LMFDB - Embedded newform 95.5.q.a.17.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [95,5,Mod(17,95)] 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("95.17"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(95, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([9, 20])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 95 = 5 \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	95.q (of order $36$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$9.82014649297$
Analytic rank:	$0$
Dimension:	$456$
Relative dimension:	$38$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			17.4
Character	$\chi$	$=$	95.17
Dual form			95.5.q.a.28.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-5.67420 + 3.97311i) q^{2} +(15.2509 - 1.33428i) q^{3} +(10.9385 - 30.0534i) q^{4} +(24.9938 - 0.558702i) q^{5} +(-81.2353 + 68.1645i) q^{6} +(-4.02130 + 15.0077i) q^{7} +(28.6531 + 106.935i) q^{8} +(151.040 - 26.6324i) q^{9} +(-139.600 + 102.473i) q^{10} +(16.2576 - 28.1591i) q^{11} +(126.723 - 472.936i) q^{12} +(19.0214 - 217.415i) q^{13} +(-36.8096 - 101.134i) q^{14} +(380.431 - 41.8694i) q^{15} +(-195.451 - 164.003i) q^{16} +(321.493 - 225.112i) q^{17} +(-751.216 + 751.216i) q^{18} +(-326.110 + 154.833i) q^{19} +(256.604 - 757.258i) q^{20} +(-41.3039 + 234.246i) q^{21} +(19.6301 + 224.373i) q^{22} +(-347.596 + 162.087i) q^{23} +(579.665 + 1592.62i) q^{24} +(624.376 - 27.9281i) q^{25} +(755.884 + 1309.23i) q^{26} +(1070.17 - 286.751i) q^{27} +(407.044 + 285.016i) q^{28} +(498.299 - 87.8636i) q^{29} +(-1992.29 + 1749.07i) q^{30} +(830.640 + 1438.71i) q^{31} +(-3.94077 - 0.344773i) q^{32} +(210.371 - 451.143i) q^{33} +(-929.818 + 2554.66i) q^{34} +(-92.1225 + 377.345i) q^{35} +(851.761 - 4830.58i) q^{36} +(-725.663 - 725.663i) q^{37} +(1235.25 - 2174.22i) q^{38} -3341.15i q^{39} +(775.892 + 2656.69i) q^{40} +(-1354.05 - 1136.19i) q^{41} +(-696.320 - 1493.26i) q^{42} +(-1431.78 + 3070.45i) q^{43} +(-668.440 - 796.616i) q^{44} +(3760.17 - 750.030i) q^{45} +(1328.34 - 2300.75i) q^{46} +(-791.553 + 1130.45i) q^{47} +(-3199.63 - 2240.40i) q^{48} +(1870.27 + 1079.80i) q^{49} +(-3431.87 + 2639.19i) q^{50} +(4602.69 - 3862.11i) q^{51} +(-6325.99 - 2949.86i) q^{52} +(2135.97 - 996.021i) q^{53} +(-4933.06 + 5878.99i) q^{54} +(390.607 - 712.884i) q^{55} -1720.06 q^{56} +(-4766.88 + 2796.46i) q^{57} +(-2478.36 + 2478.36i) q^{58} +(286.035 + 50.4357i) q^{59} +(2903.05 - 11891.2i) q^{60} +(3222.76 + 1172.99i) q^{61} +(-10429.4 - 4863.30i) q^{62} +(-207.685 + 2373.85i) q^{63} +(3559.10 - 2054.85i) q^{64} +(353.945 - 5444.65i) q^{65} +(598.754 + 3395.70i) q^{66} +(-500.675 + 715.038i) q^{67} +(-3248.71 - 12124.3i) q^{68} +(-5084.89 + 2935.76i) q^{69} +(-976.514 - 2507.14i) q^{70} +(2628.64 - 956.748i) q^{71} +(7175.68 + 15388.3i) q^{72} +(-5448.26 + 476.661i) q^{73} +(7000.70 + 1234.41i) q^{74} +(9485.02 - 1259.02i) q^{75} +(1086.07 + 11494.4i) q^{76} +(357.225 + 357.225i) q^{77} +(13274.8 + 18958.4i) q^{78} +(-5149.04 + 6136.39i) q^{79} +(-4976.68 - 3989.85i) q^{80} +(4264.66 - 1552.21i) q^{81} +(12197.4 + 1067.13i) q^{82} +(-7643.55 - 2048.08i) q^{83} +(6588.08 + 3803.63i) q^{84} +(7909.54 - 5806.00i) q^{85} +(-4075.09 - 23111.0i) q^{86} +(7482.27 - 2004.87i) q^{87} +(3477.01 + 931.662i) q^{88} +(-6047.05 - 7206.60i) q^{89} +(-18356.0 + 19195.4i) q^{90} +(3186.40 + 1159.76i) q^{91} +(1069.06 + 12219.4i) q^{92} +(14587.6 + 20833.3i) q^{93} -9559.35i q^{94} +(-8064.21 + 4052.04i) q^{95} -60.5603 q^{96} +(-4522.27 + 3166.53i) q^{97} +(-14902.4 + 1303.79i) q^{98} +(1705.61 - 4686.12i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 456 q - 12 q^{2} - 12 q^{3} - 12 q^{5} + 84 q^{6} - 96 q^{7} - 6 q^{8} - 12 q^{10} - 12 q^{11} - 6 q^{12} - 12 q^{13} - 534 q^{15} + 4092 q^{16} - 1362 q^{17} - 3864 q^{18} - 2364 q^{20} - 4776 q^{21} + 2004 q^{22}+ \cdots + 123726 q^{98}+O(q^{100}) $ 456 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 + 84 * q^6 - 96 * q^7 - 6 * q^8 - 12 * q^10 - 12 * q^11 - 6 * q^12 - 12 * q^13 - 534 * q^15 + 4092 * q^16 - 1362 * q^17 - 3864 * q^18 - 2364 * q^20 - 4776 * q^21 + 2004 * q^22 + 1968 * q^23 + 3252 * q^25 + 7332 * q^26 - 6 * q^27 - 9648 * q^28 - 6 * q^30 - 12 * q^31 + 5922 * q^32 + 16494 * q^33 - 1794 * q^35 + 9048 * q^36 - 24 * q^37 - 15222 * q^38 - 9786 * q^40 - 5640 * q^41 + 7764 * q^42 - 19032 * q^43 - 6144 * q^45 - 12 * q^46 - 4332 * q^47 + 29328 * q^48 + 18426 * q^50 - 10944 * q^51 + 84 * q^52 + 1878 * q^53 + 27018 * q^55 - 48 * q^56 - 14202 * q^57 + 16536 * q^58 - 84108 * q^60 - 14688 * q^61 - 46536 * q^62 - 46098 * q^63 - 13236 * q^65 + 42408 * q^66 + 44748 * q^67 + 20154 * q^68 + 37620 * q^70 - 24 * q^71 + 82680 * q^72 - 10542 * q^73 + 90024 * q^75 - 21600 * q^76 + 20328 * q^77 + 63426 * q^78 - 32688 * q^80 + 41976 * q^81 - 184332 * q^82 - 43476 * q^83 - 51396 * q^85 + 11316 * q^86 - 59286 * q^87 - 1254 * q^88 - 9294 * q^90 - 33312 * q^91 + 163884 * q^92 - 106566 * q^93 - 11424 * q^95 - 200208 * q^96 + 12168 * q^97 + 123726 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/95\mathbb{Z}\right)^\times$.

$n$	$21$	$77$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−5.67420	+	3.97311i	−1.41855	+	0.993279i	−0.422326	+	0.906444i	$0.638786\pi$
$2$	−5.67420	+	3.97311i	−1.41855	+	0.993279i	−0.996223	+	0.0868349i	$0.972325\pi$
$3$	15.2509	−	1.33428i	1.69454	−	0.148253i	0.801431	−	0.598087i	$-0.204072\pi$
$3$	15.2509	−	1.33428i	1.69454	−	0.148253i	0.893112	+	0.449834i	$0.148517\pi$
$4$	10.9385	−	30.0534i	0.683659	−	1.87834i
$5$	24.9938	−	0.558702i	0.999750	−	0.0223481i
$5$	24.9938	−	0.558702i	0.999750	−	0.0223481i
$6$	−81.2353	+	68.1645i	−2.25654	+	1.89346i
$7$	−4.02130	+	15.0077i	−0.0820672	+	0.306279i	−0.994743	−	0.102406i	$-0.967346\pi$
$7$	−4.02130	+	15.0077i	−0.0820672	+	0.306279i	0.912675	+	0.408685i	$0.134013\pi$
$8$	28.6531	+	106.935i	0.447704	+	1.67085i
$9$	151.040	−	26.6324i	1.86469	−	0.328795i
$10$	−139.600	+	102.473i	−1.39600	+	1.02473i
$11$	16.2576	−	28.1591i	0.134361	−	0.232719i	−0.790992	−	0.611826i	$-0.790435\pi$
$11$	16.2576	−	28.1591i	0.134361	−	0.232719i	0.925353	+	0.379107i	$0.123769\pi$
$12$	126.723	−	472.936i	0.880019	−	3.28428i
$13$	19.0214	−	217.415i	0.112552	−	1.28648i	−0.704412	−	0.709791i	$-0.748789\pi$
$13$	19.0214	−	217.415i	0.112552	−	1.28648i	0.816964	−	0.576688i	$-0.195655\pi$
$14$	−36.8096	−	101.134i	−0.187804	−	0.515988i
$15$	380.431	−	41.8694i	1.69081	−	0.186086i
$16$	−195.451	−	164.003i	−0.763481	−	0.640636i
$17$	321.493	−	225.112i	1.11243	−	0.778933i	0.135139	−	0.990827i	$-0.456852\pi$
$17$	321.493	−	225.112i	1.11243	−	0.778933i	0.977293	+	0.211894i	$0.0679630\pi$
$18$	−751.216	+	751.216i	−2.31857	+	2.31857i
$19$	−326.110	+	154.833i	−0.903352	+	0.428899i
$19$	−326.110	+	154.833i	−0.903352	+	0.428899i
$20$	256.604	−	757.258i	0.641511	−	1.89315i
$21$	−41.3039	+	234.246i	−0.0936596	+	0.531170i
$22$	19.6301	+	224.373i	0.0405581	+	0.463582i
$23$	−347.596	+	162.087i	−0.657082	+	0.306402i	−0.722414	−	0.691461i	$-0.756967\pi$
$23$	−347.596	+	162.087i	−0.657082	+	0.306402i	0.0653314	+	0.997864i	$0.479190\pi$
$24$	579.665	+	1592.62i	1.00636	+	2.76496i
$25$	624.376	−	27.9281i	0.999001	−	0.0446850i
$26$	755.884	+	1309.23i	1.11817	+	1.93673i
$27$	1070.17	−	286.751i	1.46800	−	0.393348i
$28$	407.044	+	285.016i	0.519189	+	0.363540i
$29$	498.299	−	87.8636i	0.592508	−	0.104475i	0.130649	−	0.991429i	$-0.458294\pi$
$29$	498.299	−	87.8636i	0.592508	−	0.104475i	0.461859	+	0.886953i	$0.347183\pi$
$30$	−1992.29	+	1749.07i	−2.21366	+	1.94341i
$31$	830.640	+	1438.71i	0.864350	+	1.49710i	0.867692	+	0.497103i	$0.165603\pi$
$31$	830.640	+	1438.71i	0.864350	+	1.49710i	−0.00334193	+	0.999994i	$0.501064\pi$
$32$	−3.94077	−	0.344773i	−0.00384841	−	0.000336692i
$33$	210.371	−	451.143i	0.193178	−	0.414273i
$34$	−929.818	+	2554.66i	−0.804341	+	2.20991i
$35$	−92.1225	+	377.345i	−0.0752020	+	0.308037i
$36$	851.761	−	4830.58i	0.657223	−	3.72730i
$37$	−725.663	−	725.663i	−0.530068	−	0.530068i	0.390525	−	0.920593i	$-0.372294\pi$
$37$	−725.663	−	725.663i	−0.530068	−	0.530068i	−0.920593	+	0.390525i	$0.872294\pi$
$38$	1235.25	−	2174.22i	0.855434	−	1.50569i
$39$		−	3341.15i		−	2.19668i
$40$	775.892	+	2656.69i	0.484933	+	1.66043i
$41$	−1354.05	−	1136.19i	−0.805505	−	0.675899i	0.144026	−	0.989574i	$-0.453995\pi$
$41$	−1354.05	−	1136.19i	−0.805505	−	0.675899i	−0.949530	+	0.313675i	$0.898440\pi$
$42$	−696.320	−	1493.26i	−0.394739	−	0.846521i
$43$	−1431.78	+	3070.45i	−0.774351	+	1.66060i	−0.0238651	+	0.999715i	$0.507597\pi$
$43$	−1431.78	+	3070.45i	−0.774351	+	1.66060i	−0.750486	+	0.660886i	$0.770181\pi$
$44$	−668.440	−	796.616i	−0.345269	−	0.411475i
$45$	3760.17	−	750.030i	1.85688	−	0.370385i
$46$	1328.34	−	2300.75i	0.627760	−	1.08731i
$47$	−791.553	+	1130.45i	−0.358331	+	0.511749i	−0.957329	−	0.289001i	$-0.906677\pi$
$47$	−791.553	+	1130.45i	−0.358331	+	0.511749i	0.598998	+	0.800751i	$0.295566\pi$
$48$	−3199.63	−	2240.40i	−1.38873	−	0.972397i
$49$	1870.27	+	1079.80i	0.778954	+	0.449729i
$50$	−3431.87	+	2639.19i	−1.37275	+	1.05567i
$51$	4602.69	−	3862.11i	1.76958	−	1.48486i
$52$	−6325.99	−	2949.86i	−2.33949	−	1.09092i
$53$	2135.97	−	996.021i	0.760404	−	0.354582i	−0.00343099	−	0.999994i	$-0.501092\pi$
$53$	2135.97	−	996.021i	0.760404	−	0.354582i	0.763835	+	0.645412i	$0.223314\pi$
$54$	−4933.06	+	5878.99i	−1.69172	+	2.01611i
$55$	390.607	−	712.884i	0.129126	−	0.235664i
$56$	−1720.06			−0.548490
$57$	−4766.88	+	2796.46i	−1.46718	+	0.860713i
$58$	−2478.36	+	2478.36i	−0.736729	+	0.736729i
$59$	286.035	+	50.4357i	0.0821704	+	0.0144889i	0.214582	−	0.976706i	$-0.431161\pi$
$59$	286.035	+	50.4357i	0.0821704	+	0.0144889i	−0.132412	+	0.991195i	$0.542272\pi$
$60$	2903.05	−	11891.2i	0.806402	−	3.30312i
$61$	3222.76	+	1172.99i	0.866101	+	0.315235i	0.736587	−	0.676343i	$-0.236436\pi$
$61$	3222.76	+	1172.99i	0.866101	+	0.315235i	0.129514	+	0.991578i	$0.458658\pi$
$62$	−10429.4	−	4863.30i	−2.71316	−	1.26517i
$63$	−207.685	+	2373.85i	−0.0523269	+	0.598099i
$64$	3559.10	−	2054.85i	0.868921	−	0.501672i
$65$	353.945	−	5444.65i	0.0837739	−	1.28867i
$66$	598.754	+	3395.70i	0.137455	+	0.779546i
$67$	−500.675	+	715.038i	−0.111534	+	0.159287i	−0.871038	−	0.491216i	$-0.836553\pi$
$67$	−500.675	+	715.038i	−0.111534	+	0.159287i	0.759504	+	0.650502i	$0.225442\pi$
$68$	−3248.71	−	12124.3i	−0.702575	−	2.62205i
$69$	−5084.89	+	2935.76i	−1.06803	+	0.616627i
$70$	−976.514	−	2507.14i	−0.199289	−	0.511662i
$71$	2628.64	−	956.748i	0.521453	−	0.189793i	−0.0678651	−	0.997695i	$-0.521619\pi$
$71$	2628.64	−	956.748i	0.521453	−	0.189793i	0.589318	+	0.807901i	$0.299397\pi$
$72$	7175.68	+	15388.3i	1.38420	+	2.96842i
$73$	−5448.26	+	476.661i	−1.02238	+	0.0894466i	−0.585996	−	0.810314i	$-0.699296\pi$
$73$	−5448.26	+	476.661i	−1.02238	+	0.0894466i	−0.436383	+	0.899761i	$0.643741\pi$
$74$	7000.70	+	1234.41i	1.27843	+	0.225422i
$75$	9485.02	−	1259.02i	1.68623	−	0.223826i
$76$	1086.07	+	11494.4i	0.188032	+	1.99002i
$77$	357.225	+	357.225i	0.0602505	+	0.0602505i
$78$	13274.8	+	18958.4i	2.18192	+	3.11610i
$79$	−5149.04	+	6136.39i	−0.825034	+	0.983238i	−0.999999	−	0.00133698i	$-0.999574\pi$
$79$	−5149.04	+	6136.39i	−0.825034	+	0.983238i	0.174965	+	0.984575i	$0.444019\pi$
$80$	−4976.68	−	3989.85i	−0.777607	−	0.623414i
$81$	4264.66	−	1552.21i	0.650002	−	0.236581i
$82$	12197.4	+	1067.13i	1.81400	+	0.158705i
$83$	−7643.55	−	2048.08i	−1.10953	−	0.297297i	−0.342890	−	0.939376i	$-0.611406\pi$
$83$	−7643.55	−	2048.08i	−1.10953	−	0.297297i	−0.766639	+	0.642078i	$0.778072\pi$
$84$	6588.08	+	3803.63i	0.933685	+	0.539063i
$85$	7909.54	−	5806.00i	1.09475	−	0.803599i
$86$	−4075.09	−	23111.0i	−0.550985	−	3.12479i
$87$	7482.27	−	2004.87i	0.988542	−	0.264879i
$88$	3477.01	+	931.662i	0.448994	+	0.120308i
$89$	−6047.05	−	7206.60i	−0.763420	−	0.909809i	0.234639	−	0.972083i	$-0.424609\pi$
$89$	−6047.05	−	7206.60i	−0.763420	−	0.909809i	−0.998059	+	0.0622739i	$0.980165\pi$
$90$	−18356.0	+	19195.4i	−2.26617	+	2.36980i
$91$	3186.40	+	1159.76i	0.384785	+	0.140050i
$92$	1069.06	+	12219.4i	0.126307	+	1.44370i
$93$	14587.6	+	20833.3i	1.68663	+	2.40875i
$94$		−	9559.35i		−	1.08186i
$95$	−8064.21	+	4052.04i	−0.893542	+	0.448980i
$96$	−60.5603			−0.00657121
$97$	−4522.27	+	3166.53i	−0.480632	+	0.336542i	−0.788654	−	0.614837i	$-0.789222\pi$
$97$	−4522.27	+	3166.53i	−0.480632	+	0.336542i	0.308022	+	0.951379i	$0.400333\pi$
$98$	−14902.4	+	1303.79i	−1.55169	+	0.135755i
$99$	1705.61	−	4686.12i	0.174024	−	0.478127i
$100$	5990.42	−	19070.1i	0.599042	−	1.90701i
$101$	−11277.9	+	9463.29i	−1.10557	+	0.927682i	−0.997787	−	0.0664924i	$-0.978819\pi$
$101$	−11277.9	+	9463.29i	−1.10557	+	0.927682i	−0.107782	+	0.994175i	$0.534375\pi$
$102$	−10771.9	+	40201.4i	−1.03536	+	3.86403i
$103$	−5433.39	−	20277.7i	−0.512149	−	1.91137i	−0.396368	−	0.918092i	$-0.629730\pi$
$103$	−5433.39	−	20277.7i	−0.512149	−	1.91137i	−0.115781	−	0.993275i	$-0.536937\pi$
$104$	23794.2	−	4195.57i	2.19991	−	0.387904i
$105$	−901.465	+	5877.76i	−0.0817656	+	0.533130i
$106$	−8162.63	+	14138.1i	−0.726471	+	1.25828i
$107$	5240.58	−	19558.1i	0.457732	−	1.70828i	−0.222196	−	0.975002i	$-0.571323\pi$
$107$	5240.58	−	19558.1i	0.457732	−	1.70828i	0.679929	−	0.733278i	$-0.262011\pi$
$108$	3088.25	−	35298.8i	0.264768	−	3.02631i
$109$	−868.205	−	2385.37i	−0.0730751	−	0.200772i	0.897778	−	0.440449i	$-0.145181\pi$
$109$	−868.205	−	2385.37i	−0.0730751	−	0.200772i	−0.970853	+	0.239677i	$0.922959\pi$
$110$	615.989	+	5596.97i	0.0509082	+	0.462559i
$111$	−12035.2	−	10098.8i	−0.976807	−	0.819639i
$112$	3247.27	−	2273.76i	0.258870	−	0.181263i
$113$	−2862.76	+	2862.76i	−0.224196	+	0.224196i	−0.810263	−	0.586067i	$-0.800676\pi$
$113$	−2862.76	+	2862.76i	−0.224196	+	0.224196i	0.586067	+	0.810263i	$0.300676\pi$
$114$	15937.6	−	34807.0i	1.22634	−	2.67829i
$115$	−8597.18	+	4245.36i	−0.650071	+	0.321010i
$116$	2810.07	−	15936.7i	0.208834	−	1.18435i
$117$	−2917.30	−	33344.9i	−0.213113	−	2.43589i
$118$	−1823.41	+	850.269i	−0.130954	+	0.0610650i
$119$	2085.59	+	5730.10i	0.147277	+	0.404640i
$120$	15377.8	+	39481.6i	1.06790	+	2.74178i
$121$	6791.88	+	11763.9i	0.463894	+	0.803489i
$122$	−22947.0	+	6148.63i	−1.54172	+	0.413103i
$123$	−22166.5	−	15521.2i	−1.46517	−	1.02592i
$124$	52324.1	−	9226.15i	3.40297	−	0.600036i
$125$	15589.9	−	1046.87i	0.997753	−	0.0669996i
$126$	−8253.15	−	14294.9i	−0.519851	−	0.900408i
$127$	−11574.4	−	1012.63i	−0.717617	−	0.0627834i	−0.277502	−	0.960725i	$-0.589507\pi$
$127$	−11574.4	−	1012.63i	−0.717617	−	0.0627834i	−0.440115	+	0.897942i	$0.645062\pi$
$128$	−12004.1	+	25742.9i	−0.732674	+	1.57122i
$129$	−17739.0	+	48737.5i	−1.06598	+	2.92876i
$130$	19623.9	+	32300.3i	1.16117	+	1.91126i
$131$	1403.84	−	7961.59i	0.0818042	−	0.463935i	−0.916196	−	0.400730i	$-0.868757\pi$
$131$	1403.84	−	7961.59i	0.0818042	−	0.463935i	0.998001	−	0.0632052i	$-0.0201323\pi$
$132$	−11257.2	−	11257.2i	−0.646075	−	0.646075i
$133$	−1012.29	−	5516.78i	−0.0572272	−	0.311877i
$134$		−	6046.51i		−	0.336740i
$135$	26587.3	−	7764.89i	1.45884	−	0.426057i
$136$	33284.0	+	27928.6i	1.79952	+	1.50998i
$137$	−406.258	−	871.222i	−0.0216451	−	0.0464181i	0.895188	−	0.445689i	$-0.147041\pi$
$137$	−406.258	−	871.222i	−0.0216451	−	0.0464181i	−0.916833	+	0.399271i	$0.869263\pi$
$138$	17188.5	−	36860.9i	0.902569	−	1.93557i
$139$	−3468.00	−	4133.00i	−0.179494	−	0.213912i	0.668794	−	0.743448i	$-0.266811\pi$
$139$	−3468.00	−	4133.00i	−0.179494	−	0.213912i	−0.848288	+	0.529535i	$0.822366\pi$
$140$	10332.8	+	6896.19i	0.527184	+	0.351847i
$141$	−10563.5	+	18296.6i	−0.531338	+	0.920305i
$142$	−11114.2	+	15872.7i	−0.551189	+	0.787179i
$143$	−5812.96	−	4070.28i	−0.284266	−	0.199045i
$144$	−33888.7	−	19565.6i	−1.63429	−	0.943559i
$145$	12405.3	−	2474.44i	0.590025	−	0.117690i
$146$	29020.7	−	24351.2i	1.36145	−	1.14239i
$147$	29964.0	+	13972.4i	1.38664	+	0.646603i
$148$	−29746.3	+	13870.9i	−1.35803	+	0.633260i
$149$	−10089.2	+	12023.9i	−0.454450	+	0.541592i	−0.943810	−	0.330490i	$-0.892786\pi$
$149$	−10089.2	+	12023.9i	−0.454450	+	0.541592i	0.489360	+	0.872082i	$0.337231\pi$
$150$	−48817.6	+	44829.0i	−2.16967	+	1.99240i
$151$	−8390.64			−0.367994			−0.183997	−	0.982927i	$-0.558904\pi$
$151$	−8390.64			−0.367994			−0.183997	+	0.982927i	$0.558904\pi$
$152$	−25901.0	−	30436.1i	−1.12106	−	1.31735i
$153$	42562.9	−	42562.9i	1.81823	−	1.81823i
$154$	−3446.26	−	607.669i	−0.145314	−	0.0256228i
$155$	21564.6	+	35494.7i	0.897591	+	1.47741i
$156$	−100413.	−	36547.3i	−4.12611	−	1.50178i
$157$	2635.93	+	1229.16i	0.106939	+	0.0498663i	0.475351	−	0.879796i	$-0.342321\pi$
$157$	2635.93	+	1229.16i	0.106939	+	0.0498663i	−0.368413	+	0.929662i	$0.620099\pi$
$158$	4836.09	−	55276.8i	0.193723	−	2.21426i
$159$	31246.5	−	18040.2i	1.23597	−	0.713587i
$160$	−98.6873	−	6.41545i	−0.00385497	−	0.000250604i
$161$	−1034.76	−	5868.42i	−0.0399198	−	0.226396i
$162$	−18031.4	+	25751.5i	−0.687068	+	0.981235i
$163$	350.445	+	1307.88i	0.0131900	+	0.0492258i	0.972207	−	0.234122i	$-0.0752216\pi$
$163$	350.445	+	1307.88i	0.0131900	+	0.0492258i	−0.959017	+	0.283348i	$0.908555\pi$
$164$	−48957.6	+	28265.7i	−1.82026	+	1.05092i
$165$	5005.92	−	11393.3i	0.183872	−	0.418486i
$166$	51508.2	−	18747.5i	1.86922	−	0.680341i
$167$	1900.47	+	4075.57i	0.0681441	+	0.146136i	0.937430	−	0.348175i	$-0.113198\pi$
$167$	1900.47	+	4075.57i	0.0681441	+	0.146136i	−0.869286	+	0.494310i	$0.835421\pi$
$168$	−26232.5	+	2295.05i	−0.929440	+	0.0813154i
$169$	−18780.4	−	3311.49i	−0.657554	−	0.115945i
$170$	−21812.4	+	64369.9i	−0.754753	+	2.22733i
$171$	−45132.1	+	32071.0i	−1.54345	+	1.09678i
$172$	76616.0	+	76616.0i	2.58978	+	2.58978i
$173$	11829.6	+	16894.4i	0.395254	+	0.564482i	0.966620	−	0.256214i	$-0.0824752\pi$
$173$	11829.6	+	16894.4i	0.395254	+	0.564482i	−0.571366	+	0.820695i	$0.693586\pi$
$174$	−34490.3	+	41103.9i	−1.13920	+	1.35764i
$175$	−2091.66	+	9482.74i	−0.0682992	+	0.309640i
$176$	−7795.74	+	2837.42i	−0.251670	+	0.0916005i
$177$	4429.59	+	387.539i	0.141389	+	0.0123700i
$178$	62944.8	+	16866.0i	1.98664	+	0.532319i
$179$	15900.2	+	9179.98i	0.496245	+	0.286507i	0.727162	−	0.686466i	$-0.240839\pi$
$179$	15900.2	+	9179.98i	0.496245	+	0.286507i	−0.230916	+	0.972974i	$0.574172\pi$
$180$	18589.9	−	121210.i	0.573761	−	3.74105i
$181$	−3463.16	−	19640.6i	−0.105710	−	0.599511i	−0.990934	−	0.134347i	$-0.957106\pi$
$181$	−3463.16	−	19640.6i	−0.105710	−	0.599511i	0.885225	−	0.465164i	$-0.154005\pi$
$182$	−22688.1	+	6079.27i	−0.684945	+	0.183531i
$183$	50715.1	+	13589.1i	1.51438	+	0.405777i
$184$	−27292.4	−	32525.8i	−0.806132	−	0.960711i
$185$	−18542.5	−	17731.6i	−0.541782	−	0.518090i
$186$	−165546.	−	60253.9i	−4.78513	−	1.74164i
$187$	−1112.22	−	12712.7i	−0.0318058	−	0.363542i
$188$	25315.6	+	36154.4i	0.716262	+	1.02293i
$189$			17213.9i			0.481898i
$190$	29658.7	−	55032.1i	0.821571	−	1.52444i
$191$	53662.8			1.47098			0.735490	−	0.677535i	$-0.236952\pi$
$191$	53662.8			1.47098			0.735490	+	0.677535i	$0.236952\pi$
$192$	51537.7	−	36087.1i	1.39805	−	0.978924i
$193$	−35017.6	+	3063.65i	−0.940096	+	0.0822477i	−0.546892	−	0.837203i	$-0.684189\pi$
$193$	−35017.6	+	3063.65i	−0.940096	+	0.0822477i	−0.393204	+	0.919451i	$0.628633\pi$
$194$	13079.3	−	35935.0i	0.347520	−	0.954803i
$195$	−1866.71	−	83507.9i	−0.0490916	−	2.19613i
$196$	52909.6	−	44396.4i	1.37728	−	1.15568i
$197$	6036.98	−	22530.3i	0.155556	−	0.580544i	−0.843501	−	0.537128i	$-0.819509\pi$
$197$	6036.98	−	22530.3i	0.155556	−	0.580544i	0.999057	−	0.0434158i	$-0.0138240\pi$
$198$	8940.54	+	33366.5i	0.228052	+	0.851100i
$199$	−31567.3	+	5566.16i	−0.797133	+	0.140556i	−0.557358	−	0.830272i	$-0.688185\pi$
$199$	−31567.3	+	5566.16i	−0.797133	+	0.140556i	−0.239775	+	0.970828i	$0.577074\pi$
$200$	20876.8	+	65967.2i	0.521919	+	1.64918i
$201$	−6681.68	+	11573.0i	−0.165384	+	0.286453i
$202$	26394.3	−	98505.0i	0.646856	−	2.41410i
$203$	−685.180	+	7831.64i	−0.0166269	+	0.190047i
$204$	−65722.9	−	180572.i	−1.57927	−	4.33901i
$205$	−34477.7	−	27641.0i	−0.820408	−	0.657728i
$206$	111396.	+	93472.1i	2.62503	+	2.20266i
$207$	−48184.2	+	33738.9i	−1.12451	+	0.787391i
$208$	−39374.4	+	39374.4i	−0.910097	+	0.910097i
$209$	−941.845	+	11700.2i	−0.0215619	+	0.267855i
$210$	−18237.9	−	36933.2i	−0.413559	−	0.837488i
$211$	−11649.1	+	66065.1i	−0.261653	+	1.48391i	0.516746	+	0.856139i	$0.327143\pi$
$211$	−11649.1	+	66065.1i	−0.261653	+	1.48391i	−0.778399	+	0.627770i	$0.783968\pi$
$212$	−6569.37	−	75088.2i	−0.146168	−	1.67071i
$213$	38812.6	−	18098.6i	0.855487	−	0.398920i
$214$	47970.5	+	131798.i	1.04748	+	2.87793i
$215$	−34070.0	+	77542.1i	−0.737047	+	1.67749i
$216$	61327.3	+	106222.i	1.31446	+	2.27670i
$217$	−24932.0	+	6680.50i	−0.529465	+	0.141870i
$218$	14403.7	+	10085.6i	0.303083	+	0.212221i
$219$	−82454.8	+	14539.0i	−1.71920	+	0.303142i
$220$	−17151.9	−	19537.0i	−0.354378	−	0.403656i
$221$	−42827.4	−	74179.3i	−0.876875	−	1.51879i
$222$	108414.	+	9484.99i	2.19978	+	0.192456i
$223$	−25010.7	+	53635.6i	−0.502939	+	1.07856i	0.476934	+	0.878939i	$0.341748\pi$
$223$	−25010.7	+	53635.6i	−0.502939	+	1.07856i	−0.979874	+	0.199618i	$0.936030\pi$
$224$	21.0212	−	57.7554i	0.000418950	−	0.00115106i
$225$	93561.8	−	20846.9i	1.84813	−	0.411790i
$226$	4869.78	−	27617.9i	0.0953439	−	0.540722i
$227$	−44942.2	−	44942.2i	−0.872173	−	0.872173i	0.120536	−	0.992709i	$-0.461539\pi$
$227$	−44942.2	−	44942.2i	−0.872173	−	0.872173i	−0.992709	+	0.120536i	$0.961539\pi$
$228$	31900.3	+	173850.i	0.613655	+	3.34430i
$229$		−	7841.00i		−	0.149520i	−0.997202	−	0.0747602i	$-0.976181\pi$
$229$		−	7841.00i		−	0.149520i	0.997202	−	0.0747602i	$-0.0238191\pi$
$230$	31914.8	−	58246.6i	0.603304	−	1.10107i
$231$	5924.64	+	4971.36i	0.111029	+	0.0931647i
$232$	23673.5	+	50767.9i	0.439831	+	0.943221i
$233$	24039.3	−	51552.4i	0.442802	−	0.949593i	−0.550585	−	0.834779i	$-0.685595\pi$
$233$	24039.3	−	51552.4i	0.442802	−	0.949593i	0.993387	−	0.114813i	$-0.0366270\pi$
$234$	149037.	+	177615.i	2.72183	+	3.24375i
$235$	−19152.3	+	28696.5i	−0.346805	+	0.519630i
$236$	4644.57	−	8044.63i	0.0833915	−	0.144438i
$237$	−70339.8	+	100456.i	−1.25229	+	1.78845i
$238$	−34600.4	−	24227.4i	−0.610839	−	0.427714i
$239$	79336.3	+	45804.9i	1.38892	+	0.801892i	0.993193	−	0.116478i	$-0.0371603\pi$
$239$	79336.3	+	45804.9i	1.38892	+	0.801892i	0.395724	+	0.918369i	$0.370494\pi$
$240$	−81222.4	−	54208.5i	−1.41011	−	0.941119i
$241$	−58273.0	+	48896.9i	−1.00331	+	0.841874i	−0.987439	−	0.158000i	$-0.949495\pi$
$241$	−58273.0	+	48896.9i	−1.00331	+	0.841874i	−0.0158669	+	0.999874i	$0.505051\pi$
$242$	−85277.7	−	39765.6i	−1.45615	−	0.679012i
$243$	−18364.7	+	8563.61i	−0.311008	+	0.145025i
$244$	70504.6	−	84024.1i	1.18423	−	1.41132i
$245$	47348.3	+	25943.3i	0.788810	+	0.432209i
$246$	187444.			3.09744
$247$	27459.9	+	73846.4i	0.450095	+	1.21042i
$248$	−130048.	+	130048.i	−2.11446	+	2.11446i
$249$	−119304.	−	21036.4i	−1.92422	−	0.339292i
$250$	−84300.8	+	67880.6i	−1.34881	+	1.08609i
$251$	−21604.9	−	7863.56i	−0.342930	−	0.124816i	0.164813	−	0.986325i	$-0.447298\pi$
$251$	−21604.9	−	7863.56i	−0.342930	−	0.124816i	−0.507743	+	0.861508i	$0.669520\pi$
$252$	69070.6	+	32208.1i	1.08766	+	0.507183i
$253$	−1086.88	+	12423.1i	−0.0169802	+	0.194084i
$254$	69699.0	−	40240.7i	1.08034	−	0.623733i
$255$	112881.	−	99100.3i	1.73596	−	1.52403i
$256$	−22747.6	−	129008.i	−0.347101	−	1.96851i
$257$	40872.3	−	58371.6i	0.618817	−	0.883763i	−0.380338	−	0.924847i	$-0.624192\pi$
$257$	40872.3	−	58371.6i	0.618817	−	0.883763i	0.999156	+	0.0410848i	$0.0130814\pi$
$258$	−92985.1	−	347025.i	−1.39693	−	5.21341i
$259$	13808.6	−	7972.41i	0.205850	−	0.118848i
$260$	−159758.	−	70193.7i	−2.36329	−	1.03837i
$261$	72923.0	−	26541.8i	1.07049	−	0.389627i
$262$	23666.6	+	50753.2i	0.344773	+	0.739369i
$263$	41831.4	−	3659.77i	0.604771	−	0.0529106i	0.219342	−	0.975648i	$-0.429609\pi$
$263$	41831.4	−	3659.77i	0.604771	−	0.0529106i	0.385429	+	0.922737i	$0.374053\pi$
$264$	54270.6	+	9569.37i	0.778676	+	0.137302i
$265$	52829.5	−	26087.7i	0.752289	−	0.371487i
$266$	27662.8	+	27281.4i	0.390960	+	0.385570i
$267$	−101839.	−	101839.i	−1.42853	−	1.42853i
$268$	16012.7	+	22868.4i	0.222943	+	0.318396i
$269$	−45597.8	+	54341.3i	−0.630143	+	0.750975i	−0.982779	−	0.184785i	$-0.940841\pi$
$269$	−45597.8	+	54341.3i	−0.630143	+	0.750975i	0.352636	+	0.935761i	$0.385285\pi$
$270$	−120011.	+	149694.i	−1.64624	+	2.05342i
$271$	36782.3	−	13387.7i	0.500842	−	0.182291i	−0.0792309	−	0.996856i	$-0.525246\pi$
$271$	36782.3	−	13387.7i	0.500842	−	0.182291i	0.580072	+	0.814565i	$0.303024\pi$
$272$	−99755.1	−	8727.44i	−1.34833	−	0.117964i
$273$	50142.9	+	13435.8i	0.672798	+	0.180276i
$274$	5766.65	+	3329.38i	0.0768108	+	0.0443468i
$275$	9364.44	−	18035.9i	0.123827	−	0.238491i
$276$	32608.3	+	184931.i	0.428065	+	2.42768i
$277$	26415.6	−	7078.05i	0.344272	−	0.0922473i	−0.0825402	−	0.996588i	$-0.526303\pi$
$277$	26415.6	−	7078.05i	0.344272	−	0.0922473i	0.426812	+	0.904340i	$0.359637\pi$
$278$	36099.0	+	9672.69i	0.467095	+	0.125158i
$279$	163776.	+	195181.i	2.10398	+	2.50743i
$280$	−42990.9	+	961.003i	−0.548353	+	0.0122577i
$281$	14834.4	+	5399.28i	0.187870	+	0.0683791i	0.434242	−	0.900796i	$-0.357016\pi$
$281$	14834.4	+	5399.28i	0.187870	+	0.0683791i	−0.246372	+	0.969175i	$0.579239\pi$
$282$	−12754.8	−	145789.i	−0.160390	−	1.83326i
$283$	−7185.39	−	10261.8i	−0.0897176	−	0.128130i	0.771784	−	0.635885i	$-0.219365\pi$
$283$	−7185.39	−	10261.8i	−0.0897176	−	0.128130i	−0.861502	+	0.507755i	$0.830476\pi$
$284$		−	89465.1i		−	1.10922i
$285$	−117580.	+	72557.2i	−1.44758	+	0.893287i
$286$	49155.6			0.600953
$287$	22496.6	−	15752.3i	0.273119	−	0.191240i
$288$	−604.396	+	52.8778i	−0.00728679	+	0.000637512i
$289$	24116.5	−	66259.5i	0.288747	−	0.793327i
$290$	−60558.8	+	63328.1i	−0.720080	+	0.753009i
$291$	−64743.6	+	54326.3i	−0.764558	+	0.641541i
$292$	−45270.7	+	168953.i	−0.530947	+	1.98152i
$293$	−6521.67	−	24339.2i	−0.0759668	−	0.283512i	0.917484	−	0.397773i	$-0.130217\pi$
$293$	−6521.67	−	24339.2i	−0.0759668	−	0.283512i	−0.993451	+	0.114261i	$0.963550\pi$
$294$	−225536.	+	39768.0i	−2.60928	+	0.460086i
$295$	7177.27	+	1100.77i	0.0824737	+	0.0126489i
$296$	56806.1	−	98391.0i	0.648353	−	1.12298i
$297$	9323.79	−	34796.8i	0.105701	−	0.394482i
$298$	9476.04	−	108312.i	0.106707	−	1.21967i
$299$	28628.4	+	78655.8i	0.320224	+	0.879809i
$300$	65914.4	−	298829.i	0.732382	−	3.32032i
$301$	−40322.8	−	33834.8i	−0.445059	−	0.373449i
$302$	47610.1	−	33337.0i	0.522018	−	0.365521i
$303$	−159371.	+	159371.i	−1.73590	+	1.73590i
$304$	89131.6	+	23220.8i	0.964460	+	0.251264i
$305$	81204.3	+	27516.8i	0.872930	+	0.295801i
$306$	−72403.0	+	410618.i	−0.773239	+	4.38526i
$307$	−5712.40	−	65293.0i	−0.0606097	−	0.692772i	−0.964339	−	0.264668i	$-0.914738\pi$
$307$	−5712.40	−	65293.0i	−0.0606097	−	0.692772i	0.903730	−	0.428103i	$-0.140818\pi$
$308$	14643.4	−	6828.31i	0.154362	−	0.0719800i
$309$	−109920.	−	302003.i	−1.15123	−	3.16297i
$310$	−263386.	−	115725.i	−2.74075	−	1.20422i
$311$	10464.8	+	18125.6i	0.108196	+	0.187401i	0.915039	−	0.403364i	$-0.132159\pi$
$311$	10464.8	+	18125.6i	0.108196	+	0.187401i	−0.806843	+	0.590765i	$0.798826\pi$
$312$	357285.	−	95734.3i	3.67034	−	0.983463i
$313$	48246.2	+	33782.4i	0.492464	+	0.344827i	0.793282	−	0.608854i	$-0.208371\pi$
$313$	48246.2	+	33782.4i	0.492464	+	0.344827i	−0.300818	+	0.953682i	$0.597260\pi$
$314$	−19840.4	+	3498.39i	−0.201229	+	0.0354821i
$315$	−3864.56	+	59447.6i	−0.0389474	+	0.599119i
$316$	128096.	+	221869.i	1.28281	+	2.22189i
$317$	−26015.8	−	2276.09i	−0.258892	−	0.0226501i	−0.0430291	−	0.999074i	$-0.513701\pi$
$317$	−26015.8	−	2276.09i	−0.258892	−	0.0226501i	−0.215863	+	0.976424i	$0.569256\pi$
$318$	−105623.	+	226510.i	−1.04449	+	2.23992i
$319$	5627.01	−	15460.1i	0.0552964	−	0.151926i
$320$	87807.2	−	53346.8i	0.857492	−	0.520965i
$321$	53827.5	−	305271.i	0.522389	−	2.96261i
$322$	29187.3	+	29187.3i	0.281503	+	0.281503i
$323$	−69987.5	+	123189.i	−0.670834	+	1.18077i
$324$		−	145146.i		−	1.38266i
$325$	5804.48	−	136280.i	0.0549536	−	1.29022i
$326$	−7184.86	−	6028.81i	−0.0676056	−	0.0567279i
$327$	−16423.7	−	35220.6i	−0.153594	−	0.329383i
$328$	82699.9	−	177350.i	0.768701	−	1.64848i
$329$	−13782.4	−	16425.3i	−0.127331	−	0.151747i
$330$	16862.3	+	84536.8i	0.154842	+	0.776279i
$331$	−32966.0	+	57098.7i	−0.300891	+	0.521159i	−0.976338	−	0.216250i	$-0.930617\pi$
$331$	−32966.0	+	57098.7i	−0.300891	+	0.521159i	0.675447	+	0.737409i	$0.263951\pi$
$332$	−145161.	+	207311.i	−1.31696	+	1.88082i
$333$	−128930.	−	90277.9i	−1.16270	−	0.814128i
$334$	−26976.4	−	15574.8i	−0.241819	−	0.139614i
$335$	−12114.3	+	18151.2i	−0.107946	+	0.161739i
$336$	46489.9	−	39009.7i	0.411794	−	0.345536i
$337$	−126993.	−	59217.6i	−1.11820	−	0.521424i	−0.226480	−	0.974016i	$-0.572722\pi$
$337$	−126993.	−	59217.6i	−1.11820	−	0.521424i	−0.891718	+	0.452592i	$0.850499\pi$
$338$	119721.	−	55826.6i	1.04794	−	0.488661i
$339$	−39839.9	+	47479.3i	−0.346672	+	0.413147i
$340$	−87971.3	−	301218.i	−0.760997	−	2.60569i
$341$	54017.0			0.464538
$342$	128667.	−	361292.i	1.10005	−	3.08892i
$343$	−50104.5	+	50104.5i	−0.425881	+	0.425881i
$344$	−369363.	−	65128.6i	−3.12130	−	0.550370i
$345$	−125450.	+	76216.6i	−1.05398	+	0.640341i
$346$	−134247.	−	48861.7i	−1.12137	−	0.408147i
$347$	4950.57	+	2308.49i	0.0411146	+	0.0191721i	0.443067	−	0.896489i	$-0.353890\pi$
$347$	4950.57	+	2308.49i	0.0411146	+	0.0191721i	−0.401952	+	0.915661i	$0.631668\pi$
$348$	21592.0	−	246798.i	0.178293	−	2.03790i
$349$	88407.2	−	51041.9i	0.725833	−	0.419060i	−0.0910626	−	0.995845i	$-0.529026\pi$
$349$	88407.2	−	51041.9i	0.725833	−	0.419060i	0.816896	+	0.576785i	$0.195693\pi$
$350$	−25807.5	−	62117.3i	−0.210673	−	0.507080i
$351$	−41987.9	−	238125.i	−0.340808	−	1.93282i
$352$	−73.7761	+	105.363i	−0.000595430	+	0.000850362i
$353$	52152.6	+	194636.i	0.418530	+	1.56197i	0.777659	+	0.628686i	$0.216407\pi$
$353$	52152.6	+	194636.i	0.418530	+	1.56197i	−0.359129	+	0.933288i	$0.616926\pi$
$354$	−26674.1	+	15400.3i	−0.212854	+	0.122892i
$355$	65165.1	−	25381.4i	0.517081	−	0.201399i
$356$	−282728.	+	102905.i	−2.23085	+	0.811961i
$357$	39452.6	+	84606.4i	0.309556	+	0.663845i
$358$	−126694.	+	11084.3i	−0.988530	+	0.0864851i
$359$	130682.	+	23042.8i	1.01398	+	0.178792i	0.655858	−	0.754884i	$-0.272307\pi$
$359$	130682.	+	23042.8i	1.01398	+	0.178792i	0.358119	+	0.933676i	$0.383418\pi$
$360$	187945.	+	380602.i	1.45019	+	2.93675i
$361$	82374.8	−	100985.i	0.632091	−	0.774894i
$362$	97684.9	+	97684.9i	0.745436	+	0.745436i
$363$	119278.	+	170347.i	0.905209	+	1.29277i
$364$	69709.2	−	83076.2i	0.526123	−	0.627009i
$365$	−135906.	+	14957.5i	−1.02012	+	0.112272i
$366$	−341758.	+	124390.i	−2.55127	+	0.928587i
$367$	68954.1	+	6032.70i	0.511950	+	0.0447899i	0.340205	−	0.940351i	$-0.389504\pi$
$367$	68954.1	+	6032.70i	0.511950	+	0.0447899i	0.171746	+	0.985141i	$0.445059\pi$
$368$	94520.8	+	25326.8i	0.697962	+	0.187018i
$369$	−234775.	−	135548.i	−1.72425	−	0.995495i
$370$	175663.	+	26941.3i	1.28315	+	0.196795i
$371$	6358.58	+	36061.3i	0.0461968	+	0.261995i
$372$	785679.	−	210522.i	5.67753	−	1.52129i
$373$	258559.	+	69280.6i	1.85841	+	0.497959i	0.999890	−	0.0148223i	$-0.00471826\pi$
$373$	258559.	+	69280.6i	1.85841	+	0.497959i	0.858519	+	0.512782i	$0.171385\pi$
$374$	56820.0	+	67715.5i	0.406217	+	0.484111i
$375$	236363.	−	36767.0i	1.68080	−	0.261454i
$376$	−143565.	−	52253.5i	−1.01548	−	0.369606i
$377$	−9624.54	−	110009.i	−0.0677170	−	0.774008i
$378$	−68392.7	−	97674.8i	−0.478659	−	0.683595i
$379$		−	11936.9i		−	0.0831021i	−0.999136	−	0.0415510i	$-0.986770\pi$
$379$		−	11936.9i		−	0.0831021i	0.999136	−	0.0415510i	$-0.0132299\pi$
$380$	33566.9	+	286680.i	0.232458	+	1.98532i
$381$	−177872.			−1.22534
$382$	−304493.	+	213209.i	−2.08666	+	1.46109i
$383$	162045.	−	14177.1i	1.10468	−	0.0966472i	0.479809	−	0.877373i	$-0.340706\pi$
$383$	162045.	−	14177.1i	1.10468	−	0.0966472i	0.624873	+	0.780726i	$0.285151\pi$
$384$	−148725.	+	408620.i	−1.00861	+	2.77113i
$385$	9127.98	+	8728.82i	0.0615819	+	0.0588890i
$386$	186525.	−	156513.i	1.25188	−	1.05045i
$387$	−134482.	+	501892.i	−0.897927	+	3.35111i
$388$	45697.8	+	170547.i	0.303551	+	1.13287i
$389$	−249262.	+	43951.6i	−1.64724	+	0.290452i	−0.918819	−	0.394680i	$-0.870856\pi$
$389$	−249262.	+	43951.6i	−1.64724	+	0.290452i	−0.728419	+	0.685132i	$0.759744\pi$
$390$	342379.	+	466424.i	2.25101	+	3.06656i
$391$	−75262.1	+	130358.i	−0.492292	+	0.852675i
$392$	−61879.1	+	230936.i	−0.402691	+	1.50286i
$393$	10786.9	−	123294.i	0.0698409	−	0.798285i
$394$	55260.5	+	151827.i	0.355978	+	0.978040i
$395$	−125265.	+	156248.i	−0.802855	+	1.00143i
$396$	−122177.	−	102519.i	−0.779110	−	0.653751i
$397$	2951.12	−	2066.40i	0.0187243	−	0.0131109i	−0.564177	−	0.825654i	$-0.690806\pi$
$397$	2951.12	−	2066.40i	0.0187243	−	0.0131109i	0.582901	+	0.812543i	$0.301917\pi$
$398$	157004.	−	157004.i	0.991161	−	0.991161i
$399$	−22799.3	−	82785.2i	−0.143211	−	0.520004i
$400$	−126615.	−	96940.8i	−0.791345	−	0.605880i
$401$	27839.1	−	157884.i	0.173128	−	0.981856i	−0.767155	−	0.641462i	$-0.778328\pi$
$401$	27839.1	−	157884.i	0.173128	−	0.981856i	0.940283	−	0.340395i	$-0.110561\pi$
$402$	−8067.73	−	92214.6i	−0.0499228	−	0.570621i
$403$	328597.	−	153227.i	2.02327	−	0.943466i
$404$	161040.	+	442454.i	0.986668	+	2.71085i
$405$	105723.	−	41178.2i	0.644552	−	0.251048i
$406$	−27228.2	−	47160.6i	−0.165183	−	0.286106i
$407$	−32231.6	+	8636.42i	−0.194577	+	0.0521369i
$408$	544875.	+	381526.i	3.27323	+	2.29194i
$409$	157807.	−	27825.6i	0.943365	−	0.166341i	0.319248	−	0.947671i	$-0.396570\pi$
$409$	157807.	−	27825.6i	0.943365	−	0.166341i	0.624117	+	0.781331i	$0.285459\pi$
$410$	305454.	+	19856.9i	1.81710	+	0.118126i
$411$	−7358.24	−	12744.8i	−0.0435603	−	0.0754486i
$412$	−668846.	−	58516.5i	−3.94032	−	0.344734i
$413$	−1907.15	+	4089.91i	−0.0111811	+	0.0239780i
$414$	139358.	−	382882.i	0.813075	−	2.23390i
$415$	−192185.	−	46918.8i	−1.11590	−	0.272427i
$416$	−149.918	+	850.225i	−0.000866295	+	0.00491300i
$417$	−58404.6	−	58404.6i	−0.335873	−	0.335873i
$418$	−41141.9	−	70131.1i	−0.235468	−	0.401382i
$419$			133988.i			0.763200i	0.924328	+	0.381600i	$0.124627\pi$
$419$			133988.i			0.763200i	−0.924328	+	0.381600i	$0.875373\pi$
$420$	166786.	+	91386.2i	0.945499	+	0.518062i
$421$	134135.	+	112553.i	0.756794	+	0.635026i	0.937290	−	0.348550i	$-0.113326\pi$
$421$	134135.	+	112553.i	0.756794	+	0.635026i	−0.180496	+	0.983576i	$0.557770\pi$
$422$	−196385.	−	421150.i	−1.10277	−	2.36489i
$423$	−89449.3	+	191825.i	−0.499915	+	1.07207i
$424$	167711.	+	199871.i	0.932891	+	1.11178i
$425$	194445.	−	149533.i	1.07651	−	0.827864i
$426$	−148322.	+	256902.i	−0.817311	+	1.41562i
$427$	−30563.5	+	43649.2i	−0.167628	+	0.239398i
$428$	−530463.	−	371434.i	−2.89579	−	2.02766i
$429$	−94083.7	−	54319.2i	−0.511211	−	0.295148i
$430$	−114764.	−	575353.i	−0.620680	−	3.11170i
$431$	211734.	−	177666.i	1.13982	−	0.956422i	0.140386	−	0.990097i	$-0.455166\pi$
$431$	211734.	−	177666.i	1.13982	−	0.956422i	0.999433	+	0.0336749i	$0.0107211\pi$
$432$	−256194.	−	119465.i	−1.37278	−	0.640138i
$433$	−73671.9	+	34353.8i	−0.392940	+	0.183231i	−0.609039	−	0.793141i	$-0.708445\pi$
$433$	−73671.9	+	34353.8i	−0.392940	+	0.183231i	0.216098	+	0.976372i	$0.430667\pi$
$434$	114926.	−	136964.i	0.610155	−	0.727155i
$435$	185890.	−	54289.6i	0.982375	−	0.286905i
$436$	−81185.4			−0.427076
$437$	88258.5	−	106677.i	0.462161	−	0.558611i
$438$	410099.	−	410099.i	2.13767	−	2.13767i
$439$	−15080.0	−	2659.01i	−0.0782478	−	0.0137972i	0.134387	−	0.990929i	$-0.457093\pi$
$439$	−15080.0	−	2659.01i	−0.0782478	−	0.0137972i	−0.212635	+	0.977132i	$0.568205\pi$
$440$	87424.1	+	21343.1i	0.451571	+	0.110243i
$441$	311243.	+	113283.i	1.60037	+	0.582489i
$442$	537734.	+	250750.i	2.75247	+	1.28350i
$443$	29060.3	−	332161.i	0.148079	−	1.69255i	−0.451529	−	0.892256i	$-0.649121\pi$
$443$	29060.3	−	332161.i	0.148079	−	1.69255i	0.599608	−	0.800294i	$-0.295323\pi$
$444$	−435150.	+	251234.i	−2.20736	+	1.27442i
$445$	−155165.	−	176741.i	−0.783562	−	0.892521i
$446$	−71184.8	−	403709.i	−0.357864	−	2.02955i
$447$	−137827.	+	196837.i	−0.689792	+	0.985125i
$448$	16526.3	+	61677.0i	0.0823416	+	0.307303i
$449$	−77439.4	+	44709.6i	−0.384122	+	0.221773i	−0.679610	−	0.733573i	$-0.737851\pi$
$449$	−77439.4	+	44709.6i	−0.384122	+	0.221773i	0.295488	+	0.955346i	$0.404518\pi$
$450$	−448061.	+	490021.i	−2.21265	+	2.41986i
$451$	−54007.6	+	19657.2i	−0.265523	+	0.0966424i
$452$	54721.2	+	117350.i	0.267842	+	0.574389i
$453$	−127965.	+	11195.5i	−0.623582	+	0.0545564i
$454$	433571.	+	76450.3i	2.10353	+	0.370909i
$455$	80288.2	+	27206.4i	0.387819	+	0.131416i
$456$	−435624.	−	429618.i	−2.09499	−	2.06611i
$457$	80032.0	+	80032.0i	0.383205	+	0.383205i	0.872255	−	0.489050i	$-0.162657\pi$
$457$	80032.0	+	80032.0i	0.383205	+	0.383205i	−0.489050	+	0.872255i	$0.662657\pi$
$458$	31153.2	+	44491.3i	0.148515	+	0.212102i
$459$	279501.	−	333096.i	1.32665	−	1.58104i
$460$	33546.9	+	304813.i	0.158539	+	1.44051i
$461$	56509.6	−	20567.8i	0.265901	−	0.0967802i	−0.205629	−	0.978630i	$-0.565924\pi$
$461$	56509.6	−	20567.8i	0.265901	−	0.0967802i	0.471530	+	0.881850i	$0.343702\pi$
$462$	−53369.4	−	4669.22i	−0.250039	−	0.0218756i
$463$	−188728.	−	50569.5i	−0.880388	−	0.235899i	−0.209813	−	0.977741i	$-0.567286\pi$
$463$	−188728.	−	50569.5i	−0.880388	−	0.235899i	−0.670574	+	0.741842i	$0.733952\pi$
$464$	−111803.	−	64549.5i	−0.519299	−	0.299817i
$465$	376240.	+	512552.i	1.74004	+	2.37046i
$466$	68420.1	+	388030.i	0.315073	+	1.78687i
$467$	15975.0	−	4280.49i	0.0732500	−	0.0196273i	−0.222008	−	0.975045i	$-0.571261\pi$
$467$	15975.0	−	4280.49i	0.0732500	−	0.0196273i	0.295258	+	0.955418i	$0.404594\pi$
$468$	−1.03404e6	−	277070.i	−4.72112	−	1.26502i
$469$	−8717.70	−	10389.3i	−0.0396329	−	0.0472327i
$470$	−5340.83	−	238924.i	−0.0241776	−	1.08159i
$471$	41840.3	+	15228.6i	0.188605	+	0.0686466i
$472$	2802.46	+	32032.2i	0.0125793	+	0.143782i
$473$	63183.7	+	90235.7i	0.282412	+	0.403326i
$474$		−	849473.i		−	3.78088i
$475$	−199291.	+	105781.i	−0.883285	+	0.468837i
$476$	195022.			0.860736
$477$	296091.	−	207325.i	1.30133	−	0.911202i
$478$	−632158.	+	55306.7i	−2.76675	+	0.242059i
$479$	9045.70	−	24852.8i	0.0394249	−	0.108319i	−0.918418	−	0.395611i	$-0.870533\pi$
$479$	9045.70	−	24852.8i	0.0394249	−	0.108319i	0.957843	+	0.287292i	$0.0927550\pi$
$480$	−1513.63	+	33.8352i	−0.00656957	+	0.000146854i
$481$	−171573.	+	143967.i	−0.741582	+	0.622261i
$482$	136380.	−	508976.i	0.587023	−	2.19080i
$483$	−23611.1	−	88117.9i	−0.101210	−	0.377720i
$484$	427838.	−	75439.3i	1.82637	−	0.322038i
$485$	−111259.	+	81670.0i	−0.472991	+	0.347199i
$486$	70180.8	−	121557.i	0.297129	−	0.514643i
$487$	−9495.79	+	35438.8i	−0.0400381	+	0.149424i	−0.983051	−	0.183332i	$-0.941312\pi$
$487$	−9495.79	+	35438.8i	−0.0400381	+	0.149424i	0.943013	+	0.332756i	$0.107978\pi$
$488$	−33091.3	+	378235.i	−0.138955	+	1.58826i
$489$	7089.68	+	19478.7i	0.0296489	+	0.0814598i
$490$	−371739.	+	40912.7i	−1.54827	+	0.170399i
$491$	−158639.	−	133114.i	−0.658031	−	0.552154i	0.251465	−	0.967866i	$-0.419088\pi$
$491$	−158639.	−	133114.i	−0.658031	−	0.552154i	−0.909496	+	0.415713i	$0.863532\pi$
$492$	−708932.	+	496400.i	−2.92870	+	2.05070i
$493$	140420.	−	140420.i	0.577746	−	0.577746i
$494$	−449213.	−	309918.i	−1.84076	−	1.26997i
$495$	40011.4	−	118077.i	0.163295	−	0.481896i
$496$	73603.3	−	417425.i	0.299181	−	1.69674i
$497$	3788.01	+	43297.2i	0.0153355	+	0.175286i
$498$	760532.	−	354642.i	3.06661	−	1.42998i
$499$	−110776.	−	304356.i	−0.444884	−	1.22231i	−0.936244	−	0.351351i	$-0.885722\pi$
$499$	−110776.	−	304356.i	−0.444884	−	1.22231i	0.491360	−	0.870956i	$-0.336500\pi$
$500$	139069.	−	479980.i	0.556275	−	1.91992i
$501$	34421.8	+	59620.3i	0.137138	+	0.237530i
$502$	153833.	−	41219.6i	0.610441	−	0.163567i
$503$	339447.	+	237683.i	1.34164	+	0.939426i	1.00000		0.000405580i	$-0.000129100\pi$
$503$	339447.	+	237683.i	1.34164	+	0.939426i	0.341639	+	0.939831i	$0.389018\pi$
$504$	−259798.	+	45809.4i	−1.02276	+	0.180341i
$505$	−276590.	+	242824.i	−1.08456	+	0.952158i
$506$	−43191.4	−	74809.6i	−0.168693	−	0.292184i
$507$	−290836.	−	25444.9i	−1.13144	−	0.0989884i
$508$	−157041.	+	336775.i	−0.608533	+	1.30500i
$509$	95146.8	−	261414.i	0.367247	−	1.00900i	−0.609156	−	0.793050i	$-0.708492\pi$
$509$	95146.8	−	261414.i	0.367247	−	1.00900i	0.976404	−	0.215954i	$-0.0692860\pi$
$510$	−246770.	+	1.01080e6i	−0.948752	+	3.88621i
$511$	14755.5	−	83682.5i	0.0565082	−	0.320474i
$512$	320282.	+	320282.i	1.22178	+	1.22178i
$513$	−304595.	+	259209.i	−1.15741	+	0.984954i
$514$			493602.i			1.86832i
$515$	−147130.	−	503780.i	−0.554737	−	1.89944i
$516$	1.27069e6	+	1.06623e6i	4.77243	+	4.00454i
$517$	18963.8	+	40667.9i	0.0709485	+	0.152150i
$518$	−46677.5	+	100100.i	−0.173960	+	0.373057i
$519$	202953.	+	241870.i	0.753462	+	0.897940i
$520$	592363.	−	118157.i	2.19069	−	0.436970i
$521$	36461.2	−	63152.6i	0.134324	−	0.232657i	−0.791015	−	0.611797i	$-0.790447\pi$
$521$	36461.2	−	63152.6i	0.134324	−	0.232657i	0.925339	+	0.379140i	$0.123780\pi$
$522$	−308326.	+	440335.i	−1.13154	+	1.61600i
$523$	−38102.0	−	26679.3i	−0.139298	−	0.0975375i	0.501850	−	0.864954i	$-0.332653\pi$
$523$	−38102.0	−	26679.3i	−0.139298	−	0.0975375i	−0.641148	+	0.767417i	$0.721542\pi$
$524$	−223917.	−	129278.i	−0.815500	−	0.470829i
$525$	−19247.1	+	147411.i	−0.0698307	+	0.534825i
$526$	−222819.	+	186967.i	−0.805342	+	0.675762i
$527$	590915.	+	275548.i	2.12767	+	0.992148i
$528$	−115106.	+	53674.8i	−0.412886	+	0.192532i
$529$	−85327.2	+	101689.i	−0.304913	+	0.363381i
$530$	−196116.	+	357924.i	−0.698169	+	1.27421i
$531$	44545.9			0.157986
$532$	−176871.	−	29922.8i	−0.624933	−	0.105725i
$533$	−272780.	+	272780.i	−0.960191	+	0.960191i
$534$	982468.	+	173236.i	3.44537	+	0.607512i
$535$	120055.	−	491758.i	0.419441	−	1.71808i
$536$	−90808.2	−	33051.5i	−0.316079	−	0.115043i
$537$	254741.	+	118788.i	0.883385	+	0.411929i
$538$	42826.4	−	489509.i	0.147961	−	1.69120i
$539$	60812.3	−	35110.0i	0.209321	−	0.120852i
$540$	57465.4	−	883976.i	0.197069	−	3.03147i
$541$	11725.9	+	66500.6i	0.0400636	+	0.227212i	0.998265	−	0.0588829i	$-0.0187539\pi$
$541$	11725.9	+	66500.6i	0.0400636	+	0.227212i	−0.958201	+	0.286095i	$0.907643\pi$
$542$	−155519.	+	222105.i	−0.529402	+	0.756065i
$543$	−79022.3	−	294915.i	−0.268009	−	1.00022i
$544$	−1344.54	+	776.272i	−0.00454335	+	0.00262311i
$545$	−23032.4	−	59134.4i	−0.0775437	−	0.199089i
$546$	−337903.	+	122987.i	−1.13346	+	0.412546i
$547$	−126431.	−	271132.i	−0.422550	−	0.906162i	−0.996203	−	0.0870631i	$-0.972252\pi$
$547$	−126431.	−	271132.i	−0.422550	−	0.906162i	0.573653	−	0.819099i	$-0.305526\pi$
$548$	−30627.0	+	2679.52i	−0.101987	+	0.00892269i
$549$	518005.	+	91338.2i	1.71866	+	0.303046i
$550$	18522.9	+	139545.i	0.0612328	+	0.461306i
$551$	−148896.	+	105806.i	−0.490434	+	0.348504i
$552$	−459632.	−	459632.i	−1.50845	−	1.50845i
$553$	−71387.1	−	101951.i	−0.233437	−	0.333382i
$554$	−121766.	+	145115.i	−0.396739	+	0.472815i
$555$	−306448.	−	245682.i	−0.994881	−	0.797604i
$556$	−162145.	+	59016.1i	−0.524512	+	0.190907i
$557$	380114.	+	33255.7i	1.22519	+	0.107190i	0.681324	−	0.731982i	$-0.261404\pi$
$557$	380114.	+	33255.7i	1.22519	+	0.107190i	0.543866	+	0.839172i	$0.316960\pi$
$558$	−1.70477e6	−	456792.i	−5.47518	−	1.46707i
$559$	640328.	+	369694.i	2.04917	+	1.18309i
$560$	79891.1	−	58644.1i	0.254755	−	0.187003i
$561$	−33924.6	−	192396.i	−0.107793	−	0.611323i
$562$	−105625.	+	28302.2i	−0.334422	+	0.0896081i
$563$	−259226.	−	69459.5i	−0.817829	−	0.219137i	−0.174432	−	0.984669i	$-0.555809\pi$
$563$	−259226.	−	69459.5i	−0.817829	−	0.219137i	−0.643397	+	0.765533i	$0.722476\pi$
$564$	434325.	+	517608.i	1.36539	+	1.62721i
$565$	−69951.7	+	73150.5i	−0.219130	+	0.229150i
$566$	81542.7	+	29679.1i	0.254538	+	0.0926441i
$567$	6145.60	+	70244.5i	0.0191161	+	0.218498i
$568$	177628.	+	253679.i	0.550574	+	0.786301i
$569$		−	10827.6i		−	0.0334432i	−0.999860	−	0.0167216i	$-0.994677\pi$
$569$		−	10827.6i		−	0.0334432i	0.999860	−	0.0167216i	$-0.00532290\pi$
$570$	378893.	−	878862.i	1.16618	−	2.70502i
$571$	155060.			0.475585			0.237793	−	0.971316i	$-0.423576\pi$
$571$	155060.			0.475585			0.237793	+	0.971316i	$0.423576\pi$
$572$	−185911.	+	130176.i	−0.568215	+	0.397869i
$573$	818406.	−	71601.2i	2.49264	−	0.218078i
$574$	−65064.3	+	178763.i	−0.197478	+	0.542567i
$575$	−212504.	+	110911.i	−0.642734	+	0.335458i
$576$	482840.	−	405151.i	1.45532	−	1.22116i
$577$	−99571.1	+	371604.i	−0.299076	+	1.11617i	0.638850	+	0.769331i	$0.279410\pi$
$577$	−99571.1	+	371604.i	−0.299076	+	1.11617i	−0.937926	+	0.346835i	$0.887256\pi$
$578$	126415.	+	471787.i	0.378392	+	1.41218i
$579$	−529962.	+	93446.6i	−1.58084	+	0.278745i
$580$	61330.3	−	399887.i	0.182313	−	1.18873i
$581$	61473.9	−	106476.i	0.182112	−	0.315427i
$582$	151523.	−	565492.i	0.447335	−	1.66948i
$583$	6678.88	−	76339.9i	0.0196502	−	0.224603i
$584$	−207081.	−	568950.i	−0.607175	−	1.66820i
$585$	−91544.2	−	831785.i	−0.267497	−	2.43052i
$586$	133708.	+	112194.i	0.389369	+	0.326719i
$587$	−386367.	+	270537.i	−1.12130	+	0.785146i	−0.978835	−	0.204653i	$-0.934393\pi$
$587$	−386367.	+	270537.i	−1.12130	+	0.785146i	−0.142470	+	0.989799i	$0.545504\pi$
$588$	747681.	−	747681.i	2.16253	−	2.16253i
$589$	−493639.	−	340568.i	−1.42292	−	0.981688i
$590$	−45098.7	+	22270.1i	−0.129557	+	0.0639763i
$591$	62007.6	−	351662.i	0.177529	−	1.00682i
$592$	22820.8	+	260842.i	0.0651158	+	0.744277i
$593$	−614578.	+	286583.i	−1.74770	+	0.814968i	−0.761767	+	0.647851i	$0.775668\pi$
$593$	−614578.	+	286583.i	−1.74770	+	0.814968i	−0.985937	+	0.167116i	$0.946554\pi$
$594$	85346.9	+	234489.i	0.241888	+	0.664582i
$595$	55328.0	+	142052.i	0.156283	+	0.401247i
$596$	250997.	+	434740.i	0.706604	+	1.22387i
$597$	−474002.	+	127008.i	−1.32994	+	0.356356i
$598$	−474952.	−	332565.i	−1.32815	−	0.929980i
$599$	−290324.	+	51191.9i	−0.809150	+	0.142675i	−0.562893	−	0.826530i	$-0.690312\pi$
$599$	−290324.	+	51191.9i	−0.809150	+	0.142675i	−0.246257	+	0.969205i	$0.579201\pi$
$600$	406408.	+	978203.i	1.12891	+	2.71723i
$601$	139904.	+	242321.i	0.387330	+	0.670875i	0.992089	−	0.125533i	$-0.0400641\pi$
$601$	139904.	+	242321.i	0.387330	+	0.670875i	−0.604760	+	0.796408i	$0.706731\pi$
$602$	363229.	+	31778.4i	1.00228	+	0.0876878i
$603$	−56578.7	+	121333.i	−0.155603	+	0.333692i
$604$	−91781.3	+	252167.i	−0.251582	+	0.691217i
$605$	176327.	+	290229.i	0.481735	+	0.792921i
$606$	271104.	−	1.53751e6i	0.738227	−	4.18670i
$607$	−107950.	−	107950.i	−0.292984	−	0.292984i	0.545274	−	0.838258i	$-0.316426\pi$
$607$	−107950.	−	107950.i	−0.292984	−	0.292984i	−0.838258	+	0.545274i	$0.816426\pi$
$608$	1338.51	−	497.726i	0.00362088	−	0.00134643i
$609$			120354.i			0.324508i
$610$	−570097.	+	166498.i	−1.53211	+	0.447455i
$611$	230721.	+	193598.i	0.618024	+	0.518584i
$612$	−813584.	−	1.74474e6i	−2.17220	−	4.65830i
$613$	−68993.0	+	147956.i	−0.183605	+	0.393742i	−0.976469	−	0.215656i	$-0.930811\pi$
$613$	−68993.0	+	147956.i	−0.183605	+	0.393742i	0.792865	+	0.609398i	$0.208589\pi$
$614$	291830.	+	347789.i	0.774093	+	0.922528i
$615$	−562696.	−	375547.i	−1.48773	−	0.992921i
$616$	−27964.2	+	48435.4i	−0.0736954	+	0.127644i
$617$	186363.	−	266154.i	0.489541	−	0.699137i	−0.496048	−	0.868295i	$-0.665216\pi$
$617$	186363.	−	266154.i	0.489541	−	0.699137i	0.985589	+	0.169158i	$0.0541049\pi$
$618$	1.82360e6	+	1.27690e6i	4.77478	+	3.34333i
$619$	−231224.	−	133497.i	−0.603464	−	0.348410i	0.166939	−	0.985967i	$-0.446612\pi$
$619$	−231224.	−	133497.i	−0.603464	−	0.348410i	−0.770403	+	0.637557i	$0.779945\pi$
$620$	1.30262e6	−	259830.i	3.38871	−	0.675936i
$621$	−325508.	+	273134.i	−0.844071	+	0.708260i
$622$	−131395.	−	61270.3i	−0.339623	−	0.158369i
$623$	132471.	−	61772.4i	0.341307	−	0.159154i
$624$	−547959.	+	653032.i	−1.40727	+	1.67712i
$625$	389065.	−	34875.3i	0.996007	−	0.0892807i
$626$	−407980.			−1.04109
$627$	1247.33	+	179695.i	0.00317282	+	0.457088i
$628$	65773.5	−	65773.5i	0.166775	−	0.166775i
$629$	−396651.	−	69940.2i	−1.00255	−	0.176777i
$630$	−214264.	−	352671.i	−0.539843	−	0.888565i
$631$	724031.	+	263526.i	1.81844	+	0.661858i	0.995613	+	0.0935637i	$0.0298259\pi$
$631$	724031.	+	263526.i	1.81844	+	0.661858i	0.822826	+	0.568294i	$0.192396\pi$
$632$	−803728.	−	374785.i	−2.01222	−	0.938313i
$633$	−89509.2	+	1.02309e6i	−0.223388	+	2.55334i
$634$	156662.	−	90448.7i	0.389749	−	0.225021i
$635$	−289855.	−	18842.8i	−0.718841	−	0.0467303i
$636$	−200377.	−	1.13640e6i	−0.495376	−	2.80941i
$637$	270340.	−	386085.i	0.666240	−	0.951490i
$638$	29495.9	+	110080.i	0.0724638	+	0.270438i
$639$	371549.	−	214514.i	0.909944	−	0.525357i
$640$	−285646.	+	650120.i	−0.697377	+	1.58721i
$641$	−461974.	+	168145.i	−1.12435	+	0.409230i	−0.836238	−	0.548367i	$-0.815250\pi$
$641$	−461974.	+	168145.i	−1.12435	+	0.409230i	−0.288112	+	0.957597i	$0.593027\pi$
$642$	907448.	+	1.94603e6i	2.20167	+	4.72149i
$643$	−53373.7	+	4669.59i	−0.129094	+	0.0112942i	−0.151519	−	0.988454i	$-0.548417\pi$
$643$	−53373.7	+	4669.59i	−0.129094	+	0.0112942i	0.0224258	+	0.999749i	$0.492861\pi$
$644$	−187685.	−	33093.8i	−0.452540	−	0.0797950i
$645$	−416135.	+	1.22804e6i	−1.00026	+	2.95185i
$646$	−92320.4	−	977065.i	−0.221224	−	2.34131i
$647$	242872.	+	242872.i	0.580188	+	0.580188i	0.934955	−	0.354766i	$-0.115440\pi$
$647$	242872.	+	242872.i	0.580188	+	0.580188i	−0.354766	+	0.934955i	$0.615440\pi$
$648$	288181.	+	411565.i	0.686301	+	0.980140i
$649$	6070.48	−	7234.52i	0.0144123	−	0.0171759i
$650$	508520.	+	796341.i	1.20360	+	1.88483i
$651$	−371321.	+	135150.i	−0.876168	+	0.318899i
$652$	43139.6	+	3774.23i	0.101480	+	0.00887836i
$653$	651278.	+	174509.i	1.52736	+	0.409254i	0.922155	−	0.386819i	$-0.126426\pi$
$653$	651278.	+	174509.i	1.52736	+	0.409254i	0.605200	+	0.796073i	$0.293093\pi$
$654$	233127.	+	134596.i	0.545050	+	0.314685i
$655$	30639.1	−	199774.i	0.0714158	−	0.465647i
$656$	78313.4	+	444137.i	0.181982	+	1.03207i
$657$	−810209.	+	217095.i	−1.87701	+	0.502943i
$658$	143464.	+	38441.0i	0.331352	+	0.0887856i
$659$	−128387.	−	153006.i	−0.295632	−	0.352321i	0.597698	−	0.801721i	$-0.296082\pi$
$659$	−128387.	−	153006.i	−0.295632	−	0.352321i	−0.893330	+	0.449400i	$0.851638\pi$
$660$	−287649.	−	275071.i	−0.660352	−	0.631475i
$661$	271305.	+	98746.8i	0.620947	+	0.226006i	0.633286	−	0.773918i	$-0.281706\pi$
$661$	271305.	+	98746.8i	0.620947	+	0.226006i	−0.0123393	+	0.999924i	$0.503928\pi$
$662$	−39804.4	−	454967.i	−0.0908271	−	1.03816i
$663$	−752132.	−	1.07416e6i	−1.71107	−	2.44366i
$664$		−	876044.i		−	1.98696i
$665$	−28383.2	−	137320.i	−0.0641827	−	0.310520i
$666$	1.09026e6			2.45800
$667$	−158966.	+	111309.i	−0.357315	+	0.250195i
$668$	143273.	−	12534.8i	0.321079	−	0.0280908i
$669$	−309870.	+	851361.i	−0.692353	+	1.90222i
$670$	−3378.19	−	151125.i	−0.00752550	−	0.336656i
$671$	85424.8	−	71679.9i	0.189731	−	0.159203i
$672$	243.531	−	908.869i	0.000539281	−	0.00201262i
$673$	−123765.	−	461898.i	−0.273255	−	1.01980i	−0.957002	−	0.290082i	$-0.906317\pi$
$673$	−123765.	−	461898.i	−0.273255	−	1.01980i	0.683747	−	0.729720i	$-0.260349\pi$
$674$	955859.	−	168544.i	2.10414	−	0.371016i
$675$	660179.	−	208928.i	1.44895	−	0.458553i
$676$	−304952.	+	528192.i	−0.667325	+	1.15584i
$677$	204723.	−	764038.i	0.446673	−	1.66701i	−0.264807	−	0.964301i	$-0.585308\pi$
$677$	204723.	−	764038.i	0.446673	−	1.66701i	0.711481	−	0.702706i	$-0.248025\pi$
$678$	37418.5	−	427695.i	0.0814005	−	0.930412i
$679$	−29336.8	−	80602.3i	−0.0636317	−	0.174827i
$680$	847496.	+	679445.i	1.83282	+	1.46939i
$681$	−745374.	−	625443.i	−1.60724	−	1.34863i
$682$	−306503.	+	214616.i	−0.658970	+	0.461416i
$683$	−109378.	+	109378.i	−0.234471	+	0.234471i	−0.814556	−	0.580085i	$-0.803019\pi$
$683$	−109378.	+	109378.i	−0.234471	+	0.234471i	0.580085	+	0.814556i	$0.303019\pi$
$684$	470162.	+	1.70718e6i	1.00493	+	3.64895i
$685$	−10640.7	−	21548.1i	−0.0226771	−	0.0459228i
$686$	85231.8	−	483374.i	0.181115	−	1.02715i
$687$	−10462.1	−	119582.i	−0.0221669	−	0.253369i
$688$	783405.	−	365308.i	1.65504	−	0.771760i
$689$	−175921.	−	483338.i	−0.370577	−	1.01815i
$690$	409012.	−	930896.i	0.859088	−	1.95525i
$691$	325154.	+	563183.i	0.680978	+	1.17949i	0.974683	+	0.223592i	$0.0717784\pi$
$691$	325154.	+	563183.i	0.680978	+	1.17949i	−0.293705	+	0.955896i	$0.594888\pi$
$692$	637131.	−	170719.i	1.33051	−	0.356508i
$693$	63469.0	+	44441.5i	0.132159	+	0.0925384i
$694$	−37262.4	+	6570.37i	−0.0773663	+	0.0136418i
$695$	−88987.4	−	101362.i	−0.184229	−	0.209847i
$696$	428780.	+	742669.i	0.885148	+	1.53312i
$697$	−691087.	−	60462.3i	−1.42255	−	0.124457i
$698$	−298844.	+	640874.i	−0.613387	+	1.31541i
$699$	297835.	−	818296.i	0.609567	−	1.67477i
$700$	262109.	+	166589.i	0.534916	+	0.339977i
$701$	58507.4	−	331812.i	0.119062	−	0.675236i	−0.865596	−	0.500743i	$-0.833060\pi$
$701$	58507.4	−	331812.i	0.119062	−	0.675236i	0.984658	−	0.174493i	$-0.0558288\pi$
$702$	1.18435e6	+	1.18435e6i	2.40328	+	2.40328i
$703$	349002.	+	124290.i	0.706184	+	0.251493i
$704$		−	133628.i		−	0.269620i
$705$	−253800.	+	463202.i	−0.510639	+	0.931950i
$706$	−1.06924e6	−	897195.i	−2.14518	−	1.80002i
$707$	−96670.2	−	207310.i	−0.193399	−	0.414745i
$708$	60100.0	−	128885.i	0.119897	−	0.257120i
$709$	−540475.	−	644112.i	−1.07518	−	1.28135i	−0.957541	−	0.288298i	$-0.906911\pi$
$709$	−540475.	−	644112.i	−1.07518	−	1.28135i	−0.117643	−	0.993056i	$-0.537534\pi$
$710$	−268917.	+	402927.i	−0.533459	+	0.799301i
$711$	−614283.	+	1.06397e6i	−1.21515	+	2.10470i
$712$	597368.	−	853131.i	1.17837	−	1.68289i
$713$	−521924.	−	365455.i	−1.02666	−	0.718877i
$714$	−560013.	−	323323.i	−1.09850	−	0.634221i
$715$	−147562.	−	98483.8i	−0.288644	−	0.192643i
$716$	449814.	−	377439.i	0.877419	−	0.736242i
$717$	1.27107e6	+	592708.i	2.47246	+	1.15293i
$718$	−833070.	+	388467.i	−1.61597	+	0.753538i
$719$	−163464.	+	194808.i	−0.316201	+	0.376834i	−0.900612	−	0.434624i	$-0.856881\pi$
$719$	−163464.	+	194808.i	−0.316201	+	0.376834i	0.584411	+	0.811458i	$0.301326\pi$
$720$	−857937.	−	470085.i	−1.65497	−	0.906800i
$721$	326170.			0.627442
$722$	−66185.9	+	900293.i	−0.126967	+	1.72707i
$723$	−823473.	+	823473.i	−1.57533	+	1.57533i
$724$	−628147.	−	110759.i	−1.19835	−	0.211302i
$725$	308672.	−	68776.5i	0.587248	−	0.130847i
$726$	−1.35362e6	−	492677.i	−2.56817	−	0.934736i
$727$	−346759.	−	161696.i	−0.656083	−	0.305937i	0.0659216	−	0.997825i	$-0.479001\pi$
$727$	−346759.	−	161696.i	−0.656083	−	0.305937i	−0.722005	+	0.691888i	$0.756779\pi$
$728$	−32717.9	+	373968.i	−0.0617338	+	0.705621i
$729$	−587009.	+	338910.i	−1.10456	+	0.637718i
$730$	711730.	−	624842.i	1.33558	−	1.17253i
$731$	230889.	+	1.30944e6i	0.432085	+	2.45047i
$732$	963146.	−	1.37552e6i	1.79750	−	2.56710i
$733$	−22793.9	−	85068.0i	−0.0424239	−	0.158328i	0.941464	−	0.337112i	$-0.109450\pi$
$733$	−22793.9	−	85068.0i	−0.0424239	−	0.158328i	−0.983888	+	0.178784i	$0.942784\pi$
$734$	−415228.	+	239732.i	−0.770716	+	0.444973i
$735$	756719.	+	332483.i	1.40075	+	0.615452i
$736$	1425.68	−	518.906i	0.00263188	−	0.000957928i
$737$	11995.0	+	25723.4i	0.0220834	+	0.0473579i
$738$	1.87071e6	−	163666.i	3.43473	−	0.300500i
$739$	−682163.	−	120284.i	−1.24911	−	0.220251i	−0.490291	−	0.871559i	$-0.663110\pi$
$739$	−682163.	−	120284.i	−1.24911	−	0.220251i	−0.758814	+	0.651308i	$0.774221\pi$
$740$	−735723.	+	363306.i	−1.34354	+	0.663452i
$741$	517319.	+	1.08958e6i	0.942154	+	1.98438i
$742$	−179356.	−	179356.i	−0.325767	−	0.325767i
$743$	181026.	+	258532.i	0.327916	+	0.468313i	0.948930	−	0.315487i	$-0.102168\pi$
$743$	181026.	+	258532.i	0.327916	+	0.468313i	−0.621014	+	0.783800i	$0.713279\pi$
$744$	−1.80982e6	+	2.15686e6i	−3.26957	+	3.89652i
$745$	−245450.	+	306159.i	−0.442233	+	0.551613i
$746$	−1.74237e6	+	634172.i	−3.13086	+	1.13954i
$747$	−1.20903e6	−	105776.i	−2.16668	−	0.189560i
$748$	−394226.	−	105633.i	−0.704599	−	0.188797i
$749$	272448.	+	157298.i	0.485646	+	0.280388i
$750$	−1.19509e6	+	1.14772e6i	−2.12460	+	2.04039i
$751$	−95991.2	−	544393.i	−0.170197	−	0.965234i	−0.943543	−	0.331250i	$-0.892530\pi$
$751$	−95991.2	−	544393.i	−0.170197	−	0.965234i	0.773346	−	0.633984i	$-0.218581\pi$
$752$	340108.	−	91131.6i	0.601424	−	0.161151i
$753$	−339987.	−	91099.2i	−0.599614	−	0.160666i
$754$	491690.	+	585973.i	0.864866	+	1.03071i
$755$	−209714.	+	4687.87i	−0.367902	+	0.00822397i
$756$	517335.	+	188295.i	0.905166	+	0.329453i
$757$	−81379.3	−	930170.i	−0.142011	−	1.62319i	−0.648686	−	0.761056i	$-0.724681\pi$
$757$	−81379.3	−	930170.i	−0.142011	−	1.62319i	0.506675	−	0.862137i	$-0.330875\pi$
$758$	47426.5	+	67732.1i	0.0825435	+	0.117884i
$759$			190914.i			0.331402i
$760$	−664369.	−	746241.i	−1.15022	−	1.29197i
$761$	187526.			0.323811			0.161906	−	0.986806i	$-0.448236\pi$
$761$	187526.			0.323811			0.161906	+	0.986806i	$0.448236\pi$
$762$	1.00928e6	−	706705.i	1.73821	−	1.21711i
$763$	39290.2	−	3437.45i	0.0674894	−	0.00590456i
$764$	586993.	−	1.61275e6i	1.00565	−	2.76300i
$765$	1.04003e6	−	1.08759e6i	1.77714	−	1.85841i
$766$	−863146.	+	724266.i	−1.47105	+	1.23436i
$767$	16406.3	−	61229.0i	0.0278881	−	0.104080i
$768$	−519055.	−	1.93714e6i	−0.880016	−	3.28426i
$769$	1.02789e6	−	181244.i	1.73817	−	0.306487i	0.787416	−	0.616422i	$-0.211419\pi$
$769$	1.02789e6	−	181244.i	1.73817	−	0.306487i	0.950758	+	0.309936i	$0.100307\pi$
$770$	−86474.6	−	13262.5i	−0.145850	−	0.0223689i
$771$	545454.	−	944754.i	0.917592	−	1.58932i
$772$	−290969.	+	1.08591e6i	−0.488216	+	1.82205i
$773$	−40716.3	+	465390.i	−0.0681412	+	0.778857i	0.882853	+	0.469649i	$0.155620\pi$
$773$	−40716.3	+	465390.i	−0.0681412	+	0.778857i	−0.950994	+	0.309208i	$0.899936\pi$
$774$	−1.23100e6	−	3.38215e6i	−2.05483	−	5.64560i
$775$	558812.	+	875098.i	0.930384	+	1.45698i
$776$	−468188.	−	392857.i	−0.777494	−	0.652395i
$777$	199956.	−	140011.i	0.331202	−	0.231910i
$778$	1.23973e6	−	1.23973e6i	2.04819	−	2.04819i
$779$	617489.	+	160870.i	1.01755	+	0.265095i
$780$	−2.53012e6	−	857354.i	−4.15864	−	1.40919i
$781$	15794.4	−	89574.6i	0.0258941	−	0.146853i
$782$	−90874.5	−	1.03870e6i	−0.148603	−	1.69854i
$783$	508070.	−	236917.i	0.828704	−	0.386431i
$784$	−188455.	−	517777.i	−0.306603	−	0.842385i
$785$	66568.6	+	29248.5i	0.108026	+	0.0474640i
$786$	428656.	+	742454.i	0.693847	+	1.20178i
$787$	1.06969e6	−	286622.i	1.72706	−	0.462765i	0.747558	−	0.664196i	$-0.231226\pi$
$787$	1.06969e6	−	286622.i	1.72706	−	0.462765i	0.979503	+	0.201432i	$0.0645595\pi$
$788$	−611077.	−	427880.i	−0.984109	−	0.689080i
$789$	633083.	−	111630.i	1.01697	−	0.179319i
$790$	89988.9	−	1.38428e6i	0.144190	−	2.21804i
$791$	−31451.4	−	54475.3i	−0.0502674	−	0.0870657i
$792$	549980.	+	48117.0i	0.876791	+	0.0767093i
$793$	316327.	−	678365.i	0.503025	−	1.07874i
$794$	−8535.21	+	23450.3i	−0.0135386	+	0.0371969i
$795$	770889.	−	468350.i	1.21971	−	0.741030i
$796$	−178018.	+	1.00959e6i	−0.280955	+	1.59338i
$797$	258826.	+	258826.i	0.407466	+	0.407466i	0.880854	−	0.473388i	$-0.156969\pi$
$797$	258826.	+	258826.i	0.407466	+	0.407466i	−0.473388	+	0.880854i	$0.656969\pi$
$798$	458283.	+	379155.i	0.719660	+	0.595403i
$799$			541621.i			0.848402i
$800$	−2470.15	−	105.209i	−0.00385961	−	0.000164390i
$801$	−1.10527e6	−	927435.i	−1.72268	−	1.44550i
$802$	469325.	+	1.00647e6i	0.729667	+	1.56478i
$803$	−75153.5	+	161167.i	−0.116552	+	0.249946i
$804$	274720.	+	327399.i	0.424990	+	0.506483i
$805$	−29141.2	−	146096.i	−0.0449693	−	0.225448i
$806$	−1.25574e6	+	2.17500e6i	−1.93298	+	3.34802i
$807$	−622900.	+	889594.i	−0.956470	+	1.36598i
$808$	−1.33510e6	−	934847.i	−2.04499	−	1.43192i
$809$	−986652.	−	569644.i	−1.50753	−	0.870375i	−0.999962	−	0.00876578i	$-0.997210\pi$
$809$	−986652.	−	569644.i	−1.50753	−	0.870375i	−0.507572	−	0.861609i	$-0.669457\pi$
$810$	−436285.	+	653702.i	−0.664968	+	0.996344i
$811$	455320.	−	382059.i	0.692269	−	0.580882i	−0.227294	−	0.973826i	$-0.572988\pi$
$811$	455320.	−	382059.i	0.692269	−	0.580882i	0.919562	+	0.392944i	$0.128543\pi$
$812$	227872.	+	106259.i	0.345605	+	0.161158i
$813$	543100.	−	253252.i	0.821672	−	0.383152i
$814$	148575.	−	177064.i	0.224231	−	0.267228i
$815$	9489.66	+	32493.0i	0.0142868	+	0.0489187i
$816$	−1.53300e6			−2.30230
$817$	−8489.25	−	1.22299e6i	−0.0127182	−	1.83223i
$818$	−784874.	+	784874.i	−1.17299	+	1.17299i
$819$	512161.	+	90307.8i	0.763552	+	0.134635i
$820$	−1.20784e6	+	733818.i	−1.79631	+	1.09134i
$821$	504684.	+	183690.i	0.748744	+	0.272520i	0.688077	−	0.725638i	$-0.258455\pi$
$821$	504684.	+	183690.i	0.748744	+	0.272520i	0.0606667	+	0.998158i	$0.480677\pi$
$822$	92388.9	+	43081.6i	0.136734	+	0.0637600i
$823$	−25279.1	+	288941.i	−0.0373217	+	0.426589i	0.954432	+	0.298429i	$0.0964627\pi$
$823$	−25279.1	+	288941.i	−0.0373217	+	0.426589i	−0.991753	+	0.128160i	$0.959093\pi$
$824$	2.01271e6	−	1.16204e6i	2.96432	−	1.71145i
$825$	118751.	−	287558.i	0.174474	−	0.422491i
$826$	−5428.10	−	30784.3i	−0.00795587	−	0.0451200i
$827$	−422504.	+	603398.i	−0.617760	+	0.882252i	−0.999110	−	0.0421782i	$-0.986570\pi$
$827$	−422504.	+	603398.i	−0.617760	+	0.882252i	0.381350	+	0.924431i	$0.375459\pi$
$828$	486904.	+	1.81715e6i	0.710204	+	2.65052i
$829$	216409.	−	124944.i	0.314896	−	0.181805i	−0.334219	−	0.942495i	$-0.608473\pi$
$829$	216409.	−	124944.i	0.314896	−	0.181805i	0.649115	+	0.760690i	$0.275139\pi$
$830$	1.27691e6	−	497347.i	1.85355	−	0.721944i
$831$	393418.	−	143192.i	0.569707	−	0.207357i
$832$	−379056.	−	812888.i	−0.547591	−	1.17431i
$833$	844353.	−	73871.3i	1.21684	−	0.106460i
$834$	563448.	+	99351.0i	0.810068	+	0.142837i
$835$	49776.9	+	100802.i	0.0713929	+	0.144576i
$836$	341327.	+	156288.i	0.488381	+	0.223622i
$837$	1.30148e6	+	1.30148e6i	1.85774	+	1.85774i
$838$	−532350.	−	760275.i	−0.758070	−	1.08264i
$839$	398540.	−	474961.i	0.566171	−	0.674737i	−0.404669	−	0.914463i	$-0.632613\pi$
$839$	398540.	−	474961.i	0.566171	−	0.674737i	0.970840	+	0.239726i	$0.0770577\pi$
$840$	−654366.	+	72018.0i	−0.927390	+	0.102066i
$841$	−424045.	+	154340.i	−0.599542	+	0.218215i
$842$	−1.20829e6	−	105712.i	−1.70431	−	0.149108i
$843$	233442.	+	62550.6i	0.328491	+	0.0880189i
$844$	1.85806e6	+	1.07275e6i	2.60840	+	1.50596i
$845$	−471243.	−	72274.0i	−0.659981	−	0.101220i
$846$	−254588.	−	1.44384e6i	−0.355711	−	2.01734i
$847$	−203861.	+	54624.3i	−0.284162	+	0.0761411i
$848$	−580829.	−	155633.i	−0.807711	−	0.216426i
$849$	−123276.	−	146914.i	−0.171026	−	0.203821i
$850$	−509209.	+	1.62103e6i	−0.704788	+	2.24364i
$851$	369858.	+	134617.i	0.510712	+	0.185884i
$852$	−119371.	−	1.36442e6i	−0.164445	−	1.87962i
$853$	606287.	+	865868.i	0.833260	+	1.19002i	0.979635	+	0.200789i	$0.0643506\pi$
$853$	606287.	+	865868.i	0.833260	+	1.19002i	−0.146375	+	0.989229i	$0.546761\pi$
$854$		−	369107.i		−	0.506100i
$855$	−1.11010e6	+	826790.i	−1.51856	+	1.13100i
$856$	2.24160e6			3.05922
$857$	3543.64	−	2481.28i	0.00482490	−	0.00337843i	−0.571162	−	0.820838i	$-0.693507\pi$
$857$	3543.64	−	2481.28i	0.00482490	−	0.00337843i	0.575986	+	0.817459i	$0.304618\pi$
$858$	749666.	−	65587.3i	1.01834	−	0.0890933i
$859$	126982.	−	348880.i	0.172090	−	0.472814i	−0.823424	−	0.567426i	$-0.807939\pi$
$859$	126982.	−	348880.i	0.172090	−	0.472814i	0.995514	+	0.0946129i	$0.0301613\pi$
$860$	1.95773e6	+	1.87211e6i	2.64701	+	2.53125i
$861$	322074.	−	270253.i	0.434460	−	0.364555i
$862$	−495533.	+	1.84935e6i	−0.666896	+	2.48889i
$863$	−52640.7	−	196458.i	−0.0706806	−	0.263784i	0.921539	−	0.388287i	$-0.126933\pi$
$863$	−52640.7	−	196458.i	−0.0706806	−	0.263784i	−0.992219	+	0.124503i	$0.960266\pi$
$864$	−4316.16	+	761.055i	−0.00578189	+	0.00101950i
$865$	305104.	+	415644.i	0.407771	+	0.555507i
$866$	281538.	−	487637.i	0.375405	−	0.650221i
$867$	279389.	−	1.04269e6i	0.371682	−	1.38713i
$868$	−71947.6	+	822364.i	−0.0954941	+	1.09150i
$869$	89083.6	+	244755.i	0.117966	+	0.324110i
$870$	−839077.	+	1.04661e6i	−1.10857	+	1.38276i
$871$	145937.	+	122455.i	0.192366	+	0.161414i
$872$	230202.	−	161189.i	0.302745	−	0.211984i
$873$	−598710.	+	598710.i	−0.785576	+	0.785576i
$874$	−76954.0	+	955970.i	−0.100742	+	1.25147i
$875$	−46980.5	+	238178.i	−0.0613623	+	0.311089i
$876$	−464988.	+	2.63708e6i	−0.605946	+	3.43649i
$877$	4624.52	+	52858.5i	0.00601267	+	0.0687252i	0.998608	−	0.0527413i	$-0.0167959\pi$
$877$	4624.52	+	52858.5i	0.00601267	+	0.0687252i	−0.992596	+	0.121466i	$0.961240\pi$
$878$	96131.4	−	44826.8i	0.124703	−	0.0581499i
$879$	−131937.	−	362493.i	−0.170761	−	0.469161i
$880$	−193260.	+	75273.2i	−0.249560	+	0.0972020i
$881$	−392676.	−	680135.i	−0.505921	−	0.876281i	−0.999977	−	0.00685049i	$-0.997819\pi$
$881$	−392676.	−	680135.i	−0.505921	−	0.876281i	0.494056	−	0.869430i	$-0.335514\pi$
$882$	−2.21614e6	+	593812.i	−2.84878	+	0.763329i
$883$	−819168.	−	573588.i	−1.05063	−	0.735662i	−0.0852148	−	0.996363i	$-0.527158\pi$
$883$	−819168.	−	573588.i	−1.05063	−	0.735662i	−0.965420	+	0.260700i	$0.916047\pi$
$884$	−2.69781e6	+	475696.i	−3.45228	+	0.608731i
$885$	110929.	+	7211.23i	0.141630	+	0.00920709i
$886$	1.15482e6	+	2.00021e6i	1.47112	+	2.54805i
$887$	−864156.	−	75603.9i	−1.09836	−	0.0960941i	−0.476465	−	0.879194i	$-0.658082\pi$
$887$	−864156.	−	75603.9i	−1.09836	−	0.0960941i	−0.621896	+	0.783100i	$0.713638\pi$
$888$	735062.	−	1.57635e6i	0.932176	−	1.99906i
$889$	61741.5	−	169633.i	0.0781221	−	0.214639i
$890$	1.58265e6	+	386377.i	1.99804	+	0.487789i
$891$	25624.6	−	145324.i	0.0322776	−	0.183055i
$892$	1.33835e6	+	1.33835e6i	1.68205	+	1.68205i
$893$	83102.3	−	491211.i	0.104210	−	0.615978i
$894$		−	1.66449e6i		−	2.08260i
$895$	402534.	+	220559.i	0.502524	+	0.275346i
$896$	−338070.	−	283674.i	−0.421105	−	0.353349i
$897$	541557.	+	1.16137e6i	0.673069	+	1.44340i
$898$	261770.	−	561367.i	0.324613	−	0.696136i
$899$	540318.	+	643925.i	0.668544	+	0.796739i
$900$	396910.	−	3.03988e6i	0.490012	−	3.75294i
$901$	462484.	−	801046.i	0.569701	−	0.986752i
$902$	228350.	−	326117.i	0.280664	−	0.400830i
$903$	−660103.	−	462209.i	−0.809536	−	0.566843i
$904$	−388155.	−	224101.i	−0.474972	−	0.274225i
$905$	−97530.6	−	488957.i	−0.119081	−	0.596998i
$906$	681616.	−	571944.i	0.830392	−	0.696782i
$907$	1.22973e6	+	573433.i	1.49484	+	0.697057i	0.986449	−	0.164067i	$-0.0524614\pi$
$907$	1.22973e6	+	573433.i	1.49484	+	0.697057i	0.508395	+	0.861124i	$0.330239\pi$
$908$	−1.84227e6	+	859063.i	−2.23450	+	1.04197i
$909$	−1.45138e6	+	1.72969e6i	−1.75652	+	2.09334i
$910$	−563665.	+	164620.i	−0.680673	+	0.198792i
$911$	−621933.			−0.749389			−0.374694	−	0.927148i	$-0.622252\pi$
$911$	−621933.			−0.749389			−0.374694	+	0.927148i	$0.622252\pi$
$912$	1.39032e6	+	235212.i	1.67157	+	0.282794i
$913$	−181938.	+	181938.i	−0.218264	+	0.218264i
$914$	−772094.	−	136141.i	−0.924225	−	0.162966i
$915$	1.27515e6	+	311307.i	1.52307	+	0.371832i
$916$	−235648.	−	85769.0i	−0.280850	−	0.102221i
$917$	113840.	+	53084.3i	0.135380	+	0.0631288i
$918$	−262513.	+	3.00054e6i	−0.311506	+	3.56052i
$919$	964562.	−	556890.i	1.14209	−	0.659384i	0.195140	−	0.980775i	$-0.437484\pi$
$919$	964562.	−	556890.i	1.14209	−	0.659384i	0.946946	+	0.321391i	$0.104150\pi$
$920$	−700312.	−	797695.i	−0.827401	−	0.942456i
$921$	−174238.	−	988155.i	−0.205411	−	1.16495i
$922$	−238928.	+	341225.i	−0.281065	+	0.401402i
$923$	−158011.	−	589705.i	−0.185474	−	0.692200i
$924$	214213.	−	123676.i	0.250901	−	0.144858i
$925$	−473353.	−	432820.i	−0.553225	−	0.505852i
$926$	1.27180e6	−	462896.i	1.48319	−	0.539836i
$927$	−1.36070e6	−	2.91803e6i	−1.58345	−	3.39571i
$928$	−1993.98	+	174.450i	−0.00231539	+	0.000202570i
$929$	278642.	+	49132.2i	0.322861	+	0.0569291i	0.332730	−	0.943022i	$-0.392030\pi$
$929$	278642.	+	49132.2i	0.322861	+	0.0569291i	−0.00986883	+	0.999951i	$0.503141\pi$
$930$	−4.17129e6	−	1.41348e6i	−4.82285	−	1.63427i
$931$	−777101.	−	62555.4i	−0.896558	−	0.0721715i
$932$	−1.28637e6	−	1.28637e6i	−1.48093	−	1.48093i
$933$	183783.	+	262469.i	0.211126	+	0.301519i
$934$	−73638.5	+	87758.9i	−0.0844133	+	0.100600i
$935$	−34901.1	−	317117.i	−0.0399224	−	0.362741i
$936$	3.48214e6	−	1.26739e6i	3.97461	−	1.44664i
$937$	1.39851e6	+	122354.i	1.59289	+	0.139360i	0.848799	−	0.528716i	$-0.177326\pi$
$937$	1.39851e6	+	122354.i	1.59289	+	0.139360i	0.744093	+	0.668076i	$0.232882\pi$
$938$	90744.0	+	24314.8i	0.103136	+	0.0276353i
$939$	780873.	+	450837.i	0.885624	+	0.511315i
$940$	652930.	+	889489.i	0.738943	+	1.00667i
$941$	221211.	+	1.25455e6i	0.249820	+	1.41680i	0.809027	+	0.587772i	$0.199995\pi$
$941$	221211.	+	1.25455e6i	0.249820	+	1.41680i	−0.559207	+	0.829028i	$0.688894\pi$
$942$	−297915.	+	79826.2i	−0.335731	+	0.0899588i
$943$	654825.	+	175460.i	0.736380	+	0.197312i
$944$	−47634.3	−	56768.3i	−0.0534534	−	0.0637033i
$945$	9617.42	+	430239.i	0.0107695	+	0.481777i
$946$	−717034.	−	260979.i	−0.801230	−	0.291624i
$947$	5521.41	+	63110.0i	0.00615673	+	0.0703718i	0.998651	−	0.0519155i	$-0.0165326\pi$
$947$	5521.41	+	63110.0i	0.00615673	+	0.0703718i	−0.992495	+	0.122287i	$0.960977\pi$
$948$	2.24962e6	+	3.21279e6i	2.50318	+	3.57491i
$949$			1.19360e6i			1.32534i
$950$	710536.	−	1.39203e6i	0.787297	−	1.54242i
$951$	−399801.			−0.442061
$952$	−552988.	+	387206.i	−0.610157	+	0.427237i
$953$	−395436.	+	34596.2i	−0.435402	+	0.0380928i	−0.302750	−	0.953070i	$-0.597905\pi$
$953$	−395436.	+	34596.2i	−0.435402	+	0.0380928i	−0.132652	+	0.991163i	$0.542349\pi$
$954$	−856351.	+	2.35280e6i	−0.940925	+	2.58517i
$955$	1.34124e6	−	29981.5i	1.47061	−	0.0328736i
$956$	2.24441e6	−	1.88329e6i	2.45577	−	2.06063i
$957$	65188.9	−	243288.i	0.0711786	−	0.265642i
$958$	47416.2	+	176960.i	0.0516649	+	0.192816i
$959$	14708.7	−	2593.54i	0.0159933	−	0.00282004i
$960$	1.26796e6	−	930746.i	1.37582	−	1.00992i
$961$	−918165.	+	1.59031e6i	−0.994200	+	1.72201i
$962$	401542.	−	1.49858e6i	0.433892	−	1.61931i
$963$	270657.	−	3.09362e6i	0.291854	−	3.33591i
$964$	832095.	+	2.28616e6i	0.895403	+	2.46010i
$965$	−873510.	+	96136.4i	−0.938023	+	0.103237i
$966$	484077.	+	406188.i	0.518752	+	0.435285i
$967$	−443134.	+	310286.i	−0.473895	+	0.331825i	−0.786004	−	0.618221i	$-0.787854\pi$
$967$	−443134.	+	310286.i	−0.473895	+	0.331825i	0.312109	+	0.950046i	$0.398965\pi$
$968$	−1.06336e6	+	1.06336e6i	−1.13483	+	1.13483i
$969$	−903003.	+	1.97212e6i	−0.961704	+	2.10032i
$970$	306823.	−	905457.i	0.326095	−	0.962331i
$971$	−850.920	+	4825.81i	−0.000902507	+	0.00511837i	−0.985256	−	0.171088i	$-0.945272\pi$
$971$	−850.920	+	4825.81i	−0.000902507	+	0.00511837i	0.984353	+	0.176207i	$0.0563827\pi$
$972$	56482.2	+	645595.i	0.0597832	+	0.683326i
$973$	75972.6	−	35426.6i	0.0802474	−	0.0374200i
$974$	−86921.3	−	238814.i	−0.0916238	−	0.251734i
$975$	−93312.1	−	2.08613e6i	−0.0981587	−	2.19449i
$976$	−437519.	−	757804.i	−0.459300	−	0.795532i
$977$	−1.46702e6	+	393087.i	−1.53691	+	0.411813i	−0.925265	−	0.379321i	$-0.876157\pi$
$977$	−1.46702e6	+	393087.i	−1.53691	+	0.411813i	−0.611642	+	0.791134i	$0.709491\pi$
$978$	−117620.	−	82358.1i	−0.122971	−	0.0861050i
$979$	−301242.	+	53117.0i	−0.314304	+	0.0554202i
$980$	1.29761e6	−	1.13919e6i	1.35111	−	1.18617i
$981$	−194662.	−	337164.i	−0.202275	−	0.350351i
$982$	1.42902e6	+	125023.i	1.48189	+	0.129649i
$983$	−24215.6	+	51930.5i	−0.0250604	+	0.0537422i	−0.918440	−	0.395561i	$-0.870550\pi$
$983$	−24215.6	+	51930.5i	−0.0250604	+	0.0537422i	0.893379	+	0.449304i	$0.148328\pi$
$984$	1.02461e6	−	2.81510e6i	1.05820	−	2.90739i
$985$	138299.	−	566490.i	0.142543	−	0.583875i
$986$	−238867.	+	1.35468e6i	−0.245698	+	1.39342i
$987$	−232110.	−	232110.i	−0.238265	−	0.238265i
$988$	2.51970e6	−	17490.2i	2.58128	−	0.0179177i
$989$		−	1.29935e6i		−	1.32841i
$990$	242100.	+	828960.i	0.247015	+	0.845791i
$991$	−355511.	−	298310.i	−0.361998	−	0.303752i	0.443588	−	0.896231i	$-0.353705\pi$
$991$	−355511.	−	298310.i	−0.361998	−	0.303752i	−0.805587	+	0.592478i	$0.798150\pi$
$992$	−2777.33	−	5956.01i	−0.00282231	−	0.00605246i
$993$	−426574.	+	914792.i	−0.432610	+	0.927735i
$994$	−193519.	−	230627.i	−0.195862	−	0.233419i
$995$	−785874.	+	156756.i	−0.793792	+	0.158335i
$996$	−1.93722e6	+	3.35537e6i	−1.95281	+	3.38237i
$997$	175535.	−	250690.i	0.176593	−	0.252201i	−0.721091	−	0.692840i	$-0.756359\pi$
$997$	175535.	−	250690.i	0.176593	−	0.252201i	0.897685	+	0.440639i	$0.145248\pi$
$998$	1.83781e6	+	1.28685e6i	1.84518	+	1.29201i
$999$	−984667.	−	568498.i	−0.986639	−	0.569636i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	95.5.q.a.17.4	✓	456
5.3	odd	4	inner	95.5.q.a.93.35	yes	456
19.9	even	9	inner	95.5.q.a.47.35	yes	456
95.28	odd	36	inner	95.5.q.a.28.4	yes	456

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.5.q.a.17.4	✓	456	1.1	even	1	trivial
95.5.q.a.28.4	yes	456	95.28	odd	36	inner
95.5.q.a.47.35	yes	456	19.9	even	9	inner
95.5.q.a.93.35	yes	456	5.3	odd	4	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:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	95.q (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.67420 + 3.97311i) q^{2} +(15.2509 - 1.33428i) q^{3} +(10.9385 - 30.0534i) q^{4} +(24.9938 - 0.558702i) q^{5} +(-81.2353 + 68.1645i) q^{6} +(-4.02130 + 15.0077i) q^{7} +(28.6531 + 106.935i) q^{8} +(151.040 - 26.6324i) q^{9} +(-139.600 + 102.473i) q^{10} +(16.2576 - 28.1591i) q^{11} +(126.723 - 472.936i) q^{12} +(19.0214 - 217.415i) q^{13} +(-36.8096 - 101.134i) q^{14} +(380.431 - 41.8694i) q^{15} +(-195.451 - 164.003i) q^{16} +(321.493 - 225.112i) q^{17} +(-751.216 + 751.216i) q^{18} +(-326.110 + 154.833i) q^{19} +(256.604 - 757.258i) q^{20} +(-41.3039 + 234.246i) q^{21} +(19.6301 + 224.373i) q^{22} +(-347.596 + 162.087i) q^{23} +(579.665 + 1592.62i) q^{24} +(624.376 - 27.9281i) q^{25} +(755.884 + 1309.23i) q^{26} +(1070.17 - 286.751i) q^{27} +(407.044 + 285.016i) q^{28} +(498.299 - 87.8636i) q^{29} +(-1992.29 + 1749.07i) q^{30} +(830.640 + 1438.71i) q^{31} +(-3.94077 - 0.344773i) q^{32} +(210.371 - 451.143i) q^{33} +(-929.818 + 2554.66i) q^{34} +(-92.1225 + 377.345i) q^{35} +(851.761 - 4830.58i) q^{36} +(-725.663 - 725.663i) q^{37} +(1235.25 - 2174.22i) q^{38} -3341.15i q^{39} +(775.892 + 2656.69i) q^{40} +(-1354.05 - 1136.19i) q^{41} +(-696.320 - 1493.26i) q^{42} +(-1431.78 + 3070.45i) q^{43} +(-668.440 - 796.616i) q^{44} +(3760.17 - 750.030i) q^{45} +(1328.34 - 2300.75i) q^{46} +(-791.553 + 1130.45i) q^{47} +(-3199.63 - 2240.40i) q^{48} +(1870.27 + 1079.80i) q^{49} +(-3431.87 + 2639.19i) q^{50} +(4602.69 - 3862.11i) q^{51} +(-6325.99 - 2949.86i) q^{52} +(2135.97 - 996.021i) q^{53} +(-4933.06 + 5878.99i) q^{54} +(390.607 - 712.884i) q^{55} -1720.06 q^{56} +(-4766.88 + 2796.46i) q^{57} +(-2478.36 + 2478.36i) q^{58} +(286.035 + 50.4357i) q^{59} +(2903.05 - 11891.2i) q^{60} +(3222.76 + 1172.99i) q^{61} +(-10429.4 - 4863.30i) q^{62} +(-207.685 + 2373.85i) q^{63} +(3559.10 - 2054.85i) q^{64} +(353.945 - 5444.65i) q^{65} +(598.754 + 3395.70i) q^{66} +(-500.675 + 715.038i) q^{67} +(-3248.71 - 12124.3i) q^{68} +(-5084.89 + 2935.76i) q^{69} +(-976.514 - 2507.14i) q^{70} +(2628.64 - 956.748i) q^{71} +(7175.68 + 15388.3i) q^{72} +(-5448.26 + 476.661i) q^{73} +(7000.70 + 1234.41i) q^{74} +(9485.02 - 1259.02i) q^{75} +(1086.07 + 11494.4i) q^{76} +(357.225 + 357.225i) q^{77} +(13274.8 + 18958.4i) q^{78} +(-5149.04 + 6136.39i) q^{79} +(-4976.68 - 3989.85i) q^{80} +(4264.66 - 1552.21i) q^{81} +(12197.4 + 1067.13i) q^{82} +(-7643.55 - 2048.08i) q^{83} +(6588.08 + 3803.63i) q^{84} +(7909.54 - 5806.00i) q^{85} +(-4075.09 - 23111.0i) q^{86} +(7482.27 - 2004.87i) q^{87} +(3477.01 + 931.662i) q^{88} +(-6047.05 - 7206.60i) q^{89} +(-18356.0 + 19195.4i) q^{90} +(3186.40 + 1159.76i) q^{91} +(1069.06 + 12219.4i) q^{92} +(14587.6 + 20833.3i) q^{93} -9559.35i q^{94} +(-8064.21 + 4052.04i) q^{95} -60.5603 q^{96} +(-4522.27 + 3166.53i) q^{97} +(-14902.4 + 1303.79i) q^{98} +(1705.61 - 4686.12i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 456 q - 12 q^{2} - 12 q^{3} - 12 q^{5} + 84 q^{6} - 96 q^{7} - 6 q^{8} - 12 q^{10} - 12 q^{11} - 6 q^{12} - 12 q^{13} - 534 q^{15} + 4092 q^{16} - 1362 q^{17} - 3864 q^{18} - 2364 q^{20} - 4776 q^{21} + 2004 q^{22}+ \cdots + 123726 q^{98}+O(q^{100}) \) 456 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 + 84 * q^6 - 96 * q^7 - 6 * q^8 - 12 * q^10 - 12 * q^11 - 6 * q^12 - 12 * q^13 - 534 * q^15 + 4092 * q^16 - 1362 * q^17 - 3864 * q^18 - 2364 * q^20 - 4776 * q^21 + 2004 * q^22 + 1968 * q^23 + 3252 * q^25 + 7332 * q^26 - 6 * q^27 - 9648 * q^28 - 6 * q^30 - 12 * q^31 + 5922 * q^32 + 16494 * q^33 - 1794 * q^35 + 9048 * q^36 - 24 * q^37 - 15222 * q^38 - 9786 * q^40 - 5640 * q^41 + 7764 * q^42 - 19032 * q^43 - 6144 * q^45 - 12 * q^46 - 4332 * q^47 + 29328 * q^48 + 18426 * q^50 - 10944 * q^51 + 84 * q^52 + 1878 * q^53 + 27018 * q^55 - 48 * q^56 - 14202 * q^57 + 16536 * q^58 - 84108 * q^60 - 14688 * q^61 - 46536 * q^62 - 46098 * q^63 - 13236 * q^65 + 42408 * q^66 + 44748 * q^67 + 20154 * q^68 + 37620 * q^70 - 24 * q^71 + 82680 * q^72 - 10542 * q^73 + 90024 * q^75 - 21600 * q^76 + 20328 * q^77 + 63426 * q^78 - 32688 * q^80 + 41976 * q^81 - 184332 * q^82 - 43476 * q^83 - 51396 * q^85 + 11316 * q^86 - 59286 * q^87 - 1254 * q^88 - 9294 * q^90 - 33312 * q^91 + 163884 * q^92 - 106566 * q^93 - 11424 * q^95 - 200208 * q^96 + 12168 * q^97 + 123726 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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