LMFDB - Embedded newform 5915.2.a.bd.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5915,2,Mod(1,5915)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5915, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("5915.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5915 = 5 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5915.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:	$47.2315127956$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 15x^{7} + 70x^{5} - 3x^{4} - 108x^{3} + 3x^{2} + 36x + 8 $ x^9 - 15x^7 + 70x^5 - 3x^4 - 108x^3 + 3x^2 + 36x + 8
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 455)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.46507$ of defining polynomial
Character	$\chi$	$=$	5915.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.46507 q^{2} +2.66524 q^{3} +0.146416 q^{4} +1.00000 q^{5} -3.90476 q^{6} +1.00000 q^{7} +2.71562 q^{8} +4.10353 q^{9} +O(q^{10})$	\(q-1.46507 q^{2} +2.66524 q^{3} +0.146416 q^{4} +1.00000 q^{5} -3.90476 q^{6} +1.00000 q^{7} +2.71562 q^{8} +4.10353 q^{9} -1.46507 q^{10} -4.62772 q^{11} +0.390233 q^{12} -1.46507 q^{14} +2.66524 q^{15} -4.27139 q^{16} -1.28033 q^{17} -6.01194 q^{18} +1.72407 q^{19} +0.146416 q^{20} +2.66524 q^{21} +6.77992 q^{22} +7.52949 q^{23} +7.23780 q^{24} +1.00000 q^{25} +2.94117 q^{27} +0.146416 q^{28} +10.1125 q^{29} -3.90476 q^{30} +1.48695 q^{31} +0.826626 q^{32} -12.3340 q^{33} +1.87577 q^{34} +1.00000 q^{35} +0.600821 q^{36} -2.08630 q^{37} -2.52587 q^{38} +2.71562 q^{40} +1.12814 q^{41} -3.90476 q^{42} +7.90335 q^{43} -0.677571 q^{44} +4.10353 q^{45} -11.0312 q^{46} +1.21990 q^{47} -11.3843 q^{48} +1.00000 q^{49} -1.46507 q^{50} -3.41240 q^{51} -1.03088 q^{53} -4.30901 q^{54} -4.62772 q^{55} +2.71562 q^{56} +4.59507 q^{57} -14.8155 q^{58} -14.0082 q^{59} +0.390233 q^{60} -12.8043 q^{61} -2.17847 q^{62} +4.10353 q^{63} +7.33173 q^{64} +18.0701 q^{66} -11.5301 q^{67} -0.187461 q^{68} +20.0679 q^{69} -1.46507 q^{70} -7.23666 q^{71} +11.1436 q^{72} +6.70200 q^{73} +3.05657 q^{74} +2.66524 q^{75} +0.252431 q^{76} -4.62772 q^{77} +11.9357 q^{79} -4.27139 q^{80} -4.47164 q^{81} -1.65280 q^{82} +16.2863 q^{83} +0.390233 q^{84} -1.28033 q^{85} -11.5789 q^{86} +26.9523 q^{87} -12.5671 q^{88} +3.09148 q^{89} -6.01194 q^{90} +1.10243 q^{92} +3.96308 q^{93} -1.78723 q^{94} +1.72407 q^{95} +2.20316 q^{96} +9.18205 q^{97} -1.46507 q^{98} -18.9900 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 2 q^{3} + 12 q^{4} + 9 q^{5} + 12 q^{6} + 9 q^{7} + 13 q^{9}+O(q^{10}) $ 9 * q + 2 * q^3 + 12 * q^4 + 9 * q^5 + 12 * q^6 + 9 * q^7 + 13 * q^9	$ 9 q + 2 q^{3} + 12 q^{4} + 9 q^{5} + 12 q^{6} + 9 q^{7} + 13 q^{9} + 8 q^{11} - 5 q^{12} + 2 q^{15} + 26 q^{16} + 6 q^{17} - q^{18} + 6 q^{19} + 12 q^{20} + 2 q^{21} - 4 q^{22} + 12 q^{23} + 45 q^{24} + 9 q^{25} + 14 q^{27} + 12 q^{28} + 22 q^{29} + 12 q^{30} + 20 q^{31} - 15 q^{32} - 12 q^{33} + q^{34} + 9 q^{35} + 20 q^{36} + 4 q^{37} - 19 q^{38} + 8 q^{41} + 12 q^{42} + 10 q^{43} - 14 q^{44} + 13 q^{45} - 2 q^{46} - 4 q^{47} - 60 q^{48} + 9 q^{49} + 22 q^{51} + 22 q^{53} + 31 q^{54} + 8 q^{55} - 28 q^{57} - 28 q^{58} + 8 q^{59} - 5 q^{60} + 8 q^{61} - 14 q^{62} + 13 q^{63} + 46 q^{64} - 2 q^{66} - 16 q^{67} + 70 q^{68} + 30 q^{69} + 12 q^{71} - 34 q^{72} + 10 q^{73} - 44 q^{74} + 2 q^{75} - 30 q^{76} + 8 q^{77} - 2 q^{79} + 26 q^{80} + 33 q^{81} + q^{82} + 16 q^{83} - 5 q^{84} + 6 q^{85} + 28 q^{86} - 40 q^{87} + 8 q^{88} + 34 q^{89} - q^{90} + 50 q^{92} - 50 q^{93} + 40 q^{94} + 6 q^{95} + 80 q^{96} + 12 q^{97} - 30 q^{99}+O(q^{100}) $ 9 * q + 2 * q^3 + 12 * q^4 + 9 * q^5 + 12 * q^6 + 9 * q^7 + 13 * q^9 + 8 * q^11 - 5 * q^12 + 2 * q^15 + 26 * q^16 + 6 * q^17 - q^18 + 6 * q^19 + 12 * q^20 + 2 * q^21 - 4 * q^22 + 12 * q^23 + 45 * q^24 + 9 * q^25 + 14 * q^27 + 12 * q^28 + 22 * q^29 + 12 * q^30 + 20 * q^31 - 15 * q^32 - 12 * q^33 + q^34 + 9 * q^35 + 20 * q^36 + 4 * q^37 - 19 * q^38 + 8 * q^41 + 12 * q^42 + 10 * q^43 - 14 * q^44 + 13 * q^45 - 2 * q^46 - 4 * q^47 - 60 * q^48 + 9 * q^49 + 22 * q^51 + 22 * q^53 + 31 * q^54 + 8 * q^55 - 28 * q^57 - 28 * q^58 + 8 * q^59 - 5 * q^60 + 8 * q^61 - 14 * q^62 + 13 * q^63 + 46 * q^64 - 2 * q^66 - 16 * q^67 + 70 * q^68 + 30 * q^69 + 12 * q^71 - 34 * q^72 + 10 * q^73 - 44 * q^74 + 2 * q^75 - 30 * q^76 + 8 * q^77 - 2 * q^79 + 26 * q^80 + 33 * q^81 + q^82 + 16 * q^83 - 5 * q^84 + 6 * q^85 + 28 * q^86 - 40 * q^87 + 8 * q^88 + 34 * q^89 - q^90 + 50 * q^92 - 50 * q^93 + 40 * q^94 + 6 * q^95 + 80 * q^96 + 12 * q^97 - 30 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.46507	−1.03596	−0.517979	−	0.855394i	$-0.673315\pi$
$2$	−1.46507	−1.03596	−0.517979	+	0.855394i	$0.673315\pi$
$3$	2.66524	1.53878	0.769390	−	0.638780i	$-0.220560\pi$
$3$	2.66524	1.53878	0.769390	+	0.638780i	$0.220560\pi$
$4$	0.146416	0.0732078
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−3.90476	−1.59411
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	2.71562	0.960117
$9$	4.10353	1.36784
$10$	−1.46507	−0.463294
$11$	−4.62772	−1.39531	−0.697656	−	0.716433i	$-0.745773\pi$
$11$	−4.62772	−1.39531	−0.697656	+	0.716433i	$0.745773\pi$
$12$	0.390233	0.112651
$13$	0	0
$13$	0	0
$14$	−1.46507	−0.391555
$15$	2.66524	0.688163
$16$	−4.27139	−1.06785
$17$	−1.28033	−0.310526	−0.155263	−	0.987873i	$-0.549623\pi$
$17$	−1.28033	−0.310526	−0.155263	+	0.987873i	$0.549623\pi$
$18$	−6.01194	−1.41703
$19$	1.72407	0.395529	0.197764	−	0.980250i	$-0.436632\pi$
$19$	1.72407	0.395529	0.197764	+	0.980250i	$0.436632\pi$
$20$	0.146416	0.0327395
$21$	2.66524	0.581604
$22$	6.77992	1.44548
$23$	7.52949	1.57001	0.785003	−	0.619492i	$-0.212661\pi$
$23$	7.52949	1.57001	0.785003	+	0.619492i	$0.212661\pi$
$24$	7.23780	1.47741
$25$	1.00000	0.200000
$26$	0	0
$27$	2.94117	0.566029
$28$	0.146416	0.0276699
$29$	10.1125	1.87785	0.938923	−	0.344128i	$-0.111825\pi$
$29$	10.1125	1.87785	0.938923	+	0.344128i	$0.111825\pi$
$30$	−3.90476	−0.712908
$31$	1.48695	0.267064	0.133532	−	0.991045i	$-0.457368\pi$
$31$	1.48695	0.267064	0.133532	+	0.991045i	$0.457368\pi$
$32$	0.826626	0.146128
$33$	−12.3340	−2.14708
$34$	1.87577	0.321692
$35$	1.00000	0.169031
$36$	0.600821	0.100137
$37$	−2.08630	−0.342986	−0.171493	−	0.985185i	$-0.554859\pi$
$37$	−2.08630	−0.342986	−0.171493	+	0.985185i	$0.554859\pi$
$38$	−2.52587	−0.409751
$39$	0	0
$40$	2.71562	0.429378
$41$	1.12814	0.176186	0.0880930	−	0.996112i	$-0.471923\pi$
$41$	1.12814	0.176186	0.0880930	+	0.996112i	$0.471923\pi$
$42$	−3.90476	−0.602517
$43$	7.90335	1.20525	0.602625	−	0.798025i	$-0.294122\pi$
$43$	7.90335	1.20525	0.602625	+	0.798025i	$0.294122\pi$
$44$	−0.677571	−0.102148
$45$	4.10353	0.611718
$46$	−11.0312	−1.62646
$47$	1.21990	0.177940	0.0889702	−	0.996034i	$-0.471642\pi$
$47$	1.21990	0.177940	0.0889702	+	0.996034i	$0.471642\pi$
$48$	−11.3843	−1.64318
$49$	1.00000	0.142857
$50$	−1.46507	−0.207191
$51$	−3.41240	−0.477832
$52$	0	0
$53$	−1.03088	−0.141603	−0.0708014	−	0.997490i	$-0.522556\pi$
$53$	−1.03088	−0.141603	−0.0708014	+	0.997490i	$0.522556\pi$
$54$	−4.30901	−0.586382
$55$	−4.62772	−0.624002
$56$	2.71562	0.362890
$57$	4.59507	0.608632
$58$	−14.8155	−1.94537
$59$	−14.0082	−1.82371	−0.911855	−	0.410512i	$-0.865350\pi$
$59$	−14.0082	−1.82371	−0.911855	+	0.410512i	$0.865350\pi$
$60$	0.390233	0.0503789
$61$	−12.8043	−1.63943	−0.819714	−	0.572773i	$-0.805868\pi$
$61$	−12.8043	−1.63943	−0.819714	+	0.572773i	$0.805868\pi$
$62$	−2.17847	−0.276667
$63$	4.10353	0.516996
$64$	7.33173	0.916466
$65$	0	0
$66$	18.0701	2.22428
$67$	−11.5301	−1.40862	−0.704312	−	0.709890i	$-0.748745\pi$
$67$	−11.5301	−1.40862	−0.704312	+	0.709890i	$0.748745\pi$
$68$	−0.187461	−0.0227329
$69$	20.0679	2.41589
$70$	−1.46507	−0.175109
$71$	−7.23666	−0.858833	−0.429417	−	0.903107i	$-0.641281\pi$
$71$	−7.23666	−0.858833	−0.429417	+	0.903107i	$0.641281\pi$
$72$	11.1436	1.31329
$73$	6.70200	0.784409	0.392205	−	0.919878i	$-0.371713\pi$
$73$	6.70200	0.784409	0.392205	+	0.919878i	$0.371713\pi$
$74$	3.05657	0.355319
$75$	2.66524	0.307756
$76$	0.252431	0.0289558
$77$	−4.62772	−0.527378
$78$	0	0
$79$	11.9357	1.34287	0.671437	−	0.741062i	$-0.265678\pi$
$79$	11.9357	1.34287	0.671437	+	0.741062i	$0.265678\pi$
$80$	−4.27139	−0.477556
$81$	−4.47164	−0.496849
$82$	−1.65280	−0.182521
$83$	16.2863	1.78766	0.893829	−	0.448409i	$-0.148009\pi$
$83$	16.2863	1.78766	0.893829	+	0.448409i	$0.148009\pi$
$84$	0.390233	0.0425779
$85$	−1.28033	−0.138872
$86$	−11.5789	−1.24859
$87$	26.9523	2.88959
$88$	−12.5671	−1.33966
$89$	3.09148	0.327696	0.163848	−	0.986486i	$-0.447609\pi$
$89$	3.09148	0.327696	0.163848	+	0.986486i	$0.447609\pi$
$90$	−6.01194	−0.633714
$91$	0	0
$92$	1.10243	0.114937
$93$	3.96308	0.410952
$94$	−1.78723	−0.184339
$95$	1.72407	0.176886
$96$	2.20316	0.224859
$97$	9.18205	0.932296	0.466148	−	0.884707i	$-0.345641\pi$
$97$	9.18205	0.932296	0.466148	+	0.884707i	$0.345641\pi$
$98$	−1.46507	−0.147994
$99$	−18.9900	−1.90857
$100$	0.146416	0.0146416
$101$	1.07146	0.106614	0.0533071	−	0.998578i	$-0.483024\pi$
$101$	1.07146	0.106614	0.0533071	+	0.998578i	$0.483024\pi$
$102$	4.99939	0.495013
$103$	8.28838	0.816679	0.408339	−	0.912830i	$-0.366108\pi$
$103$	8.28838	0.816679	0.408339	+	0.912830i	$0.366108\pi$
$104$	0	0
$105$	2.66524	0.260101
$106$	1.51031	0.146695
$107$	12.5948	1.21759	0.608794	−	0.793329i	$-0.291654\pi$
$107$	12.5948	1.21759	0.608794	+	0.793329i	$0.291654\pi$
$108$	0.430634	0.0414378
$109$	2.14944	0.205879	0.102940	−	0.994688i	$-0.467175\pi$
$109$	2.14944	0.205879	0.102940	+	0.994688i	$0.467175\pi$
$110$	6.77992	0.646440
$111$	−5.56051	−0.527780
$112$	−4.27139	−0.403609
$113$	8.99642	0.846312	0.423156	−	0.906057i	$-0.360922\pi$
$113$	8.99642	0.846312	0.423156	+	0.906057i	$0.360922\pi$
$114$	−6.73207	−0.630516
$115$	7.52949	0.702128
$116$	1.48063	0.137473
$117$	0	0
$118$	20.5229	1.88929
$119$	−1.28033	−0.117368
$120$	7.23780	0.660717
$121$	10.4158	0.946893
$122$	18.7592	1.69838
$123$	3.00677	0.271111
$124$	0.217712	0.0195511
$125$	1.00000	0.0894427
$126$	−6.01194	−0.535586
$127$	3.62461	0.321632	0.160816	−	0.986984i	$-0.448587\pi$
$127$	3.62461	0.321632	0.160816	+	0.986984i	$0.448587\pi$
$128$	−12.3947	−1.09555
$129$	21.0644	1.85461
$130$	0	0
$131$	18.2622	1.59558	0.797788	−	0.602938i	$-0.206003\pi$
$131$	18.2622	1.59558	0.797788	+	0.602938i	$0.206003\pi$
$132$	−1.80589	−0.157183
$133$	1.72407	0.149496
$134$	16.8923	1.45928
$135$	2.94117	0.253136
$136$	−3.47690	−0.298142
$137$	−0.567292	−0.0484671	−0.0242335	−	0.999706i	$-0.507715\pi$
$137$	−0.567292	−0.0484671	−0.0242335	+	0.999706i	$0.507715\pi$
$138$	−29.4008	−2.50276
$139$	−8.48359	−0.719569	−0.359784	−	0.933035i	$-0.617150\pi$
$139$	−8.48359	−0.719569	−0.359784	+	0.933035i	$0.617150\pi$
$140$	0.146416	0.0123744
$141$	3.25133	0.273811
$142$	10.6022	0.889715
$143$	0	0
$144$	−17.5278	−1.46065
$145$	10.1125	0.839798
$146$	−9.81886	−0.812615
$147$	2.66524	0.219826
$148$	−0.305467	−0.0251093
$149$	−8.05515	−0.659904	−0.329952	−	0.943998i	$-0.607033\pi$
$149$	−8.05515	−0.659904	−0.329952	+	0.943998i	$0.607033\pi$
$150$	−3.90476	−0.318822
$151$	5.48140	0.446070	0.223035	−	0.974810i	$-0.428404\pi$
$151$	5.48140	0.446070	0.223035	+	0.974810i	$0.428404\pi$
$152$	4.68192	0.379754
$153$	−5.25388	−0.424751
$154$	6.77992	0.546341
$155$	1.48695	0.119435
$156$	0	0
$157$	20.8873	1.66699	0.833493	−	0.552531i	$-0.186338\pi$
$157$	20.8873	1.66699	0.833493	+	0.552531i	$0.186338\pi$
$158$	−17.4866	−1.39116
$159$	−2.74756	−0.217896
$160$	0.826626	0.0653505
$161$	7.52949	0.593407
$162$	6.55124	0.514714
$163$	18.6553	1.46120	0.730599	−	0.682806i	$-0.239241\pi$
$163$	18.6553	1.46120	0.730599	+	0.682806i	$0.239241\pi$
$164$	0.165177	0.0128982
$165$	−12.3340	−0.960202
$166$	−23.8605	−1.85194
$167$	−5.32179	−0.411813	−0.205906	−	0.978572i	$-0.566014\pi$
$167$	−5.32179	−0.411813	−0.205906	+	0.978572i	$0.566014\pi$
$168$	7.23780	0.558408
$169$	0	0
$170$	1.87577	0.143865
$171$	7.07477	0.541021
$172$	1.15717	0.0882336
$173$	−10.4086	−0.791351	−0.395676	−	0.918390i	$-0.629490\pi$
$173$	−10.4086	−0.791351	−0.395676	+	0.918390i	$0.629490\pi$
$174$	−39.4869	−2.99349
$175$	1.00000	0.0755929
$176$	19.7668	1.48998
$177$	−37.3352	−2.80629
$178$	−4.52922	−0.339479
$179$	−3.51830	−0.262970	−0.131485	−	0.991318i	$-0.541975\pi$
$179$	−3.51830	−0.262970	−0.131485	+	0.991318i	$0.541975\pi$
$180$	0.600821	0.0447825
$181$	−15.9978	−1.18911	−0.594555	−	0.804055i	$-0.702672\pi$
$181$	−15.9978	−1.18911	−0.594555	+	0.804055i	$0.702672\pi$
$182$	0	0
$183$	−34.1267	−2.52272
$184$	20.4472	1.50739
$185$	−2.08630	−0.153388
$186$	−5.80617	−0.425729
$187$	5.92503	0.433281
$188$	0.178612	0.0130266
$189$	2.94117	0.213939
$190$	−2.52587	−0.183246
$191$	−21.1989	−1.53390	−0.766951	−	0.641706i	$-0.778227\pi$
$191$	−21.1989	−1.53390	−0.766951	+	0.641706i	$0.778227\pi$
$192$	19.5408	1.41024
$193$	16.2263	1.16800	0.583999	−	0.811754i	$-0.301487\pi$
$193$	16.2263	1.16800	0.583999	+	0.811754i	$0.301487\pi$
$194$	−13.4523	−0.965819
$195$	0	0
$196$	0.146416	0.0104583
$197$	−2.30728	−0.164387	−0.0821935	−	0.996616i	$-0.526193\pi$
$197$	−2.30728	−0.164387	−0.0821935	+	0.996616i	$0.526193\pi$
$198$	27.8216	1.97719
$199$	−17.6911	−1.25409	−0.627044	−	0.778984i	$-0.715735\pi$
$199$	−17.6911	−1.25409	−0.627044	+	0.778984i	$0.715735\pi$
$200$	2.71562	0.192023
$201$	−30.7305	−2.16756
$202$	−1.56976	−0.110448
$203$	10.1125	0.709759
$204$	−0.499628	−0.0349810
$205$	1.12814	0.0787928
$206$	−12.1430	−0.846044
$207$	30.8975	2.14752
$208$	0	0
$209$	−7.97852	−0.551886
$210$	−3.90476	−0.269454
$211$	−6.22460	−0.428519	−0.214259	−	0.976777i	$-0.568734\pi$
$211$	−6.22460	−0.428519	−0.214259	+	0.976777i	$0.568734\pi$
$212$	−0.150938	−0.0103664
$213$	−19.2875	−1.32155
$214$	−18.4522	−1.26137
$215$	7.90335	0.539004
$216$	7.98712	0.543455
$217$	1.48695	0.100941
$218$	−3.14908	−0.213282
$219$	17.8625	1.20703
$220$	−0.677571	−0.0456818
$221$	0	0
$222$	8.14651	0.546758
$223$	−5.32179	−0.356374	−0.178187	−	0.983997i	$-0.557023\pi$
$223$	−5.32179	−0.356374	−0.178187	+	0.983997i	$0.557023\pi$
$224$	0.826626	0.0552313
$225$	4.10353	0.273569
$226$	−13.1803	−0.876743
$227$	12.9412	0.858937	0.429469	−	0.903082i	$-0.358701\pi$
$227$	12.9412	0.858937	0.429469	+	0.903082i	$0.358701\pi$
$228$	0.672789	0.0445566
$229$	26.8927	1.77712	0.888559	−	0.458763i	$-0.151707\pi$
$229$	26.8927	1.77712	0.888559	+	0.458763i	$0.151707\pi$
$230$	−11.0312	−0.727375
$231$	−12.3340	−0.811519
$232$	27.4617	1.80295
$233$	−0.643475	−0.0421554	−0.0210777	−	0.999778i	$-0.506710\pi$
$233$	−0.643475	−0.0421554	−0.0210777	+	0.999778i	$0.506710\pi$
$234$	0	0
$235$	1.21990	0.0795774
$236$	−2.05102	−0.133510
$237$	31.8116	2.06639
$238$	1.87577	0.121588
$239$	−24.1040	−1.55916	−0.779578	−	0.626306i	$-0.784566\pi$
$239$	−24.1040	−1.55916	−0.779578	+	0.626306i	$0.784566\pi$
$240$	−11.3843	−0.734854
$241$	0.781343	0.0503307	0.0251654	−	0.999683i	$-0.491989\pi$
$241$	0.781343	0.0503307	0.0251654	+	0.999683i	$0.491989\pi$
$242$	−15.2599	−0.980941
$243$	−20.7415	−1.33057
$244$	−1.87475	−0.120019
$245$	1.00000	0.0638877
$246$	−4.40511	−0.280860
$247$	0	0
$248$	4.03799	0.256412
$249$	43.4071	2.75081
$250$	−1.46507	−0.0926588
$251$	12.4807	0.787772	0.393886	−	0.919159i	$-0.371130\pi$
$251$	12.4807	0.787772	0.393886	+	0.919159i	$0.371130\pi$
$252$	0.600821	0.0378481
$253$	−34.8444	−2.19065
$254$	−5.31028	−0.333197
$255$	−3.41240	−0.213693
$256$	3.49560	0.218475
$257$	7.89115	0.492237	0.246118	−	0.969240i	$-0.420845\pi$
$257$	7.89115	0.492237	0.246118	+	0.969240i	$0.420845\pi$
$258$	−30.8606	−1.92130
$259$	−2.08630	−0.129637
$260$	0	0
$261$	41.4970	2.56860
$262$	−26.7553	−1.65295
$263$	11.9743	0.738364	0.369182	−	0.929357i	$-0.379638\pi$
$263$	11.9743	0.738364	0.369182	+	0.929357i	$0.379638\pi$
$264$	−33.4945	−2.06145
$265$	−1.03088	−0.0633267
$266$	−2.52587	−0.154871
$267$	8.23955	0.504252
$268$	−1.68818	−0.103122
$269$	1.44411	0.0880492	0.0440246	−	0.999030i	$-0.485982\pi$
$269$	1.44411	0.0880492	0.0440246	+	0.999030i	$0.485982\pi$
$270$	−4.30901	−0.262238
$271$	18.9486	1.15104	0.575522	−	0.817786i	$-0.304799\pi$
$271$	18.9486	1.15104	0.575522	+	0.817786i	$0.304799\pi$
$272$	5.46881	0.331595
$273$	0	0
$274$	0.831120	0.0502098
$275$	−4.62772	−0.279062
$276$	2.93826	0.176862
$277$	10.7652	0.646815	0.323408	−	0.946260i	$-0.395172\pi$
$277$	10.7652	0.646815	0.323408	+	0.946260i	$0.395172\pi$
$278$	12.4290	0.745443
$279$	6.10173	0.365301
$280$	2.71562	0.162289
$281$	13.8013	0.823314	0.411657	−	0.911339i	$-0.364950\pi$
$281$	13.8013	0.823314	0.411657	+	0.911339i	$0.364950\pi$
$282$	−4.76341	−0.283657
$283$	9.66944	0.574789	0.287394	−	0.957812i	$-0.407211\pi$
$283$	9.66944	0.574789	0.287394	+	0.957812i	$0.407211\pi$
$284$	−1.05956	−0.0628733
$285$	4.59507	0.272188
$286$	0	0
$287$	1.12814	0.0665920
$288$	3.39208	0.199880
$289$	−15.3607	−0.903573
$290$	−14.8155	−0.869995
$291$	24.4724	1.43460
$292$	0.981276	0.0574249
$293$	−20.3650	−1.18974	−0.594869	−	0.803822i	$-0.702796\pi$
$293$	−20.3650	−1.18974	−0.594869	+	0.803822i	$0.702796\pi$
$294$	−3.90476	−0.227730
$295$	−14.0082	−0.815588
$296$	−5.66561	−0.329307
$297$	−13.6109	−0.789787
$298$	11.8013	0.683632
$299$	0	0
$300$	0.390233	0.0225301
$301$	7.90335	0.455541
$302$	−8.03060	−0.462109
$303$	2.85570	0.164056
$304$	−7.36418	−0.422365
$305$	−12.8043	−0.733174
$306$	7.69728	0.440024
$307$	−5.66548	−0.323346	−0.161673	−	0.986844i	$-0.551689\pi$
$307$	−5.66548	−0.323346	−0.161673	+	0.986844i	$0.551689\pi$
$308$	−0.677571	−0.0386082
$309$	22.0906	1.25669
$310$	−2.17847	−0.123729
$311$	25.9435	1.47112	0.735562	−	0.677458i	$-0.236918\pi$
$311$	25.9435	1.47112	0.735562	+	0.677458i	$0.236918\pi$
$312$	0	0
$313$	−16.9839	−0.959987	−0.479994	−	0.877272i	$-0.659361\pi$
$313$	−16.9839	−0.959987	−0.479994	+	0.877272i	$0.659361\pi$
$314$	−30.6012	−1.72693
$315$	4.10353	0.231208
$316$	1.74758	0.0983088
$317$	−3.76355	−0.211382	−0.105691	−	0.994399i	$-0.533705\pi$
$317$	−3.76355	−0.211382	−0.105691	+	0.994399i	$0.533705\pi$
$318$	4.02535	0.225731
$319$	−46.7979	−2.62018
$320$	7.33173	0.409856
$321$	33.5683	1.87360
$322$	−11.0312	−0.614744
$323$	−2.20738	−0.122822
$324$	−0.654717	−0.0363732
$325$	0	0
$326$	−27.3313	−1.51374
$327$	5.72879	0.316803
$328$	3.06360	0.169159
$329$	1.21990	0.0672552
$330$	18.0701	0.994728
$331$	25.4467	1.39868	0.699339	−	0.714790i	$-0.253478\pi$
$331$	25.4467	1.39868	0.699339	+	0.714790i	$0.253478\pi$
$332$	2.38457	0.130870
$333$	−8.56121	−0.469152
$334$	7.79677	0.426620
$335$	−11.5301	−0.629956
$336$	−11.3843	−0.621065
$337$	−27.2139	−1.48244	−0.741218	−	0.671264i	$-0.765752\pi$
$337$	−27.2139	−1.48244	−0.741218	+	0.671264i	$0.765752\pi$
$338$	0	0
$339$	23.9777	1.30229
$340$	−0.187461	−0.0101665
$341$	−6.88118	−0.372637
$342$	−10.3650	−0.560475
$343$	1.00000	0.0539949
$344$	21.4625	1.15718
$345$	20.0679	1.08042
$346$	15.2493	0.819806
$347$	−16.4371	−0.882388	−0.441194	−	0.897412i	$-0.645445\pi$
$347$	−16.4371	−0.882388	−0.441194	+	0.897412i	$0.645445\pi$
$348$	3.94624	0.211540
$349$	−3.51452	−0.188128	−0.0940641	−	0.995566i	$-0.529986\pi$
$349$	−3.51452	−0.188128	−0.0940641	+	0.995566i	$0.529986\pi$
$350$	−1.46507	−0.0783110
$351$	0	0
$352$	−3.82540	−0.203894
$353$	3.76145	0.200202	0.100101	−	0.994977i	$-0.468083\pi$
$353$	3.76145	0.200202	0.100101	+	0.994977i	$0.468083\pi$
$354$	54.6986	2.90720
$355$	−7.23666	−0.384082
$356$	0.452640	0.0239899
$357$	−3.41240	−0.180603
$358$	5.15454	0.272426
$359$	−5.51209	−0.290917	−0.145459	−	0.989364i	$-0.546466\pi$
$359$	−5.51209	−0.290917	−0.145459	+	0.989364i	$0.546466\pi$
$360$	11.1436	0.587321
$361$	−16.0276	−0.843557
$362$	23.4379	1.23187
$363$	27.7607	1.45706
$364$	0	0
$365$	6.70200	0.350798
$366$	49.9978	2.61343
$367$	30.0369	1.56791	0.783957	−	0.620815i	$-0.213198\pi$
$367$	30.0369	1.56791	0.783957	+	0.620815i	$0.213198\pi$
$368$	−32.1614	−1.67653
$369$	4.62936	0.240995
$370$	3.05657	0.158904
$371$	−1.03088	−0.0535208
$372$	0.580256	0.0300849
$373$	13.9391	0.721738	0.360869	−	0.932616i	$-0.382480\pi$
$373$	13.9391	0.721738	0.360869	+	0.932616i	$0.382480\pi$
$374$	−8.68055	−0.448860
$375$	2.66524	0.137633
$376$	3.31278	0.170844
$377$	0	0
$378$	−4.30901	−0.221632
$379$	20.7459	1.06565	0.532823	−	0.846227i	$-0.321131\pi$
$379$	20.7459	1.06565	0.532823	+	0.846227i	$0.321131\pi$
$380$	0.252431	0.0129494
$381$	9.66046	0.494921
$382$	31.0578	1.58906
$383$	2.49658	0.127569	0.0637847	−	0.997964i	$-0.479683\pi$
$383$	2.49658	0.127569	0.0637847	+	0.997964i	$0.479683\pi$
$384$	−33.0349	−1.68581
$385$	−4.62772	−0.235851
$386$	−23.7726	−1.21000
$387$	32.4316	1.64859
$388$	1.34440	0.0682513
$389$	−10.5511	−0.534960	−0.267480	−	0.963563i	$-0.586191\pi$
$389$	−10.5511	−0.534960	−0.267480	+	0.963563i	$0.586191\pi$
$390$	0	0
$391$	−9.64025	−0.487528
$392$	2.71562	0.137160
$393$	48.6733	2.45524
$394$	3.38032	0.170298
$395$	11.9357	0.600551
$396$	−2.78043	−0.139722
$397$	20.3192	1.01979	0.509897	−	0.860236i	$-0.329684\pi$
$397$	20.3192	1.01979	0.509897	+	0.860236i	$0.329684\pi$
$398$	25.9186	1.29918
$399$	4.59507	0.230041
$400$	−4.27139	−0.213570
$401$	12.4731	0.622878	0.311439	−	0.950266i	$-0.399189\pi$
$401$	12.4731	0.622878	0.311439	+	0.950266i	$0.399189\pi$
$402$	45.0222	2.24550
$403$	0	0
$404$	0.156878	0.00780500
$405$	−4.47164	−0.222197
$406$	−14.8155	−0.735280
$407$	9.65484	0.478573
$408$	−9.26679	−0.458774
$409$	10.6684	0.527518	0.263759	−	0.964589i	$-0.415038\pi$
$409$	10.6684	0.527518	0.263759	+	0.964589i	$0.415038\pi$
$410$	−1.65280	−0.0816259
$411$	−1.51197	−0.0745801
$412$	1.21355	0.0597872
$413$	−14.0082	−0.689298
$414$	−45.2668	−2.22474
$415$	16.2863	0.799465
$416$	0	0
$417$	−22.6108	−1.10726
$418$	11.6890	0.571730
$419$	29.6841	1.45017	0.725083	−	0.688662i	$-0.241802\pi$
$419$	29.6841	1.45017	0.725083	+	0.688662i	$0.241802\pi$
$420$	0.390233	0.0190414
$421$	−13.4500	−0.655514	−0.327757	−	0.944762i	$-0.606293\pi$
$421$	−13.4500	−0.655514	−0.327757	+	0.944762i	$0.606293\pi$
$422$	9.11944	0.443927
$423$	5.00589	0.243395
$424$	−2.79949	−0.135955
$425$	−1.28033	−0.0621053
$426$	28.2574	1.36907
$427$	−12.8043	−0.619645
$428$	1.84408	0.0891369
$429$	0	0
$430$	−11.5789	−0.558385
$431$	−33.0749	−1.59316	−0.796581	−	0.604532i	$-0.793360\pi$
$431$	−33.0749	−1.59316	−0.796581	+	0.604532i	$0.793360\pi$
$432$	−12.5629	−0.604434
$433$	13.4972	0.648635	0.324318	−	0.945948i	$-0.394865\pi$
$433$	13.4972	0.648635	0.324318	+	0.945948i	$0.394865\pi$
$434$	−2.17847	−0.104570
$435$	26.9523	1.29226
$436$	0.314712	0.0150720
$437$	12.9814	0.620983
$438$	−26.1697	−1.25043
$439$	−10.8985	−0.520159	−0.260079	−	0.965587i	$-0.583749\pi$
$439$	−10.8985	−0.520159	−0.260079	+	0.965587i	$0.583749\pi$
$440$	−12.5671	−0.599115
$441$	4.10353	0.195406
$442$	0	0
$443$	−33.5921	−1.59601	−0.798003	−	0.602653i	$-0.794110\pi$
$443$	−33.5921	−1.59601	−0.798003	+	0.602653i	$0.794110\pi$
$444$	−0.814146	−0.0386376
$445$	3.09148	0.146550
$446$	7.79677	0.369188
$447$	−21.4690	−1.01545
$448$	7.33173	0.346392
$449$	33.7493	1.59273	0.796364	−	0.604817i	$-0.206754\pi$
$449$	33.7493	1.59273	0.796364	+	0.604817i	$0.206754\pi$
$450$	−6.01194	−0.283405
$451$	−5.22072	−0.245834
$452$	1.31722	0.0619566
$453$	14.6093	0.686403
$454$	−18.9597	−0.889822
$455$	0	0
$456$	12.4785	0.584358
$457$	−11.2789	−0.527604	−0.263802	−	0.964577i	$-0.584976\pi$
$457$	−11.2789	−0.527604	−0.263802	+	0.964577i	$0.584976\pi$
$458$	−39.3995	−1.84102
$459$	−3.76568	−0.175767
$460$	1.10243	0.0514013
$461$	38.8671	1.81022	0.905110	−	0.425178i	$-0.139789\pi$
$461$	38.8671	1.81022	0.905110	+	0.425178i	$0.139789\pi$
$462$	18.0701	0.840699
$463$	−10.8599	−0.504704	−0.252352	−	0.967636i	$-0.581204\pi$
$463$	−10.8599	−0.504704	−0.252352	+	0.967636i	$0.581204\pi$
$464$	−43.1945	−2.00525
$465$	3.96308	0.183783
$466$	0.942732	0.0436712
$467$	30.7494	1.42291	0.711455	−	0.702731i	$-0.248036\pi$
$467$	30.7494	1.42291	0.711455	+	0.702731i	$0.248036\pi$
$468$	0	0
$469$	−11.5301	−0.532410
$470$	−1.78723	−0.0824388
$471$	55.6697	2.56512
$472$	−38.0409	−1.75098
$473$	−36.5745	−1.68170
$474$	−46.6061	−2.14069
$475$	1.72407	0.0791058
$476$	−0.187461	−0.00859224
$477$	−4.23026	−0.193690
$478$	35.3139	1.61522
$479$	−31.6605	−1.44660	−0.723302	−	0.690532i	$-0.757376\pi$
$479$	−31.6605	−1.44660	−0.723302	+	0.690532i	$0.757376\pi$
$480$	2.20316	0.100560
$481$	0	0
$482$	−1.14472	−0.0521405
$483$	20.0679	0.913122
$484$	1.52504	0.0693199
$485$	9.18205	0.416935
$486$	30.3877	1.37841
$487$	7.89192	0.357617	0.178808	−	0.983884i	$-0.442776\pi$
$487$	7.89192	0.357617	0.178808	+	0.983884i	$0.442776\pi$
$488$	−34.7717	−1.57404
$489$	49.7210	2.24846
$490$	−1.46507	−0.0661849
$491$	−41.8887	−1.89041	−0.945206	−	0.326474i	$-0.894139\pi$
$491$	−41.8887	−1.89041	−0.945206	+	0.326474i	$0.894139\pi$
$492$	0.440238	0.0198475
$493$	−12.9474	−0.583120
$494$	0	0
$495$	−18.9900	−0.853537
$496$	−6.35134	−0.285184
$497$	−7.23666	−0.324608
$498$	−63.5942	−2.84972
$499$	−1.13318	−0.0507281	−0.0253640	−	0.999678i	$-0.508074\pi$
$499$	−1.13318	−0.0507281	−0.0253640	+	0.999678i	$0.508074\pi$
$500$	0.146416	0.00654790
$501$	−14.1839	−0.633689
$502$	−18.2850	−0.816099
$503$	−33.4180	−1.49004	−0.745018	−	0.667044i	$-0.767559\pi$
$503$	−33.4180	−1.49004	−0.745018	+	0.667044i	$0.767559\pi$
$504$	11.1436	0.496377
$505$	1.07146	0.0476794
$506$	51.0493	2.26942
$507$	0	0
$508$	0.530699	0.0235460
$509$	−26.3711	−1.16888	−0.584440	−	0.811437i	$-0.698686\pi$
$509$	−26.3711	−1.16888	−0.584440	+	0.811437i	$0.698686\pi$
$510$	4.99939	0.221377
$511$	6.70200	0.296479
$512$	19.6681	0.869217
$513$	5.07079	0.223881
$514$	−11.5611	−0.509936
$515$	8.28838	0.365230
$516$	3.08415	0.135772
$517$	−5.64535	−0.248282
$518$	3.05657	0.134298
$519$	−27.7415	−1.21772
$520$	0	0
$521$	−4.74619	−0.207934	−0.103967	−	0.994581i	$-0.533154\pi$
$521$	−4.74619	−0.207934	−0.103967	+	0.994581i	$0.533154\pi$
$522$	−60.7958	−2.66096
$523$	13.2476	0.579278	0.289639	−	0.957136i	$-0.406465\pi$
$523$	13.2476	0.579278	0.289639	+	0.957136i	$0.406465\pi$
$524$	2.67387	0.116809
$525$	2.66524	0.116321
$526$	−17.5431	−0.764914
$527$	−1.90379	−0.0829303
$528$	52.6834	2.29275
$529$	33.6932	1.46492
$530$	1.51031	0.0656038
$531$	−57.4830	−2.49455
$532$	0.252431	0.0109443
$533$	0	0
$534$	−12.0715	−0.522384
$535$	12.5948	0.544522
$536$	−31.3114	−1.35244
$537$	−9.37713	−0.404653
$538$	−2.11572	−0.0912152
$539$	−4.62772	−0.199330
$540$	0.430634	0.0185315
$541$	31.6007	1.35862	0.679310	−	0.733852i	$-0.262279\pi$
$541$	31.6007	1.35862	0.679310	+	0.733852i	$0.262279\pi$
$542$	−27.7609	−1.19243
$543$	−42.6382	−1.82978
$544$	−1.05836	−0.0453766
$545$	2.14944	0.0920721
$546$	0	0
$547$	15.0005	0.641376	0.320688	−	0.947185i	$-0.396086\pi$
$547$	15.0005	0.641376	0.320688	+	0.947185i	$0.396086\pi$
$548$	−0.0830604	−0.00354817
$549$	−52.5430	−2.24248
$550$	6.77992	0.289097
$551$	17.4347	0.742742
$552$	54.4969	2.31954
$553$	11.9357	0.507558
$554$	−15.7716	−0.670073
$555$	−5.56051	−0.236031
$556$	−1.24213	−0.0526780
$557$	0.755865	0.0320270	0.0160135	−	0.999872i	$-0.494903\pi$
$557$	0.755865	0.0320270	0.0160135	+	0.999872i	$0.494903\pi$
$558$	−8.93943	−0.378436
$559$	0	0
$560$	−4.27139	−0.180499
$561$	15.7916	0.666724
$562$	−20.2197	−0.852919
$563$	−14.0829	−0.593522	−0.296761	−	0.954952i	$-0.595907\pi$
$563$	−14.0829	−0.593522	−0.296761	+	0.954952i	$0.595907\pi$
$564$	0.476045	0.0200451
$565$	8.99642	0.378482
$566$	−14.1664	−0.595457
$567$	−4.47164	−0.187791
$568$	−19.6520	−0.824580
$569$	−20.0727	−0.841493	−0.420746	−	0.907178i	$-0.638232\pi$
$569$	−20.0727	−0.841493	−0.420746	+	0.907178i	$0.638232\pi$
$570$	−6.73207	−0.281976
$571$	−39.6025	−1.65731	−0.828656	−	0.559758i	$-0.810894\pi$
$571$	−39.6025	−1.65731	−0.828656	+	0.559758i	$0.810894\pi$
$572$	0	0
$573$	−56.5004	−2.36034
$574$	−1.65280	−0.0689865
$575$	7.52949	0.314001
$576$	30.0860	1.25358
$577$	−20.3402	−0.846775	−0.423387	−	0.905949i	$-0.639159\pi$
$577$	−20.3402	−0.846775	−0.423387	+	0.905949i	$0.639159\pi$
$578$	22.5045	0.936064
$579$	43.2472	1.79729
$580$	1.48063	0.0614797
$581$	16.2863	0.675671
$582$	−35.8537	−1.48618
$583$	4.77065	0.197580
$584$	18.2001	0.753125
$585$	0	0
$586$	29.8361	1.23252
$587$	−27.7622	−1.14587	−0.572934	−	0.819602i	$-0.694195\pi$
$587$	−27.7622	−1.14587	−0.572934	+	0.819602i	$0.694195\pi$
$588$	0.390233	0.0160929
$589$	2.56360	0.105631
$590$	20.5229	0.844915
$591$	−6.14947	−0.252955
$592$	8.91143	0.366257
$593$	−22.4330	−0.921211	−0.460605	−	0.887605i	$-0.652368\pi$
$593$	−22.4330	−0.921211	−0.460605	+	0.887605i	$0.652368\pi$
$594$	19.9409	0.818186
$595$	−1.28033	−0.0524885
$596$	−1.17940	−0.0483101
$597$	−47.1511	−1.92977
$598$	0	0
$599$	45.5527	1.86123	0.930617	−	0.365996i	$-0.119271\pi$
$599$	45.5527	1.86123	0.930617	+	0.365996i	$0.119271\pi$
$600$	7.23780	0.295482
$601$	−8.47654	−0.345765	−0.172883	−	0.984942i	$-0.555308\pi$
$601$	−8.47654	−0.345765	−0.172883	+	0.984942i	$0.555308\pi$
$602$	−11.5789	−0.471921
$603$	−47.3141	−1.92678
$604$	0.802562	0.0326558
$605$	10.4158	0.423463
$606$	−4.18379	−0.169955
$607$	−31.5717	−1.28145	−0.640727	−	0.767769i	$-0.721367\pi$
$607$	−31.5717	−1.28145	−0.640727	+	0.767769i	$0.721367\pi$
$608$	1.42516	0.0577979
$609$	26.9523	1.09216
$610$	18.7592	0.759537
$611$	0	0
$612$	−0.769250	−0.0310951
$613$	13.4748	0.544244	0.272122	−	0.962263i	$-0.412275\pi$
$613$	13.4748	0.544244	0.272122	+	0.962263i	$0.412275\pi$
$614$	8.30029	0.334972
$615$	3.00677	0.121245
$616$	−12.5671	−0.506345
$617$	36.6834	1.47682	0.738410	−	0.674352i	$-0.235577\pi$
$617$	36.6834	1.47682	0.738410	+	0.674352i	$0.235577\pi$
$618$	−32.3641	−1.30188
$619$	−35.3137	−1.41938	−0.709688	−	0.704516i	$-0.751164\pi$
$619$	−35.3137	−1.41938	−0.709688	+	0.704516i	$0.751164\pi$
$620$	0.217712	0.00874353
$621$	22.1455	0.888670
$622$	−38.0090	−1.52402
$623$	3.09148	0.123857
$624$	0	0
$625$	1.00000	0.0400000
$626$	24.8825	0.994506
$627$	−21.2647	−0.849230
$628$	3.05822	0.122036
$629$	2.67116	0.106506
$630$	−6.01194	−0.239521
$631$	−34.7223	−1.38227	−0.691137	−	0.722723i	$-0.742890\pi$
$631$	−34.7223	−1.38227	−0.691137	+	0.722723i	$0.742890\pi$
$632$	32.4129	1.28932
$633$	−16.5901	−0.659396
$634$	5.51385	0.218983
$635$	3.62461	0.143838
$636$	−0.402285	−0.0159517
$637$	0	0
$638$	68.5619	2.71439
$639$	−29.6958	−1.17475
$640$	−12.3947	−0.489944
$641$	12.9368	0.510971	0.255485	−	0.966813i	$-0.417765\pi$
$641$	12.9368	0.510971	0.255485	+	0.966813i	$0.417765\pi$
$642$	−49.1797	−1.94097
$643$	25.9004	1.02141	0.510707	−	0.859755i	$-0.329384\pi$
$643$	25.9004	1.02141	0.510707	+	0.859755i	$0.329384\pi$
$644$	1.10243	0.0434420
$645$	21.0644	0.829408
$646$	3.23396	0.127238
$647$	−14.5044	−0.570228	−0.285114	−	0.958494i	$-0.592031\pi$
$647$	−14.5044	−0.570228	−0.285114	+	0.958494i	$0.592031\pi$
$648$	−12.1433	−0.477033
$649$	64.8260	2.54464
$650$	0	0
$651$	3.96308	0.155325
$652$	2.73143	0.106971
$653$	23.2408	0.909481	0.454741	−	0.890624i	$-0.349732\pi$
$653$	23.2408	0.909481	0.454741	+	0.890624i	$0.349732\pi$
$654$	−8.39306	−0.328194
$655$	18.2622	0.713564
$656$	−4.81873	−0.188140
$657$	27.5018	1.07295
$658$	−1.78723	−0.0696735
$659$	−33.2905	−1.29681	−0.648407	−	0.761294i	$-0.724564\pi$
$659$	−33.2905	−1.29681	−0.648407	+	0.761294i	$0.724564\pi$
$660$	−1.80589	−0.0702942
$661$	9.24842	0.359722	0.179861	−	0.983692i	$-0.442435\pi$
$661$	9.24842	0.359722	0.179861	+	0.983692i	$0.442435\pi$
$662$	−37.2811	−1.44897
$663$	0	0
$664$	44.2275	1.71636
$665$	1.72407	0.0668566
$666$	12.5427	0.486021
$667$	76.1420	2.94823
$668$	−0.779193	−0.0301479
$669$	−14.1839	−0.548380
$670$	16.8923	0.652608
$671$	59.2549	2.28751
$672$	2.20316	0.0849888
$673$	0.808875	0.0311798	0.0155899	−	0.999878i	$-0.495037\pi$
$673$	0.808875	0.0311798	0.0155899	+	0.999878i	$0.495037\pi$
$674$	39.8702	1.53574
$675$	2.94117	0.113206
$676$	0	0
$677$	−16.7684	−0.644462	−0.322231	−	0.946661i	$-0.604433\pi$
$677$	−16.7684	−0.644462	−0.322231	+	0.946661i	$0.604433\pi$
$678$	−35.1288	−1.34911
$679$	9.18205	0.352375
$680$	−3.47690	−0.133333
$681$	34.4914	1.32171
$682$	10.0814	0.386036
$683$	−28.8879	−1.10536	−0.552682	−	0.833392i	$-0.686396\pi$
$683$	−28.8879	−1.10536	−0.552682	+	0.833392i	$0.686396\pi$
$684$	1.03586	0.0396070
$685$	−0.567292	−0.0216751
$686$	−1.46507	−0.0559364
$687$	71.6755	2.73459
$688$	−33.7583	−1.28702
$689$	0	0
$690$	−29.4008	−1.11927
$691$	20.5225	0.780712	0.390356	−	0.920664i	$-0.372352\pi$
$691$	20.5225	0.780712	0.390356	+	0.920664i	$0.372352\pi$
$692$	−1.52398	−0.0579331
$693$	−18.9900	−0.721370
$694$	24.0814	0.914117
$695$	−8.48359	−0.321801
$696$	73.1923	2.77435
$697$	−1.44440	−0.0547104
$698$	5.14901	0.194893
$699$	−1.71502	−0.0648679
$700$	0.146416	0.00553399
$701$	−18.5376	−0.700154	−0.350077	−	0.936721i	$-0.613845\pi$
$701$	−18.5376	−0.700154	−0.350077	+	0.936721i	$0.613845\pi$
$702$	0	0
$703$	−3.59694	−0.135661
$704$	−33.9292	−1.27875
$705$	3.25133	0.122452
$706$	−5.51077	−0.207401
$707$	1.07146	0.0402964
$708$	−5.46646	−0.205442
$709$	8.56864	0.321802	0.160901	−	0.986971i	$-0.448560\pi$
$709$	8.56864	0.321802	0.160901	+	0.986971i	$0.448560\pi$
$710$	10.6022	0.397892
$711$	48.9786	1.83684
$712$	8.39528	0.314627
$713$	11.1960	0.419292
$714$	4.99939	0.187097
$715$	0	0
$716$	−0.515134	−0.0192514
$717$	−64.2429	−2.39920
$718$	8.07557	0.301378
$719$	−10.7670	−0.401541	−0.200771	−	0.979638i	$-0.564345\pi$
$719$	−10.7670	−0.401541	−0.200771	+	0.979638i	$0.564345\pi$
$720$	−17.5278	−0.653222
$721$	8.28838	0.308675
$722$	23.4815	0.873889
$723$	2.08247	0.0774479
$724$	−2.34233	−0.0870521
$725$	10.1125	0.375569
$726$	−40.6712	−1.50945
$727$	−18.2670	−0.677487	−0.338743	−	0.940879i	$-0.610002\pi$
$727$	−18.2670	−0.677487	−0.338743	+	0.940879i	$0.610002\pi$
$728$	0	0
$729$	−41.8663	−1.55061
$730$	−9.81886	−0.363412
$731$	−10.1189	−0.374262
$732$	−4.99668	−0.184683
$733$	13.1869	0.487069	0.243534	−	0.969892i	$-0.421693\pi$
$733$	13.1869	0.487069	0.243534	+	0.969892i	$0.421693\pi$
$734$	−44.0060	−1.62429
$735$	2.66524	0.0983090
$736$	6.22407	0.229422
$737$	53.3581	1.96547
$738$	−6.78231	−0.249660
$739$	2.22164	0.0817243	0.0408621	−	0.999165i	$-0.486990\pi$
$739$	2.22164	0.0817243	0.0408621	+	0.999165i	$0.486990\pi$
$740$	−0.305467	−0.0112292
$741$	0	0
$742$	1.51031	0.0554453
$743$	22.2034	0.814564	0.407282	−	0.913302i	$-0.366477\pi$
$743$	22.2034	0.814564	0.407282	+	0.913302i	$0.366477\pi$
$744$	10.7622	0.394562
$745$	−8.05515	−0.295118
$746$	−20.4217	−0.747690
$747$	66.8314	2.44523
$748$	0.867516	0.0317195
$749$	12.5948	0.460205
$750$	−3.90476	−0.142582
$751$	46.9512	1.71327	0.856637	−	0.515920i	$-0.172550\pi$
$751$	46.9512	1.71327	0.856637	+	0.515920i	$0.172550\pi$
$752$	−5.21067	−0.190013
$753$	33.2640	1.21221
$754$	0	0
$755$	5.48140	0.199488
$756$	0.430634	0.0156620
$757$	−38.0694	−1.38366	−0.691828	−	0.722062i	$-0.743195\pi$
$757$	−38.0694	−1.38366	−0.691828	+	0.722062i	$0.743195\pi$
$758$	−30.3941	−1.10396
$759$	−92.8688	−3.37092
$760$	4.68192	0.169831
$761$	−35.6231	−1.29134	−0.645668	−	0.763619i	$-0.723421\pi$
$761$	−35.6231	−1.29134	−0.645668	+	0.763619i	$0.723421\pi$
$762$	−14.1532	−0.512717
$763$	2.14944	0.0778151
$764$	−3.10386	−0.112294
$765$	−5.25388	−0.189955
$766$	−3.65765	−0.132156
$767$	0	0
$768$	9.31663	0.336185
$769$	−5.26155	−0.189736	−0.0948681	−	0.995490i	$-0.530243\pi$
$769$	−5.26155	−0.189736	−0.0948681	+	0.995490i	$0.530243\pi$
$770$	6.77992	0.244331
$771$	21.0319	0.757444
$772$	2.37579	0.0855065
$773$	41.1018	1.47833	0.739165	−	0.673525i	$-0.235220\pi$
$773$	41.1018	1.47833	0.739165	+	0.673525i	$0.235220\pi$
$774$	−47.5144	−1.70787
$775$	1.48695	0.0534127
$776$	24.9350	0.895114
$777$	−5.56051	−0.199482
$778$	15.4580	0.554195
$779$	1.94499	0.0696866
$780$	0	0
$781$	33.4892	1.19834
$782$	14.1236	0.505059
$783$	29.7426	1.06292
$784$	−4.27139	−0.152550
$785$	20.8873	0.745498
$786$	−71.3095	−2.54353
$787$	−7.99614	−0.285032	−0.142516	−	0.989793i	$-0.545519\pi$
$787$	−7.99614	−0.285032	−0.142516	+	0.989793i	$0.545519\pi$
$788$	−0.337822	−0.0120344
$789$	31.9143	1.13618
$790$	−17.4866	−0.622145
$791$	8.99642	0.319876
$792$	−51.5696	−1.83245
$793$	0	0
$794$	−29.7690	−1.05646
$795$	−2.74756	−0.0974459
$796$	−2.59025	−0.0918090
$797$	18.2780	0.647439	0.323720	−	0.946153i	$-0.395067\pi$
$797$	18.2780	0.647439	0.323720	+	0.946153i	$0.395067\pi$
$798$	−6.73207	−0.238313
$799$	−1.56188	−0.0552552
$800$	0.826626	0.0292256
$801$	12.6860	0.448237
$802$	−18.2739	−0.645275
$803$	−31.0150	−1.09449
$804$	−4.49943	−0.158682
$805$	7.52949	0.265380
$806$	0	0
$807$	3.84892	0.135488
$808$	2.90968	0.102362
$809$	−37.3141	−1.31189	−0.655946	−	0.754808i	$-0.727730\pi$
$809$	−37.3141	−1.31189	−0.655946	+	0.754808i	$0.727730\pi$
$810$	6.55124	0.230187
$811$	25.5479	0.897110	0.448555	−	0.893755i	$-0.351939\pi$
$811$	25.5479	0.897110	0.448555	+	0.893755i	$0.351939\pi$
$812$	1.48063	0.0519599
$813$	50.5026	1.77120
$814$	−14.1450	−0.495781
$815$	18.6553	0.653468
$816$	14.5757	0.510252
$817$	13.6259	0.476711
$818$	−15.6299	−0.546487
$819$	0	0
$820$	0.165177	0.00576824
$821$	46.1178	1.60952	0.804762	−	0.593598i	$-0.202293\pi$
$821$	46.1178	1.60952	0.804762	+	0.593598i	$0.202293\pi$
$822$	2.21514	0.0772618
$823$	8.81111	0.307136	0.153568	−	0.988138i	$-0.450924\pi$
$823$	8.81111	0.307136	0.153568	+	0.988138i	$0.450924\pi$
$824$	22.5081	0.784107
$825$	−12.3340	−0.429415
$826$	20.5229	0.714083
$827$	29.5559	1.02776	0.513879	−	0.857862i	$-0.328208\pi$
$827$	29.5559	1.02776	0.513879	+	0.857862i	$0.328208\pi$
$828$	4.52387	0.157215
$829$	9.76643	0.339202	0.169601	−	0.985513i	$-0.445752\pi$
$829$	9.76643	0.339202	0.169601	+	0.985513i	$0.445752\pi$
$830$	−23.8605	−0.828211
$831$	28.6918	0.995306
$832$	0	0
$833$	−1.28033	−0.0443609
$834$	33.1264	1.14707
$835$	−5.32179	−0.184168
$836$	−1.16818	−0.0404023
$837$	4.37337	0.151166
$838$	−43.4892	−1.50231
$839$	−30.3025	−1.04616	−0.523080	−	0.852284i	$-0.675217\pi$
$839$	−30.3025	−1.04616	−0.523080	+	0.852284i	$0.675217\pi$
$840$	7.23780	0.249728
$841$	73.2628	2.52630
$842$	19.7052	0.679085
$843$	36.7837	1.26690
$844$	−0.911378	−0.0313709
$845$	0	0
$846$	−7.33395	−0.252146
$847$	10.4158	0.357892
$848$	4.40331	0.151210
$849$	25.7714	0.884473
$850$	1.87577	0.0643384
$851$	−15.7088	−0.538491
$852$	−2.82398	−0.0967481
$853$	−11.5388	−0.395082	−0.197541	−	0.980295i	$-0.563295\pi$
$853$	−11.5388	−0.395082	−0.197541	+	0.980295i	$0.563295\pi$
$854$	18.7592	0.641926
$855$	7.07477	0.241952
$856$	34.2028	1.16903
$857$	−30.0981	−1.02813	−0.514066	−	0.857750i	$-0.671861\pi$
$857$	−30.0981	−1.02813	−0.514066	+	0.857750i	$0.671861\pi$
$858$	0	0
$859$	17.0420	0.581467	0.290733	−	0.956804i	$-0.406101\pi$
$859$	17.0420	0.581467	0.290733	+	0.956804i	$0.406101\pi$
$860$	1.15717	0.0394593
$861$	3.00677	0.102470
$862$	48.4569	1.65045
$863$	−15.0579	−0.512577	−0.256288	−	0.966600i	$-0.582500\pi$
$863$	−15.0579	−0.512577	−0.256288	+	0.966600i	$0.582500\pi$
$864$	2.43125	0.0827128
$865$	−10.4086	−0.353903
$866$	−19.7743	−0.671958
$867$	−40.9402	−1.39040
$868$	0.217712	0.00738964
$869$	−55.2352	−1.87373
$870$	−39.4869	−1.33873
$871$	0	0
$872$	5.83708	0.197668
$873$	37.6788	1.27523
$874$	−19.0185	−0.643312
$875$	1.00000	0.0338062
$876$	2.61534	0.0883642
$877$	−23.9557	−0.808926	−0.404463	−	0.914554i	$-0.632541\pi$
$877$	−23.9557	−0.808926	−0.404463	+	0.914554i	$0.632541\pi$
$878$	15.9671	0.538862
$879$	−54.2778	−1.83075
$880$	19.7668	0.666340
$881$	44.6031	1.50272	0.751359	−	0.659894i	$-0.229399\pi$
$881$	44.6031	1.50272	0.751359	+	0.659894i	$0.229399\pi$
$882$	−6.01194	−0.202432
$883$	53.9903	1.81692	0.908459	−	0.417974i	$-0.137260\pi$
$883$	53.9903	1.81692	0.908459	+	0.417974i	$0.137260\pi$
$884$	0	0
$885$	−37.3352	−1.25501
$886$	49.2146	1.65340
$887$	−8.51255	−0.285823	−0.142912	−	0.989735i	$-0.545646\pi$
$887$	−8.51255	−0.285823	−0.142912	+	0.989735i	$0.545646\pi$
$888$	−15.1002	−0.506731
$889$	3.62461	0.121565
$890$	−4.52922	−0.151820
$891$	20.6935	0.693258
$892$	−0.779193	−0.0260893
$893$	2.10319	0.0703806
$894$	31.4534	1.05196
$895$	−3.51830	−0.117604
$896$	−12.3947	−0.414078
$897$	0	0
$898$	−49.4449	−1.65000
$899$	15.0368	0.501504
$900$	0.600821	0.0200274
$901$	1.31987	0.0439714
$902$	7.64870	0.254674
$903$	21.0644	0.700978
$904$	24.4309	0.812559
$905$	−15.9978	−0.531786
$906$	−21.4035	−0.711084
$907$	−31.8891	−1.05886	−0.529431	−	0.848353i	$-0.677594\pi$
$907$	−31.8891	−1.05886	−0.529431	+	0.848353i	$0.677594\pi$
$908$	1.89479	0.0628809
$909$	4.39677	0.145832
$910$	0	0
$911$	−32.7163	−1.08394	−0.541970	−	0.840398i	$-0.682322\pi$
$911$	−32.7163	−1.08394	−0.541970	+	0.840398i	$0.682322\pi$
$912$	−19.6273	−0.649926
$913$	−75.3686	−2.49434
$914$	16.5243	0.546575
$915$	−34.1267	−1.12819
$916$	3.93750	0.130099
$917$	18.2622	0.603071
$918$	5.51697	0.182087
$919$	−34.3802	−1.13410	−0.567050	−	0.823684i	$-0.691915\pi$
$919$	−34.3802	−1.13410	−0.567050	+	0.823684i	$0.691915\pi$
$920$	20.4472	0.674126
$921$	−15.0999	−0.497558
$922$	−56.9428	−1.87531
$923$	0	0
$924$	−1.80589	−0.0594095
$925$	−2.08630	−0.0685973
$926$	15.9105	0.522852
$927$	34.0116	1.11709
$928$	8.35926	0.274406
$929$	16.1622	0.530265	0.265132	−	0.964212i	$-0.414584\pi$
$929$	16.1622	0.530265	0.265132	+	0.964212i	$0.414584\pi$
$930$	−5.80617	−0.190392
$931$	1.72407	0.0565041
$932$	−0.0942147	−0.00308611
$933$	69.1459	2.26373
$934$	−45.0498	−1.47407
$935$	5.92503	0.193769
$936$	0	0
$937$	31.0608	1.01471	0.507356	−	0.861737i	$-0.330623\pi$
$937$	31.0608	1.01471	0.507356	+	0.861737i	$0.330623\pi$
$938$	16.8923	0.551554
$939$	−45.2663	−1.47721
$940$	0.178612	0.00582568
$941$	−60.4279	−1.96989	−0.984947	−	0.172858i	$-0.944700\pi$
$941$	−60.4279	−1.96989	−0.984947	+	0.172858i	$0.944700\pi$
$942$	−81.5597	−2.65736
$943$	8.49432	0.276613
$944$	59.8345	1.94745
$945$	2.94117	0.0956764
$946$	53.5840	1.74217
$947$	−32.7981	−1.06580	−0.532898	−	0.846180i	$-0.678897\pi$
$947$	−32.7981	−1.06580	−0.532898	+	0.846180i	$0.678897\pi$
$948$	4.65772	0.151276
$949$	0	0
$950$	−2.52587	−0.0819502
$951$	−10.0308	−0.325270
$952$	−3.47690	−0.112687
$953$	11.5855	0.375290	0.187645	−	0.982237i	$-0.439915\pi$
$953$	11.5855	0.375290	0.187645	+	0.982237i	$0.439915\pi$
$954$	6.19761	0.200655
$955$	−21.1989	−0.685982
$956$	−3.52919	−0.114142
$957$	−124.728	−4.03188
$958$	46.3846	1.49862
$959$	−0.567292	−0.0183188
$960$	19.5408	0.630678
$961$	−28.7890	−0.928677
$962$	0	0
$963$	51.6832	1.66547
$964$	0.114401	0.00368460
$965$	16.2263	0.522344
$966$	−29.4008	−0.945956
$967$	47.3045	1.52121	0.760604	−	0.649216i	$-0.224903\pi$
$967$	47.3045	1.52121	0.760604	+	0.649216i	$0.224903\pi$
$968$	28.2854	0.909128
$969$	−5.88322	−0.188996
$970$	−13.4523	−0.431927
$971$	25.7962	0.827840	0.413920	−	0.910313i	$-0.364159\pi$
$971$	25.7962	0.827840	0.413920	+	0.910313i	$0.364159\pi$
$972$	−3.03688	−0.0974081
$973$	−8.48359	−0.271971
$974$	−11.5622	−0.370476
$975$	0	0
$976$	54.6924	1.75066
$977$	21.5667	0.689980	0.344990	−	0.938606i	$-0.387882\pi$
$977$	21.5667	0.689980	0.344990	+	0.938606i	$0.387882\pi$
$978$	−72.8445	−2.32931
$979$	−14.3065	−0.457238
$980$	0.146416	0.00467707
$981$	8.82031	0.281611
$982$	61.3697	1.95839
$983$	−40.2239	−1.28294	−0.641472	−	0.767147i	$-0.721676\pi$
$983$	−40.2239	−1.28294	−0.641472	+	0.767147i	$0.721676\pi$
$984$	8.16525	0.260299
$985$	−2.30728	−0.0735161
$986$	18.9687	0.604088
$987$	3.25133	0.103491
$988$	0	0
$989$	59.5081	1.89225
$990$	27.8216	0.884228
$991$	−17.2351	−0.547490	−0.273745	−	0.961802i	$-0.588262\pi$
$991$	−17.2351	−0.547490	−0.273745	+	0.961802i	$0.588262\pi$
$992$	1.22915	0.0390255
$993$	67.8217	2.15226
$994$	10.6022	0.336280
$995$	−17.6911	−0.560845
$996$	6.35547	0.201381
$997$	0.332018	0.0105151	0.00525755	−	0.999986i	$-0.498326\pi$
$997$	0.332018	0.0105151	0.00525755	+	0.999986i	$0.498326\pi$
$998$	1.66018	0.0525521
$999$	−6.13619	−0.194140

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5915.2.a.bd.1.3		9
13.5	odd	4		455.2.d.b.246.13	yes	18
13.8	odd	4		455.2.d.b.246.6	✓	18
13.12	even	2		5915.2.a.bc.1.7		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
455.2.d.b.246.6	✓	18	13.8	odd	4
455.2.d.b.246.13	yes	18	13.5	odd	4
5915.2.a.bc.1.7		9	13.12	even	2
5915.2.a.bd.1.3		9	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:	\( N \)	\(=\)	\( 5915 = 5 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5915.a (trivial)

\(f(q)\)	\(=\)	\(q-1.46507 q^{2} +2.66524 q^{3} +0.146416 q^{4} +1.00000 q^{5} -3.90476 q^{6} +1.00000 q^{7} +2.71562 q^{8} +4.10353 q^{9} +O(q^{10})\)	\(q-1.46507 q^{2} +2.66524 q^{3} +0.146416 q^{4} +1.00000 q^{5} -3.90476 q^{6} +1.00000 q^{7} +2.71562 q^{8} +4.10353 q^{9} -1.46507 q^{10} -4.62772 q^{11} +0.390233 q^{12} -1.46507 q^{14} +2.66524 q^{15} -4.27139 q^{16} -1.28033 q^{17} -6.01194 q^{18} +1.72407 q^{19} +0.146416 q^{20} +2.66524 q^{21} +6.77992 q^{22} +7.52949 q^{23} +7.23780 q^{24} +1.00000 q^{25} +2.94117 q^{27} +0.146416 q^{28} +10.1125 q^{29} -3.90476 q^{30} +1.48695 q^{31} +0.826626 q^{32} -12.3340 q^{33} +1.87577 q^{34} +1.00000 q^{35} +0.600821 q^{36} -2.08630 q^{37} -2.52587 q^{38} +2.71562 q^{40} +1.12814 q^{41} -3.90476 q^{42} +7.90335 q^{43} -0.677571 q^{44} +4.10353 q^{45} -11.0312 q^{46} +1.21990 q^{47} -11.3843 q^{48} +1.00000 q^{49} -1.46507 q^{50} -3.41240 q^{51} -1.03088 q^{53} -4.30901 q^{54} -4.62772 q^{55} +2.71562 q^{56} +4.59507 q^{57} -14.8155 q^{58} -14.0082 q^{59} +0.390233 q^{60} -12.8043 q^{61} -2.17847 q^{62} +4.10353 q^{63} +7.33173 q^{64} +18.0701 q^{66} -11.5301 q^{67} -0.187461 q^{68} +20.0679 q^{69} -1.46507 q^{70} -7.23666 q^{71} +11.1436 q^{72} +6.70200 q^{73} +3.05657 q^{74} +2.66524 q^{75} +0.252431 q^{76} -4.62772 q^{77} +11.9357 q^{79} -4.27139 q^{80} -4.47164 q^{81} -1.65280 q^{82} +16.2863 q^{83} +0.390233 q^{84} -1.28033 q^{85} -11.5789 q^{86} +26.9523 q^{87} -12.5671 q^{88} +3.09148 q^{89} -6.01194 q^{90} +1.10243 q^{92} +3.96308 q^{93} -1.78723 q^{94} +1.72407 q^{95} +2.20316 q^{96} +9.18205 q^{97} -1.46507 q^{98} -18.9900 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 2 q^{3} + 12 q^{4} + 9 q^{5} + 12 q^{6} + 9 q^{7} + 13 q^{9}+O(q^{10}) \) 9 * q + 2 * q^3 + 12 * q^4 + 9 * q^5 + 12 * q^6 + 9 * q^7 + 13 * q^9	\( 9 q + 2 q^{3} + 12 q^{4} + 9 q^{5} + 12 q^{6} + 9 q^{7} + 13 q^{9} + 8 q^{11} - 5 q^{12} + 2 q^{15} + 26 q^{16} + 6 q^{17} - q^{18} + 6 q^{19} + 12 q^{20} + 2 q^{21} - 4 q^{22} + 12 q^{23} + 45 q^{24} + 9 q^{25} + 14 q^{27} + 12 q^{28} + 22 q^{29} + 12 q^{30} + 20 q^{31} - 15 q^{32} - 12 q^{33} + q^{34} + 9 q^{35} + 20 q^{36} + 4 q^{37} - 19 q^{38} + 8 q^{41} + 12 q^{42} + 10 q^{43} - 14 q^{44} + 13 q^{45} - 2 q^{46} - 4 q^{47} - 60 q^{48} + 9 q^{49} + 22 q^{51} + 22 q^{53} + 31 q^{54} + 8 q^{55} - 28 q^{57} - 28 q^{58} + 8 q^{59} - 5 q^{60} + 8 q^{61} - 14 q^{62} + 13 q^{63} + 46 q^{64} - 2 q^{66} - 16 q^{67} + 70 q^{68} + 30 q^{69} + 12 q^{71} - 34 q^{72} + 10 q^{73} - 44 q^{74} + 2 q^{75} - 30 q^{76} + 8 q^{77} - 2 q^{79} + 26 q^{80} + 33 q^{81} + q^{82} + 16 q^{83} - 5 q^{84} + 6 q^{85} + 28 q^{86} - 40 q^{87} + 8 q^{88} + 34 q^{89} - q^{90} + 50 q^{92} - 50 q^{93} + 40 q^{94} + 6 q^{95} + 80 q^{96} + 12 q^{97} - 30 q^{99}+O(q^{100}) \) 9 * q + 2 * q^3 + 12 * q^4 + 9 * q^5 + 12 * q^6 + 9 * q^7 + 13 * q^9 + 8 * q^11 - 5 * q^12 + 2 * q^15 + 26 * q^16 + 6 * q^17 - q^18 + 6 * q^19 + 12 * q^20 + 2 * q^21 - 4 * q^22 + 12 * q^23 + 45 * q^24 + 9 * q^25 + 14 * q^27 + 12 * q^28 + 22 * q^29 + 12 * q^30 + 20 * q^31 - 15 * q^32 - 12 * q^33 + q^34 + 9 * q^35 + 20 * q^36 + 4 * q^37 - 19 * q^38 + 8 * q^41 + 12 * q^42 + 10 * q^43 - 14 * q^44 + 13 * q^45 - 2 * q^46 - 4 * q^47 - 60 * q^48 + 9 * q^49 + 22 * q^51 + 22 * q^53 + 31 * q^54 + 8 * q^55 - 28 * q^57 - 28 * q^58 + 8 * q^59 - 5 * q^60 + 8 * q^61 - 14 * q^62 + 13 * q^63 + 46 * q^64 - 2 * q^66 - 16 * q^67 + 70 * q^68 + 30 * q^69 + 12 * q^71 - 34 * q^72 + 10 * q^73 - 44 * q^74 + 2 * q^75 - 30 * q^76 + 8 * q^77 - 2 * q^79 + 26 * q^80 + 33 * q^81 + q^82 + 16 * q^83 - 5 * q^84 + 6 * q^85 + 28 * q^86 - 40 * q^87 + 8 * q^88 + 34 * q^89 - q^90 + 50 * q^92 - 50 * q^93 + 40 * q^94 + 6 * q^95 + 80 * q^96 + 12 * q^97 - 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more