LMFDB - Embedded newform 363.3.h.n.323.3

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			323.3
Root			$1.90610 - 0.619331i$ of defining polynomial
Character	$\chi$	$=$	363.323
Dual form			363.3.h.n.245.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.17804 - 1.62143i) q^{2} +(1.88824 - 2.33121i) q^{3} +(-0.00519352 - 0.0159840i) q^{4} +(-3.22364 - 4.43696i) q^{5} +(-1.55548 - 5.80790i) q^{6} +(-1.72766 - 5.31721i) q^{7} +(7.59238 + 2.46692i) q^{8} +(-1.86912 - 8.80377i) q^{9} -10.9918 q^{10} +(-0.0470687 - 0.0180744i) q^{12} +(-7.86105 - 5.71139i) q^{13} +(-10.6567 - 3.46258i) q^{14} +(-16.4305 - 0.863040i) q^{15} +(12.9984 - 9.44391i) q^{16} +(10.5047 + 14.4584i) q^{17} +(-16.4766 - 7.34053i) q^{18} +(-5.76592 + 17.7457i) q^{19} +(-0.0541783 + 0.0745701i) q^{20} +(-15.6578 - 6.01259i) q^{21} -12.3649i q^{23} +(20.0871 - 13.0413i) q^{24} +(-1.56932 + 4.82989i) q^{25} +(-18.5212 + 6.01791i) q^{26} +(-24.0528 - 12.2663i) q^{27} +(-0.0760176 + 0.0552300i) q^{28} +(2.35608 - 0.765535i) q^{29} +(-20.7551 + 25.6242i) q^{30} +(-39.8286 - 28.9372i) q^{31} -0.268903i q^{32} +35.8182 q^{34} +(-18.0228 + 24.8063i) q^{35} +(-0.131012 + 0.0755985i) q^{36} +(-12.1539 - 37.4057i) q^{37} +(21.9809 + 30.2541i) q^{38} +(-28.1580 + 7.54133i) q^{39} +(-13.5295 - 41.6395i) q^{40} +(53.7571 + 17.4667i) q^{41} +(-28.1945 + 18.3049i) q^{42} +43.9060 q^{43} +(-33.0366 + 36.6734i) q^{45} +(-20.0488 - 14.5663i) q^{46} +(54.9558 + 17.8562i) q^{47} +(2.52835 - 48.1345i) q^{48} +(14.3540 - 10.4288i) q^{49} +(5.98260 + 8.23434i) q^{50} +(53.5409 + 2.81233i) q^{51} +(-0.0504643 + 0.155313i) q^{52} +(-25.3428 + 34.8814i) q^{53} +(-48.2241 + 24.5498i) q^{54} -44.6323i q^{56} +(30.4815 + 46.9496i) q^{57} +(1.53428 - 4.72204i) q^{58} +(85.6247 - 27.8212i) q^{59} +(0.0715372 + 0.267107i) q^{60} +(-24.9740 + 18.1446i) q^{61} +(-93.8392 + 30.4902i) q^{62} +(-43.5823 + 25.1484i) q^{63} +(51.5577 + 37.4589i) q^{64} +53.2906i q^{65} +34.0775 q^{67} +(0.176547 - 0.242996i) q^{68} +(-28.8251 - 23.3478i) q^{69} +(18.9901 + 58.4456i) q^{70} +(22.0985 + 30.4160i) q^{71} +(7.52711 - 71.4526i) q^{72} +(3.74717 + 11.5326i) q^{73} +(-74.9685 - 24.3587i) q^{74} +(8.29624 + 12.7784i) q^{75} +0.313592 q^{76} +(-20.9434 + 54.5402i) q^{78} +(-51.0852 - 37.1155i) q^{79} +(-83.8045 - 27.2297i) q^{80} +(-74.0128 + 32.9105i) q^{81} +(91.6490 - 66.5869i) q^{82} +(-5.70238 - 7.84865i) q^{83} +(-0.0147863 + 0.281501i) q^{84} +(30.2882 - 93.2174i) q^{85} +(51.7229 - 71.1904i) q^{86} +(2.66420 - 6.93803i) q^{87} -34.1289i q^{89} +(20.5449 + 96.7691i) q^{90} +(-16.7874 + 51.6662i) q^{91} +(-0.197640 + 0.0642171i) q^{92} +(-142.665 + 38.2087i) q^{93} +(93.6927 - 68.0717i) q^{94} +(97.3240 - 31.6225i) q^{95} +(-0.626871 - 0.507754i) q^{96} +(30.5992 + 22.2316i) q^{97} -35.5595i 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 $

$2$	1.17804	−	1.62143i	0.589019	−	0.810715i	−0.405629	−	0.914038i	$-0.632948\pi$
$2$	1.17804	−	1.62143i	0.589019	−	0.810715i	0.994648	+	0.103323i	$0.0329475\pi$
$3$	1.88824	−	2.33121i	0.629413	−	0.777071i
$3$	1.88824	−	2.33121i	0.629413	−	0.777071i
$4$	−0.00519352	−	0.0159840i	−0.00129838	−	0.00399600i
$5$	−3.22364	−	4.43696i	−0.644728	−	0.887392i	0.354129	−	0.935197i	$-0.384777\pi$
$5$	−3.22364	−	4.43696i	−0.644728	−	0.887392i	−0.998857	+	0.0478050i	$0.984777\pi$
$6$	−1.55548	−	5.80790i	−0.259247	−	0.967984i
$7$	−1.72766	−	5.31721i	−0.246809	−	0.759601i	−0.995334	−	0.0964935i	$-0.969237\pi$
$7$	−1.72766	−	5.31721i	−0.246809	−	0.759601i	0.748524	−	0.663107i	$-0.230763\pi$
$8$	7.59238	+	2.46692i	0.949048	+	0.308364i
$9$	−1.86912	−	8.80377i	−0.207680	−	0.978197i
$10$	−10.9918			−1.09918
$11$		0			0
$11$		0			0
$12$	−0.0470687	−	0.0180744i	−0.00392239	−	0.00150620i
$13$	−7.86105	−	5.71139i	−0.604696	−	0.439338i	0.242846	−	0.970065i	$-0.421919\pi$
$13$	−7.86105	−	5.71139i	−0.604696	−	0.439338i	−0.847543	+	0.530727i	$0.821919\pi$
$14$	−10.6567	−	3.46258i	−0.761195	−	0.247327i
$15$	−16.4305	−	0.863040i	−1.09537	−	0.0575360i
$16$	12.9984	−	9.44391i	0.812402	−	0.590245i
$17$	10.5047	+	14.4584i	0.617921	+	0.850495i	0.997199	−	0.0747875i	$-0.0238278\pi$
$17$	10.5047	+	14.4584i	0.617921	+	0.850495i	−0.379279	+	0.925282i	$0.623828\pi$
$18$	−16.4766	−	7.34053i	−0.915366	−	0.407807i
$19$	−5.76592	+	17.7457i	−0.303469	+	0.933982i	0.676775	+	0.736190i	$0.263377\pi$
$19$	−5.76592	+	17.7457i	−0.303469	+	0.933982i	−0.980244	+	0.197792i	$0.936623\pi$
$20$	−0.0541783	+	0.0745701i	−0.00270892	+	0.00372850i
$21$	−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	$-0.0866275\pi$
$24$	20.0871	−	13.0413i	0.836964	−	0.543390i
$25$	−1.56932	+	4.82989i	−0.0627730	+	0.193195i
$26$	−18.5212	+	6.01791i	−0.712355	+	0.231458i
$27$	−24.0528	−	12.2663i	−0.890845	−	0.454308i
$28$	−0.0760176	+	0.0552300i	−0.00271491	+	0.00197250i
$29$	2.35608	−	0.765535i	0.0812440	−	0.0263978i	−0.268113	−	0.963387i	$-0.586400\pi$
$29$	2.35608	−	0.765535i	0.0812440	−	0.0263978i	0.349357	+	0.936990i	$0.386400\pi$
$30$	−20.7551	+	25.6242i	−0.691837	+	0.854140i
$31$	−39.8286	−	28.9372i	−1.28479	−	0.933457i	−0.285107	−	0.958496i	$-0.592029\pi$
$31$	−39.8286	−	28.9372i	−1.28479	−	0.933457i	−0.999686	+	0.0250387i	$0.992029\pi$
$32$		−	0.268903i		−	0.00840323i
$33$		0			0
$34$	35.8182			1.05348
$35$	−18.0228	+	24.8063i	−0.514939	+	0.708752i
$36$	−0.131012	+	0.0755985i	−0.00363923	+	0.00209996i
$37$	−12.1539	−	37.4057i	−0.328483	−	1.01097i	−0.969844	−	0.243727i	$-0.921630\pi$
$37$	−12.1539	−	37.4057i	−0.328483	−	1.01097i	0.641361	−	0.767239i	$-0.278370\pi$
$38$	21.9809	+	30.2541i	0.578444	+	0.796160i
$39$	−28.1580	+	7.54133i	−0.722000	+	0.193368i
$40$	−13.5295	−	41.6395i	−0.338238	−	1.04099i
$41$	53.7571	+	17.4667i	1.31115	+	0.426018i	0.879446	−	0.475998i	$-0.157913\pi$
$41$	53.7571	+	17.4667i	1.31115	+	0.426018i	0.431703	+	0.902016i	$0.357913\pi$
$42$	−28.1945	+	18.3049i	−0.671296	+	0.435832i
$43$	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
$46$	−20.0488	−	14.5663i	−0.435842	−	0.316658i
$47$	54.9558	+	17.8562i	1.16927	+	0.379920i	0.828372	−	0.560179i	$-0.189268\pi$
$47$	54.9558	+	17.8562i	1.16927	+	0.379920i	0.340902	+	0.940099i	$0.389268\pi$
$48$	2.52835	−	48.1345i	0.0526739	−	1.00280i
$49$	14.3540	−	10.4288i	0.292939	−	0.212832i
$50$	5.98260	+	8.23434i	0.119652	+	0.164687i
$51$	53.5409	+	2.81233i	1.04982	+	0.0551438i
$52$	−0.0504643	+	0.155313i	−0.000970468	+	0.00298679i
$53$	−25.3428	+	34.8814i	−0.478167	+	0.658140i	−0.978151	−	0.207894i	$-0.933339\pi$
$53$	−25.3428	+	34.8814i	−0.478167	+	0.658140i	0.499985	+	0.866034i	$0.333339\pi$
$54$	−48.2241	+	24.5498i	−0.893038	+	0.454625i
$55$		0			0
$56$		−	44.6323i		−	0.797005i
$57$	30.4815	+	46.9496i	0.534763	+	0.823677i
$58$	1.53428	−	4.72204i	0.0264532	−	0.0814145i
$59$	85.6247	−	27.8212i	1.45127	−	0.471545i	0.525876	−	0.850561i	$-0.323738\pi$
$59$	85.6247	−	27.8212i	1.45127	−	0.471545i	0.925390	+	0.379016i	$0.123738\pi$
$60$	0.0715372	+	0.267107i	0.00119229	+	0.00445179i
$61$	−24.9740	+	18.1446i	−0.409409	+	0.297453i	−0.773363	−	0.633964i	$-0.781427\pi$
$61$	−24.9740	+	18.1446i	−0.409409	+	0.297453i	0.363953	+	0.931417i	$0.381427\pi$
$62$	−93.8392	+	30.4902i	−1.51353	+	0.491777i
$63$	−43.5823	+	25.1484i	−0.691782	+	0.399182i
$64$	51.5577	+	37.4589i	0.805589	+	0.585295i
$65$			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	$0.418152\pi$
$68$	0.176547	−	0.242996i	0.00259628	−	0.00357348i
$69$	−28.8251	−	23.3478i	−0.417756	−	0.338374i
$70$	18.9901	+	58.4456i	0.271287	+	0.834937i
$71$	22.0985	+	30.4160i	0.311247	+	0.428394i	0.935769	−	0.352612i	$-0.114707\pi$
$71$	22.0985	+	30.4160i	0.311247	+	0.428394i	−0.624523	+	0.781006i	$0.714707\pi$
$72$	7.52711	−	71.4526i	0.104543	−	0.992397i
$73$	3.74717	+	11.5326i	0.0513311	+	0.157981i	0.973436	−	0.228959i	$-0.0735321\pi$
$73$	3.74717	+	11.5326i	0.0513311	+	0.157981i	−0.922105	+	0.386940i	$0.873532\pi$
$74$	−74.9685	−	24.3587i	−1.01309	−	0.329172i
$75$	8.29624	+	12.7784i	0.110616	+	0.170379i
$76$	0.313592			0.00412621
$77$		0			0
$78$	−20.9434	+	54.5402i	−0.268506	+	0.699233i
$79$	−51.0852	−	37.1155i	−0.646648	−	0.469817i	0.215480	−	0.976508i	$-0.430868\pi$
$79$	−51.0852	−	37.1155i	−0.646648	−	0.469817i	−0.862128	+	0.506691i	$0.830868\pi$
$80$	−83.8045	−	27.2297i	−1.04756	−	0.340372i
$81$	−74.0128	+	32.9105i	−0.913738	+	0.406303i
$82$	91.6490	−	66.5869i	1.11767	−	0.812035i
$83$	−5.70238	−	7.84865i	−0.0687034	−	0.0945621i	0.773283	−	0.634062i	$-0.218613\pi$
$83$	−5.70238	−	7.84865i	−0.0687034	−	0.0945621i	−0.841986	+	0.539500i	$0.818613\pi$
$84$	−0.0147863	+	0.281501i	−0.000176027	+	0.00335120i
$85$	30.2882	−	93.2174i	0.356331	−	1.09668i
$86$	51.7229	−	71.1904i	0.601429	−	0.827795i
$87$	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	$-0.0614115\pi$
$90$	20.5449	+	96.7691i	0.228277	+	1.07521i
$91$	−16.7874	+	51.6662i	−0.184476	+	0.567760i
$92$	−0.197640	+	0.0642171i	−0.00214826	+	0.000698012i
$93$	−142.665	+	38.2087i	−1.53403	+	0.410846i
$94$	93.6927	−	68.0717i	0.996731	−	0.724167i
$95$	97.3240	−	31.6225i	1.02446	−	0.332868i
$96$	−0.626871	−	0.507754i	−0.00652991	−	0.00528910i
$97$	30.5992	+	22.2316i	0.315456	+	0.229192i	0.734234	−	0.678896i	$-0.237542\pi$
$97$	30.5992	+	22.2316i	0.315456	+	0.229192i	−0.418778	+	0.908089i	$0.637542\pi$
$98$		−	35.5595i		−	0.362852i
$99$		0			0
$100$	0.0853512			0.000853512
$101$	27.5699	−	37.9467i	0.272969	−	0.375710i	−0.650420	−	0.759575i	$-0.725407\pi$
$101$	27.5699	−	37.9467i	0.272969	−	0.375710i	0.923389	+	0.383865i	$0.125407\pi$
$102$	67.6332	−	83.4998i	0.663071	−	0.818626i
$103$	32.3840	+	99.6677i	0.314408	+	0.967647i	0.975998	+	0.217782i	$0.0698820\pi$
$103$	32.3840	+	99.6677i	0.314408	+	0.967647i	−0.661590	+	0.749866i	$0.730118\pi$
$104$	−45.5946	−	62.7556i	−0.438410	−	0.603419i
$105$	23.7974	+	88.8554i	0.226642	+	0.846241i
$106$	26.7030	+	82.1833i	0.251915	+	0.775314i
$107$	44.3479	+	14.4095i	0.414467	+	0.134668i	0.508825	−	0.860870i	$-0.330080\pi$
$107$	44.3479	+	14.4095i	0.414467	+	0.134668i	−0.0943585	+	0.995538i	$0.530080\pi$
$108$	−0.0711460	+	0.448165i	−0.000658759	+	0.00414968i
$109$	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
$112$	−72.6722	−	52.7994i	−0.648858	−	0.471423i
$113$	44.0531	+	14.3137i	0.389850	+	0.126670i	0.497382	−	0.867532i	$-0.334295\pi$
$113$	44.0531	+	14.3137i	0.389850	+	0.126670i	−0.107532	+	0.994202i	$0.534295\pi$
$114$	112.034	+	5.88477i	0.982753	+	0.0516208i
$115$	−54.8624	+	39.8598i	−0.477064	+	0.346607i
$116$	−0.0244726	−	0.0336837i	−0.000210971	−	0.000290377i
$117$	−35.5885	+	79.8821i	−0.304176	+	0.682753i
$118$	55.7591	−	171.609i	0.472535	−	1.45431i
$119$	58.7298	−	80.8347i	0.493528	−	0.679283i
$120$	−122.618	−	47.0852i	−1.02181	−	0.392376i
$121$		0			0
$122$			61.8686i			0.507120i
$123$	142.225	−	92.3379i	1.15630	−	0.750715i
$124$	−0.255681	+	0.786906i	−0.00206195	+	0.00634602i
$125$	−103.910	+	33.7624i	−0.831280	+	0.270099i
$126$	−10.5651	+	100.291i	−0.0838501	+	0.795963i
$127$	−55.2468	+	40.1392i	−0.435014	+	0.316056i	−0.783651	−	0.621202i	$-0.786645\pi$
$127$	−55.2468	+	40.1392i	−0.435014	+	0.316056i	0.348636	+	0.937258i	$0.386645\pi$
$128$	122.497	−	39.8016i	0.957006	−	0.310950i
$129$	82.9049	−	102.354i	0.642673	−	0.793443i
$130$	86.4070	+	62.7783i	0.664669	+	0.482910i
$131$		−	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
$134$	40.1446	−	55.2543i	0.299587	−	0.412346i
$135$	23.1125	+	146.263i	0.171204	+	1.08343i
$136$	44.0877	+	135.688i	0.324174	+	0.997705i
$137$	31.0745	+	42.7704i	0.226821	+	0.312192i	0.907226	−	0.420644i	$-0.138196\pi$
$137$	31.0745	+	42.7704i	0.226821	+	0.312192i	−0.680405	+	0.732837i	$0.738196\pi$
$138$	−71.8139	+	19.2333i	−0.520391	+	0.139372i
$139$	26.7410	+	82.3003i	0.192381	+	0.592089i	0.999997	+	0.00237984i	$0.000757526\pi$
$139$	26.7410	+	82.3003i	0.192381	+	0.592089i	−0.807616	+	0.589709i	$0.799242\pi$
$140$	0.490106	+	0.159245i	0.00350076	+	0.00113747i
$141$	145.396	−	94.3970i	1.03118	−	0.669482i
$142$	75.3502			0.530635
$143$		0			0
$144$	−107.438	−	96.7835i	−0.746095	−	0.672107i
$145$	−10.9918	−	7.98600i	−0.0758054	−	0.0550758i
$146$	23.1136	+	7.51007i	0.158312	+	0.0514388i
$147$	2.79202	−	53.1542i	0.0189933	−	0.361593i
$148$	−0.534772	+	0.388535i	−0.00361332	+	0.00262523i
$149$	−37.8827	−	52.1411i	−0.254246	−	0.349940i	0.662746	−	0.748844i	$-0.269391\pi$
$149$	−37.8827	−	52.1411i	−0.254246	−	0.349940i	−0.916993	+	0.398904i	$0.869391\pi$
$150$	30.4926	+	1.60168i	0.203284	+	0.0106778i
$151$	−13.7929	+	42.4502i	−0.0913437	+	0.281127i	−0.986284	−	0.165060i	$-0.947218\pi$
$151$	−13.7929	+	42.4502i	−0.0913437	+	0.281127i	0.894940	+	0.446187i	$0.147218\pi$
$152$	−87.5541	+	120.508i	−0.576014	+	0.792815i
$153$	107.654	−	119.505i	0.703622	−	0.781079i
$154$		0			0
$155$			270.001i			1.74194i
$156$	0.266780	+	0.410911i	0.00171013	+	0.00263405i
$157$	−43.5918	+	134.162i	−0.277655	+	0.854534i	0.710850	+	0.703344i	$0.248311\pi$
$157$	−43.5918	+	134.162i	−0.277655	+	0.854534i	−0.988505	+	0.151190i	$0.951689\pi$
$158$	−120.360	+	39.1075i	−0.761775	+	0.247516i
$159$	33.4628	+	124.944i	0.210458	+	0.785811i
$160$	−1.19311	+	0.866847i	−0.00745696	+	0.00541780i
$161$	−65.7465	+	21.3623i	−0.408363	+	0.132685i
$162$	−33.8277	+	158.776i	−0.208813	+	0.980101i
$163$	−97.8624	−	71.1012i	−0.600383	−	0.436204i	0.245632	−	0.969363i	$-0.421005\pi$
$163$	−97.8624	−	71.1012i	−0.600383	−	0.436204i	−0.846015	+	0.533159i	$0.821005\pi$
$164$		−	0.949967i		−	0.00579248i
$165$		0			0
$166$	−19.4437			−0.117130
$167$	−63.1468	+	86.9141i	−0.378125	+	0.520444i	−0.955086	−	0.296327i	$-0.904238\pi$
$167$	−63.1468	+	86.9141i	−0.378125	+	0.520444i	0.576962	+	0.816771i	$0.304238\pi$
$168$	−104.047	−	84.2763i	−0.619330	−	0.501645i
$169$	−23.0477	−	70.9335i	−0.136377	−	0.419725i
$170$	−115.465	−	158.924i	−0.679205	−	0.934846i
$171$	167.006	+	17.5931i	0.976643	+	0.102884i
$172$	−0.228026	−	0.701793i	−0.00132573	−	0.00408019i
$173$	−312.721	−	101.609i	−1.80763	−	0.587336i	−0.807637	−	0.589680i	$-0.799254\pi$
$173$	−312.721	−	101.609i	−1.80763	−	0.587336i	−0.999997	+	0.00234427i	$0.999254\pi$
$174$	−8.11099	−	12.4931i	−0.0466149	−	0.0717993i
$175$	28.3928			0.162244
$176$		0			0
$177$	96.8227	−	252.142i	0.547021	−	1.42453i
$178$	−55.3376	−	40.2051i	−0.310885	−	0.225872i
$179$	−45.9346	−	14.9251i	−0.256618	−	0.0833802i	0.177883	−	0.984052i	$-0.443075\pi$
$179$	−45.9346	−	14.9251i	−0.256618	−	0.0833802i	−0.434501	+	0.900671i	$0.643075\pi$
$180$	0.757763	+	0.337593i	0.00420980	+	0.00187552i
$181$	−0.0538541	+	0.0391273i	−0.000297537	+	0.000216173i	−0.587934	−	0.808909i	$-0.700059\pi$
$181$	−0.0538541	+	0.0391273i	−0.000297537	+	0.000216173i	0.587636	+	0.809125i	$0.300059\pi$
$182$	63.9969	+	88.0842i	0.351632	+	0.483979i
$183$	−4.85773	+	92.4811i	−0.0265450	+	0.505361i
$184$	30.5031	−	93.8788i	0.165778	−	0.510211i
$185$	−126.788	+	174.509i	−0.685341	+	0.943291i
$186$	−106.111	+	276.332i	−0.570492	+	1.48566i
$187$		0			0
$188$		−	0.971151i		−	0.00516570i
$189$	−23.6673	+	149.086i	−0.125224	+	0.788814i
$190$	63.3777	−	195.056i	0.333567	−	1.02661i
$191$	187.751	−	61.0042i	0.982992	−	0.319393i	0.226943	−	0.973908i	$-0.427127\pi$
$191$	187.751	−	61.0042i	0.982992	−	0.319393i	0.756049	+	0.654515i	$0.227127\pi$
$192$	184.678	−	49.4608i	0.961864	−	0.257608i
$193$	1.23267	−	0.895586i	0.00638688	−	0.00464034i	−0.584587	−	0.811331i	$-0.698744\pi$
$193$	1.23267	−	0.895586i	0.00638688	−	0.00464034i	0.590974	+	0.806691i	$0.298744\pi$
$194$	72.0941	−	23.4248i	0.371619	−	0.120746i
$195$	124.232	+	100.625i	0.637086	+	0.516027i
$196$	−0.241241	−	0.175272i	−0.00123082	−	0.000894245i
$197$			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	$0.586362\pi$
$200$	−23.8298	+	32.7990i	−0.119149	+	0.163995i
$201$	64.3465	−	79.4420i	0.320132	−	0.395234i
$202$	−29.0496	−	89.4053i	−0.143810	−	0.442601i
$203$	−8.14102	−	11.2051i	−0.0401035	−	0.0551978i
$204$	−0.233113	−	0.870404i	−0.00114271	−	0.00426669i
$205$	−95.7943	−	294.824i	−0.467289	−	1.43817i
$206$	199.754	+	64.9039i	0.969678	+	0.315068i
$207$	−108.857	+	23.1114i	−0.525881	+	0.111649i
$208$	−156.119			−0.750573
$209$		0			0
$210$	172.107	+	66.0891i	0.819557	+	0.314710i
$211$	173.797	+	126.271i	0.823684	+	0.598442i	0.917765	−	0.397123i	$-0.129991\pi$
$211$	173.797	+	126.271i	0.823684	+	0.598442i	−0.0940813	+	0.995565i	$0.529991\pi$
$212$	0.689163	+	0.223923i	0.00325077	+	0.00105624i
$213$	112.633	+	5.91627i	0.528795	+	0.0277759i
$214$	75.6075	−	54.9321i	0.353306	−	0.256692i
$215$	−141.537	−	194.809i	−0.658311	−	0.906088i
$216$	−152.358	−	152.467i	−0.705362	−	0.705865i
$217$	−85.0544	+	261.771i	−0.391956	+	1.20632i
$218$	198.397	−	273.070i	0.910078	−	1.25261i
$219$	33.9605	+	13.0408i	0.155071	+	0.0595472i
$220$		0			0
$221$		−	173.654i		−	0.785767i
$222$	−198.344	+	128.772i	−0.893440	+	0.580056i
$223$	13.8343	−	42.5777i	0.0620373	−	0.190931i	−0.915234	−	0.402922i	$-0.867995\pi$
$223$	13.8343	−	42.5777i	0.0620373	−	0.190931i	0.977272	+	0.211991i	$0.0679946\pi$
$224$	−1.42981	+	0.464575i	−0.00638310	+	0.00207400i
$225$	45.4545	+	4.78836i	0.202020	+	0.0212816i
$226$	75.1049	−	54.5669i	0.332323	−	0.241446i
$227$	−213.516	+	69.3755i	−0.940598	+	0.305619i	−0.738890	−	0.673827i	$-0.764649\pi$
$227$	−213.516	+	69.3755i	−0.940598	+	0.305619i	−0.201709	+	0.979446i	$0.564649\pi$
$228$	0.592136	−	0.731050i	0.00259709	−	0.00320636i
$229$	84.2193	+	61.1889i	0.367770	+	0.267200i	0.756286	−	0.654242i	$-0.227012\pi$
$229$	84.2193	+	61.1889i	0.367770	+	0.267200i	−0.388516	+	0.921442i	$0.627012\pi$
$230$			135.912i			0.590921i
$231$		0			0
$232$	19.7767			0.0852446
$233$	36.1658	−	49.7780i	0.155218	−	0.213640i	−0.724325	−	0.689459i	$-0.757848\pi$
$233$	36.1658	−	49.7780i	0.155218	−	0.213640i	0.879543	+	0.475819i	$0.157848\pi$
$234$	87.5986	+	151.808i	0.374353	+	0.648754i
$235$	−97.9304	−	301.399i	−0.416725	−	1.28255i
$236$	−0.889387	−	1.22414i	−0.00376859	−	0.00518702i
$237$	−182.985	+	49.0075i	−0.772089	+	0.206783i
$238$	−61.8818	−	190.453i	−0.260008	−	0.800221i
$239$	−141.955	−	46.1240i	−0.593954	−	0.192987i	−0.00341179	−	0.999994i	$-0.501086\pi$
$239$	−141.955	−	46.1240i	−0.593954	−	0.192987i	−0.590542	+	0.807007i	$0.701086\pi$
$240$	−221.721	+	143.950i	−0.923838	+	0.599792i
$241$	−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
$244$	0.419727	+	0.304949i	0.00172019	+	0.00124979i
$245$	−92.5441	−	30.0694i	−0.377731	−	0.122732i
$246$	17.8268	−	339.385i	0.0724667	−	1.37961i
$247$	146.679	−	106.568i	0.593840	−	0.431450i
$248$	−231.008	−	317.956i	−0.931486	−	1.28208i
$249$	−29.0643	−	1.52666i	−0.116724	−	0.00613115i
$250$	−67.6665	+	208.256i	−0.270666	+	0.833024i
$251$	−209.852	+	288.837i	−0.836065	+	1.15074i	0.150699	+	0.988580i	$0.451848\pi$
$251$	−209.852	+	288.837i	−0.836065	+	1.15074i	−0.986764	+	0.162165i	$0.948152\pi$
$252$	0.628318	+	0.566010i	0.00249332	+	0.00224607i
$253$		0			0
$254$			136.864i			0.538836i
$255$	−160.118	−	246.625i	−0.627915	−	0.967156i
$256$	0.997138	−	3.06887i	0.00389507	−	0.0119878i
$257$	−62.8586	+	20.4240i	−0.244586	+	0.0794708i	−0.428745	−	0.903426i	$-0.641044\pi$
$257$	−62.8586	+	20.4240i	−0.244586	+	0.0794708i	0.184159	+	0.982897i	$0.441044\pi$
$258$	−68.2950	−	255.001i	−0.264709	−	0.988378i
$259$	−177.896	+	129.249i	−0.686858	+	0.499031i
$260$	0.851797	−	0.276766i	0.00327614	−	0.00106448i
$261$	−11.1434	−	19.3115i	−0.0426949	−	0.0739903i
$262$	−263.112	−	191.162i	−1.00424	−	0.729627i
$263$			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
$266$	122.892	−	169.146i	0.461998	−	0.635886i
$267$	−79.5618	−	64.4435i	−0.297984	−	0.241361i
$268$	−0.176982	−	0.544695i	−0.000660381	−	0.00203244i
$269$	95.0942	+	130.886i	0.353510	+	0.486565i	0.948326	−	0.317297i	$-0.102775\pi$
$269$	95.0942	+	130.886i	0.353510	+	0.486565i	−0.594816	+	0.803862i	$0.702775\pi$
$270$	264.383	+	134.829i	0.979197	+	0.499365i
$271$	80.3424	+	247.269i	0.296467	+	0.912430i	0.982725	+	0.185072i	$0.0592520\pi$
$271$	80.3424	+	247.269i	0.296467	+	0.912430i	−0.686258	+	0.727358i	$0.740748\pi$
$272$	273.088	+	88.7317i	1.00400	+	0.326219i
$273$	88.7464	+	136.693i	0.325078	+	0.500707i
$274$	105.956			0.386701
$275$		0			0
$276$	−0.223487	+	0.581998i	−0.000809737	+	0.00210869i
$277$	−70.2162	−	51.0151i	−0.253488	−	0.184170i	0.453783	−	0.891112i	$-0.350074\pi$
$277$	−70.2162	−	51.0151i	−0.253488	−	0.184170i	−0.707271	+	0.706942i	$0.750074\pi$
$278$	164.946	+	53.5942i	0.593331	+	0.192785i
$279$	−180.312	+	404.729i	−0.646279	+	1.45064i
$280$	−198.031	+	143.878i	−0.707255	+	0.513851i
$281$	284.908	+	392.143i	1.01391	+	1.39553i	0.916387	+	0.400292i	$0.131091\pi$
$281$	284.908	+	392.143i	1.01391	+	1.39553i	0.0975213	+	0.995233i	$0.468909\pi$
$282$	18.2243	−	346.953i	0.0646253	−	1.23033i
$283$	−133.518	+	410.925i	−0.471794	+	1.45203i	0.378439	+	0.925626i	$0.376461\pi$
$283$	−133.518	+	410.925i	−0.471794	+	1.45203i	−0.850233	+	0.526406i	$0.823539\pi$
$284$	0.371400	−	0.511188i	0.00130775	−	0.00179996i
$285$	110.052	−	286.594i	0.386148	−	1.00559i
$286$		0			0
$287$		−	316.014i		−	1.10109i
$288$	−2.36736	+	0.502612i	−0.00822001	+	0.00174518i
$289$	−9.39211	+	28.9059i	−0.0324986	+	0.100021i
$290$	−25.8975	+	8.41460i	−0.0893016	+	0.0290159i
$291$	109.605	−	29.3547i	0.376650	−	0.100875i
$292$	0.164876	−	0.119790i	0.000564644	−	0.000410238i
$293$	−5.25894	+	1.70873i	−0.0179486	+	0.00583185i	−0.317978	−	0.948098i	$-0.603004\pi$
$293$	−5.25894	+	1.70873i	−0.0179486	+	0.00583185i	0.300029	+	0.953930i	$0.403004\pi$
$294$	−82.8967	−	67.1447i	−0.281962	−	0.228383i
$295$	−399.464	−	290.228i	−1.35412	−	0.983823i
$296$		−	313.981i		−	1.06075i
$297$		0			0
$298$	−129.170			−0.433458
$299$	−70.6205	+	97.2008i	−0.236189	+	0.325086i
$300$	0.161163	−	0.198972i	0.000537211	−	0.000663240i
$301$	−75.8548	−	233.457i	−0.252009	−	0.775604i
$302$	52.5814	+	72.3721i	0.174111	+	0.239643i
$303$	−36.4034	−	135.924i	−0.120143	−	0.448593i
$304$	92.6406	+	285.119i	0.304739	+	0.937890i
$305$	161.014	+	52.3166i	0.527915	+	0.171530i
$306$	−66.9483	−	315.335i	−0.218785	−	1.03051i
$307$	−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
$310$	437.787	+	318.071i	1.41222	+	1.02604i
$311$	−135.193	−	43.9268i	−0.434704	−	0.141244i	0.0834870	−	0.996509i	$-0.473394\pi$
$311$	−135.193	−	43.9268i	−0.434704	−	0.141244i	−0.518191	+	0.855265i	$0.673394\pi$
$312$	−232.390	−	12.2067i	−0.744840	−	0.0391240i
$313$	−76.2787	+	55.4197i	−0.243702	+	0.177060i	−0.702931	−	0.711258i	$-0.748126\pi$
$313$	−76.2787	+	55.4197i	−0.243702	+	0.177060i	0.459229	+	0.888318i	$0.348126\pi$
$314$	166.181	+	228.729i	0.529239	+	0.728435i
$315$	252.076	+	112.303i	0.800241	+	0.356518i
$316$	−0.327943	+	1.00931i	−0.00103779	+	0.00319400i
$317$	294.607	−	405.491i	0.929359	−	1.27915i	−0.0307506	−	0.999527i	$-0.509790\pi$
$317$	294.607	−	405.491i	0.929359	−	1.27915i	0.960109	−	0.279625i	$-0.0902102\pi$
$318$	242.008	+	92.9312i	0.761032	+	0.292237i
$319$		0			0
$320$		−	349.513i		−	1.09223i
$321$	117.331	−	76.1759i	0.365517	−	0.237308i
$322$	−42.8143	+	131.769i	−0.132964	+	0.409220i
$323$	−317.143	+	103.046i	−0.981867	+	0.319028i
$324$	0.910429	+	1.01210i	0.00280997	+	0.00312376i
$325$	39.9219	−	29.0050i	0.122837	−	0.0892460i
$326$	−230.571	+	74.9172i	−0.707274	+	0.229807i
$327$	318.004	−	392.607i	0.972489	−	1.20063i
$328$	365.056	+	265.228i	1.11297	+	0.808623i
$329$		−	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	$0.948903\pi$
$332$	−0.0958375	+	0.131909i	−0.000288667	+	0.000397316i
$333$	−306.595	+	176.915i	−0.920705	+	0.531278i
$334$	66.5358	+	204.776i	0.199209	+	0.613103i
$335$	−109.854	−	151.201i	−0.327921	−	0.451345i
$336$	−260.309	+	69.7165i	−0.774729	+	0.207490i
$337$	−203.755	−	627.094i	−0.604615	−	1.86081i	−0.499419	−	0.866361i	$-0.666453\pi$
$337$	−203.755	−	627.094i	−0.604615	−	1.86081i	−0.105195	−	0.994452i	$-0.533547\pi$
$338$	−142.165	−	46.1921i	−0.420606	−	0.136663i
$339$	116.551	−	75.6695i	0.343808	−	0.223214i
$340$	−1.64729			−0.00484497
$341$		0			0
$342$	225.265	−	250.063i	0.658670	−	0.731179i
$343$	−301.882	−	219.330i	−0.880122	−	0.639446i
$344$	333.351	+	108.312i	0.969043	+	0.314861i
$345$	−10.6714	+	203.161i	−0.0309315	+	0.588872i
$346$	−533.149	+	387.355i	−1.54089	+	1.11952i
$347$	163.333	+	224.809i	0.470702	+	0.647865i	0.976685	−	0.214678i	$-0.0688702\pi$
$347$	163.333	+	224.809i	0.470702	+	0.647865i	−0.505983	+	0.862543i	$0.668870\pi$
$348$	−0.124734	−	0.00655187i	−0.000358431	−	1.88272e-5i
$349$	78.1118	−	240.403i	0.223816	−	0.688835i	−0.774594	−	0.632459i	$-0.782046\pi$
$349$	78.1118	−	240.403i	0.223816	−	0.688835i	0.998410	−	0.0563757i	$-0.0179545\pi$
$350$	33.4477	−	46.0369i	0.0955650	−	0.131534i
$351$	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	$0.707818\pi$
$354$	−294.770	−	454.025i	−0.832685	−	1.28256i
$355$	63.7168	−	196.100i	0.179484	−	0.552395i
$356$	−0.545516	+	0.177249i	−0.00153235	+	0.000497891i
$357$	−77.5470	−	289.547i	−0.217219	−	0.811056i
$358$	−78.3126	+	56.8975i	−0.218750	+	0.158931i
$359$	281.573	−	91.4886i	0.784326	−	0.254843i	0.110640	−	0.993861i	$-0.464710\pi$
$359$	281.573	−	91.4886i	0.784326	−	0.254843i	0.673686	+	0.739018i	$0.264710\pi$
$360$	−341.297	+	196.940i	−0.948047	+	0.547055i
$361$	10.3923	+	7.55047i	0.0287876	+	0.0209154i
$362$			0.133414i			0.000368547i
$363$		0			0
$364$	0.913018			0.00250829
$365$	39.0901	−	53.8030i	0.107096	−	0.147405i
$366$	144.229	+	116.823i	0.394068	+	0.319187i
$367$	26.2225	+	80.7046i	0.0714510	+	0.219904i	0.980405	−	0.196993i	$-0.0631177\pi$
$367$	26.2225	+	80.7046i	0.0714510	+	0.219904i	−0.908954	+	0.416897i	$0.863118\pi$
$368$	−116.773	−	160.724i	−0.317317	−	0.436749i
$369$	53.2949	−	505.913i	0.144431	−	1.37104i
$370$	133.593	+	411.156i	0.361061	+	1.11123i
$371$	229.256	+	74.4897i	0.617940	+	0.200781i
$372$	1.35166	+	2.08191i	0.00363349	+	0.00559654i
$373$	−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
$376$	373.196	+	271.143i	0.992543	+	0.721124i
$377$	−22.8935	−	7.43855i	−0.0607255	−	0.0197309i
$378$	213.851	+	214.003i	0.565744	+	0.566147i
$379$	87.9702	−	63.9141i	0.232111	−	0.168639i	−0.465650	−	0.884969i	$-0.654180\pi$
$379$	87.9702	−	63.9141i	0.232111	−	0.168639i	0.697762	+	0.716330i	$0.254180\pi$
$380$	−1.01091	−	1.39139i	−0.00266028	−	0.00366157i
$381$	−10.7462	+	204.584i	−0.0282051	+	0.536967i
$382$	122.264	−	376.291i	0.320064	−	0.985055i
$383$	−259.809	+	357.597i	−0.678353	+	0.933673i	−0.999913	−	0.0132167i	$-0.995793\pi$
$383$	−259.809	+	357.597i	−0.678353	+	0.933673i	0.321560	+	0.946889i	$0.395793\pi$
$384$	138.517	−	360.721i	0.360721	−	0.939378i
$385$		0			0
$386$		−	3.05372i		−	0.00791119i
$387$	−82.0653	−	386.538i	−0.212055	−	0.998806i
$388$	0.196433	−	0.604558i	0.000506270	−	0.00155814i
$389$	484.656	−	157.474i	1.24590	−	0.404818i	0.389451	−	0.921047i	$-0.372665\pi$
$389$	484.656	−	157.474i	1.24590	−	0.404818i	0.856450	+	0.516229i	$0.172665\pi$
$390$	309.507	−	82.8927i	0.793607	−	0.212545i
$391$	178.776	−	129.889i	0.457228	−	0.332196i
$392$	134.708	−	43.7693i	0.343643	−	0.111656i
$393$	−378.290	−	306.408i	−0.962570	−	0.779663i
$394$	349.353	+	253.819i	0.886682	+	0.644212i
$395$			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	$0.494769\pi$
$398$	−125.653	+	172.946i	−0.315710	+	0.434538i
$399$	196.979	−	243.190i	0.493681	−	0.609498i
$400$	25.2143	+	77.6015i	0.0630356	+	0.194004i
$401$	323.050	+	444.640i	0.805611	+	1.10883i	0.991986	+	0.126350i	$0.0403262\pi$
$401$	323.050	+	444.640i	0.805611	+	1.10883i	−0.186375	+	0.982479i	$0.559674\pi$
$402$	−53.0071	−	197.919i	−0.131858	−	0.492336i
$403$	147.823	+	454.953i	0.366807	+	1.12892i
$404$	−0.749725	−	0.243601i	−0.00185576	−	0.000602972i
$405$	384.613	+	222.300i	0.949662	+	0.548889i
$406$	−27.7588			−0.0683714
$407$		0			0
$408$	399.566	+	153.433i	0.979327	+	0.376062i
$409$	500.107	+	363.349i	1.22276	+	0.888384i	0.996326	−	0.0856436i	$-0.0272946\pi$
$409$	500.107	+	363.349i	1.22276	+	0.888384i	0.226430	+	0.974028i	$0.427295\pi$
$410$	−590.886	−	191.991i	−1.44119	−	0.468270i
$411$	158.383	+	8.31934i	0.385360	+	0.0202417i
$412$	1.42490	−	1.03525i	0.00345850	−	0.00251275i
$413$	−295.862	−	407.219i	−0.716372	−	0.986001i
$414$	−90.7647	+	203.731i	−0.219238	+	0.492103i
$415$	−16.4417	+	50.6024i	−0.0396186	+	0.121934i
$416$	−1.53581	+	2.11386i	−0.00369185	+	0.00508140i
$417$	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	$-0.176110\pi$
$420$	1.29667	−	0.841850i	0.00308731	−	0.00200440i
$421$	177.447	−	546.125i	0.421489	−	1.29721i	−0.484828	−	0.874610i	$-0.661118\pi$
$421$	177.447	−	546.125i	0.421489	−	1.29721i	0.906317	−	0.422599i	$-0.138882\pi$
$422$	409.480	−	133.048i	0.970331	−	0.315280i
$423$	54.4834	−	517.194i	0.128802	−	1.22268i
$424$	−278.462	+	202.315i	−0.656750	+	0.477157i
$425$	−86.3177	+	28.0463i	−0.203100	+	0.0659913i
$426$	142.279	−	175.658i	0.333989	−	0.412342i
$427$	139.625	+	101.444i	0.326992	+	0.237573i
$428$		−	0.783693i		−	0.00183106i
$429$		0			0
$430$	−482.605			−1.12234
$431$	−388.809	+	535.150i	−0.902109	+	1.24165i	0.0676813	+	0.997707i	$0.478440\pi$
$431$	−388.809	+	535.150i	−0.902109	+	1.24165i	−0.969790	+	0.243940i	$0.921560\pi$
$432$	−428.491	+	67.7099i	−0.991877	+	0.156736i
$433$	65.7530	+	202.367i	0.151855	+	0.467360i	0.997829	−	0.0658637i	$-0.0209803\pi$
$433$	65.7530	+	202.367i	0.151855	+	0.467360i	−0.845974	+	0.533224i	$0.820980\pi$
$434$	324.245	+	446.285i	0.747109	+	1.02831i
$435$	−39.3722	+	10.5447i	−0.0905107	+	0.0242408i
$436$	−0.874656	−	2.69192i	−0.00200609	−	0.00617412i
$437$	219.423	+	71.2947i	0.502111	+	0.163146i
$438$	61.1516	−	39.7020i	0.139615	−	0.0906438i
$439$	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
$442$	−281.569	−	204.572i	−0.637033	−	0.462831i
$443$	263.223	+	85.5262i	0.594182	+	0.193061i	0.590644	−	0.806932i	$-0.298874\pi$
$443$	263.223	+	85.5262i	0.594182	+	0.193061i	0.00353800	+	0.999994i	$0.498874\pi$
$444$	−0.104019	+	1.98031i	−0.000234278	+	0.00446017i
$445$	−151.429	+	110.019i	−0.340289	+	0.247234i
$446$	−52.7393	−	72.5895i	−0.118250	−	0.162757i
$447$	−193.084	−	10.1421i	−0.431954	−	0.0226892i
$448$	110.102	−	338.859i	0.245764	−	0.756382i
$449$	292.645	−	402.791i	0.651770	−	0.897084i	−0.347405	−	0.937715i	$-0.612937\pi$
$449$	292.645	−	402.791i	0.651770	−	0.897084i	0.999174	+	0.0406314i	$0.0129369\pi$
$450$	61.3111	−	68.0603i	0.136247	−	0.151245i
$451$		0			0
$452$		−	0.778483i		−	0.00172231i
$453$	72.9162	+	112.310i	0.160963	+	0.247926i
$454$	−139.042	+	427.928i	−0.306260	+	0.942572i
$455$	283.357	−	92.0683i	0.622763	−	0.202348i
$456$	115.607	+	431.655i	0.253523	+	0.946612i
$457$	656.206	−	476.762i	1.43590	−	1.04324i	0.447021	−	0.894523i	$-0.352485\pi$
$457$	656.206	−	476.762i	1.43590	−	1.04324i	0.988879	−	0.148719i	$-0.0475151\pi$
$458$	198.427	−	64.4728i	0.433247	−	0.140770i
$459$	−75.3151	−	476.619i	−0.164085	−	1.03839i
$460$	0.922048	+	0.669907i	0.00200445	+	0.00145632i
$461$			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	$0.301658\pi$
$464$	23.3956	−	32.2013i	0.0504216	−	0.0693994i
$465$	629.430	+	509.826i	1.35361	+	1.09640i
$466$	−38.1068	−	117.281i	−0.0817743	−	0.251675i
$467$	−163.326	−	224.799i	−0.349734	−	0.481367i	0.597519	−	0.801855i	$-0.296153\pi$
$467$	−163.326	−	224.799i	−0.349734	−	0.481367i	−0.947253	+	0.320488i	$0.896153\pi$
$468$	1.46167	+	0.153978i	0.00312322	+	0.000329013i
$469$	−58.8745	−	181.197i	−0.125532	−	0.386348i
$470$	−604.063	−	196.272i	−1.28524	−	0.417600i
$471$	230.448	+	354.951i	0.489274	+	0.753612i
$472$	718.728			1.52273
$473$		0			0
$474$	−136.101	+	354.430i	−0.287133	+	0.747743i
$475$	−76.6609	−	55.6974i	−0.161391	−	0.117258i
$476$	−1.59708	−	0.518921i	−0.00335520	−	0.00109017i
$477$	354.457	+	157.915i	0.743096	+	0.331059i
$478$	−242.015	+	175.834i	−0.506308	+	0.367854i
$479$	276.392	+	380.421i	0.577019	+	0.794198i	0.993365	−	0.115008i	$-0.0366895\pi$
$479$	276.392	+	380.421i	0.577019	+	0.794198i	−0.416346	+	0.909206i	$0.636689\pi$
$480$	−0.232074	+	4.41822i	−0.000483489	+	0.00920462i
$481$	−118.097	+	363.464i	−0.245523	+	0.755642i
$482$	−422.776	+	581.901i	−0.877128	+	1.20726i
$483$	−74.3449	+	193.606i	−0.153923	+	0.400841i
$484$		0			0
$485$		−	207.434i		−	0.427699i
$486$	306.267	+	378.667i	0.630179	+	0.779151i
$487$	78.5518	−	241.757i	0.161297	−	0.496422i	−0.837447	−	0.546518i	$-0.815953\pi$
$487$	78.5518	−	241.757i	0.161297	−	0.496422i	0.998744	+	0.0500964i	$0.0159529\pi$
$488$	−234.373	+	76.1525i	−0.480273	+	0.156050i
$489$	−350.540	+	93.8823i	−0.716850	+	0.191988i
$490$	−157.776	+	114.631i	−0.321992	+	0.233941i
$491$	117.097	−	38.0472i	0.238487	−	0.0774892i	−0.187335	−	0.982296i	$-0.559985\pi$
$491$	117.097	−	38.0472i	0.238487	−	0.0774892i	0.425822	+	0.904807i	$0.359985\pi$
$492$	−2.21458	−	1.79376i	−0.00450117	−	0.00364586i
$493$	35.8182	+	26.0234i	0.0726535	+	0.0527859i
$494$		−	363.370i		−	0.735567i
$495$		0			0
$496$	−790.989			−1.59474
$497$	123.549	−	170.051i	0.248590	−	0.342155i
$498$	−36.7142	+	45.3273i	−0.0737234	+	0.0910187i
$499$	20.1875	+	62.1308i	0.0404560	+	0.124511i	0.969245	−	0.246099i	$-0.0791488\pi$
$499$	20.1875	+	62.1308i	0.0404560	+	0.124511i	−0.928789	+	0.370610i	$0.879149\pi$
$500$	1.07932	+	1.48555i	0.00215863	+	0.00297110i
$501$	83.3792	+	311.323i	0.166426	+	0.621404i
$502$	221.115	+	680.522i	0.440468	+	1.35562i
$503$	−405.054	−	131.610i	−0.805277	−	0.261650i	−0.122681	−	0.992446i	$-0.539149\pi$
$503$	−405.054	−	131.610i	−0.805277	−	0.261650i	−0.682596	+	0.730796i	$0.739149\pi$
$504$	−392.932	+	83.4229i	−0.779628	+	0.165522i
$505$	−257.243			−0.509393
$506$		0			0
$507$	−208.881	−	80.2103i	−0.411994	−	0.158206i
$508$	0.928510	+	0.674602i	0.00182778	+	0.00132796i
$509$	−66.4418	−	21.5883i	−0.130534	−	0.0424131i	0.243021	−	0.970021i	$-0.421861\pi$
$509$	−66.4418	−	21.5883i	−0.130534	−	0.0424131i	−0.373555	+	0.927608i	$0.621861\pi$
$510$	−588.510	−	30.9125i	−1.15394	−	0.0606128i
$511$	54.8473	−	39.8489i	0.107333	−	0.0779823i
$512$	299.027	+	411.576i	0.584038	+	0.803859i
$513$	356.360	−	356.107i	0.694659	−	0.694165i
$514$	−40.9337	+	125.981i	−0.0796376	+	0.245099i
$515$	337.827	−	464.979i	0.655975	−	0.902872i
$516$	−2.06660	−	0.793574i	−0.00400503	−	0.00153793i
$517$		0			0
$518$			440.706i			0.850785i
$519$	−827.364	+	537.157i	−1.59415	+	1.03498i
$520$	−131.463	+	404.603i	−0.252814	+	0.778082i
$521$	95.7147	−	31.0996i	0.183714	−	0.0596921i	−0.215716	−	0.976456i	$-0.569208\pi$
$521$	95.7147	−	31.0996i	0.183714	−	0.0596921i	0.399429	+	0.916764i	$0.369208\pi$
$522$	−44.4395	−	4.68144i	−0.0851332	−	0.00896828i
$523$	−689.238	+	500.761i	−1.31785	+	0.957477i	−0.317898	+	0.948125i	$0.602977\pi$
$523$	−689.238	+	500.761i	−1.31785	+	0.957477i	−0.999956	+	0.00935234i	$0.997023\pi$
$524$	−2.59375	+	0.842761i	−0.00494991	+	0.00160832i
$525$	53.6123	−	66.1896i	0.102119	−	0.126075i
$526$	138.502	+	100.627i	0.263311	+	0.191307i
$527$		−	879.833i		−	1.66951i
$528$		0			0
$529$	376.110			0.710983
$530$	278.563	−	383.409i	0.525590	−	0.723413i
$531$	−404.974	−	701.819i	−0.762662	−	1.32169i
$532$	−0.541782	−	1.66743i	−0.00101839	−	0.00313427i
$533$	−322.828	−	444.335i	−0.605681	−	0.833648i
$534$	−198.217	+	53.0870i	−0.371193	+	0.0994138i
$535$	−79.0273	−	243.221i	−0.147715	−	0.454619i
$536$	258.730	+	84.0664i	0.482705	+	0.156840i
$537$	−121.529	+	78.9014i	−0.226311	+	0.146930i
$538$	324.247			0.602689
$539$		0			0
$540$	2.21784	−	1.12905i	0.00410711	−	0.00209084i
$541$	591.736	+	429.921i	1.09378	+	0.794679i	0.980034	−	0.198831i	$-0.0637145\pi$
$541$	591.736	+	429.921i	1.09378	+	0.794679i	0.113747	+	0.993510i	$0.463715\pi$
$542$	495.575	+	161.022i	0.914345	+	0.297089i
$543$	−0.0104753	+	0.199427i	−1.92915e−5	+	0.000367269i
$544$	3.88792	−	2.82474i	0.00714691	−	0.00519253i
$545$	−542.903	−	747.242i	−0.996152	−	1.37109i
$546$	326.185	+	17.1334i	0.597408	+	0.0313799i
$547$	38.0953	−	117.245i	0.0696440	−	0.214342i	−0.910177	−	0.414220i	$-0.864054\pi$
$547$	38.0953	−	117.245i	0.0696440	−	0.214342i	0.979821	+	0.199878i	$0.0640545\pi$
$548$	0.522256	−	0.718823i	0.000953021	−	0.00131172i
$549$	206.421	+	185.951i	0.375994	+	0.338708i
$550$		0			0
$551$			46.2241i			0.0838913i
$552$	−161.254	−	248.375i	−0.292128	−	0.449954i
$553$	−109.093	+	335.753i	−0.197275	+	0.607149i
$554$	−165.435	+	53.7530i	−0.298619	+	0.0970271i
$555$	167.411	+	625.084i	0.301642	+	1.12628i
$556$	1.17661	−	0.854856i	0.00211620	−	0.00153751i
$557$	−191.900	+	62.3520i	−0.344524	+	0.111942i	−0.476168	−	0.879355i	$-0.657974\pi$
$557$	−191.900	+	62.3520i	−0.344524	+	0.111942i	0.131644	+	0.991297i	$0.457974\pi$
$558$	443.825	+	769.149i	0.795385	+	1.37840i
$559$	−345.147	−	250.764i	−0.617436	−	0.448594i
$560$			492.649i			0.879731i
$561$		0			0
$562$	971.465			1.72858
$563$	284.551	−	391.651i	0.505420	−	0.695651i	−0.477719	−	0.878513i	$-0.658536\pi$
$563$	284.551	−	391.651i	0.505420	−	0.695651i	0.983139	+	0.182862i	$0.0585362\pi$
$564$	−2.26396	−	1.83376i	−0.00401411	−	0.00325135i
$565$	−78.5019	−	241.604i	−0.138941	−	0.427618i
$566$	508.998	+	700.575i	0.899289	+	1.23776i
$567$	302.861	+	336.683i	0.534147	+	0.593797i
$568$	92.7467	+	285.445i	0.163286	+	0.502544i
$569$	444.542	+	144.440i	0.781268	+	0.253849i	0.672382	−	0.740205i	$-0.265271\pi$
$569$	444.542	+	144.440i	0.781268	+	0.253849i	0.108887	+	0.994054i	$0.465271\pi$
$570$	−335.046	−	516.060i	−0.587800	−	0.905368i
$571$	−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
$574$	−512.395	−	372.277i	−0.892674	−	0.648566i
$575$	59.7209	+	19.4045i	0.103862	+	0.0337469i
$576$	233.412	−	523.917i	0.405229	−	0.909579i
$577$	706.639	−	513.403i	1.22468	−	0.889780i	0.228198	−	0.973615i	$-0.426717\pi$
$577$	706.639	−	513.403i	1.22468	−	0.889780i	0.996480	+	0.0838344i	$0.0267167\pi$
$578$	35.8047	+	49.2809i	0.0619458	+	0.0852611i
$579$	0.239768	−	4.56469i	0.000414108	−	0.00788375i
$580$	−0.0705622	+	0.217168i	−0.000121659	+	0.000374428i
$581$	−31.8811	+	43.8806i	−0.0548728	+	0.0755259i
$582$	81.5225	−	212.298i	0.140073	−	0.364774i
$583$		0			0
$584$			96.8039i			0.165760i
$585$	469.158	−	99.6063i	0.801980	−	0.170267i
$586$	−3.42464	+	10.5399i	−0.00584409	+	0.0179863i
$587$	−751.908	+	244.310i	−1.28093	+	0.416201i	−0.868909	−	0.494972i	$-0.835178\pi$
$587$	−751.908	+	244.310i	−1.28093	+	0.416201i	−0.412025	+	0.911173i	$0.635178\pi$
$588$	−0.864118	+	0.231430i	−0.00146959	+	0.000393588i
$589$	743.158	−	539.936i	1.26173	−	0.916699i
$590$	−941.168	+	305.804i	−1.59520	+	0.518312i
$591$	502.282	+	406.839i	0.849886	+	0.688391i
$592$	−511.238	−	371.436i	−0.863577	−	0.627425i
$593$		−	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
$596$	−0.636679	+	0.876313i	−0.00106825	+	0.00147032i
$597$	−201.404	+	248.653i	−0.337361	+	0.416505i
$598$	74.4106	+	229.012i	0.124433	+	0.382964i
$599$	−539.215	−	742.166i	−0.900192	−	1.23901i	−0.970407	−	0.241477i	$-0.922368\pi$
$599$	−539.215	−	742.166i	−0.900192	−	1.23901i	0.0702143	−	0.997532i	$-0.477632\pi$
$600$	31.4650	+	117.485i	0.0524416	+	0.195808i
$601$	−295.316	−	908.889i	−0.491374	−	1.51229i	−0.822532	−	0.568719i	$-0.807439\pi$
$601$	−295.316	−	908.889i	−0.491374	−	1.51229i	0.331158	−	0.943575i	$-0.392561\pi$
$602$	−467.894	−	152.028i	−0.777232	−	0.252538i
$603$	−63.6949	−	300.011i	−0.105630	−	0.497530i
$604$	0.750158			0.00124198
$605$		0			0
$606$	−263.275	−	101.098i	−0.434448	−	0.166828i
$607$	−632.343	−	459.424i	−1.04175	−	0.756877i	−0.0711247	−	0.997467i	$-0.522659\pi$
$607$	−632.343	−	459.424i	−1.04175	−	0.756877i	−0.970627	+	0.240591i	$0.922659\pi$
$608$	4.77187	+	1.55047i	0.00784847	+	0.00255012i
$609$	−41.4938	−	2.17953i	−0.0681343	−	0.00357887i
$610$	274.508	−	199.442i	0.450014	−	0.326954i
$611$	−330.027	−	454.243i	−0.540142	−	0.743442i
$612$	−2.46927	−	1.10009i	−0.00403476	−	0.00179754i
$613$	−26.5687	+	81.7701i	−0.0433421	+	0.133393i	−0.970386	−	0.241560i	$-0.922341\pi$
$613$	−26.5687	+	81.7701i	−0.0433421	+	0.133393i	0.927044	+	0.374953i	$0.122341\pi$
$614$	−258.293	+	355.509i	−0.420672	+	0.579005i
$615$	−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	$-0.00192905\pi$
$618$	528.487	−	343.115i	0.855158	−	0.555202i
$619$	100.475	−	309.230i	0.162318	−	0.499564i	−0.836510	−	0.547951i	$-0.815408\pi$
$619$	100.475	−	309.230i	0.162318	−	0.499564i	0.998829	+	0.0483869i	$0.0154080\pi$
$620$	4.31569	−	1.40225i	0.00696079	−	0.00226170i
$621$	−151.671	+	297.410i	−0.244237	+	0.478921i
$622$	−230.487	+	167.458i	−0.370557	+	0.269226i
$623$	−181.470	+	58.9633i	−0.291285	+	0.0946441i
$624$	−294.790	+	363.947i	−0.472420	+	0.583249i
$625$	587.484	+	426.832i	0.939975	+	0.682932i
$626$			188.967i			0.301864i
$627$		0			0
$628$	2.37084			0.00377522
$629$	413.156	−	568.660i	0.656845	−	0.904070i
$630$	479.047	−	276.426i	0.760392	−	0.438772i
$631$	−211.843	−	651.985i	−0.335726	−	1.03326i	−0.966363	−	0.257180i	$-0.917207\pi$
$631$	−211.843	−	651.985i	−0.335726	−	1.03326i	0.630638	−	0.776077i	$-0.282793\pi$
$632$	−296.297	−	407.818i	−0.468825	−	0.645282i
$633$	622.536	−	166.729i	0.983469	−	0.263395i
$634$	−310.418	−	955.368i	−0.489618	−	1.50689i
$635$	356.192	+	115.734i	0.560932	+	0.182258i
$636$	1.82332	−	1.18377i	0.00286685	−	0.00186127i
$637$	−172.400			−0.270644
$638$		0			0
$639$	226.471	−	251.401i	0.354414	−	0.393429i
$640$	−571.484	−	415.207i	−0.892943	−	0.648761i
$641$	259.923	+	84.4540i	0.405496	+	0.131754i	0.504661	−	0.863317i	$-0.331617\pi$
$641$	259.923	+	84.4540i	0.405496	+	0.131754i	−0.0991656	+	0.995071i	$0.531617\pi$
$642$	14.7066	−	279.982i	0.0229074	−	0.436109i
$643$	−149.364	+	108.519i	−0.232292	+	0.168770i	−0.697842	−	0.716251i	$-0.745856\pi$
$643$	−149.364	+	108.519i	−0.232292	+	0.168770i	0.465550	+	0.885021i	$0.345856\pi$
$644$	0.682911	+	0.939947i	0.00106042	+	0.00145954i
$645$	−721.396	−	37.8926i	−1.11844	−	0.0587482i
$646$	−206.525	+	635.617i	−0.319698	+	0.983928i
$647$	211.660	−	291.325i	0.327141	−	0.450271i	−0.613490	−	0.789703i	$-0.710235\pi$
$647$	211.660	−	291.325i	0.327141	−	0.450271i	0.940631	+	0.339432i	$0.110235\pi$
$648$	−643.121	+	67.2862i	−0.992471	+	0.103837i
$649$		0			0
$650$		−	98.8995i		−	0.152153i
$651$	449.640	+	692.565i	0.690691	+	1.06385i
$652$	−0.628232	+	1.93350i	−0.000963546	+	0.00296549i
$653$	−979.935	+	318.400i	−1.50067	+	0.487596i	−0.940212	−	0.340589i	$-0.889374\pi$
$653$	−979.935	+	318.400i	−1.50067	+	0.487596i	−0.560455	+	0.828185i	$0.689374\pi$
$654$	−261.964	−	978.127i	−0.400557	−	1.49561i
$655$	−719.993	+	523.105i	−1.09923	+	0.798634i
$656$	863.712	−	280.637i	1.31663	−	0.427801i
$657$	94.5265	−	54.5450i	0.143876	−	0.0830213i
$658$	−523.821	−	380.578i	−0.796080	−	0.578386i
$659$			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	$0.391650\pi$
$662$	−769.834	+	1059.59i	−1.16289	+	1.60058i
$663$	−404.826	−	327.901i	−0.610597	−	0.494572i
$664$	−23.9327	−	73.6573i	−0.0360432	−	0.110930i
$665$	−336.286	−	462.859i	−0.505694	−	0.696028i
$666$	−74.3239	+	705.535i	−0.111598	+	1.05936i
$667$	−9.46574	−	29.1325i	−0.0141915	−	0.0436770i
$668$	1.71719	+	0.557949i	0.00257064	+	0.000835253i
$669$	−73.1352	−	112.648i	−0.109320	−	0.168382i
$670$	−374.573			−0.559064
$671$		0			0
$672$	−1.61681	+	4.21043i	−0.00240596	+	0.00626552i
$673$	−299.904	−	217.893i	−0.445623	−	0.323764i	0.342242	−	0.939612i	$-0.388814\pi$
$673$	−299.904	−	217.893i	−0.445623	−	0.323764i	−0.787865	+	0.615848i	$0.788814\pi$
$674$	−1256.82	−	408.365i	−1.86472	−	0.605883i
$675$	96.9915	−	96.9225i	0.143691	−	0.143589i
$676$	−1.01410	+	0.736789i	−0.00150015	+	0.00108992i
$677$	−44.2177	−	60.8605i	−0.0653142	−	0.0898973i	0.775110	−	0.631826i	$-0.217694\pi$
$677$	−44.2177	−	60.8605i	−0.0653142	−	0.0898973i	−0.840424	+	0.541929i	$0.817694\pi$
$678$	14.6088	−	278.121i	0.0215469	−	0.410208i
$679$	65.3450	−	201.111i	0.0962371	−	0.296187i
$680$	459.919	−	633.024i	0.676351	−	0.930918i
$681$	−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	$0.742892\pi$
$684$	−0.586140	−	2.76079i	−0.000856930	−	0.00403625i
$685$	89.5974	−	275.752i	0.130799	−	0.402558i
$686$	−711.257	+	231.101i	−1.03682	+	0.336882i
$687$	301.670	−	80.7940i	0.439113	−	0.117604i
$688$	570.708	−	414.644i	0.829518	−	0.602680i
$689$	398.443	−	129.462i	0.578291	−	0.187898i
$690$	316.840	+	256.634i	0.459188	+	0.371933i
$691$	−830.700	−	603.539i	−1.20217	−	0.873428i	−0.207675	−	0.978198i	$-0.566589\pi$
$691$	−830.700	−	603.539i	−1.20217	−	0.873428i	−0.994497	+	0.104770i	$0.966589\pi$
$692$			5.52624i			0.00798589i
$693$		0			0
$694$	556.925			0.802486
$695$	278.960	−	383.955i	0.401381	−	0.552454i
$696$	37.3432	−	46.1038i	0.0536540	−	0.0662411i
$697$	312.158	+	960.725i	0.447860	+	1.37837i
$698$	−297.779	−	409.857i	−0.426617	−	0.587188i
$699$	−47.7535	−	178.303i	−0.0683169	−	0.255083i
$700$	−0.147458	−	0.453830i	−0.000210655	−	0.000648328i
$701$	−177.798	−	57.7699i	−0.253634	−	0.0824107i	0.179440	−	0.983769i	$-0.442571\pi$
$701$	−177.798	−	57.7699i	−0.253634	−	0.0824107i	−0.433074	+	0.901358i	$0.642571\pi$
$702$	519.305	+	82.4393i	0.739751	+	0.117435i
$703$	733.868			1.04391
$704$		0			0
$705$	−887.541	−	340.816i	−1.25892	−	0.483427i
$706$	909.302	+	660.647i	1.28796	+	0.935760i
$707$	−249.402	−	81.0357i	−0.352761	−	0.114619i
$708$	−4.53310	−	0.238109i	−0.00640268	−	0.000336312i
$709$	577.375	−	419.488i	0.814351	−	0.591661i	−0.100738	−	0.994913i	$-0.532120\pi$
$709$	577.375	−	419.488i	0.814351	−	0.591661i	0.915089	+	0.403252i	$0.132120\pi$
$710$	−242.902	−	334.326i	−0.342115	−	0.470881i
$711$	−231.273	+	519.115i	−0.325278	+	0.730120i
$712$	84.1931	−	259.120i	0.118249	−	0.363932i
$713$	−357.804	+	492.475i	−0.501829	+	0.690708i
$714$	−560.833	−	215.360i	−0.785481	−	0.301625i
$715$		0			0
$716$			0.811733i			0.00113370i
$717$	−375.570	+	243.834i	−0.523807	+	0.340076i
$718$	183.361	−	564.328i	0.255378	−	0.785972i
$719$	474.314	−	154.114i	0.659685	−	0.214345i	0.0400055	−	0.999199i	$-0.487262\pi$
$719$	474.314	−	154.114i	0.659685	−	0.214345i	0.619680	+	0.784855i	$0.287262\pi$
$720$	−83.0840	+	788.691i	−0.115394	+	1.09540i
$721$	474.005	−	344.385i	0.657427	−	0.477649i
$722$	24.4851	−	7.95569i	0.0339129	−	0.0110190i
$723$	−677.653	+	836.629i	−0.937280	+	1.15716i
$724$	0.000905104	0	0.000657596i	1.25014e−6	0	9.08282e-7i
$725$			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	$0.404930\pi$
$728$	−254.912	+	350.857i	−0.350154	+	0.481946i
$729$	428.076	+	590.078i	0.587209	+	0.809435i
$730$	−41.1881	−	126.764i	−0.0564220	−	0.173649i
$731$	461.217	+	634.810i	0.630940	+	0.868414i
$732$	1.50345	−	0.402656i	0.00205389	−	0.000550076i
$733$	−295.860	−	910.564i	−0.403629	−	1.24224i	−0.922035	−	0.387108i	$-0.873474\pi$
$733$	−295.860	−	910.564i	−0.403629	−	1.24224i	0.518405	−	0.855135i	$-0.326526\pi$
$734$	161.748	+	52.5551i	0.220365	+	0.0716010i
$735$	−244.844	+	158.962i	−0.333120	+	0.216275i
$736$	−3.32495			−0.00451760
$737$		0			0
$738$	−757.518	−	682.398i	−1.02645	−	0.924659i
$739$	−918.220	−	667.126i	−1.24252	−	0.902741i	−0.244753	−	0.969585i	$-0.578707\pi$
$739$	−918.220	−	667.126i	−1.24252	−	0.902741i	−0.997763	+	0.0668442i	$0.978707\pi$
$740$	3.44782	+	1.12027i	0.00465922	+	0.00151387i
$741$	28.5307	−	543.165i	0.0385030	−	0.733016i
$742$	390.851	−	283.970i	0.526754	−	0.382709i
$743$	509.543	+	701.326i	0.685791	+	0.943911i	0.999985	−	0.00544821i	$-0.00173423\pi$
$743$	509.543	+	701.326i	0.685791	+	0.943911i	−0.314194	+	0.949359i	$0.601734\pi$
$744$	−1177.42	−	61.8461i	−1.58256	−	0.0831265i
$745$	−109.228	+	336.168i	−0.146614	+	0.451232i
$746$	−372.375	+	512.530i	−0.499162	+	0.687038i
$747$	−58.4393	+	64.8725i	−0.0782321	+	0.0868441i
$748$		0			0
$749$		−	260.702i		−	0.348067i
$750$	357.719	+	550.982i	0.476959	+	0.734643i
$751$	−357.678	+	1100.82i	−0.476268	+	1.46580i	0.367971	+	0.929837i	$0.380053\pi$
$751$	−357.678	+	1100.82i	−0.476268	+	1.46580i	−0.844240	+	0.535966i	$0.819947\pi$
$752$	882.972	−	286.895i	1.17417	−	0.381509i
$753$	277.090	+	1034.60i	0.367981	+	1.37398i
$754$	−39.0305	+	28.3573i	−0.0517646	+	0.0376092i
$755$	232.813	−	75.6455i	0.308362	−	0.100193i
$756$	2.50590	−	0.395982i	0.00331469	−	0.000523786i
$757$	331.936	+	241.165i	0.438488	+	0.318580i	0.785034	−	0.619453i	$-0.212645\pi$
$757$	331.936	+	241.165i	0.438488	+	0.318580i	−0.346546	+	0.938033i	$0.612645\pi$
$758$		−	217.931i		−	0.287508i
$759$		0			0
$760$	816.931			1.07491
$761$	148.998	−	205.078i	0.195792	−	0.269484i	−0.699822	−	0.714318i	$-0.746737\pi$
$761$	148.998	−	205.078i	0.195792	−	0.269484i	0.895613	+	0.444833i	$0.146737\pi$
$762$	319.060	+	258.432i	0.418714	+	0.339150i
$763$	−290.961	−	895.487i	−0.381339	−	1.17364i
$764$	−1.95018	−	2.68419i	−0.00255259	−	0.00351334i
$765$	−877.277	−	92.4160i	−1.14677	−	0.120805i
$766$	273.753	+	842.524i	0.357380	+	1.09990i
$767$	−831.998	−	270.332i	−1.08474	−	0.352454i
$768$	−5.27137	−	8.11930i	−0.00686376	−	0.0105720i
$769$	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
$772$	−0.0207169	−	0.0150517i	−2.68354e−5	−	1.94971e-5i
$773$	326.547	+	106.102i	0.422442	+	0.137260i	0.512520	−	0.858675i	$-0.328712\pi$
$773$	326.547	+	106.102i	0.422442	+	0.137260i	−0.0900787	+	0.995935i	$0.528712\pi$
$774$	−723.420	−	322.293i	−0.934651	−	0.416399i
$775$	202.267	−	146.956i	0.260990	−	0.189620i
$776$	177.477	+	244.277i	0.228708	+	0.314790i
$777$	−34.6029	+	658.767i	−0.0445340	+	0.847834i
$778$	315.609	−	971.346i	0.405668	−	1.24852i
$779$	−619.918	+	853.244i	−0.795787	+	1.09531i
$780$	0.963195	−	2.50832i	0.00123487	−	0.00321580i
$781$		0			0
$782$		−	442.887i		−	0.566351i
$783$	−66.0605	−	10.4871i	−0.0843685	−	0.0133934i
$784$	88.0908	−	271.116i	0.112361	−	0.345811i
$785$	735.795	−	239.074i	0.937318	−	0.304553i
$786$	−942.458	+	252.411i	−1.19906	+	0.321134i
$787$	−156.500	+	113.704i	−0.198856	+	0.144478i	−0.682758	−	0.730645i	$-0.739219\pi$
$787$	−156.500	+	113.704i	−0.198856	+	0.144478i	0.483901	+	0.875123i	$0.339219\pi$
$788$	3.44391	−	1.11899i	0.00437044	−	0.00142004i
$789$	199.131	+	161.292i	0.252384	+	0.204426i
$790$	561.517	+	407.966i	0.710781	+	0.516413i
$791$		−	258.969i		−	0.327394i
$792$		0			0
$793$	299.953			0.378251
$794$	15.3712	−	21.1566i	0.0193592	−	0.0266456i
$795$	446.499	−	551.247i	0.561634	−	0.693393i
$796$	0.553954	+	1.70490i	0.000695922	+	0.00214183i
$797$	312.659	+	430.338i	0.392294	+	0.539947i	0.958789	−	0.284119i	$-0.0917009\pi$
$797$	312.659	+	430.338i	0.392294	+	0.539947i	−0.566495	+	0.824065i	$0.691701\pi$
$798$	−162.266	−	605.874i	−0.203341	−	0.759241i
$799$	319.119	+	982.148i	0.399398	+	1.22922i
$800$	1.29877	+	0.421997i	0.00162347	+	0.000527496i
$801$	−300.463	+	63.7909i	−0.375110	+	0.0796391i
$802$	1101.52			1.37346
$803$		0			0
$804$	−1.60399	−	0.615931i	−0.00199501	−	0.000766083i
$805$	306.727	+	222.850i	0.381027	+	0.276832i
$806$	911.816	+	296.267i	1.13128	+	0.367577i
$807$	484.683	+	25.4588i	0.600599	+	0.0315475i
$808$	302.933	−	220.094i	0.374917	−	0.272393i
$809$	170.708	+	234.960i	0.211012	+	0.290433i	0.901383	−	0.433022i	$-0.142553\pi$
$809$	170.708	+	234.960i	0.211012	+	0.290433i	−0.690371	+	0.723455i	$0.742553\pi$
$810$	813.533	−	361.746i	1.00436	−	0.446599i
$811$	−118.833	+	365.730i	−0.146526	+	0.450962i	−0.997204	−	0.0747256i	$-0.976192\pi$
$811$	−118.833	+	365.730i	−0.146526	+	0.450962i	0.850678	+	0.525688i	$0.176192\pi$
$812$	−0.136823	+	0.188320i	−0.000168501	+	0.000231921i
$813$	728.142	+	279.607i	0.895623	+	0.343919i
$814$		0			0
$815$			663.416i			0.814008i
$816$	722.508	−	469.080i	0.885426	−	0.574853i
$817$	−253.158	+	779.140i	−0.309863	+	0.953660i
$818$	1178.29	−	382.850i	1.44045	−	0.468031i
$819$	486.235	+	51.2220i	0.593693	+	0.0625421i
$820$	−4.21497	+	3.06235i	−0.00514020	+	0.00373458i
$821$	−591.295	+	192.123i	−0.720213	+	0.234011i	−0.646115	−	0.763240i	$-0.723608\pi$
$821$	−591.295	+	192.123i	−0.720213	+	0.234011i	−0.0740974	+	0.997251i	$0.523608\pi$
$822$	200.070	−	247.006i	0.243394	−	0.300494i
$823$	231.689	+	168.332i	0.281517	+	0.204534i	0.719579	−	0.694411i	$-0.244335\pi$
$823$	231.689	+	168.332i	0.281517	+	0.204534i	−0.438062	+	0.898945i	$0.644335\pi$
$824$			836.604i			1.01530i
$825$		0			0
$826$	−1008.81			−1.22132
$827$	−245.405	+	337.771i	−0.296741	+	0.408430i	−0.931189	−	0.364536i	$-0.881228\pi$
$827$	−245.405	+	337.771i	−0.296741	+	0.408430i	0.634448	+	0.772966i	$0.281228\pi$
$828$	0.934765	+	1.61995i	0.00112894	+	0.00195646i
$829$	114.601	+	352.706i	0.138240	+	0.425460i	0.996080	−	0.0884576i	$-0.0281938\pi$
$829$	114.601	+	352.706i	0.138240	+	0.425460i	−0.857840	+	0.513917i	$0.828194\pi$
$830$	62.6793	+	86.2707i	0.0755173	+	0.103941i
$831$	−251.512	+	67.3605i	−0.302662	+	0.0810595i
$832$	−191.356	−	588.932i	−0.229995	−	0.707851i
$833$	301.567	+	97.9852i	0.362026	+	0.117629i
$834$	436.397	−	283.326i	0.523258	−	0.339719i
$835$	589.197			0.705625
$836$		0			0
$837$	603.038	+	1184.57i	0.720475	+	1.41526i
$838$	−713.983	−	518.739i	−0.852009	−	0.619020i
$839$	−823.477	−	267.564i	−0.981498	−	0.318908i	−0.226050	−	0.974116i	$-0.572581\pi$
$839$	−823.477	−	267.564i	−0.981498	−	0.318908i	−0.755449	+	0.655208i	$0.772581\pi$
$840$	−38.5195	+	733.330i	−0.0458565	+	0.873012i
$841$	−675.418	+	490.720i	−0.803113	+	0.583496i
$842$	−676.464	−	931.073i	−0.803402	−	1.10579i
$843$	1452.14	+	76.2764i	1.72259	+	0.0904821i
$844$	1.11570	−	3.43377i	0.00132192	−	0.00406845i
$845$	−240.432	+	330.926i	−0.284534	+	0.391628i
$846$	−774.410	−	697.615i	−0.915379	−	0.824604i
$847$		0			0
$848$			692.739i			0.816910i
$849$	705.841	+	1087.18i	0.831380	+	1.28055i
$850$	−56.2104	+	172.998i	−0.0661298	+	0.203527i
$851$	−462.517	+	150.281i	−0.543498	+	0.176593i
$852$	−0.490398	−	1.83106i	−0.000575584	−	0.00214913i
$853$	−1089.63	+	791.663i	−1.27741	+	0.928093i	−0.999472	−	0.0325055i	$-0.989651\pi$
$853$	−1089.63	+	791.663i	−1.27741	+	0.928093i	−0.277939	+	0.960599i	$0.589651\pi$
$854$	328.968	−	106.888i	0.385208	−	0.125162i
$855$	−460.307	−	797.712i	−0.538371	−	0.932997i
$856$	301.159	+	218.805i	0.351822	+	0.255614i
$857$		−	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	$0.603638\pi$
$860$	−2.37875	+	3.27407i	−0.00276599	+	0.00380706i
$861$	−736.697	−	596.710i	−0.855629	−	0.693043i
$862$	409.676	+	1260.85i	0.475262	+	1.46271i
$863$	644.169	+	886.623i	0.746430	+	1.02737i	0.998223	+	0.0595920i	$0.0189800\pi$
$863$	644.169	+	886.623i	0.746430	+	1.02737i	−0.251792	+	0.967781i	$0.581020\pi$
$864$	−3.29845	+	6.46788i	−0.00381765	+	0.00748598i
$865$	557.263	+	1715.08i	0.644235	+	1.98275i
$866$	405.583	+	131.782i	0.468341	+	0.152173i
$867$	49.6514	+	76.4763i	0.0572680	+	0.0882080i
$868$	4.62587			0.00532935
$869$		0			0
$870$	−29.2843	+	76.2613i	−0.0336602	+	0.0876567i
$871$	−267.885	−	194.630i	−0.307560	−	0.223456i
$872$	1278.66	+	415.461i	1.46635	+	0.476446i
$873$	138.529	−	310.942i	0.158681	−	0.356176i
$874$	374.088	−	271.791i	0.428018	−	0.310973i
$875$	359.043	+	494.181i	0.410335	+	0.564778i
$876$	0.0320703	−	0.610553i	3.66100e−5	−	0.000696978i
$877$	445.959	−	1372.52i	0.508505	−	1.56502i	−0.286293	−	0.958142i	$-0.592423\pi$
$877$	445.959	−	1372.52i	0.508505	−	1.56502i	0.794798	−	0.606875i	$-0.207577\pi$
$878$	122.298	−	168.329i	0.139292	−	0.191719i
$879$	−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	$-0.0293217\pi$
$882$	−313.058	+	66.4648i	−0.354941	+	0.0753569i
$883$	−26.9204	+	82.8525i	−0.0304875	+	0.0938307i	−0.965142	−	0.261725i	$-0.915709\pi$
$883$	−26.9204	+	82.8525i	−0.0304875	+	0.0938307i	0.934655	+	0.355556i	$0.115709\pi$
$884$	−2.77569	+	0.901877i	−0.00313992	+	0.00102022i
$885$	−1430.87	+	383.218i	−1.61680	+	0.433014i
$886$	448.761	−	326.044i	0.506502	−	0.367995i
$887$	776.279	−	252.228i	0.875174	−	0.284361i	0.163222	−	0.986589i	$-0.447811\pi$
$887$	776.279	−	252.228i	0.875174	−	0.284361i	0.711952	+	0.702228i	$0.247811\pi$
$888$	−731.957	−	592.871i	−0.824276	−	0.667648i
$889$	308.876	+	224.412i	0.347442	+	0.252432i
$890$			375.137i			0.421503i
$891$		0			0
$892$	−0.752410			−0.000843509
$893$	−633.741	+	872.270i	−0.709677	+	0.976786i
$894$	−243.904	+	301.124i	−0.272824	+	0.336828i
$895$	81.8547	+	251.923i	0.0914578	+	0.281478i
$896$	−423.267	−	582.577i	−0.472396	−	0.650197i
$897$	93.2475	+	348.170i	0.103955	+	0.388149i
$898$	−308.350	−	949.005i	−0.343375	−	1.05680i
$899$	−115.992	−	37.6879i	−0.129023	−	0.0419221i
$900$	−0.159531	−	0.751413i	−0.000177257	−	0.000834903i
$901$	−770.548			−0.855214
$902$		0			0
$903$	−687.470	−	263.989i	−0.761318	−	0.292346i
$904$	299.157	+	217.351i	0.330926	+	0.240432i
$905$	0.347213	+	0.112816i	0.000383660	+	0.000124659i
$906$	268.001	+	14.0772i	0.295807	+	0.0155378i
$907$	−451.884	+	328.313i	−0.498218	+	0.361977i	−0.808336	−	0.588721i	$-0.799632\pi$
$907$	−451.884	+	328.313i	−0.498218	+	0.361977i	0.310118	+	0.950698i	$0.399632\pi$
$908$	2.21780	+	3.05253i	0.00244251	+	0.00336182i
$909$	−385.606	−	171.792i	−0.424209	−	0.188991i
$910$	184.523	−	567.903i	0.202773	−	0.624070i
$911$	956.353	−	1316.31i	1.04978	−	1.44490i	0.160788	−	0.986989i	$-0.448597\pi$
$911$	956.353	−	1316.31i	1.04978	−	1.44490i	0.888996	−	0.457914i	$-0.151403\pi$
$912$	839.600	+	322.407i	0.920614	+	0.353516i
$913$		0			0
$914$		−	1625.64i		−	1.77860i
$915$	425.994	−	276.572i	0.465567	−	0.302264i
$916$	0.540649	−	1.66395i	0.000590228	−	0.00181654i
$917$	−862.832	+	280.351i	−0.940929	+	0.305726i
$918$	−861.528	−	439.357i	−0.938484	−	0.478602i
$919$	46.5896	−	33.8493i	0.0506960	−	0.0368328i	−0.562149	−	0.827036i	$-0.690025\pi$
$919$	46.5896	−	33.8493i	0.0506960	−	0.0368328i	0.612845	+	0.790203i	$0.290025\pi$
$920$	−514.867	+	167.290i	−0.559638	+	0.181837i
$921$	−414.009	+	511.134i	−0.449521	+	0.554977i
$922$	1281.02	+	930.716i	1.38939	+	1.00945i
$923$		−	365.315i		−	0.395791i
$924$		0			0
$925$	199.739			0.215934
$926$	636.589	−	876.189i	0.687461	−	0.946209i
$927$	816.922	−	471.392i	0.881254	−	0.508513i
$928$	−0.205855	−	0.633557i	−0.000221827	−	0.000682712i
$929$	−12.6377	−	17.3943i	−0.0136036	−	0.0187237i	0.802161	−	0.597108i	$-0.203684\pi$
$929$	−12.6377	−	17.3943i	−0.0136036	−	0.0187237i	−0.815765	+	0.578384i	$0.803684\pi$
$930$	1568.14	−	419.982i	1.68617	−	0.451593i
$931$	102.302	+	314.853i	0.109884	+	0.338187i
$932$	−0.983480	−	0.319552i	−0.00105524	−	0.000342867i
$933$	−357.679	+	232.219i	−0.383365	+	0.248895i
$934$	−556.899			−0.596251
$935$		0			0
$936$	−467.264	+	518.702i	−0.499214	+	0.554169i
$937$	−185.231	−	134.578i	−0.197685	−	0.143626i	0.484539	−	0.874769i	$-0.338987\pi$
$937$	−185.231	−	134.578i	−0.197685	−	0.143626i	−0.682224	+	0.731143i	$0.738987\pi$
$938$	−363.155	−	117.996i	−0.387159	−	0.125796i
$939$	−14.8371	+	282.468i	−0.0158010	+	0.300818i
$940$	−4.30896	+	3.13064i	−0.00458400	+	0.00333047i
$941$	507.355	+	698.315i	0.539166	+	0.742099i	0.988493	−	0.151269i	$-0.0483360\pi$
$941$	507.355	+	698.315i	0.539166	+	0.742099i	−0.449326	+	0.893368i	$0.648336\pi$
$942$	847.005	+	44.4904i	0.899156	+	0.0472297i
$943$	215.974	−	664.699i	0.229028	−	0.704877i
$944$	850.246	−	1170.26i	0.900685	−	1.23969i
$945$	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	$-0.208908\pi$
$948$	1.73367	+	2.67031i	0.00182877	+	0.00281679i
$949$	36.4105	−	112.060i	0.0383672	−	0.118082i
$950$	−180.619	+	58.6866i	−0.190125	+	0.0617754i
$951$	−388.999	−	1452.46i	−0.409043	−	1.52729i
$952$	645.312	−	468.846i	0.677849	−	0.492486i
$953$	−1709.15	+	555.337i	−1.79344	+	0.582725i	−0.999675	−	0.0254945i	$-0.991884\pi$
$953$	−1709.15	+	555.337i	−1.79344	+	0.582725i	−0.793769	+	0.608220i	$0.791884\pi$
$954$	673.612	−	388.697i	0.706092	−	0.407439i
$955$	−875.916	−	636.390i	−0.917189	−	0.666377i
$956$			2.50855i			0.00262401i
$957$		0			0
$958$	942.426			0.983743
$959$	173.732	−	239.122i	0.181160	−	0.249345i
$960$	−814.790	−	659.964i	−0.848740	−	0.687463i
$961$	451.992	+	1391.09i	0.470335	+	1.44754i
$962$	450.209	+	619.659i	0.467993	+	0.644136i
$963$	43.9667	−	417.362i	0.0456559	−	0.433398i
$964$	1.86386	+	5.73636i	0.00193346	+	0.00595058i
$965$	−7.94735	−	2.58225i	−0.00823560	−	0.00267591i
$966$	226.338	+	348.620i	0.234304	+	0.360891i
$967$	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
$970$	−336.340	−	244.365i	−0.346742	−	0.251923i
$971$	−483.830	−	157.206i	−0.498280	−	0.161901i	0.0490858	−	0.998795i	$-0.484369\pi$
$971$	−483.830	−	157.206i	−0.498280	−	0.161901i	−0.547365	+	0.836894i	$0.684369\pi$
$972$	4.07853	−	0.211321i	0.00419601	−	0.000217408i
$973$	391.408	−	284.375i	0.402270	−	0.292266i
$974$	−299.456	−	412.166i	−0.307449	−	0.423168i
$975$	7.76528	−	147.835i	0.00796439	−	0.151625i
$976$	−153.266	+	471.704i	−0.157035	+	0.483303i
$977$	831.426	−	1144.36i	0.850999	−	1.17130i	−0.132643	−	0.991164i	$-0.542346\pi$
$977$	831.426	−	1144.36i	0.850999	−	1.17130i	0.983642	−	0.180136i	$-0.0576537\pi$
$978$	−260.726	+	678.972i	−0.266590	+	0.694246i
$979$		0			0
$980$			1.63539i			0.00166877i
$981$	−314.784	−	1482.67i	−0.320880	−	1.51139i
$982$	76.2541	−	234.686i	0.0776518	−	0.238988i
$983$	1.06713	−	0.346732i	0.00108559	−	0.000352728i	−0.308474	−	0.951233i	$-0.599818\pi$
$983$	1.06713	−	0.346732i	0.00108559	−	0.000352728i	0.309560	+	0.950880i	$0.399818\pi$
$984$	1307.62	−	350.208i	1.32888	−	0.355903i
$985$	955.985	−	694.564i	0.970543	−	0.705141i
$986$	84.3903	−	27.4201i	0.0855886	−	0.0278094i
$987$	−753.124	−	610.016i	−0.763044	−	0.618051i
$988$	−2.46516	−	1.79105i	−0.00249510	−	0.00181280i
$989$		−	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	$0.756924\pi$
$992$	−7.78130	+	10.7100i	−0.00784405	+	0.0107964i
$993$	−1233.94	+	1523.42i	−1.24264	+	1.53416i
$994$	−130.180	−	400.653i	−0.130966	−	0.403071i
$995$	343.842	+	473.258i	0.345570	+	0.475636i
$996$	0.126544	+	0.472493i	0.000127052	+	0.000474391i
$997$	360.427	+	1109.28i	0.361511	+	1.11262i	0.952137	+	0.305671i	$0.0988808\pi$
$997$	360.427	+	1109.28i	0.361511	+	1.11262i	−0.590626	+	0.806945i	$0.701119\pi$
$998$	124.522	+	40.4598i	0.124772	+	0.0405409i
$999$	−166.496	+	1048.80i	−0.166662	+	1.04985i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.3.h.b.5.2	✓	16	33.2	even	10
33.3.h.b.5.3	yes	16	11.2	odd	10
33.3.h.b.20.2	yes	16	11.7	odd	10
33.3.h.b.20.3	yes	16	33.29	even	10
363.3.b.l.122.3		8	33.5	odd	10
363.3.b.l.122.6		8	11.5	even	5
363.3.b.m.122.3		8	11.6	odd	10
363.3.b.m.122.6		8	33.17	even	10
363.3.h.j.251.2		16	33.26	odd	10
363.3.h.j.251.3		16	11.4	even	5
363.3.h.j.269.2		16	11.9	even	5
363.3.h.j.269.3		16	33.20	odd	10
363.3.h.n.245.2		16	11.3	even	5	inner
363.3.h.n.245.3		16	33.14	odd	10	inner
363.3.h.n.323.2		16	3.2	odd	2	inner
363.3.h.n.323.3		16	1.1	even	1	trivial
363.3.h.o.245.2		16	33.8	even	10
363.3.h.o.245.3		16	11.8	odd	10
363.3.h.o.323.2		16	11.10	odd	2
363.3.h.o.323.3		16	33.32	even	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+(1.17804 - 1.62143i) q^{2} +(1.88824 - 2.33121i) q^{3} +(-0.00519352 - 0.0159840i) q^{4} +(-3.22364 - 4.43696i) q^{5} +(-1.55548 - 5.80790i) q^{6} +(-1.72766 - 5.31721i) q^{7} +(7.59238 + 2.46692i) q^{8} +(-1.86912 - 8.80377i) q^{9} -10.9918 q^{10} +(-0.0470687 - 0.0180744i) q^{12} +(-7.86105 - 5.71139i) q^{13} +(-10.6567 - 3.46258i) q^{14} +(-16.4305 - 0.863040i) q^{15} +(12.9984 - 9.44391i) q^{16} +(10.5047 + 14.4584i) q^{17} +(-16.4766 - 7.34053i) q^{18} +(-5.76592 + 17.7457i) q^{19} +(-0.0541783 + 0.0745701i) q^{20} +(-15.6578 - 6.01259i) q^{21} -12.3649i q^{23} +(20.0871 - 13.0413i) q^{24} +(-1.56932 + 4.82989i) q^{25} +(-18.5212 + 6.01791i) q^{26} +(-24.0528 - 12.2663i) q^{27} +(-0.0760176 + 0.0552300i) q^{28} +(2.35608 - 0.765535i) q^{29} +(-20.7551 + 25.6242i) q^{30} +(-39.8286 - 28.9372i) q^{31} -0.268903i q^{32} +35.8182 q^{34} +(-18.0228 + 24.8063i) q^{35} +(-0.131012 + 0.0755985i) q^{36} +(-12.1539 - 37.4057i) q^{37} +(21.9809 + 30.2541i) q^{38} +(-28.1580 + 7.54133i) q^{39} +(-13.5295 - 41.6395i) q^{40} +(53.7571 + 17.4667i) q^{41} +(-28.1945 + 18.3049i) q^{42} +43.9060 q^{43} +(-33.0366 + 36.6734i) q^{45} +(-20.0488 - 14.5663i) q^{46} +(54.9558 + 17.8562i) q^{47} +(2.52835 - 48.1345i) q^{48} +(14.3540 - 10.4288i) q^{49} +(5.98260 + 8.23434i) q^{50} +(53.5409 + 2.81233i) q^{51} +(-0.0504643 + 0.155313i) q^{52} +(-25.3428 + 34.8814i) q^{53} +(-48.2241 + 24.5498i) q^{54} -44.6323i q^{56} +(30.4815 + 46.9496i) q^{57} +(1.53428 - 4.72204i) q^{58} +(85.6247 - 27.8212i) q^{59} +(0.0715372 + 0.267107i) q^{60} +(-24.9740 + 18.1446i) q^{61} +(-93.8392 + 30.4902i) q^{62} +(-43.5823 + 25.1484i) q^{63} +(51.5577 + 37.4589i) q^{64} +53.2906i q^{65} +34.0775 q^{67} +(0.176547 - 0.242996i) q^{68} +(-28.8251 - 23.3478i) q^{69} +(18.9901 + 58.4456i) q^{70} +(22.0985 + 30.4160i) q^{71} +(7.52711 - 71.4526i) q^{72} +(3.74717 + 11.5326i) q^{73} +(-74.9685 - 24.3587i) q^{74} +(8.29624 + 12.7784i) q^{75} +0.313592 q^{76} +(-20.9434 + 54.5402i) q^{78} +(-51.0852 - 37.1155i) q^{79} +(-83.8045 - 27.2297i) q^{80} +(-74.0128 + 32.9105i) q^{81} +(91.6490 - 66.5869i) q^{82} +(-5.70238 - 7.84865i) q^{83} +(-0.0147863 + 0.281501i) q^{84} +(30.2882 - 93.2174i) q^{85} +(51.7229 - 71.1904i) q^{86} +(2.66420 - 6.93803i) q^{87} -34.1289i q^{89} +(20.5449 + 96.7691i) q^{90} +(-16.7874 + 51.6662i) q^{91} +(-0.197640 + 0.0642171i) q^{92} +(-142.665 + 38.2087i) q^{93} +(93.6927 - 68.0717i) q^{94} +(97.3240 - 31.6225i) q^{95} +(-0.626871 - 0.507754i) q^{96} +(30.5992 + 22.2316i) q^{97} -35.5595i 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

Varieties

Fields

Representations

Groups

Database

Properties

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