LMFDB - Embedded newform 196.4.f.c.31.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [196,4,Mod(19,196)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("196.19"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(196, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 5])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	196.f (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$11.5643743611$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} - 4 x^{15} - 78 x^{14} + 280 x^{13} + 2659 x^{12} - 8424 x^{11} - 49830 x^{10} + 138796 x^{9} + \cdots + 19109188 $ x^16 - 4x^15 - 78x^14 + 280x^13 + 2659x^12 - 8424x^11 - 49830x^10 + 138796x^9 + 531243x^8 - 1328224x^7 - 2933244x^6 + 7183032x^5 + 5477132x^4 - 20299520x^3 + 6548432x^2 + 29088320*x + 19109188
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{26} $
Twist minimal:	no (minimal twist has level 28)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.3
Root			$1.10894 + 1.32242i$ of defining polynomial
Character	$\chi$	$=$	196.31
Dual form			196.4.f.c.19.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0690906 + 2.82758i) q^{2} +(-2.39945 + 4.15597i) q^{3} +(-7.99045 - 0.390719i) q^{4} +(-14.7855 + 8.53640i) q^{5} +(-11.5856 - 7.07178i) q^{6} +(1.65685 - 22.5667i) q^{8} +(1.98528 + 3.43861i) q^{9} +(-23.1158 - 42.3969i) q^{10} +(-35.9149 - 20.7355i) q^{11} +(20.7965 - 32.2706i) q^{12} +45.3599i q^{13} -81.9306i q^{15} +(63.6947 + 6.24404i) q^{16} +(24.4974 + 14.1436i) q^{17} +(-9.86011 + 5.37597i) q^{18} +(20.7717 + 35.9776i) q^{19} +(121.478 - 62.4327i) q^{20} +(61.1127 - 100.120i) q^{22} +(81.3450 - 46.9645i) q^{23} +(89.8109 + 61.0334i) q^{24} +(83.2401 - 144.176i) q^{25} +(-128.259 - 3.13394i) q^{26} -148.625 q^{27} +27.8234 q^{29} +(231.666 + 5.66063i) q^{30} +(-40.7200 + 70.5291i) q^{31} +(-22.0562 + 179.671i) q^{32} +(172.352 - 99.5075i) q^{33} +(-41.6846 + 68.2912i) q^{34} +(-14.5198 - 28.2517i) q^{36} +(-47.4020 - 82.1027i) q^{37} +(-103.165 + 56.2480i) q^{38} +(-188.514 - 108.839i) q^{39} +(168.141 + 347.803i) q^{40} -227.302i q^{41} +171.988i q^{43} +(278.875 + 179.719i) q^{44} +(-58.7066 - 33.8943i) q^{45} +(127.176 + 233.254i) q^{46} +(-143.002 - 247.687i) q^{47} +(-178.782 + 249.731i) q^{48} +(401.919 + 245.330i) q^{50} +(-117.560 + 67.8735i) q^{51} +(17.7230 - 362.446i) q^{52} +(287.960 - 498.762i) q^{53} +(10.2686 - 420.248i) q^{54} +708.025 q^{55} -199.362 q^{57} +(-1.92233 + 78.6729i) q^{58} +(206.000 - 356.802i) q^{59} +(-32.0118 + 654.663i) q^{60} +(-674.623 + 389.494i) q^{61} +(-196.614 - 120.012i) q^{62} +(-506.510 - 74.7794i) q^{64} +(-387.210 - 670.668i) q^{65} +(269.458 + 494.215i) q^{66} +(-172.143 - 99.3867i) q^{67} +(-190.219 - 122.585i) q^{68} +450.756i q^{69} +197.762i q^{71} +(80.8873 - 39.1039i) q^{72} +(-221.347 - 127.795i) q^{73} +(235.427 - 128.361i) q^{74} +(399.461 + 691.887i) q^{75} +(-151.918 - 295.593i) q^{76} +(320.775 - 525.520i) q^{78} +(-1020.60 + 589.244i) q^{79} +(-995.057 + 451.402i) q^{80} +(303.015 - 524.837i) q^{81} +(642.716 + 15.7044i) q^{82} -938.514 q^{83} -482.940 q^{85} +(-486.310 - 11.8827i) q^{86} +(-66.7608 + 115.633i) q^{87} +(-527.437 + 776.125i) q^{88} +(1010.49 - 583.404i) q^{89} +(99.8950 - 163.656i) q^{90} +(-668.333 + 343.485i) q^{92} +(-195.411 - 338.462i) q^{93} +(710.237 - 387.238i) q^{94} +(-614.238 - 354.631i) q^{95} +(-693.783 - 522.776i) q^{96} -656.635i q^{97} -164.663i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{2} + 16 q^{4} - 64 q^{8} - 104 q^{9} - 64 q^{16} - 88 q^{18} + 480 q^{22} + 472 q^{25} - 1184 q^{29} - 256 q^{30} - 1152 q^{32} - 1952 q^{36} - 1392 q^{37} + 1184 q^{44} + 816 q^{46} + 3376 q^{50}+ \cdots + 2304 q^{93}+O(q^{100}) $ 16 * q + 8 * q^2 + 16 * q^4 - 64 * q^8 - 104 * q^9 - 64 * q^16 - 88 * q^18 + 480 * q^22 + 472 * q^25 - 1184 * q^29 - 256 * q^30 - 1152 * q^32 - 1952 * q^36 - 1392 * q^37 + 1184 * q^44 + 816 * q^46 + 3376 * q^50 + 1168 * q^53 - 384 * q^57 + 560 * q^58 - 2944 * q^60 - 6656 * q^64 - 448 * q^65 + 1184 * q^72 + 496 * q^74 + 15360 * q^78 + 4984 * q^81 + 2048 * q^85 - 240 * q^86 - 3776 * q^88 - 7616 * q^92 + 2304 * q^93

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.0690906	+	2.82758i	−0.0244272	+	0.999702i
$2$	−0.0690906	+	2.82758i	−0.0244272	+	0.999702i
$3$	−2.39945	+	4.15597i	−0.461774	+	0.799817i	−0.999049	−	0.0435904i	$-0.986120\pi$
$3$	−2.39945	+	4.15597i	−0.461774	+	0.799817i	0.537275	+	0.843407i	$0.319454\pi$
$4$	−7.99045	−	0.390719i	−0.998807	−	0.0488398i
$5$	−14.7855	+	8.53640i	−1.32245	+	0.763518i	−0.984119	−	0.177508i	$-0.943196\pi$
$5$	−14.7855	+	8.53640i	−1.32245	+	0.763518i	−0.338333	+	0.941026i	$0.609863\pi$
$6$	−11.5856	−	7.07178i	−0.788298	−	0.481174i
$7$		0			0
$7$		0			0
$8$	1.65685	−	22.5667i	0.0732233	−	0.997316i
$9$	1.98528	+	3.43861i	0.0735289	+	0.127356i
$10$	−23.1158	−	42.3969i	−0.730987	−	1.34071i
$11$	−35.9149	−	20.7355i	−0.984432	−	0.568362i	−0.0808269	−	0.996728i	$-0.525756\pi$
$11$	−35.9149	−	20.7355i	−0.984432	−	0.568362i	−0.903605	+	0.428366i	$0.859089\pi$
$12$	20.7965	−	32.2706i	0.500286	−	0.776309i
$13$			45.3599i			0.967737i	0.875141	+	0.483868i	$0.160769\pi$
$13$			45.3599i			0.967737i	−0.875141	+	0.483868i	$0.839231\pi$
$14$		0			0
$15$		−	81.9306i		−	1.41029i
$16$	63.6947	+	6.24404i	0.995229	+	0.0975631i
$17$	24.4974	+	14.1436i	0.349499	+	0.201783i	0.664465	−	0.747320i	$-0.268660\pi$
$17$	24.4974	+	14.1436i	0.349499	+	0.201783i	−0.314966	+	0.949103i	$0.601993\pi$
$18$	−9.86011	+	5.37597i	−0.129114	+	0.0703961i
$19$	20.7717	+	35.9776i	0.250808	+	0.434412i	0.963749	−	0.266812i	$-0.0859704\pi$
$19$	20.7717	+	35.9776i	0.250808	+	0.434412i	−0.712941	+	0.701225i	$0.752637\pi$
$20$	121.478	−	62.4327i	1.35816	−	0.698019i
$21$		0			0
$22$	61.1127	−	100.120i	0.592240	−	0.970255i
$23$	81.3450	−	46.9645i	0.737461	−	0.425773i	−0.0836846	−	0.996492i	$-0.526669\pi$
$23$	81.3450	−	46.9645i	0.737461	−	0.425773i	0.821145	+	0.570719i	$0.193335\pi$
$24$	89.8109	+	61.0334i	0.763857	+	0.519100i
$25$	83.2401	−	144.176i	0.665921	−	1.15341i
$26$	−128.259	−	3.13394i	−0.967448	−	0.0236391i
$27$	−148.625			−1.05936
$28$		0			0
$29$	27.8234			0.178161			0.0890805	−	0.996024i	$-0.471607\pi$
$29$	27.8234			0.178161			0.0890805	+	0.996024i	$0.471607\pi$
$30$	231.666	+	5.66063i	1.40987	+	0.0344495i
$31$	−40.7200	+	70.5291i	−0.235920	+	0.408626i	−0.959540	−	0.281573i	$-0.909144\pi$
$31$	−40.7200	+	70.5291i	−0.235920	+	0.408626i	0.723619	+	0.690199i	$0.242477\pi$
$32$	−22.0562	+	179.671i	−0.121845	+	0.992549i
$33$	172.352	−	99.5075i	0.909171	−	0.524910i
$34$	−41.6846	+	68.2912i	−0.210260	+	0.344466i
$35$		0			0
$36$	−14.5198	−	28.2517i	−0.0672212	−	0.130795i
$37$	−47.4020	−	82.1027i	−0.210617	−	0.364800i	0.741291	−	0.671184i	$-0.234214\pi$
$37$	−47.4020	−	82.1027i	−0.210617	−	0.364800i	−0.951908	+	0.306384i	$0.900881\pi$
$38$	−103.165	+	56.2480i	−0.440409	+	0.240122i
$39$	−188.514	−	108.839i	−0.774012	−	0.446876i
$40$	168.141	+	347.803i	0.664634	+	1.37481i
$41$		−	227.302i		−	0.865820i	−0.901437	−	0.432910i	$-0.857487\pi$
$41$		−	227.302i		−	0.865820i	0.901437	−	0.432910i	$-0.142513\pi$
$42$		0			0
$43$			171.988i			0.609951i	0.952360	+	0.304976i	$0.0986483\pi$
$43$			171.988i			0.609951i	−0.952360	+	0.304976i	$0.901352\pi$
$44$	278.875	+	179.719i	0.955499	+	0.615763i
$45$	−58.7066	−	33.8943i	−0.194477	−	0.112281i
$46$	127.176	+	233.254i	0.407632	+	0.747641i
$47$	−143.002	−	247.687i	−0.443809	−	0.768700i	0.554159	−	0.832411i	$-0.313040\pi$
$47$	−143.002	−	247.687i	−0.443809	−	0.768700i	−0.997968	+	0.0637105i	$0.979707\pi$
$48$	−178.782	+	249.731i	−0.537604	+	0.750949i
$49$		0			0
$50$	401.919	+	245.330i	1.13680	+	0.693897i
$51$	−117.560	+	67.8735i	−0.322779	+	0.186357i
$52$	17.7230	−	362.446i	0.0472641	−	0.966582i
$53$	287.960	−	498.762i	0.746310	−	1.29265i	−0.203271	−	0.979123i	$-0.565157\pi$
$53$	287.960	−	498.762i	0.746310	−	1.29265i	0.949580	−	0.313524i	$-0.101510\pi$
$54$	10.2686	−	420.248i	0.0258773	−	1.05905i
$55$	708.025			1.73582
$56$		0			0
$57$	−199.362			−0.463267
$58$	−1.92233	+	78.6729i	−0.00435198	+	0.178108i
$59$	206.000	−	356.802i	0.454557	−	0.787316i	−0.544106	−	0.839017i	$-0.683131\pi$
$59$	206.000	−	356.802i	0.454557	−	0.787316i	0.998663	+	0.0517011i	$0.0164643\pi$
$60$	−32.0118	+	654.663i	−0.0688785	+	1.40861i
$61$	−674.623	+	389.494i	−1.41601	+	0.817534i	−0.995945	−	0.0899604i	$-0.971326\pi$
$61$	−674.623	+	389.494i	−1.41601	+	0.817534i	−0.420065	+	0.907494i	$0.637993\pi$
$62$	−196.614	−	120.012i	−0.402741	−	0.245832i
$63$		0			0
$64$	−506.510	−	74.7794i	−0.989277	−	0.146053i
$65$	−387.210	−	670.668i	−0.738885	−	1.27979i
$66$	269.458	+	494.215i	0.502545	+	0.921722i
$67$	−172.143	−	99.3867i	−0.313889	−	0.181224i	0.334776	−	0.942298i	$-0.391339\pi$
$67$	−172.143	−	99.3867i	−0.313889	−	0.181224i	−0.648666	+	0.761074i	$0.724673\pi$
$68$	−190.219	−	122.585i	−0.339227	−	0.218612i
$69$			450.756i			0.786444i
$70$		0			0
$71$			197.762i			0.330564i	0.986246	+	0.165282i	$0.0528534\pi$
$71$			197.762i			0.330564i	−0.986246	+	0.165282i	$0.947147\pi$
$72$	80.8873	−	39.1039i	0.132398	−	0.0640061i
$73$	−221.347	−	127.795i	−0.354886	−	0.204894i	0.311949	−	0.950099i	$-0.399018\pi$
$73$	−221.347	−	127.795i	−0.354886	−	0.204894i	−0.666835	+	0.745205i	$0.732352\pi$
$74$	235.427	−	128.361i	0.369836	−	0.201644i
$75$	399.461	+	691.887i	0.615010	+	1.06523i
$76$	−151.918	−	295.593i	−0.229292	−	0.446143i
$77$		0			0
$78$	320.775	−	525.520i	0.465650	−	0.762865i
$79$	−1020.60	+	589.244i	−1.45350	+	0.839179i	−0.998678	−	0.0514035i	$-0.983631\pi$
$79$	−1020.60	+	589.244i	−1.45350	+	0.839179i	−0.454822	+	0.890582i	$0.650297\pi$
$80$	−995.057	+	451.402i	−1.39064	+	0.630853i
$81$	303.015	−	524.837i	0.415658	−	0.719941i
$82$	642.716	+	15.7044i	0.865562	+	0.0211496i
$83$	−938.514			−1.24115			−0.620574	−	0.784148i	$-0.713100\pi$
$83$	−938.514			−1.24115			−0.620574	+	0.784148i	$0.713100\pi$
$84$		0			0
$85$	−482.940			−0.616261
$86$	−486.310	−	11.8827i	−0.609769	−	0.0148994i
$87$	−66.7608	+	115.633i	−0.0822702	+	0.142496i
$88$	−527.437	+	776.125i	−0.638920	+	0.940172i
$89$	1010.49	−	583.404i	1.20350	−	0.694840i	0.242166	−	0.970235i	$-0.422142\pi$
$89$	1010.49	−	583.404i	1.20350	−	0.694840i	0.961331	+	0.275395i	$0.0888087\pi$
$90$	99.8950	−	163.656i	0.116998	−	0.191676i
$91$		0			0
$92$	−668.333	+	343.485i	−0.757375	+	0.389248i
$93$	−195.411	−	338.462i	−0.217884	−	0.377386i
$94$	710.237	−	387.238i	0.779312	−	0.424900i
$95$	−614.238	−	354.631i	−0.663363	−	0.382993i
$96$	−693.783	−	522.776i	−0.737593	−	0.555787i
$97$		−	656.635i		−	0.687332i	−0.939092	−	0.343666i	$-0.888331\pi$
$97$		−	656.635i		−	0.687332i	0.939092	−	0.343666i	$-0.111669\pi$
$98$		0			0
$99$		−	164.663i		−	0.167164i
$100$	−721.459	+	1119.51i	−0.721459	+	1.11951i
$101$	865.528	+	499.713i	0.852706	+	0.492310i	0.861563	−	0.507651i	$-0.169486\pi$
$101$	865.528	+	499.713i	0.852706	+	0.492310i	−0.00885711	+	0.999961i	$0.502819\pi$
$102$	−183.796	−	337.101i	−0.178417	−	0.327235i
$103$	−479.466	−	830.460i	−0.458672	−	0.794443i	0.540219	−	0.841524i	$-0.318341\pi$
$103$	−479.466	−	830.460i	−0.458672	−	0.794443i	−0.998891	+	0.0470813i	$0.985008\pi$
$104$	1023.62	+	75.1548i	0.965139	+	0.0708609i
$105$		0			0
$106$	1390.40	+	848.692i	1.27403	+	0.777663i
$107$	−594.001	+	342.946i	−0.536675	+	0.309849i	−0.743730	−	0.668480i	$-0.766945\pi$
$107$	−594.001	+	342.946i	−0.536675	+	0.309849i	0.207055	+	0.978329i	$0.433612\pi$
$108$	1187.58	+	58.0704i	1.05810	+	0.0517391i
$109$	−563.902	+	976.706i	−0.495523	+	0.858271i	−0.999987	−	0.00516223i	$-0.998357\pi$
$109$	−563.902	+	976.706i	−0.495523	+	0.858271i	0.504464	+	0.863433i	$0.331690\pi$
$110$	−48.9179	+	2002.00i	−0.0424012	+	1.73530i
$111$	454.955			0.389031
$112$		0			0
$113$	−10.0488			−0.00836557			−0.00418278	−	0.999991i	$-0.501331\pi$
$113$	−10.0488			−0.00836557			−0.00418278	+	0.999991i	$0.501331\pi$
$114$	13.7741	−	563.714i	0.0113163	−	0.463129i
$115$	−801.816	+	1388.79i	−0.650171	+	1.12613i
$116$	−222.321	−	10.8711i	−0.177948	−	0.00870136i
$117$	−155.975	+	90.0522i	−0.123247	+	0.0711567i
$118$	994.654	+	607.132i	0.775977	+	0.473653i
$119$		0			0
$120$	−1848.90	−	135.747i	−1.40651	−	0.103266i
$121$	194.421	+	336.747i	0.146071	+	0.253003i
$122$	−1054.72	−	1934.46i	−0.782701	−	1.43556i
$123$	944.661	+	545.400i	0.692498	+	0.399814i
$124$	352.928	−	547.650i	0.255596	−	0.396616i
$125$			708.183i			0.506735i
$126$		0			0
$127$			1347.06i			0.941198i	0.882347	+	0.470599i	$0.155962\pi$
$127$			1347.06i			0.941198i	−0.882347	+	0.470599i	$0.844038\pi$
$128$	246.440	−	1427.03i	0.170175	−	0.985414i
$129$	−714.776	−	412.676i	−0.487849	−	0.281660i
$130$	1923.12	−	1048.53i	1.29745	−	0.707403i
$131$	−240.133	−	415.922i	−0.160156	−	0.277399i	0.774768	−	0.632245i	$-0.217867\pi$
$131$	−240.133	−	415.922i	−0.160156	−	0.277399i	−0.934925	+	0.354846i	$0.884533\pi$
$132$	−1416.05	+	727.769i	−0.933723	+	0.479880i
$133$		0			0
$134$	292.918	−	479.881i	0.188838	−	0.309369i
$135$	2197.49	−	1268.72i	1.40096	−	0.808844i
$136$	359.762	−	529.390i	0.226833	−	0.333786i
$137$	123.902	−	214.604i	0.0772674	−	0.133831i	−0.824803	−	0.565421i	$-0.808714\pi$
$137$	123.902	−	214.604i	0.0772674	−	0.133831i	0.902070	+	0.431590i	$0.142047\pi$
$138$	−1274.55	−	31.1430i	−0.786210	−	0.0192106i
$139$	−1842.35			−1.12422			−0.562109	−	0.827063i	$-0.690010\pi$
$139$	−1842.35			−1.12422			−0.562109	+	0.827063i	$0.690010\pi$
$140$		0			0
$141$	1372.51			0.819759
$142$	−559.189	−	13.6635i	−0.330465	−	0.00807475i
$143$	940.560	−	1629.10i	0.550025	−	0.952671i
$144$	104.981	+	231.417i	0.0607529	+	0.133922i
$145$	−411.382	+	237.511i	−0.235610	+	0.136029i
$146$	376.643	−	617.047i	0.213501	−	0.349775i
$147$		0			0
$148$	346.685	+	674.559i	0.192549	+	0.374651i
$149$	1100.41	+	1905.97i	0.605028	+	1.04794i	0.992047	+	0.125868i	$0.0401715\pi$
$149$	1100.41	+	1905.97i	0.605028	+	1.04794i	−0.387019	+	0.922072i	$0.626495\pi$
$150$	−1983.97	+	1081.71i	−1.07993	+	0.588806i
$151$	2779.04	+	1604.48i	1.49771	+	0.864706i	0.999997	−	0.00263344i	$-0.000838251\pi$
$151$	2779.04	+	1604.48i	1.49771	+	0.864706i	0.497718	+	0.867339i	$0.334172\pi$
$152$	846.311	−	409.138i	0.451611	−	0.218326i
$153$			112.316i			0.0593477i
$154$		0			0
$155$		−	1390.41i		−	0.720518i
$156$	1463.79	+	943.328i	0.751263	+	0.484145i
$157$	−551.266	−	318.273i	−0.280228	−	0.161790i	0.353299	−	0.935511i	$-0.385060\pi$
$157$	−551.266	−	318.273i	−0.280228	−	0.161790i	−0.633527	+	0.773721i	$0.718393\pi$
$158$	−1595.62	−	2926.54i	−0.803423	−	1.47357i
$159$	1381.89	+	2393.51i	0.689253	+	1.19382i
$160$	−1207.63	−	2844.80i	−0.596696	−	1.40563i
$161$		0			0
$162$	1463.08	+	893.061i	0.709573	+	0.433120i
$163$	2130.75	−	1230.19i	1.02389	−	0.591141i	0.108660	−	0.994079i	$-0.465344\pi$
$163$	2130.75	−	1230.19i	1.02389	−	0.591141i	0.915227	+	0.402938i	$0.132011\pi$
$164$	−88.8112	+	1816.25i	−0.0422865	+	0.864787i
$165$	−1698.87	+	2942.53i	−0.801557	+	1.38834i
$166$	64.8424	−	2653.73i	0.0303178	−	1.24078i
$167$	2133.16			0.988435			0.494218	−	0.869338i	$-0.335455\pi$
$167$	2133.16			0.988435			0.494218	+	0.869338i	$0.335455\pi$
$168$		0			0
$169$	139.478			0.0634855
$170$	33.3666	−	1365.55i	0.0150535	−	0.616078i
$171$	−82.4753	+	142.851i	−0.0368833	+	0.0638837i
$172$	67.1989	−	1374.26i	0.0297899	−	0.609223i
$173$	−1266.76	+	731.366i	−0.556706	+	0.321415i	−0.751822	−	0.659366i	$-0.770825\pi$
$173$	−1266.76	+	731.366i	−0.556706	+	0.321415i	0.195116	+	0.980780i	$0.437492\pi$
$174$	−322.350	−	196.761i	−0.140444	−	0.0857264i
$175$		0			0
$176$	−2158.12	−	1544.99i	−0.924285	−	0.661695i
$177$	988.571	+	1712.26i	0.419805	+	0.727124i
$178$	1579.81	+	2897.54i	0.665234	+	1.22011i
$179$	−2631.82	−	1519.48i	−1.09895	−	0.634478i	−0.163003	−	0.986626i	$-0.552118\pi$
$179$	−2631.82	−	1519.48i	−1.09895	−	0.634478i	−0.935944	+	0.352148i	$0.885451\pi$
$180$	455.850	+	293.769i	0.188761	+	0.121646i
$181$			384.978i			0.158095i	0.996871	+	0.0790475i	$0.0251879\pi$
$181$			384.978i			0.158095i	−0.996871	+	0.0790475i	$0.974812\pi$
$182$		0			0
$183$		−	3738.28i		−	1.51006i
$184$	−925.057	−	1913.50i	−0.370631	−	0.766658i
$185$	1401.72	+	809.285i	0.557063	+	0.321621i
$186$	970.531	−	529.157i	0.382596	−	0.208600i
$187$	−586.547	−	1015.93i	−0.229372	−	0.397284i
$188$	1045.88	+	2035.01i	0.405736	+	0.789459i
$189$		0			0
$190$	1045.19	−	1712.31i	0.399083	−	0.653810i
$191$	437.867	−	252.802i	0.165879	−	0.0957704i	−0.414762	−	0.909930i	$-0.636135\pi$
$191$	437.867	−	252.802i	0.165879	−	0.0957704i	0.580641	+	0.814159i	$0.302802\pi$
$192$	1526.13	−	1925.61i	0.573639	−	0.723796i
$193$	−960.954	+	1664.42i	−0.358399	+	0.620765i	−0.987694	−	0.156402i	$-0.950011\pi$
$193$	−960.954	+	1664.42i	−0.358399	+	0.620765i	0.629295	+	0.777167i	$0.283344\pi$
$194$	1856.69	+	45.3673i	0.687127	+	0.0167896i
$195$	3716.37			1.36479
$196$		0			0
$197$	1603.63			0.579968			0.289984	−	0.957031i	$-0.406350\pi$
$197$	1603.63			0.579968			0.289984	+	0.957031i	$0.406350\pi$
$198$	465.599	+	11.3767i	0.167114	+	0.00408336i
$199$	1279.38	−	2215.95i	0.455742	−	0.789368i	−0.542989	−	0.839740i	$-0.682707\pi$
$199$	1279.38	−	2215.95i	0.455742	−	0.789368i	0.998731	+	0.0503720i	$0.0160407\pi$
$200$	−3115.66	−	2117.33i	−1.10155	−	0.748590i
$201$	826.096	−	476.947i	0.289892	−	0.167369i
$202$	−1472.78	+	2412.83i	−0.512992	+	0.840426i
$203$		0			0
$204$	965.881	−	496.407i	0.331496	−	0.170370i
$205$	1940.34	+	3360.77i	0.661070	+	1.14501i
$206$	2381.32	−	1298.35i	0.805410	−	0.439129i
$207$	322.985	+	186.476i	0.108449	+	0.0626133i
$208$	−283.229	+	2889.19i	−0.0944154	+	0.963120i
$209$		−	1722.84i		−	0.570199i
$210$		0			0
$211$			381.389i			0.124436i	0.998063	+	0.0622178i	$0.0198173\pi$
$211$			381.389i			0.124436i	−0.998063	+	0.0622178i	$0.980183\pi$
$212$	−2495.81	+	3872.82i	−0.808552	+	1.25465i
$213$	−821.893	−	474.520i	−0.264391	−	0.152646i
$214$	−928.670	−	1703.28i	−0.296647	−	0.544083i
$215$	−1468.16	−	2542.92i	−0.465709	−	0.806632i
$216$	−246.249	+	3353.96i	−0.0775701	+	1.05652i
$217$		0			0
$218$	−2722.76	−	1661.96i	−0.845910	−	0.516340i
$219$	1062.22	−	613.274i	0.327755	−	0.189229i
$220$	−5657.44	−	276.639i	−1.73375	−	0.0847772i
$221$	−641.551	+	1111.20i	−0.195273	+	0.338223i
$222$	−31.4331	+	1286.42i	−0.00950294	+	0.388915i
$223$	−2943.88			−0.884023			−0.442011	−	0.897009i	$-0.645735\pi$
$223$	−2943.88			−0.884023			−0.442011	+	0.897009i	$0.645735\pi$
$224$		0			0
$225$	661.020			0.195858
$226$	0.694275	−	28.4137i	0.000204347	−	0.00836307i
$227$	−2893.05	+	5010.91i	−0.845897	+	1.46514i	0.0389429	+	0.999241i	$0.487601\pi$
$227$	−2893.05	+	5010.91i	−0.845897	+	1.46514i	−0.884840	+	0.465895i	$0.845732\pi$
$228$	1593.00	+	77.8946i	0.462714	+	0.0226259i
$229$	3727.24	−	2151.93i	1.07556	−	0.620975i	0.145865	−	0.989305i	$-0.453404\pi$
$229$	3727.24	−	2151.93i	1.07556	−	0.620975i	0.929695	+	0.368330i	$0.120070\pi$
$230$	−3871.51	−	2363.15i	−1.10991	−	0.677486i
$231$		0			0
$232$	46.0993	−	627.881i	0.0130455	−	0.177683i
$233$	−2566.96	−	4446.10i	−0.721747	−	1.25010i	−0.960299	−	0.278972i	$-0.910006\pi$
$233$	−2566.96	−	4446.10i	−0.721747	−	1.25010i	0.238552	−	0.971130i	$-0.423327\pi$
$234$	−243.854	−	447.254i	−0.0681249	−	0.124948i
$235$	4228.71	+	2441.45i	1.17383	+	0.677713i
$236$	−1785.44	+	2770.52i	−0.492467	+	0.764175i
$237$		−	5655.44i		−	1.55004i
$238$		0			0
$239$		−	468.448i		−	0.126784i	−0.997989	−	0.0633920i	$-0.979808\pi$
$239$		−	468.448i		−	0.126784i	0.997989	−	0.0633920i	$-0.0201919\pi$
$240$	511.578	−	5218.54i	0.137593	−	1.40356i
$241$	−337.318	−	194.751i	−0.0901600	−	0.0520539i	0.454242	−	0.890878i	$-0.349910\pi$
$241$	−337.318	−	194.751i	−0.0901600	−	0.0520539i	−0.544402	+	0.838824i	$0.683243\pi$
$242$	−965.613	+	526.475i	−0.256496	+	0.139848i
$243$	−552.295	−	956.603i	−0.145801	−	0.252536i
$244$	5542.72	−	2848.64i	1.45425	−	0.747400i
$245$		0			0
$246$	−1607.43	+	2633.42i	−0.416610	+	0.682525i
$247$	−1631.94	+	942.202i	−0.420397	+	0.242716i
$248$	1524.14	+	1035.77i	0.390254	+	0.265208i
$249$	2251.92	−	3900.43i	0.573130	−	0.992691i
$250$	−2002.45	−	48.9288i	−0.506584	−	0.0123781i
$251$	−4690.59			−1.17955			−0.589776	−	0.807567i	$-0.700784\pi$
$251$	−4690.59			−1.17955			−0.589776	+	0.807567i	$0.700784\pi$
$252$		0			0
$253$	−3895.33			−0.967974
$254$	−3808.92	−	93.0690i	−0.940917	−	0.0229908i
$255$	1158.79	−	2007.08i	0.284574	−	0.492896i
$256$	4018.02	+	795.424i	0.980963	+	0.194195i
$257$	−4523.48	+	2611.63i	−1.09793	+	0.633888i	−0.935676	−	0.352861i	$-0.885209\pi$
$257$	−4523.48	+	2611.63i	−1.09793	+	0.633888i	−0.162251	+	0.986750i	$0.551875\pi$
$258$	1216.26	−	1992.58i	0.293493	−	0.480823i
$259$		0			0
$260$	2831.94	+	5510.23i	0.675499	+	1.31435i
$261$	55.2372	+	95.6737i	0.0131000	+	0.0226899i
$262$	1192.64	−	650.259i	0.281228	−	0.153333i
$263$	−4074.48	−	2352.40i	−0.955297	−	0.551541i	−0.0605744	−	0.998164i	$-0.519293\pi$
$263$	−4074.48	−	2352.40i	−0.955297	−	0.551541i	−0.894722	+	0.446623i	$0.852627\pi$
$264$	−1959.99	−	4054.28i	−0.456929	−	0.945166i
$265$			9832.58i			2.27928i
$266$		0			0
$267$			5599.40i			1.28344i
$268$	1336.67	+	861.404i	0.304664	+	0.196338i
$269$	−2983.05	−	1722.26i	−0.676132	−	0.390365i	0.122264	−	0.992498i	$-0.460985\pi$
$269$	−2983.05	−	1722.26i	−0.676132	−	0.390365i	−0.798396	+	0.602132i	$0.794318\pi$
$270$	3435.58	+	6301.23i	0.774381	+	1.42030i
$271$	2625.89	+	4548.17i	0.588603	+	1.01949i	0.994416	+	0.105534i	$0.0336553\pi$
$271$	2625.89	+	4548.17i	0.588603	+	1.01949i	−0.405813	+	0.913956i	$0.633011\pi$
$272$	1472.04	+	1053.83i	0.328145	+	0.234919i
$273$		0			0
$274$	598.250	+	365.169i	0.131904	+	0.0805134i
$275$	−5979.12	+	3452.05i	−1.31111	+	0.756969i
$276$	176.119	−	3601.75i	0.0384098	−	0.785506i
$277$	−3001.60	+	5198.92i	−0.651077	+	1.12770i	0.331785	+	0.943355i	$0.392349\pi$
$277$	−3001.60	+	5198.92i	−0.651077	+	1.12770i	−0.982862	+	0.184344i	$0.940984\pi$
$278$	127.289	−	5209.41i	0.0274615	−	1.12388i
$279$	−323.363			−0.0693879
$280$		0			0
$281$	−1870.63			−0.397125			−0.198563	−	0.980088i	$-0.563627\pi$
$281$	−1870.63			−0.397125			−0.198563	+	0.980088i	$0.563627\pi$
$282$	−94.8273	+	3880.88i	−0.0200244	+	0.819514i
$283$	1981.71	−	3432.42i	0.416256	−	0.720976i	−0.579304	−	0.815112i	$-0.696675\pi$
$283$	1981.71	−	3432.42i	0.416256	−	0.720976i	0.995559	+	0.0941357i	$0.0300087\pi$
$284$	77.2693	−	1580.21i	0.0161447	−	0.330169i
$285$	2947.67	−	1701.84i	0.612648	−	0.353713i
$286$	4541.43	+	2772.07i	0.938952	+	0.573132i
$287$		0			0
$288$	−661.605	+	280.854i	−0.135366	+	0.0574635i
$289$	−2056.42	−	3561.82i	−0.418567	−	0.724979i
$290$	−643.161	−	1179.63i	−0.130233	−	0.238862i
$291$	2728.95	+	1575.56i	0.549739	+	0.317392i
$292$	1718.73	+	1107.62i	0.344456	+	0.221982i
$293$			4654.67i			0.928084i	0.885813	+	0.464042i	$0.153601\pi$
$293$			4654.67i			0.928084i	−0.885813	+	0.464042i	$0.846399\pi$
$294$		0			0
$295$			7033.97i			1.38825i
$296$	−1931.32	+	933.674i	−0.379243	+	0.183340i
$297$	5337.84	+	3081.80i	1.04287	+	0.602102i
$298$	−5465.31	+	2979.82i	−1.06241	+	0.579249i
$299$	2130.31	+	3689.80i	0.412036	+	0.713668i
$300$	−2921.54	−	5684.56i	−0.562251	−	1.09399i
$301$		0			0
$302$	−4728.80	+	7747.10i	−0.901033	+	1.47614i
$303$	−4153.58	+	2398.07i	−0.787515	+	0.454672i
$304$	1098.40	+	2421.28i	0.207229	+	0.456809i
$305$	6649.75	−	11517.7i	1.24840	−	2.16230i
$306$	−317.582	−	7.75996i	−0.0593300	−	0.00144970i
$307$	2828.15			0.525769			0.262884	−	0.964827i	$-0.415326\pi$
$307$	2828.15			0.525769			0.262884	+	0.964827i	$0.415326\pi$
$308$		0			0
$309$	4601.82			0.847212
$310$	3931.50	+	96.0641i	0.720303	+	0.0176002i
$311$	−3279.55	+	5680.35i	−0.597962	+	1.03570i	0.395160	+	0.918613i	$0.370689\pi$
$311$	−3279.55	+	5680.35i	−0.597962	+	1.03570i	−0.993122	+	0.117088i	$0.962644\pi$
$312$	−2768.47	+	4073.81i	−0.502352	+	0.739212i
$313$	−5384.22	+	3108.58i	−0.972314	+	0.561366i	−0.899941	−	0.436012i	$-0.856391\pi$
$313$	−5384.22	+	3108.58i	−0.972314	+	0.561366i	−0.0723733	+	0.997378i	$0.523057\pi$
$314$	938.031	−	1536.76i	0.168587	−	0.276192i
$315$		0			0
$316$	8385.29	−	4309.56i	1.49275	−	0.767189i
$317$	−1627.42	−	2818.77i	−0.288344	−	0.499426i	0.685071	−	0.728476i	$-0.259771\pi$
$317$	−1627.42	−	2818.77i	−0.288344	−	0.499426i	−0.973415	+	0.229051i	$0.926438\pi$
$318$	−6863.32	+	3742.05i	−1.21030	+	0.659886i
$319$	−999.274	−	576.931i	−0.175388	−	0.101260i
$320$	8127.33	−	3218.12i	1.41979	−	0.562182i
$321$		−	3291.53i		−	0.572322i
$322$		0			0
$323$			1175.14i			0.202436i
$324$	−2626.29	+	4075.29i	−0.450324	+	0.698781i
$325$	6539.82	+	3775.76i	1.11620	+	0.644436i
$326$	3331.25	+	6109.88i	0.565954	+	1.03802i
$327$	−2706.11	−	4687.11i	−0.457639	−	0.792655i
$328$	−5129.45	−	376.607i	−0.863496	−	0.0633982i
$329$		0			0
$330$	−8202.88	−	5007.00i	−1.36834	−	0.835231i
$331$	3797.79	−	2192.65i	0.630651	−	0.364106i	−0.150353	−	0.988632i	$-0.548041\pi$
$331$	3797.79	−	2192.65i	0.630651	−	0.364106i	0.781004	+	0.624526i	$0.214708\pi$
$332$	7499.15	+	366.695i	1.23967	+	0.0606174i
$333$	188.213	−	325.994i	0.0309729	−	0.0536467i
$334$	−147.381	+	6031.68i	−0.0241447	+	0.988140i
$335$	3393.62			0.553472
$336$		0			0
$337$	−9569.41			−1.54682			−0.773411	−	0.633905i	$-0.781451\pi$
$337$	−9569.41			−1.54682			−0.773411	+	0.633905i	$0.781451\pi$
$338$	−9.63659	+	394.385i	−0.00155077	+	0.0634666i
$339$	24.1115	−	41.7624i	0.00386300	−	0.00669092i
$340$	3858.91	+	188.694i	0.615526	+	0.0300981i
$341$	2924.91	−	1688.70i	0.464495	−	0.268176i
$342$	−398.226	−	243.075i	−0.0629637	−	0.0384328i
$343$		0			0
$344$	3881.19	+	284.959i	0.608314	+	0.0446626i
$345$	−3847.83	−	6664.64i	−0.600465	−	1.04004i
$346$	−1980.48	−	3632.41i	−0.307720	−	0.564391i
$347$	−9015.01	−	5204.82i	−1.39467	−	0.805214i	−0.400843	−	0.916147i	$-0.631283\pi$
$347$	−9015.01	−	5204.82i	−1.39467	−	0.805214i	−0.993828	+	0.110933i	$0.964616\pi$
$348$	578.629	−	897.876i	0.0891315	−	0.138308i
$349$		−	12612.4i		−	1.93446i	−0.253895	−	0.967232i	$-0.581712\pi$
$349$		−	12612.4i		−	1.93446i	0.253895	−	0.967232i	$-0.418288\pi$
$350$		0			0
$351$		−	6741.60i		−	1.02519i
$352$	4517.71	−	5995.51i	0.684075	−	0.907846i
$353$	−8965.19	−	5176.06i	−1.35175	−	0.780435i	−0.363259	−	0.931688i	$-0.618336\pi$
$353$	−8965.19	−	5176.06i	−1.35175	−	0.780435i	−0.988495	+	0.151253i	$0.951669\pi$
$354$	−4909.84	+	2676.97i	−0.737162	+	0.401918i
$355$	−1688.18	−	2924.01i	−0.252392	−	0.437155i
$356$	−8302.18	+	4266.85i	−1.23600	+	0.635232i
$357$		0			0
$358$	4478.30	−	7336.72i	0.661133	−	1.08312i
$359$	−3223.20	+	1860.92i	−0.473855	+	0.273580i	−0.717852	−	0.696196i	$-0.754875\pi$
$359$	−3223.20	+	1860.92i	−0.473855	+	0.273580i	0.243997	+	0.969776i	$0.421541\pi$
$360$	−862.150	+	1268.66i	−0.126220	+	0.185733i
$361$	2566.57	−	4445.44i	0.374191	−	0.648117i
$362$	−1088.56	−	26.5983i	−0.158048	−	0.00386182i
$363$	−1866.01			−0.269808
$364$		0			0
$365$	4363.62			0.625760
$366$	10570.3	+	258.280i	1.50961	+	0.0368866i
$367$	−2338.05	+	4049.63i	−0.332549	+	0.575991i	−0.983011	−	0.183547i	$-0.941242\pi$
$367$	−2338.05	+	4049.63i	−0.332549	+	0.575991i	0.650462	+	0.759539i	$0.274575\pi$
$368$	5474.49	−	2483.47i	0.775482	−	0.351793i
$369$	781.603	−	451.259i	0.110267	−	0.0636629i
$370$	−2385.17	+	3907.57i	−0.335132	+	0.549041i
$371$		0			0
$372$	1429.18	+	2780.82i	0.199192	+	0.387577i
$373$	3300.97	+	5717.44i	0.458224	+	0.793668i	0.998867	−	0.0475845i	$-0.0151523\pi$
$373$	3300.97	+	5717.44i	0.458224	+	0.793668i	−0.540643	+	0.841252i	$0.681819\pi$
$374$	2913.15	−	1588.32i	0.402769	−	0.219599i
$375$	−2943.19	−	1699.25i	−0.405295	−	0.233997i
$376$	−5826.41	+	2816.71i	−0.799134	+	0.386331i
$377$			1262.07i			0.172413i
$378$		0			0
$379$		−	12756.2i		−	1.72887i	−0.502747	−	0.864434i	$-0.667677\pi$
$379$		−	12756.2i		−	1.72887i	0.502747	−	0.864434i	$-0.332323\pi$
$380$	4769.48	+	3073.65i	0.643867	+	0.414935i
$381$	−5598.33	−	3232.20i	−0.752786	−	0.434621i
$382$	684.567	+	1255.57i	0.0916898	+	0.168169i
$383$	−786.757	−	1362.70i	−0.104965	−	0.181804i	0.808759	−	0.588140i	$-0.200140\pi$
$383$	−786.757	−	1362.70i	−0.104965	−	0.181804i	−0.913724	+	0.406336i	$0.866806\pi$
$384$	5339.38	+	4448.29i	0.709568	+	0.591148i
$385$		0			0
$386$	−4639.89	−	2832.17i	−0.611825	−	0.373455i
$387$	−591.399	+	341.444i	−0.0776809	+	0.0448491i
$388$	−256.559	+	5246.81i	−0.0335692	+	0.686511i
$389$	2011.47	−	3483.98i	0.262174	−	0.454099i	−0.704645	−	0.709560i	$-0.748894\pi$
$389$	2011.47	−	3483.98i	0.262174	−	0.454099i	0.966819	+	0.255461i	$0.0822271\pi$
$390$	−256.766	+	10508.3i	−0.0333381	+	1.36439i
$391$	2656.98			0.343656
$392$		0			0
$393$	2304.74			0.295824
$394$	−110.796	+	4534.39i	−0.0141670	+	0.579795i
$395$	10060.0	−	17424.5i	1.28146	−	2.21955i
$396$	−64.3369	+	1315.73i	−0.00816428	+	0.166965i
$397$	3453.12	−	1993.66i	0.436542	−	0.252038i	−0.265588	−	0.964087i	$-0.585566\pi$
$397$	3453.12	−	1993.66i	0.436542	−	0.252038i	0.702130	+	0.712049i	$0.252233\pi$
$398$	6177.38	+	3770.65i	0.778000	+	0.474888i
$399$		0			0
$400$	6202.19	−	8663.50i	0.775274	−	1.08294i
$401$	−2312.23	−	4004.90i	−0.287948	−	0.498741i	0.685372	−	0.728194i	$-0.259640\pi$
$401$	−2312.23	−	4004.90i	−0.287948	−	0.498741i	−0.973320	+	0.229452i	$0.926306\pi$
$402$	1291.53	+	2368.81i	0.160238	+	0.293894i
$403$	−3199.20	−	1847.06i	−0.395442	−	0.228309i
$404$	−6720.72	−	4331.11i	−0.827644	−	0.533368i
$405$			10346.6i			1.26945i
$406$		0			0
$407$			3931.62i			0.478828i
$408$	1336.90	+	2765.40i	0.162222	+	0.335559i
$409$	−548.219	−	316.514i	−0.0662779	−	0.0382656i	0.466495	−	0.884524i	$-0.345517\pi$
$409$	−548.219	−	316.514i	−0.0662779	−	0.0382656i	−0.532773	+	0.846258i	$0.678850\pi$
$410$	−9636.92	+	5254.28i	−1.16081	+	0.632903i
$411$	594.591	+	1029.86i	0.0713602	+	0.123599i
$412$	3506.68	+	6823.09i	0.419324	+	0.815896i
$413$		0			0
$414$	−549.591	+	900.384i	−0.0652437	+	0.106888i
$415$	13876.4	−	8011.53i	1.64136	−	0.947639i
$416$	−8149.84	−	1000.47i	−0.960526	−	0.117914i
$417$	4420.64	−	7656.76i	0.519135	−	0.899169i
$418$	4871.49	+	119.032i	0.570029	+	0.0139284i
$419$	3197.39			0.372799			0.186399	−	0.982474i	$-0.440318\pi$
$419$	3197.39			0.372799			0.186399	+	0.982474i	$0.440318\pi$
$420$		0			0
$421$	−5489.09			−0.635444			−0.317722	−	0.948184i	$-0.602918\pi$
$421$	−5489.09			−0.635444			−0.317722	+	0.948184i	$0.602918\pi$
$422$	−1078.41	−	26.3504i	−0.124398	−	0.00303961i
$423$	567.800	−	983.458i	0.0652657	−	0.113043i
$424$	−10778.3	−	7324.69i	−1.23453	−	0.838958i
$425$	4078.33	−	2354.62i	0.465478	−	0.268744i
$426$	1398.53	−	2291.19i	0.159059	−	0.260583i
$427$		0			0
$428$	4880.33	−	2508.21i	0.551167	−	0.283268i
$429$	4513.65	+	7817.88i	0.507975	+	0.879838i
$430$	7291.76	−	3975.64i	0.817767	−	0.445866i
$431$	3618.55	+	2089.17i	0.404406	+	0.233484i	0.688384	−	0.725347i	$-0.258321\pi$
$431$	3618.55	+	2089.17i	0.404406	+	0.233484i	−0.283977	+	0.958831i	$0.591654\pi$
$432$	−9466.60	−	928.018i	−1.05431	−	0.103355i
$433$		−	9306.18i		−	1.03286i	−0.856331	−	0.516428i	$-0.827261\pi$
$433$		−	9306.18i		−	1.03286i	0.856331	−	0.516428i	$-0.172739\pi$
$434$		0			0
$435$		−	2279.59i		−	0.251259i
$436$	4887.45	−	7584.00i	0.536849	−	0.833045i
$437$	3379.34	+	1951.07i	0.369922	+	0.213575i
$438$	1660.69	+	3045.89i	0.181167	+	0.332279i
$439$	−1465.71	−	2538.69i	−0.159350	−	0.276002i	0.775285	−	0.631612i	$-0.217606\pi$
$439$	−1465.71	−	2538.69i	−0.159350	−	0.276002i	−0.934634	+	0.355610i	$0.884273\pi$
$440$	1173.09	−	15977.8i	0.127103	−	1.73116i
$441$		0			0
$442$	−3097.68	−	1890.81i	−0.333352	−	0.203477i
$443$	−5095.95	+	2942.15i	−0.546537	+	0.315543i	−0.747724	−	0.664010i	$-0.768853\pi$
$443$	−5095.95	+	2942.15i	−0.546537	+	0.315543i	0.201187	+	0.979553i	$0.435520\pi$
$444$	−3635.30	−	177.759i	−0.388567	−	0.0190002i
$445$	−9960.34	+	17251.8i	−1.06105	+	1.83778i
$446$	203.395	−	8324.08i	0.0215942	−	0.883759i
$447$	−10561.5			−1.11755
$448$		0			0
$449$	12856.4			1.35129			0.675646	−	0.737227i	$-0.263865\pi$
$449$	12856.4			1.35129			0.675646	+	0.737227i	$0.263865\pi$
$450$	−45.6703	+	1869.09i	−0.00478426	+	0.195799i
$451$	−4713.22	+	8163.54i	−0.492100	+	0.852342i
$452$	80.2943	+	3.92624i	0.00835558	+	0.000408573i
$453$	−13336.3	+	7699.73i	−1.38321	+	0.798598i
$454$	−13968.9	−	8526.55i	−1.44404	−	0.881434i
$455$		0			0
$456$	−330.315	+	4498.95i	−0.0339219	+	0.462023i
$457$	−915.559	−	1585.80i	−0.0937157	−	0.162320i	0.815356	−	0.578960i	$-0.196541\pi$
$457$	−915.559	−	1585.80i	−0.0937157	−	0.162320i	−0.909072	+	0.416639i	$0.863208\pi$
$458$	5827.23	+	10687.8i	0.594517	+	1.09041i
$459$	−3640.91	−	2102.08i	−0.370247	−	0.213762i
$460$	6949.50	−	10783.7i	0.704395	−	1.09303i
$461$			609.925i			0.0616205i	0.999525	+	0.0308102i	$0.00980875\pi$
$461$			609.925i			0.0616205i	−0.999525	+	0.0308102i	$0.990191\pi$
$462$		0			0
$463$			7896.96i			0.792663i	0.918107	+	0.396332i	$0.129717\pi$
$463$			7896.96i			0.792663i	−0.918107	+	0.396332i	$0.870283\pi$
$464$	1772.20	+	173.730i	0.177311	+	0.0173819i
$465$	5778.50	+	3336.22i	0.576282	+	0.332717i
$466$	12749.1	−	6951.10i	1.26736	−	0.690995i
$467$	7294.01	+	12633.6i	0.722755	+	1.25185i	0.959891	+	0.280372i	$0.0904580\pi$
$467$	7294.01	+	12633.6i	0.722755	+	1.25185i	−0.237136	+	0.971476i	$0.576209\pi$
$468$	1281.50	−	658.616i	0.126575	−	0.0650524i
$469$		0			0
$470$	−7195.57	+	11788.4i	−0.706184	+	1.15693i
$471$	2645.47	−	1527.36i	0.258804	−	0.149421i
$472$	−7710.52	−	5239.89i	−0.751918	−	0.510986i
$473$	3566.25	−	6176.93i	0.346673	−	0.600456i
$474$	15991.2	+	390.738i	1.54958	+	0.0378633i
$475$	6916.15			0.668073
$476$		0			0
$477$	2286.73			0.219501
$478$	1324.58	+	32.3653i	0.126746	+	0.00309698i
$479$	−9176.03	+	15893.4i	−0.875289	+	1.51605i	−0.0188353	+	0.999823i	$0.505996\pi$
$479$	−9176.03	+	15893.4i	−0.875289	+	1.51605i	−0.856454	+	0.516223i	$0.827338\pi$
$480$	14720.5	+	1807.08i	1.39979	+	0.171837i
$481$	3724.17	−	2150.15i	0.353030	−	0.203822i
$482$	573.979	−	940.339i	0.0542407	−	0.0888615i
$483$		0			0
$484$	−1421.94	−	2766.72i	−0.133540	−	0.259835i
$485$	5605.30	+	9708.66i	0.524790	+	0.908964i
$486$	2743.03	−	1495.57i	0.256022	−	0.139589i
$487$	12707.6	+	7336.74i	1.18242	+	0.682668i	0.956572	−	0.291496i	$-0.0941529\pi$
$487$	12707.6	+	7336.74i	1.18242	+	0.682668i	0.225843	+	0.974164i	$0.427486\pi$
$488$	7671.83	+	15869.3i	0.711654	+	1.47207i
$489$			11807.1i			1.09190i
$490$		0			0
$491$			3216.95i			0.295680i	0.989011	+	0.147840i	$0.0472321\pi$
$491$			3216.95i			0.295680i	−0.989011	+	0.147840i	$0.952768\pi$
$492$	−7335.17	−	4727.09i	−0.672144	−	0.433158i
$493$	681.600	+	393.522i	0.0622671	+	0.0359500i
$494$	−2551.40	−	4679.55i	−0.232375	−	0.426200i
$495$	1405.63	+	2434.62i	0.127633	+	0.221067i
$496$	−3034.03	+	4238.07i	−0.274662	+	0.383659i
$497$		0			0
$498$	10873.2	+	6636.97i	0.978394	+	0.597208i
$499$	7670.50	−	4428.57i	0.688134	−	0.397294i	−0.114779	−	0.993391i	$-0.536616\pi$
$499$	7670.50	−	4428.57i	0.688134	−	0.397294i	0.802913	+	0.596097i	$0.203283\pi$
$500$	276.700	−	5658.71i	0.0247488	−	0.506130i
$501$	−5118.40	+	8865.34i	−0.456434	+	0.790567i
$502$	324.076	−	13263.0i	0.0288131	−	1.17920i
$503$	−5037.58			−0.446550			−0.223275	−	0.974756i	$-0.571675\pi$
$503$	−5037.58			−0.446550			−0.223275	+	0.974756i	$0.571675\pi$
$504$		0			0
$505$	−17063.0			−1.50355
$506$	269.131	−	11014.4i	0.0236449	−	0.967685i
$507$	−334.670	+	579.665i	−0.0293160	+	0.0507768i
$508$	526.321	−	10763.6i	0.0459679	−	0.940075i
$509$	−9257.46	+	5344.80i	−0.806149	+	0.465430i	−0.845617	−	0.533791i	$-0.820767\pi$
$509$	−9257.46	+	5344.80i	−0.806149	+	0.465430i	0.0394680	+	0.999221i	$0.487434\pi$
$510$	5595.14	+	3415.25i	0.485798	+	0.296529i
$511$		0			0
$512$	−2526.73	+	11306.3i	−0.218100	+	0.975927i
$513$	−3087.18	−	5347.16i	−0.265697	−	0.460201i
$514$	−7072.08	−	12971.0i	−0.606880	−	1.11308i
$515$	14178.3	+	8185.83i	1.21314	+	0.700409i
$516$	5550.15	+	3576.75i	0.473511	+	0.305150i
$517$			11860.9i			1.00898i
$518$		0			0
$519$		−	7019.50i		−	0.593684i
$520$	−15776.3	+	7626.85i	−1.33045	+	0.643191i
$521$	11693.0	+	6750.93i	0.983259	+	0.567685i	0.903252	−	0.429110i	$-0.141173\pi$
$521$	11693.0	+	6750.93i	0.983259	+	0.567685i	0.0800063	+	0.996794i	$0.474506\pi$
$522$	−274.342	+	149.578i	−0.0230031	+	0.0125418i
$523$	−6909.97	−	11968.4i	−0.577728	−	1.00065i	−0.995739	−	0.0922123i	$-0.970606\pi$
$523$	−6909.97	−	11968.4i	−0.577728	−	1.00065i	0.418011	−	0.908442i	$-0.362727\pi$
$524$	1756.26	+	3417.23i	0.146417	+	0.284890i
$525$		0			0
$526$	6933.12	−	11358.4i	0.574711	−	0.941539i
$527$	−1995.07	+	1151.85i	−0.164908	+	0.0952096i
$528$	11599.2	−	5261.93i	0.956046	−	0.433704i
$529$	−1672.16	+	2896.27i	−0.137434	+	0.238043i
$530$	−27802.4	−	679.338i	−2.27860	−	0.0556766i
$531$	1635.87			0.133692
$532$		0			0
$533$	10310.4			0.837886
$534$	−15832.8	−	386.865i	−1.28305	−	0.0313508i
$535$	5855.05	−	10141.2i	0.473151	−	0.819522i
$536$	−2528.04	+	3720.02i	−0.203722	+	0.299777i
$537$	12629.9	−	7291.85i	1.01493	−	0.585971i
$538$	5075.94	−	8315.82i	0.406765	−	0.666395i
$539$		0			0
$540$	−18054.6	+	9279.04i	−1.43879	+	0.739456i
$541$	691.732	+	1198.11i	0.0549720	+	0.0952144i	0.892202	−	0.451637i	$-0.149160\pi$
$541$	691.732	+	1198.11i	0.0549720	+	0.0952144i	−0.837230	+	0.546851i	$0.815826\pi$
$542$	−13041.8	+	7110.69i	−1.03356	+	0.563524i
$543$	−1599.96	−	923.735i	−0.126447	−	0.0730042i
$544$	−3081.50	+	4089.50i	−0.242865	+	0.322309i
$545$		−	19254.7i		−	1.51336i
$546$		0			0
$547$			19306.3i			1.50910i	0.656243	+	0.754550i	$0.272145\pi$
$547$			19306.3i			1.50910i	−0.656243	+	0.754550i	$0.727855\pi$
$548$	−1073.88	+	1666.37i	−0.0837114	+	0.129898i
$549$	−2678.63	−	1546.51i	−0.208235	−	0.120225i
$550$	−9347.85	−	17145.0i	−0.724716	−	1.32921i
$551$	577.938	+	1001.02i	0.0446842	+	0.0773953i
$552$	10172.1	+	746.837i	0.784333	+	0.0575861i
$553$		0			0
$554$	−14493.0	−	8846.46i	−1.11146	−	0.678429i
$555$	−6726.73	+	3883.68i	−0.514475	+	0.297032i
$556$	14721.2	+	719.842i	1.12288	+	0.0549066i
$557$	−12574.5	+	21779.7i	−0.956551	+	1.65680i	−0.225774	+	0.974180i	$0.572491\pi$
$557$	−12574.5	+	21779.7i	−0.956551	+	1.65680i	−0.730777	+	0.682616i	$0.760842\pi$
$558$	22.3413	−	914.335i	0.00169495	−	0.0693672i
$559$	−7801.36			−0.590272
$560$		0			0
$561$	5629.56			0.423673
$562$	129.243	−	5289.35i	0.00970066	−	0.397007i
$563$	5563.59	−	9636.41i	0.416478	−	0.721361i	−0.579104	−	0.815253i	$-0.696598\pi$
$563$	5563.59	−	9636.41i	0.416478	−	0.721361i	0.995582	+	0.0938923i	$0.0299309\pi$
$564$	−10967.0	−	536.264i	−0.818781	−	0.0400369i
$565$	148.576	−	85.7803i	0.0110631	−	0.00638726i
$566$	9568.54	+	5840.60i	0.710593	+	0.433743i
$567$		0			0
$568$	4462.83	+	327.663i	0.329677	+	0.0242050i
$569$	1222.05	+	2116.65i	0.0900368	+	0.155948i	0.907526	−	0.419995i	$-0.137968\pi$
$569$	1222.05	+	2116.65i	0.0900368	+	0.155948i	−0.817490	+	0.575943i	$0.804635\pi$
$570$	4608.43	+	8452.36i	0.338642	+	0.621106i
$571$	6707.19	+	3872.40i	0.491571	+	0.283809i	0.725226	−	0.688511i	$-0.241735\pi$
$571$	6707.19	+	3872.40i	0.491571	+	0.283809i	−0.233655	+	0.972320i	$0.575069\pi$
$572$	−8152.02	+	12649.7i	−0.595897	+	0.924671i
$573$			2426.35i			0.176897i
$574$		0			0
$575$		−	15637.3i		−	1.13413i
$576$	−748.427	−	1890.15i	−0.0541397	−	0.136729i
$577$	−23628.1	−	13641.7i	−1.70476	−	0.984246i	−0.940784	−	0.339005i	$-0.889910\pi$
$577$	−23628.1	−	13641.7i	−1.70476	−	0.984246i	−0.763979	−	0.645241i	$-0.776757\pi$
$578$	10213.4	−	5568.61i	0.734987	−	0.400733i
$579$	−4611.52	−	7987.39i	−0.330999	−	0.573307i
$580$	3379.93	−	1737.09i	0.241972	−	0.124360i
$581$		0			0
$582$	−4643.58	+	7607.49i	−0.330726	+	0.541822i
$583$	−20684.2	+	11942.0i	−1.46938	+	0.848348i
$584$	−3250.64	+	4783.32i	−0.230330	+	0.338930i
$585$	1537.44	−	2662.93i	0.108659	−	0.188203i
$586$	−13161.5	−	321.594i	−0.927807	−	0.0226705i
$587$	3068.80			0.215780			0.107890	−	0.994163i	$-0.465591\pi$
$587$	3068.80			0.215780			0.107890	+	0.994163i	$0.465591\pi$
$588$		0			0
$589$	−3383.29			−0.236683
$590$	−19889.1	−	485.981i	−1.38784	−	0.0339111i
$591$	−3847.83	+	6664.63i	−0.267815	+	0.463868i
$592$	−2506.60	−	5525.49i	−0.174022	−	0.383608i
$593$	18899.9	−	10911.9i	1.30881	−	0.755643i	0.326914	−	0.945054i	$-0.393991\pi$
$593$	18899.9	−	10911.9i	1.30881	−	0.755643i	0.981898	+	0.189411i	$0.0606580\pi$
$594$	−9082.85	+	14880.3i	−0.627397	+	1.02785i
$595$		0			0
$596$	−8048.09	−	15659.5i	−0.553125	−	1.07624i
$597$	6139.60	+	10634.1i	0.420900	+	0.729020i
$598$	−10580.4	+	5768.69i	−0.723520	+	0.394481i
$599$	−16759.8	−	9676.28i	−1.14322	−	0.660037i	−0.195992	−	0.980605i	$-0.562793\pi$
$599$	−16759.8	−	9676.28i	−1.14322	−	0.660037i	−0.947225	+	0.320568i	$0.896126\pi$
$600$	16275.4	−	7868.15i	1.10740	−	0.535360i
$601$		−	8218.83i		−	0.557826i	−0.960316	−	0.278913i	$-0.910026\pi$
$601$		−	8218.83i		−	0.557826i	0.960316	−	0.278913i	$-0.0899740\pi$
$602$		0			0
$603$		−	789.242i		−	0.0533009i
$604$	−21578.9	−	13906.3i	−1.45369	−	0.936822i
$605$	−5749.21	−	3319.31i	−0.386345	−	0.223056i
$606$	−6493.78	−	11910.3i	−0.435300	−	0.798387i
$607$	11896.7	+	20605.6i	0.795503	+	1.37785i	0.922519	+	0.385951i	$0.126127\pi$
$607$	11896.7	+	20605.6i	0.795503	+	1.37785i	−0.127016	+	0.991901i	$0.540540\pi$
$608$	−6922.27	+	2938.53i	−0.461735	+	0.196008i
$609$		0			0
$610$	32107.8	+	19598.5i	2.13116	+	1.30085i
$611$	11235.1	−	6486.58i	0.743900	−	0.429491i
$612$	43.8839	−	897.454i	0.00289853	−	0.0592769i
$613$	−9745.06	+	16878.9i	−0.642087	+	1.11213i	0.342880	+	0.939379i	$0.388598\pi$
$613$	−9745.06	+	16878.9i	−0.642087	+	1.11213i	−0.984966	+	0.172747i	$0.944736\pi$
$614$	−195.398	+	7996.83i	−0.0128431	+	0.525612i
$615$	−18623.0			−1.22106
$616$		0			0
$617$	−12532.4			−0.817724			−0.408862	−	0.912596i	$-0.634074\pi$
$617$	−12532.4			−0.817724			−0.408862	+	0.912596i	$0.634074\pi$
$618$	−317.942	+	13012.0i	−0.0206950	+	0.846959i
$619$	−1788.57	+	3097.90i	−0.116137	+	0.201155i	−0.918234	−	0.396039i	$-0.870384\pi$
$619$	−1788.57	+	3097.90i	−0.116137	+	0.201155i	0.802097	+	0.597194i	$0.203718\pi$
$620$	−543.259	+	11110.0i	−0.0351900	+	0.719658i
$621$	−12089.9	+	6980.09i	−0.781239	+	0.451049i
$622$	−15835.1	−	9665.66i	−1.02078	−	0.623083i
$623$		0			0
$624$	−11327.8	−	8109.55i	−0.726721	−	0.520259i
$625$	4359.68	+	7551.19i	0.279020	+	0.483276i
$626$	−8417.78	−	15439.1i	−0.537447	−	0.985737i
$627$	7160.09	+	4133.88i	0.456055	+	0.263303i
$628$	4280.51	+	2758.54i	0.271992	+	0.175283i
$629$		−	2681.73i		−	0.169996i
$630$		0			0
$631$			2950.67i			0.186156i	0.995659	+	0.0930779i	$0.0296706\pi$
$631$			2950.67i			0.186156i	−0.995659	+	0.0930779i	$0.970329\pi$
$632$	11606.3	+	24007.8i	0.730496	+	1.51105i
$633$	−1585.04	−	915.124i	−0.0995256	−	0.0574611i
$634$	8082.75	−	4406.91i	0.506320	−	0.276058i
$635$	−11499.0	−	19916.9i	−0.718622	−	1.24469i
$636$	−10106.8	−	19665.2i	−0.630125	−	1.22606i
$637$		0			0
$638$	1700.36	−	2785.67i	0.105514	−	0.172862i
$639$	−680.026	+	392.613i	−0.0420993	+	0.0243060i
$640$	8537.98	+	23203.0i	0.527333	+	1.43310i
$641$	1237.01	−	2142.56i	0.0762229	−	0.132022i	−0.825395	−	0.564556i	$-0.809047\pi$
$641$	1237.01	−	2142.56i	0.0762229	−	0.132022i	0.901617	+	0.432534i	$0.142381\pi$
$642$	9307.08	+	227.414i	0.572151	+	0.0139802i
$643$	20855.1			1.27907			0.639537	−	0.768760i	$-0.279126\pi$
$643$	20855.1			1.27907			0.639537	+	0.768760i	$0.279126\pi$
$644$		0			0
$645$	14091.1			0.860210
$646$	−3322.81	−	81.1913i	−0.202375	−	0.00494493i
$647$	12264.5	−	21242.8i	0.745237	−	1.29079i	−0.204847	−	0.978794i	$-0.565670\pi$
$647$	12264.5	−	21242.8i	0.745237	−	1.29079i	0.950084	−	0.311994i	$-0.100997\pi$
$648$	−11341.8	−	7707.61i	−0.687572	−	0.467259i
$649$	−14796.9	+	8543.00i	−0.894961	+	0.516706i
$650$	−11128.1	+	18231.0i	−0.671509	+	1.10012i
$651$		0			0
$652$	−17506.4	+	8997.26i	−1.05154	+	0.540430i
$653$	−4420.01	−	7655.68i	−0.264882	−	0.458790i	0.702650	−	0.711535i	$-0.252000\pi$
$653$	−4420.01	−	7655.68i	−0.264882	−	0.458790i	−0.967533	+	0.252745i	$0.918666\pi$
$654$	13440.2	−	7327.91i	0.803597	−	0.438140i
$655$	7100.95	+	4099.73i	0.423599	+	0.244565i
$656$	1419.28	−	14477.9i	0.0844721	−	0.861690i
$657$		−	1014.83i		−	0.0602624i
$658$		0			0
$659$		−	26347.9i		−	1.55746i	−0.627356	−	0.778732i	$-0.715863\pi$
$659$		−	26347.9i		−	1.55746i	0.627356	−	0.778732i	$-0.284137\pi$
$660$	14724.5	−	22848.4i	0.868407	−	1.34753i
$661$	19658.4	+	11349.8i	1.15677	+	0.667861i	0.950527	−	0.310641i	$-0.100544\pi$
$661$	19658.4	+	11349.8i	1.15677	+	0.667861i	0.206241	+	0.978501i	$0.433877\pi$
$662$	5937.52	+	10890.1i	0.348593	+	0.639356i
$663$	−3078.74	−	5332.53i	−0.180344	−	0.312366i
$664$	−1554.98	+	21179.1i	−0.0908809	+	1.23782i
$665$		0			0
$666$	908.771	+	554.710i	0.0528741	+	0.0322741i
$667$	2263.29	−	1306.71i	0.131387	−	0.0758562i
$668$	−17044.9	−	833.464i	−0.987256	−	0.0482750i
$669$	7063.70	−	12234.7i	0.408219	−	0.707056i
$670$	−234.467	+	9595.73i	−0.0135198	+	0.553307i
$671$	32305.4			1.85862
$672$		0			0
$673$	−5208.40			−0.298319			−0.149160	−	0.988813i	$-0.547657\pi$
$673$	−5208.40			−0.298319			−0.149160	+	0.988813i	$0.547657\pi$
$674$	661.156	−	27058.3i	0.0377845	−	1.54636i
$675$	−12371.5	+	21428.1i	−0.705452	+	1.22188i
$676$	−1114.49	−	54.4965i	−0.0634097	−	0.00310062i
$677$	2723.40	−	1572.35i	0.154607	−	0.0892622i	−0.420701	−	0.907199i	$-0.638216\pi$
$677$	2723.40	−	1572.35i	0.154607	−	0.0892622i	0.575307	+	0.817937i	$0.304882\pi$
$678$	116.421	+	71.0627i	0.00659456	+	0.00402529i
$679$		0			0
$680$	−800.162	+	10898.4i	−0.0451247	+	0.614607i
$681$	−13883.5	−	24046.9i	−0.781227	−	1.35312i
$682$	4572.85	+	8387.10i	0.256750	+	0.470907i
$683$	10301.6	+	5947.66i	0.577132	+	0.333208i	0.759993	−	0.649931i	$-0.225202\pi$
$683$	10301.6	+	5947.66i	0.577132	+	0.333208i	−0.182861	+	0.983139i	$0.558536\pi$
$684$	714.830	−	1109.22i	0.0399593	−	0.0620061i
$685$			4230.69i			0.235980i
$686$		0			0
$687$			20653.8i			1.14700i
$688$	−1073.90	+	10954.7i	−0.0595087	+	0.607041i
$689$	22623.8	+	13061.9i	1.25094	+	0.722231i
$690$	19110.7	−	10419.6i	1.05439	−	0.574881i
$691$	12303.2	+	21309.8i	0.677333	+	1.17318i	0.975781	+	0.218750i	$0.0701978\pi$
$691$	12303.2	+	21309.8i	0.677333	+	1.17318i	−0.298448	+	0.954426i	$0.596469\pi$
$692$	10407.8	−	5349.00i	0.571740	−	0.293842i
$693$		0			0
$694$	15339.9	−	25131.1i	0.839042	−	1.37459i
$695$	27240.1	−	15727.1i	1.48673	−	0.858362i
$696$	2498.84	+	1698.16i	0.136090	+	0.0924834i
$697$	3214.86	−	5568.31i	0.174708	−	0.302603i
$698$	35662.7	+	871.400i	1.93389	+	0.0472535i
$699$	24637.1			1.33314
$700$		0			0
$701$	−1627.77			−0.0877033			−0.0438516	−	0.999038i	$-0.513963\pi$
$701$	−1627.77			−0.0877033			−0.0438516	+	0.999038i	$0.513963\pi$
$702$	19062.4	+	465.781i	1.02488	+	0.0250424i
$703$	1969.24	−	3410.82i	0.105649	−	0.182990i
$704$	16640.7	+	13188.4i	0.890865	+	0.706047i
$705$	−20293.2	+	11716.3i	−1.08409	+	0.625901i
$706$	15255.1	−	24992.2i	0.813222	−	1.33229i
$707$		0			0
$708$	−7230.12	−	14067.9i	−0.383792	−	0.746760i
$709$	13817.2	+	23932.0i	0.731896	+	1.26768i	0.956072	+	0.293133i	$0.0946978\pi$
$709$	13817.2	+	23932.0i	0.731896	+	1.26768i	−0.224175	+	0.974549i	$0.571969\pi$
$710$	8384.51	−	4571.43i	0.443190	−	0.241638i
$711$	−4052.36	−	2339.63i	−0.213749	−	0.123408i
$712$	−11491.3	−	23769.9i	−0.604850	−	1.25115i
$713$			7649.59i			0.401794i
$714$		0			0
$715$			32116.0i			1.67982i
$716$	20435.8	+	13169.7i	1.06665	+	0.687393i
$717$	1946.86	+	1124.02i	0.101404	+	0.0585456i
$718$	−5039.20	−	9242.44i	−0.261924	−	0.480397i
$719$	−2971.62	−	5146.99i	−0.154134	−	0.266969i	0.778609	−	0.627509i	$-0.215926\pi$
$719$	−2971.62	−	5146.99i	−0.154134	−	0.266969i	−0.932743	+	0.360541i	$0.882592\pi$
$720$	−3527.66	−	2525.45i	−0.182595	−	0.130720i
$721$		0			0
$722$	12392.5	+	7564.34i	0.638783	+	0.389911i
$723$	1618.75	−	934.588i	0.0832671	−	0.0480743i
$724$	150.418	−	3076.15i	0.00772133	−	0.157906i
$725$	2316.02	−	4011.47i	0.118641	−	0.205493i
$726$	128.924	−	5276.31i	0.00659065	−	0.269727i
$727$	−20574.9			−1.04963			−0.524816	−	0.851216i	$-0.675866\pi$
$727$	−20574.9			−1.04963			−0.524816	+	0.851216i	$0.675866\pi$
$728$		0			0
$729$	21663.6			1.10063
$730$	−301.485	+	12338.5i	−0.0152856	+	0.625573i
$731$	−2432.52	+	4213.25i	−0.123078	+	0.213177i
$732$	−1460.62	+	29870.6i	−0.0737513	+	1.50826i
$733$	14052.6	−	8113.27i	0.708110	−	0.408828i	−0.102251	−	0.994759i	$-0.532604\pi$
$733$	14052.6	−	8113.27i	0.708110	−	0.408828i	0.810361	+	0.585931i	$0.199271\pi$
$734$	−11289.1	−	6890.83i	−0.567696	−	0.346519i
$735$		0			0
$736$	6643.98	+	15651.2i	0.332745	+	0.783844i
$737$	4121.66	+	7138.93i	0.206002	+	0.356806i
$738$	1221.97	+	2241.23i	0.0609503	+	0.111790i
$739$	−23629.6	−	13642.5i	−1.17622	−	0.679092i	−0.221084	−	0.975255i	$-0.570959\pi$
$739$	−23629.6	−	13642.5i	−1.17622	−	0.679092i	−0.955137	+	0.296163i	$0.904293\pi$
$740$	−10884.2	−	7014.23i	−0.540690	−	0.348444i
$741$		−	9043.07i		−	0.448320i
$742$		0			0
$743$		−	15043.5i		−	0.742791i	−0.928475	−	0.371396i	$-0.878879\pi$
$743$		−	15043.5i		−	0.742791i	0.928475	−	0.371396i	$-0.121121\pi$
$744$	−7961.74	+	3849.00i	−0.392327	+	0.189666i
$745$	−32540.2	−	18787.1i	−1.60024	−	0.923900i
$746$	−16394.6	+	8938.74i	−0.804624	+	0.438700i
$747$	−1863.21	−	3227.18i	−0.0912603	−	0.158067i
$748$	4289.84	+	8346.92i	0.209695	+	0.408013i
$749$		0			0
$750$	5008.12	−	8204.71i	0.243828	−	0.399458i
$751$	−15537.7	+	8970.68i	−0.754964	+	0.435879i	−0.827485	−	0.561488i	$-0.810229\pi$
$751$	−15537.7	+	8970.68i	−0.754964	+	0.435879i	0.0725209	+	0.997367i	$0.476896\pi$
$752$	−7561.92	−	16669.3i	−0.366695	−	0.808332i
$753$	11254.8	−	19494.0i	0.544687	−	0.943425i
$754$	−3568.60	−	87.1969i	−0.172362	−	0.00421157i
$755$	−54785.8			−2.64088
$756$		0			0
$757$	−12961.3			−0.622305			−0.311152	−	0.950360i	$-0.600715\pi$
$757$	−12961.3			−0.622305			−0.311152	+	0.950360i	$0.600715\pi$
$758$	36069.1	+	881.331i	1.72835	+	0.0422314i
$759$	9346.65	−	16188.9i	0.446985	−	0.774201i
$760$	−9020.54	+	13273.7i	−0.430539	+	0.633539i
$761$	7678.27	−	4433.05i	0.365752	−	0.211167i	−0.305849	−	0.952080i	$-0.598940\pi$
$761$	7678.27	−	4433.05i	0.365752	−	0.211167i	0.671601	+	0.740913i	$0.265607\pi$
$762$	9526.11	−	15606.4i	0.452880	−	0.741945i
$763$		0			0
$764$	−3597.53	+	1848.92i	−0.170359	+	0.0875546i
$765$	−958.772	−	1660.64i	−0.0453131	−	0.0784845i
$766$	3907.51	−	2130.47i	0.184314	−	0.100492i
$767$	16184.5	+	9344.12i	0.761914	+	0.439891i
$768$	−12946.8	+	14790.2i	−0.608304	+	0.694916i
$769$			31664.2i			1.48484i	0.669937	+	0.742418i	$0.266321\pi$
$769$			31664.2i			1.48484i	−0.669937	+	0.742418i	$0.733679\pi$
$770$		0			0
$771$		−	25065.9i		−	1.17085i
$772$	8328.78	−	12924.0i	0.388289	−	0.602520i
$773$	−16673.7	−	9626.55i	−0.775822	−	0.447921i	0.0591256	−	0.998251i	$-0.481169\pi$
$773$	−16673.7	−	9626.55i	−0.775822	−	0.447921i	−0.834948	+	0.550330i	$0.814502\pi$
$774$	−924.602	−	1695.82i	−0.0429382	−	0.0787532i
$775$	6779.08	+	11741.7i	0.314209	+	0.544225i
$776$	−14818.1	−	1087.95i	−0.685487	−	0.0503287i
$777$		0			0
$778$	9712.26	+	5928.32i	0.447559	+	0.273188i
$779$	8177.79	−	4721.45i	0.376123	−	0.217155i
$780$	−29695.4	−	1452.05i	−1.36316	−	0.0666562i
$781$	4100.69	−	7102.61i	0.187880	−	0.325418i
$782$	−183.573	+	7512.84i	−0.00839455	+	0.343553i
$783$	−4135.24			−0.188737
$784$		0			0
$785$	10867.6			0.494118
$786$	−159.236	+	6516.86i	−0.00722616	+	0.295736i
$787$	642.360	−	1112.60i	0.0290949	−	0.0503938i	−0.851111	−	0.524985i	$-0.824071\pi$
$787$	642.360	−	1112.60i	0.0290949	−	0.0503938i	0.880206	+	0.474591i	$0.157404\pi$
$788$	−12813.7	−	626.567i	−0.579276	−	0.0283256i
$789$	19553.0	−	11288.9i	0.882263	−	0.509375i
$790$	48574.2	+	29649.5i	2.18758	+	1.33529i
$791$		0			0
$792$	−3715.90	−	272.823i	−0.166716	−	0.0122403i
$793$	−17667.4	−	30600.8i	−0.791157	−	1.37032i
$794$	5398.66	+	9901.73i	0.241299	+	0.442568i
$795$	−40863.9	−	23592.8i	−1.82301	−	1.05252i
$796$	−11088.6	+	17206.5i	−0.493751	+	0.766168i
$797$			2593.21i			0.115253i	0.998338	+	0.0576263i	$0.0183532\pi$
$797$			2593.21i			0.115253i	−0.998338	+	0.0576263i	$0.981647\pi$
$798$		0			0
$799$		−	8090.25i		−	0.358213i
$800$	24068.2	+	18135.8i	1.06368	+	0.801496i
$801$	4012.20	+	2316.44i	0.176984	+	0.102182i
$802$	11483.9	−	6261.32i	0.505626	−	0.275680i
$803$	5299.77	+	9179.47i	0.232908	+	0.403408i
$804$	−6787.23	+	3488.25i	−0.297721	+	0.153011i
$805$		0			0
$806$	5443.74	−	8918.38i	0.237900	−	0.389747i
$807$	14315.3	−	8264.97i	0.624441	−	0.360521i
$808$	12710.9	−	18704.1i	0.553426	−	0.814368i
$809$	5712.40	−	9894.17i	0.248254	−	0.429988i	−0.714788	−	0.699342i	$-0.753477\pi$
$809$	5712.40	−	9894.17i	0.248254	−	0.429988i	0.963041	+	0.269353i	$0.0868099\pi$
$810$	−29255.9	−	714.853i	−1.26907	−	0.0310091i
$811$	−32094.4			−1.38962			−0.694812	−	0.719191i	$-0.744513\pi$
$811$	−32094.4			−1.38962			−0.694812	+	0.719191i	$0.744513\pi$
$812$		0			0
$813$	−25202.8			−1.08721
$814$	−11117.0	−	271.638i	−0.478685	−	0.0116964i
$815$	−21002.8	+	36377.9i	−0.902695	+	1.56351i
$816$	−7911.78	+	3589.13i	−0.339421	+	0.153976i
$817$	−6187.71	+	3572.48i	−0.264970	+	0.152981i
$818$	932.847	−	1528.27i	0.0398732	−	0.0653234i
$819$		0			0
$820$	−14191.1	−	27612.2i	−0.604359	−	1.17593i
$821$	−1930.54	−	3343.79i	−0.0820660	−	0.142143i	0.822071	−	0.569385i	$-0.192819\pi$
$821$	−1930.54	−	3343.79i	−0.0820660	−	0.142143i	−0.904137	+	0.427242i	$0.859485\pi$
$822$	−2953.10	+	1610.10i	−0.125306	+	0.0683197i
$823$	−4191.93	−	2420.21i	−0.177548	−	0.102507i	0.408592	−	0.912717i	$-0.366020\pi$
$823$	−4191.93	−	2420.21i	−0.177548	−	0.102507i	−0.586140	+	0.810210i	$0.699353\pi$
$824$	−19535.1	+	9444.01i	−0.825896	+	0.399269i
$825$		−	33132.1i		−	1.39819i
$826$		0			0
$827$		−	831.897i		−	0.0349793i	−0.999847	−	0.0174897i	$-0.994433\pi$
$827$		−	831.897i		−	0.0349793i	0.999847	−	0.0174897i	$-0.00556741\pi$
$828$	−2507.94	−	1616.22i	−0.105262	−	0.0678352i
$829$	21387.6	+	12348.1i	0.896046	+	0.517333i	0.875915	−	0.482465i	$-0.160258\pi$
$829$	21387.6	+	12348.1i	0.896046	+	0.517333i	0.0201310	+	0.999797i	$0.493592\pi$
$830$	21694.5	+	39790.1i	0.907263	+	1.66402i
$831$	−14404.4	−	24949.1i	−0.601301	−	1.04148i
$832$	3391.99	−	22975.2i	0.141341	−	0.957359i
$833$		0			0
$834$	21344.7	+	13028.7i	0.886219	+	0.540945i
$835$	−31539.7	+	18209.5i	−1.30716	+	0.754688i
$836$	−673.147	+	13766.3i	−0.0278484	+	0.569519i
$837$	6052.00	−	10482.4i	0.249925	−	0.432884i
$838$	−220.909	+	9040.88i	−0.00910642	+	0.372687i
$839$	20023.0			0.823922			0.411961	−	0.911202i	$-0.364844\pi$
$839$	20023.0			0.823922			0.411961	+	0.911202i	$0.364844\pi$
$840$		0			0
$841$	−23614.9			−0.968259
$842$	379.244	−	15520.9i	0.0155221	−	0.635254i
$843$	4488.47	−	7774.26i	0.183382	−	0.317627i
$844$	149.016	−	3047.47i	0.00607741	−	0.124287i
$845$	−2062.24	+	1190.64i	−0.0839566	+	0.0484723i
$846$	2741.58	+	1673.45i	0.111415	+	0.0680075i
$847$		0			0
$848$	21455.8	−	29970.5i	0.868864	−	1.21367i
$849$	9510.02	+	16471.8i	0.384432	+	0.665857i
$850$	6376.12	+	11694.5i	0.257293	+	0.471903i
$851$	−7711.83	−	4452.43i	−0.310644	−	0.179350i
$852$	6381.89	+	4112.76i	0.256620	+	0.165377i
$853$		−	25542.4i		−	1.02527i	−0.858606	−	0.512636i	$-0.828669\pi$
$853$		−	25542.4i		−	1.02527i	0.858606	−	0.512636i	$-0.171331\pi$
$854$		0			0
$855$		−	2816.17i		−	0.112644i
$856$	6754.99	+	13972.8i	0.269720	+	0.557922i
$857$	22450.1	+	12961.6i	0.894844	+	0.516638i	0.875524	−	0.483175i	$-0.160516\pi$
$857$	22450.1	+	12961.6i	0.894844	+	0.516638i	0.0193202	+	0.999813i	$0.493850\pi$
$858$	−22417.5	+	12222.6i	−0.891984	+	0.486331i
$859$	−12903.9	−	22350.2i	−0.512544	−	0.887753i	−0.999894	−	0.0145459i	$-0.995370\pi$
$859$	−12903.9	−	22350.2i	−0.512544	−	0.887753i	0.487350	−	0.873207i	$-0.337964\pi$
$860$	10737.7	+	20892.7i	0.425758	+	0.828414i
$861$		0			0
$862$	−6157.30	+	10087.4i	−0.243293	+	0.398582i
$863$	−953.538	+	550.526i	−0.0376116	+	0.0217151i	−0.518688	−	0.854964i	$-0.673579\pi$
$863$	−953.538	+	550.526i	−0.0376116	+	0.0217151i	0.481076	+	0.876679i	$0.340246\pi$
$864$	3278.10	−	26703.5i	0.129078	−	1.05147i
$865$	12486.5	−	21627.2i	0.490812	−	0.850111i
$866$	26314.0	+	642.969i	1.03255	+	0.0252298i
$867$	19737.1			0.773134
$868$		0			0
$869$	48873.0			1.90783
$870$	6445.72	+	157.498i	0.251184	+	0.00613756i
$871$	4508.17	−	7808.38i	0.175377	−	0.303762i
$872$	21106.7	+	14343.6i	0.819683	+	0.557038i
$873$	2257.91	−	1303.60i	0.0875357	−	0.0505388i
$874$	−5750.28	+	9420.58i	−0.222547	+	0.364595i
$875$		0			0
$876$	−8727.25	+	4485.31i	−0.336605	+	0.172996i
$877$	−21754.6	−	37680.1i	−0.837631	−	1.45082i	−0.891871	−	0.452291i	$-0.850607\pi$
$877$	−21754.6	−	37680.1i	−0.837631	−	1.45082i	0.0542399	−	0.998528i	$-0.482726\pi$
$878$	7279.61	−	3969.02i	0.279812	−	0.152560i
$879$	−19344.7	−	11168.6i	−0.742297	−	0.428565i
$880$	45097.4	+	4420.94i	1.72754	+	0.169352i
$881$			39281.4i			1.50219i	0.660197	+	0.751093i	$0.270473\pi$
$881$			39281.4i			1.50219i	−0.660197	+	0.751093i	$0.729527\pi$
$882$		0			0
$883$			4217.95i			0.160754i	0.996765	+	0.0803768i	$0.0256123\pi$
$883$			4217.95i			0.160754i	−0.996765	+	0.0803768i	$0.974388\pi$
$884$	5560.45	−	8628.32i	0.211559	−	0.328282i
$885$	−29233.0	−	16877.7i	−1.11035	−	0.641058i
$886$	−7967.08	−	14612.5i	−0.302099	−	0.554082i
$887$	−3603.27	−	6241.05i	−0.136399	−	0.236250i	0.789732	−	0.613452i	$-0.210220\pi$
$887$	−3603.27	−	6241.05i	−0.136399	−	0.236250i	−0.926131	+	0.377202i	$0.876886\pi$
$888$	753.794	−	10266.8i	0.0284861	−	0.387987i
$889$		0			0
$890$	−48092.8	−	29355.6i	−1.81132	−	1.10562i
$891$	−21765.5	+	12566.3i	−0.818374	+	0.472489i
$892$	23523.0	+	1150.23i	0.882968	+	0.0431755i
$893$	5940.80	−	10289.8i	0.222622	−	0.385592i
$894$	729.702	−	29863.6i	0.0272985	−	1.11721i
$895$	51883.7			1.93774
$896$		0			0
$897$	−20446.3			−0.761071
$898$	−888.254	+	36352.5i	−0.0330083	+	1.35089i
$899$	−1132.97	+	1962.36i	−0.0420318	+	0.0728012i
$900$	−5281.85	−	258.273i	−0.195624	−	0.00956566i
$901$	14108.5	−	8145.57i	0.521669	−	0.301186i
$902$	−22757.4	−	13891.0i	−0.840067	−	0.512773i
$903$		0			0
$904$	−16.6494	+	226.767i	−0.000612554	+	0.00834311i
$905$	−3286.32	−	5692.08i	−0.120708	−	0.209073i
$906$	−20850.2	−	38241.5i	−0.764571	−	1.40231i
$907$	24349.5	+	14058.2i	0.891415	+	0.514659i	0.874405	−	0.485197i	$-0.161252\pi$
$907$	24349.5	+	14058.2i	0.891415	+	0.514659i	0.0170097	+	0.999855i	$0.494585\pi$
$908$	25074.7	−	38909.1i	0.916445	−	1.42207i
$909$			3968.28i			0.144796i
$910$		0			0
$911$			36758.1i			1.33683i	0.743790	+	0.668414i	$0.233026\pi$
$911$			36758.1i			1.33683i	−0.743790	+	0.668414i	$0.766974\pi$
$912$	−12698.3	−	1244.83i	−0.461057	−	0.0451977i
$913$	33706.6	+	19460.5i	1.22183	+	0.705422i
$914$	4547.23	−	2479.26i	0.164561	−	0.0897227i
$915$	31911.5	+	55272.3i	1.15296	+	1.99699i
$916$	−30623.2	+	15738.6i	−1.10460	+	0.567704i
$917$		0			0
$918$	6195.36	−	10149.7i	0.222742	−	0.364915i
$919$	−3949.63	+	2280.32i	−0.141770	+	0.0818508i	−0.569207	−	0.822194i	$-0.692750\pi$
$919$	−3949.63	+	2280.32i	−0.141770	+	0.0818508i	0.427437	+	0.904045i	$0.359416\pi$
$920$	30011.8	+	20395.3i	1.07550	+	0.730885i
$921$	−6786.00	+	11753.7i	−0.242787	+	0.420519i
$922$	−1724.61	−	42.1401i	−0.0616021	−	0.00150522i
$923$	−8970.47			−0.319899
$924$		0			0
$925$	−15783.0			−0.561018
$926$	−22329.3	−	545.606i	−0.792427	−	0.0193625i
$927$	1903.75	−	3297.39i	0.0674513	−	0.116829i
$928$	−613.679	+	4999.04i	−0.0217080	+	0.176834i
$929$	−40730.3	+	23515.6i	−1.43845	+	0.830488i	−0.997742	−	0.0671644i	$-0.978605\pi$
$929$	−40730.3	+	23515.6i	−1.43845	+	0.830488i	−0.440705	+	0.897652i	$0.645271\pi$
$930$	−9832.67	+	16108.7i	−0.346694	+	0.567983i
$931$		0			0
$932$	18774.0	+	36529.3i	0.659831	+	1.28386i
$933$	−15738.2	−	27259.4i	−0.552247	−	0.956520i
$934$	−36226.5	+	19751.6i	−1.26913	+	0.691960i
$935$	17344.8	+	10014.0i	0.606668	+	0.350260i
$936$	1773.75	+	3669.04i	0.0619411	+	0.128126i
$937$		−	958.545i		−	0.0334197i	−0.999860	−	0.0167099i	$-0.994681\pi$
$937$		−	958.545i		−	0.0334197i	0.999860	−	0.0167099i	$-0.00531916\pi$
$938$		0			0
$939$		−	29835.6i		−	1.03690i
$940$	−32835.4	−	21160.5i	−1.13933	−	0.734234i
$941$	−23092.4	−	13332.4i	−0.799989	−	0.461874i	0.0434780	−	0.999054i	$-0.486156\pi$
$941$	−23092.4	−	13332.4i	−0.799989	−	0.461874i	−0.843467	+	0.537180i	$0.819489\pi$
$942$	4135.97	+	7585.81i	0.143054	+	0.262377i
$943$	−10675.1	−	18489.9i	−0.368643	−	0.638509i
$944$	15349.0	−	21440.1i	0.529201	−	0.739212i
$945$		0			0
$946$	17219.4	+	10510.6i	0.591808	+	0.361237i
$947$	−2951.90	+	1704.28i	−0.101292	+	0.0584812i	−0.549790	−	0.835303i	$-0.685292\pi$
$947$	−2951.90	+	1704.28i	−0.101292	+	0.0584812i	0.448498	+	0.893784i	$0.351959\pi$
$948$	−2209.69	+	45189.6i	−0.0757039	+	1.54820i
$949$	5796.76	−	10040.3i	0.198283	−	0.343436i
$950$	−477.841	+	19556.0i	−0.0163192	+	0.667874i
$951$	15619.6			0.532599
$952$		0			0
$953$	−30025.2			−1.02058			−0.510290	−	0.860002i	$-0.670462\pi$
$953$	−30025.2			−1.02058			−0.510290	+	0.860002i	$0.670462\pi$
$954$	−157.991	+	6465.92i	−0.00536181	+	0.219436i
$955$	−4316.04	+	7475.61i	−0.146245	+	0.253304i
$956$	−183.031	+	3743.11i	−0.00619211	+	0.126633i
$957$	4795.42	−	2768.64i	0.161979	−	0.0935186i
$958$	−44305.8	−	27044.1i	−1.49421	−	0.912061i
$959$		0			0
$960$	−6126.72	+	41498.6i	−0.205978	+	1.39517i
$961$	11579.3	+	20055.9i	0.388683	+	0.673219i
$962$	5822.43	+	10679.0i	0.195138	+	0.357904i
$963$	−2358.52	−	1361.69i	−0.0789223	−	0.0455658i
$964$	2619.23	+	1687.94i	0.0875101	+	0.0563952i
$965$		−	32812.3i		−	1.09458i
$966$		0			0
$967$			21764.9i			0.723798i	0.932217	+	0.361899i	$0.117872\pi$
$967$			21764.9i			0.723798i	−0.932217	+	0.361899i	$0.882128\pi$
$968$	7921.39	−	3829.49i	0.263020	−	0.127153i
$969$	−4883.86	−	2819.70i	−0.161911	−	0.0934796i
$970$	−27839.3	+	15178.7i	−0.921512	+	0.502430i
$971$	10938.3	+	18945.7i	0.361511	+	0.626155i	0.988210	−	0.153107i	$-0.0489278\pi$
$971$	10938.3	+	18945.7i	0.361511	+	0.626155i	−0.626699	+	0.779261i	$0.715594\pi$
$972$	4039.33	+	7859.49i	0.133294	+	0.259355i
$973$		0			0
$974$	−21623.2	+	35424.9i	−0.711347	+	1.16539i
$975$	−31383.9	+	18119.5i	−1.03086	+	0.595168i
$976$	−45401.9	+	20596.3i	−1.48902	+	0.675483i
$977$	−16972.7	+	29397.6i	−0.555789	+	0.962655i	0.442052	+	0.896989i	$0.354251\pi$
$977$	−16972.7	+	29397.6i	−0.555789	+	0.962655i	−0.997842	+	0.0656660i	$0.979083\pi$
$978$	−33385.7	−	815.762i	−1.09157	−	0.0266720i
$979$	−48388.7			−1.57968
$980$		0			0
$981$	−4478.01			−0.145741
$982$	−9096.20	−	222.261i	−0.295592	−	0.00722264i
$983$	11714.3	−	20289.7i	0.380088	−	0.658332i	−0.610986	−	0.791641i	$-0.709227\pi$
$983$	11714.3	−	20289.7i	0.380088	−	0.658332i	0.991074	+	0.133309i	$0.0425603\pi$
$984$	13873.0	−	20414.2i	0.449447	−	0.661363i
$985$	−23710.4	+	13689.2i	−0.766981	+	0.442817i
$986$	−1159.81	+	1900.09i	−0.0374602	+	0.0613704i
$987$		0			0
$988$	13408.1	−	6890.99i	0.431749	−	0.221894i
$989$	8077.33	+	13990.3i	0.259701	+	0.449815i
$990$	−6981.21	+	3806.33i	−0.224119	+	0.122195i
$991$	−47625.2	−	27496.4i	−1.52660	−	0.881385i	−0.999501	−	0.0315834i	$-0.989945\pi$
$991$	−47625.2	−	27496.4i	−1.52660	−	0.881385i	−0.527103	−	0.849802i	$-0.676722\pi$
$992$	−11773.9	−	8871.80i	−0.376836	−	0.283951i
$993$			21044.7i			0.672540i
$994$		0			0
$995$			43685.1i			1.39187i
$996$	−19517.8	+	30286.4i	−0.620929	+	0.963514i
$997$	−1196.16	−	690.601i	−0.0379966	−	0.0219374i	0.480881	−	0.876786i	$-0.340317\pi$
$997$	−1196.16	−	690.601i	−0.0379966	−	0.0219374i	−0.518878	+	0.854848i	$0.673650\pi$
$998$	11992.2	+	21995.0i	0.380367	+	0.697633i
$999$	7045.11	+	12202.5i	0.223120	+	0.386456i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	196.4.f.c.31.3		16
4.3	odd	2	inner	196.4.f.c.31.8		16
7.2	even	3	inner	196.4.f.c.19.7		16
7.3	odd	6		28.4.d.b.27.1	✓	8
7.4	even	3		28.4.d.b.27.2	yes	8
7.5	odd	6	inner	196.4.f.c.19.8		16
7.6	odd	2	inner	196.4.f.c.31.4		16
21.11	odd	6		252.4.b.d.55.8		8
21.17	even	6		252.4.b.d.55.7		8
28.3	even	6		28.4.d.b.27.4	yes	8
28.11	odd	6		28.4.d.b.27.3	yes	8
28.19	even	6	inner	196.4.f.c.19.3		16
28.23	odd	6	inner	196.4.f.c.19.4		16
28.27	even	2	inner	196.4.f.c.31.7		16
56.3	even	6		448.4.f.d.447.3		8
56.11	odd	6		448.4.f.d.447.6		8
56.45	odd	6		448.4.f.d.447.5		8
56.53	even	6		448.4.f.d.447.4		8
84.11	even	6		252.4.b.d.55.6		8
84.59	odd	6		252.4.b.d.55.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.4.d.b.27.1	✓	8	7.3	odd	6
28.4.d.b.27.2	yes	8	7.4	even	3
28.4.d.b.27.3	yes	8	28.11	odd	6
28.4.d.b.27.4	yes	8	28.3	even	6
196.4.f.c.19.3		16	28.19	even	6	inner
196.4.f.c.19.4		16	28.23	odd	6	inner
196.4.f.c.19.7		16	7.2	even	3	inner
196.4.f.c.19.8		16	7.5	odd	6	inner
196.4.f.c.31.3		16	1.1	even	1	trivial
196.4.f.c.31.4		16	7.6	odd	2	inner
196.4.f.c.31.7		16	28.27	even	2	inner
196.4.f.c.31.8		16	4.3	odd	2	inner
252.4.b.d.55.5		8	84.59	odd	6
252.4.b.d.55.6		8	84.11	even	6
252.4.b.d.55.7		8	21.17	even	6
252.4.b.d.55.8		8	21.11	odd	6
448.4.f.d.447.3		8	56.3	even	6
448.4.f.d.447.4		8	56.53	even	6
448.4.f.d.447.5		8	56.45	odd	6
448.4.f.d.447.6		8	56.11	odd	6

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:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	196.f (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0690906 + 2.82758i) q^{2} +(-2.39945 + 4.15597i) q^{3} +(-7.99045 - 0.390719i) q^{4} +(-14.7855 + 8.53640i) q^{5} +(-11.5856 - 7.07178i) q^{6} +(1.65685 - 22.5667i) q^{8} +(1.98528 + 3.43861i) q^{9} +(-23.1158 - 42.3969i) q^{10} +(-35.9149 - 20.7355i) q^{11} +(20.7965 - 32.2706i) q^{12} +45.3599i q^{13} -81.9306i q^{15} +(63.6947 + 6.24404i) q^{16} +(24.4974 + 14.1436i) q^{17} +(-9.86011 + 5.37597i) q^{18} +(20.7717 + 35.9776i) q^{19} +(121.478 - 62.4327i) q^{20} +(61.1127 - 100.120i) q^{22} +(81.3450 - 46.9645i) q^{23} +(89.8109 + 61.0334i) q^{24} +(83.2401 - 144.176i) q^{25} +(-128.259 - 3.13394i) q^{26} -148.625 q^{27} +27.8234 q^{29} +(231.666 + 5.66063i) q^{30} +(-40.7200 + 70.5291i) q^{31} +(-22.0562 + 179.671i) q^{32} +(172.352 - 99.5075i) q^{33} +(-41.6846 + 68.2912i) q^{34} +(-14.5198 - 28.2517i) q^{36} +(-47.4020 - 82.1027i) q^{37} +(-103.165 + 56.2480i) q^{38} +(-188.514 - 108.839i) q^{39} +(168.141 + 347.803i) q^{40} -227.302i q^{41} +171.988i q^{43} +(278.875 + 179.719i) q^{44} +(-58.7066 - 33.8943i) q^{45} +(127.176 + 233.254i) q^{46} +(-143.002 - 247.687i) q^{47} +(-178.782 + 249.731i) q^{48} +(401.919 + 245.330i) q^{50} +(-117.560 + 67.8735i) q^{51} +(17.7230 - 362.446i) q^{52} +(287.960 - 498.762i) q^{53} +(10.2686 - 420.248i) q^{54} +708.025 q^{55} -199.362 q^{57} +(-1.92233 + 78.6729i) q^{58} +(206.000 - 356.802i) q^{59} +(-32.0118 + 654.663i) q^{60} +(-674.623 + 389.494i) q^{61} +(-196.614 - 120.012i) q^{62} +(-506.510 - 74.7794i) q^{64} +(-387.210 - 670.668i) q^{65} +(269.458 + 494.215i) q^{66} +(-172.143 - 99.3867i) q^{67} +(-190.219 - 122.585i) q^{68} +450.756i q^{69} +197.762i q^{71} +(80.8873 - 39.1039i) q^{72} +(-221.347 - 127.795i) q^{73} +(235.427 - 128.361i) q^{74} +(399.461 + 691.887i) q^{75} +(-151.918 - 295.593i) q^{76} +(320.775 - 525.520i) q^{78} +(-1020.60 + 589.244i) q^{79} +(-995.057 + 451.402i) q^{80} +(303.015 - 524.837i) q^{81} +(642.716 + 15.7044i) q^{82} -938.514 q^{83} -482.940 q^{85} +(-486.310 - 11.8827i) q^{86} +(-66.7608 + 115.633i) q^{87} +(-527.437 + 776.125i) q^{88} +(1010.49 - 583.404i) q^{89} +(99.8950 - 163.656i) q^{90} +(-668.333 + 343.485i) q^{92} +(-195.411 - 338.462i) q^{93} +(710.237 - 387.238i) q^{94} +(-614.238 - 354.631i) q^{95} +(-693.783 - 522.776i) q^{96} -656.635i q^{97} -164.663i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{2} + 16 q^{4} - 64 q^{8} - 104 q^{9} - 64 q^{16} - 88 q^{18} + 480 q^{22} + 472 q^{25} - 1184 q^{29} - 256 q^{30} - 1152 q^{32} - 1952 q^{36} - 1392 q^{37} + 1184 q^{44} + 816 q^{46} + 3376 q^{50}+ \cdots + 2304 q^{93}+O(q^{100}) \) 16 * q + 8 * q^2 + 16 * q^4 - 64 * q^8 - 104 * q^9 - 64 * q^16 - 88 * q^18 + 480 * q^22 + 472 * q^25 - 1184 * q^29 - 256 * q^30 - 1152 * q^32 - 1952 * q^36 - 1392 * q^37 + 1184 * q^44 + 816 * q^46 + 3376 * q^50 + 1168 * q^53 - 384 * q^57 + 560 * q^58 - 2944 * q^60 - 6656 * q^64 - 448 * q^65 + 1184 * q^72 + 496 * q^74 + 15360 * q^78 + 4984 * q^81 + 2048 * q^85 - 240 * q^86 - 3776 * q^88 - 7616 * q^92 + 2304 * q^93

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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