LMFDB - Embedded newform 60.5.f.a.19.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,5,Mod(19,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("60.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	60.f (of order $2$, degree $1$, 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:	$6.20219778503$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.19
Character	$\chi$	$=$	60.19
Dual form			60.5.f.a.19.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.44337 - 2.03548i) q^{2} -5.19615 q^{3} +(7.71364 - 14.0178i) q^{4} +(-20.5121 - 14.2918i) q^{5} +(-17.8923 + 10.5767i) q^{6} -51.0440 q^{7} +(-1.97210 - 63.9696i) q^{8} +27.0000 q^{9} +O(q^{10})$	\(q+(3.44337 - 2.03548i) q^{2} -5.19615 q^{3} +(7.71364 - 14.0178i) q^{4} +(-20.5121 - 14.2918i) q^{5} +(-17.8923 + 10.5767i) q^{6} -51.0440 q^{7} +(-1.97210 - 63.9696i) q^{8} +27.0000 q^{9} +(-99.7214 - 7.45996i) q^{10} +37.8608i q^{11} +(-40.0812 + 72.8388i) q^{12} -201.199i q^{13} +(-175.763 + 103.899i) q^{14} +(106.584 + 74.2622i) q^{15} +(-137.000 - 216.257i) q^{16} -370.875i q^{17} +(92.9711 - 54.9580i) q^{18} +474.940i q^{19} +(-358.562 + 177.293i) q^{20} +265.232 q^{21} +(77.0650 + 130.369i) q^{22} +386.396 q^{23} +(10.2473 + 332.396i) q^{24} +(216.491 + 586.308i) q^{25} +(-409.538 - 692.805i) q^{26} -140.296 q^{27} +(-393.735 + 715.526i) q^{28} +1164.83 q^{29} +(518.167 + 38.7631i) q^{30} -1459.12i q^{31} +(-911.928 - 465.794i) q^{32} -196.731i q^{33} +(-754.909 - 1277.06i) q^{34} +(1047.02 + 729.508i) q^{35} +(208.268 - 378.482i) q^{36} -609.708i q^{37} +(966.731 + 1635.40i) q^{38} +1045.46i q^{39} +(-873.787 + 1340.33i) q^{40} +731.186 q^{41} +(913.293 - 539.875i) q^{42} -1825.96 q^{43} +(530.727 + 292.045i) q^{44} +(-553.826 - 385.878i) q^{45} +(1330.50 - 786.501i) q^{46} +1394.19 q^{47} +(711.871 + 1123.70i) q^{48} +204.486 q^{49} +(1938.88 + 1578.21i) q^{50} +1927.12i q^{51} +(-2820.38 - 1551.98i) q^{52} +3052.05i q^{53} +(-483.092 + 285.570i) q^{54} +(541.098 - 776.605i) q^{55} +(100.664 + 3265.26i) q^{56} -2467.86i q^{57} +(4010.95 - 2370.99i) q^{58} -2232.89i q^{59} +(1863.15 - 921.244i) q^{60} -5509.38 q^{61} +(-2970.00 - 5024.28i) q^{62} -1378.19 q^{63} +(-4088.22 + 252.309i) q^{64} +(-2875.50 + 4127.02i) q^{65} +(-400.442 - 677.417i) q^{66} -5332.45 q^{67} +(-5198.86 - 2860.80i) q^{68} -2007.77 q^{69} +(5090.17 + 380.786i) q^{70} -5691.93i q^{71} +(-53.2467 - 1727.18i) q^{72} -4464.89i q^{73} +(-1241.05 - 2099.45i) q^{74} +(-1124.92 - 3046.54i) q^{75} +(6657.63 + 3663.52i) q^{76} -1932.57i q^{77} +(2128.02 + 3599.92i) q^{78} +3141.04i q^{79} +(-280.550 + 6393.85i) q^{80} +729.000 q^{81} +(2517.75 - 1488.31i) q^{82} +6107.15 q^{83} +(2045.91 - 3717.98i) q^{84} +(-5300.46 + 7607.42i) q^{85} +(-6287.46 + 3716.71i) q^{86} -6052.64 q^{87} +(2421.94 - 74.6654i) q^{88} +9513.18 q^{89} +(-2692.48 - 201.419i) q^{90} +10270.0i q^{91} +(2980.52 - 5416.43i) q^{92} +7581.79i q^{93} +(4800.72 - 2837.85i) q^{94} +(6787.73 - 9742.01i) q^{95} +(4738.52 + 2420.34i) q^{96} -3487.02i q^{97} +(704.121 - 416.227i) q^{98} +1022.24i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 14 q^{4} - 24 q^{5} - 18 q^{6} + 648 q^{9}+O(q^{10}) $ 24 * q + 14 * q^4 - 24 * q^5 - 18 * q^6 + 648 * q^9	$ 24 q + 14 q^{4} - 24 q^{5} - 18 q^{6} + 648 q^{9} + 274 q^{10} - 36 q^{14} + 594 q^{16} - 12 q^{20} - 594 q^{24} + 1208 q^{25} - 2868 q^{26} - 1680 q^{29} + 468 q^{30} + 3076 q^{34} + 378 q^{36} - 7222 q^{40} - 4848 q^{41} - 3828 q^{44} - 648 q^{45} - 15280 q^{46} + 5416 q^{49} + 14472 q^{50} - 486 q^{54} + 32172 q^{56} - 7506 q^{60} + 2896 q^{61} - 18298 q^{64} - 2688 q^{65} - 15588 q^{66} + 9792 q^{69} + 27608 q^{70} + 31836 q^{74} + 50136 q^{76} - 27348 q^{80} + 17496 q^{81} - 4284 q^{84} - 15680 q^{85} - 58152 q^{86} - 38544 q^{89} + 7398 q^{90} + 4808 q^{94} + 21978 q^{96}+O(q^{100}) $ 24 * q + 14 * q^4 - 24 * q^5 - 18 * q^6 + 648 * q^9 + 274 * q^10 - 36 * q^14 + 594 * q^16 - 12 * q^20 - 594 * q^24 + 1208 * q^25 - 2868 * q^26 - 1680 * q^29 + 468 * q^30 + 3076 * q^34 + 378 * q^36 - 7222 * q^40 - 4848 * q^41 - 3828 * q^44 - 648 * q^45 - 15280 * q^46 + 5416 * q^49 + 14472 * q^50 - 486 * q^54 + 32172 * q^56 - 7506 * q^60 + 2896 * q^61 - 18298 * q^64 - 2688 * q^65 - 15588 * q^66 + 9792 * q^69 + 27608 * q^70 + 31836 * q^74 + 50136 * q^76 - 27348 * q^80 + 17496 * q^81 - 4284 * q^84 - 15680 * q^85 - 58152 * q^86 - 38544 * q^89 + 7398 * q^90 + 4808 * q^94 + 21978 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	3.44337	−	2.03548i	0.860843	−	0.508870i
$2$	3.44337	−	2.03548i	0.860843	−	0.508870i
$3$	−5.19615			−0.577350
$3$	−5.19615			−0.577350
$4$	7.71364	−	14.0178i	0.482102	−	0.876115i
$5$	−20.5121	−	14.2918i	−0.820483	−	0.571671i
$5$	−20.5121	−	14.2918i	−0.820483	−	0.571671i
$6$	−17.8923	+	10.5767i	−0.497008	+	0.293796i
$7$	−51.0440			−1.04171			−0.520857	−	0.853644i	$-0.674387\pi$
$7$	−51.0440			−1.04171			−0.520857	+	0.853644i	$0.674387\pi$
$8$	−1.97210	−	63.9696i	−0.0308141	−	0.999525i
$9$	27.0000			0.333333
$10$	−99.7214	−	7.45996i	−0.997214	−	0.0745996i
$11$			37.8608i			0.312900i	0.987686	+	0.156450i	$0.0500049\pi$
$11$			37.8608i			0.312900i	−0.987686	+	0.156450i	$0.949995\pi$
$12$	−40.0812	+	72.8388i	−0.278342	+	0.505825i
$13$		−	201.199i		−	1.19053i	−0.803530	−	0.595265i	$-0.797047\pi$
$13$		−	201.199i		−	1.19053i	0.803530	−	0.595265i	$-0.202953\pi$
$14$	−175.763	+	103.899i	−0.896752	+	0.530097i
$15$	106.584	+	74.2622i	0.473706	+	0.330054i
$16$	−137.000	−	216.257i	−0.535155	−	0.844754i
$17$		−	370.875i		−	1.28330i	−0.766996	−	0.641652i	$-0.778249\pi$
$17$		−	370.875i		−	1.28330i	0.766996	−	0.641652i	$-0.221751\pi$
$18$	92.9711	−	54.9580i	0.286948	−	0.169623i
$19$			474.940i			1.31562i	0.753183	+	0.657812i	$0.228518\pi$
$19$			474.940i			1.31562i	−0.753183	+	0.657812i	$0.771482\pi$
$20$	−358.562	+	177.293i	−0.896406	+	0.443234i
$21$	265.232			0.601434
$22$	77.0650	+	130.369i	0.159225	+	0.269357i
$23$	386.396			0.730426			0.365213	−	0.930924i	$-0.380996\pi$
$23$	386.396			0.730426			0.365213	+	0.930924i	$0.380996\pi$
$24$	10.2473	+	332.396i	0.0177905	+	0.577076i
$25$	216.491	+	586.308i	0.346385	+	0.938092i
$26$	−409.538	−	692.805i	−0.605825	−	1.02486i
$27$	−140.296			−0.192450
$28$	−393.735	+	715.526i	−0.502213	+	0.912661i
$29$	1164.83			1.38505			0.692527	−	0.721392i	$-0.256497\pi$
$29$	1164.83			1.38505			0.692527	+	0.721392i	$0.256497\pi$
$30$	518.167	+	38.7631i	0.575742	+	0.0430701i
$31$		−	1459.12i		−	1.51833i	−0.650898	−	0.759166i	$-0.725607\pi$
$31$		−	1459.12i		−	1.51833i	0.650898	−	0.759166i	$-0.274393\pi$
$32$	−911.928	−	465.794i	−0.890554	−	0.454877i
$33$		−	196.731i		−	0.180653i
$34$	−754.909	−	1277.06i	−0.653035	−	1.10472i
$35$	1047.02	+	729.508i	0.854708	+	0.595517i
$36$	208.268	−	378.482i	0.160701	−	0.292038i
$37$		−	609.708i		−	0.445368i	−0.974891	−	0.222684i	$-0.928518\pi$
$37$		−	609.708i		−	0.445368i	0.974891	−	0.222684i	$-0.0714817\pi$
$38$	966.731	+	1635.40i	0.669481	+	1.13255i
$39$			1045.46i			0.687353i
$40$	−873.787	+	1340.33i	−0.546117	+	0.837709i
$41$	731.186			0.434971			0.217485	−	0.976064i	$-0.430215\pi$
$41$	731.186			0.434971			0.217485	+	0.976064i	$0.430215\pi$
$42$	913.293	−	539.875i	0.517740	−	0.306052i
$43$	−1825.96			−0.987539			−0.493770	−	0.869593i	$-0.664381\pi$
$43$	−1825.96			−0.987539			−0.493770	+	0.869593i	$0.664381\pi$
$44$	530.727	+	292.045i	0.274136	+	0.150850i
$45$	−553.826	−	385.878i	−0.273494	−	0.190557i
$46$	1330.50	−	786.501i	0.628783	−	0.371692i
$47$	1394.19			0.631141			0.315570	−	0.948902i	$-0.397804\pi$
$47$	1394.19			0.631141			0.315570	+	0.948902i	$0.397804\pi$
$48$	711.871	+	1123.70i	0.308972	+	0.487719i
$49$	204.486			0.0851670
$50$	1938.88	+	1578.21i	0.775550	+	0.631286i
$51$			1927.12i			0.740916i
$52$	−2820.38	−	1551.98i	−1.04304	−	0.573957i
$53$			3052.05i			1.08653i	0.839562	+	0.543263i	$0.182811\pi$
$53$			3052.05i			1.08653i	−0.839562	+	0.543263i	$0.817189\pi$
$54$	−483.092	+	285.570i	−0.165669	+	0.0979321i
$55$	541.098	−	776.605i	0.178876	−	0.256729i
$56$	100.664	+	3265.26i	0.0320994	+	1.04122i
$57$		−	2467.86i		−	0.759575i
$58$	4010.95	−	2370.99i	1.19231	−	0.704813i
$59$		−	2232.89i		−	0.641451i	−0.947172	−	0.320725i	$-0.896073\pi$
$59$		−	2232.89i		−	0.641451i	0.947172	−	0.320725i	$-0.103927\pi$
$60$	1863.15	−	921.244i	0.517540	−	0.255901i
$61$	−5509.38			−1.48062			−0.740309	−	0.672267i	$-0.765321\pi$
$61$	−5509.38			−1.48062			−0.740309	+	0.672267i	$0.765321\pi$
$62$	−2970.00	−	5024.28i	−0.772633	−	1.30705i
$63$	−1378.19			−0.347238
$64$	−4088.22	+	252.309i	−0.998101	+	0.0615989i
$65$	−2875.50	+	4127.02i	−0.680591	+	0.976809i
$66$	−400.442	−	677.417i	−0.0919287	−	0.155514i
$67$	−5332.45			−1.18789			−0.593946	−	0.804505i	$-0.702431\pi$
$67$	−5332.45			−1.18789			−0.593946	+	0.804505i	$0.702431\pi$
$68$	−5198.86	−	2860.80i	−1.12432	−	0.618684i
$69$	−2007.77			−0.421712
$70$	5090.17	+	380.786i	1.03881	+	0.0777114i
$71$		−	5691.93i		−	1.12913i	−0.825390	−	0.564563i	$-0.809045\pi$
$71$		−	5691.93i		−	1.12913i	0.825390	−	0.564563i	$-0.190955\pi$
$72$	−53.2467	−	1727.18i	−0.0102714	−	0.333175i
$73$		−	4464.89i		−	0.837848i	−0.908021	−	0.418924i	$-0.862407\pi$
$73$		−	4464.89i		−	0.837848i	0.908021	−	0.418924i	$-0.137593\pi$
$74$	−1241.05	−	2099.45i	−0.226634	−	0.383392i
$75$	−1124.92	−	3046.54i	−0.199986	−	0.541608i
$76$	6657.63	+	3663.52i	1.15264	+	0.634265i
$77$		−	1932.57i		−	0.325952i
$78$	2128.02	+	3599.92i	0.349773	+	0.591703i
$79$			3141.04i			0.503292i	0.967819	+	0.251646i	$0.0809718\pi$
$79$			3141.04i			0.503292i	−0.967819	+	0.251646i	$0.919028\pi$
$80$	−280.550	+	6393.85i	−0.0438360	+	0.999039i
$81$	729.000			0.111111
$82$	2517.75	−	1488.31i	0.374442	−	0.221344i
$83$	6107.15			0.886507			0.443254	−	0.896396i	$-0.353824\pi$
$83$	6107.15			0.886507			0.443254	+	0.896396i	$0.353824\pi$
$84$	2045.91	−	3717.98i	0.289953	−	0.526925i
$85$	−5300.46	+	7607.42i	−0.733628	+	1.05293i
$86$	−6287.46	+	3716.71i	−0.850117	+	0.502529i
$87$	−6052.64			−0.799661
$88$	2421.94	−	74.6654i	0.312751	−	0.00964171i
$89$	9513.18			1.20101			0.600504	−	0.799622i	$-0.294967\pi$
$89$	9513.18			1.20101			0.600504	+	0.799622i	$0.294967\pi$
$90$	−2692.48	−	201.419i	−0.332405	−	0.0248665i
$91$			10270.0i			1.24019i
$92$	2980.52	−	5416.43i	0.352140	−	0.639937i
$93$			7581.79i			0.876609i
$94$	4800.72	−	2837.85i	0.543313	−	0.321169i
$95$	6787.73	−	9742.01i	0.752103	−	1.07945i
$96$	4738.52	+	2420.34i	0.514162	+	0.262623i
$97$		−	3487.02i		−	0.370605i	−0.982682	−	0.185302i	$-0.940674\pi$
$97$		−	3487.02i		−	0.370605i	0.982682	−	0.185302i	$-0.0593264\pi$
$98$	704.121	−	416.227i	0.0733154	−	0.0433389i
$99$			1022.24i			0.104300i
$100$	9888.70	+	1487.83i	0.988870	+	0.148783i
$101$	−9548.01			−0.935987			−0.467994	−	0.883732i	$-0.655023\pi$
$101$	−9548.01			−0.935987			−0.467994	+	0.883732i	$0.655023\pi$
$102$	3922.62	+	6635.80i	0.377030	+	0.637813i
$103$	5516.29			0.519963			0.259981	−	0.965614i	$-0.416284\pi$
$103$	5516.29			0.519963			0.259981	+	0.965614i	$0.416284\pi$
$104$	−12870.7	+	396.786i	−1.18996	+	0.0366851i
$105$	−5440.46	−	3790.64i	−0.493466	−	0.343822i
$106$	6212.39	+	10509.4i	0.552901	+	0.935329i
$107$	−2923.03			−0.255309			−0.127654	−	0.991819i	$-0.540745\pi$
$107$	−2923.03			−0.255309			−0.127654	+	0.991819i	$0.540745\pi$
$108$	−1082.19	+	1966.65i	−0.0927806	+	0.168608i
$109$	21658.4			1.82294			0.911471	−	0.411364i	$-0.134947\pi$
$109$	21658.4			1.82294			0.911471	+	0.411364i	$0.134947\pi$
$110$	282.440	−	3775.53i	0.0233422	−	0.312028i
$111$			3168.14i			0.257133i
$112$	6993.00	+	11038.6i	0.557478	+	0.879992i
$113$			14588.6i			1.14250i	0.820775	+	0.571252i	$0.193542\pi$
$113$			14588.6i			1.14250i	−0.820775	+	0.571252i	$0.806458\pi$
$114$	−5023.28	−	8497.76i	−0.386525	−	0.653875i
$115$	−7925.77	−	5522.28i	−0.599302	−	0.417563i
$116$	8985.08	−	16328.4i	0.667738	−	1.21347i
$117$		−	5432.39i		−	0.396843i
$118$	−4545.00	−	7688.67i	−0.326415	−	0.552189i
$119$			18930.9i			1.33684i
$120$	4540.33	−	6964.58i	0.315301	−	0.483652i
$121$	13207.6			0.902094
$122$	−18970.9	+	11214.2i	−1.27458	+	0.753442i
$123$	−3799.35			−0.251131
$124$	−20453.7	−	11255.1i	−1.33023	−	0.731991i
$125$	3938.70	−	15120.4i	0.252077	−	0.967707i
$126$	−4745.61	+	2805.27i	−0.298917	+	0.176699i
$127$	22165.2			1.37425			0.687123	−	0.726541i	$-0.258873\pi$
$127$	22165.2			1.37425			0.687123	+	0.726541i	$0.258873\pi$
$128$	−13563.7	+	9190.29i	−0.827863	+	0.560931i
$129$	9487.97			0.570156
$130$	−1500.94	+	20063.9i	−0.0888130	+	1.18721i
$131$		−	25664.9i		−	1.49553i	−0.663961	−	0.747767i	$-0.731126\pi$
$131$		−	25664.9i		−	1.49553i	0.663961	−	0.747767i	$-0.268874\pi$
$132$	−2757.74	−	1517.51i	−0.158272	−	0.0870931i
$133$		−	24242.8i		−	1.37050i
$134$	−18361.6	+	10854.1i	−1.02259	+	0.604483i
$135$	2877.76	+	2005.08i	0.157902	+	0.110018i
$136$	−23724.7	+	731.403i	−1.28269	+	0.0395438i
$137$		−	530.885i		−	0.0282852i	−0.999900	−	0.0141426i	$-0.995498\pi$
$137$		−	530.885i		−	0.0282852i	0.999900	−	0.0141426i	$-0.00450188\pi$
$138$	−6913.50	+	4086.78i	−0.363028	+	0.214597i
$139$			20974.6i			1.08558i	0.839867	+	0.542792i	$0.182633\pi$
$139$			20974.6i			1.08558i	−0.839867	+	0.542792i	$0.817367\pi$
$140$	18302.4	−	9049.76i	0.933798	−	0.461722i
$141$	−7244.43			−0.364389
$142$	−11585.8	−	19599.4i	−0.574579	−	0.972001i
$143$	7617.58			0.372516
$144$	−3698.99	−	5838.94i	−0.178385	−	0.281585i
$145$	−23893.1	−	16647.5i	−1.13641	−	0.791795i
$146$	−9088.20	−	15374.3i	−0.426356	−	0.721256i
$147$	−1062.54			−0.0491712
$148$	−8546.79	−	4703.07i	−0.390193	−	0.214713i
$149$	31793.5			1.43207			0.716037	−	0.698062i	$-0.245954\pi$
$149$	31793.5			1.43207			0.716037	+	0.698062i	$0.245954\pi$
$150$	−10074.7	−	8200.64i	−0.447764	−	0.364473i
$151$			1630.74i			0.0715203i	0.999360	+	0.0357602i	$0.0113852\pi$
$151$			1630.74i			0.0715203i	−0.999360	+	0.0357602i	$0.988615\pi$
$152$	30381.7	−	936.629i	1.31500	−	0.0405397i
$153$		−	10013.6i		−	0.427768i
$154$	−3933.70	−	6654.55i	−0.165867	−	0.280593i
$155$	−20853.4	+	29929.5i	−0.867986	+	1.24577i
$156$	14655.1	+	8064.32i	0.602200	+	0.331374i
$157$			33255.4i			1.34916i	0.738203	+	0.674578i	$0.235675\pi$
$157$			33255.4i			1.34916i	−0.738203	+	0.674578i	$0.764325\pi$
$158$	6393.53	+	10815.8i	0.256110	+	0.433255i
$159$		−	15858.9i		−	0.627306i
$160$	12048.5	+	22587.5i	0.470645	+	0.882323i
$161$	−19723.2			−0.760895
$162$	2510.22	−	1483.87i	0.0956493	−	0.0565411i
$163$	−22085.6			−0.831255			−0.415628	−	0.909535i	$-0.636438\pi$
$163$	−22085.6			−0.831255			−0.415628	+	0.909535i	$0.636438\pi$
$164$	5640.10	−	10249.6i	0.209700	−	0.381084i
$165$	−2811.63	+	4035.36i	−0.103274	+	0.148222i
$166$	21029.2	−	12431.0i	0.763144	−	0.451117i
$167$	4028.51			0.144448			0.0722240	−	0.997388i	$-0.476990\pi$
$167$	4028.51			0.144448			0.0722240	+	0.997388i	$0.476990\pi$
$168$	−523.065	−	16966.8i	−0.0185326	−	0.601148i
$169$	−11920.2			−0.417360
$170$	−2766.71	+	36984.2i	−0.0957340	+	1.27973i
$171$			12823.4i			0.438541i
$172$	−14084.8	+	25596.0i	−0.476095	+	0.865198i
$173$		−	23111.2i		−	0.772201i	−0.922457	−	0.386100i	$-0.873822\pi$
$173$		−	23111.2i		−	0.772201i	0.922457	−	0.386100i	$-0.126178\pi$
$174$	−20841.5	+	12320.0i	−0.688383	+	0.406924i
$175$	−11050.5	−	29927.5i	−0.360834	−	0.977224i
$176$	8187.68	−	5186.92i	0.264323	−	0.167450i
$177$			11602.4i			0.370342i
$178$	32757.4	−	19363.9i	1.03388	−	0.611157i
$179$			47662.6i			1.48755i	0.668429	+	0.743776i	$0.266967\pi$
$179$			47662.6i			1.48755i	−0.668429	+	0.743776i	$0.733033\pi$
$180$	−9681.19	+	4786.92i	−0.298802	+	0.147745i
$181$	−2398.35			−0.0732073			−0.0366037	−	0.999330i	$-0.511654\pi$
$181$	−2398.35			−0.0732073			−0.0366037	+	0.999330i	$0.511654\pi$
$182$	20904.4	+	35363.5i	0.631096	+	1.06761i
$183$	28627.6			0.854835
$184$	−762.011	−	24717.6i	−0.0225074	−	0.730079i
$185$	−8713.81	+	12506.4i	−0.254604	+	0.365417i
$186$	15432.6	+	26106.9i	0.446080	+	0.754623i
$187$	14041.6			0.401545
$188$	10754.3	−	19543.5i	0.304275	−	0.552952i
$189$	7161.27			0.200478
$190$	3543.03	−	47361.7i	0.0981450	−	1.31196i
$191$		−	53842.6i		−	1.47591i	−0.674851	−	0.737954i	$-0.735792\pi$
$191$		−	53842.6i		−	1.47591i	0.674851	−	0.737954i	$-0.264208\pi$
$192$	21243.0	−	1311.04i	0.576254	−	0.0355641i
$193$			34598.0i			0.928831i	0.885618	+	0.464415i	$0.153736\pi$
$193$			34598.0i			0.928831i	−0.885618	+	0.464415i	$0.846264\pi$
$194$	−7097.76	−	12007.1i	−0.188590	−	0.319032i
$195$	14941.5	−	21444.6i	0.392939	−	0.563961i
$196$	1577.33	−	2866.45i	0.0410592	−	0.0746160i
$197$			14197.5i			0.365831i	0.983129	+	0.182915i	$0.0585535\pi$
$197$			14197.5i			0.365831i	−0.983129	+	0.182915i	$0.941447\pi$
$198$	2080.76	+	3519.96i	0.0530751	+	0.0897858i
$199$		−	64774.5i		−	1.63568i	−0.575447	−	0.817839i	$-0.695172\pi$
$199$		−	64774.5i		−	1.63568i	0.575447	−	0.817839i	$-0.304828\pi$
$200$	37078.9	−	15005.1i	0.926973	−	0.375127i
$201$	27708.2			0.685830
$202$	−32877.4	+	19434.8i	−0.805738	+	0.476296i
$203$	−59457.6			−1.44283
$204$	27014.1	+	14865.1i	0.649128	+	0.357197i
$205$	−14998.1	−	10449.9i	−0.356886	−	0.248660i
$206$	18994.6	−	11228.3i	0.447607	−	0.264594i
$207$	10432.7			0.243475
$208$	−43510.8	+	27564.2i	−1.00570	+	0.637117i
$209$	−17981.6			−0.411658
$210$	−26449.3	−	1978.62i	−0.599758	−	0.0448667i
$211$		−	16618.2i		−	0.373267i	−0.982430	−	0.186633i	$-0.940242\pi$
$211$		−	16618.2i		−	0.373267i	0.982430	−	0.186633i	$-0.0597576\pi$
$212$	42783.2	+	23542.4i	0.951922	+	0.523817i
$213$			29576.1i			0.651902i
$214$	−10065.1	+	5949.77i	−0.219781	+	0.129919i
$215$	37454.2	+	26096.2i	0.810259	+	0.564547i
$216$	276.678	+	8974.69i	0.00593017	+	0.192359i
$217$			74479.1i			1.58167i
$218$	74577.9	−	44085.2i	1.56927	−	0.927641i
$219$			23200.3i			0.483732i
$220$	−6712.48	−	13575.5i	−0.138688	−	0.280485i
$221$	−74619.8			−1.52781
$222$	6448.68	+	10909.1i	0.130847	+	0.221351i
$223$	3438.26			0.0691400			0.0345700	−	0.999402i	$-0.488994\pi$
$223$	3438.26			0.0691400			0.0345700	+	0.999402i	$0.488994\pi$
$224$	46548.4	+	23776.0i	0.927702	+	0.473851i
$225$	5845.25	+	15830.3i	0.115462	+	0.312697i
$226$	29694.9	+	50234.1i	0.581386	+	0.983517i
$227$	−69197.7			−1.34289			−0.671444	−	0.741055i	$-0.734326\pi$
$227$	−69197.7			−1.34289			−0.671444	+	0.741055i	$0.734326\pi$
$228$	−34594.1	−	19036.2i	−0.665475	−	0.366193i
$229$	27160.9			0.517933			0.258966	−	0.965886i	$-0.416618\pi$
$229$	27160.9			0.517933			0.258966	+	0.965886i	$0.416618\pi$
$230$	−38531.9	−	2882.49i	−0.728391	−	0.0544895i
$231$			10041.9i			0.188188i
$232$	−2297.16	−	74513.7i	−0.0426792	−	1.38440i
$233$		−	61634.9i		−	1.13531i	−0.823266	−	0.567655i	$-0.807851\pi$
$233$		−	61634.9i		−	1.13531i	0.823266	−	0.567655i	$-0.192149\pi$
$234$	−11057.5	−	18705.7i	−0.201942	−	0.341620i
$235$	−28597.7	−	19925.4i	−0.517840	−	0.360805i
$236$	−31300.3	−	17223.7i	−0.561985	−	0.309245i
$237$		−	16321.3i		−	0.290576i
$238$	38533.5	+	65186.2i	0.680276	+	1.15081i
$239$		−	8898.70i		−	0.155787i	−0.996962	−	0.0778934i	$-0.975181\pi$
$239$		−	8898.70i		−	0.155787i	0.996962	−	0.0778934i	$-0.0248194\pi$
$240$	1457.78	−	33223.4i	0.0253087	−	0.576795i
$241$	−13180.6			−0.226935			−0.113468	−	0.993542i	$-0.536196\pi$
$241$	−13180.6			−0.226935			−0.113468	+	0.993542i	$0.536196\pi$
$242$	45478.5	−	26883.7i	0.776561	−	0.459049i
$243$	−3788.00			−0.0641500
$244$	−42497.4	+	77229.6i	−0.713810	+	1.29719i
$245$	−4194.43	−	2922.46i	−0.0698781	−	0.0486875i
$246$	−13082.6	+	7733.51i	−0.216184	+	0.127793i
$247$	95557.7			1.56629
$248$	−93339.1	+	2877.52i	−1.51761	+	0.0467860i
$249$	−31733.7			−0.511825
$250$	−17214.9	−	60082.4i	−0.275439	−	0.961319i
$251$			104252.i			1.65476i	0.561640	+	0.827382i	$0.310171\pi$
$251$			104252.i			1.65476i	−0.561640	+	0.827382i	$0.689829\pi$
$252$	−10630.8	+	19319.2i	−0.167404	+	0.304220i
$253$			14629.3i			0.228550i
$254$	76323.1	−	45116.9i	1.18301	−	0.699313i
$255$	27542.0	−	39529.3i	0.423560	−	0.607909i
$256$	−27998.2	+	59254.2i	−0.427219	+	0.904148i
$257$		−	75052.8i		−	1.13632i	−0.822918	−	0.568160i	$-0.807656\pi$
$257$		−	75052.8i		−	1.13632i	0.822918	−	0.568160i	$-0.192344\pi$
$258$	32670.6	−	19312.6i	0.490815	−	0.290135i
$259$			31121.9i			0.463945i
$260$	35671.4	+	72142.6i	0.527683	+	1.06720i
$261$	31450.4			0.461685
$262$	−52240.3	−	88373.7i	−0.761033	−	1.28742i
$263$	10228.9			0.147882			0.0739411	−	0.997263i	$-0.476442\pi$
$263$	10228.9			0.147882			0.0739411	+	0.997263i	$0.476442\pi$
$264$	−12584.8	+	387.973i	−0.180567	+	0.00556664i
$265$	43619.2	−	62603.9i	0.621135	−	0.891476i
$266$	−49345.8	−	83477.1i	−0.697408	−	1.17979i
$267$	−49431.9			−0.693402
$268$	−41132.6	+	74749.4i	−0.572686	+	1.04073i
$269$	8355.99			0.115476			0.0577382	−	0.998332i	$-0.481611\pi$
$269$	8355.99			0.115476			0.0577382	+	0.998332i	$0.481611\pi$
$270$	13990.5	+	1046.60i	0.191914	+	0.0143567i
$271$			66166.8i			0.900952i	0.892788	+	0.450476i	$0.148746\pi$
$271$			66166.8i			0.900952i	−0.892788	+	0.450476i	$0.851254\pi$
$272$	−80204.3	+	50809.7i	−1.08408	+	0.686766i
$273$		−	53364.6i		−	0.716024i
$274$	−1080.61	−	1828.04i	−0.0143935	−	0.0243491i
$275$	−22198.1	+	8196.52i	−0.293529	+	0.108384i
$276$	−15487.2	+	28144.6i	−0.203308	+	0.369468i
$277$		−	117613.i		−	1.53283i	−0.642343	−	0.766417i	$-0.722038\pi$
$277$		−	117613.i		−	1.53283i	0.642343	−	0.766417i	$-0.277962\pi$
$278$	42693.3	+	72223.3i	0.552421	+	0.934518i
$279$		−	39396.1i		−	0.506110i
$280$	44601.5	−	68416.0i	0.568897	−	0.872653i
$281$	84024.3			1.06412			0.532062	−	0.846705i	$-0.321417\pi$
$281$	84024.3			1.06412			0.532062	+	0.846705i	$0.321417\pi$
$282$	−24945.3	+	14745.9i	−0.313682	+	0.185427i
$283$	−61114.9			−0.763087			−0.381544	−	0.924351i	$-0.624607\pi$
$283$	−61114.9			−0.763087			−0.381544	+	0.924351i	$0.624607\pi$
$284$	−79788.5	−	43905.5i	−0.989245	−	0.544355i
$285$	−35270.1	+	50620.9i	−0.434227	+	0.623219i
$286$	26230.2	−	15505.4i	0.320678	−	0.189562i
$287$	−37322.6			−0.453115
$288$	−24622.0	−	12576.4i	−0.296851	−	0.151626i
$289$	−54027.2			−0.646870
$290$	−116158.	−	8689.59i	−1.38119	−	0.103324i
$291$			18119.1i			0.213969i
$292$	−62588.1	−	34440.6i	−0.734051	−	0.403929i
$293$			64656.8i			0.753146i	0.926387	+	0.376573i	$0.122898\pi$
$293$			64656.8i			0.753146i	−0.926387	+	0.376573i	$0.877102\pi$
$294$	−3658.72	+	2162.78i	−0.0423287	+	0.0250217i
$295$	−31912.0	+	45801.2i	−0.366699	+	0.526300i
$296$	−39002.8	+	1202.41i	−0.445156	+	0.0137236i
$297$		−	5311.73i		−	0.0602175i
$298$	109477.	−	64715.0i	1.23279	−	0.728740i
$299$		−	77742.6i		−	0.869594i
$300$	−51383.2	−	7731.02i	−0.570924	−	0.0859002i
$301$	93204.2			1.02873
$302$	3319.33	+	5615.23i	0.0363946	+	0.0615678i
$303$	49612.9			0.540393
$304$	102709.	−	65066.6i	1.11138	−	0.704062i
$305$	113009.	+	78738.8i	1.21482	+	0.846426i
$306$	−20382.5	−	34480.6i	−0.217678	−	0.368241i
$307$	144462.			1.53277			0.766386	−	0.642381i	$-0.222053\pi$
$307$	144462.			1.53277			0.766386	+	0.642381i	$0.222053\pi$
$308$	−27090.4	−	14907.1i	−0.285571	−	0.157142i
$309$	−28663.5			−0.300201
$310$	−10884.9	+	145505.i	−0.113267	+	1.51410i
$311$		−	109152.i		−	1.12852i	−0.825597	−	0.564260i	$-0.809161\pi$
$311$		−	109152.i		−	1.12852i	0.825597	−	0.564260i	$-0.190839\pi$
$312$	66877.9	−	2061.76i	0.687026	−	0.0211801i
$313$			37361.4i			0.381360i	0.981652	+	0.190680i	$0.0610692\pi$
$313$			37361.4i			0.381360i	−0.981652	+	0.190680i	$0.938931\pi$
$314$	67690.7	+	114511.i	0.686546	+	1.16141i
$315$	28269.5	+	19696.7i	0.284903	+	0.198506i
$316$	44030.6	+	24228.9i	0.440941	+	0.242638i
$317$			31439.8i			0.312868i	0.987688	+	0.156434i	$0.0499999\pi$
$317$			31439.8i			0.312868i	−0.987688	+	0.156434i	$0.950000\pi$
$318$	−32280.5	−	54608.2i	−0.319217	−	0.540012i
$319$			44101.5i			0.433383i
$320$	87463.9	+	53252.5i	0.854139	+	0.520044i
$321$	15188.5			0.147403
$322$	−67914.2	+	40146.1i	−0.655011	+	0.387197i
$323$	176143.			1.68834
$324$	5623.24	−	10219.0i	0.0535669	−	0.0973461i
$325$	117965.	−	43557.8i	1.11683	−	0.412382i
$326$	−76049.1	+	44954.9i	−0.715581	+	0.423001i
$327$	−112540.			−1.05248
$328$	−1441.97	−	46773.7i	−0.0134032	−	0.434764i
$329$	−71165.0			−0.657468
$330$	−1467.60	+	19618.3i	−0.0134766	+	0.180149i
$331$			60318.3i			0.550545i	0.961366	+	0.275273i	$0.0887681\pi$
$331$			60318.3i			0.550545i	−0.961366	+	0.275273i	$0.911232\pi$
$332$	47108.3	−	85609.0i	0.427387	−	0.776682i
$333$		−	16462.1i		−	0.148456i
$334$	13871.7	−	8199.95i	0.124347	−	0.0735052i
$335$	109380.	+	76210.1i	0.974646	+	0.679083i
$336$	−36336.7	−	57358.3i	−0.321860	−	0.508063i
$337$			35916.7i			0.316254i	0.987419	+	0.158127i	$0.0505456\pi$
$337$			35916.7i			0.316254i	−0.987419	+	0.158127i	$0.949454\pi$
$338$	−41045.8	+	24263.4i	−0.359282	+	0.212382i
$339$		−	75804.7i		−	0.659625i
$340$	65753.7	+	132982.i	0.568804	+	1.15036i
$341$	55243.4			0.475085
$342$	26101.7	+	44155.7i	0.223160	+	0.377515i
$343$	112119.			0.952994
$344$	3600.98	+	116806.i	0.0304301	+	0.987070i
$345$	41183.5	+	28694.6i	0.346007	+	0.241080i
$346$	−47042.4	−	79580.5i	−0.392950	−	0.664744i
$347$	−98807.1			−0.820596			−0.410298	−	0.911952i	$-0.634575\pi$
$347$	−98807.1			−0.820596			−0.410298	+	0.911952i	$0.634575\pi$
$348$	−46687.8	+	84844.9i	−0.385519	+	0.700595i
$349$	−73220.1			−0.601145			−0.300573	−	0.953759i	$-0.597178\pi$
$349$	−73220.1			−0.601145			−0.300573	+	0.953759i	$0.597178\pi$
$350$	−98967.9	−	80558.3i	−0.807901	−	0.657619i
$351$			28227.5i			0.229118i
$352$	17635.3	−	34526.4i	0.142331	−	0.278654i
$353$			78557.6i			0.630433i	0.949020	+	0.315216i	$0.102077\pi$
$353$			78557.6i			0.630433i	−0.949020	+	0.315216i	$0.897923\pi$
$354$	23616.5	+	39951.5i	0.188456	+	0.318806i
$355$	−81347.7	+	116753.i	−0.645489	+	0.926429i
$356$	73381.2	−	133354.i	0.579009	−	1.05222i
$357$		−	98368.0i		−	0.771822i
$358$	97016.3	+	164120.i	0.756970	+	1.28055i
$359$		−	50142.5i		−	0.389060i	−0.980897	−	0.194530i	$-0.937682\pi$
$359$		−	50142.5i		−	0.389060i	0.980897	−	0.194530i	$-0.0623182\pi$
$360$	−23592.2	+	36189.0i	−0.182039	+	0.279236i
$361$	−95247.0			−0.730864
$362$	−8258.40	+	4881.78i	−0.0630200	+	0.0372530i
$363$	−68628.5			−0.520824
$364$	143963.	+	79219.2i	1.08655	+	0.597899i
$365$	−63811.2	+	91584.2i	−0.478973	+	0.687440i
$366$	98575.4	−	58270.9i	0.735879	−	0.435000i
$367$	−165475.			−1.22857			−0.614284	−	0.789085i	$-0.710555\pi$
$367$	−165475.			−1.22857			−0.614284	+	0.789085i	$0.710555\pi$
$368$	−52936.0	−	83560.8i	−0.390891	−	0.617031i
$369$	19742.0			0.144990
$370$	−4548.40	+	60800.9i	−0.0332242	+	0.444127i
$371$		−	155789.i		−	1.13185i
$372$	106280.	+	58483.2i	0.768010	+	0.422615i
$373$		−	56871.4i		−	0.408767i	−0.978891	−	0.204384i	$-0.934481\pi$
$373$		−	56871.4i		−	0.408767i	0.978891	−	0.204384i	$-0.0655190\pi$
$374$	48350.6	−	28581.5i	0.345668	−	0.204334i
$375$	−20466.1	+	78568.0i	−0.145537	+	0.558706i
$376$	−2749.48	−	89185.8i	−0.0194480	−	0.630841i
$377$		−	234363.i		−	1.64895i
$378$	24658.9	−	14576.6i	0.172580	−	0.102017i
$379$		−	166749.i		−	1.16088i	−0.814305	−	0.580438i	$-0.802882\pi$
$379$		−	166749.i		−	1.16088i	0.814305	−	0.580438i	$-0.197118\pi$
$380$	−84203.7	−	170296.i	−0.583128	−	1.17933i
$381$	−115174.			−0.793421
$382$	−109596.	−	185400.i	−0.751046	−	1.27053i
$383$	−10594.7			−0.0722257			−0.0361128	−	0.999348i	$-0.511498\pi$
$383$	−10594.7			−0.0722257			−0.0361128	+	0.999348i	$0.511498\pi$
$384$	70479.1	−	47754.1i	0.477967	−	0.323854i
$385$	−27619.8	+	39641.0i	−0.186337	+	0.267438i
$386$	70423.6	+	119134.i	0.472654	+	0.799578i
$387$	−49300.9			−0.329180
$388$	−48880.5	−	26897.6i	−0.324692	−	0.178669i
$389$	−251272.			−1.66052			−0.830262	−	0.557373i	$-0.811809\pi$
$389$	−251272.			−1.66052			−0.830262	+	0.557373i	$0.811809\pi$
$390$	7799.11	−	104255.i	0.0512762	−	0.685437i
$391$		−	143304.i		−	0.937359i
$392$	−403.267	−	13080.9i	−0.00262434	−	0.0851265i
$393$			133359.i			0.863447i
$394$	28898.8	+	48887.4i	0.186160	+	0.314923i
$395$	44891.1	−	64429.3i	0.287717	−	0.412942i
$396$	14329.6	+	7885.21i	0.0913786	+	0.0502832i
$397$			145938.i			0.925952i	0.886371	+	0.462976i	$0.153218\pi$
$397$			145938.i			0.925952i	−0.886371	+	0.462976i	$0.846782\pi$
$398$	−131847.	−	223043.i	−0.832348	−	1.40806i
$399$			125969.i			0.791260i
$400$	97134.1	−	127142.i	0.607088	−	0.794635i
$401$	−636.947			−0.00396109			−0.00198054	−	0.999998i	$-0.500630\pi$
$401$	−636.947			−0.00396109			−0.00198054	+	0.999998i	$0.500630\pi$
$402$	95409.8	−	56399.5i	0.590392	−	0.348998i
$403$	−293573.			−1.80762
$404$	−73649.9	+	133842.i	−0.451242	+	0.820032i
$405$	−14953.3	−	10418.7i	−0.0911648	−	0.0635190i
$406$	−204735.	+	121025.i	−1.24205	+	0.734213i
$407$	23084.1			0.139355
$408$	123277.	−	3800.48i	0.740564	−	0.0228306i
$409$	−280113.			−1.67450			−0.837252	−	0.546816i	$-0.815840\pi$
$409$	−280113.			−1.67450			−0.837252	+	0.546816i	$0.815840\pi$
$410$	−72914.9	−	5454.62i	−0.433759	−	0.0324486i
$411$			2758.56i			0.0163305i
$412$	42550.6	−	77326.4i	0.250675	−	0.455547i
$413$			113976.i			0.668208i
$414$	35923.6	−	21235.5i	0.209594	−	0.123897i
$415$	−125270.	−	87282.0i	−0.727364	−	0.506790i
$416$	−93717.5	+	183479.i	−0.541544	+	1.06023i
$417$		−	108987.i		−	0.626762i
$418$	−61917.5	+	36601.3i	−0.354373	+	0.209480i
$419$			7136.79i			0.0406513i	0.999793	+	0.0203257i	$0.00647031\pi$
$419$			7136.79i			0.0406513i	−0.999793	+	0.0203257i	$0.993530\pi$
$420$	−95102.3	+	47023.9i	−0.539129	+	0.266576i
$421$	127649.			0.720200			0.360100	−	0.932914i	$-0.382743\pi$
$421$	127649.			0.720200			0.360100	+	0.932914i	$0.382743\pi$
$422$	−33826.0	−	57222.7i	−0.189944	−	0.321324i
$423$	37643.1			0.210380
$424$	195239.	−	6018.95i	1.08601	−	0.0334803i
$425$	217447.	−	80291.0i	1.20386	−	0.444517i
$426$	60201.6	+	101842.i	0.331733	+	0.561185i
$427$	281221.			1.54238
$428$	−22547.2	+	40974.6i	−0.123085	+	0.223680i
$429$	−39582.1			−0.215072
$430$	182087.	+	13621.6i	0.984787	+	0.0736700i
$431$			295330.i			1.58984i	0.606717	+	0.794918i	$0.292486\pi$
$431$			295330.i			1.58984i	−0.606717	+	0.794918i	$0.707514\pi$
$432$	19220.5	+	30340.0i	0.102991	+	0.162573i
$433$		−	103955.i		−	0.554457i	−0.960804	−	0.277228i	$-0.910584\pi$
$433$		−	103955.i		−	0.554457i	0.960804	−	0.277228i	$-0.0894159\pi$
$434$	151601.	+	256459.i	0.804863	+	1.36157i
$435$	124152.	+	86502.9i	0.656109	+	0.457143i
$436$	167065.	−	303604.i	0.878845	−	1.59711i
$437$			183515.i			0.960966i
$438$	47223.7	+	79887.2i	0.246157	+	0.416417i
$439$		−	45639.3i		−	0.236815i	−0.992965	−	0.118408i	$-0.962221\pi$
$439$		−	45639.3i		−	0.236815i	0.992965	−	0.118408i	$-0.0377790\pi$
$440$	−50746.2	−	33082.3i	−0.262119	−	0.170880i
$441$	5521.12			0.0283890
$442$	−256944.	+	151887.i	−1.31521	+	0.777458i
$443$	126637.			0.645290			0.322645	−	0.946520i	$-0.395428\pi$
$443$	126637.			0.645290			0.322645	+	0.946520i	$0.395428\pi$
$444$	44410.4	+	24437.9i	0.225278	+	0.123964i
$445$	−195135.	−	135960.i	−0.985407	−	0.686581i
$446$	11839.2	−	6998.52i	0.0595187	−	0.0351833i
$447$	−165204.			−0.826808
$448$	208679.	−	12878.9i	1.03974	−	0.0641684i
$449$	98148.3			0.486844			0.243422	−	0.969920i	$-0.421730\pi$
$449$	98148.3			0.486844			0.243422	+	0.969920i	$0.421730\pi$
$450$	52349.7	+	42611.8i	0.258517	+	0.210429i
$451$			27683.3i			0.136102i
$452$	204501.	+	112531.i	1.00096	+	0.550804i
$453$		−	8473.55i		−	0.0412923i
$454$	−238274.	+	140851.i	−1.15602	+	0.683356i
$455$	146777.	−	210659.i	0.708981	−	1.01756i
$456$	−157868.	+	4866.87i	−0.759215	+	0.0234056i
$457$			323140.i			1.54724i	0.633648	+	0.773622i	$0.281557\pi$
$457$			323140.i			1.54724i	−0.633648	+	0.773622i	$0.718443\pi$
$458$	93525.1	−	55285.5i	0.445859	−	0.263560i
$459$			52032.3i			0.246972i
$460$	−138547.	+	68505.4i	−0.654759	+	0.323749i
$461$	101678.			0.478437			0.239218	−	0.970966i	$-0.423109\pi$
$461$	101678.			0.478437			0.239218	+	0.970966i	$0.423109\pi$
$462$	20440.1	+	34578.1i	0.0957634	+	0.162001i
$463$	−155652.			−0.726094			−0.363047	−	0.931771i	$-0.618264\pi$
$463$	−155652.			−0.726094			−0.363047	+	0.931771i	$0.618264\pi$
$464$	−159581.	−	251903.i	−0.741218	−	1.17003i
$465$	108357.	−	155518.i	0.501132	−	0.719243i
$466$	−125457.	−	212232.i	−0.577726	−	0.977325i
$467$	299837.			1.37484			0.687418	−	0.726262i	$-0.258744\pi$
$467$	299837.			1.37484			0.687418	+	0.726262i	$0.258744\pi$
$468$	−76150.3	−	41903.5i	−0.347680	−	0.191319i
$469$	272189.			1.23744
$470$	−139031.	−	10400.6i	−0.629382	−	0.0470829i
$471$		−	172800.i		−	0.778936i
$472$	−142837.	+	4403.48i	−0.641146	+	0.0197657i
$473$		−	69132.4i		−	0.309001i
$474$	−33221.8	−	56200.5i	−0.147865	−	0.250140i
$475$	−278461.	+	102820.i	−1.23418	+	0.455712i
$476$	265371.	+	146026.i	1.17122	+	0.644492i
$477$			82405.4i			0.362175i
$478$	−18113.1	−	30641.5i	−0.0792753	−	0.134108i
$479$		−	178034.i		−	0.775948i	−0.921670	−	0.387974i	$-0.873175\pi$
$479$		−	178034.i		−	0.775948i	0.921670	−	0.387974i	$-0.126825\pi$
$480$	−62605.9	−	117368.i	−0.271727	−	0.509409i
$481$	−122673.			−0.530223
$482$	−45385.8	+	26828.9i	−0.195356	+	0.115481i
$483$	102485.			0.439303
$484$	101878.	−	185141.i	0.434902	−	0.790338i
$485$	−49835.7	+	71526.0i	−0.211864	+	0.304075i
$486$	−13043.5	+	7710.39i	−0.0552231	+	0.0326440i
$487$	318199.			1.34165			0.670827	−	0.741614i	$-0.265939\pi$
$487$	318199.			1.34165			0.670827	+	0.741614i	$0.265939\pi$
$488$	10865.1	+	352433.i	0.0456239	+	1.47992i
$489$	114760.			0.479926
$490$	−20391.6	−	1525.46i	−0.0849296	−	0.00635342i
$491$			167000.i			0.692712i	0.938103	+	0.346356i	$0.112581\pi$
$491$			167000.i			0.692712i	−0.938103	+	0.346356i	$0.887419\pi$
$492$	−29306.8	+	53258.7i	−0.121071	+	0.220019i
$493$		−	432006.i		−	1.77745i
$494$	329041.	−	194506.i	1.34833	−	0.797037i
$495$	14609.7	−	20968.3i	0.0596252	−	0.0855763i
$496$	−315544.	+	199898.i	−1.28262	+	0.812542i
$497$			290539.i			1.17623i
$498$	−109271.	+	64593.3i	−0.440601	+	0.260453i
$499$		−	26900.7i		−	0.108034i	−0.998540	−	0.0540172i	$-0.982797\pi$
$499$		−	26900.7i		−	0.108034i	0.998540	−	0.0540172i	$-0.0172026\pi$
$500$	−181574.	−	171846.i	−0.726296	−	0.687382i
$501$	−20932.7			−0.0833971
$502$	212202.	+	358978.i	0.842060	+	1.42449i
$503$	−217917.			−0.861301			−0.430650	−	0.902519i	$-0.641716\pi$
$503$	−217917.			−0.861301			−0.430650	+	0.902519i	$0.641716\pi$
$504$	2717.92	+	88162.1i	0.0106998	+	0.347073i
$505$	195849.	+	136458.i	0.767962	+	0.535077i
$506$	29777.6	+	50374.0i	0.116302	+	0.196746i
$507$	61939.3			0.240963
$508$	170974.	−	310708.i	0.662527	−	1.20400i
$509$	294895.			1.13823			0.569117	−	0.822256i	$-0.307285\pi$
$509$	294895.			1.13823			0.569117	+	0.822256i	$0.307285\pi$
$510$	14376.3	−	192175.i	0.0552720	−	0.738852i
$511$			227906.i			0.872798i
$512$	24202.5	+	261024.i	0.0923252	+	0.995729i
$513$		−	66632.2i		−	0.253192i
$514$	−152768.	−	258435.i	−0.578239	−	0.978193i
$515$	−113150.	−	78837.5i	−0.426621	−	0.297248i
$516$	73186.7	−	133001.i	0.274874	−	0.499522i
$517$			52785.2i			0.197484i
$518$	63348.1	+	107164.i	0.236088	+	0.399384i
$519$			120089.i			0.445830i
$520$	269675.	+	175805.i	0.997317	+	0.650168i
$521$	247783.			0.912842			0.456421	−	0.889764i	$-0.349131\pi$
$521$	247783.			0.912842			0.456421	+	0.889764i	$0.349131\pi$
$522$	108296.	−	64016.7i	0.397438	−	0.234938i
$523$	90277.4			0.330047			0.165023	−	0.986290i	$-0.447230\pi$
$523$	90277.4			0.330047			0.165023	+	0.986290i	$0.447230\pi$
$524$	−359766.	−	197970.i	−1.31026	−	0.721001i
$525$	57420.3	+	155508.i	0.208328	+	0.564200i
$526$	35221.8	−	20820.6i	0.127303	−	0.0752528i
$527$	−541150.			−1.94848
$528$	−42544.4	+	26952.0i	−0.152607	+	0.0966771i
$529$	−130540.			−0.466477
$530$	22768.2	−	304355.i	0.0810544	−	1.08350i
$531$		−	60288.0i		−	0.213817i
$532$	−339832.	−	187000.i	−1.20072	−	0.660722i
$533$		−	147114.i		−	0.517846i
$534$	−170213.	+	100618.i	−0.596911	+	0.352852i
$535$	59957.4	+	41775.3i	0.209477	+	0.145953i
$536$	10516.1	+	341115.i	0.0366038	+	1.18733i
$537$		−	247662.i		−	0.858838i
$538$	28772.8	−	17008.5i	0.0994071	−	0.0587625i
$539$			7742.01i			0.0266487i
$540$	50304.9	−	24873.6i	0.172513	−	0.0853004i
$541$	153234.			0.523553			0.261777	−	0.965128i	$-0.415692\pi$
$541$	153234.			0.523553			0.261777	+	0.965128i	$0.415692\pi$
$542$	134681.	+	227837.i	0.458468	+	0.775579i
$543$	12462.2			0.0422663
$544$	−172751.	+	338211.i	−0.583745	+	1.14285i
$545$	−444258.	−	309537.i	−1.49569	−	1.04212i
$546$	−108623.	−	183754.i	−0.364363	−	0.616385i
$547$	432810.			1.44652			0.723258	−	0.690578i	$-0.242644\pi$
$547$	432810.			1.44652			0.723258	+	0.690578i	$0.242644\pi$
$548$	−7441.86	−	4095.06i	−0.0247811	−	0.0136364i
$549$	−148753.			−0.493539
$550$	−59752.5	+	73407.5i	−0.197529	+	0.242669i
$551$			553224.i			1.82221i
$552$	3959.52	+	128436.i	0.0129947	+	0.421512i
$553$		−	160331.i		−	0.524286i
$554$	−239399.	−	404985.i	−0.780013	−	1.31953i
$555$	45278.3	−	64985.1i	0.146995	−	0.210973i
$556$	294018.	+	161790.i	0.951097	+	0.523363i
$557$		−	590478.i		−	1.90324i	−0.307281	−	0.951619i	$-0.599419\pi$
$557$		−	590478.i		−	1.90324i	0.307281	−	0.951619i	$-0.400581\pi$
$558$	−80190.1	−	135656.i	−0.257544	−	0.435682i
$559$			367382.i			1.17569i
$560$	14320.4	−	326367.i	0.0456645	−	1.04071i
$561$	−72962.5			−0.231832
$562$	289327.	−	171030.i	0.916044	−	0.541501i
$563$	200378.			0.632169			0.316084	−	0.948731i	$-0.397632\pi$
$563$	200378.			0.632169			0.316084	+	0.948731i	$0.397632\pi$
$564$	−55880.9	+	101551.i	−0.175673	+	0.319247i
$565$	208497.	−	299243.i	0.653136	−	0.937405i
$566$	−210441.	+	124398.i	−0.656898	+	0.388312i
$567$	−37211.0			−0.115746
$568$	−364110.	+	11225.1i	−1.12859	+	0.0347930i
$569$	−102871.			−0.317738			−0.158869	−	0.987300i	$-0.550785\pi$
$569$	−102871.			−0.317738			−0.158869	+	0.987300i	$0.550785\pi$
$570$	−18410.1	+	246098.i	−0.0566640	+	0.757459i
$571$		−	478647.i		−	1.46806i	−0.679118	−	0.734029i	$-0.737638\pi$
$571$		−	478647.i		−	1.46806i	0.679118	−	0.734029i	$-0.262362\pi$
$572$	58759.3	−	106782.i	0.179591	−	0.326367i
$573$			279775.i			0.852116i
$574$	−128516.	+	75969.5i	−0.390061	+	0.230577i
$575$	83651.0	+	226547.i	0.253009	+	0.685207i
$576$	−110382.	+	6812.34i	−0.332700	+	0.0205330i
$577$			299722.i			0.900257i	0.892964	+	0.450128i	$0.148622\pi$
$577$			299722.i			0.900257i	−0.892964	+	0.450128i	$0.851378\pi$
$578$	−186036.	+	109971.i	−0.556854	+	0.329173i
$579$		−	179777.i		−	0.536261i
$580$	−417664.	+	206517.i	−1.24157	+	0.613902i
$581$	−311733.			−0.923487
$582$	36881.0	+	62390.7i	0.108882	+	0.184193i
$583$	−115553.			−0.339974
$584$	−285617.	+	8805.22i	−0.837450	+	0.0258175i
$585$	−77638.4	+	111430.i	−0.226864	+	0.325603i
$586$	131608.	+	222638.i	0.383253	+	0.648341i
$587$	−77803.7			−0.225800			−0.112900	−	0.993606i	$-0.536014\pi$
$587$	−77803.7			−0.225800			−0.112900	+	0.993606i	$0.536014\pi$
$588$	−8196.05	+	14894.5i	−0.0237055	+	0.0430796i
$589$	692993.			1.99755
$590$	−16657.3	+	222667.i	−0.0478520	+	0.639663i
$591$		−	73772.5i		−	0.211213i
$592$	−131854.	+	83529.8i	−0.376226	+	0.238340i
$593$			219310.i			0.623662i	0.950138	+	0.311831i	$0.100942\pi$
$593$			219310.i			0.623662i	−0.950138	+	0.311831i	$0.899058\pi$
$594$	−10811.9	−	18290.3i	−0.0306429	−	0.0518379i
$595$	270556.	−	388313.i	0.764230	−	1.09685i
$596$	245243.	−	445676.i	0.690406	−	1.25466i
$597$			336578.i			0.944360i
$598$	−158243.	−	267697.i	−0.442510	−	0.748584i
$599$			81343.8i			0.226710i	0.993555	+	0.113355i	$0.0361598\pi$
$599$			81343.8i			0.226710i	−0.993555	+	0.113355i	$0.963840\pi$
$600$	−192668.	+	77968.7i	−0.535188	+	0.216580i
$601$	−442777.			−1.22585			−0.612924	−	0.790142i	$-0.710007\pi$
$601$	−442777.			−1.22585			−0.612924	+	0.790142i	$0.710007\pi$
$602$	320937.	−	189715.i	0.885578	−	0.523491i
$603$	−143976.			−0.395964
$604$	22859.4	+	12578.9i	0.0626600	+	0.0344801i
$605$	−270914.	−	188759.i	−0.740153	−	0.515701i
$606$	170836.	−	100986.i	0.465193	−	0.274990i
$607$	−325514.			−0.883472			−0.441736	−	0.897145i	$-0.645637\pi$
$607$	−325514.			−0.883472			−0.441736	+	0.897145i	$0.645637\pi$
$608$	221224.	−	433111.i	0.598446	−	1.17163i
$609$	308950.			0.833018
$610$	549403.	+	41099.8i	1.47649	+	0.110454i
$611$		−	280510.i		−	0.751392i
$612$	−140369.	−	77241.5i	−0.374774	−	0.206228i
$613$			370093.i			0.984896i	0.870342	+	0.492448i	$0.163898\pi$
$613$			370093.i			0.984896i	−0.870342	+	0.492448i	$0.836102\pi$
$614$	497437.	−	294050.i	1.31948	−	0.779982i
$615$	77932.6	+	54299.5i	0.206048	+	0.143564i
$616$	−123626.	+	3811.22i	−0.325797	+	0.0100439i
$617$		−	64817.4i		−	0.170263i	−0.996370	−	0.0851317i	$-0.972869\pi$
$617$		−	64817.4i		−	0.170263i	0.996370	−	0.0851317i	$-0.0271311\pi$
$618$	−98699.0	+	58343.9i	−0.258426	+	0.152763i
$619$			499198.i			1.30284i	0.758716	+	0.651421i	$0.225827\pi$
$619$			499198.i			1.30284i	−0.758716	+	0.651421i	$0.774173\pi$
$620$	258692.	+	523184.i	0.672975	+	1.36104i
$621$	−54209.8			−0.140571
$622$	−222176.	−	375850.i	−0.574271	−	0.971480i
$623$	−485590.			−1.25111
$624$	226089.	−	143228.i	0.580644	−	0.367840i
$625$	−296889.	+	253860.i	−0.760035	+	0.649882i
$626$	76048.5	+	128649.i	0.194063	+	0.328291i
$627$	93435.3			0.237671
$628$	466168.	+	256520.i	1.18202	+	0.650432i
$629$	−226125.			−0.571542
$630$	137435.	+	10281.2i	0.346270	+	0.0259038i
$631$		−	541326.i		−	1.35956i	−0.733414	−	0.679782i	$-0.762074\pi$
$631$		−	541326.i		−	1.35956i	0.733414	−	0.679782i	$-0.237926\pi$
$632$	200931.	−	6194.45i	0.503053	−	0.0155085i
$633$			86350.7i			0.215506i
$634$	63995.1	+	108259.i	0.159209	+	0.269330i
$635$	−454655.	−	316780.i	−1.12755	−	0.785616i
$636$	−222308.	−	122330.i	−0.549592	−	0.302426i
$637$		−	41142.5i		−	0.101394i
$638$	89767.7	+	151858.i	0.220536	+	0.373075i
$639$		−	153682.i		−	0.376376i
$640$	409565.	+	5337.37i	0.999915	+	0.0130307i
$641$	−38288.9			−0.0931873			−0.0465936	−	0.998914i	$-0.514837\pi$
$641$	−38288.9			−0.0931873			−0.0465936	+	0.998914i	$0.514837\pi$
$642$	52299.7	−	30915.9i	0.126891	−	0.0750088i
$643$	570529.			1.37993			0.689963	−	0.723845i	$-0.257627\pi$
$643$	570529.			1.37993			0.689963	+	0.723845i	$0.257627\pi$
$644$	−152137.	+	276476.i	−0.366829	+	0.666631i
$645$	−194618.	−	135600.i	−0.467803	−	0.325942i
$646$	606527.	−	358536.i	1.45340	−	0.859148i
$647$	−415706.			−0.993066			−0.496533	−	0.868018i	$-0.665394\pi$
$647$	−415706.			−0.993066			−0.496533	+	0.868018i	$0.665394\pi$
$648$	−1437.66	−	46633.8i	−0.00342379	−	0.111058i
$649$	84539.1			0.200710
$650$	317536.	−	390101.i	0.751564	−	0.923316i
$651$		−	387005.i		−	0.913175i
$652$	−170361.	+	309593.i	−0.400750	+	0.728275i
$653$			91144.2i			0.213748i	0.994273	+	0.106874i	$0.0340842\pi$
$653$			91144.2i			0.213748i	−0.994273	+	0.106874i	$0.965916\pi$
$654$	−387518.	+	229073.i	−0.906017	+	0.535574i
$655$	−366796.	+	526440.i	−0.854953	+	1.22706i
$656$	−100172.	−	158124.i	−0.232777	−	0.367443i
$657$		−	120552.i		−	0.279283i
$658$	−245048.	+	144855.i	−0.565977	+	0.334566i
$659$			25068.2i			0.0577235i	0.999583	+	0.0288618i	$0.00918826\pi$
$659$			25068.2i			0.0577235i	−0.999583	+	0.0288618i	$0.990812\pi$
$660$	34879.1	+	70540.2i	0.0800713	+	0.161938i
$661$	−183147.			−0.419177			−0.209589	−	0.977790i	$-0.567212\pi$
$661$	−183147.			−0.419177			−0.209589	+	0.977790i	$0.567212\pi$
$662$	122777.	+	207698.i	0.280156	+	0.473933i
$663$	387736.			0.882082
$664$	−12043.9	−	390672.i	−0.0273169	−	0.886086i
$665$	−346473.	+	497271.i	−0.783476	+	1.12447i
$666$	−33508.3	−	56685.2i	−0.0755447	−	0.127797i
$667$	450085.			1.01168
$668$	31074.5	−	56471.0i	0.0696387	−	0.126553i
$669$	−17865.7			−0.0399180
$670$	531759.	+	39779.9i	1.18458	+	0.0886163i
$671$		−	208590.i		−	0.463285i
$672$	−241873.	−	123544.i	−0.535609	−	0.273578i
$673$			292902.i			0.646684i	0.946282	+	0.323342i	$0.104806\pi$
$673$			292902.i			0.646684i	−0.946282	+	0.323342i	$0.895194\pi$
$674$	73107.7	+	123675.i	0.160932	+	0.272246i
$675$	−30372.8	−	82256.7i	−0.0666618	−	0.180536i
$676$	−91948.4	+	167096.i	−0.201210	+	0.365656i
$677$			264707.i			0.577548i	0.957397	+	0.288774i	$0.0932477\pi$
$677$			264707.i			0.577548i	−0.957397	+	0.288774i	$0.906752\pi$
$678$	−154299.	−	261024.i	−0.335663	−	0.567834i
$679$			177991.i			0.386064i
$680$	497096.	+	324066.i	1.07504	+	0.700834i
$681$	359562.			0.775317
$682$	190224.	−	112447.i	0.408974	−	0.241757i
$683$	−202073.			−0.433178			−0.216589	−	0.976263i	$-0.569493\pi$
$683$	−202073.			−0.433178			−0.216589	+	0.976263i	$0.569493\pi$
$684$	179756.	+	98914.9i	0.384212	+	0.211422i
$685$	−7587.29	+	10889.6i	−0.0161698	+	0.0232075i
$686$	386067.	−	228216.i	0.820378	−	0.484950i
$687$	−141132.			−0.299029
$688$	250156.	+	394877.i	0.528486	+	0.834228i
$689$	614071.			1.29354
$690$	200218.	+	14977.9i	0.420537	+	0.0314595i
$691$		−	105012.i		−	0.219928i	−0.993936	−	0.109964i	$-0.964926\pi$
$691$		−	105012.i		−	0.219928i	0.993936	−	0.109964i	$-0.0350736\pi$
$692$	−323969.	−	178271.i	−0.676537	−	0.372280i
$693$		−	52179.3i		−	0.108651i
$694$	−340230.	+	201120.i	−0.706404	+	0.417577i
$695$	299764.	−	430232.i	0.620597	−	0.890704i
$696$	11936.4	+	387185.i	0.0246408	+	0.799281i
$697$		−	271179.i		−	0.558200i
$698$	−252124.	+	149038.i	−0.517492	+	0.305905i
$699$			320264.i			0.655472i
$700$	−504758.	−	75945.0i	−1.03012	−	0.154990i
$701$	−240544.			−0.489506			−0.244753	−	0.969585i	$-0.578707\pi$
$701$	−240544.			−0.489506			−0.244753	+	0.969585i	$0.578707\pi$
$702$	57456.5	+	97197.8i	0.116591	+	0.197234i
$703$	289575.			0.585936
$704$	−9552.63	−	154784.i	−0.0192743	−	0.312305i
$705$	148598.	+	103536.i	0.298975	+	0.208311i
$706$	159902.	+	270503.i	0.320808	+	0.542704i
$707$	487368.			0.975031
$708$	162641.	+	89497.0i	0.324462	+	0.178543i
$709$	65769.2			0.130837			0.0654184	−	0.997858i	$-0.479162\pi$
$709$	65769.2			0.130837			0.0654184	+	0.997858i	$0.479162\pi$
$710$	−42461.5	+	567607.i	−0.0842324	+	1.12598i
$711$			84808.2i			0.167764i
$712$	−18761.0	−	608555.i	−0.0370079	−	1.20044i
$713$		−	563796.i		−	1.10903i
$714$	−200226.	−	338718.i	−0.392757	−	0.664418i
$715$	−156252.	−	108869.i	−0.305643	−	0.212957i
$716$	668127.	+	367652.i	1.30327	+	0.717152i
$717$			46239.0i			0.0899436i
$718$	−102064.	−	172659.i	−0.197981	−	0.334920i
$719$			793740.i			1.53540i	0.640812	+	0.767698i	$0.278598\pi$
$719$			793740.i			1.53540i	−0.640812	+	0.767698i	$0.721402\pi$
$720$	−7574.85	+	172634.i	−0.0146120	+	0.333013i
$721$	−281573.			−0.541652
$722$	−327971.	+	193873.i	−0.629160	+	0.371915i
$723$	68488.5			0.131021
$724$	−18500.0	+	33619.6i	−0.0352934	+	0.0641380i
$725$	252175.	+	682949.i	0.479762	+	1.29931i
$726$	−236313.	+	139692.i	−0.448348	+	0.265032i
$727$	−1.00277e6			−1.89728			−0.948639	−	0.316362i	$-0.897539\pi$
$727$	−1.00277e6			−1.89728			−0.948639	+	0.316362i	$0.897539\pi$
$728$	656969.	−	20253.5i	1.23960	−	0.0382153i
$729$	19683.0			0.0370370
$730$	−33307.9	+	445245.i	−0.0625031	+	0.835513i
$731$			677203.i			1.26731i
$732$	220823.	−	401297.i	0.412118	−	0.748934i
$733$			323556.i			0.602201i	0.953592	+	0.301100i	$0.0973539\pi$
$733$			323556.i			0.602201i	−0.953592	+	0.301100i	$0.902646\pi$
$734$	−569791.	+	336820.i	−1.05760	+	0.625181i
$735$	21794.9	+	15185.6i	0.0403441	+	0.0281097i
$736$	−352365.	−	179981.i	−0.650484	−	0.332254i
$737$		−	201891.i		−	0.371691i
$738$	67979.1	−	40184.5i	0.124814	−	0.0737812i
$739$		−	954629.i		−	1.74802i	−0.485911	−	0.874008i	$-0.661512\pi$
$739$		−	954629.i		−	1.74802i	0.485911	−	0.874008i	$-0.338488\pi$
$740$	108097.	+	218618.i	0.197402	+	0.399230i
$741$	−496532.			−0.904297
$742$	−317105.	−	536439.i	−0.575964	−	0.974345i
$743$	796623.			1.44303			0.721515	−	0.692399i	$-0.243446\pi$
$743$	796623.			1.44303			0.721515	+	0.692399i	$0.243446\pi$
$744$	485004.	−	14952.1i	0.876193	−	0.0270119i
$745$	−652150.	−	454385.i	−1.17499	−	0.818675i
$746$	−115761.	−	195830.i	−0.208010	−	0.351885i
$747$	164893.			0.295502
$748$	108312.	−	196833.i	0.193586	−	0.351800i
$749$	149203.			0.265959
$750$	89451.3	+	312197.i	0.159025	+	0.555018i
$751$			294285.i			0.521782i	0.965368	+	0.260891i	$0.0840163\pi$
$751$			294285.i			0.521782i	−0.965368	+	0.260891i	$0.915984\pi$
$752$	−191003.	−	301504.i	−0.337758	−	0.533159i
$753$		−	541708.i		−	0.955378i
$754$	−477042.	−	807000.i	−0.839100	−	1.41949i
$755$	23306.1	−	33449.8i	0.0408861	−	0.0586812i
$756$	55239.4	−	100386.i	0.0966509	−	0.175642i
$757$		−	859620.i		−	1.50008i	−0.661391	−	0.750041i	$-0.730034\pi$
$757$		−	859620.i		−	1.50008i	0.661391	−	0.750041i	$-0.269966\pi$
$758$	−339415.	−	574180.i	−0.590735	−	0.999332i
$759$		−	76015.9i		−	0.131953i
$760$	−636578.	−	414996.i	−1.10211	−	0.718484i
$761$	682493.			1.17850			0.589249	−	0.807951i	$-0.299424\pi$
$761$	682493.			1.17850			0.589249	+	0.807951i	$0.299424\pi$
$762$	−396586.	+	234434.i	−0.683011	+	0.403748i
$763$	−1.10553e6			−1.89898
$764$	−754757.	−	415323.i	−1.29307	−	0.711539i
$765$	−143112.	+	205400.i	−0.244543	+	0.350977i
$766$	−36481.5	+	21565.3i	−0.0621750	+	0.0367535i
$767$	−449256.			−0.763666
$768$	145483.	−	307894.i	0.246655	−	0.522010i
$769$	452888.			0.765840			0.382920	−	0.923781i	$-0.374918\pi$
$769$	452888.			0.765840			0.382920	+	0.923781i	$0.374918\pi$
$770$	−14416.9	+	192718.i	−0.0243159	+	0.325043i
$771$			389986.i			0.656055i
$772$	484989.	+	266877.i	0.813762	+	0.447792i
$773$			30549.1i			0.0511257i	0.999673	+	0.0255628i	$0.00813779\pi$
$773$			30549.1i			0.0511257i	−0.999673	+	0.0255628i	$0.991862\pi$
$774$	−169761.	+	100351.i	−0.283372	+	0.167510i
$775$	855491.	−	315885.i	1.42434	−	0.525927i
$776$	−223063.	+	6876.75i	−0.370429	+	0.0114198i
$777$		−	161714.i		−	0.267859i
$778$	−865224.	+	511460.i	−1.42945	+	0.844991i
$779$			347269.i			0.572258i
$780$	−185354.	−	374864.i	−0.304658	−	0.616147i
$781$	215501.			0.353303
$782$	−291693.	−	493451.i	−0.476994	−	0.806919i
$783$	−163421.			−0.266554
$784$	−28014.5	−	44221.5i	−0.0455775	−	0.0719451i
$785$	475278.	−	682137.i	0.771274	−	1.10696i
$786$	271449.	+	459203.i	0.439383	+	0.743293i
$787$	171230.			0.276459			0.138229	−	0.990400i	$-0.455859\pi$
$787$	171230.			0.276459			0.138229	+	0.990400i	$0.455859\pi$
$788$	199019.	+	109515.i	0.320510	+	0.176368i
$789$	−53150.7			−0.0853798
$790$	23432.1	−	313229.i	0.0375454	−	0.501889i
$791$		−	744661.i		−	1.19016i
$792$	65392.5	−	2015.97i	0.104250	−	0.00321390i
$793$			1.10848e6i			1.76272i
$794$	297055.	+	502520.i	0.471189	+	0.797099i
$795$	−226652.	+	325300.i	−0.358613	+	0.514694i
$796$	−907999.	−	499647.i	−1.43304	−	0.788565i
$797$		−	681307.i		−	1.07257i	−0.844036	−	0.536286i	$-0.819827\pi$
$797$		−	681307.i		−	1.07257i	0.844036	−	0.536286i	$-0.180173\pi$
$798$	256408.	+	433760.i	0.402649	+	0.681151i
$799$		−	517070.i		−	0.809946i
$800$	75674.7	−	635510.i	0.118242	−	0.992985i
$801$	256856.			0.400336
$802$	−2193.25	+	1296.49i	−0.00340988	+	0.00201568i
$803$	169045.			0.262162
$804$	213731.	−	388409.i	0.330640	−	0.600866i
$805$	404563.	+	281879.i	0.624301	+	0.434981i
$806$	−1.01088e6	+	597563.i	−1.55608	+	0.919843i
$807$	−43419.0			−0.0666703
$808$	18829.6	+	610782.i	0.0288416	+	0.935543i
$809$	−67654.6			−0.103371			−0.0516857	−	0.998663i	$-0.516459\pi$
$809$	−67654.6			−0.103371			−0.0516857	+	0.998663i	$0.516459\pi$
$810$	−72696.9	−	5438.31i	−0.110802	−	0.00828884i
$811$			617988.i			0.939590i	0.882776	+	0.469795i	$0.155672\pi$
$811$			617988.i			0.939590i	−0.882776	+	0.469795i	$0.844328\pi$
$812$	−458634.	+	833466.i	−0.695591	+	1.26408i
$813$		−	343813.i		−	0.520165i
$814$	79487.1	−	46987.2i	0.119963	−	0.0709137i
$815$	453022.	+	315643.i	0.682031	+	0.475204i
$816$	416754.	−	264015.i	0.625892	−	0.396505i
$817$		−	867221.i		−	1.29923i
$818$	−964533.	+	570164.i	−1.44149	+	0.852106i
$819$			277290.i			0.413397i
$820$	−262176.	+	129634.i	−0.389911	+	0.192794i
$821$	−539888.			−0.800972			−0.400486	−	0.916303i	$-0.631159\pi$
$821$	−539888.			−0.800972			−0.400486	+	0.916303i	$0.631159\pi$
$822$	5615.00	+	9498.75i	0.00831009	+	0.0140580i
$823$	258227.			0.381242			0.190621	−	0.981664i	$-0.438950\pi$
$823$	258227.			0.381242			0.190621	+	0.981664i	$0.438950\pi$
$824$	−10878.7	−	352875.i	−0.0160222	−	0.519716i
$825$	115345.	−	42590.4i	0.169469	−	0.0625754i
$826$	231995.	+	392460.i	0.340031	+	0.575222i
$827$	475190.			0.694794			0.347397	−	0.937718i	$-0.387066\pi$
$827$	475190.			0.694794			0.347397	+	0.937718i	$0.387066\pi$
$828$	80473.9	−	146244.i	0.117380	−	0.213312i
$829$	−267309.			−0.388959			−0.194480	−	0.980907i	$-0.562302\pi$
$829$	−267309.			−0.388959			−0.194480	+	0.980907i	$0.562302\pi$
$830$	−609013.	−	45559.1i	−0.884037	−	0.0661331i
$831$			611134.i			0.884982i
$832$	50764.4	+	822548.i	0.0733353	+	1.18827i
$833$		−	75838.7i		−	0.109295i
$834$	−221841.	−	375283.i	−0.318941	−	0.539544i
$835$	−82633.1	−	57574.5i	−0.118517	−	0.0825767i
$836$	−138704.	+	252064.i	−0.198461	+	0.360660i
$837$			204708.i			0.292203i
$838$	14526.8	+	24574.6i	0.0206862	+	0.0349944i
$839$		−	266377.i		−	0.378419i	−0.981937	−	0.189209i	$-0.939408\pi$
$839$		−	266377.i		−	0.378419i	0.981937	−	0.189209i	$-0.0605925\pi$
$840$	−231756.	+	355500.i	−0.328453	+	0.503826i
$841$	649549.			0.918374
$842$	439543.	−	259827.i	0.619979	−	0.366488i
$843$	−436603.			−0.614372
$844$	−232951.	−	128187.i	−0.327024	−	0.179953i
$845$	244509.	+	170361.i	0.342437	+	0.238593i
$846$	129619.	−	76621.9i	0.181104	−	0.107056i
$847$	−674166.			−0.939723
$848$	660028.	−	418130.i	0.917848	−	0.581460i
$849$	317562.			0.440569
$850$	585320.	−	719081.i	0.810131	−	0.995267i
$851$		−	235588.i		−	0.325308i
$852$	414593.	+	228140.i	0.571141	+	0.314283i
$853$		−	1.15218e6i		−	1.58351i	−0.610839	−	0.791755i	$-0.709168\pi$
$853$		−	1.15218e6i		−	1.58351i	0.610839	−	0.791755i	$-0.290832\pi$
$854$	968347.	−	572419.i	1.32775	−	0.784871i
$855$	183269.	−	263034.i	0.250701	−	0.359816i
$856$	5764.51	+	186985.i	0.00786710	+	0.255187i
$857$			854725.i			1.16376i	0.813273	+	0.581882i	$0.197683\pi$
$857$			854725.i			1.16376i	−0.813273	+	0.581882i	$0.802317\pi$
$858$	−136296.	+	80568.6i	−0.185144	+	0.109444i
$859$			972193.i			1.31755i	0.752341	+	0.658774i	$0.228925\pi$
$859$			972193.i			1.31755i	−0.752341	+	0.658774i	$0.771075\pi$
$860$	654721.	−	323731.i	0.885236	−	0.437711i
$861$	193934.			0.261606
$862$	601137.	+	1.01693e6i	0.809020	+	1.36860i
$863$	121346.			0.162931			0.0814653	−	0.996676i	$-0.474040\pi$
$863$	121346.			0.162931			0.0814653	+	0.996676i	$0.474040\pi$
$864$	127940.	+	65349.1i	0.171387	+	0.0875411i
$865$	−330300.	+	474059.i	−0.441445	+	0.633578i
$866$	−211597.	−	357954.i	−0.282147	−	0.477300i
$867$	280734.			0.373471
$868$	1.04404e6	+	574505.i	1.38572	+	0.762525i
$869$	−118923.			−0.157480
$870$	603577.	+	45152.4i	0.797433	+	0.0596544i
$871$			1.07289e6i			1.41422i
$872$	−42712.5	−	1.38548e6i	−0.0561723	−	1.82208i
$873$		−	94149.5i		−	0.123535i
$874$	373541.	+	631910.i	0.489007	+	0.827241i
$875$	−201047.	+	771806.i	−0.262592	+	1.00807i
$876$	325217.	+	178958.i	0.423805	+	0.233208i
$877$			691356.i			0.898882i	0.893310	+	0.449441i	$0.148377\pi$
$877$			691356.i			0.898882i	−0.893310	+	0.449441i	$0.851623\pi$
$878$	−92897.9	−	157153.i	−0.120508	−	0.203861i
$879$		−	335967.i		−	0.434829i
$880$	−242076.	−	10621.9i	−0.312599	−	0.0137163i
$881$	31766.7			0.0409280			0.0204640	−	0.999791i	$-0.493486\pi$
$881$	31766.7			0.0409280			0.0204640	+	0.999791i	$0.493486\pi$
$882$	19011.3	−	11238.1i	0.0244385	−	0.0144463i
$883$	393237.			0.504351			0.252175	−	0.967682i	$-0.418854\pi$
$883$	393237.			0.504351			0.252175	+	0.967682i	$0.418854\pi$
$884$	−575590.	+	1.04601e6i	−0.736562	+	1.33854i
$885$	165819.	−	237990.i	0.211714	−	0.303859i
$886$	436060.	−	257768.i	0.555493	−	0.328369i
$887$	1.29403e6			1.64474			0.822368	−	0.568957i	$-0.192653\pi$
$887$	1.29403e6			1.64474			0.822368	+	0.568957i	$0.192653\pi$
$888$	202664.	−	6247.88i	0.257011	−	0.00792332i
$889$	−1.13140e6			−1.43157
$890$	−948667.	−	70968.0i	−1.19766	−	0.0895947i
$891$			27600.6i			0.0347666i
$892$	26521.5	−	48197.0i	0.0333326	−	0.0605746i
$893$			662157.i			0.830344i
$894$	−568858.	+	336269.i	−0.711752	+	0.420738i
$895$	681183.	−	977660.i	0.850390	−	1.22051i
$896$	692345.	−	469109.i	0.862396	−	0.584329i
$897$			403962.i			0.502060i
$898$	337961.	−	199779.i	0.419096	−	0.247740i
$899$		−	1.69962e6i		−	2.10297i
$900$	266995.	+	40171.5i	0.329623	+	0.0495945i
$901$	1.13193e6			1.39434
$902$	56348.9	+	95324.0i	0.0692583	+	0.117163i
$903$	−484303.			−0.593939
$904$	933229.	−	28770.2i	1.14196	−	0.0352052i
$905$	49195.0	+	34276.6i	0.0600654	+	0.0418505i
$906$	−17247.7	−	29177.6i	−0.0210124	−	0.0355462i
$907$	−1.05297e6			−1.27997			−0.639987	−	0.768386i	$-0.721060\pi$
$907$	−1.05297e6			−1.27997			−0.639987	+	0.768386i	$0.721060\pi$
$908$	−533766.	+	970002.i	−0.647410	+	1.17652i
$909$	−257796.			−0.311996
$910$	76613.9	−	1.02414e6i	0.0925177	−	1.23673i
$911$		−	1.11267e6i		−	1.34069i	−0.742048	−	0.670347i	$-0.766145\pi$
$911$		−	1.11267e6i		−	1.34069i	0.742048	−	0.670347i	$-0.233855\pi$
$912$	−533692.	+	338096.i	−0.641654	+	0.406490i
$913$			231222.i			0.277388i
$914$	657746.	+	1.11269e6i	0.787346	+	1.33193i
$915$	−587211.	−	409139.i	−0.701378	−	0.488684i
$916$	209509.	−	380737.i	0.249697	−	0.453769i
$917$			1.31004e6i			1.55792i
$918$	105911.	+	179167.i	0.125677	+	0.212604i
$919$		−	265960.i		−	0.314909i	−0.987526	−	0.157455i	$-0.949671\pi$
$919$		−	265960.i		−	0.314909i	0.987526	−	0.157455i	$-0.0503288\pi$
$920$	−337627.	+	517899.i	−0.398898	+	0.611885i
$921$	−750648.			−0.884946
$922$	350115.	−	206963.i	0.411859	−	0.243462i
$923$	−1.14521e6			−1.34426
$924$	140766.	+	77459.7i	0.164875	+	0.0907260i
$925$	357477.	−	131996.i	0.417796	−	0.154269i
$926$	−535968.	+	316827.i	−0.625053	+	0.369487i
$927$	148940.			0.173321
$928$	−1.06224e6	−	542571.i	−1.23347	−	0.630029i
$929$	345791.			0.400666			0.200333	−	0.979728i	$-0.435798\pi$
$929$	345791.			0.400666			0.200333	+	0.979728i	$0.435798\pi$
$930$	56559.9	−	756066.i	0.0653947	−	0.874166i
$931$			97118.5i			0.112048i
$932$	−863988.	−	475429.i	−0.994663	−	0.547336i
$933$			567169.i			0.651552i
$934$	1.03245e6	−	610311.i	1.18352	−	0.699613i
$935$	−288023.	−	200680.i	−0.329461	−	0.229552i
$936$	−347508.	+	10713.2i	−0.396655	+	0.0122284i
$937$			865910.i			0.986264i	0.869954	+	0.493132i	$0.164148\pi$
$937$			865910.i			0.986264i	−0.869954	+	0.493132i	$0.835852\pi$
$938$	937250.	−	554036.i	1.06525	−	0.629698i
$939$		−	194136.i		−	0.220178i
$940$	−499904.	+	247181.i	−0.565759	+	0.279743i
$941$	−459940.			−0.519424			−0.259712	−	0.965686i	$-0.583628\pi$
$941$	−459940.			−0.519424			−0.259712	+	0.965686i	$0.583628\pi$
$942$	−351731.	−	595015.i	−0.396377	−	0.670542i
$943$	282527.			0.317714
$944$	−482878.	+	305905.i	−0.541868	+	0.343275i
$945$	−146893.	−	102347.i	−0.164489	−	0.114607i
$946$	−140718.	−	238049.i	−0.157241	−	0.266001i
$947$	1.52574e6			1.70130			0.850651	−	0.525730i	$-0.176208\pi$
$947$	1.52574e6			1.70130			0.850651	+	0.525730i	$0.176208\pi$
$948$	−228790.	−	125897.i	−0.254578	−	0.140087i
$949$	−898334.			−0.997483
$950$	−749557.	+	920850.i	−0.830534	+	1.02033i
$951$		−	163366.i		−	0.180634i
$952$	1.21100e6	−	37333.7i	1.33620	−	0.0411933i
$953$		−	426620.i		−	0.469737i	−0.972027	−	0.234869i	$-0.924534\pi$
$953$		−	426620.i		−	0.469737i	0.972027	−	0.234869i	$-0.0754660\pi$
$954$	167735.	+	283753.i	0.184300	+	0.311776i
$955$	−769506.	+	1.10442e6i	−0.843734	+	1.21096i
$956$	−124741.	−	68641.4i	−0.136487	−	0.0751052i
$957$		−	229158.i		−	0.250214i
$958$	−362385.	−	613039.i	−0.394857	−	0.667970i
$959$			27098.5i			0.0294651i
$960$	−454476.	−	276708.i	−0.493138	−	0.300248i
$961$	−1.20550e6			−1.30533
$962$	−422409.	+	249698.i	−0.456439	+	0.269815i
$963$	−78921.8			−0.0851029
$964$	−101671.	+	184764.i	−0.109406	+	0.198821i
$965$	494467.	−	709677.i	0.530985	−	0.762090i
$966$	352892.	−	208605.i	0.378171	−	0.223548i
$967$	−178041.			−0.190400			−0.0951999	−	0.995458i	$-0.530349\pi$
$967$	−178041.			−0.190400			−0.0951999	+	0.995458i	$0.530349\pi$
$968$	−26046.6	−	844882.i	−0.0277972	−	0.901666i
$969$	−915268.			−0.974766
$970$	−26013.0	+	347730.i	−0.0276469	+	0.369572i
$971$		−	1.24791e6i		−	1.32356i	−0.749696	−	0.661782i	$-0.769800\pi$
$971$		−	1.24791e6i		−	1.32356i	0.749696	−	0.661782i	$-0.230200\pi$
$972$	−29219.2	+	53099.5i	−0.0309269	+	0.0562028i
$973$		−	1.07063e6i		−	1.13087i
$974$	1.09568e6	−	647687.i	1.15495	−	0.682727i
$975$	−612963.	+	226333.i	−0.644800	+	0.238089i
$976$	754783.	+	1.19144e6i	0.792360	+	1.25076i
$977$			106345.i			0.111411i	0.998447	+	0.0557055i	$0.0177408\pi$
$977$			106345.i			0.111411i	−0.998447	+	0.0557055i	$0.982259\pi$
$978$	395162.	−	233592.i	0.413141	−	0.244220i
$979$			360177.i			0.375795i
$980$	−73321.0	+	36254.0i	−0.0763442	+	0.0377489i
$981$	584776.			0.607648
$982$	339925.	+	575042.i	0.352500	+	0.596316i
$983$	1.12950e6			1.16891			0.584454	−	0.811427i	$-0.301309\pi$
$983$	1.12950e6			1.16891			0.584454	+	0.811427i	$0.301309\pi$
$984$	7492.71	+	243043.i	0.00773835	+	0.251011i
$985$	202908.	−	291221.i	0.209135	−	0.300158i
$986$	−879341.	−	1.48756e6i	−0.904489	−	1.53010i
$987$	369784.			0.379589
$988$	737097.	−	1.33951e6i	0.755111	−	1.37225i
$989$	−705543.			−0.721325
$990$	7625.89	−	101939.i	0.00778073	−	0.104009i
$991$		−	1.25503e6i		−	1.27793i	−0.769234	−	0.638967i	$-0.779362\pi$
$991$		−	1.25503e6i		−	1.27793i	0.769234	−	0.638967i	$-0.220638\pi$
$992$	−679647.	+	1.33061e6i	−0.690654	+	1.35216i
$993$		−	313423.i		−	0.317857i
$994$	591385.	+	1.00043e6i	0.598546	+	1.01255i
$995$	−925742.	+	1.32866e6i	−0.935070	+	1.34205i
$996$	−244782.	+	444838.i	−0.246752	+	0.448418i
$997$		−	1.24545e6i		−	1.25295i	−0.779440	−	0.626477i	$-0.784496\pi$
$997$		−	1.24545e6i		−	1.25295i	0.779440	−	0.626477i	$-0.215504\pi$
$998$	−54755.8	−	92629.1i	−0.0549755	−	0.0930007i
$999$			85539.7i			0.0857110i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.5.f.a.19.19	yes	24
3.2	odd	2		180.5.f.i.19.6		24
4.3	odd	2	inner	60.5.f.a.19.5	✓	24
5.2	odd	4		300.5.c.e.151.18		24
5.3	odd	4		300.5.c.e.151.7		24
5.4	even	2	inner	60.5.f.a.19.6	yes	24
8.3	odd	2		960.5.j.d.319.4		24
8.5	even	2		960.5.j.d.319.21		24
12.11	even	2		180.5.f.i.19.20		24
15.14	odd	2		180.5.f.i.19.19		24
20.3	even	4		300.5.c.e.151.8		24
20.7	even	4		300.5.c.e.151.17		24
20.19	odd	2	inner	60.5.f.a.19.20	yes	24
40.19	odd	2		960.5.j.d.319.16		24
40.29	even	2		960.5.j.d.319.9		24
60.59	even	2		180.5.f.i.19.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.5.f.a.19.5	✓	24	4.3	odd	2	inner
60.5.f.a.19.6	yes	24	5.4	even	2	inner
60.5.f.a.19.19	yes	24	1.1	even	1	trivial
60.5.f.a.19.20	yes	24	20.19	odd	2	inner
180.5.f.i.19.5		24	60.59	even	2
180.5.f.i.19.6		24	3.2	odd	2
180.5.f.i.19.19		24	15.14	odd	2
180.5.f.i.19.20		24	12.11	even	2
300.5.c.e.151.7		24	5.3	odd	4
300.5.c.e.151.8		24	20.3	even	4
300.5.c.e.151.17		24	20.7	even	4
300.5.c.e.151.18		24	5.2	odd	4
960.5.j.d.319.4		24	8.3	odd	2
960.5.j.d.319.9		24	40.29	even	2
960.5.j.d.319.16		24	40.19	odd	2
960.5.j.d.319.21		24	8.5	even	2

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:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	60.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(3.44337 - 2.03548i) q^{2} -5.19615 q^{3} +(7.71364 - 14.0178i) q^{4} +(-20.5121 - 14.2918i) q^{5} +(-17.8923 + 10.5767i) q^{6} -51.0440 q^{7} +(-1.97210 - 63.9696i) q^{8} +27.0000 q^{9} +O(q^{10})\)	\(q+(3.44337 - 2.03548i) q^{2} -5.19615 q^{3} +(7.71364 - 14.0178i) q^{4} +(-20.5121 - 14.2918i) q^{5} +(-17.8923 + 10.5767i) q^{6} -51.0440 q^{7} +(-1.97210 - 63.9696i) q^{8} +27.0000 q^{9} +(-99.7214 - 7.45996i) q^{10} +37.8608i q^{11} +(-40.0812 + 72.8388i) q^{12} -201.199i q^{13} +(-175.763 + 103.899i) q^{14} +(106.584 + 74.2622i) q^{15} +(-137.000 - 216.257i) q^{16} -370.875i q^{17} +(92.9711 - 54.9580i) q^{18} +474.940i q^{19} +(-358.562 + 177.293i) q^{20} +265.232 q^{21} +(77.0650 + 130.369i) q^{22} +386.396 q^{23} +(10.2473 + 332.396i) q^{24} +(216.491 + 586.308i) q^{25} +(-409.538 - 692.805i) q^{26} -140.296 q^{27} +(-393.735 + 715.526i) q^{28} +1164.83 q^{29} +(518.167 + 38.7631i) q^{30} -1459.12i q^{31} +(-911.928 - 465.794i) q^{32} -196.731i q^{33} +(-754.909 - 1277.06i) q^{34} +(1047.02 + 729.508i) q^{35} +(208.268 - 378.482i) q^{36} -609.708i q^{37} +(966.731 + 1635.40i) q^{38} +1045.46i q^{39} +(-873.787 + 1340.33i) q^{40} +731.186 q^{41} +(913.293 - 539.875i) q^{42} -1825.96 q^{43} +(530.727 + 292.045i) q^{44} +(-553.826 - 385.878i) q^{45} +(1330.50 - 786.501i) q^{46} +1394.19 q^{47} +(711.871 + 1123.70i) q^{48} +204.486 q^{49} +(1938.88 + 1578.21i) q^{50} +1927.12i q^{51} +(-2820.38 - 1551.98i) q^{52} +3052.05i q^{53} +(-483.092 + 285.570i) q^{54} +(541.098 - 776.605i) q^{55} +(100.664 + 3265.26i) q^{56} -2467.86i q^{57} +(4010.95 - 2370.99i) q^{58} -2232.89i q^{59} +(1863.15 - 921.244i) q^{60} -5509.38 q^{61} +(-2970.00 - 5024.28i) q^{62} -1378.19 q^{63} +(-4088.22 + 252.309i) q^{64} +(-2875.50 + 4127.02i) q^{65} +(-400.442 - 677.417i) q^{66} -5332.45 q^{67} +(-5198.86 - 2860.80i) q^{68} -2007.77 q^{69} +(5090.17 + 380.786i) q^{70} -5691.93i q^{71} +(-53.2467 - 1727.18i) q^{72} -4464.89i q^{73} +(-1241.05 - 2099.45i) q^{74} +(-1124.92 - 3046.54i) q^{75} +(6657.63 + 3663.52i) q^{76} -1932.57i q^{77} +(2128.02 + 3599.92i) q^{78} +3141.04i q^{79} +(-280.550 + 6393.85i) q^{80} +729.000 q^{81} +(2517.75 - 1488.31i) q^{82} +6107.15 q^{83} +(2045.91 - 3717.98i) q^{84} +(-5300.46 + 7607.42i) q^{85} +(-6287.46 + 3716.71i) q^{86} -6052.64 q^{87} +(2421.94 - 74.6654i) q^{88} +9513.18 q^{89} +(-2692.48 - 201.419i) q^{90} +10270.0i q^{91} +(2980.52 - 5416.43i) q^{92} +7581.79i q^{93} +(4800.72 - 2837.85i) q^{94} +(6787.73 - 9742.01i) q^{95} +(4738.52 + 2420.34i) q^{96} -3487.02i q^{97} +(704.121 - 416.227i) q^{98} +1022.24i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 14 q^{4} - 24 q^{5} - 18 q^{6} + 648 q^{9}+O(q^{10}) \) 24 * q + 14 * q^4 - 24 * q^5 - 18 * q^6 + 648 * q^9	\( 24 q + 14 q^{4} - 24 q^{5} - 18 q^{6} + 648 q^{9} + 274 q^{10} - 36 q^{14} + 594 q^{16} - 12 q^{20} - 594 q^{24} + 1208 q^{25} - 2868 q^{26} - 1680 q^{29} + 468 q^{30} + 3076 q^{34} + 378 q^{36} - 7222 q^{40} - 4848 q^{41} - 3828 q^{44} - 648 q^{45} - 15280 q^{46} + 5416 q^{49} + 14472 q^{50} - 486 q^{54} + 32172 q^{56} - 7506 q^{60} + 2896 q^{61} - 18298 q^{64} - 2688 q^{65} - 15588 q^{66} + 9792 q^{69} + 27608 q^{70} + 31836 q^{74} + 50136 q^{76} - 27348 q^{80} + 17496 q^{81} - 4284 q^{84} - 15680 q^{85} - 58152 q^{86} - 38544 q^{89} + 7398 q^{90} + 4808 q^{94} + 21978 q^{96}+O(q^{100}) \) 24 * q + 14 * q^4 - 24 * q^5 - 18 * q^6 + 648 * q^9 + 274 * q^10 - 36 * q^14 + 594 * q^16 - 12 * q^20 - 594 * q^24 + 1208 * q^25 - 2868 * q^26 - 1680 * q^29 + 468 * q^30 + 3076 * q^34 + 378 * q^36 - 7222 * q^40 - 4848 * q^41 - 3828 * q^44 - 648 * q^45 - 15280 * q^46 + 5416 * q^49 + 14472 * q^50 - 486 * q^54 + 32172 * q^56 - 7506 * q^60 + 2896 * q^61 - 18298 * q^64 - 2688 * q^65 - 15588 * q^66 + 9792 * q^69 + 27608 * q^70 + 31836 * q^74 + 50136 * q^76 - 27348 * q^80 + 17496 * q^81 - 4284 * q^84 - 15680 * q^85 - 58152 * q^86 - 38544 * q^89 + 7398 * q^90 + 4808 * q^94 + 21978 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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