LMFDB - Embedded newform 60.5.f.a.19.1

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			19.1
Character	$\chi$	$=$	60.19
Dual form			60.5.f.a.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.90764 - 0.854601i) q^{2} -5.19615 q^{3} +(14.5393 + 6.67895i) q^{4} +(-9.11612 - 23.2787i) q^{5} +(20.3047 + 4.44064i) q^{6} -10.5267 q^{7} +(-51.1066 - 38.5243i) q^{8} +27.0000 q^{9} +O(q^{10})$	\(q+(-3.90764 - 0.854601i) q^{2} -5.19615 q^{3} +(14.5393 + 6.67895i) q^{4} +(-9.11612 - 23.2787i) q^{5} +(20.3047 + 4.44064i) q^{6} -10.5267 q^{7} +(-51.1066 - 38.5243i) q^{8} +27.0000 q^{9} +(15.7285 + 98.7553i) q^{10} +38.4519i q^{11} +(-75.5485 - 34.7048i) q^{12} +273.709i q^{13} +(41.1345 + 8.99612i) q^{14} +(47.3687 + 120.960i) q^{15} +(166.783 + 194.215i) q^{16} +256.390i q^{17} +(-105.506 - 23.0742i) q^{18} +257.340i q^{19} +(22.9350 - 399.342i) q^{20} +54.6982 q^{21} +(32.8610 - 150.256i) q^{22} +168.293 q^{23} +(265.558 + 200.178i) q^{24} +(-458.793 + 424.422i) q^{25} +(233.912 - 1069.55i) q^{26} -140.296 q^{27} +(-153.051 - 70.3072i) q^{28} -684.931 q^{29} +(-81.7278 - 513.148i) q^{30} -754.026i q^{31} +(-485.753 - 901.455i) q^{32} -199.802i q^{33} +(219.111 - 1001.88i) q^{34} +(95.9624 + 245.047i) q^{35} +(392.561 + 180.332i) q^{36} +1654.56i q^{37} +(219.923 - 1005.59i) q^{38} -1422.23i q^{39} +(-430.900 + 1540.88i) q^{40} +1203.31 q^{41} +(-213.741 - 46.7452i) q^{42} +3419.20 q^{43} +(-256.818 + 559.064i) q^{44} +(-246.135 - 628.524i) q^{45} +(-657.629 - 143.823i) q^{46} -3242.29 q^{47} +(-866.631 - 1009.17i) q^{48} -2290.19 q^{49} +(2155.51 - 1266.40i) q^{50} -1332.24i q^{51} +(-1828.09 + 3979.53i) q^{52} -639.077i q^{53} +(548.227 + 119.897i) q^{54} +(895.108 - 350.532i) q^{55} +(537.983 + 405.533i) q^{56} -1337.18i q^{57} +(2676.47 + 585.343i) q^{58} +6777.91i q^{59} +(-119.174 + 2075.04i) q^{60} +1887.70 q^{61} +(-644.391 + 2946.46i) q^{62} -284.220 q^{63} +(1127.76 + 3937.69i) q^{64} +(6371.57 - 2495.16i) q^{65} +(-170.751 + 780.753i) q^{66} -6754.36 q^{67} +(-1712.42 + 3727.74i) q^{68} -874.476 q^{69} +(-165.569 - 1039.57i) q^{70} +5877.68i q^{71} +(-1379.88 - 1040.15i) q^{72} -7216.94i q^{73} +(1413.99 - 6465.43i) q^{74} +(2383.96 - 2205.36i) q^{75} +(-1718.76 + 3741.55i) q^{76} -404.771i q^{77} +(-1215.44 + 5557.57i) q^{78} -7382.13i q^{79} +(3000.64 - 5652.98i) q^{80} +729.000 q^{81} +(-4702.09 - 1028.35i) q^{82} -5474.87 q^{83} +(795.275 + 365.327i) q^{84} +(5968.42 - 2337.28i) q^{85} +(-13361.0 - 2922.05i) q^{86} +3559.01 q^{87} +(1481.33 - 1965.14i) q^{88} -4600.96 q^{89} +(424.670 + 2666.39i) q^{90} -2881.24i q^{91} +(2446.87 + 1124.02i) q^{92} +3918.03i q^{93} +(12669.7 + 2770.86i) q^{94} +(5990.54 - 2345.94i) q^{95} +(2524.05 + 4684.10i) q^{96} -758.641i q^{97} +(8949.24 + 1957.20i) q^{98} +1038.20i 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 $

$2$	−3.90764	−	0.854601i	−0.976910	−	0.213650i
$2$	−3.90764	−	0.854601i	−0.976910	−	0.213650i
$3$	−5.19615			−0.577350
$3$	−5.19615			−0.577350
$4$	14.5393	+	6.67895i	0.908707	+	0.417434i
$5$	−9.11612	−	23.2787i	−0.364645	−	0.931147i
$5$	−9.11612	−	23.2787i	−0.364645	−	0.931147i
$6$	20.3047	+	4.44064i	0.564019	+	0.123351i
$7$	−10.5267			−0.214830			−0.107415	−	0.994214i	$-0.534257\pi$
$7$	−10.5267			−0.214830			−0.107415	+	0.994214i	$0.534257\pi$
$8$	−51.1066	−	38.5243i	−0.798540	−	0.601942i
$9$	27.0000			0.333333
$10$	15.7285	+	98.7553i	0.157285	+	0.987553i
$11$			38.4519i			0.317784i	0.987296	+	0.158892i	$0.0507922\pi$
$11$			38.4519i			0.317784i	−0.987296	+	0.158892i	$0.949208\pi$
$12$	−75.5485	−	34.7048i	−0.524642	−	0.241006i
$13$			273.709i			1.61958i	0.586722	+	0.809789i	$0.300418\pi$
$13$			273.709i			1.61958i	−0.586722	+	0.809789i	$0.699582\pi$
$14$	41.1345	+	8.99612i	0.209870	+	0.0458986i
$15$	47.3687	+	120.960i	0.210528	+	0.537598i
$16$	166.783	+	194.215i	0.651497	+	0.758651i
$17$			256.390i			0.887163i	0.896234	+	0.443582i	$0.146292\pi$
$17$			256.390i			0.887163i	−0.896234	+	0.443582i	$0.853708\pi$
$18$	−105.506	−	23.0742i	−0.325637	−	0.0712168i
$19$			257.340i			0.712854i	0.934323	+	0.356427i	$0.116005\pi$
$19$			257.340i			0.712854i	−0.934323	+	0.356427i	$0.883995\pi$
$20$	22.9350	−	399.342i	0.0573375	−	0.998355i
$21$	54.6982			0.124032
$22$	32.8610	−	150.256i	0.0678947	−	0.310446i
$23$	168.293			0.318134			0.159067	−	0.987268i	$-0.449151\pi$
$23$	168.293			0.318134			0.159067	+	0.987268i	$0.449151\pi$
$24$	265.558	+	200.178i	0.461037	+	0.347531i
$25$	−458.793	+	424.422i	−0.734069	+	0.679075i
$26$	233.912	−	1069.55i	0.346023	−	1.58218i
$27$	−140.296			−0.192450
$28$	−153.051	−	70.3072i	−0.195218	−	0.0896775i
$29$	−684.931			−0.814425			−0.407212	−	0.913334i	$-0.633499\pi$
$29$	−684.931			−0.814425			−0.407212	+	0.913334i	$0.633499\pi$
$30$	−81.7278	−	513.148i	−0.0908087	−	0.570164i
$31$		−	754.026i		−	0.784626i	−0.919832	−	0.392313i	$-0.871675\pi$
$31$		−	754.026i		−	0.784626i	0.919832	−	0.392313i	$-0.128325\pi$
$32$	−485.753	−	901.455i	−0.474368	−	0.880327i
$33$		−	199.802i		−	0.183473i
$34$	219.111	−	1001.88i	0.189543	−	0.866679i
$35$	95.9624	+	245.047i	0.0783367	+	0.200038i
$36$	392.561	+	180.332i	0.302902	+	0.139145i
$37$			1654.56i			1.20859i	0.796761	+	0.604295i	$0.206545\pi$
$37$			1654.56i			1.20859i	−0.796761	+	0.604295i	$0.793455\pi$
$38$	219.923	−	1005.59i	0.152301	−	0.696394i
$39$		−	1422.23i		−	0.935063i
$40$	−430.900	+	1540.88i	−0.269313	+	0.963053i
$41$	1203.31			0.715827			0.357914	−	0.933755i	$-0.383488\pi$
$41$	1203.31			0.715827			0.357914	+	0.933755i	$0.383488\pi$
$42$	−213.741	−	46.7452i	−0.121168	−	0.0264995i
$43$	3419.20			1.84921			0.924607	−	0.380923i	$-0.124394\pi$
$43$	3419.20			1.84921			0.924607	+	0.380923i	$0.124394\pi$
$44$	−256.818	+	559.064i	−0.132654	+	0.288773i
$45$	−246.135	−	628.524i	−0.121548	−	0.310382i
$46$	−657.629	−	143.823i	−0.310789	−	0.0679695i
$47$	−3242.29			−1.46776			−0.733881	−	0.679278i	$-0.762293\pi$
$47$	−3242.29			−1.46776			−0.733881	+	0.679278i	$0.762293\pi$
$48$	−866.631	−	1009.17i	−0.376142	−	0.438007i
$49$	−2290.19			−0.953848
$50$	2155.51	−	1266.40i	0.862204	−	0.506562i
$51$		−	1332.24i		−	0.512204i
$52$	−1828.09	+	3979.53i	−0.676067	+	1.47172i
$53$		−	639.077i		−	0.227511i	−0.993509	−	0.113755i	$-0.963712\pi$
$53$		−	639.077i		−	0.227511i	0.993509	−	0.113755i	$-0.0362880\pi$
$54$	548.227	+	119.897i	0.188006	+	0.0411170i
$55$	895.108	−	350.532i	0.295904	−	0.115878i
$56$	537.983	+	405.533i	0.171551	+	0.129315i
$57$		−	1337.18i		−	0.411566i
$58$	2676.47	+	585.343i	0.795620	+	0.174002i
$59$			6777.91i			1.94712i	0.228440	+	0.973558i	$0.426637\pi$
$59$			6777.91i			1.94712i	−0.228440	+	0.973558i	$0.573363\pi$
$60$	−119.174	+	2075.04i	−0.0331038	+	0.576400i
$61$	1887.70			0.507309			0.253655	−	0.967295i	$-0.418367\pi$
$61$	1887.70			0.507309			0.253655	+	0.967295i	$0.418367\pi$
$62$	−644.391	+	2946.46i	−0.167636	+	0.766509i
$63$	−284.220			−0.0716101
$64$	1127.76	+	3937.69i	0.275333	+	0.961349i
$65$	6371.57	−	2495.16i	1.50806	−	0.590570i
$66$	−170.751	+	780.753i	−0.0391990	+	0.179236i
$67$	−6754.36			−1.50465			−0.752323	−	0.658794i	$-0.771067\pi$
$67$	−6754.36			−1.50465			−0.752323	+	0.658794i	$0.771067\pi$
$68$	−1712.42	+	3727.74i	−0.370333	+	0.806172i
$69$	−874.476			−0.183675
$70$	−165.569	−	1039.57i	−0.0337896	−	0.212156i
$71$			5877.68i			1.16598i	0.812481	+	0.582988i	$0.198117\pi$
$71$			5877.68i			1.16598i	−0.812481	+	0.582988i	$0.801883\pi$
$72$	−1379.88	−	1040.15i	−0.266180	−	0.200647i
$73$		−	7216.94i		−	1.35428i	−0.735856	−	0.677138i	$-0.763220\pi$
$73$		−	7216.94i		−	1.35428i	0.735856	−	0.677138i	$-0.236780\pi$
$74$	1413.99	−	6465.43i	0.258216	−	1.18068i
$75$	2383.96	−	2205.36i	0.423815	−	0.392064i
$76$	−1718.76	+	3741.55i	−0.297570	+	0.647775i
$77$		−	404.771i		−	0.0682696i
$78$	−1215.44	+	5557.57i	−0.199777	+	0.913473i
$79$		−	7382.13i		−	1.18284i	−0.806362	−	0.591422i	$-0.798567\pi$
$79$		−	7382.13i		−	1.18284i	0.806362	−	0.591422i	$-0.201433\pi$
$80$	3000.64	−	5652.98i	0.468851	−	0.883277i
$81$	729.000			0.111111
$82$	−4702.09	−	1028.35i	−0.699299	−	0.152937i
$83$	−5474.87			−0.794726			−0.397363	−	0.917661i	$-0.630075\pi$
$83$	−5474.87			−0.794726			−0.397363	+	0.917661i	$0.630075\pi$
$84$	795.275	+	365.327i	0.112709	+	0.0517753i
$85$	5968.42	−	2337.28i	0.826079	−	0.323499i
$86$	−13361.0	−	2922.05i	−1.80652	−	0.395085i
$87$	3559.01			0.470208
$88$	1481.33	−	1965.14i	0.191287	−	0.253763i
$89$	−4600.96			−0.580856			−0.290428	−	0.956897i	$-0.593798\pi$
$89$	−4600.96			−0.580856			−0.290428	+	0.956897i	$0.593798\pi$
$90$	424.670	+	2666.39i	0.0524284	+	0.329184i
$91$		−	2881.24i		−	0.347934i
$92$	2446.87	+	1124.02i	0.289091	+	0.132800i
$93$			3918.03i			0.453004i
$94$	12669.7	+	2770.86i	1.43387	+	0.313588i
$95$	5990.54	−	2345.94i	0.663772	−	0.259938i
$96$	2524.05	+	4684.10i	0.273876	+	0.508257i
$97$		−	758.641i		−	0.0806293i	−0.999187	−	0.0403146i	$-0.987164\pi$
$97$		−	758.641i		−	0.0806293i	0.999187	−	0.0403146i	$-0.0128360\pi$
$98$	8949.24	+	1957.20i	0.931824	+	0.203790i
$99$			1038.20i			0.105928i
$100$	−9505.23	+	3106.55i	−0.950523	+	0.310655i
$101$	−8930.15			−0.875419			−0.437710	−	0.899116i	$-0.644210\pi$
$101$	−8930.15			−0.875419			−0.437710	+	0.899116i	$0.644210\pi$
$102$	−1138.54	+	5205.93i	−0.109433	+	0.500377i
$103$	8127.84			0.766127			0.383063	−	0.923722i	$-0.374869\pi$
$103$	8127.84			0.766127			0.383063	+	0.923722i	$0.374869\pi$
$104$	10544.4	−	13988.3i	0.974891	−	1.29330i
$105$	−498.635	−	1273.30i	−0.0452277	−	0.115492i
$106$	−546.156	+	2497.28i	−0.0486077	+	0.222257i
$107$	947.053			0.0827193			0.0413597	−	0.999144i	$-0.486831\pi$
$107$	947.053			0.0827193			0.0413597	+	0.999144i	$0.486831\pi$
$108$	−2039.81	−	937.031i	−0.174881	−	0.0803353i
$109$	−16024.5			−1.34875			−0.674373	−	0.738391i	$-0.735586\pi$
$109$	−16024.5			−1.34875			−0.674373	+	0.738391i	$0.735586\pi$
$110$	−3797.33	+	604.791i	−0.313829	+	0.0499827i
$111$		−	8597.35i		−	0.697780i
$112$	−1755.67	−	2044.44i	−0.139961	−	0.162981i
$113$			12287.0i			0.962256i	0.876650	+	0.481128i	$0.159773\pi$
$113$			12287.0i			0.962256i	−0.876650	+	0.481128i	$0.840227\pi$
$114$	−1142.76	+	5225.22i	−0.0879313	+	0.402063i
$115$	−1534.18	−	3917.64i	−0.116006	−	0.296230i
$116$	−9958.43	−	4574.62i	−0.740073	−	0.339969i
$117$			7390.13i			0.539859i
$118$	5792.41	−	26485.6i	0.416002	−	1.90216i
$119$		−	2698.94i		−	0.190590i
$120$	2239.02	−	8006.67i	0.155488	−	0.556019i
$121$	13162.5			0.899013
$122$	−7376.44	−	1613.23i	−0.495595	−	0.108387i
$123$	−6252.56			−0.413283
$124$	5036.10	−	10963.0i	0.327530	−	0.712995i
$125$	14062.4	+	6811.01i	0.899993	+	0.435904i
$126$	1110.63	+	242.895i	0.0699566	+	0.0152995i
$127$	−1969.22			−0.122092			−0.0610459	−	0.998135i	$-0.519444\pi$
$127$	−1969.22			−0.122092			−0.0610459	+	0.998135i	$0.519444\pi$
$128$	−1041.74	−	16350.8i	−0.0635829	−	0.997977i
$129$	−17766.7			−1.06764
$130$	−27030.2	+	4305.03i	−1.59942	+	0.254736i
$131$			20194.2i			1.17675i	0.808589	+	0.588374i	$0.200232\pi$
$131$			20194.2i			1.17675i	−0.808589	+	0.588374i	$0.799768\pi$
$132$	1334.47	−	2904.98i	0.0765878	−	0.166723i
$133$		−	2708.94i		−	0.153143i
$134$	26393.6	+	5772.28i	1.46990	+	0.321468i
$135$	1278.96	+	3265.91i	0.0701759	+	0.179199i
$136$	9877.24	−	13103.2i	0.534020	−	0.708436i
$137$			9623.52i			0.512735i	0.966579	+	0.256367i	$0.0825257\pi$
$137$			9623.52i			0.512735i	−0.966579	+	0.256367i	$0.917474\pi$
$138$	3417.14	+	747.329i	0.179434	+	0.0392422i
$139$			32167.4i			1.66489i	0.554106	+	0.832446i	$0.313060\pi$
$139$			32167.4i			1.66489i	−0.554106	+	0.832446i	$0.686940\pi$
$140$	−241.430	+	4203.75i	−0.0123178	+	0.214477i
$141$	16847.4			0.847413
$142$	5023.08	−	22967.9i	0.249111	−	1.13905i
$143$	−10524.6			−0.514676
$144$	4503.15	+	5243.80i	0.217166	+	0.252884i
$145$	6243.91	+	15944.3i	0.296976	+	0.758349i
$146$	−6167.60	+	28201.2i	−0.289342	+	1.32301i
$147$	11900.2			0.550704
$148$	−11050.7	+	24056.2i	−0.504507	+	1.09825i
$149$	−14146.3			−0.637192			−0.318596	−	0.947891i	$-0.603211\pi$
$149$	−14146.3			−0.637192			−0.318596	+	0.947891i	$0.603211\pi$
$150$	−11200.4	+	6580.43i	−0.497794	+	0.292463i
$151$		−	22961.8i		−	1.00705i	−0.863980	−	0.503527i	$-0.832036\pi$
$151$		−	22961.8i		−	1.00705i	0.863980	−	0.503527i	$-0.167964\pi$
$152$	9913.84	−	13151.8i	0.429096	−	0.569242i
$153$			6922.54i			0.295721i
$154$	−345.917	+	1581.70i	−0.0145858	+	0.0666933i
$155$	−17552.7	+	6873.79i	−0.730602	+	0.286110i
$156$	9499.01	−	20678.3i	0.390328	−	0.849699i
$157$			4633.47i			0.187978i	0.995573	+	0.0939891i	$0.0299619\pi$
$157$			4633.47i			0.187978i	−0.995573	+	0.0939891i	$0.970038\pi$
$158$	−6308.77	+	28846.7i	−0.252715	+	1.15553i
$159$			3320.74i			0.131353i
$160$	−16556.5	+	19525.4i	−0.646738	+	0.762713i
$161$	−1771.57			−0.0683449
$162$	−2848.67	−	623.004i	−0.108546	−	0.0237389i
$163$	−4881.70			−0.183737			−0.0918684	−	0.995771i	$-0.529284\pi$
$163$	−4881.70			−0.183737			−0.0918684	+	0.995771i	$0.529284\pi$
$164$	17495.2	+	8036.82i	0.650477	+	0.298811i
$165$	−4651.12	+	1821.42i	−0.170840	+	0.0669023i
$166$	21393.8	+	4678.83i	0.776376	+	0.169794i
$167$	44697.6			1.60270			0.801348	−	0.598198i	$-0.204116\pi$
$167$	44697.6			1.60270			0.801348	+	0.598198i	$0.204116\pi$
$168$	−2795.44	−	2107.21i	−0.0990448	−	0.0746602i
$169$	−46355.4			−1.62303
$170$	−25319.9	+	4032.64i	−0.876121	+	0.139538i
$171$			6948.19i			0.237618i
$172$	49712.8	+	22836.6i	1.68039	+	0.771925i
$173$		−	6971.46i		−	0.232933i	−0.993195	−	0.116467i	$-0.962843\pi$
$173$		−	6971.46i		−	0.232933i	0.993195	−	0.116467i	$-0.0371568\pi$
$174$	−13907.3	−	3041.53i	−0.459351	−	0.100460i
$175$	4829.57	−	4467.76i	0.157700	−	0.145886i
$176$	−7467.92	+	6413.13i	−0.241087	+	0.207035i
$177$		−	35219.1i		−	1.12417i
$178$	17978.9	+	3931.98i	0.567444	+	0.124100i
$179$		−	22333.2i		−	0.697020i	−0.937305	−	0.348510i	$-0.886688\pi$
$179$		−	22333.2i		−	0.697020i	0.937305	−	0.348510i	$-0.113312\pi$
$180$	619.246	−	10782.2i	0.0191125	−	0.332785i
$181$	35367.4			1.07956			0.539779	−	0.841807i	$-0.318508\pi$
$181$	35367.4			1.07956			0.539779	+	0.841807i	$0.318508\pi$
$182$	−2462.31	+	11258.9i	−0.0743363	+	0.339900i
$183$	−9808.76			−0.292895
$184$	−8600.88	−	6483.37i	−0.254043	−	0.191498i
$185$	38516.0	−	15083.2i	1.12537	−	0.440706i
$186$	3348.36	−	15310.3i	0.0967845	−	0.442544i
$187$	−9858.68			−0.281926
$188$	−47140.6	−	21655.1i	−1.33377	−	0.612694i
$189$	1476.85			0.0413441
$190$	−25413.7	+	4047.58i	−0.703981	+	0.112121i
$191$		−	63007.8i		−	1.72714i	−0.504230	−	0.863570i	$-0.668224\pi$
$191$		−	63007.8i		−	1.72714i	0.504230	−	0.863570i	$-0.331776\pi$
$192$	−5860.03	−	20460.8i	−0.158963	−	0.555035i
$193$			19940.8i			0.535338i	0.963511	+	0.267669i	$0.0862534\pi$
$193$			19940.8i			0.535338i	−0.963511	+	0.267669i	$0.913747\pi$
$194$	−648.336	+	2964.50i	−0.0172265	+	0.0787676i
$195$	−33107.7	+	12965.2i	−0.870681	+	0.340966i
$196$	−33297.8	−	15296.1i	−0.866768	−	0.398169i
$197$		−	69791.4i		−	1.79833i	−0.437609	−	0.899165i	$-0.644175\pi$
$197$		−	69791.4i		−	1.79833i	0.437609	−	0.899165i	$-0.355825\pi$
$198$	887.248	−	4056.91i	0.0226316	−	0.103482i
$199$		−	4560.80i		−	0.115169i	−0.998341	−	0.0575843i	$-0.981660\pi$
$199$		−	4560.80i		−	0.115169i	0.998341	−	0.0575843i	$-0.0183398\pi$
$200$	39797.9	−	4016.10i	0.994947	−	0.100403i
$201$	35096.7			0.868708
$202$	34895.8	+	7631.72i	0.855206	+	0.187034i
$203$	7210.05			0.174963
$204$	8897.98	−	19369.9i	0.213812	−	0.465443i
$205$	−10969.5	−	28011.4i	−0.261023	−	0.666540i
$206$	−31760.7	−	6946.06i	−0.748437	−	0.163683i
$207$	4543.91			0.106045
$208$	−53158.2	+	45650.0i	−1.22869	+	1.05515i
$209$	−9895.21			−0.226534
$210$	860.323	+	5401.74i	0.0195084	+	0.122488i
$211$			50581.3i			1.13612i	0.822986	+	0.568061i	$0.192306\pi$
$211$			50581.3i			1.13612i	−0.822986	+	0.568061i	$0.807694\pi$
$212$	4268.37	−	9291.75i	0.0949708	−	0.206741i
$213$		−	30541.3i		−	0.673176i
$214$	−3700.74	−	809.353i	−0.0808093	−	0.0176730i
$215$	−31169.8	−	79594.3i	−0.674306	−	1.72189i
$216$	7170.05	+	5404.80i	0.153679	+	0.115844i
$217$			7937.39i			0.168561i
$218$	62617.8	+	13694.5i	1.31760	+	0.288160i
$219$			37500.3i			0.781892i
$220$	15355.4	+	881.894i	0.317261	+	0.0182210i
$221$	−70176.2			−1.43683
$222$	−7347.30	+	33595.3i	−0.149081	+	0.681668i
$223$	21320.1			0.428726			0.214363	−	0.976754i	$-0.431233\pi$
$223$	21320.1			0.428726			0.214363	+	0.976754i	$0.431233\pi$
$224$	5113.36	+	9489.32i	0.101909	+	0.189121i
$225$	−12387.4	+	11459.4i	−0.244690	+	0.226358i
$226$	10500.5	−	48013.4i	0.205586	−	0.940038i
$227$	23761.8			0.461135			0.230567	−	0.973056i	$-0.425942\pi$
$227$	23761.8			0.461135			0.230567	+	0.973056i	$0.425942\pi$
$228$	8930.95	−	19441.7i	0.171802	−	0.373993i
$229$	49175.6			0.937732			0.468866	−	0.883269i	$-0.344663\pi$
$229$	49175.6			0.937732			0.468866	+	0.883269i	$0.344663\pi$
$230$	2647.00	+	16619.8i	0.0500378	+	0.314175i
$231$			2103.25i			0.0394155i
$232$	35004.5	+	26386.5i	0.650351	+	0.490236i
$233$		−	60292.5i		−	1.11058i	−0.831655	−	0.555292i	$-0.812607\pi$
$233$		−	60292.5i		−	1.11058i	0.831655	−	0.555292i	$-0.187393\pi$
$234$	6315.62	−	28878.0i	0.115341	−	0.527394i
$235$	29557.1	+	75476.1i	0.535212	+	1.36670i
$236$	−45269.3	+	98546.2i	−0.812793	+	1.76936i
$237$			38358.6i			0.682915i
$238$	−2306.52	+	10546.5i	−0.0407195	+	0.186189i
$239$		−	34237.6i		−	0.599388i	−0.954035	−	0.299694i	$-0.903115\pi$
$239$		−	34237.6i		−	0.599388i	0.954035	−	0.299694i	$-0.0968845\pi$
$240$	−15591.8	+	29373.7i	−0.270691	+	0.509960i
$241$	−2512.03			−0.0432505			−0.0216253	−	0.999766i	$-0.506884\pi$
$241$	−2512.03			−0.0432505			−0.0216253	+	0.999766i	$0.506884\pi$
$242$	−51434.1	−	11248.7i	−0.878255	−	0.192075i
$243$	−3788.00			−0.0641500
$244$	27445.8	+	12607.8i	0.460995	+	0.211768i
$245$	20877.6	+	53312.6i	0.347816	+	0.888172i
$246$	24432.8	+	5343.45i	0.403741	+	0.0882981i
$247$	−70436.2			−1.15452
$248$	−29048.3	+	38535.7i	−0.472299	+	0.626555i
$249$	28448.3			0.458835
$250$	−49130.1	−	38632.7i	−0.786081	−	0.618123i
$251$			63629.7i			1.00998i	0.863125	+	0.504990i	$0.168504\pi$
$251$			63629.7i			1.00998i	−0.863125	+	0.504990i	$0.831496\pi$
$252$	−4132.37	−	1898.29i	−0.0650726	−	0.0298925i
$253$			6471.18i			0.101098i
$254$	7695.00	+	1682.90i	0.119273	+	0.0260850i
$255$	−31012.8	+	12144.9i	−0.476937	+	0.186772i
$256$	−9902.71	+	64783.5i	−0.151103	+	0.988518i
$257$			70597.1i			1.06886i	0.845213	+	0.534430i	$0.179474\pi$
$257$			70597.1i			1.06886i	−0.845213	+	0.534430i	$0.820526\pi$
$258$	69425.7	+	15183.4i	1.04299	+	0.228103i
$259$		−	17417.0i		−	0.259642i
$260$	109303.	+	6277.51i	1.61691	+	0.0928626i
$261$	−18493.1			−0.271475
$262$	17258.0	−	78911.5i	0.251413	−	1.14958i
$263$	63534.2			0.918536			0.459268	−	0.888298i	$-0.348112\pi$
$263$	63534.2			0.918536			0.459268	+	0.888298i	$0.348112\pi$
$264$	−7697.21	+	10211.2i	−0.110440	+	0.146510i
$265$	−14876.9	+	5825.90i	−0.211846	+	0.0829605i
$266$	−2315.06	+	10585.6i	−0.0327190	+	0.149607i
$267$	23907.3			0.335357
$268$	−98203.7	−	45112.0i	−1.36728	−	0.628091i
$269$	76424.0			1.05615			0.528074	−	0.849198i	$-0.322914\pi$
$269$	76424.0			1.05615			0.528074	+	0.849198i	$0.322914\pi$
$270$	−2206.65	−	13855.0i	−0.0302696	−	0.190055i
$271$		−	1217.43i		−	0.0165769i	−0.999966	−	0.00828846i	$-0.997362\pi$
$271$		−	1217.43i		−	0.0165769i	0.999966	−	0.00828846i	$-0.00263833\pi$
$272$	−49794.8	+	42761.6i	−0.673048	+	0.577984i
$273$			14971.4i			0.200880i
$274$	8224.27	−	37605.3i	0.109546	−	0.500896i
$275$	−16319.8	−	17641.4i	−0.215799	−	0.233275i
$276$	−12714.3	−	5840.58i	−0.166907	−	0.0766722i
$277$		−	10953.9i		−	0.142761i	−0.997449	−	0.0713803i	$-0.977260\pi$
$277$		−	10953.9i		−	0.142761i	0.997449	−	0.0713803i	$-0.0227404\pi$
$278$	27490.3	−	125699.i	0.355705	−	1.62645i
$279$		−	20358.7i		−	0.261542i
$280$	4535.95	−	16220.4i	0.0578565	−	0.206893i
$281$	−82058.4			−1.03923			−0.519614	−	0.854401i	$-0.673924\pi$
$281$	−82058.4			−1.03923			−0.519614	+	0.854401i	$0.673924\pi$
$282$	−65833.6	−	14397.8i	−0.827846	−	0.181050i
$283$	−50793.3			−0.634211			−0.317105	−	0.948390i	$-0.602711\pi$
$283$	−50793.3			−0.634211			−0.317105	+	0.948390i	$0.602711\pi$
$284$	−39256.8	+	85457.5i	−0.486718	+	1.05953i
$285$	−31127.8	+	12189.9i	−0.383229	+	0.150075i
$286$	41126.4	+	8994.34i	0.502792	+	0.109961i
$287$	−12666.8			−0.153781
$288$	−13115.3	−	24339.3i	−0.158123	−	0.293442i
$289$	17785.1			0.212941
$290$	−10773.0	−	67640.6i	−0.128097	−	0.804288i
$291$			3942.01i			0.0465513i
$292$	48201.6	−	104929.i	0.565321	−	1.23064i
$293$			126457.i			1.47302i	0.676425	+	0.736511i	$0.263528\pi$
$293$			126457.i			1.47302i	−0.676425	+	0.736511i	$0.736472\pi$
$294$	−46501.6	−	10169.9i	−0.537989	−	0.117658i
$295$	157781.	−	61788.2i	1.81305	−	0.710005i
$296$	63740.7	−	84558.9i	0.727501	−	0.965108i
$297$		−	5394.65i		−	0.0611576i
$298$	55278.6	+	12089.4i	0.622479	+	0.136136i
$299$			46063.3i			0.515243i
$300$	49390.6	−	16142.1i	0.548785	−	0.179357i
$301$	−35992.8			−0.397267
$302$	−19623.2	+	89726.6i	−0.215157	+	0.983801i
$303$	46402.4			0.505424
$304$	−49979.3	+	42920.0i	−0.540807	+	0.464422i
$305$	−17208.5	−	43943.1i	−0.184988	−	0.472379i
$306$	5916.01	−	27050.8i	0.0631809	−	0.288893i
$307$	−152128.			−1.61411			−0.807053	−	0.590479i	$-0.798939\pi$
$307$	−152128.			−1.61411			−0.807053	+	0.590479i	$0.798939\pi$
$308$	2703.44	−	5885.09i	0.0284981	−	0.0620371i
$309$	−42233.5			−0.442323
$310$	74464.0	−	11859.7i	0.774860	−	0.123410i
$311$			31828.3i			0.329073i	0.986371	+	0.164537i	$0.0526128\pi$
$311$			31828.3i			0.329073i	−0.986371	+	0.164537i	$0.947387\pi$
$312$	−54790.4	+	72685.4i	−0.562853	+	0.746686i
$313$			37579.2i			0.383582i	0.981436	+	0.191791i	$0.0614296\pi$
$313$			37579.2i			0.383582i	−0.981436	+	0.191791i	$0.938570\pi$
$314$	3959.77	−	18105.9i	0.0401616	−	0.183638i
$315$	2590.99	+	6616.27i	0.0261122	+	0.0666795i
$316$	49304.9	−	107331.i	0.493760	−	1.07486i
$317$			76010.0i			0.756401i	0.925724	+	0.378201i	$0.123457\pi$
$317$			76010.0i			0.756401i	−0.925724	+	0.378201i	$0.876543\pi$
$318$	2837.91	−	12976.3i	0.0280637	−	0.128320i
$319$		−	26336.9i		−	0.258811i
$320$	81383.3	−	62149.2i	0.794758	−	0.606926i
$321$	−4921.03			−0.0477580
$322$	6922.65	+	1513.98i	0.0667668	+	0.0146019i
$323$	−65979.5			−0.632418
$324$	10599.2	+	4868.96i	0.100967	+	0.0463816i
$325$	−116168.	−	125576.i	−1.09982	−	1.18888i
$326$	19075.9	+	4171.91i	0.179494	+	0.0392554i
$327$	83265.5			0.778699
$328$	−61496.8	−	46356.5i	−0.571617	−	0.430886i
$329$	34130.5			0.315320
$330$	19731.5	−	3142.59i	0.181189	−	0.0288575i
$331$		−	120219.i		−	1.09728i	−0.836060	−	0.548638i	$-0.815147\pi$
$331$		−	120219.i		−	1.09728i	0.836060	−	0.548638i	$-0.184853\pi$
$332$	−79600.8	−	36566.4i	−0.722173	−	0.331746i
$333$			44673.1i			0.402863i
$334$	−174662.	−	38198.6i	−1.56569	−	0.342417i
$335$	61573.5	+	157232.i	0.548661	+	1.40105i
$336$	9122.75	+	10623.2i	0.0808067	+	0.0940972i
$337$			81709.2i			0.719467i	0.933055	+	0.359734i	$0.117132\pi$
$337$			81709.2i			0.719467i	−0.933055	+	0.359734i	$0.882868\pi$
$338$	181140.	+	39615.4i	1.58556	+	0.346761i
$339$		−	63845.4i		−	0.555559i
$340$	102387.	+	5880.31i	0.885704	+	0.0508678i
$341$	28993.7			0.249342
$342$	5937.93	−	27151.0i	0.0507672	−	0.232131i
$343$	49382.6			0.419746
$344$	−174743.	−	131722.i	−1.47667	−	1.11312i
$345$	7971.83	+	20356.6i	0.0669761	+	0.171028i
$346$	−5957.82	+	27242.0i	−0.0497663	+	0.227555i
$347$	53216.0			0.441960			0.220980	−	0.975278i	$-0.429074\pi$
$347$	53216.0			0.441960			0.220980	+	0.975278i	$0.429074\pi$
$348$	51745.5	+	23770.4i	0.427282	+	0.196281i
$349$	134753.			1.10633			0.553167	−	0.833070i	$-0.313419\pi$
$349$	134753.			1.10633			0.553167	+	0.833070i	$0.313419\pi$
$350$	−22690.4	+	13331.0i	−0.185227	+	0.108825i
$351$		−	38400.2i		−	0.311688i
$352$	34662.6	−	18678.1i	0.279754	−	0.150747i
$353$		−	88840.8i		−	0.712956i	−0.934304	−	0.356478i	$-0.883977\pi$
$353$		−	88840.8i		−	0.712956i	0.934304	−	0.356478i	$-0.116023\pi$
$354$	−30098.3	+	137623.i	−0.240179	+	1.09821i
$355$	136825.	−	53581.6i	1.08569	−	0.425167i
$356$	−66894.8	−	30729.6i	−0.527828	−	0.242469i
$357$			14024.1i			0.110037i
$358$	−19086.0	+	87270.2i	−0.148919	+	0.680926i
$359$		−	50921.2i		−	0.395102i	−0.980293	−	0.197551i	$-0.936701\pi$
$359$		−	50921.2i		−	0.395102i	0.980293	−	0.197551i	$-0.0632988\pi$
$360$	−11634.3	+	41603.9i	−0.0897708	+	0.321018i
$361$	64097.0			0.491839
$362$	−138203.	−	30225.0i	−1.05463	−	0.230648i
$363$	−68394.1			−0.519046
$364$	19243.7	−	41891.3i	0.145240	−	0.316170i
$365$	−168001.	+	65790.4i	−1.26103	+	0.493830i
$366$	38329.1	+	8382.58i	0.286132	+	0.0625771i
$367$	−226148.			−1.67904			−0.839519	−	0.543330i	$-0.817163\pi$
$367$	−226148.			−1.67904			−0.839519	+	0.543330i	$0.817163\pi$
$368$	28068.5	+	32685.0i	0.207264	+	0.241353i
$369$	32489.3			0.238609
$370$	−163397.	+	26023.8i	−1.19355	+	0.190093i
$371$			6727.36i			0.0488762i
$372$	−26168.3	+	56965.5i	−0.189099	+	0.411648i
$373$		−	204938.i		−	1.47301i	−0.676435	−	0.736503i	$-0.736476\pi$
$373$		−	204938.i		−	1.47301i	0.676435	−	0.736503i	$-0.263524\pi$
$374$	38524.2	+	8425.24i	0.275417	+	0.0602337i
$375$	−73070.3	−	35391.0i	−0.519611	−	0.251670i
$376$	165702.	+	124907.i	1.17207	+	0.883507i
$377$		−	187472.i		−	1.31902i
$378$	−5771.01	−	1262.12i	−0.0403895	−	0.00883318i
$379$			107866.i			0.750938i	0.926835	+	0.375469i	$0.122518\pi$
$379$			107866.i			0.750938i	−0.926835	+	0.375469i	$0.877482\pi$
$380$	102767.	+	5902.10i	0.711681	+	0.0408733i
$381$	10232.4			0.0704898
$382$	−53846.5	+	246212.i	−0.369004	+	1.68726i
$383$	−112959.			−0.770055			−0.385028	−	0.922905i	$-0.625808\pi$
$383$	−112959.			−0.770055			−0.385028	+	0.922905i	$0.625808\pi$
$384$	5413.05	+	84961.5i	0.0367096	+	0.576182i
$385$	−9422.52	+	3689.94i	−0.0635690	+	0.0248941i
$386$	17041.4	−	77921.5i	0.114375	−	0.522977i
$387$	92318.3			0.616404
$388$	5066.93	−	11030.1i	0.0336574	−	0.0732684i
$389$	241784.			1.59782			0.798910	−	0.601451i	$-0.205410\pi$
$389$	241784.			1.59782			0.798910	+	0.601451i	$0.205410\pi$
$390$	140453.	−	22369.6i	0.923425	−	0.147072i
$391$			43148.7i			0.282237i
$392$	117044.	+	88227.8i	0.761686	+	0.574161i
$393$		−	104932.i		−	0.679395i
$394$	−59643.8	+	272720.i	−0.384214	+	1.75681i
$395$	−171846.	+	67296.3i	−1.10140	+	0.431317i
$396$	−6934.09	+	15094.7i	−0.0442180	+	0.0962575i
$397$		−	21464.4i		−	0.136188i	−0.997679	−	0.0680938i	$-0.978308\pi$
$397$		−	21464.4i		−	0.136188i	0.997679	−	0.0680938i	$-0.0216917\pi$
$398$	−3897.66	+	17822.0i	−0.0246058	+	0.112509i
$399$			14076.1i			0.0884169i
$400$	−158948.	−	18317.8i	−0.993425	−	0.114486i
$401$	111671.			0.694465			0.347232	−	0.937779i	$-0.387122\pi$
$401$	111671.			0.694465			0.347232	+	0.937779i	$0.387122\pi$
$402$	−137145.	−	29993.7i	−0.848650	−	0.185600i
$403$	206383.			1.27076
$404$	−129838.	−	59644.0i	−0.795500	−	0.365430i
$405$	−6645.65	−	16970.1i	−0.0405161	−	0.103461i
$406$	−28174.3	−	6161.72i	−0.170923	−	0.0373809i
$407$	−63620.9			−0.384071
$408$	−51323.7	+	68086.4i	−0.308317	+	0.409015i
$409$	42586.1			0.254578			0.127289	−	0.991866i	$-0.459372\pi$
$409$	42586.1			0.254578			0.127289	+	0.991866i	$0.459372\pi$
$410$	18926.2	+	118833.i	0.112589	+	0.706918i
$411$		−	50005.3i		−	0.296028i
$412$	118173.	+	54285.4i	0.696185	+	0.319808i
$413$		−	71348.9i		−	0.418299i
$414$	−17756.0	−	3883.23i	−0.103596	−	0.0226565i
$415$	49909.5	+	127448.i	0.289793	+	0.740007i
$416$	246736.	−	132955.i	1.42576	−	0.768276i
$417$		−	167147.i		−	0.961226i
$418$	38666.9	+	8456.46i	0.221303	+	0.0483990i
$419$			82067.7i			0.467460i	0.972302	+	0.233730i	$0.0750931\pi$
$419$			82067.7i			0.467460i	−0.972302	+	0.233730i	$0.924907\pi$
$420$	1254.51	−	21843.3i	0.00711171	−	0.123828i
$421$	−134312.			−0.757794			−0.378897	−	0.925439i	$-0.623697\pi$
$421$	−134312.			−0.757794			−0.378897	+	0.925439i	$0.623697\pi$
$422$	43226.8	−	197654.i	0.242733	−	1.10989i
$423$	−87541.7			−0.489254
$424$	−24620.0	+	32661.1i	−0.136948	+	0.181676i
$425$	−108818.	−	117630.i	−0.602451	−	0.651239i
$426$	−26100.7	+	119345.i	−0.143824	+	0.657633i
$427$	−19871.2			−0.108985
$428$	13769.5	+	6325.32i	0.0751676	+	0.0345299i
$429$	54687.5			0.297148
$430$	53778.9	+	337664.i	0.290854	+	1.82620i
$431$			164289.i			0.884411i	0.896914	+	0.442205i	$0.145804\pi$
$431$			164289.i			0.884411i	−0.896914	+	0.442205i	$0.854196\pi$
$432$	−23399.0	−	27247.6i	−0.125381	−	0.146002i
$433$			196377.i			1.04741i	0.851901	+	0.523703i	$0.175450\pi$
$433$			196377.i			1.04741i	−0.851901	+	0.523703i	$0.824550\pi$
$434$	6783.30	−	31016.5i	0.0360132	−	0.164669i
$435$	−32444.3	−	82848.9i	−0.171459	−	0.437833i
$436$	−232985.	−	107027.i	−1.22562	−	0.563013i
$437$			43308.6i			0.226783i
$438$	32047.8	−	146538.i	0.167051	−	0.763838i
$439$		−	268874.i		−	1.39514i	−0.716515	−	0.697572i	$-0.754264\pi$
$439$		−	268874.i		−	1.39514i	0.716515	−	0.697572i	$-0.245736\pi$
$440$	−59249.9	−	16568.9i	−0.306043	−	0.0855832i
$441$	−61835.1			−0.317949
$442$	274223.	+	59972.7i	1.40365	+	0.306979i
$443$	−82278.4			−0.419255			−0.209628	−	0.977781i	$-0.567225\pi$
$443$	−82278.4			−0.419255			−0.209628	+	0.977781i	$0.567225\pi$
$444$	57421.2	−	125000.i	0.291277	−	0.634077i
$445$	41942.9	+	107104.i	0.211806	+	0.540862i
$446$	−83311.3	−	18220.2i	−0.418826	−	0.0915974i
$447$	73506.3			0.367883
$448$	−11871.6	−	41450.8i	−0.0591498	−	0.206527i
$449$	62580.8			0.310419			0.155210	−	0.987882i	$-0.450395\pi$
$449$	62580.8			0.310419			0.155210	+	0.987882i	$0.450395\pi$
$450$	58198.8	−	34192.9i	0.287401	−	0.168854i
$451$			46269.4i			0.227479i
$452$	−82064.6	+	178645.i	−0.401679	+	0.874409i
$453$			119313.i			0.581423i
$454$	−92852.6	−	20306.9i	−0.450487	−	0.0985216i
$455$	−67071.5	+	26265.7i	−0.323978	+	0.126872i
$456$	−51513.8	+	68338.6i	−0.247739	+	0.328652i
$457$			203110.i			0.972520i	0.873814	+	0.486260i	$0.161639\pi$
$457$			203110.i			0.972520i	−0.873814	+	0.486260i	$0.838361\pi$
$458$	−192161.	−	42025.6i	−0.916080	−	0.200347i
$459$		−	35970.6i		−	0.170735i
$460$	3859.80	−	67206.5i	0.0182410	−	0.317611i
$461$	61108.2			0.287539			0.143770	−	0.989611i	$-0.454078\pi$
$461$	61108.2			0.287539			0.143770	+	0.989611i	$0.454078\pi$
$462$	1797.44	−	8218.74i	0.00842113	−	0.0385054i
$463$	270706.			1.26281			0.631403	−	0.775455i	$-0.282479\pi$
$463$	270706.			1.26281			0.631403	+	0.775455i	$0.282479\pi$
$464$	−114235.	−	133024.i	−0.530595	−	0.617864i
$465$	91206.6	−	35717.2i	0.421813	−	0.165186i
$466$	−51526.0	+	235601.i	−0.237277	+	1.08494i
$467$	364897.			1.67316			0.836579	−	0.547847i	$-0.184552\pi$
$467$	364897.			1.67316			0.836579	+	0.547847i	$0.184552\pi$
$468$	−49358.3	+	107447.i	−0.225356	+	0.490574i
$469$	71101.0			0.323243
$470$	−50996.4	−	320193.i	−0.230857	−	1.44949i
$471$		−	24076.2i		−	0.108529i
$472$	261114.	−	346396.i	1.17205	−	1.55485i
$473$			131474.i			0.587650i
$474$	32781.4	−	149892.i	0.145905	−	0.667147i
$475$	−109221.	−	118066.i	−0.484082	−	0.523284i
$476$	18026.1	−	39240.7i	0.0795586	−	0.173190i
$477$		−	17255.1i		−	0.0758369i
$478$	−29259.5	+	133788.i	−0.128059	+	0.585548i
$479$			185746.i			0.809557i	0.914415	+	0.404779i	$0.132651\pi$
$479$			185746.i			0.809557i	−0.914415	+	0.404779i	$0.867349\pi$
$480$	86030.0	−	101457.i	0.373394	−	0.440352i
$481$	−452867.			−1.95741
$482$	9816.12	+	2146.79i	0.0422519	+	0.00924048i
$483$	9205.33			0.0394589
$484$	191373.	+	87911.4i	0.816940	+	0.375279i
$485$	−17660.2	+	6915.86i	−0.0750777	+	0.0294010i
$486$	14802.1	+	3237.23i	0.0626688	+	0.0137057i
$487$	−275005.			−1.15953			−0.579765	−	0.814784i	$-0.696856\pi$
$487$	−275005.			−1.15953			−0.579765	+	0.814784i	$0.696856\pi$
$488$	−96473.7	−	72722.1i	−0.405107	−	0.305370i
$489$	25366.1			0.106081
$490$	−36021.3	−	226168.i	−0.150026	−	0.941976i
$491$		−	168313.i		−	0.698159i	−0.937093	−	0.349080i	$-0.886494\pi$
$491$		−	168313.i		−	0.698159i	0.937093	−	0.349080i	$-0.113506\pi$
$492$	−90907.9	−	41760.5i	−0.375553	−	0.172519i
$493$		−	175610.i		−	0.722528i
$494$	275239.	+	60194.9i	1.12786	+	0.246664i
$495$	24167.9	−	9464.36i	0.0986345	−	0.0386261i
$496$	146443.	−	125759.i	0.595258	−	0.511182i
$497$		−	61872.5i		−	0.250487i
$498$	−111166.	−	24311.9i	−0.448241	−	0.0980303i
$499$		−	332833.i		−	1.33667i	−0.743859	−	0.668337i	$-0.767006\pi$
$499$		−	332833.i		−	1.33667i	0.743859	−	0.668337i	$-0.232994\pi$
$500$	158967.	+	192949.i	0.635868	+	0.771797i
$501$	−232256.			−0.925317
$502$	54378.0	−	248642.i	0.215782	−	0.986659i
$503$	−141985.			−0.561184			−0.280592	−	0.959827i	$-0.590531\pi$
$503$	−141985.			−0.561184			−0.280592	+	0.959827i	$0.590531\pi$
$504$	14525.5	+	10949.4i	0.0571835	+	0.0431051i
$505$	81408.3	+	207882.i	0.319217	+	0.815144i
$506$	5530.28	−	25287.1i	0.0215996	−	0.0987637i
$507$	240870.			0.937057
$508$	−28631.1	−	13152.3i	−0.110946	−	0.0509654i
$509$	−388108.			−1.49802			−0.749010	−	0.662559i	$-0.769470\pi$
$509$	−388108.			−1.49802			−0.749010	+	0.662559i	$0.769470\pi$
$510$	131566.	−	20954.2i	0.505829	−	0.0805621i
$511$			75970.4i			0.290939i
$512$	94060.3	−	244688.i	0.358812	−	0.933410i
$513$		−	36103.8i		−	0.137189i
$514$	60332.4	−	275868.i	0.228362	−	1.04418i
$515$	−74094.3	−	189205.i	−0.279364	−	0.713376i
$516$	−258315.	−	118663.i	−0.970176	−	0.445671i
$517$		−	124672.i		−	0.466431i
$518$	−14884.6	+	68059.5i	−0.0554725	+	0.253647i
$519$			36224.8i			0.134484i
$520$	−421753.	−	117941.i	−1.55974	−	0.436172i
$521$	279589.			1.03002			0.515009	−	0.857185i	$-0.327789\pi$
$521$	279589.			1.03002			0.515009	+	0.857185i	$0.327789\pi$
$522$	72264.6	+	15804.3i	0.265207	+	0.0580007i
$523$	−10085.8			−0.0368729			−0.0184365	−	0.999830i	$-0.505869\pi$
$523$	−10085.8			−0.0368729			−0.0184365	+	0.999830i	$0.505869\pi$
$524$	−134876.	+	293609.i	−0.491215	+	1.06932i
$525$	−25095.2	+	23215.1i	−0.0910482	+	0.0842273i
$526$	−248269.	−	54296.4i	−0.897327	−	0.196245i
$527$	193325.			0.696092
$528$	38804.4	−	33323.6i	0.139192	−	0.119532i
$529$	−251518.			−0.898791
$530$	63112.3	−	10051.7i	0.224679	−	0.0357841i
$531$			183004.i			0.649039i
$532$	18092.9	−	39386.1i	0.0639270	−	0.139162i
$533$			329355.i			1.15934i
$534$	−93421.0	−	20431.2i	−0.327614	−	0.0716492i
$535$	−8633.45	−	22046.1i	−0.0301632	−	0.0770238i
$536$	345192.	+	260207.i	1.20152	+	0.905709i
$537$			116047.i			0.402425i
$538$	−298637.	−	65312.0i	−1.03176	−	0.225647i
$539$		−	88062.0i		−	0.303118i
$540$	−3217.69	+	56026.1i	−0.0110346	+	0.192133i
$541$	313754.			1.07200			0.536000	−	0.844218i	$-0.319935\pi$
$541$	313754.			1.07200			0.536000	+	0.844218i	$0.319935\pi$
$542$	−1040.41	+	4757.26i	−0.00354166	+	0.0161942i
$543$	−183774.			−0.623283
$544$	231124.	−	124542.i	0.780994	−	0.420842i
$545$	146081.	+	373028.i	0.491813	+	1.25588i
$546$	12794.6	−	58502.8i	0.0429181	−	0.196242i
$547$	233886.			0.781682			0.390841	−	0.920458i	$-0.372184\pi$
$547$	233886.			0.781682			0.390841	+	0.920458i	$0.372184\pi$
$548$	−64275.0	+	139919.i	−0.214033	+	0.465926i
$549$	50967.8			0.169103
$550$	48695.6	+	82883.4i	0.160977	+	0.273995i
$551$		−	176260.i		−	0.580566i
$552$	44691.5	+	33688.6i	0.146672	+	0.110562i
$553$			77709.3i			0.254110i
$554$	−9361.19	+	42803.8i	−0.0305008	+	0.139464i
$555$	−200135.	+	78374.4i	−0.649735	+	0.254442i
$556$	−214844.	+	467692.i	−0.694983	+	1.51290i
$557$		−	11592.9i		−	0.0373663i	−0.999825	−	0.0186832i	$-0.994053\pi$
$557$		−	11592.9i		−	0.0373663i	0.999825	−	0.0186832i	$-0.00594738\pi$
$558$	−17398.6	+	79554.5i	−0.0558785	+	0.255503i
$559$			935863.i			2.99494i
$560$	−31586.8	+	59507.1i	−0.100723	+	0.189755i
$561$	51227.2			0.162770
$562$	320655.	+	70127.3i	1.01523	+	0.222031i
$563$	185479.			0.585165			0.292582	−	0.956240i	$-0.405485\pi$
$563$	185479.			0.585165			0.292582	+	0.956240i	$0.405485\pi$
$564$	244950.	+	112523.i	0.770050	+	0.353739i
$565$	286026.	−	112010.i	0.896002	−	0.350882i
$566$	198482.	+	43408.0i	0.619567	+	0.135499i
$567$	−7673.95			−0.0238700
$568$	226433.	−	300388.i	0.701849	−	0.931078i
$569$	−516873.			−1.59647			−0.798233	−	0.602349i	$-0.794232\pi$
$569$	−516873.			−1.59647			−0.798233	+	0.602349i	$0.794232\pi$
$570$	132054.	−	21031.9i	0.406444	−	0.0647333i
$571$			231315.i			0.709466i	0.934968	+	0.354733i	$0.115428\pi$
$571$			231315.i			0.709466i	−0.934968	+	0.354733i	$0.884572\pi$
$572$	−153021.	−	70293.3i	−0.467690	−	0.214843i
$573$			327398.i			0.997164i
$574$	49497.4	+	10825.1i	0.150231	+	0.0328554i
$575$	−77211.7	+	71427.3i	−0.233532	+	0.216037i
$576$	30449.6	+	106318.i	0.0917776	+	0.320450i
$577$			262050.i			0.787105i	0.919302	+	0.393552i	$0.128754\pi$
$577$			262050.i			0.787105i	−0.919302	+	0.393552i	$0.871246\pi$
$578$	−69497.6	−	15199.1i	−0.208024	−	0.0454949i
$579$		−	103615.i		−	0.309078i
$580$	−15708.9	+	273522.i	−0.0466971	+	0.813085i
$581$	57632.2			0.170731
$582$	3368.85	−	15404.0i	0.00994571	−	0.0454765i
$583$	24573.7			0.0722992
$584$	−278027.	+	368833.i	−0.815195	+	1.08144i
$585$	172032.	−	67369.3i	0.502688	−	0.196857i
$586$	108071.	−	494150.i	0.314712	−	1.43901i
$587$	209922.			0.609230			0.304615	−	0.952476i	$-0.401472\pi$
$587$	209922.			0.609230			0.304615	+	0.952476i	$0.401472\pi$
$588$	173020.	+	79480.7i	0.500429	+	0.229883i
$589$	194041.			0.559324
$590$	−669355.	+	106607.i	−1.92288	+	0.306253i
$591$			362647.i			1.03827i
$592$	−321340.	+	275953.i	−0.916898	+	0.787393i
$593$		−	138829.i		−	0.394793i	−0.980324	−	0.197397i	$-0.936751\pi$
$593$		−	138829.i		−	0.394793i	0.980324	−	0.197397i	$-0.0632487\pi$
$594$	−4610.27	+	21080.3i	−0.0130663	+	0.0597454i
$595$	−62827.7	+	24603.8i	−0.177467	+	0.0694974i
$596$	−205677.	−	94482.4i	−0.579021	−	0.265986i
$597$			23698.6i			0.0664927i
$598$	39365.7	−	179999.i	0.110082	−	0.503346i
$599$		−	31392.1i		−	0.0874917i	−0.999043	−	0.0437459i	$-0.986071\pi$
$599$		−	31392.1i		−	0.0874917i	0.999043	−	0.0437459i	$-0.0139292\pi$
$600$	−206796.	+	20868.3i	−0.574433	+	0.0579675i
$601$	129781.			0.359304			0.179652	−	0.983730i	$-0.442503\pi$
$601$	129781.			0.359304			0.179652	+	0.983730i	$0.442503\pi$
$602$	140647.	+	30759.5i	0.388094	+	0.0848762i
$603$	−182368.			−0.501549
$604$	153361.	−	333849.i	0.420379	−	0.915117i
$605$	−119990.	−	306404.i	−0.327820	−	0.837113i
$606$	−181324.	−	39655.6i	−0.493753	−	0.107984i
$607$	−664466.			−1.80341			−0.901707	−	0.432349i	$-0.857685\pi$
$607$	−664466.			−1.80341			−0.901707	+	0.432349i	$0.857685\pi$
$608$	231981.	−	125004.i	0.627544	−	0.338155i
$609$	−37464.5			−0.101015
$610$	29690.7	+	186420.i	0.0797922	+	0.500995i
$611$		−	887442.i		−	2.37715i
$612$	−46235.3	+	100649.i	−0.123444	+	0.268724i
$613$		−	573113.i		−	1.52517i	−0.646886	−	0.762587i	$-0.723929\pi$
$613$		−	573113.i		−	1.52517i	0.646886	−	0.762587i	$-0.276071\pi$
$614$	594461.	+	130009.i	1.57684	+	0.344854i
$615$	56999.1	+	145551.i	0.150701	+	0.384827i
$616$	−15593.5	+	20686.4i	−0.0410943	+	0.0545160i
$617$		−	342449.i		−	0.899551i	−0.893142	−	0.449776i	$-0.851504\pi$
$617$		−	342449.i		−	0.899551i	0.893142	−	0.449776i	$-0.148496\pi$
$618$	165033.	+	36092.8i	0.432110	+	0.0945026i
$619$		−	238418.i		−	0.622239i	−0.950371	−	0.311120i	$-0.899296\pi$
$619$		−	238418.i		−	0.622239i	0.950371	−	0.311120i	$-0.100704\pi$
$620$	−301114.	−	17293.6i	−0.783335	−	0.0449885i
$621$	−23610.9			−0.0612250
$622$	27200.5	−	124373.i	0.0703066	−	0.321475i
$623$	48432.8			0.124785
$624$	276218.	−	237204.i	0.709387	−	0.609191i
$625$	30356.8	−	389444.i	0.0777133	−	0.996976i
$626$	32115.2	−	146846.i	0.0819524	−	0.374725i
$627$	51417.0			0.130789
$628$	−30946.7	+	67367.5i	−0.0784685	+	0.170817i
$629$	−424213.			−1.07222
$630$	−4470.37	−	28068.3i	−0.0112632	−	0.0707188i
$631$			105864.i			0.265882i	0.991124	+	0.132941i	$0.0424421\pi$
$631$			105864.i			0.265882i	−0.991124	+	0.132941i	$0.957558\pi$
$632$	−284391.	+	377275.i	−0.712003	+	0.944548i
$633$		−	262828.i		−	0.655940i
$634$	64958.2	−	297020.i	0.161605	−	0.738936i
$635$	17951.6	+	45840.8i	0.0445202	+	0.113685i
$636$	−22179.1	+	48281.3i	−0.0548314	+	0.119362i
$637$		−	626844.i		−	1.54483i
$638$	−22507.5	+	102915.i	−0.0552951	+	0.252835i
$639$			158697.i			0.388659i
$640$	−371129.	+	173307.i	−0.906077	+	0.423112i
$641$	575689.			1.40111			0.700554	−	0.713599i	$-0.252936\pi$
$641$	575689.			1.40111			0.700554	+	0.713599i	$0.252936\pi$
$642$	19229.6	+	4205.52i	0.0466553	+	0.0102035i
$643$	−258203.			−0.624510			−0.312255	−	0.949998i	$-0.601084\pi$
$643$	−258203.			−0.624510			−0.312255	+	0.949998i	$0.601084\pi$
$644$	−25757.4	−	11832.2i	−0.0621055	−	0.0285295i
$645$	161963.	+	413584.i	0.389311	+	0.994133i
$646$	257824.	+	56386.2i	0.617815	+	0.135116i
$647$	−59686.2			−0.142582			−0.0712911	−	0.997456i	$-0.522712\pi$
$647$	−59686.2			−0.142582			−0.0712911	+	0.997456i	$0.522712\pi$
$648$	−37256.7	−	28084.2i	−0.0887267	−	0.0668824i
$649$	−260623.			−0.618762
$650$	346626.	+	589981.i	0.820416	+	1.39641i
$651$		−	41243.9i		−	0.0973190i
$652$	−70976.6	−	32604.7i	−0.166963	−	0.0766981i
$653$		−	424956.i		−	0.996592i	−0.867007	−	0.498296i	$-0.833959\pi$
$653$		−	424956.i		−	0.996592i	0.867007	−	0.498296i	$-0.166041\pi$
$654$	−325372.	−	71158.8i	−0.760719	−	0.166369i
$655$	470093.	−	184092.i	1.09572	−	0.429095i
$656$	200691.	+	233700.i	0.466359	+	0.543063i
$657$		−	194857.i		−	0.451425i
$658$	−133370.	−	29168.0i	−0.308039	−	0.0673682i
$659$		−	623821.i		−	1.43644i	−0.695814	−	0.718222i	$-0.744956\pi$
$659$		−	623821.i		−	1.43644i	0.695814	−	0.718222i	$-0.255044\pi$
$660$	−79789.2	−	4582.46i	−0.183171	−	0.0105199i
$661$	314221.			0.719172			0.359586	−	0.933112i	$-0.382918\pi$
$661$	314221.			0.719172			0.359586	+	0.933112i	$0.382918\pi$
$662$	−102739.	+	469771.i	−0.234433	+	1.07194i
$663$	364646.			0.829554
$664$	279802.	+	210915.i	0.634621	+	0.478379i
$665$	−63060.5	+	24695.0i	−0.142598	+	0.0558426i
$666$	38177.7	−	174567.i	0.0860719	−	0.393561i
$667$	−115269.			−0.259096
$668$	649872.	+	298533.i	1.45638	+	0.669021i
$669$	−110782.			−0.247525
$670$	−106236.	−	667029.i	−0.236659	−	1.48592i
$671$			72585.5i			0.161215i
$672$	−26569.8	−	49308.0i	−0.0588369	−	0.109189i
$673$			305155.i			0.673736i	0.941552	+	0.336868i	$0.109368\pi$
$673$			305155.i			0.673736i	−0.941552	+	0.336868i	$0.890632\pi$
$674$	69828.8	−	319290.i	0.153714	−	0.702855i
$675$	64366.9	−	59544.8i	0.141272	−	0.130688i
$676$	−673975.	−	309605.i	−1.47486	−	0.677509i
$677$			612904.i			1.33726i	0.743596	+	0.668629i	$0.233119\pi$
$677$			612904.i			1.33726i	−0.743596	+	0.668629i	$0.766881\pi$
$678$	−54562.3	+	249485.i	−0.118695	+	0.542731i
$679$			7985.97i			0.0173216i
$680$	−395068.	−	110479.i	−0.854385	−	0.238924i
$681$	−123470.			−0.266236
$682$	−113297.	−	24778.1i	−0.243584	−	0.0532719i
$683$	−144495.			−0.309749			−0.154875	−	0.987934i	$-0.549497\pi$
$683$	−144495.			−0.309749			−0.154875	+	0.987934i	$0.549497\pi$
$684$	−46406.6	+	101022.i	−0.0991899	+	0.215925i
$685$	224023.	−	87729.1i	0.477431	−	0.186966i
$686$	−192970.	−	42202.5i	−0.410054	−	0.0896788i
$687$	−255524.			−0.541400
$688$	570265.	+	664058.i	1.20476	+	1.40291i
$689$	174921.			0.368471
$690$	−13754.2	−	86359.2i	−0.0288894	−	0.181389i
$691$		−	908289.i		−	1.90225i	−0.308804	−	0.951126i	$-0.599929\pi$
$691$		−	908289.i		−	1.90225i	0.308804	−	0.951126i	$-0.400071\pi$
$692$	46562.0	−	101360.i	0.0972344	−	0.211668i
$693$		−	10928.8i		−	0.0227565i
$694$	−207949.	−	45478.4i	−0.431755	−	0.0944249i
$695$	748814.	−	293242.i	1.55026	−	0.607094i
$696$	−181889.	−	137108.i	−0.375480	−	0.283038i
$697$			308516.i			0.635056i
$698$	−526565.	−	115160.i	−1.08079	−	0.236369i
$699$			313289.i			0.641196i
$700$	100058.	−	32701.7i	0.204201	−	0.0667381i
$701$	−74505.2			−0.151618			−0.0758089	−	0.997122i	$-0.524154\pi$
$701$	−74505.2			−0.151618			−0.0758089	+	0.997122i	$0.524154\pi$
$702$	−32816.9	+	150054.i	−0.0665922	+	0.304491i
$703$	−425785.			−0.861548
$704$	−151411.	+	43364.6i	−0.305501	+	0.0874964i
$705$	−153583.	−	392185.i	−0.309005	−	0.789066i
$706$	−75923.5	+	347158.i	−0.152323	+	0.696494i
$707$	94004.9			0.188066
$708$	235226.	−	512061.i	0.469266	−	1.02154i
$709$	−802973.			−1.59738			−0.798690	−	0.601742i	$-0.794473\pi$
$709$	−802973.			−1.59738			−0.798690	+	0.601742i	$0.794473\pi$
$710$	−580453.	+	92447.3i	−1.15146	+	0.183391i
$711$		−	199317.i		−	0.394281i
$712$	235139.	+	177248.i	0.463837	+	0.349641i
$713$		−	126897.i		−	0.249616i
$714$	11985.0	−	54801.1i	0.0235094	−	0.107496i
$715$	95943.5	+	244999.i	0.187674	+	0.479239i
$716$	149162.	−	324710.i	0.290960	−	0.633387i
$717$			177904.i			0.346057i
$718$	−43517.3	+	198982.i	−0.0844137	+	0.385979i
$719$			555301.i			1.07416i	0.843530	+	0.537082i	$0.180474\pi$
$719$			555301.i			1.07416i	−0.843530	+	0.537082i	$0.819526\pi$
$720$	81017.4	−	152630.i	0.156284	−	0.294426i
$721$	−85559.2			−0.164587
$722$	−250468.	−	54777.4i	−0.480483	−	0.105082i
$723$	13052.9			0.0249707
$724$	514218.	+	236217.i	0.981002	+	0.450645i
$725$	314242.	−	290700.i	0.597844	−	0.553056i
$726$	267260.	+	58449.7i	0.507061	+	0.110894i
$727$	268018.			0.507101			0.253551	−	0.967322i	$-0.418402\pi$
$727$	268018.			0.507101			0.253551	+	0.967322i	$0.418402\pi$
$728$	−110998.	+	147250.i	−0.209436	+	0.277839i
$729$	19683.0			0.0370370
$730$	712711.	−	113512.i	1.33742	−	0.213008i
$731$			876648.i			1.64055i
$732$	−142613.	−	65512.2i	−0.266156	−	0.122264i
$733$			657569.i			1.22386i	0.790910	+	0.611932i	$0.209607\pi$
$733$			657569.i			1.22386i	−0.790910	+	0.611932i	$0.790393\pi$
$734$	883705.	+	193266.i	1.64027	+	0.358727i
$735$	−108483.	−	277020.i	−0.200811	−	0.512787i
$736$	−81748.8	−	151709.i	−0.150913	−	0.280062i
$737$		−	259718.i		−	0.478153i
$738$	−126956.	−	27765.4i	−0.233100	−	0.0509789i
$739$			249798.i			0.457404i	0.973497	+	0.228702i	$0.0734481\pi$
$739$			249798.i			0.457404i	−0.973497	+	0.228702i	$0.926552\pi$
$740$	660735.	+	37947.4i	1.20660	+	0.0692976i
$741$	365997.			0.666564
$742$	5749.21	−	26288.1i	0.0104424	−	0.0477476i
$743$	250352.			0.453496			0.226748	−	0.973953i	$-0.427191\pi$
$743$	250352.			0.453496			0.226748	+	0.973953i	$0.427191\pi$
$744$	150939.	−	200237.i	0.272682	−	0.361742i
$745$	128959.	+	329307.i	0.232349	+	0.593319i
$746$	−175140.	+	800823.i	−0.314708	+	1.43899i
$747$	−147821.			−0.264909
$748$	−143338.	−	65845.7i	−0.256188	−	0.117686i
$749$	−9969.33			−0.0177706
$750$	255287.	+	200741.i	0.453844	+	0.356874i
$751$			697780.i			1.23720i	0.785707	+	0.618599i	$0.212299\pi$
$751$			697780.i			1.23720i	−0.785707	+	0.618599i	$0.787701\pi$
$752$	−540759.	−	629700.i	−0.956243	−	1.11352i
$753$		−	330630.i		−	0.583112i
$754$	−160213.	+	732571.i	−0.281810	+	1.28857i
$755$	−534521.	+	209323.i	−0.937715	+	0.367217i
$756$	21472.4	+	9863.82i	0.0375697	+	0.0172584i
$757$			87729.0i			0.153092i	0.997066	+	0.0765458i	$0.0243891\pi$
$757$			87729.0i			0.153092i	−0.997066	+	0.0765458i	$0.975611\pi$
$758$	92182.0	−	421500.i	0.160438	−	0.733599i
$759$		−	33625.2i		−	0.0583690i
$760$	−396532.	−	110888.i	−0.686516	−	0.191980i
$761$	1587.45			0.00274113			0.00137057	−	0.999999i	$-0.499564\pi$
$761$	1587.45			0.00274113			0.00137057	+	0.999999i	$0.499564\pi$
$762$	−39984.4	−	8744.60i	−0.0688622	−	0.0150602i
$763$	168684.			0.289752
$764$	420826.	−	916090.i	0.720967	−	1.56946i
$765$	161147.	−	63106.6i	0.275360	−	0.107833i
$766$	441402.	+	96534.6i	0.752275	+	0.164523i
$767$	−1.85517e6			−3.15350
$768$	51456.0	−	336625.i	0.0872395	−	0.570721i
$769$	−30299.3			−0.0512366			−0.0256183	−	0.999672i	$-0.508155\pi$
$769$	−30299.3			−0.0512366			−0.0256183	+	0.999672i	$0.508155\pi$
$770$	39973.2	−	6366.44i	0.0674199	−	0.0107378i
$771$		−	366833.i		−	0.617106i
$772$	−133184.	+	289926.i	−0.223469	+	0.486466i
$773$			644896.i			1.07927i	0.841899	+	0.539635i	$0.181438\pi$
$773$			644896.i			1.07927i	−0.841899	+	0.539635i	$0.818562\pi$
$774$	−360747.	−	78895.3i	−0.602172	−	0.131695i
$775$	320025.	+	345942.i	0.532820	+	0.575969i
$776$	−29226.1	+	38771.5i	−0.0485341	+	0.0643857i
$777$			90501.5i			0.149904i
$778$	−944804.	−	206629.i	−1.56093	−	0.341375i
$779$			309659.i			0.510280i
$780$	−567957.	−	32618.9i	−0.933525	−	0.0536142i
$781$	−226008.			−0.370528
$782$	36874.9	−	168610.i	0.0603001	−	0.275720i
$783$	96093.2			0.156736
$784$	−381965.	−	444788.i	−0.621429	−	0.723638i
$785$	107861.	−	42239.3i	0.175035	−	0.0685452i
$786$	−89675.0	+	410036.i	−0.145153	+	0.663708i
$787$	899059.			1.45157			0.725786	−	0.687920i	$-0.241476\pi$
$787$	899059.			1.45157			0.725786	+	0.687920i	$0.241476\pi$
$788$	466133.	−	1.01472e6i	0.750685	−	1.63416i
$789$	−330133.			−0.530317
$790$	729024.	−	116110.i	1.16812	−	0.186044i
$791$		−	129342.i		−	0.206722i
$792$	39995.9	−	53058.9i	0.0637625	−	0.0845878i
$793$			516679.i			0.821626i
$794$	−18343.5	+	83875.1i	−0.0290965	+	0.133043i
$795$	77302.5	−	30272.3i	0.122309	−	0.0478973i
$796$	30461.3	−	66310.8i	0.0480754	−	0.104655i
$797$			489490.i			0.770596i	0.922792	+	0.385298i	$0.125901\pi$
$797$			489490.i			0.770596i	−0.922792	+	0.385298i	$0.874099\pi$
$798$	12029.4	−	55004.2i	0.0188903	−	0.0863754i
$799$		−	831291.i		−	1.30214i
$800$	605457.	+	207417.i	0.946027	+	0.324089i
$801$	−124226.			−0.193619
$802$	−436369.	−	95433.9i	−0.678430	−	0.148373i
$803$	277505.			0.430367
$804$	510281.	+	234409.i	0.789401	+	0.362629i
$805$	16149.8	+	41239.7i	0.0249216	+	0.0636391i
$806$	−806472.	−	176375.i	−1.24142	−	0.271499i
$807$	−397111.			−0.609768
$808$	456389.	+	344027.i	0.699057	+	0.526951i
$809$	244826.			0.374076			0.187038	−	0.982353i	$-0.440111\pi$
$809$	244826.			0.374076			0.187038	+	0.982353i	$0.440111\pi$
$810$	11466.1	+	71992.6i	0.0174761	+	0.109728i
$811$			1.03351e6i			1.57135i	0.618638	+	0.785676i	$0.287685\pi$
$811$			1.03351e6i			1.57135i	−0.618638	+	0.785676i	$0.712315\pi$
$812$	104829.	+	48155.6i	0.158990	+	0.0730356i
$813$			6325.93i			0.00957069i
$814$	248608.	+	54370.5i	0.375203	+	0.0820568i
$815$	44502.2	+	113640.i	0.0669987	+	0.171086i
$816$	258741.	−	222196.i	0.388584	−	0.333699i
$817$			879897.i			1.31822i
$818$	−166411.	−	36394.1i	−0.248700	−	0.0543907i
$819$		−	77793.6i		−	0.115978i
$820$	27597.8	−	480530.i	0.0410438	−	0.714650i
$821$	−809789.			−1.20140			−0.600698	−	0.799476i	$-0.705110\pi$
$821$	−809789.			−1.20140			−0.600698	+	0.799476i	$0.705110\pi$
$822$	−42734.6	+	195403.i	−0.0632464	+	0.289192i
$823$	293041.			0.432641			0.216321	−	0.976322i	$-0.430594\pi$
$823$	293041.			0.432641			0.216321	+	0.976322i	$0.430594\pi$
$824$	−415386.	−	313119.i	−0.611783	−	0.461164i
$825$	84800.3	+	91667.6i	0.124592	+	0.134682i
$826$	−60974.9	+	278806.i	−0.0893698	+	0.408641i
$827$	694600.			1.01560			0.507802	−	0.861474i	$-0.330458\pi$
$827$	694600.			1.01560			0.507802	+	0.861474i	$0.330458\pi$
$828$	66065.4	+	30348.6i	0.0963636	+	0.0442667i
$829$	65048.8			0.0946521			0.0473260	−	0.998879i	$-0.484930\pi$
$829$	65048.8			0.0946521			0.0473260	+	0.998879i	$0.484930\pi$
$830$	−86111.6	−	540672.i	−0.124999	−	0.784834i
$831$			56918.0i			0.0824228i
$832$	−1.07778e6	+	308678.i	−1.55698	+	0.445923i
$833$		−	587182.i		−	0.846219i
$834$	−142844.	+	653149.i	−0.205366	+	0.939032i
$835$	−407469.	−	1.04050e6i	−0.584415	−	1.49235i
$836$	−143870.	−	66089.6i	−0.205853	−	0.0945629i
$837$			105787.i			0.151001i
$838$	70135.2	−	320691.i	0.0998729	−	0.456666i
$839$		−	393104.i		−	0.558448i	−0.960226	−	0.279224i	$-0.909923\pi$
$839$		−	393104.i		−	0.558448i	0.960226	−	0.279224i	$-0.0900773\pi$
$840$	−23569.5	+	84283.7i	−0.0334034	+	0.119450i
$841$	−238150.			−0.336712
$842$	524844.	+	114783.i	0.740297	+	0.161903i
$843$	426388.			0.599998
$844$	−337830.	+	735417.i	−0.474257	+	1.03240i
$845$	422581.	+	1.07909e6i	0.591829	+	1.51128i
$846$	342082.	+	74813.3i	0.477957	+	0.104529i
$847$	−138557.			−0.193135
$848$	124118.	−	106587.i	0.172601	−	0.148223i
$849$	263930.			0.366162
$850$	324694.	+	552652.i	0.449403	+	0.764916i
$851$			278451.i			0.384494i
$852$	203984.	−	444050.i	0.281007	−	0.611720i
$853$		−	321668.i		−	0.442089i	−0.975264	−	0.221044i	$-0.929053\pi$
$853$		−	321668.i		−	0.442089i	0.975264	−	0.221044i	$-0.0709466\pi$
$854$	77649.4	+	16981.9i	0.106469	+	0.0232848i
$855$	161745.	−	63340.5i	0.221257	−	0.0866461i
$856$	−48400.6	−	36484.5i	−0.0660547	−	0.0497922i
$857$			128881.i			0.175480i	0.996143	+	0.0877399i	$0.0279644\pi$
$857$			128881.i			0.175480i	−0.996143	+	0.0877399i	$0.972036\pi$
$858$	−213699.	−	46736.0i	−0.290287	−	0.0634858i
$859$			706876.i			0.957981i	0.877820	+	0.478991i	$0.158997\pi$
$859$			706876.i			0.957981i	−0.877820	+	0.478991i	$0.841003\pi$
$860$	78419.3	−	1.36543e6i	0.106029	−	1.84617i
$861$	65818.7			0.0887857
$862$	140402.	−	641983.i	0.188955	−	0.863990i
$863$	1.00795e6			1.35337			0.676686	−	0.736272i	$-0.263415\pi$
$863$	1.00795e6			1.35337			0.676686	+	0.736272i	$0.263415\pi$
$864$	68149.2	+	126471.i	0.0912922	+	0.169419i
$865$	−162286.	+	63552.6i	−0.216895	+	0.0849379i
$866$	167824.	−	767372.i	0.223779	−	1.02322i
$867$	−92413.9			−0.122942
$868$	−53013.4	+	115404.i	−0.0703633	+	0.153173i
$869$	283856.			0.375889
$870$	55977.9	+	351471.i	0.0739568	+	0.464356i
$871$		−	1.84873e6i		−	2.43689i
$872$	818955.	+	617330.i	1.07703	+	0.811867i
$873$		−	20483.3i		−	0.0268764i
$874$	37011.6	−	169234.i	0.0484523	−	0.221547i
$875$	−148030.	−	71697.3i	−0.193346	−	0.0936454i
$876$	−250463.	+	545229.i	−0.326388	+	0.710510i
$877$		−	738902.i		−	0.960699i	−0.877077	−	0.480350i	$-0.840510\pi$
$877$		−	738902.i		−	0.960699i	0.877077	−	0.480350i	$-0.159490\pi$
$878$	−229780.	+	1.05066e6i	−0.298073	+	1.36293i
$879$		−	657092.i		−	0.850450i
$880$	217367.	+	115380.i	0.280691	+	0.148993i
$881$	−1.01171e6			−1.30347			−0.651737	−	0.758445i	$-0.725959\pi$
$881$	−1.01171e6			−1.30347			−0.651737	+	0.758445i	$0.725959\pi$
$882$	241629.	+	52844.4i	0.310608	+	0.0679300i
$883$	−642982.			−0.824665			−0.412333	−	0.911033i	$-0.635286\pi$
$883$	−642982.			−0.824665			−0.412333	+	0.911033i	$0.635286\pi$
$884$	−1.02031e6	−	468703.i	−1.30566	−	0.599782i
$885$	−819853.	+	321061.i	−1.04677	+	0.409922i
$886$	321514.	+	70315.2i	0.409574	+	0.0895740i
$887$	−307209.			−0.390470			−0.195235	−	0.980757i	$-0.562547\pi$
$887$	−307209.			−0.390470			−0.195235	+	0.980757i	$0.562547\pi$
$888$	−331206.	+	439381.i	−0.420023	+	0.557205i
$889$	20729.3			0.0262290
$890$	−72366.3	−	454369.i	−0.0913600	−	0.573626i
$891$			28031.4i			0.0353093i
$892$	309980.	+	142396.i	0.389586	+	0.178965i
$893$		−	834371.i		−	1.04630i
$894$	−287236.	−	62818.6i	−0.359389	−	0.0785983i
$895$	−519888.	+	203592.i	−0.649028	+	0.254165i
$896$	10966.1	+	172120.i	0.0136595	+	0.214396i
$897$		−	239352.i		−	0.297476i
$898$	−244543.	−	53481.6i	−0.303252	−	0.0663212i
$899$			516456.i			0.639019i
$900$	−256641.	+	83876.9i	−0.316841	+	0.103552i
$901$	163853.			0.201839
$902$	39541.9	−	180804.i	0.0486009	−	0.222226i
$903$	187024.			0.229362
$904$	473349.	−	627949.i	0.579222	−	0.768400i
$905$	−322413.	−	823306.i	−0.393655	−	1.00523i
$906$	101965.	−	466233.i	0.124221	−	0.567998i
$907$	1.19090e6			1.44764			0.723820	−	0.689988i	$-0.242384\pi$
$907$	1.19090e6			1.44764			0.723820	+	0.689988i	$0.242384\pi$
$908$	345480.	+	158704.i	0.419036	+	0.192493i
$909$	−241114.			−0.291806
$910$	284538.	−	45317.7i	0.343603	−	0.0547249i
$911$			775058.i			0.933894i	0.884285	+	0.466947i	$0.154646\pi$
$911$			775058.i			0.933894i	−0.884285	+	0.466947i	$0.845354\pi$
$912$	259700.	−	223019.i	0.312235	−	0.268134i
$913$		−	210519.i		−	0.252551i
$914$	173578.	−	793680.i	0.207779	−	0.950065i
$915$	89417.8	+	228335.i	0.106803	+	0.272728i
$916$	714980.	+	328442.i	0.852124	+	0.391442i
$917$		−	212578.i		−	0.252801i
$918$	−30740.5	+	140560.i	−0.0364775	+	0.166792i
$919$		−	533514.i		−	0.631705i	−0.948808	−	0.315853i	$-0.897709\pi$
$919$		−	533514.i		−	0.631705i	0.948808	−	0.315853i	$-0.102291\pi$
$920$	−72517.5	+	259320.i	−0.0856776	+	0.306380i
$921$	790480.			0.931905
$922$	−238789.	−	52223.1i	−0.280900	−	0.0614329i
$923$	−1.60877e6			−1.88839
$924$	−14047.5	+	30579.8i	−0.0164534	+	0.0358171i
$925$	−702232.	−	759100.i	−0.820724	−	0.887188i
$926$	−1.05782e6	−	231346.i	−1.23365	−	0.269799i
$927$	219452.			0.255376
$928$	332707.	+	617434.i	0.386337	+	0.716960i
$929$	959719.			1.11202			0.556010	−	0.831176i	$-0.312332\pi$
$929$	959719.			1.11202			0.556010	+	0.831176i	$0.312332\pi$
$930$	−386927.	+	61624.9i	−0.447366	+	0.0712509i
$931$		−	589358.i		−	0.679954i
$932$	402691.	−	876611.i	0.463596	−	1.00920i
$933$		−	165385.i		−	0.189990i
$934$	−1.42589e6	−	311842.i	−1.63452	−	0.357471i
$935$	89872.9	+	229497.i	0.102803	+	0.262515i
$936$	284699.	−	377684.i	0.324964	−	0.431099i
$937$		−	1.06136e6i		−	1.20889i	−0.796648	−	0.604443i	$-0.793396\pi$
$937$		−	1.06136e6i		−	1.20889i	0.796648	−	0.604443i	$-0.206604\pi$
$938$	−277837.	−	60763.0i	−0.315780	−	0.0690611i
$939$		−	195267.i		−	0.221461i
$940$	−74361.9	+	1.29478e6i	−0.0841579	+	1.46535i
$941$	411089.			0.464255			0.232128	−	0.972685i	$-0.425431\pi$
$941$	411089.			0.464255			0.232128	+	0.972685i	$0.425431\pi$
$942$	−20575.6	+	94081.3i	−0.0231873	+	0.106023i
$943$	202508.			0.227729
$944$	−1.31637e6	+	1.13044e6i	−1.47718	+	1.26854i
$945$	−13463.2	−	34379.2i	−0.0150759	−	0.0384974i
$946$	112358.	−	513755.i	0.125552	−	0.574082i
$947$	−133138.			−0.148458			−0.0742290	−	0.997241i	$-0.523650\pi$
$947$	−133138.			−0.148458			−0.0742290	+	0.997241i	$0.523650\pi$
$948$	−256196.	+	557708.i	−0.285072	+	0.620570i
$949$	1.97534e6			2.19335
$950$	325897.	+	554699.i	0.361104	+	0.614625i
$951$		−	394960.i		−	0.436708i
$952$	−103975.	+	137933.i	−0.114724	+	0.152193i
$953$			1.31368e6i			1.44645i	0.690611	+	0.723226i	$0.257342\pi$
$953$			1.31368e6i			1.44645i	−0.690611	+	0.723226i	$0.742658\pi$
$954$	−14746.2	+	67426.7i	−0.0162026	+	0.0740858i
$955$	−1.46674e6	+	574386.i	−1.60822	+	0.629792i
$956$	228671.	−	497792.i	0.250205	−	0.544668i
$957$			136850.i			0.149425i
$958$	158738.	−	725827.i	0.172962	−	0.790865i
$959$		−	101304.i		−	0.110151i
$960$	−422880.	+	322937.i	−0.458854	+	0.350409i
$961$	354966.			0.384362
$962$	1.76964e6	+	387021.i	1.91221	+	0.418200i
$963$	25570.4			0.0275731
$964$	−36523.2	−	16777.7i	−0.0393020	−	0.0180542i
$965$	464196.	−	181783.i	0.498478	−	0.195208i
$966$	−35971.1	−	7866.89i	−0.0385478	−	0.00843041i
$967$	314926.			0.336787			0.168394	−	0.985720i	$-0.446142\pi$
$967$	314926.			0.336787			0.168394	+	0.985720i	$0.446142\pi$
$968$	−672688.	−	507074.i	−0.717898	−	0.541153i
$969$	342840.			0.365127
$970$	74919.8	−	11932.3i	0.0796257	−	0.0126818i
$971$			1.35538e6i			1.43754i	0.695246	+	0.718772i	$0.255295\pi$
$971$			1.35538e6i			1.43754i	−0.695246	+	0.718772i	$0.744705\pi$
$972$	−55074.8	−	25299.8i	−0.0582936	−	0.0267784i
$973$		−	338616.i		−	0.357669i
$974$	1.07462e6	+	235019.i	1.13276	+	0.247734i
$975$	603626.	+	652510.i	0.634979	+	0.686401i
$976$	314836.	+	366619.i	0.330510	+	0.384871i
$977$		−	1.16094e6i		−	1.21625i	−0.793842	−	0.608123i	$-0.791923\pi$
$977$		−	1.16094e6i		−	1.21625i	0.793842	−	0.608123i	$-0.208077\pi$
$978$	−99121.5	−	21677.9i	−0.103631	−	0.0226641i
$979$		−	176915.i		−	0.184587i
$980$	−52525.5	+	914569.i	−0.0546913	+	0.952279i
$981$	−432660.			−0.449582
$982$	−143840.	+	657707.i	−0.149162	+	0.682039i
$983$	108544.			0.112331			0.0561655	−	0.998421i	$-0.482113\pi$
$983$	108544.			0.112331			0.0561655	+	0.998421i	$0.482113\pi$
$984$	319547.	+	240875.i	0.330023	+	0.248772i
$985$	−1.62465e6	+	636227.i	−1.67451	+	0.655752i
$986$	−150076.	+	686219.i	−0.154368	+	0.705845i
$987$	−177347.			−0.182050
$988$	−1.02409e6	−	470440.i	−1.04912	−	0.481937i
$989$	575427.			0.588298
$990$	−102528.	+	16329.4i	−0.104610	+	0.0166609i
$991$			231812.i			0.236041i	0.993011	+	0.118021i	$0.0376549\pi$
$991$			231812.i			0.236041i	−0.993011	+	0.118021i	$0.962345\pi$
$992$	−679720.	+	366270.i	−0.690727	+	0.372201i
$993$			624674.i			0.633512i
$994$	−52876.3	+	241776.i	−0.0535166	+	0.244703i
$995$	−106169.	+	41576.7i	−0.107239	+	0.0419956i
$996$	413618.	+	190004.i	0.416947	+	0.191534i
$997$		−	1.21724e6i		−	1.22458i	−0.790633	−	0.612291i	$-0.790248\pi$
$997$		−	1.21724e6i		−	1.22458i	0.790633	−	0.612291i	$-0.209752\pi$
$998$	−284440.	+	1.30059e6i	−0.285581	+	1.30581i
$999$		−	232128.i		−	0.232593i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.5.f.a.19.1	✓	24
3.2	odd	2		180.5.f.i.19.24		24
4.3	odd	2	inner	60.5.f.a.19.23	yes	24
5.2	odd	4		300.5.c.e.151.13		24
5.3	odd	4		300.5.c.e.151.12		24
5.4	even	2	inner	60.5.f.a.19.24	yes	24
8.3	odd	2		960.5.j.d.319.7		24
8.5	even	2		960.5.j.d.319.18		24
12.11	even	2		180.5.f.i.19.2		24
15.14	odd	2		180.5.f.i.19.1		24
20.3	even	4		300.5.c.e.151.11		24
20.7	even	4		300.5.c.e.151.14		24
20.19	odd	2	inner	60.5.f.a.19.2	yes	24
40.19	odd	2		960.5.j.d.319.19		24
40.29	even	2		960.5.j.d.319.6		24
60.59	even	2		180.5.f.i.19.23		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.5.f.a.19.1	✓	24	1.1	even	1	trivial
60.5.f.a.19.2	yes	24	20.19	odd	2	inner
60.5.f.a.19.23	yes	24	4.3	odd	2	inner
60.5.f.a.19.24	yes	24	5.4	even	2	inner
180.5.f.i.19.1		24	15.14	odd	2
180.5.f.i.19.2		24	12.11	even	2
180.5.f.i.19.23		24	60.59	even	2
180.5.f.i.19.24		24	3.2	odd	2
300.5.c.e.151.11		24	20.3	even	4
300.5.c.e.151.12		24	5.3	odd	4
300.5.c.e.151.13		24	5.2	odd	4
300.5.c.e.151.14		24	20.7	even	4
960.5.j.d.319.6		24	40.29	even	2
960.5.j.d.319.7		24	8.3	odd	2
960.5.j.d.319.18		24	8.5	even	2
960.5.j.d.319.19		24	40.19	odd	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)

\(f(q)\)	\(=\)	\(q+(-3.90764 - 0.854601i) q^{2} -5.19615 q^{3} +(14.5393 + 6.67895i) q^{4} +(-9.11612 - 23.2787i) q^{5} +(20.3047 + 4.44064i) q^{6} -10.5267 q^{7} +(-51.1066 - 38.5243i) q^{8} +27.0000 q^{9} +O(q^{10})\)	\(q+(-3.90764 - 0.854601i) q^{2} -5.19615 q^{3} +(14.5393 + 6.67895i) q^{4} +(-9.11612 - 23.2787i) q^{5} +(20.3047 + 4.44064i) q^{6} -10.5267 q^{7} +(-51.1066 - 38.5243i) q^{8} +27.0000 q^{9} +(15.7285 + 98.7553i) q^{10} +38.4519i q^{11} +(-75.5485 - 34.7048i) q^{12} +273.709i q^{13} +(41.1345 + 8.99612i) q^{14} +(47.3687 + 120.960i) q^{15} +(166.783 + 194.215i) q^{16} +256.390i q^{17} +(-105.506 - 23.0742i) q^{18} +257.340i q^{19} +(22.9350 - 399.342i) q^{20} +54.6982 q^{21} +(32.8610 - 150.256i) q^{22} +168.293 q^{23} +(265.558 + 200.178i) q^{24} +(-458.793 + 424.422i) q^{25} +(233.912 - 1069.55i) q^{26} -140.296 q^{27} +(-153.051 - 70.3072i) q^{28} -684.931 q^{29} +(-81.7278 - 513.148i) q^{30} -754.026i q^{31} +(-485.753 - 901.455i) q^{32} -199.802i q^{33} +(219.111 - 1001.88i) q^{34} +(95.9624 + 245.047i) q^{35} +(392.561 + 180.332i) q^{36} +1654.56i q^{37} +(219.923 - 1005.59i) q^{38} -1422.23i q^{39} +(-430.900 + 1540.88i) q^{40} +1203.31 q^{41} +(-213.741 - 46.7452i) q^{42} +3419.20 q^{43} +(-256.818 + 559.064i) q^{44} +(-246.135 - 628.524i) q^{45} +(-657.629 - 143.823i) q^{46} -3242.29 q^{47} +(-866.631 - 1009.17i) q^{48} -2290.19 q^{49} +(2155.51 - 1266.40i) q^{50} -1332.24i q^{51} +(-1828.09 + 3979.53i) q^{52} -639.077i q^{53} +(548.227 + 119.897i) q^{54} +(895.108 - 350.532i) q^{55} +(537.983 + 405.533i) q^{56} -1337.18i q^{57} +(2676.47 + 585.343i) q^{58} +6777.91i q^{59} +(-119.174 + 2075.04i) q^{60} +1887.70 q^{61} +(-644.391 + 2946.46i) q^{62} -284.220 q^{63} +(1127.76 + 3937.69i) q^{64} +(6371.57 - 2495.16i) q^{65} +(-170.751 + 780.753i) q^{66} -6754.36 q^{67} +(-1712.42 + 3727.74i) q^{68} -874.476 q^{69} +(-165.569 - 1039.57i) q^{70} +5877.68i q^{71} +(-1379.88 - 1040.15i) q^{72} -7216.94i q^{73} +(1413.99 - 6465.43i) q^{74} +(2383.96 - 2205.36i) q^{75} +(-1718.76 + 3741.55i) q^{76} -404.771i q^{77} +(-1215.44 + 5557.57i) q^{78} -7382.13i q^{79} +(3000.64 - 5652.98i) q^{80} +729.000 q^{81} +(-4702.09 - 1028.35i) q^{82} -5474.87 q^{83} +(795.275 + 365.327i) q^{84} +(5968.42 - 2337.28i) q^{85} +(-13361.0 - 2922.05i) q^{86} +3559.01 q^{87} +(1481.33 - 1965.14i) q^{88} -4600.96 q^{89} +(424.670 + 2666.39i) q^{90} -2881.24i q^{91} +(2446.87 + 1124.02i) q^{92} +3918.03i q^{93} +(12669.7 + 2770.86i) q^{94} +(5990.54 - 2345.94i) q^{95} +(2524.05 + 4684.10i) q^{96} -758.641i q^{97} +(8949.24 + 1957.20i) q^{98} +1038.20i 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

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