LMFDB - Embedded newform 95.5.q.a.17.3

Error: no document with id 240499420 found in table mf_hecke_traces.

Error: table True does not exist

Error: no document with id 275160291 found in table mf_hecke_traces.

Error: table True does not exist

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			17.3
Character	$\chi$	$=$	95.17
Dual form			95.5.q.a.28.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-5.80689 + 4.06603i) q^{2} +(6.77670 - 0.592885i) q^{3} +(11.7151 - 32.1869i) q^{4} +(-24.5342 - 4.80323i) q^{5} +(-36.9409 + 30.9971i) q^{6} +(-12.2458 + 45.7020i) q^{7} +(33.4888 + 124.982i) q^{8} +(-34.1972 + 6.02989i) q^{9} +(161.998 - 71.8651i) q^{10} +(99.3086 - 172.008i) q^{11} +(60.3065 - 225.067i) q^{12} +(-3.17658 + 36.3084i) q^{13} +(-114.715 - 315.178i) q^{14} +(-169.109 - 18.0041i) q^{15} +(-282.823 - 237.317i) q^{16} +(118.227 - 82.7838i) q^{17} +(174.062 - 174.062i) q^{18} +(342.347 - 114.540i) q^{19} +(-442.022 + 733.411i) q^{20} +(-55.8902 + 316.969i) q^{21} +(122.713 + 1402.62i) q^{22} +(783.000 - 365.119i) q^{23} +(301.044 + 827.112i) q^{24} +(578.858 + 235.687i) q^{25} +(-129.185 - 223.755i) q^{26} +(-760.404 + 203.750i) q^{27} +(1327.54 + 929.557i) q^{28} +(106.411 - 18.7632i) q^{29} +(1055.20 - 583.055i) q^{30} +(-24.7771 - 42.9151i) q^{31} +(544.880 + 47.6708i) q^{32} +(571.005 - 1224.52i) q^{33} +(-349.933 + 961.433i) q^{34} +(519.958 - 1062.44i) q^{35} +(-206.540 + 1171.34i) q^{36} +(1622.55 + 1622.55i) q^{37} +(-1522.25 + 2057.11i) q^{38} +247.935i q^{39} +(-221.306 - 3227.20i) q^{40} +(-979.089 - 821.554i) q^{41} +(-964.257 - 2067.86i) q^{42} +(670.423 - 1437.73i) q^{43} +(-4372.99 - 5211.52i) q^{44} +(867.966 + 16.3181i) q^{45} +(-3062.21 + 5303.91i) q^{46} +(1367.42 - 1952.88i) q^{47} +(-2057.31 - 1440.54i) q^{48} +(140.617 + 81.1854i) q^{49} +(-4319.68 + 985.045i) q^{50} +(752.111 - 631.096i) q^{51} +(1131.44 + 527.600i) q^{52} +(2745.22 - 1280.12i) q^{53} +(3587.13 - 4274.98i) q^{54} +(-3262.65 + 3743.07i) q^{55} -6122.02 q^{56} +(2252.08 - 979.175i) q^{57} +(-541.627 + 541.627i) q^{58} +(-4329.95 - 763.488i) q^{59} +(-2560.62 + 5232.18i) q^{60} +(-1604.78 - 584.093i) q^{61} +(318.372 + 148.459i) q^{62} +(143.195 - 1636.72i) q^{63} +(1757.88 - 1014.91i) q^{64} +(252.332 - 875.542i) q^{65} +(1663.19 + 9432.40i) q^{66} +(727.031 - 1038.31i) q^{67} +(-1279.51 - 4775.20i) q^{68} +(5089.69 - 2938.53i) q^{69} +(1300.59 + 8283.66i) q^{70} +(3896.69 - 1418.28i) q^{71} +(-1898.85 - 4072.11i) q^{72} +(-115.243 + 10.0824i) q^{73} +(-16019.3 - 2824.64i) q^{74} +(4062.48 + 1253.98i) q^{75} +(323.942 - 12360.9i) q^{76} +(6644.97 + 6644.97i) q^{77} +(-1008.11 - 1439.73i) q^{78} +(2920.50 - 3480.51i) q^{79} +(5798.96 + 7180.84i) q^{80} +(-2389.15 + 869.581i) q^{81} +(9025.93 + 789.666i) q^{82} +(-10594.8 - 2838.87i) q^{83} +(9547.50 + 5512.25i) q^{84} +(-3298.25 + 1463.16i) q^{85} +(1952.77 + 11074.7i) q^{86} +(709.993 - 190.242i) q^{87} +(24823.6 + 6651.46i) q^{88} +(6503.04 + 7750.03i) q^{89} +(-5106.54 + 3434.42i) q^{90} +(-1620.47 - 589.802i) q^{91} +(-2579.14 - 29479.8i) q^{92} +(-193.351 - 276.133i) q^{93} +16900.1i q^{94} +(-8949.39 + 1165.78i) q^{95} +3720.75 q^{96} +(-11805.0 + 8265.94i) q^{97} +(-1146.65 + 100.319i) q^{98} +(-2358.89 + 6481.00i) 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 $

$2$	−5.80689	+	4.06603i	−1.45172	+	1.01651i	−0.460027	+	0.887905i	$0.652160\pi$
$2$	−5.80689	+	4.06603i	−1.45172	+	1.01651i	−0.991696	+	0.128602i	$0.958951\pi$
$3$	6.77670	−	0.592885i	0.752967	−	0.0658761i	0.295791	−	0.955253i	$-0.404417\pi$
$3$	6.77670	−	0.592885i	0.752967	−	0.0658761i	0.457176	+	0.889376i	$0.348861\pi$
$4$	11.7151	−	32.1869i	0.732192	−	2.01168i
$5$	−24.5342	−	4.80323i	−0.981370	−	0.192129i
$5$	−24.5342	−	4.80323i	−0.981370	−	0.192129i
$6$	−36.9409	+	30.9971i	−1.02614	+	0.861031i
$7$	−12.2458	+	45.7020i	−0.249914	+	0.932693i	0.720935	+	0.693003i	$0.243713\pi$
$7$	−12.2458	+	45.7020i	−0.249914	+	0.932693i	−0.970849	+	0.239690i	$0.922954\pi$
$8$	33.4888	+	124.982i	0.523263	+	1.95285i
$9$	−34.1972	+	6.02989i	−0.422188	+	0.0744431i
$10$	161.998	−	71.8651i	1.61998	−	0.718651i
$11$	99.3086	−	172.008i	0.820733	−	1.42155i	−0.0844050	−	0.996432i	$-0.526899\pi$
$11$	99.3086	−	172.008i	0.820733	−	1.42155i	0.905138	−	0.425119i	$-0.139768\pi$
$12$	60.3065	−	225.067i	0.418795	−	1.56296i
$13$	−3.17658	+	36.3084i	−0.0187963	+	0.214843i	0.980988	+	0.194069i	$0.0621685\pi$
$13$	−3.17658	+	36.3084i	−0.0187963	+	0.214843i	−0.999784	+	0.0207738i	$0.993387\pi$
$14$	−114.715	−	315.178i	−0.585283	−	1.60805i
$15$	−169.109	−	18.0041i	−0.751596	−	0.0800180i
$16$	−282.823	−	237.317i	−1.10478	−	0.927018i
$17$	118.227	−	82.7838i	0.409092	−	0.286449i	−0.350861	−	0.936428i	$-0.614111\pi$
$17$	118.227	−	82.7838i	0.409092	−	0.286449i	0.759953	+	0.649979i	$0.225222\pi$
$18$	174.062	−	174.062i	0.537228	−	0.537228i
$19$	342.347	−	114.540i	0.948330	−	0.317285i
$19$	342.347	−	114.540i	0.948330	−	0.317285i
$20$	−442.022	+	733.411i	−1.10505	+	1.83353i
$21$	−55.8902	+	316.969i	−0.126735	+	0.718751i
$22$	122.713	+	1402.62i	0.253540	+	2.89798i
$23$	783.000	−	365.119i	1.48015	−	0.690206i	0.496129	−	0.868249i	$-0.334754\pi$
$23$	783.000	−	365.119i	1.48015	−	0.690206i	0.984023	+	0.178043i	$0.0569766\pi$
$24$	301.044	+	827.112i	0.522646	+	1.43596i
$25$	578.858	+	235.687i	0.926173	+	0.377099i
$26$	−129.185	−	223.755i	−0.191102	−	0.330999i
$27$	−760.404	+	203.750i	−1.04308	+	0.279492i
$28$	1327.54	+	929.557i	1.69330	+	1.18566i
$29$	106.411	−	18.7632i	0.126529	−	0.0223106i	−0.110025	−	0.993929i	$-0.535093\pi$
$29$	106.411	−	18.7632i	0.126529	−	0.0223106i	0.236554	+	0.971618i	$0.423982\pi$
$30$	1055.20	−	583.055i	1.17245	−	0.647839i
$31$	−24.7771	−	42.9151i	−0.0257826	−	0.0446567i	0.852846	−	0.522162i	$-0.174874\pi$
$31$	−24.7771	−	42.9151i	−0.0257826	−	0.0446567i	−0.878629	+	0.477505i	$0.841541\pi$
$32$	544.880	+	47.6708i	0.532110	+	0.0465536i
$33$	571.005	−	1224.52i	0.524338	−	1.12445i
$34$	−349.933	+	961.433i	−0.302710	+	0.831689i
$35$	519.958	−	1062.44i	0.424456	−	0.867301i
$36$	−206.540	+	1171.34i	−0.159367	+	0.903815i
$37$	1622.55	+	1622.55i	1.18521	+	1.18521i	0.978376	+	0.206832i	$0.0663154\pi$
$37$	1622.55	+	1622.55i	1.18521	+	1.18521i	0.206832	+	0.978376i	$0.433685\pi$
$38$	−1522.25	+	2057.11i	−1.05419	+	1.42459i
$39$			247.935i			0.163008i
$40$	−221.306	−	3227.20i	−0.138316	−	2.01700i
$41$	−979.089	−	821.554i	−0.582445	−	0.488729i	0.303304	−	0.952894i	$-0.401910\pi$
$41$	−979.089	−	821.554i	−0.582445	−	0.488729i	−0.885749	+	0.464165i	$0.846355\pi$
$42$	−964.257	−	2067.86i	−0.546631	−	1.17225i
$43$	670.423	−	1437.73i	0.362587	−	0.777570i	−0.637388	−	0.770543i	$-0.719985\pi$
$43$	670.423	−	1437.73i	0.362587	−	0.777570i	0.999975	−	0.00702757i	$-0.00223696\pi$
$44$	−4372.99	−	5211.52i	−2.25877	−	2.69190i
$45$	867.966	+	16.3181i	0.428625	+	0.00805834i
$46$	−3062.21	+	5303.91i	−1.44717	+	2.50657i
$47$	1367.42	−	1952.88i	0.619023	−	0.884056i	−0.380142	−	0.924928i	$-0.624125\pi$
$47$	1367.42	−	1952.88i	0.619023	−	0.884056i	0.999164	+	0.0408724i	$0.0130137\pi$
$48$	−2057.31	−	1440.54i	−0.892929	−	0.625235i
$49$	140.617	+	81.1854i	0.0585661	+	0.0338132i
$50$	−4319.68	+	985.045i	−1.72787	+	0.394018i
$51$	752.111	−	631.096i	0.289162	−	0.242636i
$52$	1131.44	+	527.600i	0.418433	+	0.195118i
$53$	2745.22	−	1280.12i	0.977295	−	0.455720i	0.132718	−	0.991154i	$-0.457630\pi$
$53$	2745.22	−	1280.12i	0.977295	−	0.455720i	0.844577	+	0.535434i	$0.179852\pi$
$54$	3587.13	−	4274.98i	1.23016	−	1.46604i
$55$	−3262.65	+	3743.07i	−1.07856	+	1.23738i
$56$	−6122.02			−1.95218
$57$	2252.08	−	979.175i	0.693160	−	0.301377i
$58$	−541.627	+	541.627i	−0.161007	+	0.161007i
$59$	−4329.95	−	763.488i	−1.24388	−	0.219330i	−0.487304	−	0.873233i	$-0.662019\pi$
$59$	−4329.95	−	763.488i	−1.24388	−	0.219330i	−0.756579	+	0.653903i	$0.773131\pi$
$60$	−2560.62	+	5232.18i	−0.711284	+	1.45338i
$61$	−1604.78	−	584.093i	−0.431277	−	0.156972i	0.117254	−	0.993102i	$-0.462591\pi$
$61$	−1604.78	−	584.093i	−0.431277	−	0.156972i	−0.548532	+	0.836130i	$0.684813\pi$
$62$	318.372	+	148.459i	0.0828231	+	0.0386210i
$63$	143.195	−	1636.72i	0.0360782	−	0.412376i
$64$	1757.88	−	1014.91i	0.429170	−	0.247781i
$65$	252.332	−	875.542i	0.0597236	−	0.207229i
$66$	1663.19	+	9432.40i	0.381815	+	2.16538i
$67$	727.031	−	1038.31i	0.161958	−	0.231301i	−0.729968	−	0.683482i	$-0.760465\pi$
$67$	727.031	−	1038.31i	0.161958	−	0.231301i	0.891926	+	0.452181i	$0.149354\pi$
$68$	−1279.51	−	4775.20i	−0.276711	−	1.03270i
$69$	5089.69	−	2938.53i	1.06904	−	0.617209i
$70$	1300.59	+	8283.66i	0.265426	+	1.69054i
$71$	3896.69	−	1418.28i	0.772999	−	0.281349i	0.0747487	−	0.997202i	$-0.476185\pi$
$71$	3896.69	−	1418.28i	0.772999	−	0.281349i	0.698250	+	0.715854i	$0.253962\pi$
$72$	−1898.85	−	4072.11i	−0.366291	−	0.785514i
$73$	−115.243	+	10.0824i	−0.0216256	+	0.00189199i	−0.0979634	−	0.995190i	$-0.531233\pi$
$73$	−115.243	+	10.0824i	−0.0216256	+	0.00189199i	0.0763378	+	0.997082i	$0.475677\pi$
$74$	−16019.3	−	2824.64i	−2.92537	−	0.515821i
$75$	4062.48	+	1253.98i	0.722220	+	0.222931i
$76$	323.942	−	12360.9i	0.0560842	−	2.14005i
$77$	6644.97	+	6644.97i	1.12076	+	1.12076i
$78$	−1008.11	−	1439.73i	−0.165699	−	0.236642i
$79$	2920.50	−	3480.51i	0.467953	−	0.557685i	−0.479515	−	0.877533i	$-0.659188\pi$
$79$	2920.50	−	3480.51i	0.467953	−	0.557685i	0.947469	+	0.319848i	$0.103632\pi$
$80$	5798.96	+	7180.84i	0.906087	+	1.12201i
$81$	−2389.15	+	869.581i	−0.364145	+	0.132538i
$82$	9025.93	+	789.666i	1.34234	+	0.117440i
$83$	−10594.8	−	2838.87i	−1.53793	−	0.412087i	−0.612334	−	0.790599i	$-0.709769\pi$
$83$	−10594.8	−	2838.87i	−1.53793	−	0.412087i	−0.925596	+	0.378512i	$0.876436\pi$
$84$	9547.50	+	5512.25i	1.35310	+	0.781215i
$85$	−3298.25	+	1463.16i	−0.456505	+	0.202514i
$86$	1952.77	+	11074.7i	0.264030	+	1.49739i
$87$	709.993	−	190.242i	0.0938028	−	0.0251344i
$88$	24823.6	+	6651.46i	3.20553	+	0.858918i
$89$	6503.04	+	7750.03i	0.820988	+	0.978415i	0.999985	−	0.00543438i	$-0.00172983\pi$
$89$	6503.04	+	7750.03i	0.820988	+	0.978415i	−0.178997	+	0.983850i	$0.557285\pi$
$90$	−5106.54	+	3434.42i	−0.630436	+	0.424002i
$91$	−1620.47	−	589.802i	−0.195685	−	0.0712235i
$92$	−2579.14	−	29479.8i	−0.304719	−	3.48296i
$93$	−193.351	−	276.133i	−0.0223553	−	0.0319266i
$94$			16900.1i			1.91265i
$95$	−8949.39	+	1165.78i	−0.991622	+	0.129172i
$96$	3720.75			0.403728
$97$	−11805.0	+	8265.94i	−1.25465	+	0.878514i	−0.996164	−	0.0875011i	$-0.972112\pi$
$97$	−11805.0	+	8265.94i	−1.25465	+	0.878514i	−0.258484	+	0.966016i	$0.583223\pi$
$98$	−1146.65	+	100.319i	−0.119393	+	0.0104455i
$99$	−2358.89	+	6481.00i	−0.240679	+	0.661259i
$100$	14367.4	−	15870.6i	1.43674	−	1.58706i
$101$	1172.22	−	983.609i	0.114912	−	0.0964228i	−0.583521	−	0.812098i	$-0.698325\pi$
$101$	1172.22	−	983.609i	0.114912	−	0.0964228i	0.698433	+	0.715675i	$0.253881\pi$
$102$	−1801.37	+	6722.81i	−0.173142	+	0.646176i
$103$	1040.69	+	3883.89i	0.0980947	+	0.366094i	0.997470	−	0.0710821i	$-0.0226452\pi$
$103$	1040.69	+	3883.89i	0.0980947	+	0.366094i	−0.899376	+	0.437176i	$0.855979\pi$
$104$	−4644.28	+	818.912i	−0.429390	+	0.0757130i
$105$	2893.70	−	7508.14i	0.262467	−	0.681011i
$106$	−10736.2	+	18595.7i	−0.955519	+	1.65501i
$107$	3997.99	−	14920.7i	0.349200	−	1.30323i	−0.538429	−	0.842671i	$-0.680982\pi$
$107$	3997.99	−	14920.7i	0.349200	−	1.30323i	0.887629	−	0.460560i	$-0.152351\pi$
$108$	−2350.12	+	26862.0i	−0.201485	+	2.30298i
$109$	−5756.20	−	15815.0i	−0.484488	−	1.33112i	−0.905608	−	0.424115i	$-0.860585\pi$
$109$	−5756.20	−	15815.0i	−0.484488	−	1.33112i	0.421120	−	0.907005i	$-0.361637\pi$
$110$	3726.43	−	35001.7i	0.307969	−	2.89270i
$111$	11957.5	+	10033.6i	0.970500	+	0.814346i
$112$	14309.2	−	10019.4i	1.14072	−	0.798743i
$113$	−3709.90	+	3709.90i	−0.290540	+	0.290540i	−0.837294	−	0.546754i	$-0.815863\pi$
$113$	−3709.90	+	3709.90i	−0.290540	+	0.290540i	0.546754	+	0.837294i	$0.315863\pi$
$114$	−9096.22	+	14843.0i	−0.699924	+	1.14212i
$115$	−20964.1	+	5196.99i	−1.58518	+	0.392967i
$116$	642.688	−	3644.86i	0.0477622	−	0.270873i
$117$	−110.306	−	1260.80i	−0.00805799	−	0.0921033i
$118$	28247.9	−	13172.2i	2.02872	−	0.946009i
$119$	2335.59	+	6416.98i	0.164931	+	0.453145i
$120$	−3413.08	−	21738.5i	−0.237020	−	1.50962i
$121$	−12403.9	−	21484.2i	−0.847204	−	1.46740i
$122$	11693.7	−	3133.33i	0.785658	−	0.210517i
$123$	−7122.08	−	4986.94i	−0.470757	−	0.329628i
$124$	−1671.57	+	294.743i	−0.108713	+	0.0191690i
$125$	−13069.8	−	8562.79i	−0.836466	−	0.548018i
$126$	5823.44	+	10086.5i	0.366808	+	0.635330i
$127$	7204.70	+	630.330i	0.446693	+	0.0390805i	0.308283	−	0.951295i	$-0.400246\pi$
$127$	7204.70	+	630.330i	0.446693	+	0.0390805i	0.138409	+	0.990375i	$0.455801\pi$
$128$	−9779.65	+	20972.5i	−0.596902	+	1.28006i
$129$	3690.85	−	10140.5i	0.221793	−	0.609371i
$130$	2094.71	+	6110.17i	0.123947	+	0.361548i
$131$	3841.39	−	21785.6i	0.223844	−	1.26948i	−0.641039	−	0.767508i	$-0.721496\pi$
$131$	3841.39	−	21785.6i	0.223844	−	1.26948i	0.864883	−	0.501974i	$-0.167393\pi$
$132$	−32724.3	−	32724.3i	−1.87811	−	1.87811i
$133$	1042.38	+	17048.6i	0.0589279	+	0.963795i
$134$			8985.47i			0.500416i
$135$	19634.6	−	1346.45i	1.07734	−	0.0738793i
$136$	14305.8	+	12004.0i	0.773453	+	0.649004i
$137$	9579.79	+	20543.9i	0.510405	+	1.09457i	0.977611	+	0.210419i	$0.0674827\pi$
$137$	9579.79	+	20543.9i	0.510405	+	1.09457i	−0.467207	+	0.884148i	$0.654740\pi$
$138$	−17607.1	+	37758.6i	−0.924549	+	1.98270i
$139$	−14768.5	−	17600.4i	−0.764375	−	0.910947i	0.233741	−	0.972299i	$-0.424903\pi$
$139$	−14768.5	−	17600.4i	−0.764375	−	0.910947i	−0.998116	+	0.0613523i	$0.980459\pi$
$140$	−28105.4	−	29182.5i	−1.43395	−	1.48890i
$141$	8108.77	−	14044.8i	0.407865	−	0.706444i
$142$	−16860.9	+	24079.8i	−0.836187	+	1.19420i
$143$	5929.86	+	4152.13i	0.289983	+	0.203048i
$144$	11102.7	+	6410.18i	0.535434	+	0.309133i
$145$	−2700.84	−	50.7770i	−0.128459	−	0.00241508i
$146$	628.207	−	527.128i	0.0294712	−	0.0247292i
$147$	1001.05	+	466.800i	0.0463258	+	0.0216021i
$148$	71233.2	−	33216.6i	3.25206	−	1.51646i
$149$	−11283.3	+	13446.9i	−0.508232	+	0.605688i	−0.957756	−	0.287581i	$-0.907149\pi$
$149$	−11283.3	+	13446.9i	−0.508232	+	0.605688i	0.449524	+	0.893268i	$0.351594\pi$
$150$	−28689.2	+	9236.43i	−1.27507	+	0.410508i
$151$	41515.5			1.82077			0.910387	−	0.413758i	$-0.135784\pi$
$151$	41515.5			1.82077			0.910387	+	0.413758i	$0.135784\pi$
$152$	25780.2	+	38951.5i	1.11583	+	1.68592i
$153$	−3543.87	+	3543.87i	−0.151389	+	0.151389i
$154$	−65605.3	−	11568.0i	−2.76629	−	0.487771i
$155$	401.755	+	1171.90i	0.0167224	+	0.0487784i
$156$	7980.25	+	2904.58i	0.327920	+	0.119353i
$157$	2729.94	+	1272.99i	0.110752	+	0.0516447i	0.477205	−	0.878792i	$-0.341650\pi$
$157$	2729.94	+	1272.99i	0.110752	+	0.0516447i	−0.366452	+	0.930437i	$0.619428\pi$
$158$	−2807.14	+	32085.8i	−0.112448	+	1.28528i
$159$	17844.6	−	10302.6i	0.705850	−	0.407523i
$160$	−13139.2	−	3786.75i	−0.513252	−	0.147920i
$161$	7098.19	+	40255.8i	0.273839	+	1.55302i
$162$	10337.8	−	14763.9i	0.393911	−	0.562564i
$163$	−2773.89	−	10352.3i	−0.104403	−	0.389639i	0.893873	−	0.448319i	$-0.147977\pi$
$163$	−2773.89	−	10352.3i	−0.104403	−	0.389639i	−0.998277	+	0.0586806i	$0.981311\pi$
$164$	−37913.4	+	21889.3i	−1.40963	+	0.813850i
$165$	−19890.8	+	27300.1i	−0.730609	+	1.00276i
$166$	73065.8	−	26593.8i	2.65154	−	0.965081i
$167$	12181.4	+	26123.2i	0.436783	+	0.936683i	0.994310	+	0.106525i	$0.0339723\pi$
$167$	12181.4	+	26123.2i	0.436783	+	0.936683i	−0.557527	+	0.830158i	$0.688250\pi$
$168$	−41487.1	+	3629.66i	−1.46992	+	0.128602i
$169$	26818.9	+	4728.89i	0.939004	+	0.165572i
$170$	13203.3	−	21907.2i	0.456862	−	0.758035i
$171$	−11016.7	+	5981.26i	−0.376754	+	0.204550i
$172$	−38422.0	−	38422.0i	−1.29874	−	1.29874i
$173$	−4991.66	−	7128.83i	−0.166783	−	0.238192i	0.727056	−	0.686578i	$-0.240888\pi$
$173$	−4991.66	−	7128.83i	−0.166783	−	0.238192i	−0.893840	+	0.448386i	$0.851999\pi$
$174$	−3349.32	+	3991.57i	−0.110626	+	0.131839i
$175$	−17859.9	+	23568.8i	−0.583182	+	0.769593i
$176$	−68907.0	+	25080.1i	−2.22453	+	0.809662i
$177$	−29795.5	−	2606.77i	−0.951051	−	0.0832062i
$178$	−69274.3	−	18562.0i	−2.18641	−	0.585848i
$179$	19990.1	+	11541.3i	0.623891	+	0.360204i	0.778382	−	0.627790i	$-0.216040\pi$
$179$	19990.1	+	11541.3i	0.623891	+	0.360204i	−0.154491	+	0.987994i	$0.549374\pi$
$180$	10693.5	−	27746.0i	0.330047	−	0.856357i
$181$	224.698	+	1274.33i	0.00685870	+	0.0388976i	0.988045	−	0.154165i	$-0.0492689\pi$
$181$	224.698	+	1274.33i	0.00685870	+	0.0388976i	−0.981186	+	0.193063i	$0.938158\pi$
$182$	11808.0	−	3163.95i	0.356479	−	0.0955184i
$183$	−11221.4	−	3006.77i	−0.335078	−	0.0897840i
$184$	71855.1	+	85633.6i	2.12237	+	2.52935i
$185$	−32014.6	−	47601.5i	−0.935415	−	1.39084i
$186$	2245.53	+	817.307i	0.0649073	+	0.0236243i
$187$	−2498.43	−	28557.2i	−0.0714469	−	0.816642i
$188$	−46837.7	−	66891.2i	−1.32520	−	1.89258i
$189$		−	37247.0i		−	1.04272i
$190$	47228.1	−	43158.0i	1.30826	−	1.19551i
$191$	−27347.0			−0.749623			−0.374811	−	0.927101i	$-0.622293\pi$
$191$	−27347.0			−0.749623			−0.374811	+	0.927101i	$0.622293\pi$
$192$	11310.9	−	7919.98i	0.306828	−	0.214843i
$193$	15167.7	−	1327.00i	0.407196	−	0.0356251i	0.118282	−	0.992980i	$-0.462261\pi$
$193$	15167.7	−	1327.00i	0.407196	−	0.0356251i	0.288914	+	0.957355i	$0.406706\pi$
$194$	34940.7	−	95998.9i	0.928386	−	2.55072i
$195$	1190.89	−	6082.89i	0.0313185	−	0.159971i
$196$	4260.45	−	3574.94i	0.110903	−	0.0930587i
$197$	−7814.09	+	29162.6i	−0.201347	+	0.751438i	0.789185	+	0.614156i	$0.210503\pi$
$197$	−7814.09	+	29162.6i	−0.201347	+	0.751438i	−0.990532	+	0.137282i	$0.956163\pi$
$198$	−12654.1	−	47225.8i	−0.322776	−	1.20462i
$199$	50731.6	−	8945.35i	1.28107	−	0.225887i	0.508635	−	0.860983i	$-0.330150\pi$
$199$	50731.6	−	8945.35i	1.28107	−	0.225887i	0.772433	+	0.635096i	$0.219039\pi$
$200$	−10071.4	+	80239.8i	−0.251784	+	2.00599i
$201$	4311.28	−	7467.35i	0.106712	−	0.184831i
$202$	−2807.57	+	10478.0i	−0.0688062	+	0.256788i
$203$	−445.577	+	5092.97i	−0.0108126	+	0.123589i
$204$	−11502.0	−	31601.5i	−0.276384	−	0.759359i
$205$	20075.1	+	24859.0i	0.477694	+	0.591528i
$206$	−21835.2	−	18321.9i	−0.514544	−	0.431754i
$207$	−24574.8	+	17207.5i	−0.573521	+	0.401584i
$208$	9515.00	−	9515.00i	0.219929	−	0.219929i
$209$	14296.3	−	70261.1i	0.327289	−	1.60851i
$210$	13724.9	+	55364.8i	0.311223	+	1.25544i
$211$	−8228.19	+	46664.4i	−0.184816	+	1.04814i	0.741376	+	0.671090i	$0.234174\pi$
$211$	−8228.19	+	46664.4i	−0.184816	+	1.04814i	−0.926192	+	0.377053i	$0.876937\pi$
$212$	−9042.56	−	103357.i	−0.201196	−	2.29968i
$213$	25565.8	−	11921.5i	0.563509	−	0.262768i
$214$	37452.1	+	102899.i	0.817802	+	2.24689i
$215$	−23354.1	+	32053.4i	−0.505226	+	0.693420i
$216$	−50930.1	−	88213.5i	−1.09161	−	1.89072i
$217$	2264.72	−	606.830i	0.0480945	−	0.0128869i
$218$	97730.0	+	68431.3i	2.05644	+	1.43993i
$219$	−774.989	+	136.651i	−0.0161587	+	0.00284922i
$220$	82255.8	+	148865.i	1.69950	+	3.07573i
$221$	2630.19	+	4555.62i	0.0538521	+	0.0932745i
$222$	−110233.	−	9644.12i	−2.23669	−	0.195685i
$223$	−36046.8	+	77302.6i	−0.724865	+	1.55448i	0.103715	+	0.994607i	$0.466927\pi$
$223$	−36046.8	+	77302.6i	−0.724865	+	1.55448i	−0.828580	+	0.559870i	$0.810851\pi$
$224$	−8851.15	+	24318.3i	−0.176402	+	0.484661i
$225$	−21216.5	−	4569.39i	−0.419092	−	0.0902596i
$226$	6458.43	−	36627.6i	0.126448	−	0.717120i
$227$	47720.9	+	47720.9i	0.926097	+	0.926097i	0.997451	−	0.0713541i	$-0.0227320\pi$
$227$	47720.9	+	47720.9i	0.926097	+	0.926097i	−0.0713541	+	0.997451i	$0.522732\pi$
$228$	−5133.35	−	83958.5i	−0.0987487	−	1.61508i
$229$		−	90603.8i		−	1.72773i	−0.503725	−	0.863864i	$-0.668037\pi$
$229$		−	90603.8i		−	1.72773i	0.503725	−	0.863864i	$-0.331963\pi$
$230$	100605.	−	115419.i	1.90179	−	2.18183i
$231$	48970.7	+	41091.3i	0.917725	+	0.770062i
$232$	5908.65	+	12671.1i	0.109777	+	0.235418i
$233$	−30774.1	+	65995.2i	−0.566856	+	1.21563i	0.388849	+	0.921302i	$0.372873\pi$
$233$	−30774.1	+	65995.2i	−0.566856	+	1.21563i	−0.955705	+	0.294326i	$0.904905\pi$
$234$	5766.99	+	6872.83i	0.105322	+	0.125517i
$235$	−42928.8	+	41344.4i	−0.777343	+	0.748653i
$236$	−75300.1	+	130424.i	−1.35198	+	2.34170i
$237$	17727.8	−	25317.9i	0.315615	−	0.450745i
$238$	−39654.2	−	27766.1i	−0.700059	−	0.490187i
$239$	13250.7	+	7650.31i	0.231976	+	0.133932i	0.611483	−	0.791257i	$-0.290573\pi$
$239$	13250.7	+	7650.31i	0.231976	+	0.133932i	−0.379507	+	0.925189i	$0.623906\pi$
$240$	43555.2	+	45224.3i	0.756167	+	0.785145i
$241$	−9741.00	+	8173.67i	−0.167714	+	0.140729i	−0.722782	−	0.691076i	$-0.757137\pi$
$241$	−9741.00	+	8173.67i	−0.167714	+	0.140729i	0.555068	+	0.831805i	$0.312692\pi$
$242$	159384.	+	74321.8i	2.72153	+	1.26907i
$243$	42116.1	−	19639.1i	0.713240	−	0.332589i
$244$	−37600.3	+	44810.3i	−0.631556	+	0.752659i
$245$	−3059.99	−	2667.24i	−0.0509785	−	0.0444355i
$246$	61634.2			1.01848
$247$	3071.27	+	12793.9i	0.0503412	+	0.209706i
$248$	4533.87	−	4533.87i	0.0737166	−	0.0737166i
$249$	−73480.9	−	12956.7i	−1.18516	−	0.208975i
$250$	110711.	−	3418.95i	1.77138	−	0.0547032i
$251$	53084.9	+	19321.3i	0.842604	+	0.306683i	0.727021	−	0.686615i	$-0.240904\pi$
$251$	53084.9	+	19321.3i	0.842604	+	0.306683i	0.115583	+	0.993298i	$0.463126\pi$
$252$	−51003.5	−	23783.3i	−0.803154	−	0.374517i
$253$	14955.4	−	170941.i	0.233646	−	2.67058i
$254$	−44399.9	+	25634.3i	−0.688199	+	0.397332i
$255$	−21483.8	+	11870.9i	−0.330393	+	0.182559i
$256$	−22845.9	−	129566.i	−0.348601	−	1.97702i
$257$	41391.6	−	59113.4i	0.626681	−	0.894993i	−0.372777	−	0.927921i	$-0.621594\pi$
$257$	41391.6	−	59113.4i	0.626681	−	0.894993i	0.999458	+	0.0329280i	$0.0104832\pi$
$258$	19799.3	+	73892.1i	0.297448	+	1.11009i
$259$	−94023.2	+	54284.3i	−1.40164	+	0.809235i
$260$	−25224.9	−	18378.8i	−0.373149	−	0.271876i
$261$	−3525.83	+	1283.30i	−0.0517583	+	0.0188385i
$262$	66274.3	+	142126.i	0.965479	+	2.07048i
$263$	−72977.2	+	6384.68i	−1.05506	+	0.0923055i	−0.601461	−	0.798902i	$-0.705414\pi$
$263$	−72977.2	+	6384.68i	−1.05506	+	0.0923055i	−0.453595	+	0.891208i	$0.649859\pi$
$264$	172166.	+	30357.5i	2.47024	+	0.435570i
$265$	−73500.6	+	18220.8i	−1.04664	+	0.259463i
$266$	−75373.0	−	94760.9i	−1.06525	−	1.33926i
$267$	48664.1	+	48664.1i	0.682631	+	0.682631i
$268$	−24902.7	−	35564.8i	−0.346719	−	0.495165i
$269$	54082.3	−	64452.8i	0.747396	−	0.890712i	−0.249585	−	0.968353i	$-0.580294\pi$
$269$	54082.3	−	64452.8i	0.747396	−	0.890712i	0.996981	+	0.0776409i	$0.0247388\pi$
$270$	−108541.	+	87653.5i	−1.48891	+	1.20238i
$271$	−18570.0	+	6758.91i	−0.252855	+	0.0920318i	−0.465338	−	0.885133i	$-0.654067\pi$
$271$	−18570.0	+	6758.91i	−0.252855	+	0.0920318i	0.212483	+	0.977165i	$0.431845\pi$
$272$	−53083.4	−	4644.19i	−0.717498	−	0.0627729i
$273$	−11331.1	−	3036.16i	−0.152036	−	0.0407380i
$274$	−139161.	−	80344.6i	−1.85360	−	1.07018i
$275$	98025.6	−	76162.2i	1.29621	−	1.00710i
$276$	−34956.2	−	198246.i	−0.458887	−	2.60248i
$277$	28877.0	−	7737.57i	0.376351	−	0.100843i	−0.0656849	−	0.997840i	$-0.520923\pi$
$277$	28877.0	−	7737.57i	0.376351	−	0.100843i	0.442035	+	0.896998i	$0.354257\pi$
$278$	157323.	+	42154.5i	2.03564	+	0.545449i
$279$	1106.08	+	1318.18i	0.0142095	+	0.0169342i
$280$	150199.	+	29405.5i	1.91581	+	0.375070i
$281$	−65135.2	−	23707.3i	−0.824904	−	0.300240i	−0.105138	−	0.994458i	$-0.533529\pi$
$281$	−65135.2	−	23707.3i	−0.824904	−	0.300240i	−0.719766	+	0.694217i	$0.755751\pi$
$282$	10019.8	+	114527.i	0.125998	+	1.44016i
$283$	52392.9	+	74824.8i	0.654183	+	0.934270i	0.999992	−	0.00403475i	$-0.00128430\pi$
$283$	52392.9	+	74824.8i	0.654183	+	0.934270i	−0.345809	+	0.938305i	$0.612395\pi$
$284$		−	142038.i		−	1.76103i
$285$	−59956.2	+	13206.1i	−0.738150	+	0.162586i
$286$	−51316.8			−0.627375
$287$	49536.3	−	34685.7i	0.601395	−	0.421102i
$288$	−18920.8	+	1655.36i	−0.228116	+	0.0199576i
$289$	−21441.3	+	58909.4i	−0.256717	+	0.705325i
$290$	15890.0	−	10686.9i	0.188941	−	0.127073i
$291$	−75098.2	+	63014.8i	−0.886836	+	0.744144i
$292$	−1025.56	+	3827.43i	−0.0120280	+	0.0448891i
$293$	10278.5	+	38359.7i	0.119727	+	0.446828i	0.999597	−	0.0283867i	$-0.00903699\pi$
$293$	10278.5	+	38359.7i	0.119727	+	0.446828i	−0.879870	+	0.475215i	$0.842370\pi$
$294$	−7711.04	+	1359.66i	−0.0892110	+	0.0157303i
$295$	102565.	+	39529.3i	1.17857	+	0.454230i
$296$	−148452.	+	257127.i	−1.69435	+	2.93471i
$297$	−40468.2	+	151029.i	−0.458776	+	1.71218i
$298$	10845.3	−	123963.i	0.122127	−	1.39591i
$299$	10769.6	+	29589.3i	0.120464	+	0.330973i
$300$	87954.2	−	116068.i	0.977269	−	1.28965i
$301$	57497.1	+	48245.8i	0.634619	+	0.532508i
$302$	−241076.	+	168803.i	−2.64326	+	1.85083i
$303$	7360.62	−	7360.62i	0.0801732	−	0.0801732i
$304$	−124006.	−	48850.2i	−1.34182	−	0.528590i
$305$	36566.6	+	22038.4i	0.393084	+	0.236909i
$306$	6169.40	−	34988.4i	0.0658870	−	0.373664i
$307$	−12025.8	−	137456.i	−0.127596	−	1.45843i	−0.742510	−	0.669835i	$-0.766365\pi$
$307$	−12025.8	−	137456.i	−0.127596	−	1.45843i	0.614913	−	0.788595i	$-0.289191\pi$
$308$	291727.	−	136035.i	3.07522	−	1.43400i
$309$	9355.12	+	25703.0i	0.0979789	+	0.269195i
$310$	−7097.93	−	5171.55i	−0.0738599	−	0.0538142i
$311$	−75161.7	−	130184.i	−0.777098	−	1.34597i	−0.933608	−	0.358297i	$-0.883358\pi$
$311$	−75161.7	−	130184.i	−0.777098	−	1.34597i	0.156509	−	0.987676i	$-0.449976\pi$
$312$	−30987.4	+	8303.05i	−0.318329	+	0.0852960i
$313$	−70297.1	−	49222.5i	−0.717544	−	0.502430i	0.156864	−	0.987620i	$-0.449861\pi$
$313$	−70297.1	−	49222.5i	−0.717544	−	0.502430i	−0.874409	+	0.485190i	$0.838750\pi$
$314$	−21028.5	+	3707.88i	−0.213279	+	0.0376068i
$315$	−11374.7	+	39467.9i	−0.114636	+	0.397762i
$316$	−77813.1	−	134776.i	−0.779253	−	1.34971i
$317$	−33500.9	−	2930.95i	−0.333379	−	0.0291669i	−0.0807624	−	0.996733i	$-0.525736\pi$
$317$	−33500.9	−	2930.95i	−0.333379	−	0.0291669i	−0.252616	+	0.967567i	$0.581291\pi$
$318$	−61731.0	+	132383.i	−0.610449	+	1.30911i
$319$	7340.15	−	20166.9i	0.0721313	−	0.198179i
$320$	−48003.1	+	16456.6i	−0.468780	+	0.160709i
$321$	18246.9	−	103483.i	0.177084	−	1.00429i
$322$	−204900.	−	204900.i	−1.97619	−	1.97619i
$323$	30992.8	−	41882.5i	0.297068	−	0.401447i
$324$			87086.7i			0.829586i
$325$	−10396.2	+	20268.7i	−0.0984257	+	0.191893i
$326$	58200.5	+	48836.0i	0.547636	+	0.459521i
$327$	−48384.6	−	103761.i	−0.452492	−	0.970373i
$328$	69890.9	−	149882.i	0.649640	−	1.39316i
$329$	72505.2	+	86408.4i	0.669850	+	0.798296i
$330$	4500.92	−	239405.i	0.0413308	−	2.19840i
$331$	−40592.5	+	70308.3i	−0.370501	+	0.641727i	−0.989643	−	0.143552i	$-0.954147\pi$
$331$	−40592.5	+	70308.3i	−0.370501	+	0.641727i	0.619141	+	0.785279i	$0.287481\pi$
$332$	−215493.	+	307756.i	−1.95505	+	2.79210i
$333$	−65270.5	−	45702.9i	−0.588612	−	0.412150i
$334$	−176954.	−	102164.i	−1.58623	−	0.915812i
$335$	−22824.4	+	21982.0i	−0.203381	+	0.195874i
$336$	91029.0	−	76382.4i	0.806309	−	0.676573i
$337$	−130136.	−	60683.3i	−1.14587	−	0.534330i	−0.245478	−	0.969402i	$-0.578945\pi$
$337$	−130136.	−	60683.3i	−1.14587	−	0.534330i	−0.900396	+	0.435072i	$0.856723\pi$
$338$	−174962.	+	81586.2i	−1.53148	+	0.714140i
$339$	−22941.4	+	27340.5i	−0.199627	+	0.237907i
$340$	8455.46	+	123302.i	0.0731441	+	1.06662i
$341$	−9842.31			−0.0846424
$342$	39652.6	−	79526.6i	0.339015	−	0.679924i
$343$	−85760.5	+	85760.5i	−0.728953	+	0.728953i
$344$	202142.	+	35643.1i	1.70820	+	0.301202i
$345$	−138986.	+	47647.7i	−1.16770	+	0.400317i
$346$	57972.1	+	21100.1i	0.484247	+	0.176251i
$347$	107777.	+	50257.2i	0.895090	+	0.417387i	0.815041	−	0.579404i	$-0.196715\pi$
$347$	107777.	+	50257.2i	0.895090	+	0.417387i	0.0800489	+	0.996791i	$0.474492\pi$
$348$	2194.32	−	25081.2i	0.0181193	−	0.207105i
$349$	21487.2	−	12405.6i	0.176412	−	0.101851i	−0.409194	−	0.912447i	$-0.634190\pi$
$349$	21487.2	−	12405.6i	0.176412	−	0.101851i	0.585606	+	0.810596i	$0.300857\pi$
$350$	7879.43	−	209480.i	0.0643219	−	1.71004i
$351$	−4982.35	−	28256.3i	−0.0404408	−	0.229351i
$352$	62311.1	−	88989.4i	0.502898	−	0.718213i
$353$	−24109.1	−	89976.3i	−0.193478	−	0.722069i	−0.992656	−	0.120974i	$-0.961398\pi$
$353$	−24109.1	−	89976.3i	−0.193478	−	0.722069i	0.799178	−	0.601095i	$-0.205269\pi$
$354$	183618.	−	106012.i	1.46524	−	0.845958i
$355$	−102415.	+	16079.7i	−0.812653	+	0.127591i
$356$	325633.	−	118521.i	2.56938	−	0.935178i
$357$	19632.1	+	42101.2i	0.154039	+	0.330338i
$358$	−163008.	+	14261.3i	−1.27187	+	0.111274i
$359$	144660.	+	25507.4i	1.12243	+	0.197914i	0.703907	−	0.710292i	$-0.251437\pi$
$359$	144660.	+	25507.4i	1.12243	+	0.197914i	0.418522	+	0.908207i	$0.362548\pi$
$360$	27027.7	+	109027.i	0.208547	+	0.841255i
$361$	104082.	−	78424.8i	0.798661	−	0.601781i
$362$	−6486.24	−	6486.24i	−0.0494967	−	0.0494967i
$363$	−96795.3	−	138238.i	−0.734583	−	1.04909i
$364$	−37967.8	+	45248.2i	−0.286558	+	0.341506i
$365$	2875.82	+	306.172i	0.0215862	+	0.00229816i
$366$	77387.3	−	28166.7i	0.577707	−	0.210268i
$367$	197204.	+	17253.1i	1.46414	+	0.128096i	0.791182	−	0.611581i	$-0.209466\pi$
$367$	197204.	+	17253.1i	1.46414	+	0.128096i	0.672962	+	0.739677i	$0.265022\pi$
$368$	−308099.	−	82554.9i	−2.27507	−	0.609603i
$369$	38436.0	+	22191.0i	0.282284	+	0.162977i
$370$	379454.	+	146245.i	2.77176	+	1.06826i
$371$	24886.5	+	141138.i	0.180807	+	1.02541i
$372$	−11153.0	+	2988.44i	−0.0805945	+	0.0215952i
$373$	−89684.8	−	24031.0i	−0.644616	−	0.172724i	−0.0783227	−	0.996928i	$-0.524956\pi$
$373$	−89684.8	−	24031.0i	−0.644616	−	0.172724i	−0.566293	+	0.824204i	$0.691623\pi$
$374$	130622.	+	155670.i	0.933844	+	1.11291i
$375$	−93646.8	−	50278.6i	−0.665933	−	0.357537i
$376$	289868.	+	105503.i	2.05034	+	0.746261i
$377$	343.238	+	3923.23i	0.00241497	+	0.0276033i
$378$	151448.	+	216290.i	1.05993	+	1.51374i
$379$			76209.3i			0.530554i	0.964172	+	0.265277i	$0.0854634\pi$
$379$			76209.3i			0.530554i	−0.964172	+	0.265277i	$0.914537\pi$
$380$	−67320.1	+	301710.i	−0.466206	+	2.08941i
$381$	49197.9			0.338919
$382$	158801.	−	111194.i	1.08824	−	0.761997i
$383$	−90698.9	+	7935.13i	−0.618308	+	0.0540949i	−0.392007	−	0.919962i	$-0.628219\pi$
$383$	−90698.9	+	7935.13i	−0.618308	+	0.0540949i	−0.226301	+	0.974057i	$0.572663\pi$
$384$	−53839.5	+	147923.i	−0.365122	+	1.00317i
$385$	−131112.	−	194947.i	−0.884547	−	1.31521i
$386$	−82681.3	+	69377.9i	−0.554923	+	0.465636i
$387$	−14257.3	+	53208.9i	−0.0951951	+	0.355273i
$388$	127759.	+	476802.i	0.848648	+	3.16720i
$389$	−22463.5	+	3960.92i	−0.148449	+	0.0261756i	−0.247379	−	0.968919i	$-0.579569\pi$
$389$	−22463.5	+	3960.92i	−0.148449	+	0.0261756i	0.0989297	+	0.995094i	$0.468458\pi$
$390$	17817.9	+	40164.9i	0.117146	+	0.264069i
$391$	62346.2	−	107987.i	0.407809	−	0.706345i
$392$	−5437.61	+	20293.4i	−0.0353864	+	0.132064i
$393$	13115.6	−	149912.i	0.0849186	−	0.970624i
$394$	−73200.3	−	201116.i	−0.471542	−	1.29555i
$395$	−88369.9	+	71363.9i	−0.566383	+	0.457388i
$396$	180969.	+	151851.i	1.15402	+	0.968338i
$397$	−119275.	+	83517.2i	−0.756777	+	0.529901i	−0.887104	−	0.461570i	$-0.847286\pi$
$397$	−119275.	+	83517.2i	−0.756777	+	0.529901i	0.130327	+	0.991471i	$0.458397\pi$
$398$	−258221.	+	258221.i	−1.63014	+	1.63014i
$399$	17171.7	+	114915.i	0.107862	+	0.721824i
$400$	−107782.	−	204030.i	−0.673637	−	1.27519i
$401$	−44606.3	+	252975.i	−0.277401	+	1.57322i	0.453831	+	0.891088i	$0.350057\pi$
$401$	−44606.3	+	252975.i	−0.277401	+	1.57322i	−0.731232	+	0.682129i	$0.761054\pi$
$402$	5327.35	+	60891.9i	0.0329655	+	0.376797i
$403$	1636.89	−	763.293i	0.0100788	−	0.00469982i
$404$	−17926.7	−	49253.2i	−0.109834	−	0.301767i
$405$	62792.8	−	9858.86i	0.382825	−	0.0601058i
$406$	−18120.8	−	31386.1i	−0.109932	−	0.190408i
$407$	440224.	−	117958.i	2.65757	−	0.712095i
$408$	104063.	+	72865.7i	0.625139	+	0.437727i
$409$	−17683.9	+	3118.15i	−0.105714	+	0.0186402i	−0.226255	−	0.974068i	$-0.572648\pi$
$409$	−17683.9	+	3118.15i	−0.105714	+	0.0186402i	0.120541	+	0.992708i	$0.461537\pi$
$410$	−217651.	−	62727.4i	−1.29477	−	0.373155i
$411$	77099.6	+	133540.i	0.456424	+	0.790549i
$412$	137202.	+	12003.6i	0.808289	+	0.0707162i
$413$	87916.7	−	188538.i	0.515432	−	1.10535i
$414$	72737.2	−	199844.i	0.424381	−	1.16598i
$415$	246300.	+	120539.i	1.43010	+	0.699891i
$416$	−3461.71	+	19632.3i	−0.0200034	+	0.113445i
$417$	−110517.	−	110517.i	−0.635559	−	0.635559i
$418$	202667.	+	466128.i	1.15992	+	2.66780i
$419$		−	216406.i		−	1.23265i	−0.787490	−	0.616327i	$-0.788620\pi$
$419$		−	216406.i		−	1.23265i	0.787490	−	0.616327i	$-0.211380\pi$
$420$	−207764.	−	181098.i	−1.17780	−	1.02663i
$421$	143072.	+	120051.i	0.807216	+	0.677335i	0.949942	−	0.312428i	$-0.101142\pi$
$421$	143072.	+	120051.i	0.807216	+	0.677335i	−0.142726	+	0.989762i	$0.545587\pi$
$422$	−141959.	−	304431.i	−0.797144	−	1.70948i
$423$	−34986.3	+	75028.5i	−0.195532	+	0.419320i
$424$	251926.	+	300234.i	1.40133	+	1.67004i
$425$	87948.0	−	20055.4i	0.486909	−	0.111033i
$426$	−99984.6	+	173178.i	−0.550952	+	0.954277i
$427$	46346.1	−	66189.0i	0.254189	−	0.363020i
$428$	−433414.	−	303480.i	−2.36600	−	1.65669i
$429$	42646.7	+	24622.1i	0.231724	+	0.133786i
$430$	5284.59	−	281089.i	0.0285808	−	1.52022i
$431$	241536.	−	202673.i	1.30025	−	1.09104i	0.310148	−	0.950688i	$-0.399621\pi$
$431$	241536.	−	202673.i	1.30025	−	1.09104i	0.990102	−	0.140351i	$-0.0448232\pi$
$432$	263413.	+	122831.i	1.41146	+	0.658176i
$433$	149265.	−	69603.2i	0.796125	−	0.371239i	0.0183894	−	0.999831i	$-0.494146\pi$
$433$	149265.	−	69603.2i	0.796125	−	0.371239i	0.777735	+	0.628592i	$0.216368\pi$
$434$	−10683.6	+	12732.2i	−0.0567203	+	0.0675966i
$435$	−18332.9	+	1257.19i	−0.0968842	+	0.00664388i
$436$	−576471.			−3.03253
$437$	226237.	−	214682.i	1.18468	−	1.12417i
$438$	3944.65	−	3944.65i	0.0205617	−	0.0205617i
$439$	−45791.0	−	8074.18i	−0.237602	−	0.0418957i	0.0535789	−	0.998564i	$-0.482937\pi$
$439$	−45791.0	−	8074.18i	−0.237602	−	0.0418957i	−0.291181	+	0.956668i	$0.594048\pi$
$440$	−577080.	−	282422.i	−2.98078	−	1.45879i
$441$	−5298.26	−	1928.41i	−0.0272431	−	0.00991567i
$442$	−33796.5	−	15759.6i	−0.172993	−	0.0806678i
$443$	13971.4	−	159694.i	0.0711924	−	0.813733i	−0.873724	−	0.486422i	$-0.838302\pi$
$443$	13971.4	−	159694.i	0.0711924	−	0.813733i	0.944916	−	0.327311i	$-0.106143\pi$
$444$	463033.	−	267332.i	2.34880	−	1.35608i
$445$	−122322.	−	221377.i	−0.617711	−	1.11792i
$446$	−104995.	−	595455.i	−0.527835	−	2.99350i
$447$	−68490.9	+	97815.1i	−0.342782	+	0.489543i
$448$	24856.8	+	92767.0i	0.123848	+	0.462208i
$449$	84961.4	−	49052.5i	0.421433	−	0.243315i	−0.274257	−	0.961656i	$-0.588432\pi$
$449$	84961.4	−	49052.5i	0.421433	−	0.243315i	0.695690	+	0.718342i	$0.255099\pi$
$450$	141781.	−	59733.0i	0.700154	−	0.294978i
$451$	−238545.	+	86823.5i	−1.17278	+	0.426859i
$452$	75948.6	+	162872.i	0.371743	+	0.797205i
$453$	281338.	−	24613.9i	1.37098	−	0.119945i
$454$	−471144.	−	83075.4i	−2.28582	−	0.403052i
$455$	36924.0	+	22253.8i	0.178355	+	0.107493i
$456$	197799.	+	248678.i	0.951248	+	1.19593i
$457$	−99457.9	−	99457.9i	−0.476219	−	0.476219i	0.427701	−	0.903920i	$-0.359324\pi$
$457$	−99457.9	−	99457.9i	−0.476219	−	0.476219i	−0.903920	+	0.427701i	$0.859324\pi$
$458$	368398.	+	526127.i	1.75625	+	2.50818i
$459$	−73033.5	+	87037.9i	−0.346654	+	0.413126i
$460$	−78320.6	+	735652.i	−0.370135	+	3.47661i
$461$	−59424.1	+	21628.6i	−0.279615	+	0.101772i	−0.478021	−	0.878348i	$-0.658646\pi$
$461$	−59424.1	+	21628.6i	−0.279615	+	0.101772i	0.198406	+	0.980120i	$0.436424\pi$
$462$	−451446.	−	39496.4i	−2.11506	−	0.185043i
$463$	77945.4	+	20885.4i	0.363604	+	0.0974273i	0.435995	−	0.899949i	$-0.356396\pi$
$463$	77945.4	+	20885.4i	0.363604	+	0.0974273i	−0.0723915	+	0.997376i	$0.523063\pi$
$464$	−34548.3	−	19946.5i	−0.160469	−	0.0926469i
$465$	3417.38	+	7703.43i	0.0158047	+	0.0356269i
$466$	−89636.7	−	508355.i	−0.412776	−	2.34097i
$467$	−164721.	+	44136.9i	−0.755293	+	0.202380i	−0.615865	−	0.787852i	$-0.711193\pi$
$467$	−164721.	+	44136.9i	−0.755293	+	0.202380i	−0.139428	+	0.990232i	$0.544526\pi$
$468$	−41873.6	−	11220.0i	−0.191183	−	0.0512272i
$469$	38549.6	+	45941.7i	0.175257	+	0.208863i
$470$	81175.2	−	414632.i	0.367475	−	1.87701i
$471$	19254.7	+	7008.14i	0.0867950	+	0.0315908i
$472$	−49582.9	−	566735.i	−0.222560	−	2.54388i
$473$	−180721.	−	258097.i	−0.807769	−	1.15361i
$474$			219100.i			0.975183i
$475$	225166.	+	14384.5i	0.997966	+	0.0637541i
$476$	233904.			1.03234
$477$	−86160.0	+	60329.9i	−0.378677	+	0.265152i
$478$	−108052.	+	9453.32i	−0.472908	+	0.0413741i
$479$	−72189.9	+	198340.i	−0.314634	+	0.864449i	0.677072	+	0.735917i	$0.263249\pi$
$479$	−72189.9	+	198340.i	−0.314634	+	0.864449i	−0.991705	+	0.128532i	$0.958973\pi$
$480$	−91285.9	−	17871.6i	−0.396206	−	0.0775678i
$481$	−64066.4	+	53758.1i	−0.276911	+	0.232356i
$482$	23330.6	−	87070.9i	0.100423	−	0.374782i
$483$	71969.4	+	268593.i	0.308499	+	1.15133i
$484$	−836823.	+	147554.i	−3.57226	+	0.629886i
$485$	329330.	−	146097.i	1.40006	−	0.621093i
$486$	−164711.	+	285287.i	−0.697348	+	1.20784i
$487$	7618.01	−	28430.8i	0.0321206	−	0.119876i	−0.948004	−	0.318258i	$-0.896902\pi$
$487$	7618.01	−	28430.8i	0.0321206	−	0.119876i	0.980125	+	0.198382i	$0.0635688\pi$
$488$	19258.9	−	220130.i	0.0808706	−	0.924355i
$489$	−24935.6	−	68510.0i	−0.104280	−	0.286508i
$490$	28614.1	+	3046.38i	0.119176	+	0.0126879i
$491$	−348569.	−	292484.i	−1.44586	−	1.21322i	−0.935534	−	0.353238i	$-0.885081\pi$
$491$	−348569.	−	292484.i	−1.44586	−	1.21322i	−0.510325	−	0.859982i	$-0.670475\pi$
$492$	−243950.	+	170816.i	−1.00779	+	0.705663i
$493$	11027.4	−	11027.4i	0.0453713	−	0.0453713i
$494$	−69855.0	−	61805.1i	−0.286249	−	0.253262i
$495$	89003.4	−	147676.i	0.363242	−	0.602699i
$496$	−3176.95	+	18017.4i	−0.0129136	+	0.0732366i
$497$	17100.0	+	195454.i	0.0692284	+	0.791284i
$498$	479378.	−	223538.i	1.93294	−	0.901347i
$499$	76730.3	+	210815.i	0.308152	+	0.846642i	0.993017	+	0.117972i	$0.0376392\pi$
$499$	76730.3	+	210815.i	0.308152	+	0.846642i	−0.684864	+	0.728670i	$0.740139\pi$
$500$	−428723.	+	320362.i	−1.71489	+	1.28145i
$501$	98038.0	+	169807.i	0.390588	+	0.676518i
$502$	−386819.	+	103648.i	−1.53497	+	0.411295i
$503$	−186991.	−	130933.i	−0.739070	−	0.517502i	0.142361	−	0.989815i	$-0.454531\pi$
$503$	−186991.	−	130933.i	−0.739070	−	0.517502i	−0.881431	+	0.472312i	$0.843419\pi$
$504$	209356.	−	36915.2i	0.824185	−	0.145326i
$505$	−33484.0	+	18501.7i	−0.131297	+	0.0725485i
$506$	608208.	+	1.05345e6i	2.37548	+	4.11445i
$507$	184547.	+	16145.8i	0.717946	+	0.0628121i
$508$	104692.	−	224513.i	0.405682	−	0.869989i
$509$	−106717.	+	293203.i	−0.411906	+	1.13170i	0.544270	+	0.838910i	$0.316807\pi$
$509$	−106717.	+	293203.i	−0.411906	+	1.13170i	−0.956176	+	0.292793i	$0.905415\pi$
$510$	76486.5	−	156287.i	0.294066	−	0.600872i
$511$	950.454	−	5390.29i	0.00363990	−	0.0206429i
$512$	397676.	+	397676.i	1.51701	+	1.51701i
$513$	−236985.	+	156850.i	−0.900504	+	0.596003i
$514$			511565.i			1.93631i
$515$	−6877.23	−	100287.i	−0.0259298	−	0.378121i
$516$	−283154.	−	237594.i	−1.06347	−	0.892353i
$517$	−200113.	−	429145.i	−0.748678	−	1.60555i
$518$	325261.	−	697524.i	1.21219	−	2.59956i
$519$	−38053.6	−	45350.5i	−0.141274	−	0.168363i
$520$	117877.	+	2216.15i	0.435937	+	0.00819580i
$521$	−118818.	+	205799.i	−0.437731	+	0.758173i	−0.997514	−	0.0704664i	$-0.977551\pi$
$521$	−118818.	+	205799.i	−0.437731	+	0.758173i	0.559783	+	0.828639i	$0.310885\pi$
$522$	15256.2	−	21788.1i	0.0559893	−	0.0799610i
$523$	248685.	+	174131.i	0.909173	+	0.636610i	0.931736	−	0.363135i	$-0.118294\pi$
$523$	248685.	+	174131.i	0.909173	+	0.636610i	−0.0225631	+	0.999745i	$0.507183\pi$
$524$	−656209.	−	378862.i	−2.38990	−	1.37981i
$525$	−107058.	+	170307.i	−0.388419	+	0.617896i
$526$	397810.	−	333803.i	1.43782	−	1.20647i
$527$	−6482.01	−	3022.61i	−0.0233393	−	0.0108833i
$528$	−452093.	+	210814.i	−1.62166	+	0.756192i
$529$	299899.	−	357406.i	1.07168	−	1.27717i
$530$	352724.	−	404662.i	1.25569	−	1.44059i
$531$	152676.			0.541480
$532$	560952.	+	166175.i	1.98200	+	0.587139i
$533$	32939.5	−	32939.5i	0.115948	−	0.115948i
$534$	−480457.	−	84717.5i	−1.68489	−	0.297092i
$535$	−169755.	+	346864.i	−0.593082	+	1.21186i
$536$	154117.	+	56094.1i	0.536441	+	0.195249i
$537$	142310.	+	66360.1i	0.493498	+	0.230122i
$538$	−51983.2	+	594171.i	−0.179597	+	2.05280i
$539$	27929.0	−	16124.8i	0.0961342	−	0.0555031i
$540$	186683.	−	647751.i	0.640201	−	2.22137i
$541$	−52821.7	−	299567.i	−0.180475	−	1.02353i	−0.931632	−	0.363402i	$-0.881615\pi$
$541$	−52821.7	−	299567.i	−0.180475	−	1.02353i	0.751157	−	0.660123i	$-0.229496\pi$
$542$	80351.8	−	114754.i	0.273525	−	0.390634i
$543$	2278.24	+	8502.51i	0.00772680	+	0.0288368i
$544$	68366.2	−	39471.2i	0.231017	−	0.133378i
$545$	65260.9	+	415658.i	0.219715	+	1.39940i
$546$	78143.6	−	28442.0i	0.262125	−	0.0954057i
$547$	152451.	+	326932.i	0.509512	+	1.09265i	0.977889	+	0.209124i	$0.0670613\pi$
$547$	152451.	+	326932.i	0.509512	+	1.09265i	−0.468377	+	0.883529i	$0.655161\pi$
$548$	773473.	−	67670.2i	2.57563	−	0.225339i
$549$	58401.1	+	10297.7i	0.193766	+	0.0341661i
$550$	−259546.	+	840841.i	−0.858003	+	2.77964i
$551$	34280.5	−	18611.8i	0.112913	−	0.0613036i
$552$	537712.	+	537712.i	1.76470	+	1.76470i
$553$	123302.	+	176094.i	0.403201	+	0.575830i
$554$	−136224.	+	162346.i	−0.443849	+	0.528959i
$555$	−245175.	−	303600.i	−0.795960	−	0.985636i
$556$	−739517.	+	269162.i	−2.39220	+	0.870691i
$557$	−581918.	−	50911.2i	−1.87565	−	0.164098i	−0.908428	−	0.418042i	$-0.862717\pi$
$557$	−581918.	−	50911.2i	−1.87565	−	0.164098i	−0.967219	+	0.253944i	$0.918272\pi$
$558$	−11782.6	−	3157.15i	−0.0378420	−	0.0101397i
$559$	50072.0	+	28909.1i	0.160240	+	0.0925146i
$560$	−399192.	+	177089.i	−1.27293	+	0.564696i
$561$	−33862.2	−	192042.i	−0.107594	−	0.610198i
$562$	474628.	−	127176.i	1.50273	−	0.402655i
$563$	121436.	+	32538.6i	0.383115	+	0.102655i	0.445236	−	0.895413i	$-0.353120\pi$
$563$	121436.	+	32538.6i	0.383115	+	0.102655i	−0.0621209	+	0.998069i	$0.519786\pi$
$564$	−357064.	−	425532.i	−1.12250	−	1.33775i
$565$	108839.	−	73200.2i	0.340948	−	0.229306i
$566$	−608480.	−	221468.i	−1.89939	−	0.691320i
$567$	−10484.4	−	119838.i	−0.0326121	−	0.372758i
$568$	307755.	+	439520.i	0.953912	+	1.36233i
$569$		−	198885.i		−	0.614294i	−0.951662	−	0.307147i	$-0.900626\pi$
$569$		−	198885.i		−	0.614294i	0.951662	−	0.307147i	$-0.0993744\pi$
$570$	294463.	−	320470.i	0.906319	−	0.986365i
$571$	−359098.			−1.10139			−0.550695	−	0.834706i	$-0.685637\pi$
$571$	−359098.			−1.10139			−0.550695	+	0.834706i	$0.685637\pi$
$572$	203113.	−	142221.i	0.620792	−	0.434683i
$573$	−185322.	+	16213.6i	−0.564441	+	0.0493822i
$574$	−146619.	+	402833.i	−0.445007	+	1.22265i
$575$	539300.	−	26809.1i	1.63115	−	0.0810861i
$576$	−53994.8	+	45307.0i	−0.162745	+	0.136559i
$577$	−2789.83	+	10411.8i	−0.00837966	+	0.0312733i	−0.969989	−	0.243148i	$-0.921820\pi$
$577$	−2789.83	+	10411.8i	−0.00837966	+	0.0312733i	0.961609	+	0.274422i	$0.0884864\pi$
$578$	−115020.	−	429262.i	−0.344286	−	1.28489i
$579$	102000.	−	17985.3i	0.304259	−	0.0536490i
$580$	−33274.9	+	86337.0i	−0.0989148	+	0.256650i
$581$	259484.	−	449439.i	0.768702	−	1.33143i
$582$	179867.	−	671272.i	0.531013	−	1.98177i
$583$	52434.2	−	599326.i	0.154269	−	1.76330i
$584$	−5119.47	−	14065.6i	−0.0150107	−	0.0412414i
$585$	−3349.64	+	31462.6i	−0.00978784	+	0.0919355i
$586$	−215658.	−	180958.i	−0.628015	−	0.526967i
$587$	−445057.	+	311633.i	−1.29163	+	0.904413i	−0.998662	−	0.0517083i	$-0.983533\pi$
$587$	−445057.	+	311633.i	−1.29163	+	0.904413i	−0.292973	+	0.956121i	$0.594645\pi$
$588$	26752.3	−	26752.3i	0.0773760	−	0.0773760i
$589$	−13397.9	−	11853.9i	−0.0386193	−	0.0341689i
$590$	−756311.	+	187489.i	−2.17268	+	0.538608i
$591$	−35663.7	+	202259.i	−0.102106	+	0.579072i
$592$	−73836.3	−	843952.i	−0.210681	−	2.40810i
$593$	−39419.9	+	18381.8i	−0.112100	+	0.0522731i	−0.477859	−	0.878436i	$-0.658587\pi$
$593$	−39419.9	+	18381.8i	−0.112100	+	0.0522731i	0.365759	+	0.930709i	$0.380809\pi$
$594$	−379095.	−	1.04156e6i	−1.07442	−	2.95196i
$595$	−26479.7	−	168654.i	−0.0747962	−	0.476390i
$596$	300629.	+	520705.i	0.846327	+	1.46588i
$597$	338489.	−	90697.9i	0.949722	−	0.254477i
$598$	−182849.	−	128032.i	−0.511318	−	0.358028i
$599$	−251788.	+	44397.1i	−0.701749	+	0.123737i	−0.513127	−	0.858312i	$-0.671513\pi$
$599$	−251788.	+	44397.1i	−0.701749	+	0.123737i	−0.188622	+	0.982050i	$0.560402\pi$
$600$	−20677.7	+	549732.i	−0.0574381	+	1.52703i
$601$	−16144.9	−	27963.7i	−0.0446978	−	0.0774188i	0.842811	−	0.538210i	$-0.180899\pi$
$601$	−16144.9	−	27963.7i	−0.0446978	−	0.0774188i	−0.887509	+	0.460791i	$0.847566\pi$
$602$	−530048.	−	46373.2i	−1.46259	−	0.127960i
$603$	−18601.6	+	39891.2i	−0.0511582	+	0.109709i
$604$	486357.	−	1.33625e6i	1.33316	−	3.66282i
$605$	201127.	+	586677.i	0.549490	+	1.60283i
$606$	−12813.8	+	72670.8i	−0.0348926	+	0.197886i
$607$	−261984.	−	261984.i	−0.711046	−	0.711046i	0.255708	−	0.966754i	$-0.417691\pi$
$607$	−261984.	−	261984.i	−0.711046	−	0.711046i	−0.966754	+	0.255708i	$0.917691\pi$
$608$	191998.	−	46090.5i	0.519386	−	0.124682i
$609$			34777.8i			0.0937706i
$610$	−301947.	+	20706.2i	−0.811468	+	0.0556468i
$611$	66562.2	+	55852.4i	0.178298	+	0.149609i
$612$	72549.6	+	155583.i	0.193701	+	0.415393i
$613$	−18878.0	+	40484.0i	−0.0502384	+	0.107736i	−0.929825	−	0.368003i	$-0.880042\pi$
$613$	−18878.0	+	40484.0i	−0.0502384	+	0.107736i	0.879586	+	0.475739i	$0.157819\pi$
$614$	628731.	+	749292.i	1.66774	+	1.98753i
$615$	150782.	+	156560.i	0.398656	+	0.413933i
$616$	−607970.	+	1.05303e6i	−1.60221	+	2.77512i
$617$	13529.5	−	19322.2i	0.0355396	−	0.0507557i	−0.800989	−	0.598679i	$-0.795693\pi$
$617$	13529.5	−	19322.2i	0.0355396	−	0.0507557i	0.836529	+	0.547923i	$0.184581\pi$
$618$	−158833.	−	111216.i	−0.415877	−	0.291200i
$619$	242363.	+	139928.i	0.632536	+	0.365195i	0.781733	−	0.623613i	$-0.214336\pi$
$619$	242363.	+	139928.i	0.632536	+	0.365195i	−0.149198	+	0.988807i	$0.547669\pi$
$620$	42426.4	+	797.636i	0.110371	+	0.00207501i
$621$	−521004.	+	437174.i	−1.35101	+	1.13363i
$622$	965788.	+	450354.i	2.49632	+	1.16405i
$623$	−433826.	+	202297.i	−1.11774	+	0.521210i
$624$	58839.0	−	70121.6i	0.151111	−	0.180087i
$625$	279528.	+	272859.i	0.715592	+	0.698518i
$626$	608348.			1.55240
$627$	55225.2	−	484615.i	0.140476	−	1.23271i
$628$	72955.0	−	72955.0i	0.184985	−	0.184985i
$629$	326151.	+	57509.2i	0.824361	+	0.145357i
$630$	−94426.0	−	275436.i	−0.237909	−	0.693968i
$631$	−280809.	−	102206.i	−0.705265	−	0.256696i	−0.0356081	−	0.999366i	$-0.511337\pi$
$631$	−280809.	−	102206.i	−0.705265	−	0.256696i	−0.669657	+	0.742670i	$0.733559\pi$
$632$	532806.	+	248451.i	1.33394	+	0.622024i
$633$	−28093.4	+	321109.i	−0.0701127	+	0.801392i
$634$	206453.	−	119196.i	0.513622	−	0.296540i
$635$	−173734.	−	50070.5i	−0.430862	−	0.124175i
$636$	−122557.	−	695058.i	−0.302988	−	1.71833i
$637$	−3394.39	+	4847.70i	−0.00836534	+	0.0119469i
$638$	39375.7	+	146952.i	0.0967358	+	0.361023i
$639$	−124704.	+	71997.8i	−0.305406	+	0.176326i
$640$	340672.	−	467571.i	0.831719	−	1.14153i
$641$	−515432.	+	187602.i	−1.25445	+	0.456584i	−0.881905	−	0.471428i	$-0.843739\pi$
$641$	−515432.	+	187602.i	−1.25445	+	0.456584i	−0.372550	+	0.928012i	$0.621516\pi$
$642$	314809.	+	675109.i	0.763795	+	1.63796i
$643$	13081.9	−	1144.51i	0.0316408	−	0.00276821i	−0.0713244	−	0.997453i	$-0.522723\pi$
$643$	13081.9	−	1144.51i	0.0316408	−	0.00276821i	0.102965	+	0.994685i	$0.467167\pi$
$644$	1.37887e6	+	243131.i	3.32468	+	0.586232i
$645$	−139260.	+	231062.i	−0.334739	+	0.555405i
$646$	−9676.26	+	369225.i	−0.0231869	+	0.884761i
$647$	−225425.	−	225425.i	−0.538510	−	0.538510i	0.384581	−	0.923091i	$-0.374346\pi$
$647$	−225425.	−	225425.i	−0.538510	−	0.538510i	−0.923091	+	0.384581i	$0.874346\pi$
$648$	−188692.	−	269480.i	−0.449369	−	0.641766i
$649$	−561328.	+	668964.i	−1.33268	+	1.58823i
$650$	−22043.6	−	159970.i	−0.0521743	−	0.378627i
$651$	14987.6	−	5455.03i	0.0353646	−	0.0128717i
$652$	−365705.	−	31995.1i	−0.860273	−	0.0752641i
$653$	−216881.	−	58113.1i	−0.508622	−	0.136285i	−0.00462340	−	0.999989i	$-0.501472\pi$
$653$	−216881.	−	58113.1i	−0.508622	−	0.136285i	−0.503999	+	0.863704i	$0.668138\pi$
$654$	702859.	+	405796.i	1.64329	+	0.948751i
$655$	−198887.	+	516042.i	−0.463578	+	1.20282i
$656$	81940.6	+	464708.i	0.190411	+	1.07987i
$657$	3880.19	−	1039.69i	0.00898922	−	0.00240865i
$658$	−772369.	−	206956.i	−1.78391	−	0.477998i
$659$	149785.	+	178507.i	0.344903	+	0.411040i	0.910412	−	0.413702i	$-0.135765\pi$
$659$	149785.	+	178507.i	0.344903	+	0.411040i	−0.565509	+	0.824742i	$0.691320\pi$
$660$	645683.	+	960047.i	1.48228	+	2.20396i
$661$	56376.4	+	20519.3i	0.129031	+	0.0469634i	0.405729	−	0.913994i	$-0.367018\pi$
$661$	56376.4	+	20519.3i	0.129031	+	0.0469634i	−0.276698	+	0.960957i	$0.589240\pi$
$662$	−50159.2	−	573323.i	−0.114455	−	1.30823i
$663$	20525.0	+	29312.7i	0.0466934	+	0.0666851i
$664$		−	1.41923e6i		−	3.21897i
$665$	56314.2	−	423281.i	0.127343	−	0.957161i
$666$	564848.			1.27345
$667$	76469.2	−	53544.3i	0.171884	−	0.120354i
$668$	983530.	−	86047.8i	2.20412	−	0.192835i
$669$	−198447.	+	545228.i	−0.443396	+	1.21822i
$670$	43159.3	−	220452.i	0.0961445	−	0.491093i
$671$	−259837.	+	218029.i	−0.577107	+	0.484250i
$672$	−45563.6	+	170046.i	−0.100897	+	0.376554i
$673$	−168870.	−	630231.i	−0.372840	−	1.39146i	−0.856476	−	0.516187i	$-0.827351\pi$
$673$	−168870.	−	630231.i	−0.372840	−	1.39146i	0.483636	−	0.875269i	$-0.339316\pi$
$674$	1.00242e6	−	176754.i	2.20664	−	0.389091i
$675$	−488187.	−	61275.2i	−1.07147	−	0.134486i
$676$	466394.	−	807818.i	1.02061	−	1.76775i
$677$	−28005.8	+	104519.i	−0.0611042	+	0.228044i	−0.989725	−	0.142987i	$-0.954329\pi$
$677$	−28005.8	+	104519.i	−0.0611042	+	0.228044i	0.928620	+	0.371031i	$0.120996\pi$
$678$	22051.0	−	252044.i	0.0479698	−	0.548297i
$679$	−233208.	−	640734.i	−0.505830	−	1.38976i
$680$	−293324.	−	363223.i	−0.634351	−	0.785516i
$681$	351683.	+	295097.i	0.758328	+	0.636313i
$682$	57153.2	−	40019.1i	0.122877	−	0.0860397i
$683$	343232.	−	343232.i	0.735776	−	0.735776i	−0.235981	−	0.971758i	$-0.575830\pi$
$683$	343232.	−	343232.i	0.735776	−	0.735776i	0.971758	+	0.235981i	$0.0758304\pi$
$684$	63457.2	+	424663.i	0.135634	+	0.907680i
$685$	−136356.	−	550043.i	−0.290598	−	1.17224i
$686$	149297.	−	846707.i	0.317252	−	1.79922i
$687$	−53717.6	−	613995.i	−0.113816	−	1.30092i
$688$	−530808.	+	247520.i	−1.12140	+	0.522917i
$689$	37758.7	+	103741.i	0.0795386	+	0.218531i
$690$	613340.	−	841807.i	1.28826	−	1.76813i
$691$	−407922.	−	706542.i	−0.854322	−	1.47973i	−0.877273	−	0.479992i	$-0.840639\pi$
$691$	−407922.	−	706542.i	−0.854322	−	1.47973i	0.0229507	−	0.999737i	$-0.492694\pi$
$692$	−287933.	+	77151.4i	−0.601283	+	0.161113i
$693$	−267308.	−	187171.i	−0.556603	−	0.389738i
$694$	−830196.	+	146386.i	−1.72370	+	0.303935i
$695$	277795.	+	502749.i	0.575115	+	1.04083i
$696$	47553.7	+	82365.4i	0.0981671	+	0.170030i
$697$	−183767.	−	16077.5i	−0.378269	−	0.0330943i
$698$	−74332.0	+	159405.i	−0.152569	+	0.327184i
$699$	−169419.	+	465475.i	−0.346743	+	0.952670i
$700$	549375.	+	850966.i	1.12117	+	1.73667i
$701$	−109062.	+	618521.i	−0.221941	+	1.25869i	0.646507	+	0.762908i	$0.276229\pi$
$701$	−109062.	+	618521.i	−0.221941	+	1.25869i	−0.868448	+	0.495780i	$0.834882\pi$
$702$	143823.	+	143823.i	0.291846	+	0.291846i
$703$	741322.	+	369629.i	1.50002	+	0.747921i
$704$		−	403158.i		−	0.813449i
$705$	−266403.	+	305630.i	−0.535995	+	0.614920i
$706$	505845.	+	424455.i	1.01486	+	0.851573i
$707$	30598.1	+	65617.8i	0.0612147	+	0.131275i
$708$	−432960.	+	928486.i	−0.863737	+	1.85229i
$709$	137489.	+	163853.i	0.273511	+	0.325958i	0.885262	−	0.465093i	$-0.153979\pi$
$709$	137489.	+	163853.i	0.273511	+	0.325958i	−0.611751	+	0.791050i	$0.709535\pi$
$710$	529330.	−	509794.i	1.05005	−	1.01130i
$711$	−78885.8	+	136634.i	−0.156048	+	0.270284i
$712$	−750835.	+	1.07230e6i	−1.48110	+	2.11523i
$713$	−35069.6	−	24556.0i	−0.0689845	−	0.0483035i
$714$	−285187.	−	164653.i	−0.559413	−	0.322977i
$715$	−125541.	−	130352.i	−0.245569	−	0.254980i
$716$	605664.	−	508213.i	1.18142	−	0.991332i
$717$	94332.0	+	43987.7i	0.183493	+	0.0855644i
$718$	−943737.	+	440072.i	−1.83064	+	0.853640i
$719$	−526231.	+	627137.i	−1.01793	+	1.21312i	−0.0410905	+	0.999155i	$0.513083\pi$
$719$	−526231.	+	627137.i	−1.01793	+	1.21312i	−0.976841	+	0.213968i	$0.931361\pi$
$720$	−241608.	−	210598.i	−0.466065	−	0.406246i
$721$	−190246.			−0.365969
$722$	−285517.	+	878606.i	−0.547719	+	1.68546i
$723$	−61165.9	+	61165.9i	−0.117013	+	0.117013i
$724$	43649.0	+	7696.49i	0.0832716	+	0.0146830i
$725$	66019.3	+	14218.5i	0.125601	+	0.0270507i
$726$	1.12416e6	+	409161.i	2.13282	+	0.776284i
$727$	742453.	+	346211.i	1.40475	+	0.655047i	0.969462	−	0.245242i	$-0.0788675\pi$
$727$	742453.	+	346211.i	1.40475	+	0.655047i	0.435291	+	0.900290i	$0.356645\pi$
$728$	19447.1	−	222281.i	0.0366937	−	0.419411i
$729$	452115.	−	261029.i	0.850734	−	0.491172i
$730$	−17944.5	+	9915.27i	−0.0336733	+	0.0186063i
$731$	−39758.0	−	225479.i	−0.0744030	−	0.421960i
$732$	−228239.	+	325959.i	−0.425959	+	0.608332i
$733$	85817.9	+	320277.i	0.159724	+	0.596098i	0.998654	+	0.0518592i	$0.0165147\pi$
$733$	85817.9	+	320277.i	0.159724	+	0.596098i	−0.838930	+	0.544239i	$0.816819\pi$
$734$	−1.21530e6	+	701651.i	−2.25574	+	1.30235i
$735$	−22318.0	−	16260.9i	−0.0413124	−	0.0301002i
$736$	444047.	−	161620.i	0.819734	−	0.298359i
$737$	−106396.	−	228168.i	−0.195881	−	0.420068i
$738$	−313423.	+	27421.0i	−0.575465	+	0.0503466i
$739$	−269215.	−	47469.9i	−0.492959	−	0.0869219i	−0.0783578	−	0.996925i	$-0.524968\pi$
$739$	−269215.	−	47469.9i	−0.492959	−	0.0869219i	−0.414601	+	0.910003i	$0.636079\pi$
$740$	−1.90720e6	+	472795.i	−3.48283	+	0.863394i
$741$	28398.4	+	84879.8i	0.0517199	+	0.154585i
$742$	−718385.	−	718385.i	−1.30482	−	1.30482i
$743$	354221.	+	505880.i	0.641648	+	0.916368i	0.999851	−	0.0172760i	$-0.00549940\pi$
$743$	354221.	+	505880.i	0.641648	+	0.916368i	−0.358203	+	0.933644i	$0.616611\pi$
$744$	28036.6	−	33412.7i	0.0506500	−	0.0603624i
$745$	341415.	−	275713.i	0.615134	−	0.496757i
$746$	618501.	−	225116.i	1.11138	−	0.404509i
$747$	379431.	+	33195.9i	0.679973	+	0.0594899i
$748$	−948436.	−	254133.i	−1.69514	−	0.454211i
$749$	632946.	+	365432.i	1.12824	+	0.651392i
$750$	748231.	−	88808.3i	1.33019	−	0.157881i
$751$	47040.5	+	266780.i	0.0834050	+	0.473013i	0.997689	+	0.0679402i	$0.0216427\pi$
$751$	47040.5	+	266780.i	0.0834050	+	0.473013i	−0.914284	+	0.405073i	$0.867246\pi$
$752$	−850188.	+	227807.i	−1.50342	+	0.402839i
$753$	371196.	+	99461.6i	0.654656	+	0.175415i
$754$	−17945.1	−	21386.1i	−0.0315648	−	0.0376175i
$755$	−1.01855e6	−	199408.i	−1.78685	−	0.349823i
$756$	−1.19887e6	−	436352.i	−2.09762	−	0.763472i
$757$	72391.0	+	827433.i	0.126326	+	1.44391i	0.749590	+	0.661902i	$0.230250\pi$
$757$	72391.0	+	827433.i	0.126326	+	1.44391i	−0.623264	+	0.782011i	$0.714194\pi$
$758$	−309869.	−	442539.i	−0.539312	−	0.770217i
$759$		−	1.16729e6i		−	2.02625i
$760$	−445406.	−	1.07947e6i	−0.771132	−	1.86889i
$761$	510015.			0.880671			0.440336	−	0.897833i	$-0.354859\pi$
$761$	510015.			0.880671			0.440336	+	0.897833i	$0.354859\pi$
$762$	−285687.	+	200040.i	−0.492017	+	0.344514i
$763$	793267.	−	69401.9i	1.36261	−	0.119213i
$764$	−320372.	+	880215.i	−0.548868	+	1.50800i
$765$	103968.	−	69924.2i	0.177655	−	0.119483i
$766$	494415.	−	414863.i	0.842624	−	0.707045i
$767$	41475.5	−	154789.i	0.0705018	−	0.263116i
$768$	−231638.	−	864484.i	−0.392723	−	1.46566i
$769$	627057.	−	110567.i	1.06036	−	0.186971i	0.383845	−	0.923397i	$-0.374600\pi$
$769$	627057.	−	110567.i	1.06036	−	0.186971i	0.676517	+	0.736427i	$0.263488\pi$
$770$	1.55401e6	+	598929.i	2.62104	+	1.01017i
$771$	245451.	−	425134.i	0.412911	−	0.715184i
$772$	134978.	−	503746.i	0.226480	−	0.845234i
$773$	−660.506	+	7549.62i	−0.00110540	+	0.0126347i	−0.996727	−	0.0808366i	$-0.974241\pi$
$773$	−660.506	+	7549.62i	−0.00110540	+	0.0126347i	0.995622	+	0.0934714i	$0.0297964\pi$
$774$	−133558.	−	366949.i	−0.222941	−	0.612525i
$775$	−4227.86	−	30681.4i	−0.00703911	−	0.0510825i
$776$	−1.42843e6	−	1.19860e6i	−2.37211	−	1.99044i
$777$	−604983.	+	423614.i	−1.00208	+	0.701662i
$778$	114338.	−	114338.i	0.188899	−	0.188899i
$779$	−429289.	−	169112.i	−0.707416	−	0.278676i
$780$	−181838.	−	109593.i	−0.298879	−	0.180132i
$781$	143020.	−	811107.i	0.234474	−	1.32977i
$782$	77039.8	+	880569.i	0.125980	+	1.43996i
$783$	−77092.6	+	35948.9i	−0.125744	+	0.0586356i
$784$	−20503.1	−	56331.9i	−0.0333571	−	0.0916478i
$785$	−60862.4	−	44344.3i	−0.0987666	−	0.0719613i
$786$	533386.	+	923851.i	0.863368	+	1.49540i
$787$	−1.02778e6	+	275393.i	−1.65940	+	0.444634i	−0.962222	−	0.272266i	$-0.912227\pi$
$787$	−1.02778e6	+	275393.i	−1.65940	+	0.444634i	−0.697176	+	0.716900i	$0.745560\pi$
$788$	847111.	+	593153.i	1.36423	+	0.955244i
$789$	−490759.	+	86534.1i	−0.788342	+	0.139006i
$790$	222986.	−	773717.i	0.357293	−	1.23973i
$791$	−124119.	−	214981.i	−0.198375	−	0.343595i
$792$	−889006.	−	77777.9i	−1.41728	−	0.123996i
$793$	26305.2	−	56411.7i	0.0418307	−	0.0897063i
$794$	353033.	−	969950.i	0.559982	−	1.53854i
$795$	−487289.	+	167054.i	−0.770997	+	0.264316i
$796$	306401.	−	1.73769e6i	0.483576	−	2.74249i
$797$	652673.	+	652673.i	1.02749	+	1.02749i	0.999611	+	0.0278825i	$0.00887643\pi$
$797$	652673.	+	652673.i	1.02749	+	1.02749i	0.0278825	+	0.999611i	$0.491124\pi$
$798$	−566963.	−	597479.i	−0.890325	−	0.938246i
$799$		−	344084.i		−	0.538978i
$800$	304173.	+	156016.i	0.475270	+	0.243775i
$801$	−269118.	−	225817.i	−0.419447	−	0.351958i
$802$	−769579.	−	1.65037e6i	−1.19648	−	2.56586i
$803$	−9710.35	+	20823.9i	−0.0150593	+	0.0322947i
$804$	−189844.	−	226247.i	−0.293687	−	0.350003i
$805$	19209.2	−	1.02174e6i	0.0296426	−	1.57670i
$806$	−6401.66	+	11088.0i	−0.00985422	+	0.0170680i
$807$	328287.	−	468842.i	0.504088	−	0.719912i
$808$	162190.	+	113567.i	0.248428	+	0.173951i
$809$	661029.	+	381645.i	1.01000	+	0.583126i	0.911193	−	0.411980i	$-0.135163\pi$
$809$	661029.	+	381645.i	1.01000	+	0.583126i	0.0988113	+	0.995106i	$0.468496\pi$
$810$	−324545.	+	312567.i	−0.494658	+	0.476401i
$811$	299708.	−	251485.i	0.455676	−	0.382358i	−0.385861	−	0.922557i	$-0.626096\pi$
$811$	299708.	−	251485.i	0.455676	−	0.382358i	0.841537	+	0.540199i	$0.181651\pi$
$812$	158707.	+	74006.4i	0.240705	+	0.112242i
$813$	−121836.	+	56813.0i	−0.184329	+	0.0859541i
$814$	−2.07672e6	+	2.47493e6i	−3.13421	+	3.73521i
$815$	18330.9	+	267310.i	0.0275974	+	0.402439i
$816$	−362484.			−0.544388
$817$	64840.6	−	568992.i	0.0971410	−	0.852437i
$818$	90010.1	−	90010.1i	0.134519	−	0.134519i
$819$	58971.9	+	10398.3i	0.0879179	+	0.0155023i
$820$	1.03532e6	−	354931.i	1.53973	−	0.527857i
$821$	818843.	+	298034.i	1.21483	+	0.442161i	0.868376	−	0.495907i	$-0.165164\pi$
$821$	818843.	+	298034.i	1.21483	+	0.442161i	0.346451	+	0.938068i	$0.387387\pi$
$822$	−990688.	−	461965.i	−1.46620	−	0.683700i
$823$	68122.6	−	778645.i	0.100575	−	1.14958i	−0.763358	−	0.645976i	$-0.776451\pi$
$823$	68122.6	−	778645.i	0.100575	−	1.14958i	0.863933	−	0.503606i	$-0.167994\pi$
$824$	−450566.	+	260134.i	−0.663596	+	0.383127i
$825$	619135.	−	574247.i	0.909656	−	0.843705i
$826$	256078.	+	1.45229e6i	0.375329	+	2.12860i
$827$	−284588.	+	406434.i	−0.416108	+	0.594263i	−0.971417	−	0.237381i	$-0.923711\pi$
$827$	−284588.	+	406434.i	−0.416108	+	0.594263i	0.555309	+	0.831644i	$0.312600\pi$
$828$	265959.	+	992574.i	0.387931	+	1.44778i
$829$	346178.	−	199866.i	0.503721	−	0.290823i	−0.226528	−	0.974005i	$-0.572737\pi$
$829$	346178.	−	199866.i	0.503721	−	0.290823i	0.730249	+	0.683181i	$0.239404\pi$
$830$	−1.92035e6	+	301506.i	−2.78756	+	0.437664i
$831$	191103.	−	69556.0i	0.276736	−	0.100724i
$832$	31265.8	+	67049.8i	0.0451672	+	0.0968614i
$833$	23345.6	−	2042.48i	0.0336446	−	0.00294353i
$834$	1.09112e6	+	192394.i	1.56871	+	0.276605i
$835$	−173387.	−	699422.i	−0.248681	−	1.00315i
$836$	−2.09401e6	−	1.28327e6i	−2.99616	−	1.83614i
$837$	27584.5	+	27584.5i	0.0393745	+	0.0393745i
$838$	879913.	+	1.25665e6i	1.25300	+	1.78947i
$839$	150255.	−	179067.i	0.213454	−	0.254385i	−0.648684	−	0.761058i	$-0.724680\pi$
$839$	150255.	−	179067.i	0.213454	−	0.254385i	0.862138	+	0.506673i	$0.169125\pi$
$840$	1.03529e6	+	110221.i	1.46725	+	0.156209i
$841$	−653655.	+	237911.i	−0.924181	+	0.336374i
$842$	−1.31894e6	−	115392.i	−1.86037	−	0.162761i
$843$	−455458.	−	122040.i	−0.640904	−	0.171730i
$844$	1.40559e6	+	811517.i	1.97321	+	1.13923i
$845$	−635267.	−	244837.i	−0.889699	−	0.342897i
$846$	−101906.	−	577938.i	−0.142383	−	0.807496i
$847$	1.13377e6	−	303792.i	1.58036	−	0.423457i
$848$	−1.08020e6	−	289440.i	−1.50215	−	0.402501i
$849$	399413.	+	476002.i	0.554124	+	0.660380i
$850$	−429159.	+	474058.i	−0.593991	+	0.656136i
$851$	1.86288e6	+	678033.i	2.57233	+	0.936250i
$852$	−84211.9	−	962547.i	−0.116010	−	1.32600i
$853$	134534.	+	192134.i	0.184898	+	0.264062i	0.900891	−	0.434046i	$-0.142914\pi$
$853$	134534.	+	192134.i	0.184898	+	0.264062i	−0.715992	+	0.698108i	$0.754026\pi$
$854$			572797.i			0.785389i
$855$	299015.	−	93830.2i	0.409035	−	0.128354i
$856$	1.99871e6			2.72773
$857$	35333.0	−	24740.5i	0.0481082	−	0.0336857i	−0.549275	−	0.835642i	$-0.685096\pi$
$857$	35333.0	−	24740.5i	0.0481082	−	0.0336857i	0.597383	+	0.801956i	$0.296207\pi$
$858$	−347759.	+	30424.9i	−0.472393	+	0.0413290i
$859$	344999.	−	947878.i	0.467554	−	1.28459i	−0.452136	−	0.891949i	$-0.649338\pi$
$859$	344999.	−	947878.i	0.467554	−	1.28459i	0.919690	−	0.392645i	$-0.128440\pi$
$860$	758104.	+	1.12720e6i	1.02502	+	1.52407i
$861$	315128.	−	264424.i	0.425090	−	0.356693i
$862$	−578500.	+	2.15899e6i	−0.778554	+	2.90560i
$863$	−25406.0	−	94816.4i	−0.0341126	−	0.127310i	0.946770	−	0.321911i	$-0.104325\pi$
$863$	−25406.0	−	94816.4i	−0.0341126	−	0.127310i	−0.980882	+	0.194602i	$0.937659\pi$
$864$	−424042.	+	74770.0i	−0.568043	+	0.100161i
$865$	88225.3	+	198877.i	0.117913	+	0.265798i
$866$	−583755.	+	1.01109e6i	−0.778385	+	1.34820i
$867$	−110375.	+	411924.i	−0.146836	+	0.547998i
$868$	6999.39	−	80003.4i	0.00929011	−	0.106186i
$869$	−308644.	−	847993.i	−0.408713	−	1.12293i
$870$	101346.	−	81842.6i	0.133896	−	0.108129i
$871$	35389.9	+	29695.6i	0.0466490	+	0.0391432i
$872$	1.78383e6	−	1.24905e6i	2.34596	−	1.64266i
$873$	353855.	−	353855.i	0.464298	−	0.464298i
$874$	−440832.	+	2.16652e6i	−0.577098	+	2.83622i
$875$	551386.	−	492457.i	0.720178	−	0.643209i
$876$	−4680.67	+	26545.4i	−0.00609957	+	0.0345924i
$877$	30381.3	+	347260.i	0.0395009	+	0.451497i	0.990029	+	0.140860i	$0.0449868\pi$
$877$	30381.3	+	347260.i	0.0395009	+	0.451497i	−0.950529	+	0.310637i	$0.899458\pi$
$878$	298733.	−	139301.i	0.387520	−	0.180704i
$879$	92397.0	+	253859.i	0.119586	+	0.328560i
$880$	1.81105e6	−	284345.i	2.33864	−	0.367181i
$881$	200517.	+	347306.i	0.258345	+	0.447467i	0.965799	−	0.259293i	$-0.0834895\pi$
$881$	200517.	+	347306.i	0.258345	+	0.447467i	−0.707454	+	0.706760i	$0.750156\pi$
$882$	38607.4	−	10344.8i	0.0496287	−	0.0132980i
$883$	342355.	+	239720.i	0.439092	+	0.307456i	0.772138	−	0.635455i	$-0.219187\pi$
$883$	342355.	+	239720.i	0.439092	+	0.307456i	−0.333046	+	0.942911i	$0.608076\pi$
$884$	177444.	−	31288.2i	0.227069	−	0.0400384i
$885$	718489.	+	207069.i	0.917346	+	0.264381i
$886$	568191.	+	984136.i	0.723814	+	1.25368i
$887$	−1.08445e6	−	94877.3i	−1.37836	−	0.120591i	−0.626248	−	0.779624i	$-0.715410\pi$
$887$	−1.08445e6	−	94877.3i	−1.37836	−	0.120591i	−0.752114	+	0.659033i	$0.770966\pi$
$888$	−853571.	+	1.83049e6i	−1.08246	+	2.32135i
$889$	−117035.	+	321550.i	−0.148085	+	0.406860i
$890$	1.61044e6	+	788145.i	2.03312	+	0.995007i
$891$	−87689.0	+	497309.i	−0.110456	+	0.626428i
$892$	2.06584e6	+	2.06584e6i	2.59637	+	2.59637i
$893$	244450.	−	825187.i	0.306540	−	1.03478i
$894$		−	846488.i		−	1.05912i
$895$	−435007.	−	379174.i	−0.543062	−	0.473361i
$896$	−838726.	−	703775.i	−1.04473	−	0.876632i
$897$	90525.7	+	194133.i	0.112509	+	0.241276i
$898$	−293913.	+	630298.i	−0.364473	+	0.781616i
$899$	−3441.78	−	4101.76i	−0.00425857	−	0.00507517i
$900$	−395628.	+	629363.i	−0.488429	+	0.776992i
$901$	218588.	−	378605.i	0.269263	−	0.466376i
$902$	1.03218e6	−	1.47411e6i	1.26865	−	1.81182i
$903$	418245.	+	292858.i	0.512927	+	0.359155i
$904$	−587912.	−	339431.i	−0.719408	−	0.415351i
$905$	608.079	−	32343.9i	0.000742442	−	0.0394907i
$906$	−1.53362e6	+	1.28686e6i	−1.86836	+	1.56774i
$907$	−32611.1	−	15206.8i	−0.0396416	−	0.0184852i	0.402696	−	0.915334i	$-0.368073\pi$
$907$	−32611.1	−	15206.8i	−0.0396416	−	0.0184852i	−0.442338	+	0.896848i	$0.645851\pi$
$908$	2.09504e6	−	976933.i	2.54109	−	1.18493i
$909$	−34155.6	+	40705.1i	−0.0413366	+	0.0492630i
$910$	−304898.	+	20908.5i	−0.368190	+	0.0252488i
$911$	−781627.			−0.941809			−0.470905	−	0.882184i	$-0.656072\pi$
$911$	−781627.			−0.941809			−0.470905	+	0.882184i	$0.656072\pi$
$912$	−869313.	−	257522.i	−1.04517	−	0.309617i
$913$	−1.54046e6	+	1.54046e6i	−1.84803	+	1.84803i
$914$	981940.	+	173143.i	1.17542	+	0.207258i
$915$	260867.	+	127668.i	0.311586	+	0.152490i
$916$	−2.91626e6	−	1.06143e6i	−3.47564	−	1.26503i
$917$	948603.	+	442341.i	1.12810	+	0.526040i
$918$	70198.8	−	802376.i	0.0832999	−	0.952122i
$919$	417461.	−	241021.i	0.494293	−	0.285380i	−0.232061	−	0.972701i	$-0.574547\pi$
$919$	417461.	−	241021.i	0.494293	−	0.285380i	0.726354	+	0.687321i	$0.241213\pi$
$920$	−1.35159e6	−	2.44609e6i	−1.59687	−	2.88999i
$921$	−162991.	−	924366.i	−0.192151	−	1.08974i
$922$	257127.	−	367215.i	0.302472	−	0.431975i
$923$	39117.3	+	145988.i	0.0459162	+	0.171361i
$924$	1.89630e6	−	1.09483e6i	2.22107	−	1.28234i
$925$	556812.	+	1.32164e6i	0.650767	+	1.54465i
$926$	−537541.	+	195649.i	−0.626888	+	0.228168i
$927$	−59008.0	−	126543.i	−0.0686676	−	0.147258i
$928$	58875.8	−	5150.97i	0.0683662	−	0.00598126i
$929$	−1.25246e6	−	220843.i	−1.45122	−	0.255889i	−0.608204	−	0.793781i	$-0.708110\pi$
$929$	−1.25246e6	−	220843.i	−1.45122	−	0.255889i	−0.843014	+	0.537892i	$0.819221\pi$
$930$	−51166.7	−	30837.8i	−0.0591591	−	0.0356548i
$931$	57438.9	+	11687.3i	0.0662684	+	0.0134839i
$932$	1.76366e6	+	1.76366e6i	2.03041	+	2.03041i
$933$	−586533.	−	837655.i	−0.673797	−	0.962282i
$934$	777056.	−	926059.i	0.890755	−	1.06156i
$935$	−75869.5	+	712629.i	−0.0867848	+	0.815155i
$936$	153884.	−	56009.1i	0.175647	−	0.0639303i
$937$	−189429.	−	16572.9i	−0.215758	−	0.0188764i	−0.0212360	−	0.999774i	$-0.506760\pi$
$937$	−189429.	−	16572.9i	−0.215758	−	0.0188764i	−0.194522	+	0.980898i	$0.562316\pi$
$938$	−410654.	−	110034.i	−0.466735	−	0.125061i
$939$	−505566.	−	291889.i	−0.573385	−	0.331044i
$940$	827834.	+	1.86610e6i	0.936888	+	2.11192i
$941$	−183412.	−	1.04018e6i	−0.207132	−	1.17471i	−0.894049	−	0.447970i	$-0.852147\pi$
$941$	−183412.	−	1.04018e6i	−0.207132	−	1.17471i	0.686916	−	0.726737i	$-0.258964\pi$
$942$	−140305.	+	37594.7i	−0.158115	+	0.0423667i
$943$	−1.06659e6	−	285792.i	−1.19943	−	0.321386i
$944$	1.04342e6	+	1.24350e6i	1.17089	+	1.39541i
$945$	−178906.	+	913828.i	−0.200337	+	1.02329i
$946$	2.09886e6	+	763922.i	2.34531	+	0.853624i
$947$	−128235.	−	1.46573e6i	−0.142990	−	1.63438i	−0.641233	−	0.767346i	$-0.721577\pi$
$947$	−128235.	−	1.46573e6i	−0.142990	−	1.63438i	0.498243	−	0.867037i	$-0.333979\pi$
$948$	−607223.	−	867205.i	−0.675665	−	0.964950i
$949$		−	4216.31i		−	0.00468166i
$950$	−1.36600e6	+	832002.i	−1.51358	+	0.921886i
$951$	−228763.			−0.252945
$952$	−723791.	+	506804.i	−0.798619	+	0.559199i
$953$	−1.03996e6	+	90985.1i	−1.14507	+	0.100181i	−0.643860	−	0.765144i	$-0.722668\pi$
$953$	−1.03996e6	+	90985.1i	−1.14507	+	0.100181i	−0.501212	+	0.865324i	$0.667112\pi$
$954$	255019.	−	700658.i	0.280205	−	0.769856i
$955$	670937.	+	131354.i	0.735657	+	0.144024i
$956$	401473.	−	336876.i	0.439279	−	0.368599i
$957$	37785.4	−	141017.i	0.0412572	−	0.153974i
$958$	−387258.	−	1.44527e6i	−0.421958	−	1.57477i
$959$	−1.05621e6	+	186238.i	−1.14845	+	0.202503i
$960$	−315546.	+	139982.i	−0.342389	+	0.151890i
$961$	460533.	−	797666.i	0.498671	−	0.863723i
$962$	153445.	−	572663.i	0.165807	−	0.618799i
$963$	−46749.9	+	534353.i	−0.0504113	+	0.576204i
$964$	148969.	+	409288.i	0.160303	+	0.440428i
$965$	−378501.	−	40296.8i	−0.406455	−	0.0432729i
$966$	−1.51003e6	−	1.26706e6i	−1.61819	−	1.35783i
$967$	−300928.	+	210712.i	−0.321818	+	0.225339i	−0.723310	−	0.690523i	$-0.757380\pi$
$967$	−300928.	+	210712.i	−0.321818	+	0.225339i	0.401493	+	0.915862i	$0.368492\pi$
$968$	2.26975e6	−	2.26975e6i	2.42229	−	2.42229i
$969$	185198.	−	302201.i	0.197237	−	0.321846i
$970$	−1.31835e6	+	2.18743e6i	−1.40116	+	2.32483i
$971$	−111713.	+	633553.i	−0.118485	+	0.671962i	0.866481	+	0.499211i	$0.166377\pi$
$971$	−111713.	+	633553.i	−0.118485	+	0.671962i	−0.984966	+	0.172751i	$0.944734\pi$
$972$	−138727.	−	1.58566e6i	−0.146835	−	1.67833i
$973$	985225.	−	459418.i	1.04066	−	0.485269i
$974$	71363.6	+	196070.i	0.0752244	+	0.206677i
$975$	−58435.0	+	143519.i	−0.0614701	+	0.150973i
$976$	315254.	+	546036.i	0.330949	+	0.573221i
$977$	−769198.	+	206106.i	−0.805841	+	0.215924i	−0.638147	−	0.769915i	$-0.720299\pi$
$977$	−769198.	+	206106.i	−0.805841	+	0.215924i	−0.167694	+	0.985839i	$0.553632\pi$
$978$	423362.	+	296441.i	0.442623	+	0.309928i
$979$	1.97887e6	−	348929.i	2.06468	−	0.364058i
$980$	−121698.	+	67244.6i	−0.126716	+	0.0700173i
$981$	292209.	+	506121.i	0.303638	+	0.525916i
$982$	3.21335e6	+	281132.i	3.33223	+	0.291533i
$983$	−482033.	+	1.03372e6i	−0.498850	+	1.06979i	0.482206	+	0.876058i	$0.339836\pi$
$983$	−482033.	+	1.03372e6i	−0.498850	+	1.06979i	−0.981055	+	0.193728i	$0.937942\pi$
$984$	384767.	−	1.05714e6i	0.397382	−	1.09180i
$985$	331787.	−	677949.i	0.341969	−	0.698754i
$986$	−19197.3	+	108873.i	−0.0197463	+	0.111987i
$987$	542577.	+	542577.i	0.556964	+	0.556964i
$988$	447777.	+	51027.3i	0.458721	+	0.0522744i
$989$		−	1.37053e6i		−	1.40118i
$990$	83623.0	+	1.21943e6i	0.0853208	+	1.24419i
$991$	1.40008e6	+	1.17481e6i	1.42563	+	1.19624i	0.948242	+	0.317548i	$0.102859\pi$
$991$	1.40008e6	+	1.17481e6i	1.42563	+	1.19624i	0.477384	+	0.878695i	$0.341585\pi$
$992$	−11454.7	−	24564.8i	−0.0116402	−	0.0249626i
$993$	−233399.	+	500525.i	−0.236701	+	0.507606i
$994$	−894021.	−	1.06545e6i	−0.904846	−	1.07835i
$995$	−1.28763e6	−	24207.9i	−1.30060	−	0.0244519i
$996$	−1.27787e6	+	2.21334e6i	−1.28815	+	2.23115i
$997$	192249.	−	274560.i	0.193408	−	0.276215i	−0.710722	−	0.703473i	$-0.751632\pi$
$997$	192249.	−	274560.i	0.193408	−	0.276215i	0.904130	+	0.427258i	$0.140520\pi$
$998$	−1.30274e6	−	912191.i	−1.30797	−	0.915850i
$999$	−1.56439e6	−	903200.i	−1.56752	−	0.905009i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	95.5.q.a.17.3	✓	456
5.3	odd	4	inner	95.5.q.a.93.36	yes	456
19.9	even	9	inner	95.5.q.a.47.36	yes	456
95.28	odd	36	inner	95.5.q.a.28.3	yes	456

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.5.q.a.17.3	✓	456	1.1	even	1	trivial
95.5.q.a.28.3	yes	456	95.28	odd	36	inner
95.5.q.a.47.36	yes	456	19.9	even	9	inner
95.5.q.a.93.36	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+(-5.80689 + 4.06603i) q^{2} +(6.77670 - 0.592885i) q^{3} +(11.7151 - 32.1869i) q^{4} +(-24.5342 - 4.80323i) q^{5} +(-36.9409 + 30.9971i) q^{6} +(-12.2458 + 45.7020i) q^{7} +(33.4888 + 124.982i) q^{8} +(-34.1972 + 6.02989i) q^{9} +(161.998 - 71.8651i) q^{10} +(99.3086 - 172.008i) q^{11} +(60.3065 - 225.067i) q^{12} +(-3.17658 + 36.3084i) q^{13} +(-114.715 - 315.178i) q^{14} +(-169.109 - 18.0041i) q^{15} +(-282.823 - 237.317i) q^{16} +(118.227 - 82.7838i) q^{17} +(174.062 - 174.062i) q^{18} +(342.347 - 114.540i) q^{19} +(-442.022 + 733.411i) q^{20} +(-55.8902 + 316.969i) q^{21} +(122.713 + 1402.62i) q^{22} +(783.000 - 365.119i) q^{23} +(301.044 + 827.112i) q^{24} +(578.858 + 235.687i) q^{25} +(-129.185 - 223.755i) q^{26} +(-760.404 + 203.750i) q^{27} +(1327.54 + 929.557i) q^{28} +(106.411 - 18.7632i) q^{29} +(1055.20 - 583.055i) q^{30} +(-24.7771 - 42.9151i) q^{31} +(544.880 + 47.6708i) q^{32} +(571.005 - 1224.52i) q^{33} +(-349.933 + 961.433i) q^{34} +(519.958 - 1062.44i) q^{35} +(-206.540 + 1171.34i) q^{36} +(1622.55 + 1622.55i) q^{37} +(-1522.25 + 2057.11i) q^{38} +247.935i q^{39} +(-221.306 - 3227.20i) q^{40} +(-979.089 - 821.554i) q^{41} +(-964.257 - 2067.86i) q^{42} +(670.423 - 1437.73i) q^{43} +(-4372.99 - 5211.52i) q^{44} +(867.966 + 16.3181i) q^{45} +(-3062.21 + 5303.91i) q^{46} +(1367.42 - 1952.88i) q^{47} +(-2057.31 - 1440.54i) q^{48} +(140.617 + 81.1854i) q^{49} +(-4319.68 + 985.045i) q^{50} +(752.111 - 631.096i) q^{51} +(1131.44 + 527.600i) q^{52} +(2745.22 - 1280.12i) q^{53} +(3587.13 - 4274.98i) q^{54} +(-3262.65 + 3743.07i) q^{55} -6122.02 q^{56} +(2252.08 - 979.175i) q^{57} +(-541.627 + 541.627i) q^{58} +(-4329.95 - 763.488i) q^{59} +(-2560.62 + 5232.18i) q^{60} +(-1604.78 - 584.093i) q^{61} +(318.372 + 148.459i) q^{62} +(143.195 - 1636.72i) q^{63} +(1757.88 - 1014.91i) q^{64} +(252.332 - 875.542i) q^{65} +(1663.19 + 9432.40i) q^{66} +(727.031 - 1038.31i) q^{67} +(-1279.51 - 4775.20i) q^{68} +(5089.69 - 2938.53i) q^{69} +(1300.59 + 8283.66i) q^{70} +(3896.69 - 1418.28i) q^{71} +(-1898.85 - 4072.11i) q^{72} +(-115.243 + 10.0824i) q^{73} +(-16019.3 - 2824.64i) q^{74} +(4062.48 + 1253.98i) q^{75} +(323.942 - 12360.9i) q^{76} +(6644.97 + 6644.97i) q^{77} +(-1008.11 - 1439.73i) q^{78} +(2920.50 - 3480.51i) q^{79} +(5798.96 + 7180.84i) q^{80} +(-2389.15 + 869.581i) q^{81} +(9025.93 + 789.666i) q^{82} +(-10594.8 - 2838.87i) q^{83} +(9547.50 + 5512.25i) q^{84} +(-3298.25 + 1463.16i) q^{85} +(1952.77 + 11074.7i) q^{86} +(709.993 - 190.242i) q^{87} +(24823.6 + 6651.46i) q^{88} +(6503.04 + 7750.03i) q^{89} +(-5106.54 + 3434.42i) q^{90} +(-1620.47 - 589.802i) q^{91} +(-2579.14 - 29479.8i) q^{92} +(-193.351 - 276.133i) q^{93} +16900.1i q^{94} +(-8949.39 + 1165.78i) q^{95} +3720.75 q^{96} +(-11805.0 + 8265.94i) q^{97} +(-1146.65 + 100.319i) q^{98} +(-2358.89 + 6481.00i) 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

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Groups

Database

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