LMFDB - Embedded newform 363.3.h.j.269.2

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,-10,8,0,33,-6] 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			269.2
Root			$-1.90610 + 0.619331i$ of defining polynomial
Character	$\chi$	$=$	363.269
Dual form			363.3.h.j.251.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.90610 + 0.619331i) q^{2} +(-1.63362 - 2.51621i) q^{3} +(0.0135968 - 0.00987866i) q^{4} +(5.21596 + 1.69477i) q^{5} +(4.67221 + 3.78440i) q^{6} +(4.52308 - 3.28621i) q^{7} +(4.69235 - 6.45847i) q^{8} +(-3.66258 + 8.22104i) q^{9} -10.9918 q^{10} +(-0.0470687 - 0.0180744i) q^{12} +(3.00265 + 9.24122i) q^{13} +(-6.58622 + 9.06515i) q^{14} +(-4.25650 - 15.8930i) q^{15} +(-4.96496 + 15.2806i) q^{16} +(-16.9969 - 5.52262i) q^{17} +(1.88972 - 17.9385i) q^{18} +(15.0954 + 10.9674i) q^{19} +(0.0876624 - 0.0284832i) q^{20} +(-15.6578 - 6.01259i) q^{21} -12.3649i q^{23} +(-23.9163 - 1.25625i) q^{24} +(4.10855 + 2.98503i) q^{25} +(-11.4467 - 15.7551i) q^{26} +(26.6691 - 4.21424i) q^{27} +(0.0290361 - 0.0893640i) q^{28} +(1.45613 + 2.00420i) q^{29} +(17.9564 + 27.6576i) q^{30} +(15.2132 + 46.8213i) q^{31} -0.268903i q^{32} +35.8182 q^{34} +(29.1616 - 9.47517i) q^{35} +(0.0314134 + 0.147961i) q^{36} +(31.8192 - 23.1180i) q^{37} +(-35.5658 - 11.5560i) q^{38} +(18.3476 - 22.6519i) q^{39} +(35.4207 - 25.7346i) q^{40} +(33.2237 - 45.7285i) q^{41} +(33.5692 + 1.76328i) q^{42} +43.9060 q^{43} +(-33.0366 + 36.6734i) q^{45} +(7.65794 + 23.5687i) q^{46} +(33.9646 - 46.7482i) q^{47} +(46.5599 - 12.4698i) q^{48} +(-5.48274 + 16.8741i) q^{49} +(-9.68004 - 3.14524i) q^{50} +(13.8704 + 51.7895i) q^{51} +(0.132117 + 0.0959889i) q^{52} +(41.0056 - 13.3235i) q^{53} +(-48.2241 + 24.5498i) q^{54} -44.6323i q^{56} +(2.93623 - 55.8996i) q^{57} +(-4.01681 - 2.91838i) q^{58} +(52.9190 + 72.8367i) q^{59} +(-0.214877 - 0.174046i) q^{60} +(9.53920 - 29.3587i) q^{61} +(-57.9958 - 79.8244i) q^{62} +(10.4499 + 49.2205i) q^{63} +(-19.6933 - 60.6097i) q^{64} +53.2906i q^{65} +34.0775 q^{67} +(-0.285659 + 0.0928164i) q^{68} +(-31.1125 + 20.1995i) q^{69} +(-49.7168 + 36.1213i) q^{70} +(-35.7561 - 11.6179i) q^{71} +(35.9092 + 62.2307i) q^{72} +(-9.81022 + 7.12754i) q^{73} +(-46.3331 + 63.7720i) q^{74} +(0.799160 - 15.2144i) q^{75} +0.313592 q^{76} +(-20.9434 + 54.5402i) q^{78} +(19.5128 + 60.0542i) q^{79} +(-51.7940 + 71.2884i) q^{80} +(-54.1710 - 60.2204i) q^{81} +(-35.0068 + 107.740i) q^{82} +(9.22665 + 2.99792i) q^{83} +(-0.272292 + 0.0729258i) q^{84} +(-79.2955 - 57.6115i) q^{85} +(-83.6893 + 27.1923i) q^{86} +(2.66420 - 6.93803i) q^{87} -34.1289i q^{89} +(40.2583 - 90.3639i) q^{90} +(43.9499 + 31.9315i) q^{91} +(-0.122148 - 0.168123i) q^{92} +(92.9595 - 114.768i) q^{93} +(-35.7874 + 110.142i) q^{94} +(60.1495 + 82.7887i) q^{95} +(-0.676616 + 0.439286i) q^{96} +(-11.6879 - 35.9715i) q^{97} -35.5595i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 10 q^{3} + 8 q^{4} + 33 q^{6} - 6 q^{7} - 28 q^{9} + 12 q^{10} + 106 q^{12} + 42 q^{13} + 82 q^{15} - 88 q^{16} + 43 q^{18} + 134 q^{19} + 12 q^{21} - 41 q^{24} + 134 q^{25} + 80 q^{27} - 264 q^{28}+ \cdots + 72 q^{97}+O(q^{100}) $ 16 * q - 10 * q^3 + 8 * q^4 + 33 * q^6 - 6 * q^7 - 28 * q^9 + 12 * q^10 + 106 * q^12 + 42 * q^13 + 82 * q^15 - 88 * q^16 + 43 * q^18 + 134 * q^19 + 12 * q^21 - 41 * q^24 + 134 * q^25 + 80 * q^27 - 264 * q^28 + 120 * q^30 + 124 * q^31 - 132 * q^34 - 219 * q^36 + 90 * q^37 + 174 * q^39 + 284 * q^40 - 102 * q^42 + 156 * q^43 - 72 * q^45 + 22 * q^46 + 30 * q^48 - 30 * q^49 - 111 * q^51 - 326 * q^52 - 1046 * q^54 - 281 * q^57 - 116 * q^58 + 54 * q^60 + 126 * q^61 + 138 * q^63 + 236 * q^64 + 368 * q^67 + 198 * q^69 - 322 * q^70 + 562 * q^72 - 24 * q^73 - 21 * q^75 + 900 * q^76 - 492 * q^78 + 314 * q^79 - 388 * q^81 - 270 * q^84 - 318 * q^85 - 132 * q^87 - 176 * q^90 + 374 * q^91 - 10 * q^93 - 990 * q^94 + 332 * q^96 + 72 * 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 $

$2$	−1.90610	+	0.619331i	−0.953052	+	0.309666i	−0.743955	−	0.668229i	$-0.767052\pi$
$2$	−1.90610	+	0.619331i	−0.953052	+	0.309666i	−0.209097	+	0.977895i	$0.567052\pi$
$3$	−1.63362	−	2.51621i	−0.544540	−	0.838735i
$3$	−1.63362	−	2.51621i	−0.544540	−	0.838735i
$4$	0.0135968	−	0.00987866i	0.00339920	−	0.00246966i
$5$	5.21596	+	1.69477i	1.04319	+	0.338953i	0.779993	−	0.625788i	$-0.215223\pi$
$5$	5.21596	+	1.69477i	1.04319	+	0.338953i	0.263198	+	0.964742i	$0.415223\pi$
$6$	4.67221	+	3.78440i	0.778702	+	0.630733i
$7$	4.52308	−	3.28621i	0.646155	−	0.469459i	−0.215804	−	0.976437i	$-0.569237\pi$
$7$	4.52308	−	3.28621i	0.646155	−	0.469459i	0.861959	+	0.506978i	$0.169237\pi$
$8$	4.69235	−	6.45847i	0.586544	−	0.807308i
$9$	−3.66258	+	8.22104i	−0.406953	+	0.913449i
$10$	−10.9918			−1.09918
$11$		0			0
$11$		0			0
$12$	−0.0470687	−	0.0180744i	−0.00392239	−	0.00150620i
$13$	3.00265	+	9.24122i	0.230973	+	0.710863i	0.997630	+	0.0688058i	$0.0219189\pi$
$13$	3.00265	+	9.24122i	0.230973	+	0.710863i	−0.766657	+	0.642057i	$0.778081\pi$
$14$	−6.58622	+	9.06515i	−0.470444	+	0.647511i
$15$	−4.25650	−	15.8930i	−0.283767	−	1.05953i
$16$	−4.96496	+	15.2806i	−0.310310	+	0.955036i
$17$	−16.9969	−	5.52262i	−0.999817	−	0.324860i	−0.237024	−	0.971504i	$-0.576172\pi$
$17$	−16.9969	−	5.52262i	−0.999817	−	0.324860i	−0.762792	+	0.646643i	$0.776172\pi$
$18$	1.88972	−	17.9385i	0.104984	−	0.996584i
$19$	15.0954	+	10.9674i	0.794493	+	0.577233i	0.909293	−	0.416156i	$-0.136623\pi$
$19$	15.0954	+	10.9674i	0.794493	+	0.577233i	−0.114801	+	0.993389i	$0.536623\pi$
$20$	0.0876624	−	0.0284832i	0.00438312	−	0.00142416i
$21$	−15.6578	−	6.01259i	−0.745609	−	0.286314i
$22$		0			0
$23$		−	12.3649i		−	0.537603i	−0.963196	−	0.268801i	$-0.913372\pi$
$23$		−	12.3649i		−	0.537603i	0.963196	−	0.268801i	$-0.0866275\pi$
$24$	−23.9163	−	1.25625i	−0.996514	−	0.0523437i
$25$	4.10855	+	2.98503i	0.164342	+	0.119401i
$26$	−11.4467	−	15.7551i	−0.440260	−	0.605965i
$27$	26.6691	−	4.21424i	0.987744	−	0.156083i
$28$	0.0290361	−	0.0893640i	0.00103700	−	0.00319157i
$29$	1.45613	+	2.00420i	0.0502115	+	0.0691102i	0.833384	−	0.552694i	$-0.186400\pi$
$29$	1.45613	+	2.00420i	0.0502115	+	0.0691102i	−0.783173	+	0.621804i	$0.786400\pi$
$30$	17.9564	+	27.6576i	0.598546	+	0.921919i
$31$	15.2132	+	46.8213i	0.490747	+	1.51037i	0.823481	+	0.567344i	$0.192029\pi$
$31$	15.2132	+	46.8213i	0.490747	+	1.51037i	−0.332733	+	0.943021i	$0.607971\pi$
$32$		−	0.268903i		−	0.00840323i
$33$		0			0
$34$	35.8182			1.05348
$35$	29.1616	−	9.47517i	0.833188	−	0.270719i
$36$	0.0314134	+	0.147961i	0.000872596	+	0.00411003i
$37$	31.8192	−	23.1180i	0.859979	−	0.624811i	−0.0679003	−	0.997692i	$-0.521630\pi$
$37$	31.8192	−	23.1180i	0.859979	−	0.624811i	0.927879	+	0.372881i	$0.121630\pi$
$38$	−35.5658	−	11.5560i	−0.935942	−	0.304106i
$39$	18.3476	−	22.6519i	0.470452	−	0.580819i
$40$	35.4207	−	25.7346i	0.885518	−	0.643366i
$41$	33.2237	−	45.7285i	0.810335	−	1.11533i	−0.180937	−	0.983495i	$-0.557913\pi$
$41$	33.2237	−	45.7285i	0.810335	−	1.11533i	0.991272	−	0.131835i	$-0.0420870\pi$
$42$	33.5692	+	1.76328i	0.799266	+	0.0419828i
$43$	43.9060			1.02107			0.510534	−	0.859857i	$-0.329448\pi$
$43$	43.9060			1.02107			0.510534	+	0.859857i	$0.329448\pi$
$44$		0			0
$45$	−33.0366	+	36.6734i	−0.734147	+	0.814964i
$46$	7.65794	+	23.5687i	0.166477	+	0.512364i
$47$	33.9646	−	46.7482i	0.722651	−	0.994643i	−0.276781	−	0.960933i	$-0.589268\pi$
$47$	33.9646	−	46.7482i	0.722651	−	0.994643i	0.999432	−	0.0337102i	$-0.0107323\pi$
$48$	46.5599	−	12.4698i	0.969998	−	0.259787i
$49$	−5.48274	+	16.8741i	−0.111893	+	0.344370i
$50$	−9.68004	−	3.14524i	−0.193601	−	0.0629047i
$51$	13.8704	+	51.7895i	0.271968	+	1.01548i
$52$	0.132117	+	0.0959889i	0.00254072	+	0.00184594i
$53$	41.0056	−	13.3235i	0.773690	−	0.251387i	0.104546	−	0.994520i	$-0.466661\pi$
$53$	41.0056	−	13.3235i	0.773690	−	0.251387i	0.669144	+	0.743133i	$0.266661\pi$
$54$	−48.2241	+	24.5498i	−0.893038	+	0.454625i
$55$		0			0
$56$		−	44.6323i		−	0.797005i
$57$	2.93623	−	55.8996i	0.0515127	−	0.980695i
$58$	−4.01681	−	2.91838i	−0.0692553	−	0.0503169i
$59$	52.9190	+	72.8367i	0.896932	+	1.23452i	0.971436	+	0.237300i	$0.0762625\pi$
$59$	52.9190	+	72.8367i	0.896932	+	1.23452i	−0.0745046	+	0.997221i	$0.523738\pi$
$60$	−0.214877	−	0.174046i	−0.00358128	−	0.00290076i
$61$	9.53920	−	29.3587i	0.156380	−	0.481289i	−0.841918	−	0.539606i	$-0.818573\pi$
$61$	9.53920	−	29.3587i	0.156380	−	0.481289i	0.998298	+	0.0583165i	$0.0185733\pi$
$62$	−57.9958	−	79.8244i	−0.935416	−	1.28749i
$63$	10.4499	+	49.2205i	0.165872	+	0.781278i
$64$	−19.6933	−	60.6097i	−0.307708	−	0.947027i
$65$			53.2906i			0.819855i
$66$		0			0
$67$	34.0775			0.508620			0.254310	−	0.967123i	$-0.418152\pi$
$67$	34.0775			0.508620			0.254310	+	0.967123i	$0.418152\pi$
$68$	−0.285659	+	0.0928164i	−0.00420087	+	0.00136495i
$69$	−31.1125	+	20.1995i	−0.450906	+	0.292746i
$70$	−49.7168	+	36.1213i	−0.710240	+	0.516019i
$71$	−35.7561	−	11.6179i	−0.503607	−	0.163632i	0.0461856	−	0.998933i	$-0.485293\pi$
$71$	−35.7561	−	11.6179i	−0.503607	−	0.163632i	−0.549793	+	0.835301i	$0.685293\pi$
$72$	35.9092	+	62.2307i	0.498739	+	0.864315i
$73$	−9.81022	+	7.12754i	−0.134387	+	0.0976375i	−0.652948	−	0.757403i	$-0.726468\pi$
$73$	−9.81022	+	7.12754i	−0.134387	+	0.0976375i	0.518561	+	0.855041i	$0.326468\pi$
$74$	−46.3331	+	63.7720i	−0.626123	+	0.861784i
$75$	0.799160	−	15.2144i	0.0106555	−	0.202858i
$76$	0.313592			0.00412621
$77$		0			0
$78$	−20.9434	+	54.5402i	−0.268506	+	0.699233i
$79$	19.5128	+	60.0542i	0.246997	+	0.760180i	0.995302	+	0.0968240i	$0.0308684\pi$
$79$	19.5128	+	60.0542i	0.246997	+	0.760180i	−0.748304	+	0.663356i	$0.769132\pi$
$80$	−51.7940	+	71.2884i	−0.647425	+	0.891104i
$81$	−54.1710	−	60.2204i	−0.668778	−	0.743462i
$82$	−35.0068	+	107.740i	−0.426912	+	1.31390i
$83$	9.22665	+	2.99792i	0.111164	+	0.0361195i	0.364071	−	0.931371i	$-0.381387\pi$
$83$	9.22665	+	2.99792i	0.111164	+	0.0361195i	−0.252907	+	0.967491i	$0.581387\pi$
$84$	−0.272292	+	0.0729258i	−0.00324157	+	0.000868165i
$85$	−79.2955	−	57.6115i	−0.932888	−	0.677783i
$86$	−83.6893	+	27.1923i	−0.973132	+	0.316190i
$87$	2.66420	−	6.93803i	0.0306230	−	0.0797474i
$88$		0			0
$89$		−	34.1289i		−	0.383471i	−0.981447	−	0.191735i	$-0.938588\pi$
$89$		−	34.1289i		−	0.383471i	0.981447	−	0.191735i	$-0.0614115\pi$
$90$	40.2583	−	90.3639i	0.447314	−	1.00404i
$91$	43.9499	+	31.9315i	0.482966	+	0.350895i
$92$	−0.122148	−	0.168123i	−0.00132770	−	0.00182742i
$93$	92.9595	−	114.768i	0.999565	−	1.23406i
$94$	−35.7874	+	110.142i	−0.380717	+	1.17173i
$95$	60.1495	+	82.7887i	0.633153	+	0.871460i
$96$	−0.676616	+	0.439286i	−0.00704809	+	0.00457589i
$97$	−11.6879	−	35.9715i	−0.120493	−	0.370841i	0.872560	−	0.488507i	$-0.162458\pi$
$97$	−11.6879	−	35.9715i	−0.120493	−	0.370841i	−0.993053	+	0.117667i	$0.962458\pi$
$98$		−	35.5595i		−	0.362852i
$99$		0			0
$100$	0.0853512			0.000853512
$101$	−44.6091	+	14.4944i	−0.441674	+	0.143509i	−0.521408	−	0.853308i	$-0.674593\pi$
$101$	−44.6091	+	14.4944i	−0.441674	+	0.143509i	0.0797339	+	0.996816i	$0.474593\pi$
$102$	−58.5132	−	90.1259i	−0.573659	−	0.883587i
$103$	−84.7824	+	61.5980i	−0.823130	+	0.598039i	−0.917607	−	0.397488i	$-0.869882\pi$
$103$	−84.7824	+	61.5980i	−0.823130	+	0.598039i	0.0944773	+	0.995527i	$0.469882\pi$
$104$	73.7736	+	23.9705i	0.709362	+	0.230486i
$105$	−71.4804	−	57.8977i	−0.680766	−	0.551407i
$106$	−69.9092	+	50.7920i	−0.659521	+	0.479170i
$107$	27.4085	−	37.7246i	0.256154	−	0.352566i	−0.661500	−	0.749945i	$-0.730080\pi$
$107$	27.4085	−	37.7246i	0.256154	−	0.352566i	0.917655	+	0.397378i	$0.130080\pi$
$108$	0.320983	−	0.320755i	0.00297207	−	0.00296995i
$109$	168.413			1.54507			0.772537	−	0.634969i	$-0.218987\pi$
$109$	168.413			1.54507			0.772537	+	0.634969i	$0.218987\pi$
$110$		0			0
$111$	−110.150	−	42.2977i	−0.992344	−	0.381060i
$112$	27.7583	+	85.4312i	0.247842	+	0.762779i
$113$	27.2263	−	37.4738i	0.240941	−	0.331627i	−0.671372	−	0.741121i	$-0.734295\pi$
$113$	27.2263	−	37.4738i	0.240941	−	0.331627i	0.912313	+	0.409494i	$0.134295\pi$
$114$	29.0236	+	108.369i	0.254593	+	0.950606i
$115$	20.9556	−	64.4946i	0.182222	−	0.560822i
$116$	0.0395975	+	0.0128660i	0.000341358	+	0.000110914i
$117$	−86.9699	−	9.16177i	−0.743332	−	0.0783057i
$118$	−145.979	−	106.060i	−1.23711	−	0.898814i
$119$	−95.0269	+	30.8761i	−0.798545	+	0.259463i
$120$	−122.618	−	47.0852i	−1.02181	−	0.392376i
$121$		0			0
$122$			61.8686i			0.507120i
$123$	−169.337	−	8.89474i	−1.37673	−	0.0723149i
$124$	0.669382	+	0.486335i	0.00539824	+	0.00392205i
$125$	−64.2199	−	88.3911i	−0.513759	−	0.707129i
$126$	−50.4024	−	87.3474i	−0.400019	−	0.693234i
$127$	21.1024	−	64.9465i	0.166161	−	0.511390i	−0.832959	−	0.553334i	$-0.813355\pi$
$127$	21.1024	−	64.9465i	0.166161	−	0.511390i	0.999120	+	0.0419443i	$0.0133552\pi$
$128$	75.7072	+	104.202i	0.591462	+	0.814078i
$129$	−71.7256	−	110.476i	−0.556012	−	0.856406i
$130$	−33.0045	−	101.577i	−0.253881	−	0.781365i
$131$		−	162.272i		−	1.23872i	−0.785109	−	0.619358i	$-0.787393\pi$
$131$		−	162.272i		−	1.23872i	0.785109	−	0.619358i	$-0.212607\pi$
$132$		0			0
$133$	104.319			0.784353
$134$	−64.9553	+	21.1053i	−0.484741	+	0.157502i
$135$	146.247	+	23.2166i	1.08331	+	0.171975i
$136$	−115.423	+	83.8598i	−0.848699	+	0.616616i
$137$	−50.2796	−	16.3368i	−0.367004	−	0.119247i	0.119708	−	0.992809i	$-0.461804\pi$
$137$	−50.2796	−	16.3368i	−0.367004	−	0.119247i	−0.486713	+	0.873562i	$0.661804\pi$
$138$	46.7936	−	57.7713i	0.339084	−	0.418632i
$139$	−70.0088	+	50.8644i	−0.503661	+	0.365931i	−0.810414	−	0.585858i	$-0.800758\pi$
$139$	−70.0088	+	50.8644i	−0.503661	+	0.365931i	0.306753	+	0.951789i	$0.400758\pi$
$140$	0.302902	−	0.416909i	0.00216359	−	0.00297792i
$141$	−173.113	−	9.09308i	−1.22775	−	0.0644899i
$142$	75.3502			0.530635
$143$		0			0
$144$	−107.438	−	96.7835i	−0.746095	−	0.672107i
$145$	4.19849	+	12.9216i	0.0289551	+	0.0891146i
$146$	14.2850	−	19.6616i	0.0978424	−	0.134669i
$147$	51.4155	−	13.7702i	0.349765	−	0.0936748i
$148$	0.204265	−	0.628662i	0.00138017	−	0.00424772i
$149$	61.2955	+	19.9161i	0.411379	+	0.133665i	0.507393	−	0.861715i	$-0.330609\pi$
$149$	61.2955	+	19.9161i	0.411379	+	0.133665i	−0.0960136	+	0.995380i	$0.530609\pi$
$150$	7.89944	+	29.4951i	0.0526629	+	0.196634i
$151$	36.1103	+	26.2357i	0.239141	+	0.173746i	0.700901	−	0.713259i	$-0.252782\pi$
$151$	36.1103	+	26.2357i	0.239141	+	0.173746i	−0.461760	+	0.887005i	$0.652782\pi$
$152$	141.666	−	46.0299i	0.932010	−	0.302828i
$153$	107.654	−	119.505i	0.703622	−	0.781079i
$154$		0			0
$155$			270.001i			1.74194i
$156$	0.0256984	−	0.489244i	0.000164733	−	0.00313618i
$157$	114.125	+	82.9166i	0.726910	+	0.528131i	0.888584	−	0.458713i	$-0.151689\pi$
$157$	114.125	+	82.9166i	0.726910	+	0.528131i	−0.161675	+	0.986844i	$0.551689\pi$
$158$	−74.3869	−	102.385i	−0.470803	−	0.648005i
$159$	−100.512	−	81.4129i	−0.632152	−	0.512031i
$160$	0.455729	−	1.40259i	0.00284830	−	0.00876618i
$161$	−40.6336	−	55.9273i	−0.252382	−	0.347375i
$162$	140.552	+	81.2367i	0.867605	+	0.501461i
$163$	37.3801	+	115.044i	0.229326	+	0.705793i	0.997824	+	0.0659401i	$0.0210046\pi$
$163$	37.3801	+	115.044i	0.229326	+	0.705793i	−0.768498	+	0.639853i	$0.778995\pi$
$164$		−	0.949967i		−	0.00579248i
$165$		0			0
$166$	−19.4437			−0.117130
$167$	102.174	−	33.1982i	0.611819	−	0.198792i	0.0133141	−	0.999911i	$-0.495762\pi$
$167$	102.174	−	33.1982i	0.611819	−	0.198792i	0.598504	+	0.801119i	$0.295762\pi$
$168$	−112.304	+	72.9121i	−0.668476	+	0.434001i
$169$	60.3397	−	43.8393i	0.357039	−	0.259404i
$170$	186.826	+	60.7035i	1.09898	+	0.357079i
$171$	−145.452	+	83.9305i	−0.850594	+	0.490822i
$172$	0.596981	−	0.433732i	0.00347082	−	0.00252170i
$173$	−193.272	+	266.016i	−1.11718	+	1.53767i	−0.306787	+	0.951778i	$0.599254\pi$
$173$	−193.272	+	266.016i	−1.11718	+	1.53767i	−0.810393	+	0.585887i	$0.800746\pi$
$174$	−0.781316	+	14.8746i	−0.00449032	+	0.0854864i
$175$	28.3928			0.162244
$176$		0			0
$177$	96.8227	−	252.142i	0.547021	−	1.42453i
$178$	21.1371	+	65.0533i	0.118748	+	0.365468i
$179$	−28.3892	+	39.0743i	−0.158599	+	0.218292i	−0.880920	−	0.473265i	$-0.843075\pi$
$179$	−28.3892	+	39.0743i	−0.158599	+	0.218292i	0.722321	+	0.691558i	$0.243075\pi$
$180$	−0.0869087	+	0.824998i	−0.000482826	+	0.00458332i
$181$	0.0205705	−	0.0633093i	0.000113649	−	0.000349775i	−0.951000	−	0.309192i	$-0.899941\pi$
$181$	0.0205705	−	0.0633093i	0.000113649	−	0.000349775i	0.951113	+	0.308842i	$0.0999415\pi$
$182$	−103.549	−	33.6452i	−0.568952	−	0.184864i
$183$	−89.4558	+	23.9582i	−0.488830	+	0.130919i
$184$	−79.8581	−	58.0203i	−0.434011	−	0.315328i
$185$	205.147	−	66.6564i	1.10890	−	0.360305i
$186$	−106.111	+	276.332i	−0.570492	+	1.48566i
$187$		0			0
$188$		−	0.971151i		−	0.00516570i
$189$	106.778	−	106.702i	0.564961	−	0.564559i
$190$	−165.925	−	120.552i	−0.873289	−	0.634482i
$191$	116.037	+	159.711i	0.607523	+	0.836183i	0.996371	−	0.0851188i	$-0.0271270\pi$
$191$	116.037	+	159.711i	0.607523	+	0.836183i	−0.388848	+	0.921302i	$0.627127\pi$
$192$	−120.335	+	148.566i	−0.626746	+	0.773779i
$193$	−0.470837	+	1.44909i	−0.00243957	+	0.00750823i	−0.952269	−	0.305260i	$-0.901256\pi$
$193$	−0.470837	+	1.44909i	−0.00243957	+	0.00750823i	0.949829	+	0.312769i	$0.101256\pi$
$194$	44.5566	+	61.3269i	0.229673	+	0.316118i
$195$	134.090	−	87.0565i	0.687642	−	0.446444i
$196$	0.0921460	+	0.283596i	0.000470133	+	0.00144692i
$197$			215.460i			1.09370i	0.837229	+	0.546852i	$0.184174\pi$
$197$			215.460i			1.09370i	−0.837229	+	0.546852i	$0.815826\pi$
$198$		0			0
$199$	−106.663			−0.535993			−0.267997	−	0.963420i	$-0.586362\pi$
$199$	−106.663			−0.535993			−0.267997	+	0.963420i	$0.586362\pi$
$200$	38.5575	−	12.5281i	0.192787	−	0.0626404i
$201$	−55.6697	−	85.7461i	−0.276964	−	0.426597i
$202$	76.0527	−	55.2555i	0.376499	−	0.273542i
$203$	13.1724	+	4.27999i	0.0648889	+	0.0210837i
$204$	0.700204	+	0.567151i	0.00343237	+	0.00278015i
$205$	250.793	−	182.212i	1.22338	−	0.888837i
$206$	123.455	−	169.921i	0.599294	−	0.824858i
$207$	101.652	+	45.2873i	0.491073	+	0.218779i
$208$	−156.119			−0.750573
$209$		0			0
$210$	172.107	+	66.0891i	0.819557	+	0.314710i
$211$	−66.3847	−	204.311i	−0.314619	−	0.968299i	−0.975911	−	0.218170i	$-0.929991\pi$
$211$	−66.3847	−	204.311i	−0.314619	−	0.968299i	0.661291	−	0.750129i	$-0.270009\pi$
$212$	0.425926	−	0.586237i	0.00200909	−	0.00276527i
$213$	29.1789	+	108.949i	0.136990	+	0.511497i
$214$	−28.8795	+	88.8820i	−0.134951	+	0.415336i
$215$	229.012	+	74.4104i	1.06517	+	0.346095i
$216$	97.9232	−	192.016i	0.453348	−	0.888964i
$217$	222.675	+	161.783i	1.02615	+	0.745544i
$218$	−321.013	+	104.303i	−1.47254	+	0.478456i
$219$	33.9605	+	13.0408i	0.155071	+	0.0595472i
$220$		0			0
$221$		−	173.654i		−	0.785767i
$222$	236.154	+	12.4044i	1.06376	+	0.0558757i
$223$	−36.2187	−	26.3144i	−0.162416	−	0.118002i	0.503609	−	0.863932i	$-0.332005\pi$
$223$	−36.2187	−	26.3144i	−0.162416	−	0.118002i	−0.666024	+	0.745930i	$0.732005\pi$
$224$	−0.883674	−	1.21627i	−0.00394497	−	0.00542979i
$225$	−39.5880	+	22.8436i	−0.175946	+	0.101527i
$226$	−28.6875	+	88.2911i	−0.126936	+	0.390669i
$227$	−131.960	−	181.627i	−0.581322	−	0.800121i	0.412518	−	0.910950i	$-0.364649\pi$
$227$	−131.960	−	181.627i	−0.581322	−	0.800121i	−0.993840	+	0.110829i	$0.964649\pi$
$228$	−0.512290	−	0.789062i	−0.00224689	−	0.00346080i
$229$	−32.1689	−	99.0057i	−0.140476	−	0.432339i	0.855926	−	0.517099i	$-0.172988\pi$
$229$	−32.1689	−	99.0057i	−0.140476	−	0.432339i	−0.996401	+	0.0847591i	$0.972988\pi$
$230$			135.912i			0.590921i
$231$		0			0
$232$	19.7767			0.0852446
$233$	−58.5176	+	19.0135i	−0.251148	+	0.0816030i	−0.431886	−	0.901928i	$-0.642152\pi$
$233$	−58.5176	+	19.0135i	−0.251148	+	0.0816030i	0.180737	+	0.983531i	$0.442152\pi$
$234$	171.448	−	36.3999i	0.732683	−	0.155555i
$235$	256.385	−	186.275i	1.09100	−	0.792658i
$236$	1.43906	+	0.467578i	0.00609770	+	0.00198126i
$237$	119.232	−	147.204i	0.503090	−	0.621113i
$238$	162.009	−	117.706i	0.680709	−	0.494564i
$239$	−87.7330	+	120.754i	−0.367084	+	0.505247i	−0.952105	−	0.305770i	$-0.901086\pi$
$239$	−87.7330	+	120.754i	−0.367084	+	0.505247i	0.585022	+	0.811018i	$0.301086\pi$
$240$	263.988	+	13.8664i	1.09995	+	0.0577768i
$241$	−358.881			−1.48913			−0.744567	−	0.667548i	$-0.767344\pi$
$241$	−358.881			−1.48913			−0.744567	+	0.667548i	$0.767344\pi$
$242$		0			0
$243$	−63.0323	+	234.683i	−0.259392	+	0.965772i
$244$	−0.160321	−	0.493418i	−0.000657055	−	0.00202221i
$245$	−57.1954	+	78.7227i	−0.233451	+	0.321317i
$246$	328.283	−	87.9215i	1.33449	−	0.357405i
$247$	−56.0262	+	172.431i	−0.226827	+	0.698101i
$248$	373.780	+	121.448i	1.50718	+	0.489711i
$249$	−7.52944	−	28.1136i	−0.0302387	−	0.112906i
$250$	177.153	+	128.709i	0.708613	+	0.514837i
$251$	339.548	−	110.326i	1.35278	−	0.439545i	0.459155	−	0.888356i	$-0.348152\pi$
$251$	339.548	−	110.326i	1.35278	−	0.439545i	0.893627	+	0.448811i	$0.148152\pi$
$252$	0.628318	+	0.566010i	0.00249332	+	0.00224607i
$253$		0			0
$254$			136.864i			0.538836i
$255$	−15.4239	+	293.639i	−0.0604859	+	1.15153i
$256$	−2.61054	−	1.89667i	−0.0101974	−	0.00740886i
$257$	−38.8488	−	53.4707i	−0.151162	−	0.208057i	0.726720	−	0.686934i	$-0.241044\pi$
$257$	−38.8488	−	53.4707i	−0.151162	−	0.208057i	−0.877882	+	0.478877i	$0.841044\pi$
$258$	205.138	+	166.158i	0.795108	+	0.644022i
$259$	67.9503	−	209.130i	0.262356	−	0.807450i
$260$	0.526440	+	0.724582i	0.00202477	+	0.00278685i
$261$	−21.8098	+	4.63041i	−0.0835624	+	0.0177410i
$262$	100.500	+	309.307i	0.383587	+	1.18056i
$263$			85.4194i			0.324789i	0.986726	+	0.162394i	$0.0519216\pi$
$263$			85.4194i			0.324789i	−0.986726	+	0.162394i	$0.948078\pi$
$264$		0			0
$265$	236.464			0.892315
$266$	−198.843	+	64.6079i	−0.747529	+	0.242887i
$267$	−85.8753	+	55.7536i	−0.321630	+	0.208815i
$268$	0.463345	−	0.336640i	0.00172890	−	0.00125612i
$269$	−153.866	−	49.9940i	−0.571991	−	0.185851i	0.00871848	−	0.999962i	$-0.497225\pi$
$269$	−153.866	−	49.9940i	−0.571991	−	0.185851i	−0.580710	+	0.814111i	$0.697225\pi$
$270$	−293.141	+	46.3220i	−1.08571	+	0.171563i
$271$	−210.339	+	152.820i	−0.776160	+	0.563913i	−0.903824	−	0.427904i	$-0.859252\pi$
$271$	−210.339	+	152.820i	−0.776160	+	0.563913i	0.127664	+	0.991817i	$0.459252\pi$
$272$	168.778	−	232.303i	0.620506	−	0.854053i
$273$	8.54877	−	162.751i	0.0313142	−	0.596157i
$274$	105.956			0.386701
$275$		0			0
$276$	−0.223487	+	0.581998i	−0.000809737	+	0.00210869i
$277$	26.8202	+	82.5441i	0.0968239	+	0.297993i	0.987725	−	0.156205i	$-0.0499259\pi$
$277$	26.8202	+	82.5441i	0.0968239	+	0.297993i	−0.890901	+	0.454198i	$0.849926\pi$
$278$	101.942	−	140.312i	0.366699	−	0.504718i
$279$	−440.639	−	46.4188i	−1.57935	−	0.166376i
$280$	75.6413	−	232.800i	0.270147	−	0.831429i
$281$	−460.991	−	149.785i	−1.64054	−	0.533043i	−0.663880	−	0.747839i	$-0.731091\pi$
$281$	−460.991	−	149.785i	−1.64054	−	0.533043i	−0.976659	+	0.214796i	$0.931091\pi$
$282$	335.604	−	89.8821i	1.19008	−	0.318731i
$283$	349.554	+	253.966i	1.23517	+	0.897406i	0.997267	−	0.0738826i	$-0.0235390\pi$
$283$	349.554	+	253.966i	1.23517	+	0.897406i	0.237906	+	0.971288i	$0.423539\pi$
$284$	−0.600938	+	0.195257i	−0.00211598	+	0.000687523i
$285$	110.052	−	286.594i	0.386148	−	1.00559i
$286$		0			0
$287$		−	316.014i		−	1.10109i
$288$	2.21067	+	0.984880i	0.00767592	+	0.00341972i
$289$	24.5889	+	17.8649i	0.0850826	+	0.0618161i
$290$	−16.0055	−	22.0297i	−0.0551914	−	0.0759645i
$291$	−71.4183	+	88.1728i	−0.245424	+	0.302999i
$292$	−0.0629771	+	0.193823i	−0.000215675	+	0.000663779i
$293$	−3.25020	−	4.47352i	−0.0110928	−	0.0152680i	0.803435	−	0.595393i	$-0.203004\pi$
$293$	−3.25020	−	4.47352i	−0.0110928	−	0.0152680i	−0.814527	+	0.580125i	$0.803004\pi$
$294$	−89.4750	+	58.0906i	−0.304337	+	0.197587i
$295$	152.582	+	469.599i	0.517227	+	1.59186i
$296$		−	313.981i		−	1.06075i
$297$		0			0
$298$	−129.170			−0.433458
$299$	114.266	−	37.1274i	0.382162	−	0.124172i
$300$	−0.139431	−	0.214761i	−0.000464771	−	0.000715871i
$301$	198.590	−	144.284i	0.659769	−	0.479350i
$302$	−85.0786	−	27.6437i	−0.281717	−	0.0915354i
$303$	109.345	+	88.5673i	0.360874	+	0.292301i
$304$	−242.536	+	176.213i	−0.797817	+	0.579648i
$305$	99.5122	−	136.967i	0.326269	−	0.449071i
$306$	−131.187	+	294.463i	−0.428716	+	0.962296i
$307$	−219.257			−0.714191			−0.357095	−	0.934068i	$-0.616233\pi$
$307$	−219.257			−0.714191			−0.357095	+	0.934068i	$0.616233\pi$
$308$		0			0
$309$	293.495	+	112.702i	0.949823	+	0.364732i
$310$	−167.220	−	514.650i	−0.539419	−	1.66016i
$311$	−83.5538	+	115.002i	−0.268662	+	0.369781i	−0.921937	−	0.387339i	$-0.873394\pi$
$311$	−83.5538	+	115.002i	−0.268662	+	0.369781i	0.653276	+	0.757120i	$0.273394\pi$
$312$	−60.2033	−	224.788i	−0.192959	−	0.720475i
$313$	29.1359	−	89.6710i	0.0930859	−	0.286489i	−0.893664	−	0.448736i	$-0.851874\pi$
$313$	29.1359	−	89.6710i	0.0930859	−	0.286489i	0.986750	+	0.162247i	$0.0518743\pi$
$314$	−268.887	−	87.3666i	−0.856327	−	0.278238i
$315$	−28.9109	+	274.442i	−0.0917805	+	0.871245i
$316$	0.858566	+	0.623785i	0.00271698	+	0.00197400i
$317$	−476.684	+	154.884i	−1.50373	+	0.488593i	−0.941104	−	0.338116i	$-0.890210\pi$
$317$	−476.684	+	154.884i	−1.50373	+	0.488593i	−0.562630	+	0.826709i	$0.690210\pi$
$318$	242.008	+	92.9312i	0.761032	+	0.292237i
$319$		0			0
$320$		−	349.513i		−	1.09223i
$321$	−139.698	−	7.33788i	−0.435196	−	0.0228594i
$322$	112.089	+	81.4377i	0.348104	+	0.252912i
$323$	−196.005	−	269.778i	−0.606827	−	0.835226i
$324$	−1.33145	−	0.283669i	−0.00410941	−	0.000875521i
$325$	−15.2488	+	46.9310i	−0.0469194	+	0.144403i
$326$	−142.501	−	196.136i	−0.437119	−	0.601643i
$327$	−275.123	−	423.762i	−0.841354	−	1.29591i
$328$	−139.439	−	429.149i	−0.425118	−	1.30838i
$329$		−	323.061i		−	0.981948i
$330$		0			0
$331$	−653.489			−1.97429			−0.987143	−	0.159839i	$-0.948903\pi$
$331$	−653.489			−1.97429			−0.987143	+	0.159839i	$0.948903\pi$
$332$	0.155068	−	0.0503847i	0.000467073	−	0.000151761i
$333$	73.5137	+	346.259i	0.220762	+	1.03982i
$334$	−174.193	+	126.559i	−0.521536	+	0.378918i
$335$	177.747	+	57.7535i	0.530588	+	0.172398i
$336$	169.616	−	209.408i	0.504810	−	0.623237i
$337$	533.438	−	387.565i	1.58290	−	1.15005i	0.669629	−	0.742696i	$-0.266453\pi$
$337$	533.438	−	387.565i	1.58290	−	1.15005i	0.913272	−	0.407349i	$-0.133547\pi$
$338$	−87.8627	+	120.933i	−0.259949	+	0.357789i
$339$	−138.769	−	7.28910i	−0.409349	−	0.0215018i
$340$	−1.64729			−0.00484497
$341$		0			0
$342$	225.265	−	250.063i	0.658670	−	0.731179i
$343$	115.309	+	354.884i	0.336177	+	1.03465i
$344$	206.022	−	283.565i	0.598902	−	0.824317i
$345$	−196.515	+	52.6311i	−0.569609	+	0.152554i
$346$	203.645	−	626.754i	0.588569	−	1.81143i
$347$	−264.279	−	85.8695i	−0.761611	−	0.247463i	−0.0976413	−	0.995222i	$-0.531130\pi$
$347$	−264.279	−	85.8695i	−0.761611	−	0.247463i	−0.663970	+	0.747759i	$0.731130\pi$
$348$	−0.0323137	−	0.120654i	−9.28556e−5	−	0.000346706i
$349$	−204.499	−	148.578i	−0.585958	−	0.425724i	0.254909	−	0.966965i	$-0.417954\pi$
$349$	−204.499	−	148.578i	−0.585958	−	0.425724i	−0.840867	+	0.541242i	$0.817954\pi$
$350$	−54.1196	+	17.5845i	−0.154627	+	0.0502415i
$351$	119.023	+	233.801i	0.339096	+	0.666100i
$352$		0			0
$353$			560.803i			1.58868i	0.607476	+	0.794338i	$0.292182\pi$
$353$			560.803i			1.58868i	−0.607476	+	0.794338i	$0.707818\pi$
$354$	−28.3947	+	540.575i	−0.0802109	+	1.52705i
$355$	−166.813	−	121.197i	−0.469895	−	0.341399i
$356$	−0.337148	−	0.464044i	−0.000947044	−	0.00130349i
$357$	232.928	+	188.667i	0.652460	+	0.528480i
$358$	29.9128	−	92.0620i	0.0835552	−	0.257157i
$359$	174.022	+	239.520i	0.484740	+	0.667187i	0.979407	−	0.201895i	$-0.0647100\pi$
$359$	174.022	+	239.520i	0.484740	+	0.667187i	−0.494667	+	0.869083i	$0.664710\pi$
$360$	81.8344	+	385.450i	0.227318	+	1.07070i
$361$	−3.96952	−	12.2169i	−0.0109959	−	0.0338419i
$362$			0.133414i			0.000368547i
$363$		0			0
$364$	0.913018			0.00250829
$365$	−63.2492	+	20.5509i	−0.173285	+	0.0563038i
$366$	155.674	−	101.070i	0.425339	−	0.276147i
$367$	−68.6514	+	49.8782i	−0.187061	+	0.135908i	−0.677375	−	0.735638i	$-0.736882\pi$
$367$	−68.6514	+	49.8782i	−0.187061	+	0.135908i	0.490313	+	0.871546i	$0.336882\pi$
$368$	188.942	+	61.3910i	0.513430	+	0.166823i
$369$	254.252	+	440.618i	0.689028	+	1.19409i
$370$	−349.750	+	254.108i	−0.945270	+	0.686779i
$371$	141.688	−	195.016i	0.381908	−	0.525651i
$372$	0.130203	−	2.47879i	0.000350007	−	0.00666341i
$373$	−316.098			−0.847447			−0.423724	−	0.905792i	$-0.639277\pi$
$373$	−316.098			−0.847447			−0.423724	+	0.905792i	$0.639277\pi$
$374$		0			0
$375$	−117.499	+	305.988i	−0.313332	+	0.815968i
$376$	−142.548	−	438.718i	−0.379118	−	1.16680i
$377$	−14.1490	+	19.4744i	−0.0375304	+	0.0516562i
$378$	−137.446	+	269.515i	−0.363613	+	0.713003i
$379$	−33.6016	+	103.415i	−0.0886586	+	0.272863i	−0.985549	−	0.169389i	$-0.945820\pi$
$379$	−33.6016	+	103.415i	−0.0886586	+	0.272863i	0.896891	+	0.442253i	$0.145820\pi$
$380$	1.63568	+	0.531466i	0.00430443	+	0.00139859i
$381$	−197.892	+	52.9999i	−0.519402	+	0.139107i
$382$	−320.092	−	232.561i	−0.837938	−	0.608797i
$383$	420.380	−	136.590i	1.09760	−	0.356631i	0.296420	−	0.955058i	$-0.404207\pi$
$383$	420.380	−	136.590i	1.09760	−	0.356631i	0.801178	+	0.598426i	$0.204207\pi$
$384$	138.517	−	360.721i	0.360721	−	0.939378i
$385$		0			0
$386$		−	3.05372i		−	0.00791119i
$387$	−160.809	+	360.953i	−0.415527	+	0.932694i
$388$	−0.514268	−	0.373638i	−0.00132543	−	0.000962983i
$389$	299.534	+	412.273i	0.770010	+	1.05983i	0.996315	+	0.0857708i	$0.0273353\pi$
$389$	299.534	+	412.273i	0.770010	+	1.05983i	−0.226305	+	0.974056i	$0.572665\pi$
$390$	−201.673	+	248.985i	−0.517110	+	0.638423i
$391$	−68.2865	+	210.164i	−0.174646	+	0.537504i
$392$	83.2541	+	114.589i	0.212383	+	0.292320i
$393$	−408.309	+	265.090i	−1.03895	+	0.674529i
$394$	−133.441	−	410.689i	−0.338682	−	1.04236i
$395$			346.310i			0.876734i
$396$		0			0
$397$	13.0481			0.0328668			0.0164334	−	0.999865i	$-0.494769\pi$
$397$	13.0481			0.0328668			0.0164334	+	0.999865i	$0.494769\pi$
$398$	203.310	−	66.0595i	0.510830	−	0.165979i
$399$	−170.417	−	262.488i	−0.427111	−	0.657864i
$400$	−66.0118	+	47.9604i	−0.165029	+	0.119901i
$401$	−522.706	−	169.837i	−1.30351	−	0.423535i	−0.426706	−	0.904390i	$-0.640326\pi$
$401$	−522.706	−	169.837i	−1.30351	−	0.423535i	−0.876800	+	0.480855i	$0.840326\pi$
$402$	159.217	+	128.963i	0.396063	+	0.320804i
$403$	−387.006	+	281.176i	−0.960313	+	0.697708i
$404$	−0.463356	+	0.637754i	−0.00114692	+	0.00157860i
$405$	−180.494	−	405.914i	−0.445664	−	1.00226i
$406$	−27.7588			−0.0683714
$407$		0			0
$408$	399.566	+	153.433i	0.979327	+	0.376062i
$409$	−191.024	−	587.911i	−0.467051	−	1.43744i	−0.856385	−	0.516339i	$-0.827295\pi$
$409$	−191.024	−	587.911i	−0.467051	−	1.43744i	0.389334	−	0.921097i	$-0.372705\pi$
$410$	−365.188	+	502.638i	−0.890702	+	1.22595i
$411$	41.0308	+	153.202i	0.0998317	+	0.372754i
$412$	−0.544264	+	1.67507i	−0.00132103	+	0.00406571i
$413$	478.714	+	155.544i	1.15911	+	0.376619i
$414$	−221.807	−	23.3661i	−0.535766	−	0.0564398i
$415$	43.0450	+	31.2740i	0.103723	+	0.0753591i
$416$	2.48500	−	0.807424i	0.00597355	−	0.00194092i
$417$	242.353	+	93.0636i	0.581182	+	0.223174i
$418$		0			0
$419$		−	440.342i		−	1.05094i	−0.850814	−	0.525468i	$-0.823890\pi$
$419$		−	440.342i		−	1.05094i	0.850814	−	0.525468i	$-0.176110\pi$
$420$	−1.54386	−	0.0810938i	−0.00367585	−	0.000193080i
$421$	−464.562	−	337.524i	−1.10347	−	0.801719i	−0.121849	−	0.992549i	$-0.538882\pi$
$421$	−464.562	−	337.524i	−1.10347	−	0.801719i	−0.981623	+	0.190829i	$0.938882\pi$
$422$	253.072	+	348.324i	0.599697	+	0.825413i
$423$	259.921	+	450.443i	0.614471	+	1.06488i
$424$	106.363	−	327.352i	0.250856	−	0.772056i
$425$	−53.3473	−	73.4262i	−0.125523	−	0.172768i
$426$	−123.094	−	189.597i	−0.288952	−	0.445063i
$427$	−53.3322	−	164.140i	−0.124900	−	0.384402i
$428$		−	0.783693i		−	0.00183106i
$429$		0			0
$430$	−482.605			−1.12234
$431$	629.106	−	204.409i	1.45964	−	0.474267i	0.531682	−	0.846944i	$-0.321560\pi$
$431$	629.106	−	204.409i	1.45964	−	0.474267i	0.927961	+	0.372677i	$0.121560\pi$
$432$	−68.0149	+	428.442i	−0.157442	+	0.991765i
$433$	−172.144	+	125.070i	−0.397560	+	0.288845i	−0.768547	−	0.639794i	$-0.779020\pi$
$433$	−172.144	+	125.070i	−0.397560	+	0.288845i	0.370986	+	0.928638i	$0.379020\pi$
$434$	−524.640	−	170.466i	−1.20885	−	0.392778i
$435$	25.6547	−	31.6732i	0.0589764	−	0.0728121i
$436$	2.28988	−	1.66370i	0.00525202	−	0.00381581i
$437$	135.611	−	186.652i	0.310322	−	0.427121i
$438$	−72.8089	−	3.82441i	−0.166230	−	0.00873154i
$439$	103.815			0.236482			0.118241	−	0.992985i	$-0.462275\pi$
$439$	103.815			0.236482			0.118241	+	0.992985i	$0.462275\pi$
$440$		0			0
$441$	−118.642	−	106.877i	−0.269029	−	0.242351i
$442$	107.550	+	331.004i	0.243325	+	0.748877i
$443$	162.680	−	223.910i	0.367225	−	0.505441i	−0.584919	−	0.811092i	$-0.698874\pi$
$443$	162.680	−	223.910i	0.367225	−	0.505441i	0.952144	+	0.305650i	$0.0988738\pi$
$444$	−1.91553	+	0.513022i	−0.00431427	+	0.00115546i
$445$	57.8405	−	178.015i	0.129979	−	0.400033i
$446$	85.3340	+	27.7267i	0.191332	+	0.0621675i
$447$	−50.0205	−	186.768i	−0.111903	−	0.417824i
$448$	−288.251	−	209.427i	−0.643417	−	0.467470i
$449$	−473.509	+	153.852i	−1.05459	+	0.342656i	−0.784466	−	0.620171i	$-0.787063\pi$
$449$	−473.509	+	153.852i	−1.05459	+	0.342656i	−0.270119	+	0.962827i	$0.587063\pi$
$450$	61.3111	−	68.0603i	0.136247	−	0.151245i
$451$		0			0
$452$		−	0.778483i		−	0.00172231i
$453$	7.02388	−	133.720i	0.0155052	−	0.295188i
$454$	364.017	+	264.474i	0.801800	+	0.582542i
$455$	175.124	+	241.038i	0.384889	+	0.529754i
$456$	−347.248	−	281.264i	−0.761509	−	0.616807i
$457$	−250.649	+	771.417i	−0.548465	+	1.68800i	0.164140	+	0.986437i	$0.447515\pi$
$457$	−250.649	+	771.417i	−0.548465	+	1.68800i	−0.712605	+	0.701565i	$0.752485\pi$
$458$	122.635	+	168.792i	0.267761	+	0.368542i
$459$	−476.565	−	75.6544i	−1.03827	−	0.164824i
$460$	−0.352191	−	1.08393i	−0.000765633	−	0.00235638i
$461$			790.057i			1.71379i	0.515492	+	0.856894i	$0.327609\pi$
$461$			790.057i			1.71379i	−0.515492	+	0.856894i	$0.672391\pi$
$462$		0			0
$463$	540.381			1.16713			0.583565	−	0.812067i	$-0.301658\pi$
$463$	540.381			1.16713			0.583565	+	0.812067i	$0.301658\pi$
$464$	−37.8549	+	12.2998i	−0.0815839	+	0.0265082i
$465$	679.377	−	441.078i	1.46103	−	0.948555i
$466$	99.7650	−	72.4835i	0.214088	−	0.155544i
$467$	264.267	+	85.8654i	0.565881	+	0.183866i	0.577966	−	0.816061i	$-0.303847\pi$
$467$	264.267	+	85.8654i	0.565881	+	0.183866i	−0.0120845	+	0.999927i	$0.503847\pi$
$468$	−1.27302	+	0.734575i	−0.00272013	+	0.00156960i
$469$	154.136	−	111.986i	0.328647	−	0.238776i
$470$	−373.331	+	513.846i	−0.794322	+	1.09329i
$471$	22.1986	−	422.616i	0.0471308	−	0.897273i
$472$	718.728			1.52273
$473$		0			0
$474$	−136.101	+	354.430i	−0.287133	+	0.747743i
$475$	29.2819	+	90.1203i	0.0616460	+	0.189727i
$476$	−0.987047	+	1.35855i	−0.00207363	+	0.00285411i
$477$	−40.6530	+	385.907i	−0.0852265	+	0.809029i
$478$	92.4415	−	284.506i	0.193392	−	0.595200i
$479$	−447.212	−	145.308i	−0.933636	−	0.303357i	−0.197587	−	0.980285i	$-0.563311\pi$
$479$	−447.212	−	145.308i	−0.933636	−	0.303357i	−0.736049	+	0.676929i	$0.763311\pi$
$480$	−4.27369	+	1.14459i	−0.00890352	+	0.00238456i
$481$	309.181	+	224.633i	0.642787	+	0.467012i
$482$	684.065	−	222.266i	1.41922	−	0.461133i
$483$	−74.3449	+	193.606i	−0.153923	+	0.400841i
$484$		0			0
$485$		−	207.434i		−	0.427699i
$486$	−25.2001	−	486.368i	−0.0518521	−	1.00076i
$487$	−205.651	−	149.414i	−0.422282	−	0.306806i	0.356274	−	0.934382i	$-0.384047\pi$
$487$	−205.651	−	149.414i	−0.422282	−	0.306806i	−0.778555	+	0.627576i	$0.784047\pi$
$488$	−144.851	−	199.370i	−0.296825	−	0.408545i
$489$	228.410	−	281.994i	0.467096	−	0.576676i
$490$	60.2650	−	185.477i	0.122990	−	0.378524i
$491$	72.3701	+	99.6089i	0.147393	+	0.202869i	0.876329	−	0.481712i	$-0.159985\pi$
$491$	72.3701	+	99.6089i	0.147393	+	0.202869i	−0.728936	+	0.684582i	$0.759985\pi$
$492$	−2.39031	+	1.55188i	−0.00485836	+	0.00315424i
$493$	−13.6813	−	42.1068i	−0.0277512	−	0.0854093i
$494$		−	363.370i		−	0.735567i
$495$		0			0
$496$	−790.989			−1.59474
$497$	−199.907	+	64.9537i	−0.402227	+	0.130691i
$498$	31.7635	+	48.9242i	0.0637822	+	0.0982414i
$499$	−52.8516	+	38.3990i	−0.105915	+	0.0769518i	−0.639482	−	0.768806i	$-0.720851\pi$
$499$	−52.8516	+	38.3990i	−0.105915	+	0.0769518i	0.533567	+	0.845758i	$0.320851\pi$
$500$	−1.74637	−	0.567430i	−0.00349274	−	0.00113486i
$501$	−250.446	−	202.857i	−0.499893	−	0.404904i
$502$	−578.886	+	420.585i	−1.15316	+	0.837820i
$503$	−250.337	+	344.560i	−0.497688	+	0.685009i	−0.981783	−	0.190007i	$-0.939149\pi$
$503$	−250.337	+	344.560i	−0.497688	+	0.685009i	0.484095	+	0.875016i	$0.339149\pi$
$504$	366.924	+	163.469i	0.728023	+	0.324344i
$505$	−257.243			−0.509393
$506$		0			0
$507$	−208.881	−	80.2103i	−0.411994	−	0.158206i
$508$	−0.354659	−	1.09153i	−0.000698148	−	0.00214868i
$509$	−41.0633	+	56.5188i	−0.0806745	+	0.111039i	−0.847447	−	0.530880i	$-0.821861\pi$
$509$	−41.0633	+	56.5188i	−0.0806745	+	0.111039i	0.766772	+	0.641919i	$0.221861\pi$
$510$	−152.460	−	569.259i	−0.298941	−	1.11619i
$511$	−20.9498	+	64.4769i	−0.0409977	+	0.126178i
$512$	−483.837	−	157.208i	−0.944993	−	0.307047i
$513$	448.799	+	228.876i	0.874852	+	0.446151i
$514$	107.166	+	77.8606i	0.208494	+	0.151480i
$515$	−546.616	+	177.606i	−1.06139	+	0.344866i
$516$	−2.06660	−	0.793574i	−0.00400503	−	0.00153793i
$517$		0			0
$518$			440.706i			0.850785i
$519$	985.084	+	51.7433i	1.89804	+	0.0996980i
$520$	344.176	+	250.058i	0.661876	+	0.480881i
$521$	59.1550	+	81.4198i	0.113541	+	0.156276i	0.862005	−	0.506899i	$-0.169208\pi$
$521$	59.1550	+	81.4198i	0.113541	+	0.156276i	−0.748464	+	0.663175i	$0.769208\pi$
$522$	38.7040	−	22.3335i	0.0741456	−	0.0427845i
$523$	263.265	−	810.248i	0.503376	−	1.54923i	−0.300109	−	0.953905i	$-0.597023\pi$
$523$	263.265	−	810.248i	0.503376	−	1.54923i	0.803484	−	0.595326i	$-0.202977\pi$
$524$	−1.60303	−	2.20638i	−0.00305921	−	0.00421064i
$525$	−46.3829	−	71.4420i	−0.0883485	−	0.136080i
$526$	−52.9029	−	162.818i	−0.100576	−	0.309541i
$527$		−	879.833i		−	1.66951i
$528$		0			0
$529$	376.110			0.710983
$530$	−450.724	+	146.449i	−0.850423	+	0.276319i
$531$	−792.614	+	168.279i	−1.49268	+	0.316909i
$532$	1.41840	−	1.03053i	0.00266617	−	0.00193709i
$533$	522.347	+	169.721i	0.980013	+	0.318425i
$534$	129.157	−	159.457i	0.241868	−	0.298610i
$535$	206.896	−	150.319i	0.386722	−	0.280970i
$536$	159.904	−	220.089i	0.298328	−	0.410613i
$537$	144.696	+	7.60041i	0.269453	+	0.0141535i
$538$	324.247			0.602689
$539$		0			0
$540$	2.21784	−	1.12905i	0.00410711	−	0.00209084i
$541$	−226.023	−	695.627i	−0.417787	−	1.28582i	−0.909734	−	0.415192i	$-0.863715\pi$
$541$	−226.023	−	695.627i	−0.417787	−	1.28582i	0.491947	−	0.870625i	$-0.336285\pi$
$542$	306.282	−	421.561i	0.565096	−	0.777788i
$543$	−0.192904	+	0.0516638i	−0.000355255	+	9.51452e-5i
$544$	−1.48505	+	4.57052i	−0.00272988	+	0.00840169i
$545$	878.436	+	285.421i	1.61181	+	0.523708i
$546$	84.5017	+	315.515i	0.154765	+	0.577865i
$547$	−99.7347	−	72.4615i	−0.182330	−	0.132471i	0.492876	−	0.870099i	$-0.335946\pi$
$547$	−99.7347	−	72.4615i	−0.182330	−	0.132471i	−0.675207	+	0.737629i	$0.735946\pi$
$548$	−0.845027	+	0.274566i	−0.00154202	+	0.000501033i
$549$	206.421	+	185.951i	0.375994	+	0.338708i
$550$		0			0
$551$			46.2241i			0.0838913i
$552$	−15.5333	+	295.722i	−0.0281401	+	0.535729i
$553$	285.609	+	207.507i	0.516472	+	0.375239i
$554$	−102.244	−	140.727i	−0.184556	−	0.254020i
$555$	−502.854	−	407.302i	−0.906043	−	0.733877i
$556$	−0.449425	+	1.38319i	−0.000808318	+	0.00248775i
$557$	−118.600	−	163.240i	−0.212927	−	0.293069i	0.689172	−	0.724598i	$-0.257974\pi$
$557$	−118.600	−	163.240i	−0.212927	−	0.293069i	−0.902099	+	0.431529i	$0.857974\pi$
$558$	868.654	−	184.423i	1.55673	−	0.330506i
$559$	131.834	+	405.745i	0.235840	+	0.725840i
$560$			492.649i			0.879731i
$561$		0			0
$562$	971.465			1.72858
$563$	−460.414	+	149.597i	−0.817786	+	0.265715i	−0.687892	−	0.725813i	$-0.741464\pi$
$563$	−460.414	+	149.597i	−0.817786	+	0.265715i	−0.129894	+	0.991528i	$0.541464\pi$
$564$	−2.44362	+	1.58649i	−0.00433265	+	0.00281293i
$565$	205.521	−	149.319i	0.363753	−	0.264282i
$566$	−823.575	−	267.596i	−1.45508	−	0.472784i
$567$	−442.917	−	94.3647i	−0.781159	−	0.166428i
$568$	−242.814	+	176.415i	−0.427489	+	0.310589i
$569$	274.742	−	378.150i	0.482850	−	0.664586i	−0.496199	−	0.868209i	$-0.665271\pi$
$569$	274.742	−	378.150i	0.482850	−	0.664586i	0.979050	+	0.203622i	$0.0652714\pi$
$570$	−32.2744	+	614.437i	−0.0566217	+	1.07796i
$571$	−656.796			−1.15026			−0.575128	−	0.818064i	$-0.695048\pi$
$571$	−656.796			−1.15026			−0.575128	+	0.818064i	$0.695048\pi$
$572$		0			0
$573$	212.306	−	552.879i	0.370516	−	0.964885i
$574$	195.717	+	602.356i	0.340971	+	1.04940i
$575$	36.9095	−	50.8016i	0.0641905	−	0.0883506i
$576$	570.403	+	60.0886i	0.990284	+	0.104321i
$577$	−269.912	+	830.704i	−0.467785	+	1.43969i	0.387660	+	0.921802i	$0.373283\pi$
$577$	−269.912	+	830.704i	−0.467785	+	1.43969i	−0.855446	+	0.517893i	$0.826717\pi$
$578$	−57.9332	−	18.8236i	−0.100230	−	0.0325669i
$579$	4.41537	−	1.18253i	0.00762586	−	0.00204237i
$580$	0.184734	+	0.134217i	0.000318507	+	0.000231409i
$581$	51.5847	−	16.7609i	0.0887861	−	0.0288483i
$582$	81.5225	−	212.298i	0.140073	−	0.364774i
$583$		0			0
$584$			96.8039i			0.165760i
$585$	−438.104	−	195.181i	−0.748896	−	0.333643i
$586$	8.96581	+	6.51405i	0.0153000	+	0.0111161i
$587$	−464.705	−	639.611i	−0.791661	−	1.08963i	−0.993899	−	0.110291i	$-0.964822\pi$
$587$	−464.705	−	639.611i	−0.791661	−	1.08963i	0.202239	−	0.979336i	$-0.435178\pi$
$588$	0.563055	−	0.695146i	0.000957576	−	0.00118222i
$589$	−283.861	+	873.634i	−0.481937	+	1.48325i
$590$	−581.674	−	800.605i	−0.985888	−	1.35696i
$591$	542.141	−	351.979i	0.917328	−	0.595565i
$592$	195.275	+	600.996i	0.329857	+	1.01520i
$593$		−	928.634i		−	1.56599i	−0.622026	−	0.782997i	$-0.713690\pi$
$593$		−	928.634i		−	1.56599i	0.622026	−	0.782997i	$-0.286310\pi$
$594$		0			0
$595$	−547.984			−0.920981
$596$	1.03017	−	0.334722i	0.00172847	−	0.000561614i
$597$	174.246	+	268.385i	0.291870	+	0.449556i
$598$	−194.810	+	141.537i	−0.325769	+	0.236685i
$599$	872.469	+	283.482i	1.45654	+	0.473259i	0.927012	−	0.375032i	$-0.122368\pi$
$599$	872.469	+	283.482i	1.45654	+	0.473259i	0.529530	+	0.848291i	$0.322368\pi$
$600$	−94.5115	−	76.5524i	−0.157519	−	0.127587i
$601$	773.147	−	561.724i	1.28643	−	0.934649i	0.286708	−	0.958018i	$-0.407439\pi$
$601$	773.147	−	561.724i	1.28643	−	0.934649i	0.999727	+	0.0233687i	$0.00743915\pi$
$602$	−289.174	+	398.014i	−0.480356	+	0.661153i
$603$	−124.812	+	280.153i	−0.206985	+	0.464598i
$604$	0.750158			0.00124198
$605$		0			0
$606$	−263.275	−	101.098i	−0.434448	−	0.166828i
$607$	241.534	+	743.364i	0.397914	+	1.22465i	0.926669	+	0.375878i	$0.122659\pi$
$607$	241.534	+	743.364i	0.397914	+	1.22465i	−0.528756	+	0.848774i	$0.677341\pi$
$608$	2.94918	−	4.05919i	0.00485062	−	0.00667631i
$609$	−10.7494	−	40.1364i	−0.0176509	−	0.0659055i
$610$	−104.853	+	322.704i	−0.171890	+	0.529023i
$611$	533.995	+	173.505i	0.873968	+	0.283969i
$612$	0.283204	−	2.68836i	0.000462751	−	0.00439275i
$613$	69.5578	+	50.5367i	0.113471	+	0.0824416i	0.643074	−	0.765804i	$-0.277659\pi$
$613$	69.5578	+	50.5367i	0.113471	+	0.0824416i	−0.529603	+	0.848246i	$0.677659\pi$
$614$	417.926	−	135.792i	0.680661	−	0.221160i
$615$	−868.181	−	333.382i	−1.41168	−	0.542084i
$616$		0			0
$617$		−	7.47837i		−	0.0121205i	−0.999982	−	0.00606027i	$-0.998071\pi$
$617$		−	7.47837i		−	0.0121205i	0.999982	−	0.00606027i	$-0.00192905\pi$
$618$	−629.233	−	33.0516i	−1.01818	−	0.0534815i
$619$	−263.047	−	191.115i	−0.424955	−	0.308748i	0.354674	−	0.934990i	$-0.384592\pi$
$619$	−263.047	−	191.115i	−0.424955	−	0.308748i	−0.779628	+	0.626243i	$0.784592\pi$
$620$	2.66724	+	3.67115i	0.00430201	+	0.00592121i
$621$	−52.1085	−	329.760i	−0.0839106	−	0.531014i
$622$	88.0380	−	270.953i	0.141540	−	0.435616i
$623$	−112.155	−	154.368i	−0.180024	−	0.247782i
$624$	255.039	+	392.828i	0.408717	+	0.629532i
$625$	−224.399	−	690.629i	−0.359038	−	1.10501i
$626$			188.967i			0.301864i
$627$		0			0
$628$	2.37084			0.00377522
$629$	−668.500	+	217.209i	−1.06280	+	0.345324i
$630$	−114.863	−	541.021i	−0.182323	−	0.858763i
$631$	554.612	−	402.949i	0.878941	−	0.638588i	−0.0540299	−	0.998539i	$-0.517207\pi$
$631$	554.612	−	402.949i	0.878941	−	0.638588i	0.932971	+	0.359951i	$0.117207\pi$
$632$	479.419	+	155.773i	0.758574	+	0.246476i
$633$	−405.641	+	500.804i	−0.640824	+	0.791159i
$634$	812.685	−	590.450i	1.28184	−	0.931309i
$635$	220.139	−	302.995i	0.346675	−	0.477157i
$636$	−2.17089	−	0.114030i	−0.00341336	−	0.000179292i
$637$	−172.400			−0.270644
$638$		0			0
$639$	226.471	−	251.401i	0.354414	−	0.393429i
$640$	218.287	+	671.819i	0.341074	+	1.04972i
$641$	160.641	−	221.104i	0.250610	−	0.344935i	−0.665115	−	0.746741i	$-0.731617\pi$
$641$	160.641	−	221.104i	0.250610	−	0.344935i	0.915725	+	0.401806i	$0.131617\pi$
$642$	270.823	−	72.5325i	0.421843	−	0.112979i
$643$	57.0519	−	175.588i	0.0887277	−	0.273076i	−0.896841	−	0.442354i	$-0.854144\pi$
$643$	57.0519	−	175.588i	0.0887277	−	0.273076i	0.985568	+	0.169278i	$0.0541436\pi$
$644$	−1.10497	−	0.359028i	−0.00171580	−	0.000557496i
$645$	−186.886	−	697.798i	−0.289745	−	1.08186i
$646$	540.688	+	392.833i	0.836979	+	0.608101i
$647$	−342.473	+	111.276i	−0.529325	+	0.171988i	−0.561473	−	0.827495i	$-0.689765\pi$
$647$	−342.473	+	111.276i	−0.529325	+	0.171988i	0.0321480	+	0.999483i	$0.489765\pi$
$648$	−643.121	+	67.2862i	−0.992471	+	0.103837i
$649$		0			0
$650$		−	98.8995i		−	0.152153i
$651$	43.3130	−	824.589i	0.0665330	−	1.26665i
$652$	1.64473	+	1.19497i	0.00252260	+	0.00183277i
$653$	−605.633	−	833.583i	−0.927463	−	1.27654i	−0.960841	−	0.277101i	$-0.910626\pi$
$653$	−605.633	−	833.583i	−0.927463	−	1.27654i	0.0333778	−	0.999443i	$-0.489374\pi$
$654$	786.862	+	637.343i	1.20315	+	0.974530i
$655$	275.013	−	846.402i	0.419867	−	1.29222i
$656$	533.804	+	734.718i	0.813725	+	1.12000i
$657$	−22.6651	−	106.755i	−0.0344978	−	0.162489i
$658$	200.082	+	615.788i	0.304076	+	0.935848i
$659$			1071.63i			1.62614i	0.582166	+	0.813070i	$0.302205\pi$
$659$			1071.63i			1.62614i	−0.582166	+	0.813070i	$0.697795\pi$
$660$		0			0
$661$	441.357			0.667712			0.333856	−	0.942624i	$-0.391650\pi$
$661$	441.357			0.667712			0.333856	+	0.942624i	$0.391650\pi$
$662$	1245.62	−	404.726i	1.88160	−	0.611368i
$663$	−436.950	+	283.685i	−0.659050	+	0.427881i
$664$	62.6566	−	45.5227i	0.0943624	−	0.0685583i
$665$	544.123	+	176.796i	0.818230	+	0.265859i
$666$	−354.574	−	614.476i	−0.532393	−	0.922637i
$667$	24.7816	−	18.0049i	0.0371539	−	0.0269939i
$668$	1.06128	−	1.46073i	0.00158874	−	0.00218672i
$669$	−7.04497	+	134.122i	−0.0105306	+	0.200481i
$670$	−374.573			−0.559064
$671$		0			0
$672$	−1.61681	+	4.21043i	−0.00240596	+	0.00626552i
$673$	114.553	+	352.559i	0.170213	+	0.523861i	0.999383	−	0.0351357i	$-0.0111864\pi$
$673$	114.553	+	352.559i	0.170213	+	0.523861i	−0.829170	+	0.558997i	$0.811186\pi$
$674$	−776.757	+	1069.11i	−1.15246	+	1.58622i
$675$	122.151	+	62.2937i	0.180964	+	0.0922870i
$676$	0.387353	−	1.19215i	0.000573007	−	0.00176353i
$677$	71.5458	+	23.2466i	0.105681	+	0.0343377i	0.361380	−	0.932419i	$-0.382306\pi$
$677$	71.5458	+	23.2466i	0.105681	+	0.0343377i	−0.255699	+	0.966756i	$0.582306\pi$
$678$	269.023	−	72.0503i	0.396789	−	0.106269i
$679$	−171.075	−	124.294i	−0.251952	−	0.183054i
$680$	−744.164	+	241.794i	−1.09436	+	0.355579i
$681$	−241.440	+	628.749i	−0.354537	+	0.923272i
$682$		0			0
$683$			987.234i			1.44544i	0.691142	+	0.722719i	$0.257108\pi$
$683$			987.234i			1.44544i	−0.691142	+	0.722719i	$0.742892\pi$
$684$	−1.14856	+	2.57805i	−0.00167918	+	0.00376908i
$685$	−234.569	−	170.424i	−0.342436	−	0.248795i
$686$	−439.581	−	605.031i	−0.640788	−	0.881970i
$687$	−196.567	+	242.681i	−0.286124	+	0.353248i
$688$	−217.991	+	670.908i	−0.316848	+	0.975157i
$689$	246.251	+	338.936i	0.357404	+	0.491924i
$690$	341.982	−	222.028i	0.495626	−	0.321780i
$691$	317.299	+	976.547i	0.459188	+	1.41324i	0.866147	+	0.499790i	$0.166589\pi$
$691$	317.299	+	976.547i	0.459188	+	1.41324i	−0.406958	+	0.913447i	$0.633411\pi$
$692$			5.52624i			0.00798589i
$693$		0			0
$694$	556.925			0.802486
$695$	−451.366	+	146.658i	−0.649448	+	0.211018i
$696$	−32.3076	−	49.7623i	−0.0464190	−	0.0714976i
$697$	−817.241	+	593.760i	−1.17251	+	0.851880i
$698$	481.816	+	156.551i	0.690281	+	0.224286i
$699$	143.437	+	116.181i	0.205204	+	0.166211i
$700$	0.386051	−	0.280482i	0.000551501	−	0.000400689i
$701$	−109.885	+	151.244i	−0.156754	+	0.215754i	−0.880170	−	0.474659i	$-0.842571\pi$
$701$	−109.885	+	151.244i	−0.156754	+	0.215754i	0.723415	+	0.690413i	$0.242571\pi$
$702$	−371.670	−	371.935i	−0.529444	−	0.529822i
$703$	733.868			1.04391
$704$		0			0
$705$	−887.541	−	340.816i	−1.25892	−	0.483427i
$706$	−347.322	−	1068.95i	−0.491958	−	1.51409i
$707$	−154.139	+	212.154i	−0.218018	+	0.300077i
$708$	−1.17435	−	4.38481i	−0.00165868	−	0.00619323i
$709$	−220.538	+	678.745i	−0.311055	+	0.957327i	0.666294	+	0.745690i	$0.267880\pi$
$709$	−220.538	+	678.745i	−0.311055	+	0.957327i	−0.977348	+	0.211638i	$0.932120\pi$
$710$	393.024	+	127.701i	0.553554	+	0.179861i
$711$	−565.175	−	59.5379i	−0.794902	−	0.0837383i
$712$	−220.420	−	160.145i	−0.309579	−	0.224922i
$713$	578.939	−	188.109i	0.811976	−	0.263827i
$714$	−560.833	−	215.360i	−0.785481	−	0.301625i
$715$		0			0
$716$			0.811733i			0.00113370i
$717$	447.164	+	23.4881i	0.623660	+	0.0327588i
$718$	−480.046	−	348.774i	−0.668588	−	0.485757i
$719$	293.142	+	403.475i	0.407708	+	0.561162i	0.962658	−	0.270722i	$-0.0872624\pi$
$719$	293.142	+	403.475i	0.407708	+	0.561162i	−0.554950	+	0.831884i	$0.687262\pi$
$720$	−396.365	−	686.900i	−0.550506	−	0.954028i
$721$	−181.054	+	557.226i	−0.251115	+	0.772852i
$722$	15.1326	+	20.8283i	0.0209593	+	0.0288480i
$723$	586.275	+	903.019i	0.810892	+	1.24899i
$724$	−0.000345719	−	0.00106401i	−4.77512e−7	−	1.46963e-6i
$725$			12.5809i			0.0173530i
$726$		0			0
$727$	427.838			0.588498			0.294249	−	0.955729i	$-0.404930\pi$
$727$	427.838			0.588498			0.294249	+	0.955729i	$0.404930\pi$
$728$	412.457	−	134.015i	0.566561	−	0.184087i
$729$	693.480	−	224.780i	0.951276	−	0.308340i
$730$	107.832	−	78.3444i	0.147715	−	0.107321i
$731$	−746.264	−	242.476i	−1.02088	−	0.331705i
$732$	−0.979638	+	1.20946i	−0.00133830	+	0.00165227i
$733$	774.572	−	562.759i	1.05671	−	0.767748i	0.0832370	−	0.996530i	$-0.473474\pi$
$733$	774.572	−	562.759i	1.05671	−	0.767748i	0.973478	+	0.228782i	$0.0734742\pi$
$734$	99.9657	−	137.591i	0.136193	−	0.187454i
$735$	291.518	+	15.3125i	0.396623	+	0.0208333i
$736$	−3.32495			−0.00451760
$737$		0			0
$738$	−757.518	−	682.398i	−1.02645	−	0.924659i
$739$	350.729	+	1079.43i	0.474599	+	1.46067i	0.846498	+	0.532392i	$0.178707\pi$
$739$	350.729	+	1079.43i	0.474599	+	1.46067i	−0.371899	+	0.928273i	$0.621293\pi$
$740$	2.13087	−	2.93289i	0.00287956	−	0.00396337i
$741$	525.397	−	140.713i	0.709038	−	0.189896i
$742$	−149.292	+	459.473i	−0.201202	+	0.619236i
$743$	−824.458	−	267.883i	−1.10963	−	0.360542i	−0.303831	−	0.952726i	$-0.598266\pi$
$743$	−824.458	−	267.883i	−1.10963	−	0.360542i	−0.805803	+	0.592184i	$0.798266\pi$
$744$	−305.024	−	1138.91i	−0.409979	−	1.53079i
$745$	285.962	+	207.763i	0.383841	+	0.278877i
$746$	602.516	−	195.769i	0.807662	−	0.262425i
$747$	−58.4393	+	64.8725i	−0.0782321	+	0.0868441i
$748$		0			0
$749$		−	260.702i		−	0.348067i
$750$	34.4584	−	656.016i	0.0459445	−	0.874688i
$751$	936.412	+	680.343i	1.24689	+	0.905916i	0.998037	−	0.0626258i	$-0.0199475\pi$
$751$	936.412	+	680.343i	1.24689	+	0.905916i	0.248850	+	0.968542i	$0.419947\pi$
$752$	545.707	+	751.101i	0.725674	+	0.998805i
$753$	−832.295	−	674.143i	−1.10531	−	0.895276i
$754$	14.9083	−	45.8831i	0.0197723	−	0.0608529i
$755$	143.886	+	198.043i	0.190578	+	0.262308i
$756$	0.397766	−	2.50562i	0.000526145	−	0.00331431i
$757$	−126.788	−	390.214i	−0.167488	−	0.515474i	0.831723	−	0.555190i	$-0.187355\pi$
$757$	−126.788	−	390.214i	−0.167488	−	0.515474i	−0.999211	+	0.0397163i	$0.987355\pi$
$758$		−	217.931i		−	0.287508i
$759$		0			0
$760$	816.931			1.07491
$761$	−241.083	+	78.3326i	−0.316798	+	0.102934i	−0.463100	−	0.886306i	$-0.653263\pi$
$761$	−241.083	+	78.3326i	−0.316798	+	0.102934i	0.146302	+	0.989240i	$0.453263\pi$
$762$	344.379	−	223.584i	0.451941	−	0.293417i
$763$	761.747	−	553.442i	0.998358	−	0.725349i
$764$	3.15546	+	1.02527i	0.00413018	+	0.00134198i
$765$	764.053	−	440.884i	0.998762	−	0.576319i
$766$	−716.694	+	520.709i	−0.935632	+	0.679776i
$767$	−514.203	+	707.739i	−0.670408	+	0.922737i
$768$	−0.507781	+	9.66709i	−0.000661173	+	0.0125874i
$769$	788.887			1.02586			0.512931	−	0.858430i	$-0.328560\pi$
$769$	788.887			1.02586			0.512931	+	0.858430i	$0.328560\pi$
$770$		0			0
$771$	−71.0793	+	185.102i	−0.0921910	+	0.240081i
$772$	0.00791316	+	0.0243542i	1.02502e−5	+	3.15469e-5i
$773$	201.817	−	277.778i	0.261083	−	0.359350i	−0.658271	−	0.752781i	$-0.728712\pi$
$773$	201.817	−	277.778i	0.261083	−	0.359350i	0.919354	+	0.393431i	$0.128712\pi$
$774$	82.9698	−	787.608i	0.107196	−	1.01758i
$775$	−77.2592	+	237.779i	−0.0996893	+	0.306812i
$776$	−287.165	−	93.3054i	−0.370057	−	0.120239i
$777$	−637.218	+	170.661i	−0.820100	+	0.219641i
$778$	−826.276	−	600.325i	−1.06205	−	0.771625i
$779$	1003.05	−	325.910i	1.28761	−	0.418370i
$780$	0.963195	−	2.50832i	0.00123487	−	0.00321580i
$781$		0			0
$782$		−	442.887i		−	0.566351i
$783$	47.2799	+	47.3136i	0.0603831	+	0.0604261i
$784$	−230.625	−	167.559i	−0.294164	−	0.213723i
$785$	454.746	+	625.904i	0.579294	+	0.797330i
$786$	614.101	−	758.168i	0.781299	−	0.964590i
$787$	59.7777	−	183.977i	0.0759564	−	0.233770i	−0.905868	−	0.423559i	$-0.860781\pi$
$787$	59.7777	−	183.977i	0.0759564	−	0.233770i	0.981825	+	0.189789i	$0.0607805\pi$
$788$	2.12845	+	2.92956i	0.00270108	+	0.00371772i
$789$	214.933	−	139.543i	0.272412	−	0.176860i
$790$	−214.480	−	660.103i	−0.271494	−	0.835573i
$791$		−	258.969i		−	0.327394i
$792$		0			0
$793$	299.953			0.378251
$794$	−24.8711	+	8.08110i	−0.0313238	+	0.0101777i
$795$	−386.291	−	594.991i	−0.485901	−	0.748416i
$796$	−1.45027	+	1.05368i	−0.00182195	+	0.00132372i
$797$	−505.892	−	164.374i	−0.634745	−	0.206241i	−0.0260694	−	0.999660i	$-0.508299\pi$
$797$	−505.892	−	164.374i	−0.634745	−	0.206241i	−0.608676	+	0.793419i	$0.708299\pi$
$798$	487.400	+	394.785i	0.610777	+	0.494717i
$799$	−835.465	+	607.001i	−1.04564	+	0.759701i
$800$	0.802686	−	1.10480i	0.00100336	−	0.00138100i
$801$	280.575	+	125.000i	0.350281	+	0.156055i
$802$	1101.52			1.37346
$803$		0			0
$804$	−1.60399	−	0.615931i	−0.00199501	−	0.000766083i
$805$	−117.159	−	360.579i	−0.145539	−	0.447924i
$806$	563.533	−	775.637i	0.699173	−	0.962328i
$807$	125.563	+	468.829i	0.155592	+	0.580952i
$808$	−115.710	+	356.119i	−0.143205	+	0.440741i
$809$	−276.212	−	89.7467i	−0.341424	−	0.110935i	0.133286	−	0.991078i	$-0.457447\pi$
$809$	−276.212	−	89.7467i	−0.341424	−	0.110935i	−0.474710	+	0.880142i	$0.657447\pi$
$810$	595.436	+	661.930i	0.735106	+	0.817198i
$811$	311.109	+	226.034i	0.383611	+	0.278710i	0.762833	−	0.646596i	$-0.223808\pi$
$811$	311.109	+	226.034i	0.383611	+	0.278710i	−0.379221	+	0.925306i	$0.623808\pi$
$812$	0.221384	−	0.0719319i	0.000272640	−	8.85861e-5i
$813$	728.142	+	279.607i	0.895623	+	0.343919i
$814$		0			0
$815$			663.416i			0.814008i
$816$	−860.239	−	45.1856i	−1.05421	−	0.0553745i
$817$	662.776	+	481.535i	0.811232	+	0.589394i
$818$	728.223	+	1002.31i	0.890248	+	1.22532i
$819$	−423.480	+	244.362i	−0.517069	+	0.298367i
$820$	1.60997	−	4.95499i	0.00196338	−	0.00604267i
$821$	−365.440	−	502.985i	−0.445116	−	0.612650i	0.526223	−	0.850346i	$-0.323608\pi$
$821$	−365.440	−	502.985i	−0.445116	−	0.612650i	−0.971339	+	0.237697i	$0.923608\pi$
$822$	−173.092	−	266.607i	−0.210574	−	0.324340i
$823$	−88.4972	−	272.366i	−0.107530	−	0.330943i	0.882786	−	0.469776i	$-0.155665\pi$
$823$	−88.4972	−	272.366i	−0.107530	−	0.330943i	−0.990316	+	0.138832i	$0.955665\pi$
$824$			836.604i			1.01530i
$825$		0			0
$826$	−1008.81			−1.22132
$827$	397.074	−	129.017i	0.480138	−	0.156006i	−0.0589412	−	0.998261i	$-0.518772\pi$
$827$	397.074	−	129.017i	0.480138	−	0.156006i	0.539079	+	0.842255i	$0.318772\pi$
$828$	1.82952	−	0.388423i	0.00220957	−	0.000469110i
$829$	−300.030	+	217.984i	−0.361918	+	0.262949i	−0.753852	−	0.657045i	$-0.771806\pi$
$829$	−300.030	+	217.984i	−0.361918	+	0.262949i	0.391934	+	0.919993i	$0.371806\pi$
$830$	−101.417	−	32.9525i	−0.122189	−	0.0397018i
$831$	163.884	−	202.331i	0.197213	−	0.243479i
$832$	500.976	−	363.980i	0.602134	−	0.437476i
$833$	186.379	−	256.528i	0.223744	−	0.307957i
$834$	−519.588	−	27.2922i	−0.623007	−	0.0327245i
$835$	589.197			0.705625
$836$		0			0
$837$	603.038	+	1184.57i	0.720475	+	1.41526i
$838$	272.717	+	839.338i	0.325438	+	1.00160i
$839$	−508.937	+	700.492i	−0.606599	+	0.834912i	−0.996292	−	0.0860324i	$-0.972581\pi$
$839$	−508.937	+	700.492i	−0.606599	+	0.834912i	0.389693	+	0.920945i	$0.372581\pi$
$840$	−709.342	+	189.977i	−0.844454	+	0.226163i
$841$	257.987	−	794.002i	0.306762	−	0.944116i
$842$	1094.54	+	355.638i	1.29993	+	0.422373i
$843$	376.194	+	1404.64i	0.446256	+	1.66624i
$844$	−2.92094	−	2.12219i	−0.00346083	−	0.00251444i
$845$	389.027	−	126.402i	0.460386	−	0.149589i
$846$	−774.410	−	697.615i	−0.915379	−	0.824604i
$847$		0			0
$848$			692.739i			0.816910i
$849$	67.9923	−	1294.43i	0.0800852	−	1.52466i
$850$	147.161	+	106.918i	0.173130	+	0.125786i
$851$	−285.851	−	393.440i	−0.335900	−	0.462327i
$852$	1.47301	+	1.19311i	0.00172888	+	0.00140036i
$853$	416.202	−	1280.94i	0.487927	−	1.50169i	−0.339768	−	0.940509i	$-0.610349\pi$
$853$	416.202	−	1280.94i	0.487927	−	1.50169i	0.827696	−	0.561177i	$-0.189651\pi$
$854$	203.313	+	279.837i	0.238072	+	0.327678i
$855$	−900.912	+	191.271i	−1.05370	+	0.223709i
$856$	−115.033	−	354.034i	−0.134384	−	0.413591i
$857$		−	770.599i		−	0.899182i	−0.893235	−	0.449591i	$-0.851570\pi$
$857$		−	770.599i		−	0.899182i	0.893235	−	0.449591i	$-0.148430\pi$
$858$		0			0
$859$	−549.532			−0.639735			−0.319867	−	0.947462i	$-0.603638\pi$
$859$	−549.532			−0.639735			−0.319867	+	0.947462i	$0.603638\pi$
$860$	3.84890	−	1.25058i	0.00447546	−	0.00145417i
$861$	−795.157	+	516.247i	−0.923527	+	0.599590i
$862$	−1072.55	+	779.250i	−1.24425	+	0.904002i
$863$	−1042.29	−	338.660i	−1.20775	−	0.392422i	−0.365143	−	0.930951i	$-0.618980\pi$
$863$	−1042.29	−	338.660i	−1.20775	−	0.392422i	−0.842607	+	0.538530i	$0.818980\pi$
$864$	−1.13322	−	7.17141i	−0.00131160	−	0.00830024i
$865$	−1458.93	+	1059.98i	−1.68663	+	1.22541i
$866$	250.664	−	345.010i	0.289451	−	0.398395i
$867$	4.78282	−	91.0550i	0.00551652	−	0.105023i
$868$	4.62587			0.00532935
$869$		0			0
$870$	−29.2843	+	76.2613i	−0.0336602	+	0.0876567i
$871$	102.323	+	314.918i	0.117478	+	0.361559i
$872$	790.254	−	1087.69i	0.906254	−	1.24735i
$873$	338.531	+	35.6623i	0.387779	+	0.0408503i
$874$	−142.889	+	439.766i	−0.163488	+	0.503165i
$875$	−580.944	−	188.760i	−0.663936	−	0.215726i
$876$	0.590580	−	0.158170i	0.000674178	−	0.000180560i
$877$	−1167.54	−	848.264i	−1.33128	−	0.967234i	−0.999717	−	0.0238017i	$-0.992423\pi$
$877$	−1167.54	−	848.264i	−1.33128	−	0.967234i	−0.331566	−	0.943432i	$-0.607577\pi$
$878$	−197.883	+	64.2961i	−0.225379	+	0.0732302i
$879$	−5.94670	+	15.4862i	−0.00676531	+	0.0176180i
$880$		0			0
$881$		−	162.080i		−	0.183973i	−0.995760	−	0.0919866i	$-0.970678\pi$
$881$		−	162.080i		−	0.183973i	0.995760	−	0.0919866i	$-0.0293217\pi$
$882$	292.336	+	130.239i	0.331447	+	0.147664i
$883$	70.4786	+	51.2057i	0.0798172	+	0.0579906i	0.626978	−	0.779037i	$-0.284291\pi$
$883$	70.4786	+	51.2057i	0.0798172	+	0.0579906i	−0.547161	+	0.837027i	$0.684291\pi$
$884$	−1.71547	−	2.36115i	−0.00194058	−	0.00267098i
$885$	932.346	−	1151.07i	1.05350	−	1.30065i
$886$	−171.411	+	527.550i	−0.193467	+	0.595429i
$887$	479.767	+	660.342i	0.540887	+	0.744467i	0.988741	−	0.149640i	$-0.0478114\pi$
$887$	479.767	+	660.342i	0.540887	+	0.744467i	−0.447853	+	0.894107i	$0.647811\pi$
$888$	−790.041	+	512.926i	−0.889686	+	0.577619i
$889$	−117.980	−	363.106i	−0.132711	−	0.408443i
$890$			375.137i			0.421503i
$891$		0			0
$892$	−0.752410			−0.000843509
$893$	1025.42	−	333.178i	1.14828	−	0.373099i
$894$	211.015	+	325.019i	0.236035	+	0.363556i
$895$	−214.298	+	155.697i	−0.239440	+	0.173963i
$896$	684.860	+	222.525i	0.764353	+	0.248353i
$897$	−280.088	−	226.866i	−0.312250	−	0.252916i
$898$	807.272	−	586.517i	0.898967	−	0.653137i
$899$	−71.6867	+	98.6683i	−0.0797405	+	0.109753i
$900$	−0.312606	+	0.701676i	−0.000347340	+	0.000779640i
$901$	−770.548			−0.855214
$902$		0			0
$903$	−687.470	−	263.989i	−0.761318	−	0.292346i
$904$	−114.268	−	351.681i	−0.126403	−	0.389027i
$905$	0.214589	−	0.295357i	0.000237115	−	0.000326361i
$906$	69.4287	+	259.234i	0.0766321	+	0.286131i
$907$	172.604	−	531.221i	0.190302	−	0.585691i	−0.809697	−	0.586848i	$-0.800368\pi$
$907$	172.604	−	531.221i	0.190302	−	0.585691i	0.999999	+	0.00115761i	$0.000368480\pi$
$908$	−3.58847	−	1.16596i	−0.00395206	−	0.00128410i
$909$	44.2255	−	419.820i	0.0486530	−	0.461848i
$910$	−483.088	−	350.984i	−0.530865	−	0.385696i
$911$	−1547.41	+	502.785i	−1.69859	+	0.551904i	−0.988368	−	0.152078i	$-0.951403\pi$
$911$	−1547.41	+	502.785i	−1.69859	+	0.551904i	−0.710217	+	0.703982i	$0.751403\pi$
$912$	839.600	+	322.407i	0.920614	+	0.353516i
$913$		0			0
$914$		−	1625.64i		−	1.77860i
$915$	−507.201	−	26.6416i	−0.554318	−	0.0291165i
$916$	−1.41544	−	1.02838i	−0.00154524	−	0.00112268i
$917$	−533.259	−	733.969i	−0.581526	−	0.800402i
$918$	955.238	−	150.946i	1.04056	−	0.164430i
$919$	−17.7957	+	54.7694i	−0.0193642	+	0.0595967i	−0.960272	−	0.279067i	$-0.909975\pi$
$919$	−17.7957	+	54.7694i	−0.0193642	+	0.0595967i	0.940908	+	0.338664i	$0.109975\pi$
$920$	−318.205	−	437.972i	−0.345875	−	0.476057i
$921$	358.182	+	551.695i	0.388905	+	0.599017i
$922$	−489.307	−	1505.93i	−0.530701	−	1.63333i
$923$		−	365.315i		−	0.395791i
$924$		0			0
$925$	199.739			0.215934
$926$	−1030.02	+	334.675i	−1.11234	+	0.361420i
$927$	−195.877	−	922.607i	−0.211303	−	0.995261i
$928$	0.538935	−	0.391560i	0.000580749	−	0.000421939i
$929$	20.4483	+	6.64405i	0.0220111	+	0.00715183i	0.320002	−	0.947417i	$-0.396316\pi$
$929$	20.4483	+	6.64405i	0.0220111	+	0.00715183i	−0.297991	+	0.954569i	$0.596316\pi$
$930$	−1021.79	+	1261.50i	−1.09870	+	1.35645i
$931$	−267.830	+	194.590i	−0.287679	+	0.209011i
$932$	−0.607824	+	0.836598i	−0.000652172	+	0.000897637i
$933$	425.864	+	22.3692i	0.456445	+	0.0239756i
$934$	−556.899			−0.596251
$935$		0			0
$936$	−467.264	+	518.702i	−0.499214	+	0.554169i
$937$	70.7518	+	217.752i	0.0755089	+	0.232393i	0.981686	−	0.190506i	$-0.0610128\pi$
$937$	70.7518	+	217.752i	0.0755089	+	0.232393i	−0.906177	+	0.422898i	$0.861013\pi$
$938$	−224.442	+	308.918i	−0.239277	+	0.329337i
$939$	−273.228	+	73.1764i	−0.290977	+	0.0779301i
$940$	1.64587	−	5.06548i	0.00175093	−	0.00538881i
$941$	−820.918	−	266.732i	−0.872389	−	0.283456i	−0.161596	−	0.986857i	$-0.551664\pi$
$941$	−820.918	−	266.732i	−0.872389	−	0.283456i	−0.710794	+	0.703401i	$0.751664\pi$
$942$	219.426	+	819.298i	0.232936	+	0.869743i
$943$	−565.427	−	410.807i	−0.599604	−	0.435638i
$944$	−1375.73	+	447.001i	−1.45734	+	0.473518i
$945$	737.782	−	375.588i	0.780722	−	0.397448i
$946$		0			0
$947$		−	1155.70i		−	1.22038i	−0.792253	−	0.610192i	$-0.791092\pi$
$947$		−	1155.70i		−	1.22038i	0.792253	−	0.610192i	$-0.208908\pi$
$948$	0.167001	−	3.17936i	0.000176162	−	0.00335375i
$949$	−95.3238	−	69.2568i	−0.100447	−	0.0729787i
$950$	−111.629	−	153.644i	−0.117504	−	0.161730i
$951$	1168.44	+	946.413i	1.22864	+	0.995176i
$952$	−246.487	+	758.610i	−0.258915	+	0.796859i
$953$	−1056.31	−	1453.89i	−1.10841	−	1.52559i	−0.823739	−	0.566969i	$-0.808116\pi$
$953$	−1056.31	−	1453.89i	−1.10841	−	1.52559i	−0.284670	−	0.958626i	$-0.591884\pi$
$954$	−161.515	−	760.757i	−0.169303	−	0.797439i
$955$	334.570	+	1029.70i	0.350335	+	1.07822i
$956$			2.50855i			0.00262401i
$957$		0			0
$958$	942.426			0.983743
$959$	−281.105	+	91.3366i	−0.293123	+	0.0952415i
$960$	−879.447	+	570.971i	−0.916091	+	0.594762i
$961$	−1183.33	+	859.740i	−1.23135	+	0.894630i
$962$	−728.453	−	236.689i	−0.757228	−	0.246038i
$963$	209.750	+	363.496i	0.217808	+	0.377462i
$964$	−4.87964	+	3.54526i	−0.00506186	+	0.00367766i
$965$	−4.91173	+	6.76042i	−0.00508988	+	0.00700562i
$966$	21.8027	−	415.078i	0.0225701	−	0.429687i
$967$	1767.36			1.82767			0.913835	−	0.406085i	$-0.133106\pi$
$967$	1767.36			1.82767			0.913835	+	0.406085i	$0.133106\pi$
$968$		0			0
$969$	−358.619	+	933.904i	−0.370092	+	0.963781i
$970$	128.470	+	395.391i	0.132444	+	0.407620i
$971$	−299.023	+	411.570i	−0.307954	+	0.423862i	−0.934742	−	0.355328i	$-0.884369\pi$
$971$	−299.023	+	411.570i	−0.307954	+	0.423862i	0.626788	+	0.779190i	$0.284369\pi$
$972$	1.46131	+	3.81361i	0.00150341	+	0.00392346i
$973$	−149.505	+	460.128i	−0.153653	+	0.472896i
$974$	484.530	+	157.433i	0.497464	+	0.161636i
$975$	142.999	−	38.2982i	0.146665	−	0.0392802i
$976$	401.255	+	291.529i	0.411122	+	0.298698i
$977$	−1345.28	+	437.107i	−1.37695	+	0.447397i	−0.901664	−	0.432437i	$-0.857654\pi$
$977$	−1345.28	+	437.107i	−1.37695	+	0.447397i	−0.475281	+	0.879834i	$0.657654\pi$
$978$	−260.726	+	678.972i	−0.266590	+	0.694246i
$979$		0			0
$980$			1.63539i			0.00166877i
$981$	−616.827	+	1384.53i	−0.628773	+	1.41135i
$982$	−199.636	−	145.044i	−0.203295	−	0.147703i
$983$	0.659524	+	0.907756i	0.000670929	+	0.000923455i	0.809352	−	0.587323i	$-0.199818\pi$
$983$	0.659524	+	0.907756i	0.000670929	+	0.000923455i	−0.808681	+	0.588247i	$0.799818\pi$
$984$	−852.036	+	1051.92i	−0.865891	+	1.06903i
$985$	−365.154	+	1123.83i	−0.370715	+	1.14094i
$986$	52.1561	+	71.7867i	0.0528966	+	0.0728060i
$987$	−812.888	+	527.759i	−0.823595	+	0.534710i
$988$	0.941609	+	2.89797i	0.000953045	+	0.00293317i
$989$		−	542.891i		−	0.548929i
$990$		0			0
$991$	−1431.64			−1.44464			−0.722320	−	0.691559i	$-0.756924\pi$
$991$	−1431.64			−1.44464			−0.722320	+	0.691559i	$0.756924\pi$
$992$	12.5904	−	4.09087i	0.0126919	−	0.00412386i
$993$	1067.55	+	1644.31i	1.07508	+	1.65590i
$994$	340.816	−	247.617i	0.342873	−	0.249112i
$995$	−556.348	−	180.768i	−0.559144	−	0.181677i
$996$	−0.380101	−	0.307874i	−0.000381627	−	0.000309111i
$997$	−943.609	+	685.572i	−0.946448	+	0.687635i	−0.949964	−	0.312359i	$-0.898881\pi$
$997$	−943.609	+	685.572i	−0.946448	+	0.687635i	0.00351594	+	0.999994i	$0.498881\pi$
$998$	76.9591	−	105.925i	0.0771133	−	0.106137i
$999$	751.165	−	750.630i	0.751917	−	0.751382i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.3.h.j.269.2		16
3.2	odd	2	inner	363.3.h.j.269.3		16
11.2	odd	10		33.3.h.b.20.2	yes	16
11.3	even	5		363.3.b.l.122.6		8
11.4	even	5		363.3.h.n.245.2		16
11.5	even	5		363.3.h.n.323.3		16
11.6	odd	10		363.3.h.o.323.2		16
11.7	odd	10		363.3.h.o.245.3		16
11.8	odd	10		363.3.b.m.122.3		8
11.9	even	5	inner	363.3.h.j.251.3		16
11.10	odd	2		33.3.h.b.5.3	yes	16
33.2	even	10		33.3.h.b.20.3	yes	16
33.5	odd	10		363.3.h.n.323.2		16
33.8	even	10		363.3.b.m.122.6		8
33.14	odd	10		363.3.b.l.122.3		8
33.17	even	10		363.3.h.o.323.3		16
33.20	odd	10	inner	363.3.h.j.251.2		16
33.26	odd	10		363.3.h.n.245.3		16
33.29	even	10		363.3.h.o.245.2		16
33.32	even	2		33.3.h.b.5.2	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.3.h.b.5.2	✓	16	33.32	even	2
33.3.h.b.5.3	yes	16	11.10	odd	2
33.3.h.b.20.2	yes	16	11.2	odd	10
33.3.h.b.20.3	yes	16	33.2	even	10
363.3.b.l.122.3		8	33.14	odd	10
363.3.b.l.122.6		8	11.3	even	5
363.3.b.m.122.3		8	11.8	odd	10
363.3.b.m.122.6		8	33.8	even	10
363.3.h.j.251.2		16	33.20	odd	10	inner
363.3.h.j.251.3		16	11.9	even	5	inner
363.3.h.j.269.2		16	1.1	even	1	trivial
363.3.h.j.269.3		16	3.2	odd	2	inner
363.3.h.n.245.2		16	11.4	even	5
363.3.h.n.245.3		16	33.26	odd	10
363.3.h.n.323.2		16	33.5	odd	10
363.3.h.n.323.3		16	11.5	even	5
363.3.h.o.245.2		16	33.29	even	10
363.3.h.o.245.3		16	11.7	odd	10
363.3.h.o.323.2		16	11.6	odd	10
363.3.h.o.323.3		16	33.17	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.90610 + 0.619331i) q^{2} +(-1.63362 - 2.51621i) q^{3} +(0.0135968 - 0.00987866i) q^{4} +(5.21596 + 1.69477i) q^{5} +(4.67221 + 3.78440i) q^{6} +(4.52308 - 3.28621i) q^{7} +(4.69235 - 6.45847i) q^{8} +(-3.66258 + 8.22104i) q^{9} -10.9918 q^{10} +(-0.0470687 - 0.0180744i) q^{12} +(3.00265 + 9.24122i) q^{13} +(-6.58622 + 9.06515i) q^{14} +(-4.25650 - 15.8930i) q^{15} +(-4.96496 + 15.2806i) q^{16} +(-16.9969 - 5.52262i) q^{17} +(1.88972 - 17.9385i) q^{18} +(15.0954 + 10.9674i) q^{19} +(0.0876624 - 0.0284832i) q^{20} +(-15.6578 - 6.01259i) q^{21} -12.3649i q^{23} +(-23.9163 - 1.25625i) q^{24} +(4.10855 + 2.98503i) q^{25} +(-11.4467 - 15.7551i) q^{26} +(26.6691 - 4.21424i) q^{27} +(0.0290361 - 0.0893640i) q^{28} +(1.45613 + 2.00420i) q^{29} +(17.9564 + 27.6576i) q^{30} +(15.2132 + 46.8213i) q^{31} -0.268903i q^{32} +35.8182 q^{34} +(29.1616 - 9.47517i) q^{35} +(0.0314134 + 0.147961i) q^{36} +(31.8192 - 23.1180i) q^{37} +(-35.5658 - 11.5560i) q^{38} +(18.3476 - 22.6519i) q^{39} +(35.4207 - 25.7346i) q^{40} +(33.2237 - 45.7285i) q^{41} +(33.5692 + 1.76328i) q^{42} +43.9060 q^{43} +(-33.0366 + 36.6734i) q^{45} +(7.65794 + 23.5687i) q^{46} +(33.9646 - 46.7482i) q^{47} +(46.5599 - 12.4698i) q^{48} +(-5.48274 + 16.8741i) q^{49} +(-9.68004 - 3.14524i) q^{50} +(13.8704 + 51.7895i) q^{51} +(0.132117 + 0.0959889i) q^{52} +(41.0056 - 13.3235i) q^{53} +(-48.2241 + 24.5498i) q^{54} -44.6323i q^{56} +(2.93623 - 55.8996i) q^{57} +(-4.01681 - 2.91838i) q^{58} +(52.9190 + 72.8367i) q^{59} +(-0.214877 - 0.174046i) q^{60} +(9.53920 - 29.3587i) q^{61} +(-57.9958 - 79.8244i) q^{62} +(10.4499 + 49.2205i) q^{63} +(-19.6933 - 60.6097i) q^{64} +53.2906i q^{65} +34.0775 q^{67} +(-0.285659 + 0.0928164i) q^{68} +(-31.1125 + 20.1995i) q^{69} +(-49.7168 + 36.1213i) q^{70} +(-35.7561 - 11.6179i) q^{71} +(35.9092 + 62.2307i) q^{72} +(-9.81022 + 7.12754i) q^{73} +(-46.3331 + 63.7720i) q^{74} +(0.799160 - 15.2144i) q^{75} +0.313592 q^{76} +(-20.9434 + 54.5402i) q^{78} +(19.5128 + 60.0542i) q^{79} +(-51.7940 + 71.2884i) q^{80} +(-54.1710 - 60.2204i) q^{81} +(-35.0068 + 107.740i) q^{82} +(9.22665 + 2.99792i) q^{83} +(-0.272292 + 0.0729258i) q^{84} +(-79.2955 - 57.6115i) q^{85} +(-83.6893 + 27.1923i) q^{86} +(2.66420 - 6.93803i) q^{87} -34.1289i q^{89} +(40.2583 - 90.3639i) q^{90} +(43.9499 + 31.9315i) q^{91} +(-0.122148 - 0.168123i) q^{92} +(92.9595 - 114.768i) q^{93} +(-35.7874 + 110.142i) q^{94} +(60.1495 + 82.7887i) q^{95} +(-0.676616 + 0.439286i) q^{96} +(-11.6879 - 35.9715i) q^{97} -35.5595i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 10 q^{3} + 8 q^{4} + 33 q^{6} - 6 q^{7} - 28 q^{9} + 12 q^{10} + 106 q^{12} + 42 q^{13} + 82 q^{15} - 88 q^{16} + 43 q^{18} + 134 q^{19} + 12 q^{21} - 41 q^{24} + 134 q^{25} + 80 q^{27} - 264 q^{28}+ \cdots + 72 q^{97}+O(q^{100}) \) 16 * q - 10 * q^3 + 8 * q^4 + 33 * q^6 - 6 * q^7 - 28 * q^9 + 12 * q^10 + 106 * q^12 + 42 * q^13 + 82 * q^15 - 88 * q^16 + 43 * q^18 + 134 * q^19 + 12 * q^21 - 41 * q^24 + 134 * q^25 + 80 * q^27 - 264 * q^28 + 120 * q^30 + 124 * q^31 - 132 * q^34 - 219 * q^36 + 90 * q^37 + 174 * q^39 + 284 * q^40 - 102 * q^42 + 156 * q^43 - 72 * q^45 + 22 * q^46 + 30 * q^48 - 30 * q^49 - 111 * q^51 - 326 * q^52 - 1046 * q^54 - 281 * q^57 - 116 * q^58 + 54 * q^60 + 126 * q^61 + 138 * q^63 + 236 * q^64 + 368 * q^67 + 198 * q^69 - 322 * q^70 + 562 * q^72 - 24 * q^73 - 21 * q^75 + 900 * q^76 - 492 * q^78 + 314 * q^79 - 388 * q^81 - 270 * q^84 - 318 * q^85 - 132 * q^87 - 176 * q^90 + 374 * q^91 - 10 * q^93 - 990 * q^94 + 332 * q^96 + 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more