LMFDB - Embedded newform 8470.2.a.cx.1.2

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			1.2
Root			$2.67544$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.67544 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.67544 q^{6} +1.00000 q^{7} -1.00000 q^{8} +4.15798 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.67544 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.67544 q^{6} +1.00000 q^{7} -1.00000 q^{8} +4.15798 q^{9} +1.00000 q^{10} -2.67544 q^{12} -3.11654 q^{13} -1.00000 q^{14} +2.67544 q^{15} +1.00000 q^{16} -0.564586 q^{17} -4.15798 q^{18} +7.52404 q^{19} -1.00000 q^{20} -2.67544 q^{21} +4.63400 q^{23} +2.67544 q^{24} +1.00000 q^{25} +3.11654 q^{26} -3.09812 q^{27} +1.00000 q^{28} +6.24003 q^{29} -2.67544 q^{30} +2.72257 q^{31} -1.00000 q^{32} +0.564586 q^{34} -1.00000 q^{35} +4.15798 q^{36} -0.240027 q^{37} -7.52404 q^{38} +8.33813 q^{39} +1.00000 q^{40} -2.28644 q^{41} +2.67544 q^{42} -3.78866 q^{43} -4.15798 q^{45} -4.63400 q^{46} -0.981558 q^{47} -2.67544 q^{48} +1.00000 q^{49} -1.00000 q^{50} +1.51052 q^{51} -3.11654 q^{52} -1.14198 q^{53} +3.09812 q^{54} -1.00000 q^{56} -20.1301 q^{57} -6.24003 q^{58} +8.79892 q^{59} +2.67544 q^{60} +11.9594 q^{61} -2.72257 q^{62} +4.15798 q^{63} +1.00000 q^{64} +3.11654 q^{65} -6.80218 q^{67} -0.564586 q^{68} -12.3980 q^{69} +1.00000 q^{70} +11.4260 q^{71} -4.15798 q^{72} +13.2594 q^{73} +0.240027 q^{74} -2.67544 q^{75} +7.52404 q^{76} -8.33813 q^{78} -15.3694 q^{79} -1.00000 q^{80} -4.18512 q^{81} +2.28644 q^{82} +10.5208 q^{83} -2.67544 q^{84} +0.564586 q^{85} +3.78866 q^{86} -16.6948 q^{87} -4.33244 q^{89} +4.15798 q^{90} -3.11654 q^{91} +4.63400 q^{92} -7.28408 q^{93} +0.981558 q^{94} -7.52404 q^{95} +2.67544 q^{96} -9.05134 q^{97} -1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.67544	−1.54467	−0.772333	−	0.635217i	$-0.780910\pi$
$3$	−2.67544	−1.54467	−0.772333	+	0.635217i	$0.780910\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.67544	1.09224
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	4.15798	1.38599
$10$	1.00000	0.316228
$11$	0	0
$11$	0	0
$12$	−2.67544	−0.772333
$13$	−3.11654	−0.864374	−0.432187	−	0.901784i	$-0.642258\pi$
$13$	−3.11654	−0.864374	−0.432187	+	0.901784i	$0.642258\pi$
$14$	−1.00000	−0.267261
$15$	2.67544	0.690796
$16$	1.00000	0.250000
$17$	−0.564586	−0.136932	−0.0684661	−	0.997653i	$-0.521810\pi$
$17$	−0.564586	−0.136932	−0.0684661	+	0.997653i	$0.521810\pi$
$18$	−4.15798	−0.980046
$19$	7.52404	1.72613	0.863066	−	0.505091i	$-0.168541\pi$
$19$	7.52404	1.72613	0.863066	+	0.505091i	$0.168541\pi$
$20$	−1.00000	−0.223607
$21$	−2.67544	−0.583829
$22$	0	0
$23$	4.63400	0.966256	0.483128	−	0.875550i	$-0.339501\pi$
$23$	4.63400	0.966256	0.483128	+	0.875550i	$0.339501\pi$
$24$	2.67544	0.546122
$25$	1.00000	0.200000
$26$	3.11654	0.611204
$27$	−3.09812	−0.596233
$28$	1.00000	0.188982
$29$	6.24003	1.15874	0.579372	−	0.815063i	$-0.303298\pi$
$29$	6.24003	1.15874	0.579372	+	0.815063i	$0.303298\pi$
$30$	−2.67544	−0.488466
$31$	2.72257	0.488988	0.244494	−	0.969651i	$-0.421378\pi$
$31$	2.72257	0.488988	0.244494	+	0.969651i	$0.421378\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	0.564586	0.0968257
$35$	−1.00000	−0.169031
$36$	4.15798	0.692997
$37$	−0.240027	−0.0394602	−0.0197301	−	0.999805i	$-0.506281\pi$
$37$	−0.240027	−0.0394602	−0.0197301	+	0.999805i	$0.506281\pi$
$38$	−7.52404	−1.22056
$39$	8.33813	1.33517
$40$	1.00000	0.158114
$41$	−2.28644	−0.357082	−0.178541	−	0.983932i	$-0.557138\pi$
$41$	−2.28644	−0.357082	−0.178541	+	0.983932i	$0.557138\pi$
$42$	2.67544	0.412830
$43$	−3.78866	−0.577765	−0.288883	−	0.957365i	$-0.593284\pi$
$43$	−3.78866	−0.577765	−0.288883	+	0.957365i	$0.593284\pi$
$44$	0	0
$45$	−4.15798	−0.619836
$46$	−4.63400	−0.683246
$47$	−0.981558	−0.143175	−0.0715875	−	0.997434i	$-0.522807\pi$
$47$	−0.981558	−0.143175	−0.0715875	+	0.997434i	$0.522807\pi$
$48$	−2.67544	−0.386167
$49$	1.00000	0.142857
$50$	−1.00000	−0.141421
$51$	1.51052	0.211515
$52$	−3.11654	−0.432187
$53$	−1.14198	−0.156862	−0.0784312	−	0.996920i	$-0.524991\pi$
$53$	−1.14198	−0.156862	−0.0784312	+	0.996920i	$0.524991\pi$
$54$	3.09812	0.421601
$55$	0	0
$56$	−1.00000	−0.133631
$57$	−20.1301	−2.66630
$58$	−6.24003	−0.819356
$59$	8.79892	1.14552	0.572761	−	0.819722i	$-0.305872\pi$
$59$	8.79892	1.14552	0.572761	+	0.819722i	$0.305872\pi$
$60$	2.67544	0.345398
$61$	11.9594	1.53125	0.765625	−	0.643287i	$-0.222430\pi$
$61$	11.9594	1.53125	0.765625	+	0.643287i	$0.222430\pi$
$62$	−2.72257	−0.345767
$63$	4.15798	0.523857
$64$	1.00000	0.125000
$65$	3.11654	0.386560
$66$	0	0
$67$	−6.80218	−0.831018	−0.415509	−	0.909589i	$-0.636397\pi$
$67$	−6.80218	−0.831018	−0.415509	+	0.909589i	$0.636397\pi$
$68$	−0.564586	−0.0684661
$69$	−12.3980	−1.49254
$70$	1.00000	0.119523
$71$	11.4260	1.35601	0.678007	−	0.735055i	$-0.262844\pi$
$71$	11.4260	1.35601	0.678007	+	0.735055i	$0.262844\pi$
$72$	−4.15798	−0.490023
$73$	13.2594	1.55190	0.775948	−	0.630797i	$-0.217272\pi$
$73$	13.2594	1.55190	0.775948	+	0.630797i	$0.217272\pi$
$74$	0.240027	0.0279026
$75$	−2.67544	−0.308933
$76$	7.52404	0.863066
$77$	0	0
$78$	−8.33813	−0.944107
$79$	−15.3694	−1.72919	−0.864595	−	0.502470i	$-0.832425\pi$
$79$	−15.3694	−1.72919	−0.864595	+	0.502470i	$0.832425\pi$
$80$	−1.00000	−0.111803
$81$	−4.18512	−0.465013
$82$	2.28644	0.252495
$83$	10.5208	1.15481	0.577403	−	0.816459i	$-0.304066\pi$
$83$	10.5208	1.15481	0.577403	+	0.816459i	$0.304066\pi$
$84$	−2.67544	−0.291915
$85$	0.564586	0.0612379
$86$	3.78866	0.408542
$87$	−16.6948	−1.78987
$88$	0	0
$89$	−4.33244	−0.459238	−0.229619	−	0.973281i	$-0.573748\pi$
$89$	−4.33244	−0.459238	−0.229619	+	0.973281i	$0.573748\pi$
$90$	4.15798	0.438290
$91$	−3.11654	−0.326703
$92$	4.63400	0.483128
$93$	−7.28408	−0.755324
$94$	0.981558	0.101240
$95$	−7.52404	−0.771950
$96$	2.67544	0.273061
$97$	−9.05134	−0.919025	−0.459512	−	0.888171i	$-0.651976\pi$
$97$	−9.05134	−0.919025	−0.459512	+	0.888171i	$0.651976\pi$
$98$	−1.00000	−0.101015
$99$	0	0
$100$	1.00000	0.100000
$101$	5.47395	0.544679	0.272339	−	0.962201i	$-0.412203\pi$
$101$	5.47395	0.544679	0.272339	+	0.962201i	$0.412203\pi$
$102$	−1.51052	−0.149563
$103$	12.5991	1.24143	0.620715	−	0.784036i	$-0.286842\pi$
$103$	12.5991	1.24143	0.620715	+	0.784036i	$0.286842\pi$
$104$	3.11654	0.305602
$105$	2.67544	0.261096
$106$	1.14198	0.110919
$107$	9.86211	0.953406	0.476703	−	0.879064i	$-0.341832\pi$
$107$	9.86211	0.953406	0.476703	+	0.879064i	$0.341832\pi$
$108$	−3.09812	−0.298117
$109$	−14.9188	−1.42896	−0.714480	−	0.699656i	$-0.753337\pi$
$109$	−14.9188	−1.42896	−0.714480	+	0.699656i	$0.753337\pi$
$110$	0	0
$111$	0.642178	0.0609528
$112$	1.00000	0.0944911
$113$	−1.87415	−0.176305	−0.0881527	−	0.996107i	$-0.528096\pi$
$113$	−1.87415	−0.176305	−0.0881527	+	0.996107i	$0.528096\pi$
$114$	20.1301	1.88536
$115$	−4.63400	−0.432123
$116$	6.24003	0.579372
$117$	−12.9585	−1.19802
$118$	−8.79892	−0.810007
$119$	−0.564586	−0.0517555
$120$	−2.67544	−0.244233
$121$	0	0
$122$	−11.9594	−1.08276
$123$	6.11724	0.551573
$124$	2.72257	0.244494
$125$	−1.00000	−0.0894427
$126$	−4.15798	−0.370423
$127$	−13.7604	−1.22104	−0.610519	−	0.792002i	$-0.709039\pi$
$127$	−13.7604	−1.22104	−0.610519	+	0.792002i	$0.709039\pi$
$128$	−1.00000	−0.0883883
$129$	10.1363	0.892455
$130$	−3.11654	−0.273339
$131$	8.75625	0.765037	0.382519	−	0.923948i	$-0.375057\pi$
$131$	8.75625	0.765037	0.382519	+	0.923948i	$0.375057\pi$
$132$	0	0
$133$	7.52404	0.652417
$134$	6.80218	0.587619
$135$	3.09812	0.266644
$136$	0.564586	0.0484128
$137$	−3.81831	−0.326220	−0.163110	−	0.986608i	$-0.552153\pi$
$137$	−3.81831	−0.326220	−0.163110	+	0.986608i	$0.552153\pi$
$138$	12.3980	1.05539
$139$	−0.0485569	−0.00411855	−0.00205927	−	0.999998i	$-0.500655\pi$
$139$	−0.0485569	−0.00411855	−0.00205927	+	0.999998i	$0.500655\pi$
$140$	−1.00000	−0.0845154
$141$	2.62610	0.221158
$142$	−11.4260	−0.958847
$143$	0	0
$144$	4.15798	0.346499
$145$	−6.24003	−0.518206
$146$	−13.2594	−1.09736
$147$	−2.67544	−0.220667
$148$	−0.240027	−0.0197301
$149$	10.5863	0.867266	0.433633	−	0.901090i	$-0.357231\pi$
$149$	10.5863	0.867266	0.433633	+	0.901090i	$0.357231\pi$
$150$	2.67544	0.218449
$151$	−10.5581	−0.859203	−0.429601	−	0.903019i	$-0.641346\pi$
$151$	−10.5581	−0.859203	−0.429601	+	0.903019i	$0.641346\pi$
$152$	−7.52404	−0.610280
$153$	−2.34754	−0.189787
$154$	0	0
$155$	−2.72257	−0.218682
$156$	8.33813	0.667585
$157$	20.5831	1.64271	0.821356	−	0.570416i	$-0.193218\pi$
$157$	20.5831	1.64271	0.821356	+	0.570416i	$0.193218\pi$
$158$	15.3694	1.22272
$159$	3.05529	0.242300
$160$	1.00000	0.0790569
$161$	4.63400	0.365210
$162$	4.18512	0.328814
$163$	−19.3407	−1.51488	−0.757439	−	0.652906i	$-0.773550\pi$
$163$	−19.3407	−1.51488	−0.757439	+	0.652906i	$0.773550\pi$
$164$	−2.28644	−0.178541
$165$	0	0
$166$	−10.5208	−0.816571
$167$	7.83259	0.606104	0.303052	−	0.952974i	$-0.401994\pi$
$167$	7.83259	0.606104	0.303052	+	0.952974i	$0.401994\pi$
$168$	2.67544	0.206415
$169$	−3.28716	−0.252858
$170$	−0.564586	−0.0433018
$171$	31.2848	2.39241
$172$	−3.78866	−0.288883
$173$	−12.1772	−0.925819	−0.462909	−	0.886406i	$-0.653194\pi$
$173$	−12.1772	−0.925819	−0.462909	+	0.886406i	$0.653194\pi$
$174$	16.6948	1.26563
$175$	1.00000	0.0755929
$176$	0	0
$177$	−23.5410	−1.76945
$178$	4.33244	0.324730
$179$	1.01844	0.0761219	0.0380610	−	0.999275i	$-0.487882\pi$
$179$	1.01844	0.0761219	0.0380610	+	0.999275i	$0.487882\pi$
$180$	−4.15798	−0.309918
$181$	1.18721	0.0882445	0.0441223	−	0.999026i	$-0.485951\pi$
$181$	1.18721	0.0882445	0.0441223	+	0.999026i	$0.485951\pi$
$182$	3.11654	0.231014
$183$	−31.9968	−2.36527
$184$	−4.63400	−0.341623
$185$	0.240027	0.0176471
$186$	7.28408	0.534094
$187$	0	0
$188$	−0.981558	−0.0715875
$189$	−3.09812	−0.225355
$190$	7.52404	0.545851
$191$	16.9155	1.22396	0.611980	−	0.790873i	$-0.290373\pi$
$191$	16.9155	1.22396	0.611980	+	0.790873i	$0.290373\pi$
$192$	−2.67544	−0.193083
$193$	15.2274	1.09609	0.548045	−	0.836449i	$-0.315372\pi$
$193$	15.2274	1.09609	0.548045	+	0.836449i	$0.315372\pi$
$194$	9.05134	0.649849
$195$	−8.33813	−0.597106
$196$	1.00000	0.0714286
$197$	−2.83965	−0.202317	−0.101158	−	0.994870i	$-0.532255\pi$
$197$	−2.83965	−0.202317	−0.101158	+	0.994870i	$0.532255\pi$
$198$	0	0
$199$	4.77593	0.338556	0.169278	−	0.985568i	$-0.445856\pi$
$199$	4.77593	0.338556	0.169278	+	0.985568i	$0.445856\pi$
$200$	−1.00000	−0.0707107
$201$	18.1988	1.28365
$202$	−5.47395	−0.385146
$203$	6.24003	0.437964
$204$	1.51052	0.105757
$205$	2.28644	0.159692
$206$	−12.5991	−0.877824
$207$	19.2681	1.33923
$208$	−3.11654	−0.216093
$209$	0	0
$210$	−2.67544	−0.184623
$211$	−26.0899	−1.79610	−0.898052	−	0.439889i	$-0.855018\pi$
$211$	−26.0899	−1.79610	−0.898052	+	0.439889i	$0.855018\pi$
$212$	−1.14198	−0.0784312
$213$	−30.5695	−2.09459
$214$	−9.86211	−0.674160
$215$	3.78866	0.258385
$216$	3.09812	0.210800
$217$	2.72257	0.184820
$218$	14.9188	1.01043
$219$	−35.4748	−2.39716
$220$	0	0
$221$	1.75956	0.118361
$222$	−0.642178	−0.0431002
$223$	8.25283	0.552650	0.276325	−	0.961064i	$-0.410883\pi$
$223$	8.25283	0.552650	0.276325	+	0.961064i	$0.410883\pi$
$224$	−1.00000	−0.0668153
$225$	4.15798	0.277199
$226$	1.87415	0.124667
$227$	−5.55836	−0.368921	−0.184461	−	0.982840i	$-0.559054\pi$
$227$	−5.55836	−0.368921	−0.184461	+	0.982840i	$0.559054\pi$
$228$	−20.1301	−1.33315
$229$	−5.96188	−0.393972	−0.196986	−	0.980406i	$-0.563115\pi$
$229$	−5.96188	−0.393972	−0.196986	+	0.980406i	$0.563115\pi$
$230$	4.63400	0.305557
$231$	0	0
$232$	−6.24003	−0.409678
$233$	2.50193	0.163907	0.0819533	−	0.996636i	$-0.473884\pi$
$233$	2.50193	0.163907	0.0819533	+	0.996636i	$0.473884\pi$
$234$	12.9585	0.847126
$235$	0.981558	0.0640298
$236$	8.79892	0.572761
$237$	41.1199	2.67102
$238$	0.564586	0.0365967
$239$	−28.8313	−1.86494	−0.932472	−	0.361242i	$-0.882353\pi$
$239$	−28.8313	−1.86494	−0.932472	+	0.361242i	$0.882353\pi$
$240$	2.67544	0.172699
$241$	−1.67379	−0.107818	−0.0539092	−	0.998546i	$-0.517168\pi$
$241$	−1.67379	−0.107818	−0.0539092	+	0.998546i	$0.517168\pi$
$242$	0	0
$243$	20.4914	1.31452
$244$	11.9594	0.765625
$245$	−1.00000	−0.0638877
$246$	−6.11724	−0.390021
$247$	−23.4490	−1.49202
$248$	−2.72257	−0.172883
$249$	−28.1477	−1.78379
$250$	1.00000	0.0632456
$251$	−7.91255	−0.499436	−0.249718	−	0.968319i	$-0.580338\pi$
$251$	−7.91255	−0.499436	−0.249718	+	0.968319i	$0.580338\pi$
$252$	4.15798	0.261928
$253$	0	0
$254$	13.7604	0.863404
$255$	−1.51052	−0.0945922
$256$	1.00000	0.0625000
$257$	−9.58983	−0.598197	−0.299099	−	0.954222i	$-0.596686\pi$
$257$	−9.58983	−0.598197	−0.299099	+	0.954222i	$0.596686\pi$
$258$	−10.1363	−0.631061
$259$	−0.240027	−0.0149145
$260$	3.11654	0.193280
$261$	25.9459	1.60601
$262$	−8.75625	−0.540963
$263$	−23.6980	−1.46128	−0.730642	−	0.682761i	$-0.760779\pi$
$263$	−23.6980	−1.46128	−0.730642	+	0.682761i	$0.760779\pi$
$264$	0	0
$265$	1.14198	0.0701510
$266$	−7.52404	−0.461328
$267$	11.5912	0.709369
$268$	−6.80218	−0.415509
$269$	3.41365	0.208134	0.104067	−	0.994570i	$-0.466814\pi$
$269$	3.41365	0.208134	0.104067	+	0.994570i	$0.466814\pi$
$270$	−3.09812	−0.188546
$271$	−23.1613	−1.40695	−0.703474	−	0.710721i	$-0.748369\pi$
$271$	−23.1613	−1.40695	−0.703474	+	0.710721i	$0.748369\pi$
$272$	−0.564586	−0.0342331
$273$	8.33813	0.504646
$274$	3.81831	0.230672
$275$	0	0
$276$	−12.3980	−0.746271
$277$	4.39966	0.264350	0.132175	−	0.991226i	$-0.457804\pi$
$277$	4.39966	0.264350	0.132175	+	0.991226i	$0.457804\pi$
$278$	0.0485569	0.00291225
$279$	11.3204	0.677735
$280$	1.00000	0.0597614
$281$	−13.5746	−0.809794	−0.404897	−	0.914362i	$-0.632693\pi$
$281$	−13.5746	−0.809794	−0.404897	+	0.914362i	$0.632693\pi$
$282$	−2.62610	−0.156382
$283$	−23.5943	−1.40254	−0.701268	−	0.712897i	$-0.747383\pi$
$283$	−23.5943	−1.40254	−0.701268	+	0.712897i	$0.747383\pi$
$284$	11.4260	0.678007
$285$	20.1301	1.19240
$286$	0	0
$287$	−2.28644	−0.134964
$288$	−4.15798	−0.245012
$289$	−16.6812	−0.981250
$290$	6.24003	0.366427
$291$	24.2163	1.41959
$292$	13.2594	0.775948
$293$	−30.2362	−1.76642	−0.883209	−	0.468979i	$-0.844622\pi$
$293$	−30.2362	−1.76642	−0.883209	+	0.468979i	$0.844622\pi$
$294$	2.67544	0.156035
$295$	−8.79892	−0.512293
$296$	0.240027	0.0139513
$297$	0	0
$298$	−10.5863	−0.613250
$299$	−14.4421	−0.835206
$300$	−2.67544	−0.154467
$301$	−3.78866	−0.218375
$302$	10.5581	0.607548
$303$	−14.6452	−0.841347
$304$	7.52404	0.431533
$305$	−11.9594	−0.684796
$306$	2.34754	0.134200
$307$	5.66685	0.323424	0.161712	−	0.986838i	$-0.448298\pi$
$307$	5.66685	0.323424	0.161712	+	0.986838i	$0.448298\pi$
$308$	0	0
$309$	−33.7082	−1.91760
$310$	2.72257	0.154632
$311$	29.7071	1.68454	0.842269	−	0.539058i	$-0.181219\pi$
$311$	29.7071	1.68454	0.842269	+	0.539058i	$0.181219\pi$
$312$	−8.33813	−0.472054
$313$	−7.84976	−0.443695	−0.221847	−	0.975081i	$-0.571209\pi$
$313$	−7.84976	−0.443695	−0.221847	+	0.975081i	$0.571209\pi$
$314$	−20.5831	−1.16157
$315$	−4.15798	−0.234276
$316$	−15.3694	−0.864595
$317$	6.99148	0.392681	0.196340	−	0.980536i	$-0.437094\pi$
$317$	6.99148	0.392681	0.196340	+	0.980536i	$0.437094\pi$
$318$	−3.05529	−0.171332
$319$	0	0
$320$	−1.00000	−0.0559017
$321$	−26.3855	−1.47270
$322$	−4.63400	−0.258243
$323$	−4.24796	−0.236363
$324$	−4.18512	−0.232507
$325$	−3.11654	−0.172875
$326$	19.3407	1.07118
$327$	39.9143	2.20727
$328$	2.28644	0.126248
$329$	−0.981558	−0.0541150
$330$	0	0
$331$	25.4265	1.39757	0.698784	−	0.715333i	$-0.253725\pi$
$331$	25.4265	1.39757	0.698784	+	0.715333i	$0.253725\pi$
$332$	10.5208	0.577403
$333$	−0.998028	−0.0546916
$334$	−7.83259	−0.428580
$335$	6.80218	0.371643
$336$	−2.67544	−0.145957
$337$	−15.5179	−0.845313	−0.422656	−	0.906290i	$-0.638902\pi$
$337$	−15.5179	−0.845313	−0.422656	+	0.906290i	$0.638902\pi$
$338$	3.28716	0.178798
$339$	5.01418	0.272333
$340$	0.564586	0.0306190
$341$	0	0
$342$	−31.2848	−1.69169
$343$	1.00000	0.0539949
$344$	3.78866	0.204271
$345$	12.3980	0.667486
$346$	12.1772	0.654653
$347$	12.5627	0.674403	0.337202	−	0.941432i	$-0.390520\pi$
$347$	12.5627	0.674403	0.337202	+	0.941432i	$0.390520\pi$
$348$	−16.6948	−0.894937
$349$	20.3193	1.08767	0.543833	−	0.839194i	$-0.316973\pi$
$349$	20.3193	1.08767	0.543833	+	0.839194i	$0.316973\pi$
$350$	−1.00000	−0.0534522
$351$	9.65543	0.515368
$352$	0	0
$353$	32.3745	1.72312	0.861560	−	0.507656i	$-0.169488\pi$
$353$	32.3745	1.72312	0.861560	+	0.507656i	$0.169488\pi$
$354$	23.5410	1.25119
$355$	−11.4260	−0.606428
$356$	−4.33244	−0.229619
$357$	1.51052	0.0799450
$358$	−1.01844	−0.0538263
$359$	23.2783	1.22858	0.614291	−	0.789079i	$-0.289442\pi$
$359$	23.2783	1.22858	0.614291	+	0.789079i	$0.289442\pi$
$360$	4.15798	0.219145
$361$	37.6111	1.97953
$362$	−1.18721	−0.0623983
$363$	0	0
$364$	−3.11654	−0.163351
$365$	−13.2594	−0.694029
$366$	31.9968	1.67250
$367$	−4.14641	−0.216441	−0.108221	−	0.994127i	$-0.534515\pi$
$367$	−4.14641	−0.216441	−0.108221	+	0.994127i	$0.534515\pi$
$368$	4.63400	0.241564
$369$	−9.50699	−0.494914
$370$	−0.240027	−0.0124784
$371$	−1.14198	−0.0592884
$372$	−7.28408	−0.377662
$373$	−21.9641	−1.13726	−0.568628	−	0.822595i	$-0.692526\pi$
$373$	−21.9641	−1.13726	−0.568628	+	0.822595i	$0.692526\pi$
$374$	0	0
$375$	2.67544	0.138159
$376$	0.981558	0.0506200
$377$	−19.4473	−1.00159
$378$	3.09812	0.159350
$379$	20.9655	1.07692	0.538462	−	0.842650i	$-0.319005\pi$
$379$	20.9655	1.07692	0.538462	+	0.842650i	$0.319005\pi$
$380$	−7.52404	−0.385975
$381$	36.8151	1.88610
$382$	−16.9155	−0.865471
$383$	−36.1904	−1.84925	−0.924623	−	0.380885i	$-0.875619\pi$
$383$	−36.1904	−1.84925	−0.924623	+	0.380885i	$0.875619\pi$
$384$	2.67544	0.136531
$385$	0	0
$386$	−15.2274	−0.775053
$387$	−15.7532	−0.800780
$388$	−9.05134	−0.459512
$389$	27.3801	1.38823	0.694113	−	0.719866i	$-0.255797\pi$
$389$	27.3801	1.38823	0.694113	+	0.719866i	$0.255797\pi$
$390$	8.33813	0.422218
$391$	−2.61629	−0.132312
$392$	−1.00000	−0.0505076
$393$	−23.4268	−1.18173
$394$	2.83965	0.143060
$395$	15.3694	0.773317
$396$	0	0
$397$	−2.72549	−0.136788	−0.0683942	−	0.997658i	$-0.521788\pi$
$397$	−2.72549	−0.136788	−0.0683942	+	0.997658i	$0.521788\pi$
$398$	−4.77593	−0.239396
$399$	−20.1301	−1.00777
$400$	1.00000	0.0500000
$401$	26.3810	1.31741	0.658703	−	0.752403i	$-0.271105\pi$
$401$	26.3810	1.31741	0.658703	+	0.752403i	$0.271105\pi$
$402$	−18.1988	−0.907675
$403$	−8.48501	−0.422668
$404$	5.47395	0.272339
$405$	4.18512	0.207960
$406$	−6.24003	−0.309687
$407$	0	0
$408$	−1.51052	−0.0747817
$409$	31.2447	1.54495	0.772476	−	0.635044i	$-0.219018\pi$
$409$	31.2447	1.54495	0.772476	+	0.635044i	$0.219018\pi$
$410$	−2.28644	−0.112919
$411$	10.2157	0.503901
$412$	12.5991	0.620715
$413$	8.79892	0.432967
$414$	−19.2681	−0.946975
$415$	−10.5208	−0.516445
$416$	3.11654	0.152801
$417$	0.129911	0.00636178
$418$	0	0
$419$	0.716042	0.0349809	0.0174905	−	0.999847i	$-0.494432\pi$
$419$	0.716042	0.0349809	0.0174905	+	0.999847i	$0.494432\pi$
$420$	2.67544	0.130548
$421$	28.3733	1.38283	0.691416	−	0.722457i	$-0.256987\pi$
$421$	28.3733	1.38283	0.691416	+	0.722457i	$0.256987\pi$
$422$	26.0899	1.27004
$423$	−4.08130	−0.198440
$424$	1.14198	0.0554593
$425$	−0.564586	−0.0273864
$426$	30.5695	1.48110
$427$	11.9594	0.578758
$428$	9.86211	0.476703
$429$	0	0
$430$	−3.78866	−0.182705
$431$	−15.8511	−0.763519	−0.381760	−	0.924262i	$-0.624682\pi$
$431$	−15.8511	−0.763519	−0.381760	+	0.924262i	$0.624682\pi$
$432$	−3.09812	−0.149058
$433$	22.2137	1.06752	0.533761	−	0.845635i	$-0.320778\pi$
$433$	22.2137	1.06752	0.533761	+	0.845635i	$0.320778\pi$
$434$	−2.72257	−0.130688
$435$	16.6948	0.800456
$436$	−14.9188	−0.714480
$437$	34.8664	1.66789
$438$	35.4748	1.69505
$439$	−16.3478	−0.780238	−0.390119	−	0.920764i	$-0.627566\pi$
$439$	−16.3478	−0.780238	−0.390119	+	0.920764i	$0.627566\pi$
$440$	0	0
$441$	4.15798	0.197999
$442$	−1.75956	−0.0836936
$443$	28.6492	1.36117	0.680583	−	0.732671i	$-0.261727\pi$
$443$	28.6492	1.36117	0.680583	+	0.732671i	$0.261727\pi$
$444$	0.642178	0.0304764
$445$	4.33244	0.205377
$446$	−8.25283	−0.390783
$447$	−28.3231	−1.33964
$448$	1.00000	0.0472456
$449$	23.2905	1.09914	0.549572	−	0.835446i	$-0.314791\pi$
$449$	23.2905	1.09914	0.549572	+	0.835446i	$0.314791\pi$
$450$	−4.15798	−0.196009
$451$	0	0
$452$	−1.87415	−0.0881527
$453$	28.2475	1.32718
$454$	5.55836	0.260867
$455$	3.11654	0.146106
$456$	20.1301	0.942679
$457$	10.3649	0.484849	0.242424	−	0.970170i	$-0.422057\pi$
$457$	10.3649	0.484849	0.242424	+	0.970170i	$0.422057\pi$
$458$	5.96188	0.278580
$459$	1.74915	0.0816436
$460$	−4.63400	−0.216061
$461$	−0.698098	−0.0325137	−0.0162568	−	0.999868i	$-0.505175\pi$
$461$	−0.698098	−0.0325137	−0.0162568	+	0.999868i	$0.505175\pi$
$462$	0	0
$463$	10.4790	0.487002	0.243501	−	0.969901i	$-0.421704\pi$
$463$	10.4790	0.487002	0.243501	+	0.969901i	$0.421704\pi$
$464$	6.24003	0.289686
$465$	7.28408	0.337791
$466$	−2.50193	−0.115900
$467$	−39.3583	−1.82129	−0.910644	−	0.413193i	$-0.864414\pi$
$467$	−39.3583	−1.82129	−0.910644	+	0.413193i	$0.864414\pi$
$468$	−12.9585	−0.599009
$469$	−6.80218	−0.314095
$470$	−0.981558	−0.0452759
$471$	−55.0689	−2.53744
$472$	−8.79892	−0.405003
$473$	0	0
$474$	−41.1199	−1.88870
$475$	7.52404	0.345226
$476$	−0.564586	−0.0258778
$477$	−4.74832	−0.217411
$478$	28.8313	1.31871
$479$	−27.4511	−1.25427	−0.627136	−	0.778910i	$-0.715773\pi$
$479$	−27.4511	−1.25427	−0.627136	+	0.778910i	$0.715773\pi$
$480$	−2.67544	−0.122117
$481$	0.748054	0.0341083
$482$	1.67379	0.0762391
$483$	−12.3980	−0.564128
$484$	0	0
$485$	9.05134	0.411000
$486$	−20.4914	−0.929508
$487$	−36.5980	−1.65841	−0.829206	−	0.558943i	$-0.811207\pi$
$487$	−36.5980	−1.65841	−0.829206	+	0.558943i	$0.811207\pi$
$488$	−11.9594	−0.541379
$489$	51.7448	2.33998
$490$	1.00000	0.0451754
$491$	3.39001	0.152989	0.0764944	−	0.997070i	$-0.475627\pi$
$491$	3.39001	0.152989	0.0764944	+	0.997070i	$0.475627\pi$
$492$	6.11724	0.275786
$493$	−3.52303	−0.158669
$494$	23.4490	1.05502
$495$	0	0
$496$	2.72257	0.122247
$497$	11.4260	0.512525
$498$	28.1477	1.26133
$499$	22.9786	1.02867	0.514333	−	0.857591i	$-0.328040\pi$
$499$	22.9786	1.02867	0.514333	+	0.857591i	$0.328040\pi$
$500$	−1.00000	−0.0447214
$501$	−20.9556	−0.936228
$502$	7.91255	0.353154
$503$	31.6613	1.41171	0.705854	−	0.708357i	$-0.250563\pi$
$503$	31.6613	1.41171	0.705854	+	0.708357i	$0.250563\pi$
$504$	−4.15798	−0.185211
$505$	−5.47395	−0.243588
$506$	0	0
$507$	8.79459	0.390582
$508$	−13.7604	−0.610519
$509$	0.742359	0.0329045	0.0164522	−	0.999865i	$-0.494763\pi$
$509$	0.742359	0.0329045	0.0164522	+	0.999865i	$0.494763\pi$
$510$	1.51052	0.0668868
$511$	13.2594	0.586562
$512$	−1.00000	−0.0441942
$513$	−23.3104	−1.02918
$514$	9.58983	0.422989
$515$	−12.5991	−0.555184
$516$	10.1363	0.446227
$517$	0	0
$518$	0.240027	0.0105462
$519$	32.5795	1.43008
$520$	−3.11654	−0.136669
$521$	20.2911	0.888969	0.444485	−	0.895786i	$-0.353387\pi$
$521$	20.2911	0.888969	0.444485	+	0.895786i	$0.353387\pi$
$522$	−25.9459	−1.13562
$523$	−31.4418	−1.37485	−0.687426	−	0.726255i	$-0.741259\pi$
$523$	−31.4418	−1.37485	−0.687426	+	0.726255i	$0.741259\pi$
$524$	8.75625	0.382519
$525$	−2.67544	−0.116766
$526$	23.6980	1.03328
$527$	−1.53713	−0.0669582
$528$	0	0
$529$	−1.52605	−0.0663498
$530$	−1.14198	−0.0496043
$531$	36.5858	1.58769
$532$	7.52404	0.326208
$533$	7.12580	0.308652
$534$	−11.5912	−0.501600
$535$	−9.86211	−0.426376
$536$	6.80218	0.293809
$537$	−2.72478	−0.117583
$538$	−3.41365	−0.147173
$539$	0	0
$540$	3.09812	0.133322
$541$	−3.03964	−0.130684	−0.0653422	−	0.997863i	$-0.520814\pi$
$541$	−3.03964	−0.130684	−0.0653422	+	0.997863i	$0.520814\pi$
$542$	23.1613	0.994863
$543$	−3.17631	−0.136308
$544$	0.564586	0.0242064
$545$	14.9188	0.639050
$546$	−8.33813	−0.356839
$547$	18.1983	0.778102	0.389051	−	0.921216i	$-0.372803\pi$
$547$	18.1983	0.778102	0.389051	+	0.921216i	$0.372803\pi$
$548$	−3.81831	−0.163110
$549$	49.7272	2.12231
$550$	0	0
$551$	46.9502	2.00015
$552$	12.3980	0.527694
$553$	−15.3694	−0.653572
$554$	−4.39966	−0.186924
$555$	−0.642178	−0.0272589
$556$	−0.0485569	−0.00205927
$557$	12.1608	0.515268	0.257634	−	0.966243i	$-0.417057\pi$
$557$	12.1608	0.515268	0.257634	+	0.966243i	$0.417057\pi$
$558$	−11.3204	−0.479231
$559$	11.8075	0.499405
$560$	−1.00000	−0.0422577
$561$	0	0
$562$	13.5746	0.572611
$563$	38.4298	1.61962	0.809812	−	0.586689i	$-0.199569\pi$
$563$	38.4298	1.61962	0.809812	+	0.586689i	$0.199569\pi$
$564$	2.62610	0.110579
$565$	1.87415	0.0788462
$566$	23.5943	0.991743
$567$	−4.18512	−0.175758
$568$	−11.4260	−0.479424
$569$	−19.7245	−0.826893	−0.413446	−	0.910528i	$-0.635675\pi$
$569$	−19.7245	−0.826893	−0.413446	+	0.910528i	$0.635675\pi$
$570$	−20.1301	−0.843158
$571$	25.4847	1.06650	0.533251	−	0.845957i	$-0.320970\pi$
$571$	25.4847	1.06650	0.533251	+	0.845957i	$0.320970\pi$
$572$	0	0
$573$	−45.2563	−1.89061
$574$	2.28644	0.0954342
$575$	4.63400	0.193251
$576$	4.15798	0.173249
$577$	−27.2044	−1.13254	−0.566268	−	0.824221i	$-0.691613\pi$
$577$	−27.2044	−1.13254	−0.566268	+	0.824221i	$0.691613\pi$
$578$	16.6812	0.693848
$579$	−40.7400	−1.69309
$580$	−6.24003	−0.259103
$581$	10.5208	0.436476
$582$	−24.2163	−1.00380
$583$	0	0
$584$	−13.2594	−0.548678
$585$	12.9585	0.535770
$586$	30.2362	1.24905
$587$	28.3154	1.16870	0.584350	−	0.811502i	$-0.301350\pi$
$587$	28.3154	1.16870	0.584350	+	0.811502i	$0.301350\pi$
$588$	−2.67544	−0.110333
$589$	20.4847	0.844058
$590$	8.79892	0.362246
$591$	7.59732	0.312512
$592$	−0.240027	−0.00986505
$593$	−0.594543	−0.0244150	−0.0122075	−	0.999925i	$-0.503886\pi$
$593$	−0.594543	−0.0244150	−0.0122075	+	0.999925i	$0.503886\pi$
$594$	0	0
$595$	0.564586	0.0231458
$596$	10.5863	0.433633
$597$	−12.7777	−0.522957
$598$	14.4421	0.590580
$599$	5.55684	0.227046	0.113523	−	0.993535i	$-0.463786\pi$
$599$	5.55684	0.227046	0.113523	+	0.993535i	$0.463786\pi$
$600$	2.67544	0.109224
$601$	3.76921	0.153749	0.0768747	−	0.997041i	$-0.475506\pi$
$601$	3.76921	0.153749	0.0768747	+	0.997041i	$0.475506\pi$
$602$	3.78866	0.154414
$603$	−28.2834	−1.15179
$604$	−10.5581	−0.429601
$605$	0	0
$606$	14.6452	0.594922
$607$	20.3035	0.824092	0.412046	−	0.911163i	$-0.364814\pi$
$607$	20.3035	0.824092	0.412046	+	0.911163i	$0.364814\pi$
$608$	−7.52404	−0.305140
$609$	−16.6948	−0.676508
$610$	11.9594	0.484224
$611$	3.05907	0.123757
$612$	−2.34754	−0.0948937
$613$	36.3948	1.46997	0.734986	−	0.678082i	$-0.237189\pi$
$613$	36.3948	1.46997	0.734986	+	0.678082i	$0.237189\pi$
$614$	−5.66685	−0.228696
$615$	−6.11724	−0.246671
$616$	0	0
$617$	25.2056	1.01474	0.507371	−	0.861728i	$-0.330618\pi$
$617$	25.2056	1.01474	0.507371	+	0.861728i	$0.330618\pi$
$618$	33.7082	1.35594
$619$	42.8248	1.72128	0.860638	−	0.509218i	$-0.170065\pi$
$619$	42.8248	1.72128	0.860638	+	0.509218i	$0.170065\pi$
$620$	−2.72257	−0.109341
$621$	−14.3567	−0.576114
$622$	−29.7071	−1.19115
$623$	−4.33244	−0.173576
$624$	8.33813	0.333792
$625$	1.00000	0.0400000
$626$	7.84976	0.313739
$627$	0	0
$628$	20.5831	0.821356
$629$	0.135516	0.00540337
$630$	4.15798	0.165658
$631$	−10.9354	−0.435331	−0.217666	−	0.976023i	$-0.569844\pi$
$631$	−10.9354	−0.435331	−0.217666	+	0.976023i	$0.569844\pi$
$632$	15.3694	0.611361
$633$	69.8021	2.77438
$634$	−6.99148	−0.277667
$635$	13.7604	0.546065
$636$	3.05529	0.121150
$637$	−3.11654	−0.123482
$638$	0	0
$639$	47.5091	1.87943
$640$	1.00000	0.0395285
$641$	21.8420	0.862708	0.431354	−	0.902183i	$-0.358036\pi$
$641$	21.8420	0.862708	0.431354	+	0.902183i	$0.358036\pi$
$642$	26.3855	1.04135
$643$	0.551560	0.0217514	0.0108757	−	0.999941i	$-0.496538\pi$
$643$	0.551560	0.0217514	0.0108757	+	0.999941i	$0.496538\pi$
$644$	4.63400	0.182605
$645$	−10.1363	−0.399118
$646$	4.24796	0.167134
$647$	1.00700	0.0395894	0.0197947	−	0.999804i	$-0.493699\pi$
$647$	1.00700	0.0395894	0.0197947	+	0.999804i	$0.493699\pi$
$648$	4.18512	0.164407
$649$	0	0
$650$	3.11654	0.122241
$651$	−7.28408	−0.285485
$652$	−19.3407	−0.757439
$653$	−19.2293	−0.752500	−0.376250	−	0.926518i	$-0.622787\pi$
$653$	−19.2293	−0.752500	−0.376250	+	0.926518i	$0.622787\pi$
$654$	−39.9143	−1.56077
$655$	−8.75625	−0.342135
$656$	−2.28644	−0.0892706
$657$	55.1324	2.15092
$658$	0.981558	0.0382651
$659$	−2.36031	−0.0919447	−0.0459723	−	0.998943i	$-0.514639\pi$
$659$	−2.36031	−0.0919447	−0.0459723	+	0.998943i	$0.514639\pi$
$660$	0	0
$661$	24.9127	0.968991	0.484495	−	0.874794i	$-0.339003\pi$
$661$	24.9127	0.968991	0.484495	+	0.874794i	$0.339003\pi$
$662$	−25.4265	−0.988229
$663$	−4.70759	−0.182828
$664$	−10.5208	−0.408285
$665$	−7.52404	−0.291770
$666$	0.998028	0.0386728
$667$	28.9163	1.11964
$668$	7.83259	0.303052
$669$	−22.0800	−0.853661
$670$	−6.80218	−0.262791
$671$	0	0
$672$	2.67544	0.103207
$673$	−4.02852	−0.155288	−0.0776440	−	0.996981i	$-0.524740\pi$
$673$	−4.02852	−0.155288	−0.0776440	+	0.996981i	$0.524740\pi$
$674$	15.5179	0.597726
$675$	−3.09812	−0.119247
$676$	−3.28716	−0.126429
$677$	15.2440	0.585874	0.292937	−	0.956132i	$-0.405367\pi$
$677$	15.2440	0.585874	0.292937	+	0.956132i	$0.405367\pi$
$678$	−5.01418	−0.192569
$679$	−9.05134	−0.347359
$680$	−0.564586	−0.0216509
$681$	14.8711	0.569861
$682$	0	0
$683$	33.8181	1.29401	0.647006	−	0.762485i	$-0.276021\pi$
$683$	33.8181	1.29401	0.647006	+	0.762485i	$0.276021\pi$
$684$	31.2848	1.19621
$685$	3.81831	0.145890
$686$	−1.00000	−0.0381802
$687$	15.9507	0.608556
$688$	−3.78866	−0.144441
$689$	3.55902	0.135588
$690$	−12.3980	−0.471984
$691$	1.75430	0.0667368	0.0333684	−	0.999443i	$-0.489377\pi$
$691$	1.75430	0.0667368	0.0333684	+	0.999443i	$0.489377\pi$
$692$	−12.1772	−0.462909
$693$	0	0
$694$	−12.5627	−0.476875
$695$	0.0485569	0.00184187
$696$	16.6948	0.632816
$697$	1.29089	0.0488961
$698$	−20.3193	−0.769096
$699$	−6.69376	−0.253181
$700$	1.00000	0.0377964
$701$	13.1026	0.494877	0.247438	−	0.968904i	$-0.420411\pi$
$701$	13.1026	0.494877	0.247438	+	0.968904i	$0.420411\pi$
$702$	−9.65543	−0.364421
$703$	−1.80597	−0.0681135
$704$	0	0
$705$	−2.62610	−0.0989047
$706$	−32.3745	−1.21843
$707$	5.47395	0.205869
$708$	−23.5410	−0.884725
$709$	−5.43312	−0.204045	−0.102023	−	0.994782i	$-0.532531\pi$
$709$	−5.43312	−0.204045	−0.102023	+	0.994782i	$0.532531\pi$
$710$	11.4260	0.428810
$711$	−63.9056	−2.39665
$712$	4.33244	0.162365
$713$	12.6164	0.472488
$714$	−1.51052	−0.0565297
$715$	0	0
$716$	1.01844	0.0380610
$717$	77.1366	2.88072
$718$	−23.2783	−0.868739
$719$	−48.9750	−1.82646	−0.913230	−	0.407445i	$-0.866420\pi$
$719$	−48.9750	−1.82646	−0.913230	+	0.407445i	$0.866420\pi$
$720$	−4.15798	−0.154959
$721$	12.5991	0.469216
$722$	−37.6111	−1.39974
$723$	4.47813	0.166543
$724$	1.18721	0.0441223
$725$	6.24003	0.231749
$726$	0	0
$727$	17.7501	0.658316	0.329158	−	0.944275i	$-0.393235\pi$
$727$	17.7501	0.658316	0.329158	+	0.944275i	$0.393235\pi$
$728$	3.11654	0.115507
$729$	−42.2682	−1.56549
$730$	13.2594	0.490753
$731$	2.13902	0.0791147
$732$	−31.9968	−1.18264
$733$	−28.0948	−1.03770	−0.518852	−	0.854864i	$-0.673641\pi$
$733$	−28.0948	−1.03770	−0.518852	+	0.854864i	$0.673641\pi$
$734$	4.14641	0.153047
$735$	2.67544	0.0986851
$736$	−4.63400	−0.170811
$737$	0	0
$738$	9.50699	0.349957
$739$	10.5129	0.386723	0.193361	−	0.981128i	$-0.438061\pi$
$739$	10.5129	0.386723	0.193361	+	0.981128i	$0.438061\pi$
$740$	0.240027	0.00882357
$741$	62.7364	2.30468
$742$	1.14198	0.0419233
$743$	−33.7047	−1.23650	−0.618252	−	0.785980i	$-0.712159\pi$
$743$	−33.7047	−1.23650	−0.618252	+	0.785980i	$0.712159\pi$
$744$	7.28408	0.267047
$745$	−10.5863	−0.387853
$746$	21.9641	0.804161
$747$	43.7452	1.60055
$748$	0	0
$749$	9.86211	0.360354
$750$	−2.67544	−0.0976933
$751$	−21.5277	−0.785557	−0.392778	−	0.919633i	$-0.628486\pi$
$751$	−21.5277	−0.785557	−0.392778	+	0.919633i	$0.628486\pi$
$752$	−0.981558	−0.0357937
$753$	21.1696	0.771462
$754$	19.4473	0.708229
$755$	10.5581	0.384247
$756$	−3.09812	−0.112678
$757$	30.8831	1.12247	0.561233	−	0.827658i	$-0.310327\pi$
$757$	30.8831	1.12247	0.561233	+	0.827658i	$0.310327\pi$
$758$	−20.9655	−0.761501
$759$	0	0
$760$	7.52404	0.272925
$761$	−7.53569	−0.273169	−0.136584	−	0.990628i	$-0.543612\pi$
$761$	−7.53569	−0.273169	−0.136584	+	0.990628i	$0.543612\pi$
$762$	−36.8151	−1.33367
$763$	−14.9188	−0.540096
$764$	16.9155	0.611980
$765$	2.34754	0.0848755
$766$	36.1904	1.30761
$767$	−27.4222	−0.990159
$768$	−2.67544	−0.0965417
$769$	−52.9068	−1.90787	−0.953934	−	0.300017i	$-0.903008\pi$
$769$	−52.9068	−1.90787	−0.953934	+	0.300017i	$0.903008\pi$
$770$	0	0
$771$	25.6570	0.924015
$772$	15.2274	0.548045
$773$	40.8245	1.46836	0.734178	−	0.678957i	$-0.237568\pi$
$773$	40.8245	1.46836	0.734178	+	0.678957i	$0.237568\pi$
$774$	15.7532	0.566237
$775$	2.72257	0.0977976
$776$	9.05134	0.324924
$777$	0.642178	0.0230380
$778$	−27.3801	−0.981623
$779$	−17.2033	−0.616371
$780$	−8.33813	−0.298553
$781$	0	0
$782$	2.61629	0.0935584
$783$	−19.3324	−0.690882
$784$	1.00000	0.0357143
$785$	−20.5831	−0.734643
$786$	23.4268	0.835607
$787$	30.7705	1.09685	0.548425	−	0.836200i	$-0.315228\pi$
$787$	30.7705	1.09685	0.548425	+	0.836200i	$0.315228\pi$
$788$	−2.83965	−0.101158
$789$	63.4027	2.25720
$790$	−15.3694	−0.546818
$791$	−1.87415	−0.0666372
$792$	0	0
$793$	−37.2721	−1.32357
$794$	2.72549	0.0967240
$795$	−3.05529	−0.108360
$796$	4.77593	0.169278
$797$	48.5308	1.71905	0.859525	−	0.511093i	$-0.170759\pi$
$797$	48.5308	1.71905	0.859525	+	0.511093i	$0.170759\pi$
$798$	20.1301	0.712598
$799$	0.554174	0.0196053
$800$	−1.00000	−0.0353553
$801$	−18.0142	−0.636501
$802$	−26.3810	−0.931547
$803$	0	0
$804$	18.1988	0.641823
$805$	−4.63400	−0.163327
$806$	8.48501	0.298872
$807$	−9.13301	−0.321497
$808$	−5.47395	−0.192573
$809$	4.68981	0.164885	0.0824424	−	0.996596i	$-0.473728\pi$
$809$	4.68981	0.164885	0.0824424	+	0.996596i	$0.473728\pi$
$810$	−4.18512	−0.147050
$811$	−30.7640	−1.08027	−0.540135	−	0.841578i	$-0.681627\pi$
$811$	−30.7640	−1.08027	−0.540135	+	0.841578i	$0.681627\pi$
$812$	6.24003	0.218982
$813$	61.9667	2.17327
$814$	0	0
$815$	19.3407	0.677474
$816$	1.51052	0.0528786
$817$	−28.5060	−0.997299
$818$	−31.2447	−1.09245
$819$	−12.9585	−0.452808
$820$	2.28644	0.0798460
$821$	55.6318	1.94156	0.970782	−	0.239961i	$-0.0771347\pi$
$821$	55.6318	1.94156	0.970782	+	0.239961i	$0.0771347\pi$
$822$	−10.2157	−0.356312
$823$	−31.3173	−1.09165	−0.545826	−	0.837898i	$-0.683784\pi$
$823$	−31.3173	−1.09165	−0.545826	+	0.837898i	$0.683784\pi$
$824$	−12.5991	−0.438912
$825$	0	0
$826$	−8.79892	−0.306154
$827$	−37.9025	−1.31800	−0.659000	−	0.752143i	$-0.729020\pi$
$827$	−37.9025	−1.31800	−0.659000	+	0.752143i	$0.729020\pi$
$828$	19.2681	0.669613
$829$	52.1297	1.81054	0.905269	−	0.424838i	$-0.139669\pi$
$829$	52.1297	1.81054	0.905269	+	0.424838i	$0.139669\pi$
$830$	10.5208	0.365182
$831$	−11.7710	−0.408333
$832$	−3.11654	−0.108047
$833$	−0.564586	−0.0195617
$834$	−0.129911	−0.00449846
$835$	−7.83259	−0.271058
$836$	0	0
$837$	−8.43485	−0.291551
$838$	−0.716042	−0.0247353
$839$	−22.4013	−0.773380	−0.386690	−	0.922210i	$-0.626382\pi$
$839$	−22.4013	−0.773380	−0.386690	+	0.922210i	$0.626382\pi$
$840$	−2.67544	−0.0923115
$841$	9.93794	0.342687
$842$	−28.3733	−0.977810
$843$	36.3181	1.25086
$844$	−26.0899	−0.898052
$845$	3.28716	0.113082
$846$	4.08130	0.140318
$847$	0	0
$848$	−1.14198	−0.0392156
$849$	63.1252	2.16645
$850$	0.564586	0.0193651
$851$	−1.11228	−0.0381286
$852$	−30.5695	−1.04730
$853$	−20.6326	−0.706447	−0.353223	−	0.935539i	$-0.614914\pi$
$853$	−20.6326	−0.706447	−0.353223	+	0.935539i	$0.614914\pi$
$854$	−11.9594	−0.409244
$855$	−31.2848	−1.06992
$856$	−9.86211	−0.337080
$857$	−18.5793	−0.634656	−0.317328	−	0.948316i	$-0.602786\pi$
$857$	−18.5793	−0.634656	−0.317328	+	0.948316i	$0.602786\pi$
$858$	0	0
$859$	−52.2925	−1.78420	−0.892099	−	0.451840i	$-0.850768\pi$
$859$	−52.2925	−1.78420	−0.892099	+	0.451840i	$0.850768\pi$
$860$	3.78866	0.129192
$861$	6.11724	0.208475
$862$	15.8511	0.539890
$863$	8.28381	0.281984	0.140992	−	0.990011i	$-0.454971\pi$
$863$	8.28381	0.281984	0.140992	+	0.990011i	$0.454971\pi$
$864$	3.09812	0.105400
$865$	12.1772	0.414039
$866$	−22.2137	−0.754853
$867$	44.6297	1.51570
$868$	2.72257	0.0924101
$869$	0	0
$870$	−16.6948	−0.566008
$871$	21.1993	0.718310
$872$	14.9188	0.505213
$873$	−37.6354	−1.27376
$874$	−34.8664	−1.17937
$875$	−1.00000	−0.0338062
$876$	−35.4748	−1.19858
$877$	35.7102	1.20585	0.602923	−	0.797799i	$-0.294003\pi$
$877$	35.7102	1.20585	0.602923	+	0.797799i	$0.294003\pi$
$878$	16.3478	0.551712
$879$	80.8952	2.72853
$880$	0	0
$881$	−31.7041	−1.06814	−0.534069	−	0.845441i	$-0.679338\pi$
$881$	−31.7041	−1.06814	−0.534069	+	0.845441i	$0.679338\pi$
$882$	−4.15798	−0.140007
$883$	−48.1427	−1.62013	−0.810065	−	0.586340i	$-0.800568\pi$
$883$	−48.1427	−1.62013	−0.810065	+	0.586340i	$0.800568\pi$
$884$	1.75956	0.0591803
$885$	23.5410	0.791322
$886$	−28.6492	−0.962489
$887$	39.9088	1.34001	0.670004	−	0.742358i	$-0.266293\pi$
$887$	39.9088	1.34001	0.670004	+	0.742358i	$0.266293\pi$
$888$	−0.642178	−0.0215501
$889$	−13.7604	−0.461509
$890$	−4.33244	−0.145224
$891$	0	0
$892$	8.25283	0.276325
$893$	−7.38528	−0.247139
$894$	28.3231	0.947267
$895$	−1.01844	−0.0340428
$896$	−1.00000	−0.0334077
$897$	38.6389	1.29011
$898$	−23.2905	−0.777213
$899$	16.9889	0.566612
$900$	4.15798	0.138599
$901$	0.644744	0.0214795
$902$	0	0
$903$	10.1363	0.337316
$904$	1.87415	0.0623334
$905$	−1.18721	−0.0394642
$906$	−28.2475	−0.938459
$907$	−43.4697	−1.44339	−0.721693	−	0.692213i	$-0.756636\pi$
$907$	−43.4697	−1.44339	−0.721693	+	0.692213i	$0.756636\pi$
$908$	−5.55836	−0.184461
$909$	22.7606	0.754922
$910$	−3.11654	−0.103312
$911$	−19.2575	−0.638028	−0.319014	−	0.947750i	$-0.603352\pi$
$911$	−19.2575	−0.638028	−0.319014	+	0.947750i	$0.603352\pi$
$912$	−20.1301	−0.666575
$913$	0	0
$914$	−10.3649	−0.342840
$915$	31.9968	1.05778
$916$	−5.96188	−0.196986
$917$	8.75625	0.289157
$918$	−1.74915	−0.0577307
$919$	−8.40644	−0.277303	−0.138651	−	0.990341i	$-0.544277\pi$
$919$	−8.40644	−0.277303	−0.138651	+	0.990341i	$0.544277\pi$
$920$	4.63400	0.152778
$921$	−15.1613	−0.499583
$922$	0.698098	0.0229906
$923$	−35.6096	−1.17210
$924$	0	0
$925$	−0.240027	−0.00789204
$926$	−10.4790	−0.344362
$927$	52.3870	1.72062
$928$	−6.24003	−0.204839
$929$	35.8044	1.17470	0.587351	−	0.809332i	$-0.300171\pi$
$929$	35.8044	1.17470	0.587351	+	0.809332i	$0.300171\pi$
$930$	−7.28408	−0.238854
$931$	7.52404	0.246590
$932$	2.50193	0.0819533
$933$	−79.4797	−2.60205
$934$	39.3583	1.28784
$935$	0	0
$936$	12.9585	0.423563
$937$	51.9019	1.69556	0.847780	−	0.530348i	$-0.177939\pi$
$937$	51.9019	1.69556	0.847780	+	0.530348i	$0.177939\pi$
$938$	6.80218	0.222099
$939$	21.0016	0.685360
$940$	0.981558	0.0320149
$941$	−56.8484	−1.85321	−0.926603	−	0.376042i	$-0.877285\pi$
$941$	−56.8484	−1.85321	−0.926603	+	0.376042i	$0.877285\pi$
$942$	55.0689	1.79424
$943$	−10.5954	−0.345033
$944$	8.79892	0.286381
$945$	3.09812	0.100782
$946$	0	0
$947$	−20.4586	−0.664815	−0.332408	−	0.943136i	$-0.607861\pi$
$947$	−20.4586	−0.664815	−0.332408	+	0.943136i	$0.607861\pi$
$948$	41.1199	1.33551
$949$	−41.3235	−1.34142
$950$	−7.52404	−0.244112
$951$	−18.7053	−0.606561
$952$	0.564586	0.0182983
$953$	55.2868	1.79091	0.895457	−	0.445148i	$-0.146849\pi$
$953$	55.2868	1.79091	0.895457	+	0.445148i	$0.146849\pi$
$954$	4.74832	0.153732
$955$	−16.9155	−0.547372
$956$	−28.8313	−0.932472
$957$	0	0
$958$	27.4511	0.886904
$959$	−3.81831	−0.123300
$960$	2.67544	0.0863495
$961$	−23.5876	−0.760891
$962$	−0.748054	−0.0241182
$963$	41.0065	1.32142
$964$	−1.67379	−0.0539092
$965$	−15.2274	−0.490187
$966$	12.3980	0.398899
$967$	−56.2874	−1.81008	−0.905040	−	0.425327i	$-0.860159\pi$
$967$	−56.2874	−1.81008	−0.905040	+	0.425327i	$0.860159\pi$
$968$	0	0
$969$	11.3652	0.365102
$970$	−9.05134	−0.290621
$971$	−5.39008	−0.172976	−0.0864880	−	0.996253i	$-0.527564\pi$
$971$	−5.39008	−0.172976	−0.0864880	+	0.996253i	$0.527564\pi$
$972$	20.4914	0.657262
$973$	−0.0485569	−0.00155666
$974$	36.5980	1.17267
$975$	8.33813	0.267034
$976$	11.9594	0.382813
$977$	10.2278	0.327217	0.163609	−	0.986525i	$-0.447687\pi$
$977$	10.2278	0.327217	0.163609	+	0.986525i	$0.447687\pi$
$978$	−51.7448	−1.65462
$979$	0	0
$980$	−1.00000	−0.0319438
$981$	−62.0320	−1.98053
$982$	−3.39001	−0.108179
$983$	29.2357	0.932474	0.466237	−	0.884660i	$-0.345609\pi$
$983$	29.2357	0.932474	0.466237	+	0.884660i	$0.345609\pi$
$984$	−6.11724	−0.195010
$985$	2.83965	0.0904788
$986$	3.52303	0.112196
$987$	2.62610	0.0835897
$988$	−23.4490	−0.746012
$989$	−17.5567	−0.558269
$990$	0	0
$991$	51.3625	1.63158	0.815792	−	0.578346i	$-0.196302\pi$
$991$	51.3625	1.63158	0.815792	+	0.578346i	$0.196302\pi$
$992$	−2.72257	−0.0864417
$993$	−68.0271	−2.15878
$994$	−11.4260	−0.362410
$995$	−4.77593	−0.151407
$996$	−28.1477	−0.891895
$997$	29.1018	0.921664	0.460832	−	0.887487i	$-0.347551\pi$
$997$	29.1018	0.921664	0.460832	+	0.887487i	$0.347551\pi$
$998$	−22.9786	−0.727376
$999$	0.743632	0.0235275

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8470.2.a.cx.1.2	✓	6
11.10	odd	2		8470.2.a.dd.1.2	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8470.2.a.cx.1.2	✓	6	1.1	even	1	trivial
8470.2.a.dd.1.2	yes	6	11.10	odd	2

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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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.67544 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.67544 q^{6} +1.00000 q^{7} -1.00000 q^{8} +4.15798 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.67544 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.67544 q^{6} +1.00000 q^{7} -1.00000 q^{8} +4.15798 q^{9} +1.00000 q^{10} -2.67544 q^{12} -3.11654 q^{13} -1.00000 q^{14} +2.67544 q^{15} +1.00000 q^{16} -0.564586 q^{17} -4.15798 q^{18} +7.52404 q^{19} -1.00000 q^{20} -2.67544 q^{21} +4.63400 q^{23} +2.67544 q^{24} +1.00000 q^{25} +3.11654 q^{26} -3.09812 q^{27} +1.00000 q^{28} +6.24003 q^{29} -2.67544 q^{30} +2.72257 q^{31} -1.00000 q^{32} +0.564586 q^{34} -1.00000 q^{35} +4.15798 q^{36} -0.240027 q^{37} -7.52404 q^{38} +8.33813 q^{39} +1.00000 q^{40} -2.28644 q^{41} +2.67544 q^{42} -3.78866 q^{43} -4.15798 q^{45} -4.63400 q^{46} -0.981558 q^{47} -2.67544 q^{48} +1.00000 q^{49} -1.00000 q^{50} +1.51052 q^{51} -3.11654 q^{52} -1.14198 q^{53} +3.09812 q^{54} -1.00000 q^{56} -20.1301 q^{57} -6.24003 q^{58} +8.79892 q^{59} +2.67544 q^{60} +11.9594 q^{61} -2.72257 q^{62} +4.15798 q^{63} +1.00000 q^{64} +3.11654 q^{65} -6.80218 q^{67} -0.564586 q^{68} -12.3980 q^{69} +1.00000 q^{70} +11.4260 q^{71} -4.15798 q^{72} +13.2594 q^{73} +0.240027 q^{74} -2.67544 q^{75} +7.52404 q^{76} -8.33813 q^{78} -15.3694 q^{79} -1.00000 q^{80} -4.18512 q^{81} +2.28644 q^{82} +10.5208 q^{83} -2.67544 q^{84} +0.564586 q^{85} +3.78866 q^{86} -16.6948 q^{87} -4.33244 q^{89} +4.15798 q^{90} -3.11654 q^{91} +4.63400 q^{92} -7.28408 q^{93} +0.981558 q^{94} -7.52404 q^{95} +2.67544 q^{96} -9.05134 q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 6 q^{4} - 6 q^{5} + 6 q^{7} - 6 q^{8} + 18 q^{9}+O(q^{10}) \) 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

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Groups

Database

Properties

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