LMFDB - Embedded newform 95.5.q.a.28.2

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			28.2
Character	$\chi$	$=$	95.28
Dual form			95.5.q.a.17.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-6.07197 - 4.25164i) q^{2} +(-0.946507 - 0.0828086i) q^{3} +(13.3201 + 36.5966i) q^{4} +(2.51310 + 24.8734i) q^{5} +(5.39509 + 4.52702i) q^{6} +(19.4176 + 72.4674i) q^{7} +(44.0206 - 164.287i) q^{8} +(-78.8804 - 13.9087i) q^{9} +(90.4932 - 161.715i) q^{10} +(-65.5179 - 113.480i) q^{11} +(-9.57704 - 35.7420i) q^{12} +(8.15917 + 93.2598i) q^{13} +(190.202 - 522.576i) q^{14} +(-0.318941 - 23.7509i) q^{15} +(-488.440 + 409.850i) q^{16} +(-134.575 - 94.2306i) q^{17} +(419.825 + 419.825i) q^{18} +(57.2339 - 356.434i) q^{19} +(-876.807 + 423.287i) q^{20} +(-12.3779 - 70.1988i) q^{21} +(-84.6548 + 967.609i) q^{22} +(242.486 + 113.073i) q^{23} +(-55.2702 + 151.854i) q^{24} +(-612.369 + 125.019i) q^{25} +(346.965 - 600.961i) q^{26} +(147.847 + 39.6154i) q^{27} +(-2393.42 + 1675.89i) q^{28} +(-980.177 - 172.832i) q^{29} +(-99.0438 + 145.571i) q^{30} +(14.0593 - 24.3514i) q^{31} +(1997.37 - 174.747i) q^{32} +(52.6160 + 112.835i) q^{33} +(416.503 + 1144.33i) q^{34} +(-1753.71 + 665.098i) q^{35} +(-541.681 - 3072.02i) q^{36} +(106.529 - 106.529i) q^{37} +(-1862.95 + 1920.92i) q^{38} -88.9467i q^{39} +(4197.00 + 682.070i) q^{40} +(2177.88 - 1827.46i) q^{41} +(-223.302 + 478.872i) q^{42} +(-567.889 - 1217.84i) q^{43} +(3280.30 - 3909.30i) q^{44} +(147.723 - 1996.98i) q^{45} +(-991.623 - 1717.54i) q^{46} +(-1043.35 - 1490.05i) q^{47} +(496.252 - 347.479i) q^{48} +(-2795.15 + 1613.78i) q^{49} +(4249.82 + 1844.46i) q^{50} +(119.573 + 100.334i) q^{51} +(-3304.31 + 1540.83i) q^{52} +(2173.48 + 1013.51i) q^{53} +(-729.291 - 869.135i) q^{54} +(2657.99 - 1914.84i) q^{55} +12760.2 q^{56} +(-83.6881 + 332.628i) q^{57} +(5216.79 + 5216.79i) q^{58} +(-6460.67 + 1139.19i) q^{59} +(864.956 - 328.037i) q^{60} +(-5624.43 + 2047.12i) q^{61} +(-188.901 + 88.0860i) q^{62} +(-523.736 - 5986.33i) q^{63} +(-4035.90 - 2330.13i) q^{64} +(-2299.18 + 437.317i) q^{65} +(160.253 - 908.838i) q^{66} +(2806.46 + 4008.05i) q^{67} +(1655.97 - 6180.16i) q^{68} +(-220.151 - 127.104i) q^{69} +(13476.2 + 3417.68i) q^{70} +(-2002.19 - 728.737i) q^{71} +(-5757.39 + 12346.8i) q^{72} +(-10178.3 - 890.482i) q^{73} +(-1099.76 + 193.918i) q^{74} +(589.964 - 67.6217i) q^{75} +(13806.7 - 2653.16i) q^{76} +(6951.42 - 6951.42i) q^{77} +(-378.169 + 540.082i) q^{78} +(-2857.18 - 3405.05i) q^{79} +(-11421.9 - 11119.2i) q^{80} +(5959.95 + 2169.25i) q^{81} +(-20993.7 + 1836.71i) q^{82} +(2735.12 - 732.872i) q^{83} +(2404.17 - 1388.05i) q^{84} +(2005.63 - 3584.15i) q^{85} +(-1729.62 + 9809.16i) q^{86} +(913.433 + 244.754i) q^{87} +(-21527.5 + 5768.28i) q^{88} +(2825.45 - 3367.24i) q^{89} +(-9387.39 + 11497.5i) q^{90} +(-6599.86 + 2402.15i) q^{91} +(-908.161 + 10380.3i) q^{92} +(-15.3237 + 21.8845i) q^{93} +13483.5i q^{94} +(9009.55 + 527.845i) q^{95} -1904.99 q^{96} +(-732.295 - 512.759i) q^{97} +(23833.3 + 2085.14i) q^{98} +(3589.71 + 9862.65i) 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 $\left(\mathbb{Z}/95\mathbb{Z}\right)^\times$.

$n$	$21$	$77$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−6.07197	−	4.25164i	−1.51799	−	1.06291i	−0.974740	−	0.223342i	$-0.928303\pi$
$2$	−6.07197	−	4.25164i	−1.51799	−	1.06291i	−0.543253	−	0.839569i	$-0.682808\pi$
$3$	−0.946507	−	0.0828086i	−0.105167	−	0.00920096i	0.0344505	−	0.999406i	$-0.489032\pi$
$3$	−0.946507	−	0.0828086i	−0.105167	−	0.00920096i	−0.139618	+	0.990205i	$0.544587\pi$
$4$	13.3201	+	36.5966i	0.832506	+	2.28729i
$5$	2.51310	+	24.8734i	0.100524	+	0.994935i
$5$	2.51310	+	24.8734i	0.100524	+	0.994935i
$6$	5.39509	+	4.52702i	0.149864	+	0.125751i
$7$	19.4176	+	72.4674i	0.396277	+	1.47893i	0.819594	+	0.572944i	$0.194199\pi$
$7$	19.4176	+	72.4674i	0.396277	+	1.47893i	−0.423317	+	0.905981i	$0.639135\pi$
$8$	44.0206	−	164.287i	0.687822	−	2.56699i
$9$	−78.8804	−	13.9087i	−0.973832	−	0.171713i
$10$	90.4932	−	161.715i	0.904932	−	1.61715i
$11$	−65.5179	−	113.480i	−0.541470	−	0.937854i	−0.998820	−	0.0485672i	$-0.984534\pi$
$11$	−65.5179	−	113.480i	−0.541470	−	0.937854i	0.457350	−	0.889287i	$-0.348799\pi$
$12$	−9.57704	−	35.7420i	−0.0665072	−	0.248208i
$13$	8.15917	+	93.2598i	0.0482791	+	0.551833i	0.981362	+	0.192170i	$0.0615526\pi$
$13$	8.15917	+	93.2598i	0.0482791	+	0.551833i	−0.933082	+	0.359662i	$0.882892\pi$
$14$	190.202	−	522.576i	0.970420	−	2.66621i
$15$	−0.318941	−	23.7509i	−0.00141751	−	0.105560i
$16$	−488.440	+	409.850i	−1.90797	+	1.60098i
$17$	−134.575	−	94.2306i	−0.465658	−	0.326057i	0.317091	−	0.948395i	$-0.397294\pi$
$17$	−134.575	−	94.2306i	−0.465658	−	0.326057i	−0.782749	+	0.622338i	$0.786183\pi$
$18$	419.825	+	419.825i	1.29576	+	1.29576i
$19$	57.2339	−	356.434i	0.158543	−	0.987352i
$19$	57.2339	−	356.434i	0.158543	−	0.987352i
$20$	−876.807	+	423.287i	−2.19202	+	1.05822i
$21$	−12.3779	−	70.1988i	−0.0280679	−	0.159181i
$22$	−84.6548	+	967.609i	−0.174907	+	1.99919i
$23$	242.486	+	113.073i	0.458386	+	0.213749i	0.638074	−	0.769975i	$-0.279731\pi$
$23$	242.486	+	113.073i	0.458386	+	0.213749i	−0.179689	+	0.983724i	$0.557509\pi$
$24$	−55.2702	+	151.854i	−0.0959552	+	0.263635i
$25$	−612.369	+	125.019i	−0.979790	+	0.200030i
$26$	346.965	−	600.961i	0.513262	−	0.888995i
$27$	147.847	+	39.6154i	0.202808	+	0.0543421i
$28$	−2393.42	+	1675.89i	−3.05283	+	2.13761i
$29$	−980.177	−	172.832i	−1.16549	−	0.205507i	−0.442762	−	0.896639i	$-0.646001\pi$
$29$	−980.177	−	172.832i	−1.16549	−	0.205507i	−0.722729	+	0.691132i	$0.757112\pi$
$30$	−99.0438	+	145.571i	−0.110049	+	0.161746i
$31$	14.0593	−	24.3514i	0.0146298	−	0.0253396i	−0.858618	−	0.512616i	$-0.828676\pi$
$31$	14.0593	−	24.3514i	0.0146298	−	0.0253396i	0.873248	+	0.487277i	$0.162010\pi$
$32$	1997.37	−	174.747i	1.95056	−	0.170652i
$33$	52.6160	+	112.835i	0.0483159	+	0.103614i
$34$	416.503	+	1144.33i	0.360296	+	0.989906i
$35$	−1753.71	+	665.098i	−1.43160	+	0.542937i
$36$	−541.681	−	3072.02i	−0.417964	−	2.37039i
$37$	106.529	−	106.529i	0.0778150	−	0.0778150i	−0.667128	−	0.744943i	$-0.732477\pi$
$37$	106.529	−	106.529i	0.0778150	−	0.0778150i	0.744943	+	0.667128i	$0.232477\pi$
$38$	−1862.95	+	1920.92i	−1.29013	+	1.33028i
$39$		−	88.9467i		−	0.0584791i
$40$	4197.00	+	682.070i	2.62313	+	0.426294i
$41$	2177.88	−	1827.46i	1.29558	−	1.08712i	0.304694	−	0.952450i	$-0.401446\pi$
$41$	2177.88	−	1827.46i	1.29558	−	1.08712i	0.990890	−	0.134673i	$-0.0429985\pi$
$42$	−223.302	+	478.872i	−0.126588	+	0.271469i
$43$	−567.889	−	1217.84i	−0.307133	−	0.658649i	0.690791	−	0.723055i	$-0.257263\pi$
$43$	−567.889	−	1217.84i	−0.307133	−	0.658649i	−0.997924	+	0.0644060i	$0.979485\pi$
$44$	3280.30	−	3909.30i	1.69437	−	2.01927i
$45$	147.723	−	1996.98i	0.0729495	−	0.986161i
$46$	−991.623	−	1717.54i	−0.468631	−	0.811693i
$47$	−1043.35	−	1490.05i	−0.472316	−	0.674537i	0.510341	−	0.859972i	$-0.329519\pi$
$47$	−1043.35	−	1490.05i	−0.472316	−	0.674537i	−0.982656	+	0.185436i	$0.940630\pi$
$48$	496.252	−	347.479i	0.215387	−	0.150816i
$49$	−2795.15	+	1613.78i	−1.16416	+	0.672128i
$50$	4249.82	+	1844.46i	1.69993	+	0.737785i
$51$	119.573	+	100.334i	0.0459720	+	0.0385751i
$52$	−3304.31	+	1540.83i	−1.22201	+	0.569832i
$53$	2173.48	+	1013.51i	0.773755	+	0.360808i	0.769056	−	0.639181i	$-0.220727\pi$
$53$	2173.48	+	1013.51i	0.773755	+	0.360808i	0.00469885	+	0.999989i	$0.498504\pi$
$54$	−729.291	−	869.135i	−0.250100	−	0.298057i
$55$	2657.99	−	1914.84i	0.878673	−	0.633005i
$56$	12760.2			4.06895
$57$	−83.6881	+	332.628i	−0.0257581	+	0.102379i
$58$	5216.79	+	5216.79i	1.55077	+	1.55077i
$59$	−6460.67	+	1139.19i	−1.85598	+	0.327260i	−0.986120	−	0.166035i	$-0.946903\pi$
$59$	−6460.67	+	1139.19i	−1.85598	+	0.327260i	−0.869862	+	0.493295i	$0.835792\pi$
$60$	864.956	−	328.037i	0.240265	−	0.0911213i
$61$	−5624.43	+	2047.12i	−1.51154	+	0.550154i	−0.959018	−	0.283346i	$-0.908555\pi$
$61$	−5624.43	+	2047.12i	−1.51154	+	0.550154i	−0.552519	+	0.833501i	$0.686333\pi$
$62$	−188.901	+	88.0860i	−0.0491418	+	0.0229152i
$63$	−523.736	−	5986.33i	−0.131957	−	1.50827i
$64$	−4035.90	−	2330.13i	−0.985327	−	0.568879i
$65$	−2299.18	+	437.317i	−0.544184	+	0.103507i
$66$	160.253	−	908.838i	0.0367890	−	0.208641i
$67$	2806.46	+	4008.05i	0.625187	+	0.892860i	0.999405	−	0.0344809i	$-0.0109778\pi$
$67$	2806.46	+	4008.05i	0.625187	+	0.892860i	−0.374218	+	0.927341i	$0.622089\pi$
$68$	1655.97	−	6180.16i	0.358125	−	1.33654i
$69$	−220.151	−	127.104i	−0.0462406	−	0.0266970i
$70$	13476.2	+	3417.68i	2.75025	+	0.697486i
$71$	−2002.19	−	728.737i	−0.397181	−	0.144562i	0.135705	−	0.990749i	$-0.456670\pi$
$71$	−2002.19	−	728.737i	−0.397181	−	0.144562i	−0.532885	+	0.846187i	$0.678892\pi$
$72$	−5757.39	+	12346.8i	−1.11061	+	2.38171i
$73$	−10178.3	−	890.482i	−1.90998	−	0.167101i	−0.930180	−	0.367103i	$-0.880350\pi$
$73$	−10178.3	−	890.482i	−1.90998	−	0.167101i	−0.979796	+	0.200002i	$0.935905\pi$
$74$	−1099.76	+	193.918i	−0.200833	+	0.0354123i
$75$	589.964	−	67.6217i	0.104882	−	0.0120216i
$76$	13806.7	−	2653.16i	2.39035	−	0.459343i
$77$	6951.42	−	6951.42i	1.17244	−	1.17244i
$78$	−378.169	+	540.082i	−0.0621580	+	0.0887709i
$79$	−2857.18	−	3405.05i	−0.457807	−	0.545593i	0.486922	−	0.873446i	$-0.338120\pi$
$79$	−2857.18	−	3405.05i	−0.457807	−	0.545593i	−0.944729	+	0.327852i	$0.893675\pi$
$80$	−11421.9	−	11119.2i	−1.78467	−	1.73737i
$81$	5959.95	+	2169.25i	0.908391	+	0.330627i
$82$	−20993.7	+	1836.71i	−3.12220	+	0.273157i
$83$	2735.12	−	732.872i	0.397027	−	0.106383i	−0.0547809	−	0.998498i	$-0.517446\pi$
$83$	2735.12	−	732.872i	0.397027	−	0.106383i	0.451808	+	0.892115i	$0.350779\pi$
$84$	2404.17	−	1388.05i	0.340726	−	0.196718i
$85$	2005.63	−	3584.15i	0.277596	−	0.496076i
$86$	−1729.62	+	9809.16i	−0.233859	+	1.32628i
$87$	913.433	+	244.754i	0.120681	+	0.0323363i
$88$	−21527.5	+	5768.28i	−2.77989	+	0.744871i
$89$	2825.45	−	3367.24i	0.356704	−	0.425103i	−0.557614	−	0.830100i	$-0.688283\pi$
$89$	2825.45	−	3367.24i	0.356704	−	0.425103i	0.914318	+	0.404997i	$0.132728\pi$
$90$	−9387.39	+	11497.5i	−1.15894	+	1.41945i
$91$	−6599.86	+	2402.15i	−0.796988	+	0.290080i
$92$	−908.161	+	10380.3i	−0.107297	+	1.22641i
$93$	−15.3237	+	21.8845i	−0.00177173	+	0.00253030i
$94$			13483.5i			1.52597i
$95$	9009.55	+	527.845i	0.998288	+	0.0584869i
$96$	−1904.99			−0.206705
$97$	−732.295	−	512.759i	−0.0778292	−	0.0544966i	0.534014	−	0.845475i	$-0.320683\pi$
$97$	−732.295	−	512.759i	−0.0778292	−	0.0544966i	−0.611843	+	0.790979i	$0.709572\pi$
$98$	23833.3	+	2085.14i	2.48160	+	0.217112i
$99$	3589.71	+	9862.65i	0.366260	+	1.00629i
$100$	−12732.1	−	20745.4i	−1.27321	−	2.07454i
$101$	10948.9	+	9187.22i	1.07332	+	0.900620i	0.995349	−	0.0963359i	$-0.0307123\pi$
$101$	10948.9	+	9187.22i	1.07332	+	0.900620i	0.0779682	+	0.996956i	$0.475157\pi$
$102$	−299.462	−	1117.61i	−0.0287834	−	0.107421i
$103$	−3055.22	+	11402.3i	−0.287984	+	1.07477i	0.658647	+	0.752452i	$0.271129\pi$
$103$	−3055.22	+	11402.3i	−0.287984	+	1.07477i	−0.946631	+	0.322319i	$0.895537\pi$
$104$	15680.6	+	2764.90i	1.44976	+	0.255631i
$105$	1714.97	−	484.298i	0.155553	−	0.0439273i
$106$	−8888.22	−	15394.9i	−0.791049	−	1.37014i
$107$	1090.22	+	4068.77i	0.0952244	+	0.355382i	0.997053	−	0.0767109i	$-0.0244419\pi$
$107$	1090.22	+	4068.77i	0.0952244	+	0.355382i	−0.901829	+	0.432093i	$0.857775\pi$
$108$	519.540	+	5938.37i	0.0445422	+	0.509120i
$109$	4654.97	−	12789.4i	0.391799	−	1.07646i	−0.574380	−	0.818589i	$-0.694757\pi$
$109$	4654.97	−	12789.4i	0.391799	−	1.07646i	0.966179	−	0.257871i	$-0.0830210\pi$
$110$	−24280.4	+	326.051i	−2.00665	+	0.0269464i
$111$	−109.652	+	92.0087i	−0.00889958	+	0.00746763i
$112$	−39185.1	−	27437.7i	−3.12381	−	2.18732i
$113$	−16427.1	−	16427.1i	−1.28648	−	1.28648i	−0.936910	−	0.349572i	$-0.886327\pi$
$113$	−16427.1	−	16427.1i	−1.28648	−	1.28648i	−0.349572	−	0.936910i	$-0.613673\pi$
$114$	1922.37	−	1663.90i	0.147920	−	0.128031i
$115$	−2203.12	+	6315.61i	−0.166587	+	0.477551i
$116$	−6730.99	−	38173.3i	−0.500222	−	2.83690i
$117$	653.527	−	7469.85i	0.0477411	−	0.545683i
$118$	44072.5	+	20551.3i	3.16522	+	1.47596i
$119$	4215.52	−	11582.0i	0.297685	−	0.817883i
$120$	−3916.01	−	993.132i	−0.271945	−	0.0689675i
$121$	−1264.69	+	2190.52i	−0.0863803	+	0.149615i
$122$	42855.0	+	11483.0i	2.87927	+	0.771497i
$123$	−2212.70	+	1549.35i	−0.146256	+	0.102409i
$124$	1078.45	+	190.160i	0.0701385	+	0.0123673i
$125$	−4648.58	−	14917.5i	−0.297509	−	0.954719i
$126$	−22271.6	+	38575.6i	−1.40285	+	2.42980i
$127$	23216.3	−	2031.16i	1.43941	−	0.125932i	0.659445	−	0.751753i	$-0.270791\pi$
$127$	23216.3	−	2031.16i	1.43941	−	0.125932i	0.779967	+	0.625821i	$0.215236\pi$
$128$	1041.43	+	2233.35i	0.0635637	+	0.136313i
$129$	436.663	+	1199.72i	0.0262402	+	0.0720943i
$130$	15819.9	+	7119.91i	0.936087	+	0.421296i
$131$	−122.412	−	694.234i	−0.00713316	−	0.0404542i	0.981033	−	0.193839i	$-0.0620938\pi$
$131$	−122.412	−	694.234i	−0.00713316	−	0.0404542i	−0.988167	+	0.153384i	$0.950983\pi$
$132$	−3428.55	+	3428.55i	−0.196772	+	0.196772i
$133$	26941.2	−	2773.49i	1.52305	−	0.156792i
$134$		−	36268.8i		−	2.01987i
$135$	−613.814	+	3777.00i	−0.0336798	+	0.207243i
$136$	−21405.0	+	17960.9i	−1.15727	+	0.971069i
$137$	−13920.0	+	29851.5i	−0.741647	+	1.59047i	0.0639154	+	0.997955i	$0.479641\pi$
$137$	−13920.0	+	29851.5i	−0.741647	+	1.59047i	−0.805562	+	0.592511i	$0.798137\pi$
$138$	796.351	+	1707.78i	0.0418164	+	0.0896755i
$139$	−12024.3	+	14330.0i	−0.622346	+	0.741683i	−0.981472	−	0.191606i	$-0.938630\pi$
$139$	−12024.3	+	14330.0i	−0.622346	+	0.741683i	0.359126	+	0.933289i	$0.383075\pi$
$140$	−47699.9	−	55320.7i	−2.43367	−	2.82248i
$141$	864.145	+	1496.74i	0.0434659	+	0.0752851i
$142$	9058.90	+	12937.5i	0.449261	+	0.641612i
$143$	10048.6	−	7036.09i	0.491397	−	0.344080i
$144$	44228.9	−	25535.6i	2.13295	−	1.23146i
$145$	1835.62	−	24814.7i	0.0873065	−	1.18025i
$146$	58016.1	+	48681.3i	2.72172	+	2.28379i
$147$	2779.26	−	1295.99i	0.128616	−	0.0599746i
$148$	5317.57	+	2479.62i	0.242767	+	0.113204i
$149$	−11247.9	−	13404.7i	−0.506639	−	0.603789i	0.450729	−	0.892661i	$-0.351164\pi$
$149$	−11247.9	−	13404.7i	−0.506639	−	0.603789i	−0.957368	+	0.288872i	$0.906720\pi$
$150$	−3869.75	−	2097.72i	−0.171989	−	0.0932319i
$151$	2346.63			0.102918			0.0514589	−	0.998675i	$-0.483613\pi$
$151$	2346.63			0.102918			0.0514589	+	0.998675i	$0.483613\pi$
$152$	−56038.1	−	25093.2i	−2.42547	−	1.08610i
$153$	9304.72	+	9304.72i	0.397485	+	0.397485i
$154$	−71763.8	+	12653.9i	−3.02597	+	0.533560i
$155$	641.034	+	288.504i	0.0266819	+	0.0120085i
$156$	3255.15	−	1184.78i	0.133759	−	0.0486842i
$157$	−7596.70	+	3542.40i	−0.308195	+	0.143714i	−0.570562	−	0.821254i	$-0.693275\pi$
$157$	−7596.70	+	3542.40i	−0.308195	+	0.143714i	0.262367	+	0.964968i	$0.415497\pi$
$158$	2871.65	+	32823.1i	0.115031	+	1.31482i
$159$	−1973.29	−	1139.28i	−0.0780541	−	0.0450645i
$160$	9366.14	+	49242.1i	0.365865	+	1.92352i
$161$	−3485.62	+	19767.9i	−0.134471	+	0.762622i
$162$	−26965.8	−	38511.2i	−1.02750	−	1.46743i
$163$	−3995.95	+	14913.1i	−0.150399	+	0.561296i	0.849057	+	0.528302i	$0.177171\pi$
$163$	−3995.95	+	14913.1i	−0.150399	+	0.561296i	−0.999456	+	0.0329945i	$0.989496\pi$
$164$	95888.2	+	55361.1i	3.56515	+	2.05834i
$165$	−2674.37	+	1592.30i	−0.0982320	+	0.0584869i
$166$	−19723.5	−	7178.76i	−0.715759	−	0.260515i
$167$	−10182.0	+	21835.4i	−0.365091	+	0.782941i	0.634855	+	0.772631i	$0.281060\pi$
$167$	−10182.0	+	21835.4i	−0.365091	+	0.782941i	−0.999947	+	0.0103102i	$0.996718\pi$
$168$	−12077.6	−	1056.66i	−0.427921	−	0.0374382i
$169$	19496.3	−	3437.72i	0.682619	−	0.120364i
$170$	−27416.7	+	13235.6i	−0.948673	+	0.457981i
$171$	−9472.19	+	27319.6i	−0.323935	+	0.934291i
$172$	37004.6	−	37004.6i	1.25083	−	1.25083i
$173$	3860.31	−	5513.09i	0.128982	−	0.184206i	−0.749467	−	0.662042i	$-0.769690\pi$
$173$	3860.31	−	5513.09i	0.128982	−	0.184206i	0.878449	+	0.477836i	$0.158579\pi$
$174$	−4505.74	−	5369.73i	−0.148822	−	0.177359i
$175$	−20950.5	−	41949.2i	−0.684097	−	1.36977i
$176$	78511.6	+	28575.9i	2.53459	+	0.922516i
$177$	6209.41	−	543.253i	0.198200	−	0.0173403i
$178$	−31472.4	+	8432.99i	−0.993320	+	0.266159i
$179$	−48099.4	+	27770.2i	−1.50118	+	0.866708i	−0.501184	+	0.865341i	$0.667102\pi$
$179$	−48099.4	+	27770.2i	−1.50118	+	0.866708i	−0.999999	+	0.00136746i	$0.999565\pi$
$180$	75050.3	−	21193.7i	2.31637	−	0.654128i
$181$	2116.60	−	12003.8i	0.0646072	−	0.366405i	−0.935314	−	0.353820i	$-0.884883\pi$
$181$	2116.60	−	12003.8i	0.0646072	−	0.366405i	0.999921	−	0.0125857i	$-0.00400626\pi$
$182$	50287.2	+	13474.4i	1.51815	+	0.406787i
$183$	5493.08	−	1471.87i	0.164026	−	0.0439507i
$184$	29250.9	−	34859.8i	0.863978	−	1.02965i
$185$	2917.45	+	2382.01i	0.0852431	+	0.0695986i
$186$	186.090	−	67.7314i	0.00537896	−	0.00195778i
$187$	−1876.23	+	21445.4i	−0.0536542	+	0.613270i
$188$	40633.4	−	58030.6i	1.14966	−	1.64188i
$189$			11483.3i			0.321472i
$190$	−52461.6	−	41510.4i	−1.45323	−	1.14987i
$191$	−2203.85			−0.0604110			−0.0302055	−	0.999544i	$-0.509616\pi$
$191$	−2203.85			−0.0604110			−0.0302055	+	0.999544i	$0.509616\pi$
$192$	3627.05	+	2539.69i	0.0983901	+	0.0688935i
$193$	751.294	+	65.7297i	0.0201695	+	0.00176460i	0.0972360	−	0.995261i	$-0.469000\pi$
$193$	751.294	+	65.7297i	0.0201695	+	0.00176460i	−0.0770665	+	0.997026i	$0.524555\pi$
$194$	2266.41	+	6226.91i	0.0602192	+	0.165451i
$195$	2212.40	−	223.532i	0.0581829	−	0.00587856i
$196$	−96290.5	−	80797.4i	−2.50652	−	2.10322i
$197$	−8174.83	−	30508.9i	−0.210643	−	0.786129i	−0.987655	−	0.156644i	$-0.949933\pi$
$197$	−8174.83	−	30508.9i	−0.210643	−	0.786129i	0.777013	−	0.629485i	$-0.216734\pi$
$198$	20135.8	−	75147.9i	0.513617	−	1.91684i
$199$	3707.86	+	653.795i	0.0936304	+	0.0165096i	0.220267	−	0.975440i	$-0.429307\pi$
$199$	3707.86	+	653.795i	0.0936304	+	0.0165096i	−0.126637	+	0.991949i	$0.540418\pi$
$200$	−6417.88	+	106108.i	−0.160447	+	2.65269i
$201$	−2324.44	−	4026.04i	−0.0575342	−	0.0996521i
$202$	−27420.7	−	102335.i	−0.672010	−	2.50798i
$203$	−6508.01	−	74386.8i	−0.157927	−	1.80511i
$204$	−2079.16	+	5712.44i	−0.0499605	+	0.137265i
$205$	50928.2	+	49578.5i	1.21185	+	1.17974i
$206$	67029.6	−	56244.5i	1.57954	−	1.32540i
$207$	−17554.7	−	12291.9i	−0.409687	−	0.286866i
$208$	−42207.8	−	42207.8i	−0.975587	−	0.975587i
$209$	−44198.1	+	16857.9i	−1.01184	+	0.385932i
$210$	−12472.3	−	4350.81i	−0.282819	−	0.0986578i
$211$	−7641.04	−	43334.5i	−0.171628	−	0.973350i	−0.941965	−	0.335712i	$-0.891023\pi$
$211$	−7641.04	−	43334.5i	−0.171628	−	0.973350i	0.770337	−	0.637637i	$-0.220088\pi$
$212$	−8140.12	+	93042.1i	−0.181117	+	2.07018i
$213$	1834.74	+	855.553i	0.0404404	+	0.0188577i
$214$	10679.1	−	29340.7i	0.233189	−	0.640683i
$215$	28864.7	−	17185.9i	0.624438	−	0.371787i
$216$	13016.6	−	22545.4i	0.278991	−	0.483227i
$217$	2037.68	+	545.994i	0.0432729	+	0.0115949i
$218$	−82640.9	+	57865.8i	−1.73893	+	1.21761i
$219$	9560.06	+	1685.70i	0.199330	+	0.0351472i
$220$	105481.	+	71767.5i	2.17937	+	1.48280i
$221$	7689.90	−	13319.3i	0.157448	−	0.272707i
$222$	1056.99	−	92.4747i	0.0214469	−	0.00187636i
$223$	−3271.81	−	7016.42i	−0.0657928	−	0.141093i	0.870662	−	0.491883i	$-0.163691\pi$
$223$	−3271.81	−	7016.42i	−0.0657928	−	0.141093i	−0.936454	+	0.350789i	$0.885913\pi$
$224$	51447.5	+	141351.i	1.02534	+	2.81710i
$225$	50042.7	−	1344.25i	0.988499	−	0.0265530i
$226$	29902.7	+	169587.i	0.585456	+	3.32029i
$227$	−53915.5	+	53915.5i	−1.04631	+	1.04631i	−0.0474403	+	0.998874i	$0.515106\pi$
$227$	−53915.5	+	53915.5i	−1.04631	+	1.04631i	−0.998874	+	0.0474403i	$0.984894\pi$
$228$	−13287.8	+	1367.93i	−0.255613	+	0.0263144i
$229$			31865.9i			0.607652i	0.952728	+	0.303826i	$0.0982642\pi$
$229$			31865.9i			0.607652i	−0.952728	+	0.303826i	$0.901736\pi$
$230$	40229.0	−	28981.4i	0.760472	−	0.547852i
$231$	−7155.21	+	6003.93i	−0.134091	+	0.112515i
$232$	−71542.0	+	153422.i	−1.32918	+	2.85045i
$233$	12739.8	+	27320.7i	0.234667	+	0.503245i	0.988011	−	0.154381i	$-0.0493384\pi$
$233$	12739.8	+	27320.7i	0.234667	+	0.503245i	−0.753344	+	0.657626i	$0.771561\pi$
$234$	−35727.3	+	42578.2i	−0.652483	+	0.777598i
$235$	34440.6	−	29696.2i	0.623641	−	0.537730i
$236$	−127747.	−	221265.i	−2.29365	−	3.97272i
$237$	2422.37	+	3459.50i	0.0431264	+	0.0615909i
$238$	−74839.2	+	52403.0i	−1.32122	+	0.925128i
$239$	−92415.4	+	53356.0i	−1.61789	+	0.934088i	−0.630422	+	0.776253i	$0.717118\pi$
$239$	−92415.4	+	53356.0i	−1.61789	+	0.934088i	−0.987465	+	0.157835i	$0.949549\pi$
$240$	9890.11	+	11470.2i	0.171703	+	0.199135i
$241$	41350.8	+	34697.5i	0.711951	+	0.597398i	0.925146	−	0.379612i	$-0.123942\pi$
$241$	41350.8	+	34697.5i	0.711951	+	0.597398i	−0.213195	+	0.977010i	$0.568387\pi$
$242$	16992.5	−	7923.72i	0.290152	−	0.135300i
$243$	−16697.9	−	7786.38i	−0.282781	−	0.131863i
$244$	−149836.	−	178567.i	−2.51672	−	2.99932i
$245$	−47164.6	−	65469.2i	−0.785750	−	1.09070i
$246$	20022.8			0.330867
$247$	33707.9	+	2429.42i	0.552508	+	0.0398206i
$248$	−3381.72	−	3381.72i	−0.0549838	−	0.0549838i
$249$	−2649.50	+	467.177i	−0.0427331	+	0.00753500i
$250$	−35197.7	+	110343.i	−0.563164	+	1.76548i
$251$	−83512.3	+	30396.0i	−1.32557	+	0.482468i	−0.905239	−	0.424903i	$-0.860308\pi$
$251$	−83512.3	+	30396.0i	−1.32557	+	0.482468i	−0.420331	+	0.907371i	$0.638086\pi$
$252$	212103.	−	98905.4i	3.34000	−	1.55747i
$253$	−3055.61	−	34925.7i	−0.0477371	−	0.545638i
$254$	−149604.	−	86374.2i	−2.31887	−	1.33880i
$255$	−2195.14	+	3226.34i	−0.0337584	+	0.0496169i
$256$	−9776.04	+	55442.7i	−0.149171	+	0.845988i
$257$	5893.44	+	8416.71i	0.0892283	+	0.127431i	0.861284	−	0.508123i	$-0.169661\pi$
$257$	5893.44	+	8416.71i	0.0892283	+	0.127431i	−0.772056	+	0.635554i	$0.780772\pi$
$258$	2449.38	−	9141.21i	0.0367974	−	0.137330i
$259$	9788.39	+	5651.33i	0.145919	+	0.0842463i
$260$	−46629.6	−	78317.1i	−0.689787	−	1.15854i
$261$	74912.9	+	27266.1i	1.09970	+	0.400259i
$262$	−2208.35	+	4735.82i	−0.0321711	+	0.0689911i
$263$	−17852.8	−	1561.92i	−0.258104	−	0.0225812i	−0.0426307	−	0.999091i	$-0.513574\pi$
$263$	−17852.8	−	1561.92i	−0.258104	−	0.0225812i	−0.215473	+	0.976510i	$0.569129\pi$
$264$	20853.6	−	3677.05i	0.299208	−	0.0527584i
$265$	−19747.2	+	56608.8i	−0.281199	+	0.806106i
$266$	−175378.	−	97703.7i	−2.47863	−	1.38085i
$267$	−2953.15	+	2953.15i	−0.0414250	+	0.0414250i
$268$	−109299.	+	156095.i	−1.52176	+	2.17330i
$269$	−7318.93	−	8722.36i	−0.101145	−	0.120539i	0.713098	−	0.701065i	$-0.247292\pi$
$269$	−7318.93	−	8722.36i	−0.101145	−	0.120539i	−0.814242	+	0.580525i	$0.802847\pi$
$270$	19785.5	−	20324.1i	0.271406	−	0.278795i
$271$	15930.7	+	5798.29i	0.216918	+	0.0789517i	0.448193	−	0.893937i	$-0.352068\pi$
$271$	15930.7	+	5798.29i	0.216918	+	0.0789517i	−0.231275	+	0.972888i	$0.574290\pi$
$272$	104352.	−	9129.65i	1.41047	−	0.123400i
$273$	6445.73	−	1727.13i	0.0864862	−	0.0231739i
$274$	211439.	−	122075.i	2.81634	−	1.62601i
$275$	54308.3	+	61300.8i	0.718126	+	0.810590i
$276$	1719.16	−	9749.85i	0.0225683	−	0.127991i
$277$	91247.3	+	24449.6i	1.18921	+	0.318649i	0.798576	−	0.601895i	$-0.205587\pi$
$277$	91247.3	+	24449.6i	1.18921	+	0.318649i	0.390639	+	0.920544i	$0.372254\pi$
$278$	133938.	−	35888.5i	1.73306	−	0.464372i
$279$	−1447.70	+	1725.30i	−0.0185982	+	0.0221644i
$280$	32067.8	+	317390.i	0.409028	+	4.04834i
$281$	78435.9	−	28548.3i	0.993349	−	0.361550i	0.206333	−	0.978482i	$-0.433847\pi$
$281$	78435.9	−	28548.3i	0.993349	−	0.361550i	0.787016	+	0.616932i	$0.211625\pi$
$282$	1116.55	−	12762.2i	0.0140404	−	0.160483i
$283$	−38158.4	+	54495.8i	−0.476450	+	0.680440i	−0.983383	−	0.181545i	$-0.941890\pi$
$283$	−38158.4	+	54495.8i	−0.476450	+	0.680440i	0.506933	+	0.861985i	$0.330779\pi$
$284$		−	82980.2i		−	1.02882i
$285$	−8483.89	−	1245.68i	−0.104449	−	0.0153361i
$286$	−90929.6			−1.11166
$287$	174720.	+	122340.i	2.12119	+	1.48527i
$288$	−159984.	−	13996.8i	−1.92882	−	0.168750i
$289$	−19334.8	−	53121.9i	−0.231496	−	0.636030i
$290$	−116649.	+	142870.i	−1.38703	+	1.69881i
$291$	650.662	+	545.970i	0.00768368	+	0.00644737i
$292$	−102987.	−	384351.i	−1.20786	−	4.50778i
$293$	14626.9	−	54588.4i	0.170379	−	0.635865i	−0.826913	−	0.562330i	$-0.809905\pi$
$293$	14626.9	−	54588.4i	0.170379	−	0.635865i	0.997293	−	0.0735352i	$-0.0234281\pi$
$294$	−22385.7	−	3947.20i	−0.258986	−	0.0456662i
$295$	−44571.9	−	157836.i	−0.512173	−	1.81368i
$296$	−12811.8	−	22190.8i	−0.146227	−	0.253273i
$297$	−5191.04	−	19373.2i	−0.0588493	−	0.219629i
$298$	11304.9	+	129215.i	0.127301	+	1.45506i
$299$	−8566.69	+	23536.8i	−0.0958232	+	0.263272i
$300$	10333.1	+	20690.0i	0.114812	+	0.229889i
$301$	77226.7	−	64800.9i	0.852383	−	0.715234i
$302$	−14248.7	−	9977.02i	−0.156229	−	0.109392i
$303$	−9602.44	−	9602.44i	−0.104591	−	0.104591i
$304$	118129.	+	197554.i	1.27823	+	2.13766i
$305$	−65053.6	−	134754.i	−0.699313	−	1.44858i
$306$	−16937.7	−	96058.3i	−0.180889	−	1.02587i
$307$	−9964.41	+	113894.i	−0.105724	+	1.20843i	0.739177	+	0.673511i	$0.235215\pi$
$307$	−9964.41	+	113894.i	−0.105724	+	1.20843i	−0.844901	+	0.534922i	$0.820341\pi$
$308$	346992.	+	161805.i	3.65779	+	1.70565i
$309$	3836.00	−	10539.3i	0.0401755	−	0.110381i
$310$	−2665.72	−	4477.23i	−0.0277391	−	0.0465893i
$311$	−33754.2	+	58464.0i	−0.348985	+	0.604460i	−0.986069	−	0.166334i	$-0.946807\pi$
$311$	−33754.2	+	58464.0i	−0.348985	+	0.604460i	0.637084	+	0.770794i	$0.280140\pi$
$312$	−14612.8	−	3915.49i	−0.150115	−	0.0402232i
$313$	52391.5	−	36684.9i	0.534776	−	0.374454i	−0.274770	−	0.961510i	$-0.588602\pi$
$313$	52391.5	−	36684.9i	0.534776	−	0.374454i	0.809547	+	0.587055i	$0.199713\pi$
$314$	61188.0	+	10789.1i	0.620593	+	0.109427i
$315$	147584.	−	28071.3i	1.48737	−	0.282906i
$316$	86555.5	−	149919.i	0.866804	−	1.50135i
$317$	−113641.	+	9942.28i	−1.13088	+	0.0989390i	−0.637195	−	0.770703i	$-0.719905\pi$
$317$	−113641.	+	9942.28i	−1.13088	+	0.0989390i	−0.493683	+	0.869642i	$0.664350\pi$
$318$	7137.94	+	15307.4i	0.0705860	+	0.151372i
$319$	44606.2	+	122554.i	0.438343	+	1.20434i
$320$	47815.5	−	106242.i	0.466948	−	1.03752i
$321$	−694.975	−	3941.40i	−0.00674465	−	0.0382508i
$322$	105211.	−	105211.i	1.01473	−	1.01473i
$323$	−41289.3	+	42574.0i	−0.395760	+	0.408075i
$324$			247009.i			2.35300i
$325$	−16655.6	−	56089.3i	−0.157686	−	0.531023i
$326$	87668.4	−	73562.5i	0.824912	−	0.692184i
$327$	−5465.04	+	11719.8i	−0.0511090	+	0.109604i
$328$	−204356.	−	438243.i	−1.89950	−	4.07349i
$329$	87720.9	−	104542.i	0.810422	−	0.965823i
$330$	23008.6	+	1702.02i	0.211282	+	0.0156292i
$331$	68438.5	+	118539.i	0.624661	+	1.08195i	0.988606	+	0.150525i	$0.0480963\pi$
$331$	68438.5	+	118539.i	0.624661	+	1.08195i	−0.363945	+	0.931420i	$0.618570\pi$
$332$	63252.7	+	90334.2i	0.573856	+	0.819551i
$333$	−9884.71	+	6921.35i	−0.0891406	+	0.0624169i
$334$	154662.	−	89293.9i	1.38640	−	0.800440i
$335$	−92640.7	+	79878.9i	−0.825491	+	0.711774i
$336$	34816.9	+	29214.8i	0.308398	+	0.258777i
$337$	−14838.8	+	6919.44i	−0.130659	+	0.0609272i	−0.486848	−	0.873487i	$-0.661854\pi$
$337$	−14838.8	+	6919.44i	−0.130659	+	0.0609272i	0.356189	+	0.934414i	$0.384076\pi$
$338$	−132997.	−	62017.5i	−1.16415	−	0.542851i
$339$	14188.0	+	16908.7i	0.123459	+	0.147133i
$340$	157883.	+	25658.1i	1.36577	+	0.221956i
$341$	−3684.54			−0.0316865
$342$	173668.	−	125612.i	1.48480	−	1.07393i
$343$	−43848.8	−	43848.8i	−0.372709	−	0.372709i
$344$	−225075.	+	39686.7i	−1.90200	+	0.335373i
$345$	2608.25	−	5795.33i	0.0219135	−	0.0486900i
$346$	−46879.4	+	17062.7i	−0.391588	+	0.142526i
$347$	53263.2	−	24837.0i	0.442352	−	0.206272i	−0.188664	−	0.982042i	$-0.560416\pi$
$347$	53263.2	−	24837.0i	0.442352	−	0.206272i	0.631016	+	0.775769i	$0.282638\pi$
$348$	3209.85	+	36688.7i	0.0265049	+	0.302952i
$349$	25034.6	+	14453.7i	0.205537	+	0.118667i	0.599235	−	0.800573i	$-0.295471\pi$
$349$	25034.6	+	14453.7i	0.205537	+	0.118667i	−0.393699	+	0.919240i	$0.628805\pi$
$350$	−51142.1	+	343788.i	−0.417486	+	2.80643i
$351$	−2488.22	+	14111.4i	−0.0201964	+	0.114539i
$352$	−150694.	−	215213.i	−1.21621	−	1.73693i
$353$	−14537.7	+	54255.5i	−0.116667	+	0.435406i	−0.999406	−	0.0344567i	$-0.989030\pi$
$353$	−14537.7	+	54255.5i	−0.116667	+	0.435406i	0.882740	+	0.469863i	$0.155697\pi$
$354$	−40013.1	−	23101.6i	−0.319297	−	0.184346i
$355$	13094.4	−	51632.5i	0.103903	−	0.409701i
$356$	160865.	+	58550.0i	1.26929	+	0.461984i
$357$	−4949.11	+	10613.4i	−0.0388321	+	0.0832757i
$358$	410127.	+	35881.5i	3.20002	+	0.279965i
$359$	12574.3	−	2217.19i	0.0975651	−	0.0172034i	−0.124652	−	0.992200i	$-0.539782\pi$
$359$	12574.3	−	2217.19i	0.0975651	−	0.0172034i	0.222218	+	0.974997i	$0.428670\pi$
$360$	−321575.	−	112177.i	−2.48129	−	0.865563i
$361$	−123770.	−	40800.3i	−0.949728	−	0.313075i
$362$	−63887.8	+	63887.8i	−0.487530	+	0.487530i
$363$	1378.44	−	1968.61i	0.0104610	−	0.0149399i
$364$	−175821.	−	209536.i	−1.32699	−	1.58145i
$365$	−3429.73	−	255405.i	−0.0257439	−	1.91710i
$366$	−39611.7	−	14417.5i	−0.295707	−	0.107628i
$367$	−136607.	+	11951.5i	−1.01424	+	0.0887344i	−0.582137	−	0.813091i	$-0.697783\pi$
$367$	−136607.	+	11951.5i	−1.01424	+	0.0887344i	−0.432101	+	0.901825i	$0.642228\pi$
$368$	−164783.	+	44153.5i	−1.21679	+	0.326039i
$369$	−197209.	+	113859.i	−1.44835	+	0.836208i
$370$	−7587.20	−	26867.4i	−0.0554215	−	0.196256i
$371$	−31242.7	+	177186.i	−0.226987	+	1.28731i
$372$	−1005.01	−	269.293i	−0.00726250	−	0.00194598i
$373$	1935.53	−	518.625i	0.0139118	−	0.00372765i	−0.251856	−	0.967765i	$-0.581041\pi$
$373$	1935.53	−	518.625i	0.0139118	−	0.00372765i	0.265768	+	0.964037i	$0.414374\pi$
$374$	102571.	−	122239.i	0.733298	−	0.873910i
$375$	3164.62	+	14504.4i	0.0225040	+	0.103143i
$376$	−290725.	+	105815.i	−2.05640	+	0.748467i
$377$	8120.81	−	92821.3i	0.0571369	−	0.653078i
$378$	48822.9	−	69726.3i	0.341696	−	0.487992i
$379$		−	60084.7i		−	0.418298i	−0.977884	−	0.209149i	$-0.932931\pi$
$379$		−	60084.7i		−	0.418298i	0.977884	−	0.209149i	$-0.0670693\pi$
$380$	100691.	+	336750.i	0.697304	+	2.33207i
$381$	−22142.6			−0.152538
$382$	13381.7	+	9370.00i	0.0917035	+	0.0642115i
$383$	65449.4	+	5726.08i	0.446178	+	0.0390355i	0.308031	−	0.951376i	$-0.400330\pi$
$383$	65449.4	+	5726.08i	0.446178	+	0.0390355i	0.138147	+	0.990412i	$0.455885\pi$
$384$	−800.778	−	2200.12i	−0.00543062	−	0.0149205i
$385$	190375.	+	155436.i	1.28436	+	1.04865i
$386$	−4282.38	−	3593.34i	−0.0287416	−	0.0241170i
$387$	27856.7	+	103962.i	0.185997	+	0.694152i
$388$	9011.01	−	33629.5i	0.0598563	−	0.223387i
$389$	−67856.4	−	11964.9i	−0.448427	−	0.0790698i	−0.0551257	−	0.998479i	$-0.517556\pi$
$389$	−67856.4	−	11964.9i	−0.448427	−	0.0790698i	−0.393301	+	0.919410i	$0.628667\pi$
$390$	−14384.0	−	8049.06i	−0.0945696	−	0.0529196i
$391$	−21977.7	−	38066.4i	−0.143757	−	0.248994i
$392$	142079.	+	530247.i	0.924609	+	3.45069i
$393$	58.3754	+	667.234i	0.000377959	+	0.00432009i
$394$	−80075.5	+	220006.i	−0.515831	+	1.41723i
$395$	77514.6	−	79624.8i	0.496809	−	0.510334i
$396$	−313125.	+	262743.i	−1.99676	+	1.67548i
$397$	−97430.7	−	68221.7i	−0.618179	−	0.432854i	0.222088	−	0.975027i	$-0.428713\pi$
$397$	−97430.7	−	68221.7i	−0.618179	−	0.432854i	−0.840267	+	0.542173i	$0.817602\pi$
$398$	−19734.3	−	19734.3i	−0.124582	−	0.124582i
$399$	−25729.7	+	394.168i	−0.161618	+	0.00247591i
$400$	247867.	−	312044.i	1.54917	−	1.95027i
$401$	5595.52	+	31733.8i	0.0347978	+	0.197348i	0.997251	−	0.0741003i	$-0.0236085\pi$
$401$	5595.52	+	31733.8i	0.0347978	+	0.197348i	−0.962453	+	0.271448i	$0.912497\pi$
$402$	−3003.37	+	34328.7i	−0.0185848	+	0.212425i
$403$	2385.72	+	1112.48i	0.0146896	+	0.00684985i
$404$	−190381.	+	523068.i	−1.16644	+	3.20476i
$405$	−38978.5	+	153696.i	−0.237637	+	0.937026i
$406$	−276750.	+	479345.i	−1.67894	+	2.90801i
$407$	−19068.5	−	5109.38i	−0.115114	−	0.0308446i
$408$	21747.3	−	15227.6i	0.130642	−	0.0914768i
$409$	187074.	+	32986.2i	1.11832	+	0.197191i	0.702104	−	0.712074i	$-0.252244\pi$
$409$	187074.	+	32986.2i	1.11832	+	0.197191i	0.416219	+	0.909265i	$0.363355\pi$
$410$	−98444.5	−	517568.i	−0.585630	−	3.07893i
$411$	15647.3	−	27101.9i	0.0926309	−	0.160441i
$412$	−457980.	+	40068.1i	−2.69806	+	0.236050i
$413$	−208005.	−	446068.i	−1.21948	−	2.61517i
$414$	54330.8	+	149273.i	0.316990	+	0.870922i
$415$	25102.6	+	66189.8i	0.145755	+	0.384321i
$416$	32593.8	+	184848.i	0.188342	+	1.06814i
$417$	12567.8	−	12567.8i	0.0722747	−	0.0722747i
$418$	340044.	+	85553.9i	1.94618	+	0.489652i
$419$		−	227173.i		−	1.29398i	−0.762498	−	0.646990i	$-0.776027\pi$
$419$		−	227173.i		−	1.29398i	0.762498	−	0.646990i	$-0.223973\pi$
$420$	40567.3	+	56311.4i	0.229973	+	0.319226i
$421$	178299.	−	149611.i	1.00597	−	0.844111i	0.0181714	−	0.999835i	$-0.494216\pi$
$421$	178299.	−	149611.i	1.00597	−	0.844111i	0.987801	+	0.155724i	$0.0497711\pi$
$422$	−137847.	+	295613.i	−0.774054	+	1.65996i
$423$	61574.8	+	132047.i	0.344130	+	0.737988i
$424$	262184.	−	312459.i	1.45840	−	1.73805i
$425$	94190.2	+	40879.4i	0.521468	+	0.226322i
$426$	−7502.98	−	12995.5i	−0.0413442	−	0.0716103i
$427$	−257562.	−	367837.i	−1.41262	−	2.01744i
$428$	−134381.	+	94094.9i	−0.733587	+	0.513663i
$429$	−10093.7	+	5827.60i	−0.0548448	+	0.0316647i
$430$	−248334.	−	18370.0i	−1.34307	−	0.0993512i
$431$	100876.	+	84644.7i	0.543040	+	0.455665i	0.872576	−	0.488478i	$-0.162448\pi$
$431$	100876.	+	84644.7i	0.543040	+	0.455665i	−0.329536	+	0.944143i	$0.606892\pi$
$432$	−88450.7	+	41245.2i	−0.473951	+	0.221007i
$433$	−140863.	−	65685.6i	−0.751314	−	0.350344i	0.00894787	−	0.999960i	$-0.497152\pi$
$433$	−140863.	−	65685.6i	−0.751314	−	0.350344i	−0.760262	+	0.649616i	$0.774930\pi$
$434$	−10051.4	−	11978.7i	−0.0533636	−	0.0635963i
$435$	−3792.29	+	23335.2i	−0.0200412	+	0.123320i
$436$	530055.			2.78835
$437$	54181.6	−	79958.7i	0.283719	−	0.418700i
$438$	−50881.4	−	50881.4i	−0.265223	−	0.265223i
$439$	47391.4	−	8356.39i	0.245907	−	0.0433600i	−0.0493360	−	0.998782i	$-0.515711\pi$
$439$	47391.4	−	8356.39i	0.245907	−	0.0433600i	0.295243	+	0.955422i	$0.404599\pi$
$440$	−197577.	−	520965.i	−1.02054	−	2.69094i
$441$	242928.	−	88418.6i	1.24911	−	0.454639i
$442$	−103322.	+	48179.7i	−0.528868	+	0.246615i
$443$	−18201.6	−	208045.i	−0.0927476	−	1.06011i	−0.889846	−	0.456260i	$-0.849189\pi$
$443$	−18201.6	−	208045.i	−0.0927476	−	1.06011i	0.797099	−	0.603849i	$-0.206367\pi$
$444$	−4827.78	−	2787.32i	−0.0244896	−	0.0141391i
$445$	90855.2	+	61816.2i	0.458807	+	0.312164i
$446$	−9964.97	+	56514.1i	−0.0500963	+	0.284111i
$447$	9536.19	+	13619.1i	0.0477265	+	0.0681605i
$448$	90490.8	−	337716.i	0.450867	−	1.68266i
$449$	250341.	+	144535.i	1.24177	+	0.716934i	0.969453	−	0.245275i	$-0.0788784\pi$
$449$	250341.	+	144535.i	1.24177	+	0.716934i	0.272312	+	0.962209i	$0.412212\pi$
$450$	−309573.	−	204602.i	−1.52876	−	1.01038i
$451$	−350070.	−	127415.i	−1.72108	−	0.626423i
$452$	382366.	−	819986.i	1.87155	−	4.01356i
$453$	−2221.10	−	194.321i	−0.0108236	−	0.000946942i
$454$	556603.	−	98144.2i	2.70044	−	0.476160i
$455$	−76335.7	−	158124.i	−0.368727	−	0.763791i
$456$	50962.5	+	28391.4i	0.245087	+	0.136539i
$457$	62459.4	−	62459.4i	0.299065	−	0.299065i	−0.541583	−	0.840648i	$-0.682175\pi$
$457$	62459.4	−	62459.4i	0.299065	−	0.299065i	0.840648	+	0.541583i	$0.182175\pi$
$458$	135482.	−	193489.i	0.645880	−	0.922412i
$459$	−16163.5	−	19262.9i	−0.0767203	−	0.0914317i
$460$	−260476.	+	3497.81i	−1.23098	+	0.0165303i
$461$	−215935.	−	78593.8i	−1.01606	−	0.369817i	−0.220305	−	0.975431i	$-0.570705\pi$
$461$	−215935.	−	78593.8i	−1.01606	−	0.369817i	−0.795758	+	0.605615i	$0.792927\pi$
$462$	68972.8	−	6034.34i	0.323142	−	0.0282713i
$463$	−341647.	+	91544.0i	−1.59373	+	0.427039i	−0.943142	−	0.332390i	$-0.892145\pi$
$463$	−341647.	+	91544.0i	−1.59373	+	0.427039i	−0.650590	+	0.759429i	$0.725478\pi$
$464$	549593.	−	317308.i	2.55273	−	1.47382i
$465$	−582.852	−	326.154i	−0.00269558	−	0.00150840i
$466$	38801.7	−	220056.i	0.178681	−	1.01335i
$467$	−89851.8	−	24075.7i	−0.411996	−	0.110394i	0.0468668	−	0.998901i	$-0.485076\pi$
$467$	−89851.8	−	24075.7i	−0.411996	−	0.110394i	−0.458863	+	0.888507i	$0.651743\pi$
$468$	282077.	−	75582.2i	1.28788	−	0.345086i
$469$	−235958.	+	281204.i	−1.07273	+	1.27842i
$470$	−335380.	+	33885.4i	−1.51824	+	0.153397i
$471$	7483.67	−	2723.83i	0.0337344	−	0.0122783i
$472$	−97248.3	+	1.11155e6i	−0.436514	+	4.98938i
$473$	−100994.	+	144235.i	−0.451413	+	0.644685i
$474$		−	31305.1i		−	0.139334i
$475$	9512.66	+	225424.i	0.0421614	+	0.999111i
$476$	480015.			2.11856
$477$	−157348.	−	110176.i	−0.691552	−	0.484230i
$478$	787994.	+	68940.6i	3.44879	+	0.301730i
$479$	66159.0	+	181770.i	0.288349	+	0.792232i	0.996298	+	0.0859683i	$0.0273984\pi$
$479$	66159.0	+	181770.i	0.288349	+	0.792232i	−0.707949	+	0.706263i	$0.750379\pi$
$480$	−4787.45	−	47383.6i	−0.0207789	−	0.205658i
$481$	10804.0	+	9065.66i	0.0466977	+	0.0391840i
$482$	−103560.	−	386491.i	−0.445757	−	1.66359i
$483$	4936.12	−	18421.8i	0.0211588	−	0.0789658i
$484$	−97011.4	−	17105.7i	−0.414125	−	0.0730215i
$485$	10913.7	−	19503.3i	0.0463969	−	0.0829132i
$486$	68284.6	+	118272.i	0.289101	+	0.500738i
$487$	35650.2	+	133048.i	0.150315	+	0.560985i	0.999461	+	0.0328262i	$0.0104508\pi$
$487$	35650.2	+	133048.i	0.150315	+	0.560985i	−0.849146	+	0.528159i	$0.822883\pi$
$488$	88725.5	+	1.01414e6i	0.372571	+	4.25850i
$489$	5017.13	−	13784.4i	0.0209815	−	0.0576463i
$490$	8031.00	+	598054.i	0.0334486	+	2.49085i
$491$	−24837.1	+	20840.8i	−0.103024	+	0.0864475i	−0.692845	−	0.721087i	$-0.743643\pi$
$491$	−24837.1	+	20840.8i	−0.103024	+	0.0864475i	0.589821	+	0.807534i	$0.299198\pi$
$492$	−86174.5	−	60340.0i	−0.355999	−	0.249273i
$493$	115622.	+	115622.i	0.475713	+	0.475713i
$494$	−194345.	−	158065.i	−0.796377	−	0.647714i
$495$	−236296.	+	114074.i	−0.964375	+	0.465561i
$496$	3113.30	+	17656.4i	0.0126549	+	0.0717693i
$497$	13932.0	−	159244.i	0.0564028	−	0.644687i
$498$	18073.9	+	8428.02i	0.0728776	+	0.0339834i
$499$	84981.4	−	233485.i	0.341290	−	0.937685i	−0.643732	−	0.765251i	$-0.722615\pi$
$499$	84981.4	−	233485.i	0.341290	−	0.937685i	0.985021	−	0.172434i	$-0.0551631\pi$
$500$	484010.	−	368825.i	1.93604	−	1.47530i
$501$	11445.5	−	19824.2i	0.0455996	−	0.0789807i
$502$	636317.	+	170501.i	2.52503	+	0.676579i
$503$	−294970.	+	206540.i	−1.16585	+	0.816335i	−0.985899	−	0.167341i	$-0.946482\pi$
$503$	−294970.	+	206540.i	−1.16585	+	0.816335i	−0.179948	+	0.983676i	$0.557593\pi$
$504$	−1.00653e6	−	177479.i	−3.96247	−	0.698691i
$505$	−201001.	+	295425.i	−0.788164	+	1.15841i
$506$	−129938.	+	225059.i	−0.507500	+	0.879015i
$507$	−18738.0	+	1639.37i	−0.0728968	+	0.00637764i
$508$	383577.	+	822583.i	1.48636	+	3.18751i
$509$	−30430.6	−	83607.4i	−0.117456	−	0.322707i	0.867008	−	0.498294i	$-0.166040\pi$
$509$	−30430.6	−	83607.4i	−0.117456	−	0.322707i	−0.984464	+	0.175587i	$0.943818\pi$
$510$	27046.1	−	10257.3i	0.103983	−	0.0394360i
$511$	−133106.	−	754883.i	−0.509749	−	2.89093i
$512$	322962.	−	322962.i	1.23200	−	1.23200i
$513$	22582.1	−	50430.3i	0.0858085	−	0.191627i
$514$		−	76162.8i		−	0.288281i
$515$	−291291.	−	47338.7i	−1.09828	−	0.178485i
$516$	−38089.4	+	31960.8i	−0.143056	+	0.120038i
$517$	−100734.	+	216024.i	−0.376872	+	0.808205i
$518$	−35407.4	−	75931.4i	−0.131958	−	0.282984i
$519$	−4110.34	+	4898.51i	−0.0152596	+	0.0181857i
$520$	−29365.6	+	396977.i	−0.108601	+	1.46811i
$521$	−198963.	−	344613.i	−0.732987	−	1.26957i	−0.955601	−	0.294664i	$-0.904792\pi$
$521$	−198963.	−	344613.i	−0.732987	−	1.26957i	0.222614	−	0.974907i	$-0.428541\pi$
$522$	−338944.	−	484062.i	−1.24390	−	1.77648i
$523$	−340410.	+	238358.i	−1.24451	+	0.871416i	−0.995282	−	0.0970287i	$-0.969066\pi$
$523$	−340410.	+	238358.i	−1.24451	+	0.871416i	−0.249229	+	0.968445i	$0.580177\pi$
$524$	23776.1	−	13727.1i	0.0865920	−	0.0499939i
$525$	16356.0	+	41440.1i	0.0593416	+	0.150349i
$526$	101761.	+	85387.7i	0.367799	+	0.308620i
$527$	−4186.68	+	1952.28i	−0.0150747	+	0.00702944i
$528$	−71945.4	−	33548.7i	−0.258069	−	0.120339i
$529$	−133864.	−	159533.i	−0.478359	−	0.570086i
$530$	360585.	−	259769.i	1.28368	−	0.924774i
$531$	525465.			1.86361
$532$	460359.	+	949014.i	1.62657	+	3.35312i
$533$	188198.	+	188198.i	0.662460	+	0.662460i
$534$	30487.1	−	5375.70i	0.106914	−	0.0188518i
$535$	−98464.2	+	37342.8i	−0.344010	+	0.130466i
$536$	782013.	−	284629.i	2.72198	−	0.990718i
$537$	47826.0	−	22301.6i	0.165850	−	0.0773372i
$538$	7355.99	+	84079.4i	0.0254142	+	0.290486i
$539$	366265.	+	211463.i	1.26072	+	0.727875i
$540$	−146402.	+	27846.5i	−0.502063	+	0.0954954i
$541$	−63748.6	+	361536.i	−0.217809	+	1.23526i	0.658156	+	0.752882i	$0.271337\pi$
$541$	−63748.6	+	361536.i	−0.217809	+	1.23526i	−0.875965	+	0.482375i	$0.839774\pi$
$542$	−72078.4	−	102939.i	−0.245362	−	0.350413i
$543$	−2997.39	+	11186.4i	−0.0101659	+	0.0379395i
$544$	−285263.	−	164697.i	−0.963934	−	0.556528i
$545$	329814.	+	83643.6i	1.11039	+	0.281605i
$546$	−46481.4	−	16917.9i	−0.155917	−	0.0567492i
$547$	44638.4	−	95727.4i	0.149188	−	0.319935i	−0.817485	−	0.575951i	$-0.804632\pi$
$547$	44638.4	−	95727.4i	0.149188	−	0.319935i	0.966673	+	0.256016i	$0.0824098\pi$
$548$	−1.27788e6	−	111800.i	−4.25528	−	0.372289i
$549$	472130.	−	83249.3i	1.56645	−	0.276208i
$550$	−69129.2	−	603117.i	−0.228526	−	1.99377i
$551$	−117703.	+	339477.i	−0.387688	+	1.11817i
$552$	−30572.8	+	30572.8i	−0.100336	+	0.100336i
$553$	191275.	−	273170.i	0.625474	−	0.893269i
$554$	−450100.	−	536408.i	−1.46653	−	1.74774i
$555$	−2564.13	−	2496.18i	−0.00832443	−	0.00810382i
$556$	−684597.	−	249173.i	−2.21455	−	0.806030i
$557$	−226978.	+	19858.0i	−0.731600	+	0.0640067i	−0.446867	−	0.894600i	$-0.647460\pi$
$557$	−226978.	+	19858.0i	−0.731600	+	0.0640067i	−0.284733	+	0.958607i	$0.591905\pi$
$558$	16125.8	−	4320.88i	0.0517907	−	0.0138773i
$559$	108942.	−	62897.7i	0.348636	−	0.201285i
$560$	583992.	−	1.04362e6i	1.86222	−	3.32787i
$561$	3551.73	−	20142.9i	0.0112853	−	0.0640024i
$562$	−597638.	−	160137.i	−1.89219	−	0.507011i
$563$	182740.	−	48965.2i	0.576525	−	0.154479i	0.0412374	−	0.999149i	$-0.486870\pi$
$563$	182740.	−	48965.2i	0.576525	−	0.154479i	0.535287	+	0.844670i	$0.320203\pi$
$564$	−43265.3	+	51561.5i	−0.136013	+	0.162094i
$565$	367314.	−	449880.i	1.15064	−	1.40929i
$566$	463393.	−	168661.i	1.44649	−	0.526481i
$567$	−41471.7	+	474024.i	−0.128999	+	1.47446i
$568$	−207860.	+	296854.i	−0.644278	+	0.920124i
$569$			193564.i			0.597862i	0.954275	+	0.298931i	$0.0966301\pi$
$569$			193564.i			0.597862i	−0.954275	+	0.298931i	$0.903370\pi$
$570$	46217.8	+	43634.2i	0.142252	+	0.134300i
$571$	−4012.63			−0.0123071			−0.00615357	−	0.999981i	$-0.501959\pi$
$571$	−4012.63			−0.0123071			−0.00615357	+	0.999981i	$0.501959\pi$
$572$	391345.	+	274023.i	1.19610	+	0.837519i
$573$	2085.96	+	182.498i	0.00635327	+	0.000555839i
$574$	−540748.	−	1.48569e6i	−1.64124	−	4.50926i
$575$	−162627.	−	38927.1i	−0.491878	−	0.117738i
$576$	285944.	+	239936.i	0.861860	+	0.723186i
$577$	108895.	+	406403.i	0.327083	+	1.22069i	0.912201	+	0.409743i	$0.134382\pi$
$577$	108895.	+	406403.i	0.327083	+	1.22069i	−0.585118	+	0.810948i	$0.698952\pi$
$578$	−108455.	+	404759.i	−0.324634	+	1.21155i
$579$	−705.662	−	124.427i	−0.00210494	−	0.000371157i
$580$	932584.	−	263356.i	2.77225	−	0.782865i
$581$	106219.	+	183976.i	0.314665	+	0.545016i
$582$	−1629.53	−	6081.50i	−0.00481080	−	0.0179541i
$583$	−27388.3	−	313050.i	−0.0805802	−	0.921036i
$584$	−594348.	+	1.63296e6i	−1.74267	+	4.78795i
$585$	187443.	−	2517.09i	0.547718	−	0.00735506i
$586$	−320904.	+	269271.i	−0.934502	+	0.784141i
$587$	50844.7	+	35601.8i	0.147560	+	0.103323i	0.645025	−	0.764161i	$-0.276847\pi$
$587$	50844.7	+	35601.8i	0.147560	+	0.103323i	−0.497465	+	0.867484i	$0.665736\pi$
$588$	84449.0	+	84449.0i	0.244253	+	0.244253i
$589$	−7875.00	−	6404.93i	−0.0226997	−	0.0184622i
$590$	−400422.	+	1.14788e6i	−1.15031	+	3.29755i
$591$	5211.14	+	29553.8i	0.0149196	+	0.0846133i
$592$	−8372.12	+	95693.8i	−0.0238887	+	0.273049i
$593$	−119463.	−	55706.4i	−0.339722	−	0.158415i	0.245268	−	0.969455i	$-0.421124\pi$
$593$	−119463.	−	55706.4i	−0.339722	−	0.158415i	−0.584990	+	0.811040i	$0.698902\pi$
$594$	−50848.1	+	139704.i	−0.144113	+	0.395946i
$595$	298678.	+	75747.2i	0.843664	+	0.213960i
$596$	340745.	−	590187.i	0.959261	−	1.66149i
$597$	−3455.37	−	925.864i	−0.00969496	−	0.00259776i
$598$	152087.	−	106492.i	0.425294	−	0.297794i
$599$	317256.	+	55940.8i	0.884211	+	0.155910i	0.597272	−	0.802039i	$-0.296251\pi$
$599$	317256.	+	55940.8i	0.884211	+	0.155910i	0.286939	+	0.957949i	$0.407362\pi$
$600$	14861.2	−	99900.2i	0.0412811	−	0.277501i
$601$	260773.	−	451673.i	0.721962	−	1.25048i	−0.238250	−	0.971204i	$-0.576574\pi$
$601$	260773.	−	451673.i	0.721962	−	1.25048i	0.960212	−	0.279271i	$-0.0900929\pi$
$602$	−744429.	+	65129.1i	−2.05414	+	0.179714i
$603$	−165628.	−	355191.i	−0.455512	−	0.976848i
$604$	31257.3	+	85878.7i	0.0856796	+	0.235403i
$605$	−57663.8	−	25952.2i	−0.157541	−	0.0709029i
$606$	17479.6	+	99131.9i	0.0475978	+	0.269941i
$607$	−41951.2	+	41951.2i	−0.113859	+	0.113859i	−0.761741	−	0.647882i	$-0.775655\pi$
$607$	−41951.2	+	41951.2i	−0.113859	+	0.113859i	0.647882	+	0.761741i	$0.275655\pi$
$608$	52031.4	−	721932.i	0.140753	−	1.95294i
$609$			70946.6i			0.191292i
$610$	−177921.	+	1.09481e6i	−0.478154	+	2.94224i
$611$	130449.	−	109460.i	0.349429	−	0.293205i
$612$	−216582.	+	464461.i	−0.578255	+	1.24007i
$613$	203208.	+	435781.i	0.540779	+	1.15970i	0.966928	+	0.255051i	$0.0820924\pi$
$613$	203208.	+	435781.i	0.540779	+	1.15970i	−0.426148	+	0.904653i	$0.640130\pi$
$614$	544739.	−	649194.i	1.44495	−	1.72202i
$615$	−44098.4	−	51143.7i	−0.116593	−	0.135220i
$616$	−836024.	−	1.44804e6i	−2.20322	−	3.81608i
$617$	40500.8	+	57841.2i	0.106388	+	0.151938i	0.868816	−	0.495135i	$-0.164882\pi$
$617$	40500.8	+	57841.2i	0.106388	+	0.151938i	−0.762428	+	0.647074i	$0.775993\pi$
$618$	−68101.5	+	47685.2i	−0.178312	+	0.124855i
$619$	−500671.	+	289063.i	−1.30669	+	0.754416i	−0.981542	−	0.191248i	$-0.938746\pi$
$619$	−500671.	+	289063.i	−1.30669	+	0.754416i	−0.325145	+	0.945664i	$0.605413\pi$
$620$	−2019.66	+	27302.6i	−0.00525406	+	0.0710265i
$621$	31371.3	+	26323.7i	0.0813485	+	0.0682595i
$622$	453522.	−	211481.i	1.17224	−	0.546626i
$623$	298878.	+	139369.i	0.770049	+	0.359080i
$624$	36454.8	+	43445.2i	0.0936237	+	0.111576i
$625$	359366.	−	153115.i	0.919976	−	0.391974i
$626$	−474091.			−1.20980
$627$	43229.8	−	12296.1i	0.109963	−	0.0312776i
$628$	−230829.	−	230829.i	−0.585289	−	0.585289i
$629$	−24374.4	+	4297.86i	−0.0616073	+	0.0108630i
$630$	−1.01548e6	−	457026.i	−2.55852	−	1.15149i
$631$	478542.	−	174175.i	1.20188	−	0.437449i	0.338000	−	0.941146i	$-0.390249\pi$
$631$	478542.	−	174175.i	1.20188	−	0.437449i	0.863880	+	0.503697i	$0.168027\pi$
$632$	−685180.	+	319505.i	−1.71542	+	0.799914i
$633$	3643.83	+	41649.1i	0.00909391	+	0.103944i
$634$	732295.	+	422791.i	1.82183	+	1.05183i
$635$	108867.	+	572362.i	0.269990	+	1.41946i
$636$	15409.4	−	87390.9i	0.0380952	−	0.216049i
$637$	−173307.	−	247508.i	−0.427107	−	0.609972i
$638$	250210.	−	933797.i	0.614701	−	2.29409i
$639$	147798.	+	85331.0i	0.361964	+	0.208980i
$640$	−52933.7	+	31516.4i	−0.129233	+	0.0769444i
$641$	−495800.	−	180456.i	−1.20667	−	0.439194i	−0.341126	−	0.940018i	$-0.610808\pi$
$641$	−495800.	−	180456.i	−1.20667	−	0.439194i	−0.865549	+	0.500824i	$0.833030\pi$
$642$	−12537.6	+	26886.9i	−0.0304188	+	0.0652334i
$643$	545957.	+	47765.1i	1.32049	+	0.115528i	0.725512	−	0.688210i	$-0.241603\pi$
$643$	545957.	+	47765.1i	1.32049	+	0.115528i	0.594983	+	0.803738i	$0.297159\pi$
$644$	−769869.	+	135749.i	−1.85629	+	0.327313i
$645$	−28743.7	+	13876.3i	−0.0690914	+	0.0333545i
$646$	431717.	−	82961.1i	1.03451	−	0.198797i
$647$	207066.	−	207066.i	0.494652	−	0.494652i	−0.415116	−	0.909768i	$-0.636259\pi$
$647$	207066.	−	207066.i	0.494652	−	0.494652i	0.909768	+	0.415116i	$0.136259\pi$
$648$	618740.	−	883652.i	1.47353	−	2.10442i
$649$	552566.	+	658522.i	1.31188	+	1.56344i
$650$	−137339.	+	411387.i	−0.325063	+	0.973696i
$651$	−1883.46	−	685.525i	−0.00444422	−	0.00161756i
$652$	−598995.	+	52405.3i	−1.40906	+	0.123276i
$653$	−643795.	+	172504.i	−1.50981	+	0.404551i	−0.916371	−	0.400330i	$-0.868896\pi$
$653$	−643795.	+	172504.i	−1.50981	+	0.404551i	−0.593436	+	0.804881i	$0.702229\pi$
$654$	83012.0	−	47927.0i	0.194082	−	0.112053i
$655$	16960.3	−	4789.48i	0.0395322	−	0.0111636i
$656$	−314780.	+	1.78521e6i	−0.731475	+	4.14840i
$657$	790480.	+	211808.i	1.83130	+	0.490696i
$658$	−977113.	+	261817.i	−2.25680	+	0.604707i
$659$	153291.	−	182686.i	0.352978	−	0.420662i	−0.560115	−	0.828415i	$-0.689243\pi$
$659$	153291.	−	182686.i	0.352978	−	0.420662i	0.913092	+	0.407753i	$0.133687\pi$
$660$	−93895.8	−	76663.2i	−0.215555	−	0.175995i
$661$	−40916.1	+	14892.2i	−0.0936464	+	0.0340845i	−0.388418	−	0.921483i	$-0.626978\pi$
$661$	−40916.1	+	14892.2i	−0.0936464	+	0.0340845i	0.294772	+	0.955568i	$0.404756\pi$
$662$	88428.5	−	1.01074e6i	0.201779	−	2.30635i
$663$	−8381.50	+	11970.0i	−0.0190675	+	0.0272313i
$664$		−	481606.i		−	1.09233i
$665$	136692.	+	663148.i	0.309101	+	1.49957i
$666$	89446.8			0.201658
$667$	−218137.	−	152741.i	−0.490317	−	0.343324i
$668$	−934730.	−	81778.3i	−2.09475	−	0.183267i
$669$	2515.77	+	6912.03i	0.00562107	+	0.0154438i
$670$	902128.	−	91147.4i	2.00964	−	0.203046i
$671$	600809.	+	504139.i	1.33442	+	1.11971i
$672$	−36990.4	−	138050.i	−0.0819125	−	0.305702i
$673$	134788.	−	503034.i	0.297591	−	1.11062i	−0.641547	−	0.767084i	$-0.721707\pi$
$673$	134788.	−	503034.i	0.297591	−	1.11062i	0.939138	−	0.343541i	$-0.111626\pi$
$674$	119520.	+	21074.6i	0.263099	+	0.0463915i
$675$	−95489.3	−	5775.63i	−0.209579	−	0.0126763i
$676$	385501.	+	667708.i	0.843592	+	1.46114i
$677$	−133051.	−	496552.i	−0.290295	−	1.08340i	−0.944882	−	0.327410i	$-0.893824\pi$
$677$	−133051.	−	496552.i	−0.290295	−	1.08340i	0.654587	−	0.755986i	$-0.272842\pi$
$678$	−14259.9	−	162991.i	−0.0310211	−	0.354573i
$679$	22938.9	−	63024.0i	0.0497545	−	0.136699i
$680$	−500541.	−	487276.i	−1.08248	−	1.05380i
$681$	55496.1	−	46566.8i	0.119665	−	0.100411i
$682$	22372.4	+	15665.3i	0.0480999	+	0.0336799i
$683$	−470368.	−	470368.i	−1.00831	−	1.00831i	−0.999965	−	0.00834977i	$-0.997342\pi$
$683$	−470368.	−	470368.i	−1.00831	−	1.00831i	−0.00834977	−	0.999965i	$-0.502658\pi$
$684$	−1.12598e6	+	17249.5i	−2.40667	+	0.0368692i
$685$	−777489.	−	271217.i	−1.65696	−	0.578010i
$686$	79819.4	+	452678.i	0.169613	+	0.961925i
$687$	2638.77	−	30161.3i	0.00559098	−	0.0639052i
$688$	776512.	+	362094.i	1.64048	+	0.764969i
$689$	−76785.9	+	210967.i	−0.161749	+	0.444403i
$690$	−40476.9	+	24099.8i	−0.0850177	+	0.0506191i
$691$	172486.	−	298754.i	0.361241	−	0.625687i	−0.626925	−	0.779080i	$-0.715687\pi$
$691$	172486.	−	298754.i	0.361241	−	0.625687i	0.988165	+	0.153393i	$0.0490200\pi$
$692$	253180.	+	67839.5i	0.528710	+	0.141667i
$693$	−645017.	+	451646.i	−1.34309	+	0.940440i
$694$	−429011.	−	75646.2i	−0.890737	−	0.157061i
$695$	−386655.	−	263073.i	−0.800486	−	0.544636i
$696$	80419.8	−	139291.i	0.166014	−	0.287544i
$697$	−465290.	+	40707.6i	−0.957764	+	0.0837935i
$698$	−90557.3	−	194201.i	−0.185871	−	0.398602i
$699$	−9795.95	−	26914.2i	−0.0200490	−	0.0550841i
$700$	1.25614e6	−	1.32548e6i	2.56354	−	2.70507i
$701$	151070.	+	856763.i	0.307428	+	1.74351i	0.611850	+	0.790974i	$0.290426\pi$
$701$	151070.	+	856763.i	0.307428	+	1.74351i	−0.304422	+	0.952537i	$0.598463\pi$
$702$	75104.9	−	75104.9i	0.152403	−	0.152403i
$703$	−31873.4	−	44067.5i	−0.0644938	−	0.0891678i
$704$			610661.i			1.23212i
$705$	−35057.3	+	25255.7i	−0.0705343	+	0.0508136i
$706$	318948.	−	267629.i	0.639897	−	0.536937i
$707$	−453173.	+	971832.i	−0.906619	+	1.94425i
$708$	102591.	+	220007.i	0.204665	+	0.438905i
$709$	260539.	−	310499.i	0.518299	−	0.617685i	−0.441878	−	0.897075i	$-0.645688\pi$
$709$	260539.	−	310499.i	0.518299	−	0.617685i	0.960178	+	0.279390i	$0.0901322\pi$
$710$	−299032.	+	257839.i	−0.593200	+	0.511483i
$711$	178015.	+	308331.i	0.352142	+	0.609928i
$712$	−428816.	−	612413.i	−0.845885	−	1.20805i
$713$	6162.67	−	4315.15i	0.0121224	−	0.00848822i
$714$	75175.2	−	43402.4i	0.147461	−	0.0851369i
$715$	200264.	+	232260.i	0.391734	+	0.454320i
$716$	−1.65698e6	−	1.39038e6i	−3.23216	−	2.71210i
$717$	91890.1	−	42849.1i	0.178744	−	0.0833495i
$718$	−85777.4	−	39998.7i	−0.166389	−	0.0775884i
$719$	448581.	+	534598.i	0.867726	+	1.03412i	0.999084	+	0.0427812i	$0.0136218\pi$
$719$	448581.	+	534598.i	0.867726	+	1.03412i	−0.131358	+	0.991335i	$0.541934\pi$
$720$	746307.	+	1.03595e6i	1.43964	+	1.99836i
$721$	−885616.			−1.70363
$722$	578057.	+	773962.i	1.10891	+	1.48472i
$723$	−36265.6	−	36265.6i	−0.0693774	−	0.0693774i
$724$	467492.	−	82431.5i	0.891861	−	0.157259i
$725$	621837.	−	16703.8i	1.18304	−	0.0317789i
$726$	−16739.7	+	6092.74i	−0.0317595	+	0.0115595i
$727$	104306.	−	48638.8i	0.197352	−	0.0920268i	−0.321430	−	0.946933i	$-0.604163\pi$
$727$	104306.	−	48638.8i	0.197352	−	0.0920268i	0.518782	+	0.854907i	$0.326386\pi$
$728$	104113.	+	1.19002e6i	0.196445	+	2.24538i
$729$	−429751.	−	248117.i	−0.808652	−	0.466875i
$730$	−1.06507e6	+	1.56540e6i	−1.99863	+	2.93751i
$731$	−38334.1	+	217404.i	−0.0717383	+	0.406848i
$732$	127034.	+	181423.i	0.237081	+	0.338587i
$733$	−98173.1	+	366387.i	−0.182719	+	0.681918i	0.812388	+	0.583118i	$0.198167\pi$
$733$	−98173.1	+	366387.i	−0.182719	+	0.681918i	−0.995107	+	0.0988007i	$0.968499\pi$
$734$	880287.	+	508234.i	1.63392	+	0.943347i
$735$	39220.2	+	65872.7i	0.0725998	+	0.121936i
$736$	504093.	+	183475.i	0.930584	+	0.338705i
$737$	270961.	−	581078.i	0.498852	−	1.06979i
$738$	1.68154e6	+	147115.i	3.08741	+	0.270113i
$739$	71785.7	−	12657.8i	0.131447	−	0.0231776i	−0.107538	−	0.994201i	$-0.534297\pi$
$739$	71785.7	−	12657.8i	0.131447	−	0.0231776i	0.238984	+	0.971023i	$0.423186\pi$
$740$	−48313.0	+	138497.i	−0.0882267	+	0.252917i
$741$	−31703.6	−	5090.77i	−0.0577394	−	0.00927143i
$742$	943037.	−	943037.i	1.71286	−	1.71286i
$743$	381349.	−	544623.i	0.690789	−	0.986549i	−0.308586	−	0.951196i	$-0.599856\pi$
$743$	381349.	−	544623.i	0.690789	−	0.986549i	0.999375	−	0.0353525i	$-0.0112554\pi$
$744$	2920.79	+	3480.86i	0.00527660	+	0.00628841i
$745$	305153.	−	313461.i	0.549801	−	0.564768i
$746$	−13957.5	−	5080.12i	−0.0250802	−	0.00912844i
$747$	−225940.	+	19767.2i	−0.404905	+	0.0354246i
$748$	−809822.	+	216991.i	−1.44739	+	0.387828i
$749$	−273684.	+	158011.i	−0.487849	+	0.281659i
$750$	42452.2	−	101525.i	0.0754706	−	0.180490i
$751$	−23346.5	+	132404.i	−0.0413944	+	0.234759i	−0.998485	−	0.0550308i	$-0.982474\pi$
$751$	−23346.5	+	132404.i	−0.0413944	+	0.234759i	0.957090	+	0.289790i	$0.0935854\pi$
$752$	1.12031e6	+	300186.i	1.98108	+	0.530829i
$753$	81562.0	−	21854.5i	0.143846	−	0.0385434i
$754$	−443952.	+	529082.i	−0.780897	+	0.930636i
$755$	5897.32	+	58368.5i	0.0103457	+	0.102396i
$756$	−420250.	+	152958.i	−0.735299	+	0.267627i
$757$	51284.1	−	586179.i	0.0894933	−	1.02291i	−0.810131	−	0.586249i	$-0.800604\pi$
$757$	51284.1	−	586179.i	0.0894933	−	1.02291i	0.899624	−	0.436664i	$-0.143840\pi$
$758$	−255459.	+	364833.i	−0.444613	+	0.634973i
$759$			33310.5i			0.0578226i
$760$	483324.	−	1.45692e6i	0.836780	−	2.52236i
$761$	−1.08350e6			−1.87094			−0.935471	−	0.353404i	$-0.885024\pi$
$761$	−1.08350e6			−1.87094			−0.935471	+	0.353404i	$0.885024\pi$
$762$	134449.	+	94142.3i	0.231552	+	0.162134i
$763$	1.01720e6	+	88993.8i	1.74727	+	0.152866i
$764$	−29355.5	−	80653.7i	−0.0502925	−	0.138178i
$765$	−208056.	+	254823.i	−0.355514	+	0.435428i
$766$	−373062.	−	313036.i	−0.635804	−	0.533503i
$767$	−158954.	−	593226.i	−0.270198	−	1.00839i
$768$	13844.2	−	51667.4i	0.0234718	−	0.0875979i
$769$	−304273.	−	53651.5i	−0.514529	−	0.0907254i	−0.0896463	−	0.995974i	$-0.528574\pi$
$769$	−304273.	−	53651.5i	−0.514529	−	0.0907254i	−0.424883	+	0.905248i	$0.639685\pi$
$770$	−495095.	−	1.75321e6i	−0.835040	−	2.95700i
$771$	−4881.21	−	8454.50i	−0.00821142	−	0.0142226i
$772$	7601.81	+	28370.3i	0.0127551	+	0.0476025i
$773$	49550.2	+	566361.i	0.0829252	+	0.947839i	0.917707	+	0.397258i	$0.130038\pi$
$773$	49550.2	+	566361.i	0.0829252	+	0.947839i	−0.834782	+	0.550581i	$0.814406\pi$
$774$	272866.	−	749694.i	0.455479	−	1.25142i
$775$	−5565.08	+	16669.7i	−0.00926549	+	0.0277539i
$776$	−116476.	+	97734.7i	−0.193425	+	0.162303i
$777$	−8796.80	−	6159.58i	−0.0145708	−	0.0102026i
$778$	361152.	+	361152.i	0.596665	+	0.596665i
$779$	−526719.	−	880862.i	−0.867969	−	1.45155i
$780$	37649.9	+	77989.1i	0.0618835	+	0.128187i
$781$	48481.9	+	274954.i	0.0794835	+	0.450774i
$782$	−28397.0	+	324580.i	−0.0464365	+	0.530772i
$783$	−138069.	−	64382.7i	−0.225203	−	0.105014i
$784$	703856.	−	1.93383e6i	1.14512	−	3.14619i
$785$	−107203.	−	180053.i	−0.173967	−	0.292187i
$786$	2482.39	−	4299.62i	0.00401813	−	0.00695961i
$787$	−22031.6	−	5903.36i	−0.0355711	−	0.00953124i	0.240990	−	0.970528i	$-0.422528\pi$
$787$	−22031.6	−	5903.36i	−0.0355711	−	0.00953124i	−0.276561	+	0.960996i	$0.589195\pi$
$788$	1.00763e6	−	705552.i	1.62274	−	1.13626i
$789$	16768.5	+	2956.73i	0.0269364	+	0.00474961i
$790$	−809203.	+	153915.i	−1.29659	+	0.246619i
$791$	871453.	−	1.50940e6i	1.39281	−	2.41241i
$792$	1.77833e6	−	155584.i	2.83505	−	0.248035i
$793$	−236805.	−	507830.i	−0.376569	−	0.807554i
$794$	301542.	+	828481.i	0.478307	+	1.31414i
$795$	23378.6	−	51945.4i	0.0369900	−	0.0821888i
$796$	25462.3	+	144404.i	0.0401856	+	0.227904i
$797$	−323786.	+	323786.i	−0.509731	+	0.509731i	−0.914444	−	0.404713i	$-0.867372\pi$
$797$	−323786.	+	323786.i	−0.509731	+	0.509731i	0.404713	+	0.914444i	$0.367372\pi$
$798$	157906.	+	107000.i	0.247966	+	0.168027i
$799$			298839.i			0.468105i
$800$	−1.20128e6	+	356718.i	−1.87700	+	0.557372i
$801$	−269707.	+	226311.i	−0.420365	+	0.352728i
$802$	100945.	−	216477.i	0.156941	−	0.336560i
$803$	565806.	+	1.21338e6i	0.877479	+	1.88176i
$804$	116378.	−	138694.i	0.180036	−	0.214558i
$805$	−500455.	−	37020.2i	−0.772277	−	0.0571278i
$806$	−9756.15	−	16898.2i	−0.0150179	−	0.0260117i
$807$	6205.13	+	8861.84i	0.00952804	+	0.0136075i
$808$	1.99132e6	−	1.39434e6i	3.05013	−	2.13572i
$809$	395833.	−	228534.i	0.604804	−	0.349184i	−0.166125	−	0.986105i	$-0.553126\pi$
$809$	395833.	−	228534.i	0.604804	−	0.349184i	0.770929	+	0.636921i	$0.219792\pi$
$810$	890135.	−	767514.i	1.35671	−	1.16981i
$811$	−240222.	−	201570.i	−0.365234	−	0.306467i	0.441639	−	0.897193i	$-0.354397\pi$
$811$	−240222.	−	201570.i	−0.365234	−	0.306467i	−0.806873	+	0.590725i	$0.798842\pi$
$812$	2.63562e6	−	1.22901e6i	3.99734	−	1.86399i
$813$	−14598.4	−	6807.32i	−0.0220863	−	0.0102990i
$814$	94060.0	+	112096.i	0.141957	+	0.169177i
$815$	−380981.	−	61914.6i	−0.573572	−	0.0932132i
$816$	−99526.3			−0.149471
$817$	−466583.	+	132713.i	−0.699012	+	0.198824i
$818$	−995664.	−	995664.i	−1.48801	−	1.48801i
$819$	554010.	−	97687.0i	0.825943	−	0.145636i
$820$	−1.13604e6	+	2.52419e6i	−1.68953	+	3.75400i
$821$	−19326.1	+	7034.12i	−0.0286720	+	0.0104357i	−0.356316	−	0.934365i	$-0.615967\pi$
$821$	−19326.1	+	7034.12i	−0.0286720	+	0.0104357i	0.327644	+	0.944801i	$0.393745\pi$
$822$	−210238.	+	98035.5i	−0.311148	+	0.145091i
$823$	−43095.0	−	492578.i	−0.0636249	−	0.727236i	−0.959275	−	0.282475i	$-0.908844\pi$
$823$	−43095.0	−	492578.i	−0.0636249	−	0.727236i	0.895650	−	0.444760i	$-0.146711\pi$
$824$	1.73875e6	+	1.00387e6i	2.56084	+	1.47850i
$825$	−46326.9	−	62518.9i	−0.0680653	−	0.0918551i
$826$	−633520.	+	3.59287e6i	−0.928540	+	5.26601i
$827$	−42723.8	−	61015.9i	−0.0624681	−	0.0892138i	0.786703	−	0.617332i	$-0.211787\pi$
$827$	−42723.8	−	61015.9i	−0.0624681	−	0.0892138i	−0.849171	+	0.528119i	$0.822898\pi$
$828$	216013.	−	806173.i	0.315079	−	1.17589i
$829$	−866970.	−	500545.i	−1.26152	−	0.728340i	−0.288154	−	0.957584i	$-0.593041\pi$
$829$	−866970.	−	500545.i	−1.26152	−	0.728340i	−0.973369	+	0.229244i	$0.926375\pi$
$830$	128993.	−	508630.i	0.187244	−	0.738322i
$831$	−84341.6	−	30697.8i	−0.122135	−	0.0444534i
$832$	184378.	−	395399.i	0.266355	−	0.571201i
$833$	528225.	+	46213.7i	0.761253	+	0.0666010i
$834$	−129745.	+	22877.5i	−0.186534	+	0.0328910i
$835$	−568710.	−	198387.i	−0.815676	−	0.284538i
$836$	−1.20567e6	−	1.39295e6i	−1.72510	−	1.99308i
$837$	3043.31	−	3043.31i	0.00434405	−	0.00434405i
$838$	−965856.	+	1.37939e6i	−1.37539	+	1.96425i
$839$	−290305.	−	345972.i	−0.412411	−	0.491492i	0.519352	−	0.854561i	$-0.326174\pi$
$839$	−290305.	−	345972.i	−0.412411	−	0.491492i	−0.931762	+	0.363069i	$0.881729\pi$
$840$	−4069.76	−	303067.i	−0.00576779	−	0.429517i
$841$	266250.	+	96907.2i	0.376442	+	0.137014i
$842$	−1.71872e6	+	150369.i	−2.42427	+	0.212096i
$843$	−76604.1	+	20526.0i	−0.107795	+	0.0288835i
$844$	1.48412e6	−	856856.i	2.08345	−	1.20288i
$845$	134504.	+	476299.i	0.188374	+	0.667062i
$846$	187538.	−	1.06358e6i	0.262029	−	1.48604i
$847$	−183298.	−	49114.6i	−0.255500	−	0.0684611i
$848$	−1.47700e6	+	395761.i	−2.05395	+	0.550354i
$849$	40629.9	−	48420.8i	0.0563677	−	0.0671764i
$850$	−398116.	−	648682.i	−0.551025	−	0.897830i
$851$	37877.3	−	13786.2i	0.0523022	−	0.0190364i
$852$	−6871.48	+	78541.3i	−0.00946609	+	0.108198i
$853$	32584.5	−	46535.5i	0.0447830	−	0.0639568i	−0.796136	−	0.605118i	$-0.793126\pi$
$853$	32584.5	−	46535.5i	0.0447830	−	0.0639568i	0.840919	+	0.541161i	$0.182015\pi$
$854$			3.32856e6i			4.56395i
$855$	−703335.	−	166948.i	−0.962122	−	0.228375i
$856$	716439.			0.977759
$857$	231984.	+	162437.i	0.315862	+	0.221169i	0.720746	−	0.693199i	$-0.243799\pi$
$857$	231984.	+	162437.i	0.315862	+	0.221169i	−0.404884	+	0.914368i	$0.632688\pi$
$858$	86065.6	+	7529.76i	0.116911	+	0.0102284i
$859$	−325799.	−	895125.i	−0.441533	−	1.21310i	−0.938484	−	0.345323i	$-0.887769\pi$
$859$	−325799.	−	895125.i	−0.441533	−	1.21310i	0.496951	−	0.867779i	$-0.334453\pi$
$860$	1.01342e6	+	827432.i	1.37023	+	1.11876i
$861$	−155243.	−	130264.i	−0.209414	−	0.175719i
$862$	−252635.	−	942848.i	−0.340001	−	1.26890i
$863$	−238775.	+	891121.i	−0.320603	+	1.19651i	0.598056	+	0.801455i	$0.295940\pi$
$863$	−238775.	+	891121.i	−0.320603	+	1.19651i	−0.918659	+	0.395052i	$0.870727\pi$
$864$	302227.	+	53290.8i	0.404861	+	0.0713879i
$865$	146830.	+	82163.9i	0.196238	+	0.109812i
$866$	576046.	+	997741.i	0.768106	+	1.33040i
$867$	13901.6	+	51881.3i	0.0184938	+	0.0690197i
$868$	7160.50	+	81844.9i	0.00950394	+	0.108631i
$869$	−199210.	+	547325.i	−0.263798	+	0.724779i
$870$	122240.	−	125568.i	0.161501	−	0.165897i
$871$	−350891.	+	294433.i	−0.462526	+	0.388105i
$872$	−1.89622e6	−	1.32775e6i	−2.49377	−	1.74616i
$873$	50631.9	+	50631.9i	0.0664348	+	0.0664348i
$874$	−668945.	+	255147.i	−0.875724	+	0.334016i
$875$	990766.	−	626532.i	1.29406	−	0.818327i
$876$	65650.0	+	372320.i	0.0855513	+	0.485185i
$877$	−21034.0	+	240419.i	−0.0273478	+	0.312586i	0.970184	+	0.242370i	$0.0779247\pi$
$877$	−21034.0	+	240419.i	−0.0273478	+	0.312586i	−0.997532	+	0.0702168i	$0.977631\pi$
$878$	−323288.	−	150752.i	−0.419373	−	0.195557i
$879$	−18364.9	+	50457.0i	−0.0237689	+	0.0653046i
$880$	−513470.	+	2.02466e6i	−0.663056	+	2.61449i
$881$	169205.	−	293072.i	0.218003	−	0.377592i	−0.736195	−	0.676770i	$-0.763379\pi$
$881$	169205.	−	293072.i	0.218003	−	0.377592i	0.954197	+	0.299178i	$0.0967125\pi$
$882$	−1.85098e6	−	495968.i	−2.37938	−	0.637553i
$883$	530700.	−	371600.i	0.680656	−	0.476601i	−0.181402	−	0.983409i	$-0.558064\pi$
$883$	530700.	−	371600.i	0.680656	−	0.476601i	0.862059	+	0.506808i	$0.169175\pi$
$884$	589872.	+	104010.i	0.754837	+	0.133098i
$885$	29117.4	+	153084.i	0.0371763	+	0.195453i
$886$	−774015.	+	1.34063e6i	−0.986011	+	1.70782i
$887$	1.17181e6	−	102520.i	1.48939	−	0.130305i	0.686807	−	0.726840i	$-0.259012\pi$
$887$	1.17181e6	−	102520.i	1.48939	−	0.130305i	0.802587	+	0.596535i	$0.203456\pi$
$888$	10288.9	+	22064.6i	0.0130480	+	0.0279815i
$889$	597997.	+	1.64298e6i	0.756650	+	2.07888i
$890$	−288850.	−	761631.i	−0.364664	−	0.961533i
$891$	−144317.	−	818462.i	−0.181787	−	1.03096i
$892$	213197.	−	213197.i	0.267948	−	0.267948i
$893$	−590820.	+	286602.i	−0.740887	+	0.359399i
$894$		−	123239.i		−	0.154196i
$895$	−811617.	−	1.12660e6i	−1.01322	−	1.40645i
$896$	−141623.	+	118836.i	−0.176408	+	0.148024i
$897$	10057.5	−	21568.3i	0.0124998	−	0.0268060i
$898$	−905556.	−	1.94197e6i	−1.12296	−	2.40819i
$899$	−17989.3	+	21438.8i	−0.0222584	+	0.0265266i
$900$	715769.	+	1.81349e6i	0.883665	+	2.23888i
$901$	−196993.	−	341201.i	−0.242661	−	0.420302i
$902$	1.58389e6	+	2.26203e6i	1.94676	+	2.78026i
$903$	−78461.7	+	54939.5i	−0.0962238	+	0.0673766i
$904$	−3.42189e6	+	1.97563e6i	−4.18725	+	2.41751i
$905$	303894.	+	22480.0i	0.371044	+	0.0274473i
$906$	12660.3	+	10623.2i	0.0154236	+	0.0129420i
$907$	−1.21439e6	+	566280.i	−1.47620	+	0.688362i	−0.983345	−	0.181750i	$-0.941824\pi$
$907$	−1.21439e6	+	566280.i	−1.47620	+	0.688362i	−0.492853	+	0.870113i	$0.664046\pi$
$908$	−2.69129e6	−	1.25497e6i	−3.26429	−	1.52216i
$909$	−735872.	−	876978.i	−0.890583	−	1.06136i
$910$	−208777.	+	1.28468e6i	−0.252116	+	1.55135i
$911$	215497.			0.259659			0.129830	−	0.991536i	$-0.458557\pi$
$911$	215497.			0.259659			0.129830	+	0.991536i	$0.458557\pi$
$912$	−95451.0	−	196769.i	−0.114760	−	0.236573i
$913$	−262366.	−	262366.i	−0.314750	−	0.314750i
$914$	−644807.	+	113697.i	−0.771858	+	0.136099i
$915$	50414.9	+	132932.i	0.0602167	+	0.158777i
$916$	−1.16618e6	+	424456.i	−1.38988	+	0.505874i
$917$	47932.3	−	22351.2i	0.0570020	−	0.0265805i
$918$	16245.4	+	185686.i	0.0192772	+	0.220340i
$919$	−573521.	−	331122.i	−0.679075	−	0.392064i	0.120431	−	0.992722i	$-0.461572\pi$
$919$	−573521.	−	331122.i	−0.679075	−	0.392064i	−0.799507	+	0.600657i	$0.794906\pi$
$920$	940591.	+	639961.i	1.11128	+	0.756097i
$921$	18862.8	−	106976.i	0.0222375	−	0.126115i
$922$	976997.	+	1.39530e6i	1.14929	+	1.64136i
$923$	51625.6	−	192669.i	0.0605985	−	0.226157i
$924$	−315032.	−	181884.i	−0.368987	−	0.213034i
$925$	−51916.8	+	78552.9i	−0.0606770	+	0.0918077i
$926$	2.46368e6	+	896707.i	2.87318	+	1.04575i
$927$	399588.	−	856920.i	0.465001	−	0.997197i
$928$	−1.98798e6	−	173926.i	−2.30842	−	0.201961i
$929$	1.14351e6	−	201632.i	1.32498	−	0.233629i	0.534005	−	0.845481i	$-0.320686\pi$
$929$	1.14351e6	−	201632.i	1.32498	−	0.233629i	0.790972	+	0.611852i	$0.209575\pi$
$930$	2152.37	+	4458.48i	0.00248858	+	0.00515491i
$931$	415229.	+	1.08865e6i	0.479058	+	1.25600i
$932$	−830149.	+	830149.i	−0.955705	+	0.955705i
$933$	36789.9	−	52541.4i	0.0422635	−	0.0603585i
$934$	443216.	+	528205.i	0.508068	+	0.605492i
$935$	−538135.	+	7226.38i	−0.615557	+	0.00826604i
$936$	−1.19843e6	−	436194.i	−1.36792	−	0.497883i
$937$	1.27349e6	−	111416.i	1.45050	−	0.126902i	0.665500	−	0.746398i	$-0.268218\pi$
$937$	1.27349e6	−	111416.i	1.45050	−	0.126902i	0.785000	+	0.619496i	$0.212663\pi$
$938$	2.62831e6	−	704253.i	2.98724	−	0.800429i
$939$	−52626.8	+	30384.1i	−0.0596864	+	0.0344600i
$940$	1.54553e6	+	864853.i	1.74913	+	0.978784i
$941$	−102325.	+	580315.i	−0.115559	+	0.655367i	0.870913	+	0.491437i	$0.163528\pi$
$941$	−102325.	+	580315.i	−0.115559	+	0.655367i	−0.986472	+	0.163930i	$0.947583\pi$
$942$	−57021.4	−	15278.9i	−0.0642594	−	0.0172182i
$943$	734741.	−	196873.i	0.826249	−	0.221393i
$944$	2.68876e6	−	3.20434e6i	3.01722	−	3.59579i
$945$	−285628.	+	28858.7i	−0.319843	+	0.0323157i
$946$	1.22647e6	−	446398.i	1.37048	−	0.498815i
$947$	−85448.2	+	976677.i	−0.0952802	+	1.08906i	0.786561	+	0.617512i	$0.211859\pi$
$947$	−85448.2	+	976677.i	−0.0952802	+	1.08906i	−0.881842	+	0.471546i	$0.843696\pi$
$948$	−94340.0	+	134731.i	−0.104973	+	0.149917i
$949$		−	956488.i		−	1.06205i
$950$	900663.	−	1.40922e6i	0.997965	−	1.56146i
$951$	108385.			0.119842
$952$	−1.71721e6	−	1.20240e6i	−1.89474	−	1.32671i
$953$	360143.	+	31508.5i	0.396542	+	0.0346930i	0.283683	−	0.958918i	$-0.408444\pi$
$953$	360143.	+	31508.5i	0.396542	+	0.0346930i	0.112859	+	0.993611i	$0.463999\pi$
$954$	486984.	+	1.33798e6i	0.535079	+	1.47012i
$955$	−5538.51	−	54817.3i	−0.00607276	−	0.0601050i
$956$	−3.18363e6	−	2.67138e6i	−3.48343	−	2.92295i
$957$	−32071.5	−	119692.i	−0.0350183	−	0.130690i
$958$	371107.	−	1.38499e6i	0.404360	−	1.50909i
$959$	−2.43355e6	−	429100.i	−2.64608	−	0.466575i
$960$	−54055.5	+	96599.5i	−0.0586540	+	0.104817i
$961$	461365.	+	799108.i	0.499572	+	0.865284i
$962$	−27057.9	−	100981.i	−0.0292377	−	0.109117i
$963$	−29405.8	−	336110.i	−0.0317089	−	0.362434i
$964$	−719014.	+	1.97547e6i	−0.773719	+	2.12578i
$965$	253.160	+	18852.4i	0.000271857	+	0.0202447i
$966$	−108295.	+	90870.4i	−0.116053	+	0.0973796i
$967$	479829.	+	335980.i	0.513137	+	0.359302i	0.801284	−	0.598284i	$-0.204150\pi$
$967$	479829.	+	335980.i	0.513137	+	0.359302i	−0.288147	+	0.957586i	$0.593039\pi$
$968$	304201.	+	304201.i	0.324646	+	0.324646i
$969$	42606.1	−	36877.5i	0.0453758	−	0.0392748i
$970$	−149189.	+	72022.2i	−0.158559	+	0.0765460i
$971$	−124390.	−	705449.i	−0.131931	−	0.748217i	−0.976948	−	0.213478i	$-0.931521\pi$
$971$	−124390.	−	705449.i	−0.131931	−	0.748217i	0.845017	−	0.534739i	$-0.179590\pi$
$972$	62537.2	−	714804.i	0.0661921	−	0.756579i
$973$	−1.27194e6	−	593117.i	−1.34351	−	0.626491i
$974$	349207.	−	959437.i	0.368099	−	1.01134i
$975$	11120.0	+	54468.1i	0.0116976	+	0.0572972i
$976$	1.90818e6	−	3.30507e6i	2.00318	−	3.46961i
$977$	−746163.	−	199934.i	−0.781708	−	0.209458i	−0.154171	−	0.988044i	$-0.549271\pi$
$977$	−746163.	−	199934.i	−0.781708	−	0.209458i	−0.627538	+	0.778586i	$0.715937\pi$
$978$	−89070.4	+	62367.7i	−0.0931227	+	0.0652052i
$979$	−567233.	−	100019.i	−0.591829	−	0.104355i
$980$	1.76771e6	−	2.59812e6i	1.84060	−	2.70525i
$981$	−545071.	+	944090.i	−0.566389	+	0.981014i
$982$	239418.	−	20946.4i	0.248276	−	0.0217213i
$983$	−358590.	−	768998.i	−0.371100	−	0.795826i	−0.999834	−	0.0182059i	$-0.994205\pi$
$983$	−358590.	−	768998.i	−0.371100	−	0.795826i	0.628735	−	0.777620i	$-0.283573\pi$
$984$	157134.	+	431722.i	0.162286	+	0.445876i
$985$	738314.	−	280008.i	0.760972	−	0.288601i
$986$	−210470.	−	1.19363e6i	−0.216489	−	1.22777i
$987$	−91685.4	+	91685.4i	−0.0941165	+	0.0941165i
$988$	360084.	+	1.26596e6i	0.368884	+	1.29690i
$989$		−	359523.i		−	0.367565i
$990$	1.91979e6	+	311991.i	1.95876	+	0.318326i
$991$	−537369.	+	450906.i	−0.547174	+	0.459133i	−0.873983	−	0.485957i	$-0.838471\pi$
$991$	−537369.	+	450906.i	−0.547174	+	0.459133i	0.326809	+	0.945090i	$0.394027\pi$
$992$	23826.2	−	51095.5i	0.0242121	−	0.0519230i
$993$	−54961.5	−	117865.i	−0.0557391	−	0.119533i
$994$	−761641.	+	907689.i	−0.770864	+	0.918680i
$995$	−6943.86	+	93869.9i	−0.00701382	+	0.0948157i
$996$	−52388.6	−	90739.8i	−0.0528103	−	0.0914701i
$997$	353815.	+	505300.i	0.355948	+	0.508346i	0.956695	−	0.291093i	$-0.0940190\pi$
$997$	353815.	+	505300.i	0.355948	+	0.508346i	−0.600747	+	0.799439i	$0.705130\pi$
$998$	−1.50870e6	+	1.05640e6i	−1.51475	+	1.06064i
$999$	19970.1	−	11529.7i	0.0200101	−	0.0115528i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	95.5.q.a.28.2	yes	456
5.2	odd	4	inner	95.5.q.a.47.37	yes	456
19.17	even	9	inner	95.5.q.a.93.37	yes	456
95.17	odd	36	inner	95.5.q.a.17.2	✓	456

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.5.q.a.17.2	✓	456	95.17	odd	36	inner
95.5.q.a.28.2	yes	456	1.1	even	1	trivial
95.5.q.a.47.37	yes	456	5.2	odd	4	inner
95.5.q.a.93.37	yes	456	19.17	even	9	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+(-6.07197 - 4.25164i) q^{2} +(-0.946507 - 0.0828086i) q^{3} +(13.3201 + 36.5966i) q^{4} +(2.51310 + 24.8734i) q^{5} +(5.39509 + 4.52702i) q^{6} +(19.4176 + 72.4674i) q^{7} +(44.0206 - 164.287i) q^{8} +(-78.8804 - 13.9087i) q^{9} +(90.4932 - 161.715i) q^{10} +(-65.5179 - 113.480i) q^{11} +(-9.57704 - 35.7420i) q^{12} +(8.15917 + 93.2598i) q^{13} +(190.202 - 522.576i) q^{14} +(-0.318941 - 23.7509i) q^{15} +(-488.440 + 409.850i) q^{16} +(-134.575 - 94.2306i) q^{17} +(419.825 + 419.825i) q^{18} +(57.2339 - 356.434i) q^{19} +(-876.807 + 423.287i) q^{20} +(-12.3779 - 70.1988i) q^{21} +(-84.6548 + 967.609i) q^{22} +(242.486 + 113.073i) q^{23} +(-55.2702 + 151.854i) q^{24} +(-612.369 + 125.019i) q^{25} +(346.965 - 600.961i) q^{26} +(147.847 + 39.6154i) q^{27} +(-2393.42 + 1675.89i) q^{28} +(-980.177 - 172.832i) q^{29} +(-99.0438 + 145.571i) q^{30} +(14.0593 - 24.3514i) q^{31} +(1997.37 - 174.747i) q^{32} +(52.6160 + 112.835i) q^{33} +(416.503 + 1144.33i) q^{34} +(-1753.71 + 665.098i) q^{35} +(-541.681 - 3072.02i) q^{36} +(106.529 - 106.529i) q^{37} +(-1862.95 + 1920.92i) q^{38} -88.9467i q^{39} +(4197.00 + 682.070i) q^{40} +(2177.88 - 1827.46i) q^{41} +(-223.302 + 478.872i) q^{42} +(-567.889 - 1217.84i) q^{43} +(3280.30 - 3909.30i) q^{44} +(147.723 - 1996.98i) q^{45} +(-991.623 - 1717.54i) q^{46} +(-1043.35 - 1490.05i) q^{47} +(496.252 - 347.479i) q^{48} +(-2795.15 + 1613.78i) q^{49} +(4249.82 + 1844.46i) q^{50} +(119.573 + 100.334i) q^{51} +(-3304.31 + 1540.83i) q^{52} +(2173.48 + 1013.51i) q^{53} +(-729.291 - 869.135i) q^{54} +(2657.99 - 1914.84i) q^{55} +12760.2 q^{56} +(-83.6881 + 332.628i) q^{57} +(5216.79 + 5216.79i) q^{58} +(-6460.67 + 1139.19i) q^{59} +(864.956 - 328.037i) q^{60} +(-5624.43 + 2047.12i) q^{61} +(-188.901 + 88.0860i) q^{62} +(-523.736 - 5986.33i) q^{63} +(-4035.90 - 2330.13i) q^{64} +(-2299.18 + 437.317i) q^{65} +(160.253 - 908.838i) q^{66} +(2806.46 + 4008.05i) q^{67} +(1655.97 - 6180.16i) q^{68} +(-220.151 - 127.104i) q^{69} +(13476.2 + 3417.68i) q^{70} +(-2002.19 - 728.737i) q^{71} +(-5757.39 + 12346.8i) q^{72} +(-10178.3 - 890.482i) q^{73} +(-1099.76 + 193.918i) q^{74} +(589.964 - 67.6217i) q^{75} +(13806.7 - 2653.16i) q^{76} +(6951.42 - 6951.42i) q^{77} +(-378.169 + 540.082i) q^{78} +(-2857.18 - 3405.05i) q^{79} +(-11421.9 - 11119.2i) q^{80} +(5959.95 + 2169.25i) q^{81} +(-20993.7 + 1836.71i) q^{82} +(2735.12 - 732.872i) q^{83} +(2404.17 - 1388.05i) q^{84} +(2005.63 - 3584.15i) q^{85} +(-1729.62 + 9809.16i) q^{86} +(913.433 + 244.754i) q^{87} +(-21527.5 + 5768.28i) q^{88} +(2825.45 - 3367.24i) q^{89} +(-9387.39 + 11497.5i) q^{90} +(-6599.86 + 2402.15i) q^{91} +(-908.161 + 10380.3i) q^{92} +(-15.3237 + 21.8845i) q^{93} +13483.5i q^{94} +(9009.55 + 527.845i) q^{95} -1904.99 q^{96} +(-732.295 - 512.759i) q^{97} +(23833.3 + 2085.14i) q^{98} +(3589.71 + 9862.65i) 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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