LMFDB - Embedded newform 196.4.f.c.19.7

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			19.7
Root			$4.18996 + 0.456399i$ of defining polynomial
Character	$\chi$	$=$	196.19
Dual form			196.4.f.c.31.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.48330 - 1.35396i) q^{2} +(-2.39945 - 4.15597i) q^{3} +(4.33360 - 6.72458i) 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} +(48.2747 + 1.17957i) q^{10} +(35.9149 - 20.7355i) q^{11} +(-38.3454 - 1.87502i) q^{12} +45.3599i q^{13} -81.9306i q^{15} +(-26.4398 - 58.2832i) q^{16} +(-24.4974 + 14.1436i) q^{17} +(0.274328 - 11.2271i) 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} +(-97.7619 + 47.2618i) q^{24} +(83.2401 + 144.176i) q^{25} +(61.4154 + 112.642i) q^{26} -148.625 q^{27} +27.8234 q^{29} +(-110.931 - 203.459i) q^{30} +(-40.7200 - 70.5291i) q^{31} +(-144.571 - 108.937i) 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} +(2.87026 - 117.467i) q^{38} +(188.514 - 108.839i) q^{39} +(217.135 - 319.515i) q^{40} -227.302i q^{41} +171.988i q^{43} +(16.2035 - 331.372i) q^{44} +(58.7066 - 33.8943i) q^{45} +(-265.592 - 6.48961i) 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} +(305.026 + 196.572i) q^{52} +(287.960 + 498.762i) q^{53} +(-369.080 + 201.231i) q^{54} +708.025 q^{55} -199.362 q^{57} +(69.0939 - 37.6717i) q^{58} +(206.000 + 356.802i) q^{59} +(-550.949 - 355.054i) 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} +(-562.732 - 13.7501i) q^{66} +(172.143 - 99.3867i) q^{67} +(-11.0523 + 226.027i) q^{68} +450.756i q^{69} +197.762i q^{71} +(-74.3086 - 50.4985i) q^{72} +(221.347 - 127.795i) q^{73} +(-6.55006 + 268.066i) 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} +(106.603 - 1087.45i) q^{80} +(303.015 + 524.837i) q^{81} +(-307.757 - 564.460i) q^{82} -938.514 q^{83} -482.940 q^{85} +(232.864 + 427.098i) q^{86} +(-66.7608 - 115.633i) q^{87} +(-408.425 - 844.836i) 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} +(-19.7602 + 808.702i) q^{94} +(614.238 - 354.631i) q^{95} +(-105.846 + 862.221i) 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 $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	2.48330	−	1.35396i	0.877981	−	0.478696i
$2$	2.48330	−	1.35396i	0.877981	−	0.478696i
$3$	−2.39945	−	4.15597i	−0.461774	−	0.799817i	0.537275	−	0.843407i	$-0.319454\pi$
$3$	−2.39945	−	4.15597i	−0.461774	−	0.799817i	−0.999049	+	0.0435904i	$0.986120\pi$
$4$	4.33360	−	6.72458i	0.541700	−	0.840572i
$5$	14.7855	+	8.53640i	1.32245	+	0.763518i	0.984119	−	0.177508i	$-0.0568035\pi$
$5$	14.7855	+	8.53640i	1.32245	+	0.763518i	0.338333	+	0.941026i	$0.390137\pi$
$6$	−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
$10$	48.2747	+	1.17957i	1.52658	+	0.0373012i
$11$	35.9149	−	20.7355i	0.984432	−	0.568362i	0.0808269	−	0.996728i	$-0.474244\pi$
$11$	35.9149	−	20.7355i	0.984432	−	0.568362i	0.903605	+	0.428366i	$0.140911\pi$
$12$	−38.3454	−	1.87502i	−0.922447	−	0.0451060i
$13$			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
$16$	−26.4398	−	58.2832i	−0.413123	−	0.910675i
$17$	−24.4974	+	14.1436i	−0.349499	+	0.201783i	−0.664465	−	0.747320i	$-0.731340\pi$
$17$	−24.4974	+	14.1436i	−0.349499	+	0.201783i	0.314966	+	0.949103i	$0.398007\pi$
$18$	0.274328	−	11.2271i	0.00359221	−	0.147014i
$19$	20.7717	−	35.9776i	0.250808	−	0.434412i	−0.712941	−	0.701225i	$-0.752637\pi$
$19$	20.7717	−	35.9776i	0.250808	−	0.434412i	0.963749	+	0.266812i	$0.0859704\pi$
$20$	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	$-0.473331\pi$
$23$	−81.3450	−	46.9645i	−0.737461	−	0.425773i	−0.821145	+	0.570719i	$0.806665\pi$
$24$	−97.7619	+	47.2618i	−0.831482	+	0.401970i
$25$	83.2401	+	144.176i	0.665921	+	1.15341i
$26$	61.4154	+	112.642i	0.463252	+	0.849654i
$27$	−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	$0.471607\pi$
$30$	−110.931	−	203.459i	−0.675102	−	1.23821i
$31$	−40.7200	−	70.5291i	−0.235920	−	0.408626i	0.723619	−	0.690199i	$-0.242477\pi$
$31$	−40.7200	−	70.5291i	−0.235920	−	0.408626i	−0.959540	+	0.281573i	$0.909144\pi$
$32$	−144.571	−	108.937i	−0.798650	−	0.601795i
$33$	−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	−0.951908	−	0.306384i	$-0.900881\pi$
$37$	−47.4020	+	82.1027i	−0.210617	+	0.364800i	0.741291	+	0.671184i	$0.234214\pi$
$38$	2.87026	−	117.467i	0.0122531	−	0.501466i
$39$	188.514	−	108.839i	0.774012	−	0.446876i
$40$	217.135	−	319.515i	0.858303	−	1.26300i
$41$		−	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	$0.901352\pi$
$44$	16.2035	−	331.372i	0.0555174	−	1.13537i
$45$	58.7066	−	33.8943i	0.194477	−	0.112281i
$46$	−265.592	−	6.48961i	−0.851292	−	0.0208009i
$47$	−143.002	+	247.687i	−0.443809	+	0.768700i	−0.997968	−	0.0637105i	$-0.979707\pi$
$47$	−143.002	+	247.687i	−0.443809	+	0.768700i	0.554159	+	0.832411i	$0.313040\pi$
$48$	−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
$52$	305.026	+	196.572i	0.813452	+	0.524223i
$53$	287.960	+	498.762i	0.746310	+	1.29265i	0.949580	+	0.313524i	$0.101510\pi$
$53$	287.960	+	498.762i	0.746310	+	1.29265i	−0.203271	+	0.979123i	$0.565157\pi$
$54$	−369.080	+	201.231i	−0.930101	+	0.507113i
$55$	708.025			1.73582
$56$		0			0
$57$	−199.362			−0.463267
$58$	69.0939	−	37.6717i	0.156422	−	0.0852850i
$59$	206.000	+	356.802i	0.454557	+	0.787316i	0.998663	−	0.0517011i	$-0.0164643\pi$
$59$	206.000	+	356.802i	0.454557	+	0.787316i	−0.544106	+	0.839017i	$0.683131\pi$
$60$	−550.949	−	355.054i	−1.18545	−	0.763955i
$61$	674.623	+	389.494i	1.41601	+	0.817534i	0.995945	−	0.0899604i	$-0.0286741\pi$
$61$	674.623	+	389.494i	1.41601	+	0.817534i	0.420065	+	0.907494i	$0.362007\pi$
$62$	−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
$66$	−562.732	−	13.7501i	−1.04951	−	0.0256442i
$67$	172.143	−	99.3867i	0.313889	−	0.181224i	−0.334776	−	0.942298i	$-0.608661\pi$
$67$	172.143	−	99.3867i	0.313889	−	0.181224i	0.648666	+	0.761074i	$0.275327\pi$
$68$	−11.0523	+	226.027i	−0.0197101	+	0.403085i
$69$			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	$0.947147\pi$
$72$	−74.3086	−	50.4985i	−0.121630	−	0.0826570i
$73$	221.347	−	127.795i	0.354886	−	0.204894i	−0.311949	−	0.950099i	$-0.600982\pi$
$73$	221.347	−	127.795i	0.354886	−	0.204894i	0.666835	+	0.745205i	$0.267648\pi$
$74$	−6.55006	+	268.066i	−0.0102896	+	0.421109i
$75$	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	$-0.0163694\pi$
$79$	1020.60	+	589.244i	1.45350	+	0.839179i	0.454822	+	0.890582i	$0.349703\pi$
$80$	106.603	−	1087.45i	0.148982	−	1.51975i
$81$	303.015	+	524.837i	0.415658	+	0.719941i
$82$	−307.757	−	564.460i	−0.414465	−	0.760174i
$83$	−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
$86$	232.864	+	427.098i	0.291981	+	0.535525i
$87$	−66.7608	−	115.633i	−0.0822702	−	0.142496i
$88$	−408.425	−	844.836i	−0.494753	−	1.02341i
$89$	−1010.49	−	583.404i	−1.20350	−	0.694840i	−0.242166	−	0.970235i	$-0.577858\pi$
$89$	−1010.49	−	583.404i	−1.20350	−	0.694840i	−0.961331	+	0.275395i	$0.911191\pi$
$90$	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
$94$	−19.7602	+	808.702i	−0.0216820	+	0.887354i
$95$	614.238	−	354.631i	0.663363	−	0.382993i
$96$	−105.846	+	862.221i	−0.112529	+	0.916667i
$97$		−	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
$100$	1330.25	+	65.0469i	1.33025	+	0.0650469i
$101$	−865.528	+	499.713i	−0.852706	+	0.492310i	−0.861563	−	0.507651i	$-0.830514\pi$
$101$	−865.528	+	499.713i	−0.852706	+	0.492310i	0.00885711	+	0.999961i	$0.497181\pi$
$102$	383.836	+	9.37884i	0.372602	+	0.00910435i
$103$	−479.466	+	830.460i	−0.458672	+	0.794443i	−0.998891	−	0.0470813i	$-0.985008\pi$
$103$	−479.466	+	830.460i	−0.458672	+	0.794443i	0.540219	+	0.841524i	$0.318341\pi$
$104$	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	$-0.233055\pi$
$107$	594.001	+	342.946i	0.536675	+	0.309849i	−0.207055	+	0.978329i	$0.566388\pi$
$108$	−644.079	+	999.438i	−0.573857	+	0.890472i
$109$	−563.902	−	976.706i	−0.495523	−	0.858271i	0.504464	−	0.863433i	$-0.331690\pi$
$109$	−563.902	−	976.706i	−0.495523	−	0.858271i	−0.999987	+	0.00516223i	$0.998357\pi$
$110$	1758.24	−	958.636i	1.52402	−	0.830931i
$111$	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	$0.501331\pi$
$114$	−495.078	+	269.928i	−0.406739	+	0.221764i
$115$	−801.816	−	1388.79i	−0.650171	−	1.12613i
$116$	120.575	−	187.100i	0.0965098	−	0.149757i
$117$	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
$122$	2202.65	+	53.8207i	1.63458	+	0.0399401i
$123$	−944.661	+	545.400i	−0.692498	+	0.399814i
$124$	−650.743	−	31.8201i	−0.471278	−	0.0230446i
$125$			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	$0.844038\pi$
$128$	−1359.07	+	500.093i	−0.938481	+	0.345331i
$129$	714.776	−	412.676i	0.487849	−	0.281660i
$130$	−53.5051	+	2189.74i	−0.0360978	+	1.47733i
$131$	−240.133	+	415.922i	−0.160156	+	0.277399i	−0.934925	−	0.354846i	$-0.884533\pi$
$131$	−240.133	+	415.922i	−0.160156	+	0.277399i	0.774768	+	0.632245i	$0.217867\pi$
$132$	−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
$136$	278.585	+	576.258i	0.175650	+	0.363336i
$137$	123.902	+	214.604i	0.0772674	+	0.133831i	0.902070	−	0.431590i	$-0.142047\pi$
$137$	123.902	+	214.604i	0.0772674	+	0.133831i	−0.824803	+	0.565421i	$0.808714\pi$
$138$	610.305	+	1119.36i	0.376468	+	0.690483i
$139$	−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
$142$	267.761	+	491.103i	0.158240	+	0.290229i
$143$	940.560	+	1629.10i	0.550025	+	0.952671i
$144$	−252.904	−	24.7923i	−0.146356	−	0.0143474i
$145$	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	−0.387019	−	0.922072i	$-0.626495\pi$
$149$	1100.41	−	1905.97i	0.605028	−	1.04794i	0.992047	−	0.125868i	$-0.0401715\pi$
$150$	55.1980	−	2259.02i	0.0300460	−	1.22965i
$151$	−2779.04	+	1604.48i	−1.49771	+	0.864706i	−0.999997	−	0.00263344i	$-0.999162\pi$
$151$	−2779.04	+	1604.48i	−1.49771	+	0.864706i	−0.497718	+	0.867339i	$0.665828\pi$
$152$	−777.480	−	528.358i	−0.414881	−	0.281944i
$153$			112.316i			0.0593477i
$154$		0			0
$155$		−	1390.41i		−	0.720518i
$156$	85.0507	−	1739.34i	0.0436507	−	0.892685i
$157$	551.266	−	318.273i	0.280228	−	0.161790i	−0.353299	−	0.935511i	$-0.614940\pi$
$157$	551.266	−	318.273i	0.280228	−	0.161790i	0.633527	+	0.773721i	$0.281607\pi$
$158$	3332.27	+	81.4224i	1.67786	+	0.0409976i
$159$	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	$-0.534656\pi$
$163$	−2130.75	−	1230.19i	−1.02389	−	0.591141i	−0.915227	+	0.402938i	$0.867989\pi$
$164$	−1528.51	−	985.036i	−0.727784	−	0.469015i
$165$	−1698.87	−	2942.53i	−0.801557	−	1.38834i
$166$	−2330.62	+	1270.71i	−1.08970	+	0.594133i
$167$	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
$170$	−1199.29	+	653.881i	−0.541066	+	0.295002i
$171$	−82.4753	−	142.851i	−0.0368833	−	0.0638837i
$172$	1156.55	+	745.326i	0.512708	+	0.330410i
$173$	1266.76	+	731.366i	0.556706	+	0.321415i	0.751822	−	0.659366i	$-0.229175\pi$
$173$	1266.76	+	731.366i	0.556706	+	0.321415i	−0.195116	+	0.980780i	$0.562508\pi$
$174$	−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
$178$	−3299.25	−	80.6154i	−1.38926	−	0.0339460i
$179$	2631.82	−	1519.48i	1.09895	−	0.634478i	0.163003	−	0.986626i	$-0.447882\pi$
$179$	2631.82	−	1519.48i	1.09895	−	0.634478i	0.935944	+	0.352148i	$0.114549\pi$
$180$	26.4863	−	541.662i	0.0109676	−	0.224295i
$181$			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
$184$	−1194.61	+	1757.87i	−0.478630	+	0.704305i
$185$	−1401.72	+	809.285i	−0.557063	+	0.321621i
$186$	−27.0021	+	1105.08i	−0.0106446	+	0.435638i
$187$	−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	$-0.363865\pi$
$191$	−437.867	−	252.802i	−0.165879	−	0.0957704i	−0.580641	+	0.814159i	$0.697198\pi$
$192$	904.564	+	2284.47i	0.340007	+	0.858684i
$193$	−960.954	−	1664.42i	−0.358399	−	0.620765i	0.629295	−	0.777167i	$-0.283344\pi$
$193$	−960.954	−	1664.42i	−0.358399	−	0.620765i	−0.987694	+	0.156402i	$0.950011\pi$
$194$	−889.056	−	1630.62i	−0.329023	−	0.603464i
$195$	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	$0.406350\pi$
$198$	−222.947	−	408.909i	−0.0800209	−	0.146767i
$199$	1279.38	+	2215.95i	0.455742	+	0.789368i	0.998731	−	0.0503720i	$-0.0160407\pi$
$199$	1279.38	+	2215.95i	0.455742	+	0.789368i	−0.542989	+	0.839740i	$0.682707\pi$
$200$	3391.49	−	1639.57i	1.19907	−	0.579677i
$201$	−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
$206$	−66.2532	+	2711.46i	−0.0224081	+	0.917070i
$207$	−322.985	+	186.476i	−0.108449	+	0.0626133i
$208$	2643.72	−	1199.31i	0.881294	−	0.399794i
$209$		−	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	$0.980183\pi$
$212$	4601.87	+	225.023i	1.49084	+	0.0728993i
$213$	821.893	−	474.520i	0.264391	−	0.152646i
$214$	1939.42	+	47.3887i	0.619514	+	0.0151375i
$215$	−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
$220$	3068.30	−	4761.17i	0.940294	−	1.45908i
$221$	−641.551	−	1111.20i	−0.195273	−	0.338223i
$222$	1129.79	−	615.990i	0.341562	−	0.186228i
$223$	−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
$226$	−24.9542	+	13.6056i	−0.00734481	+	0.00400457i
$227$	−2893.05	−	5010.91i	−0.845897	−	1.46514i	−0.884840	−	0.465895i	$-0.845732\pi$
$227$	−2893.05	−	5010.91i	−0.845897	−	1.46514i	0.0389429	−	0.999241i	$-0.487601\pi$
$228$	−863.957	+	1340.63i	−0.250952	+	0.389409i
$229$	−3727.24	−	2151.93i	−1.07556	−	0.620975i	−0.145865	−	0.989305i	$-0.546596\pi$
$229$	−3727.24	−	2151.93i	−1.07556	−	0.620975i	−0.929695	+	0.368330i	$0.879930\pi$
$230$	−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	0.238552	+	0.971130i	$0.423327\pi$
$233$	−2566.96	+	4446.10i	−0.721747	+	1.25010i	−0.960299	+	0.278972i	$0.910006\pi$
$234$	509.260	+	12.4435i	0.142271	+	0.00347632i
$235$	−4228.71	+	2441.45i	−1.17383	+	0.677713i
$236$	3292.06	+	160.976i	0.908029	+	0.0444010i
$237$		−	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	$-0.0201919\pi$
$240$	−4775.18	+	2166.23i	−1.28432	+	0.582624i
$241$	337.318	−	194.751i	0.0901600	−	0.0520539i	−0.454242	−	0.890878i	$-0.650090\pi$
$241$	337.318	−	194.751i	0.0901600	−	0.0520539i	0.544402	+	0.838824i	$0.316757\pi$
$242$	26.8653	−	1099.48i	0.00713623	−	0.292055i
$243$	−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
$248$	−1659.08	+	802.059i	−0.424804	+	0.205366i
$249$	2251.92	+	3900.43i	0.573130	+	0.992691i
$250$	958.850	+	1758.63i	0.242572	+	0.444903i
$251$	−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
$254$	1823.86	+	3345.16i	0.450548	+	0.826353i
$255$	1158.79	+	2007.08i	0.284574	+	0.492896i
$256$	−2697.87	+	3082.00i	−0.658659	+	0.752441i
$257$	4523.48	+	2611.63i	1.09793	+	0.633888i	0.935676	−	0.352861i	$-0.114791\pi$
$257$	4523.48	+	2611.63i	1.09793	+	0.633888i	0.162251	+	0.986750i	$0.448125\pi$
$258$	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
$262$	−33.1818	+	1357.99i	−0.00782434	+	0.320217i
$263$	4074.48	−	2352.40i	0.955297	−	0.551541i	0.0605744	−	0.998164i	$-0.480707\pi$
$263$	4074.48	−	2352.40i	0.955297	−	0.551541i	0.894722	+	0.446623i	$0.147373\pi$
$264$	−2531.12	+	3724.54i	−0.590074	+	0.868295i
$265$			9832.58i			2.27928i
$266$		0			0
$267$			5599.40i			1.28344i
$268$	77.6645	−	1588.29i	0.0177019	−	0.362016i
$269$	2983.05	−	1722.26i	0.676132	−	0.390365i	−0.122264	−	0.992498i	$-0.539015\pi$
$269$	2983.05	−	1722.26i	0.676132	−	0.390365i	0.798396	+	0.602132i	$0.205682\pi$
$270$	−7174.81	−	175.313i	−1.61720	−	0.0395156i
$271$	2625.89	−	4548.17i	0.588603	−	1.01949i	−0.405813	−	0.913956i	$-0.633011\pi$
$271$	2625.89	−	4548.17i	0.588603	−	1.01949i	0.994416	−	0.105534i	$-0.0336553\pi$
$272$	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
$276$	3031.14	+	1953.40i	0.661063	+	0.426017i
$277$	−3001.60	−	5198.92i	−0.651077	−	1.12770i	−0.982862	−	0.184344i	$-0.940984\pi$
$277$	−3001.60	−	5198.92i	−0.651077	−	1.12770i	0.331785	−	0.943355i	$-0.392349\pi$
$278$	−4575.12	+	2494.47i	−0.987042	+	0.538159i
$279$	−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	$0.563627\pi$
$282$	3408.35	−	1858.32i	0.719732	−	0.392416i
$283$	1981.71	+	3432.42i	0.416256	+	0.720976i	0.995559	−	0.0941357i	$-0.0300087\pi$
$283$	1981.71	+	3432.42i	0.416256	+	0.720976i	−0.579304	+	0.815112i	$0.696675\pi$
$284$	1329.87	+	857.021i	0.277863	+	0.179066i
$285$	−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
$290$	1343.17	+	32.8196i	0.271977	+	0.00664563i
$291$	−2728.95	+	1575.56i	−0.549739	+	0.317392i
$292$	99.8635	−	2042.27i	0.0200139	−	0.409298i
$293$			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
$296$	1774.25	+	1205.74i	0.348399	+	0.236764i
$297$	−5337.84	+	3081.80i	−1.04287	+	0.602102i
$298$	152.056	−	6223.01i	0.0295583	−	1.20970i
$299$	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
$304$	−2646.09	−	259.398i	−0.499223	−	0.0489392i
$305$	6649.75	+	11517.7i	1.24840	+	2.16230i
$306$	152.071	+	278.914i	0.0284095	+	0.0521061i
$307$	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
$310$	−1882.55	−	3452.81i	−0.344909	−	0.632601i
$311$	−3279.55	−	5680.35i	−0.597962	−	1.03570i	−0.993122	−	0.117088i	$-0.962644\pi$
$311$	−3279.55	−	5680.35i	−0.597962	−	1.03570i	0.395160	−	0.918613i	$-0.370689\pi$
$312$	−2143.79	−	4434.47i	−0.389001	−	0.804656i
$313$	5384.22	+	3108.58i	0.972314	+	0.561366i	0.899941	−	0.436012i	$-0.143609\pi$
$313$	5384.22	+	3108.58i	0.972314	+	0.561366i	0.0723733	+	0.997378i	$0.476943\pi$
$314$	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	−0.973415	−	0.229051i	$-0.926438\pi$
$317$	−1627.42	+	2818.77i	−0.288344	+	0.499426i	0.685071	+	0.728476i	$0.259771\pi$
$318$	190.952	−	7814.84i	0.0336731	−	1.37810i
$319$	999.274	−	576.931i	0.175388	−	0.101260i
$320$	−6850.64	−	5429.42i	−1.19676	−	0.948480i
$321$		−	3291.53i		−	0.572322i
$322$		0			0
$323$			1175.14i			0.202436i
$324$	4842.45	+	236.787i	0.830324	+	0.0406013i
$325$	−6539.82	+	3775.76i	−1.11620	+	0.644436i
$326$	−6956.94	−	169.989i	−1.18193	−	0.0288799i
$327$	−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	$-0.451959\pi$
$331$	−3797.79	−	2192.65i	−0.630651	−	0.364106i	−0.781004	+	0.624526i	$0.785292\pi$
$332$	−4067.14	+	6311.11i	−0.672330	+	1.04327i
$333$	188.213	+	325.994i	0.0309729	+	0.0536467i
$334$	5297.28	−	2888.20i	0.867827	−	0.473160i
$335$	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	$0.781451\pi$
$338$	346.365	−	188.847i	0.0557390	−	0.0303903i
$339$	24.1115	+	41.7624i	0.00386300	+	0.00669092i
$340$	−2092.87	+	3247.57i	−0.333829	+	0.518012i
$341$	−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
$346$	4136.00	+	101.061i	0.642637	+	0.0157025i
$347$	9015.01	−	5204.82i	1.39467	−	0.805214i	0.400843	−	0.916147i	$-0.368717\pi$
$347$	9015.01	−	5204.82i	1.39467	−	0.805214i	0.993828	+	0.110933i	$0.0353838\pi$
$348$	−1066.90	−	52.1694i	−0.164344	−	0.00803613i
$349$		−	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
$352$	−7451.11	−	914.694i	−1.12825	−	0.138504i
$353$	8965.19	−	5176.06i	1.35175	−	0.780435i	0.363259	−	0.931688i	$-0.381664\pi$
$353$	8965.19	−	5176.06i	1.35175	−	0.780435i	0.988495	+	0.151253i	$0.0483308\pi$
$354$	136.602	−	5590.53i	0.0205093	−	0.839360i
$355$	−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	$-0.245125\pi$
$359$	3223.20	+	1860.92i	0.473855	+	0.273580i	−0.243997	+	0.969776i	$0.578459\pi$
$360$	−667.613	−	1380.97i	−0.0977397	−	0.202177i
$361$	2566.57	+	4445.44i	0.374191	+	0.648117i
$362$	521.244	+	956.017i	0.0756794	+	0.138804i
$363$	−1866.01			−0.269808
$364$		0			0
$365$	4363.62			0.625760
$366$	−5061.48	−	9283.29i	−0.722862	−	1.32581i
$367$	−2338.05	−	4049.63i	−0.332549	−	0.575991i	0.650462	−	0.759539i	$-0.274575\pi$
$367$	−2338.05	−	4049.63i	−0.332549	−	0.575991i	−0.983011	+	0.183547i	$0.941242\pi$
$368$	−586.497	+	5982.78i	−0.0830795	+	0.847484i
$369$	−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	−0.540643	−	0.841252i	$-0.681819\pi$
$373$	3300.97	−	5717.44i	0.458224	−	0.793668i	0.998867	+	0.0475845i	$0.0151523\pi$
$374$	−81.0498	+	3317.02i	−0.0112058	+	0.458607i
$375$	2943.19	−	1699.25i	0.405295	−	0.233997i
$376$	5352.55	+	3637.47i	0.734140	+	0.498905i
$377$			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	$-0.332323\pi$
$380$	277.122	−	5667.32i	0.0374106	−	0.765072i
$381$	5598.33	−	3232.20i	0.752786	−	0.434621i
$382$	−1429.64	−	34.9325i	−0.191484	−	0.00467880i
$383$	−786.757	+	1362.70i	−0.104965	+	0.181804i	−0.913724	−	0.406336i	$-0.866806\pi$
$383$	−786.757	+	1362.70i	−0.104965	+	0.181804i	0.808759	+	0.588140i	$0.200140\pi$
$384$	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
$388$	−4415.59	−	2845.59i	−0.577752	−	0.372327i
$389$	2011.47	+	3483.98i	0.262174	+	0.454099i	0.966819	−	0.255461i	$-0.0822271\pi$
$389$	2011.47	+	3483.98i	0.262174	+	0.454099i	−0.704645	+	0.709560i	$0.748894\pi$
$390$	9228.87	−	5031.80i	1.19826	−	0.653321i
$391$	2656.98			0.343656
$392$		0			0
$393$	2304.74			0.295824
$394$	3982.30	−	2171.24i	0.509201	−	0.277629i
$395$	10060.0	+	17424.5i	1.28146	+	2.21955i
$396$	−1107.29	−	713.584i	−0.140514	−	0.0905529i
$397$	−3453.12	−	1993.66i	−0.436542	−	0.252038i	0.265588	−	0.964087i	$-0.414434\pi$
$397$	−3453.12	−	1993.66i	−0.436542	−	0.252038i	−0.702130	+	0.712049i	$0.747767\pi$
$398$	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	−0.973320	−	0.229452i	$-0.926306\pi$
$401$	−2312.23	+	4004.90i	−0.287948	+	0.498741i	0.685372	+	0.728194i	$0.259640\pi$
$402$	−2697.21	−	65.9050i	−0.334639	−	0.00817673i
$403$	3199.20	−	1847.06i	0.395442	−	0.228309i
$404$	−390.494	+	7985.87i	−0.0480887	+	0.983445i
$405$			10346.6i			1.26945i
$406$		0			0
$407$			3931.62i			0.478828i
$408$	1726.46	−	2540.49i	0.209492	−	0.308267i
$409$	548.219	−	316.514i	0.0662779	−	0.0382656i	−0.466495	−	0.884524i	$-0.654483\pi$
$409$	548.219	−	316.514i	0.0662779	−	0.0382656i	0.532773	+	0.846258i	$0.321150\pi$
$410$	268.119	−	10973.0i	0.0322962	−	1.32175i
$411$	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
$416$	4941.35	−	6557.74i	0.582379	−	0.772883i
$417$	4420.64	+	7656.76i	0.519135	+	0.899169i
$418$	−2332.66	−	4278.35i	−0.272952	−	0.500624i
$419$	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	$0.602918\pi$
$422$	516.384	+	947.105i	0.0595668	+	0.109252i
$423$	567.800	+	983.458i	0.0652657	+	0.113043i
$424$	11732.5	−	5671.93i	1.34382	−	0.649654i
$425$	−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
$430$	−202.872	+	8302.67i	−0.0227519	+	0.931140i
$431$	−3618.55	+	2089.17i	−0.404406	+	0.233484i	−0.688384	−	0.725347i	$-0.741679\pi$
$431$	−3618.55	+	2089.17i	−0.404406	+	0.233484i	0.283977	+	0.958831i	$0.408346\pi$
$432$	3929.61	+	8662.32i	0.437647	+	0.964737i
$433$		−	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
$436$	−9011.66	−	440.654i	−0.989863	−	0.0484025i
$437$	−3379.34	+	1951.07i	−0.369922	+	0.213575i
$438$	−3468.16	−	84.7428i	−0.378345	−	0.00924468i
$439$	−1465.71	+	2538.69i	−0.159350	+	0.276002i	−0.934634	−	0.355610i	$-0.884273\pi$
$439$	−1465.71	+	2538.69i	−0.159350	+	0.276002i	0.775285	+	0.631612i	$0.217606\pi$
$440$	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	$-0.231147\pi$
$443$	5095.95	+	2942.15i	0.546537	+	0.315543i	−0.201187	+	0.979553i	$0.564480\pi$
$444$	1971.59	−	3059.38i	0.210738	−	0.327008i
$445$	−9960.34	−	17251.8i	−1.06105	−	1.83778i
$446$	−7310.56	+	3985.89i	−0.776155	+	0.423178i
$447$	−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	$0.263865\pi$
$450$	1641.51	−	894.993i	0.171959	−	0.0937564i
$451$	−4713.22	−	8163.54i	−0.492100	−	0.852342i
$452$	−43.5474	+	67.5737i	−0.00453163	+	0.00703186i
$453$	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	−0.909072	−	0.416639i	$-0.863208\pi$
$457$	−915.559	+	1585.80i	−0.0937157	+	0.162320i	0.815356	+	0.578960i	$0.196541\pi$
$458$	−12169.5	−	297.356i	−1.24158	−	0.0303374i
$459$	3640.91	−	2102.08i	0.370247	−	0.213762i
$460$	−12813.7	−	626.569i	−1.29879	−	0.0635085i
$461$			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	$0.870283\pi$
$464$	−735.646	−	1621.64i	−0.0736024	−	0.162247i
$465$	−5778.50	+	3336.22i	−0.576282	+	0.332717i
$466$	−354.705	+	14516.6i	−0.0352605	+	1.44306i
$467$	7294.01	−	12633.6i	0.722755	−	1.25185i	−0.237136	−	0.971476i	$-0.576209\pi$
$467$	7294.01	−	12633.6i	0.722755	−	1.25185i	0.959891	−	0.280372i	$-0.0904580\pi$
$468$	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
$472$	8393.14	−	4057.56i	0.818486	−	0.395687i
$473$	3566.25	+	6176.93i	0.346673	+	0.600456i
$474$	−7657.23	−	14044.2i	−0.742001	−	1.36091i
$475$	6916.15			0.668073
$476$		0			0
$477$	2286.73			0.219501
$478$	−634.259	−	1163.30i	−0.0606911	−	0.111314i
$479$	−9176.03	−	15893.4i	−0.875289	−	1.51605i	−0.856454	−	0.516223i	$-0.827338\pi$
$479$	−9176.03	−	15893.4i	−0.875289	−	1.51605i	−0.0188353	−	0.999823i	$-0.505996\pi$
$480$	−8925.24	+	11844.8i	−0.848707	+	1.12633i
$481$	−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
$486$	−76.3168	+	3123.32i	−0.00712304	+	0.291516i
$487$	−12707.6	+	7336.74i	−1.18242	+	0.682668i	−0.956572	−	0.291496i	$-0.905847\pi$
$487$	−12707.6	+	7336.74i	−1.18242	+	0.682668i	−0.225843	+	0.974164i	$0.572514\pi$
$488$	9907.33	−	14578.7i	0.919024	−	1.35235i
$489$			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	$0.952768\pi$
$492$	−426.196	+	8715.99i	−0.0390537	+	0.798673i
$493$	−681.600	+	393.522i	−0.0622671	+	0.0359500i
$494$	5328.31	+	130.195i	0.485287	+	0.0118578i
$495$	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	$-0.463384\pi$
$499$	−7670.50	−	4428.57i	−0.688134	−	0.397294i	−0.802913	+	0.596097i	$0.796717\pi$
$500$	4762.23	+	3068.98i	0.425947	+	0.274498i
$501$	−5118.40	−	8865.34i	−0.456434	−	0.790567i
$502$	−11648.2	+	6350.86i	−1.03562	+	0.564647i
$503$	−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
$506$	−9673.29	+	5274.11i	−0.849862	+	0.463365i
$507$	−334.670	−	579.665i	−0.0293160	−	0.0507768i
$508$	9058.40	+	5837.61i	0.791145	+	0.509847i
$509$	9257.46	+	5344.80i	0.806149	+	0.465430i	0.845617	−	0.533791i	$-0.179233\pi$
$509$	9257.46	+	5344.80i	0.806149	+	0.465430i	−0.0394680	+	0.999221i	$0.512566\pi$
$510$	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
$514$	14769.2	+	360.879i	1.26740	+	0.0309682i
$515$	−14178.3	+	8185.83i	−1.21314	+	0.700409i
$516$	322.481	−	6594.94i	0.0275124	−	0.562647i
$517$			11860.9i			1.00898i
$518$		0			0
$519$		−	7019.50i		−	0.593684i
$520$	14493.2	+	9849.25i	1.22225	+	0.830612i
$521$	−11693.0	+	6750.93i	−0.983259	+	0.567685i	−0.903252	−	0.429110i	$-0.858827\pi$
$521$	−11693.0	+	6750.93i	−0.983259	+	0.567685i	−0.0800063	+	0.996794i	$0.525494\pi$
$522$	7.63274	−	312.376i	0.000639992	−	0.0261922i
$523$	−6909.97	+	11968.4i	−0.577728	+	1.00065i	0.418011	+	0.908442i	$0.362727\pi$
$523$	−6909.97	+	11968.4i	−0.577728	+	1.00065i	−0.995739	+	0.0922123i	$0.970606\pi$
$524$	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
$528$	−1242.66	+	12676.2i	−0.102424	+	1.04481i
$529$	−1672.16	−	2896.27i	−0.137434	−	0.238043i
$530$	13312.9	+	24417.3i	1.09109	+	2.00117i
$531$	1635.87			0.133692
$532$		0			0
$533$	10310.4			0.837886
$534$	7581.34	+	13905.0i	0.614376	+	1.12683i
$535$	5855.05	+	10141.2i	0.473151	+	0.819522i
$536$	−1957.61	−	4049.36i	−0.157754	−	0.326317i
$537$	−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	−0.837230	−	0.546851i	$-0.815826\pi$
$541$	691.732	−	1198.11i	0.0549720	−	0.0952144i	0.892202	+	0.451637i	$0.149160\pi$
$542$	362.848	−	14849.8i	0.0287559	−	1.17686i
$543$	1599.96	−	923.735i	0.126447	−	0.0730042i
$544$	5082.37	+	623.908i	0.400560	+	0.0491725i
$545$		−	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	$0.727855\pi$
$548$	1980.06	+	96.8213i	0.154350	+	0.00754745i
$549$	2678.63	−	1546.51i	0.208235	−	0.120225i
$550$	19521.9	+	477.008i	1.51349	+	0.0369813i
$551$	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
$556$	−7984.02	+	12389.0i	−0.608989	+	0.944987i
$557$	−12574.5	−	21779.7i	−0.956551	−	1.65680i	−0.730777	−	0.682616i	$-0.760842\pi$
$557$	−12574.5	−	21779.7i	−0.956551	−	1.65680i	−0.225774	−	0.974180i	$-0.572491\pi$
$558$	−803.008	+	437.819i	−0.0609212	+	0.0332157i
$559$	−7801.36			−0.590272
$560$		0			0
$561$	5629.56			0.423673
$562$	−4645.33	+	2532.75i	−0.348668	+	0.190102i
$563$	5563.59	+	9636.41i	0.416478	+	0.721361i	0.995582	−	0.0938923i	$-0.0299309\pi$
$563$	5563.59	+	9636.41i	0.416478	+	0.721361i	−0.579104	+	0.815253i	$0.696598\pi$
$564$	5947.90	−	9229.53i	0.444063	−	0.689066i
$565$	−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	−0.817490	−	0.575943i	$-0.804635\pi$
$569$	1222.05	−	2116.65i	0.0900368	−	0.155948i	0.907526	+	0.419995i	$0.137968\pi$
$570$	−9624.17	−	235.162i	−0.707214	−	0.0172804i
$571$	−6707.19	+	3872.40i	−0.491571	+	0.283809i	−0.725226	−	0.688511i	$-0.758265\pi$
$571$	−6707.19	+	3872.40i	−0.491571	+	0.283809i	0.233655	+	0.972320i	$0.424931\pi$
$572$	15031.0	+	734.989i	1.09874	+	0.0537263i
$573$			2426.35i			0.176897i
$574$		0			0
$575$		−	15637.3i		−	1.13413i
$576$	−1262.70	+	1593.23i	−0.0913412	+	0.115251i
$577$	23628.1	−	13641.7i	1.70476	−	0.984246i	0.763979	−	0.645241i	$-0.223243\pi$
$577$	23628.1	−	13641.7i	1.70476	−	0.984246i	0.940784	−	0.339005i	$-0.110090\pi$
$578$	−284.158	+	11629.4i	−0.0204488	+	0.836884i
$579$	−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
$584$	−2517.16	−	5206.80i	−0.178358	−	0.368936i
$585$	1537.44	+	2662.93i	0.108659	+	0.188203i
$586$	6302.22	+	11559.0i	0.444270	+	0.814840i
$587$	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
$590$	9523.70	+	17467.5i	0.664550	+	1.21886i
$591$	−3847.83	−	6664.63i	−0.267815	−	0.463868i
$592$	6038.51	+	591.960i	0.419225	+	0.0410970i
$593$	−18899.9	−	10911.9i	−1.30881	−	0.755643i	−0.326914	−	0.945054i	$-0.606009\pi$
$593$	−18899.9	−	10911.9i	−1.30881	−	0.755643i	−0.981898	+	0.189411i	$0.939342\pi$
$594$	−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
$598$	294.368	−	12047.2i	0.0201298	−	0.823827i
$599$	16759.8	−	9676.28i	1.14322	−	0.660037i	0.195992	−	0.980605i	$-0.437207\pi$
$599$	16759.8	−	9676.28i	1.14322	−	0.660037i	0.947225	+	0.320568i	$0.103874\pi$
$600$	−14951.7	−	10160.9i	−1.01734	−	0.691359i
$601$		−	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
$604$	−1253.80	+	25641.0i	−0.0844642	+	1.72735i
$605$	5749.21	−	3319.31i	0.386345	−	0.223056i
$606$	13561.5	+	331.368i	0.909073	+	0.0222127i
$607$	11896.7	−	20605.6i	0.795503	−	1.37785i	−0.127016	−	0.991901i	$-0.540540\pi$
$607$	11896.7	−	20605.6i	0.795503	−	1.37785i	0.922519	−	0.385951i	$-0.126127\pi$
$608$	−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
$612$	755.276	+	486.732i	0.0498860	+	0.0321486i
$613$	−9745.06	−	16878.9i	−0.642087	−	1.11213i	−0.984966	−	0.172747i	$-0.944736\pi$
$613$	−9745.06	−	16878.9i	−0.642087	−	1.11213i	0.342880	−	0.939379i	$-0.388598\pi$
$614$	7023.16	−	3829.19i	0.461615	−	0.251684i
$615$	−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	$0.634074\pi$
$618$	11427.7	−	6230.67i	0.743835	−	0.405557i
$619$	−1788.57	−	3097.90i	−0.116137	−	0.201155i	0.802097	−	0.597194i	$-0.203718\pi$
$619$	−1788.57	−	3097.90i	−0.116137	−	0.201155i	−0.918234	+	0.396039i	$0.870384\pi$
$620$	−9349.91	−	6025.47i	−0.605647	−	0.390305i
$621$	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
$626$	17579.6	+	429.548i	1.12240	+	0.0274252i
$627$	−7160.09	+	4133.88i	−0.456055	+	0.263303i
$628$	248.711	−	5086.30i	0.0158036	−	0.323193i
$629$		−	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	$0.970329\pi$
$632$	14988.3	−	22055.3i	0.943356	−	1.38815i
$633$	1585.04	−	915.124i	0.0995256	−	0.0574611i
$634$	−224.879	+	9203.32i	−0.0140869	+	0.576515i
$635$	−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
$640$	−24363.4	−	4207.42i	−1.50476	−	0.259864i
$641$	1237.01	+	2142.56i	0.0762229	+	0.132022i	0.901617	−	0.432534i	$-0.142381\pi$
$641$	1237.01	+	2142.56i	0.0762229	+	0.132022i	−0.825395	+	0.564556i	$0.809047\pi$
$642$	−4456.59	−	8173.87i	−0.273968	−	0.502488i
$643$	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
$646$	1591.09	+	2918.24i	0.0969051	+	0.177735i
$647$	12264.5	+	21242.8i	0.745237	+	1.29079i	0.950084	+	0.311994i	$0.100997\pi$
$647$	12264.5	+	21242.8i	0.745237	+	1.29079i	−0.204847	+	0.978794i	$0.565670\pi$
$648$	12345.9	−	5968.46i	0.748444	−	0.361826i
$649$	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	−0.967533	−	0.252745i	$-0.918666\pi$
$653$	−4420.01	+	7655.68i	−0.264882	+	0.458790i	0.702650	+	0.711535i	$0.252000\pi$
$654$	−373.933	+	15303.5i	−0.0223577	+	0.915006i
$655$	−7100.95	+	4099.73i	−0.423599	+	0.244565i
$656$	−13247.9	+	6009.83i	−0.788481	+	0.357690i
$657$		−	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	$-0.284137\pi$
$660$	−27149.5	−	1327.56i	−1.60120	−	0.0782958i
$661$	−19658.4	+	11349.8i	−1.15677	+	0.667861i	−0.950527	−	0.310641i	$-0.899456\pi$
$661$	−19658.4	+	11349.8i	−1.15677	+	0.667861i	−0.206241	+	0.978501i	$0.566123\pi$
$662$	−12399.8	−	302.983i	−0.727995	−	0.0177882i
$663$	−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
$668$	9244.25	−	14344.6i	0.535435	−	0.830851i
$669$	7063.70	+	12234.7i	0.408219	+	0.707056i
$670$	8427.38	−	4594.81i	0.485938	−	0.264945i
$671$	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	$0.547657\pi$
$674$	−23763.8	+	12956.6i	−1.35808	+	0.740458i
$675$	−12371.5	−	21428.1i	−0.705452	−	1.22188i
$676$	604.440	−	937.928i	0.0343901	−	0.0533641i
$677$	−2723.40	−	1572.35i	−0.154607	−	0.0892622i	0.420701	−	0.907199i	$-0.361784\pi$
$677$	−2723.40	−	1572.35i	−0.154607	−	0.0892622i	−0.575307	+	0.817937i	$0.695118\pi$
$678$	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
$682$	−9549.87	−	233.346i	−0.536193	−	0.0131016i
$683$	−10301.6	+	5947.66i	−0.577132	+	0.333208i	−0.759993	−	0.649931i	$-0.774798\pi$
$683$	−10301.6	+	5947.66i	−0.577132	+	0.333208i	0.182861	+	0.983139i	$0.441464\pi$
$684$	−1318.03	−	64.4493i	−0.0736786	−	0.00360275i
$685$			4230.69i			0.235980i
$686$		0			0
$687$			20653.8i			1.14700i
$688$	10024.0	−	4547.33i	0.555468	−	0.251985i
$689$	−22623.8	+	13061.9i	−1.25094	+	0.722231i
$690$	−531.698	+	21760.1i	−0.0293354	+	1.20057i
$691$	12303.2	−	21309.8i	0.677333	−	1.17318i	−0.298448	−	0.954426i	$-0.596469\pi$
$691$	12303.2	−	21309.8i	0.677333	−	1.17318i	0.975781	−	0.218750i	$-0.0701978\pi$
$692$	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
$696$	−2720.07	+	1314.98i	−0.148138	+	0.0716153i
$697$	3214.86	+	5568.31i	0.174708	+	0.302603i
$698$	−17076.7	−	31320.5i	−0.926020	−	1.69842i
$699$	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	$0.513963\pi$
$702$	−9127.84	−	16741.4i	−0.490752	−	0.900093i
$703$	1969.24	+	3410.82i	0.105649	+	0.182990i
$704$	−19741.8	+	7817.03i	−1.05689	+	0.418488i
$705$	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	−0.224175	−	0.974549i	$-0.571969\pi$
$709$	13817.2	−	23932.0i	0.731896	−	1.26768i	0.956072	−	0.293133i	$-0.0946978\pi$
$710$	−233.274	+	9546.91i	−0.0123304	+	0.504633i
$711$	4052.36	−	2339.63i	0.213749	−	0.123408i
$712$	−14839.7	+	21836.7i	−0.781098	+	1.14939i
$713$			7649.59i			0.401794i
$714$		0			0
$715$			32116.0i			1.67982i
$716$	1187.38	−	24282.7i	0.0619756	−	1.26744i
$717$	−1946.86	+	1124.02i	−0.101404	+	0.0585456i
$718$	10523.8	+	257.143i	0.546998	+	0.0133656i
$719$	−2971.62	+	5146.99i	−0.154134	+	0.266969i	−0.932743	−	0.360541i	$-0.882592\pi$
$719$	−2971.62	+	5146.99i	−0.154134	+	0.266969i	0.778609	+	0.627509i	$0.215926\pi$
$720$	−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
$724$	2588.81	+	1668.34i	0.132890	+	0.0856400i
$725$	2316.02	+	4011.47i	0.118641	+	0.205493i
$726$	−4633.88	+	2526.50i	−0.236886	+	0.129156i
$727$	−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
$730$	10836.2	−	5908.16i	0.549405	−	0.299549i
$731$	−2432.52	−	4213.25i	−0.123078	−	0.213177i
$732$	−25138.4	−	16200.2i	−1.26932	−	0.818002i
$733$	−14052.6	−	8113.27i	−0.708110	−	0.408828i	0.102251	−	0.994759i	$-0.467396\pi$
$733$	−14052.6	−	8113.27i	−0.708110	−	0.408828i	−0.810361	+	0.585931i	$0.800729\pi$
$734$	−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
$738$	−2551.94	−	62.3554i	−0.127288	−	0.00311021i
$739$	23629.6	−	13642.5i	1.17622	−	0.679092i	0.221084	−	0.975255i	$-0.429041\pi$
$739$	23629.6	−	13642.5i	1.17622	−	0.679092i	0.955137	+	0.296163i	$0.0957072\pi$
$740$	−632.405	+	12933.1i	−0.0314158	+	0.642474i
$741$		−	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	$-0.121121\pi$
$744$	7314.20	+	4970.56i	0.360419	+	0.244932i
$745$	32540.2	−	18787.1i	1.60024	−	0.923900i
$746$	456.131	−	18667.5i	0.0223863	−	0.916175i
$747$	−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	$-0.189771\pi$
$751$	15537.7	+	8970.68i	0.754964	+	0.435879i	−0.0725209	+	0.997367i	$0.523104\pi$
$752$	18217.0	+	1785.82i	0.883384	+	0.0865988i
$753$	11254.8	+	19494.0i	0.544687	+	0.943425i
$754$	1708.78	+	3134.09i	0.0825335	+	0.151375i
$755$	−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	$0.600715\pi$
$758$	−17271.3	−	31677.5i	−0.827602	−	1.51791i
$759$	9346.65	+	16188.9i	0.446985	+	0.774201i
$760$	−6985.13	−	14448.9i	−0.333391	−	0.689627i
$761$	−7678.27	−	4433.05i	−0.365752	−	0.211167i	0.305849	−	0.952080i	$-0.401060\pi$
$761$	−7678.27	−	4433.05i	−0.365752	−	0.211167i	−0.671601	+	0.740913i	$0.734393\pi$
$762$	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
$766$	−108.715	+	4449.24i	−0.00512798	+	0.209866i
$767$	−16184.5	+	9344.12i	−0.761914	+	0.439891i
$768$	19282.1	+	3817.16i	0.905967	+	0.179349i
$769$			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
$772$	−15356.9	−	750.925i	−0.715942	−	0.0350083i
$773$	16673.7	−	9626.55i	0.775822	−	0.447921i	−0.0591256	−	0.998251i	$-0.518831\pi$
$773$	16673.7	−	9626.55i	0.775822	−	0.447921i	0.834948	+	0.550330i	$0.185498\pi$
$774$	1930.92	+	47.1812i	0.0896714	+	0.00219107i
$775$	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
$780$	16105.2	−	24991.0i	0.739308	−	1.14721i
$781$	4100.69	+	7102.61i	0.187880	+	0.325418i
$782$	6598.10	−	3597.44i	0.301723	−	0.164507i
$783$	−4135.24			−0.188737
$784$		0			0
$785$	10867.6			0.494118
$786$	5723.38	−	3120.53i	0.259728	−	0.141610i
$787$	642.360	+	1112.60i	0.0290949	+	0.0503938i	0.880206	−	0.474591i	$-0.157404\pi$
$787$	642.360	+	1112.60i	0.0290949	+	0.0503938i	−0.851111	+	0.524985i	$0.824071\pi$
$788$	6949.48	−	10783.7i	0.314169	−	0.487505i
$789$	−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
$794$	−11274.5	−	275.486i	−0.503925	−	0.0123132i
$795$	40863.9	−	23592.8i	1.82301	−	1.05252i
$796$	20445.6	+	999.753i	0.910396	+	0.0445167i
$797$			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
$800$	3671.93	−	29911.6i	0.162278	−	1.32192i
$801$	−4012.20	+	2316.44i	−0.176984	+	0.102182i
$802$	−319.507	+	13076.0i	−0.0140675	+	0.575725i
$803$	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
$808$	9842.81	+	20360.0i	0.428550	+	0.886465i
$809$	5712.40	+	9894.17i	0.248254	+	0.429988i	0.963041	−	0.269353i	$-0.0868099\pi$
$809$	5712.40	+	9894.17i	0.248254	+	0.429988i	−0.714788	+	0.699342i	$0.753477\pi$
$810$	14008.9	+	25693.8i	0.607681	+	1.11455i
$811$	−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
$814$	5323.24	+	9763.40i	0.229213	+	0.420402i
$815$	−21002.8	−	36377.9i	−0.902695	−	1.56351i
$816$	847.610	−	8646.37i	0.0363631	−	0.370936i
$817$	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	−0.904137	−	0.427242i	$-0.859485\pi$
$821$	−1930.54	+	3343.79i	−0.0820660	+	0.142143i	0.822071	+	0.569385i	$0.192819\pi$
$822$	82.1613	−	3362.51i	0.00348626	−	0.142678i
$823$	4191.93	−	2420.21i	0.177548	−	0.102507i	−0.408592	−	0.912717i	$-0.633980\pi$
$823$	4191.93	−	2420.21i	0.177548	−	0.102507i	0.586140	+	0.810210i	$0.300647\pi$
$824$	17946.3	+	12195.9i	0.758725	+	0.515612i
$825$		−	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	$-0.00556741\pi$
$828$	−145.719	+	2980.05i	−0.00611605	+	0.125077i
$829$	−21387.6	+	12348.1i	−0.896046	+	0.517333i	−0.875915	−	0.482465i	$-0.839742\pi$
$829$	−21387.6	+	12348.1i	−0.896046	+	0.517333i	−0.0201310	+	0.999797i	$0.506408\pi$
$830$	−45306.5	−	1107.04i	−1.89471	−	0.0462964i
$831$	−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
$836$	−11585.4	−	7466.12i	−0.479293	−	0.308877i
$837$	6052.00	+	10482.4i	0.249925	+	0.432884i
$838$	7940.08	−	4329.13i	0.327310	−	0.178457i
$839$	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
$842$	−13631.1	+	7432.00i	−0.557908	+	0.304185i
$843$	4488.47	+	7774.26i	0.183382	+	0.317627i
$844$	2564.68	+	1652.79i	0.104597	+	0.0674067i
$845$	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
$850$	−13315.8	−	325.365i	−0.537327	−	0.0131293i
$851$	7711.83	−	4452.43i	0.310644	−	0.179350i
$852$	370.808	−	7583.26i	0.0149104	−	0.304928i
$853$		−	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
$856$	8723.33	−	12836.4i	0.348315	−	0.512546i
$857$	−22450.1	+	12961.6i	−0.894844	+	0.516638i	−0.875524	−	0.483175i	$-0.839484\pi$
$857$	−22450.1	+	12961.6i	−0.894844	+	0.516638i	−0.0193202	+	0.999813i	$0.506150\pi$
$858$	623.702	−	25525.5i	0.0248168	−	1.01565i
$859$	−12903.9	+	22350.2i	−0.512544	+	0.887753i	0.487350	+	0.873207i	$0.337964\pi$
$859$	−12903.9	+	22350.2i	−0.512544	+	0.887753i	−0.999894	+	0.0145459i	$0.995370\pi$
$860$	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	$-0.326421\pi$
$863$	953.538	+	550.526i	0.0376116	+	0.0217151i	−0.481076	+	0.876679i	$0.659754\pi$
$864$	21486.8	+	16190.7i	0.846061	+	0.637520i
$865$	12486.5	+	21627.2i	0.490812	+	0.850111i
$866$	−12600.2	−	23110.1i	−0.494424	−	0.906827i
$867$	19737.1			0.773134
$868$		0			0
$869$	48873.0			1.90783
$870$	−3086.46	−	5660.91i	−0.120277	−	0.220601i
$871$	4508.17	+	7808.38i	0.175377	+	0.303762i
$872$	−22975.3	+	11107.1i	−0.892250	+	0.431347i
$873$	−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	0.0542399	+	0.998528i	$0.482726\pi$
$877$	−21754.6	+	37680.1i	−0.837631	+	1.45082i	−0.891871	+	0.452291i	$0.850607\pi$
$878$	−202.534	+	8288.84i	−0.00778494	+	0.318604i
$879$	19344.7	−	11168.6i	0.742297	−	0.428565i
$880$	−18720.1	−	41266.0i	−0.717107	−	1.58077i
$881$			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	$0.974388\pi$
$884$	−10252.6	−	501.332i	−0.390080	−	0.0190742i
$885$	29233.0	−	16877.7i	1.11035	−	0.641058i
$886$	16638.3	+	406.549i	0.630898	+	0.0154157i
$887$	−3603.27	+	6241.05i	−0.136399	+	0.236250i	−0.926131	−	0.377202i	$-0.876886\pi$
$887$	−3603.27	+	6241.05i	−0.136399	+	0.236250i	0.789732	+	0.613452i	$0.210220\pi$
$888$	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
$892$	−12757.6	+	19796.4i	−0.478875	+	0.743085i
$893$	5940.80	+	10289.8i	0.222622	+	0.385592i
$894$	−26227.5	+	14299.9i	−0.981184	+	0.534965i
$895$	51883.7			1.93774
$896$		0			0
$897$	−20446.3			−0.761071
$898$	31926.3	−	17407.0i	1.18641	−	0.646858i
$899$	−1132.97	−	1962.36i	−0.0420318	−	0.0728012i
$900$	2864.60	−	4445.08i	0.106096	−	0.164633i
$901$	−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
$906$	43543.2	+	1063.96i	1.59672	+	0.0390150i
$907$	−24349.5	+	14058.2i	−0.891415	+	0.514659i	−0.874405	−	0.485197i	$-0.838748\pi$
$907$	−24349.5	+	14058.2i	−0.891415	+	0.514659i	−0.0170097	+	0.999855i	$0.505415\pi$
$908$	−46233.6	−	2260.74i	−1.68978	−	0.0826269i
$909$			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	$0.766974\pi$
$912$	5271.11	+	11619.5i	0.191386	+	0.421886i
$913$	−33706.6	+	19460.5i	−1.22183	+	0.705422i
$914$	−126.513	+	5177.64i	−0.00457842	+	0.187375i
$915$	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	$-0.307250\pi$
$919$	3949.63	+	2280.32i	0.141770	+	0.0818508i	−0.427437	+	0.904045i	$0.640584\pi$
$920$	−32668.8	+	15793.3i	−1.17071	+	0.565967i
$921$	−6786.00	−	11753.7i	−0.242787	−	0.420519i
$922$	825.812	+	1514.63i	0.0294975	+	0.0541016i
$923$	−8970.47			−0.319899
$924$		0			0
$925$	−15783.0			−0.561018
$926$	10692.2	+	19610.6i	0.379445	+	0.695943i
$927$	1903.75	+	3297.39i	0.0674513	+	0.116829i
$928$	−4022.46	−	3030.98i	−0.142288	−	0.107216i
$929$	40730.3	+	23515.6i	1.43845	+	0.830488i	0.997742	−	0.0671644i	$-0.0213952\pi$
$929$	40730.3	+	23515.6i	1.43845	+	0.830488i	0.440705	+	0.897652i	$0.354729\pi$
$930$	−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
$934$	1007.90	−	41248.9i	0.0353098	−	1.44508i
$935$	−17344.8	+	10014.0i	−0.606668	+	0.350260i
$936$	2290.61	−	3370.63i	0.0799902	−	0.117706i
$937$		−	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
$940$	−1907.84	+	39016.6i	−0.0661988	+	1.35381i
$941$	23092.4	−	13332.4i	0.799989	−	0.461874i	−0.0434780	−	0.999054i	$-0.513844\pi$
$941$	23092.4	−	13332.4i	0.799989	−	0.461874i	0.843467	+	0.537180i	$0.180511\pi$
$942$	−8637.48	−	211.053i	−0.298752	−	0.00729986i
$943$	−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	$-0.314708\pi$
$947$	2951.90	+	1704.28i	0.101292	+	0.0584812i	−0.448498	+	0.893784i	$0.648041\pi$
$948$	−38030.5	−	24508.4i	−1.30292	−	0.839659i
$949$	5796.76	+	10040.3i	0.198283	+	0.343436i
$950$	17174.9	−	9364.17i	0.586555	−	0.319804i
$951$	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	$0.670462\pi$
$954$	5678.65	−	3096.14i	0.192718	−	0.105075i
$955$	−4316.04	−	7475.61i	−0.146245	−	0.253304i
$956$	−3150.12	−	2030.07i	−0.106571	−	0.0686789i
$957$	−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
$962$	−12159.5	−	297.110i	−0.407523	−	0.00995761i
$963$	2358.52	−	1361.69i	0.0789223	−	0.0455658i
$964$	152.185	−	3112.29i	0.00508461	−	0.103984i
$965$		−	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	$0.882128\pi$
$968$	−7277.13	−	4945.37i	−0.241628	−	0.164205i
$969$	4883.86	−	2819.70i	0.161911	−	0.0934796i
$970$	774.546	−	31698.9i	0.0256383	−	1.04927i
$971$	10938.3	−	18945.7i	0.361511	−	0.626155i	−0.626699	−	0.779261i	$-0.715594\pi$
$971$	10938.3	−	18945.7i	0.361511	−	0.626155i	0.988210	+	0.153107i	$0.0489278\pi$
$972$	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
$976$	4864.03	−	49617.4i	0.159522	−	1.62727i
$977$	−16972.7	−	29397.6i	−0.555789	−	0.962655i	−0.997842	−	0.0656660i	$-0.979083\pi$
$977$	−16972.7	−	29397.6i	−0.555789	−	0.962655i	0.442052	−	0.896989i	$-0.354251\pi$
$978$	15986.4	+	29320.7i	0.522686	+	0.958663i
$979$	−48388.7			−1.57968
$980$		0			0
$981$	−4478.01			−0.145741
$982$	4355.62	+	7988.67i	0.141541	+	0.259602i
$983$	11714.3	+	20289.7i	0.380088	+	0.658332i	0.991074	−	0.133309i	$-0.0425603\pi$
$983$	11714.3	+	20289.7i	0.380088	+	0.658332i	−0.610986	+	0.791641i	$0.709227\pi$
$984$	10742.7	+	22221.5i	0.348033	+	0.719914i
$985$	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
$990$	194.231	−	7949.07i	0.00623544	−	0.255190i
$991$	47625.2	−	27496.4i	1.52660	−	0.881385i	0.527103	−	0.849802i	$-0.323278\pi$
$991$	47625.2	−	27496.4i	1.52660	−	0.881385i	0.999501	−	0.0315834i	$-0.0100550\pi$
$992$	−1796.26	+	14632.4i	−0.0574913	+	0.468325i
$993$			21044.7i			0.672540i
$994$		0			0
$995$			43685.1i			1.39187i
$996$	35987.7	+	1759.73i	1.14489	+	0.0559832i
$997$	1196.16	−	690.601i	0.0379966	−	0.0219374i	−0.480881	−	0.876786i	$-0.659683\pi$
$997$	1196.16	−	690.601i	0.0379966	−	0.0219374i	0.518878	+	0.854848i	$0.326350\pi$
$998$	−25044.3	−	611.944i	−0.794352	−	0.0194096i
$999$	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.19.7		16
4.3	odd	2	inner	196.4.f.c.19.4		16
7.2	even	3		28.4.d.b.27.2	yes	8
7.3	odd	6	inner	196.4.f.c.31.4		16
7.4	even	3	inner	196.4.f.c.31.3		16
7.5	odd	6		28.4.d.b.27.1	✓	8
7.6	odd	2	inner	196.4.f.c.19.8		16
21.2	odd	6		252.4.b.d.55.8		8
21.5	even	6		252.4.b.d.55.7		8
28.3	even	6	inner	196.4.f.c.31.7		16
28.11	odd	6	inner	196.4.f.c.31.8		16
28.19	even	6		28.4.d.b.27.4	yes	8
28.23	odd	6		28.4.d.b.27.3	yes	8
28.27	even	2	inner	196.4.f.c.19.3		16
56.5	odd	6		448.4.f.d.447.5		8
56.19	even	6		448.4.f.d.447.3		8
56.37	even	6		448.4.f.d.447.4		8
56.51	odd	6		448.4.f.d.447.6		8
84.23	even	6		252.4.b.d.55.6		8
84.47	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	7.5	odd	6
28.4.d.b.27.2	yes	8	7.2	even	3
28.4.d.b.27.3	yes	8	28.23	odd	6
28.4.d.b.27.4	yes	8	28.19	even	6
196.4.f.c.19.3		16	28.27	even	2	inner
196.4.f.c.19.4		16	4.3	odd	2	inner
196.4.f.c.19.7		16	1.1	even	1	trivial
196.4.f.c.19.8		16	7.6	odd	2	inner
196.4.f.c.31.3		16	7.4	even	3	inner
196.4.f.c.31.4		16	7.3	odd	6	inner
196.4.f.c.31.7		16	28.3	even	6	inner
196.4.f.c.31.8		16	28.11	odd	6	inner
252.4.b.d.55.5		8	84.47	odd	6
252.4.b.d.55.6		8	84.23	even	6
252.4.b.d.55.7		8	21.5	even	6
252.4.b.d.55.8		8	21.2	odd	6
448.4.f.d.447.3		8	56.19	even	6
448.4.f.d.447.4		8	56.37	even	6
448.4.f.d.447.5		8	56.5	odd	6
448.4.f.d.447.6		8	56.51	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+(2.48330 - 1.35396i) q^{2} +(-2.39945 - 4.15597i) q^{3} +(4.33360 - 6.72458i) 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} +(48.2747 + 1.17957i) q^{10} +(35.9149 - 20.7355i) q^{11} +(-38.3454 - 1.87502i) q^{12} +45.3599i q^{13} -81.9306i q^{15} +(-26.4398 - 58.2832i) q^{16} +(-24.4974 + 14.1436i) q^{17} +(0.274328 - 11.2271i) 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} +(-97.7619 + 47.2618i) q^{24} +(83.2401 + 144.176i) q^{25} +(61.4154 + 112.642i) q^{26} -148.625 q^{27} +27.8234 q^{29} +(-110.931 - 203.459i) q^{30} +(-40.7200 - 70.5291i) q^{31} +(-144.571 - 108.937i) 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} +(2.87026 - 117.467i) q^{38} +(188.514 - 108.839i) q^{39} +(217.135 - 319.515i) q^{40} -227.302i q^{41} +171.988i q^{43} +(16.2035 - 331.372i) q^{44} +(58.7066 - 33.8943i) q^{45} +(-265.592 - 6.48961i) 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} +(305.026 + 196.572i) q^{52} +(287.960 + 498.762i) q^{53} +(-369.080 + 201.231i) q^{54} +708.025 q^{55} -199.362 q^{57} +(69.0939 - 37.6717i) q^{58} +(206.000 + 356.802i) q^{59} +(-550.949 - 355.054i) 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} +(-562.732 - 13.7501i) q^{66} +(172.143 - 99.3867i) q^{67} +(-11.0523 + 226.027i) q^{68} +450.756i q^{69} +197.762i q^{71} +(-74.3086 - 50.4985i) q^{72} +(221.347 - 127.795i) q^{73} +(-6.55006 + 268.066i) 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} +(106.603 - 1087.45i) q^{80} +(303.015 + 524.837i) q^{81} +(-307.757 - 564.460i) q^{82} -938.514 q^{83} -482.940 q^{85} +(232.864 + 427.098i) q^{86} +(-66.7608 - 115.633i) q^{87} +(-408.425 - 844.836i) 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} +(-19.7602 + 808.702i) q^{94} +(614.238 - 354.631i) q^{95} +(-105.846 + 862.221i) 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

Fields

Representations

Groups

Database

Properties

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