LMFDB - Embedded newform 7381.2.a.l.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7381,2,Mod(1,7381)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7381, 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("7381.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7381 = 11^{2} \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7381.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:	$58.9375817319$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	7381.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.933034 q^{2} +0.244187 q^{3} -1.12945 q^{4} -1.38011 q^{5} +0.227834 q^{6} +4.47715 q^{7} -2.91988 q^{8} -2.94037 q^{9} +O(q^{10})$	\(q+0.933034 q^{2} +0.244187 q^{3} -1.12945 q^{4} -1.38011 q^{5} +0.227834 q^{6} +4.47715 q^{7} -2.91988 q^{8} -2.94037 q^{9} -1.28769 q^{10} -0.275796 q^{12} -3.28313 q^{13} +4.17733 q^{14} -0.337004 q^{15} -0.465450 q^{16} +4.80044 q^{17} -2.74347 q^{18} -4.66648 q^{19} +1.55876 q^{20} +1.09326 q^{21} -5.54639 q^{23} -0.712996 q^{24} -3.09530 q^{25} -3.06327 q^{26} -1.45056 q^{27} -5.05671 q^{28} -0.148189 q^{29} -0.314436 q^{30} +6.11172 q^{31} +5.40548 q^{32} +4.47897 q^{34} -6.17895 q^{35} +3.32100 q^{36} +3.43147 q^{37} -4.35398 q^{38} -0.801697 q^{39} +4.02975 q^{40} -4.62730 q^{41} +1.02005 q^{42} +4.15262 q^{43} +4.05804 q^{45} -5.17497 q^{46} +7.71527 q^{47} -0.113657 q^{48} +13.0448 q^{49} -2.88802 q^{50} +1.17220 q^{51} +3.70813 q^{52} +1.58839 q^{53} -1.35342 q^{54} -13.0727 q^{56} -1.13949 q^{57} -0.138266 q^{58} +4.86290 q^{59} +0.380629 q^{60} -1.00000 q^{61} +5.70244 q^{62} -13.1645 q^{63} +5.97439 q^{64} +4.53108 q^{65} +0.456794 q^{67} -5.42185 q^{68} -1.35435 q^{69} -5.76517 q^{70} -12.6725 q^{71} +8.58554 q^{72} -13.6593 q^{73} +3.20168 q^{74} -0.755831 q^{75} +5.27055 q^{76} -0.748010 q^{78} +0.677972 q^{79} +0.642372 q^{80} +8.46691 q^{81} -4.31743 q^{82} +13.5258 q^{83} -1.23478 q^{84} -6.62513 q^{85} +3.87454 q^{86} -0.0361858 q^{87} -2.17593 q^{89} +3.78628 q^{90} -14.6991 q^{91} +6.26436 q^{92} +1.49240 q^{93} +7.19861 q^{94} +6.44025 q^{95} +1.31995 q^{96} +11.1898 q^{97} +12.1713 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 5 q^{2} - 2 q^{3} + 27 q^{4} - 4 q^{5} + 12 q^{6} + 6 q^{7} + 9 q^{8} + 26 q^{9}+O(q^{10}) $ 24 * q + 5 * q^2 - 2 * q^3 + 27 * q^4 - 4 * q^5 + 12 * q^6 + 6 * q^7 + 9 * q^8 + 26 * q^9	\( 24 q + 5 q^{2} - 2 q^{3} + 27 q^{4} - 4 q^{5} + 12 q^{6} + 6 q^{7} + 9 q^{8} + 26 q^{9} + 12 q^{10} + q^{12} + 3 q^{13} - q^{14} - 5 q^{15} + 17 q^{16} + 8 q^{17} + 20 q^{18} + 8 q^{19} + 16 q^{20} + 11 q^{21} + 2 q^{23} + q^{24} + 4 q^{25} + 4 q^{26} + 13 q^{27} - 7 q^{28} + 43 q^{29} + 30 q^{30} - 4 q^{31} + 23 q^{32} + 31 q^{35} - 35 q^{36} - 4 q^{37} - 13 q^{38} + 11 q^{39} + 57 q^{40} + 29 q^{41} + 48 q^{42} + 10 q^{43} - 10 q^{45} - 14 q^{46} - 13 q^{47} + 42 q^{48} + 26 q^{49} - 6 q^{50} + 56 q^{51} + 25 q^{52} - 15 q^{53} + 35 q^{54} - 9 q^{56} - 3 q^{57} - 84 q^{58} - 13 q^{59} + 34 q^{60} - 24 q^{61} + 55 q^{62} + 22 q^{63} + 61 q^{64} + 41 q^{65} - q^{67} - 4 q^{68} - 27 q^{69} + 55 q^{70} - 6 q^{71} + 22 q^{72} + 18 q^{73} + 28 q^{74} + 47 q^{75} + 36 q^{76} - 10 q^{78} + 9 q^{79} - 40 q^{80} + 40 q^{81} + 15 q^{82} + 10 q^{83} + 93 q^{84} - 9 q^{85} + 38 q^{86} + 51 q^{87} - 17 q^{89} - 44 q^{90} - 22 q^{91} + 11 q^{92} + 32 q^{93} - 47 q^{94} + 54 q^{95} + 44 q^{96} - q^{97} + 45 q^{98}+O(q^{100}) \) 24 * q + 5 * q^2 - 2 * q^3 + 27 * q^4 - 4 * q^5 + 12 * q^6 + 6 * q^7 + 9 * q^8 + 26 * q^9 + 12 * q^10 + q^12 + 3 * q^13 - q^14 - 5 * q^15 + 17 * q^16 + 8 * q^17 + 20 * q^18 + 8 * q^19 + 16 * q^20 + 11 * q^21 + 2 * q^23 + q^24 + 4 * q^25 + 4 * q^26 + 13 * q^27 - 7 * q^28 + 43 * q^29 + 30 * q^30 - 4 * q^31 + 23 * q^32 + 31 * q^35 - 35 * q^36 - 4 * q^37 - 13 * q^38 + 11 * q^39 + 57 * q^40 + 29 * q^41 + 48 * q^42 + 10 * q^43 - 10 * q^45 - 14 * q^46 - 13 * q^47 + 42 * q^48 + 26 * q^49 - 6 * q^50 + 56 * q^51 + 25 * q^52 - 15 * q^53 + 35 * q^54 - 9 * q^56 - 3 * q^57 - 84 * q^58 - 13 * q^59 + 34 * q^60 - 24 * q^61 + 55 * q^62 + 22 * q^63 + 61 * q^64 + 41 * q^65 - q^67 - 4 * q^68 - 27 * q^69 + 55 * q^70 - 6 * q^71 + 22 * q^72 + 18 * q^73 + 28 * q^74 + 47 * q^75 + 36 * q^76 - 10 * q^78 + 9 * q^79 - 40 * q^80 + 40 * q^81 + 15 * q^82 + 10 * q^83 + 93 * q^84 - 9 * q^85 + 38 * q^86 + 51 * q^87 - 17 * q^89 - 44 * q^90 - 22 * q^91 + 11 * q^92 + 32 * q^93 - 47 * q^94 + 54 * q^95 + 44 * q^96 - q^97 + 45 * q^98

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 $

$2$	0.933034	0.659754	0.329877	−	0.944024i	$-0.392993\pi$
$2$	0.933034	0.659754	0.329877	+	0.944024i	$0.392993\pi$
$3$	0.244187	0.140981	0.0704906	−	0.997512i	$-0.477544\pi$
$3$	0.244187	0.140981	0.0704906	+	0.997512i	$0.477544\pi$
$4$	−1.12945	−0.564724
$5$	−1.38011	−0.617204	−0.308602	−	0.951191i	$-0.599861\pi$
$5$	−1.38011	−0.617204	−0.308602	+	0.951191i	$0.599861\pi$
$6$	0.227834	0.0930130
$7$	4.47715	1.69220	0.846101	−	0.533022i	$-0.178944\pi$
$7$	4.47715	1.69220	0.846101	+	0.533022i	$0.178944\pi$
$8$	−2.91988	−1.03233
$9$	−2.94037	−0.980124
$10$	−1.28769	−0.407203
$11$	0	0
$11$	0	0
$12$	−0.275796	−0.0796155
$13$	−3.28313	−0.910577	−0.455288	−	0.890344i	$-0.650464\pi$
$13$	−3.28313	−0.910577	−0.455288	+	0.890344i	$0.650464\pi$
$14$	4.17733	1.11644
$15$	−0.337004	−0.0870142
$16$	−0.465450	−0.116363
$17$	4.80044	1.16428	0.582139	−	0.813089i	$-0.302216\pi$
$17$	4.80044	1.16428	0.582139	+	0.813089i	$0.302216\pi$
$18$	−2.74347	−0.646641
$19$	−4.66648	−1.07056	−0.535282	−	0.844673i	$-0.679795\pi$
$19$	−4.66648	−1.07056	−0.535282	+	0.844673i	$0.679795\pi$
$20$	1.55876	0.348550
$21$	1.09326	0.238569
$22$	0	0
$23$	−5.54639	−1.15650	−0.578251	−	0.815859i	$-0.696265\pi$
$23$	−5.54639	−1.15650	−0.578251	+	0.815859i	$0.696265\pi$
$24$	−0.712996	−0.145540
$25$	−3.09530	−0.619060
$26$	−3.06327	−0.600757
$27$	−1.45056	−0.279160
$28$	−5.05671	−0.955628
$29$	−0.148189	−0.0275180	−0.0137590	−	0.999905i	$-0.504380\pi$
$29$	−0.148189	−0.0275180	−0.0137590	+	0.999905i	$0.504380\pi$
$30$	−0.314436	−0.0574080
$31$	6.11172	1.09770	0.548849	−	0.835921i	$-0.315066\pi$
$31$	6.11172	1.09770	0.548849	+	0.835921i	$0.315066\pi$
$32$	5.40548	0.955563
$33$	0	0
$34$	4.47897	0.768137
$35$	−6.17895	−1.04443
$36$	3.32100	0.553500
$37$	3.43147	0.564130	0.282065	−	0.959395i	$-0.408981\pi$
$37$	3.43147	0.564130	0.282065	+	0.959395i	$0.408981\pi$
$38$	−4.35398	−0.706309
$39$	−0.801697	−0.128374
$40$	4.02975	0.637160
$41$	−4.62730	−0.722663	−0.361331	−	0.932437i	$-0.617678\pi$
$41$	−4.62730	−0.722663	−0.361331	+	0.932437i	$0.617678\pi$
$42$	1.02005	0.157397
$43$	4.15262	0.633269	0.316634	−	0.948548i	$-0.397447\pi$
$43$	4.15262	0.633269	0.316634	+	0.948548i	$0.397447\pi$
$44$	0	0
$45$	4.05804	0.604936
$46$	−5.17497	−0.763007
$47$	7.71527	1.12539	0.562694	−	0.826665i	$-0.309765\pi$
$47$	7.71527	1.12539	0.562694	+	0.826665i	$0.309765\pi$
$48$	−0.113657	−0.0164049
$49$	13.0448	1.86355
$50$	−2.88802	−0.408427
$51$	1.17220	0.164141
$52$	3.70813	0.514225
$53$	1.58839	0.218182	0.109091	−	0.994032i	$-0.465206\pi$
$53$	1.58839	0.218182	0.109091	+	0.994032i	$0.465206\pi$
$54$	−1.35342	−0.184177
$55$	0	0
$56$	−13.0727	−1.74692
$57$	−1.13949	−0.150929
$58$	−0.138266	−0.0181552
$59$	4.86290	0.633095	0.316548	−	0.948577i	$-0.397476\pi$
$59$	4.86290	0.633095	0.316548	+	0.948577i	$0.397476\pi$
$60$	0.380629	0.0491390
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	5.70244	0.724211
$63$	−13.1645	−1.65857
$64$	5.97439	0.746799
$65$	4.53108	0.562011
$66$	0	0
$67$	0.456794	0.0558063	0.0279032	−	0.999611i	$-0.491117\pi$
$67$	0.456794	0.0558063	0.0279032	+	0.999611i	$0.491117\pi$
$68$	−5.42185	−0.657496
$69$	−1.35435	−0.163045
$70$	−5.76517	−0.689070
$71$	−12.6725	−1.50395	−0.751973	−	0.659194i	$-0.770898\pi$
$71$	−12.6725	−1.50395	−0.751973	+	0.659194i	$0.770898\pi$
$72$	8.58554	1.01182
$73$	−13.6593	−1.59870	−0.799352	−	0.600863i	$-0.794824\pi$
$73$	−13.6593	−1.59870	−0.799352	+	0.600863i	$0.794824\pi$
$74$	3.20168	0.372187
$75$	−0.755831	−0.0872758
$76$	5.27055	0.604573
$77$	0	0
$78$	−0.748010	−0.0846955
$79$	0.677972	0.0762778	0.0381389	−	0.999272i	$-0.487857\pi$
$79$	0.677972	0.0762778	0.0381389	+	0.999272i	$0.487857\pi$
$80$	0.642372	0.0718194
$81$	8.46691	0.940768
$82$	−4.31743	−0.476780
$83$	13.5258	1.48465	0.742325	−	0.670040i	$-0.233723\pi$
$83$	13.5258	1.48465	0.742325	+	0.670040i	$0.233723\pi$
$84$	−1.23478	−0.134726
$85$	−6.62513	−0.718596
$86$	3.87454	0.417802
$87$	−0.0361858	−0.00387953
$88$	0	0
$89$	−2.17593	−0.230648	−0.115324	−	0.993328i	$-0.536791\pi$
$89$	−2.17593	−0.230648	−0.115324	+	0.993328i	$0.536791\pi$
$90$	3.78628	0.399109
$91$	−14.6991	−1.54088
$92$	6.26436	0.653105
$93$	1.49240	0.154755
$94$	7.19861	0.742480
$95$	6.44025	0.660756
$96$	1.31995	0.134717
$97$	11.1898	1.13615	0.568077	−	0.822975i	$-0.307687\pi$
$97$	11.1898	1.13615	0.568077	+	0.822975i	$0.307687\pi$
$98$	12.1713	1.22949
$99$	0	0
$100$	3.49598	0.349598
$101$	16.5342	1.64522	0.822608	−	0.568609i	$-0.192518\pi$
$101$	16.5342	1.64522	0.822608	+	0.568609i	$0.192518\pi$
$102$	1.09371	0.108293
$103$	19.9238	1.96315	0.981574	−	0.191085i	$-0.0612006\pi$
$103$	19.9238	1.96315	0.981574	+	0.191085i	$0.0612006\pi$
$104$	9.58635	0.940019
$105$	−1.50882	−0.147246
$106$	1.48202	0.143947
$107$	2.20721	0.213379	0.106689	−	0.994292i	$-0.465975\pi$
$107$	2.20721	0.213379	0.106689	+	0.994292i	$0.465975\pi$
$108$	1.63833	0.157649
$109$	−5.80459	−0.555978	−0.277989	−	0.960584i	$-0.589668\pi$
$109$	−5.80459	−0.555978	−0.277989	+	0.960584i	$0.589668\pi$
$110$	0	0
$111$	0.837919	0.0795318
$112$	−2.08389	−0.196909
$113$	7.17258	0.674739	0.337370	−	0.941372i	$-0.390463\pi$
$113$	7.17258	0.674739	0.337370	+	0.941372i	$0.390463\pi$
$114$	−1.06319	−0.0995764
$115$	7.65462	0.713797
$116$	0.167372	0.0155401
$117$	9.65363	0.892478
$118$	4.53725	0.417687
$119$	21.4923	1.97019
$120$	0.984013	0.0898276
$121$	0	0
$122$	−0.933034	−0.0844729
$123$	−1.12993	−0.101882
$124$	−6.90288	−0.619897
$125$	11.1724	0.999289
$126$	−12.2829	−1.09425
$127$	−20.5325	−1.82197	−0.910983	−	0.412444i	$-0.864675\pi$
$127$	−20.5325	−1.82197	−0.910983	+	0.412444i	$0.864675\pi$
$128$	−5.23665	−0.462859
$129$	1.01402	0.0892791
$130$	4.22765	0.370789
$131$	−10.7539	−0.939571	−0.469786	−	0.882781i	$-0.655669\pi$
$131$	−10.7539	−0.939571	−0.469786	+	0.882781i	$0.655669\pi$
$132$	0	0
$133$	−20.8925	−1.81161
$134$	0.426204	0.0368185
$135$	2.00193	0.172299
$136$	−14.0167	−1.20192
$137$	0.673567	0.0575467	0.0287733	−	0.999586i	$-0.490840\pi$
$137$	0.673567	0.0575467	0.0287733	+	0.999586i	$0.490840\pi$
$138$	−1.26366	−0.107570
$139$	18.8140	1.59578	0.797891	−	0.602802i	$-0.205949\pi$
$139$	18.8140	1.59578	0.797891	+	0.602802i	$0.205949\pi$
$140$	6.97881	0.589817
$141$	1.88397	0.158659
$142$	−11.8238	−0.992235
$143$	0	0
$144$	1.36860	0.114050
$145$	0.204517	0.0169842
$146$	−12.7446	−1.05475
$147$	3.18538	0.262726
$148$	−3.87567	−0.318578
$149$	−15.1132	−1.23812	−0.619060	−	0.785343i	$-0.712486\pi$
$149$	−15.1132	−1.23812	−0.619060	+	0.785343i	$0.712486\pi$
$150$	−0.705216	−0.0575806
$151$	−3.97243	−0.323272	−0.161636	−	0.986850i	$-0.551677\pi$
$151$	−3.97243	−0.323272	−0.161636	+	0.986850i	$0.551677\pi$
$152$	13.6256	1.10518
$153$	−14.1151	−1.14114
$154$	0	0
$155$	−8.43485	−0.677503
$156$	0.905475	0.0724961
$157$	−8.78898	−0.701437	−0.350719	−	0.936481i	$-0.614063\pi$
$157$	−8.78898	−0.701437	−0.350719	+	0.936481i	$0.614063\pi$
$158$	0.632571	0.0503246
$159$	0.387864	0.0307596
$160$	−7.46015	−0.589777
$161$	−24.8320	−1.95704
$162$	7.89991	0.620676
$163$	4.49408	0.352004	0.176002	−	0.984390i	$-0.443684\pi$
$163$	4.49408	0.352004	0.176002	+	0.984390i	$0.443684\pi$
$164$	5.22630	0.408105
$165$	0	0
$166$	12.6200	0.979504
$167$	21.9270	1.69677	0.848383	−	0.529383i	$-0.177577\pi$
$167$	21.9270	1.69677	0.848383	+	0.529383i	$0.177577\pi$
$168$	−3.19219	−0.246283
$169$	−2.22105	−0.170850
$170$	−6.18147	−0.474097
$171$	13.7212	1.04929
$172$	−4.69017	−0.357622
$173$	−8.55065	−0.650094	−0.325047	−	0.945698i	$-0.605380\pi$
$173$	−8.55065	−0.650094	−0.325047	+	0.945698i	$0.605380\pi$
$174$	−0.0337626	−0.00255954
$175$	−13.8581	−1.04757
$176$	0	0
$177$	1.18746	0.0892546
$178$	−2.03021	−0.152171
$179$	22.9432	1.71485	0.857426	−	0.514608i	$-0.172062\pi$
$179$	22.9432	1.71485	0.857426	+	0.514608i	$0.172062\pi$
$180$	−4.58334	−0.341622
$181$	7.21049	0.535951	0.267976	−	0.963426i	$-0.413645\pi$
$181$	7.21049	0.535951	0.267976	+	0.963426i	$0.413645\pi$
$182$	−13.7147	−1.01660
$183$	−0.244187	−0.0180508
$184$	16.1948	1.19390
$185$	−4.73580	−0.348183
$186$	1.39246	0.102100
$187$	0	0
$188$	−8.71400	−0.635534
$189$	−6.49437	−0.472396
$190$	6.00897	0.435937
$191$	−13.2300	−0.957287	−0.478643	−	0.878009i	$-0.658871\pi$
$191$	−13.2300	−0.957287	−0.478643	+	0.878009i	$0.658871\pi$
$192$	1.45887	0.105285
$193$	16.5218	1.18926	0.594632	−	0.803998i	$-0.297298\pi$
$193$	16.5218	1.18926	0.594632	+	0.803998i	$0.297298\pi$
$194$	10.4405	0.749583
$195$	1.10643	0.0792331
$196$	−14.7335	−1.05239
$197$	25.0464	1.78448	0.892241	−	0.451559i	$-0.149132\pi$
$197$	25.0464	1.78448	0.892241	+	0.451559i	$0.149132\pi$
$198$	0	0
$199$	−14.9242	−1.05795	−0.528973	−	0.848639i	$-0.677423\pi$
$199$	−14.9242	−1.05795	−0.528973	+	0.848639i	$0.677423\pi$
$200$	9.03790	0.639076
$201$	0.111543	0.00786764
$202$	15.4270	1.08544
$203$	−0.663465	−0.0465661
$204$	−1.32394	−0.0926946
$205$	6.38618	0.446030
$206$	18.5895	1.29519
$207$	16.3084	1.13352
$208$	1.52813	0.105957
$209$	0	0
$210$	−1.40778	−0.0971459
$211$	18.8797	1.29973	0.649866	−	0.760049i	$-0.274825\pi$
$211$	18.8797	1.29973	0.649866	+	0.760049i	$0.274825\pi$
$212$	−1.79400	−0.123213
$213$	−3.09445	−0.212028
$214$	2.05940	0.140778
$215$	−5.73107	−0.390856
$216$	4.23546	0.288187
$217$	27.3631	1.85753
$218$	−5.41587	−0.366809
$219$	−3.33543	−0.225387
$220$	0	0
$221$	−15.7605	−1.06016
$222$	0.781807	0.0524714
$223$	13.4441	0.900286	0.450143	−	0.892956i	$-0.351373\pi$
$223$	13.4441	0.900286	0.450143	+	0.892956i	$0.351373\pi$
$224$	24.2011	1.61701
$225$	9.10133	0.606755
$226$	6.69225	0.445162
$227$	−6.06435	−0.402505	−0.201252	−	0.979539i	$-0.564501\pi$
$227$	−6.06435	−0.402505	−0.201252	+	0.979539i	$0.564501\pi$
$228$	1.28700	0.0852335
$229$	−3.18934	−0.210757	−0.105379	−	0.994432i	$-0.533605\pi$
$229$	−3.18934	−0.210757	−0.105379	+	0.994432i	$0.533605\pi$
$230$	7.14202	0.470931
$231$	0	0
$232$	0.432695	0.0284078
$233$	−6.57966	−0.431048	−0.215524	−	0.976499i	$-0.569146\pi$
$233$	−6.57966	−0.431048	−0.215524	+	0.976499i	$0.569146\pi$
$234$	9.00716	0.588817
$235$	−10.6479	−0.694593
$236$	−5.49239	−0.357524
$237$	0.165552	0.0107537
$238$	20.0530	1.29984
$239$	13.8196	0.893912	0.446956	−	0.894556i	$-0.352508\pi$
$239$	13.8196	0.893912	0.446956	+	0.894556i	$0.352508\pi$
$240$	0.156859	0.0101252
$241$	4.60018	0.296324	0.148162	−	0.988963i	$-0.452664\pi$
$241$	4.60018	0.296324	0.148162	+	0.988963i	$0.452664\pi$
$242$	0	0
$243$	6.41919	0.411791
$244$	1.12945	0.0723055
$245$	−18.0033	−1.15019
$246$	−1.05426	−0.0672171
$247$	15.3207	0.974831
$248$	−17.8455	−1.13319
$249$	3.30282	0.209308
$250$	10.4242	0.659286
$251$	16.5208	1.04279	0.521393	−	0.853317i	$-0.325413\pi$
$251$	16.5208	1.04279	0.521393	+	0.853317i	$0.325413\pi$
$252$	14.8686	0.936634
$253$	0	0
$254$	−19.1575	−1.20205
$255$	−1.61777	−0.101309
$256$	−16.8348	−1.05217
$257$	−2.57342	−0.160526	−0.0802628	−	0.996774i	$-0.525576\pi$
$257$	−2.57342	−0.160526	−0.0802628	+	0.996774i	$0.525576\pi$
$258$	0.946110	0.0589023
$259$	15.3632	0.954622
$260$	−5.11762	−0.317381
$261$	0.435732	0.0269711
$262$	−10.0337	−0.619886
$263$	−10.5405	−0.649958	−0.324979	−	0.945721i	$-0.605357\pi$
$263$	−10.5405	−0.649958	−0.324979	+	0.945721i	$0.605357\pi$
$264$	0	0
$265$	−2.19215	−0.134663
$266$	−19.4934	−1.19522
$267$	−0.531332	−0.0325170
$268$	−0.515925	−0.0315152
$269$	6.26056	0.381713	0.190857	−	0.981618i	$-0.438873\pi$
$269$	6.26056	0.381713	0.190857	+	0.981618i	$0.438873\pi$
$270$	1.86787	0.113675
$271$	30.0820	1.82735	0.913675	−	0.406446i	$-0.133232\pi$
$271$	30.0820	1.82735	0.913675	+	0.406446i	$0.133232\pi$
$272$	−2.23436	−0.135478
$273$	−3.58932	−0.217235
$274$	0.628460	0.0379667
$275$	0	0
$276$	1.52967	0.0920755
$277$	0.834158	0.0501197	0.0250598	−	0.999686i	$-0.492022\pi$
$277$	0.834158	0.0501197	0.0250598	+	0.999686i	$0.492022\pi$
$278$	17.5541	1.05282
$279$	−17.9707	−1.07588
$280$	18.0418	1.07820
$281$	22.1834	1.32335	0.661676	−	0.749789i	$-0.269845\pi$
$281$	22.1834	1.32335	0.661676	+	0.749789i	$0.269845\pi$
$282$	1.75780	0.104676
$283$	−2.88128	−0.171274	−0.0856372	−	0.996326i	$-0.527293\pi$
$283$	−2.88128	−0.171274	−0.0856372	+	0.996326i	$0.527293\pi$
$284$	14.3129	0.849315
$285$	1.57262	0.0931542
$286$	0	0
$287$	−20.7171	−1.22289
$288$	−15.8941	−0.936570
$289$	6.04421	0.355542
$290$	0.190822	0.0112054
$291$	2.73241	0.160177
$292$	15.4275	0.902827
$293$	24.4317	1.42732	0.713658	−	0.700495i	$-0.247037\pi$
$293$	24.4317	1.42732	0.713658	+	0.700495i	$0.247037\pi$
$294$	2.97207	0.173334
$295$	−6.71133	−0.390749
$296$	−10.0195	−0.582370
$297$	0	0
$298$	−14.1011	−0.816856
$299$	18.2095	1.05308
$300$	0.853672	0.0492868
$301$	18.5919	1.07162
$302$	−3.70641	−0.213280
$303$	4.03743	0.231945
$304$	2.17201	0.124574
$305$	1.38011	0.0790248
$306$	−13.1698	−0.752870
$307$	−24.1282	−1.37707	−0.688534	−	0.725204i	$-0.741745\pi$
$307$	−24.1282	−1.37707	−0.688534	+	0.725204i	$0.741745\pi$
$308$	0	0
$309$	4.86512	0.276767
$310$	−7.87000	−0.446986
$311$	−29.8651	−1.69349	−0.846747	−	0.531996i	$-0.821442\pi$
$311$	−29.8651	−1.69349	−0.846747	+	0.531996i	$0.821442\pi$
$312$	2.34086	0.132525
$313$	8.51520	0.481307	0.240654	−	0.970611i	$-0.422638\pi$
$313$	8.51520	0.481307	0.240654	+	0.970611i	$0.422638\pi$
$314$	−8.20042	−0.462776
$315$	18.1684	1.02367
$316$	−0.765734	−0.0430759
$317$	18.7613	1.05374	0.526870	−	0.849946i	$-0.323366\pi$
$317$	18.7613	1.05374	0.526870	+	0.849946i	$0.323366\pi$
$318$	0.361890	0.0202938
$319$	0	0
$320$	−8.24532	−0.460927
$321$	0.538971	0.0300824
$322$	−23.1691	−1.29116
$323$	−22.4012	−1.24643
$324$	−9.56294	−0.531274
$325$	10.1623	0.563701
$326$	4.19313	0.232236
$327$	−1.41740	−0.0783826
$328$	13.5112	0.746029
$329$	34.5424	1.90438
$330$	0	0
$331$	−31.9965	−1.75869	−0.879343	−	0.476190i	$-0.842018\pi$
$331$	−31.9965	−1.75869	−0.879343	+	0.476190i	$0.842018\pi$
$332$	−15.2767	−0.838418
$333$	−10.0898	−0.552917
$334$	20.4587	1.11945
$335$	−0.630426	−0.0344438
$336$	−0.508858	−0.0277605
$337$	7.66496	0.417537	0.208768	−	0.977965i	$-0.433055\pi$
$337$	7.66496	0.417537	0.208768	+	0.977965i	$0.433055\pi$
$338$	−2.07231	−0.112719
$339$	1.75145	0.0951256
$340$	7.48274	0.405809
$341$	0	0
$342$	12.8023	0.692271
$343$	27.0637	1.46130
$344$	−12.1252	−0.653745
$345$	1.86916	0.100632
$346$	−7.97805	−0.428903
$347$	−9.82527	−0.527448	−0.263724	−	0.964598i	$-0.584951\pi$
$347$	−9.82527	−0.527448	−0.263724	+	0.964598i	$0.584951\pi$
$348$	0.0408700	0.00219086
$349$	22.0005	1.17766	0.588830	−	0.808257i	$-0.299589\pi$
$349$	22.0005	1.17766	0.588830	+	0.808257i	$0.299589\pi$
$350$	−12.9301	−0.691142
$351$	4.76238	0.254197
$352$	0	0
$353$	−2.69665	−0.143528	−0.0717641	−	0.997422i	$-0.522863\pi$
$353$	−2.69665	−0.143528	−0.0717641	+	0.997422i	$0.522863\pi$
$354$	1.10794	0.0588861
$355$	17.4894	0.928241
$356$	2.45760	0.130252
$357$	5.24813	0.277760
$358$	21.4067	1.13138
$359$	−7.08835	−0.374109	−0.187054	−	0.982350i	$-0.559894\pi$
$359$	−7.08835	−0.374109	−0.187054	+	0.982350i	$0.559894\pi$
$360$	−11.8490	−0.624496
$361$	2.77604	0.146107
$362$	6.72762	0.353596
$363$	0	0
$364$	16.6018	0.870172
$365$	18.8514	0.986726
$366$	−0.227834	−0.0119091
$367$	30.0528	1.56875	0.784373	−	0.620290i	$-0.212985\pi$
$367$	30.0528	1.56875	0.784373	+	0.620290i	$0.212985\pi$
$368$	2.58157	0.134573
$369$	13.6060	0.708299
$370$	−4.41866	−0.229715
$371$	7.11145	0.369208
$372$	−1.68559	−0.0873938
$373$	23.0912	1.19562	0.597808	−	0.801639i	$-0.296038\pi$
$373$	23.0912	1.19562	0.597808	+	0.801639i	$0.296038\pi$
$374$	0	0
$375$	2.72815	0.140881
$376$	−22.5277	−1.16178
$377$	0.486525	0.0250573
$378$	−6.05947	−0.311665
$379$	−11.1329	−0.571858	−0.285929	−	0.958251i	$-0.592302\pi$
$379$	−11.1329	−0.571858	−0.285929	+	0.958251i	$0.592302\pi$
$380$	−7.27393	−0.373145
$381$	−5.01377	−0.256863
$382$	−12.3440	−0.631574
$383$	−17.8548	−0.912338	−0.456169	−	0.889893i	$-0.650779\pi$
$383$	−17.8548	−0.912338	−0.456169	+	0.889893i	$0.650779\pi$
$384$	−1.27872	−0.0652544
$385$	0	0
$386$	15.4154	0.784622
$387$	−12.2103	−0.620682
$388$	−12.6383	−0.641614
$389$	36.6023	1.85581	0.927906	−	0.372815i	$-0.121607\pi$
$389$	36.6023	1.85581	0.927906	+	0.372815i	$0.121607\pi$
$390$	1.03234	0.0522744
$391$	−26.6251	−1.34649
$392$	−38.0894	−1.92381
$393$	−2.62596	−0.132462
$394$	23.3691	1.17732
$395$	−0.935675	−0.0470789
$396$	0	0
$397$	15.0892	0.757307	0.378653	−	0.925539i	$-0.376387\pi$
$397$	15.0892	0.757307	0.378653	+	0.925539i	$0.376387\pi$
$398$	−13.9247	−0.697984
$399$	−5.10168	−0.255403
$400$	1.44071	0.0720353
$401$	−18.8866	−0.943150	−0.471575	−	0.881826i	$-0.656314\pi$
$401$	−18.8866	−0.943150	−0.471575	+	0.881826i	$0.656314\pi$
$402$	0.104073	0.00519071
$403$	−20.0656	−0.999538
$404$	−18.6745	−0.929093
$405$	−11.6853	−0.580645
$406$	−0.619035	−0.0307222
$407$	0	0
$408$	−3.42269	−0.169449
$409$	19.2551	0.952101	0.476051	−	0.879418i	$-0.342068\pi$
$409$	19.2551	0.952101	0.476051	+	0.879418i	$0.342068\pi$
$410$	5.95852	0.294270
$411$	0.164476	0.00811300
$412$	−22.5029	−1.10864
$413$	21.7719	1.07133
$414$	15.2163	0.747842
$415$	−18.6671	−0.916331
$416$	−17.7469	−0.870113
$417$	4.59413	0.224975
$418$	0	0
$419$	9.09958	0.444544	0.222272	−	0.974985i	$-0.428653\pi$
$419$	9.09958	0.444544	0.222272	+	0.974985i	$0.428653\pi$
$420$	1.70413	0.0831531
$421$	−27.2060	−1.32594	−0.662968	−	0.748647i	$-0.730704\pi$
$421$	−27.2060	−1.32594	−0.662968	+	0.748647i	$0.730704\pi$
$422$	17.6154	0.857504
$423$	−22.6858	−1.10302
$424$	−4.63791	−0.225237
$425$	−14.8588	−0.720757
$426$	−2.88723	−0.139887
$427$	−4.47715	−0.216664
$428$	−2.49293	−0.120500
$429$	0	0
$430$	−5.34728	−0.257869
$431$	−20.4941	−0.987167	−0.493583	−	0.869699i	$-0.664313\pi$
$431$	−20.4941	−0.987167	−0.493583	+	0.869699i	$0.664313\pi$
$432$	0.675163	0.0324838
$433$	−17.0762	−0.820632	−0.410316	−	0.911943i	$-0.634582\pi$
$433$	−17.0762	−0.820632	−0.410316	+	0.911943i	$0.634582\pi$
$434$	25.5307	1.22551
$435$	0.0499404	0.00239446
$436$	6.55598	0.313974
$437$	25.8821	1.23811
$438$	−3.11207	−0.148700
$439$	17.6859	0.844104	0.422052	−	0.906572i	$-0.361310\pi$
$439$	17.6859	0.844104	0.422052	+	0.906572i	$0.361310\pi$
$440$	0	0
$441$	−38.3567	−1.82651
$442$	−14.7050	−0.699448
$443$	31.5402	1.49852	0.749261	−	0.662275i	$-0.230409\pi$
$443$	31.5402	1.49852	0.749261	+	0.662275i	$0.230409\pi$
$444$	−0.946386	−0.0449135
$445$	3.00302	0.142357
$446$	12.5438	0.593968
$447$	−3.69044	−0.174552
$448$	26.7482	1.26374
$449$	14.2815	0.673988	0.336994	−	0.941507i	$-0.390590\pi$
$449$	14.2815	0.673988	0.336994	+	0.941507i	$0.390590\pi$
$450$	8.49185	0.400310
$451$	0	0
$452$	−8.10105	−0.381042
$453$	−0.970016	−0.0455753
$454$	−5.65824	−0.265554
$455$	20.2863	0.951037
$456$	3.32718	0.155810
$457$	−5.22152	−0.244252	−0.122126	−	0.992515i	$-0.538971\pi$
$457$	−5.22152	−0.244252	−0.122126	+	0.992515i	$0.538971\pi$
$458$	−2.97576	−0.139048
$459$	−6.96333	−0.325020
$460$	−8.64550	−0.403098
$461$	26.2946	1.22466	0.612331	−	0.790602i	$-0.290232\pi$
$461$	26.2946	1.22466	0.612331	+	0.790602i	$0.290232\pi$
$462$	0	0
$463$	22.6835	1.05419	0.527096	−	0.849806i	$-0.323281\pi$
$463$	22.6835	1.05419	0.527096	+	0.849806i	$0.323281\pi$
$464$	0.0689747	0.00320207
$465$	−2.05968	−0.0955153
$466$	−6.13905	−0.284386
$467$	6.35831	0.294228	0.147114	−	0.989120i	$-0.453002\pi$
$467$	6.35831	0.294228	0.147114	+	0.989120i	$0.453002\pi$
$468$	−10.9033	−0.504004
$469$	2.04514	0.0944356
$470$	−9.93486	−0.458261
$471$	−2.14615	−0.0988895
$472$	−14.1991	−0.653566
$473$	0	0
$474$	0.154465	0.00709483
$475$	14.4442	0.662743
$476$	−24.2744	−1.11262
$477$	−4.67046	−0.213846
$478$	12.8941	0.589763
$479$	4.58446	0.209469	0.104735	−	0.994500i	$-0.466601\pi$
$479$	4.58446	0.209469	0.104735	+	0.994500i	$0.466601\pi$
$480$	−1.82167	−0.0831475
$481$	−11.2660	−0.513684
$482$	4.29212	0.195501
$483$	−6.06364	−0.275905
$484$	0	0
$485$	−15.4432	−0.701239
$486$	5.98932	0.271681
$487$	29.8861	1.35427	0.677134	−	0.735860i	$-0.263222\pi$
$487$	29.8861	1.35427	0.677134	+	0.735860i	$0.263222\pi$
$488$	2.91988	0.132177
$489$	1.09740	0.0496259
$490$	−16.7977	−0.758843
$491$	23.7665	1.07257	0.536283	−	0.844038i	$-0.319828\pi$
$491$	23.7665	1.07257	0.536283	+	0.844038i	$0.319828\pi$
$492$	1.27619	0.0575352
$493$	−0.711373	−0.0320386
$494$	14.2947	0.643149
$495$	0	0
$496$	−2.84470	−0.127731
$497$	−56.7365	−2.54498
$498$	3.08164	0.138092
$499$	16.7604	0.750297	0.375148	−	0.926965i	$-0.377592\pi$
$499$	16.7604	0.750297	0.375148	+	0.926965i	$0.377592\pi$
$500$	−12.6186	−0.564323
$501$	5.35429	0.239212
$502$	15.4145	0.687982
$503$	−9.07226	−0.404512	−0.202256	−	0.979333i	$-0.564827\pi$
$503$	−9.07226	−0.404512	−0.202256	+	0.979333i	$0.564827\pi$
$504$	38.4387	1.71220
$505$	−22.8190	−1.01543
$506$	0	0
$507$	−0.542351	−0.0240867
$508$	23.1904	1.02891
$509$	−14.9348	−0.661974	−0.330987	−	0.943635i	$-0.607382\pi$
$509$	−14.9348	−0.661974	−0.330987	+	0.943635i	$0.607382\pi$
$510$	−1.50943	−0.0668388
$511$	−61.1548	−2.70533
$512$	−5.23410	−0.231317
$513$	6.76901	0.298859
$514$	−2.40109	−0.105907
$515$	−27.4970	−1.21166
$516$	−1.14528	−0.0504180
$517$	0	0
$518$	14.3344	0.629816
$519$	−2.08796	−0.0916511
$520$	−13.2302	−0.580183
$521$	18.6596	0.817490	0.408745	−	0.912649i	$-0.365966\pi$
$521$	18.6596	0.817490	0.408745	+	0.912649i	$0.365966\pi$
$522$	0.406552	0.0177943
$523$	−12.4402	−0.543971	−0.271985	−	0.962301i	$-0.587680\pi$
$523$	−12.4402	−0.543971	−0.271985	+	0.962301i	$0.587680\pi$
$524$	12.1460	0.530598
$525$	−3.38397	−0.147688
$526$	−9.83468	−0.428813
$527$	29.3390	1.27803
$528$	0	0
$529$	7.76242	0.337497
$530$	−2.04535	−0.0888444
$531$	−14.2987	−0.620512
$532$	23.5970	1.02306
$533$	15.1920	0.658040
$534$	−0.495751	−0.0214532
$535$	−3.04619	−0.131698
$536$	−1.33378	−0.0576107
$537$	5.60241	0.241762
$538$	5.84132	0.251837
$539$	0	0
$540$	−2.26108	−0.0973013
$541$	−42.7815	−1.83932	−0.919661	−	0.392714i	$-0.871536\pi$
$541$	−42.7815	−1.83932	−0.919661	+	0.392714i	$0.871536\pi$
$542$	28.0675	1.20560
$543$	1.76070	0.0755591
$544$	25.9487	1.11254
$545$	8.01096	0.343152
$546$	−3.34895	−0.143322
$547$	−27.7867	−1.18808	−0.594038	−	0.804437i	$-0.702467\pi$
$547$	−27.7867	−1.18808	−0.594038	+	0.804437i	$0.702467\pi$
$548$	−0.760759	−0.0324980
$549$	2.94037	0.125492
$550$	0	0
$551$	0.691522	0.0294598
$552$	3.95455	0.168317
$553$	3.03538	0.129078
$554$	0.778297	0.0330667
$555$	−1.15642	−0.0490873
$556$	−21.2494	−0.901176
$557$	23.3758	0.990463	0.495231	−	0.868761i	$-0.335083\pi$
$557$	23.3758	0.990463	0.495231	+	0.868761i	$0.335083\pi$
$558$	−16.7673	−0.709817
$559$	−13.6336	−0.576640
$560$	2.87599	0.121533
$561$	0	0
$562$	20.6979	0.873088
$563$	5.75581	0.242578	0.121289	−	0.992617i	$-0.461297\pi$
$563$	5.75581	0.242578	0.121289	+	0.992617i	$0.461297\pi$
$564$	−2.12784	−0.0895984
$565$	−9.89894	−0.416451
$566$	−2.68833	−0.112999
$567$	37.9076	1.59197
$568$	37.0021	1.55257
$569$	−38.2631	−1.60407	−0.802036	−	0.597276i	$-0.796250\pi$
$569$	−38.2631	−1.60407	−0.802036	+	0.597276i	$0.796250\pi$
$570$	1.46731	0.0614589
$571$	4.39036	0.183731	0.0918654	−	0.995771i	$-0.470717\pi$
$571$	4.39036	0.183731	0.0918654	+	0.995771i	$0.470717\pi$
$572$	0	0
$573$	−3.23058	−0.134960
$574$	−19.3298	−0.806808
$575$	17.1677	0.715944
$576$	−17.5669	−0.731956
$577$	−32.7400	−1.36299	−0.681493	−	0.731825i	$-0.738669\pi$
$577$	−32.7400	−1.36299	−0.681493	+	0.731825i	$0.738669\pi$
$578$	5.63945	0.234570
$579$	4.03440	0.167664
$580$	−0.230992	−0.00959141
$581$	60.5570	2.51233
$582$	2.54943	0.105677
$583$	0	0
$584$	39.8836	1.65040
$585$	−13.3231	−0.550841
$586$	22.7956	0.941678
$587$	−38.4380	−1.58651	−0.793253	−	0.608893i	$-0.791614\pi$
$587$	−38.4380	−1.58651	−0.793253	+	0.608893i	$0.791614\pi$
$588$	−3.59772	−0.148368
$589$	−28.5202	−1.17516
$590$	−6.26190	−0.257798
$591$	6.11600	0.251579
$592$	−1.59718	−0.0656436
$593$	13.5538	0.556590	0.278295	−	0.960496i	$-0.410231\pi$
$593$	13.5538	0.556590	0.278295	+	0.960496i	$0.410231\pi$
$594$	0	0
$595$	−29.6617	−1.21601
$596$	17.0696	0.699197
$597$	−3.64428	−0.149151
$598$	16.9901	0.694777
$599$	−2.85600	−0.116693	−0.0583465	−	0.998296i	$-0.518583\pi$
$599$	−2.85600	−0.116693	−0.0583465	+	0.998296i	$0.518583\pi$
$600$	2.20694	0.0900978
$601$	39.2074	1.59930	0.799652	−	0.600464i	$-0.205017\pi$
$601$	39.2074	1.59930	0.799652	+	0.600464i	$0.205017\pi$
$602$	17.3469	0.707006
$603$	−1.34315	−0.0546971
$604$	4.48666	0.182560
$605$	0	0
$606$	3.76706	0.153026
$607$	−3.04304	−0.123513	−0.0617566	−	0.998091i	$-0.519670\pi$
$607$	−3.04304	−0.123513	−0.0617566	+	0.998091i	$0.519670\pi$
$608$	−25.2246	−1.02299
$609$	−0.162009	−0.00656495
$610$	1.28769	0.0521370
$611$	−25.3302	−1.02475
$612$	15.9423	0.644427
$613$	−18.7949	−0.759117	−0.379559	−	0.925168i	$-0.623924\pi$
$613$	−18.7949	−0.759117	−0.379559	+	0.925168i	$0.623924\pi$
$614$	−22.5124	−0.908526
$615$	1.55942	0.0628819
$616$	0	0
$617$	7.84270	0.315735	0.157868	−	0.987460i	$-0.449538\pi$
$617$	7.84270	0.315735	0.157868	+	0.987460i	$0.449538\pi$
$618$	4.53932	0.182598
$619$	−36.6241	−1.47205	−0.736023	−	0.676957i	$-0.763298\pi$
$619$	−36.6241	−1.47205	−0.736023	+	0.676957i	$0.763298\pi$
$620$	9.52672	0.382602
$621$	8.04537	0.322850
$622$	−27.8651	−1.11729
$623$	−9.74194	−0.390303
$624$	0.373150	0.0149380
$625$	0.0573676	0.00229470
$626$	7.94497	0.317545
$627$	0	0
$628$	9.92670	0.396119
$629$	16.4726	0.656804
$630$	16.9517	0.675374
$631$	6.78809	0.270230	0.135115	−	0.990830i	$-0.456860\pi$
$631$	6.78809	0.270230	0.135115	+	0.990830i	$0.456860\pi$
$632$	−1.97960	−0.0787442
$633$	4.61017	0.183238
$634$	17.5049	0.695209
$635$	28.3371	1.12452
$636$	−0.438072	−0.0173707
$637$	−42.8279	−1.69691
$638$	0	0
$639$	37.2618	1.47405
$640$	7.22715	0.285678
$641$	−13.2070	−0.521646	−0.260823	−	0.965387i	$-0.583994\pi$
$641$	−13.2070	−0.521646	−0.260823	+	0.965387i	$0.583994\pi$
$642$	0.502878	0.0198470
$643$	−27.7811	−1.09558	−0.547791	−	0.836615i	$-0.684531\pi$
$643$	−27.7811	−1.09558	−0.547791	+	0.836615i	$0.684531\pi$
$644$	28.0465	1.10519
$645$	−1.39945	−0.0551034
$646$	−20.9010	−0.822340
$647$	−8.52081	−0.334988	−0.167494	−	0.985873i	$-0.553567\pi$
$647$	−8.52081	−0.334988	−0.167494	+	0.985873i	$0.553567\pi$
$648$	−24.7224	−0.971186
$649$	0	0
$650$	9.48174	0.371904
$651$	6.68170	0.261877
$652$	−5.07583	−0.198785
$653$	−0.646840	−0.0253128	−0.0126564	−	0.999920i	$-0.504029\pi$
$653$	−0.646840	−0.0253128	−0.0126564	+	0.999920i	$0.504029\pi$
$654$	−1.32248	−0.0517132
$655$	14.8415	0.579907
$656$	2.15378	0.0840909
$657$	40.1635	1.56693
$658$	32.2292	1.25643
$659$	17.4642	0.680308	0.340154	−	0.940370i	$-0.389521\pi$
$659$	17.4642	0.680308	0.340154	+	0.940370i	$0.389521\pi$
$660$	0	0
$661$	8.57228	0.333423	0.166712	−	0.986006i	$-0.446685\pi$
$661$	8.57228	0.333423	0.166712	+	0.986006i	$0.446685\pi$
$662$	−29.8538	−1.16030
$663$	−3.84850	−0.149463
$664$	−39.4937	−1.53265
$665$	28.8340	1.11813
$666$	−9.41412	−0.364790
$667$	0.821915	0.0318247
$668$	−24.7655	−0.958205
$669$	3.28288	0.126924
$670$	−0.588209	−0.0227245
$671$	0	0
$672$	5.90960	0.227968
$673$	24.1228	0.929864	0.464932	−	0.885346i	$-0.346079\pi$
$673$	24.1228	0.929864	0.464932	+	0.885346i	$0.346079\pi$
$674$	7.15166	0.275472
$675$	4.48992	0.172817
$676$	2.50856	0.0964831
$677$	37.3493	1.43545	0.717726	−	0.696326i	$-0.245183\pi$
$677$	37.3493	1.43545	0.717726	+	0.696326i	$0.245183\pi$
$678$	1.63416	0.0627595
$679$	50.0985	1.92260
$680$	19.3446	0.741831
$681$	−1.48083	−0.0567457
$682$	0	0
$683$	−17.4491	−0.667669	−0.333835	−	0.942632i	$-0.608343\pi$
$683$	−17.4491	−0.667669	−0.333835	+	0.942632i	$0.608343\pi$
$684$	−15.4974	−0.592557
$685$	−0.929595	−0.0355180
$686$	25.2513	0.964100
$687$	−0.778794	−0.0297128
$688$	−1.93284	−0.0736888
$689$	−5.21489	−0.198672
$690$	1.74399	0.0663924
$691$	−22.4902	−0.855566	−0.427783	−	0.903881i	$-0.640705\pi$
$691$	−22.4902	−0.855566	−0.427783	+	0.903881i	$0.640705\pi$
$692$	9.65752	0.367124
$693$	0	0
$694$	−9.16731	−0.347986
$695$	−25.9653	−0.984922
$696$	0.105658	0.00400497
$697$	−22.2131	−0.841380
$698$	20.5272	0.776966
$699$	−1.60667	−0.0607697
$700$	15.6520	0.591591
$701$	−28.6456	−1.08193	−0.540965	−	0.841045i	$-0.681941\pi$
$701$	−28.6456	−1.08193	−0.540965	+	0.841045i	$0.681941\pi$
$702$	4.44346	0.167708
$703$	−16.0129	−0.603937
$704$	0	0
$705$	−2.60008	−0.0979247
$706$	−2.51606	−0.0946933
$707$	74.0261	2.78404
$708$	−1.34117	−0.0504042
$709$	6.45477	0.242414	0.121207	−	0.992627i	$-0.461324\pi$
$709$	6.45477	0.242414	0.121207	+	0.992627i	$0.461324\pi$
$710$	16.3182	0.612411
$711$	−1.99349	−0.0747617
$712$	6.35344	0.238105
$713$	−33.8980	−1.26949
$714$	4.89668	0.183254
$715$	0	0
$716$	−25.9131	−0.968418
$717$	3.37455	0.126025
$718$	−6.61367	−0.246820
$719$	−23.6768	−0.882994	−0.441497	−	0.897263i	$-0.645552\pi$
$719$	−23.6768	−0.882994	−0.441497	+	0.897263i	$0.645552\pi$
$720$	−1.88881	−0.0703919
$721$	89.2016	3.32204
$722$	2.59014	0.0963949
$723$	1.12330	0.0417761
$724$	−8.14387	−0.302665
$725$	0.458690	0.0170353
$726$	0	0
$727$	−20.6645	−0.766405	−0.383203	−	0.923664i	$-0.625179\pi$
$727$	−20.6645	−0.766405	−0.383203	+	0.923664i	$0.625179\pi$
$728$	42.9195	1.59070
$729$	−23.8333	−0.882713
$730$	17.5890	0.650997
$731$	19.9344	0.737301
$732$	0.275796	0.0101937
$733$	−22.3971	−0.827254	−0.413627	−	0.910446i	$-0.635738\pi$
$733$	−22.3971	−0.827254	−0.413627	+	0.910446i	$0.635738\pi$
$734$	28.0403	1.03499
$735$	−4.39617	−0.162155
$736$	−29.9809	−1.10511
$737$	0	0
$738$	12.6948	0.467304
$739$	−6.88503	−0.253270	−0.126635	−	0.991949i	$-0.540418\pi$
$739$	−6.88503	−0.253270	−0.126635	+	0.991949i	$0.540418\pi$
$740$	5.34884	0.196627
$741$	3.74110	0.137433
$742$	6.63523	0.243587
$743$	20.7862	0.762571	0.381285	−	0.924457i	$-0.375482\pi$
$743$	20.7862	0.762571	0.381285	+	0.924457i	$0.375482\pi$
$744$	−4.35764	−0.159759
$745$	20.8579	0.764173
$746$	21.5449	0.788813
$747$	−39.7709	−1.45514
$748$	0	0
$749$	9.88200	0.361080
$750$	2.54546	0.0929469
$751$	−41.2877	−1.50661	−0.753304	−	0.657672i	$-0.771541\pi$
$751$	−41.2877	−1.50661	−0.753304	+	0.657672i	$0.771541\pi$
$752$	−3.59107	−0.130953
$753$	4.03417	0.147013
$754$	0.453944	0.0165317
$755$	5.48239	0.199525
$756$	7.33506	0.266773
$757$	29.2249	1.06220	0.531099	−	0.847310i	$-0.321779\pi$
$757$	29.2249	1.06220	0.531099	+	0.847310i	$0.321779\pi$
$758$	−10.3873	−0.377286
$759$	0	0
$760$	−18.8048	−0.682121
$761$	−7.63299	−0.276696	−0.138348	−	0.990384i	$-0.544179\pi$
$761$	−7.63299	−0.276696	−0.138348	+	0.990384i	$0.544179\pi$
$762$	−4.67801	−0.169467
$763$	−25.9880	−0.940828
$764$	14.9426	0.540603
$765$	19.4804	0.704314
$766$	−16.6591	−0.601919
$767$	−15.9655	−0.576482
$768$	−4.11083	−0.148337
$769$	−35.8764	−1.29374	−0.646868	−	0.762602i	$-0.723922\pi$
$769$	−35.8764	−1.29374	−0.646868	+	0.762602i	$0.723922\pi$
$770$	0	0
$771$	−0.628395	−0.0226311
$772$	−18.6605	−0.671606
$773$	36.7613	1.32221	0.661105	−	0.750293i	$-0.270088\pi$
$773$	36.7613	1.32221	0.661105	+	0.750293i	$0.270088\pi$
$774$	−11.3926	−0.409498
$775$	−18.9176	−0.679541
$776$	−32.6730	−1.17289
$777$	3.75149	0.134584
$778$	34.1512	1.22438
$779$	21.5932	0.773657
$780$	−1.24965	−0.0447448
$781$	0	0
$782$	−24.8421	−0.888352
$783$	0.214957	0.00768195
$784$	−6.07173	−0.216847
$785$	12.1298	0.432930
$786$	−2.45011	−0.0873924
$787$	8.98838	0.320401	0.160201	−	0.987084i	$-0.448786\pi$
$787$	8.98838	0.320401	0.160201	+	0.987084i	$0.448786\pi$
$788$	−28.2886	−1.00774
$789$	−2.57386	−0.0916319
$790$	−0.873017	−0.0310605
$791$	32.1127	1.14180
$792$	0	0
$793$	3.28313	0.116587
$794$	14.0788	0.499636
$795$	−0.535294	−0.0189849
$796$	16.8561	0.597448
$797$	25.0967	0.888971	0.444485	−	0.895786i	$-0.353387\pi$
$797$	25.0967	0.888971	0.444485	+	0.895786i	$0.353387\pi$
$798$	−4.76004	−0.168503
$799$	37.0367	1.31026
$800$	−16.7316	−0.591551
$801$	6.39803	0.226063
$802$	−17.6218	−0.622247
$803$	0	0
$804$	−0.125982	−0.00444305
$805$	34.2709	1.20789
$806$	−18.7219	−0.659450
$807$	1.52875	0.0538144
$808$	−48.2779	−1.69841
$809$	−3.00189	−0.105541	−0.0527705	−	0.998607i	$-0.516805\pi$
$809$	−3.00189	−0.105541	−0.0527705	+	0.998607i	$0.516805\pi$
$810$	−10.9027	−0.383083
$811$	−44.6668	−1.56846	−0.784232	−	0.620467i	$-0.786943\pi$
$811$	−44.6668	−1.56846	−0.784232	+	0.620467i	$0.786943\pi$
$812$	0.749349	0.0262970
$813$	7.34562	0.257622
$814$	0	0
$815$	−6.20233	−0.217258
$816$	−0.545602	−0.0190999
$817$	−19.3781	−0.677955
$818$	17.9656	0.628153
$819$	43.2207	1.51025
$820$	−7.21286	−0.251884
$821$	−4.40238	−0.153644	−0.0768221	−	0.997045i	$-0.524477\pi$
$821$	−4.40238	−0.153644	−0.0768221	+	0.997045i	$0.524477\pi$
$822$	0.153462	0.00535259
$823$	−12.7236	−0.443516	−0.221758	−	0.975102i	$-0.571180\pi$
$823$	−12.7236	−0.443516	−0.221758	+	0.975102i	$0.571180\pi$
$824$	−58.1750	−2.02662
$825$	0	0
$826$	20.3139	0.706812
$827$	3.91459	0.136124	0.0680619	−	0.997681i	$-0.478318\pi$
$827$	3.91459	0.136124	0.0680619	+	0.997681i	$0.478318\pi$
$828$	−18.4195	−0.640124
$829$	2.45366	0.0852193	0.0426097	−	0.999092i	$-0.486433\pi$
$829$	2.45366	0.0852193	0.0426097	+	0.999092i	$0.486433\pi$
$830$	−17.4170	−0.604553
$831$	0.203690	0.00706594
$832$	−19.6147	−0.680018
$833$	62.6210	2.16969
$834$	4.28647	0.148428
$835$	−30.2617	−1.04725
$836$	0	0
$837$	−8.86543	−0.306434
$838$	8.49021	0.293290
$839$	−9.04468	−0.312257	−0.156129	−	0.987737i	$-0.549901\pi$
$839$	−9.04468	−0.312257	−0.156129	+	0.987737i	$0.549901\pi$
$840$	4.40557	0.152007
$841$	−28.9780	−0.999243
$842$	−25.3841	−0.874793
$843$	5.41690	0.186568
$844$	−21.3237	−0.733990
$845$	3.06529	0.105449
$846$	−21.1666	−0.727722
$847$	0	0
$848$	−0.739316	−0.0253882
$849$	−0.703571	−0.0241465
$850$	−13.8638	−0.475523
$851$	−19.0323	−0.652417
$852$	3.49502	0.119737
$853$	31.7140	1.08587	0.542934	−	0.839775i	$-0.317313\pi$
$853$	31.7140	1.08587	0.542934	+	0.839775i	$0.317313\pi$
$854$	−4.17733	−0.142945
$855$	−18.9367	−0.647623
$856$	−6.44479	−0.220278
$857$	−1.52490	−0.0520895	−0.0260448	−	0.999661i	$-0.508291\pi$
$857$	−1.52490	−0.0520895	−0.0260448	+	0.999661i	$0.508291\pi$
$858$	0	0
$859$	26.5000	0.904168	0.452084	−	0.891975i	$-0.350681\pi$
$859$	26.5000	0.904168	0.452084	+	0.891975i	$0.350681\pi$
$860$	6.47295	0.220726
$861$	−5.05884	−0.172405
$862$	−19.1217	−0.651287
$863$	−42.1050	−1.43327	−0.716636	−	0.697447i	$-0.754319\pi$
$863$	−42.1050	−1.43327	−0.716636	+	0.697447i	$0.754319\pi$
$864$	−7.84098	−0.266755
$865$	11.8008	0.401240
$866$	−15.9327	−0.541416
$867$	1.47592	0.0501248
$868$	−30.9052	−1.04899
$869$	0	0
$870$	0.0465961	0.00157976
$871$	−1.49972	−0.0508159
$872$	16.9487	0.573955
$873$	−32.9023	−1.11357
$874$	24.1489	0.816848
$875$	50.0205	1.69100
$876$	3.76719	0.127282
$877$	−46.5109	−1.57056	−0.785281	−	0.619139i	$-0.787482\pi$
$877$	−46.5109	−1.57056	−0.785281	+	0.619139i	$0.787482\pi$
$878$	16.5016	0.556901
$879$	5.96590	0.201225
$880$	0	0
$881$	44.7347	1.50715	0.753576	−	0.657361i	$-0.228327\pi$
$881$	44.7347	1.50715	0.753576	+	0.657361i	$0.228327\pi$
$882$	−35.7881	−1.20505
$883$	34.2821	1.15368	0.576842	−	0.816856i	$-0.304285\pi$
$883$	34.2821	1.15368	0.576842	+	0.816856i	$0.304285\pi$
$884$	17.8006	0.598700
$885$	−1.63882	−0.0550883
$886$	29.4281	0.988657
$887$	5.53889	0.185978	0.0929888	−	0.995667i	$-0.470358\pi$
$887$	5.53889	0.185978	0.0929888	+	0.995667i	$0.470358\pi$
$888$	−2.44662	−0.0821033
$889$	−91.9271	−3.08314
$890$	2.80191	0.0939204
$891$	0	0
$892$	−15.1845	−0.508413
$893$	−36.0032	−1.20480
$894$	−3.44331	−0.115161
$895$	−31.6641	−1.05841
$896$	−23.4453	−0.783251
$897$	4.44652	0.148465
$898$	13.3252	0.444666
$899$	−0.905692	−0.0302065
$900$	−10.2795	−0.342649
$901$	7.62497	0.254025
$902$	0	0
$903$	4.53990	0.151078
$904$	−20.9431	−0.696556
$905$	−9.95126	−0.330791
$906$	−0.905057	−0.0300685
$907$	−11.4483	−0.380134	−0.190067	−	0.981771i	$-0.560871\pi$
$907$	−11.4483	−0.380134	−0.190067	+	0.981771i	$0.560871\pi$
$908$	6.84937	0.227304
$909$	−48.6167	−1.61252
$910$	18.9278	0.627451
$911$	−16.3921	−0.543095	−0.271547	−	0.962425i	$-0.587535\pi$
$911$	−16.3921	−0.543095	−0.271547	+	0.962425i	$0.587535\pi$
$912$	0.530377	0.0175625
$913$	0	0
$914$	−4.87185	−0.161146
$915$	0.337004	0.0111410
$916$	3.60219	0.119020
$917$	−48.1467	−1.58994
$918$	−6.49702	−0.214434
$919$	−52.4650	−1.73066	−0.865330	−	0.501203i	$-0.832891\pi$
$919$	−52.4650	−1.73066	−0.865330	+	0.501203i	$0.832891\pi$
$920$	−22.3506	−0.736877
$921$	−5.89178	−0.194141
$922$	24.5338	0.807976
$923$	41.6054	1.36946
$924$	0	0
$925$	−10.6214	−0.349230
$926$	21.1645	0.695508
$927$	−58.5833	−1.92413
$928$	−0.801034	−0.0262952
$929$	30.6935	1.00702	0.503511	−	0.863989i	$-0.332041\pi$
$929$	30.6935	1.00702	0.503511	+	0.863989i	$0.332041\pi$
$930$	−1.92175	−0.0630166
$931$	−60.8735	−1.99505
$932$	7.43139	0.243423
$933$	−7.29266	−0.238751
$934$	5.93252	0.194118
$935$	0	0
$936$	−28.1874	−0.921335
$937$	−18.4070	−0.601329	−0.300665	−	0.953730i	$-0.597208\pi$
$937$	−18.4070	−0.601329	−0.300665	+	0.953730i	$0.597208\pi$
$938$	1.90818	0.0623043
$939$	2.07930	0.0678554
$940$	12.0263	0.392254
$941$	17.2438	0.562133	0.281067	−	0.959688i	$-0.409312\pi$
$941$	17.2438	0.562133	0.281067	+	0.959688i	$0.409312\pi$
$942$	−2.00243	−0.0652428
$943$	25.6648	0.835761
$944$	−2.26344	−0.0736686
$945$	8.96294	0.291565
$946$	0	0
$947$	31.3401	1.01842	0.509208	−	0.860644i	$-0.329939\pi$
$947$	31.3401	1.01842	0.509208	+	0.860644i	$0.329939\pi$
$948$	−0.186982	−0.00607290
$949$	44.8454	1.45574
$950$	13.4769	0.437248
$951$	4.58126	0.148558
$952$	−62.7549	−2.03390
$953$	−4.20814	−0.136315	−0.0681574	−	0.997675i	$-0.521712\pi$
$953$	−4.20814	−0.136315	−0.0681574	+	0.997675i	$0.521712\pi$
$954$	−4.35769	−0.141086
$955$	18.2588	0.590841
$956$	−15.6085	−0.504814
$957$	0	0
$958$	4.27746	0.138198
$959$	3.01566	0.0973806
$960$	−2.01340	−0.0649821
$961$	6.35318	0.204941
$962$	−10.5115	−0.338905
$963$	−6.49002	−0.209138
$964$	−5.19567	−0.167341
$965$	−22.8019	−0.734018
$966$	−5.65758	−0.182030
$967$	5.55361	0.178592	0.0892960	−	0.996005i	$-0.471538\pi$
$967$	5.55361	0.178592	0.0892960	+	0.996005i	$0.471538\pi$
$968$	0	0
$969$	−5.47007	−0.175724
$970$	−14.4090	−0.462645
$971$	−28.6931	−0.920807	−0.460403	−	0.887710i	$-0.652295\pi$
$971$	−28.6931	−0.920807	−0.460403	+	0.887710i	$0.652295\pi$
$972$	−7.25014	−0.232548
$973$	84.2330	2.70039
$974$	27.8847	0.893484
$975$	2.48149	0.0794714
$976$	0.465450	0.0148987
$977$	9.99679	0.319825	0.159913	−	0.987131i	$-0.448879\pi$
$977$	9.99679	0.319825	0.159913	+	0.987131i	$0.448879\pi$
$978$	1.02391	0.0327409
$979$	0	0
$980$	20.3338	0.649540
$981$	17.0676	0.544928
$982$	22.1749	0.707630
$983$	−48.4411	−1.54503	−0.772516	−	0.634996i	$-0.781002\pi$
$983$	−48.4411	−1.54503	−0.772516	+	0.634996i	$0.781002\pi$
$984$	3.29925	0.105176
$985$	−34.5668	−1.10139
$986$	−0.663735	−0.0211376
$987$	8.43480	0.268483
$988$	−17.3039	−0.550510
$989$	−23.0321	−0.732377
$990$	0	0
$991$	−43.3277	−1.37635	−0.688174	−	0.725545i	$-0.741588\pi$
$991$	−43.3277	−1.37635	−0.688174	+	0.725545i	$0.741588\pi$
$992$	33.0368	1.04892
$993$	−7.81311	−0.247942
$994$	−52.9371	−1.67906
$995$	20.5970	0.652968
$996$	−3.73037	−0.118201
$997$	−34.4455	−1.09090	−0.545450	−	0.838143i	$-0.683641\pi$
$997$	−34.4455	−1.09090	−0.545450	+	0.838143i	$0.683641\pi$
$998$	15.6380	0.495011
$999$	−4.97755	−0.157483

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7381.2.a.l.1.14	yes	24
11.10	odd	2		7381.2.a.k.1.11	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7381.2.a.k.1.11	✓	24	11.10	odd	2
7381.2.a.l.1.14	yes	24	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:	\( N \)	\(=\)	\( 7381 = 11^{2} \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7381.a (trivial)

\(f(q)\)	\(=\)	\(q+0.933034 q^{2} +0.244187 q^{3} -1.12945 q^{4} -1.38011 q^{5} +0.227834 q^{6} +4.47715 q^{7} -2.91988 q^{8} -2.94037 q^{9} +O(q^{10})\)	\(q+0.933034 q^{2} +0.244187 q^{3} -1.12945 q^{4} -1.38011 q^{5} +0.227834 q^{6} +4.47715 q^{7} -2.91988 q^{8} -2.94037 q^{9} -1.28769 q^{10} -0.275796 q^{12} -3.28313 q^{13} +4.17733 q^{14} -0.337004 q^{15} -0.465450 q^{16} +4.80044 q^{17} -2.74347 q^{18} -4.66648 q^{19} +1.55876 q^{20} +1.09326 q^{21} -5.54639 q^{23} -0.712996 q^{24} -3.09530 q^{25} -3.06327 q^{26} -1.45056 q^{27} -5.05671 q^{28} -0.148189 q^{29} -0.314436 q^{30} +6.11172 q^{31} +5.40548 q^{32} +4.47897 q^{34} -6.17895 q^{35} +3.32100 q^{36} +3.43147 q^{37} -4.35398 q^{38} -0.801697 q^{39} +4.02975 q^{40} -4.62730 q^{41} +1.02005 q^{42} +4.15262 q^{43} +4.05804 q^{45} -5.17497 q^{46} +7.71527 q^{47} -0.113657 q^{48} +13.0448 q^{49} -2.88802 q^{50} +1.17220 q^{51} +3.70813 q^{52} +1.58839 q^{53} -1.35342 q^{54} -13.0727 q^{56} -1.13949 q^{57} -0.138266 q^{58} +4.86290 q^{59} +0.380629 q^{60} -1.00000 q^{61} +5.70244 q^{62} -13.1645 q^{63} +5.97439 q^{64} +4.53108 q^{65} +0.456794 q^{67} -5.42185 q^{68} -1.35435 q^{69} -5.76517 q^{70} -12.6725 q^{71} +8.58554 q^{72} -13.6593 q^{73} +3.20168 q^{74} -0.755831 q^{75} +5.27055 q^{76} -0.748010 q^{78} +0.677972 q^{79} +0.642372 q^{80} +8.46691 q^{81} -4.31743 q^{82} +13.5258 q^{83} -1.23478 q^{84} -6.62513 q^{85} +3.87454 q^{86} -0.0361858 q^{87} -2.17593 q^{89} +3.78628 q^{90} -14.6991 q^{91} +6.26436 q^{92} +1.49240 q^{93} +7.19861 q^{94} +6.44025 q^{95} +1.31995 q^{96} +11.1898 q^{97} +12.1713 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 5 q^{2} - 2 q^{3} + 27 q^{4} - 4 q^{5} + 12 q^{6} + 6 q^{7} + 9 q^{8} + 26 q^{9}+O(q^{10}) \) 24 * q + 5 * q^2 - 2 * q^3 + 27 * q^4 - 4 * q^5 + 12 * q^6 + 6 * q^7 + 9 * q^8 + 26 * q^9	\( 24 q + 5 q^{2} - 2 q^{3} + 27 q^{4} - 4 q^{5} + 12 q^{6} + 6 q^{7} + 9 q^{8} + 26 q^{9} + 12 q^{10} + q^{12} + 3 q^{13} - q^{14} - 5 q^{15} + 17 q^{16} + 8 q^{17} + 20 q^{18} + 8 q^{19} + 16 q^{20} + 11 q^{21} + 2 q^{23} + q^{24} + 4 q^{25} + 4 q^{26} + 13 q^{27} - 7 q^{28} + 43 q^{29} + 30 q^{30} - 4 q^{31} + 23 q^{32} + 31 q^{35} - 35 q^{36} - 4 q^{37} - 13 q^{38} + 11 q^{39} + 57 q^{40} + 29 q^{41} + 48 q^{42} + 10 q^{43} - 10 q^{45} - 14 q^{46} - 13 q^{47} + 42 q^{48} + 26 q^{49} - 6 q^{50} + 56 q^{51} + 25 q^{52} - 15 q^{53} + 35 q^{54} - 9 q^{56} - 3 q^{57} - 84 q^{58} - 13 q^{59} + 34 q^{60} - 24 q^{61} + 55 q^{62} + 22 q^{63} + 61 q^{64} + 41 q^{65} - q^{67} - 4 q^{68} - 27 q^{69} + 55 q^{70} - 6 q^{71} + 22 q^{72} + 18 q^{73} + 28 q^{74} + 47 q^{75} + 36 q^{76} - 10 q^{78} + 9 q^{79} - 40 q^{80} + 40 q^{81} + 15 q^{82} + 10 q^{83} + 93 q^{84} - 9 q^{85} + 38 q^{86} + 51 q^{87} - 17 q^{89} - 44 q^{90} - 22 q^{91} + 11 q^{92} + 32 q^{93} - 47 q^{94} + 54 q^{95} + 44 q^{96} - q^{97} + 45 q^{98}+O(q^{100}) \) 24 * q + 5 * q^2 - 2 * q^3 + 27 * q^4 - 4 * q^5 + 12 * q^6 + 6 * q^7 + 9 * q^8 + 26 * q^9 + 12 * q^10 + q^12 + 3 * q^13 - q^14 - 5 * q^15 + 17 * q^16 + 8 * q^17 + 20 * q^18 + 8 * q^19 + 16 * q^20 + 11 * q^21 + 2 * q^23 + q^24 + 4 * q^25 + 4 * q^26 + 13 * q^27 - 7 * q^28 + 43 * q^29 + 30 * q^30 - 4 * q^31 + 23 * q^32 + 31 * q^35 - 35 * q^36 - 4 * q^37 - 13 * q^38 + 11 * q^39 + 57 * q^40 + 29 * q^41 + 48 * q^42 + 10 * q^43 - 10 * q^45 - 14 * q^46 - 13 * q^47 + 42 * q^48 + 26 * q^49 - 6 * q^50 + 56 * q^51 + 25 * q^52 - 15 * q^53 + 35 * q^54 - 9 * q^56 - 3 * q^57 - 84 * q^58 - 13 * q^59 + 34 * q^60 - 24 * q^61 + 55 * q^62 + 22 * q^63 + 61 * q^64 + 41 * q^65 - q^67 - 4 * q^68 - 27 * q^69 + 55 * q^70 - 6 * q^71 + 22 * q^72 + 18 * q^73 + 28 * q^74 + 47 * q^75 + 36 * q^76 - 10 * q^78 + 9 * q^79 - 40 * q^80 + 40 * q^81 + 15 * q^82 + 10 * q^83 + 93 * q^84 - 9 * q^85 + 38 * q^86 + 51 * q^87 - 17 * q^89 - 44 * q^90 - 22 * q^91 + 11 * q^92 + 32 * q^93 - 47 * q^94 + 54 * q^95 + 44 * q^96 - q^97 + 45 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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