LMFDB - Embedded newform 552.2.bb.a.133.24

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [552,2,Mod(13,552)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(552, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 11, 0, 14])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("552.13"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.bb (of order $22$, degree $10$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$48$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			133.24
Character	$\chi$	$=$	552.133
Dual form			552.2.bb.a.469.24

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.162597 - 1.40484i) q^{2} +(-0.755750 - 0.654861i) q^{3} +(-1.94712 - 0.456843i) q^{4} +(-2.88170 - 0.414326i) q^{5} +(-1.04285 + 0.955226i) q^{6} +(-2.13746 - 4.68038i) q^{7} +(-0.958385 + 2.66111i) q^{8} +(0.142315 + 0.989821i) q^{9} +(-1.05062 + 3.98095i) q^{10} +(0.715560 + 2.43697i) q^{11} +(1.17237 + 1.62035i) q^{12} +(1.25459 + 0.572954i) q^{13} +(-6.92271 + 2.24176i) q^{14} +(1.90652 + 2.20024i) q^{15} +(3.58259 + 1.77906i) q^{16} +(5.83669 - 3.75101i) q^{17} +(1.41368 - 0.0389872i) q^{18} +(-2.30229 + 3.58243i) q^{19} +(5.42175 + 2.12323i) q^{20} +(-1.44961 + 4.93693i) q^{21} +(3.53989 - 0.609000i) q^{22} +(-4.40270 + 1.90164i) q^{23} +(2.46695 - 1.38352i) q^{24} +(3.33508 + 0.979269i) q^{25} +(1.00890 - 1.66934i) q^{26} +(0.540641 - 0.841254i) q^{27} +(2.02370 + 10.0898i) q^{28} +(1.59036 + 2.47465i) q^{29} +(3.40097 - 2.32059i) q^{30} +(-2.10247 - 2.42638i) q^{31} +(3.08180 - 4.74368i) q^{32} +(1.05509 - 2.31033i) q^{33} +(-4.32053 - 8.80948i) q^{34} +(4.22032 + 14.3731i) q^{35} +(0.175088 - 1.99232i) q^{36} +(-4.72967 + 0.680024i) q^{37} +(4.65838 + 3.81683i) q^{38} +(-0.572954 - 1.25459i) q^{39} +(3.86435 - 7.27144i) q^{40} +(-1.63493 + 11.3712i) q^{41} +(6.69988 + 2.83920i) q^{42} +(-8.98707 - 7.78734i) q^{43} +(-0.279970 - 5.07199i) q^{44} -2.91134i q^{45} +(1.95563 + 6.49427i) q^{46} +3.21794 q^{47} +(-1.54250 - 3.69062i) q^{48} +(-12.7532 + 14.7180i) q^{49} +(1.91799 - 4.52602i) q^{50} +(-6.86746 - 0.987392i) q^{51} +(-2.18110 - 1.68877i) q^{52} +(-2.87684 + 1.31381i) q^{53} +(-1.09392 - 0.896296i) q^{54} +(-1.05233 - 7.31911i) q^{55} +(14.5035 - 1.20240i) q^{56} +(4.08595 - 1.19974i) q^{57} +(3.73506 - 1.83183i) q^{58} +(-2.75622 - 1.25872i) q^{59} +(-2.70707 - 5.15513i) q^{60} +(1.30434 - 1.13022i) q^{61} +(-3.75052 + 2.55910i) q^{62} +(4.32855 - 2.78179i) q^{63} +(-6.16299 - 5.10073i) q^{64} +(-3.37798 - 2.17090i) q^{65} +(-3.07408 - 1.85789i) q^{66} +(2.56768 - 8.74472i) q^{67} +(-13.0784 + 4.63723i) q^{68} +(4.57265 + 1.44599i) q^{69} +(20.8780 - 3.59183i) q^{70} +(3.77544 + 1.10857i) q^{71} +(-2.77041 - 0.569915i) q^{72} +(-1.93535 - 1.24377i) q^{73} +(0.186293 + 6.75498i) q^{74} +(-1.87920 - 2.92410i) q^{75} +(6.11945 - 5.92366i) q^{76} +(9.87649 - 8.55802i) q^{77} +(-1.85566 + 0.600913i) q^{78} +(1.06170 - 2.32479i) q^{79} +(-9.58685 - 6.61109i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(15.7088 + 4.14573i) q^{82} +(7.37017 - 1.05967i) q^{83} +(5.07798 - 8.95058i) q^{84} +(-18.3737 + 8.39101i) q^{85} +(-12.4012 + 11.3592i) q^{86} +(0.418637 - 2.91168i) q^{87} +(-7.17083 - 0.431377i) q^{88} +(1.62551 - 1.87594i) q^{89} +(-4.08995 - 0.473374i) q^{90} -7.09665i q^{91} +(9.44136 - 1.69139i) q^{92} +3.21056i q^{93} +(0.523226 - 4.52067i) q^{94} +(8.11881 - 9.36961i) q^{95} +(-5.43552 + 1.56688i) q^{96} +(-1.91268 + 13.3030i) q^{97} +(18.6027 + 20.3093i) q^{98} +(-2.31033 + 1.05509i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32}+ \cdots - 132 q^{98}+O(q^{100}) $ 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{6}{11}\right)$	$1$	$-1$	$1$

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 $

$2$	0.162597	−	1.40484i	0.114973	−	0.993369i
$2$	0.162597	−	1.40484i	0.114973	−	0.993369i
$3$	−0.755750	−	0.654861i	−0.436332	−	0.378084i
$3$	−0.755750	−	0.654861i	−0.436332	−	0.378084i
$4$	−1.94712	−	0.456843i	−0.973562	−	0.228422i
$5$	−2.88170	−	0.414326i	−1.28874	−	0.185292i	−0.536340	−	0.844002i	$-0.680193\pi$
$5$	−2.88170	−	0.414326i	−1.28874	−	0.185292i	−0.752397	+	0.658710i	$0.771103\pi$
$6$	−1.04285	+	0.955226i	−0.425743	+	0.389969i
$7$	−2.13746	−	4.68038i	−0.807883	−	1.76902i	−0.616249	−	0.787551i	$-0.711349\pi$
$7$	−2.13746	−	4.68038i	−0.807883	−	1.76902i	−0.191634	−	0.981466i	$-0.561379\pi$
$8$	−0.958385	+	2.66111i	−0.338840	+	0.940844i
$9$	0.142315	+	0.989821i	0.0474383	+	0.329940i
$10$	−1.05062	+	3.98095i	−0.332234	+	1.25889i
$11$	0.715560	+	2.43697i	0.215749	+	0.734775i	0.994245	+	0.107126i	$0.0341647\pi$
$11$	0.715560	+	2.43697i	0.215749	+	0.734775i	−0.778496	+	0.627650i	$0.784017\pi$
$12$	1.17237	+	1.62035i	0.338434	+	0.467756i
$13$	1.25459	+	0.572954i	0.347962	+	0.158909i	0.581727	−	0.813384i	$-0.302377\pi$
$13$	1.25459	+	0.572954i	0.347962	+	0.158909i	−0.233765	+	0.972293i	$0.575105\pi$
$14$	−6.92271	+	2.24176i	−1.85017	+	0.599136i
$15$	1.90652	+	2.20024i	0.492261	+	0.568100i
$16$	3.58259	+	1.77906i	0.895647	+	0.444765i
$17$	5.83669	−	3.75101i	1.41560	−	0.909754i	0.415604	−	0.909546i	$-0.363570\pi$
$17$	5.83669	−	3.75101i	1.41560	−	0.909754i	1.00000		0.000207890i	$-6.61735e-5\pi$
$18$	1.41368	−	0.0389872i	0.333207	−	0.00918938i
$19$	−2.30229	+	3.58243i	−0.528181	+	0.821866i	−0.998149	−	0.0608174i	$-0.980629\pi$
$19$	−2.30229	+	3.58243i	−0.528181	+	0.821866i	0.469967	+	0.882684i	$0.344266\pi$
$20$	5.42175	+	2.12323i	1.21234	+	0.474769i
$21$	−1.44961	+	4.93693i	−0.316332	+	1.07733i
$22$	3.53989	−	0.609000i	0.754708	−	0.129839i
$23$	−4.40270	+	1.90164i	−0.918026	+	0.396520i
$23$	−4.40270	+	1.90164i	−0.918026	+	0.396520i
$24$	2.46695	−	1.38352i	0.503565	−	0.282410i
$25$	3.33508	+	0.979269i	0.667017	+	0.195854i
$26$	1.00890	−	1.66934i	0.197861	−	0.327384i
$27$	0.540641	−	0.841254i	0.104046	−	0.161899i
$28$	2.02370	+	10.0898i	0.382443	+	1.90679i
$29$	1.59036	+	2.47465i	0.295323	+	0.459531i	0.956930	−	0.290320i	$-0.0937616\pi$
$29$	1.59036	+	2.47465i	0.295323	+	0.459531i	−0.661607	+	0.749851i	$0.730125\pi$
$30$	3.40097	−	2.32059i	0.620930	−	0.423681i
$31$	−2.10247	−	2.42638i	−0.377615	−	0.435791i	0.534849	−	0.844948i	$-0.320368\pi$
$31$	−2.10247	−	2.42638i	−0.377615	−	0.435791i	−0.912464	+	0.409157i	$0.865823\pi$
$32$	3.08180	−	4.74368i	0.544791	−	0.838572i
$33$	1.05509	−	2.31033i	0.183668	−	0.402178i
$34$	−4.32053	−	8.80948i	−0.740964	−	1.51081i
$35$	4.22032	+	14.3731i	0.713364	+	2.42949i
$36$	0.175088	−	1.99232i	0.0291814	−	0.332054i
$37$	−4.72967	+	0.680024i	−0.777554	+	0.111795i	−0.519654	−	0.854377i	$-0.673939\pi$
$37$	−4.72967	+	0.680024i	−0.777554	+	0.111795i	−0.257899	+	0.966172i	$0.583030\pi$
$38$	4.65838	+	3.81683i	0.755689	+	0.619171i
$39$	−0.572954	−	1.25459i	−0.0917461	−	0.200896i
$40$	3.86435	−	7.27144i	0.611007	−	1.14972i
$41$	−1.63493	+	11.3712i	−0.255334	+	1.77588i	0.309718	+	0.950829i	$0.399765\pi$
$41$	−1.63493	+	11.3712i	−0.255334	+	1.77588i	−0.565051	+	0.825056i	$0.691144\pi$
$42$	6.69988	+	2.83920i	1.03381	+	0.438098i
$43$	−8.98707	−	7.78734i	−1.37051	−	1.18756i	−0.961426	−	0.275063i	$-0.911301\pi$
$43$	−8.98707	−	7.78734i	−1.37051	−	1.18756i	−0.409089	−	0.912495i	$-0.634153\pi$
$44$	−0.279970	−	5.07199i	−0.0422070	−	0.764631i
$45$		−	2.91134i		−	0.433996i
$46$	1.95563	+	6.49427i	0.288342	+	0.957527i
$47$	3.21794			0.469384			0.234692	−	0.972070i	$-0.424592\pi$
$47$	3.21794			0.469384			0.234692	+	0.972070i	$0.424592\pi$
$48$	−1.54250	−	3.69062i	−0.222641	−	0.532695i
$49$	−12.7532	+	14.7180i	−1.82189	+	2.10257i
$50$	1.91799	−	4.52602i	0.271244	−	0.640076i
$51$	−6.86746	−	0.987392i	−0.961637	−	0.138263i
$52$	−2.18110	−	1.68877i	−0.302464	−	0.234190i
$53$	−2.87684	+	1.31381i	−0.395164	+	0.180465i	−0.603079	−	0.797682i	$-0.706060\pi$
$53$	−2.87684	+	1.31381i	−0.395164	+	0.180465i	0.207915	+	0.978147i	$0.433332\pi$
$54$	−1.09392	−	0.896296i	−0.148863	−	0.121970i
$55$	−1.05233	−	7.31911i	−0.141896	−	0.986909i
$56$	14.5035	−	1.20240i	1.93811	−	0.160677i
$57$	4.08595	−	1.19974i	0.541197	−	0.158910i
$58$	3.73506	−	1.83183i	0.490438	−	0.240531i
$59$	−2.75622	−	1.25872i	−0.358829	−	0.163872i	0.227840	−	0.973699i	$-0.426834\pi$
$59$	−2.75622	−	1.25872i	−0.358829	−	0.163872i	−0.586669	+	0.809827i	$0.699561\pi$
$60$	−2.70707	−	5.15513i	−0.349481	−	0.665524i
$61$	1.30434	−	1.13022i	0.167003	−	0.144709i	−0.567350	−	0.823477i	$-0.692031\pi$
$61$	1.30434	−	1.13022i	0.167003	−	0.144709i	0.734353	+	0.678768i	$0.237486\pi$
$62$	−3.75052	+	2.55910i	−0.476317	+	0.325007i
$63$	4.32855	−	2.78179i	0.545346	−	0.350473i
$64$	−6.16299	−	5.10073i	−0.770374	−	0.637592i
$65$	−3.37798	−	2.17090i	−0.418987	−	0.269267i
$66$	−3.07408	−	1.85789i	−0.378394	−	0.228690i
$67$	2.56768	−	8.74472i	0.313692	−	1.06834i	−0.640205	−	0.768204i	$-0.721151\pi$
$67$	2.56768	−	8.74472i	0.313692	−	1.06834i	0.953897	−	0.300133i	$-0.0970311\pi$
$68$	−13.0784	+	4.63723i	−1.58599	+	0.562347i
$69$	4.57265	+	1.44599i	0.550482	+	0.174077i
$70$	20.8780	−	3.59183i	2.49540	−	0.429306i
$71$	3.77544	+	1.10857i	0.448062	+	0.131563i	0.497976	−	0.867191i	$-0.334077\pi$
$71$	3.77544	+	1.10857i	0.448062	+	0.131563i	−0.0499142	+	0.998754i	$0.515895\pi$
$72$	−2.77041	−	0.569915i	−0.326496	−	0.0671652i
$73$	−1.93535	−	1.24377i	−0.226516	−	0.145573i	0.422461	−	0.906381i	$-0.361166\pi$
$73$	−1.93535	−	1.24377i	−0.226516	−	0.145573i	−0.648977	+	0.760808i	$0.724803\pi$
$74$	0.186293	+	6.75498i	0.0216561	+	0.785251i
$75$	−1.87920	−	2.92410i	−0.216992	−	0.337646i
$76$	6.11945	−	5.92366i	0.701950	−	0.679490i
$77$	9.87649	−	8.55802i	1.12553	−	0.975277i
$78$	−1.85566	+	0.600913i	−0.210112	+	0.0680400i
$79$	1.06170	−	2.32479i	0.119450	−	0.261559i	−0.840457	−	0.541879i	$-0.817713\pi$
$79$	1.06170	−	2.32479i	0.119450	−	0.261559i	0.959907	+	0.280320i	$0.0904404\pi$
$80$	−9.58685	−	6.61109i	−1.07184	−	0.739142i
$81$	−0.959493	+	0.281733i	−0.106610	+	0.0313036i
$82$	15.7088	+	4.14573i	1.73475	+	0.457820i
$83$	7.37017	−	1.05967i	0.808981	−	0.116314i	0.274601	−	0.961558i	$-0.411454\pi$
$83$	7.37017	−	1.05967i	0.808981	−	0.116314i	0.534380	+	0.845244i	$0.320545\pi$
$84$	5.07798	−	8.95058i	0.554054	−	0.976588i
$85$	−18.3737	+	8.39101i	−1.99291	+	0.910132i
$86$	−12.4012	+	11.3592i	−1.33726	+	1.22489i
$87$	0.418637	−	2.91168i	0.0448826	−	0.312165i
$88$	−7.17083	−	0.431377i	−0.764413	−	0.0459850i
$89$	1.62551	−	1.87594i	0.172304	−	0.198849i	−0.663029	−	0.748594i	$-0.730729\pi$
$89$	1.62551	−	1.87594i	0.172304	−	0.198849i	0.835333	+	0.549744i	$0.185275\pi$
$90$	−4.08995	−	0.473374i	−0.431118	−	0.0498980i
$91$		−	7.09665i		−	0.743931i
$92$	9.44136	−	1.69139i	0.984329	−	0.176340i
$93$			3.21056i			0.332920i
$94$	0.523226	−	4.52067i	0.0539666	−	0.466271i
$95$	8.11881	−	9.36961i	0.832973	−	0.961302i
$96$	−5.43552	+	1.56688i	−0.554761	+	0.159919i
$97$	−1.91268	+	13.3030i	−0.194203	+	1.35071i	0.626529	+	0.779398i	$0.284475\pi$
$97$	−1.91268	+	13.3030i	−0.194203	+	1.35071i	−0.820732	+	0.571314i	$0.806434\pi$
$98$	18.6027	+	20.3093i	1.87916	+	2.05155i
$99$	−2.31033	+	1.05509i	−0.232197	+	0.106041i
$100$	−6.04645	−	3.43037i	−0.604645	−	0.343037i
$101$	−9.62641	+	1.38407i	−0.957863	+	0.137720i	−0.603478	−	0.797380i	$-0.706219\pi$
$101$	−9.62641	+	1.38407i	−0.957863	+	0.137720i	−0.354385	+	0.935100i	$0.615310\pi$
$102$	−2.50375	+	9.48711i	−0.247908	+	0.939363i
$103$	−4.13129	+	1.21306i	−0.407068	+	0.119526i	−0.478855	−	0.877894i	$-0.658948\pi$
$103$	−4.13129	+	1.21306i	−0.407068	+	0.119526i	0.0717868	+	0.997420i	$0.477130\pi$
$104$	−2.72708	+	2.78950i	−0.267412	+	0.273533i
$105$	6.22286	−	13.6262i	0.607289	−	1.32978i
$106$	1.37792	+	4.25510i	0.133835	+	0.413292i
$107$	−11.0595	+	9.58309i	−1.06916	+	0.926433i	−0.997477	−	0.0709947i	$-0.977383\pi$
$107$	−11.0595	+	9.58309i	−1.06916	+	0.926433i	−0.0716837	+	0.997427i	$0.522837\pi$
$108$	−1.43702	+	1.39104i	−0.138277	+	0.133853i
$109$	−0.101876	−	0.158522i	−0.00975793	−	0.0151836i	0.836340	−	0.548211i	$-0.184691\pi$
$109$	−0.101876	−	0.158522i	−0.00975793	−	0.0151836i	−0.846098	+	0.533027i	$0.821054\pi$
$110$	−10.4533	+	0.288286i	−0.996678	+	0.0274870i
$111$	4.01977	+	2.58335i	0.381540	+	0.245201i
$112$	0.669049	−	20.5705i	0.0632192	−	1.94373i
$113$	−10.1075	−	2.96782i	−0.950830	−	0.279189i	−0.230698	−	0.973025i	$-0.574101\pi$
$113$	−10.1075	−	2.96782i	−0.950830	−	0.279189i	−0.720133	+	0.693837i	$0.755919\pi$
$114$	−1.02108	−	5.93516i	−0.0956328	−	0.555879i
$115$	13.4752	−	3.65582i	1.25657	−	0.340907i
$116$	−1.96610	−	5.54500i	−0.182548	−	0.514840i
$117$	−0.388575	+	1.32336i	−0.0359238	+	0.122345i
$118$	−2.21645	+	3.66737i	−0.204041	+	0.337609i
$119$	−30.0318	−	19.3003i	−2.75301	−	1.76925i
$120$	−7.68226	+	2.96478i	−0.701291	+	0.270646i
$121$	3.82697	−	2.45945i	0.347907	−	0.223586i
$122$	−1.37569	−	2.01615i	−0.124549	−	0.182534i
$123$	8.68216	−	7.52313i	0.782844	−	0.678338i
$124$	2.98530	+	5.68497i	0.268088	+	0.510525i
$125$	4.03624	+	1.84329i	0.361012	+	0.164869i
$126$	−3.20415	−	6.53321i	−0.285448	−	0.582025i
$127$	−17.1333	+	5.03078i	−1.52033	+	0.446409i	−0.932075	−	0.362266i	$-0.882003\pi$
$127$	−17.1333	+	5.03078i	−1.52033	+	0.446409i	−0.588256	+	0.808675i	$0.700185\pi$
$128$	−8.16777	+	7.82863i	−0.721936	+	0.691960i
$129$	1.69235	+	11.7706i	0.149003	+	1.03634i
$130$	−3.59900	+	4.39253i	−0.315653	+	0.385250i
$131$	−13.7058	+	6.25921i	−1.19748	+	0.546870i	−0.911474	−	0.411359i	$-0.865054\pi$
$131$	−13.7058	+	6.25921i	−1.19748	+	0.546870i	−0.286004	+	0.958228i	$0.592327\pi$
$132$	−3.10986	+	4.01650i	−0.270679	+	0.349591i
$133$	21.6882	+	3.11829i	1.88061	+	0.270390i
$134$	−11.8674	−	5.02903i	−1.02519	−	0.434442i
$135$	−1.90652	+	2.20024i	−0.164087	+	0.189367i
$136$	4.38805	+	19.1270i	0.376272	+	1.64012i
$137$	14.8577			1.26938			0.634691	−	0.772766i	$-0.281128\pi$
$137$	14.8577			1.26938			0.634691	+	0.772766i	$0.281128\pi$
$138$	2.77487	−	6.18871i	0.236213	−	0.526818i
$139$			4.29106i			0.363963i	0.983302	+	0.181981i	$0.0582510\pi$
$139$			4.29106i			0.363963i	−0.983302	+	0.181981i	$0.941749\pi$
$140$	−1.65124	−	29.9142i	−0.139555	−	2.52821i
$141$	−2.43195	−	2.10730i	−0.204807	−	0.177467i
$142$	2.17123	−	5.12362i	0.182206	−	0.429965i
$143$	−0.498536	+	3.46740i	−0.0416897	+	0.289958i
$144$	−1.25110	+	3.79931i	−0.104258	+	0.316609i
$145$	−3.55764	−	7.79014i	−0.295446	−	0.646936i
$146$	−2.06198	+	2.51662i	−0.170651	+	0.208277i
$147$	19.2765	−	2.77154i	1.58990	−	0.228593i
$148$	9.51993	+	0.836627i	0.782533	+	0.0687703i
$149$	3.37208	+	11.4843i	0.276252	+	0.940826i	0.974390	+	0.224864i	$0.0721937\pi$
$149$	3.37208	+	11.4843i	0.276252	+	0.940826i	−0.698139	+	0.715963i	$0.745988\pi$
$150$	−4.41343	+	2.16452i	−0.360355	+	0.176733i
$151$	1.01002	−	2.21163i	0.0821940	−	0.179980i	−0.864073	−	0.503367i	$-0.832094\pi$
$151$	1.01002	−	2.21163i	0.0821940	−	0.179980i	0.946267	+	0.323387i	$0.104822\pi$
$152$	−7.32676	−	9.55999i	−0.594279	−	0.775418i
$153$	4.54348	+	5.24345i	0.367318	+	0.423908i
$154$	−10.4167	−	15.2663i	−0.839404	−	1.23020i
$155$	5.05339	+	7.86322i	0.405898	+	0.631589i
$156$	0.542460	+	2.70460i	0.0434316	+	0.216541i
$157$	2.65498	−	4.13124i	0.211891	−	0.329709i	−0.718997	−	0.695013i	$-0.755399\pi$
$157$	2.65498	−	4.13124i	0.211891	−	0.329709i	0.930888	+	0.365304i	$0.119035\pi$
$158$	−3.09332	−	1.86951i	−0.246091	−	0.148730i
$159$	3.03453	+	0.891018i	0.240654	+	0.0706623i
$160$	−10.8463	+	12.3930i	−0.857474	+	0.979753i
$161$	18.3110	+	16.5416i	1.44311	+	1.30366i
$162$	0.239777	+	1.39374i	0.0188387	+	0.109502i
$163$	−0.269801	+	0.918858i	−0.0211324	+	0.0719705i	−0.969384	−	0.245549i	$-0.921032\pi$
$163$	−0.269801	+	0.918858i	−0.0211324	+	0.0719705i	0.948252	+	0.317520i	$0.102850\pi$
$164$	8.37828	−	21.3942i	0.654233	−	1.67061i
$165$	−3.99770	+	6.22054i	−0.311221	+	0.484269i
$166$	−0.290297	−	10.5262i	−0.0225314	−	0.816989i
$167$	−4.33192	+	2.78396i	−0.335214	+	0.215429i	−0.697409	−	0.716673i	$-0.745664\pi$
$167$	−4.33192	+	2.78396i	−0.335214	+	0.215429i	0.362195	+	0.932102i	$0.382027\pi$
$168$	−11.7484	−	8.58907i	−0.906411	−	0.662661i
$169$	−7.26746	−	8.38709i	−0.559035	−	0.645161i
$170$	8.80047	+	27.1764i	0.674965	+	2.08434i
$171$	−3.87362	−	1.76902i	−0.296223	−	0.135281i
$172$	13.9413	+	19.2686i	1.06302	+	1.46922i
$173$	−1.42175	−	4.84203i	−0.108093	−	0.368133i	0.887625	−	0.460566i	$-0.152354\pi$
$173$	−1.42175	−	4.84203i	−0.108093	−	0.368133i	−0.995719	+	0.0924336i	$0.970535\pi$
$174$	−4.02236	−	1.06155i	−0.304935	−	0.0804755i
$175$	−2.54525	−	17.7026i	−0.192403	−	1.33819i
$176$	−1.77197	+	10.0037i	−0.133567	+	0.754057i
$177$	1.25872	+	2.75622i	0.0946114	+	0.207170i
$178$	−2.37109	−	2.58860i	−0.177720	−	0.194024i
$179$	2.70878	+	0.389464i	0.202464	+	0.0291099i	0.242801	−	0.970076i	$-0.421934\pi$
$179$	2.70878	+	0.389464i	0.202464	+	0.0291099i	−0.0403366	+	0.999186i	$0.512843\pi$
$180$	−1.33002	+	5.66874i	−0.0991342	+	0.422523i
$181$	−9.26925	−	8.03185i	−0.688978	−	0.597003i	0.238383	−	0.971171i	$-0.423383\pi$
$181$	−9.26925	−	8.03185i	−0.688978	−	0.597003i	−0.927361	+	0.374168i	$0.877928\pi$
$182$	−9.96962	−	1.15389i	−0.738997	−	0.0855321i
$183$	−1.72589			−0.127581
$184$	−0.840996	−	13.5386i	−0.0619991	−	0.998076i
$185$	13.9113			1.02278
$186$	4.51031	+	0.522027i	0.330712	+	0.0382769i
$187$	13.3176	+	11.5398i	0.973880	+	0.843872i
$188$	−6.26572	−	1.47009i	−0.456975	−	0.107217i
$189$	−5.09298	−	0.732261i	−0.370460	−	0.0532641i
$190$	−11.8427	−	12.9291i	−0.859157	−	0.937973i
$191$	−6.85801	−	15.0169i	−0.496228	−	1.08659i	−0.977677	−	0.210114i	$-0.932616\pi$
$191$	−6.85801	−	15.0169i	−0.496228	−	1.08659i	0.481449	−	0.876474i	$-0.340111\pi$
$192$	1.31741	+	7.89078i	0.0950759	+	0.569468i
$193$	−1.62645	−	11.3122i	−0.117075	−	0.814272i	−0.960749	−	0.277418i	$-0.910521\pi$
$193$	−1.62645	−	11.3122i	−0.117075	−	0.814272i	0.843675	−	0.536855i	$-0.180388\pi$
$194$	18.3775	+	4.85002i	1.31943	+	0.348211i
$195$	1.13127	+	3.85276i	0.0810121	+	0.275902i
$196$	31.5559	−	22.8315i	2.25399	−	1.63082i
$197$	−20.9427	−	9.56420i	−1.49210	−	0.681421i	−0.508384	−	0.861131i	$-0.669757\pi$
$197$	−20.9427	−	9.56420i	−1.49210	−	0.681421i	−0.983720	+	0.179710i	$0.942484\pi$
$198$	1.10658	+	3.41719i	0.0786413	+	0.242849i
$199$	−3.41985	−	3.94672i	−0.242427	−	0.279775i	0.621477	−	0.783432i	$-0.286533\pi$
$199$	−3.41985	−	3.94672i	−0.242427	−	0.279775i	−0.863904	+	0.503657i	$0.831987\pi$
$200$	−5.80224	+	7.93650i	−0.410280	+	0.561196i
$201$	−7.66709	+	4.92734i	−0.540795	+	0.347548i
$202$	0.379166	+	13.7486i	0.0266780	+	0.967346i
$203$	8.18298	−	12.7330i	0.574332	−	0.893679i
$204$	12.9207	+	5.05993i	0.904631	+	0.354266i
$205$	9.42278	−	32.0911i	0.658116	−	2.24134i
$206$	1.03241	+	6.00102i	0.0719314	+	0.418111i
$207$	−2.50886	−	4.08725i	−0.174378	−	0.284084i
$208$	3.47538	+	4.28466i	0.240974	+	0.297088i
$209$	−10.3777	−	3.04717i	−0.717842	−	0.210777i
$210$	−18.1307	−	10.9577i	−1.25114	−	0.756151i
$211$	11.8696	−	18.4694i	0.817134	−	1.27148i	−0.142377	−	0.989812i	$-0.545475\pi$
$211$	11.8696	−	18.4694i	0.817134	−	1.27148i	0.959511	−	0.281672i	$-0.0908891\pi$
$212$	6.20176	−	1.24388i	0.425939	−	0.0854303i
$213$	−2.12733	−	3.31019i	−0.145762	−	0.226810i
$214$	11.6644	+	17.0949i	0.797364	+	1.16859i
$215$	22.6716	+	26.1644i	1.54619	+	1.78440i
$216$	1.72052	+	2.24495i	0.117067	+	0.152749i
$217$	−6.86244	+	15.0267i	−0.465853	+	1.02008i
$218$	−0.239262	+	0.117344i	−0.0162049	+	0.00794751i
$219$	0.648142	+	2.20737i	0.0437973	+	0.149160i
$220$	−1.29467	+	14.7320i	−0.0872866	+	0.993229i
$221$	9.47183	−	1.36184i	0.637144	−	0.0916075i
$222$	4.28278	−	5.22707i	0.287442	−	0.350818i
$223$	9.97705	+	21.8467i	0.668112	+	1.46296i	0.874765	+	0.484548i	$0.161016\pi$
$223$	9.97705	+	21.8467i	0.668112	+	1.46296i	−0.206652	+	0.978414i	$0.566257\pi$
$224$	−28.7894	−	4.28461i	−1.92358	−	0.286277i
$225$	−0.494670	+	3.44050i	−0.0329780	+	0.229367i
$226$	−5.81274	+	13.7168i	−0.386658	+	0.912426i
$227$	−15.5515	−	13.4755i	−1.03219	−	0.894399i	−0.0377072	−	0.999289i	$-0.512005\pi$
$227$	−15.5515	−	13.4755i	−1.03219	−	0.894399i	−0.994484	+	0.104890i	$0.966551\pi$
$228$	−8.50395	+	0.469411i	−0.563188	+	0.0310875i
$229$			22.5665i			1.49123i	0.666375	+	0.745617i	$0.267845\pi$
$229$			22.5665i			1.49123i	−0.666375	+	0.745617i	$0.732155\pi$
$230$	−2.94480	−	19.5248i	−0.194175	−	1.28743i
$231$	−13.0685			−0.859842
$232$	−8.10949	+	1.86046i	−0.532414	+	0.122145i
$233$	−11.5404	+	13.3183i	−0.756035	+	0.872511i	−0.995139	−	0.0984834i	$-0.968601\pi$
$233$	−11.5404	+	13.3183i	−0.756035	+	0.872511i	0.239104	+	0.970994i	$0.423146\pi$
$234$	1.79593	+	0.761058i	0.117404	+	0.0497519i
$235$	−9.27314	−	1.33328i	−0.604913	−	0.0869733i
$236$	4.79166	+	3.71005i	0.311911	+	0.241504i
$237$	−2.32479	+	1.06170i	−0.151011	+	0.0689646i
$238$	−31.9968	+	39.0516i	−2.07404	+	2.53134i
$239$	2.14486	+	14.9178i	0.138739	+	0.964954i	0.933640	+	0.358213i	$0.116614\pi$
$239$	2.14486	+	14.9178i	0.138739	+	0.964954i	−0.794900	+	0.606740i	$0.792477\pi$
$240$	2.91591	+	11.2744i	0.188221	+	0.727758i
$241$	15.7174	−	4.61506i	1.01245	−	0.297282i	0.266894	−	0.963726i	$-0.414003\pi$
$241$	15.7174	−	4.61506i	1.01245	−	0.297282i	0.745555	+	0.666444i	$0.232184\pi$
$242$	−2.83286	−	5.77617i	−0.182103	−	0.371306i
$243$	0.909632	+	0.415415i	0.0583529	+	0.0266489i
$244$	−3.05604	+	1.60479i	−0.195643	+	0.102736i
$245$	42.8490	−	37.1289i	2.73752	−	2.37208i
$246$	−9.15707	−	13.4202i	−0.583834	−	0.855643i
$247$	−4.94101	+	3.17539i	−0.314389	+	0.202045i
$248$	8.47184	−	3.26950i	0.537962	−	0.207613i
$249$	−6.26394	−	4.02559i	−0.396961	−	0.255111i
$250$	3.24579	−	5.37054i	0.205282	−	0.339663i
$251$	1.62696	−	5.54090i	0.102692	−	0.349739i	−0.892077	−	0.451883i	$-0.850752\pi$
$251$	1.62696	−	5.54090i	0.102692	−	0.349739i	0.994770	+	0.102145i	$0.0325705\pi$
$252$	−9.69907	+	3.43902i	−0.610984	+	0.216638i
$253$	−7.78465	−	9.36852i	−0.489417	−	0.588994i
$254$	4.28160	+	24.8874i	0.268652	+	1.56157i
$255$	19.3809	+	5.69074i	1.21368	+	0.356368i
$256$	9.66988	+	12.7473i	0.604368	+	0.796706i
$257$	7.21011	+	4.63366i	0.449754	+	0.289040i	0.745844	−	0.666121i	$-0.232046\pi$
$257$	7.21011	+	4.63366i	0.449754	+	0.289040i	−0.296090	+	0.955160i	$0.595683\pi$
$258$	16.8109	−	0.463620i	1.04660	−	0.0288637i
$259$	13.2923	+	20.6832i	0.825941	+	1.28519i
$260$	5.58559	+	5.77021i	0.346404	+	0.357853i
$261$	−2.22313	+	1.92635i	−0.137608	+	0.119238i
$262$	6.56465	+	20.2721i	0.405565	+	1.25241i
$263$	4.52533	−	9.90909i	0.279044	−	0.611021i	−0.717271	−	0.696795i	$-0.754609\pi$
$263$	4.52533	−	9.90909i	0.279044	−	0.611021i	0.996315	+	0.0857737i	$0.0273362\pi$
$264$	5.13686	+	5.02191i	0.316152	+	0.309077i
$265$	8.83454	−	2.59405i	0.542701	−	0.159351i
$266$	7.90712	−	29.9613i	0.484816	−	1.83705i
$267$	−2.45696	+	0.353258i	−0.150364	+	0.0216190i
$268$	−8.99456	+	15.8540i	−0.549430	+	0.968439i
$269$	10.4702	−	4.78156i	0.638377	−	0.291537i	−0.0698120	−	0.997560i	$-0.522240\pi$
$269$	10.4702	−	4.78156i	0.638377	−	0.291537i	0.708189	+	0.706023i	$0.249513\pi$
$270$	2.78098	+	3.03610i	0.169245	+	0.184771i
$271$	−0.584465	+	4.06504i	−0.0355037	+	0.246934i	−0.999843	−	0.0177364i	$-0.994354\pi$
$271$	−0.584465	+	4.06504i	−0.0355037	+	0.246934i	0.964339	+	0.264670i	$0.0852631\pi$
$272$	27.5837	−	3.05451i	1.67251	−	0.185207i
$273$	−4.64732	+	5.36329i	−0.281268	+	0.324601i
$274$	2.41582	−	20.8727i	0.145945	−	1.26096i
$275$			8.82824i			0.532363i
$276$	−8.24293	−	4.90450i	−0.496166	−	0.295216i
$277$		−	12.2540i		−	0.736269i	−0.929773	−	0.368135i	$-0.879997\pi$
$277$		−	12.2540i		−	0.736269i	0.929773	−	0.368135i	$-0.120003\pi$
$278$	6.02823	+	0.697712i	0.361549	+	0.0418460i
$279$	2.10247	−	2.42638i	0.125872	−	0.145264i
$280$	−42.2930	−	2.54423i	−2.52749	−	0.152047i
$281$	0.766558	−	5.33153i	0.0457290	−	0.318052i	−0.954099	−	0.299492i	$-0.903183\pi$
$281$	0.766558	−	5.33153i	0.0457290	−	0.318052i	0.999828	−	0.0185600i	$-0.00590818\pi$
$282$	−3.35584	+	3.07385i	−0.199837	+	0.183045i
$283$	6.76217	−	3.08818i	0.401969	−	0.183573i	−0.204163	−	0.978937i	$-0.565447\pi$
$283$	6.76217	−	3.08818i	0.401969	−	0.183573i	0.606133	+	0.795364i	$0.292720\pi$
$284$	−6.84481	−	3.88330i	−0.406165	−	0.230432i
$285$	−12.2716	+	1.76439i	−0.726906	+	0.104513i
$286$	4.79006	+	1.26415i	0.283242	+	0.0747507i
$287$	56.7162	−	16.6534i	3.34785	−	0.983018i
$288$	5.13398	+	2.37534i	0.302523	+	0.139968i
$289$	12.9348	−	28.3232i	0.760868	−	1.66607i
$290$	−11.5223	+	3.73124i	−0.676614	+	0.219106i
$291$	10.1571	−	8.80118i	0.595420	−	0.515934i
$292$	3.20016	+	3.30594i	0.187275	+	0.193465i
$293$	−10.5923	−	16.4819i	−0.618807	−	0.962882i	−0.999274	−	0.0380879i	$-0.987873\pi$
$293$	−10.5923	−	16.4819i	−0.618807	−	0.962882i	0.380468	−	0.924794i	$-0.375763\pi$
$294$	−0.759264	−	27.5309i	−0.0442812	−	1.60564i
$295$	7.42108	+	4.76924i	0.432072	+	0.277676i
$296$	2.72323	−	13.2379i	0.158285	−	0.769437i
$297$	2.43697	+	0.715560i	0.141408	+	0.0415210i
$298$	16.6818	−	2.86992i	0.966349	−	0.166250i
$299$	−6.61316	−	0.136753i	−0.382449	−	0.00790864i
$300$	2.32319	+	6.55209i	0.134129	+	0.378285i
$301$	−17.2382	+	58.7080i	−0.993595	+	3.38387i
$302$	−2.94275	−	1.77851i	−0.169336	−	0.102342i
$303$	8.18153	+	5.25795i	0.470016	+	0.302061i
$304$	−14.6215	+	8.73847i	−0.838602	+	0.501186i
$305$	−4.22699	+	2.71652i	−0.242037	+	0.155548i
$306$	8.10494	−	5.53027i	0.463329	−	0.316144i
$307$	11.3650	−	9.84782i	0.648634	−	0.562045i	−0.267180	−	0.963647i	$-0.586092\pi$
$307$	11.3650	−	9.84782i	0.648634	−	0.562045i	0.915814	+	0.401602i	$0.131546\pi$
$308$	−23.1404	+	12.1515i	−1.31855	+	0.692398i
$309$	3.91660	+	1.78865i	0.222808	+	0.101753i
$310$	11.8682	−	5.82064i	0.674068	−	0.330590i
$311$	−18.6304	+	5.47038i	−1.05643	+	0.310197i	−0.763414	−	0.645910i	$-0.776478\pi$
$311$	−18.6304	+	5.47038i	−1.05643	+	0.310197i	−0.293020	+	0.956106i	$0.594660\pi$
$312$	3.88772	−	0.322308i	0.220099	−	0.0182471i
$313$	2.42059	+	16.8356i	0.136820	+	0.951602i	0.936373	+	0.351007i	$0.114161\pi$
$313$	2.42059	+	16.8356i	0.136820	+	0.951602i	−0.799553	+	0.600595i	$0.794930\pi$
$314$	−5.37201	−	4.40154i	−0.303160	−	0.248393i
$315$	−13.6262	+	6.22286i	−0.767747	+	0.350619i
$316$	−3.12932	+	4.04163i	−0.176038	+	0.227359i
$317$	−7.00911	−	1.00776i	−0.393671	−	0.0566013i	−0.0573629	−	0.998353i	$-0.518269\pi$
$317$	−7.00911	−	1.00776i	−0.393671	−	0.0566013i	−0.336308	+	0.941752i	$0.609178\pi$
$318$	1.74514	−	4.11814i	0.0978625	−	0.230934i
$319$	−4.89266	+	5.64643i	−0.273936	+	0.316139i
$320$	15.6466	+	17.2523i	0.874669	+	0.964433i
$321$	14.6338			0.816779
$322$	26.2156	−	23.0343i	1.46094	−	1.28365i
$323$			29.5454i			1.64395i
$324$	1.99696	−	0.110231i	0.110942	−	0.00612392i
$325$	3.62310	+	3.13944i	0.200974	+	0.174145i
$326$	1.24698	+	0.528429i	0.0690636	+	0.0292670i
$327$	−0.0268171	+	0.186517i	−0.00148299	+	0.0103144i
$328$	−28.6931	−	15.2487i	−1.58431	−	0.841970i
$329$	−6.87820	−	15.0612i	−0.379208	−	0.830349i
$330$	8.08883	+	6.62755i	0.445275	+	0.364835i
$331$	−24.0842	+	3.46279i	−1.32379	+	0.190332i	−0.767710	−	0.640798i	$-0.778604\pi$
$331$	−24.0842	+	3.46279i	−1.32379	+	0.190332i	−0.556079	+	0.831130i	$0.687695\pi$
$332$	−14.8347	−	1.30370i	−0.814162	−	0.0715499i
$333$	−1.34621	−	4.58476i	−0.0737716	−	0.251243i
$334$	3.20664	+	6.53830i	0.175460	+	0.357760i
$335$	−11.0225	+	24.1358i	−0.602221	+	1.31868i
$336$	−13.9765	+	15.1080i	−0.762479	+	0.824212i
$337$	−15.9988	−	18.4636i	−0.871510	−	1.00578i	−0.999901	−	0.0140527i	$-0.995527\pi$
$337$	−15.9988	−	18.4636i	−0.871510	−	1.00578i	0.128391	−	0.991724i	$-0.459019\pi$
$338$	−12.9642	+	8.84587i	−0.705157	+	0.481152i
$339$	5.69520	+	8.86191i	0.309321	+	0.481313i
$340$	39.6093	−	7.94442i	2.14812	−	0.430847i
$341$	4.40858	−	6.85989i	0.238738	−	0.371484i
$342$	−3.11502	+	5.15416i	−0.168441	+	0.278705i
$343$	61.5867	+	18.0835i	3.32537	+	0.976417i
$344$	29.3360	−	16.4523i	1.58169	−	0.887048i
$345$	−12.5779	−	6.06148i	−0.677172	−	0.326339i
$346$	−7.03342	+	1.21002i	−0.378119	+	0.0650513i
$347$	2.26794	−	7.72389i	0.121749	−	0.414640i	−0.875953	−	0.482397i	$-0.839766\pi$
$347$	2.26794	−	7.72389i	0.121749	−	0.414640i	0.997702	+	0.0677573i	$0.0215844\pi$
$348$	−2.14532	+	5.47816i	−0.115001	+	0.293660i
$349$	−2.40400	+	3.74069i	−0.128683	+	0.200235i	−0.899616	−	0.436681i	$-0.856154\pi$
$349$	−2.40400	+	3.74069i	−0.128683	+	0.200235i	0.770933	+	0.636916i	$0.219790\pi$
$350$	−25.2831	+	0.697273i	−1.35144	+	0.0372708i
$351$	1.16028	−	0.745670i	0.0619314	−	0.0398009i
$352$	13.7654	+	4.11589i	0.733700	+	0.219378i
$353$	1.86960	+	2.15764i	0.0995089	+	0.114839i	0.803320	−	0.595548i	$-0.203065\pi$
$353$	1.86960	+	2.15764i	0.0995089	+	0.114839i	−0.703811	+	0.710388i	$0.748520\pi$
$354$	4.07670	−	1.32015i	0.216674	−	0.0701650i
$355$	−10.4204	−	4.75883i	−0.553057	−	0.252573i
$356$	−4.02209	+	2.91009i	−0.213170	+	0.154234i
$357$	10.0575	+	34.2528i	0.532302	+	1.81285i
$358$	0.987573	−	3.74207i	0.0521948	−	0.197775i
$359$	−4.11318	−	28.6078i	−0.217085	−	1.50986i	−0.748720	−	0.662886i	$-0.769331\pi$
$359$	−4.11318	−	28.6078i	−0.217085	−	1.50986i	0.531635	−	0.846974i	$-0.321578\pi$
$360$	7.74738	+	2.79018i	0.408323	+	0.147056i
$361$	0.359601	+	0.787416i	0.0189264	+	0.0414429i
$362$	−12.7906	+	11.7158i	−0.672258	+	0.615770i
$363$	−4.50283	−	0.647409i	−0.236337	−	0.0339802i
$364$	−3.24205	+	13.8181i	−0.169930	+	0.724263i
$365$	5.06178	+	4.38606i	0.264946	+	0.229577i
$366$	−0.280623	+	2.42459i	−0.0146684	+	0.126735i
$367$	−35.0592			−1.83008			−0.915039	−	0.403366i	$-0.867840\pi$
$367$	−35.0592			−1.83008			−0.915039	+	0.403366i	$0.867840\pi$
$368$	−19.1562	−	1.01986i	−0.998586	−	0.0531641i
$369$	−11.4881			−0.598049
$370$	2.26193	−	19.5430i	0.117592	−	1.01599i
$371$	12.2982	+	10.6565i	0.638493	+	0.553257i
$372$	1.46672	−	6.25137i	0.0760461	−	0.324118i
$373$	35.8483	+	5.15421i	1.85616	+	0.266875i	0.977555	−	0.210681i	$-0.0675683\pi$
$373$	35.8483	+	5.15421i	1.85616	+	0.266875i	0.878601	+	0.477556i	$0.158477\pi$
$374$	18.3769	−	16.8327i	0.950246	−	0.870399i
$375$	−1.84329	−	4.03624i	−0.0951870	−	0.208430i
$376$	−3.08402	+	8.56327i	−0.159046	+	0.441617i
$377$	0.577398	+	4.01589i	0.0297375	+	0.206829i
$378$	−1.85681	+	7.03574i	−0.0955039	+	0.361879i
$379$	−10.4363	−	35.5429i	−0.536079	−	1.82572i	−0.563533	−	0.826094i	$-0.690558\pi$
$379$	−10.4363	−	35.5429i	−0.536079	−	1.82572i	0.0274537	−	0.999623i	$-0.491260\pi$
$380$	−20.0888	+	14.5348i	−1.03053	+	0.745618i
$381$	16.2429	+	7.41789i	0.832149	+	0.380030i
$382$	−22.2114	+	7.19267i	−1.13644	+	0.368009i
$383$	15.1779	+	17.5163i	0.775555	+	0.895039i	0.996780	−	0.0801842i	$-0.0255509\pi$
$383$	15.1779	+	17.5163i	0.775555	+	0.895039i	−0.221225	+	0.975223i	$0.571005\pi$
$384$	11.2995	−	0.567729i	0.576623	−	0.0289718i
$385$	−32.0069	+	20.5696i	−1.63122	+	1.04832i
$386$	−16.1563	+	0.445568i	−0.822333	+	0.0226788i
$387$	6.42908	−	10.0038i	0.326809	−	0.508524i
$388$	9.80160	−	25.0288i	0.497601	−	1.27064i
$389$	0.488808	−	1.66473i	0.0247835	−	0.0844050i	−0.946173	−	0.323662i	$-0.895086\pi$
$389$	0.488808	−	1.66473i	0.0247835	−	0.0844050i	0.970956	+	0.239257i	$0.0769040\pi$
$390$	5.59643	−	0.962805i	0.283386	−	0.0487536i
$391$	−18.5641	+	27.6139i	−0.938826	+	1.39649i
$392$	−26.9437	−	48.0432i	−1.36086	−	2.42655i
$393$	14.4570	+	4.24497i	0.729261	+	0.214130i
$394$	−16.8413	+	27.8659i	−0.848454	+	1.40386i
$395$	−4.02271	+	6.25947i	−0.202405	+	0.314948i
$396$	4.98052	−	0.998940i	0.250281	−	0.0501986i
$397$	−1.56478	−	2.43485i	−0.0785342	−	0.122202i	0.799765	−	0.600314i	$-0.204958\pi$
$397$	−1.56478	−	2.43485i	−0.0785342	−	0.122202i	−0.878299	+	0.478112i	$0.841321\pi$
$398$	−6.10054	+	4.16260i	−0.305793	+	0.208652i
$399$	−14.3488	−	16.5594i	−0.718338	−	0.829007i
$400$	10.2061	+	9.44164i	0.510303	+	0.472082i
$401$	−1.52979	+	3.34978i	−0.0763943	+	0.167280i	−0.943976	−	0.330015i	$-0.892946\pi$
$401$	−1.52979	+	3.34978i	−0.0763943	+	0.167280i	0.867581	+	0.497295i	$0.165673\pi$
$402$	5.67546	+	11.5722i	0.283066	+	0.577168i
$403$	−1.24754	−	4.24874i	−0.0621446	−	0.211645i
$404$	19.3761	+	1.70280i	0.963998	+	0.0847177i
$405$	2.88170	−	0.414326i	0.143193	−	0.0205880i
$406$	−16.5572	−	13.5661i	−0.821720	−	0.673273i
$407$	−5.04157	−	11.0395i	−0.249901	−	0.547207i
$408$	9.20923	−	17.3288i	0.455925	−	0.857901i
$409$	1.30324	−	9.06425i	0.0644412	−	0.448198i	−0.931899	−	0.362718i	$-0.881849\pi$
$409$	1.30324	−	9.06425i	0.0644412	−	0.448198i	0.996340	−	0.0854796i	$-0.0272423\pi$
$410$	−43.5505	−	18.4554i	−2.15081	−	0.911445i
$411$	−11.2287	−	9.72974i	−0.553872	−	0.479933i
$412$	8.59832	−	0.474620i	0.423609	−	0.0233829i
$413$			15.5906i			0.767164i
$414$	−6.14985	+	2.85996i	−0.302249	+	0.140559i
$415$	−21.6777			−1.06412
$416$	6.58433	−	4.18566i	0.322823	−	0.205219i
$417$	2.81004	−	3.24296i	0.137608	−	0.158809i
$418$	−5.96816	+	14.0835i	−0.291912	+	0.688848i
$419$	−15.6690	−	2.25286i	−0.765480	−	0.110059i	−0.251495	−	0.967859i	$-0.580922\pi$
$419$	−15.6690	−	2.25286i	−0.765480	−	0.110059i	−0.513985	+	0.857799i	$0.671831\pi$
$420$	−18.3417	+	23.6890i	−0.894984	+	1.15590i
$421$	4.81909	−	2.20081i	0.234868	−	0.107261i	−0.294505	−	0.955650i	$-0.595155\pi$
$421$	4.81909	−	2.20081i	0.234868	−	0.107261i	0.529373	+	0.848389i	$0.322427\pi$
$422$	−24.0165	−	19.6778i	−1.16910	−	0.957902i
$423$	0.457960	+	3.18518i	0.0222668	+	0.154869i
$424$	−0.739065	−	8.91471i	−0.0358922	−	0.432937i
$425$	23.1391	−	6.79425i	1.12241	−	0.329569i
$426$	−4.99616	+	2.45032i	−0.242065	+	0.118718i
$427$	−8.07781	−	3.68901i	−0.390913	−	0.178524i
$428$	25.9122	−	13.6070i	1.25251	−	0.657721i
$429$	2.64743	−	2.29401i	0.127819	−	0.110756i
$430$	40.4430	−	27.5956i	1.95033	−	1.33078i
$431$	−12.2635	+	7.88127i	−0.590712	+	0.379627i	−0.801580	−	0.597887i	$-0.796007\pi$
$431$	−12.2635	+	7.88127i	−0.590712	+	0.379627i	0.210869	+	0.977514i	$0.432371\pi$
$432$	3.43354	−	2.05203i	0.165196	−	0.0987285i
$433$	−21.1049	−	13.5633i	−1.01424	−	0.651810i	−0.0757499	−	0.997127i	$-0.524135\pi$
$433$	−21.1049	−	13.5633i	−1.01424	−	0.651810i	−0.938486	+	0.345317i	$0.887771\pi$
$434$	19.9942	+	12.0839i	0.959751	+	0.580045i
$435$	−2.41277	+	8.21715i	−0.115684	+	0.393982i
$436$	0.125945	+	0.355203i	0.00603168	+	0.0170111i
$437$	3.32378	−	20.1505i	0.158998	−	0.963929i
$438$	3.20637	−	0.551622i	0.153206	−	0.0263575i
$439$	6.43616	+	1.88983i	0.307181	+	0.0901965i	0.431690	−	0.902022i	$-0.357917\pi$
$439$	6.43616	+	1.88983i	0.307181	+	0.0901965i	−0.124509	+	0.992218i	$0.539736\pi$
$440$	20.4855	+	4.21417i	0.976607	+	0.200903i
$441$	−16.3832	−	10.5288i	−0.780150	−	0.501372i
$442$	−0.373078	−	13.5278i	−0.0177455	−	0.643452i
$443$	6.08182	+	9.46350i	0.288956	+	0.449624i	0.955136	−	0.296166i	$-0.0957083\pi$
$443$	6.08182	+	9.46350i	0.288956	+	0.449624i	−0.666180	+	0.745791i	$0.732072\pi$
$444$	−6.64681	−	6.86651i	−0.315444	−	0.325870i
$445$	−5.46150	+	4.73242i	−0.258900	+	0.224338i
$446$	32.3132	−	10.4639i	1.53008	−	0.495480i
$447$	4.97214	−	10.8875i	0.235174	−	0.514959i
$448$	−10.7002	+	39.7478i	−0.505539	+	1.87791i
$449$	−10.0307	+	2.94528i	−0.473378	+	0.138996i	−0.509715	−	0.860343i	$-0.670249\pi$
$449$	−10.0307	+	2.94528i	−0.473378	+	0.138996i	0.0363371	+	0.999340i	$0.488431\pi$
$450$	4.75291	+	1.25434i	0.224054	+	0.0591303i
$451$	−28.8812	+	4.15249i	−1.35996	+	0.195533i
$452$	18.3247	+	10.3962i	0.861920	+	0.488998i
$453$	−2.21163	+	1.01002i	−0.103911	+	0.0474547i
$454$	−21.4594	+	19.6563i	−1.00714	+	0.922514i
$455$	−2.94033	+	20.4504i	−0.137845	+	0.958731i
$456$	−0.723268	+	12.0230i	−0.0338701	+	0.563027i
$457$	−8.01044	+	9.24454i	−0.374712	+	0.432441i	−0.911515	−	0.411267i	$-0.865087\pi$
$457$	−8.01044	+	9.24454i	−0.374712	+	0.432441i	0.536803	+	0.843708i	$0.319632\pi$
$458$	31.7022	+	3.66923i	1.48134	+	0.171452i
$459$		−	6.93808i		−	0.323842i
$460$	−27.9080	+	0.962292i	−1.30122	+	0.0448671i
$461$			8.28230i			0.385745i	0.981224	+	0.192873i	$0.0617804\pi$
$461$			8.28230i			0.385745i	−0.981224	+	0.192873i	$0.938220\pi$
$462$	−2.12489	+	18.3590i	−0.0988588	+	0.854140i
$463$	−5.05565	+	5.83453i	−0.234956	+	0.271153i	−0.860967	−	0.508660i	$-0.830141\pi$
$463$	−5.05565	+	5.83453i	−0.234956	+	0.271153i	0.626011	+	0.779814i	$0.284686\pi$
$464$	1.29506	+	11.6950i	0.0601215	+	0.542927i
$465$	1.33022	−	9.25189i	0.0616875	−	0.429046i
$466$	16.8336	+	18.3778i	0.779801	+	0.851336i
$467$	28.9123	−	13.2038i	1.33790	−	0.611000i	0.387457	−	0.921888i	$-0.373354\pi$
$467$	28.9123	−	13.2038i	1.33790	−	0.611000i	0.950447	+	0.310888i	$0.100626\pi$
$468$	1.36117	−	2.39924i	0.0629203	−	0.110905i
$469$	−46.4169	+	6.67374i	−2.14333	+	0.308165i
$470$	−3.38081	+	12.8104i	−0.155945	+	0.590902i
$471$	−4.71189	+	1.38354i	−0.217112	+	0.0637499i
$472$	5.99112	−	6.12826i	0.275764	−	0.282076i
$473$	12.5467	−	27.4736i	0.576900	−	1.26324i
$474$	1.11350	+	3.43858i	0.0511450	+	0.157939i
$475$	−11.1865	+	9.69315i	−0.513272	+	0.444752i
$476$	49.6585	+	51.2999i	2.27609	+	2.35133i
$477$	−1.70985	−	2.66058i	−0.0782887	−	0.121820i
$478$	21.3058	−	0.587585i	0.974506	−	0.0268755i
$479$	−0.171049	−	0.109926i	−0.00781542	−	0.00502267i	0.536727	−	0.843756i	$-0.319660\pi$
$479$	−0.171049	−	0.109926i	−0.00781542	−	0.00502267i	−0.544543	+	0.838733i	$0.683297\pi$
$480$	16.3128	−	2.26320i	0.744572	−	0.103301i
$481$	−6.32345	−	1.85673i	−0.288324	−	0.0846597i
$482$	−3.92779	−	22.8308i	−0.178906	−	1.03992i
$483$	−3.00607	−	24.4925i	−0.136781	−	1.11445i
$484$	−8.57518	+	3.04052i	−0.389781	+	0.138206i
$485$	11.0235	−	37.5428i	0.500553	−	1.70473i
$486$	0.731493	−	1.21034i	0.0331812	−	0.0549020i
$487$	−0.292873	−	0.188218i	−0.0132713	−	0.00852896i	0.533988	−	0.845492i	$-0.320693\pi$
$487$	−0.292873	−	0.188218i	−0.0132713	−	0.00852896i	−0.547260	+	0.836963i	$0.684329\pi$
$488$	1.75757	+	4.55417i	0.0795613	+	0.206157i
$489$	0.805626	−	0.517744i	0.0364317	−	0.0234132i
$490$	−45.1929	−	66.2329i	−2.04161	−	2.99210i
$491$	−28.4707	+	24.6700i	−1.28487	+	1.11334i	−0.297528	+	0.954713i	$0.596162\pi$
$491$	−28.4707	+	24.6700i	−1.28487	+	1.11334i	−0.987338	+	0.158630i	$0.949292\pi$
$492$	−20.3421	+	10.6821i	−0.917094	+	0.481586i
$493$	18.5649	+	8.47830i	0.836120	+	0.381843i
$494$	3.65751	+	7.45761i	0.164559	+	0.335534i
$495$	7.09485	−	2.08324i	0.318890	−	0.0936345i
$496$	−3.21561	−	12.4332i	−0.144385	−	0.558265i
$497$	−2.88132	−	20.0400i	−0.129245	−	0.898917i
$498$	−6.67378	+	8.14525i	−0.299059	+	0.364998i
$499$	18.7539	−	8.56462i	0.839540	−	0.383405i	0.0512329	−	0.998687i	$-0.483685\pi$
$499$	18.7539	−	8.56462i	0.839540	−	0.383405i	0.788308	+	0.615281i	$0.210958\pi$
$500$	−7.01696	−	5.43304i	−0.313808	−	0.242973i
$501$	5.09695	+	0.732831i	0.227715	+	0.0327405i
$502$	−7.51951	−	3.18654i	−0.335612	−	0.142222i
$503$	−2.54269	+	2.93442i	−0.113373	+	0.130839i	−0.809599	−	0.586983i	$-0.800316\pi$
$503$	−2.54269	+	2.93442i	−0.113373	+	0.130839i	0.696226	+	0.717822i	$0.254861\pi$
$504$	3.25423	+	14.1848i	0.144955	+	0.631840i
$505$	28.3139			1.25995
$506$	−14.4270	+	9.41286i	−0.641358	+	0.418453i
$507$			11.0977i			0.492867i
$508$	35.6589	−	1.96834i	1.58211	−	0.0873310i
$509$	6.41130	+	5.55543i	0.284176	+	0.246240i	0.785271	−	0.619152i	$-0.212524\pi$
$509$	6.41130	+	5.55543i	0.284176	+	0.246240i	−0.501095	+	0.865392i	$0.667069\pi$
$510$	11.1458	−	26.3017i	0.493545	−	1.16466i
$511$	−1.68461	+	11.7167i	−0.0745226	+	0.518316i
$512$	19.4801	−	11.5119i	0.860908	−	0.508760i
$513$	1.76902	+	3.87362i	0.0781042	+	0.171024i
$514$	7.68187	−	9.37560i	0.338833	−	0.413540i
$515$	12.4078	−	1.78397i	0.546751	−	0.0786110i
$516$	2.08208	−	23.6919i	0.0916585	−	1.04298i
$517$	2.30263	+	7.84202i	0.101269	+	0.344892i
$518$	31.2177	−	15.3104i	1.37163	−	0.672701i
$519$	−2.09637	+	4.59041i	−0.0920204	+	0.201497i
$520$	9.01440	−	6.90862i	0.395307	−	0.302963i
$521$	−17.7426	−	20.4761i	−0.777318	−	0.897073i	0.219594	−	0.975591i	$-0.429527\pi$
$521$	−17.7426	−	20.4761i	−0.777318	−	0.897073i	−0.996913	+	0.0785180i	$0.974981\pi$
$522$	2.34474	+	3.43635i	0.102626	+	0.150405i
$523$	−14.1956	−	22.0888i	−0.620732	−	0.965877i	−0.999189	−	0.0402588i	$-0.987182\pi$
$523$	−14.1956	−	22.0888i	−0.620732	−	0.965877i	0.378458	−	0.925619i	$-0.376455\pi$
$524$	29.5463	−	5.92608i	1.29074	−	0.258882i
$525$	−9.66917	+	15.0455i	−0.421997	+	0.656641i
$526$	−13.1848	−	7.96853i	−0.574886	−	0.347444i
$527$	−21.3728	−	6.27563i	−0.931016	−	0.273371i
$528$	7.89019	−	6.39990i	0.343377	−	0.278520i
$529$	15.7675	−	16.7447i	0.685544	−	0.728031i
$530$	−2.20775	−	12.8329i	−0.0958986	−	0.557424i
$531$	0.853660	−	2.90730i	0.0370457	−	0.126166i
$532$	−40.8051	−	15.9798i	−1.76912	−	0.692812i
$533$	−8.56636	+	13.3295i	−0.371050	+	0.577365i
$534$	0.0967752	+	3.50907i	0.00418787	+	0.151852i
$535$	35.8407	−	23.0334i	1.54953	−	0.995821i
$536$	20.8098	+	15.2137i	0.898847	+	0.657131i
$537$	−1.79212	−	2.06821i	−0.0773356	−	0.0892500i
$538$	−5.01489	−	15.4863i	−0.216207	−	0.667662i
$539$	−44.9930	−	20.5476i	−1.93799	−	0.885049i
$540$	4.71740	−	3.41316i	0.203004	−	0.146879i
$541$	−6.36432	−	21.6749i	−0.273623	−	0.931876i	−0.975578	−	0.219654i	$-0.929507\pi$
$541$	−6.36432	−	21.6749i	−0.273623	−	0.931876i	0.701954	−	0.712222i	$-0.252311\pi$
$542$	5.61568	+	1.48204i	0.241214	+	0.0636591i
$543$	1.74549	+	12.1401i	0.0749061	+	0.520983i
$544$	0.193943	−	39.2472i	0.00831525	−	1.68271i
$545$	0.227896	+	0.499023i	0.00976200	+	0.0213758i
$546$	6.77890	+	7.40077i	0.290110	+	0.316724i
$547$	−19.7747	−	2.84318i	−0.845507	−	0.121566i	−0.294072	−	0.955783i	$-0.595011\pi$
$547$	−19.7747	−	2.84318i	−0.845507	−	0.121566i	−0.551435	+	0.834218i	$0.685920\pi$
$548$	−28.9298	−	6.78765i	−1.23582	−	0.289954i
$549$	1.30434	+	1.13022i	0.0556678	+	0.0482364i
$550$	12.4022	+	1.43544i	0.528833	+	0.0612075i
$551$	−12.5267			−0.533657
$552$	−8.23029	+	10.7825i	−0.350304	+	0.458934i
$553$	−13.1502			−0.559205
$554$	−17.2148	−	1.99245i	−0.731387	−	0.0846512i
$555$	−10.5134	−	9.10995i	−0.446271	−	0.386696i
$556$	1.96034	−	8.35522i	0.0831369	−	0.354340i
$557$	−32.4121	−	4.66015i	−1.37334	−	0.197457i	−0.584172	−	0.811630i	$-0.698581\pi$
$557$	−32.4121	−	4.66015i	−1.37334	−	0.197457i	−0.789171	+	0.614173i	$0.789490\pi$
$558$	−3.06681	−	3.34815i	−0.129828	−	0.141738i
$559$	−6.81334	−	14.9191i	−0.288173	−	0.631012i
$560$	−10.4509	+	59.0010i	−0.441632	+	2.49325i
$561$	−2.50783	−	17.4424i	−0.105881	−	0.736417i
$562$	−7.36528	−	1.94378i	−0.310686	−	0.0819933i
$563$	6.30982	+	21.4893i	0.265927	+	0.905665i	0.978877	+	0.204450i	$0.0655406\pi$
$563$	6.30982	+	21.4893i	0.265927	+	0.905665i	−0.712950	+	0.701215i	$0.752641\pi$
$564$	3.77261	+	5.21420i	0.158856	+	0.219557i
$565$	27.8971	+	12.7402i	1.17364	+	0.535983i
$566$	−3.23888	−	10.0019i	−0.136140	−	0.420410i
$567$	3.36949	+	3.88860i	0.141505	+	0.163306i
$568$	−6.56835	+	8.98441i	−0.275602	+	0.376978i
$569$	−6.36323	+	4.08940i	−0.266761	+	0.171437i	−0.667183	−	0.744894i	$-0.732500\pi$
$569$	−6.36323	+	4.08940i	−0.266761	+	0.171437i	0.400422	+	0.916331i	$0.368864\pi$
$570$	0.483355	+	17.5264i	0.0202455	+	0.734101i
$571$	−15.7363	+	24.4861i	−0.658543	+	1.02471i	0.337960	+	0.941160i	$0.390263\pi$
$571$	−15.7363	+	24.4861i	−0.658543	+	1.02471i	−0.996503	+	0.0835525i	$0.973373\pi$
$572$	2.55477	−	6.52370i	0.106820	−	0.272770i
$573$	−4.65107	+	15.8401i	−0.194301	+	0.661729i
$574$	−14.1734	−	82.3847i	−0.591586	−	3.43867i
$575$	−16.5456	+	2.03071i	−0.689999	+	0.0846866i
$576$	4.17173	−	6.82617i	0.173822	−	0.284424i
$577$	4.96694	+	1.45842i	0.206776	+	0.0607150i	0.383480	−	0.923549i	$-0.374725\pi$
$577$	4.96694	+	1.45842i	0.206776	+	0.0607150i	−0.176704	+	0.984264i	$0.556544\pi$
$578$	−37.6863	−	22.7765i	−1.56754	−	0.947376i
$579$	−6.17875	+	9.61432i	−0.256780	+	0.399557i
$580$	3.36829	+	16.7937i	0.139861	+	0.697319i
$581$	−20.7131	−	32.2302i	−0.859324	−	1.33713i
$582$	−10.7127	−	15.7001i	−0.444055	−	0.650790i
$583$	−5.26026	−	6.07067i	−0.217858	−	0.251421i
$584$	5.16463	−	3.95816i	0.213714	−	0.163790i
$585$	1.66806	−	3.65255i	0.0689659	−	0.151014i
$586$	−24.8766	+	12.2005i	−1.02764	+	0.503998i
$587$	6.32925	+	21.5555i	0.261236	+	0.889689i	0.980759	+	0.195220i	$0.0625422\pi$
$587$	6.32925	+	21.5555i	0.261236	+	0.889689i	−0.719523	+	0.694468i	$0.755640\pi$
$588$	−38.7998	−	3.40979i	−1.60008	−	0.140618i
$589$	13.5328	−	1.94573i	0.557611	−	0.0801724i
$590$	7.90664	−	9.64994i	0.325511	−	0.397282i
$591$	9.56420	+	20.9427i	0.393419	+	0.861466i
$592$	−18.1543	−	5.97813i	−0.746136	−	0.245700i
$593$	−0.379025	+	2.63618i	−0.0155647	+	0.108255i	−0.996123	−	0.0879745i	$-0.971961\pi$
$593$	−0.379025	+	2.63618i	−0.0155647	+	0.108255i	0.980558	+	0.196229i	$0.0628697\pi$
$594$	1.40149	−	3.30720i	0.0575037	−	0.135696i
$595$	78.5462	+	68.0607i	3.22008	+	2.79022i
$596$	−1.31936	−	23.9018i	−0.0540431	−	0.979055i
$597$			5.22225i			0.213733i
$598$	−1.26739	+	9.26816i	−0.0518276	+	0.379003i
$599$	24.7861			1.01273			0.506366	−	0.862318i	$-0.330988\pi$
$599$	24.7861			1.01273			0.506366	+	0.862318i	$0.330988\pi$
$600$	9.58234	−	2.19835i	0.391198	−	0.0897473i
$601$	9.54701	−	11.0178i	0.389431	−	0.449427i	−0.526853	−	0.849956i	$-0.676628\pi$
$601$	9.54701	−	11.0178i	0.389431	−	0.449427i	0.916284	+	0.400529i	$0.131174\pi$
$602$	79.6722	+	33.7626i	3.24720	+	1.37606i
$603$	9.02113	+	1.29704i	0.367369	+	0.0528196i
$604$	−2.97699	+	3.84489i	−0.121132	+	0.156447i
$605$	−12.0472	+	5.50178i	−0.489789	+	0.223679i
$606$	8.71684	−	10.6388i	0.354097	−	0.432171i
$607$	1.04648	+	7.27845i	0.0424754	+	0.295423i	0.999976	+	0.00699035i	$0.00222512\pi$
$607$	1.04648	+	7.27845i	0.0424754	+	0.295423i	−0.957500	+	0.288433i	$0.906866\pi$
$608$	9.89870	+	21.9617i	0.401445	+	0.890664i
$609$	−14.5226	+	4.26422i	−0.588485	+	0.172795i
$610$	3.12897	+	6.37993i	0.126688	+	0.258316i
$611$	4.03720	+	1.84373i	0.163328	+	0.0745893i
$612$	−6.45128	−	12.2853i	−0.260778	−	0.496604i
$613$	12.7486	−	11.0467i	0.514911	−	0.446173i	−0.358235	−	0.933631i	$-0.616621\pi$
$613$	12.7486	−	11.0467i	0.514911	−	0.446173i	0.873146	+	0.487458i	$0.162076\pi$
$614$	−11.9867	−	17.5672i	−0.483742	−	0.708953i
$615$	−28.1364	+	18.0822i	−1.13457	+	0.729144i
$616$	13.3083	+	34.4843i	0.536209	+	1.38941i
$617$	−13.0904	−	8.41268i	−0.526999	−	0.338682i	0.249936	−	0.968262i	$-0.419590\pi$
$617$	−13.0904	−	8.41268i	−0.526999	−	0.338682i	−0.776935	+	0.629581i	$0.783227\pi$
$618$	3.14959	−	5.21136i	0.126695	−	0.209631i
$619$	9.16555	−	31.2150i	0.368395	−	1.25464i	−0.541818	−	0.840496i	$-0.682264\pi$
$619$	9.16555	−	31.2150i	0.368395	−	1.25464i	0.910213	−	0.414141i	$-0.135918\pi$
$620$	−6.24731	−	17.6193i	−0.250898	−	0.707607i
$621$	−0.780515	+	4.73189i	−0.0313210	+	0.189884i
$622$	4.65574	+	27.0621i	0.186678	+	1.08509i
$623$	−12.2546	−	3.59827i	−0.490970	−	0.144162i
$624$	0.179341	−	5.51402i	0.00717940	−	0.220737i
$625$	−25.4880	−	16.3801i	−1.01952	−	0.655206i
$626$	24.0448	−	0.663121i	0.961022	−	0.0265037i
$627$	5.84748	+	9.09886i	0.233526	+	0.363374i
$628$	−7.05691	+	6.83112i	−0.281601	+	0.272591i
$629$	−25.0548	+	21.7101i	−0.999002	+	0.865640i
$630$	6.52653	+	20.1543i	0.260023	+	0.802968i
$631$	3.76163	−	8.23682i	0.149748	−	0.327902i	−0.819861	−	0.572563i	$-0.805949\pi$
$631$	3.76163	−	8.23682i	0.149748	−	0.327902i	0.969609	+	0.244660i	$0.0786765\pi$
$632$	5.16900	+	5.05333i	0.205612	+	0.201011i
$633$	−21.0653	+	6.18532i	−0.837270	+	0.245845i
$634$	−2.55539	+	9.68279i	−0.101488	+	0.384553i
$635$	51.4574	−	7.39845i	2.04202	−	0.293599i
$636$	−5.50155	−	3.12123i	−0.218151	−	0.123765i
$637$	−24.4328	+	11.1581i	−0.968065	+	0.442100i
$638$	7.13678	+	7.79147i	0.282548	+	0.308467i
$639$	−0.559984	+	3.89478i	−0.0221526	+	0.154075i
$640$	26.7807	−	19.1757i	1.05860	−	0.757985i
$641$	21.7830	−	25.1389i	0.860376	−	0.992927i	−0.139620	−	0.990205i	$-0.544588\pi$
$641$	21.7830	−	25.1389i	0.860376	−	0.992927i	0.999996	−	0.00272173i	$-0.000866354\pi$
$642$	2.37941	−	20.5581i	0.0939077	−	0.811362i
$643$			19.8397i			0.782401i	0.920305	+	0.391201i	$0.127940\pi$
$643$			19.8397i			0.782401i	−0.920305	+	0.391201i	$0.872060\pi$
$644$	−28.0969	−	40.5739i	−1.10717	−	1.59883i
$645$		−	34.6204i		−	1.36318i
$646$	41.5065	+	4.80399i	1.63305	+	0.189010i
$647$	4.14787	−	4.78690i	0.163070	−	0.188193i	−0.668334	−	0.743861i	$-0.732992\pi$
$647$	4.14787	−	4.78690i	0.163070	−	0.188193i	0.831404	+	0.555669i	$0.187538\pi$
$648$	0.169843	−	2.82332i	0.00667207	−	0.110911i
$649$	1.09523	−	7.61752i	0.0429917	−	0.299014i
$650$	4.99950	−	4.57940i	0.196096	−	0.179619i
$651$	15.0267	−	6.86244i	0.588941	−	0.268960i
$652$	0.945110	−	1.66587i	0.0370134	−	0.0652407i
$653$	−25.1800	+	3.62034i	−0.985370	+	0.141675i	−0.616118	−	0.787654i	$-0.711295\pi$
$653$	−25.1800	+	3.62034i	−0.985370	+	0.141675i	−0.369253	+	0.929329i	$0.620386\pi$
$654$	0.257666	+	0.0680008i	0.0100755	+	0.00265904i
$655$	42.0893	−	12.3585i	1.64456	−	0.482888i
$656$	−26.0874	+	37.8297i	−1.01854	+	1.47700i
$657$	0.955686	−	2.09266i	0.0372848	−	0.0816424i
$658$	−22.2768	+	7.21385i	−0.868441	+	0.281225i
$659$	11.0289	−	9.55656i	0.429623	−	0.372271i	−0.413039	−	0.910713i	$-0.635533\pi$
$659$	11.0289	−	9.55656i	0.429623	−	0.372271i	0.842662	+	0.538443i	$0.180987\pi$
$660$	10.6258	−	10.2859i	0.413610	−	0.400376i
$661$	19.3917	+	30.1741i	0.754251	+	1.17364i	0.979912	+	0.199432i	$0.0639096\pi$
$661$	19.3917	+	30.1741i	0.754251	+	1.17364i	−0.225661	+	0.974206i	$0.572454\pi$
$662$	0.948633	+	34.3974i	0.0368697	+	1.33689i
$663$	−8.05015	−	5.17352i	−0.312642	−	0.200923i
$664$	−4.24356	+	20.6284i	−0.164682	+	0.800537i
$665$	−61.2070	−	17.9720i	−2.37350	−	0.696924i
$666$	−6.65972	+	1.14573i	−0.258059	+	0.0443962i
$667$	−11.7078	−	7.87084i	−0.453327	−	0.304760i
$668$	9.70662	−	3.44170i	0.375560	−	0.133163i
$669$	6.76639	−	23.0442i	0.261604	−	0.890940i
$670$	32.1146	+	19.4091i	1.24070	+	0.749841i
$671$	3.68764	+	2.36990i	0.142360	+	0.0914890i
$672$	18.9518	+	22.0912i	0.731081	+	0.852185i
$673$	−0.204334	+	0.131317i	−0.00787648	+	0.00506191i	−0.544573	−	0.838713i	$-0.683308\pi$
$673$	−0.204334	+	0.131317i	−0.00787648	+	0.00506191i	0.536697	+	0.843775i	$0.319672\pi$
$674$	−28.5397	+	19.4736i	−1.09931	+	0.750093i
$675$	2.62690	−	2.27622i	0.101109	−	0.0876117i
$676$	10.3191	+	19.6508i	0.396887	+	0.755800i
$677$	−29.3762	−	13.4157i	−1.12902	−	0.515606i	−0.238768	−	0.971077i	$-0.576744\pi$
$677$	−29.3762	−	13.4157i	−1.12902	−	0.515606i	−0.890251	+	0.455471i	$0.849471\pi$
$678$	13.3755	−	6.55991i	0.513685	−	0.251932i
$679$	66.3513	−	19.4825i	2.54633	−	0.747669i
$680$	−4.72025	−	56.9363i	−0.181013	−	2.18341i
$681$	2.92850	+	20.3682i	0.112220	+	0.780510i
$682$	−8.92019	−	7.30873i	−0.341572	−	0.279866i
$683$	−27.3749	+	12.5017i	−1.04747	+	0.478364i	−0.863385	−	0.504546i	$-0.831660\pi$
$683$	−27.3749	+	12.5017i	−1.04747	+	0.478364i	−0.184087	+	0.982910i	$0.558933\pi$
$684$	6.73425	+	5.21414i	0.257491	+	0.199368i
$685$	−42.8156	−	6.15595i	−1.63590	−	0.235207i
$686$	35.4181	−	83.5789i	1.35227	−	3.19106i
$687$	14.7779	−	17.0546i	0.563811	−	0.650673i
$688$	−18.3428	−	43.8874i	−0.699313	−	1.67319i
$689$	−4.36202			−0.166180
$690$	−10.5605	+	16.6843i	−0.402032	+	0.635161i
$691$			25.5785i			0.973053i	0.873666	+	0.486527i	$0.161736\pi$
$691$			25.5785i			0.973053i	−0.873666	+	0.486527i	$0.838264\pi$
$692$	0.556273	+	10.0775i	0.0211463	+	0.383091i
$693$	9.87649	+	8.55802i	0.375177	+	0.325092i
$694$	−10.4820	−	4.44196i	−0.397892	−	0.168614i
$695$	1.77790	−	12.3656i	0.0674395	−	0.469052i
$696$	7.34709	+	3.90455i	0.278491	+	0.148002i
$697$	33.1109	+	72.5028i	1.25417	+	2.74624i
$698$	4.86418	+	3.98545i	0.184112	+	0.150851i
$699$	17.4433	−	2.50796i	0.659765	−	0.0948598i
$700$	−3.13140	+	35.6320i	−0.118356	+	1.34676i
$701$	−8.35296	−	28.4476i	−0.315487	−	1.07445i	−0.952738	−	0.303794i	$-0.901747\pi$
$701$	−8.35296	−	28.4476i	−0.315487	−	1.07445i	0.637251	−	0.770656i	$-0.280071\pi$
$702$	−0.858885	−	1.75125i	−0.0324165	−	0.0660968i
$703$	8.45294	−	18.5094i	0.318809	−	0.698093i
$704$	8.02036	−	18.6689i	0.302279	−	0.703612i
$705$	6.13506	+	7.08023i	0.231060	+	0.266657i
$706$	3.33512	−	2.27566i	0.125519	−	0.0856456i
$707$	27.0540	+	42.0969i	1.01747	+	1.58322i
$708$	−1.19173	−	5.94174i	−0.0447880	−	0.223304i
$709$	26.0403	−	40.5195i	0.977964	−	1.52174i	0.130118	−	0.991499i	$-0.458464\pi$
$709$	26.0403	−	40.5195i	0.977964	−	1.52174i	0.847846	−	0.530243i	$-0.177899\pi$
$710$	−8.37969	+	13.8652i	−0.314484	+	0.520350i
$711$	2.45222	+	0.720037i	0.0919655	+	0.0270035i
$712$	3.43422	+	6.12354i	0.128703	+	0.229489i
$713$	13.8707	+	6.68447i	0.519460	+	0.250336i
$714$	49.7549	−	8.55979i	1.86203	−	0.320342i
$715$	2.87327	−	9.78545i	0.107454	−	0.365955i
$716$	−5.09642	−	1.99582i	−0.190462	−	0.0745875i
$717$	8.14812	−	12.6787i	0.304297	−	0.473495i
$718$	−40.8580	+	1.12681i	−1.52481	+	0.0420521i
$719$	−3.32775	+	2.13861i	−0.124104	+	0.0797568i	−0.601220	−	0.799083i	$-0.705318\pi$
$719$	−3.32775	+	2.13861i	−0.124104	+	0.0797568i	0.477116	+	0.878840i	$0.341682\pi$
$720$	5.17945	−	10.4301i	0.193027	−	0.388708i
$721$	14.5080	+	16.7432i	0.540307	+	0.623548i
$722$	1.16466	−	0.377149i	0.0433441	−	0.0140360i
$723$	−14.9007	−	6.80491i	−0.554162	−	0.253077i
$724$	14.3791	+	19.8736i	0.534395	+	0.738597i
$725$	2.88064	+	9.81056i	0.106984	+	0.364355i
$726$	−1.64165	+	6.22047i	−0.0609273	+	0.230863i
$727$	4.78992	+	33.3147i	0.177648	+	1.23557i	0.862185	+	0.506594i	$0.169096\pi$
$727$	4.78992	+	33.3147i	0.177648	+	1.23557i	−0.684536	+	0.728979i	$0.739995\pi$
$728$	18.8849	+	6.80132i	0.699923	+	0.252074i
$729$	−0.415415	−	0.909632i	−0.0153857	−	0.0336901i
$730$	6.98472	−	6.39781i	0.258516	−	0.236794i
$731$	−81.6651	−	11.7417i	−3.02049	−	0.434281i
$732$	3.36052	+	0.788460i	0.124208	+	0.0291423i
$733$	−15.9163	−	13.7916i	−0.587883	−	0.509403i	0.309358	−	0.950946i	$-0.399886\pi$
$733$	−15.9163	−	13.7916i	−0.587883	−	0.509403i	−0.897240	+	0.441542i	$0.854431\pi$
$734$	−5.70052	+	49.2524i	−0.210410	+	1.81794i
$735$	−56.6974			−2.09131
$736$	−4.54748	+	26.7455i	−0.167622	+	0.985851i
$737$	23.1480			0.852666
$738$	−1.86793	+	16.1389i	−0.0687596	+	0.594083i
$739$	33.6546	+	29.1619i	1.23800	+	1.07274i	0.994703	+	0.102786i	$0.0327758\pi$
$739$	33.6546	+	29.1619i	1.23800	+	1.07274i	0.243301	+	0.969951i	$0.421770\pi$
$740$	−27.0870	−	6.35527i	−0.995737	−	0.233624i
$741$	5.81361	+	0.835870i	0.213568	+	0.0307065i
$742$	16.9703	−	15.5443i	0.622998	−	0.570649i
$743$	16.7505	+	36.6786i	0.614518	+	1.34561i	0.919441	+	0.393229i	$0.128642\pi$
$743$	16.7505	+	36.6786i	0.614518	+	1.34561i	−0.304923	+	0.952377i	$0.598631\pi$
$744$	−8.54365	−	3.07696i	−0.313226	−	0.112807i
$745$	−4.95911	−	34.4913i	−0.181688	−	1.26367i
$746$	13.0696	−	49.5229i	0.478513	−	1.81316i
$747$	2.09777	+	7.14434i	0.0767533	+	0.261398i
$748$	−20.6592	−	28.5534i	−0.755374	−	1.04402i
$749$	68.4917	+	31.2791i	2.50263	+	1.14291i
$750$	−5.96996	+	1.93324i	−0.217992	+	0.0705918i
$751$	6.56295	+	7.57405i	0.239485	+	0.276381i	0.862751	−	0.505630i	$-0.168740\pi$
$751$	6.56295	+	7.57405i	0.239485	+	0.276381i	−0.623265	+	0.782010i	$0.714194\pi$
$752$	11.5285	+	5.72490i	0.420403	+	0.208766i
$753$	−4.85809	+	3.12210i	−0.177039	+	0.113776i
$754$	5.73554	−	0.158178i	0.208876	−	0.00576052i
$755$	−3.82690	+	5.95478i	−0.139275	+	0.216717i
$756$	9.58215	+	3.75250i	0.348499	+	0.136477i
$757$	−10.7893	+	36.7449i	−0.392143	+	1.33552i	0.492932	+	0.870068i	$0.335925\pi$
$757$	−10.7893	+	36.7449i	−0.392143	+	1.33552i	−0.885075	+	0.465449i	$0.845893\pi$
$758$	−51.6289	+	8.88218i	−1.87524	+	0.322615i
$759$	−0.251831	+	12.1781i	−0.00914088	+	0.442038i
$760$	17.1526	+	30.5847i	0.622190	+	1.10942i
$761$	−24.4923	−	7.19158i	−0.887844	−	0.260694i	−0.194156	−	0.980971i	$-0.562197\pi$
$761$	−24.4923	−	7.19158i	−0.887844	−	0.260694i	−0.693687	+	0.720276i	$0.744015\pi$
$762$	13.0620	−	21.6125i	0.473185	−	0.782938i
$763$	−0.524187	+	0.815651i	−0.0189769	+	0.0295286i
$764$	6.49301	+	32.3729i	0.234909	+	1.17121i
$765$	−10.9205	−	16.9926i	−0.394830	−	0.614367i
$766$	27.0753	−	18.4744i	0.978271	−	0.667507i
$767$	−2.73675	−	3.15837i	−0.0988182	−	0.114042i
$768$	1.03969	−	15.9662i	0.0375165	−	0.576130i
$769$	7.22408	−	15.8185i	0.260507	−	0.570430i	−0.733507	−	0.679682i	$-0.762118\pi$
$769$	7.22408	−	15.8185i	0.260507	−	0.570430i	0.994014	+	0.109251i	$0.0348453\pi$
$770$	23.6927	+	48.3090i	0.853825	+	1.74094i
$771$	−2.41464	−	8.22350i	−0.0869611	−	0.296162i
$772$	−2.00101	+	22.7694i	−0.0720179	+	0.819487i
$773$	43.8931	−	6.31088i	1.57873	−	0.226987i	0.703498	−	0.710697i	$-0.251620\pi$
$773$	43.8931	−	6.31088i	1.57873	−	0.226987i	0.875228	+	0.483711i	$0.160711\pi$
$774$	−13.0084	−	10.6584i	−0.467578	−	0.383108i
$775$	−4.63584	−	10.1511i	−0.166524	−	0.364637i
$776$	−33.5676	−	17.8392i	−1.20501	−	0.640391i
$777$	3.49897	−	24.3359i	0.125525	−	0.873044i
$778$	−2.25919	−	0.957374i	−0.0809958	−	0.0343235i
$779$	−36.9725	−	32.0368i	−1.32468	−	1.14784i
$780$	−0.442621	−	8.01862i	−0.0158484	−	0.287113i
$781$			9.99389i			0.357610i
$782$	35.7745	+	30.5694i	1.27929	+	1.09316i
$783$	2.94162			0.105125
$784$	−71.8737	+	30.0398i	−2.56692	+	1.07285i
$785$	−9.36256	+	10.8050i	−0.334164	+	0.385646i
$786$	8.31415	−	19.6195i	0.296556	−	0.699805i
$787$	−39.4912	−	5.67798i	−1.40771	−	0.202398i	−0.603794	−	0.797141i	$-0.706345\pi$
$787$	−39.4912	−	5.67798i	−1.40771	−	0.202398i	−0.803916	+	0.594742i	$0.797254\pi$
$788$	36.4087	+	28.1902i	1.29700	+	1.00423i
$789$	−9.90909	+	4.52533i	−0.352773	+	0.161106i
$790$	8.13944	+	6.66902i	0.289588	+	0.237273i
$791$	7.71376	+	53.6504i	0.274270	+	1.90759i
$792$	−0.593530	−	7.15924i	−0.0210902	−	0.254392i
$793$	2.28398	−	0.670636i	0.0811064	−	0.0238150i
$794$	−3.67499	+	1.80236i	−0.130421	+	0.0639635i
$795$	−8.37544	−	3.82494i	−0.297046	−	0.135657i
$796$	4.85584	+	9.24708i	0.172111	+	0.327754i
$797$	−4.90169	+	4.24734i	−0.173627	+	0.150449i	−0.737339	−	0.675523i	$-0.763918\pi$
$797$	−4.90169	+	4.24734i	−0.173627	+	0.150449i	0.563712	+	0.825971i	$0.309373\pi$
$798$	−25.5963	+	17.4652i	−0.906099	+	0.618261i
$799$	18.7821	−	12.0705i	0.664462	−	0.427024i
$800$	14.9234	−	12.8027i	0.527623	−	0.452642i
$801$	2.08818	+	1.34199i	0.0737823	+	0.0474170i
$802$	4.45715	+	2.69377i	0.157388	+	0.0951204i
$803$	1.64619	−	5.60639i	0.0580926	−	0.197845i
$804$	17.1798	−	6.09149i	0.605885	−	0.214830i
$805$	−45.9132	−	55.2548i	−1.61823	−	1.94748i
$806$	−6.17163	+	1.06176i	−0.217387	+	0.0373990i
$807$	−11.0441	−	3.24283i	−0.388770	−	0.114153i
$808$	5.54265	−	26.9434i	0.194990	−	0.947865i
$809$	−18.7058	−	12.0215i	−0.657659	−	0.422652i	0.168799	−	0.985651i	$-0.446011\pi$
$809$	−18.7058	−	12.0215i	−0.657659	−	0.422652i	−0.826458	+	0.562999i	$0.809648\pi$
$810$	−0.113505	−	4.11569i	−0.00398816	−	0.144611i
$811$	7.37302	+	11.4726i	0.258902	+	0.402859i	0.946233	−	0.323485i	$-0.104854\pi$
$811$	7.37302	+	11.4726i	0.258902	+	0.402859i	−0.687332	+	0.726344i	$0.741218\pi$
$812$	−21.7502	+	21.0543i	−0.763284	+	0.738862i
$813$	3.10375	−	2.68941i	0.108853	−	0.0943218i
$814$	−16.3284	+	5.28759i	−0.572311	+	0.185330i
$815$	1.15819	−	2.53609i	0.0405698	−	0.0888354i
$816$	−22.8467	−	15.7551i	−0.799793	−	0.551537i
$817$	48.5884	−	14.2669i	1.69989	−	0.499134i
$818$	−12.5219	−	3.30466i	−0.437817	−	0.115545i
$819$	7.02441	−	1.00996i	0.245453	−	0.0352908i
$820$	−33.0079	+	58.1805i	−1.15269	+	2.03175i
$821$	−10.5327	+	4.81012i	−0.367594	+	0.167874i	−0.590644	−	0.806933i	$-0.701126\pi$
$821$	−10.5327	+	4.81012i	−0.367594	+	0.167874i	0.223050	+	0.974807i	$0.428399\pi$
$822$	−15.4944	+	14.1925i	−0.540431	+	0.495020i
$823$	−1.86760	+	12.9894i	−0.0651004	+	0.452783i	0.931033	+	0.364934i	$0.118908\pi$
$823$	−1.86760	+	12.9894i	−0.0651004	+	0.452783i	−0.996134	+	0.0878492i	$0.972001\pi$
$824$	0.731294	−	12.1564i	0.0254758	−	0.423488i
$825$	5.78127	−	6.67194i	0.201278	−	0.232287i
$826$	21.9023	+	2.53498i	0.762077	+	0.0882034i
$827$			6.26926i			0.218004i	0.994042	+	0.109002i	$0.0347654\pi$
$827$			6.26926i			0.218004i	−0.994042	+	0.109002i	$0.965235\pi$
$828$	3.01782	+	9.10455i	0.104877	+	0.316405i
$829$			23.2097i			0.806108i	0.915176	+	0.403054i	$0.132051\pi$
$829$			23.2097i			0.806108i	−0.915176	+	0.403054i	$0.867949\pi$
$830$	−3.52472	+	30.4536i	−0.122345	+	1.05706i
$831$	−8.02464	+	9.26093i	−0.278372	+	0.321258i
$832$	−4.80957	−	9.93047i	−0.166742	−	0.344277i
$833$	−19.2292	+	133.742i	−0.666251	+	4.63388i
$834$	−4.09893	−	4.47494i	−0.141934	−	0.154955i
$835$	13.6368	−	6.22771i	0.471920	−	0.215519i
$836$	18.8146	+	10.6742i	0.650718	+	0.369175i
$837$	−3.17788	+	0.456911i	−0.109844	+	0.0157931i
$838$	−5.71262	+	21.6460i	−0.197339	+	0.747750i
$839$	−31.5297	+	9.25795i	−1.08853	+	0.319620i	−0.776285	−	0.630383i	$-0.782898\pi$
$839$	−31.5297	+	9.25795i	−1.08853	+	0.319620i	−0.312241	+	0.950003i	$0.601080\pi$
$840$	30.2968	+	29.6188i	1.04534	+	1.02195i
$841$	8.45239	−	18.5081i	0.291462	−	0.638212i
$842$	−2.30820	−	7.12787i	−0.0795459	−	0.245643i
$843$	−4.07073	+	3.52731i	−0.140204	+	0.121487i
$844$	−31.5491	+	30.5397i	−1.08597	+	1.05122i
$845$	17.4677	+	27.1802i	0.600906	+	0.935028i
$846$	4.54912	−	0.125458i	0.156402	−	0.00431335i
$847$	−19.6911	−	12.6547i	−0.676596	−	0.434822i
$848$	−12.6439	−	0.411237i	−0.434192	−	0.0141219i
$849$	−7.13283	−	2.09439i	−0.244798	−	0.0718792i
$850$	−5.78246	−	33.6113i	−0.198337	−	1.15286i
$851$	19.5302	−	11.9881i	0.669485	−	0.410947i
$852$	2.62994	+	7.41720i	0.0901001	+	0.254109i
$853$	−5.22145	+	17.7826i	−0.178779	+	0.608865i	0.820527	+	0.571608i	$0.193680\pi$
$853$	−5.22145	+	17.7826i	−0.178779	+	0.608865i	−0.999306	+	0.0372570i	$0.988138\pi$
$854$	−6.49588	+	10.7482i	−0.222284	+	0.367795i
$855$	10.4297	+	6.70274i	0.356687	+	0.229229i
$856$	−14.9024	−	38.6148i	−0.509354	−	1.31983i
$857$	17.0166	−	10.9359i	0.581275	−	0.373563i	−0.216713	−	0.976235i	$-0.569534\pi$
$857$	17.0166	−	10.9359i	0.581275	−	0.373563i	0.797989	+	0.602672i	$0.205897\pi$
$858$	−2.79225	−	4.09220i	−0.0953257	−	0.139706i
$859$	6.39720	−	5.54321i	0.218270	−	0.189132i	−0.538862	−	0.842394i	$-0.681146\pi$
$859$	6.39720	−	5.54321i	0.218270	−	0.189132i	0.757132	+	0.653262i	$0.226600\pi$
$860$	−32.1913	−	61.3026i	−1.09772	−	2.09040i
$861$	−53.7689	−	24.5554i	−1.83244	−	0.836847i
$862$	9.07788	+	18.5097i	0.309194	+	0.630442i
$863$	−17.7093	+	5.19991i	−0.602830	+	0.177007i	−0.568885	−	0.822417i	$-0.692625\pi$
$863$	−17.7093	+	5.19991i	−0.602830	+	0.177007i	−0.0339448	+	0.999424i	$0.510807\pi$
$864$	−2.32449	−	5.15721i	−0.0790806	−	0.175452i
$865$	2.09088	+	14.5424i	0.0710919	+	0.494455i
$866$	−22.4858	+	27.4435i	−0.764098	+	0.932570i
$867$	−28.3232	+	12.9348i	−0.961906	+	0.439288i
$868$	20.2269	−	26.1237i	0.686544	−	0.886697i
$869$	6.42516	+	0.923798i	0.217959	+	0.0313377i
$870$	11.1514	+	4.72563i	0.378069	+	0.160214i
$871$	8.23172	−	9.49991i	0.278921	−	0.321892i
$872$	0.519480	−	0.119178i	0.0175918	−	0.00403586i
$873$	−13.4398			−0.454867
$874$	−27.7677	−	7.94577i	−0.939257	−	0.268770i
$875$		−	22.8311i		−	0.771831i
$876$	−0.253592	−	4.59412i	−0.00856807	−	0.155221i
$877$	5.01047	+	4.34160i	0.169192	+	0.146605i	0.735341	−	0.677697i	$-0.237022\pi$
$877$	5.01047	+	4.34160i	0.169192	+	0.146605i	−0.566149	+	0.824303i	$0.691567\pi$
$878$	3.70139	−	8.73447i	0.124916	−	0.294774i
$879$	−2.78824	+	19.3926i	−0.0940450	+	0.654097i
$880$	9.25108	−	28.0935i	0.311854	−	0.947033i
$881$	−22.8995	−	50.1429i	−0.771504	−	1.68936i	−0.723314	−	0.690520i	$-0.757382\pi$
$881$	−22.8995	−	50.1429i	−0.771504	−	1.68936i	−0.0481902	−	0.998838i	$-0.515345\pi$
$882$	−17.4551	+	21.3037i	−0.587744	+	0.717332i
$883$	6.19835	−	0.891188i	0.208591	−	0.0299909i	−0.0372270	−	0.999307i	$-0.511852\pi$
$883$	6.19835	−	0.891188i	0.208591	−	0.0299909i	0.245818	+	0.969316i	$0.420943\pi$
$884$	−19.0650	−	1.67546i	−0.641225	−	0.0563519i
$885$	−2.48529	−	8.46413i	−0.0835422	−	0.284519i
$886$	14.2835	−	7.00522i	0.479865	−	0.235345i
$887$	−2.62118	+	5.73958i	−0.0880105	+	0.192716i	−0.948519	−	0.316720i	$-0.897419\pi$
$887$	−2.62118	+	5.73958i	−0.0880105	+	0.192716i	0.860509	+	0.509436i	$0.170146\pi$
$888$	−10.7271	+	8.22120i	−0.359977	+	0.275885i
$889$	60.1676	+	69.4371i	2.01796	+	2.32885i
$890$	5.76024	+	8.44198i	0.193084	+	0.282976i
$891$	−1.37315	−	2.13666i	−0.0460022	−	0.0715809i
$892$	−9.44604	−	47.0962i	−0.316277	−	1.57690i
$893$	−7.40862	+	11.5280i	−0.247920	+	0.385771i
$894$	−14.4866	−	8.75530i	−0.484506	−	0.292821i
$895$	−7.64455	−	2.24464i	−0.255529	−	0.0750301i
$896$	54.0993	+	21.4949i	1.80733	+	0.718095i
$897$	4.90834	+	4.43405i	0.163885	+	0.148049i
$898$	2.50667	+	14.5704i	0.0836488	+	0.486220i
$899$	2.66076	−	9.06171i	0.0887412	−	0.302225i
$900$	2.53495	−	6.47310i	0.0844985	−	0.215770i
$901$	−11.8631	+	18.4593i	−0.395217	+	0.614969i
$902$	1.13758	+	41.2485i	0.0378772	+	1.37343i
$903$	51.4733	−	33.0799i	1.71293	−	1.10083i
$904$	17.5845	−	24.0527i	0.584853	−	0.799982i
$905$	23.3834	+	26.9859i	0.777292	+	0.897042i
$906$	1.05930	+	3.27120i	0.0351930	+	0.108678i
$907$	8.64528	+	3.94817i	0.287062	+	0.131097i	0.553742	−	0.832688i	$-0.313199\pi$
$907$	8.64528	+	3.94817i	0.287062	+	0.131097i	−0.266680	+	0.963785i	$0.585927\pi$
$908$	24.1246	+	33.3430i	0.800602	+	1.10653i
$909$	−2.73996	−	9.33145i	−0.0908788	−	0.309505i
$910$	28.2514	+	7.45585i	0.936525	+	0.247159i
$911$	1.51017	+	10.5035i	0.0500341	+	0.347995i	0.999425	+	0.0338988i	$0.0107924\pi$
$911$	1.51017	+	10.5035i	0.0500341	+	0.347995i	−0.949391	+	0.314096i	$0.898299\pi$
$912$	16.7727	+	2.97097i	0.555399	+	0.0983786i
$913$	7.85619	+	17.2026i	0.260002	+	0.569325i
$914$	11.6846	+	12.7565i	0.386492	+	0.421947i
$915$	4.97349	+	0.715081i	0.164419	+	0.0236398i
$916$	10.3093	−	43.9397i	0.340630	−	1.45181i
$917$	58.5910	+	50.7694i	1.93484	+	1.67655i
$918$	−9.74686	−	1.12811i	−0.321694	−	0.0372331i
$919$	−59.5481			−1.96431			−0.982156	−	0.188070i	$-0.939777\pi$
$919$	−59.5481			−1.96431			−0.982156	+	0.188070i	$0.939777\pi$
$920$	−3.18588	+	39.3626i	−0.105035	+	1.29775i
$921$	−15.0380			−0.495520
$922$	11.6353	+	1.34667i	0.383187	+	0.0443504i
$923$	4.10149	+	3.55396i	0.135002	+	0.116980i
$924$	25.4459	+	5.97024i	0.837110	+	0.196406i
$925$	−16.4398	−	2.36369i	−0.540537	−	0.0777175i
$926$	7.37452	+	8.05103i	0.242342	+	0.264573i
$927$	−1.78865	−	3.91660i	−0.0587471	−	0.128638i
$928$	16.6401	+	0.0822286i	0.546239	+	0.00269928i
$929$	3.38480	+	23.5418i	0.111052	+	0.772382i	0.966900	+	0.255155i	$0.0821265\pi$
$929$	3.38480	+	23.5418i	0.111052	+	0.772382i	−0.855848	+	0.517227i	$0.826964\pi$
$930$	−12.7811	−	3.37307i	−0.419109	−	0.110607i
$931$	−23.3646	−	79.5726i	−0.765745	−	2.60789i
$932$	28.5549	−	20.6602i	0.935347	−	0.676749i
$933$	17.6623	+	8.06608i	0.578236	+	0.264072i
$934$	−13.8481	−	42.7640i	−0.453125	−	1.39928i
$935$	−33.5962	−	38.7721i	−1.09871	−	1.26798i
$936$	−3.14921	−	2.30233i	−0.102935	−	0.0752541i
$937$	−33.8599	+	21.7604i	−1.10615	+	0.710882i	−0.960452	−	0.278447i	$-0.910180\pi$
$937$	−33.8599	+	21.7604i	−1.10615	+	0.710882i	−0.145702	+	0.989329i	$0.546544\pi$
$938$	1.82828	+	66.2932i	0.0596953	+	2.16455i
$939$	9.19559	−	14.3086i	0.300087	−	0.466944i
$940$	17.4469	+	6.83242i	0.569054	+	0.222849i
$941$	−13.8499	+	47.1685i	−0.451495	+	1.53765i	0.348304	+	0.937382i	$0.386758\pi$
$941$	−13.8499	+	47.1685i	−0.451495	+	1.53765i	−0.799799	+	0.600268i	$0.795061\pi$
$942$	1.17750	+	6.84438i	0.0383651	+	0.223002i
$943$	−14.4259	−	53.1731i	−0.469771	−	1.73155i
$944$	−7.63505	−	9.41297i	−0.248500	−	0.306366i
$945$	14.3731	+	4.22032i	0.467556	+	0.137287i
$946$	−36.5558	−	22.0932i	−1.18853	−	0.718313i
$947$	24.6425	−	38.3445i	0.800774	−	1.24603i	−0.164910	−	0.986309i	$-0.552733\pi$
$947$	24.6425	−	38.3445i	0.800774	−	1.24603i	0.965684	−	0.259720i	$-0.0836303\pi$
$948$	5.01168	−	1.00519i	0.162772	−	0.0326471i
$949$	−1.71546	−	2.66930i	−0.0556860	−	0.0866492i
$950$	11.7984	+	17.2913i	0.382791	+	0.561003i
$951$	4.63719	+	5.35160i	0.150371	+	0.173538i
$952$	80.1422	−	61.4208i	2.59742	−	1.99066i
$953$	7.78552	−	17.0479i	0.252198	−	0.552236i	−0.740613	−	0.671932i	$-0.765465\pi$
$953$	7.78552	−	17.0479i	0.252198	−	0.552236i	0.992811	+	0.119696i	$0.0381920\pi$
$954$	−4.01569	+	1.96946i	−0.130013	+	0.0637636i
$955$	13.5408	+	46.1159i	0.438171	+	1.49227i
$956$	2.63880	−	30.0267i	0.0853448	−	0.971133i
$957$	7.39525	−	1.06328i	0.239055	−	0.0343709i
$958$	−0.182240	+	0.222422i	−0.00588792	+	0.00718612i
$959$	−31.7578	−	69.5398i	−1.02551	−	2.24556i
$960$	−0.527025	−	23.2847i	−0.0170097	−	0.751511i
$961$	2.94482	−	20.4817i	0.0949942	−	0.660699i
$962$	−3.63657	+	8.58150i	−0.117248	+	0.276679i
$963$	−11.0595	−	9.58309i	−0.356387	−	0.308811i
$964$	−32.7122	+	1.80569i	−1.05359	+	0.0581572i
$965$			33.2724i			1.07108i
$966$	−34.8967	+	0.240638i	−1.12278	+	0.00774239i
$967$	7.14131			0.229649			0.114825	−	0.993386i	$-0.463369\pi$
$967$	7.14131			0.229649			0.114825	+	0.993386i	$0.463369\pi$
$968$	2.87714	+	12.5411i	0.0924747	+	0.403086i
$969$	19.3481	−	22.3290i	0.621552	−	0.717309i
$970$	−50.9490	−	21.5906i	−1.63587	−	0.693232i
$971$	33.5001	+	4.81658i	1.07507	+	0.154572i	0.657035	−	0.753860i	$-0.271810\pi$
$971$	33.5001	+	4.81658i	1.07507	+	0.154572i	0.418034	+	0.908432i	$0.362719\pi$
$972$	−1.58139	−	1.22442i	−0.0507230	−	0.0392734i
$973$	20.0838	−	9.17195i	0.643856	−	0.294039i
$974$	−0.312035	+	0.380834i	−0.00999825	+	0.0122027i
$975$	−0.682265	−	4.74526i	−0.0218500	−	0.151970i
$976$	6.68363	−	1.72860i	0.213938	−	0.0553311i
$977$	−0.0613739	+	0.0180210i	−0.00196352	+	0.000576543i	−0.282714	−	0.959204i	$-0.591235\pi$
$977$	−0.0613739	+	0.0180210i	−0.00196352	+	0.000576543i	0.280751	+	0.959781i	$0.409417\pi$
$978$	−0.596353	−	1.21596i	−0.0190693	−	0.0388820i
$979$	5.73477	+	2.61898i	0.183284	+	0.0837031i
$980$	−100.394	+	52.7193i	−3.20698	+	1.68406i
$981$	0.142410	−	0.123399i	0.00454680	−	0.00393982i
$982$	30.0281	+	44.0080i	0.958235	+	1.40435i
$983$	27.1875	−	17.4723i	0.867146	−	0.557281i	−0.0297323	−	0.999558i	$-0.509465\pi$
$983$	27.1875	−	17.4723i	0.867146	−	0.557281i	0.896879	+	0.442277i	$0.145829\pi$
$984$	11.6990	+	30.3142i	0.372951	+	0.966382i
$985$	56.3879	+	36.2383i	1.79667	+	1.15465i
$986$	14.9292	−	24.7021i	0.475443	−	0.786674i
$987$	−4.66477	+	15.8867i	−0.148481	+	0.505680i
$988$	11.0714	−	3.92562i	0.352229	−	0.124891i
$989$	54.3761	+	17.1951i	1.72906	+	0.546773i
$990$	−1.77300	−	10.3058i	−0.0563498	−	0.327541i
$991$	14.5937	+	4.28509i	0.463584	+	0.136120i	0.505180	−	0.863014i	$-0.331426\pi$
$991$	14.5937	+	4.28509i	0.463584	+	0.136120i	−0.0415962	+	0.999135i	$0.513244\pi$
$992$	−17.9894	+	2.49581i	−0.571163	+	0.0792421i
$993$	20.4693	+	13.1548i	0.649573	+	0.417455i
$994$	−28.6214	+	0.789339i	−0.907816	+	0.0250363i
$995$	8.21976	+	12.7902i	0.260584	+	0.405477i
$996$	10.3576	+	10.7000i	0.328193	+	0.339041i
$997$	25.2909	−	21.9147i	0.800971	−	0.694045i	−0.154868	−	0.987935i	$-0.549495\pi$
$997$	25.2909	−	21.9147i	0.800971	−	0.694045i	0.955839	+	0.293890i	$0.0949499\pi$
$998$	−8.98256	−	27.7387i	−0.284338	−	0.878054i
$999$	−1.98498	+	4.34650i	−0.0628020	+	0.137517i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.bb.a.133.24	yes	480
8.5	even	2	inner	552.2.bb.a.133.16	✓	480
23.9	even	11	inner	552.2.bb.a.469.16	yes	480
184.101	even	22	inner	552.2.bb.a.469.24	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.bb.a.133.16	✓	480	8.5	even	2	inner
552.2.bb.a.133.24	yes	480	1.1	even	1	trivial
552.2.bb.a.469.16	yes	480	23.9	even	11	inner
552.2.bb.a.469.24	yes	480	184.101	even	22	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.bb (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.162597 - 1.40484i) q^{2} +(-0.755750 - 0.654861i) q^{3} +(-1.94712 - 0.456843i) q^{4} +(-2.88170 - 0.414326i) q^{5} +(-1.04285 + 0.955226i) q^{6} +(-2.13746 - 4.68038i) q^{7} +(-0.958385 + 2.66111i) q^{8} +(0.142315 + 0.989821i) q^{9} +(-1.05062 + 3.98095i) q^{10} +(0.715560 + 2.43697i) q^{11} +(1.17237 + 1.62035i) q^{12} +(1.25459 + 0.572954i) q^{13} +(-6.92271 + 2.24176i) q^{14} +(1.90652 + 2.20024i) q^{15} +(3.58259 + 1.77906i) q^{16} +(5.83669 - 3.75101i) q^{17} +(1.41368 - 0.0389872i) q^{18} +(-2.30229 + 3.58243i) q^{19} +(5.42175 + 2.12323i) q^{20} +(-1.44961 + 4.93693i) q^{21} +(3.53989 - 0.609000i) q^{22} +(-4.40270 + 1.90164i) q^{23} +(2.46695 - 1.38352i) q^{24} +(3.33508 + 0.979269i) q^{25} +(1.00890 - 1.66934i) q^{26} +(0.540641 - 0.841254i) q^{27} +(2.02370 + 10.0898i) q^{28} +(1.59036 + 2.47465i) q^{29} +(3.40097 - 2.32059i) q^{30} +(-2.10247 - 2.42638i) q^{31} +(3.08180 - 4.74368i) q^{32} +(1.05509 - 2.31033i) q^{33} +(-4.32053 - 8.80948i) q^{34} +(4.22032 + 14.3731i) q^{35} +(0.175088 - 1.99232i) q^{36} +(-4.72967 + 0.680024i) q^{37} +(4.65838 + 3.81683i) q^{38} +(-0.572954 - 1.25459i) q^{39} +(3.86435 - 7.27144i) q^{40} +(-1.63493 + 11.3712i) q^{41} +(6.69988 + 2.83920i) q^{42} +(-8.98707 - 7.78734i) q^{43} +(-0.279970 - 5.07199i) q^{44} -2.91134i q^{45} +(1.95563 + 6.49427i) q^{46} +3.21794 q^{47} +(-1.54250 - 3.69062i) q^{48} +(-12.7532 + 14.7180i) q^{49} +(1.91799 - 4.52602i) q^{50} +(-6.86746 - 0.987392i) q^{51} +(-2.18110 - 1.68877i) q^{52} +(-2.87684 + 1.31381i) q^{53} +(-1.09392 - 0.896296i) q^{54} +(-1.05233 - 7.31911i) q^{55} +(14.5035 - 1.20240i) q^{56} +(4.08595 - 1.19974i) q^{57} +(3.73506 - 1.83183i) q^{58} +(-2.75622 - 1.25872i) q^{59} +(-2.70707 - 5.15513i) q^{60} +(1.30434 - 1.13022i) q^{61} +(-3.75052 + 2.55910i) q^{62} +(4.32855 - 2.78179i) q^{63} +(-6.16299 - 5.10073i) q^{64} +(-3.37798 - 2.17090i) q^{65} +(-3.07408 - 1.85789i) q^{66} +(2.56768 - 8.74472i) q^{67} +(-13.0784 + 4.63723i) q^{68} +(4.57265 + 1.44599i) q^{69} +(20.8780 - 3.59183i) q^{70} +(3.77544 + 1.10857i) q^{71} +(-2.77041 - 0.569915i) q^{72} +(-1.93535 - 1.24377i) q^{73} +(0.186293 + 6.75498i) q^{74} +(-1.87920 - 2.92410i) q^{75} +(6.11945 - 5.92366i) q^{76} +(9.87649 - 8.55802i) q^{77} +(-1.85566 + 0.600913i) q^{78} +(1.06170 - 2.32479i) q^{79} +(-9.58685 - 6.61109i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(15.7088 + 4.14573i) q^{82} +(7.37017 - 1.05967i) q^{83} +(5.07798 - 8.95058i) q^{84} +(-18.3737 + 8.39101i) q^{85} +(-12.4012 + 11.3592i) q^{86} +(0.418637 - 2.91168i) q^{87} +(-7.17083 - 0.431377i) q^{88} +(1.62551 - 1.87594i) q^{89} +(-4.08995 - 0.473374i) q^{90} -7.09665i q^{91} +(9.44136 - 1.69139i) q^{92} +3.21056i q^{93} +(0.523226 - 4.52067i) q^{94} +(8.11881 - 9.36961i) q^{95} +(-5.43552 + 1.56688i) q^{96} +(-1.91268 + 13.3030i) q^{97} +(18.6027 + 20.3093i) q^{98} +(-2.31033 + 1.05509i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32}+ \cdots - 132 q^{98}+O(q^{100}) \) 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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