LMFDB - Embedded newform 7935.2.a.bl.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7935,2,Mod(1,7935)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7935, 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("7935.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7935 = 3 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7935.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:	$63.3612940039$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 16x^{10} + 92x^{8} - 4x^{7} - 234x^{6} + 32x^{5} + 252x^{4} - 68x^{3} - 76x^{2} + 32x - 2 $ x^12 - 16x^10 + 92x^8 - 4x^7 - 234x^6 + 32x^5 + 252x^4 - 68x^3 - 76x^2 + 32*x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$2.61103$ of defining polynomial
Character	$\chi$	$=$	7935.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.61103 q^{2} +1.00000 q^{3} +4.81746 q^{4} -1.00000 q^{5} +2.61103 q^{6} +4.73661 q^{7} +7.35645 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.61103 q^{2} +1.00000 q^{3} +4.81746 q^{4} -1.00000 q^{5} +2.61103 q^{6} +4.73661 q^{7} +7.35645 q^{8} +1.00000 q^{9} -2.61103 q^{10} +3.07512 q^{11} +4.81746 q^{12} -6.05956 q^{13} +12.3674 q^{14} -1.00000 q^{15} +9.57297 q^{16} +6.93369 q^{17} +2.61103 q^{18} +1.19411 q^{19} -4.81746 q^{20} +4.73661 q^{21} +8.02923 q^{22} +7.35645 q^{24} +1.00000 q^{25} -15.8217 q^{26} +1.00000 q^{27} +22.8184 q^{28} -4.71195 q^{29} -2.61103 q^{30} +5.07039 q^{31} +10.2824 q^{32} +3.07512 q^{33} +18.1040 q^{34} -4.73661 q^{35} +4.81746 q^{36} -1.65119 q^{37} +3.11785 q^{38} -6.05956 q^{39} -7.35645 q^{40} -3.95403 q^{41} +12.3674 q^{42} -11.9318 q^{43} +14.8143 q^{44} -1.00000 q^{45} -5.37718 q^{47} +9.57297 q^{48} +15.4355 q^{49} +2.61103 q^{50} +6.93369 q^{51} -29.1917 q^{52} -6.44486 q^{53} +2.61103 q^{54} -3.07512 q^{55} +34.8447 q^{56} +1.19411 q^{57} -12.3030 q^{58} -9.32751 q^{59} -4.81746 q^{60} -4.11660 q^{61} +13.2389 q^{62} +4.73661 q^{63} +7.70160 q^{64} +6.05956 q^{65} +8.02923 q^{66} -3.93311 q^{67} +33.4027 q^{68} -12.3674 q^{70} -7.33554 q^{71} +7.35645 q^{72} +2.18243 q^{73} -4.31129 q^{74} +1.00000 q^{75} +5.75257 q^{76} +14.5657 q^{77} -15.8217 q^{78} +3.68919 q^{79} -9.57297 q^{80} +1.00000 q^{81} -10.3241 q^{82} +9.41994 q^{83} +22.8184 q^{84} -6.93369 q^{85} -31.1542 q^{86} -4.71195 q^{87} +22.6220 q^{88} +10.5183 q^{89} -2.61103 q^{90} -28.7018 q^{91} +5.07039 q^{93} -14.0400 q^{94} -1.19411 q^{95} +10.2824 q^{96} +11.9404 q^{97} +40.3025 q^{98} +3.07512 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{3} + 8 q^{4} - 12 q^{5} + 4 q^{7} + 12 q^{9}+O(q^{10}) $ 12 * q + 12 * q^3 + 8 * q^4 - 12 * q^5 + 4 * q^7 + 12 * q^9	$ 12 q + 12 q^{3} + 8 q^{4} - 12 q^{5} + 4 q^{7} + 12 q^{9} + 24 q^{11} + 8 q^{12} - 8 q^{13} + 16 q^{14} - 12 q^{15} + 28 q^{17} + 16 q^{19} - 8 q^{20} + 4 q^{21} + 12 q^{25} - 36 q^{26} + 12 q^{27} + 8 q^{28} - 16 q^{29} + 20 q^{32} + 24 q^{33} + 16 q^{34} - 4 q^{35} + 8 q^{36} + 20 q^{37} + 16 q^{38} - 8 q^{39} - 4 q^{41} + 16 q^{42} - 12 q^{43} + 16 q^{44} - 12 q^{45} + 4 q^{47} + 24 q^{49} + 28 q^{51} - 36 q^{52} + 28 q^{53} - 24 q^{55} + 56 q^{56} + 16 q^{57} + 20 q^{59} - 8 q^{60} + 32 q^{61} + 12 q^{62} + 4 q^{63} - 4 q^{64} + 8 q^{65} - 4 q^{67} + 64 q^{68} - 16 q^{70} - 8 q^{71} + 4 q^{73} - 36 q^{74} + 12 q^{75} + 8 q^{76} - 28 q^{77} - 36 q^{78} + 40 q^{79} + 12 q^{81} - 28 q^{82} + 100 q^{83} + 8 q^{84} - 28 q^{85} - 20 q^{86} - 16 q^{87} + 80 q^{89} - 24 q^{91} + 44 q^{94} - 16 q^{95} + 20 q^{96} - 8 q^{97} + 28 q^{98} + 24 q^{99}+O(q^{100}) $ 12 * q + 12 * q^3 + 8 * q^4 - 12 * q^5 + 4 * q^7 + 12 * q^9 + 24 * q^11 + 8 * q^12 - 8 * q^13 + 16 * q^14 - 12 * q^15 + 28 * q^17 + 16 * q^19 - 8 * q^20 + 4 * q^21 + 12 * q^25 - 36 * q^26 + 12 * q^27 + 8 * q^28 - 16 * q^29 + 20 * q^32 + 24 * q^33 + 16 * q^34 - 4 * q^35 + 8 * q^36 + 20 * q^37 + 16 * q^38 - 8 * q^39 - 4 * q^41 + 16 * q^42 - 12 * q^43 + 16 * q^44 - 12 * q^45 + 4 * q^47 + 24 * q^49 + 28 * q^51 - 36 * q^52 + 28 * q^53 - 24 * q^55 + 56 * q^56 + 16 * q^57 + 20 * q^59 - 8 * q^60 + 32 * q^61 + 12 * q^62 + 4 * q^63 - 4 * q^64 + 8 * q^65 - 4 * q^67 + 64 * q^68 - 16 * q^70 - 8 * q^71 + 4 * q^73 - 36 * q^74 + 12 * q^75 + 8 * q^76 - 28 * q^77 - 36 * q^78 + 40 * q^79 + 12 * q^81 - 28 * q^82 + 100 * q^83 + 8 * q^84 - 28 * q^85 - 20 * q^86 - 16 * q^87 + 80 * q^89 - 24 * q^91 + 44 * q^94 - 16 * q^95 + 20 * q^96 - 8 * q^97 + 28 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.61103	1.84627	0.923137	−	0.384471i	$-0.125616\pi$
$2$	2.61103	1.84627	0.923137	+	0.384471i	$0.125616\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.81746	2.40873
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.61103	1.06595
$7$	4.73661	1.79027	0.895136	−	0.445794i	$-0.147079\pi$
$7$	4.73661	1.79027	0.895136	+	0.445794i	$0.147079\pi$
$8$	7.35645	2.60090
$9$	1.00000	0.333333
$10$	−2.61103	−0.825679
$11$	3.07512	0.927184	0.463592	−	0.886049i	$-0.346560\pi$
$11$	3.07512	0.927184	0.463592	+	0.886049i	$0.346560\pi$
$12$	4.81746	1.39068
$13$	−6.05956	−1.68062	−0.840310	−	0.542106i	$-0.817627\pi$
$13$	−6.05956	−1.68062	−0.840310	+	0.542106i	$0.817627\pi$
$14$	12.3674	3.30533
$15$	−1.00000	−0.258199
$16$	9.57297	2.39324
$17$	6.93369	1.68167	0.840833	−	0.541294i	$-0.182066\pi$
$17$	6.93369	1.68167	0.840833	+	0.541294i	$0.182066\pi$
$18$	2.61103	0.615425
$19$	1.19411	0.273947	0.136974	−	0.990575i	$-0.456262\pi$
$19$	1.19411	0.273947	0.136974	+	0.990575i	$0.456262\pi$
$20$	−4.81746	−1.07722
$21$	4.73661	1.03361
$22$	8.02923	1.71184
$23$	0	0
$23$	0	0
$24$	7.35645	1.50163
$25$	1.00000	0.200000
$26$	−15.8217	−3.10289
$27$	1.00000	0.192450
$28$	22.8184	4.31228
$29$	−4.71195	−0.874987	−0.437493	−	0.899222i	$-0.644134\pi$
$29$	−4.71195	−0.874987	−0.437493	+	0.899222i	$0.644134\pi$
$30$	−2.61103	−0.476706
$31$	5.07039	0.910669	0.455334	−	0.890320i	$-0.349520\pi$
$31$	5.07039	0.910669	0.455334	+	0.890320i	$0.349520\pi$
$32$	10.2824	1.81768
$33$	3.07512	0.535310
$34$	18.1040	3.10482
$35$	−4.73661	−0.800634
$36$	4.81746	0.802909
$37$	−1.65119	−0.271454	−0.135727	−	0.990746i	$-0.543337\pi$
$37$	−1.65119	−0.271454	−0.135727	+	0.990746i	$0.543337\pi$
$38$	3.11785	0.505782
$39$	−6.05956	−0.970307
$40$	−7.35645	−1.16316
$41$	−3.95403	−0.617516	−0.308758	−	0.951141i	$-0.599913\pi$
$41$	−3.95403	−0.617516	−0.308758	+	0.951141i	$0.599913\pi$
$42$	12.3674	1.90833
$43$	−11.9318	−1.81958	−0.909790	−	0.415068i	$-0.863758\pi$
$43$	−11.9318	−1.81958	−0.909790	+	0.415068i	$0.863758\pi$
$44$	14.8143	2.23334
$45$	−1.00000	−0.149071
$46$	0	0
$47$	−5.37718	−0.784343	−0.392171	−	0.919892i	$-0.628276\pi$
$47$	−5.37718	−0.784343	−0.392171	+	0.919892i	$0.628276\pi$
$48$	9.57297	1.38174
$49$	15.4355	2.20507
$50$	2.61103	0.369255
$51$	6.93369	0.970910
$52$	−29.1917	−4.04816
$53$	−6.44486	−0.885270	−0.442635	−	0.896702i	$-0.645956\pi$
$53$	−6.44486	−0.885270	−0.442635	+	0.896702i	$0.645956\pi$
$54$	2.61103	0.355316
$55$	−3.07512	−0.414649
$56$	34.8447	4.65631
$57$	1.19411	0.158164
$58$	−12.3030	−1.61547
$59$	−9.32751	−1.21434	−0.607169	−	0.794572i	$-0.707695\pi$
$59$	−9.32751	−1.21434	−0.607169	+	0.794572i	$0.707695\pi$
$60$	−4.81746	−0.621931
$61$	−4.11660	−0.527077	−0.263538	−	0.964649i	$-0.584890\pi$
$61$	−4.11660	−0.527077	−0.263538	+	0.964649i	$0.584890\pi$
$62$	13.2389	1.68134
$63$	4.73661	0.596757
$64$	7.70160	0.962700
$65$	6.05956	0.751596
$66$	8.02923	0.988329
$67$	−3.93311	−0.480506	−0.240253	−	0.970710i	$-0.577230\pi$
$67$	−3.93311	−0.480506	−0.240253	+	0.970710i	$0.577230\pi$
$68$	33.4027	4.05068
$69$	0	0
$70$	−12.3674	−1.47819
$71$	−7.33554	−0.870569	−0.435284	−	0.900293i	$-0.643352\pi$
$71$	−7.33554	−0.870569	−0.435284	+	0.900293i	$0.643352\pi$
$72$	7.35645	0.866966
$73$	2.18243	0.255434	0.127717	−	0.991811i	$-0.459235\pi$
$73$	2.18243	0.255434	0.127717	+	0.991811i	$0.459235\pi$
$74$	−4.31129	−0.501178
$75$	1.00000	0.115470
$76$	5.75257	0.659865
$77$	14.5657	1.65991
$78$	−15.8217	−1.79145
$79$	3.68919	0.415066	0.207533	−	0.978228i	$-0.433457\pi$
$79$	3.68919	0.415066	0.207533	+	0.978228i	$0.433457\pi$
$80$	−9.57297	−1.07029
$81$	1.00000	0.111111
$82$	−10.3241	−1.14010
$83$	9.41994	1.03397	0.516986	−	0.855994i	$-0.327054\pi$
$83$	9.41994	1.03397	0.516986	+	0.855994i	$0.327054\pi$
$84$	22.8184	2.48969
$85$	−6.93369	−0.752064
$86$	−31.1542	−3.35944
$87$	−4.71195	−0.505174
$88$	22.6220	2.41151
$89$	10.5183	1.11494	0.557470	−	0.830197i	$-0.311772\pi$
$89$	10.5183	1.11494	0.557470	+	0.830197i	$0.311772\pi$
$90$	−2.61103	−0.275226
$91$	−28.7018	−3.00877
$92$	0	0
$93$	5.07039	0.525775
$94$	−14.0400	−1.44811
$95$	−1.19411	−0.122513
$96$	10.2824	1.04944
$97$	11.9404	1.21237	0.606184	−	0.795324i	$-0.292699\pi$
$97$	11.9404	1.21237	0.606184	+	0.795324i	$0.292699\pi$
$98$	40.3025	4.07117
$99$	3.07512	0.309061
$100$	4.81746	0.481746
$101$	−2.79740	−0.278352	−0.139176	−	0.990268i	$-0.544445\pi$
$101$	−2.79740	−0.278352	−0.139176	+	0.990268i	$0.544445\pi$
$102$	18.1040	1.79257
$103$	−0.121041	−0.0119266	−0.00596329	−	0.999982i	$-0.501898\pi$
$103$	−0.121041	−0.0119266	−0.00596329	+	0.999982i	$0.501898\pi$
$104$	−44.5769	−4.37112
$105$	−4.73661	−0.462246
$106$	−16.8277	−1.63445
$107$	5.74677	0.555562	0.277781	−	0.960644i	$-0.410401\pi$
$107$	5.74677	0.555562	0.277781	+	0.960644i	$0.410401\pi$
$108$	4.81746	0.463560
$109$	−3.76646	−0.360762	−0.180381	−	0.983597i	$-0.557733\pi$
$109$	−3.76646	−0.360762	−0.180381	+	0.983597i	$0.557733\pi$
$110$	−8.02923	−0.765557
$111$	−1.65119	−0.156724
$112$	45.3435	4.28455
$113$	−0.665423	−0.0625977	−0.0312989	−	0.999510i	$-0.509964\pi$
$113$	−0.665423	−0.0625977	−0.0312989	+	0.999510i	$0.509964\pi$
$114$	3.11785	0.292013
$115$	0	0
$116$	−22.6996	−2.10761
$117$	−6.05956	−0.560207
$118$	−24.3544	−2.24200
$119$	32.8422	3.01064
$120$	−7.35645	−0.671549
$121$	−1.54362	−0.140329
$122$	−10.7486	−0.973128
$123$	−3.95403	−0.356523
$124$	24.4264	2.19355
$125$	−1.00000	−0.0894427
$126$	12.3674	1.10178
$127$	−1.93046	−0.171300	−0.0856501	−	0.996325i	$-0.527297\pi$
$127$	−1.93046	−0.171300	−0.0856501	+	0.996325i	$0.527297\pi$
$128$	−0.455668	−0.0402758
$129$	−11.9318	−1.05054
$130$	15.8217	1.38765
$131$	3.49573	0.305424	0.152712	−	0.988271i	$-0.451199\pi$
$131$	3.49573	0.305424	0.152712	+	0.988271i	$0.451199\pi$
$132$	14.8143	1.28942
$133$	5.65603	0.490440
$134$	−10.2694	−0.887145
$135$	−1.00000	−0.0860663
$136$	51.0073	4.37384
$137$	−10.1966	−0.871157	−0.435579	−	0.900151i	$-0.643456\pi$
$137$	−10.1966	−0.871157	−0.435579	+	0.900151i	$0.643456\pi$
$138$	0	0
$139$	−21.8465	−1.85299	−0.926497	−	0.376303i	$-0.877195\pi$
$139$	−21.8465	−1.85299	−0.926497	+	0.376303i	$0.877195\pi$
$140$	−22.8184	−1.92851
$141$	−5.37718	−0.452840
$142$	−19.1533	−1.60731
$143$	−18.6339	−1.55825
$144$	9.57297	0.797748
$145$	4.71195	0.391306
$146$	5.69837	0.471600
$147$	15.4355	1.27310
$148$	−7.95452	−0.653858
$149$	20.8113	1.70493	0.852465	−	0.522783i	$-0.175106\pi$
$149$	20.8113	1.70493	0.852465	+	0.522783i	$0.175106\pi$
$150$	2.61103	0.213189
$151$	7.20673	0.586476	0.293238	−	0.956040i	$-0.405267\pi$
$151$	7.20673	0.586476	0.293238	+	0.956040i	$0.405267\pi$
$152$	8.78441	0.712509
$153$	6.93369	0.560555
$154$	38.0313	3.06465
$155$	−5.07039	−0.407264
$156$	−29.1917	−2.33721
$157$	−17.5980	−1.40447	−0.702235	−	0.711945i	$-0.747814\pi$
$157$	−17.5980	−1.40447	−0.702235	+	0.711945i	$0.747814\pi$
$158$	9.63256	0.766325
$159$	−6.44486	−0.511111
$160$	−10.2824	−0.812893
$161$	0	0
$162$	2.61103	0.205142
$163$	23.8451	1.86769	0.933846	−	0.357674i	$-0.116430\pi$
$163$	23.8451	1.86769	0.933846	+	0.357674i	$0.116430\pi$
$164$	−19.0484	−1.48743
$165$	−3.07512	−0.239398
$166$	24.5957	1.90900
$167$	2.07675	0.160704	0.0803518	−	0.996767i	$-0.474396\pi$
$167$	2.07675	0.160704	0.0803518	+	0.996767i	$0.474396\pi$
$168$	34.8447	2.68832
$169$	23.7183	1.82449
$170$	−18.1040	−1.38852
$171$	1.19411	0.0913158
$172$	−57.4809	−4.38287
$173$	9.23081	0.701806	0.350903	−	0.936412i	$-0.385875\pi$
$173$	9.23081	0.701806	0.350903	+	0.936412i	$0.385875\pi$
$174$	−12.3030	−0.932689
$175$	4.73661	0.358054
$176$	29.4381	2.21898
$177$	−9.32751	−0.701099
$178$	27.4636	2.05849
$179$	2.63972	0.197302	0.0986510	−	0.995122i	$-0.468547\pi$
$179$	2.63972	0.197302	0.0986510	+	0.995122i	$0.468547\pi$
$180$	−4.81746	−0.359072
$181$	−2.45221	−0.182272	−0.0911358	−	0.995838i	$-0.529050\pi$
$181$	−2.45221	−0.182272	−0.0911358	+	0.995838i	$0.529050\pi$
$182$	−74.9412	−5.55501
$183$	−4.11660	−0.304308
$184$	0	0
$185$	1.65119	0.121398
$186$	13.2389	0.970725
$187$	21.3219	1.55921
$188$	−25.9043	−1.88927
$189$	4.73661	0.344538
$190$	−3.11785	−0.226193
$191$	−15.5298	−1.12369	−0.561847	−	0.827241i	$-0.689909\pi$
$191$	−15.5298	−1.12369	−0.561847	+	0.827241i	$0.689909\pi$
$192$	7.70160	0.555815
$193$	7.69118	0.553624	0.276812	−	0.960924i	$-0.410722\pi$
$193$	7.69118	0.553624	0.276812	+	0.960924i	$0.410722\pi$
$194$	31.1768	2.23837
$195$	6.05956	0.433934
$196$	74.3598	5.31142
$197$	9.85276	0.701980	0.350990	−	0.936379i	$-0.385845\pi$
$197$	9.85276	0.701980	0.350990	+	0.936379i	$0.385845\pi$
$198$	8.02923	0.570612
$199$	14.4397	1.02361	0.511803	−	0.859103i	$-0.328978\pi$
$199$	14.4397	1.02361	0.511803	+	0.859103i	$0.328978\pi$
$200$	7.35645	0.520180
$201$	−3.93311	−0.277420
$202$	−7.30409	−0.513914
$203$	−22.3187	−1.56646
$204$	33.4027	2.33866
$205$	3.95403	0.276161
$206$	−0.316042	−0.0220197
$207$	0	0
$208$	−58.0080	−4.02213
$209$	3.67203	0.254000
$210$	−12.3674	−0.853433
$211$	0.924349	0.0636348	0.0318174	−	0.999494i	$-0.489871\pi$
$211$	0.924349	0.0636348	0.0318174	+	0.999494i	$0.489871\pi$
$212$	−31.0478	−2.13237
$213$	−7.33554	−0.502623
$214$	15.0050	1.02572
$215$	11.9318	0.813741
$216$	7.35645	0.500543
$217$	24.0165	1.63034
$218$	−9.83433	−0.666065
$219$	2.18243	0.147475
$220$	−14.8143	−0.998778
$221$	−42.0151	−2.82624
$222$	−4.31129	−0.289355
$223$	−9.54389	−0.639106	−0.319553	−	0.947568i	$-0.603533\pi$
$223$	−9.54389	−0.639106	−0.319553	+	0.947568i	$0.603533\pi$
$224$	48.7036	3.25415
$225$	1.00000	0.0666667
$226$	−1.73744	−0.115573
$227$	5.84623	0.388028	0.194014	−	0.980999i	$-0.437849\pi$
$227$	5.84623	0.388028	0.194014	+	0.980999i	$0.437849\pi$
$228$	5.75257	0.380973
$229$	13.5935	0.898281	0.449140	−	0.893461i	$-0.351730\pi$
$229$	13.5935	0.898281	0.449140	+	0.893461i	$0.351730\pi$
$230$	0	0
$231$	14.5657	0.958350
$232$	−34.6632	−2.27575
$233$	−15.3077	−1.00284	−0.501421	−	0.865204i	$-0.667189\pi$
$233$	−15.3077	−1.00284	−0.501421	+	0.865204i	$0.667189\pi$
$234$	−15.8217	−1.03430
$235$	5.37718	0.350769
$236$	−44.9349	−2.92501
$237$	3.68919	0.239638
$238$	85.7518	5.55846
$239$	−23.1859	−1.49977	−0.749887	−	0.661566i	$-0.769892\pi$
$239$	−23.1859	−1.49977	−0.749887	+	0.661566i	$0.769892\pi$
$240$	−9.57297	−0.617933
$241$	−25.8756	−1.66679	−0.833396	−	0.552677i	$-0.813607\pi$
$241$	−25.8756	−1.66679	−0.833396	+	0.552677i	$0.813607\pi$
$242$	−4.03043	−0.259086
$243$	1.00000	0.0641500
$244$	−19.8315	−1.26958
$245$	−15.4355	−0.986138
$246$	−10.3241	−0.658239
$247$	−7.23578	−0.460402
$248$	37.3001	2.36856
$249$	9.41994	0.596964
$250$	−2.61103	−0.165136
$251$	−1.74717	−0.110281	−0.0551403	−	0.998479i	$-0.517561\pi$
$251$	−1.74717	−0.110281	−0.0551403	+	0.998479i	$0.517561\pi$
$252$	22.8184	1.43743
$253$	0	0
$254$	−5.04047	−0.316267
$255$	−6.93369	−0.434204
$256$	−16.5930	−1.03706
$257$	15.5910	0.972542	0.486271	−	0.873808i	$-0.338357\pi$
$257$	15.5910	0.972542	0.486271	+	0.873808i	$0.338357\pi$
$258$	−31.1542	−1.93958
$259$	−7.82104	−0.485976
$260$	29.1917	1.81039
$261$	−4.71195	−0.291662
$262$	9.12745	0.563896
$263$	−5.74141	−0.354030	−0.177015	−	0.984208i	$-0.556644\pi$
$263$	−5.74141	−0.354030	−0.177015	+	0.984208i	$0.556644\pi$
$264$	22.6220	1.39229
$265$	6.44486	0.395905
$266$	14.7680	0.905487
$267$	10.5183	0.643711
$268$	−18.9476	−1.15741
$269$	−8.81335	−0.537359	−0.268680	−	0.963230i	$-0.586587\pi$
$269$	−8.81335	−0.537359	−0.268680	+	0.963230i	$0.586587\pi$
$270$	−2.61103	−0.158902
$271$	16.6833	1.01344	0.506719	−	0.862112i	$-0.330858\pi$
$271$	16.6833	1.01344	0.506719	+	0.862112i	$0.330858\pi$
$272$	66.3760	4.02464
$273$	−28.7018	−1.73711
$274$	−26.6237	−1.60840
$275$	3.07512	0.185437
$276$	0	0
$277$	5.32772	0.320111	0.160056	−	0.987108i	$-0.448833\pi$
$277$	5.32772	0.320111	0.160056	+	0.987108i	$0.448833\pi$
$278$	−57.0417	−3.42113
$279$	5.07039	0.303556
$280$	−34.8447	−2.08237
$281$	16.3304	0.974191	0.487096	−	0.873349i	$-0.338056\pi$
$281$	16.3304	0.974191	0.487096	+	0.873349i	$0.338056\pi$
$282$	−14.0400	−0.836068
$283$	16.3765	0.973483	0.486741	−	0.873546i	$-0.338185\pi$
$283$	16.3765	0.973483	0.486741	+	0.873546i	$0.338185\pi$
$284$	−35.3387	−2.09696
$285$	−1.19411	−0.0707329
$286$	−48.6536	−2.87695
$287$	−18.7287	−1.10552
$288$	10.2824	0.605895
$289$	31.0760	1.82800
$290$	12.3030	0.722458
$291$	11.9404	0.699961
$292$	10.5137	0.615270
$293$	−0.184472	−0.0107770	−0.00538849	−	0.999985i	$-0.501715\pi$
$293$	−0.184472	−0.0107770	−0.00538849	+	0.999985i	$0.501715\pi$
$294$	40.3025	2.35049
$295$	9.32751	0.543069
$296$	−12.1469	−0.706023
$297$	3.07512	0.178437
$298$	54.3389	3.14777
$299$	0	0
$300$	4.81746	0.278136
$301$	−56.5163	−3.25754
$302$	18.8170	1.08279
$303$	−2.79740	−0.160707
$304$	11.4312	0.655623
$305$	4.11660	0.235716
$306$	18.1040	1.03494
$307$	−20.5275	−1.17156	−0.585782	−	0.810469i	$-0.699212\pi$
$307$	−20.5275	−1.17156	−0.585782	+	0.810469i	$0.699212\pi$
$308$	70.1695	3.99828
$309$	−0.121041	−0.00688581
$310$	−13.2389	−0.751920
$311$	28.3811	1.60934	0.804672	−	0.593720i	$-0.202341\pi$
$311$	28.3811	1.60934	0.804672	+	0.593720i	$0.202341\pi$
$312$	−44.5769	−2.52367
$313$	−18.5106	−1.04628	−0.523139	−	0.852247i	$-0.675239\pi$
$313$	−18.5106	−1.04628	−0.523139	+	0.852247i	$0.675239\pi$
$314$	−45.9487	−2.59304
$315$	−4.73661	−0.266878
$316$	17.7725	0.999781
$317$	−9.71309	−0.545541	−0.272771	−	0.962079i	$-0.587940\pi$
$317$	−9.71309	−0.545541	−0.272771	+	0.962079i	$0.587940\pi$
$318$	−16.8277	−0.943650
$319$	−14.4898	−0.811274
$320$	−7.70160	−0.430533
$321$	5.74677	0.320754
$322$	0	0
$323$	8.27958	0.460688
$324$	4.81746	0.267636
$325$	−6.05956	−0.336124
$326$	62.2602	3.44827
$327$	−3.76646	−0.208286
$328$	−29.0876	−1.60610
$329$	−25.4696	−1.40419
$330$	−8.02923	−0.441994
$331$	−23.7013	−1.30274	−0.651370	−	0.758760i	$-0.725806\pi$
$331$	−23.7013	−1.30274	−0.651370	+	0.758760i	$0.725806\pi$
$332$	45.3801	2.49056
$333$	−1.65119	−0.0904845
$334$	5.42244	0.296703
$335$	3.93311	0.214889
$336$	45.3435	2.47369
$337$	−1.60445	−0.0874000	−0.0437000	−	0.999045i	$-0.513915\pi$
$337$	−1.60445	−0.0874000	−0.0437000	+	0.999045i	$0.513915\pi$
$338$	61.9291	3.36850
$339$	−0.665423	−0.0361408
$340$	−33.4027	−1.81152
$341$	15.5921	0.844358
$342$	3.11785	0.168594
$343$	39.9557	2.15740
$344$	−87.7756	−4.73254
$345$	0	0
$346$	24.1019	1.29573
$347$	31.1377	1.67156	0.835779	−	0.549066i	$-0.185016\pi$
$347$	31.1377	1.67156	0.835779	+	0.549066i	$0.185016\pi$
$348$	−22.6996	−1.21683
$349$	−34.6747	−1.85610	−0.928048	−	0.372461i	$-0.878514\pi$
$349$	−34.6747	−1.85610	−0.928048	+	0.372461i	$0.878514\pi$
$350$	12.3674	0.661066
$351$	−6.05956	−0.323436
$352$	31.6196	1.68533
$353$	−3.35735	−0.178694	−0.0893469	−	0.996001i	$-0.528478\pi$
$353$	−3.35735	−0.178694	−0.0893469	+	0.996001i	$0.528478\pi$
$354$	−24.3544	−1.29442
$355$	7.33554	0.389330
$356$	50.6716	2.68559
$357$	32.8422	1.73819
$358$	6.89238	0.364274
$359$	8.35993	0.441220	0.220610	−	0.975362i	$-0.429195\pi$
$359$	8.35993	0.441220	0.220610	+	0.975362i	$0.429195\pi$
$360$	−7.35645	−0.387719
$361$	−17.5741	−0.924953
$362$	−6.40279	−0.336523
$363$	−1.54362	−0.0810190
$364$	−138.270	−7.24730
$365$	−2.18243	−0.114233
$366$	−10.7486	−0.561836
$367$	2.49541	0.130259	0.0651296	−	0.997877i	$-0.479254\pi$
$367$	2.49541	0.130259	0.0651296	+	0.997877i	$0.479254\pi$
$368$	0	0
$369$	−3.95403	−0.205839
$370$	4.31129	0.224134
$371$	−30.5268	−1.58487
$372$	24.4264	1.26645
$373$	−24.1942	−1.25273	−0.626365	−	0.779530i	$-0.715458\pi$
$373$	−24.1942	−1.25273	−0.626365	+	0.779530i	$0.715458\pi$
$374$	55.6721	2.87874
$375$	−1.00000	−0.0516398
$376$	−39.5570	−2.04000
$377$	28.5524	1.47052
$378$	12.3674	0.636111
$379$	8.14589	0.418426	0.209213	−	0.977870i	$-0.432910\pi$
$379$	8.14589	0.418426	0.209213	+	0.977870i	$0.432910\pi$
$380$	−5.75257	−0.295101
$381$	−1.93046	−0.0989003
$382$	−40.5486	−2.07465
$383$	−4.05024	−0.206958	−0.103479	−	0.994632i	$-0.532997\pi$
$383$	−4.05024	−0.206958	−0.103479	+	0.994632i	$0.532997\pi$
$384$	−0.455668	−0.0232532
$385$	−14.5657	−0.742335
$386$	20.0819	1.02214
$387$	−11.9318	−0.606527
$388$	57.5226	2.92027
$389$	−0.724098	−0.0367132	−0.0183566	−	0.999832i	$-0.505843\pi$
$389$	−0.724098	−0.0367132	−0.0183566	+	0.999832i	$0.505843\pi$
$390$	15.8217	0.801162
$391$	0	0
$392$	113.550	5.73516
$393$	3.49573	0.176336
$394$	25.7258	1.29605
$395$	−3.68919	−0.185623
$396$	14.8143	0.744445
$397$	22.1993	1.11415	0.557075	−	0.830462i	$-0.311923\pi$
$397$	22.1993	1.11415	0.557075	+	0.830462i	$0.311923\pi$
$398$	37.7026	1.88986
$399$	5.65603	0.283156
$400$	9.57297	0.478649
$401$	−21.1621	−1.05679	−0.528393	−	0.849000i	$-0.677205\pi$
$401$	−21.1621	−1.05679	−0.528393	+	0.849000i	$0.677205\pi$
$402$	−10.2694	−0.512194
$403$	−30.7244	−1.53049
$404$	−13.4764	−0.670474
$405$	−1.00000	−0.0496904
$406$	−58.2746	−2.89212
$407$	−5.07761	−0.251688
$408$	51.0073	2.52524
$409$	1.54061	0.0761784	0.0380892	−	0.999274i	$-0.487873\pi$
$409$	1.54061	0.0761784	0.0380892	+	0.999274i	$0.487873\pi$
$410$	10.3241	0.509870
$411$	−10.1966	−0.502963
$412$	−0.583112	−0.0287279
$413$	−44.1808	−2.17400
$414$	0	0
$415$	−9.41994	−0.462407
$416$	−62.3067	−3.05484
$417$	−21.8465	−1.06983
$418$	9.58777	0.468953
$419$	−21.5140	−1.05103	−0.525515	−	0.850784i	$-0.676127\pi$
$419$	−21.5140	−1.05103	−0.525515	+	0.850784i	$0.676127\pi$
$420$	−22.8184	−1.11342
$421$	12.0377	0.586681	0.293340	−	0.956008i	$-0.405233\pi$
$421$	12.0377	0.586681	0.293340	+	0.956008i	$0.405233\pi$
$422$	2.41350	0.117487
$423$	−5.37718	−0.261448
$424$	−47.4113	−2.30250
$425$	6.93369	0.336333
$426$	−19.1533	−0.927980
$427$	−19.4987	−0.943610
$428$	27.6848	1.33820
$429$	−18.6339	−0.899653
$430$	31.1542	1.50239
$431$	25.9586	1.25038	0.625190	−	0.780473i	$-0.285022\pi$
$431$	25.9586	1.25038	0.625190	+	0.780473i	$0.285022\pi$
$432$	9.57297	0.460580
$433$	20.9385	1.00624	0.503120	−	0.864217i	$-0.332186\pi$
$433$	20.9385	1.00624	0.503120	+	0.864217i	$0.332186\pi$
$434$	62.7076	3.01006
$435$	4.71195	0.225921
$436$	−18.1448	−0.868977
$437$	0	0
$438$	5.69837	0.272279
$439$	37.6127	1.79516	0.897579	−	0.440854i	$-0.145324\pi$
$439$	37.6127	1.79516	0.897579	+	0.440854i	$0.145324\pi$
$440$	−22.6220	−1.07846
$441$	15.4355	0.735024
$442$	−109.703	−5.21802
$443$	38.0121	1.80601	0.903004	−	0.429633i	$-0.141357\pi$
$443$	38.0121	1.80601	0.903004	+	0.429633i	$0.141357\pi$
$444$	−7.95452	−0.377505
$445$	−10.5183	−0.498616
$446$	−24.9194	−1.17997
$447$	20.8113	0.984342
$448$	36.4795	1.72349
$449$	−0.0715265	−0.00337555	−0.00168777	−	0.999999i	$-0.500537\pi$
$449$	−0.0715265	−0.00337555	−0.00168777	+	0.999999i	$0.500537\pi$
$450$	2.61103	0.123085
$451$	−12.1591	−0.572551
$452$	−3.20565	−0.150781
$453$	7.20673	0.338602
$454$	15.2647	0.716406
$455$	28.7018	1.34556
$456$	8.78441	0.411368
$457$	−12.8162	−0.599517	−0.299759	−	0.954015i	$-0.596906\pi$
$457$	−12.8162	−0.599517	−0.299759	+	0.954015i	$0.596906\pi$
$458$	35.4929	1.65847
$459$	6.93369	0.323637
$460$	0	0
$461$	−24.0264	−1.11902	−0.559510	−	0.828824i	$-0.689011\pi$
$461$	−24.0264	−1.11902	−0.559510	+	0.828824i	$0.689011\pi$
$462$	38.0313	1.76938
$463$	−34.1088	−1.58517	−0.792585	−	0.609761i	$-0.791265\pi$
$463$	−34.1088	−1.58517	−0.792585	+	0.609761i	$0.791265\pi$
$464$	−45.1073	−2.09406
$465$	−5.07039	−0.235134
$466$	−39.9688	−1.85152
$467$	24.9701	1.15548	0.577738	−	0.816222i	$-0.303935\pi$
$467$	24.9701	1.15548	0.577738	+	0.816222i	$0.303935\pi$
$468$	−29.1917	−1.34939
$469$	−18.6296	−0.860235
$470$	14.0400	0.647615
$471$	−17.5980	−0.810871
$472$	−68.6174	−3.15837
$473$	−36.6917	−1.68709
$474$	9.63256	0.442438
$475$	1.19411	0.0547895
$476$	158.216	7.25181
$477$	−6.44486	−0.295090
$478$	−60.5391	−2.76899
$479$	6.32629	0.289056	0.144528	−	0.989501i	$-0.453834\pi$
$479$	6.32629	0.289056	0.144528	+	0.989501i	$0.453834\pi$
$480$	−10.2824	−0.469324
$481$	10.0055	0.456211
$482$	−67.5618	−3.07735
$483$	0	0
$484$	−7.43632	−0.338014
$485$	−11.9404	−0.542188
$486$	2.61103	0.118439
$487$	7.91241	0.358545	0.179273	−	0.983799i	$-0.442626\pi$
$487$	7.91241	0.358545	0.179273	+	0.983799i	$0.442626\pi$
$488$	−30.2836	−1.37087
$489$	23.8451	1.07831
$490$	−40.3025	−1.82068
$491$	−20.1842	−0.910898	−0.455449	−	0.890262i	$-0.650521\pi$
$491$	−20.1842	−0.910898	−0.455449	+	0.890262i	$0.650521\pi$
$492$	−19.0484	−0.858767
$493$	−32.6712	−1.47144
$494$	−18.8928	−0.850028
$495$	−3.07512	−0.138216
$496$	48.5387	2.17945
$497$	−34.7456	−1.55855
$498$	24.5957	1.10216
$499$	−1.71063	−0.0765782	−0.0382891	−	0.999267i	$-0.512191\pi$
$499$	−1.71063	−0.0765782	−0.0382891	+	0.999267i	$0.512191\pi$
$500$	−4.81746	−0.215443
$501$	2.07675	0.0927822
$502$	−4.56191	−0.203608
$503$	−43.8310	−1.95433	−0.977163	−	0.212491i	$-0.931842\pi$
$503$	−43.8310	−1.95433	−0.977163	+	0.212491i	$0.931842\pi$
$504$	34.8447	1.55210
$505$	2.79740	0.124483
$506$	0	0
$507$	23.7183	1.05337
$508$	−9.29989	−0.412616
$509$	2.56312	0.113608	0.0568041	−	0.998385i	$-0.481909\pi$
$509$	2.56312	0.113608	0.0568041	+	0.998385i	$0.481909\pi$
$510$	−18.1040	−0.801660
$511$	10.3373	0.457295
$512$	−42.4133	−1.87442
$513$	1.19411	0.0527212
$514$	40.7086	1.79558
$515$	0.121041	0.00533373
$516$	−57.4809	−2.53045
$517$	−16.5355	−0.727230
$518$	−20.4209	−0.897244
$519$	9.23081	0.405188
$520$	44.5769	1.95483
$521$	27.5020	1.20488	0.602442	−	0.798163i	$-0.294194\pi$
$521$	27.5020	1.20488	0.602442	+	0.798163i	$0.294194\pi$
$522$	−12.3030	−0.538488
$523$	−26.4686	−1.15739	−0.578695	−	0.815544i	$-0.696438\pi$
$523$	−26.4686	−1.15739	−0.578695	+	0.815544i	$0.696438\pi$
$524$	16.8405	0.735682
$525$	4.73661	0.206723
$526$	−14.9910	−0.653637
$527$	35.1565	1.53144
$528$	29.4381	1.28113
$529$	0	0
$530$	16.8277	0.730948
$531$	−9.32751	−0.404780
$532$	27.2477	1.18134
$533$	23.9597	1.03781
$534$	27.4636	1.18847
$535$	−5.74677	−0.248455
$536$	−28.9337	−1.24975
$537$	2.63972	0.113912
$538$	−23.0119	−0.992112
$539$	47.4660	2.04451
$540$	−4.81746	−0.207310
$541$	−40.9163	−1.75913	−0.879564	−	0.475781i	$-0.842166\pi$
$541$	−40.9163	−1.75913	−0.879564	+	0.475781i	$0.842166\pi$
$542$	43.5605	1.87108
$543$	−2.45221	−0.105235
$544$	71.2948	3.05674
$545$	3.76646	0.161338
$546$	−74.9412	−3.20719
$547$	−5.59736	−0.239326	−0.119663	−	0.992815i	$-0.538181\pi$
$547$	−5.59736	−0.239326	−0.119663	+	0.992815i	$0.538181\pi$
$548$	−49.1218	−2.09838
$549$	−4.11660	−0.175692
$550$	8.02923	0.342367
$551$	−5.62658	−0.239700
$552$	0	0
$553$	17.4742	0.743080
$554$	13.9108	0.591013
$555$	1.65119	0.0700890
$556$	−105.244	−4.46336
$557$	−4.11449	−0.174337	−0.0871683	−	0.996194i	$-0.527782\pi$
$557$	−4.11449	−0.174337	−0.0871683	+	0.996194i	$0.527782\pi$
$558$	13.2389	0.560448
$559$	72.3014	3.05802
$560$	−45.3435	−1.91611
$561$	21.3219	0.900213
$562$	42.6391	1.79862
$563$	43.9985	1.85432	0.927158	−	0.374671i	$-0.122244\pi$
$563$	43.9985	1.85432	0.927158	+	0.374671i	$0.122244\pi$
$564$	−25.9043	−1.09077
$565$	0.665423	0.0279945
$566$	42.7595	1.79732
$567$	4.73661	0.198919
$568$	−53.9636	−2.26426
$569$	18.8292	0.789361	0.394681	−	0.918818i	$-0.370855\pi$
$569$	18.8292	0.789361	0.394681	+	0.918818i	$0.370855\pi$
$570$	−3.11785	−0.130592
$571$	−16.0666	−0.672366	−0.336183	−	0.941797i	$-0.609136\pi$
$571$	−16.0666	−0.672366	−0.336183	+	0.941797i	$0.609136\pi$
$572$	−89.7680	−3.75339
$573$	−15.5298	−0.648765
$574$	−48.9011	−2.04109
$575$	0	0
$576$	7.70160	0.320900
$577$	−8.70931	−0.362573	−0.181287	−	0.983430i	$-0.558026\pi$
$577$	−8.70931	−0.362573	−0.181287	+	0.983430i	$0.558026\pi$
$578$	81.1403	3.37499
$579$	7.69118	0.319635
$580$	22.6996	0.942550
$581$	44.6186	1.85109
$582$	31.1768	1.29232
$583$	−19.8187	−0.820808
$584$	16.0549	0.664357
$585$	6.05956	0.250532
$586$	−0.481661	−0.0198972
$587$	−19.4053	−0.800944	−0.400472	−	0.916309i	$-0.631154\pi$
$587$	−19.4053	−0.800944	−0.400472	+	0.916309i	$0.631154\pi$
$588$	74.3598	3.06655
$589$	6.05460	0.249475
$590$	24.3544	1.00265
$591$	9.85276	0.405289
$592$	−15.8068	−0.649654
$593$	−25.9312	−1.06487	−0.532434	−	0.846472i	$-0.678722\pi$
$593$	−25.9312	−1.06487	−0.532434	+	0.846472i	$0.678722\pi$
$594$	8.02923	0.329443
$595$	−32.8422	−1.34640
$596$	100.258	4.10672
$597$	14.4397	0.590979
$598$	0	0
$599$	−46.2901	−1.89136	−0.945681	−	0.325097i	$-0.894603\pi$
$599$	−46.2901	−1.89136	−0.945681	+	0.325097i	$0.894603\pi$
$600$	7.35645	0.300326
$601$	−18.2065	−0.742660	−0.371330	−	0.928501i	$-0.621098\pi$
$601$	−18.2065	−0.742660	−0.371330	+	0.928501i	$0.621098\pi$
$602$	−147.565	−6.01432
$603$	−3.93311	−0.160169
$604$	34.7181	1.41266
$605$	1.54362	0.0627570
$606$	−7.30409	−0.296708
$607$	−0.974973	−0.0395729	−0.0197865	−	0.999804i	$-0.506299\pi$
$607$	−0.974973	−0.0395729	−0.0197865	+	0.999804i	$0.506299\pi$
$608$	12.2783	0.497950
$609$	−22.3187	−0.904398
$610$	10.7486	0.435196
$611$	32.5834	1.31818
$612$	33.4027	1.35023
$613$	−17.9195	−0.723762	−0.361881	−	0.932224i	$-0.617865\pi$
$613$	−17.9195	−0.723762	−0.361881	+	0.932224i	$0.617865\pi$
$614$	−53.5977	−2.16303
$615$	3.95403	0.159442
$616$	107.152	4.31726
$617$	35.7617	1.43971	0.719856	−	0.694123i	$-0.244208\pi$
$617$	35.7617	1.43971	0.719856	+	0.694123i	$0.244208\pi$
$618$	−0.316042	−0.0127131
$619$	45.1183	1.81346	0.906728	−	0.421716i	$-0.138572\pi$
$619$	45.1183	1.81346	0.906728	+	0.421716i	$0.138572\pi$
$620$	−24.4264	−0.980987
$621$	0	0
$622$	74.1037	2.97129
$623$	49.8212	1.99605
$624$	−58.0080	−2.32218
$625$	1.00000	0.0400000
$626$	−48.3315	−1.93172
$627$	3.67203	0.146647
$628$	−84.7774	−3.38298
$629$	−11.4488	−0.456494
$630$	−12.3674	−0.492730
$631$	−2.82695	−0.112539	−0.0562696	−	0.998416i	$-0.517921\pi$
$631$	−2.82695	−0.112539	−0.0562696	+	0.998416i	$0.517921\pi$
$632$	27.1393	1.07954
$633$	0.924349	0.0367396
$634$	−25.3611	−1.00722
$635$	1.93046	0.0766078
$636$	−31.0478	−1.23113
$637$	−93.5324	−3.70589
$638$	−37.8333	−1.49783
$639$	−7.33554	−0.290190
$640$	0.455668	0.0180119
$641$	−5.90822	−0.233361	−0.116680	−	0.993170i	$-0.537225\pi$
$641$	−5.90822	−0.233361	−0.116680	+	0.993170i	$0.537225\pi$
$642$	15.0050	0.592199
$643$	−2.59929	−0.102506	−0.0512530	−	0.998686i	$-0.516321\pi$
$643$	−2.59929	−0.102506	−0.0512530	+	0.998686i	$0.516321\pi$
$644$	0	0
$645$	11.9318	0.469814
$646$	21.6182	0.850557
$647$	19.5243	0.767578	0.383789	−	0.923421i	$-0.374619\pi$
$647$	19.5243	0.767578	0.383789	+	0.923421i	$0.374619\pi$
$648$	7.35645	0.288989
$649$	−28.6832	−1.12592
$650$	−15.8217	−0.620577
$651$	24.0165	0.941280
$652$	114.873	4.49876
$653$	9.45131	0.369858	0.184929	−	0.982752i	$-0.440794\pi$
$653$	9.45131	0.369858	0.184929	+	0.982752i	$0.440794\pi$
$654$	−9.83433	−0.384553
$655$	−3.49573	−0.136590
$656$	−37.8518	−1.47787
$657$	2.18243	0.0851445
$658$	−66.5019	−2.59251
$659$	10.4127	0.405620	0.202810	−	0.979218i	$-0.434993\pi$
$659$	10.4127	0.405620	0.202810	+	0.979218i	$0.434993\pi$
$660$	−14.8143	−0.576645
$661$	6.20997	0.241540	0.120770	−	0.992681i	$-0.461464\pi$
$661$	6.20997	0.241540	0.120770	+	0.992681i	$0.461464\pi$
$662$	−61.8847	−2.40522
$663$	−42.0151	−1.63173
$664$	69.2973	2.68926
$665$	−5.65603	−0.219332
$666$	−4.31129	−0.167059
$667$	0	0
$668$	10.0046	0.387091
$669$	−9.54389	−0.368988
$670$	10.2694	0.396743
$671$	−12.6591	−0.488697
$672$	48.7036	1.87878
$673$	0.361577	0.0139378	0.00696889	−	0.999976i	$-0.497782\pi$
$673$	0.361577	0.0139378	0.00696889	+	0.999976i	$0.497782\pi$
$674$	−4.18926	−0.161364
$675$	1.00000	0.0384900
$676$	114.262	4.39469
$677$	40.5949	1.56019	0.780094	−	0.625662i	$-0.215171\pi$
$677$	40.5949	1.56019	0.780094	+	0.625662i	$0.215171\pi$
$678$	−1.73744	−0.0667258
$679$	56.5573	2.17047
$680$	−51.0073	−1.95604
$681$	5.84623	0.224028
$682$	40.7113	1.55892
$683$	−20.3735	−0.779569	−0.389784	−	0.920906i	$-0.627450\pi$
$683$	−20.3735	−0.779569	−0.389784	+	0.920906i	$0.627450\pi$
$684$	5.75257	0.219955
$685$	10.1966	0.389593
$686$	104.325	3.98316
$687$	13.5935	0.518623
$688$	−114.223	−4.35470
$689$	39.0530	1.48780
$690$	0	0
$691$	21.0372	0.800293	0.400147	−	0.916451i	$-0.368959\pi$
$691$	21.0372	0.800293	0.400147	+	0.916451i	$0.368959\pi$
$692$	44.4690	1.69046
$693$	14.5657	0.553304
$694$	81.3013	3.08615
$695$	21.8465	0.828684
$696$	−34.6632	−1.31391
$697$	−27.4160	−1.03846
$698$	−90.5366	−3.42686
$699$	−15.3077	−0.578991
$700$	22.8184	0.862455
$701$	32.2684	1.21876	0.609380	−	0.792878i	$-0.291418\pi$
$701$	32.2684	1.21876	0.609380	+	0.792878i	$0.291418\pi$
$702$	−15.8217	−0.597151
$703$	−1.97170	−0.0743640
$704$	23.6834	0.892600
$705$	5.37718	0.202516
$706$	−8.76613	−0.329918
$707$	−13.2502	−0.498326
$708$	−44.9349	−1.68876
$709$	−39.4004	−1.47971	−0.739856	−	0.672765i	$-0.765107\pi$
$709$	−39.4004	−1.47971	−0.739856	+	0.672765i	$0.765107\pi$
$710$	19.1533	0.718810
$711$	3.68919	0.138355
$712$	77.3775	2.89985
$713$	0	0
$714$	85.7518	3.20918
$715$	18.6339	0.696869
$716$	12.7167	0.475247
$717$	−23.1859	−0.865894
$718$	21.8280	0.814614
$719$	44.1497	1.64651	0.823254	−	0.567674i	$-0.192157\pi$
$719$	44.1497	1.64651	0.823254	+	0.567674i	$0.192157\pi$
$720$	−9.57297	−0.356764
$721$	−0.573327	−0.0213518
$722$	−45.8864	−1.70772
$723$	−25.8756	−0.962323
$724$	−11.8134	−0.439043
$725$	−4.71195	−0.174997
$726$	−4.03043	−0.149583
$727$	−7.60866	−0.282189	−0.141095	−	0.989996i	$-0.545062\pi$
$727$	−7.60866	−0.282189	−0.141095	+	0.989996i	$0.545062\pi$
$728$	−211.143	−7.82550
$729$	1.00000	0.0370370
$730$	−5.69837	−0.210906
$731$	−82.7313	−3.05993
$732$	−19.8315	−0.732995
$733$	39.7470	1.46809	0.734044	−	0.679102i	$-0.237630\pi$
$733$	39.7470	1.46809	0.734044	+	0.679102i	$0.237630\pi$
$734$	6.51558	0.240494
$735$	−15.4355	−0.569347
$736$	0	0
$737$	−12.0948	−0.445517
$738$	−10.3241	−0.380034
$739$	3.28084	0.120688	0.0603439	−	0.998178i	$-0.480780\pi$
$739$	3.28084	0.120688	0.0603439	+	0.998178i	$0.480780\pi$
$740$	7.95452	0.292414
$741$	−7.23578	−0.265813
$742$	−79.7063	−2.92611
$743$	11.1652	0.409612	0.204806	−	0.978803i	$-0.434344\pi$
$743$	11.1652	0.409612	0.204806	+	0.978803i	$0.434344\pi$
$744$	37.3001	1.36749
$745$	−20.8113	−0.762468
$746$	−63.1718	−2.31288
$747$	9.41994	0.344658
$748$	102.718	3.75572
$749$	27.2202	0.994606
$750$	−2.61103	−0.0953412
$751$	3.15592	0.115161	0.0575806	−	0.998341i	$-0.481661\pi$
$751$	3.15592	0.115161	0.0575806	+	0.998341i	$0.481661\pi$
$752$	−51.4756	−1.87712
$753$	−1.74717	−0.0636705
$754$	74.5509	2.71498
$755$	−7.20673	−0.262280
$756$	22.8184	0.829898
$757$	−25.0049	−0.908817	−0.454409	−	0.890793i	$-0.650149\pi$
$757$	−25.0049	−0.908817	−0.454409	+	0.890793i	$0.650149\pi$
$758$	21.2691	0.772529
$759$	0	0
$760$	−8.78441	−0.318644
$761$	−20.9727	−0.760260	−0.380130	−	0.924933i	$-0.624121\pi$
$761$	−20.9727	−0.760260	−0.380130	+	0.924933i	$0.624121\pi$
$762$	−5.04047	−0.182597
$763$	−17.8403	−0.645861
$764$	−74.8139	−2.70667
$765$	−6.93369	−0.250688
$766$	−10.5753	−0.382101
$767$	56.5207	2.04084
$768$	−16.5930	−0.598747
$769$	47.8452	1.72534	0.862671	−	0.505765i	$-0.168790\pi$
$769$	47.8452	1.72534	0.862671	+	0.505765i	$0.168790\pi$
$770$	−38.0313	−1.37055
$771$	15.5910	0.561498
$772$	37.0519	1.33353
$773$	−35.8153	−1.28819	−0.644093	−	0.764947i	$-0.722765\pi$
$773$	−35.8153	−1.28819	−0.644093	+	0.764947i	$0.722765\pi$
$774$	−31.1542	−1.11981
$775$	5.07039	0.182134
$776$	87.8393	3.15325
$777$	−7.82104	−0.280578
$778$	−1.89064	−0.0677826
$779$	−4.72154	−0.169167
$780$	29.1917	1.04523
$781$	−22.5577	−0.807178
$782$	0	0
$783$	−4.71195	−0.168391
$784$	147.764	5.27727
$785$	17.5980	0.628098
$786$	9.12745	0.325565
$787$	17.6597	0.629499	0.314750	−	0.949175i	$-0.398079\pi$
$787$	17.6597	0.629499	0.314750	+	0.949175i	$0.398079\pi$
$788$	47.4653	1.69088
$789$	−5.74141	−0.204400
$790$	−9.63256	−0.342711
$791$	−3.15185	−0.112067
$792$	22.6220	0.803837
$793$	24.9448	0.885816
$794$	57.9629	2.05703
$795$	6.44486	0.228576
$796$	69.5628	2.46559
$797$	−2.14080	−0.0758309	−0.0379155	−	0.999281i	$-0.512072\pi$
$797$	−2.14080	−0.0758309	−0.0379155	+	0.999281i	$0.512072\pi$
$798$	14.7680	0.522783
$799$	−37.2837	−1.31900
$800$	10.2824	0.363537
$801$	10.5183	0.371647
$802$	−55.2548	−1.95112
$803$	6.71123	0.236834
$804$	−18.9476	−0.668230
$805$	0	0
$806$	−80.2221	−2.82570
$807$	−8.81335	−0.310244
$808$	−20.5790	−0.723965
$809$	−4.96602	−0.174596	−0.0872981	−	0.996182i	$-0.527823\pi$
$809$	−4.96602	−0.174596	−0.0872981	+	0.996182i	$0.527823\pi$
$810$	−2.61103	−0.0917421
$811$	54.2124	1.90365	0.951827	−	0.306635i	$-0.0992029\pi$
$811$	54.2124	1.90365	0.951827	+	0.306635i	$0.0992029\pi$
$812$	−107.519	−3.77318
$813$	16.6833	0.585108
$814$	−13.2578	−0.464684
$815$	−23.8451	−0.835258
$816$	66.3760	2.32362
$817$	−14.2479	−0.498469
$818$	4.02258	0.140646
$819$	−28.7018	−1.00292
$820$	19.0484	0.665198
$821$	−44.0655	−1.53790	−0.768949	−	0.639310i	$-0.779220\pi$
$821$	−44.0655	−1.53790	−0.768949	+	0.639310i	$0.779220\pi$
$822$	−26.6237	−0.928607
$823$	2.91262	0.101528	0.0507638	−	0.998711i	$-0.483834\pi$
$823$	2.91262	0.101528	0.0507638	+	0.998711i	$0.483834\pi$
$824$	−0.890436	−0.0310198
$825$	3.07512	0.107062
$826$	−115.357	−4.01379
$827$	11.3045	0.393097	0.196548	−	0.980494i	$-0.437027\pi$
$827$	11.3045	0.393097	0.196548	+	0.980494i	$0.437027\pi$
$828$	0	0
$829$	−38.6777	−1.34333	−0.671666	−	0.740854i	$-0.734421\pi$
$829$	−38.6777	−1.34333	−0.671666	+	0.740854i	$0.734421\pi$
$830$	−24.5957	−0.853729
$831$	5.32772	0.184816
$832$	−46.6683	−1.61793
$833$	107.025	3.70819
$834$	−57.0417	−1.97519
$835$	−2.07675	−0.0718688
$836$	17.6899	0.611817
$837$	5.07039	0.175258
$838$	−56.1737	−1.94049
$839$	28.3558	0.978950	0.489475	−	0.872017i	$-0.337188\pi$
$839$	28.3558	0.978950	0.489475	+	0.872017i	$0.337188\pi$
$840$	−34.8447	−1.20225
$841$	−6.79755	−0.234398
$842$	31.4307	1.08317
$843$	16.3304	0.562450
$844$	4.45301	0.153279
$845$	−23.7183	−0.815935
$846$	−14.0400	−0.482704
$847$	−7.31153	−0.251227
$848$	−61.6965	−2.11866
$849$	16.3765	0.562041
$850$	18.1040	0.620963
$851$	0	0
$852$	−35.3387	−1.21068
$853$	51.4522	1.76169	0.880844	−	0.473406i	$-0.156976\pi$
$853$	51.4522	1.76169	0.880844	+	0.473406i	$0.156976\pi$
$854$	−50.9117	−1.74216
$855$	−1.19411	−0.0408377
$856$	42.2759	1.44496
$857$	51.2894	1.75201	0.876006	−	0.482301i	$-0.160199\pi$
$857$	51.2894	1.75201	0.876006	+	0.482301i	$0.160199\pi$
$858$	−48.6536	−1.66101
$859$	−30.7456	−1.04903	−0.524513	−	0.851402i	$-0.675753\pi$
$859$	−30.7456	−1.04903	−0.524513	+	0.851402i	$0.675753\pi$
$860$	57.4809	1.96008
$861$	−18.7287	−0.638273
$862$	67.7785	2.30854
$863$	10.3681	0.352933	0.176467	−	0.984307i	$-0.443533\pi$
$863$	10.3681	0.352933	0.176467	+	0.984307i	$0.443533\pi$
$864$	10.2824	0.349813
$865$	−9.23081	−0.313857
$866$	54.6709	1.85779
$867$	31.0760	1.05540
$868$	115.698	3.92706
$869$	11.3447	0.384843
$870$	12.3030	0.417111
$871$	23.8329	0.807548
$872$	−27.7078	−0.938305
$873$	11.9404	0.404123
$874$	0	0
$875$	−4.73661	−0.160127
$876$	10.5137	0.355226
$877$	−9.39749	−0.317331	−0.158665	−	0.987332i	$-0.550719\pi$
$877$	−9.39749	−0.317331	−0.158665	+	0.987332i	$0.550719\pi$
$878$	98.2078	3.31435
$879$	−0.184472	−0.00622209
$880$	−29.4381	−0.992357
$881$	29.7727	1.00307	0.501533	−	0.865138i	$-0.332769\pi$
$881$	29.7727	1.00307	0.501533	+	0.865138i	$0.332769\pi$
$882$	40.3025	1.35706
$883$	46.3232	1.55890	0.779450	−	0.626465i	$-0.215499\pi$
$883$	46.3232	1.55890	0.779450	+	0.626465i	$0.215499\pi$
$884$	−202.406	−6.80765
$885$	9.32751	0.313541
$886$	99.2505	3.33438
$887$	−5.32767	−0.178886	−0.0894428	−	0.995992i	$-0.528509\pi$
$887$	−5.32767	−0.178886	−0.0894428	+	0.995992i	$0.528509\pi$
$888$	−12.1469	−0.407623
$889$	−9.14382	−0.306674
$890$	−27.4636	−0.920583
$891$	3.07512	0.103020
$892$	−45.9773	−1.53943
$893$	−6.42094	−0.214869
$894$	54.3389	1.81737
$895$	−2.63972	−0.0882362
$896$	−2.15832	−0.0721046
$897$	0	0
$898$	−0.186758	−0.00623218
$899$	−23.8914	−0.796823
$900$	4.81746	0.160582
$901$	−44.6866	−1.48873
$902$	−31.7478	−1.05709
$903$	−56.5163	−1.88074
$904$	−4.89515	−0.162810
$905$	2.45221	0.0815143
$906$	18.8170	0.625152
$907$	−48.9813	−1.62640	−0.813198	−	0.581987i	$-0.802275\pi$
$907$	−48.9813	−1.62640	−0.813198	+	0.581987i	$0.802275\pi$
$908$	28.1639	0.934653
$909$	−2.79740	−0.0927840
$910$	74.9412	2.48428
$911$	29.8683	0.989579	0.494790	−	0.869013i	$-0.335245\pi$
$911$	29.8683	0.989579	0.494790	+	0.869013i	$0.335245\pi$
$912$	11.4312	0.378524
$913$	28.9675	0.958683
$914$	−33.4635	−1.10687
$915$	4.11660	0.136091
$916$	65.4859	2.16371
$917$	16.5579	0.546791
$918$	18.1040	0.597522
$919$	−35.3263	−1.16531	−0.582654	−	0.812720i	$-0.697986\pi$
$919$	−35.3263	−1.16531	−0.582654	+	0.812720i	$0.697986\pi$
$920$	0	0
$921$	−20.5275	−0.676403
$922$	−62.7335	−2.06602
$923$	44.4502	1.46310
$924$	70.1695	2.30841
$925$	−1.65119	−0.0542907
$926$	−89.0589	−2.92666
$927$	−0.121041	−0.00397552
$928$	−48.4500	−1.59045
$929$	27.9685	0.917615	0.458808	−	0.888536i	$-0.348277\pi$
$929$	27.9685	0.917615	0.458808	+	0.888536i	$0.348277\pi$
$930$	−13.2389	−0.434121
$931$	18.4317	0.604074
$932$	−73.7442	−2.41557
$933$	28.3811	0.929155
$934$	65.1975	2.13333
$935$	−21.3219	−0.697302
$936$	−44.5769	−1.45704
$937$	−6.55597	−0.214174	−0.107087	−	0.994250i	$-0.534152\pi$
$937$	−6.55597	−0.214174	−0.107087	+	0.994250i	$0.534152\pi$
$938$	−48.6424	−1.58823
$939$	−18.5106	−0.604069
$940$	25.9043	0.844906
$941$	−8.46984	−0.276109	−0.138054	−	0.990425i	$-0.544085\pi$
$941$	−8.46984	−0.276109	−0.138054	+	0.990425i	$0.544085\pi$
$942$	−45.9487	−1.49709
$943$	0	0
$944$	−89.2920	−2.90621
$945$	−4.73661	−0.154082
$946$	−95.8030	−3.11482
$947$	−1.66902	−0.0542358	−0.0271179	−	0.999632i	$-0.508633\pi$
$947$	−1.66902	−0.0542358	−0.0271179	+	0.999632i	$0.508633\pi$
$948$	17.7725	0.577224
$949$	−13.2245	−0.429287
$950$	3.11785	0.101156
$951$	−9.71309	−0.314968
$952$	241.602	7.83036
$953$	43.9420	1.42342	0.711710	−	0.702474i	$-0.247921\pi$
$953$	43.9420	1.42342	0.711710	+	0.702474i	$0.247921\pi$
$954$	−16.8277	−0.544817
$955$	15.5298	0.502531
$956$	−111.697	−3.61255
$957$	−14.4898	−0.468389
$958$	16.5181	0.533676
$959$	−48.2975	−1.55961
$960$	−7.70160	−0.248568
$961$	−5.29115	−0.170682
$962$	26.1246	0.842290
$963$	5.74677	0.185187
$964$	−124.654	−4.01485
$965$	−7.69118	−0.247588
$966$	0	0
$967$	0.969288	0.0311702	0.0155851	−	0.999879i	$-0.495039\pi$
$967$	0.969288	0.0311702	0.0155851	+	0.999879i	$0.495039\pi$
$968$	−11.3556	−0.364981
$969$	8.27958	0.265978
$970$	−31.1768	−1.00103
$971$	−4.57014	−0.146663	−0.0733314	−	0.997308i	$-0.523363\pi$
$971$	−4.57014	−0.146663	−0.0733314	+	0.997308i	$0.523363\pi$
$972$	4.81746	0.154520
$973$	−103.478	−3.31736
$974$	20.6595	0.661973
$975$	−6.05956	−0.194061
$976$	−39.4081	−1.26142
$977$	−26.7895	−0.857071	−0.428536	−	0.903525i	$-0.640970\pi$
$977$	−26.7895	−0.857071	−0.428536	+	0.903525i	$0.640970\pi$
$978$	62.2602	1.99086
$979$	32.3451	1.03376
$980$	−74.3598	−2.37534
$981$	−3.76646	−0.120254
$982$	−52.7013	−1.68177
$983$	−38.5526	−1.22964	−0.614818	−	0.788669i	$-0.710771\pi$
$983$	−38.5526	−1.22964	−0.614818	+	0.788669i	$0.710771\pi$
$984$	−29.0876	−0.927280
$985$	−9.85276	−0.313935
$986$	−85.3053	−2.71667
$987$	−25.4696	−0.810707
$988$	−34.8581	−1.10898
$989$	0	0
$990$	−8.02923	−0.255186
$991$	41.1983	1.30871	0.654353	−	0.756189i	$-0.272941\pi$
$991$	41.1983	1.30871	0.654353	+	0.756189i	$0.272941\pi$
$992$	52.1356	1.65531
$993$	−23.7013	−0.752138
$994$	−90.7217	−2.87752
$995$	−14.4397	−0.457771
$996$	45.3801	1.43792
$997$	−33.5263	−1.06179	−0.530894	−	0.847438i	$-0.678144\pi$
$997$	−33.5263	−1.06179	−0.530894	+	0.847438i	$0.678144\pi$
$998$	−4.46649	−0.141384
$999$	−1.65119	−0.0522413

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.bl.1.12	✓	12
23.22	odd	2		7935.2.a.bm.1.12	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7935.2.a.bl.1.12	✓	12	1.1	even	1	trivial
7935.2.a.bm.1.12	yes	12	23.22	odd	2

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:	\( N \)	\(=\)	\( 7935 = 3 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7935.a (trivial)

\(f(q)\)	\(=\)	\(q+2.61103 q^{2} +1.00000 q^{3} +4.81746 q^{4} -1.00000 q^{5} +2.61103 q^{6} +4.73661 q^{7} +7.35645 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.61103 q^{2} +1.00000 q^{3} +4.81746 q^{4} -1.00000 q^{5} +2.61103 q^{6} +4.73661 q^{7} +7.35645 q^{8} +1.00000 q^{9} -2.61103 q^{10} +3.07512 q^{11} +4.81746 q^{12} -6.05956 q^{13} +12.3674 q^{14} -1.00000 q^{15} +9.57297 q^{16} +6.93369 q^{17} +2.61103 q^{18} +1.19411 q^{19} -4.81746 q^{20} +4.73661 q^{21} +8.02923 q^{22} +7.35645 q^{24} +1.00000 q^{25} -15.8217 q^{26} +1.00000 q^{27} +22.8184 q^{28} -4.71195 q^{29} -2.61103 q^{30} +5.07039 q^{31} +10.2824 q^{32} +3.07512 q^{33} +18.1040 q^{34} -4.73661 q^{35} +4.81746 q^{36} -1.65119 q^{37} +3.11785 q^{38} -6.05956 q^{39} -7.35645 q^{40} -3.95403 q^{41} +12.3674 q^{42} -11.9318 q^{43} +14.8143 q^{44} -1.00000 q^{45} -5.37718 q^{47} +9.57297 q^{48} +15.4355 q^{49} +2.61103 q^{50} +6.93369 q^{51} -29.1917 q^{52} -6.44486 q^{53} +2.61103 q^{54} -3.07512 q^{55} +34.8447 q^{56} +1.19411 q^{57} -12.3030 q^{58} -9.32751 q^{59} -4.81746 q^{60} -4.11660 q^{61} +13.2389 q^{62} +4.73661 q^{63} +7.70160 q^{64} +6.05956 q^{65} +8.02923 q^{66} -3.93311 q^{67} +33.4027 q^{68} -12.3674 q^{70} -7.33554 q^{71} +7.35645 q^{72} +2.18243 q^{73} -4.31129 q^{74} +1.00000 q^{75} +5.75257 q^{76} +14.5657 q^{77} -15.8217 q^{78} +3.68919 q^{79} -9.57297 q^{80} +1.00000 q^{81} -10.3241 q^{82} +9.41994 q^{83} +22.8184 q^{84} -6.93369 q^{85} -31.1542 q^{86} -4.71195 q^{87} +22.6220 q^{88} +10.5183 q^{89} -2.61103 q^{90} -28.7018 q^{91} +5.07039 q^{93} -14.0400 q^{94} -1.19411 q^{95} +10.2824 q^{96} +11.9404 q^{97} +40.3025 q^{98} +3.07512 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{3} + 8 q^{4} - 12 q^{5} + 4 q^{7} + 12 q^{9}+O(q^{10}) \) 12 * q + 12 * q^3 + 8 * q^4 - 12 * q^5 + 4 * q^7 + 12 * q^9	\( 12 q + 12 q^{3} + 8 q^{4} - 12 q^{5} + 4 q^{7} + 12 q^{9} + 24 q^{11} + 8 q^{12} - 8 q^{13} + 16 q^{14} - 12 q^{15} + 28 q^{17} + 16 q^{19} - 8 q^{20} + 4 q^{21} + 12 q^{25} - 36 q^{26} + 12 q^{27} + 8 q^{28} - 16 q^{29} + 20 q^{32} + 24 q^{33} + 16 q^{34} - 4 q^{35} + 8 q^{36} + 20 q^{37} + 16 q^{38} - 8 q^{39} - 4 q^{41} + 16 q^{42} - 12 q^{43} + 16 q^{44} - 12 q^{45} + 4 q^{47} + 24 q^{49} + 28 q^{51} - 36 q^{52} + 28 q^{53} - 24 q^{55} + 56 q^{56} + 16 q^{57} + 20 q^{59} - 8 q^{60} + 32 q^{61} + 12 q^{62} + 4 q^{63} - 4 q^{64} + 8 q^{65} - 4 q^{67} + 64 q^{68} - 16 q^{70} - 8 q^{71} + 4 q^{73} - 36 q^{74} + 12 q^{75} + 8 q^{76} - 28 q^{77} - 36 q^{78} + 40 q^{79} + 12 q^{81} - 28 q^{82} + 100 q^{83} + 8 q^{84} - 28 q^{85} - 20 q^{86} - 16 q^{87} + 80 q^{89} - 24 q^{91} + 44 q^{94} - 16 q^{95} + 20 q^{96} - 8 q^{97} + 28 q^{98} + 24 q^{99}+O(q^{100}) \) 12 * q + 12 * q^3 + 8 * q^4 - 12 * q^5 + 4 * q^7 + 12 * q^9 + 24 * q^11 + 8 * q^12 - 8 * q^13 + 16 * q^14 - 12 * q^15 + 28 * q^17 + 16 * q^19 - 8 * q^20 + 4 * q^21 + 12 * q^25 - 36 * q^26 + 12 * q^27 + 8 * q^28 - 16 * q^29 + 20 * q^32 + 24 * q^33 + 16 * q^34 - 4 * q^35 + 8 * q^36 + 20 * q^37 + 16 * q^38 - 8 * q^39 - 4 * q^41 + 16 * q^42 - 12 * q^43 + 16 * q^44 - 12 * q^45 + 4 * q^47 + 24 * q^49 + 28 * q^51 - 36 * q^52 + 28 * q^53 - 24 * q^55 + 56 * q^56 + 16 * q^57 + 20 * q^59 - 8 * q^60 + 32 * q^61 + 12 * q^62 + 4 * q^63 - 4 * q^64 + 8 * q^65 - 4 * q^67 + 64 * q^68 - 16 * q^70 - 8 * q^71 + 4 * q^73 - 36 * q^74 + 12 * q^75 + 8 * q^76 - 28 * q^77 - 36 * q^78 + 40 * q^79 + 12 * q^81 - 28 * q^82 + 100 * q^83 + 8 * q^84 - 28 * q^85 - 20 * q^86 - 16 * q^87 + 80 * q^89 - 24 * q^91 + 44 * q^94 - 16 * q^95 + 20 * q^96 - 8 * q^97 + 28 * q^98 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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