LMFDB - Embedded newform 175.4.x.a.3.53

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,4,Mod(3,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([21, 10]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("175.3");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	175.x (of order $60$, degree $16$, 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:	$10.3253342510$
Analytic rank:	$0$
Dimension:	$928$
Relative dimension:	$58$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			3.53
Character	$\chi$	$=$	175.3
Dual form			175.4.x.a.117.53

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.67058 - 4.11233i) q^{2} +(-3.22886 + 8.41147i) q^{3} +(-6.52539 - 14.6563i) q^{4} +(-4.17384 + 10.3720i) q^{5} +(25.9678 + 35.7416i) q^{6} +(5.00240 - 17.8319i) q^{7} +(-38.9538 - 6.16967i) q^{8} +(-40.2623 - 36.2524i) q^{9} +(31.5067 + 44.8636i) q^{10} +(-31.6717 - 35.1750i) q^{11} +(144.350 - 7.56508i) q^{12} +(-77.7071 - 39.5937i) q^{13} +(-59.9713 - 68.1930i) q^{14} +(-73.7673 - 68.5980i) q^{15} +(-43.5206 + 48.3345i) q^{16} +(2.55681 - 3.15740i) q^{17} +(-256.606 + 68.7573i) q^{18} +(31.7797 + 14.1492i) q^{19} +(179.251 - 6.50867i) q^{20} +(133.840 + 99.6542i) q^{21} +(-229.233 + 36.3070i) q^{22} +(120.455 + 78.2245i) q^{23} +(177.672 - 307.738i) q^{24} +(-90.1581 - 86.5824i) q^{25} +(-370.346 + 213.819i) q^{26} +(218.184 - 111.171i) q^{27} +(-293.991 + 43.0435i) q^{28} +(-107.290 + 147.672i) q^{29} +(-479.099 + 120.159i) q^{30} +(-143.118 + 15.0423i) q^{31} +(0.881111 + 3.28835i) q^{32} +(398.137 - 152.830i) q^{33} +(-6.15611 - 18.9466i) q^{34} +(164.074 + 126.312i) q^{35} +(-268.597 + 826.656i) q^{36} +(-4.53293 - 86.4934i) q^{37} +(143.057 - 92.9020i) q^{38} +(583.947 - 525.788i) q^{39} +(226.579 - 378.279i) q^{40} +(30.3689 - 9.86746i) q^{41} +(767.242 - 284.261i) q^{42} +(-68.8788 - 68.8788i) q^{43} +(-308.864 + 693.720i) q^{44} +(544.059 - 266.291i) q^{45} +(643.370 - 286.447i) q^{46} +(-165.555 + 134.064i) q^{47} +(-266.042 - 522.137i) q^{48} +(-292.952 - 178.404i) q^{49} +(-596.830 + 139.535i) q^{50} +(18.3028 + 31.7014i) q^{51} +(-73.2273 + 1397.26i) q^{52} +(111.265 + 42.7105i) q^{53} +(125.509 - 1194.14i) q^{54} +(497.029 - 181.685i) q^{55} +(-304.879 + 663.756i) q^{56} +(-221.628 + 221.628i) q^{57} +(320.751 + 835.584i) q^{58} +(-590.246 - 125.461i) q^{59} +(-524.029 + 1528.78i) q^{60} +(88.3600 + 415.701i) q^{61} +(-320.350 + 628.722i) q^{62} +(-847.856 + 536.605i) q^{63} +(-478.982 - 155.631i) q^{64} +(735.005 - 640.723i) q^{65} +(434.767 - 2045.42i) q^{66} +(-251.164 - 203.389i) q^{67} +(-62.9599 - 16.8701i) q^{68} +(-1046.92 + 760.629i) q^{69} +(957.611 - 337.398i) q^{70} +(471.023 + 342.218i) q^{71} +(1344.71 + 1660.57i) q^{72} +(397.047 + 20.8084i) q^{73} +(-367.795 - 212.347i) q^{74} +(1019.39 - 478.800i) q^{75} -558.101i q^{76} +(-785.671 + 388.807i) q^{77} +(-602.739 - 3805.54i) q^{78} +(1007.08 + 105.849i) q^{79} +(-319.679 - 653.137i) q^{80} +(77.7145 + 739.404i) q^{81} +(40.5244 - 151.239i) q^{82} +(73.2488 - 462.475i) q^{83} +(587.198 - 2611.88i) q^{84} +(22.0770 + 39.6978i) q^{85} +(-467.199 + 99.3062i) q^{86} +(-895.716 - 1379.28i) q^{87} +(1016.72 + 1565.60i) q^{88} +(480.162 - 102.061i) q^{89} +(357.878 - 2948.50i) q^{90} +(-1094.75 + 1187.60i) q^{91} +(360.462 - 2275.87i) q^{92} +(335.581 - 1252.40i) q^{93} +(109.187 + 1038.84i) q^{94} +(-279.400 + 270.563i) q^{95} +(-30.5049 - 3.20619i) q^{96} +(-83.1014 - 524.682i) q^{97} +(-1516.01 + 728.273i) q^{98} +2564.40i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 928 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 24 q^{7} + 84 q^{8} - 10 q^{9} - 96 q^{10} - 6 q^{11} - 72 q^{12} - 20 q^{14} - 368 q^{15} - 1670 q^{16} + 120 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} - 880 q^{22}+ \cdots - 19478 q^{98}+O(q^{100}) $ 928 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 24 * q^7 + 84 * q^8 - 10 * q^9 - 96 * q^10 - 6 * q^11 - 72 * q^12 - 20 * q^14 - 368 * q^15 - 1670 * q^16 + 120 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 - 880 * q^22 + 296 * q^23 + 32 * q^25 - 48 * q^26 + 226 * q^28 - 200 * q^29 - 38 * q^30 - 18 * q^31 - 964 * q^32 - 1092 * q^33 + 288 * q^35 + 7400 * q^36 - 392 * q^37 + 5424 * q^38 + 2430 * q^39 + 2172 * q^40 - 2098 * q^42 + 1560 * q^43 - 10 * q^44 - 4224 * q^45 - 6 * q^46 + 96 * q^47 + 6232 * q^50 - 16 * q^51 - 8928 * q^52 - 2384 * q^53 - 30 * q^54 + 244 * q^56 + 1556 * q^57 + 640 * q^58 + 4890 * q^59 + 3676 * q^60 - 18 * q^61 + 224 * q^63 - 9700 * q^64 - 1116 * q^65 - 2610 * q^66 - 2404 * q^67 - 13614 * q^68 - 1700 * q^70 - 24 * q^71 - 518 * q^72 - 4200 * q^73 - 16104 * q^75 - 722 * q^77 - 356 * q^78 - 10 * q^79 + 6414 * q^80 - 6810 * q^81 + 1692 * q^82 + 20620 * q^84 + 2712 * q^85 - 6 * q^86 + 9102 * q^87 + 1650 * q^88 + 20370 * q^89 - 12 * q^91 + 1612 * q^92 - 4604 * q^93 - 30 * q^94 + 1652 * q^95 - 2610 * q^96 - 19478 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{20}\right)$

Coefficient data

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

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

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

$2$	2.67058	−	4.11233i	0.944193	−	1.45393i	0.0538967	−	0.998547i	$-0.482836\pi$
$2$	2.67058	−	4.11233i	0.944193	−	1.45393i	0.890296	−	0.455383i	$-0.150498\pi$
$3$	−3.22886	+	8.41147i	−0.621394	+	1.61879i	0.154549	+	0.987985i	$0.450608\pi$
$3$	−3.22886	+	8.41147i	−0.621394	+	1.61879i	−0.775943	+	0.630803i	$0.782726\pi$
$4$	−6.52539	−	14.6563i	−0.815674	−	1.83203i
$5$	−4.17384	+	10.3720i	−0.373319	+	0.927703i
$5$	−4.17384	+	10.3720i	−0.373319	+	0.927703i
$6$	25.9678	+	35.7416i	1.76689	+	2.43191i
$7$	5.00240	−	17.8319i	0.270104	−	0.962831i
$7$	5.00240	−	17.8319i	0.270104	−	0.962831i
$8$	−38.9538	−	6.16967i	−1.72153	−	0.272664i
$9$	−40.2623	−	36.2524i	−1.49120	−	1.34268i
$10$	31.5067	+	44.8636i	0.996329	+	1.41871i
$11$	−31.6717	−	35.1750i	−0.868126	−	0.964151i	0.131505	−	0.991315i	$-0.458019\pi$
$11$	−31.6717	−	35.1750i	−0.868126	−	0.964151i	−0.999631	+	0.0271642i	$0.991352\pi$
$12$	144.350	−	7.56508i	3.47253	−	0.181987i
$13$	−77.7071	−	39.5937i	−1.65785	−	0.844718i	−0.995420	−	0.0955952i	$-0.969525\pi$
$13$	−77.7071	−	39.5937i	−1.65785	−	0.844718i	−0.662431	−	0.749123i	$-0.730475\pi$
$14$	−59.9713	−	68.1930i	−1.14486	−	1.30181i
$15$	−73.7673	−	68.5980i	−1.26978	−	1.18079i
$16$	−43.5206	+	48.3345i	−0.680009	+	0.755227i
$17$	2.55681	−	3.15740i	0.0364776	−	0.0450460i	−0.758581	−	0.651579i	$-0.774107\pi$
$17$	2.55681	−	3.15740i	0.0364776	−	0.0450460i	0.795058	+	0.606533i	$0.207440\pi$
$18$	−256.606	+	68.7573i	−3.36014	+	0.900347i
$19$	31.7797	+	14.1492i	0.383724	+	0.170845i	0.589527	−	0.807748i	$-0.299314\pi$
$19$	31.7797	+	14.1492i	0.383724	+	0.170845i	−0.205803	+	0.978593i	$0.565981\pi$
$20$	179.251	−	6.50867i	2.00409	−	0.0727691i
$21$	133.840	+	99.6542i	1.39078	+	1.03554i
$22$	−229.233	+	36.3070i	−2.22149	+	0.351849i
$23$	120.455	+	78.2245i	1.09203	+	0.709171i	0.959415	−	0.281997i	$-0.0909968\pi$
$23$	120.455	+	78.2245i	1.09203	+	0.709171i	0.132612	+	0.991168i	$0.457663\pi$
$24$	177.672	−	307.738i	1.51113	−	2.61736i
$25$	−90.1581	−	86.5824i	−0.721265	−	0.692659i
$26$	−370.346	+	213.819i	−2.79349	+	1.61282i
$27$	218.184	−	111.171i	1.55517	−	0.792399i
$28$	−293.991	+	43.0435i	−1.98425	+	0.290516i
$29$	−107.290	+	147.672i	−0.687010	+	0.945589i	−0.999991	−	0.00417070i	$-0.998672\pi$
$29$	−107.290	+	147.672i	−0.687010	+	0.945589i	0.312981	+	0.949759i	$0.398672\pi$
$30$	−479.099	+	120.159i	−2.91570	+	0.731266i
$31$	−143.118	+	15.0423i	−0.829187	+	0.0871511i	−0.509606	−	0.860408i	$-0.670209\pi$
$31$	−143.118	+	15.0423i	−0.829187	+	0.0871511i	−0.319581	+	0.947559i	$0.603542\pi$
$32$	0.881111	+	3.28835i	0.00486750	+	0.0181658i
$33$	398.137	−	152.830i	2.10020	−	0.806193i
$34$	−6.15611	−	18.9466i	−0.0310519	−	0.0955679i
$35$	164.074	+	126.312i	0.792386	+	0.610020i
$36$	−268.597	+	826.656i	−1.24350	+	3.82711i
$37$	−4.53293	−	86.4934i	−0.0201408	−	0.384309i	−0.990039	−	0.140796i	$-0.955034\pi$
$37$	−4.53293	−	86.4934i	−0.0201408	−	0.384309i	0.969898	−	0.243512i	$-0.0782996\pi$
$38$	143.057	−	92.9020i	0.610706	−	0.396597i
$39$	583.947	−	525.788i	2.39760	−	2.15881i
$40$	226.579	−	378.279i	0.895632	−	1.49528i
$41$	30.3689	−	9.86746i	0.115679	−	0.0375863i	−0.250606	−	0.968089i	$-0.580630\pi$
$41$	30.3689	−	9.86746i	0.115679	−	0.0375863i	0.366284	+	0.930503i	$0.380630\pi$
$42$	767.242	−	284.261i	2.81876	−	1.04434i
$43$	−68.8788	−	68.8788i	−0.244277	−	0.244277i	0.574340	−	0.818617i	$-0.305259\pi$
$43$	−68.8788	−	68.8788i	−0.244277	−	0.244277i	−0.818617	+	0.574340i	$0.805259\pi$
$44$	−308.864	+	693.720i	−1.05825	+	2.37687i
$45$	544.059	−	266.291i	1.80230	−	0.882140i
$46$	643.370	−	286.447i	2.06217	−	0.918137i
$47$	−165.555	+	134.064i	−0.513801	+	0.416068i	−0.850842	−	0.525422i	$-0.823907\pi$
$47$	−165.555	+	134.064i	−0.513801	+	0.416068i	0.337041	+	0.941490i	$0.390574\pi$
$48$	−266.042	−	522.137i	−0.799998	−	1.57008i
$49$	−292.952	−	178.404i	−0.854088	−	0.520129i
$50$	−596.830	+	139.535i	−1.68809	+	0.394665i
$51$	18.3028	+	31.7014i	0.0502530	+	0.0870408i
$52$	−73.2273	+	1397.26i	−0.195285	+	3.72625i
$53$	111.265	+	42.7105i	0.288366	+	0.110693i	0.498251	−	0.867033i	$-0.333976\pi$
$53$	111.265	+	42.7105i	0.288366	+	0.110693i	−0.209885	+	0.977726i	$0.567309\pi$
$54$	125.509	−	1194.14i	0.316289	−	3.00929i
$55$	497.029	−	181.685i	1.21853	−	0.445426i
$56$	−304.879	+	663.756i	−0.727521	+	1.58390i
$57$	−221.628	+	221.628i	−0.515006	+	0.515006i
$58$	320.751	+	835.584i	0.726149	+	1.89168i
$59$	−590.246	−	125.461i	−1.30243	−	0.276840i	−0.496080	−	0.868277i	$-0.665228\pi$
$59$	−590.246	−	125.461i	−1.30243	−	0.276840i	−0.806351	+	0.591437i	$0.798561\pi$
$60$	−524.029	+	1528.78i	−1.12753	+	3.28941i
$61$	88.3600	+	415.701i	0.185465	+	0.872542i	0.968198	+	0.250185i	$0.0804914\pi$
$61$	88.3600	+	415.701i	0.185465	+	0.872542i	−0.782734	+	0.622357i	$0.786175\pi$
$62$	−320.350	+	628.722i	−0.656201	+	1.28787i
$63$	−847.856	+	536.605i	−1.69555	+	1.07311i
$64$	−478.982	−	155.631i	−0.935511	−	0.303966i
$65$	735.005	−	640.723i	1.40256	−	1.22264i
$66$	434.767	−	2045.42i	0.810850	−	3.81475i
$67$	−251.164	−	203.389i	−0.457979	−	0.370864i	0.372391	−	0.928076i	$-0.378538\pi$
$67$	−251.164	−	203.389i	−0.457979	−	0.370864i	−0.830371	+	0.557212i	$0.811871\pi$
$68$	−62.9599	−	16.8701i	−0.112280	−	0.0300852i
$69$	−1046.92	+	760.629i	−1.82658	+	1.32709i
$70$	957.611	−	337.398i	1.63509	−	0.576097i
$71$	471.023	+	342.218i	0.787327	+	0.572026i	0.907169	−	0.420767i	$-0.138239\pi$
$71$	471.023	+	342.218i	0.787327	+	0.572026i	−0.119842	+	0.992793i	$0.538239\pi$
$72$	1344.71	+	1660.57i	2.20104	+	2.71806i
$73$	397.047	+	20.8084i	0.636587	+	0.0333621i	0.367900	−	0.929865i	$-0.380077\pi$
$73$	397.047	+	20.8084i	0.636587	+	0.0333621i	0.268687	+	0.963228i	$0.413410\pi$
$74$	−367.795	−	212.347i	−0.577774	−	0.333578i
$75$	1019.39	−	478.800i	1.56946	−	0.737161i
$76$		−	558.101i		−	0.842349i
$77$	−785.671	+	388.807i	−1.16280	+	0.575437i
$78$	−602.739	−	3805.54i	−0.874958	−	5.52427i
$79$	1007.08	+	105.849i	1.43425	+	0.150746i	0.789548	−	0.613688i	$-0.210315\pi$
$79$	1007.08	+	105.849i	1.43425	+	0.150746i	0.644702	+	0.764434i	$0.276981\pi$
$80$	−319.679	−	653.137i	−0.446765	−	0.912787i
$81$	77.7145	+	739.404i	0.106604	+	1.01427i
$82$	40.5244	−	151.239i	0.0545752	−	0.203677i
$83$	73.2488	−	462.475i	0.0968686	−	0.611604i	−0.890721	−	0.454550i	$-0.849800\pi$
$83$	73.2488	−	462.475i	0.0968686	−	0.611604i	0.987590	−	0.157055i	$-0.0501999\pi$
$84$	587.198	−	2611.88i	0.762720	−	3.39261i
$85$	22.0770	+	39.6978i	0.0281715	+	0.0506569i
$86$	−467.199	+	99.3062i	−0.585807	+	0.124517i
$87$	−895.716	−	1379.28i	−1.10380	−	1.69971i
$88$	1016.72	+	1565.60i	1.23162	+	1.89652i
$89$	480.162	−	102.061i	0.571877	−	0.121556i	0.0871085	−	0.996199i	$-0.472237\pi$
$89$	480.162	−	102.061i	0.571877	−	0.121556i	0.484768	+	0.874643i	$0.338904\pi$
$90$	357.878	−	2948.50i	0.419152	−	3.45333i
$91$	−1094.75	+	1187.60i	−1.26111	+	1.36807i
$92$	360.462	−	2275.87i	0.408487	−	2.57908i
$93$	335.581	−	1252.40i	0.374173	−	1.39643i
$94$	109.187	+	1038.84i	0.119806	+	1.13988i
$95$	−279.400	+	270.563i	−0.301745	+	0.292202i
$96$	−30.5049	−	3.20619i	−0.0324311	−	0.00340865i
$97$	−83.1014	−	524.682i	−0.0869863	−	0.549210i	−0.992240	−	0.124338i	$-0.960319\pi$
$97$	−83.1014	−	524.682i	−0.0869863	−	0.549210i	0.905254	−	0.424872i	$-0.139681\pi$
$98$	−1516.01	+	728.273i	−1.56265	+	0.750681i
$99$			2564.40i			2.60336i
$100$	−680.657	+	1886.36i	−0.680657	+	1.88636i
$101$	419.295	+	242.080i	0.413083	+	0.238494i	0.692114	−	0.721789i	$-0.256680\pi$
$101$	419.295	+	242.080i	0.413083	+	0.238494i	−0.279030	+	0.960282i	$0.590013\pi$
$102$	179.246	+	9.39387i	0.174000	+	0.00911893i
$103$	−489.853	−	604.918i	−0.468608	−	0.578683i	0.486971	−	0.873418i	$-0.338102\pi$
$103$	−489.853	−	604.918i	−0.468608	−	0.578683i	−0.955579	+	0.294736i	$0.904768\pi$
$104$	2782.71	+	2021.75i	2.62372	+	1.90624i
$105$	−1592.24	+	972.255i	−1.47988	+	0.903642i
$106$	472.781	−	343.495i	0.433213	−	0.314747i
$107$	−768.917	−	206.031i	−0.694711	−	0.186147i	−0.105850	−	0.994382i	$-0.533756\pi$
$107$	−768.917	−	206.031i	−0.694711	−	0.186147i	−0.588860	+	0.808235i	$0.700423\pi$
$108$	−3053.08	−	2472.34i	−2.72021	−	2.20278i
$109$	1.29106	−	6.07395i	0.00113450	−	0.00533743i	−0.977577	−	0.210580i	$-0.932465\pi$
$109$	1.29106	−	6.07395i	0.00113450	−	0.00533743i	0.978711	+	0.205242i	$0.0657982\pi$
$110$	580.205	−	2529.15i	0.502913	−	2.19223i
$111$	742.172	+	241.146i	0.634630	+	0.206204i
$112$	644.188	+	1017.84i	0.543482	+	0.858724i
$113$	968.995	−	1901.76i	0.806685	−	1.58321i	−0.00562592	−	0.999984i	$-0.501791\pi$
$113$	968.995	−	1901.76i	0.806685	−	1.58321i	0.812311	−	0.583224i	$-0.198209\pi$
$114$	319.533	+	1503.28i	0.262517	+	1.23505i
$115$	−1314.11	+	922.869i	−1.06558	+	0.748330i
$116$	2864.44	+	608.855i	2.29273	+	0.487334i
$117$	1693.30	+	4411.20i	1.33800	+	3.48561i
$118$	−2092.23	+	2092.23i	−1.63225	+	1.63225i
$119$	−43.5122	−	61.3874i	−0.0335190	−	0.0472888i
$120$	2450.29	+	3127.27i	1.86400	+	2.37900i
$121$	−95.0560	+	904.397i	−0.0714170	+	0.679487i
$122$	1945.47	+	746.797i	1.44373	+	0.554195i
$123$	−15.0572	+	287.308i	−0.0110379	+	0.210615i
$124$	1154.37	+	1999.42i	0.836009	+	1.44801i
$125$	1274.34	−	573.742i	0.911844	−	0.410537i
$126$	−57.5717	+	4919.71i	−0.0407055	+	3.47844i
$127$	−923.154	−	1811.79i	−0.645013	−	1.26591i	−0.949612	−	0.313429i	$-0.898522\pi$
$127$	−923.154	−	1811.79i	−0.645013	−	1.26591i	0.304598	−	0.952481i	$-0.401478\pi$
$128$	−1940.33	+	1571.25i	−1.33986	+	1.08500i
$129$	801.772	−	356.972i	0.547226	−	0.243641i
$130$	−671.976	−	4733.68i	−0.453356	−	3.19363i
$131$	−17.6492	+	39.6408i	−0.0117711	+	0.0264384i	−0.919335	−	0.393475i	$-0.871273\pi$
$131$	−17.6492	+	39.6408i	−0.0117711	+	0.0264384i	0.907564	+	0.419913i	$0.137940\pi$
$132$	−4837.92	−	4837.92i	−3.19005	−	3.19005i
$133$	411.282	−	495.912i	0.268140	−	0.323316i
$134$	−1507.16	+	489.705i	−0.971631	+	0.315702i
$135$	242.398	+	2727.02i	0.154535	+	1.73855i
$136$	−119.078	+	107.218i	−0.0750796	+	0.0676020i
$137$	−1061.06	+	689.061i	−0.661697	+	0.429711i	−0.831317	−	0.555798i	$-0.812413\pi$
$137$	−1061.06	+	689.061i	−0.661697	+	0.429711i	0.169620	+	0.985510i	$0.445746\pi$
$138$	332.086	+	6336.59i	0.204848	+	3.90874i
$139$	−360.479	+	1109.44i	−0.219967	+	0.676989i	0.778797	+	0.627276i	$0.215830\pi$
$139$	−360.479	+	1109.44i	−0.219967	+	0.676989i	−0.998764	+	0.0497121i	$0.984170\pi$
$140$	780.624	−	3228.94i	0.471248	−	1.94925i
$141$	−593.119	−	1825.43i	−0.354252	−	1.09028i
$142$	2665.22	−	1023.08i	1.57507	−	0.604614i
$143$	1068.41	+	3987.35i	0.624788	+	2.33174i
$144$	3504.48	−	368.336i	2.02806	−	0.213157i
$145$	−1083.85	−	1729.18i	−0.620751	−	0.990348i
$146$	1145.92	−	1577.22i	0.649567	−	0.894052i
$147$	2446.54	−	1888.11i	1.37270	−	1.05938i
$148$	−1238.09	+	630.839i	−0.687638	+	0.350369i
$149$	1402.51	−	809.738i	0.771127	−	0.445210i	−0.0621498	−	0.998067i	$-0.519796\pi$
$149$	1402.51	−	809.738i	0.771127	−	0.445210i	0.833276	+	0.552857i	$0.186462\pi$
$150$	753.386	−	5470.76i	0.410091	−	2.97790i
$151$	−1133.48	+	1963.25i	−0.610870	+	1.05806i	0.380224	+	0.924894i	$0.375847\pi$
$151$	−1133.48	+	1963.25i	−0.610870	+	1.05806i	−0.991094	+	0.133163i	$0.957487\pi$
$152$	−1150.64	−	747.237i	−0.614010	−	0.398743i
$153$	−217.407	+	34.4338i	−0.114878	+	0.0181948i
$154$	−499.294	+	4269.28i	−0.261261	+	2.23395i
$155$	441.333	−	1547.21i	0.228701	−	0.801774i
$156$	−11516.6	−	5127.51i	−5.91066	−	2.63160i
$157$	−396.190	+	106.159i	−0.201397	+	0.0539643i	−0.358107	−	0.933680i	$-0.616578\pi$
$157$	−396.190	+	106.159i	−0.201397	+	0.0539643i	0.156710	+	0.987645i	$0.449911\pi$
$158$	3124.78	−	3858.79i	1.57338	−	1.94297i
$159$	−718.516	+	797.993i	−0.358378	+	0.398019i
$160$	−37.7845	−	4.58614i	−0.0186696	−	0.00226604i
$161$	1997.45	−	1756.63i	0.977773	−	0.859888i
$162$	3248.22	+	1655.05i	1.57533	+	0.802672i
$163$	−2866.68	+	150.236i	−1.37752	+	0.0721927i	−0.726655	−	0.687003i	$-0.758926\pi$
$163$	−2866.68	+	150.236i	−1.37752	+	0.0721927i	−0.650863	+	0.759195i	$0.725593\pi$
$164$	−342.789	−	380.706i	−0.163215	−	0.181269i
$165$	−76.5969	+	4767.38i	−0.0361397	+	2.24933i
$166$	−1706.23	−	1536.30i	−0.797767	−	0.718313i
$167$	−4006.75	−	634.607i	−1.85660	−	0.294056i	−0.874870	−	0.484357i	$-0.839054\pi$
$167$	−4006.75	−	634.607i	−1.85660	−	0.294056i	−0.981726	+	0.190301i	$0.939054\pi$
$168$	−4598.75	−	4707.66i	−2.11191	−	2.16193i
$169$	3179.37	+	4376.02i	1.44714	+	1.99182i
$170$	222.209	+	15.2285i	0.100251	+	0.00687043i
$171$	−766.582	−	1721.77i	−0.342819	−	0.769983i
$172$	−560.045	+	1458.97i	−0.248273	+	0.646774i
$173$	912.661	−	1405.37i	0.401089	−	0.617622i	−0.579202	−	0.815184i	$-0.696636\pi$
$173$	912.661	−	1405.37i	0.401089	−	0.617622i	0.980290	+	0.197562i	$0.0633023\pi$
$174$	−8064.15			−3.51346
$175$	−1994.93	+	1174.57i	−0.861730	+	0.507366i
$176$	3078.54			1.31849
$177$	2961.13	−	4559.74i	1.25747	−	1.93633i
$178$	862.599	−	2247.15i	0.363228	−	0.946241i
$179$	338.479	+	760.237i	0.141336	+	0.317446i	0.970319	−	0.241828i	$-0.0777469\pi$
$179$	338.479	+	760.237i	0.141336	+	0.317446i	−0.828983	+	0.559273i	$0.811080\pi$
$180$	−7453.03	−	6236.23i	−3.08620	−	2.58234i
$181$	−270.354	−	372.110i	−0.111023	−	0.152811i	0.749889	−	0.661563i	$-0.230107\pi$
$181$	−270.354	−	372.110i	−0.111023	−	0.152811i	−0.860913	+	0.508753i	$0.830107\pi$
$182$	1960.18	+	7673.57i	0.798343	+	3.12529i
$183$	−3781.96	−	599.003i	−1.52771	−	0.241965i
$184$	−4209.57	−	3790.31i	−1.68659	−	1.51862i
$185$	916.032	+	313.994i	0.364043	+	0.124785i
$186$	−4254.11	−	4724.66i	−1.67702	−	1.86252i
$187$	−192.040	+	10.0644i	−0.0750983	+	0.00393573i
$188$	3045.18	+	1551.60i	1.18134	+	0.601925i
$189$	−890.934	−	4446.76i	−0.342889	−	1.71140i
$190$	366.488	+	1871.55i	0.139936	+	0.714612i
$191$	2285.69	−	2538.51i	0.865898	−	0.961677i	−0.133671	−	0.991026i	$-0.542677\pi$
$191$	2285.69	−	2538.51i	0.865898	−	0.961677i	0.999569	+	0.0293483i	$0.00934320\pi$
$192$	2855.65	−	3526.43i	1.07338	−	1.32551i
$193$	1414.42	−	378.993i	0.527524	−	0.141350i	0.0147794	−	0.999891i	$-0.495295\pi$
$193$	1414.42	−	378.993i	0.527524	−	0.141350i	0.512745	+	0.858541i	$0.328629\pi$
$194$	−2379.59	−	1059.46i	−0.880644	−	0.392088i
$195$	3016.19	+	8251.27i	1.10766	+	3.03018i
$196$	−703.115	+	5457.74i	−0.256237	+	1.98897i
$197$	2738.56	−	433.746i	0.990429	−	0.156869i	0.359864	−	0.933005i	$-0.382823\pi$
$197$	2738.56	−	433.746i	0.990429	−	0.156869i	0.630565	+	0.776136i	$0.282823\pi$
$198$	10545.7	+	6848.44i	3.78510	+	2.45807i
$199$	1561.60	−	2704.77i	0.556275	−	0.963497i	−0.441528	−	0.897248i	$-0.645563\pi$
$199$	1561.60	−	2704.77i	0.556275	−	0.963497i	0.997803	−	0.0662495i	$-0.0211033\pi$
$200$	2977.82	+	3928.96i	1.05282	+	1.38910i
$201$	2521.77	−	1455.95i	0.884936	−	0.510918i
$202$	2115.27	−	1077.79i	0.736783	−	0.375410i
$203$	2096.57	+	2651.90i	0.724878	+	0.916882i
$204$	345.191	−	475.114i	0.118471	−	0.163062i
$205$	−24.4094	+	356.173i	−0.00831621	+	0.121347i
$206$	−3795.81	+	398.956i	−1.28382	+	0.134935i
$207$	−2013.98	−	7516.29i	−0.676239	−	2.52376i
$208$	5295.60	−	2032.79i	1.76531	−	0.677638i
$209$	−508.818	−	1565.98i	−0.168400	−	0.518283i
$210$	−253.978	+	9144.32i	−0.0834577	+	3.00485i
$211$	−710.477	+	2186.62i	−0.231807	+	0.713429i	0.765722	+	0.643172i	$0.222382\pi$
$211$	−710.477	+	2186.62i	−0.231807	+	0.713429i	−0.997529	+	0.0702569i	$0.977618\pi$
$212$	−100.069	−	1909.43i	−0.0324186	−	0.618585i
$213$	−4399.43	+	2857.02i	−1.41523	+	0.919061i
$214$	−2900.72	+	2611.82i	−0.926585	+	0.834301i
$215$	1001.90	−	426.924i	0.317810	−	0.135423i
$216$	−9185.00	+	2984.39i	−2.89333	+	0.940101i
$217$	−447.701	+	2627.32i	−0.140055	+	0.821907i
$218$	−21.5302	−	21.5302i	−0.00668905	−	0.00668905i
$219$	−1457.04	+	3272.56i	−0.449578	+	1.00977i
$220$	−5906.13	−	6099.02i	−1.80996	−	1.86907i
$221$	−323.696	+	144.119i	−0.0985256	+	0.0438664i
$222$	2973.70	−	2408.06i	0.899018	−	0.728010i
$223$	40.2496	+	78.9943i	0.0120866	+	0.0237213i	0.896971	−	0.442090i	$-0.145763\pi$
$223$	40.2496	+	78.9943i	0.0120866	+	0.0237213i	−0.884884	+	0.465811i	$0.845763\pi$
$224$	63.0452	+	0.737771i	0.0188053	+	0.000220064i
$225$	491.161	+	6754.46i	0.145529	+	2.00132i
$226$	−5232.89	−	9063.63i	−1.54021	−	2.66772i
$227$	−9.56648	+	182.539i	−0.00279713	+	0.0533725i	−0.999671	−	0.0256310i	$-0.991841\pi$
$227$	−9.56648	+	182.539i	−0.00279713	+	0.0533725i	0.996874	+	0.0790035i	$0.0251738\pi$
$228$	4694.45	+	1802.03i	1.36358	+	0.523431i
$229$	−4.89539	+	46.5766i	−0.00141265	+	0.0134405i	−0.995206	−	0.0978058i	$-0.968818\pi$
$229$	−4.89539	+	46.5766i	−0.00141265	+	0.0134405i	0.993793	+	0.111246i	$0.0354842\pi$
$230$	285.713	+	7868.64i	0.0819103	+	2.25584i
$231$	−733.616	−	7864.05i	−0.208954	−	2.23990i
$232$	5090.45	−	5090.45i	1.44054	−	1.44054i
$233$	−553.070	−	1440.80i	−0.155506	−	0.405106i	0.833590	−	0.552384i	$-0.186282\pi$
$233$	−553.070	−	1440.80i	−0.155506	−	0.405106i	−0.989095	+	0.147279i	$0.952949\pi$
$234$	22662.4	+	4817.05i	6.33115	+	1.34573i
$235$	−699.513	−	2276.70i	−0.194175	−	0.631981i
$236$	2012.80	+	9469.47i	0.555178	+	2.61191i
$237$	−4142.08	+	8129.28i	−1.13526	+	2.22807i
$238$	−368.648	+	14.9968i	−0.100403	+	0.00408445i
$239$	−6952.28	−	2258.93i	−1.88161	−	0.611373i	−0.986053	−	0.166430i	$-0.946776\pi$
$239$	−6952.28	−	2258.93i	−1.88161	−	0.611373i	−0.895559	−	0.444943i	$-0.853224\pi$
$240$	6526.04	−	580.082i	1.75523	−	0.156017i
$241$	−569.492	+	2679.25i	−0.152217	+	0.716123i	0.834147	+	0.551542i	$0.185960\pi$
$241$	−569.492	+	2679.25i	−0.152217	+	0.716123i	−0.986364	+	0.164581i	$0.947373\pi$
$242$	3465.33	+	2806.17i	0.920495	+	0.745402i
$243$	−84.0845	−	22.5304i	−0.0221976	−	0.00594784i
$244$	5516.04	−	4007.64i	1.44725	−	1.05149i
$245$	3073.15	−	2293.88i	0.801373	−	0.598165i
$246$	1141.29	+	829.199i	0.295798	+	0.214910i
$247$	−1909.29	−	2357.77i	−0.491842	−	0.607375i
$248$	5667.80	+	297.037i	1.45123	+	0.0760559i
$249$	3653.58	+	2109.40i	0.929864	+	0.536857i
$250$	1043.81	−	6772.74i	0.264065	−	1.71338i
$251$		−	134.048i		−	0.0337093i	−0.999858	−	0.0168546i	$-0.994635\pi$
$251$		−	134.048i		−	0.0337093i	0.999858	−	0.0168546i	$-0.00536525\pi$
$252$	13397.2	+	8924.85i	3.34899	+	2.23100i
$253$	−1063.47	−	6714.52i	−0.264269	−	1.66853i
$254$	−9916.05	−	1042.22i	−2.44956	−	0.257459i
$255$	−405.201	+	57.5208i	−0.0995084	+	0.0141258i
$256$	858.538	+	8168.44i	0.209604	+	1.99425i
$257$	1284.02	−	4792.04i	0.311654	−	1.16311i	−0.615410	−	0.788207i	$-0.711010\pi$
$257$	1284.02	−	4792.04i	0.311654	−	1.16311i	0.927064	−	0.374902i	$-0.122324\pi$
$258$	673.209	−	4250.48i	0.162450	−	1.02567i
$259$	−1565.01	−	351.844i	−0.375464	−	0.0844112i
$260$	−14186.8	−	6591.45i	−3.38395	−	1.57225i
$261$	9673.23	−	2056.11i	2.29409	−	0.487624i
$262$	115.882	+	178.443i	0.0273253	+	0.0420773i
$263$	−1322.23	−	2036.06i	−0.310009	−	0.477372i	0.648984	−	0.760802i	$-0.275194\pi$
$263$	−1322.23	−	2036.06i	−0.310009	−	0.477372i	−0.958993	+	0.283430i	$0.908528\pi$
$264$	−16451.9	+	3496.95i	−3.83539	+	0.815236i
$265$	−907.395	+	975.774i	−0.210343	+	0.226194i
$266$	−940.992	−	3015.70i	−0.216902	−	0.695130i
$267$	−691.888	+	4368.41i	−0.158587	+	1.00128i
$268$	−1341.98	+	5008.32i	−0.305874	+	1.14154i
$269$	−45.3808	−	431.769i	−0.0102859	−	0.0978641i	0.988174	−	0.153334i	$-0.0490010\pi$
$269$	−45.3808	−	431.769i	−0.0102859	−	0.0978641i	−0.998460	+	0.0554698i	$0.982334\pi$
$270$	11861.8	+	6285.92i	2.67365	+	1.41685i
$271$	−2436.19	−	256.054i	−0.546081	−	0.0573954i	−0.172529	−	0.985005i	$-0.555194\pi$
$271$	−2436.19	−	256.054i	−0.546081	−	0.0573954i	−0.373552	+	0.927609i	$0.621860\pi$
$272$	41.3374	+	260.994i	0.00921489	+	0.0581805i
$273$	−6454.66	−	13043.1i	−1.43097	−	2.89159i
$274$			6203.63i			1.36779i
$275$	−190.073	+	5913.53i	−0.0416793	+	1.29672i
$276$	17979.5	+	10380.5i	3.92116	+	2.26388i
$277$	2727.35	+	142.934i	0.591591	+	0.0310040i	0.345783	−	0.938315i	$-0.387613\pi$
$277$	2727.35	+	142.934i	0.591591	+	0.0310040i	0.245808	+	0.969319i	$0.420947\pi$
$278$	3599.70	+	4445.25i	0.776602	+	0.959024i
$279$	6307.60	+	4582.74i	1.35350	+	0.983374i
$280$	−5611.98	−	5932.63i	−1.19779	−	1.26622i
$281$	1988.17	−	1444.49i	0.422079	−	0.306659i	−0.356395	−	0.934336i	$-0.615994\pi$
$281$	1988.17	−	1444.49i	0.422079	−	0.306659i	0.778474	+	0.627677i	$0.215994\pi$
$282$	−9090.75	−	2435.86i	−1.91967	−	0.514373i
$283$	−5813.73	−	4707.86i	−1.22117	−	0.988881i	−0.999907	−	0.0136663i	$-0.995650\pi$
$283$	−5813.73	−	4707.86i	−1.22117	−	0.988881i	−0.221260	−	0.975215i	$-0.571017\pi$
$284$	1942.03	−	9136.55i	0.405769	−	1.90899i
$285$	−1373.69	−	3223.77i	−0.285511	−	0.670034i
$286$	19250.6	+	6254.89i	3.98011	+	1.29322i
$287$	−24.0380	−	590.896i	−0.00494397	−	0.121531i
$288$	83.7350	−	164.339i	0.0171324	−	0.0336242i
$289$	1018.04	+	4789.49i	0.207213	+	0.974861i
$290$	−10005.5	−	160.757i	−2.02600	−	0.0325515i
$291$	4681.67	+	995.119i	0.943107	+	0.200464i
$292$	−2285.91	−	5955.01i	−0.458127	−	1.19346i
$293$	−100.749	+	100.749i	−0.0200881	+	0.0200881i	−0.717080	−	0.696991i	$-0.754522\pi$
$293$	−100.749	+	100.749i	−0.0200881	+	0.0200881i	0.696991	+	0.717080i	$0.254522\pi$
$294$	−1230.86	−	15103.4i	−0.244168	−	2.99607i
$295$	3764.87	−	5598.40i	0.743049	−	1.10492i
$296$	−357.061	+	3397.21i	−0.0701141	+	0.667091i
$297$	−10820.7	−	4153.68i	−2.11408	−	0.811518i
$298$	415.596	−	7930.05i	0.0807880	−	1.54153i
$299$	−6263.02	−	10847.9i	−1.21137	−	2.09816i
$300$	−13669.4	−	11816.1i	−2.63067	−	2.27402i
$301$	−1572.80	+	883.680i	−0.301178	+	0.169217i
$302$	5046.47	+	9904.25i	0.961562	+	1.88717i
$303$	−3390.09	+	2745.24i	−0.642758	+	0.520495i
$304$	−2066.97	+	920.273i	−0.389963	+	0.173623i
$305$	−4680.46	−	818.596i	−0.878697	−	0.153681i
$306$	−438.998	+	986.007i	−0.0820127	+	0.184203i
$307$	6766.34	+	6766.34i	1.25790	+	1.25790i	0.952094	+	0.305806i	$0.0989257\pi$
$307$	6766.34	+	6766.34i	1.25790	+	1.25790i	0.305806	+	0.952094i	$0.401074\pi$
$308$	10825.3	+	8977.89i	2.00268	+	1.66092i
$309$	6669.91	−	2167.19i	1.22795	−	0.398987i
$310$	−5184.03	−	5946.86i	−0.949785	−	1.08954i
$311$	−2382.97	+	2145.64i	−0.434488	+	0.391215i	−0.857145	−	0.515075i	$-0.827764\pi$
$311$	−2382.97	+	2145.64i	−0.434488	+	0.391215i	0.422657	+	0.906290i	$0.361097\pi$
$312$	−25990.9	+	16878.7i	−4.71617	+	3.06271i
$313$	−253.946	−	4845.57i	−0.0458590	−	0.875041i	−0.920614	−	0.390475i	$-0.872311\pi$
$313$	−253.946	−	4845.57i	−0.0458590	−	0.875041i	0.874755	−	0.484566i	$-0.161023\pi$
$314$	−621.497	+	1912.77i	−0.111698	+	0.343770i
$315$	−2026.86	−	11033.7i	−0.362543	−	1.97358i
$316$	−5020.27	−	15450.8i	−0.893709	−	2.75055i
$317$	3374.10	−	1295.20i	0.597818	−	0.229481i	−0.0405937	−	0.999176i	$-0.512925\pi$
$317$	3374.10	−	1295.20i	0.597818	−	0.229481i	0.638412	+	0.769695i	$0.279592\pi$
$318$	1362.76	+	5085.88i	0.240313	+	0.896862i
$319$	8592.44	−	903.102i	1.50810	−	0.158508i
$320$	3613.40	−	4318.44i	0.631234	−	0.754400i
$321$	4215.75	−	5802.48i	0.733022	−	1.00892i
$322$	−1889.49	−	12905.4i	−0.327011	−	2.23351i
$323$	125.930	−	64.1643i	0.0216932	−	0.0110532i
$324$	10329.8	−	5963.90i	1.77122	−	1.02262i
$325$	3577.81	+	10297.8i	0.610649	+	1.75759i
$326$	−7037.87	+	12189.9i	−1.19568	+	2.07098i
$327$	46.9222	+	30.4717i	0.00793518	+	0.00515317i
$328$	−1243.86	+	197.009i	−0.209393	+	0.0331646i
$329$	1562.44	+	3622.79i	0.261823	+	0.607085i
$330$	19400.5	+	13046.7i	3.23625	+	2.17635i
$331$	2674.80	+	1190.90i	0.444170	+	0.197757i	0.616620	−	0.787261i	$-0.288502\pi$
$331$	2674.80	+	1190.90i	0.444170	+	0.197757i	−0.172450	+	0.985018i	$0.555168\pi$
$332$	−7256.12	+	1944.27i	−1.19949	+	0.321403i
$333$	−2953.08	+	3646.76i	−0.485970	+	0.600123i
$334$	−13310.1	+	14782.3i	−2.18052	+	2.42171i
$335$	3157.88	−	1756.17i	0.515024	−	0.286418i
$336$	−10641.5	+	2132.10i	−1.72781	+	0.346177i
$337$	101.949	+	51.9456i	0.0164793	+	0.00839660i	0.462211	−	0.886770i	$-0.347056\pi$
$337$	101.949	+	51.9456i	0.0164793	+	0.00839660i	−0.445731	+	0.895167i	$0.647056\pi$
$338$	26486.4	−	1388.09i	4.26234	−	0.223380i
$339$	12867.8	+	14291.2i	2.06161	+	2.28965i
$340$	437.761	−	582.609i	0.0698263	−	0.0929307i
$341$	5061.92	+	4557.77i	0.803865	+	0.723804i
$342$	−9127.71	−	1445.69i	−1.44319	−	0.228578i
$343$	−4646.75	+	4331.44i	−0.731489	+	0.681853i
$344$	2258.13	+	3108.05i	0.353925	+	0.487136i
$345$	−3519.61	−	14033.4i	−0.549245	−	2.18995i
$346$	−3342.03	−	7506.33i	−0.519274	−	1.16631i
$347$	−2761.51	+	7193.99i	−0.427222	+	1.11295i	0.535994	+	0.844222i	$0.319937\pi$
$347$	−2761.51	+	7193.99i	−0.427222	+	1.11295i	−0.963216	+	0.268729i	$0.913397\pi$
$348$	−14370.2	+	22128.2i	−2.21358	+	3.40861i
$349$	−6249.45			−0.958525			−0.479262	−	0.877672i	$-0.659096\pi$
$349$	−6249.45			−0.958525			−0.479262	+	0.877672i	$0.659096\pi$
$350$	−497.408	+	11340.6i	−0.0759645	+	1.73195i
$351$	−21356.1			−3.24760
$352$	87.7615	−	135.141i	0.0132889	−	0.0204632i
$353$	2773.29	−	7224.68i	0.418152	−	1.08932i	−0.549157	−	0.835719i	$-0.685051\pi$
$353$	2773.29	−	7224.68i	0.418152	−	1.08932i	0.967308	−	0.253603i	$-0.0816157\pi$
$354$	−10843.2	−	24354.3i	−1.62800	−	3.65654i
$355$	−5515.48	+	3457.10i	−0.824595	+	0.516857i
$356$	−4629.08	−	6371.38i	−0.689160	−	0.948547i
$357$	656.853	−	167.790i	0.0973791	−	0.0248751i
$358$	4030.28	+	638.334i	0.594992	+	0.0942375i
$359$	5094.22	+	4586.85i	0.748921	+	0.674331i	0.952435	−	0.304741i	$-0.0985698\pi$
$359$	5094.22	+	4586.85i	0.748921	+	0.674331i	−0.203515	+	0.979072i	$0.565236\pi$
$360$	−22836.1	+	7016.37i	−3.34325	+	1.02721i
$361$	−3779.82	−	4197.91i	−0.551074	−	0.612030i
$362$	−2252.24	+	118.035i	−0.327003	+	0.0171375i
$363$	−7300.39	−	3719.73i	−1.05557	−	0.537838i
$364$	24549.5	+	8295.43i	3.53500	+	1.19450i
$365$	−1873.04	+	4031.33i	−0.268600	+	0.578109i
$366$	−12563.3	+	13953.0i	−1.79425	+	1.99272i
$367$	7452.70	−	9203.31i	1.06002	−	1.30902i	0.110994	−	0.993821i	$-0.464597\pi$
$367$	7452.70	−	9203.31i	1.06002	−	1.30902i	0.949027	−	0.315196i	$-0.102070\pi$
$368$	−9023.22	+	2417.77i	−1.27817	+	0.342486i
$369$	−1580.44	−	703.659i	−0.222966	−	0.0992710i
$370$	3737.58	−	2928.48i	0.525156	−	0.411472i
$371$	1318.20	−	1770.40i	0.184468	−	0.247749i
$372$	−20545.4	+	3254.06i	−2.86351	+	0.453536i
$373$	−7071.93	−	4592.57i	−0.981691	−	0.637518i	−0.0492300	−	0.998787i	$-0.515677\pi$
$373$	−7071.93	−	4592.57i	−0.981691	−	0.637518i	−0.932461	+	0.361270i	$0.882343\pi$
$374$	−471.471	+	816.612i	−0.0651850	+	0.112904i
$375$	711.347	+	12571.6i	0.0979568	+	1.73119i
$376$	7276.11	−	4200.87i	0.997971	−	0.576179i
$377$	14184.1	−	7227.17i	1.93772	−	0.987316i
$378$	−20665.9	−	8211.60i	−2.81200	−	1.11735i
$379$	1808.96	−	2489.82i	0.245172	−	0.337450i	−0.668641	−	0.743585i	$-0.733124\pi$
$379$	1808.96	−	2489.82i	0.245172	−	0.337450i	0.913813	+	0.406135i	$0.133124\pi$
$380$	5788.64	+	2329.42i	0.781450	+	0.314465i
$381$	18220.6	−	1915.06i	2.45005	−	0.257510i
$382$	−4335.10	−	16178.8i	−0.580636	−	2.16696i
$383$	8861.65	−	3401.67i	1.18227	−	0.453831i	0.313760	−	0.949502i	$-0.398411\pi$
$383$	8861.65	−	3401.67i	1.18227	−	0.453831i	0.868510	+	0.495672i	$0.165078\pi$
$384$	−6951.45	−	21394.3i	−0.923801	−	2.84317i
$385$	−753.455	−	9771.82i	−0.0997392	−	1.29355i
$386$	2218.78	−	6828.70i	0.292572	−	0.900444i
$387$	276.202	+	5270.24i	0.0362794	+	0.692252i
$388$	−7147.60	+	4641.71i	−0.935218	+	0.607338i
$389$	−2745.93	+	2472.44i	−0.357902	+	0.322257i	−0.828392	−	0.560149i	$-0.810744\pi$
$389$	−2745.93	+	2472.44i	−0.357902	+	0.322257i	0.470490	+	0.882406i	$0.344077\pi$
$390$	41987.0	+	9632.10i	5.45152	+	1.25062i
$391$	554.968	−	180.320i	0.0717798	−	0.0233227i
$392$	10310.9	+	8756.94i	1.32852	+	1.12830i
$393$	−276.450	−	276.450i	−0.0354836	−	0.0354836i
$394$	5529.84	−	12420.2i	0.707080	−	1.58813i
$395$	−5301.27	+	10003.7i	−0.675281	+	1.27428i
$396$	37584.6	−	16733.7i	4.76943	−	2.12349i
$397$	−6291.78	+	5094.99i	−0.795404	+	0.644106i	−0.938374	−	0.345621i	$-0.887668\pi$
$397$	−6291.78	+	5094.99i	−0.795404	+	0.644106i	0.142970	+	0.989727i	$0.454335\pi$
$398$	−6952.53	−	13645.1i	−0.875625	−	1.71851i
$399$	2843.37	+	5060.72i	0.356759	+	0.634969i
$400$	8108.65	−	589.633i	1.01358	−	0.0737041i
$401$	−3346.04	−	5795.52i	−0.416692	−	0.721731i	0.578913	−	0.815390i	$-0.303477\pi$
$401$	−3346.04	−	5795.52i	−0.416692	−	0.721731i	−0.995604	+	0.0936582i	$0.970144\pi$
$402$	747.261	−	14258.6i	0.0927115	−	1.76904i
$403$	11716.9	+	4497.69i	1.44829	+	0.555945i
$404$	811.926	−	7724.96i	0.0999872	−	0.951315i
$405$	−7993.49	−	2280.09i	−0.980740	−	0.279750i
$406$	16504.6	−	1539.66i	2.01751	−	0.188208i
$407$	−2898.84	+	2898.84i	−0.353047	+	0.353047i
$408$	−517.376	−	1347.81i	−0.0627792	−	0.163546i
$409$	−14876.2	−	3162.02i	−1.79848	−	0.382279i	−0.817430	−	0.576028i	$-0.804602\pi$
$409$	−14876.2	−	3162.02i	−1.79848	−	0.382279i	−0.981051	+	0.193750i	$0.937935\pi$
$410$	1399.51	+	1051.57i	0.168578	+	0.126666i
$411$	−2370.00	−	11150.0i	−0.284436	−	1.33817i
$412$	−5669.35	+	11126.7i	−0.677934	+	1.33052i
$413$	−5189.84	+	9897.59i	−0.618342	+	1.17925i
$414$	−36288.0	−	11790.7i	−4.30787	−	1.39971i
$415$	4491.07	+	2690.03i	0.531224	+	0.318189i
$416$	61.7296	−	290.415i	0.00727534	−	0.0342278i
$417$	−8168.08	−	6614.38i	−0.959215	−	0.776757i
$418$	−7798.68	−	2089.65i	−0.912550	−	0.244517i
$419$	−2922.72	+	2123.48i	−0.340774	+	0.247587i	−0.744988	−	0.667077i	$-0.767545\pi$
$419$	−2922.72	+	2123.48i	−0.340774	+	0.247587i	0.404214	+	0.914664i	$0.367545\pi$
$420$	24639.6	+	16992.0i	2.86260	+	1.97411i
$421$	−4616.53	−	3354.11i	−0.534432	−	0.388288i	0.287581	−	0.957756i	$-0.407149\pi$
$421$	−4616.53	−	3354.11i	−0.534432	−	0.388288i	−0.822013	+	0.569469i	$0.807149\pi$
$422$	7094.74	+	8761.28i	0.818404	+	1.01065i
$423$	11525.7	+	604.039i	1.32483	+	0.0694311i
$424$	−4070.67	−	2350.20i	−0.466248	−	0.269188i
$425$	−503.893	+	63.2905i	−0.0575115	+	0.00722362i
$426$			25721.8i			2.92541i
$427$	7854.74	+	503.877i	0.890205	+	0.0571061i
$428$	1997.84	+	12613.9i	0.225629	+	1.42457i
$429$	−36989.2	−	3887.72i	−4.16283	−	0.437531i
$430$	920.006	−	5260.29i	0.103178	−	0.589939i
$431$	−1048.38	−	9974.64i	−0.117166	−	1.11476i	−0.882234	−	0.470811i	$-0.843961\pi$
$431$	−1048.38	−	9974.64i	−0.117166	−	1.11476i	0.765068	−	0.643949i	$-0.222705\pi$
$432$	−4122.14	+	15384.0i	−0.459089	+	1.71334i
$433$	−1186.22	+	7489.49i	−0.131654	+	0.831229i	0.830160	+	0.557525i	$0.188249\pi$
$433$	−1186.22	+	7489.49i	−0.131654	+	0.831229i	−0.961814	+	0.273704i	$0.911751\pi$
$434$	9608.77	+	8857.55i	1.06276	+	0.979668i
$435$	18044.5	−	3533.50i	1.98889	−	0.389467i
$436$	−97.4461	+	20.7128i	−0.0107037	+	0.00227515i
$437$	2721.21	+	4190.30i	0.297879	+	0.458694i
$438$	9566.72	+	14731.5i	1.04364	+	1.60707i
$439$	−8026.68	+	1706.12i	−0.872648	+	0.185487i	−0.622404	−	0.782696i	$-0.713844\pi$
$439$	−8026.68	+	1706.12i	−0.872648	+	0.185487i	−0.250244	+	0.968183i	$0.580511\pi$
$440$	−20482.1	+	4010.82i	−2.21920	+	0.434565i
$441$	5327.36	+	17803.2i	0.575246	+	1.92238i
$442$	−271.792	+	1716.03i	−0.0292485	+	0.184668i
$443$	−3438.84	+	12833.9i	−0.368813	+	1.37643i	0.493364	+	0.869823i	$0.335767\pi$
$443$	−3438.84	+	12833.9i	−0.368813	+	1.37643i	−0.862177	+	0.506607i	$0.830900\pi$
$444$	−1308.66	−	12451.0i	−0.139879	−	1.33086i
$445$	−945.532	+	5406.24i	−0.100725	+	0.575911i
$446$	432.340	+	45.4408i	0.0459011	+	0.00482441i
$447$	2282.58	+	14411.7i	0.241527	+	1.52494i
$448$	−5171.24	+	7762.62i	−0.545353	+	0.818637i
$449$			11553.6i			1.21436i	0.794563	+	0.607181i	$0.207700\pi$
$449$			11553.6i			1.21436i	−0.794563	+	0.607181i	$0.792300\pi$
$450$	29088.3	+	16018.5i	3.04719	+	1.67804i
$451$	−1308.92	−	755.708i	−0.136663	−	0.0789022i
$452$	−34195.8	−	1792.12i	−3.55848	−	0.186492i
$453$	−12853.9	−	15873.3i	−1.33318	−	1.64634i
$454$	725.114	+	526.826i	0.0749588	+	0.0544608i
$455$	−7748.51	−	16311.7i	−0.798364	−	1.68067i
$456$	10000.6	−	7265.88i	1.02702	−	0.746175i
$457$	5822.06	+	1560.02i	0.595939	+	0.159681i	0.544166	−	0.838977i	$-0.316846\pi$
$457$	5822.06	+	1560.02i	0.595939	+	0.159681i	0.0517732	+	0.998659i	$0.483513\pi$
$458$	178.465	+	144.518i	0.0182077	+	0.0147443i
$459$	206.847	−	973.138i	0.0210344	−	0.0989590i
$460$	22100.9	+	13237.8i	2.24013	+	1.34178i
$461$	−4358.33	−	1416.11i	−0.440320	−	0.143069i	0.0804631	−	0.996758i	$-0.474360\pi$
$461$	−4358.33	−	1416.11i	−0.440320	−	0.143069i	−0.520783	+	0.853689i	$0.674360\pi$
$462$	−34298.8	−	17984.7i	−3.45395	−	1.81109i
$463$	−17.3044	+	33.9618i	−0.00173694	+	0.00340894i	−0.891873	−	0.452285i	$-0.850609\pi$
$463$	−17.3044	+	33.9618i	−0.00173694	+	0.00340894i	0.890136	+	0.455694i	$0.150609\pi$
$464$	−2468.34	−	11612.6i	−0.246960	−	1.16186i
$465$	11589.3	+	8707.99i	1.15579	+	0.868437i
$466$	−7402.05	−	1573.35i	−0.735822	−	0.156404i
$467$	−331.109	−	862.570i	−0.0328092	−	0.0854710i	0.916197	−	0.400728i	$-0.131243\pi$
$467$	−331.109	−	862.570i	−0.0328092	−	0.0854710i	−0.949006	+	0.315257i	$0.897909\pi$
$468$	53602.3	−	53602.3i	5.29438	−	5.29438i
$469$	−4883.23	+	3461.30i	−0.480782	+	0.340785i
$470$	−11230.7	−	3203.48i	−1.10219	−	0.314394i
$471$	386.291	−	3675.31i	0.0377905	−	0.359553i
$472$	22218.3	+	8528.79i	2.16669	+	0.831715i
$473$	−241.302	+	4604.32i	−0.0234569	+	0.447584i
$474$	22368.6	+	38743.5i	2.16756	+	3.75432i
$475$	−1640.12	−	4027.23i	−0.158430	−	0.389015i
$476$	−615.775	+	1038.30i	−0.0592942	+	0.0999801i
$477$	−2931.42	−	5753.23i	−0.281385	−	0.552248i
$478$	−27856.1	+	22557.4i	−2.66550	+	2.15848i
$479$	18303.8	−	8149.36i	1.74597	−	0.777357i	0.753136	−	0.657864i	$-0.228540\pi$
$479$	18303.8	−	8149.36i	1.74597	−	0.777357i	0.992835	−	0.119492i	$-0.0381267\pi$
$480$	160.577	−	303.015i	0.0152694	−	0.0288139i
$481$	−3072.36	+	6900.62i	−0.291242	+	0.654140i
$482$	9497.09	+	9497.09i	0.897470	+	0.897470i
$483$	8326.36	+	22473.4i	0.784394	+	2.11714i
$484$	13875.4	−	4508.38i	1.30310	−	0.423401i
$485$	5788.87	+	1328.01i	0.541977	+	0.124333i
$486$	−317.207	+	285.614i	−0.0296066	+	0.0266579i
$487$	386.342	−	250.893i	0.0359483	−	0.0233451i	−0.526540	−	0.850150i	$-0.676511\pi$
$487$	386.342	−	250.893i	0.0359483	−	0.0233451i	0.562488	+	0.826805i	$0.309844\pi$
$488$	−877.216	−	16738.3i	−0.0813724	−	1.55268i
$489$	7992.39	−	24598.0i	0.739117	−	2.27477i
$490$	−1226.09	−	18763.8i	−0.113039	−	1.72992i
$491$	5284.71	+	16264.7i	0.485734	+	1.49494i	0.830914	+	0.556400i	$0.187818\pi$
$491$	5284.71	+	16264.7i	0.485734	+	1.49494i	−0.345180	+	0.938537i	$0.612182\pi$
$492$	4309.11	−	1654.11i	0.394857	−	0.151572i
$493$	191.940	+	716.329i	0.0175346	+	0.0654399i
$494$	−14794.9	+	1555.00i	−1.34747	+	0.141625i
$495$	−26598.1	−	10703.4i	−2.41514	−	0.971884i
$496$	5501.53	−	7572.20i	0.498036	−	0.685488i
$497$	8458.65	−	6687.32i	0.763425	−	0.603556i
$498$	18431.7	−	9391.43i	1.65852	−	0.845060i
$499$	786.343	−	453.996i	0.0705442	−	0.0407287i	−0.464313	−	0.885671i	$-0.653699\pi$
$499$	786.343	−	453.996i	0.0705442	−	0.0407287i	0.534857	+	0.844942i	$0.320365\pi$
$500$	−16724.5	−	14933.2i	−1.49588	−	1.33566i
$501$	18275.2	−	31653.6i	1.62969	−	2.82271i
$502$	−551.249	−	357.986i	−0.0490109	−	0.0318280i
$503$	−7814.08	+	1237.63i	−0.692669	+	0.109708i	−0.492836	−	0.870122i	$-0.664040\pi$
$503$	−7814.08	+	1237.63i	−0.692669	+	0.109708i	−0.199833	+	0.979830i	$0.564040\pi$
$504$	36337.9	−	15671.8i	3.21154	−	1.38507i
$505$	−4260.93	+	3338.54i	−0.375463	+	0.294184i
$506$	−30452.4	−	13558.3i	−2.67544	−	1.19118i
$507$	−47074.5	+	12613.6i	−4.12357	+	1.10491i
$508$	−20530.2	+	25352.6i	−1.79307	+	2.21425i
$509$	8305.86	−	9224.60i	0.723283	−	0.803287i	−0.263616	−	0.964628i	$-0.584915\pi$
$509$	8305.86	−	9224.60i	0.723283	−	0.803287i	0.986899	+	0.161341i	$0.0515818\pi$
$510$	−845.576	+	1819.93i	−0.0734171	+	0.158016i
$511$	2357.24	−	6976.00i	0.204067	−	0.603914i
$512$	18087.3	+	9215.92i	1.56123	+	0.795489i
$513$	8506.81	−	445.823i	0.732134	−	0.0383695i
$514$	−16277.4	−	18077.8i	−1.39682	−	1.55132i
$515$	8318.79	−	2555.94i	0.711786	−	0.218695i
$516$	−10463.7	−	9421.60i	−0.892715	−	0.803804i
$517$	9959.09	+	1577.37i	0.847196	+	0.134183i
$518$	−5626.40	+	5496.24i	−0.477239	+	0.466198i
$519$	8874.41	+	12214.6i	0.750565	+	1.03306i
$520$	−32584.3	+	20423.8i	−2.74791	+	1.72239i
$521$	5028.04	+	11293.2i	0.422807	+	0.949640i	0.991859	+	0.127339i	$0.0406436\pi$
$521$	5028.04	+	11293.2i	0.422807	+	0.949640i	−0.569052	+	0.822301i	$0.692690\pi$
$522$	17377.7	−	45270.6i	1.45709	−	3.79586i
$523$	5503.02	−	8473.90i	0.460096	−	0.708485i	−0.530137	−	0.847912i	$-0.677859\pi$
$523$	5503.02	−	8473.90i	0.460096	−	0.708485i	0.990232	+	0.139427i	$0.0445260\pi$
$524$	696.153			0.0580374
$525$	−3438.50	−	20572.8i	−0.285844	−	1.71023i
$526$	−11904.1			−0.986773
$527$	−318.432	+	490.342i	−0.0263209	+	0.0405306i
$528$	−9940.17	+	25895.0i	−0.819300	+	2.13435i
$529$	3441.61	+	7729.99i	0.282864	+	0.635324i
$530$	1589.43	+	6337.39i	0.130265	+	0.519394i
$531$	19216.4	+	26449.1i	1.57047	+	2.16157i
$532$	−9951.99	−	2791.84i	−0.811040	−	0.227522i
$533$	−2750.57	−	435.648i	−0.223528	−	0.0354034i
$534$	16116.6	+	14511.4i	1.30606	+	1.17598i
$535$	5346.29	−	7115.30i	0.432038	−	0.574993i
$536$	8528.96	+	9472.37i	0.687304	+	0.763328i
$537$	−7487.61	+	392.409i	−0.601703	+	0.0315339i
$538$	−1896.77	−	966.454i	−0.151999	−	0.0774476i
$539$	3002.92	+	15955.0i	0.239972	+	1.27501i
$540$	38386.2	−	21347.5i	3.05904	−	1.70121i
$541$	4186.00	−	4649.02i	0.332662	−	0.369459i	−0.553488	−	0.832857i	$-0.686703\pi$
$541$	4186.00	−	4649.02i	0.332662	−	0.369459i	0.886150	+	0.463398i	$0.153370\pi$
$542$	−7559.01	+	9334.60i	−0.599054	+	0.739770i
$543$	4002.92	−	1072.58i	0.316357	−	0.0847676i
$544$	12.6355	+	5.62568i	0.000995849	+	0.000443381i
$545$	57.6106	+	38.7426i	0.00452801	+	0.00304505i
$546$	−70875.1	−	8288.87i	−5.55527	−	0.649690i
$547$	−22813.7	+	3613.34i	−1.78326	+	0.282441i	−0.958925	−	0.283659i	$-0.908452\pi$
$547$	−22813.7	+	3613.34i	−1.78326	+	0.282441i	−0.824337	+	0.566100i	$0.808452\pi$
$548$	17022.9	+	11054.8i	1.32697	+	0.861747i
$549$	11512.6	−	19940.4i	0.894981	−	1.55015i
$550$	23810.8	+	16574.2i	1.84599	+	1.28496i
$551$	−5499.10	+	3174.91i	−0.425172	+	0.245473i
$552$	45474.2	−	23170.2i	3.50636	−	1.78658i
$553$	6925.32	−	17428.7i	0.532540	−	1.34022i
$554$	7871.40	−	10834.1i	0.603653	−	0.830857i
$555$	−5598.89	+	6691.33i	−0.428215	+	0.511768i
$556$	18612.5	−	1956.25i	1.41969	−	0.149215i
$557$	−331.872	−	1238.56i	−0.0252457	−	0.0942184i	0.952153	−	0.305620i	$-0.0988638\pi$
$557$	−331.872	−	1238.56i	−0.0252457	−	0.0942184i	−0.977399	+	0.211402i	$0.932197\pi$
$558$	35690.7	−	13700.4i	2.70772	−	1.03940i
$559$	2625.20	+	8079.54i	0.198630	+	0.611321i
$560$	−13245.8	+	2433.23i	−0.999533	+	0.183612i
$561$	535.415	−	1647.84i	0.0402945	−	0.124014i
$562$	−630.656	−	12033.6i	−0.0473357	−	0.903218i
$563$	10380.2	−	6741.01i	0.777043	−	0.504618i	−0.0941500	−	0.995558i	$-0.530013\pi$
$563$	10380.2	−	6741.01i	0.777043	−	0.504618i	0.871193	+	0.490940i	$0.163347\pi$
$564$	−22883.7	+	20604.5i	−1.70847	+	1.53831i
$565$	15680.7	+	17988.1i	1.16760	+	1.33941i
$566$	−34886.3	+	11335.3i	−2.59078	+	0.841795i
$567$	13573.7	+	2313.00i	1.00537	+	0.171317i
$568$	−16236.8	−	16236.8i	−1.19944	−	1.19944i
$569$	6587.47	−	14795.7i	0.485345	−	1.09010i	−0.490461	−	0.871463i	$-0.663172\pi$
$569$	6587.47	−	14795.7i	0.485345	−	1.09010i	0.975806	−	0.218639i	$-0.0701617\pi$
$570$	−16925.8	−	2960.26i	−1.24376	−	0.217529i
$571$	3596.99	−	1601.48i	0.263624	−	0.117373i	−0.270668	−	0.962673i	$-0.587245\pi$
$571$	3596.99	−	1601.48i	0.263624	−	0.117373i	0.534293	+	0.845300i	$0.320578\pi$
$572$	51467.9	−	41677.9i	3.76220	−	3.04657i
$573$	13972.5	+	27422.5i	1.01869	+	1.99929i
$574$	−2494.16	−	1479.18i	−0.181366	−	0.107561i
$575$	−4087.15	−	17481.9i	−0.296428	−	1.26790i
$576$	13642.9	+	23630.3i	0.986903	+	1.70937i
$577$	206.672	−	3943.53i	0.0149114	−	0.284526i	−0.980989	−	0.194065i	$-0.937833\pi$
$577$	206.672	−	3943.53i	0.0149114	−	0.284526i	0.995900	−	0.0904608i	$-0.0288340\pi$
$578$	22414.7	+	8604.21i	1.61303	+	0.619184i
$579$	−1379.08	+	13121.1i	−0.0989854	+	0.941784i
$580$	−18270.8	+	27168.8i	−1.30802	+	1.94504i
$581$	−7880.37	−	3619.64i	−0.562707	−	0.258465i
$582$	16595.0	−	16595.0i	1.18193	−	1.18193i
$583$	−2021.60	−	5266.45i	−0.143613	−	0.374124i
$584$	−15338.1	−	3260.21i	−1.08681	−	0.231008i
$585$	−52820.7	−	848.664i	−3.73311	−	0.0599794i
$586$	145.255	+	683.372i	0.0102396	+	0.0481738i
$587$	10221.7	−	20061.2i	0.718730	−	1.41059i	−0.185111	−	0.982718i	$-0.559264\pi$
$587$	10221.7	−	20061.2i	0.718730	−	1.41059i	0.903841	−	0.427869i	$-0.140736\pi$
$588$	−43637.3	−	23536.5i	−3.06050	−	1.65073i
$589$	−4761.09	−	1546.97i	−0.333069	−	0.108221i
$590$	−12968.1	−	30433.4i	−0.904893	−	2.12360i
$591$	−5194.00	+	24435.8i	−0.361510	+	1.70077i
$592$	4377.89	+	3545.14i	0.303936	+	0.246123i
$593$	5331.11	+	1428.47i	0.369178	+	0.0989209i	0.438638	−	0.898664i	$-0.355461\pi$
$593$	5331.11	+	1428.47i	0.369178	+	0.0989209i	−0.0694603	+	0.997585i	$0.522128\pi$
$594$	−45978.8	+	33405.6i	−3.17598	+	2.30749i
$595$	818.325	−	195.089i	0.0563833	−	0.0134418i
$596$	−21019.6	−	15271.7i	−1.44463	−	1.04958i
$597$	17708.9	+	21868.7i	1.21403	+	1.49920i
$598$	−61336.0	−	3214.48i	−4.19434	−	0.219816i
$599$	−6205.52	−	3582.76i	−0.423290	−	0.244387i	0.273194	−	0.961959i	$-0.411920\pi$
$599$	−6205.52	−	3582.76i	−0.423290	−	0.244387i	−0.696484	+	0.717572i	$0.745253\pi$
$600$	−42663.3	+	12361.7i	−2.90287	+	0.841110i
$601$			15331.0i			1.04054i	0.854002	+	0.520270i	$0.174169\pi$
$601$			15331.0i			1.04054i	−0.854002	+	0.520270i	$0.825831\pi$
$602$	−566.298	+	8827.81i	−0.0383399	+	0.597665i
$603$	2739.14	+	17294.2i	0.184985	+	1.16795i
$604$	36170.2	+	3801.65i	2.43667	+	0.256104i
$605$	−8983.69	−	4760.73i	−0.603701	−	0.319920i
$606$	2235.84	+	21272.6i	0.149876	+	1.42597i
$607$	−3394.70	+	12669.2i	−0.226996	+	0.847161i	0.754599	+	0.656186i	$0.227832\pi$
$607$	−3394.70	+	12669.2i	−0.226996	+	0.847161i	−0.981595	+	0.190975i	$0.938835\pi$
$608$	−18.5262	+	116.970i	−0.00123575	+	0.00780223i
$609$	−29075.9	+	9072.59i	−1.93467	+	0.603678i
$610$	−15865.9	+	17061.5i	−1.05310	+	1.13246i
$611$	18172.9	−	3862.76i	1.20327	−	0.255762i
$612$	1923.33	+	2961.67i	0.127036	+	0.195619i
$613$	6400.57	+	9856.02i	0.421724	+	0.649398i	0.984127	−	0.177465i	$-0.0567897\pi$
$613$	6400.57	+	9856.02i	0.421724	+	0.649398i	−0.562403	+	0.826863i	$0.690123\pi$
$614$	45895.5	−	9755.38i	3.01660	−	0.641197i
$615$	−2917.12	−	1355.35i	−0.191268	−	0.0888667i
$616$	33003.7	−	10298.2i	2.15870	−	0.673580i
$617$	−2743.15	+	17319.6i	−0.178987	+	1.13008i	0.720604	+	0.693347i	$0.243864\pi$
$617$	−2743.15	+	17319.6i	−0.178987	+	1.13008i	−0.899591	+	0.436733i	$0.856136\pi$
$618$	8900.34	−	33216.5i	0.579327	−	2.16208i
$619$	2471.96	+	23519.1i	0.160511	+	1.52716i	0.717452	+	0.696608i	$0.245308\pi$
$619$	2471.96	+	23519.1i	0.160511	+	1.52716i	−0.556940	+	0.830552i	$0.688025\pi$
$620$	−25556.2	+	3627.86i	−1.65542	+	0.234998i
$621$	34977.7	+	3676.30i	2.26024	+	0.237560i
$622$	2459.66	+	15529.7i	0.158558	+	1.00110i
$623$	582.010	−	9072.74i	0.0374282	−	0.583454i
$624$			51107.4i			3.27874i
$625$	631.981	+	15612.2i	0.0404468	+	0.999182i
$626$	−20604.8	−	11896.2i	−1.31555	−	0.759532i
$627$	14815.1	+	776.427i	0.943634	+	0.0494538i
$628$	4141.18	+	5113.94i	0.263139	+	0.324949i
$629$	−284.684	−	206.835i	−0.0180463	−	0.0131114i
$630$	−50787.1	−	21131.2i	−3.21176	−	1.33633i
$631$	20104.4	−	14606.7i	1.26837	−	0.921526i	0.269235	−	0.963074i	$-0.413229\pi$
$631$	20104.4	−	14606.7i	1.26837	−	0.921526i	0.999136	+	0.0415484i	$0.0132291\pi$
$632$	−38576.7	−	10336.6i	−2.42800	−	0.650581i
$633$	−16098.7	−	13036.5i	−1.01085	−	0.818567i
$634$	3684.53	−	17334.4i	0.230807	−	1.08586i
$635$	22645.1	−	2012.86i	1.41518	−	0.125792i
$636$	16384.2	+	5323.55i	1.02150	+	0.331906i
$637$	15700.8	+	25462.4i	0.976588	+	1.58376i
$638$	19233.0	−	37746.8i	1.19348	−	2.34234i
$639$	−6558.27	−	30854.2i	−0.406011	−	1.91013i
$640$	−8198.41	−	26683.3i	−0.506360	−	1.64805i
$641$	−19743.1	−	4196.52i	−1.21654	−	0.258584i	−0.445450	−	0.895307i	$-0.646956\pi$
$641$	−19743.1	−	4196.52i	−1.21654	−	0.258584i	−0.771093	+	0.636723i	$0.780290\pi$
$642$	−12603.2	−	32832.5i	−0.774782	−	2.01838i
$643$	−22074.7	+	22074.7i	−1.35387	+	1.35387i	−0.472593	+	0.881281i	$0.656682\pi$
$643$	−22074.7	+	22074.7i	−1.35387	+	1.35387i	−0.881281	+	0.472593i	$0.843318\pi$
$644$	−38779.8	−	17812.5i	−2.37289	−	1.08992i
$645$	356.057	+	9805.95i	0.0217360	+	0.598618i
$646$	72.4400	−	689.220i	0.00441194	−	0.0419768i
$647$	19851.7	+	7620.36i	1.20626	+	0.463041i	0.876674	−	0.481085i	$-0.159757\pi$
$647$	19851.7	+	7620.36i	1.20626	+	0.463041i	0.329588	+	0.944125i	$0.393090\pi$
$648$	1534.61	−	29282.1i	0.0930325	−	1.77517i
$649$	14281.0	+	24735.5i	0.863758	+	1.49607i
$650$	51902.7	+	12787.9i	3.13198	+	0.771664i
$651$	−20654.0	−	12249.1i	−1.24346	−	0.737448i
$652$	20908.1	+	41034.4i	1.25586	+	2.46477i
$653$	20424.8	−	16539.7i	1.22402	−	0.991193i	0.224159	−	0.974552i	$-0.428036\pi$
$653$	20424.8	−	16539.7i	1.22402	−	0.991193i	0.999862	−	0.0166401i	$-0.00529696\pi$
$654$	250.619	−	111.583i	0.0149847	−	0.00667161i
$655$	−337.490	−	348.512i	−0.0201326	−	0.0207901i
$656$	−844.735	+	1897.31i	−0.0502764	+	0.112923i
$657$	−15231.7	−	15231.7i	−0.904482	−	0.904482i
$658$	19070.7	+	3249.70i	1.12987	+	0.192533i
$659$	−72.2301	+	23.4690i	−0.00426963	+	0.00138729i	−0.311151	−	0.950360i	$-0.600715\pi$
$659$	−72.2301	+	23.4690i	−0.00426963	+	0.00138729i	0.306881	+	0.951748i	$0.400715\pi$
$660$	70371.8	−	29986.4i	4.15033	−	1.76851i
$661$	−17702.0	+	15938.9i	−1.04165	+	0.937902i	−0.998129	−	0.0611509i	$-0.980523\pi$
$661$	−17702.0	+	15938.9i	−1.04165	+	0.937902i	−0.0435170	+	0.999053i	$0.513856\pi$
$662$	12040.6	−	7819.28i	0.706907	−	0.459071i
$663$	−167.081	−	3188.10i	−0.00978717	−	0.186750i
$664$	−5706.63	+	17563.2i	−0.333525	+	1.02648i
$665$	3426.99	+	6335.69i	0.199839	+	0.369455i
$666$	7110.22	+	21883.0i	0.413687	+	1.27320i
$667$	−24475.3	+	9395.17i	−1.42082	+	0.545401i
$668$	16844.6	+	62865.0i	0.975656	+	3.64120i
$669$	−794.418	+	83.4967i	−0.0459103	+	0.00482536i
$670$	1211.39	−	17676.2i	0.0698511	−	1.01924i
$671$	11823.8	−	16274.0i	0.680256	−	0.936292i
$672$	−209.770	+	527.920i	−0.0120417	+	0.0303050i
$673$	−10492.9	+	5346.42i	−0.601000	+	0.306225i	−0.727892	−	0.685692i	$-0.759500\pi$
$673$	−10492.9	+	5346.42i	−0.601000	+	0.306225i	0.126892	+	0.991917i	$0.459500\pi$
$674$	485.880	−	280.523i	0.0277677	−	0.0160317i
$675$	−29296.5	−	8868.00i	−1.67055	−	0.505673i
$676$	43389.5	−	75152.8i	2.46868	−	4.27588i
$677$	−14073.5	−	9139.46i	−0.798951	−	0.518845i	0.0794101	−	0.996842i	$-0.474696\pi$
$677$	−14073.5	−	9139.46i	−0.798951	−	0.518845i	−0.878362	+	0.477997i	$0.841363\pi$
$678$	93134.7	−	14751.1i	5.27554	−	0.835564i
$679$	−9771.77	−	1142.81i	−0.552292	−	0.0645907i
$680$	−615.058	−	1682.59i	−0.0346859	−	0.0948887i
$681$	−1504.53	−	669.862i	−0.0846606	−	0.0376933i
$682$	32261.3	−	8644.39i	1.81136	−	0.485353i
$683$	−1630.99	+	2014.10i	−0.0913733	+	0.112837i	−0.820782	−	0.571242i	$-0.806462\pi$
$683$	−1630.99	+	2014.10i	−0.0913733	+	0.112837i	0.729409	+	0.684078i	$0.239795\pi$
$684$	−20232.5	+	22470.4i	−1.13101	+	1.25611i
$685$	−2718.27	−	13881.4i	−0.151620	−	0.774278i
$686$	5402.80	+	30676.4i	0.300699	+	1.70733i
$687$	−375.971	−	191.567i	−0.0208794	−	0.0106386i
$688$	6326.87	−	331.577i	0.350595	−	0.0183739i
$689$	−6954.99	−	7724.29i	−0.384563	−	0.427100i
$690$	−67109.4	−	23003.5i	−3.70262	−	1.26917i
$691$	−6612.29	−	5953.74i	−0.364028	−	0.327773i	0.466736	−	0.884397i	$-0.345430\pi$
$691$	−6612.29	−	5953.74i	−0.364028	−	0.327773i	−0.830765	+	0.556624i	$0.812096\pi$
$692$	−26553.0	−	4205.58i	−1.45866	−	0.231029i
$693$	45728.1	+	12828.2i	2.50659	+	0.703177i
$694$	22209.2	+	30568.4i	1.21477	+	1.67199i
$695$	−10002.6	−	8369.52i	−0.545926	−	0.456797i
$696$	26381.8	+	59254.5i	1.43678	+	3.22707i
$697$	46.4922	−	121.116i	0.00252656	−	0.00658193i
$698$	−16689.6	+	25699.8i	−0.905032	+	1.39363i
$699$	13905.0			0.752411
$700$	30232.5	+	21573.7i	1.63240	+	1.16487i
$701$	−8579.73			−0.462271			−0.231135	−	0.972922i	$-0.574244\pi$
$701$	−8579.73			−0.462271			−0.231135	+	0.972922i	$0.574244\pi$
$702$	−57033.3	+	87823.5i	−3.06636	+	4.72177i
$703$	1079.76	−	2812.87i	0.0579288	−	0.150910i
$704$	9695.86	+	21777.3i	0.519072	+	1.16585i
$705$	21409.0	+	1467.21i	1.14370	+	0.0783806i
$706$	−22304.0	−	30698.8i	−1.18898	−	1.63649i
$707$	6414.22	−	6265.84i	0.341205	−	0.333311i
$708$	−86151.2	−	13645.0i	−4.57311	−	0.724309i
$709$	10222.4	+	9204.30i	0.541482	+	0.487552i	0.893885	−	0.448296i	$-0.147969\pi$
$709$	10222.4	+	9204.30i	0.541482	+	0.487552i	−0.352404	+	0.935848i	$0.614636\pi$
$710$	−512.757	+	31913.9i	−0.0271034	+	1.68691i
$711$	−36710.3	−	40770.9i	−1.93635	−	2.15053i
$712$	−19333.8	+	1013.24i	−1.01765	+	0.0533326i
$713$	−18416.0	−	9383.43i	−0.967300	−	0.492864i
$714$	1064.17	−	3149.30i	0.0557780	−	0.165069i
$715$	−45816.3	−	5561.00i	−2.39641	−	0.290867i
$716$	8933.52	−	9921.68i	0.466287	−	0.517864i
$717$	41448.9	−	51185.1i	2.15891	−	2.66603i
$718$	32467.2	−	8699.56i	1.68756	−	0.452179i
$719$	−33022.8	−	14702.7i	−1.71286	−	0.762613i	−0.997991	−	0.0633499i	$-0.979822\pi$
$719$	−33022.8	−	14702.7i	−1.71286	−	0.762613i	−0.714865	−	0.699263i	$-0.753512\pi$
$720$	−10806.7	+	37886.0i	−0.559366	+	1.96101i
$721$	−13237.3	+	5708.96i	−0.683746	+	0.294886i
$722$	−27357.5	+	4333.01i	−1.41017	+	0.223349i
$723$	−20697.6	−	13441.2i	−1.06466	−	0.691401i
$724$	−3689.58	+	6390.53i	−0.189395	+	0.328042i
$725$	22458.9	−	4024.42i	1.15049	−	0.206156i
$726$	−34793.0	+	20087.8i	−1.77864	+	1.02690i
$727$	−26031.9	+	13263.9i	−1.32802	+	0.676658i	−0.966731	−	0.255797i	$-0.917662\pi$
$727$	−26031.9	+	13263.9i	−1.32802	+	0.676658i	−0.361286	+	0.932455i	$0.617662\pi$
$728$	49971.9	−	39507.3i	2.54407	−	2.01131i
$729$	−11338.1	+	15605.6i	−0.576036	+	0.792845i
$730$	11576.1	+	18468.5i	0.586919	+	0.936372i
$731$	−393.588	+	41.3678i	−0.0199144	+	0.00209308i
$732$	15899.6	+	59338.1i	0.802822	+	2.99617i
$733$	25736.0	−	9879.11i	1.29683	−	0.497808i	0.390591	−	0.920565i	$-0.372271\pi$
$733$	25736.0	−	9879.11i	1.29683	−	0.497808i	0.906243	+	0.422757i	$0.138938\pi$
$734$	−17944.1	−	55226.2i	−0.902354	−	2.77716i
$735$	9372.11	+	33256.3i	0.470334	+	1.66895i
$736$	−151.095	+	465.024i	−0.00756718	+	0.0232894i
$737$	800.601	+	15276.4i	0.0400143	+	0.763518i
$738$	−7114.38	+	4620.13i	−0.354856	+	0.230446i
$739$	−21443.0	+	19307.3i	−1.06738	+	0.961072i	−0.999330	−	0.0366105i	$-0.988344\pi$
$739$	−21443.0	+	19307.3i	−1.06738	+	0.961072i	−0.0680485	+	0.997682i	$0.521677\pi$
$740$	−1375.49	−	15474.5i	−0.0683297	−	0.768723i
$741$	25997.2	−	8446.99i	1.28884	−	0.418769i
$742$	−3760.13	−	10148.9i	−0.186036	−	0.502125i
$743$	−14244.0	−	14244.0i	−0.703314	−	0.703314i	0.261806	−	0.965120i	$-0.415682\pi$
$743$	−14244.0	−	14244.0i	−0.703314	−	0.703314i	−0.965120	+	0.261806i	$0.915682\pi$
$744$	−20799.1	+	46715.5i	−1.02491	+	2.30198i
$745$	2544.79	+	17926.6i	0.125146	+	0.881582i
$746$	−37772.3	+	16817.3i	−1.85381	+	0.825370i
$747$	−19715.0	+	15964.9i	−0.965640	+	0.781960i
$748$	1400.64	+	2748.92i	0.0684661	+	0.134372i
$749$	−7520.35	+	12680.6i	−0.366872	+	0.618610i
$750$	53598.4	+	30648.2i	2.60951	+	1.49215i
$751$	−16788.6	−	29078.6i	−0.815743	−	1.41291i	−0.908793	−	0.417247i	$-0.862995\pi$
$751$	−16788.6	−	29078.6i	−0.815743	−	1.41291i	0.0930502	−	0.995661i	$-0.470338\pi$
$752$	725.142	−	13836.5i	0.0351638	−	0.670966i
$753$	1127.54	+	432.822i	0.0545681	+	0.0209467i
$754$	8159.30	−	77630.5i	0.394090	−	3.74952i
$755$	−15631.9	−	19950.8i	−0.753513	−	0.961699i
$756$	−59359.2	+	42074.6i	−2.85565	+	2.02412i
$757$	18598.1	−	18598.1i	0.892946	−	0.892946i	−0.101853	−	0.994799i	$-0.532477\pi$
$757$	18598.1	−	18598.1i	0.892946	−	0.892946i	0.994799	+	0.101853i	$0.0324772\pi$
$758$	−5408.00	−	14088.3i	−0.259139	−	0.675081i
$759$	59912.8	+	12734.8i	2.86521	+	0.609019i
$760$	12553.0	−	8815.67i	0.599137	−	0.420760i
$761$	8495.29	+	39967.2i	0.404670	+	1.90382i	0.427362	+	0.904081i	$0.359443\pi$
$761$	8495.29	+	39967.2i	0.404670	+	1.90382i	−0.0226918	+	0.999743i	$0.507224\pi$
$762$	40784.1	−	80043.3i	1.93891	−	3.80533i
$763$	−101.852	−	53.4063i	−0.00483260	−	0.00253400i
$764$	−52120.1	−	16934.9i	−2.46811	−	0.801939i
$765$	550.271	−	2398.67i	0.0260067	−	0.113365i
$766$	9676.96	−	45526.5i	0.456453	−	2.14744i
$767$	40898.8	+	33119.2i	1.92539	+	1.55915i
$768$	−71480.7

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	175.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(2.67058 - 4.11233i) q^{2} +(-3.22886 + 8.41147i) q^{3} +(-6.52539 - 14.6563i) q^{4} +(-4.17384 + 10.3720i) q^{5} +(25.9678 + 35.7416i) q^{6} +(5.00240 - 17.8319i) q^{7} +(-38.9538 - 6.16967i) q^{8} +(-40.2623 - 36.2524i) q^{9} +(31.5067 + 44.8636i) q^{10} +(-31.6717 - 35.1750i) q^{11} +(144.350 - 7.56508i) q^{12} +(-77.7071 - 39.5937i) q^{13} +(-59.9713 - 68.1930i) q^{14} +(-73.7673 - 68.5980i) q^{15} +(-43.5206 + 48.3345i) q^{16} +(2.55681 - 3.15740i) q^{17} +(-256.606 + 68.7573i) q^{18} +(31.7797 + 14.1492i) q^{19} +(179.251 - 6.50867i) q^{20} +(133.840 + 99.6542i) q^{21} +(-229.233 + 36.3070i) q^{22} +(120.455 + 78.2245i) q^{23} +(177.672 - 307.738i) q^{24} +(-90.1581 - 86.5824i) q^{25} +(-370.346 + 213.819i) q^{26} +(218.184 - 111.171i) q^{27} +(-293.991 + 43.0435i) q^{28} +(-107.290 + 147.672i) q^{29} +(-479.099 + 120.159i) q^{30} +(-143.118 + 15.0423i) q^{31} +(0.881111 + 3.28835i) q^{32} +(398.137 - 152.830i) q^{33} +(-6.15611 - 18.9466i) q^{34} +(164.074 + 126.312i) q^{35} +(-268.597 + 826.656i) q^{36} +(-4.53293 - 86.4934i) q^{37} +(143.057 - 92.9020i) q^{38} +(583.947 - 525.788i) q^{39} +(226.579 - 378.279i) q^{40} +(30.3689 - 9.86746i) q^{41} +(767.242 - 284.261i) q^{42} +(-68.8788 - 68.8788i) q^{43} +(-308.864 + 693.720i) q^{44} +(544.059 - 266.291i) q^{45} +(643.370 - 286.447i) q^{46} +(-165.555 + 134.064i) q^{47} +(-266.042 - 522.137i) q^{48} +(-292.952 - 178.404i) q^{49} +(-596.830 + 139.535i) q^{50} +(18.3028 + 31.7014i) q^{51} +(-73.2273 + 1397.26i) q^{52} +(111.265 + 42.7105i) q^{53} +(125.509 - 1194.14i) q^{54} +(497.029 - 181.685i) q^{55} +(-304.879 + 663.756i) q^{56} +(-221.628 + 221.628i) q^{57} +(320.751 + 835.584i) q^{58} +(-590.246 - 125.461i) q^{59} +(-524.029 + 1528.78i) q^{60} +(88.3600 + 415.701i) q^{61} +(-320.350 + 628.722i) q^{62} +(-847.856 + 536.605i) q^{63} +(-478.982 - 155.631i) q^{64} +(735.005 - 640.723i) q^{65} +(434.767 - 2045.42i) q^{66} +(-251.164 - 203.389i) q^{67} +(-62.9599 - 16.8701i) q^{68} +(-1046.92 + 760.629i) q^{69} +(957.611 - 337.398i) q^{70} +(471.023 + 342.218i) q^{71} +(1344.71 + 1660.57i) q^{72} +(397.047 + 20.8084i) q^{73} +(-367.795 - 212.347i) q^{74} +(1019.39 - 478.800i) q^{75} -558.101i q^{76} +(-785.671 + 388.807i) q^{77} +(-602.739 - 3805.54i) q^{78} +(1007.08 + 105.849i) q^{79} +(-319.679 - 653.137i) q^{80} +(77.7145 + 739.404i) q^{81} +(40.5244 - 151.239i) q^{82} +(73.2488 - 462.475i) q^{83} +(587.198 - 2611.88i) q^{84} +(22.0770 + 39.6978i) q^{85} +(-467.199 + 99.3062i) q^{86} +(-895.716 - 1379.28i) q^{87} +(1016.72 + 1565.60i) q^{88} +(480.162 - 102.061i) q^{89} +(357.878 - 2948.50i) q^{90} +(-1094.75 + 1187.60i) q^{91} +(360.462 - 2275.87i) q^{92} +(335.581 - 1252.40i) q^{93} +(109.187 + 1038.84i) q^{94} +(-279.400 + 270.563i) q^{95} +(-30.5049 - 3.20619i) q^{96} +(-83.1014 - 524.682i) q^{97} +(-1516.01 + 728.273i) q^{98} +2564.40i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 928 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 24 q^{7} + 84 q^{8} - 10 q^{9} - 96 q^{10} - 6 q^{11} - 72 q^{12} - 20 q^{14} - 368 q^{15} - 1670 q^{16} + 120 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} - 880 q^{22}+ \cdots - 19478 q^{98}+O(q^{100}) \) 928 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 24 * q^7 + 84 * q^8 - 10 * q^9 - 96 * q^10 - 6 * q^11 - 72 * q^12 - 20 * q^14 - 368 * q^15 - 1670 * q^16 + 120 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 - 880 * q^22 + 296 * q^23 + 32 * q^25 - 48 * q^26 + 226 * q^28 - 200 * q^29 - 38 * q^30 - 18 * q^31 - 964 * q^32 - 1092 * q^33 + 288 * q^35 + 7400 * q^36 - 392 * q^37 + 5424 * q^38 + 2430 * q^39 + 2172 * q^40 - 2098 * q^42 + 1560 * q^43 - 10 * q^44 - 4224 * q^45 - 6 * q^46 + 96 * q^47 + 6232 * q^50 - 16 * q^51 - 8928 * q^52 - 2384 * q^53 - 30 * q^54 + 244 * q^56 + 1556 * q^57 + 640 * q^58 + 4890 * q^59 + 3676 * q^60 - 18 * q^61 + 224 * q^63 - 9700 * q^64 - 1116 * q^65 - 2610 * q^66 - 2404 * q^67 - 13614 * q^68 - 1700 * q^70 - 24 * q^71 - 518 * q^72 - 4200 * q^73 - 16104 * q^75 - 722 * q^77 - 356 * q^78 - 10 * q^79 + 6414 * q^80 - 6810 * q^81 + 1692 * q^82 + 20620 * q^84 + 2712 * q^85 - 6 * q^86 + 9102 * q^87 + 1650 * q^88 + 20370 * q^89 - 12 * q^91 + 1612 * q^92 - 4604 * q^93 - 30 * q^94 + 1652 * q^95 - 2610 * q^96 - 19478 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more