LMFDB - Embedded newform 6026.2.a.m.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.a (trivial)

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:	yes
Analytic conductor:	$48.1178522580$
Analytic rank:	$0$
Dimension:	$41$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.35219 q^{3} +1.00000 q^{4} +0.827343 q^{5} -2.35219 q^{6} +0.166684 q^{7} +1.00000 q^{8} +2.53280 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.35219 q^{3} +1.00000 q^{4} +0.827343 q^{5} -2.35219 q^{6} +0.166684 q^{7} +1.00000 q^{8} +2.53280 q^{9} +0.827343 q^{10} -5.71499 q^{11} -2.35219 q^{12} -3.76006 q^{13} +0.166684 q^{14} -1.94607 q^{15} +1.00000 q^{16} +1.08060 q^{17} +2.53280 q^{18} -7.95687 q^{19} +0.827343 q^{20} -0.392072 q^{21} -5.71499 q^{22} +1.00000 q^{23} -2.35219 q^{24} -4.31550 q^{25} -3.76006 q^{26} +1.09895 q^{27} +0.166684 q^{28} -4.77718 q^{29} -1.94607 q^{30} +2.25920 q^{31} +1.00000 q^{32} +13.4427 q^{33} +1.08060 q^{34} +0.137905 q^{35} +2.53280 q^{36} +10.9997 q^{37} -7.95687 q^{38} +8.84437 q^{39} +0.827343 q^{40} +4.45111 q^{41} -0.392072 q^{42} -12.2404 q^{43} -5.71499 q^{44} +2.09549 q^{45} +1.00000 q^{46} +10.5540 q^{47} -2.35219 q^{48} -6.97222 q^{49} -4.31550 q^{50} -2.54177 q^{51} -3.76006 q^{52} +10.2774 q^{53} +1.09895 q^{54} -4.72826 q^{55} +0.166684 q^{56} +18.7161 q^{57} -4.77718 q^{58} -3.08748 q^{59} -1.94607 q^{60} +5.61729 q^{61} +2.25920 q^{62} +0.422176 q^{63} +1.00000 q^{64} -3.11086 q^{65} +13.4427 q^{66} +0.392856 q^{67} +1.08060 q^{68} -2.35219 q^{69} +0.137905 q^{70} -3.94659 q^{71} +2.53280 q^{72} +8.69129 q^{73} +10.9997 q^{74} +10.1509 q^{75} -7.95687 q^{76} -0.952597 q^{77} +8.84437 q^{78} +10.4255 q^{79} +0.827343 q^{80} -10.1833 q^{81} +4.45111 q^{82} +5.44253 q^{83} -0.392072 q^{84} +0.894023 q^{85} -12.2404 q^{86} +11.2368 q^{87} -5.71499 q^{88} +10.2049 q^{89} +2.09549 q^{90} -0.626741 q^{91} +1.00000 q^{92} -5.31406 q^{93} +10.5540 q^{94} -6.58306 q^{95} -2.35219 q^{96} -11.9980 q^{97} -6.97222 q^{98} -14.4749 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9}+O(q^{10}) $ 41 * q + 41 * q^2 + 4 * q^3 + 41 * q^4 + 9 * q^5 + 4 * q^6 + 12 * q^7 + 41 * q^8 + 63 * q^9	\( 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9} + 9 q^{10} + 4 q^{11} + 4 q^{12} + 16 q^{13} + 12 q^{14} + 10 q^{15} + 41 q^{16} + 10 q^{17} + 63 q^{18} + 16 q^{19} + 9 q^{20} + 16 q^{21} + 4 q^{22} + 41 q^{23} + 4 q^{24} + 76 q^{25} + 16 q^{26} + 7 q^{27} + 12 q^{28} + 28 q^{29} + 10 q^{30} + 25 q^{31} + 41 q^{32} + 5 q^{33} + 10 q^{34} + 4 q^{35} + 63 q^{36} + 26 q^{37} + 16 q^{38} + 50 q^{39} + 9 q^{40} + 27 q^{41} + 16 q^{42} + 12 q^{43} + 4 q^{44} + 44 q^{45} + 41 q^{46} + 18 q^{47} + 4 q^{48} + 87 q^{49} + 76 q^{50} + 24 q^{51} + 16 q^{52} + 63 q^{53} + 7 q^{54} + 18 q^{55} + 12 q^{56} - 12 q^{57} + 28 q^{58} + 33 q^{59} + 10 q^{60} + 24 q^{61} + 25 q^{62} + 48 q^{63} + 41 q^{64} + 21 q^{65} + 5 q^{66} - 9 q^{67} + 10 q^{68} + 4 q^{69} + 4 q^{70} + 36 q^{71} + 63 q^{72} + 36 q^{73} + 26 q^{74} + 6 q^{75} + 16 q^{76} + 48 q^{77} + 50 q^{78} + 51 q^{79} + 9 q^{80} + 149 q^{81} + 27 q^{82} - 27 q^{83} + 16 q^{84} + 52 q^{85} + 12 q^{86} - 3 q^{87} + 4 q^{88} + 68 q^{89} + 44 q^{90} + 22 q^{91} + 41 q^{92} + 45 q^{93} + 18 q^{94} + 46 q^{95} + 4 q^{96} + 16 q^{97} + 87 q^{98} - 10 q^{99}+O(q^{100}) \) 41 * q + 41 * q^2 + 4 * q^3 + 41 * q^4 + 9 * q^5 + 4 * q^6 + 12 * q^7 + 41 * q^8 + 63 * q^9 + 9 * q^10 + 4 * q^11 + 4 * q^12 + 16 * q^13 + 12 * q^14 + 10 * q^15 + 41 * q^16 + 10 * q^17 + 63 * q^18 + 16 * q^19 + 9 * q^20 + 16 * q^21 + 4 * q^22 + 41 * q^23 + 4 * q^24 + 76 * q^25 + 16 * q^26 + 7 * q^27 + 12 * q^28 + 28 * q^29 + 10 * q^30 + 25 * q^31 + 41 * q^32 + 5 * q^33 + 10 * q^34 + 4 * q^35 + 63 * q^36 + 26 * q^37 + 16 * q^38 + 50 * q^39 + 9 * q^40 + 27 * q^41 + 16 * q^42 + 12 * q^43 + 4 * q^44 + 44 * q^45 + 41 * q^46 + 18 * q^47 + 4 * q^48 + 87 * q^49 + 76 * q^50 + 24 * q^51 + 16 * q^52 + 63 * q^53 + 7 * q^54 + 18 * q^55 + 12 * q^56 - 12 * q^57 + 28 * q^58 + 33 * q^59 + 10 * q^60 + 24 * q^61 + 25 * q^62 + 48 * q^63 + 41 * q^64 + 21 * q^65 + 5 * q^66 - 9 * q^67 + 10 * q^68 + 4 * q^69 + 4 * q^70 + 36 * q^71 + 63 * q^72 + 36 * q^73 + 26 * q^74 + 6 * q^75 + 16 * q^76 + 48 * q^77 + 50 * q^78 + 51 * q^79 + 9 * q^80 + 149 * q^81 + 27 * q^82 - 27 * q^83 + 16 * q^84 + 52 * q^85 + 12 * q^86 - 3 * q^87 + 4 * q^88 + 68 * q^89 + 44 * q^90 + 22 * q^91 + 41 * q^92 + 45 * q^93 + 18 * q^94 + 46 * q^95 + 4 * q^96 + 16 * q^97 + 87 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.35219	−1.35804	−0.679019	−	0.734121i	$-0.737594\pi$
$3$	−2.35219	−1.35804	−0.679019	+	0.734121i	$0.737594\pi$
$4$	1.00000	0.500000
$5$	0.827343	0.369999	0.184999	−	0.982739i	$-0.440772\pi$
$5$	0.827343	0.369999	0.184999	+	0.982739i	$0.440772\pi$
$6$	−2.35219	−0.960277
$7$	0.166684	0.0630006	0.0315003	−	0.999504i	$-0.489971\pi$
$7$	0.166684	0.0630006	0.0315003	+	0.999504i	$0.489971\pi$
$8$	1.00000	0.353553
$9$	2.53280	0.844266
$10$	0.827343	0.261629
$11$	−5.71499	−1.72313	−0.861567	−	0.507643i	$-0.830517\pi$
$11$	−5.71499	−1.72313	−0.861567	+	0.507643i	$0.830517\pi$
$12$	−2.35219	−0.679019
$13$	−3.76006	−1.04285	−0.521426	−	0.853296i	$-0.674600\pi$
$13$	−3.76006	−1.04285	−0.521426	+	0.853296i	$0.674600\pi$
$14$	0.166684	0.0445481
$15$	−1.94607	−0.502472
$16$	1.00000	0.250000
$17$	1.08060	0.262083	0.131041	−	0.991377i	$-0.458168\pi$
$17$	1.08060	0.262083	0.131041	+	0.991377i	$0.458168\pi$
$18$	2.53280	0.596986
$19$	−7.95687	−1.82543	−0.912715	−	0.408596i	$-0.866019\pi$
$19$	−7.95687	−1.82543	−0.912715	+	0.408596i	$0.866019\pi$
$20$	0.827343	0.184999
$21$	−0.392072	−0.0855571
$22$	−5.71499	−1.21844
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−2.35219	−0.480139
$25$	−4.31550	−0.863101
$26$	−3.76006	−0.737408
$27$	1.09895	0.211493
$28$	0.166684	0.0315003
$29$	−4.77718	−0.887101	−0.443550	−	0.896249i	$-0.646281\pi$
$29$	−4.77718	−0.887101	−0.443550	+	0.896249i	$0.646281\pi$
$30$	−1.94607	−0.355302
$31$	2.25920	0.405764	0.202882	−	0.979203i	$-0.434969\pi$
$31$	2.25920	0.405764	0.202882	+	0.979203i	$0.434969\pi$
$32$	1.00000	0.176777
$33$	13.4427	2.34008
$34$	1.08060	0.185321
$35$	0.137905	0.0233101
$36$	2.53280	0.422133
$37$	10.9997	1.80835	0.904173	−	0.427167i	$-0.140488\pi$
$37$	10.9997	1.80835	0.904173	+	0.427167i	$0.140488\pi$
$38$	−7.95687	−1.29077
$39$	8.84437	1.41623
$40$	0.827343	0.130814
$41$	4.45111	0.695146	0.347573	−	0.937653i	$-0.387006\pi$
$41$	4.45111	0.695146	0.347573	+	0.937653i	$0.387006\pi$
$42$	−0.392072	−0.0604980
$43$	−12.2404	−1.86664	−0.933322	−	0.359040i	$-0.883104\pi$
$43$	−12.2404	−1.86664	−0.933322	+	0.359040i	$0.883104\pi$
$44$	−5.71499	−0.861567
$45$	2.09549	0.312377
$46$	1.00000	0.147442
$47$	10.5540	1.53947	0.769733	−	0.638366i	$-0.220389\pi$
$47$	10.5540	1.53947	0.769733	+	0.638366i	$0.220389\pi$
$48$	−2.35219	−0.339509
$49$	−6.97222	−0.996031
$50$	−4.31550	−0.610304
$51$	−2.54177	−0.355918
$52$	−3.76006	−0.521426
$53$	10.2774	1.41171	0.705853	−	0.708358i	$-0.250564\pi$
$53$	10.2774	1.41171	0.705853	+	0.708358i	$0.250564\pi$
$54$	1.09895	0.149548
$55$	−4.72826	−0.637558
$56$	0.166684	0.0222741
$57$	18.7161	2.47900
$58$	−4.77718	−0.627275
$59$	−3.08748	−0.401955	−0.200978	−	0.979596i	$-0.564412\pi$
$59$	−3.08748	−0.401955	−0.200978	+	0.979596i	$0.564412\pi$
$60$	−1.94607	−0.251236
$61$	5.61729	0.719220	0.359610	−	0.933103i	$-0.382910\pi$
$61$	5.61729	0.719220	0.359610	+	0.933103i	$0.382910\pi$
$62$	2.25920	0.286918
$63$	0.422176	0.0531892
$64$	1.00000	0.125000
$65$	−3.11086	−0.385854
$66$	13.4427	1.65469
$67$	0.392856	0.0479950	0.0239975	−	0.999712i	$-0.492361\pi$
$67$	0.392856	0.0479950	0.0239975	+	0.999712i	$0.492361\pi$
$68$	1.08060	0.131041
$69$	−2.35219	−0.283170
$70$	0.137905	0.0164828
$71$	−3.94659	−0.468374	−0.234187	−	0.972192i	$-0.575243\pi$
$71$	−3.94659	−0.468374	−0.234187	+	0.972192i	$0.575243\pi$
$72$	2.53280	0.298493
$73$	8.69129	1.01724	0.508620	−	0.860991i	$-0.330156\pi$
$73$	8.69129	1.01724	0.508620	+	0.860991i	$0.330156\pi$
$74$	10.9997	1.27869
$75$	10.1509	1.17212
$76$	−7.95687	−0.912715
$77$	−0.952597	−0.108558
$78$	8.84437	1.00143
$79$	10.4255	1.17296	0.586479	−	0.809964i	$-0.300514\pi$
$79$	10.4255	1.17296	0.586479	+	0.809964i	$0.300514\pi$
$80$	0.827343	0.0924997
$81$	−10.1833	−1.13148
$82$	4.45111	0.491543
$83$	5.44253	0.597395	0.298698	−	0.954348i	$-0.403448\pi$
$83$	5.44253	0.597395	0.298698	+	0.954348i	$0.403448\pi$
$84$	−0.392072	−0.0427786
$85$	0.894023	0.0969704
$86$	−12.2404	−1.31992
$87$	11.2368	1.20472
$88$	−5.71499	−0.609220
$89$	10.2049	1.08171	0.540857	−	0.841115i	$-0.318100\pi$
$89$	10.2049	1.08171	0.540857	+	0.841115i	$0.318100\pi$
$90$	2.09549	0.220884
$91$	−0.626741	−0.0657003
$92$	1.00000	0.104257
$93$	−5.31406	−0.551042
$94$	10.5540	1.08857
$95$	−6.58306	−0.675408
$96$	−2.35219	−0.240069
$97$	−11.9980	−1.21821	−0.609104	−	0.793091i	$-0.708471\pi$
$97$	−11.9980	−1.21821	−0.609104	+	0.793091i	$0.708471\pi$
$98$	−6.97222	−0.704300
$99$	−14.4749	−1.45478
$100$	−4.31550	−0.431550
$101$	15.2903	1.52145	0.760723	−	0.649077i	$-0.224845\pi$
$101$	15.2903	1.52145	0.760723	+	0.649077i	$0.224845\pi$
$102$	−2.54177	−0.251672
$103$	−3.23199	−0.318457	−0.159228	−	0.987242i	$-0.550901\pi$
$103$	−3.23199	−0.318457	−0.159228	+	0.987242i	$0.550901\pi$
$104$	−3.76006	−0.368704
$105$	−0.324378	−0.0316561
$106$	10.2774	0.998227
$107$	16.9302	1.63670	0.818350	−	0.574720i	$-0.194889\pi$
$107$	16.9302	1.63670	0.818350	+	0.574720i	$0.194889\pi$
$108$	1.09895	0.105747
$109$	6.86879	0.657911	0.328955	−	0.944345i	$-0.393303\pi$
$109$	6.86879	0.657911	0.328955	+	0.944345i	$0.393303\pi$
$110$	−4.72826	−0.450822
$111$	−25.8735	−2.45580
$112$	0.166684	0.0157501
$113$	9.12158	0.858086	0.429043	−	0.903284i	$-0.358851\pi$
$113$	9.12158	0.858086	0.429043	+	0.903284i	$0.358851\pi$
$114$	18.7161	1.75292
$115$	0.827343	0.0771501
$116$	−4.77718	−0.443550
$117$	−9.52347	−0.880445
$118$	−3.08748	−0.284225
$119$	0.180118	0.0165114
$120$	−1.94607	−0.177651
$121$	21.6611	1.96919
$122$	5.61729	0.508565
$123$	−10.4698	−0.944034
$124$	2.25920	0.202882
$125$	−7.70711	−0.689345
$126$	0.422176	0.0376105
$127$	15.2686	1.35487	0.677436	−	0.735582i	$-0.263091\pi$
$127$	15.2686	1.35487	0.677436	+	0.735582i	$0.263091\pi$
$128$	1.00000	0.0883883
$129$	28.7918	2.53497
$130$	−3.11086	−0.272840
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	13.4427	1.17004
$133$	−1.32628	−0.115003
$134$	0.392856	0.0339376
$135$	0.909209	0.0782522
$136$	1.08060	0.0926603
$137$	−3.36301	−0.287321	−0.143661	−	0.989627i	$-0.545887\pi$
$137$	−3.36301	−0.287321	−0.143661	+	0.989627i	$0.545887\pi$
$138$	−2.35219	−0.200232
$139$	−17.8648	−1.51527	−0.757635	−	0.652678i	$-0.773645\pi$
$139$	−17.8648	−1.51527	−0.757635	+	0.652678i	$0.773645\pi$
$140$	0.137905	0.0116551
$141$	−24.8251	−2.09065
$142$	−3.94659	−0.331191
$143$	21.4887	1.79698
$144$	2.53280	0.211066
$145$	−3.95237	−0.328226
$146$	8.69129	0.719297
$147$	16.4000	1.35265
$148$	10.9997	0.904173
$149$	−11.9413	−0.978269	−0.489134	−	0.872208i	$-0.662687\pi$
$149$	−11.9413	−0.978269	−0.489134	+	0.872208i	$0.662687\pi$
$150$	10.1509	0.828816
$151$	−8.47742	−0.689882	−0.344941	−	0.938624i	$-0.612101\pi$
$151$	−8.47742	−0.689882	−0.344941	+	0.938624i	$0.612101\pi$
$152$	−7.95687	−0.645387
$153$	2.73693	0.221268
$154$	−0.952597	−0.0767624
$155$	1.86913	0.150132
$156$	8.84437	0.708117
$157$	−6.28255	−0.501402	−0.250701	−	0.968065i	$-0.580661\pi$
$157$	−6.28255	−0.501402	−0.250701	+	0.968065i	$0.580661\pi$
$158$	10.4255	0.829407
$159$	−24.1743	−1.91715
$160$	0.827343	0.0654072
$161$	0.166684	0.0131365
$162$	−10.1833	−0.800078
$163$	−24.3171	−1.90466	−0.952332	−	0.305064i	$-0.901322\pi$
$163$	−24.3171	−1.90466	−0.952332	+	0.305064i	$0.901322\pi$
$164$	4.45111	0.347573
$165$	11.1218	0.865828
$166$	5.44253	0.422422
$167$	−17.9184	−1.38657	−0.693283	−	0.720665i	$-0.743837\pi$
$167$	−17.9184	−1.38657	−0.693283	+	0.720665i	$0.743837\pi$
$168$	−0.392072	−0.0302490
$169$	1.13805	0.0875422
$170$	0.894023	0.0685684
$171$	−20.1531	−1.54115
$172$	−12.2404	−0.933322
$173$	−16.4739	−1.25249	−0.626244	−	0.779627i	$-0.715408\pi$
$173$	−16.4739	−1.25249	−0.626244	+	0.779627i	$0.715408\pi$
$174$	11.2368	0.851863
$175$	−0.719325	−0.0543758
$176$	−5.71499	−0.430784
$177$	7.26234	0.545871
$178$	10.2049	0.764887
$179$	−15.9566	−1.19265	−0.596325	−	0.802743i	$-0.703373\pi$
$179$	−15.9566	−1.19265	−0.596325	+	0.802743i	$0.703373\pi$
$180$	2.09549	0.156189
$181$	−3.02973	−0.225198	−0.112599	−	0.993641i	$-0.535918\pi$
$181$	−3.02973	−0.225198	−0.112599	+	0.993641i	$0.535918\pi$
$182$	−0.626741	−0.0464572
$183$	−13.2129	−0.976727
$184$	1.00000	0.0737210
$185$	9.10055	0.669086
$186$	−5.31406	−0.389646
$187$	−6.17559	−0.451604
$188$	10.5540	0.769733
$189$	0.183177	0.0133242
$190$	−6.58306	−0.477585
$191$	−18.7658	−1.35785	−0.678923	−	0.734209i	$-0.737553\pi$
$191$	−18.7658	−1.35785	−0.678923	+	0.734209i	$0.737553\pi$
$192$	−2.35219	−0.169755
$193$	16.4115	1.18132	0.590662	−	0.806919i	$-0.298867\pi$
$193$	16.4115	1.18132	0.590662	+	0.806919i	$0.298867\pi$
$194$	−11.9980	−0.861403
$195$	7.31733	0.524005
$196$	−6.97222	−0.498015
$197$	−3.89836	−0.277746	−0.138873	−	0.990310i	$-0.544348\pi$
$197$	−3.89836	−0.277746	−0.138873	+	0.990310i	$0.544348\pi$
$198$	−14.4749	−1.02869
$199$	9.50685	0.673923	0.336961	−	0.941518i	$-0.390601\pi$
$199$	9.50685	0.673923	0.336961	+	0.941518i	$0.390601\pi$
$200$	−4.31550	−0.305152
$201$	−0.924071	−0.0651790
$202$	15.2903	1.07582
$203$	−0.796280	−0.0558879
$204$	−2.54177	−0.177959
$205$	3.68259	0.257203
$206$	−3.23199	−0.225183
$207$	2.53280	0.176042
$208$	−3.76006	−0.260713
$209$	45.4734	3.14546
$210$	−0.324378	−0.0223842
$211$	26.9077	1.85240	0.926201	−	0.377029i	$-0.123054\pi$
$211$	26.9077	1.85240	0.926201	+	0.377029i	$0.123054\pi$
$212$	10.2774	0.705853
$213$	9.28314	0.636070
$214$	16.9302	1.15732
$215$	−10.1270	−0.690657
$216$	1.09895	0.0747741
$217$	0.376571	0.0255633
$218$	6.86879	0.465213
$219$	−20.4436	−1.38145
$220$	−4.72826	−0.318779
$221$	−4.06310	−0.273314
$222$	−25.8735	−1.73651
$223$	25.1509	1.68423	0.842115	−	0.539298i	$-0.181310\pi$
$223$	25.1509	1.68423	0.842115	+	0.539298i	$0.181310\pi$
$224$	0.166684	0.0111370
$225$	−10.9303	−0.728686
$226$	9.12158	0.606759
$227$	18.4514	1.22466	0.612330	−	0.790603i	$-0.290233\pi$
$227$	18.4514	1.22466	0.612330	+	0.790603i	$0.290233\pi$
$228$	18.7161	1.23950
$229$	−4.94343	−0.326671	−0.163335	−	0.986571i	$-0.552225\pi$
$229$	−4.94343	−0.326671	−0.163335	+	0.986571i	$0.552225\pi$
$230$	0.827343	0.0545534
$231$	2.24069	0.147426
$232$	−4.77718	−0.313638
$233$	26.2180	1.71760	0.858801	−	0.512310i	$-0.171210\pi$
$233$	26.2180	1.71760	0.858801	+	0.512310i	$0.171210\pi$
$234$	−9.52347	−0.622569
$235$	8.73182	0.569601
$236$	−3.08748	−0.200978
$237$	−24.5227	−1.59292
$238$	0.180118	0.0116753
$239$	17.8873	1.15703	0.578516	−	0.815671i	$-0.303632\pi$
$239$	17.8873	1.15703	0.578516	+	0.815671i	$0.303632\pi$
$240$	−1.94607	−0.125618
$241$	−6.79664	−0.437810	−0.218905	−	0.975746i	$-0.570248\pi$
$241$	−6.79664	−0.437810	−0.218905	+	0.975746i	$0.570248\pi$
$242$	21.6611	1.39243
$243$	20.6563	1.32510
$244$	5.61729	0.359610
$245$	−5.76841	−0.368530
$246$	−10.4698	−0.667533
$247$	29.9183	1.90366
$248$	2.25920	0.143459
$249$	−12.8019	−0.811285
$250$	−7.70711	−0.487441
$251$	6.74267	0.425593	0.212797	−	0.977097i	$-0.431743\pi$
$251$	6.74267	0.425593	0.212797	+	0.977097i	$0.431743\pi$
$252$	0.422176	0.0265946
$253$	−5.71499	−0.359298
$254$	15.2686	0.958039
$255$	−2.10291	−0.131689
$256$	1.00000	0.0625000
$257$	11.8732	0.740632	0.370316	−	0.928906i	$-0.379249\pi$
$257$	11.8732	0.740632	0.370316	+	0.928906i	$0.379249\pi$
$258$	28.7918	1.79250
$259$	1.83348	0.113927
$260$	−3.11086	−0.192927
$261$	−12.0996	−0.748949
$262$	1.00000	0.0617802
$263$	−24.7110	−1.52375	−0.761873	−	0.647726i	$-0.775720\pi$
$263$	−24.7110	−1.52375	−0.761873	+	0.647726i	$0.775720\pi$
$264$	13.4427	0.827344
$265$	8.50291	0.522330
$266$	−1.32628	−0.0813195
$267$	−24.0038	−1.46901
$268$	0.392856	0.0239975
$269$	9.51456	0.580113	0.290056	−	0.957010i	$-0.406326\pi$
$269$	9.51456	0.580113	0.290056	+	0.957010i	$0.406326\pi$
$270$	0.909209	0.0553327
$271$	−4.93482	−0.299769	−0.149884	−	0.988704i	$-0.547890\pi$
$271$	−4.93482	−0.299769	−0.149884	+	0.988704i	$0.547890\pi$
$272$	1.08060	0.0655207
$273$	1.47421	0.0892235
$274$	−3.36301	−0.203167
$275$	24.6631	1.48724
$276$	−2.35219	−0.141585
$277$	18.6218	1.11887	0.559436	−	0.828873i	$-0.311018\pi$
$277$	18.6218	1.11887	0.559436	+	0.828873i	$0.311018\pi$
$278$	−17.8648	−1.07146
$279$	5.72208	0.342572
$280$	0.137905	0.00824138
$281$	−0.483280	−0.0288301	−0.0144150	−	0.999896i	$-0.504589\pi$
$281$	−0.483280	−0.0288301	−0.0144150	+	0.999896i	$0.504589\pi$
$282$	−24.8251	−1.47831
$283$	−1.00303	−0.0596241	−0.0298120	−	0.999556i	$-0.509491\pi$
$283$	−1.00303	−0.0596241	−0.0298120	+	0.999556i	$0.509491\pi$
$284$	−3.94659	−0.234187
$285$	15.4846	0.917229
$286$	21.4887	1.27065
$287$	0.741928	0.0437946
$288$	2.53280	0.149246
$289$	−15.8323	−0.931313
$290$	−3.95237	−0.232091
$291$	28.2215	1.65437
$292$	8.69129	0.508620
$293$	15.3741	0.898166	0.449083	−	0.893490i	$-0.351751\pi$
$293$	15.3741	0.898166	0.449083	+	0.893490i	$0.351751\pi$
$294$	16.4000	0.956466
$295$	−2.55440	−0.148723
$296$	10.9997	0.639347
$297$	−6.28049	−0.364431
$298$	−11.9413	−0.691740
$299$	−3.76006	−0.217450
$300$	10.1509	0.586062
$301$	−2.04028	−0.117600
$302$	−8.47742	−0.487821
$303$	−35.9658	−2.06618
$304$	−7.95687	−0.456358
$305$	4.64742	0.266111
$306$	2.73693	0.156460
$307$	9.21067	0.525681	0.262840	−	0.964839i	$-0.415341\pi$
$307$	9.21067	0.525681	0.262840	+	0.964839i	$0.415341\pi$
$308$	−0.952597	−0.0542792
$309$	7.60224	0.432476
$310$	1.86913	0.106159
$311$	13.7769	0.781214	0.390607	−	0.920558i	$-0.372265\pi$
$311$	13.7769	0.781214	0.390607	+	0.920558i	$0.372265\pi$
$312$	8.84437	0.500714
$313$	−14.8034	−0.836740	−0.418370	−	0.908277i	$-0.637398\pi$
$313$	−14.8034	−0.836740	−0.418370	+	0.908277i	$0.637398\pi$
$314$	−6.28255	−0.354545
$315$	0.349285	0.0196800
$316$	10.4255	0.586479
$317$	4.40316	0.247306	0.123653	−	0.992326i	$-0.460539\pi$
$317$	4.40316	0.247306	0.123653	+	0.992326i	$0.460539\pi$
$318$	−24.1743	−1.35563
$319$	27.3016	1.52859
$320$	0.827343	0.0462499
$321$	−39.8230	−2.22270
$322$	0.166684	0.00928893
$323$	−8.59816	−0.478414
$324$	−10.1833	−0.565741
$325$	16.2266	0.900087
$326$	−24.3171	−1.34680
$327$	−16.1567	−0.893468
$328$	4.45111	0.245771
$329$	1.75919	0.0969873
$330$	11.1218	0.612233
$331$	10.5681	0.580878	0.290439	−	0.956894i	$-0.406199\pi$
$331$	10.5681	0.580878	0.290439	+	0.956894i	$0.406199\pi$
$332$	5.44253	0.298698
$333$	27.8601	1.52672
$334$	−17.9184	−0.980451
$335$	0.325026	0.0177581
$336$	−0.392072	−0.0213893
$337$	23.4087	1.27515	0.637576	−	0.770387i	$-0.279937\pi$
$337$	23.4087	1.27515	0.637576	+	0.770387i	$0.279937\pi$
$338$	1.13805	0.0619017
$339$	−21.4557	−1.16531
$340$	0.894023	0.0484852
$341$	−12.9113	−0.699185
$342$	−20.1531	−1.08976
$343$	−2.32894	−0.125751
$344$	−12.2404	−0.659959
$345$	−1.94607	−0.104773
$346$	−16.4739	−0.885642
$347$	28.9904	1.55629	0.778144	−	0.628086i	$-0.216161\pi$
$347$	28.9904	1.55629	0.778144	+	0.628086i	$0.216161\pi$
$348$	11.2368	0.602358
$349$	−33.0837	−1.77093	−0.885464	−	0.464708i	$-0.846159\pi$
$349$	−33.0837	−1.77093	−0.885464	+	0.464708i	$0.846159\pi$
$350$	−0.719325	−0.0384495
$351$	−4.13212	−0.220556
$352$	−5.71499	−0.304610
$353$	26.4808	1.40943	0.704715	−	0.709491i	$-0.251075\pi$
$353$	26.4808	1.40943	0.704715	+	0.709491i	$0.251075\pi$
$354$	7.26234	0.385989
$355$	−3.26519	−0.173298
$356$	10.2049	0.540857
$357$	−0.423671	−0.0224231
$358$	−15.9566	−0.843331
$359$	−3.42465	−0.180746	−0.0903731	−	0.995908i	$-0.528806\pi$
$359$	−3.42465	−0.180746	−0.0903731	+	0.995908i	$0.528806\pi$
$360$	2.09549	0.110442
$361$	44.3118	2.33220
$362$	−3.02973	−0.159239
$363$	−50.9511	−2.67424
$364$	−0.626741	−0.0328502
$365$	7.19068	0.376377
$366$	−13.2129	−0.690651
$367$	9.45363	0.493476	0.246738	−	0.969082i	$-0.420641\pi$
$367$	9.45363	0.493476	0.246738	+	0.969082i	$0.420641\pi$
$368$	1.00000	0.0521286
$369$	11.2738	0.586888
$370$	9.10055	0.473115
$371$	1.71307	0.0889383
$372$	−5.31406	−0.275521
$373$	33.3389	1.72622	0.863111	−	0.505014i	$-0.168513\pi$
$373$	33.3389	1.72622	0.863111	+	0.505014i	$0.168513\pi$
$374$	−6.17559	−0.319332
$375$	18.1286	0.936157
$376$	10.5540	0.544284
$377$	17.9625	0.925116
$378$	0.183177	0.00942162
$379$	10.9804	0.564024	0.282012	−	0.959411i	$-0.408998\pi$
$379$	10.9804	0.564024	0.282012	+	0.959411i	$0.408998\pi$
$380$	−6.58306	−0.337704
$381$	−35.9147	−1.83997
$382$	−18.7658	−0.960143
$383$	−5.07001	−0.259065	−0.129533	−	0.991575i	$-0.541348\pi$
$383$	−5.07001	−0.259065	−0.129533	+	0.991575i	$0.541348\pi$
$384$	−2.35219	−0.120035
$385$	−0.788124	−0.0401665
$386$	16.4115	0.835322
$387$	−31.0025	−1.57594
$388$	−11.9980	−0.609104
$389$	−15.3033	−0.775906	−0.387953	−	0.921679i	$-0.626818\pi$
$389$	−15.3033	−0.775906	−0.387953	+	0.921679i	$0.626818\pi$
$390$	7.31733	0.370527
$391$	1.08060	0.0546481
$392$	−6.97222	−0.352150
$393$	−2.35219	−0.118652
$394$	−3.89836	−0.196396
$395$	8.62545	0.433993
$396$	−14.4749	−0.727392
$397$	6.62716	0.332607	0.166304	−	0.986075i	$-0.446817\pi$
$397$	6.62716	0.332607	0.166304	+	0.986075i	$0.446817\pi$
$398$	9.50685	0.476535
$399$	3.11967	0.156179
$400$	−4.31550	−0.215775
$401$	37.1211	1.85374	0.926870	−	0.375383i	$-0.122489\pi$
$401$	37.1211	1.85374	0.926870	+	0.375383i	$0.122489\pi$
$402$	−0.924071	−0.0460885
$403$	−8.49471	−0.423152
$404$	15.2903	0.760723
$405$	−8.42511	−0.418647
$406$	−0.796280	−0.0395187
$407$	−62.8634	−3.11602
$408$	−2.54177	−0.125836
$409$	20.9320	1.03502	0.517512	−	0.855676i	$-0.326858\pi$
$409$	20.9320	1.03502	0.517512	+	0.855676i	$0.326858\pi$
$410$	3.68259	0.181870
$411$	7.91043	0.390193
$412$	−3.23199	−0.159228
$413$	−0.514633	−0.0253234
$414$	2.53280	0.124480
$415$	4.50284	0.221036
$416$	−3.76006	−0.184352
$417$	42.0213	2.05779
$418$	45.4734	2.22418
$419$	−19.7627	−0.965471	−0.482735	−	0.875766i	$-0.660357\pi$
$419$	−19.7627	−0.965471	−0.482735	+	0.875766i	$0.660357\pi$
$420$	−0.324378	−0.0158280
$421$	37.8493	1.84466	0.922331	−	0.386401i	$-0.126282\pi$
$421$	37.8493	1.84466	0.922331	+	0.386401i	$0.126282\pi$
$422$	26.9077	1.30985
$423$	26.7313	1.29972
$424$	10.2774	0.499113
$425$	−4.66331	−0.226204
$426$	9.28314	0.449769
$427$	0.936311	0.0453113
$428$	16.9302	0.818350
$429$	−50.5455	−2.44036
$430$	−10.1270	−0.488368
$431$	−9.26786	−0.446417	−0.223209	−	0.974771i	$-0.571653\pi$
$431$	−9.26786	−0.446417	−0.223209	+	0.974771i	$0.571653\pi$
$432$	1.09895	0.0528733
$433$	−6.35839	−0.305565	−0.152782	−	0.988260i	$-0.548823\pi$
$433$	−6.35839	−0.305565	−0.152782	+	0.988260i	$0.548823\pi$
$434$	0.376571	0.0180760
$435$	9.29672	0.445744
$436$	6.86879	0.328955
$437$	−7.95687	−0.380629
$438$	−20.4436	−0.976832
$439$	−31.0689	−1.48284	−0.741419	−	0.671042i	$-0.765847\pi$
$439$	−31.0689	−1.48284	−0.741419	+	0.671042i	$0.765847\pi$
$440$	−4.72826	−0.225411
$441$	−17.6592	−0.840915
$442$	−4.06310	−0.193262
$443$	−22.7770	−1.08217	−0.541083	−	0.840969i	$-0.681986\pi$
$443$	−22.7770	−1.08217	−0.541083	+	0.840969i	$0.681986\pi$
$444$	−25.8735	−1.22790
$445$	8.44292	0.400233
$446$	25.1509	1.19093
$447$	28.0882	1.32853
$448$	0.166684	0.00787507
$449$	4.67328	0.220546	0.110273	−	0.993901i	$-0.464828\pi$
$449$	4.67328	0.220546	0.110273	+	0.993901i	$0.464828\pi$
$450$	−10.9303	−0.515259
$451$	−25.4380	−1.19783
$452$	9.12158	0.429043
$453$	19.9405	0.936886
$454$	18.4514	0.865965
$455$	−0.518530	−0.0243091
$456$	18.7161	0.876460
$457$	−1.19996	−0.0561317	−0.0280658	−	0.999606i	$-0.508935\pi$
$457$	−1.19996	−0.0561317	−0.0280658	+	0.999606i	$0.508935\pi$
$458$	−4.94343	−0.230991
$459$	1.18752	0.0554287
$460$	0.827343	0.0385751
$461$	−14.6364	−0.681685	−0.340842	−	0.940120i	$-0.610712\pi$
$461$	−14.6364	−0.681685	−0.340842	+	0.940120i	$0.610712\pi$
$462$	2.24069	0.104246
$463$	−36.1038	−1.67788	−0.838942	−	0.544221i	$-0.816825\pi$
$463$	−36.1038	−1.67788	−0.838942	+	0.544221i	$0.816825\pi$
$464$	−4.77718	−0.221775
$465$	−4.39655	−0.203885
$466$	26.2180	1.21453
$467$	10.8575	0.502427	0.251213	−	0.967932i	$-0.419170\pi$
$467$	10.8575	0.502427	0.251213	+	0.967932i	$0.419170\pi$
$468$	−9.52347	−0.440222
$469$	0.0654827	0.00302371
$470$	8.73182	0.402769
$471$	14.7778	0.680923
$472$	−3.08748	−0.142113
$473$	69.9538	3.21648
$474$	−24.5227	−1.12637
$475$	34.3379	1.57553
$476$	0.180118	0.00825569
$477$	26.0305	1.19185
$478$	17.8873	0.818145
$479$	−31.1140	−1.42163	−0.710817	−	0.703377i	$-0.751675\pi$
$479$	−31.1140	−1.42163	−0.710817	+	0.703377i	$0.751675\pi$
$480$	−1.94607	−0.0888254
$481$	−41.3597	−1.88584
$482$	−6.79664	−0.309578
$483$	−0.392072	−0.0178399
$484$	21.6611	0.984597
$485$	−9.92642	−0.450735
$486$	20.6563	0.936988
$487$	38.2817	1.73471	0.867355	−	0.497691i	$-0.165819\pi$
$487$	38.2817	1.73471	0.867355	+	0.497691i	$0.165819\pi$
$488$	5.61729	0.254283
$489$	57.1985	2.58660
$490$	−5.76841	−0.260590
$491$	10.6610	0.481123	0.240562	−	0.970634i	$-0.422668\pi$
$491$	10.6610	0.481123	0.240562	+	0.970634i	$0.422668\pi$
$492$	−10.4698	−0.472017
$493$	−5.16220	−0.232494
$494$	29.9183	1.34609
$495$	−11.9757	−0.538268
$496$	2.25920	0.101441
$497$	−0.657833	−0.0295079
$498$	−12.8019	−0.573665
$499$	−21.8687	−0.978977	−0.489489	−	0.872010i	$-0.662817\pi$
$499$	−21.8687	−0.978977	−0.489489	+	0.872010i	$0.662817\pi$
$500$	−7.70711	−0.344673
$501$	42.1475	1.88301
$502$	6.74267	0.300940
$503$	14.5587	0.649140	0.324570	−	0.945862i	$-0.394780\pi$
$503$	14.5587	0.649140	0.324570	+	0.945862i	$0.394780\pi$
$504$	0.422176	0.0188052
$505$	12.6504	0.562933
$506$	−5.71499	−0.254062
$507$	−2.67691	−0.118886
$508$	15.2686	0.677436
$509$	−35.7577	−1.58493	−0.792467	−	0.609915i	$-0.791204\pi$
$509$	−35.7577	−1.58493	−0.792467	+	0.609915i	$0.791204\pi$
$510$	−2.10291	−0.0931185
$511$	1.44870	0.0640866
$512$	1.00000	0.0441942
$513$	−8.74421	−0.386066
$514$	11.8732	0.523706
$515$	−2.67396	−0.117829
$516$	28.7918	1.26749
$517$	−60.3163	−2.65271
$518$	1.83348	0.0805584
$519$	38.7497	1.70092
$520$	−3.11086	−0.136420
$521$	−17.0249	−0.745872	−0.372936	−	0.927857i	$-0.621649\pi$
$521$	−17.0249	−0.745872	−0.372936	+	0.927857i	$0.621649\pi$
$522$	−12.0996	−0.529587
$523$	−13.8591	−0.606014	−0.303007	−	0.952988i	$-0.597991\pi$
$523$	−13.8591	−0.606014	−0.303007	+	0.952988i	$0.597991\pi$
$524$	1.00000	0.0436852
$525$	1.69199	0.0738444
$526$	−24.7110	−1.07745
$527$	2.44128	0.106344
$528$	13.4427	0.585020
$529$	1.00000	0.0434783
$530$	8.50291	0.369343
$531$	−7.81996	−0.339357
$532$	−1.32628	−0.0575016
$533$	−16.7364	−0.724935
$534$	−24.0038	−1.03875
$535$	14.0070	0.605577
$536$	0.392856	0.0169688
$537$	37.5329	1.61966
$538$	9.51456	0.410202
$539$	39.8462	1.71630
$540$	0.909209	0.0391261
$541$	34.5077	1.48360	0.741801	−	0.670620i	$-0.233972\pi$
$541$	34.5077	1.48360	0.741801	+	0.670620i	$0.233972\pi$
$542$	−4.93482	−0.211969
$543$	7.12650	0.305828
$544$	1.08060	0.0463302
$545$	5.68284	0.243426
$546$	1.47421	0.0630906
$547$	10.7550	0.459849	0.229924	−	0.973209i	$-0.426152\pi$
$547$	10.7550	0.459849	0.229924	+	0.973209i	$0.426152\pi$
$548$	−3.36301	−0.143661
$549$	14.2274	0.607213
$550$	24.6631	1.05164
$551$	38.0114	1.61934
$552$	−2.35219	−0.100116
$553$	1.73776	0.0738971
$554$	18.6218	0.791162
$555$	−21.4062	−0.908644
$556$	−17.8648	−0.757635
$557$	−6.14095	−0.260200	−0.130100	−	0.991501i	$-0.541530\pi$
$557$	−6.14095	−0.260200	−0.130100	+	0.991501i	$0.541530\pi$
$558$	5.72208	0.242235
$559$	46.0247	1.94664
$560$	0.137905	0.00582754
$561$	14.5262	0.613295
$562$	−0.483280	−0.0203859
$563$	−4.07810	−0.171871	−0.0859356	−	0.996301i	$-0.527388\pi$
$563$	−4.07810	−0.171871	−0.0859356	+	0.996301i	$0.527388\pi$
$564$	−24.8251	−1.04533
$565$	7.54668	0.317491
$566$	−1.00303	−0.0421606
$567$	−1.69740	−0.0712840
$568$	−3.94659	−0.165595
$569$	−0.0320363	−0.00134303	−0.000671515	−	1.00000i	$-0.500214\pi$
$569$	−0.0320363	−0.00134303	−0.000671515		1.00000i	$0.500214\pi$
$570$	15.4846	0.648579
$571$	−28.3576	−1.18673	−0.593365	−	0.804934i	$-0.702201\pi$
$571$	−28.3576	−1.18673	−0.593365	+	0.804934i	$0.702201\pi$
$572$	21.4887	0.898488
$573$	44.1408	1.84401
$574$	0.741928	0.0309675
$575$	−4.31550	−0.179969
$576$	2.53280	0.105533
$577$	2.69310	0.112115	0.0560575	−	0.998428i	$-0.482147\pi$
$577$	2.69310	0.112115	0.0560575	+	0.998428i	$0.482147\pi$
$578$	−15.8323	−0.658537
$579$	−38.6029	−1.60428
$580$	−3.95237	−0.164113
$581$	0.907182	0.0376362
$582$	28.2215	1.16982
$583$	−58.7351	−2.43256
$584$	8.69129	0.359648
$585$	−7.87917	−0.325764
$586$	15.3741	0.635099
$587$	−35.6404	−1.47104	−0.735518	−	0.677505i	$-0.763061\pi$
$587$	−35.6404	−1.47104	−0.735518	+	0.677505i	$0.763061\pi$
$588$	16.4000	0.676324
$589$	−17.9761	−0.740693
$590$	−2.55440	−0.105163
$591$	9.16968	0.377190
$592$	10.9997	0.452086
$593$	−17.6267	−0.723843	−0.361921	−	0.932209i	$-0.617879\pi$
$593$	−17.6267	−0.723843	−0.361921	+	0.932209i	$0.617879\pi$
$594$	−6.28049	−0.257692
$595$	0.149019	0.00610919
$596$	−11.9413	−0.489134
$597$	−22.3619	−0.915212
$598$	−3.76006	−0.153760
$599$	−18.6112	−0.760433	−0.380216	−	0.924898i	$-0.624150\pi$
$599$	−18.6112	−0.760433	−0.380216	+	0.924898i	$0.624150\pi$
$600$	10.1509	0.414408
$601$	−34.6598	−1.41380	−0.706902	−	0.707312i	$-0.749908\pi$
$601$	−34.6598	−1.41380	−0.706902	+	0.707312i	$0.749908\pi$
$602$	−2.04028	−0.0831555
$603$	0.995024	0.0405205
$604$	−8.47742	−0.344941
$605$	17.9212	0.728599
$606$	−35.9658	−1.46101
$607$	3.04094	0.123428	0.0617139	−	0.998094i	$-0.480343\pi$
$607$	3.04094	0.123428	0.0617139	+	0.998094i	$0.480343\pi$
$608$	−7.95687	−0.322694
$609$	1.87300	0.0758978
$610$	4.64742	0.188169
$611$	−39.6839	−1.60544
$612$	2.73693	0.110634
$613$	−18.5211	−0.748059	−0.374030	−	0.927417i	$-0.622024\pi$
$613$	−18.5211	−0.748059	−0.374030	+	0.927417i	$0.622024\pi$
$614$	9.21067	0.371712
$615$	−8.66215	−0.349292
$616$	−0.952597	−0.0383812
$617$	15.9358	0.641549	0.320775	−	0.947156i	$-0.396057\pi$
$617$	15.9358	0.641549	0.320775	+	0.947156i	$0.396057\pi$
$618$	7.60224	0.305807
$619$	6.71291	0.269815	0.134907	−	0.990858i	$-0.456926\pi$
$619$	6.71291	0.269815	0.134907	+	0.990858i	$0.456926\pi$
$620$	1.86913	0.0750660
$621$	1.09895	0.0440994
$622$	13.7769	0.552402
$623$	1.70099	0.0681486
$624$	8.84437	0.354058
$625$	15.2011	0.608044
$626$	−14.8034	−0.591664
$627$	−106.962	−4.27166
$628$	−6.28255	−0.250701
$629$	11.8863	0.473937
$630$	0.349285	0.0139158
$631$	34.4510	1.37147	0.685736	−	0.727850i	$-0.259480\pi$
$631$	34.4510	1.37147	0.685736	+	0.727850i	$0.259480\pi$
$632$	10.4255	0.414703
$633$	−63.2920	−2.51563
$634$	4.40316	0.174872
$635$	12.6324	0.501301
$636$	−24.1743	−0.958575
$637$	26.2160	1.03871
$638$	27.3016	1.08088
$639$	−9.99592	−0.395432
$640$	0.827343	0.0327036
$641$	0.108864	0.00429989	0.00214994	−	0.999998i	$-0.499316\pi$
$641$	0.108864	0.00429989	0.00214994	+	0.999998i	$0.499316\pi$
$642$	−39.8230	−1.57169
$643$	−49.4323	−1.94942	−0.974710	−	0.223474i	$-0.928260\pi$
$643$	−49.4323	−1.94942	−0.974710	+	0.223474i	$0.928260\pi$
$644$	0.166684	0.00656826
$645$	23.8207	0.937937
$646$	−8.59816	−0.338290
$647$	39.2984	1.54498	0.772490	−	0.635027i	$-0.219011\pi$
$647$	39.2984	1.54498	0.772490	+	0.635027i	$0.219011\pi$
$648$	−10.1833	−0.400039
$649$	17.6449	0.692623
$650$	16.2266	0.636458
$651$	−0.885768	−0.0347160
$652$	−24.3171	−0.952332
$653$	−13.0887	−0.512200	−0.256100	−	0.966650i	$-0.582438\pi$
$653$	−13.0887	−0.512200	−0.256100	+	0.966650i	$0.582438\pi$
$654$	−16.1567	−0.631777
$655$	0.827343	0.0323270
$656$	4.45111	0.173787
$657$	22.0133	0.858820
$658$	1.75919	0.0685803
$659$	−10.7392	−0.418338	−0.209169	−	0.977879i	$-0.567076\pi$
$659$	−10.7392	−0.418338	−0.209169	+	0.977879i	$0.567076\pi$
$660$	11.1218	0.432914
$661$	28.4049	1.10482	0.552412	−	0.833571i	$-0.313708\pi$
$661$	28.4049	1.10482	0.552412	+	0.833571i	$0.313708\pi$
$662$	10.5681	0.410743
$663$	9.55719	0.371171
$664$	5.44253	0.211211
$665$	−1.09729	−0.0425511
$666$	27.8601	1.07956
$667$	−4.77718	−0.184973
$668$	−17.9184	−0.693283
$669$	−59.1597	−2.28725
$670$	0.325026	0.0125569
$671$	−32.1027	−1.23931
$672$	−0.392072	−0.0151245
$673$	26.1258	1.00707	0.503537	−	0.863973i	$-0.332032\pi$
$673$	26.1258	1.00707	0.503537	+	0.863973i	$0.332032\pi$
$674$	23.4087	0.901669
$675$	−4.74253	−0.182540
$676$	1.13805	0.0437711
$677$	−15.3129	−0.588521	−0.294260	−	0.955725i	$-0.595073\pi$
$677$	−15.3129	−0.588521	−0.294260	+	0.955725i	$0.595073\pi$
$678$	−21.4557	−0.824001
$679$	−1.99986	−0.0767478
$680$	0.894023	0.0342842
$681$	−43.4011	−1.66313
$682$	−12.9113	−0.494399
$683$	−20.7824	−0.795218	−0.397609	−	0.917555i	$-0.630160\pi$
$683$	−20.7824	−0.795218	−0.397609	+	0.917555i	$0.630160\pi$
$684$	−20.1531	−0.770574
$685$	−2.78236	−0.106309
$686$	−2.32894	−0.0889195
$687$	11.6279	0.443631
$688$	−12.2404	−0.466661
$689$	−38.6435	−1.47220
$690$	−1.94607	−0.0740855
$691$	46.3581	1.76354	0.881772	−	0.471675i	$-0.156351\pi$
$691$	46.3581	1.76354	0.881772	+	0.471675i	$0.156351\pi$
$692$	−16.4739	−0.626244
$693$	−2.41273	−0.0916522
$694$	28.9904	1.10046
$695$	−14.7803	−0.560649
$696$	11.2368	0.425932
$697$	4.80985	0.182186
$698$	−33.0837	−1.25224
$699$	−61.6698	−2.33257
$700$	−0.719325	−0.0271879
$701$	−43.7317	−1.65172	−0.825862	−	0.563872i	$-0.809311\pi$
$701$	−43.7317	−1.65172	−0.825862	+	0.563872i	$0.809311\pi$
$702$	−4.13212	−0.155957
$703$	−87.5235	−3.30101
$704$	−5.71499	−0.215392
$705$	−20.5389	−0.773539
$706$	26.4808	0.996617
$707$	2.54865	0.0958520
$708$	7.26234	0.272935
$709$	4.94657	0.185772	0.0928862	−	0.995677i	$-0.470391\pi$
$709$	4.94657	0.185772	0.0928862	+	0.995677i	$0.470391\pi$
$710$	−3.26519	−0.122540
$711$	26.4056	0.990289
$712$	10.2049	0.382444
$713$	2.25920	0.0846075
$714$	−0.423671	−0.0158555
$715$	17.7785	0.664879
$716$	−15.9566	−0.596325
$717$	−42.0743	−1.57129
$718$	−3.42465	−0.127807
$719$	41.3503	1.54211	0.771053	−	0.636771i	$-0.219730\pi$
$719$	41.3503	1.54211	0.771053	+	0.636771i	$0.219730\pi$
$720$	2.09549	0.0780943
$721$	−0.538720	−0.0200630
$722$	44.3118	1.64911
$723$	15.9870	0.594562
$724$	−3.02973	−0.112599
$725$	20.6160	0.765658
$726$	−50.9511	−1.89097
$727$	−18.8038	−0.697394	−0.348697	−	0.937236i	$-0.613376\pi$
$727$	−18.8038	−0.697394	−0.348697	+	0.937236i	$0.613376\pi$
$728$	−0.626741	−0.0232286
$729$	−18.0375	−0.668055
$730$	7.19068	0.266139
$731$	−13.2269	−0.489216
$732$	−13.2129	−0.488364
$733$	−37.0971	−1.37021	−0.685105	−	0.728444i	$-0.740244\pi$
$733$	−37.0971	−1.37021	−0.685105	+	0.728444i	$0.740244\pi$
$734$	9.45363	0.348940
$735$	13.5684	0.500478
$736$	1.00000	0.0368605
$737$	−2.24517	−0.0827018
$738$	11.2738	0.414992
$739$	−11.6646	−0.429089	−0.214545	−	0.976714i	$-0.568827\pi$
$739$	−11.6646	−0.429089	−0.214545	+	0.976714i	$0.568827\pi$
$740$	9.10055	0.334543
$741$	−70.3735	−2.58524
$742$	1.71307	0.0628889
$743$	−10.6657	−0.391288	−0.195644	−	0.980675i	$-0.562680\pi$
$743$	−10.6657	−0.391288	−0.195644	+	0.980675i	$0.562680\pi$
$744$	−5.31406	−0.194823
$745$	−9.87954	−0.361958
$746$	33.3389	1.22062
$747$	13.7848	0.504360
$748$	−6.17559	−0.225802
$749$	2.82198	0.103113
$750$	18.1286	0.661963
$751$	43.8675	1.60075	0.800375	−	0.599500i	$-0.204634\pi$
$751$	43.8675	1.60075	0.800375	+	0.599500i	$0.204634\pi$
$752$	10.5540	0.384867
$753$	−15.8600	−0.577972
$754$	17.9625	0.654156
$755$	−7.01373	−0.255256
$756$	0.183177	0.00666209
$757$	18.7154	0.680224	0.340112	−	0.940385i	$-0.389535\pi$
$757$	18.7154	0.680224	0.340112	+	0.940385i	$0.389535\pi$
$758$	10.9804	0.398825
$759$	13.4427	0.487941
$760$	−6.58306	−0.238793
$761$	48.6044	1.76191	0.880954	−	0.473202i	$-0.156902\pi$
$761$	48.6044	1.76191	0.880954	+	0.473202i	$0.156902\pi$
$762$	−35.9147	−1.30105
$763$	1.14492	0.0414488
$764$	−18.7658	−0.678923
$765$	2.26438	0.0818688
$766$	−5.07001	−0.183187
$767$	11.6091	0.419180
$768$	−2.35219	−0.0848773
$769$	48.3037	1.74187	0.870937	−	0.491394i	$-0.163513\pi$
$769$	48.3037	1.74187	0.870937	+	0.491394i	$0.163513\pi$
$770$	−0.788124	−0.0284020
$771$	−27.9281	−1.00581
$772$	16.4115	0.590662
$773$	−20.1481	−0.724678	−0.362339	−	0.932046i	$-0.618022\pi$
$773$	−20.1481	−0.724678	−0.362339	+	0.932046i	$0.618022\pi$
$774$	−31.0025	−1.11436
$775$	−9.74957	−0.350215
$776$	−11.9980	−0.430701
$777$	−4.31269	−0.154717
$778$	−15.3033	−0.548648
$779$	−35.4169	−1.26894
$780$	7.31733	0.262002
$781$	22.5547	0.807072
$782$	1.08060	0.0386420
$783$	−5.24989	−0.187616
$784$	−6.97222	−0.249008
$785$	−5.19782	−0.185518
$786$	−2.35219	−0.0838998
$787$	−40.1933	−1.43274	−0.716368	−	0.697722i	$-0.754197\pi$
$787$	−40.1933	−1.43274	−0.716368	+	0.697722i	$0.754197\pi$
$788$	−3.89836	−0.138873
$789$	58.1250	2.06930
$790$	8.62545	0.306880
$791$	1.52042	0.0540599
$792$	−14.4749	−0.514344
$793$	−21.1213	−0.750040
$794$	6.62716	0.235189
$795$	−20.0005	−0.709343
$796$	9.50685	0.336961
$797$	7.42637	0.263055	0.131528	−	0.991312i	$-0.458012\pi$
$797$	7.42637	0.263055	0.131528	+	0.991312i	$0.458012\pi$
$798$	3.11967	0.110435
$799$	11.4047	0.403468
$800$	−4.31550	−0.152576
$801$	25.8469	0.913254
$802$	37.1211	1.31079
$803$	−49.6707	−1.75284
$804$	−0.924071	−0.0325895
$805$	0.137905	0.00486050
$806$	−8.49471	−0.299213
$807$	−22.3801	−0.787815
$808$	15.2903	0.537912
$809$	−24.3037	−0.854473	−0.427236	−	0.904140i	$-0.640513\pi$
$809$	−24.3037	−0.854473	−0.427236	+	0.904140i	$0.640513\pi$
$810$	−8.42511	−0.296028
$811$	10.6487	0.373927	0.186964	−	0.982367i	$-0.440135\pi$
$811$	10.6487	0.373927	0.186964	+	0.982367i	$0.440135\pi$
$812$	−0.796280	−0.0279439
$813$	11.6076	0.407097
$814$	−62.8634	−2.20336
$815$	−20.1186	−0.704724
$816$	−2.54177	−0.0889796
$817$	97.3953	3.40743
$818$	20.9320	0.731872
$819$	−1.58741	−0.0554685
$820$	3.68259	0.128602
$821$	0.984963	0.0343754	0.0171877	−	0.999852i	$-0.494529\pi$
$821$	0.984963	0.0343754	0.0171877	+	0.999852i	$0.494529\pi$
$822$	7.91043	0.275908
$823$	4.50790	0.157136	0.0785678	−	0.996909i	$-0.474965\pi$
$823$	4.50790	0.157136	0.0785678	+	0.996909i	$0.474965\pi$
$824$	−3.23199	−0.112592
$825$	−58.0122	−2.01973
$826$	−0.514633	−0.0179064
$827$	−45.5191	−1.58285	−0.791426	−	0.611265i	$-0.790661\pi$
$827$	−45.5191	−1.58285	−0.791426	+	0.611265i	$0.790661\pi$
$828$	2.53280	0.0880208
$829$	18.0069	0.625406	0.312703	−	0.949851i	$-0.398766\pi$
$829$	18.0069	0.625406	0.312703	+	0.949851i	$0.398766\pi$
$830$	4.50284	0.156296
$831$	−43.8019	−1.51947
$832$	−3.76006	−0.130357
$833$	−7.53415	−0.261043
$834$	42.0213	1.45508
$835$	−14.8247	−0.513028
$836$	45.4734	1.57273
$837$	2.48274	0.0858162
$838$	−19.7627	−0.682691
$839$	6.40628	0.221169	0.110585	−	0.993867i	$-0.464728\pi$
$839$	6.40628	0.221169	0.110585	+	0.993867i	$0.464728\pi$
$840$	−0.324378	−0.0111921
$841$	−6.17851	−0.213052
$842$	37.8493	1.30437
$843$	1.13677	0.0391523
$844$	26.9077	0.926201
$845$	0.941557	0.0323905
$846$	26.7313	0.919040
$847$	3.61056	0.124060
$848$	10.2774	0.352926
$849$	2.35932	0.0809717
$850$	−4.66331	−0.159950
$851$	10.9997	0.377066
$852$	9.28314	0.318035
$853$	20.2994	0.695038	0.347519	−	0.937673i	$-0.387024\pi$
$853$	20.2994	0.695038	0.347519	+	0.937673i	$0.387024\pi$
$854$	0.936311	0.0320399
$855$	−16.6735	−0.570223
$856$	16.9302	0.578661
$857$	36.7838	1.25651	0.628256	−	0.778007i	$-0.283769\pi$
$857$	36.7838	1.25651	0.628256	+	0.778007i	$0.283769\pi$
$858$	−50.5455	−1.72560
$859$	28.8951	0.985887	0.492943	−	0.870061i	$-0.335921\pi$
$859$	28.8951	0.985887	0.492943	+	0.870061i	$0.335921\pi$
$860$	−10.1270	−0.345328
$861$	−1.74515	−0.0594747
$862$	−9.26786	−0.315664
$863$	17.7272	0.603439	0.301720	−	0.953397i	$-0.402439\pi$
$863$	17.7272	0.603439	0.301720	+	0.953397i	$0.402439\pi$
$864$	1.09895	0.0373871
$865$	−13.6296	−0.463419
$866$	−6.35839	−0.216067
$867$	37.2406	1.26476
$868$	0.376571	0.0127817
$869$	−59.5815	−2.02117
$870$	9.29672	0.315188
$871$	−1.47716	−0.0500517
$872$	6.86879	0.232607
$873$	−30.3884	−1.02849
$874$	−7.95687	−0.269145
$875$	−1.28465	−0.0434292
$876$	−20.4436	−0.690724
$877$	11.5184	0.388949	0.194475	−	0.980908i	$-0.437700\pi$
$877$	11.5184	0.388949	0.194475	+	0.980908i	$0.437700\pi$
$878$	−31.0689	−1.04853
$879$	−36.1628	−1.21974
$880$	−4.72826	−0.159390
$881$	−13.1580	−0.443304	−0.221652	−	0.975126i	$-0.571145\pi$
$881$	−13.1580	−0.443304	−0.221652	+	0.975126i	$0.571145\pi$
$882$	−17.6592	−0.594616
$883$	31.0629	1.04535	0.522675	−	0.852532i	$-0.324934\pi$
$883$	31.0629	1.04535	0.522675	+	0.852532i	$0.324934\pi$
$884$	−4.06310	−0.136657
$885$	6.00844	0.201972
$886$	−22.7770	−0.765207
$887$	1.73226	0.0581636	0.0290818	−	0.999577i	$-0.490742\pi$
$887$	1.73226	0.0581636	0.0290818	+	0.999577i	$0.490742\pi$
$888$	−25.8735	−0.868257
$889$	2.54503	0.0853577
$890$	8.44292	0.283007
$891$	58.1976	1.94969
$892$	25.1509	0.842115
$893$	−83.9772	−2.81019
$894$	28.0882	0.939409
$895$	−13.2016	−0.441279
$896$	0.166684	0.00556852
$897$	8.84437	0.295305
$898$	4.67328	0.155949
$899$	−10.7926	−0.359953
$900$	−10.9303	−0.364343
$901$	11.1057	0.369984
$902$	−25.4380	−0.846994
$903$	4.79912	0.159705
$904$	9.12158	0.303379
$905$	−2.50663	−0.0833231
$906$	19.9405	0.662479
$907$	4.87670	0.161928	0.0809642	−	0.996717i	$-0.474200\pi$
$907$	4.87670	0.161928	0.0809642	+	0.996717i	$0.474200\pi$
$908$	18.4514	0.612330
$909$	38.7273	1.28450
$910$	−0.518530	−0.0171891
$911$	−0.558150	−0.0184923	−0.00924617	−	0.999957i	$-0.502943\pi$
$911$	−0.558150	−0.0184923	−0.00924617	+	0.999957i	$0.502943\pi$
$912$	18.7161	0.619751
$913$	−31.1040	−1.02939
$914$	−1.19996	−0.0396911
$915$	−10.9316	−0.361388
$916$	−4.94343	−0.163335
$917$	0.166684	0.00550439
$918$	1.18752	0.0391940
$919$	30.6926	1.01246	0.506228	−	0.862400i	$-0.331039\pi$
$919$	30.6926	1.01246	0.506228	+	0.862400i	$0.331039\pi$
$920$	0.827343	0.0272767
$921$	−21.6652	−0.713894
$922$	−14.6364	−0.482024
$923$	14.8394	0.488446
$924$	2.24069	0.0737132
$925$	−47.4694	−1.56078
$926$	−36.1038	−1.18644
$927$	−8.18596	−0.268862
$928$	−4.77718	−0.156819
$929$	−41.6335	−1.36595	−0.682976	−	0.730441i	$-0.739315\pi$
$929$	−41.6335	−1.36595	−0.682976	+	0.730441i	$0.739315\pi$
$930$	−4.39655	−0.144168
$931$	55.4770	1.81819
$932$	26.2180	0.858801
$933$	−32.4058	−1.06092
$934$	10.8575	0.355269
$935$	−5.10933	−0.167093
$936$	−9.52347	−0.311284
$937$	1.02085	0.0333497	0.0166748	−	0.999861i	$-0.494692\pi$
$937$	1.02085	0.0333497	0.0166748	+	0.999861i	$0.494692\pi$
$938$	0.0654827	0.00213809
$939$	34.8205	1.13632
$940$	8.73182	0.284800
$941$	7.09160	0.231180	0.115590	−	0.993297i	$-0.463124\pi$
$941$	7.09160	0.231180	0.115590	+	0.993297i	$0.463124\pi$
$942$	14.7778	0.481485
$943$	4.45111	0.144948
$944$	−3.08748	−0.100489
$945$	0.151550	0.00492994
$946$	69.9538	2.27439
$947$	53.1654	1.72764	0.863822	−	0.503798i	$-0.168064\pi$
$947$	53.1654	1.72764	0.863822	+	0.503798i	$0.168064\pi$
$948$	−24.5227	−0.796461
$949$	−32.6798	−1.06083
$950$	34.3379	1.11407
$951$	−10.3571	−0.335851
$952$	0.180118	0.00583765
$953$	−9.90477	−0.320847	−0.160423	−	0.987048i	$-0.551286\pi$
$953$	−9.90477	−0.320847	−0.160423	+	0.987048i	$0.551286\pi$
$954$	26.0305	0.842769
$955$	−15.5258	−0.502402
$956$	17.8873	0.578516
$957$	−64.2185	−2.07589
$958$	−31.1140	−1.00525
$959$	−0.560559	−0.0181014
$960$	−1.94607	−0.0628091
$961$	−25.8960	−0.835356
$962$	−41.3597	−1.33349
$963$	42.8807	1.38181
$964$	−6.79664	−0.218905
$965$	13.5779	0.437089
$966$	−0.392072	−0.0126147
$967$	−5.17143	−0.166302	−0.0831510	−	0.996537i	$-0.526498\pi$
$967$	−5.17143	−0.166302	−0.0831510	+	0.996537i	$0.526498\pi$
$968$	21.6611	0.696215
$969$	20.2245	0.649705
$970$	−9.92642	−0.318718
$971$	36.0523	1.15697	0.578486	−	0.815692i	$-0.303644\pi$
$971$	36.0523	1.15697	0.578486	+	0.815692i	$0.303644\pi$
$972$	20.6563	0.662550
$973$	−2.97777	−0.0954629
$974$	38.2817	1.22662
$975$	−38.1679	−1.22235
$976$	5.61729	0.179805
$977$	−44.0667	−1.40982	−0.704910	−	0.709297i	$-0.749013\pi$
$977$	−44.0667	−1.40982	−0.704910	+	0.709297i	$0.749013\pi$
$978$	57.1985	1.82901
$979$	−58.3207	−1.86394
$980$	−5.76841	−0.184265
$981$	17.3973	0.555452
$982$	10.6610	0.340206
$983$	9.93196	0.316780	0.158390	−	0.987377i	$-0.449370\pi$
$983$	9.93196	0.316780	0.158390	+	0.987377i	$0.449370\pi$
$984$	−10.4698	−0.333767
$985$	−3.22528	−0.102766
$986$	−5.16220	−0.164398
$987$	−4.13795	−0.131712
$988$	29.9183	0.951828
$989$	−12.2404	−0.389222
$990$	−11.9757	−0.380613
$991$	8.83218	0.280563	0.140282	−	0.990112i	$-0.455199\pi$
$991$	8.83218	0.280563	0.140282	+	0.990112i	$0.455199\pi$
$992$	2.25920	0.0717295
$993$	−24.8583	−0.788854
$994$	−0.657833	−0.0208652
$995$	7.86542	0.249351
$996$	−12.8019	−0.405642
$997$	1.41911	0.0449435	0.0224718	−	0.999747i	$-0.492846\pi$
$997$	1.41911	0.0449435	0.0224718	+	0.999747i	$0.492846\pi$
$998$	−21.8687	−0.692242
$999$	12.0882	0.382453

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.m.1.7	✓	41

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.m.1.7	✓	41	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.35219 q^{3} +1.00000 q^{4} +0.827343 q^{5} -2.35219 q^{6} +0.166684 q^{7} +1.00000 q^{8} +2.53280 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.35219 q^{3} +1.00000 q^{4} +0.827343 q^{5} -2.35219 q^{6} +0.166684 q^{7} +1.00000 q^{8} +2.53280 q^{9} +0.827343 q^{10} -5.71499 q^{11} -2.35219 q^{12} -3.76006 q^{13} +0.166684 q^{14} -1.94607 q^{15} +1.00000 q^{16} +1.08060 q^{17} +2.53280 q^{18} -7.95687 q^{19} +0.827343 q^{20} -0.392072 q^{21} -5.71499 q^{22} +1.00000 q^{23} -2.35219 q^{24} -4.31550 q^{25} -3.76006 q^{26} +1.09895 q^{27} +0.166684 q^{28} -4.77718 q^{29} -1.94607 q^{30} +2.25920 q^{31} +1.00000 q^{32} +13.4427 q^{33} +1.08060 q^{34} +0.137905 q^{35} +2.53280 q^{36} +10.9997 q^{37} -7.95687 q^{38} +8.84437 q^{39} +0.827343 q^{40} +4.45111 q^{41} -0.392072 q^{42} -12.2404 q^{43} -5.71499 q^{44} +2.09549 q^{45} +1.00000 q^{46} +10.5540 q^{47} -2.35219 q^{48} -6.97222 q^{49} -4.31550 q^{50} -2.54177 q^{51} -3.76006 q^{52} +10.2774 q^{53} +1.09895 q^{54} -4.72826 q^{55} +0.166684 q^{56} +18.7161 q^{57} -4.77718 q^{58} -3.08748 q^{59} -1.94607 q^{60} +5.61729 q^{61} +2.25920 q^{62} +0.422176 q^{63} +1.00000 q^{64} -3.11086 q^{65} +13.4427 q^{66} +0.392856 q^{67} +1.08060 q^{68} -2.35219 q^{69} +0.137905 q^{70} -3.94659 q^{71} +2.53280 q^{72} +8.69129 q^{73} +10.9997 q^{74} +10.1509 q^{75} -7.95687 q^{76} -0.952597 q^{77} +8.84437 q^{78} +10.4255 q^{79} +0.827343 q^{80} -10.1833 q^{81} +4.45111 q^{82} +5.44253 q^{83} -0.392072 q^{84} +0.894023 q^{85} -12.2404 q^{86} +11.2368 q^{87} -5.71499 q^{88} +10.2049 q^{89} +2.09549 q^{90} -0.626741 q^{91} +1.00000 q^{92} -5.31406 q^{93} +10.5540 q^{94} -6.58306 q^{95} -2.35219 q^{96} -11.9980 q^{97} -6.97222 q^{98} -14.4749 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9}+O(q^{10}) \) 41 * q + 41 * q^2 + 4 * q^3 + 41 * q^4 + 9 * q^5 + 4 * q^6 + 12 * q^7 + 41 * q^8 + 63 * q^9	\( 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9} + 9 q^{10} + 4 q^{11} + 4 q^{12} + 16 q^{13} + 12 q^{14} + 10 q^{15} + 41 q^{16} + 10 q^{17} + 63 q^{18} + 16 q^{19} + 9 q^{20} + 16 q^{21} + 4 q^{22} + 41 q^{23} + 4 q^{24} + 76 q^{25} + 16 q^{26} + 7 q^{27} + 12 q^{28} + 28 q^{29} + 10 q^{30} + 25 q^{31} + 41 q^{32} + 5 q^{33} + 10 q^{34} + 4 q^{35} + 63 q^{36} + 26 q^{37} + 16 q^{38} + 50 q^{39} + 9 q^{40} + 27 q^{41} + 16 q^{42} + 12 q^{43} + 4 q^{44} + 44 q^{45} + 41 q^{46} + 18 q^{47} + 4 q^{48} + 87 q^{49} + 76 q^{50} + 24 q^{51} + 16 q^{52} + 63 q^{53} + 7 q^{54} + 18 q^{55} + 12 q^{56} - 12 q^{57} + 28 q^{58} + 33 q^{59} + 10 q^{60} + 24 q^{61} + 25 q^{62} + 48 q^{63} + 41 q^{64} + 21 q^{65} + 5 q^{66} - 9 q^{67} + 10 q^{68} + 4 q^{69} + 4 q^{70} + 36 q^{71} + 63 q^{72} + 36 q^{73} + 26 q^{74} + 6 q^{75} + 16 q^{76} + 48 q^{77} + 50 q^{78} + 51 q^{79} + 9 q^{80} + 149 q^{81} + 27 q^{82} - 27 q^{83} + 16 q^{84} + 52 q^{85} + 12 q^{86} - 3 q^{87} + 4 q^{88} + 68 q^{89} + 44 q^{90} + 22 q^{91} + 41 q^{92} + 45 q^{93} + 18 q^{94} + 46 q^{95} + 4 q^{96} + 16 q^{97} + 87 q^{98} - 10 q^{99}+O(q^{100}) \) 41 * q + 41 * q^2 + 4 * q^3 + 41 * q^4 + 9 * q^5 + 4 * q^6 + 12 * q^7 + 41 * q^8 + 63 * q^9 + 9 * q^10 + 4 * q^11 + 4 * q^12 + 16 * q^13 + 12 * q^14 + 10 * q^15 + 41 * q^16 + 10 * q^17 + 63 * q^18 + 16 * q^19 + 9 * q^20 + 16 * q^21 + 4 * q^22 + 41 * q^23 + 4 * q^24 + 76 * q^25 + 16 * q^26 + 7 * q^27 + 12 * q^28 + 28 * q^29 + 10 * q^30 + 25 * q^31 + 41 * q^32 + 5 * q^33 + 10 * q^34 + 4 * q^35 + 63 * q^36 + 26 * q^37 + 16 * q^38 + 50 * q^39 + 9 * q^40 + 27 * q^41 + 16 * q^42 + 12 * q^43 + 4 * q^44 + 44 * q^45 + 41 * q^46 + 18 * q^47 + 4 * q^48 + 87 * q^49 + 76 * q^50 + 24 * q^51 + 16 * q^52 + 63 * q^53 + 7 * q^54 + 18 * q^55 + 12 * q^56 - 12 * q^57 + 28 * q^58 + 33 * q^59 + 10 * q^60 + 24 * q^61 + 25 * q^62 + 48 * q^63 + 41 * q^64 + 21 * q^65 + 5 * q^66 - 9 * q^67 + 10 * q^68 + 4 * q^69 + 4 * q^70 + 36 * q^71 + 63 * q^72 + 36 * q^73 + 26 * q^74 + 6 * q^75 + 16 * q^76 + 48 * q^77 + 50 * q^78 + 51 * q^79 + 9 * q^80 + 149 * q^81 + 27 * q^82 - 27 * q^83 + 16 * q^84 + 52 * q^85 + 12 * q^86 - 3 * q^87 + 4 * q^88 + 68 * q^89 + 44 * q^90 + 22 * q^91 + 41 * q^92 + 45 * q^93 + 18 * q^94 + 46 * q^95 + 4 * q^96 + 16 * q^97 + 87 * q^98 - 10 * q^99

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