LMFDB - Embedded newform 70.5.h.a.59.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [70,5,Mod(19,70)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(70, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

N = Newforms(chi, 5, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("70.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 70 = 2 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	70.h (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.23589741587$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			59.2
Character	$\chi$	$=$	70.59
Dual form			70.5.h.a.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.44949 + 1.41421i) q^{2} +(-6.27030 + 10.8605i) q^{3} +(4.00000 - 6.92820i) q^{4} +(10.1380 - 22.8521i) q^{5} -35.4702i q^{6} +(-32.1106 - 37.0123i) q^{7} +22.6274i q^{8} +(-38.1334 - 66.0490i) q^{9} +O(q^{10})$	\(q+(-2.44949 + 1.41421i) q^{2} +(-6.27030 + 10.8605i) q^{3} +(4.00000 - 6.92820i) q^{4} +(10.1380 - 22.8521i) q^{5} -35.4702i q^{6} +(-32.1106 - 37.0123i) q^{7} +22.6274i q^{8} +(-38.1334 - 66.0490i) q^{9} +(7.48477 + 70.3134i) q^{10} +(3.60139 - 6.23778i) q^{11} +(50.1624 + 86.8839i) q^{12} +292.752 q^{13} +(130.998 + 45.2500i) q^{14} +(184.617 + 253.394i) q^{15} +(-32.0000 - 55.4256i) q^{16} +(61.4709 - 106.471i) q^{17} +(186.815 + 107.858i) q^{18} +(-75.8198 + 43.7746i) q^{19} +(-117.772 - 161.647i) q^{20} +(603.315 - 116.658i) q^{21} +20.3725i q^{22} +(445.403 - 257.154i) q^{23} +(-245.745 - 141.881i) q^{24} +(-419.440 - 463.352i) q^{25} +(-717.094 + 414.014i) q^{26} -59.3570 q^{27} +(-384.871 + 74.4194i) q^{28} +931.646 q^{29} +(-810.570 - 359.598i) q^{30} +(-12.4789 - 7.20472i) q^{31} +(156.767 + 90.5097i) q^{32} +(45.1636 + 78.2256i) q^{33} +347.732i q^{34} +(-1171.35 + 358.563i) q^{35} -610.135 q^{36} +(1496.98 - 864.280i) q^{37} +(123.813 - 214.451i) q^{38} +(-1835.65 + 3179.43i) q^{39} +(517.085 + 229.398i) q^{40} -2540.41i q^{41} +(-1312.83 + 1138.97i) q^{42} -410.931i q^{43} +(-28.8111 - 49.9023i) q^{44} +(-1895.96 + 201.822i) q^{45} +(-727.340 + 1259.79i) q^{46} +(-1519.41 - 2631.70i) q^{47} +802.599 q^{48} +(-338.821 + 2376.97i) q^{49} +(1682.69 + 541.798i) q^{50} +(770.882 + 1335.21i) q^{51} +(1171.01 - 2028.25i) q^{52} +(-1721.93 - 994.156i) q^{53} +(145.394 - 83.9435i) q^{54} +(-106.036 - 145.538i) q^{55} +(837.493 - 726.580i) q^{56} -1097.92i q^{57} +(-2282.06 + 1317.55i) q^{58} +(-3389.27 - 1956.80i) q^{59} +(2494.03 - 265.486i) q^{60} +(4131.01 - 2385.04i) q^{61} +40.7560 q^{62} +(-1220.14 + 3532.28i) q^{63} -512.000 q^{64} +(2967.94 - 6690.02i) q^{65} +(-221.255 - 127.742i) q^{66} +(6625.07 + 3824.99i) q^{67} +(-491.767 - 851.766i) q^{68} +6449.73i q^{69} +(2362.12 - 2534.83i) q^{70} +1844.25 q^{71} +(1494.52 - 862.860i) q^{72} +(-5299.30 + 9178.65i) q^{73} +(-2444.55 + 4234.09i) q^{74} +(7662.24 - 1649.97i) q^{75} +700.394i q^{76} +(-346.517 + 67.0033i) q^{77} -10384.0i q^{78} +(1890.26 + 3274.03i) q^{79} +(-1591.01 + 169.361i) q^{80} +(3460.99 - 5994.61i) q^{81} +(3592.68 + 6222.71i) q^{82} +3661.83 q^{83} +(1605.03 - 4646.52i) q^{84} +(-1809.89 - 2484.15i) q^{85} +(581.144 + 1006.57i) q^{86} +(-5841.71 + 10118.1i) q^{87} +(141.145 + 81.4901i) q^{88} +(129.635 - 74.8449i) q^{89} +(4358.71 - 3175.65i) q^{90} +(-9400.45 - 10835.4i) q^{91} -4114.46i q^{92} +(156.493 - 90.3515i) q^{93} +(7443.58 + 4297.55i) q^{94} +(231.678 + 2176.43i) q^{95} +(-1965.96 + 1135.05i) q^{96} -12754.1 q^{97} +(-2531.61 - 6301.54i) q^{98} -549.333 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 128 q^{4} + 54 q^{5} - 516 q^{9}+O(q^{10}) $ 32 * q + 128 * q^4 + 54 * q^5 - 516 * q^9	$ 32 q + 128 q^{4} + 54 q^{5} - 516 q^{9} - 96 q^{10} - 144 q^{11} + 96 q^{14} - 76 q^{15} - 1024 q^{16} - 816 q^{19} + 1084 q^{21} + 768 q^{24} + 294 q^{25} - 576 q^{26} + 912 q^{29} + 608 q^{30} + 6468 q^{31} + 1398 q^{35} - 8256 q^{36} - 2424 q^{39} - 768 q^{40} + 1152 q^{44} - 8256 q^{45} + 1664 q^{46} - 7712 q^{49} + 15744 q^{50} + 2708 q^{51} + 7776 q^{54} - 768 q^{56} + 3924 q^{59} - 304 q^{60} + 41556 q^{61} - 16384 q^{64} + 936 q^{65} - 15360 q^{66} + 15104 q^{70} - 53808 q^{71} - 6336 q^{74} - 29058 q^{75} - 24076 q^{79} - 3456 q^{80} + 17680 q^{81} - 19232 q^{84} + 8324 q^{85} + 6624 q^{86} - 41436 q^{89} + 12928 q^{91} + 62880 q^{94} + 42990 q^{95} + 6144 q^{96} + 101048 q^{99}+O(q^{100}) $ 32 * q + 128 * q^4 + 54 * q^5 - 516 * q^9 - 96 * q^10 - 144 * q^11 + 96 * q^14 - 76 * q^15 - 1024 * q^16 - 816 * q^19 + 1084 * q^21 + 768 * q^24 + 294 * q^25 - 576 * q^26 + 912 * q^29 + 608 * q^30 + 6468 * q^31 + 1398 * q^35 - 8256 * q^36 - 2424 * q^39 - 768 * q^40 + 1152 * q^44 - 8256 * q^45 + 1664 * q^46 - 7712 * q^49 + 15744 * q^50 + 2708 * q^51 + 7776 * q^54 - 768 * q^56 + 3924 * q^59 - 304 * q^60 + 41556 * q^61 - 16384 * q^64 + 936 * q^65 - 15360 * q^66 + 15104 * q^70 - 53808 * q^71 - 6336 * q^74 - 29058 * q^75 - 24076 * q^79 - 3456 * q^80 + 17680 * q^81 - 19232 * q^84 + 8324 * q^85 + 6624 * q^86 - 41436 * q^89 + 12928 * q^91 + 62880 * q^94 + 42990 * q^95 + 6144 * q^96 + 101048 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/70\mathbb{Z}\right)^\times$.

$n$	$31$	$57$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.44949	+	1.41421i	−0.612372	+	0.353553i
$2$	−2.44949	+	1.41421i	−0.612372	+	0.353553i
$3$	−6.27030	+	10.8605i	−0.696700	+	1.20672i	0.272904	+	0.962041i	$0.412016\pi$
$3$	−6.27030	+	10.8605i	−0.696700	+	1.20672i	−0.969604	+	0.244679i	$0.921317\pi$
$4$	4.00000	−	6.92820i	0.250000	−	0.433013i
$5$	10.1380	−	22.8521i	0.405522	−	0.914085i
$5$	10.1380	−	22.8521i	0.405522	−	0.914085i
$6$		−	35.4702i		−	0.985283i
$7$	−32.1106	−	37.0123i	−0.655318	−	0.755353i
$7$	−32.1106	−	37.0123i	−0.655318	−	0.755353i
$8$			22.6274i			0.353553i
$9$	−38.1334	−	66.0490i	−0.470783	−	0.815420i
$10$	7.48477	+	70.3134i	0.0748477	+	0.703134i
$11$	3.60139	−	6.23778i	0.0297635	−	0.0515519i	−0.850760	−	0.525554i	$-0.823858\pi$
$11$	3.60139	−	6.23778i	0.0297635	−	0.0515519i	0.880523	+	0.474003i	$0.157191\pi$
$12$	50.1624	+	86.8839i	0.348350	+	0.603360i
$13$	292.752			1.73226			0.866131	−	0.499816i	$-0.166599\pi$
$13$	292.752			1.73226			0.866131	+	0.499816i	$0.166599\pi$
$14$	130.998	+	45.2500i	0.668356	+	0.230868i
$15$	184.617	+	253.394i	0.820518	+	1.12619i
$16$	−32.0000	−	55.4256i	−0.125000	−	0.216506i
$17$	61.4709	−	106.471i	0.212702	−	0.368411i	−0.739857	−	0.672764i	$-0.765107\pi$
$17$	61.4709	−	106.471i	0.212702	−	0.368411i	0.952559	+	0.304353i	$0.0984403\pi$
$18$	186.815	+	107.858i	0.576589	+	0.332894i
$19$	−75.8198	+	43.7746i	−0.210027	+	0.121259i	−0.601324	−	0.799005i	$-0.705360\pi$
$19$	−75.8198	+	43.7746i	−0.210027	+	0.121259i	0.391297	+	0.920265i	$0.372027\pi$
$20$	−117.772	−	161.647i	−0.294430	−	0.404117i
$21$	603.315	−	116.658i	1.36806	−	0.264531i
$22$			20.3725i			0.0420920i
$23$	445.403	−	257.154i	0.841972	−	0.486113i	−0.0159620	−	0.999873i	$-0.505081\pi$
$23$	445.403	−	257.154i	0.841972	−	0.486113i	0.857934	+	0.513760i	$0.171748\pi$
$24$	−245.745	−	141.881i	−0.426640	−	0.246321i
$25$	−419.440	−	463.352i	−0.671104	−	0.741363i
$26$	−717.094	+	414.014i	−1.06079	+	0.612447i
$27$	−59.3570			−0.0814225
$28$	−384.871	+	74.4194i	−0.490907	+	0.0949227i
$29$	931.646			1.10778			0.553892	−	0.832589i	$-0.313142\pi$
$29$	931.646			1.10778			0.553892	+	0.832589i	$0.313142\pi$
$30$	−810.570	−	359.598i	−0.900633	−	0.399554i
$31$	−12.4789	−	7.20472i	−0.0129854	−	0.00749711i	0.493493	−	0.869750i	$-0.335720\pi$
$31$	−12.4789	−	7.20472i	−0.0129854	−	0.00749711i	−0.506479	+	0.862253i	$0.669053\pi$
$32$	156.767	+	90.5097i	0.153093	+	0.0883883i
$33$	45.1636	+	78.2256i	0.0414725	+	0.0718325i
$34$			347.732i			0.300806i
$35$	−1171.35	+	358.563i	−0.956203	+	0.292705i
$36$	−610.135			−0.470783
$37$	1496.98	−	864.280i	1.09348	−	0.631322i	0.158980	−	0.987282i	$-0.449179\pi$
$37$	1496.98	−	864.280i	1.09348	−	0.631322i	0.934501	+	0.355960i	$0.115846\pi$
$38$	123.813	−	214.451i	0.0857433	−	0.148512i
$39$	−1835.65	+	3179.43i	−1.20687	+	2.09036i
$40$	517.085	+	229.398i	0.323178	+	0.143374i
$41$		−	2540.41i		−	1.51125i	−0.655005	−	0.755625i	$-0.727333\pi$
$41$		−	2540.41i		−	1.51125i	0.655005	−	0.755625i	$-0.272667\pi$
$42$	−1312.83	+	1138.97i	−0.744237	+	0.645674i
$43$		−	410.931i		−	0.222245i	−0.993807	−	0.111122i	$-0.964555\pi$
$43$		−	410.931i		−	0.222245i	0.993807	−	0.111122i	$-0.0354446\pi$
$44$	−28.8111	−	49.9023i	−0.0148818	−	0.0257760i
$45$	−1895.96	+	201.822i	−0.936276	+	0.0996653i
$46$	−727.340	+	1259.79i	−0.343734	+	0.595364i
$47$	−1519.41	−	2631.70i	−0.687829	−	1.19136i	−0.972539	−	0.232741i	$-0.925230\pi$
$47$	−1519.41	−	2631.70i	−0.687829	−	1.19136i	0.284709	−	0.958614i	$-0.408103\pi$
$48$	802.599			0.348350
$49$	−338.821	+	2376.97i	−0.141117	+	0.989993i
$50$	1682.69	+	541.798i	0.673077	+	0.216719i
$51$	770.882	+	1335.21i	0.296379	+	0.513344i
$52$	1171.01	−	2028.25i	0.433066	−	0.750092i
$53$	−1721.93	−	994.156i	−0.613004	−	0.353918i	0.161136	−	0.986932i	$-0.448484\pi$
$53$	−1721.93	−	994.156i	−0.613004	−	0.353918i	−0.774140	+	0.633014i	$0.781818\pi$
$54$	145.394	−	83.9435i	0.0498609	−	0.0287872i
$55$	−106.036	−	145.538i	−0.0350531	−	0.0481118i
$56$	837.493	−	726.580i	0.267058	−	0.231690i
$57$		−	1097.92i		−	0.337926i
$58$	−2282.06	+	1317.55i	−0.678376	+	0.391661i
$59$	−3389.27	−	1956.80i	−0.973649	−	0.562136i	−0.0733020	−	0.997310i	$-0.523354\pi$
$59$	−3389.27	−	1956.80i	−0.973649	−	0.562136i	−0.900347	+	0.435173i	$0.856687\pi$
$60$	2494.03	−	265.486i	0.692786	−	0.0737462i
$61$	4131.01	−	2385.04i	1.11019	−	0.640968i	0.171310	−	0.985217i	$-0.445200\pi$
$61$	4131.01	−	2385.04i	1.11019	−	0.640968i	0.938878	+	0.344250i	$0.111867\pi$
$62$	40.7560			0.0106025
$63$	−1220.14	+	3532.28i	−0.307417	+	0.889966i
$64$	−512.000			−0.125000
$65$	2967.94	−	6690.02i	0.702470	−	1.58344i
$66$	−221.255	−	127.742i	−0.0507933	−	0.0293255i
$67$	6625.07	+	3824.99i	1.47585	+	0.852080i	0.999629	−	0.0272481i	$-0.00867441\pi$
$67$	6625.07	+	3824.99i	1.47585	+	0.852080i	0.476217	+	0.879328i	$0.342008\pi$
$68$	−491.767	−	851.766i	−0.106351	−	0.184205i
$69$			6449.73i			1.35470i
$70$	2362.12	−	2534.83i	0.482066	−	0.517313i
$71$	1844.25			0.365849			0.182925	−	0.983127i	$-0.441444\pi$
$71$	1844.25			0.365849			0.182925	+	0.983127i	$0.441444\pi$
$72$	1494.52	−	862.860i	0.288294	−	0.166447i
$73$	−5299.30	+	9178.65i	−0.994426	+	1.72240i	−0.405901	+	0.913917i	$0.633042\pi$
$73$	−5299.30	+	9178.65i	−0.994426	+	1.72240i	−0.588525	+	0.808479i	$0.700291\pi$
$74$	−2444.55	+	4234.09i	−0.446412	+	0.773208i
$75$	7662.24	−	1649.97i	1.36218	−	0.293327i
$76$			700.394i			0.121259i
$77$	−346.517	+	67.0033i	−0.0584445	+	0.0113009i
$78$		−	10384.0i		−	1.70677i
$79$	1890.26	+	3274.03i	0.302878	+	0.524600i	0.976787	−	0.214215i	$-0.0687192\pi$
$79$	1890.26	+	3274.03i	0.302878	+	0.524600i	−0.673909	+	0.738815i	$0.735386\pi$
$80$	−1591.01	+	169.361i	−0.248596	+	0.0264627i
$81$	3460.99	−	5994.61i	0.527510	−	0.913674i
$82$	3592.68	+	6222.71i	0.534307	+	0.925447i
$83$	3661.83			0.531547			0.265774	−	0.964035i	$-0.414373\pi$
$83$	3661.83			0.531547			0.265774	+	0.964035i	$0.414373\pi$
$84$	1605.03	−	4646.52i	0.227470	−	0.658520i
$85$	−1809.89	−	2484.15i	−0.250504	−	0.343826i
$86$	581.144	+	1006.57i	0.0785754	+	0.136097i
$87$	−5841.71	+	10118.1i	−0.771794	+	1.33679i
$88$	141.145	+	81.4901i	0.0182264	+	0.0105230i
$89$	129.635	−	74.8449i	0.0163660	−	0.00944892i	−0.491795	−	0.870711i	$-0.663659\pi$
$89$	129.635	−	74.8449i	0.0163660	−	0.00944892i	0.508161	+	0.861262i	$0.330326\pi$
$90$	4358.71	−	3175.65i	0.538113	−	0.392056i
$91$	−9400.45	−	10835.4i	−1.13518	−	1.30847i
$92$		−	4114.46i		−	0.486113i
$93$	156.493	−	90.3515i	0.0180938	−	0.0104465i
$94$	7443.58	+	4297.55i	0.842415	+	0.486369i
$95$	231.678	+	2176.43i	0.0256707	+	0.241156i
$96$	−1965.96	+	1135.05i	−0.213320	+	0.123160i
$97$	−12754.1			−1.35552			−0.677759	−	0.735284i	$-0.737049\pi$
$97$	−12754.1			−1.35552			−0.677759	+	0.735284i	$0.737049\pi$
$98$	−2531.61	−	6301.54i	−0.263599	−	0.656137i
$99$	−549.333			−0.0560486
$100$	−4887.96	+	1052.56i	−0.488796	+	0.105256i
$101$	−9960.79	−	5750.87i	−0.976453	−	0.563755i	−0.0752554	−	0.997164i	$-0.523977\pi$
$101$	−9960.79	−	5750.87i	−0.976453	−	0.563755i	−0.901197	+	0.433409i	$0.857311\pi$
$102$	−3776.54	−	2180.38i	−0.362989	−	0.209572i
$103$	3786.56	+	6558.51i	0.356919	+	0.618203i	0.987445	−	0.157966i	$-0.0504937\pi$
$103$	3786.56	+	6558.51i	0.356919	+	0.618203i	−0.630525	+	0.776169i	$0.717160\pi$
$104$			6624.23i			0.612447i
$105$	3450.54	−	14969.7i	0.312974	−	1.35780i
$106$	5623.80			0.500516
$107$	5473.23	−	3159.97i	0.478053	−	0.276004i	−0.241552	−	0.970388i	$-0.577656\pi$
$107$	5473.23	−	3159.97i	0.478053	−	0.276004i	0.719605	+	0.694384i	$0.244323\pi$
$108$	−237.428	+	411.238i	−0.0203556	+	0.0352570i
$109$	−9805.80	+	16984.1i	−0.825335	+	1.42952i	0.0763284	+	0.997083i	$0.475680\pi$
$109$	−9805.80	+	16984.1i	−0.825335	+	1.42952i	−0.901663	+	0.432439i	$0.857653\pi$
$110$	465.556	+	206.537i	0.0384757	+	0.0170692i
$111$			21677.2i			1.75937i
$112$	−1023.89	+	2964.14i	−0.0816240	+	0.236300i
$113$		−	15860.1i		−	1.24208i	−0.783780	−	0.621039i	$-0.786711\pi$
$113$		−	15860.1i		−	1.24208i	0.783780	−	0.621039i	$-0.213289\pi$
$114$	1552.69	+	2689.34i	0.119475	+	0.206936i
$115$	−1360.99	−	12785.5i	−0.102911	−	0.966764i
$116$	3726.59	−	6454.64i	0.276946	−	0.479685i
$117$	−11163.6	−	19336.0i	−0.815520	−	1.41252i
$118$	11069.3			0.794981
$119$	−5914.59	+	1143.66i	−0.417668	+	0.0807611i
$120$	−5733.65	+	4177.40i	−0.398170	+	0.290097i
$121$	7294.56	+	12634.5i	0.498228	+	0.862957i
$122$	−6745.91	+	11684.3i	−0.453232	+	0.785022i
$123$	27590.1	+	15929.1i	1.82366	+	1.05289i
$124$	−99.8315	+	57.6378i	−0.00649268	+	0.00374855i
$125$	−14840.9	+	4887.62i	−0.949816	+	0.312808i
$126$	−2006.67	−	10377.8i	−0.126397	−	0.653679i
$127$			3905.57i			0.242146i	0.992644	+	0.121073i	$0.0386335\pi$
$127$			3905.57i			0.242146i	−0.992644	+	0.121073i	$0.961367\pi$
$128$	1254.14	−	724.077i	0.0765466	−	0.0441942i
$129$	4462.91	+	2576.66i	0.268187	+	0.154838i
$130$	2191.18	+	20584.4i	0.129656	+	1.21801i
$131$	−28422.1	+	16409.5i	−1.65620	+	0.956208i	−0.681756	+	0.731579i	$0.738784\pi$
$131$	−28422.1	+	16409.5i	−1.65620	+	0.956208i	−0.974444	+	0.224629i	$0.927883\pi$
$132$	722.617			0.0414725
$133$	4054.82	+	1400.64i	0.229228	+	0.0791813i
$134$	−21637.4			−1.20502
$135$	−601.764	+	1356.43i	−0.0330186	+	0.0744272i
$136$	2409.16	+	1390.93i	0.130253	+	0.0752015i
$137$	12543.3	+	7241.86i	0.668297	+	0.385842i	0.795431	−	0.606044i	$-0.207244\pi$
$137$	12543.3	+	7241.86i	0.668297	+	0.385842i	−0.127134	+	0.991886i	$0.540578\pi$
$138$	−9121.29	−	15798.5i	−0.478959	−	0.829581i
$139$		−	20012.6i		−	1.03580i	−0.855442	−	0.517899i	$-0.826714\pi$
$139$		−	20012.6i		−	1.03580i	0.855442	−	0.517899i	$-0.173286\pi$
$140$	−2201.20	+	9549.59i	−0.112306	+	0.487224i
$141$	38108.8			1.91684
$142$	−4517.46	+	2608.16i	−0.224036	+	0.129347i
$143$	1054.31	−	1826.13i	0.0515582	−	0.0893015i
$144$	−2440.54	+	4227.14i	−0.117696	+	0.203855i
$145$	9445.07	−	21290.1i	0.449230	−	1.01261i
$146$		−	29977.3i		−	1.40633i
$147$	−23690.6	−	18584.1i	−1.09633	−	0.860017i
$148$		−	13828.5i		−	0.631322i
$149$	−9030.06	−	15640.5i	−0.406741	−	0.704496i	0.587781	−	0.809020i	$-0.300002\pi$
$149$	−9030.06	−	15640.5i	−0.406741	−	0.704496i	−0.994522	+	0.104524i	$0.966668\pi$
$150$	−16435.2	+	14877.6i	−0.730452	+	0.661228i
$151$	8980.40	−	15554.5i	0.393860	−	0.682186i	−0.599095	−	0.800678i	$-0.704473\pi$
$151$	8980.40	−	15554.5i	0.393860	−	0.682186i	0.992955	+	0.118492i	$0.0378061\pi$
$152$	−990.506	−	1715.61i	−0.0428716	−	0.0742558i
$153$	−9376.38			−0.400546
$154$	754.034	−	654.173i	0.0317943	−	0.0275836i
$155$	−291.155	+	212.129i	−0.0121188	+	0.00882950i
$156$	14685.2	+	25435.5i	0.603434	+	1.04518i
$157$	−7351.76	+	12733.6i	−0.298258	+	0.516598i	−0.975737	−	0.218944i	$-0.929739\pi$
$157$	−7351.76	+	12733.6i	−0.298258	+	0.516598i	0.677480	+	0.735542i	$0.263072\pi$
$158$	−9260.35	−	5346.47i	−0.370948	−	0.214167i
$159$	21594.0	−	12467.3i	0.854160	−	0.493150i
$160$	3657.65	−	2664.88i	0.142877	−	0.104097i
$161$	−23820.0	−	8228.05i	−0.918946	−	0.317428i
$162$			19578.3i			0.746012i
$163$	−12197.0	+	7041.92i	−0.459067	+	0.265043i	−0.711652	−	0.702532i	$-0.752053\pi$
$163$	−12197.0	+	7041.92i	−0.459067	+	0.265043i	0.252585	+	0.967575i	$0.418719\pi$
$164$	−17600.5	−	10161.6i	−0.654390	−	0.377812i
$165$	2245.49	−	239.030i	0.0824791	−	0.00877978i
$166$	−8969.61	+	5178.61i	−0.325505	+	0.187930i
$167$	43007.4			1.54209			0.771045	−	0.636781i	$-0.219734\pi$
$167$	43007.4			1.54209			0.771045	+	0.636781i	$0.219734\pi$
$168$	2639.67	+	13651.5i	0.0935258	+	0.483682i
$169$	57143.0			2.00073
$170$	7946.42	+	3525.32i	0.274963	+	0.121983i
$171$	5782.54	+	3338.55i	0.197754	+	0.114174i
$172$	−2847.01	−	1643.72i	−0.0962348	−	0.0555612i
$173$	11398.8	+	19743.2i	0.380860	+	0.659670i	0.991185	−	0.132482i	$-0.0422945\pi$
$173$	11398.8	+	19743.2i	0.380860	+	0.659670i	−0.610325	+	0.792151i	$0.708961\pi$
$174$		−	33045.7i		−	1.09148i
$175$	−3681.25	+	30402.9i	−0.120204	+	0.992749i
$176$	−460.977			−0.0148818
$177$	42503.5	−	24539.4i	1.35668	−	0.783281i
$178$	−211.693	+	366.663i	−0.00668139	+	0.0115725i
$179$	6165.35	−	10678.7i	0.192421	−	0.333283i	−0.753631	−	0.657298i	$-0.771699\pi$
$179$	6165.35	−	10678.7i	0.192421	−	0.333283i	0.946052	+	0.324015i	$0.105033\pi$
$180$	−6185.57	+	13942.9i	−0.190913	+	0.430336i
$181$		−	35555.8i		−	1.08531i	−0.839956	−	0.542655i	$-0.817419\pi$
$181$		−	35555.8i		−	1.08531i	0.839956	−	0.542655i	$-0.182581\pi$
$182$	38349.9	+	13247.1i	1.15777	+	0.399923i
$183$			59819.7i			1.78625i
$184$	5818.72	+	10078.3i	0.171867	+	0.297682i
$185$	−4574.23	−	42971.2i	−0.133652	−	1.25555i
$186$	−255.553	+	442.630i	−0.00738677	+	0.0127943i
$187$	−442.761	−	766.884i	−0.0126615	−	0.0219304i
$188$	−24310.6			−0.687829
$189$	1905.99	+	2196.94i	0.0533577	+	0.0615028i
$190$	−3645.44	−	5003.51i	−0.100982	−	0.138601i
$191$	26972.8	+	46718.3i	0.739366	+	1.28062i	0.952781	+	0.303657i	$0.0982078\pi$
$191$	26972.8	+	46718.3i	0.739366	+	1.28062i	−0.213416	+	0.976961i	$0.568459\pi$
$192$	3210.40	−	5560.57i	0.0870875	−	0.150840i
$193$	−2091.52	−	1207.54i	−0.0561497	−	0.0324181i	0.471662	−	0.881779i	$-0.343654\pi$
$193$	−2091.52	−	1207.54i	−0.0561497	−	0.0324181i	−0.527812	+	0.849361i	$0.676987\pi$
$194$	31241.0	−	18037.0i	0.830082	−	0.479248i
$195$	54047.0	+	74181.7i	1.42135	+	1.95087i
$196$	15112.9	+	11855.3i	0.393400	+	0.308604i
$197$		−	26051.4i		−	0.671272i	−0.941992	−	0.335636i	$-0.891049\pi$
$197$		−	26051.4i		−	0.671272i	0.941992	−	0.335636i	$-0.108951\pi$
$198$	1345.58	−	776.874i	0.0343226	−	0.0198162i
$199$	1143.89	+	660.427i	0.0288854	+	0.0166770i	0.514373	−	0.857566i	$-0.328025\pi$
$199$	1143.89	+	660.427i	0.0288854	+	0.0166770i	−0.485488	+	0.874243i	$0.661358\pi$
$200$	10484.5	−	9490.85i	0.262111	−	0.237271i
$201$	−83082.4	+	47967.6i	−2.05644	+	1.18729i
$202$	32531.8			0.797270
$203$	−29915.7	−	34482.4i	−0.725951	−	0.836768i
$204$	12334.1			0.296379
$205$	−58053.8	−	25754.8i	−1.38141	−	0.612844i
$206$	−18550.3	−	10710.0i	−0.437135	−	0.252380i
$207$	−33969.5	−	19612.3i	−0.792772	−	0.457707i
$208$	−9368.08	−	16226.0i	−0.216533	−	0.375046i
$209$			630.597i			0.0144364i
$210$	12718.3	+	41548.0i	0.288397	+	0.942131i
$211$	−5370.71			−0.120633			−0.0603166	−	0.998179i	$-0.519211\pi$
$211$	−5370.71			−0.120633			−0.0603166	+	0.998179i	$0.519211\pi$
$212$	−13775.4	+	7953.25i	−0.306502	+	0.176959i
$213$	−11564.0	+	20029.4i	−0.254887	+	0.441478i
$214$	−8937.75	+	15480.6i	−0.195164	+	0.338035i
$215$	−9390.64	−	4166.03i	−0.203151	−	0.0901251i
$216$		−	1343.10i		−	0.0287872i
$217$	134.043	+	693.222i	0.00284658	+	0.0147215i
$218$		−	55470.0i		−	1.16720i
$219$	−66456.4	−	115106.i	−1.38563	−	2.39999i
$220$	−1432.46	+	152.484i	−0.0295963	+	0.00315049i
$221$	17995.8	−	31169.6i	0.368456	−	0.638184i
$222$	−30656.2	−	53098.0i	−0.622031	−	1.07739i
$223$	−63898.3			−1.28493			−0.642465	−	0.766315i	$-0.722088\pi$
$223$	−63898.3			−1.28493			−0.642465	+	0.766315i	$0.722088\pi$
$224$	−1683.92	−	8708.64i	−0.0335603	−	0.173562i
$225$	−14609.2	+	45372.8i	−0.288578	+	0.896253i
$226$	22429.6	+	38849.1i	0.439141	+	0.760614i
$227$	12345.9	−	21383.7i	0.239591	−	0.414984i	−0.721006	−	0.692929i	$-0.756320\pi$
$227$	12345.9	−	21383.7i	0.239591	−	0.414984i	0.960597	+	0.277945i	$0.0896533\pi$
$228$	−7606.61	−	4391.68i	−0.146326	−	0.0844814i
$229$	29099.2	−	16800.4i	0.554894	−	0.320368i	−0.196199	−	0.980564i	$-0.562860\pi$
$229$	29099.2	−	16800.4i	0.554894	−	0.320368i	0.751094	+	0.660196i	$0.229527\pi$
$230$	21415.1	+	29393.1i	0.404822	+	0.555635i
$231$	1445.08	−	4183.48i	0.0270812	−	0.0783995i
$232$			21080.8i			0.391661i
$233$	−22348.3	+	12902.8i	−0.411655	+	0.237669i	−0.691500	−	0.722376i	$-0.743050\pi$
$233$	−22348.3	+	12902.8i	−0.411655	+	0.237669i	0.279846	+	0.960045i	$0.409717\pi$
$234$	54690.5	+	31575.6i	0.998803	+	0.576659i
$235$	−75543.9	+	8041.55i	−1.36793	+	0.145614i
$236$	−27114.2	+	15654.4i	−0.486824	+	0.281068i
$237$	−47410.1			−0.844061
$238$	12870.4	−	11165.9i	0.227215	−	0.197124i
$239$	−31292.6			−0.547830			−0.273915	−	0.961754i	$-0.588319\pi$
$239$	−31292.6			−0.547830			−0.273915	+	0.961754i	$0.588319\pi$
$240$	8136.78	−	18341.1i	0.141264	−	0.318422i
$241$	31606.1	+	18247.8i	0.544172	+	0.314178i	0.746768	−	0.665084i	$-0.231604\pi$
$241$	31606.1	+	18247.8i	0.544172	+	0.314178i	−0.202596	+	0.979262i	$0.564938\pi$
$242$	−35735.9	−	20632.1i	−0.610203	−	0.352301i
$243$	40999.0	+	71012.3i	0.694321	+	1.20260i
$244$		−	38160.6i		−	0.640968i
$245$	50883.9	+	31840.6i	0.847712	+	0.530456i
$246$	−90108.8			−1.48901
$247$	−22196.4	+	12815.1i	−0.363822	+	0.210053i
$248$	163.024	−	282.366i	0.00265063	−	0.00459102i
$249$	−22960.8	+	39769.2i	−0.370329	+	0.641429i
$250$	29440.4	−	32960.4i	0.471047	−	0.527366i
$251$			69357.1i			1.10089i	0.834872	+	0.550444i	$0.185542\pi$
$251$			69357.1i			1.10089i	−0.834872	+	0.550444i	$0.814458\pi$
$252$	19591.8	+	22582.5i	0.308512	+	0.355607i
$253$		−	3704.44i		−	0.0578737i
$254$	−5523.31	−	9566.65i	−0.0856114	−	0.148283i
$255$	38327.6	−	4079.92i	0.589428	−	0.0627439i
$256$	−2048.00	+	3547.24i	−0.0312500	+	0.0541266i
$257$	55043.3	+	95337.8i	0.833371	+	1.44344i	0.895350	+	0.445363i	$0.146925\pi$
$257$	55043.3	+	95337.8i	0.833371	+	1.44344i	−0.0619795	+	0.998077i	$0.519741\pi$
$258$	−14575.8			−0.218974
$259$	−80057.8	−	27654.0i	−1.19345	−	0.412248i
$260$	−34478.1	−	47322.5i	−0.510030	−	0.700038i
$261$	−35526.8	−	61534.3i	−0.521526	−	0.903309i
$262$	46413.0	−	80389.7i	0.676141	−	1.17111i
$263$	493.097	+	284.690i	0.00712888	+	0.00411586i	0.503560	−	0.863960i	$-0.332023\pi$
$263$	493.097	+	284.690i	0.00712888	+	0.00411586i	−0.496431	+	0.868076i	$0.665357\pi$
$264$	−1770.04	+	1021.93i	−0.0253966	+	0.0146627i
$265$	−40175.6	+	29270.9i	−0.572098	+	0.416817i
$266$	−11913.0	+	2303.53i	−0.168368	+	0.0325559i
$267$			1877.20i			0.0263323i
$268$	53000.6	−	30599.9i	0.737923	−	0.426040i
$269$	49537.8	+	28600.7i	0.684593	+	0.395250i	0.801583	−	0.597883i	$-0.203991\pi$
$269$	49537.8	+	28600.7i	0.684593	+	0.395250i	−0.116990	+	0.993133i	$0.537325\pi$
$270$	−444.274	−	4173.60i	−0.00609429	−	0.0572510i
$271$	72714.2	−	41981.6i	0.990104	−	0.571637i	0.0847985	−	0.996398i	$-0.472975\pi$
$271$	72714.2	−	41981.6i	0.990104	−	0.571637i	0.905305	+	0.424761i	$0.139642\pi$
$272$	−7868.28			−0.106351
$273$	176622.	−	34151.9i	2.36984	−	0.458237i
$274$	−40966.2			−0.545663
$275$	−4400.86	+	947.668i	−0.0581931	+	0.0125312i
$276$	44685.0	+	25798.9i	0.586602	+	0.338675i
$277$	50543.2	+	29181.1i	0.658723	+	0.380314i	0.791790	−	0.610793i	$-0.209149\pi$
$277$	50543.2	+	29181.1i	0.658723	+	0.380314i	−0.133067	+	0.991107i	$0.542483\pi$
$278$	28302.1	+	49020.7i	0.366210	+	0.634294i
$279$			1098.96i			0.0141180i
$280$	−8113.36	−	26504.6i	−0.103487	−	0.338069i
$281$	29284.0			0.370867			0.185434	−	0.982657i	$-0.440631\pi$
$281$	29284.0			0.370867			0.185434	+	0.982657i	$0.440631\pi$
$282$	−93347.0	+	53893.9i	−1.17382	+	0.677707i
$283$	64277.9	−	111333.i	0.802581	−	1.39011i	−0.115332	−	0.993327i	$-0.536793\pi$
$283$	64277.9	−	111333.i	0.802581	−	1.39011i	0.917912	−	0.396783i	$-0.129874\pi$
$284$	7376.98	−	12777.3i	0.0914623	−	0.158417i
$285$	−25089.8	−	11130.8i	−0.308893	−	0.137036i
$286$			5964.10i			0.0729144i
$287$	−94026.4	+	81574.0i	−1.14153	+	0.990349i
$288$		−	13805.8i		−	0.166447i
$289$	34203.2	+	59241.6i	0.409516	+	0.709302i
$290$	6973.16	+	65507.2i	0.0829151	+	0.778921i
$291$	79971.9	−	138515.i	0.944390	−	1.63573i
$292$	42394.4	+	73429.2i	0.497213	+	0.861198i
$293$	−127398.			−1.48398			−0.741990	−	0.670411i	$-0.766118\pi$
$293$	−127398.			−1.48398			−0.741990	+	0.670411i	$0.766118\pi$
$294$	84311.7	+	12018.1i	0.975423	+	0.139040i
$295$	−79077.6	+	57614.0i	−0.908676	+	0.662040i
$296$	19556.4	+	33872.7i	0.223206	+	0.386604i
$297$	−213.768	+	370.256i	−0.00242342	+	0.00419749i
$298$	44238.1	+	25540.9i	0.498154	+	0.287609i
$299$	130393.	−	75282.4i	1.45852	−	0.842075i
$300$	19217.7	−	59685.4i	0.213530	−	0.663172i
$301$	−15209.5	+	13195.2i	−0.167873	+	0.145641i
$302$			50800.8i			0.557002i
$303$	124914.	−	72119.4i	1.36059	−	0.785537i
$304$	4852.47	+	2801.57i	0.0525068	+	0.0303148i
$305$	−12622.9	−	118582.i	−0.135694	−	1.27473i
$306$	22967.3	−	13260.2i	0.245283	−	0.141614i
$307$	−63793.8			−0.676865			−0.338432	−	0.940991i	$-0.609897\pi$
$307$	−63793.8			−0.676865			−0.338432	+	0.940991i	$0.609897\pi$
$308$	−921.857	+	2668.76i	−0.00971767	+	0.0281324i
$309$	−94971.5			−0.994664
$310$	413.187	−	931.363i	0.00429955	−	0.00969160i
$311$	−17599.8	−	10161.2i	−0.181964	−	0.105057i	0.406251	−	0.913762i	$-0.366836\pi$
$311$	−17599.8	−	10161.2i	−0.181964	−	0.105057i	−0.588215	+	0.808704i	$0.700169\pi$
$312$	−71942.4	−	41535.9i	−0.739053	−	0.426692i
$313$	48519.0	+	84037.5i	0.495249	+	0.857796i	0.999985	−	0.00547733i	$-0.00174350\pi$
$313$	48519.0	+	84037.5i	0.495249	+	0.857796i	−0.504736	+	0.863274i	$0.668410\pi$
$314$		−	41587.8i		−	0.421800i
$315$	68350.2	+	63693.2i	0.688841	+	0.641906i
$316$	30244.2			0.302878
$317$	18486.9	−	10673.4i	0.183969	−	0.106215i	−0.405187	−	0.914234i	$-0.632794\pi$
$317$	18486.9	−	10673.4i	0.183969	−	0.106215i	0.589156	+	0.808019i	$0.299460\pi$
$318$	−35262.9	+	61077.1i	−0.348710	+	0.603983i
$319$	3355.22	−	5811.41i	0.0329716	−	0.0571084i
$320$	−5190.68	+	11700.3i	−0.0506902	+	0.114261i
$321$			79255.9i			0.769169i
$322$	69983.1	−	13532.1i	0.674965	−	0.130513i
$323$			10763.5i			0.103168i
$324$	−27687.9	−	47956.9i	−0.263755	−	0.456837i
$325$	−122792.	−	135647.i	−1.16253	−	1.28424i
$326$	19917.6	−	34498.2i	0.187414	−	0.324610i
$327$	−122971.	−	212992.i	−1.15002	−	1.99190i
$328$	57482.9			0.534307
$329$	−48616.1	+	140743.i	−0.449147	+	1.30027i
$330$	−5162.27	+	3761.11i	−0.0474038	+	0.0345372i
$331$	−29010.4	−	50247.5i	−0.264788	−	0.458626i	0.702720	−	0.711466i	$-0.251969\pi$
$331$	−29010.4	−	50247.5i	−0.264788	−	0.458626i	−0.967508	+	0.252841i	$0.918635\pi$
$332$	14647.3	−	25369.9i	0.132887	−	0.230167i
$333$	−114170.	−	65915.9i	−1.02958	−	0.594431i
$334$	−105346.	+	60821.6i	−0.944334	+	0.545211i
$335$	154574.	−	112619.i	1.37736	−	1.00351i
$336$	−25771.9	−	29706.0i	−0.228280	−	0.263127i
$337$			98548.0i			0.867737i	0.900976	+	0.433869i	$0.142852\pi$
$337$			98548.0i			0.867737i	−0.900976	+	0.433869i	$0.857148\pi$
$338$	−139971.	+	80812.4i	−1.22519	+	0.707367i
$339$	172248.	+	99447.6i	1.49884	+	0.865356i
$340$	−24450.2	+	2602.69i	−0.211507	+	0.0225146i
$341$	−89.8830	+	51.8940i	−0.000772981	+	0.000446281i
$342$	−18885.7			−0.161466
$343$	98857.0	−	63785.4i	0.840271	−	0.542167i
$344$	9298.30			0.0785754
$345$	147390.	+	65387.6i	1.23831	+	0.549360i
$346$	−55842.3	−	32240.6i	−0.466457	−	0.269309i
$347$	39760.1	+	22955.5i	0.330209	+	0.190646i	0.655934	−	0.754818i	$-0.272275\pi$
$347$	39760.1	+	22955.5i	0.330209	+	0.190646i	−0.325725	+	0.945465i	$0.605608\pi$
$348$	46733.6	+	80945.0i	0.385897	+	0.668393i
$349$		−	14058.4i		−	0.115421i	−0.998333	−	0.0577104i	$-0.981620\pi$
$349$		−	14058.4i		−	0.115421i	0.998333	−	0.0577104i	$-0.0183800\pi$
$350$	−33979.1	−	79677.8i	−0.277380	−	0.650431i
$351$	−17376.9			−0.141045
$352$	1129.16	−	651.921i	0.00911318	−	0.00526150i
$353$	−6711.88	+	11625.3i	−0.0538635	+	0.0932944i	−0.891700	−	0.452627i	$-0.850487\pi$
$353$	−6711.88	+	11625.3i	−0.0538635	+	0.0932944i	0.837836	+	0.545921i	$0.183820\pi$
$354$	−69407.9	+	120218.i	−0.553863	+	0.959320i
$355$	18697.0	−	42144.9i	0.148360	−	0.334417i
$356$		−	1197.52i		−	0.00944892i
$357$	24665.6	−	71406.4i	0.193533	−	0.560274i
$358$			34876.5i			0.272124i
$359$	48550.5	+	84091.9i	0.376708	+	0.652477i	0.990581	−	0.136927i	$-0.0437227\pi$
$359$	48550.5	+	84091.9i	0.376708	+	0.652477i	−0.613873	+	0.789405i	$0.710389\pi$
$360$	−4566.72	−	42900.6i	−0.0352370	−	0.331024i
$361$	−61328.1	+	106223.i	−0.470592	+	0.815090i
$362$	50283.6	+	87093.7i	0.383715	+	0.664614i
$363$	−182956.			−1.38846
$364$	−112672.	+	21786.5i	−0.850380	+	0.164431i
$365$	156027.	+	214154.i	1.17116	+	1.60746i
$366$	−84597.8	−	146528.i	−0.631534	−	1.09385i
$367$	−5836.08	+	10108.4i	−0.0433301	+	0.0750499i	−0.886877	−	0.462005i	$-0.847130\pi$
$367$	−5836.08	+	10108.4i	−0.0433301	+	0.0750499i	0.843547	+	0.537055i	$0.180463\pi$
$368$	−28505.8	−	16457.8i	−0.210493	−	0.121528i
$369$	−167792.	+	96874.5i	−1.23230	+	0.711470i
$370$	71975.0	+	98788.6i	0.525749	+	0.721611i
$371$	18496.1	+	95655.5i	0.134379	+	0.694963i
$372$		−	1445.62i		−	0.0104465i
$373$	−171258.	+	98875.9i	−1.23093	+	0.710678i	−0.967224	−	0.253925i	$-0.918278\pi$
$373$	−171258.	+	98875.9i	−1.23093	+	0.710678i	−0.263707	+	0.964603i	$0.584945\pi$
$374$	2169.08	+	1252.32i	0.0155071	+	0.00895305i
$375$	39974.9	−	191826.i	0.284266	−	1.36410i
$376$	59548.7	−	34380.4i	0.421208	−	0.243184i
$377$	272742.			1.91897
$378$	−7775.64	−	2685.91i	−0.0544193	−	0.0187978i
$379$	−8503.45			−0.0591993			−0.0295997	−	0.999562i	$-0.509423\pi$
$379$	−8503.45			−0.0591993			−0.0295997	+	0.999562i	$0.509423\pi$
$380$	16005.5	+	7100.62i	0.110841	+	0.0491733i
$381$	−42416.4	−	24489.1i	−0.292202	−	0.168703i
$382$	−132139.	−	76290.6i	−0.905534	−	0.522810i
$383$	−115090.	−	199342.i	−0.784584	−	1.35894i	−0.929247	−	0.369459i	$-0.879543\pi$
$383$	−115090.	−	199342.i	−0.784584	−	1.35894i	0.144663	−	0.989481i	$-0.453790\pi$
$384$			18160.7i			0.123160i
$385$	−1981.84	+	8597.94i	−0.0133705	+	0.0580060i
$386$	6830.88			0.0458461
$387$	−27141.6	+	15670.2i	−0.181223	+	0.104629i
$388$	−51016.3	+	88362.8i	−0.338879	+	0.586956i
$389$	−40004.1	+	69289.1i	−0.264366	+	0.457895i	−0.967397	−	0.253264i	$-0.918496\pi$
$389$	−40004.1	+	69289.1i	−0.264366	+	0.457895i	0.703032	+	0.711159i	$0.251829\pi$
$390$	−237296.	−	105273.i	−1.56013	−	0.692132i
$391$		−	63229.9i		−	0.413589i
$392$	−53784.8	−	7666.65i	−0.350015	−	0.0498923i
$393$		−	411570.i		−	2.66476i
$394$	36842.3	+	63812.7i	0.237331	+	0.411069i
$395$	93982.1	−	10004.3i	0.602353	−	0.0641197i
$396$	−2197.33	+	3805.89i	−0.0140122	+	0.0242698i
$397$	23855.6	+	41319.0i	0.151359	+	0.262162i	0.931727	−	0.363159i	$-0.118302\pi$
$397$	23855.6	+	41319.0i	0.151359	+	0.262162i	−0.780368	+	0.625320i	$0.784968\pi$
$398$	−3735.94			−0.0235849
$399$	−40636.6	+	35254.9i	−0.255253	+	0.221449i
$400$	−12259.5	+	38075.0i	−0.0766217	+	0.237969i
$401$	−27054.9	−	46860.4i	−0.168251	−	0.291419i	0.769554	−	0.638582i	$-0.220478\pi$
$401$	−27054.9	−	46860.4i	−0.168251	−	0.291419i	−0.937805	+	0.347163i	$0.887145\pi$
$402$	135673.	−	234993.i	0.839540	−	1.45413i
$403$	−3653.24	−	2109.20i	−0.0224941	−	0.0129870i
$404$	−79686.4	+	46006.9i	−0.488226	+	0.281878i
$405$	−101902.	−	139865.i	−0.621259	−	0.852704i
$406$	122044.	+	42157.0i	0.740394	+	0.255751i
$407$		−	12450.4i		−	0.0751615i
$408$	−30212.3	+	17443.1i	−0.181494	+	0.104786i
$409$	−157861.	−	91141.0i	−0.943687	−	0.544838i	−0.0525726	−	0.998617i	$-0.516742\pi$
$409$	−157861.	−	91141.0i	−0.943687	−	0.544838i	−0.891114	+	0.453779i	$0.850075\pi$
$410$	178625.	−	19014.4i	1.06261	−	0.113114i
$411$	−157300.	+	90817.3i	−0.931206	+	0.537632i
$412$	60584.9			0.356919
$413$	36405.9	+	188279.i	0.213438	+	1.10383i
$414$	110944.			0.647296
$415$	37123.8	−	83680.6i	0.215554	−	0.485879i
$416$	45894.0	+	26496.9i	0.265198	+	0.153112i
$417$	217347.	+	125485.i	1.24992	+	0.721640i
$418$	−891.799	−	1544.64i	−0.00510404	−	0.00884046i
$419$			50823.7i			0.289493i	0.989469	+	0.144746i	$0.0462366\pi$
$419$			50823.7i			0.289493i	−0.989469	+	0.144746i	$0.953763\pi$
$420$	−89911.0	−	83784.9i	−0.509700	−	0.474971i
$421$	10731.4			0.0605471			0.0302735	−	0.999542i	$-0.490362\pi$
$421$	10731.4			0.0605471			0.0302735	+	0.999542i	$0.490362\pi$
$422$	13155.5	−	7595.33i	0.0738725	−	0.0426503i
$423$	−115881.	+	200712.i	−0.647636	+	1.12174i
$424$	22495.2	−	38962.8i	0.125129	−	0.216730i
$425$	−75116.8	+	16175.4i	−0.415871	+	0.0895526i
$426$		−	65415.7i		−	0.360465i
$427$	−220925.	−	76313.2i	−1.21168	−	0.418547i
$428$		−	50559.6i		−	0.276004i
$429$	13221.7	+	22900.7i	0.0718413	+	0.124433i
$430$	28893.9	−	3075.72i	0.156268	−	0.0166345i
$431$	−41981.9	+	72714.7i	−0.225999	+	0.391442i	−0.956619	−	0.291343i	$-0.905898\pi$
$431$	−41981.9	+	72714.7i	−0.225999	+	0.391442i	0.730619	+	0.682785i	$0.239231\pi$
$432$	1899.42	+	3289.90i	0.0101778	+	0.0176285i
$433$	7149.73			0.0381342			0.0190671	−	0.999818i	$-0.493930\pi$
$433$	7149.73			0.0381342			0.0190671	+	0.999818i	$0.493930\pi$
$434$	−1308.70	−	1508.48i	−0.00694801	−	0.00800864i
$435$	171997.	+	236073.i	0.908957	+	1.24758i
$436$	78446.4	+	135873.i	0.412667	+	0.714761i
$437$	−22513.6	+	38994.7i	−0.117891	+	0.204194i
$438$	325568.	+	187967.i	1.69705	+	0.979791i
$439$	−219582.	+	126775.i	−1.13938	+	0.657819i	−0.946276	−	0.323361i	$-0.895187\pi$
$439$	−219582.	+	126775.i	−1.13938	+	0.657819i	−0.193099	+	0.981179i	$0.561854\pi$
$440$	3293.16	−	2399.31i	0.0170101	−	0.0123931i
$441$	169917.	−	68263.3i	0.873695	−	0.351002i
$442$			101799.i			0.521075i
$443$	−61839.7	+	35703.2i	−0.315108	+	0.181928i	−0.649210	−	0.760609i	$-0.724900\pi$
$443$	−61839.7	+	35703.2i	−0.315108	+	0.181928i	0.334102	+	0.942537i	$0.391567\pi$
$444$	150184.	+	86708.7i	0.761829	+	0.439842i
$445$	−396.119	−	3721.22i	−0.00200035	−	0.0187917i
$446$	156518.	−	90365.8i	0.786855	−	0.454291i
$447$	226485.			1.13351
$448$	16440.6	+	18950.3i	0.0819147	+	0.0944191i
$449$	315051.			1.56275			0.781373	−	0.624064i	$-0.214520\pi$
$449$	315051.			1.56275			0.781373	+	0.624064i	$0.214520\pi$
$450$	−28381.6	−	131801.i	−0.140156	−	0.650868i
$451$	−15846.5	−	9149.00i	−0.0779078	−	0.0449801i
$452$	−109882.	−	63440.4i	−0.537836	−	0.310520i
$453$	112620.	+	195063.i	0.548805	+	0.950558i
$454$			69838.9i			0.338833i
$455$	−342915.	+	104970.i	−1.65639	+	0.507041i
$456$	24843.1			0.119475
$457$	60108.5	−	34703.6i	0.287808	−	0.166166i	−0.349145	−	0.937069i	$-0.613528\pi$
$457$	60108.5	−	34703.6i	0.287808	−	0.166166i	0.636953	+	0.770903i	$0.280195\pi$
$458$	−47518.8	+	82305.0i	−0.226535	+	0.392370i
$459$	−3648.73	+	6319.79i	−0.0173187	+	0.0299969i
$460$	−94024.2	−	41712.6i	−0.444349	−	0.197129i
$461$		−	166851.i		−	0.785104i	−0.919730	−	0.392552i	$-0.871592\pi$
$461$		−	166851.i		−	0.785104i	0.919730	−	0.392552i	$-0.128408\pi$
$462$	2376.62	+	12291.0i	0.0111346	+	0.0575844i
$463$		−	166871.i		−	0.778429i	−0.921147	−	0.389214i	$-0.872747\pi$
$463$		−	166871.i		−	0.778429i	0.921147	−	0.389214i	$-0.127253\pi$
$464$	−29812.7	−	51637.1i	−0.138473	−	0.239842i
$465$	−478.188	−	4492.20i	−0.00221153	−	0.0207756i
$466$	36494.6	−	63210.6i	0.168057	−	0.291084i
$467$	−91273.3	−	158090.i	−0.418514	−	0.724888i	0.577276	−	0.816549i	$-0.304116\pi$
$467$	−91273.3	−	158090.i	−0.418514	−	0.724888i	−0.995790	+	0.0916612i	$0.970782\pi$
$468$	−178618.			−0.815520
$469$	−71163.3	−	368032.i	−0.323527	−	1.67317i
$470$	173672.	−	126533.i	0.786200	−	0.572807i
$471$	−92195.5	−	159687.i	−0.415593	−	0.719828i
$472$	44277.2	−	76690.4i	0.198745	−	0.344237i
$473$	−2563.30	−	1479.92i	−0.0114571	−	0.00661479i
$474$	116130.	−	67047.9i	0.516880	−	0.298421i
$475$	52084.9	+	16770.4i	0.230847	+	0.0743288i
$476$	−15734.9	+	45552.1i	−0.0694464	+	0.201046i
$477$			151642.i			0.666474i
$478$	76650.9	−	44254.4i	0.335476	−	0.193687i
$479$	62412.7	+	36034.0i	0.272021	+	0.157051i	0.629806	−	0.776753i	$-0.283135\pi$
$479$	62412.7	+	36034.0i	0.272021	+	0.157051i	−0.357785	+	0.933804i	$0.616468\pi$
$480$	6007.27	+	56433.5i	0.0260732	+	0.244937i
$481$	438243.	−	253020.i	1.89420	−	1.09362i
$482$	−103225.			−0.444315
$483$	238719.	−	207104.i	1.02328	−	0.887759i
$484$	116713.			0.498228
$485$	−129301.	+	291458.i	−0.549692	+	1.23906i
$486$	−200853.	−	115963.i	−0.850367	−	0.490959i
$487$	−74054.8	−	42755.5i	−0.312245	−	0.180275i	0.335686	−	0.941974i	$-0.391032\pi$
$487$	−74054.8	−	42755.5i	−0.312245	−	0.180275i	−0.647931	+	0.761699i	$0.724365\pi$
$488$	53967.3	+	93474.1i	0.226616	+	0.392511i
$489$		−	176620.i		−	0.738621i
$490$	−169669.	−	6032.58i	−0.706660	−	0.0251253i
$491$	−360859.			−1.49684			−0.748418	−	0.663227i	$-0.769186\pi$
$491$	−360859.			−1.49684			−0.748418	+	0.663227i	$0.769186\pi$
$492$	220721.	−	127433.i	0.911828	−	0.526444i
$493$	57269.1	−	99193.1i	0.235628	−	0.408120i
$494$	36246.6	−	62781.0i	0.148530	−	0.257261i
$495$	−5569.16	+	12553.4i	−0.0227289	+	0.0512332i
$496$			922.204i			0.00374855i
$497$	−59219.8	−	68259.8i	−0.239747	−	0.276345i
$498$		−	129886.i		−	0.523724i
$499$	193248.	+	334716.i	0.776094	+	1.34423i	0.934177	+	0.356809i	$0.116135\pi$
$499$	193248.	+	334716.i	0.776094	+	1.34423i	−0.158083	+	0.987426i	$0.550531\pi$
$500$	−25501.1	+	122371.i	−0.102004	+	0.489485i
$501$	−269669.	+	467081.i	−1.07437	+	1.86087i
$502$	−98085.7	−	169889.i	−0.389223	−	0.674154i
$503$	125251.			0.495044			0.247522	−	0.968882i	$-0.420384\pi$
$503$	125251.			0.495044			0.247522	+	0.968882i	$0.420384\pi$
$504$	−79926.3	−	27608.6i	−0.314651	−	0.108688i
$505$	−232403.	+	169323.i	−0.911293	+	0.663946i
$506$	5238.87	+	9073.99i	0.0204615	+	0.0354403i
$507$	−358304.	+	620600.i	−1.39391	+	2.41433i
$508$	27058.6	+	15622.3i	0.104852	+	0.0605364i
$509$	299969.	−	173187.i	1.15782	−	0.668468i	0.207040	−	0.978333i	$-0.433617\pi$
$509$	299969.	−	173187.i	1.15782	−	0.668468i	0.950781	+	0.309865i	$0.100284\pi$
$510$	−88113.1	+	64197.1i	−0.338766	+	0.246817i
$511$	509886.	−	98592.6i	1.95268	−	0.377574i
$512$		−	11585.2i		−	0.0441942i
$513$	4500.44	−	2598.33i	0.0171010	−	0.00987324i
$514$	−269656.	−	155686.i	−1.02067	−	0.589282i
$515$	188264.	−	20040.5i	0.709829	−	0.0755603i
$516$	35703.2	−	20613.3i	0.134094	−	0.0774190i
$517$	−21888.0			−0.0818889
$518$	235209.	−	45480.5i	0.876587	−	0.169499i
$519$	−285895.			−1.06138
$520$	151378.	+	67156.7i	0.559829	+	0.248361i
$521$	18587.3	+	10731.4i	0.0684764	+	0.0395349i	0.533847	−	0.845581i	$-0.320746\pi$
$521$	18587.3	+	10731.4i	0.0684764	+	0.0395349i	−0.465371	+	0.885116i	$0.654079\pi$
$522$	174045.	+	100485.i	0.638736	+	0.368774i
$523$	177435.	+	307327.i	0.648689	+	1.12356i	0.983436	+	0.181254i	$0.0580157\pi$
$523$	177435.	+	307327.i	0.648689	+	1.12356i	−0.334747	+	0.942308i	$0.608651\pi$
$524$			262552.i			0.956208i
$525$	−307108.	−	230616.i	−1.11422	−	0.836701i
$526$	−1610.45			−0.00582070
$527$	−1534.18	+	885.761i	−0.00552403	+	0.00318930i
$528$	2890.47	−	5006.44i	0.0103681	−	0.0179581i
$529$	−7664.46	+	13275.2i	−0.0273886	+	0.0474385i
$530$	57014.3	−	128516.i	0.202970	−	0.457514i
$531$			298477.i			1.05858i
$532$	25923.2	−	22490.0i	0.0915936	−	0.0794634i
$533$		−	743711.i		−	2.61788i
$534$	−2654.76	−	4598.18i	−0.00930986	−	0.0161251i
$535$	−16724.3	−	157111.i	−0.0584304	−	0.548907i
$536$	−86549.6	+	149908.i	−0.301256	+	0.521790i
$537$	77317.3	+	133917.i	0.268119	+	0.464396i
$538$	−161790.			−0.558968
$539$	13606.8	+	10673.9i	0.0468359	+	0.0367405i
$540$	6990.60	+	9594.88i	0.0239733	+	0.0329043i
$541$	−27795.2	−	48142.6i	−0.0949675	−	0.164488i	0.814628	−	0.579984i	$-0.196941\pi$
$541$	−27795.2	−	48142.6i	−0.0949675	−	0.164488i	−0.909595	+	0.415496i	$0.863608\pi$
$542$	−118742.	+	205667.i	−0.404208	+	0.700109i
$543$	386154.	+	222946.i	1.30967	+	0.756136i
$544$	19273.3	−	11127.4i	0.0651264	−	0.0376008i
$545$	288712.	+	396270.i	0.972014	+	1.33413i
$546$	−384335.	+	333436.i	−1.28921	+	1.11848i
$547$		−	486947.i		−	1.62745i	−0.581251	−	0.813725i	$-0.697436\pi$
$547$		−	486947.i		−	1.62745i	0.581251	−	0.813725i	$-0.302564\pi$
$548$	100346.	−	57934.9i	0.334149	−	0.192921i
$549$	−315059.	−	181899.i	−1.04532	−	0.603513i
$550$	9439.64	−	8545.05i	0.0312054	−	0.0282481i
$551$	−70637.3	+	40782.4i	−0.232665	+	0.134329i
$552$	−145941.			−0.478959
$553$	60482.0	−	175094.i	0.197777	−	0.572560i
$554$	−165073.			−0.537845
$555$	495370.	+	219764.i	1.60821	+	0.713462i
$556$	−138652.	−	80050.5i	−0.448513	−	0.258949i
$557$	113373.	+	65455.7i	0.365424	+	0.210978i	0.671458	−	0.741043i	$-0.265669\pi$
$557$	113373.	+	65455.7i	0.365424	+	0.210978i	−0.306033	+	0.952021i	$0.599002\pi$
$558$	−1554.17	−	2691.90i	−0.00499148	−	0.00864549i
$559$		−	120301.i		−	0.384986i
$560$	57356.7	+	53448.7i	0.182898	+	0.170436i
$561$	11105.0			0.0352852
$562$	−71730.9	+	41413.9i	−0.227109	+	0.131121i
$563$	−246241.	+	426503.i	−0.776863	+	1.34557i	0.156879	+	0.987618i	$0.449857\pi$
$563$	−246241.	+	426503.i	−0.776863	+	1.34557i	−0.933742	+	0.357948i	$0.883477\pi$
$564$	152435.	−	264025.i	0.479211	−	0.830018i
$565$	−362437.	−	160790.i	−1.13537	−	0.503690i
$566$			363611.i			1.13502i
$567$	−333009.	+	64391.3i	−1.03583	+	0.200291i
$568$			41730.5i			0.129347i
$569$	−43040.5	−	74548.3i	−0.132939	−	0.230257i	0.791869	−	0.610691i	$-0.209108\pi$
$569$	−43040.5	−	74548.3i	−0.132939	−	0.230257i	−0.924808	+	0.380434i	$0.875775\pi$
$570$	77198.5	−	8217.68i	0.237607	−	0.0252929i
$571$	−13812.5	+	23923.9i	−0.0423642	+	0.0733769i	−0.886430	−	0.462863i	$-0.846822\pi$
$571$	−13812.5	+	23923.9i	−0.0423642	+	0.0733769i	0.844066	+	0.536240i	$0.180156\pi$
$572$	−8434.52	−	14609.0i	−0.0257791	−	0.0446508i
$573$	−676510.			−2.06047
$574$	114954.	−	332788.i	0.348898	−	1.01005i
$575$	−305973.	−	98517.8i	−0.925437	−	0.297975i
$576$	19524.3	+	33817.1i	0.0588478	+	0.101927i
$577$	150729.	−	261070.i	0.452736	−	0.784162i	−0.545819	−	0.837903i	$-0.683781\pi$
$577$	150729.	−	261070.i	0.452736	−	0.784162i	0.998555	+	0.0537410i	$0.0171145\pi$
$578$	−167561.	−	96741.1i	−0.501552	−	0.289571i
$579$	26228.9	−	15143.3i	0.0782391	−	0.0451713i
$580$	−109722.	−	150598.i	−0.326165	−	0.447675i
$581$	−117583.	−	135533.i	−0.348332	−	0.401506i
$582$			452389.i			1.33557i
$583$	−12402.7	+	7160.68i	−0.0364903	+	0.0210677i
$584$	−207689.	−	119909.i	−0.608959	−	0.351583i
$585$	−555047.	+	59083.9i	−1.62188	+	0.172646i
$586$	312061.	−	180168.i	0.908749	−	0.524666i
$587$	−155451.			−0.451147			−0.225574	−	0.974226i	$-0.572426\pi$
$587$	−155451.			−0.451147			−0.225574	+	0.974226i	$0.572426\pi$
$588$	−223517.	+	89796.6i	−0.646480	+	0.259720i
$589$	1261.53			0.00363638
$590$	112221.	−	252957.i	0.322382	−	0.726680i
$591$	282931.	+	163350.i	0.810038	+	0.467676i
$592$	−95806.5	−	55313.9i	−0.273370	−	0.157830i
$593$	45364.7	+	78574.0i	0.129006	+	0.223445i	0.923292	−	0.384100i	$-0.125488\pi$
$593$	45364.7	+	78574.0i	0.129006	+	0.223445i	−0.794286	+	0.607544i	$0.792155\pi$
$594$		−	1209.25i		−	0.00342724i
$595$	−33827.4	+	146756.i	−0.0955508	+	0.414534i
$596$	−144481.			−0.406741
$597$	−14345.1	+	8282.15i	−0.0402490	+	0.0232378i
$598$	−212931.	+	368807.i	−0.595437	+	1.03133i
$599$	66299.8	−	114835.i	0.184782	−	0.320051i	−0.758721	−	0.651415i	$-0.774176\pi$
$599$	66299.8	−	114835.i	0.184782	−	0.320051i	0.943503	+	0.331364i	$0.107509\pi$
$600$	37334.5	+	173377.i	0.103707	+	0.481602i
$601$			247185.i			0.684343i	0.939638	+	0.342171i	$0.111162\pi$
$601$			247185.i			0.684343i	−0.939638	+	0.342171i	$0.888838\pi$
$602$	18594.6	−	53831.0i	0.0513091	−	0.148539i
$603$		−	583439.i		−	1.60458i
$604$	−71843.2	−	124436.i	−0.196930	−	0.341093i
$605$	362679.	−	38606.7i	0.990858	−	0.105476i
$606$	−203984.	+	353311.i	−0.555459	+	0.962082i
$607$	48474.3	+	83960.0i	0.131563	+	0.227874i	0.924279	−	0.381717i	$-0.124667\pi$
$607$	48474.3	+	83960.0i	0.131563	+	0.227874i	−0.792716	+	0.609591i	$0.791334\pi$
$608$	−15848.1			−0.0428716
$609$	562076.	−	108684.i	1.51552	−	0.293043i
$610$	198620.	+	272614.i	0.533781	+	0.732637i
$611$	−444812.	−	770438.i	−1.19150	−	2.06374i
$612$	−37505.5	+	64961.5i	−0.100136	+	0.173441i
$613$	−190621.	−	110055.i	−0.507284	−	0.292880i	0.224433	−	0.974490i	$-0.427947\pi$
$613$	−190621.	−	110055.i	−0.507284	−	0.292880i	−0.731716	+	0.681609i	$0.761280\pi$
$614$	156262.	−	90218.1i	0.414493	−	0.239308i
$615$	643724.	−	469002.i	1.70196	−	1.24001i
$616$	−1516.11	−	7840.79i	−0.00399549	−	0.0206632i
$617$		−	219063.i		−	0.575438i	−0.957715	−	0.287719i	$-0.907103\pi$
$617$		−	219063.i		−	0.575438i	0.957715	−	0.287719i	$-0.0928970\pi$
$618$	232632.	−	134310.i	0.609105	−	0.351667i
$619$	−15226.7	−	8791.15i	−0.0397398	−	0.0229438i	0.479999	−	0.877269i	$-0.340637\pi$
$619$	−15226.7	−	8791.15i	−0.0397398	−	0.0229438i	−0.519738	+	0.854326i	$0.673971\pi$
$620$	305.050	+	2865.70i	0.000793573	+	0.00745499i
$621$	−26437.8	+	15263.9i	−0.0685555	+	0.0395805i
$622$	57480.6			0.148573
$623$	−6932.84	−	2394.78i	−0.0178622	−	0.00617007i
$624$	234963.			0.603434
$625$	−38764.9	+	388697.i	−0.0992380	+	0.995064i
$626$	−237694.	−	137233.i	−0.606554	−	0.350194i
$627$	−6848.59	−	3954.03i	−0.0174207	−	0.0100579i
$628$	58814.1	+	101869.i	0.149129	+	0.258299i
$629$		−	212512.i		−	0.537134i
$630$	−257499.	−	59353.9i	−0.648775	−	0.149544i
$631$	541622.			1.36031			0.680154	−	0.733069i	$-0.261913\pi$
$631$	541622.			1.36031			0.680154	+	0.733069i	$0.261913\pi$
$632$	−74082.8	+	42771.7i	−0.185474	+	0.107084i
$633$	33676.0	−	58328.5i	0.0840452	−	0.145571i
$634$	−30189.0	+	52288.8i	−0.0751052	+	0.130086i
$635$	89250.6	+	39594.8i	0.221342	+	0.0981953i
$636$		−	199477.i		−	0.493150i
$637$	−99190.7	+	695865.i	−0.244451	+	1.71493i
$638$			18980.0i			0.0466288i
$639$	−70327.3	−	121811.i	−0.172235	−	0.298321i
$640$	−3832.20	−	36000.5i	−0.00935596	−	0.0878918i
$641$	−190385.	+	329757.i	−0.463358	+	0.802560i	−0.999126	−	0.0418055i	$-0.986689\pi$
$641$	−190385.	+	329757.i	−0.463358	+	0.802560i	0.535768	+	0.844366i	$0.320022\pi$
$642$	−112085.	−	194137.i	−0.271942	−	0.471018i
$643$	−209750.			−0.507319			−0.253659	−	0.967294i	$-0.581634\pi$
$643$	−209750.			−0.507319			−0.253659	+	0.967294i	$0.581634\pi$
$644$	−152286.	+	132118.i	−0.367187	+	0.318558i
$645$	104127.	−	75864.6i	0.250291	−	0.182356i
$646$	−15221.8	−	26365.0i	−0.0364755	−	0.0631775i
$647$	212293.	−	367702.i	0.507139	−	0.878391i	−0.492827	−	0.870127i	$-0.664036\pi$
$647$	212293.	−	367702.i	0.507139	−	0.878391i	0.999966	−	0.00826322i	$-0.00263029\pi$
$648$	135643.	+	78313.3i	0.323033	+	0.186503i
$649$	−24412.1	+	14094.4i	−0.0579584	+	0.0334623i
$650$	492612.	+	158613.i	1.16595	+	0.375414i
$651$	−8369.21	−	2890.94i	−0.0197480	−	0.00682146i
$652$			112671.i			0.265043i
$653$	−308491.	+	178107.i	−0.723463	+	0.417691i	−0.816026	−	0.578016i	$-0.803827\pi$
$653$	−308491.	+	178107.i	−0.723463	+	0.417691i	0.0925633	+	0.995707i	$0.470494\pi$
$654$	602431.	+	347814.i	1.40848	+	0.813188i
$655$	86847.7	+	815865.i	0.202430	+	1.90167i
$656$	−140804.	+	81293.1i	−0.327195	+	0.188906i
$657$	808321.			1.87263
$658$	−79955.4	−	413501.i	−0.184670	−	0.955047i
$659$	252669.			0.581810			0.290905	−	0.956752i	$-0.406044\pi$
$659$	252669.			0.581810			0.290905	+	0.956752i	$0.406044\pi$
$660$	7325.92	−	16513.3i	0.0168180	−	0.0379094i
$661$	245541.	+	141763.i	0.561980	+	0.324459i	0.753940	−	0.656943i	$-0.228151\pi$
$661$	245541.	+	141763.i	0.561980	+	0.324459i	−0.191960	+	0.981403i	$0.561484\pi$
$662$	142121.	+	82053.8i	0.324297	+	0.187233i
$663$	225678.	+	390885.i	0.513407	+	0.889247i
$664$			82857.7i			0.187930i
$665$	73115.5	−	78461.5i	0.165336	−	0.177424i
$666$	372876.			0.840652
$667$	414958.	−	239576.i	0.932723	−	0.538508i
$668$	172029.	−	297964.i	0.385523	−	0.667745i
$669$	400662.	−	693966.i	0.895211	−	1.55055i
$670$	−219361.	+	494461.i	−0.488663	+	1.10149i
$671$		−	34357.8i		−	0.0763098i
$672$	105139.	+	36317.6i	0.232822	+	0.0804227i
$673$			859774.i			1.89825i	0.314896	+	0.949126i	$0.398030\pi$
$673$			859774.i			1.89825i	−0.314896	+	0.949126i	$0.601970\pi$
$674$	−139368.	−	241392.i	−0.306791	−	0.531378i
$675$	24896.7	+	27503.2i	0.0546430	+	0.0603637i
$676$	228572.	−	395898.i	0.500184	−	0.866344i
$677$	−385171.	−	667136.i	−0.840382	−	1.45558i	−0.889572	−	0.456795i	$-0.848997\pi$
$677$	−385171.	−	667136.i	−0.840382	−	1.45558i	0.0491904	−	0.998789i	$-0.484336\pi$
$678$	−562561.			−1.22380
$679$	409540.	+	472057.i	0.888295	+	1.02389i
$680$	56209.8	−	40953.1i	0.121561	−	0.0885664i
$681$	154825.	+	268165.i	0.333847	+	0.578239i
$682$	146.778	−	254.227i	0.000315568	−	0.000546580i
$683$	781529.	+	451216.i	1.67534	+	0.967260i	0.964566	+	0.263842i	$0.0849899\pi$
$683$	781529.	+	451216.i	1.67534	+	0.967260i	0.710777	+	0.703417i	$0.248343\pi$
$684$	46260.3	−	26708.4i	0.0988772	−	0.0570868i
$685$	292656.	−	213222.i	0.623701	−	0.454414i
$686$	−151943.	+	296047.i	−0.322873	+	0.629089i
$687$			421375.i			0.892803i
$688$	−22776.1	+	13149.8i	−0.0481174	+	0.0277806i
$689$	−504099.	−	291042.i	−1.06188	−	0.613079i
$690$	−453502.	+	48274.7i	−0.952536	+	0.101396i
$691$	−199508.	+	115186.i	−0.417835	+	0.241237i	−0.694151	−	0.719830i	$-0.744220\pi$
$691$	−199508.	+	115186.i	−0.417835	+	0.241237i	0.276316	+	0.961067i	$0.410887\pi$
$692$	182380.			0.380860
$693$	17639.4	+	20332.1i	0.0367297	+	0.0423365i
$694$	−129856.			−0.269614
$695$	−457331.	−	202889.i	−0.946807	−	0.420038i
$696$	−228947.	−	132183.i	−0.472625	−	0.272870i
$697$	−270479.	−	156161.i	−0.556761	−	0.321446i
$698$	19881.5	+	34435.8i	0.0408074	+	0.0706805i
$699$		−	323618.i		−	0.662336i
$700$	195913.	+	147116.i	0.399822	+	0.300237i
$701$	236661.			0.481604			0.240802	−	0.970574i	$-0.422590\pi$
$701$	236661.			0.481604			0.240802	+	0.970574i	$0.422590\pi$
$702$	42564.6	−	24574.7i	0.0863722	−	0.0498670i
$703$	−75667.0	+	131059.i	−0.153107	+	0.265190i
$704$	−1843.91	+	3193.75i	−0.00372044	+	0.00644399i
$705$	386348.	−	870867.i	0.777322	−	1.75216i
$706$		−	37968.1i		−	0.0761746i
$707$	106994.	+	553336.i	0.214053	+	1.10701i
$708$		−	392631.i		−	0.783281i
$709$	31409.8	+	54403.4i	0.0624845	+	0.108226i	0.895575	−	0.444910i	$-0.146764\pi$
$709$	31409.8	+	54403.4i	0.0624845	+	0.108226i	−0.833091	+	0.553136i	$0.813431\pi$
$710$	13803.7	+	129675.i	0.0273830	+	0.257241i
$711$	144164.	−	249700.i	0.285180	−	0.493945i
$712$	1693.55	+	2933.31i	0.00334070	+	0.00578626i
$713$	−7410.88			−0.0145778
$714$	40565.7	+	209792.i	0.0795725	+	0.411521i
$715$	−31042.2	−	42606.7i	−0.0607212	−	0.0833423i
$716$	−49322.8	−	85429.7i	−0.0962104	−	0.166641i
$717$	196214.	−	339853.i	0.381674	−	0.661078i
$718$	−237848.	−	137322.i	−0.461371	−	0.266373i
$719$	−444505.	+	256635.i	−0.859843	+	0.496431i	−0.863960	−	0.503561i	$-0.832023\pi$
$719$	−444505.	+	256635.i	−0.859843	+	0.496431i	0.00411680	+	0.999992i	$0.498690\pi$
$720$	71856.8	+	98626.4i	0.138613	+	0.190252i
$721$	121157.	−	350747.i	0.233066	−	0.674720i
$722$		−	346924.i		−	0.665518i
$723$	−396359.	+	228838.i	−0.758250	+	0.437776i
$724$	−246338.	−	142223.i	−0.469953	−	0.271328i
$725$	−390770.	−	431680.i	−0.743439	−	0.821270i
$726$	448150.	−	258739.i	0.850257	−	0.490896i
$727$	−724922.			−1.37158			−0.685792	−	0.727797i	$-0.740544\pi$
$727$	−724922.			−1.37158			−0.685792	+	0.727797i	$0.740544\pi$
$728$	245178.	−	212708.i	0.462614	−	0.401348i
$729$	−467624.			−0.879916
$730$	−685046.	−	303912.i	−1.28551	−	0.570298i
$731$	−43752.1	−	25260.3i	−0.0818774	−	0.0472719i
$732$	414443.	+	239279.i	0.773469	+	0.446562i
$733$	165689.	+	286981.i	0.308379	+	0.534128i	0.978008	−	0.208568i	$-0.0668802\pi$
$733$	165689.	+	286981.i	0.308379	+	0.534128i	−0.669629	+	0.742696i	$0.733547\pi$
$734$		−	33013.9i		−	0.0612780i
$735$	−664862.	+	352974.i	−1.23071	+	0.653383i
$736$	93099.6			0.171867
$737$	47718.9	−	27550.5i	0.0878527	−	0.0507218i
$738$	274002.	−	474586.i	0.503085	−	0.871369i
$739$	−132295.	+	229141.i	−0.242244	+	0.419580i	−0.961353	−	0.275318i	$-0.911217\pi$
$739$	−132295.	+	229141.i	−0.242244	+	0.419580i	0.719109	+	0.694897i	$0.244550\pi$
$740$	−316010.	−	140194.i	−0.577082	−	0.256015i
$741$		−	321419.i		−	0.585376i
$742$	−180583.	−	208150.i	−0.327997	−	0.378066i
$743$		−	105627.i		−	0.191337i	−0.995413	−	0.0956683i	$-0.969501\pi$
$743$		−	105627.i		−	0.191337i	0.995413	−	0.0956683i	$-0.0304988\pi$
$744$	2044.42	+	3541.04i	0.00369339	+	0.00639713i
$745$	−448966.	+	47791.9i	−0.808912	+	0.0861076i
$746$	279663.	−	484391.i	0.502525	−	0.870399i
$747$	−139638.	−	241860.i	−0.250243	−	0.433434i
$748$	−7084.18			−0.0126615
$749$	−292707.	−	101108.i	−0.521758	−	0.180229i
$750$	173365.	+	526409.i	0.308204	+	0.935838i
$751$	477793.	+	827562.i	0.847149	+	1.46731i	0.883741	+	0.467976i	$0.155017\pi$
$751$	477793.	+	827562.i	0.847149	+	1.46731i	−0.0365919	+	0.999330i	$0.511650\pi$
$752$	−97242.6	+	168429.i	−0.171957	+	0.297839i
$753$	−753251.	−	434890.i	−1.32846	−	0.766989i
$754$	−668078.	+	385715.i	−1.17513	+	0.678459i
$755$	−264410.	−	362914.i	−0.463857	−	0.636663i
$756$	22844.8	−	4417.32i	0.0399709	−	0.00772885i
$757$			1.03602e6i			1.80791i	0.427624	+	0.903957i	$0.359351\pi$
$757$			1.03602e6i			1.80791i	−0.427624	+	0.903957i	$0.640649\pi$
$758$	20829.1	−	12025.7i	0.0362520	−	0.0209301i
$759$	40232.0	+	23228.0i	0.0698374	+	0.0403206i
$760$	−49247.1	+	5242.28i	−0.0852616	+	0.00907598i
$761$	−950676.	+	548873.i	−1.64158	+	0.947769i	−0.661314	+	0.750109i	$0.730001\pi$
$761$	−950676.	+	548873.i	−1.64158	+	0.947769i	−0.980271	+	0.197660i	$0.936666\pi$
$762$	138531.			0.238582
$763$	943492.	−	182436.i	1.62065	−	0.313372i
$764$	431565.			0.739366
$765$	−95058.1	+	214270.i	−0.162430	+	0.366133i
$766$	563823.	+	325523.i	0.960916	+	0.554785i
$767$	−992217.	−	572857.i	−1.68662	−	0.973768i
$768$	−25683.2	−	44484.5i	−0.0435438	−	0.0754200i
$769$			610743.i			1.03278i	0.856355	+	0.516388i	$0.172724\pi$
$769$			610743.i			1.03278i	−0.856355	+	0.516388i	$0.827276\pi$
$770$	−7304.83	−	23863.3i	−0.0123205	−	0.0402485i
$771$	−1.38055e6			−2.32244
$772$	−16732.2	+	9660.32i	−0.0280749	+	0.0162090i
$773$	−55423.0	+	95995.4i	−0.0927536	+	0.160654i	−0.908669	−	0.417518i	$-0.862900\pi$
$773$	−55423.0	+	95995.4i	−0.0927536	+	0.160654i	0.815915	+	0.578172i	$0.196234\pi$
$774$	44322.0	−	76767.9i	0.0739839	−	0.128144i
$775$	1895.85	+	8804.09i	0.00315646	+	0.0146582i
$776$		−	288592.i		−	0.479248i
$777$	802323.	−	696067.i	1.32894	−	1.15295i
$778$		−	226297.i		−	0.373870i
$779$	111205.	+	192613.i	0.183253	+	0.317404i
$780$	730134.	−	77721.7i	1.20009	−	0.127748i
$781$	6641.84	−	11504.0i	0.0108890	−	0.0188602i
$782$	89420.6	+	154881.i	0.146226	+	0.253270i
$783$	−55299.8			−0.0901986
$784$	142587.	−	57283.8i	0.231979	−	0.0931965i
$785$	216458.	+	297097.i	0.351264	+	0.482125i
$786$	582048.	+	1.00814e6i	0.942136	+	1.63183i
$787$	13760.1	−	23833.1i	0.0222163	−	0.0384797i	−0.854704	−	0.519116i	$-0.826261\pi$
$787$	13760.1	−	23833.1i	0.0222163	−	0.0384797i	0.876920	+	0.480637i	$0.159594\pi$
$788$	−180489.	−	104206.i	−0.290669	−	0.167818i
$789$	−6183.74	+	3570.18i	−0.00993338	+	0.00573504i
$790$	−216060.	+	157416.i	−0.346195	+	0.252229i
$791$	−587019.	+	509277.i	−0.938207	+	0.813956i
$792$		−	12430.0i		−	0.0198162i
$793$	1.20936e6	−	698226.i	1.92314	−	1.11032i
$794$	−116868.	−	67473.7i	−0.185376	−	0.107027i
$795$	−65983.7	−	619864.i	−0.104400	−	0.980758i
$796$	9151.14	−	5283.41i	0.0144427	−	0.00833851i
$797$	793651.			1.24943			0.624717	−	0.780852i	$-0.285214\pi$
$797$	793651.			1.24943			0.624717	+	0.780852i	$0.285214\pi$
$798$	49680.9	−	143825.i	0.0780160	−	0.225855i
$799$	−373599.			−0.585211
$800$	−23816.7	−	110602.i	−0.0372136	−	0.172815i
$801$	−9886.86	−	5708.18i	−0.0154097	−	0.00889678i
$802$	132541.	+	76522.8i	0.206064	+	0.118971i
$803$	38169.6	+	66111.7i	0.0591952	+	0.102529i
$804$			767482.i			1.18729i
$805$	−429517.	+	460922.i	−0.662809	+	0.711272i
$806$	11931.4			0.0183663
$807$	−621235.	+	358670.i	−0.953912	+	0.550742i
$808$	130127.	−	225387.i	0.199318	−	0.345228i
$809$	−67222.0	+	116432.i	−0.102710	+	0.177900i	−0.912800	−	0.408406i	$-0.866085\pi$
$809$	−67222.0	+	116432.i	−0.102710	+	0.177900i	0.810090	+	0.586305i	$0.199418\pi$
$810$	447407.	+	198486.i	0.681918	+	0.302524i
$811$		−	1.12692e6i		−	1.71337i	−0.515838	−	0.856686i	$-0.672519\pi$
$811$		−	1.12692e6i		−	1.71337i	0.515838	−	0.856686i	$-0.327481\pi$
$812$	−358564.	+	69332.6i	−0.543819	+	0.105154i
$813$			1.05295e6i			1.59304i
$814$	17607.6	+	30497.2i	0.0265736	+	0.0460268i
$815$	37269.6	+	350118.i	0.0561099	+	0.527107i
$816$	49336.5	−	85453.3i	0.0740948	−	0.128336i
$817$	17988.3	+	31156.7i	0.0269492	+	0.0466775i
$818$	515571.			0.770517
$819$	−357199.	+	1.03408e6i	−0.532528	+	1.54166i
$820$	−410650.	+	299189.i	−0.610722	+	0.444957i
$821$	−178657.	−	309443.i	−0.265054	−	0.459087i	0.702524	−	0.711660i	$-0.252056\pi$
$821$	−178657.	−	309443.i	−0.265054	−	0.459087i	−0.967578	+	0.252574i	$0.918723\pi$
$822$	256870.	−	444912.i	0.380163	−	0.658462i
$823$	496211.	+	286488.i	0.732600	+	0.422967i	0.819372	−	0.573262i	$-0.194322\pi$
$823$	496211.	+	286488.i	0.732600	+	0.422967i	−0.0867728	+	0.996228i	$0.527655\pi$
$824$	−148402.	+	85680.0i	−0.218568	+	0.126190i
$825$	17302.6	−	53737.6i	0.0254216	−	0.0789533i
$826$	−355442.	−	409701.i	−0.520965	−	0.600491i
$827$		−	985411.i		−	1.44081i	−0.693554	−	0.720405i	$-0.743956\pi$
$827$		−	985411.i		−	1.44081i	0.693554	−	0.720405i	$-0.256044\pi$
$828$	−271756.	+	156898.i	−0.396386	+	0.228854i
$829$	98948.8	+	57128.1i	0.143980	+	0.0831267i	0.570259	−	0.821465i	$-0.306843\pi$
$829$	98948.8	+	57128.1i	0.143980	+	0.0831267i	−0.426280	+	0.904591i	$0.640176\pi$
$830$	27407.9	+	257476.i	0.0397851	+	0.373749i
$831$	−633842.	+	365949.i	−0.917865	+	0.529930i
$832$	−149889.			−0.216533
$833$	232250.	+	182189.i	0.334708	+	0.262562i
$834$	−709852.			−1.02055
$835$	436010.	−	982810.i	0.625351	−	1.40960i
$836$	4368.90	+	2522.39i	0.00625115	+	0.00360910i
$837$	740.713	+	427.651i	0.00105730	+	0.000610433i
$838$	−71875.5	−	124492.i	−0.102351	−	0.177277i
$839$			808131.i			1.14804i	0.818841	+	0.574021i	$0.194617\pi$
$839$			808131.i			1.14804i	−0.818841	+	0.574021i	$0.805383\pi$
$840$	338726.	+	78076.9i	0.480054	+	0.110653i
$841$	160684.			0.227185
$842$	−26286.5	+	15176.5i	−0.0370773	+	0.0214066i
$843$	−183620.	+	318039.i	−0.258383	+	0.447533i
$844$	−21482.8	+	37209.4i	−0.0301583	+	0.0522357i
$845$	579318.	−	1.30584e6i	0.811341	−	1.82884i
$846$		−	655522.i		−	0.915896i
$847$	233401.	−	675691.i	0.325339	−	0.941849i
$848$			127252.i			0.176959i
$849$	806083.	+	1.39618e6i	1.11832	+	1.93698i
$850$	161122.	−	145853.i	0.223007	−	0.201872i
$851$	444505.	−	769906.i	0.613787	−	1.06311i
$852$	92511.8	+	160235.i	0.127444	+	0.220739i
$853$	−1.24179e6			−1.70668			−0.853338	−	0.521358i	$-0.825426\pi$
$853$	−1.24179e6			−1.70668			−0.853338	+	0.521358i	$0.825426\pi$
$854$	649077.	−	125507.i	0.889980	−	0.172088i
$855$	134917.	−	98297.0i	0.184558	−	0.134465i
$856$	71502.0	+	123845.i	0.0975822	+	0.169017i
$857$	21176.8	−	36679.3i	0.0288336	−	0.0499413i	−0.851249	−	0.524763i	$-0.824154\pi$
$857$	21176.8	−	36679.3i	0.0288336	−	0.0499413i	0.880082	+	0.474821i	$0.157487\pi$
$858$	−64773.1	−	37396.7i	−0.0879873	−	0.0507995i
$859$	756574.	−	436808.i	1.02533	−	0.591976i	0.109689	−	0.993966i	$-0.465015\pi$
$859$	756574.	−	436808.i	1.02533	−	0.591976i	0.915644	+	0.401990i	$0.131681\pi$
$860$	−66425.7	+	48396.1i	−0.0898130	+	0.0654356i
$861$	−296359.	−	1.53267e6i	−0.399772	−	2.06748i
$862$		−	237485.i		−	0.319611i
$863$	−1.02453e6	+	591510.i	−1.37563	+	0.794219i	−0.991630	−	0.129114i	$-0.958787\pi$
$863$	−1.02453e6	+	591510.i	−1.37563	+	0.794219i	−0.383999	+	0.923334i	$0.625453\pi$
$864$	−9305.24	−	5372.39i	−0.0124652	−	0.00719680i
$865$	566737.	−	60328.3i	0.757441	−	0.0806286i
$866$	−17513.2	+	10111.3i	−0.0233523	+	0.0134825i
$867$	−857857.			−1.14124
$868$	5338.95	+	1844.21i	0.00708625	+	0.00244778i
$869$	27230.3			0.0360589
$870$	−755164.	−	335018.i	−0.997707	−	0.442619i
$871$	1.93951e6	+	1.11977e6i	2.55655	+	1.47603i
$872$	−384307.	−	221880.i	−0.505412	−	0.291800i
$873$	486356.	+	842393.i	0.638154	+	1.10532i
$874$		−	127356.i		−	0.166724i
$875$	657452.	+	392351.i	0.858712	+	0.512458i
$876$	−1.06330e6			−1.38563
$877$	−15337.8	+	8855.27i	−0.0199418	+	0.0115134i	−0.509938	−	0.860211i	$-0.670332\pi$
$877$	−15337.8	+	8855.27i	−0.0199418	+	0.0115134i	0.489996	+	0.871725i	$0.336998\pi$
$878$	358575.	−	621070.i	0.465148	−	0.805660i
$879$	798826.	−	1.38361e6i	1.03389	−	1.79075i
$880$	−4673.41	+	10534.3i	−0.00603488	+	0.0136032i
$881$			761550.i			0.981175i	0.871392	+	0.490588i	$0.163218\pi$
$881$			761550.i			0.981175i	−0.871392	+	0.490588i	$0.836782\pi$
$882$	−319671.	+	407509.i	−0.410929	+	0.523842i
$883$		−	1.12110e6i		−	1.43789i	−0.695069	−	0.718943i	$-0.744626\pi$
$883$		−	1.12110e6i		−	1.43789i	0.695069	−	0.718943i	$-0.255374\pi$
$884$	−143966.	−	249357.i	−0.184228	−	0.319092i
$885$	−129876.	−	1.22008e6i	−0.165822	−	1.55776i
$886$	100984.	−	174909.i	0.128642	−	0.222815i
$887$	247341.	+	428407.i	0.314376	+	0.544514i	0.979305	−	0.202392i	$-0.0648716\pi$
$887$	247341.	+	428407.i	0.314376	+	0.544514i	−0.664929	+	0.746907i	$0.731538\pi$
$888$	−490499.			−0.622031
$889$	144554.	−	125410.i	0.182906	−	0.158682i
$890$	6232.89	+	8554.89i	0.00786881	+	0.0108003i
$891$	−24928.7	−	43177.8i	−0.0314011	−	0.0543883i
$892$	−255593.	+	442700.i	−0.321232	+	0.556391i
$893$	230404.	+	133024.i	0.288926	+	0.166811i
$894$	−554772.	+	320298.i	−0.694128	+	0.400755i
$895$	−181527.	−	249153.i	−0.226618	−	0.311042i
$896$	−67070.9	−	23168.0i	−0.0835445	−	0.0288584i
$897$			1.88817e6i			2.34670i
$898$	−771715.	+	445550.i	−0.956983	+	0.552514i
$899$	−11626.0	−	6712.25i	−0.0143850	−	0.00830517i
$900$	255915.	+	282707.i	0.315944	+	0.349021i
$901$	−211697.	+	122223.i	−0.260775	+	0.150558i
$902$	51754.5			0.0636115
$903$	−47938.4	−	247920.i	−0.0587906	−	0.304044i
$904$	358873.			0.439141
$905$	−812527.	−	360467.i	−0.992066	−	0.440117i
$906$	−551722.	−	318537.i	−0.672146	−	0.388064i
$907$	108222.	+	62482.2i	0.131554	+	0.0759525i	0.564332	−	0.825548i	$-0.309134\pi$
$907$	108222.	+	62482.2i	0.131554	+	0.0759525i	−0.432779	+	0.901500i	$0.642467\pi$
$908$	−98767.2	−	171070.i	−0.119796	−	0.207492i
$909$			877201.i			1.06163i
$910$	691517.	−	742079.i	0.835064	−	0.896122i
$911$	1.43305e6			1.72673			0.863366	−	0.504578i	$-0.168352\pi$
$911$	1.43305e6			1.72673			0.863366	+	0.504578i	$0.168352\pi$
$912$	−60852.9	+	35133.4i	−0.0731630	+	0.0422407i
$913$	13187.7	−	22841.7i	0.0158207	−	0.0274023i
$914$	−98156.7	+	170012.i	−0.117497	+	0.203511i
$915$	1.36701e6	+	606455.i	1.63278	+	0.724363i
$916$		−	268807.i		−	0.320368i
$917$	1.52000e6	+	525048.i	1.80761	+	0.624396i
$918$		−	20640.3i		−	0.0244924i
$919$	−721700.	−	1.25002e6i	−0.854527	−	1.48008i	−0.877084	−	0.480338i	$-0.840514\pi$
$919$	−721700.	−	1.25002e6i	−0.854527	−	1.48008i	0.0225570	−	0.999746i	$-0.492819\pi$
$920$	289302.	−	30795.8i	0.341803	−	0.0363844i
$921$	400006.	−	692832.i	0.471572	−	0.816786i
$922$	235963.	+	408700.i	0.277576	+	0.480776i
$923$	539907.			0.633747
$924$	−23203.7	−	26745.7i	−0.0271777	−	0.0313264i
$925$	−1.02836e6	−	331113.i	−1.20188	−	0.386984i
$926$	235991.	+	408749.i	0.275216	+	0.476688i
$927$	288789.	−	500197.i	0.336063	−	0.582078i
$928$	146052.	+	84323.0i	0.169594	+	0.0979152i
$929$	457017.	−	263859.i	0.529542	−	0.305731i	−0.211288	−	0.977424i	$-0.567766\pi$
$929$	457017.	−	263859.i	0.529542	−	0.305731i	0.740830	+	0.671693i	$0.234432\pi$
$930$	7524.24	+	10327.3i	0.00869955	+	0.0119405i
$931$	−78361.7	−	195053.i	−0.0904075	−	0.225037i
$932$			206445.i			0.237669i
$933$	220712.	−	127428.i	0.253549	−	0.146387i
$934$	447146.	+	258160.i	0.512573	+	0.295934i
$935$	−22013.7	+	2343.33i	−0.0251808	+	0.00268046i
$936$	437524.	−	252605.i	0.499402	−	0.288330i
$937$	−37174.4			−0.0423413			−0.0211707	−	0.999776i	$-0.506739\pi$
$937$	−37174.4			−0.0423413			−0.0211707	+	0.999776i	$0.506739\pi$
$938$	694789.	+	800850.i	0.789673	+	0.910218i
$939$	−1.21692e6			−1.38016
$940$	−246462.	+	555550.i	−0.278930	+	0.628735i
$941$	672093.	+	388033.i	0.759014	+	0.438217i	0.828942	−	0.559335i	$-0.188943\pi$
$941$	672093.	+	388033.i	0.759014	+	0.438217i	−0.0699274	+	0.997552i	$0.522277\pi$
$942$	451664.	+	260768.i	0.508995	+	0.293868i
$943$	−653276.	−	1.13151e6i	−0.734638	−	1.27243i
$944$			250470.i			0.281068i
$945$	69527.8	−	21283.2i	0.0778565	−	0.0238327i
$946$	8371.69			0.00935472
$947$	−214846.	+	124041.i	−0.239567	+	0.138314i	−0.614978	−	0.788545i	$-0.710835\pi$
$947$	−214846.	+	124041.i	−0.239567	+	0.138314i	0.375411	+	0.926858i	$0.377502\pi$
$948$	−189640.	+	328467.i	−0.211015	+	0.365489i
$949$	−1.55138e6	+	2.68707e6i	−1.72261	+	2.98364i
$950$	−151298.	+	32580.2i	−0.167644	+	0.0361000i
$951$			267702.i			0.295999i
$952$	−25878.0	−	133832.i	−0.0285533	−	0.147668i
$953$		−	899097.i		−	0.989968i	−0.868902	−	0.494984i	$-0.835174\pi$
$953$		−	899097.i		−	0.989968i	0.868902	−	0.494984i	$-0.164826\pi$
$954$	−214454.	−	371446.i	−0.235634	−	0.408130i
$955$	1.34106e6	−	142754.i	1.47042	−	0.156525i
$956$	−125170.	+	216802.i	−0.136958	+	0.237217i
$957$	42076.5	+	72878.6i	0.0459426	+	0.0795749i
$958$	−203839.			−0.222104
$959$	−134734.	−	696796.i	−0.146501	−	0.757650i
$960$	−94523.7	−	129738.i	−0.102565	−	0.140774i
$961$	−461657.	−	799613.i	−0.499888	−	0.865831i
$962$	−715649.	+	1.23954e6i	−0.773303	+	1.33940i
$963$	−417426.	−	241001.i	−0.450119	−	0.259876i
$964$	252848.	−	145982.i	0.272086	−	0.157089i
$965$	−48798.8	+	35553.6i	−0.0524028	+	0.0381794i
$966$	−291850.	+	844900.i	−0.312756	+	0.905422i
$967$			603847.i			0.645764i	0.946439	+	0.322882i	$0.104652\pi$
$967$			603847.i			0.645764i	−0.946439	+	0.322882i	$0.895348\pi$
$968$	−285887.	+	165057.i	−0.305101	+	0.176150i
$969$	−116896.	−	67490.1i	−0.124495	−	0.0718775i
$970$	−95461.2	−	896782.i	−0.101457	−	0.953111i
$971$	−1.02176e6	+	589916.i	−1.08371	+	0.625679i	−0.931894	−	0.362730i	$-0.881845\pi$
$971$	−1.02176e6	+	589916.i	−1.08371	+	0.625679i	−0.151814	+	0.988409i	$0.548511\pi$
$972$	655984.			0.694321
$973$	−740714.	+	642617.i	−0.782393	+	0.678776i
$974$	241862.			0.254947
$975$	2.24314e6	−	483032.i	2.35965	−	0.508120i
$976$	−264385.	−	152643.i	−0.277547	−	0.160242i
$977$	−1.15311e6	−	665749.i	−1.20804	−	0.697463i	−0.245710	−	0.969343i	$-0.579021\pi$
$977$	−1.15311e6	−	665749.i	−1.20804	−	0.697463i	−0.962331	+	0.271880i	$0.912355\pi$
$978$	249778.	+	432629.i	0.261142	+	0.452311i
$979$		−	1078.18i		−	0.00112493i
$980$	424134.	−	225172.i	0.441622	−	0.234456i
$981$	1.49571e6			1.55421
$982$	883920.	−	510331.i	0.916621	−	0.529211i
$983$	−227444.	+	393944.i	−0.235378	+	0.407687i	−0.959383	−	0.282108i	$-0.908966\pi$
$983$	−227444.	+	393944.i	−0.235378	+	0.407687i	0.724004	+	0.689796i	$0.242300\pi$
$984$	−360435.	+	624292.i	−0.372252	+	0.644760i
$985$	−595330.	−	264110.i	−0.613600	−	0.272216i
$986$			323963.i			0.333228i
$987$	−1.22369e6	−	1.41049e6i	−1.25614	−	1.44789i
$988$			205042.i			0.210053i
$989$	−105672.	−	183030.i	−0.108036	−	0.187124i
$990$	−4111.63	−	38625.5i	−0.00419511	−	0.0394097i
$991$	632867.	−	1.09616e6i	0.644415	−	1.11616i	−0.340022	−	0.940418i	$-0.610434\pi$
$991$	632867.	−	1.09616e6i	0.644415	−	1.11616i	0.984436	−	0.175741i	$-0.0562323\pi$
$992$	−1304.19	−	2258.93i	−0.00132531	−	0.00229551i
$993$	727616.			0.737911
$994$	241592.	+	83452.2i	0.244518	+	0.0844627i
$995$	26689.0	−	19445.0i	0.0269579	−	0.0196409i
$996$	183686.	+	318154.i	0.185164	+	0.320714i
$997$	721126.	−	1.24903e6i	0.725472	−	1.25655i	−0.233307	−	0.972403i	$-0.574955\pi$
$997$	721126.	−	1.24903e6i	0.725472	−	1.25655i	0.958779	−	0.284151i	$-0.0917118\pi$
$998$	−946719.	−	546589.i	−0.950517	−	0.548781i
$999$	−88856.1	+	51301.1i	−0.0890341	+	0.0514038i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	70.5.h.a.59.2	yes	32
5.2	odd	4		350.5.k.e.101.1		32
5.3	odd	4		350.5.k.e.101.16		32
5.4	even	2	inner	70.5.h.a.59.15	yes	32
7.3	odd	6		490.5.d.a.489.17		32
7.4	even	3		490.5.d.a.489.19		32
7.5	odd	6	inner	70.5.h.a.19.15	yes	32
35.4	even	6		490.5.d.a.489.18		32
35.12	even	12		350.5.k.e.201.1		32
35.19	odd	6	inner	70.5.h.a.19.2	✓	32
35.24	odd	6		490.5.d.a.489.20		32
35.33	even	12		350.5.k.e.201.16		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.5.h.a.19.2	✓	32	35.19	odd	6	inner
70.5.h.a.19.15	yes	32	7.5	odd	6	inner
70.5.h.a.59.2	yes	32	1.1	even	1	trivial
70.5.h.a.59.15	yes	32	5.4	even	2	inner
350.5.k.e.101.1		32	5.2	odd	4
350.5.k.e.101.16		32	5.3	odd	4
350.5.k.e.201.1		32	35.12	even	12
350.5.k.e.201.16		32	35.33	even	12
490.5.d.a.489.17		32	7.3	odd	6
490.5.d.a.489.18		32	35.4	even	6
490.5.d.a.489.19		32	7.4	even	3
490.5.d.a.489.20		32	35.24	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 70 = 2 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	70.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.44949 + 1.41421i) q^{2} +(-6.27030 + 10.8605i) q^{3} +(4.00000 - 6.92820i) q^{4} +(10.1380 - 22.8521i) q^{5} -35.4702i q^{6} +(-32.1106 - 37.0123i) q^{7} +22.6274i q^{8} +(-38.1334 - 66.0490i) q^{9} +O(q^{10})\)	\(q+(-2.44949 + 1.41421i) q^{2} +(-6.27030 + 10.8605i) q^{3} +(4.00000 - 6.92820i) q^{4} +(10.1380 - 22.8521i) q^{5} -35.4702i q^{6} +(-32.1106 - 37.0123i) q^{7} +22.6274i q^{8} +(-38.1334 - 66.0490i) q^{9} +(7.48477 + 70.3134i) q^{10} +(3.60139 - 6.23778i) q^{11} +(50.1624 + 86.8839i) q^{12} +292.752 q^{13} +(130.998 + 45.2500i) q^{14} +(184.617 + 253.394i) q^{15} +(-32.0000 - 55.4256i) q^{16} +(61.4709 - 106.471i) q^{17} +(186.815 + 107.858i) q^{18} +(-75.8198 + 43.7746i) q^{19} +(-117.772 - 161.647i) q^{20} +(603.315 - 116.658i) q^{21} +20.3725i q^{22} +(445.403 - 257.154i) q^{23} +(-245.745 - 141.881i) q^{24} +(-419.440 - 463.352i) q^{25} +(-717.094 + 414.014i) q^{26} -59.3570 q^{27} +(-384.871 + 74.4194i) q^{28} +931.646 q^{29} +(-810.570 - 359.598i) q^{30} +(-12.4789 - 7.20472i) q^{31} +(156.767 + 90.5097i) q^{32} +(45.1636 + 78.2256i) q^{33} +347.732i q^{34} +(-1171.35 + 358.563i) q^{35} -610.135 q^{36} +(1496.98 - 864.280i) q^{37} +(123.813 - 214.451i) q^{38} +(-1835.65 + 3179.43i) q^{39} +(517.085 + 229.398i) q^{40} -2540.41i q^{41} +(-1312.83 + 1138.97i) q^{42} -410.931i q^{43} +(-28.8111 - 49.9023i) q^{44} +(-1895.96 + 201.822i) q^{45} +(-727.340 + 1259.79i) q^{46} +(-1519.41 - 2631.70i) q^{47} +802.599 q^{48} +(-338.821 + 2376.97i) q^{49} +(1682.69 + 541.798i) q^{50} +(770.882 + 1335.21i) q^{51} +(1171.01 - 2028.25i) q^{52} +(-1721.93 - 994.156i) q^{53} +(145.394 - 83.9435i) q^{54} +(-106.036 - 145.538i) q^{55} +(837.493 - 726.580i) q^{56} -1097.92i q^{57} +(-2282.06 + 1317.55i) q^{58} +(-3389.27 - 1956.80i) q^{59} +(2494.03 - 265.486i) q^{60} +(4131.01 - 2385.04i) q^{61} +40.7560 q^{62} +(-1220.14 + 3532.28i) q^{63} -512.000 q^{64} +(2967.94 - 6690.02i) q^{65} +(-221.255 - 127.742i) q^{66} +(6625.07 + 3824.99i) q^{67} +(-491.767 - 851.766i) q^{68} +6449.73i q^{69} +(2362.12 - 2534.83i) q^{70} +1844.25 q^{71} +(1494.52 - 862.860i) q^{72} +(-5299.30 + 9178.65i) q^{73} +(-2444.55 + 4234.09i) q^{74} +(7662.24 - 1649.97i) q^{75} +700.394i q^{76} +(-346.517 + 67.0033i) q^{77} -10384.0i q^{78} +(1890.26 + 3274.03i) q^{79} +(-1591.01 + 169.361i) q^{80} +(3460.99 - 5994.61i) q^{81} +(3592.68 + 6222.71i) q^{82} +3661.83 q^{83} +(1605.03 - 4646.52i) q^{84} +(-1809.89 - 2484.15i) q^{85} +(581.144 + 1006.57i) q^{86} +(-5841.71 + 10118.1i) q^{87} +(141.145 + 81.4901i) q^{88} +(129.635 - 74.8449i) q^{89} +(4358.71 - 3175.65i) q^{90} +(-9400.45 - 10835.4i) q^{91} -4114.46i q^{92} +(156.493 - 90.3515i) q^{93} +(7443.58 + 4297.55i) q^{94} +(231.678 + 2176.43i) q^{95} +(-1965.96 + 1135.05i) q^{96} -12754.1 q^{97} +(-2531.61 - 6301.54i) q^{98} -549.333 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 128 q^{4} + 54 q^{5} - 516 q^{9}+O(q^{10}) \) 32 * q + 128 * q^4 + 54 * q^5 - 516 * q^9	\( 32 q + 128 q^{4} + 54 q^{5} - 516 q^{9} - 96 q^{10} - 144 q^{11} + 96 q^{14} - 76 q^{15} - 1024 q^{16} - 816 q^{19} + 1084 q^{21} + 768 q^{24} + 294 q^{25} - 576 q^{26} + 912 q^{29} + 608 q^{30} + 6468 q^{31} + 1398 q^{35} - 8256 q^{36} - 2424 q^{39} - 768 q^{40} + 1152 q^{44} - 8256 q^{45} + 1664 q^{46} - 7712 q^{49} + 15744 q^{50} + 2708 q^{51} + 7776 q^{54} - 768 q^{56} + 3924 q^{59} - 304 q^{60} + 41556 q^{61} - 16384 q^{64} + 936 q^{65} - 15360 q^{66} + 15104 q^{70} - 53808 q^{71} - 6336 q^{74} - 29058 q^{75} - 24076 q^{79} - 3456 q^{80} + 17680 q^{81} - 19232 q^{84} + 8324 q^{85} + 6624 q^{86} - 41436 q^{89} + 12928 q^{91} + 62880 q^{94} + 42990 q^{95} + 6144 q^{96} + 101048 q^{99}+O(q^{100}) \) 32 * q + 128 * q^4 + 54 * q^5 - 516 * q^9 - 96 * q^10 - 144 * q^11 + 96 * q^14 - 76 * q^15 - 1024 * q^16 - 816 * q^19 + 1084 * q^21 + 768 * q^24 + 294 * q^25 - 576 * q^26 + 912 * q^29 + 608 * q^30 + 6468 * q^31 + 1398 * q^35 - 8256 * q^36 - 2424 * q^39 - 768 * q^40 + 1152 * q^44 - 8256 * q^45 + 1664 * q^46 - 7712 * q^49 + 15744 * q^50 + 2708 * q^51 + 7776 * q^54 - 768 * q^56 + 3924 * q^59 - 304 * q^60 + 41556 * q^61 - 16384 * q^64 + 936 * q^65 - 15360 * q^66 + 15104 * q^70 - 53808 * q^71 - 6336 * q^74 - 29058 * q^75 - 24076 * q^79 - 3456 * q^80 + 17680 * q^81 - 19232 * q^84 + 8324 * q^85 + 6624 * q^86 - 41436 * q^89 + 12928 * q^91 + 62880 * q^94 + 42990 * q^95 + 6144 * q^96 + 101048 * q^99

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