LMFDB - Embedded newform 6041.2.a.f.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6041,2,Mod(1,6041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6041, 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("6041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6041 = 7 \cdot 863 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6041.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:	$48.2376278611$
Analytic rank:	$0$
Dimension:	$132$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	6041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.62362 q^{2} -1.27143 q^{3} +4.88340 q^{4} +1.41870 q^{5} +3.33576 q^{6} +1.00000 q^{7} -7.56495 q^{8} -1.38346 q^{9} +O(q^{10})$	\(q-2.62362 q^{2} -1.27143 q^{3} +4.88340 q^{4} +1.41870 q^{5} +3.33576 q^{6} +1.00000 q^{7} -7.56495 q^{8} -1.38346 q^{9} -3.72213 q^{10} +1.00335 q^{11} -6.20891 q^{12} +2.84063 q^{13} -2.62362 q^{14} -1.80378 q^{15} +10.0808 q^{16} -0.358679 q^{17} +3.62968 q^{18} +5.52965 q^{19} +6.92806 q^{20} -1.27143 q^{21} -2.63241 q^{22} -1.69823 q^{23} +9.61832 q^{24} -2.98730 q^{25} -7.45275 q^{26} +5.57327 q^{27} +4.88340 q^{28} +5.52479 q^{29} +4.73243 q^{30} +5.40586 q^{31} -11.3183 q^{32} -1.27569 q^{33} +0.941039 q^{34} +1.41870 q^{35} -6.75599 q^{36} +7.60429 q^{37} -14.5077 q^{38} -3.61167 q^{39} -10.7324 q^{40} +7.89719 q^{41} +3.33576 q^{42} -1.43388 q^{43} +4.89975 q^{44} -1.96271 q^{45} +4.45551 q^{46} -3.18421 q^{47} -12.8170 q^{48} +1.00000 q^{49} +7.83754 q^{50} +0.456036 q^{51} +13.8719 q^{52} -12.9323 q^{53} -14.6222 q^{54} +1.42345 q^{55} -7.56495 q^{56} -7.03057 q^{57} -14.4950 q^{58} +0.388087 q^{59} -8.80856 q^{60} +4.85277 q^{61} -14.1829 q^{62} -1.38346 q^{63} +9.53330 q^{64} +4.03000 q^{65} +3.34693 q^{66} -8.67990 q^{67} -1.75157 q^{68} +2.15918 q^{69} -3.72213 q^{70} -11.8443 q^{71} +10.4658 q^{72} +13.4684 q^{73} -19.9508 q^{74} +3.79815 q^{75} +27.0035 q^{76} +1.00335 q^{77} +9.47567 q^{78} +2.15817 q^{79} +14.3016 q^{80} -2.93565 q^{81} -20.7193 q^{82} +8.98617 q^{83} -6.20891 q^{84} -0.508857 q^{85} +3.76195 q^{86} -7.02439 q^{87} -7.59028 q^{88} +11.1380 q^{89} +5.14942 q^{90} +2.84063 q^{91} -8.29312 q^{92} -6.87318 q^{93} +8.35418 q^{94} +7.84490 q^{95} +14.3904 q^{96} -10.7738 q^{97} -2.62362 q^{98} -1.38809 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 8 q^{2} + 10 q^{3} + 174 q^{4} + 11 q^{5} + 16 q^{6} + 132 q^{7} + 30 q^{8} + 178 q^{9}+O(q^{10}) $ 132 * q + 8 * q^2 + 10 * q^3 + 174 * q^4 + 11 * q^5 + 16 * q^6 + 132 * q^7 + 30 * q^8 + 178 * q^9	\( 132 q + 8 q^{2} + 10 q^{3} + 174 q^{4} + 11 q^{5} + 16 q^{6} + 132 q^{7} + 30 q^{8} + 178 q^{9} + 22 q^{10} + 32 q^{11} + 30 q^{12} + 16 q^{13} + 8 q^{14} + 59 q^{15} + 254 q^{16} + 11 q^{17} + 33 q^{18} + 40 q^{19} + 4 q^{20} + 10 q^{21} + 66 q^{22} + 62 q^{23} + 36 q^{24} + 235 q^{25} + 25 q^{26} + 37 q^{27} + 174 q^{28} + 28 q^{29} + 45 q^{30} + 121 q^{31} + 53 q^{32} - 13 q^{33} + 44 q^{34} + 11 q^{35} + 274 q^{36} + 61 q^{37} - 28 q^{38} + 114 q^{39} + 32 q^{40} - q^{41} + 16 q^{42} + 105 q^{43} + 54 q^{44} + 29 q^{45} + 104 q^{46} + 33 q^{47} + 16 q^{48} + 132 q^{49} - 14 q^{50} + 53 q^{51} - 11 q^{52} + 48 q^{53} + 11 q^{54} + 118 q^{55} + 30 q^{56} + 93 q^{57} + 87 q^{58} + 12 q^{59} + 41 q^{60} + 54 q^{61} - 28 q^{62} + 178 q^{63} + 376 q^{64} + 22 q^{65} + 6 q^{66} + 123 q^{67} - 47 q^{68} + 58 q^{69} + 22 q^{70} + 108 q^{71} + 97 q^{72} + q^{73} - 10 q^{74} + 23 q^{75} + 71 q^{76} + 32 q^{77} + 5 q^{78} + 204 q^{79} - 10 q^{80} + 296 q^{81} + 80 q^{82} - 10 q^{83} + 30 q^{84} + 94 q^{85} + 48 q^{86} + 4 q^{87} + 155 q^{88} + q^{89} - 66 q^{90} + 16 q^{91} + 49 q^{92} + 90 q^{93} + 79 q^{94} + 100 q^{95} + q^{96} + 18 q^{97} + 8 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q + 8 * q^2 + 10 * q^3 + 174 * q^4 + 11 * q^5 + 16 * q^6 + 132 * q^7 + 30 * q^8 + 178 * q^9 + 22 * q^10 + 32 * q^11 + 30 * q^12 + 16 * q^13 + 8 * q^14 + 59 * q^15 + 254 * q^16 + 11 * q^17 + 33 * q^18 + 40 * q^19 + 4 * q^20 + 10 * q^21 + 66 * q^22 + 62 * q^23 + 36 * q^24 + 235 * q^25 + 25 * q^26 + 37 * q^27 + 174 * q^28 + 28 * q^29 + 45 * q^30 + 121 * q^31 + 53 * q^32 - 13 * q^33 + 44 * q^34 + 11 * q^35 + 274 * q^36 + 61 * q^37 - 28 * q^38 + 114 * q^39 + 32 * q^40 - q^41 + 16 * q^42 + 105 * q^43 + 54 * q^44 + 29 * q^45 + 104 * q^46 + 33 * q^47 + 16 * q^48 + 132 * q^49 - 14 * q^50 + 53 * q^51 - 11 * q^52 + 48 * q^53 + 11 * q^54 + 118 * q^55 + 30 * q^56 + 93 * q^57 + 87 * q^58 + 12 * q^59 + 41 * q^60 + 54 * q^61 - 28 * q^62 + 178 * q^63 + 376 * q^64 + 22 * q^65 + 6 * q^66 + 123 * q^67 - 47 * q^68 + 58 * q^69 + 22 * q^70 + 108 * q^71 + 97 * q^72 + q^73 - 10 * q^74 + 23 * q^75 + 71 * q^76 + 32 * q^77 + 5 * q^78 + 204 * q^79 - 10 * q^80 + 296 * q^81 + 80 * q^82 - 10 * q^83 + 30 * q^84 + 94 * q^85 + 48 * q^86 + 4 * q^87 + 155 * q^88 + q^89 - 66 * q^90 + 16 * q^91 + 49 * q^92 + 90 * q^93 + 79 * q^94 + 100 * q^95 + q^96 + 18 * q^97 + 8 * q^98 + 96 * 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 $

$2$	−2.62362	−1.85518	−0.927591	−	0.373598i	$-0.878124\pi$
$2$	−2.62362	−1.85518	−0.927591	+	0.373598i	$0.878124\pi$
$3$	−1.27143	−0.734062	−0.367031	−	0.930209i	$-0.619626\pi$
$3$	−1.27143	−0.734062	−0.367031	+	0.930209i	$0.619626\pi$
$4$	4.88340	2.44170
$5$	1.41870	0.634461	0.317230	−	0.948348i	$-0.397247\pi$
$5$	1.41870	0.634461	0.317230	+	0.948348i	$0.397247\pi$
$6$	3.33576	1.36182
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−7.56495	−2.67461
$9$	−1.38346	−0.461154
$10$	−3.72213	−1.17704
$11$	1.00335	0.302521	0.151261	−	0.988494i	$-0.451667\pi$
$11$	1.00335	0.302521	0.151261	+	0.988494i	$0.451667\pi$
$12$	−6.20891	−1.79236
$13$	2.84063	0.787850	0.393925	−	0.919143i	$-0.371117\pi$
$13$	2.84063	0.787850	0.393925	+	0.919143i	$0.371117\pi$
$14$	−2.62362	−0.701193
$15$	−1.80378	−0.465733
$16$	10.0808	2.52019
$17$	−0.358679	−0.0869925	−0.0434962	−	0.999054i	$-0.513850\pi$
$17$	−0.358679	−0.0869925	−0.0434962	+	0.999054i	$0.513850\pi$
$18$	3.62968	0.855524
$19$	5.52965	1.26859	0.634294	−	0.773092i	$-0.281291\pi$
$19$	5.52965	1.26859	0.634294	+	0.773092i	$0.281291\pi$
$20$	6.92806	1.54916
$21$	−1.27143	−0.277449
$22$	−2.63241	−0.561232
$23$	−1.69823	−0.354105	−0.177052	−	0.984201i	$-0.556656\pi$
$23$	−1.69823	−0.354105	−0.177052	+	0.984201i	$0.556656\pi$
$24$	9.61832	1.96333
$25$	−2.98730	−0.597459
$26$	−7.45275	−1.46160
$27$	5.57327	1.07258
$28$	4.88340	0.922875
$29$	5.52479	1.02593	0.512964	−	0.858410i	$-0.328548\pi$
$29$	5.52479	1.02593	0.512964	+	0.858410i	$0.328548\pi$
$30$	4.73243	0.864020
$31$	5.40586	0.970921	0.485460	−	0.874259i	$-0.338652\pi$
$31$	5.40586	0.970921	0.485460	+	0.874259i	$0.338652\pi$
$32$	−11.3183	−2.00081
$33$	−1.27569	−0.222069
$34$	0.941039	0.161387
$35$	1.41870	0.239804
$36$	−6.75599	−1.12600
$37$	7.60429	1.25014	0.625068	−	0.780570i	$-0.285071\pi$
$37$	7.60429	1.25014	0.625068	+	0.780570i	$0.285071\pi$
$38$	−14.5077	−2.35346
$39$	−3.61167	−0.578330
$40$	−10.7324	−1.69694
$41$	7.89719	1.23333	0.616667	−	0.787224i	$-0.288482\pi$
$41$	7.89719	1.23333	0.616667	+	0.787224i	$0.288482\pi$
$42$	3.33576	0.514719
$43$	−1.43388	−0.218664	−0.109332	−	0.994005i	$-0.534871\pi$
$43$	−1.43388	−0.218664	−0.109332	+	0.994005i	$0.534871\pi$
$44$	4.89975	0.738665
$45$	−1.96271	−0.292584
$46$	4.45551	0.656929
$47$	−3.18421	−0.464465	−0.232233	−	0.972660i	$-0.574603\pi$
$47$	−3.18421	−0.464465	−0.232233	+	0.972660i	$0.574603\pi$
$48$	−12.8170	−1.84998
$49$	1.00000	0.142857
$50$	7.83754	1.10840
$51$	0.456036	0.0638578
$52$	13.8719	1.92369
$53$	−12.9323	−1.77639	−0.888197	−	0.459462i	$-0.848042\pi$
$53$	−12.9323	−1.77639	−0.888197	+	0.459462i	$0.848042\pi$
$54$	−14.6222	−1.98982
$55$	1.42345	0.191938
$56$	−7.56495	−1.01091
$57$	−7.03057	−0.931222
$58$	−14.4950	−1.90328
$59$	0.388087	0.0505246	0.0252623	−	0.999681i	$-0.491958\pi$
$59$	0.388087	0.0505246	0.0252623	+	0.999681i	$0.491958\pi$
$60$	−8.80856	−1.13718
$61$	4.85277	0.621334	0.310667	−	0.950519i	$-0.399448\pi$
$61$	4.85277	0.621334	0.310667	+	0.950519i	$0.399448\pi$
$62$	−14.1829	−1.80123
$63$	−1.38346	−0.174300
$64$	9.53330	1.19166
$65$	4.03000	0.499860
$66$	3.34693	0.411978
$67$	−8.67990	−1.06042	−0.530209	−	0.847867i	$-0.677887\pi$
$67$	−8.67990	−1.06042	−0.530209	+	0.847867i	$0.677887\pi$
$68$	−1.75157	−0.212409
$69$	2.15918	0.259935
$70$	−3.72213	−0.444879
$71$	−11.8443	−1.40566	−0.702831	−	0.711357i	$-0.748081\pi$
$71$	−11.8443	−1.40566	−0.702831	+	0.711357i	$0.748081\pi$
$72$	10.4658	1.23341
$73$	13.4684	1.57635	0.788177	−	0.615449i	$-0.211025\pi$
$73$	13.4684	1.57635	0.788177	+	0.615449i	$0.211025\pi$
$74$	−19.9508	−2.31923
$75$	3.79815	0.438572
$76$	27.0035	3.09751
$77$	1.00335	0.114342
$78$	9.47567	1.07291
$79$	2.15817	0.242813	0.121406	−	0.992603i	$-0.461260\pi$
$79$	2.15817	0.242813	0.121406	+	0.992603i	$0.461260\pi$
$80$	14.3016	1.59896
$81$	−2.93565	−0.326184
$82$	−20.7193	−2.28806
$83$	8.98617	0.986361	0.493180	−	0.869927i	$-0.335834\pi$
$83$	8.98617	0.986361	0.493180	+	0.869927i	$0.335834\pi$
$84$	−6.20891	−0.677447
$85$	−0.508857	−0.0551933
$86$	3.76195	0.405662
$87$	−7.02439	−0.753094
$88$	−7.59028	−0.809127
$89$	11.1380	1.18063	0.590314	−	0.807173i	$-0.299004\pi$
$89$	11.1380	1.18063	0.590314	+	0.807173i	$0.299004\pi$
$90$	5.14942	0.542796
$91$	2.84063	0.297779
$92$	−8.29312	−0.864617
$93$	−6.87318	−0.712716
$94$	8.35418	0.861668
$95$	7.84490	0.804869
$96$	14.3904	1.46871
$97$	−10.7738	−1.09391	−0.546957	−	0.837161i	$-0.684214\pi$
$97$	−10.7738	−1.09391	−0.546957	+	0.837161i	$0.684214\pi$
$98$	−2.62362	−0.265026
$99$	−1.38809	−0.139509
$100$	−14.5882	−1.45882
$101$	4.40333	0.438147	0.219074	−	0.975708i	$-0.429697\pi$
$101$	4.40333	0.438147	0.219074	+	0.975708i	$0.429697\pi$
$102$	−1.19647	−0.118468
$103$	8.24817	0.812717	0.406358	−	0.913714i	$-0.366798\pi$
$103$	8.24817	0.812717	0.406358	+	0.913714i	$0.366798\pi$
$104$	−21.4892	−2.10719
$105$	−1.80378	−0.176031
$106$	33.9296	3.29554
$107$	20.5661	1.98820	0.994098	−	0.108489i	$-0.0346013\pi$
$107$	20.5661	1.98820	0.994098	+	0.108489i	$0.0346013\pi$
$108$	27.2165	2.61891
$109$	5.76817	0.552490	0.276245	−	0.961087i	$-0.410910\pi$
$109$	5.76817	0.552490	0.276245	+	0.961087i	$0.410910\pi$
$110$	−3.73459	−0.356079
$111$	−9.66833	−0.917677
$112$	10.0808	0.952544
$113$	−10.4969	−0.987468	−0.493734	−	0.869613i	$-0.664368\pi$
$113$	−10.4969	−0.987468	−0.493734	+	0.869613i	$0.664368\pi$
$114$	18.4456	1.72759
$115$	−2.40927	−0.224666
$116$	26.9797	2.50501
$117$	−3.92991	−0.363320
$118$	−1.01819	−0.0937322
$119$	−0.358679	−0.0328801
$120$	13.6455	1.24566
$121$	−9.99329	−0.908481
$122$	−12.7318	−1.15269
$123$	−10.0407	−0.905343
$124$	26.3990	2.37070
$125$	−11.3316	−1.01353
$126$	3.62968	0.323358
$127$	−7.74654	−0.687394	−0.343697	−	0.939081i	$-0.611679\pi$
$127$	−7.74654	−0.687394	−0.343697	+	0.939081i	$0.611679\pi$
$128$	−2.37526	−0.209945
$129$	1.82308	0.160513
$130$	−10.5732	−0.927331
$131$	−10.6972	−0.934616	−0.467308	−	0.884095i	$-0.654776\pi$
$131$	−10.6972	−0.934616	−0.467308	+	0.884095i	$0.654776\pi$
$132$	−6.22970	−0.542226
$133$	5.52965	0.479481
$134$	22.7728	1.96727
$135$	7.90679	0.680508
$136$	2.71339	0.232671
$137$	−15.1157	−1.29142	−0.645711	−	0.763582i	$-0.723439\pi$
$137$	−15.1157	−1.29142	−0.645711	+	0.763582i	$0.723439\pi$
$138$	−5.66487	−0.482226
$139$	10.2572	0.870008	0.435004	−	0.900429i	$-0.356747\pi$
$139$	10.2572	0.870008	0.435004	+	0.900429i	$0.356747\pi$
$140$	6.92806	0.585528
$141$	4.04851	0.340946
$142$	31.0750	2.60776
$143$	2.85015	0.238341
$144$	−13.9464	−1.16220
$145$	7.83800	0.650911
$146$	−35.3359	−2.92442
$147$	−1.27143	−0.104866
$148$	37.1347	3.05246
$149$	−7.02431	−0.575454	−0.287727	−	0.957713i	$-0.592900\pi$
$149$	−7.02431	−0.575454	−0.287727	+	0.957713i	$0.592900\pi$
$150$	−9.96490	−0.813631
$151$	14.6847	1.19502	0.597512	−	0.801860i	$-0.296156\pi$
$151$	14.6847	1.19502	0.597512	+	0.801860i	$0.296156\pi$
$152$	−41.8315	−3.39298
$153$	0.496219	0.0401169
$154$	−2.63241	−0.212126
$155$	7.66928	0.616011
$156$	−17.6372	−1.41211
$157$	16.7482	1.33665	0.668324	−	0.743870i	$-0.267012\pi$
$157$	16.7482	1.33665	0.668324	+	0.743870i	$0.267012\pi$
$158$	−5.66222	−0.450462
$159$	16.4426	1.30398
$160$	−16.0572	−1.26943
$161$	−1.69823	−0.133839
$162$	7.70205	0.605130
$163$	21.2624	1.66540	0.832698	−	0.553727i	$-0.186795\pi$
$163$	21.2624	1.66540	0.832698	+	0.553727i	$0.186795\pi$
$164$	38.5651	3.01143
$165$	−1.80982	−0.140894
$166$	−23.5763	−1.82988
$167$	14.3356	1.10932	0.554661	−	0.832077i	$-0.312848\pi$
$167$	14.3356	1.10932	0.554661	+	0.832077i	$0.312848\pi$
$168$	9.61832	0.742069
$169$	−4.93080	−0.379292
$170$	1.33505	0.102394
$171$	−7.65005	−0.585014
$172$	−7.00219	−0.533912
$173$	13.5304	1.02870	0.514350	−	0.857580i	$-0.328033\pi$
$173$	13.5304	1.02870	0.514350	+	0.857580i	$0.328033\pi$
$174$	18.4294	1.39713
$175$	−2.98730	−0.225818
$176$	10.1145	0.762412
$177$	−0.493426	−0.0370881
$178$	−29.2220	−2.19028
$179$	−12.8676	−0.961771	−0.480886	−	0.876783i	$-0.659685\pi$
$179$	−12.8676	−0.961771	−0.480886	+	0.876783i	$0.659685\pi$
$180$	−9.58471	−0.714402
$181$	−12.1559	−0.903540	−0.451770	−	0.892134i	$-0.649207\pi$
$181$	−12.1559	−0.903540	−0.451770	+	0.892134i	$0.649207\pi$
$182$	−7.45275	−0.552435
$183$	−6.16997	−0.456097
$184$	12.8470	0.947093
$185$	10.7882	0.793163
$186$	18.0326	1.32222
$187$	−0.359880	−0.0263171
$188$	−15.5498	−1.13408
$189$	5.57327	0.405396
$190$	−20.5821	−1.49318
$191$	4.58823	0.331993	0.165996	−	0.986126i	$-0.446916\pi$
$191$	4.58823	0.331993	0.165996	+	0.986126i	$0.446916\pi$
$192$	−12.1209	−0.874754
$193$	−12.2706	−0.883254	−0.441627	−	0.897199i	$-0.645599\pi$
$193$	−12.2706	−0.883254	−0.441627	+	0.897199i	$0.645599\pi$
$194$	28.2664	2.02941
$195$	−5.12387	−0.366928
$196$	4.88340	0.348814
$197$	1.99005	0.141785	0.0708926	−	0.997484i	$-0.477415\pi$
$197$	1.99005	0.141785	0.0708926	+	0.997484i	$0.477415\pi$
$198$	3.64184	0.258814
$199$	−7.22899	−0.512449	−0.256225	−	0.966617i	$-0.582479\pi$
$199$	−7.22899	−0.512449	−0.256225	+	0.966617i	$0.582479\pi$
$200$	22.5988	1.59797
$201$	11.0359	0.778412
$202$	−11.5527	−0.812843
$203$	5.52479	0.387764
$204$	2.22701	0.155922
$205$	11.2037	0.782502
$206$	−21.6401	−1.50774
$207$	2.34943	0.163297
$208$	28.6358	1.98554
$209$	5.54817	0.383775
$210$	4.73243	0.326569
$211$	12.7426	0.877234	0.438617	−	0.898674i	$-0.355469\pi$
$211$	12.7426	0.877234	0.438617	+	0.898674i	$0.355469\pi$
$212$	−63.1538	−4.33742
$213$	15.0592	1.03184
$214$	−53.9576	−3.68846
$215$	−2.03424	−0.138734
$216$	−42.1615	−2.86873
$217$	5.40586	0.366974
$218$	−15.1335	−1.02497
$219$	−17.1241	−1.15714
$220$	6.95127	0.468654
$221$	−1.01888	−0.0685370
$222$	25.3661	1.70246
$223$	−25.5811	−1.71303	−0.856517	−	0.516119i	$-0.827376\pi$
$223$	−25.5811	−1.71303	−0.856517	+	0.516119i	$0.827376\pi$
$224$	−11.3183	−0.756233
$225$	4.13281	0.275521
$226$	27.5400	1.83193
$227$	−0.774330	−0.0513941	−0.0256970	−	0.999670i	$-0.508181\pi$
$227$	−0.774330	−0.0513941	−0.0256970	+	0.999670i	$0.508181\pi$
$228$	−34.3331	−2.27376
$229$	20.2797	1.34012	0.670061	−	0.742306i	$-0.266268\pi$
$229$	20.2797	1.34012	0.670061	+	0.742306i	$0.266268\pi$
$230$	6.32102	0.416796
$231$	−1.27569	−0.0839342
$232$	−41.7947	−2.74396
$233$	−3.89638	−0.255260	−0.127630	−	0.991822i	$-0.540737\pi$
$233$	−3.89638	−0.255260	−0.127630	+	0.991822i	$0.540737\pi$
$234$	10.3106	0.674024
$235$	−4.51744	−0.294685
$236$	1.89518	0.123366
$237$	−2.74396	−0.178240
$238$	0.941039	0.0609985
$239$	11.2504	0.727727	0.363864	−	0.931452i	$-0.381457\pi$
$239$	11.2504	0.727727	0.363864	+	0.931452i	$0.381457\pi$
$240$	−18.1835	−1.17374
$241$	13.1433	0.846637	0.423318	−	0.905981i	$-0.360865\pi$
$241$	13.1433	0.846637	0.423318	+	0.905981i	$0.360865\pi$
$242$	26.2186	1.68540
$243$	−12.9873	−0.833138
$244$	23.6980	1.51711
$245$	1.41870	0.0906373
$246$	26.3431	1.67958
$247$	15.7077	0.999457
$248$	−40.8950	−2.59684
$249$	−11.4253	−0.724049
$250$	29.7297	1.88027
$251$	20.4839	1.29293	0.646465	−	0.762944i	$-0.276247\pi$
$251$	20.4839	1.29293	0.646465	+	0.762944i	$0.276247\pi$
$252$	−6.75599	−0.425587
$253$	−1.70391	−0.107124
$254$	20.3240	1.27524
$255$	0.646977	0.0405153
$256$	−12.8348	−0.802176
$257$	−29.4392	−1.83637	−0.918185	−	0.396152i	$-0.870345\pi$
$257$	−29.4392	−1.83637	−0.918185	+	0.396152i	$0.870345\pi$
$258$	−4.78306	−0.297781
$259$	7.60429	0.472507
$260$	19.6801	1.22051
$261$	−7.64333	−0.473110
$262$	28.0653	1.73388
$263$	−30.4121	−1.87529	−0.937644	−	0.347597i	$-0.886998\pi$
$263$	−30.4121	−1.87529	−0.937644	+	0.347597i	$0.886998\pi$
$264$	9.65053	0.593949
$265$	−18.3471	−1.12705
$266$	−14.5077	−0.889525
$267$	−14.1612	−0.866654
$268$	−42.3874	−2.58922
$269$	1.92312	0.117254	0.0586272	−	0.998280i	$-0.481328\pi$
$269$	1.92312	0.117254	0.0586272	+	0.998280i	$0.481328\pi$
$270$	−20.7444	−1.26247
$271$	−8.56791	−0.520463	−0.260232	−	0.965546i	$-0.583799\pi$
$271$	−8.56791	−0.520463	−0.260232	+	0.965546i	$0.583799\pi$
$272$	−3.61576	−0.219238
$273$	−3.61167	−0.218588
$274$	39.6579	2.39582
$275$	−2.99730	−0.180744
$276$	10.5441	0.634682
$277$	−12.0706	−0.725249	−0.362625	−	0.931935i	$-0.618119\pi$
$277$	−12.0706	−0.725249	−0.362625	+	0.931935i	$0.618119\pi$
$278$	−26.9111	−1.61402
$279$	−7.47880	−0.447744
$280$	−10.7324	−0.641382
$281$	−24.4139	−1.45641	−0.728206	−	0.685359i	$-0.759645\pi$
$281$	−24.4139	−1.45641	−0.728206	+	0.685359i	$0.759645\pi$
$282$	−10.6218	−0.632517
$283$	1.38787	0.0825001	0.0412501	−	0.999149i	$-0.486866\pi$
$283$	1.38787	0.0825001	0.0412501	+	0.999149i	$0.486866\pi$
$284$	−57.8405	−3.43220
$285$	−9.97425	−0.590824
$286$	−7.47771	−0.442166
$287$	7.89719	0.466157
$288$	15.6584	0.922679
$289$	−16.8713	−0.992432
$290$	−20.5640	−1.20756
$291$	13.6982	0.803000
$292$	65.7714	3.84898
$293$	−14.5443	−0.849688	−0.424844	−	0.905267i	$-0.639671\pi$
$293$	−14.5443	−0.849688	−0.424844	+	0.905267i	$0.639671\pi$
$294$	3.33576	0.194545
$295$	0.550577	0.0320559
$296$	−57.5260	−3.34363
$297$	5.59194	0.324477
$298$	18.4291	1.06757
$299$	−4.82404	−0.278982
$300$	18.5479	1.07086
$301$	−1.43388	−0.0826473
$302$	−38.5271	−2.21699
$303$	−5.59853	−0.321627
$304$	55.7431	3.19709
$305$	6.88461	0.394212
$306$	−1.30189	−0.0744241
$307$	−9.31668	−0.531731	−0.265866	−	0.964010i	$-0.585658\pi$
$307$	−9.31668	−0.531731	−0.265866	+	0.964010i	$0.585658\pi$
$308$	4.89975	0.279189
$309$	−10.4870	−0.596584
$310$	−20.1213	−1.14281
$311$	−19.4038	−1.10029	−0.550145	−	0.835069i	$-0.685428\pi$
$311$	−19.4038	−1.10029	−0.550145	+	0.835069i	$0.685428\pi$
$312$	27.3221	1.54681
$313$	7.37349	0.416774	0.208387	−	0.978046i	$-0.433179\pi$
$313$	7.37349	0.416774	0.208387	+	0.978046i	$0.433179\pi$
$314$	−43.9409	−2.47973
$315$	−1.96271	−0.110586
$316$	10.5392	0.592876
$317$	13.4956	0.757990	0.378995	−	0.925399i	$-0.376270\pi$
$317$	13.4956	0.757990	0.378995	+	0.925399i	$0.376270\pi$
$318$	−43.1392	−2.41913
$319$	5.54329	0.310365
$320$	13.5249	0.756063
$321$	−26.1483	−1.45946
$322$	4.45551	0.248296
$323$	−1.98337	−0.110358
$324$	−14.3360	−0.796442
$325$	−8.48582	−0.470708
$326$	−55.7844	−3.08961
$327$	−7.33383	−0.405562
$328$	−59.7419	−3.29869
$329$	−3.18421	−0.175551
$330$	4.74828	0.261384
$331$	28.7446	1.57994	0.789972	−	0.613143i	$-0.210095\pi$
$331$	28.7446	1.57994	0.789972	+	0.613143i	$0.210095\pi$
$332$	43.8831	2.40840
$333$	−10.5202	−0.576505
$334$	−37.6112	−2.05799
$335$	−12.3142	−0.672794
$336$	−12.8170	−0.699226
$337$	−10.8952	−0.593502	−0.296751	−	0.954955i	$-0.595903\pi$
$337$	−10.8952	−0.593502	−0.296751	+	0.954955i	$0.595903\pi$
$338$	12.9366	0.703656
$339$	13.3461	0.724863
$340$	−2.48495	−0.134765
$341$	5.42396	0.293724
$342$	20.0709	1.08531
$343$	1.00000	0.0539949
$344$	10.8472	0.584842
$345$	3.06322	0.164918
$346$	−35.4988	−1.90843
$347$	−36.3110	−1.94927	−0.974637	−	0.223790i	$-0.928157\pi$
$347$	−36.3110	−1.94927	−0.974637	+	0.223790i	$0.928157\pi$
$348$	−34.3029	−1.83883
$349$	4.74346	0.253912	0.126956	−	0.991908i	$-0.459479\pi$
$349$	4.74346	0.253912	0.126956	+	0.991908i	$0.459479\pi$
$350$	7.83754	0.418934
$351$	15.8316	0.845030
$352$	−11.3562	−0.605286
$353$	24.8401	1.32210	0.661052	−	0.750340i	$-0.270110\pi$
$353$	24.8401	1.32210	0.661052	+	0.750340i	$0.270110\pi$
$354$	1.29456	0.0688052
$355$	−16.8035	−0.891837
$356$	54.3914	2.88274
$357$	0.456036	0.0241360
$358$	33.7598	1.78426
$359$	−0.364763	−0.0192514	−0.00962572	−	0.999954i	$-0.503064\pi$
$359$	−0.364763	−0.0192514	−0.00962572	+	0.999954i	$0.503064\pi$
$360$	14.8478	0.782549
$361$	11.5770	0.609316
$362$	31.8925	1.67623
$363$	12.7058	0.666881
$364$	13.8719	0.727087
$365$	19.1075	1.00013
$366$	16.1877	0.846143
$367$	−16.7597	−0.874848	−0.437424	−	0.899255i	$-0.644109\pi$
$367$	−16.7597	−0.874848	−0.437424	+	0.899255i	$0.644109\pi$
$368$	−17.1195	−0.892413
$369$	−10.9255	−0.568757
$370$	−28.3041	−1.47146
$371$	−12.9323	−0.671414
$372$	−33.5645	−1.74024
$373$	4.97701	0.257700	0.128850	−	0.991664i	$-0.458871\pi$
$373$	4.97701	0.257700	0.128850	+	0.991664i	$0.458871\pi$
$374$	0.944190	0.0488229
$375$	14.4073	0.743990
$376$	24.0884	1.24227
$377$	15.6939	0.808277
$378$	−14.6222	−0.752083
$379$	−4.43273	−0.227694	−0.113847	−	0.993498i	$-0.536317\pi$
$379$	−4.43273	−0.227694	−0.113847	+	0.993498i	$0.536317\pi$
$380$	38.3097	1.96525
$381$	9.84920	0.504590
$382$	−12.0378	−0.615907
$383$	0.741365	0.0378820	0.0189410	−	0.999821i	$-0.493971\pi$
$383$	0.741365	0.0378820	0.0189410	+	0.999821i	$0.493971\pi$
$384$	3.01998	0.154113
$385$	1.42345	0.0725457
$386$	32.1933	1.63860
$387$	1.98371	0.100838
$388$	−52.6128	−2.67101
$389$	19.8357	1.00571	0.502854	−	0.864371i	$-0.332283\pi$
$389$	19.8357	1.00571	0.502854	+	0.864371i	$0.332283\pi$
$390$	13.4431	0.680718
$391$	0.609119	0.0308045
$392$	−7.56495	−0.382088
$393$	13.6007	0.686066
$394$	−5.22114	−0.263037
$395$	3.06179	0.154055
$396$	−6.77862	−0.340638
$397$	−0.940959	−0.0472254	−0.0236127	−	0.999721i	$-0.507517\pi$
$397$	−0.940959	−0.0472254	−0.0236127	+	0.999721i	$0.507517\pi$
$398$	18.9661	0.950686
$399$	−7.03057	−0.351969
$400$	−30.1143	−1.50571
$401$	27.1068	1.35365	0.676825	−	0.736144i	$-0.263355\pi$
$401$	27.1068	1.35365	0.676825	+	0.736144i	$0.263355\pi$
$402$	−28.9540	−1.44410
$403$	15.3561	0.764940
$404$	21.5032	1.06982
$405$	−4.16480	−0.206951
$406$	−14.4950	−0.719373
$407$	7.62975	0.378193
$408$	−3.44989	−0.170795
$409$	6.45681	0.319268	0.159634	−	0.987176i	$-0.448969\pi$
$409$	6.45681	0.319268	0.159634	+	0.987176i	$0.448969\pi$
$410$	−29.3944	−1.45168
$411$	19.2186	0.947984
$412$	40.2791	1.98441
$413$	0.388087	0.0190965
$414$	−6.16402	−0.302945
$415$	12.7487	0.625807
$416$	−32.1510	−1.57633
$417$	−13.0414	−0.638639
$418$	−14.5563	−0.711972
$419$	0.669887	0.0327261	0.0163631	−	0.999866i	$-0.494791\pi$
$419$	0.669887	0.0327261	0.0163631	+	0.999866i	$0.494791\pi$
$420$	−8.80856	−0.429814
$421$	7.71126	0.375824	0.187912	−	0.982186i	$-0.439828\pi$
$421$	7.71126	0.375824	0.187912	+	0.982186i	$0.439828\pi$
$422$	−33.4317	−1.62743
$423$	4.40524	0.214190
$424$	97.8326	4.75117
$425$	1.07148	0.0519745
$426$	−39.5098	−1.91426
$427$	4.85277	0.234842
$428$	100.432	4.85457
$429$	−3.62377	−0.174957
$430$	5.33707	0.257376
$431$	−6.20495	−0.298882	−0.149441	−	0.988771i	$-0.547747\pi$
$431$	−6.20495	−0.298882	−0.149441	+	0.988771i	$0.547747\pi$
$432$	56.1829	2.70310
$433$	27.0266	1.29882	0.649409	−	0.760440i	$-0.275017\pi$
$433$	27.0266	1.29882	0.649409	+	0.760440i	$0.275017\pi$
$434$	−14.1829	−0.680803
$435$	−9.96549	−0.477809
$436$	28.1683	1.34901
$437$	−9.39060	−0.449213
$438$	44.9272	2.14671
$439$	7.68565	0.366816	0.183408	−	0.983037i	$-0.441287\pi$
$439$	7.68565	0.366816	0.183408	+	0.983037i	$0.441287\pi$
$440$	−10.7683	−0.513359
$441$	−1.38346	−0.0658791
$442$	2.67315	0.127149
$443$	−3.68603	−0.175128	−0.0875642	−	0.996159i	$-0.527908\pi$
$443$	−3.68603	−0.175128	−0.0875642	+	0.996159i	$0.527908\pi$
$444$	−47.2143	−2.24069
$445$	15.8015	0.749063
$446$	67.1150	3.17799
$447$	8.93093	0.422418
$448$	9.53330	0.450406
$449$	8.92995	0.421431	0.210715	−	0.977547i	$-0.432421\pi$
$449$	8.92995	0.421431	0.210715	+	0.977547i	$0.432421\pi$
$450$	−10.8429	−0.511141
$451$	7.92364	0.373110
$452$	−51.2607	−2.41110
$453$	−18.6706	−0.877221
$454$	2.03155	0.0953453
$455$	4.03000	0.188929
$456$	53.1859	2.49066
$457$	16.5931	0.776190	0.388095	−	0.921619i	$-0.373133\pi$
$457$	16.5931	0.776190	0.388095	+	0.921619i	$0.373133\pi$
$458$	−53.2064	−2.48617
$459$	−1.99902	−0.0933061
$460$	−11.7654	−0.548566
$461$	31.7615	1.47928	0.739640	−	0.673003i	$-0.234996\pi$
$461$	31.7615	1.47928	0.739640	+	0.673003i	$0.234996\pi$
$462$	3.34693	0.155713
$463$	−9.40780	−0.437218	−0.218609	−	0.975813i	$-0.570152\pi$
$463$	−9.40780	−0.437218	−0.218609	+	0.975813i	$0.570152\pi$
$464$	55.6942	2.58554
$465$	−9.75096	−0.452190
$466$	10.2226	0.473554
$467$	−34.8129	−1.61095	−0.805475	−	0.592629i	$-0.798090\pi$
$467$	−34.8129	−1.61095	−0.805475	+	0.592629i	$0.798090\pi$
$468$	−19.1913	−0.887118
$469$	−8.67990	−0.400801
$470$	11.8521	0.546694
$471$	−21.2941	−0.981182
$472$	−2.93585	−0.135134
$473$	−1.43868	−0.0661505
$474$	7.19913	0.330667
$475$	−16.5187	−0.757930
$476$	−1.75157	−0.0802832
$477$	17.8914	0.819191
$478$	−29.5168	−1.35007
$479$	21.8378	0.997796	0.498898	−	0.866661i	$-0.333738\pi$
$479$	21.8378	0.997796	0.498898	+	0.866661i	$0.333738\pi$
$480$	20.4156	0.931841
$481$	21.6010	0.984920
$482$	−34.4832	−1.57066
$483$	2.15918	0.0982461
$484$	−48.8012	−2.21824
$485$	−15.2848	−0.694046
$486$	34.0739	1.54562
$487$	37.6515	1.70615	0.853077	−	0.521785i	$-0.174734\pi$
$487$	37.6515	1.70615	0.853077	+	0.521785i	$0.174734\pi$
$488$	−36.7110	−1.66183
$489$	−27.0336	−1.22250
$490$	−3.72213	−0.168149
$491$	−10.1391	−0.457571	−0.228785	−	0.973477i	$-0.573475\pi$
$491$	−10.1391	−0.457571	−0.228785	+	0.973477i	$0.573475\pi$
$492$	−49.0329	−2.21058
$493$	−1.98163	−0.0892480
$494$	−41.2111	−1.85417
$495$	−1.96929	−0.0885128
$496$	54.4953	2.44691
$497$	−11.8443	−0.531290
$498$	29.9757	1.34324
$499$	−5.93453	−0.265666	−0.132833	−	0.991138i	$-0.542407\pi$
$499$	−5.93453	−0.265666	−0.132833	+	0.991138i	$0.542407\pi$
$500$	−55.3365	−2.47472
$501$	−18.2267	−0.814310
$502$	−53.7419	−2.39862
$503$	−4.78204	−0.213221	−0.106610	−	0.994301i	$-0.534000\pi$
$503$	−4.78204	−0.213221	−0.106610	+	0.994301i	$0.534000\pi$
$504$	10.4658	0.466184
$505$	6.24699	0.277987
$506$	4.47043	0.198735
$507$	6.26918	0.278424
$508$	−37.8294	−1.67841
$509$	41.8774	1.85618	0.928092	−	0.372350i	$-0.121448\pi$
$509$	41.8774	1.85618	0.928092	+	0.372350i	$0.121448\pi$
$510$	−1.69742	−0.0751632
$511$	13.4684	0.595806
$512$	38.4242	1.69813
$513$	30.8182	1.36066
$514$	77.2375	3.40680
$515$	11.7017	0.515637
$516$	8.90280	0.391924
$517$	−3.19488	−0.140511
$518$	−19.9508	−0.876587
$519$	−17.2030	−0.755129
$520$	−30.4867	−1.33693
$521$	−16.9223	−0.741381	−0.370691	−	0.928756i	$-0.620879\pi$
$521$	−16.9223	−0.741381	−0.370691	+	0.928756i	$0.620879\pi$
$522$	20.0532	0.877705
$523$	1.70053	0.0743589	0.0371794	−	0.999309i	$-0.488163\pi$
$523$	1.70053	0.0743589	0.0371794	+	0.999309i	$0.488163\pi$
$524$	−52.2385	−2.28205
$525$	3.79815	0.165765
$526$	79.7898	3.47900
$527$	−1.93897	−0.0844628
$528$	−12.8599	−0.559657
$529$	−20.1160	−0.874610
$530$	48.1359	2.09089
$531$	−0.536903	−0.0232996
$532$	27.0035	1.17075
$533$	22.4330	0.971683
$534$	37.1538	1.60780
$535$	29.1770	1.26143
$536$	65.6630	2.83621
$537$	16.3603	0.705999
$538$	−5.04553	−0.217528
$539$	1.00335	0.0432173
$540$	38.6120	1.66160
$541$	24.6674	1.06053	0.530267	−	0.847831i	$-0.322092\pi$
$541$	24.6674	1.06053	0.530267	+	0.847831i	$0.322092\pi$
$542$	22.4790	0.965554
$543$	15.4554	0.663254
$544$	4.05962	0.174055
$545$	8.18328	0.350533
$546$	9.47567	0.405521
$547$	−36.5380	−1.56225	−0.781125	−	0.624374i	$-0.785354\pi$
$547$	−36.5380	−1.56225	−0.781125	+	0.624374i	$0.785354\pi$
$548$	−73.8160	−3.15326
$549$	−6.71362	−0.286530
$550$	7.86379	0.335313
$551$	30.5501	1.30148
$552$	−16.3341	−0.695225
$553$	2.15817	0.0917747
$554$	31.6686	1.34547
$555$	−13.7164	−0.582230
$556$	50.0902	2.12430
$557$	−12.5265	−0.530763	−0.265381	−	0.964144i	$-0.585498\pi$
$557$	−12.5265	−0.530763	−0.265381	+	0.964144i	$0.585498\pi$
$558$	19.6215	0.830646
$559$	−4.07312	−0.172274
$560$	14.3016	0.604352
$561$	0.457563	0.0193183
$562$	64.0529	2.70191
$563$	41.0593	1.73044	0.865221	−	0.501391i	$-0.167178\pi$
$563$	41.0593	1.73044	0.865221	+	0.501391i	$0.167178\pi$
$564$	19.7705	0.832488
$565$	−14.8920	−0.626510
$566$	−3.64124	−0.153053
$567$	−2.93565	−0.123286
$568$	89.6017	3.75960
$569$	10.7698	0.451495	0.225747	−	0.974186i	$-0.427518\pi$
$569$	10.7698	0.451495	0.225747	+	0.974186i	$0.427518\pi$
$570$	26.1687	1.09609
$571$	12.5226	0.524055	0.262028	−	0.965060i	$-0.415609\pi$
$571$	12.5226	0.524055	0.262028	+	0.965060i	$0.415609\pi$
$572$	13.9184	0.581958
$573$	−5.83362	−0.243703
$574$	−20.7193	−0.864805
$575$	5.07311	0.211563
$576$	−13.1889	−0.549540
$577$	−6.88690	−0.286705	−0.143353	−	0.989672i	$-0.545788\pi$
$577$	−6.88690	−0.286705	−0.143353	+	0.989672i	$0.545788\pi$
$578$	44.2641	1.84114
$579$	15.6012	0.648363
$580$	38.2761	1.58933
$581$	8.98617	0.372809
$582$	−35.9388	−1.48971
$583$	−12.9757	−0.537397
$584$	−101.888	−4.21614
$585$	−5.57535	−0.230512
$586$	38.1588	1.57633
$587$	39.2707	1.62087	0.810437	−	0.585826i	$-0.199230\pi$
$587$	39.2707	1.62087	0.810437	+	0.585826i	$0.199230\pi$
$588$	−6.20891	−0.256051
$589$	29.8925	1.23170
$590$	−1.44451	−0.0594694
$591$	−2.53021	−0.104079
$592$	76.6571	3.15059
$593$	−15.6776	−0.643803	−0.321901	−	0.946773i	$-0.604322\pi$
$593$	−15.6776	−0.643803	−0.321901	+	0.946773i	$0.604322\pi$
$594$	−14.6711	−0.601964
$595$	−0.508857	−0.0208611
$596$	−34.3025	−1.40508
$597$	9.19116	0.376169
$598$	12.6565	0.517561
$599$	−45.7991	−1.87130	−0.935650	−	0.352929i	$-0.885186\pi$
$599$	−45.7991	−1.87130	−0.935650	+	0.352929i	$0.885186\pi$
$600$	−28.7328	−1.17301
$601$	−6.99513	−0.285337	−0.142669	−	0.989771i	$-0.545568\pi$
$601$	−6.99513	−0.285337	−0.142669	+	0.989771i	$0.545568\pi$
$602$	3.76195	0.153326
$603$	12.0083	0.489016
$604$	71.7112	2.91789
$605$	−14.1775	−0.576396
$606$	14.6884	0.596677
$607$	26.5766	1.07871	0.539356	−	0.842078i	$-0.318668\pi$
$607$	26.5766	1.07871	0.539356	+	0.842078i	$0.318668\pi$
$608$	−62.5860	−2.53820
$609$	−7.02439	−0.284643
$610$	−18.0626	−0.731335
$611$	−9.04519	−0.365929
$612$	2.42323	0.0979534
$613$	38.4416	1.55264	0.776322	−	0.630337i	$-0.217083\pi$
$613$	38.4416	1.55264	0.776322	+	0.630337i	$0.217083\pi$
$614$	24.4435	0.986458
$615$	−14.2448	−0.574405
$616$	−7.59028	−0.305821
$617$	−31.4730	−1.26705	−0.633527	−	0.773721i	$-0.718393\pi$
$617$	−31.4730	−1.26705	−0.633527	+	0.773721i	$0.718393\pi$
$618$	27.5139	1.10677
$619$	39.5958	1.59149	0.795745	−	0.605631i	$-0.207079\pi$
$619$	39.5958	1.59149	0.795745	+	0.605631i	$0.207079\pi$
$620$	37.4521	1.50411
$621$	−9.46468	−0.379805
$622$	50.9083	2.04124
$623$	11.1380	0.446236
$624$	−36.4085	−1.45751
$625$	−1.13957	−0.0455827
$626$	−19.3452	−0.773192
$627$	−7.05411	−0.281714
$628$	81.7879	3.26369
$629$	−2.72750	−0.108752
$630$	5.14942	0.205158
$631$	43.3957	1.72755	0.863777	−	0.503875i	$-0.168093\pi$
$631$	43.3957	1.72755	0.863777	+	0.503875i	$0.168093\pi$
$632$	−16.3264	−0.649431
$633$	−16.2013	−0.643944
$634$	−35.4075	−1.40621
$635$	−10.9900	−0.436125
$636$	80.2958	3.18393
$637$	2.84063	0.112550
$638$	−14.5435	−0.575783
$639$	16.3862	0.648226
$640$	−3.36977	−0.133202
$641$	−33.7650	−1.33364	−0.666818	−	0.745220i	$-0.732344\pi$
$641$	−33.7650	−1.33364	−0.666818	+	0.745220i	$0.732344\pi$
$642$	68.6034	2.70756
$643$	37.5203	1.47966	0.739829	−	0.672795i	$-0.234906\pi$
$643$	37.5203	1.47966	0.739829	+	0.672795i	$0.234906\pi$
$644$	−8.29312	−0.326795
$645$	2.58639	0.101839
$646$	5.20361	0.204733
$647$	−0.762837	−0.0299902	−0.0149951	−	0.999888i	$-0.504773\pi$
$647$	−0.762837	−0.0299902	−0.0149951	+	0.999888i	$0.504773\pi$
$648$	22.2081	0.872415
$649$	0.389386	0.0152847
$650$	22.2636	0.873250
$651$	−6.87318	−0.269381
$652$	103.833	4.06640
$653$	−24.0453	−0.940963	−0.470482	−	0.882410i	$-0.655920\pi$
$653$	−24.0453	−0.940963	−0.470482	+	0.882410i	$0.655920\pi$
$654$	19.2412	0.752391
$655$	−15.1760	−0.592977
$656$	79.6099	3.10824
$657$	−18.6330	−0.726941
$658$	8.35418	0.325680
$659$	10.7830	0.420046	0.210023	−	0.977696i	$-0.432646\pi$
$659$	10.7830	0.420046	0.210023	+	0.977696i	$0.432646\pi$
$660$	−8.83806	−0.344021
$661$	−27.0293	−1.05132	−0.525660	−	0.850695i	$-0.676181\pi$
$661$	−27.0293	−1.05132	−0.525660	+	0.850695i	$0.676181\pi$
$662$	−75.4149	−2.93108
$663$	1.29543	0.0503104
$664$	−67.9799	−2.63813
$665$	7.84490	0.304212
$666$	27.6011	1.06952
$667$	−9.38235	−0.363286
$668$	70.0064	2.70863
$669$	32.5246	1.25747
$670$	32.3077	1.24815
$671$	4.86902	0.187967
$672$	14.3904	0.555122
$673$	−23.2270	−0.895336	−0.447668	−	0.894200i	$-0.647745\pi$
$673$	−23.2270	−0.895336	−0.447668	+	0.894200i	$0.647745\pi$
$674$	28.5850	1.10105
$675$	−16.6490	−0.640821
$676$	−24.0791	−0.926118
$677$	21.5465	0.828098	0.414049	−	0.910255i	$-0.364114\pi$
$677$	21.5465	0.828098	0.414049	+	0.910255i	$0.364114\pi$
$678$	−35.0152	−1.34475
$679$	−10.7738	−0.413461
$680$	3.84948	0.147621
$681$	0.984507	0.0377264
$682$	−14.2304	−0.544911
$683$	36.8466	1.40990	0.704948	−	0.709259i	$-0.250970\pi$
$683$	36.8466	1.40990	0.704948	+	0.709259i	$0.250970\pi$
$684$	−37.3582	−1.42843
$685$	−21.4446	−0.819357
$686$	−2.62362	−0.100170
$687$	−25.7843	−0.983732
$688$	−14.4546	−0.551076
$689$	−36.7361	−1.39953
$690$	−8.03674	−0.305954
$691$	32.3596	1.23102	0.615508	−	0.788131i	$-0.288951\pi$
$691$	32.3596	1.23102	0.615508	+	0.788131i	$0.288951\pi$
$692$	66.0745	2.51178
$693$	−1.38809	−0.0527293
$694$	95.2663	3.61626
$695$	14.5519	0.551986
$696$	53.1392	2.01423
$697$	−2.83256	−0.107291
$698$	−12.4451	−0.471052
$699$	4.95398	0.187377
$700$	−14.5882	−0.551381
$701$	−10.2804	−0.388286	−0.194143	−	0.980973i	$-0.562193\pi$
$701$	−10.2804	−0.388286	−0.194143	+	0.980973i	$0.562193\pi$
$702$	−41.5362	−1.56768
$703$	42.0490	1.58591
$704$	9.56523	0.360503
$705$	5.74361	0.216317
$706$	−65.1710	−2.45274
$707$	4.40333	0.165604
$708$	−2.40959	−0.0905581
$709$	−2.01430	−0.0756488	−0.0378244	−	0.999284i	$-0.512043\pi$
$709$	−2.01430	−0.0756488	−0.0378244	+	0.999284i	$0.512043\pi$
$710$	44.0861	1.65452
$711$	−2.98574	−0.111974
$712$	−84.2586	−3.15773
$713$	−9.18038	−0.343808
$714$	−1.19647	−0.0447766
$715$	4.04350	0.151218
$716$	−62.8377	−2.34836
$717$	−14.3041	−0.534197
$718$	0.957000	0.0357149
$719$	6.09844	0.227433	0.113717	−	0.993513i	$-0.463724\pi$
$719$	6.09844	0.227433	0.113717	+	0.993513i	$0.463724\pi$
$720$	−19.7857	−0.737368
$721$	8.24817	0.307178
$722$	−30.3737	−1.13039
$723$	−16.7109	−0.621483
$724$	−59.3620	−2.20617
$725$	−16.5042	−0.612950
$726$	−33.3352	−1.23719
$727$	16.2330	0.602049	0.301024	−	0.953616i	$-0.402671\pi$
$727$	16.2330	0.602049	0.301024	+	0.953616i	$0.402671\pi$
$728$	−21.4892	−0.796445
$729$	25.3195	0.937758
$730$	−50.1310	−1.85543
$731$	0.514301	0.0190221
$732$	−30.1304	−1.11365
$733$	−29.7793	−1.09992	−0.549961	−	0.835190i	$-0.685357\pi$
$733$	−29.7793	−1.09992	−0.549961	+	0.835190i	$0.685357\pi$
$734$	43.9711	1.62300
$735$	−1.80378	−0.0665333
$736$	19.2210	0.708495
$737$	−8.70897	−0.320799
$738$	28.6643	1.05515
$739$	24.2669	0.892671	0.446335	−	0.894866i	$-0.352729\pi$
$739$	24.2669	0.892671	0.446335	+	0.894866i	$0.352729\pi$
$740$	52.6830	1.93666
$741$	−19.9713	−0.733663
$742$	33.9296	1.24560
$743$	−12.6911	−0.465593	−0.232797	−	0.972525i	$-0.574788\pi$
$743$	−12.6911	−0.465593	−0.232797	+	0.972525i	$0.574788\pi$
$744$	51.9953	1.90624
$745$	−9.96537	−0.365103
$746$	−13.0578	−0.478080
$747$	−12.4320	−0.454864
$748$	−1.75744	−0.0642583
$749$	20.5661	0.751467
$750$	−37.7993	−1.38024
$751$	0.551230	0.0201147	0.0100573	−	0.999949i	$-0.496799\pi$
$751$	0.551230	0.0201147	0.0100573	+	0.999949i	$0.496799\pi$
$752$	−32.0994	−1.17054
$753$	−26.0438	−0.949090
$754$	−41.1749	−1.49950
$755$	20.8331	0.758196
$756$	27.2165	0.989855
$757$	14.1085	0.512784	0.256392	−	0.966573i	$-0.417466\pi$
$757$	14.1085	0.512784	0.256392	+	0.966573i	$0.417466\pi$
$758$	11.6298	0.422414
$759$	2.16641	0.0786357
$760$	−59.3462	−2.15271
$761$	7.29511	0.264448	0.132224	−	0.991220i	$-0.457788\pi$
$761$	7.29511	0.264448	0.132224	+	0.991220i	$0.457788\pi$
$762$	−25.8406	−0.936106
$763$	5.76817	0.208822
$764$	22.4062	0.810626
$765$	0.703984	0.0254526
$766$	−1.94506	−0.0702779
$767$	1.10241	0.0398058
$768$	16.3186	0.588846
$769$	38.3516	1.38300	0.691498	−	0.722379i	$-0.256951\pi$
$769$	38.3516	1.38300	0.691498	+	0.722379i	$0.256951\pi$
$770$	−3.73459	−0.134585
$771$	37.4300	1.34801
$772$	−59.9220	−2.15664
$773$	−7.46079	−0.268346	−0.134173	−	0.990958i	$-0.542838\pi$
$773$	−7.46079	−0.268346	−0.134173	+	0.990958i	$0.542838\pi$
$774$	−5.20451	−0.187072
$775$	−16.1489	−0.580086
$776$	81.5033	2.92580
$777$	−9.66833	−0.346849
$778$	−52.0413	−1.86577
$779$	43.6687	1.56459
$780$	−25.0219	−0.895928
$781$	−11.8840	−0.425242
$782$	−1.59810	−0.0571479
$783$	30.7911	1.10039
$784$	10.0808	0.360028
$785$	23.7606	0.848051
$786$	−35.6832	−1.27278
$787$	−42.7412	−1.52356	−0.761779	−	0.647837i	$-0.775674\pi$
$787$	−42.7412	−1.52356	−0.761779	+	0.647837i	$0.775674\pi$
$788$	9.71821	0.346197
$789$	38.6669	1.37658
$790$	−8.03298	−0.285801
$791$	−10.4969	−0.373228
$792$	10.5009	0.373132
$793$	13.7849	0.489518
$794$	2.46872	0.0876117
$795$	23.3271	0.827326
$796$	−35.3020	−1.25125
$797$	24.8675	0.880852	0.440426	−	0.897789i	$-0.354827\pi$
$797$	24.8675	0.880852	0.440426	+	0.897789i	$0.354827\pi$
$798$	18.4456	0.652966
$799$	1.14211	0.0404050
$800$	33.8110	1.19540
$801$	−15.4090	−0.544451
$802$	−71.1181	−2.51127
$803$	13.5135	0.476880
$804$	53.8927	1.90065
$805$	−2.40927	−0.0849156
$806$	−40.2885	−1.41910
$807$	−2.44511	−0.0860720
$808$	−33.3109	−1.17187
$809$	−35.2861	−1.24059	−0.620296	−	0.784368i	$-0.712988\pi$
$809$	−35.2861	−1.24059	−0.620296	+	0.784368i	$0.712988\pi$
$810$	10.9269	0.383931
$811$	52.0766	1.82866	0.914329	−	0.404972i	$-0.132719\pi$
$811$	52.0766	1.82866	0.914329	+	0.404972i	$0.132719\pi$
$812$	26.9797	0.946803
$813$	10.8935	0.382052
$814$	−20.0176	−0.701616
$815$	30.1649	1.05663
$816$	4.59720	0.160934
$817$	−7.92883	−0.277395
$818$	−16.9402	−0.592301
$819$	−3.92991	−0.137322
$820$	54.7123	1.91064
$821$	27.5507	0.961526	0.480763	−	0.876851i	$-0.340360\pi$
$821$	27.5507	0.961526	0.480763	+	0.876851i	$0.340360\pi$
$822$	−50.4224	−1.75868
$823$	−18.6228	−0.649149	−0.324574	−	0.945860i	$-0.605221\pi$
$823$	−18.6228	−0.649149	−0.324574	+	0.945860i	$0.605221\pi$
$824$	−62.3970	−2.17370
$825$	3.81086	0.132677
$826$	−1.01819	−0.0354275
$827$	−41.2752	−1.43528	−0.717639	−	0.696415i	$-0.754777\pi$
$827$	−41.2752	−1.43528	−0.717639	+	0.696415i	$0.754777\pi$
$828$	11.4732	0.398721
$829$	−41.5670	−1.44368	−0.721841	−	0.692059i	$-0.756704\pi$
$829$	−41.5670	−1.44368	−0.721841	+	0.692059i	$0.756704\pi$
$830$	−33.4477	−1.16099
$831$	15.3469	0.532378
$832$	27.0806	0.938851
$833$	−0.358679	−0.0124275
$834$	34.2157	1.18479
$835$	20.3379	0.703821
$836$	27.0939	0.937062
$837$	30.1283	1.04139
$838$	−1.75753	−0.0607129
$839$	25.6470	0.885434	0.442717	−	0.896661i	$-0.354015\pi$
$839$	25.6470	0.885434	0.442717	+	0.896661i	$0.354015\pi$
$840$	13.6455	0.470814
$841$	1.52329	0.0525272
$842$	−20.2314	−0.697221
$843$	31.0406	1.06910
$844$	62.2270	2.14194
$845$	−6.99531	−0.240646
$846$	−11.5577	−0.397361
$847$	−9.99329	−0.343374
$848$	−130.368	−4.47686
$849$	−1.76458	−0.0605602
$850$	−2.81116	−0.0964221
$851$	−12.9138	−0.442679
$852$	73.5403	2.51945
$853$	26.0641	0.892416	0.446208	−	0.894929i	$-0.352774\pi$
$853$	26.0641	0.892416	0.446208	+	0.894929i	$0.352774\pi$
$854$	−12.7318	−0.435675
$855$	−10.8531	−0.371168
$856$	−155.581	−5.31765
$857$	−36.3613	−1.24208	−0.621039	−	0.783780i	$-0.713289\pi$
$857$	−36.3613	−1.24208	−0.621039	+	0.783780i	$0.713289\pi$
$858$	9.50740	0.324577
$859$	−30.8138	−1.05135	−0.525677	−	0.850684i	$-0.676188\pi$
$859$	−30.8138	−1.05135	−0.525677	+	0.850684i	$0.676188\pi$
$860$	−9.93399	−0.338746
$861$	−10.0407	−0.342188
$862$	16.2794	0.554480
$863$	−1.00000	−0.0340404
$863$	−1.00000	−0.0340404
$864$	−63.0798	−2.14602
$865$	19.1956	0.652670
$866$	−70.9077	−2.40954
$867$	21.4508	0.728506
$868$	26.3990	0.896039
$869$	2.16540	0.0734560
$870$	26.1457	0.886422
$871$	−24.6564	−0.835451
$872$	−43.6359	−1.47770
$873$	14.9051	0.504463
$874$	24.6374	0.833372
$875$	−11.3316	−0.383077
$876$	−83.6239	−2.82539
$877$	−23.5148	−0.794037	−0.397019	−	0.917811i	$-0.629955\pi$
$877$	−23.5148	−0.794037	−0.397019	+	0.917811i	$0.629955\pi$
$878$	−20.1642	−0.680510
$879$	18.4921	0.623723
$880$	14.3495	0.483720
$881$	43.2880	1.45841	0.729206	−	0.684295i	$-0.239890\pi$
$881$	43.2880	1.45841	0.729206	+	0.684295i	$0.239890\pi$
$882$	3.62968	0.122218
$883$	53.1004	1.78697	0.893485	−	0.449092i	$-0.148253\pi$
$883$	53.1004	1.78697	0.893485	+	0.449092i	$0.148253\pi$
$884$	−4.97558	−0.167347
$885$	−0.700022	−0.0235310
$886$	9.67074	0.324895
$887$	15.4190	0.517719	0.258859	−	0.965915i	$-0.416653\pi$
$887$	15.4190	0.517719	0.258859	+	0.965915i	$0.416653\pi$
$888$	73.1404	2.45443
$889$	−7.74654	−0.259811
$890$	−41.4572	−1.38965
$891$	−2.94548	−0.0986774
$892$	−124.922	−4.18271
$893$	−17.6076	−0.589215
$894$	−23.4314	−0.783663
$895$	−18.2553	−0.610206
$896$	−2.37526	−0.0793518
$897$	6.13344	0.204790
$898$	−23.4288	−0.781830
$899$	29.8662	0.996094
$900$	20.1822	0.672738
$901$	4.63856	0.154533
$902$	−20.7886	−0.692186
$903$	1.82308	0.0606682
$904$	79.4088	2.64110
$905$	−17.2455	−0.573261
$906$	48.9846	1.62740
$907$	33.3959	1.10889	0.554447	−	0.832219i	$-0.312930\pi$
$907$	33.3959	1.10889	0.554447	+	0.832219i	$0.312930\pi$
$908$	−3.78136	−0.125489
$909$	−6.09183	−0.202053
$910$	−10.5732	−0.350498
$911$	46.6324	1.54500	0.772501	−	0.635014i	$-0.219006\pi$
$911$	46.6324	1.54500	0.772501	+	0.635014i	$0.219006\pi$
$912$	−70.8736	−2.34686
$913$	9.01627	0.298395
$914$	−43.5339	−1.43997
$915$	−8.75332	−0.289376
$916$	99.0340	3.27218
$917$	−10.6972	−0.353252
$918$	5.24466	0.173100
$919$	−1.44613	−0.0477035	−0.0238518	−	0.999716i	$-0.507593\pi$
$919$	−1.44613	−0.0477035	−0.0238518	+	0.999716i	$0.507593\pi$
$920$	18.2260	0.600894
$921$	11.8455	0.390323
$922$	−83.3302	−2.74433
$923$	−33.6454	−1.10745
$924$	−6.22970	−0.204942
$925$	−22.7163	−0.746906
$926$	24.6825	0.811118
$927$	−11.4110	−0.374787
$928$	−62.5310	−2.05268
$929$	−2.65734	−0.0871846	−0.0435923	−	0.999049i	$-0.513880\pi$
$929$	−2.65734	−0.0871846	−0.0435923	+	0.999049i	$0.513880\pi$
$930$	25.5829	0.838895
$931$	5.52965	0.181227
$932$	−19.0276	−0.623269
$933$	24.6707	0.807681
$934$	91.3360	2.98861
$935$	−0.510561	−0.0166971
$936$	29.7295	0.971740
$937$	0.769474	0.0251376	0.0125688	−	0.999921i	$-0.495999\pi$
$937$	0.769474	0.0251376	0.0125688	+	0.999921i	$0.495999\pi$
$938$	22.7728	0.743558
$939$	−9.37489	−0.305938
$940$	−22.0604	−0.719532
$941$	−37.8046	−1.23239	−0.616197	−	0.787592i	$-0.711328\pi$
$941$	−37.8046	−1.23239	−0.616197	+	0.787592i	$0.711328\pi$
$942$	55.8678	1.82027
$943$	−13.4112	−0.436730
$944$	3.91221	0.127332
$945$	7.90679	0.257208
$946$	3.77455	0.122721
$947$	0.244560	0.00794712	0.00397356	−	0.999992i	$-0.498735\pi$
$947$	0.244560	0.00794712	0.00397356	+	0.999992i	$0.498735\pi$
$948$	−13.3999	−0.435208
$949$	38.2587	1.24193
$950$	43.3388	1.40610
$951$	−17.1588	−0.556412
$952$	2.71339	0.0879414
$953$	−37.9064	−1.22791	−0.613955	−	0.789341i	$-0.710422\pi$
$953$	−37.9064	−1.22791	−0.613955	+	0.789341i	$0.710422\pi$
$954$	−46.9403	−1.51975
$955$	6.50931	0.210636
$956$	54.9401	1.77689
$957$	−7.04792	−0.227827
$958$	−57.2943	−1.85109
$959$	−15.1157	−0.488112
$960$	−17.1959	−0.554997
$961$	−1.77669	−0.0573126
$962$	−56.6729	−1.82721
$963$	−28.4523	−0.916864
$964$	64.1841	2.06723
$965$	−17.4082	−0.560390
$966$	−5.66487	−0.182264
$967$	−4.93632	−0.158741	−0.0793707	−	0.996845i	$-0.525291\pi$
$967$	−4.93632	−0.158741	−0.0793707	+	0.996845i	$0.525291\pi$
$968$	75.5987	2.42984
$969$	2.52172	0.0810093
$970$	40.1015	1.28758
$971$	46.5158	1.49276	0.746381	−	0.665519i	$-0.231790\pi$
$971$	46.5158	1.49276	0.746381	+	0.665519i	$0.231790\pi$
$972$	−63.4223	−2.03427
$973$	10.2572	0.328832
$974$	−98.7835	−3.16523
$975$	10.7891	0.345529
$976$	48.9197	1.56588
$977$	23.0833	0.738499	0.369250	−	0.929330i	$-0.379615\pi$
$977$	23.0833	0.738499	0.369250	+	0.929330i	$0.379615\pi$
$978$	70.9261	2.26797
$979$	11.1753	0.357165
$980$	6.92806	0.221309
$981$	−7.98003	−0.254783
$982$	26.6011	0.848877
$983$	4.63684	0.147892	0.0739461	−	0.997262i	$-0.476441\pi$
$983$	4.63684	0.147892	0.0739461	+	0.997262i	$0.476441\pi$
$984$	75.9577	2.42144
$985$	2.82328	0.0899572
$986$	5.19904	0.165571
$987$	4.04851	0.128866
$988$	76.7070	2.44037
$989$	2.43505	0.0774300
$990$	5.16666	0.164207
$991$	−49.5792	−1.57494	−0.787468	−	0.616356i	$-0.788608\pi$
$991$	−49.5792	−1.57494	−0.787468	+	0.616356i	$0.788608\pi$
$992$	−61.1849	−1.94262
$993$	−36.5468	−1.15978
$994$	31.0750	0.985640
$995$	−10.2557	−0.325129
$996$	−55.7943	−1.76791
$997$	−38.6510	−1.22409	−0.612045	−	0.790823i	$-0.709653\pi$
$997$	−38.6510	−1.22409	−0.612045	+	0.790823i	$0.709653\pi$
$998$	15.5700	0.492859
$999$	42.3808	1.34087

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6041.2.a.f.1.7	✓	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6041.2.a.f.1.7	✓	132	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:	\( N \)	\(=\)	\( 6041 = 7 \cdot 863 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.62362 q^{2} -1.27143 q^{3} +4.88340 q^{4} +1.41870 q^{5} +3.33576 q^{6} +1.00000 q^{7} -7.56495 q^{8} -1.38346 q^{9} +O(q^{10})\)	\(q-2.62362 q^{2} -1.27143 q^{3} +4.88340 q^{4} +1.41870 q^{5} +3.33576 q^{6} +1.00000 q^{7} -7.56495 q^{8} -1.38346 q^{9} -3.72213 q^{10} +1.00335 q^{11} -6.20891 q^{12} +2.84063 q^{13} -2.62362 q^{14} -1.80378 q^{15} +10.0808 q^{16} -0.358679 q^{17} +3.62968 q^{18} +5.52965 q^{19} +6.92806 q^{20} -1.27143 q^{21} -2.63241 q^{22} -1.69823 q^{23} +9.61832 q^{24} -2.98730 q^{25} -7.45275 q^{26} +5.57327 q^{27} +4.88340 q^{28} +5.52479 q^{29} +4.73243 q^{30} +5.40586 q^{31} -11.3183 q^{32} -1.27569 q^{33} +0.941039 q^{34} +1.41870 q^{35} -6.75599 q^{36} +7.60429 q^{37} -14.5077 q^{38} -3.61167 q^{39} -10.7324 q^{40} +7.89719 q^{41} +3.33576 q^{42} -1.43388 q^{43} +4.89975 q^{44} -1.96271 q^{45} +4.45551 q^{46} -3.18421 q^{47} -12.8170 q^{48} +1.00000 q^{49} +7.83754 q^{50} +0.456036 q^{51} +13.8719 q^{52} -12.9323 q^{53} -14.6222 q^{54} +1.42345 q^{55} -7.56495 q^{56} -7.03057 q^{57} -14.4950 q^{58} +0.388087 q^{59} -8.80856 q^{60} +4.85277 q^{61} -14.1829 q^{62} -1.38346 q^{63} +9.53330 q^{64} +4.03000 q^{65} +3.34693 q^{66} -8.67990 q^{67} -1.75157 q^{68} +2.15918 q^{69} -3.72213 q^{70} -11.8443 q^{71} +10.4658 q^{72} +13.4684 q^{73} -19.9508 q^{74} +3.79815 q^{75} +27.0035 q^{76} +1.00335 q^{77} +9.47567 q^{78} +2.15817 q^{79} +14.3016 q^{80} -2.93565 q^{81} -20.7193 q^{82} +8.98617 q^{83} -6.20891 q^{84} -0.508857 q^{85} +3.76195 q^{86} -7.02439 q^{87} -7.59028 q^{88} +11.1380 q^{89} +5.14942 q^{90} +2.84063 q^{91} -8.29312 q^{92} -6.87318 q^{93} +8.35418 q^{94} +7.84490 q^{95} +14.3904 q^{96} -10.7738 q^{97} -2.62362 q^{98} -1.38809 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 8 q^{2} + 10 q^{3} + 174 q^{4} + 11 q^{5} + 16 q^{6} + 132 q^{7} + 30 q^{8} + 178 q^{9}+O(q^{10}) \) 132 * q + 8 * q^2 + 10 * q^3 + 174 * q^4 + 11 * q^5 + 16 * q^6 + 132 * q^7 + 30 * q^8 + 178 * q^9	\( 132 q + 8 q^{2} + 10 q^{3} + 174 q^{4} + 11 q^{5} + 16 q^{6} + 132 q^{7} + 30 q^{8} + 178 q^{9} + 22 q^{10} + 32 q^{11} + 30 q^{12} + 16 q^{13} + 8 q^{14} + 59 q^{15} + 254 q^{16} + 11 q^{17} + 33 q^{18} + 40 q^{19} + 4 q^{20} + 10 q^{21} + 66 q^{22} + 62 q^{23} + 36 q^{24} + 235 q^{25} + 25 q^{26} + 37 q^{27} + 174 q^{28} + 28 q^{29} + 45 q^{30} + 121 q^{31} + 53 q^{32} - 13 q^{33} + 44 q^{34} + 11 q^{35} + 274 q^{36} + 61 q^{37} - 28 q^{38} + 114 q^{39} + 32 q^{40} - q^{41} + 16 q^{42} + 105 q^{43} + 54 q^{44} + 29 q^{45} + 104 q^{46} + 33 q^{47} + 16 q^{48} + 132 q^{49} - 14 q^{50} + 53 q^{51} - 11 q^{52} + 48 q^{53} + 11 q^{54} + 118 q^{55} + 30 q^{56} + 93 q^{57} + 87 q^{58} + 12 q^{59} + 41 q^{60} + 54 q^{61} - 28 q^{62} + 178 q^{63} + 376 q^{64} + 22 q^{65} + 6 q^{66} + 123 q^{67} - 47 q^{68} + 58 q^{69} + 22 q^{70} + 108 q^{71} + 97 q^{72} + q^{73} - 10 q^{74} + 23 q^{75} + 71 q^{76} + 32 q^{77} + 5 q^{78} + 204 q^{79} - 10 q^{80} + 296 q^{81} + 80 q^{82} - 10 q^{83} + 30 q^{84} + 94 q^{85} + 48 q^{86} + 4 q^{87} + 155 q^{88} + q^{89} - 66 q^{90} + 16 q^{91} + 49 q^{92} + 90 q^{93} + 79 q^{94} + 100 q^{95} + q^{96} + 18 q^{97} + 8 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q + 8 * q^2 + 10 * q^3 + 174 * q^4 + 11 * q^5 + 16 * q^6 + 132 * q^7 + 30 * q^8 + 178 * q^9 + 22 * q^10 + 32 * q^11 + 30 * q^12 + 16 * q^13 + 8 * q^14 + 59 * q^15 + 254 * q^16 + 11 * q^17 + 33 * q^18 + 40 * q^19 + 4 * q^20 + 10 * q^21 + 66 * q^22 + 62 * q^23 + 36 * q^24 + 235 * q^25 + 25 * q^26 + 37 * q^27 + 174 * q^28 + 28 * q^29 + 45 * q^30 + 121 * q^31 + 53 * q^32 - 13 * q^33 + 44 * q^34 + 11 * q^35 + 274 * q^36 + 61 * q^37 - 28 * q^38 + 114 * q^39 + 32 * q^40 - q^41 + 16 * q^42 + 105 * q^43 + 54 * q^44 + 29 * q^45 + 104 * q^46 + 33 * q^47 + 16 * q^48 + 132 * q^49 - 14 * q^50 + 53 * q^51 - 11 * q^52 + 48 * q^53 + 11 * q^54 + 118 * q^55 + 30 * q^56 + 93 * q^57 + 87 * q^58 + 12 * q^59 + 41 * q^60 + 54 * q^61 - 28 * q^62 + 178 * q^63 + 376 * q^64 + 22 * q^65 + 6 * q^66 + 123 * q^67 - 47 * q^68 + 58 * q^69 + 22 * q^70 + 108 * q^71 + 97 * q^72 + q^73 - 10 * q^74 + 23 * q^75 + 71 * q^76 + 32 * q^77 + 5 * q^78 + 204 * q^79 - 10 * q^80 + 296 * q^81 + 80 * q^82 - 10 * q^83 + 30 * q^84 + 94 * q^85 + 48 * q^86 + 4 * q^87 + 155 * q^88 + q^89 - 66 * q^90 + 16 * q^91 + 49 * q^92 + 90 * q^93 + 79 * q^94 + 100 * q^95 + q^96 + 18 * q^97 + 8 * q^98 + 96 * q^99

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