LMFDB - Embedded newform 99.3.k.a.46.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [99,3,Mod(19,99)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(99, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 3])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("99.19"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	99.k (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,5,0,-9] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$2.69755461717$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 11)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			46.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	99.46
Dual form			99.3.k.a.28.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.690983 + 0.224514i) q^{2} +(-2.80902 - 2.04087i) q^{4} +(-1.23607 - 3.80423i) q^{5} +(5.85410 - 8.05748i) q^{7} +(-3.19098 - 4.39201i) q^{8} -2.90617i q^{10} +(10.3713 + 3.66547i) q^{11} +(-5.00000 - 1.62460i) q^{13} +(5.85410 - 4.25325i) q^{14} +(3.07295 + 9.45756i) q^{16} +(-14.5344 + 4.72253i) q^{17} +(1.21885 + 1.67760i) q^{19} +(-4.29180 + 13.2088i) q^{20} +(6.34346 + 4.86128i) q^{22} +2.76393 q^{23} +(7.28115 - 5.29007i) q^{25} +(-3.09017 - 2.24514i) q^{26} +(-32.8885 + 10.6861i) q^{28} +(16.7082 - 22.9969i) q^{29} +(-2.20163 + 6.77591i) q^{31} +28.9402i q^{32} -11.1033 q^{34} +(-37.8885 - 12.3107i) q^{35} +(32.5623 + 23.6579i) q^{37} +(0.465558 + 1.43284i) q^{38} +(-12.7639 + 17.5680i) q^{40} +(41.2426 + 56.7656i) q^{41} +23.0624i q^{43} +(-21.6525 - 31.4629i) q^{44} +(1.90983 + 0.620541i) q^{46} +(22.0344 - 16.0090i) q^{47} +(-15.5106 - 47.7369i) q^{49} +(6.21885 - 2.02063i) q^{50} +(10.7295 + 14.7679i) q^{52} +(3.54102 - 10.8981i) q^{53} +(1.12461 - 43.9856i) q^{55} -54.0689 q^{56} +(16.7082 - 12.1392i) q^{58} +(-1.83688 - 1.33457i) q^{59} +(21.5066 - 6.98791i) q^{61} +(-3.04257 + 4.18774i) q^{62} +(5.79431 - 17.8330i) q^{64} +21.0292i q^{65} -38.4934 q^{67} +(50.4656 + 16.3973i) q^{68} +(-23.4164 - 17.0130i) q^{70} +(-23.5836 - 72.5828i) q^{71} +(60.4656 - 83.2237i) q^{73} +(17.1885 + 23.6579i) q^{74} -7.19991i q^{76} +(90.2492 - 62.1087i) q^{77} +(-3.74265 - 1.21606i) q^{79} +(32.1803 - 23.3804i) q^{80} +(15.7533 + 48.4836i) q^{82} +(-79.1697 + 25.7238i) q^{83} +(35.9311 + 49.4549i) q^{85} +(-5.17783 + 15.9357i) q^{86} +(-16.9959 - 57.2474i) q^{88} -123.297 q^{89} +(-42.3607 + 30.7768i) q^{91} +(-7.76393 - 5.64083i) q^{92} +(18.8197 - 6.11488i) q^{94} +(4.87539 - 6.71040i) q^{95} +(-23.9205 + 73.6196i) q^{97} -36.4677i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 5 q^{2} - 9 q^{4} + 4 q^{5} + 10 q^{7} - 15 q^{8} - q^{11} - 20 q^{13} + 10 q^{14} + 19 q^{16} + 25 q^{19} - 44 q^{20} - 35 q^{22} + 20 q^{23} + 9 q^{25} + 10 q^{26} - 60 q^{28} + 40 q^{29} - 58 q^{31}+ \cdots - 165 q^{97}+O(q^{100}) $ 4 * q + 5 * q^2 - 9 * q^4 + 4 * q^5 + 10 * q^7 - 15 * q^8 - q^11 - 20 * q^13 + 10 * q^14 + 19 * q^16 + 25 * q^19 - 44 * q^20 - 35 * q^22 + 20 * q^23 + 9 * q^25 + 10 * q^26 - 60 * q^28 + 40 * q^29 - 58 * q^31 + 130 * q^34 - 80 * q^35 + 90 * q^37 + 60 * q^38 - 60 * q^40 + 80 * q^41 - 24 * q^44 + 30 * q^46 + 30 * q^47 - 109 * q^49 + 45 * q^50 + 110 * q^52 - 120 * q^53 - 76 * q^55 - 100 * q^56 + 40 * q^58 - 23 * q^59 + 10 * q^61 - 200 * q^62 - 149 * q^64 - 230 * q^67 + 260 * q^68 - 40 * q^70 - 148 * q^71 + 300 * q^73 + 270 * q^74 + 200 * q^77 + 70 * q^79 + 84 * q^80 + 25 * q^82 - 225 * q^83 + 260 * q^85 - 175 * q^86 + 55 * q^88 - 122 * q^89 - 80 * q^91 - 40 * q^92 + 120 * q^94 + 100 * q^95 - 165 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$1$

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 $

$2$	0.690983	+	0.224514i	0.345492	+	0.112257i	0.476623	−	0.879108i	$-0.341861\pi$
$2$	0.690983	+	0.224514i	0.345492	+	0.112257i	−0.131131	+	0.991365i	$0.541861\pi$
$3$		0			0
$3$		0			0
$4$	−2.80902	−	2.04087i	−0.702254	−	0.510218i
$5$	−1.23607	−	3.80423i	−0.247214	−	0.760845i	−0.995264	−	0.0972039i	$-0.969010\pi$
$5$	−1.23607	−	3.80423i	−0.247214	−	0.760845i	0.748051	−	0.663641i	$-0.230990\pi$
$6$		0			0
$7$	5.85410	−	8.05748i	0.836300	−	1.15107i	−0.150417	−	0.988623i	$-0.548062\pi$
$7$	5.85410	−	8.05748i	0.836300	−	1.15107i	0.986717	−	0.162446i	$-0.0519383\pi$
$8$	−3.19098	−	4.39201i	−0.398873	−	0.549001i
$9$		0			0
$10$		−	2.90617i		−	0.290617i
$11$	10.3713	+	3.66547i	0.942848	+	0.333224i
$11$	10.3713	+	3.66547i	0.942848	+	0.333224i
$12$		0			0
$13$	−5.00000	−	1.62460i	−0.384615	−	0.124969i	0.110326	−	0.993895i	$-0.464810\pi$
$13$	−5.00000	−	1.62460i	−0.384615	−	0.124969i	−0.494941	+	0.868926i	$0.664810\pi$
$14$	5.85410	−	4.25325i	0.418150	−	0.303804i
$15$		0			0
$16$	3.07295	+	9.45756i	0.192059	+	0.591098i
$17$	−14.5344	+	4.72253i	−0.854967	+	0.277796i	−0.703525	−	0.710670i	$-0.748392\pi$
$17$	−14.5344	+	4.72253i	−0.854967	+	0.277796i	−0.151442	+	0.988466i	$0.548392\pi$
$18$		0			0
$19$	1.21885	+	1.67760i	0.0641498	+	0.0882947i	0.839886	−	0.542762i	$-0.182621\pi$
$19$	1.21885	+	1.67760i	0.0641498	+	0.0882947i	−0.775737	+	0.631057i	$0.782621\pi$
$20$	−4.29180	+	13.2088i	−0.214590	+	0.660440i
$21$		0			0
$22$	6.34346	+	4.86128i	0.288339	+	0.220967i
$23$	2.76393			0.120171			0.0600855	−	0.998193i	$-0.480863\pi$
$23$	2.76393			0.120171			0.0600855	+	0.998193i	$0.480863\pi$
$24$		0			0
$25$	7.28115	−	5.29007i	0.291246	−	0.211603i
$26$	−3.09017	−	2.24514i	−0.118853	−	0.0863515i
$27$		0			0
$28$	−32.8885	+	10.6861i	−1.17459	+	0.381648i
$29$	16.7082	−	22.9969i	0.576145	−	0.792996i	−0.417121	−	0.908851i	$-0.636961\pi$
$29$	16.7082	−	22.9969i	0.576145	−	0.792996i	0.993266	+	0.115855i	$0.0369609\pi$
$30$		0			0
$31$	−2.20163	+	6.77591i	−0.0710202	+	0.218578i	−0.980266	−	0.197681i	$-0.936659\pi$
$31$	−2.20163	+	6.77591i	−0.0710202	+	0.218578i	0.909246	+	0.416259i	$0.136659\pi$
$32$			28.9402i			0.904382i
$33$		0			0
$34$	−11.1033			−0.326568
$35$	−37.8885	−	12.3107i	−1.08253	−	0.351735i
$36$		0			0
$37$	32.5623	+	23.6579i	0.880062	+	0.639403i	0.933268	−	0.359181i	$-0.116944\pi$
$37$	32.5623	+	23.6579i	0.880062	+	0.639403i	−0.0532056	+	0.998584i	$0.516944\pi$
$38$	0.465558	+	1.43284i	0.0122515	+	0.0377063i
$39$		0			0
$40$	−12.7639	+	17.5680i	−0.319098	+	0.439201i
$41$	41.2426	+	56.7656i	1.00592	+	1.38453i	0.921623	+	0.388087i	$0.126864\pi$
$41$	41.2426	+	56.7656i	1.00592	+	1.38453i	0.0842954	+	0.996441i	$0.473136\pi$
$42$		0			0
$43$			23.0624i			0.536334i	0.963372	+	0.268167i	$0.0864180\pi$
$43$			23.0624i			0.536334i	−0.963372	+	0.268167i	$0.913582\pi$
$44$	−21.6525	−	31.4629i	−0.492102	−	0.715066i
$45$		0			0
$46$	1.90983	+	0.620541i	0.0415180	+	0.0134900i
$47$	22.0344	−	16.0090i	0.468818	−	0.340616i	−0.328163	−	0.944621i	$-0.606429\pi$
$47$	22.0344	−	16.0090i	0.468818	−	0.340616i	0.796980	+	0.604005i	$0.206429\pi$
$48$		0			0
$49$	−15.5106	−	47.7369i	−0.316544	−	0.974221i
$50$	6.21885	−	2.02063i	0.124377	−	0.0404125i
$51$		0			0
$52$	10.7295	+	14.7679i	0.206336	+	0.283998i
$53$	3.54102	−	10.8981i	0.0668117	−	0.205625i	−0.912077	−	0.410019i	$-0.865522\pi$
$53$	3.54102	−	10.8981i	0.0668117	−	0.205625i	0.978889	+	0.204393i	$0.0655222\pi$
$54$		0			0
$55$	1.12461	−	43.9856i	0.0204475	−	0.799739i
$56$	−54.0689			−0.965516
$57$		0			0
$58$	16.7082	−	12.1392i	0.288072	−	0.209297i
$59$	−1.83688	−	1.33457i	−0.0311336	−	0.0226199i	0.572110	−	0.820177i	$-0.306125\pi$
$59$	−1.83688	−	1.33457i	−0.0311336	−	0.0226199i	−0.603243	+	0.797557i	$0.706125\pi$
$60$		0			0
$61$	21.5066	−	6.98791i	0.352567	−	0.114556i	−0.127379	−	0.991854i	$-0.540656\pi$
$61$	21.5066	−	6.98791i	0.352567	−	0.114556i	0.479946	+	0.877298i	$0.340656\pi$
$62$	−3.04257	+	4.18774i	−0.0490737	+	0.0675442i
$63$		0			0
$64$	5.79431	−	17.8330i	0.0905361	−	0.278641i
$65$			21.0292i			0.323527i
$66$		0			0
$67$	−38.4934			−0.574529			−0.287264	−	0.957851i	$-0.592746\pi$
$67$	−38.4934			−0.574529			−0.287264	+	0.957851i	$0.592746\pi$
$68$	50.4656	+	16.3973i	0.742141	+	0.241136i
$69$		0			0
$70$	−23.4164	−	17.0130i	−0.334520	−	0.243043i
$71$	−23.5836	−	72.5828i	−0.332163	−	1.02229i	−0.968103	−	0.250554i	$-0.919387\pi$
$71$	−23.5836	−	72.5828i	−0.332163	−	1.02229i	0.635939	−	0.771739i	$-0.280613\pi$
$72$		0			0
$73$	60.4656	−	83.2237i	0.828295	−	1.14005i	−0.159943	−	0.987126i	$-0.551131\pi$
$73$	60.4656	−	83.2237i	0.828295	−	1.14005i	0.988238	−	0.152924i	$-0.0488691\pi$
$74$	17.1885	+	23.6579i	0.232277	+	0.319701i
$75$		0			0
$76$		−	7.19991i		−	0.0947357i
$77$	90.2492	−	62.1087i	1.17207	−	0.806606i
$78$		0			0
$79$	−3.74265	−	1.21606i	−0.0473753	−	0.0153932i	0.285233	−	0.958458i	$-0.407929\pi$
$79$	−3.74265	−	1.21606i	−0.0473753	−	0.0153932i	−0.332609	+	0.943065i	$0.607929\pi$
$80$	32.1803	−	23.3804i	0.402254	−	0.292255i
$81$		0			0
$82$	15.7533	+	48.4836i	0.192113	+	0.591264i
$83$	−79.1697	+	25.7238i	−0.953852	+	0.309925i	−0.744280	−	0.667868i	$-0.767207\pi$
$83$	−79.1697	+	25.7238i	−0.953852	+	0.309925i	−0.209572	+	0.977793i	$0.567207\pi$
$84$		0			0
$85$	35.9311	+	49.4549i	0.422719	+	0.581823i
$86$	−5.17783	+	15.9357i	−0.0602073	+	0.185299i
$87$		0			0
$88$	−16.9959	−	57.2474i	−0.193136	−	0.650539i
$89$	−123.297			−1.38536			−0.692679	−	0.721246i	$-0.743570\pi$
$89$	−123.297			−1.38536			−0.692679	+	0.721246i	$0.743570\pi$
$90$		0			0
$91$	−42.3607	+	30.7768i	−0.465502	+	0.338207i
$92$	−7.76393	−	5.64083i	−0.0843906	−	0.0613133i
$93$		0			0
$94$	18.8197	−	6.11488i	0.200209	−	0.0650519i
$95$	4.87539	−	6.71040i	0.0513199	−	0.0706357i
$96$		0			0
$97$	−23.9205	+	73.6196i	−0.246603	+	0.758965i	0.748766	+	0.662835i	$0.230647\pi$
$97$	−23.9205	+	73.6196i	−0.246603	+	0.758965i	−0.995369	+	0.0961309i	$0.969353\pi$
$98$		−	36.4677i		−	0.372119i
$99$		0			0
$100$	−31.2492			−0.312492
$101$	107.159	+	34.8181i	1.06098	+	0.344734i	0.786969	−	0.616993i	$-0.211649\pi$
$101$	107.159	+	34.8181i	1.06098	+	0.344734i	0.274012	+	0.961726i	$0.411649\pi$
$102$		0			0
$103$	−74.9230	−	54.4347i	−0.727408	−	0.528493i	0.161335	−	0.986900i	$-0.448420\pi$
$103$	−74.9230	−	54.4347i	−0.727408	−	0.528493i	−0.888742	+	0.458407i	$0.848420\pi$
$104$	8.81966	+	27.1441i	0.0848044	+	0.261001i
$105$		0			0
$106$	4.89357	−	6.73542i	0.0461657	−	0.0635417i
$107$	49.8607	+	68.6273i	0.465988	+	0.641377i	0.975737	−	0.218946i	$-0.0702619\pi$
$107$	49.8607	+	68.6273i	0.465988	+	0.641377i	−0.509749	+	0.860323i	$0.670262\pi$
$108$		0			0
$109$			94.0766i			0.863088i	0.902092	+	0.431544i	$0.142031\pi$
$109$			94.0766i			0.863088i	−0.902092	+	0.431544i	$0.857969\pi$
$110$	10.6525	−	30.1408i	0.0968407	−	0.274008i
$111$		0			0
$112$	94.1935	+	30.6053i	0.841013	+	0.273262i
$113$	−6.87132	+	4.99231i	−0.0608082	+	0.0441797i	−0.617774	−	0.786356i	$-0.711965\pi$
$113$	−6.87132	+	4.99231i	−0.0608082	+	0.0441797i	0.556966	+	0.830535i	$0.311965\pi$
$114$		0			0
$115$	−3.41641	−	10.5146i	−0.0297079	−	0.0914315i
$116$	−93.8673	+	30.4993i	−0.809200	+	0.262925i
$117$		0			0
$118$	−0.969623	−	1.33457i	−0.00821715	−	0.0113099i
$119$	−47.0344	+	144.757i	−0.395247	+	1.21645i
$120$		0			0
$121$	94.1287	+	76.0315i	0.777923	+	0.628360i
$122$	16.4296			0.134669
$123$		0			0
$124$	20.0132	−	14.5404i	0.161396	−	0.117261i
$125$	−110.026	−	79.9388i	−0.880210	−	0.639510i
$126$		0			0
$127$	−179.039	+	58.1734i	−1.40976	+	0.458059i	−0.912334	−	0.409448i	$-0.865721\pi$
$127$	−179.039	+	58.1734i	−1.40976	+	0.458059i	−0.497426	+	0.867506i	$0.665721\pi$
$128$	76.0501	−	104.674i	0.594141	−	0.817766i
$129$		0			0
$130$	−4.72136	+	14.5309i	−0.0363182	+	0.111776i
$131$			141.932i			1.08345i	0.840556	+	0.541725i	$0.182229\pi$
$131$			141.932i			1.08345i	−0.840556	+	0.541725i	$0.817771\pi$
$132$		0			0
$133$	20.6525			0.155282
$134$	−26.5983	−	8.64231i	−0.198495	−	0.0644949i
$135$		0			0
$136$	67.1205	+	48.7659i	0.493533	+	0.358573i
$137$	−5.02380	−	15.4617i	−0.0366701	−	0.112859i	0.931046	−	0.364902i	$-0.118898\pi$
$137$	−5.02380	−	15.4617i	−0.0366701	−	0.112859i	−0.967716	+	0.252043i	$0.918898\pi$
$138$		0			0
$139$	−133.108	+	183.208i	−0.957614	+	1.31804i	−0.00955293	+	0.999954i	$0.503041\pi$
$139$	−133.108	+	183.208i	−0.957614	+	1.31804i	−0.948061	+	0.318088i	$0.896959\pi$
$140$	81.3050	+	111.907i	0.580750	+	0.799333i
$141$		0			0
$142$		−	55.4484i		−	0.390481i
$143$	−45.9017	−	35.1766i	−0.320991	−	0.245990i
$144$		0			0
$145$	−108.138	−	35.1361i	−0.745778	−	0.242318i
$146$	60.4656	−	43.9308i	0.414148	−	0.300896i
$147$		0			0
$148$	−43.1854	−	132.911i	−0.291793	−	0.898047i
$149$	63.8967	−	20.7613i	0.428837	−	0.139338i	−0.0866427	−	0.996239i	$-0.527614\pi$
$149$	63.8967	−	20.7613i	0.428837	−	0.139338i	0.515479	+	0.856902i	$0.327614\pi$
$150$		0			0
$151$	59.0871	+	81.3264i	0.391305	+	0.538585i	0.958535	−	0.284974i	$-0.0919850\pi$
$151$	59.0871	+	81.3264i	0.391305	+	0.538585i	−0.567230	+	0.823559i	$0.691985\pi$
$152$	3.47871	−	10.7064i	0.0228863	−	0.0704367i
$153$		0			0
$154$	76.3050	−	22.6538i	0.495487	−	0.147103i
$155$	28.4984			0.183861
$156$		0			0
$157$	199.520	−	144.960i	1.27083	−	0.923309i	0.271591	−	0.962413i	$-0.412450\pi$
$157$	199.520	−	144.960i	1.27083	−	0.923309i	0.999235	+	0.0391033i	$0.0124502\pi$
$158$	−2.31308	−	1.68055i	−0.0146398	−	0.0106364i
$159$		0			0
$160$	110.095	−	35.7721i	0.688095	−	0.223576i
$161$	16.1803	−	22.2703i	0.100499	−	0.138325i
$162$		0			0
$163$	53.8820	−	165.832i	0.330564	−	1.01737i	−0.638302	−	0.769786i	$-0.720363\pi$
$163$	53.8820	−	165.832i	0.330564	−	1.01737i	0.968866	−	0.247586i	$-0.0796372\pi$
$164$		−	243.627i		−	1.48553i
$165$		0			0
$166$	−60.4803			−0.364339
$167$	−234.864	−	76.3120i	−1.40637	−	0.456958i	−0.495126	−	0.868821i	$-0.664878\pi$
$167$	−234.864	−	76.3120i	−1.40637	−	0.456958i	−0.911246	+	0.411863i	$0.864878\pi$
$168$		0			0
$169$	−114.363	−	83.0897i	−0.676705	−	0.491655i
$170$	13.7245	+	42.2396i	0.0807321	+	0.248468i
$171$		0			0
$172$	47.0673	−	64.7826i	0.273647	−	0.376643i
$173$	29.2411	+	40.2469i	0.169024	+	0.232641i	0.885123	−	0.465357i	$-0.154074\pi$
$173$	29.2411	+	40.2469i	0.169024	+	0.232641i	−0.716099	+	0.697999i	$0.754074\pi$
$174$		0			0
$175$		−	89.6363i		−	0.512208i
$176$	−2.79586	+	109.351i	−0.0158856	+	0.621314i
$177$		0			0
$178$	−85.1960	−	27.6819i	−0.478629	−	0.155516i
$179$	177.134	−	128.695i	0.989574	−	0.718967i	0.0297461	−	0.999557i	$-0.490530\pi$
$179$	177.134	−	128.695i	0.989574	−	0.718967i	0.959828	+	0.280590i	$0.0905301\pi$
$180$		0			0
$181$	12.0213	+	36.9977i	0.0664159	+	0.204407i	0.978757	−	0.205024i	$-0.0657272\pi$
$181$	12.0213	+	36.9977i	0.0664159	+	0.204407i	−0.912341	+	0.409431i	$0.865727\pi$
$182$	−36.1803	+	11.7557i	−0.198793	+	0.0645918i
$183$		0			0
$184$	−8.81966	−	12.1392i	−0.0479329	−	0.0659740i
$185$	49.7508	−	153.117i	0.268923	−	0.827660i
$186$		0			0
$187$	−168.052	−	4.29670i	−0.898672	−	0.0229770i
$188$	−94.5673			−0.503018
$189$		0			0
$190$	4.87539	−	3.54218i	0.0256599	−	0.0186430i
$191$	96.9230	+	70.4187i	0.507450	+	0.368684i	0.811855	−	0.583858i	$-0.198458\pi$
$191$	96.9230	+	70.4187i	0.507450	+	0.368684i	−0.304405	+	0.952543i	$0.598458\pi$
$192$		0			0
$193$	27.7933	−	9.03061i	0.144007	−	0.0467907i	−0.236127	−	0.971722i	$-0.575878\pi$
$193$	27.7933	−	9.03061i	0.144007	−	0.0467907i	0.380134	+	0.924932i	$0.375878\pi$
$194$	−33.0573	+	45.4994i	−0.170398	+	0.234533i
$195$		0			0
$196$	−53.8551	+	165.749i	−0.274771	+	0.845657i
$197$			282.037i			1.43166i	0.698275	+	0.715830i	$0.253951\pi$
$197$			282.037i			1.43166i	−0.698275	+	0.715830i	$0.746049\pi$
$198$		0			0
$199$	177.469			0.891804			0.445902	−	0.895082i	$-0.352883\pi$
$199$	177.469			0.891804			0.445902	+	0.895082i	$0.352883\pi$
$200$	−46.4681	−	15.0984i	−0.232340	−	0.0754920i
$201$		0			0
$202$	66.2279	+	48.1174i	0.327861	+	0.238205i
$203$	−87.4853	−	269.252i	−0.430962	−	1.32636i
$204$		0			0
$205$	164.971	−	227.063i	0.804735	−	1.10762i
$206$	−39.5492	−	54.4347i	−0.191986	−	0.264246i
$207$		0			0
$208$		−	52.2801i		−	0.251347i
$209$	6.49187	+	21.8666i	0.0310616	+	0.104625i
$210$		0			0
$211$	93.5354	+	30.3915i	0.443296	+	0.144036i	0.522156	−	0.852850i	$-0.325128\pi$
$211$	93.5354	+	30.3915i	0.443296	+	0.144036i	−0.0788599	+	0.996886i	$0.525128\pi$
$212$	−32.1885	+	23.3863i	−0.151832	+	0.110313i
$213$		0			0
$214$	19.0451	+	58.6147i	0.0889957	+	0.273901i
$215$	87.7345	−	28.5067i	0.408068	−	0.132589i
$216$		0			0
$217$	41.7082	+	57.4064i	0.192204	+	0.264546i
$218$	−21.1215	+	65.0053i	−0.0968876	+	0.298190i
$219$		0			0
$220$	−92.9280	+	121.261i	−0.422400	+	0.551187i
$221$	80.3444			0.363549
$222$		0			0
$223$	−215.220	+	156.366i	−0.965111	+	0.701194i	−0.954332	−	0.298748i	$-0.903431\pi$
$223$	−215.220	+	156.366i	−0.965111	+	0.701194i	−0.0107791	+	0.999942i	$0.503431\pi$
$224$	233.185	+	169.419i	1.04101	+	0.756335i
$225$		0			0
$226$	−5.86881	+	1.90689i	−0.0259682	+	0.00843758i
$227$	−149.606	+	205.915i	−0.659057	+	0.907114i	−0.999450	−	0.0331697i	$-0.989440\pi$
$227$	−149.606	+	205.915i	−0.659057	+	0.907114i	0.340393	+	0.940283i	$0.389440\pi$
$228$		0			0
$229$	−12.4245	+	38.2388i	−0.0542556	+	0.166982i	−0.974513	−	0.224333i	$-0.927980\pi$
$229$	−12.4245	+	38.2388i	−0.0542556	+	0.166982i	0.920257	+	0.391315i	$0.127980\pi$
$230$		−	8.03246i		−	0.0349237i
$231$		0			0
$232$	−154.318			−0.665164
$233$	219.639	+	71.3649i	0.942655	+	0.306287i	0.739728	−	0.672906i	$-0.234954\pi$
$233$	219.639	+	71.3649i	0.942655	+	0.306287i	0.202928	+	0.979194i	$0.434954\pi$
$234$		0			0
$235$	−88.1378	−	64.0358i	−0.375054	−	0.272493i
$236$	2.43614	+	7.49767i	0.0103226	+	0.0317698i
$237$		0			0
$238$	−65.0000	+	89.4648i	−0.273109	+	0.375903i
$239$	−185.249	−	254.974i	−0.775101	−	1.06684i	−0.995806	−	0.0914947i	$-0.970836\pi$
$239$	−185.249	−	254.974i	−0.775101	−	1.06684i	0.220704	−	0.975341i	$-0.429164\pi$
$240$		0			0
$241$			270.933i			1.12420i	0.827069	+	0.562101i	$0.190007\pi$
$241$			270.933i			1.12420i	−0.827069	+	0.562101i	$0.809993\pi$
$242$	47.9712	+	73.6697i	0.198228	+	0.304420i
$243$		0			0
$244$	−74.6738	−	24.2630i	−0.306040	−	0.0994384i
$245$	−162.430	+	118.012i	−0.662978	+	0.481682i
$246$		0			0
$247$	−3.36881	−	10.3681i	−0.0136389	−	0.0419762i
$248$	36.7852	−	11.9522i	0.148327	−	0.0481945i
$249$		0			0
$250$	−58.0789	−	79.9388i	−0.232316	−	0.319755i
$251$	−3.44080	+	10.5897i	−0.0137084	+	0.0421900i	−0.957677	−	0.287846i	$-0.907061\pi$
$251$	−3.44080	+	10.5897i	−0.0137084	+	0.0421900i	0.943968	+	0.330036i	$0.107061\pi$
$252$		0			0
$253$	28.6656	+	10.1311i	0.113303	+	0.0400439i
$254$	−136.774			−0.538480
$255$		0			0
$256$	15.3713	−	11.1679i	0.0600442	−	0.0436247i
$257$	−326.261	−	237.042i	−1.26950	−	0.922344i	−0.270315	−	0.962772i	$-0.587128\pi$
$257$	−326.261	−	237.042i	−1.26950	−	0.922344i	−0.999182	+	0.0404281i	$0.987128\pi$
$258$		0			0
$259$	381.246	−	123.874i	1.47199	−	0.478279i
$260$	42.9180	−	59.0715i	0.165069	−	0.227198i
$261$		0			0
$262$	−31.8657	+	98.0726i	−0.121625	+	0.374323i
$263$		−	42.6636i		−	0.162219i	−0.996705	−	0.0811094i	$-0.974154\pi$
$263$		−	42.6636i		−	0.162219i	0.996705	−	0.0811094i	$-0.0258463\pi$
$264$		0			0
$265$	−45.8359			−0.172966
$266$	14.2705	+	4.63677i	0.0536485	+	0.0174315i
$267$		0			0
$268$	108.129	+	78.5601i	0.403465	+	0.293135i
$269$	126.695	+	389.927i	0.470985	+	1.44954i	0.851296	+	0.524685i	$0.175817\pi$
$269$	126.695	+	389.927i	0.470985	+	1.44954i	−0.380311	+	0.924859i	$0.624183\pi$
$270$		0			0
$271$	−136.400	+	187.739i	−0.503322	+	0.692763i	−0.982775	−	0.184804i	$-0.940835\pi$
$271$	−136.400	+	187.739i	−0.503322	+	0.692763i	0.479454	+	0.877567i	$0.340835\pi$
$272$	−89.3272	−	122.948i	−0.328409	−	0.452016i
$273$		0			0
$274$		−	11.8117i		−	0.0431082i
$275$	94.9058	−	28.1762i	0.345112	−	0.102459i
$276$		0			0
$277$	291.305	+	94.6507i	1.05164	+	0.341699i	0.783313	−	0.621628i	$-0.213528\pi$
$277$	291.305	+	94.6507i	1.05164	+	0.341699i	0.268330	+	0.963327i	$0.413528\pi$
$278$	−133.108	+	96.7089i	−0.478807	+	0.347874i
$279$		0			0
$280$	66.8328	+	205.690i	0.238689	+	0.734608i
$281$	123.114	−	40.0022i	0.438128	−	0.142356i	−0.0816438	−	0.996662i	$-0.526017\pi$
$281$	123.114	−	40.0022i	0.438128	−	0.142356i	0.519772	+	0.854305i	$0.326017\pi$
$282$		0			0
$283$	−247.984	−	341.320i	−0.876268	−	1.20608i	−0.977441	−	0.211210i	$-0.932260\pi$
$283$	−247.984	−	341.320i	−0.876268	−	1.20608i	0.101173	−	0.994869i	$-0.467740\pi$
$284$	−81.8854	+	252.017i	−0.288329	+	0.887385i
$285$		0			0
$286$	−23.8197	−	34.6120i	−0.0832855	−	0.121021i
$287$	698.827			2.43494
$288$		0			0
$289$	−44.8582	+	32.5914i	−0.155219	+	0.112773i
$290$	−66.8328	−	48.5569i	−0.230458	−	0.167438i
$291$		0			0
$292$	−339.698	+	110.374i	−1.16335	+	0.377995i
$293$	37.8998	−	52.1646i	0.129351	−	0.178036i	−0.739429	−	0.673234i	$-0.764905\pi$
$293$	37.8998	−	52.1646i	0.129351	−	0.178036i	0.868780	+	0.495198i	$0.164905\pi$
$294$		0			0
$295$	−2.80650	+	8.63753i	−0.00951357	+	0.0292798i
$296$		−	218.506i		−	0.738196i
$297$		0			0
$298$	48.8127			0.163801
$299$	−13.8197	−	4.49028i	−0.0462196	−	0.0150177i
$300$		0			0
$301$	185.825	+	135.010i	0.617358	+	0.448537i
$302$	22.5693	+	69.4610i	0.0747326	+	0.230003i
$303$		0			0
$304$	−12.1205	+	16.6825i	−0.0398702	+	0.0548766i
$305$	−53.1672	−	73.1784i	−0.174319	−	0.239929i
$306$		0			0
$307$		−	356.512i		−	1.16128i	−0.814161	−	0.580639i	$-0.802803\pi$
$307$		−	356.512i		−	1.16128i	0.814161	−	0.580639i	$-0.197197\pi$
$308$	−380.267	−	9.72257i	−1.23463	−	0.0315668i
$309$		0			0
$310$	19.6919	+	6.39830i	0.0635224	+	0.0206397i
$311$	−449.177	+	326.346i	−1.44430	+	1.04935i	−0.457178	+	0.889375i	$0.651140\pi$
$311$	−449.177	+	326.346i	−1.44430	+	1.04935i	−0.987122	+	0.159970i	$0.948860\pi$
$312$		0			0
$313$	−102.405	−	315.170i	−0.327172	−	1.00693i	−0.970451	−	0.241300i	$-0.922426\pi$
$313$	−102.405	−	315.170i	−0.327172	−	1.00693i	0.643279	−	0.765632i	$-0.277574\pi$
$314$	170.410	−	55.3696i	0.542708	−	0.176336i
$315$		0			0
$316$	8.03134	+	11.0542i	0.0254156	+	0.0349816i
$317$	159.740	−	491.628i	0.503910	−	1.55088i	−0.298685	−	0.954352i	$-0.596548\pi$
$317$	159.740	−	491.628i	0.503910	−	1.55088i	0.802595	−	0.596524i	$-0.203452\pi$
$318$		0			0
$319$	257.580	−	177.265i	0.807462	−	0.555688i
$320$	−75.0031			−0.234385
$321$		0			0
$322$	16.1803	−	11.7557i	0.0502495	−	0.0365084i
$323$	−25.6378	−	18.6269i	−0.0793739	−	0.0576685i
$324$		0			0
$325$	−45.0000	+	14.6214i	−0.138462	+	0.0449889i
$326$	74.4630	−	102.490i	0.228414	−	0.314385i
$327$		0			0
$328$	117.711	−	362.276i	0.358874	−	1.10450i
$329$		−	271.260i		−	0.824499i
$330$		0			0
$331$	208.884			0.631068			0.315534	−	0.948914i	$-0.397816\pi$
$331$	208.884			0.631068			0.315534	+	0.948914i	$0.397816\pi$
$332$	274.888	+	89.3165i	0.827976	+	0.269026i
$333$		0			0
$334$	−145.154	−	105.461i	−0.434593	−	0.315750i
$335$	47.5805	+	146.438i	0.142031	+	0.437127i
$336$		0			0
$337$	−79.3090	+	109.159i	−0.235338	+	0.323915i	−0.910309	−	0.413929i	$-0.864156\pi$
$337$	−79.3090	+	109.159i	−0.235338	+	0.323915i	0.674971	+	0.737844i	$0.264156\pi$
$338$	−60.3682	−	83.0897i	−0.178604	−	0.245828i
$339$		0			0
$340$		−	212.251i		−	0.624266i
$341$	−47.6707	+	62.2051i	−0.139797	+	0.182420i
$342$		0			0
$343$	−11.3050	−	3.67320i	−0.0329590	−	0.0107090i
$344$	101.290	−	73.5917i	0.294448	−	0.213929i
$345$		0			0
$346$	11.1691	+	34.3750i	0.0322806	+	0.0993496i
$347$	90.1393	−	29.2880i	0.259767	−	0.0844036i	−0.176238	−	0.984348i	$-0.556393\pi$
$347$	90.1393	−	29.2880i	0.259767	−	0.0844036i	0.436005	+	0.899944i	$0.356393\pi$
$348$		0			0
$349$	−100.997	−	139.010i	−0.289389	−	0.398310i	0.639426	−	0.768852i	$-0.279172\pi$
$349$	−100.997	−	139.010i	−0.289389	−	0.398310i	−0.928816	+	0.370542i	$0.879172\pi$
$350$	20.1246	−	61.9372i	0.0574989	−	0.176963i
$351$		0			0
$352$	−106.080	+	300.149i	−0.301362	+	0.852695i
$353$	119.644			0.338936			0.169468	−	0.985536i	$-0.445795\pi$
$353$	119.644			0.338936			0.169468	+	0.985536i	$0.445795\pi$
$354$		0			0
$355$	−246.971	+	179.435i	−0.695692	+	0.505450i
$356$	346.343	+	251.633i	0.972873	+	0.706834i
$357$		0			0
$358$	151.290	−	49.1572i	0.422598	−	0.137311i
$359$	−274.681	+	378.066i	−0.765127	+	1.05311i	0.231643	+	0.972801i	$0.425590\pi$
$359$	−274.681	+	378.066i	−0.765127	+	1.05311i	−0.996770	+	0.0803065i	$0.974410\pi$
$360$		0			0
$361$	110.226	−	339.242i	0.305336	−	0.939728i
$362$			28.2637i			0.0780766i
$363$		0			0
$364$	181.803			0.499460
$365$	−391.341	−	127.155i	−1.07217	−	0.348368i
$366$		0			0
$367$	266.026	+	193.279i	0.724867	+	0.526647i	0.887936	−	0.459968i	$-0.152139\pi$
$367$	266.026	+	193.279i	0.724867	+	0.526647i	−0.163068	+	0.986615i	$0.552139\pi$
$368$	8.49342	+	26.1401i	0.0230800	+	0.0710328i
$369$		0			0
$370$	68.7539	−	94.6316i	0.185821	−	0.255761i
$371$	−67.0820	−	92.3305i	−0.180814	−	0.248869i
$372$		0			0
$373$			214.135i			0.574088i	0.957917	+	0.287044i	$0.0926726\pi$
$373$			214.135i			0.574088i	−0.957917	+	0.287044i	$0.907327\pi$
$374$	−115.156	−	40.6989i	−0.307904	−	0.108821i
$375$		0			0
$376$	−140.623	−	45.6912i	−0.373997	−	0.121519i
$377$	−120.902	+	87.8402i	−0.320694	+	0.232998i
$378$		0			0
$379$	98.9630	+	304.577i	0.261116	+	0.803633i	0.992563	+	0.121734i	$0.0388456\pi$
$379$	98.9630	+	304.577i	0.261116	+	0.803633i	−0.731447	+	0.681899i	$0.761154\pi$
$380$	−27.3901	+	8.89958i	−0.0720792	+	0.0234200i
$381$		0			0
$382$	51.1622	+	70.4187i	0.133932	+	0.184342i
$383$	169.205	−	520.759i	0.441788	−	1.35968i	−0.444181	−	0.895937i	$-0.646505\pi$
$383$	169.205	−	520.759i	0.441788	−	1.35968i	0.885968	−	0.463746i	$-0.153495\pi$
$384$		0			0
$385$	−347.830	−	266.558i	−0.903454	−	0.692358i
$386$	21.2322			0.0550058
$387$		0			0
$388$	217.441	−	157.980i	0.560415	−	0.407166i
$389$	272.259	+	197.808i	0.699895	+	0.508504i	0.879898	−	0.475162i	$-0.157611\pi$
$389$	272.259	+	197.808i	0.699895	+	0.508504i	−0.180003	+	0.983666i	$0.557611\pi$
$390$		0			0
$391$	−40.1722	+	13.0527i	−0.102742	+	0.0333830i
$392$	−160.167	+	220.450i	−0.408588	+	0.562373i
$393$		0			0
$394$	−63.3212	+	194.883i	−0.160714	+	0.494626i
$395$			15.7410i			0.0398506i
$396$		0			0
$397$	115.374			0.290614			0.145307	−	0.989387i	$-0.453583\pi$
$397$	115.374			0.290614			0.145307	+	0.989387i	$0.453583\pi$
$398$	122.628	+	39.8443i	0.308111	+	0.100111i
$399$		0			0
$400$	72.4058	+	52.6059i	0.181014	+	0.131515i
$401$	−19.7138	−	60.6729i	−0.0491617	−	0.151304i	0.923462	−	0.383690i	$-0.125347\pi$
$401$	−19.7138	−	60.6729i	−0.0491617	−	0.151304i	−0.972624	+	0.232386i	$0.925347\pi$
$402$		0			0
$403$	22.0163	−	30.3028i	0.0546309	−	0.0751930i
$404$	−229.952	−	316.502i	−0.569189	−	0.783422i
$405$		0			0
$406$		−	205.690i		−	0.506626i
$407$	250.997	+	364.720i	0.616700	+	0.896118i
$408$		0			0
$409$	−581.745	−	189.020i	−1.42236	−	0.462152i	−0.506008	−	0.862529i	$-0.668879\pi$
$409$	−581.745	−	189.020i	−1.42236	−	0.462152i	−0.916351	+	0.400377i	$0.868879\pi$
$410$	164.971	−	119.858i	0.402367	−	0.292337i
$411$		0			0
$412$	99.3657	+	305.816i	0.241179	+	0.742272i
$413$	−21.5066	+	6.98791i	−0.0520740	+	0.0169199i
$414$		0			0
$415$	195.718	+	269.383i	0.471610	+	0.649116i
$416$	47.0163	−	144.701i	0.113020	−	0.347839i
$417$		0			0
$418$	−0.423579	+	16.5669i	−0.00101335	+	0.0396338i
$419$	−146.156			−0.348821			−0.174410	−	0.984673i	$-0.555802\pi$
$419$	−146.156			−0.348821			−0.174410	+	0.984673i	$0.555802\pi$
$420$		0			0
$421$	−480.079	+	348.798i	−1.14033	+	0.828498i	−0.987165	−	0.159702i	$-0.948947\pi$
$421$	−480.079	+	348.798i	−1.14033	+	0.828498i	−0.153165	+	0.988201i	$0.548947\pi$
$422$	57.8081	+	42.0000i	0.136986	+	0.0995261i
$423$		0			0
$424$	−59.1641	+	19.2236i	−0.139538	+	0.0453386i
$425$	−80.8450	+	111.274i	−0.190224	+	0.261820i
$426$		0			0
$427$	69.5967	−	214.197i	0.162990	−	0.501632i
$428$		−	294.535i		−	0.688165i
$429$		0			0
$430$	67.0232			0.155868
$431$	−165.807	−	53.8738i	−0.384702	−	0.124997i	0.110280	−	0.993901i	$-0.464825\pi$
$431$	−165.807	−	53.8738i	−0.384702	−	0.124997i	−0.494982	+	0.868903i	$0.664825\pi$
$432$		0			0
$433$	−502.109	−	364.804i	−1.15961	−	0.842503i	−0.169878	−	0.985465i	$-0.554337\pi$
$433$	−502.109	−	364.804i	−1.15961	−	0.842503i	−0.989728	+	0.142962i	$0.954337\pi$
$434$	15.9311	+	49.0309i	0.0367076	+	0.112975i
$435$		0			0
$436$	191.998	−	264.263i	0.440363	−	0.606107i
$437$	3.36881	+	4.63677i	0.00770895	+	0.0106105i
$438$		0			0
$439$			676.778i			1.54164i	0.637055	+	0.770818i	$0.280152\pi$
$439$			676.778i			1.54164i	−0.637055	+	0.770818i	$0.719848\pi$
$440$	−196.774	+	135.418i	−0.447214	+	0.307768i
$441$		0			0
$442$	55.5166	+	18.0384i	0.125603	+	0.0408110i
$443$	−209.784	+	152.417i	−0.473552	+	0.344056i	−0.798824	−	0.601565i	$-0.794544\pi$
$443$	−209.784	+	152.417i	−0.473552	+	0.344056i	0.325272	+	0.945621i	$0.394544\pi$
$444$		0			0
$445$	152.403	+	469.049i	0.342479	+	1.05404i
$446$	−183.820	+	59.7266i	−0.412152	+	0.133916i
$447$		0			0
$448$	−109.769	−	151.084i	−0.245020	−	0.337241i
$449$	−124.349	+	382.707i	−0.276947	+	0.852354i	0.711751	+	0.702432i	$0.247902\pi$
$449$	−124.349	+	382.707i	−0.276947	+	0.852354i	−0.988698	+	0.149923i	$0.952098\pi$
$450$		0			0
$451$	219.668	+	739.908i	0.487069	+	1.64059i
$452$	29.4903			0.0652441
$453$		0			0
$454$	−149.606	+	108.695i	−0.329528	+	0.239416i
$455$	169.443	+	123.107i	0.372402	+	0.270566i
$456$		0			0
$457$	243.209	−	79.0234i	0.532186	−	0.172918i	−0.0305823	−	0.999532i	$-0.509736\pi$
$457$	243.209	−	79.0234i	0.532186	−	0.172918i	0.562769	+	0.826614i	$0.309736\pi$
$458$	−17.1703	+	23.6329i	−0.0374897	+	0.0516002i
$459$		0			0
$460$	−11.8622	+	36.5082i	−0.0257875	+	0.0793656i
$461$			446.274i			0.968056i	0.875053	+	0.484028i	$0.160827\pi$
$461$			446.274i			0.968056i	−0.875053	+	0.484028i	$0.839173\pi$
$462$		0			0
$463$	73.1308			0.157950			0.0789750	−	0.996877i	$-0.474835\pi$
$463$	73.1308			0.157950			0.0789750	+	0.996877i	$0.474835\pi$
$464$	268.838	+	87.3507i	0.579392	+	0.188256i
$465$		0			0
$466$	135.744	+	98.6239i	0.291297	+	0.211639i
$467$	−3.43459	−	10.5706i	−0.00735458	−	0.0226351i	0.947312	−	0.320313i	$-0.103788\pi$
$467$	−3.43459	−	10.5706i	−0.00735458	−	0.0226351i	−0.954666	+	0.297678i	$0.903788\pi$
$468$		0			0
$469$	−225.344	+	310.160i	−0.480479	+	0.661322i
$470$	−46.5248	−	64.0358i	−0.0989888	−	0.136246i
$471$		0			0
$472$			12.3262i			0.0261148i
$473$	−84.5344	+	239.187i	−0.178720	+	0.505682i
$474$		0			0
$475$	17.7492	+	5.76707i	0.0373668	+	0.0121412i
$476$	427.551	−	310.634i	0.898217	−	0.652593i
$477$		0			0
$478$	−70.7589	−	217.774i	−0.148031	−	0.455593i
$479$	545.546	−	177.259i	1.13893	−	0.370060i	0.321965	−	0.946752i	$-0.395657\pi$
$479$	545.546	−	177.259i	1.13893	−	0.370060i	0.816962	+	0.576692i	$0.195657\pi$
$480$		0			0
$481$	−124.377	−	171.190i	−0.258580	−	0.355905i
$482$	−60.8282	+	187.210i	−0.126199	+	0.388402i
$483$		0			0
$484$	−109.239	−	405.678i	−0.225700	−	0.838178i
$485$	309.633			0.638419
$486$		0			0
$487$	510.363	−	370.800i	1.04797	−	0.761397i	0.0761466	−	0.997097i	$-0.475738\pi$
$487$	510.363	−	370.800i	1.04797	−	0.761397i	0.971826	+	0.235700i	$0.0757383\pi$
$488$	−99.3181	−	72.1588i	−0.203521	−	0.147866i
$489$		0			0
$490$	−138.731	+	45.0766i	−0.283125	+	0.0919930i
$491$	256.297	−	352.763i	0.521990	−	0.718458i	−0.463893	−	0.885891i	$-0.653548\pi$
$491$	256.297	−	352.763i	0.521990	−	0.718458i	0.985883	+	0.167433i	$0.0535479\pi$
$492$		0			0
$493$	−134.241	+	413.152i	−0.272294	+	0.838036i
$494$		−	7.92055i		−	0.0160335i
$495$		0			0
$496$	−70.8491			−0.142841
$497$	−722.895	−	234.883i	−1.45452	−	0.472602i
$498$		0			0
$499$	376.446	+	273.504i	0.754401	+	0.548105i	0.897188	−	0.441649i	$-0.145606\pi$
$499$	376.446	+	273.504i	0.754401	+	0.548105i	−0.142787	+	0.989753i	$0.545606\pi$
$500$	145.921	+	449.099i	0.291842	+	0.898198i
$501$		0			0
$502$	−4.75507	+	6.54479i	−0.00947225	+	0.0130374i
$503$	−270.059	−	371.704i	−0.536896	−	0.738974i	0.451265	−	0.892390i	$-0.350973\pi$
$503$	−270.059	−	371.704i	−0.536896	−	0.738974i	−0.988162	+	0.153415i	$0.950973\pi$
$504$		0			0
$505$		−	450.695i		−	0.892465i
$506$	17.5329	+	13.4363i	0.0346500	+	0.0265539i
$507$		0			0
$508$	621.649	+	201.986i	1.22372	+	0.397610i
$509$	−194.705	+	141.462i	−0.382525	+	0.277920i	−0.762385	−	0.647123i	$-0.775972\pi$
$509$	−194.705	+	141.462i	−0.382525	+	0.277920i	0.379861	+	0.925044i	$0.375972\pi$
$510$		0			0
$511$	−316.602	−	974.400i	−0.619573	−	1.90685i
$512$	−479.078	+	155.662i	−0.935699	+	0.304027i
$513$		0			0
$514$	−172.221	−	237.042i	−0.335061	−	0.461172i
$515$	−114.472	+	352.309i	−0.222276	+	0.684095i
$516$		0			0
$517$	287.207	−	85.2675i	0.555525	−	0.164928i
$518$	291.246			0.562251
$519$		0			0
$520$	92.3607	−	67.1040i	0.177617	−	0.129046i
$521$	−564.504	−	410.136i	−1.08350	−	0.787210i	−0.105212	−	0.994450i	$-0.533552\pi$
$521$	−564.504	−	410.136i	−1.08350	−	0.787210i	−0.978290	+	0.207240i	$0.933552\pi$
$522$		0			0
$523$	−353.526	+	114.868i	−0.675959	+	0.219632i	−0.626825	−	0.779160i	$-0.715646\pi$
$523$	−353.526	+	114.868i	−0.675959	+	0.219632i	−0.0491334	+	0.998792i	$0.515646\pi$
$524$	289.665	−	398.689i	0.552795	−	0.760857i
$525$		0			0
$526$	9.57857	−	29.4798i	0.0182102	−	0.0560452i
$527$		−	108.881i		−	0.206606i
$528$		0			0
$529$	−521.361			−0.985559
$530$	−31.6718	−	10.2908i	−0.0597582	−	0.0194166i
$531$		0			0
$532$	−58.0132	−	42.1490i	−0.109047	−	0.0792275i
$533$	−113.992	−	350.831i	−0.213868	−	0.658219i
$534$		0			0
$535$	199.443	−	274.509i	0.372790	−	0.513102i
$536$	122.832	+	169.064i	0.229164	+	0.315417i
$537$		0			0
$538$			297.878i			0.553676i
$539$	14.1120	−	551.948i	0.0261819	−	1.02402i
$540$		0			0
$541$	−64.3657	−	20.9137i	−0.118975	−	0.0386575i	0.248924	−	0.968523i	$-0.419923\pi$
$541$	−64.3657	−	20.9137i	−0.118975	−	0.0386575i	−0.367900	+	0.929866i	$0.619923\pi$
$542$	−136.400	+	99.1005i	−0.251661	+	0.182842i
$543$		0			0
$544$	−136.671	−	420.630i	−0.251233	−	0.773217i
$545$	357.889	−	116.285i	0.656676	−	0.213367i
$546$		0			0
$547$	−436.380	−	600.625i	−0.797769	−	1.09804i	−0.993097	−	0.117297i	$-0.962577\pi$
$547$	−436.380	−	600.625i	−0.797769	−	1.09804i	0.195328	−	0.980738i	$-0.437423\pi$
$548$	−17.4433	+	53.6850i	−0.0318309	+	0.0979653i
$549$		0			0
$550$	71.9042	+	1.83843i	0.130735	+	0.00334259i
$551$	58.9443			0.106977
$552$		0			0
$553$	−31.7082	+	23.0374i	−0.0573385	+	0.0416589i
$554$	180.036	+	130.804i	0.324975	+	0.236108i
$555$		0			0
$556$	747.807	−	242.977i	1.34498	−	0.437010i
$557$	441.323	−	607.429i	0.792322	−	1.09054i	−0.201494	−	0.979490i	$-0.564579\pi$
$557$	441.323	−	607.429i	0.792322	−	1.09054i	0.993815	−	0.111047i	$-0.0354205\pi$
$558$		0			0
$559$	37.4671	−	115.312i	0.0670252	−	0.206282i
$560$		−	396.164i		−	0.707435i
$561$		0			0
$562$	94.0507			0.167350
$563$	991.673	+	322.214i	1.76141	+	0.572316i	0.997345	−	0.0728240i	$-0.0232011\pi$
$563$	991.673	+	322.214i	1.76141	+	0.572316i	0.764064	+	0.645140i	$0.223201\pi$
$564$		0			0
$565$	27.4853	+	19.9692i	0.0486465	+	0.0353438i
$566$	−94.7214	−	291.522i	−0.167352	−	0.515057i
$567$		0			0
$568$	−243.530	+	335.190i	−0.428750	+	0.590123i
$569$	136.967	+	188.518i	0.240714	+	0.331315i	0.912232	−	0.409673i	$-0.134357\pi$
$569$	136.967	+	188.518i	0.240714	+	0.331315i	−0.671518	+	0.740988i	$0.734357\pi$
$570$		0			0
$571$		−	196.324i		−	0.343825i	−0.985112	−	0.171912i	$-0.945005\pi$
$571$		−	196.324i		−	0.343825i	0.985112	−	0.171912i	$-0.0549946\pi$
$572$	57.1478	+	192.491i	0.0999088	+	0.336523i
$573$		0			0
$574$	482.877	+	156.896i	0.841250	+	0.273339i
$575$	20.1246	−	14.6214i	0.0349993	−	0.0254285i
$576$		0			0
$577$	43.9884	+	135.382i	0.0762364	+	0.234631i	0.981911	−	0.189341i	$-0.0606352\pi$
$577$	43.9884	+	135.382i	0.0762364	+	0.234631i	−0.905675	+	0.423973i	$0.860635\pi$
$578$	−38.3134	+	12.4488i	−0.0662862	+	0.0215377i
$579$		0			0
$580$	232.053	+	319.393i	0.400091	+	0.550678i
$581$	−256.199	+	788.498i	−0.440961	+	1.35714i
$582$		0			0
$583$	76.6718	−	100.049i	0.131513	−	0.171610i
$584$	−558.464			−0.956274
$585$		0			0
$586$	37.8998	−	27.5358i	0.0646754	−	0.0469894i
$587$	−193.847	−	140.838i	−0.330233	−	0.239929i	0.410296	−	0.911952i	$-0.365425\pi$
$587$	−193.847	−	140.838i	−0.330233	−	0.239929i	−0.740530	+	0.672024i	$0.765425\pi$
$588$		0			0
$589$	−14.0507	+	4.56535i	−0.0238552	+	0.00775102i
$590$	−3.87849	+	5.33829i	−0.00657372	+	0.00904795i
$591$		0			0
$592$	−123.684	+	380.660i	−0.208925	+	0.643006i
$593$			598.782i			1.00975i	0.863192	+	0.504875i	$0.168462\pi$
$593$			598.782i			1.00975i	−0.863192	+	0.504875i	$0.831538\pi$
$594$		0			0
$595$	608.827			1.02324
$596$	−221.858	−	72.0860i	−0.372245	−	0.120950i
$597$		0			0
$598$	−8.54102	−	6.20541i	−0.0142826	−	0.0103769i
$599$	−93.8359	−	288.797i	−0.156654	−	0.482132i	0.841670	−	0.539992i	$-0.181573\pi$
$599$	−93.8359	−	288.797i	−0.156654	−	0.482132i	−0.998325	+	0.0578592i	$0.981573\pi$
$600$		0			0
$601$	−107.416	+	147.845i	−0.178729	+	0.245999i	−0.888977	−	0.457953i	$-0.848583\pi$
$601$	−107.416	+	147.845i	−0.178729	+	0.245999i	0.710248	+	0.703952i	$0.248583\pi$
$602$	98.0902	+	135.010i	0.162940	+	0.224268i
$603$		0			0
$604$		−	349.036i		−	0.577874i
$605$	172.892	−	452.067i	0.285771	−	0.747218i
$606$		0			0
$607$	−769.237	−	249.940i	−1.26728	−	0.411763i	−0.403195	−	0.915114i	$-0.632100\pi$
$607$	−769.237	−	249.940i	−1.26728	−	0.411763i	−0.864082	+	0.503351i	$0.832100\pi$
$608$	−48.5501	+	35.2737i	−0.0798522	+	0.0580160i
$609$		0			0
$610$	−20.3081	−	62.5018i	−0.0332919	−	0.102462i
$611$	−136.180	+	44.2477i	−0.222881	+	0.0724185i
$612$		0			0
$613$	701.597	+	965.666i	1.14453	+	1.57531i	0.756946	+	0.653478i	$0.226691\pi$
$613$	701.597	+	965.666i	1.14453	+	1.57531i	0.387585	+	0.921834i	$0.373309\pi$
$614$	80.0420	−	246.344i	0.130362	−	0.401212i
$615$		0			0
$616$	−560.766	−	198.188i	−0.910334	−	0.321733i
$617$	−107.900			−0.174878			−0.0874390	−	0.996170i	$-0.527868\pi$
$617$	−107.900			−0.174878			−0.0874390	+	0.996170i	$0.527868\pi$
$618$		0			0
$619$	457.719	−	332.552i	0.739449	−	0.537241i	−0.153089	−	0.988212i	$-0.548922\pi$
$619$	457.719	−	332.552i	0.739449	−	0.537241i	0.892539	+	0.450971i	$0.148922\pi$
$620$	−80.0526	−	58.1616i	−0.129117	−	0.0938091i
$621$		0			0
$622$	−383.643	+	124.653i	−0.616790	+	0.200407i
$623$	−721.792	+	993.462i	−1.15857	+	1.59464i
$624$		0			0
$625$	−98.5764	+	303.387i	−0.157722	+	0.485419i
$626$		−	240.768i		−	0.384614i
$627$		0			0
$628$	−856.298			−1.36353
$629$	−585.000	−	190.078i	−0.930048	−	0.302191i
$630$		0			0
$631$	−558.872	−	406.044i	−0.885693	−	0.643494i	0.0490585	−	0.998796i	$-0.484378\pi$
$631$	−558.872	−	406.044i	−0.885693	−	0.643494i	−0.934751	+	0.355302i	$0.884378\pi$
$632$	6.60177	+	20.3182i	0.0104458	+	0.0321490i
$633$		0			0
$634$	220.755	−	303.843i	0.348193	−	0.479247i
$635$	442.610	+	609.200i	0.697023	+	0.959371i
$636$		0			0
$637$			263.883i			0.414259i
$638$	217.782	−	64.6564i	0.341351	−	0.101342i
$639$		0			0
$640$	−492.207	−	159.928i	−0.769073	−	0.249887i
$641$	624.756	−	453.912i	0.974659	−	0.708131i	0.0181501	−	0.999835i	$-0.494222\pi$
$641$	624.756	−	453.912i	0.974659	−	0.708131i	0.956509	+	0.291704i	$0.0942223\pi$
$642$		0			0
$643$	291.864	+	898.264i	0.453909	+	1.39699i	0.872411	+	0.488773i	$0.162555\pi$
$643$	291.864	+	898.264i	0.453909	+	1.39699i	−0.418502	+	0.908216i	$0.637445\pi$
$644$	−90.9017	+	29.5358i	−0.141152	+	0.0458630i
$645$		0			0
$646$	−13.5333	−	18.6269i	−0.0209493	−	0.0288343i
$647$	301.400	−	927.614i	0.465843	−	1.43372i	−0.392077	−	0.919932i	$-0.628243\pi$
$647$	301.400	−	927.614i	0.465843	−	1.43372i	0.857920	−	0.513784i	$-0.171757\pi$
$648$		0			0
$649$	−14.1591	−	20.5743i	−0.0218167	−	0.0317016i
$650$	−34.3769			−0.0528876
$651$		0			0
$652$	−489.796	+	355.858i	−0.751221	+	0.545794i
$653$	194.615	+	141.396i	0.298032	+	0.216533i	0.726744	−	0.686908i	$-0.241033\pi$
$653$	194.615	+	141.396i	0.298032	+	0.216533i	−0.428712	+	0.903441i	$0.641033\pi$
$654$		0			0
$655$	539.941	−	175.438i	0.824338	−	0.267844i
$656$	−410.128	+	564.493i	−0.625195	+	0.860507i
$657$		0			0
$658$	60.9017	−	187.436i	0.0925558	−	0.284857i
$659$			937.713i			1.42293i	0.702720	+	0.711467i	$0.251969\pi$
$659$			937.713i			1.42293i	−0.702720	+	0.711467i	$0.748031\pi$
$660$		0			0
$661$	133.305			0.201672			0.100836	−	0.994903i	$-0.467848\pi$
$661$	133.305			0.201672			0.100836	+	0.994903i	$0.467848\pi$
$662$	144.335	+	46.8973i	0.218029	+	0.0708418i
$663$		0			0
$664$	365.608	+	265.630i	0.550615	+	0.400045i
$665$	−25.5279	−	78.5667i	−0.0383878	−	0.118145i
$666$		0			0
$667$	46.1803	−	63.5618i	0.0692359	−	0.0952950i
$668$	503.995	+	693.689i	0.754483	+	1.03846i
$669$		0			0
$670$			111.868i			0.166968i
$671$	248.666	+	6.35781i	0.370590	+	0.00947513i
$672$		0			0
$673$	860.230	+	279.506i	1.27820	+	0.415313i	0.867947	−	0.496657i	$-0.165439\pi$
$673$	860.230	+	279.506i	1.27820	+	0.415313i	0.410256	+	0.911971i	$0.365439\pi$
$674$	−79.3090	+	57.6214i	−0.117669	+	0.0854917i
$675$		0			0
$676$	151.673	+	466.801i	0.224368	+	0.690534i
$677$	−574.798	+	186.763i	−0.849037	+	0.275869i	−0.701043	−	0.713119i	$-0.747282\pi$
$677$	−574.798	+	186.763i	−0.849037	+	0.275869i	−0.147995	+	0.988988i	$0.547282\pi$
$678$		0			0
$679$	453.156	+	623.716i	0.667387	+	0.918580i
$680$	102.551	−	315.620i	0.150810	−	0.464147i
$681$		0			0
$682$	−46.9055	+	32.2800i	−0.0687764	+	0.0473313i
$683$	−1261.32			−1.84673			−0.923367	−	0.383919i	$-0.874574\pi$
$683$	−1261.32			−1.84673			−0.923367	+	0.383919i	$0.874574\pi$
$684$		0			0
$685$	−52.6099	+	38.2233i	−0.0768028	+	0.0558005i
$686$	−6.98684	−	5.07624i	−0.0101849	−	0.00739977i
$687$		0			0
$688$	−218.114	+	70.8695i	−0.317026	+	0.103008i
$689$	−35.4102	+	48.7380i	−0.0513936	+	0.0707372i
$690$		0			0
$691$	−132.915	+	409.071i	−0.192352	+	0.591999i	0.807645	+	0.589669i	$0.200742\pi$
$691$	−132.915	+	409.071i	−0.192352	+	0.591999i	−0.999997	+	0.00232993i	$0.999258\pi$
$692$		−	172.732i		−	0.249612i
$693$		0			0
$694$	68.8603			0.0992224
$695$	861.495	+	279.917i	1.23956	+	0.402758i
$696$		0			0
$697$	−867.516	−	630.287i	−1.24464	−	0.904286i
$698$	−38.5774	−	118.729i	−0.0552685	−	0.170099i
$699$		0			0
$700$	−182.936	+	251.790i	−0.261337	+	0.359700i
$701$	299.098	+	411.673i	0.426674	+	0.587266i	0.967186	−	0.254070i	$-0.0817694\pi$
$701$	299.098	+	411.673i	0.426674	+	0.587266i	−0.540512	+	0.841336i	$0.681769\pi$
$702$		0			0
$703$			83.4619i			0.118722i
$704$	125.461	−	163.713i	0.178212	−	0.232548i
$705$		0			0
$706$	82.6722	+	26.8618i	0.117099	+	0.0380479i
$707$	907.866	−	659.603i	1.28411	−	0.932961i
$708$		0			0
$709$	−227.956	−	701.577i	−0.321518	−	0.989531i	−0.972988	−	0.230856i	$-0.925847\pi$
$709$	−227.956	−	701.577i	−0.321518	−	0.989531i	0.651470	−	0.758674i	$-0.274153\pi$
$710$	−210.938	+	68.5379i	−0.297096	+	0.0965323i
$711$		0			0
$712$	393.438	+	541.521i	0.552582	+	0.760563i
$713$	−6.08514	+	18.7282i	−0.00853457	+	0.0262667i
$714$		0			0
$715$	−77.0820	+	218.101i	−0.107807	+	0.305036i
$716$	−760.222			−1.06176
$717$		0			0
$718$	−274.681	+	199.567i	−0.382564	+	0.277949i
$719$	−425.782	−	309.349i	−0.592187	−	0.430249i	0.250910	−	0.968010i	$-0.419270\pi$
$719$	−425.782	−	309.349i	−0.592187	−	0.430249i	−0.843097	+	0.537762i	$0.819270\pi$
$720$		0			0
$721$	−877.214	+	285.024i	−1.21666	+	0.395318i
$722$	152.329	−	209.663i	0.210982	−	0.290392i
$723$		0			0
$724$	41.7395	−	128.461i	0.0576513	−	0.177432i
$725$		−	255.831i		−	0.352871i
$726$		0			0
$727$	−756.122			−1.04006			−0.520029	−	0.854149i	$-0.674079\pi$
$727$	−756.122			−1.04006			−0.520029	+	0.854149i	$0.674079\pi$
$728$	270.344	+	87.8402i	0.371352	+	0.120660i
$729$		0			0
$730$	−241.862	−	175.723i	−0.331318	−	0.240717i
$731$	−108.913	−	335.199i	−0.148991	−	0.458548i
$732$		0			0
$733$	250.381	−	344.620i	0.341584	−	0.470149i	−0.603320	−	0.797500i	$-0.706156\pi$
$733$	250.381	−	344.620i	0.341584	−	0.470149i	0.944903	+	0.327350i	$0.106156\pi$
$734$	140.426	+	193.279i	0.191316	+	0.263323i
$735$		0			0
$736$			79.9888i			0.108680i
$737$	−399.228	−	141.096i	−0.541693	−	0.191447i
$738$		0			0
$739$	184.618	+	59.9862i	0.249822	+	0.0811721i	0.431251	−	0.902232i	$-0.358072\pi$
$739$	184.618	+	59.9862i	0.249822	+	0.0811721i	−0.181429	+	0.983404i	$0.558072\pi$
$740$	−452.243	+	328.574i	−0.611139	+	0.444019i
$741$		0			0
$742$	−25.6231	−	78.8597i	−0.0345324	−	0.106280i
$743$	−211.584	+	68.7477i	−0.284769	+	0.0925272i	−0.447919	−	0.894074i	$-0.647835\pi$
$743$	−211.584	+	68.7477i	−0.284769	+	0.0925272i	0.163150	+	0.986601i	$0.447835\pi$
$744$		0			0
$745$	−157.961	−	217.415i	−0.212029	−	0.291832i
$746$	−48.0763	+	147.964i	−0.0644454	+	0.198343i
$747$		0			0
$748$	463.291	+	355.041i	0.619373	+	0.474654i
$749$	844.853			1.12797
$750$		0			0
$751$	1186.49	−	862.033i	1.57987	−	1.14785i	0.663037	−	0.748587i	$-0.269267\pi$
$751$	1186.49	−	862.033i	1.57987	−	1.14785i	0.916838	−	0.399260i	$-0.130733\pi$
$752$	219.116	+	159.197i	0.291378	+	0.211699i
$753$		0			0
$754$	−103.262	+	33.5520i	−0.136953	+	0.0444986i
$755$	236.348	−	325.305i	0.313044	−	0.430868i
$756$		0			0
$757$	410.832	−	1264.41i	0.542710	−	1.67029i	−0.183663	−	0.982989i	$-0.558795\pi$
$757$	410.832	−	1264.41i	0.542710	−	1.67029i	0.726373	−	0.687301i	$-0.241205\pi$
$758$			232.676i			0.306961i
$759$		0			0
$760$	−45.0294			−0.0592492
$761$	−654.725	−	212.733i	−0.860348	−	0.279544i	−0.154574	−	0.987981i	$-0.549401\pi$
$761$	−654.725	−	212.733i	−0.860348	−	0.279544i	−0.705774	+	0.708437i	$0.749401\pi$
$762$		0			0
$763$	758.020	+	550.734i	0.993473	+	0.721801i
$764$	−128.543	−	395.614i	−0.168250	−	0.517820i
$765$		0			0
$766$	233.835	−	321.847i	0.305268	−	0.420165i
$767$	7.01626	+	9.65706i	0.00914767	+	0.0125907i
$768$		0			0
$769$		−	695.838i		−	0.904860i	−0.891800	−	0.452430i	$-0.850557\pi$
$769$		−	695.838i		−	0.904860i	0.891800	−	0.452430i	$-0.149443\pi$
$770$	−180.498	−	262.280i	−0.234414	−	0.340623i
$771$		0			0
$772$	−96.5023	−	31.3555i	−0.125003	−	0.0406159i
$773$	67.1591	−	48.7939i	0.0868811	−	0.0631228i	−0.543497	−	0.839411i	$-0.682900\pi$
$773$	67.1591	−	48.7939i	0.0868811	−	0.0631228i	0.630378	+	0.776288i	$0.282900\pi$
$774$		0			0
$775$	19.8146	+	60.9832i	0.0255673	+	0.0786880i
$776$	399.668	−	129.860i	0.515036	−	0.167345i
$777$		0			0
$778$	143.716	+	197.808i	0.184725	+	0.254252i
$779$	−44.9615	+	138.377i	−0.0577169	+	0.177634i
$780$		0			0
$781$	21.4571	−	839.225i	0.0274738	−	1.07455i
$782$	−30.6888			−0.0392440
$783$		0			0
$784$	403.811	−	293.386i	0.515065	−	0.374217i
$785$	−798.079	−	579.838i	−1.01666	−	0.738647i
$786$		0			0
$787$	103.159	−	33.5185i	0.131079	−	0.0425903i	−0.242743	−	0.970091i	$-0.578047\pi$
$787$	103.159	−	33.5185i	0.131079	−	0.0425903i	0.373822	+	0.927500i	$0.378047\pi$
$788$	575.601	−	792.246i	0.730458	−	1.00539i
$789$		0			0
$790$	−3.53408	+	10.8768i	−0.00447351	+	0.0137681i
$791$			84.5910i			0.106942i
$792$		0			0
$793$	−118.885			−0.149919
$794$	79.7214	+	25.9030i	0.100405	+	0.0326235i
$795$		0			0
$796$	−498.514	−	362.191i	−0.626273	−	0.455014i
$797$	308.596	+	949.759i	0.387196	+	1.19167i	0.934874	+	0.354979i	$0.115512\pi$
$797$	308.596	+	949.759i	0.387196	+	1.19167i	−0.547678	+	0.836689i	$0.684488\pi$
$798$		0			0
$799$	−244.656	+	336.740i	−0.306202	+	0.421451i
$800$	153.096	+	210.718i	0.191370	+	0.263398i
$801$		0			0
$802$		−	46.3500i		−	0.0577930i
$803$	932.162	−	641.505i	1.16085	−	0.798886i
$804$		0			0
$805$	−104.721	−	34.0260i	−0.130089	−	0.0422684i
$806$	22.0163	−	15.9958i	0.0273155	−	0.0198458i
$807$		0			0
$808$	−189.021	−	581.748i	−0.233937	−	0.719985i
$809$	−71.6823	+	23.2910i	−0.0886060	+	0.0287898i	−0.352985	−	0.935629i	$-0.614833\pi$
$809$	−71.6823	+	23.2910i	−0.0886060	+	0.0287898i	0.264379	+	0.964419i	$0.414833\pi$
$810$		0			0
$811$	−583.402	−	802.984i	−0.719361	−	0.990115i	−0.999545	−	0.0301690i	$-0.990395\pi$
$811$	−583.402	−	802.984i	−0.719361	−	0.990115i	0.280184	−	0.959946i	$-0.409605\pi$
$812$	−303.761	+	934.880i	−0.374090	+	1.15133i
$813$		0			0
$814$	91.5499	+	308.368i	0.112469	+	0.378830i
$815$	−697.463			−0.855783
$816$		0			0
$817$	−38.6894	+	28.1095i	−0.0473555	+	0.0344058i
$818$	−359.538	−	261.220i	−0.439533	−	0.319339i
$819$		0			0
$820$	−926.810	+	301.139i	−1.13026	+	0.367243i
$821$	733.079	−	1009.00i	0.892910	−	1.22898i	−0.0797652	−	0.996814i	$-0.525417\pi$
$821$	733.079	−	1009.00i	0.892910	−	1.22898i	0.972675	−	0.232171i	$-0.0745830\pi$
$822$		0			0
$823$	−165.319	+	508.800i	−0.200874	+	0.618227i	0.798984	+	0.601353i	$0.205371\pi$
$823$	−165.319	+	508.800i	−0.200874	+	0.618227i	−0.999858	+	0.0168738i	$0.994629\pi$
$824$			502.763i			0.610149i
$825$		0			0
$826$	−16.4296			−0.0198905
$827$	−53.4969	−	17.3822i	−0.0646879	−	0.0210184i	0.276494	−	0.961016i	$-0.410827\pi$
$827$	−53.4969	−	17.3822i	−0.0646879	−	0.0210184i	−0.341182	+	0.939997i	$0.610827\pi$
$828$		0			0
$829$	660.320	+	479.751i	0.796526	+	0.578710i	0.909893	−	0.414843i	$-0.136164\pi$
$829$	660.320	+	479.751i	0.796526	+	0.578710i	−0.113367	+	0.993553i	$0.536164\pi$
$830$	74.7577	+	230.081i	0.0900695	+	0.277206i
$831$		0			0
$832$	−57.9431	+	79.7518i	−0.0696431	+	0.0958555i
$833$	450.877	+	620.579i	0.541269	+	0.744993i
$834$		0			0
$835$			987.803i			1.18300i
$836$	26.3911	−	74.6726i	0.0315682	−	0.0893213i
$837$		0			0
$838$	−100.991	−	32.8141i	−0.120515	−	0.0391576i
$839$	49.8216	−	36.1975i	0.0593821	−	0.0431436i	−0.557698	−	0.830044i	$-0.688315\pi$
$839$	49.8216	−	36.1975i	0.0593821	−	0.0431436i	0.617080	+	0.786900i	$0.288315\pi$
$840$		0			0
$841$	10.1913	+	31.3657i	0.0121181	+	0.0372958i
$842$	−410.036	+	133.229i	−0.486979	+	0.158229i
$843$		0			0
$844$	−200.717	−	276.264i	−0.237817	−	0.327327i
$845$	−174.731	+	537.768i	−0.206783	+	0.636412i
$846$		0			0
$847$	1163.66	−	313.344i	1.37386	−	0.369945i
$848$	113.951			0.134376
$849$		0			0
$850$	−80.8450	+	58.7373i	−0.0951118	+	0.0691028i
$851$	90.0000	+	65.3888i	0.105758	+	0.0768376i
$852$		0			0
$853$	1347.24	−	437.746i	1.57942	−	0.513184i	0.617511	−	0.786562i	$-0.288141\pi$
$853$	1347.24	−	437.746i	1.57942	−	0.513184i	0.961907	+	0.273379i	$0.0881412\pi$
$854$	96.1803	−	132.381i	0.112623	−	0.155013i
$855$		0			0
$856$	142.307	−	437.977i	0.166247	−	0.511656i
$857$		−	1249.64i		−	1.45815i	−0.684432	−	0.729077i	$-0.739950\pi$
$857$		−	1249.64i		−	1.45815i	0.684432	−	0.729077i	$-0.260050\pi$
$858$		0			0
$859$	−345.229			−0.401896			−0.200948	−	0.979602i	$-0.564402\pi$
$859$	−345.229			−0.401896			−0.200948	+	0.979602i	$0.564402\pi$
$860$	−304.626	−	98.9790i	−0.354216	−	0.115092i
$861$		0			0
$862$	−102.474	−	74.4518i	−0.118879	−	0.0863710i
$863$	125.242	+	385.456i	0.145124	+	0.446647i	0.997027	−	0.0770535i	$-0.0245512\pi$
$863$	125.242	+	385.456i	0.145124	+	0.446647i	−0.851903	+	0.523700i	$0.824551\pi$
$864$		0			0
$865$	116.964	−	160.988i	0.135219	−	0.186113i
$866$	−265.045	−	364.804i	−0.306057	−	0.421251i
$867$		0			0
$868$		−	246.377i		−	0.283844i
$869$	−34.3588	−	26.3307i	−0.0395383	−	0.0303000i
$870$		0			0
$871$	192.467	+	62.5364i	0.220973	+	0.0717983i
$872$	413.185	−	300.197i	0.473836	−	0.344262i
$873$		0			0
$874$	1.28677	+	3.96027i	0.00147228	+	0.00453121i
$875$	−1288.21	+	418.565i	−1.47224	+	0.478360i
$876$		0			0
$877$	209.069	+	287.759i	0.238391	+	0.328117i	0.911403	−	0.411514i	$-0.135000\pi$
$877$	209.069	+	287.759i	0.238391	+	0.328117i	−0.673012	+	0.739631i	$0.735000\pi$
$878$	−151.946	+	467.642i	−0.173059	+	0.532622i
$879$		0			0
$880$	419.453	−	124.529i	0.476651	−	0.141511i
$881$	883.370			1.00269			0.501345	−	0.865248i	$-0.332839\pi$
$881$	883.370			1.00269			0.501345	+	0.865248i	$0.332839\pi$
$882$		0			0
$883$	−674.512	+	490.062i	−0.763887	+	0.554996i	−0.900100	−	0.435683i	$-0.856507\pi$
$883$	−674.512	+	490.062i	−0.763887	+	0.554996i	0.136213	+	0.990680i	$0.456507\pi$
$884$	−225.689	−	163.973i	−0.255304	−	0.185489i
$885$		0			0
$886$	−179.177	+	58.2180i	−0.202231	+	0.0657088i
$887$	−54.3406	+	74.7934i	−0.0612633	+	0.0843217i	−0.838549	−	0.544826i	$-0.816596\pi$
$887$	−54.3406	+	74.7934i	−0.0612633	+	0.0843217i	0.777286	+	0.629147i	$0.216596\pi$
$888$		0			0
$889$	−579.384	+	1783.16i	−0.651725	+	2.00580i
$890$			358.322i			0.402608i
$891$		0			0
$892$	923.680			1.03552
$893$	53.7132	+	17.4525i	0.0601492	+	0.0195437i
$894$		0			0
$895$	−708.535	−	514.781i	−0.791659	−	0.575174i
$896$	−398.204	−	1225.54i	−0.444424	−	1.36780i
$897$		0			0
$898$	−171.846	+	236.526i	−0.191365	+	0.263392i
$899$	119.039	+	163.844i	0.132413	+	0.182251i
$900$		0			0
$901$			175.121i			0.194363i
$902$	−14.3328	+	560.583i	−0.0158900	+	0.621489i
$903$		0			0
$904$	43.8525	+	14.2486i	0.0485095	+	0.0157617i
$905$	125.889	−	91.4634i	0.139103	−	0.101065i
$906$		0			0
$907$	−454.784	−	1399.68i	−0.501415	−	1.54320i	−0.806715	−	0.590941i	$-0.798757\pi$
$907$	−454.784	−	1399.68i	−0.501415	−	1.54320i	0.305299	−	0.952256i	$-0.401243\pi$
$908$	840.491	−	273.092i	0.925651	−	0.300762i
$909$		0			0
$910$	89.4427	+	123.107i	0.0982887	+	0.135283i
$911$	−54.3525	+	167.280i	−0.0596625	+	0.183622i	−0.976446	−	0.215763i	$-0.930776\pi$
$911$	−54.3525	+	167.280i	−0.0596625	+	0.183622i	0.916783	+	0.399385i	$0.130776\pi$
$912$		0			0
$913$	−915.384	−	23.4043i	−1.00261	−	0.0256345i
$914$	185.795			0.203277
$915$		0			0
$916$	112.941	−	82.0566i	0.123298	−	0.0895814i
$917$	1143.61	+	830.884i	1.24713	+	0.906089i
$918$		0			0
$919$	−1636.12	+	531.609i	−1.78033	+	0.578465i	−0.998960	−	0.0456019i	$-0.985479\pi$
$919$	−1636.12	+	531.609i	−1.78033	+	0.578465i	−0.781371	+	0.624066i	$0.785479\pi$
$920$	−35.2786	+	48.5569i	−0.0383463	+	0.0527792i
$921$		0			0
$922$	−100.195	+	308.368i	−0.108671	+	0.334455i
$923$			401.228i			0.434700i
$924$		0			0
$925$	362.243			0.391614
$926$	50.5322	+	16.4189i	0.0545704	+	0.0177310i
$927$		0			0
$928$	665.535	+	483.539i	0.717171	+	0.521055i
$929$	−288.957	−	889.317i	−0.311040	−	0.957284i	−0.977354	−	0.211612i	$-0.932129\pi$
$929$	−288.957	−	889.317i	−0.311040	−	0.957284i	0.666313	−	0.745672i	$-0.267871\pi$
$930$		0			0
$931$	61.1782	−	84.2046i	0.0657123	−	0.0904453i
$932$	−471.322	−	648.720i	−0.505711	−	0.696051i
$933$		0			0
$934$		−	8.07520i		−	0.00864583i
$935$	191.378	+	644.618i	0.204682	+	0.689431i
$936$		0			0
$937$	−853.544	−	277.333i	−0.910933	−	0.295980i	−0.184191	−	0.982890i	$-0.558967\pi$
$937$	−853.544	−	277.333i	−0.910933	−	0.295980i	−0.726742	+	0.686910i	$0.758967\pi$
$938$	−225.344	+	163.722i	−0.240239	+	0.174544i
$939$		0			0
$940$	116.892	+	359.756i	0.124353	+	0.382719i
$941$	−437.800	+	142.250i	−0.465250	+	0.151169i	−0.532256	−	0.846584i	$-0.678655\pi$
$941$	−437.800	+	142.250i	−0.465250	+	0.151169i	0.0670056	+	0.997753i	$0.478655\pi$
$942$		0			0
$943$	113.992	+	156.896i	0.120882	+	0.166380i
$944$	6.97716	−	21.4735i	0.00739106	−	0.0227473i
$945$		0			0
$946$	−112.113	+	146.295i	−0.118512	+	0.154646i
$947$	−1781.44			−1.88114			−0.940570	−	0.339600i	$-0.889708\pi$
$947$	−1781.44			−1.88114			−0.940570	+	0.339600i	$0.889708\pi$
$948$		0			0
$949$	−437.533	+	317.886i	−0.461046	+	0.334970i
$950$	10.9696	+	7.96990i	0.0115470	+	0.00838937i
$951$		0			0
$952$	785.861	−	255.342i	0.825484	−	0.268216i
$953$	−472.394	+	650.194i	−0.495691	+	0.682260i	−0.981425	−	0.191847i	$-0.938552\pi$
$953$	−472.394	+	650.194i	−0.495691	+	0.682260i	0.485734	+	0.874107i	$0.338552\pi$
$954$		0			0
$955$	148.085	−	455.759i	0.155063	−	0.477235i
$956$			1094.30i			1.14466i
$957$		0			0
$958$	416.760			0.435031
$959$	−153.992	−	50.0350i	−0.160575	−	0.0521741i
$960$		0			0
$961$	736.400	+	535.026i	0.766285	+	0.556738i
$962$	−47.5078	−	146.214i	−0.0493844	−	0.151989i
$963$		0			0
$964$	552.938	−	761.054i	0.573587	−	0.789475i
$965$	−68.7089	−	94.5697i	−0.0712010	−	0.0979997i
$966$		0			0
$967$			915.454i			0.946695i	0.880876	+	0.473347i	$0.156954\pi$
$967$			915.454i			0.946695i	−0.880876	+	0.473347i	$0.843046\pi$
$968$	33.5683	−	656.030i	0.0346780	−	0.677716i
$969$		0			0
$970$	213.951	+	69.5170i	0.220568	+	0.0716670i
$971$	596.366	−	433.285i	0.614177	−	0.446226i	−0.236706	−	0.971581i	$-0.576068\pi$
$971$	596.366	−	433.285i	0.614177	−	0.446226i	0.850883	+	0.525356i	$0.176068\pi$
$972$		0			0
$973$	696.964	+	2145.04i	0.716305	+	2.20456i
$974$	435.902	−	141.633i	0.447538	−	0.145414i
$975$		0			0
$976$	132.177	+	181.926i	0.135427	+	0.186400i
$977$	−59.1165	+	181.942i	−0.0605082	+	0.186225i	−0.976742	−	0.214420i	$-0.931214\pi$
$977$	−59.1165	+	181.942i	−0.0605082	+	0.186225i	0.916233	+	0.400645i	$0.131214\pi$
$978$		0			0
$979$	−1278.75	−	451.941i	−1.30618	−	0.461635i
$980$	697.115			0.711341
$981$		0			0
$982$	256.297	−	186.211i	0.260995	−	0.189624i
$983$	772.503	+	561.257i	0.785863	+	0.570963i	0.906733	−	0.421705i	$-0.138568\pi$
$983$	772.503	+	561.257i	0.785863	+	0.570963i	−0.120870	+	0.992668i	$0.538568\pi$
$984$		0			0
$985$	1072.93	−	348.617i	1.08927	−	0.353926i
$986$	−185.517	+	255.342i	−0.188151	+	0.258967i
$987$		0			0
$988$	−11.6970	+	35.9996i	−0.0118390	+	0.0364368i
$989$			63.7429i			0.0644518i
$990$		0			0
$991$	−1076.02			−1.08580			−0.542898	−	0.839799i	$-0.682673\pi$
$991$	−1076.02			−1.08580			−0.542898	+	0.839799i	$0.682673\pi$
$992$	−196.096	−	63.7156i	−0.197678	−	0.0642294i
$993$		0			0
$994$	−446.774	−	324.600i	−0.449471	−	0.326560i
$995$	−219.364	−	675.132i	−0.220466	−	0.678525i
$996$		0			0
$997$	283.439	−	390.120i	0.284292	−	0.391294i	−0.642858	−	0.765986i	$-0.722251\pi$
$997$	283.439	−	390.120i	0.284292	−	0.391294i	0.927150	+	0.374692i	$0.122251\pi$
$998$	198.712	+	273.504i	0.199111	+	0.274052i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.3.k.a.46.1		4
3.2	odd	2		11.3.d.a.2.1	✓	4
11.4	even	5		1089.3.c.e.604.3		4
11.6	odd	10	inner	99.3.k.a.28.1		4
11.7	odd	10		1089.3.c.e.604.2		4
12.11	even	2		176.3.n.a.145.1		4
15.2	even	4		275.3.q.d.24.2		8
15.8	even	4		275.3.q.d.24.1		8
15.14	odd	2		275.3.x.e.101.1		4
33.2	even	10		121.3.d.c.118.1		4
33.5	odd	10		121.3.d.d.94.1		4
33.8	even	10		121.3.d.a.40.1		4
33.14	odd	10		121.3.d.c.40.1		4
33.17	even	10		11.3.d.a.6.1	yes	4
33.20	odd	10		121.3.d.a.118.1		4
33.26	odd	10		121.3.b.b.120.2		4
33.29	even	10		121.3.b.b.120.3		4
33.32	even	2		121.3.d.d.112.1		4
132.83	odd	10		176.3.n.a.17.1		4
165.17	odd	20		275.3.q.d.149.1		8
165.83	odd	20		275.3.q.d.149.2		8
165.149	even	10		275.3.x.e.226.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.3.d.a.2.1	✓	4	3.2	odd	2
11.3.d.a.6.1	yes	4	33.17	even	10
99.3.k.a.28.1		4	11.6	odd	10	inner
99.3.k.a.46.1		4	1.1	even	1	trivial
121.3.b.b.120.2		4	33.26	odd	10
121.3.b.b.120.3		4	33.29	even	10
121.3.d.a.40.1		4	33.8	even	10
121.3.d.a.118.1		4	33.20	odd	10
121.3.d.c.40.1		4	33.14	odd	10
121.3.d.c.118.1		4	33.2	even	10
121.3.d.d.94.1		4	33.5	odd	10
121.3.d.d.112.1		4	33.32	even	2
176.3.n.a.17.1		4	132.83	odd	10
176.3.n.a.145.1		4	12.11	even	2
275.3.q.d.24.1		8	15.8	even	4
275.3.q.d.24.2		8	15.2	even	4
275.3.q.d.149.1		8	165.17	odd	20
275.3.q.d.149.2		8	165.83	odd	20
275.3.x.e.101.1		4	15.14	odd	2
275.3.x.e.226.1		4	165.149	even	10
1089.3.c.e.604.2		4	11.7	odd	10
1089.3.c.e.604.3		4	11.4	even	5

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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	99.k (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.690983 + 0.224514i) q^{2} +(-2.80902 - 2.04087i) q^{4} +(-1.23607 - 3.80423i) q^{5} +(5.85410 - 8.05748i) q^{7} +(-3.19098 - 4.39201i) q^{8} -2.90617i q^{10} +(10.3713 + 3.66547i) q^{11} +(-5.00000 - 1.62460i) q^{13} +(5.85410 - 4.25325i) q^{14} +(3.07295 + 9.45756i) q^{16} +(-14.5344 + 4.72253i) q^{17} +(1.21885 + 1.67760i) q^{19} +(-4.29180 + 13.2088i) q^{20} +(6.34346 + 4.86128i) q^{22} +2.76393 q^{23} +(7.28115 - 5.29007i) q^{25} +(-3.09017 - 2.24514i) q^{26} +(-32.8885 + 10.6861i) q^{28} +(16.7082 - 22.9969i) q^{29} +(-2.20163 + 6.77591i) q^{31} +28.9402i q^{32} -11.1033 q^{34} +(-37.8885 - 12.3107i) q^{35} +(32.5623 + 23.6579i) q^{37} +(0.465558 + 1.43284i) q^{38} +(-12.7639 + 17.5680i) q^{40} +(41.2426 + 56.7656i) q^{41} +23.0624i q^{43} +(-21.6525 - 31.4629i) q^{44} +(1.90983 + 0.620541i) q^{46} +(22.0344 - 16.0090i) q^{47} +(-15.5106 - 47.7369i) q^{49} +(6.21885 - 2.02063i) q^{50} +(10.7295 + 14.7679i) q^{52} +(3.54102 - 10.8981i) q^{53} +(1.12461 - 43.9856i) q^{55} -54.0689 q^{56} +(16.7082 - 12.1392i) q^{58} +(-1.83688 - 1.33457i) q^{59} +(21.5066 - 6.98791i) q^{61} +(-3.04257 + 4.18774i) q^{62} +(5.79431 - 17.8330i) q^{64} +21.0292i q^{65} -38.4934 q^{67} +(50.4656 + 16.3973i) q^{68} +(-23.4164 - 17.0130i) q^{70} +(-23.5836 - 72.5828i) q^{71} +(60.4656 - 83.2237i) q^{73} +(17.1885 + 23.6579i) q^{74} -7.19991i q^{76} +(90.2492 - 62.1087i) q^{77} +(-3.74265 - 1.21606i) q^{79} +(32.1803 - 23.3804i) q^{80} +(15.7533 + 48.4836i) q^{82} +(-79.1697 + 25.7238i) q^{83} +(35.9311 + 49.4549i) q^{85} +(-5.17783 + 15.9357i) q^{86} +(-16.9959 - 57.2474i) q^{88} -123.297 q^{89} +(-42.3607 + 30.7768i) q^{91} +(-7.76393 - 5.64083i) q^{92} +(18.8197 - 6.11488i) q^{94} +(4.87539 - 6.71040i) q^{95} +(-23.9205 + 73.6196i) q^{97} -36.4677i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 5 q^{2} - 9 q^{4} + 4 q^{5} + 10 q^{7} - 15 q^{8} - q^{11} - 20 q^{13} + 10 q^{14} + 19 q^{16} + 25 q^{19} - 44 q^{20} - 35 q^{22} + 20 q^{23} + 9 q^{25} + 10 q^{26} - 60 q^{28} + 40 q^{29} - 58 q^{31}+ \cdots - 165 q^{97}+O(q^{100}) \) 4 * q + 5 * q^2 - 9 * q^4 + 4 * q^5 + 10 * q^7 - 15 * q^8 - q^11 - 20 * q^13 + 10 * q^14 + 19 * q^16 + 25 * q^19 - 44 * q^20 - 35 * q^22 + 20 * q^23 + 9 * q^25 + 10 * q^26 - 60 * q^28 + 40 * q^29 - 58 * q^31 + 130 * q^34 - 80 * q^35 + 90 * q^37 + 60 * q^38 - 60 * q^40 + 80 * q^41 - 24 * q^44 + 30 * q^46 + 30 * q^47 - 109 * q^49 + 45 * q^50 + 110 * q^52 - 120 * q^53 - 76 * q^55 - 100 * q^56 + 40 * q^58 - 23 * q^59 + 10 * q^61 - 200 * q^62 - 149 * q^64 - 230 * q^67 + 260 * q^68 - 40 * q^70 - 148 * q^71 + 300 * q^73 + 270 * q^74 + 200 * q^77 + 70 * q^79 + 84 * q^80 + 25 * q^82 - 225 * q^83 + 260 * q^85 - 175 * q^86 + 55 * q^88 - 122 * q^89 - 80 * q^91 - 40 * q^92 + 120 * q^94 + 100 * q^95 - 165 * q^97

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