LMFDB - Embedded newform 363.3.h.n.323.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [363,3,Mod(245,363)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [16,0,5,18,0,-32,34] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$9.89103359628$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 12x^{14} + 180x^{12} - 2562x^{10} + 25179x^{8} - 96398x^{6} + 239275x^{4} - 536393x^{2} + 1771561 $ x^16 - 12x^14 + 180x^12 - 2562x^10 + 25179x^8 - 96398x^6 + 239275x^4 - 536393*x^2 + 1771561
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			323.1
Root			$-2.91048 + 0.945671i$ of defining polynomial
Character	$\chi$	$=$	363.323
Dual form			363.3.h.n.245.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.79877 + 2.47580i) q^{2} +(2.88971 + 0.805978i) q^{3} +(-1.65793 - 5.10257i) q^{4} +(-3.90250 - 5.37133i) q^{5} +(-7.19336 + 5.70456i) q^{6} +(0.946512 + 2.91306i) q^{7} +(3.97326 + 1.29099i) q^{8} +(7.70080 + 4.65808i) q^{9} +20.3180 q^{10} +(-0.678356 - 16.0812i) q^{12} +(13.1422 + 9.54837i) q^{13} +(-8.91472 - 2.89657i) q^{14} +(-6.94789 - 18.6669i) q^{15} +(7.01879 - 5.09945i) q^{16} +(-0.473548 - 0.651783i) q^{17} +(-25.3845 + 10.6868i) q^{18} +(-6.39720 + 19.6886i) q^{19} +(-20.9375 + 28.8180i) q^{20} +(0.387274 + 9.18076i) q^{21} +27.3224i q^{23} +(10.4410 + 6.93295i) q^{24} +(-5.89623 + 18.1467i) q^{25} +(-47.2797 + 15.3621i) q^{26} +(18.4987 + 19.6672i) q^{27} +(13.2949 - 9.65928i) q^{28} +(-3.59755 + 1.16891i) q^{29} +(58.7131 + 16.3759i) q^{30} +(16.8114 + 12.2142i) q^{31} +43.2608i q^{32} +2.46549 q^{34} +(11.9533 - 16.4522i) q^{35} +(11.0008 - 47.0166i) q^{36} +(11.9137 + 36.6667i) q^{37} +(-37.2378 - 51.2534i) q^{38} +(30.2813 + 38.1843i) q^{39} +(-8.57131 - 26.3798i) q^{40} +(12.7181 + 4.13237i) q^{41} +(-23.4263 - 15.5553i) q^{42} -43.4125 q^{43} +(-5.03227 - 59.5416i) q^{45} +(-67.6447 - 49.1468i) q^{46} +(18.9168 + 6.14644i) q^{47} +(24.3923 - 9.07892i) q^{48} +(32.0518 - 23.2870i) q^{49} +(-34.3217 - 47.2397i) q^{50} +(-0.843091 - 2.26513i) q^{51} +(26.9324 - 82.8895i) q^{52} +(-10.3894 + 14.2997i) q^{53} +(-81.9669 + 10.4224i) q^{54} +12.7963i q^{56} +(-34.3546 + 51.7382i) q^{57} +(3.57717 - 11.0094i) q^{58} +(-41.3952 + 13.4501i) q^{59} +(-83.7299 + 66.4004i) q^{60} +(8.61986 - 6.26270i) q^{61} +(-60.4797 + 19.6510i) q^{62} +(-6.28039 + 26.8418i) q^{63} +(-79.0299 - 57.4185i) q^{64} -107.854i q^{65} +72.2963 q^{67} +(-2.54066 + 3.49692i) q^{68} +(-22.0213 + 78.9537i) q^{69} +(19.2312 + 59.1877i) q^{70} +(-1.51055 - 2.07909i) q^{71} +(24.5838 + 28.4494i) q^{72} +(14.0537 + 43.2529i) q^{73} +(-112.209 - 36.4590i) q^{74} +(-31.6643 + 47.6865i) q^{75} +111.068 q^{76} +(-149.006 + 6.28555i) q^{78} +(-79.4797 - 57.7454i) q^{79} +(-54.7816 - 17.7996i) q^{80} +(37.6046 + 71.7419i) q^{81} +(-33.1080 + 24.0543i) q^{82} +(-18.7507 - 25.8081i) q^{83} +(46.2034 - 17.1971i) q^{84} +(-1.65292 + 5.08716i) q^{85} +(78.0893 - 107.481i) q^{86} +(-11.3380 + 0.478272i) q^{87} +18.5409i q^{89} +(156.465 + 94.6430i) q^{90} +(-15.3758 + 47.3217i) q^{91} +(139.414 - 45.2985i) q^{92} +(38.7356 + 48.8450i) q^{93} +(-49.2443 + 35.7781i) q^{94} +(130.719 - 42.4731i) q^{95} +(-34.8673 + 125.011i) q^{96} +(51.2123 + 37.2079i) q^{97} +121.242i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 5 q^{3} + 18 q^{4} - 32 q^{6} + 34 q^{7} + 17 q^{9} + 12 q^{10} + 106 q^{12} + 2 q^{13} - 28 q^{15} + 102 q^{16} - 42 q^{18} - 66 q^{19} + 12 q^{21} + 74 q^{24} - 176 q^{25} - 55 q^{27} + 146 q^{28}+ \cdots + 252 q^{97}+O(q^{100}) $ 16 * q + 5 * q^3 + 18 * q^4 - 32 * q^6 + 34 * q^7 + 17 * q^9 + 12 * q^10 + 106 * q^12 + 2 * q^13 - 28 * q^15 + 102 * q^16 - 42 * q^18 - 66 * q^19 + 12 * q^21 + 74 * q^24 - 176 * q^25 - 55 * q^27 + 146 * q^28 - 110 * q^30 - 126 * q^31 - 132 * q^34 + 226 * q^36 - 230 * q^37 - 136 * q^39 - 226 * q^40 - 72 * q^42 + 156 * q^43 - 72 * q^45 - 308 * q^46 + 255 * q^48 + 170 * q^49 + 169 * q^51 + 224 * q^52 - 1046 * q^54 + 259 * q^57 + 184 * q^58 - 316 * q^60 - 104 * q^61 + 108 * q^63 - 184 * q^64 + 368 * q^67 - 22 * q^69 - 52 * q^70 - 73 * q^72 - 354 * q^73 + 54 * q^75 + 900 * q^76 - 492 * q^78 - 566 * q^79 + 377 * q^81 + 200 * q^82 + 720 * q^84 + 162 * q^85 - 132 * q^87 + 774 * q^90 - 226 * q^91 - 370 * q^93 + 530 * q^94 + 67 * q^96 + 252 * q^97

Character values

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

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

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 $

$2$	−1.79877	+	2.47580i	−0.899386	+	1.23790i	0.0712771	+	0.997457i	$0.477293\pi$
$2$	−1.79877	+	2.47580i	−0.899386	+	1.23790i	−0.970663	+	0.240443i	$0.922707\pi$
$3$	2.88971	+	0.805978i	0.963235	+	0.268659i
$3$	2.88971	+	0.805978i	0.963235	+	0.268659i
$4$	−1.65793	−	5.10257i	−0.414481	−	1.27564i
$5$	−3.90250	−	5.37133i	−0.780499	−	1.07427i	−0.995227	−	0.0975910i	$-0.968886\pi$
$5$	−3.90250	−	5.37133i	−0.780499	−	1.07427i	0.214727	−	0.976674i	$-0.431114\pi$
$6$	−7.19336	+	5.70456i	−1.19889	+	0.950759i
$7$	0.946512	+	2.91306i	0.135216	+	0.416152i	0.995624	−	0.0934546i	$-0.0297910\pi$
$7$	0.946512	+	2.91306i	0.135216	+	0.416152i	−0.860408	+	0.509607i	$0.829791\pi$
$8$	3.97326	+	1.29099i	0.496658	+	0.161374i
$9$	7.70080	+	4.65808i	0.855644	+	0.517564i
$10$	20.3180			2.03180
$11$		0			0
$11$		0			0
$12$	−0.678356	−	16.0812i	−0.0565297	−	1.34010i
$13$	13.1422	+	9.54837i	1.01094	+	0.734490i	0.964406	−	0.264427i	$-0.0851827\pi$
$13$	13.1422	+	9.54837i	1.01094	+	0.734490i	0.0465330	+	0.998917i	$0.485183\pi$
$14$	−8.91472	−	2.89657i	−0.636765	−	0.206898i
$15$	−6.94789	−	18.6669i	−0.463193	−	1.24446i
$16$	7.01879	−	5.09945i	0.438674	−	0.318716i
$17$	−0.473548	−	0.651783i	−0.0278557	−	0.0383401i	0.794862	−	0.606790i	$-0.207543\pi$
$17$	−0.473548	−	0.651783i	−0.0278557	−	0.0383401i	−0.822718	+	0.568450i	$0.807543\pi$
$18$	−25.3845	+	10.6868i	−1.41025	+	0.593711i
$19$	−6.39720	+	19.6886i	−0.336695	+	1.03624i	0.629186	+	0.777255i	$0.283388\pi$
$19$	−6.39720	+	19.6886i	−0.336695	+	1.03624i	−0.965881	+	0.258986i	$0.916612\pi$
$20$	−20.9375	+	28.8180i	−1.04688	+	1.44090i
$21$	0.387274	+	9.18076i	0.0184416	+	0.437179i
$22$		0			0
$23$			27.3224i			1.18793i	0.804491	+	0.593965i	$0.202438\pi$
$23$			27.3224i			1.18793i	−0.804491	+	0.593965i	$0.797562\pi$
$24$	10.4410	+	6.93295i	0.435044	+	0.288873i
$25$	−5.89623	+	18.1467i	−0.235849	+	0.725870i
$26$	−47.2797	+	15.3621i	−1.81845	+	0.590850i
$27$	18.4987	+	19.6672i	0.685138	+	0.728413i
$28$	13.2949	−	9.65928i	0.474817	−	0.344974i
$29$	−3.59755	+	1.16891i	−0.124053	+	0.0403074i	−0.370386	−	0.928878i	$-0.620774\pi$
$29$	−3.59755	+	1.16891i	−0.124053	+	0.0403074i	0.246332	+	0.969185i	$0.420774\pi$
$30$	58.7131	+	16.3759i	1.95710	+	0.545863i
$31$	16.8114	+	12.2142i	0.542302	+	0.394006i	0.824939	−	0.565221i	$-0.191209\pi$
$31$	16.8114	+	12.2142i	0.542302	+	0.394006i	−0.282637	+	0.959227i	$0.591209\pi$
$32$			43.2608i			1.35190i
$33$		0			0
$34$	2.46549			0.0725143
$35$	11.9533	−	16.4522i	0.341522	−	0.470064i
$36$	11.0008	−	47.0166i	0.305579	−	1.30602i
$37$	11.9137	+	36.6667i	0.321993	+	0.990991i	0.972780	+	0.231731i	$0.0744390\pi$
$37$	11.9137	+	36.6667i	0.321993	+	0.990991i	−0.650787	+	0.759260i	$0.725561\pi$
$38$	−37.2378	−	51.2534i	−0.979942	−	1.34877i
$39$	30.2813	+	38.1843i	0.776444	+	0.979085i
$40$	−8.57131	−	26.3798i	−0.214283	−	0.659494i
$41$	12.7181	+	4.13237i	0.310199	+	0.100790i	0.459979	−	0.887930i	$-0.347857\pi$
$41$	12.7181	+	4.13237i	0.310199	+	0.100790i	−0.149781	+	0.988719i	$0.547857\pi$
$42$	−23.4263	−	15.5553i	−0.557770	−	0.370364i
$43$	−43.4125			−1.00959			−0.504797	−	0.863238i	$-0.668433\pi$
$43$	−43.4125			−1.00959			−0.504797	+	0.863238i	$0.668433\pi$
$44$		0			0
$45$	−5.03227	−	59.5416i	−0.111828	−	1.32315i
$46$	−67.6447	−	49.1468i	−1.47054	−	1.06841i
$47$	18.9168	+	6.14644i	0.402485	+	0.130775i	0.503262	−	0.864134i	$-0.332133\pi$
$47$	18.9168	+	6.14644i	0.402485	+	0.130775i	−0.100777	+	0.994909i	$0.532133\pi$
$48$	24.3923	−	9.07892i	0.508173	−	0.189144i
$49$	32.0518	−	23.2870i	0.654118	−	0.475244i
$50$	−34.3217	−	47.2397i	−0.686434	−	0.944795i
$51$	−0.843091	−	2.26513i	−0.0165312	−	0.0444143i
$52$	26.9324	−	82.8895i	0.517931	−	1.59403i
$53$	−10.3894	+	14.2997i	−0.196026	+	0.269806i	−0.895703	−	0.444653i	$-0.853327\pi$
$53$	−10.3894	+	14.2997i	−0.196026	+	0.269806i	0.699677	+	0.714459i	$0.253327\pi$
$54$	−81.9669	+	10.4224i	−1.51791	+	0.193007i
$55$		0			0
$56$			12.7963i			0.228505i
$57$	−34.3546	+	51.7382i	−0.602712	+	0.907687i
$58$	3.57717	−	11.0094i	0.0616754	−	0.189817i
$59$	−41.3952	+	13.4501i	−0.701614	+	0.227968i	−0.638034	−	0.770009i	$-0.720252\pi$
$59$	−41.3952	+	13.4501i	−0.701614	+	0.227968i	−0.0635803	+	0.997977i	$0.520252\pi$
$60$	−83.7299	+	66.4004i	−1.39550	+	1.10667i
$61$	8.61986	−	6.26270i	0.141309	−	0.102667i	−0.514885	−	0.857259i	$-0.672165\pi$
$61$	8.61986	−	6.26270i	0.141309	−	0.102667i	0.656194	+	0.754592i	$0.272165\pi$
$62$	−60.4797	+	19.6510i	−0.975479	+	0.316952i
$63$	−6.28039	+	26.8418i	−0.0996887	+	0.426061i
$64$	−79.0299	−	57.4185i	−1.23484	−	0.897165i
$65$		−	107.854i		−	1.65929i
$66$		0			0
$67$	72.2963			1.07905			0.539525	−	0.841970i	$-0.318604\pi$
$67$	72.2963			1.07905			0.539525	+	0.841970i	$0.318604\pi$
$68$	−2.54066	+	3.49692i	−0.0373626	+	0.0514253i
$69$	−22.0213	+	78.9537i	−0.319149	+	1.14426i
$70$	19.2312	+	59.1877i	0.274732	+	0.845538i
$71$	−1.51055	−	2.07909i	−0.0212753	−	0.0292830i	0.798247	−	0.602330i	$-0.205761\pi$
$71$	−1.51055	−	2.07909i	−0.0212753	−	0.0292830i	−0.819522	+	0.573047i	$0.805761\pi$
$72$	24.5838	+	28.4494i	0.341441	+	0.395131i
$73$	14.0537	+	43.2529i	0.192517	+	0.592505i	0.999997	+	0.00261035i	$0.000830900\pi$
$73$	14.0537	+	43.2529i	0.192517	+	0.592505i	−0.807480	+	0.589895i	$0.799169\pi$
$74$	−112.209	−	36.4590i	−1.51634	−	0.492690i
$75$	−31.6643	+	47.6865i	−0.422190	+	0.635820i
$76$	111.068			1.46143
$77$		0			0
$78$	−149.006	+	6.28555i	−1.91033	+	0.0805840i
$79$	−79.4797	−	57.7454i	−1.00607	−	0.730954i	−0.0426901	−	0.999088i	$-0.513593\pi$
$79$	−79.4797	−	57.7454i	−1.00607	−	0.730954i	−0.963381	+	0.268135i	$0.913593\pi$
$80$	−54.7816	−	17.7996i	−0.684770	−	0.222495i
$81$	37.6046	+	71.7419i	0.464254	+	0.885702i
$82$	−33.1080	+	24.0543i	−0.403756	+	0.293346i
$83$	−18.7507	−	25.8081i	−0.225912	−	0.310941i	0.680982	−	0.732300i	$-0.261553\pi$
$83$	−18.7507	−	25.8081i	−0.225912	−	0.310941i	−0.906894	+	0.421359i	$0.861553\pi$
$84$	46.2034	−	17.1971i	0.550041	−	0.204728i
$85$	−1.65292	+	5.08716i	−0.0194461	+	0.0598489i
$86$	78.0893	−	107.481i	0.908015	−	1.24978i
$87$	−11.3380	+	0.478272i	−0.130321	+	0.00549738i
$88$		0			0
$89$			18.5409i			0.208325i	0.994560	+	0.104162i	$0.0332161\pi$
$89$			18.5409i			0.208325i	−0.994560	+	0.104162i	$0.966784\pi$
$90$	156.465	+	94.6430i	1.73850	+	1.05159i
$91$	−15.3758	+	47.3217i	−0.168964	+	0.520019i
$92$	139.414	−	45.2985i	1.51537	−	0.492375i
$93$	38.7356	+	48.8450i	0.416511	+	0.525215i
$94$	−49.2443	+	35.7781i	−0.523876	+	0.380618i
$95$	130.719	−	42.4731i	1.37599	−	0.447085i
$96$	−34.8673	+	125.011i	−0.363201	+	1.30220i
$97$	51.2123	+	37.2079i	0.527962	+	0.383587i	0.819595	−	0.572943i	$-0.194199\pi$
$97$	51.2123	+	37.2079i	0.527962	+	0.383587i	−0.291633	+	0.956530i	$0.594199\pi$
$98$			121.242i			1.23716i
$99$		0			0
$100$	102.371			1.02371
$101$	88.3786	−	121.643i	0.875036	−	1.20438i	−0.102735	−	0.994709i	$-0.532759\pi$
$101$	88.3786	−	121.643i	0.875036	−	1.20438i	0.977771	−	0.209675i	$-0.0672406\pi$
$102$	7.12453	+	1.98713i	0.0698483	+	0.0194817i
$103$	−46.2807	−	142.437i	−0.449327	−	1.38289i	−0.877668	−	0.479269i	$-0.840902\pi$
$103$	−46.2807	−	142.437i	−0.449327	−	1.38289i	0.428341	−	0.903617i	$-0.359098\pi$
$104$	39.8906	+	54.9047i	0.383563	+	0.527929i
$105$	47.8015	−	37.9081i	0.455253	−	0.361029i
$106$	−16.7152	−	51.4440i	−0.157690	−	0.485320i
$107$	19.7358	+	6.41256i	0.184447	+	0.0599305i	0.399784	−	0.916609i	$-0.369085\pi$
$107$	19.7358	+	6.41256i	0.184447	+	0.0599305i	−0.215337	+	0.976540i	$0.569085\pi$
$108$	69.6835	−	126.998i	0.645218	−	1.17590i
$109$	105.794			0.970583			0.485291	−	0.874352i	$-0.338714\pi$
$109$	105.794			0.970583			0.485291	+	0.874352i	$0.338714\pi$
$110$		0			0
$111$	4.87462	+	115.558i	0.0439155	+	1.04106i
$112$	21.4984	+	15.6195i	0.191950	+	0.139460i
$113$	126.271	+	41.0279i	1.11744	+	0.363078i	0.808790	−	0.588097i	$-0.200123\pi$
$113$	126.271	+	41.0279i	1.11744	+	0.363078i	0.308650	+	0.951176i	$0.400123\pi$
$114$	−66.2971	−	178.120i	−0.581554	−	1.56246i
$115$	146.757	−	106.626i	1.27615	−	0.927179i
$116$	11.9289	+	16.4188i	0.102836	+	0.141541i
$117$	56.7284	+	134.748i	0.484858	+	1.15169i
$118$	41.1608	−	126.680i	0.348820	−	1.07356i
$119$	1.45047	−	1.99639i	0.0121888	−	0.0167764i
$120$	−3.50703	−	83.1381i	−0.0292253	−	0.692817i
$121$		0			0
$122$			32.6062i			0.267264i
$123$	33.4211	+	22.1919i	0.271716	+	0.180422i
$124$	34.4517	−	106.031i	0.277836	−	0.855092i
$125$	−37.3772	+	12.1446i	−0.299018	+	0.0971568i
$126$	−55.1580	−	63.8313i	−0.437762	−	0.506598i
$127$	−118.647	+	86.2019i	−0.934226	+	0.678755i	−0.947024	−	0.321163i	$-0.895926\pi$
$127$	−118.647	+	86.2019i	−0.934226	+	0.678755i	0.0127976	+	0.999918i	$0.495926\pi$
$128$	119.740	−	38.9058i	0.935466	−	0.303951i
$129$	−125.449	−	34.9896i	−0.972476	−	0.271237i
$130$	267.024	+	194.004i	2.05403	+	1.49234i
$131$		−	149.467i		−	1.14097i	−0.821309	−	0.570484i	$-0.806756\pi$
$131$		−	149.467i		−	1.14097i	0.821309	−	0.570484i	$-0.193244\pi$
$132$		0			0
$133$	−63.4091			−0.476760
$134$	−130.045	+	178.991i	−0.970482	+	1.33575i
$135$	33.4475	−	176.114i	0.247759	−	1.30455i
$136$	−1.04008	−	3.20105i	−0.00764768	−	0.0235371i
$137$	89.4650	+	123.138i	0.653029	+	0.898817i	0.999226	−	0.0393446i	$-0.0125270\pi$
$137$	89.4650	+	123.138i	0.653029	+	0.898817i	−0.346197	+	0.938162i	$0.612527\pi$
$138$	−155.862	−	196.540i	−1.12944	−	1.42420i
$139$	−34.5591	−	106.362i	−0.248627	−	0.765194i	−0.995019	−	0.0996878i	$-0.968216\pi$
$139$	−34.5591	−	106.362i	−0.248627	−	0.765194i	0.746392	−	0.665506i	$-0.231784\pi$
$140$	−103.766	−	33.7157i	−0.741188	−	0.240827i
$141$	49.7100	+	33.0079i	0.352554	+	0.234099i
$142$	7.86454			0.0553841
$143$		0			0
$144$	77.8039	−	6.57574i	0.540305	−	0.0456649i
$145$	20.3180	+	14.7619i	0.140124	+	0.101806i
$146$	−132.365	−	43.0080i	−0.906609	−	0.294575i
$147$	111.389	−	41.4595i	0.757748	−	0.282037i
$148$	167.342	−	121.581i	1.13069	−	0.821495i
$149$	152.645	+	210.098i	1.02446	+	1.41005i	0.909026	+	0.416739i	$0.136827\pi$
$149$	152.645	+	210.098i	1.02446	+	1.41005i	0.115437	+	0.993315i	$0.463173\pi$
$150$	−61.1054	−	164.171i	−0.407369	−	1.09448i
$151$	−27.1990	+	83.7098i	−0.180126	+	0.554370i	−0.999830	−	0.0184166i	$-0.994137\pi$
$151$	−27.1990	+	83.7098i	−0.180126	+	0.554370i	0.819705	+	0.572786i	$0.194137\pi$
$152$	−50.8355	+	69.9691i	−0.334444	+	0.460323i
$153$	−0.610640	−	7.22507i	−0.00399111	−	0.0472227i
$154$		0			0
$155$		−	137.965i		−	0.890098i
$156$	144.634	−	217.819i	0.927141	−	1.39628i
$157$	−2.36562	+	7.28062i	−0.0150676	+	0.0463734i	−0.958308	−	0.285738i	$-0.907761\pi$
$157$	−2.36562	+	7.28062i	−0.0150676	+	0.0463734i	0.943240	+	0.332112i	$0.107761\pi$
$158$	285.932	−	92.9048i	1.80969	−	0.588005i
$159$	−41.5475	+	32.9484i	−0.261305	+	0.207223i
$160$	232.368	−	168.825i	1.45230	−	1.05516i
$161$	−79.5919	+	25.8610i	−0.494360	+	0.160627i
$162$	−245.260	−	35.9460i	−1.51395	−	0.221889i
$163$	−212.405	−	154.321i	−1.30310	−	0.946756i	−0.303117	−	0.952953i	$-0.598027\pi$
$163$	−212.405	−	154.321i	−1.30310	−	0.946756i	−0.999981	+	0.00619729i	$0.998027\pi$
$164$		−	71.7464i		−	0.437478i
$165$		0			0
$166$	97.6240			0.588096
$167$	−94.0494	+	129.448i	−0.563170	+	0.775137i	−0.991725	−	0.128379i	$-0.959023\pi$
$167$	−94.0494	+	129.448i	−0.563170	+	0.775137i	0.428555	+	0.903515i	$0.359023\pi$
$168$	−10.3135	+	36.9776i	−0.0613901	+	0.220105i
$169$	29.3223	+	90.2447i	0.173505	+	0.533992i
$170$	−9.62155	−	13.2429i	−0.0565974	−	0.0778996i
$171$	−140.974	+	121.819i	−0.824412	+	0.712392i
$172$	71.9747	+	221.515i	0.418458	+	1.28788i
$173$	157.422	+	51.1497i	0.909956	+	0.295663i	0.726340	−	0.687335i	$-0.241220\pi$
$173$	157.422	+	51.1497i	0.909956	+	0.295663i	0.183616	+	0.982998i	$0.441220\pi$
$174$	19.2103	−	28.9308i	0.110404	−	0.166269i
$175$	−58.4435			−0.333963
$176$		0			0
$177$	−130.461	+	5.50325i	−0.737065	+	0.0310918i
$178$	−45.9035	−	33.3508i	−0.257885	−	0.187364i
$179$	55.6720	+	18.0889i	0.311017	+	0.101056i	0.460367	−	0.887729i	$-0.347718\pi$
$179$	55.6720	+	18.0889i	0.311017	+	0.101056i	−0.149350	+	0.988784i	$0.547718\pi$
$180$	−295.472	+	124.393i	−1.64151	+	0.691073i
$181$	−230.309	+	167.330i	−1.27243	+	0.924473i	−0.999296	−	0.0375044i	$-0.988059\pi$
$181$	−230.309	+	167.330i	−1.27243	+	0.924473i	−0.273131	+	0.961977i	$0.588059\pi$
$182$	−89.5015	−	123.188i	−0.491767	−	0.676859i
$183$	29.9565	−	11.1499i	0.163696	−	0.0609286i
$184$	−35.2730	+	108.559i	−0.191701	+	0.589995i
$185$	150.455	−	207.084i	0.813272	−	1.11937i
$186$	−190.607	+	8.04041i	−1.02477	+	0.0432280i
$187$		0			0
$188$		−	106.715i		−	0.567631i
$189$	−39.7824	+	72.5032i	−0.210489	+	0.383615i
$190$	−129.979	+	400.033i	−0.684097	+	2.10544i
$191$	−130.716	+	42.4721i	−0.684375	+	0.222367i	−0.630510	−	0.776181i	$-0.717154\pi$
$191$	−130.716	+	42.4721i	−0.684375	+	0.222367i	−0.0538652	+	0.998548i	$0.517154\pi$
$192$	−182.095	−	229.619i	−0.948411	−	1.19593i
$193$	241.163	−	175.215i	1.24955	−	0.907852i	0.251356	−	0.967895i	$-0.419124\pi$
$193$	241.163	−	175.215i	1.24955	−	0.907852i	0.998196	+	0.0600426i	$0.0191237\pi$
$194$	−184.239	+	59.8628i	−0.949684	+	0.308571i
$195$	86.9276	−	311.665i	0.445783	−	1.59828i
$196$	−171.963	−	124.938i	−0.877362	−	0.637441i
$197$			58.1375i			0.295114i	0.989054	+	0.147557i	$0.0471410\pi$
$197$			58.1375i			0.295114i	−0.989054	+	0.147557i	$0.952859\pi$
$198$		0			0
$199$	−125.049			−0.628385			−0.314193	−	0.949359i	$-0.601734\pi$
$199$	−125.049			−0.628385			−0.314193	+	0.949359i	$0.601734\pi$
$200$	−46.8546	+	64.4898i	−0.234273	+	0.322449i
$201$	208.915	+	58.2693i	1.03938	+	0.289897i
$202$	142.190	+	437.615i	0.703910	+	2.16641i
$203$	−6.81024	−	9.37349i	−0.0335480	−	0.0461748i
$204$	−10.1602	+	8.05735i	−0.0498049	+	0.0394968i
$205$	−27.4362	−	84.4398i	−0.133835	−	0.411902i
$206$	435.894	+	141.631i	2.11599	+	0.687527i
$207$	−127.270	+	210.404i	−0.614831	+	1.01645i
$208$	140.934			0.677566
$209$		0			0
$210$	7.86865	+	186.535i	0.0374698	+	0.888262i
$211$	−39.1505	−	28.4445i	−0.185547	−	0.134808i	0.491134	−	0.871084i	$-0.336583\pi$
$211$	−39.1505	−	28.4445i	−0.185547	−	0.134808i	−0.676681	+	0.736276i	$0.736583\pi$
$212$	90.1902	+	29.3046i	0.425425	+	0.138229i
$213$	−2.68934	−	7.22543i	−0.0126260	−	0.0339222i
$214$	−51.3765	+	37.3272i	−0.240077	+	0.174426i
$215$	169.417	+	233.183i	0.787987	+	1.08457i
$216$	48.1102	+	102.024i	0.222732	+	0.472336i
$217$	−19.6685	+	60.5335i	−0.0906383	+	0.278956i
$218$	−190.298	+	261.923i	−0.872929	+	1.20148i
$219$	5.75021	+	136.315i	0.0262567	+	0.622444i
$220$		0			0
$221$		−	13.0875i		−	0.0592193i
$222$	−294.867	−	195.794i	−1.32823	−	0.881956i
$223$	65.4240	−	201.354i	0.293381	−	0.902934i	−0.690379	−	0.723448i	$-0.742556\pi$
$223$	65.4240	−	201.354i	0.293381	−	0.902934i	0.983760	−	0.179487i	$-0.0574437\pi$
$224$	−126.021	+	40.9469i	−0.562596	+	0.182798i
$225$	−129.935	+	112.279i	−0.577487	+	0.499019i
$226$	−328.709	+	238.821i	−1.45447	+	1.05673i
$227$	115.444	−	37.5101i	0.508565	−	0.165243i	−0.0434848	−	0.999054i	$-0.513846\pi$
$227$	115.444	−	37.5101i	0.508565	−	0.165243i	0.552049	+	0.833811i	$0.313846\pi$
$228$	320.955	+	89.5187i	1.40770	+	0.392626i
$229$	−261.267	−	189.822i	−1.14090	−	0.828915i	−0.153659	−	0.988124i	$-0.549106\pi$
$229$	−261.267	−	189.822i	−1.14090	−	0.828915i	−0.987245	+	0.159209i	$0.949106\pi$
$230$			555.137i			2.41364i
$231$		0			0
$232$	−15.8030			−0.0681166
$233$	236.530	−	325.556i	1.01515	−	1.39724i	0.0996031	−	0.995027i	$-0.468243\pi$
$233$	236.530	−	325.556i	1.01515	−	1.39724i	0.915548	−	0.402209i	$-0.131757\pi$
$234$	−435.649	−	101.932i	−1.86175	−	0.435607i
$235$	−40.8082	−	125.595i	−0.173652	−	0.534445i
$236$	137.260	+	188.923i	0.581612	+	0.800520i
$237$	−183.131	−	230.926i	−0.772706	−	0.974371i
$238$	2.33361	+	7.18212i	0.00980509	+	0.0301770i
$239$	−0.305711	−	0.0993315i	−0.00127912	−	0.000415613i	0.308377	−	0.951264i	$-0.400214\pi$
$239$	−0.305711	−	0.0993315i	−0.00127912	−	0.000415613i	−0.309656	+	0.950848i	$0.600214\pi$
$240$	−143.957	−	95.5885i	−0.599819	−	0.398285i
$241$	−290.799			−1.20664			−0.603318	−	0.797500i	$-0.706155\pi$
$241$	−290.799			−1.20664			−0.603318	+	0.797500i	$0.706155\pi$
$242$		0			0
$243$	50.8438	+	237.621i	0.209234	+	0.977866i
$244$	−46.2469	−	33.6004i	−0.189537	−	0.137706i
$245$	−250.164	−	81.2832i	−1.02108	−	0.331768i
$246$	−115.060	+	42.8257i	−0.467722	+	0.174088i
$247$	−272.067	+	197.668i	−1.10149	+	0.800276i
$248$	51.0276	+	70.2335i	0.205756	+	0.283199i
$249$	−33.3832	−	89.6906i	−0.134069	−	0.360203i
$250$	37.1656	−	114.384i	0.148662	−	0.457535i
$251$	−66.1972	+	91.1127i	−0.263734	+	0.362999i	−0.920262	−	0.391303i	$-0.872024\pi$
$251$	−66.1972	+	91.1127i	−0.263734	+	0.362999i	0.656528	+	0.754302i	$0.272024\pi$
$252$	147.375	−	12.4557i	0.584821	−	0.0494272i
$253$		0			0
$254$		−	448.803i		−	1.76694i
$255$	−8.87658	+	13.3682i	−0.0348101	+	0.0524242i
$256$	1.68535	−	5.18697i	0.00658339	−	0.0202616i
$257$	−186.948	+	60.7430i	−0.727423	+	0.236354i	−0.649238	−	0.760585i	$-0.724912\pi$
$257$	−186.948	+	60.7430i	−0.727423	+	0.236354i	−0.0781844	+	0.996939i	$0.524912\pi$
$258$	312.282	−	247.649i	1.21040	−	0.959881i
$259$	−95.5359	+	69.4109i	−0.368864	+	0.267996i
$260$	−550.330	+	178.813i	−2.11665	+	0.687743i
$261$	−33.1489	−	7.75609i	−0.127007	−	0.0297168i
$262$	370.050	+	268.857i	1.41240	+	1.02617i
$263$		−	378.327i		−	1.43850i	−0.694749	−	0.719252i	$-0.744485\pi$
$263$		−	378.327i		−	1.43850i	0.694749	−	0.719252i	$-0.255515\pi$
$264$		0			0
$265$	117.353			0.442842
$266$	114.059	−	156.988i	0.428791	−	0.590181i
$267$	−14.9435	+	53.5777i	−0.0559683	+	0.200666i
$268$	−119.862	−	368.897i	−0.447246	−	1.37648i
$269$	−118.235	−	162.737i	−0.439537	−	0.604971i	0.530572	−	0.847640i	$-0.321977\pi$
$269$	−118.235	−	162.737i	−0.439537	−	0.604971i	−0.970109	+	0.242669i	$0.921977\pi$
$270$	375.858	+	399.598i	1.39206	+	1.47999i
$271$	−24.7877	−	76.2886i	−0.0914674	−	0.281508i	0.894850	−	0.446368i	$-0.147283\pi$
$271$	−24.7877	−	76.2886i	−0.0914674	−	0.281508i	−0.986317	+	0.164860i	$0.947283\pi$
$272$	−6.64746	−	2.15989i	−0.0244392	−	0.00794078i
$273$	−82.5717	+	124.353i	−0.302460	+	0.455507i
$274$	−465.792			−1.69997
$275$		0			0
$276$	439.376	−	18.5343i	1.59194	−	0.0671533i
$277$	177.106	+	128.675i	0.639371	+	0.464530i	0.859634	−	0.510910i	$-0.170692\pi$
$277$	177.106	+	128.675i	0.639371	+	0.464530i	−0.220263	+	0.975441i	$0.570692\pi$
$278$	325.495	+	105.760i	1.17084	+	0.380430i
$279$	72.5664	+	172.368i	0.260095	+	0.617805i
$280$	68.7331	−	49.9375i	0.245475	−	0.178348i
$281$	−291.798	−	401.626i	−1.03843	−	1.42927i	−0.898427	−	0.439123i	$-0.855289\pi$
$281$	−291.798	−	401.626i	−1.03843	−	1.42927i	−0.140001	−	0.990151i	$-0.544711\pi$
$282$	−171.138	+	63.6983i	−0.606872	+	0.225881i
$283$	95.0850	−	292.642i	0.335990	−	1.03407i	−0.630243	−	0.776398i	$-0.717045\pi$
$283$	95.0850	−	292.642i	0.335990	−	1.03407i	0.966233	−	0.257672i	$-0.0829553\pi$
$284$	−8.10433	+	11.1547i	−0.0285364	+	0.0392770i
$285$	411.971	−	17.3783i	1.44551	−	0.0609764i
$286$		0			0
$287$			40.9601i			0.142718i
$288$	−201.512	+	333.143i	−0.699695	+	1.15675i
$289$	89.1053	−	274.238i	0.308323	−	0.948921i
$290$	−73.0950	+	23.7500i	−0.252052	+	0.0818966i
$291$	118.000	+	148.796i	0.405497	+	0.511326i
$292$	197.401	−	143.420i	0.676030	−	0.491165i
$293$	−323.072	+	104.972i	−1.10263	+	0.358268i	−0.803116	−	0.595823i	$-0.796826\pi$
$293$	−323.072	+	104.972i	−1.10263	+	0.358268i	−0.299519	+	0.954090i	$0.596826\pi$
$294$	−97.7182	+	350.353i	−0.332375	+	1.19168i
$295$	233.790	+	169.858i	0.792507	+	0.575790i
$296$			161.067i			0.544145i
$297$		0			0
$298$	−794.734			−2.66689
$299$	−260.884	+	359.077i	−0.872523	+	1.20092i
$300$	295.821	+	82.5084i	0.986069	+	0.275028i
$301$	−41.0905	−	126.463i	−0.136513	−	0.420144i
$302$	−158.324	−	217.914i	−0.524251	−	0.721570i
$303$	353.430	−	280.281i	1.16643	−	0.925018i
$304$	55.5002	+	170.812i	0.182567	+	0.561882i
$305$	−67.2779	−	21.8599i	−0.220583	−	0.0716719i
$306$	18.9862	+	11.4844i	0.0620465	+	0.0375308i
$307$	396.129			1.29032			0.645161	−	0.764047i	$-0.276790\pi$
$307$	396.129			1.29032			0.645161	+	0.764047i	$0.276790\pi$
$308$		0			0
$309$	−18.9362	−	448.903i	−0.0612821	−	1.45276i
$310$	341.574	+	248.168i	1.10185	+	0.800542i
$311$	−82.7760	−	26.8955i	−0.266161	−	0.0864808i	0.172896	−	0.984940i	$-0.444687\pi$
$311$	−82.7760	−	26.8955i	−0.266161	−	0.0864808i	−0.439057	+	0.898459i	$0.644687\pi$
$312$	71.0200	+	190.809i	0.227628	+	0.611568i
$313$	484.531	−	352.033i	1.54802	−	1.12471i	0.602982	−	0.797755i	$-0.293979\pi$
$313$	484.531	−	352.033i	1.54802	−	1.12471i	0.945041	−	0.326951i	$-0.106021\pi$
$314$	−13.7701	−	18.9530i	−0.0438539	−	0.0603598i
$315$	168.685	−	71.0162i	0.535509	−	0.225448i
$316$	−162.878	+	501.288i	−0.515438	+	1.58635i
$317$	−1.44295	+	1.98605i	−0.00455190	+	0.00626516i	−0.811287	−	0.584648i	$-0.801233\pi$
$317$	−1.44295	+	1.98605i	−0.00455190	+	0.00626516i	0.806735	+	0.590913i	$0.201233\pi$
$318$	−6.83917	−	162.130i	−0.0215068	−	0.509843i
$319$		0			0
$320$			648.571i			2.02678i
$321$	51.8624	+	34.4371i	0.161565	+	0.107281i
$322$	79.1412	−	243.571i	0.245780	−	0.756433i
$323$	15.8620	−	5.15389i	0.0491085	−	0.0159563i
$324$	303.722	−	310.823i	0.937414	−	0.959329i
$325$	−250.761	+	182.189i	−0.771573	+	0.560581i
$326$	764.136	−	248.283i	2.34398	−	0.761604i
$327$	305.712	+	85.2673i	0.934900	+	0.260756i
$328$	45.1977	+	32.8380i	0.137798	+	0.100116i
$329$			60.9235i			0.185178i
$330$		0			0
$331$	368.074			1.11200			0.556002	−	0.831181i	$-0.312335\pi$
$331$	368.074			1.11200			0.556002	+	0.831181i	$0.312335\pi$
$332$	−100.601	+	138.465i	−0.303014	+	0.417063i
$333$	−79.0511	+	337.858i	−0.237391	+	1.01459i
$334$	−151.313	−	465.694i	−0.453034	−	1.39429i
$335$	−282.136	−	388.327i	−0.842197	−	1.15919i
$336$	49.5350	+	62.4630i	0.147426	+	0.185902i
$337$	−182.901	−	562.911i	−0.542733	−	1.67036i	−0.726321	−	0.687356i	$-0.758771\pi$
$337$	−182.901	−	562.911i	−0.542733	−	1.67036i	0.183588	−	0.983003i	$-0.441229\pi$
$338$	−276.172	−	89.7336i	−0.817076	−	0.265484i
$339$	331.818	+	220.330i	0.978814	+	0.649941i
$340$	28.6980			0.0844059
$341$		0			0
$342$	−48.0182	−	568.149i	−0.140404	−	1.66125i
$343$	219.596	+	159.546i	0.640221	+	0.465148i
$344$	−172.489	−	56.0452i	−0.501423	−	0.162922i
$345$	510.024	−	189.833i	1.47833	−	0.550241i
$346$	−409.803	+	297.740i	−1.18440	+	0.860519i
$347$	173.162	+	238.337i	0.499026	+	0.686851i	0.982021	−	0.188773i	$-0.0604509\pi$
$347$	173.162	+	238.337i	0.499026	+	0.686851i	−0.482994	+	0.875623i	$0.660451\pi$
$348$	21.2379	+	57.0598i	0.0610285	+	0.163965i
$349$	−127.318	+	391.843i	−0.364807	+	1.12276i	0.585295	+	0.810820i	$0.300979\pi$
$349$	−127.318	+	391.843i	−0.364807	+	1.12276i	−0.950102	+	0.311939i	$0.899021\pi$
$350$	105.127	−	144.694i	0.300361	−	0.413412i
$351$	55.3248	+	435.102i	0.157620	+	1.23961i
$352$		0			0
$353$		−	135.577i		−	0.384070i	−0.981388	−	0.192035i	$-0.938491\pi$
$353$		−	135.577i		−	0.384070i	0.981388	−	0.192035i	$-0.0615086\pi$
$354$	221.044	−	332.893i	0.624418	−	0.940376i
$355$	−5.27257	+	16.2273i	−0.0148523	+	0.0457107i
$356$	94.6061	−	30.7394i	0.265748	−	0.0863466i
$357$	5.80047	−	4.59995i	0.0162478	−	0.0128850i
$358$	−144.926	+	105.295i	−0.404821	+	0.294120i
$359$	265.131	−	86.1464i	0.738527	−	0.239962i	0.0844899	−	0.996424i	$-0.473074\pi$
$359$	265.131	−	86.1464i	0.738527	−	0.239962i	0.654037	+	0.756462i	$0.273074\pi$
$360$	56.8732	−	243.071i	0.157981	−	0.675198i
$361$	−54.6603	−	39.7131i	−0.151414	−	0.110008i
$362$		−	871.187i		−	2.40659i
$363$		0			0
$364$	266.954			0.733391
$365$	177.481	−	244.281i	0.486249	−	0.669264i
$366$	−26.2799	+	94.2223i	−0.0718030	+	0.257438i
$367$	−54.5068	−	167.755i	−0.148520	−	0.457097i	0.848927	−	0.528510i	$-0.177249\pi$
$367$	−54.5068	−	167.755i	−0.148520	−	0.457097i	−0.997447	+	0.0714131i	$0.977249\pi$
$368$	139.329	+	191.770i	0.378612	+	0.521115i
$369$	78.6909	+	91.0647i	0.213254	+	0.246788i
$370$	242.063	+	744.994i	0.654225	+	2.01350i
$371$	−51.4897	−	16.7300i	−0.138786	−	0.0450944i
$372$	185.014	−	278.632i	0.497350	−	0.749011i
$373$	−163.109			−0.437289			−0.218645	−	0.975805i	$-0.570164\pi$
$373$	−163.109			−0.437289			−0.218645	+	0.975805i	$0.570164\pi$
$374$		0			0
$375$	−117.797	+	4.96908i	−0.314126	+	0.0132509i
$376$	67.2264	+	48.8428i	0.178794	+	0.129901i
$377$	−58.4409	−	18.9886i	−0.155016	−	0.0503676i
$378$	−107.944	−	228.910i	−0.285565	−	0.605582i
$379$	−43.0644	+	31.2881i	−0.113626	+	0.0825545i	−0.643147	−	0.765742i	$-0.722372\pi$
$379$	−43.0644	+	31.2881i	−0.113626	+	0.0825545i	0.529521	+	0.848297i	$0.322372\pi$
$380$	−433.444	−	596.584i	−1.14064	−	1.56996i
$381$	−412.331	+	153.471i	−1.08223	+	0.402812i
$382$	129.975	−	400.023i	0.340250	−	1.04718i
$383$	52.7039	−	72.5408i	0.137608	−	0.189401i	−0.734651	−	0.678445i	$-0.762654\pi$
$383$	52.7039	−	72.5408i	0.137608	−	0.189401i	0.872259	+	0.489044i	$0.162654\pi$
$384$	377.369	−	15.9187i	0.982733	−	0.0414549i
$385$		0			0
$386$			912.245i			2.36333i
$387$	−334.311	−	202.219i	−0.863853	−	0.522530i
$388$	104.950	−	323.002i	0.270489	−	0.832480i
$389$	−256.406	+	83.3113i	−0.659141	+	0.214168i	−0.619440	−	0.785044i	$-0.712640\pi$
$389$	−256.406	+	83.3113i	−0.659141	+	0.214168i	−0.0397008	+	0.999212i	$0.512640\pi$
$390$	615.257	+	775.830i	1.57758	+	1.98931i
$391$	17.8083	−	12.9385i	0.0455454	−	0.0330907i
$392$	157.413	−	51.1467i	0.401565	−	0.130476i
$393$	120.467	−	431.915i	0.306532	−	1.09902i
$394$	−143.937	−	104.576i	−0.365322	−	0.265422i
$395$			652.262i			1.65130i
$396$		0			0
$397$	211.490			0.532720			0.266360	−	0.963874i	$-0.414179\pi$
$397$	211.490			0.532720			0.266360	+	0.963874i	$0.414179\pi$
$398$	224.934	−	309.595i	0.565161	−	0.777877i
$399$	−183.234	−	51.1063i	−0.459232	−	0.128086i
$400$	51.1540	+	157.436i	0.127885	+	0.393589i
$401$	264.385	+	363.894i	0.659314	+	0.907468i	0.999458	−	0.0329055i	$-0.0104760\pi$
$401$	264.385	+	363.894i	0.659314	+	0.907468i	−0.340145	+	0.940373i	$0.610476\pi$
$402$	−520.054	+	412.418i	−1.29367	+	1.02592i
$403$	104.313	+	321.042i	0.258841	+	0.796631i
$404$	−767.216	−	249.284i	−1.89905	−	0.617038i
$405$	238.597	−	481.959i	0.589129	−	1.19002i
$406$	35.4569			0.0873323
$407$		0			0
$408$	−0.425560	−	10.0884i	−0.00104304	−	0.0247264i
$409$	−124.826	−	90.6917i	−0.305199	−	0.221740i	0.424635	−	0.905365i	$-0.360403\pi$
$409$	−124.826	−	90.6917i	−0.305199	−	0.221740i	−0.729834	+	0.683625i	$0.760403\pi$
$410$	258.407	+	83.9617i	0.630262	+	0.204785i
$411$	159.281	+	427.939i	0.387545	+	1.04122i
$412$	−650.066	+	472.301i	−1.57783	+	1.14636i
$413$	−78.3621	−	107.856i	−0.189739	−	0.261153i
$414$	−291.989	−	693.564i	−0.705287	−	1.67528i
$415$	−65.4493	+	201.432i	−0.157709	+	0.485379i
$416$	−413.070	+	568.542i	−0.992957	+	1.36669i
$417$	−14.1402	−	335.209i	−0.0339093	−	0.803858i
$418$		0			0
$419$			755.530i			1.80317i	0.432599	+	0.901587i	$0.357597\pi$
$419$			755.530i			1.80317i	−0.432599	+	0.901587i	$0.642403\pi$
$420$	−272.680	−	181.062i	−0.649238	−	0.431100i
$421$	−135.007	+	415.507i	−0.320681	+	0.986954i	0.652672	+	0.757641i	$0.273648\pi$
$421$	−135.007	+	415.507i	−0.320681	+	0.986954i	−0.973353	+	0.229313i	$0.926352\pi$
$422$	140.846	−	45.7635i	0.333758	−	0.108444i
$423$	117.044	+	135.448i	0.276699	+	0.320209i
$424$	−59.7405	+	43.4040i	−0.140897	+	0.102368i
$425$	14.6199	−	4.75029i	0.0343997	−	0.0111771i
$426$	22.7262	+	6.33865i	0.0533479	+	0.0148795i
$427$	26.4024	+	19.1825i	0.0618324	+	0.0449239i
$428$		−	111.335i		−	0.260129i
$429$		0			0
$430$	−882.057			−2.05129
$431$	−5.72154	+	7.87503i	−0.0132750	+	0.0182715i	−0.815603	−	0.578612i	$-0.803595\pi$
$431$	−5.72154	+	7.87503i	−0.0132750	+	0.0182715i	0.802328	+	0.596884i	$0.203595\pi$
$432$	230.130	+	43.7063i	0.532709	+	0.101172i
$433$	−18.3169	−	56.3736i	−0.0423023	−	0.130193i	0.927675	−	0.373389i	$-0.121804\pi$
$433$	−18.3169	−	56.3736i	−0.0423023	−	0.130193i	−0.969977	+	0.243196i	$0.921804\pi$
$434$	−114.489	−	157.581i	−0.263801	−	0.363090i
$435$	46.8153	+	59.0334i	0.107621	+	0.135709i
$436$	−175.398	−	539.819i	−0.402288	−	1.23812i
$437$	−537.939	−	174.787i	−1.23098	−	0.399970i
$438$	−347.832	−	230.964i	−0.794137	−	0.527314i
$439$	−444.724			−1.01304			−0.506519	−	0.862229i	$-0.669068\pi$
$439$	−444.724			−1.01304			−0.506519	+	0.862229i	$0.669068\pi$
$440$		0			0
$441$	355.297	−	30.0286i	0.805662	−	0.0680920i
$442$	32.4019	+	23.5414i	0.0733075	+	0.0532610i
$443$	−509.149	−	165.433i	−1.14932	−	0.373437i	−0.328434	−	0.944527i	$-0.606521\pi$
$443$	−509.149	−	165.433i	−1.14932	−	0.373437i	−0.820888	+	0.571090i	$0.806521\pi$
$444$	581.562	−	216.460i	1.30982	−	0.487522i
$445$	99.5891	−	72.3557i	0.223796	−	0.162597i
$446$	380.830	+	524.167i	0.853878	+	1.17526i
$447$	271.765	+	730.150i	0.607975	+	1.63344i
$448$	92.4612	−	284.566i	0.206387	−	0.635193i
$449$	452.250	−	622.469i	1.00724	−	1.38635i	0.0864624	−	0.996255i	$-0.472444\pi$
$449$	452.250	−	622.469i	1.00724	−	1.38635i	0.920777	−	0.390090i	$-0.127556\pi$
$450$	−44.2578	−	523.657i	−0.0983508	−	1.16368i
$451$		0			0
$452$		−	712.327i		−	1.57594i
$453$	−146.065	+	219.975i	−0.322440	+	0.485596i
$454$	−114.790	+	353.289i	−0.252842	+	0.778169i
$455$	314.184	−	102.085i	0.690515	−	0.224362i
$456$	−203.293	+	161.218i	−0.445819	+	0.353548i
$457$	137.254	−	99.7207i	0.300337	−	0.218207i	−0.427402	−	0.904061i	$-0.640571\pi$
$457$	137.254	−	99.7207i	0.300337	−	0.218207i	0.727739	+	0.685854i	$0.240571\pi$
$458$	939.919	−	305.398i	2.05223	−	0.666809i
$459$	4.05868	−	21.3705i	0.00884244	−	0.0465588i
$460$	−787.377	−	572.063i	−1.71169	−	1.24362i
$461$			266.355i			0.577777i	0.957363	+	0.288888i	$0.0932857\pi$
$461$			266.355i			0.577777i	−0.957363	+	0.288888i	$0.906714\pi$
$462$		0			0
$463$	−704.848			−1.52235			−0.761175	−	0.648547i	$-0.775377\pi$
$463$	−704.848			−1.52235			−0.761175	+	0.648547i	$0.775377\pi$
$464$	−19.2896	+	26.5499i	−0.0415724	+	0.0572195i
$465$	111.197	−	398.679i	0.239133	−	0.857373i
$466$	380.547	+	1171.20i	0.816624	+	2.51331i
$467$	−396.859	−	546.230i	−0.849806	−	1.16966i	−0.983905	−	0.178690i	$-0.942814\pi$
$467$	−396.859	−	546.230i	−0.849806	−	1.16966i	0.134099	−	0.990968i	$-0.457186\pi$
$468$	593.507	−	512.862i	1.26818	−	1.09586i
$469$	68.4293	+	210.604i	0.145905	+	0.449049i
$470$	384.352	+	124.883i	0.817769	+	0.265709i
$471$	−12.7040	+	19.1322i	−0.0269723	+	0.0406204i
$472$	−181.838			−0.385250
$473$		0			0
$474$	901.138	−	38.0129i	1.90113	−	0.0801960i
$475$	−319.564	−	232.177i	−0.672766	−	0.488793i
$476$	−12.5915	−	4.09123i	−0.0264527	−	0.00859502i
$477$	−146.616	+	61.7249i	−0.307371	+	0.129402i
$478$	0.795829	−	0.578204i	0.00166491	−	0.00120963i
$479$	−411.336	−	566.156i	−0.858740	−	1.18195i	−0.981868	−	0.189563i	$-0.939293\pi$
$479$	−411.336	−	566.156i	−0.858740	−	1.18195i	0.123128	−	0.992391i	$-0.460707\pi$
$480$	807.544	−	300.571i	1.68238	−	0.626191i
$481$	−193.534	+	595.638i	−0.402358	+	1.23833i
$482$	523.082	−	719.961i	1.08523	−	1.49369i
$483$	−250.841	+	10.5813i	−0.519339	+	0.0219074i
$484$		0			0
$485$		−	420.282i		−	0.866560i
$486$	−679.759	−	301.548i	−1.39868	−	0.620469i
$487$	−201.895	+	621.370i	−0.414569	+	1.27591i	0.498066	+	0.867139i	$0.334044\pi$
$487$	−201.895	+	621.370i	−0.414569	+	1.27591i	−0.912636	+	0.408774i	$0.865956\pi$
$488$	42.3341	−	13.7552i	0.0867501	−	0.0281868i
$489$	−489.408	−	617.137i	−1.00083	−	1.26204i
$490$	651.229	−	473.145i	1.32904	−	0.965603i
$491$	−58.8107	+	19.1088i	−0.119777	+	0.0389180i	−0.368292	−	0.929710i	$-0.620057\pi$
$491$	−58.8107	+	19.1088i	−0.119777	+	0.0389180i	0.248515	+	0.968628i	$0.420057\pi$
$492$	57.8260	−	207.326i	0.117533	−	0.421394i
$493$	2.46549	+	1.79128i	0.00500099	+	0.00363343i
$494$		−	1029.14i		−	2.08329i
$495$		0			0
$496$	180.281			0.363470
$497$	4.62677	−	6.36821i	0.00930940	−	0.0128133i
$498$	282.105	+	78.6828i	0.566475	+	0.157998i
$499$	101.973	+	313.842i	0.204356	+	0.628942i	0.999739	+	0.0228356i	$0.00726941\pi$
$499$	101.973	+	313.842i	0.204356	+	0.628942i	−0.795384	+	0.606106i	$0.792731\pi$
$500$	123.937	+	170.585i	0.247875	+	0.341170i
$501$	−376.107	+	298.264i	−0.750713	+	0.595338i
$502$	−106.503	−	327.782i	−0.212157	−	0.652952i
$503$	−330.187	−	107.284i	−0.656436	−	0.213289i	−0.0381861	−	0.999271i	$-0.512158\pi$
$503$	−330.187	−	107.284i	−0.656436	−	0.213289i	−0.618250	+	0.785982i	$0.712158\pi$
$504$	−59.6062	+	98.5418i	−0.118266	+	0.195519i
$505$	−998.280			−1.97679
$506$		0			0
$507$	11.9975	+	284.414i	0.0236637	+	0.560974i
$508$	636.559	+	462.487i	1.25307	+	0.910407i
$509$	814.289	+	264.578i	1.59978	+	0.519800i	0.967053	−	0.254574i	$-0.0819352\pi$
$509$	814.289	+	264.578i	1.59978	+	0.519800i	0.632728	+	0.774374i	$0.281935\pi$
$510$	−17.1299	−	46.0229i	−0.0335881	−	0.0902410i
$511$	−112.696	+	81.8787i	−0.220541	+	0.160232i
$512$	305.823	+	420.929i	0.597310	+	0.822127i
$513$	−505.558	+	238.399i	−0.985494	+	0.464715i
$514$	185.889	−	572.108i	0.361652	−	1.11305i
$515$	−584.467	+	804.449i	−1.13489	+	1.56204i
$516$	29.4492	+	698.125i	0.0570720	+	1.35295i
$517$		0			0
$518$		−	361.382i		−	0.697649i
$519$	413.679	+	274.687i	0.797069	+	0.529261i
$520$	139.238	−	428.530i	0.267765	−	0.824097i
$521$	677.779	−	220.224i	1.30092	−	0.422695i	0.425019	−	0.905185i	$-0.360268\pi$
$521$	677.779	−	220.224i	1.30092	−	0.422695i	0.875901	+	0.482490i	$0.160268\pi$
$522$	78.8298	−	68.1184i	0.151015	−	0.130495i
$523$	407.684	−	296.200i	0.779510	−	0.566347i	−0.125322	−	0.992116i	$-0.539996\pi$
$523$	407.684	−	296.200i	0.779510	−	0.566347i	0.904832	+	0.425769i	$0.139996\pi$
$524$	−762.665	+	247.805i	−1.45547	+	0.472910i
$525$	−168.884	−	47.1042i	−0.321685	−	0.0897222i
$526$	936.660	+	680.524i	1.78072	+	1.29377i
$527$		−	16.7414i		−	0.0317673i
$528$		0			0
$529$	−217.513			−0.411179
$530$	−211.091	+	290.542i	−0.398286	+	0.548193i
$531$	−381.428	−	89.2456i	−0.718320	−	0.168071i
$532$	105.128	+	323.549i	0.197608	+	0.608175i
$533$	127.687	+	175.746i	0.239563	+	0.329730i
$534$	−105.768	−	133.371i	−0.198066	−	0.249759i
$535$	−42.5751	−	131.033i	−0.0795796	−	0.244921i
$536$	287.252	+	93.3339i	0.535918	+	0.174130i
$537$	146.297	+	97.1422i	0.272433	+	0.180898i
$538$	615.583			1.14421
$539$		0			0
$540$	−954.086	+	121.315i	−1.76683	+	0.224658i
$541$	−474.599	−	344.817i	−0.877263	−	0.637369i	0.0552628	−	0.998472i	$-0.482400\pi$
$541$	−474.599	−	344.817i	−0.877263	−	0.637369i	−0.932526	+	0.361103i	$0.882400\pi$
$542$	233.463	+	75.8566i	0.430743	+	0.139957i
$543$	−800.390	+	297.909i	−1.47402	+	0.548635i
$544$	28.1966	−	20.4861i	0.0518320	−	0.0376582i
$545$	−412.859	−	568.251i	−0.757539	−	1.04266i
$546$	−159.346	−	428.114i	−0.291842	−	0.784092i
$547$	−212.865	+	655.132i	−0.389151	+	1.19768i	0.544273	+	0.838908i	$0.316805\pi$
$547$	−212.865	+	655.132i	−0.389151	+	1.19768i	−0.933424	+	0.358775i	$0.883195\pi$
$548$	479.994	−	660.655i	0.875901	−	1.20557i
$549$	95.5519	−	8.07575i	0.174047	−	0.0147099i
$550$		0			0
$551$		−	78.3083i		−	0.142120i
$552$	−189.425	+	285.275i	−0.343161	+	0.516802i
$553$	92.9875	−	286.186i	0.168151	−	0.517515i
$554$	−637.146	+	207.021i	−1.15008	+	0.373685i
$555$	601.677	−	477.148i	1.08410	−	0.859727i
$556$	−485.423	+	352.681i	−0.873063	+	0.634317i
$557$	−588.519	+	191.222i	−1.05659	+	0.343306i	−0.785250	−	0.619178i	$-0.787466\pi$
$557$	−588.519	+	191.222i	−1.05659	+	0.343306i	−0.271337	+	0.962484i	$0.587466\pi$
$558$	−557.278	−	130.390i	−0.998706	−	0.233675i
$559$	−570.536	−	414.519i	−1.02064	−	0.741536i
$560$		−	176.430i		−	0.315053i
$561$		0			0
$562$	1519.22			2.70325
$563$	−334.609	+	460.549i	−0.594331	+	0.818027i	−0.995175	−	0.0981198i	$-0.968717\pi$
$563$	−334.609	+	460.549i	−0.594331	+	0.818027i	0.400843	+	0.916147i	$0.368717\pi$
$564$	86.0096	−	308.374i	0.152499	−	0.546762i
$565$	−272.397	−	838.353i	−0.482119	−	1.48381i
$566$	553.485	+	761.807i	0.977889	+	1.34595i
$567$	−173.395	+	177.449i	−0.305812	+	0.312961i
$568$	−3.31772	−	10.2109i	−0.00584105	−	0.0179769i
$569$	857.404	+	278.588i	1.50686	+	0.489609i	0.942010	−	0.335584i	$-0.108934\pi$
$569$	857.404	+	278.588i	1.50686	+	0.489609i	0.564851	+	0.825193i	$0.308934\pi$
$570$	−698.017	+	1051.22i	−1.22459	+	1.84424i
$571$	804.182			1.40837			0.704187	−	0.710014i	$-0.251312\pi$
$571$	804.182			1.40837			0.704187	+	0.710014i	$0.251312\pi$
$572$		0			0
$573$	−411.961	+	17.3779i	−0.718955	+	0.0303279i
$574$	−101.409	−	73.6779i	−0.176671	−	0.128359i
$575$	−495.812	−	161.099i	−0.862283	−	0.280173i
$576$	−341.133	−	810.296i	−0.592244	−	1.40676i
$577$	636.777	−	462.646i	1.10360	−	0.801812i	0.121956	−	0.992535i	$-0.461083\pi$
$577$	636.777	−	462.646i	1.10360	−	0.801812i	0.981644	+	0.190723i	$0.0610833\pi$
$578$	518.678	+	713.899i	0.897366	+	1.23512i
$579$	838.111	−	311.949i	1.44751	−	0.538771i
$580$	41.6379	−	128.148i	0.0717895	−	0.220945i
$581$	57.4330	−	79.0497i	0.0988519	−	0.136058i
$582$	−580.643	+	24.4934i	−0.997669	+	0.0420849i
$583$		0			0
$584$			189.998i			0.325340i
$585$	502.390	−	830.558i	0.858787	−	1.41976i
$586$	321.243	−	988.683i	0.548195	−	1.68717i
$587$	173.593	−	56.4039i	0.295730	−	0.0960884i	−0.157395	−	0.987536i	$-0.550309\pi$
$587$	173.593	−	56.4039i	0.295730	−	0.0960884i	0.453124	+	0.891447i	$0.350309\pi$
$588$	−396.225	−	499.633i	−0.673851	−	0.849717i
$589$	−348.025	+	252.855i	−0.590875	+	0.429296i
$590$	−841.069	+	273.280i	−1.42554	+	0.463186i
$591$	−46.8576	+	168.000i	−0.0792852	+	0.284264i
$592$	270.600	+	196.602i	0.457094	+	0.332098i
$593$			685.071i			1.15526i	0.816297	+	0.577632i	$0.196023\pi$
$593$			685.071i			1.15526i	−0.816297	+	0.577632i	$0.803977\pi$
$594$		0			0
$595$	−16.3837			−0.0275357
$596$	818.965	−	1127.21i	1.37410	−	1.89129i
$597$	−361.354	−	100.786i	−0.605283	−	0.168822i
$598$	−419.729	−	1291.79i	−0.701889	−	2.16019i
$599$	212.117	+	291.955i	0.354119	+	0.487403i	0.948499	−	0.316782i	$-0.102602\pi$
$599$	212.117	+	291.955i	0.354119	+	0.487403i	−0.594379	+	0.804185i	$0.702602\pi$
$600$	−187.373	+	148.593i	−0.312289	+	0.247655i
$601$	129.629	+	398.956i	0.215688	+	0.663820i	0.999104	+	0.0423223i	$0.0134756\pi$
$601$	129.629	+	398.956i	0.215688	+	0.663820i	−0.783416	+	0.621498i	$0.786524\pi$
$602$	387.010	+	125.747i	0.642874	+	0.208883i
$603$	556.739	+	336.762i	0.923282	+	0.558478i
$604$	472.229			0.781836
$605$		0			0
$606$	58.1783	+	1379.18i	0.0960039	+	2.27588i
$607$	815.264	+	592.324i	1.34310	+	0.975822i	0.999324	+	0.0367717i	$0.0117074\pi$
$607$	815.264	+	592.324i	1.34310	+	0.975822i	0.343780	+	0.939050i	$0.388293\pi$
$608$	−851.743	−	276.748i	−1.40089	−	0.455178i
$609$	−12.1248	−	32.5755i	−0.0199093	−	0.0534902i
$610$	175.138	−	127.246i	0.287112	−	0.208599i
$611$	189.920	+	261.402i	0.310834	+	0.427827i
$612$	−35.8540	+	15.0945i	−0.0585850	+	0.0246642i
$613$	170.654	−	525.219i	0.278391	−	0.856800i	−0.709911	−	0.704292i	$-0.751265\pi$
$613$	170.654	−	525.219i	0.278391	−	0.856800i	0.988302	−	0.152509i	$-0.0487352\pi$
$614$	−712.546	+	980.735i	−1.16050	+	1.59729i
$615$	−11.2258	−	266.119i	−0.0182533	−	0.432714i
$616$		0			0
$617$		−	675.556i		−	1.09490i	−0.836837	−	0.547452i	$-0.815598\pi$
$617$		−	675.556i		−	1.09490i	0.836837	−	0.547452i	$-0.184402\pi$
$618$	1145.45	+	760.592i	1.85349	+	1.23073i
$619$	−83.1625	+	255.948i	−0.134350	+	0.413486i	−0.995488	−	0.0948843i	$-0.969752\pi$
$619$	−83.1625	+	255.948i	−0.134350	+	0.413486i	0.861139	+	0.508370i	$0.169752\pi$
$620$	−703.977	+	228.736i	−1.13545	+	0.368929i
$621$	−537.354	+	505.430i	−0.865304	+	0.813896i
$622$	215.483	−	156.558i	0.346436	−	0.251700i
$623$	−54.0108	+	17.5492i	−0.0866947	+	0.0281688i
$624$	407.257	+	113.590i	0.652656	+	0.182035i
$625$	597.010	+	433.754i	0.955217	+	0.694006i
$626$			1832.83i			2.92784i
$627$		0			0
$628$	41.0719			0.0654011
$629$	18.2570	−	25.1286i	0.0290254	−	0.0399501i
$630$	−127.605	+	545.373i	−0.202548	+	0.865672i
$631$	28.8464	+	88.7801i	0.0457154	+	0.140697i	0.971309	−	0.237822i	$-0.0764334\pi$
$631$	28.8464	+	88.7801i	0.0457154	+	0.140697i	−0.925593	+	0.378519i	$0.876433\pi$
$632$	−241.245	−	332.045i	−0.381716	−	0.525388i
$633$	−90.2078	−	113.751i	−0.142508	−	0.179701i
$634$	−2.32153	−	7.14492i	−0.00366171	−	0.0112696i
$635$	926.037	+	300.888i	1.45833	+	0.473839i
$636$	237.004	+	157.373i	0.372648	+	0.247442i
$637$	643.584			1.01034
$638$		0			0
$639$	−1.94785	−	23.0469i	−0.00304828	−	0.0360672i
$640$	−676.259	−	491.331i	−1.05665	−	0.767704i
$641$	−14.0474	−	4.56426i	−0.0219148	−	0.00712054i	0.298039	−	0.954554i	$-0.403667\pi$
$641$	−14.0474	−	4.56426i	−0.0219148	−	0.00712054i	−0.319954	+	0.947433i	$0.603667\pi$
$642$	−178.548	+	66.4563i	−0.278112	+	0.103515i
$643$	352.763	−	256.298i	0.548621	−	0.398597i	−0.278656	−	0.960391i	$-0.589889\pi$
$643$	352.763	−	256.298i	0.548621	−	0.398597i	0.827277	+	0.561794i	$0.189889\pi$
$644$	263.915	+	363.248i	0.409806	+	0.564049i
$645$	301.626	+	810.376i	0.467637	+	1.25640i
$646$	−15.7722	+	48.5419i	−0.0244152	+	0.0751423i
$647$	−184.783	+	254.332i	−0.285600	+	0.393095i	−0.927579	−	0.373628i	$-0.878114\pi$
$647$	−184.783	+	254.332i	−0.285600	+	0.393095i	0.641979	+	0.766722i	$0.278114\pi$
$648$	56.7948	+	333.596i	0.0876462	+	0.514809i
$649$		0			0
$650$		−	948.550i		−	1.45931i
$651$	−105.625	+	159.071i	−0.162250	+	0.244349i
$652$	−435.283	+	1339.66i	−0.667612	+	2.05470i
$653$	182.526	−	59.3063i	0.279519	−	0.0908213i	−0.165903	−	0.986142i	$-0.553054\pi$
$653$	182.526	−	59.3063i	0.279519	−	0.0908213i	0.445422	+	0.895321i	$0.353054\pi$
$654$	−761.011	+	603.505i	−1.16363	+	0.922791i
$655$	−802.835	+	583.294i	−1.22570	+	0.890525i
$656$	110.339	−	35.8512i	0.168199	−	0.0546513i
$657$	−93.2506	+	398.545i	−0.141934	+	0.606614i
$658$	−150.834	−	109.587i	−0.229231	−	0.166546i
$659$		−	127.678i		−	0.193745i	−0.995297	−	0.0968724i	$-0.969116\pi$
$659$		−	127.678i		−	0.193745i	0.995297	−	0.0968724i	$-0.0308839\pi$
$660$		0			0
$661$	580.599			0.878364			0.439182	−	0.898398i	$-0.355268\pi$
$661$	580.599			0.878364			0.439182	+	0.898398i	$0.355268\pi$
$662$	−662.081	+	911.276i	−1.00012	+	1.37655i
$663$	10.5482	−	37.8189i	0.0159098	−	0.0570421i
$664$	−41.1834	−	126.750i	−0.0620232	−	0.190888i
$665$	247.454	+	340.591i	0.372111	+	0.512167i
$666$	−694.273	−	803.444i	−1.04245	−	1.20637i
$667$	−31.9375	−	98.2936i	−0.0478823	−	0.147367i
$668$	816.443	+	265.279i	1.22222	+	0.397124i
$669$	351.343	−	529.124i	0.525177	−	0.790918i
$670$	1468.92			2.19241
$671$		0			0
$672$	−397.167	+	16.7538i	−0.591023	+	0.0249313i
$673$	−442.096	−	321.202i	−0.656904	−	0.477268i	0.208712	−	0.977977i	$-0.433073\pi$
$673$	−442.096	−	321.202i	−0.656904	−	0.477268i	−0.865616	+	0.500709i	$0.833073\pi$
$674$	1722.65	+	559.723i	2.55586	+	0.830450i
$675$	−465.968	+	219.729i	−0.690322	+	0.325525i
$676$	411.866	−	299.238i	0.609269	−	0.442660i
$677$	17.1436	+	23.5961i	0.0253229	+	0.0348540i	0.821491	−	0.570222i	$-0.193143\pi$
$677$	17.1436	+	23.5961i	0.0253229	+	0.0348540i	−0.796168	+	0.605076i	$0.793143\pi$
$678$	−1142.36	+	425.191i	−1.68489	+	0.627125i
$679$	−59.9160	+	184.402i	−0.0882415	+	0.271579i
$680$	−13.1350	+	18.0787i	−0.0193161	+	0.0265863i
$681$	363.832	−	15.3476i	0.534261	−	0.0225369i
$682$		0			0
$683$		−	82.4506i		−	0.120718i	−0.998177	−	0.0603592i	$-0.980775\pi$
$683$		−	82.4506i		−	0.120718i	0.998177	−	0.0603592i	$-0.0192246\pi$
$684$	855.315	+	517.365i	1.25046	+	0.756382i
$685$	312.277	−	961.091i	0.455879	−	1.40305i
$686$	−790.006	+	256.688i	−1.15161	+	0.374181i
$687$	−601.992	−	759.104i	−0.876263	−	1.10495i
$688$	−304.703	+	221.380i	−0.442883	+	0.321773i
$689$	−273.078	+	88.7285i	−0.396340	+	0.128779i
$690$	−447.428	+	1604.18i	−0.648447	+	2.32490i
$691$	−782.898	−	568.809i	−1.13299	−	0.823168i	−0.146865	−	0.989156i	$-0.546918\pi$
$691$	−782.898	−	568.809i	−1.13299	−	0.823168i	−0.986128	+	0.165989i	$0.946918\pi$
$692$		−	888.061i		−	1.28333i
$693$		0			0
$694$	−901.554			−1.29907
$695$	−436.438	+	600.705i	−0.627968	+	0.864324i
$696$	−45.6662	−	12.7369i	−0.0656123	−	0.0183002i
$697$	−3.32924	−	10.2463i	−0.00477652	−	0.0147006i
$698$	−741.109	−	1020.05i	−1.06176	−	1.46139i
$699$	945.894	−	750.123i	1.35321	−	1.07314i
$700$	96.8949	+	298.212i	0.138421	+	0.426017i
$701$	−298.727	−	97.0623i	−0.426144	−	0.138463i	0.0880898	−	0.996113i	$-0.471924\pi$
$701$	−298.727	−	97.0623i	−0.426144	−	0.138463i	−0.514234	+	0.857650i	$0.671924\pi$
$702$	−1176.74	−	645.677i	−1.67627	−	0.919768i
$703$	−798.129			−1.13532
$704$		0			0
$705$	−16.6971	−	395.822i	−0.0236838	−	0.561450i
$706$	335.660	+	243.871i	0.475439	+	0.345427i
$707$	438.005	+	142.316i	0.619525	+	0.201296i
$708$	244.375	+	656.560i	0.345162	+	0.927344i
$709$	−264.833	+	192.413i	−0.373531	+	0.271386i	−0.758673	−	0.651471i	$-0.774152\pi$
$709$	−264.833	+	192.413i	−0.373531	+	0.271386i	0.385143	+	0.922857i	$0.374152\pi$
$710$	−30.6913	−	42.2430i	−0.0432272	−	0.0594972i
$711$	−343.074	−	814.908i	−0.482524	−	1.14614i
$712$	−23.9361	+	73.6678i	−0.0336181	+	0.103466i
$713$	−333.721	+	459.327i	−0.468051	+	0.644217i
$714$	0.954820	+	22.6351i	0.00133728	+	0.0317018i
$715$		0			0
$716$		−	314.061i		−	0.438632i
$717$	−0.803355	−	0.533435i	−0.00112044	−	0.000743982i
$718$	−263.630	+	811.369i	−0.367172	+	1.13004i
$719$	1052.06	−	341.836i	1.46323	−	0.475433i	0.534176	−	0.845373i	$-0.320622\pi$
$719$	1052.06	−	341.836i	1.46323	−	0.475433i	0.929056	+	0.369940i	$0.120622\pi$
$720$	−338.950	−	392.248i	−0.470764	−	0.544789i
$721$	371.124	−	269.637i	0.514735	−	0.373977i
$722$	196.643	−	63.8932i	0.272359	−	0.0884947i
$723$	−840.325	−	234.378i	−1.16228	−	0.324174i
$724$	1235.65	+	897.750i	1.70669	+	1.23999i
$725$		−	72.1759i		−	0.0995530i
$726$		0			0
$727$	577.040			0.793727			0.396864	−	0.917878i	$-0.370099\pi$
$727$	577.040			0.793727			0.396864	+	0.917878i	$0.370099\pi$
$728$	−122.184	+	168.172i	−0.167835	+	0.231005i
$729$	−44.5941	+	727.635i	−0.0611716	+	0.998127i
$730$	285.544	+	878.813i	0.391156	+	1.20385i
$731$	20.5579	+	28.2955i	0.0281230	+	0.0387080i
$732$	−106.559	−	134.369i	−0.145572	−	0.183564i
$733$	−191.375	−	588.991i	−0.261084	−	0.803535i	−0.992570	−	0.121678i	$-0.961173\pi$
$733$	−191.375	−	588.991i	−0.261084	−	0.803535i	0.731485	−	0.681857i	$-0.238827\pi$
$734$	513.372	+	166.805i	0.699417	+	0.227254i
$735$	−657.388	−	436.511i	−0.894405	−	0.593893i
$736$	−1181.99			−1.60596
$737$		0			0
$738$	−367.005	+	31.0181i	−0.497297	+	0.0420299i
$739$	−905.537	−	657.911i	−1.22535	−	0.890272i	−0.228821	−	0.973468i	$-0.573487\pi$
$739$	−905.537	−	657.911i	−1.22535	−	0.890272i	−0.996533	+	0.0831961i	$0.973487\pi$
$740$	−1306.10	−	424.379i	−1.76501	−	0.573485i
$741$	−945.510	+	351.923i	−1.27599	+	0.474930i
$742$	134.038	−	97.3846i	0.180645	−	0.131246i
$743$	675.116	+	929.218i	0.908636	+	1.25063i	0.967630	+	0.252371i	$0.0812105\pi$
$743$	675.116	+	929.218i	0.908636	+	1.25063i	−0.0589948	+	0.998258i	$0.518790\pi$
$744$	90.8481	+	244.081i	0.122108	+	0.328066i
$745$	532.808	−	1639.81i	0.715178	−	2.20109i
$746$	293.396	−	403.825i	0.393292	−	0.541320i
$747$	−24.1791	−	286.086i	−0.0323682	−	0.382979i
$748$		0			0
$749$			63.5613i			0.0848616i
$750$	199.588	−	300.581i	0.266118	−	0.400775i
$751$	−84.5649	+	260.264i	−0.112603	+	0.346556i	−0.991440	−	0.130567i	$-0.958320\pi$
$751$	−84.5649	+	260.264i	−0.112603	+	0.346556i	0.878837	+	0.477123i	$0.158320\pi$
$752$	164.116	−	53.3246i	0.218240	−	0.0709104i
$753$	−264.725	+	209.935i	−0.351561	+	0.278798i
$754$	152.134	−	110.532i	0.201769	−	0.146594i
$755$	555.776	−	180.583i	0.736128	−	0.239182i
$756$	435.909	+	82.7877i	0.576599	+	0.109508i
$757$	451.436	+	327.988i	0.596349	+	0.433273i	0.844581	−	0.535428i	$-0.179850\pi$
$757$	451.436	+	327.988i	0.596349	+	0.433273i	−0.248232	+	0.968701i	$0.579850\pi$
$758$		−	162.899i		−	0.214906i
$759$		0			0
$760$	574.212			0.755543
$761$	247.901	−	341.207i	0.325757	−	0.448366i	−0.614457	−	0.788950i	$-0.710625\pi$
$761$	247.901	−	341.207i	0.325757	−	0.448366i	0.940214	+	0.340584i	$0.110625\pi$
$762$	361.725	−	1296.91i	0.474705	−	1.70198i
$763$	100.135	+	308.183i	0.131238	+	0.403910i
$764$	433.434	+	596.570i	0.567321	+	0.780851i
$765$	−36.4252	+	31.4758i	−0.0476146	+	0.0411448i
$766$	84.7939	+	260.969i	0.110697	+	0.340690i
$767$	−672.451	−	218.493i	−0.876729	−	0.284867i
$768$	9.05074	−	13.6305i	0.0117848	−	0.0177480i
$769$	108.997			0.141738			0.0708692	−	0.997486i	$-0.477423\pi$
$769$	108.997			0.141738			0.0708692	+	0.997486i	$0.477423\pi$
$770$		0			0
$771$	−589.181	+	24.8536i	−0.764178	+	0.0322355i
$772$	−1293.88	−	940.059i	−1.67601	−	1.21769i
$773$	−981.122	−	318.786i	−1.26924	−	0.412401i	−0.404461	−	0.914555i	$-0.632541\pi$
$773$	−981.122	−	318.786i	−1.26924	−	0.412401i	−0.864778	+	0.502154i	$0.832541\pi$
$774$	1102.00	−	463.941i	1.42378	−	0.599407i
$775$	−320.771	+	233.054i	−0.413898	+	0.300715i
$776$	155.445	+	213.952i	0.200316	+	0.275711i
$777$	−332.014	+	123.577i	−0.427303	+	0.159044i
$778$	254.954	−	784.668i	0.327704	−	1.00857i
$779$	−162.721	+	223.966i	−0.208885	+	0.287505i
$780$	−1734.41	+	73.1631i	−2.22360	+	0.0937988i
$781$		0			0
$782$			67.3630i			0.0861420i
$783$	−89.5392	−	49.1301i	−0.114354	−	0.0627459i
$784$	106.214	−	326.893i	0.135477	−	0.416955i
$785$	48.3384	−	15.7061i	0.0615776	−	0.0200078i
$786$	852.642	+	1075.17i	1.08479	+	1.36790i
$787$	167.812	−	121.923i	0.213230	−	0.154921i	−0.476044	−	0.879422i	$-0.657930\pi$
$787$	167.812	−	121.923i	0.213230	−	0.154921i	0.689274	+	0.724501i	$0.257930\pi$
$788$	296.651	−	96.3877i	0.376460	−	0.122319i
$789$	304.923	−	1093.25i	0.386468	−	1.38562i
$790$	−1614.87	−	1173.27i	−2.04414	−	1.48515i
$791$			406.668i			0.514119i
$792$		0			0
$793$	173.082			0.218263
$794$	−380.422	+	523.606i	−0.479121	+	0.659453i
$795$	339.116	+	94.5840i	0.426561	+	0.118974i
$796$	207.321	+	638.069i	0.260454	+	0.801595i
$797$	130.723	+	179.925i	0.164019	+	0.225753i	0.883113	−	0.469160i	$-0.155443\pi$
$797$	130.723	+	179.925i	0.164019	+	0.225753i	−0.719094	+	0.694912i	$0.755443\pi$
$798$	456.125	−	361.721i	0.571585	−	0.453284i
$799$	−4.95186	−	15.2403i	−0.00619757	−	0.0190742i
$800$	−785.043	−	255.076i	−0.981303	−	0.318845i
$801$	−86.3649	+	142.780i	−0.107821	+	0.178252i
$802$	−1376.50			−1.71633
$803$		0			0
$804$	−49.0426	−	1162.61i	−0.0609983	−	1.44603i
$805$	449.515	+	326.592i	0.558403	+	0.405704i
$806$	−982.472	−	319.224i	−1.21895	−	0.396060i
$807$	−210.503	−	565.558i	−0.260846	−	0.700815i
$808$	508.191	−	369.223i	0.628950	−	0.456959i
$809$	−442.375	−	608.877i	−0.546817	−	0.752630i	0.442759	−	0.896641i	$-0.354000\pi$
$809$	−442.375	−	608.877i	−0.546817	−	0.752630i	−0.989576	+	0.144011i	$0.954000\pi$
$810$	764.051	+	1457.65i	0.943272	+	1.79957i
$811$	−71.7678	+	220.879i	−0.0884930	+	0.272354i	−0.985503	−	0.169656i	$-0.945734\pi$
$811$	−71.7678	+	220.879i	−0.0884930	+	0.272354i	0.897010	+	0.442010i	$0.145734\pi$
$812$	−36.5380	+	50.2903i	−0.0449976	+	0.0619338i
$813$	−10.1421	−	240.430i	−0.0124749	−	0.295732i
$814$		0			0
$815$			1743.13i			2.13881i
$816$	−17.4684	−	11.5992i	−0.0214073	−	0.0142147i
$817$	277.719	−	854.730i	0.339925	−	1.04618i
$818$	449.069	−	145.911i	0.548984	−	0.178376i
$819$	−338.834	+	292.793i	−0.413717	+	0.357501i
$820$	−385.373	+	279.990i	−0.469967	+	0.341451i
$821$	−461.227	+	149.862i	−0.561787	+	0.182536i	−0.576125	−	0.817361i	$-0.695436\pi$
$821$	−461.227	+	149.862i	−0.561787	+	0.182536i	0.0143379	+	0.999897i	$0.495436\pi$
$822$	−1346.00	−	375.418i	−1.63747	−	0.456713i
$823$	−126.927	−	92.2181i	−0.154225	−	0.112051i	0.507997	−	0.861359i	$-0.330386\pi$
$823$	−126.927	−	92.2181i	−0.154225	−	0.112051i	−0.662222	+	0.749308i	$0.730386\pi$
$824$		−	625.689i		−	0.759331i
$825$		0			0
$826$	407.986			0.493930
$827$	92.7092	−	127.603i	0.112103	−	0.154297i	−0.749279	−	0.662255i	$-0.769600\pi$
$827$	92.7092	−	127.603i	0.112103	−	0.154297i	0.861382	+	0.507958i	$0.169600\pi$
$828$	1284.61	+	300.569i	1.55146	+	0.363006i
$829$	403.767	+	1242.67i	0.487053	+	1.49900i	0.828985	+	0.559271i	$0.188919\pi$
$829$	403.767	+	1242.67i	0.487053	+	1.49900i	−0.341931	+	0.939725i	$0.611081\pi$
$830$	−380.977	−	524.370i	−0.459009	−	0.631771i
$831$	408.074	+	514.576i	0.491064	+	0.619225i
$832$	−490.373	−	1509.21i	−0.589390	−	1.81396i
$833$	−30.3561	−	9.86329i	−0.0364419	−	0.0118407i
$834$	855.344	+	567.956i	1.02559	+	0.681002i
$835$	1062.33			1.27226
$836$		0			0
$837$	70.7709	+	556.579i	0.0845530	+	0.664969i
$838$	−1870.54	−	1359.03i	−2.23215	−	1.62175i
$839$	1220.51	+	396.569i	1.45472	+	0.472668i	0.926454	−	0.376409i	$-0.122841\pi$
$839$	1220.51	+	396.569i	1.45472	+	0.472668i	0.528269	+	0.849077i	$0.322841\pi$
$840$	238.867	−	88.9074i	0.284366	−	0.105842i
$841$	−668.807	+	485.917i	−0.795252	+	0.577785i
$842$	−785.866	−	1081.65i	−0.933333	−	1.28462i
$843$	−519.510	−	1395.76i	−0.616263	−	1.65571i
$844$	−80.2314	+	246.927i	−0.0950610	+	0.292568i
$845$	370.304	−	509.679i	0.438229	−	0.603170i
$846$	−545.878	+	46.1359i	−0.645246	+	0.0545342i
$847$		0			0
$848$			153.347i			0.180834i
$849$	510.631	−	769.012i	0.601449	−	0.905785i
$850$	−14.5371	+	44.7405i	−0.0171025	+	0.0526359i
$851$	−1001.82	+	325.512i	−1.17723	+	0.382505i
$852$	−32.4095	+	25.7018i	−0.0380394	+	0.0301664i
$853$	401.784	−	291.913i	0.471025	−	0.342219i	−0.326816	−	0.945088i	$-0.605976\pi$
$853$	401.784	−	291.913i	0.471025	−	0.342219i	0.797840	+	0.602869i	$0.205976\pi$
$854$	−94.9839	+	30.8621i	−0.111222	+	0.0361383i
$855$	1204.48	+	281.822i	1.40875	+	0.329616i
$856$	70.1371	+	50.9576i	0.0819359	+	0.0595299i
$857$		−	479.970i		−	0.560059i	−0.959991	−	0.280029i	$-0.909656\pi$
$857$		−	479.970i		−	0.560059i	0.959991	−	0.280029i	$-0.0903442\pi$
$858$		0			0
$859$	658.810			0.766950			0.383475	−	0.923551i	$-0.374727\pi$
$859$	658.810			0.766950			0.383475	+	0.923551i	$0.374727\pi$
$860$	908.950	−	1251.06i	1.05692	−	1.45472i
$861$	−33.0129	+	118.363i	−0.0383426	+	0.137471i
$862$	−9.20523	−	28.3308i	−0.0106789	−	0.0328663i
$863$	316.707	+	435.910i	0.366984	+	0.505110i	0.952078	−	0.305855i	$-0.0989424\pi$
$863$	316.707	+	435.910i	0.366984	+	0.505110i	−0.585094	+	0.810965i	$0.698942\pi$
$864$	−850.817	+	800.270i	−0.984742	+	0.926238i
$865$	−339.599	−	1045.18i	−0.392600	−	1.20830i
$866$	172.518	+	56.0544i	0.199212	+	0.0647279i
$867$	478.518	−	720.650i	0.551924	−	0.831200i
$868$	341.485			0.393416
$869$		0			0
$870$	−230.365	+	9.71754i	−0.264787	+	0.0111696i
$871$	950.133	+	690.312i	1.09085	+	0.792551i
$872$	420.345	+	136.579i	0.482048	+	0.156627i
$873$	221.058	+	525.082i	0.253217	+	0.601468i
$874$	1400.37	−	1017.43i	1.60225	−	1.16410i
$875$	−70.7560	−	97.3872i	−0.0808639	−	0.111300i
$876$	686.024	−	255.341i	0.783132	−	0.291485i
$877$	−26.1783	+	80.5685i	−0.0298498	+	0.0918683i	−0.964872	−	0.262722i	$-0.915380\pi$
$877$	−26.1783	+	80.5685i	−0.0298498	+	0.0918683i	0.935022	+	0.354591i	$0.115380\pi$
$878$	799.957	−	1101.05i	0.911113	−	1.25404i
$879$	−1018.19	+	42.9505i	−1.15835	+	0.0488629i
$880$		0			0
$881$			364.734i			0.414000i	0.978341	+	0.207000i	$0.0663701\pi$
$881$			364.734i			0.414000i	−0.978341	+	0.207000i	$0.933630\pi$
$882$	−564.754	+	933.658i	−0.640310	+	1.05857i
$883$	68.8459	−	211.886i	0.0779682	−	0.239961i	−0.904474	−	0.426529i	$-0.859736\pi$
$883$	68.8459	−	211.886i	0.0779682	−	0.239961i	0.982442	+	0.186567i	$0.0597363\pi$
$884$	−66.7797	+	21.6980i	−0.0755427	+	0.0245453i
$885$	538.681	+	679.269i	0.608680	+	0.767536i
$886$	1325.42	−	962.975i	1.49596	−	1.08688i
$887$	1296.73	−	421.334i	1.46193	−	0.475010i	0.533272	−	0.845944i	$-0.320962\pi$
$887$	1296.73	−	421.334i	1.46193	−	0.475010i	0.928659	+	0.370934i	$0.120962\pi$
$888$	−129.816	+	465.436i	−0.146190	+	0.524140i
$889$	−363.412	−	264.034i	−0.408788	−	0.297002i
$890$			376.714i			0.423274i
$891$		0			0
$892$	−1135.89			−1.27342
$893$	−242.029	+	333.124i	−0.271029	+	0.373040i
$894$	−2296.55	−	640.538i	−2.56884	−	0.716486i
$895$	−120.098	−	369.625i	−0.134188	−	0.412989i
$896$	226.670	+	311.984i	0.252980	+	0.348197i
$897$	−1043.29	+	827.358i	−1.16308	+	0.922362i
$898$	727.612	+	2239.36i	0.810259	+	2.49372i
$899$	−74.7570	−	24.2900i	−0.0831557	−	0.0270189i
$900$	788.335	+	476.850i	0.875927	+	0.529833i
$901$	14.2402			0.0158049
$902$		0			0
$903$	−16.8126	−	398.560i	−0.0186186	−	0.441373i
$904$	448.740	+	326.029i	0.496394	+	0.360652i
$905$	1797.56	+	584.064i	1.98626	+	0.645374i
$906$	−281.875	−	757.313i	−0.311121	−	0.835886i
$907$	−531.719	+	386.317i	−0.586239	+	0.425928i	−0.840968	−	0.541085i	$-0.818014\pi$
$907$	−531.719	+	386.317i	−0.586239	+	0.425928i	0.254729	+	0.967013i	$0.418014\pi$
$908$	−382.796	−	526.873i	−0.421581	−	0.580257i
$909$	1247.21	−	525.072i	1.37207	−	0.577636i
$910$	−312.405	+	961.484i	−0.343302	+	1.05658i
$911$	204.809	−	281.895i	0.224818	−	0.309435i	−0.681676	−	0.731654i	$-0.738749\pi$
$911$	204.809	−	281.895i	0.224818	−	0.309435i	0.906494	+	0.422219i	$0.138749\pi$
$912$	22.7085	+	538.329i	0.0248996	+	0.590273i
$913$		0			0
$914$			519.188i			0.568039i
$915$	−176.795	−	117.393i	−0.193218	−	0.128299i
$916$	−535.416	+	1647.84i	−0.584516	+	1.79895i
$917$	435.407	−	141.472i	0.474816	−	0.154277i
$918$	45.6084	+	48.4891i	0.0496823	+	0.0528204i
$919$	517.293	−	375.836i	0.562887	−	0.408961i	−0.269627	−	0.962965i	$-0.586901\pi$
$919$	517.293	−	375.836i	0.562887	−	0.408961i	0.832514	+	0.554003i	$0.186901\pi$
$920$	720.759	−	234.189i	0.783433	−	0.254553i
$921$	1144.70	+	319.271i	1.24288	+	0.346657i
$922$	−659.442	−	479.112i	−0.715229	−	0.519645i
$923$		−	41.7471i		−	0.0452298i
$924$		0			0
$925$	−735.627			−0.795272
$926$	1267.86	−	1745.06i	1.36918	−	1.88452i
$927$	307.086	−	1312.46i	0.331269	−	1.41581i
$928$	−50.5681	−	155.633i	−0.0544915	−	0.167708i
$929$	−184.827	−	254.392i	−0.198952	−	0.273834i	0.697871	−	0.716224i	$-0.254131\pi$
$929$	−184.827	−	254.392i	−0.198952	−	0.273834i	−0.896823	+	0.442389i	$0.854131\pi$
$930$	787.030	+	992.433i	0.846269	+	1.06713i
$931$	253.446	+	780.025i	0.272229	+	0.837836i
$932$	−2053.32	−	667.165i	−2.20313	−	0.715842i
$933$	−217.521	−	144.436i	−0.233141	−	0.154808i
$934$	2066.22			2.21222
$935$		0			0
$936$	51.4389	+	608.623i	0.0549561	+	0.650238i
$937$	1229.78	+	893.489i	1.31247	+	0.953564i	0.999993	+	0.00363731i	$0.00115779\pi$
$937$	1229.78	+	893.489i	1.31247	+	0.953564i	0.312474	+	0.949926i	$0.398842\pi$
$938$	−644.501	−	209.411i	−0.687101	−	0.223253i
$939$	1683.88	−	626.749i	1.79327	−	0.667464i
$940$	−573.199	+	416.453i	−0.609786	+	0.443035i
$941$	659.673	+	907.963i	0.701034	+	0.964891i	0.999944	+	0.0106096i	$0.00337722\pi$
$941$	659.673	+	907.963i	0.701034	+	0.964891i	−0.298909	+	0.954282i	$0.596623\pi$
$942$	−24.5160	−	65.8669i	−0.0260254	−	0.0699224i
$943$	−112.906	+	347.490i	−0.119731	+	0.368494i
$944$	−221.956	+	305.496i	−0.235123	+	0.323619i
$945$	544.689	−	69.2591i	0.576390	−	0.0732900i
$946$		0			0
$947$		−	865.333i		−	0.913762i	−0.889528	−	0.456881i	$-0.848967\pi$
$947$		−	865.333i		−	0.913762i	0.889528	−	0.456881i	$-0.151033\pi$
$948$	−874.698	+	1317.30i	−0.922677	+	1.38956i
$949$	−228.298	+	702.628i	−0.240567	+	0.740388i
$950$	1149.65	−	373.543i	1.21015	−	0.393203i
$951$	−5.77043	+	4.57612i	−0.00606775	+	0.00481191i
$952$	8.34041	−	6.05966i	0.00876093	−	0.00636519i
$953$	482.372	−	156.732i	0.506162	−	0.164462i	−0.0447943	−	0.998996i	$-0.514263\pi$
$953$	482.372	−	156.732i	0.506162	−	0.164462i	0.550956	+	0.834534i	$0.314263\pi$
$954$	110.910	−	474.020i	0.116258	−	0.496876i
$955$	738.249	+	536.369i	0.773035	+	0.561643i
$956$			1.72460i			0.00180397i
$957$		0			0
$958$	2141.59			2.23548
$959$	−274.029	+	377.169i	−0.285745	+	0.393294i
$960$	−522.734	+	1874.18i	−0.544514	+	1.95227i
$961$	−163.529	−	503.291i	−0.170166	−	0.523716i
$962$	−1126.55	−	1550.57i	−1.17105	−	1.61182i
$963$	122.111	+	141.313i	0.126803	+	0.146742i
$964$	482.124	+	1483.82i	0.500128	+	1.53924i
$965$	−1882.28	−	611.589i	−1.95055	−	0.633771i
$966$	425.008	−	640.064i	0.439967	−	0.662592i
$967$	569.116			0.588537			0.294269	−	0.955723i	$-0.404924\pi$
$967$	569.116			0.588537			0.294269	+	0.955723i	$0.404924\pi$
$968$		0			0
$969$	49.9906	−	2.10876i	0.0515899	−	0.00217623i
$970$	1040.53	+	755.991i	1.07271	+	0.779373i
$971$	−1192.00	−	387.303i	−1.22760	−	0.398871i	−0.377754	−	0.925906i	$-0.623304\pi$
$971$	−1192.00	−	387.303i	−1.22760	−	0.398871i	−0.849843	+	0.527035i	$0.823304\pi$
$972$	1128.18	−	653.392i	1.16068	−	0.672214i
$973$	277.129	−	201.346i	0.284819	−	0.206933i
$974$	−1175.22	−	1617.55i	−1.20659	−	1.66073i
$975$	−871.466	+	324.364i	−0.893812	+	0.332681i
$976$	28.5647	−	87.9131i	0.0292671	−	0.0900749i
$977$	−671.043	+	923.611i	−0.686840	+	0.945354i	−0.999991	−	0.00434910i	$-0.998616\pi$
$977$	−671.043	+	923.611i	−0.686840	+	0.945354i	0.313150	+	0.949704i	$0.398616\pi$
$978$	2408.24	−	101.587i	2.46241	−	0.103873i
$979$		0			0
$980$			1411.24i			1.44004i
$981$	814.695	+	492.795i	0.830474	+	0.502339i
$982$	58.4777	−	179.976i	0.0595496	−	0.183275i
$983$	−632.701	+	205.577i	−0.643643	+	0.209132i	−0.612609	−	0.790386i	$-0.709880\pi$
$983$	−632.701	+	205.577i	−0.643643	+	0.209132i	−0.0310339	+	0.999518i	$0.509880\pi$
$984$	104.141	+	131.321i	0.105835	+	0.133456i
$985$	312.275	−	226.881i	0.317031	−	0.230336i
$986$	−8.86970	+	2.88194i	−0.00899564	+	0.00292286i
$987$	−49.1030	+	176.051i	−0.0497497	+	0.178370i
$988$	1459.68	+	1060.52i	1.47741	+	1.07340i
$989$		−	1186.13i		−	1.19933i
$990$		0			0
$991$	−1471.97			−1.48534			−0.742670	−	0.669658i	$-0.766441\pi$
$991$	−1471.97			−1.48534			−0.742670	+	0.669658i	$0.766441\pi$
$992$	−528.395	+	727.273i	−0.532656	+	0.733139i
$993$	1063.62	+	296.659i	1.07112	+	0.298751i
$994$	7.44388	+	22.9099i	0.00748881	+	0.0230482i
$995$	488.002	+	671.677i	0.490454	+	0.675052i
$996$	−402.306	+	319.041i	−0.403921	+	0.320322i
$997$	−191.835	−	590.409i	−0.192413	−	0.592185i	−0.999997	−	0.00243317i	$-0.999225\pi$
$997$	−191.835	−	590.409i	−0.192413	−	0.592185i	0.807584	−	0.589752i	$-0.200775\pi$
$998$	−960.436	−	312.065i	−0.962361	−	0.312690i
$999$	−500.741	+	912.596i	−0.501242	+	0.913510i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.3.h.n.323.1		16
3.2	odd	2	inner	363.3.h.n.323.4		16
11.2	odd	10		33.3.h.b.5.1	✓	16
11.3	even	5	inner	363.3.h.n.245.4		16
11.4	even	5		363.3.h.j.251.1		16
11.5	even	5		363.3.b.l.122.2		8
11.6	odd	10		363.3.b.m.122.7		8
11.7	odd	10		33.3.h.b.20.4	yes	16
11.8	odd	10		363.3.h.o.245.1		16
11.9	even	5		363.3.h.j.269.4		16
11.10	odd	2		363.3.h.o.323.4		16
33.2	even	10		33.3.h.b.5.4	yes	16
33.5	odd	10		363.3.b.l.122.7		8
33.8	even	10		363.3.h.o.245.4		16
33.14	odd	10	inner	363.3.h.n.245.1		16
33.17	even	10		363.3.b.m.122.2		8
33.20	odd	10		363.3.h.j.269.1		16
33.26	odd	10		363.3.h.j.251.4		16
33.29	even	10		33.3.h.b.20.1	yes	16
33.32	even	2		363.3.h.o.323.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.3.h.b.5.1	✓	16	11.2	odd	10
33.3.h.b.5.4	yes	16	33.2	even	10
33.3.h.b.20.1	yes	16	33.29	even	10
33.3.h.b.20.4	yes	16	11.7	odd	10
363.3.b.l.122.2		8	11.5	even	5
363.3.b.l.122.7		8	33.5	odd	10
363.3.b.m.122.2		8	33.17	even	10
363.3.b.m.122.7		8	11.6	odd	10
363.3.h.j.251.1		16	11.4	even	5
363.3.h.j.251.4		16	33.26	odd	10
363.3.h.j.269.1		16	33.20	odd	10
363.3.h.j.269.4		16	11.9	even	5
363.3.h.n.245.1		16	33.14	odd	10	inner
363.3.h.n.245.4		16	11.3	even	5	inner
363.3.h.n.323.1		16	1.1	even	1	trivial
363.3.h.n.323.4		16	3.2	odd	2	inner
363.3.h.o.245.1		16	11.8	odd	10
363.3.h.o.245.4		16	33.8	even	10
363.3.h.o.323.1		16	33.32	even	2
363.3.h.o.323.4		16	11.10	odd	2

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+(-1.79877 + 2.47580i) q^{2} +(2.88971 + 0.805978i) q^{3} +(-1.65793 - 5.10257i) q^{4} +(-3.90250 - 5.37133i) q^{5} +(-7.19336 + 5.70456i) q^{6} +(0.946512 + 2.91306i) q^{7} +(3.97326 + 1.29099i) q^{8} +(7.70080 + 4.65808i) q^{9} +20.3180 q^{10} +(-0.678356 - 16.0812i) q^{12} +(13.1422 + 9.54837i) q^{13} +(-8.91472 - 2.89657i) q^{14} +(-6.94789 - 18.6669i) q^{15} +(7.01879 - 5.09945i) q^{16} +(-0.473548 - 0.651783i) q^{17} +(-25.3845 + 10.6868i) q^{18} +(-6.39720 + 19.6886i) q^{19} +(-20.9375 + 28.8180i) q^{20} +(0.387274 + 9.18076i) q^{21} +27.3224i q^{23} +(10.4410 + 6.93295i) q^{24} +(-5.89623 + 18.1467i) q^{25} +(-47.2797 + 15.3621i) q^{26} +(18.4987 + 19.6672i) q^{27} +(13.2949 - 9.65928i) q^{28} +(-3.59755 + 1.16891i) q^{29} +(58.7131 + 16.3759i) q^{30} +(16.8114 + 12.2142i) q^{31} +43.2608i q^{32} +2.46549 q^{34} +(11.9533 - 16.4522i) q^{35} +(11.0008 - 47.0166i) q^{36} +(11.9137 + 36.6667i) q^{37} +(-37.2378 - 51.2534i) q^{38} +(30.2813 + 38.1843i) q^{39} +(-8.57131 - 26.3798i) q^{40} +(12.7181 + 4.13237i) q^{41} +(-23.4263 - 15.5553i) q^{42} -43.4125 q^{43} +(-5.03227 - 59.5416i) q^{45} +(-67.6447 - 49.1468i) q^{46} +(18.9168 + 6.14644i) q^{47} +(24.3923 - 9.07892i) q^{48} +(32.0518 - 23.2870i) q^{49} +(-34.3217 - 47.2397i) q^{50} +(-0.843091 - 2.26513i) q^{51} +(26.9324 - 82.8895i) q^{52} +(-10.3894 + 14.2997i) q^{53} +(-81.9669 + 10.4224i) q^{54} +12.7963i q^{56} +(-34.3546 + 51.7382i) q^{57} +(3.57717 - 11.0094i) q^{58} +(-41.3952 + 13.4501i) q^{59} +(-83.7299 + 66.4004i) q^{60} +(8.61986 - 6.26270i) q^{61} +(-60.4797 + 19.6510i) q^{62} +(-6.28039 + 26.8418i) q^{63} +(-79.0299 - 57.4185i) q^{64} -107.854i q^{65} +72.2963 q^{67} +(-2.54066 + 3.49692i) q^{68} +(-22.0213 + 78.9537i) q^{69} +(19.2312 + 59.1877i) q^{70} +(-1.51055 - 2.07909i) q^{71} +(24.5838 + 28.4494i) q^{72} +(14.0537 + 43.2529i) q^{73} +(-112.209 - 36.4590i) q^{74} +(-31.6643 + 47.6865i) q^{75} +111.068 q^{76} +(-149.006 + 6.28555i) q^{78} +(-79.4797 - 57.7454i) q^{79} +(-54.7816 - 17.7996i) q^{80} +(37.6046 + 71.7419i) q^{81} +(-33.1080 + 24.0543i) q^{82} +(-18.7507 - 25.8081i) q^{83} +(46.2034 - 17.1971i) q^{84} +(-1.65292 + 5.08716i) q^{85} +(78.0893 - 107.481i) q^{86} +(-11.3380 + 0.478272i) q^{87} +18.5409i q^{89} +(156.465 + 94.6430i) q^{90} +(-15.3758 + 47.3217i) q^{91} +(139.414 - 45.2985i) q^{92} +(38.7356 + 48.8450i) q^{93} +(-49.2443 + 35.7781i) q^{94} +(130.719 - 42.4731i) q^{95} +(-34.8673 + 125.011i) q^{96} +(51.2123 + 37.2079i) q^{97} +121.242i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 5 q^{3} + 18 q^{4} - 32 q^{6} + 34 q^{7} + 17 q^{9} + 12 q^{10} + 106 q^{12} + 2 q^{13} - 28 q^{15} + 102 q^{16} - 42 q^{18} - 66 q^{19} + 12 q^{21} + 74 q^{24} - 176 q^{25} - 55 q^{27} + 146 q^{28}+ \cdots + 252 q^{97}+O(q^{100}) \) 16 * q + 5 * q^3 + 18 * q^4 - 32 * q^6 + 34 * q^7 + 17 * q^9 + 12 * q^10 + 106 * q^12 + 2 * q^13 - 28 * q^15 + 102 * q^16 - 42 * q^18 - 66 * q^19 + 12 * q^21 + 74 * q^24 - 176 * q^25 - 55 * q^27 + 146 * q^28 - 110 * q^30 - 126 * q^31 - 132 * q^34 + 226 * q^36 - 230 * q^37 - 136 * q^39 - 226 * q^40 - 72 * q^42 + 156 * q^43 - 72 * q^45 - 308 * q^46 + 255 * q^48 + 170 * q^49 + 169 * q^51 + 224 * q^52 - 1046 * q^54 + 259 * q^57 + 184 * q^58 - 316 * q^60 - 104 * q^61 + 108 * q^63 - 184 * q^64 + 368 * q^67 - 22 * q^69 - 52 * q^70 - 73 * q^72 - 354 * q^73 + 54 * q^75 + 900 * q^76 - 492 * q^78 - 566 * q^79 + 377 * q^81 + 200 * q^82 + 720 * q^84 + 162 * q^85 - 132 * q^87 + 774 * q^90 - 226 * q^91 - 370 * q^93 + 530 * q^94 + 67 * q^96 + 252 * q^97

Introduction

L-functions

Modular forms

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