LMFDB - Embedded newform 966.2.y.d.823.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(25,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 44, 6]))

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

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

chi := DirichletCharacter("966.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.y (of order $33$, degree $20$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$8$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			823.5
Character	$\chi$	$=$	966.823
Dual form			966.2.y.d.331.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.235759 + 0.971812i) q^{2} +(-0.327068 - 0.945001i) q^{3} +(-0.888835 + 0.458227i) q^{4} +(-0.262927 + 0.105260i) q^{5} +(0.841254 - 0.540641i) q^{6} +(-1.94492 - 1.79368i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(-0.786053 + 0.618159i) q^{9} +O(q^{10})$	\(q+(0.235759 + 0.971812i) q^{2} +(-0.327068 - 0.945001i) q^{3} +(-0.888835 + 0.458227i) q^{4} +(-0.262927 + 0.105260i) q^{5} +(0.841254 - 0.540641i) q^{6} +(-1.94492 - 1.79368i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(-0.786053 + 0.618159i) q^{9} +(-0.164280 - 0.230699i) q^{10} +(0.182192 - 0.751005i) q^{11} +(0.723734 + 0.690079i) q^{12} +(-0.0379206 + 0.0830345i) q^{13} +(1.28459 - 2.31297i) q^{14} +(0.185466 + 0.214039i) q^{15} +(0.580057 - 0.814576i) q^{16} +(0.140280 + 2.94484i) q^{17} +(-0.786053 - 0.618159i) q^{18} +(-0.369874 + 7.76461i) q^{19} +(0.185466 - 0.214039i) q^{20} +(-1.05891 + 2.42460i) q^{21} +0.772788 q^{22} +(1.20638 + 4.64162i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-3.56062 + 3.39504i) q^{25} +(-0.0896340 - 0.0172755i) q^{26} +(0.841254 + 0.540641i) q^{27} +(2.55062 + 0.703076i) q^{28} +(-1.47402 + 0.947298i) q^{29} +(-0.164280 + 0.230699i) q^{30} +(2.38821 - 0.460289i) q^{31} +(0.928368 + 0.371662i) q^{32} +(-0.769289 + 0.0734582i) q^{33} +(-2.82876 + 0.830598i) q^{34} +(0.700174 + 0.266885i) q^{35} +(0.415415 - 0.909632i) q^{36} +(-1.53089 + 1.20391i) q^{37} +(-7.63294 + 1.47113i) q^{38} +(0.0908703 + 0.00867706i) q^{39} +(0.251731 + 0.129776i) q^{40} +(-0.0592609 + 0.412169i) q^{41} +(-2.60591 - 0.457440i) q^{42} +(-2.78289 + 3.21162i) q^{43} +(0.182192 + 0.751005i) q^{44} +(0.141607 - 0.245271i) q^{45} +(-4.22637 + 2.26668i) q^{46} +(-3.32370 - 5.75682i) q^{47} +(-0.959493 - 0.281733i) q^{48} +(0.565406 + 6.97713i) q^{49} +(-4.13879 - 2.65984i) q^{50} +(2.73699 - 1.09573i) q^{51} +(-0.00434345 - 0.0911802i) q^{52} +(-0.993994 - 0.0949149i) q^{53} +(-0.327068 + 0.945001i) q^{54} +(0.0311477 + 0.216637i) q^{55} +(-0.0819249 + 2.64448i) q^{56} +(7.45854 - 2.19002i) q^{57} +(-1.26811 - 1.20914i) q^{58} +(-1.73300 - 2.43366i) q^{59} +(-0.262927 - 0.105260i) q^{60} +(-3.39590 + 9.81182i) q^{61} +(1.01035 + 2.21237i) q^{62} +(2.63759 + 0.207662i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(0.00123013 - 0.0258235i) q^{65} +(-0.252754 - 0.730286i) q^{66} +(8.56166 - 8.16353i) q^{67} +(-1.47409 - 2.55320i) q^{68} +(3.99177 - 2.65815i) q^{69} +(-0.0942899 + 0.743358i) q^{70} +(0.539661 + 0.158459i) q^{71} +(0.981929 + 0.189251i) q^{72} +(-12.3359 + 6.35959i) q^{73} +(-1.53089 - 1.20391i) q^{74} +(4.37288 + 2.25438i) q^{75} +(-3.22919 - 7.07095i) q^{76} +(-1.70141 + 1.13385i) q^{77} +(0.0129910 + 0.0903545i) q^{78} +(12.1226 - 1.15757i) q^{79} +(-0.0667703 + 0.275231i) q^{80} +(0.235759 - 0.971812i) q^{81} +(-0.414522 + 0.0395820i) q^{82} +(1.85626 + 12.9106i) q^{83} +(-0.169820 - 2.64030i) q^{84} +(-0.346857 - 0.759512i) q^{85} +(-3.77718 - 1.94727i) q^{86} +(1.37730 + 1.08312i) q^{87} +(-0.686882 + 0.354112i) q^{88} +(-17.6868 - 3.40886i) q^{89} +(0.271742 + 0.0797906i) q^{90} +(0.222690 - 0.0934778i) q^{91} +(-3.19919 - 3.57284i) q^{92} +(-1.21608 - 2.10631i) q^{93} +(4.81095 - 4.58723i) q^{94} +(-0.720053 - 2.08046i) q^{95} +(0.0475819 - 0.998867i) q^{96} +(-1.50876 + 10.4936i) q^{97} +(-6.64715 + 2.19439i) q^{98} +(0.321028 + 0.702953i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{5} - 16 q^{6} + 6 q^{7} - 16 q^{8} + 8 q^{9}+O(q^{10}) $ 160 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^5 - 16 * q^6 + 6 * q^7 - 16 * q^8 + 8 * q^9	\( 160 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{5} - 16 q^{6} + 6 q^{7} - 16 q^{8} + 8 q^{9} - 2 q^{10} - 4 q^{11} + 8 q^{12} - 4 q^{13} + 5 q^{14} + 26 q^{15} + 8 q^{16} - 13 q^{17} + 8 q^{18} + 4 q^{19} + 26 q^{20} + 11 q^{21} - 124 q^{22} + 26 q^{23} - 80 q^{24} + 14 q^{25} + 2 q^{26} - 16 q^{27} - 22 q^{28} + 54 q^{29} - 2 q^{30} + 15 q^{31} + 8 q^{32} - 4 q^{33} + 4 q^{34} - 2 q^{35} - 16 q^{36} + 7 q^{37} - 7 q^{38} + 2 q^{39} + 9 q^{40} - 30 q^{41} + 6 q^{42} + 36 q^{43} - 4 q^{44} + 20 q^{45} + 4 q^{46} - 6 q^{47} - 16 q^{48} + 14 q^{49} - 28 q^{50} + 9 q^{51} + 2 q^{52} - 24 q^{53} + 8 q^{54} - 14 q^{55} + 6 q^{56} - 30 q^{57} - 5 q^{58} + 4 q^{59} - 2 q^{60} + 32 q^{61} - 8 q^{62} - 6 q^{63} - 16 q^{64} + 38 q^{65} - 4 q^{66} + 6 q^{67} + 42 q^{68} - 30 q^{69} - 8 q^{70} - 180 q^{71} + 8 q^{72} - 32 q^{73} + 7 q^{74} + 14 q^{75} - 8 q^{76} + 61 q^{77} + 18 q^{78} - 66 q^{79} - 2 q^{80} + 8 q^{81} - 7 q^{82} + 130 q^{83} + 5 q^{84} - 70 q^{85} - 40 q^{86} + 6 q^{87} - 15 q^{88} - 4 q^{89} + 4 q^{90} - 6 q^{91} + 58 q^{92} - 18 q^{93} + 16 q^{94} + 19 q^{95} + 8 q^{96} + 40 q^{97} + 43 q^{98} + 8 q^{99}+O(q^{100}) \) 160 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^5 - 16 * q^6 + 6 * q^7 - 16 * q^8 + 8 * q^9 - 2 * q^10 - 4 * q^11 + 8 * q^12 - 4 * q^13 + 5 * q^14 + 26 * q^15 + 8 * q^16 - 13 * q^17 + 8 * q^18 + 4 * q^19 + 26 * q^20 + 11 * q^21 - 124 * q^22 + 26 * q^23 - 80 * q^24 + 14 * q^25 + 2 * q^26 - 16 * q^27 - 22 * q^28 + 54 * q^29 - 2 * q^30 + 15 * q^31 + 8 * q^32 - 4 * q^33 + 4 * q^34 - 2 * q^35 - 16 * q^36 + 7 * q^37 - 7 * q^38 + 2 * q^39 + 9 * q^40 - 30 * q^41 + 6 * q^42 + 36 * q^43 - 4 * q^44 + 20 * q^45 + 4 * q^46 - 6 * q^47 - 16 * q^48 + 14 * q^49 - 28 * q^50 + 9 * q^51 + 2 * q^52 - 24 * q^53 + 8 * q^54 - 14 * q^55 + 6 * q^56 - 30 * q^57 - 5 * q^58 + 4 * q^59 - 2 * q^60 + 32 * q^61 - 8 * q^62 - 6 * q^63 - 16 * q^64 + 38 * q^65 - 4 * q^66 + 6 * q^67 + 42 * q^68 - 30 * q^69 - 8 * q^70 - 180 * q^71 + 8 * q^72 - 32 * q^73 + 7 * q^74 + 14 * q^75 - 8 * q^76 + 61 * q^77 + 18 * q^78 - 66 * q^79 - 2 * q^80 + 8 * q^81 - 7 * q^82 + 130 * q^83 + 5 * q^84 - 70 * q^85 - 40 * q^86 + 6 * q^87 - 15 * q^88 - 4 * q^89 + 4 * q^90 - 6 * q^91 + 58 * q^92 - 18 * q^93 + 16 * q^94 + 19 * q^95 + 8 * q^96 + 40 * q^97 + 43 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{6}{11}\right)$

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 $

$2$	0.235759	+	0.971812i	0.166707	+	0.687175i
$2$	0.235759	+	0.971812i	0.166707	+	0.687175i
$3$	−0.327068	−	0.945001i	−0.188833	−	0.545596i
$3$	−0.327068	−	0.945001i	−0.188833	−	0.545596i
$4$	−0.888835	+	0.458227i	−0.444418	+	0.229113i
$5$	−0.262927	+	0.105260i	−0.117584	+	0.0470737i	−0.429709	−	0.902968i	$-0.641384\pi$
$5$	−0.262927	+	0.105260i	−0.117584	+	0.0470737i	0.312124	+	0.950041i	$0.398959\pi$
$6$	0.841254	−	0.540641i	0.343440	−	0.220716i
$7$	−1.94492	−	1.79368i	−0.735110	−	0.677948i
$7$	−1.94492	−	1.79368i	−0.735110	−	0.677948i
$8$	−0.654861	−	0.755750i	−0.231528	−	0.267198i
$9$	−0.786053	+	0.618159i	−0.262018	+	0.206053i
$10$	−0.164280	−	0.230699i	−0.0519500	−	0.0729536i
$11$	0.182192	−	0.751005i	0.0549329	−	0.226436i	−0.937728	−	0.347372i	$-0.887074\pi$
$11$	0.182192	−	0.751005i	0.0549329	−	0.226436i	0.992660	+	0.120935i	$0.0385894\pi$
$12$	0.723734	+	0.690079i	0.208924	+	0.199209i
$13$	−0.0379206	+	0.0830345i	−0.0105173	+	0.0230296i	−0.914818	−	0.403867i	$-0.867666\pi$
$13$	−0.0379206	+	0.0830345i	−0.0105173	+	0.0230296i	0.904300	+	0.426897i	$0.140393\pi$
$14$	1.28459	−	2.31297i	0.343321	−	0.618167i
$15$	0.185466	+	0.214039i	0.0478871	+	0.0552646i
$16$	0.580057	−	0.814576i	0.145014	−	0.203644i
$17$	0.140280	+	2.94484i	0.0340229	+	0.714229i	0.949859	+	0.312677i	$0.101226\pi$
$17$	0.140280	+	2.94484i	0.0340229	+	0.714229i	−0.915837	+	0.401551i	$0.868471\pi$
$18$	−0.786053	−	0.618159i	−0.185274	−	0.145701i
$19$	−0.369874	+	7.76461i	−0.0848549	+	1.78132i	0.409742	+	0.912201i	$0.365619\pi$
$19$	−0.369874	+	7.76461i	−0.0848549	+	1.78132i	−0.494597	+	0.869122i	$0.664684\pi$
$20$	0.185466	−	0.214039i	0.0414714	−	0.0478606i
$21$	−1.05891	+	2.42460i	−0.231073	+	0.529092i
$22$	0.772788			0.164759
$23$	1.20638	+	4.64162i	0.251547	+	0.967845i
$23$	1.20638	+	4.64162i	0.251547	+	0.967845i
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	−3.56062	+	3.39504i	−0.712124	+	0.679009i
$26$	−0.0896340	−	0.0172755i	−0.0175787	−	0.00338801i
$27$	0.841254	+	0.540641i	0.161899	+	0.104046i
$28$	2.55062	+	0.703076i	0.482023	+	0.132869i
$29$	−1.47402	+	0.947298i	−0.273720	+	0.175909i	−0.670298	−	0.742092i	$-0.733834\pi$
$29$	−1.47402	+	0.947298i	−0.273720	+	0.175909i	0.396579	+	0.918001i	$0.370197\pi$
$30$	−0.164280	+	0.230699i	−0.0299933	+	0.0421198i
$31$	2.38821	−	0.460289i	0.428934	−	0.0826703i	0.0297852	−	0.999556i	$-0.490518\pi$
$31$	2.38821	−	0.460289i	0.428934	−	0.0826703i	0.399149	+	0.916886i	$0.369306\pi$
$32$	0.928368	+	0.371662i	0.164114	+	0.0657013i
$33$	−0.769289	+	0.0734582i	−0.133916	+	0.0127874i
$34$	−2.82876	+	0.830598i	−0.485128	+	0.142446i
$35$	0.700174	+	0.266885i	0.118351	+	0.0451118i
$36$	0.415415	−	0.909632i	0.0692358	−	0.151605i
$37$	−1.53089	+	1.20391i	−0.251677	+	0.197921i	−0.736025	−	0.676954i	$-0.763299\pi$
$37$	−1.53089	+	1.20391i	−0.251677	+	0.197921i	0.484348	+	0.874876i	$0.339057\pi$
$38$	−7.63294	+	1.47113i	−1.23823	+	0.238649i
$39$	0.0908703	+	0.00867706i	0.0145509	+	0.00138944i
$40$	0.251731	+	0.129776i	0.0398021	+	0.0205194i
$41$	−0.0592609	+	0.412169i	−0.00925500	+	0.0643700i	−0.993926	−	0.110055i	$-0.964897\pi$
$41$	−0.0592609	+	0.412169i	−0.00925500	+	0.0643700i	0.984671	+	0.174425i	$0.0558065\pi$
$42$	−2.60591	−	0.457440i	−0.402100	−	0.0705845i
$43$	−2.78289	+	3.21162i	−0.424386	+	0.489768i	−0.927168	−	0.374646i	$-0.877764\pi$
$43$	−2.78289	+	3.21162i	−0.424386	+	0.489768i	0.502782	+	0.864413i	$0.332310\pi$
$44$	0.182192	+	0.751005i	0.0274664	+	0.113218i
$45$	0.141607	−	0.245271i	0.0211095	−	0.0365628i
$46$	−4.22637	+	2.26668i	−0.623144	+	0.334203i
$47$	−3.32370	−	5.75682i	−0.484811	−	0.839718i	0.515036	−	0.857168i	$-0.327778\pi$
$47$	−3.32370	−	5.75682i	−0.484811	−	0.839718i	−0.999848	+	0.0174503i	$0.994445\pi$
$48$	−0.959493	−	0.281733i	−0.138491	−	0.0406646i
$49$	0.565406	+	6.97713i	0.0807723	+	0.996733i
$50$	−4.13879	−	2.65984i	−0.585313	−	0.376158i
$51$	2.73699	−	1.09573i	0.383256	−	0.153433i
$52$	−0.00434345	−	0.0911802i	−0.000602328	−	0.0126444i
$53$	−0.993994	−	0.0949149i	−0.136536	−	0.0130376i	0.0265645	−	0.999647i	$-0.491543\pi$
$53$	−0.993994	−	0.0949149i	−0.136536	−	0.0130376i	−0.163100	+	0.986610i	$0.552149\pi$
$54$	−0.327068	+	0.945001i	−0.0445083	+	0.128598i
$55$	0.0311477	+	0.216637i	0.00419995	+	0.0292113i
$56$	−0.0819249	+	2.64448i	−0.0109477	+	0.353384i
$57$	7.45854	−	2.19002i	0.987907	−	0.290076i
$58$	−1.26811	−	1.20914i	−0.166511	−	0.158768i
$59$	−1.73300	−	2.43366i	−0.225617	−	0.316835i	0.686214	−	0.727399i	$-0.259271\pi$
$59$	−1.73300	−	2.43366i	−0.225617	−	0.316835i	−0.911832	+	0.410564i	$0.865332\pi$
$60$	−0.262927	−	0.105260i	−0.0339437	−	0.0135890i
$61$	−3.39590	+	9.81182i	−0.434801	+	1.25627i	0.488624	+	0.872495i	$0.337499\pi$
$61$	−3.39590	+	9.81182i	−0.434801	+	1.25627i	−0.923425	+	0.383780i	$0.874622\pi$
$62$	1.01035	+	2.21237i	0.128315	+	0.280971i
$63$	2.63759	+	0.207662i	0.332305	+	0.0261629i
$64$	−0.142315	+	0.989821i	−0.0177894	+	0.123728i
$65$	0.00123013	−	0.0258235i	0.000152578	−	0.00320301i
$66$	−0.252754	−	0.730286i	−0.0311119	−	0.0898919i
$67$	8.56166	−	8.16353i	1.04597	−	0.997334i	0.0459748	−	0.998943i	$-0.485361\pi$
$67$	8.56166	−	8.16353i	1.04597	−	0.997334i	0.999999	+	0.00160889i	$0.000512127\pi$
$68$	−1.47409	−	2.55320i	−0.178760	−	0.309621i
$69$	3.99177	−	2.65815i	0.480552	−	0.320004i
$70$	−0.0942899	+	0.743358i	−0.0112698	+	0.0888483i
$71$	0.539661	+	0.158459i	0.0640460	+	0.0188056i	0.313599	−	0.949556i	$-0.398465\pi$
$71$	0.539661	+	0.158459i	0.0640460	+	0.0188056i	−0.249553	+	0.968361i	$0.580284\pi$
$72$	0.981929	+	0.189251i	0.115721	+	0.0223035i
$73$	−12.3359	+	6.35959i	−1.44381	+	0.744333i	−0.989229	−	0.146374i	$-0.953240\pi$
$73$	−12.3359	+	6.35959i	−1.44381	+	0.744333i	−0.454576	+	0.890708i	$0.650209\pi$
$74$	−1.53089	−	1.20391i	−0.177963	−	0.139951i
$75$	4.37288	+	2.25438i	0.504937	+	0.260313i
$76$	−3.22919	−	7.07095i	−0.370414	−	0.811093i
$77$	−1.70141	+	1.13385i	−0.193894	+	0.129214i
$78$	0.0129910	+	0.0903545i	0.00147094	+	0.0102306i
$79$	12.1226	−	1.15757i	1.36390	−	0.130237i	0.612704	−	0.790312i	$-0.290082\pi$
$79$	12.1226	−	1.15757i	1.36390	−	0.130237i	0.751199	+	0.660075i	$0.229476\pi$
$80$	−0.0667703	+	0.275231i	−0.00746514	+	0.0307717i
$81$	0.235759	−	0.971812i	0.0261954	−	0.107979i
$82$	−0.414522	+	0.0395820i	−0.0457763	+	0.00437110i
$83$	1.85626	+	12.9106i	0.203751	+	1.41712i	0.793026	+	0.609187i	$0.208504\pi$
$83$	1.85626	+	12.9106i	0.203751	+	1.41712i	−0.589275	+	0.807932i	$0.700587\pi$
$84$	−0.169820	−	2.64030i	−0.0185289	−	0.288080i
$85$	−0.346857	−	0.759512i	−0.0376220	−	0.0823806i
$86$	−3.77718	−	1.94727i	−0.407304	−	0.209980i
$87$	1.37730	+	1.08312i	0.147662	+	0.116123i
$88$	−0.686882	+	0.354112i	−0.0732218	+	0.0377485i
$89$	−17.6868	−	3.40886i	−1.87480	−	0.361338i	−0.881057	−	0.473011i	$-0.843167\pi$
$89$	−17.6868	−	3.40886i	−1.87480	−	0.361338i	−0.993745	+	0.111672i	$0.964379\pi$
$90$	0.271742	+	0.0797906i	0.0286441	+	0.00841067i
$91$	0.222690	−	0.0934778i	0.0233443	−	0.00979913i
$92$	−3.19919	−	3.57284i	−0.333538	−	0.372495i
$93$	−1.21608	−	2.10631i	−0.126102	−	0.218414i
$94$	4.81095	−	4.58723i	0.496212	−	0.473137i
$95$	−0.720053	−	2.08046i	−0.0738759	−	0.213450i
$96$	0.0475819	−	0.998867i	0.00485631	−	0.101946i
$97$	−1.50876	+	10.4936i	−0.153191	+	1.06547i	0.757636	+	0.652678i	$0.226354\pi$
$97$	−1.50876	+	10.4936i	−0.153191	+	1.06547i	−0.910827	+	0.412789i	$0.864555\pi$
$98$	−6.64715	+	2.19439i	−0.671464	+	0.221667i
$99$	0.321028	+	0.702953i	0.0322645	+	0.0706494i
$100$	1.60911	−	4.64921i	0.160911	−	0.464921i
$101$	−4.73447	−	1.89540i	−0.471098	−	0.188599i	0.123952	−	0.992288i	$-0.460443\pi$
$101$	−4.73447	−	1.89540i	−0.471098	−	0.188599i	−0.595049	+	0.803689i	$0.702867\pi$
$102$	1.71011	+	2.40152i	0.169326	+	0.237785i
$103$	−5.07320	−	4.83729i	−0.499878	−	0.476632i	0.397683	−	0.917523i	$-0.369814\pi$
$103$	−5.07320	−	4.83729i	−0.499878	−	0.476632i	−0.897561	+	0.440890i	$0.854663\pi$
$104$	0.0875860	−	0.0257176i	0.00858851	−	0.00252182i
$105$	0.0232023	−	0.748955i	0.00226431	−	0.0730905i
$106$	−0.142104	−	0.988352i	−0.0138023	−	0.0959972i
$107$	5.73968	−	16.5837i	0.554876	−	1.60321i	−0.223020	−	0.974814i	$-0.571591\pi$
$107$	5.73968	−	16.5837i	0.554876	−	1.60321i	0.777895	−	0.628394i	$-0.216287\pi$
$108$	−0.995472	−	0.0950560i	−0.0957893	−	0.00914677i
$109$	0.350906	+	7.36642i	0.0336107	+	0.705575i	0.951298	+	0.308272i	$0.0997507\pi$
$109$	0.350906	+	7.36642i	0.0336107	+	0.705575i	−0.917688	+	0.397303i	$0.869946\pi$
$110$	−0.203187	+	0.0813437i	−0.0193731	+	0.00775582i
$111$	1.63840	+	1.05293i	0.155510	+	0.0999402i
$112$	−2.58925	+	0.543845i	−0.244661	+	0.0513885i
$113$	2.25427	+	0.661914i	0.212064	+	0.0622676i	0.386039	−	0.922482i	$-0.373843\pi$
$113$	2.25427	+	0.661914i	0.212064	+	0.0622676i	−0.173975	+	0.984750i	$0.555661\pi$
$114$	3.88671	+	6.73197i	0.364023	+	0.630507i
$115$	−0.805767	−	1.09342i	−0.0751381	−	0.101962i
$116$	0.876088	−	1.51743i	0.0813428	−	0.140890i
$117$	−0.0215209	−	0.0887105i	−0.00198961	−	0.00820129i
$118$	1.95649	−	2.25791i	0.180109	−	0.207857i
$119$	5.00927	−	5.97909i	0.459199	−	0.548102i
$120$	0.0403056	−	0.280331i	0.00367938	−	0.0255906i
$121$	9.24638	+	4.76684i	0.840580	+	0.433349i
$122$	−10.3359	−	0.986954i	−0.935764	−	0.0893546i
$123$	0.408882	−	0.0788056i	0.0368677	−	0.00710566i
$124$	−1.91181	+	1.50346i	−0.171685	+	0.135015i
$125$	1.16708	−	2.55554i	0.104387	−	0.228575i
$126$	0.420027	+	2.61220i	0.0374190	+	0.232713i
$127$	−5.89425	+	1.73071i	−0.523030	+	0.153575i	−0.532581	−	0.846379i	$-0.678778\pi$
$127$	−5.89425	+	1.73071i	−0.523030	+	0.153575i	0.00955121	+	0.999954i	$0.496960\pi$
$128$	−0.995472	+	0.0950560i	−0.0879881	+	0.00840185i
$129$	3.94518	+	1.57941i	0.347354	+	0.139059i
$130$	0.0253856	−	0.00489268i	0.00222647	−	0.000429116i
$131$	−7.21599	+	10.1334i	−0.630464	+	0.885363i	−0.999021	−	0.0442424i	$-0.985913\pi$
$131$	−7.21599	+	10.1334i	−0.630464	+	0.885363i	0.368557	+	0.929605i	$0.379852\pi$
$132$	0.650111	−	0.417801i	0.0565849	−	0.0363649i
$133$	14.6466	−	14.4381i	1.27002	−	1.25194i
$134$	9.95190	+	6.39570i	0.859713	+	0.552504i
$135$	−0.278096	−	0.0535986i	−0.0239347	−	0.00461303i
$136$	2.13370	−	2.03448i	0.182963	−	0.174455i
$137$	9.48623	−	16.4306i	0.810464	−	1.40376i	−0.102076	−	0.994777i	$-0.532549\pi$
$137$	9.48623	−	16.4306i	0.810464	−	1.40376i	0.912540	−	0.408988i	$-0.134118\pi$
$138$	3.52432	+	3.25256i	0.300010	+	0.276877i
$139$	1.58902			0.134779			0.0673893	−	0.997727i	$-0.478533\pi$
$139$	1.58902			0.134779			0.0673893	+	0.997727i	$0.478533\pi$
$140$	−0.744633	+	0.0836212i	−0.0629330	+	0.00706729i
$141$	−4.35312	+	5.02377i	−0.366599	+	0.423078i
$142$	−0.0267622	+	0.561807i	−0.00224583	+	0.0471458i
$143$	0.0554505	+	0.0436067i	0.00463700	+	0.00364658i
$144$	0.0475819	+	0.998867i	0.00396516	+	0.0832389i
$145$	0.287848	−	0.404226i	0.0239045	−	0.0335691i
$146$	−9.08861	−	10.4888i	−0.752179	−	0.868061i
$147$	6.40847	−	2.81630i	0.528561	−	0.232285i
$148$	0.809049	−	1.77157i	0.0665034	−	0.145622i
$149$	−9.28221	−	8.85057i	−0.760428	−	0.725067i	0.206964	−	0.978349i	$-0.433642\pi$
$149$	−9.28221	−	8.85057i	−0.760428	−	0.725067i	−0.967393	+	0.253282i	$0.918490\pi$
$150$	−1.15988	+	4.78111i	−0.0947042	+	0.390376i
$151$	5.41593	+	7.60561i	0.440742	+	0.618936i	0.973872	−	0.227098i	$-0.0729237\pi$
$151$	5.41593	+	7.60561i	0.440742	+	0.618936i	−0.533130	+	0.846033i	$0.678984\pi$
$152$	6.11032	−	4.80521i	0.495612	−	0.389754i
$153$	−1.93065	−	2.22809i	−0.156084	−	0.180130i
$154$	−1.50301	−	1.38614i	−0.121116	−	0.111698i
$155$	−0.579473	+	0.372405i	−0.0465444	+	0.0299123i
$156$	−0.0847448	+	0.0339267i	−0.00678501	+	0.00271631i
$157$	13.1873	−	6.79853i	1.05246	−	0.542582i	0.156944	−	0.987608i	$-0.449836\pi$
$157$	13.1873	−	6.79853i	1.05246	−	0.542582i	0.895518	+	0.445026i	$0.146806\pi$
$158$	3.98296	+	11.5080i	0.316867	+	0.915528i
$159$	0.235409	+	0.970369i	0.0186691	+	0.0769553i
$160$	−0.283214			−0.0223900
$161$	5.97929	−	11.1914i	0.471234	−	0.882008i
$162$	1.00000			0.0785674
$163$	0.912771	+	3.76249i	0.0714937	+	0.294701i	0.996322	−	0.0856826i	$-0.0273071\pi$
$163$	0.912771	+	3.76249i	0.0714937	+	0.294701i	−0.924829	+	0.380384i	$0.875792\pi$
$164$	−0.136193	−	0.393505i	−0.0106349	−	0.0307276i
$165$	0.194535	−	0.100290i	0.0151445	−	0.00780753i
$166$	−12.1090	+	4.84772i	−0.939842	+	0.376256i
$167$	1.16014	−	0.745575i	0.0897741	−	0.0576943i	−0.494984	−	0.868902i	$-0.664826\pi$
$167$	1.16014	−	0.745575i	0.0897741	−	0.0576943i	0.584758	+	0.811208i	$0.301190\pi$
$168$	2.52583	−	0.787506i	0.194872	−	0.0607574i
$169$	8.50773	+	9.81845i	0.654441	+	0.755265i
$170$	0.656327	−	0.516142i	0.0503380	−	0.0395863i
$171$	−4.50902	−	6.33204i	−0.344814	−	0.484223i
$172$	1.00188	−	4.12980i	0.0763925	−	0.314894i
$173$	−7.46007	−	7.11316i	−0.567178	−	0.540804i	0.351306	−	0.936261i	$-0.385738\pi$
$173$	−7.46007	−	7.11316i	−0.567178	−	0.540804i	−0.918484	+	0.395457i	$0.870586\pi$
$174$	−0.727881	+	1.59384i	−0.0551805	+	0.120828i
$175$	13.0147	−	0.216458i	0.983822	−	0.0163627i
$176$	−0.506069	−	0.584034i	−0.0381464	−	0.0440233i
$177$	−1.73300	+	2.43366i	−0.130260	+	0.182925i
$178$	−0.857062	−	17.9919i	−0.0642395	−	1.34855i
$179$	−6.82482	−	5.36710i	−0.510111	−	0.401156i	0.329657	−	0.944101i	$-0.393067\pi$
$179$	−6.82482	−	5.36710i	−0.510111	−	0.401156i	−0.839768	+	0.542945i	$0.817309\pi$
$180$	−0.0134759	+	0.282893i	−0.00100443	+	0.0210856i
$181$	2.39422	−	2.76307i	0.177961	−	0.205378i	−0.659760	−	0.751476i	$-0.729342\pi$
$181$	2.39422	−	2.76307i	0.177961	−	0.205378i	0.837721	+	0.546099i	$0.183888\pi$
$182$	0.143344	+	0.194374i	0.0106254	+	0.0144080i
$183$	10.3829			0.767524
$184$	2.71789	−	3.95134i	0.200366	−	0.291296i
$185$	0.275789	−	0.477681i	0.0202764	−	0.0351198i
$186$	1.76024	−	1.67838i	0.129067	−	0.123065i
$187$	2.23715	+	0.431175i	0.163596	+	0.0315306i
$188$	5.59215	+	3.59386i	0.407849	+	0.262109i
$189$	−0.666430	−	2.56044i	−0.0484757	−	0.186245i
$190$	1.85205	−	1.19024i	0.134362	−	0.0863493i
$191$	12.8822	−	18.0906i	0.932125	−	1.30899i	−0.0188832	−	0.999822i	$-0.506011\pi$
$191$	12.8822	−	18.0906i	0.932125	−	1.30899i	0.951008	−	0.309165i	$-0.100050\pi$
$192$	0.981929	−	0.189251i	0.0708646	−	0.0136580i
$193$	−16.6558	−	6.66796i	−1.19891	−	0.479970i	−0.315658	−	0.948873i	$-0.602225\pi$
$193$	−16.6558	−	6.66796i	−1.19891	−	0.479970i	−0.883250	+	0.468903i	$0.844649\pi$
$194$	−10.5535	+	1.00774i	−0.757700	+	0.0723516i
$195$	−0.0248056	+	0.00728358i	−0.00177637	+	0.000521588i
$196$	−3.69966	−	5.94243i	−0.264261	−	0.424460i
$197$	−7.16360	+	15.6861i	−0.510386	+	1.11759i	0.462567	+	0.886584i	$0.346928\pi$
$197$	−7.16360	+	15.6861i	−0.510386	+	1.11759i	−0.972953	+	0.231004i	$0.925799\pi$
$198$	−0.607453	+	0.477706i	−0.0431698	+	0.0339491i
$199$	−2.35535	+	0.453956i	−0.166966	+	0.0321801i	−0.272049	−	0.962283i	$-0.587701\pi$
$199$	−2.35535	+	0.453956i	−0.166966	+	0.0321801i	0.105083	+	0.994463i	$0.466489\pi$
$200$	4.89751	+	0.467656i	0.346306	+	0.0330683i
$201$	−10.5148	−	5.42075i	−0.741656	−	0.382350i
$202$	0.725774	−	5.04787i	0.0510653	−	0.355167i
$203$	4.56601	+	0.801516i	0.320471	+	0.0562554i
$204$	−1.93065	+	2.22809i	−0.135172	+	0.155997i
$205$	−0.0278036	−	0.114608i	−0.00194189	−	0.00800458i
$206$	3.50488	−	6.07063i	0.244197	−	0.422961i
$207$	−3.81754	−	2.90283i	−0.265337	−	0.201760i
$208$	0.0456418	+	0.0790540i	0.00316469	+	0.00548141i
$209$	5.76387	+	1.69242i	0.398695	+	0.117067i
$210$	0.733313	−	0.154025i	0.0506034	−	0.0106287i
$211$	−1.26773	−	0.814724i	−0.0872745	−	0.0560879i	0.496276	−	0.868165i	$-0.334700\pi$
$211$	−1.26773	−	0.814724i	−0.0872745	−	0.0560879i	−0.583550	+	0.812077i	$0.698337\pi$
$212$	0.926990	−	0.371111i	0.0636659	−	0.0254880i
$213$	−0.0267622	−	0.561807i	−0.00183371	−	0.0384944i
$214$	17.4694	+	1.66813i	1.19419	+	0.114031i
$215$	0.393640	−	1.13735i	0.0268460	−	0.0775665i
$216$	−0.142315	−	0.989821i	−0.00968330	−	0.0673488i
$217$	−5.47047	−	3.38846i	−0.371360	−	0.230024i
$218$	−7.07604	+	2.07771i	−0.479250	+	0.140720i
$219$	10.0445	+	9.57740i	0.678743	+	0.647181i
$220$	−0.126954	−	0.178282i	−0.00855923	−	0.0120198i
$221$	−0.249843	−	0.100022i	−0.0168062	−	0.00672821i
$222$	−0.636987	+	1.84045i	−0.0427518	+	0.123523i
$223$	0.0296424	+	0.0649079i	0.00198500	+	0.00434655i	0.910622	−	0.413241i	$-0.135603\pi$
$223$	0.0296424	+	0.0649079i	0.00198500	+	0.00434655i	−0.908637	+	0.417587i	$0.862876\pi$
$224$	−1.13895	−	2.38805i	−0.0760996	−	0.159558i
$225$	0.700159	−	4.86971i	0.0466773	−	0.324648i
$226$	−0.111791	+	2.34678i	−0.00743621	+	0.156105i
$227$	−3.51125	−	10.1451i	−0.233050	−	0.673353i	−0.999517	−	0.0310701i	$-0.990108\pi$
$227$	−3.51125	−	10.1451i	−0.233050	−	0.673353i	0.766467	−	0.642283i	$-0.222013\pi$
$228$	−5.62588	+	5.36427i	−0.372583	+	0.355257i
$229$	9.69105	+	16.7854i	0.640403	+	1.10921i	0.985343	+	0.170585i	$0.0545659\pi$
$229$	9.69105	+	16.7854i	0.640403	+	1.10921i	−0.344940	+	0.938625i	$0.612101\pi$
$230$	0.872635	−	1.04084i	0.0575399	−	0.0686308i
$231$	1.62796	+	1.23699i	0.107112	+	0.0813880i
$232$	1.68120	+	0.493645i	0.110376	+	0.0324094i
$233$	−12.9666	−	2.49910i	−0.849468	−	0.163722i	−0.254103	−	0.967177i	$-0.581780\pi$
$233$	−12.9666	−	2.49910i	−0.849468	−	0.163722i	−0.595365	+	0.803456i	$0.702992\pi$
$234$	0.0811361	−	0.0418286i	0.00530404	−	0.00273442i
$235$	1.47985	+	1.16377i	0.0965350	+	0.0759159i
$236$	2.65552	+	1.36901i	0.172860	+	0.0891153i
$237$	−5.05883	−	11.0773i	−0.328606	−	0.719548i
$238$	6.99153	+	3.45845i	0.453193	+	0.224178i
$239$	1.67825	+	11.6725i	0.108557	+	0.755029i	0.969281	+	0.245957i	$0.0791022\pi$
$239$	1.67825	+	11.6725i	0.108557	+	0.755029i	−0.860724	+	0.509072i	$0.829989\pi$
$240$	0.281932	−	0.0269212i	0.0181986	−	0.00173776i
$241$	−3.92207	+	16.1670i	−0.252643	+	1.04141i	0.694218	+	0.719765i	$0.255750\pi$
$241$	−3.92207	+	16.1670i	−0.252643	+	1.04141i	−0.946861	+	0.321643i	$0.895765\pi$
$242$	−2.45255	+	10.1096i	−0.157656	+	0.649867i
$243$	−0.995472	+	0.0950560i	−0.0638596	+	0.00609785i
$244$	−1.47764	−	10.2772i	−0.0945960	−	0.657929i
$245$	−0.883073	−	1.77496i	−0.0564175	−	0.113398i
$246$	0.172982	+	0.378777i	0.0110289	+	0.0241500i
$247$	−0.630705	−	0.325151i	−0.0401308	−	0.0206889i
$248$	−1.91181	−	1.50346i	−0.121400	−	0.0954698i
$249$	11.5934	−	5.97680i	0.734700	−	0.378764i
$250$	2.75865	+	0.531687i	0.174473	+	0.0336268i
$251$	11.1594	+	3.27669i	0.704374	+	0.206823i	0.614254	−	0.789108i	$-0.289457\pi$
$251$	11.1594	+	3.27669i	0.704374	+	0.206823i	0.0901196	+	0.995931i	$0.471275\pi$
$252$	−2.43954	+	1.02404i	−0.153677	+	0.0645082i
$253$	3.70567	−	0.0603304i	0.232974	−	0.00379294i
$254$	−3.07154	−	5.32007i	−0.192726	−	0.333811i
$255$	−0.604293	+	0.576192i	−0.0378423	+	0.0360826i
$256$	−0.327068	−	0.945001i	−0.0204417	−	0.0590626i
$257$	0.736153	−	15.4537i	0.0459200	−	0.963978i	−0.851924	−	0.523665i	$-0.824564\pi$
$257$	0.736153	−	15.4537i	0.0459200	−	0.963978i	0.897844	−	0.440313i	$-0.145133\pi$
$258$	−0.604779	+	4.20633i	−0.0376519	+	0.261875i
$259$	5.13688	+	0.404435i	0.319191	+	0.0251304i
$260$	0.0107396	+	0.0235165i	0.000666045	+	0.00145843i
$261$	0.573081	−	1.65581i	0.0354728	−	0.102492i
$262$	−11.5490	−	4.62353i	−0.713501	−	0.285643i
$263$	14.7394	+	20.6986i	0.908869	+	1.27633i	0.960676	+	0.277671i	$0.0895624\pi$
$263$	14.7394	+	20.6986i	0.908869	+	1.27633i	−0.0518075	+	0.998657i	$0.516498\pi$
$264$	0.559293	+	0.533285i	0.0344221	+	0.0328214i
$265$	0.271339	−	0.0796722i	0.0166682	−	0.00489422i
$266$	17.4842	+	10.8298i	1.07202	+	0.664020i
$267$	2.56342	+	17.8290i	0.156879	+	1.09112i
$268$	−3.86916	+	11.1792i	−0.236347	+	0.682879i
$269$	−21.4106	−	2.04447i	−1.30543	−	0.124653i	−0.580944	−	0.813944i	$-0.697316\pi$
$269$	−21.4106	−	2.04447i	−1.30543	−	0.124653i	−0.724485	+	0.689290i	$0.757922\pi$
$270$	−0.0134759	−	0.282893i	−0.000820115	−	0.0172163i
$271$	0.236088	−	0.0945156i	0.0143414	−	0.00574141i	−0.364481	−	0.931211i	$-0.618753\pi$
$271$	0.236088	−	0.0945156i	0.0143414	−	0.00574141i	0.378822	+	0.925470i	$0.376329\pi$
$272$	2.48017	+	1.59391i	0.150382	+	0.0966447i
$273$	−0.161171	−	0.179869i	−0.00975453	−	0.0108861i
$274$	18.2039	+	5.34516i	1.09974	+	0.322913i
$275$	1.90098	+	3.29259i	0.114633	+	0.198551i
$276$	−2.32999	+	4.19180i	−0.140249	+	0.252316i
$277$	3.74954	−	6.49439i	0.225288	−	0.390210i	−0.731118	−	0.682251i	$-0.761001\pi$
$277$	3.74954	−	6.49439i	0.225288	−	0.390210i	0.956406	+	0.292041i	$0.0943344\pi$
$278$	0.374625	+	1.54422i	0.0224685	+	0.0926164i
$279$	−1.59272	+	1.83810i	−0.0953539	+	0.110044i
$280$	−0.256818	−	0.703929i	−0.0153478	−	0.0420678i
$281$	−0.558186	+	3.88227i	−0.0332986	+	0.231597i	−0.999674	−	0.0255393i	$-0.991870\pi$
$281$	−0.558186	+	3.88227i	−0.0332986	+	0.231597i	0.966375	+	0.257136i	$0.0827788\pi$
$282$	−5.90844	−	3.04601i	−0.351843	−	0.181388i
$283$	4.09933	+	0.391439i	0.243680	+	0.0232686i	0.216181	−	0.976353i	$-0.430640\pi$
$283$	4.09933	+	0.391439i	0.243680	+	0.0232686i	0.0274986	+	0.999622i	$0.491246\pi$
$284$	−0.552280	+	0.106443i	−0.0327718	+	0.00631625i
$285$	−1.73053	+	1.36090i	−0.102508	+	0.0806129i
$286$	−0.0293046	+	0.0641681i	−0.00173282	+	0.00379434i
$287$	0.854558	−	0.695339i	0.0504430	−	0.0410446i
$288$	−0.959493	+	0.281733i	−0.0565387	+	0.0166013i
$289$	8.27062	−	0.789748i	0.486507	−	0.0464558i
$290$	0.460694	+	0.184434i	0.0270529	+	0.0108303i
$291$	10.4100	−	2.00635i	0.610242	−	0.117615i
$292$	8.05043	−	11.3053i	0.471116	−	0.661590i
$293$	16.4099	−	10.5460i	0.958674	−	0.616102i	0.0350430	−	0.999386i	$-0.488843\pi$
$293$	16.4099	−	10.5460i	0.958674	−	0.616102i	0.923631	+	0.383284i	$0.125207\pi$
$294$	4.24777	+	5.56385i	0.247735	+	0.324490i
$295$	0.711819	+	0.457458i	0.0414437	+	0.0266343i
$296$	1.91237	+	0.368580i	0.111154	+	0.0214233i
$297$	0.559293	−	0.533285i	0.0324535	−	0.0309443i
$298$	6.41272	−	11.1072i	0.371479	−	0.643421i
$299$	−0.431161	−	0.0758420i	−0.0249347	−	0.00438606i
$300$	−4.91979			−0.284044
$301$	11.1731	−	1.25472i	0.644008	−	0.0723211i
$302$	−6.11437	+	7.05635i	−0.351842	+	0.406048i
$303$	−0.242657	+	5.09400i	−0.0139403	+	0.292643i
$304$	6.11032	+	4.80521i	0.350451	+	0.275597i
$305$	−0.139918	−	2.93724i	−0.00801169	−	0.168186i
$306$	1.71011	−	2.40152i	0.0977606	−	0.137286i
$307$	−17.1688	−	19.8139i	−0.979877	−	1.13084i	−0.991395	−	0.130905i	$-0.958212\pi$
$307$	−17.1688	−	19.8139i	−0.979877	−	1.13084i	0.0115178	−	0.999934i	$-0.496334\pi$
$308$	0.992716	−	1.78744i	0.0565652	−	0.101849i
$309$	−2.91196	+	6.37630i	−0.165656	+	0.362735i
$310$	−0.498523	−	0.475341i	−0.0283142	−	0.0269976i
$311$	−3.46429	+	14.2800i	−0.196442	+	0.809744i	0.785236	+	0.619197i	$0.212542\pi$
$311$	−3.46429	+	14.2800i	−0.196442	+	0.809744i	−0.981678	+	0.190548i	$0.938974\pi$
$312$	−0.0529497	−	0.0743575i	−0.00299769	−	0.00420966i
$313$	−23.7135	+	18.6485i	−1.34037	+	1.05408i	−0.347149	+	0.937810i	$0.612850\pi$
$313$	−23.7135	+	18.6485i	−1.34037	+	1.05408i	−0.993218	+	0.116266i	$0.962907\pi$
$314$	9.71591	+	11.2128i	0.548301	+	0.632773i
$315$	−0.715352	+	0.223033i	−0.0403055	+	0.0125665i
$316$	−10.2446	+	6.58380i	−0.576304	+	0.370368i
$317$	14.2714	−	5.71341i	0.801562	−	0.320897i	0.0655359	−	0.997850i	$-0.479124\pi$
$317$	14.2714	−	5.71341i	0.801562	−	0.320897i	0.736026	+	0.676953i	$0.236700\pi$
$318$	−0.887516	+	0.457546i	−0.0497694	+	0.0256579i
$319$	0.442870	+	1.27959i	0.0247960	+	0.0716433i
$320$	−0.0667703	−	0.275231i	−0.00373257	−	0.0153859i
$321$	−17.5489			−0.979483
$322$	12.2856	+	3.17226i	0.684651	+	0.176783i
$323$	−22.9174			−1.27516
$324$	0.235759	+	0.971812i	0.0130977	+	0.0539895i
$325$	−0.146885	−	0.424396i	−0.00814771	−	0.0235413i
$326$	−3.44124	+	1.77408i	−0.190593	+	0.0982573i
$327$	6.84650	−	2.74093i	0.378612	−	0.151574i
$328$	0.350304	−	0.225127i	0.0193423	−	0.0124305i
$329$	−3.86158	+	17.1582i	−0.212896	+	0.945962i
$330$	0.143326	+	0.165407i	0.00788983	+	0.00910534i
$331$	3.18889	−	2.50777i	0.175277	−	0.137839i	−0.526666	−	0.850072i	$-0.676558\pi$
$331$	3.18889	−	2.50777i	0.175277	−	0.137839i	0.701944	+	0.712233i	$0.252316\pi$
$332$	−7.56588	−	10.6248i	−0.415231	−	0.583111i
$333$	0.459157	−	1.89267i	0.0251616	−	0.103718i
$334$	0.998071	+	0.951659i	0.0546120	+	0.0520724i
$335$	−1.39180	+	3.04761i	−0.0760420	+	0.166509i
$336$	1.36080	+	2.26897i	0.0742375	+	0.123783i
$337$	1.73956	+	2.00756i	0.0947600	+	0.109359i	0.801149	−	0.598465i	$-0.204222\pi$
$337$	1.73956	+	2.00756i	0.0947600	+	0.109359i	−0.706389	+	0.707824i	$0.749677\pi$
$338$	−7.53591	+	10.5827i	−0.409899	+	0.575623i
$339$	−0.111791	−	2.34678i	−0.00607164	−	0.127459i
$340$	0.656327	+	0.516142i	0.0355944	+	0.0279917i
$341$	0.0894323	−	1.87741i	0.00484303	−	0.101668i
$342$	5.09050	−	5.87475i	0.275263	−	0.317670i
$343$	11.4151	−	14.5841i	0.616357	−	0.787467i
$344$	4.24958			0.229122
$345$	−0.769746	+	1.11907i	−0.0414417	+	0.0602489i
$346$	5.15387	−	8.92677i	0.277074	−	0.479906i
$347$	11.7154	−	11.1706i	0.628915	−	0.599669i	−0.307080	−	0.951684i	$-0.599352\pi$
$347$	11.7154	−	11.1706i	0.628915	−	0.599669i	0.935994	+	0.352015i	$0.114503\pi$
$348$	−1.72051	−	0.331602i	−0.0922292	−	0.0177757i
$349$	14.1930	+	9.12131i	0.759736	+	0.488252i	0.862252	−	0.506479i	$-0.169053\pi$
$349$	14.1930	+	9.12131i	0.759736	+	0.488252i	−0.102517	+	0.994731i	$0.532690\pi$
$350$	3.27870	+	12.5968i	0.175254	+	0.673330i
$351$	−0.0767927	+	0.0493517i	−0.00409889	+	0.00263420i
$352$	0.448261	−	0.629495i	0.0238924	−	0.0335522i
$353$	−20.8948	+	4.02714i	−1.11212	+	0.214343i	−0.712040	−	0.702138i	$-0.752229\pi$
$353$	−20.8948	+	4.02714i	−1.11212	+	0.214343i	−0.400077	+	0.916481i	$0.631017\pi$
$354$	−2.77363	−	1.11039i	−0.147417	−	0.0590167i
$355$	−0.158571	+	0.0151417i	−0.00841607	+	0.000803637i
$356$	17.2827	−	5.07467i	0.915983	−	0.268957i
$357$	−7.28862	−	2.77820i	−0.385754	−	0.147038i
$358$	3.60680	−	7.89778i	0.190625	−	0.417411i
$359$	19.2704	−	15.1544i	1.01705	−	0.799818i	0.0371521	−	0.999310i	$-0.488171\pi$
$359$	19.2704	−	15.1544i	1.01705	−	0.799818i	0.979900	+	0.199491i	$0.0639290\pi$
$360$	−0.278096	+	0.0535986i	−0.0146569	+	0.00282490i
$361$	−41.2384	−	3.93779i	−2.17044	−	0.207252i
$362$	3.24964	+	1.67531i	0.170797	+	0.0880522i
$363$	1.48047	−	10.2969i	0.0777047	−	0.540448i
$364$	−0.155101	+	0.185129i	−0.00812949	+	0.00970339i
$365$	2.57402	−	2.97058i	0.134731	−	0.155487i
$366$	2.44785	+	10.0902i	0.127951	+	0.527423i
$367$	10.3881	−	17.9928i	0.542256	−	0.939214i	−0.456519	−	0.889714i	$-0.650904\pi$
$367$	10.3881	−	17.9928i	0.542256	−	0.939214i	0.998774	−	0.0495002i	$-0.0157629\pi$
$368$	4.48072	+	1.70972i	0.233574	+	0.0891252i
$369$	−0.208204	−	0.360619i	−0.0108386	−	0.0187731i
$370$	0.529236	+	0.155398i	0.0275137	+	0.00807874i
$371$	1.76299	+	1.96751i	0.0915298	+	0.102148i
$372$	2.04606	+	1.31492i	0.106083	+	0.0681756i
$373$	11.8881	−	4.75927i	0.615542	−	0.246426i	−0.0428735	−	0.999081i	$-0.513651\pi$
$373$	11.8881	−	4.75927i	0.615542	−	0.246426i	0.658416	+	0.752655i	$0.271227\pi$
$374$	0.108407	+	2.27574i	0.00560558	+	0.117676i
$375$	−2.79670	−	0.267053i	−0.144421	−	0.0137905i
$376$	−2.17415	+	6.28180i	−0.112123	+	0.323959i
$377$	−0.0227626	−	0.158317i	−0.00117233	−	0.00815374i
$378$	2.33115	−	1.25129i	0.119901	−	0.0643595i
$379$	−31.9909	+	9.39337i	−1.64326	+	0.482505i	−0.967131	−	0.254277i	$-0.918163\pi$
$379$	−31.9909	+	9.39337i	−1.64326	+	0.482505i	−0.676130	+	0.736782i	$0.736344\pi$
$380$	1.59333	+	1.51924i	0.0817361	+	0.0779352i
$381$	3.56334	+	5.00401i	0.182555	+	0.256363i
$382$	20.6177	+	8.25409i	1.05489	+	0.422316i
$383$	−7.49856	+	21.6657i	−0.383158	+	1.10706i	0.574338	+	0.818618i	$0.305260\pi$
$383$	−7.49856	+	21.6657i	−0.383158	+	1.10706i	−0.957496	+	0.288445i	$0.906862\pi$
$384$	0.415415	+	0.909632i	0.0211991	+	0.0464195i
$385$	0.327998	−	0.477210i	0.0167163	−	0.0243209i
$386$	2.55326	−	17.7583i	0.129957	−	0.903873i
$387$	0.202203	−	4.24477i	0.0102786	−	0.215774i
$388$	−3.46742	−	10.0185i	−0.176032	−	0.508610i
$389$	−9.61401	+	9.16694i	−0.487450	+	0.464782i	−0.893497	−	0.449070i	$-0.851755\pi$
$389$	−9.61401	+	9.16694i	−0.487450	+	0.464782i	0.406047	+	0.913852i	$0.366907\pi$
$390$	−0.0129264	−	0.0223892i	−0.000654554	−	0.00113372i
$391$	−13.4996	+	4.20372i	−0.682704	+	0.212591i
$392$	4.90270	−	4.99635i	0.247624	−	0.252354i
$393$	11.9362	+	3.50479i	0.602103	+	0.176793i
$394$	−16.9328	−	3.26353i	−0.853063	−	0.164414i
$395$	−3.06552	+	1.58039i	−0.154243	+	0.0795179i
$396$	−0.607453	−	0.477706i	−0.0305256	−	0.0240056i
$397$	8.91755	+	4.59732i	0.447559	+	0.230733i	0.667246	−	0.744838i	$-0.267473\pi$
$397$	8.91755	+	4.59732i	0.447559	+	0.230733i	−0.219686	+	0.975571i	$0.570503\pi$
$398$	−0.996453	−	2.18193i	−0.0499477	−	0.109370i
$399$	−18.4344	−	9.11883i	−0.922876	−	0.456513i
$400$	0.700159	+	4.86971i	0.0350080	+	0.243486i
$401$	1.78501	−	0.170448i	0.0891393	−	0.00851177i	−0.0503911	−	0.998730i	$-0.516047\pi$
$401$	1.78501	−	0.170448i	0.0891393	−	0.00851177i	0.139530	+	0.990218i	$0.455441\pi$
$402$	2.78899	−	11.4964i	0.139102	−	0.573387i
$403$	−0.0523423	+	0.215758i	−0.00260736	+	0.0107477i
$404$	5.07669	−	0.484765i	0.252575	−	0.0241180i
$405$	0.0403056	+	0.280331i	0.00200280	+	0.0139298i
$406$	0.297555	+	4.62626i	0.0147674	+	0.229598i
$407$	0.625224	+	1.36905i	0.0309912	+	0.0678612i
$408$	−2.62045	−	1.35093i	−0.129731	−	0.0668812i
$409$	−12.7216	−	10.0044i	−0.629042	−	0.494684i	0.251997	−	0.967728i	$-0.418913\pi$
$409$	−12.7216	−	10.0044i	−0.629042	−	0.494684i	−0.881039	+	0.473044i	$0.843155\pi$
$410$	0.104823	−	0.0540398i	0.00517682	−	0.00266883i
$411$	−18.6296	−	3.59056i	−0.918931	−	0.177109i
$412$	6.72582	+	1.97488i	0.331357	+	0.0972953i
$413$	−0.994668	+	7.84172i	−0.0489444	+	0.385866i
$414$	1.92098	−	4.39429i	0.0944112	−	0.215968i
$415$	−1.84703	−	3.19915i	−0.0906670	−	0.157040i
$416$	−0.0660651	+	0.0629929i	−0.00323911	+	0.00308848i
$417$	−0.519716	−	1.50162i	−0.0254506	−	0.0735347i
$418$	−0.285834	+	6.00040i	−0.0139806	+	0.293489i
$419$	−3.43151	+	23.8667i	−0.167640	+	1.16596i	0.716104	+	0.697994i	$0.245924\pi$
$419$	−3.43151	+	23.8667i	−0.167640	+	1.16596i	−0.883744	+	0.467970i	$0.844985\pi$
$420$	0.322568	+	0.676329i	0.0157397	+	0.0330015i
$421$	−11.9894	−	26.2531i	−0.584328	−	1.27950i	−0.938810	−	0.344437i	$-0.888070\pi$
$421$	−11.9894	−	26.2531i	−0.584328	−	1.27950i	0.354482	−	0.935063i	$-0.384657\pi$
$422$	0.492878	−	1.42408i	0.0239929	−	0.0693230i
$423$	6.17123	+	2.47059i	0.300056	+	0.120124i
$424$	0.579196	+	0.813367i	0.0281282	+	0.0395006i
$425$	−10.4973	−	10.0092i	−0.509196	−	0.485517i
$426$	0.539661	−	0.158459i	0.0261467	−	0.00767736i
$427$	24.2040	−	12.9920i	1.17132	−	0.628727i
$428$	2.49747	+	17.3703i	0.120720	+	0.839623i
$429$	0.0230723	−	0.0666631i	0.00111394	−	0.00321853i
$430$	1.19809	+	0.114404i	0.0577772	+	0.00551705i
$431$	−0.929042	−	19.5030i	−0.0447504	−	0.939426i	−0.903911	−	0.427720i	$-0.859317\pi$
$431$	−0.929042	−	19.5030i	−0.0447504	−	0.939426i	0.859161	−	0.511706i	$-0.170986\pi$
$432$	0.928368	−	0.371662i	0.0446661	−	0.0178816i
$433$	−0.368053	−	0.236533i	−0.0176875	−	0.0113671i	0.531767	−	0.846891i	$-0.321528\pi$
$433$	−0.368053	−	0.236533i	−0.0176875	−	0.0113671i	−0.549455	+	0.835524i	$0.685164\pi$
$434$	2.00323	−	6.11513i	0.0961581	−	0.293536i
$435$	−0.476140	−	0.139807i	−0.0228292	−	0.00670325i
$436$	−3.68738	−	6.38674i	−0.176594	−	0.305869i
$437$	−36.4866	+	7.65024i	−1.74539	+	0.365961i
$438$	−6.93935	+	12.0193i	−0.331575	+	0.574305i
$439$	1.49206	+	6.15036i	0.0712122	+	0.293541i	0.996271	−	0.0862842i	$-0.0274993\pi$
$439$	1.49206	+	6.15036i	0.0712122	+	0.293541i	−0.925058	+	0.379825i	$0.875984\pi$
$440$	0.143326	−	0.165407i	0.00683279	−	0.00788546i
$441$	−4.75741	−	5.13488i	−0.226543	−	0.244518i
$442$	0.0382998	−	0.266381i	0.00182174	−	0.0126705i
$443$	14.6915	+	7.57400i	0.698015	+	0.359852i	0.770431	−	0.637523i	$-0.220041\pi$
$443$	14.6915	+	7.57400i	0.698015	+	0.359852i	−0.0724168	+	0.997374i	$0.523071\pi$
$444$	−1.93875	−	0.185128i	−0.0920090	−	0.00878579i
$445$	5.00916	−	0.965437i	0.237457	−	0.0457661i
$446$	−0.0560898	+	0.0441095i	−0.00265593	+	0.00208864i
$447$	−5.32788	+	11.6664i	−0.252000	+	0.551803i
$448$	2.05222	−	1.66985i	0.0969581	−	0.0788931i
$449$	−5.13812	+	1.50869i	−0.242483	+	0.0711994i	−0.400716	−	0.916202i	$-0.631239\pi$
$449$	−5.13812	+	1.50869i	−0.242483	+	0.0711994i	0.158233	+	0.987402i	$0.449420\pi$
$450$	4.89751	−	0.467656i	0.230871	−	0.0220455i
$451$	0.298744	+	0.119599i	0.0140673	+	0.00563170i
$452$	−2.30698	+	0.444634i	−0.108511	+	0.0209138i
$453$	5.41593	−	7.60561i	0.254463	−	0.357343i
$454$	9.03131	−	5.80407i	0.423860	−	0.272398i
$455$	−0.0487117	+	0.0480182i	−0.00228364	+	0.00225113i
$456$	−6.53941	−	4.20262i	−0.306236	−	0.196806i
$457$	−8.42562	−	1.62391i	−0.394134	−	0.0759631i	−0.0116662	−	0.999932i	$-0.503714\pi$
$457$	−8.42562	−	1.62391i	−0.394134	−	0.0759631i	−0.382468	+	0.923969i	$0.624926\pi$
$458$	−14.0275	+	13.3752i	−0.655461	+	0.624981i
$459$	−1.47409	+	2.55320i	−0.0688046	+	0.119173i
$460$	1.21723	+	0.602650i	0.0567536	+	0.0280987i
$461$	−35.6889			−1.66220			−0.831099	−	0.556124i	$-0.812288\pi$
$461$	−35.6889			−1.66220			−0.831099	+	0.556124i	$0.812288\pi$
$462$	−0.818314	+	1.87371i	−0.0380714	+	0.0871727i
$463$	−13.8512	+	15.9851i	−0.643720	+	0.742893i	−0.980028	−	0.198860i	$-0.936276\pi$
$463$	−13.8512	+	15.9851i	−0.643720	+	0.742893i	0.336308	+	0.941752i	$0.390822\pi$
$464$	−0.0833719	+	1.75019i	−0.00387044	+	0.0812506i
$465$	0.541450	+	0.425801i	0.0251091	+	0.0197461i
$466$	−0.628329	−	13.1902i	−0.0291068	−	0.611026i
$467$	6.67401	−	9.37233i	0.308836	−	0.433700i	−0.630763	−	0.775975i	$-0.717258\pi$
$467$	6.67401	−	9.37233i	0.308836	−	0.433700i	0.939600	+	0.342275i	$0.111198\pi$
$468$	0.0597781	+	0.0689876i	0.00276324	+	0.00318895i
$469$	−31.2945	+	0.520483i	−1.44505	+	0.0240337i
$470$	−0.782076	+	1.71251i	−0.0360745	+	0.0789921i
$471$	−10.7378	−	10.2384i	−0.494770	−	0.471762i
$472$	−0.704362	+	2.90342i	−0.0324209	+	0.133641i
$473$	1.90492	+	2.67509i	0.0875885	+	0.123001i
$474$	9.57238	−	7.52780i	0.439674	−	0.345763i
$475$	−25.0442	−	28.9026i	−1.14911	−	1.32614i
$476$	−1.71264	+	7.60981i	−0.0784989	+	0.348795i
$477$	0.840005	−	0.539838i	0.0384612	−	0.0247175i
$478$	−10.9478	+	4.38283i	−0.500740	+	0.200466i
$479$	−11.6538	+	6.00794i	−0.532475	+	0.274510i	−0.703425	−	0.710770i	$-0.748347\pi$
$479$	−11.6538	+	6.00794i	−0.532475	+	0.274510i	0.170950	+	0.985280i	$0.445316\pi$
$480$	0.0926303	+	0.267638i	0.00422797	+	0.0122159i
$481$	−0.0419135	−	0.172770i	−0.00191109	−	0.00787762i
$482$	−16.6359			−0.757746
$483$	−12.5315	−	1.99008i	−0.570205	−	0.0905516i
$484$	−10.4028			−0.472854
$485$	−0.707868	−	2.91787i	−0.0321426	−	0.132494i
$486$	−0.327068	−	0.945001i	−0.0148361	−	0.0428661i
$487$	−37.6988	+	19.4351i	−1.70830	+	0.880688i	−0.727385	+	0.686229i	$0.759265\pi$
$487$	−37.6988	+	19.4351i	−1.70830	+	0.880688i	−0.980911	+	0.194459i	$0.937705\pi$
$488$	9.63912	−	3.85892i	0.436343	−	0.174685i
$489$	3.25702	−	2.09316i	0.147288	−	0.0946559i
$490$	1.51673	−	1.27664i	0.0685191	−	0.0576729i
$491$	6.92330	+	7.98991i	0.312444	+	0.360580i	0.890152	−	0.455664i	$-0.150598\pi$
$491$	6.92330	+	7.98991i	0.312444	+	0.360580i	−0.577708	+	0.816244i	$0.696053\pi$
$492$	−0.327318	+	0.257406i	−0.0147566	+	0.0116048i
$493$	−2.99642	−	4.20788i	−0.134952	−	0.189513i
$494$	0.167291	−	0.689583i	0.00752678	−	0.0310258i
$495$	−0.158400	−	0.151034i	−0.00711954	−	0.00678847i
$496$	1.01035	−	2.21237i	0.0453663	−	0.0993383i
$497$	−0.765372	−	1.27617i	−0.0343316	−	0.0572441i
$498$	8.54157	+	9.85749i	0.382757	+	0.441725i
$499$	−4.90215	+	6.88411i	−0.219450	+	0.308175i	−0.909595	−	0.415497i	$-0.863608\pi$
$499$	−4.90215	+	6.88411i	−0.219450	+	0.308175i	0.690144	+	0.723672i	$0.257547\pi$
$500$	0.133678	+	2.80624i	0.00597825	+	0.125499i
$501$	−1.08401	−	0.852477i	−0.0484301	−	0.0380859i
$502$	−0.553401	+	11.6173i	−0.0246995	+	0.518507i
$503$	12.1962	−	14.0752i	0.543803	−	0.627582i	−0.415625	−	0.909536i	$-0.636437\pi$
$503$	12.1962	−	14.0752i	0.543803	−	0.627582i	0.959428	+	0.281954i	$0.0909826\pi$
$504$	−1.57031	−	2.12935i	−0.0699473	−	0.0948486i
$505$	1.44433			0.0642718
$506$	0.932275	+	3.58699i	0.0414447	+	0.159461i
$507$	6.49583	−	11.2511i	0.288490	−	0.499680i
$508$	4.44596	−	4.23922i	0.197258	−	0.188085i
$509$	40.3315	+	7.77326i	1.78766	+	0.344543i	0.972179	−	0.234239i	$-0.0752597\pi$
$509$	40.3315	+	7.77326i	1.78766	+	0.344543i	0.815482	+	0.578782i	$0.196472\pi$
$510$	−0.702418	−	0.451417i	−0.0311036	−	0.0199891i
$511$	35.3993	+	9.75778i	1.56597	+	0.431659i
$512$	0.841254	−	0.540641i	0.0371785	−	0.0238932i
$513$	−4.50902	+	6.33204i	−0.199078	+	0.279566i
$514$	15.1917	−	2.92796i	0.670077	−	0.129147i
$515$	1.84305	+	0.737848i	0.0812147	+	0.0325135i
$516$	−4.23034	+	0.403949i	−0.186230	+	0.0177829i
$517$	−4.92895	+	1.44727i	−0.216775	+	0.0636508i
$518$	0.818032	+	5.08743i	0.0359422	+	0.223529i
$519$	−4.28199	+	9.37626i	−0.187959	+	0.411572i
$520$	−0.0203217	+	0.0159811i	−0.000891165	+	0.000700820i
$521$	−15.2442	+	2.93809i	−0.667862	+	0.128720i	−0.511903	−	0.859043i	$-0.671059\pi$
$521$	−15.2442	+	2.93809i	−0.667862	+	0.128720i	−0.155960	+	0.987763i	$0.549847\pi$
$522$	1.74424	+	0.166555i	0.0763434	+	0.00728991i
$523$	1.61556	+	0.832881i	0.0706436	+	0.0364193i	0.493186	−	0.869924i	$-0.335832\pi$
$523$	1.61556	+	0.832881i	0.0706436	+	0.0364193i	−0.422543	+	0.906343i	$0.638862\pi$
$524$	1.77042	−	12.3135i	0.0773410	−	0.537919i
$525$	−4.46126	−	12.2281i	−0.194705	−	0.533680i
$526$	−16.6402	+	19.2038i	−0.725545	+	0.837324i
$527$	1.69049	+	6.96831i	0.0736391	+	0.303544i
$528$	−0.386394	+	0.669254i	−0.0168156	+	0.0291256i
$529$	−20.0893	+	11.1991i	−0.873448	+	0.486918i
$530$	0.141397	+	0.244907i	0.00614189	+	0.0106381i
$531$	2.86662	+	0.841715i	0.124401	+	0.0365273i
$532$	−6.40252	+	19.5446i	−0.277584	+	0.847364i
$533$	−0.0319770	−	0.0205504i	−0.00138508	−	0.000890136i
$534$	−16.7221	+	6.69451i	−0.723636	+	0.289700i
$535$	0.236486	+	4.96446i	0.0102242	+	0.214632i
$536$	−11.7763	−	1.12450i	−0.508658	−	0.0485709i
$537$	−2.83973	+	8.20487i	−0.122543	+	0.354066i
$538$	−3.06091	−	21.2891i	−0.131965	−	0.917838i
$539$	5.34287	+	0.846553i	0.230134	+	0.0364636i
$540$	0.271742	−	0.0797906i	0.0116939	−	0.00343364i
$541$	17.5706	+	16.7535i	0.755418	+	0.720290i	0.966356	−	0.257210i	$-0.0828032\pi$
$541$	17.5706	+	16.7535i	0.755418	+	0.720290i	−0.210938	+	0.977500i	$0.567652\pi$
$542$	0.147511	+	0.207151i	0.00633615	+	0.00889788i
$543$	−3.39418	−	1.35882i	−0.145658	−	0.0583127i
$544$	−0.964255	+	2.78603i	−0.0413421	+	0.119450i
$545$	−0.867652	−	1.89989i	−0.0371661	−	0.0813825i
$546$	0.136801	−	0.199034i	0.00585454	−	0.00851786i
$547$	−0.159348	+	1.10829i	−0.00681322	+	0.0473870i	−0.992944	−	0.118581i	$-0.962166\pi$
$547$	−0.159348	+	1.10829i	−0.00681322	+	0.0473870i	0.986131	+	0.165968i	$0.0530747\pi$
$548$	−0.902746	+	18.9510i	−0.0385634	+	0.809546i
$549$	−3.39590	−	9.81182i	−0.144934	−	0.418758i
$550$	−2.75161	+	2.62365i	−0.117329	+	0.111873i
$551$	−6.81020	−	11.7956i	−0.290124	−	0.502510i
$552$	−4.62295	−	1.27606i	−0.196766	−	0.0543126i
$553$	−25.6538	−	19.4928i	−1.09091	−	0.828917i
$554$	7.19531	+	2.11273i	0.305700	+	0.0897615i
$555$	−0.541611	−	0.104387i	−0.0229901	−	0.00443098i
$556$	−1.41237	+	0.728129i	−0.0598980	+	0.0308795i
$557$	5.77256	+	4.53959i	0.244591	+	0.192349i	0.732927	−	0.680307i	$-0.238154\pi$
$557$	5.77256	+	4.53959i	0.244591	+	0.192349i	−0.488336	+	0.872656i	$0.662396\pi$
$558$	−2.16179	−	1.11448i	−0.0915158	−	0.0471797i
$559$	−0.161147	−	0.352862i	−0.00681578	−	0.0149245i
$560$	0.623539	−	0.415536i	0.0263493	−	0.0175596i
$561$	−0.324239	−	2.25513i	−0.0136894	−	0.0952116i
$562$	−3.90443	+	0.372828i	−0.164698	+	0.0157268i
$563$	0.405256	−	1.67049i	0.0170795	−	0.0704027i	−0.962634	−	0.270806i	$-0.912710\pi$
$563$	0.405256	−	1.67049i	0.0170795	−	0.0704027i	0.979714	+	0.200403i	$0.0642251\pi$
$564$	1.56718	−	6.46002i	0.0659903	−	0.272016i
$565$	−0.662381	+	0.0632497i	−0.0278666	+	0.00266094i
$566$	0.586049	+	4.07606i	0.0246335	+	0.171330i
$567$	−2.20165	+	1.46722i	−0.0924607	+	0.0616173i
$568$	−0.233648	−	0.511617i	−0.00980364	−	0.0214670i
$569$	37.7294	+	19.4508i	1.58170	+	0.815421i	0.999998	+	0.00201717i	$0.000642086\pi$
$569$	37.7294	+	19.4508i	1.58170	+	0.815421i	0.581699	+	0.813404i	$0.302388\pi$
$570$	−1.73053	−	1.36090i	−0.0724838	−	0.0570019i
$571$	−2.70029	+	1.39210i	−0.113004	+	0.0582574i	−0.513802	−	0.857909i	$-0.671763\pi$
$571$	−2.70029	+	1.39210i	−0.113004	+	0.0582574i	0.400798	+	0.916166i	$0.368733\pi$
$572$	−0.0692681	−	0.0133503i	−0.00289625	−	0.000558206i
$573$	−21.3090	−	6.25687i	−0.890194	−	0.261385i
$574$	0.877208	+	0.666537i	0.0366140	+	0.0278207i
$575$	−20.0540	−	12.4313i	−0.836308	−	0.518423i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	6.72287	−	6.41024i	0.279877	−	0.266862i	−0.537118	−	0.843507i	$-0.680487\pi$
$577$	6.72287	−	6.41024i	0.279877	−	0.266862i	0.816995	+	0.576645i	$0.195639\pi$
$578$	2.71736	+	7.85129i	0.113027	+	0.326571i
$579$	−0.853662	+	17.9206i	−0.0354770	+	0.744754i
$580$	−0.0706225	+	0.491190i	−0.00293244	+	0.0203956i
$581$	19.5472	−	28.4395i	0.810954	−	1.17987i
$582$	4.40404	+	9.64350i	0.182553	+	0.399736i
$583$	−0.252379	+	0.729202i	−0.0104525	+	0.0302004i
$584$	12.8845	+	5.15819i	0.533166	+	0.213447i
$585$	0.0149961	+	0.0210591i	0.000620013	+	0.000870686i
$586$	14.1175	+	13.4610i	0.583187	+	0.556068i
$587$	26.8290	−	7.87771i	1.10735	−	0.325148i	0.323583	−	0.946200i	$-0.395113\pi$
$587$	26.8290	−	7.87771i	1.10735	−	0.325148i	0.783770	+	0.621052i	$0.213294\pi$
$588$	−4.40557	+	5.43976i	−0.181682	+	0.224332i
$589$	2.69063	+	18.7137i	0.110865	+	0.771086i
$590$	−0.276746	+	0.799604i	−0.0113934	+	0.0329192i
$591$	17.1664	+	1.63919i	0.706130	+	0.0674272i
$592$	0.0926690	+	1.94536i	0.00380867	+	0.0799539i
$593$	5.32697	−	2.13260i	0.218752	−	0.0875752i	−0.259698	−	0.965690i	$-0.583623\pi$
$593$	5.32697	−	2.13260i	0.218752	−	0.0875752i	0.478450	+	0.878115i	$0.341199\pi$
$594$	0.650111	+	0.417801i	0.0266744	+	0.0171426i
$595$	−0.687714	+	2.09934i	−0.0281935	+	0.0860645i
$596$	12.3059	+	3.61335i	0.504070	+	0.148008i
$597$	1.19935	+	2.07733i	0.0490860	+	0.0850194i
$598$	−0.0279460	−	0.436888i	−0.00114280	−	0.0178657i
$599$	−6.39632	+	11.0788i	−0.261347	+	0.452666i	−0.966600	−	0.256290i	$-0.917500\pi$
$599$	−6.39632	+	11.0788i	−0.261347	+	0.452666i	0.705253	+	0.708955i	$0.250833\pi$
$600$	−1.15988	−	4.78111i	−0.0473521	−	0.195188i
$601$	−22.6452	+	26.1339i	−0.923716	+	1.06603i	0.0739167	+	0.997264i	$0.476450\pi$
$601$	−22.6452	+	26.1339i	−0.923716	+	1.06603i	−0.997633	+	0.0687612i	$0.978095\pi$
$602$	3.85352	+	10.5623i	0.157058	+	0.430489i
$603$	−1.68356	+	11.7094i	−0.0685600	+	0.476845i
$604$	−8.29896	−	4.27841i	−0.337680	−	0.174086i
$605$	−2.93288	−	0.280056i	−0.119238	−	0.0113859i
$606$	−5.00762	+	0.965140i	−0.203421	+	0.0392061i
$607$	9.47481	−	7.45108i	0.384571	−	0.302430i	−0.407093	−	0.913387i	$-0.633458\pi$
$607$	9.47481	−	7.45108i	0.384571	−	0.302430i	0.791664	+	0.610957i	$0.209215\pi$
$608$	−3.22919	+	7.07095i	−0.130961	+	0.286765i
$609$	−0.735962	−	4.57703i	−0.0298227	−	0.185471i
$610$	2.82146	−	0.828456i	0.114238	−	0.0335432i
$611$	0.604051	−	0.0576799i	0.0244373	−	0.00233348i
$612$	2.73699	+	1.09573i	0.110636	+	0.0442922i
$613$	−41.6572	+	8.02878i	−1.68252	+	0.324279i	−0.938865	−	0.344284i	$-0.888122\pi$
$613$	−41.6572	+	8.02878i	−1.68252	+	0.324279i	−0.743655	+	0.668564i	$0.766909\pi$
$614$	15.2077	−	21.3562i	0.613731	−	0.861865i
$615$	−0.0992111	+	0.0637591i	−0.00400058	+	0.00257101i
$616$	1.97109	+	0.543329i	0.0794176	+	0.0218913i
$617$	−1.06395	−	0.683761i	−0.0428331	−	0.0275272i	0.519049	−	0.854744i	$-0.326286\pi$
$617$	−1.06395	−	0.683761i	−0.0428331	−	0.0275272i	−0.561882	+	0.827217i	$0.689923\pi$
$618$	−6.88309	−	1.32661i	−0.276878	−	0.0533639i
$619$	25.2019	−	24.0300i	1.01295	−	0.965846i	0.0135307	−	0.999908i	$-0.495693\pi$
$619$	25.2019	−	24.0300i	1.01295	−	0.965846i	0.999420	+	0.0340622i	$0.0108444\pi$
$620$	0.344411	−	0.596537i	0.0138319	−	0.0239575i
$621$	−1.49458	+	4.55700i	−0.0599754	+	0.182866i
$622$	−14.6942			−0.589184
$623$	28.2850	+	38.3545i	1.13322	+	1.53664i
$624$	0.0597781	−	0.0689876i	0.00239304	−	0.00276171i
$625$	1.13261	−	23.7763i	0.0453042	−	0.951053i
$626$	−23.7135	−	18.6485i	−0.947783	−	0.745344i
$627$	−0.285834	−	6.00040i	−0.0114151	−	0.239633i
$628$	−8.60608	+	12.0855i	−0.343420	+	0.482266i
$629$	−3.76007	−	4.33935i	−0.149924	−	0.173021i
$630$	−0.385396	−	0.642605i	−0.0153546	−	0.0256020i
$631$	−15.5515	+	34.0530i	−0.619094	+	1.35563i	0.297082	+	0.954852i	$0.403987\pi$
$631$	−15.5515	+	34.0530i	−0.619094	+	1.35563i	−0.916176	+	0.400775i	$0.868741\pi$
$632$	−8.81347	−	8.40363i	−0.350581	−	0.334278i
$633$	−0.355279	+	1.46448i	−0.0141211	+	0.0582079i
$634$	8.91697	+	12.5221i	0.354138	+	0.497317i
$635$	1.36758	−	1.07548i	0.0542708	−	0.0426791i
$636$	−0.653889	−	0.754628i	−0.0259284	−	0.0299229i
$637$	−0.600783	−	0.217629i	−0.0238039	−	0.00862276i
$638$	−1.13911	+	0.732061i	−0.0450978	+	0.0289826i
$639$	−0.522155	+	0.209039i	−0.0206561	+	0.00826947i
$640$	0.251731	−	0.129776i	0.00995053	−	0.00512985i
$641$	−11.1226	−	32.1365i	−0.439315	−	1.26932i	−0.919825	−	0.392328i	$-0.871670\pi$
$641$	−11.1226	−	32.1365i	−0.439315	−	1.26932i	0.480511	−	0.876989i	$-0.340451\pi$
$642$	−4.13731	−	17.0542i	−0.163286	−	0.673076i
$643$	13.3995			0.528424			0.264212	−	0.964465i	$-0.414888\pi$
$643$	13.3995			0.528424			0.264212	+	0.964465i	$0.414888\pi$
$644$	−0.186395	+	12.6872i	−0.00734500	+	0.499946i
$645$	−1.20354			−0.0473894
$646$	−5.40299	−	22.2714i	−0.212578	−	0.876257i
$647$	6.23318	+	18.0096i	0.245052	+	0.708030i	0.998711	+	0.0507645i	$0.0161658\pi$
$647$	6.23318	+	18.0096i	0.245052	+	0.708030i	−0.753659	+	0.657266i	$0.771713\pi$
$648$	−0.888835	+	0.458227i	−0.0349168	+	0.0180008i
$649$	−2.14343	+	0.858099i	−0.0841369	+	0.0336833i
$650$	0.377804	−	0.242800i	0.0148187	−	0.00952339i
$651$	−1.41288	+	6.27786i	−0.0553751	+	0.246049i
$652$	−2.53538	−	2.92598i	−0.0992930	−	0.114590i
$653$	19.6832	−	15.4790i	0.770263	−	0.605742i	−0.153747	−	0.988110i	$-0.549134\pi$
$653$	19.6832	−	15.4790i	0.770263	−	0.605742i	0.924010	+	0.382368i	$0.124891\pi$
$654$	4.27779	+	6.00731i	0.167275	+	0.234904i
$655$	0.830631	−	3.42391i	0.0324555	−	0.133783i
$656$	0.301368	+	0.287354i	0.0117664	+	0.0112193i
$657$	5.76542	−	12.6245i	0.224930	−	0.492529i
$658$	−17.5849	+	0.292469i	−0.685532	+	0.0114016i
$659$	13.5880	+	15.6814i	0.529313	+	0.610859i	0.955938	−	0.293569i	$-0.0948431\pi$
$659$	13.5880	+	15.6814i	0.529313	+	0.610859i	−0.426625	+	0.904429i	$0.640298\pi$
$660$	−0.126954	+	0.178282i	−0.00494167	+	0.00693961i
$661$	0.289715	+	6.08186i	0.0112686	+	0.236557i	0.997474	+	0.0710314i	$0.0226291\pi$
$661$	0.289715	+	6.08186i	0.0112686	+	0.236557i	−0.986205	+	0.165526i	$0.947068\pi$
$662$	3.18889	+	2.50777i	0.123940	+	0.0974672i
$663$	−0.0128053	+	0.268816i	−0.000497315	+	0.0104399i
$664$	8.54157	−	9.85749i	0.331477	−	0.382545i
$665$	−2.33124	+	5.33786i	−0.0904015	+	0.206994i
$666$	1.94757			0.0754667
$667$	−6.17523	−	5.69907i	−0.239106	−	0.220669i
$668$	−0.689529	+	1.19430i	−0.0266787	+	0.0462088i
$669$	0.0516429	−	0.0492414i	0.00199663	−	0.00190378i
$670$	−3.28983	−	0.634063i	−0.127097	−	0.0244960i
$671$	6.75002	+	4.33797i	0.260581	+	0.167466i
$672$	−1.88419	+	1.85737i	−0.0726844	+	0.0716495i
$673$	5.24795	−	3.37265i	0.202294	−	0.130006i	−0.435572	−	0.900154i	$-0.643454\pi$
$673$	5.24795	−	3.37265i	0.202294	−	0.130006i	0.637866	+	0.770148i	$0.279818\pi$
$674$	−1.54085	+	2.16383i	−0.0593515	+	0.0833475i
$675$	−4.83088	+	0.931076i	−0.185941	+	0.0358371i
$676$	−12.0610	−	4.82851i	−0.463886	−	0.185712i
$677$	23.5008	−	2.24405i	0.903208	−	0.0862459i	0.366892	−	0.930263i	$-0.380422\pi$
$677$	23.5008	−	2.24405i	0.903208	−	0.0862459i	0.536316	+	0.844018i	$0.319816\pi$
$678$	2.25427	−	0.661914i	0.0865747	−	0.0254206i
$679$	21.7567	−	17.7030i	0.834944	−	0.679379i
$680$	−0.346857	+	0.759512i	−0.0133014	+	0.0291259i
$681$	−8.43870	+	6.63627i	−0.323372	+	0.254302i
$682$	1.84558	−	0.355706i	0.0706708	−	0.0136207i
$683$	−3.35931	−	0.320775i	−0.128540	−	0.0122741i	0.0305875	−	0.999532i	$-0.490262\pi$
$683$	−3.35931	−	0.320775i	−0.128540	−	0.0122741i	−0.159128	+	0.987258i	$0.550868\pi$
$684$	6.90929	+	3.56198i	0.264183	+	0.136196i
$685$	−0.764696	+	5.31858i	−0.0292175	+	0.203212i
$686$	16.8642	+	7.65498i	0.643878	+	0.292269i
$687$	12.6926	−	14.6480i	0.484252	−	0.558857i
$688$	1.00188	+	4.12980i	0.0381962	+	0.157447i
$689$	0.0455741	−	0.0789366i	0.00173623	−	0.00300725i
$690$	−1.26900	−	0.484216i	−0.0483101	−	0.0184338i
$691$	−14.2125	−	24.6168i	−0.540670	−	0.936468i	−0.998866	−	0.0476167i	$-0.984837\pi$
$691$	−14.2125	−	24.6168i	−0.540670	−	0.936468i	0.458196	−	0.888851i	$-0.348496\pi$
$692$	9.89021	+	2.90403i	0.375969	+	0.110395i
$693$	0.636502	−	1.94301i	0.0241787	−	0.0738088i
$694$	13.6177	+	8.75158i	0.516922	+	0.332205i
$695$	−0.417795	+	0.167260i	−0.0158479	+	0.00634453i
$696$	−0.0833719	−	1.75019i	−0.00316020	−	0.0663409i
$697$	−1.22208	−	0.116695i	−0.0462898	−	0.00442014i
$698$	−5.51806	+	15.9434i	−0.208862	+	0.603466i
$699$	1.87930	+	13.0708i	0.0710815	+	0.494383i
$700$	−11.4688	+	6.15609i	−0.433479	+	0.232679i
$701$	44.8129	−	13.1583i	1.69256	−	0.496980i	0.713518	−	0.700637i	$-0.247101\pi$
$701$	44.8129	−	13.1583i	1.69256	−	0.496980i	0.979042	+	0.203657i	$0.0652826\pi$
$702$	−0.0660651	−	0.0629929i	−0.00249347	−	0.00237751i
$703$	−8.78163	−	12.3321i	−0.331205	−	0.465113i
$704$	0.717432	+	0.287216i	0.0270392	+	0.0108249i
$705$	0.615750	−	1.77909i	0.0231905	−	0.0670045i
$706$	−8.83976	−	19.3564i	−0.332689	−	0.728486i
$707$	5.80842	+	12.1785i	0.218448	+	0.458021i
$708$	0.425185	−	2.95723i	0.0159794	−	0.111139i
$709$	−0.631116	+	13.2488i	−0.0237021	+	0.497568i	0.955539	+	0.294866i	$0.0952751\pi$
$709$	−0.631116	+	13.2488i	−0.0237021	+	0.497568i	−0.979241	+	0.202701i	$0.935028\pi$
$710$	−0.0520994	−	0.150531i	−0.00195525	−	0.00564934i
$711$	−8.81347	+	8.40363i	−0.330531	+	0.315161i
$712$	9.00618	+	15.5992i	0.337521	+	0.584603i
$713$	5.01757	+	10.5299i	0.187909	+	0.394347i
$714$	0.981531	−	7.73815i	0.0367329	−	0.289593i
$715$	−0.0191695	−	0.00562866i	−0.000716898	−	0.000210500i
$716$	8.52549	+	1.64315i	0.318612	+	0.0614075i
$717$	10.4816	−	5.40364i	0.391442	−	0.201802i
$718$	19.2704	+	15.1544i	0.719164	+	0.565557i
$719$	8.43929	+	4.35076i	0.314733	+	0.162256i	0.608354	−	0.793666i	$-0.291830\pi$
$719$	8.43929	+	4.35076i	0.314733	+	0.162256i	−0.293621	+	0.955922i	$0.594860\pi$
$720$	−0.117651	−	0.257621i	−0.00438461	−	0.00960095i
$721$	1.19040	+	18.5078i	0.0443328	+	0.689268i
$722$	−5.89553	−	41.0043i	−0.219409	−	1.52602i
$723$	16.5606	−	1.58135i	0.615896	−	0.0588109i
$724$	−0.861951	+	3.55301i	−0.0320342	+	0.132047i
$725$	2.03232	−	8.37735i	0.0754786	−	0.311127i
$726$	10.3557	−	0.988849i	0.384336	−	0.0366996i
$727$	5.86686	+	40.8049i	0.217590	+	1.51337i	0.746897	+	0.664939i	$0.231543\pi$
$727$	5.86686	+	40.8049i	0.217590	+	1.51337i	−0.529308	+	0.848430i	$0.677548\pi$
$728$	−0.216477	−	0.107083i	−0.00802316	−	0.00396876i
$729$	0.415415	+	0.909632i	0.0153857	+	0.0336901i
$730$	3.49369	+	1.80112i	0.129307	+	0.0666626i
$731$	−9.84810	−	7.74463i	−0.364245	−	0.286445i
$732$	−9.22866	+	4.75771i	−0.341101	+	0.175850i
$733$	22.7254	+	4.37997i	0.839383	+	0.161778i	0.590785	−	0.806829i	$-0.298818\pi$
$733$	22.7254	+	4.37997i	0.839383	+	0.161778i	0.248598	+	0.968607i	$0.420030\pi$
$734$	19.9347	+	5.85334i	0.735802	+	0.216051i
$735$	−1.38851	+	1.41504i	−0.0512161	+	0.0521944i
$736$	−0.605154	+	4.75750i	−0.0223063	+	0.175364i
$737$	−4.57098	−	7.91718i	−0.168374	−	0.291633i
$738$	0.301368	−	0.287354i	0.0110935	−	0.0105776i
$739$	−8.90044	−	25.7161i	−0.327408	−	0.945984i	−0.981815	−	0.189841i	$-0.939203\pi$
$739$	−8.90044	−	25.7161i	−0.327408	−	0.945984i	0.654407	−	0.756143i	$-0.272918\pi$
$740$	−0.0262452	+	0.550954i	−0.000964792	+	0.0202535i
$741$	−0.100985	+	0.702363i	−0.00370976	+	0.0258019i
$742$	−1.49641	+	2.17715i	−0.0549349	+	0.0799258i
$743$	−4.48064	−	9.81123i	−0.164379	−	0.359939i	0.809462	−	0.587173i	$-0.199759\pi$
$743$	−4.48064	−	9.81123i	−0.164379	−	0.359939i	−0.973840	+	0.227234i	$0.927032\pi$
$744$	−0.795481	+	2.29839i	−0.0291637	+	0.0842631i
$745$	3.37215	+	1.35001i	0.123546	+	0.0494604i
$746$	7.42784	+	10.4309i	0.271953	+	0.381904i
$747$	−9.43990	−	9.00093i	−0.345388	−	0.329327i
$748$	−2.18603	+	0.641876i	−0.0799292	+	0.0234693i
$749$	−40.9091	+	21.9588i	−1.49479	+	0.802356i
$750$	−0.399823	−	2.78083i	−0.0145995	−	0.101541i
$751$	6.75501	−	19.5173i	0.246494	−	0.712197i	−0.752093	−	0.659057i	$-0.770956\pi$
$751$	6.75501	−	19.5173i	0.246494	−	0.712197i	0.998587	−	0.0531403i	$-0.0169231\pi$
$752$	−6.61730	−	0.631876i	−0.241308	−	0.0230421i
$753$	−0.553401	−	11.6173i	−0.0201671	−	0.423359i
$754$	0.148488	−	0.0594456i	0.00540761	−	0.00216488i
$755$	−2.22456	−	1.42964i	−0.0809600	−	0.0520299i
$756$	1.76561	+	1.97044i	0.0642146	+	0.0716641i
$757$	20.8838	+	6.13205i	0.759036	+	0.222873i	0.638275	−	0.769808i	$-0.279648\pi$
$757$	20.8838	+	6.13205i	0.759036	+	0.222873i	0.120761	+	0.992682i	$0.461466\pi$
$758$	−16.6707	−	28.8745i	−0.605508	−	1.04877i
$759$	−1.26902	−	3.48213i	−0.0460625	−	0.126393i
$760$	−1.10077	+	1.90659i	−0.0399291	+	0.0691593i
$761$	6.12955	+	25.2664i	0.222196	+	0.915905i	0.968243	+	0.250011i	$0.0804344\pi$
$761$	6.12955	+	25.2664i	0.222196	+	0.915905i	−0.746047	+	0.665894i	$0.768050\pi$
$762$	−4.02287	+	4.64263i	−0.145733	+	0.168185i
$763$	12.5305	−	14.9565i	0.453636	−	0.541461i
$764$	−3.16061	+	21.9825i	−0.114347	+	0.795299i
$765$	0.742147	+	0.382603i	0.0268324	+	0.0138331i
$766$	−22.8228	−	2.17931i	−0.824621	−	0.0787417i
$767$	0.267794	−	0.0516131i	0.00966948	−	0.00186364i
$768$	−0.786053	+	0.618159i	−0.0283642	+	0.0223059i
$769$	−17.4237	+	38.1525i	−0.628313	+	1.37581i	0.281002	+	0.959707i	$0.409333\pi$
$769$	−17.4237	+	38.1525i	−0.628313	+	1.37581i	−0.909315	+	0.416107i	$0.863394\pi$
$770$	0.541086	+	0.206246i	0.0194994	+	0.00743258i
$771$	−14.8446	+	4.35876i	−0.534614	+	0.156977i
$772$	17.8597	−	1.70539i	0.642783	−	0.0613784i
$773$	21.4768	+	8.59800i	0.772466	+	0.309249i	0.724204	−	0.689586i	$-0.242208\pi$
$773$	21.4768	+	8.59800i	0.772466	+	0.309249i	0.0482619	+	0.998835i	$0.484632\pi$
$774$	4.17279	−	0.804239i	0.149988	−	0.0289078i
$775$	−6.94079	+	9.74698i	−0.249321	+	0.350122i
$776$	8.91858	−	5.73163i	0.320158	−	0.205753i
$777$	−1.29792	−	4.98664i	−0.0465626	−	0.178895i
$778$	−11.1751	−	7.18182i	−0.400648	−	0.257481i
$779$	−3.17841	−	0.612589i	−0.113878	−	0.0219483i
$780$	0.0187106	−	0.0178405i	0.000669946	−	0.000638792i
$781$	0.217325	−	0.376418i	0.00777651	−	0.0134693i
$782$	−7.26787	−	12.1280i	−0.259899	−	0.433697i
$783$	−1.75218			−0.0626177
$784$	6.01137	+	3.58657i	0.214692	+	0.128092i
$785$	−2.75168	+	3.17561i	−0.0982118	+	0.113342i
$786$	−0.591926	+	12.4261i	−0.0211133	+	0.443223i
$787$	41.6966	+	32.7906i	1.48632	+	1.16886i	0.944565	+	0.328325i	$0.106484\pi$
$787$	41.6966	+	32.7906i	1.48632	+	1.16886i	0.541760	+	0.840533i	$0.317758\pi$
$788$	−0.820524	−	17.2249i	−0.0292300	−	0.613612i
$789$	14.7394	−	20.6986i	0.524736	−	0.736888i
$790$	−2.25856	−	2.60652i	−0.0803560	−	0.0927358i
$791$	−3.19711	−	5.33081i	−0.113676	−	0.189542i
$792$	0.321028	−	0.702953i	0.0114072	−	0.0249783i
$793$	−0.685945	−	0.654047i	−0.0243586	−	0.0232259i
$794$	−2.36533	+	9.75004i	−0.0839426	+	0.346016i
$795$	−0.164036	−	0.230357i	−0.00581777	−	0.00816992i
$796$	1.88550	−	1.48277i	0.0668298	−	0.0525555i
$797$	15.5663	+	17.9645i	0.551386	+	0.636334i	0.961206	−	0.275833i	$-0.0889536\pi$
$797$	15.5663	+	17.9645i	0.551386	+	0.636334i	−0.409819	+	0.912167i	$0.634408\pi$
$798$	4.51570	−	20.0647i	0.159854	−	0.710281i
$799$	16.4867	−	10.5953i	0.583256	−	0.374836i
$800$	−4.56738	+	1.82850i	−0.161481	+	0.0646473i
$801$	16.0100	−	8.25374i	0.565686	−	0.291631i
$802$	0.586476	+	1.69451i	0.0207092	+	0.0598353i
$803$	2.52858	+	10.4230i	0.0892318	+	0.367818i
$804$	11.8298			0.417206
$805$	−0.394106	+	3.57191i	−0.0138904	+	0.125893i
$806$	−0.222016			−0.00782019
$807$	5.07071	+	20.9017i	0.178497	+	0.735776i
$808$	1.66797	+	4.81930i	0.0586791	+	0.169542i
$809$	−12.7522	+	6.57422i	−0.448344	+	0.231137i	−0.667585	−	0.744533i	$-0.732672\pi$
$809$	−12.7522	+	6.57422i	−0.448344	+	0.231137i	0.219241	+	0.975671i	$0.429642\pi$
$810$	−0.262927	+	0.105260i	−0.00923831	+	0.00369846i
$811$	6.14183	−	3.94711i	0.215669	−	0.138602i	−0.428346	−	0.903615i	$-0.640904\pi$
$811$	6.14183	−	3.94711i	0.215669	−	0.138602i	0.644015	+	0.765013i	$0.277267\pi$
$812$	−4.42571	+	1.37985i	−0.155312	+	0.0484233i
$813$	−0.166534	−	0.192191i	−0.00584061	−	0.00674042i
$814$	−1.18306	+	0.930365i	−0.0414661	+	0.0326093i
$815$	−0.636032	−	0.893182i	−0.0222792	−	0.0312868i
$816$	0.695060	−	2.86507i	0.0243320	−	0.100298i
$817$	−23.9077	−	22.7959i	−0.836424	−	0.797528i
$818$	6.72313	−	14.7216i	0.235069	−	0.514729i
$819$	−0.117262	+	0.211136i	−0.00409747	+	0.00737770i
$820$	0.0772293	+	0.0891274i	0.00269696	+	0.00311246i
$821$	24.7270	−	34.7242i	0.862977	−	1.21188i	−0.112909	−	0.993605i	$-0.536017\pi$
$821$	24.7270	−	34.7242i	0.862977	−	1.21188i	0.975887	−	0.218277i	$-0.0700436\pi$
$822$	−0.902746	−	18.9510i	−0.0314869	−	0.660991i
$823$	7.67955	+	6.03926i	0.267692	+	0.210515i	0.742978	−	0.669316i	$-0.233413\pi$
$823$	7.67955	+	6.03926i	0.267692	+	0.210515i	−0.475286	+	0.879832i	$0.657655\pi$
$824$	−0.333538	+	7.00182i	−0.0116193	+	0.243920i
$825$	2.48975	−	2.87333i	0.0866820	−	0.100036i
$826$	−7.85517	+	0.882124i	−0.273316	+	0.0306930i
$827$	18.2887			0.635959			0.317980	−	0.948098i	$-0.396996\pi$
$827$	18.2887			0.635959			0.317980	+	0.948098i	$0.396996\pi$
$828$	4.72332	+	0.830839i	0.164147	+	0.0288737i
$829$	−10.0951	+	17.4851i	−0.350616	+	0.607284i	−0.986357	−	0.164618i	$-0.947361\pi$
$829$	−10.0951	+	17.4851i	−0.350616	+	0.607284i	0.635742	+	0.771902i	$0.280694\pi$
$830$	2.67351	−	2.54919i	0.0927990	−	0.0884837i
$831$	−7.36356	−	1.41921i	−0.255439	−	0.0492319i
$832$	−0.0767927	−	0.0493517i	−0.00266231	−	0.00171096i
$833$	−20.4672	+	2.64378i	−0.709147	+	0.0916016i
$834$	1.33676	−	0.859087i	0.0462884	−	0.0297477i
$835$	−0.226552	+	0.318148i	−0.00784015	+	0.0110100i
$836$	−5.89865	+	1.13687i	−0.204009	+	0.0393195i
$837$	2.25794	+	0.903942i	0.0780457	+	0.0312448i
$838$	−24.0029	+	2.29200i	−0.829168	+	0.0791759i
$839$	−16.1257	+	4.73493i	−0.556721	+	0.163468i	−0.547977	−	0.836494i	$-0.684602\pi$
$839$	−16.1257	+	4.73493i	−0.556721	+	0.163468i	−0.00874453	+	0.999962i	$0.502784\pi$
$840$	−0.581216	+	0.472926i	−0.0200539	+	0.0163175i
$841$	−10.7717	+	23.5866i	−0.371437	+	0.813333i
$842$	22.6865	−	17.8409i	0.781828	−	0.614836i
$843$	3.85131	−	0.742279i	0.132646	−	0.0255655i
$844$	1.50014	+	0.143246i	0.0516368	+	0.00493072i
$845$	−3.27040	−	1.68601i	−0.112505	−	0.0580005i
$846$	−0.946024	+	6.57974i	−0.0325250	+	0.226216i
$847$	−9.43324	−	25.8562i	−0.324130	−	0.888428i
$848$	−0.653889	+	0.754628i	−0.0224546	+	0.0259140i
$849$	−0.970850	−	4.00190i	−0.0333195	−	0.137345i
$850$	7.25221	−	12.5612i	0.248749	−	0.430846i
$851$	−7.43491	−	5.65345i	−0.254866	−	0.193798i
$852$	0.281222	+	0.487091i	0.00963451	+	0.0166875i
$853$	37.7247	+	11.0770i	1.29167	+	0.379268i	0.854191	−	0.519960i	$-0.174053\pi$
$853$	37.7247	+	11.0770i	1.29167	+	0.379268i	0.437479	+	0.899229i	$0.355871\pi$
$854$	18.3321	+	20.4588i	0.627311	+	0.700085i
$855$	1.85205	+	1.19024i	0.0633389	+	0.0407054i
$856$	−16.2918	+	6.52226i	−0.556843	+	0.222926i
$857$	1.14431	+	24.0220i	0.0390888	+	0.820575i	0.930259	+	0.366905i	$0.119582\pi$
$857$	1.14431	+	24.0220i	0.0390888	+	0.820575i	−0.891170	+	0.453670i	$0.850114\pi$
$858$	0.0702235	+	0.00670553i	0.00239739	+	0.000228923i
$859$	14.6053	−	42.1994i	0.498328	−	1.43982i	−0.363007	−	0.931787i	$-0.618250\pi$
$859$	14.6053	−	42.1994i	0.498328	−	1.43982i	0.861335	−	0.508038i	$-0.169629\pi$
$860$	0.171282	+	1.19129i	0.00584067	+	0.0406227i
$861$	−0.936594	−	0.580135i	−0.0319191	−	0.0197709i
$862$	18.7342	−	5.50086i	0.638090	−	0.187360i
$863$	9.33160	+	8.89766i	0.317651	+	0.302880i	0.832083	−	0.554652i	$-0.187148\pi$
$863$	9.33160	+	8.89766i	0.317651	+	0.302880i	−0.514431	+	0.857532i	$0.671997\pi$
$864$	0.580057	+	0.814576i	0.0197339	+	0.0277124i
$865$	2.71018	+	1.08499i	0.0921490	+	0.0368909i
$866$	0.143094	−	0.413443i	0.00486253	−	0.0140494i
$867$	−3.45137	−	7.55744i	−0.117215	−	0.256664i
$868$	6.41503	+	0.505066i	0.217740	+	0.0171431i
$869$	1.33930	−	9.31506i	0.0454327	−	0.315992i
$870$	0.0236121	−	0.495679i	0.000800525	−	0.0168051i
$871$	0.353191	+	1.02048i	0.0119674	+	0.0345776i
$872$	5.33737	−	5.08917i	0.180746	−	0.172341i
$873$	−5.30077	−	9.18120i	−0.179404	−	0.310737i
$874$	−16.0366	−	33.6545i	−0.542447	−	1.13838i
$875$	−6.85370	+	2.87695i	−0.231697	+	0.0972587i
$876$	−13.3165	−	3.91008i	−0.449923	−	0.132109i
$877$	−31.9490	−	6.15766i	−1.07884	−	0.207930i	−0.381283	−	0.924458i	$-0.624518\pi$
$877$	−31.9490	−	6.15766i	−1.07884	−	0.207930i	−0.697558	+	0.716529i	$0.745730\pi$
$878$	−5.62523	+	2.90001i	−0.189842	+	0.0978705i
$879$	−15.3331	−	12.0581i	−0.517172	−	0.406709i
$880$	0.194535	+	0.100290i	0.00655776	+	0.00338076i
$881$	1.04737	+	2.29343i	0.0352869	+	0.0772676i	0.926455	−	0.376406i	$-0.122840\pi$
$881$	1.04737	+	2.29343i	0.0352869	+	0.0772676i	−0.891168	+	0.453674i	$0.850113\pi$
$882$	3.86854	−	5.83390i	0.130260	−	0.196438i
$883$	0.980594	+	6.82018i	0.0329996	+	0.229517i	0.999646	−	0.0265965i	$-0.00846692\pi$
$883$	0.980594	+	6.82018i	0.0329996	+	0.229517i	−0.966647	+	0.256114i	$0.917558\pi$
$884$	0.267902	−	0.0255815i	0.00901052	−	0.000860400i
$885$	0.199485	−	0.822290i	0.00670563	−	0.0276410i
$886$	−3.89685	+	16.0630i	−0.130917	+	0.539648i
$887$	8.92195	−	0.851943i	0.299570	−	0.0286054i	0.0558111	−	0.998441i	$-0.482226\pi$
$887$	8.92195	−	0.851943i	0.299570	−	0.0286054i	0.243759	+	0.969836i	$0.421619\pi$
$888$	−0.277168	−	1.92774i	−0.00930114	−	0.0646909i
$889$	14.5682	+	7.20633i	0.488601	+	0.241692i
$890$	2.11918	+	4.64035i	0.0710350	+	0.155545i
$891$	−0.686882	−	0.354112i	−0.0230114	−	0.0118632i
$892$	−0.0560898	−	0.0441095i	−0.00187802	−	0.00147689i
$893$	45.9288	−	23.6779i	1.53695	−	0.792352i
$894$	−12.5937	−	2.42723i	−0.421195	−	0.0811788i
$895$	2.35937	+	0.692773i	0.0788650	+	0.0231569i
$896$	2.10661	+	1.60068i	0.0703769	+	0.0534751i
$897$	0.0693483	+	0.432253i	0.00231547	+	0.0144325i
$898$	−2.67752	−	4.63760i	−0.0893500	−	0.154759i
$899$	−3.08424	+	2.94082i	−0.102865	+	0.0980818i
$900$	1.60911	+	4.64921i	0.0536369	+	0.154974i
$901$	0.140072	−	2.94047i	0.00466647	−	0.0979612i
$902$	−0.0457962	+	0.318519i	−0.00152485	+	0.0106055i
$903$	−4.84008	−	10.1482i	−0.161068	−	0.337712i
$904$	−0.975992	−	2.13713i	−0.0324610	−	0.0710797i
$905$	−0.338663	+	0.978501i	−0.0112575	+	0.0325265i
$906$	8.66807	+	3.47017i	0.287977	+	0.115289i
$907$	−0.973907	−	1.36766i	−0.0323381	−	0.0454124i	0.798090	−	0.602538i	$-0.205844\pi$
$907$	−0.973907	−	1.36766i	−0.0323381	−	0.0454124i	−0.830428	+	0.557125i	$0.811904\pi$
$908$	7.76967	+	7.40837i	0.257846	+	0.245855i
$909$	4.89320	−	1.43677i	0.162297	−	0.0476548i
$910$	−0.0581488	−	0.0360179i	−0.00192762	−	0.00119398i
$911$	2.71679	+	18.8957i	0.0900113	+	0.626042i	0.984029	+	0.178010i	$0.0569659\pi$
$911$	2.71679	+	18.8957i	0.0900113	+	0.626042i	−0.894017	+	0.448032i	$0.852125\pi$
$912$	2.54243	−	7.34588i	0.0841884	−	0.243246i
$913$	10.0341	+	0.958140i	0.332080	+	0.0317098i
$914$	−0.408285	−	8.57096i	−0.0135049	−	0.283502i
$915$	−2.72993	+	1.09290i	−0.0902489	+	0.0361302i
$916$	−16.3053	−	10.4788i	−0.538741	−	0.346228i
$917$	32.2107	−	6.76551i	1.06369	−	0.223417i
$918$	−2.82876	−	0.830598i	−0.0933629	−	0.0274138i
$919$	19.7076	+	34.1346i	0.650094	+	1.12600i	0.983100	+	0.183071i	$0.0586038\pi$
$919$	19.7076	+	34.1346i	0.650094	+	1.12600i	−0.333006	+	0.942925i	$0.608063\pi$
$920$	−0.298690	+	1.32500i	−0.00984750	+	0.0436839i
$921$	−13.1088	+	22.7051i	−0.431949	+	0.748157i
$922$	−8.41398	−	34.6829i	−0.277100	−	1.14222i
$923$	−0.0336218	+	0.0388017i	−0.00110668	+	0.00127717i
$924$	−2.01381	−	0.353504i	−0.0662496	−	0.0116294i
$925$	1.36361	−	9.48410i	0.0448351	−	0.311835i
$926$	−18.8001	−	9.69212i	−0.617809	−	0.318503i
$927$	6.97802	+	0.666320i	0.229188	+	0.0218848i
$928$	−1.72051	+	0.331602i	−0.0564786	+	0.0108854i
$929$	−23.3931	+	18.3965i	−0.767502	+	0.603571i	−0.923238	−	0.384228i	$-0.874468\pi$
$929$	−23.3931	+	18.3965i	−0.767502	+	0.603571i	0.155736	+	0.987799i	$0.450225\pi$
$930$	−0.286147	+	0.626574i	−0.00938312	+	0.0205462i
$931$	−54.3838	+	1.80950i	−1.78236	+	0.0593039i
$932$	12.6703	−	3.72033i	0.415029	−	0.121864i
$933$	14.6277	−	1.39677i	0.478888	−	0.0457283i
$934$	10.6816	+	4.27627i	0.349513	+	0.139924i
$935$	−0.633591	+	0.122115i	−0.0207207	+	0.00399358i
$936$	−0.0529497	+	0.0743575i	−0.00173072	+	0.00243045i
$937$	18.3492	−	11.7923i	0.599441	−	0.385237i	−0.205443	−	0.978669i	$-0.565864\pi$
$937$	18.3492	−	11.7923i	0.599441	−	0.385237i	0.804884	+	0.593432i	$0.202227\pi$
$938$	−7.88377	−	30.2897i	−0.257414	−	0.988992i
$939$	25.3788	+	16.3100i	0.828206	+	0.532255i
$940$	−1.84862	−	0.356291i	−0.0602952	−	0.0116209i
$941$	21.4034	−	20.4081i	0.697730	−	0.665284i	−0.255749	−	0.966743i	$-0.582322\pi$
$941$	21.4034	−	20.4081i	0.697730	−	0.665284i	0.953479	+	0.301459i	$0.0974737\pi$
$942$	7.41831	−	12.8489i	0.241701	−	0.418639i
$943$	−1.98462	+	0.222165i	−0.0646282	+	0.00723468i
$944$	−2.98764			−0.0972393
$945$	0.444735	+	0.603061i	0.0144672	+	0.0196176i
$946$	−2.15058	+	2.48190i	−0.0699215	+	0.0806937i
$947$	2.59739	−	54.5259i	0.0844038	−	1.77185i	−0.419176	−	0.907905i	$-0.637681\pi$
$947$	2.59739	−	54.5259i	0.0844038	−	1.77185i	0.503580	−	0.863949i	$-0.332016\pi$
$948$	9.57238	+	7.52780i	0.310897	+	0.244492i
$949$	−0.0602814	−	1.26546i	−0.00195682	−	0.0410787i
$950$	22.1834	−	31.1523i	0.719726	−	1.01071i
$951$	−10.0669	−	11.6178i	−0.326441	−	0.376734i
$952$	−7.79907	+	0.129712i	−0.252769	+	0.00420400i
$953$	5.82580	−	12.7567i	0.188716	−	0.413230i	−0.791498	−	0.611172i	$-0.790698\pi$
$953$	5.82580	−	12.7567i	0.188716	−	0.413230i	0.980214	+	0.197942i	$0.0634256\pi$
$954$	0.722660	+	0.689055i	0.0233970	+	0.0223090i
$955$	−1.48287	+	6.11248i	−0.0479846	+	0.197795i
$956$	−6.84032	−	9.60588i	−0.221232	−	0.310677i
$957$	1.06436	−	0.837025i	0.0344060	−	0.0270572i
$958$	−8.58607	−	9.90886i	−0.277403	−	0.320141i
$959$	−47.9213	+	14.9409i	−1.54746	+	0.482468i
$960$	−0.238255	+	0.153117i	−0.00768964	+	0.00494183i
$961$	−23.2877	+	9.32301i	−0.751218	+	0.300742i
$962$	0.158018	−	0.0814640i	0.00509471	−	0.00262651i
$963$	5.73968	+	16.5837i	0.184959	+	0.534403i
$964$	−3.92207	−	16.1670i	−0.126321	−	0.520704i
$965$	5.08112			0.163567
$966$	−1.02044	−	12.6475i	−0.0328323	−	0.406926i
$967$	−33.9492			−1.09173			−0.545867	−	0.837872i	$-0.683799\pi$
$967$	−33.9492			−1.09173			−0.545867	+	0.837872i	$0.683799\pi$
$968$	−2.45255	−	10.1096i	−0.0788280	−	0.324934i
$969$	7.49555	+	21.6570i	0.240792	+	0.695722i
$970$	2.66873	−	1.37583i	0.0856879	−	0.0441752i
$971$	−23.2828	+	9.32102i	−0.747180	+	0.299126i	−0.713831	−	0.700318i	$-0.753042\pi$
$971$	−23.2828	+	9.32102i	−0.747180	+	0.299126i	−0.0333492	+	0.999444i	$0.510617\pi$
$972$	0.841254	−	0.540641i	0.0269832	−	0.0173411i
$973$	−3.09050	−	2.85019i	−0.0990770	−	0.0913729i
$974$	−27.7751	−	32.0541i	−0.889971	−	1.02708i
$975$	−0.353014	+	0.277613i	−0.0113055	+	0.00889073i
$976$	6.02265	+	8.45763i	0.192780	+	0.270722i
$977$	4.47550	−	18.4483i	0.143184	−	0.590212i	−0.854329	−	0.519732i	$-0.826032\pi$
$977$	4.47550	−	18.4483i	0.143184	−	0.590212i	0.997513	−	0.0704802i	$-0.0224532\pi$
$978$	2.80203	+	2.67173i	0.0895990	+	0.0854324i
$979$	−5.78247	+	12.6618i	−0.184808	+	0.404674i
$980$	1.59824	+	1.17300i	0.0510539	+	0.0374701i
$981$	−4.82945	−	5.57348i	−0.154192	−	0.177947i
$982$	−6.13246	+	8.61184i	−0.195695	+	0.274815i
$983$	−2.77369	−	58.2269i	−0.0884669	−	1.85715i	−0.412316	−	0.911041i	$-0.635280\pi$
$983$	−2.77369	−	58.2269i	−0.0884669	−	1.85715i	0.323849	−	0.946109i	$-0.395023\pi$
$984$	−0.327318	−	0.257406i	−0.0104345	−	0.00820580i
$985$	0.232384	−	4.87834i	0.00740437	−	0.155437i
$986$	3.38283	−	3.90400i	0.107731	−	0.124329i
$987$	17.4775	−	1.96270i	0.556315	−	0.0624734i
$988$	0.709586			0.0225749
$989$	−18.2643	−	9.04267i	−0.580772	−	0.287540i
$990$	0.109432	−	0.189542i	0.00347799	−	0.00602405i
$991$	19.6337	−	18.7207i	0.623685	−	0.594682i	−0.310891	−	0.950446i	$-0.600627\pi$
$991$	19.6337	−	18.7207i	0.623685	−	0.594682i	0.934576	+	0.355763i	$0.115779\pi$
$992$	2.38821	+	0.460289i	0.0758256	+	0.0146142i
$993$	−3.41283	−	2.19329i	−0.108303	−	0.0696019i
$994$	1.05975	−	1.04467i	0.0336134	−	0.0331348i
$995$	0.571500	−	0.367281i	0.0181178	−	0.0116436i
$996$	−7.56588	+	10.6248i	−0.239734	+	0.336659i
$997$	34.5989	−	6.66839i	1.09576	−	0.211190i	0.390826	−	0.920465i	$-0.372190\pi$
$997$	34.5989	−	6.66839i	1.09576	−	0.211190i	0.704932	+	0.709275i	$0.250977\pi$
$998$	−7.84578	−	3.14098i	−0.248354	−	0.0994259i
$999$	−1.93875	+	0.185128i	−0.0613393	+	0.00585719i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.y.d.823.5	yes	160
7.2	even	3	inner	966.2.y.d.961.4	yes	160
23.9	even	11	inner	966.2.y.d.193.4	✓	160
161.9	even	33	inner	966.2.y.d.331.5	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.y.d.193.4	✓	160	23.9	even	11	inner
966.2.y.d.331.5	yes	160	161.9	even	33	inner
966.2.y.d.823.5	yes	160	1.1	even	1	trivial
966.2.y.d.961.4	yes	160	7.2	even	3	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.235759 + 0.971812i) q^{2} +(-0.327068 - 0.945001i) q^{3} +(-0.888835 + 0.458227i) q^{4} +(-0.262927 + 0.105260i) q^{5} +(0.841254 - 0.540641i) q^{6} +(-1.94492 - 1.79368i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(-0.786053 + 0.618159i) q^{9} +O(q^{10})\)	\(q+(0.235759 + 0.971812i) q^{2} +(-0.327068 - 0.945001i) q^{3} +(-0.888835 + 0.458227i) q^{4} +(-0.262927 + 0.105260i) q^{5} +(0.841254 - 0.540641i) q^{6} +(-1.94492 - 1.79368i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(-0.786053 + 0.618159i) q^{9} +(-0.164280 - 0.230699i) q^{10} +(0.182192 - 0.751005i) q^{11} +(0.723734 + 0.690079i) q^{12} +(-0.0379206 + 0.0830345i) q^{13} +(1.28459 - 2.31297i) q^{14} +(0.185466 + 0.214039i) q^{15} +(0.580057 - 0.814576i) q^{16} +(0.140280 + 2.94484i) q^{17} +(-0.786053 - 0.618159i) q^{18} +(-0.369874 + 7.76461i) q^{19} +(0.185466 - 0.214039i) q^{20} +(-1.05891 + 2.42460i) q^{21} +0.772788 q^{22} +(1.20638 + 4.64162i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-3.56062 + 3.39504i) q^{25} +(-0.0896340 - 0.0172755i) q^{26} +(0.841254 + 0.540641i) q^{27} +(2.55062 + 0.703076i) q^{28} +(-1.47402 + 0.947298i) q^{29} +(-0.164280 + 0.230699i) q^{30} +(2.38821 - 0.460289i) q^{31} +(0.928368 + 0.371662i) q^{32} +(-0.769289 + 0.0734582i) q^{33} +(-2.82876 + 0.830598i) q^{34} +(0.700174 + 0.266885i) q^{35} +(0.415415 - 0.909632i) q^{36} +(-1.53089 + 1.20391i) q^{37} +(-7.63294 + 1.47113i) q^{38} +(0.0908703 + 0.00867706i) q^{39} +(0.251731 + 0.129776i) q^{40} +(-0.0592609 + 0.412169i) q^{41} +(-2.60591 - 0.457440i) q^{42} +(-2.78289 + 3.21162i) q^{43} +(0.182192 + 0.751005i) q^{44} +(0.141607 - 0.245271i) q^{45} +(-4.22637 + 2.26668i) q^{46} +(-3.32370 - 5.75682i) q^{47} +(-0.959493 - 0.281733i) q^{48} +(0.565406 + 6.97713i) q^{49} +(-4.13879 - 2.65984i) q^{50} +(2.73699 - 1.09573i) q^{51} +(-0.00434345 - 0.0911802i) q^{52} +(-0.993994 - 0.0949149i) q^{53} +(-0.327068 + 0.945001i) q^{54} +(0.0311477 + 0.216637i) q^{55} +(-0.0819249 + 2.64448i) q^{56} +(7.45854 - 2.19002i) q^{57} +(-1.26811 - 1.20914i) q^{58} +(-1.73300 - 2.43366i) q^{59} +(-0.262927 - 0.105260i) q^{60} +(-3.39590 + 9.81182i) q^{61} +(1.01035 + 2.21237i) q^{62} +(2.63759 + 0.207662i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(0.00123013 - 0.0258235i) q^{65} +(-0.252754 - 0.730286i) q^{66} +(8.56166 - 8.16353i) q^{67} +(-1.47409 - 2.55320i) q^{68} +(3.99177 - 2.65815i) q^{69} +(-0.0942899 + 0.743358i) q^{70} +(0.539661 + 0.158459i) q^{71} +(0.981929 + 0.189251i) q^{72} +(-12.3359 + 6.35959i) q^{73} +(-1.53089 - 1.20391i) q^{74} +(4.37288 + 2.25438i) q^{75} +(-3.22919 - 7.07095i) q^{76} +(-1.70141 + 1.13385i) q^{77} +(0.0129910 + 0.0903545i) q^{78} +(12.1226 - 1.15757i) q^{79} +(-0.0667703 + 0.275231i) q^{80} +(0.235759 - 0.971812i) q^{81} +(-0.414522 + 0.0395820i) q^{82} +(1.85626 + 12.9106i) q^{83} +(-0.169820 - 2.64030i) q^{84} +(-0.346857 - 0.759512i) q^{85} +(-3.77718 - 1.94727i) q^{86} +(1.37730 + 1.08312i) q^{87} +(-0.686882 + 0.354112i) q^{88} +(-17.6868 - 3.40886i) q^{89} +(0.271742 + 0.0797906i) q^{90} +(0.222690 - 0.0934778i) q^{91} +(-3.19919 - 3.57284i) q^{92} +(-1.21608 - 2.10631i) q^{93} +(4.81095 - 4.58723i) q^{94} +(-0.720053 - 2.08046i) q^{95} +(0.0475819 - 0.998867i) q^{96} +(-1.50876 + 10.4936i) q^{97} +(-6.64715 + 2.19439i) q^{98} +(0.321028 + 0.702953i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{5} - 16 q^{6} + 6 q^{7} - 16 q^{8} + 8 q^{9}+O(q^{10}) \) 160 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^5 - 16 * q^6 + 6 * q^7 - 16 * q^8 + 8 * q^9	\( 160 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{5} - 16 q^{6} + 6 q^{7} - 16 q^{8} + 8 q^{9} - 2 q^{10} - 4 q^{11} + 8 q^{12} - 4 q^{13} + 5 q^{14} + 26 q^{15} + 8 q^{16} - 13 q^{17} + 8 q^{18} + 4 q^{19} + 26 q^{20} + 11 q^{21} - 124 q^{22} + 26 q^{23} - 80 q^{24} + 14 q^{25} + 2 q^{26} - 16 q^{27} - 22 q^{28} + 54 q^{29} - 2 q^{30} + 15 q^{31} + 8 q^{32} - 4 q^{33} + 4 q^{34} - 2 q^{35} - 16 q^{36} + 7 q^{37} - 7 q^{38} + 2 q^{39} + 9 q^{40} - 30 q^{41} + 6 q^{42} + 36 q^{43} - 4 q^{44} + 20 q^{45} + 4 q^{46} - 6 q^{47} - 16 q^{48} + 14 q^{49} - 28 q^{50} + 9 q^{51} + 2 q^{52} - 24 q^{53} + 8 q^{54} - 14 q^{55} + 6 q^{56} - 30 q^{57} - 5 q^{58} + 4 q^{59} - 2 q^{60} + 32 q^{61} - 8 q^{62} - 6 q^{63} - 16 q^{64} + 38 q^{65} - 4 q^{66} + 6 q^{67} + 42 q^{68} - 30 q^{69} - 8 q^{70} - 180 q^{71} + 8 q^{72} - 32 q^{73} + 7 q^{74} + 14 q^{75} - 8 q^{76} + 61 q^{77} + 18 q^{78} - 66 q^{79} - 2 q^{80} + 8 q^{81} - 7 q^{82} + 130 q^{83} + 5 q^{84} - 70 q^{85} - 40 q^{86} + 6 q^{87} - 15 q^{88} - 4 q^{89} + 4 q^{90} - 6 q^{91} + 58 q^{92} - 18 q^{93} + 16 q^{94} + 19 q^{95} + 8 q^{96} + 40 q^{97} + 43 q^{98} + 8 q^{99}+O(q^{100}) \) 160 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^5 - 16 * q^6 + 6 * q^7 - 16 * q^8 + 8 * q^9 - 2 * q^10 - 4 * q^11 + 8 * q^12 - 4 * q^13 + 5 * q^14 + 26 * q^15 + 8 * q^16 - 13 * q^17 + 8 * q^18 + 4 * q^19 + 26 * q^20 + 11 * q^21 - 124 * q^22 + 26 * q^23 - 80 * q^24 + 14 * q^25 + 2 * q^26 - 16 * q^27 - 22 * q^28 + 54 * q^29 - 2 * q^30 + 15 * q^31 + 8 * q^32 - 4 * q^33 + 4 * q^34 - 2 * q^35 - 16 * q^36 + 7 * q^37 - 7 * q^38 + 2 * q^39 + 9 * q^40 - 30 * q^41 + 6 * q^42 + 36 * q^43 - 4 * q^44 + 20 * q^45 + 4 * q^46 - 6 * q^47 - 16 * q^48 + 14 * q^49 - 28 * q^50 + 9 * q^51 + 2 * q^52 - 24 * q^53 + 8 * q^54 - 14 * q^55 + 6 * q^56 - 30 * q^57 - 5 * q^58 + 4 * q^59 - 2 * q^60 + 32 * q^61 - 8 * q^62 - 6 * q^63 - 16 * q^64 + 38 * q^65 - 4 * q^66 + 6 * q^67 + 42 * q^68 - 30 * q^69 - 8 * q^70 - 180 * q^71 + 8 * q^72 - 32 * q^73 + 7 * q^74 + 14 * q^75 - 8 * q^76 + 61 * q^77 + 18 * q^78 - 66 * q^79 - 2 * q^80 + 8 * q^81 - 7 * q^82 + 130 * q^83 + 5 * q^84 - 70 * q^85 - 40 * q^86 + 6 * q^87 - 15 * q^88 - 4 * q^89 + 4 * q^90 - 6 * q^91 + 58 * q^92 - 18 * q^93 + 16 * q^94 + 19 * q^95 + 8 * q^96 + 40 * q^97 + 43 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

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