LMFDB - Embedded newform 196.4.f.c.19.8

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			19.8
Root			$-0.608943 + 0.456399i$ of defining polynomial
Character	$\chi$	$=$	196.19
Dual form			196.4.f.c.31.8

$q$-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	0.999049	−	0.0435904i	$-0.0138797\pi$
$3$	2.39945	+	4.15597i	0.461774	+	0.799817i	−0.537275	+	0.843407i	$0.680546\pi$
$4$	4.33360	−	6.72458i	0.541700	−	0.840572i
$5$	−14.7855	−	8.53640i	−1.32245	−	0.763518i	−0.338333	−	0.941026i	$-0.609863\pi$
$5$	−14.7855	−	8.53640i	−1.32245	−	0.763518i	−0.984119	+	0.177508i	$0.943196\pi$
$6$	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	$-0.839231\pi$
$13$		−	45.3599i		−	0.967737i	0.875141	−	0.483868i	$-0.160769\pi$
$14$		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	−0.314966	−	0.949103i	$-0.601993\pi$
$17$	24.4974	−	14.1436i	0.349499	−	0.201783i	0.664465	+	0.747320i	$0.268660\pi$
$18$	0.274328	−	11.2271i	0.00359221	−	0.147014i
$19$	−20.7717	+	35.9776i	−0.250808	+	0.434412i	−0.963749	−	0.266812i	$-0.914030\pi$
$19$	−20.7717	+	35.9776i	−0.250808	+	0.434412i	0.712941	+	0.701225i	$0.247363\pi$
$20$	−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	0.959540	−	0.281573i	$-0.0908562\pi$
$31$	40.7200	+	70.5291i	0.235920	+	0.408626i	−0.723619	+	0.690199i	$0.757523\pi$
$32$	−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	$0.142513\pi$
$41$			227.302i			0.865820i	−0.901437	+	0.432910i	$0.857487\pi$
$42$		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	−0.554159	−	0.832411i	$-0.686960\pi$
$47$	143.002	−	247.687i	0.443809	−	0.768700i	0.997968	+	0.0637105i	$0.0202934\pi$
$48$	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	0.544106	−	0.839017i	$-0.316869\pi$
$59$	−206.000	−	356.802i	−0.454557	−	0.787316i	−0.998663	+	0.0517011i	$0.983536\pi$
$60$	−550.949	−	355.054i	−1.18545	−	0.763955i
$61$	−674.623	−	389.494i	−1.41601	−	0.817534i	−0.420065	−	0.907494i	$-0.637993\pi$
$61$	−674.623	−	389.494i	−1.41601	−	0.817534i	−0.995945	+	0.0899604i	$0.971326\pi$
$62$	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	−0.666835	−	0.745205i	$-0.732352\pi$
$73$	−221.347	+	127.795i	−0.354886	+	0.204894i	0.311949	+	0.950099i	$0.399018\pi$
$74$	−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	$-0.286900\pi$
$83$	938.514			1.24115			0.620574	+	0.784148i	$0.286900\pi$
$84$		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	0.961331	−	0.275395i	$-0.0888087\pi$
$89$	1010.49	+	583.404i	1.20350	+	0.694840i	0.242166	+	0.970235i	$0.422142\pi$
$90$	−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	$0.111669\pi$
$97$			656.635i			0.687332i	−0.939092	+	0.343666i	$0.888331\pi$
$98$		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	−0.00885711	−	0.999961i	$-0.502819\pi$
$101$	865.528	−	499.713i	0.852706	−	0.492310i	0.861563	+	0.507651i	$0.169486\pi$
$102$	383.836	+	9.37884i	0.372602	+	0.00910435i
$103$	479.466	−	830.460i	0.458672	−	0.794443i	−0.540219	−	0.841524i	$-0.681659\pi$
$103$	479.466	−	830.460i	0.458672	−	0.794443i	0.998891	+	0.0470813i	$0.0149920\pi$
$104$	−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	−0.774768	−	0.632245i	$-0.782133\pi$
$131$	240.133	−	415.922i	0.160156	−	0.277399i	0.934925	+	0.354846i	$0.115467\pi$
$132$	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	$-0.309990\pi$
$139$	1842.35			1.12422			0.562109	+	0.827063i	$0.309990\pi$
$140$		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	−0.633527	−	0.773721i	$-0.718393\pi$
$157$	−551.266	+	318.273i	−0.280228	+	0.161790i	0.353299	+	0.935511i	$0.385060\pi$
$158$	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	$-0.664545\pi$
$167$	−2133.16			−0.988435			−0.494218	+	0.869338i	$0.664545\pi$
$168$		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	0.195116	−	0.980780i	$-0.437492\pi$
$173$	−1266.76	−	731.366i	−0.556706	−	0.321415i	−0.751822	+	0.659366i	$0.770825\pi$
$174$	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	$-0.974812\pi$
$181$		−	384.978i		−	0.158095i	0.996871	−	0.0790475i	$-0.0251879\pi$
$182$		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	0.542989	−	0.839740i	$-0.317293\pi$
$199$	−1279.38	−	2215.95i	−0.455742	−	0.789368i	−0.998731	+	0.0503720i	$0.983959\pi$
$200$	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	$-0.354265\pi$
$223$	2943.88			0.884023			0.442011	+	0.897009i	$0.354265\pi$
$224$		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	$0.154268\pi$
$227$	2893.05	+	5010.91i	0.845897	+	1.46514i	−0.0389429	+	0.999241i	$0.512399\pi$
$228$	−863.957	+	1340.63i	−0.250952	+	0.389409i
$229$	3727.24	+	2151.93i	1.07556	+	0.620975i	0.929695	−	0.368330i	$-0.120070\pi$
$229$	3727.24	+	2151.93i	1.07556	+	0.620975i	0.145865	+	0.989305i	$0.453404\pi$
$230$	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	−0.544402	−	0.838824i	$-0.683243\pi$
$241$	−337.318	+	194.751i	−0.0901600	+	0.0520539i	0.454242	+	0.890878i	$0.349910\pi$
$242$	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	$-0.299216\pi$
$251$	4690.59			1.17955			0.589776	+	0.807567i	$0.299216\pi$
$252$		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	−0.162251	−	0.986750i	$-0.551875\pi$
$257$	−4523.48	−	2611.63i	−1.09793	−	0.633888i	−0.935676	+	0.352861i	$0.885209\pi$
$258$	−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	−0.798396	−	0.602132i	$-0.794318\pi$
$269$	−2983.05	+	1722.26i	−0.676132	+	0.390365i	0.122264	+	0.992498i	$0.460985\pi$
$270$	−7174.81	−	175.313i	−1.61720	−	0.0395156i
$271$	−2625.89	+	4548.17i	−0.588603	+	1.01949i	0.405813	+	0.913956i	$0.366989\pi$
$271$	−2625.89	+	4548.17i	−0.588603	+	1.01949i	−0.994416	+	0.105534i	$0.966345\pi$
$272$	−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	0.579304	−	0.815112i	$-0.303325\pi$
$283$	−1981.71	−	3432.42i	−0.416256	−	0.720976i	−0.995559	+	0.0941357i	$0.969991\pi$
$284$	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	$-0.846399\pi$
$293$		−	4654.67i		−	0.928084i	0.885813	−	0.464042i	$-0.153601\pi$
$294$		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	$-0.584674\pi$
$307$	−2828.15			−0.525769			−0.262884	+	0.964827i	$0.584674\pi$
$308$		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	$0.0373560\pi$
$311$	3279.55	+	5680.35i	0.597962	+	1.03570i	−0.395160	+	0.918613i	$0.629311\pi$
$312$	−2143.79	−	4434.47i	−0.389001	−	0.804656i
$313$	−5384.22	−	3108.58i	−0.972314	−	0.561366i	−0.0723733	−	0.997378i	$-0.523057\pi$
$313$	−5384.22	−	3108.58i	−0.972314	−	0.561366i	−0.899941	+	0.436012i	$0.856391\pi$
$314$	−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	$0.418288\pi$
$349$			12612.4i			1.93446i	−0.253895	+	0.967232i	$0.581712\pi$
$350$		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	−0.988495	−	0.151253i	$-0.951669\pi$
$353$	−8965.19	+	5176.06i	−1.35175	+	0.780435i	−0.363259	+	0.931688i	$0.618336\pi$
$354$	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	0.983011	−	0.183547i	$-0.0587581\pi$
$367$	2338.05	+	4049.63i	0.332549	+	0.575991i	−0.650462	+	0.759539i	$0.725425\pi$
$368$	−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	−0.808759	−	0.588140i	$-0.799860\pi$
$383$	786.757	−	1362.70i	0.104965	−	0.181804i	0.913724	+	0.406336i	$0.133194\pi$
$384$	−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	0.702130	−	0.712049i	$-0.252233\pi$
$397$	3453.12	+	1993.66i	0.436542	+	0.252038i	−0.265588	+	0.964087i	$0.585566\pi$
$398$	−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	−0.532773	−	0.846258i	$-0.678850\pi$
$409$	−548.219	+	316.514i	−0.0662779	+	0.0382656i	0.466495	+	0.884524i	$0.345517\pi$
$410$	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	$-0.559682\pi$
$419$	−3197.39			−0.372799			−0.186399	+	0.982474i	$0.559682\pi$
$420$		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	$0.172739\pi$
$433$			9306.18i			1.03286i	−0.856331	+	0.516428i	$0.827261\pi$
$434$		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	−0.775285	−	0.631612i	$-0.782394\pi$
$439$	1465.71	−	2538.69i	0.159350	−	0.276002i	0.934634	+	0.355610i	$0.115727\pi$
$440$	−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	$-0.990191\pi$
$461$		−	609.925i		−	0.0616205i	0.999525	−	0.0308102i	$-0.00980875\pi$
$462$		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	$0.423791\pi$
$467$	−7294.01	+	12633.6i	−0.722755	+	1.25185i	−0.959891	+	0.280372i	$0.909542\pi$
$468$	−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	$0.172662\pi$
$479$	9176.03	+	15893.4i	0.875289	+	1.51605i	0.0188353	+	0.999823i	$0.494004\pi$
$480$	−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	$-0.428325\pi$
$503$	5037.58			0.446550			0.223275	+	0.974756i	$0.428325\pi$
$504$		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	0.0394680	−	0.999221i	$-0.487434\pi$
$509$	−9257.46	−	5344.80i	−0.806149	−	0.465430i	−0.845617	+	0.533791i	$0.820767\pi$
$510$	−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	0.0800063	−	0.996794i	$-0.474506\pi$
$521$	11693.0	−	6750.93i	0.983259	−	0.567685i	0.903252	+	0.429110i	$0.141173\pi$
$522$	7.63274	−	312.376i	0.000639992	−	0.0261922i
$523$	6909.97	−	11968.4i	0.577728	−	1.00065i	−0.418011	−	0.908442i	$-0.637273\pi$
$523$	6909.97	−	11968.4i	0.577728	−	1.00065i	0.995739	−	0.0922123i	$-0.0293938\pi$
$524$	−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	0.579104	−	0.815253i	$-0.303402\pi$
$563$	−5563.59	−	9636.41i	−0.416478	−	0.721361i	−0.995582	+	0.0938923i	$0.970069\pi$
$564$	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	$0.776757\pi$
$577$	−23628.1	+	13641.7i	−1.70476	+	0.984246i	−0.940784	+	0.339005i	$0.889910\pi$
$578$	−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	$-0.534409\pi$
$587$	−3068.80			−0.215780			−0.107890	+	0.994163i	$0.534409\pi$
$588$		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	0.981898	−	0.189411i	$-0.0606580\pi$
$593$	18899.9	+	10911.9i	1.30881	+	0.755643i	0.326914	+	0.945054i	$0.393991\pi$
$594$	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	$0.0899740\pi$
$601$			8218.83i			0.557826i	−0.960316	+	0.278913i	$0.910026\pi$
$602$		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	$0.459460\pi$
$607$	−11896.7	+	20605.6i	−0.795503	+	1.37785i	−0.922519	+	0.385951i	$0.873873\pi$
$608$	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	0.918234	−	0.396039i	$-0.129616\pi$
$619$	1788.57	+	3097.90i	0.116137	+	0.201155i	−0.802097	+	0.597194i	$0.796282\pi$
$620$	−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	$-0.720874\pi$
$643$	−20855.1			−1.27907			−0.639537	+	0.768760i	$0.720874\pi$
$644$		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	$-0.899003\pi$
$647$	−12264.5	−	21242.8i	−0.745237	−	1.29079i	0.204847	−	0.978794i	$-0.434330\pi$
$648$	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	0.206241	−	0.978501i	$-0.433877\pi$
$661$	19658.4	−	11349.8i	1.15677	−	0.667861i	0.950527	+	0.310641i	$0.100544\pi$
$662$	−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	0.575307	−	0.817937i	$-0.304882\pi$
$677$	2723.40	+	1572.35i	0.154607	+	0.0892622i	−0.420701	+	0.907199i	$0.638216\pi$
$678$	−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	$0.403531\pi$
$691$	−12303.2	+	21309.8i	−0.677333	+	1.17318i	−0.975781	+	0.218750i	$0.929802\pi$
$692$	−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	−0.778609	−	0.627509i	$-0.784074\pi$
$719$	2971.62	−	5146.99i	0.154134	−	0.266969i	0.932743	+	0.360541i	$0.117408\pi$
$720$	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	$-0.324134\pi$
$727$	20574.9			1.04963			0.524816	+	0.851216i	$0.324134\pi$
$728$		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	0.810361	−	0.585931i	$-0.199271\pi$
$733$	14052.6	+	8113.27i	0.708110	+	0.408828i	−0.102251	+	0.994759i	$0.532604\pi$
$734$	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	0.671601	−	0.740913i	$-0.265607\pi$
$761$	7678.27	+	4433.05i	0.365752	+	0.211167i	−0.305849	+	0.952080i	$0.598940\pi$
$762$	−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	$-0.733679\pi$
$769$		−	31664.2i		−	1.48484i	0.669937	−	0.742418i	$-0.266321\pi$
$770$		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	−0.834948	−	0.550330i	$-0.814502\pi$
$773$	−16673.7	+	9626.55i	−0.775822	+	0.447921i	0.0591256	+	0.998251i	$0.481169\pi$
$774$	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	0.851111	−	0.524985i	$-0.175929\pi$
$787$	−642.360	−	1112.60i	−0.0290949	−	0.0503938i	−0.880206	+	0.474591i	$0.842596\pi$
$788$	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	$-0.981647\pi$
$797$		−	2593.21i		−	0.115253i	0.998338	−	0.0576263i	$-0.0183532\pi$
$798$		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	$-0.255487\pi$
$811$	32094.4			1.38962			0.694812	+	0.719191i	$0.255487\pi$
$812$		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	0.0201310	−	0.999797i	$-0.493592\pi$
$829$	21387.6	−	12348.1i	0.896046	−	0.517333i	0.875915	+	0.482465i	$0.160258\pi$
$830$	−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	$-0.635156\pi$
$839$	−20023.0			−0.823922			−0.411961	+	0.911202i	$0.635156\pi$
$840$		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	$0.171331\pi$
$853$			25542.4i			1.02527i	−0.858606	+	0.512636i	$0.828669\pi$
$854$		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	0.0193202	−	0.999813i	$-0.493850\pi$
$857$	22450.1	−	12961.6i	0.894844	−	0.516638i	0.875524	+	0.483175i	$0.160516\pi$
$858$	623.702	−	25525.5i	0.0248168	−	1.01565i
$859$	12903.9	−	22350.2i	0.512544	−	0.887753i	−0.487350	−	0.873207i	$-0.662036\pi$
$859$	12903.9	−	22350.2i	0.512544	−	0.887753i	0.999894	−	0.0145459i	$-0.00463028\pi$
$860$	−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	$-0.729527\pi$
$881$		−	39281.4i		−	1.50219i	0.660197	−	0.751093i	$-0.270473\pi$
$882$		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	−0.789732	−	0.613452i	$-0.789780\pi$
$887$	3603.27	−	6241.05i	0.136399	−	0.236250i	0.926131	+	0.377202i	$0.123114\pi$
$888$	−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	−0.440705	−	0.897652i	$-0.645271\pi$
$929$	−40730.3	−	23515.6i	−1.43845	−	0.830488i	−0.997742	+	0.0671644i	$0.978605\pi$
$930$	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	$0.00531916\pi$
$937$			958.545i			0.0334197i	−0.999860	+	0.0167099i	$0.994681\pi$
$938$		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	−0.843467	−	0.537180i	$-0.819489\pi$
$941$	−23092.4	+	13332.4i	−0.799989	+	0.461874i	0.0434780	+	0.999054i	$0.486156\pi$
$942$	−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	−0.988210	−	0.153107i	$-0.951072\pi$
$971$	−10938.3	+	18945.7i	−0.361511	+	0.626155i	0.626699	+	0.779261i	$0.284406\pi$
$972$	−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	0.610986	−	0.791641i	$-0.290773\pi$
$983$	−11714.3	−	20289.7i	−0.380088	−	0.658332i	−0.991074	+	0.133309i	$0.957440\pi$
$984$	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	−0.518878	−	0.854848i	$-0.673650\pi$
$997$	−1196.16	+	690.601i	−0.0379966	+	0.0219374i	0.480881	+	0.876786i	$0.340317\pi$
$998$	−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.19.8		16
4.3	odd	2	inner	196.4.f.c.19.3		16
7.2	even	3		28.4.d.b.27.1	✓	8
7.3	odd	6	inner	196.4.f.c.31.3		16
7.4	even	3	inner	196.4.f.c.31.4		16
7.5	odd	6		28.4.d.b.27.2	yes	8
7.6	odd	2	inner	196.4.f.c.19.7		16
21.2	odd	6		252.4.b.d.55.7		8
21.5	even	6		252.4.b.d.55.8		8
28.3	even	6	inner	196.4.f.c.31.8		16
28.11	odd	6	inner	196.4.f.c.31.7		16
28.19	even	6		28.4.d.b.27.3	yes	8
28.23	odd	6		28.4.d.b.27.4	yes	8
28.27	even	2	inner	196.4.f.c.19.4		16
56.5	odd	6		448.4.f.d.447.4		8
56.19	even	6		448.4.f.d.447.6		8
56.37	even	6		448.4.f.d.447.5		8
56.51	odd	6		448.4.f.d.447.3		8
84.23	even	6		252.4.b.d.55.5		8
84.47	odd	6		252.4.b.d.55.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.4.d.b.27.1	✓	8	7.2	even	3
28.4.d.b.27.2	yes	8	7.5	odd	6
28.4.d.b.27.3	yes	8	28.19	even	6
28.4.d.b.27.4	yes	8	28.23	odd	6
196.4.f.c.19.3		16	4.3	odd	2	inner
196.4.f.c.19.4		16	28.27	even	2	inner
196.4.f.c.19.7		16	7.6	odd	2	inner
196.4.f.c.19.8		16	1.1	even	1	trivial
196.4.f.c.31.3		16	7.3	odd	6	inner
196.4.f.c.31.4		16	7.4	even	3	inner
196.4.f.c.31.7		16	28.11	odd	6	inner
196.4.f.c.31.8		16	28.3	even	6	inner
252.4.b.d.55.5		8	84.23	even	6
252.4.b.d.55.6		8	84.47	odd	6
252.4.b.d.55.7		8	21.2	odd	6
252.4.b.d.55.8		8	21.5	even	6
448.4.f.d.447.3		8	56.51	odd	6
448.4.f.d.447.4		8	56.5	odd	6
448.4.f.d.447.5		8	56.37	even	6
448.4.f.d.447.6		8	56.19	even	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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