LMFDB - Embedded newform 99.3.k.a.28.1

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			28.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	99.28
Dual form			99.3.k.a.46.1

$q$-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 $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$1$

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	−0.131131	−	0.991365i	$-0.541861\pi$
$2$	0.690983	−	0.224514i	0.345492	−	0.112257i	0.476623	+	0.879108i	$0.341861\pi$
$3$		0			0
$3$		0			0
$4$	−2.80902	+	2.04087i	−0.702254	+	0.510218i
$5$	−1.23607	+	3.80423i	−0.247214	+	0.760845i	0.748051	+	0.663641i	$0.230990\pi$
$5$	−1.23607	+	3.80423i	−0.247214	+	0.760845i	−0.995264	+	0.0972039i	$0.969010\pi$
$6$		0			0
$7$	5.85410	+	8.05748i	0.836300	+	1.15107i	0.986717	+	0.162446i	$0.0519383\pi$
$7$	5.85410	+	8.05748i	0.836300	+	1.15107i	−0.150417	+	0.988623i	$0.548062\pi$
$8$	−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	−0.494941	−	0.868926i	$-0.664810\pi$
$13$	−5.00000	+	1.62460i	−0.384615	+	0.124969i	0.110326	+	0.993895i	$0.464810\pi$
$14$	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	−0.151442	−	0.988466i	$-0.548392\pi$
$17$	−14.5344	−	4.72253i	−0.854967	−	0.277796i	−0.703525	+	0.710670i	$0.748392\pi$
$18$		0			0
$19$	1.21885	−	1.67760i	0.0641498	−	0.0882947i	−0.775737	−	0.631057i	$-0.782621\pi$
$19$	1.21885	−	1.67760i	0.0641498	−	0.0882947i	0.839886	+	0.542762i	$0.182621\pi$
$20$	−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	0.993266	−	0.115855i	$-0.0369609\pi$
$29$	16.7082	+	22.9969i	0.576145	+	0.792996i	−0.417121	+	0.908851i	$0.636961\pi$
$30$		0			0
$31$	−2.20163	−	6.77591i	−0.0710202	−	0.218578i	0.909246	−	0.416259i	$-0.136659\pi$
$31$	−2.20163	−	6.77591i	−0.0710202	−	0.218578i	−0.980266	+	0.197681i	$0.936659\pi$
$32$		−	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	−0.0532056	−	0.998584i	$-0.516944\pi$
$37$	32.5623	−	23.6579i	0.880062	−	0.639403i	0.933268	+	0.359181i	$0.116944\pi$
$38$	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	0.0842954	−	0.996441i	$-0.473136\pi$
$41$	41.2426	−	56.7656i	1.00592	−	1.38453i	0.921623	−	0.388087i	$-0.126864\pi$
$42$		0			0
$43$		−	23.0624i		−	0.536334i	−0.963372	−	0.268167i	$-0.913582\pi$
$43$		−	23.0624i		−	0.536334i	0.963372	−	0.268167i	$-0.0864180\pi$
$44$	−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	0.796980	−	0.604005i	$-0.206429\pi$
$47$	22.0344	+	16.0090i	0.468818	+	0.340616i	−0.328163	+	0.944621i	$0.606429\pi$
$48$		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	0.978889	−	0.204393i	$-0.0655222\pi$
$53$	3.54102	+	10.8981i	0.0668117	+	0.205625i	−0.912077	+	0.410019i	$0.865522\pi$
$54$		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	−0.603243	−	0.797557i	$-0.706125\pi$
$59$	−1.83688	+	1.33457i	−0.0311336	+	0.0226199i	0.572110	+	0.820177i	$0.306125\pi$
$60$		0			0
$61$	21.5066	+	6.98791i	0.352567	+	0.114556i	0.479946	−	0.877298i	$-0.340656\pi$
$61$	21.5066	+	6.98791i	0.352567	+	0.114556i	−0.127379	+	0.991854i	$0.540656\pi$
$62$	−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	0.635939	+	0.771739i	$0.280613\pi$
$71$	−23.5836	+	72.5828i	−0.332163	+	1.02229i	−0.968103	+	0.250554i	$0.919387\pi$
$72$		0			0
$73$	60.4656	+	83.2237i	0.828295	+	1.14005i	0.988238	+	0.152924i	$0.0488691\pi$
$73$	60.4656	+	83.2237i	0.828295	+	1.14005i	−0.159943	+	0.987126i	$0.551131\pi$
$74$	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	−0.332609	−	0.943065i	$-0.607929\pi$
$79$	−3.74265	+	1.21606i	−0.0473753	+	0.0153932i	0.285233	+	0.958458i	$0.407929\pi$
$80$	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	−0.209572	−	0.977793i	$-0.567207\pi$
$83$	−79.1697	−	25.7238i	−0.953852	−	0.309925i	−0.744280	+	0.667868i	$0.767207\pi$
$84$		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	−0.995369	−	0.0961309i	$-0.969353\pi$
$97$	−23.9205	−	73.6196i	−0.246603	−	0.758965i	0.748766	−	0.662835i	$-0.230647\pi$
$98$			36.4677i			0.372119i
$99$		0			0
$100$	−31.2492			−0.312492
$101$	107.159	−	34.8181i	1.06098	−	0.344734i	0.274012	−	0.961726i	$-0.411649\pi$
$101$	107.159	−	34.8181i	1.06098	−	0.344734i	0.786969	+	0.616993i	$0.211649\pi$
$102$		0			0
$103$	−74.9230	+	54.4347i	−0.727408	+	0.528493i	−0.888742	−	0.458407i	$-0.848420\pi$
$103$	−74.9230	+	54.4347i	−0.727408	+	0.528493i	0.161335	+	0.986900i	$0.448420\pi$
$104$	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	−0.509749	−	0.860323i	$-0.670262\pi$
$107$	49.8607	−	68.6273i	0.465988	−	0.641377i	0.975737	+	0.218946i	$0.0702619\pi$
$108$		0			0
$109$		−	94.0766i		−	0.863088i	−0.902092	−	0.431544i	$-0.857969\pi$
$109$		−	94.0766i		−	0.863088i	0.902092	−	0.431544i	$-0.142031\pi$
$110$	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	0.556966	−	0.830535i	$-0.311965\pi$
$113$	−6.87132	−	4.99231i	−0.0608082	−	0.0441797i	−0.617774	+	0.786356i	$0.711965\pi$
$114$		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	−0.497426	−	0.867506i	$-0.665721\pi$
$127$	−179.039	−	58.1734i	−1.40976	−	0.458059i	−0.912334	+	0.409448i	$0.865721\pi$
$128$	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	$-0.817771\pi$
$131$		−	141.932i		−	1.08345i	0.840556	−	0.541725i	$-0.182229\pi$
$132$		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	−0.967716	−	0.252043i	$-0.918898\pi$
$137$	−5.02380	+	15.4617i	−0.0366701	+	0.112859i	0.931046	+	0.364902i	$0.118898\pi$
$138$		0			0
$139$	−133.108	−	183.208i	−0.957614	−	1.31804i	−0.948061	−	0.318088i	$-0.896959\pi$
$139$	−133.108	−	183.208i	−0.957614	−	1.31804i	−0.00955293	−	0.999954i	$-0.503041\pi$
$140$	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	0.515479	−	0.856902i	$-0.327614\pi$
$149$	63.8967	+	20.7613i	0.428837	+	0.139338i	−0.0866427	+	0.996239i	$0.527614\pi$
$150$		0			0
$151$	59.0871	−	81.3264i	0.391305	−	0.538585i	−0.567230	−	0.823559i	$-0.691985\pi$
$151$	59.0871	−	81.3264i	0.391305	−	0.538585i	0.958535	+	0.284974i	$0.0919850\pi$
$152$	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	0.999235	−	0.0391033i	$-0.0124502\pi$
$157$	199.520	+	144.960i	1.27083	+	0.923309i	0.271591	+	0.962413i	$0.412450\pi$
$158$	−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	0.968866	+	0.247586i	$0.0796372\pi$
$163$	53.8820	+	165.832i	0.330564	+	1.01737i	−0.638302	+	0.769786i	$0.720363\pi$
$164$			243.627i			1.48553i
$165$		0			0
$166$	−60.4803			−0.364339
$167$	−234.864	+	76.3120i	−1.40637	+	0.456958i	−0.911246	−	0.411863i	$-0.864878\pi$
$167$	−234.864	+	76.3120i	−1.40637	+	0.456958i	−0.495126	+	0.868821i	$0.664878\pi$
$168$		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	−0.716099	−	0.697999i	$-0.754074\pi$
$173$	29.2411	−	40.2469i	0.169024	−	0.232641i	0.885123	+	0.465357i	$0.154074\pi$
$174$		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	0.959828	−	0.280590i	$-0.0905301\pi$
$179$	177.134	+	128.695i	0.989574	+	0.718967i	0.0297461	+	0.999557i	$0.490530\pi$
$180$		0			0
$181$	12.0213	−	36.9977i	0.0664159	−	0.204407i	−0.912341	−	0.409431i	$-0.865727\pi$
$181$	12.0213	−	36.9977i	0.0664159	−	0.204407i	0.978757	+	0.205024i	$0.0657272\pi$
$182$	−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	−0.304405	−	0.952543i	$-0.598458\pi$
$191$	96.9230	−	70.4187i	0.507450	−	0.368684i	0.811855	+	0.583858i	$0.198458\pi$
$192$		0			0
$193$	27.7933	+	9.03061i	0.144007	+	0.0467907i	0.380134	−	0.924932i	$-0.375878\pi$
$193$	27.7933	+	9.03061i	0.144007	+	0.0467907i	−0.236127	+	0.971722i	$0.575878\pi$
$194$	−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	$-0.746049\pi$
$197$		−	282.037i		−	1.43166i	0.698275	−	0.715830i	$-0.253951\pi$
$198$		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	−0.0788599	−	0.996886i	$-0.525128\pi$
$211$	93.5354	−	30.3915i	0.443296	−	0.144036i	0.522156	+	0.852850i	$0.325128\pi$
$212$	−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	−0.0107791	−	0.999942i	$-0.503431\pi$
$223$	−215.220	−	156.366i	−0.965111	−	0.701194i	−0.954332	+	0.298748i	$0.903431\pi$
$224$	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	0.340393	−	0.940283i	$-0.389440\pi$
$227$	−149.606	−	205.915i	−0.659057	−	0.907114i	−0.999450	+	0.0331697i	$0.989440\pi$
$228$		0			0
$229$	−12.4245	−	38.2388i	−0.0542556	−	0.166982i	0.920257	−	0.391315i	$-0.127980\pi$
$229$	−12.4245	−	38.2388i	−0.0542556	−	0.166982i	−0.974513	+	0.224333i	$0.927980\pi$
$230$			8.03246i			0.0349237i
$231$		0			0
$232$	−154.318			−0.665164
$233$	219.639	−	71.3649i	0.942655	−	0.306287i	0.202928	−	0.979194i	$-0.434954\pi$
$233$	219.639	−	71.3649i	0.942655	−	0.306287i	0.739728	+	0.672906i	$0.234954\pi$
$234$		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	0.220704	+	0.975341i	$0.429164\pi$
$239$	−185.249	+	254.974i	−0.775101	+	1.06684i	−0.995806	+	0.0914947i	$0.970836\pi$
$240$		0			0
$241$		−	270.933i		−	1.12420i	−0.827069	−	0.562101i	$-0.809993\pi$
$241$		−	270.933i		−	1.12420i	0.827069	−	0.562101i	$-0.190007\pi$
$242$	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	0.943968	−	0.330036i	$-0.107061\pi$
$251$	−3.44080	−	10.5897i	−0.0137084	−	0.0421900i	−0.957677	+	0.287846i	$0.907061\pi$
$252$		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	−0.999182	−	0.0404281i	$-0.987128\pi$
$257$	−326.261	+	237.042i	−1.26950	+	0.922344i	−0.270315	+	0.962772i	$0.587128\pi$
$258$		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	$0.0258463\pi$
$263$			42.6636i			0.162219i	−0.996705	+	0.0811094i	$0.974154\pi$
$264$		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	−0.380311	−	0.924859i	$-0.624183\pi$
$269$	126.695	−	389.927i	0.470985	−	1.44954i	0.851296	−	0.524685i	$-0.175817\pi$
$270$		0			0
$271$	−136.400	−	187.739i	−0.503322	−	0.692763i	0.479454	−	0.877567i	$-0.340835\pi$
$271$	−136.400	−	187.739i	−0.503322	−	0.692763i	−0.982775	+	0.184804i	$0.940835\pi$
$272$	−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	0.268330	−	0.963327i	$-0.413528\pi$
$277$	291.305	−	94.6507i	1.05164	−	0.341699i	0.783313	+	0.621628i	$0.213528\pi$
$278$	−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	0.519772	−	0.854305i	$-0.326017\pi$
$281$	123.114	+	40.0022i	0.438128	+	0.142356i	−0.0816438	+	0.996662i	$0.526017\pi$
$282$		0			0
$283$	−247.984	+	341.320i	−0.876268	+	1.20608i	0.101173	+	0.994869i	$0.467740\pi$
$283$	−247.984	+	341.320i	−0.876268	+	1.20608i	−0.977441	+	0.211210i	$0.932260\pi$
$284$	−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	0.868780	−	0.495198i	$-0.164905\pi$
$293$	37.8998	+	52.1646i	0.129351	+	0.178036i	−0.739429	+	0.673234i	$0.764905\pi$
$294$		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	$0.197197\pi$
$307$			356.512i			1.16128i	−0.814161	+	0.580639i	$0.802803\pi$
$308$	−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	−0.987122	−	0.159970i	$-0.948860\pi$
$311$	−449.177	−	326.346i	−1.44430	−	1.04935i	−0.457178	−	0.889375i	$-0.651140\pi$
$312$		0			0
$313$	−102.405	+	315.170i	−0.327172	+	1.00693i	0.643279	+	0.765632i	$0.277574\pi$
$313$	−102.405	+	315.170i	−0.327172	+	1.00693i	−0.970451	+	0.241300i	$0.922426\pi$
$314$	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	0.802595	+	0.596524i	$0.203452\pi$
$317$	159.740	+	491.628i	0.503910	+	1.55088i	−0.298685	+	0.954352i	$0.596548\pi$
$318$		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	0.674971	−	0.737844i	$-0.264156\pi$
$337$	−79.3090	−	109.159i	−0.235338	−	0.323915i	−0.910309	+	0.413929i	$0.864156\pi$
$338$	−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	0.436005	−	0.899944i	$-0.356393\pi$
$347$	90.1393	+	29.2880i	0.259767	+	0.0844036i	−0.176238	+	0.984348i	$0.556393\pi$
$348$		0			0
$349$	−100.997	+	139.010i	−0.289389	+	0.398310i	−0.928816	−	0.370542i	$-0.879172\pi$
$349$	−100.997	+	139.010i	−0.289389	+	0.398310i	0.639426	+	0.768852i	$0.279172\pi$
$350$	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	−0.996770	−	0.0803065i	$-0.974410\pi$
$359$	−274.681	−	378.066i	−0.765127	−	1.05311i	0.231643	−	0.972801i	$-0.425590\pi$
$360$		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	−0.163068	−	0.986615i	$-0.552139\pi$
$367$	266.026	−	193.279i	0.724867	−	0.526647i	0.887936	+	0.459968i	$0.152139\pi$
$368$	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	$-0.907327\pi$
$373$		−	214.135i		−	0.574088i	0.957917	−	0.287044i	$-0.0926726\pi$
$374$	−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	−0.731447	−	0.681899i	$-0.761154\pi$
$379$	98.9630	−	304.577i	0.261116	−	0.803633i	0.992563	−	0.121734i	$-0.0388456\pi$
$380$	−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	0.885968	+	0.463746i	$0.153495\pi$
$383$	169.205	+	520.759i	0.441788	+	1.35968i	−0.444181	+	0.895937i	$0.646505\pi$
$384$		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	−0.180003	−	0.983666i	$-0.557611\pi$
$389$	272.259	−	197.808i	0.699895	−	0.508504i	0.879898	+	0.475162i	$0.157611\pi$
$390$		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	−0.972624	−	0.232386i	$-0.925347\pi$
$401$	−19.7138	+	60.6729i	−0.0491617	+	0.151304i	0.923462	+	0.383690i	$0.125347\pi$
$402$		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	−0.916351	−	0.400377i	$-0.868879\pi$
$409$	−581.745	+	189.020i	−1.42236	+	0.462152i	−0.506008	+	0.862529i	$0.668879\pi$
$410$	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	−0.153165	−	0.988201i	$-0.548947\pi$
$421$	−480.079	−	348.798i	−1.14033	−	0.828498i	−0.987165	+	0.159702i	$0.948947\pi$
$422$	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	−0.494982	−	0.868903i	$-0.664825\pi$
$431$	−165.807	+	53.8738i	−0.384702	+	0.124997i	0.110280	+	0.993901i	$0.464825\pi$
$432$		0			0
$433$	−502.109	+	364.804i	−1.15961	+	0.842503i	−0.989728	−	0.142962i	$-0.954337\pi$
$433$	−502.109	+	364.804i	−1.15961	+	0.842503i	−0.169878	+	0.985465i	$0.554337\pi$
$434$	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	$-0.719848\pi$
$439$		−	676.778i		−	1.54164i	0.637055	−	0.770818i	$-0.280152\pi$
$440$	−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	0.325272	−	0.945621i	$-0.394544\pi$
$443$	−209.784	−	152.417i	−0.473552	−	0.344056i	−0.798824	+	0.601565i	$0.794544\pi$
$444$		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	−0.988698	−	0.149923i	$-0.952098\pi$
$449$	−124.349	−	382.707i	−0.276947	−	0.852354i	0.711751	−	0.702432i	$-0.247902\pi$
$450$		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	0.562769	−	0.826614i	$-0.309736\pi$
$457$	243.209	+	79.0234i	0.532186	+	0.172918i	−0.0305823	+	0.999532i	$0.509736\pi$
$458$	−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	$-0.839173\pi$
$461$		−	446.274i		−	0.968056i	0.875053	−	0.484028i	$-0.160827\pi$
$462$		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	−0.954666	−	0.297678i	$-0.903788\pi$
$467$	−3.43459	+	10.5706i	−0.00735458	+	0.0226351i	0.947312	+	0.320313i	$0.103788\pi$
$468$		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	0.816962	−	0.576692i	$-0.195657\pi$
$479$	545.546	+	177.259i	1.13893	+	0.370060i	0.321965	+	0.946752i	$0.395657\pi$
$480$		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	0.971826	−	0.235700i	$-0.0757383\pi$
$487$	510.363	+	370.800i	1.04797	+	0.761397i	0.0761466	+	0.997097i	$0.475738\pi$
$488$	−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	0.985883	−	0.167433i	$-0.0535479\pi$
$491$	256.297	+	352.763i	0.521990	+	0.718458i	−0.463893	+	0.885891i	$0.653548\pi$
$492$		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	−0.142787	−	0.989753i	$-0.545606\pi$
$499$	376.446	−	273.504i	0.754401	−	0.548105i	0.897188	+	0.441649i	$0.145606\pi$
$500$	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	−0.988162	−	0.153415i	$-0.950973\pi$
$503$	−270.059	+	371.704i	−0.536896	+	0.738974i	0.451265	+	0.892390i	$0.350973\pi$
$504$		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	0.379861	−	0.925044i	$-0.375972\pi$
$509$	−194.705	−	141.462i	−0.382525	−	0.277920i	−0.762385	+	0.647123i	$0.775972\pi$
$510$		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	−0.978290	−	0.207240i	$-0.933552\pi$
$521$	−564.504	+	410.136i	−1.08350	+	0.787210i	−0.105212	+	0.994450i	$0.533552\pi$
$522$		0			0
$523$	−353.526	−	114.868i	−0.675959	−	0.219632i	−0.0491334	−	0.998792i	$-0.515646\pi$
$523$	−353.526	−	114.868i	−0.675959	−	0.219632i	−0.626825	+	0.779160i	$0.715646\pi$
$524$	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	−0.367900	−	0.929866i	$-0.619923\pi$
$541$	−64.3657	+	20.9137i	−0.118975	+	0.0386575i	0.248924	+	0.968523i	$0.419923\pi$
$542$	−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	0.195328	+	0.980738i	$0.437423\pi$
$547$	−436.380	+	600.625i	−0.797769	+	1.09804i	−0.993097	+	0.117297i	$0.962577\pi$
$548$	−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	0.993815	+	0.111047i	$0.0354205\pi$
$557$	441.323	+	607.429i	0.792322	+	1.09054i	−0.201494	+	0.979490i	$0.564579\pi$
$558$		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	0.764064	−	0.645140i	$-0.223201\pi$
$563$	991.673	−	322.214i	1.76141	−	0.572316i	0.997345	+	0.0728240i	$0.0232011\pi$
$564$		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	−0.671518	−	0.740988i	$-0.734357\pi$
$569$	136.967	−	188.518i	0.240714	−	0.331315i	0.912232	+	0.409673i	$0.134357\pi$
$570$		0			0
$571$			196.324i			0.343825i	0.985112	+	0.171912i	$0.0549946\pi$
$571$			196.324i			0.343825i	−0.985112	+	0.171912i	$0.945005\pi$
$572$	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	−0.905675	−	0.423973i	$-0.860635\pi$
$577$	43.9884	−	135.382i	0.0762364	−	0.234631i	0.981911	+	0.189341i	$0.0606352\pi$
$578$	−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	−0.740530	−	0.672024i	$-0.765425\pi$
$587$	−193.847	+	140.838i	−0.330233	+	0.239929i	0.410296	+	0.911952i	$0.365425\pi$
$588$		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	$-0.831538\pi$
$593$		−	598.782i		−	1.00975i	0.863192	−	0.504875i	$-0.168462\pi$
$594$		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	−0.998325	−	0.0578592i	$-0.981573\pi$
$599$	−93.8359	+	288.797i	−0.156654	+	0.482132i	0.841670	+	0.539992i	$0.181573\pi$
$600$		0			0
$601$	−107.416	−	147.845i	−0.178729	−	0.245999i	0.710248	−	0.703952i	$-0.248583\pi$
$601$	−107.416	−	147.845i	−0.178729	−	0.245999i	−0.888977	+	0.457953i	$0.848583\pi$
$602$	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	−0.864082	−	0.503351i	$-0.832100\pi$
$607$	−769.237	+	249.940i	−1.26728	+	0.411763i	−0.403195	+	0.915114i	$0.632100\pi$
$608$	−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	0.387585	−	0.921834i	$-0.373309\pi$
$613$	701.597	−	965.666i	1.14453	−	1.57531i	0.756946	−	0.653478i	$-0.226691\pi$
$614$	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	0.892539	−	0.450971i	$-0.148922\pi$
$619$	457.719	+	332.552i	0.739449	+	0.537241i	−0.153089	+	0.988212i	$0.548922\pi$
$620$	−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	−0.934751	−	0.355302i	$-0.884378\pi$
$631$	−558.872	+	406.044i	−0.885693	+	0.643494i	0.0490585	+	0.998796i	$0.484378\pi$
$632$	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	0.956509	−	0.291704i	$-0.0942223\pi$
$641$	624.756	+	453.912i	0.974659	+	0.708131i	0.0181501	+	0.999835i	$0.494222\pi$
$642$		0			0
$643$	291.864	−	898.264i	0.453909	−	1.39699i	−0.418502	−	0.908216i	$-0.637445\pi$
$643$	291.864	−	898.264i	0.453909	−	1.39699i	0.872411	−	0.488773i	$-0.162555\pi$
$644$	−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	0.857920	+	0.513784i	$0.171757\pi$
$647$	301.400	+	927.614i	0.465843	+	1.43372i	−0.392077	+	0.919932i	$0.628243\pi$
$648$		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	−0.428712	−	0.903441i	$-0.641033\pi$
$653$	194.615	−	141.396i	0.298032	−	0.216533i	0.726744	+	0.686908i	$0.241033\pi$
$654$		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	$-0.748031\pi$
$659$		−	937.713i		−	1.42293i	0.702720	−	0.711467i	$-0.251969\pi$
$660$		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	0.410256	−	0.911971i	$-0.365439\pi$
$673$	860.230	−	279.506i	1.27820	−	0.415313i	0.867947	+	0.496657i	$0.165439\pi$
$674$	−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	−0.147995	−	0.988988i	$-0.547282\pi$
$677$	−574.798	−	186.763i	−0.849037	−	0.275869i	−0.701043	+	0.713119i	$0.747282\pi$
$678$		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	−0.999997	−	0.00232993i	$-0.999258\pi$
$691$	−132.915	−	409.071i	−0.192352	−	0.591999i	0.807645	−	0.589669i	$-0.200742\pi$
$692$			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	−0.540512	−	0.841336i	$-0.681769\pi$
$701$	299.098	−	411.673i	0.426674	−	0.587266i	0.967186	+	0.254070i	$0.0817694\pi$
$702$		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	0.651470	+	0.758674i	$0.274153\pi$
$709$	−227.956	+	701.577i	−0.321518	+	0.989531i	−0.972988	+	0.230856i	$0.925847\pi$
$710$	−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	−0.843097	−	0.537762i	$-0.819270\pi$
$719$	−425.782	+	309.349i	−0.592187	+	0.430249i	0.250910	+	0.968010i	$0.419270\pi$
$720$		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	0.944903	−	0.327350i	$-0.106156\pi$
$733$	250.381	+	344.620i	0.341584	+	0.470149i	−0.603320	+	0.797500i	$0.706156\pi$
$734$	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	−0.181429	−	0.983404i	$-0.558072\pi$
$739$	184.618	−	59.9862i	0.249822	−	0.0811721i	0.431251	+	0.902232i	$0.358072\pi$
$740$	−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	0.163150	−	0.986601i	$-0.447835\pi$
$743$	−211.584	−	68.7477i	−0.284769	−	0.0925272i	−0.447919	+	0.894074i	$0.647835\pi$
$744$		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	0.916838	+	0.399260i	$0.130733\pi$
$751$	1186.49	+	862.033i	1.57987	+	1.14785i	0.663037	+	0.748587i	$0.269267\pi$
$752$	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	0.726373	+	0.687301i	$0.241205\pi$
$757$	410.832	+	1264.41i	0.542710	+	1.67029i	−0.183663	+	0.982989i	$0.558795\pi$
$758$		−	232.676i		−	0.306961i
$759$		0			0
$760$	−45.0294			−0.0592492
$761$	−654.725	+	212.733i	−0.860348	+	0.279544i	−0.705774	−	0.708437i	$-0.749401\pi$
$761$	−654.725	+	212.733i	−0.860348	+	0.279544i	−0.154574	+	0.987981i	$0.549401\pi$
$762$		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	$0.149443\pi$
$769$			695.838i			0.904860i	−0.891800	+	0.452430i	$0.850557\pi$
$770$	−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	0.630378	−	0.776288i	$-0.282900\pi$
$773$	67.1591	+	48.7939i	0.0868811	+	0.0631228i	−0.543497	+	0.839411i	$0.682900\pi$
$774$		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	0.373822	−	0.927500i	$-0.378047\pi$
$787$	103.159	+	33.5185i	0.131079	+	0.0425903i	−0.242743	+	0.970091i	$0.578047\pi$
$788$	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	−0.547678	−	0.836689i	$-0.684488\pi$
$797$	308.596	−	949.759i	0.387196	−	1.19167i	0.934874	−	0.354979i	$-0.115512\pi$
$798$		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	0.264379	−	0.964419i	$-0.414833\pi$
$809$	−71.6823	−	23.2910i	−0.0886060	−	0.0287898i	−0.352985	+	0.935629i	$0.614833\pi$
$810$		0			0
$811$	−583.402	+	802.984i	−0.719361	+	0.990115i	0.280184	+	0.959946i	$0.409605\pi$
$811$	−583.402	+	802.984i	−0.719361	+	0.990115i	−0.999545	+	0.0301690i	$0.990395\pi$
$812$	−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	0.972675	+	0.232171i	$0.0745830\pi$
$821$	733.079	+	1009.00i	0.892910	+	1.22898i	−0.0797652	+	0.996814i	$0.525417\pi$
$822$		0			0
$823$	−165.319	−	508.800i	−0.200874	−	0.618227i	−0.999858	−	0.0168738i	$-0.994629\pi$
$823$	−165.319	−	508.800i	−0.200874	−	0.618227i	0.798984	−	0.601353i	$-0.205371\pi$
$824$		−	502.763i		−	0.610149i
$825$		0			0
$826$	−16.4296			−0.0198905
$827$	−53.4969	+	17.3822i	−0.0646879	+	0.0210184i	−0.341182	−	0.939997i	$-0.610827\pi$
$827$	−53.4969	+	17.3822i	−0.0646879	+	0.0210184i	0.276494	+	0.961016i	$0.410827\pi$
$828$		0			0
$829$	660.320	−	479.751i	0.796526	−	0.578710i	−0.113367	−	0.993553i	$-0.536164\pi$
$829$	660.320	−	479.751i	0.796526	−	0.578710i	0.909893	+	0.414843i	$0.136164\pi$
$830$	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	0.617080	−	0.786900i	$-0.288315\pi$
$839$	49.8216	+	36.1975i	0.0593821	+	0.0431436i	−0.557698	+	0.830044i	$0.688315\pi$
$840$		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	0.961907	−	0.273379i	$-0.0881412\pi$
$853$	1347.24	+	437.746i	1.57942	+	0.513184i	0.617511	+	0.786562i	$0.288141\pi$
$854$	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	$0.260050\pi$
$857$			1249.64i			1.45815i	−0.684432	+	0.729077i	$0.739950\pi$
$858$		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	−0.851903	−	0.523700i	$-0.824551\pi$
$863$	125.242	−	385.456i	0.145124	−	0.446647i	0.997027	+	0.0770535i	$0.0245512\pi$
$864$		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	−0.673012	−	0.739631i	$-0.735000\pi$
$877$	209.069	−	287.759i	0.238391	−	0.328117i	0.911403	+	0.411514i	$0.135000\pi$
$878$	−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	0.136213	−	0.990680i	$-0.456507\pi$
$883$	−674.512	−	490.062i	−0.763887	−	0.554996i	−0.900100	+	0.435683i	$0.856507\pi$
$884$	−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	0.777286	−	0.629147i	$-0.216596\pi$
$887$	−54.3406	−	74.7934i	−0.0612633	−	0.0843217i	−0.838549	+	0.544826i	$0.816596\pi$
$888$		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	0.305299	+	0.952256i	$0.401243\pi$
$907$	−454.784	+	1399.68i	−0.501415	+	1.54320i	−0.806715	+	0.590941i	$0.798757\pi$
$908$	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	0.916783	−	0.399385i	$-0.130776\pi$
$911$	−54.3525	−	167.280i	−0.0596625	−	0.183622i	−0.976446	+	0.215763i	$0.930776\pi$
$912$		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	−0.781371	−	0.624066i	$-0.785479\pi$
$919$	−1636.12	−	531.609i	−1.78033	−	0.578465i	−0.998960	+	0.0456019i	$0.985479\pi$
$920$	−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	0.666313	+	0.745672i	$0.267871\pi$
$929$	−288.957	+	889.317i	−0.311040	+	0.957284i	−0.977354	+	0.211612i	$0.932129\pi$
$930$		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	−0.726742	−	0.686910i	$-0.758967\pi$
$937$	−853.544	+	277.333i	−0.910933	+	0.295980i	−0.184191	+	0.982890i	$0.558967\pi$
$938$	−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	0.0670056	−	0.997753i	$-0.478655\pi$
$941$	−437.800	−	142.250i	−0.465250	−	0.151169i	−0.532256	+	0.846584i	$0.678655\pi$
$942$		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	0.485734	−	0.874107i	$-0.338552\pi$
$953$	−472.394	−	650.194i	−0.495691	−	0.682260i	−0.981425	+	0.191847i	$0.938552\pi$
$954$		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	$-0.843046\pi$
$967$		−	915.454i		−	0.946695i	0.880876	−	0.473347i	$-0.156954\pi$
$968$	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	0.850883	−	0.525356i	$-0.176068\pi$
$971$	596.366	+	433.285i	0.614177	+	0.446226i	−0.236706	+	0.971581i	$0.576068\pi$
$972$		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	0.916233	−	0.400645i	$-0.131214\pi$
$977$	−59.1165	−	181.942i	−0.0605082	−	0.186225i	−0.976742	+	0.214420i	$0.931214\pi$
$978$		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	−0.120870	−	0.992668i	$-0.538568\pi$
$983$	772.503	−	561.257i	0.785863	−	0.570963i	0.906733	+	0.421705i	$0.138568\pi$
$984$		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	0.927150	−	0.374692i	$-0.122251\pi$
$997$	283.439	+	390.120i	0.284292	+	0.391294i	−0.642858	+	0.765986i	$0.722251\pi$
$998$	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.28.1		4
3.2	odd	2		11.3.d.a.6.1	yes	4
11.2	odd	10	inner	99.3.k.a.46.1		4
11.3	even	5		1089.3.c.e.604.2		4
11.8	odd	10		1089.3.c.e.604.3		4
12.11	even	2		176.3.n.a.17.1		4
15.2	even	4		275.3.q.d.149.1		8
15.8	even	4		275.3.q.d.149.2		8
15.14	odd	2		275.3.x.e.226.1		4
33.2	even	10		11.3.d.a.2.1	✓	4
33.5	odd	10		121.3.d.a.40.1		4
33.8	even	10		121.3.b.b.120.2		4
33.14	odd	10		121.3.b.b.120.3		4
33.17	even	10		121.3.d.c.40.1		4
33.20	odd	10		121.3.d.d.112.1		4
33.26	odd	10		121.3.d.c.118.1		4
33.29	even	10		121.3.d.a.118.1		4
33.32	even	2		121.3.d.d.94.1		4
132.35	odd	10		176.3.n.a.145.1		4
165.2	odd	20		275.3.q.d.24.2		8
165.68	odd	20		275.3.q.d.24.1		8
165.134	even	10		275.3.x.e.101.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.3.d.a.2.1	✓	4	33.2	even	10
11.3.d.a.6.1	yes	4	3.2	odd	2
99.3.k.a.28.1		4	1.1	even	1	trivial
99.3.k.a.46.1		4	11.2	odd	10	inner
121.3.b.b.120.2		4	33.8	even	10
121.3.b.b.120.3		4	33.14	odd	10
121.3.d.a.40.1		4	33.5	odd	10
121.3.d.a.118.1		4	33.29	even	10
121.3.d.c.40.1		4	33.17	even	10
121.3.d.c.118.1		4	33.26	odd	10
121.3.d.d.94.1		4	33.32	even	2
121.3.d.d.112.1		4	33.20	odd	10
176.3.n.a.17.1		4	12.11	even	2
176.3.n.a.145.1		4	132.35	odd	10
275.3.q.d.24.1		8	165.68	odd	20
275.3.q.d.24.2		8	165.2	odd	20
275.3.q.d.149.1		8	15.2	even	4
275.3.q.d.149.2		8	15.8	even	4
275.3.x.e.101.1		4	165.134	even	10
275.3.x.e.226.1		4	15.14	odd	2
1089.3.c.e.604.2		4	11.3	even	5
1089.3.c.e.604.3		4	11.8	odd	10

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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