LMFDB - Embedded newform 4719.2.a.bn.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4719,2,Mod(1,4719)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4719, 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("4719.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4719 = 3 \cdot 11^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4719.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:	$37.6814047138$
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} - 3x^{9} - 10x^{8} + 32x^{7} + 27x^{6} - 101x^{5} - 21x^{4} + 116x^{3} - 8x^{2} - 40x + 11 $ x^10 - 3x^9 - 10x^8 + 32x^7 + 27x^6 - 101x^5 - 21x^4 + 116x^3 - 8x^2 - 40*x + 11
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 429)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$0.368322$ of defining polynomial
Character	$\chi$	$=$	4719.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.368322 q^{2} -1.00000 q^{3} -1.86434 q^{4} +1.06229 q^{5} -0.368322 q^{6} +3.52340 q^{7} -1.42332 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.368322 q^{2} -1.00000 q^{3} -1.86434 q^{4} +1.06229 q^{5} -0.368322 q^{6} +3.52340 q^{7} -1.42332 q^{8} +1.00000 q^{9} +0.391264 q^{10} +1.86434 q^{12} -1.00000 q^{13} +1.29775 q^{14} -1.06229 q^{15} +3.20444 q^{16} +3.96148 q^{17} +0.368322 q^{18} -7.95302 q^{19} -1.98046 q^{20} -3.52340 q^{21} -1.09078 q^{23} +1.42332 q^{24} -3.87154 q^{25} -0.368322 q^{26} -1.00000 q^{27} -6.56880 q^{28} +3.07216 q^{29} -0.391264 q^{30} -7.15646 q^{31} +4.02691 q^{32} +1.45910 q^{34} +3.74286 q^{35} -1.86434 q^{36} -2.83369 q^{37} -2.92927 q^{38} +1.00000 q^{39} -1.51198 q^{40} -9.15381 q^{41} -1.29775 q^{42} -3.48063 q^{43} +1.06229 q^{45} -0.401760 q^{46} +5.79558 q^{47} -3.20444 q^{48} +5.41431 q^{49} -1.42598 q^{50} -3.96148 q^{51} +1.86434 q^{52} +7.92215 q^{53} -0.368322 q^{54} -5.01493 q^{56} +7.95302 q^{57} +1.13155 q^{58} -6.96053 q^{59} +1.98046 q^{60} -4.35854 q^{61} -2.63588 q^{62} +3.52340 q^{63} -4.92567 q^{64} -1.06229 q^{65} +14.3737 q^{67} -7.38554 q^{68} +1.09078 q^{69} +1.37858 q^{70} +12.4295 q^{71} -1.42332 q^{72} -6.59251 q^{73} -1.04371 q^{74} +3.87154 q^{75} +14.8271 q^{76} +0.368322 q^{78} +8.58641 q^{79} +3.40403 q^{80} +1.00000 q^{81} -3.37155 q^{82} -12.1426 q^{83} +6.56880 q^{84} +4.20823 q^{85} -1.28199 q^{86} -3.07216 q^{87} -5.44615 q^{89} +0.391264 q^{90} -3.52340 q^{91} +2.03359 q^{92} +7.15646 q^{93} +2.13464 q^{94} -8.44840 q^{95} -4.02691 q^{96} -4.03329 q^{97} +1.99421 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 3 q^{2} - 10 q^{3} + 9 q^{4} - 8 q^{5} - 3 q^{6} + q^{7} + 9 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q + 3 * q^2 - 10 * q^3 + 9 * q^4 - 8 * q^5 - 3 * q^6 + q^7 + 9 * q^8 + 10 * q^9	$ 10 q + 3 q^{2} - 10 q^{3} + 9 q^{4} - 8 q^{5} - 3 q^{6} + q^{7} + 9 q^{8} + 10 q^{9} - q^{10} - 9 q^{12} - 10 q^{13} - 8 q^{14} + 8 q^{15} + 15 q^{16} + q^{17} + 3 q^{18} - 6 q^{19} - 30 q^{20} - q^{21} + 3 q^{23} - 9 q^{24} + 4 q^{25} - 3 q^{26} - 10 q^{27} - 4 q^{28} - 12 q^{29} + q^{30} - 20 q^{31} + 21 q^{32} - 12 q^{34} + q^{35} + 9 q^{36} - 3 q^{37} - 4 q^{38} + 10 q^{39} - 60 q^{40} + 12 q^{41} + 8 q^{42} + 14 q^{43} - 8 q^{45} - 6 q^{46} - 6 q^{47} - 15 q^{48} - 19 q^{49} + 28 q^{50} - q^{51} - 9 q^{52} - 22 q^{53} - 3 q^{54} - 18 q^{56} + 6 q^{57} - 4 q^{58} - 28 q^{59} + 30 q^{60} - 12 q^{61} - 65 q^{62} + q^{63} + 49 q^{64} + 8 q^{65} + 28 q^{67} - 20 q^{68} - 3 q^{69} + 23 q^{70} - 9 q^{71} + 9 q^{72} - 5 q^{73} - 2 q^{74} - 4 q^{75} + 30 q^{76} + 3 q^{78} - 10 q^{79} - 76 q^{80} + 10 q^{81} + 22 q^{82} - 12 q^{83} + 4 q^{84} + 25 q^{85} - 53 q^{86} + 12 q^{87} - 63 q^{89} - q^{90} - q^{91} - 34 q^{92} + 20 q^{93} + 11 q^{94} - 19 q^{95} - 21 q^{96} - 26 q^{97} - 27 q^{98}+O(q^{100}) $ 10 * q + 3 * q^2 - 10 * q^3 + 9 * q^4 - 8 * q^5 - 3 * q^6 + q^7 + 9 * q^8 + 10 * q^9 - q^10 - 9 * q^12 - 10 * q^13 - 8 * q^14 + 8 * q^15 + 15 * q^16 + q^17 + 3 * q^18 - 6 * q^19 - 30 * q^20 - q^21 + 3 * q^23 - 9 * q^24 + 4 * q^25 - 3 * q^26 - 10 * q^27 - 4 * q^28 - 12 * q^29 + q^30 - 20 * q^31 + 21 * q^32 - 12 * q^34 + q^35 + 9 * q^36 - 3 * q^37 - 4 * q^38 + 10 * q^39 - 60 * q^40 + 12 * q^41 + 8 * q^42 + 14 * q^43 - 8 * q^45 - 6 * q^46 - 6 * q^47 - 15 * q^48 - 19 * q^49 + 28 * q^50 - q^51 - 9 * q^52 - 22 * q^53 - 3 * q^54 - 18 * q^56 + 6 * q^57 - 4 * q^58 - 28 * q^59 + 30 * q^60 - 12 * q^61 - 65 * q^62 + q^63 + 49 * q^64 + 8 * q^65 + 28 * q^67 - 20 * q^68 - 3 * q^69 + 23 * q^70 - 9 * q^71 + 9 * q^72 - 5 * q^73 - 2 * q^74 - 4 * q^75 + 30 * q^76 + 3 * q^78 - 10 * q^79 - 76 * q^80 + 10 * q^81 + 22 * q^82 - 12 * q^83 + 4 * q^84 + 25 * q^85 - 53 * q^86 + 12 * q^87 - 63 * q^89 - q^90 - q^91 - 34 * q^92 + 20 * q^93 + 11 * q^94 - 19 * q^95 - 21 * q^96 - 26 * q^97 - 27 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0.368322	0.260443	0.130222	−	0.991485i	$-0.458431\pi$
$2$	0.368322	0.260443	0.130222	+	0.991485i	$0.458431\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.86434	−0.932169
$5$	1.06229	0.475070	0.237535	−	0.971379i	$-0.423661\pi$
$5$	1.06229	0.475070	0.237535	+	0.971379i	$0.423661\pi$
$6$	−0.368322	−0.150367
$7$	3.52340	1.33172	0.665859	−	0.746077i	$-0.268065\pi$
$7$	3.52340	1.33172	0.665859	+	0.746077i	$0.268065\pi$
$8$	−1.42332	−0.503220
$9$	1.00000	0.333333
$10$	0.391264	0.123729
$11$	0	0
$11$	0	0
$12$	1.86434	0.538188
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	1.29775	0.346837
$15$	−1.06229	−0.274282
$16$	3.20444	0.801109
$17$	3.96148	0.960800	0.480400	−	0.877049i	$-0.340491\pi$
$17$	3.96148	0.960800	0.480400	+	0.877049i	$0.340491\pi$
$18$	0.368322	0.0868144
$19$	−7.95302	−1.82455	−0.912274	−	0.409581i	$-0.865675\pi$
$19$	−7.95302	−1.82455	−0.912274	+	0.409581i	$0.865675\pi$
$20$	−1.98046	−0.442845
$21$	−3.52340	−0.768868
$22$	0	0
$23$	−1.09078	−0.227444	−0.113722	−	0.993513i	$-0.536277\pi$
$23$	−1.09078	−0.227444	−0.113722	+	0.993513i	$0.536277\pi$
$24$	1.42332	0.290534
$25$	−3.87154	−0.774309
$26$	−0.368322	−0.0722339
$27$	−1.00000	−0.192450
$28$	−6.56880	−1.24139
$29$	3.07216	0.570486	0.285243	−	0.958455i	$-0.407926\pi$
$29$	3.07216	0.570486	0.285243	+	0.958455i	$0.407926\pi$
$30$	−0.391264	−0.0714348
$31$	−7.15646	−1.28534	−0.642669	−	0.766144i	$-0.722173\pi$
$31$	−7.15646	−1.28534	−0.642669	+	0.766144i	$0.722173\pi$
$32$	4.02691	0.711864
$33$	0	0
$34$	1.45910	0.250234
$35$	3.74286	0.632659
$36$	−1.86434	−0.310723
$37$	−2.83369	−0.465856	−0.232928	−	0.972494i	$-0.574831\pi$
$37$	−2.83369	−0.465856	−0.232928	+	0.972494i	$0.574831\pi$
$38$	−2.92927	−0.475191
$39$	1.00000	0.160128
$40$	−1.51198	−0.239065
$41$	−9.15381	−1.42958	−0.714792	−	0.699337i	$-0.753479\pi$
$41$	−9.15381	−1.42958	−0.714792	+	0.699337i	$0.753479\pi$
$42$	−1.29775	−0.200246
$43$	−3.48063	−0.530790	−0.265395	−	0.964140i	$-0.585502\pi$
$43$	−3.48063	−0.530790	−0.265395	+	0.964140i	$0.585502\pi$
$44$	0	0
$45$	1.06229	0.158357
$46$	−0.401760	−0.0592363
$47$	5.79558	0.845372	0.422686	−	0.906276i	$-0.361087\pi$
$47$	5.79558	0.845372	0.422686	+	0.906276i	$0.361087\pi$
$48$	−3.20444	−0.462521
$49$	5.41431	0.773473
$50$	−1.42598	−0.201663
$51$	−3.96148	−0.554718
$52$	1.86434	0.258537
$53$	7.92215	1.08819	0.544095	−	0.839023i	$-0.316873\pi$
$53$	7.92215	1.08819	0.544095	+	0.839023i	$0.316873\pi$
$54$	−0.368322	−0.0501223
$55$	0	0
$56$	−5.01493	−0.670148
$57$	7.95302	1.05340
$58$	1.13155	0.148579
$59$	−6.96053	−0.906184	−0.453092	−	0.891464i	$-0.649679\pi$
$59$	−6.96053	−0.906184	−0.453092	+	0.891464i	$0.649679\pi$
$60$	1.98046	0.255677
$61$	−4.35854	−0.558054	−0.279027	−	0.960283i	$-0.590012\pi$
$61$	−4.35854	−0.558054	−0.279027	+	0.960283i	$0.590012\pi$
$62$	−2.63588	−0.334758
$63$	3.52340	0.443906
$64$	−4.92567	−0.615709
$65$	−1.06229	−0.131761
$66$	0	0
$67$	14.3737	1.75603	0.878014	−	0.478636i	$-0.158869\pi$
$67$	14.3737	1.75603	0.878014	+	0.478636i	$0.158869\pi$
$68$	−7.38554	−0.895628
$69$	1.09078	0.131315
$70$	1.37858	0.164772
$71$	12.4295	1.47511	0.737554	−	0.675288i	$-0.235981\pi$
$71$	12.4295	1.47511	0.737554	+	0.675288i	$0.235981\pi$
$72$	−1.42332	−0.167740
$73$	−6.59251	−0.771595	−0.385797	−	0.922584i	$-0.626074\pi$
$73$	−6.59251	−0.771595	−0.385797	+	0.922584i	$0.626074\pi$
$74$	−1.04371	−0.121329
$75$	3.87154	0.447047
$76$	14.8271	1.70079
$77$	0	0
$78$	0.368322	0.0417043
$79$	8.58641	0.966047	0.483023	−	0.875607i	$-0.339539\pi$
$79$	8.58641	0.966047	0.483023	+	0.875607i	$0.339539\pi$
$80$	3.40403	0.380583
$81$	1.00000	0.111111
$82$	−3.37155	−0.372325
$83$	−12.1426	−1.33282	−0.666412	−	0.745584i	$-0.732171\pi$
$83$	−12.1426	−1.33282	−0.666412	+	0.745584i	$0.732171\pi$
$84$	6.56880	0.716715
$85$	4.20823	0.456447
$86$	−1.28199	−0.138241
$87$	−3.07216	−0.329370
$88$	0	0
$89$	−5.44615	−0.577290	−0.288645	−	0.957436i	$-0.593205\pi$
$89$	−5.44615	−0.577290	−0.288645	+	0.957436i	$0.593205\pi$
$90$	0.391264	0.0412429
$91$	−3.52340	−0.369352
$92$	2.03359	0.212016
$93$	7.15646	0.742090
$94$	2.13464	0.220171
$95$	−8.44840	−0.866787
$96$	−4.02691	−0.410995
$97$	−4.03329	−0.409518	−0.204759	−	0.978812i	$-0.565641\pi$
$97$	−4.03329	−0.409518	−0.204759	+	0.978812i	$0.565641\pi$
$98$	1.99421	0.201446
$99$	0	0
$100$	7.21787	0.721787
$101$	−10.8698	−1.08159	−0.540793	−	0.841156i	$-0.681876\pi$
$101$	−10.8698	−1.08159	−0.540793	+	0.841156i	$0.681876\pi$
$102$	−1.45910	−0.144473
$103$	−7.57313	−0.746203	−0.373101	−	0.927791i	$-0.621706\pi$
$103$	−7.57313	−0.746203	−0.373101	+	0.927791i	$0.621706\pi$
$104$	1.42332	0.139568
$105$	−3.74286	−0.365266
$106$	2.91790	0.283412
$107$	6.73419	0.651019	0.325509	−	0.945539i	$-0.394464\pi$
$107$	6.73419	0.651019	0.325509	+	0.945539i	$0.394464\pi$
$108$	1.86434	0.179396
$109$	10.1222	0.969529	0.484764	−	0.874645i	$-0.338905\pi$
$109$	10.1222	0.969529	0.484764	+	0.874645i	$0.338905\pi$
$110$	0	0
$111$	2.83369	0.268962
$112$	11.2905	1.06685
$113$	−14.9917	−1.41030	−0.705149	−	0.709060i	$-0.749120\pi$
$113$	−14.9917	−1.41030	−0.705149	+	0.709060i	$0.749120\pi$
$114$	2.92927	0.274352
$115$	−1.15873	−0.108052
$116$	−5.72755	−0.531790
$117$	−1.00000	−0.0924500
$118$	−2.56372	−0.236010
$119$	13.9579	1.27952
$120$	1.51198	0.138024
$121$	0	0
$122$	−1.60535	−0.145341
$123$	9.15381	0.825371
$124$	13.3421	1.19815
$125$	−9.42414	−0.842920
$126$	1.29775	0.115612
$127$	−8.59519	−0.762700	−0.381350	−	0.924431i	$-0.624541\pi$
$127$	−8.59519	−0.762700	−0.381350	+	0.924431i	$0.624541\pi$
$128$	−9.86805	−0.872221
$129$	3.48063	0.306452
$130$	−0.391264	−0.0343162
$131$	11.6022	1.01369	0.506845	−	0.862037i	$-0.330812\pi$
$131$	11.6022	1.01369	0.506845	+	0.862037i	$0.330812\pi$
$132$	0	0
$133$	−28.0216	−2.42978
$134$	5.29415	0.457345
$135$	−1.06229	−0.0914272
$136$	−5.63846	−0.483494
$137$	−16.5517	−1.41411	−0.707054	−	0.707160i	$-0.749976\pi$
$137$	−16.5517	−1.41411	−0.707054	+	0.707160i	$0.749976\pi$
$138$	0.401760	0.0342001
$139$	13.6048	1.15395	0.576973	−	0.816763i	$-0.304234\pi$
$139$	13.6048	1.15395	0.576973	+	0.816763i	$0.304234\pi$
$140$	−6.97796	−0.589745
$141$	−5.79558	−0.488076
$142$	4.57805	0.384182
$143$	0	0
$144$	3.20444	0.267036
$145$	3.26352	0.271021
$146$	−2.42817	−0.200957
$147$	−5.41431	−0.446565
$148$	5.28296	0.434257
$149$	10.6803	0.874967	0.437484	−	0.899226i	$-0.355870\pi$
$149$	10.6803	0.874967	0.437484	+	0.899226i	$0.355870\pi$
$150$	1.42598	0.116430
$151$	−1.92213	−0.156421	−0.0782105	−	0.996937i	$-0.524921\pi$
$151$	−1.92213	−0.156421	−0.0782105	+	0.996937i	$0.524921\pi$
$152$	11.3197	0.918149
$153$	3.96148	0.320267
$154$	0	0
$155$	−7.60222	−0.610625
$156$	−1.86434	−0.149267
$157$	−20.2889	−1.61923	−0.809617	−	0.586959i	$-0.800325\pi$
$157$	−20.2889	−1.61923	−0.809617	+	0.586959i	$0.800325\pi$
$158$	3.16257	0.251600
$159$	−7.92215	−0.628267
$160$	4.27774	0.338185
$161$	−3.84326	−0.302892
$162$	0.368322	0.0289381
$163$	12.4345	0.973945	0.486972	−	0.873417i	$-0.338101\pi$
$163$	12.4345	0.973945	0.486972	+	0.873417i	$0.338101\pi$
$164$	17.0658	1.33261
$165$	0	0
$166$	−4.47239	−0.347125
$167$	−18.6968	−1.44680	−0.723400	−	0.690429i	$-0.757422\pi$
$167$	−18.6968	−1.44680	−0.723400	+	0.690429i	$0.757422\pi$
$168$	5.01493	0.386910
$169$	1.00000	0.0769231
$170$	1.54999	0.118879
$171$	−7.95302	−0.608182
$172$	6.48907	0.494787
$173$	−15.7538	−1.19774	−0.598870	−	0.800846i	$-0.704383\pi$
$173$	−15.7538	−1.19774	−0.598870	+	0.800846i	$0.704383\pi$
$174$	−1.13155	−0.0857823
$175$	−13.6410	−1.03116
$176$	0	0
$177$	6.96053	0.523186
$178$	−2.00594	−0.150351
$179$	−14.0386	−1.04929	−0.524647	−	0.851320i	$-0.675803\pi$
$179$	−14.0386	−1.04929	−0.524647	+	0.851320i	$0.675803\pi$
$180$	−1.98046	−0.147615
$181$	−6.68784	−0.497103	−0.248552	−	0.968619i	$-0.579955\pi$
$181$	−6.68784	−0.497103	−0.248552	+	0.968619i	$0.579955\pi$
$182$	−1.29775	−0.0961953
$183$	4.35854	0.322193
$184$	1.55254	0.114455
$185$	−3.01020	−0.221314
$186$	2.63588	0.193272
$187$	0	0
$188$	−10.8049	−0.788030
$189$	−3.52340	−0.256289
$190$	−3.11173	−0.225749
$191$	−4.58019	−0.331411	−0.165706	−	0.986175i	$-0.552990\pi$
$191$	−4.58019	−0.331411	−0.165706	+	0.986175i	$0.552990\pi$
$192$	4.92567	0.355480
$193$	0.116173	0.00836231	0.00418116	−	0.999991i	$-0.498669\pi$
$193$	0.116173	0.00836231	0.00418116	+	0.999991i	$0.498669\pi$
$194$	−1.48555	−0.106656
$195$	1.06229	0.0760720
$196$	−10.0941	−0.721008
$197$	12.6011	0.897791	0.448895	−	0.893584i	$-0.351818\pi$
$197$	12.6011	0.897791	0.448895	+	0.893584i	$0.351818\pi$
$198$	0	0
$199$	−20.1515	−1.42850	−0.714251	−	0.699890i	$-0.753232\pi$
$199$	−20.1515	−1.42850	−0.714251	+	0.699890i	$0.753232\pi$
$200$	5.51045	0.389648
$201$	−14.3737	−1.01384
$202$	−4.00359	−0.281692
$203$	10.8244	0.759727
$204$	7.38554	0.517091
$205$	−9.72398	−0.679152
$206$	−2.78935	−0.194343
$207$	−1.09078	−0.0758147
$208$	−3.20444	−0.222188
$209$	0	0
$210$	−1.37858	−0.0951310
$211$	13.4813	0.928093	0.464047	−	0.885811i	$-0.346397\pi$
$211$	13.4813	0.928093	0.464047	+	0.885811i	$0.346397\pi$
$212$	−14.7696	−1.01438
$213$	−12.4295	−0.851654
$214$	2.48035	0.169553
$215$	−3.69743	−0.252162
$216$	1.42332	0.0968448
$217$	−25.2150	−1.71171
$218$	3.72822	0.252507
$219$	6.59251	0.445480
$220$	0	0
$221$	−3.96148	−0.266478
$222$	1.04371	0.0700493
$223$	2.95010	0.197553	0.0987766	−	0.995110i	$-0.468507\pi$
$223$	2.95010	0.197553	0.0987766	+	0.995110i	$0.468507\pi$
$224$	14.1884	0.948002
$225$	−3.87154	−0.258103
$226$	−5.52176	−0.367302
$227$	−14.9390	−0.991534	−0.495767	−	0.868456i	$-0.665113\pi$
$227$	−14.9390	−0.991534	−0.495767	+	0.868456i	$0.665113\pi$
$228$	−14.8271	−0.981950
$229$	−10.0056	−0.661190	−0.330595	−	0.943773i	$-0.607249\pi$
$229$	−10.0056	−0.661190	−0.330595	+	0.943773i	$0.607249\pi$
$230$	−0.426785	−0.0281414
$231$	0	0
$232$	−4.37268	−0.287080
$233$	−20.6005	−1.34958	−0.674791	−	0.738009i	$-0.735766\pi$
$233$	−20.6005	−1.34958	−0.674791	+	0.738009i	$0.735766\pi$
$234$	−0.368322	−0.0240780
$235$	6.15657	0.401611
$236$	12.9768	0.844717
$237$	−8.58641	−0.557747
$238$	5.14099	0.333241
$239$	25.5897	1.65526	0.827630	−	0.561274i	$-0.189689\pi$
$239$	25.5897	1.65526	0.827630	+	0.561274i	$0.189689\pi$
$240$	−3.40403	−0.219729
$241$	4.71356	0.303627	0.151814	−	0.988409i	$-0.451489\pi$
$241$	4.71356	0.303627	0.151814	+	0.988409i	$0.451489\pi$
$242$	0	0
$243$	−1.00000	−0.0641500
$244$	8.12580	0.520201
$245$	5.75156	0.367454
$246$	3.37155	0.214962
$247$	7.95302	0.506038
$248$	10.1859	0.646808
$249$	12.1426	0.769506
$250$	−3.47112	−0.219533
$251$	−21.5477	−1.36008	−0.680039	−	0.733176i	$-0.738037\pi$
$251$	−21.5477	−1.36008	−0.680039	+	0.733176i	$0.738037\pi$
$252$	−6.56880	−0.413796
$253$	0	0
$254$	−3.16580	−0.198640
$255$	−4.20823	−0.263530
$256$	6.21672	0.388545
$257$	6.87996	0.429160	0.214580	−	0.976706i	$-0.431162\pi$
$257$	6.87996	0.429160	0.214580	+	0.976706i	$0.431162\pi$
$258$	1.28199	0.0798133
$259$	−9.98421	−0.620389
$260$	1.98046	0.122823
$261$	3.07216	0.190162
$262$	4.27335	0.264009
$263$	−23.0579	−1.42181	−0.710904	−	0.703289i	$-0.751714\pi$
$263$	−23.0579	−1.42181	−0.710904	+	0.703289i	$0.751714\pi$
$264$	0	0
$265$	8.41560	0.516966
$266$	−10.3210	−0.632820
$267$	5.44615	0.333299
$268$	−26.7974	−1.63691
$269$	5.78224	0.352549	0.176275	−	0.984341i	$-0.443595\pi$
$269$	5.78224	0.352549	0.176275	+	0.984341i	$0.443595\pi$
$270$	−0.391264	−0.0238116
$271$	−20.0927	−1.22054	−0.610272	−	0.792192i	$-0.708940\pi$
$271$	−20.0927	−1.22054	−0.610272	+	0.792192i	$0.708940\pi$
$272$	12.6943	0.769706
$273$	3.52340	0.213246
$274$	−6.09636	−0.368295
$275$	0	0
$276$	−2.03359	−0.122408
$277$	−9.74785	−0.585691	−0.292846	−	0.956160i	$-0.594602\pi$
$277$	−9.74785	−0.585691	−0.292846	+	0.956160i	$0.594602\pi$
$278$	5.01096	0.300537
$279$	−7.15646	−0.428446
$280$	−5.32730	−0.318367
$281$	27.9563	1.66773	0.833867	−	0.551966i	$-0.186122\pi$
$281$	27.9563	1.66773	0.833867	+	0.551966i	$0.186122\pi$
$282$	−2.13464	−0.127116
$283$	14.6880	0.873113	0.436556	−	0.899677i	$-0.356198\pi$
$283$	14.6880	0.873113	0.436556	+	0.899677i	$0.356198\pi$
$284$	−23.1728	−1.37505
$285$	8.44840	0.500440
$286$	0	0
$287$	−32.2525	−1.90380
$288$	4.02691	0.237288
$289$	−1.30667	−0.0768631
$290$	1.20203	0.0705855
$291$	4.03329	0.236436
$292$	12.2907	0.719257
$293$	21.6252	1.26336	0.631680	−	0.775229i	$-0.282366\pi$
$293$	21.6252	1.26336	0.631680	+	0.775229i	$0.282366\pi$
$294$	−1.99421	−0.116305
$295$	−7.39409	−0.430501
$296$	4.03325	0.234428
$297$	0	0
$298$	3.93381	0.227879
$299$	1.09078	0.0630817
$300$	−7.21787	−0.416724
$301$	−12.2636	−0.706863
$302$	−0.707965	−0.0407388
$303$	10.8698	0.624454
$304$	−25.4849	−1.46166
$305$	−4.63003	−0.265115
$306$	1.45910	0.0834113
$307$	4.28458	0.244534	0.122267	−	0.992497i	$-0.460984\pi$
$307$	4.28458	0.244534	0.122267	+	0.992497i	$0.460984\pi$
$308$	0	0
$309$	7.57313	0.430820
$310$	−2.80007	−0.159033
$311$	−5.38203	−0.305187	−0.152593	−	0.988289i	$-0.548762\pi$
$311$	−5.38203	−0.305187	−0.152593	+	0.988289i	$0.548762\pi$
$312$	−1.42332	−0.0805797
$313$	−12.4006	−0.700922	−0.350461	−	0.936577i	$-0.613975\pi$
$313$	−12.4006	−0.700922	−0.350461	+	0.936577i	$0.613975\pi$
$314$	−7.47287	−0.421718
$315$	3.74286	0.210886
$316$	−16.0080	−0.900519
$317$	−5.61388	−0.315307	−0.157653	−	0.987495i	$-0.550393\pi$
$317$	−5.61388	−0.315307	−0.157653	+	0.987495i	$0.550393\pi$
$318$	−2.91790	−0.163628
$319$	0	0
$320$	−5.23248	−0.292505
$321$	−6.73419	−0.375866
$322$	−1.41556	−0.0788860
$323$	−31.5057	−1.75303
$324$	−1.86434	−0.103574
$325$	3.87154	0.214755
$326$	4.57990	0.253657
$327$	−10.1222	−0.559758
$328$	13.0288	0.719396
$329$	20.4201	1.12580
$330$	0	0
$331$	−6.69231	−0.367843	−0.183921	−	0.982941i	$-0.558879\pi$
$331$	−6.69231	−0.367843	−0.183921	+	0.982941i	$0.558879\pi$
$332$	22.6379	1.24242
$333$	−2.83369	−0.155285
$334$	−6.88644	−0.376809
$335$	15.2690	0.834235
$336$	−11.2905	−0.615947
$337$	16.1781	0.881280	0.440640	−	0.897684i	$-0.354752\pi$
$337$	16.1781	0.881280	0.440640	+	0.897684i	$0.354752\pi$
$338$	0.368322	0.0200341
$339$	14.9917	0.814235
$340$	−7.84557	−0.425486
$341$	0	0
$342$	−2.92927	−0.158397
$343$	−5.58700	−0.301669
$344$	4.95405	0.267105
$345$	1.15873	0.0623838
$346$	−5.80248	−0.311943
$347$	6.04668	0.324603	0.162302	−	0.986741i	$-0.448108\pi$
$347$	6.04668	0.324603	0.162302	+	0.986741i	$0.448108\pi$
$348$	5.72755	0.307029
$349$	−3.47588	−0.186059	−0.0930297	−	0.995663i	$-0.529655\pi$
$349$	−3.47588	−0.186059	−0.0930297	+	0.995663i	$0.529655\pi$
$350$	−5.02428	−0.268559
$351$	1.00000	0.0533761
$352$	0	0
$353$	−25.1212	−1.33706	−0.668532	−	0.743683i	$-0.733077\pi$
$353$	−25.1212	−1.33706	−0.668532	+	0.743683i	$0.733077\pi$
$354$	2.56372	0.136260
$355$	13.2037	0.700779
$356$	10.1535	0.538133
$357$	−13.9579	−0.738728
$358$	−5.17073	−0.273281
$359$	27.3774	1.44493	0.722463	−	0.691410i	$-0.243010\pi$
$359$	27.3774	1.44493	0.722463	+	0.691410i	$0.243010\pi$
$360$	−1.51198	−0.0796882
$361$	44.2505	2.32897
$362$	−2.46328	−0.129467
$363$	0	0
$364$	6.56880	0.344299
$365$	−7.00314	−0.366561
$366$	1.60535	0.0839129
$367$	−5.39313	−0.281519	−0.140759	−	0.990044i	$-0.544954\pi$
$367$	−5.39313	−0.281519	−0.140759	+	0.990044i	$0.544954\pi$
$368$	−3.49535	−0.182208
$369$	−9.15381	−0.476528
$370$	−1.10872	−0.0576397
$371$	27.9129	1.44916
$372$	−13.3421	−0.691754
$373$	−7.81933	−0.404869	−0.202435	−	0.979296i	$-0.564885\pi$
$373$	−7.81933	−0.404869	−0.202435	+	0.979296i	$0.564885\pi$
$374$	0	0
$375$	9.42414	0.486660
$376$	−8.24898	−0.425408
$377$	−3.07216	−0.158224
$378$	−1.29775	−0.0667488
$379$	−2.13133	−0.109479	−0.0547395	−	0.998501i	$-0.517433\pi$
$379$	−2.13133	−0.109479	−0.0547395	+	0.998501i	$0.517433\pi$
$380$	15.7507	0.807992
$381$	8.59519	0.440345
$382$	−1.68699	−0.0863138
$383$	−6.78330	−0.346610	−0.173305	−	0.984868i	$-0.555445\pi$
$383$	−6.78330	−0.346610	−0.173305	+	0.984868i	$0.555445\pi$
$384$	9.86805	0.503577
$385$	0	0
$386$	0.0427891	0.00217791
$387$	−3.48063	−0.176930
$388$	7.51942	0.381741
$389$	−32.6015	−1.65296	−0.826480	−	0.562966i	$-0.809660\pi$
$389$	−32.6015	−1.65296	−0.826480	+	0.562966i	$0.809660\pi$
$390$	0.391264	0.0198124
$391$	−4.32112	−0.218528
$392$	−7.70631	−0.389228
$393$	−11.6022	−0.585254
$394$	4.64126	0.233823
$395$	9.12124	0.458940
$396$	0	0
$397$	34.0969	1.71128	0.855638	−	0.517575i	$-0.173165\pi$
$397$	34.0969	1.71128	0.855638	+	0.517575i	$0.173165\pi$
$398$	−7.42224	−0.372043
$399$	28.0216	1.40284
$400$	−12.4061	−0.620306
$401$	−30.5696	−1.52658	−0.763288	−	0.646059i	$-0.776416\pi$
$401$	−30.5696	−1.52658	−0.763288	+	0.646059i	$0.776416\pi$
$402$	−5.29415	−0.264048
$403$	7.15646	0.356489
$404$	20.2650	1.00822
$405$	1.06229	0.0527855
$406$	3.98688	0.197866
$407$	0	0
$408$	5.63846	0.279145
$409$	4.19895	0.207625	0.103812	−	0.994597i	$-0.466896\pi$
$409$	4.19895	0.207625	0.103812	+	0.994597i	$0.466896\pi$
$410$	−3.58156	−0.176881
$411$	16.5517	0.816435
$412$	14.1189	0.695587
$413$	−24.5247	−1.20678
$414$	−0.401760	−0.0197454
$415$	−12.8989	−0.633184
$416$	−4.02691	−0.197435
$417$	−13.6048	−0.666231
$418$	0	0
$419$	−6.59017	−0.321951	−0.160975	−	0.986958i	$-0.551464\pi$
$419$	−6.59017	−0.321951	−0.160975	+	0.986958i	$0.551464\pi$
$420$	6.97796	0.340490
$421$	−30.4011	−1.48166	−0.740830	−	0.671693i	$-0.765568\pi$
$421$	−30.4011	−1.48166	−0.740830	+	0.671693i	$0.765568\pi$
$422$	4.96548	0.241716
$423$	5.79558	0.281791
$424$	−11.2758	−0.547600
$425$	−15.3370	−0.743956
$426$	−4.57805	−0.221807
$427$	−15.3569	−0.743171
$428$	−12.5548	−0.606860
$429$	0	0
$430$	−1.36185	−0.0656740
$431$	−36.0682	−1.73735	−0.868673	−	0.495386i	$-0.835027\pi$
$431$	−36.0682	−1.73735	−0.868673	+	0.495386i	$0.835027\pi$
$432$	−3.20444	−0.154174
$433$	16.8920	0.811780	0.405890	−	0.913922i	$-0.366962\pi$
$433$	16.8920	0.811780	0.405890	+	0.913922i	$0.366962\pi$
$434$	−9.28726	−0.445803
$435$	−3.26352	−0.156474
$436$	−18.8712	−0.903765
$437$	8.67502	0.414983
$438$	2.42817	0.116022
$439$	−28.5683	−1.36349	−0.681746	−	0.731589i	$-0.738779\pi$
$439$	−28.5683	−1.36349	−0.681746	+	0.731589i	$0.738779\pi$
$440$	0	0
$441$	5.41431	0.257824
$442$	−1.45910	−0.0694024
$443$	20.9469	0.995218	0.497609	−	0.867401i	$-0.334211\pi$
$443$	20.9469	0.995218	0.497609	+	0.867401i	$0.334211\pi$
$444$	−5.28296	−0.250718
$445$	−5.78538	−0.274253
$446$	1.08659	0.0514514
$447$	−10.6803	−0.505163
$448$	−17.3551	−0.819951
$449$	−39.0549	−1.84311	−0.921556	−	0.388245i	$-0.873081\pi$
$449$	−39.0549	−1.84311	−0.921556	+	0.388245i	$0.873081\pi$
$450$	−1.42598	−0.0672212
$451$	0	0
$452$	27.9495	1.31464
$453$	1.92213	0.0903098
$454$	−5.50235	−0.258238
$455$	−3.74286	−0.175468
$456$	−11.3197	−0.530094
$457$	−28.1326	−1.31599	−0.657994	−	0.753023i	$-0.728595\pi$
$457$	−28.1326	−1.31599	−0.657994	+	0.753023i	$0.728595\pi$
$458$	−3.68529	−0.172202
$459$	−3.96148	−0.184906
$460$	2.16026	0.100723
$461$	−8.49269	−0.395544	−0.197772	−	0.980248i	$-0.563371\pi$
$461$	−8.49269	−0.395544	−0.197772	+	0.980248i	$0.563371\pi$
$462$	0	0
$463$	5.51870	0.256476	0.128238	−	0.991743i	$-0.459068\pi$
$463$	5.51870	0.256476	0.128238	+	0.991743i	$0.459068\pi$
$464$	9.84455	0.457022
$465$	7.60222	0.352545
$466$	−7.58762	−0.351490
$467$	−31.8102	−1.47200	−0.735999	−	0.676982i	$-0.763287\pi$
$467$	−31.8102	−1.47200	−0.735999	+	0.676982i	$0.763287\pi$
$468$	1.86434	0.0861791
$469$	50.6442	2.33853
$470$	2.26760	0.104597
$471$	20.2889	0.934865
$472$	9.90708	0.456010
$473$	0	0
$474$	−3.16257	−0.145261
$475$	30.7905	1.41276
$476$	−26.0222	−1.19272
$477$	7.92215	0.362730
$478$	9.42526	0.431101
$479$	−9.16859	−0.418923	−0.209462	−	0.977817i	$-0.567171\pi$
$479$	−9.16859	−0.418923	−0.209462	+	0.977817i	$0.567171\pi$
$480$	−4.27774	−0.195251
$481$	2.83369	0.129205
$482$	1.73611	0.0790776
$483$	3.84326	0.174875
$484$	0	0
$485$	−4.28451	−0.194550
$486$	−0.368322	−0.0167074
$487$	0.610094	0.0276460	0.0138230	−	0.999904i	$-0.495600\pi$
$487$	0.610094	0.0276460	0.0138230	+	0.999904i	$0.495600\pi$
$488$	6.20361	0.280824
$489$	−12.4345	−0.562307
$490$	2.11843	0.0957008
$491$	19.6595	0.887219	0.443610	−	0.896220i	$-0.353698\pi$
$491$	19.6595	0.887219	0.443610	+	0.896220i	$0.353698\pi$
$492$	−17.0658	−0.769385
$493$	12.1703	0.548123
$494$	2.92927	0.131794
$495$	0	0
$496$	−22.9324	−1.02970
$497$	43.7940	1.96443
$498$	4.47239	0.200413
$499$	11.5068	0.515116	0.257558	−	0.966263i	$-0.417082\pi$
$499$	11.5068	0.515116	0.257558	+	0.966263i	$0.417082\pi$
$500$	17.5698	0.785745
$501$	18.6968	0.835310
$502$	−7.93649	−0.354223
$503$	14.0809	0.627836	0.313918	−	0.949450i	$-0.398358\pi$
$503$	14.0809	0.627836	0.313918	+	0.949450i	$0.398358\pi$
$504$	−5.01493	−0.223383
$505$	−11.5469	−0.513829
$506$	0	0
$507$	−1.00000	−0.0444116
$508$	16.0243	0.710965
$509$	−12.9169	−0.572529	−0.286265	−	0.958151i	$-0.592414\pi$
$509$	−12.9169	−0.572529	−0.286265	+	0.958151i	$0.592414\pi$
$510$	−1.54999	−0.0686345
$511$	−23.2280	−1.02755
$512$	22.0259	0.973415
$513$	7.95302	0.351134
$514$	2.53404	0.111772
$515$	−8.04485	−0.354498
$516$	−6.48907	−0.285665
$517$	0	0
$518$	−3.67741	−0.161576
$519$	15.7538	0.691516
$520$	1.51198	0.0663046
$521$	−26.0705	−1.14217	−0.571085	−	0.820891i	$-0.693477\pi$
$521$	−26.0705	−1.14217	−0.571085	+	0.820891i	$0.693477\pi$
$522$	1.13155	0.0495264
$523$	−34.1515	−1.49334	−0.746670	−	0.665194i	$-0.768349\pi$
$523$	−34.1515	−1.49334	−0.746670	+	0.665194i	$0.768349\pi$
$524$	−21.6304	−0.944930
$525$	13.6410	0.595341
$526$	−8.49272	−0.370300
$527$	−28.3502	−1.23495
$528$	0	0
$529$	−21.8102	−0.948269
$530$	3.09965	0.134640
$531$	−6.96053	−0.302061
$532$	52.2418	2.26497
$533$	9.15381	0.396495
$534$	2.00594	0.0868054
$535$	7.15365	0.309279
$536$	−20.4584	−0.883669
$537$	14.0386	0.605810
$538$	2.12973	0.0918191
$539$	0	0
$540$	1.98046	0.0852256
$541$	24.3338	1.04619	0.523096	−	0.852274i	$-0.324777\pi$
$541$	24.3338	1.04619	0.523096	+	0.852274i	$0.324777\pi$
$542$	−7.40058	−0.317882
$543$	6.68784	0.287003
$544$	15.9525	0.683959
$545$	10.7527	0.460594
$546$	1.29775	0.0555384
$547$	7.44778	0.318444	0.159222	−	0.987243i	$-0.449101\pi$
$547$	7.44778	0.318444	0.159222	+	0.987243i	$0.449101\pi$
$548$	30.8580	1.31819
$549$	−4.35854	−0.186018
$550$	0	0
$551$	−24.4330	−1.04088
$552$	−1.55254	−0.0660804
$553$	30.2533	1.28650
$554$	−3.59035	−0.152539
$555$	3.01020	0.127776
$556$	−25.3640	−1.07567
$557$	4.34564	0.184131	0.0920653	−	0.995753i	$-0.470653\pi$
$557$	4.34564	0.184131	0.0920653	+	0.995753i	$0.470653\pi$
$558$	−2.63588	−0.111586
$559$	3.48063	0.147215
$560$	11.9938	0.506829
$561$	0	0
$562$	10.2969	0.434350
$563$	33.1181	1.39576	0.697880	−	0.716215i	$-0.254127\pi$
$563$	33.1181	1.39576	0.697880	+	0.716215i	$0.254127\pi$
$564$	10.8049	0.454969
$565$	−15.9255	−0.669989
$566$	5.40993	0.227396
$567$	3.52340	0.147969
$568$	−17.6912	−0.742304
$569$	23.1588	0.970868	0.485434	−	0.874273i	$-0.338662\pi$
$569$	23.1588	0.970868	0.485434	+	0.874273i	$0.338662\pi$
$570$	3.11173	0.130336
$571$	37.7891	1.58142	0.790712	−	0.612188i	$-0.209711\pi$
$571$	37.7891	1.58142	0.790712	+	0.612188i	$0.209711\pi$
$572$	0	0
$573$	4.58019	0.191340
$574$	−11.8793	−0.495833
$575$	4.22302	0.176112
$576$	−4.92567	−0.205236
$577$	29.3083	1.22012	0.610059	−	0.792356i	$-0.291146\pi$
$577$	29.3083	1.22012	0.610059	+	0.792356i	$0.291146\pi$
$578$	−0.481277	−0.0200185
$579$	−0.116173	−0.00482798
$580$	−6.08431	−0.252637
$581$	−42.7832	−1.77495
$582$	1.48555	0.0615780
$583$	0	0
$584$	9.38326	0.388282
$585$	−1.06229	−0.0439202
$586$	7.96505	0.329033
$587$	25.3406	1.04592	0.522960	−	0.852357i	$-0.324828\pi$
$587$	25.3406	1.04592	0.522960	+	0.852357i	$0.324828\pi$
$588$	10.0941	0.416274
$589$	56.9154	2.34516
$590$	−2.72341	−0.112121
$591$	−12.6011	−0.518340
$592$	−9.08038	−0.373201
$593$	3.80759	0.156359	0.0781795	−	0.996939i	$-0.475089\pi$
$593$	3.80759	0.156359	0.0781795	+	0.996939i	$0.475089\pi$
$594$	0	0
$595$	14.8273	0.607859
$596$	−19.9118	−0.815618
$597$	20.1515	0.824746
$598$	0.401760	0.0164292
$599$	45.6779	1.86635	0.933174	−	0.359426i	$-0.117027\pi$
$599$	45.6779	1.86635	0.933174	+	0.359426i	$0.117027\pi$
$600$	−5.51045	−0.224963
$601$	27.2343	1.11091	0.555455	−	0.831546i	$-0.312544\pi$
$601$	27.2343	1.11091	0.555455	+	0.831546i	$0.312544\pi$
$602$	−4.51697	−0.184098
$603$	14.3737	0.585342
$604$	3.58351	0.145811
$605$	0	0
$606$	4.00359	0.162635
$607$	−38.3072	−1.55484	−0.777420	−	0.628982i	$-0.783472\pi$
$607$	−38.3072	−1.55484	−0.777420	+	0.628982i	$0.783472\pi$
$608$	−32.0261	−1.29883
$609$	−10.8244	−0.438628
$610$	−1.70534	−0.0690473
$611$	−5.79558	−0.234464
$612$	−7.38554	−0.298543
$613$	−2.58995	−0.104607	−0.0523035	−	0.998631i	$-0.516656\pi$
$613$	−2.58995	−0.104607	−0.0523035	+	0.998631i	$0.516656\pi$
$614$	1.57811	0.0636872
$615$	9.72398	0.392109
$616$	0	0
$617$	9.07593	0.365383	0.182692	−	0.983170i	$-0.441519\pi$
$617$	9.07593	0.365383	0.182692	+	0.983170i	$0.441519\pi$
$618$	2.78935	0.112204
$619$	35.3414	1.42049	0.710245	−	0.703955i	$-0.248584\pi$
$619$	35.3414	1.42049	0.710245	+	0.703955i	$0.248584\pi$
$620$	14.1731	0.569206
$621$	1.09078	0.0437717
$622$	−1.98232	−0.0794838
$623$	−19.1889	−0.768788
$624$	3.20444	0.128280
$625$	9.34657	0.373863
$626$	−4.56741	−0.182550
$627$	0	0
$628$	37.8254	1.50940
$629$	−11.2256	−0.447594
$630$	1.37858	0.0549239
$631$	41.6778	1.65917	0.829584	−	0.558382i	$-0.188578\pi$
$631$	41.6778	1.65917	0.829584	+	0.558382i	$0.188578\pi$
$632$	−12.2212	−0.486134
$633$	−13.4813	−0.535835
$634$	−2.06772	−0.0821195
$635$	−9.13057	−0.362335
$636$	14.7696	0.585651
$637$	−5.41431	−0.214523
$638$	0	0
$639$	12.4295	0.491703
$640$	−10.4827	−0.414366
$641$	−21.6222	−0.854024	−0.427012	−	0.904246i	$-0.640434\pi$
$641$	−21.6222	−0.854024	−0.427012	+	0.904246i	$0.640434\pi$
$642$	−2.48035	−0.0978917
$643$	−42.1655	−1.66284	−0.831422	−	0.555641i	$-0.812473\pi$
$643$	−42.1655	−1.66284	−0.831422	+	0.555641i	$0.812473\pi$
$644$	7.16514	0.282346
$645$	3.69743	0.145586
$646$	−11.6043	−0.456563
$647$	−0.359473	−0.0141324	−0.00706618	−	0.999975i	$-0.502249\pi$
$647$	−0.359473	−0.0141324	−0.00706618	+	0.999975i	$0.502249\pi$
$648$	−1.42332	−0.0559134
$649$	0	0
$650$	1.42598	0.0559314
$651$	25.2150	0.988255
$652$	−23.1821	−0.907881
$653$	45.9279	1.79730	0.898648	−	0.438670i	$-0.144550\pi$
$653$	45.9279	1.79730	0.898648	+	0.438670i	$0.144550\pi$
$654$	−3.72822	−0.145785
$655$	12.3249	0.481573
$656$	−29.3328	−1.14525
$657$	−6.59251	−0.257198
$658$	7.52118	0.293206
$659$	5.87720	0.228943	0.114472	−	0.993427i	$-0.463483\pi$
$659$	5.87720	0.228943	0.114472	+	0.993427i	$0.463483\pi$
$660$	0	0
$661$	27.8313	1.08251	0.541256	−	0.840858i	$-0.317949\pi$
$661$	27.8313	1.08251	0.541256	+	0.840858i	$0.317949\pi$
$662$	−2.46493	−0.0958021
$663$	3.96148	0.153851
$664$	17.2828	0.670704
$665$	−29.7670	−1.15432
$666$	−1.04371	−0.0404430
$667$	−3.35106	−0.129754
$668$	34.8571	1.34866
$669$	−2.95010	−0.114057
$670$	5.62392	0.217271
$671$	0	0
$672$	−14.1884	−0.547329
$673$	21.4148	0.825481	0.412741	−	0.910849i	$-0.364572\pi$
$673$	21.4148	0.825481	0.412741	+	0.910849i	$0.364572\pi$
$674$	5.95877	0.229523
$675$	3.87154	0.149016
$676$	−1.86434	−0.0717053
$677$	27.0439	1.03938	0.519692	−	0.854354i	$-0.326047\pi$
$677$	27.0439	1.03938	0.519692	+	0.854354i	$0.326047\pi$
$678$	5.52176	0.212062
$679$	−14.2109	−0.545363
$680$	−5.98967	−0.229693
$681$	14.9390	0.572462
$682$	0	0
$683$	−34.2998	−1.31245	−0.656223	−	0.754567i	$-0.727847\pi$
$683$	−34.2998	−1.31245	−0.656223	+	0.754567i	$0.727847\pi$
$684$	14.8271	0.566929
$685$	−17.5827	−0.671800
$686$	−2.05782	−0.0785678
$687$	10.0056	0.381738
$688$	−11.1534	−0.425221
$689$	−7.92215	−0.301810
$690$	0.426785	0.0162474
$691$	23.4590	0.892422	0.446211	−	0.894928i	$-0.352773\pi$
$691$	23.4590	0.892422	0.446211	+	0.894928i	$0.352773\pi$
$692$	29.3704	1.11650
$693$	0	0
$694$	2.22713	0.0845407
$695$	14.4522	0.548205
$696$	4.37268	0.165746
$697$	−36.2626	−1.37354
$698$	−1.28024	−0.0484579
$699$	20.6005	0.779182
$700$	25.4314	0.961217
$701$	−14.2278	−0.537377	−0.268689	−	0.963227i	$-0.586590\pi$
$701$	−14.2278	−0.537377	−0.268689	+	0.963227i	$0.586590\pi$
$702$	0.368322	0.0139014
$703$	22.5364	0.849976
$704$	0	0
$705$	−6.15657	−0.231870
$706$	−9.25269	−0.348229
$707$	−38.2986	−1.44037
$708$	−12.9768	−0.487698
$709$	3.84623	0.144448	0.0722242	−	0.997388i	$-0.476990\pi$
$709$	3.84623	0.144448	0.0722242	+	0.997388i	$0.476990\pi$
$710$	4.86321	0.182513
$711$	8.58641	0.322016
$712$	7.75162	0.290504
$713$	7.80615	0.292343
$714$	−5.14099	−0.192397
$715$	0	0
$716$	26.1727	0.978119
$717$	−25.5897	−0.955665
$718$	10.0837	0.376321
$719$	19.7962	0.738275	0.369138	−	0.929375i	$-0.379653\pi$
$719$	19.7962	0.738275	0.369138	+	0.929375i	$0.379653\pi$
$720$	3.40403	0.126861
$721$	−26.6831	−0.993732
$722$	16.2984	0.606565
$723$	−4.71356	−0.175299
$724$	12.4684	0.463384
$725$	−11.8940	−0.441732
$726$	0	0
$727$	−15.5435	−0.576476	−0.288238	−	0.957559i	$-0.593069\pi$
$727$	−15.5435	−0.576476	−0.288238	+	0.957559i	$0.593069\pi$
$728$	5.01493	0.185866
$729$	1.00000	0.0370370
$730$	−2.57941	−0.0954684
$731$	−13.7884	−0.509984
$732$	−8.12580	−0.300338
$733$	24.4468	0.902963	0.451481	−	0.892281i	$-0.350896\pi$
$733$	24.4468	0.902963	0.451481	+	0.892281i	$0.350896\pi$
$734$	−1.98641	−0.0733197
$735$	−5.75156	−0.212150
$736$	−4.39249	−0.161909
$737$	0	0
$738$	−3.37155	−0.124108
$739$	−13.2396	−0.487026	−0.243513	−	0.969898i	$-0.578300\pi$
$739$	−13.2396	−0.487026	−0.243513	+	0.969898i	$0.578300\pi$
$740$	5.61202	0.206302
$741$	−7.95302	−0.292161
$742$	10.2809	0.377425
$743$	−7.06953	−0.259356	−0.129678	−	0.991556i	$-0.541394\pi$
$743$	−7.06953	−0.259356	−0.129678	+	0.991556i	$0.541394\pi$
$744$	−10.1859	−0.373435
$745$	11.3456	0.415670
$746$	−2.88003	−0.105445
$747$	−12.1426	−0.444274
$748$	0	0
$749$	23.7272	0.866974
$750$	3.47112	0.126747
$751$	17.9325	0.654366	0.327183	−	0.944961i	$-0.393901\pi$
$751$	17.9325	0.654366	0.327183	+	0.944961i	$0.393901\pi$
$752$	18.5716	0.677235
$753$	21.5477	0.785241
$754$	−1.13155	−0.0412085
$755$	−2.04186	−0.0743109
$756$	6.56880	0.238905
$757$	−29.6207	−1.07658	−0.538290	−	0.842759i	$-0.680930\pi$
$757$	−29.6207	−1.07658	−0.538290	+	0.842759i	$0.680930\pi$
$758$	−0.785015	−0.0285130
$759$	0	0
$760$	12.0248	0.436185
$761$	−6.44430	−0.233606	−0.116803	−	0.993155i	$-0.537265\pi$
$761$	−6.44430	−0.233606	−0.116803	+	0.993155i	$0.537265\pi$
$762$	3.16580	0.114685
$763$	35.6644	1.29114
$764$	8.53903	0.308931
$765$	4.20823	0.152149
$766$	−2.49844	−0.0902723
$767$	6.96053	0.251330
$768$	−6.21672	−0.224327
$769$	−22.1539	−0.798890	−0.399445	−	0.916757i	$-0.630797\pi$
$769$	−22.1539	−0.798890	−0.399445	+	0.916757i	$0.630797\pi$
$770$	0	0
$771$	−6.87996	−0.247776
$772$	−0.216586	−0.00779509
$773$	16.8647	0.606582	0.303291	−	0.952898i	$-0.401915\pi$
$773$	16.8647	0.606582	0.303291	+	0.952898i	$0.401915\pi$
$774$	−1.28199	−0.0460803
$775$	27.7065	0.995249
$776$	5.74067	0.206078
$777$	9.98421	0.358182
$778$	−12.0078	−0.430502
$779$	72.8004	2.60834
$780$	−1.98046	−0.0709120
$781$	0	0
$782$	−1.59156	−0.0569142
$783$	−3.07216	−0.109790
$784$	17.3498	0.619637
$785$	−21.5527	−0.769249
$786$	−4.27335	−0.152425
$787$	46.5238	1.65839	0.829196	−	0.558957i	$-0.188798\pi$
$787$	46.5238	1.65839	0.829196	+	0.558957i	$0.188798\pi$
$788$	−23.4927	−0.836893
$789$	23.0579	0.820882
$790$	3.35956	0.119528
$791$	−52.8216	−1.87812
$792$	0	0
$793$	4.35854	0.154776
$794$	12.5587	0.445690
$795$	−8.41560	−0.298471
$796$	37.5692	1.33161
$797$	−25.7007	−0.910365	−0.455183	−	0.890398i	$-0.650426\pi$
$797$	−25.7007	−0.910365	−0.455183	+	0.890398i	$0.650426\pi$
$798$	10.3210	0.365359
$799$	22.9591	0.812234
$800$	−15.5904	−0.551202
$801$	−5.44615	−0.192430
$802$	−11.2595	−0.397586
$803$	0	0
$804$	26.7974	0.945073
$805$	−4.08265	−0.143895
$806$	2.63588	0.0928450
$807$	−5.78224	−0.203545
$808$	15.4712	0.544276
$809$	13.5704	0.477108	0.238554	−	0.971129i	$-0.423327\pi$
$809$	13.5704	0.477108	0.238554	+	0.971129i	$0.423327\pi$
$810$	0.391264	0.0137476
$811$	29.5576	1.03791	0.518953	−	0.854803i	$-0.326322\pi$
$811$	29.5576	1.03791	0.518953	+	0.854803i	$0.326322\pi$
$812$	−20.1804	−0.708194
$813$	20.0927	0.704681
$814$	0	0
$815$	13.2090	0.462692
$816$	−12.6943	−0.444390
$817$	27.6815	0.968452
$818$	1.54657	0.0540744
$819$	−3.52340	−0.123117
$820$	18.1288	0.633085
$821$	−15.0898	−0.526638	−0.263319	−	0.964709i	$-0.584817\pi$
$821$	−15.0898	−0.526638	−0.263319	+	0.964709i	$0.584817\pi$
$822$	6.09636	0.212635
$823$	36.9069	1.28649	0.643247	−	0.765659i	$-0.277587\pi$
$823$	36.9069	1.28649	0.643247	+	0.765659i	$0.277587\pi$
$824$	10.7790	0.375504
$825$	0	0
$826$	−9.03300	−0.314298
$827$	−18.8845	−0.656679	−0.328340	−	0.944560i	$-0.606489\pi$
$827$	−18.8845	−0.656679	−0.328340	+	0.944560i	$0.606489\pi$
$828$	2.03359	0.0706722
$829$	−18.6945	−0.649286	−0.324643	−	0.945837i	$-0.605244\pi$
$829$	−18.6945	−0.649286	−0.324643	+	0.945837i	$0.605244\pi$
$830$	−4.75097	−0.164908
$831$	9.74785	0.338149
$832$	4.92567	0.170767
$833$	21.4487	0.743153
$834$	−5.01096	−0.173515
$835$	−19.8614	−0.687331
$836$	0	0
$837$	7.15646	0.247363
$838$	−2.42731	−0.0838499
$839$	−3.17529	−0.109623	−0.0548115	−	0.998497i	$-0.517456\pi$
$839$	−3.17529	−0.109623	−0.0548115	+	0.998497i	$0.517456\pi$
$840$	5.32730	0.183809
$841$	−19.5618	−0.674546
$842$	−11.1974	−0.385888
$843$	−27.9563	−0.962866
$844$	−25.1338	−0.865140
$845$	1.06229	0.0365438
$846$	2.13464	0.0733905
$847$	0	0
$848$	25.3860	0.871759
$849$	−14.6880	−0.504092
$850$	−5.64898	−0.193758
$851$	3.09094	0.105956
$852$	23.1728	0.793886
$853$	9.82277	0.336325	0.168163	−	0.985759i	$-0.446217\pi$
$853$	9.82277	0.336325	0.168163	+	0.985759i	$0.446217\pi$
$854$	−5.65628	−0.193554
$855$	−8.44840	−0.288929
$856$	−9.58492	−0.327606
$857$	−28.6512	−0.978705	−0.489352	−	0.872086i	$-0.662767\pi$
$857$	−28.6512	−0.978705	−0.489352	+	0.872086i	$0.662767\pi$
$858$	0	0
$859$	54.2057	1.84947	0.924737	−	0.380606i	$-0.124285\pi$
$859$	54.2057	1.84947	0.924737	+	0.380606i	$0.124285\pi$
$860$	6.89326	0.235058
$861$	32.2525	1.09916
$862$	−13.2847	−0.452480
$863$	−7.13319	−0.242817	−0.121408	−	0.992603i	$-0.538741\pi$
$863$	−7.13319	−0.242817	−0.121408	+	0.992603i	$0.538741\pi$
$864$	−4.02691	−0.136998
$865$	−16.7351	−0.569010
$866$	6.22172	0.211423
$867$	1.30667	0.0443769
$868$	47.0094	1.59560
$869$	0	0
$870$	−1.20203	−0.0407525
$871$	−14.3737	−0.487034
$872$	−14.4071	−0.487887
$873$	−4.03329	−0.136506
$874$	3.19520	0.108079
$875$	−33.2050	−1.12253
$876$	−12.2907	−0.415263
$877$	28.6989	0.969094	0.484547	−	0.874765i	$-0.338985\pi$
$877$	28.6989	0.969094	0.484547	+	0.874765i	$0.338985\pi$
$878$	−10.5224	−0.355112
$879$	−21.6252	−0.729401
$880$	0	0
$881$	−10.0032	−0.337015	−0.168508	−	0.985700i	$-0.553895\pi$
$881$	−10.0032	−0.337015	−0.168508	+	0.985700i	$0.553895\pi$
$882$	1.99421	0.0671486
$883$	29.4810	0.992114	0.496057	−	0.868290i	$-0.334781\pi$
$883$	29.4810	0.992114	0.496057	+	0.868290i	$0.334781\pi$
$884$	7.38554	0.248403
$885$	7.39409	0.248550
$886$	7.71522	0.259198
$887$	10.1976	0.342403	0.171201	−	0.985236i	$-0.445235\pi$
$887$	10.1976	0.342403	0.171201	+	0.985236i	$0.445235\pi$
$888$	−4.03325	−0.135347
$889$	−30.2842	−1.01570
$890$	−2.13088	−0.0714274
$891$	0	0
$892$	−5.49998	−0.184153
$893$	−46.0923	−1.54242
$894$	−3.93381	−0.131566
$895$	−14.9130	−0.498488
$896$	−34.7691	−1.16155
$897$	−1.09078	−0.0364202
$898$	−14.3848	−0.480026
$899$	−21.9858	−0.733268
$900$	7.21787	0.240596
$901$	31.3834	1.04553
$902$	0	0
$903$	12.2636	0.408108
$904$	21.3380	0.709690
$905$	−7.10441	−0.236159
$906$	0.707965	0.0235206
$907$	−57.6071	−1.91281	−0.956406	−	0.292040i	$-0.905666\pi$
$907$	−57.6071	−1.91281	−0.956406	+	0.292040i	$0.905666\pi$
$908$	27.8513	0.924277
$909$	−10.8698	−0.360529
$910$	−1.37858	−0.0456995
$911$	−23.4593	−0.777241	−0.388621	−	0.921398i	$-0.627048\pi$
$911$	−23.4593	−0.777241	−0.388621	+	0.921398i	$0.627048\pi$
$912$	25.4849	0.843891
$913$	0	0
$914$	−10.3619	−0.342740
$915$	4.63003	0.153064
$916$	18.6539	0.616341
$917$	40.8792	1.34995
$918$	−1.45910	−0.0481575
$919$	15.8060	0.521392	0.260696	−	0.965421i	$-0.416048\pi$
$919$	15.8060	0.521392	0.260696	+	0.965421i	$0.416048\pi$
$920$	1.64924	0.0543739
$921$	−4.28458	−0.141182
$922$	−3.12805	−0.103017
$923$	−12.4295	−0.409121
$924$	0	0
$925$	10.9708	0.360716
$926$	2.03266	0.0667973
$927$	−7.57313	−0.248734
$928$	12.3713	0.406108
$929$	47.8839	1.57102	0.785510	−	0.618849i	$-0.212401\pi$
$929$	47.8839	1.57102	0.785510	+	0.618849i	$0.212401\pi$
$930$	2.80007	0.0918178
$931$	−43.0601	−1.41124
$932$	38.4063	1.25804
$933$	5.38203	0.176200
$934$	−11.7164	−0.383372
$935$	0	0
$936$	1.42332	0.0465227
$937$	27.2562	0.890423	0.445211	−	0.895426i	$-0.353129\pi$
$937$	27.2562	0.890423	0.445211	+	0.895426i	$0.353129\pi$
$938$	18.6534	0.609055
$939$	12.4006	0.404677
$940$	−11.4779	−0.374369
$941$	−5.62897	−0.183499	−0.0917496	−	0.995782i	$-0.529246\pi$
$941$	−5.62897	−0.183499	−0.0917496	+	0.995782i	$0.529246\pi$
$942$	7.47287	0.243479
$943$	9.98482	0.325151
$944$	−22.3046	−0.725952
$945$	−3.74286	−0.121755
$946$	0	0
$947$	−30.3760	−0.987086	−0.493543	−	0.869721i	$-0.664299\pi$
$947$	−30.3760	−0.987086	−0.493543	+	0.869721i	$0.664299\pi$
$948$	16.0080	0.519915
$949$	6.59251	0.214002
$950$	11.3408	0.367944
$951$	5.61388	0.182042
$952$	−19.8665	−0.643878
$953$	−47.0427	−1.52386	−0.761931	−	0.647659i	$-0.775748\pi$
$953$	−47.0427	−1.52386	−0.761931	+	0.647659i	$0.775748\pi$
$954$	2.91790	0.0944706
$955$	−4.86548	−0.157443
$956$	−47.7079	−1.54298
$957$	0	0
$958$	−3.37699	−0.109106
$959$	−58.3182	−1.88319
$960$	5.23248	0.168878
$961$	20.2149	0.652094
$962$	1.04371	0.0336506
$963$	6.73419	0.217006
$964$	−8.78768	−0.283032
$965$	0.123409	0.00397268
$966$	1.41556	0.0455449
$967$	−25.5851	−0.822760	−0.411380	−	0.911464i	$-0.634953\pi$
$967$	−25.5851	−0.822760	−0.411380	+	0.911464i	$0.634953\pi$
$968$	0	0
$969$	31.5057	1.01211
$970$	−1.57808	−0.0506692
$971$	26.9659	0.865377	0.432689	−	0.901543i	$-0.357565\pi$
$971$	26.9659	0.865377	0.432689	+	0.901543i	$0.357565\pi$
$972$	1.86434	0.0597987
$973$	47.9351	1.53673
$974$	0.224711	0.00720022
$975$	−3.87154	−0.123989
$976$	−13.9667	−0.447062
$977$	−40.1413	−1.28423	−0.642117	−	0.766607i	$-0.721944\pi$
$977$	−40.1413	−1.28423	−0.642117	+	0.766607i	$0.721944\pi$
$978$	−4.57990	−0.146449
$979$	0	0
$980$	−10.7229	−0.342529
$981$	10.1222	0.323176
$982$	7.24102	0.231070
$983$	7.02955	0.224208	0.112104	−	0.993696i	$-0.464241\pi$
$983$	7.02955	0.224208	0.112104	+	0.993696i	$0.464241\pi$
$984$	−13.0288	−0.415343
$985$	13.3860	0.426513
$986$	4.48260	0.142755
$987$	−20.4201	−0.649979
$988$	−14.8271	−0.471713
$989$	3.79661	0.120725
$990$	0	0
$991$	−0.142470	−0.00452571	−0.00226286	−	0.999997i	$-0.500720\pi$
$991$	−0.142470	−0.00452571	−0.00226286	+	0.999997i	$0.500720\pi$
$992$	−28.8184	−0.914986
$993$	6.69231	0.212374
$994$	16.1303	0.511622
$995$	−21.4067	−0.678638
$996$	−22.6379	−0.717310
$997$	−3.96103	−0.125447	−0.0627235	−	0.998031i	$-0.519979\pi$
$997$	−3.96103	−0.125447	−0.0627235	+	0.998031i	$0.519979\pi$
$998$	4.23822	0.134159
$999$	2.83369	0.0896540

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4719.2.a.bn.1.5		10
11.5	even	5		429.2.n.b.157.3	✓	20
11.9	even	5		429.2.n.b.235.3	yes	20
11.10	odd	2		4719.2.a.bi.1.6		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.n.b.157.3	✓	20	11.5	even	5
429.2.n.b.235.3	yes	20	11.9	even	5
4719.2.a.bi.1.6		10	11.10	odd	2
4719.2.a.bn.1.5		10	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 4719 = 3 \cdot 11^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4719.a (trivial)

\(f(q)\)	\(=\)	\(q+0.368322 q^{2} -1.00000 q^{3} -1.86434 q^{4} +1.06229 q^{5} -0.368322 q^{6} +3.52340 q^{7} -1.42332 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.368322 q^{2} -1.00000 q^{3} -1.86434 q^{4} +1.06229 q^{5} -0.368322 q^{6} +3.52340 q^{7} -1.42332 q^{8} +1.00000 q^{9} +0.391264 q^{10} +1.86434 q^{12} -1.00000 q^{13} +1.29775 q^{14} -1.06229 q^{15} +3.20444 q^{16} +3.96148 q^{17} +0.368322 q^{18} -7.95302 q^{19} -1.98046 q^{20} -3.52340 q^{21} -1.09078 q^{23} +1.42332 q^{24} -3.87154 q^{25} -0.368322 q^{26} -1.00000 q^{27} -6.56880 q^{28} +3.07216 q^{29} -0.391264 q^{30} -7.15646 q^{31} +4.02691 q^{32} +1.45910 q^{34} +3.74286 q^{35} -1.86434 q^{36} -2.83369 q^{37} -2.92927 q^{38} +1.00000 q^{39} -1.51198 q^{40} -9.15381 q^{41} -1.29775 q^{42} -3.48063 q^{43} +1.06229 q^{45} -0.401760 q^{46} +5.79558 q^{47} -3.20444 q^{48} +5.41431 q^{49} -1.42598 q^{50} -3.96148 q^{51} +1.86434 q^{52} +7.92215 q^{53} -0.368322 q^{54} -5.01493 q^{56} +7.95302 q^{57} +1.13155 q^{58} -6.96053 q^{59} +1.98046 q^{60} -4.35854 q^{61} -2.63588 q^{62} +3.52340 q^{63} -4.92567 q^{64} -1.06229 q^{65} +14.3737 q^{67} -7.38554 q^{68} +1.09078 q^{69} +1.37858 q^{70} +12.4295 q^{71} -1.42332 q^{72} -6.59251 q^{73} -1.04371 q^{74} +3.87154 q^{75} +14.8271 q^{76} +0.368322 q^{78} +8.58641 q^{79} +3.40403 q^{80} +1.00000 q^{81} -3.37155 q^{82} -12.1426 q^{83} +6.56880 q^{84} +4.20823 q^{85} -1.28199 q^{86} -3.07216 q^{87} -5.44615 q^{89} +0.391264 q^{90} -3.52340 q^{91} +2.03359 q^{92} +7.15646 q^{93} +2.13464 q^{94} -8.44840 q^{95} -4.02691 q^{96} -4.03329 q^{97} +1.99421 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 3 q^{2} - 10 q^{3} + 9 q^{4} - 8 q^{5} - 3 q^{6} + q^{7} + 9 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 3 * q^2 - 10 * q^3 + 9 * q^4 - 8 * q^5 - 3 * q^6 + q^7 + 9 * q^8 + 10 * q^9	\( 10 q + 3 q^{2} - 10 q^{3} + 9 q^{4} - 8 q^{5} - 3 q^{6} + q^{7} + 9 q^{8} + 10 q^{9} - q^{10} - 9 q^{12} - 10 q^{13} - 8 q^{14} + 8 q^{15} + 15 q^{16} + q^{17} + 3 q^{18} - 6 q^{19} - 30 q^{20} - q^{21} + 3 q^{23} - 9 q^{24} + 4 q^{25} - 3 q^{26} - 10 q^{27} - 4 q^{28} - 12 q^{29} + q^{30} - 20 q^{31} + 21 q^{32} - 12 q^{34} + q^{35} + 9 q^{36} - 3 q^{37} - 4 q^{38} + 10 q^{39} - 60 q^{40} + 12 q^{41} + 8 q^{42} + 14 q^{43} - 8 q^{45} - 6 q^{46} - 6 q^{47} - 15 q^{48} - 19 q^{49} + 28 q^{50} - q^{51} - 9 q^{52} - 22 q^{53} - 3 q^{54} - 18 q^{56} + 6 q^{57} - 4 q^{58} - 28 q^{59} + 30 q^{60} - 12 q^{61} - 65 q^{62} + q^{63} + 49 q^{64} + 8 q^{65} + 28 q^{67} - 20 q^{68} - 3 q^{69} + 23 q^{70} - 9 q^{71} + 9 q^{72} - 5 q^{73} - 2 q^{74} - 4 q^{75} + 30 q^{76} + 3 q^{78} - 10 q^{79} - 76 q^{80} + 10 q^{81} + 22 q^{82} - 12 q^{83} + 4 q^{84} + 25 q^{85} - 53 q^{86} + 12 q^{87} - 63 q^{89} - q^{90} - q^{91} - 34 q^{92} + 20 q^{93} + 11 q^{94} - 19 q^{95} - 21 q^{96} - 26 q^{97} - 27 q^{98}+O(q^{100}) \) 10 * q + 3 * q^2 - 10 * q^3 + 9 * q^4 - 8 * q^5 - 3 * q^6 + q^7 + 9 * q^8 + 10 * q^9 - q^10 - 9 * q^12 - 10 * q^13 - 8 * q^14 + 8 * q^15 + 15 * q^16 + q^17 + 3 * q^18 - 6 * q^19 - 30 * q^20 - q^21 + 3 * q^23 - 9 * q^24 + 4 * q^25 - 3 * q^26 - 10 * q^27 - 4 * q^28 - 12 * q^29 + q^30 - 20 * q^31 + 21 * q^32 - 12 * q^34 + q^35 + 9 * q^36 - 3 * q^37 - 4 * q^38 + 10 * q^39 - 60 * q^40 + 12 * q^41 + 8 * q^42 + 14 * q^43 - 8 * q^45 - 6 * q^46 - 6 * q^47 - 15 * q^48 - 19 * q^49 + 28 * q^50 - q^51 - 9 * q^52 - 22 * q^53 - 3 * q^54 - 18 * q^56 + 6 * q^57 - 4 * q^58 - 28 * q^59 + 30 * q^60 - 12 * q^61 - 65 * q^62 + q^63 + 49 * q^64 + 8 * q^65 + 28 * q^67 - 20 * q^68 - 3 * q^69 + 23 * q^70 - 9 * q^71 + 9 * q^72 - 5 * q^73 - 2 * q^74 - 4 * q^75 + 30 * q^76 + 3 * q^78 - 10 * q^79 - 76 * q^80 + 10 * q^81 + 22 * q^82 - 12 * q^83 + 4 * q^84 + 25 * q^85 - 53 * q^86 + 12 * q^87 - 63 * q^89 - q^90 - q^91 - 34 * q^92 + 20 * q^93 + 11 * q^94 - 19 * q^95 - 21 * q^96 - 26 * q^97 - 27 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more