LMFDB - Embedded newform 8043.2.a.u.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8043,2,Mod(1,8043)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8043, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8043.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8043 = 3 \cdot 7 \cdot 383 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8043.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:	$64.2236783457$
Analytic rank:	$0$
Dimension:	$53$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	8043.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.805347 q^{2} +1.00000 q^{3} -1.35142 q^{4} +3.29338 q^{5} -0.805347 q^{6} +1.00000 q^{7} +2.69905 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.805347 q^{2} +1.00000 q^{3} -1.35142 q^{4} +3.29338 q^{5} -0.805347 q^{6} +1.00000 q^{7} +2.69905 q^{8} +1.00000 q^{9} -2.65231 q^{10} +4.32435 q^{11} -1.35142 q^{12} +3.38473 q^{13} -0.805347 q^{14} +3.29338 q^{15} +0.529158 q^{16} -5.22369 q^{17} -0.805347 q^{18} -4.55757 q^{19} -4.45072 q^{20} +1.00000 q^{21} -3.48260 q^{22} +8.09788 q^{23} +2.69905 q^{24} +5.84633 q^{25} -2.72588 q^{26} +1.00000 q^{27} -1.35142 q^{28} -0.959913 q^{29} -2.65231 q^{30} +6.16960 q^{31} -5.82426 q^{32} +4.32435 q^{33} +4.20689 q^{34} +3.29338 q^{35} -1.35142 q^{36} -8.89277 q^{37} +3.67043 q^{38} +3.38473 q^{39} +8.88900 q^{40} -5.39184 q^{41} -0.805347 q^{42} +0.927492 q^{43} -5.84400 q^{44} +3.29338 q^{45} -6.52160 q^{46} +10.6833 q^{47} +0.529158 q^{48} +1.00000 q^{49} -4.70832 q^{50} -5.22369 q^{51} -4.57417 q^{52} +2.90889 q^{53} -0.805347 q^{54} +14.2417 q^{55} +2.69905 q^{56} -4.55757 q^{57} +0.773063 q^{58} -1.67399 q^{59} -4.45072 q^{60} +5.47360 q^{61} -4.96867 q^{62} +1.00000 q^{63} +3.63224 q^{64} +11.1472 q^{65} -3.48260 q^{66} +1.46291 q^{67} +7.05938 q^{68} +8.09788 q^{69} -2.65231 q^{70} +6.80562 q^{71} +2.69905 q^{72} +2.39924 q^{73} +7.16176 q^{74} +5.84633 q^{75} +6.15918 q^{76} +4.32435 q^{77} -2.72588 q^{78} +6.36562 q^{79} +1.74272 q^{80} +1.00000 q^{81} +4.34230 q^{82} -9.75203 q^{83} -1.35142 q^{84} -17.2036 q^{85} -0.746953 q^{86} -0.959913 q^{87} +11.6716 q^{88} -2.40120 q^{89} -2.65231 q^{90} +3.38473 q^{91} -10.9436 q^{92} +6.16960 q^{93} -8.60377 q^{94} -15.0098 q^{95} -5.82426 q^{96} +18.7872 q^{97} -0.805347 q^{98} +4.32435 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 53 q + 11 q^{2} + 53 q^{3} + 63 q^{4} + 24 q^{5} + 11 q^{6} + 53 q^{7} + 30 q^{8} + 53 q^{9}+O(q^{10}) $ 53 * q + 11 * q^2 + 53 * q^3 + 63 * q^4 + 24 * q^5 + 11 * q^6 + 53 * q^7 + 30 * q^8 + 53 * q^9	\( 53 q + 11 q^{2} + 53 q^{3} + 63 q^{4} + 24 q^{5} + 11 q^{6} + 53 q^{7} + 30 q^{8} + 53 q^{9} + 2 q^{10} + 46 q^{11} + 63 q^{12} + 32 q^{13} + 11 q^{14} + 24 q^{15} + 67 q^{16} + 46 q^{17} + 11 q^{18} + 14 q^{19} + 53 q^{20} + 53 q^{21} + 13 q^{22} + 68 q^{23} + 30 q^{24} + 71 q^{25} + 11 q^{26} + 53 q^{27} + 63 q^{28} + 55 q^{29} + 2 q^{30} - 2 q^{31} + 51 q^{32} + 46 q^{33} - 7 q^{34} + 24 q^{35} + 63 q^{36} + 53 q^{37} + 16 q^{38} + 32 q^{39} - 20 q^{40} + 38 q^{41} + 11 q^{42} + 36 q^{43} + 70 q^{44} + 24 q^{45} + 4 q^{46} + 51 q^{47} + 67 q^{48} + 53 q^{49} + 32 q^{50} + 46 q^{51} + 10 q^{52} + 104 q^{53} + 11 q^{54} + 11 q^{55} + 30 q^{56} + 14 q^{57} + 4 q^{58} + 36 q^{59} + 53 q^{60} + 3 q^{61} + 25 q^{62} + 53 q^{63} + 82 q^{64} + 46 q^{65} + 13 q^{66} + 54 q^{67} + 88 q^{68} + 68 q^{69} + 2 q^{70} + 101 q^{71} + 30 q^{72} + q^{73} + 32 q^{74} + 71 q^{75} - 35 q^{76} + 46 q^{77} + 11 q^{78} + 14 q^{79} + 39 q^{80} + 53 q^{81} - 29 q^{82} + 38 q^{83} + 63 q^{84} + 16 q^{85} + 23 q^{86} + 55 q^{87} - 8 q^{88} + 52 q^{89} + 2 q^{90} + 32 q^{91} + 76 q^{92} - 2 q^{93} - 53 q^{94} + 46 q^{95} + 51 q^{96} - 3 q^{97} + 11 q^{98} + 46 q^{99}+O(q^{100}) \) 53 * q + 11 * q^2 + 53 * q^3 + 63 * q^4 + 24 * q^5 + 11 * q^6 + 53 * q^7 + 30 * q^8 + 53 * q^9 + 2 * q^10 + 46 * q^11 + 63 * q^12 + 32 * q^13 + 11 * q^14 + 24 * q^15 + 67 * q^16 + 46 * q^17 + 11 * q^18 + 14 * q^19 + 53 * q^20 + 53 * q^21 + 13 * q^22 + 68 * q^23 + 30 * q^24 + 71 * q^25 + 11 * q^26 + 53 * q^27 + 63 * q^28 + 55 * q^29 + 2 * q^30 - 2 * q^31 + 51 * q^32 + 46 * q^33 - 7 * q^34 + 24 * q^35 + 63 * q^36 + 53 * q^37 + 16 * q^38 + 32 * q^39 - 20 * q^40 + 38 * q^41 + 11 * q^42 + 36 * q^43 + 70 * q^44 + 24 * q^45 + 4 * q^46 + 51 * q^47 + 67 * q^48 + 53 * q^49 + 32 * q^50 + 46 * q^51 + 10 * q^52 + 104 * q^53 + 11 * q^54 + 11 * q^55 + 30 * q^56 + 14 * q^57 + 4 * q^58 + 36 * q^59 + 53 * q^60 + 3 * q^61 + 25 * q^62 + 53 * q^63 + 82 * q^64 + 46 * q^65 + 13 * q^66 + 54 * q^67 + 88 * q^68 + 68 * q^69 + 2 * q^70 + 101 * q^71 + 30 * q^72 + q^73 + 32 * q^74 + 71 * q^75 - 35 * q^76 + 46 * q^77 + 11 * q^78 + 14 * q^79 + 39 * q^80 + 53 * q^81 - 29 * q^82 + 38 * q^83 + 63 * q^84 + 16 * q^85 + 23 * q^86 + 55 * q^87 - 8 * q^88 + 52 * q^89 + 2 * q^90 + 32 * q^91 + 76 * q^92 - 2 * q^93 - 53 * q^94 + 46 * q^95 + 51 * q^96 - 3 * q^97 + 11 * q^98 + 46 * 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 $

$2$	−0.805347	−0.569466	−0.284733	−	0.958607i	$-0.591905\pi$
$2$	−0.805347	−0.569466	−0.284733	+	0.958607i	$0.591905\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.35142	−0.675708
$5$	3.29338	1.47284	0.736421	−	0.676523i	$-0.236514\pi$
$5$	3.29338	1.47284	0.736421	+	0.676523i	$0.236514\pi$
$6$	−0.805347	−0.328782
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	2.69905	0.954259
$9$	1.00000	0.333333
$10$	−2.65231	−0.838734
$11$	4.32435	1.30384	0.651920	−	0.758288i	$-0.273964\pi$
$11$	4.32435	1.30384	0.651920	+	0.758288i	$0.273964\pi$
$12$	−1.35142	−0.390120
$13$	3.38473	0.938754	0.469377	−	0.882998i	$-0.344479\pi$
$13$	3.38473	0.938754	0.469377	+	0.882998i	$0.344479\pi$
$14$	−0.805347	−0.215238
$15$	3.29338	0.850346
$16$	0.529158	0.132289
$17$	−5.22369	−1.26693	−0.633466	−	0.773771i	$-0.718368\pi$
$17$	−5.22369	−1.26693	−0.633466	+	0.773771i	$0.718368\pi$
$18$	−0.805347	−0.189822
$19$	−4.55757	−1.04558	−0.522789	−	0.852462i	$-0.675109\pi$
$19$	−4.55757	−1.04558	−0.522789	+	0.852462i	$0.675109\pi$
$20$	−4.45072	−0.995212
$21$	1.00000	0.218218
$22$	−3.48260	−0.742493
$23$	8.09788	1.68852	0.844262	−	0.535931i	$-0.180039\pi$
$23$	8.09788	1.68852	0.844262	+	0.535931i	$0.180039\pi$
$24$	2.69905	0.550942
$25$	5.84633	1.16927
$26$	−2.72588	−0.534589
$27$	1.00000	0.192450
$28$	−1.35142	−0.255394
$29$	−0.959913	−0.178251	−0.0891257	−	0.996020i	$-0.528407\pi$
$29$	−0.959913	−0.178251	−0.0891257	+	0.996020i	$0.528407\pi$
$30$	−2.65231	−0.484244
$31$	6.16960	1.10809	0.554046	−	0.832486i	$-0.313083\pi$
$31$	6.16960	1.10809	0.554046	+	0.832486i	$0.313083\pi$
$32$	−5.82426	−1.02959
$33$	4.32435	0.752773
$34$	4.20689	0.721475
$35$	3.29338	0.556682
$36$	−1.35142	−0.225236
$37$	−8.89277	−1.46196	−0.730981	−	0.682398i	$-0.760937\pi$
$37$	−8.89277	−1.46196	−0.730981	+	0.682398i	$0.760937\pi$
$38$	3.67043	0.595422
$39$	3.38473	0.541990
$40$	8.88900	1.40547
$41$	−5.39184	−0.842064	−0.421032	−	0.907046i	$-0.638332\pi$
$41$	−5.39184	−0.842064	−0.421032	+	0.907046i	$0.638332\pi$
$42$	−0.805347	−0.124268
$43$	0.927492	0.141441	0.0707206	−	0.997496i	$-0.477470\pi$
$43$	0.927492	0.141441	0.0707206	+	0.997496i	$0.477470\pi$
$44$	−5.84400	−0.881016
$45$	3.29338	0.490948
$46$	−6.52160	−0.961558
$47$	10.6833	1.55832	0.779160	−	0.626825i	$-0.215646\pi$
$47$	10.6833	1.55832	0.779160	+	0.626825i	$0.215646\pi$
$48$	0.529158	0.0763773
$49$	1.00000	0.142857
$50$	−4.70832	−0.665858
$51$	−5.22369	−0.731463
$52$	−4.57417	−0.634324
$53$	2.90889	0.399566	0.199783	−	0.979840i	$-0.435976\pi$
$53$	2.90889	0.399566	0.199783	+	0.979840i	$0.435976\pi$
$54$	−0.805347	−0.109594
$55$	14.2417	1.92035
$56$	2.69905	0.360676
$57$	−4.55757	−0.603665
$58$	0.773063	0.101508
$59$	−1.67399	−0.217935	−0.108967	−	0.994045i	$-0.534754\pi$
$59$	−1.67399	−0.217935	−0.108967	+	0.994045i	$0.534754\pi$
$60$	−4.45072	−0.574586
$61$	5.47360	0.700823	0.350411	−	0.936596i	$-0.386042\pi$
$61$	5.47360	0.700823	0.350411	+	0.936596i	$0.386042\pi$
$62$	−4.96867	−0.631022
$63$	1.00000	0.125988
$64$	3.63224	0.454030
$65$	11.1472	1.38264
$66$	−3.48260	−0.428679
$67$	1.46291	0.178723	0.0893615	−	0.995999i	$-0.471517\pi$
$67$	1.46291	0.178723	0.0893615	+	0.995999i	$0.471517\pi$
$68$	7.05938	0.856076
$69$	8.09788	0.974870
$70$	−2.65231	−0.317012
$71$	6.80562	0.807678	0.403839	−	0.914830i	$-0.367676\pi$
$71$	6.80562	0.807678	0.403839	+	0.914830i	$0.367676\pi$
$72$	2.69905	0.318086
$73$	2.39924	0.280810	0.140405	−	0.990094i	$-0.455160\pi$
$73$	2.39924	0.280810	0.140405	+	0.990094i	$0.455160\pi$
$74$	7.16176	0.832538
$75$	5.84633	0.675076
$76$	6.15918	0.706506
$77$	4.32435	0.492805
$78$	−2.72588	−0.308645
$79$	6.36562	0.716188	0.358094	−	0.933686i	$-0.383427\pi$
$79$	6.36562	0.716188	0.358094	+	0.933686i	$0.383427\pi$
$80$	1.74272	0.194841
$81$	1.00000	0.111111
$82$	4.34230	0.479527
$83$	−9.75203	−1.07042	−0.535212	−	0.844718i	$-0.679768\pi$
$83$	−9.75203	−1.07042	−0.535212	+	0.844718i	$0.679768\pi$
$84$	−1.35142	−0.147452
$85$	−17.2036	−1.86599
$86$	−0.746953	−0.0805460
$87$	−0.959913	−0.102913
$88$	11.6716	1.24420
$89$	−2.40120	−0.254526	−0.127263	−	0.991869i	$-0.540619\pi$
$89$	−2.40120	−0.254526	−0.127263	+	0.991869i	$0.540619\pi$
$90$	−2.65231	−0.279578
$91$	3.38473	0.354816
$92$	−10.9436	−1.14095
$93$	6.16960	0.639758
$94$	−8.60377	−0.887411
$95$	−15.0098	−1.53997
$96$	−5.82426	−0.594436
$97$	18.7872	1.90755	0.953777	−	0.300517i	$-0.0971591\pi$
$97$	18.7872	1.90755	0.953777	+	0.300517i	$0.0971591\pi$
$98$	−0.805347	−0.0813523
$99$	4.32435	0.434614
$100$	−7.90082	−0.790082
$101$	−8.71506	−0.867181	−0.433591	−	0.901110i	$-0.642754\pi$
$101$	−8.71506	−0.867181	−0.433591	+	0.901110i	$0.642754\pi$
$102$	4.20689	0.416544
$103$	−5.79861	−0.571354	−0.285677	−	0.958326i	$-0.592219\pi$
$103$	−5.79861	−0.571354	−0.285677	+	0.958326i	$0.592219\pi$
$104$	9.13555	0.895815
$105$	3.29338	0.321401
$106$	−2.34266	−0.227540
$107$	−4.48625	−0.433702	−0.216851	−	0.976205i	$-0.569579\pi$
$107$	−4.48625	−0.433702	−0.216851	+	0.976205i	$0.569579\pi$
$108$	−1.35142	−0.130040
$109$	6.74775	0.646318	0.323159	−	0.946345i	$-0.395255\pi$
$109$	6.74775	0.646318	0.323159	+	0.946345i	$0.395255\pi$
$110$	−11.4695	−1.09358
$111$	−8.89277	−0.844064
$112$	0.529158	0.0500007
$113$	3.16067	0.297331	0.148666	−	0.988888i	$-0.452502\pi$
$113$	3.16067	0.297331	0.148666	+	0.988888i	$0.452502\pi$
$114$	3.67043	0.343767
$115$	26.6694	2.48693
$116$	1.29724	0.120446
$117$	3.38473	0.312918
$118$	1.34814	0.124106
$119$	−5.22369	−0.478855
$120$	8.88900	0.811451
$121$	7.70000	0.700000
$122$	−4.40815	−0.399095
$123$	−5.39184	−0.486166
$124$	−8.33770	−0.748747
$125$	2.78728	0.249302
$126$	−0.805347	−0.0717460
$127$	−20.7064	−1.83739	−0.918697	−	0.394964i	$-0.870757\pi$
$127$	−20.7064	−1.83739	−0.918697	+	0.394964i	$0.870757\pi$
$128$	8.72331	0.771039
$129$	0.927492	0.0816611
$130$	−8.97734	−0.787365
$131$	−13.9172	−1.21595	−0.607977	−	0.793954i	$-0.708019\pi$
$131$	−13.9172	−1.21595	−0.607977	+	0.793954i	$0.708019\pi$
$132$	−5.84400	−0.508655
$133$	−4.55757	−0.395192
$134$	−1.17815	−0.101777
$135$	3.29338	0.283449
$136$	−14.0990	−1.20898
$137$	18.4978	1.58037	0.790186	−	0.612867i	$-0.209984\pi$
$137$	18.4978	1.58037	0.790186	+	0.612867i	$0.209984\pi$
$138$	−6.52160	−0.555156
$139$	11.5518	0.979815	0.489907	−	0.871775i	$-0.337031\pi$
$139$	11.5518	0.979815	0.489907	+	0.871775i	$0.337031\pi$
$140$	−4.45072	−0.376155
$141$	10.6833	0.899696
$142$	−5.48088	−0.459946
$143$	14.6367	1.22399
$144$	0.529158	0.0440965
$145$	−3.16135	−0.262536
$146$	−1.93222	−0.159912
$147$	1.00000	0.0824786
$148$	12.0178	0.987859
$149$	−1.28531	−0.105297	−0.0526483	−	0.998613i	$-0.516766\pi$
$149$	−1.28531	−0.105297	−0.0526483	+	0.998613i	$0.516766\pi$
$150$	−4.70832	−0.384433
$151$	16.6605	1.35581	0.677906	−	0.735149i	$-0.262888\pi$
$151$	16.6605	1.35581	0.677906	+	0.735149i	$0.262888\pi$
$152$	−12.3011	−0.997753
$153$	−5.22369	−0.422311
$154$	−3.48260	−0.280636
$155$	20.3188	1.63205
$156$	−4.57417	−0.366227
$157$	10.5914	0.845282	0.422641	−	0.906297i	$-0.361103\pi$
$157$	10.5914	0.845282	0.422641	+	0.906297i	$0.361103\pi$
$158$	−5.12653	−0.407845
$159$	2.90889	0.230690
$160$	−19.1815	−1.51643
$161$	8.09788	0.638202
$162$	−0.805347	−0.0632740
$163$	13.5955	1.06488	0.532441	−	0.846467i	$-0.321275\pi$
$163$	13.5955	1.06488	0.532441	+	0.846467i	$0.321275\pi$
$164$	7.28662	0.568989
$165$	14.2417	1.10872
$166$	7.85377	0.609570
$167$	−11.1562	−0.863292	−0.431646	−	0.902043i	$-0.642067\pi$
$167$	−11.1562	−0.863292	−0.431646	+	0.902043i	$0.642067\pi$
$168$	2.69905	0.208236
$169$	−1.54364	−0.118741
$170$	13.8549	1.06262
$171$	−4.55757	−0.348526
$172$	−1.25343	−0.0955730
$173$	8.14783	0.619468	0.309734	−	0.950823i	$-0.399760\pi$
$173$	8.14783	0.619468	0.309734	+	0.950823i	$0.399760\pi$
$174$	0.773063	0.0586058
$175$	5.84633	0.441941
$176$	2.28826	0.172484
$177$	−1.67399	−0.125825
$178$	1.93380	0.144944
$179$	0.784737	0.0586540	0.0293270	−	0.999570i	$-0.490664\pi$
$179$	0.784737	0.0586540	0.0293270	+	0.999570i	$0.490664\pi$
$180$	−4.45072	−0.331737
$181$	−11.2109	−0.833303	−0.416652	−	0.909066i	$-0.636796\pi$
$181$	−11.2109	−0.833303	−0.416652	+	0.909066i	$0.636796\pi$
$182$	−2.72588	−0.202056
$183$	5.47360	0.404620
$184$	21.8566	1.61129
$185$	−29.2872	−2.15324
$186$	−4.96867	−0.364320
$187$	−22.5891	−1.65188
$188$	−14.4376	−1.05297
$189$	1.00000	0.0727393
$190$	12.0881	0.876963
$191$	11.0232	0.797613	0.398806	−	0.917035i	$-0.369425\pi$
$191$	11.0232	0.797613	0.398806	+	0.917035i	$0.369425\pi$
$192$	3.63224	0.262134
$193$	−21.0502	−1.51523	−0.757615	−	0.652702i	$-0.773635\pi$
$193$	−21.0502	−1.51523	−0.757615	+	0.652702i	$0.773635\pi$
$194$	−15.1302	−1.08629
$195$	11.1472	0.798266
$196$	−1.35142	−0.0965297
$197$	−24.4801	−1.74413	−0.872066	−	0.489388i	$-0.837220\pi$
$197$	−24.4801	−1.74413	−0.872066	+	0.489388i	$0.837220\pi$
$198$	−3.48260	−0.247498
$199$	6.16127	0.436761	0.218381	−	0.975864i	$-0.429923\pi$
$199$	6.16127	0.436761	0.218381	+	0.975864i	$0.429923\pi$
$200$	15.7796	1.11578
$201$	1.46291	0.103186
$202$	7.01865	0.493831
$203$	−0.959913	−0.0673727
$204$	7.05938	0.494256
$205$	−17.7574	−1.24023
$206$	4.66990	0.325367
$207$	8.09788	0.562841
$208$	1.79105	0.124187
$209$	−19.7085	−1.36327
$210$	−2.65231	−0.183027
$211$	5.24961	0.361398	0.180699	−	0.983538i	$-0.442164\pi$
$211$	5.24961	0.361398	0.180699	+	0.983538i	$0.442164\pi$
$212$	−3.93112	−0.269990
$213$	6.80562	0.466313
$214$	3.61299	0.246979
$215$	3.05458	0.208321
$216$	2.69905	0.183647
$217$	6.16960	0.418820
$218$	−5.43428	−0.368056
$219$	2.39924	0.162126
$220$	−19.2465	−1.29760
$221$	−17.6808	−1.18934
$222$	7.16176	0.480666
$223$	20.1682	1.35057	0.675283	−	0.737559i	$-0.264022\pi$
$223$	20.1682	1.35057	0.675283	+	0.737559i	$0.264022\pi$
$224$	−5.82426	−0.389150
$225$	5.84633	0.389755
$226$	−2.54544	−0.169320
$227$	−9.83651	−0.652872	−0.326436	−	0.945219i	$-0.605848\pi$
$227$	−9.83651	−0.652872	−0.326436	+	0.945219i	$0.605848\pi$
$228$	6.15918	0.407901
$229$	−21.5695	−1.42535	−0.712675	−	0.701494i	$-0.752517\pi$
$229$	−21.5695	−1.42535	−0.712675	+	0.701494i	$0.752517\pi$
$230$	−21.4781	−1.41622
$231$	4.32435	0.284521
$232$	−2.59086	−0.170098
$233$	−16.2112	−1.06203	−0.531015	−	0.847362i	$-0.678189\pi$
$233$	−16.2112	−1.06203	−0.531015	+	0.847362i	$0.678189\pi$
$234$	−2.72588	−0.178196
$235$	35.1841	2.29516
$236$	2.26225	0.147260
$237$	6.36562	0.413491
$238$	4.20689	0.272692
$239$	−3.35466	−0.216995	−0.108498	−	0.994097i	$-0.534604\pi$
$239$	−3.35466	−0.216995	−0.108498	+	0.994097i	$0.534604\pi$
$240$	1.74272	0.112492
$241$	−15.7044	−1.01161	−0.505804	−	0.862648i	$-0.668804\pi$
$241$	−15.7044	−1.01161	−0.505804	+	0.862648i	$0.668804\pi$
$242$	−6.20117	−0.398627
$243$	1.00000	0.0641500
$244$	−7.39711	−0.473552
$245$	3.29338	0.210406
$246$	4.34230	0.276855
$247$	−15.4261	−0.981541
$248$	16.6521	1.05741
$249$	−9.75203	−0.618010
$250$	−2.24473	−0.141969
$251$	−18.7298	−1.18221	−0.591107	−	0.806593i	$-0.701309\pi$
$251$	−18.7298	−1.18221	−0.591107	+	0.806593i	$0.701309\pi$
$252$	−1.35142	−0.0851312
$253$	35.0181	2.20157
$254$	16.6758	1.04633
$255$	−17.2036	−1.07733
$256$	−14.2898	−0.893111
$257$	−24.5392	−1.53071	−0.765356	−	0.643607i	$-0.777437\pi$
$257$	−24.5392	−1.53071	−0.765356	+	0.643607i	$0.777437\pi$
$258$	−0.746953	−0.0465033
$259$	−8.89277	−0.552570
$260$	−15.0645	−0.934259
$261$	−0.959913	−0.0594171
$262$	11.2082	0.692445
$263$	0.965263	0.0595207	0.0297603	−	0.999557i	$-0.490526\pi$
$263$	0.965263	0.0595207	0.0297603	+	0.999557i	$0.490526\pi$
$264$	11.6716	0.718340
$265$	9.58006	0.588499
$266$	3.67043	0.225048
$267$	−2.40120	−0.146951
$268$	−1.97700	−0.120765
$269$	−2.12210	−0.129387	−0.0646933	−	0.997905i	$-0.520607\pi$
$269$	−2.12210	−0.129387	−0.0646933	+	0.997905i	$0.520607\pi$
$270$	−2.65231	−0.161415
$271$	−24.3236	−1.47755	−0.738776	−	0.673951i	$-0.764596\pi$
$271$	−24.3236	−1.47755	−0.738776	+	0.673951i	$0.764596\pi$
$272$	−2.76416	−0.167602
$273$	3.38473	0.204853
$274$	−14.8971	−0.899968
$275$	25.2816	1.52454
$276$	−10.9436	−0.658727
$277$	1.26002	0.0757072	0.0378536	−	0.999283i	$-0.487948\pi$
$277$	1.26002	0.0757072	0.0378536	+	0.999283i	$0.487948\pi$
$278$	−9.30324	−0.557971
$279$	6.16960	0.369364
$280$	8.88900	0.531219
$281$	20.7033	1.23506	0.617528	−	0.786549i	$-0.288134\pi$
$281$	20.7033	1.23506	0.617528	+	0.786549i	$0.288134\pi$
$282$	−8.60377	−0.512347
$283$	17.0287	1.01225	0.506125	−	0.862460i	$-0.331078\pi$
$283$	17.0287	1.01225	0.506125	+	0.862460i	$0.331078\pi$
$284$	−9.19722	−0.545755
$285$	−15.0098	−0.889104
$286$	−11.7877	−0.697018
$287$	−5.39184	−0.318270
$288$	−5.82426	−0.343198
$289$	10.2870	0.605116
$290$	2.54599	0.149506
$291$	18.7872	1.10133
$292$	−3.24237	−0.189745
$293$	−0.783476	−0.0457712	−0.0228856	−	0.999738i	$-0.507285\pi$
$293$	−0.783476	−0.0457712	−0.0228856	+	0.999738i	$0.507285\pi$
$294$	−0.805347	−0.0469688
$295$	−5.51307	−0.320983
$296$	−24.0020	−1.39509
$297$	4.32435	0.250924
$298$	1.03512	0.0599629
$299$	27.4091	1.58511
$300$	−7.90082	−0.456154
$301$	0.927492	0.0534598
$302$	−13.4175	−0.772089
$303$	−8.71506	−0.500667
$304$	−2.41167	−0.138319
$305$	18.0266	1.03220
$306$	4.20689	0.240492
$307$	0.992960	0.0566712	0.0283356	−	0.999598i	$-0.490979\pi$
$307$	0.992960	0.0566712	0.0283356	+	0.999598i	$0.490979\pi$
$308$	−5.84400	−0.332993
$309$	−5.79861	−0.329872
$310$	−16.3637	−0.929396
$311$	10.3733	0.588215	0.294108	−	0.955772i	$-0.404978\pi$
$311$	10.3733	0.588215	0.294108	+	0.955772i	$0.404978\pi$
$312$	9.13555	0.517199
$313$	1.68846	0.0954375	0.0477188	−	0.998861i	$-0.484805\pi$
$313$	1.68846	0.0954375	0.0477188	+	0.998861i	$0.484805\pi$
$314$	−8.52972	−0.481360
$315$	3.29338	0.185561
$316$	−8.60260	−0.483934
$317$	25.7611	1.44689	0.723443	−	0.690384i	$-0.242558\pi$
$317$	25.7611	1.44689	0.723443	+	0.690384i	$0.242558\pi$
$318$	−2.34266	−0.131370
$319$	−4.15100	−0.232411
$320$	11.9623	0.668714
$321$	−4.48625	−0.250398
$322$	−6.52160	−0.363435
$323$	23.8074	1.32468
$324$	−1.35142	−0.0750787
$325$	19.7882	1.09765
$326$	−10.9491	−0.606414
$327$	6.74775	0.373152
$328$	−14.5529	−0.803547
$329$	10.6833	0.588990
$330$	−11.4695	−0.631376
$331$	1.85315	0.101858	0.0509292	−	0.998702i	$-0.483782\pi$
$331$	1.85315	0.101858	0.0509292	+	0.998702i	$0.483782\pi$
$332$	13.1790	0.723294
$333$	−8.89277	−0.487321
$334$	8.98461	0.491616
$335$	4.81792	0.263231
$336$	0.529158	0.0288679
$337$	−23.9333	−1.30373	−0.651865	−	0.758335i	$-0.726013\pi$
$337$	−23.9333	−1.30373	−0.651865	+	0.758335i	$0.726013\pi$
$338$	1.24316	0.0676192
$339$	3.16067	0.171664
$340$	23.2492	1.26087
$341$	26.6795	1.44478
$342$	3.67043	0.198474
$343$	1.00000	0.0539949
$344$	2.50335	0.134972
$345$	26.6694	1.43583
$346$	−6.56183	−0.352766
$347$	19.4760	1.04553	0.522763	−	0.852478i	$-0.324901\pi$
$347$	19.4760	1.04553	0.522763	+	0.852478i	$0.324901\pi$
$348$	1.29724	0.0695395
$349$	4.92962	0.263876	0.131938	−	0.991258i	$-0.457880\pi$
$349$	4.92962	0.263876	0.131938	+	0.991258i	$0.457880\pi$
$350$	−4.70832	−0.251671
$351$	3.38473	0.180663
$352$	−25.1861	−1.34243
$353$	−15.9833	−0.850703	−0.425351	−	0.905028i	$-0.639849\pi$
$353$	−15.9833	−0.850703	−0.425351	+	0.905028i	$0.639849\pi$
$354$	1.34814	0.0716529
$355$	22.4135	1.18958
$356$	3.24502	0.171986
$357$	−5.22369	−0.276467
$358$	−0.631986	−0.0334015
$359$	9.51759	0.502319	0.251159	−	0.967946i	$-0.419188\pi$
$359$	9.51759	0.502319	0.251159	+	0.967946i	$0.419188\pi$
$360$	8.88900	0.468491
$361$	1.77146	0.0932349
$362$	9.02870	0.474538
$363$	7.70000	0.404145
$364$	−4.57417	−0.239752
$365$	7.90160	0.413588
$366$	−4.40815	−0.230418
$367$	−0.360545	−0.0188203	−0.00941015	−	0.999956i	$-0.502995\pi$
$367$	−0.360545	−0.0188203	−0.00941015	+	0.999956i	$0.502995\pi$
$368$	4.28505	0.223374
$369$	−5.39184	−0.280688
$370$	23.5864	1.22620
$371$	2.90889	0.151022
$372$	−8.33770	−0.432289
$373$	5.60272	0.290098	0.145049	−	0.989424i	$-0.453666\pi$
$373$	5.60272	0.290098	0.145049	+	0.989424i	$0.453666\pi$
$374$	18.1920	0.940688
$375$	2.78728	0.143935
$376$	28.8348	1.48704
$377$	−3.24904	−0.167334
$378$	−0.805347	−0.0414226
$379$	36.1602	1.85742	0.928711	−	0.370803i	$-0.120918\pi$
$379$	36.1602	1.85742	0.928711	+	0.370803i	$0.120918\pi$
$380$	20.2845	1.04057
$381$	−20.7064	−1.06082
$382$	−8.87753	−0.454214
$383$	1.00000	0.0510976
$383$	1.00000	0.0510976
$384$	8.72331	0.445160
$385$	14.2417	0.725825
$386$	16.9527	0.862872
$387$	0.927492	0.0471471
$388$	−25.3894	−1.28895
$389$	27.2470	1.38148	0.690738	−	0.723105i	$-0.257286\pi$
$389$	27.2470	1.38148	0.690738	+	0.723105i	$0.257286\pi$
$390$	−8.97734	−0.454585
$391$	−42.3008	−2.13924
$392$	2.69905	0.136323
$393$	−13.9172	−0.702032
$394$	19.7149	0.993225
$395$	20.9644	1.05483
$396$	−5.84400	−0.293672
$397$	−28.8380	−1.44734	−0.723670	−	0.690146i	$-0.757546\pi$
$397$	−28.8380	−1.44734	−0.723670	+	0.690146i	$0.757546\pi$
$398$	−4.96196	−0.248721
$399$	−4.55757	−0.228164
$400$	3.09363	0.154681
$401$	20.3418	1.01582	0.507910	−	0.861410i	$-0.330418\pi$
$401$	20.3418	1.01582	0.507910	+	0.861410i	$0.330418\pi$
$402$	−1.17815	−0.0587608
$403$	20.8824	1.04023
$404$	11.7777	0.585961
$405$	3.29338	0.163649
$406$	0.773063	0.0383665
$407$	−38.4554	−1.90616
$408$	−14.0990	−0.698006
$409$	6.23181	0.308143	0.154072	−	0.988060i	$-0.450761\pi$
$409$	6.23181	0.308143	0.154072	+	0.988060i	$0.450761\pi$
$410$	14.3008	0.706268
$411$	18.4978	0.912428
$412$	7.83634	0.386069
$413$	−1.67399	−0.0823715
$414$	−6.52160	−0.320519
$415$	−32.1171	−1.57657
$416$	−19.7135	−0.966535
$417$	11.5518	0.565696
$418$	15.8722	0.776335
$419$	−1.46890	−0.0717607	−0.0358803	−	0.999356i	$-0.511424\pi$
$419$	−1.46890	−0.0717607	−0.0358803	+	0.999356i	$0.511424\pi$
$420$	−4.45072	−0.217173
$421$	−23.4869	−1.14468	−0.572341	−	0.820015i	$-0.693965\pi$
$421$	−23.4869	−1.14468	−0.572341	+	0.820015i	$0.693965\pi$
$422$	−4.22776	−0.205804
$423$	10.6833	0.519440
$424$	7.85124	0.381290
$425$	−30.5394	−1.48138
$426$	−5.48088	−0.265550
$427$	5.47360	0.264886
$428$	6.06279	0.293056
$429$	14.6367	0.706668
$430$	−2.46000	−0.118632
$431$	−9.70679	−0.467559	−0.233780	−	0.972290i	$-0.575109\pi$
$431$	−9.70679	−0.467559	−0.233780	+	0.972290i	$0.575109\pi$
$432$	0.529158	0.0254591
$433$	7.75314	0.372592	0.186296	−	0.982494i	$-0.440352\pi$
$433$	7.75314	0.372592	0.186296	+	0.982494i	$0.440352\pi$
$434$	−4.96867	−0.238504
$435$	−3.16135	−0.151575
$436$	−9.11902	−0.436722
$437$	−36.9067	−1.76548
$438$	−1.93222	−0.0923250
$439$	−1.58451	−0.0756248	−0.0378124	−	0.999285i	$-0.512039\pi$
$439$	−1.58451	−0.0756248	−0.0378124	+	0.999285i	$0.512039\pi$
$440$	38.4391	1.83251
$441$	1.00000	0.0476190
$442$	14.2392	0.677288
$443$	39.3056	1.86747	0.933734	−	0.357968i	$-0.116530\pi$
$443$	39.3056	1.86747	0.933734	+	0.357968i	$0.116530\pi$
$444$	12.0178	0.570341
$445$	−7.90805	−0.374877
$446$	−16.2424	−0.769102
$447$	−1.28531	−0.0607930
$448$	3.63224	0.171607
$449$	−40.7619	−1.92367	−0.961837	−	0.273623i	$-0.911778\pi$
$449$	−40.7619	−1.92367	−0.961837	+	0.273623i	$0.911778\pi$
$450$	−4.70832	−0.221953
$451$	−23.3162	−1.09792
$452$	−4.27139	−0.200909
$453$	16.6605	0.782779
$454$	7.92181	0.371789
$455$	11.1472	0.522588
$456$	−12.3011	−0.576053
$457$	26.4544	1.23749	0.618743	−	0.785594i	$-0.287642\pi$
$457$	26.4544	1.23749	0.618743	+	0.785594i	$0.287642\pi$
$458$	17.3709	0.811689
$459$	−5.22369	−0.243821
$460$	−36.0414	−1.68044
$461$	−14.5445	−0.677407	−0.338703	−	0.940893i	$-0.609988\pi$
$461$	−14.5445	−0.677407	−0.338703	+	0.940893i	$0.609988\pi$
$462$	−3.48260	−0.162025
$463$	−29.9501	−1.39190	−0.695950	−	0.718091i	$-0.745016\pi$
$463$	−29.9501	−1.39190	−0.695950	+	0.718091i	$0.745016\pi$
$464$	−0.507945	−0.0235808
$465$	20.3188	0.942262
$466$	13.0556	0.604791
$467$	14.4742	0.669787	0.334894	−	0.942256i	$-0.391300\pi$
$467$	14.4742	0.669787	0.334894	+	0.942256i	$0.391300\pi$
$468$	−4.57417	−0.211441
$469$	1.46291	0.0675509
$470$	−28.3354	−1.30702
$471$	10.5914	0.488024
$472$	−4.51818	−0.207966
$473$	4.01080	0.184417
$474$	−5.12653	−0.235469
$475$	−26.6451	−1.22256
$476$	7.05938	0.323566
$477$	2.90889	0.133189
$478$	2.70167	0.123571
$479$	−4.42677	−0.202264	−0.101132	−	0.994873i	$-0.532246\pi$
$479$	−4.42677	−0.202264	−0.101132	+	0.994873i	$0.532246\pi$
$480$	−19.1815	−0.875511
$481$	−30.0996	−1.37242
$482$	12.6475	0.576077
$483$	8.09788	0.368466
$484$	−10.4059	−0.472996
$485$	61.8734	2.80953
$486$	−0.805347	−0.0365313
$487$	−26.4181	−1.19712	−0.598559	−	0.801079i	$-0.704260\pi$
$487$	−26.4181	−1.19712	−0.598559	+	0.801079i	$0.704260\pi$
$488$	14.7735	0.668767
$489$	13.5955	0.614809
$490$	−2.65231	−0.119819
$491$	−10.4528	−0.471730	−0.235865	−	0.971786i	$-0.575792\pi$
$491$	−10.4528	−0.471730	−0.235865	+	0.971786i	$0.575792\pi$
$492$	7.28662	0.328506
$493$	5.01429	0.225832
$494$	12.4234	0.558955
$495$	14.2417	0.640117
$496$	3.26469	0.146589
$497$	6.80562	0.305274
$498$	7.85377	0.351936
$499$	8.20793	0.367437	0.183719	−	0.982979i	$-0.441186\pi$
$499$	8.20793	0.367437	0.183719	+	0.982979i	$0.441186\pi$
$500$	−3.76678	−0.168455
$501$	−11.1562	−0.498422
$502$	15.0840	0.673231
$503$	17.0121	0.758532	0.379266	−	0.925288i	$-0.376177\pi$
$503$	17.0121	0.758532	0.379266	+	0.925288i	$0.376177\pi$
$504$	2.69905	0.120225
$505$	−28.7020	−1.27722
$506$	−28.2017	−1.25372
$507$	−1.54364	−0.0685553
$508$	27.9829	1.24154
$509$	28.2982	1.25429	0.627147	−	0.778901i	$-0.284222\pi$
$509$	28.2982	1.25429	0.627147	+	0.778901i	$0.284222\pi$
$510$	13.8549	0.613504
$511$	2.39924	0.106136
$512$	−5.93840	−0.262443
$513$	−4.55757	−0.201222
$514$	19.7626	0.871690
$515$	−19.0970	−0.841515
$516$	−1.25343	−0.0551791
$517$	46.1983	2.03180
$518$	7.16176	0.314670
$519$	8.14783	0.357650
$520$	30.0868	1.31939
$521$	18.9759	0.831348	0.415674	−	0.909514i	$-0.363546\pi$
$521$	18.9759	0.831348	0.415674	+	0.909514i	$0.363546\pi$
$522$	0.773063	0.0338361
$523$	6.91989	0.302586	0.151293	−	0.988489i	$-0.451656\pi$
$523$	6.91989	0.302586	0.151293	+	0.988489i	$0.451656\pi$
$524$	18.8080	0.821630
$525$	5.84633	0.255155
$526$	−0.777372	−0.0338950
$527$	−32.2281	−1.40388
$528$	2.28826	0.0995838
$529$	42.5756	1.85111
$530$	−7.71528	−0.335130
$531$	−1.67399	−0.0726449
$532$	6.15918	0.267034
$533$	−18.2499	−0.790490
$534$	1.93380	0.0836836
$535$	−14.7749	−0.638775
$536$	3.94847	0.170548
$537$	0.784737	0.0338639
$538$	1.70902	0.0736813
$539$	4.32435	0.186263
$540$	−4.45072	−0.191529
$541$	33.2954	1.43148	0.715741	−	0.698366i	$-0.246089\pi$
$541$	33.2954	1.43148	0.715741	+	0.698366i	$0.246089\pi$
$542$	19.5889	0.841417
$543$	−11.2109	−0.481108
$544$	30.4242	1.30443
$545$	22.2229	0.951924
$546$	−2.72588	−0.116657
$547$	−23.5845	−1.00840	−0.504201	−	0.863586i	$-0.668213\pi$
$547$	−23.5845	−1.00840	−0.504201	+	0.863586i	$0.668213\pi$
$548$	−24.9982	−1.06787
$549$	5.47360	0.233608
$550$	−20.3604	−0.868172
$551$	4.37487	0.186376
$552$	21.8566	0.930279
$553$	6.36562	0.270694
$554$	−1.01475	−0.0431127
$555$	−29.2872	−1.24317
$556$	−15.6113	−0.662069
$557$	−30.3870	−1.28754	−0.643770	−	0.765219i	$-0.722630\pi$
$557$	−30.3870	−1.28754	−0.643770	+	0.765219i	$0.722630\pi$
$558$	−4.96867	−0.210341
$559$	3.13931	0.132779
$560$	1.74272	0.0736432
$561$	−22.5891	−0.953712
$562$	−16.6734	−0.703323
$563$	22.4592	0.946543	0.473272	−	0.880917i	$-0.343073\pi$
$563$	22.4592	0.946543	0.473272	+	0.880917i	$0.343073\pi$
$564$	−14.4376	−0.607932
$565$	10.4093	0.437922
$566$	−13.7140	−0.576442
$567$	1.00000	0.0419961
$568$	18.3687	0.770734
$569$	33.4529	1.40242	0.701210	−	0.712955i	$-0.252644\pi$
$569$	33.4529	1.40242	0.701210	+	0.712955i	$0.252644\pi$
$570$	12.0881	0.506315
$571$	−10.4740	−0.438324	−0.219162	−	0.975688i	$-0.570332\pi$
$571$	−10.4740	−0.438324	−0.219162	+	0.975688i	$0.570332\pi$
$572$	−19.7803	−0.827057
$573$	11.0232	0.460502
$574$	4.34230	0.181244
$575$	47.3429	1.97433
$576$	3.63224	0.151343
$577$	9.47350	0.394387	0.197194	−	0.980365i	$-0.436817\pi$
$577$	9.47350	0.394387	0.197194	+	0.980365i	$0.436817\pi$
$578$	−8.28459	−0.344593
$579$	−21.0502	−0.874818
$580$	4.27231	0.177398
$581$	−9.75203	−0.404582
$582$	−15.1302	−0.627168
$583$	12.5790	0.520971
$584$	6.47567	0.267965
$585$	11.1472	0.460879
$586$	0.630970	0.0260651
$587$	9.04434	0.373300	0.186650	−	0.982427i	$-0.440237\pi$
$587$	9.04434	0.373300	0.186650	+	0.982427i	$0.440237\pi$
$588$	−1.35142	−0.0557315
$589$	−28.1184	−1.15860
$590$	4.43994	0.182789
$591$	−24.4801	−1.00698
$592$	−4.70567	−0.193402
$593$	−27.1101	−1.11328	−0.556640	−	0.830754i	$-0.687910\pi$
$593$	−27.1101	−1.11328	−0.556640	+	0.830754i	$0.687910\pi$
$594$	−3.48260	−0.142893
$595$	−17.2036	−0.705278
$596$	1.73699	0.0711498
$597$	6.16127	0.252164
$598$	−22.0738	−0.902666
$599$	16.4425	0.671822	0.335911	−	0.941894i	$-0.390956\pi$
$599$	16.4425	0.671822	0.335911	+	0.941894i	$0.390956\pi$
$600$	15.7796	0.644198
$601$	9.11319	0.371735	0.185867	−	0.982575i	$-0.440490\pi$
$601$	9.11319	0.371735	0.185867	+	0.982575i	$0.440490\pi$
$602$	−0.746953	−0.0304435
$603$	1.46291	0.0595743
$604$	−22.5153	−0.916133
$605$	25.3590	1.03099
$606$	7.01865	0.285113
$607$	−12.5336	−0.508723	−0.254362	−	0.967109i	$-0.581865\pi$
$607$	−12.5336	−0.508723	−0.254362	+	0.967109i	$0.581865\pi$
$608$	26.5445	1.07652
$609$	−0.959913	−0.0388976
$610$	−14.5177	−0.587804
$611$	36.1600	1.46288
$612$	7.05938	0.285359
$613$	0.0593808	0.00239837	0.00119918	−	0.999999i	$-0.499618\pi$
$613$	0.0593808	0.00239837	0.00119918	+	0.999999i	$0.499618\pi$
$614$	−0.799677	−0.0322724
$615$	−17.7574	−0.716046
$616$	11.6716	0.470264
$617$	3.61460	0.145518	0.0727592	−	0.997350i	$-0.476820\pi$
$617$	3.61460	0.145518	0.0727592	+	0.997350i	$0.476820\pi$
$618$	4.66990	0.187851
$619$	0.924473	0.0371577	0.0185789	−	0.999827i	$-0.494086\pi$
$619$	0.924473	0.0371577	0.0185789	+	0.999827i	$0.494086\pi$
$620$	−27.4592	−1.10279
$621$	8.09788	0.324957
$622$	−8.35410	−0.334969
$623$	−2.40120	−0.0962019
$624$	1.79105	0.0716995
$625$	−20.0521	−0.802083
$626$	−1.35980	−0.0543485
$627$	−19.7085	−0.787083
$628$	−14.3133	−0.571164
$629$	46.4531	1.85221
$630$	−2.65231	−0.105671
$631$	−42.4951	−1.69170	−0.845852	−	0.533418i	$-0.820907\pi$
$631$	−42.4951	−1.69170	−0.845852	+	0.533418i	$0.820907\pi$
$632$	17.1811	0.683429
$633$	5.24961	0.208653
$634$	−20.7466	−0.823953
$635$	−68.1939	−2.70619
$636$	−3.93112	−0.155879
$637$	3.38473	0.134108
$638$	3.34300	0.132350
$639$	6.80562	0.269226
$640$	28.7292	1.13562
$641$	39.8377	1.57349	0.786747	−	0.617275i	$-0.211763\pi$
$641$	39.8377	1.57349	0.786747	+	0.617275i	$0.211763\pi$
$642$	3.61299	0.142593
$643$	−20.7522	−0.818388	−0.409194	−	0.912447i	$-0.634190\pi$
$643$	−20.7522	−0.818388	−0.409194	+	0.912447i	$0.634190\pi$
$644$	−10.9436	−0.431238
$645$	3.05458	0.120274
$646$	−19.1732	−0.754359
$647$	42.3708	1.66577	0.832884	−	0.553448i	$-0.186688\pi$
$647$	42.3708	1.66577	0.832884	+	0.553448i	$0.186688\pi$
$648$	2.69905	0.106029
$649$	−7.23891	−0.284152
$650$	−15.9364	−0.625076
$651$	6.16960	0.241806
$652$	−18.3732	−0.719549
$653$	−44.4636	−1.74000	−0.869998	−	0.493055i	$-0.835880\pi$
$653$	−44.4636	−1.74000	−0.869998	+	0.493055i	$0.835880\pi$
$654$	−5.43428	−0.212497
$655$	−45.8347	−1.79091
$656$	−2.85313	−0.111396
$657$	2.39924	0.0936032
$658$	−8.60377	−0.335410
$659$	−35.4301	−1.38016	−0.690081	−	0.723733i	$-0.742425\pi$
$659$	−35.4301	−1.38016	−0.690081	+	0.723733i	$0.742425\pi$
$660$	−19.2465	−0.749168
$661$	−1.94957	−0.0758296	−0.0379148	−	0.999281i	$-0.512072\pi$
$661$	−1.94957	−0.0758296	−0.0379148	+	0.999281i	$0.512072\pi$
$662$	−1.49243	−0.0580049
$663$	−17.6808	−0.686664
$664$	−26.3212	−1.02146
$665$	−15.0098	−0.582055
$666$	7.16176	0.277513
$667$	−7.77326	−0.300982
$668$	15.0767	0.583333
$669$	20.1682	0.779749
$670$	−3.88009	−0.149901
$671$	23.6698	0.913761
$672$	−5.82426	−0.224676
$673$	32.9114	1.26864	0.634321	−	0.773070i	$-0.281280\pi$
$673$	32.9114	1.26864	0.634321	+	0.773070i	$0.281280\pi$
$674$	19.2746	0.742430
$675$	5.84633	0.225025
$676$	2.08609	0.0802344
$677$	−4.40751	−0.169394	−0.0846971	−	0.996407i	$-0.526992\pi$
$677$	−4.40751	−0.169394	−0.0846971	+	0.996407i	$0.526992\pi$
$678$	−2.54544	−0.0977570
$679$	18.7872	0.720987
$680$	−46.4334	−1.78064
$681$	−9.83651	−0.376936
$682$	−21.4863	−0.822752
$683$	38.8811	1.48774	0.743872	−	0.668322i	$-0.232987\pi$
$683$	38.8811	1.48774	0.743872	+	0.668322i	$0.232987\pi$
$684$	6.15918	0.235502
$685$	60.9201	2.32764
$686$	−0.805347	−0.0307483
$687$	−21.5695	−0.822926
$688$	0.490790	0.0187112
$689$	9.84579	0.375095
$690$	−21.4781	−0.817657
$691$	−0.295619	−0.0112459	−0.00562294	−	0.999984i	$-0.501790\pi$
$691$	−0.295619	−0.0112459	−0.00562294	+	0.999984i	$0.501790\pi$
$692$	−11.0111	−0.418580
$693$	4.32435	0.164268
$694$	−15.6849	−0.595392
$695$	38.0446	1.44311
$696$	−2.59086	−0.0982062
$697$	28.1653	1.06684
$698$	−3.97005	−0.150269
$699$	−16.2112	−0.613164
$700$	−7.90082	−0.298623
$701$	29.9604	1.13159	0.565793	−	0.824547i	$-0.308570\pi$
$701$	29.9604	1.13159	0.565793	+	0.824547i	$0.308570\pi$
$702$	−2.72588	−0.102882
$703$	40.5294	1.52860
$704$	15.7071	0.591982
$705$	35.1841	1.32511
$706$	12.8721	0.484447
$707$	−8.71506	−0.327764
$708$	2.26225	0.0850207
$709$	−39.5808	−1.48649	−0.743244	−	0.669020i	$-0.766714\pi$
$709$	−39.5808	−1.48649	−0.743244	+	0.669020i	$0.766714\pi$
$710$	−18.0506	−0.677427
$711$	6.36562	0.238729
$712$	−6.48096	−0.242884
$713$	49.9607	1.87104
$714$	4.20689	0.157439
$715$	48.2043	1.80274
$716$	−1.06051	−0.0396330
$717$	−3.35466	−0.125282
$718$	−7.66496	−0.286054
$719$	−46.0346	−1.71680	−0.858400	−	0.512980i	$-0.828541\pi$
$719$	−46.0346	−1.71680	−0.858400	+	0.512980i	$0.828541\pi$
$720$	1.74272	0.0649472
$721$	−5.79861	−0.215952
$722$	−1.42664	−0.0530941
$723$	−15.7044	−0.584052
$724$	15.1507	0.563070
$725$	−5.61197	−0.208423
$726$	−6.20117	−0.230147
$727$	−25.6123	−0.949907	−0.474954	−	0.880011i	$-0.657535\pi$
$727$	−25.6123	−0.949907	−0.474954	+	0.880011i	$0.657535\pi$
$728$	9.13555	0.338586
$729$	1.00000	0.0370370
$730$	−6.36353	−0.235525
$731$	−4.84494	−0.179196
$732$	−7.39711	−0.273405
$733$	−4.90406	−0.181136	−0.0905678	−	0.995890i	$-0.528868\pi$
$733$	−4.90406	−0.181136	−0.0905678	+	0.995890i	$0.528868\pi$
$734$	0.290364	0.0107175
$735$	3.29338	0.121478
$736$	−47.1642	−1.73849
$737$	6.32614	0.233026
$738$	4.34230	0.159842
$739$	−44.0329	−1.61978	−0.809888	−	0.586585i	$-0.800472\pi$
$739$	−44.0329	−1.61978	−0.809888	+	0.586585i	$0.800472\pi$
$740$	39.5792	1.45496
$741$	−15.4261	−0.566693
$742$	−2.34266	−0.0860019
$743$	−20.7185	−0.760088	−0.380044	−	0.924968i	$-0.624091\pi$
$743$	−20.7185	−0.760088	−0.380044	+	0.924968i	$0.624091\pi$
$744$	16.6521	0.610495
$745$	−4.23301	−0.155085
$746$	−4.51213	−0.165201
$747$	−9.75203	−0.356808
$748$	30.5272	1.11619
$749$	−4.48625	−0.163924
$750$	−2.24473	−0.0819659
$751$	−44.7414	−1.63264	−0.816318	−	0.577602i	$-0.803988\pi$
$751$	−44.7414	−1.63264	−0.816318	+	0.577602i	$0.803988\pi$
$752$	5.65315	0.206149
$753$	−18.7298	−0.682551
$754$	2.61661	0.0952912
$755$	54.8693	1.99690
$756$	−1.35142	−0.0491505
$757$	−34.6447	−1.25918	−0.629592	−	0.776926i	$-0.716778\pi$
$757$	−34.6447	−1.25918	−0.629592	+	0.776926i	$0.716778\pi$
$758$	−29.1215	−1.05774
$759$	35.0181	1.27107
$760$	−40.5123	−1.46953
$761$	7.50117	0.271917	0.135959	−	0.990715i	$-0.456589\pi$
$761$	7.50117	0.271917	0.135959	+	0.990715i	$0.456589\pi$
$762$	16.6758	0.604101
$763$	6.74775	0.244285
$764$	−14.8970	−0.538953
$765$	−17.2036	−0.621997
$766$	−0.805347	−0.0290984
$767$	−5.66599	−0.204587
$768$	−14.2898	−0.515638
$769$	31.1009	1.12153	0.560763	−	0.827976i	$-0.310508\pi$
$769$	31.1009	1.12153	0.560763	+	0.827976i	$0.310508\pi$
$770$	−11.4695	−0.413333
$771$	−24.5392	−0.883758
$772$	28.4476	1.02385
$773$	31.7962	1.14363	0.571814	−	0.820383i	$-0.306240\pi$
$773$	31.7962	1.14363	0.571814	+	0.820383i	$0.306240\pi$
$774$	−0.746953	−0.0268487
$775$	36.0695	1.29566
$776$	50.7077	1.82030
$777$	−8.89277	−0.319026
$778$	−21.9433	−0.786705
$779$	24.5737	0.880444
$780$	−15.0645	−0.539395
$781$	29.4299	1.05308
$782$	34.0669	1.21823
$783$	−0.959913	−0.0343045
$784$	0.529158	0.0188985
$785$	34.8813	1.24497
$786$	11.2082	0.399784
$787$	−3.36249	−0.119860	−0.0599299	−	0.998203i	$-0.519088\pi$
$787$	−3.36249	−0.119860	−0.0599299	+	0.998203i	$0.519088\pi$
$788$	33.0828	1.17852
$789$	0.965263	0.0343643
$790$	−16.8836	−0.600692
$791$	3.16067	0.112381
$792$	11.6716	0.414734
$793$	18.5266	0.657900
$794$	23.2246	0.824211
$795$	9.58006	0.339770
$796$	−8.32644	−0.295123
$797$	4.61495	0.163470	0.0817349	−	0.996654i	$-0.473954\pi$
$797$	4.61495	0.163470	0.0817349	+	0.996654i	$0.473954\pi$
$798$	3.67043	0.129932
$799$	−55.8063	−1.97429
$800$	−34.0506	−1.20387
$801$	−2.40120	−0.0848421
$802$	−16.3822	−0.578475
$803$	10.3751	0.366131
$804$	−1.97700	−0.0697235
$805$	26.6694	0.939971
$806$	−16.8176	−0.592374
$807$	−2.12210	−0.0747014
$808$	−23.5224	−0.827516
$809$	−21.0545	−0.740238	−0.370119	−	0.928984i	$-0.620683\pi$
$809$	−21.0545	−0.740238	−0.370119	+	0.928984i	$0.620683\pi$
$810$	−2.65231	−0.0931927
$811$	−22.2674	−0.781916	−0.390958	−	0.920409i	$-0.627856\pi$
$811$	−22.2674	−0.781916	−0.390958	+	0.920409i	$0.627856\pi$
$812$	1.29724	0.0455243
$813$	−24.3236	−0.853066
$814$	30.9700	1.08550
$815$	44.7751	1.56840
$816$	−2.76416	−0.0967649
$817$	−4.22711	−0.147888
$818$	−5.01877	−0.175477
$819$	3.38473	0.118272
$820$	23.9976	0.838032
$821$	−8.80088	−0.307153	−0.153576	−	0.988137i	$-0.549079\pi$
$821$	−8.80088	−0.307153	−0.153576	+	0.988137i	$0.549079\pi$
$822$	−14.8971	−0.519597
$823$	−11.2277	−0.391374	−0.195687	−	0.980666i	$-0.562694\pi$
$823$	−11.2277	−0.391374	−0.195687	+	0.980666i	$0.562694\pi$
$824$	−15.6508	−0.545220
$825$	25.2816	0.880191
$826$	1.34814	0.0469078
$827$	20.0759	0.698107	0.349053	−	0.937103i	$-0.386503\pi$
$827$	20.0759	0.698107	0.349053	+	0.937103i	$0.386503\pi$
$828$	−10.9436	−0.380316
$829$	11.9970	0.416673	0.208336	−	0.978057i	$-0.433195\pi$
$829$	11.9970	0.416673	0.208336	+	0.978057i	$0.433195\pi$
$830$	25.8654	0.897801
$831$	1.26002	0.0437096
$832$	12.2941	0.426222
$833$	−5.22369	−0.180990
$834$	−9.30324	−0.322145
$835$	−36.7415	−1.27149
$836$	26.6344	0.921171
$837$	6.16960	0.213253
$838$	1.18298	0.0408653
$839$	37.5523	1.29645	0.648225	−	0.761449i	$-0.275511\pi$
$839$	37.5523	1.29645	0.648225	+	0.761449i	$0.275511\pi$
$840$	8.88900	0.306700
$841$	−28.0786	−0.968226
$842$	18.9151	0.651858
$843$	20.7033	0.713060
$844$	−7.09441	−0.244200
$845$	−5.08378	−0.174887
$846$	−8.60377	−0.295804
$847$	7.70000	0.264575
$848$	1.53926	0.0528584
$849$	17.0287	0.584422
$850$	24.5948	0.843596
$851$	−72.0125	−2.46856
$852$	−9.19722	−0.315092
$853$	30.1307	1.03165	0.515827	−	0.856693i	$-0.327485\pi$
$853$	30.1307	1.03165	0.515827	+	0.856693i	$0.327485\pi$
$854$	−4.40815	−0.150844
$855$	−15.0098	−0.513324
$856$	−12.1086	−0.413864
$857$	−20.8452	−0.712059	−0.356030	−	0.934475i	$-0.615870\pi$
$857$	−20.8452	−0.712059	−0.356030	+	0.934475i	$0.615870\pi$
$858$	−11.7877	−0.402424
$859$	32.9819	1.12533	0.562663	−	0.826686i	$-0.309777\pi$
$859$	32.9819	1.12533	0.562663	+	0.826686i	$0.309777\pi$
$860$	−4.12801	−0.140764
$861$	−5.39184	−0.183753
$862$	7.81733	0.266259
$863$	−28.2037	−0.960064	−0.480032	−	0.877251i	$-0.659375\pi$
$863$	−28.2037	−0.960064	−0.480032	+	0.877251i	$0.659375\pi$
$864$	−5.82426	−0.198145
$865$	26.8339	0.912379
$866$	−6.24397	−0.212179
$867$	10.2870	0.349364
$868$	−8.33770	−0.283000
$869$	27.5272	0.933795
$870$	2.54599	0.0863171
$871$	4.95155	0.167777
$872$	18.2125	0.616755
$873$	18.7872	0.635851
$874$	29.7227	1.00538
$875$	2.78728	0.0942273
$876$	−3.24237	−0.109550
$877$	53.6770	1.81254	0.906271	−	0.422697i	$-0.138916\pi$
$877$	53.6770	1.81254	0.906271	+	0.422697i	$0.138916\pi$
$878$	1.27608	0.0430658
$879$	−0.783476	−0.0264260
$880$	7.53611	0.254042
$881$	−28.4799	−0.959512	−0.479756	−	0.877402i	$-0.659275\pi$
$881$	−28.4799	−0.959512	−0.479756	+	0.877402i	$0.659275\pi$
$882$	−0.805347	−0.0271174
$883$	3.34610	0.112605	0.0563026	−	0.998414i	$-0.482069\pi$
$883$	3.34610	0.112605	0.0563026	+	0.998414i	$0.482069\pi$
$884$	23.8941	0.803645
$885$	−5.51307	−0.185320
$886$	−31.6547	−1.06346
$887$	−9.19076	−0.308595	−0.154298	−	0.988024i	$-0.549311\pi$
$887$	−9.19076	−0.308595	−0.154298	+	0.988024i	$0.549311\pi$
$888$	−24.0020	−0.805456
$889$	−20.7064	−0.694469
$890$	6.36872	0.213480
$891$	4.32435	0.144871
$892$	−27.2557	−0.912588
$893$	−48.6899	−1.62935
$894$	1.03512	0.0346196
$895$	2.58444	0.0863882
$896$	8.72331	0.291425
$897$	27.4091	0.915163
$898$	32.8275	1.09547
$899$	−5.92228	−0.197519
$900$	−7.90082	−0.263361
$901$	−15.1951	−0.506224
$902$	18.7776	0.625227
$903$	0.927492	0.0308650
$904$	8.53083	0.283731
$905$	−36.9219	−1.22732
$906$	−13.4175	−0.445766
$907$	40.1442	1.33297	0.666484	−	0.745519i	$-0.267798\pi$
$907$	40.1442	1.33297	0.666484	+	0.745519i	$0.267798\pi$
$908$	13.2932	0.441151
$909$	−8.71506	−0.289060
$910$	−8.97734	−0.297596
$911$	43.1750	1.43045	0.715226	−	0.698893i	$-0.246324\pi$
$911$	43.1750	1.43045	0.715226	+	0.698893i	$0.246324\pi$
$912$	−2.41167	−0.0798585
$913$	−42.1712	−1.39566
$914$	−21.3050	−0.704706
$915$	18.0266	0.595942
$916$	29.1493	0.963120
$917$	−13.9172	−0.459588
$918$	4.20689	0.138848
$919$	−10.6944	−0.352774	−0.176387	−	0.984321i	$-0.556441\pi$
$919$	−10.6944	−0.352774	−0.176387	+	0.984321i	$0.556441\pi$
$920$	71.9820	2.37318
$921$	0.992960	0.0327191
$922$	11.7134	0.385760
$923$	23.0351	0.758211
$924$	−5.84400	−0.192253
$925$	−51.9900	−1.70942
$926$	24.1202	0.792640
$927$	−5.79861	−0.190451
$928$	5.59078	0.183526
$929$	2.18836	0.0717977	0.0358989	−	0.999355i	$-0.488571\pi$
$929$	2.18836	0.0717977	0.0358989	+	0.999355i	$0.488571\pi$
$930$	−16.3637	−0.536587
$931$	−4.55757	−0.149368
$932$	21.9081	0.717623
$933$	10.3733	0.339606
$934$	−11.6568	−0.381421
$935$	−74.3943	−2.43296
$936$	9.13555	0.298605
$937$	59.0456	1.92894	0.964468	−	0.264199i	$-0.0851077\pi$
$937$	59.0456	1.92894	0.964468	+	0.264199i	$0.0851077\pi$
$938$	−1.17815	−0.0384680
$939$	1.68846	0.0551009
$940$	−47.5484	−1.55086
$941$	−14.3785	−0.468727	−0.234363	−	0.972149i	$-0.575301\pi$
$941$	−14.3785	−0.468727	−0.234363	+	0.972149i	$0.575301\pi$
$942$	−8.52972	−0.277913
$943$	−43.6624	−1.42184
$944$	−0.885803	−0.0288304
$945$	3.29338	0.107134
$946$	−3.23009	−0.105019
$947$	−1.19838	−0.0389422	−0.0194711	−	0.999810i	$-0.506198\pi$
$947$	−1.19838	−0.0389422	−0.0194711	+	0.999810i	$0.506198\pi$
$948$	−8.60260	−0.279399
$949$	8.12076	0.263611
$950$	21.4585	0.696207
$951$	25.7611	0.835360
$952$	−14.0990	−0.456952
$953$	28.4228	0.920706	0.460353	−	0.887736i	$-0.347723\pi$
$953$	28.4228	0.920706	0.460353	+	0.887736i	$0.347723\pi$
$954$	−2.34266	−0.0758466
$955$	36.3036	1.17476
$956$	4.53354	0.146625
$957$	−4.15100	−0.134183
$958$	3.56509	0.115183
$959$	18.4978	0.597324
$960$	11.9623	0.386082
$961$	7.06396	0.227870
$962$	24.2406	0.781548
$963$	−4.48625	−0.144567
$964$	21.2232	0.683552
$965$	−69.3264	−2.23169
$966$	−6.52160	−0.209829
$967$	54.3684	1.74837	0.874185	−	0.485593i	$-0.161396\pi$
$967$	54.3684	1.74837	0.874185	+	0.485593i	$0.161396\pi$
$968$	20.7827	0.667982
$969$	23.8074	0.764803
$970$	−49.8296	−1.59993
$971$	27.1145	0.870147	0.435073	−	0.900395i	$-0.356722\pi$
$971$	27.1145	0.870147	0.435073	+	0.900395i	$0.356722\pi$
$972$	−1.35142	−0.0433467
$973$	11.5518	0.370335
$974$	21.2757	0.681719
$975$	19.7882	0.633730
$976$	2.89640	0.0927114
$977$	−29.8977	−0.956511	−0.478256	−	0.878221i	$-0.658731\pi$
$977$	−29.8977	−0.956511	−0.478256	+	0.878221i	$0.658731\pi$
$978$	−10.9491	−0.350113
$979$	−10.3836	−0.331862
$980$	−4.45072	−0.142173
$981$	6.74775	0.215439
$982$	8.41816	0.268634
$983$	35.6240	1.13623	0.568115	−	0.822949i	$-0.307673\pi$
$983$	35.6240	1.13623	0.568115	+	0.822949i	$0.307673\pi$
$984$	−14.5529	−0.463928
$985$	−80.6221	−2.56883
$986$	−4.03825	−0.128604
$987$	10.6833	0.340053
$988$	20.8471	0.663235
$989$	7.51072	0.238827
$990$	−11.4695	−0.364525
$991$	54.0317	1.71637	0.858187	−	0.513338i	$-0.171591\pi$
$991$	54.0317	1.71637	0.858187	+	0.513338i	$0.171591\pi$
$992$	−35.9334	−1.14089
$993$	1.85315	0.0588080
$994$	−5.48088	−0.173843
$995$	20.2914	0.643280
$996$	13.1790	0.417594
$997$	−22.2319	−0.704090	−0.352045	−	0.935983i	$-0.614514\pi$
$997$	−22.2319	−0.704090	−0.352045	+	0.935983i	$0.614514\pi$
$998$	−6.61023	−0.209243
$999$	−8.89277	−0.281355

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.u.1.19	✓	53

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.u.1.19	✓	53	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:	\( N \)	\(=\)	\( 8043 = 3 \cdot 7 \cdot 383 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8043.a (trivial)

\(f(q)\)	\(=\)	\(q-0.805347 q^{2} +1.00000 q^{3} -1.35142 q^{4} +3.29338 q^{5} -0.805347 q^{6} +1.00000 q^{7} +2.69905 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.805347 q^{2} +1.00000 q^{3} -1.35142 q^{4} +3.29338 q^{5} -0.805347 q^{6} +1.00000 q^{7} +2.69905 q^{8} +1.00000 q^{9} -2.65231 q^{10} +4.32435 q^{11} -1.35142 q^{12} +3.38473 q^{13} -0.805347 q^{14} +3.29338 q^{15} +0.529158 q^{16} -5.22369 q^{17} -0.805347 q^{18} -4.55757 q^{19} -4.45072 q^{20} +1.00000 q^{21} -3.48260 q^{22} +8.09788 q^{23} +2.69905 q^{24} +5.84633 q^{25} -2.72588 q^{26} +1.00000 q^{27} -1.35142 q^{28} -0.959913 q^{29} -2.65231 q^{30} +6.16960 q^{31} -5.82426 q^{32} +4.32435 q^{33} +4.20689 q^{34} +3.29338 q^{35} -1.35142 q^{36} -8.89277 q^{37} +3.67043 q^{38} +3.38473 q^{39} +8.88900 q^{40} -5.39184 q^{41} -0.805347 q^{42} +0.927492 q^{43} -5.84400 q^{44} +3.29338 q^{45} -6.52160 q^{46} +10.6833 q^{47} +0.529158 q^{48} +1.00000 q^{49} -4.70832 q^{50} -5.22369 q^{51} -4.57417 q^{52} +2.90889 q^{53} -0.805347 q^{54} +14.2417 q^{55} +2.69905 q^{56} -4.55757 q^{57} +0.773063 q^{58} -1.67399 q^{59} -4.45072 q^{60} +5.47360 q^{61} -4.96867 q^{62} +1.00000 q^{63} +3.63224 q^{64} +11.1472 q^{65} -3.48260 q^{66} +1.46291 q^{67} +7.05938 q^{68} +8.09788 q^{69} -2.65231 q^{70} +6.80562 q^{71} +2.69905 q^{72} +2.39924 q^{73} +7.16176 q^{74} +5.84633 q^{75} +6.15918 q^{76} +4.32435 q^{77} -2.72588 q^{78} +6.36562 q^{79} +1.74272 q^{80} +1.00000 q^{81} +4.34230 q^{82} -9.75203 q^{83} -1.35142 q^{84} -17.2036 q^{85} -0.746953 q^{86} -0.959913 q^{87} +11.6716 q^{88} -2.40120 q^{89} -2.65231 q^{90} +3.38473 q^{91} -10.9436 q^{92} +6.16960 q^{93} -8.60377 q^{94} -15.0098 q^{95} -5.82426 q^{96} +18.7872 q^{97} -0.805347 q^{98} +4.32435 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 53 q + 11 q^{2} + 53 q^{3} + 63 q^{4} + 24 q^{5} + 11 q^{6} + 53 q^{7} + 30 q^{8} + 53 q^{9}+O(q^{10}) \) 53 * q + 11 * q^2 + 53 * q^3 + 63 * q^4 + 24 * q^5 + 11 * q^6 + 53 * q^7 + 30 * q^8 + 53 * q^9	\( 53 q + 11 q^{2} + 53 q^{3} + 63 q^{4} + 24 q^{5} + 11 q^{6} + 53 q^{7} + 30 q^{8} + 53 q^{9} + 2 q^{10} + 46 q^{11} + 63 q^{12} + 32 q^{13} + 11 q^{14} + 24 q^{15} + 67 q^{16} + 46 q^{17} + 11 q^{18} + 14 q^{19} + 53 q^{20} + 53 q^{21} + 13 q^{22} + 68 q^{23} + 30 q^{24} + 71 q^{25} + 11 q^{26} + 53 q^{27} + 63 q^{28} + 55 q^{29} + 2 q^{30} - 2 q^{31} + 51 q^{32} + 46 q^{33} - 7 q^{34} + 24 q^{35} + 63 q^{36} + 53 q^{37} + 16 q^{38} + 32 q^{39} - 20 q^{40} + 38 q^{41} + 11 q^{42} + 36 q^{43} + 70 q^{44} + 24 q^{45} + 4 q^{46} + 51 q^{47} + 67 q^{48} + 53 q^{49} + 32 q^{50} + 46 q^{51} + 10 q^{52} + 104 q^{53} + 11 q^{54} + 11 q^{55} + 30 q^{56} + 14 q^{57} + 4 q^{58} + 36 q^{59} + 53 q^{60} + 3 q^{61} + 25 q^{62} + 53 q^{63} + 82 q^{64} + 46 q^{65} + 13 q^{66} + 54 q^{67} + 88 q^{68} + 68 q^{69} + 2 q^{70} + 101 q^{71} + 30 q^{72} + q^{73} + 32 q^{74} + 71 q^{75} - 35 q^{76} + 46 q^{77} + 11 q^{78} + 14 q^{79} + 39 q^{80} + 53 q^{81} - 29 q^{82} + 38 q^{83} + 63 q^{84} + 16 q^{85} + 23 q^{86} + 55 q^{87} - 8 q^{88} + 52 q^{89} + 2 q^{90} + 32 q^{91} + 76 q^{92} - 2 q^{93} - 53 q^{94} + 46 q^{95} + 51 q^{96} - 3 q^{97} + 11 q^{98} + 46 q^{99}+O(q^{100}) \) 53 * q + 11 * q^2 + 53 * q^3 + 63 * q^4 + 24 * q^5 + 11 * q^6 + 53 * q^7 + 30 * q^8 + 53 * q^9 + 2 * q^10 + 46 * q^11 + 63 * q^12 + 32 * q^13 + 11 * q^14 + 24 * q^15 + 67 * q^16 + 46 * q^17 + 11 * q^18 + 14 * q^19 + 53 * q^20 + 53 * q^21 + 13 * q^22 + 68 * q^23 + 30 * q^24 + 71 * q^25 + 11 * q^26 + 53 * q^27 + 63 * q^28 + 55 * q^29 + 2 * q^30 - 2 * q^31 + 51 * q^32 + 46 * q^33 - 7 * q^34 + 24 * q^35 + 63 * q^36 + 53 * q^37 + 16 * q^38 + 32 * q^39 - 20 * q^40 + 38 * q^41 + 11 * q^42 + 36 * q^43 + 70 * q^44 + 24 * q^45 + 4 * q^46 + 51 * q^47 + 67 * q^48 + 53 * q^49 + 32 * q^50 + 46 * q^51 + 10 * q^52 + 104 * q^53 + 11 * q^54 + 11 * q^55 + 30 * q^56 + 14 * q^57 + 4 * q^58 + 36 * q^59 + 53 * q^60 + 3 * q^61 + 25 * q^62 + 53 * q^63 + 82 * q^64 + 46 * q^65 + 13 * q^66 + 54 * q^67 + 88 * q^68 + 68 * q^69 + 2 * q^70 + 101 * q^71 + 30 * q^72 + q^73 + 32 * q^74 + 71 * q^75 - 35 * q^76 + 46 * q^77 + 11 * q^78 + 14 * q^79 + 39 * q^80 + 53 * q^81 - 29 * q^82 + 38 * q^83 + 63 * q^84 + 16 * q^85 + 23 * q^86 + 55 * q^87 - 8 * q^88 + 52 * q^89 + 2 * q^90 + 32 * q^91 + 76 * q^92 - 2 * q^93 - 53 * q^94 + 46 * q^95 + 51 * q^96 - 3 * q^97 + 11 * q^98 + 46 * q^99

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