LMFDB - Embedded newform 8470.2.a.cx.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8470,2,Mod(1,8470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8470, 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("8470.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8470.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:	$67.6332905120$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.745749504.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 18x^{4} - 4x^{3} + 81x^{2} + 36x - 44 $ x^6 - 18x^4 - 4x^3 + 81x^2 + 36x - 44
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.567932$ of defining polynomial
Character	$\chi$	$=$	8470.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.567932 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.567932 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.67745 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.567932 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.567932 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.67745 q^{9} +1.00000 q^{10} -0.567932 q^{12} +5.26170 q^{13} -1.00000 q^{14} +0.567932 q^{15} +1.00000 q^{16} +5.00401 q^{17} +2.67745 q^{18} -2.96172 q^{19} -1.00000 q^{20} -0.567932 q^{21} +0.983687 q^{23} +0.567932 q^{24} +1.00000 q^{25} -5.26170 q^{26} +3.22441 q^{27} +1.00000 q^{28} -1.43608 q^{29} -0.567932 q^{30} -9.68146 q^{31} -1.00000 q^{32} -5.00401 q^{34} -1.00000 q^{35} -2.67745 q^{36} +7.43608 q^{37} +2.96172 q^{38} -2.98829 q^{39} +1.00000 q^{40} +9.74211 q^{41} +0.567932 q^{42} -5.89617 q^{43} +2.67745 q^{45} -0.983687 q^{46} -5.70949 q^{47} -0.567932 q^{48} +1.00000 q^{49} -1.00000 q^{50} -2.84194 q^{51} +5.26170 q^{52} +10.1844 q^{53} -3.22441 q^{54} -1.00000 q^{56} +1.68205 q^{57} +1.43608 q^{58} +7.39355 q^{59} +0.567932 q^{60} +7.04229 q^{61} +9.68146 q^{62} -2.67745 q^{63} +1.00000 q^{64} -5.26170 q^{65} -2.77639 q^{67} +5.00401 q^{68} -0.558667 q^{69} +1.00000 q^{70} -2.71008 q^{71} +2.67745 q^{72} -9.81960 q^{73} -7.43608 q^{74} -0.567932 q^{75} -2.96172 q^{76} +2.98829 q^{78} +0.874198 q^{79} -1.00000 q^{80} +6.20112 q^{81} -9.74211 q^{82} +2.65545 q^{83} -0.567932 q^{84} -5.00401 q^{85} +5.89617 q^{86} +0.815593 q^{87} -4.84535 q^{89} -2.67745 q^{90} +5.26170 q^{91} +0.983687 q^{92} +5.49841 q^{93} +5.70949 q^{94} +2.96172 q^{95} +0.567932 q^{96} +17.2128 q^{97} -1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 6 q^{4} - 6 q^{5} + 6 q^{7} - 6 q^{8} + 18 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 + 6 * q^4 - 6 * q^5 + 6 * q^7 - 6 * q^8 + 18 * q^9	$ 6 q - 6 q^{2} + 6 q^{4} - 6 q^{5} + 6 q^{7} - 6 q^{8} + 18 q^{9} + 6 q^{10} - 6 q^{14} + 6 q^{16} + 6 q^{17} - 18 q^{18} - 6 q^{20} + 6 q^{25} - 12 q^{27} + 6 q^{28} + 12 q^{29} - 6 q^{32} - 6 q^{34} - 6 q^{35} + 18 q^{36} + 24 q^{37} - 24 q^{39} + 6 q^{40} + 12 q^{41} - 18 q^{43} - 18 q^{45} + 24 q^{47} + 6 q^{49} - 6 q^{50} - 12 q^{51} + 36 q^{53} + 12 q^{54} - 6 q^{56} - 12 q^{57} - 12 q^{58} + 30 q^{59} + 36 q^{61} + 18 q^{63} + 6 q^{64} - 12 q^{67} + 6 q^{68} + 6 q^{70} + 6 q^{71} - 18 q^{72} - 6 q^{73} - 24 q^{74} + 24 q^{78} - 24 q^{79} - 6 q^{80} + 54 q^{81} - 12 q^{82} + 24 q^{83} - 6 q^{85} + 18 q^{86} - 24 q^{87} + 36 q^{89} + 18 q^{90} - 24 q^{94} - 6 q^{98}+O(q^{100}) $ 6 * q - 6 * q^2 + 6 * q^4 - 6 * q^5 + 6 * q^7 - 6 * q^8 + 18 * q^9 + 6 * q^10 - 6 * q^14 + 6 * q^16 + 6 * q^17 - 18 * q^18 - 6 * q^20 + 6 * q^25 - 12 * q^27 + 6 * q^28 + 12 * q^29 - 6 * q^32 - 6 * q^34 - 6 * q^35 + 18 * q^36 + 24 * q^37 - 24 * q^39 + 6 * q^40 + 12 * q^41 - 18 * q^43 - 18 * q^45 + 24 * q^47 + 6 * q^49 - 6 * q^50 - 12 * q^51 + 36 * q^53 + 12 * q^54 - 6 * q^56 - 12 * q^57 - 12 * q^58 + 30 * q^59 + 36 * q^61 + 18 * q^63 + 6 * q^64 - 12 * q^67 + 6 * q^68 + 6 * q^70 + 6 * q^71 - 18 * q^72 - 6 * q^73 - 24 * q^74 + 24 * q^78 - 24 * q^79 - 6 * q^80 + 54 * q^81 - 12 * q^82 + 24 * q^83 - 6 * q^85 + 18 * q^86 - 24 * q^87 + 36 * q^89 + 18 * q^90 - 24 * q^94 - 6 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−0.567932	−0.327896	−0.163948	−	0.986469i	$-0.552423\pi$
$3$	−0.567932	−0.327896	−0.163948	+	0.986469i	$0.552423\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.567932	0.231857
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	−2.67745	−0.892484
$10$	1.00000	0.316228
$11$	0	0
$11$	0	0
$12$	−0.567932	−0.163948
$13$	5.26170	1.45933	0.729666	−	0.683803i	$-0.239675\pi$
$13$	5.26170	1.45933	0.729666	+	0.683803i	$0.239675\pi$
$14$	−1.00000	−0.267261
$15$	0.567932	0.146639
$16$	1.00000	0.250000
$17$	5.00401	1.21365	0.606825	−	0.794835i	$-0.292443\pi$
$17$	5.00401	1.21365	0.606825	+	0.794835i	$0.292443\pi$
$18$	2.67745	0.631082
$19$	−2.96172	−0.679464	−0.339732	−	0.940522i	$-0.610336\pi$
$19$	−2.96172	−0.679464	−0.339732	+	0.940522i	$0.610336\pi$
$20$	−1.00000	−0.223607
$21$	−0.567932	−0.123933
$22$	0	0
$23$	0.983687	0.205113	0.102556	−	0.994727i	$-0.467298\pi$
$23$	0.983687	0.205113	0.102556	+	0.994727i	$0.467298\pi$
$24$	0.567932	0.115929
$25$	1.00000	0.200000
$26$	−5.26170	−1.03190
$27$	3.22441	0.620537
$28$	1.00000	0.188982
$29$	−1.43608	−0.266672	−0.133336	−	0.991071i	$-0.542569\pi$
$29$	−1.43608	−0.266672	−0.133336	+	0.991071i	$0.542569\pi$
$30$	−0.567932	−0.103690
$31$	−9.68146	−1.73884	−0.869421	−	0.494072i	$-0.835508\pi$
$31$	−9.68146	−1.73884	−0.869421	+	0.494072i	$0.835508\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	−5.00401	−0.858180
$35$	−1.00000	−0.169031
$36$	−2.67745	−0.446242
$37$	7.43608	1.22248	0.611242	−	0.791444i	$-0.290670\pi$
$37$	7.43608	1.22248	0.611242	+	0.791444i	$0.290670\pi$
$38$	2.96172	0.480454
$39$	−2.98829	−0.478509
$40$	1.00000	0.158114
$41$	9.74211	1.52146	0.760731	−	0.649067i	$-0.224841\pi$
$41$	9.74211	1.52146	0.760731	+	0.649067i	$0.224841\pi$
$42$	0.567932	0.0876338
$43$	−5.89617	−0.899157	−0.449579	−	0.893241i	$-0.648426\pi$
$43$	−5.89617	−0.899157	−0.449579	+	0.893241i	$0.648426\pi$
$44$	0	0
$45$	2.67745	0.399131
$46$	−0.983687	−0.145037
$47$	−5.70949	−0.832814	−0.416407	−	0.909178i	$-0.636711\pi$
$47$	−5.70949	−0.832814	−0.416407	+	0.909178i	$0.636711\pi$
$48$	−0.567932	−0.0819739
$49$	1.00000	0.142857
$50$	−1.00000	−0.141421
$51$	−2.84194	−0.397951
$52$	5.26170	0.729666
$53$	10.1844	1.39894	0.699470	−	0.714662i	$-0.253419\pi$
$53$	10.1844	1.39894	0.699470	+	0.714662i	$0.253419\pi$
$54$	−3.22441	−0.438786
$55$	0	0
$56$	−1.00000	−0.133631
$57$	1.68205	0.222793
$58$	1.43608	0.188566
$59$	7.39355	0.962559	0.481279	−	0.876567i	$-0.340172\pi$
$59$	7.39355	0.962559	0.481279	+	0.876567i	$0.340172\pi$
$60$	0.567932	0.0733197
$61$	7.04229	0.901673	0.450837	−	0.892607i	$-0.351126\pi$
$61$	7.04229	0.901673	0.450837	+	0.892607i	$0.351126\pi$
$62$	9.68146	1.22955
$63$	−2.67745	−0.337327
$64$	1.00000	0.125000
$65$	−5.26170	−0.652633
$66$	0	0
$67$	−2.77639	−0.339190	−0.169595	−	0.985514i	$-0.554246\pi$
$67$	−2.77639	−0.339190	−0.169595	+	0.985514i	$0.554246\pi$
$68$	5.00401	0.606825
$69$	−0.558667	−0.0672556
$70$	1.00000	0.119523
$71$	−2.71008	−0.321627	−0.160814	−	0.986985i	$-0.551412\pi$
$71$	−2.71008	−0.321627	−0.160814	+	0.986985i	$0.551412\pi$
$72$	2.67745	0.315541
$73$	−9.81960	−1.14930	−0.574649	−	0.818400i	$-0.694861\pi$
$73$	−9.81960	−1.14930	−0.574649	+	0.818400i	$0.694861\pi$
$74$	−7.43608	−0.864426
$75$	−0.567932	−0.0655791
$76$	−2.96172	−0.339732
$77$	0	0
$78$	2.98829	0.338357
$79$	0.874198	0.0983550	0.0491775	−	0.998790i	$-0.484340\pi$
$79$	0.874198	0.0983550	0.0491775	+	0.998790i	$0.484340\pi$
$80$	−1.00000	−0.111803
$81$	6.20112	0.689013
$82$	−9.74211	−1.07584
$83$	2.65545	0.291473	0.145737	−	0.989323i	$-0.453445\pi$
$83$	2.65545	0.291473	0.145737	+	0.989323i	$0.453445\pi$
$84$	−0.567932	−0.0619665
$85$	−5.00401	−0.542761
$86$	5.89617	0.635800
$87$	0.815593	0.0874408
$88$	0	0
$89$	−4.84535	−0.513606	−0.256803	−	0.966464i	$-0.582669\pi$
$89$	−4.84535	−0.513606	−0.256803	+	0.966464i	$0.582669\pi$
$90$	−2.67745	−0.282228
$91$	5.26170	0.551576
$92$	0.983687	0.102556
$93$	5.49841	0.570159
$94$	5.70949	0.588889
$95$	2.96172	0.303866
$96$	0.567932	0.0579643
$97$	17.2128	1.74769	0.873847	−	0.486201i	$-0.161618\pi$
$97$	17.2128	1.74769	0.873847	+	0.486201i	$0.161618\pi$
$98$	−1.00000	−0.101015
$99$	0	0
$100$	1.00000	0.100000
$101$	−15.0324	−1.49578	−0.747888	−	0.663825i	$-0.768932\pi$
$101$	−15.0324	−1.49578	−0.747888	+	0.663825i	$0.768932\pi$
$102$	2.84194	0.281394
$103$	−7.80766	−0.769311	−0.384656	−	0.923060i	$-0.625680\pi$
$103$	−7.80766	−0.769311	−0.384656	+	0.923060i	$0.625680\pi$
$104$	−5.26170	−0.515952
$105$	0.567932	0.0554245
$106$	−10.1844	−0.989200
$107$	−4.64943	−0.449477	−0.224739	−	0.974419i	$-0.572153\pi$
$107$	−4.64943	−0.449477	−0.224739	+	0.974419i	$0.572153\pi$
$108$	3.22441	0.310269
$109$	4.78588	0.458404	0.229202	−	0.973379i	$-0.426388\pi$
$109$	4.78588	0.458404	0.229202	+	0.973379i	$0.426388\pi$
$110$	0	0
$111$	−4.22319	−0.400847
$112$	1.00000	0.0944911
$113$	−0.418079	−0.0393295	−0.0196648	−	0.999807i	$-0.506260\pi$
$113$	−0.418079	−0.0393295	−0.0196648	+	0.999807i	$0.506260\pi$
$114$	−1.68205	−0.157539
$115$	−0.983687	−0.0917293
$116$	−1.43608	−0.133336
$117$	−14.0880	−1.30243
$118$	−7.39355	−0.680632
$119$	5.00401	0.458717
$120$	−0.567932	−0.0518449
$121$	0	0
$122$	−7.04229	−0.637579
$123$	−5.53286	−0.498881
$124$	−9.68146	−0.869421
$125$	−1.00000	−0.0894427
$126$	2.67745	0.238526
$127$	18.7745	1.66597	0.832983	−	0.553299i	$-0.186631\pi$
$127$	18.7745	1.66597	0.832983	+	0.553299i	$0.186631\pi$
$128$	−1.00000	−0.0883883
$129$	3.34862	0.294830
$130$	5.26170	0.461481
$131$	−17.7838	−1.55378	−0.776891	−	0.629635i	$-0.783204\pi$
$131$	−17.7838	−1.55378	−0.776891	+	0.629635i	$0.783204\pi$
$132$	0	0
$133$	−2.96172	−0.256813
$134$	2.77639	0.239844
$135$	−3.22441	−0.277513
$136$	−5.00401	−0.429090
$137$	12.9900	1.10981	0.554904	−	0.831914i	$-0.312755\pi$
$137$	12.9900	1.10981	0.554904	+	0.831914i	$0.312755\pi$
$138$	0.558667	0.0475569
$139$	−13.2415	−1.12313	−0.561563	−	0.827434i	$-0.689800\pi$
$139$	−13.2415	−1.12313	−0.561563	+	0.827434i	$0.689800\pi$
$140$	−1.00000	−0.0845154
$141$	3.24260	0.273076
$142$	2.71008	0.227425
$143$	0	0
$144$	−2.67745	−0.223121
$145$	1.43608	0.119260
$146$	9.81960	0.812676
$147$	−0.567932	−0.0468422
$148$	7.43608	0.611242
$149$	−9.63123	−0.789021	−0.394511	−	0.918891i	$-0.629086\pi$
$149$	−9.63123	−0.789021	−0.394511	+	0.918891i	$0.629086\pi$
$150$	0.567932	0.0463715
$151$	−12.9025	−1.04999	−0.524996	−	0.851105i	$-0.675933\pi$
$151$	−12.9025	−1.04999	−0.524996	+	0.851105i	$0.675933\pi$
$152$	2.96172	0.240227
$153$	−13.3980	−1.08316
$154$	0	0
$155$	9.68146	0.777634
$156$	−2.98829	−0.239254
$157$	−4.31464	−0.344346	−0.172173	−	0.985067i	$-0.555079\pi$
$157$	−4.31464	−0.344346	−0.172173	+	0.985067i	$0.555079\pi$
$158$	−0.874198	−0.0695475
$159$	−5.78407	−0.458706
$160$	1.00000	0.0790569
$161$	0.983687	0.0775254
$162$	−6.20112	−0.487206
$163$	−11.3379	−0.888053	−0.444027	−	0.896014i	$-0.646450\pi$
$163$	−11.3379	−0.888053	−0.444027	+	0.896014i	$0.646450\pi$
$164$	9.74211	0.760731
$165$	0	0
$166$	−2.65545	−0.206103
$167$	−5.03663	−0.389746	−0.194873	−	0.980828i	$-0.562430\pi$
$167$	−5.03663	−0.389746	−0.194873	+	0.980828i	$0.562430\pi$
$168$	0.567932	0.0438169
$169$	14.6855	1.12965
$170$	5.00401	0.383790
$171$	7.92985	0.606411
$172$	−5.89617	−0.449579
$173$	19.9314	1.51536	0.757680	−	0.652626i	$-0.226333\pi$
$173$	19.9314	1.51536	0.757680	+	0.652626i	$0.226333\pi$
$174$	−0.815593	−0.0618300
$175$	1.00000	0.0755929
$176$	0	0
$177$	−4.19904	−0.315619
$178$	4.84535	0.363174
$179$	−3.70949	−0.277260	−0.138630	−	0.990344i	$-0.544270\pi$
$179$	−3.70949	−0.277260	−0.138630	+	0.990344i	$0.544270\pi$
$180$	2.67745	0.199566
$181$	15.6470	1.16303	0.581514	−	0.813536i	$-0.302460\pi$
$181$	15.6470	1.16303	0.581514	+	0.813536i	$0.302460\pi$
$182$	−5.26170	−0.390023
$183$	−3.99954	−0.295655
$184$	−0.983687	−0.0725184
$185$	−7.43608	−0.546711
$186$	−5.49841	−0.403163
$187$	0	0
$188$	−5.70949	−0.416407
$189$	3.22441	0.234541
$190$	−2.96172	−0.214865
$191$	7.13186	0.516043	0.258022	−	0.966139i	$-0.416929\pi$
$191$	7.13186	0.516043	0.258022	+	0.966139i	$0.416929\pi$
$192$	−0.567932	−0.0409870
$193$	12.9824	0.934496	0.467248	−	0.884126i	$-0.345245\pi$
$193$	12.9824	0.934496	0.467248	+	0.884126i	$0.345245\pi$
$194$	−17.2128	−1.23581
$195$	2.98829	0.213996
$196$	1.00000	0.0714286
$197$	−8.92115	−0.635606	−0.317803	−	0.948157i	$-0.602945\pi$
$197$	−8.92115	−0.635606	−0.317803	+	0.948157i	$0.602945\pi$
$198$	0	0
$199$	−2.90018	−0.205588	−0.102794	−	0.994703i	$-0.532778\pi$
$199$	−2.90018	−0.205588	−0.102794	+	0.994703i	$0.532778\pi$
$200$	−1.00000	−0.0707107
$201$	1.57680	0.111219
$202$	15.0324	1.05767
$203$	−1.43608	−0.100793
$204$	−2.84194	−0.198975
$205$	−9.74211	−0.680419
$206$	7.80766	0.543985
$207$	−2.63378	−0.183060
$208$	5.26170	0.364833
$209$	0	0
$210$	−0.567932	−0.0391910
$211$	−23.6547	−1.62845	−0.814227	−	0.580547i	$-0.802839\pi$
$211$	−23.6547	−1.62845	−0.814227	+	0.580547i	$0.802839\pi$
$212$	10.1844	0.699470
$213$	1.53914	0.105460
$214$	4.64943	0.317828
$215$	5.89617	0.402115
$216$	−3.22441	−0.219393
$217$	−9.68146	−0.657220
$218$	−4.78588	−0.324141
$219$	5.57687	0.376850
$220$	0	0
$221$	26.3296	1.77112
$222$	4.22319	0.283442
$223$	0.387500	0.0259489	0.0129745	−	0.999916i	$-0.495870\pi$
$223$	0.387500	0.0259489	0.0129745	+	0.999916i	$0.495870\pi$
$224$	−1.00000	−0.0668153
$225$	−2.67745	−0.178497
$226$	0.418079	0.0278102
$227$	15.0347	0.997887	0.498943	−	0.866635i	$-0.333722\pi$
$227$	15.0347	0.997887	0.498943	+	0.866635i	$0.333722\pi$
$228$	1.68205	0.111397
$229$	8.17418	0.540165	0.270083	−	0.962837i	$-0.412949\pi$
$229$	8.17418	0.540165	0.270083	+	0.962837i	$0.412949\pi$
$230$	0.983687	0.0648624
$231$	0	0
$232$	1.43608	0.0942830
$233$	−17.6289	−1.15491	−0.577454	−	0.816423i	$-0.695954\pi$
$233$	−17.6289	−1.15491	−0.577454	+	0.816423i	$0.695954\pi$
$234$	14.0880	0.920958
$235$	5.70949	0.372446
$236$	7.39355	0.481279
$237$	−0.496485	−0.0322502
$238$	−5.00401	−0.324362
$239$	28.2746	1.82893	0.914467	−	0.404660i	$-0.132610\pi$
$239$	28.2746	1.82893	0.914467	+	0.404660i	$0.132610\pi$
$240$	0.567932	0.0366599
$241$	7.13172	0.459395	0.229697	−	0.973262i	$-0.426226\pi$
$241$	7.13172	0.459395	0.229697	+	0.973262i	$0.426226\pi$
$242$	0	0
$243$	−13.1950	−0.846462
$244$	7.04229	0.450837
$245$	−1.00000	−0.0638877
$246$	5.53286	0.352762
$247$	−15.5837	−0.991564
$248$	9.68146	0.614773
$249$	−1.50811	−0.0955729
$250$	1.00000	0.0632456
$251$	26.8166	1.69265	0.846323	−	0.532670i	$-0.178811\pi$
$251$	26.8166	1.69265	0.846323	+	0.532670i	$0.178811\pi$
$252$	−2.67745	−0.168664
$253$	0	0
$254$	−18.7745	−1.17802
$255$	2.84194	0.177969
$256$	1.00000	0.0625000
$257$	20.6513	1.28819	0.644096	−	0.764945i	$-0.277234\pi$
$257$	20.6513	1.28819	0.644096	+	0.764945i	$0.277234\pi$
$258$	−3.34862	−0.208476
$259$	7.43608	0.462055
$260$	−5.26170	−0.326317
$261$	3.84502	0.238001
$262$	17.7838	1.09869
$263$	18.9482	1.16840	0.584198	−	0.811611i	$-0.301409\pi$
$263$	18.9482	1.16840	0.584198	+	0.811611i	$0.301409\pi$
$264$	0	0
$265$	−10.1844	−0.625625
$266$	2.96172	0.181594
$267$	2.75183	0.168409
$268$	−2.77639	−0.169595
$269$	26.3034	1.60375	0.801874	−	0.597493i	$-0.203836\pi$
$269$	26.3034	1.60375	0.801874	+	0.597493i	$0.203836\pi$
$270$	3.22441	0.196231
$271$	−6.40481	−0.389064	−0.194532	−	0.980896i	$-0.562319\pi$
$271$	−6.40481	−0.389064	−0.194532	+	0.980896i	$0.562319\pi$
$272$	5.00401	0.303413
$273$	−2.98829	−0.180859
$274$	−12.9900	−0.784753
$275$	0	0
$276$	−0.558667	−0.0336278
$277$	−3.41388	−0.205120	−0.102560	−	0.994727i	$-0.532703\pi$
$277$	−3.41388	−0.205120	−0.102560	+	0.994727i	$0.532703\pi$
$278$	13.2415	0.794170
$279$	25.9217	1.55189
$280$	1.00000	0.0597614
$281$	9.93058	0.592409	0.296204	−	0.955125i	$-0.404279\pi$
$281$	9.93058	0.592409	0.296204	+	0.955125i	$0.404279\pi$
$282$	−3.24260	−0.193094
$283$	−14.3247	−0.851516	−0.425758	−	0.904837i	$-0.639992\pi$
$283$	−14.3247	−0.851516	−0.425758	+	0.904837i	$0.639992\pi$
$284$	−2.71008	−0.160814
$285$	−1.68205	−0.0996362
$286$	0	0
$287$	9.74211	0.575059
$288$	2.67745	0.157770
$289$	8.04009	0.472946
$290$	−1.43608	−0.0843292
$291$	−9.77569	−0.573061
$292$	−9.81960	−0.574649
$293$	−13.0495	−0.762359	−0.381180	−	0.924501i	$-0.624482\pi$
$293$	−13.0495	−0.762359	−0.381180	+	0.924501i	$0.624482\pi$
$294$	0.567932	0.0331225
$295$	−7.39355	−0.430469
$296$	−7.43608	−0.432213
$297$	0	0
$298$	9.63123	0.557922
$299$	5.17586	0.299328
$300$	−0.567932	−0.0327896
$301$	−5.89617	−0.339850
$302$	12.9025	0.742456
$303$	8.53736	0.490458
$304$	−2.96172	−0.169866
$305$	−7.04229	−0.403240
$306$	13.3980	0.765912
$307$	−12.2190	−0.697378	−0.348689	−	0.937239i	$-0.613373\pi$
$307$	−12.2190	−0.697378	−0.348689	+	0.937239i	$0.613373\pi$
$308$	0	0
$309$	4.43422	0.252254
$310$	−9.68146	−0.549870
$311$	32.3753	1.83583	0.917917	−	0.396772i	$-0.129870\pi$
$311$	32.3753	1.83583	0.917917	+	0.396772i	$0.129870\pi$
$312$	2.98829	0.169178
$313$	−33.0363	−1.86732	−0.933660	−	0.358159i	$-0.883404\pi$
$313$	−33.0363	−1.86732	−0.933660	+	0.358159i	$0.883404\pi$
$314$	4.31464	0.243489
$315$	2.67745	0.150857
$316$	0.874198	0.0491775
$317$	−18.7597	−1.05365	−0.526826	−	0.849973i	$-0.676618\pi$
$317$	−18.7597	−1.05365	−0.526826	+	0.849973i	$0.676618\pi$
$318$	5.78407	0.324354
$319$	0	0
$320$	−1.00000	−0.0559017
$321$	2.64056	0.147382
$322$	−0.983687	−0.0548187
$323$	−14.8204	−0.824632
$324$	6.20112	0.344506
$325$	5.26170	0.291867
$326$	11.3379	0.627948
$327$	−2.71806	−0.150309
$328$	−9.74211	−0.537918
$329$	−5.70949	−0.314774
$330$	0	0
$331$	17.5094	0.962403	0.481201	−	0.876610i	$-0.340201\pi$
$331$	17.5094	0.962403	0.481201	+	0.876610i	$0.340201\pi$
$332$	2.65545	0.145737
$333$	−19.9097	−1.09105
$334$	5.03663	0.275592
$335$	2.77639	0.151690
$336$	−0.567932	−0.0309832
$337$	19.9652	1.08757	0.543786	−	0.839224i	$-0.316990\pi$
$337$	19.9652	1.08757	0.543786	+	0.839224i	$0.316990\pi$
$338$	−14.6855	−0.798784
$339$	0.237440	0.0128960
$340$	−5.00401	−0.271380
$341$	0	0
$342$	−7.92985	−0.428797
$343$	1.00000	0.0539949
$344$	5.89617	0.317900
$345$	0.558667	0.0300776
$346$	−19.9314	−1.07152
$347$	35.7762	1.92057	0.960284	−	0.279026i	$-0.0900115\pi$
$347$	35.7762	1.92057	0.960284	+	0.279026i	$0.0900115\pi$
$348$	0.815593	0.0437204
$349$	−3.27265	−0.175181	−0.0875904	−	0.996157i	$-0.527917\pi$
$349$	−3.27265	−0.175181	−0.0875904	+	0.996157i	$0.527917\pi$
$350$	−1.00000	−0.0534522
$351$	16.9659	0.905571
$352$	0	0
$353$	−3.21106	−0.170907	−0.0854537	−	0.996342i	$-0.527234\pi$
$353$	−3.21106	−0.170907	−0.0854537	+	0.996342i	$0.527234\pi$
$354$	4.19904	0.223176
$355$	2.71008	0.143836
$356$	−4.84535	−0.256803
$357$	−2.84194	−0.150411
$358$	3.70949	0.196052
$359$	5.16418	0.272555	0.136278	−	0.990671i	$-0.456486\pi$
$359$	5.16418	0.272555	0.136278	+	0.990671i	$0.456486\pi$
$360$	−2.67745	−0.141114
$361$	−10.2282	−0.538329
$362$	−15.6470	−0.822386
$363$	0	0
$364$	5.26170	0.275788
$365$	9.81960	0.513981
$366$	3.99954	0.209059
$367$	−21.0921	−1.10100	−0.550500	−	0.834835i	$-0.685563\pi$
$367$	−21.0921	−1.10100	−0.550500	+	0.834835i	$0.685563\pi$
$368$	0.983687	0.0512782
$369$	−26.0841	−1.35788
$370$	7.43608	0.386583
$371$	10.1844	0.528750
$372$	5.49841	0.285079
$373$	−20.7449	−1.07413	−0.537066	−	0.843540i	$-0.680467\pi$
$373$	−20.7449	−1.07413	−0.537066	+	0.843540i	$0.680467\pi$
$374$	0	0
$375$	0.567932	0.0293279
$376$	5.70949	0.294444
$377$	−7.55620	−0.389164
$378$	−3.22441	−0.165846
$379$	31.1753	1.60137	0.800683	−	0.599088i	$-0.204470\pi$
$379$	31.1753	1.60137	0.800683	+	0.599088i	$0.204470\pi$
$380$	2.96172	0.151933
$381$	−10.6626	−0.546263
$382$	−7.13186	−0.364898
$383$	−23.5582	−1.20377	−0.601883	−	0.798584i	$-0.705583\pi$
$383$	−23.5582	−1.20377	−0.601883	+	0.798584i	$0.705583\pi$
$384$	0.567932	0.0289822
$385$	0	0
$386$	−12.9824	−0.660789
$387$	15.7867	0.802484
$388$	17.2128	0.873847
$389$	−7.39973	−0.375181	−0.187591	−	0.982247i	$-0.560068\pi$
$389$	−7.39973	−0.375181	−0.187591	+	0.982247i	$0.560068\pi$
$390$	−2.98829	−0.151318
$391$	4.92238	0.248935
$392$	−1.00000	−0.0505076
$393$	10.1000	0.509478
$394$	8.92115	0.449441
$395$	−0.874198	−0.0439857
$396$	0	0
$397$	−15.2670	−0.766227	−0.383113	−	0.923701i	$-0.625148\pi$
$397$	−15.2670	−0.766227	−0.383113	+	0.923701i	$0.625148\pi$
$398$	2.90018	0.145373
$399$	1.68205	0.0842080
$400$	1.00000	0.0500000
$401$	35.4584	1.77071	0.885355	−	0.464916i	$-0.153916\pi$
$401$	35.4584	1.77071	0.885355	+	0.464916i	$0.153916\pi$
$402$	−1.57680	−0.0786437
$403$	−50.9409	−2.53755
$404$	−15.0324	−0.747888
$405$	−6.20112	−0.308136
$406$	1.43608	0.0712712
$407$	0	0
$408$	2.84194	0.140697
$409$	17.2938	0.855123	0.427562	−	0.903986i	$-0.359373\pi$
$409$	17.2938	0.855123	0.427562	+	0.903986i	$0.359373\pi$
$410$	9.74211	0.481129
$411$	−7.37742	−0.363901
$412$	−7.80766	−0.384656
$413$	7.39355	0.363813
$414$	2.63378	0.129443
$415$	−2.65545	−0.130351
$416$	−5.26170	−0.257976
$417$	7.52025	0.368268
$418$	0	0
$419$	−3.77494	−0.184418	−0.0922088	−	0.995740i	$-0.529393\pi$
$419$	−3.77494	−0.184418	−0.0922088	+	0.995740i	$0.529393\pi$
$420$	0.567932	0.0277122
$421$	3.56528	0.173761	0.0868806	−	0.996219i	$-0.472310\pi$
$421$	3.56528	0.173761	0.0868806	+	0.996219i	$0.472310\pi$
$422$	23.6547	1.15149
$423$	15.2869	0.743274
$424$	−10.1844	−0.494600
$425$	5.00401	0.242730
$426$	−1.53914	−0.0745716
$427$	7.04229	0.340800
$428$	−4.64943	−0.224739
$429$	0	0
$430$	−5.89617	−0.284339
$431$	2.54773	0.122720	0.0613600	−	0.998116i	$-0.480456\pi$
$431$	2.54773	0.122720	0.0613600	+	0.998116i	$0.480456\pi$
$432$	3.22441	0.155134
$433$	−2.45692	−0.118072	−0.0590360	−	0.998256i	$-0.518803\pi$
$433$	−2.45692	−0.118072	−0.0590360	+	0.998256i	$0.518803\pi$
$434$	9.68146	0.464725
$435$	−0.815593	−0.0391047
$436$	4.78588	0.229202
$437$	−2.91340	−0.139367
$438$	−5.57687	−0.266473
$439$	5.99413	0.286084	0.143042	−	0.989717i	$-0.454312\pi$
$439$	5.99413	0.286084	0.143042	+	0.989717i	$0.454312\pi$
$440$	0	0
$441$	−2.67745	−0.127498
$442$	−26.3296	−1.25237
$443$	18.2630	0.867701	0.433850	−	0.900985i	$-0.357155\pi$
$443$	18.2630	0.867701	0.433850	+	0.900985i	$0.357155\pi$
$444$	−4.22319	−0.200423
$445$	4.84535	0.229692
$446$	−0.387500	−0.0183487
$447$	5.46989	0.258717
$448$	1.00000	0.0472456
$449$	−4.60321	−0.217239	−0.108619	−	0.994083i	$-0.534643\pi$
$449$	−4.60321	−0.217239	−0.108619	+	0.994083i	$0.534643\pi$
$450$	2.67745	0.126216
$451$	0	0
$452$	−0.418079	−0.0196648
$453$	7.32775	0.344288
$454$	−15.0347	−0.705613
$455$	−5.26170	−0.246672
$456$	−1.68205	−0.0787693
$457$	−20.3512	−0.951990	−0.475995	−	0.879448i	$-0.657912\pi$
$457$	−20.3512	−0.951990	−0.475995	+	0.879448i	$0.657912\pi$
$458$	−8.17418	−0.381954
$459$	16.1350	0.753115
$460$	−0.983687	−0.0458646
$461$	22.1050	1.02953	0.514765	−	0.857331i	$-0.327879\pi$
$461$	22.1050	1.02953	0.514765	+	0.857331i	$0.327879\pi$
$462$	0	0
$463$	30.5074	1.41780	0.708899	−	0.705310i	$-0.249192\pi$
$463$	30.5074	1.41780	0.708899	+	0.705310i	$0.249192\pi$
$464$	−1.43608	−0.0666681
$465$	−5.49841	−0.254983
$466$	17.6289	0.816644
$467$	10.5885	0.489978	0.244989	−	0.969526i	$-0.421216\pi$
$467$	10.5885	0.489978	0.244989	+	0.969526i	$0.421216\pi$
$468$	−14.0880	−0.651216
$469$	−2.77639	−0.128202
$470$	−5.70949	−0.263359
$471$	2.45042	0.112910
$472$	−7.39355	−0.340316
$473$	0	0
$474$	0.496485	0.0228043
$475$	−2.96172	−0.135893
$476$	5.00401	0.229358
$477$	−27.2684	−1.24853
$478$	−28.2746	−1.29325
$479$	39.9165	1.82383	0.911915	−	0.410378i	$-0.134603\pi$
$479$	39.9165	1.82383	0.911915	+	0.410378i	$0.134603\pi$
$480$	−0.567932	−0.0259224
$481$	39.1264	1.78401
$482$	−7.13172	−0.324841
$483$	−0.558667	−0.0254202
$484$	0	0
$485$	−17.2128	−0.781593
$486$	13.1950	0.598539
$487$	38.0184	1.72278	0.861390	−	0.507944i	$-0.169594\pi$
$487$	38.0184	1.72278	0.861390	+	0.507944i	$0.169594\pi$
$488$	−7.04229	−0.318790
$489$	6.43916	0.291189
$490$	1.00000	0.0451754
$491$	−19.3973	−0.875387	−0.437693	−	0.899124i	$-0.644204\pi$
$491$	−19.3973	−0.875387	−0.437693	+	0.899124i	$0.644204\pi$
$492$	−5.53286	−0.249440
$493$	−7.18613	−0.323647
$494$	15.5837	0.701142
$495$	0	0
$496$	−9.68146	−0.434710
$497$	−2.71008	−0.121564
$498$	1.50811	0.0675802
$499$	2.76107	0.123603	0.0618013	−	0.998088i	$-0.480316\pi$
$499$	2.76107	0.123603	0.0618013	+	0.998088i	$0.480316\pi$
$500$	−1.00000	−0.0447214
$501$	2.86047	0.127796
$502$	−26.8166	−1.19688
$503$	−8.34764	−0.372203	−0.186102	−	0.982531i	$-0.559585\pi$
$503$	−8.34764	−0.372203	−0.186102	+	0.982531i	$0.559585\pi$
$504$	2.67745	0.119263
$505$	15.0324	0.668931
$506$	0	0
$507$	−8.34035	−0.370408
$508$	18.7745	0.832983
$509$	13.2459	0.587115	0.293557	−	0.955941i	$-0.405161\pi$
$509$	13.2459	0.587115	0.293557	+	0.955941i	$0.405161\pi$
$510$	−2.84194	−0.125843
$511$	−9.81960	−0.434394
$512$	−1.00000	−0.0441942
$513$	−9.54978	−0.421633
$514$	−20.6513	−0.910889
$515$	7.80766	0.344047
$516$	3.34862	0.147415
$517$	0	0
$518$	−7.43608	−0.326722
$519$	−11.3197	−0.496880
$520$	5.26170	0.230741
$521$	31.8038	1.39335	0.696674	−	0.717388i	$-0.254662\pi$
$521$	31.8038	1.39335	0.696674	+	0.717388i	$0.254662\pi$
$522$	−3.84502	−0.168292
$523$	19.7709	0.864519	0.432260	−	0.901749i	$-0.357716\pi$
$523$	19.7709	0.864519	0.432260	+	0.901749i	$0.357716\pi$
$524$	−17.7838	−0.776891
$525$	−0.567932	−0.0247866
$526$	−18.9482	−0.826180
$527$	−48.4461	−2.11035
$528$	0	0
$529$	−22.0324	−0.957929
$530$	10.1844	0.442384
$531$	−19.7959	−0.859069
$532$	−2.96172	−0.128407
$533$	51.2601	2.22032
$534$	−2.75183	−0.119083
$535$	4.64943	0.201012
$536$	2.77639	0.119922
$537$	2.10674	0.0909124
$538$	−26.3034	−1.13402
$539$	0	0
$540$	−3.22441	−0.138756
$541$	−14.0034	−0.602052	−0.301026	−	0.953616i	$-0.597329\pi$
$541$	−14.0034	−0.602052	−0.301026	+	0.953616i	$0.597329\pi$
$542$	6.40481	0.275110
$543$	−8.88641	−0.381352
$544$	−5.00401	−0.214545
$545$	−4.78588	−0.205005
$546$	2.98829	0.127887
$547$	31.9169	1.36467	0.682334	−	0.731041i	$-0.260965\pi$
$547$	31.9169	1.36467	0.682334	+	0.731041i	$0.260965\pi$
$548$	12.9900	0.554904
$549$	−18.8554	−0.804729
$550$	0	0
$551$	4.25325	0.181194
$552$	0.558667	0.0237785
$553$	0.874198	0.0371747
$554$	3.41388	0.145042
$555$	4.22319	0.179264
$556$	−13.2415	−0.561563
$557$	−34.1317	−1.44621	−0.723103	−	0.690740i	$-0.757285\pi$
$557$	−34.1317	−1.44621	−0.723103	+	0.690740i	$0.757285\pi$
$558$	−25.9217	−1.09735
$559$	−31.0239	−1.31217
$560$	−1.00000	−0.0422577
$561$	0	0
$562$	−9.93058	−0.418896
$563$	17.9194	0.755215	0.377607	−	0.925966i	$-0.376747\pi$
$563$	17.9194	0.755215	0.377607	+	0.925966i	$0.376747\pi$
$564$	3.24260	0.136538
$565$	0.418079	0.0175887
$566$	14.3247	0.602113
$567$	6.20112	0.260422
$568$	2.71008	0.113712
$569$	28.7622	1.20578	0.602888	−	0.797826i	$-0.294017\pi$
$569$	28.7622	1.20578	0.602888	+	0.797826i	$0.294017\pi$
$570$	1.68205	0.0704534
$571$	3.85772	0.161441	0.0807203	−	0.996737i	$-0.474278\pi$
$571$	3.85772	0.161441	0.0807203	+	0.996737i	$0.474278\pi$
$572$	0	0
$573$	−4.05041	−0.169208
$574$	−9.74211	−0.406628
$575$	0.983687	0.0410226
$576$	−2.67745	−0.111561
$577$	−11.3881	−0.474094	−0.237047	−	0.971498i	$-0.576180\pi$
$577$	−11.3881	−0.474094	−0.237047	+	0.971498i	$0.576180\pi$
$578$	−8.04009	−0.334424
$579$	−7.37314	−0.306417
$580$	1.43608	0.0596298
$581$	2.65545	0.110167
$582$	9.77569	0.405216
$583$	0	0
$584$	9.81960	0.406338
$585$	14.0880	0.582465
$586$	13.0495	0.539069
$587$	5.98730	0.247122	0.123561	−	0.992337i	$-0.460568\pi$
$587$	5.98730	0.247122	0.123561	+	0.992337i	$0.460568\pi$
$588$	−0.567932	−0.0234211
$589$	28.6737	1.18148
$590$	7.39355	0.304388
$591$	5.06661	0.208412
$592$	7.43608	0.305621
$593$	−7.70485	−0.316400	−0.158200	−	0.987407i	$-0.550569\pi$
$593$	−7.70485	−0.316400	−0.158200	+	0.987407i	$0.550569\pi$
$594$	0	0
$595$	−5.00401	−0.205144
$596$	−9.63123	−0.394511
$597$	1.64710	0.0674114
$598$	−5.17586	−0.211657
$599$	−18.3628	−0.750285	−0.375142	−	0.926967i	$-0.622406\pi$
$599$	−18.3628	−0.750285	−0.375142	+	0.926967i	$0.622406\pi$
$600$	0.567932	0.0231857
$601$	−17.7182	−0.722740	−0.361370	−	0.932423i	$-0.617691\pi$
$601$	−17.7182	−0.722740	−0.361370	+	0.932423i	$0.617691\pi$
$602$	5.89617	0.240310
$603$	7.43365	0.302722
$604$	−12.9025	−0.524996
$605$	0	0
$606$	−8.53736	−0.346806
$607$	−7.88194	−0.319918	−0.159959	−	0.987124i	$-0.551136\pi$
$607$	−7.88194	−0.319918	−0.159959	+	0.987124i	$0.551136\pi$
$608$	2.96172	0.120113
$609$	0.815593	0.0330495
$610$	7.04229	0.285134
$611$	−30.0416	−1.21535
$612$	−13.3980	−0.541582
$613$	−37.3291	−1.50771	−0.753855	−	0.657041i	$-0.771808\pi$
$613$	−37.3291	−1.50771	−0.753855	+	0.657041i	$0.771808\pi$
$614$	12.2190	0.493120
$615$	5.53286	0.223106
$616$	0	0
$617$	7.79365	0.313761	0.156880	−	0.987618i	$-0.449856\pi$
$617$	7.79365	0.313761	0.156880	+	0.987618i	$0.449856\pi$
$618$	−4.43422	−0.178370
$619$	−9.04031	−0.363361	−0.181680	−	0.983358i	$-0.558154\pi$
$619$	−9.04031	−0.363361	−0.181680	+	0.983358i	$0.558154\pi$
$620$	9.68146	0.388817
$621$	3.17181	0.127280
$622$	−32.3753	−1.29813
$623$	−4.84535	−0.194125
$624$	−2.98829	−0.119627
$625$	1.00000	0.0400000
$626$	33.0363	1.32040
$627$	0	0
$628$	−4.31464	−0.172173
$629$	37.2102	1.48367
$630$	−2.67745	−0.106672
$631$	44.5917	1.77517	0.887585	−	0.460644i	$-0.152382\pi$
$631$	44.5917	1.77517	0.887585	+	0.460644i	$0.152382\pi$
$632$	−0.874198	−0.0347737
$633$	13.4342	0.533963
$634$	18.7597	0.745045
$635$	−18.7745	−0.745042
$636$	−5.78407	−0.229353
$637$	5.26170	0.208476
$638$	0	0
$639$	7.25611	0.287047
$640$	1.00000	0.0395285
$641$	5.36041	0.211723	0.105862	−	0.994381i	$-0.466240\pi$
$641$	5.36041	0.211723	0.105862	+	0.994381i	$0.466240\pi$
$642$	−2.64056	−0.104215
$643$	11.9636	0.471799	0.235899	−	0.971777i	$-0.424196\pi$
$643$	11.9636	0.471799	0.235899	+	0.971777i	$0.424196\pi$
$644$	0.983687	0.0387627
$645$	−3.34862	−0.131852
$646$	14.8204	0.583103
$647$	6.61351	0.260004	0.130002	−	0.991514i	$-0.458502\pi$
$647$	6.61351	0.260004	0.130002	+	0.991514i	$0.458502\pi$
$648$	−6.20112	−0.243603
$649$	0	0
$650$	−5.26170	−0.206381
$651$	5.49841	0.215500
$652$	−11.3379	−0.444027
$653$	21.7705	0.851947	0.425974	−	0.904736i	$-0.359932\pi$
$653$	21.7705	0.851947	0.425974	+	0.904736i	$0.359932\pi$
$654$	2.71806	0.106284
$655$	17.7838	0.694872
$656$	9.74211	0.380366
$657$	26.2915	1.02573
$658$	5.70949	0.222579
$659$	43.1812	1.68210	0.841051	−	0.540957i	$-0.181938\pi$
$659$	43.1812	1.68210	0.841051	+	0.540957i	$0.181938\pi$
$660$	0	0
$661$	33.9413	1.32016	0.660081	−	0.751195i	$-0.270522\pi$
$661$	33.9413	1.32016	0.660081	+	0.751195i	$0.270522\pi$
$662$	−17.5094	−0.680522
$663$	−14.9534	−0.580742
$664$	−2.65545	−0.103051
$665$	2.96172	0.114850
$666$	19.9097	0.771487
$667$	−1.41265	−0.0546980
$668$	−5.03663	−0.194873
$669$	−0.220074	−0.00850854
$670$	−2.77639	−0.107261
$671$	0	0
$672$	0.567932	0.0219085
$673$	25.9366	0.999784	0.499892	−	0.866088i	$-0.333373\pi$
$673$	25.9366	0.999784	0.499892	+	0.866088i	$0.333373\pi$
$674$	−19.9652	−0.769029
$675$	3.22441	0.124107
$676$	14.6855	0.564826
$677$	34.3810	1.32137	0.660684	−	0.750664i	$-0.270266\pi$
$677$	34.3810	1.32137	0.660684	+	0.750664i	$0.270266\pi$
$678$	−0.237440	−0.00911884
$679$	17.2128	0.660566
$680$	5.00401	0.191895
$681$	−8.53868	−0.327203
$682$	0	0
$683$	36.4734	1.39562	0.697808	−	0.716284i	$-0.254159\pi$
$683$	36.4734	1.39562	0.697808	+	0.716284i	$0.254159\pi$
$684$	7.92985	0.303206
$685$	−12.9900	−0.496321
$686$	−1.00000	−0.0381802
$687$	−4.64238	−0.177118
$688$	−5.89617	−0.224789
$689$	53.5874	2.04152
$690$	−0.558667	−0.0212681
$691$	18.5975	0.707483	0.353741	−	0.935343i	$-0.384909\pi$
$691$	18.5975	0.707483	0.353741	+	0.935343i	$0.384909\pi$
$692$	19.9314	0.757680
$693$	0	0
$694$	−35.7762	−1.35805
$695$	13.2415	0.502277
$696$	−0.815593	−0.0309150
$697$	48.7496	1.84652
$698$	3.27265	0.123871
$699$	10.0120	0.378689
$700$	1.00000	0.0377964
$701$	−49.2961	−1.86189	−0.930943	−	0.365164i	$-0.881013\pi$
$701$	−49.2961	−1.86189	−0.930943	+	0.365164i	$0.881013\pi$
$702$	−16.9659	−0.640335
$703$	−22.0235	−0.830634
$704$	0	0
$705$	−3.24260	−0.122123
$706$	3.21106	0.120850
$707$	−15.0324	−0.565350
$708$	−4.19904	−0.157809
$709$	35.1026	1.31831	0.659153	−	0.752009i	$-0.270915\pi$
$709$	35.1026	1.31831	0.659153	+	0.752009i	$0.270915\pi$
$710$	−2.71008	−0.101707
$711$	−2.34062	−0.0877803
$712$	4.84535	0.181587
$713$	−9.52353	−0.356659
$714$	2.84194	0.106357
$715$	0	0
$716$	−3.70949	−0.138630
$717$	−16.0581	−0.599700
$718$	−5.16418	−0.192726
$719$	13.5610	0.505741	0.252871	−	0.967500i	$-0.418625\pi$
$719$	13.5610	0.505741	0.252871	+	0.967500i	$0.418625\pi$
$720$	2.67745	0.0997828
$721$	−7.80766	−0.290772
$722$	10.2282	0.380656
$723$	−4.05033	−0.150633
$724$	15.6470	0.581514
$725$	−1.43608	−0.0533345
$726$	0	0
$727$	22.6155	0.838762	0.419381	−	0.907810i	$-0.362247\pi$
$727$	22.6155	0.838762	0.419381	+	0.907810i	$0.362247\pi$
$728$	−5.26170	−0.195012
$729$	−11.1095	−0.411462
$730$	−9.81960	−0.363440
$731$	−29.5045	−1.09126
$732$	−3.99954	−0.147827
$733$	20.1667	0.744873	0.372436	−	0.928058i	$-0.378522\pi$
$733$	20.1667	0.744873	0.372436	+	0.928058i	$0.378522\pi$
$734$	21.0921	0.778525
$735$	0.567932	0.0209485
$736$	−0.983687	−0.0362592
$737$	0	0
$738$	26.0841	0.960167
$739$	6.91436	0.254349	0.127174	−	0.991880i	$-0.459409\pi$
$739$	6.91436	0.254349	0.127174	+	0.991880i	$0.459409\pi$
$740$	−7.43608	−0.273356
$741$	8.85045	0.325130
$742$	−10.1844	−0.373883
$743$	−25.7485	−0.944622	−0.472311	−	0.881432i	$-0.656580\pi$
$743$	−25.7485	−0.944622	−0.472311	+	0.881432i	$0.656580\pi$
$744$	−5.49841	−0.201582
$745$	9.63123	0.352861
$746$	20.7449	0.759526
$747$	−7.10984	−0.260136
$748$	0	0
$749$	−4.64943	−0.169886
$750$	−0.567932	−0.0207379
$751$	−25.4150	−0.927405	−0.463703	−	0.885991i	$-0.653479\pi$
$751$	−25.4150	−0.927405	−0.463703	+	0.885991i	$0.653479\pi$
$752$	−5.70949	−0.208204
$753$	−15.2300	−0.555011
$754$	7.55620	0.275180
$755$	12.9025	0.469571
$756$	3.22441	0.117271
$757$	−17.5209	−0.636809	−0.318404	−	0.947955i	$-0.603147\pi$
$757$	−17.5209	−0.636809	−0.318404	+	0.947955i	$0.603147\pi$
$758$	−31.1753	−1.13234
$759$	0	0
$760$	−2.96172	−0.107433
$761$	11.5164	0.417470	0.208735	−	0.977972i	$-0.433065\pi$
$761$	11.5164	0.417470	0.208735	+	0.977972i	$0.433065\pi$
$762$	10.6626	0.386266
$763$	4.78588	0.173261
$764$	7.13186	0.258022
$765$	13.3980	0.484406
$766$	23.5582	0.851191
$767$	38.9027	1.40469
$768$	−0.567932	−0.0204935
$769$	−24.9065	−0.898153	−0.449077	−	0.893493i	$-0.648247\pi$
$769$	−24.9065	−0.898153	−0.449077	+	0.893493i	$0.648247\pi$
$770$	0	0
$771$	−11.7285	−0.422392
$772$	12.9824	0.467248
$773$	−12.8193	−0.461078	−0.230539	−	0.973063i	$-0.574049\pi$
$773$	−12.8193	−0.461078	−0.230539	+	0.973063i	$0.574049\pi$
$774$	−15.7867	−0.567442
$775$	−9.68146	−0.347768
$776$	−17.2128	−0.617903
$777$	−4.22319	−0.151506
$778$	7.39973	0.265293
$779$	−28.8534	−1.03378
$780$	2.98829	0.106998
$781$	0	0
$782$	−4.92238	−0.176024
$783$	−4.63049	−0.165480
$784$	1.00000	0.0357143
$785$	4.31464	0.153996
$786$	−10.1000	−0.360256
$787$	−12.4754	−0.444699	−0.222349	−	0.974967i	$-0.571373\pi$
$787$	−12.4754	−0.444699	−0.222349	+	0.974967i	$0.571373\pi$
$788$	−8.92115	−0.317803
$789$	−10.7613	−0.383112
$790$	0.874198	0.0311026
$791$	−0.418079	−0.0148652
$792$	0	0
$793$	37.0544	1.31584
$794$	15.2670	0.541804
$795$	5.78407	0.205140
$796$	−2.90018	−0.102794
$797$	−5.21655	−0.184780	−0.0923898	−	0.995723i	$-0.529451\pi$
$797$	−5.21655	−0.184780	−0.0923898	+	0.995723i	$0.529451\pi$
$798$	−1.68205	−0.0595440
$799$	−28.5703	−1.01075
$800$	−1.00000	−0.0353553
$801$	12.9732	0.458385
$802$	−35.4584	−1.25208
$803$	0	0
$804$	1.57680	0.0556095
$805$	−0.983687	−0.0346704
$806$	50.9409	1.79432
$807$	−14.9386	−0.525862
$808$	15.0324	0.528837
$809$	−6.12370	−0.215298	−0.107649	−	0.994189i	$-0.534332\pi$
$809$	−6.12370	−0.215298	−0.107649	+	0.994189i	$0.534332\pi$
$810$	6.20112	0.217885
$811$	7.24103	0.254267	0.127133	−	0.991886i	$-0.459422\pi$
$811$	7.24103	0.254267	0.127133	+	0.991886i	$0.459422\pi$
$812$	−1.43608	−0.0503964
$813$	3.63749	0.127573
$814$	0	0
$815$	11.3379	0.397149
$816$	−2.84194	−0.0994877
$817$	17.4628	0.610945
$818$	−17.2938	−0.604663
$819$	−14.0880	−0.492273
$820$	−9.74211	−0.340209
$821$	25.8519	0.902236	0.451118	−	0.892464i	$-0.351025\pi$
$821$	25.8519	0.902236	0.451118	+	0.892464i	$0.351025\pi$
$822$	7.37742	0.257317
$823$	−49.9541	−1.74129	−0.870646	−	0.491910i	$-0.836299\pi$
$823$	−49.9541	−1.74129	−0.870646	+	0.491910i	$0.836299\pi$
$824$	7.80766	0.271993
$825$	0	0
$826$	−7.39355	−0.257255
$827$	−36.9973	−1.28652	−0.643261	−	0.765647i	$-0.722419\pi$
$827$	−36.9973	−1.28652	−0.643261	+	0.765647i	$0.722419\pi$
$828$	−2.63378	−0.0915300
$829$	20.0676	0.696978	0.348489	−	0.937313i	$-0.386695\pi$
$829$	20.0676	0.696978	0.348489	+	0.937313i	$0.386695\pi$
$830$	2.65545	0.0921720
$831$	1.93885	0.0672579
$832$	5.26170	0.182417
$833$	5.00401	0.173379
$834$	−7.52025	−0.260405
$835$	5.03663	0.174300
$836$	0	0
$837$	−31.2170	−1.07902
$838$	3.77494	0.130403
$839$	31.8473	1.09949	0.549745	−	0.835332i	$-0.314725\pi$
$839$	31.8473	1.09949	0.549745	+	0.835332i	$0.314725\pi$
$840$	−0.567932	−0.0195955
$841$	−26.9377	−0.928886
$842$	−3.56528	−0.122868
$843$	−5.63989	−0.194248
$844$	−23.6547	−0.814227
$845$	−14.6855	−0.505195
$846$	−15.2869	−0.525574
$847$	0	0
$848$	10.1844	0.349735
$849$	8.13546	0.279208
$850$	−5.00401	−0.171636
$851$	7.31477	0.250747
$852$	1.53914	0.0527301
$853$	54.3232	1.85999	0.929996	−	0.367569i	$-0.119810\pi$
$853$	54.3232	1.85999	0.929996	+	0.367569i	$0.119810\pi$
$854$	−7.04229	−0.240982
$855$	−7.92985	−0.271195
$856$	4.64943	0.158914
$857$	50.4050	1.72180	0.860902	−	0.508772i	$-0.169900\pi$
$857$	50.4050	1.72180	0.860902	+	0.508772i	$0.169900\pi$
$858$	0	0
$859$	32.4311	1.10654	0.553268	−	0.833003i	$-0.313380\pi$
$859$	32.4311	1.10654	0.553268	+	0.833003i	$0.313380\pi$
$860$	5.89617	0.201058
$861$	−5.53286	−0.188559
$862$	−2.54773	−0.0867761
$863$	5.57666	0.189832	0.0949159	−	0.995485i	$-0.469742\pi$
$863$	5.57666	0.189832	0.0949159	+	0.995485i	$0.469742\pi$
$864$	−3.22441	−0.109697
$865$	−19.9314	−0.677689
$866$	2.45692	0.0834895
$867$	−4.56622	−0.155077
$868$	−9.68146	−0.328610
$869$	0	0
$870$	0.815593	0.0276512
$871$	−14.6085	−0.494991
$872$	−4.78588	−0.162070
$873$	−46.0864	−1.55979
$874$	2.91340	0.0985473
$875$	−1.00000	−0.0338062
$876$	5.57687	0.188425
$877$	55.2215	1.86470	0.932349	−	0.361559i	$-0.117755\pi$
$877$	55.2215	1.86470	0.932349	+	0.361559i	$0.117755\pi$
$878$	−5.99413	−0.202292
$879$	7.41122	0.249974
$880$	0	0
$881$	−29.3724	−0.989582	−0.494791	−	0.869012i	$-0.664755\pi$
$881$	−29.3724	−0.989582	−0.494791	+	0.869012i	$0.664755\pi$
$882$	2.67745	0.0901545
$883$	53.4760	1.79961	0.899805	−	0.436292i	$-0.143708\pi$
$883$	53.4760	1.79961	0.899805	+	0.436292i	$0.143708\pi$
$884$	26.3296	0.885559
$885$	4.19904	0.141149
$886$	−18.2630	−0.613557
$887$	−29.0365	−0.974950	−0.487475	−	0.873137i	$-0.662082\pi$
$887$	−29.0365	−0.974950	−0.487475	+	0.873137i	$0.662082\pi$
$888$	4.22319	0.141721
$889$	18.7745	0.629676
$890$	−4.84535	−0.162417
$891$	0	0
$892$	0.387500	0.0129745
$893$	16.9099	0.565867
$894$	−5.46989	−0.182940
$895$	3.70949	0.123994
$896$	−1.00000	−0.0334077
$897$	−2.93954	−0.0981483
$898$	4.60321	0.153611
$899$	13.9033	0.463701
$900$	−2.67745	−0.0892484
$901$	50.9630	1.69782
$902$	0	0
$903$	3.34862	0.111435
$904$	0.418079	0.0139051
$905$	−15.6470	−0.520122
$906$	−7.32775	−0.243448
$907$	−36.4927	−1.21172	−0.605860	−	0.795571i	$-0.707171\pi$
$907$	−36.4927	−1.21172	−0.605860	+	0.795571i	$0.707171\pi$
$908$	15.0347	0.498943
$909$	40.2484	1.33496
$910$	5.26170	0.174424
$911$	14.9704	0.495993	0.247996	−	0.968761i	$-0.420228\pi$
$911$	14.9704	0.495993	0.247996	+	0.968761i	$0.420228\pi$
$912$	1.68205	0.0556983
$913$	0	0
$914$	20.3512	0.673159
$915$	3.99954	0.132221
$916$	8.17418	0.270083
$917$	−17.7838	−0.587274
$918$	−16.1350	−0.532533
$919$	−46.3079	−1.52756	−0.763778	−	0.645479i	$-0.776658\pi$
$919$	−46.3079	−1.52756	−0.763778	+	0.645479i	$0.776658\pi$
$920$	0.983687	0.0324312
$921$	6.93959	0.228667
$922$	−22.1050	−0.727988
$923$	−14.2596	−0.469361
$924$	0	0
$925$	7.43608	0.244497
$926$	−30.5074	−1.00253
$927$	20.9046	0.686598
$928$	1.43608	0.0471415
$929$	−51.7132	−1.69666	−0.848328	−	0.529471i	$-0.822390\pi$
$929$	−51.7132	−1.69666	−0.848328	+	0.529471i	$0.822390\pi$
$930$	5.49841	0.180300
$931$	−2.96172	−0.0970663
$932$	−17.6289	−0.577454
$933$	−18.3870	−0.601962
$934$	−10.5885	−0.346467
$935$	0	0
$936$	14.0880	0.460479
$937$	10.4357	0.340921	0.170460	−	0.985365i	$-0.445474\pi$
$937$	10.4357	0.340921	0.170460	+	0.985365i	$0.445474\pi$
$938$	2.77639	0.0906523
$939$	18.7624	0.612286
$940$	5.70949	0.186223
$941$	47.0321	1.53320	0.766601	−	0.642124i	$-0.221946\pi$
$941$	47.0321	1.53320	0.766601	+	0.642124i	$0.221946\pi$
$942$	−2.45042	−0.0798391
$943$	9.58319	0.312072
$944$	7.39355	0.240640
$945$	−3.22441	−0.104890
$946$	0	0
$947$	30.3259	0.985461	0.492730	−	0.870182i	$-0.335999\pi$
$947$	30.3259	0.985461	0.492730	+	0.870182i	$0.335999\pi$
$948$	−0.496485	−0.0161251
$949$	−51.6678	−1.67721
$950$	2.96172	0.0960907
$951$	10.6543	0.345488
$952$	−5.00401	−0.162181
$953$	0.609007	0.0197277	0.00986384	−	0.999951i	$-0.496860\pi$
$953$	0.609007	0.0197277	0.00986384	+	0.999951i	$0.496860\pi$
$954$	27.2684	0.882846
$955$	−7.13186	−0.230781
$956$	28.2746	0.914467
$957$	0	0
$958$	−39.9165	−1.28964
$959$	12.9900	0.419468
$960$	0.567932	0.0183299
$961$	62.7307	2.02357
$962$	−39.1264	−1.26149
$963$	12.4486	0.401151
$964$	7.13172	0.229697
$965$	−12.9824	−0.417919
$966$	0.558667	0.0179748
$967$	14.2048	0.456796	0.228398	−	0.973568i	$-0.426651\pi$
$967$	14.2048	0.456796	0.228398	+	0.973568i	$0.426651\pi$
$968$	0	0
$969$	8.41701	0.270393
$970$	17.2128	0.552669
$971$	49.1969	1.57880	0.789402	−	0.613877i	$-0.210391\pi$
$971$	49.1969	1.57880	0.789402	+	0.613877i	$0.210391\pi$
$972$	−13.1950	−0.423231
$973$	−13.2415	−0.424502
$974$	−38.0184	−1.21819
$975$	−2.98829	−0.0957018
$976$	7.04229	0.225418
$977$	19.6319	0.628080	0.314040	−	0.949410i	$-0.398317\pi$
$977$	19.6319	0.628080	0.314040	+	0.949410i	$0.398317\pi$
$978$	−6.43916	−0.205902
$979$	0	0
$980$	−1.00000	−0.0319438
$981$	−12.8140	−0.409119
$982$	19.3973	0.618992
$983$	−21.3138	−0.679804	−0.339902	−	0.940461i	$-0.610394\pi$
$983$	−21.3138	−0.679804	−0.339902	+	0.940461i	$0.610394\pi$
$984$	5.53286	0.176381
$985$	8.92115	0.284252
$986$	7.18613	0.228853
$987$	3.24260	0.103213
$988$	−15.5837	−0.495782
$989$	−5.79999	−0.184429
$990$	0	0
$991$	−27.8962	−0.886152	−0.443076	−	0.896484i	$-0.646113\pi$
$991$	−27.8962	−0.886152	−0.443076	+	0.896484i	$0.646113\pi$
$992$	9.68146	0.307387
$993$	−9.94414	−0.315568
$994$	2.71008	0.0859585
$995$	2.90018	0.0919418
$996$	−1.50811	−0.0477864
$997$	36.3507	1.15124	0.575619	−	0.817718i	$-0.304761\pi$
$997$	36.3507	1.15124	0.575619	+	0.817718i	$0.304761\pi$
$998$	−2.76107	−0.0874002
$999$	23.9769	0.758597

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8470.2.a.cx.1.3	✓	6
11.10	odd	2		8470.2.a.dd.1.3	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8470.2.a.cx.1.3	✓	6	1.1	even	1	trivial
8470.2.a.dd.1.3	yes	6	11.10	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:	\( N \)	\(=\)	\( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8470.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.567932 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.567932 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.67745 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.567932 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.567932 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.67745 q^{9} +1.00000 q^{10} -0.567932 q^{12} +5.26170 q^{13} -1.00000 q^{14} +0.567932 q^{15} +1.00000 q^{16} +5.00401 q^{17} +2.67745 q^{18} -2.96172 q^{19} -1.00000 q^{20} -0.567932 q^{21} +0.983687 q^{23} +0.567932 q^{24} +1.00000 q^{25} -5.26170 q^{26} +3.22441 q^{27} +1.00000 q^{28} -1.43608 q^{29} -0.567932 q^{30} -9.68146 q^{31} -1.00000 q^{32} -5.00401 q^{34} -1.00000 q^{35} -2.67745 q^{36} +7.43608 q^{37} +2.96172 q^{38} -2.98829 q^{39} +1.00000 q^{40} +9.74211 q^{41} +0.567932 q^{42} -5.89617 q^{43} +2.67745 q^{45} -0.983687 q^{46} -5.70949 q^{47} -0.567932 q^{48} +1.00000 q^{49} -1.00000 q^{50} -2.84194 q^{51} +5.26170 q^{52} +10.1844 q^{53} -3.22441 q^{54} -1.00000 q^{56} +1.68205 q^{57} +1.43608 q^{58} +7.39355 q^{59} +0.567932 q^{60} +7.04229 q^{61} +9.68146 q^{62} -2.67745 q^{63} +1.00000 q^{64} -5.26170 q^{65} -2.77639 q^{67} +5.00401 q^{68} -0.558667 q^{69} +1.00000 q^{70} -2.71008 q^{71} +2.67745 q^{72} -9.81960 q^{73} -7.43608 q^{74} -0.567932 q^{75} -2.96172 q^{76} +2.98829 q^{78} +0.874198 q^{79} -1.00000 q^{80} +6.20112 q^{81} -9.74211 q^{82} +2.65545 q^{83} -0.567932 q^{84} -5.00401 q^{85} +5.89617 q^{86} +0.815593 q^{87} -4.84535 q^{89} -2.67745 q^{90} +5.26170 q^{91} +0.983687 q^{92} +5.49841 q^{93} +5.70949 q^{94} +2.96172 q^{95} +0.567932 q^{96} +17.2128 q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 6 q^{4} - 6 q^{5} + 6 q^{7} - 6 q^{8} + 18 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 + 6 * q^4 - 6 * q^5 + 6 * q^7 - 6 * q^8 + 18 * q^9	\( 6 q - 6 q^{2} + 6 q^{4} - 6 q^{5} + 6 q^{7} - 6 q^{8} + 18 q^{9} + 6 q^{10} - 6 q^{14} + 6 q^{16} + 6 q^{17} - 18 q^{18} - 6 q^{20} + 6 q^{25} - 12 q^{27} + 6 q^{28} + 12 q^{29} - 6 q^{32} - 6 q^{34} - 6 q^{35} + 18 q^{36} + 24 q^{37} - 24 q^{39} + 6 q^{40} + 12 q^{41} - 18 q^{43} - 18 q^{45} + 24 q^{47} + 6 q^{49} - 6 q^{50} - 12 q^{51} + 36 q^{53} + 12 q^{54} - 6 q^{56} - 12 q^{57} - 12 q^{58} + 30 q^{59} + 36 q^{61} + 18 q^{63} + 6 q^{64} - 12 q^{67} + 6 q^{68} + 6 q^{70} + 6 q^{71} - 18 q^{72} - 6 q^{73} - 24 q^{74} + 24 q^{78} - 24 q^{79} - 6 q^{80} + 54 q^{81} - 12 q^{82} + 24 q^{83} - 6 q^{85} + 18 q^{86} - 24 q^{87} + 36 q^{89} + 18 q^{90} - 24 q^{94} - 6 q^{98}+O(q^{100}) \) 6 * q - 6 * q^2 + 6 * q^4 - 6 * q^5 + 6 * q^7 - 6 * q^8 + 18 * q^9 + 6 * q^10 - 6 * q^14 + 6 * q^16 + 6 * q^17 - 18 * q^18 - 6 * q^20 + 6 * q^25 - 12 * q^27 + 6 * q^28 + 12 * q^29 - 6 * q^32 - 6 * q^34 - 6 * q^35 + 18 * q^36 + 24 * q^37 - 24 * q^39 + 6 * q^40 + 12 * q^41 - 18 * q^43 - 18 * q^45 + 24 * q^47 + 6 * q^49 - 6 * q^50 - 12 * q^51 + 36 * q^53 + 12 * q^54 - 6 * q^56 - 12 * q^57 - 12 * q^58 + 30 * q^59 + 36 * q^61 + 18 * q^63 + 6 * q^64 - 12 * q^67 + 6 * q^68 + 6 * q^70 + 6 * q^71 - 18 * q^72 - 6 * q^73 - 24 * q^74 + 24 * q^78 - 24 * q^79 - 6 * q^80 + 54 * q^81 - 12 * q^82 + 24 * q^83 - 6 * q^85 + 18 * q^86 - 24 * q^87 + 36 * q^89 + 18 * q^90 - 24 * q^94 - 6 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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