LMFDB - Embedded newform 82.5.h.b.13.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [82,5,Mod(7,82)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(82, base_ring=CyclotomicField(40)) chi = DirichletCharacter(H, H._module([39])) N = Newforms(chi, 5, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("82.7"); S:= CuspForms(chi, 5); N := Newforms(S);

Level:	$ N $	$=$	$ 82 = 2 \cdot 41 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	82.h (of order $40$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [112,56] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$8.47633697288$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$7$ over $\Q(\zeta_{40})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{40}]$

Embedding invariants

Embedding label			13.7
Character	$\chi$	$=$	82.13
Dual form			82.5.h.b.19.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.52015 - 1.28408i) q^{2} +(5.90673 - 14.2601i) q^{3} +(4.70228 + 6.47214i) q^{4} +(-12.4829 - 1.97710i) q^{5} +(-33.1970 + 28.3529i) q^{6} +(-27.9835 - 23.9001i) q^{7} +(-3.53971 - 22.3488i) q^{8} +(-111.186 - 111.186i) q^{9} +(28.9200 + 21.0116i) q^{10} +(13.0886 + 21.3587i) q^{11} +(120.069 - 28.8259i) q^{12} +(17.5069 + 1.37782i) q^{13} +(39.8328 + 96.1648i) q^{14} +(-101.927 + 166.329i) q^{15} +(-19.7771 + 60.8676i) q^{16} +(-27.1543 + 113.106i) q^{17} +(137.433 + 422.976i) q^{18} +(-165.362 + 13.0143i) q^{19} +(-45.9020 - 90.0878i) q^{20} +(-506.110 + 257.876i) q^{21} +(-5.55902 - 70.6340i) q^{22} +(189.162 - 61.4626i) q^{23} +(-339.605 - 81.5320i) q^{24} +(-442.497 - 143.776i) q^{25} +(-42.3506 - 25.9525i) q^{26} +(-1087.20 + 450.332i) q^{27} +(23.0988 - 293.498i) q^{28} +(-155.132 - 646.171i) q^{29} +(470.450 - 288.292i) q^{30} +(-1024.55 + 1410.18i) q^{31} +(128.000 - 128.000i) q^{32} +(381.889 - 60.4853i) q^{33} +(213.670 - 250.175i) q^{34} +(302.062 + 353.669i) q^{35} +(196.783 - 1242.44i) q^{36} +(1709.37 - 1241.93i) q^{37} +(433.449 + 179.540i) q^{38} +(123.056 - 241.511i) q^{39} +285.976i q^{40} +(1477.24 - 802.194i) q^{41} +1606.60 q^{42} +(-1474.01 - 751.045i) q^{43} +(-76.6901 + 185.146i) q^{44} +(1168.10 + 1607.75i) q^{45} +(-555.640 - 88.0047i) q^{46} +(427.273 - 364.925i) q^{47} +(751.161 + 641.552i) q^{48} +(-163.741 - 1033.82i) q^{49} +(930.537 + 930.537i) q^{50} +(1452.51 + 1055.31i) q^{51} +(73.4047 + 119.786i) q^{52} +(2618.25 - 628.586i) q^{53} +(3318.16 + 261.145i) q^{54} +(-121.156 - 292.496i) q^{55} +(-435.087 + 709.997i) q^{56} +(-791.166 + 2434.96i) q^{57} +(-438.779 + 1827.65i) q^{58} +(-1947.28 - 5993.11i) q^{59} +(-1555.79 + 122.444i) q^{60} +(-2812.51 - 5519.86i) q^{61} +(4392.80 - 2238.24i) q^{62} +(454.008 + 5768.72i) q^{63} +(-486.941 + 158.217i) q^{64} +(-215.812 - 51.8119i) q^{65} +(-1040.08 - 337.944i) q^{66} +(-5038.26 - 3087.45i) q^{67} +(-859.723 + 356.109i) q^{68} +(240.868 - 3060.52i) q^{69} +(-307.101 - 1279.17i) q^{70} +(175.267 - 107.404i) q^{71} +(-2091.31 + 2878.44i) q^{72} +(-1621.82 + 1621.82i) q^{73} +(-5902.62 + 934.883i) q^{74} +(-4663.97 + 5460.81i) q^{75} +(-861.811 - 1009.05i) q^{76} +(144.211 - 910.511i) q^{77} +(-620.240 + 450.630i) q^{78} +(5090.15 + 2108.41i) q^{79} +(367.216 - 720.702i) q^{80} +5427.10i q^{81} +(-4752.95 + 124.750i) q^{82} +11667.4 q^{83} +(-4048.88 - 2063.01i) q^{84} +(562.585 - 1358.20i) q^{85} +(2750.32 + 3785.49i) q^{86} +(-10130.8 - 1604.56i) q^{87} +(431.013 - 368.120i) q^{88} +(2053.55 + 1753.90i) q^{89} +(-879.300 - 5551.68i) q^{90} +(-456.972 - 456.972i) q^{91} +(1287.29 + 935.270i) q^{92} +(14057.5 + 22939.8i) q^{93} +(-1545.38 + 371.014i) q^{94} +(2089.93 + 164.481i) q^{95} +(-1069.23 - 2581.36i) q^{96} +(-7145.87 + 11661.0i) q^{97} +(-914.858 + 2815.64i) q^{98} +(919.516 - 3830.06i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 56 q^{2} - 16 q^{3} + 16 q^{6} - 448 q^{8} - 24 q^{9} + 512 q^{11} - 576 q^{12} + 348 q^{13} - 192 q^{14} - 1036 q^{15} + 1792 q^{16} + 552 q^{17} + 416 q^{18} + 504 q^{19} + 876 q^{21} + 16 q^{22}+ \cdots + 36896 q^{99}+O(q^{100}) $ 112 * q + 56 * q^2 - 16 * q^3 + 16 * q^6 - 448 * q^8 - 24 * q^9 + 512 * q^11 - 576 * q^12 + 348 * q^13 - 192 * q^14 - 1036 * q^15 + 1792 * q^16 + 552 * q^17 + 416 * q^18 + 504 * q^19 + 876 * q^21 + 16 * q^22 + 800 * q^23 - 384 * q^24 - 3360 * q^25 + 1656 * q^26 - 964 * q^27 + 768 * q^28 + 4 * q^29 - 3544 * q^30 + 1380 * q^31 + 14336 * q^32 - 7392 * q^33 + 4224 * q^34 + 2264 * q^35 + 2048 * q^36 + 6212 * q^37 + 2624 * q^38 + 4928 * q^39 - 7460 * q^41 + 5056 * q^42 - 19816 * q^43 - 6560 * q^44 - 26000 * q^45 - 4400 * q^46 - 14660 * q^47 - 1536 * q^48 - 17808 * q^49 - 28720 * q^50 + 17948 * q^51 + 1152 * q^52 + 19032 * q^53 + 20152 * q^54 + 3160 * q^55 - 1536 * q^56 + 23432 * q^57 - 6752 * q^58 + 25136 * q^59 - 9536 * q^60 + 10080 * q^61 + 10496 * q^62 - 968 * q^63 - 57460 * q^65 - 2480 * q^66 + 280 * q^67 + 1568 * q^68 - 1876 * q^69 + 6792 * q^70 + 49672 * q^71 + 4480 * q^72 + 16196 * q^73 - 30984 * q^74 + 58748 * q^75 + 13312 * q^76 + 6444 * q^77 + 4928 * q^78 + 34556 * q^79 + 6888 * q^82 + 17304 * q^83 + 7008 * q^84 - 104144 * q^85 + 30800 * q^86 - 28492 * q^87 - 3648 * q^88 + 26732 * q^89 - 70336 * q^90 - 132748 * q^91 + 4160 * q^92 + 35360 * q^93 - 11160 * q^94 - 5644 * q^95 - 1024 * q^96 + 14036 * q^97 - 6528 * q^98 + 36896 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/82\mathbb{Z}\right)^\times$.

$n$	$47$
$\chi(n)$	$e\left(\frac{31}{40}\right)$

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 $

$2$	−2.52015	−	1.28408i	−0.630037	−	0.321020i
$2$	−2.52015	−	1.28408i	−0.630037	−	0.321020i
$3$	5.90673	−	14.2601i	0.656304	−	1.58446i	−0.147166	−	0.989112i	$-0.547015\pi$
$3$	5.90673	−	14.2601i	0.656304	−	1.58446i	0.803470	−	0.595346i	$-0.202985\pi$
$4$	4.70228	+	6.47214i	0.293893	+	0.404508i
$5$	−12.4829	−	1.97710i	−0.499316	−	0.0790838i	−0.0983033	−	0.995157i	$-0.531342\pi$
$5$	−12.4829	−	1.97710i	−0.499316	−	0.0790838i	−0.401012	+	0.916073i	$0.631342\pi$
$6$	−33.1970	+	28.3529i	−0.922138	+	0.787580i
$7$	−27.9835	−	23.9001i	−0.571091	−	0.487758i	0.316373	−	0.948635i	$-0.397535\pi$
$7$	−27.9835	−	23.9001i	−0.571091	−	0.487758i	−0.887464	+	0.460877i	$0.847535\pi$
$8$	−3.53971	−	22.3488i	−0.0553079	−	0.349201i
$9$	−111.186	−	111.186i	−1.37266	−	1.37266i
$10$	28.9200	+	21.0116i	0.289200	+	0.210116i
$11$	13.0886	+	21.3587i	0.108171	+	0.176518i	0.902145	−	0.431433i	$-0.141992\pi$
$11$	13.0886	+	21.3587i	0.108171	+	0.176518i	−0.793975	+	0.607951i	$0.791992\pi$
$12$	120.069	−	28.8259i	0.833809	−	0.200180i
$13$	17.5069	+	1.37782i	0.103591	+	0.00815278i	0.130149	−	0.991495i	$-0.458455\pi$
$13$	17.5069	+	1.37782i	0.103591	+	0.00815278i	−0.0265577	+	0.999647i	$0.508455\pi$
$14$	39.8328	+	96.1648i	0.203228	+	0.490637i
$15$	−101.927	+	166.329i	−0.453008	+	0.739241i
$16$	−19.7771	+	60.8676i	−0.0772542	+	0.237764i
$17$	−27.1543	+	113.106i	−0.0939595	+	0.391370i	−0.999456	−	0.0329845i	$-0.989499\pi$
$17$	−27.1543	+	113.106i	−0.0939595	+	0.391370i	0.905496	+	0.424354i	$0.139499\pi$
$18$	137.433	+	422.976i	0.424177	+	1.30548i
$19$	−165.362	+	13.0143i	−0.458067	+	0.0360507i	−0.305394	−	0.952226i	$-0.598788\pi$
$19$	−165.362	+	13.0143i	−0.458067	+	0.0360507i	−0.152673	+	0.988277i	$0.548788\pi$
$20$	−45.9020	−	90.0878i	−0.114755	−	0.225220i
$21$	−506.110	+	257.876i	−1.14764	+	0.584752i
$22$	−5.55902	−	70.6340i	−0.0114856	−	0.145938i
$23$	189.162	−	61.4626i	0.357585	−	0.116186i	−0.124715	−	0.992193i	$-0.539802\pi$
$23$	189.162	−	61.4626i	0.357585	−	0.116186i	0.482300	+	0.876006i	$0.339802\pi$
$24$	−339.605	−	81.5320i	−0.589592	−	0.141549i
$25$	−442.497	−	143.776i	−0.707995	−	0.230041i
$26$	−42.3506	−	25.9525i	−0.0626489	−	0.0383913i
$27$	−1087.20	+	450.332i	−1.49136	+	0.617740i
$28$	23.0988	−	293.498i	0.0294627	−	0.374360i
$29$	−155.132	−	646.171i	−0.184461	−	0.768336i	−0.985493	−	0.169715i	$-0.945715\pi$
$29$	−155.132	−	646.171i	−0.184461	−	0.768336i	0.801032	−	0.598621i	$-0.204285\pi$
$30$	470.450	−	288.292i	0.522723	−	0.320325i
$31$	−1024.55	+	1410.18i	−1.06613	+	1.46741i	−0.192201	+	0.981356i	$0.561563\pi$
$31$	−1024.55	+	1410.18i	−1.06613	+	1.46741i	−0.873931	+	0.486050i	$0.838437\pi$
$32$	128.000	−	128.000i	0.125000	−	0.125000i
$33$	381.889	−	60.4853i	0.350679	−	0.0555421i
$34$	213.670	−	250.175i	0.184835	−	0.216414i
$35$	302.062	+	353.669i	0.246581	+	0.288709i
$36$	196.783	−	1242.44i	0.151838	−	0.958671i
$37$	1709.37	−	1241.93i	1.24863	−	0.907183i	0.250489	−	0.968120i	$-0.419409\pi$
$37$	1709.37	−	1241.93i	1.24863	−	0.907183i	0.998142	+	0.0609366i	$0.0194088\pi$
$38$	433.449	+	179.540i	0.300172	+	0.124335i
$39$	123.056	−	241.511i	0.0809048	−	0.158785i
$40$			285.976i			0.178735i
$41$	1477.24	−	802.194i	0.878788	−	0.477212i
$41$	1477.24	−	802.194i	0.878788	−	0.477212i
$42$	1606.60			0.910773
$43$	−1474.01	−	751.045i	−0.797192	−	0.406190i	0.00743312	−	0.999972i	$-0.497634\pi$
$43$	−1474.01	−	751.045i	−0.797192	−	0.406190i	−0.804626	+	0.593783i	$0.797634\pi$
$44$	−76.6901	+	185.146i	−0.0396126	+	0.0956334i
$45$	1168.10	+	1607.75i	0.576837	+	0.793948i
$46$	−555.640	−	88.0047i	−0.262590	−	0.0415901i
$47$	427.273	−	364.925i	0.193424	−	0.165199i	−0.547462	−	0.836830i	$-0.684406\pi$
$47$	427.273	−	364.925i	0.193424	−	0.165199i	0.740886	+	0.671631i	$0.234406\pi$
$48$	751.161	+	641.552i	0.326025	+	0.278452i
$49$	−163.741	−	1033.82i	−0.0681972	−	0.430580i
$50$	930.537	+	930.537i	0.372215	+	0.372215i
$51$	1452.51	+	1055.31i	0.558442	+	0.405732i
$52$	73.4047	+	119.786i	0.0271467	+	0.0442994i
$53$	2618.25	−	628.586i	0.932093	−	0.223776i	0.261161	−	0.965295i	$-0.415895\pi$
$53$	2618.25	−	628.586i	0.932093	−	0.223776i	0.670931	+	0.741520i	$0.265895\pi$
$54$	3318.16	+	261.145i	1.13792	+	0.0895559i
$55$	−121.156	−	292.496i	−0.0400515	−	0.0966929i
$56$	−435.087	+	709.997i	−0.138739	+	0.226402i
$57$	−791.166	+	2434.96i	−0.243511	+	0.749449i
$58$	−438.779	+	1827.65i	−0.130434	+	0.543296i
$59$	−1947.28	−	5993.11i	−0.559402	−	1.72166i	−0.684025	−	0.729458i	$-0.739772\pi$
$59$	−1947.28	−	5993.11i	−0.559402	−	1.72166i	0.124623	−	0.992204i	$-0.460228\pi$
$60$	−1555.79	+	122.444i	−0.432165	+	0.0340121i
$61$	−2812.51	−	5519.86i	−0.755847	−	1.48343i	−0.871633	−	0.490159i	$-0.836939\pi$
$61$	−2812.51	−	5519.86i	−0.755847	−	1.48343i	0.115786	−	0.993274i	$-0.463061\pi$
$62$	4392.80	−	2238.24i	1.14277	−	0.582270i
$63$	454.008	+	5768.72i	0.114389	+	1.45344i
$64$	−486.941	+	158.217i	−0.118882	+	0.0386271i
$65$	−215.812	−	51.8119i	−0.0510798	−	0.0122632i
$66$	−1040.08	−	337.944i	−0.238771	−	0.0775813i
$67$	−5038.26	−	3087.45i	−1.12236	−	0.687781i	−0.167804	−	0.985820i	$-0.553667\pi$
$67$	−5038.26	−	3087.45i	−1.12236	−	0.687781i	−0.954554	+	0.298039i	$0.903667\pi$
$68$	−859.723	+	356.109i	−0.185926	+	0.0770132i
$69$	240.868	−	3060.52i	0.0505920	−	0.642832i
$70$	−307.101	−	1279.17i	−0.0626737	−	0.261055i
$71$	175.267	−	107.404i	0.0347683	−	0.0213060i	−0.505006	−	0.863116i	$-0.668510\pi$
$71$	175.267	−	107.404i	0.0347683	−	0.0213060i	0.539774	+	0.841810i	$0.318510\pi$
$72$	−2091.31	+	2878.44i	−0.403416	+	0.555255i
$73$	−1621.82	+	1621.82i	−0.304339	+	0.304339i	−0.842709	−	0.538370i	$-0.819040\pi$
$73$	−1621.82	+	1621.82i	−0.304339	+	0.304339i	0.538370	+	0.842709i	$0.319040\pi$
$74$	−5902.62	+	934.883i	−1.07791	+	0.170724i
$75$	−4663.97	+	5460.81i	−0.829151	+	0.970811i
$76$	−861.811	−	1009.05i	−0.149205	−	0.174697i
$77$	144.211	−	910.511i	0.0243230	−	0.153569i
$78$	−620.240	+	450.630i	−0.101946	+	0.0740681i
$79$	5090.15	+	2108.41i	0.815599	+	0.337832i	0.751186	−	0.660091i	$-0.229482\pi$
$79$	5090.15	+	2108.41i	0.815599	+	0.337832i	0.0644136	+	0.997923i	$0.479482\pi$
$80$	367.216	−	720.702i	0.0573775	−	0.112610i
$81$			5427.10i			0.827175i
$82$	−4752.95	+	124.750i	−0.706863	+	0.0185529i
$83$	11667.4			1.69363			0.846815	−	0.531888i	$-0.178517\pi$
$83$	11667.4			1.69363			0.846815	+	0.531888i	$0.178517\pi$
$84$	−4048.88	−	2063.01i	−0.573820	−	0.292376i
$85$	562.585	−	1358.20i	0.0778664	−	0.187986i
$86$	2750.32	+	3785.49i	0.371866	+	0.511829i
$87$	−10130.8	−	1604.56i	−1.33846	−	0.211991i
$88$	431.013	−	368.120i	0.0556576	−	0.0475361i
$89$	2053.55	+	1753.90i	0.259254	+	0.221424i	0.769569	−	0.638564i	$-0.220471\pi$
$89$	2053.55	+	1753.90i	0.259254	+	0.221424i	−0.510315	+	0.859988i	$0.670471\pi$
$90$	−879.300	−	5551.68i	−0.108556	−	0.685393i
$91$	−456.972	−	456.972i	−0.0551832	−	0.0551832i
$92$	1287.29	+	935.270i	0.152090	+	0.110500i
$93$	14057.5	+	22939.8i	1.62533	+	2.65231i
$94$	−1545.38	+	371.014i	−0.174896	+	0.0419889i
$95$	2089.93	+	164.481i	0.231571	+	0.0182251i
$96$	−1069.23	−	2581.36i	−0.116019	−	0.280095i
$97$	−7145.87	+	11661.0i	−0.759471	+	1.23934i	0.205928	+	0.978567i	$0.433979\pi$
$97$	−7145.87	+	11661.0i	−0.759471	+	1.23934i	−0.965399	+	0.260777i	$0.916021\pi$
$98$	−914.858	+	2815.64i	−0.0952580	+	0.293174i
$99$	919.516	−	3830.06i	0.0938186	−	0.390783i
$100$	−1150.21	−	3539.97i	−0.115021	−	0.353997i
$101$	−950.842	+	74.8329i	−0.0932107	+	0.00733584i	−0.124979	−	0.992159i	$-0.539886\pi$
$101$	−950.842	+	74.8329i	−0.0932107	+	0.00733584i	0.0317680	+	0.999495i	$0.489886\pi$
$102$	−2305.44	−	4524.67i	−0.221591	−	0.434897i
$103$	4318.00	−	2200.13i	0.407013	−	0.207383i	−0.238484	−	0.971146i	$-0.576650\pi$
$103$	4318.00	−	2200.13i	0.407013	−	0.207383i	0.645497	+	0.763763i	$0.276650\pi$
$104$	−31.1765	−	396.135i	−0.00288244	−	0.0366249i
$105$	6827.55	−	2218.41i	0.619279	−	0.201216i
$106$	−7405.52	−	1777.91i	−0.659089	−	0.158233i
$107$	−8894.08	−	2889.86i	−0.776843	−	0.252412i	−0.106351	−	0.994329i	$-0.533917\pi$
$107$	−8894.08	−	2889.86i	−0.776843	−	0.252412i	−0.670492	+	0.741917i	$0.733917\pi$
$108$	−8026.93	−	4918.91i	−0.688180	−	0.421717i
$109$	3275.73	−	1356.85i	0.275711	−	0.114203i	−0.240544	−	0.970638i	$-0.577326\pi$
$109$	3275.73	−	1356.85i	0.275711	−	0.114203i	0.516255	+	0.856435i	$0.327326\pi$
$110$	−70.2576	+	892.707i	−0.00580641	+	0.0737774i
$111$	−7613.30	−	31711.7i	−0.617912	−	2.57379i
$112$	2008.18	−	1230.61i	0.160091	−	0.0981036i
$113$	−1159.69	+	1596.17i	−0.0908204	+	0.125004i	−0.852009	−	0.523527i	$-0.824616\pi$
$113$	−1159.69	+	1596.17i	−0.0908204	+	0.125004i	0.761189	+	0.648530i	$0.224616\pi$
$114$	5120.53	−	5120.53i	0.394009	−	0.394009i
$115$	−2482.81	+	393.239i	−0.187736	+	0.0297345i
$116$	3452.63	−	4042.51i	0.256587	−	0.300424i
$117$	−1793.32	−	2099.71i	−0.131004	−	0.153387i
$118$	−2788.20	+	17604.0i	−0.200244	+	1.26429i
$119$	3463.11	−	2516.10i	0.244553	−	0.177678i
$120$	4078.06	+	1689.19i	0.283198	+	0.117305i
$121$	6361.99	−	12486.1i	0.434533	−	0.852818i
$122$			17522.3i			1.17726i
$123$	−2713.70	−	25804.0i	−0.179371	−	1.70560i
$124$	−13944.6			−0.906906
$125$	12277.5	+	6255.69i	0.785759	+	0.400364i
$126$	6263.33	−	15121.0i	0.394515	−	0.952444i
$127$	1356.44	+	1866.98i	0.0840995	+	0.115753i	0.848994	−	0.528403i	$-0.177209\pi$
$127$	1356.44	+	1866.98i	0.0840995	+	0.115753i	−0.764894	+	0.644156i	$0.777209\pi$
$128$	1430.33	+	226.541i	0.0873001	+	0.0138270i
$129$	−19416.6	+	16583.3i	−1.16679	+	0.996534i
$130$	477.348	+	407.693i	0.0282454	+	0.0241239i
$131$	3394.79	+	21433.9i	0.197820	+	1.24899i	0.864113	+	0.503297i	$0.167880\pi$
$131$	3394.79	+	21433.9i	0.197820	+	1.24899i	−0.666293	+	0.745690i	$0.732120\pi$
$132$	2187.22	+	2187.22i	0.125529	+	0.125529i
$133$	4938.45	+	3588.00i	0.279182	+	0.202838i
$134$	8732.63	+	14250.4i	0.486335	+	0.793626i
$135$	14461.7	−	3471.95i	0.793511	−	0.190505i
$136$	2623.90	+	206.505i	0.141863	+	0.0111649i
$137$	5205.78	+	12567.9i	0.277360	+	0.669607i	0.999761	−	0.0218678i	$-0.00696131\pi$
$137$	5205.78	+	12567.9i	0.277360	+	0.669607i	−0.722401	+	0.691475i	$0.756961\pi$
$138$	−4536.98	+	7403.67i	−0.238236	+	0.388767i
$139$	−115.337	+	354.969i	−0.00596949	+	0.0183722i	−0.953997	−	0.299816i	$-0.903075\pi$
$139$	−115.337	+	354.969i	−0.00596949	+	0.0183722i	0.948027	+	0.318189i	$0.103075\pi$
$140$	−868.613	+	3618.03i	−0.0443170	+	0.184594i
$141$	−2680.09	−	8248.48i	−0.134807	−	0.414892i
$142$	−579.613	+	45.6165i	−0.0287449	+	0.00226228i
$143$	199.713	+	391.958i	0.00976637	+	0.0191676i
$144$	8966.55	−	4568.68i	0.432415	−	0.220326i
$145$	658.953	+	8372.79i	0.0313414	+	0.398230i
$146$	6169.78	−	2004.68i	0.289444	−	0.0940460i
$147$	−15709.6	−	3771.54i	−0.726994	−	0.174536i
$148$	16075.9	+	5223.38i	0.733926	+	0.238467i
$149$	20292.3	+	12435.1i	0.914027	+	0.560116i	0.898117	−	0.439757i	$-0.144935\pi$
$149$	20292.3	+	12435.1i	0.914027	+	0.560116i	0.0159101	+	0.999873i	$0.494935\pi$
$150$	18766.0	−	7773.14i	0.834045	−	0.345473i
$151$	2296.63	−	29181.4i	0.100725	−	1.27983i	−0.714067	−	0.700078i	$-0.753149\pi$
$151$	2296.63	−	29181.4i	0.100725	−	1.27983i	0.814792	−	0.579754i	$-0.196851\pi$
$152$	876.189	+	3649.59i	0.0379237	+	0.157964i
$153$	15594.9	−	9556.59i	0.666194	−	0.408244i
$154$	−1532.60	+	2109.44i	−0.0646231	+	0.0889461i
$155$	15577.4	−	15577.4i	0.648384	−	0.648384i
$156$	2141.74	−	339.218i	0.0880071	−	0.0139390i
$157$	−18975.5	+	22217.4i	−0.769827	+	0.901352i	−0.997375	−	0.0724150i	$-0.976929\pi$
$157$	−18975.5	+	22217.4i	−0.769827	+	0.901352i	0.227547	+	0.973767i	$0.426929\pi$
$158$	−10120.6	−	11849.7i	−0.405407	−	0.474670i
$159$	6501.59	−	41049.4i	0.257173	−	1.62373i
$160$	−1850.88	+	1344.74i	−0.0722999	+	0.0525290i
$161$	−6762.38	−	2801.07i	−0.260884	−	0.108062i
$162$	6968.82	−	13677.1i	0.265540	−	0.521151i
$163$			47435.7i			1.78538i	0.450672	+	0.892690i	$0.351184\pi$
$163$			47435.7i			1.78538i	−0.450672	+	0.892690i	$0.648816\pi$
$164$	12138.3	+	5788.77i	0.451306	+	0.215228i
$165$	−4886.66			−0.179492
$166$	−29403.6	−	14981.9i	−1.06705	−	0.543689i
$167$	13301.0	−	32111.4i	0.476925	−	1.15140i	−0.484118	−	0.875003i	$-0.660859\pi$
$167$	13301.0	−	32111.4i	0.476925	−	1.15140i	0.961044	−	0.276397i	$-0.0891405\pi$
$168$	7554.70	+	10398.2i	0.267669	+	0.368415i
$169$	−27904.8	−	4419.68i	−0.977024	−	0.154745i
$170$	−3161.83	+	2700.46i	−0.109406	+	0.0934415i
$171$	19833.0	+	16938.9i	0.678259	+	0.579288i
$172$	−2070.34	−	13071.6i	−0.0699817	−	0.441847i
$173$	37452.4	+	37452.4i	1.25138	+	1.25138i	0.955103	+	0.296273i	$0.0957439\pi$
$173$	37452.4	+	37452.4i	1.25138	+	1.25138i	0.296273	+	0.955103i	$0.404256\pi$
$174$	23470.7	+	17052.5i	0.775225	+	0.563234i
$175$	8946.33	+	14599.1i	0.292125	+	0.476705i
$176$	−1558.91	+	374.261i	−0.0503264	+	0.0120823i
$177$	−96964.5	−	7631.27i	−3.09504	−	0.243585i
$178$	−2923.11	−	7057.00i	−0.0922581	−	0.222731i
$179$	6871.01	−	11212.5i	0.214444	−	0.349942i	−0.727272	−	0.686349i	$-0.759212\pi$
$179$	6871.01	−	11212.5i	0.214444	−	0.349942i	0.941716	+	0.336408i	$0.109212\pi$
$180$	−4912.83	+	15120.1i	−0.151631	+	0.466671i
$181$	12628.3	−	52600.5i	0.385466	−	1.60558i	−0.355928	−	0.934513i	$-0.615835\pi$
$181$	12628.3	−	52600.5i	0.385466	−	1.60558i	0.741395	−	0.671069i	$-0.234165\pi$
$182$	564.849	+	1738.43i	0.0170526	+	0.0524824i
$183$	−95326.5	+	7502.36i	−2.84650	+	0.224025i
$184$	−2043.20	−	4010.00i	−0.0603496	−	0.118443i
$185$	−23793.4	+	12123.3i	−0.695204	+	0.354224i
$186$	−5970.52	−	75862.6i	−0.172578	−	2.19281i
$187$	−2771.21	+	900.420i	−0.0792476	+	0.0257491i
$188$	4371.00	+	1049.38i	0.123670	+	0.0296906i
$189$	41186.6	+	13382.3i	1.15301	+	0.374635i
$190$	−5055.72	−	3098.15i	−0.140048	−	0.0858214i
$191$	−19038.3	+	7885.94i	−0.521870	+	0.216166i	−0.628038	−	0.778183i	$-0.716142\pi$
$191$	−19038.3	+	7885.94i	−0.521870	+	0.216166i	0.106168	+	0.994348i	$0.466142\pi$
$192$	−620.042	+	7878.38i	−0.0168197	+	0.213715i
$193$	236.527	+	985.208i	0.00634990	+	0.0264492i	0.975455	−	0.220199i	$-0.0706707\pi$
$193$	236.527	+	985.208i	0.00634990	+	0.0264492i	−0.969105	+	0.246648i	$0.920671\pi$
$194$	32982.3	−	20211.6i	0.876349	−	0.537027i
$195$	−2013.59	+	2771.47i	−0.0529543	+	0.0728854i
$196$	5921.08	−	5921.08i	0.154131	−	0.154131i
$197$	48470.2	−	7676.93i	1.24894	−	0.197813i	0.503273	−	0.864128i	$-0.332129\pi$
$197$	48470.2	−	7676.93i	1.24894	−	0.197813i	0.745671	+	0.666314i	$0.232129\pi$
$198$	−7235.42	+	8471.58i	−0.184558	+	0.216090i
$199$	−6022.10	−	7050.97i	−0.152069	−	0.178050i	0.679142	−	0.734007i	$-0.262352\pi$
$199$	−6022.10	−	7050.97i	−0.152069	−	0.178050i	−0.831211	+	0.555957i	$0.812352\pi$
$200$	−1646.91	+	10398.2i	−0.0411729	+	0.259955i
$201$	−73787.1	+	53609.5i	−1.82637	+	1.32693i
$202$	2492.35	+	1032.37i	0.0610811	+	0.0253006i
$203$	−11102.4	+	21789.8i	−0.269418	+	0.528762i
$204$			14363.2i			0.345136i
$205$	−20026.3	+	7093.04i	−0.476532	+	0.168782i
$206$	−13707.1			−0.323007
$207$	−27866.0	−	14198.4i	−0.650329	−	0.331359i
$208$	−430.099	+	1038.35i	−0.00994127	+	0.0240004i
$209$	−2442.34	−	3361.59i	−0.0559131	−	0.0769577i
$210$	−20055.1	−	3176.41i	−0.454763	−	0.0720274i
$211$	−50282.6	+	42945.4i	−1.12941	+	0.964609i	−0.999637	−	0.0269342i	$-0.991426\pi$
$211$	−50282.6	+	42945.4i	−1.12941	+	0.964609i	−0.129775	+	0.991543i	$0.541426\pi$
$212$	16380.0	+	13989.9i	0.364454	+	0.311273i
$213$	−496.334	−	3133.73i	−0.0109399	−	0.0690721i
$214$	18703.6	+	18703.6i	0.408411	+	0.408411i
$215$	16915.0	+	12289.5i	0.365928	+	0.265862i
$216$	13912.8	+	22703.6i	0.298199	+	0.486617i
$217$	62374.0	−	14974.7i	1.32460	−	0.318008i
$218$	−9997.62	−	786.830i	−0.210370	−	0.0165565i
$219$	13547.7	+	32707.1i	0.282474	+	0.681952i
$220$	1323.37	−	2159.54i	0.0273423	−	0.0446185i
$221$	−631.226	+	1942.71i	−0.0129241	+	0.0397763i
$222$	−21533.7	+	89694.1i	−0.436930	+	1.81994i
$223$	−6677.21	−	20550.3i	−0.134272	−	0.413246i	0.861204	−	0.508259i	$-0.169711\pi$
$223$	−6677.21	−	20550.3i	−0.134272	−	0.413246i	−0.995476	+	0.0950128i	$0.969711\pi$
$224$	−6641.10	+	522.666i	−0.132356	+	0.0104167i
$225$	33213.5	+	65185.2i	0.656070	+	1.28761i
$226$	4972.19	−	2533.46i	0.0973488	−	0.0496017i
$227$	−5698.76	−	72409.6i	−0.110593	−	1.40522i	−0.762533	−	0.646949i	$-0.776045\pi$
$227$	−5698.76	−	72409.6i	−0.110593	−	1.40522i	0.651940	−	0.758270i	$-0.273955\pi$
$228$	−19479.7	+	6329.33i	−0.374724	+	0.121755i
$229$	85618.1	+	20555.1i	1.63265	+	0.391966i	0.943164	−	0.332328i	$-0.107834\pi$
$229$	85618.1	+	20555.1i	1.63265	+	0.391966i	0.689491	+	0.724294i	$0.257834\pi$
$230$	6762.00	+	2197.11i	0.127826	+	0.0415332i
$231$	−12132.2	−	7434.61i	−0.227361	−	0.139327i
$232$	−13892.0	+	5754.27i	−0.258101	+	0.106909i
$233$	4581.73	−	58216.4i	0.0843952	−	1.07234i	−0.798257	−	0.602316i	$-0.794245\pi$
$233$	4581.73	−	58216.4i	0.0843952	−	1.07234i	0.882653	−	0.470026i	$-0.155755\pi$
$234$	1823.24	+	7594.34i	0.0332975	+	0.138694i
$235$	−6055.09	+	3710.56i	−0.109644	+	0.0671899i
$236$	29631.6	−	40784.3i	0.532023	−	0.732267i
$237$	60132.4	−	60132.4i	1.07056	−	1.07056i
$238$	−11958.4	+	1894.03i	−0.211116	+	0.0334374i
$239$	−32276.7	+	37791.2i	−0.565059	+	0.661599i	−0.967211	−	0.253974i	$-0.918262\pi$
$239$	−32276.7	+	37791.2i	−0.565059	+	0.661599i	0.402152	+	0.915573i	$0.368262\pi$
$240$	−8108.25	−	9493.55i	−0.140768	−	0.164818i
$241$	2849.07	−	17988.3i	0.0490535	−	0.309711i	−0.950946	−	0.309355i	$-0.899887\pi$
$241$	2849.07	−	17988.3i	0.0490535	−	0.309711i	1.00000		0.000355876i	$-0.000113279\pi$
$242$	−32066.3	+	23297.5i	−0.547543	+	0.397813i
$243$	−10672.0	−	4420.51i	−0.180732	−	0.0748616i
$244$	22500.1	−	44158.8i	0.377923	−	0.741717i
$245$			13228.8i			0.220389i
$246$	−26295.5	+	68514.5i	−0.434521	+	1.13217i
$247$	−2912.91			−0.0477455
$248$	35142.4	+	17906.0i	0.571384	+	0.291135i
$249$	68916.3	−	166379.i	1.11154	−	2.68348i
$250$	−22908.3	−	31530.5i	−0.366532	−	0.504488i
$251$	−72769.9	−	11525.6i	−1.15506	−	0.182943i	−0.450626	−	0.892713i	$-0.648799\pi$
$251$	−72769.9	−	11525.6i	−1.15506	−	0.182943i	−0.704434	+	0.709770i	$0.748799\pi$
$252$	−35201.1	+	30064.6i	−0.554313	+	0.473428i
$253$	3788.64	+	3235.81i	0.0591892	+	0.0505524i
$254$	−1021.08	−	6446.85i	−0.0158268	−	0.0999263i
$255$	−16045.1	−	16045.1i	−0.246752	−	0.246752i
$256$	−3313.73	−	2407.57i	−0.0505636	−	0.0367366i
$257$	3715.42	+	6063.02i	0.0562525	+	0.0917957i	0.879530	−	0.475843i	$-0.157857\pi$
$257$	3715.42	+	6063.02i	0.0562525	+	0.0917957i	−0.823278	+	0.567639i	$0.807857\pi$
$258$	70226.9	−	16860.0i	1.05503	−	0.253290i
$259$	−77516.6	−	6100.69i	−1.15557	−	0.0909451i
$260$	−679.476	−	1640.40i	−0.0100514	−	0.0242663i
$261$	−54596.6	+	89093.5i	−0.801464	+	1.30787i
$262$	18967.4	−	58375.7i	0.276316	−	0.850412i
$263$	−11887.7	+	49515.8i	−0.171864	+	0.715867i	0.818162	+	0.574987i	$0.194993\pi$
$263$	−11887.7	+	49515.8i	−0.171864	+	0.715867i	−0.990027	+	0.140880i	$0.955007\pi$
$264$	−2703.55	−	8320.68i	−0.0387906	−	0.119385i
$265$	−33926.1	+	2670.04i	−0.483105	+	0.0380212i
$266$	−7838.36	−	15383.6i	−0.110780	−	0.217418i
$267$	37140.6	−	18924.1i	0.520986	−	0.265456i
$268$	−3708.93	−	47126.4i	−0.0516391	−	0.656137i
$269$	39975.4	−	12988.8i	0.552444	−	0.179500i	−0.0194747	−	0.999810i	$-0.506199\pi$
$269$	39975.4	−	12988.8i	0.552444	−	0.179500i	0.571918	+	0.820311i	$0.306199\pi$
$270$	−40904.0	−	9820.17i	−0.561097	−	0.134707i
$271$	106812.	+	34705.3i	1.45439	+	0.472560i	0.926351	−	0.376661i	$-0.122928\pi$
$271$	106812.	+	34705.3i	1.45439	+	0.472560i	0.528038	+	0.849221i	$0.322928\pi$
$272$	−6347.45	−	3889.72i	−0.0857949	−	0.0525752i
$273$	−9215.69	+	3817.27i	−0.123652	+	0.0512185i
$274$	3018.80	−	38357.5i	0.0402099	−	0.510915i
$275$	−2720.81	−	11333.0i	−0.0359777	−	0.149858i
$276$	20940.7	−	12832.5i	0.274900	−	0.168459i
$277$	36843.9	−	50711.3i	0.480182	−	0.660914i	−0.498358	−	0.866972i	$-0.666063\pi$
$277$	36843.9	−	50711.3i	0.480182	−	0.660914i	0.978540	+	0.206057i	$0.0660633\pi$
$278$	746.474	−	746.474i	0.00965884	−	0.00965884i
$279$	270707.	−	42875.8i	3.47770	−	0.550813i
$280$	6834.87	−	8002.61i	0.0871795	−	0.102074i
$281$	−47718.2	−	55870.9i	−0.604326	−	0.707575i	0.370928	−	0.928662i	$-0.379040\pi$
$281$	−47718.2	−	55870.9i	−0.604326	−	0.707575i	−0.975254	+	0.221086i	$0.929040\pi$
$282$	−3837.47	+	24228.8i	−0.0482555	+	0.304673i
$283$	60153.1	−	43703.8i	0.751078	−	0.545690i	−0.145083	−	0.989420i	$-0.546345\pi$
$283$	60153.1	−	43703.8i	0.751078	−	0.545690i	0.896161	+	0.443729i	$0.146345\pi$
$284$	1519.29	+	629.309i	0.0188366	+	0.00780238i
$285$	14690.2	−	28831.1i	0.180858	−	0.354954i
$286$		−	1244.24i		−	0.0152115i
$287$	−60510.9	−	12858.1i	−0.734632	−	0.156104i
$288$	−28463.6			−0.343166
$289$	62362.2	+	31775.1i	0.746665	+	0.380445i
$290$	9090.66	−	21946.8i	0.108093	−	0.260961i
$291$	124078.	+	170779.i	1.46525	+	2.01674i
$292$	−18122.9	−	2870.39i	−0.212551	−	0.0336647i
$293$	56855.2	−	48558.9i	0.662270	−	0.565632i	−0.253500	−	0.967335i	$-0.581582\pi$
$293$	56855.2	−	48558.9i	0.662270	−	0.565632i	0.915770	+	0.401704i	$0.131582\pi$
$294$	34747.6	+	29677.2i	0.402004	+	0.343343i
$295$	12458.7	+	78661.2i	0.143162	+	0.903892i
$296$	−33806.5	−	33806.5i	−0.385848	−	0.385848i
$297$	−23848.5	−	17326.9i	−0.270363	−	0.196431i
$298$	−35171.9	−	57395.3i	−0.396062	−	0.646315i
$299$	3396.32	−	815.385i	0.0379898	−	0.00912054i
$300$	−57274.4	−	4507.59i	−0.636382	−	0.0500844i
$301$	23297.8	+	56245.8i	0.257147	+	0.620808i
$302$	−43259.1	+	70592.5i	−0.474312	+	0.774006i
$303$	−4549.25	+	14001.1i	−0.0495512	+	0.152503i
$304$	2478.24	−	10322.6i	0.0268161	−	0.111697i
$305$	24194.9	+	74464.3i	0.260091	+	0.800476i
$306$	−51572.9	+	4058.88i	−0.550781	+	0.0433474i
$307$	34715.3	+	68132.5i	0.368335	+	0.722899i	0.998567	−	0.0535078i	$-0.0170402\pi$
$307$	34715.3	+	68132.5i	0.368335	+	0.722899i	−0.630232	+	0.776407i	$0.717040\pi$
$308$	6571.07	−	3348.13i	0.0692684	−	0.0352940i
$309$	−5868.85	−	74570.8i	−0.0614661	−	0.781001i
$310$	−59260.1	+	19254.8i	−0.616650	+	0.200362i
$311$	51454.5	+	12353.1i	0.531989	+	0.127719i	0.490536	−	0.871421i	$-0.336801\pi$
$311$	51454.5	+	12353.1i	0.531989	+	0.127719i	0.0414534	+	0.999140i	$0.486801\pi$
$312$	−5833.08	−	1895.28i	−0.0599224	−	0.0194700i
$313$	3742.88	+	2293.64i	0.0382047	+	0.0234119i	0.541470	−	0.840720i	$-0.317868\pi$
$313$	3742.88	+	2293.64i	0.0382047	+	0.0234119i	−0.503265	+	0.864132i	$0.667868\pi$
$314$	76349.9	−	31625.2i	0.774371	−	0.320755i
$315$	5737.98	−	72907.9i	0.0578279	−	0.734774i
$316$	10289.4	+	42858.5i	0.103043	+	0.429203i
$317$	−125527.	+	76923.0i	−1.24916	+	0.765487i	−0.980266	−	0.197683i	$-0.936658\pi$
$317$	−125527.	+	76923.0i	−1.24916	+	0.765487i	−0.268895	+	0.963170i	$0.586658\pi$
$318$	−69095.7	+	95102.0i	−0.683277	+	0.940449i
$319$	11770.9	−	11770.9i	0.115672	−	0.115672i
$320$	6391.24	−	1012.27i	0.0624144	−	0.00988548i
$321$	−93744.7	+	109761.i	−0.909781	+	1.06522i
$322$	13445.4	+	15742.5i	0.129677	+	0.151832i
$323$	3018.31	−	19056.8i	0.0289307	−	0.182661i
$324$	−35124.9	+	25519.7i	−0.334599	+	0.243101i
$325$	−7548.63	−	3126.74i	−0.0714663	−	0.0296023i
$326$	60911.2	−	119545.i	0.573142	−	1.12485i
$327$		−	54726.8i		−	0.511805i
$328$	−23157.1	−	30175.1i	−0.215247	−	0.280480i
$329$	−20678.3			−0.191040
$330$	12315.1	+	6274.86i	0.113086	+	0.0576204i
$331$	−9811.95	+	23688.1i	−0.0895569	+	0.216210i	−0.962311	−	0.271950i	$-0.912332\pi$
$331$	−9811.95	+	23688.1i	−0.0895569	+	0.216210i	0.872755	+	0.488159i	$0.162332\pi$
$332$	54863.5	+	75513.1i	0.497745	+	0.685088i
$333$	−328144.	−	51972.8i	−2.95921	−	0.468693i
$334$	−74754.0	+	63845.9i	−0.670103	+	0.572322i
$335$	56787.9	+	48501.4i	0.506018	+	0.432180i
$336$	−5686.91	−	35905.7i	−0.0503730	−	0.318042i
$337$	−62073.7	−	62073.7i	−0.546573	−	0.546573i	0.378875	−	0.925448i	$-0.376311\pi$
$337$	−62073.7	−	62073.7i	−0.546573	−	0.546573i	−0.925448	+	0.378875i	$0.876311\pi$
$338$	64648.9	+	46970.2i	0.565885	+	0.411139i
$339$	15911.6	+	25965.4i	0.138457	+	0.225941i
$340$	11435.9	−	2745.51i	0.0989264	−	0.0237501i
$341$	−43529.6	−	3425.85i	−0.374348	−	0.0294618i
$342$	−28231.0	−	68155.7i	−0.241365	−	0.582707i
$343$	−66293.6	+	108181.i	−0.563486	+	0.919526i
$344$	−11567.4	+	35600.9i	−0.0977507	+	0.300846i
$345$	−9057.68	+	37727.9i	−0.0760989	+	0.316975i
$346$	−46293.8	−	142478.i	−0.386697	−	1.19013i
$347$	−134970.	+	10622.4i	−1.12093	+	0.0882189i	−0.625350	−	0.780344i	$-0.715044\pi$
$347$	−134970.	+	10622.4i	−1.12093	+	0.0882189i	−0.495578	+	0.868563i	$0.665044\pi$
$348$	−37252.9	−	73113.0i	−0.307611	−	0.603720i
$349$	67195.7	−	34237.9i	0.551684	−	0.281097i	−0.155845	−	0.987782i	$-0.549810\pi$
$349$	67195.7	−	34237.9i	0.551684	−	0.281097i	0.707529	+	0.706684i	$0.249810\pi$
$350$	−3799.69	−	48279.6i	−0.0310179	−	0.394119i
$351$	−19653.9	+	6385.94i	−0.159527	+	0.0518335i
$352$	4409.26	+	1058.57i	0.0355861	+	0.00854347i
$353$	12372.0	+	4019.92i	0.0992870	+	0.0322603i	0.358239	−	0.933630i	$-0.383377\pi$
$353$	12372.0	+	4019.92i	0.0992870	+	0.0322603i	−0.258952	+	0.965890i	$0.583377\pi$
$354$	234566.	+	143742.i	1.87179	+	1.14704i
$355$	−2400.18	+	994.189i	−0.0190453	+	0.00788882i
$356$	−1695.09	+	21538.2i	−0.0133750	+	0.169945i
$357$	−15424.2	−	64246.4i	−0.121022	−	0.504095i
$358$	−31713.7	+	19434.2i	−0.247446	+	0.151635i
$359$	16317.9	−	22459.6i	0.126612	−	0.174266i	−0.741005	−	0.671499i	$-0.765651\pi$
$359$	16317.9	−	22459.6i	0.126612	−	0.174266i	0.867617	+	0.497233i	$0.165651\pi$
$360$	31796.5	−	31796.5i	0.245344	−	0.245344i
$361$	−101541.	+	16082.5i	−0.779162	+	0.123407i
$362$	−99368.3	+	116345.i	−0.758282	+	0.887834i
$363$	−140475.	−	164475.i	−1.06607	−	1.24821i
$364$	808.774	−	5106.40i	0.00610414	−	0.0385400i
$365$	23451.5	−	17038.5i	0.176030	−	0.127893i
$366$	249870.	+	103500.i	1.86532	+	0.772640i
$367$	−26514.4	+	52037.5i	−0.196857	+	0.386353i	−0.968242	−	0.250016i	$-0.919564\pi$
$367$	−26514.4	+	52037.5i	−0.196857	+	0.386353i	0.771385	+	0.636369i	$0.219564\pi$
$368$			12729.4i			0.0939968i
$369$	−253441.	−	75055.9i	−1.86133	−	0.551229i
$370$	75530.0			0.551717
$371$	−88290.9	−	44986.5i	−0.641458	−	0.326839i
$372$	−82367.0	+	198852.i	−0.595206	+	1.43695i
$373$	41813.1	+	57550.9i	0.300535	+	0.413651i	0.932400	−	0.361427i	$-0.117710\pi$
$373$	41813.1	+	57550.9i	0.300535	+	0.413651i	−0.631865	+	0.775078i	$0.717710\pi$
$374$	8140.06	+	1289.26i	0.0581949	+	0.00921716i
$375$	161727.	−	138128.i	1.15006	−	0.982242i
$376$	−9668.08	−	8257.32i	−0.0683856	−	0.0584068i
$377$	−1825.56	−	11526.2i	−0.0128444	−	0.0810965i
$378$	−86612.3	−	86612.3i	−0.606172	−	0.606172i
$379$	40302.4	+	29281.4i	0.280577	+	0.203851i	0.719169	−	0.694835i	$-0.244523\pi$
$379$	40302.4	+	29281.4i	0.280577	+	0.203851i	−0.438592	+	0.898686i	$0.644523\pi$
$380$	8762.90	+	14299.7i	0.0606849	+	0.0990287i
$381$	34635.5	−	8315.25i	0.238601	−	0.0572830i
$382$	58105.6	+	4573.01i	0.398191	+	0.0313383i
$383$	−106087.	−	256116.i	−0.723209	−	1.74598i	−0.663998	−	0.747734i	$-0.731142\pi$
$383$	−106087.	−	256116.i	−0.723209	−	1.74598i	−0.0592105	−	0.998246i	$-0.518858\pi$
$384$	11679.1	−	19058.5i	0.0792037	−	0.129249i
$385$	−3600.34	+	11080.7i	−0.0242897	+	0.0747559i
$386$	669.001	−	2786.59i	0.00449006	−	0.0187024i
$387$	80383.3	+	247394.i	0.536715	+	1.65184i
$388$	−109073.	+	8584.26i	−0.724528	+	0.0570216i
$389$	−91550.1	−	179677.i	−0.605006	−	1.18739i	−0.966896	−	0.255170i	$-0.917868\pi$
$389$	−91550.1	−	179677.i	−0.605006	−	1.18739i	0.361890	−	0.932221i	$-0.382132\pi$
$390$	8633.32	−	4398.90i	0.0567608	−	0.0289211i
$391$	1815.20	+	23064.3i	0.0118733	+	0.150865i
$392$	−22525.1	+	7318.86i	−0.146587	+	0.0476290i
$393$	325702.	+	78194.1i	2.10880	+	0.506277i
$394$	−132010.	−	42892.6i	−0.850382	−	0.276306i
$395$	−59371.3	−	36382.8i	−0.380524	−	0.233186i
$396$	29112.5	−	12058.8i	0.185647	−	0.0768977i
$397$	−7836.39	+	99570.7i	−0.0497204	+	0.631758i	0.920690	+	0.390295i	$0.127627\pi$
$397$	−7836.39	+	99570.7i	−0.0497204	+	0.631758i	−0.970410	+	0.241463i	$0.922373\pi$
$398$	6122.57	+	25502.3i	0.0386516	+	0.160995i
$399$	80335.4	−	49229.6i	0.504616	−	0.309229i
$400$	17502.6	−	24090.3i	0.109391	−	0.150564i
$401$	28036.2	−	28036.2i	0.174353	−	0.174353i	−0.614536	−	0.788889i	$-0.710657\pi$
$401$	28036.2	−	28036.2i	0.174353	−	0.174353i	0.788889	+	0.614536i	$0.210657\pi$
$402$	254793.	−	40355.3i	1.57665	−	0.249717i
$403$	−19879.7	+	23276.1i	−0.122405	+	0.143318i
$404$	−4955.46	−	5802.09i	−0.0303613	−	0.0355486i
$405$	10729.9	−	67745.9i	0.0654162	−	0.413022i
$406$	55959.6	−	40657.0i	0.339486	−	0.246651i
$407$	48899.5	+	20254.8i	0.295200	+	0.122276i
$408$	18443.5	−	36197.4i	0.110796	−	0.217449i
$409$			3529.73i			0.0211006i	0.999944	+	0.0105503i	$0.00335833\pi$
$409$			3529.73i			0.0211006i	−0.999944	+	0.0105503i	$0.996642\pi$
$410$	59577.2	+	7839.80i	0.354415	+	0.0466377i
$411$	209968.			1.24300
$412$	34544.0	+	17601.0i	0.203506	+	0.103692i
$413$	−88744.5	+	214248.i	−0.520285	+	1.25608i
$414$	51994.4	+	71564.2i	0.303358	+	0.417537i
$415$	−145643.	−	23067.6i	−0.845656	−	0.133939i
$416$	2417.24	−	2064.52i	0.0139680	−	0.0119298i
$417$	4380.64	+	3741.42i	0.0251922	+	0.0215162i
$418$	1838.50	+	11607.9i	0.0105223	+	0.0664354i
$419$	128717.	+	128717.i	0.733175	+	0.733175i	0.971247	−	0.238072i	$-0.0765155\pi$
$419$	128717.	+	128717.i	0.733175	+	0.733175i	−0.238072	+	0.971247i	$0.576516\pi$
$420$	46462.9	+	33757.3i	0.263395	+	0.191368i
$421$	103513.	+	168917.i	0.584021	+	0.953036i	0.999065	+	0.0432348i	$0.0137663\pi$
$421$	103513.	+	168917.i	0.584021	+	0.953036i	−0.415044	+	0.909802i	$0.636234\pi$
$422$	181865.	−	43661.9i	1.02123	−	0.245176i
$423$	−88081.2	−	6932.14i	−0.492269	−	0.0387424i
$424$	−23316.0	−	56289.8i	−0.129695	−	0.313111i
$425$	28277.6	−	46144.8i	0.156554	−	0.255473i
$426$	−2773.12	+	8534.80i	−0.0152809	+	0.0470299i
$427$	−53221.6	+	221684.i	−0.291899	+	1.21585i
$428$	−23118.9	−	71152.6i	−0.126206	−	0.388422i
$429$	6769.02	−	532.733i	0.0367799	−	0.00289464i
$430$	−26847.6	−	52691.5i	−0.145201	−	0.284973i
$431$	−31990.7	+	16300.1i	−0.172214	+	0.0877476i	−0.537973	−	0.842962i	$-0.680810\pi$
$431$	−31990.7	+	16300.1i	−0.172214	+	0.0877476i	0.365758	+	0.930710i	$0.380810\pi$
$432$	−5909.04	−	75081.5i	−0.0316628	−	0.402314i
$433$	273572.	−	88889.0i	1.45914	−	0.474102i	0.531331	−	0.847164i	$-0.321692\pi$
$433$	273572.	−	88889.0i	1.45914	−	0.474102i	0.927806	+	0.373062i	$0.121692\pi$
$434$	−176420.	−	42354.7i	−0.936632	−	0.224865i
$435$	123289.	+	40059.1i	0.651548	+	0.211701i
$436$	24185.1	+	14820.7i	0.127226	+	0.0779641i
$437$	−30480.5	+	12625.4i	−0.159609	+	0.0661124i
$438$	7856.24	−	99823.0i	0.0409512	−	0.520334i
$439$	−38125.0	−	158802.i	−0.197825	−	0.823999i	−0.979685	−	0.200545i	$-0.935729\pi$
$439$	−38125.0	−	158802.i	−0.197825	−	0.823999i	0.781860	−	0.623454i	$-0.214271\pi$
$440$	−6108.09	+	3743.04i	−0.0315501	+	0.0193339i
$441$	−96740.7	+	133152.i	−0.497430	+	0.684654i
$442$	4085.38	−	4085.38i	0.0209116	−	0.0209116i
$443$	−114833.	+	18187.8i	−0.585141	+	0.0926772i	−0.441984	−	0.897023i	$-0.645725\pi$
$443$	−114833.	+	18187.8i	−0.585141	+	0.0926772i	−0.143157	+	0.989700i	$0.545725\pi$
$444$	169442.	−	198391.i	0.859520	−	1.00637i
$445$	−22166.6	−	25953.8i	−0.111938	−	0.131063i
$446$	−9560.71	+	60363.9i	−0.0480640	+	0.303464i
$447$	297188.	−	215920.i	1.48736	−	1.08063i
$448$	17407.7	+	7210.50i	0.0867332	+	0.0359261i
$449$	−101048.	+	198319.i	−0.501230	+	0.983719i	0.492330	+	0.870409i	$0.336145\pi$
$449$	−101048.	+	198319.i	−0.501230	+	0.983719i	−0.993560	+	0.113310i	$0.963855\pi$
$450$		−	206925.i		−	1.02185i
$451$	36468.9	+	21052.4i	0.179296	+	0.103502i
$452$	−15783.8			−0.0772565
$453$	−402565.	−	205117.i	−1.96173	−	0.999553i
$454$	−78617.9	+	189800.i	−0.381425	+	0.920843i
$455$	4800.86	+	6607.81i	0.0231897	+	0.0319179i
$456$	57219.0	+	9062.60i	0.275176	+	0.0435836i
$457$	199035.	−	169992.i	0.953008	−	0.813946i	−0.0296146	−	0.999561i	$-0.509428\pi$
$457$	199035.	−	169992.i	0.953008	−	0.813946i	0.982622	+	0.185616i	$0.0594280\pi$
$458$	−189376.	−	161742.i	−0.902804	−	0.771067i
$459$	−21413.1	−	135197.i	−0.101638	−	0.641714i
$460$	−14220.0	−	14220.0i	−0.0672021	−	0.0672021i
$461$	−125932.	−	91495.2i	−0.592564	−	0.430523i	0.250668	−	0.968073i	$-0.419350\pi$
$461$	−125932.	−	91495.2i	−0.592564	−	0.430523i	−0.843232	+	0.537550i	$0.819350\pi$
$462$	21028.3	+	34315.0i	0.0985189	+	0.160768i
$463$	−241437.	+	57964.0i	−1.12627	+	0.270393i	−0.753447	−	0.657509i	$-0.771610\pi$
$463$	−241437.	+	57964.0i	−1.12627	+	0.270393i	−0.372823	+	0.927902i	$0.621610\pi$
$464$	42398.9	+	3336.87i	0.196933	+	0.0154990i
$465$	−130124.	−	314148.i	−0.601801	−	1.45287i
$466$	−86301.1	+	140831.i	−0.397415	+	0.648522i
$467$	−1459.29	+	4491.24i	−0.00669128	+	0.0205936i	−0.954346	−	0.298702i	$-0.903446\pi$
$467$	−1459.29	+	4491.24i	−0.00669128	+	0.0205936i	0.947655	+	0.319296i	$0.103446\pi$
$468$	5156.90	−	21480.0i	0.0235449	−	0.0980716i
$469$	67197.5	+	206813.i	0.305497	+	0.940224i
$470$	20024.4	−	1575.95i	0.0906490	−	0.00713423i
$471$	204740.	+	401825.i	0.922913	+	1.81132i
$472$	−127046.	+	64733.3i	−0.570266	+	0.290565i
$473$	−3251.41	−	41313.1i	−0.0145328	−	0.184657i
$474$	−228757.	+	74327.7i	−1.01816	+	0.330822i
$475$	75043.4	+	18016.3i	0.332603	+	0.0798508i
$476$	32569.1	+	10582.3i	0.143745	+	0.0467055i
$477$	−361002.	−	221222.i	−1.58662	−	0.972282i
$478$	129869.	−	53793.5i	0.568394	−	0.235437i
$479$	9424.83	−	119754.i	0.0410773	−	0.521937i	−0.941615	−	0.336692i	$-0.890692\pi$
$479$	9424.83	−	119754.i	0.0410773	−	0.521937i	0.982692	−	0.185245i	$-0.0593080\pi$
$480$	8243.53	+	34336.8i	0.0357792	+	0.149031i
$481$	31636.9	−	19387.1i	0.136743	−	0.0837961i
$482$	−30278.5	+	41674.8i	−0.130329	+	0.179382i
$483$	−79887.2	+	79887.2i	−0.342439	+	0.342439i
$484$	110728.	−	17537.5i	0.472678	−	0.0748649i
$485$	112256.	−	131435.i	0.477228	−	0.558762i
$486$	21218.8	+	24844.1i	0.0898357	+	0.105184i
$487$	20625.7	−	130226.i	0.0869664	−	0.549084i	−0.905282	−	0.424812i	$-0.860340\pi$
$487$	20625.7	−	130226.i	0.0869664	−	0.549084i	0.992248	−	0.124273i	$-0.0396597\pi$
$488$	−113407.	+	82394.9i	−0.476211	+	0.345988i
$489$	676439.	+	280190.i	2.82886	+	1.17175i
$490$	16986.9	−	33338.6i	0.0707491	−	0.138853i
$491$			267648.i			1.11020i	0.831784	+	0.555100i	$0.187320\pi$
$491$			267648.i			1.11020i	−0.831784	+	0.555100i	$0.812680\pi$
$492$	154246.	−	138901.i	0.637214	−	0.573820i
$493$	77298.1			0.318035
$494$	7340.95	+	3740.40i	0.0300814	+	0.0153273i
$495$	−19050.6	+	45992.2i	−0.0777497	+	0.187704i
$496$	−65571.4	−	90251.3i	−0.266533	−	0.366851i
$497$	−7471.54	−	1183.38i	−0.0302480	−	0.00479082i
$498$	−387323.	+	330805.i	−1.56176	+	1.33387i
$499$	332121.	+	283658.i	1.33381	+	1.13918i	0.978913	+	0.204280i	$0.0654852\pi$
$499$	332121.	+	283658.i	1.33381	+	1.13918i	0.354900	+	0.934904i	$0.384515\pi$
$500$	17244.5	+	108878.i	0.0689781	+	0.435510i
$501$	−379347.	−	379347.i	−1.51134	−	1.51134i
$502$	168591.	+	122489.i	0.669002	+	0.486058i
$503$	−100157.	−	163442.i	−0.395865	−	0.645993i	0.591161	−	0.806554i	$-0.298670\pi$
$503$	−100157.	−	163442.i	−0.395865	−	0.645993i	−0.987026	+	0.160561i	$0.948670\pi$
$504$	127317.	−	30566.1i	0.501217	−	0.120332i
$505$	12017.2	+	945.775i	0.0471217	+	0.00370856i
$506$	−5392.91	−	13019.6i	−0.0210631	−	0.0508508i
$507$	−227851.	+	371820.i	−0.886412	+	1.44649i
$508$	−5704.99	+	17558.1i	−0.0221069	+	0.0680380i
$509$	65456.9	−	272648.i	0.252650	−	1.05236i	−0.691376	−	0.722495i	$-0.742995\pi$
$509$	65456.9	−	272648.i	0.252650	−	1.05236i	0.944026	−	0.329870i	$-0.107005\pi$
$510$	19832.8	+	61039.0i	0.0762506	+	0.234675i
$511$	84146.0	−	6622.44i	0.322249	−	0.0253616i
$512$	5259.59	+	10322.5i	0.0200637	+	0.0393773i
$513$	173921.	−	88617.2i	0.660872	−	0.336731i
$514$	−1578.02	−	20050.6i	−0.00597290	−	0.0758928i
$515$	−58251.0	+	18926.9i	−0.219629	+	0.0713616i
$516$	−198632.	−	47687.2i	−0.746018	−	0.179103i
$517$	13386.8	+	4349.62i	0.0500835	+	0.0162731i
$518$	187519.	+	114912.i	0.698855	+	0.428259i
$519$	755298.	−	312855.i	2.80404	−	1.16147i
$520$	−394.024	+	5006.55i	−0.00145719	+	0.0185153i
$521$	−15285.5	−	63668.8i	−0.0563125	−	0.234558i	0.937115	−	0.349020i	$-0.113486\pi$
$521$	−15285.5	−	63668.8i	−0.0563125	−	0.234558i	−0.993428	+	0.114462i	$0.963486\pi$
$522$	251994.	−	154422.i	0.924804	−	0.566721i
$523$	106210.	−	146186.i	0.388296	−	0.534444i	−0.569462	−	0.822018i	$-0.692848\pi$
$523$	106210.	−	146186.i	0.388296	−	0.534444i	0.957759	+	0.287573i	$0.0928485\pi$
$524$	−122760.	+	122760.i	−0.447088	+	0.447088i
$525$	261028.	−	41342.8i	0.947041	−	0.149997i
$526$	93540.9	−	109522.i	0.338088	−	0.395851i
$527$	−131678.	−	154175.i	−0.474124	−	0.555128i
$528$	−3871.06	+	24440.9i	−0.0138855	+	0.0876697i
$529$	−194391.	+	141234.i	−0.694649	+	0.504692i
$530$	88927.2	+	36834.9i	0.316580	+	0.131132i
$531$	−449839.	+	882858.i	−1.59539	+	3.13114i
$532$			48834.1i			0.172544i
$533$	26967.2	−	12008.5i	0.0949250	−	0.0422703i
$534$	−117900.			−0.413457
$535$	105310.	+	53658.3i	0.367928	+	0.187469i
$536$	−51167.0	+	123528.i	−0.178098	+	0.429968i
$537$	−119306.	−	164211.i	−0.413727	−	0.569446i
$538$	−117422.	−	18597.9i	−0.405683	−	0.0642538i
$539$	19938.0	−	17028.6i	0.0686284	−	0.0586142i
$540$	90474.1	+	77272.2i	0.310268	+	0.264994i
$541$	−50115.6	−	316417.i	−0.171229	−	1.08110i	−0.912255	−	0.409623i	$-0.865660\pi$
$541$	−50115.6	−	316417.i	−0.171229	−	1.08110i	0.741026	−	0.671477i	$-0.234340\pi$
$542$	−224617.	−	224617.i	−0.764618	−	0.764618i
$543$	−675498.	−	490778.i	−2.29099	−	1.66451i
$544$	11001.8	+	17953.3i	0.0371763	+	0.0606661i
$545$	−43573.2	+	10461.0i	−0.146699	+	0.0352192i
$546$	28126.6	+	2213.61i	0.0943478	+	0.00742533i
$547$	−38996.5	−	94146.0i	−0.130332	−	0.314650i	0.845220	−	0.534419i	$-0.179470\pi$
$547$	−38996.5	−	94146.0i	−0.130332	−	0.314650i	−0.975552	+	0.219769i	$0.929470\pi$
$548$	−56861.8	+	92790.1i	−0.189348	+	0.308987i
$549$	−301019.	+	926441.i	−0.998732	+	3.07378i
$550$	−7695.62	+	32054.6i	−0.0254401	+	0.105965i
$551$	34062.4	+	104833.i	0.112195	+	0.345300i
$552$	−69251.7	+	5450.23i	−0.227275	+	0.0178870i
$553$	−92048.8	−	180656.i	−0.301001	−	0.590748i
$554$	−157969.	+	80489.4i	−0.514699	+	0.262252i
$555$	32338.9	+	410905.i	0.104988	+	1.33400i
$556$	−2839.75	+	922.692i	−0.00918610	+	0.00298475i
$557$	504168.	+	121040.i	1.62504	+	0.390139i	0.940759	−	0.339076i	$-0.110114\pi$
$557$	504168.	+	121040.i	1.62504	+	0.390139i	0.684285	+	0.729214i	$0.260114\pi$
$558$	−737279.	−	239556.i	−2.36790	−	0.769377i
$559$	−24770.5	−	15179.4i	−0.0792703	−	0.0485769i
$560$	−27500.9	+	11391.2i	−0.0876941	+	0.0363241i
$561$	−3528.69	+	44836.3i	−0.0112121	+	0.142464i
$562$	48514.3	+	202077.i	0.153602	+	0.639799i
$563$	−8937.63	+	5476.99i	−0.0281972	+	0.0172793i	−0.536526	−	0.843884i	$-0.680264\pi$
$563$	−8937.63	+	5476.99i	−0.0281972	+	0.0172793i	0.508329	+	0.861163i	$0.330264\pi$
$564$	40782.7	−	56132.6i	0.128209	−	0.176464i
$565$	17632.0	−	17632.0i	0.0552338	−	0.0552338i
$566$	−207714.	+	32898.6i	−0.648384	+	0.102694i
$567$	129708.	−	151869.i	0.403461	−	0.472392i
$568$	−3020.74	−	3536.83i	−0.00936304	−	0.0109627i
$569$	40539.6	−	255957.i	0.125215	−	0.790574i	−0.842532	−	0.538647i	$-0.818936\pi$
$569$	40539.6	−	255957.i	0.125215	−	0.790574i	0.967746	−	0.251927i	$-0.0810643\pi$
$570$	−74042.8	+	53795.3i	−0.227894	+	0.165575i
$571$	−507301.	−	210131.i	−1.55594	−	0.644492i	−0.571564	−	0.820558i	$-0.693663\pi$
$571$	−507301.	−	210131.i	−1.55594	−	0.644492i	−0.984378	+	0.176065i	$0.943663\pi$
$572$	−1597.70	+	3135.66i	−0.00488319	+	0.00958379i
$573$			318069.i			0.968751i
$574$	135986.	+	110105.i	0.412733	+	0.334183i
$575$	−92540.6			−0.279896
$576$	71732.4	+	36549.5i	0.216207	+	0.110163i
$577$	50733.2	−	122481.i	0.152385	−	0.367889i	−0.829190	−	0.558966i	$-0.811198\pi$
$577$	50733.2	−	122481.i	0.152385	−	0.367889i	0.981575	+	0.191077i	$0.0611981\pi$
$578$	−116360.	−	160156.i	−0.348296	−	0.479388i
$579$	15446.3	+	2446.45i	0.0460752	+	0.00729759i
$580$	−51091.2	+	43636.0i	−0.151876	+	0.129715i
$581$	−326495.	−	278853.i	−0.967217	−	0.826081i
$582$	−93401.7	−	589715.i	−0.275746	−	1.74099i
$583$	47695.1	+	47695.1i	0.140326	+	0.140326i
$584$	41986.6	+	30505.1i	0.123108	+	0.0894430i
$585$	18234.5	+	29756.0i	0.0532822	+	0.0869486i
$586$	−205637.	+	49369.1i	−0.598833	+	0.143767i
$587$	−160775.	−	12653.2i	−0.466597	−	0.0367219i	−0.157018	−	0.987596i	$-0.550188\pi$
$587$	−160775.	−	12653.2i	−0.466597	−	0.0367219i	−0.309579	+	0.950874i	$0.600188\pi$
$588$	−49461.1	−	119410.i	−0.143057	−	0.345370i
$589$	151070.	−	246524.i	0.435460	−	0.710605i
$590$	69609.5	−	214236.i	0.199970	−	0.615443i
$591$	176827.	−	736537.i	0.506260	−	2.10872i
$592$	41787.1	+	128607.i	0.119234	+	0.366963i
$593$	574860.	−	45242.5i	1.63476	−	0.128658i	0.772460	−	0.635063i	$-0.219026\pi$
$593$	574860.	−	45242.5i	1.63476	−	0.128658i	0.862296	+	0.506405i	$0.169026\pi$
$594$	37852.5	+	74289.8i	0.107281	+	0.210550i
$595$	−48204.2	+	24561.3i	−0.136161	+	0.0693773i
$596$	14938.2	+	189808.i	0.0420539	+	0.534346i
$597$	−136119.	+	44227.6i	−0.381917	+	0.124092i
$598$	−9606.25	−	2306.26i	−0.0268628	−	0.00644919i
$599$	−269860.	−	87682.7i	−0.752115	−	0.244377i	−0.0922241	−	0.995738i	$-0.529398\pi$
$599$	−269860.	−	87682.7i	−0.752115	−	0.244377i	−0.659891	+	0.751361i	$0.729398\pi$
$600$	138552.	+	84904.7i	0.384866	+	0.235846i
$601$	517498.	−	214355.i	1.43271	−	0.593449i	0.474694	−	0.880151i	$-0.342559\pi$
$601$	517498.	−	214355.i	1.43271	−	0.593449i	0.958020	+	0.286702i	$0.0925589\pi$
$602$	13510.3	−	171664.i	0.0372795	−	0.473681i
$603$	216903.	+	903464.i	0.596527	+	2.48471i
$604$	199666.	−	122355.i	0.547305	−	0.335389i
$605$	−104102.	+	143284.i	−0.284413	+	0.391461i
$606$	29443.3	−	29443.3i	0.0801755	−	0.0801755i
$607$	215210.	−	34085.9i	0.584097	−	0.0925118i	0.142609	−	0.989779i	$-0.454451\pi$
$607$	215210.	−	34085.9i	0.584097	−	0.0925118i	0.441488	+	0.897267i	$0.354451\pi$
$608$	−19500.6	+	22832.2i	−0.0527521	+	0.0617648i
$609$	245145.	+	287028.i	0.660981	+	0.773910i
$610$	34643.3	−	218729.i	0.0931021	−	0.587824i
$611$	7983.00	−	5799.99i	0.0213837	−	0.0155362i
$612$	135183.	+	55994.8i	0.360928	+	0.149501i
$613$	−232346.	+	456005.i	−0.618321	+	1.21352i	0.343321	+	0.939218i	$0.388448\pi$
$613$	−232346.	+	456005.i	−0.618321	+	1.21352i	−0.961643	+	0.274306i	$0.911552\pi$
$614$		−	216281.i		−	0.573696i
$615$	−17142.2	+	327474.i	−0.0453227	+	0.865817i
$616$	−20859.3			−0.0549717
$617$	154209.	+	78573.6i	0.405080	+	0.206398i	0.644645	−	0.764482i	$-0.277005\pi$
$617$	154209.	+	78573.6i	0.405080	+	0.206398i	−0.239566	+	0.970880i	$0.577005\pi$
$618$	−80964.4	+	195465.i	−0.211991	+	0.511791i
$619$	−267285.	−	367887.i	−0.697580	−	0.960136i	−0.999976	−	0.00695379i	$-0.997787\pi$
$619$	−267285.	−	367887.i	−0.697580	−	0.960136i	0.302396	−	0.953182i	$-0.402213\pi$
$620$	174069.	+	27569.8i	0.452832	+	0.0717216i
$621$	−177979.	+	152008.i	−0.461514	+	0.394170i
$622$	−113811.	−	97203.4i	−0.294172	−	0.251247i
$623$	−15547.1	−	98160.2i	−0.0400564	−	0.252906i
$624$	12266.5	+	12266.5i	0.0315031	+	0.0315031i
$625$	94366.0	+	68560.9i	0.241577	+	0.175516i
$626$	−6487.39	−	10586.5i	−0.0165547	−	0.0270148i
$627$	−62362.9	+	14972.0i	−0.158632	+	0.0380842i
$628$	−233022.	−	18339.2i	−0.590851	−	0.0465010i
$629$	94053.0	+	227064.i	0.237723	+	0.573914i
$630$	−108080.	+	176371.i	−0.272311	+	0.444370i
$631$	−43688.6	+	134460.i	−0.109726	+	0.337702i	−0.990811	−	0.135257i	$-0.956814\pi$
$631$	−43688.6	+	134460.i	−0.109726	+	0.337702i	0.881085	+	0.472959i	$0.156814\pi$
$632$	29102.9	−	121222.i	0.0728621	−	0.303492i
$633$	315400.	+	970702.i	0.787145	+	2.42258i
$634$	415121.	−	32670.8i	1.03275	−	0.0812795i
$635$	−13241.1	−	25987.1i	−0.0328380	−	0.0644482i
$636$	296250.	−	150947.i	0.732392	−	0.373172i
$637$	−1442.18	−	18324.6i	−0.00355418	−	0.0451602i
$638$	−44779.2	+	14549.7i	−0.110011	+	0.0357447i
$639$	−31429.0	−	7545.43i	−0.0769712	−	0.0184792i
$640$	−17406.7	−	5655.78i	−0.0424968	−	0.0138081i
$641$	−246452.	−	151026.i	−0.599814	−	0.367567i	0.189203	−	0.981938i	$-0.439410\pi$
$641$	−246452.	−	151026.i	−0.599814	−	0.367567i	−0.789017	+	0.614372i	$0.789410\pi$
$642$	377192.	−	156238.i	0.915151	−	0.379068i
$643$	−38162.3	+	484898.i	−0.0923023	+	1.17281i	0.760057	+	0.649856i	$0.225171\pi$
$643$	−38162.3	+	484898.i	−0.0923023	+	1.17281i	−0.852360	+	0.522956i	$0.824829\pi$
$644$	−13669.7	−	56938.5i	−0.0329601	−	0.137289i
$645$	275162.	−	168619.i	0.661407	−	0.405310i
$646$	−32077.1	+	44150.3i	−0.0768651	+	0.105796i
$647$	−487716.	+	487716.i	−1.16509	+	1.16509i	−0.181740	+	0.983347i	$0.558173\pi$
$647$	−487716.	+	487716.i	−1.16509	+	1.16509i	−0.983347	+	0.181740i	$0.941827\pi$
$648$	121289.	−	19210.3i	0.288850	−	0.0457494i
$649$	102518.	−	120033.i	0.243394	−	0.284978i
$650$	15008.7	+	17572.9i	0.0355235	+	0.0415926i
$651$	154886.	−	977911.i	0.365469	−	2.30748i
$652$	−307011.	+	223056.i	−0.722201	+	0.524710i
$653$	139979.	+	57981.2i	0.328274	+	0.135975i	0.540733	−	0.841195i	$-0.318147\pi$
$653$	139979.	+	57981.2i	0.328274	+	0.135975i	−0.212459	+	0.977170i	$0.568147\pi$
$654$	−70273.6	+	137920.i	−0.164300	+	0.322456i
$655$		−	274268.i		−	0.639283i
$656$	19612.1	+	105781.i	0.0455738	+	0.245811i
$657$	360648.			0.835511
$658$	52112.4	+	26552.6i	0.120362	+	0.0613275i
$659$	108452.	−	261826.i	0.249727	−	0.602895i	−0.748453	−	0.663187i	$-0.769203\pi$
$659$	108452.	−	261826.i	0.249727	−	0.602895i	0.998181	+	0.0602920i	$0.0192032\pi$
$660$	−22978.5	−	31627.2i	−0.0527513	−	0.0726060i
$661$	524425.	+	83060.7i	1.20027	+	0.190105i	0.724381	−	0.689399i	$-0.242125\pi$
$661$	524425.	+	83060.7i	1.20027	+	0.190105i	0.475892	+	0.879504i	$0.342125\pi$
$662$	55145.0	−	47098.3i	0.125832	−	0.107470i
$663$	23974.8	+	20476.4i	0.0545417	+	0.0465830i
$664$	−41299.2	−	260753.i	−0.0936712	−	0.591416i
$665$	−54552.4	−	54552.4i	−0.123359	−	0.123359i
$666$	760233.	+	552342.i	1.71395	+	1.24526i
$667$	−69060.4	−	112696.i	−0.155231	−	0.253314i
$668$	270374.	−	64911.1i	0.605916	−	0.145468i
$669$	−332491.	−	26167.6i	−0.742895	−	0.0584671i
$670$	−80834.1	−	195151.i	−0.180072	−	0.434731i
$671$	81085.2	−	132319.i	0.180093	−	0.293885i
$672$	−31773.9	+	97790.1i	−0.0703611	+	0.216549i
$673$	153508.	−	639407.i	0.338923	−	1.41172i	−0.499320	−	0.866418i	$-0.666417\pi$
$673$	153508.	−	639407.i	0.338923	−	1.41172i	0.838243	−	0.545298i	$-0.183583\pi$
$674$	76727.3	+	236142.i	0.168900	+	0.519821i
$675$	545829.	−	42957.7i	1.19798	−	0.0942829i
$676$	−102611.	−	201386.i	−0.224544	−	0.440693i
$677$	−403954.	+	205825.i	−0.881364	+	0.449077i	−0.835257	−	0.549859i	$-0.814681\pi$
$677$	−403954.	+	205825.i	−0.881364	+	0.449077i	−0.0461063	+	0.998937i	$0.514681\pi$
$678$	−6757.99	−	85868.4i	−0.0147014	−	0.186799i
$679$	478665.	−	155528.i	1.03823	−	0.337341i
$680$	−32345.6	−	7765.49i	−0.0699515	−	0.0167939i
$681$	−1.06623e6	−	346439.i	−2.29909	−	0.747021i
$682$	105302.	+	64529.1i	0.226395	+	0.138735i
$683$	802355.	−	332346.i	1.71999	−	0.712442i	0.720161	−	0.693807i	$-0.244068\pi$
$683$	802355.	−	332346.i	1.71999	−	0.712442i	0.999826	−	0.0186352i	$-0.00593212\pi$
$684$	−16371.0	+	208013.i	−0.0349915	+	0.444610i
$685$	−40135.3	−	167175.i	−0.0855352	−	0.356280i
$686$	305983.	−	187507.i	0.650203	−	0.398445i
$687$	798841.	−	1.09951e6i	1.69257	−	2.32962i
$688$	74865.9	−	74865.9i	0.158164	−	0.158164i
$689$	46703.4	−	7397.09i	0.0983807	−	0.0155820i
$690$	71272.3	−	83449.2i	0.149700	−	0.175277i
$691$	−264484.	−	309671.i	−0.553916	−	0.648553i	0.410837	−	0.911709i	$-0.365237\pi$
$691$	−264484.	−	309671.i	−0.553916	−	0.648553i	−0.964753	+	0.263156i	$0.915237\pi$
$692$	−66285.4	+	418509.i	−0.138422	+	0.873963i
$693$	−117270.	+	85201.8i	−0.244186	+	0.177412i
$694$	353784.	+	146542.i	0.734546	+	0.304259i
$695$	2141.54	−	4203.01i	0.00443360	−	0.00870144i
$696$			232091.i			0.479115i
$697$	50619.3	+	188868.i	0.104196	+	0.388769i
$698$	−213307.			−0.437819
$699$	−803110.	−	409205.i	−1.64369	−	0.837503i
$700$	−52419.1	+	126551.i	−0.106978	+	0.258267i
$701$	−250691.	−	345047.i	−0.510156	−	0.702170i	0.473789	−	0.880638i	$-0.342886\pi$
$701$	−250691.	−	345047.i	−0.510156	−	0.702170i	−0.983946	+	0.178468i	$0.942886\pi$
$702$	57730.8	+	9143.66i	0.117148	+	0.0185544i
$703$	−266503.	+	227615.i	−0.539252	+	0.460565i
$704$	−9752.70	−	8329.60i	−0.0196779	−	0.0168066i
$705$	17147.3	+	108264.i	0.0344998	+	0.217823i
$706$	−26017.5	−	26017.5i	−0.0521982	−	0.0521982i
$707$	28396.4	+	20631.2i	0.0568099	+	0.0412748i
$708$	−406564.	−	663452.i	−0.811077	−	1.32356i
$709$	−582038.	+	139735.i	−1.15787	+	0.277980i	−0.766494	−	0.642252i	$-0.778000\pi$
$709$	−582038.	+	139735.i	−1.15787	+	0.277980i	−0.391374	+	0.920232i	$0.628000\pi$
$710$	7325.43	+	576.524i	0.0145317	+	0.00114367i
$711$	−331528.	−	800378.i	−0.655814	−	1.58327i
$712$	31928.6	−	52102.7i	0.0629825	−	0.102778i
$713$	−107134.	+	329724.i	−0.210740	+	0.648592i
$714$	−43626.2	+	181716.i	−0.0855758	+	0.356449i
$715$	−1718.05	−	5287.62i	−0.00336066	−	0.0103430i
$716$	104878.	−	8254.09i	0.204578	−	0.0161006i
$717$	348257.	+	683493.i	0.677425	+	1.32952i
$718$	−69963.3	+	35648.1i	−0.135713	+	0.0691492i
$719$	38702.1	+	491756.i	0.0748646	+	0.951245i	0.913576	+	0.406668i	$0.133310\pi$
$719$	38702.1	+	491756.i	0.0748646	+	0.951245i	−0.838711	+	0.544576i	$0.816690\pi$
$720$	−120961.	+	39302.7i	−0.233336	+	0.0758153i
$721$	−173416.	−	41633.5i	−0.333594	−	0.0800889i
$722$	276550.	+	89856.5i	0.530517	+	0.172375i
$723$	−239687.	−	146880.i	−0.458530	−	0.280988i
$724$	399819.	−	165611.i	0.762758	−	0.315945i
$725$	−24258.4	+	308233.i	−0.0461516	+	0.586412i
$726$	142818.	+	594882.i	0.270964	+	1.12865i
$727$	−361248.	+	221373.i	−0.683497	+	0.418848i	−0.820441	−	0.571731i	$-0.806272\pi$
$727$	−361248.	+	221373.i	−0.683497	+	0.418848i	0.136944	+	0.990579i	$0.456272\pi$
$728$	−8595.25	+	11830.3i	−0.0162179	+	0.0223221i
$729$	−436914.	+	436914.i	−0.822132	+	0.822132i
$730$	−80980.2	+	12826.0i	−0.151961	+	0.0240683i
$731$	124973.	−	146325.i	0.233874	−	0.273831i
$732$	−496808.	−	581688.i	−0.927186	−	1.08560i
$733$	69438.2	−	438415.i	0.129238	−	0.815977i	−0.834866	−	0.550453i	$-0.814455\pi$
$733$	69438.2	−	438415.i	0.129238	−	0.815977i	0.964104	−	0.265524i	$-0.0855449\pi$
$734$	133640.	−	97095.5i	0.248054	−	0.180222i
$735$	188645.	+	78139.2i	0.349196	+	0.144642i
$736$	16345.6	−	32080.0i	0.0301748	−	0.0592214i
$737$		−	148021.i		−	0.272514i
$738$	542331.	+	514590.i	0.995753	+	0.944819i
$739$	65217.0			0.119419			0.0597093	−	0.998216i	$-0.480983\pi$
$739$	65217.0			0.119419			0.0597093	+	0.998216i	$0.480983\pi$
$740$	−190347.	−	96986.6i	−0.347602	−	0.177112i
$741$	−17205.8	+	41538.4i	−0.0313356	+	0.0756508i
$742$	164740.	+	226745.i	0.299220	+	0.411841i
$743$	239025.	+	37857.8i	0.432977	+	0.0685768i	0.369119	−	0.929382i	$-0.379659\pi$
$743$	239025.	+	37857.8i	0.432977	+	0.0685768i	0.0638581	+	0.997959i	$0.479659\pi$
$744$	462918.	−	395369.i	0.836293	−	0.714261i
$745$	−228721.	−	195346.i	−0.412092	−	0.351960i
$746$	−31475.4	−	198728.i	−0.0565580	−	0.357093i
$747$	−1.29725e6	−	1.29725e6i	−2.32479	−	2.32479i
$748$	−18858.6	−	13701.6i	−0.0337060	−	0.0244889i
$749$	179819.	+	293438.i	0.320532	+	0.523061i
$750$	−584942.	+	140432.i	−1.03990	+	0.249657i
$751$	−490865.	−	38631.9i	−0.870326	−	0.0684961i	−0.364573	−	0.931175i	$-0.618785\pi$
$751$	−490865.	−	38631.9i	−0.870326	−	0.0684961i	−0.505753	+	0.862679i	$0.668785\pi$
$752$	13761.9	+	33224.2i	0.0243357	+	0.0587515i
$753$	−594189.	+	969629.i	−1.04794	+	1.71008i
$754$	−10199.8	+	31391.8i	−0.0179411	+	0.0552171i
$755$	−86363.0	+	359728.i	−0.151507	+	0.631074i
$756$	107059.	+	329493.i	0.187317	+	0.576504i
$757$	−35444.1	+	2789.51i	−0.0618518	+	0.00486785i	−0.109347	−	0.994004i	$-0.534876\pi$
$757$	−35444.1	+	2789.51i	−0.0618518	+	0.00486785i	0.0474954	+	0.998871i	$0.484876\pi$
$758$	−63968.4	−	125545.i	−0.111334	−	0.218505i
$759$	68521.5	−	34913.4i	0.118944	−	0.0606051i
$760$	−3721.78	−	47289.7i	−0.00644353	−	0.0818728i
$761$	329549.	−	107077.i	0.569050	−	0.184896i	−0.0103390	−	0.999947i	$-0.503291\pi$
$761$	329549.	−	107077.i	0.569050	−	0.184896i	0.579389	+	0.815051i	$0.303291\pi$
$762$	−97964.0	−	23519.1i	−0.168716	−	0.0405052i
$763$	−124095.	−	40320.9i	−0.213160	−	0.0692599i
$764$	−140562.	−	86136.8i	−0.240815	−	0.147571i
$765$	−213564.	+	88461.1i	−0.364926	+	0.151158i
$766$	−61519.1	+	781674.i	−0.104846	+	1.33220i
$767$	−25833.3	−	107603.i	−0.0439126	−	0.182909i
$768$	−53905.6	+	33033.4i	−0.0913926	+	0.0560055i
$769$	−521873.	+	718296.i	−0.882494	+	1.21465i	0.0932298	+	0.995645i	$0.470281\pi$
$769$	−521873.	+	718296.i	−0.882494	+	1.21465i	−0.975724	+	0.219004i	$0.929719\pi$
$770$	23301.9	−	23301.9i	0.0393015	−	0.0393015i
$771$	108405.	−	17169.7i	0.182365	−	0.0288838i
$772$	−5264.18	+	6163.56i	−0.00883275	+	0.0103418i
$773$	657688.	+	770054.i	1.10068	+	1.28873i	0.954086	+	0.299534i	$0.0968313\pi$
$773$	657688.	+	770054.i	1.10068	+	1.28873i	0.146595	+	0.989197i	$0.453169\pi$
$774$	115096.	−	726689.i	0.192123	−	1.21302i
$775$	656111.	−	476692.i	1.09238	−	0.793661i
$776$	285904.	+	118425.i	0.474785	+	0.196662i
$777$	−544867.	+	1.06936e6i	−0.902502	+	1.77126i
$778$			570370.i			0.942319i
$779$	−233840.	+	151878.i	−0.385340	+	0.250276i
$780$	−27405.8			−0.0450456
$781$	4588.01	+	2337.71i	0.00752181	+	0.00383255i
$782$	25041.9	−	60456.4i	0.0409499	−	0.0988618i
$783$	459651.	+	632655.i	0.749729	+	1.03191i
$784$	66164.7	+	10479.5i	0.107645	+	0.0170493i
$785$	280795.	−	239821.i	0.455669	−	0.389178i
$786$	−720409.	−	615287.i	−1.16609	−	0.995939i
$787$	152796.	+	964715.i	0.246696	+	1.55758i	0.730816	+	0.682575i	$0.239140\pi$
$787$	152796.	+	964715.i	0.246696	+	1.55758i	−0.484120	+	0.875002i	$0.660860\pi$
$788$	277607.	+	277607.i	0.447072	+	0.447072i
$789$	635884.	+	461997.i	1.02147	+	0.742138i
$790$	102906.	+	167927.i	0.164887	+	0.269071i
$791$	70600.7	−	16949.7i	0.112838	−	0.0270901i
$792$	−88852.2	−	6992.82i	−0.141650	−	0.0111481i
$793$	−41632.8	−	100510.i	−0.0662047	−	0.159832i
$794$	147606.	−	240870.i	0.234133	−	0.382070i
$795$	−162317.	+	499561.i	−0.256821	+	0.790413i
$796$	17317.2	−	72131.5i	0.0273308	−	0.113841i
$797$	293001.	+	901765.i	0.461267	+	1.41963i	0.863617	+	0.504149i	$0.168194\pi$
$797$	293001.	+	901765.i	0.461267	+	1.41963i	−0.402350	+	0.915486i	$0.631806\pi$
$798$	−265672.	+	20908.8i	−0.417195	+	0.0328340i
$799$	29672.9	+	58236.3i	0.0464800	+	0.0912221i
$800$	−75042.9	+	38236.3i	−0.117255	+	0.0597442i
$801$	−33317.1	−	423334.i	−0.0519281	−	0.659809i
$802$	−106656.	+	34654.6i	−0.165820	+	0.0538781i
$803$	−55867.6	−	13412.6i	−0.0866420	−	0.0208009i
$804$	−693935.	−	225473.i	−1.07351	−	0.348805i
$805$	78876.1	+	48335.3i	0.121718	+	0.0745887i
$806$	79988.1	−	33132.1i	0.123128	−	0.0510011i
$807$	50902.3	−	646775.i	0.0781610	−	0.993130i
$808$	5038.13	+	20985.3i	0.00771697	+	0.0321435i
$809$	−818113.	+	501340.i	−1.25002	+	0.766012i	−0.980412	−	0.196959i	$-0.936894\pi$
$809$	−818113.	+	501340.i	−1.25002	+	0.766012i	−0.269606	+	0.962971i	$0.586894\pi$
$810$	−114032.	+	156951.i	−0.173803	+	0.239219i
$811$	−636894.	+	636894.i	−0.968335	+	0.968335i	−0.999514	−	0.0311786i	$-0.990074\pi$
$811$	−636894.	+	636894.i	−0.968335	+	0.968335i	0.0311786	+	0.999514i	$0.490074\pi$
$812$	−193233.	+	30605.1i	−0.293069	+	0.0464175i
$813$	1.12581e6	−	1.31815e6i	1.70327	−	1.99428i
$814$	−97225.2	−	113836.i	−0.146734	−	0.171803i
$815$	93785.0	−	592135.i	0.141195	−	0.891467i
$816$	−92960.6	+	67539.8i	−0.139611	+	0.101433i
$817$	253520.	+	105011.i	0.379811	+	0.157323i
$818$	4532.46	−	8895.45i	0.00677372	−	0.0132942i
$819$			101618.i			0.151496i
$820$	−140076.	−	96259.2i	−0.208323	−	0.143158i
$821$	838289.			1.24368			0.621838	−	0.783146i	$-0.286386\pi$
$821$	838289.			1.24368			0.621838	+	0.783146i	$0.286386\pi$
$822$	−529151.	−	269616.i	−0.783133	−	0.399026i
$823$	−383328.	+	925437.i	−0.565941	+	1.36630i	0.339008	+	0.940783i	$0.389909\pi$
$823$	−383328.	+	925437.i	−0.565941	+	1.36630i	−0.904949	+	0.425519i	$0.860091\pi$
$824$	−64454.8	−	88714.5i	−0.0949295	−	0.130659i
$825$	−177681.	−	28141.9i	−0.261056	−	0.0413472i
$826$	498761.	−	425982.i	0.731025	−	0.624354i
$827$	709788.	+	606216.i	1.03781	+	0.886373i	0.993635	−	0.112651i	$-0.0359342\pi$
$827$	709788.	+	606216.i	1.03781	+	0.886373i	0.0441747	+	0.999024i	$0.485934\pi$
$828$	−39139.5	−	247117.i	−0.0570893	−	0.360448i
$829$	−781749.	−	781749.i	−1.13752	−	1.13752i	−0.988894	−	0.148624i	$-0.952516\pi$
$829$	−781749.	−	781749.i	−1.13752	−	1.13752i	−0.148624	−	0.988894i	$-0.547484\pi$
$830$	337421.	+	245151.i	0.489797	+	0.355858i
$831$	−505522.	−	824937.i	−0.732045	−	1.19459i
$832$	−8742.80	+	2098.96i	−0.0126300	+	0.00303220i
$833$	121378.	+	9552.63i	0.174924	+	0.0137668i
$834$	−6235.58	−	15054.0i	−0.00896489	−	0.0216432i
$835$	−229522.	+	374546.i	−0.329193	+	0.537195i
$836$	10272.1	−	31614.3i	0.0146976	−	0.0452346i
$837$	478845.	−	1.99453e6i	0.683508	−	2.84702i
$838$	−159103.	−	489668.i	−0.226564	−	0.697291i
$839$	−37806.5	+	2975.44i	−0.0537084	+	0.00422695i	−0.105285	−	0.994442i	$-0.533575\pi$
$839$	−37806.5	+	2975.44i	−0.0537084	+	0.00422695i	0.0515764	+	0.998669i	$0.483575\pi$
$840$	−73746.4	−	144735.i	−0.104516	−	0.205124i
$841$	236721.	−	120616.i	0.334692	−	0.170534i
$842$	−43963.9	−	558614.i	−0.0620115	−	0.787930i
$843$	−1.07858e6	+	350453.i	−1.51774	+	0.493145i
$844$	−514391.	−	123494.i	−0.722119	−	0.173365i
$845$	339594.	+	110341.i	0.475605	+	0.154534i
$846$	213076.	+	130573.i	0.297710	+	0.182437i
$847$	−476450.	+	197352.i	−0.664126	+	0.275090i
$848$	−13520.8	+	171798.i	−0.0188023	+	0.238906i
$849$	−267913.	−	1.11594e6i	−0.371688	−	1.54819i
$850$	−130517.	+	79981.1i	−0.180647	+	0.110700i
$851$	247017.	−	339990.i	0.341089	−	0.469469i
$852$	17948.0	−	17948.0i	0.0247251	−	0.0247251i
$853$	−105171.	+	16657.4i	−0.144543	+	0.0228934i	−0.228287	−	0.973594i	$-0.573312\pi$
$853$	−105171.	+	16657.4i	−0.144543	+	0.0228934i	0.0837435	+	0.996487i	$0.473312\pi$
$854$	418786.	−	490335.i	0.574217	−	0.672322i
$855$	−214083.	−	250659.i	−0.292853	−	0.342887i
$856$	−33102.6	+	209002.i	−0.0451767	+	0.285234i
$857$	−355165.	+	258042.i	−0.483580	+	0.351341i	−0.802710	−	0.596370i	$-0.796609\pi$
$857$	−355165.	+	258042.i	−0.483580	+	0.351341i	0.319130	+	0.947711i	$0.396609\pi$
$858$	−17743.0	−	7349.39i	−0.0241020	−	0.00998335i
$859$	267792.	−	525572.i	0.362921	−	0.712272i	−0.635277	−	0.772284i	$-0.719114\pi$
$859$	267792.	−	525572.i	0.362921	−	0.712272i	0.998198	+	0.0600126i	$0.0191141\pi$
$860$			167265.i			0.226156i
$861$	−540780.	+	786943.i	−0.729482	+	1.06154i
$862$	101552.			0.136670
$863$	649619.	+	330997.i	0.872242	+	0.444429i	0.832010	−	0.554761i	$-0.187190\pi$
$863$	649619.	+	330997.i	0.872242	+	0.444429i	0.0402321	+	0.999190i	$0.487190\pi$
$864$	−81518.9	+	196804.i	−0.109202	+	0.263637i
$865$	−393468.	−	541562.i	−0.525868	−	0.723795i
$866$	−803583.	−	127275.i	−1.07151	−	0.169710i
$867$	821474.	−	701605.i	1.09284	−	0.933371i
$868$	390218.	+	333278.i	0.517926	+	0.442351i
$869$	21590.2	+	136315.i	0.0285903	+	0.180512i
$870$	−259268.	−	259268.i	−0.342539	−	0.342539i
$871$	−83950.2	−	60993.4i	−0.110659	−	0.0803982i
$872$	−41919.1	−	68405.8i	−0.0551289	−	0.0899622i
$873$	2.09106e6	−	502018.i	2.74370	−	0.658705i
$874$	93027.3	+	7321.40i	0.121783	+	0.00958454i
$875$	−194055.	−	468490.i	−0.253459	−	0.611905i
$876$	−147979.	+	241481.i	−0.192838	+	0.314683i
$877$	17093.2	−	52607.5i	0.0222241	−	0.0683988i	−0.939329	−	0.343017i	$-0.888551\pi$
$877$	17093.2	−	52607.5i	0.0222241	−	0.0683988i	0.961553	+	0.274618i	$0.0885513\pi$
$878$	−107834.	+	449159.i	−0.139883	+	0.582655i
$879$	−356627.	−	1.09759e6i	−0.461569	−	1.42056i
$880$	20199.7	−	1589.75i	0.0260843	−	0.00205288i
$881$	203310.	+	399018.i	0.261943	+	0.514092i	0.984095	−	0.177642i	$-0.0568470\pi$
$881$	203310.	+	399018.i	0.261943	+	0.514092i	−0.722152	+	0.691734i	$0.756847\pi$
$882$	414779.	−	211340.i	0.533187	−	0.271672i
$883$	18974.9	+	241099.i	0.0243365	+	0.309225i	0.997023	+	0.0771028i	$0.0245670\pi$
$883$	18974.9	+	241099.i	0.0243365	+	0.309225i	−0.972687	+	0.232122i	$0.925433\pi$
$884$	−15541.7	+	5049.81i	−0.0198881	+	0.00646205i
$885$	1.19531e6	+	286968.i	1.52614	+	0.366393i
$886$	312751.	+	101619.i	0.398412	+	0.129452i
$887$	1.30287e6	+	798398.i	1.65597	+	1.01478i	0.952724	+	0.303836i	$0.0982676\pi$
$887$	1.30287e6	+	798398.i	1.65597	+	1.01478i	0.703248	+	0.710945i	$0.251732\pi$
$888$	−681770.	+	282398.i	−0.864593	+	0.358126i
$889$	6663.18	−	84663.7i	0.00843098	−	0.107126i
$890$	22536.4	+	93871.0i	0.0284515	+	0.118509i
$891$	−115916.	+	71033.4i	−0.146012	+	0.0894761i
$892$	101606.	−	139849.i	0.127700	−	0.175764i
$893$	−65905.6	+	65905.6i	−0.0826455	+	0.0826455i
$894$	−1.02622e6	+	162537.i	−1.28400	+	0.203365i
$895$	−107938.	+	126379.i	−0.134750	+	0.157772i
$896$	−34611.1	−	40524.4i	−0.0431121	−	0.0504778i
$897$	8433.69	−	53248.2i	0.0104817	−	0.0661790i
$898$	509314.	−	370038.i	0.631586	−	0.458874i
$899$	1.07016e6	+	443273.i	1.32412	+	0.548469i
$900$	−265708.	+	521482.i	−0.328035	+	0.643805i
$901$			313208.i			0.385818i
$902$	−64874.2	−	99884.1i	−0.0797368	−	0.122768i
$903$	939686.			1.15241
$904$	39777.5	+	20267.7i	0.0486744	+	0.0248008i
$905$	−261633.	+	631639.i	−0.319445	+	0.771208i
$906$	751137.	+	1.03385e6i	0.915088	+	1.25951i
$907$	−785707.	−	124444.i	−0.955093	−	0.151272i	−0.340613	−	0.940204i	$-0.610634\pi$
$907$	−785707.	−	124444.i	−0.955093	−	0.151272i	−0.614481	+	0.788932i	$0.710634\pi$
$908$	441847.	−	377373.i	0.535921	−	0.457720i
$909$	114041.	+	97399.8i	0.138017	+	0.117877i
$910$	−3613.91	−	22817.3i	−0.00436410	−	0.0275538i
$911$	−1.05281e6	−	1.05281e6i	−1.26856	−	1.26856i	−0.946830	−	0.321735i	$-0.895734\pi$
$911$	−1.05281e6	−	1.05281e6i	−1.26856	−	1.26856i	−0.321735	−	0.946830i	$-0.604266\pi$
$912$	−132563.	−	96312.8i	−0.159380	−	0.115796i
$913$	152711.	+	249201.i	0.183201	+	0.298957i
$914$	−719880.	+	172828.i	−0.861723	+	0.206881i
$915$	1.20478e6	+	94818.5i	1.43902	+	0.113253i
$916$	269565.	+	650787.i	0.321272	+	0.775619i
$917$	417274.	−	680930.i	0.496230	−	0.809774i
$918$	−119639.	+	368212.i	−0.141968	+	0.436931i
$919$	23432.7	−	97604.1i	0.0277454	−	0.115568i	−0.956779	−	0.290817i	$-0.906073\pi$
$919$	23432.7	−	97604.1i	0.0277454	−	0.115568i	0.984524	+	0.175249i	$0.0560730\pi$
$920$	17576.8	+	54096.0i	0.0207666	+	0.0639130i
$921$	1.17663e6	−	92602.9i	1.38714	−	0.109171i
$922$	199881.	+	392288.i	0.235131	+	0.461470i
$923$	3216.35	−	1638.81i	0.00377538	−	0.00192365i
$924$	−8931.13	−	113481.i	−0.0104607	−	0.132916i
$925$	−934953.	+	303785.i	−1.09271	+	0.355044i
$926$	682888.	+	163947.i	0.796393	+	0.191197i
$927$	−724724.	−	235477.i	−0.843360	−	0.274024i
$928$	−102567.	−	62853.0i	−0.119100	−	0.0729844i
$929$	300097.	−	124304.i	0.347721	−	0.144031i	−0.201986	−	0.979388i	$-0.564740\pi$
$929$	300097.	−	124304.i	0.347721	−	0.144031i	0.549707	+	0.835358i	$0.314740\pi$
$930$	−75458.3	+	958789.i	−0.0872451	+	1.10855i
$931$	40531.2	+	168824.i	0.0467616	+	0.194776i
$932$	398329.	−	244096.i	0.458575	−	0.281015i
$933$	480085.	−	660781.i	0.551512	−	0.759091i
$934$	9444.75	−	9444.75i	0.0108267	−	0.0108267i
$935$	36372.9	−	5760.90i	0.0416059	−	0.00658972i
$936$	−40578.2	+	47511.0i	−0.0463171	+	0.0542303i
$937$	−677832.	−	793640.i	−0.772046	−	0.903950i	0.225480	−	0.974248i	$-0.427605\pi$
$937$	−677832.	−	793640.i	−0.772046	−	0.903950i	−0.997526	+	0.0702981i	$0.977605\pi$
$938$	96216.2	−	607485.i	0.109356	−	0.690447i
$939$	54815.8	−	39826.0i	0.0621691	−	0.0451685i
$940$	−52488.0	−	21741.2i	−0.0594024	−	0.0246053i
$941$	429001.	−	841962.i	0.484484	−	0.950853i	−0.511324	−	0.859388i	$-0.670845\pi$
$941$	429001.	−	841962.i	0.484484	−	0.950853i	0.995808	−	0.0914653i	$-0.0291551\pi$
$942$		−	1.27556e6i		−	1.43747i
$943$	230134.	−	242540.i	0.258796	−	0.272747i
$944$	403298.			0.452566
$945$	−487669.	−	248480.i	−0.546087	−	0.278245i
$946$	−44855.3	+	108290.i	−0.0501223	+	0.121006i
$947$	873309.	+	1.20201e6i	0.973796	+	1.34032i	0.940106	+	0.340883i	$0.110726\pi$
$947$	873309.	+	1.20201e6i	0.973796	+	1.34032i	0.0336907	+	0.999432i	$0.489274\pi$
$948$	671944.	+	106426.i	0.747682	+	0.118421i
$949$	−30627.6	+	26158.5i	−0.0340080	+	0.0290456i
$950$	−165986.	−	141766.i	−0.183918	−	0.157081i
$951$	355477.	+	2.24439e6i	0.393052	+	2.48163i
$952$	−68490.3	−	68490.3i	−0.0755710	−	0.0755710i
$953$	−53484.3	−	38858.6i	−0.0588899	−	0.0427860i	0.557951	−	0.829874i	$-0.311588\pi$
$953$	−53484.3	−	38858.6i	−0.0588899	−	0.0427860i	−0.616841	+	0.787088i	$0.711588\pi$
$954$	625711.	+	1.02107e6i	0.687507	+	1.12191i
$955$	253245.	−	60798.7i	0.277673	−	0.0666634i
$956$	−396364.	−	31194.5i	−0.433689	−	0.0341321i
$957$	−98327.0	−	237382.i	−0.107362	−	0.259194i
$958$	−177525.	+	289695.i	−0.193432	+	0.315653i
$959$	154698.	−	476111.i	0.168208	−	0.517691i
$960$	23316.2	−	97119.1i	0.0252997	−	0.105381i
$961$	−653505.	−	2.01128e6i	−0.707623	−	2.17784i
$962$	−104624.	+	8234.12i	−0.113053	+	0.00889748i
$963$	667584.	+	1.31021e6i	0.719869	+	1.41282i
$964$	129820.	−	66146.7i	0.139697	−	0.0711793i
$965$	−1004.70	−	12765.9i	−0.00107890	−	0.0137087i
$966$	303909.	−	98746.0i	0.325679	−	0.105819i
$967$	−271366.	−	65149.1i	−0.290203	−	0.0696716i	0.0857301	−	0.996318i	$-0.472678\pi$
$967$	−271366.	−	65149.1i	−0.290203	−	0.0696716i	−0.375933	+	0.926647i	$0.622678\pi$
$968$	−301570.	−	97985.9i	−0.321838	−	0.104571i
$969$	−253924.	−	155605.i	−0.270431	−	0.165720i
$970$	−451674.	+	187090.i	−0.480045	+	0.198841i
$971$	−24966.0	+	317223.i	−0.0264796	+	0.336455i	0.969381	+	0.245561i	$0.0789722\pi$
$971$	−24966.0	+	317223.i	−0.0264796	+	0.336455i	−0.995861	+	0.0908934i	$0.971028\pi$
$972$	−21572.8	−	89857.4i	−0.0228336	−	0.0951089i
$973$	11711.3	−	7176.71i	0.0123703	−	0.00758054i
$974$	−219200.	+	301703.i	−0.231059	+	0.318025i
$975$	−89175.5	+	89175.5i	−0.0938072	+	0.0938072i
$976$	391604.	−	62023.9i	0.411100	−	0.0651118i
$977$	−972625.	+	1.13880e6i	−1.01896	+	1.19305i	−0.0379095	+	0.999281i	$0.512070\pi$
$977$	−972625.	+	1.13880e6i	−1.01896	+	1.19305i	−0.981048	+	0.193765i	$0.937930\pi$
$978$	−1.34494e6	−	1.57472e6i	−1.40613	−	1.64637i
$979$	−10582.8	+	66817.4i	−0.0110417	+	0.0697146i
$980$	−85618.8	+	62205.7i	−0.0891491	+	0.0647706i
$981$	−515077.	−	213352.i	−0.535222	−	0.221696i
$982$	343681.	−	674513.i	0.356396	−	0.699467i
$983$			951578.i			0.984776i	0.870376	+	0.492388i	$0.163876\pi$
$983$			951578.i			0.984776i	−0.870376	+	0.492388i	$0.836124\pi$
$984$	−567084.	+	151987.i	−0.585675	+	0.156969i
$985$	−620227.			−0.639261
$986$	−194803.	−	99256.9i	−0.200374	−	0.102096i
$987$	−122141.	+	294875.i	−0.125380	+	0.302694i
$988$	−13697.3	−	18852.7i	−0.0140321	−	0.0193135i
$989$	−324988.	−	51473.1i	−0.332258	−	0.0526245i
$990$	107068.	−	91444.7i	0.109242	−	0.0933014i
$991$	−411543.	−	351491.i	−0.419052	−	0.357904i	0.414781	−	0.909921i	$-0.363858\pi$
$991$	−411543.	−	351491.i	−0.419052	−	0.357904i	−0.833833	+	0.552017i	$0.813858\pi$
$992$	49359.8	+	311645.i	0.0501591	+	0.316692i
$993$	279839.	+	279839.i	0.283798	+	0.283798i
$994$	17309.8	+	12576.3i	0.0175194	+	0.0127286i
$995$	61232.7	+	99922.7i	0.0618497	+	0.100929i
$996$	1.40089e6	−	336324.i	1.41216	−	0.339031i
$997$	−1.12583e6	−	88604.9i	−1.13262	−	0.0891389i	−0.501738	−	0.865020i	$-0.667306\pi$
$997$	−1.12583e6	−	88604.9i	−1.13262	−	0.0891389i	−0.630880	+	0.775881i	$0.717306\pi$
$998$	−472754.	−	1.14133e6i	−0.474651	−	1.14591i
$999$	−1.29915e6	+	2.12002e6i	−1.30175	+	2.12426i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	82.5.h.b.13.7	✓	112
41.19	odd	40	inner	82.5.h.b.19.7	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
82.5.h.b.13.7	✓	112	1.1	even	1	trivial
82.5.h.b.19.7	yes	112	41.19	odd	40	inner

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:	\( N \)	\(=\)	\( 82 = 2 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	82.h (of order \(40\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.52015 - 1.28408i) q^{2} +(5.90673 - 14.2601i) q^{3} +(4.70228 + 6.47214i) q^{4} +(-12.4829 - 1.97710i) q^{5} +(-33.1970 + 28.3529i) q^{6} +(-27.9835 - 23.9001i) q^{7} +(-3.53971 - 22.3488i) q^{8} +(-111.186 - 111.186i) q^{9} +(28.9200 + 21.0116i) q^{10} +(13.0886 + 21.3587i) q^{11} +(120.069 - 28.8259i) q^{12} +(17.5069 + 1.37782i) q^{13} +(39.8328 + 96.1648i) q^{14} +(-101.927 + 166.329i) q^{15} +(-19.7771 + 60.8676i) q^{16} +(-27.1543 + 113.106i) q^{17} +(137.433 + 422.976i) q^{18} +(-165.362 + 13.0143i) q^{19} +(-45.9020 - 90.0878i) q^{20} +(-506.110 + 257.876i) q^{21} +(-5.55902 - 70.6340i) q^{22} +(189.162 - 61.4626i) q^{23} +(-339.605 - 81.5320i) q^{24} +(-442.497 - 143.776i) q^{25} +(-42.3506 - 25.9525i) q^{26} +(-1087.20 + 450.332i) q^{27} +(23.0988 - 293.498i) q^{28} +(-155.132 - 646.171i) q^{29} +(470.450 - 288.292i) q^{30} +(-1024.55 + 1410.18i) q^{31} +(128.000 - 128.000i) q^{32} +(381.889 - 60.4853i) q^{33} +(213.670 - 250.175i) q^{34} +(302.062 + 353.669i) q^{35} +(196.783 - 1242.44i) q^{36} +(1709.37 - 1241.93i) q^{37} +(433.449 + 179.540i) q^{38} +(123.056 - 241.511i) q^{39} +285.976i q^{40} +(1477.24 - 802.194i) q^{41} +1606.60 q^{42} +(-1474.01 - 751.045i) q^{43} +(-76.6901 + 185.146i) q^{44} +(1168.10 + 1607.75i) q^{45} +(-555.640 - 88.0047i) q^{46} +(427.273 - 364.925i) q^{47} +(751.161 + 641.552i) q^{48} +(-163.741 - 1033.82i) q^{49} +(930.537 + 930.537i) q^{50} +(1452.51 + 1055.31i) q^{51} +(73.4047 + 119.786i) q^{52} +(2618.25 - 628.586i) q^{53} +(3318.16 + 261.145i) q^{54} +(-121.156 - 292.496i) q^{55} +(-435.087 + 709.997i) q^{56} +(-791.166 + 2434.96i) q^{57} +(-438.779 + 1827.65i) q^{58} +(-1947.28 - 5993.11i) q^{59} +(-1555.79 + 122.444i) q^{60} +(-2812.51 - 5519.86i) q^{61} +(4392.80 - 2238.24i) q^{62} +(454.008 + 5768.72i) q^{63} +(-486.941 + 158.217i) q^{64} +(-215.812 - 51.8119i) q^{65} +(-1040.08 - 337.944i) q^{66} +(-5038.26 - 3087.45i) q^{67} +(-859.723 + 356.109i) q^{68} +(240.868 - 3060.52i) q^{69} +(-307.101 - 1279.17i) q^{70} +(175.267 - 107.404i) q^{71} +(-2091.31 + 2878.44i) q^{72} +(-1621.82 + 1621.82i) q^{73} +(-5902.62 + 934.883i) q^{74} +(-4663.97 + 5460.81i) q^{75} +(-861.811 - 1009.05i) q^{76} +(144.211 - 910.511i) q^{77} +(-620.240 + 450.630i) q^{78} +(5090.15 + 2108.41i) q^{79} +(367.216 - 720.702i) q^{80} +5427.10i q^{81} +(-4752.95 + 124.750i) q^{82} +11667.4 q^{83} +(-4048.88 - 2063.01i) q^{84} +(562.585 - 1358.20i) q^{85} +(2750.32 + 3785.49i) q^{86} +(-10130.8 - 1604.56i) q^{87} +(431.013 - 368.120i) q^{88} +(2053.55 + 1753.90i) q^{89} +(-879.300 - 5551.68i) q^{90} +(-456.972 - 456.972i) q^{91} +(1287.29 + 935.270i) q^{92} +(14057.5 + 22939.8i) q^{93} +(-1545.38 + 371.014i) q^{94} +(2089.93 + 164.481i) q^{95} +(-1069.23 - 2581.36i) q^{96} +(-7145.87 + 11661.0i) q^{97} +(-914.858 + 2815.64i) q^{98} +(919.516 - 3830.06i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 56 q^{2} - 16 q^{3} + 16 q^{6} - 448 q^{8} - 24 q^{9} + 512 q^{11} - 576 q^{12} + 348 q^{13} - 192 q^{14} - 1036 q^{15} + 1792 q^{16} + 552 q^{17} + 416 q^{18} + 504 q^{19} + 876 q^{21} + 16 q^{22}+ \cdots + 36896 q^{99}+O(q^{100}) \) 112 * q + 56 * q^2 - 16 * q^3 + 16 * q^6 - 448 * q^8 - 24 * q^9 + 512 * q^11 - 576 * q^12 + 348 * q^13 - 192 * q^14 - 1036 * q^15 + 1792 * q^16 + 552 * q^17 + 416 * q^18 + 504 * q^19 + 876 * q^21 + 16 * q^22 + 800 * q^23 - 384 * q^24 - 3360 * q^25 + 1656 * q^26 - 964 * q^27 + 768 * q^28 + 4 * q^29 - 3544 * q^30 + 1380 * q^31 + 14336 * q^32 - 7392 * q^33 + 4224 * q^34 + 2264 * q^35 + 2048 * q^36 + 6212 * q^37 + 2624 * q^38 + 4928 * q^39 - 7460 * q^41 + 5056 * q^42 - 19816 * q^43 - 6560 * q^44 - 26000 * q^45 - 4400 * q^46 - 14660 * q^47 - 1536 * q^48 - 17808 * q^49 - 28720 * q^50 + 17948 * q^51 + 1152 * q^52 + 19032 * q^53 + 20152 * q^54 + 3160 * q^55 - 1536 * q^56 + 23432 * q^57 - 6752 * q^58 + 25136 * q^59 - 9536 * q^60 + 10080 * q^61 + 10496 * q^62 - 968 * q^63 - 57460 * q^65 - 2480 * q^66 + 280 * q^67 + 1568 * q^68 - 1876 * q^69 + 6792 * q^70 + 49672 * q^71 + 4480 * q^72 + 16196 * q^73 - 30984 * q^74 + 58748 * q^75 + 13312 * q^76 + 6444 * q^77 + 4928 * q^78 + 34556 * q^79 + 6888 * q^82 + 17304 * q^83 + 7008 * q^84 - 104144 * q^85 + 30800 * q^86 - 28492 * q^87 - 3648 * q^88 + 26732 * q^89 - 70336 * q^90 - 132748 * q^91 + 4160 * q^92 + 35360 * q^93 - 11160 * q^94 - 5644 * q^95 - 1024 * q^96 + 14036 * q^97 - 6528 * q^98 + 36896 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

Properties

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