LMFDB - Embedded newform 966.2.be.a.19.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(19,966)]

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, 55, 45]))

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

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

chi := DirichletCharacter("966.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.be (of order $66$, 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:	$320$
Relative dimension:	$16$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			19.11
Character	$\chi$	$=$	966.19
Dual form			966.2.be.a.661.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.995472 + 0.0950560i) q^{2} +(0.690079 - 0.723734i) q^{3} +(0.981929 + 0.189251i) q^{4} +(-1.59513 + 0.822347i) q^{5} +(0.755750 - 0.654861i) q^{6} +(-1.53650 + 2.15387i) q^{7} +(0.959493 + 0.281733i) q^{8} +(-0.0475819 - 0.998867i) q^{9} +O(q^{10})$	\(q+(0.995472 + 0.0950560i) q^{2} +(0.690079 - 0.723734i) q^{3} +(0.981929 + 0.189251i) q^{4} +(-1.59513 + 0.822347i) q^{5} +(0.755750 - 0.654861i) q^{6} +(-1.53650 + 2.15387i) q^{7} +(0.959493 + 0.281733i) q^{8} +(-0.0475819 - 0.998867i) q^{9} +(-1.66608 + 0.666996i) q^{10} +(0.455072 + 4.76573i) q^{11} +(0.814576 - 0.580057i) q^{12} +(0.860526 + 0.123725i) q^{13} +(-1.73428 + 1.99807i) q^{14} +(-0.505605 + 1.72193i) q^{15} +(0.928368 + 0.371662i) q^{16} +(0.00822747 - 0.0237717i) q^{17} +(0.0475819 - 0.998867i) q^{18} +(1.70293 + 4.92029i) q^{19} +(-1.72193 + 0.505605i) q^{20} +(0.498526 + 2.59836i) q^{21} +4.78741i q^{22} +(-1.43339 - 4.57661i) q^{23} +(0.866025 - 0.500000i) q^{24} +(-1.03210 + 1.44938i) q^{25} +(0.844869 + 0.204963i) q^{26} +(-0.755750 - 0.654861i) q^{27} +(-1.91636 + 1.82417i) q^{28} +(3.22932 + 3.72683i) q^{29} +(-0.666996 + 1.66608i) q^{30} +(-3.08610 + 0.748681i) q^{31} +(0.888835 + 0.458227i) q^{32} +(3.76316 + 2.95938i) q^{33} +(0.0104499 - 0.0228820i) q^{34} +(0.679684 - 4.69924i) q^{35} +(0.142315 - 0.989821i) q^{36} +(7.95815 - 0.379093i) q^{37} +(1.22752 + 5.05989i) q^{38} +(0.683375 - 0.537412i) q^{39} +(-1.76220 + 0.339636i) q^{40} +(-1.20695 + 1.87805i) q^{41} +(0.249279 + 2.63398i) q^{42} +(2.56923 + 8.74999i) q^{43} +(-0.455072 + 4.76573i) q^{44} +(0.897315 + 1.55419i) q^{45} +(-0.991865 - 4.69214i) q^{46} +(-3.07852 - 1.77738i) q^{47} +(0.909632 - 0.415415i) q^{48} +(-2.27834 - 6.61885i) q^{49} +(-1.16520 + 1.34471i) q^{50} +(-0.0115268 - 0.0223589i) q^{51} +(0.821560 + 0.284345i) q^{52} +(0.792805 + 1.00813i) q^{53} +(-0.690079 - 0.723734i) q^{54} +(-4.64498 - 7.22773i) q^{55} +(-2.08108 + 1.63375i) q^{56} +(4.73614 + 2.16292i) q^{57} +(2.86044 + 4.01692i) q^{58} +(-3.78672 - 9.45876i) q^{59} +(-0.822347 + 1.59513i) q^{60} +(6.74829 - 6.43448i) q^{61} +(-3.14330 + 0.451938i) q^{62} +(2.22454 + 1.43227i) q^{63} +(0.841254 + 0.540641i) q^{64} +(-1.47440 + 0.510293i) q^{65} +(3.46481 + 3.30369i) q^{66} +(2.85806 + 2.03521i) q^{67} +(0.0125776 - 0.0217851i) q^{68} +(-4.30140 - 2.12083i) q^{69} +(1.12330 - 4.61336i) q^{70} +(0.134708 + 0.294968i) q^{71} +(0.235759 - 0.971812i) q^{72} +(-0.614684 + 3.18928i) q^{73} +(7.95815 + 0.379093i) q^{74} +(0.336736 + 1.74715i) q^{75} +(0.740984 + 5.15366i) q^{76} +(-10.9640 - 6.34237i) q^{77} +(0.731365 - 0.470020i) q^{78} +(9.24853 - 11.7605i) q^{79} +(-1.78650 + 0.170590i) q^{80} +(-0.995472 + 0.0950560i) q^{81} +(-1.38000 + 1.75482i) q^{82} +(-8.52400 + 5.47804i) q^{83} +(-0.00222539 + 2.64575i) q^{84} +(0.00642471 + 0.0446848i) q^{85} +(1.72586 + 8.95459i) q^{86} +(4.92572 + 0.234641i) q^{87} +(-0.906023 + 4.70089i) q^{88} +(3.70075 - 15.2547i) q^{89} +(0.745516 + 1.63245i) q^{90} +(-1.58869 + 1.66336i) q^{91} +(-0.541358 - 4.76518i) q^{92} +(-1.58781 + 2.75017i) q^{93} +(-2.89563 - 2.06197i) q^{94} +(-6.76258 - 6.44811i) q^{95} +(0.945001 - 0.327068i) q^{96} +(-6.67740 - 4.29131i) q^{97} +(-1.63887 - 6.80545i) q^{98} +(4.73868 - 0.681319i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 16 q^{9}+O(q^{10}) $ 320 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 16 * q^9	$ 320 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 16 q^{9} - 22 q^{14} + 16 q^{16} + 66 q^{17} + 16 q^{18} + 40 q^{23} - 48 q^{25} + 12 q^{26} + 44 q^{28} - 24 q^{29} + 24 q^{31} - 16 q^{32} + 98 q^{35} + 32 q^{36} - 22 q^{37} - 66 q^{38} - 8 q^{39} - 88 q^{43} + 4 q^{46} - 144 q^{47} - 24 q^{49} + 80 q^{50} - 22 q^{51} + 12 q^{52} + 44 q^{53} + 44 q^{57} + 10 q^{58} + 12 q^{59} - 32 q^{64} + 108 q^{70} - 16 q^{71} + 16 q^{72} - 180 q^{73} - 22 q^{74} - 12 q^{75} + 18 q^{77} - 16 q^{78} + 44 q^{79} + 16 q^{81} + 36 q^{82} + 22 q^{84} + 68 q^{85} - 22 q^{86} + 48 q^{87} + 22 q^{88} + 8 q^{92} + 8 q^{93} - 12 q^{94} + 66 q^{95} - 90 q^{98}+O(q^{100}) $ 320 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 16 * q^9 - 22 * q^14 + 16 * q^16 + 66 * q^17 + 16 * q^18 + 40 * q^23 - 48 * q^25 + 12 * q^26 + 44 * q^28 - 24 * q^29 + 24 * q^31 - 16 * q^32 + 98 * q^35 + 32 * q^36 - 22 * q^37 - 66 * q^38 - 8 * q^39 - 88 * q^43 + 4 * q^46 - 144 * q^47 - 24 * q^49 + 80 * q^50 - 22 * q^51 + 12 * q^52 + 44 * q^53 + 44 * q^57 + 10 * q^58 + 12 * q^59 - 32 * q^64 + 108 * q^70 - 16 * q^71 + 16 * q^72 - 180 * q^73 - 22 * q^74 - 12 * q^75 + 18 * q^77 - 16 * q^78 + 44 * q^79 + 16 * q^81 + 36 * q^82 + 22 * q^84 + 68 * q^85 - 22 * q^86 + 48 * q^87 + 22 * q^88 + 8 * q^92 + 8 * q^93 - 12 * q^94 + 66 * q^95 - 90 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{15}{22}\right)$

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 $

$2$	0.995472	+	0.0950560i	0.703905	+	0.0672148i
$2$	0.995472	+	0.0950560i	0.703905	+	0.0672148i
$3$	0.690079	−	0.723734i	0.398417	−	0.417848i
$3$	0.690079	−	0.723734i	0.398417	−	0.417848i
$4$	0.981929	+	0.189251i	0.490964	+	0.0946256i
$5$	−1.59513	+	0.822347i	−0.713364	+	0.367765i	−0.776395	−	0.630247i	$-0.782954\pi$
$5$	−1.59513	+	0.822347i	−0.713364	+	0.367765i	0.0630309	+	0.998012i	$0.479923\pi$
$6$	0.755750	−	0.654861i	0.308533	−	0.267346i
$7$	−1.53650	+	2.15387i	−0.580742	+	0.814088i
$7$	−1.53650	+	2.15387i	−0.580742	+	0.814088i
$8$	0.959493	+	0.281733i	0.339232	+	0.0996075i
$9$	−0.0475819	−	0.998867i	−0.0158606	−	0.332956i
$10$	−1.66608	+	0.666996i	−0.526860	+	0.210923i
$11$	0.455072	+	4.76573i	0.137209	+	1.43692i	0.757646	+	0.652665i	$0.226349\pi$
$11$	0.455072	+	4.76573i	0.137209	+	1.43692i	−0.620437	+	0.784256i	$0.713045\pi$
$12$	0.814576	−	0.580057i	0.235148	−	0.167448i
$13$	0.860526	+	0.123725i	0.238667	+	0.0343151i	0.260610	−	0.965444i	$-0.416076\pi$
$13$	0.860526	+	0.123725i	0.238667	+	0.0343151i	−0.0219433	+	0.999759i	$0.506985\pi$
$14$	−1.73428	+	1.99807i	−0.463506	+	0.534006i
$15$	−0.505605	+	1.72193i	−0.130547	+	0.444601i
$16$	0.928368	+	0.371662i	0.232092	+	0.0929156i
$17$	0.00822747	−	0.0237717i	0.00199546	−	0.00576549i	−0.943999	−	0.329949i	$-0.892968\pi$
$17$	0.00822747	−	0.0237717i	0.00199546	−	0.00576549i	0.945994	+	0.324184i	$0.105090\pi$
$18$	0.0475819	−	0.998867i	0.0112152	−	0.235435i
$19$	1.70293	+	4.92029i	0.390679	+	1.12879i	0.953286	+	0.302069i	$0.0976772\pi$
$19$	1.70293	+	4.92029i	0.390679	+	1.12879i	−0.562607	+	0.826724i	$0.690202\pi$
$20$	−1.72193	+	0.505605i	−0.385036	+	0.113057i
$21$	0.498526	+	2.59836i	0.108787	+	0.567009i
$22$			4.78741i			1.02068i
$23$	−1.43339	−	4.57661i	−0.298883	−	0.954290i
$23$	−1.43339	−	4.57661i	−0.298883	−	0.954290i
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$	−1.03210	+	1.44938i	−0.206420	+	0.289876i
$26$	0.844869	+	0.204963i	0.165692	+	0.0401965i
$27$	−0.755750	−	0.654861i	−0.145444	−	0.126028i
$28$	−1.91636	+	1.82417i	−0.362157	+	0.344735i
$29$	3.22932	+	3.72683i	0.599669	+	0.692055i	0.971714	−	0.236159i	$-0.0758887\pi$
$29$	3.22932	+	3.72683i	0.599669	+	0.692055i	−0.372045	+	0.928215i	$0.621343\pi$
$30$	−0.666996	+	1.66608i	−0.121776	+	0.304183i
$31$	−3.08610	+	0.748681i	−0.554281	+	0.134467i	−0.503109	−	0.864223i	$-0.667811\pi$
$31$	−3.08610	+	0.748681i	−0.554281	+	0.134467i	−0.0511715	+	0.998690i	$0.516296\pi$
$32$	0.888835	+	0.458227i	0.157125	+	0.0810038i
$33$	3.76316	+	2.95938i	0.655081	+	0.515162i
$34$	0.0104499	−	0.0228820i	0.00179214	−	0.00392423i
$35$	0.679684	−	4.69924i	0.114888	−	0.794317i
$36$	0.142315	−	0.989821i	0.0237191	−	0.164970i
$37$	7.95815	−	0.379093i	1.30831	−	0.0623226i	0.618197	−	0.786023i	$-0.287863\pi$
$37$	7.95815	−	0.379093i	1.30831	−	0.0623226i	0.690114	+	0.723700i	$0.257560\pi$
$38$	1.22752	+	5.05989i	0.199129	+	0.820822i
$39$	0.683375	−	0.537412i	0.109428	−	0.0860548i
$40$	−1.76220	+	0.339636i	−0.278628	+	0.0537011i
$41$	−1.20695	+	1.87805i	−0.188494	+	0.293302i	−0.922619	−	0.385712i	$-0.873956\pi$
$41$	−1.20695	+	1.87805i	−0.188494	+	0.293302i	0.734126	+	0.679014i	$0.237592\pi$
$42$	0.249279	+	2.63398i	0.0384646	+	0.406432i
$43$	2.56923	+	8.74999i	0.391804	+	1.33436i	0.885465	+	0.464707i	$0.153840\pi$
$43$	2.56923	+	8.74999i	0.391804	+	1.33436i	−0.493661	+	0.869655i	$0.664341\pi$
$44$	−0.455072	+	4.76573i	−0.0686047	+	0.718461i
$45$	0.897315	+	1.55419i	0.133764	+	0.231686i
$46$	−0.991865	−	4.69214i	−0.146243	−	0.691819i
$47$	−3.07852	−	1.77738i	−0.449048	−	0.259258i	0.258380	−	0.966043i	$-0.416811\pi$
$47$	−3.07852	−	1.77738i	−0.449048	−	0.259258i	−0.707428	+	0.706785i	$0.750145\pi$
$48$	0.909632	−	0.415415i	0.131294	−	0.0599600i
$49$	−2.27834	−	6.61885i	−0.325478	−	0.945550i
$50$	−1.16520	+	1.34471i	−0.164784	+	0.190171i
$51$	−0.0115268	−	0.0223589i	−0.00161407	−	0.00313087i
$52$	0.821560	+	0.284345i	0.113930	+	0.0394315i
$53$	0.792805	+	1.00813i	0.108900	+	0.138478i	0.837448	−	0.546517i	$-0.184047\pi$
$53$	0.792805	+	1.00813i	0.108900	+	0.138478i	−0.728548	+	0.684995i	$0.759804\pi$
$54$	−0.690079	−	0.723734i	−0.0939079	−	0.0984877i
$55$	−4.64498	−	7.22773i	−0.626329	−	0.974587i
$56$	−2.08108	+	1.63375i	−0.278095	+	0.218318i
$57$	4.73614	+	2.16292i	0.627317	+	0.286486i
$58$	2.86044	+	4.01692i	0.375594	+	0.527448i
$59$	−3.78672	−	9.45876i	−0.492989	−	1.23143i	−0.941307	−	0.337552i	$-0.890401\pi$
$59$	−3.78672	−	9.45876i	−0.492989	−	1.23143i	0.448318	−	0.893874i	$-0.352023\pi$
$60$	−0.822347	+	1.59513i	−0.106165	+	0.205930i
$61$	6.74829	−	6.43448i	0.864030	−	0.823851i	−0.121634	−	0.992575i	$-0.538813\pi$
$61$	6.74829	−	6.43448i	0.864030	−	0.823851i	0.985663	+	0.168724i	$0.0539648\pi$
$62$	−3.14330	+	0.451938i	−0.399199	+	0.0573962i
$63$	2.22454	+	1.43227i	0.280266	+	0.180449i
$64$	0.841254	+	0.540641i	0.105157	+	0.0675801i
$65$	−1.47440	+	0.510293i	−0.182876	+	0.0632941i
$66$	3.46481	+	3.30369i	0.426489	+	0.406656i
$67$	2.85806	+	2.03521i	0.349167	+	0.248641i	0.741161	−	0.671327i	$-0.234275\pi$
$67$	2.85806	+	2.03521i	0.349167	+	0.248641i	−0.391994	+	0.919968i	$0.628215\pi$
$68$	0.0125776	−	0.0217851i	0.00152526	−	0.00264183i
$69$	−4.30140	−	2.12083i	−0.517828	−	0.255318i
$70$	1.12330	−	4.61336i	0.134260	−	0.551402i
$71$	0.134708	+	0.294968i	0.0159868	+	0.0350063i	0.917457	−	0.397835i	$-0.130238\pi$
$71$	0.134708	+	0.294968i	0.0159868	+	0.0350063i	−0.901470	+	0.432841i	$0.857511\pi$
$72$	0.235759	−	0.971812i	0.0277845	−	0.114529i
$73$	−0.614684	+	3.18928i	−0.0719433	+	0.373277i	0.928056	+	0.372440i	$0.121479\pi$
$73$	−0.614684	+	3.18928i	−0.0719433	+	0.373277i	−1.00000		0.000837487i	$0.999733\pi$
$74$	7.95815	+	0.379093i	0.925116	+	0.0440687i
$75$	0.336736	+	1.74715i	0.0388829	+	0.201744i
$76$	0.740984	+	5.15366i	0.0849967	+	0.591165i
$77$	−10.9640	−	6.34237i	−1.24946	−	0.722780i
$78$	0.731365	−	0.470020i	0.0828108	−	0.0532192i
$79$	9.24853	−	11.7605i	1.04054	−	1.32316i	0.0957769	−	0.995403i	$-0.469466\pi$
$79$	9.24853	−	11.7605i	1.04054	−	1.32316i	0.944764	−	0.327752i	$-0.106291\pi$
$80$	−1.78650	+	0.170590i	−0.199737	+	0.0190726i
$81$	−0.995472	+	0.0950560i	−0.110608	+	0.0105618i
$82$	−1.38000	+	1.75482i	−0.152396	+	0.193787i
$83$	−8.52400	+	5.47804i	−0.935631	+	0.601294i	−0.917153	−	0.398536i	$-0.869518\pi$
$83$	−8.52400	+	5.47804i	−0.935631	+	0.601294i	−0.0184782	+	0.999829i	$0.505882\pi$
$84$	−0.00222539	+	2.64575i	−0.000242810	+	0.288675i
$85$	0.00642471	+	0.0446848i	0.000696857	+	0.00484675i
$86$	1.72586	+	8.95459i	0.186104	+	0.965599i
$87$	4.92572	+	0.234641i	0.528093	+	0.0251562i
$88$	−0.906023	+	4.70089i	−0.0965824	+	0.501117i
$89$	3.70075	−	15.2547i	0.392279	−	1.61700i	−0.343072	−	0.939309i	$-0.611468\pi$
$89$	3.70075	−	15.2547i	0.392279	−	1.61700i	0.735351	−	0.677686i	$-0.237017\pi$
$90$	0.745516	+	1.63245i	0.0785843	+	0.172076i
$91$	−1.58869	+	1.66336i	−0.166539	+	0.174368i
$92$	−0.541358	−	4.76518i	−0.0564404	−	0.496804i
$93$	−1.58781	+	2.75017i	−0.164648	+	0.285179i
$94$	−2.89563	−	2.06197i	−0.298661	−	0.212676i
$95$	−6.76258	−	6.44811i	−0.693826	−	0.661562i
$96$	0.945001	−	0.327068i	0.0964487	−	0.0333812i
$97$	−6.67740	−	4.29131i	−0.677988	−	0.435716i	0.155809	−	0.987787i	$-0.450201\pi$
$97$	−6.67740	−	4.29131i	−0.677988	−	0.435716i	−0.833797	+	0.552071i	$0.813838\pi$
$98$	−1.63887	−	6.80545i	−0.165551	−	0.687454i
$99$	4.73868	−	0.681319i	0.476255	−	0.0684751i
$100$	−1.28774	+	1.22786i	−0.128774	+	0.122786i
$101$	2.19072	−	4.24941i	0.217985	−	0.422832i	−0.754333	−	0.656492i	$-0.772040\pi$
$101$	2.19072	−	4.24941i	0.217985	−	0.422832i	0.972319	+	0.233659i	$0.0750700\pi$
$102$	−0.00934926	−	0.0233533i	−0.000925715	−	0.00231232i
$103$	3.16613	+	4.44620i	0.311968	+	0.438097i	0.940555	−	0.339642i	$-0.110306\pi$
$103$	3.16613	+	4.44620i	0.311968	+	0.438097i	−0.628587	+	0.777739i	$0.716366\pi$
$104$	0.790811	+	0.361151i	0.0775454	+	0.0354138i
$105$	−2.93197	−	3.73476i	−0.286131	−	0.364475i
$106$	0.693386	+	1.07893i	0.0673476	+	0.104795i
$107$	0.241361	+	0.253132i	0.0233332	+	0.0244712i	0.735297	−	0.677745i	$-0.237043\pi$
$107$	0.241361	+	0.253132i	0.0233332	+	0.0244712i	−0.711964	+	0.702216i	$0.752194\pi$
$108$	−0.618159	−	0.786053i	−0.0594824	−	0.0756380i
$109$	6.66969	+	2.30840i	0.638840	+	0.221105i	0.627238	−	0.778828i	$-0.284186\pi$
$109$	6.66969	+	2.30840i	0.638840	+	0.221105i	0.0116025	+	0.999933i	$0.496307\pi$
$110$	−3.93691	−	7.63654i	−0.375370	−	0.728115i
$111$	5.21739	−	6.02119i	0.495213	−	0.571506i
$112$	−2.22695	+	1.42853i	−0.210427	+	0.134983i
$113$	−4.92805	+	2.25056i	−0.463592	+	0.211715i	−0.633497	−	0.773745i	$-0.718381\pi$
$113$	−4.92805	+	2.25056i	−0.463592	+	0.211715i	0.169905	+	0.985460i	$0.445654\pi$
$114$	4.50910	+	2.60333i	0.422316	+	0.243824i
$115$	6.05001	+	6.12155i	0.564166	+	0.570837i
$116$	2.46565	+	4.27064i	0.228930	+	0.396519i
$117$	0.0826394	−	0.865439i	0.00764001	−	0.0800098i
$118$	−2.87046	−	9.77588i	−0.264247	−	0.899943i
$119$	0.0385598	+	0.0542462i	0.00353477	+	0.00497274i
$120$	−0.970250	+	1.50974i	−0.0885713	+	0.137820i
$121$	−11.7039	+	2.25574i	−1.06399	+	0.205067i
$122$	7.32937	−	5.76388i	0.663570	−	0.521837i
$123$	0.526318	+	2.16951i	0.0474565	+	0.195618i
$124$	−3.17202	+	0.151102i	−0.284856	+	0.0135694i
$125$	1.73145	−	12.0425i	0.154866	−	1.07711i
$126$	2.07832	+	1.63724i	0.185152	+	0.145857i
$127$	−2.59751	+	5.68776i	−0.230492	+	0.504707i	−0.989173	−	0.146755i	$-0.953117\pi$
$127$	−2.59751	+	5.68776i	−0.230492	+	0.504707i	0.758681	+	0.651463i	$0.225844\pi$
$128$	0.786053	+	0.618159i	0.0694779	+	0.0546381i
$129$	8.10564	+	4.17875i	0.713662	+	0.367918i
$130$	−1.51623	+	0.367833i	−0.132982	+	0.0322610i
$131$	1.74844	−	4.36739i	0.152762	−	0.381581i	−0.832171	−	0.554519i	$-0.812902\pi$
$131$	1.74844	−	4.36739i	0.152762	−	0.381581i	0.984933	+	0.172939i	$0.0553263\pi$
$132$	3.13509	+	3.61808i	0.272874	+	0.314914i
$133$	−13.2142	−	3.89213i	−1.14582	−	0.337490i
$134$	2.65166	+	2.29767i	0.229068	+	0.198489i
$135$	1.74404	+	0.423100i	0.150103	+	0.0364146i
$136$	0.0145915	−	0.0204909i	0.00125121	−	0.00175708i
$137$	−17.3002	+	9.98829i	−1.47806	+	0.853358i	−0.999692	−	0.0248028i	$-0.992104\pi$
$137$	−17.3002	+	9.98829i	−1.47806	+	0.853358i	−0.478366	+	0.878160i	$0.658771\pi$
$138$	−4.08033	−	2.52010i	−0.347341	−	0.214525i
$139$			1.81073i			0.153584i	0.997047	+	0.0767921i	$0.0244678\pi$
$139$			1.81073i			0.153584i	−0.997047	+	0.0767921i	$0.975532\pi$
$140$	1.55674	−	4.48569i	0.131568	−	0.379110i
$141$	−3.41077	+	1.00149i	−0.287239	+	0.0843409i
$142$	0.106059	+	0.306437i	0.00890028	+	0.0257157i
$143$	−0.198038	+	4.15734i	−0.0165608	+	0.347654i
$144$	0.327068	−	0.945001i	0.0272557	−	0.0787501i
$145$	−8.21593	−	3.28916i	−0.682296	−	0.273150i
$146$	−0.915061	+	3.11641i	−0.0757310	+	0.257916i
$147$	−6.36252	−	2.91861i	−0.524772	−	0.240723i
$148$	7.88608	+	1.13385i	0.648232	+	0.0932017i
$149$	6.11999	−	4.35803i	0.501369	−	0.357024i	−0.301221	−	0.953554i	$-0.597394\pi$
$149$	6.11999	−	4.35803i	0.501369	−	0.357024i	0.802590	+	0.596531i	$0.203455\pi$
$150$	0.169134	+	1.77125i	0.0138097	+	0.144622i
$151$	13.2806	−	5.31673i	1.08076	−	0.432670i	0.238166	−	0.971224i	$-0.423454\pi$
$151$	13.2806	−	5.31673i	1.08076	−	0.432670i	0.842591	+	0.538555i	$0.181029\pi$
$152$	0.247743	+	5.20076i	0.0200946	+	0.421837i
$153$	−0.0241363	−	0.00708705i	−0.00195130	−	0.000572954i
$154$	−10.3115	−	7.35584i	−0.830922	−	0.592751i
$155$	4.30706	−	3.73209i	0.345952	−	0.299769i
$156$	0.772731	−	0.398371i	0.0618680	−	0.0318952i
$157$	−3.02830	−	0.583656i	−0.241684	−	0.0465808i	0.0669705	−	0.997755i	$-0.478667\pi$
$157$	−3.02830	−	0.583656i	−0.241684	−	0.0465808i	−0.308655	+	0.951174i	$0.599879\pi$
$158$	10.3246	−	10.8281i	0.821377	−	0.861436i
$159$	1.27672	+	0.121912i	0.101250	+	0.00966824i
$160$	−1.79463			−0.141878
$161$	12.0599	+	3.94462i	0.950449	+	0.310879i
$162$	−1.00000			−0.0785674
$163$	11.9632	+	1.14235i	0.937033	+	0.0894758i	0.552386	−	0.833588i	$-0.313717\pi$
$163$	11.9632	+	1.14235i	0.937033	+	0.0894758i	0.384646	+	0.923064i	$0.374323\pi$
$164$	−1.54056	+	1.61569i	−0.120298	+	0.126164i
$165$	−8.43636	−	1.62597i	−0.656770	−	0.126582i
$166$	−9.00613	+	4.64298i	−0.699011	+	0.360365i
$167$	−4.21752	+	3.65450i	−0.326361	+	0.282794i	−0.802594	−	0.596526i	$-0.796547\pi$
$167$	−4.21752	+	3.65450i	−0.326361	+	0.282794i	0.476233	+	0.879319i	$0.342002\pi$
$168$	−0.253710	+	2.63356i	−0.0195741	+	0.203183i
$169$	−11.7482	−	3.44959i	−0.903709	−	0.265353i
$170$	0.00214805	+	0.0450932i	0.000164748	+	0.00345849i
$171$	4.83369	−	1.93512i	0.369642	−	0.147982i
$172$	0.866854	+	9.07810i	0.0660970	+	0.692199i
$173$	3.45136	−	2.45770i	0.262402	−	0.186855i	−0.441283	−	0.897368i	$-0.645476\pi$
$173$	3.45136	−	2.45770i	0.262402	−	0.186855i	0.703684	+	0.710513i	$0.251537\pi$
$174$	4.88111	+	0.701798i	0.370036	+	0.0532032i
$175$	−1.53596	−	4.44998i	−0.116108	−	0.336387i
$176$	−1.34877	+	4.59348i	−0.101667	+	0.346247i
$177$	−9.45876	−	3.78672i	−0.710964	−	0.284627i
$178$	5.13405	−	14.8339i	0.384813	−	1.11184i
$179$	−0.0390473	+	0.819703i	−0.00291853	+	0.0612675i	−0.999857	−	0.0169258i	$-0.994612\pi$
$179$	−0.0390473	+	0.819703i	−0.00291853	+	0.0612675i	0.996938	+	0.0781933i	$0.0249151\pi$
$180$	0.586966	+	1.69593i	0.0437498	+	0.126407i
$181$	−12.1778	+	3.57574i	−0.905172	+	0.265782i	−0.701007	−	0.713154i	$-0.747266\pi$
$181$	−12.1778	+	3.57574i	−0.905172	+	0.265782i	−0.204165	+	0.978937i	$0.565448\pi$
$182$	−1.73960	+	1.50482i	−0.128948	+	0.111544i
$183$		−	9.32426i		−	0.689269i
$184$	−0.0859472	−	4.79506i	−0.00633611	−	0.353497i
$185$	−12.3825	+	7.14906i	−0.910382	+	0.525609i
$186$	−1.84204	+	2.58678i	−0.135065	+	0.189672i
$187$	0.117034	+	0.0283921i	0.00855835	+	0.00207623i
$188$	−2.68651	−	2.32788i	−0.195934	−	0.169778i
$189$	2.57170	−	0.621597i	0.187063	−	0.0452145i
$190$	−6.11903	−	7.06174i	−0.443921	−	0.512312i
$191$	−7.75098	+	19.3610i	−0.560841	+	1.40091i	0.328863	+	0.944377i	$0.393334\pi$
$191$	−7.75098	+	19.3610i	−0.560841	+	1.40091i	−0.889705	+	0.456536i	$0.849090\pi$
$192$	0.971812	−	0.235759i	0.0701345	−	0.0170144i
$193$	14.4644	+	7.45690i	1.04117	+	0.536759i	0.891992	−	0.452051i	$-0.149308\pi$
$193$	14.4644	+	7.45690i	1.04117	+	0.536759i	0.149176	+	0.988811i	$0.452338\pi$
$194$	−6.23925	−	4.90660i	−0.447952	−	0.352274i
$195$	−0.648133	+	1.41921i	−0.0464138	+	0.101632i
$196$	−0.984547	−	6.93042i	−0.0703248	−	0.495030i
$197$	2.03270	−	14.1377i	0.144824	−	1.00727i	−0.779702	−	0.626151i	$-0.784629\pi$
$197$	2.03270	−	14.1377i	0.144824	−	1.00727i	0.924525	−	0.381120i	$-0.124462\pi$
$198$	4.78198	−	0.227794i	0.339841	−	0.0161886i
$199$	4.72791	+	19.4887i	0.335153	+	1.38152i	0.851148	+	0.524927i	$0.175907\pi$
$199$	4.72791	+	19.4887i	0.335153	+	1.38152i	−0.515995	+	0.856592i	$0.672578\pi$
$200$	−1.39863	+	1.09989i	−0.0988980	+	0.0777743i
$201$	3.44524	−	0.664015i	0.243008	−	0.0468360i
$202$	2.58474	−	4.02193i	0.181861	−	0.282982i
$203$	−12.9890	+	1.22927i	−0.911647	+	0.0862780i
$204$	−0.00708705	−	0.0241363i	−0.000496193	−	0.00168988i
$205$	0.380833	−	3.98826i	0.0265985	−	0.278552i
$206$	2.72915	+	4.72703i	0.190149	+	0.329348i
$207$	−4.50323	+	1.64953i	−0.312996	+	0.114650i
$208$	0.752901	+	0.434688i	0.0522043	+	0.0301402i
$209$	−22.6738	+	10.3548i	−1.56838	+	0.716256i
$210$	−2.56368	−	3.99655i	−0.176911	−	0.275788i
$211$	1.76738	−	2.03966i	0.121671	−	0.140416i	−0.691646	−	0.722237i	$-0.743114\pi$
$211$	1.76738	−	2.03966i	0.121671	−	0.140416i	0.813317	+	0.581821i	$0.197659\pi$
$212$	0.587688	+	1.13995i	0.0403626	+	0.0782924i
$213$	0.306437	+	0.106059i	0.0209967	+	0.00726704i
$214$	0.216206	+	0.274928i	0.0147795	+	0.0187937i
$215$	−11.2938	−	11.8446i	−0.770230	−	0.807794i
$216$	−0.540641	−	0.841254i	−0.0367859	−	0.0572401i
$217$	3.12923	−	7.79743i	0.212426	−	0.529324i
$218$	6.42006	+	2.93194i	0.434821	+	0.198576i
$219$	1.88401	+	2.64572i	0.127310	+	0.178782i
$220$	−3.19318	−	7.97619i	−0.215284	−	0.537754i
$221$	0.0100211	−	0.0194382i	0.000674093	−	0.00130756i
$222$	5.76612	−	5.49798i	0.386996	−	0.369000i
$223$	21.7178	−	3.12255i	1.45433	−	0.209101i	0.630612	−	0.776099i	$-0.282804\pi$
$223$	21.7178	−	3.12255i	1.45433	−	0.209101i	0.823720	+	0.566997i	$0.191895\pi$
$224$	−2.35266	+	1.21037i	−0.157193	+	0.0808716i
$225$	1.49685	+	0.961965i	0.0997898	+	0.0641310i
$226$	−5.11966	+	1.77193i	−0.340555	+	0.117867i
$227$	−2.07575	−	1.97922i	−0.137772	−	0.131366i	0.618060	−	0.786131i	$-0.287919\pi$
$227$	−2.07575	−	1.97922i	−0.137772	−	0.131366i	−0.755832	+	0.654765i	$0.772767\pi$
$228$	4.24122	+	3.02016i	0.280881	+	0.200015i
$229$	11.0249	−	19.0957i	0.728548	−	1.26188i	−0.228949	−	0.973438i	$-0.573529\pi$
$229$	11.0249	−	19.0957i	0.728548	−	1.26188i	0.957497	−	0.288444i	$-0.0931377\pi$
$230$	5.44072	+	6.66892i	0.358751	+	0.439736i
$231$	−12.1562	+	3.55828i	−0.799820	+	0.234118i
$232$	2.04854	+	4.48567i	0.134493	+	0.294499i
$233$	−0.829761	+	3.42032i	−0.0543594	+	0.224073i	−0.992512	−	0.122151i	$-0.961021\pi$
$233$	−0.829761	+	3.42032i	−0.0543594	+	0.224073i	0.938152	+	0.346223i	$0.112536\pi$
$234$	0.164530	−	0.853664i	0.0107557	−	0.0558058i
$235$	6.37226	+	0.303548i	0.415680	+	0.0198013i
$236$	−1.92820	−	10.0045i	−0.125515	−	0.651236i
$237$	−2.12923	−	14.8091i	−0.138308	−	0.961956i
$238$	0.0332288	+	0.0576659i	0.00215390	+	0.00373792i
$239$	21.6113	−	13.8887i	1.39792	−	0.898388i	0.398098	−	0.917343i	$-0.369670\pi$
$239$	21.6113	−	13.8887i	1.39792	−	0.898388i	0.999820	+	0.0189549i	$0.00603390\pi$
$240$	−1.10937	+	1.41067i	−0.0716093	+	0.0910586i
$241$	12.8138	−	1.22357i	0.825408	−	0.0788169i	0.326202	−	0.945300i	$-0.394231\pi$
$241$	12.8138	−	1.22357i	0.825408	−	0.0788169i	0.499206	+	0.866483i	$0.333625\pi$
$242$	−11.8653	+	1.13300i	−0.762730	+	0.0728319i
$243$	−0.618159	+	0.786053i	−0.0396549	+	0.0504253i
$244$	7.84407	−	5.04108i	0.502165	−	0.322722i
$245$	9.07724	+	8.68433i	0.579924	+	0.554822i
$246$	0.317709	+	2.20972i	0.0202564	+	0.140886i
$247$	0.856653	+	4.44474i	0.0545075	+	0.282812i
$248$	−3.17202	−	0.151102i	−0.201424	−	0.00959499i
$249$	−1.91759	+	9.94940i	−0.121522	+	0.630517i
$250$	2.86832	−	11.8234i	0.181409	−	0.747777i
$251$	−0.671561	−	1.47051i	−0.0423885	−	0.0928179i	0.887253	−	0.461283i	$-0.152611\pi$
$251$	−0.671561	−	1.47051i	−0.0423885	−	0.0928179i	−0.929642	+	0.368465i	$0.879883\pi$
$252$	1.91328	+	1.82739i	0.120526	+	0.115115i
$253$	21.1586	−	8.91384i	1.33023	−	0.560408i
$254$	−3.12641	+	5.41510i	−0.196168	+	0.339773i
$255$	0.0367735	+	0.0261863i	0.00230284	+	0.00163985i
$256$	0.723734	+	0.690079i	0.0452334	+	0.0431299i
$257$	15.6328	−	5.41057i	0.975149	−	0.337502i	0.207402	−	0.978256i	$-0.433499\pi$
$257$	15.6328	−	5.41057i	0.975149	−	0.337502i	0.767747	+	0.640754i	$0.221378\pi$
$258$	7.67172	+	4.93032i	0.477621	+	0.306948i
$259$	−11.4112	+	17.7233i	−0.709055	+	1.10127i
$260$	−1.54433	+	0.222040i	−0.0957750	+	0.0137704i
$261$	3.56895	−	3.40299i	0.220913	−	0.210640i
$262$	2.15567	−	4.18141i	0.133178	−	0.258329i
$263$	−7.23722	−	18.0777i	−0.446266	−	1.11472i	−0.965573	−	0.260132i	$-0.916234\pi$
$263$	−7.23722	−	18.0777i	−0.446266	−	1.11472i	0.519307	−	0.854588i	$-0.326190\pi$
$264$	2.77697	+	3.89971i	0.170911	+	0.240010i
$265$	−2.09366	−	0.956144i	−0.128613	−	0.0587354i
$266$	−12.7844	−	5.13060i	−0.783864	−	0.314577i
$267$	−8.48654	−	13.2053i	−0.519368	−	0.808152i
$268$	2.42124	+	2.53932i	0.147901	+	0.155114i
$269$	−11.5864	−	14.7333i	−0.706433	−	0.898302i	0.291875	−	0.956456i	$-0.405721\pi$
$269$	−11.5864	−	14.7333i	−0.706433	−	0.898302i	−0.998308	+	0.0581544i	$0.981478\pi$
$270$	1.69593	+	0.586966i	0.103211	+	0.0357216i
$271$	6.00611	+	11.6502i	0.364845	+	0.707701i	0.997786	−	0.0664989i	$-0.0211829\pi$
$271$	6.00611	+	11.6502i	0.364845	+	0.707701i	−0.632941	+	0.774200i	$0.718153\pi$
$272$	0.0164732	−	0.0190111i	0.000998833	−	0.00115271i
$273$	0.107513	+	2.29764i	0.00650698	+	0.139059i
$274$	−18.1713	+	8.29858i	−1.09777	+	0.501335i
$275$	−7.37703	−	4.25913i	−0.444852	−	0.256835i
$276$	−3.82230	−	2.89655i	−0.230076	−	0.174352i
$277$	−0.396002	−	0.685896i	−0.0237935	−	0.0412115i	0.853883	−	0.520464i	$-0.174241\pi$
$277$	−0.396002	−	0.685896i	−0.0237935	−	0.0412115i	−0.877677	+	0.479253i	$0.840908\pi$
$278$	−0.172121	+	1.80253i	−0.0103231	+	0.108109i
$279$	0.894676	+	3.04699i	0.0535628	+	0.182418i
$280$	1.97608	−	4.31740i	0.118093	−	0.258014i
$281$	1.05610	−	1.64333i	0.0630018	−	0.0980327i	−0.808323	−	0.588739i	$-0.799625\pi$
$281$	1.05610	−	1.64333i	0.0630018	−	0.0980327i	0.871325	+	0.490706i	$0.163261\pi$
$282$	−3.49053	+	0.672744i	−0.207858	+	0.0400613i
$283$	−24.4280	+	19.2104i	−1.45209	+	1.14194i	−0.489159	+	0.872195i	$0.662696\pi$
$283$	−24.4280	+	19.2104i	−1.45209	+	1.14194i	−0.962932	+	0.269743i	$0.913061\pi$
$284$	0.0764500	+	0.315131i	0.00453648	+	0.0186996i
$285$	−9.33343	+	0.444606i	−0.552865	+	0.0263362i
$286$	−0.592322	+	4.11969i	−0.0350247	+	0.243602i
$287$	−2.19061	−	5.48523i	−0.129307	−	0.323783i
$288$	0.415415	−	0.909632i	0.0244786	−	0.0536006i
$289$	13.3624	+	10.5083i	0.786024	+	0.618136i
$290$	−7.86607	−	4.05524i	−0.461912	−	0.238132i
$291$	−7.71370	+	1.87132i	−0.452185	+	0.109699i
$292$	−1.20715	+	3.01532i	−0.0706432	+	0.176458i
$293$	7.13606	+	8.23546i	0.416893	+	0.481121i	0.924888	−	0.380240i	$-0.124159\pi$
$293$	7.13606	+	8.23546i	0.416893	+	0.481121i	−0.507995	+	0.861360i	$0.669613\pi$
$294$	−6.05628	−	3.51019i	−0.353210	−	0.204719i
$295$	13.8187	+	11.9740i	0.804555	+	0.697151i
$296$	7.74259	+	1.87833i	0.450029	+	0.109176i
$297$	2.77697	−	3.89971i	0.161136	−	0.226284i
$298$	6.50654	−	3.75655i	0.376914	−	0.217611i
$299$	−0.667229	−	4.11564i	−0.0385868	−	0.238014i
$300$			1.77931i			0.102728i
$301$	−22.7940	−	7.91056i	−1.31382	−	0.455957i
$302$	13.7258	−	4.03026i	0.789832	−	0.231916i
$303$	−1.56367	−	4.51793i	−0.0898306	−	0.259548i
$304$	−0.247743	+	5.20076i	−0.0142090	+	0.298284i
$305$	−5.47302	+	15.8133i	−0.313384	+	0.905465i
$306$	−0.0233533	−	0.00934926i	−0.00133502	−	0.000534462i
$307$	5.18129	−	17.6458i	0.295712	−	1.00710i	−0.668884	−	0.743367i	$-0.733228\pi$
$307$	5.18129	−	17.6458i	0.295712	−	1.00710i	0.964595	−	0.263734i	$-0.0849542\pi$
$308$	−9.56556	−	8.30270i	−0.545049	−	0.473090i
$309$	5.40274	+	0.776797i	0.307351	+	0.0441904i
$310$	4.64232	−	3.30578i	0.263666	−	0.187756i
$311$	−0.690308	−	7.22923i	−0.0391438	−	0.409932i	−0.993714	−	0.111947i	$-0.964291\pi$
$311$	−0.690308	−	7.22923i	−0.0391438	−	0.409932i	0.954570	−	0.297985i	$-0.0963146\pi$
$312$	0.807100	−	0.323114i	0.0456930	−	0.0182927i
$313$	−1.00244	−	21.0437i	−0.0566611	−	1.18946i	−0.830846	−	0.556503i	$-0.812143\pi$
$313$	−1.00244	−	21.0437i	−0.0566611	−	1.18946i	0.774185	−	0.632960i	$-0.218160\pi$
$314$	−2.95910	−	0.868871i	−0.166992	−	0.0490332i
$315$	−4.72626	−	0.455315i	−0.266295	−	0.0256541i
$316$	11.3071	−	9.79764i	0.636073	−	0.551160i
$317$	29.2016	−	15.0545i	1.64012	−	0.845543i	0.643325	−	0.765593i	$-0.277554\pi$
$317$	29.2016	−	15.0545i	1.64012	−	0.845543i	0.996799	−	0.0799493i	$-0.0254759\pi$
$318$	1.25935	+	0.242720i	0.0706208	+	0.0136110i
$319$	−16.2915	+	17.0860i	−0.912149	+	0.956634i
$320$	−1.78650	−	0.170590i	−0.0998686	−	0.00953629i
$321$	0.349758			0.0195216
$322$	11.6303	+	5.07312i	0.648130	+	0.282714i
$323$	0.130975			0.00728763
$324$	−0.995472	−	0.0950560i	−0.0553040	−	0.00528089i
$325$	−1.06747	+	1.11953i	−0.0592127	+	0.0621005i
$326$	11.8005	+	2.27436i	0.653568	+	0.125965i
$327$	6.27328	−	3.23410i	0.346913	−	0.178846i
$328$	−1.68717	+	1.46194i	−0.0931582	+	0.0807220i
$329$	8.55839	−	3.89979i	0.471840	−	0.215002i
$330$	−8.24360	−	2.42054i	−0.453795	−	0.133246i
$331$	0.664530	+	13.9502i	0.0365259	+	0.766773i	0.940625	+	0.339449i	$0.110241\pi$
$331$	0.664530	+	13.9502i	0.0365259	+	0.766773i	−0.904099	+	0.427324i	$0.859456\pi$
$332$	−9.40669	+	3.76587i	−0.516259	+	0.206679i
$333$	−0.757328	−	7.93110i	−0.0415013	−	0.434622i
$334$	−4.54580	+	3.23705i	−0.248735	+	0.177124i
$335$	−6.23262	−	0.896116i	−0.340525	−	0.0489600i
$336$	−0.502897	+	2.59752i	−0.0274353	+	0.141706i
$337$	3.76726	−	12.8301i	0.205216	−	0.698901i	−0.790986	−	0.611834i	$-0.790432\pi$
$337$	3.76726	−	12.8301i	0.205216	−	0.698901i	0.996202	−	0.0870677i	$-0.0277496\pi$
$338$	−11.3671	−	4.55070i	−0.618289	−	0.247526i
$339$	−1.77193	+	5.11966i	−0.0962382	+	0.278062i
$340$	−0.00214805	+	0.0450932i	−0.000116495	+	0.00244552i
$341$	−4.97241	−	14.3668i	−0.269271	−	0.778008i
$342$	4.99575	−	1.46688i	0.270139	−	0.0793200i
$343$	17.7568	+	5.26258i	0.958779	+	0.284153i
$344$			9.11939i			0.491685i
$345$	8.60536	−	0.154243i	0.463297	−	0.00830419i
$346$	3.66935	−	2.11850i	0.197265	−	0.113891i
$347$	−11.4034	+	16.0139i	−0.612169	+	0.859671i	−0.998020	−	0.0628897i	$-0.979968\pi$
$347$	−11.4034	+	16.0139i	−0.612169	+	0.859671i	0.385851	+	0.922561i	$0.373908\pi$
$348$	4.79230	+	1.16260i	0.256894	+	0.0623219i
$349$	16.7873	+	14.5463i	0.898605	+	0.778646i	0.975867	−	0.218365i	$-0.0700723\pi$
$349$	16.7873	+	14.5463i	0.898605	+	0.778646i	−0.0772618	+	0.997011i	$0.524618\pi$
$350$	−1.10601	−	4.57583i	−0.0591188	−	0.244589i
$351$	−0.569320	−	0.657030i	−0.0303880	−	0.0350697i
$352$	−1.77930	+	4.44448i	−0.0948370	+	0.236891i
$353$	−26.3880	+	6.40165i	−1.40449	+	0.340726i	−0.865214	−	0.501403i	$-0.832817\pi$
$353$	−26.3880	+	6.40165i	−1.40449	+	0.340726i	−0.539277	+	0.842129i	$0.681302\pi$
$354$	−9.05598	−	4.66868i	−0.481320	−	0.248138i
$355$	−0.457442	−	0.359737i	−0.0242785	−	0.0190928i
$356$	6.52085	−	14.2787i	0.345604	−	0.756768i
$357$	0.0658691	+	0.00952710i	0.00348616	+	0.000504228i
$358$	−0.116788	+	0.812280i	−0.00617245	+	0.0429303i
$359$	33.0511	−	1.57442i	1.74437	−	0.0830946i	0.848993	−	0.528403i	$-0.177209\pi$
$359$	33.0511	−	1.57442i	1.74437	−	0.0830946i	0.895377	+	0.445309i	$0.146906\pi$
$360$	0.423100	+	1.74404i	0.0222993	+	0.0919191i
$361$	−6.37432	+	5.01282i	−0.335490	+	0.263833i
$362$	−12.4626	+	2.40197i	−0.655020	+	0.126245i
$363$	−6.44404	+	10.0271i	−0.338225	+	0.526288i
$364$	−1.87477	+	1.33264i	−0.0982646	+	0.0698494i
$365$	−1.64220	−	5.59280i	−0.0859564	−	0.292741i
$366$	0.886328	−	9.28204i	0.0463291	−	0.485180i
$367$	15.5448	+	26.9243i	0.811431	+	1.40544i	0.911863	+	0.410495i	$0.134644\pi$
$367$	15.5448	+	26.9243i	0.811431	+	1.40544i	−0.100432	+	0.994944i	$0.532023\pi$
$368$	0.370242	−	4.78152i	0.0193002	−	0.249254i
$369$	1.93335	+	1.11622i	0.100646	+	0.0581081i
$370$	−13.0060	+	5.93966i	−0.676151	+	0.308788i
$371$	−3.38954	+	0.158606i	−0.175976	+	0.00823442i
$372$	−2.07959	+	2.39997i	−0.107822	+	0.124433i
$373$	9.82196	+	19.0519i	0.508562	+	0.986472i	0.993704	+	0.112037i	$0.0357375\pi$
$373$	9.82196	+	19.0519i	0.508562	+	0.986472i	−0.485142	+	0.874435i	$0.661232\pi$
$374$	0.113805	+	0.0393883i	0.00588471	+	0.00203672i
$375$	−7.52073	−	9.56339i	−0.388369	−	0.493851i
$376$	−2.45307	−	2.57270i	−0.126507	−	0.132677i
$377$	2.31781	+	3.60658i	0.119373	+	0.185749i
$378$	2.61914	−	0.374327i	0.134714	−	0.0192533i
$379$	22.8620	+	10.4407i	1.17434	+	0.536305i	0.904448	−	0.426584i	$-0.140283\pi$
$379$	22.8620	+	10.4407i	1.17434	+	0.536305i	0.269897	+	0.962889i	$0.413011\pi$
$380$	−5.42006	−	7.61141i	−0.278043	−	0.390457i
$381$	2.32394	+	5.80491i	0.119059	+	0.297395i
$382$	−9.55627	+	18.5366i	−0.488941	+	0.948413i
$383$	−10.8430	+	10.3388i	−0.554051	+	0.528287i	−0.914550	−	0.404473i	$-0.867455\pi$
$383$	−10.8430	+	10.3388i	−0.554051	+	0.528287i	0.360499	+	0.932760i	$0.382607\pi$
$384$	0.989821	−	0.142315i	0.0505116	−	0.00726247i
$385$	22.7046	+	1.10070i	1.15713	+	0.0560967i
$386$	13.6900	+	8.79806i	0.696805	+	0.447809i
$387$	8.61783	−	2.98266i	0.438069	−	0.151617i
$388$	−5.74460	−	5.47746i	−0.291638	−	0.278076i
$389$	−24.7712	−	17.6395i	−1.25595	−	0.894359i	−0.258521	−	0.966006i	$-0.583235\pi$
$389$	−24.7712	−	17.6395i	−1.25595	−	0.894359i	−0.997430	+	0.0716466i	$0.977175\pi$
$390$	−0.780103	+	1.35118i	−0.0395021	+	0.0684196i
$391$	−0.120587	−	0.00357980i	−0.00609836	−	0.000181038i
$392$	−0.321311	−	6.99262i	−0.0162286	−	0.353181i
$393$	−1.95427	−	4.27925i	−0.0985797	−	0.215860i
$394$	3.36737	−	13.8805i	0.169646	−	0.699289i
$395$	−5.08143	+	26.3650i	−0.255674	+	1.32656i
$396$	4.78198	+	0.227794i	0.240304	+	0.0114471i
$397$	−6.68261	−	34.6727i	−0.335390	−	1.74017i	−0.622817	−	0.782368i	$-0.714012\pi$
$397$	−6.68261	−	34.6727i	−0.335390	−	1.74017i	0.287426	−	0.957803i	$-0.407200\pi$
$398$	2.85398	+	19.8499i	0.143057	+	0.994985i
$399$	−11.9357	+	6.87772i	−0.597534	+	0.344317i
$400$	−1.49685	+	0.961965i	−0.0748424	+	0.0480983i
$401$	10.8698	−	13.8221i	0.542812	−	0.690241i	−0.434831	−	0.900512i	$-0.643192\pi$
$401$	10.8698	−	13.8221i	0.542812	−	0.690241i	0.977643	+	0.210271i	$0.0674345\pi$
$402$	3.49276	−	0.333518i	0.174203	−	0.0166344i
$403$	−2.74830	+	0.262431i	−0.136903	+	0.0130726i
$404$	2.95534	−	3.75802i	0.147034	−	0.186969i
$405$	1.50974	−	0.970250i	0.0750195	−	0.0482121i
$406$	−13.0470	−	0.0109741i	−0.647512	−	0.000544634i
$407$	5.42819	+	37.7539i	0.269065	+	1.87139i
$408$	−0.00476066	−	0.0247007i	−0.000235688	−	0.00122286i
$409$	15.4208	+	0.734583i	0.762509	+	0.0363228i	0.425234	−	0.905083i	$-0.360192\pi$
$409$	15.4208	+	0.734583i	0.762509	+	0.0363228i	0.337275	+	0.941406i	$0.390495\pi$
$410$	0.758217	−	3.93400i	0.0374457	−	0.194287i
$411$	−4.70966	+	19.4135i	−0.232310	+	0.957596i
$412$	2.26746	+	4.96504i	0.111710	+	0.244610i
$413$	26.1913	+	6.37726i	1.28879	+	0.313805i
$414$	−4.63963	+	1.21400i	−0.228026	+	0.0596650i
$415$	9.09204	−	15.7479i	0.446311	−	0.773033i
$416$	0.708172	+	0.504287i	0.0347210	+	0.0247247i
$417$	1.31049	+	1.24955i	0.0641748	+	0.0611906i
$418$	−23.5555	+	8.15262i	−1.15213	+	0.398758i
$419$	5.53631	+	3.55797i	0.270467	+	0.173818i	0.668843	−	0.743404i	$-0.266790\pi$
$419$	5.53631	+	3.55797i	0.270467	+	0.173818i	−0.398376	+	0.917222i	$0.630426\pi$
$420$	−2.17217	−	4.22215i	−0.105991	−	0.206020i
$421$	−29.1100	+	4.18539i	−1.41874	+	0.203983i	−0.808621	−	0.588330i	$-0.799786\pi$
$421$	−29.1100	+	4.18539i	−1.41874	+	0.203983i	−0.610115	+	0.792313i	$0.708877\pi$
$422$	1.95326	−	1.86243i	0.0950832	−	0.0906616i
$423$	−1.62889	+	3.15960i	−0.0791992	+	0.153625i
$424$	0.476667	+	1.19066i	0.0231490	+	0.0578234i
$425$	0.0259627	+	0.0364595i	0.00125938	+	0.00176855i
$426$	0.294968	+	0.134708i	0.0142913	+	0.00652660i
$427$	3.49032	+	24.4215i	0.168909	+	1.18184i
$428$	0.189093	+	0.294235i	0.00914017	+	0.0142224i
$429$	2.87215	+	3.01222i	0.138668	+	0.145431i
$430$	−10.1167	−	12.8645i	−0.487873	−	0.620381i
$431$	11.6518	+	4.03271i	0.561246	+	0.194249i	0.592937	−	0.805249i	$-0.297968\pi$
$431$	11.6518	+	4.03271i	0.561246	+	0.194249i	−0.0316916	+	0.999498i	$0.510089\pi$
$432$	−0.458227	−	0.888835i	−0.0220464	−	0.0427641i
$433$	19.9807	−	23.0590i	0.960213	−	1.10814i	−0.0338599	−	0.999427i	$-0.510780\pi$
$433$	19.9807	−	23.0590i	0.960213	−	1.10814i	0.994073	−	0.108718i	$-0.0346746\pi$
$434$	3.85625	−	7.46467i	0.185106	−	0.358315i
$435$	−8.05012	+	3.67637i	−0.385974	+	0.176268i
$436$	6.11229	+	3.52893i	0.292726	+	0.169005i
$437$	20.0773	−	14.8464i	0.960429	−	0.710198i
$438$	1.62399	+	2.81283i	0.0775972	+	0.134402i
$439$	−0.186138	+	1.94932i	−0.00888386	+	0.0930360i	−0.998826	−	0.0484342i	$-0.984577\pi$
$439$	−0.186138	+	1.94932i	−0.00888386	+	0.0930360i	0.989943	+	0.141470i	$0.0451829\pi$
$440$	−2.42054	−	8.24360i	−0.115395	−	0.392998i
$441$	−6.50294	+	2.59070i	−0.309664	+	0.123367i
$442$	0.0118235	−	0.0183977i	0.000562385	−	0.000875087i
$443$	−18.7510	+	3.61397i	−0.890889	+	0.171705i	−0.614102	−	0.789226i	$-0.710482\pi$
$443$	−18.7510	+	3.61397i	−0.890889	+	0.171705i	−0.276787	+	0.960931i	$0.589270\pi$
$444$	6.26262	−	4.92498i	0.297211	−	0.233729i
$445$	6.64148	+	27.3765i	0.314836	+	1.29777i
$446$	21.9163	−	1.04400i	1.03777	−	0.0494349i
$447$	1.06923	−	7.43663i	0.0505727	−	0.351741i
$448$	−2.45706	+	0.981260i	−0.116085	+	0.0463602i
$449$	−10.7391	+	23.5154i	−0.506811	+	1.10976i	0.467384	+	0.884054i	$0.345196\pi$
$449$	−10.7391	+	23.5154i	−0.506811	+	1.10976i	−0.974195	+	0.225707i	$0.927531\pi$
$450$	1.39863	+	1.09989i	0.0659320	+	0.0518495i
$451$	−9.49952	−	4.89734i	−0.447315	−	0.230607i
$452$	−5.26492	+	1.27725i	−0.247641	+	0.0600770i
$453$	5.31673	−	13.2806i	0.249802	−	0.623975i
$454$	−1.87821	−	2.16757i	−0.0881488	−	0.101729i
$455$	1.16630	−	3.95973i	0.0546770	−	0.185635i
$456$	3.93493	+	3.40963i	0.184270	+	0.159671i
$457$	−34.5965	−	8.39302i	−1.61836	−	0.392609i	−0.678614	−	0.734495i	$-0.737419\pi$
$457$	−34.5965	−	8.39302i	−1.61836	−	0.392609i	−0.939741	+	0.341886i	$0.888934\pi$
$458$	12.7902	−	17.9613i	0.597646	−	0.839276i
$459$	−0.0217851	+	0.0125776i	−0.00101684	+	0.000587073i
$460$	4.78217	+	7.15590i	0.222970	+	0.333645i
$461$			32.7567i			1.52563i	0.646616	+	0.762816i	$0.276184\pi$
$461$			32.7567i			1.52563i	−0.646616	+	0.762816i	$0.723816\pi$
$462$	−12.4394	+	2.38665i	−0.578733	+	0.111037i
$463$	−2.33689	+	0.686173i	−0.108605	+	0.0318892i	−0.335583	−	0.942011i	$-0.608933\pi$
$463$	−2.33689	+	0.686173i	−0.108605	+	0.0318892i	0.226979	+	0.973900i	$0.427115\pi$
$464$	1.61287	+	4.66009i	0.0748757	+	0.216339i
$465$	0.271172	−	5.69261i	0.0125753	−	0.263988i
$466$	−1.15113	+	3.32596i	−0.0533249	+	0.154072i
$467$	−20.2034	−	8.08820i	−0.934900	−	0.374277i	−0.146339	−	0.989234i	$-0.546749\pi$
$467$	−20.2034	−	8.08820i	−0.934900	−	0.374277i	−0.788561	+	0.614957i	$0.789173\pi$
$468$	0.244931	−	0.834159i	0.0113220	−	0.0385590i
$469$	−8.77499	+	3.02879i	−0.405191	+	0.139857i
$470$	6.31455	+	0.907895i	0.291269	+	0.0418781i
$471$	−2.51218	+	1.78891i	−0.115755	+	0.0824287i
$472$	−0.968487	−	10.1425i	−0.0445782	−	0.466844i
$473$	−40.5309	+	16.2261i	−1.86361	+	0.746078i
$474$	−0.711892	−	14.9445i	−0.0326983	−	0.686422i
$475$	−8.88897	−	2.61004i	−0.407854	−	0.119757i
$476$	0.0275968	+	0.0605633i	0.00126490	+	0.00277592i
$477$	0.969269	−	0.839876i	0.0443798	−	0.0384553i
$478$	22.8336	−	11.7716i	1.04439	−	0.538419i
$479$	33.1959	+	6.39799i	1.51676	+	0.292332i	0.878595	−	0.477567i	$-0.158481\pi$
$479$	33.1959	+	6.39799i	1.51676	+	0.292332i	0.638166	+	0.769899i	$0.279693\pi$
$480$	−1.23844	+	1.29883i	−0.0565266	+	0.0592834i
$481$	6.89510	+	0.658402i	0.314389	+	0.0300206i
$482$	12.8721			0.586307
$483$	11.1771	−	6.00603i	0.508576	−	0.273284i
$484$	−11.9193			−0.541785
$485$	14.1803	+	1.35405i	0.643893	+	0.0614843i
$486$	−0.690079	+	0.723734i	−0.0313026	+	0.0328292i
$487$	−4.18125	−	0.805869i	−0.189470	−	0.0365174i	0.0936332	−	0.995607i	$-0.470152\pi$
$487$	−4.18125	−	0.805869i	−0.189470	−	0.0365174i	−0.283104	+	0.959089i	$0.591364\pi$
$488$	8.28774	−	4.27262i	0.375168	−	0.193413i
$489$	9.08234	−	7.86989i	0.410717	−	0.355889i
$490$	8.21064	+	9.50786i	0.370919	+	0.429521i
$491$	6.91875	+	2.03153i	0.312239	+	0.0916816i	0.434098	−	0.900866i	$-0.357067\pi$
$491$	6.91875	+	2.03153i	0.312239	+	0.0916816i	−0.121859	+	0.992547i	$0.538885\pi$
$492$	0.106224	+	2.22991i	0.00478894	+	0.100532i
$493$	0.115162	−	0.0461041i	0.00518665	−	0.00207642i
$494$	0.430275	+	4.50604i	0.0193590	+	0.202736i
$495$	−6.99853	+	4.98363i	−0.314560	+	0.223997i
$496$	−3.14330	−	0.451938i	−0.141138	−	0.0202926i
$497$	−0.842302	−	0.163075i	−0.0377824	−	0.00731493i
$498$	−2.85466	+	9.72207i	−0.127920	+	0.435656i
$499$	3.05036	+	1.22118i	0.136553	+	0.0546676i	0.438933	−	0.898520i	$-0.355357\pi$
$499$	3.05036	+	1.22118i	0.136553	+	0.0546676i	−0.302379	+	0.953188i	$0.597781\pi$
$500$	3.97922	−	11.4972i	0.177956	−	0.514170i
$501$	−0.265534	+	5.57425i	−0.0118632	+	0.249039i
$502$	−0.528739	−	1.52769i	−0.0235988	−	0.0681841i
$503$	−37.9112	+	11.1317i	−1.69038	+	0.496340i	−0.978549	−	0.206013i	$-0.933951\pi$
$503$	−37.9112	+	11.1317i	−1.69038	+	0.496340i	−0.711829	+	0.702353i	$0.752133\pi$
$504$	1.73092	+	2.00098i	0.0771011	+	0.0891308i
$505$			8.57990i			0.381801i
$506$	21.9101	−	6.86222i	0.974023	−	0.305063i
$507$	−10.6038	+	6.12209i	−0.470930	+	0.271892i
$508$	−3.62699	+	5.09339i	−0.160922	+	0.225983i
$509$	28.1899	+	6.83879i	1.24949	+	0.303124i	0.805333	−	0.592823i	$-0.201986\pi$
$509$	28.1899	+	6.83879i	1.24949	+	0.303124i	0.444162	+	0.895947i	$0.353502\pi$
$510$	0.0341178	+	0.0295632i	0.00151076	+	0.00130908i
$511$	−5.92485	−	6.22428i	−0.262100	−	0.275346i
$512$	0.654861	+	0.755750i	0.0289410	+	0.0333997i
$513$	1.93512	−	4.83369i	0.0854376	−	0.213413i
$514$	16.0763	−	3.90008i	0.709097	−	0.172025i
$515$	−8.70670	−	4.48862i	−0.383663	−	0.197792i
$516$	7.16833	+	5.63724i	0.315568	+	0.248165i
$517$	7.06958	−	15.4802i	0.310920	−	0.680819i
$518$	−13.0442	+	16.5584i	−0.573130	+	0.727533i
$519$	0.602988	−	4.19387i	0.0264682	−	0.184090i
$520$	−1.55844	+	0.0742376i	−0.0683421	+	0.00325553i
$521$	5.94515	+	24.5062i	0.260462	+	1.07364i	0.940319	+	0.340294i	$0.110526\pi$
$521$	5.94515	+	24.5062i	0.260462	+	1.07364i	−0.679857	+	0.733344i	$0.737958\pi$
$522$	3.87627	−	3.04833i	0.169660	−	0.133422i
$523$	−39.5297	+	7.61872i	−1.72851	+	0.333144i	−0.954089	−	0.299523i	$-0.903172\pi$
$523$	−39.5297	+	7.61872i	−1.72851	+	0.333144i	−0.774424	+	0.632667i	$0.781960\pi$
$524$	2.54338	−	3.95757i	0.111108	−	0.172887i
$525$	−4.28054	−	1.95921i	−0.186818	−	0.0855069i
$526$	−5.48606	−	18.6838i	−0.239203	−	0.814652i
$527$	−0.00759341	+	0.0795218i	−0.000330774	+	0.00346402i
$528$	2.39370	+	4.14602i	0.104173	+	0.180432i
$529$	−18.8908	+	13.1201i	−0.821338	+	0.570441i
$530$	−1.99330	−	1.15083i	−0.0865832	−	0.0499888i
$531$	−9.26787	+	4.23249i	−0.402191	+	0.183675i
$532$	−12.2389	−	6.32260i	−0.530622	−	0.274120i
$533$	−1.27097	+	1.46678i	−0.0550519	+	0.0635333i
$534$	−7.19287	−	13.9522i	−0.311266	−	0.603771i
$535$	−0.593163	−	0.205296i	−0.0256447	−	0.00887571i
$536$	2.16890	+	2.75798i	0.0936822	+	0.119127i
$537$	0.566301	+	0.593920i	0.0244377	+	0.0256295i
$538$	−10.1334	−	15.7679i	−0.436882	−	0.679802i
$539$	30.5068	−	13.8700i	1.31402	−	0.597424i
$540$	1.63245	+	0.745516i	0.0702496	+	0.0320819i
$541$	−22.9533	−	32.2334i	−0.986838	−	1.38582i	−0.921682	−	0.387946i	$-0.873185\pi$
$541$	−22.9533	−	32.2334i	−0.986838	−	1.38582i	−0.0651561	−	0.997875i	$-0.520755\pi$
$542$	4.87149	+	12.1684i	0.209248	+	0.522677i
$543$	−5.81579	+	11.2811i	−0.249579	+	0.484117i
$544$	0.0182057	−	0.0173591i	0.000780563	−	0.000744265i
$545$	−12.5373	+	1.80260i	−0.537040	+	0.0772147i
$546$	−0.111378	+	2.29745i	−0.00476654	+	0.0983219i
$547$	−19.8943	−	12.7853i	−0.850620	−	0.546661i	0.0411478	−	0.999153i	$-0.486899\pi$
$547$	−19.8943	−	12.7853i	−0.850620	−	0.546661i	−0.891768	+	0.452493i	$0.850535\pi$
$548$	−18.8779	+	6.53370i	−0.806424	+	0.279106i
$549$	−6.74829	−	6.43448i	−0.288010	−	0.274617i
$550$	−6.93877	−	4.94108i	−0.295870	−	0.210688i
$551$	−12.8378	+	22.2357i	−0.546909	+	0.947274i
$552$	−3.52966	−	3.24677i	−0.150232	−	0.138192i
$553$	11.1202	+	37.9901i	0.472879	+	1.61550i
$554$	−0.329010	−	0.720432i	−0.0139783	−	0.0306082i
$555$	−3.37091	+	13.8951i	−0.143087	+	0.589813i
$556$	−0.342683	+	1.77801i	−0.0145330	+	0.0754043i
$557$	0.635131	+	0.0302550i	0.0269113	+	0.00128195i	0.0610333	−	0.998136i	$-0.480560\pi$
$557$	0.635131	+	0.0302550i	0.0269113	+	0.00128195i	−0.0341219	+	0.999418i	$0.510863\pi$
$558$	0.600990	+	3.11823i	0.0254419	+	0.132005i
$559$	1.12830	+	7.84748i	0.0477219	+	0.331913i
$560$	2.37753	−	4.11001i	0.100469	−	0.173680i
$561$	0.101311	−	0.0651085i	0.00427735	−	0.00274888i
$562$	1.20753	−	1.53550i	0.0509365	−	0.0647711i
$563$	27.1031	−	2.58803i	1.14226	−	0.109073i	0.493275	−	0.869874i	$-0.335800\pi$
$563$	27.1031	−	2.58803i	1.14226	−	0.109073i	0.648985	+	0.760801i	$0.275194\pi$
$564$	−3.53867	+	0.337902i	−0.149005	+	0.0142282i
$565$	6.01014	−	7.64251i	0.252848	−	0.321523i
$566$	−26.1434	+	16.8013i	−1.09889	+	0.706213i
$567$	1.32480	−	2.29017i	0.0556365	−	0.0961783i
$568$	0.0461487	+	0.320971i	0.00193636	+	0.0134677i
$569$	5.88023	+	30.5095i	0.246512	+	1.27903i	0.868378	+	0.495902i	$0.165163\pi$
$569$	5.88023	+	30.5095i	0.246512	+	1.27903i	−0.621866	+	0.783123i	$0.713625\pi$
$570$	−9.33343	−	0.444606i	−0.390935	−	0.0186225i
$571$	−3.52171	+	18.2724i	−0.147379	+	0.764675i	0.830745	+	0.556653i	$0.187915\pi$
$571$	−3.52171	+	18.2724i	−0.147379	+	0.764675i	−0.978124	+	0.208022i	$0.933297\pi$
$572$	−0.981241	+	4.04473i	−0.0410278	+	0.169119i
$573$	8.66344	+	18.9703i	0.361920	+	0.792495i
$574$	−1.65928	−	5.66863i	−0.0692571	−	0.236604i
$575$	8.11265	+	2.64599i	0.338321	+	0.110345i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	1.48293	+	1.05599i	0.0617350	+	0.0439613i	0.610508	−	0.792010i	$-0.290965\pi$
$577$	1.48293	+	1.05599i	0.0617350	+	0.0439613i	−0.548773	+	0.835972i	$0.684905\pi$
$578$	12.3030	+	11.7309i	0.511738	+	0.487941i
$579$	15.3784	−	5.32250i	0.639103	−	0.221196i
$580$	−7.44498	−	4.78460i	−0.309136	−	0.198670i
$581$	1.29810	−	26.7766i	0.0538544	−	1.11088i
$582$	−7.85665	+	1.12962i	−0.325669	+	0.0468241i
$583$	−4.44371	+	4.23707i	−0.184040	+	0.175481i
$584$	−1.48831	+	2.88692i	−0.0615867	+	0.119462i
$585$	0.579870	+	1.44845i	0.0239747	+	0.0598858i
$586$	6.32092	+	8.87649i	0.261115	+	0.366684i
$587$	2.66424	+	1.21672i	0.109965	+	0.0502194i	0.469638	−	0.882859i	$-0.344384\pi$
$587$	2.66424	+	1.21672i	0.109965	+	0.0502194i	−0.359673	+	0.933078i	$0.617112\pi$
$588$	−5.69519	−	4.06998i	−0.234866	−	0.167843i
$589$	−8.93915	−	13.9096i	−0.368331	−	0.573135i
$590$	12.6179	+	13.2333i	0.519471	+	0.544806i
$591$	−8.82923	−	11.2273i	−0.363186	−	0.461829i
$592$	7.52899	+	2.60581i	0.309439	+	0.107098i
$593$	11.7894	+	22.8683i	0.484134	+	0.939090i	0.996757	+	0.0804755i	$0.0256439\pi$
$593$	11.7894	+	22.8683i	0.484134	+	0.939090i	−0.512622	+	0.858614i	$0.671326\pi$
$594$	3.13509	−	3.61808i	0.128634	−	0.148452i
$595$	−0.106117	−	0.0548202i	−0.00435037	−	0.00224741i
$596$	6.83416	−	3.12106i	0.279938	−	0.127843i
$597$	17.3673	+	10.0270i	0.710795	+	0.410378i
$598$	−0.272991	−	4.16043i	−0.0111634	−	0.170133i
$599$	3.90791	+	6.76869i	0.159673	+	0.276561i	0.934751	−	0.355304i	$-0.115623\pi$
$599$	3.90791	+	6.76869i	0.159673	+	0.276561i	−0.775078	+	0.631866i	$0.782289\pi$
$600$	−0.169134	+	1.77125i	−0.00690486	+	0.0723109i
$601$	−7.42334	−	25.2816i	−0.302804	−	1.03126i	−0.960571	−	0.278035i	$-0.910317\pi$
$601$	−7.42334	−	25.2816i	−0.302804	−	1.03126i	0.657767	−	0.753222i	$-0.271501\pi$
$602$	−21.9388	−	10.0414i	−0.894160	−	0.409259i
$603$	1.89692	−	2.95166i	0.0772484	−	0.120201i
$604$	14.0468	−	2.70729i	0.571555	−	0.110158i
$605$	16.8142	−	13.2228i	0.683594	−	0.537585i
$606$	−1.12713	−	4.64611i	−0.0457867	−	0.188735i
$607$	15.1764	−	0.722940i	0.615990	−	0.0293432i	0.262731	−	0.964869i	$-0.415377\pi$
$607$	15.1764	−	0.722940i	0.615990	−	0.0293432i	0.353258	+	0.935526i	$0.385074\pi$
$608$	−0.740984	+	5.15366i	−0.0300509	+	0.209009i
$609$	−8.07375	+	10.2489i	−0.327165	+	0.415305i
$610$	−6.95139	+	15.2214i	−0.281453	+	0.616297i
$611$	−2.42924	−	1.91037i	−0.0982764	−	0.0772854i
$612$	−0.0223589	−	0.0115268i	−0.000903804	−	0.000465943i
$613$	−5.11514	+	1.24092i	−0.206598	+	0.0501202i	−0.337722	−	0.941246i	$-0.609657\pi$
$613$	−5.11514	+	1.24092i	−0.206598	+	0.0501202i	0.131124	+	0.991366i	$0.458141\pi$
$614$	6.83517	−	17.0734i	0.275845	−	0.689028i
$615$	−2.62364	−	3.02784i	−0.105795	−	0.122094i
$616$	−8.73303	−	9.17437i	−0.351864	−	0.369646i
$617$	15.1505	+	13.1280i	0.609935	+	0.528512i	0.904143	−	0.427230i	$-0.140510\pi$
$617$	15.1505	+	13.1280i	0.609935	+	0.528512i	−0.294208	+	0.955741i	$0.595056\pi$
$618$	5.30444	+	1.28684i	0.213376	+	0.0517644i
$619$	−2.38546	+	3.34991i	−0.0958797	+	0.134644i	−0.859729	−	0.510750i	$-0.829368\pi$
$619$	−2.38546	+	3.34991i	−0.0958797	+	0.134644i	0.763849	+	0.645395i	$0.223307\pi$
$620$	4.93553	−	2.84953i	0.198216	−	0.114440i
$621$	−1.91376	+	4.39744i	−0.0767965	+	0.176463i
$622$		−	7.26211i		−	0.291184i
$623$	27.1705	+	31.4098i	1.08856	+	1.25841i
$624$	0.834159	−	0.244931i	0.0333931	−	0.00980510i
$625$	4.23145	+	12.2260i	0.169258	+	0.489039i
$626$	1.00244	−	21.0437i	0.0400654	−	0.841077i
$627$	−8.15262	+	23.5555i	−0.325584	+	0.940714i
$628$	−2.86311	−	1.14622i	−0.114251	−	0.0457391i
$629$	0.0564638	−	0.192298i	0.00225136	−	0.00766742i
$630$	−4.66158	−	0.902513i	−0.185722	−	0.0359570i
$631$	−10.4912	−	1.50840i	−0.417646	−	0.0600485i	−0.0697115	−	0.997567i	$-0.522208\pi$
$631$	−10.4912	−	1.50840i	−0.417646	−	0.0600485i	−0.347935	+	0.937519i	$0.613117\pi$
$632$	12.1872	−	8.67847i	0.484781	−	0.345211i
$633$	−0.256543	−	2.68664i	−0.0101967	−	0.106784i
$634$	30.5004	−	12.2105i	1.21132	−	0.484941i
$635$	−0.533940	−	11.2088i	−0.0211888	−	0.444807i
$636$	1.23058	+	0.361329i	0.0487955	+	0.0143276i
$637$	−1.14166	−	5.97758i	−0.0452341	−	0.236840i
$638$	−17.8419	+	15.4601i	−0.706366	+	0.612070i
$639$	0.288225	−	0.148590i	0.0114020	−	0.00587813i
$640$	−1.76220	−	0.339636i	−0.0696570	−	0.0134253i
$641$	14.0095	−	14.6928i	0.553344	−	0.580330i	−0.386348	−	0.922353i	$-0.626264\pi$
$641$	14.0095	−	14.6928i	0.553344	−	0.580330i	0.939692	+	0.342023i	$0.111112\pi$
$642$	0.348174	+	0.0332466i	0.0137413	+	0.00131214i
$643$	15.0682			0.594231			0.297115	−	0.954842i	$-0.403975\pi$
$643$	15.0682			0.594231			0.297115	+	0.954842i	$0.403975\pi$
$644$	11.0954	+	6.15567i	0.437220	+	0.242568i
$645$	−16.3659			−0.644408
$646$	0.130382	+	0.0124499i	0.00512980	+	0.000489836i
$647$	−2.68040	+	2.81113i	−0.105378	+	0.110517i	−0.774310	−	0.632806i	$-0.781903\pi$
$647$	−2.68040	+	2.81113i	−0.105378	+	0.110517i	0.668933	+	0.743323i	$0.266751\pi$
$648$	−0.981929	−	0.189251i	−0.0385738	−	0.00743449i
$649$	43.3547	−	22.3509i	1.70182	−	0.877349i
$650$	−1.16906	+	1.01299i	−0.0458542	+	0.0397329i
$651$	−3.48385	−	7.64557i	−0.136543	−	0.299654i
$652$	11.5309	+	3.38576i	0.451583	+	0.132597i
$653$	−0.745635	−	15.6528i	−0.0291790	−	0.612542i	−0.965344	−	0.260981i	$-0.915954\pi$
$653$	−0.745635	−	15.6528i	−0.0291790	−	0.612542i	0.936165	−	0.351561i	$-0.114349\pi$
$654$	6.55229	−	2.62314i	0.256215	−	0.102573i
$655$	0.802521	+	8.40438i	0.0313571	+	0.328386i
$656$	−1.81849	+	1.29494i	−0.0710002	+	0.0505590i
$657$	3.21492	+	0.462235i	0.125426	+	0.0180335i
$658$	8.89034	−	3.06861i	0.346582	−	0.119627i
$659$	−8.63387	+	29.4043i	−0.336328	+	1.14543i	0.601658	+	0.798754i	$0.294507\pi$
$659$	−8.63387	+	29.4043i	−0.336328	+	1.14543i	−0.937986	+	0.346673i	$0.887311\pi$
$660$	−7.97619	−	3.19318i	−0.310473	−	0.124294i
$661$	−5.08542	+	14.6934i	−0.197800	+	0.571506i	−0.999662	−	0.0260039i	$-0.991722\pi$
$661$	−5.08542	+	14.6934i	−0.197800	+	0.571506i	0.801862	+	0.597510i	$0.203843\pi$
$662$	−0.664530	+	13.9502i	−0.0258277	+	0.542190i
$663$	−0.00715276	−	0.0206665i	−0.000277790	−	0.000802622i
$664$	−9.72207	+	2.85466i	−0.377289	+	0.110782i
$665$	24.2791	−	4.65824i	0.941504	−	0.180639i
$666$		−	7.96717i		−	0.308722i
$667$	12.4274	−	20.1214i	0.481191	−	0.779102i
$668$	−4.83292	+	2.79029i	−0.186991	+	0.107959i
$669$	12.7271	−	17.8727i	0.492058	−	0.690999i
$670$	−6.11922	−	1.48451i	−0.236406	−	0.0573515i
$671$	33.7359	+	29.2324i	1.30236	+	1.12850i
$672$	−0.747529	+	2.53795i	−0.0288366	+	0.0979036i
$673$	−24.8092	−	28.6314i	−0.956326	−	1.10366i	−0.994537	−	0.104389i	$-0.966711\pi$
$673$	−24.8092	−	28.6314i	−0.956326	−	1.10366i	0.0382106	−	0.999270i	$-0.487834\pi$
$674$	4.96979	−	12.4139i	0.191429	−	0.478167i
$675$	1.72915	−	0.419487i	0.0665550	−	0.0161461i
$676$	−10.8831	−	5.61061i	−0.418580	−	0.215793i
$677$	−32.4061	−	25.4845i	−1.24547	−	0.979447i	−0.999949	−	0.0100552i	$-0.996799\pi$
$677$	−32.4061	−	25.4845i	−1.24547	−	0.979447i	−0.245519	−	0.969392i	$-0.578958\pi$
$678$	−2.25056	+	4.92805i	−0.0864324	+	0.189261i
$679$	19.5028	−	7.78870i	0.748447	−	0.298903i
$680$	−0.00642471	+	0.0446848i	−0.000246376	+	0.00171358i
$681$	−2.86486	+	0.136470i	−0.109782	+	0.00522954i
$682$	−3.58424	−	14.7744i	−0.137248	−	0.565742i
$683$	35.7716	−	28.1311i	1.36876	−	1.07641i	0.380314	−	0.924857i	$-0.375816\pi$
$683$	35.7716	−	28.1311i	1.36876	−	1.07641i	0.988450	−	0.151550i	$-0.0484265\pi$
$684$	5.11257	−	0.985366i	0.195484	−	0.0376764i
$685$	19.3823	−	30.1594i	0.740559	−	1.15233i
$686$	17.1762	+	6.92665i	0.655790	+	0.264461i
$687$	−6.21216	−	21.1567i	−0.237009	−	0.807178i
$688$	−0.866854	+	9.07810i	−0.0330485	+	0.346099i
$689$	0.557498	+	0.965615i	0.0212390	+	0.0367870i
$690$	8.58105	+	0.664446i	0.326675	+	0.0252950i
$691$	12.7988	+	7.38937i	0.486888	+	0.281105i	0.723283	−	0.690552i	$-0.242632\pi$
$691$	12.7988	+	7.38937i	0.486888	+	0.281105i	−0.236395	+	0.971657i	$0.575966\pi$
$692$	3.85411	−	1.76011i	0.146511	−	0.0669094i
$693$	−5.81350	+	11.2534i	−0.220836	+	0.427480i
$694$	−12.8740	+	14.8574i	−0.488692	+	0.563980i
$695$	−1.48905	−	2.88835i	−0.0564828	−	0.109561i
$696$	4.66009	+	1.61287i	0.176640	+	0.0611358i
$697$	0.0347143	+	0.0441428i	0.00131490	+	0.00167203i
$698$	15.3286	+	16.0762i	0.580196	+	0.608492i
$699$	1.90280	+	2.96082i	0.0719706	+	0.111988i
$700$	−0.666042	−	4.66025i	−0.0251740	−	0.176141i
$701$	15.4753	+	7.06733i	0.584494	+	0.266929i	0.685638	−	0.727942i	$-0.259523\pi$
$701$	15.4753	+	7.06733i	0.584494	+	0.266929i	−0.101145	+	0.994872i	$0.532250\pi$
$702$	−0.504287	−	0.708172i	−0.0190331	−	0.0267282i
$703$	15.4174	+	38.5109i	0.581479	+	1.45247i
$704$	−2.19372	+	4.25522i	−0.0826788	+	0.160375i
$705$	4.61705	−	4.40235i	0.173888	−	0.165802i
$706$	−26.8770	+	3.86433i	−1.01153	+	0.145436i
$707$	5.78665	+	11.2478i	0.217630	+	0.423016i
$708$	−8.57119	−	5.50837i	−0.322125	−	0.207017i
$709$	−3.42387	+	1.18501i	−0.128586	+	0.0445041i	−0.390603	−	0.920559i	$-0.627734\pi$
$709$	−3.42387	+	1.18501i	−0.128586	+	0.0445041i	0.262017	+	0.965063i	$0.415612\pi$
$710$	−0.421176	−	0.401590i	−0.0158064	−	0.0150714i
$711$	−12.1872	−	8.67847i	−0.457056	−	0.325468i
$712$	7.84859	−	13.5942i	0.294138	−	0.509463i
$713$	7.85002	+	13.0508i	0.293985	+	0.488755i
$714$	0.0646652	+	0.0157452i	0.00242004	+	0.000589250i
$715$	−3.10288	−	6.79435i	−0.116041	−	0.254094i
$716$	−0.193472	+	0.797500i	−0.00723037	+	0.0298040i
$717$	4.86175	−	25.2252i	0.181565	−	0.942051i
$718$	33.0511	+	1.57442i	1.23346	+	0.0587568i
$719$	−4.72834	−	24.5330i	−0.176338	−	0.914926i	−0.957025	−	0.290005i	$-0.906343\pi$
$719$	−4.72834	−	24.5330i	−0.176338	−	0.914926i	0.780688	−	0.624921i	$-0.214869\pi$
$720$	0.255402	+	1.77636i	0.00951828	+	0.0662011i
$721$	−14.4413	−	0.0121468i	−0.537822	−	0.000452372i
$722$	−6.82195	+	4.38420i	−0.253887	+	0.163163i
$723$	7.95699	−	10.1181i	0.295923	−	0.376297i
$724$	−12.6345	+	1.20645i	−0.469557	+	0.0448373i
$725$	−8.73457	+	0.834050i	−0.324394	+	0.0309759i
$726$	−7.36800	+	9.36918i	−0.273452	+	0.347723i
$727$	−35.5320	+	22.8350i	−1.31781	+	0.846905i	−0.995031	−	0.0995692i	$-0.968254\pi$
$727$	−35.5320	+	22.8350i	−1.31781	+	0.846905i	−0.322779	+	0.946474i	$0.604617\pi$
$728$	−1.99296	+	1.14840i	−0.0738638	+	0.0425625i
$729$	0.142315	+	0.989821i	0.00527092	+	0.0366601i
$730$	−1.10313	−	5.72358i	−0.0408287	−	0.211839i
$731$	0.229141	+	0.0109153i	0.00847508	+	0.000403718i
$732$	1.76463	−	9.15576i	0.0652225	−	0.338407i
$733$	−4.46952	+	18.4236i	−0.165085	+	0.680492i	0.827760	+	0.561083i	$0.189615\pi$
$733$	−4.46952	+	18.4236i	−0.165085	+	0.680492i	−0.992845	+	0.119409i	$0.961900\pi$
$734$	12.9151	+	28.2800i	0.476704	+	1.04384i
$735$	12.5492	−	0.576633i	0.462883	−	0.0212694i
$736$	0.823077	−	4.72467i	0.0303390	−	0.174154i
$737$	−8.39865	+	14.5469i	−0.309368	+	0.535842i
$738$	1.81849	+	1.29494i	0.0669396	+	0.0476675i
$739$	−30.4976	−	29.0794i	−1.12187	−	1.06970i	−0.996990	−	0.0775302i	$-0.975297\pi$
$739$	−30.4976	−	29.0794i	−1.12187	−	1.06970i	−0.124881	−	0.992172i	$-0.539855\pi$
$740$	−13.5117	+	4.67646i	−0.496701	+	0.171910i
$741$	3.80797	+	2.44723i	0.139889	+	0.0899013i
$742$	−3.38927	−	0.164308i	−0.124424	−	0.00603194i
$743$	38.0384	−	5.46909i	1.39549	−	0.200641i	0.596804	−	0.802387i	$-0.296437\pi$
$743$	38.0384	−	5.46909i	1.39549	−	0.200641i	0.798688	+	0.601746i	$0.205528\pi$
$744$	−2.29830	+	2.19143i	−0.0842599	+	0.0803417i
$745$	−6.17838	+	11.9844i	−0.226358	+	0.439074i
$746$	7.96648	+	19.8993i	0.291674	+	0.728566i
$747$	5.87743	+	8.25369i	0.215044	+	0.301987i
$748$	0.109546	+	0.0500278i	0.00400538	+	0.00182920i
$749$	−0.916064	+	0.130924i	−0.0334722	+	0.00478385i
$750$	−6.57762	−	10.2350i	−0.240181	−	0.373729i
$751$	−20.4347	−	21.4313i	−0.745671	−	0.782038i	0.236176	−	0.971710i	$-0.424106\pi$
$751$	−20.4347	−	21.4313i	−0.745671	−	0.782038i	−0.981847	+	0.189673i	$0.939257\pi$
$752$	−2.19741	−	2.79423i	−0.0801313	−	0.101895i
$753$	−1.52769	−	0.528739i	−0.0556721	−	0.0192683i
$754$	1.96449	+	3.81058i	0.0715424	+	0.138773i
$755$	−16.8120	+	19.4021i	−0.611852	+	0.706115i
$756$	2.64286	−	0.123667i	0.0961199	−	0.00449773i
$757$	−34.6520	+	15.8251i	−1.25945	+	0.575172i	−0.929498	−	0.368826i	$-0.879760\pi$
$757$	−34.6520	+	15.8251i	−1.25945	+	0.575172i	−0.329952	+	0.943998i	$0.607032\pi$
$758$	21.7661	+	12.5666i	0.790579	+	0.456441i
$759$	8.14986	−	21.4645i	0.295821	−	0.779110i
$760$	−4.67201	−	8.09216i	−0.169472	−	0.293533i
$761$	4.30246	−	45.0574i	0.155964	−	1.63333i	−0.491249	−	0.871019i	$-0.663459\pi$
$761$	4.30246	−	45.0574i	0.155964	−	1.63333i	0.647213	−	0.762309i	$-0.275934\pi$
$762$	1.76162	+	5.99953i	0.0638168	+	0.217340i
$763$	−15.2200	+	10.8188i	−0.551000	+	0.391667i
$764$	−11.2750	+	17.5443i	−0.407915	+	0.634729i
$765$	0.0443285	−	0.00854362i	0.00160270	−	0.000308895i
$766$	−11.7767	+	9.26127i	−0.425508	+	0.334623i
$767$	−2.08828	−	8.60802i	−0.0754036	−	0.310818i
$768$	0.998867	−	0.0475819i	0.0360435	−	0.00171696i
$769$	−6.62458	+	46.0750i	−0.238888	+	1.66151i	0.418697	+	0.908126i	$0.362487\pi$
$769$	−6.62458	+	46.0750i	−0.238888	+	1.66151i	−0.657586	+	0.753380i	$0.728422\pi$
$770$	22.4972	+	3.25392i	0.810743	+	0.117263i
$771$	6.87207	−	15.0477i	0.247491	−	0.541931i
$772$	12.7917	+	10.0595i	0.460385	+	0.362051i
$773$	−28.2053	−	14.5408i	−1.01447	−	0.522998i	−0.130953	−	0.991389i	$-0.541804\pi$
$773$	−28.2053	−	14.5408i	−1.01447	−	0.522998i	−0.883522	+	0.468391i	$0.844834\pi$
$774$	8.86233	−	2.14998i	0.318550	−	0.0772794i
$775$	2.10004	−	5.24565i	0.0754357	−	0.188429i
$776$	−5.19792	−	5.99872i	−0.186595	−	0.215342i
$777$	4.95237	+	20.4891i	0.177665	+	0.735044i
$778$	−22.9823	−	19.9143i	−0.823956	−	0.713962i
$779$	−11.2959	−	2.74036i	−0.404718	−	0.0981835i
$780$	−0.905008	+	1.27091i	−0.0324045	+	0.0455057i
$781$	−1.34444	+	0.776211i	−0.0481078	+	0.0277750i
$782$	−0.119701	−	0.0150261i	−0.00428049	−	0.000537333i
$783$		−	4.93131i		−	0.176230i
$784$	0.344835	−	6.99150i	0.0123155	−	0.249696i
$785$	5.31049	−	1.55930i	0.189540	−	0.0556539i
$786$	−1.53865	−	4.44564i	−0.0548818	−	0.158571i
$787$	−0.597602	+	12.5452i	−0.0213022	+	0.447189i	0.962869	+	0.269969i	$0.0870134\pi$
$787$	−0.597602	+	12.5452i	−0.0213022	+	0.447189i	−0.984171	+	0.177220i	$0.943290\pi$
$788$	4.67155	−	13.4975i	0.166417	−	0.480830i
$789$	−18.0777	−	7.23722i	−0.643584	−	0.257652i
$790$	−7.56457	+	25.7626i	−0.269135	+	0.916591i
$791$	2.72451	−	14.0724i	0.0968724	−	0.500356i
$792$	4.73868	+	0.681319i	0.168382	+	0.0242096i
$793$	6.60318	−	4.70211i	0.234486	−	0.166977i
$794$	−3.35650	−	35.1509i	−0.119118	−	1.24746i
$795$	−2.13679	+	0.855440i	−0.0757840	+	0.0303393i
$796$	0.954208	+	20.0313i	0.0338210	+	0.709990i
$797$	6.39070	+	1.87648i	0.226370	+	0.0664683i	0.392951	−	0.919560i	$-0.371454\pi$
$797$	6.39070	+	1.87648i	0.226370	+	0.0664683i	−0.166580	+	0.986028i	$0.553273\pi$
$798$	−12.5355	+	5.71202i	−0.443751	+	0.202203i
$799$	−0.0675799	+	0.0585583i	−0.00239080	+	0.00207164i
$800$	−1.58151	+	0.815325i	−0.0559148	+	0.0288261i
$801$	−15.4135	−	2.97071i	−0.544610	−	0.104965i
$802$	12.1344	−	12.7262i	0.428482	−	0.449379i
$803$	−15.4790	−	1.47806i	−0.546242	−	0.0521597i
$804$	3.50864			0.123740
$805$	−22.4809	+	3.62520i	−0.792347	+	0.127772i
$806$	−2.76081			−0.0972452
$807$	−18.6585	−	1.78167i	−0.656809	−	0.0627176i
$808$	3.29918	−	3.46008i	0.116065	−	0.121725i
$809$	29.6103	+	5.70692i	1.04104	+	0.200645i	0.680995	−	0.732288i	$-0.261548\pi$
$809$	29.6103	+	5.70692i	1.04104	+	0.200645i	0.360049	+	0.932933i	$0.382760\pi$
$810$	1.59513	−	0.822347i	0.0560472	−	0.0288943i
$811$	−16.5634	+	14.3522i	−0.581618	+	0.503975i	−0.895247	−	0.445571i	$-0.853001\pi$
$811$	−16.5634	+	14.3522i	−0.581618	+	0.503975i	0.313629	+	0.949546i	$0.398455\pi$
$812$	−12.9869	−	1.25112i	−0.455750	−	0.0439057i
$813$	12.5764	+	3.69275i	0.441072	+	0.129510i
$814$	1.81487	+	38.0989i	0.0636113	+	1.33537i
$815$	−20.0223	+	8.01573i	−0.701351	+	0.280779i
$816$	−0.00239116	−	0.0250413i	−8.37073e−5	−	0.000876622i
$817$	−38.6773	+	27.5420i	−1.35315	+	0.963573i
$818$	15.2811	+	2.19710i	0.534293	+	0.0768197i
$819$	1.73707	+	1.50774i	0.0606981	+	0.0526847i
$820$	1.12873	−	3.84412i	0.0394171	−	0.134242i
$821$	−21.0405	−	8.42333i	−0.734317	−	0.293976i	−0.0257975	−	0.999667i	$-0.508213\pi$
$821$	−21.0405	−	8.42333i	−0.734317	−	0.293976i	−0.708520	+	0.705691i	$0.750637\pi$
$822$	−6.53370	+	18.8779i	−0.227889	+	0.658442i
$823$	0.607849	−	12.7603i	0.0211883	−	0.444797i	−0.963200	−	0.268786i	$-0.913378\pi$
$823$	0.607849	−	12.7603i	0.0211883	−	0.444797i	0.984388	−	0.176011i	$-0.0563194\pi$
$824$	1.78524	+	5.15810i	0.0621916	+	0.179691i
$825$	−8.17321	+	2.39987i	−0.284555	+	0.0835528i
$826$	25.4665	+	8.83802i	0.886092	+	0.307514i
$827$			16.1650i			0.562113i	0.959691	+	0.281057i	$0.0906849\pi$
$827$			16.1650i			0.562113i	−0.959691	+	0.281057i	$0.909315\pi$
$828$	−4.73402	+	0.767481i	−0.164519	+	0.0266718i
$829$	−17.3154	+	9.99704i	−0.601388	+	0.347211i	−0.769587	−	0.638541i	$-0.779538\pi$
$829$	−17.3154	+	9.99704i	−0.601388	+	0.347211i	0.168199	+	0.985753i	$0.446205\pi$
$830$	10.5478	−	14.8123i	0.366120	−	0.514143i
$831$	−0.769679	−	0.186722i	−0.0266999	−	0.00647732i
$832$	0.657030	+	0.569320i	0.0227784	+	0.0197376i
$833$	−0.176086		0.000296219i	−0.00610103		1.02634e-5i
$834$	1.18578	+	1.36846i	0.0410601	+	0.0473858i
$835$	3.72222	−	9.29766i	0.128813	−	0.321759i
$836$	−24.2237	+	5.87662i	−0.837796	+	0.203247i
$837$	2.82260	+	1.45515i	0.0975635	+	0.0502975i
$838$	5.17304	+	4.06812i	0.178700	+	0.140531i
$839$	−0.214048	+	0.468701i	−0.00738977	+	0.0161813i	−0.913291	−	0.407308i	$-0.866468\pi$
$839$	−0.214048	+	0.468701i	−0.00738977	+	0.0161813i	0.905901	+	0.423489i	$0.139195\pi$
$840$	−1.76100	−	4.40951i	−0.0607602	−	0.152142i
$841$	0.666350	−	4.63456i	0.0229776	−	0.159813i
$842$	−29.3761	+	1.39935i	−1.01237	+	0.0482249i
$843$	−0.460538	−	1.89836i	−0.0158618	−	0.0653831i
$844$	2.12145	−	1.66833i	0.0730233	−	0.0574262i
$845$	21.5767	−	4.15856i	0.742260	−	0.143059i
$846$	−1.92185	+	2.99046i	−0.0660746	+	0.102814i
$847$	13.1244	−	28.6746i	0.450960	−	0.985271i
$848$	0.361329	+	1.23058i	0.0124081	+	0.0422581i
$849$	−2.95403	+	30.9360i	−0.101382	+	1.06172i
$850$	0.0223794	+	0.0387623i	0.000767608	+	0.00132954i
$851$	−13.1421	−	35.8780i	−0.450505	−	1.22988i
$852$	0.280828	+	0.162136i	0.00962100	+	0.00555469i
$853$	22.8530	−	10.4366i	0.782472	−	0.357343i	0.0162079	−	0.999869i	$-0.494841\pi$
$853$	22.8530	−	10.4366i	0.782472	−	0.357343i	0.766264	+	0.642526i	$0.222113\pi$
$854$	1.15310	+	24.6427i	0.0394584	+	0.843256i
$855$	−6.11903	+	7.06174i	−0.209266	+	0.241506i
$856$	0.160268	+	0.310877i	0.00547786	+	0.0106256i
$857$	1.33877	+	0.463354i	0.0457316	+	0.0158279i	0.349838	−	0.936810i	$-0.386237\pi$
$857$	1.33877	+	0.463354i	0.0457316	+	0.0158279i	−0.304106	+	0.952638i	$0.598358\pi$
$858$	2.57281	+	3.27159i	0.0878343	+	0.111690i
$859$	0.785811	+	0.824135i	0.0268115	+	0.0281191i	0.737003	−	0.675889i	$-0.236240\pi$
$859$	0.785811	+	0.824135i	0.0268115	+	0.0281191i	−0.710192	+	0.704008i	$0.751392\pi$
$860$	−8.84809	−	13.7679i	−0.301717	−	0.469481i
$861$	−5.48154	−	2.19983i	−0.186810	−	0.0749700i
$862$	11.2157	+	5.12202i	0.382007	+	0.174457i
$863$	−25.6284	−	35.9901i	−0.872402	−	1.22512i	−0.973142	−	0.230204i	$-0.926061\pi$
$863$	−25.6284	−	35.9901i	−0.872402	−	1.22512i	0.100741	−	0.994913i	$-0.467879\pi$
$864$	−0.371662	−	0.928368i	−0.0126442	−	0.0315837i
$865$	−3.48428	+	6.75856i	−0.118469	+	0.229798i
$866$	22.0822	−	21.0553i	0.750382	−	0.715488i
$867$	16.8263	−	2.41926i	0.571452	−	0.0821625i
$868$	4.54835	−	7.06431i	0.154381	−	0.239778i
$869$	60.2559	+	38.7241i	2.04404	+	1.31363i
$870$	−8.36313	+	2.89451i	−0.283537	+	0.0981330i
$871$	2.20763	+	2.10497i	0.0748025	+	0.0713241i
$872$	5.74917	+	4.09396i	0.194691	+	0.138639i
$873$	−3.96872	+	6.87403i	−0.134321	+	0.232651i
$874$	21.3976	−	12.8707i	0.723786	−	0.435357i
$875$	23.2777	+	22.2326i	0.786929	+	0.751600i
$876$	1.34926	+	2.95446i	0.0455872	+	0.0998221i
$877$	11.8138	−	48.6972i	0.398924	−	1.64439i	−0.318625	−	0.947881i	$-0.603221\pi$
$877$	11.8138	−	48.6972i	0.398924	−	1.64439i	0.717549	−	0.696508i	$-0.245264\pi$
$878$	−0.370590	+	1.92280i	−0.0125068	+	0.0648914i
$879$	10.8847	+	0.518504i	0.367133	+	0.0174887i
$880$	−1.62597	−	8.43636i	−0.0548116	−	0.284390i
$881$	−4.46358	−	31.0449i	−0.150382	−	1.04593i	−0.915580	−	0.402135i	$-0.868268\pi$
$881$	−4.46358	−	31.0449i	−0.150382	−	1.04593i	0.765199	−	0.643794i	$-0.222641\pi$
$882$	−6.71976	+	1.96083i	−0.226266	+	0.0660245i
$883$	33.8858	−	21.7771i	1.14035	−	0.732858i	0.172654	−	0.984982i	$-0.444766\pi$
$883$	33.8858	−	21.7771i	1.14035	−	0.732858i	0.967695	+	0.252124i	$0.0811292\pi$
$884$	0.0135187	−	0.0171905i	0.000454684	−	0.000578178i
$885$	18.2020	−	1.73808i	0.611852	−	0.0584248i
$886$	−19.0097	+	1.81520i	−0.638642	+	0.0609830i
$887$	−21.8295	+	27.7584i	−0.732962	+	0.932037i	−0.999495	−	0.0317891i	$-0.989880\pi$
$887$	−21.8295	+	27.7584i	−0.732962	+	0.932037i	0.266533	+	0.963826i	$0.414122\pi$
$888$	6.70241	−	4.30738i	0.224918	−	0.144546i
$889$	−8.25964	−	14.3340i	−0.277020	−	0.480745i
$890$	4.00910	+	27.8839i	0.134385	+	0.934670i
$891$	−0.906023	−	4.70089i	−0.0303529	−	0.157486i
$892$	21.9163	+	1.04400i	0.733811	+	0.0349557i
$893$	3.50275	−	18.1740i	0.117215	−	0.608169i
$894$	1.77128	−	7.30132i	0.0592405	−	0.244193i
$895$	−0.611795	−	1.33964i	−0.0204500	−	0.0447794i
$896$	−2.53921	+	0.743259i	−0.0848289	+	0.0248305i
$897$	−3.43907	−	2.35722i	−0.114827	−	0.0787053i
$898$	−12.9258	+	22.3881i	−0.431339	+	0.747101i
$899$	−12.7562	−	9.08366i	−0.425444	−	0.302957i
$900$	1.28774	+	1.22786i	0.0429248	+	0.0409287i
$901$	0.0304879	−	0.0105520i	0.00101570	−	0.000351536i
$902$	−8.99099	−	5.77816i	−0.299367	−	0.192392i
$903$	−21.4548	+	11.0379i	−0.713971	+	0.367318i
$904$	−5.36249	+	0.771009i	−0.178354	+	0.0256434i
$905$	16.4847	−	15.7182i	0.547972	−	0.522490i
$906$	6.55506	−	12.7150i	0.217777	−	0.422429i
$907$	−4.53077	−	11.3173i	−0.150442	−	0.375786i	0.833934	−	0.551864i	$-0.186083\pi$
$907$	−4.53077	−	11.3173i	−0.150442	−	0.375786i	−0.984376	+	0.176078i	$0.943659\pi$
$908$	−1.66367	−	2.33629i	−0.0552107	−	0.0775326i
$909$	−4.34884	−	1.98605i	−0.144242	−	0.0658731i
$910$	1.53741	−	3.83093i	0.0509648	−	0.126994i
$911$	−19.7511	−	30.7333i	−0.654383	−	1.01824i	−0.996896	−	0.0787265i	$-0.974915\pi$
$911$	−19.7511	−	30.7333i	−0.654383	−	1.01824i	0.342514	−	0.939513i	$-0.388722\pi$
$912$	3.59300	+	3.76823i	0.118976	+	0.124779i
$913$	−29.9859	−	38.1302i	−0.992389	−	1.26193i
$914$	−33.6420	−	11.6436i	−1.11278	−	0.385137i
$915$	7.66778	+	14.8734i	0.253489	+	0.491700i
$916$	14.4396	−	16.6642i	0.477097	−	0.550600i
$917$	6.72033	+	10.4764i	0.221925	+	0.345961i
$918$	−0.0228820	+	0.0104499i	−0.000755219	+	0.000344897i
$919$	−18.7422	−	10.8208i	−0.618247	−	0.356945i	0.157939	−	0.987449i	$-0.449515\pi$
$919$	−18.7422	−	10.8208i	−0.618247	−	0.356945i	−0.776186	+	0.630504i	$0.782848\pi$
$920$	4.08030	+	7.57807i	0.134524	+	0.249842i
$921$	−9.19540	−	15.9269i	−0.302999	−	0.524809i
$922$	−3.11372	+	32.6084i	−0.102545	+	1.07390i
$923$	0.0794244	+	0.270495i	0.00261429	+	0.00890344i
$924$	−12.6099	+	1.19340i	−0.414837	+	0.0392600i
$925$	−7.66415	+	11.9256i	−0.251996	+	0.392113i
$926$	−2.39153	+	0.460930i	−0.0785907	+	0.0151471i
$927$	4.29051	−	3.37410i	0.140919	−	0.110820i
$928$	1.16260	+	4.79230i	0.0381642	+	0.157315i
$929$	5.22709	−	0.248997i	0.171495	−	0.00816933i	0.0383414	−	0.999265i	$-0.487793\pi$
$929$	5.22709	−	0.248997i	0.171495	−	0.00816933i	0.133154	+	0.991095i	$0.457490\pi$
$930$	0.811061	−	5.64105i	0.0265957	−	0.184977i
$931$	28.6868	−	22.4816i	0.940173	−	0.736804i
$932$	−1.46207	+	3.20148i	−0.0478915	+	0.104868i
$933$	−5.70840	−	4.48914i	−0.186885	−	0.146968i
$934$	−19.3430	−	9.97203i	−0.632923	−	0.326295i
$935$	−0.210032	+	0.0509532i	−0.00686878	+	0.00166635i
$936$	0.323114	−	0.807100i	0.0105613	−	0.0263809i
$937$	−36.4082	−	42.0173i	−1.18940	−	1.37264i	−0.911118	−	0.412146i	$-0.864779\pi$
$937$	−36.4082	−	42.0173i	−1.18940	−	1.37264i	−0.278286	−	0.960498i	$-0.589766\pi$
$938$	−9.02316	+	2.18096i	−0.294617	+	0.0712109i
$939$	−15.9218	−	13.7963i	−0.519589	−	0.450227i
$940$	6.19966	+	1.50402i	0.202211	+	0.0490557i
$941$	4.45872	−	6.26140i	0.145350	−	0.204116i	−0.735482	−	0.677544i	$-0.763044\pi$
$941$	4.45872	−	6.26140i	0.145350	−	0.204116i	0.880832	+	0.473428i	$0.156984\pi$
$942$	−2.67085	+	1.54201i	−0.0870209	+	0.0502415i
$943$	10.3251	+	2.83176i	0.336233	+	0.0922148i
$944$		−	10.1886i		−	0.331610i
$945$	−3.59102	+	3.10635i	−0.116816	+	0.101050i
$946$	−41.8898	+	12.3000i	−1.36195	+	0.399906i
$947$	1.07627	+	3.10967i	0.0349740	+	0.101051i	0.961136	−	0.276075i	$-0.0890337\pi$
$947$	1.07627	+	3.10967i	0.0349740	+	0.101051i	−0.926162	+	0.377126i	$0.876913\pi$
$948$	0.711892	−	14.9445i	0.0231212	−	0.485373i
$949$	−0.923545	+	2.66841i	−0.0299796	+	0.0866202i
$950$	−8.60062	−	3.44317i	−0.279041	−	0.111711i
$951$	9.25597	−	31.5229i	0.300145	−	1.02220i
$952$	0.0217149	+	0.0629124i	0.000703785	+	0.00203900i
$953$	5.48394	+	0.788472i	0.177642	+	0.0255411i	0.230562	−	0.973058i	$-0.425944\pi$
$953$	5.48394	+	0.788472i	0.177642	+	0.0255411i	−0.0529195	+	0.998599i	$0.516853\pi$
$954$	1.04472	−	0.743938i	0.0338239	−	0.0240859i
$955$	−3.55764	−	37.2573i	−0.115123	−	1.20562i
$956$	23.8492	−	9.54779i	0.771339	−	0.308797i
$957$	1.12332	+	23.5814i	0.0363118	+	0.762279i
$958$	32.4375	+	9.52450i	1.04801	+	0.307723i
$959$	5.06826	−	52.6095i	0.163663	−	1.69885i
$960$	−1.35629	+	1.17523i	−0.0437741	+	0.0379305i
$961$	−18.5904	+	9.58401i	−0.599690	+	0.309162i
$962$	6.80129	+	1.31084i	0.219282	+	0.0422632i
$963$	0.241361	−	0.253132i	0.00777774	−	0.00815705i
$964$	12.8138	+	1.22357i	0.412704	+	0.0394085i
$965$	−29.2047			−0.940133
$966$	11.6974	−	4.91638i	0.376358	−	0.158182i
$967$	−15.4124			−0.495629			−0.247815	−	0.968807i	$-0.579712\pi$
$967$	−15.4124			−0.495629			−0.247815	+	0.968807i	$0.579712\pi$
$968$	−11.8653	−	1.13300i	−0.381365	−	0.0364160i
$969$	0.0903829	−	0.0947908i	0.00290352	−	0.00304512i
$970$	13.9874	+	2.69584i	0.449107	+	0.0865582i
$971$	40.3717	−	20.8130i	1.29559	−	0.667922i	0.334041	−	0.942559i	$-0.391588\pi$
$971$	40.3717	−	20.8130i	1.29559	−	0.667922i	0.961548	+	0.274636i	$0.0885574\pi$
$972$	−0.755750	+	0.654861i	−0.0242407	+	0.0210047i
$973$	−3.90008	−	2.78218i	−0.125031	−	0.0891927i
$974$	−4.08571	−	1.19967i	−0.130915	−	0.0384400i
$975$	0.0736037	+	1.54513i	0.00235721	+	0.0494838i
$976$	8.65635	−	3.46548i	0.277083	−	0.110927i
$977$	−2.98878	−	31.3000i	−0.0956197	−	1.00137i	−0.908203	−	0.418530i	$-0.862546\pi$
$977$	−2.98878	−	31.3000i	−0.0956197	−	1.00137i	0.812583	−	0.582845i	$-0.198061\pi$
$978$	9.78929	−	6.97092i	0.313027	−	0.222906i
$979$	74.3839	+	10.6948i	2.37732	+	0.341807i
$980$	7.26968	+	10.2453i	0.232222	+	0.327273i
$981$	1.98843	−	6.77197i	0.0634857	−	0.216212i
$982$	6.69431	+	2.68000i	0.213624	+	0.0855222i
$983$	8.32332	−	24.0487i	0.265473	−	0.767033i	−0.730943	−	0.682439i	$-0.760919\pi$
$983$	8.32332	−	24.0487i	0.265473	−	0.767033i	0.996415	−	0.0845942i	$-0.0269594\pi$
$984$	−0.106224	+	2.22991i	−0.00338629	+	0.0710870i
$985$	8.38370	+	24.2231i	0.267127	+	0.771812i
$986$	0.119023	−	0.0349484i	0.00379048	−	0.00111298i
$987$	3.08356	−	8.88516i	0.0981507	−	0.282818i
$988$			4.52654i			0.144008i
$989$	36.3626	−	24.3005i	1.15626	−	0.772712i
$990$	−7.44056	+	4.29581i	−0.236477	+	0.136530i
$991$	26.4517	−	37.1463i	0.840267	−	1.17999i	−0.141507	−	0.989937i	$-0.545195\pi$
$991$	26.4517	−	37.1463i	0.840267	−	1.17999i	0.981774	−	0.190053i	$-0.0608659\pi$
$992$	−3.08610	−	0.748681i	−0.0979839	−	0.0237706i
$993$	10.5548	+	9.14580i	0.334947	+	0.290233i
$994$	−0.822987	−	0.242403i	−0.0261036	−	0.00768855i
$995$	−23.5681	−	27.1991i	−0.747159	−	0.862268i
$996$	−3.76587	+	9.40669i	−0.119326	+	0.298062i
$997$	−30.4256	+	7.38117i	−0.963588	+	0.233764i	−0.686540	−	0.727092i	$-0.740871\pi$
$997$	−30.4256	+	7.38117i	−0.963588	+	0.233764i	−0.277048	+	0.960856i	$0.589356\pi$
$998$	2.92047	+	1.50561i	0.0924459	+	0.0476592i
$999$	−6.26262	−	4.92498i	−0.198141	−	0.155819i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.be.a.19.11	✓	320
7.3	odd	6	inner	966.2.be.a.157.11	yes	320
23.17	odd	22	inner	966.2.be.a.523.11	yes	320
161.17	even	66	inner	966.2.be.a.661.11	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.be.a.19.11	✓	320	1.1	even	1	trivial
966.2.be.a.157.11	yes	320	7.3	odd	6	inner
966.2.be.a.523.11	yes	320	23.17	odd	22	inner
966.2.be.a.661.11	yes	320	161.17	even	66	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.be (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.995472 + 0.0950560i) q^{2} +(0.690079 - 0.723734i) q^{3} +(0.981929 + 0.189251i) q^{4} +(-1.59513 + 0.822347i) q^{5} +(0.755750 - 0.654861i) q^{6} +(-1.53650 + 2.15387i) q^{7} +(0.959493 + 0.281733i) q^{8} +(-0.0475819 - 0.998867i) q^{9} +O(q^{10})\)	\(q+(0.995472 + 0.0950560i) q^{2} +(0.690079 - 0.723734i) q^{3} +(0.981929 + 0.189251i) q^{4} +(-1.59513 + 0.822347i) q^{5} +(0.755750 - 0.654861i) q^{6} +(-1.53650 + 2.15387i) q^{7} +(0.959493 + 0.281733i) q^{8} +(-0.0475819 - 0.998867i) q^{9} +(-1.66608 + 0.666996i) q^{10} +(0.455072 + 4.76573i) q^{11} +(0.814576 - 0.580057i) q^{12} +(0.860526 + 0.123725i) q^{13} +(-1.73428 + 1.99807i) q^{14} +(-0.505605 + 1.72193i) q^{15} +(0.928368 + 0.371662i) q^{16} +(0.00822747 - 0.0237717i) q^{17} +(0.0475819 - 0.998867i) q^{18} +(1.70293 + 4.92029i) q^{19} +(-1.72193 + 0.505605i) q^{20} +(0.498526 + 2.59836i) q^{21} +4.78741i q^{22} +(-1.43339 - 4.57661i) q^{23} +(0.866025 - 0.500000i) q^{24} +(-1.03210 + 1.44938i) q^{25} +(0.844869 + 0.204963i) q^{26} +(-0.755750 - 0.654861i) q^{27} +(-1.91636 + 1.82417i) q^{28} +(3.22932 + 3.72683i) q^{29} +(-0.666996 + 1.66608i) q^{30} +(-3.08610 + 0.748681i) q^{31} +(0.888835 + 0.458227i) q^{32} +(3.76316 + 2.95938i) q^{33} +(0.0104499 - 0.0228820i) q^{34} +(0.679684 - 4.69924i) q^{35} +(0.142315 - 0.989821i) q^{36} +(7.95815 - 0.379093i) q^{37} +(1.22752 + 5.05989i) q^{38} +(0.683375 - 0.537412i) q^{39} +(-1.76220 + 0.339636i) q^{40} +(-1.20695 + 1.87805i) q^{41} +(0.249279 + 2.63398i) q^{42} +(2.56923 + 8.74999i) q^{43} +(-0.455072 + 4.76573i) q^{44} +(0.897315 + 1.55419i) q^{45} +(-0.991865 - 4.69214i) q^{46} +(-3.07852 - 1.77738i) q^{47} +(0.909632 - 0.415415i) q^{48} +(-2.27834 - 6.61885i) q^{49} +(-1.16520 + 1.34471i) q^{50} +(-0.0115268 - 0.0223589i) q^{51} +(0.821560 + 0.284345i) q^{52} +(0.792805 + 1.00813i) q^{53} +(-0.690079 - 0.723734i) q^{54} +(-4.64498 - 7.22773i) q^{55} +(-2.08108 + 1.63375i) q^{56} +(4.73614 + 2.16292i) q^{57} +(2.86044 + 4.01692i) q^{58} +(-3.78672 - 9.45876i) q^{59} +(-0.822347 + 1.59513i) q^{60} +(6.74829 - 6.43448i) q^{61} +(-3.14330 + 0.451938i) q^{62} +(2.22454 + 1.43227i) q^{63} +(0.841254 + 0.540641i) q^{64} +(-1.47440 + 0.510293i) q^{65} +(3.46481 + 3.30369i) q^{66} +(2.85806 + 2.03521i) q^{67} +(0.0125776 - 0.0217851i) q^{68} +(-4.30140 - 2.12083i) q^{69} +(1.12330 - 4.61336i) q^{70} +(0.134708 + 0.294968i) q^{71} +(0.235759 - 0.971812i) q^{72} +(-0.614684 + 3.18928i) q^{73} +(7.95815 + 0.379093i) q^{74} +(0.336736 + 1.74715i) q^{75} +(0.740984 + 5.15366i) q^{76} +(-10.9640 - 6.34237i) q^{77} +(0.731365 - 0.470020i) q^{78} +(9.24853 - 11.7605i) q^{79} +(-1.78650 + 0.170590i) q^{80} +(-0.995472 + 0.0950560i) q^{81} +(-1.38000 + 1.75482i) q^{82} +(-8.52400 + 5.47804i) q^{83} +(-0.00222539 + 2.64575i) q^{84} +(0.00642471 + 0.0446848i) q^{85} +(1.72586 + 8.95459i) q^{86} +(4.92572 + 0.234641i) q^{87} +(-0.906023 + 4.70089i) q^{88} +(3.70075 - 15.2547i) q^{89} +(0.745516 + 1.63245i) q^{90} +(-1.58869 + 1.66336i) q^{91} +(-0.541358 - 4.76518i) q^{92} +(-1.58781 + 2.75017i) q^{93} +(-2.89563 - 2.06197i) q^{94} +(-6.76258 - 6.44811i) q^{95} +(0.945001 - 0.327068i) q^{96} +(-6.67740 - 4.29131i) q^{97} +(-1.63887 - 6.80545i) q^{98} +(4.73868 - 0.681319i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 16 q^{9}+O(q^{10}) \) 320 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 16 * q^9	\( 320 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 16 q^{9} - 22 q^{14} + 16 q^{16} + 66 q^{17} + 16 q^{18} + 40 q^{23} - 48 q^{25} + 12 q^{26} + 44 q^{28} - 24 q^{29} + 24 q^{31} - 16 q^{32} + 98 q^{35} + 32 q^{36} - 22 q^{37} - 66 q^{38} - 8 q^{39} - 88 q^{43} + 4 q^{46} - 144 q^{47} - 24 q^{49} + 80 q^{50} - 22 q^{51} + 12 q^{52} + 44 q^{53} + 44 q^{57} + 10 q^{58} + 12 q^{59} - 32 q^{64} + 108 q^{70} - 16 q^{71} + 16 q^{72} - 180 q^{73} - 22 q^{74} - 12 q^{75} + 18 q^{77} - 16 q^{78} + 44 q^{79} + 16 q^{81} + 36 q^{82} + 22 q^{84} + 68 q^{85} - 22 q^{86} + 48 q^{87} + 22 q^{88} + 8 q^{92} + 8 q^{93} - 12 q^{94} + 66 q^{95} - 90 q^{98}+O(q^{100}) \) 320 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 16 * q^9 - 22 * q^14 + 16 * q^16 + 66 * q^17 + 16 * q^18 + 40 * q^23 - 48 * q^25 + 12 * q^26 + 44 * q^28 - 24 * q^29 + 24 * q^31 - 16 * q^32 + 98 * q^35 + 32 * q^36 - 22 * q^37 - 66 * q^38 - 8 * q^39 - 88 * q^43 + 4 * q^46 - 144 * q^47 - 24 * q^49 + 80 * q^50 - 22 * q^51 + 12 * q^52 + 44 * q^53 + 44 * q^57 + 10 * q^58 + 12 * q^59 - 32 * q^64 + 108 * q^70 - 16 * q^71 + 16 * q^72 - 180 * q^73 - 22 * q^74 - 12 * q^75 + 18 * q^77 - 16 * q^78 + 44 * q^79 + 16 * q^81 + 36 * q^82 + 22 * q^84 + 68 * q^85 - 22 * q^86 + 48 * q^87 + 22 * q^88 + 8 * q^92 + 8 * q^93 - 12 * q^94 + 66 * q^95 - 90 * q^98

Introduction

L-functions

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