LMFDB - Embedded newform 2695.2.a.w.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2695,2,Mod(1,2695)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2695, 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("2695.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2695 = 5 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2695.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:	$21.5196833447$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 13x^{8} + 24x^{7} + 56x^{6} - 92x^{5} - 86x^{4} + 116x^{3} + 31x^{2} - 22x + 1 $ x^10 - 2x^9 - 13x^8 + 24x^7 + 56x^6 - 92x^5 - 86x^4 + 116x^3 + 31x^2 - 22*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.47696$ of defining polynomial
Character	$\chi$	$=$	2695.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.47696 q^{2} -2.93275 q^{3} +0.181403 q^{4} -1.00000 q^{5} +4.33154 q^{6} +2.68599 q^{8} +5.60100 q^{9} +O(q^{10})$	\(q-1.47696 q^{2} -2.93275 q^{3} +0.181403 q^{4} -1.00000 q^{5} +4.33154 q^{6} +2.68599 q^{8} +5.60100 q^{9} +1.47696 q^{10} -1.00000 q^{11} -0.532008 q^{12} +3.85395 q^{13} +2.93275 q^{15} -4.32990 q^{16} -5.44952 q^{17} -8.27243 q^{18} -7.63698 q^{19} -0.181403 q^{20} +1.47696 q^{22} -0.920232 q^{23} -7.87733 q^{24} +1.00000 q^{25} -5.69211 q^{26} -7.62806 q^{27} -4.04263 q^{29} -4.33154 q^{30} +6.90394 q^{31} +1.02309 q^{32} +2.93275 q^{33} +8.04871 q^{34} +1.01604 q^{36} +8.92096 q^{37} +11.2795 q^{38} -11.3026 q^{39} -2.68599 q^{40} -10.9981 q^{41} +7.66162 q^{43} -0.181403 q^{44} -5.60100 q^{45} +1.35914 q^{46} +7.25899 q^{47} +12.6985 q^{48} -1.47696 q^{50} +15.9821 q^{51} +0.699116 q^{52} +1.55316 q^{53} +11.2663 q^{54} +1.00000 q^{55} +22.3973 q^{57} +5.97079 q^{58} +12.5344 q^{59} +0.532008 q^{60} -8.45566 q^{61} -10.1968 q^{62} +7.14873 q^{64} -3.85395 q^{65} -4.33154 q^{66} -2.23246 q^{67} -0.988558 q^{68} +2.69881 q^{69} +8.70188 q^{71} +15.0442 q^{72} +2.53683 q^{73} -13.1759 q^{74} -2.93275 q^{75} -1.38537 q^{76} +16.6935 q^{78} +5.04832 q^{79} +4.32990 q^{80} +5.56817 q^{81} +16.2438 q^{82} +8.75498 q^{83} +5.44952 q^{85} -11.3159 q^{86} +11.8560 q^{87} -2.68599 q^{88} -6.26273 q^{89} +8.27243 q^{90} -0.166933 q^{92} -20.2475 q^{93} -10.7212 q^{94} +7.63698 q^{95} -3.00048 q^{96} -13.3102 q^{97} -5.60100 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{2} + 10 q^{4} - 10 q^{5} - 4 q^{6} + 6 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q + 2 * q^2 + 10 * q^4 - 10 * q^5 - 4 * q^6 + 6 * q^8 + 10 * q^9	$ 10 q + 2 q^{2} + 10 q^{4} - 10 q^{5} - 4 q^{6} + 6 q^{8} + 10 q^{9} - 2 q^{10} - 10 q^{11} - 4 q^{12} - 8 q^{13} + 6 q^{16} - 28 q^{17} - 10 q^{18} - 8 q^{19} - 10 q^{20} - 2 q^{22} - 8 q^{23} - 32 q^{24} + 10 q^{25} - 12 q^{26} - 8 q^{29} + 4 q^{30} + 4 q^{31} + 14 q^{32} - 20 q^{34} - 22 q^{36} + 28 q^{37} - 24 q^{38} - 24 q^{39} - 6 q^{40} - 44 q^{41} + 20 q^{43} - 10 q^{44} - 10 q^{45} - 12 q^{46} - 12 q^{47} - 16 q^{48} + 2 q^{50} - 4 q^{51} - 36 q^{52} + 8 q^{54} + 10 q^{55} + 12 q^{57} - 8 q^{58} - 16 q^{59} + 4 q^{60} - 16 q^{61} - 36 q^{62} - 34 q^{64} + 8 q^{65} + 4 q^{66} + 20 q^{67} - 8 q^{68} - 4 q^{69} - 4 q^{71} + 10 q^{72} - 20 q^{73} - 16 q^{74} - 4 q^{76} + 52 q^{78} - 20 q^{79} - 6 q^{80} + 10 q^{81} + 32 q^{82} - 16 q^{83} + 28 q^{85} - 20 q^{86} - 20 q^{87} - 6 q^{88} - 44 q^{89} + 10 q^{90} - 24 q^{92} + 16 q^{93} - 24 q^{94} + 8 q^{95} + 4 q^{97} - 10 q^{99}+O(q^{100}) $ 10 * q + 2 * q^2 + 10 * q^4 - 10 * q^5 - 4 * q^6 + 6 * q^8 + 10 * q^9 - 2 * q^10 - 10 * q^11 - 4 * q^12 - 8 * q^13 + 6 * q^16 - 28 * q^17 - 10 * q^18 - 8 * q^19 - 10 * q^20 - 2 * q^22 - 8 * q^23 - 32 * q^24 + 10 * q^25 - 12 * q^26 - 8 * q^29 + 4 * q^30 + 4 * q^31 + 14 * q^32 - 20 * q^34 - 22 * q^36 + 28 * q^37 - 24 * q^38 - 24 * q^39 - 6 * q^40 - 44 * q^41 + 20 * q^43 - 10 * q^44 - 10 * q^45 - 12 * q^46 - 12 * q^47 - 16 * q^48 + 2 * q^50 - 4 * q^51 - 36 * q^52 + 8 * q^54 + 10 * q^55 + 12 * q^57 - 8 * q^58 - 16 * q^59 + 4 * q^60 - 16 * q^61 - 36 * q^62 - 34 * q^64 + 8 * q^65 + 4 * q^66 + 20 * q^67 - 8 * q^68 - 4 * q^69 - 4 * q^71 + 10 * q^72 - 20 * q^73 - 16 * q^74 - 4 * q^76 + 52 * q^78 - 20 * q^79 - 6 * q^80 + 10 * q^81 + 32 * q^82 - 16 * q^83 + 28 * q^85 - 20 * q^86 - 20 * q^87 - 6 * q^88 - 44 * q^89 + 10 * q^90 - 24 * q^92 + 16 * q^93 - 24 * q^94 + 8 * q^95 + 4 * q^97 - 10 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.47696	−1.04437	−0.522183	−	0.852833i	$-0.674882\pi$
$2$	−1.47696	−1.04437	−0.522183	+	0.852833i	$0.674882\pi$
$3$	−2.93275	−1.69322	−0.846611	−	0.532213i	$-0.821361\pi$
$3$	−2.93275	−1.69322	−0.846611	+	0.532213i	$0.821361\pi$
$4$	0.181403	0.0907014
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	4.33154	1.76834
$7$	0	0
$7$	0	0
$8$	2.68599	0.949641
$9$	5.60100	1.86700
$10$	1.47696	0.467055
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.532008	−0.153578
$13$	3.85395	1.06889	0.534446	−	0.845203i	$-0.320520\pi$
$13$	3.85395	1.06889	0.534446	+	0.845203i	$0.320520\pi$
$14$	0	0
$15$	2.93275	0.757232
$16$	−4.32990	−1.08247
$17$	−5.44952	−1.32170	−0.660851	−	0.750517i	$-0.729805\pi$
$17$	−5.44952	−1.32170	−0.660851	+	0.750517i	$0.729805\pi$
$18$	−8.27243	−1.94983
$19$	−7.63698	−1.75204	−0.876022	−	0.482272i	$-0.839812\pi$
$19$	−7.63698	−1.75204	−0.876022	+	0.482272i	$0.839812\pi$
$20$	−0.181403	−0.0405629
$21$	0	0
$22$	1.47696	0.314888
$23$	−0.920232	−0.191882	−0.0959409	−	0.995387i	$-0.530586\pi$
$23$	−0.920232	−0.191882	−0.0959409	+	0.995387i	$0.530586\pi$
$24$	−7.87733	−1.60795
$25$	1.00000	0.200000
$26$	−5.69211	−1.11632
$27$	−7.62806	−1.46802
$28$	0	0
$29$	−4.04263	−0.750697	−0.375349	−	0.926884i	$-0.622477\pi$
$29$	−4.04263	−0.750697	−0.375349	+	0.926884i	$0.622477\pi$
$30$	−4.33154	−0.790827
$31$	6.90394	1.23998	0.619992	−	0.784608i	$-0.287136\pi$
$31$	6.90394	1.23998	0.619992	+	0.784608i	$0.287136\pi$
$32$	1.02309	0.180859
$33$	2.93275	0.510525
$34$	8.04871	1.38034
$35$	0	0
$36$	1.01604	0.169339
$37$	8.92096	1.46660	0.733299	−	0.679907i	$-0.237980\pi$
$37$	8.92096	1.46660	0.733299	+	0.679907i	$0.237980\pi$
$38$	11.2795	1.82978
$39$	−11.3026	−1.80987
$40$	−2.68599	−0.424692
$41$	−10.9981	−1.71762	−0.858811	−	0.512292i	$-0.828796\pi$
$41$	−10.9981	−1.71762	−0.858811	+	0.512292i	$0.828796\pi$
$42$	0	0
$43$	7.66162	1.16839	0.584193	−	0.811615i	$-0.301411\pi$
$43$	7.66162	1.16839	0.584193	+	0.811615i	$0.301411\pi$
$44$	−0.181403	−0.0273475
$45$	−5.60100	−0.834947
$46$	1.35914	0.200395
$47$	7.25899	1.05883	0.529416	−	0.848362i	$-0.322411\pi$
$47$	7.25899	1.05883	0.529416	+	0.848362i	$0.322411\pi$
$48$	12.6985	1.83287
$49$	0	0
$50$	−1.47696	−0.208873
$51$	15.9821	2.23793
$52$	0.699116	0.0969500
$53$	1.55316	0.213343	0.106672	−	0.994294i	$-0.465981\pi$
$53$	1.55316	0.213343	0.106672	+	0.994294i	$0.465981\pi$
$54$	11.2663	1.53315
$55$	1.00000	0.134840
$56$	0	0
$57$	22.3973	2.96660
$58$	5.97079	0.784003
$59$	12.5344	1.63184	0.815920	−	0.578165i	$-0.196231\pi$
$59$	12.5344	1.63184	0.815920	+	0.578165i	$0.196231\pi$
$60$	0.532008	0.0686820
$61$	−8.45566	−1.08264	−0.541318	−	0.840818i	$-0.682075\pi$
$61$	−8.45566	−1.08264	−0.541318	+	0.840818i	$0.682075\pi$
$62$	−10.1968	−1.29500
$63$	0	0
$64$	7.14873	0.893591
$65$	−3.85395	−0.478023
$66$	−4.33154	−0.533176
$67$	−2.23246	−0.272738	−0.136369	−	0.990658i	$-0.543543\pi$
$67$	−2.23246	−0.272738	−0.136369	+	0.990658i	$0.543543\pi$
$68$	−0.988558	−0.119880
$69$	2.69881	0.324898
$70$	0	0
$71$	8.70188	1.03272	0.516362	−	0.856371i	$-0.327286\pi$
$71$	8.70188	1.03272	0.516362	+	0.856371i	$0.327286\pi$
$72$	15.0442	1.77298
$73$	2.53683	0.296914	0.148457	−	0.988919i	$-0.452569\pi$
$73$	2.53683	0.296914	0.148457	+	0.988919i	$0.452569\pi$
$74$	−13.1759	−1.53166
$75$	−2.93275	−0.338644
$76$	−1.38537	−0.158913
$77$	0	0
$78$	16.6935	1.89017
$79$	5.04832	0.567980	0.283990	−	0.958827i	$-0.408342\pi$
$79$	5.04832	0.567980	0.283990	+	0.958827i	$0.408342\pi$
$80$	4.32990	0.484097
$81$	5.56817	0.618685
$82$	16.2438	1.79383
$83$	8.75498	0.960984	0.480492	−	0.876999i	$-0.340458\pi$
$83$	8.75498	0.960984	0.480492	+	0.876999i	$0.340458\pi$
$84$	0	0
$85$	5.44952	0.591083
$86$	−11.3159	−1.22022
$87$	11.8560	1.27110
$88$	−2.68599	−0.286328
$89$	−6.26273	−0.663848	−0.331924	−	0.943306i	$-0.607698\pi$
$89$	−6.26273	−0.663848	−0.331924	+	0.943306i	$0.607698\pi$
$90$	8.27243	0.871991
$91$	0	0
$92$	−0.166933	−0.0174039
$93$	−20.2475	−2.09957
$94$	−10.7212	−1.10581
$95$	7.63698	0.783538
$96$	−3.00048	−0.306235
$97$	−13.3102	−1.35144	−0.675722	−	0.737157i	$-0.736168\pi$
$97$	−13.3102	−1.35144	−0.675722	+	0.737157i	$0.736168\pi$
$98$	0	0
$99$	−5.60100	−0.562921
$100$	0.181403	0.0181403
$101$	−10.4604	−1.04085	−0.520423	−	0.853909i	$-0.674226\pi$
$101$	−10.4604	−1.04085	−0.520423	+	0.853909i	$0.674226\pi$
$102$	−23.6048	−2.33722
$103$	6.95847	0.685638	0.342819	−	0.939401i	$-0.388618\pi$
$103$	6.95847	0.685638	0.342819	+	0.939401i	$0.388618\pi$
$104$	10.3517	1.01506
$105$	0	0
$106$	−2.29396	−0.222809
$107$	15.3967	1.48846	0.744228	−	0.667926i	$-0.232818\pi$
$107$	15.3967	1.48846	0.744228	+	0.667926i	$0.232818\pi$
$108$	−1.38375	−0.133151
$109$	−8.78335	−0.841292	−0.420646	−	0.907225i	$-0.638197\pi$
$109$	−8.78335	−0.841292	−0.420646	+	0.907225i	$0.638197\pi$
$110$	−1.47696	−0.140822
$111$	−26.1629	−2.48327
$112$	0	0
$113$	0.0968326	0.00910924	0.00455462	−	0.999990i	$-0.498550\pi$
$113$	0.0968326	0.00910924	0.00455462	+	0.999990i	$0.498550\pi$
$114$	−33.0799	−3.09822
$115$	0.920232	0.0858121
$116$	−0.733344	−0.0680893
$117$	21.5859	1.99562
$118$	−18.5128	−1.70424
$119$	0	0
$120$	7.87733	0.719098
$121$	1.00000	0.0909091
$122$	12.4886	1.13067
$123$	32.2548	2.90831
$124$	1.25239	0.112468
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	−16.5320	−1.46698	−0.733488	−	0.679702i	$-0.762109\pi$
$127$	−16.5320	−1.46698	−0.733488	+	0.679702i	$0.762109\pi$
$128$	−12.6046	−1.11410
$129$	−22.4696	−1.97834
$130$	5.69211	0.499231
$131$	−0.569864	−0.0497892	−0.0248946	−	0.999690i	$-0.507925\pi$
$131$	−0.569864	−0.0497892	−0.0248946	+	0.999690i	$0.507925\pi$
$132$	0.532008	0.0463054
$133$	0	0
$134$	3.29725	0.284839
$135$	7.62806	0.656519
$136$	−14.6374	−1.25514
$137$	−10.8931	−0.930661	−0.465331	−	0.885137i	$-0.654065\pi$
$137$	−10.8931	−0.930661	−0.465331	+	0.885137i	$0.654065\pi$
$138$	−3.98602	−0.339313
$139$	−4.90123	−0.415717	−0.207858	−	0.978159i	$-0.566649\pi$
$139$	−4.90123	−0.415717	−0.207858	+	0.978159i	$0.566649\pi$
$140$	0	0
$141$	−21.2888	−1.79284
$142$	−12.8523	−1.07854
$143$	−3.85395	−0.322283
$144$	−24.2517	−2.02098
$145$	4.04263	0.335722
$146$	−3.74680	−0.310087
$147$	0	0
$148$	1.61829	0.133022
$149$	9.12128	0.747244	0.373622	−	0.927581i	$-0.378116\pi$
$149$	9.12128	0.747244	0.373622	+	0.927581i	$0.378116\pi$
$150$	4.33154	0.353669
$151$	8.72572	0.710089	0.355045	−	0.934849i	$-0.384466\pi$
$151$	8.72572	0.710089	0.355045	+	0.934849i	$0.384466\pi$
$152$	−20.5129	−1.66381
$153$	−30.5227	−2.46762
$154$	0	0
$155$	−6.90394	−0.554538
$156$	−2.05033	−0.164158
$157$	10.0872	0.805043	0.402522	−	0.915410i	$-0.368134\pi$
$157$	10.0872	0.805043	0.402522	+	0.915410i	$0.368134\pi$
$158$	−7.45615	−0.593179
$159$	−4.55503	−0.361238
$160$	−1.02309	−0.0808827
$161$	0	0
$162$	−8.22394	−0.646134
$163$	11.8766	0.930249	0.465125	−	0.885245i	$-0.346010\pi$
$163$	11.8766	0.930249	0.465125	+	0.885245i	$0.346010\pi$
$164$	−1.99509	−0.155791
$165$	−2.93275	−0.228314
$166$	−12.9307	−1.00362
$167$	0.734903	0.0568685	0.0284343	−	0.999596i	$-0.490948\pi$
$167$	0.734903	0.0568685	0.0284343	+	0.999596i	$0.490948\pi$
$168$	0	0
$169$	1.85289	0.142530
$170$	−8.04871	−0.617308
$171$	−42.7747	−3.27106
$172$	1.38984	0.105974
$173$	−0.115941	−0.00881485	−0.00440743	−	0.999990i	$-0.501403\pi$
$173$	−0.115941	−0.00881485	−0.00440743	+	0.999990i	$0.501403\pi$
$174$	−17.5108	−1.32749
$175$	0	0
$176$	4.32990	0.326378
$177$	−36.7602	−2.76307
$178$	9.24979	0.693301
$179$	18.9678	1.41772	0.708862	−	0.705348i	$-0.249209\pi$
$179$	18.9678	1.41772	0.708862	+	0.705348i	$0.249209\pi$
$180$	−1.01604	−0.0757309
$181$	15.1542	1.12641	0.563203	−	0.826319i	$-0.309569\pi$
$181$	15.1542	1.12641	0.563203	+	0.826319i	$0.309569\pi$
$182$	0	0
$183$	24.7983	1.83314
$184$	−2.47174	−0.182219
$185$	−8.92096	−0.655882
$186$	29.9047	2.19272
$187$	5.44952	0.398508
$188$	1.31680	0.0960376
$189$	0	0
$190$	−11.2795	−0.818301
$191$	−14.9110	−1.07893	−0.539463	−	0.842010i	$-0.681373\pi$
$191$	−14.9110	−1.07893	−0.539463	+	0.842010i	$0.681373\pi$
$192$	−20.9654	−1.51305
$193$	10.7855	0.776355	0.388178	−	0.921585i	$-0.373105\pi$
$193$	10.7855	0.776355	0.388178	+	0.921585i	$0.373105\pi$
$194$	19.6586	1.41140
$195$	11.3026	0.809399
$196$	0	0
$197$	5.21883	0.371826	0.185913	−	0.982566i	$-0.440476\pi$
$197$	5.21883	0.371826	0.185913	+	0.982566i	$0.440476\pi$
$198$	8.27243	0.587896
$199$	19.4576	1.37931	0.689655	−	0.724138i	$-0.257762\pi$
$199$	19.4576	1.37931	0.689655	+	0.724138i	$0.257762\pi$
$200$	2.68599	0.189928
$201$	6.54724	0.461806
$202$	15.4495	1.08702
$203$	0	0
$204$	2.89919	0.202984
$205$	10.9981	0.768144
$206$	−10.2774	−0.716058
$207$	−5.15422	−0.358243
$208$	−16.6872	−1.15705
$209$	7.63698	0.528261
$210$	0	0
$211$	−6.69431	−0.460855	−0.230428	−	0.973089i	$-0.574013\pi$
$211$	−6.69431	−0.460855	−0.230428	+	0.973089i	$0.574013\pi$
$212$	0.281748	0.0193505
$213$	−25.5204	−1.74863
$214$	−22.7403	−1.55449
$215$	−7.66162	−0.522518
$216$	−20.4889	−1.39409
$217$	0	0
$218$	12.9726	0.878618
$219$	−7.43989	−0.502741
$220$	0.181403	0.0122302
$221$	−21.0021	−1.41276
$222$	38.6415	2.59345
$223$	18.3906	1.23152	0.615762	−	0.787932i	$-0.288848\pi$
$223$	18.3906	1.23152	0.615762	+	0.787932i	$0.288848\pi$
$224$	0	0
$225$	5.60100	0.373400
$226$	−0.143018	−0.00951339
$227$	−15.7354	−1.04439	−0.522196	−	0.852825i	$-0.674887\pi$
$227$	−15.7354	−1.04439	−0.522196	+	0.852825i	$0.674887\pi$
$228$	4.06294	0.269074
$229$	3.84103	0.253822	0.126911	−	0.991914i	$-0.459494\pi$
$229$	3.84103	0.253822	0.126911	+	0.991914i	$0.459494\pi$
$230$	−1.35914	−0.0896193
$231$	0	0
$232$	−10.8585	−0.712893
$233$	−6.65771	−0.436161	−0.218081	−	0.975931i	$-0.569980\pi$
$233$	−6.65771	−0.436161	−0.218081	+	0.975931i	$0.569980\pi$
$234$	−31.8815	−2.08416
$235$	−7.25899	−0.473524
$236$	2.27377	0.148010
$237$	−14.8054	−0.961716
$238$	0	0
$239$	−23.1848	−1.49970	−0.749850	−	0.661607i	$-0.769875\pi$
$239$	−23.1848	−1.49970	−0.749850	+	0.661607i	$0.769875\pi$
$240$	−12.6985	−0.819684
$241$	22.9431	1.47789	0.738947	−	0.673764i	$-0.235323\pi$
$241$	22.9431	1.47789	0.738947	+	0.673764i	$0.235323\pi$
$242$	−1.47696	−0.0949424
$243$	6.55416	0.420450
$244$	−1.53388	−0.0981966
$245$	0	0
$246$	−47.6389	−3.03735
$247$	−29.4325	−1.87275
$248$	18.5439	1.17754
$249$	−25.6761	−1.62716
$250$	1.47696	0.0934110
$251$	−17.9640	−1.13388	−0.566940	−	0.823759i	$-0.691873\pi$
$251$	−17.9640	−1.13388	−0.566940	+	0.823759i	$0.691873\pi$
$252$	0	0
$253$	0.920232	0.0578545
$254$	24.4170	1.53206
$255$	−15.9821	−1.00083
$256$	4.31893	0.269933
$257$	−28.8496	−1.79959	−0.899795	−	0.436312i	$-0.856284\pi$
$257$	−28.8496	−1.79959	−0.899795	+	0.436312i	$0.856284\pi$
$258$	33.1866	2.06611
$259$	0	0
$260$	−0.699116	−0.0433574
$261$	−22.6428	−1.40155
$262$	0.841664	0.0519982
$263$	−10.3206	−0.636393	−0.318197	−	0.948025i	$-0.603077\pi$
$263$	−10.3206	−0.636393	−0.318197	+	0.948025i	$0.603077\pi$
$264$	7.87733	0.484816
$265$	−1.55316	−0.0954101
$266$	0	0
$267$	18.3670	1.12404
$268$	−0.404974	−0.0247378
$269$	5.83566	0.355806	0.177903	−	0.984048i	$-0.443069\pi$
$269$	5.83566	0.355806	0.177903	+	0.984048i	$0.443069\pi$
$270$	−11.2663	−0.685646
$271$	−29.5757	−1.79660	−0.898299	−	0.439385i	$-0.855196\pi$
$271$	−29.5757	−1.79660	−0.898299	+	0.439385i	$0.855196\pi$
$272$	23.5959	1.43071
$273$	0	0
$274$	16.0887	0.971951
$275$	−1.00000	−0.0603023
$276$	0.489571	0.0294687
$277$	4.80119	0.288475	0.144238	−	0.989543i	$-0.453927\pi$
$277$	4.80119	0.288475	0.144238	+	0.989543i	$0.453927\pi$
$278$	7.23891	0.434161
$279$	38.6689	2.31505
$280$	0	0
$281$	−8.17990	−0.487972	−0.243986	−	0.969779i	$-0.578455\pi$
$281$	−8.17990	−0.487972	−0.243986	+	0.969779i	$0.578455\pi$
$282$	31.4426	1.87238
$283$	22.8767	1.35988	0.679940	−	0.733268i	$-0.262006\pi$
$283$	22.8767	1.35988	0.679940	+	0.733268i	$0.262006\pi$
$284$	1.57854	0.0936694
$285$	−22.3973	−1.32670
$286$	5.69211	0.336582
$287$	0	0
$288$	5.73035	0.337664
$289$	12.6973	0.746897
$290$	−5.97079	−0.350617
$291$	39.0353	2.28829
$292$	0.460189	0.0269305
$293$	−21.8968	−1.27923	−0.639613	−	0.768697i	$-0.720905\pi$
$293$	−21.8968	−1.27923	−0.639613	+	0.768697i	$0.720905\pi$
$294$	0	0
$295$	−12.5344	−0.729781
$296$	23.9616	1.39274
$297$	7.62806	0.442625
$298$	−13.4717	−0.780397
$299$	−3.54653	−0.205101
$300$	−0.532008	−0.0307155
$301$	0	0
$302$	−12.8875	−0.741594
$303$	30.6776	1.76238
$304$	33.0674	1.89654
$305$	8.45566	0.484170
$306$	45.0808	2.57710
$307$	0.763802	0.0435925	0.0217962	−	0.999762i	$-0.493061\pi$
$307$	0.763802	0.0435925	0.0217962	+	0.999762i	$0.493061\pi$
$308$	0	0
$309$	−20.4074	−1.16094
$310$	10.1968	0.579140
$311$	−29.9622	−1.69900	−0.849501	−	0.527587i	$-0.823097\pi$
$311$	−29.9622	−1.69900	−0.849501	+	0.527587i	$0.823097\pi$
$312$	−30.3588	−1.71873
$313$	−7.56256	−0.427461	−0.213731	−	0.976893i	$-0.568561\pi$
$313$	−7.56256	−0.427461	−0.213731	+	0.976893i	$0.568561\pi$
$314$	−14.8983	−0.840760
$315$	0	0
$316$	0.915779	0.0515166
$317$	11.1375	0.625543	0.312771	−	0.949828i	$-0.398743\pi$
$317$	11.1375	0.625543	0.312771	+	0.949828i	$0.398743\pi$
$318$	6.72759	0.377265
$319$	4.04263	0.226344
$320$	−7.14873	−0.399626
$321$	−45.1546	−2.52028
$322$	0	0
$323$	41.6179	2.31568
$324$	1.01008	0.0561156
$325$	3.85395	0.213778
$326$	−17.5413	−0.971521
$327$	25.7593	1.42449
$328$	−29.5409	−1.63112
$329$	0	0
$330$	4.33154	0.238443
$331$	−31.0570	−1.70705	−0.853523	−	0.521055i	$-0.825538\pi$
$331$	−31.0570	−1.70705	−0.853523	+	0.521055i	$0.825538\pi$
$332$	1.58818	0.0871626
$333$	49.9663	2.73813
$334$	−1.08542	−0.0593916
$335$	2.23246	0.121972
$336$	0	0
$337$	7.54460	0.410981	0.205490	−	0.978659i	$-0.434121\pi$
$337$	7.54460	0.410981	0.205490	+	0.978659i	$0.434121\pi$
$338$	−2.73665	−0.148854
$339$	−0.283985	−0.0154240
$340$	0.988558	0.0536121
$341$	−6.90394	−0.373869
$342$	63.1764	3.41619
$343$	0	0
$344$	20.5790	1.10955
$345$	−2.69881	−0.145299
$346$	0.171240	0.00920594
$347$	−14.7583	−0.792267	−0.396134	−	0.918193i	$-0.629648\pi$
$347$	−14.7583	−0.792267	−0.396134	+	0.918193i	$0.629648\pi$
$348$	2.15071	0.115290
$349$	−17.1364	−0.917293	−0.458646	−	0.888619i	$-0.651666\pi$
$349$	−17.1364	−0.917293	−0.458646	+	0.888619i	$0.651666\pi$
$350$	0	0
$351$	−29.3981	−1.56916
$352$	−1.02309	−0.0545311
$353$	4.14453	0.220591	0.110296	−	0.993899i	$-0.464820\pi$
$353$	4.14453	0.220591	0.110296	+	0.993899i	$0.464820\pi$
$354$	54.2932	2.88565
$355$	−8.70188	−0.461848
$356$	−1.13608	−0.0602120
$357$	0	0
$358$	−28.0147	−1.48062
$359$	−19.2515	−1.01605	−0.508026	−	0.861341i	$-0.669625\pi$
$359$	−19.2515	−1.01605	−0.508026	+	0.861341i	$0.669625\pi$
$360$	−15.0442	−0.792900
$361$	39.3235	2.06966
$362$	−22.3822	−1.17638
$363$	−2.93275	−0.153929
$364$	0	0
$365$	−2.53683	−0.132784
$366$	−36.6260	−1.91447
$367$	−33.4524	−1.74620	−0.873100	−	0.487542i	$-0.837894\pi$
$367$	−33.4524	−1.74620	−0.873100	+	0.487542i	$0.837894\pi$
$368$	3.98451	0.207707
$369$	−61.6006	−3.20680
$370$	13.1759	0.684981
$371$	0	0
$372$	−3.67295	−0.190434
$373$	−2.41632	−0.125112	−0.0625561	−	0.998041i	$-0.519925\pi$
$373$	−2.41632	−0.125112	−0.0625561	+	0.998041i	$0.519925\pi$
$374$	−8.04871	−0.416189
$375$	2.93275	0.151446
$376$	19.4976	1.00551
$377$	−15.5801	−0.802415
$378$	0	0
$379$	−21.4843	−1.10357	−0.551786	−	0.833986i	$-0.686054\pi$
$379$	−21.4843	−1.10357	−0.551786	+	0.833986i	$0.686054\pi$
$380$	1.38537	0.0710680
$381$	48.4841	2.48391
$382$	22.0230	1.12679
$383$	−17.1501	−0.876331	−0.438166	−	0.898894i	$-0.644372\pi$
$383$	−17.1501	−0.876331	−0.438166	+	0.898894i	$0.644372\pi$
$384$	36.9660	1.88641
$385$	0	0
$386$	−15.9297	−0.810800
$387$	42.9127	2.18138
$388$	−2.41450	−0.122578
$389$	−24.0392	−1.21884	−0.609419	−	0.792848i	$-0.708597\pi$
$389$	−24.0392	−1.21884	−0.609419	+	0.792848i	$0.708597\pi$
$390$	−16.6935	−0.845309
$391$	5.01482	0.253611
$392$	0	0
$393$	1.67126	0.0843042
$394$	−7.70799	−0.388323
$395$	−5.04832	−0.254008
$396$	−1.01604	−0.0510577
$397$	−12.6111	−0.632933	−0.316466	−	0.948604i	$-0.602496\pi$
$397$	−12.6111	−0.632933	−0.316466	+	0.948604i	$0.602496\pi$
$398$	−28.7380	−1.44051
$399$	0	0
$400$	−4.32990	−0.216495
$401$	−29.8565	−1.49096	−0.745482	−	0.666526i	$-0.767781\pi$
$401$	−29.8565	−1.49096	−0.745482	+	0.666526i	$0.767781\pi$
$402$	−9.66999	−0.482295
$403$	26.6074	1.32541
$404$	−1.89754	−0.0944061
$405$	−5.56817	−0.276684
$406$	0	0
$407$	−8.92096	−0.442196
$408$	42.9276	2.12523
$409$	27.3955	1.35462	0.677311	−	0.735697i	$-0.263145\pi$
$409$	27.3955	1.35462	0.677311	+	0.735697i	$0.263145\pi$
$410$	−16.2438	−0.802224
$411$	31.9467	1.57582
$412$	1.26229	0.0621884
$413$	0	0
$414$	7.61256	0.374137
$415$	−8.75498	−0.429765
$416$	3.94295	0.193319
$417$	14.3741	0.703901
$418$	−11.2795	−0.551698
$419$	17.3501	0.847606	0.423803	−	0.905754i	$-0.360695\pi$
$419$	17.3501	0.847606	0.423803	+	0.905754i	$0.360695\pi$
$420$	0	0
$421$	16.1245	0.785859	0.392929	−	0.919569i	$-0.371462\pi$
$421$	16.1245	0.785859	0.392929	+	0.919569i	$0.371462\pi$
$422$	9.88721	0.481302
$423$	40.6576	1.97684
$424$	4.17178	0.202600
$425$	−5.44952	−0.264340
$426$	37.6925	1.82621
$427$	0	0
$428$	2.79300	0.135005
$429$	11.3026	0.545697
$430$	11.3159	0.545701
$431$	6.74000	0.324654	0.162327	−	0.986737i	$-0.448100\pi$
$431$	6.74000	0.324654	0.162327	+	0.986737i	$0.448100\pi$
$432$	33.0287	1.58909
$433$	1.28906	0.0619483	0.0309742	−	0.999520i	$-0.490139\pi$
$433$	1.28906	0.0619483	0.0309742	+	0.999520i	$0.490139\pi$
$434$	0	0
$435$	−11.8560	−0.568452
$436$	−1.59332	−0.0763064
$437$	7.02780	0.336185
$438$	10.9884	0.525046
$439$	26.4186	1.26089	0.630445	−	0.776234i	$-0.282872\pi$
$439$	26.4186	1.26089	0.630445	+	0.776234i	$0.282872\pi$
$440$	2.68599	0.128050
$441$	0	0
$442$	31.0193	1.47544
$443$	29.9528	1.42310	0.711550	−	0.702636i	$-0.247994\pi$
$443$	29.9528	1.42310	0.711550	+	0.702636i	$0.247994\pi$
$444$	−4.74602	−0.225236
$445$	6.26273	0.296882
$446$	−27.1621	−1.28616
$447$	−26.7504	−1.26525
$448$	0	0
$449$	−10.5268	−0.496792	−0.248396	−	0.968659i	$-0.579903\pi$
$449$	−10.5268	−0.496792	−0.248396	+	0.968659i	$0.579903\pi$
$450$	−8.27243	−0.389966
$451$	10.9981	0.517883
$452$	0.0175657	0.000826221 0
$453$	−25.5903	−1.20234
$454$	23.2404	1.09073
$455$	0	0
$456$	60.1590	2.81720
$457$	−22.6842	−1.06112	−0.530562	−	0.847646i	$-0.678019\pi$
$457$	−22.6842	−1.06112	−0.530562	+	0.847646i	$0.678019\pi$
$458$	−5.67303	−0.265084
$459$	41.5692	1.94029
$460$	0.166933	0.00778328
$461$	−16.7700	−0.781058	−0.390529	−	0.920591i	$-0.627708\pi$
$461$	−16.7700	−0.781058	−0.390529	+	0.920591i	$0.627708\pi$
$462$	0	0
$463$	−14.3522	−0.667004	−0.333502	−	0.942749i	$-0.608230\pi$
$463$	−14.3522	−0.667004	−0.333502	+	0.942749i	$0.608230\pi$
$464$	17.5042	0.812611
$465$	20.2475	0.938955
$466$	9.83315	0.455512
$467$	−26.6010	−1.23095	−0.615474	−	0.788157i	$-0.711035\pi$
$467$	−26.6010	−1.23095	−0.615474	+	0.788157i	$0.711035\pi$
$468$	3.91575	0.181005
$469$	0	0
$470$	10.7212	0.494533
$471$	−29.5831	−1.36312
$472$	33.6673	1.54966
$473$	−7.66162	−0.352282
$474$	21.8670	1.00438
$475$	−7.63698	−0.350409
$476$	0	0
$477$	8.69926	0.398312
$478$	34.2430	1.56624
$479$	−37.5372	−1.71512	−0.857558	−	0.514387i	$-0.828019\pi$
$479$	−37.5372	−1.71512	−0.857558	+	0.514387i	$0.828019\pi$
$480$	3.00048	0.136952
$481$	34.3809	1.56763
$482$	−33.8859	−1.54346
$483$	0	0
$484$	0.181403	0.00824558
$485$	13.3102	0.604384
$486$	−9.68022	−0.439104
$487$	8.14330	0.369008	0.184504	−	0.982832i	$-0.440932\pi$
$487$	8.14330	0.369008	0.184504	+	0.982832i	$0.440932\pi$
$488$	−22.7118	−1.02812
$489$	−34.8311	−1.57512
$490$	0	0
$491$	20.3351	0.917711	0.458856	−	0.888511i	$-0.348260\pi$
$491$	20.3351	0.917711	0.458856	+	0.888511i	$0.348260\pi$
$492$	5.85110	0.263788
$493$	22.0304	0.992199
$494$	43.4706	1.95583
$495$	5.60100	0.251746
$496$	−29.8933	−1.34225
$497$	0	0
$498$	37.9225	1.69935
$499$	−17.0819	−0.764691	−0.382346	−	0.924019i	$-0.624884\pi$
$499$	−17.0819	−0.764691	−0.382346	+	0.924019i	$0.624884\pi$
$500$	−0.181403	−0.00811258
$501$	−2.15528	−0.0962910
$502$	26.5321	1.18419
$503$	13.0824	0.583317	0.291659	−	0.956522i	$-0.405793\pi$
$503$	13.0824	0.583317	0.291659	+	0.956522i	$0.405793\pi$
$504$	0	0
$505$	10.4604	0.465480
$506$	−1.35914	−0.0604213
$507$	−5.43407	−0.241335
$508$	−2.99895	−0.133057
$509$	11.9106	0.527926	0.263963	−	0.964533i	$-0.414970\pi$
$509$	11.9106	0.527926	0.263963	+	0.964533i	$0.414970\pi$
$510$	23.6048	1.04524
$511$	0	0
$512$	18.8302	0.832187
$513$	58.2553	2.57204
$514$	42.6097	1.87943
$515$	−6.95847	−0.306627
$516$	−4.07605	−0.179438
$517$	−7.25899	−0.319250
$518$	0	0
$519$	0.340026	0.0149255
$520$	−10.3517	−0.453950
$521$	38.5872	1.69054	0.845268	−	0.534342i	$-0.179441\pi$
$521$	38.5872	1.69054	0.845268	+	0.534342i	$0.179441\pi$
$522$	33.4424	1.46373
$523$	−39.2940	−1.71821	−0.859103	−	0.511803i	$-0.828978\pi$
$523$	−39.2940	−1.71821	−0.859103	+	0.511803i	$0.828978\pi$
$524$	−0.103375	−0.00451595
$525$	0	0
$526$	15.2430	0.664628
$527$	−37.6231	−1.63889
$528$	−12.6985	−0.552631
$529$	−22.1532	−0.963181
$530$	2.29396	0.0996431
$531$	70.2051	3.04664
$532$	0	0
$533$	−42.3863	−1.83595
$534$	−27.1273	−1.17391
$535$	−15.3967	−0.665657
$536$	−5.99637	−0.259004
$537$	−55.6279	−2.40052
$538$	−8.61902	−0.371592
$539$	0	0
$540$	1.38375	0.0595472
$541$	10.1380	0.435868	0.217934	−	0.975964i	$-0.430068\pi$
$541$	10.1380	0.435868	0.217934	+	0.975964i	$0.430068\pi$
$542$	43.6821	1.87631
$543$	−44.4435	−1.90725
$544$	−5.57537	−0.239042
$545$	8.78335	0.376237
$546$	0	0
$547$	−25.1517	−1.07541	−0.537704	−	0.843134i	$-0.680708\pi$
$547$	−25.1517	−1.07541	−0.537704	+	0.843134i	$0.680708\pi$
$548$	−1.97604	−0.0844122
$549$	−47.3601	−2.02128
$550$	1.47696	0.0629777
$551$	30.8735	1.31525
$552$	7.24897	0.308537
$553$	0	0
$554$	−7.09115	−0.301274
$555$	26.1629	1.11055
$556$	−0.889097	−0.0377061
$557$	−25.0976	−1.06342	−0.531709	−	0.846927i	$-0.678450\pi$
$557$	−25.0976	−1.06342	−0.531709	+	0.846927i	$0.678450\pi$
$558$	−57.1123	−2.41776
$559$	29.5275	1.24888
$560$	0	0
$561$	−15.9821	−0.674763
$562$	12.0814	0.509622
$563$	18.1832	0.766329	0.383164	−	0.923680i	$-0.374834\pi$
$563$	18.1832	0.766329	0.383164	+	0.923680i	$0.374834\pi$
$564$	−3.86184	−0.162613
$565$	−0.0968326	−0.00407378
$566$	−33.7879	−1.42021
$567$	0	0
$568$	23.3732	0.980716
$569$	8.17679	0.342789	0.171394	−	0.985202i	$-0.445173\pi$
$569$	8.17679	0.342789	0.171394	+	0.985202i	$0.445173\pi$
$570$	33.0799	1.38556
$571$	−3.85555	−0.161350	−0.0806750	−	0.996740i	$-0.525708\pi$
$571$	−3.85555	−0.161350	−0.0806750	+	0.996740i	$0.525708\pi$
$572$	−0.699116	−0.0292315
$573$	43.7303	1.82686
$574$	0	0
$575$	−0.920232	−0.0383763
$576$	40.0400	1.66833
$577$	−10.6634	−0.443922	−0.221961	−	0.975056i	$-0.571246\pi$
$577$	−10.6634	−0.443922	−0.221961	+	0.975056i	$0.571246\pi$
$578$	−18.7533	−0.780035
$579$	−31.6311	−1.31454
$580$	0.733344	0.0304505
$581$	0	0
$582$	−57.6535	−2.38982
$583$	−1.55316	−0.0643255
$584$	6.81391	0.281962
$585$	−21.5859	−0.892468
$586$	32.3407	1.33598
$587$	28.4806	1.17552	0.587761	−	0.809035i	$-0.300010\pi$
$587$	28.4806	1.17552	0.587761	+	0.809035i	$0.300010\pi$
$588$	0	0
$589$	−52.7252	−2.17251
$590$	18.5128	0.762159
$591$	−15.3055	−0.629584
$592$	−38.6269	−1.58755
$593$	−33.1579	−1.36163	−0.680816	−	0.732454i	$-0.738375\pi$
$593$	−33.1579	−1.36163	−0.680816	+	0.732454i	$0.738375\pi$
$594$	−11.2663	−0.462263
$595$	0	0
$596$	1.65462	0.0677761
$597$	−57.0641	−2.33548
$598$	5.23807	0.214200
$599$	−30.5597	−1.24864	−0.624319	−	0.781170i	$-0.714623\pi$
$599$	−30.5597	−1.24864	−0.624319	+	0.781170i	$0.714623\pi$
$600$	−7.87733	−0.321590
$601$	39.7363	1.62088	0.810440	−	0.585822i	$-0.199228\pi$
$601$	39.7363	1.62088	0.810440	+	0.585822i	$0.199228\pi$
$602$	0	0
$603$	−12.5040	−0.509202
$604$	1.58287	0.0644061
$605$	−1.00000	−0.0406558
$606$	−45.3095	−1.84057
$607$	14.6902	0.596256	0.298128	−	0.954526i	$-0.403638\pi$
$607$	14.6902	0.596256	0.298128	+	0.954526i	$0.403638\pi$
$608$	−7.81335	−0.316873
$609$	0	0
$610$	−12.4886	−0.505651
$611$	27.9758	1.13178
$612$	−5.53691	−0.223816
$613$	−26.3863	−1.06573	−0.532866	−	0.846199i	$-0.678885\pi$
$613$	−26.3863	−1.06573	−0.532866	+	0.846199i	$0.678885\pi$
$614$	−1.12810	−0.0455265
$615$	−32.2548	−1.30064
$616$	0	0
$617$	28.4145	1.14392	0.571962	−	0.820280i	$-0.306182\pi$
$617$	28.4145	1.14392	0.571962	+	0.820280i	$0.306182\pi$
$618$	30.1409	1.21244
$619$	13.8476	0.556580	0.278290	−	0.960497i	$-0.410232\pi$
$619$	13.8476	0.556580	0.278290	+	0.960497i	$0.410232\pi$
$620$	−1.25239	−0.0502973
$621$	7.01959	0.281686
$622$	44.2529	1.77438
$623$	0	0
$624$	48.9393	1.95914
$625$	1.00000	0.0400000
$626$	11.1696	0.446426
$627$	−22.3973	−0.894463
$628$	1.82984	0.0730185
$629$	−48.6149	−1.93840
$630$	0	0
$631$	−35.4313	−1.41050	−0.705249	−	0.708959i	$-0.749165\pi$
$631$	−35.4313	−1.41050	−0.705249	+	0.708959i	$0.749165\pi$
$632$	13.5597	0.539377
$633$	19.6327	0.780330
$634$	−16.4496	−0.653296
$635$	16.5320	0.656052
$636$	−0.826296	−0.0327648
$637$	0	0
$638$	−5.97079	−0.236386
$639$	48.7392	1.92809
$640$	12.6046	0.498239
$641$	−0.749731	−0.0296126	−0.0148063	−	0.999890i	$-0.504713\pi$
$641$	−0.749731	−0.0296126	−0.0148063	+	0.999890i	$0.504713\pi$
$642$	66.6914	2.63210
$643$	35.4511	1.39806	0.699028	−	0.715095i	$-0.253616\pi$
$643$	35.4511	1.39806	0.699028	+	0.715095i	$0.253616\pi$
$644$	0	0
$645$	22.4696	0.884739
$646$	−61.4678	−2.41842
$647$	29.9925	1.17913	0.589563	−	0.807722i	$-0.299300\pi$
$647$	29.9925	1.17913	0.589563	+	0.807722i	$0.299300\pi$
$648$	14.9560	0.587529
$649$	−12.5344	−0.492018
$650$	−5.69211	−0.223263
$651$	0	0
$652$	2.15445	0.0843749
$653$	−0.852307	−0.0333533	−0.0166767	−	0.999861i	$-0.505309\pi$
$653$	−0.852307	−0.0333533	−0.0166767	+	0.999861i	$0.505309\pi$
$654$	−38.0454	−1.48769
$655$	0.569864	0.0222664
$656$	47.6209	1.85928
$657$	14.2088	0.554338
$658$	0	0
$659$	−6.72961	−0.262148	−0.131074	−	0.991373i	$-0.541843\pi$
$659$	−6.72961	−0.262148	−0.131074	+	0.991373i	$0.541843\pi$
$660$	−0.532008	−0.0207084
$661$	−34.1278	−1.32742	−0.663708	−	0.747992i	$-0.731018\pi$
$661$	−34.1278	−1.32742	−0.663708	+	0.747992i	$0.731018\pi$
$662$	45.8698	1.78278
$663$	61.5940	2.39211
$664$	23.5158	0.912590
$665$	0	0
$666$	−73.7980	−2.85962
$667$	3.72016	0.144045
$668$	0.133313	0.00515805
$669$	−53.9349	−2.08524
$670$	−3.29725	−0.127384
$671$	8.45566	0.326427
$672$	0	0
$673$	−0.323964	−0.0124879	−0.00624396	−	0.999981i	$-0.501988\pi$
$673$	−0.323964	−0.0124879	−0.00624396	+	0.999981i	$0.501988\pi$
$674$	−11.1431	−0.429214
$675$	−7.62806	−0.293604
$676$	0.336120	0.0129277
$677$	23.6614	0.909380	0.454690	−	0.890650i	$-0.349750\pi$
$677$	23.6614	0.909380	0.454690	+	0.890650i	$0.349750\pi$
$678$	0.419434	0.0161083
$679$	0	0
$680$	14.6374	0.561317
$681$	46.1478	1.76839
$682$	10.1968	0.390456
$683$	−16.0822	−0.615369	−0.307685	−	0.951488i	$-0.599554\pi$
$683$	−16.0822	−0.615369	−0.307685	+	0.951488i	$0.599554\pi$
$684$	−7.75945	−0.296690
$685$	10.8931	0.416204
$686$	0	0
$687$	−11.2648	−0.429777
$688$	−33.1740	−1.26475
$689$	5.98581	0.228041
$690$	3.98602	0.151745
$691$	47.5451	1.80870	0.904350	−	0.426791i	$-0.140356\pi$
$691$	47.5451	1.80870	0.904350	+	0.426791i	$0.140356\pi$
$692$	−0.0210321	−0.000799519 0
$693$	0	0
$694$	21.7974	0.827417
$695$	4.90123	0.185914
$696$	31.8451	1.20709
$697$	59.9346	2.27019
$698$	25.3098	0.957990
$699$	19.5254	0.738517
$700$	0	0
$701$	−28.6954	−1.08381	−0.541905	−	0.840440i	$-0.682297\pi$
$701$	−28.6954	−1.08381	−0.541905	+	0.840440i	$0.682297\pi$
$702$	43.4198	1.63877
$703$	−68.1292	−2.56954
$704$	−7.14873	−0.269428
$705$	21.2888	0.801782
$706$	−6.12130	−0.230378
$707$	0	0
$708$	−6.66840	−0.250614
$709$	−15.9184	−0.597830	−0.298915	−	0.954280i	$-0.596625\pi$
$709$	−15.9184	−0.597830	−0.298915	+	0.954280i	$0.596625\pi$
$710$	12.8523	0.482338
$711$	28.2756	1.06042
$712$	−16.8216	−0.630418
$713$	−6.35323	−0.237930
$714$	0	0
$715$	3.85395	0.144129
$716$	3.44082	0.128589
$717$	67.9952	2.53933
$718$	28.4336	1.06113
$719$	−38.3995	−1.43206	−0.716030	−	0.698070i	$-0.754042\pi$
$719$	−38.3995	−1.43206	−0.716030	+	0.698070i	$0.754042\pi$
$720$	24.2517	0.903809
$721$	0	0
$722$	−58.0791	−2.16148
$723$	−67.2862	−2.50240
$724$	2.74902	0.102167
$725$	−4.04263	−0.150139
$726$	4.33154	0.160759
$727$	−30.6277	−1.13592	−0.567959	−	0.823057i	$-0.692267\pi$
$727$	−30.6277	−1.13592	−0.567959	+	0.823057i	$0.692267\pi$
$728$	0	0
$729$	−35.9262	−1.33060
$730$	3.74680	0.138675
$731$	−41.7522	−1.54426
$732$	4.49848	0.166269
$733$	46.3411	1.71165	0.855825	−	0.517266i	$-0.173050\pi$
$733$	46.3411	1.71165	0.855825	+	0.517266i	$0.173050\pi$
$734$	49.4077	1.82367
$735$	0	0
$736$	−0.941485	−0.0347036
$737$	2.23246	0.0822337
$738$	90.9814	3.34907
$739$	−34.9071	−1.28408	−0.642039	−	0.766672i	$-0.721911\pi$
$739$	−34.9071	−1.28408	−0.642039	+	0.766672i	$0.721911\pi$
$740$	−1.61829	−0.0594894
$741$	86.3180	3.17097
$742$	0	0
$743$	6.43418	0.236047	0.118024	−	0.993011i	$-0.462344\pi$
$743$	6.43418	0.236047	0.118024	+	0.993011i	$0.462344\pi$
$744$	−54.3846	−1.99383
$745$	−9.12128	−0.334178
$746$	3.56880	0.130663
$747$	49.0366	1.79416
$748$	0.988558	0.0361453
$749$	0	0
$750$	−4.33154	−0.158165
$751$	17.8456	0.651197	0.325598	−	0.945508i	$-0.394434\pi$
$751$	17.8456	0.651197	0.325598	+	0.945508i	$0.394434\pi$
$752$	−31.4307	−1.14616
$753$	52.6839	1.91991
$754$	23.0111	0.838015
$755$	−8.72572	−0.317562
$756$	0	0
$757$	−45.5199	−1.65445	−0.827224	−	0.561873i	$-0.810081\pi$
$757$	−45.5199	−1.65445	−0.827224	+	0.561873i	$0.810081\pi$
$758$	31.7313	1.15253
$759$	−2.69881	−0.0979605
$760$	20.5129	0.744080
$761$	−0.800500	−0.0290181	−0.0145091	−	0.999895i	$-0.504619\pi$
$761$	−0.800500	−0.0290181	−0.0145091	+	0.999895i	$0.504619\pi$
$762$	−71.6089	−2.59412
$763$	0	0
$764$	−2.70490	−0.0978600
$765$	30.5227	1.10355
$766$	25.3300	0.915211
$767$	48.3069	1.74426
$768$	−12.6663	−0.457057
$769$	23.0989	0.832969	0.416484	−	0.909143i	$-0.363262\pi$
$769$	23.0989	0.832969	0.416484	+	0.909143i	$0.363262\pi$
$770$	0	0
$771$	84.6086	3.04711
$772$	1.95651	0.0704165
$773$	9.89330	0.355837	0.177919	−	0.984045i	$-0.443064\pi$
$773$	9.89330	0.355837	0.177919	+	0.984045i	$0.443064\pi$
$774$	−63.3802	−2.27816
$775$	6.90394	0.247997
$776$	−35.7510	−1.28339
$777$	0	0
$778$	35.5049	1.27291
$779$	83.9927	3.00935
$780$	2.05033	0.0734136
$781$	−8.70188	−0.311378
$782$	−7.40668	−0.264862
$783$	30.8374	1.10204
$784$	0	0
$785$	−10.0872	−0.360026
$786$	−2.46839	−0.0880444
$787$	−38.7279	−1.38050	−0.690250	−	0.723571i	$-0.742499\pi$
$787$	−38.7279	−1.38050	−0.690250	+	0.723571i	$0.742499\pi$
$788$	0.946711	0.0337252
$789$	30.2676	1.07755
$790$	7.45615	0.265278
$791$	0	0
$792$	−15.0442	−0.534573
$793$	−32.5876	−1.15722
$794$	18.6260	0.661014
$795$	4.55503	0.161550
$796$	3.52966	0.125105
$797$	−38.7875	−1.37392	−0.686962	−	0.726693i	$-0.741056\pi$
$797$	−38.7875	−1.37392	−0.686962	+	0.726693i	$0.741056\pi$
$798$	0	0
$799$	−39.5580	−1.39946
$800$	1.02309	0.0361718
$801$	−35.0775	−1.23940
$802$	44.0968	1.55711
$803$	−2.53683	−0.0895229
$804$	1.18769	0.0418865
$805$	0	0
$806$	−39.2980	−1.38421
$807$	−17.1145	−0.602459
$808$	−28.0964	−0.988429
$809$	2.76679	0.0972751	0.0486375	−	0.998816i	$-0.484512\pi$
$809$	2.76679	0.0972751	0.0486375	+	0.998816i	$0.484512\pi$
$810$	8.22394	0.288960
$811$	52.5651	1.84581	0.922905	−	0.385028i	$-0.125808\pi$
$811$	52.5651	1.84581	0.922905	+	0.385028i	$0.125808\pi$
$812$	0	0
$813$	86.7381	3.04204
$814$	13.1759	0.461814
$815$	−11.8766	−0.416020
$816$	−69.2007	−2.42251
$817$	−58.5117	−2.04706
$818$	−40.4620	−1.41472
$819$	0	0
$820$	1.99509	0.0696717
$821$	−15.3836	−0.536893	−0.268446	−	0.963295i	$-0.586510\pi$
$821$	−15.3836	−0.536893	−0.268446	+	0.963295i	$0.586510\pi$
$822$	−47.1839	−1.64573
$823$	6.03044	0.210208	0.105104	−	0.994461i	$-0.466482\pi$
$823$	6.03044	0.210208	0.105104	+	0.994461i	$0.466482\pi$
$824$	18.6904	0.651110
$825$	2.93275	0.102105
$826$	0	0
$827$	−30.3526	−1.05546	−0.527732	−	0.849411i	$-0.676957\pi$
$827$	−30.3526	−1.05546	−0.527732	+	0.849411i	$0.676957\pi$
$828$	−0.934989	−0.0324931
$829$	51.3476	1.78337	0.891687	−	0.452652i	$-0.149522\pi$
$829$	51.3476	1.78337	0.891687	+	0.452652i	$0.149522\pi$
$830$	12.9307	0.448832
$831$	−14.0807	−0.488453
$832$	27.5508	0.955153
$833$	0	0
$834$	−21.2299	−0.735130
$835$	−0.734903	−0.0254324
$836$	1.38537	0.0479140
$837$	−52.6636	−1.82032
$838$	−25.6253	−0.885211
$839$	8.81050	0.304172	0.152086	−	0.988367i	$-0.451401\pi$
$839$	8.81050	0.304172	0.152086	+	0.988367i	$0.451401\pi$
$840$	0	0
$841$	−12.6571	−0.436453
$842$	−23.8152	−0.820724
$843$	23.9896	0.826245
$844$	−1.21437	−0.0418002
$845$	−1.85289	−0.0637415
$846$	−60.0495	−2.06454
$847$	0	0
$848$	−6.72504	−0.230939
$849$	−67.0916	−2.30258
$850$	8.04871	0.276068
$851$	−8.20936	−0.281413
$852$	−4.62947	−0.158603
$853$	−1.80061	−0.0616518	−0.0308259	−	0.999525i	$-0.509814\pi$
$853$	−1.80061	−0.0616518	−0.0308259	+	0.999525i	$0.509814\pi$
$854$	0	0
$855$	42.7747	1.46286
$856$	41.3554	1.41350
$857$	0.693596	0.0236928	0.0118464	−	0.999930i	$-0.496229\pi$
$857$	0.693596	0.0236928	0.0118464	+	0.999930i	$0.496229\pi$
$858$	−16.6935	−0.569907
$859$	52.9238	1.80574	0.902868	−	0.429919i	$-0.141458\pi$
$859$	52.9238	1.80574	0.902868	+	0.429919i	$0.141458\pi$
$860$	−1.38984	−0.0473931
$861$	0	0
$862$	−9.95469	−0.339058
$863$	−23.4022	−0.796621	−0.398310	−	0.917251i	$-0.630403\pi$
$863$	−23.4022	−0.796621	−0.398310	+	0.917251i	$0.630403\pi$
$864$	−7.80422	−0.265505
$865$	0.115941	0.00394212
$866$	−1.90389	−0.0646967
$867$	−37.2378	−1.26466
$868$	0	0
$869$	−5.04832	−0.171252
$870$	17.5108	0.593672
$871$	−8.60378	−0.291528
$872$	−23.5920	−0.798926
$873$	−74.5502	−2.52314
$874$	−10.3798	−0.351100
$875$	0	0
$876$	−1.34962	−0.0455993
$877$	−0.759491	−0.0256462	−0.0128231	−	0.999918i	$-0.504082\pi$
$877$	−0.759491	−0.0256462	−0.0128231	+	0.999918i	$0.504082\pi$
$878$	−39.0191	−1.31683
$879$	64.2178	2.16601
$880$	−4.32990	−0.145961
$881$	−15.0156	−0.505889	−0.252945	−	0.967481i	$-0.581399\pi$
$881$	−15.0156	−0.505889	−0.252945	+	0.967481i	$0.581399\pi$
$882$	0	0
$883$	−5.84038	−0.196545	−0.0982723	−	0.995160i	$-0.531332\pi$
$883$	−5.84038	−0.196545	−0.0982723	+	0.995160i	$0.531332\pi$
$884$	−3.80985	−0.128139
$885$	36.7602	1.23568
$886$	−44.2390	−1.48624
$887$	8.77944	0.294785	0.147392	−	0.989078i	$-0.452912\pi$
$887$	8.77944	0.294785	0.147392	+	0.989078i	$0.452912\pi$
$888$	−70.2733	−2.35822
$889$	0	0
$890$	−9.24979	−0.310054
$891$	−5.56817	−0.186541
$892$	3.33610	0.111701
$893$	−55.4368	−1.85512
$894$	39.5092	1.32138
$895$	−18.9678	−0.634025
$896$	0	0
$897$	10.4011	0.347281
$898$	15.5477	0.518833
$899$	−27.9101	−0.930853
$900$	1.01604	0.0338679
$901$	−8.46400	−0.281977
$902$	−16.2438	−0.540859
$903$	0	0
$904$	0.260091	0.00865051
$905$	−15.1542	−0.503744
$906$	37.7958	1.25568
$907$	10.1133	0.335807	0.167904	−	0.985803i	$-0.446300\pi$
$907$	10.1133	0.335807	0.167904	+	0.985803i	$0.446300\pi$
$908$	−2.85444	−0.0947278
$909$	−58.5885	−1.94326
$910$	0	0
$911$	53.7077	1.77942	0.889708	−	0.456531i	$-0.150908\pi$
$911$	53.7077	1.77942	0.889708	+	0.456531i	$0.150908\pi$
$912$	−96.9781	−3.21127
$913$	−8.75498	−0.289748
$914$	33.5036	1.10820
$915$	−24.7983	−0.819806
$916$	0.696773	0.0230220
$917$	0	0
$918$	−61.3960	−2.02637
$919$	4.42072	0.145826	0.0729131	−	0.997338i	$-0.476770\pi$
$919$	4.42072	0.145826	0.0729131	+	0.997338i	$0.476770\pi$
$920$	2.47174	0.0814907
$921$	−2.24004	−0.0738117
$922$	24.7686	0.815710
$923$	33.5366	1.10387
$924$	0	0
$925$	8.92096	0.293319
$926$	21.1976	0.696597
$927$	38.9744	1.28009
$928$	−4.13599	−0.135771
$929$	21.4323	0.703173	0.351586	−	0.936155i	$-0.385642\pi$
$929$	21.4323	0.703173	0.351586	+	0.936155i	$0.385642\pi$
$930$	−29.9047	−0.980613
$931$	0	0
$932$	−1.20773	−0.0395604
$933$	87.8716	2.87679
$934$	39.2886	1.28556
$935$	−5.44952	−0.178218
$936$	57.9796	1.89512
$937$	−54.1049	−1.76753	−0.883764	−	0.467932i	$-0.844999\pi$
$937$	−54.1049	−1.76753	−0.883764	+	0.467932i	$0.844999\pi$
$938$	0	0
$939$	22.1791	0.723786
$940$	−1.31680	−0.0429493
$941$	−2.87994	−0.0938835	−0.0469417	−	0.998898i	$-0.514948\pi$
$941$	−2.87994	−0.0938835	−0.0469417	+	0.998898i	$0.514948\pi$
$942$	43.6930	1.42359
$943$	10.1209	0.329580
$944$	−54.2727	−1.76642
$945$	0	0
$946$	11.3159	0.367911
$947$	−5.50887	−0.179014	−0.0895072	−	0.995986i	$-0.528529\pi$
$947$	−5.50887	−0.179014	−0.0895072	+	0.995986i	$0.528529\pi$
$948$	−2.68575	−0.0872290
$949$	9.77682	0.317369
$950$	11.2795	0.365955
$951$	−32.6634	−1.05918
$952$	0	0
$953$	−49.5783	−1.60600	−0.802999	−	0.595980i	$-0.796764\pi$
$953$	−49.5783	−1.60600	−0.802999	+	0.595980i	$0.796764\pi$
$954$	−12.8484	−0.415984
$955$	14.9110	0.482510
$956$	−4.20579	−0.136025
$957$	−11.8560	−0.383250
$958$	55.4408	1.79121
$959$	0	0
$960$	20.9654	0.676656
$961$	16.6644	0.537560
$962$	−50.7791	−1.63718
$963$	86.2368	2.77894
$964$	4.16194	0.134047
$965$	−10.7855	−0.347197
$966$	0	0
$967$	−4.63070	−0.148913	−0.0744567	−	0.997224i	$-0.523722\pi$
$967$	−4.63070	−0.148913	−0.0744567	+	0.997224i	$0.523722\pi$
$968$	2.68599	0.0863310
$969$	−122.055	−3.92096
$970$	−19.6586	−0.631198
$971$	−2.94032	−0.0943593	−0.0471797	−	0.998886i	$-0.515023\pi$
$971$	−2.94032	−0.0943593	−0.0471797	+	0.998886i	$0.515023\pi$
$972$	1.18894	0.0381354
$973$	0	0
$974$	−12.0273	−0.385380
$975$	−11.3026	−0.361974
$976$	36.6121	1.17193
$977$	39.1292	1.25185	0.625927	−	0.779881i	$-0.284721\pi$
$977$	39.1292	1.25185	0.625927	+	0.779881i	$0.284721\pi$
$978$	51.4441	1.64500
$979$	6.26273	0.200158
$980$	0	0
$981$	−49.1955	−1.57069
$982$	−30.0341	−0.958427
$983$	−38.1640	−1.21724	−0.608621	−	0.793461i	$-0.708277\pi$
$983$	−38.1640	−1.21724	−0.608621	+	0.793461i	$0.708277\pi$
$984$	86.6360	2.76185
$985$	−5.21883	−0.166286
$986$	−32.5379	−1.03622
$987$	0	0
$988$	−5.33914	−0.169861
$989$	−7.05047	−0.224192
$990$	−8.27243	−0.262915
$991$	−30.4826	−0.968312	−0.484156	−	0.874982i	$-0.660873\pi$
$991$	−30.4826	−0.968312	−0.484156	+	0.874982i	$0.660873\pi$
$992$	7.06338	0.224263
$993$	91.0822	2.89041
$994$	0	0
$995$	−19.4576	−0.616847
$996$	−4.65772	−0.147586
$997$	−58.0855	−1.83959	−0.919794	−	0.392402i	$-0.871644\pi$
$997$	−58.0855	−1.83959	−0.919794	+	0.392402i	$0.871644\pi$
$998$	25.2292	0.798618
$999$	−68.0496	−2.15299

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2695.2.a.w.1.3	✓	10
7.6	odd	2		2695.2.a.x.1.3	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2695.2.a.w.1.3	✓	10	1.1	even	1	trivial
2695.2.a.x.1.3	yes	10	7.6	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:	\( N \)	\(=\)	\( 2695 = 5 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2695.a (trivial)

\(f(q)\)	\(=\)	\(q-1.47696 q^{2} -2.93275 q^{3} +0.181403 q^{4} -1.00000 q^{5} +4.33154 q^{6} +2.68599 q^{8} +5.60100 q^{9} +O(q^{10})\)	\(q-1.47696 q^{2} -2.93275 q^{3} +0.181403 q^{4} -1.00000 q^{5} +4.33154 q^{6} +2.68599 q^{8} +5.60100 q^{9} +1.47696 q^{10} -1.00000 q^{11} -0.532008 q^{12} +3.85395 q^{13} +2.93275 q^{15} -4.32990 q^{16} -5.44952 q^{17} -8.27243 q^{18} -7.63698 q^{19} -0.181403 q^{20} +1.47696 q^{22} -0.920232 q^{23} -7.87733 q^{24} +1.00000 q^{25} -5.69211 q^{26} -7.62806 q^{27} -4.04263 q^{29} -4.33154 q^{30} +6.90394 q^{31} +1.02309 q^{32} +2.93275 q^{33} +8.04871 q^{34} +1.01604 q^{36} +8.92096 q^{37} +11.2795 q^{38} -11.3026 q^{39} -2.68599 q^{40} -10.9981 q^{41} +7.66162 q^{43} -0.181403 q^{44} -5.60100 q^{45} +1.35914 q^{46} +7.25899 q^{47} +12.6985 q^{48} -1.47696 q^{50} +15.9821 q^{51} +0.699116 q^{52} +1.55316 q^{53} +11.2663 q^{54} +1.00000 q^{55} +22.3973 q^{57} +5.97079 q^{58} +12.5344 q^{59} +0.532008 q^{60} -8.45566 q^{61} -10.1968 q^{62} +7.14873 q^{64} -3.85395 q^{65} -4.33154 q^{66} -2.23246 q^{67} -0.988558 q^{68} +2.69881 q^{69} +8.70188 q^{71} +15.0442 q^{72} +2.53683 q^{73} -13.1759 q^{74} -2.93275 q^{75} -1.38537 q^{76} +16.6935 q^{78} +5.04832 q^{79} +4.32990 q^{80} +5.56817 q^{81} +16.2438 q^{82} +8.75498 q^{83} +5.44952 q^{85} -11.3159 q^{86} +11.8560 q^{87} -2.68599 q^{88} -6.26273 q^{89} +8.27243 q^{90} -0.166933 q^{92} -20.2475 q^{93} -10.7212 q^{94} +7.63698 q^{95} -3.00048 q^{96} -13.3102 q^{97} -5.60100 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} + 10 q^{4} - 10 q^{5} - 4 q^{6} + 6 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 2 * q^2 + 10 * q^4 - 10 * q^5 - 4 * q^6 + 6 * q^8 + 10 * q^9	\( 10 q + 2 q^{2} + 10 q^{4} - 10 q^{5} - 4 q^{6} + 6 q^{8} + 10 q^{9} - 2 q^{10} - 10 q^{11} - 4 q^{12} - 8 q^{13} + 6 q^{16} - 28 q^{17} - 10 q^{18} - 8 q^{19} - 10 q^{20} - 2 q^{22} - 8 q^{23} - 32 q^{24} + 10 q^{25} - 12 q^{26} - 8 q^{29} + 4 q^{30} + 4 q^{31} + 14 q^{32} - 20 q^{34} - 22 q^{36} + 28 q^{37} - 24 q^{38} - 24 q^{39} - 6 q^{40} - 44 q^{41} + 20 q^{43} - 10 q^{44} - 10 q^{45} - 12 q^{46} - 12 q^{47} - 16 q^{48} + 2 q^{50} - 4 q^{51} - 36 q^{52} + 8 q^{54} + 10 q^{55} + 12 q^{57} - 8 q^{58} - 16 q^{59} + 4 q^{60} - 16 q^{61} - 36 q^{62} - 34 q^{64} + 8 q^{65} + 4 q^{66} + 20 q^{67} - 8 q^{68} - 4 q^{69} - 4 q^{71} + 10 q^{72} - 20 q^{73} - 16 q^{74} - 4 q^{76} + 52 q^{78} - 20 q^{79} - 6 q^{80} + 10 q^{81} + 32 q^{82} - 16 q^{83} + 28 q^{85} - 20 q^{86} - 20 q^{87} - 6 q^{88} - 44 q^{89} + 10 q^{90} - 24 q^{92} + 16 q^{93} - 24 q^{94} + 8 q^{95} + 4 q^{97} - 10 q^{99}+O(q^{100}) \) 10 * q + 2 * q^2 + 10 * q^4 - 10 * q^5 - 4 * q^6 + 6 * q^8 + 10 * q^9 - 2 * q^10 - 10 * q^11 - 4 * q^12 - 8 * q^13 + 6 * q^16 - 28 * q^17 - 10 * q^18 - 8 * q^19 - 10 * q^20 - 2 * q^22 - 8 * q^23 - 32 * q^24 + 10 * q^25 - 12 * q^26 - 8 * q^29 + 4 * q^30 + 4 * q^31 + 14 * q^32 - 20 * q^34 - 22 * q^36 + 28 * q^37 - 24 * q^38 - 24 * q^39 - 6 * q^40 - 44 * q^41 + 20 * q^43 - 10 * q^44 - 10 * q^45 - 12 * q^46 - 12 * q^47 - 16 * q^48 + 2 * q^50 - 4 * q^51 - 36 * q^52 + 8 * q^54 + 10 * q^55 + 12 * q^57 - 8 * q^58 - 16 * q^59 + 4 * q^60 - 16 * q^61 - 36 * q^62 - 34 * q^64 + 8 * q^65 + 4 * q^66 + 20 * q^67 - 8 * q^68 - 4 * q^69 - 4 * q^71 + 10 * q^72 - 20 * q^73 - 16 * q^74 - 4 * q^76 + 52 * q^78 - 20 * q^79 - 6 * q^80 + 10 * q^81 + 32 * q^82 - 16 * q^83 + 28 * q^85 - 20 * q^86 - 20 * q^87 - 6 * q^88 - 44 * q^89 + 10 * q^90 - 24 * q^92 + 16 * q^93 - 24 * q^94 + 8 * q^95 + 4 * q^97 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more