LMFDB - Embedded newform 6069.2.a.z.1.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [6069,2,Mod(1,6069)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("6069.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(6069, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 6069 = 3 \cdot 7 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6069.a (trivial)

Newform invariants

comment:select newform

sage:traces = [9,0,-9,6,3,0,-9] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.4612089867$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 12x^{7} - 3x^{6} + 45x^{5} + 21x^{4} - 53x^{3} - 39x^{2} + 3 $ x^9 - 12x^7 - 3x^6 + 45x^5 + 21x^4 - 53x^3 - 39x^2 + 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$0.244764$ of defining polynomial
Character	$\chi$	$=$	6069.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.244764 q^{2} -1.00000 q^{3} -1.94009 q^{4} -2.06843 q^{5} -0.244764 q^{6} -1.00000 q^{7} -0.964391 q^{8} +1.00000 q^{9} -0.506278 q^{10} +3.04983 q^{11} +1.94009 q^{12} -6.80516 q^{13} -0.244764 q^{14} +2.06843 q^{15} +3.64413 q^{16} +0.244764 q^{18} -0.484930 q^{19} +4.01295 q^{20} +1.00000 q^{21} +0.746487 q^{22} +0.437369 q^{23} +0.964391 q^{24} -0.721577 q^{25} -1.66566 q^{26} -1.00000 q^{27} +1.94009 q^{28} -8.45427 q^{29} +0.506278 q^{30} -2.11063 q^{31} +2.82073 q^{32} -3.04983 q^{33} +2.06843 q^{35} -1.94009 q^{36} -8.74194 q^{37} -0.118693 q^{38} +6.80516 q^{39} +1.99478 q^{40} -3.31075 q^{41} +0.244764 q^{42} +6.29062 q^{43} -5.91694 q^{44} -2.06843 q^{45} +0.107052 q^{46} -11.1100 q^{47} -3.64413 q^{48} +1.00000 q^{49} -0.176616 q^{50} +13.2026 q^{52} +0.0579193 q^{53} -0.244764 q^{54} -6.30837 q^{55} +0.964391 q^{56} +0.484930 q^{57} -2.06930 q^{58} -8.36804 q^{59} -4.01295 q^{60} +12.4737 q^{61} -0.516605 q^{62} -1.00000 q^{63} -6.59786 q^{64} +14.0760 q^{65} -0.746487 q^{66} -11.2390 q^{67} -0.437369 q^{69} +0.506278 q^{70} -2.15979 q^{71} -0.964391 q^{72} +6.96494 q^{73} -2.13971 q^{74} +0.721577 q^{75} +0.940808 q^{76} -3.04983 q^{77} +1.66566 q^{78} -2.30069 q^{79} -7.53765 q^{80} +1.00000 q^{81} -0.810352 q^{82} -17.2398 q^{83} -1.94009 q^{84} +1.53972 q^{86} +8.45427 q^{87} -2.94123 q^{88} -12.6380 q^{89} -0.506278 q^{90} +6.80516 q^{91} -0.848535 q^{92} +2.11063 q^{93} -2.71932 q^{94} +1.00305 q^{95} -2.82073 q^{96} +4.63222 q^{97} +0.244764 q^{98} +3.04983 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 9 q^{3} + 6 q^{4} + 3 q^{5} - 9 q^{7} + 9 q^{8} + 9 q^{9} + 12 q^{10} + 18 q^{11} - 6 q^{12} - 21 q^{13} - 3 q^{15} - 9 q^{19} + 15 q^{20} + 9 q^{21} + 6 q^{22} - 9 q^{24} + 3 q^{26} - 9 q^{27} - 6 q^{28}+ \cdots + 18 q^{99}+O(q^{100}) $ 9 * q - 9 * q^3 + 6 * q^4 + 3 * q^5 - 9 * q^7 + 9 * q^8 + 9 * q^9 + 12 * q^10 + 18 * q^11 - 6 * q^12 - 21 * q^13 - 3 * q^15 - 9 * q^19 + 15 * q^20 + 9 * q^21 + 6 * q^22 - 9 * q^24 + 3 * q^26 - 9 * q^27 - 6 * q^28 + 6 * q^29 - 12 * q^30 + 30 * q^31 + 3 * q^32 - 18 * q^33 - 3 * q^35 + 6 * q^36 + 12 * q^37 - 36 * q^38 + 21 * q^39 + 30 * q^40 + 9 * q^41 + 30 * q^44 + 3 * q^45 + 33 * q^46 - 9 * q^47 + 9 * q^49 - 12 * q^50 - 12 * q^52 + 30 * q^55 - 9 * q^56 + 9 * q^57 + 9 * q^58 - 3 * q^59 - 15 * q^60 + 33 * q^61 - 12 * q^62 - 9 * q^63 - 15 * q^64 - 15 * q^65 - 6 * q^66 - 15 * q^67 - 12 * q^70 + 9 * q^72 + 21 * q^73 + 6 * q^74 + 3 * q^76 - 18 * q^77 - 3 * q^78 + 30 * q^79 + 9 * q^81 + 9 * q^82 + 6 * q^84 + 72 * q^86 - 6 * q^87 + 48 * q^88 - 12 * q^89 + 12 * q^90 + 21 * q^91 + 48 * q^92 - 30 * q^93 + 48 * q^94 - 18 * q^95 - 3 * q^96 + 18 * q^99

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 $

$2$	0.244764	0.173074	0.0865370	−	0.996249i	$-0.472420\pi$
$2$	0.244764	0.173074	0.0865370	+	0.996249i	$0.472420\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.94009	−0.970045
$5$	−2.06843	−0.925032	−0.462516	−	0.886611i	$-0.653053\pi$
$5$	−2.06843	−0.925032	−0.462516	+	0.886611i	$0.653053\pi$
$6$	−0.244764	−0.0999243
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−0.964391	−0.340964
$9$	1.00000	0.333333
$10$	−0.506278	−0.160099
$11$	3.04983	0.919558	0.459779	−	0.888033i	$-0.347929\pi$
$11$	3.04983	0.919558	0.459779	+	0.888033i	$0.347929\pi$
$12$	1.94009	0.560056
$13$	−6.80516	−1.88741	−0.943706	−	0.330786i	$-0.892686\pi$
$13$	−6.80516	−1.88741	−0.943706	+	0.330786i	$0.892686\pi$
$14$	−0.244764	−0.0654158
$15$	2.06843	0.534068
$16$	3.64413	0.911033
$17$	0	0
$17$	0	0
$18$	0.244764	0.0576913
$19$	−0.484930	−0.111250	−0.0556252	−	0.998452i	$-0.517715\pi$
$19$	−0.484930	−0.111250	−0.0556252	+	0.998452i	$0.517715\pi$
$20$	4.01295	0.897323
$21$	1.00000	0.218218
$22$	0.746487	0.159152
$23$	0.437369	0.0911977	0.0455988	−	0.998960i	$-0.485480\pi$
$23$	0.437369	0.0911977	0.0455988	+	0.998960i	$0.485480\pi$
$24$	0.964391	0.196855
$25$	−0.721577	−0.144315
$26$	−1.66566	−0.326662
$27$	−1.00000	−0.192450
$28$	1.94009	0.366643
$29$	−8.45427	−1.56992	−0.784959	−	0.619547i	$-0.787316\pi$
$29$	−8.45427	−1.56992	−0.784959	+	0.619547i	$0.787316\pi$
$30$	0.506278	0.0924332
$31$	−2.11063	−0.379080	−0.189540	−	0.981873i	$-0.560700\pi$
$31$	−2.11063	−0.379080	−0.189540	+	0.981873i	$0.560700\pi$
$32$	2.82073	0.498640
$33$	−3.04983	−0.530907
$34$	0	0
$35$	2.06843	0.349629
$36$	−1.94009	−0.323348
$37$	−8.74194	−1.43717	−0.718583	−	0.695441i	$-0.755209\pi$
$37$	−8.74194	−1.43717	−0.718583	+	0.695441i	$0.755209\pi$
$38$	−0.118693	−0.0192546
$39$	6.80516	1.08970
$40$	1.99478	0.315402
$41$	−3.31075	−0.517053	−0.258526	−	0.966004i	$-0.583237\pi$
$41$	−3.31075	−0.517053	−0.258526	+	0.966004i	$0.583237\pi$
$42$	0.244764	0.0377678
$43$	6.29062	0.959311	0.479655	−	0.877457i	$-0.340762\pi$
$43$	6.29062	0.959311	0.479655	+	0.877457i	$0.340762\pi$
$44$	−5.91694	−0.892013
$45$	−2.06843	−0.308344
$46$	0.107052	0.0157839
$47$	−11.1100	−1.62056	−0.810280	−	0.586043i	$-0.800685\pi$
$47$	−11.1100	−1.62056	−0.810280	+	0.586043i	$0.800685\pi$
$48$	−3.64413	−0.525985
$49$	1.00000	0.142857
$50$	−0.176616	−0.0249772
$51$	0	0
$52$	13.2026	1.83087
$53$	0.0579193	0.00795582	0.00397791	−	0.999992i	$-0.498734\pi$
$53$	0.0579193	0.00795582	0.00397791	+	0.999992i	$0.498734\pi$
$54$	−0.244764	−0.0333081
$55$	−6.30837	−0.850621
$56$	0.964391	0.128872
$57$	0.484930	0.0642305
$58$	−2.06930	−0.271712
$59$	−8.36804	−1.08943	−0.544713	−	0.838623i	$-0.683361\pi$
$59$	−8.36804	−1.08943	−0.544713	+	0.838623i	$0.683361\pi$
$60$	−4.01295	−0.518070
$61$	12.4737	1.59709	0.798546	−	0.601933i	$-0.205603\pi$
$61$	12.4737	1.59709	0.798546	+	0.601933i	$0.205603\pi$
$62$	−0.516605	−0.0656089
$63$	−1.00000	−0.125988
$64$	−6.59786	−0.824732
$65$	14.0760	1.74592
$66$	−0.746487	−0.0918862
$67$	−11.2390	−1.37306	−0.686530	−	0.727101i	$-0.740867\pi$
$67$	−11.2390	−1.37306	−0.686530	+	0.727101i	$0.740867\pi$
$68$	0	0
$69$	−0.437369	−0.0526530
$70$	0.506278	0.0605117
$71$	−2.15979	−0.256320	−0.128160	−	0.991754i	$-0.540907\pi$
$71$	−2.15979	−0.256320	−0.128160	+	0.991754i	$0.540907\pi$
$72$	−0.964391	−0.113655
$73$	6.96494	0.815185	0.407592	−	0.913164i	$-0.366368\pi$
$73$	6.96494	0.815185	0.407592	+	0.913164i	$0.366368\pi$
$74$	−2.13971	−0.248736
$75$	0.721577	0.0833205
$76$	0.940808	0.107918
$77$	−3.04983	−0.347560
$78$	1.66566	0.188598
$79$	−2.30069	−0.258848	−0.129424	−	0.991589i	$-0.541313\pi$
$79$	−2.30069	−0.258848	−0.129424	+	0.991589i	$0.541313\pi$
$80$	−7.53765	−0.842735
$81$	1.00000	0.111111
$82$	−0.810352	−0.0894884
$83$	−17.2398	−1.89231	−0.946157	−	0.323709i	$-0.895070\pi$
$83$	−17.2398	−1.89231	−0.946157	+	0.323709i	$0.895070\pi$
$84$	−1.94009	−0.211681
$85$	0	0
$86$	1.53972	0.166032
$87$	8.45427	0.906393
$88$	−2.94123	−0.313536
$89$	−12.6380	−1.33962	−0.669812	−	0.742530i	$-0.733626\pi$
$89$	−12.6380	−1.33962	−0.669812	+	0.742530i	$0.733626\pi$
$90$	−0.506278	−0.0533663
$91$	6.80516	0.713375
$92$	−0.848535	−0.0884659
$93$	2.11063	0.218862
$94$	−2.71932	−0.280477
$95$	1.00305	0.102910
$96$	−2.82073	−0.287890
$97$	4.63222	0.470331	0.235165	−	0.971955i	$-0.424437\pi$
$97$	4.63222	0.470331	0.235165	+	0.971955i	$0.424437\pi$
$98$	0.244764	0.0247249
$99$	3.04983	0.306519
$100$	1.39992	0.139992
$101$	−10.3253	−1.02741	−0.513704	−	0.857967i	$-0.671727\pi$
$101$	−10.3253	−1.02741	−0.513704	+	0.857967i	$0.671727\pi$
$102$	0	0
$103$	−15.0477	−1.48269	−0.741347	−	0.671121i	$-0.765813\pi$
$103$	−15.0477	−1.48269	−0.741347	+	0.671121i	$0.765813\pi$
$104$	6.56283	0.643539
$105$	−2.06843	−0.201859
$106$	0.0141765	0.00137695
$107$	13.1879	1.27492	0.637462	−	0.770482i	$-0.279984\pi$
$107$	13.1879	1.27492	0.637462	+	0.770482i	$0.279984\pi$
$108$	1.94009	0.186685
$109$	1.05221	0.100783	0.0503916	−	0.998730i	$-0.483953\pi$
$109$	1.05221	0.100783	0.0503916	+	0.998730i	$0.483953\pi$
$110$	−1.54406	−0.147220
$111$	8.74194	0.829748
$112$	−3.64413	−0.344338
$113$	−13.9040	−1.30798	−0.653990	−	0.756503i	$-0.726906\pi$
$113$	−13.9040	−1.30798	−0.653990	+	0.756503i	$0.726906\pi$
$114$	0.118693	0.0111166
$115$	−0.904669	−0.0843608
$116$	16.4021	1.52289
$117$	−6.80516	−0.629137
$118$	−2.04819	−0.188551
$119$	0	0
$120$	−1.99478	−0.182098
$121$	−1.69855	−0.154414
$122$	3.05311	0.276415
$123$	3.31075	0.298520
$124$	4.09481	0.367725
$125$	11.8347	1.05853
$126$	−0.244764	−0.0218053
$127$	−1.31580	−0.116758	−0.0583792	−	0.998294i	$-0.518593\pi$
$127$	−1.31580	−0.116758	−0.0583792	+	0.998294i	$0.518593\pi$
$128$	−7.25638	−0.641379
$129$	−6.29062	−0.553858
$130$	3.44530	0.302173
$131$	3.96658	0.346562	0.173281	−	0.984872i	$-0.444563\pi$
$131$	3.96658	0.346562	0.173281	+	0.984872i	$0.444563\pi$
$132$	5.91694	0.515004
$133$	0.484930	0.0420487
$134$	−2.75089	−0.237641
$135$	2.06843	0.178023
$136$	0	0
$137$	19.1881	1.63935	0.819674	−	0.572831i	$-0.194155\pi$
$137$	19.1881	1.63935	0.819674	+	0.572831i	$0.194155\pi$
$138$	−0.107052	−0.00911287
$139$	−7.59329	−0.644054	−0.322027	−	0.946730i	$-0.604364\pi$
$139$	−7.59329	−0.644054	−0.322027	+	0.946730i	$0.604364\pi$
$140$	−4.01295	−0.339156
$141$	11.1100	0.935630
$142$	−0.528638	−0.0443623
$143$	−20.7546	−1.73558
$144$	3.64413	0.303678
$145$	17.4871	1.45223
$146$	1.70476	0.141087
$147$	−1.00000	−0.0824786
$148$	16.9602	1.39412
$149$	10.3536	0.848199	0.424099	−	0.905616i	$-0.360591\pi$
$149$	10.3536	0.848199	0.424099	+	0.905616i	$0.360591\pi$
$150$	0.176616	0.0144206
$151$	0.741505	0.0603428	0.0301714	−	0.999545i	$-0.490395\pi$
$151$	0.741505	0.0603428	0.0301714	+	0.999545i	$0.490395\pi$
$152$	0.467662	0.0379324
$153$	0	0
$154$	−0.746487	−0.0601536
$155$	4.36570	0.350661
$156$	−13.2026	−1.05706
$157$	0.196509	0.0156831	0.00784155	−	0.999969i	$-0.497504\pi$
$157$	0.196509	0.0156831	0.00784155	+	0.999969i	$0.497504\pi$
$158$	−0.563125	−0.0447998
$159$	−0.0579193	−0.00459330
$160$	−5.83450	−0.461258
$161$	−0.437369	−0.0344695
$162$	0.244764	0.0192304
$163$	5.24513	0.410830	0.205415	−	0.978675i	$-0.434146\pi$
$163$	5.24513	0.410830	0.205415	+	0.978675i	$0.434146\pi$
$164$	6.42316	0.501564
$165$	6.30837	0.491106
$166$	−4.21967	−0.327510
$167$	−8.52493	−0.659679	−0.329839	−	0.944037i	$-0.606995\pi$
$167$	−8.52493	−0.659679	−0.329839	+	0.944037i	$0.606995\pi$
$168$	−0.964391	−0.0744044
$169$	33.3102	2.56232
$170$	0	0
$171$	−0.484930	−0.0370835
$172$	−12.2044	−0.930575
$173$	21.3404	1.62248	0.811242	−	0.584711i	$-0.198792\pi$
$173$	21.3404	1.62248	0.811242	+	0.584711i	$0.198792\pi$
$174$	2.06930	0.156873
$175$	0.721577	0.0545461
$176$	11.1140	0.837748
$177$	8.36804	0.628980
$178$	−3.09332	−0.231854
$179$	0.927253	0.0693062	0.0346531	−	0.999399i	$-0.488967\pi$
$179$	0.927253	0.0693062	0.0346531	+	0.999399i	$0.488967\pi$
$180$	4.01295	0.299108
$181$	10.5650	0.785293	0.392647	−	0.919689i	$-0.371560\pi$
$181$	10.5650	0.785293	0.392647	+	0.919689i	$0.371560\pi$
$182$	1.66566	0.123467
$183$	−12.4737	−0.922082
$184$	−0.421794	−0.0310951
$185$	18.0821	1.32943
$186$	0.516605	0.0378793
$187$	0	0
$188$	21.5544	1.57202
$189$	1.00000	0.0727393
$190$	0.245509	0.0178111
$191$	−12.9048	−0.933757	−0.466879	−	0.884321i	$-0.654622\pi$
$191$	−12.9048	−0.933757	−0.466879	+	0.884321i	$0.654622\pi$
$192$	6.59786	0.476159
$193$	−23.0947	−1.66239	−0.831197	−	0.555977i	$-0.812344\pi$
$193$	−23.0947	−1.66239	−0.831197	+	0.555977i	$0.812344\pi$
$194$	1.13380	0.0814020
$195$	−14.0760	−1.00801
$196$	−1.94009	−0.138578
$197$	22.8435	1.62753	0.813767	−	0.581192i	$-0.197413\pi$
$197$	22.8435	1.62753	0.813767	+	0.581192i	$0.197413\pi$
$198$	0.746487	0.0530505
$199$	−1.43344	−0.101614	−0.0508069	−	0.998708i	$-0.516179\pi$
$199$	−1.43344	−0.101614	−0.0508069	+	0.998708i	$0.516179\pi$
$200$	0.695882	0.0492063
$201$	11.2390	0.792737
$202$	−2.52726	−0.177818
$203$	8.45427	0.593374
$204$	0	0
$205$	6.84807	0.478290
$206$	−3.68313	−0.256616
$207$	0.437369	0.0303992
$208$	−24.7989	−1.71950
$209$	−1.47895	−0.102301
$210$	−0.506278	−0.0349365
$211$	13.0883	0.901033	0.450516	−	0.892768i	$-0.351240\pi$
$211$	13.0883	0.901033	0.450516	+	0.892768i	$0.351240\pi$
$212$	−0.112369	−0.00771751
$213$	2.15979	0.147986
$214$	3.22792	0.220656
$215$	−13.0117	−0.887393
$216$	0.964391	0.0656185
$217$	2.11063	0.143279
$218$	0.257542	0.0174430
$219$	−6.96494	−0.470647
$220$	12.2388	0.825141
$221$	0	0
$222$	2.13971	0.143608
$223$	6.38093	0.427299	0.213649	−	0.976910i	$-0.431465\pi$
$223$	6.38093	0.427299	0.213649	+	0.976910i	$0.431465\pi$
$224$	−2.82073	−0.188468
$225$	−0.721577	−0.0481051
$226$	−3.40320	−0.226377
$227$	7.36433	0.488788	0.244394	−	0.969676i	$-0.421411\pi$
$227$	7.36433	0.488788	0.244394	+	0.969676i	$0.421411\pi$
$228$	−0.940808	−0.0623065
$229$	−17.7227	−1.17115	−0.585574	−	0.810619i	$-0.699131\pi$
$229$	−17.7227	−1.17115	−0.585574	+	0.810619i	$0.699131\pi$
$230$	−0.221430	−0.0146007
$231$	3.04983	0.200664
$232$	8.15322	0.535285
$233$	21.5513	1.41187	0.705935	−	0.708277i	$-0.250527\pi$
$233$	21.5513	1.41187	0.705935	+	0.708277i	$0.250527\pi$
$234$	−1.66566	−0.108887
$235$	22.9803	1.49907
$236$	16.2348	1.05679
$237$	2.30069	0.149446
$238$	0	0
$239$	3.92600	0.253952	0.126976	−	0.991906i	$-0.459473\pi$
$239$	3.92600	0.253952	0.126976	+	0.991906i	$0.459473\pi$
$240$	7.53765	0.486553
$241$	−6.32423	−0.407379	−0.203690	−	0.979035i	$-0.565293\pi$
$241$	−6.32423	−0.407379	−0.203690	+	0.979035i	$0.565293\pi$
$242$	−0.415743	−0.0267250
$243$	−1.00000	−0.0641500
$244$	−24.2001	−1.54925
$245$	−2.06843	−0.132147
$246$	0.810352	0.0516661
$247$	3.30002	0.209975
$248$	2.03547	0.129252
$249$	17.2398	1.09253
$250$	2.89671	0.183204
$251$	1.27935	0.0807517	0.0403759	−	0.999185i	$-0.487144\pi$
$251$	1.27935	0.0807517	0.0403759	+	0.999185i	$0.487144\pi$
$252$	1.94009	0.122214
$253$	1.33390	0.0838615
$254$	−0.322060	−0.0202079
$255$	0	0
$256$	11.4196	0.713726
$257$	−16.4715	−1.02747	−0.513733	−	0.857950i	$-0.671738\pi$
$257$	−16.4715	−1.02747	−0.513733	+	0.857950i	$0.671738\pi$
$258$	−1.53972	−0.0958585
$259$	8.74194	0.543198
$260$	−27.3088	−1.69362
$261$	−8.45427	−0.523306
$262$	0.970875	0.0599809
$263$	19.5085	1.20295	0.601473	−	0.798893i	$-0.294581\pi$
$263$	19.5085	1.20295	0.601473	+	0.798893i	$0.294581\pi$
$264$	2.94123	0.181020
$265$	−0.119802	−0.00735939
$266$	0.118693	0.00727754
$267$	12.6380	0.773433
$268$	21.8047	1.33193
$269$	12.6844	0.773379	0.386690	−	0.922210i	$-0.373618\pi$
$269$	12.6844	0.773379	0.386690	+	0.922210i	$0.373618\pi$
$270$	0.506278	0.0308111
$271$	−3.17103	−0.192626	−0.0963132	−	0.995351i	$-0.530705\pi$
$271$	−3.17103	−0.192626	−0.0963132	+	0.995351i	$0.530705\pi$
$272$	0	0
$273$	−6.80516	−0.411867
$274$	4.69654	0.283728
$275$	−2.20069	−0.132706
$276$	0.848535	0.0510758
$277$	−4.89244	−0.293958	−0.146979	−	0.989140i	$-0.546955\pi$
$277$	−4.89244	−0.293958	−0.146979	+	0.989140i	$0.546955\pi$
$278$	−1.85856	−0.111469
$279$	−2.11063	−0.126360
$280$	−1.99478	−0.119211
$281$	21.7835	1.29949	0.649747	−	0.760150i	$-0.274875\pi$
$281$	21.7835	1.29949	0.649747	+	0.760150i	$0.274875\pi$
$282$	2.71932	0.161933
$283$	−2.41799	−0.143735	−0.0718673	−	0.997414i	$-0.522896\pi$
$283$	−2.41799	−0.143735	−0.0718673	+	0.997414i	$0.522896\pi$
$284$	4.19019	0.248642
$285$	−1.00305	−0.0594153
$286$	−5.07996	−0.300384
$287$	3.31075	0.195428
$288$	2.82073	0.166213
$289$	0	0
$290$	4.28021	0.251342
$291$	−4.63222	−0.271546
$292$	−13.5126	−0.790766
$293$	−0.919352	−0.0537091	−0.0268546	−	0.999639i	$-0.508549\pi$
$293$	−0.919352	−0.0537091	−0.0268546	+	0.999639i	$0.508549\pi$
$294$	−0.244764	−0.0142749
$295$	17.3087	1.00775
$296$	8.43065	0.490021
$297$	−3.04983	−0.176969
$298$	2.53418	0.146801
$299$	−2.97636	−0.172128
$300$	−1.39992	−0.0808247
$301$	−6.29062	−0.362585
$302$	0.181493	0.0104438
$303$	10.3253	0.593175
$304$	−1.76715	−0.101353
$305$	−25.8010	−1.47736
$306$	0	0
$307$	21.4469	1.22404	0.612020	−	0.790842i	$-0.290357\pi$
$307$	21.4469	1.22404	0.612020	+	0.790842i	$0.290357\pi$
$308$	5.91694	0.337149
$309$	15.0477	0.856034
$310$	1.06856	0.0606903
$311$	11.2511	0.637993	0.318996	−	0.947756i	$-0.396654\pi$
$311$	11.2511	0.637993	0.318996	+	0.947756i	$0.396654\pi$
$312$	−6.56283	−0.371547
$313$	−16.3252	−0.922756	−0.461378	−	0.887204i	$-0.652645\pi$
$313$	−16.3252	−0.922756	−0.461378	+	0.887204i	$0.652645\pi$
$314$	0.0480982	0.00271434
$315$	2.06843	0.116543
$316$	4.46355	0.251094
$317$	−8.48366	−0.476490	−0.238245	−	0.971205i	$-0.576572\pi$
$317$	−8.48366	−0.476490	−0.238245	+	0.971205i	$0.576572\pi$
$318$	−0.0141765	−0.000794980 0
$319$	−25.7841	−1.44363
$320$	13.6472	0.762904
$321$	−13.1879	−0.736077
$322$	−0.107052	−0.00596577
$323$	0	0
$324$	−1.94009	−0.107783
$325$	4.91045	0.272383
$326$	1.28382	0.0711040
$327$	−1.05221	−0.0581873
$328$	3.19286	0.176296
$329$	11.1100	0.612514
$330$	1.54406	0.0849977
$331$	−31.2405	−1.71713	−0.858567	−	0.512701i	$-0.828645\pi$
$331$	−31.2405	−1.71713	−0.858567	+	0.512701i	$0.828645\pi$
$332$	33.4468	1.83563
$333$	−8.74194	−0.479055
$334$	−2.08659	−0.114173
$335$	23.2471	1.27013
$336$	3.64413	0.198804
$337$	10.3464	0.563605	0.281802	−	0.959472i	$-0.409068\pi$
$337$	10.3464	0.563605	0.281802	+	0.959472i	$0.409068\pi$
$338$	8.15312	0.443471
$339$	13.9040	0.755163
$340$	0	0
$341$	−6.43705	−0.348586
$342$	−0.118693	−0.00641819
$343$	−1.00000	−0.0539949
$344$	−6.06662	−0.327090
$345$	0.904669	0.0487057
$346$	5.22336	0.280810
$347$	−26.2393	−1.40860	−0.704300	−	0.709903i	$-0.748739\pi$
$347$	−26.2393	−1.40860	−0.704300	+	0.709903i	$0.748739\pi$
$348$	−16.4021	−0.879242
$349$	19.4377	1.04047	0.520237	−	0.854022i	$-0.325844\pi$
$349$	19.4377	1.04047	0.520237	+	0.854022i	$0.325844\pi$
$350$	0.176616	0.00944051
$351$	6.80516	0.363233
$352$	8.60275	0.458528
$353$	22.2508	1.18429	0.592145	−	0.805831i	$-0.298281\pi$
$353$	22.2508	1.18429	0.592145	+	0.805831i	$0.298281\pi$
$354$	2.04819	0.108860
$355$	4.46739	0.237104
$356$	24.5189	1.29950
$357$	0	0
$358$	0.226958	0.0119951
$359$	10.2274	0.539779	0.269889	−	0.962891i	$-0.413013\pi$
$359$	10.2274	0.539779	0.269889	+	0.962891i	$0.413013\pi$
$360$	1.99478	0.105134
$361$	−18.7648	−0.987623
$362$	2.58594	0.135914
$363$	1.69855	0.0891507
$364$	−13.2026	−0.692006
$365$	−14.4065	−0.754072
$366$	−3.05311	−0.159588
$367$	−26.7526	−1.39647	−0.698236	−	0.715868i	$-0.746031\pi$
$367$	−26.7526	−1.39647	−0.698236	+	0.715868i	$0.746031\pi$
$368$	1.59383	0.0830842
$369$	−3.31075	−0.172351
$370$	4.42585	0.230089
$371$	−0.0579193	−0.00300702
$372$	−4.09481	−0.212306
$373$	3.15373	0.163294	0.0816470	−	0.996661i	$-0.473982\pi$
$373$	3.15373	0.163294	0.0816470	+	0.996661i	$0.473982\pi$
$374$	0	0
$375$	−11.8347	−0.611142
$376$	10.7144	0.552552
$377$	57.5327	2.96308
$378$	0.244764	0.0125893
$379$	21.4269	1.10063	0.550313	−	0.834958i	$-0.314508\pi$
$379$	21.4269	1.10063	0.550313	+	0.834958i	$0.314508\pi$
$380$	−1.94600	−0.0998276
$381$	1.31580	0.0674105
$382$	−3.15862	−0.161609
$383$	−38.2727	−1.95564	−0.977822	−	0.209440i	$-0.932836\pi$
$383$	−38.2727	−1.95564	−0.977822	+	0.209440i	$0.932836\pi$
$384$	7.25638	0.370301
$385$	6.30837	0.321504
$386$	−5.65275	−0.287717
$387$	6.29062	0.319770
$388$	−8.98693	−0.456242
$389$	−12.4104	−0.629233	−0.314616	−	0.949219i	$-0.601876\pi$
$389$	−12.4104	−0.629233	−0.314616	+	0.949219i	$0.601876\pi$
$390$	−3.44530	−0.174460
$391$	0	0
$392$	−0.964391	−0.0487091
$393$	−3.96658	−0.200088
$394$	5.59126	0.281684
$395$	4.75883	0.239443
$396$	−5.91694	−0.297338
$397$	−22.7184	−1.14021	−0.570103	−	0.821573i	$-0.693097\pi$
$397$	−22.7184	−1.14021	−0.570103	+	0.821573i	$0.693097\pi$
$398$	−0.350853	−0.0175867
$399$	−0.484930	−0.0242768
$400$	−2.62952	−0.131476
$401$	35.7224	1.78389	0.891946	−	0.452142i	$-0.149340\pi$
$401$	35.7224	1.78389	0.891946	+	0.452142i	$0.149340\pi$
$402$	2.75089	0.137202
$403$	14.3632	0.715480
$404$	20.0321	0.996633
$405$	−2.06843	−0.102781
$406$	2.06930	0.102698
$407$	−26.6614	−1.32156
$408$	0	0
$409$	−1.35245	−0.0668742	−0.0334371	−	0.999441i	$-0.510645\pi$
$409$	−1.35245	−0.0668742	−0.0334371	+	0.999441i	$0.510645\pi$
$410$	1.67616	0.0827796
$411$	−19.1881	−0.946478
$412$	29.1939	1.43828
$413$	8.36804	0.411764
$414$	0.107052	0.00526132
$415$	35.6594	1.75045
$416$	−19.1955	−0.941139
$417$	7.59329	0.371845
$418$	−0.361994	−0.0177057
$419$	−5.72061	−0.279470	−0.139735	−	0.990189i	$-0.544625\pi$
$419$	−5.72061	−0.279470	−0.139735	+	0.990189i	$0.544625\pi$
$420$	4.01295	0.195812
$421$	30.2660	1.47508	0.737538	−	0.675306i	$-0.235988\pi$
$421$	30.2660	1.47508	0.737538	+	0.675306i	$0.235988\pi$
$422$	3.20353	0.155945
$423$	−11.1100	−0.540186
$424$	−0.0558568	−0.00271265
$425$	0	0
$426$	0.528638	0.0256126
$427$	−12.4737	−0.603644
$428$	−25.5857	−1.23673
$429$	20.7546	1.00204
$430$	−3.18480	−0.153585
$431$	23.5045	1.13217	0.566085	−	0.824347i	$-0.308457\pi$
$431$	23.5045	1.13217	0.566085	+	0.824347i	$0.308457\pi$
$432$	−3.64413	−0.175328
$433$	−15.3332	−0.736866	−0.368433	−	0.929654i	$-0.620106\pi$
$433$	−15.3332	−0.736866	−0.368433	+	0.929654i	$0.620106\pi$
$434$	0.516605	0.0247978
$435$	−17.4871	−0.838443
$436$	−2.04138	−0.0977644
$437$	−0.212093	−0.0101458
$438$	−1.70476	−0.0814568
$439$	9.66520	0.461295	0.230648	−	0.973037i	$-0.425916\pi$
$439$	9.66520	0.461295	0.230648	+	0.973037i	$0.425916\pi$
$440$	6.08373	0.290031
$441$	1.00000	0.0476190
$442$	0	0
$443$	29.9624	1.42356	0.711778	−	0.702404i	$-0.247890\pi$
$443$	29.9624	1.42356	0.711778	+	0.702404i	$0.247890\pi$
$444$	−16.9602	−0.804894
$445$	26.1409	1.23920
$446$	1.56182	0.0739543
$447$	−10.3536	−0.489708
$448$	6.59786	0.311719
$449$	−30.2211	−1.42622	−0.713110	−	0.701052i	$-0.752714\pi$
$449$	−30.2211	−1.42622	−0.713110	+	0.701052i	$0.752714\pi$
$450$	−0.176616	−0.00832575
$451$	−10.0972	−0.475460
$452$	26.9751	1.26880
$453$	−0.741505	−0.0348390
$454$	1.80252	0.0845964
$455$	−14.0760	−0.659894
$456$	−0.467662	−0.0219003
$457$	−21.9582	−1.02716	−0.513580	−	0.858042i	$-0.671681\pi$
$457$	−21.9582	−1.02716	−0.513580	+	0.858042i	$0.671681\pi$
$458$	−4.33787	−0.202695
$459$	0	0
$460$	1.75514	0.0818338
$461$	13.2021	0.614882	0.307441	−	0.951567i	$-0.400527\pi$
$461$	13.2021	0.614882	0.307441	+	0.951567i	$0.400527\pi$
$462$	0.746487	0.0347297
$463$	15.8832	0.738157	0.369079	−	0.929398i	$-0.379673\pi$
$463$	15.8832	0.738157	0.369079	+	0.929398i	$0.379673\pi$
$464$	−30.8085	−1.43025
$465$	−4.36570	−0.202454
$466$	5.27496	0.244358
$467$	33.5795	1.55388	0.776938	−	0.629578i	$-0.216772\pi$
$467$	33.5795	1.55388	0.776938	+	0.629578i	$0.216772\pi$
$468$	13.2026	0.610292
$469$	11.2390	0.518968
$470$	5.62474	0.259450
$471$	−0.196509	−0.00905464
$472$	8.07006	0.371455
$473$	19.1853	0.882142
$474$	0.563125	0.0258652
$475$	0.349914	0.0160552
$476$	0	0
$477$	0.0579193	0.00265194
$478$	0.960941	0.0439524
$479$	30.5865	1.39753	0.698766	−	0.715350i	$-0.253733\pi$
$479$	30.5865	1.39753	0.698766	+	0.715350i	$0.253733\pi$
$480$	5.83450	0.266307
$481$	59.4903	2.71252
$482$	−1.54794	−0.0705068
$483$	0.437369	0.0199010
$484$	3.29534	0.149788
$485$	−9.58144	−0.435071
$486$	−0.244764	−0.0111027
$487$	−24.5531	−1.11260	−0.556302	−	0.830980i	$-0.687780\pi$
$487$	−24.5531	−1.11260	−0.556302	+	0.830980i	$0.687780\pi$
$488$	−12.0295	−0.544550
$489$	−5.24513	−0.237193
$490$	−0.506278	−0.0228713
$491$	24.1370	1.08929	0.544645	−	0.838667i	$-0.316665\pi$
$491$	24.1370	1.08929	0.544645	+	0.838667i	$0.316665\pi$
$492$	−6.42316	−0.289578
$493$	0	0
$494$	0.807726	0.0363413
$495$	−6.30837	−0.283540
$496$	−7.69141	−0.345355
$497$	2.15979	0.0968799
$498$	4.21967	0.189088
$499$	16.2537	0.727614	0.363807	−	0.931474i	$-0.381477\pi$
$499$	16.2537	0.727614	0.363807	+	0.931474i	$0.381477\pi$
$500$	−22.9604	−1.02682
$501$	8.52493	0.380866
$502$	0.313138	0.0139760
$503$	−33.6235	−1.49920	−0.749599	−	0.661892i	$-0.769754\pi$
$503$	−33.6235	−1.49920	−0.749599	+	0.661892i	$0.769754\pi$
$504$	0.964391	0.0429574
$505$	21.3573	0.950386
$506$	0.326490	0.0145143
$507$	−33.3102	−1.47936
$508$	2.55277	0.113261
$509$	−1.81291	−0.0803558	−0.0401779	−	0.999193i	$-0.512792\pi$
$509$	−1.81291	−0.0803558	−0.0401779	+	0.999193i	$0.512792\pi$
$510$	0	0
$511$	−6.96494	−0.308111
$512$	17.3079	0.764907
$513$	0.484930	0.0214102
$514$	−4.03163	−0.177828
$515$	31.1252	1.37154
$516$	12.2044	0.537268
$517$	−33.8836	−1.49020
$518$	2.13971	0.0940134
$519$	−21.3404	−0.936741
$520$	−13.5748	−0.595294
$521$	−24.3784	−1.06804	−0.534019	−	0.845472i	$-0.679319\pi$
$521$	−24.3784	−1.06804	−0.534019	+	0.845472i	$0.679319\pi$
$522$	−2.06930	−0.0905707
$523$	−13.3601	−0.584196	−0.292098	−	0.956388i	$-0.594353\pi$
$523$	−13.3601	−0.584196	−0.292098	+	0.956388i	$0.594353\pi$
$524$	−7.69553	−0.336181
$525$	−0.721577	−0.0314922
$526$	4.77497	0.208199
$527$	0	0
$528$	−11.1140	−0.483674
$529$	−22.8087	−0.991683
$530$	−0.0293232	−0.00127372
$531$	−8.36804	−0.363142
$532$	−0.940808	−0.0407892
$533$	22.5302	0.975891
$534$	3.09332	0.133861
$535$	−27.2783	−1.17935
$536$	10.8388	0.468164
$537$	−0.927253	−0.0400139
$538$	3.10467	0.133852
$539$	3.04983	0.131365
$540$	−4.01295	−0.172690
$541$	22.8144	0.980868	0.490434	−	0.871478i	$-0.336838\pi$
$541$	22.8144	0.980868	0.490434	+	0.871478i	$0.336838\pi$
$542$	−0.776153	−0.0333386
$543$	−10.5650	−0.453389
$544$	0	0
$545$	−2.17642	−0.0932278
$546$	−1.66566	−0.0712835
$547$	−11.5617	−0.494341	−0.247170	−	0.968972i	$-0.579501\pi$
$547$	−11.5617	−0.494341	−0.247170	+	0.968972i	$0.579501\pi$
$548$	−37.2266	−1.59024
$549$	12.4737	0.532364
$550$	−0.538648	−0.0229680
$551$	4.09973	0.174654
$552$	0.421794	0.0179528
$553$	2.30069	0.0978353
$554$	−1.19749	−0.0508765
$555$	−18.0821	−0.767544
$556$	14.7317	0.624762
$557$	−32.6258	−1.38240	−0.691200	−	0.722664i	$-0.742918\pi$
$557$	−32.6258	−1.38240	−0.691200	+	0.722664i	$0.742918\pi$
$558$	−0.516605	−0.0218696
$559$	−42.8087	−1.81061
$560$	7.53765	0.318524
$561$	0	0
$562$	5.33181	0.224909
$563$	29.3944	1.23883	0.619413	−	0.785065i	$-0.287371\pi$
$563$	29.3944	1.23883	0.619413	+	0.785065i	$0.287371\pi$
$564$	−21.5544	−0.907604
$565$	28.7596	1.20992
$566$	−0.591836	−0.0248767
$567$	−1.00000	−0.0419961
$568$	2.08288	0.0873958
$569$	3.20394	0.134316	0.0671581	−	0.997742i	$-0.478607\pi$
$569$	3.20394	0.134316	0.0671581	+	0.997742i	$0.478607\pi$
$570$	−0.245509	−0.0102832
$571$	18.7057	0.782810	0.391405	−	0.920218i	$-0.371989\pi$
$571$	18.7057	0.782810	0.391405	+	0.920218i	$0.371989\pi$
$572$	40.2657	1.68360
$573$	12.9048	0.539105
$574$	0.810352	0.0338234
$575$	−0.315595	−0.0131612
$576$	−6.59786	−0.274911
$577$	−37.2105	−1.54909	−0.774546	−	0.632517i	$-0.782022\pi$
$577$	−37.2105	−1.54909	−0.774546	+	0.632517i	$0.782022\pi$
$578$	0	0
$579$	23.0947	0.959784
$580$	−33.9266	−1.40872
$581$	17.2398	0.715227
$582$	−1.13380	−0.0469975
$583$	0.176644	0.00731584
$584$	−6.71692	−0.277948
$585$	14.0760	0.581972
$586$	−0.225024	−0.00929565
$587$	0.898553	0.0370872	0.0185436	−	0.999828i	$-0.494097\pi$
$587$	0.898553	0.0370872	0.0185436	+	0.999828i	$0.494097\pi$
$588$	1.94009	0.0800080
$589$	1.02351	0.0421728
$590$	4.23655	0.174416
$591$	−22.8435	−0.939657
$592$	−31.8568	−1.30931
$593$	36.3966	1.49463	0.747314	−	0.664471i	$-0.231343\pi$
$593$	36.3966	1.49463	0.747314	+	0.664471i	$0.231343\pi$
$594$	−0.746487	−0.0306287
$595$	0	0
$596$	−20.0869	−0.822791
$597$	1.43344	0.0586667
$598$	−0.728506	−0.0297908
$599$	−31.9088	−1.30376	−0.651878	−	0.758324i	$-0.726019\pi$
$599$	−31.9088	−1.30376	−0.651878	+	0.758324i	$0.726019\pi$
$600$	−0.695882	−0.0284093
$601$	22.4172	0.914415	0.457208	−	0.889360i	$-0.348850\pi$
$601$	22.4172	0.914415	0.457208	+	0.889360i	$0.348850\pi$
$602$	−1.53972	−0.0627541
$603$	−11.2390	−0.457687
$604$	−1.43859	−0.0585353
$605$	3.51334	0.142838
$606$	2.52726	0.102663
$607$	−18.7457	−0.760865	−0.380433	−	0.924809i	$-0.624225\pi$
$607$	−18.7457	−0.760865	−0.380433	+	0.924809i	$0.624225\pi$
$608$	−1.36786	−0.0554739
$609$	−8.45427	−0.342584
$610$	−6.31515	−0.255693
$611$	75.6053	3.05866
$612$	0	0
$613$	−47.4839	−1.91786	−0.958928	−	0.283649i	$-0.908455\pi$
$613$	−47.4839	−1.91786	−0.958928	+	0.283649i	$0.908455\pi$
$614$	5.24943	0.211850
$615$	−6.84807	−0.276141
$616$	2.94123	0.118505
$617$	−35.0887	−1.41262	−0.706309	−	0.707904i	$-0.749641\pi$
$617$	−35.0887	−1.41262	−0.706309	+	0.707904i	$0.749641\pi$
$618$	3.68313	0.148157
$619$	−42.0340	−1.68949	−0.844745	−	0.535170i	$-0.820248\pi$
$619$	−42.0340	−1.68949	−0.844745	+	0.535170i	$0.820248\pi$
$620$	−8.46985	−0.340157
$621$	−0.437369	−0.0175510
$622$	2.75387	0.110420
$623$	12.6380	0.506331
$624$	24.7989	0.992751
$625$	−20.8714	−0.834858
$626$	−3.99582	−0.159705
$627$	1.47895	0.0590637
$628$	−0.381245	−0.0152133
$629$	0	0
$630$	0.506278	0.0201706
$631$	2.46401	0.0980907	0.0490453	−	0.998797i	$-0.484382\pi$
$631$	2.46401	0.0980907	0.0490453	+	0.998797i	$0.484382\pi$
$632$	2.21876	0.0882577
$633$	−13.0883	−0.520211
$634$	−2.07649	−0.0824680
$635$	2.72165	0.108005
$636$	0.112369	0.00445571
$637$	−6.80516	−0.269630
$638$	−6.31100	−0.249855
$639$	−2.15979	−0.0854400
$640$	15.0093	0.593297
$641$	−40.9372	−1.61692	−0.808461	−	0.588550i	$-0.799699\pi$
$641$	−40.9372	−1.61692	−0.808461	+	0.588550i	$0.799699\pi$
$642$	−3.22792	−0.127396
$643$	15.1296	0.596652	0.298326	−	0.954464i	$-0.403572\pi$
$643$	15.1296	0.596652	0.298326	+	0.954464i	$0.403572\pi$
$644$	0.848535	0.0334370
$645$	13.0117	0.512337
$646$	0	0
$647$	−32.4261	−1.27480	−0.637401	−	0.770532i	$-0.719990\pi$
$647$	−32.4261	−1.27480	−0.637401	+	0.770532i	$0.719990\pi$
$648$	−0.964391	−0.0378848
$649$	−25.5211	−1.00179
$650$	1.20190	0.0471423
$651$	−2.11063	−0.0827220
$652$	−10.1760	−0.398524
$653$	−7.14395	−0.279564	−0.139782	−	0.990182i	$-0.544640\pi$
$653$	−7.14395	−0.279564	−0.139782	+	0.990182i	$0.544640\pi$
$654$	−0.257542	−0.0100707
$655$	−8.20462	−0.320581
$656$	−12.0648	−0.471052
$657$	6.96494	0.271728
$658$	2.71932	0.106010
$659$	27.0371	1.05321	0.526607	−	0.850109i	$-0.323464\pi$
$659$	27.0371	1.05321	0.526607	+	0.850109i	$0.323464\pi$
$660$	−12.2388	−0.476395
$661$	36.7309	1.42867	0.714333	−	0.699806i	$-0.246730\pi$
$661$	36.7309	1.42867	0.714333	+	0.699806i	$0.246730\pi$
$662$	−7.64654	−0.297191
$663$	0	0
$664$	16.6259	0.645210
$665$	−1.00305	−0.0388964
$666$	−2.13971	−0.0829120
$667$	−3.69763	−0.143173
$668$	16.5391	0.639918
$669$	−6.38093	−0.246701
$670$	5.69005	0.219826
$671$	38.0426	1.46862
$672$	2.82073	0.108812
$673$	−15.9029	−0.613013	−0.306507	−	0.951869i	$-0.599160\pi$
$673$	−15.9029	−0.613013	−0.306507	+	0.951869i	$0.599160\pi$
$674$	2.53242	0.0975453
$675$	0.721577	0.0277735
$676$	−64.6248	−2.48557
$677$	−25.7282	−0.988815	−0.494407	−	0.869230i	$-0.664615\pi$
$677$	−25.7282	−0.988815	−0.494407	+	0.869230i	$0.664615\pi$
$678$	3.40320	0.130699
$679$	−4.63222	−0.177768
$680$	0	0
$681$	−7.36433	−0.282202
$682$	−1.57556	−0.0603312
$683$	−42.8235	−1.63860	−0.819298	−	0.573368i	$-0.805637\pi$
$683$	−42.8235	−1.63860	−0.819298	+	0.573368i	$0.805637\pi$
$684$	0.940808	0.0359727
$685$	−39.6893	−1.51645
$686$	−0.244764	−0.00934512
$687$	17.7227	0.676163
$688$	22.9239	0.873964
$689$	−0.394150	−0.0150159
$690$	0.221430	0.00842970
$691$	30.4402	1.15800	0.579000	−	0.815327i	$-0.303443\pi$
$691$	30.4402	1.15800	0.579000	+	0.815327i	$0.303443\pi$
$692$	−41.4024	−1.57388
$693$	−3.04983	−0.115853
$694$	−6.42243	−0.243792
$695$	15.7062	0.595771
$696$	−8.15322	−0.309047
$697$	0	0
$698$	4.75763	0.180079
$699$	−21.5513	−0.815143
$700$	−1.39992	−0.0529122
$701$	14.5317	0.548853	0.274427	−	0.961608i	$-0.411512\pi$
$701$	14.5317	0.548853	0.274427	+	0.961608i	$0.411512\pi$
$702$	1.66566	0.0628661
$703$	4.23923	0.159885
$704$	−20.1223	−0.758389
$705$	−22.9803	−0.865488
$706$	5.44618	0.204970
$707$	10.3253	0.388324
$708$	−16.2348	−0.610140
$709$	−26.8134	−1.00700	−0.503499	−	0.863996i	$-0.667954\pi$
$709$	−26.8134	−1.00700	−0.503499	+	0.863996i	$0.667954\pi$
$710$	1.09345	0.0410366
$711$	−2.30069	−0.0862826
$712$	12.1880	0.456763
$713$	−0.923123	−0.0345712
$714$	0	0
$715$	42.9295	1.60547
$716$	−1.79896	−0.0672301
$717$	−3.92600	−0.146619
$718$	2.50328	0.0934217
$719$	−2.03789	−0.0760005	−0.0380003	−	0.999278i	$-0.512099\pi$
$719$	−2.03789	−0.0760005	−0.0380003	+	0.999278i	$0.512099\pi$
$720$	−7.53765	−0.280912
$721$	15.0477	0.560406
$722$	−4.59295	−0.170932
$723$	6.32423	0.235201
$724$	−20.4971	−0.761770
$725$	6.10041	0.226563
$726$	0.415743	0.0154297
$727$	47.5511	1.76357	0.881787	−	0.471648i	$-0.156341\pi$
$727$	47.5511	1.76357	0.881787	+	0.471648i	$0.156341\pi$
$728$	−6.56283	−0.243235
$729$	1.00000	0.0370370
$730$	−3.52619	−0.130510
$731$	0	0
$732$	24.2001	0.894461
$733$	0.552854	0.0204201	0.0102101	−	0.999948i	$-0.496750\pi$
$733$	0.552854	0.0204201	0.0102101	+	0.999948i	$0.496750\pi$
$734$	−6.54805	−0.241693
$735$	2.06843	0.0762954
$736$	1.23370	0.0454748
$737$	−34.2770	−1.26261
$738$	−0.810352	−0.0298295
$739$	22.3783	0.823199	0.411600	−	0.911365i	$-0.364970\pi$
$739$	22.3783	0.823199	0.411600	+	0.911365i	$0.364970\pi$
$740$	−35.0810	−1.28960
$741$	−3.30002	−0.121229
$742$	−0.0141765	−0.000520437 0
$743$	−20.8678	−0.765564	−0.382782	−	0.923839i	$-0.625034\pi$
$743$	−20.8678	−0.765564	−0.382782	+	0.923839i	$0.625034\pi$
$744$	−2.03547	−0.0746240
$745$	−21.4157	−0.784611
$746$	0.771919	0.0282620
$747$	−17.2398	−0.630771
$748$	0	0
$749$	−13.1879	−0.481876
$750$	−2.89671	−0.105773
$751$	5.44466	0.198678	0.0993392	−	0.995054i	$-0.468327\pi$
$751$	5.44466	0.198678	0.0993392	+	0.995054i	$0.468327\pi$
$752$	−40.4863	−1.47638
$753$	−1.27935	−0.0466220
$754$	14.0819	0.512833
$755$	−1.53376	−0.0558191
$756$	−1.94009	−0.0705604
$757$	−9.01630	−0.327703	−0.163851	−	0.986485i	$-0.552392\pi$
$757$	−9.01630	−0.327703	−0.163851	+	0.986485i	$0.552392\pi$
$758$	5.24453	0.190490
$759$	−1.33390	−0.0484175
$760$	−0.967328	−0.0350887
$761$	−19.5596	−0.709035	−0.354518	−	0.935049i	$-0.615355\pi$
$761$	−19.5596	−0.709035	−0.354518	+	0.935049i	$0.615355\pi$
$762$	0.322060	0.0116670
$763$	−1.05221	−0.0380925
$764$	25.0364	0.905787
$765$	0	0
$766$	−9.36776	−0.338471
$767$	56.9458	2.05620
$768$	−11.4196	−0.412070
$769$	29.9914	1.08152	0.540758	−	0.841178i	$-0.318137\pi$
$769$	29.9914	1.08152	0.540758	+	0.841178i	$0.318137\pi$
$770$	1.54406	0.0556440
$771$	16.4715	0.593208
$772$	44.8059	1.61260
$773$	3.07006	0.110422	0.0552111	−	0.998475i	$-0.482417\pi$
$773$	3.07006	0.110422	0.0552111	+	0.998475i	$0.482417\pi$
$774$	1.53972	0.0553439
$775$	1.52298	0.0547071
$776$	−4.46727	−0.160366
$777$	−8.74194	−0.313615
$778$	−3.03762	−0.108904
$779$	1.60548	0.0575224
$780$	27.3088	0.977811
$781$	−6.58699	−0.235701
$782$	0	0
$783$	8.45427	0.302131
$784$	3.64413	0.130148
$785$	−0.406465	−0.0145074
$786$	−0.970875	−0.0346300
$787$	37.3431	1.33114	0.665569	−	0.746336i	$-0.268189\pi$
$787$	37.3431	1.33114	0.665569	+	0.746336i	$0.268189\pi$
$788$	−44.3185	−1.57878
$789$	−19.5085	−0.694522
$790$	1.16479	0.0414413
$791$	13.9040	0.494370
$792$	−2.94123	−0.104512
$793$	−84.8855	−3.01437
$794$	−5.56065	−0.197340
$795$	0.119802	0.00424895
$796$	2.78100	0.0985699
$797$	−21.7299	−0.769713	−0.384856	−	0.922977i	$-0.625749\pi$
$797$	−21.7299	−0.769713	−0.384856	+	0.922977i	$0.625749\pi$
$798$	−0.118693	−0.00420169
$799$	0	0
$800$	−2.03538	−0.0719614
$801$	−12.6380	−0.446542
$802$	8.74354	0.308745
$803$	21.2419	0.749609
$804$	−21.8047	−0.768991
$805$	0.904669	0.0318854
$806$	3.51558	0.123831
$807$	−12.6844	−0.446511
$808$	9.95765	0.350309
$809$	−8.70389	−0.306012	−0.153006	−	0.988225i	$-0.548895\pi$
$809$	−8.70389	−0.306012	−0.153006	+	0.988225i	$0.548895\pi$
$810$	−0.506278	−0.0177888
$811$	22.5668	0.792427	0.396214	−	0.918158i	$-0.370324\pi$
$811$	22.5668	0.792427	0.396214	+	0.918158i	$0.370324\pi$
$812$	−16.4021	−0.575599
$813$	3.17103	0.111213
$814$	−6.52574	−0.228727
$815$	−10.8492	−0.380031
$816$	0	0
$817$	−3.05051	−0.106724
$818$	−0.331030	−0.0115742
$819$	6.80516	0.237792
$820$	−13.2859	−0.463963
$821$	−15.0708	−0.525975	−0.262987	−	0.964799i	$-0.584708\pi$
$821$	−15.0708	−0.525975	−0.262987	+	0.964799i	$0.584708\pi$
$822$	−4.69654	−0.163811
$823$	33.1355	1.15503	0.577515	−	0.816380i	$-0.304022\pi$
$823$	33.1355	1.15503	0.577515	+	0.816380i	$0.304022\pi$
$824$	14.5119	0.505545
$825$	2.20069	0.0766180
$826$	2.04819	0.0712657
$827$	25.7615	0.895814	0.447907	−	0.894080i	$-0.352170\pi$
$827$	25.7615	0.895814	0.447907	+	0.894080i	$0.352170\pi$
$828$	−0.848535	−0.0294886
$829$	−24.4892	−0.850546	−0.425273	−	0.905065i	$-0.639822\pi$
$829$	−24.4892	−0.850546	−0.425273	+	0.905065i	$0.639822\pi$
$830$	8.72812	0.302957
$831$	4.89244	0.169717
$832$	44.8995	1.55661
$833$	0	0
$834$	1.85856	0.0643567
$835$	17.6333	0.610224
$836$	2.86930	0.0992369
$837$	2.11063	0.0729540
$838$	−1.40020	−0.0483690
$839$	−10.1531	−0.350523	−0.175262	−	0.984522i	$-0.556077\pi$
$839$	−10.1531	−0.350523	−0.175262	+	0.984522i	$0.556077\pi$
$840$	1.99478	0.0688264
$841$	42.4747	1.46464
$842$	7.40802	0.255297
$843$	−21.7835	−0.750263
$844$	−25.3924	−0.874043
$845$	−68.9000	−2.37023
$846$	−2.71932	−0.0934922
$847$	1.69855	0.0583628
$848$	0.211066	0.00724802
$849$	2.41799	0.0829852
$850$	0	0
$851$	−3.82345	−0.131066
$852$	−4.19019	−0.143554
$853$	−30.6769	−1.05036	−0.525179	−	0.850992i	$-0.676002\pi$
$853$	−30.6769	−1.05036	−0.525179	+	0.850992i	$0.676002\pi$
$854$	−3.05311	−0.104475
$855$	1.00305	0.0343034
$856$	−12.7183	−0.434702
$857$	−4.88180	−0.166759	−0.0833795	−	0.996518i	$-0.526571\pi$
$857$	−4.88180	−0.166759	−0.0833795	+	0.996518i	$0.526571\pi$
$858$	5.07996	0.173427
$859$	12.8261	0.437621	0.218810	−	0.975767i	$-0.429782\pi$
$859$	12.8261	0.437621	0.218810	+	0.975767i	$0.429782\pi$
$860$	25.2440	0.860812
$861$	−3.31075	−0.112830
$862$	5.75304	0.195949
$863$	38.0099	1.29387	0.646936	−	0.762544i	$-0.276050\pi$
$863$	38.0099	1.29387	0.646936	+	0.762544i	$0.276050\pi$
$864$	−2.82073	−0.0959633
$865$	−44.1413	−1.50085
$866$	−3.75300	−0.127532
$867$	0	0
$868$	−4.09481	−0.138987
$869$	−7.01671	−0.238026
$870$	−4.28021	−0.145113
$871$	76.4831	2.59153
$872$	−1.01474	−0.0343634
$873$	4.63222	0.156777
$874$	−0.0519127	−0.00175597
$875$	−11.8347	−0.400086
$876$	13.5126	0.456549
$877$	37.5705	1.26867	0.634333	−	0.773060i	$-0.281275\pi$
$877$	37.5705	1.26867	0.634333	+	0.773060i	$0.281275\pi$
$878$	2.36569	0.0798382
$879$	0.919352	0.0310090
$880$	−22.9885	−0.774944
$881$	36.6424	1.23451	0.617256	−	0.786762i	$-0.288244\pi$
$881$	36.6424	1.23451	0.617256	+	0.786762i	$0.288244\pi$
$882$	0.244764	0.00824162
$883$	−39.2293	−1.32017	−0.660086	−	0.751190i	$-0.729480\pi$
$883$	−39.2293	−1.32017	−0.660086	+	0.751190i	$0.729480\pi$
$884$	0	0
$885$	−17.3087	−0.581827
$886$	7.33371	0.246381
$887$	−11.0075	−0.369596	−0.184798	−	0.982777i	$-0.559163\pi$
$887$	−11.0075	−0.369596	−0.184798	+	0.982777i	$0.559163\pi$
$888$	−8.43065	−0.282914
$889$	1.31580	0.0441306
$890$	6.39833	0.214473
$891$	3.04983	0.102173
$892$	−12.3796	−0.414499
$893$	5.38757	0.180288
$894$	−2.53418	−0.0847557
$895$	−1.91796	−0.0641104
$896$	7.25638	0.242419
$897$	2.97636	0.0993779
$898$	−7.39701	−0.246842
$899$	17.8438	0.595125
$900$	1.39992	0.0466642
$901$	0	0
$902$	−2.47143	−0.0822897
$903$	6.29062	0.209339
$904$	13.4089	0.445974
$905$	−21.8531	−0.726421
$906$	−0.181493	−0.00602972
$907$	32.6185	1.08308	0.541540	−	0.840675i	$-0.317841\pi$
$907$	32.6185	1.08308	0.541540	+	0.840675i	$0.317841\pi$
$908$	−14.2875	−0.474146
$909$	−10.3253	−0.342470
$910$	−3.44530	−0.114211
$911$	35.7285	1.18374	0.591869	−	0.806034i	$-0.298390\pi$
$911$	35.7285	1.18374	0.591869	+	0.806034i	$0.298390\pi$
$912$	1.76715	0.0585161
$913$	−52.5784	−1.74009
$914$	−5.37456	−0.177775
$915$	25.8010	0.852955
$916$	34.3836	1.13607
$917$	−3.96658	−0.130988
$918$	0	0
$919$	−17.0877	−0.563672	−0.281836	−	0.959463i	$-0.590943\pi$
$919$	−17.0877	−0.563672	−0.281836	+	0.959463i	$0.590943\pi$
$920$	0.872454	0.0287640
$921$	−21.4469	−0.706700
$922$	3.23138	0.106420
$923$	14.6977	0.483781
$924$	−5.91694	−0.194653
$925$	6.30798	0.207405
$926$	3.88764	0.127756
$927$	−15.0477	−0.494232
$928$	−23.8472	−0.782824
$929$	18.2862	0.599950	0.299975	−	0.953947i	$-0.403022\pi$
$929$	18.2862	0.599950	0.299975	+	0.953947i	$0.403022\pi$
$930$	−1.06856	−0.0350396
$931$	−0.484930	−0.0158929
$932$	−41.8114	−1.36958
$933$	−11.2511	−0.368345
$934$	8.21905	0.268935
$935$	0	0
$936$	6.56283	0.214513
$937$	43.6001	1.42435	0.712177	−	0.702000i	$-0.247710\pi$
$937$	43.6001	1.42435	0.712177	+	0.702000i	$0.247710\pi$
$938$	2.75089	0.0898199
$939$	16.3252	0.532753
$940$	−44.5839	−1.45417
$941$	−12.4575	−0.406102	−0.203051	−	0.979168i	$-0.565086\pi$
$941$	−12.4575	−0.406102	−0.203051	+	0.979168i	$0.565086\pi$
$942$	−0.0480982	−0.00156712
$943$	−1.44802	−0.0471540
$944$	−30.4943	−0.992504
$945$	−2.06843	−0.0672862
$946$	4.69587	0.152676
$947$	19.6352	0.638057	0.319028	−	0.947745i	$-0.396643\pi$
$947$	19.6352	0.638057	0.319028	+	0.947745i	$0.396643\pi$
$948$	−4.46355	−0.144969
$949$	−47.3975	−1.53859
$950$	0.0856462	0.00277873
$951$	8.48366	0.275102
$952$	0	0
$953$	5.04661	0.163476	0.0817379	−	0.996654i	$-0.473953\pi$
$953$	5.04661	0.163476	0.0817379	+	0.996654i	$0.473953\pi$
$954$	0.0141765	0.000458982 0
$955$	26.6927	0.863756
$956$	−7.61679	−0.246345
$957$	25.7841	0.833481
$958$	7.48646	0.241876
$959$	−19.1881	−0.619615
$960$	−13.6472	−0.440463
$961$	−26.5452	−0.856298
$962$	14.5611	0.469467
$963$	13.1879	0.424974
$964$	12.2696	0.395177
$965$	47.7699	1.53777
$966$	0.107052	0.00344434
$967$	−52.9923	−1.70412	−0.852058	−	0.523447i	$-0.824646\pi$
$967$	−52.9923	−1.70412	−0.852058	+	0.523447i	$0.824646\pi$
$968$	1.63806	0.0526494
$969$	0	0
$970$	−2.34519	−0.0752995
$971$	38.0711	1.22176	0.610880	−	0.791723i	$-0.290816\pi$
$971$	38.0711	1.22176	0.610880	+	0.791723i	$0.290816\pi$
$972$	1.94009	0.0622284
$973$	7.59329	0.243430
$974$	−6.00969	−0.192563
$975$	−4.91045	−0.157260
$976$	45.4558	1.45500
$977$	33.9575	1.08640	0.543199	−	0.839604i	$-0.317213\pi$
$977$	33.9575	1.08640	0.543199	+	0.839604i	$0.317213\pi$
$978$	−1.28382	−0.0410519
$979$	−38.5437	−1.23186
$980$	4.01295	0.128189
$981$	1.05221	0.0335944
$982$	5.90787	0.188528
$983$	−2.08074	−0.0663653	−0.0331826	−	0.999449i	$-0.510564\pi$
$983$	−2.08074	−0.0663653	−0.0331826	+	0.999449i	$0.510564\pi$
$984$	−3.19286	−0.101785
$985$	−47.2503	−1.50552
$986$	0	0
$987$	−11.1100	−0.353635
$988$	−6.40234	−0.203686
$989$	2.75132	0.0874869
$990$	−1.54406	−0.0490734
$991$	−18.0029	−0.571881	−0.285941	−	0.958247i	$-0.592306\pi$
$991$	−18.0029	−0.571881	−0.285941	+	0.958247i	$0.592306\pi$
$992$	−5.95352	−0.189024
$993$	31.2405	0.991388
$994$	0.528638	0.0167674
$995$	2.96497	0.0939960
$996$	−33.4468	−1.05980
$997$	17.8497	0.565304	0.282652	−	0.959222i	$-0.408786\pi$
$997$	17.8497	0.565304	0.282652	+	0.959222i	$0.408786\pi$
$998$	3.97831	0.125931
$999$	8.74194	0.276583

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6069.2.a.z.1.6	✓	9
17.16	even	2		6069.2.a.bc.1.6	yes	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6069.2.a.z.1.6	✓	9	1.1	even	1	trivial
6069.2.a.bc.1.6	yes	9	17.16	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 6069 = 3 \cdot 7 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6069.a (trivial)

\(f(q)\)	\(=\)	\(q+0.244764 q^{2} -1.00000 q^{3} -1.94009 q^{4} -2.06843 q^{5} -0.244764 q^{6} -1.00000 q^{7} -0.964391 q^{8} +1.00000 q^{9} -0.506278 q^{10} +3.04983 q^{11} +1.94009 q^{12} -6.80516 q^{13} -0.244764 q^{14} +2.06843 q^{15} +3.64413 q^{16} +0.244764 q^{18} -0.484930 q^{19} +4.01295 q^{20} +1.00000 q^{21} +0.746487 q^{22} +0.437369 q^{23} +0.964391 q^{24} -0.721577 q^{25} -1.66566 q^{26} -1.00000 q^{27} +1.94009 q^{28} -8.45427 q^{29} +0.506278 q^{30} -2.11063 q^{31} +2.82073 q^{32} -3.04983 q^{33} +2.06843 q^{35} -1.94009 q^{36} -8.74194 q^{37} -0.118693 q^{38} +6.80516 q^{39} +1.99478 q^{40} -3.31075 q^{41} +0.244764 q^{42} +6.29062 q^{43} -5.91694 q^{44} -2.06843 q^{45} +0.107052 q^{46} -11.1100 q^{47} -3.64413 q^{48} +1.00000 q^{49} -0.176616 q^{50} +13.2026 q^{52} +0.0579193 q^{53} -0.244764 q^{54} -6.30837 q^{55} +0.964391 q^{56} +0.484930 q^{57} -2.06930 q^{58} -8.36804 q^{59} -4.01295 q^{60} +12.4737 q^{61} -0.516605 q^{62} -1.00000 q^{63} -6.59786 q^{64} +14.0760 q^{65} -0.746487 q^{66} -11.2390 q^{67} -0.437369 q^{69} +0.506278 q^{70} -2.15979 q^{71} -0.964391 q^{72} +6.96494 q^{73} -2.13971 q^{74} +0.721577 q^{75} +0.940808 q^{76} -3.04983 q^{77} +1.66566 q^{78} -2.30069 q^{79} -7.53765 q^{80} +1.00000 q^{81} -0.810352 q^{82} -17.2398 q^{83} -1.94009 q^{84} +1.53972 q^{86} +8.45427 q^{87} -2.94123 q^{88} -12.6380 q^{89} -0.506278 q^{90} +6.80516 q^{91} -0.848535 q^{92} +2.11063 q^{93} -2.71932 q^{94} +1.00305 q^{95} -2.82073 q^{96} +4.63222 q^{97} +0.244764 q^{98} +3.04983 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 9 q^{3} + 6 q^{4} + 3 q^{5} - 9 q^{7} + 9 q^{8} + 9 q^{9} + 12 q^{10} + 18 q^{11} - 6 q^{12} - 21 q^{13} - 3 q^{15} - 9 q^{19} + 15 q^{20} + 9 q^{21} + 6 q^{22} - 9 q^{24} + 3 q^{26} - 9 q^{27} - 6 q^{28}+ \cdots + 18 q^{99}+O(q^{100}) \) 9 * q - 9 * q^3 + 6 * q^4 + 3 * q^5 - 9 * q^7 + 9 * q^8 + 9 * q^9 + 12 * q^10 + 18 * q^11 - 6 * q^12 - 21 * q^13 - 3 * q^15 - 9 * q^19 + 15 * q^20 + 9 * q^21 + 6 * q^22 - 9 * q^24 + 3 * q^26 - 9 * q^27 - 6 * q^28 + 6 * q^29 - 12 * q^30 + 30 * q^31 + 3 * q^32 - 18 * q^33 - 3 * q^35 + 6 * q^36 + 12 * q^37 - 36 * q^38 + 21 * q^39 + 30 * q^40 + 9 * q^41 + 30 * q^44 + 3 * q^45 + 33 * q^46 - 9 * q^47 + 9 * q^49 - 12 * q^50 - 12 * q^52 + 30 * q^55 - 9 * q^56 + 9 * q^57 + 9 * q^58 - 3 * q^59 - 15 * q^60 + 33 * q^61 - 12 * q^62 - 9 * q^63 - 15 * q^64 - 15 * q^65 - 6 * q^66 - 15 * q^67 - 12 * q^70 + 9 * q^72 + 21 * q^73 + 6 * q^74 + 3 * q^76 - 18 * q^77 - 3 * q^78 + 30 * q^79 + 9 * q^81 + 9 * q^82 + 6 * q^84 + 72 * q^86 - 6 * q^87 + 48 * q^88 - 12 * q^89 + 12 * q^90 + 21 * q^91 + 48 * q^92 - 30 * q^93 + 48 * q^94 - 18 * q^95 - 3 * q^96 + 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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