.226936	+	0.109286i
$76$	5.43737	−	0.819551i	0.623709	−	0.0940090i
$77$	0.908209	+	0.619206i	0.103500	+	0.0705651i
$78$	8.01218	−	10.0470i	0.907201	−	1.13759i
$79$	−2.85473	−	4.94453i	−0.321182	−	0.556303i	0.659550	−	0.751660i	$-0.270747\pi$
$79$	−2.85473	−	4.94453i	−0.321182	−	0.556303i	−0.980732	+	0.195357i	$0.937413\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	−4.08572	−	10.4102i	−0.453969	−	1.15669i
$82$	10.7839	+	5.19326i	1.19089	+	0.573500i
$83$	−5.58127	−	1.72159i	−0.612624	−	0.188969i	−0.0271108	−	0.999632i	$-0.508631\pi$
$83$	−5.58127	−	1.72159i	−0.612624	−	0.188969i	−0.585513	+	0.810663i	$0.699107\pi$
$84$	1.59050	−	6.96841i	0.173537	−	0.760316i
$85$	−7.30161			−0.791970
$86$	6.40444	−	1.40825i	0.690608	−	0.151856i
$87$	3.11471			0.333932
$88$	−0.0746471	+	0.327050i	−0.00795741	+	0.0348637i
$89$	3.29612	+	1.01672i	0.349388	+	0.107772i	0.464482	−	0.885583i	$-0.346241\pi$
$89$	3.29612	+	1.01672i	0.349388	+	0.107772i	−0.115094	+	0.993355i	$0.536717\pi$
$90$	−1.58413	−	0.762874i	−0.166981	−	0.0804140i
$91$	7.05236	+	17.9691i	0.739288	+	1.88368i
$92$	−0.0861244	+	0.149172i	−0.00897909	+	0.0155522i
$93$	−10.8238	−	18.7473i	−1.12237	−	1.94401i
$94$	−6.65147	+	8.34068i	−0.686047	+	0.860275i
$95$	4.54331	+	3.09757i	0.466134	+	0.317804i
$96$	2.15698	−	0.325112i	0.220146	−	0.0331816i
$97$	2.99123	−	1.44050i	0.303713	−	0.146261i	−0.275820	−	0.961209i	$-0.588949\pi$
$97$	2.99123	−	1.44050i	0.303713	−	0.146261i	0.579533	+	0.814949i	$0.303235\pi$
$98$	2.73929	+	2.54169i	0.276710	+	0.256749i
$99$	0.583235	+	0.0879086i	0.0586174	+	0.00883515i
$100$	0.955573	−	0.294755i	0.0955573	−	0.0294755i
$101$	0.667671	+	8.90945i	0.0664357	+	0.886523i	0.926490	+	0.376320i	$0.122811\pi$
$101$	0.667671	+	8.90945i	0.0664357	+	0.886523i	−0.860054	+	0.510203i	$0.829570\pi$
$102$	−9.93050	−	12.4525i	−0.983266	−	1.23298i
$103$	−2.55943	+	6.52132i	−0.252188	+	0.642565i	−0.999767	−	0.0216089i	$-0.993121\pi$
$103$	−2.55943	+	6.52132i	−0.252188	+	0.642565i	0.747578	+	0.664173i	$0.231216\pi$
$104$	−4.31850	+	4.00698i	−0.423464	+	0.392917i
$105$	5.90564	−	4.02640i	0.576332	−	0.392936i
$106$	0.337857	−	4.50838i	0.0328155	−	0.437893i
$107$	−3.17666	−	13.9179i	−0.307099	−	1.34549i	−0.859169	−	0.511692i	$-0.829019\pi$
$107$	−3.17666	−	13.9179i	−0.307099	−	1.34549i	0.552070	−	0.833798i	$-0.313838\pi$
$108$	0.602740	+	2.64078i	0.0579987	+	0.254109i
$109$	−0.0409561	+	0.546521i	−0.00392288	+	0.0523472i	−0.998822	−	0.0485307i	$-0.984546\pi$
$109$	−0.0409561	+	0.546521i	−0.00392288	+	0.0523472i	0.994899	+	0.100878i	$0.0321652\pi$
$110$	−0.277171	+	0.188972i	−0.0264272	+	0.0180178i
$111$	−11.5318	+	10.7000i	−1.09455	+	1.01560i
$112$	−1.19712	+	3.05020i	−0.113117	+	0.288217i
$113$	3.75345	+	4.70667i	0.353095	+	0.442767i	0.926381	−	0.376589i	$-0.122903\pi$
$113$	3.75345	+	4.70667i	0.353095	+	0.442767i	−0.573286	+	0.819355i	$0.694332\pi$
$114$	0.896366	+	11.9612i	0.0839524	+	1.12027i
$115$	−0.164596	+	0.0507712i	−0.0153487	+	0.00473444i
$116$	−1.41194	−	0.212816i	−0.131095	−	0.0197594i
$117$	7.59298	+	7.04526i	0.701972	+	0.651334i
$118$	−5.22318	+	2.51535i	−0.480833	+	0.231557i
$119$	23.6580	−	3.56587i	2.16873	−	0.326883i
$120$	1.80231	+	1.22879i	0.164527	+	0.112173i
$121$	−6.78822	+	8.51216i	−0.617111	+	0.773833i
$122$	−5.44961	−	9.43900i	−0.493385	−	0.854567i
$123$	−13.0545	+	22.6111i	−1.17709	+	2.03877i
$124$	3.62563	+	9.23795i	0.325591	+	0.829593i
$125$	0.900969	+	0.433884i	0.0805851	+	0.0388077i
$126$	5.50531	+	1.69816i	0.490452	+	0.151284i
$127$	−0.872891	+	3.82439i	−0.0774566	+	0.339359i	−0.998777	−	0.0494451i	$-0.984255\pi$
$127$	−0.872891	+	3.82439i	−0.0774566	+	0.339359i	0.921320	+	0.388804i	$0.127112\pi$
$128$	−1.00000			−0.0883883
$129$	2.01929	+	14.1608i	0.177789	+	1.24679i
$130$	−5.89112			−0.516686
$131$	−1.71757	+	7.52516i	−0.150065	+	0.657476i	0.842800	+	0.538227i	$0.180906\pi$
$131$	−1.71757	+	7.52516i	−0.150065	+	0.657476i	−0.992864	+	0.119249i	$0.961951\pi$
$132$	−0.699245	−	0.215689i	−0.0608615	−	0.0187733i
$133$	−16.2336	−	7.81768i	−1.40763	−	0.677879i
$134$	5.37696	+	13.7003i	0.464498	+	1.18352i
$135$	−1.35434	+	2.34579i	−0.116563	+	0.201894i
$136$	3.65080	+	6.32338i	0.313054	+	0.542225i
$137$	−0.590371	+	0.740302i	−0.0504388	+	0.0632483i	−0.806411	−	0.591355i	$-0.798593\pi$
$137$	−0.590371	+	0.740302i	−0.0504388	+	0.0632483i	0.755972	+	0.654604i	$0.227164\pi$
$138$	−0.310445	−	0.211658i	−0.0264269	−	0.0180175i
$139$	5.76669	−	0.869189i	0.489125	−	0.0737237i	0.100150	−	0.994972i	$-0.468068\pi$
$139$	5.76669	−	0.869189i	0.489125	−	0.0737237i	0.388974	+	0.921249i	$0.372830\pi$
$140$	−2.95221	+	1.42171i	−0.249508	+	0.120157i
$141$	−17.0587	−	15.8282i	−1.43660	−	1.33297i
$142$	1.39277	+	0.209927i	0.116879	+	0.0176166i
$143$	1.88844	−	0.582508i	0.157920	−	0.0487117i
$144$	0.131394	+	1.75333i	0.0109495	+	0.146111i
$145$	−0.890274	−	1.11637i	−0.0739332	−	0.0927093i
$146$	1.29905	−	3.30993i	0.107510	−	0.273932i
$147$	−5.97532	+	5.54429i	−0.492836	+	0.457285i
$148$	5.95862	−	4.06252i	0.489796	−	0.333937i
$149$	1.33777	−	17.8514i	0.109595	−	1.46244i	−0.623239	−	0.782032i	$-0.714184\pi$
$149$	1.33777	−	17.8514i	0.109595	−	1.46244i	0.732833	−	0.680408i	$-0.238197\pi$
$150$	0.485394	+	2.12665i	0.0396322	+	0.173640i
$151$	−0.352834	−	1.54587i	−0.0287132	−	0.125801i	0.958540	−	0.284958i	$-0.0919796\pi$
$151$	−0.352834	−	1.54587i	−0.0287132	−	0.125801i	−0.987253	+	0.159157i	$0.949122\pi$
$152$	0.410925	−	5.48341i	0.0333304	−	0.444763i
$153$	10.6073	−	7.23191i	0.857547	−	0.584666i
$154$	0.805777	−	0.747652i	0.0649314	−	0.0602475i
$155$	−3.62563	+	9.23795i	−0.291218	+	0.742010i
$156$	−8.01218	−	10.0470i	−0.641488	−	0.804400i
$157$	−1.33448	−	17.8075i	−0.106503	−	1.42119i	−0.752873	−	0.658166i	$-0.771333\pi$
$157$	−1.33448	−	17.8075i	−0.106503	−	1.42119i	0.646370	−	0.763024i	$-0.276286\pi$
$158$	−5.45580	+	1.68289i	−0.434040	+	0.133884i
$159$	9.75175	+	1.46984i	0.773364	+	0.116566i
$160$	−0.733052	−	0.680173i	−0.0579528	−	0.0537724i
$161$	0.508515	−	0.244888i	0.0400766	−	0.0192999i
$162$	−11.0584	+	1.66679i	−0.868830	+	0.130955i
$163$	−8.61768	−	5.87543i	−0.674989	−	0.460200i	0.176688	−	0.984267i	$-0.443462\pi$
$163$	−8.61768	−	5.87543i	−0.674989	−	0.460200i	−0.851677	+	0.524067i	$0.824414\pi$
$164$	7.46271	−	9.35794i	0.582739	−	0.730732i
$165$	−0.365877	−	0.633718i	−0.0284835	−	0.0493349i
$166$	−2.92038	+	5.05824i	−0.226665	+	0.392596i
$167$	4.02583	+	10.2576i	0.311528	+	0.793761i	0.997793	+	0.0664086i	$0.0211541\pi$
$167$	4.02583	+	10.2576i	0.311528	+	0.793761i	−0.686264	+	0.727352i	$0.740751\pi$
$168$	−6.43978	−	3.10124i	−0.496840	−	0.239266i
$169$	20.7410	+	6.39775i	1.59546	+	0.492135i
$170$	−1.62476	+	7.11854i	−0.124613	+	0.545967i
$171$	−9.66821			−0.739347
$172$	0.0521753	−	6.55723i	0.00397833	−	0.499984i
$173$	−14.0726			−1.06992			−0.534961	−	0.844877i	$-0.679674\pi$
$173$	−14.0726			−1.06992			−0.534961	+	0.844877i	$0.679674\pi$
$174$	0.693088	−	3.03662i	0.0525429	−	0.230205i
$175$	−3.13114	−	0.965827i	−0.236692	−	0.0730097i
$176$	0.302240	+	0.145551i	0.0227822	+	0.0109713i
$177$	−4.62006	−	11.7717i	−0.347265	−	0.884816i
$178$	1.72468	−	2.98724i	0.129270	−	0.223903i
$179$	10.3482	+	17.9236i	0.773461	+	1.33967i	0.935655	+	0.352915i	$0.114809\pi$
$179$	10.3482	+	17.9236i	0.773461	+	1.33967i	−0.162194	+	0.986759i	$0.551857\pi$
$180$	−1.09625	+	1.37465i	−0.0817095	+	0.102461i
$181$	−3.80377	−	2.59337i	−0.282732	−	0.192764i	0.413647	−	0.910437i	$-0.364255\pi$
$181$	−3.80377	−	2.59337i	−0.282732	−	0.192764i	−0.696380	+	0.717674i	$0.745207\pi$
$182$	19.0879	−	2.87704i	1.41489	−	0.213260i
$183$	21.4205	−	10.3155i	1.58345	−	0.762547i
$184$	0.126267	+	0.117159i	0.00930855	+	0.00863707i
$185$	7.13120	+	1.07485i	0.524296	+	0.0790249i
$186$	−20.6858	+	6.38072i	−1.51676	+	0.467857i
$187$	−0.183044	−	2.44256i	−0.0133855	−	0.178617i
$188$	6.65147	+	8.34068i	0.485108	+	0.608306i
$189$	3.24262	−	8.26205i	0.235866	−	0.600976i
$190$	4.03089	−	3.74012i	0.292432	−	0.271337i
$191$	16.6136	−	11.3270i	1.20212	−	0.819592i	0.214542	−	0.976715i	$-0.431174\pi$
$191$	16.6136	−	11.3270i	1.20212	−	0.819592i	0.987579	+	0.157123i	$0.0502219\pi$
$192$	0.163012	−	2.17524i	0.0117644	−	0.156984i
$193$	−0.323044	−	1.41535i	−0.0232532	−	0.101879i	0.961970	−	0.273156i	$-0.0880677\pi$
$193$	−0.323044	−	1.41535i	−0.0232532	−	0.101879i	−0.985223	+	0.171277i	$0.945211\pi$
$194$	−0.738772	−	3.23677i	−0.0530408	−	0.232387i
$195$	0.960322	−	12.8146i	0.0687701	−	0.917673i
$196$	3.08751	−	2.10503i	0.220537	−	0.150359i
$197$	13.2164	−	12.2631i	0.941631	−	0.873706i	−0.0505233	−	0.998723i	$-0.516089\pi$
$197$	13.2164	−	12.2631i	0.941631	−	0.873706i	0.992155	+	0.125017i	$0.0398984\pi$
$198$	0.215487	−	0.549051i	0.0153140	−	0.0390194i
$199$	−11.9207	−	14.9481i	−0.845039	−	1.05965i	−0.997453	−	0.0713284i	$-0.977276\pi$
$199$	−11.9207	−	14.9481i	−0.845039	−	1.05965i	0.152414	−	0.988317i	$-0.451295\pi$
$200$	−0.0747301	−	0.997204i	−0.00528422	−	0.0705130i
$201$	−30.6779	+	9.46287i	−2.16385	+	0.667459i
$202$	8.83464	+	1.33161i	0.621603	+	0.0936916i
$203$	3.42979	+	3.18238i	0.240724	+	0.223359i
$204$	−14.3500	+	6.91059i	−1.00470	+	0.483838i
$205$	11.8356	−	1.78392i	0.826632	−	0.124595i
$206$	5.78829	+	3.94639i	0.403289	+	0.274958i
$207$	0.188827	−	0.236782i	0.0131244	−	0.0164575i
$208$	2.94556	+	5.10186i	0.204238	+	0.353750i
$209$	−0.922314	+	1.59749i	−0.0637978	+	0.110501i
$210$	−2.61132	−	6.65353i	−0.180198	−	0.459137i
$211$	17.4446	+	8.40086i	1.20093	+	0.578339i	0.923942	−	0.382533i	$-0.124948\pi$
$211$	17.4446	+	8.40086i	1.20093	+	0.578339i	0.276991	+	0.960872i	$0.410663\pi$
$212$	−4.32017	−	1.33260i	−0.296710	−	0.0915231i
$213$	−0.683679	+	2.99539i	−0.0468449	+	0.205241i
$214$	−14.2758			−0.975872
$215$	4.49830	−	4.77130i	0.306781	−	0.325400i
$216$	2.70869			0.184303
$217$	7.23592	−	31.7027i	0.491206	−	2.15212i
$218$	0.523705	+	0.161542i	0.0354698	+	0.0109410i
$219$	6.98814	+	3.36531i	0.472215	+	0.227407i
$220$	0.122558	+	0.312272i	0.00826284	+	0.0210534i
$221$	21.5073	−	37.2518i	1.44674	−	2.50583i
$222$	7.86564	+	13.6237i	0.527907	+	0.914362i
$223$	2.04041	−	2.55859i	0.136636	−	0.171336i	−0.708806	−	0.705404i	$-0.750766\pi$
$223$	2.04041	−	2.55859i	0.136636	−	0.171336i	0.845442	+	0.534068i	$0.179337\pi$
$224$	2.70734	+	1.84584i	0.180892	+	0.123330i
$225$	−1.73861	+	0.262053i	−0.115907	+	0.0174702i
$226$	5.42389	−	2.61201i	0.360792	−	0.173748i
$227$	−3.46159	−	3.21189i	−0.229754	−	0.213180i	0.556892	−	0.830585i	$-0.311994\pi$
$227$	−3.46159	−	3.21189i	−0.229754	−	0.213180i	−0.786646	+	0.617404i	$0.788184\pi$
$228$	11.8607	+	1.78772i	0.785497	+	0.118395i
$229$	11.6500	−	3.59354i	0.769851	−	0.237467i	0.115142	−	0.993349i	$-0.463268\pi$
$229$	11.6500	−	3.59354i	0.769851	−	0.237467i	0.654708	+	0.755882i	$0.272791\pi$
$230$	0.0128722	+	0.171767i	0.000848765	+	0.0113260i
$231$	1.49497	+	1.87464i	0.0983619	+	0.123342i
$232$	−0.521666	+	1.32918i	−0.0342491	+	0.0872652i
$233$	−10.7553	+	9.97946i	−0.704603	+	0.653776i	−0.948774	−	0.315956i	$-0.897675\pi$
$233$	−10.7553	+	9.97946i	−0.704603	+	0.653776i	0.244171	+	0.969732i	$0.421484\pi$
$234$	8.55822	−	5.83489i	0.559468	−	0.381439i
$235$	−0.797230	+	10.6383i	−0.0520056	+	0.693966i
$236$	1.29002	+	5.65194i	0.0839731	+	0.367910i
$237$	−2.77133	−	12.1420i	−0.180017	−	0.788708i
$238$	1.78794	−	23.8583i	0.115895	−	1.54651i
$239$	13.7372	−	9.36588i	0.888587	−	0.605828i	−0.0306514	−	0.999530i	$-0.509758\pi$
$239$	13.7372	−	9.36588i	0.888587	−	0.605828i	0.919238	+	0.393702i	$0.128806\pi$
$240$	1.59904	−	1.48369i	0.103217	−	0.0957717i
$241$	−7.32399	+	18.6612i	−0.471780	+	1.20208i	0.474940	+	0.880018i	$0.342470\pi$
$241$	−7.32399	+	18.6612i	−0.471780	+	1.20208i	−0.946720	+	0.322057i	$0.895626\pi$
$242$	6.78822	+	8.51216i	0.436364	+	0.547183i
$243$	−1.21575	−	16.2231i	−0.0779904	−	1.04071i
$244$	−10.4150	+	3.21260i	−0.666752	+	0.205666i
$245$	3.69509	+	0.556945i	0.236071	+	0.0355819i
$246$	19.1393	+	17.7586i	1.22027	+	1.13225i
$247$	−29.1860	+	14.0552i	−1.85706	+	0.894313i
$248$	9.81312	−	1.47909i	0.623134	−	0.0939223i
$249$	−10.5268	−	7.17708i	−0.667112	−	0.454829i
$250$	0.623490	−	0.781831i	0.0394330	−	0.0494474i
$251$	−0.400419	−	0.693547i	−0.0252742	−	0.0437763i	0.853112	−	0.521728i	$-0.174713\pi$
$251$	−0.400419	−	0.693547i	−0.0252742	−	0.0437763i	−0.878386	+	0.477952i	$0.841379\pi$
$252$	2.88063	−	4.98940i	0.181463	−	0.314303i
$253$	−0.0211104	−	0.0537885i	−0.00132720	−	0.00338165i
$254$	3.53426	+	1.70201i	0.221759	+	0.106794i
$255$	−15.2197	−	4.69465i	−0.953094	−	0.293990i
$256$	−0.222521	+	0.974928i	−0.0139076	+	0.0609330i
$257$	20.8610			1.30128			0.650638	−	0.759388i	$-0.274502\pi$
$257$	20.8610			1.30128			0.650638	+	0.759388i	$0.274502\pi$
$258$	14.2551	+	1.18240i	0.887481	+	0.0736130i
$259$	−23.6308			−1.46835
$260$	−1.31090	+	5.74342i	−0.0812984	+	0.356192i
$261$	2.39904	+	0.740006i	0.148497	+	0.0458052i
$262$	6.95429	+	3.34901i	0.429638	+	0.206903i
$263$	−7.29241	−	18.5808i	−0.449669	−	1.14574i	−0.958556	−	0.284905i	$-0.908038\pi$
$263$	−7.29241	−	18.5808i	−0.449669	−	1.14574i	0.508886	−	0.860834i	$-0.330057\pi$
$264$	−0.365877	+	0.633718i	−0.0225182	+	0.0390027i
$265$	−2.26051	−	3.91532i	−0.138862	−	0.240516i
$266$	−11.2340	+	14.0870i	−0.688800	+	0.863728i
$267$	6.21682	+	4.23856i	0.380463	+	0.259395i
$268$	14.5533	−	2.19355i	0.888981	−	0.133992i
$269$	5.23542	−	2.52125i	0.319209	−	0.153723i	−0.267417	−	0.963581i	$-0.586170\pi$
$269$	5.23542	−	2.52125i	0.319209	−	0.153723i	0.586626	+	0.809858i	$0.300456\pi$
$270$	1.98561	+	1.84238i	0.120840	+	0.112123i
$271$	4.51650	+	0.680754i	0.274358	+	0.0413528i	0.284780	−	0.958593i	$-0.408079\pi$
$271$	4.51650	+	0.680754i	0.274358	+	0.0413528i	−0.0104220	+	0.999946i	$0.503317\pi$
$272$	6.97722	−	2.15219i	0.423056	−	0.130495i
$273$	3.14670	+	41.9898i	0.190447	+	2.54134i
$274$	0.590371	+	0.740302i	0.0356656	+	0.0447233i
$275$	−0.122558	+	0.312272i	−0.00739051	+	0.0188307i
$276$	−0.275432	+	0.255563i	−0.0165791	+	0.0153831i
$277$	13.0802	−	8.91794i	0.785914	−	0.535827i	−0.102575	−	0.994725i	$-0.532708\pi$
$277$	13.0802	−	8.91794i	0.785914	−	0.535827i	0.888489	+	0.458898i	$0.151756\pi$
$278$	0.435813	−	5.81552i	0.0261383	−	0.348792i
$279$	−3.88272	−	17.0113i	−0.232452	−	1.01844i
$280$	0.729137	+	3.19456i	0.0435742	+	0.190911i
$281$	−0.605850	+	8.08451i	−0.0361420	+	0.482281i	0.949538	+	0.313653i	$0.101553\pi$
$281$	−0.605850	+	8.08451i	−0.0361420	+	0.482281i	−0.985680	+	0.168628i	$0.946066\pi$
$282$	−19.2273	+	13.1089i	−1.14497	+	0.780625i
$283$	−8.01518	+	7.43700i	−0.476453	+	0.442084i	−0.881480	−	0.472221i	$-0.843453\pi$
$283$	−8.01518	+	7.43700i	−0.476453	+	0.442084i	0.405027	+	0.914305i	$0.367262\pi$
$284$	0.514584	−	1.31114i	0.0305349	−	0.0778018i
$285$	7.47858	+	9.37785i	0.442993	+	0.555496i
$286$	−0.147685	−	1.97072i	−0.00873278	−	0.116531i
$287$	−37.4773	+	11.5602i	−2.21222	+	0.682379i
$288$	1.73861	+	0.262053i	0.102448	+	0.0154416i
$289$	−26.6196	−	24.6994i	−1.56586	−	1.45291i
$290$	−1.28648	+	0.619538i	−0.0755449	+	0.0363805i
$291$	7.16119	−	1.07938i	0.419796	−	0.0632741i
$292$	−2.93788	−	2.00301i	−0.171926	−	0.117217i
$293$	11.5336	−	14.4627i	0.673800	−	0.844919i	−0.320967	−	0.947091i	$-0.604008\pi$
$293$	11.5336	−	14.4627i	0.673800	−	0.844919i	0.994767	+	0.102172i	$0.0325791\pi$
$294$	4.07565	+	7.05923i	0.237697	+	0.411703i
$295$	−2.89865	+	5.02060i	−0.168766	+	0.292311i
$296$	−2.63475	−	6.71322i	−0.153142	−	0.390198i
$297$	−0.818674	−	0.394253i	−0.0475043	−	0.0228769i
$298$	−17.1061	−	5.27653i	−0.990930	−	0.305661i
$299$	0.225801	−	0.989297i	0.0130584	−	0.0572125i
$300$	2.18134			0.125940
$301$	−12.2448	+	17.6564i	−0.705780	+	1.01770i
$302$	−1.58562			−0.0912422
$303$	−4.33672	+	19.0004i	−0.249138	+	1.09154i
$304$	−5.25449	−	1.62079i	−0.301366	−	0.0929590i
$305$	−9.81986	−	4.72899i	−0.562283	−	0.270781i
$306$	−4.69026	−	11.9506i	−0.268124	−	0.683169i
$307$	2.68497	−	4.65051i	0.153240	−	0.265419i	−0.779177	−	0.626804i	$-0.784363\pi$
$307$	2.68497	−	4.65051i	0.153240	−	0.265419i	0.932417	+	0.361385i	$0.117696\pi$
$308$	−0.549604	−	0.951943i	−0.0313166	−	0.0542420i
$309$	−9.52791	+	11.9476i	−0.542024	+	0.679676i
$310$	8.19956	+	5.59037i	0.465704	+	0.317511i
$311$	10.5025	−	1.58299i	0.595541	−	0.0897633i	0.155646	−	0.987813i	$-0.450254\pi$
$311$	10.5025	−	1.58299i	0.595541	−	0.0897633i	0.439894	+	0.898050i	$0.355016\pi$
$312$	−11.5779	+	5.57564i	−0.655472	+	0.315659i
$313$	13.2998	+	12.3404i	0.751749	+	0.697521i	0.959827	−	0.280591i	$-0.0905305\pi$
$313$	13.2998	+	12.3404i	0.751749	+	0.697521i	−0.208079	+	0.978112i	$0.566721\pi$
$314$	−17.6579	−	2.66151i	−0.996495	−	0.150197i
$315$	5.50531	−	1.69816i	0.310189	−	0.0956806i
$316$	0.426668	+	5.69349i	0.0240020	+	0.320284i
$317$	8.75039	+	10.9726i	0.491471	+	0.616285i	0.964282	−	0.264879i	$-0.0853321\pi$
$317$	8.75039	+	10.9726i	0.491471	+	0.616285i	−0.472811	+	0.881164i	$0.656761\pi$
$318$	3.60296	−	9.18018i	0.202044	−	0.514799i
$319$	0.351133	−	0.325804i	0.0196597	−	0.0182415i
$320$	−0.826239	+	0.563320i	−0.0461882	+	0.0314905i
$321$	2.32712	−	31.0533i	0.129887	−	1.73322i
$322$	−0.125593	−	0.550258i	−0.00699902	−	0.0306647i
$323$	8.93420	+	39.1433i	0.497112	+	2.17799i
$324$	−0.835730	+	11.1520i	−0.0464294	+	0.619558i
$325$	−4.86747	+	3.31859i	−0.269999	+	0.184082i
$326$	−7.64574	+	7.09421i	−0.423458	+	0.392912i
$327$	−0.436762	+	1.11285i	−0.0241530	+	0.0615408i
$328$	−7.46271	−	9.35794i	−0.412059	−	0.516706i
$329$	−2.61229	−	34.8586i	−0.144020	−	1.92182i
$330$	−0.699245	+	0.215689i	−0.0384922	+	0.0118733i
$331$	11.2381	+	1.69388i	0.617704	+	0.0931039i	0.450438	−	0.892808i	$-0.351268\pi$
$331$	11.2381	+	1.69388i	0.617704	+	0.0931039i	0.167266	+	0.985912i	$0.446506\pi$
$332$	4.28158	+	3.97272i	0.234982	+	0.218032i
$333$	−11.4243	+	5.50166i	−0.626048	+	0.301489i
$334$	10.8963	−	1.64235i	0.596219	−	0.0898656i
$335$	12.1603	+	8.29074i	0.664387	+	0.452971i
$336$	−4.45647	+	5.58823i	−0.243120	+	0.304863i
$337$	10.6378	+	18.4252i	0.579476	+	1.00368i	0.995539	+	0.0943464i	$0.0300761\pi$
$337$	10.6378	+	18.4252i	0.579476	+	1.00368i	−0.416063	+	0.909336i	$0.636591\pi$
$338$	10.8527	−	18.7974i	0.590307	−	1.02244i
$339$	4.79759	+	12.2240i	0.260569	+	0.663919i
$340$	6.57852	+	3.16805i	0.356770	+	0.171812i
$341$	−3.18120	−	0.981270i	−0.172272	−	0.0531388i
$342$	−2.15138	+	9.42581i	−0.116333	+	0.509690i
$343$	10.6925			0.577339
$344$	−6.38122	−	1.50999i	−0.344052	−	0.0814131i
$345$	−0.375733			−0.0202288
$346$	−3.13145	+	13.7198i	−0.168348	+	0.737580i
$347$	−8.95183	−	2.76127i	−0.480559	−	0.148233i	0.0450050	−	0.998987i	$-0.485670\pi$
$347$	−8.95183	−	2.76127i	−0.480559	−	0.148233i	−0.525564	+	0.850754i	$0.676146\pi$
$348$	−2.80626	−	1.35142i	−0.150431	−	0.0724439i
$349$	4.77749	+	12.1728i	0.255733	+	0.651597i	0.999865	−	0.0164354i	$-0.00523180\pi$
$349$	4.77749	+	12.1728i	0.255733	+	0.651597i	−0.744132	+	0.668033i	$0.767137\pi$
$350$	−1.63836	+	2.83771i	−0.0875738	+	0.151682i
$351$	−7.97860	−	13.8193i	−0.425866	−	0.737622i
$352$	0.209157	−	0.262274i	0.0111481	−	0.0139793i
$353$	−7.09560	−	4.83769i	−0.377660	−	0.257485i	0.359581	−	0.933114i	$-0.382920\pi$
$353$	−7.09560	−	4.83769i	−0.377660	−	0.257485i	−0.737241	+	0.675629i	$0.763872\pi$
$354$	−12.5046	+	1.88477i	−0.664614	+	0.100174i
$355$	1.26902	−	0.611127i	0.0673525	−	0.0324352i
$356$	−2.52856	−	2.34616i	−0.134014	−	0.124346i
$357$	51.6062	+	7.77838i	2.73129	+	0.411676i
$358$	19.7769	−	6.10037i	1.04524	−	0.322415i
$359$	0.414475	+	5.53078i	0.0218751	+	0.291903i	0.997403	+	0.0720264i	$0.0229466\pi$
$359$	0.414475	+	5.53078i	0.0218751	+	0.291903i	−0.975528	+	0.219877i	$0.929434\pi$
$360$	1.09625	+	1.37465i	0.0577774	+	0.0724505i
$361$	4.10520	−	10.4599i	0.216063	−	0.550519i
$362$	−3.37477	+	3.13133i	−0.177374	+	0.164579i
$363$	−19.6226	+	13.3784i	−1.02992	+	0.702186i
$364$	1.44255	−	19.2495i	0.0756103	−	1.00895i
$365$	−0.791224	−	3.46658i	−0.0414146	−	0.181449i
$366$	−5.29042	−	23.1788i	−0.276534	−	1.21158i
$367$	−2.13731	+	28.5205i	−0.111567	+	1.48876i	0.607780	+	0.794105i	$0.292060\pi$
$367$	−2.13731	+	28.5205i	−0.111567	+	1.48876i	−0.719347	+	0.694651i	$0.755559\pi$
$368$	0.142319	−	0.0970312i	0.00741887	−	0.00505810i
$369$	−15.4270	+	14.3142i	−0.803097	+	0.745165i
$370$	2.63475	−	6.71322i	0.136974	−	0.349004i
$371$	9.23643	+	11.5821i	0.479532	+	0.601314i
$372$	1.61772	+	21.5870i	0.0838750	+	1.11923i
$373$	−9.84458	+	3.03665i	−0.509733	+	0.157232i	−0.538944	−	0.842341i	$-0.681177\pi$
$373$	−9.84458	+	3.03665i	−0.509733	+	0.157232i	0.0292111	+	0.999573i	$0.490700\pi$
$374$	−2.42205	−	0.365065i	−0.125241	−	0.0188771i
$375$	1.59904	+	1.48369i	0.0825738	+	0.0766173i
$376$	9.61165	−	4.62873i	0.495683	−	0.238708i
$377$	8.31791	−	1.25372i	0.428394	−	0.0645700i
$378$	−7.33335	−	4.99979i	−0.377187	−	0.257162i
$379$	−8.55582	+	10.7287i	−0.439483	+	0.551094i	−0.951407	−	0.307936i	$-0.900362\pi$
$379$	−8.55582	+	10.7287i	−0.439483	+	0.551094i	0.511924	+	0.859031i	$0.328933\pi$
$380$	−2.74939	−	4.76209i	−0.141041	−	0.244290i
$381$	−4.27841	+	7.41043i	−0.219190	+	0.379648i
$382$	−7.34611	−	18.7176i	−0.375860	−	0.957675i
$383$	17.6066	+	8.47888i	0.899654	+	0.433250i	0.825764	−	0.564016i	$-0.190744\pi$
$383$	17.6066	+	8.47888i	0.899654	+	0.433250i	0.0738899	+	0.997266i	$0.476459\pi$
$384$	−2.08443	−	0.642961i	−0.106371	−	0.0328110i
$385$	0.244597	−	1.07165i	0.0124658	−	0.0546163i
$386$	−1.45175			−0.0738919
$387$	−1.80905	+	11.3868i	−0.0919594	+	0.578823i
$388$	−3.32001			−0.168548
$389$	−1.88190	+	8.24516i	−0.0954163	+	0.418046i	−0.999965	−	0.00832334i	$-0.997351\pi$
$389$	−1.88190	+	8.24516i	−0.0954163	+	0.418046i	0.904549	+	0.426370i	$0.140208\pi$
$390$	−12.2796	−	3.78776i	−0.621803	−	0.191801i
$391$	−1.13314	−	0.545692i	−0.0573054	−	0.0275968i
$392$	−1.36522	−	3.47852i	−0.0689539	−	0.175692i
$393$	−8.41854	+	14.5813i	−0.424659	+	0.735531i
$394$	−9.01466	−	15.6138i	−0.454152	−	0.786614i
$395$	−3.55979	+	4.46383i	−0.179112	+	0.224600i
$396$	−0.487335	−	0.332259i	−0.0244895	−	0.0166967i
$397$	−3.15578	+	0.475657i	−0.158384	+	0.0238725i	−0.227756	−	0.973718i	$-0.573139\pi$
$397$	−3.15578	+	0.475657i	−0.158384	+	0.0238725i	0.0693715	+	0.997591i	$0.477901\pi$
$398$	−17.2260	+	8.29559i	−0.863460	+	0.415820i
$399$	−28.8113	−	26.7330i	−1.44237	−	1.33832i
$400$	−0.988831	−	0.149042i	−0.0494415	−	0.00745211i
$401$	−25.0506	+	7.72709i	−1.25097	+	0.385872i	−0.848321	−	0.529483i	$-0.822386\pi$
$401$	−25.0506	+	7.72709i	−1.25097	+	0.385872i	−0.402647	+	0.915355i	$0.631910\pi$
$402$	2.39915	+	32.0144i	0.119659	+	1.59673i
$403$	−36.4512	−	45.7084i	−1.81577	−	2.27690i
$404$	3.26411	−	8.31683i	0.162396	−	0.413778i
$405$	−8.19795	+	7.60658i	−0.407359	+	0.377974i
$406$	3.86579	−	2.63565i	0.191856	−	0.130805i
$407$	−0.180792	+	2.41250i	−0.00896150	+	0.119583i
$408$	3.54416	+	15.5280i	0.175462	+	0.768748i
$409$	3.80774	+	16.6828i	0.188281	+	0.824912i	0.977523	+	0.210830i	$0.0676165\pi$
$409$	3.80774	+	16.6828i	0.188281	+	0.824912i	−0.789242	+	0.614082i	$0.789526\pi$
$410$	0.894463	−	11.9358i	0.0441744	−	0.589466i
$411$	−1.70657	+	1.16352i	−0.0841790	+	0.0573923i
$412$	5.13546	−	4.76501i	0.253006	−	0.234755i
$413$	6.94004	−	17.6829i	0.341497	−	0.870120i
$414$	−0.188827	−	0.236782i	−0.00928036	−	0.0116372i
$415$	0.436480	+	5.82443i	0.0214260	+	0.285910i
$416$	5.62940	−	1.73644i	0.276004	−	0.0851359i
$417$	12.5791	+	1.89600i	0.616002	+	0.0928474i
$418$	1.35221	+	1.25467i	0.0661387	+	0.0613677i
$419$	20.3783	−	9.81365i	0.995543	−	0.479428i	0.136120	−	0.990692i	$-0.456537\pi$
$419$	20.3783	−	9.81365i	0.995543	−	0.479428i	0.859424	+	0.511264i	$0.170823\pi$
$420$	−7.06779	+	1.06530i	−0.344873	+	0.0519812i
$421$	15.7563	+	10.7425i	0.767915	+	0.523556i	0.882758	−	0.469828i	$-0.155684\pi$
$421$	15.7563	+	10.7425i	0.767915	+	0.523556i	−0.114843	+	0.993384i	$0.536636\pi$
$422$	12.0720	−	15.1378i	0.587656	−	0.736898i
$423$	−9.37860	−	16.2442i	−0.456003	−	0.789820i
$424$	−2.26051	+	3.91532i	−0.109780	+	0.190145i
$425$	2.66758	+	6.79687i	0.129396	+	0.329697i
$426$	2.76816	+	1.33308i	0.134118	+	0.0645877i
$427$	34.1269	+	10.5268i	1.65152	+	0.509426i
$428$	−3.17666	+	13.9179i	−0.153550	+	0.672745i
$429$	4.31086			0.208130
$430$	−3.65071	−	5.44723i	−0.176053	−	0.262689i
$431$	3.17560			0.152963			0.0764817	−	0.997071i	$-0.475631\pi$
$431$	3.17560			0.152963			0.0764817	+	0.997071i	$0.475631\pi$
$432$	0.602740	−	2.64078i	0.0289993	−	0.127054i
$433$	−19.8230	−	6.11457i	−0.952630	−	0.293847i	−0.220788	−	0.975322i	$-0.570863\pi$
$433$	−19.8230	−	6.11457i	−0.952630	−	0.293847i	−0.731842	+	0.681474i	$0.761339\pi$
$434$	−29.2977	−	14.1090i	−1.40633	−	0.677254i
$435$	−1.13793	−	2.89940i	−0.0545597	−	0.139016i
$436$	0.274027	−	0.474628i	0.0131235	−	0.0227306i
$437$	0.473579	+	0.820263i	0.0226544	+	0.0392385i
$438$	4.83595	−	6.06408i	0.231070	−	0.289753i
$439$	11.4162	+	7.78341i	0.544864	+	0.371482i	0.804249	−	0.594292i	$-0.202568\pi$
$439$	11.4162	+	7.78341i	0.544864	+	0.371482i	−0.259385	+	0.965774i	$0.583520\pi$
$440$	0.331714	−	0.0499979i	0.0158139	−	0.00238356i
$441$	−5.91961	+	2.85073i	−0.281886	+	0.135749i
$442$	−31.5320	−	29.2574i	−1.49982	−	1.39163i
$443$	34.3657	+	5.17980i	1.63276	+	0.246100i	0.900480	−	0.434898i	$-0.143216\pi$
$443$	34.3657	+	5.17980i	1.63276	+	0.246100i	0.732285	+	0.680998i	$0.238454\pi$
$444$	15.0324	−	4.63687i	0.713405	−	0.220056i
$445$	−0.257771	−	3.43972i	−0.0122195	−	0.163058i
$446$	−2.04041	−	2.55859i	−0.0966161	−	0.121153i
$447$	14.2662	−	36.3497i	0.674769	−	1.71928i
$448$	2.40200	−	2.22873i	0.113484	−	0.105298i
$449$	−15.2872	+	10.4226i	−0.721447	+	0.491874i	−0.867522	−	0.497399i	$-0.834288\pi$
$449$	−15.2872	+	10.4226i	−0.721447	+	0.491874i	0.146075	+	0.989274i	$0.453336\pi$
$450$	−0.131394	+	1.75333i	−0.00619397	+	0.0826528i
$451$	0.893470	+	3.91455i	0.0420719	+	0.184329i
$452$	−1.33959	−	5.86913i	−0.0630090	−	0.276060i
$453$	0.258475	−	3.44911i	0.0121442	−	0.162053i
$454$	−3.90164	+	2.66009i	−0.183113	+	0.124844i
$455$	14.1505	−	13.1297i	0.663384	−	0.615530i
$456$	4.38216	−	11.1656i	0.205214	−	0.522876i
$457$	−3.26697	−	4.09665i	−0.152822	−	0.191633i	0.699527	−	0.714606i	$-0.253394\pi$
$457$	−3.26697	−	4.09665i	−0.152822	−	0.191633i	−0.852349	+	0.522973i	$0.824823\pi$
$458$	−0.911079	−	12.1575i	−0.0425719	−	0.568083i
$459$	−18.8991	+	5.82960i	−0.882134	+	0.272102i
$460$	0.170325	+	0.0256723i	0.00794144	+	0.00119698i
$461$	6.14937	+	5.70578i	0.286405	+	0.265745i	0.810271	−	0.586056i	$-0.199320\pi$
$461$	6.14937	+	5.70578i	0.286405	+	0.265745i	−0.523866	+	0.851801i	$0.675511\pi$
$462$	2.16030	−	1.04034i	0.100506	−	0.0484012i
$463$	27.9814	−	4.21752i	1.30041	−	0.196005i	0.537913	−	0.843000i	$-0.319213\pi$
$463$	27.9814	−	4.21752i	1.30041	−	0.196005i	0.762494	+	0.646995i	$0.223975\pi$
$464$	1.17978	+	0.804358i	0.0547698	+	0.0373414i
$465$	−13.4970	+	16.9247i	−0.625909	+	0.784865i
$466$	7.33597	+	12.7063i	0.339832	+	0.588607i
$467$	−5.75876	+	9.97446i	−0.266484	+	0.461563i	−0.967951	−	0.251138i	$-0.919195\pi$
$467$	−5.75876	+	9.97446i	−0.266484	+	0.461563i	0.701468	+	0.712701i	$0.252528\pi$
$468$	−3.78422	−	9.64203i	−0.174926	−	0.445703i
$469$	−43.4496	−	20.9242i	−2.00632	−	0.966191i
$470$	10.1942	+	3.14449i	0.470222	+	0.145044i
$471$	8.66787	−	37.9764i	0.399394	−	1.74986i
$472$	5.79729			0.266842
$473$	1.70888	+	1.38517i	0.0785743	+	0.0636903i
$474$	−12.4543			−0.572043
$475$	1.22359	−	5.36092i	0.0561424	−	0.245976i
$476$	−22.8623	−	7.05209i	−1.04789	−	0.323232i
$477$	7.16187	+	3.44898i	0.327920	+	0.157918i
$478$	−6.07424	−	15.4769i	−0.277829	−	0.707897i
$479$	0.560171	−	0.970244i	0.0255949	−	0.0443316i	−0.852944	−	0.522002i	$-0.825185\pi$
$479$	0.560171	−	0.970244i	0.0255949	−	0.0443316i	0.878539	+	0.477670i	$0.158519\pi$
$480$	−1.09067	−	1.88910i	−0.0497821	−	0.0862251i
$481$	−26.4891	+	33.2163i	−1.20780	+	1.51453i
$482$	16.5636	+	11.2929i	0.754452	+	0.514376i
$483$	1.21742	−	0.183496i	0.0553944	−	0.00834937i
$484$	9.80927	−	4.72389i	0.445876	−	0.214722i
$485$	−2.43374	−	2.25818i	−0.110511	−	0.102539i
$486$	−16.0868	−	2.42470i	−0.729714	−	0.109987i
$487$	−30.1085	+	9.28724i	−1.36435	+	0.420845i	−0.888578	−	0.458726i	$-0.848306\pi$
$487$	−30.1085	+	9.28724i	−1.36435	+	0.420845i	−0.475768	+	0.879571i	$0.657830\pi$
$488$	0.814500	+	10.8687i	0.0368707	+	0.492005i
$489$	−14.1853	−	17.7878i	−0.641480	−	0.804390i
$490$	1.36522	−	3.47852i	0.0616742	−	0.157143i
$491$	−11.3329	+	10.5154i	−0.511446	+	0.474552i	−0.893167	−	0.449725i	$-0.851522\pi$
$491$	−11.3329	+	10.5154i	−0.511446	+	0.474552i	0.381721	+	0.924277i	$0.375331\pi$
$492$	21.5723	−	14.7077i	0.972553	−	0.663076i
$493$	0.779127	−	10.3967i	0.0350901	−	0.468245i
$494$	7.20834	+	31.5818i	0.324319	+	1.42093i
$495$	−0.131248	−	0.575035i	−0.00589916	−	0.0258459i
$496$	0.741619	−	9.89621i	0.0332997	−	0.444353i
$497$	−3.81330	+	2.59987i	−0.171050	+	0.116620i
$498$	−9.33958	+	8.66586i	−0.418517	+	0.388327i
$499$	4.63786	−	11.8171i	0.207619	−	0.529005i	−0.788695	−	0.614785i	$-0.789243\pi$
$499$	4.63786	−	11.8171i	0.207619	−	0.529005i	0.996314	+	0.0857798i	$0.0273382\pi$
$500$	−0.623490	−	0.781831i	−0.0278833	−	0.0349646i
$501$	1.79629	+	23.9698i	0.0802522	+	1.07089i
$502$	−0.765260	+	0.236051i	−0.0341552	+	0.0105355i
$503$	−6.50348	−	0.980242i	−0.289976	−	0.0437068i	0.00244352	−	0.999997i	$-0.499222\pi$
$503$	−6.50348	−	0.980242i	−0.289976	−	0.0437068i	−0.292419	+	0.956290i	$0.594460\pi$
$504$	−4.22330	−	3.91865i	−0.188121	−	0.174551i
$505$	8.04964	−	3.87650i	0.358204	−	0.172502i
$506$	−0.0571374	+	0.00861207i	−0.00254007	+	0.000382853i
$507$	39.1197	+	26.6713i	1.73737	+	1.18452i
$508$	2.44579	−	3.06692i	0.108514	−	0.136073i
$509$	−2.35385	−	4.07698i	−0.104332	−	0.180709i	0.809133	−	0.587626i	$-0.199937\pi$
$509$	−2.35385	−	4.07698i	−0.104332	−	0.180709i	−0.913465	+	0.406917i	$0.866604\pi$
$510$	−7.96364	+	13.7934i	−0.352636	+	0.610784i
$511$	4.25662	+	10.8457i	0.188302	+	0.479785i
$512$	0.900969	+	0.433884i	0.0398176	+	0.0191751i
$513$	14.2328	+	4.39023i	0.628392	+	0.193833i
$514$	4.64202	−	20.3380i	0.204751	−	0.897071i
$515$	7.00559			0.308703
$516$	4.32480	−	13.6345i	0.190389	−	0.600227i
$517$	−3.57874			−0.157393
$518$	−5.25835	+	23.0383i	−0.231039	+	1.01225i
$519$	−29.3334	−	9.04815i	−1.28759	−	0.397170i
$520$	5.30772	+	2.55606i	0.232759	+	0.112091i
$521$	−0.158702	−	0.404366i	−0.00695286	−	0.0177156i	0.927355	−	0.374182i	$-0.122077\pi$
$521$	−0.158702	−	0.404366i	−0.00695286	−	0.0177156i	−0.934308	+	0.356467i	$0.883981\pi$
$522$	1.25529	−	2.17423i	0.0549425	−	0.0951633i
$523$	−5.11821	−	8.86500i	−0.223804	−	0.387639i	0.732156	−	0.681137i	$-0.238514\pi$
$523$	−5.11821	−	8.86500i	−0.223804	−	0.387639i	−0.955960	+	0.293497i	$0.905181\pi$
$524$	4.81252	−	6.03471i	0.210236	−	0.263627i
$525$	−5.90564	−	4.02640i	−0.257743	−	0.175726i
$526$	−19.7376	+	2.97497i	−0.860601	+	0.129715i
$527$	−65.2850	+	31.4396i	−2.84386	+	1.36953i
$528$	0.536414	+	0.497720i	0.0233444	+	0.0216605i
$529$	22.7138	+	3.42355i	0.987555	+	0.148850i
$530$	−4.32017	+	1.33260i	−0.187656	+	0.0578843i
$531$	−0.761729	−	10.1646i	−0.0330562	−	0.441105i
$532$	11.2340	+	14.0870i	0.487055	+	0.610748i
$533$	−25.7610	+	65.6381i	−1.11583	+	2.84310i
$534$	5.51566	−	5.11778i	0.238686	−	0.221468i
$535$	−11.7952	+	8.04183i	−0.509951	+	0.347679i
$536$	1.09985	−	14.6765i	0.0475063	−	0.633927i
$537$	10.0459	+	44.0140i	0.433513	+	1.89934i
$538$	−1.29304	−	5.66519i	−0.0557470	−	0.244244i
$539$	−0.0936787	+	1.25006i	−0.00403503	+	0.0538437i
$540$	2.23802	−	1.52586i	0.0963092	−	0.0656625i
$541$	23.6013	−	21.8989i	1.01470	−	0.941505i	0.0164056	−	0.999865i	$-0.494778\pi$
$541$	23.6013	−	21.8989i	1.01470	−	0.941505i	0.998296	+	0.0583603i	$0.0185872\pi$
$542$	1.66870	−	4.25178i	0.0716769	−	0.182630i
$543$	−6.26126	−	7.85138i	−0.268697	−	0.336935i
$544$	−0.545650	−	7.28119i	−0.0233945	−	0.312178i
$545$	0.523705	−	0.161542i	0.0224331	−	0.00691968i
$546$	41.6372	+	6.27580i	1.78191	+	0.268579i
$547$	18.9418	+	17.5754i	0.809892	+	0.751470i	0.971919	−	0.235317i	$-0.0756127\pi$
$547$	18.9418	+	17.5754i	0.809892	+	0.751470i	−0.162027	+	0.986786i	$0.551803\pi$
$548$	0.853111	−	0.410837i	0.0364431	−	0.0175501i
$549$	18.9495	−	2.85617i	0.808744	−	0.121899i
$550$	0.277171	+	0.188972i	0.0118186	+	0.00805779i
$551$	−4.89542	+	6.13867i	−0.208552	+	0.261516i
$552$	0.187867	+	0.325394i	0.00799613	+	0.0138497i
$553$	9.35411	−	16.2018i	0.397777	−	0.688971i
$554$	−5.78373	−	14.7367i	−0.245727	−	0.626102i
$555$	14.1734	+	6.82554i	0.601627	+	0.289728i
$556$	−5.57274	−	1.71896i	−0.236337	−	0.0729002i
$557$	−0.444040	+	1.94546i	−0.0188146	+	0.0824320i	−0.983464	−	0.181106i	$-0.942032\pi$
$557$	−0.444040	+	1.94546i	−0.0188146	+	0.0824320i	0.964649	+	0.263538i	$0.0848894\pi$
$558$	−17.4488			−0.738665
$559$	11.0925	+	37.0038i	0.469163	+	1.56510i
$560$	3.27671			0.138466
$561$	1.18893	−	5.20903i	0.0501965	−	0.219925i
$562$	7.74700	+	2.38963i	0.326787	+	0.100801i
$563$	0.0785491	+	0.0378272i	0.00331045	+	0.00159423i	0.435538	−	0.900170i	$-0.356558\pi$
$563$	0.0785491	+	0.0378272i	0.00331045	+	0.00159423i	−0.432228	+	0.901764i	$0.642272\pi$
$564$	8.50178	+	21.6622i	0.357990	+	0.912143i
$565$	3.01003	−	5.21353i	0.126633	−	0.219335i
$566$	5.46700	+	9.46911i	0.229795	+	0.398017i
$567$	22.8474	−	28.6498i	0.959503	−	1.20318i
$568$	−1.16376	−	0.793438i	−0.0488303	−	0.0332919i
$569$	−44.9994	+	6.78257i	−1.88647	+	0.284340i	−0.987972	−	0.154632i	$-0.950581\pi$
$569$	−44.9994	+	6.78257i	−1.88647	+	0.284340i	−0.898501	+	0.438972i	$0.855343\pi$
$570$	10.8069	−	5.20431i	0.452650	−	0.217985i
$571$	8.37036	+	7.76656i	0.350289	+	0.325020i	0.835618	−	0.549311i	$-0.185110\pi$
$571$	8.37036	+	7.76656i	0.350289	+	0.325020i	−0.485329	+	0.874331i	$0.661300\pi$
$572$	−1.95417	−	0.294544i	−0.0817079	−	0.0123155i
$573$	41.9128	−	12.9284i	1.75093	−	0.540091i
$574$	2.93090	+	39.1101i	0.122333	+	1.63242i
$575$	0.107395	+	0.134669i	0.00447870	+	0.00561611i
$576$	0.642359	−	1.63671i	0.0267650	−	0.0681961i
$577$	−3.57451	+	3.31666i	−0.148809	+	0.138074i	−0.751064	−	0.660229i	$-0.770459\pi$
$577$	−3.57451	+	3.31666i	−0.148809	+	0.138074i	0.602256	+	0.798303i	$0.294269\pi$
$578$	−30.0036	+	20.4561i	−1.24798	+	0.850861i
$579$	0.236652	−	3.15790i	0.00983491	−	0.131238i
$580$	0.317735	+	1.39209i	0.0131932	+	0.0578033i
$581$	−4.25871	−	18.6586i	−0.176681	−	0.774090i
$582$	0.541201	−	7.22183i	0.0224335	−	0.299354i
$583$	1.25310	−	0.854347i	0.0518980	−	0.0353834i
$584$	−2.60653	+	2.41851i	−0.107859	+	0.100079i
$585$	3.78422	−	9.64203i	0.156458	−	0.398649i
$586$	−11.5336	−	14.4627i	−0.476449	−	0.597448i
$587$	−3.29957	−	44.0297i	−0.136188	−	1.81730i	−0.478911	−	0.877864i	$-0.658968\pi$
$587$	−3.29957	−	44.0297i	−0.136188	−	1.81730i	0.342723	−	0.939436i	$-0.388651\pi$
$588$	7.78916	−	2.40264i	0.321219	−	0.0990831i
$589$	53.9602	+	8.13319i	2.22339	+	0.335122i
$590$	4.24972	+	3.94316i	0.174958	+	0.162337i
$591$	35.4334	−	17.0638i	1.45753	−	0.701912i
$592$	−7.13120	+	1.07485i	−0.293090	+	0.0441763i
$593$	−33.3902	−	22.7651i	−1.37117	−	0.934850i	−0.999980	−	0.00629372i	$-0.997997\pi$
$593$	−33.3902	−	22.7651i	−1.37117	−	0.934850i	−0.371192	−	0.928556i	$-0.621051\pi$
$594$	−0.566540	+	0.710419i	−0.0232454	+	0.0291488i
$595$	−11.9626	−	20.7199i	−0.490420	−	0.849432i
$596$	−8.95070	+	15.5031i	−0.366635	+	0.635031i
$597$	−15.2369	−	38.8229i	−0.623604	−	1.58892i
$598$	−0.914248	−	0.440279i	−0.0373864	−	0.0180043i
$599$	−32.1551	−	9.91853i	−1.31382	−	0.405260i	−0.442851	−	0.896595i	$-0.646033\pi$
$599$	−32.1551	−	9.91853i	−1.31382	−	0.405260i	−0.870971	+	0.491335i	$0.836509\pi$
$600$	0.485394	−	2.12665i	0.0198161	−	0.0868201i
$601$	28.6116			1.16709			0.583545	−	0.812081i	$-0.301665\pi$
$601$	28.6116			1.16709			0.583545	+	0.812081i	$0.301665\pi$
$602$	14.4890	+	15.8667i	0.590526	+	0.646680i
$603$	−25.8772			−1.05380
$604$	−0.352834	+	1.54587i	−0.0143566	+	0.0629004i
$605$	10.4038	+	3.20914i	0.422973	+	0.130470i
$606$	17.5590	+	8.45598i	0.713286	+	0.343501i
$607$	1.12972	+	2.87849i	0.0458540	+	0.116834i	0.951966	−	0.306204i	$-0.0990589\pi$
$607$	1.12972	+	2.87849i	0.0458540	+	0.116834i	−0.906112	+	0.423038i	$0.860964\pi$
$608$	−2.74939	+	4.76209i	−0.111503	+	0.193128i
$609$	5.10300	+	8.83866i	0.206784	+	0.358161i
$610$	−6.79555	+	8.52135i	−0.275144	+	0.345020i
$611$	−51.9268	−	35.4031i	−2.10073	−	1.43226i
$612$	−12.6946	+	1.91341i	−0.513150	+	0.0773449i
$613$	−32.3592	+	15.5834i	−1.30697	+	0.629406i	−0.952180	−	0.305538i	$-0.901164\pi$
$613$	−32.3592	+	15.5834i	−1.30697	+	0.629406i	−0.354795	+	0.934944i	$0.615449\pi$
$614$	−3.93645	−	3.65249i	−0.158862	−	0.147403i
$615$	25.8174	+	3.89135i	1.04106	+	0.156914i
$616$	−1.05037	+	0.323998i	−0.0423208	+	0.0130542i
$617$	1.74954	+	23.3460i	0.0704337	+	0.939873i	0.914748	+	0.404025i	$0.132389\pi$
$617$	1.74954	+	23.3460i	0.0704337	+	0.939873i	−0.844314	+	0.535848i	$0.819992\pi$
$618$	9.52791	+	11.9476i	0.383269	+	0.480604i
$619$	12.5810	−	32.0558i	0.505673	−	1.28843i	−0.419109	−	0.907936i	$-0.637658\pi$
$619$	12.5810	−	32.0558i	0.505673	−	1.28843i	0.924782	−	0.380497i	$-0.124247\pi$
$620$	7.27478	−	6.75001i	0.292162	−	0.271087i
$621$	−0.385497	+	0.262827i	−0.0154694	+	0.0105469i
$622$	0.793716	−	10.5914i	0.0318251	−	0.424677i
$623$	2.51506	+	11.0192i	0.100764	+	0.441475i
$624$	2.85951	+	12.5284i	0.114472	+	0.501536i
$625$	0.0747301	−	0.997204i	0.00298920	−	0.0398882i
$626$	14.9905	−	10.2203i	0.599140	−	0.408487i
$627$	−2.94963	+	2.73685i	−0.117797	+	0.109299i
$628$	−6.52404	+	16.6230i	−0.260337	+	0.663329i
$629$	32.8313	+	41.1692i	1.30907	+	1.64152i
$630$	−0.430540	−	5.74515i	−0.0171531	−	0.228892i
$631$	−36.9625	+	11.4014i	−1.47145	+	0.453883i	−0.923818	−	0.382833i	$-0.874948\pi$
$631$	−36.9625	+	11.4014i	−1.47145	+	0.453883i	−0.547636	+	0.836716i	$0.684472\pi$
$632$	5.64568	+	0.850950i	0.224573	+	0.0338490i
$633$	30.9605	+	28.7272i	1.23057	+	1.14180i
$634$	12.6447	−	6.08935i	0.502184	−	0.241839i
$635$	3.87892	−	0.584654i	0.153930	−	0.0232013i
$636$	−8.14828	−	5.55540i	−0.323100	−	0.220286i
$637$	−13.7256	+	17.2113i	−0.543827	+	0.681938i
$638$	−0.239501	−	0.414827i	−0.00948192	−	0.0164232i
$639$	−1.23825	+	2.14471i	−0.0489843	+	0.0848433i
$640$	0.365341	+	0.930874i	0.0144414	+	0.0367960i
$641$	10.8994	+	5.24886i	0.430499	+	0.207317i	0.636569	−	0.771220i	$-0.280353\pi$
$641$	10.8994	+	5.24886i	0.430499	+	0.207317i	−0.206070	+	0.978537i	$0.566067\pi$
$642$	−29.7569	−	9.17877i	−1.17441	−	0.362257i
$643$	3.02536	−	13.2550i	0.119309	−	0.522725i	−0.879587	−	0.475738i	$-0.842181\pi$
$643$	3.02536	−	13.2550i	0.119309	−	0.522725i	0.998896	−	0.0469868i	$-0.0149619\pi$
$644$	−0.564409			−0.0222408
$645$	12.4441	−	7.05321i	0.489988	−	0.277720i
$646$	40.1499			1.57968
$647$	5.91808	−	25.9288i	0.232664	−	1.01937i	−0.714756	−	0.699374i	$-0.753462\pi$
$647$	5.91808	−	25.9288i	0.232664	−	1.01937i	0.947420	−	0.319993i	$-0.103681\pi$
$648$	10.6865	+	3.29634i	0.419804	+	0.129492i
$649$	−1.75217	−	0.843803i	−0.0687789	−	0.0331222i
$650$	2.15227	+	5.48389i	0.0844189	+	0.215096i
$651$	35.4664	−	61.4295i	1.39004	−	2.40761i
$652$	5.21501	+	9.03265i	0.204235	+	0.353746i
$653$	−16.9344	+	21.2351i	−0.662694	+	0.830992i	−0.993634	−	0.112660i	$-0.964063\pi$
$653$	−16.9344	+	21.2351i	−0.662694	+	0.830992i	0.330939	+	0.943652i	$0.392634\pi$
$654$	0.987761	+	0.673444i	0.0386245	+	0.0263338i
$655$	7.63247	−	1.15041i	0.298225	−	0.0449502i
$656$	−10.7839	+	5.19326i	−0.421041	+	0.202763i
$657$	4.58293	+	4.25234i	0.178797	+	0.165899i
$658$	−34.5659	−	5.20998i	−1.34752	−	0.203106i
$659$	12.8408	−	3.96086i	0.500207	−	0.154293i	−0.0343769	−	0.999409i	$-0.510945\pi$
$659$	12.8408	−	3.96086i	0.500207	−	0.154293i	0.534584	+	0.845116i	$0.320468\pi$
$660$	0.0546841	+	0.729709i	0.00212858	+	0.0284039i
$661$	−7.95083	−	9.97003i	−0.309252	−	0.387789i	0.602781	−	0.797907i	$-0.294059\pi$
$661$	−7.95083	−	9.97003i	−0.309252	−	0.387789i	−0.912033	+	0.410117i	$0.865488\pi$
$662$	4.15213	−	10.5795i	0.161377	−	0.411182i
$663$	68.7820	−	63.8203i	2.67127	−	2.47858i
$664$	4.82586	−	3.29022i	0.187280	−	0.127685i
$665$	−1.34648	+	17.9675i	−0.0522143	+	0.696751i
$666$	2.82157	+	12.3621i	0.109334	+	0.479022i
$667$	−0.0547295	−	0.239786i	−0.00211913	−	0.00928453i
$668$	0.823479	−	10.9886i	0.0318614	−	0.425160i
$669$	5.89816	−	4.02130i	0.228036	−	0.155472i
$670$	10.7888	−	10.0105i	0.416807	−	0.386741i
$671$	1.33578	−	3.40352i	0.0515674	−	0.131391i
$672$	4.45647	+	5.58823i	0.171912	+	0.215571i
$673$	−3.16977	−	42.2976i	−0.122186	−	1.63045i	−0.635394	−	0.772188i	$-0.719162\pi$
$673$	−3.16977	−	42.2976i	−0.122186	−	1.63045i	0.513208	−	0.858264i	$-0.328457\pi$
$674$	20.3303	−	6.27107i	0.783095	−	0.241553i
$675$	2.67843	+	0.403709i	0.103093	+	0.0155388i
$676$	−15.9111	−	14.7634i	−0.611966	−	0.567822i
$677$	−32.2754	+	15.5430i	−1.24044	+	0.597366i	−0.934933	−	0.354823i	$-0.884541\pi$
$677$	−32.2754	+	15.5430i	−1.24044	+	0.597366i	−0.305510	+	0.952189i	$0.598827\pi$
$678$	12.9851	−	1.95719i	0.498691	−	0.0751656i
$679$	8.98842	+	6.12820i	0.344944	+	0.235179i
$680$	4.55248	−	5.70863i	0.174580	−	0.218916i
$681$	−5.15032	−	8.92062i	−0.197361	−	0.341839i
$682$	−1.66455	+	2.88309i	−0.0637390	+	0.110399i
$683$	−17.4374	−	44.4299i	−0.667225	−	1.70006i	−0.713051	−	0.701112i	$-0.752687\pi$
$683$	−17.4374	−	44.4299i	−0.667225	−	1.70006i	0.0458260	−	0.998949i	$-0.485408\pi$
$684$	8.71076	+	4.19488i	0.333064	+	0.160395i
$685$	0.904815	+	0.279098i	0.0345712	+	0.0106638i
$686$	2.37930	−	10.4244i	0.0908420	−	0.398005i
$687$	26.5940			1.01462
$688$	−2.89208	+	5.88522i	−0.110260	+	0.224372i
$689$	26.6339			1.01467
$690$	−0.0836085	+	0.366313i	−0.00318292	+	0.0139453i
$691$	26.7493	+	8.25108i	1.01759	+	0.313886i	0.758295	−	0.651912i	$-0.226033\pi$
$691$	26.7493	+	8.25108i	1.01759	+	0.313886i	0.259298	+	0.965797i	$0.416509\pi$
$692$	12.6790	+	6.10588i	0.481983	+	0.232111i
$693$	0.706087	+	1.79908i	0.0268220	+	0.0683414i
$694$	−4.68401	+	8.11295i	−0.177803	+	0.307963i
$695$	−2.91592	−	5.05051i	−0.110607	−	0.191577i
$696$	−1.94199	+	2.43518i	−0.0736110	+	0.0923052i
$697$	72.2089	+	49.2312i	2.73511	+	1.86477i
$698$	12.9307	−	1.94899i	0.489436	−	0.0737705i
$699$	−28.8351	+	13.8862i	−1.09064	+	0.525226i
$700$	2.40200	+	2.22873i	0.0907870	+	0.0842380i
$701$	2.46993	+	0.372282i	0.0932879	+	0.0140609i	0.195520	−	0.980700i	$-0.437360\pi$
$701$	2.46993	+	0.372282i	0.0932879	+	0.0140609i	−0.102232	+	0.994761i	$0.532599\pi$
$702$	−15.2483	+	4.70347i	−0.575509	+	0.177521i
$703$	−2.96348	−	39.5449i	−0.111770	−	1.49147i
$704$	−0.209157	−	0.262274i	−0.00788289	−	0.00988483i
$705$	−8.50178	+	21.6622i	−0.320196	+	0.815845i
$706$	−6.29532	+	5.84121i	−0.236928	+	0.219837i
$707$	−24.1886	+	16.4915i	−0.909705	+	0.620227i
$708$	−0.945027	+	12.6105i	−0.0355163	+	0.473932i
$709$	−2.11344	−	9.25958i	−0.0793718	−	0.347751i	0.919612	−	0.392829i	$-0.128503\pi$
$709$	−2.11344	−	9.25958i	−0.0793718	−	0.347751i	−0.998983	+	0.0450781i	$0.985646\pi$
$710$	−0.313421	−	1.37319i	−0.0117625	−	0.0515349i
$711$	0.750187	−	10.0106i	0.0281342	−	0.375425i
$712$	−2.85000	+	1.94310i	−0.106808	+	0.0728206i
$713$	−1.25307	+	1.16268i	−0.0469279	+	0.0435427i
$714$	19.0668	−	48.5815i	0.713558	−	1.81812i
$715$	−1.23217	−	1.54509i	−0.0460804	−	0.0577830i
$716$	−1.54664	−	20.6385i	−0.0578008	−	0.771298i
$717$	34.6562	−	10.6900i	1.29426	−	0.399226i
$718$	5.48434	+	0.826632i	0.204674	+	0.0308496i
$719$	−0.241157	−	0.223761i	−0.00899362	−	0.00834486i	0.675663	−	0.737211i	$-0.263857\pi$
$719$	−0.241157	−	0.223761i	−0.00899362	−	0.00834486i	−0.684657	+	0.728866i	$0.740048\pi$
$720$	1.58413	−	0.762874i	0.0590369	−	0.0284307i
$721$	−22.6989	+	3.42131i	−0.845351	+	0.127416i
$722$	−9.28413	−	6.32981i	−0.345519	−	0.235571i
$723$	−27.2648	+	34.1890i	−1.01399	+	1.27150i
$724$	2.30186	+	3.98694i	0.0855480	+	0.148173i
$725$	−0.713944	+	1.23659i	−0.0265152	+	0.0459257i
$726$	8.67658	+	22.1076i	0.322018	+	0.820489i
$727$	39.0405	+	18.8009i	1.44793	+	0.697287i	0.982235	−	0.187657i	$-0.0600894\pi$
$727$	39.0405	+	18.8009i	1.44793	+	0.697287i	0.465697	+	0.884944i	$0.345804\pi$
$728$	−18.4459	−	5.68981i	−0.683650	−	0.210878i
$729$	0.431090	−	1.88873i	0.0159663	−	0.0699529i
$730$	−3.55573			−0.131603
$731$	47.7729	−	3.19805i	1.76694	−	0.118284i
$732$	−23.7749			−0.878746
$733$	8.83231	−	38.6969i	0.326229	−	1.42930i	−0.500029	−	0.866009i	$-0.666677\pi$
$733$	8.83231	−	38.6969i	0.326229	−	1.42930i	0.826257	−	0.563293i	$-0.190466\pi$
$734$	27.3298	+	8.43013i	1.00876	+	0.311162i
$735$	7.34406	+	3.53672i	0.270890	+	0.130454i
$736$	−0.0629295	−	0.160342i	−0.00231961	−	0.00591028i
$737$	−2.46860	+	4.27574i	−0.0909319	+	0.157499i
$738$	10.5224	+	18.2254i	0.387337	+	0.670887i
$739$	−7.96739	+	9.99079i	−0.293085	+	0.367517i	−0.906472	−	0.422265i	$-0.861235\pi$
$739$	−7.96739	+	9.99079i	−0.293085	+	0.367517i	0.613387	+	0.789782i	$0.289807\pi$
$740$	−5.95862	−	4.06252i	−0.219043	−	0.149341i
$741$	−69.8731	+	10.5317i	−2.56685	+	0.386891i
$742$	13.3470	−	6.42759i	0.489985	−	0.235964i
$743$	−14.2752	−	13.2455i	−0.523707	−	0.485929i	0.373444	−	0.927653i	$-0.378177\pi$
$743$	−14.2752	−	13.2455i	−0.523707	−	0.485929i	−0.897151	+	0.441724i	$0.854367\pi$
$744$	21.4058	+	3.22640i	0.784773	+	0.118285i
$745$	−17.1061	+	5.27653i	−0.626719	+	0.193317i
$746$	0.769891	+	10.2735i	0.0281877	+	0.376139i
$747$	−6.40292	−	8.02901i	−0.234271	−	0.293766i
$748$	−0.894868	+	2.28009i	−0.0327196	+	0.0833682i
$749$	34.2904	−	31.8168i	1.25294	−	1.16256i
$750$	1.80231	−	1.22879i	0.0658110	−	0.0448692i
$751$	−1.06990	+	14.2768i	−0.0390411	+	0.520968i	0.943061	+	0.332619i	$0.107932\pi$
$751$	−1.06990	+	14.2768i	−0.0390411	+	0.520968i	−0.982102	+	0.188348i	$0.939687\pi$
$752$	−2.37388	−	10.4007i	−0.0865666	−	0.379273i
$753$	−0.388722	−	1.70310i	−0.0141658	−	0.0620645i
$754$	0.628620	−	8.38834i	0.0228930	−	0.305485i
$755$	−1.31010	+	0.893212i	−0.0476795	+	0.0325073i
$756$	−6.50626	+	6.03693i	−0.236631	+	0.219561i
$757$	−8.20504	+	20.9061i	−0.298217	+	0.759845i	0.700706	+	0.713450i	$0.252868\pi$
$757$	−8.20504	+	20.9061i	−0.298217	+	0.759845i	−0.998923	+	0.0463949i	$0.985227\pi$
$758$	8.55582	+	10.7287i	0.310762	+	0.389683i
$759$	−0.00941927	−	0.125691i	−0.000341898	−	0.00456231i
$760$	−5.25449	+	1.62079i	−0.190600	+	0.0587924i
$761$	7.91891	+	1.19358i	0.287060	+	0.0432674i	0.290994	−	0.956725i	$-0.406014\pi$
$761$	7.91891	+	1.19358i	0.287060	+	0.0432674i	−0.00393361	+	0.999992i	$0.501252\pi$
$762$	6.27260	+	5.82012i	0.227232	+	0.210841i
$763$	−1.61797	+	0.779174i	−0.0585745	+	0.0282080i
$764$	−19.8830	+	2.99687i	−0.719340	+	0.108423i
$765$	−10.6073	−	7.23191i	−0.383507	−	0.261470i
$766$	12.1841	−	15.2784i	0.440230	−	0.552031i
$767$	−17.0763	−	29.5770i	−0.616589	−	1.06796i
$768$	−1.09067	+	1.88910i	−0.0393562	+	0.0681669i
$769$	11.3199	+	28.8427i	0.408207	+	1.04009i	0.976164	+	0.217036i	$0.0696390\pi$
$769$	11.3199	+	28.8427i	0.408207	+	1.04009i	−0.567956	+	0.823059i	$0.692266\pi$
$770$	−0.990353	−	0.476929i	−0.0356898	−	0.0171873i
$771$	43.4834	+	13.4128i	1.56601	+	0.483052i
$772$	−0.323044	+	1.41535i	−0.0116266	+	0.0509395i
$773$	−41.3051			−1.48564			−0.742821	−	0.669490i	$-0.766513\pi$
$773$	−41.3051			−1.48564			−0.742821	+	0.669490i	$0.766513\pi$
$774$	10.6987	+	4.29750i	0.384558	+	0.154470i
$775$	9.92396			0.356479
$776$	−0.738772	+	3.23677i	−0.0265204	+	0.116193i
$777$	−49.2567	−	15.1937i	−1.76708	−	0.545071i
$778$	7.61968	+	3.66944i	0.273179	+	0.131556i
$779$	−24.0454	−	61.2667i	−0.861516	−	2.19511i
$780$	−6.42527	+	11.1289i	−0.230062	+	0.398478i
$781$	0.236249	+	0.409195i	0.00845366	+	0.0146422i
$782$	−0.784158	+	0.983304i	−0.0280414	+	0.0351629i
$783$	−3.19565	−	2.17876i	−0.114203	−	0.0778624i
$784$	−3.69509	+	0.556945i	−0.131968	+	0.0198909i
$785$	−16.0890	+	7.74803i	−0.574239	+	0.276539i
$786$	12.3424	+	11.4521i	0.440241	+	0.408483i
$787$	−34.3599	−	5.17893i	−1.22480	−	0.184609i	−0.495380	−	0.868676i	$-0.664971\pi$
$787$	−34.3599	−	5.17893i	−1.22480	−	0.184609i	−0.729419	+	0.684067i	$0.760209\pi$
$788$	−17.2283	+	5.31423i	−0.613734	+	0.189312i
$789$	−3.25381	−	43.4190i	−0.115839	−	1.54576i
$790$	3.55979	+	4.46383i	0.126652	+	0.158816i
$791$	−7.20671	+	18.3624i	−0.256241	+	0.652892i
$792$	−0.432371	+	0.401182i	−0.0153636	+	0.0142554i
$793$	53.0517	−	36.1700i	1.88392	−	1.28443i
$794$	−0.238495	+	3.18250i	−0.00846389	+	0.112943i
$795$	−2.19448	−	9.61464i	−0.0778301	−	0.340996i
$796$	4.25446	+	18.6400i	0.150795	+	0.660678i
$797$	2.61143	−	34.8471i	0.0925016	−	1.23435i	−0.737019	−	0.675872i	$-0.763767\pi$
$797$	2.61143	−	34.8471i	0.0925016	−	1.23435i	0.829520	−	0.558476i	$-0.188614\pi$
$798$	−32.4738	+	22.1403i	−1.14956	+	0.783758i
$799$	−57.1007	+	52.9817i	−2.02008	+	1.87436i
$800$	−0.365341	+	0.930874i	−0.0129168	+	0.0329114i
$801$	3.78136	+	4.74168i	0.133608	+	0.167539i
$802$	1.95907	+	26.1420i	0.0691772	+	0.923105i
$803$	1.13982	−	0.351587i	0.0402232	−	0.0124072i
$804$	31.7456	+	4.78488i	1.11958	+	0.168750i
$805$	−0.413741	−	0.383896i	−0.0145825	−	0.0135305i
$806$	−52.6736	+	25.3663i	−1.85535	+	0.893488i
$807$	12.5339	−	1.88919i	0.441215	−	0.0665025i
$808$	−7.38197	−	5.03294i	−0.259697	−	0.177058i
$809$	−18.5986	+	23.3220i	−0.653893	+	0.819956i	−0.992663	−	0.120913i	$-0.961418\pi$
$809$	−18.5986	+	23.3220i	−0.653893	+	0.819956i	0.338770	+	0.940869i	$0.389989\pi$
$810$	5.59165	+	9.68503i	0.196471	+	0.340297i
$811$	3.45765	−	5.98883i	0.121415	−	0.210296i	−0.798911	−	0.601449i	$-0.794590\pi$
$811$	3.45765	−	5.98883i	0.121415	−	0.210296i	0.920326	+	0.391153i	$0.127924\pi$
$812$	−1.70935	−	4.35535i	−0.0599864	−	0.152843i
$813$	8.97664	+	4.32292i	0.314824	+	0.151611i
$814$	2.31178	+	0.713089i	0.0810278	+	0.0249938i
$815$	−2.32090	+	10.1685i	−0.0812974	+	0.356187i
$816$	15.9273			0.557567
$817$	−31.0826	−	18.2769i	−1.08744	−	0.639426i
$818$	17.1118			0.598301
$819$	−7.55243	+	33.0894i	−0.263903	+	1.15624i
$820$	−11.4375	−	3.52800i	−0.399415	−	0.123203i
$821$	4.83746	+	2.32960i	0.168828	+	0.0813035i	0.516389	−	0.856354i	$-0.327276\pi$
$821$	4.83746	+	2.32960i	0.168828	+	0.0813035i	−0.347561	+	0.937657i	$0.612990\pi$
$822$	0.754602	+	1.92269i	0.0263198	+	0.0670616i
$823$	0.396448	−	0.686669i	0.0138193	−	0.0239358i	−0.859033	−	0.511920i	$-0.828934\pi$
$823$	0.396448	−	0.686669i	0.0138193	−	0.0239358i	0.872852	+	0.487984i	$0.162268\pi$
$824$	−3.50279	−	6.06702i	−0.122026	−	0.211355i
$825$	−0.456242	+	0.572109i	−0.0158843	+	0.0199183i
$826$	−15.6953	−	10.7009i	−0.546109	−	0.372330i
$827$	4.99152	−	0.752350i	0.173572	−	0.0261618i	−0.0616811	−	0.998096i	$-0.519646\pi$
$827$	4.99152	−	0.752350i	0.173572	−	0.0261618i	0.235253	+	0.971934i	$0.424408\pi$
$828$	−0.272864	+	0.131404i	−0.00948266	+	0.00456661i
$829$	13.6416	+	12.6575i	0.473791	+	0.439614i	0.880572	−	0.473912i	$-0.157158\pi$
$829$	13.6416	+	12.6575i	0.473791	+	0.439614i	−0.406781	+	0.913526i	$0.633349\pi$
$830$	5.77552	+	0.870520i	0.200471	+	0.0302162i
$831$	32.9987	−	10.1787i	1.14471	−	0.353097i
$832$	−0.440244	−	5.87465i	−0.0152627	−	0.203667i
$833$	17.0118	+	21.3322i	0.589425	+	0.739115i
$834$	4.64758	−	11.8418i	0.160933	−	0.410049i
$835$	8.07778	−	7.49508i	0.279543	−	0.259378i
$836$	1.52410	−	1.03912i	0.0527122	−	0.0359386i
$837$	−2.00881	+	26.8057i	−0.0694347	+	0.926542i
$838$	−5.03302	−	22.0511i	−0.173863	−	0.761742i
$839$	−4.60977	−	20.1967i	−0.159147	−	0.697268i	−0.990034	−	0.140827i	$-0.955024\pi$
$839$	−4.60977	−	20.1967i	−0.159147	−	0.697268i	0.830887	−	0.556441i	$-0.187833\pi$
$840$	−0.534142	+	7.12763i	−0.0184297	+	0.245927i
$841$	−22.2763	+	15.1877i	−0.768149	+	0.523715i
$842$	13.9792	−	12.9708i	0.481756	−	0.447005i
$843$	−6.46088	+	16.4620i	−0.222524	+	0.566983i
$844$	−12.0720	−	15.1378i	−0.415536	−	0.521065i
$845$	−1.62204	−	21.6446i	−0.0557999	−	0.744598i
$846$	−17.9239	+	5.52878i	−0.616235	+	0.190083i
$847$	−35.2766	−	5.31709i	−1.21212	−	0.182697i
$848$	3.31415	+	3.07508i	0.113808	+	0.105599i
$849$	−21.4888	+	10.3485i	−0.737493	+	0.355158i
$850$	7.22005	−	1.08825i	0.247646	−	0.0373266i
$851$	1.02637	+	0.699764i	0.0351834	+	0.0239876i
$852$	1.91563	−	2.40212i	0.0656283	−	0.0822952i
$853$	20.3560	+	35.2577i	0.696977	+	1.20720i	0.969510	+	0.245053i	$0.0788052\pi$
$853$	20.3560	+	35.2577i	0.696977	+	1.20720i	−0.272533	+	0.962146i	$0.587861\pi$
$854$	17.8568	−	30.9289i	0.611047	−	1.05836i
$855$	3.53220	+	8.99989i	0.120799	+	0.307790i
$856$	12.8620	+	6.19403i	0.439615	+	0.211708i
$857$	4.57179	+	1.41021i	0.156169	+	0.0481719i	0.371854	−	0.928291i	$-0.378722\pi$
$857$	4.57179	+	1.41021i	0.156169	+	0.0481719i	−0.215685	+	0.976463i	$0.569198\pi$
$858$	0.959256	−	4.20278i	0.0327485	−	0.143480i
$859$	−15.5976			−0.532185			−0.266092	−	0.963948i	$-0.585733\pi$
$859$	−15.5976			−0.532185			−0.266092	+	0.963948i	$0.585733\pi$
$860$	−6.12302	+	2.34706i	−0.208793	+	0.0800340i
$861$	−85.5517			−2.91559
$862$	0.706638	−	3.09598i	0.0240682	−	0.105450i
$863$	42.0342	+	12.9658i	1.43086	+	0.441362i	0.910828	−	0.412785i	$-0.135444\pi$
$863$	42.0342	+	12.9658i	1.43086	+	0.441362i	0.520032	+	0.854147i	$0.325920\pi$
$864$	−2.44044	−	1.17526i	−0.0830256	−	0.0399830i
$865$	5.14130	+	13.0998i	0.174810	+	0.445408i
$866$	−10.3723	+	17.9653i	−0.352465	+	0.610487i
$867$	−39.6060	−	68.5996i	−1.34509	−	2.32976i
$868$	−20.2746	+	25.4236i	−0.688165	+	0.862932i
$869$	−1.58249	−	1.07893i	−0.0536825	−	0.0366001i
$870$	−3.07992	+	0.464224i	−0.104419	+	0.0157387i
$871$	−78.1171	+	37.6192i	−2.64690	+	1.27468i
$872$	−0.401752	−	0.372771i	−0.0136050	−	0.0126236i
$873$	5.77220	+	0.870019i	0.195359	+	0.0294457i
$874$	0.905079	−	0.279180i	0.0306148	−	0.00944340i
$875$	0.244869	+	3.26755i	0.00827808	+	0.110463i
$876$	−4.83595	−	6.06408i	−0.163391	−	0.204886i
$877$	6.13710	−	15.6371i	0.207235	−	0.528026i	−0.789032	−	0.614352i	$-0.789417\pi$
$877$	6.13710	−	15.6371i	0.207235	−	0.528026i	0.996267	+	0.0863259i	$0.0275126\pi$
$878$	10.1286	−	9.39797i	0.341824	−	0.317166i
$879$	33.3399	−	22.7308i	1.12453	−	0.766690i
$880$	0.0250690	−	0.334523i	0.000845077	−	0.0112768i
$881$	−8.31159	−	36.4155i	−0.280025	−	1.22687i	−0.897761	−	0.440483i	$-0.854807\pi$
$881$	−8.31159	−	36.4155i	−0.280025	−	1.22687i	0.617736	−	0.786385i	$-0.288050\pi$
$882$	1.46202	+	6.40554i	0.0492288	+	0.215686i
$883$	0.126043	−	1.68193i	0.00424169	−	0.0566014i	−0.994681	−	0.103001i	$-0.967156\pi$
$883$	0.126043	−	1.68193i	0.00424169	−	0.0566014i	0.998923	+	0.0463993i	$0.0147747\pi$
$884$	−35.5404	+	24.2310i	−1.19535	+	0.814977i
$885$	−9.27008	+	8.60138i	−0.311610	+	0.289132i
$886$	12.6970	−	32.3515i	0.426565	−	1.08687i
$887$	7.45791	+	9.35192i	0.250412	+	0.314007i	0.891111	−	0.453785i	$-0.149927\pi$
$887$	7.45791	+	9.35192i	0.250412	+	0.314007i	−0.640699	+	0.767792i	$0.721355\pi$
$888$	−1.17560	−	15.6873i	−0.0394505	−	0.526431i
$889$	−12.2826	+	3.78869i	−0.411946	+	0.127068i
$890$	−3.41084	−	0.514101i	−0.114332	−	0.0172327i
$891$	−2.75009	−	2.55171i	−0.0921316	−	0.0854856i
$892$	−2.94848	+	1.41991i	−0.0987223	+	0.0475421i
$893$	58.0065	−	8.74307i	1.94111	−	0.292576i
$894$	−32.2639	−	21.9971i	−1.07906	−	0.735694i
$895$	12.9040	−	16.1811i	0.431333	−	0.540875i
$896$	−1.63836	−	2.83771i	−0.0547336	−	0.0948014i
$897$	1.10674	−	1.91694i	0.0369531	−	0.0640047i
$898$	6.75959	+	17.2232i	0.225570	+	0.574744i
$899$	−12.7670	−	6.14827i	−0.425804	−	0.205056i
$900$	1.68013	+	0.518252i	0.0560044	+	0.0172751i
$901$	7.34558	−	32.1831i	0.244717	−	1.07217i
$902$	4.01522			0.133692
$903$	−36.8759	+	28.9305i	−1.22715	+	0.962748i
$904$	−6.02006			−0.200224
$905$	−1.02442	+	4.48830i	−0.0340530	+	0.149196i
$906$	−3.30511	−	1.01949i	−0.109805	−	0.0338704i
$907$	24.0105	+	11.5628i	0.797254	+	0.383937i	0.787733	−	0.616017i	$-0.211255\pi$
$907$	24.0105	+	11.5628i	0.797254	+	0.383937i	0.00952146	+	0.999955i	$0.496969\pi$
$908$	1.72520	+	4.39574i	0.0572528	+	0.145878i
$909$	−7.85447	+	13.6043i	−0.260516	+	0.451227i
$910$	−9.65175	−	16.7173i	−0.319952	−	0.554174i
$911$	−14.7986	+	18.5569i	−0.490300	+	0.614817i	−0.964011	−	0.265864i	$-0.914343\pi$
$911$	−14.7986	+	18.5569i	−0.490300	+	0.614817i	0.473711	+	0.880681i	$0.342914\pi$
$912$	−9.91050	−	6.75687i	−0.328169	−	0.223742i
$913$	−1.93746	+	0.292026i	−0.0641207	+	0.00966463i
$914$	−4.72091	+	2.27347i	−0.156154	+	0.0751997i
$915$	−17.4282	−	16.1710i	−0.576160	−	0.534598i
$916$	−12.0554	−	1.81706i	−0.398322	−	0.0600374i
$917$	−24.1682	+	7.45491i	−0.798105	+	0.246183i
$918$	1.47799	+	19.7225i	0.0487811	+	0.650938i
$919$	16.1631	+	20.2679i	0.533172	+	0.668576i	0.973347	−	0.229335i	$-0.0736553\pi$
$919$	16.1631	+	20.2679i	0.533172	+	0.668576i	−0.440176	+	0.897912i	$0.645084\pi$
$920$	0.0629295	−	0.160342i	0.00207473	−	0.00528631i
$921$	8.58674	−	7.96733i	0.282943	−	0.262532i
$922$	6.93109	−	4.72554i	0.228263	−	0.155627i
$923$	−0.620085	+	8.27446i	−0.0204104	+	0.272357i
$924$	−0.533549	−	2.33763i	−0.0175525	−	0.0769025i
$925$	−1.60476	−	7.03093i	−0.0527643	−	0.231176i
$926$	2.11467	−	28.2184i	0.0694925	−	0.927313i
$927$	−10.1772	+	6.93872i	−0.334264	+	0.227898i
$928$	1.04672	−	0.971211i	0.0343601	−	0.0318816i
$929$	−15.1930	+	38.7112i	−0.498467	+	1.27007i	0.431395	+	0.902163i	$0.358022\pi$
$929$	−15.1930	+	38.7112i	−0.498467	+	1.27007i	−0.929862	+	0.367910i	$0.880074\pi$
$930$	13.4970	+	16.9247i	0.442585	+	0.554984i
$931$	−1.53555	−	20.4906i	−0.0503258	−	0.671551i
$932$	14.0201	−	4.32463i	0.459244	−	0.141658i
$933$	22.9095	+	3.45305i	0.750023	+	0.113048i
$934$	8.44294	+	7.83390i	0.276261	+	0.256333i
$935$	−2.20684	+	1.06276i	−0.0721713	+	0.0347559i
$936$	−10.2424	+	1.54379i	−0.334782	+	0.0504602i
$937$	−23.7793	−	16.2125i	−0.776837	−	0.529639i	0.108774	−	0.994067i	$-0.465308\pi$
$937$	−23.7793	−	16.2125i	−0.776837	−	0.529639i	−0.885611	+	0.464428i	$0.846260\pi$
$938$	−30.0681	+	37.7042i	−0.981757	+	1.23108i
$939$	19.7881	+	34.2740i	0.645759	+	1.11849i
$940$	5.33406	−	9.23887i	0.173978	−	0.301339i
$941$	11.0588	+	28.1773i	0.360506	+	0.918554i	0.989938	+	0.141499i	$0.0451921\pi$
$941$	11.0588	+	28.1773i	0.360506	+	0.918554i	−0.629433	+	0.777055i	$0.716713\pi$
$942$	−35.0955	−	16.9011i	−1.14347	−	0.550668i
$943$	1.97009	+	0.607693i	0.0641551	+	0.0197892i
$944$	1.29002	−	5.65194i	0.0419866	−	0.183955i
$945$	−8.87558			−0.288723
$946$	1.73070	−	1.35780i	0.0562701	−	0.0441460i
$947$	3.74583			0.121723			0.0608616	−	0.998146i	$-0.480615\pi$
$947$	3.74583			0.121723			0.0608616	+	0.998146i	$0.480615\pi$
$948$	−2.77133	+	12.1420i	−0.0900087	+	0.394354i
$949$	20.0166	+	6.17430i	0.649766	+	0.200426i
$950$	−4.95423	−	2.38583i	−0.160737	−	0.0774066i
$951$	11.1846	+	28.4979i	0.362685	+	0.924106i
$952$	−11.9626	+	20.7199i	−0.387711	+	0.671535i
$953$	−10.1942	−	17.6569i	−0.330223	−	0.571964i	0.652332	−	0.757933i	$-0.273791\pi$
$953$	−10.1942	−	17.6569i	−0.330223	−	0.571964i	−0.982556	+	0.185969i	$0.940457\pi$
$954$	4.95617	−	6.21484i	0.160462	−	0.201213i
$955$	−16.6136	−	11.3270i	−0.537605	−	0.366533i
$956$	−16.4405	+	2.47801i	−0.531724	+	0.0801445i
$957$	0.941390	−	0.453350i	0.0304308	−	0.0146547i
$958$	−0.821268	−	0.762026i	−0.0265340	−	0.0246199i
$959$	−3.06800	−	0.462427i	−0.0990710	−	0.0149326i
$960$	−2.08443	+	0.642961i	−0.0672747	+	0.0207515i
$961$	5.04316	+	67.2963i	0.162683	+	2.17085i
$962$	26.4891	+	33.2163i	0.854044	+	1.07094i
$963$	9.17018	−	23.3652i	0.295505	−	0.752934i
$964$	14.6955	−	13.6354i	0.473310	−	0.439167i
$965$	−1.19949	+	0.817798i	−0.0386129	+	0.0263258i
$966$	0.0920054	−	1.22773i	0.00296022	−	0.0395014i
$967$	4.22591	+	18.5149i	0.135896	+	0.595400i	0.996312	+	0.0858068i	$0.0273468\pi$
$967$	4.22591	+	18.5149i	0.135896	+	0.595400i	−0.860416	+	0.509593i	$0.829796\pi$
$968$	−2.42269	−	10.6145i	−0.0778682	−	0.341163i
$969$	−6.54491	+	87.3358i	−0.210253	+	2.80563i
$970$	−2.74312	+	1.87023i	−0.0880764	+	0.0600495i
$971$	26.3291	−	24.4299i	0.844942	−	0.783991i	−0.133384	−	0.991064i	$-0.542584\pi$
$971$	26.3291	−	24.4299i	0.844942	−	0.783991i	0.978325	+	0.207073i	$0.0663938\pi$
$972$	−5.94357	+	15.1440i	−0.190640	+	0.485743i
$973$	11.9144	+	14.9402i	0.381958	+	0.478961i
$974$	2.35462	+	31.4202i	0.0754469	+	1.00677i
$975$	−12.2796	+	3.78776i	−0.393263	+	0.121306i
$976$	10.7775	+	1.62444i	0.344979	+	0.0519972i
$977$	5.39798	+	5.00859i	0.172697	+	0.160239i	0.761786	−	0.647829i	$-0.224323\pi$
$977$	5.39798	+	5.00859i	0.172697	+	0.160239i	−0.589089	+	0.808068i	$0.700513\pi$
$978$	−20.4983	+	9.87146i	−0.655464	+	0.315655i
$979$	1.14420	−	0.172461i	0.0365689	−	0.00551188i
$980$	−3.08751	−	2.10503i	−0.0986270	−	0.0672427i
$981$	−0.600803	+	0.753383i	−0.0191822	+	0.0240537i
$982$	7.72993	+	13.3886i	0.246672	+	0.427248i
$983$	−3.29900	+	5.71404i	−0.105222	+	0.182250i	−0.913829	−	0.406100i	$-0.866889\pi$
$983$	−3.29900	+	5.71404i	−0.105222	+	0.182250i	0.808607	+	0.588349i	$0.200222\pi$
$984$	−9.53869	−	24.3042i	−0.304082	−	0.774789i
$985$	−16.2439	−	7.82263i	−0.517572	−	0.249250i
$986$	−9.96269	−	3.07308i	−0.317277	−	0.0978669i
$987$	16.9676	−	74.3399i	0.540085	−	2.36627i
$988$	32.3940			1.03059
$989$	1.05468	−	0.404278i	0.0335369	−	0.0128553i
$990$	−0.589823			−0.0187458
$991$	−10.8469	+	47.5236i	−0.344565	+	1.50964i	0.444754	+	0.895653i	$0.353291\pi$
$991$	−10.8469	+	47.5236i	−0.344565	+	1.50964i	−0.789319	+	0.613984i	$0.789566\pi$
$992$	−9.48307	−	2.92514i	−0.301088	−	0.0928733i
$993$	22.3360	+	10.7565i	0.708812	+	0.341346i
$994$	1.68614	+	4.29622i	0.0534812	+	0.136268i
$995$	−9.55969	+	16.5579i	−0.303063	+	0.524920i
$996$	6.37034	+	11.0338i	0.201852	+	0.349618i
$997$	30.7686	−	38.5826i	0.974451	−	1.22192i	−0.000613692	−	1.00000i	$-0.500195\pi$
$997$	30.7686	−	38.5826i	0.974451	−	1.22192i	0.975064	−	0.221923i	$-0.0712332\pi$
$998$	−10.4888	−	7.15112i	−0.332016	−	0.226365i
$999$	19.3162	−	2.91145i	0.611137	−	0.0921141i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.q.d.81.4	✓	60
43.17	even	21	inner	430.2.q.d.361.4	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.q.d.81.4	✓	60	1.1	even	1	trivial
430.2.q.d.361.4	yes	60	43.17	even	21	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.q (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.222521 - 0.974928i) q^{2} +(2.08443 + 0.642961i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(-0.365341 - 0.930874i) q^{5} +(1.09067 - 1.88910i) q^{6} +(1.63836 + 2.83771i) q^{7} +(-0.623490 + 0.781831i) q^{8} +(1.45273 + 0.990455i) q^{9} +O(q^{10})\)	\(q+(0.222521 - 0.974928i) q^{2} +(2.08443 + 0.642961i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(-0.365341 - 0.930874i) q^{5} +(1.09067 - 1.88910i) q^{6} +(1.63836 + 2.83771i) q^{7} +(-0.623490 + 0.781831i) q^{8} +(1.45273 + 0.990455i) q^{9} +(-0.988831 + 0.149042i) q^{10} +(0.302240 - 0.145551i) q^{11} +(-1.59904 - 1.48369i) q^{12} +(5.82532 + 0.878026i) q^{13} +(3.13114 - 0.965827i) q^{14} +(-0.163012 - 2.17524i) q^{15} +(0.623490 + 0.781831i) q^{16} +(2.66758 - 6.79687i) q^{17} +(1.28889 - 1.19591i) q^{18} +(-4.54331 + 3.09757i) q^{19} +(-0.0747301 + 0.997204i) q^{20} +(1.59050 + 6.96841i) q^{21} +(-0.0746471 - 0.327050i) q^{22} +(0.0128722 - 0.171767i) q^{23} +(-1.80231 + 1.22879i) q^{24} +(-0.733052 + 0.680173i) q^{25} +(2.15227 - 5.48389i) q^{26} +(-1.68884 - 2.11774i) q^{27} +(-0.244869 - 3.26755i) q^{28} +(1.36445 - 0.420878i) q^{29} +(-2.15698 - 0.325112i) q^{30} +(-7.27478 - 6.75001i) q^{31} +(0.900969 - 0.433884i) q^{32} +(0.723582 - 0.109062i) q^{33} +(-6.03287 - 4.11314i) q^{34} +(2.04300 - 2.56184i) q^{35} +(-0.879123 - 1.52269i) q^{36} +(-3.60587 + 6.24555i) q^{37} +(2.00893 + 5.11867i) q^{38} +(11.5779 + 5.57564i) q^{39} +(0.955573 + 0.294755i) q^{40} +(-2.66341 + 11.6692i) q^{41} +7.14762 q^{42} +(2.79807 + 5.93050i) q^{43} -0.335461 q^{44} +(0.391247 - 1.71416i) q^{45} +(-0.164596 - 0.0507712i) q^{46} +(-9.61165 - 4.62873i) q^{47} +(0.796933 + 2.03055i) q^{48} +(-1.86841 + 3.23619i) q^{49} +(0.500000 + 0.866025i) q^{50} +(9.93050 - 12.4525i) q^{51} +(-4.86747 - 3.31859i) q^{52} +(4.47053 - 0.673824i) q^{53} +(-2.44044 + 1.17526i) q^{54} +(-0.245910 - 0.228172i) q^{55} +(-3.24011 - 0.488368i) q^{56} +(-11.4618 + 3.53551i) q^{57} +(-0.106706 - 1.42390i) q^{58} +(-3.61455 - 4.53251i) q^{59} +(-0.796933 + 2.03055i) q^{60} +(7.98969 - 7.41335i) q^{61} +(-8.19956 + 5.59037i) q^{62} +(-0.430540 + 5.74515i) q^{63} +(-0.222521 - 0.974928i) q^{64} +(-1.31090 - 5.74342i) q^{65} +(0.0546841 - 0.729709i) q^{66} +(-12.1603 + 8.29074i) q^{67} +(-5.35246 + 4.96635i) q^{68} +(0.137271 - 0.349760i) q^{69} +(-2.04300 - 2.56184i) q^{70} +(0.105258 + 1.40456i) q^{71} +(-1.68013 + 0.518252i) q^{72} +(3.51601 + 0.529954i) q^{73} +(5.28658 + 4.90523i) q^{74} +(-1.96532 + 0.946448i) q^{75} +(5.43737 - 0.819551i) q^{76} +(0.908209 + 0.619206i) q^{77} +(8.01218 - 10.0470i) q^{78} +(-2.85473 - 4.94453i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-4.08572 - 10.4102i) q^{81} +(10.7839 + 5.19326i) q^{82} +(-5.58127 - 1.72159i) q^{83} +(1.59050 - 6.96841i) q^{84} -7.30161 q^{85} +(6.40444 - 1.40825i) q^{86} +3.11471 q^{87} +(-0.0746471 + 0.327050i) q^{88} +(3.29612 + 1.01672i) q^{89} +(-1.58413 - 0.762874i) q^{90} +(7.05236 + 17.9691i) q^{91} +(-0.0861244 + 0.149172i) q^{92} +(-10.8238 - 18.7473i) q^{93} +(-6.65147 + 8.34068i) q^{94} +(4.54331 + 3.09757i) q^{95} +(2.15698 - 0.325112i) q^{96} +(2.99123 - 1.44050i) q^{97} +(2.73929 + 2.54169i) q^{98} +(0.583235 + 0.0879086i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 10 q^{2} - q^{3} - 10 q^{4} - 5 q^{5} - 6 q^{6} + q^{7} + 10 q^{8} + 8 q^{9}+O(q^{10}) \) 60 * q + 10 * q^2 - q^3 - 10 * q^4 - 5 * q^5 - 6 * q^6 + q^7 + 10 * q^8 + 8 * q^9	\( 60 q + 10 q^{2} - q^{3} - 10 q^{4} - 5 q^{5} - 6 q^{6} + q^{7} + 10 q^{8} + 8 q^{9} + 5 q^{10} + 3 q^{11} - q^{12} + 13 q^{13} - 15 q^{14} + q^{15} - 10 q^{16} + 38 q^{17} + 6 q^{18} + 17 q^{19} - 5 q^{20} + 4 q^{21} + 11 q^{22} - 8 q^{23} + q^{24} + 5 q^{25} + 29 q^{26} - 16 q^{27} - 6 q^{28} - 41 q^{29} - q^{30} + 15 q^{31} + 10 q^{32} + 63 q^{33} - 10 q^{34} + 2 q^{35} - 48 q^{36} + 7 q^{37} + 25 q^{38} - 64 q^{39} + 5 q^{40} - 22 q^{41} - 60 q^{42} + 6 q^{43} - 4 q^{44} + 30 q^{45} - 20 q^{46} - 13 q^{47} - q^{48} - 93 q^{49} + 30 q^{50} + 18 q^{51} - 15 q^{52} + 71 q^{53} - 5 q^{54} - 16 q^{55} - q^{56} - 94 q^{57} - 22 q^{58} + 20 q^{59} + q^{60} + 91 q^{61} + 69 q^{62} - 50 q^{63} - 10 q^{64} + 5 q^{65} + 14 q^{66} - 26 q^{67} - 18 q^{68} - 94 q^{69} - 2 q^{70} + 20 q^{71} - 36 q^{72} - 56 q^{73} - 7 q^{74} + 2 q^{75} + 38 q^{76} + 41 q^{77} - 13 q^{78} - 46 q^{79} + 30 q^{80} + 39 q^{81} + 8 q^{82} - 115 q^{83} + 4 q^{84} + 6 q^{85} + 29 q^{86} + 20 q^{87} + 11 q^{88} + 30 q^{89} - 16 q^{90} - 53 q^{91} - 8 q^{92} + 16 q^{93} + 41 q^{94} - 17 q^{95} + q^{96} + 113 q^{97} + 2 q^{98} + 139 q^{99}+O(q^{100}) \) 60 * q + 10 * q^2 - q^3 - 10 * q^4 - 5 * q^5 - 6 * q^6 + q^7 + 10 * q^8 + 8 * q^9 + 5 * q^10 + 3 * q^11 - q^12 + 13 * q^13 - 15 * q^14 + q^15 - 10 * q^16 + 38 * q^17 + 6 * q^18 + 17 * q^19 - 5 * q^20 + 4 * q^21 + 11 * q^22 - 8 * q^23 + q^24 + 5 * q^25 + 29 * q^26 - 16 * q^27 - 6 * q^28 - 41 * q^29 - q^30 + 15 * q^31 + 10 * q^32 + 63 * q^33 - 10 * q^34 + 2 * q^35 - 48 * q^36 + 7 * q^37 + 25 * q^38 - 64 * q^39 + 5 * q^40 - 22 * q^41 - 60 * q^42 + 6 * q^43 - 4 * q^44 + 30 * q^45 - 20 * q^46 - 13 * q^47 - q^48 - 93 * q^49 + 30 * q^50 + 18 * q^51 - 15 * q^52 + 71 * q^53 - 5 * q^54 - 16 * q^55 - q^56 - 94 * q^57 - 22 * q^58 + 20 * q^59 + q^60 + 91 * q^61 + 69 * q^62 - 50 * q^63 - 10 * q^64 + 5 * q^65 + 14 * q^66 - 26 * q^67 - 18 * q^68 - 94 * q^69 - 2 * q^70 + 20 * q^71 - 36 * q^72 - 56 * q^73 - 7 * q^74 + 2 * q^75 + 38 * q^76 + 41 * q^77 - 13 * q^78 - 46 * q^79 + 30 * q^80 + 39 * q^81 + 8 * q^82 - 115 * q^83 + 4 * q^84 + 6 * q^85 + 29 * q^86 + 20 * q^87 + 11 * q^88 + 30 * q^89 - 16 * q^90 - 53 * q^91 - 8 * q^92 + 16 * q^93 + 41 * q^94 - 17 * q^95 + q^96 + 113 * q^97 + 2 * q^98 + 139 * q^99

Introduction

L-functions

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