LMFDB - Embedded newform 363.3.h.q.269.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,3,Mod(245,363)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(363, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 8]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("363.245");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	363.h (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$9.89103359628$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			269.5
Character	$\chi$	$=$	363.269
Dual form			363.3.h.q.251.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.73676 - 0.889226i) q^{2} +(-0.444035 - 2.96696i) q^{3} +(3.46304 - 2.51605i) q^{4} +(-4.70571 - 1.52898i) q^{5} +(-3.85351 - 7.72499i) q^{6} +(9.04489 - 6.57149i) q^{7} +(0.474528 - 0.653131i) q^{8} +(-8.60567 + 2.63486i) q^{9} -14.2380 q^{10} +(-9.00271 - 9.15748i) q^{12} +(-5.22225 - 16.0724i) q^{13} +(18.9101 - 26.0275i) q^{14} +(-2.44691 + 14.6406i) q^{15} +(-4.57317 + 14.0748i) q^{16} +(-0.0595216 - 0.0193397i) q^{17} +(-21.2086 + 14.8634i) q^{18} +(-4.35333 - 3.16288i) q^{19} +(-20.1430 + 6.54487i) q^{20} +(-23.5136 - 23.9178i) q^{21} -8.69537i q^{23} +(-2.14852 - 1.11789i) q^{24} +(-0.419501 - 0.304785i) q^{25} +(-28.5840 - 39.3425i) q^{26} +(11.6387 + 24.3627i) q^{27} +(14.7886 - 45.5147i) q^{28} +(29.3632 + 40.4149i) q^{29} +(6.32215 + 42.2435i) q^{30} +(-7.59453 - 23.3736i) q^{31} +45.8150i q^{32} -0.180094 q^{34} +(-52.6103 + 17.0941i) q^{35} +(-23.1723 + 30.7769i) q^{36} +(31.7618 - 23.0763i) q^{37} +(-14.7265 - 4.78493i) q^{38} +(-45.3673 + 22.6309i) q^{39} +(-3.23161 + 2.34790i) q^{40} +(25.8089 - 35.5228i) q^{41} +(-85.6193 - 44.5483i) q^{42} +0.201842 q^{43} +(44.5244 + 0.758975i) q^{45} +(-7.73215 - 23.7971i) q^{46} +(-8.76165 + 12.0594i) q^{47} +(43.7899 + 7.31871i) q^{48} +(23.4836 - 72.2751i) q^{49} +(-1.41909 - 0.461092i) q^{50} +(-0.0309505 + 0.185186i) q^{51} +(-58.5238 - 42.5200i) q^{52} +(93.1486 - 30.2658i) q^{53} +(53.5163 + 56.3252i) q^{54} -9.02585i q^{56} +(-7.45110 + 14.3206i) q^{57} +(116.298 + 84.4953i) q^{58} +(8.51816 + 11.7242i) q^{59} +(28.3625 + 56.8574i) q^{60} +(9.06134 - 27.8879i) q^{61} +(-41.5687 - 57.2145i) q^{62} +(-60.5223 + 80.3841i) q^{63} +(22.4472 + 69.0854i) q^{64} +83.6168i q^{65} +82.8515 q^{67} +(-0.254785 + 0.0827848i) q^{68} +(-25.7988 + 3.86104i) q^{69} +(-128.781 + 93.5648i) q^{70} +(25.3986 + 8.25251i) q^{71} +(-2.36272 + 6.87094i) q^{72} +(-11.3022 + 8.21153i) q^{73} +(66.4042 - 91.3976i) q^{74} +(-0.718012 + 1.37998i) q^{75} -23.0337 q^{76} +(-104.035 + 102.277i) q^{78} +(15.5088 + 47.7311i) q^{79} +(43.0400 - 59.2395i) q^{80} +(67.1150 - 45.3495i) q^{81} +(39.0447 - 120.167i) q^{82} +(-57.2933 - 18.6157i) q^{83} +(-141.607 - 23.6671i) q^{84} +(0.250521 + 0.182014i) q^{85} +(0.552394 - 0.179484i) q^{86} +(106.871 - 105.065i) q^{87} +40.3489i q^{89} +(122.527 - 37.5151i) q^{90} +(-152.854 - 111.055i) q^{91} +(-21.8779 - 30.1124i) q^{92} +(-65.9761 + 32.9113i) q^{93} +(-13.2550 + 40.7946i) q^{94} +(15.6495 + 21.5397i) q^{95} +(135.931 - 20.3435i) q^{96} +(-9.52170 - 29.3048i) q^{97} -218.681i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{3} + 18 q^{4} + 10 q^{6} + 22 q^{9} + 72 q^{10} + 56 q^{12} + 42 q^{13} - 28 q^{15} - 30 q^{16} - 94 q^{18} - 84 q^{19} - 112 q^{21} - 48 q^{24} + 108 q^{25} + 38 q^{27} - 132 q^{28} + 148 q^{30}+ \cdots - 126 q^{97}+O(q^{100}) $ 24 * q - 4 * q^3 + 18 * q^4 + 10 * q^6 + 22 * q^9 + 72 * q^10 + 56 * q^12 + 42 * q^13 - 28 * q^15 - 30 * q^16 - 94 * q^18 - 84 * q^19 - 112 * q^21 - 48 * q^24 + 108 * q^25 + 38 * q^27 - 132 * q^28 + 148 * q^30 + 264 * q^34 - 46 * q^36 + 42 * q^37 + 82 * q^39 + 294 * q^40 + 206 * q^42 - 624 * q^43 - 472 * q^45 + 60 * q^46 + 88 * q^48 - 138 * q^49 - 182 * q^51 - 114 * q^52 + 560 * q^54 + 24 * q^57 + 54 * q^58 + 562 * q^60 - 264 * q^61 + 122 * q^63 - 294 * q^64 + 96 * q^67 - 152 * q^69 - 336 * q^70 + 306 * q^72 - 72 * q^73 - 62 * q^75 - 1632 * q^76 - 776 * q^78 + 250 * q^81 - 798 * q^82 - 328 * q^84 - 330 * q^85 + 1848 * q^87 + 230 * q^90 - 300 * q^91 + 266 * q^93 - 120 * q^94 + 386 * q^96 - 126 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$-1$	$e\left(\frac{2}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.73676	−	0.889226i	1.36838	−	0.444613i	0.469546	−	0.882908i	$-0.344417\pi$
$2$	2.73676	−	0.889226i	1.36838	−	0.444613i	0.898831	+	0.438295i	$0.144417\pi$
$3$	−0.444035	−	2.96696i	−0.148012	−	0.988986i
$3$	−0.444035	−	2.96696i	−0.148012	−	0.988986i
$4$	3.46304	−	2.51605i	0.865760	−	0.629011i
$5$	−4.70571	−	1.52898i	−0.941142	−	0.305796i	−0.202031	−	0.979379i	$-0.564754\pi$
$5$	−4.70571	−	1.52898i	−0.941142	−	0.305796i	−0.739111	+	0.673584i	$0.764754\pi$
$6$	−3.85351	−	7.72499i	−0.642251	−	1.28750i
$7$	9.04489	−	6.57149i	1.29213	−	0.938785i	0.292280	−	0.956333i	$-0.405586\pi$
$7$	9.04489	−	6.57149i	1.29213	−	0.938785i	0.999846	+	0.0175478i	$0.00558591\pi$
$8$	0.474528	−	0.653131i	0.0593159	−	0.0816414i
$9$	−8.60567	+	2.63486i	−0.956185	+	0.292762i
$10$	−14.2380			−1.42380
$11$		0			0
$11$		0			0
$12$	−9.00271	−	9.15748i	−0.750226	−	0.763123i
$13$	−5.22225	−	16.0724i	−0.401711	−	1.23634i	−0.923610	−	0.383333i	$-0.874776\pi$
$13$	−5.22225	−	16.0724i	−0.401711	−	1.23634i	0.521899	−	0.853007i	$-0.325224\pi$
$14$	18.9101	−	26.0275i	1.35072	−	1.85911i
$15$	−2.44691	+	14.6406i	−0.163128	+	0.976037i
$16$	−4.57317	+	14.0748i	−0.285823	+	0.879673i
$17$	−0.0595216	−	0.0193397i	−0.00350127	−	0.00113763i	0.307266	−	0.951624i	$-0.400586\pi$
$17$	−0.0595216	−	0.0193397i	−0.00350127	−	0.00113763i	−0.310767	+	0.950486i	$0.600586\pi$
$18$	−21.2086	+	14.8634i	−1.17826	+	0.825742i
$19$	−4.35333	−	3.16288i	−0.229123	−	0.166467i	0.467301	−	0.884098i	$-0.345226\pi$
$19$	−4.35333	−	3.16288i	−0.229123	−	0.166467i	−0.696424	+	0.717631i	$0.745226\pi$
$20$	−20.1430	+	6.54487i	−1.00715	+	0.327243i
$21$	−23.5136	−	23.9178i	−1.11969	−	1.13894i
$22$		0			0
$23$		−	8.69537i		−	0.378060i	−0.981971	−	0.189030i	$-0.939466\pi$
$23$		−	8.69537i		−	0.378060i	0.981971	−	0.189030i	$-0.0605343\pi$
$24$	−2.14852	−	1.11789i	−0.0895216	−	0.0465787i
$25$	−0.419501	−	0.304785i	−0.0167800	−	0.0121914i
$26$	−28.5840	−	39.3425i	−1.09939	−	1.51317i
$27$	11.6387	+	24.3627i	0.431064	+	0.902321i
$28$	14.7886	−	45.5147i	0.528165	−	1.62552i
$29$	29.3632	+	40.4149i	1.01252	+	1.39362i	0.917316	+	0.398160i	$0.130351\pi$
$29$	29.3632	+	40.4149i	1.01252	+	1.39362i	0.0952067	+	0.995458i	$0.469649\pi$
$30$	6.32215	+	42.2435i	0.210738	+	1.40812i
$31$	−7.59453	−	23.3736i	−0.244985	−	0.753986i	−0.995639	−	0.0932904i	$-0.970261\pi$
$31$	−7.59453	−	23.3736i	−0.244985	−	0.753986i	0.750654	−	0.660695i	$-0.229739\pi$
$32$			45.8150i			1.43172i
$33$		0			0
$34$	−0.180094			−0.00529687
$35$	−52.6103	+	17.0941i	−1.50315	+	0.488403i
$36$	−23.1723	+	30.7769i	−0.643676	+	0.854913i
$37$	31.7618	−	23.0763i	0.858427	−	0.623684i	−0.0690298	−	0.997615i	$-0.521990\pi$
$37$	31.7618	−	23.0763i	0.858427	−	0.623684i	0.927456	+	0.373931i	$0.121990\pi$
$38$	−14.7265	−	4.78493i	−0.387540	−	0.125919i
$39$	−45.3673	+	22.6309i	−1.16326	+	0.580279i
$40$	−3.23161	+	2.34790i	−0.0807903	+	0.0586976i
$41$	25.8089	−	35.5228i	0.629484	−	0.866411i	−0.368516	−	0.929621i	$-0.620134\pi$
$41$	25.8089	−	35.5228i	0.629484	−	0.866411i	0.998000	+	0.0632106i	$0.0201340\pi$
$42$	−85.6193	−	44.5483i	−2.03855	−	1.06067i
$43$	0.201842			0.00469401			0.00234701	−	0.999997i	$-0.499253\pi$
$43$	0.201842			0.00469401			0.00234701	+	0.999997i	$0.499253\pi$
$44$		0			0
$45$	44.5244	+	0.758975i	0.989431	+	0.0168661i
$46$	−7.73215	−	23.7971i	−0.168090	−	0.517328i
$47$	−8.76165	+	12.0594i	−0.186418	+	0.256582i	−0.891989	−	0.452057i	$-0.850691\pi$
$47$	−8.76165	+	12.0594i	−0.186418	+	0.256582i	0.705571	+	0.708639i	$0.250691\pi$
$48$	43.7899	+	7.31871i	0.912289	+	0.152473i
$49$	23.4836	−	72.2751i	0.479257	−	1.47500i
$50$	−1.41909	−	0.461092i	−0.0283819	−	0.00922183i
$51$	−0.0309505	+	0.185186i	−0.000606873	+	0.00363109i
$52$	−58.5238	−	42.5200i	−1.12546	−	0.817693i
$53$	93.1486	−	30.2658i	1.75752	−	0.571053i	0.760582	−	0.649242i	$-0.224914\pi$
$53$	93.1486	−	30.2658i	1.75752	−	0.571053i	0.996939	+	0.0781891i	$0.0249138\pi$
$54$	53.5163	+	56.3252i	0.991042	+	1.04306i
$55$		0			0
$56$		−	9.02585i		−	0.161176i
$57$	−7.45110	+	14.3206i	−0.130721	+	0.251238i
$58$	116.298	+	84.4953i	2.00513	+	1.45681i
$59$	8.51816	+	11.7242i	0.144376	+	0.198716i	0.875080	−	0.483978i	$-0.160808\pi$
$59$	8.51816	+	11.7242i	0.144376	+	0.198716i	−0.730705	+	0.682694i	$0.760808\pi$
$60$	28.3625	+	56.8574i	0.472709	+	0.947623i
$61$	9.06134	−	27.8879i	0.148547	−	0.457179i	−0.848903	−	0.528548i	$-0.822737\pi$
$61$	9.06134	−	27.8879i	0.148547	−	0.457179i	0.997450	+	0.0713686i	$0.0227366\pi$
$62$	−41.5687	−	57.2145i	−0.670464	−	0.922814i
$63$	−60.5223	+	80.3841i	−0.960671	+	1.27594i
$64$	22.4472	+	69.0854i	0.350738	+	1.07946i
$65$			83.6168i			1.28641i
$66$		0			0
$67$	82.8515			1.23659			0.618294	−	0.785947i	$-0.287824\pi$
$67$	82.8515			1.23659			0.618294	+	0.785947i	$0.287824\pi$
$68$	−0.254785	+	0.0827848i	−0.00374684	+	0.00121742i
$69$	−25.7988	+	3.86104i	−0.373895	+	0.0559572i
$70$	−128.781	+	93.5648i	−1.83973	+	1.33664i
$71$	25.3986	+	8.25251i	0.357727	+	0.116232i	0.482366	−	0.875970i	$-0.339777\pi$
$71$	25.3986	+	8.25251i	0.357727	+	0.116232i	−0.124640	+	0.992202i	$0.539777\pi$
$72$	−2.36272	+	6.87094i	−0.0328155	+	0.0954298i
$73$	−11.3022	+	8.21153i	−0.154825	+	0.112487i	−0.662501	−	0.749061i	$-0.730505\pi$
$73$	−11.3022	+	8.21153i	−0.154825	+	0.112487i	0.507676	+	0.861548i	$0.330505\pi$
$74$	66.4042	−	91.3976i	0.897354	−	1.23510i
$75$	−0.718012	+	1.37998i	−0.00957349	+	0.0183997i
$76$	−23.0337			−0.303075
$77$		0			0
$78$	−104.035	+	102.277i	−1.33379	+	1.31124i
$79$	15.5088	+	47.7311i	0.196314	+	0.604191i	0.999959	+	0.00908239i	$0.00289105\pi$
$79$	15.5088	+	47.7311i	0.196314	+	0.604191i	−0.803645	+	0.595109i	$0.797109\pi$
$80$	43.0400	−	59.2395i	0.538000	−	0.740493i
$81$	67.1150	−	45.3495i	0.828580	−	0.559870i
$82$	39.0447	−	120.167i	0.476155	−	1.46545i
$83$	−57.2933	−	18.6157i	−0.690281	−	0.224286i	−0.0571899	−	0.998363i	$-0.518214\pi$
$83$	−57.2933	−	18.6157i	−0.690281	−	0.224286i	−0.633091	+	0.774078i	$0.718214\pi$
$84$	−141.607	−	23.6671i	−1.68579	−	0.281751i
$85$	0.250521	+	0.182014i	0.00294731	+	0.00214135i
$86$	0.552394	−	0.179484i	0.00642318	−	0.00208702i
$87$	106.871	−	105.065i	1.22840	−	1.20764i
$88$		0			0
$89$			40.3489i			0.453359i	0.973969	+	0.226679i	$0.0727869\pi$
$89$			40.3489i			0.453359i	−0.973969	+	0.226679i	$0.927213\pi$
$90$	122.527	−	37.5151i	1.36141	−	0.416835i
$91$	−152.854	−	111.055i	−1.67972	−	1.22039i
$92$	−21.8779	−	30.1124i	−0.237804	−	0.327309i
$93$	−65.9761	+	32.9113i	−0.709421	+	0.353885i
$94$	−13.2550	+	40.7946i	−0.141010	+	0.433986i
$95$	15.6495	+	21.5397i	0.164732	+	0.226734i
$96$	135.931	−	20.3435i	1.41595	−	0.211911i
$97$	−9.52170	−	29.3048i	−0.0981619	−	0.302111i	0.889903	−	0.456150i	$-0.150772\pi$
$97$	−9.52170	−	29.3048i	−0.0981619	−	0.302111i	−0.988065	+	0.154039i	$0.950772\pi$
$98$		−	218.681i		−	2.23144i
$99$		0			0
$100$	−2.21960			−0.0221960
$101$	49.3806	−	16.0447i	0.488917	−	0.158859i	−0.0541757	−	0.998531i	$-0.517253\pi$
$101$	49.3806	−	16.0447i	0.488917	−	0.158859i	0.543093	+	0.839673i	$0.317253\pi$
$102$	0.0799677	+	0.534330i	0.000783997	+	0.00523853i
$103$	41.3843	−	30.0674i	0.401789	−	0.291917i	−0.368480	−	0.929636i	$-0.620122\pi$
$103$	41.3843	−	30.0674i	0.401789	−	0.291917i	0.770269	+	0.637719i	$0.220122\pi$
$104$	−12.9755	−	4.21599i	−0.124764	−	0.0405384i
$105$	74.0783	+	148.502i	0.705507	+	1.41430i
$106$	228.012	−	165.660i	2.15105	−	1.56283i
$107$	−40.2296	+	55.3713i	−0.375978	+	0.517489i	−0.954513	−	0.298168i	$-0.903624\pi$
$107$	−40.2296	+	55.3713i	−0.375978	+	0.517489i	0.578536	+	0.815657i	$0.303624\pi$
$108$	101.603	+	55.0853i	0.940768	+	0.510049i
$109$	−125.737			−1.15355			−0.576773	−	0.816904i	$-0.695688\pi$
$109$	−125.737			−1.15355			−0.576773	+	0.816904i	$0.695688\pi$
$110$		0			0
$111$	−82.5697	−	83.9892i	−0.743871	−	0.756659i
$112$	51.1284	+	157.357i	0.456504	+	1.40497i
$113$	−58.0332	+	79.8758i	−0.513568	+	0.706866i	−0.984516	−	0.175295i	$-0.943912\pi$
$113$	−58.0332	+	79.8758i	−0.513568	+	0.706866i	0.470948	+	0.882161i	$0.343912\pi$
$114$	−7.65761	+	45.8176i	−0.0671720	+	0.401909i
$115$	−13.2950	+	40.9179i	−0.115609	+	0.355808i
$116$	203.372	+	66.0794i	1.75320	+	0.569650i
$117$	87.2895	+	124.554i	0.746064	+	1.06456i
$118$	33.7376	+	24.5118i	0.285912	+	0.207727i
$119$	−0.665457	+	0.216220i	−0.00559208	+	0.00181698i
$120$	8.40107	+	8.54550i	0.0700089	+	0.0712125i
$121$		0			0
$122$		−	84.3801i		−	0.691640i
$123$	−116.855	−	60.8004i	−0.950039	−	0.494312i
$124$	−85.1091	−	61.8354i	−0.686364	−	0.498672i
$125$	74.2152	+	102.149i	0.593722	+	0.817188i
$126$	−94.1551	+	273.810i	−0.747262	+	2.17309i
$127$	−6.44270	+	19.8286i	−0.0507299	+	0.156131i	−0.973212	−	0.229909i	$-0.926157\pi$
$127$	−6.44270	+	19.8286i	−0.0507299	+	0.156131i	0.922482	+	0.386040i	$0.126157\pi$
$128$	15.1475	+	20.8488i	0.118340	+	0.162881i
$129$	−0.0896250	−	0.598858i	−0.000694768	−	0.00464231i
$130$	74.3542	+	228.839i	0.571956	+	1.76030i
$131$		−	29.0290i		−	0.221595i	−0.993843	−	0.110798i	$-0.964659\pi$
$131$		−	29.0290i		−	0.221595i	0.993843	−	0.110798i	$-0.0353405\pi$
$132$		0			0
$133$	−60.1602			−0.452332
$134$	226.744	−	73.6736i	1.69212	−	0.549803i
$135$	−17.5185	−	132.439i	−0.129767	−	0.981030i
$136$	−0.0408760	+	0.0296982i	−0.000300559	+	0.000218369i
$137$	−144.285	−	46.8811i	−1.05318	−	0.342198i	−0.269263	−	0.963067i	$-0.586780\pi$
$137$	−144.285	−	46.8811i	−1.05318	−	0.342198i	−0.783915	+	0.620869i	$0.786780\pi$
$138$	−67.1716	+	33.5077i	−0.486751	+	0.242809i
$139$	15.5515	−	11.2988i	0.111881	−	0.0812863i	−0.530438	−	0.847724i	$-0.677972\pi$
$139$	15.5515	−	11.2988i	0.111881	−	0.0812863i	0.642319	+	0.766437i	$0.277972\pi$
$140$	−139.182	+	191.567i	−0.994156	+	1.36834i
$141$	39.6701	+	20.6407i	0.281348	+	0.146388i
$142$	76.8481			0.541184
$143$		0			0
$144$	2.27009	−	133.172i	0.0157645	−	0.924808i
$145$	−76.3810	−	235.076i	−0.526765	−	1.62122i
$146$	−23.6295	+	32.5232i	−0.161846	+	0.222761i
$147$	−224.865	−	37.5822i	−1.52969	−	0.255661i
$148$	51.9313	−	159.828i	0.350887	−	1.07992i
$149$	172.775	+	56.1381i	1.15957	+	0.376766i	0.824739	−	0.565514i	$-0.191322\pi$
$149$	172.775	+	56.1381i	1.15957	+	0.376766i	0.334827	+	0.942280i	$0.391322\pi$
$150$	−0.737912	+	4.41513i	−0.00491941	+	0.0294342i
$151$	−113.418	−	82.4026i	−0.751109	−	0.545713i	0.145061	−	0.989423i	$-0.453662\pi$
$151$	−113.418	−	82.4026i	−0.751109	−	0.545713i	−0.896171	+	0.443710i	$0.853662\pi$
$152$	−4.13155	+	1.34242i	−0.0271812	+	0.00883172i
$153$	0.563181	+	0.00960013i	0.00368092	+	6.27460e-5i
$154$		0			0
$155$			121.601i			0.784523i
$156$	−100.168	+	192.518i	−0.642106	+	1.23409i
$157$	145.309	+	105.573i	0.925536	+	0.672441i	0.944896	−	0.327371i	$-0.106163\pi$
$157$	145.309	+	105.573i	0.925536	+	0.672441i	−0.0193599	+	0.999813i	$0.506163\pi$
$158$	84.8875	+	116.838i	0.537262	+	0.739478i
$159$	−131.159	−	262.929i	−0.824896	−	1.65364i
$160$	70.0501	−	215.592i	0.437813	−	1.34745i
$161$	−57.1416	−	78.6486i	−0.354917	−	0.488501i
$162$	143.351	−	183.791i	0.884885	−	1.13451i
$163$	68.3722	+	210.428i	0.419461	+	1.29097i	0.908199	+	0.418538i	$0.137457\pi$
$163$	68.3722	+	210.428i	0.419461	+	1.29097i	−0.488738	+	0.872431i	$0.662543\pi$
$164$		−	187.953i		−	1.14606i
$165$		0			0
$166$	−173.351			−1.04428
$167$	−175.393	+	56.9886i	−1.05026	+	0.341249i	−0.782769	−	0.622312i	$-0.786194\pi$
$167$	−175.393	+	56.9886i	−1.05026	+	0.341249i	−0.267488	+	0.963561i	$0.586194\pi$
$168$	−26.7793	+	4.00779i	−0.159401	+	0.0238559i
$169$	−94.3269	+	68.5325i	−0.558148	+	0.405518i
$170$	0.847468	+	0.275359i	0.00498510	+	0.00161976i
$171$	45.7970	+	15.7483i	0.267819	+	0.0920951i
$172$	0.698988	−	0.507845i	0.00406389	−	0.00295259i
$173$	−143.153	+	197.033i	−0.827472	+	1.13892i	0.160916	+	0.986968i	$0.448555\pi$
$173$	−143.153	+	197.033i	−0.827472	+	1.13892i	−0.988388	+	0.151950i	$0.951445\pi$
$174$	199.054	−	382.569i	1.14399	−	2.19867i
$175$	−5.79723			−0.0331270
$176$		0			0
$177$	31.0030	−	30.4790i	0.175158	−	0.172198i
$178$	35.8793	+	110.425i	0.201569	+	0.620366i
$179$	−186.107	+	256.154i	−1.03970	+	1.43103i	−0.142295	+	0.989824i	$0.545448\pi$
$179$	−186.107	+	256.154i	−1.03970	+	1.43103i	−0.897407	+	0.441203i	$0.854552\pi$
$180$	156.099	−	109.397i	0.867219	−	0.607761i
$181$	−9.54820	+	29.3863i	−0.0527525	+	0.162355i	−0.973962	−	0.226712i	$-0.927203\pi$
$181$	−9.54820	+	29.3863i	−0.0527525	+	0.162355i	0.921209	+	0.389067i	$0.127203\pi$
$182$	−517.078	−	168.009i	−2.84109	−	0.923126i
$183$	−86.7659	−	14.5014i	−0.474131	−	0.0792427i
$184$	−5.67922	−	4.12619i	−0.0308653	−	0.0224250i
$185$	−184.745	+	60.0272i	−0.998621	+	0.324472i
$186$	−151.295	+	148.738i	−0.813413	+	0.799666i
$187$		0			0
$188$			63.8068i			0.339398i
$189$	265.370	+	143.874i	1.40408	+	0.761237i
$190$	61.9826	+	45.0330i	0.326224	+	0.237016i
$191$	−173.938	−	239.405i	−0.910669	−	1.25343i	−0.966938	−	0.255013i	$-0.917920\pi$
$191$	−173.938	−	239.405i	−0.910669	−	1.25343i	0.0562681	−	0.998416i	$-0.482080\pi$
$192$	195.006	−	97.2763i	1.01566	−	0.506647i
$193$	−24.5692	+	75.6161i	−0.127301	+	0.391793i	−0.994313	−	0.106494i	$-0.966038\pi$
$193$	−24.5692	+	75.6161i	−0.127301	+	0.391793i	0.867012	+	0.498287i	$0.166038\pi$
$194$	−52.1171	−	71.7331i	−0.268645	−	0.369758i
$195$	248.088	−	37.1288i	1.27224	−	0.190404i
$196$	−100.523	−	309.377i	−0.512871	−	1.57845i
$197$			360.331i			1.82909i	0.404485	+	0.914544i	$0.367451\pi$
$197$			360.331i			1.82909i	−0.404485	+	0.914544i	$0.632549\pi$
$198$		0			0
$199$	369.874			1.85866			0.929332	−	0.369245i	$-0.120384\pi$
$199$	369.874			1.85866			0.929332	+	0.369245i	$0.120384\pi$
$200$	−0.398129	+	0.129360i	−0.00199065	+	0.000646800i
$201$	−36.7889	−	245.817i	−0.183029	−	1.22297i
$202$	120.875	−	87.8211i	0.598393	−	0.434758i
$203$	531.173	+	172.588i	2.61661	+	0.850190i
$204$	0.358752	+	0.719178i	0.00175859	+	0.00352538i
$205$	−175.763	+	127.699i	−0.857379	+	0.622922i
$206$	86.5219	−	119.087i	0.420009	−	0.578093i
$207$	22.9111	+	74.8294i	0.110682	+	0.361495i
$208$	250.098			1.20239
$209$		0			0
$210$	334.786	+	340.541i	1.59422	+	1.62163i
$211$	−47.8204	−	147.176i	−0.226637	−	0.697517i	−0.998121	−	0.0612686i	$-0.980485\pi$
$211$	−47.8204	−	147.176i	−0.226637	−	0.697517i	0.771484	−	0.636248i	$-0.219515\pi$
$212$	246.427	−	339.178i	1.16239	−	1.59989i
$213$	13.2070	−	79.0209i	0.0620046	−	0.370990i
$214$	−60.8610	+	187.311i	−0.284397	+	0.875285i
$215$	−0.949812	−	0.308613i	−0.00441773	−	0.00143541i
$216$	21.4349	+	3.95914i	0.0992357	+	0.0183293i
$217$	−222.291	−	161.504i	−1.02438	−	0.744257i
$218$	−344.110	+	111.808i	−1.57849	+	0.512882i
$219$	29.3818	+	29.8870i	0.134164	+	0.136470i
$220$		0			0
$221$			1.05765i			0.00478576i
$222$	−300.658	−	156.435i	−1.35432	−	0.704661i
$223$	289.076	+	210.026i	1.29631	+	0.941821i	0.999912	−	0.0132452i	$-0.00421621\pi$
$223$	289.076	+	210.026i	1.29631	+	0.941821i	0.296393	+	0.955066i	$0.404216\pi$
$224$	301.073	+	414.392i	1.34408	+	1.84996i
$225$	4.41315	+	1.51755i	0.0196140	+	0.00674468i
$226$	−87.7950	+	270.205i	−0.388473	+	1.19560i
$227$	−60.2830	−	82.9725i	−0.265564	−	0.365517i	0.655322	−	0.755350i	$-0.272533\pi$
$227$	−60.2830	−	82.9725i	−0.265564	−	0.365517i	−0.920886	+	0.389832i	$0.872533\pi$
$228$	10.2278	+	68.3400i	0.0448586	+	0.299737i
$229$	−114.140	−	351.286i	−0.498426	−	1.53400i	−0.811548	−	0.584285i	$-0.801375\pi$
$229$	−114.140	−	351.286i	−0.498426	−	1.53400i	0.313122	−	0.949713i	$-0.398625\pi$
$230$			123.804i			0.538280i
$231$		0			0
$232$	40.3299			0.173836
$233$	16.4775	−	5.35387i	0.0707190	−	0.0229780i	−0.273444	−	0.961888i	$-0.588163\pi$
$233$	16.4775	−	5.35387i	0.0707190	−	0.0229780i	0.344163	+	0.938910i	$0.388163\pi$
$234$	349.647	+	263.254i	1.49422	+	1.12502i
$235$	59.6683	−	43.3516i	0.253908	−	0.184475i
$236$	58.9975	+	19.1694i	0.249989	+	0.0812264i
$237$	134.730	−	67.2081i	0.568480	−	0.283579i
$238$	−1.62893	+	1.18348i	−0.00684422	+	0.00497262i
$239$	128.623	−	177.035i	0.538172	−	0.740730i	−0.450176	−	0.892940i	$-0.648639\pi$
$239$	128.623	−	177.035i	0.538172	−	0.740730i	0.988348	+	0.152209i	$0.0486388\pi$
$240$	−194.872	−	101.393i	−0.811968	−	0.422473i
$241$	118.033			0.489765			0.244883	−	0.969553i	$-0.421251\pi$
$241$	118.033			0.489765			0.244883	+	0.969553i	$0.421251\pi$
$242$		0			0
$243$	−164.351	−	178.991i	−0.676343	−	0.736587i
$244$	−38.7876	−	119.376i	−0.158965	−	0.489245i
$245$	−221.014	+	304.199i	−0.902097	+	1.24163i
$246$	−373.868	−	62.4855i	−1.51979	−	0.254006i
$247$	−28.1010	+	86.4859i	−0.113769	+	0.350145i
$248$	−18.8698	−	6.13117i	−0.0760880	−	0.0247225i
$249$	−29.7918	+	178.253i	−0.119646	+	0.715875i
$250$	293.942	+	213.561i	1.17577	+	0.854246i
$251$	152.702	−	49.6160i	0.608376	−	0.197673i	0.0114036	−	0.999935i	$-0.496370\pi$
$251$	152.702	−	49.6160i	0.608376	−	0.197673i	0.596973	+	0.802262i	$0.296370\pi$
$252$	−7.34098	+	430.650i	−0.0291309	+	1.70893i
$253$		0			0
$254$			59.9950i			0.236201i
$255$	0.428789	−	0.824107i	0.00168153	−	0.00323179i
$256$	−175.076	−	127.200i	−0.683891	−	0.496876i
$257$	15.3895	+	21.1818i	0.0598811	+	0.0824193i	0.837907	−	0.545813i	$-0.183779\pi$
$257$	15.3895	+	21.1818i	0.0598811	+	0.0824193i	−0.778026	+	0.628232i	$0.783779\pi$
$258$	−0.777802	−	1.55923i	−0.00301474	−	0.00604353i
$259$	135.636	−	417.445i	0.523691	−	1.61176i
$260$	210.384	+	289.568i	0.809168	+	1.11372i
$261$	−359.177	−	270.429i	−1.37616	−	1.03613i
$262$	−25.8133	−	79.4451i	−0.0985240	−	0.303226i
$263$		−	221.020i		−	0.840378i	−0.907437	−	0.420189i	$-0.861964\pi$
$263$		−	221.020i		−	0.840378i	0.907437	−	0.420189i	$-0.138036\pi$
$264$		0			0
$265$	−484.606			−1.82870
$266$	−164.644	+	53.4960i	−0.618961	+	0.201113i
$267$	119.713	−	17.9163i	0.448365	−	0.0671023i
$268$	286.918	−	208.458i	1.07059	−	0.777828i
$269$	−119.300	−	38.7629i	−0.443494	−	0.144100i	0.0787531	−	0.996894i	$-0.474906\pi$
$269$	−119.300	−	38.7629i	−0.443494	−	0.144100i	−0.522247	+	0.852794i	$0.674906\pi$
$270$	−165.712	−	346.875i	−0.613748	−	1.28472i
$271$	−323.549	+	235.072i	−1.19391	+	0.867425i	−0.993672	−	0.112323i	$-0.964171\pi$
$271$	−323.549	+	235.072i	−1.19391	+	0.867425i	−0.200236	+	0.979748i	$0.564171\pi$
$272$	0.544405	−	0.749309i	0.00200149	−	0.00275481i
$273$	−261.623	+	502.825i	−0.958328	+	1.84185i
$274$	−436.561			−1.59329
$275$		0			0
$276$	−79.6276	+	78.2819i	−0.288506	+	0.283630i
$277$	22.7480	+	70.0112i	0.0821228	+	0.252748i	0.983684	−	0.179903i	$-0.0575783\pi$
$277$	22.7480	+	70.0112i	0.0821228	+	0.252748i	−0.901562	+	0.432651i	$0.857578\pi$
$278$	32.5134	−	44.7508i	0.116955	−	0.160974i
$279$	126.942	+	181.135i	0.454990	+	0.649228i
$280$	−13.8003	+	42.4730i	−0.0492869	+	0.151689i
$281$	−398.855	−	129.596i	−1.41941	−	0.461195i	−0.503996	−	0.863706i	$-0.668137\pi$
$281$	−398.855	−	129.596i	−1.41941	−	0.461195i	−0.915415	+	0.402511i	$0.868137\pi$
$282$	126.922	+	21.2127i	0.450077	+	0.0752225i
$283$	214.669	+	155.966i	0.758548	+	0.551117i	0.898465	−	0.439046i	$-0.144683\pi$
$283$	214.669	+	155.966i	0.758548	+	0.551117i	−0.139917	+	0.990163i	$0.544683\pi$
$284$	108.720	−	35.3253i	0.382817	−	0.124385i
$285$	56.9585	−	55.9959i	0.199854	−	0.196477i
$286$		0			0
$287$		−	490.903i		−	1.71046i
$288$	−120.716	−	394.269i	−0.419154	−	1.36899i
$289$	−233.803	−	169.868i	−0.809006	−	0.587777i
$290$	−418.072	−	575.427i	−1.44163	−	1.98423i
$291$	−82.7181	+	41.2628i	−0.284255	+	0.141797i
$292$	−18.4794	+	56.8737i	−0.0632856	+	0.194773i
$293$	−111.987	−	154.137i	−0.382209	−	0.526065i	0.573959	−	0.818884i	$-0.305407\pi$
$293$	−111.987	−	154.137i	−0.382209	−	0.526065i	−0.956168	+	0.292819i	$0.905407\pi$
$294$	−648.818	+	97.1021i	−2.20686	+	0.330279i
$295$	−22.1579	−	68.1950i	−0.0751115	−	0.231169i
$296$		−	31.6949i		−	0.107078i
$297$		0			0
$298$	522.763			1.75424
$299$	−139.756	+	45.4094i	−0.467410	+	0.151871i
$300$	0.985580	+	6.58546i	0.00328527	+	0.0219515i
$301$	1.82564	−	1.32641i	0.00606526	−	0.00440667i
$302$	−383.671	−	124.662i	−1.27043	−	0.412788i
$303$	−69.5308	−	139.386i	−0.229474	−	0.460019i
$304$	64.4253	−	46.8077i	0.211925	−	0.153973i
$305$	−85.2801	+	117.378i	−0.279607	+	0.384846i
$306$	1.54982	−	0.474522i	0.00506479	−	0.00155072i
$307$	−285.254			−0.929166			−0.464583	−	0.885530i	$-0.653796\pi$
$307$	−285.254			−0.929166			−0.464583	+	0.885530i	$0.653796\pi$
$308$		0			0
$309$	−107.585	−	109.434i	−0.348171	−	0.354156i
$310$	108.131	+	332.792i	0.348809	+	1.07352i
$311$	296.766	−	408.463i	0.954230	−	1.31339i	0.00460774	−	0.999989i	$-0.498533\pi$
$311$	296.766	−	408.463i	0.954230	−	1.31339i	0.949623	−	0.313396i	$-0.101467\pi$
$312$	−6.74711	+	40.3698i	−0.0216253	+	0.129390i
$313$	24.7740	−	76.2465i	0.0791501	−	0.243599i	−0.903650	−	0.428272i	$-0.859123\pi$
$313$	24.7740	−	76.2465i	0.0791501	−	0.243599i	0.982800	+	0.184673i	$0.0591225\pi$
$314$	491.554	+	159.716i	1.56546	+	0.508648i
$315$	407.706	−	285.727i	1.29430	−	0.907070i
$316$	173.801	+	126.274i	0.550004	+	0.399601i
$317$	−8.23294	+	2.67505i	−0.0259714	+	0.00843863i	−0.321974	−	0.946749i	$-0.604346\pi$
$317$	−8.23294	+	2.67505i	−0.0259714	+	0.00843863i	0.296002	+	0.955187i	$0.404346\pi$
$318$	−592.752	−	602.942i	−1.86400	−	1.89604i
$319$		0			0
$320$		−	359.417i		−	1.12318i
$321$	182.148	+	94.7728i	0.567438	+	0.295242i
$322$	−226.319	−	164.430i	−0.702854	−	0.510653i
$323$	0.197948	+	0.272452i	0.000612842	+	0.000843504i
$324$	118.320	−	325.911i	0.365187	−	1.00590i
$325$	−2.70790	+	8.33406i	−0.00833200	+	0.0256433i
$326$	374.236	+	515.091i	1.14796	+	1.58003i
$327$	55.8314	+	373.055i	0.170738	+	1.14084i
$328$	−10.9541	−	33.7131i	−0.0333965	−	0.102784i
$329$			166.653i			0.506544i
$330$		0			0
$331$	28.2554			0.0853638			0.0426819	−	0.999089i	$-0.486410\pi$
$331$	28.2554			0.0853638			0.0426819	+	0.999089i	$0.486410\pi$
$332$	−245.247	+	79.6856i	−0.738696	+	0.240017i
$333$	−212.529	+	282.275i	−0.638224	+	0.847672i
$334$	−429.332	+	311.928i	−1.28542	+	0.933916i
$335$	−389.875	−	126.678i	−1.16381	−	0.378143i
$336$	444.169	−	221.568i	1.32193	−	0.659428i
$337$	233.420	−	169.589i	0.692640	−	0.503232i	−0.184887	−	0.982760i	$-0.559192\pi$
$337$	233.420	−	169.589i	0.692640	−	0.503232i	0.877527	+	0.479527i	$0.159192\pi$
$338$	−197.209	+	271.435i	−0.583458	+	0.803061i
$339$	262.757	+	136.714i	0.775094	+	0.403287i
$340$	1.32552			0.00389859
$341$		0			0
$342$	139.339	+	2.37521i	0.407424	+	0.00694506i
$343$	−93.2616	−	287.030i	−0.271900	−	0.836821i
$344$	0.0957798	−	0.131830i	0.000278430	−	0.000383226i
$345$	127.305	+	21.2768i	0.369000	+	0.0616719i
$346$	−216.567	+	666.526i	−0.625917	+	1.92637i
$347$	250.710	+	81.4606i	0.722507	+	0.234757i	0.647110	−	0.762397i	$-0.275977\pi$
$347$	250.710	+	81.4606i	0.722507	+	0.234757i	0.0753975	+	0.997154i	$0.475977\pi$
$348$	105.751	−	632.736i	0.303882	−	1.81821i
$349$	394.738	+	286.794i	1.13106	+	0.821760i	0.985848	−	0.167641i	$-0.0536150\pi$
$349$	394.738	+	286.794i	1.13106	+	0.821760i	0.145207	+	0.989401i	$0.453615\pi$
$350$	−15.8656	+	5.15505i	−0.0453303	+	0.0147287i
$351$	330.787	−	314.291i	0.942412	−	0.895415i
$352$		0			0
$353$			437.345i			1.23894i	0.785021	+	0.619469i	$0.212652\pi$
$353$			437.345i			1.23894i	−0.785021	+	0.619469i	$0.787348\pi$
$354$	57.7448	−	110.982i	0.163121	−	0.313509i
$355$	−106.901	−	77.6678i	−0.301128	−	0.218782i
$356$	101.520	+	139.730i	0.285168	+	0.392500i
$357$	0.937002	+	1.87837i	0.00262466	+	0.00526155i
$358$	−281.550	+	866.521i	−0.786452	+	2.42045i
$359$	−144.007	−	198.208i	−0.401132	−	0.552111i	0.559895	−	0.828563i	$-0.310841\pi$
$359$	−144.007	−	198.208i	−0.401132	−	0.552111i	−0.961028	+	0.276452i	$0.910841\pi$
$360$	21.6238	−	28.7201i	0.0600660	−	0.0797781i
$361$	−102.607	−	315.793i	−0.284231	−	0.874774i
$362$			88.9137i			0.245618i
$363$		0			0
$364$	−808.761			−2.22187
$365$	65.7402	−	21.3603i	0.180110	−	0.0585213i
$366$	−250.352	+	37.4677i	−0.684022	+	0.102371i
$367$	−182.111	+	132.311i	−0.496216	+	0.360522i	−0.807570	−	0.589772i	$-0.799217\pi$
$367$	−182.111	+	132.311i	−0.496216	+	0.360522i	0.311354	+	0.950294i	$0.399217\pi$
$368$	122.385	+	39.7654i	0.332569	+	0.108058i
$369$	−128.505	+	373.701i	−0.348251	+	1.01274i
$370$	−452.224	+	328.560i	−1.22223	+	0.887999i
$371$	643.627	−	885.876i	1.73484	−	2.38781i
$372$	−145.672	+	279.972i	−0.391590	+	0.752613i
$373$	−283.156			−0.759131			−0.379566	−	0.925165i	$-0.623927\pi$
$373$	−283.156			−0.759131			−0.379566	+	0.925165i	$0.623927\pi$
$374$		0			0
$375$	270.116	−	265.551i	0.720310	−	0.708136i
$376$	3.71871	+	11.4450i	0.00989019	+	0.0304389i
$377$	496.224	−	682.994i	1.31624	−	1.81165i
$378$	854.189	+	157.773i	2.25976	+	0.417389i
$379$	−141.092	+	434.237i	−0.372275	+	1.14574i	0.573024	+	0.819538i	$0.305770\pi$
$379$	−141.092	+	434.237i	−0.372275	+	1.14574i	−0.945299	+	0.326205i	$0.894230\pi$
$380$	108.390	+	35.2180i	0.285236	+	0.0926789i
$381$	61.6914	+	10.3106i	0.161920	+	0.0270620i
$382$	−688.910	−	500.523i	−1.80343	−	1.31027i
$383$	305.540	−	99.2761i	0.797755	−	0.259206i	0.118352	−	0.992972i	$-0.462239\pi$
$383$	305.540	−	99.2761i	0.797755	−	0.259206i	0.679403	+	0.733765i	$0.262239\pi$
$384$	55.1314	−	54.1997i	0.143571	−	0.141145i
$385$		0			0
$386$			228.790i			0.592721i
$387$	−1.73699	+	0.531827i	−0.00448834	+	0.00137423i
$388$	−106.706	−	77.5266i	−0.275016	−	0.199811i
$389$	−185.407	−	255.190i	−0.476624	−	0.656017i	0.501228	−	0.865315i	$-0.332882\pi$
$389$	−185.407	−	255.190i	−0.476624	−	0.656017i	−0.977852	+	0.209299i	$0.932882\pi$
$390$	645.939	−	322.218i	1.65625	−	0.826200i
$391$	−0.168166	+	0.517562i	−0.000430093	+	0.00132369i
$392$	−36.0615	−	49.6344i	−0.0919936	−	0.126618i
$393$	−86.1276	+	12.8899i	−0.219154	+	0.0327986i
$394$	320.415	+	986.136i	0.813236	+	2.50288i
$395$		−	248.321i		−	0.628661i
$396$		0			0
$397$	−338.199			−0.851885			−0.425943	−	0.904750i	$-0.640057\pi$
$397$	−338.199			−0.851885			−0.425943	+	0.904750i	$0.640057\pi$
$398$	1012.25	−	328.902i	2.54335	−	0.826386i
$399$	26.7132	+	178.493i	0.0669504	+	0.447350i
$400$	6.20823	−	4.51054i	0.0155206	−	0.0112764i
$401$	343.284	+	111.540i	0.856070	+	0.278154i	0.703986	−	0.710214i	$-0.251402\pi$
$401$	343.284	+	111.540i	0.856070	+	0.278154i	0.152084	+	0.988368i	$0.451402\pi$
$402$	−319.269	−	640.027i	−0.794201	−	1.59211i
$403$	−336.009	+	244.125i	−0.833770	+	0.605769i
$404$	130.638	−	179.807i	0.323361	−	0.445068i
$405$	−385.162	+	110.784i	−0.951017	+	0.273541i
$406$	1607.16			3.95852
$407$		0			0
$408$	0.106264	+	0.108090i	0.000260450	+	0.000264928i
$409$	136.320	+	419.551i	0.333302	+	1.02580i	0.967553	+	0.252670i	$0.0813087\pi$
$409$	136.320	+	419.551i	0.333302	+	1.02580i	−0.634251	+	0.773127i	$0.718691\pi$
$410$	−367.466	+	505.774i	−0.896259	+	1.23359i
$411$	−75.0267	+	448.905i	−0.182547	+	1.09223i
$412$	67.6643	−	208.249i	0.164234	−	0.505460i
$413$	154.092	+	50.0674i	0.373103	+	0.121229i
$414$	129.242	+	184.417i	0.312180	+	0.445451i
$415$	241.143	+	175.200i	0.581066	+	0.422169i
$416$	736.358	−	239.257i	1.77009	−	0.575138i
$417$	−40.4284	−	41.1235i	−0.0969507	−	0.0986174i
$418$		0			0
$419$			393.180i			0.938377i	0.883098	+	0.469188i	$0.155453\pi$
$419$			393.180i			0.938377i	−0.883098	+	0.469188i	$0.844547\pi$
$420$	630.174	+	327.884i	1.50041	+	0.780676i
$421$	569.050	+	413.439i	1.35166	+	0.982041i	0.998927	+	0.0463181i	$0.0147488\pi$
$421$	569.050	+	413.439i	1.35166	+	0.982041i	0.352737	+	0.935723i	$0.385251\pi$
$422$	−261.745	−	360.262i	−0.620250	−	0.853701i
$423$	43.6250	−	126.865i	0.103132	−	0.299917i
$424$	24.4340	−	75.2002i	0.0576274	−	0.177359i
$425$	0.0190749	+	0.0262544i	4.48821e−5	+	6.17749e-5i
$426$	−34.1232	−	228.005i	−0.0801014	−	0.535223i
$427$	−101.307	−	311.790i	−0.237252	−	0.730187i
$428$			292.973i			0.684515i
$429$		0			0
$430$	−2.87383			−0.00668332
$431$	143.851	−	46.7401i	0.333762	−	0.108446i	−0.137342	−	0.990524i	$-0.543856\pi$
$431$	143.851	−	46.7401i	0.333762	−	0.108446i	0.471103	+	0.882078i	$0.343856\pi$
$432$	−396.125	+	52.3979i	−0.916956	+	0.121291i
$433$	381.538	−	277.204i	0.881150	−	0.640193i	−0.0524055	−	0.998626i	$-0.516689\pi$
$433$	381.538	−	277.204i	0.881150	−	0.640193i	0.933555	+	0.358433i	$0.116689\pi$
$434$	−751.969	−	244.330i	−1.73265	−	0.562971i
$435$	−663.546	+	331.001i	−1.52539	+	0.760922i
$436$	−435.431	+	316.359i	−0.998695	+	0.725594i
$437$	−27.5024	+	37.8538i	−0.0629345	+	0.0866220i
$438$	106.987	+	55.6662i	0.244263	+	0.127092i
$439$	506.417			1.15357			0.576784	−	0.816897i	$-0.304307\pi$
$439$	506.417			1.15357			0.576784	+	0.816897i	$0.304307\pi$
$440$		0			0
$441$	−11.6571	+	683.851i	−0.0264334	+	1.55068i
$442$	0.940493	+	2.89454i	0.00212781	+	0.00654873i
$443$	−375.325	+	516.591i	−0.847235	+	1.16612i	0.137230	+	0.990539i	$0.456180\pi$
$443$	−375.325	+	516.591i	−0.847235	+	1.16612i	−0.984465	+	0.175580i	$0.943820\pi$
$444$	−497.263	−	83.1088i	−1.11996	−	0.187182i
$445$	61.6926	−	189.870i	0.138635	−	0.426675i
$446$	977.891	+	317.736i	2.19258	+	0.712413i
$447$	89.8411	−	537.544i	0.200987	−	1.20256i
$448$	657.027	+	477.358i	1.46658	+	1.06553i
$449$	315.250	−	102.431i	0.702116	−	0.228131i	0.0638637	−	0.997959i	$-0.479658\pi$
$449$	315.250	−	102.431i	0.702116	−	0.228131i	0.638252	+	0.769827i	$0.279658\pi$
$450$	13.4272	+	0.228883i	0.0298381	+	0.000508629i
$451$		0			0
$452$			422.627i			0.935016i
$453$	−194.124	+	373.094i	−0.428529	+	0.823608i
$454$	−238.761	−	173.470i	−0.525906	−	0.382093i
$455$	549.487	+	756.305i	1.20766	+	1.66221i
$456$	5.81746	+	11.6620i	0.0127576	+	0.0255747i
$457$	−26.5560	+	81.7309i	−0.0581094	+	0.178842i	−0.975898	−	0.218227i	$-0.929973\pi$
$457$	−26.5560	+	81.7309i	−0.0581094	+	0.178842i	0.917789	+	0.397069i	$0.129973\pi$
$458$	−624.744	−	859.887i	−1.36407	−	1.87748i
$459$	−0.221589	−	1.67520i	−0.000482764	−	0.00364966i
$460$	56.9100	+	175.151i	0.123717	+	0.380763i
$461$			65.3245i			0.141702i	0.997487	+	0.0708508i	$0.0225714\pi$
$461$			65.3245i			0.141702i	−0.997487	+	0.0708508i	$0.977429\pi$
$462$		0			0
$463$	535.374			1.15632			0.578158	−	0.815925i	$-0.303772\pi$
$463$	535.374			1.15632			0.578158	+	0.815925i	$0.303772\pi$
$464$	−703.113	+	228.455i	−1.51533	+	0.492361i
$465$	360.785	−	53.9951i	0.775882	−	0.116118i
$466$	40.3341	−	29.3045i	0.0865539	−	0.0628851i
$467$	473.636	+	153.894i	1.01421	+	0.329537i	0.768530	−	0.639814i	$-0.220989\pi$
$467$	473.636	+	153.894i	1.01421	+	0.329537i	0.245681	+	0.969351i	$0.420989\pi$
$468$	615.670	+	211.711i	1.31554	+	0.452374i
$469$	749.382	−	544.458i	1.59783	−	1.16089i
$470$	124.748	−	171.701i	0.265422	−	0.365322i
$471$	248.709	−	478.004i	0.528045	−	1.01487i
$472$	11.6996			0.0247872
$473$		0			0
$474$	308.959	−	303.737i	0.651812	−	0.640796i
$475$	0.862227	+	2.65366i	0.00181521	+	0.00558665i
$476$	−1.76048	+	2.42310i	−0.00369850	+	0.00509055i
$477$	−721.859	+	505.891i	−1.51333	+	1.06057i
$478$	194.586	−	598.875i	0.407084	−	1.25288i
$479$	−826.166	−	268.438i	−1.72477	−	0.560412i	−0.732094	−	0.681204i	$-0.761457\pi$
$479$	−826.166	−	268.438i	−1.72477	−	0.560412i	−0.992678	+	0.120791i	$0.961457\pi$
$480$	−670.757	−	112.105i	−1.39741	−	0.233553i
$481$	−536.760	−	389.979i	−1.11592	−	0.810767i
$482$	323.029	−	104.958i	0.670184	−	0.217756i
$483$	−207.974	+	204.459i	−0.430588	+	0.423311i
$484$		0			0
$485$			152.458i			0.314347i
$486$	−608.953	−	343.708i	−1.25299	−	0.707218i
$487$	−195.067	−	141.725i	−0.400549	−	0.291016i	0.369216	−	0.929344i	$-0.379626\pi$
$487$	−195.067	−	141.725i	−0.400549	−	0.291016i	−0.769764	+	0.638328i	$0.779626\pi$
$488$	−13.9146	−	19.1518i	−0.0285136	−	0.0392456i
$489$	593.971	−	296.295i	1.21466	−	0.605919i
$490$	−334.359	+	1029.05i	−0.682365	+	2.10010i
$491$	293.922	+	404.549i	0.598619	+	0.823928i	0.995581	−	0.0939071i	$-0.0299357\pi$
$491$	293.922	+	404.549i	0.598619	+	0.823928i	−0.396962	+	0.917835i	$0.629936\pi$
$492$	−557.649	+	83.4577i	−1.13343	+	0.169630i
$493$	−0.966128	−	2.97344i	−0.00195969	−	0.00603131i
$494$			261.679i			0.529714i
$495$		0			0
$496$	363.708			0.733283
$497$	283.959	−	92.2638i	0.571346	−	0.185641i
$498$	76.9740	+	514.326i	0.154566	+	1.03278i
$499$	448.855	−	326.112i	0.899509	−	0.653531i	−0.0388311	−	0.999246i	$-0.512363\pi$
$499$	448.855	−	326.112i	0.899509	−	0.653531i	0.938340	+	0.345715i	$0.112363\pi$
$500$	514.021	+	167.015i	1.02804	+	0.334031i
$501$	246.963	+	495.078i	0.492941	+	0.988181i
$502$	373.789	−	271.574i	0.744600	−	0.540984i
$503$	−395.277	+	544.051i	−0.785838	+	1.08161i	0.208776	+	0.977964i	$0.433052\pi$
$503$	−395.277	+	544.051i	−0.785838	+	1.08161i	−0.994614	+	0.103650i	$0.966948\pi$
$504$	23.7819	+	77.6735i	0.0471863	+	0.154114i
$505$	−256.903			−0.508719
$506$		0			0
$507$	245.217	+	249.433i	0.483664	+	0.491979i
$508$	27.5783	+	84.8773i	0.0542880	+	0.167081i
$509$	378.324	−	520.719i	0.743270	−	1.02302i	−0.255154	−	0.966900i	$-0.582126\pi$
$509$	378.324	−	520.719i	0.743270	−	1.02302i	0.998424	−	0.0561224i	$-0.0178737\pi$
$510$	0.440673	−	2.63667i	0.000864065	−	0.00516994i
$511$	−48.2651	+	148.545i	−0.0944523	+	0.290694i
$512$	−690.287	−	224.288i	−1.34822	−	0.438062i
$513$	26.3889	−	142.871i	0.0514404	−	0.278500i
$514$	60.9525	+	44.2846i	0.118585	+	0.0861568i
$515$	−240.715	+	78.2130i	−0.467407	+	0.151870i
$516$	−1.81713	−	1.84837i	−0.00352157	−	0.00358211i
$517$		0			0
$518$		−	1263.06i		−	2.43833i
$519$	648.152	+	337.239i	1.24885	+	0.649785i
$520$	54.6127	+	39.6785i	0.105025	+	0.0763048i
$521$	−313.882	−	432.022i	−0.602462	−	0.829217i	0.393469	−	0.919338i	$-0.371275\pi$
$521$	−313.882	−	432.022i	−0.602462	−	0.829217i	−0.995931	+	0.0901206i	$0.971275\pi$
$522$	−1223.45	−	420.709i	−2.34378	−	0.805957i
$523$	307.507	−	946.409i	0.587967	−	1.80958i	0.000954046	−	1.00000i	$-0.499696\pi$
$523$	307.507	−	946.409i	0.587967	−	1.80958i	0.587013	−	0.809577i	$-0.300304\pi$
$524$	−73.0382	−	100.528i	−0.139386	−	0.191848i
$525$	2.57417	+	17.2001i	0.00490318	+	0.0327622i
$526$	−196.536	−	604.876i	−0.373643	−	1.14996i
$527$			1.53811i			0.00291861i
$528$		0			0
$529$	453.391			0.857071
$530$	−1326.25	+	430.924i	−2.50235	+	0.813064i
$531$	−104.196	−	78.4508i	−0.196226	−	0.147742i
$532$	−208.337	+	151.366i	−0.391611	+	0.284522i
$533$	−705.718	−	229.302i	−1.32405	−	0.430210i
$534$	311.695	−	155.485i	0.583698	−	0.291170i
$535$	273.970	−	199.051i	0.512094	−	0.372058i
$536$	39.3153	−	54.1129i	0.0733494	−	0.100957i
$537$	842.635	+	438.429i	1.56915	+	0.816442i
$538$	−360.964			−0.670936
$539$		0			0
$540$	−393.890	−	414.564i	−0.729426	−	0.767711i
$541$	213.440	+	656.899i	0.394528	+	1.21423i	0.929329	+	0.369254i	$0.120387\pi$
$541$	213.440	+	656.899i	0.394528	+	1.21423i	−0.534801	+	0.844978i	$0.679613\pi$
$542$	−676.442	+	931.043i	−1.24805	+	1.71779i
$543$	91.4277	+	15.2805i	0.168375	+	0.0281410i
$544$	0.886051	−	2.72698i	0.00162877	−	0.00501284i
$545$	591.680	+	192.248i	1.08565	+	0.352749i
$546$	−268.875	+	1608.75i	−0.492444	+	2.94643i
$547$	−70.3505	−	51.1127i	−0.128612	−	0.0934418i	0.521620	−	0.853178i	$-0.325328\pi$
$547$	−70.3505	−	51.1127i	−0.128612	−	0.0934418i	−0.650231	+	0.759736i	$0.725328\pi$
$548$	−617.621	+	200.677i	−1.12705	+	0.366199i
$549$	−4.49800	+	263.870i	−0.00819307	+	0.480637i
$550$		0			0
$551$		−	268.812i		−	0.487861i
$552$	−9.72047	+	18.6822i	−0.0176095	+	0.0338445i
$553$	453.940	+	329.807i	0.820868	+	0.596395i
$554$	124.511	+	171.375i	0.224750	+	0.309342i
$555$	260.131	+	521.476i	0.468705	+	0.939596i
$556$	25.4270	−	78.2564i	0.0457321	−	0.140749i
$557$	432.298	+	595.007i	0.776118	+	1.06824i	0.995700	+	0.0926409i	$0.0295308\pi$
$557$	432.298	+	595.007i	0.776118	+	1.06824i	−0.219581	+	0.975594i	$0.570469\pi$
$558$	508.479	+	382.841i	0.911253	+	0.686094i
$559$	−1.05407	−	3.24410i	−0.00188564	−	0.00580339i
$560$		−	818.651i		−	1.46188i
$561$		0			0
$562$	−1206.81			−2.14734
$563$	542.073	−	176.130i	0.962829	−	0.312842i	0.214911	−	0.976634i	$-0.431054\pi$
$563$	542.073	−	176.130i	0.962829	−	0.312842i	0.747918	+	0.663792i	$0.231054\pi$
$564$	189.312	−	28.3324i	0.335660	−	0.0502348i
$565$	395.216	−	287.141i	0.699497	−	0.508214i
$566$	726.186	+	235.952i	1.28301	+	0.416876i
$567$	309.034	−	851.227i	0.545033	−	1.50128i
$568$	17.4423	−	12.6726i	0.0307083	−	0.0223109i
$569$	−333.772	+	459.398i	−0.586594	+	0.807378i	−0.994399	−	0.105691i	$-0.966294\pi$
$569$	−333.772	+	459.398i	−0.586594	+	0.807378i	0.407805	+	0.913069i	$0.366294\pi$
$570$	106.089	−	203.896i	0.186120	−	0.357712i
$571$	229.442			0.401825			0.200912	−	0.979609i	$-0.435609\pi$
$571$	229.442			0.401825			0.200912	+	0.979609i	$0.435609\pi$
$572$		0			0
$573$	−633.070	+	622.370i	−1.10483	+	1.08616i
$574$	−436.523	−	1343.48i	−0.760494	−	2.34056i
$575$	−2.65022	+	3.64771i	−0.00460908	+	0.00634385i
$576$	−375.204	−	535.381i	−0.651396	−	0.929481i
$577$	−222.195	+	683.846i	−0.385087	+	1.18518i	0.551331	+	0.834287i	$0.314120\pi$
$577$	−222.195	+	683.846i	−0.385087	+	1.18518i	−0.936417	+	0.350888i	$0.885880\pi$
$578$	−790.912	−	256.983i	−1.36836	−	0.444607i
$579$	235.259	+	39.3195i	0.406320	+	0.0679093i
$580$	−855.973	−	621.901i	−1.47582	−	1.07224i
$581$	−640.544	+	208.125i	−1.10249	+	0.358219i
$582$	−189.687	+	186.481i	−0.325923	+	0.320415i
$583$		0			0
$584$			11.2784i			0.0193124i
$585$	−220.319	−	719.579i	−0.376613	−	1.23005i
$586$	−443.544	−	322.254i	−0.756902	−	0.549921i
$587$	300.738	+	413.930i	0.512331	+	0.705162i	0.984310	−	0.176447i	$-0.0564604\pi$
$587$	300.738	+	413.930i	0.512331	+	0.705162i	−0.471980	+	0.881609i	$0.656460\pi$
$588$	−873.273	+	435.621i	−1.48516	+	0.740852i
$589$	−40.8662	+	125.773i	−0.0693824	+	0.213537i
$590$	−121.281	−	166.930i	−0.205562	−	0.282931i
$591$	1069.09	−	159.999i	1.80894	−	0.270726i
$592$	179.541	+	552.571i	0.303279	+	0.933398i
$593$		−	241.775i		−	0.407715i	−0.979001	−	0.203858i	$-0.934652\pi$
$593$		−	241.775i		−	0.407715i	0.979001	−	0.203858i	$-0.0653480\pi$
$594$		0			0
$595$	3.46204			0.00581856
$596$	739.573	−	240.302i	1.24089	−	0.403191i
$597$	−164.237	−	1097.40i	−0.275104	−	1.83819i
$598$	−342.098	+	248.549i	−0.572070	+	0.415633i
$599$	−460.604	−	149.659i	−0.768955	−	0.249849i	−0.101837	−	0.994801i	$-0.532472\pi$
$599$	−460.604	−	149.659i	−0.768955	−	0.249849i	−0.667118	+	0.744952i	$0.732472\pi$
$600$	0.560589	+	1.12379i	0.000934315	+	0.00187299i
$601$	−391.082	+	284.138i	−0.650719	+	0.472775i	−0.863516	−	0.504321i	$-0.831743\pi$
$601$	−391.082	+	284.138i	−0.650719	+	0.472775i	0.212797	+	0.977096i	$0.431743\pi$
$602$	3.81686	−	5.25346i	0.00634030	−	0.00872668i
$603$	−712.992	+	218.302i	−1.18241	+	0.362027i
$604$	−600.098			−0.993540
$605$		0			0
$606$	−314.234	−	319.636i	−0.518538	−	0.527453i
$607$	−153.768	−	473.248i	−0.253324	−	0.779651i	−0.994155	−	0.107960i	$-0.965568\pi$
$607$	−153.768	−	473.248i	−0.253324	−	0.779651i	0.740831	−	0.671691i	$-0.234432\pi$
$608$	144.907	−	199.448i	0.238334	−	0.328039i
$609$	276.204	−	1652.60i	0.453536	−	2.71363i
$610$	−129.015	+	397.068i	−0.211500	+	0.650931i
$611$	239.579	+	77.8439i	0.392109	+	0.127404i
$612$	1.97447	−	1.38374i	0.00322626	−	0.00226102i
$613$	847.792	+	615.957i	1.38302	+	1.00482i	0.996591	+	0.0825060i	$0.0262924\pi$
$613$	847.792	+	615.957i	1.38302	+	1.00482i	0.386431	+	0.922318i	$0.373708\pi$
$614$	−780.670	+	253.655i	−1.27145	+	0.413119i
$615$	456.922	+	464.777i	0.742963	+	0.755735i
$616$		0			0
$617$			322.739i			0.523078i	0.965193	+	0.261539i	$0.0842301\pi$
$617$			322.739i			0.523078i	−0.965193	+	0.261539i	$0.915770\pi$
$618$	−391.745	−	203.828i	−0.633892	−	0.329819i
$619$	−435.469	−	316.387i	−0.703504	−	0.511126i	0.177567	−	0.984109i	$-0.443177\pi$
$619$	−435.469	−	316.387i	−0.703504	−	0.511126i	−0.881072	+	0.472983i	$0.843177\pi$
$620$	305.954	+	421.109i	0.493474	+	0.679208i
$621$	211.842	−	101.203i	0.341131	−	0.162968i
$622$	448.959	−	1381.75i	0.721799	−	2.22147i
$623$	265.153	+	364.951i	0.425606	+	0.585797i
$624$	−111.052	−	742.029i	−0.177968	−	1.18915i
$625$	−189.047	−	581.826i	−0.302475	−	0.930921i
$626$		−	230.698i		−	0.368527i
$627$		0			0
$628$	768.838			1.22426
$629$	−2.33680	+	0.759273i	−0.00371511	+	0.00120711i
$630$	861.715	−	1144.51i	1.36780	−	1.81668i
$631$	−714.632	+	519.211i	−1.13254	+	0.822838i	−0.986062	−	0.166376i	$-0.946793\pi$
$631$	−714.632	+	519.211i	−1.13254	+	0.822838i	−0.146477	+	0.989214i	$0.546793\pi$
$632$	38.5340	+	12.5205i	0.0609715	+	0.0198109i
$633$	−415.431	+	207.232i	−0.656289	+	0.327381i
$634$	−20.1528	+	14.6419i	−0.0317868	+	0.0230945i
$635$	60.6349	−	83.4568i	0.0954881	−	0.131428i
$636$	−1115.75	−	580.532i	−1.75432	−	0.912786i
$637$	−1284.27			−2.01613
$638$		0			0
$639$	−240.316	−	4.09649i	−0.376082	−	0.00641079i
$640$	−39.4025	−	121.269i	−0.0615665	−	0.189482i
$641$	173.396	−	238.659i	0.270509	−	0.372323i	−0.652053	−	0.758174i	$-0.726092\pi$
$641$	173.396	−	238.659i	0.270509	−	0.372323i	0.922561	+	0.385850i	$0.126092\pi$
$642$	582.768	+	97.3995i	0.907738	+	0.151713i
$643$	258.185	−	794.613i	0.401532	−	1.23579i	−0.522224	−	0.852809i	$-0.674897\pi$
$643$	258.185	−	794.613i	0.401532	−	1.23579i	0.923756	−	0.382981i	$-0.125103\pi$
$644$	−395.767	−	128.592i	−0.614545	−	0.199678i
$645$	−0.493891	+	2.95509i	−0.000765723	+	0.00458153i
$646$	0.784006	+	0.569614i	0.00121363	+	0.000881755i
$647$	−777.637	+	252.670i	−1.20191	+	0.390525i	−0.840464	−	0.541867i	$-0.817718\pi$
$647$	−777.637	+	252.670i	−1.20191	+	0.390525i	−0.361448	+	0.932392i	$0.617718\pi$
$648$	2.22875	−	65.3545i	0.00343943	−	0.100856i
$649$		0			0
$650$			25.2162i			0.0387942i
$651$	−380.470	+	731.241i	−0.584439	+	1.12326i
$652$	766.222	+	556.693i	1.17519	+	0.853823i
$653$	162.445	+	223.586i	0.248767	+	0.342399i	0.915079	−	0.403275i	$-0.132128\pi$
$653$	162.445	+	223.586i	0.248767	+	0.342399i	−0.666312	+	0.745673i	$0.732128\pi$
$654$	484.527	+	971.314i	0.740867	+	1.48519i
$655$	−44.3846	+	136.602i	−0.0677628	+	0.208552i
$656$	381.947	+	525.706i	0.582237	+	0.801380i
$657$	75.6268	−	100.445i	0.115109	−	0.152885i
$658$	148.192	+	456.088i	0.225216	+	0.693143i
$659$		−	881.372i		−	1.33744i	−0.743515	−	0.668719i	$-0.766843\pi$
$659$		−	881.372i		−	1.33744i	0.743515	−	0.668719i	$-0.233157\pi$
$660$		0			0
$661$	−501.036			−0.757997			−0.378999	−	0.925397i	$-0.623731\pi$
$661$	−501.036			−0.757997			−0.378999	+	0.925397i	$0.623731\pi$
$662$	77.3282	−	25.1255i	0.116810	−	0.0379539i
$663$	3.13801	−	0.469635i	0.00473305	−	0.000708348i
$664$	−39.3458	+	28.5864i	−0.0592557	+	0.0430518i
$665$	283.096	+	91.9836i	0.425709	+	0.138321i
$666$	−330.633	+	961.503i	−0.496445	+	1.44370i
$667$	351.423	−	255.323i	0.526870	−	0.382794i
$668$	−464.007	+	638.650i	−0.694621	+	0.956064i
$669$	494.779	−	950.935i	0.739579	−	1.42143i
$670$	−1179.64			−1.76065
$671$		0			0
$672$	1095.80	−	1077.28i	1.63065	−	1.60309i
$673$	−1.37662	−	4.23681i	−0.00204550	−	0.00629541i	0.950029	−	0.312163i	$-0.101054\pi$
$673$	−1.37662	−	4.23681i	−0.00204550	−	0.00629541i	−0.952074	+	0.305868i	$0.901054\pi$
$674$	488.009	−	671.687i	0.724049	−	0.996568i
$675$	2.54292	−	13.7675i	0.00376729	−	0.0203963i
$676$	−154.227	+	474.662i	−0.228146	+	0.702162i
$677$	16.4345	+	5.33989i	0.0242755	+	0.00788758i	0.321130	−	0.947035i	$-0.395938\pi$
$677$	16.4345	+	5.33989i	0.0242755	+	0.00788758i	−0.296854	+	0.954923i	$0.595938\pi$
$678$	840.671	+	140.504i	1.23993	+	0.207232i
$679$	−278.699	−	202.487i	−0.410455	−	0.298213i
$680$	0.237759	−	0.0772525i	0.000349645	−	0.000113607i
$681$	−219.408	+	215.700i	−0.322185	+	0.316740i
$682$		0			0
$683$		−	1085.69i		−	1.58958i	−0.606882	−	0.794792i	$-0.707580\pi$
$683$		−	1085.69i		−	1.58958i	0.606882	−	0.794792i	$-0.292420\pi$
$684$	198.220	−	60.6906i	0.289796	−	0.0887290i
$685$	607.284	+	441.218i	0.886547	+	0.644114i
$686$	−510.468	−	702.600i	−0.744123	−	1.02420i
$687$	−991.567	+	494.630i	−1.44333	+	0.719986i
$688$	−0.923060	+	2.84089i	−0.00134166	+	0.00412919i
$689$	−972.890	−	1339.07i	−1.41203	−	1.94349i
$690$	367.323	−	54.9735i	0.532352	−	0.0796717i
$691$	−62.2864	−	191.698i	−0.0901395	−	0.277421i	0.895817	−	0.444423i	$-0.146591\pi$
$691$	−62.2864	−	191.698i	−0.0901395	−	0.277421i	−0.985957	+	0.167002i	$0.946591\pi$
$692$			1042.51i			1.50652i
$693$		0			0
$694$	758.569			1.09304
$695$	−90.4563	+	29.3910i	−0.130153	+	0.0422892i
$696$	−17.9079	−	119.657i	−0.0257297	−	0.171921i
$697$	−2.22319	+	1.61524i	−0.00318965	+	0.00231742i
$698$	1335.33	+	433.874i	1.91308	+	0.621596i
$699$	−23.2013	−	46.5108i	−0.0331921	−	0.0665390i
$700$	−20.0760	+	14.5861i	−0.0286801	+	0.0208373i
$701$	−252.573	+	347.637i	−0.360304	+	0.495916i	−0.950233	−	0.311539i	$-0.899155\pi$
$701$	−252.573	+	347.637i	−0.360304	+	0.495916i	0.589930	+	0.807455i	$0.299155\pi$
$702$	625.807	−	1154.28i	0.891463	−	1.64427i
$703$	−211.257			−0.300508
$704$		0			0
$705$	−155.117	−	157.784i	−0.220024	−	0.223807i
$706$	388.899	+	1196.91i	0.550848	+	1.69534i
$707$	341.204	−	469.627i	0.482609	−	0.664254i
$708$	30.6780	−	183.555i	0.0433305	−	0.259258i
$709$	231.622	−	712.859i	0.326688	−	1.00544i	−0.643985	−	0.765038i	$-0.722720\pi$
$709$	231.622	−	712.859i	0.326688	−	1.00544i	0.970673	−	0.240404i	$-0.0772801\pi$
$710$	−361.625	−	117.499i	−0.509331	−	0.165492i
$711$	−259.228	−	369.894i	−0.364597	−	0.520245i
$712$	26.3531	+	19.1467i	0.0370128	+	0.0268914i
$713$	−203.242	+	66.0372i	−0.285052	+	0.0926189i
$714$	4.23464	+	4.30744i	0.00593087	+	0.00603283i
$715$		0			0
$716$			1355.32i			1.89291i
$717$	−582.367	−	303.010i	−0.812227	−	0.422608i
$718$	−570.362	−	414.392i	−0.794376	−	0.577148i
$719$	265.207	+	365.026i	0.368855	+	0.507685i	0.952589	−	0.304260i	$-0.0984090\pi$
$719$	265.207	+	365.026i	0.368855	+	0.507685i	−0.583734	+	0.811945i	$0.698409\pi$
$720$	−214.300	+	623.200i	−0.297639	+	0.865555i
$721$	176.728	−	543.913i	0.245115	−	0.754387i
$722$	−561.623	−	773.008i	−0.777871	−	1.07065i
$723$	−52.4109	−	350.200i	−0.0724909	−	0.484371i
$724$	40.8716	+	125.790i	0.0564524	+	0.173743i
$725$		−	25.9035i		−	0.0357290i
$726$		0			0
$727$	300.631			0.413523			0.206761	−	0.978391i	$-0.433708\pi$
$727$	300.631			0.413523			0.206761	+	0.978391i	$0.433708\pi$
$728$	−145.067	+	47.1352i	−0.199268	+	0.0647462i
$729$	−458.080	+	567.101i	−0.628367	+	0.777917i
$730$	160.921	−	116.916i	0.220439	−	0.160158i
$731$	−0.0120140	−	0.00390358i	−1.64350e−5	−	5.34006e-6i
$732$	−336.960	+	168.088i	−0.460328	+	0.229628i
$733$	−1078.72	+	783.739i	−1.47166	+	1.06922i	−0.491526	+	0.870863i	$0.663561\pi$
$733$	−1078.72	+	783.739i	−1.47166	+	1.06922i	−0.980130	+	0.198357i	$0.936439\pi$
$734$	−380.739	+	524.042i	−0.518718	+	0.713954i
$735$	1000.68	+	520.664i	1.36148	+	0.708386i
$736$	398.379			0.541275
$737$		0			0
$738$	−19.3815	+	1137.00i	−0.0262623	+	1.54065i
$739$	−326.316	−	1004.30i	−0.441565	−	1.35900i	−0.886207	−	0.463289i	$-0.846669\pi$
$739$	−326.316	−	1004.30i	−0.441565	−	1.35900i	0.444643	−	0.895708i	$-0.353331\pi$
$740$	−488.747	+	672.703i	−0.660469	+	0.909058i
$741$	269.078	+	44.9716i	0.363128	+	0.0606905i
$742$	973.705	−	2996.76i	1.31227	−	4.03875i
$743$	−959.620	−	311.799i	−1.29155	−	0.419649i	−0.418914	−	0.908026i	$-0.637589\pi$
$743$	−959.620	−	311.799i	−1.29155	−	0.419649i	−0.872633	+	0.488377i	$0.837589\pi$
$744$	−9.81208	+	58.7084i	−0.0131883	+	0.0789091i
$745$	−727.196	−	528.339i	−0.976102	−	0.709180i
$746$	−774.928	+	251.789i	−1.03878	+	0.337519i
$747$	542.097	+	9.24073i	0.725699	+	0.0123705i
$748$		0			0
$749$			765.196i			1.02162i
$750$	503.107	−	966.942i	0.670809	−	1.28926i
$751$	40.6835	+	29.5583i	0.0541725	+	0.0393586i	0.614542	−	0.788884i	$-0.289341\pi$
$751$	40.6835	+	29.5583i	0.0541725	+	0.0393586i	−0.560369	+	0.828243i	$0.689341\pi$
$752$	−129.664	−	178.468i	−0.172426	−	0.237324i
$753$	−215.014	−	431.030i	−0.285543	−	0.572418i
$754$	750.708	−	2310.44i	0.995634	−	3.06425i
$755$	407.718	+	561.176i	0.540024	+	0.743279i
$756$	1280.98	−	169.443i	1.69442	−	0.224131i
$757$	97.8844	+	301.257i	0.129306	+	0.397962i	0.994661	−	0.103197i	$-0.0329072\pi$
$757$	97.8844	+	301.257i	0.129306	+	0.397962i	−0.865355	+	0.501159i	$0.832907\pi$
$758$			1313.86i			1.73333i
$759$		0			0
$760$	21.4944			0.0282821
$761$	−67.8819	+	22.0562i	−0.0892009	+	0.0289831i	−0.353277	−	0.935519i	$-0.614933\pi$
$761$	−67.8819	+	22.0562i	−0.0892009	+	0.0289831i	0.264077	+	0.964502i	$0.414933\pi$
$762$	178.003	−	26.6399i	0.233599	−	0.0349604i
$763$	−1137.27	+	826.277i	−1.49053	+	1.08293i
$764$	−1204.71	−	391.433i	−1.57684	−	0.512347i
$765$	−2.63549	−	0.906266i	−0.00344508	−	0.00118466i
$766$	747.910	−	543.389i	0.976384	−	0.709384i
$767$	143.953	−	198.134i	0.187683	−	0.258324i
$768$	−299.658	+	575.924i	−0.390179	+	0.749901i
$769$	634.282			0.824814			0.412407	−	0.911000i	$-0.364688\pi$
$769$	634.282			0.824814			0.412407	+	0.911000i	$0.364688\pi$
$770$		0			0
$771$	56.0119	−	55.0653i	0.0726484	−	0.0714206i
$772$	105.170	+	323.679i	0.136230	+	0.419273i
$773$	−507.637	+	698.702i	−0.656710	+	0.903884i	−0.999367	−	0.0355767i	$-0.988673\pi$
$773$	−507.637	+	698.702i	−0.656710	+	0.903884i	0.342657	+	0.939461i	$0.388673\pi$
$774$	−4.28080	+	3.00006i	−0.00553075	+	0.00387604i
$775$	−3.93800	+	12.1199i	−0.00508130	+	0.0156386i
$776$	−23.6582	−	7.68701i	−0.0304873	−	0.00990594i
$777$	−1298.77	−	217.066i	−1.67152	−	0.279365i
$778$	−734.335	−	533.525i	−0.943875	−	0.685765i
$779$	−224.709	+	73.0123i	−0.288458	+	0.0937257i
$780$	765.719	−	752.778i	0.981691	−	0.965100i
$781$		0			0
$782$			1.56598i			0.00200253i
$783$	−642.865	+	1185.74i	−0.821029	+	1.51436i
$784$	909.860	+	661.052i	1.16054	+	0.843179i
$785$	−522.363	−	718.971i	−0.665431	−	0.915887i
$786$	−224.248	+	111.863i	−0.285303	+	0.142320i
$787$	−371.943	+	1144.72i	−0.472609	+	1.45454i	0.376546	+	0.926398i	$0.377112\pi$
$787$	−371.943	+	1144.72i	−0.472609	+	1.45454i	−0.849155	+	0.528143i	$0.822888\pi$
$788$	906.608	+	1247.84i	1.15052	+	1.58355i
$789$	−655.755	+	98.1403i	−0.831122	+	0.124386i
$790$	−220.814	−	679.595i	−0.279511	−	0.860246i
$791$			1103.83i			1.39549i
$792$		0			0
$793$	−495.547			−0.624902
$794$	−925.567	+	300.735i	−1.16570	+	0.378759i
$795$	215.182	+	1437.80i	0.270669	+	1.80856i
$796$	1280.89	−	930.620i	1.60916	−	1.16912i
$797$	−595.973	−	193.643i	−0.747770	−	0.242965i	−0.0897487	−	0.995964i	$-0.528606\pi$
$797$	−595.973	−	193.643i	−0.747770	−	0.242965i	−0.658021	+	0.752999i	$0.728606\pi$
$798$	231.828	+	464.737i	0.290511	+	0.582377i
$799$	0.754733	−	0.548346i	0.000944597	−	0.000686290i
$800$	13.9637	−	19.2194i	0.0174547	−	0.0240243i
$801$	−106.314	−	347.229i	−0.132726	−	0.433495i
$802$	1038.67			1.29510
$803$		0			0
$804$	−745.887	−	758.710i	−0.927721	−	0.943670i
$805$	148.640	+	457.466i	0.184645	+	0.568280i
$806$	−702.493	+	966.898i	−0.871579	+	1.19963i
$807$	−62.0345	+	371.170i	−0.0768706	+	0.459938i
$808$	12.9532	−	39.8657i	0.0160311	−	0.0493387i
$809$	382.449	+	124.265i	0.472743	+	0.153604i	0.535692	−	0.844413i	$-0.320051\pi$
$809$	382.449	+	124.265i	0.472743	+	0.153604i	−0.0629493	+	0.998017i	$0.520051\pi$
$810$	−955.582	+	645.685i	−1.17973	+	0.797142i
$811$	448.052	+	325.529i	0.552469	+	0.401392i	0.828695	−	0.559701i	$-0.189084\pi$
$811$	448.052	+	325.529i	0.552469	+	0.401392i	−0.276226	+	0.961093i	$0.589084\pi$
$812$	2273.71	−	738.774i	2.80014	−	0.909820i
$813$	841.116	+	855.576i	1.03458	+	1.05237i
$814$		0			0
$815$		−	1094.75i		−	1.34325i
$816$	−2.46490	−	1.28251i	−0.00302071	−	0.00157170i
$817$	−0.878687	−	0.638403i	−0.00107550	−	0.000781399i
$818$	746.151	+	1026.99i	0.912165	+	1.25549i
$819$	1608.03	+	552.954i	1.96341	+	0.675157i
$820$	−287.376	+	884.453i	−0.350459	+	1.07860i
$821$	129.901	+	178.794i	0.158223	+	0.217776i	0.880767	−	0.473549i	$-0.157027\pi$
$821$	129.901	+	178.794i	0.158223	+	0.217776i	−0.722544	+	0.691325i	$0.757027\pi$
$822$	193.848	+	1295.26i	0.235825	+	1.57574i
$823$	222.107	+	683.574i	0.269875	+	0.830589i	0.990530	+	0.137295i	$0.0438409\pi$
$823$	222.107	+	683.574i	0.269875	+	0.830589i	−0.720656	+	0.693293i	$0.756159\pi$
$824$		−	41.2972i		−	0.0501179i
$825$		0			0
$826$	466.232			0.564446
$827$	610.949	−	198.509i	0.738753	−	0.240035i	0.0846182	−	0.996413i	$-0.473033\pi$
$827$	610.949	−	198.509i	0.738753	−	0.240035i	0.654135	+	0.756378i	$0.273033\pi$
$828$	267.616	+	201.492i	0.323208	+	0.243348i
$829$	−664.227	+	482.589i	−0.801239	+	0.582134i	−0.911277	−	0.411793i	$-0.864903\pi$
$829$	−664.227	+	482.589i	−0.801239	+	0.582134i	0.110038	+	0.993927i	$0.464903\pi$
$830$	815.741	+	265.050i	0.982820	+	0.319338i
$831$	197.619	−	98.5797i	0.237809	−	0.118628i
$832$	993.145	−	721.562i	1.19368	−	0.867262i
$833$	−2.79556	+	3.84776i	−0.00335602	+	0.00461916i
$834$	−147.211	−	76.5949i	−0.176512	−	0.0918404i
$835$	912.483			1.09279
$836$		0			0
$837$	481.052	−	457.062i	0.574733	−	0.546071i
$838$	349.626	+	1076.04i	0.417214	+	1.28405i
$839$	−202.110	+	278.180i	−0.240894	+	0.331562i	−0.912296	−	0.409531i	$-0.865692\pi$
$839$	−202.110	+	278.180i	−0.240894	+	0.331562i	0.671402	+	0.741093i	$0.265692\pi$
$840$	132.143	+	22.0855i	0.157314	+	0.0262922i
$841$	−511.287	+	1573.58i	−0.607952	+	1.87108i
$842$	1924.99	+	625.468i	2.28621	+	0.742836i
$843$	−207.400	+	1240.93i	−0.246026	+	1.47204i
$844$	−535.906	−	389.358i	−0.634959	−	0.461325i
$845$	548.660	−	178.270i	0.649302	−	0.210971i
$846$	6.57969	−	385.990i	0.00777741	−	0.456253i
$847$		0			0
$848$			1449.45i			1.70926i
$849$	367.424	−	706.168i	0.432773	−	0.831765i
$850$	0.0755494	+	0.0548898i	8.88816e−5	+	6.45763e-5i
$851$	−200.657	−	276.180i	−0.235789	−	0.324536i
$852$	−153.084	−	306.882i	−0.179676	−	0.360190i
$853$	−105.689	+	325.277i	−0.123903	+	0.381333i	−0.993700	−	0.112077i	$-0.964250\pi$
$853$	−105.689	+	325.277i	−0.123903	+	0.381333i	0.869797	+	0.493410i	$0.164250\pi$
$854$	−554.503	−	763.208i	−0.649301	−	0.893686i
$855$	−191.429	−	144.129i	−0.223893	−	0.168572i
$856$	17.0747	+	52.5504i	0.0199470	+	0.0613907i
$857$		−	1404.79i		−	1.63920i	−0.572937	−	0.819600i	$-0.694196\pi$
$857$		−	1404.79i		−	1.63920i	0.572937	−	0.819600i	$-0.305804\pi$
$858$		0			0
$859$	759.128			0.883735			0.441867	−	0.897080i	$-0.354316\pi$
$859$	759.128			0.883735			0.441867	+	0.897080i	$0.354316\pi$
$860$	−4.06572	+	1.32103i	−0.00472758	+	0.00153608i
$861$	−1456.49	+	217.978i	−1.69162	+	0.253168i
$862$	352.123	−	255.832i	0.408496	−	0.296789i
$863$	376.240	+	122.248i	0.435968	+	0.141655i	0.518775	−	0.854911i	$-0.326388\pi$
$863$	376.240	+	122.248i	0.435968	+	0.141655i	−0.0828067	+	0.996566i	$0.526388\pi$
$864$	−1116.18	+	533.229i	−1.29187	+	0.617163i
$865$	974.894	−	708.302i	1.12704	−	0.818846i
$866$	797.679	−	1097.91i	0.921108	−	1.26780i
$867$	−400.173	+	769.110i	−0.461561	+	0.887093i
$868$	−1176.15			−1.35501
$869$		0			0
$870$	−1521.63	+	1495.91i	−1.74900	+	1.71944i
$871$	−432.671	−	1331.62i	−0.496752	−	1.52884i
$872$	−59.6655	+	82.1225i	−0.0684237	+	0.0941772i
$873$	159.155	+	227.099i	0.182308	+	0.260136i
$874$	−41.6068	+	128.052i	−0.0476050	+	0.146513i
$875$	1342.54	+	436.217i	1.53433	+	0.498533i
$876$	176.947	+	29.5737i	0.201995	+	0.0337599i
$877$	−917.111	−	666.320i	−1.04574	−	0.759772i	−0.0743391	−	0.997233i	$-0.523685\pi$
$877$	−917.111	−	666.320i	−1.04574	−	0.759772i	−0.971397	+	0.237461i	$0.923685\pi$
$878$	1385.94	−	450.319i	1.57852	−	0.512891i
$879$	−407.592	+	400.703i	−0.463700	+	0.455863i
$880$		0			0
$881$		−	894.628i		−	1.01547i	−0.861514	−	0.507735i	$-0.830483\pi$
$881$		−	894.628i		−	1.01547i	0.861514	−	0.507735i	$-0.169517\pi$
$882$	576.195	+	1881.90i	0.653283	+	2.13367i
$883$	−25.6769	−	18.6553i	−0.0290791	−	0.0211272i	0.573151	−	0.819450i	$-0.305721\pi$
$883$	−25.6769	−	18.6553i	−0.0290791	−	0.0211272i	−0.602230	+	0.798323i	$0.705721\pi$
$884$	2.66110	+	3.66270i	0.00301030	+	0.00414332i
$885$	−192.493	+	96.0224i	−0.217506	+	0.108500i
$886$	−567.807	+	1747.53i	−0.640866	+	1.97238i
$887$	−796.758	−	1096.64i	−0.898262	−	1.23635i	−0.971019	−	0.239002i	$-0.923180\pi$
$887$	−796.758	−	1096.64i	−0.898262	−	1.23635i	0.0727570	−	0.997350i	$-0.476820\pi$
$888$	−94.0375	+	14.0736i	−0.105898	+	0.0158487i
$889$	72.0300	+	221.686i	0.0810236	+	0.249365i
$890$		−	574.487i		−	0.645491i
$891$		0			0
$892$	1529.52			1.71470
$893$	76.2847	−	24.7864i	0.0854252	−	0.0277563i
$894$	−232.125	−	1551.02i	−0.259647	−	1.73492i
$895$	1267.42	−	920.833i	1.41611	−	1.02886i
$896$	274.015	+	89.0330i	0.305821	+	0.0993672i
$897$	196.784	+	394.486i	0.219380	+	0.439783i
$898$	771.678	−	560.657i	0.859330	−	0.624339i
$899$	721.641	−	993.254i	0.802715	−	1.10484i
$900$	19.1011	−	5.84834i	0.0212235	−	0.00649816i
$901$	−6.12969			−0.00680321
$902$		0			0
$903$	−4.74604	−	4.82763i	−0.00525586	−	0.00534621i
$904$	24.6310	+	75.8066i	0.0272467	+	0.0838568i
$905$	89.8621	−	123.685i	0.0992951	−	0.136668i
$906$	−199.504	+	1193.69i	−0.220203	+	1.31754i
$907$	278.095	−	855.889i	0.306610	−	0.943648i	−0.672462	−	0.740132i	$-0.734763\pi$
$907$	278.095	−	855.889i	0.306610	−	0.943648i	0.979072	−	0.203516i	$-0.0652370\pi$
$908$	−417.525	−	135.662i	−0.459829	−	0.149408i
$909$	−382.678	+	268.187i	−0.420987	+	0.295035i
$910$	2176.34	+	1581.20i	2.39158	+	1.73758i
$911$	304.231	−	98.8506i	0.333953	−	0.108508i	−0.137241	−	0.990538i	$-0.543823\pi$
$911$	304.231	−	98.8506i	0.333953	−	0.108508i	0.471193	+	0.882030i	$0.343823\pi$
$912$	−167.483	−	170.363i	−0.183644	−	0.186801i
$913$		0			0
$914$			247.292i			0.270560i
$915$	386.123	+	200.902i	0.421992	+	0.219566i
$916$	−1279.12	−	929.335i	−1.39642	−	1.01456i
$917$	−190.764	−	262.564i	−0.208030	−	0.286329i
$918$	−2.09606	−	4.38756i	−0.00228329	−	0.00477948i
$919$	−138.542	+	426.387i	−0.150752	+	0.463968i	−0.997706	−	0.0676988i	$-0.978434\pi$
$919$	−138.542	+	426.387i	−0.150752	+	0.463968i	0.846953	+	0.531667i	$0.178434\pi$
$920$	20.4159	+	28.1001i	0.0221912	+	0.0305435i
$921$	126.663	+	846.336i	0.137527	+	0.918932i
$922$	58.0882	+	178.777i	0.0630024	+	0.193901i
$923$		−	451.314i		−	0.488964i
$924$		0			0
$925$	−20.3574			−0.0220080
$926$	1465.19	−	476.069i	1.58228	−	0.514113i
$927$	−276.916	+	367.792i	−0.298722	+	0.396755i
$928$	−1851.61	+	1345.27i	−1.99527	+	1.44965i
$929$	−278.538	−	90.5026i	−0.299826	−	0.0974193i	0.155241	−	0.987877i	$-0.450385\pi$
$929$	−278.538	−	90.5026i	−0.299826	−	0.0974193i	−0.455067	+	0.890457i	$0.650385\pi$
$930$	939.367	−	468.591i	1.01007	−	0.503861i
$931$	−330.829	+	240.361i	−0.355348	+	0.258175i
$932$	43.5917	−	59.9988i	0.0467722	−	0.0643764i
$933$	−1343.67	−	699.119i	−1.44016	−	0.749324i
$934$	1433.07			1.53434
$935$		0			0
$936$	122.771	+	2.09279i	0.131166	+	0.00223589i
$937$	45.6193	+	140.402i	0.0486865	+	0.149842i	0.972444	−	0.233136i	$-0.0748987\pi$
$937$	45.6193	+	140.402i	0.0486865	+	0.149842i	−0.923758	+	0.382978i	$0.874899\pi$
$938$	1566.73	−	2156.42i	1.67029	−	2.29895i
$939$	−237.221	−	39.6473i	−0.252631	−	0.0422229i
$940$	97.5592	−	300.256i	0.103786	−	0.319422i
$941$	33.1918	+	10.7847i	0.0352729	+	0.0114609i	0.326600	−	0.945163i	$-0.394097\pi$
$941$	33.1918	+	10.7847i	0.0352729	+	0.0114609i	−0.291327	+	0.956623i	$0.594097\pi$
$942$	255.602	−	1529.34i	0.271340	−	1.62350i
$943$	−308.884	−	224.418i	−0.327555	−	0.237983i
$944$	−203.971	+	66.2742i	−0.216071	+	0.0702057i
$945$	−1028.78	−	1082.77i	−1.08865	−	1.14579i
$946$		0			0
$947$		−	867.513i		−	0.916064i	−0.888936	−	0.458032i	$-0.848554\pi$
$947$		−	867.513i		−	0.916064i	0.888936	−	0.458032i	$-0.151446\pi$
$948$	297.476	−	571.730i	0.313793	−	0.603091i
$949$	191.002	+	138.771i	0.201267	+	0.146229i
$950$	4.71941	+	6.49571i	0.00496780	+	0.00683758i
$951$	11.5925	+	23.2390i	0.0121898	+	0.0244364i
$952$	−0.174558	+	0.537233i	−0.000183359	+	0.000564321i
$953$	764.359	+	1052.05i	0.802056	+	1.10394i	0.992501	+	0.122237i	$0.0390069\pi$
$953$	764.359	+	1052.05i	0.802056	+	1.10394i	−0.190445	+	0.981698i	$0.560993\pi$
$954$	−1525.70	+	2026.40i	−1.59927	+	2.12411i
$955$	452.456	+	1392.52i	0.473776	+	1.45813i
$956$		−	936.699i		−	0.979811i
$957$		0			0
$958$	−2499.72			−2.60931
$959$	−1613.12	+	524.135i	−1.68209	+	0.546544i
$960$	−1066.38	+	159.594i	−1.11081	+	0.166243i
$961$	288.819	−	209.839i	0.300540	−	0.218355i
$962$	−1815.76	−	589.976i	−1.88748	−	0.613280i
$963$	200.307	−	582.507i	0.208003	−	0.604887i
$964$	408.754	−	296.977i	0.424019	−	0.308068i
$965$	231.231	−	318.262i	0.239617	−	0.329805i
$966$	−387.364	+	744.491i	−0.400998	+	0.770695i
$967$	−1422.62			−1.47117			−0.735585	−	0.677433i	$-0.763093\pi$
$967$	−1422.62			−1.47117			−0.735585	+	0.677433i	$0.763093\pi$
$968$		0			0
$969$	0.720457	−	0.708281i	0.000743506	−	0.000730940i
$970$	135.570	+	417.241i	0.139763	+	0.430145i
$971$	204.126	−	280.955i	0.210222	−	0.289346i	−0.690865	−	0.722984i	$-0.742770\pi$
$971$	204.126	−	280.955i	0.210222	−	0.289346i	0.901087	+	0.433638i	$0.142770\pi$
$972$	−1019.50	−	206.336i	−1.04887	−	0.212280i
$973$	66.4112	−	204.393i	0.0682541	−	0.210064i
$974$	−659.877	−	214.407i	−0.677491	−	0.220130i
$975$	25.9292	+	4.33361i	0.0265940	+	0.00444473i
$976$	351.077	+	255.073i	0.359710	+	0.261345i
$977$	443.757	−	144.185i	0.454204	−	0.147580i	−0.0729757	−	0.997334i	$-0.523250\pi$
$977$	443.757	−	144.185i	0.454204	−	0.147580i	0.527180	+	0.849754i	$0.323250\pi$
$978$	1362.08	−	1339.06i	1.39272	−	1.36918i
$979$		0			0
$980$			1609.54i			1.64238i
$981$	1082.05	−	331.299i	1.10300	−	0.337715i
$982$	1164.13	+	845.788i	1.18547	+	0.861291i
$983$	−595.696	−	819.905i	−0.605998	−	0.834084i	0.390243	−	0.920712i	$-0.372391\pi$
$983$	−595.696	−	819.905i	−0.605998	−	0.834084i	−0.996241	+	0.0866277i	$0.972391\pi$
$984$	−95.1614	+	47.4700i	−0.0967088	+	0.0482419i
$985$	550.937	−	1695.61i	0.559327	−	1.72143i
$986$	−5.28811	−	7.27846i	−0.00536320	−	0.00738181i
$987$	494.452	−	73.9996i	0.500964	−	0.0749743i
$988$	120.288	+	370.207i	0.121749	+	0.374704i
$989$		−	1.75510i		−	0.00177462i
$990$		0			0
$991$	−1208.63			−1.21960			−0.609802	−	0.792554i	$-0.708751\pi$
$991$	−1208.63			−1.21960			−0.609802	+	0.792554i	$0.708751\pi$
$992$	1070.86	−	347.944i	1.07950	−	0.350750i
$993$	−12.5464	−	83.8327i	−0.0126348	−	0.0844236i
$994$	695.082	−	505.007i	0.699278	−	0.508055i
$995$	−1740.52	−	565.529i	−1.74927	−	0.568371i
$996$	345.322	+	692.254i	0.346709	+	0.695034i
$997$	−116.802	+	84.8616i	−0.117153	+	0.0851170i	−0.644819	−	0.764335i	$-0.723067\pi$
$997$	−116.802	+	84.8616i	−0.117153	+	0.0851170i	0.527666	+	0.849452i	$0.323067\pi$
$998$	938.418	−	1291.62i	0.940299	−	1.29421i
$999$	931.867	+	505.223i	0.932800	+	0.505729i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.3.h.q.269.5		24
3.2	odd	2	inner	363.3.h.q.269.2		24
11.2	odd	10		363.3.h.p.251.5		24
11.3	even	5		363.3.b.j.122.2	✓	6
11.4	even	5	inner	363.3.h.q.245.5		24
11.5	even	5	inner	363.3.h.q.323.2		24
11.6	odd	10		363.3.h.p.323.5		24
11.7	odd	10		363.3.h.p.245.2		24
11.8	odd	10		363.3.b.k.122.5	yes	6
11.9	even	5	inner	363.3.h.q.251.2		24
11.10	odd	2		363.3.h.p.269.2		24
33.2	even	10		363.3.h.p.251.2		24
33.5	odd	10	inner	363.3.h.q.323.5		24
33.8	even	10		363.3.b.k.122.2	yes	6
33.14	odd	10		363.3.b.j.122.5	yes	6
33.17	even	10		363.3.h.p.323.2		24
33.20	odd	10	inner	363.3.h.q.251.5		24
33.26	odd	10	inner	363.3.h.q.245.2		24
33.29	even	10		363.3.h.p.245.5		24
33.32	even	2		363.3.h.p.269.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
363.3.b.j.122.2	✓	6	11.3	even	5
363.3.b.j.122.5	yes	6	33.14	odd	10
363.3.b.k.122.2	yes	6	33.8	even	10
363.3.b.k.122.5	yes	6	11.8	odd	10
363.3.h.p.245.2		24	11.7	odd	10
363.3.h.p.245.5		24	33.29	even	10
363.3.h.p.251.2		24	33.2	even	10
363.3.h.p.251.5		24	11.2	odd	10
363.3.h.p.269.2		24	11.10	odd	2
363.3.h.p.269.5		24	33.32	even	2
363.3.h.p.323.2		24	33.17	even	10
363.3.h.p.323.5		24	11.6	odd	10
363.3.h.q.245.2		24	33.26	odd	10	inner
363.3.h.q.245.5		24	11.4	even	5	inner
363.3.h.q.251.2		24	11.9	even	5	inner
363.3.h.q.251.5		24	33.20	odd	10	inner
363.3.h.q.269.2		24	3.2	odd	2	inner
363.3.h.q.269.5		24	1.1	even	1	trivial
363.3.h.q.323.2		24	11.5	even	5	inner
363.3.h.q.323.5		24	33.5	odd	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	363.h (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.73676 - 0.889226i) q^{2} +(-0.444035 - 2.96696i) q^{3} +(3.46304 - 2.51605i) q^{4} +(-4.70571 - 1.52898i) q^{5} +(-3.85351 - 7.72499i) q^{6} +(9.04489 - 6.57149i) q^{7} +(0.474528 - 0.653131i) q^{8} +(-8.60567 + 2.63486i) q^{9} -14.2380 q^{10} +(-9.00271 - 9.15748i) q^{12} +(-5.22225 - 16.0724i) q^{13} +(18.9101 - 26.0275i) q^{14} +(-2.44691 + 14.6406i) q^{15} +(-4.57317 + 14.0748i) q^{16} +(-0.0595216 - 0.0193397i) q^{17} +(-21.2086 + 14.8634i) q^{18} +(-4.35333 - 3.16288i) q^{19} +(-20.1430 + 6.54487i) q^{20} +(-23.5136 - 23.9178i) q^{21} -8.69537i q^{23} +(-2.14852 - 1.11789i) q^{24} +(-0.419501 - 0.304785i) q^{25} +(-28.5840 - 39.3425i) q^{26} +(11.6387 + 24.3627i) q^{27} +(14.7886 - 45.5147i) q^{28} +(29.3632 + 40.4149i) q^{29} +(6.32215 + 42.2435i) q^{30} +(-7.59453 - 23.3736i) q^{31} +45.8150i q^{32} -0.180094 q^{34} +(-52.6103 + 17.0941i) q^{35} +(-23.1723 + 30.7769i) q^{36} +(31.7618 - 23.0763i) q^{37} +(-14.7265 - 4.78493i) q^{38} +(-45.3673 + 22.6309i) q^{39} +(-3.23161 + 2.34790i) q^{40} +(25.8089 - 35.5228i) q^{41} +(-85.6193 - 44.5483i) q^{42} +0.201842 q^{43} +(44.5244 + 0.758975i) q^{45} +(-7.73215 - 23.7971i) q^{46} +(-8.76165 + 12.0594i) q^{47} +(43.7899 + 7.31871i) q^{48} +(23.4836 - 72.2751i) q^{49} +(-1.41909 - 0.461092i) q^{50} +(-0.0309505 + 0.185186i) q^{51} +(-58.5238 - 42.5200i) q^{52} +(93.1486 - 30.2658i) q^{53} +(53.5163 + 56.3252i) q^{54} -9.02585i q^{56} +(-7.45110 + 14.3206i) q^{57} +(116.298 + 84.4953i) q^{58} +(8.51816 + 11.7242i) q^{59} +(28.3625 + 56.8574i) q^{60} +(9.06134 - 27.8879i) q^{61} +(-41.5687 - 57.2145i) q^{62} +(-60.5223 + 80.3841i) q^{63} +(22.4472 + 69.0854i) q^{64} +83.6168i q^{65} +82.8515 q^{67} +(-0.254785 + 0.0827848i) q^{68} +(-25.7988 + 3.86104i) q^{69} +(-128.781 + 93.5648i) q^{70} +(25.3986 + 8.25251i) q^{71} +(-2.36272 + 6.87094i) q^{72} +(-11.3022 + 8.21153i) q^{73} +(66.4042 - 91.3976i) q^{74} +(-0.718012 + 1.37998i) q^{75} -23.0337 q^{76} +(-104.035 + 102.277i) q^{78} +(15.5088 + 47.7311i) q^{79} +(43.0400 - 59.2395i) q^{80} +(67.1150 - 45.3495i) q^{81} +(39.0447 - 120.167i) q^{82} +(-57.2933 - 18.6157i) q^{83} +(-141.607 - 23.6671i) q^{84} +(0.250521 + 0.182014i) q^{85} +(0.552394 - 0.179484i) q^{86} +(106.871 - 105.065i) q^{87} +40.3489i q^{89} +(122.527 - 37.5151i) q^{90} +(-152.854 - 111.055i) q^{91} +(-21.8779 - 30.1124i) q^{92} +(-65.9761 + 32.9113i) q^{93} +(-13.2550 + 40.7946i) q^{94} +(15.6495 + 21.5397i) q^{95} +(135.931 - 20.3435i) q^{96} +(-9.52170 - 29.3048i) q^{97} -218.681i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{3} + 18 q^{4} + 10 q^{6} + 22 q^{9} + 72 q^{10} + 56 q^{12} + 42 q^{13} - 28 q^{15} - 30 q^{16} - 94 q^{18} - 84 q^{19} - 112 q^{21} - 48 q^{24} + 108 q^{25} + 38 q^{27} - 132 q^{28} + 148 q^{30}+ \cdots - 126 q^{97}+O(q^{100}) \) 24 * q - 4 * q^3 + 18 * q^4 + 10 * q^6 + 22 * q^9 + 72 * q^10 + 56 * q^12 + 42 * q^13 - 28 * q^15 - 30 * q^16 - 94 * q^18 - 84 * q^19 - 112 * q^21 - 48 * q^24 + 108 * q^25 + 38 * q^27 - 132 * q^28 + 148 * q^30 + 264 * q^34 - 46 * q^36 + 42 * q^37 + 82 * q^39 + 294 * q^40 + 206 * q^42 - 624 * q^43 - 472 * q^45 + 60 * q^46 + 88 * q^48 - 138 * q^49 - 182 * q^51 - 114 * q^52 + 560 * q^54 + 24 * q^57 + 54 * q^58 + 562 * q^60 - 264 * q^61 + 122 * q^63 - 294 * q^64 + 96 * q^67 - 152 * q^69 - 336 * q^70 + 306 * q^72 - 72 * q^73 - 62 * q^75 - 1632 * q^76 - 776 * q^78 + 250 * q^81 - 798 * q^82 - 328 * q^84 - 330 * q^85 + 1848 * q^87 + 230 * q^90 - 300 * q^91 + 266 * q^93 - 120 * q^94 + 386 * q^96 - 126 * q^97

Introduction

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Modular forms

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