LMFDB - Embedded newform 2842.2.a.z.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2842,2,Mod(1,2842)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2842, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("2842.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2842 = 2 \cdot 7^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2842.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:	$22.6934842544$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.1019601.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 10x^{3} - x^{2} + 24x + 7 $ x^5 - 10x^3 - x^2 + 24x + 7
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 406)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.20194$ of defining polynomial
Character	$\chi$	$=$	2842.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.515089 q^{3} +1.00000 q^{4} +3.68685 q^{5} +0.515089 q^{6} +1.00000 q^{8} -2.73468 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.515089 q^{3} +1.00000 q^{4} +3.68685 q^{5} +0.515089 q^{6} +1.00000 q^{8} -2.73468 q^{9} +3.68685 q^{10} +6.45172 q^{11} +0.515089 q^{12} +2.84856 q^{13} +1.89906 q^{15} +1.00000 q^{16} -1.53541 q^{17} -2.73468 q^{18} -3.91898 q^{19} +3.68685 q^{20} +6.45172 q^{22} +0.380892 q^{23} +0.515089 q^{24} +8.59290 q^{25} +2.84856 q^{26} -2.95387 q^{27} -1.00000 q^{29} +1.89906 q^{30} +7.98405 q^{31} +1.00000 q^{32} +3.32321 q^{33} -1.53541 q^{34} -2.73468 q^{36} -7.46896 q^{37} -3.91898 q^{38} +1.46726 q^{39} +3.68685 q^{40} -4.98713 q^{41} -11.5673 q^{43} +6.45172 q^{44} -10.0824 q^{45} +0.380892 q^{46} +7.85862 q^{47} +0.515089 q^{48} +8.59290 q^{50} -0.790874 q^{51} +2.84856 q^{52} -1.22186 q^{53} -2.95387 q^{54} +23.7865 q^{55} -2.01862 q^{57} -1.00000 q^{58} -0.696710 q^{59} +1.89906 q^{60} -3.10100 q^{61} +7.98405 q^{62} +1.00000 q^{64} +10.5022 q^{65} +3.32321 q^{66} -7.22494 q^{67} -1.53541 q^{68} +0.196193 q^{69} -13.2927 q^{71} -2.73468 q^{72} +14.9513 q^{73} -7.46896 q^{74} +4.42611 q^{75} -3.91898 q^{76} +1.46726 q^{78} +5.13590 q^{79} +3.68685 q^{80} +6.68254 q^{81} -4.98713 q^{82} +12.8154 q^{83} -5.66084 q^{85} -11.5673 q^{86} -0.515089 q^{87} +6.45172 q^{88} +9.39630 q^{89} -10.0824 q^{90} +0.380892 q^{92} +4.11250 q^{93} +7.85862 q^{94} -14.4487 q^{95} +0.515089 q^{96} -2.56729 q^{97} -17.6434 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 5 q^{2} + 3 q^{3} + 5 q^{4} + 7 q^{5} + 3 q^{6} + 5 q^{8} + 8 q^{9}+O(q^{10}) $ 5 * q + 5 * q^2 + 3 * q^3 + 5 * q^4 + 7 * q^5 + 3 * q^6 + 5 * q^8 + 8 * q^9	$ 5 q + 5 q^{2} + 3 q^{3} + 5 q^{4} + 7 q^{5} + 3 q^{6} + 5 q^{8} + 8 q^{9} + 7 q^{10} + 3 q^{12} + 10 q^{13} - 10 q^{15} + 5 q^{16} + 8 q^{17} + 8 q^{18} + 2 q^{19} + 7 q^{20} + q^{23} + 3 q^{24} + 12 q^{25} + 10 q^{26} + 15 q^{27} - 5 q^{29} - 10 q^{30} + 11 q^{31} + 5 q^{32} + 9 q^{33} + 8 q^{34} + 8 q^{36} - 8 q^{37} + 2 q^{38} + 18 q^{39} + 7 q^{40} + 23 q^{41} - 3 q^{43} + 4 q^{45} + q^{46} + 16 q^{47} + 3 q^{48} + 12 q^{50} + 7 q^{51} + 10 q^{52} + 7 q^{53} + 15 q^{54} + 6 q^{55} - 34 q^{57} - 5 q^{58} - 9 q^{59} - 10 q^{60} + 15 q^{61} + 11 q^{62} + 5 q^{64} + 5 q^{65} + 9 q^{66} - 4 q^{67} + 8 q^{68} + 14 q^{69} - 22 q^{71} + 8 q^{72} - 8 q^{74} - 34 q^{75} + 2 q^{76} + 18 q^{78} - 13 q^{79} + 7 q^{80} + 17 q^{81} + 23 q^{82} + 28 q^{83} - 7 q^{85} - 3 q^{86} - 3 q^{87} + 17 q^{89} + 4 q^{90} + q^{92} + 17 q^{93} + 16 q^{94} - 9 q^{95} + 3 q^{96} + 42 q^{97} - 42 q^{99}+O(q^{100}) $ 5 * q + 5 * q^2 + 3 * q^3 + 5 * q^4 + 7 * q^5 + 3 * q^6 + 5 * q^8 + 8 * q^9 + 7 * q^10 + 3 * q^12 + 10 * q^13 - 10 * q^15 + 5 * q^16 + 8 * q^17 + 8 * q^18 + 2 * q^19 + 7 * q^20 + q^23 + 3 * q^24 + 12 * q^25 + 10 * q^26 + 15 * q^27 - 5 * q^29 - 10 * q^30 + 11 * q^31 + 5 * q^32 + 9 * q^33 + 8 * q^34 + 8 * q^36 - 8 * q^37 + 2 * q^38 + 18 * q^39 + 7 * q^40 + 23 * q^41 - 3 * q^43 + 4 * q^45 + q^46 + 16 * q^47 + 3 * q^48 + 12 * q^50 + 7 * q^51 + 10 * q^52 + 7 * q^53 + 15 * q^54 + 6 * q^55 - 34 * q^57 - 5 * q^58 - 9 * q^59 - 10 * q^60 + 15 * q^61 + 11 * q^62 + 5 * q^64 + 5 * q^65 + 9 * q^66 - 4 * q^67 + 8 * q^68 + 14 * q^69 - 22 * q^71 + 8 * q^72 - 8 * q^74 - 34 * q^75 + 2 * q^76 + 18 * q^78 - 13 * q^79 + 7 * q^80 + 17 * q^81 + 23 * q^82 + 28 * q^83 - 7 * q^85 - 3 * q^86 - 3 * q^87 + 17 * q^89 + 4 * q^90 + q^92 + 17 * q^93 + 16 * q^94 - 9 * q^95 + 3 * q^96 + 42 * q^97 - 42 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0.515089	0.297387	0.148693	−	0.988883i	$-0.452493\pi$
$3$	0.515089	0.297387	0.148693	+	0.988883i	$0.452493\pi$
$4$	1.00000	0.500000
$5$	3.68685	1.64881	0.824406	−	0.565999i	$-0.191509\pi$
$5$	3.68685	1.64881	0.824406	+	0.565999i	$0.191509\pi$
$6$	0.515089	0.210284
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	−2.73468	−0.911561
$10$	3.68685	1.16589
$11$	6.45172	1.94527	0.972633	−	0.232348i	$-0.0746407\pi$
$11$	6.45172	1.94527	0.972633	+	0.232348i	$0.0746407\pi$
$12$	0.515089	0.148693
$13$	2.84856	0.790048	0.395024	−	0.918671i	$-0.370736\pi$
$13$	2.84856	0.790048	0.395024	+	0.918671i	$0.370736\pi$
$14$	0	0
$15$	1.89906	0.490335
$16$	1.00000	0.250000
$17$	−1.53541	−0.372392	−0.186196	−	0.982513i	$-0.559616\pi$
$17$	−1.53541	−0.372392	−0.186196	+	0.982513i	$0.559616\pi$
$18$	−2.73468	−0.644571
$19$	−3.91898	−0.899075	−0.449537	−	0.893261i	$-0.648411\pi$
$19$	−3.91898	−0.899075	−0.449537	+	0.893261i	$0.648411\pi$
$20$	3.68685	0.824406
$21$	0	0
$22$	6.45172	1.37551
$23$	0.380892	0.0794214	0.0397107	−	0.999211i	$-0.487356\pi$
$23$	0.380892	0.0794214	0.0397107	+	0.999211i	$0.487356\pi$
$24$	0.515089	0.105142
$25$	8.59290	1.71858
$26$	2.84856	0.558648
$27$	−2.95387	−0.568473
$28$	0	0
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	1.89906	0.346719
$31$	7.98405	1.43398	0.716989	−	0.697085i	$-0.245520\pi$
$31$	7.98405	1.43398	0.716989	+	0.697085i	$0.245520\pi$
$32$	1.00000	0.176777
$33$	3.32321	0.578496
$34$	−1.53541	−0.263321
$35$	0	0
$36$	−2.73468	−0.455781
$37$	−7.46896	−1.22789	−0.613945	−	0.789349i	$-0.710418\pi$
$37$	−7.46896	−1.22789	−0.613945	+	0.789349i	$0.710418\pi$
$38$	−3.91898	−0.635742
$39$	1.46726	0.234950
$40$	3.68685	0.582943
$41$	−4.98713	−0.778859	−0.389429	−	0.921056i	$-0.627328\pi$
$41$	−4.98713	−0.778859	−0.389429	+	0.921056i	$0.627328\pi$
$42$	0	0
$43$	−11.5673	−1.76400	−0.881998	−	0.471254i	$-0.843802\pi$
$43$	−11.5673	−1.76400	−0.881998	+	0.471254i	$0.843802\pi$
$44$	6.45172	0.972633
$45$	−10.0824	−1.50299
$46$	0.380892	0.0561594
$47$	7.85862	1.14630	0.573149	−	0.819451i	$-0.305722\pi$
$47$	7.85862	1.14630	0.573149	+	0.819451i	$0.305722\pi$
$48$	0.515089	0.0743467
$49$	0	0
$50$	8.59290	1.21522
$51$	−0.790874	−0.110745
$52$	2.84856	0.395024
$53$	−1.22186	−0.167836	−0.0839179	−	0.996473i	$-0.526743\pi$
$53$	−1.22186	−0.167836	−0.0839179	+	0.996473i	$0.526743\pi$
$54$	−2.95387	−0.401971
$55$	23.7865	3.20738
$56$	0	0
$57$	−2.01862	−0.267373
$58$	−1.00000	−0.131306
$59$	−0.696710	−0.0907039	−0.0453519	−	0.998971i	$-0.514441\pi$
$59$	−0.696710	−0.0907039	−0.0453519	+	0.998971i	$0.514441\pi$
$60$	1.89906	0.245167
$61$	−3.10100	−0.397043	−0.198521	−	0.980097i	$-0.563614\pi$
$61$	−3.10100	−0.397043	−0.198521	+	0.980097i	$0.563614\pi$
$62$	7.98405	1.01398
$63$	0	0
$64$	1.00000	0.125000
$65$	10.5022	1.30264
$66$	3.32321	0.409059
$67$	−7.22494	−0.882667	−0.441333	−	0.897343i	$-0.645494\pi$
$67$	−7.22494	−0.882667	−0.441333	+	0.897343i	$0.645494\pi$
$68$	−1.53541	−0.186196
$69$	0.196193	0.0236189
$70$	0	0
$71$	−13.2927	−1.57755	−0.788776	−	0.614681i	$-0.789285\pi$
$71$	−13.2927	−1.57755	−0.788776	+	0.614681i	$0.789285\pi$
$72$	−2.73468	−0.322286
$73$	14.9513	1.74991	0.874956	−	0.484202i	$-0.160890\pi$
$73$	14.9513	1.74991	0.874956	+	0.484202i	$0.160890\pi$
$74$	−7.46896	−0.868249
$75$	4.42611	0.511083
$76$	−3.91898	−0.449537
$77$	0	0
$78$	1.46726	0.166135
$79$	5.13590	0.577834	0.288917	−	0.957354i	$-0.406705\pi$
$79$	5.13590	0.577834	0.288917	+	0.957354i	$0.406705\pi$
$80$	3.68685	0.412203
$81$	6.68254	0.742505
$82$	−4.98713	−0.550736
$83$	12.8154	1.40667	0.703334	−	0.710859i	$-0.251694\pi$
$83$	12.8154	1.40667	0.703334	+	0.710859i	$0.251694\pi$
$84$	0	0
$85$	−5.66084	−0.614005
$86$	−11.5673	−1.24733
$87$	−0.515089	−0.0552233
$88$	6.45172	0.687755
$89$	9.39630	0.996006	0.498003	−	0.867175i	$-0.334067\pi$
$89$	9.39630	0.996006	0.498003	+	0.867175i	$0.334067\pi$
$90$	−10.0824	−1.06278
$91$	0	0
$92$	0.380892	0.0397107
$93$	4.11250	0.426446
$94$	7.85862	0.810555
$95$	−14.4487	−1.48241
$96$	0.515089	0.0525711
$97$	−2.56729	−0.260669	−0.130334	−	0.991470i	$-0.541605\pi$
$97$	−2.56729	−0.260669	−0.130334	+	0.991470i	$0.541605\pi$
$98$	0	0
$99$	−17.6434	−1.77323
$100$	8.59290	0.859290
$101$	−10.0344	−0.998456	−0.499228	−	0.866471i	$-0.666383\pi$
$101$	−10.0344	−0.998456	−0.499228	+	0.866471i	$0.666383\pi$
$102$	−0.790874	−0.0783082
$103$	−9.34353	−0.920646	−0.460323	−	0.887752i	$-0.652266\pi$
$103$	−9.34353	−0.920646	−0.460323	+	0.887752i	$0.652266\pi$
$104$	2.84856	0.279324
$105$	0	0
$106$	−1.22186	−0.118678
$107$	−11.7990	−1.14065	−0.570327	−	0.821418i	$-0.693183\pi$
$107$	−11.7990	−1.14065	−0.570327	+	0.821418i	$0.693183\pi$
$108$	−2.95387	−0.284237
$109$	−6.05447	−0.579913	−0.289957	−	0.957040i	$-0.593641\pi$
$109$	−6.05447	−0.579913	−0.289957	+	0.957040i	$0.593641\pi$
$110$	23.7865	2.26796
$111$	−3.84718	−0.365158
$112$	0	0
$113$	−3.50810	−0.330015	−0.165007	−	0.986292i	$-0.552765\pi$
$113$	−3.50810	−0.330015	−0.165007	+	0.986292i	$0.552765\pi$
$114$	−2.01862	−0.189061
$115$	1.40429	0.130951
$116$	−1.00000	−0.0928477
$117$	−7.78990	−0.720177
$118$	−0.696710	−0.0641373
$119$	0	0
$120$	1.89906	0.173360
$121$	30.6246	2.78406
$122$	−3.10100	−0.280752
$123$	−2.56882	−0.231622
$124$	7.98405	0.716989
$125$	13.2465	1.18480
$126$	0	0
$127$	2.64032	0.234291	0.117145	−	0.993115i	$-0.462626\pi$
$127$	2.64032	0.234291	0.117145	+	0.993115i	$0.462626\pi$
$128$	1.00000	0.0883883
$129$	−5.95819	−0.524589
$130$	10.5022	0.921105
$131$	−10.7569	−0.939832	−0.469916	−	0.882711i	$-0.655716\pi$
$131$	−10.7569	−0.939832	−0.469916	+	0.882711i	$0.655716\pi$
$132$	3.32321	0.289248
$133$	0	0
$134$	−7.22494	−0.624140
$135$	−10.8905	−0.937305
$136$	−1.53541	−0.131661
$137$	8.47238	0.723845	0.361922	−	0.932208i	$-0.382121\pi$
$137$	8.47238	0.723845	0.361922	+	0.932208i	$0.382121\pi$
$138$	0.196193	0.0167011
$139$	−2.40081	−0.203634	−0.101817	−	0.994803i	$-0.532466\pi$
$139$	−2.40081	−0.203634	−0.101817	+	0.994803i	$0.532466\pi$
$140$	0	0
$141$	4.04789	0.340894
$142$	−13.2927	−1.11550
$143$	18.3781	1.53685
$144$	−2.73468	−0.227890
$145$	−3.68685	−0.306177
$146$	14.9513	1.23738
$147$	0	0
$148$	−7.46896	−0.613945
$149$	−10.3750	−0.849954	−0.424977	−	0.905204i	$-0.639718\pi$
$149$	−10.3750	−0.849954	−0.424977	+	0.905204i	$0.639718\pi$
$150$	4.42611	0.361390
$151$	6.75687	0.549866	0.274933	−	0.961463i	$-0.411344\pi$
$151$	6.75687	0.549866	0.274933	+	0.961463i	$0.411344\pi$
$152$	−3.91898	−0.317871
$153$	4.19887	0.339458
$154$	0	0
$155$	29.4360	2.36436
$156$	1.46726	0.117475
$157$	−3.89720	−0.311030	−0.155515	−	0.987834i	$-0.549704\pi$
$157$	−3.89720	−0.311030	−0.155515	+	0.987834i	$0.549704\pi$
$158$	5.13590	0.408590
$159$	−0.629368	−0.0499121
$160$	3.68685	0.291471
$161$	0	0
$162$	6.68254	0.525030
$163$	0.389316	0.0304935	0.0152468	−	0.999884i	$-0.495147\pi$
$163$	0.389316	0.0304935	0.0152468	+	0.999884i	$0.495147\pi$
$164$	−4.98713	−0.389429
$165$	12.2522	0.953832
$166$	12.8154	0.994665
$167$	10.3042	0.797362	0.398681	−	0.917090i	$-0.369468\pi$
$167$	10.3042	0.797362	0.398681	+	0.917090i	$0.369468\pi$
$168$	0	0
$169$	−4.88572	−0.375825
$170$	−5.66084	−0.434167
$171$	10.7172	0.819562
$172$	−11.5673	−0.881998
$173$	23.0407	1.75175	0.875876	−	0.482536i	$-0.160284\pi$
$173$	23.0407	1.75175	0.875876	+	0.482536i	$0.160284\pi$
$174$	−0.515089	−0.0390488
$175$	0	0
$176$	6.45172	0.486316
$177$	−0.358868	−0.0269741
$178$	9.39630	0.704283
$179$	−6.69801	−0.500632	−0.250316	−	0.968164i	$-0.580535\pi$
$179$	−6.69801	−0.500632	−0.250316	+	0.968164i	$0.580535\pi$
$180$	−10.0824	−0.751496
$181$	13.2453	0.984513	0.492256	−	0.870450i	$-0.336172\pi$
$181$	13.2453	0.984513	0.492256	+	0.870450i	$0.336172\pi$
$182$	0	0
$183$	−1.59729	−0.118075
$184$	0.380892	0.0280797
$185$	−27.5370	−2.02456
$186$	4.11250	0.301543
$187$	−9.90604	−0.724402
$188$	7.85862	0.573149
$189$	0	0
$190$	−14.4487	−1.04822
$191$	−20.3346	−1.47136	−0.735681	−	0.677328i	$-0.763138\pi$
$191$	−20.3346	−1.47136	−0.735681	+	0.677328i	$0.763138\pi$
$192$	0.515089	0.0371734
$193$	13.2040	0.950448	0.475224	−	0.879865i	$-0.342367\pi$
$193$	13.2040	0.950448	0.475224	+	0.879865i	$0.342367\pi$
$194$	−2.56729	−0.184321
$195$	5.40958	0.387388
$196$	0	0
$197$	−9.01237	−0.642104	−0.321052	−	0.947061i	$-0.604037\pi$
$197$	−9.01237	−0.642104	−0.321052	+	0.947061i	$0.604037\pi$
$198$	−17.6434	−1.25386
$199$	−5.86360	−0.415659	−0.207830	−	0.978165i	$-0.566640\pi$
$199$	−5.86360	−0.415659	−0.207830	+	0.978165i	$0.566640\pi$
$200$	8.59290	0.607610
$201$	−3.72149	−0.262494
$202$	−10.0344	−0.706015
$203$	0	0
$204$	−0.790874	−0.0553723
$205$	−18.3868	−1.28419
$206$	−9.34353	−0.650995
$207$	−1.04162	−0.0723975
$208$	2.84856	0.197512
$209$	−25.2841	−1.74894
$210$	0	0
$211$	20.9741	1.44391	0.721957	−	0.691938i	$-0.243243\pi$
$211$	20.9741	1.44391	0.721957	+	0.691938i	$0.243243\pi$
$212$	−1.22186	−0.0839179
$213$	−6.84692	−0.469143
$214$	−11.7990	−0.806564
$215$	−42.6469	−2.90850
$216$	−2.95387	−0.200986
$217$	0	0
$218$	−6.05447	−0.410060
$219$	7.70123	0.520401
$220$	23.7865	1.60369
$221$	−4.37371	−0.294208
$222$	−3.84718	−0.258206
$223$	−1.10629	−0.0740825	−0.0370412	−	0.999314i	$-0.511793\pi$
$223$	−1.10629	−0.0740825	−0.0370412	+	0.999314i	$0.511793\pi$
$224$	0	0
$225$	−23.4989	−1.56659
$226$	−3.50810	−0.233356
$227$	−0.869629	−0.0577193	−0.0288596	−	0.999583i	$-0.509188\pi$
$227$	−0.869629	−0.0577193	−0.0288596	+	0.999583i	$0.509188\pi$
$228$	−2.01862	−0.133687
$229$	−7.00356	−0.462809	−0.231404	−	0.972858i	$-0.574332\pi$
$229$	−7.00356	−0.462809	−0.231404	+	0.972858i	$0.574332\pi$
$230$	1.40429	0.0925963
$231$	0	0
$232$	−1.00000	−0.0656532
$233$	0.411278	0.0269437	0.0134719	−	0.999909i	$-0.495712\pi$
$233$	0.411278	0.0269437	0.0134719	+	0.999909i	$0.495712\pi$
$234$	−7.78990	−0.509242
$235$	28.9736	1.89003
$236$	−0.696710	−0.0453519
$237$	2.64545	0.171840
$238$	0	0
$239$	−12.6415	−0.817713	−0.408857	−	0.912599i	$-0.634072\pi$
$239$	−12.6415	−0.817713	−0.408857	+	0.912599i	$0.634072\pi$
$240$	1.89906	0.122584
$241$	20.9092	1.34688	0.673439	−	0.739242i	$-0.264816\pi$
$241$	20.9092	1.34688	0.673439	+	0.739242i	$0.264816\pi$
$242$	30.6246	1.96863
$243$	12.3037	0.789284
$244$	−3.10100	−0.198521
$245$	0	0
$246$	−2.56882	−0.163782
$247$	−11.1634	−0.710312
$248$	7.98405	0.506988
$249$	6.60105	0.418325
$250$	13.2465	0.837782
$251$	−23.2297	−1.46624	−0.733121	−	0.680098i	$-0.761937\pi$
$251$	−23.2297	−1.46624	−0.733121	+	0.680098i	$0.761937\pi$
$252$	0	0
$253$	2.45741	0.154496
$254$	2.64032	0.165669
$255$	−2.91584	−0.182597
$256$	1.00000	0.0625000
$257$	−15.5148	−0.967784	−0.483892	−	0.875128i	$-0.660777\pi$
$257$	−15.5148	−0.967784	−0.483892	+	0.875128i	$0.660777\pi$
$258$	−5.95819	−0.370940
$259$	0	0
$260$	10.5022	0.651320
$261$	2.73468	0.169273
$262$	−10.7569	−0.664562
$263$	−2.94512	−0.181604	−0.0908021	−	0.995869i	$-0.528943\pi$
$263$	−2.94512	−0.181604	−0.0908021	+	0.995869i	$0.528943\pi$
$264$	3.32321	0.204529
$265$	−4.50483	−0.276729
$266$	0	0
$267$	4.83993	0.296199
$268$	−7.22494	−0.441333
$269$	−6.76917	−0.412724	−0.206362	−	0.978476i	$-0.566162\pi$
$269$	−6.76917	−0.412724	−0.206362	+	0.978476i	$0.566162\pi$
$270$	−10.8905	−0.662775
$271$	16.8757	1.02513	0.512564	−	0.858649i	$-0.328696\pi$
$271$	16.8757	1.02513	0.512564	+	0.858649i	$0.328696\pi$
$272$	−1.53541	−0.0930980
$273$	0	0
$274$	8.47238	0.511835
$275$	55.4389	3.34309
$276$	0.196193	0.0118094
$277$	26.3155	1.58115	0.790573	−	0.612368i	$-0.209783\pi$
$277$	26.3155	1.58115	0.790573	+	0.612368i	$0.209783\pi$
$278$	−2.40081	−0.143991
$279$	−21.8338	−1.30716
$280$	0	0
$281$	0.662563	0.0395252	0.0197626	−	0.999805i	$-0.493709\pi$
$281$	0.662563	0.0395252	0.0197626	+	0.999805i	$0.493709\pi$
$282$	4.04789	0.241048
$283$	−24.9296	−1.48191	−0.740955	−	0.671555i	$-0.765627\pi$
$283$	−24.9296	−1.48191	−0.740955	+	0.671555i	$0.765627\pi$
$284$	−13.2927	−0.788776
$285$	−7.44237	−0.440848
$286$	18.3781	1.08672
$287$	0	0
$288$	−2.73468	−0.161143
$289$	−14.6425	−0.861324
$290$	−3.68685	−0.216500
$291$	−1.32238	−0.0775195
$292$	14.9513	0.874956
$293$	9.98069	0.583078	0.291539	−	0.956559i	$-0.405833\pi$
$293$	9.98069	0.583078	0.291539	+	0.956559i	$0.405833\pi$
$294$	0	0
$295$	−2.56867	−0.149554
$296$	−7.46896	−0.434125
$297$	−19.0575	−1.10583
$298$	−10.3750	−0.601008
$299$	1.08499	0.0627467
$300$	4.42611	0.255541
$301$	0	0
$302$	6.75687	0.388814
$303$	−5.16859	−0.296928
$304$	−3.91898	−0.224769
$305$	−11.4329	−0.654649
$306$	4.19887	0.240033
$307$	−2.78572	−0.158990	−0.0794948	−	0.996835i	$-0.525331\pi$
$307$	−2.78572	−0.158990	−0.0794948	+	0.996835i	$0.525331\pi$
$308$	0	0
$309$	−4.81275	−0.273788
$310$	29.4360	1.67185
$311$	15.2581	0.865209	0.432605	−	0.901584i	$-0.357595\pi$
$311$	15.2581	0.865209	0.432605	+	0.901584i	$0.357595\pi$
$312$	1.46726	0.0830673
$313$	34.3024	1.93889	0.969443	−	0.245318i	$-0.0788922\pi$
$313$	34.3024	1.93889	0.969443	+	0.245318i	$0.0788922\pi$
$314$	−3.89720	−0.219931
$315$	0	0
$316$	5.13590	0.288917
$317$	−23.5203	−1.32103	−0.660516	−	0.750812i	$-0.729662\pi$
$317$	−23.5203	−1.32103	−0.660516	+	0.750812i	$0.729662\pi$
$318$	−0.629368	−0.0352932
$319$	−6.45172	−0.361227
$320$	3.68685	0.206101
$321$	−6.07754	−0.339215
$322$	0	0
$323$	6.01725	0.334808
$324$	6.68254	0.371252
$325$	24.4774	1.35776
$326$	0.389316	0.0215622
$327$	−3.11859	−0.172459
$328$	−4.98713	−0.275368
$329$	0	0
$330$	12.2522	0.674461
$331$	−20.9170	−1.14970	−0.574851	−	0.818258i	$-0.694940\pi$
$331$	−20.9170	−1.14970	−0.574851	+	0.818258i	$0.694940\pi$
$332$	12.8154	0.703334
$333$	20.4252	1.11930
$334$	10.3042	0.563820
$335$	−26.6373	−1.45535
$336$	0	0
$337$	35.1825	1.91651	0.958256	−	0.285910i	$-0.0922959\pi$
$337$	35.1825	1.91651	0.958256	+	0.285910i	$0.0922959\pi$
$338$	−4.88572	−0.265748
$339$	−1.80699	−0.0981420
$340$	−5.66084	−0.307002
$341$	51.5108	2.78947
$342$	10.7172	0.579518
$343$	0	0
$344$	−11.5673	−0.623667
$345$	0.723336	0.0389431
$346$	23.0407	1.23868
$347$	−14.8661	−0.798053	−0.399026	−	0.916939i	$-0.630652\pi$
$347$	−14.8661	−0.798053	−0.399026	+	0.916939i	$0.630652\pi$
$348$	−0.515089	−0.0276117
$349$	−20.1456	−1.07837	−0.539185	−	0.842187i	$-0.681268\pi$
$349$	−20.1456	−1.07837	−0.539185	+	0.842187i	$0.681268\pi$
$350$	0	0
$351$	−8.41428	−0.449121
$352$	6.45172	0.343878
$353$	−9.55582	−0.508605	−0.254302	−	0.967125i	$-0.581846\pi$
$353$	−9.55582	−0.508605	−0.254302	+	0.967125i	$0.581846\pi$
$354$	−0.358868	−0.0190736
$355$	−49.0082	−2.60109
$356$	9.39630	0.498003
$357$	0	0
$358$	−6.69801	−0.354001
$359$	12.6878	0.669637	0.334818	−	0.942283i	$-0.391325\pi$
$359$	12.6878	0.669637	0.334818	+	0.942283i	$0.391325\pi$
$360$	−10.0824	−0.531388
$361$	−3.64162	−0.191664
$362$	13.2453	0.696156
$363$	15.7744	0.827942
$364$	0	0
$365$	55.1231	2.88528
$366$	−1.59729	−0.0834918
$367$	−33.0253	−1.72391	−0.861953	−	0.506989i	$-0.830759\pi$
$367$	−33.0253	−1.72391	−0.861953	+	0.506989i	$0.830759\pi$
$368$	0.380892	0.0198554
$369$	13.6382	0.709977
$370$	−27.5370	−1.43158
$371$	0	0
$372$	4.11250	0.213223
$373$	−19.9474	−1.03284	−0.516420	−	0.856336i	$-0.672735\pi$
$373$	−19.9474	−1.03284	−0.516420	+	0.856336i	$0.672735\pi$
$374$	−9.90604	−0.512229
$375$	6.82313	0.352345
$376$	7.85862	0.405277
$377$	−2.84856	−0.146708
$378$	0	0
$379$	27.8725	1.43171	0.715857	−	0.698247i	$-0.246036\pi$
$379$	27.8725	1.43171	0.715857	+	0.698247i	$0.246036\pi$
$380$	−14.4487	−0.741203
$381$	1.36000	0.0696750
$382$	−20.3346	−1.04041
$383$	21.1598	1.08122	0.540609	−	0.841274i	$-0.318194\pi$
$383$	21.1598	1.08122	0.540609	+	0.841274i	$0.318194\pi$
$384$	0.515089	0.0262855
$385$	0	0
$386$	13.2040	0.672068
$387$	31.6329	1.60799
$388$	−2.56729	−0.130334
$389$	8.79804	0.446078	0.223039	−	0.974810i	$-0.428402\pi$
$389$	8.79804	0.446078	0.223039	+	0.974810i	$0.428402\pi$
$390$	5.40958	0.273925
$391$	−0.584826	−0.0295759
$392$	0	0
$393$	−5.54075	−0.279494
$394$	−9.01237	−0.454036
$395$	18.9353	0.952739
$396$	−17.6434	−0.886614
$397$	−7.58413	−0.380637	−0.190318	−	0.981722i	$-0.560952\pi$
$397$	−7.58413	−0.380637	−0.190318	+	0.981722i	$0.560952\pi$
$398$	−5.86360	−0.293916
$399$	0	0
$400$	8.59290	0.429645
$401$	11.8271	0.590616	0.295308	−	0.955402i	$-0.404578\pi$
$401$	11.8271	0.590616	0.295308	+	0.955402i	$0.404578\pi$
$402$	−3.72149	−0.185611
$403$	22.7430	1.13291
$404$	−10.0344	−0.499228
$405$	24.6376	1.22425
$406$	0	0
$407$	−48.1876	−2.38857
$408$	−0.790874	−0.0391541
$409$	11.8506	0.585975	0.292987	−	0.956116i	$-0.405351\pi$
$409$	11.8506	0.585975	0.292987	+	0.956116i	$0.405351\pi$
$410$	−18.3868	−0.908060
$411$	4.36403	0.215262
$412$	−9.34353	−0.460323
$413$	0	0
$414$	−1.04162	−0.0511928
$415$	47.2484	2.31933
$416$	2.84856	0.139662
$417$	−1.23663	−0.0605581
$418$	−25.2841	−1.23669
$419$	0.933145	0.0455871	0.0227935	−	0.999740i	$-0.492744\pi$
$419$	0.933145	0.0455871	0.0227935	+	0.999740i	$0.492744\pi$
$420$	0	0
$421$	−3.17478	−0.154729	−0.0773647	−	0.997003i	$-0.524651\pi$
$421$	−3.17478	−0.154729	−0.0773647	+	0.997003i	$0.524651\pi$
$422$	20.9741	1.02100
$423$	−21.4908	−1.04492
$424$	−1.22186	−0.0593389
$425$	−13.1936	−0.639986
$426$	−6.84692	−0.331734
$427$	0	0
$428$	−11.7990	−0.570327
$429$	9.46635	0.457040
$430$	−42.6469	−2.05662
$431$	−25.2882	−1.21809	−0.609044	−	0.793137i	$-0.708447\pi$
$431$	−25.2882	−1.21809	−0.609044	+	0.793137i	$0.708447\pi$
$432$	−2.95387	−0.142118
$433$	25.3900	1.22017	0.610084	−	0.792337i	$-0.291136\pi$
$433$	25.3900	1.22017	0.610084	+	0.792337i	$0.291136\pi$
$434$	0	0
$435$	−1.89906	−0.0910529
$436$	−6.05447	−0.289957
$437$	−1.49271	−0.0714058
$438$	7.70123	0.367979
$439$	−9.95941	−0.475337	−0.237668	−	0.971346i	$-0.576383\pi$
$439$	−9.95941	−0.475337	−0.237668	+	0.971346i	$0.576383\pi$
$440$	23.7865	1.13398
$441$	0	0
$442$	−4.37371	−0.208036
$443$	−9.69053	−0.460411	−0.230206	−	0.973142i	$-0.573940\pi$
$443$	−9.69053	−0.460411	−0.230206	+	0.973142i	$0.573940\pi$
$444$	−3.84718	−0.182579
$445$	34.6428	1.64223
$446$	−1.10629	−0.0523842
$447$	−5.34405	−0.252765
$448$	0	0
$449$	13.7314	0.648025	0.324013	−	0.946053i	$-0.394968\pi$
$449$	13.7314	0.648025	0.324013	+	0.946053i	$0.394968\pi$
$450$	−23.4989	−1.10775
$451$	−32.1755	−1.51509
$452$	−3.50810	−0.165007
$453$	3.48039	0.163523
$454$	−0.869629	−0.0408137
$455$	0	0
$456$	−2.01862	−0.0945306
$457$	12.3389	0.577188	0.288594	−	0.957452i	$-0.406812\pi$
$457$	12.3389	0.577188	0.288594	+	0.957452i	$0.406812\pi$
$458$	−7.00356	−0.327255
$459$	4.53541	0.211695
$460$	1.40429	0.0654755
$461$	−11.8322	−0.551081	−0.275540	−	0.961290i	$-0.588857\pi$
$461$	−11.8322	−0.551081	−0.275540	+	0.961290i	$0.588857\pi$
$462$	0	0
$463$	−30.3189	−1.40904	−0.704519	−	0.709685i	$-0.748837\pi$
$463$	−30.3189	−1.40904	−0.704519	+	0.709685i	$0.748837\pi$
$464$	−1.00000	−0.0464238
$465$	15.1622	0.703129
$466$	0.411278	0.0190521
$467$	−8.31097	−0.384586	−0.192293	−	0.981338i	$-0.561592\pi$
$467$	−8.31097	−0.384586	−0.192293	+	0.981338i	$0.561592\pi$
$468$	−7.78990	−0.360088
$469$	0	0
$470$	28.9736	1.33645
$471$	−2.00740	−0.0924962
$472$	−0.696710	−0.0320687
$473$	−74.6289	−3.43144
$474$	2.64545	0.121509
$475$	−33.6754	−1.54513
$476$	0	0
$477$	3.34141	0.152992
$478$	−12.6415	−0.578210
$479$	31.3096	1.43057	0.715286	−	0.698832i	$-0.246297\pi$
$479$	31.3096	1.43057	0.715286	+	0.698832i	$0.246297\pi$
$480$	1.89906	0.0866798
$481$	−21.2758	−0.970091
$482$	20.9092	0.952387
$483$	0	0
$484$	30.6246	1.39203
$485$	−9.46523	−0.429794
$486$	12.3037	0.558108
$487$	−21.7094	−0.983748	−0.491874	−	0.870666i	$-0.663688\pi$
$487$	−21.7094	−0.983748	−0.491874	+	0.870666i	$0.663688\pi$
$488$	−3.10100	−0.140376
$489$	0.200532	0.00906838
$490$	0	0
$491$	−28.6142	−1.29134	−0.645670	−	0.763616i	$-0.723422\pi$
$491$	−28.6142	−1.29134	−0.645670	+	0.763616i	$0.723422\pi$
$492$	−2.56882	−0.115811
$493$	1.53541	0.0691515
$494$	−11.1634	−0.502266
$495$	−65.0487	−2.92372
$496$	7.98405	0.358494
$497$	0	0
$498$	6.60105	0.295800
$499$	−22.3287	−0.999572	−0.499786	−	0.866149i	$-0.666588\pi$
$499$	−22.3287	−0.999572	−0.499786	+	0.866149i	$0.666588\pi$
$500$	13.2465	0.592401
$501$	5.30757	0.237125
$502$	−23.2297	−1.03679
$503$	−13.7215	−0.611810	−0.305905	−	0.952062i	$-0.598959\pi$
$503$	−13.7215	−0.611810	−0.305905	+	0.952062i	$0.598959\pi$
$504$	0	0
$505$	−36.9952	−1.64627
$506$	2.45741	0.109245
$507$	−2.51658	−0.111765
$508$	2.64032	0.117145
$509$	−6.80605	−0.301673	−0.150836	−	0.988559i	$-0.548197\pi$
$509$	−6.80605	−0.301673	−0.150836	+	0.988559i	$0.548197\pi$
$510$	−2.91584	−0.129115
$511$	0	0
$512$	1.00000	0.0441942
$513$	11.5762	0.511100
$514$	−15.5148	−0.684327
$515$	−34.4482	−1.51797
$516$	−5.95819	−0.262294
$517$	50.7016	2.22985
$518$	0	0
$519$	11.8680	0.520948
$520$	10.5022	0.460553
$521$	5.55924	0.243555	0.121777	−	0.992557i	$-0.461141\pi$
$521$	5.55924	0.243555	0.121777	+	0.992557i	$0.461141\pi$
$522$	2.73468	0.119694
$523$	−12.0800	−0.528221	−0.264111	−	0.964492i	$-0.585078\pi$
$523$	−12.0800	−0.528221	−0.264111	+	0.964492i	$0.585078\pi$
$524$	−10.7569	−0.469916
$525$	0	0
$526$	−2.94512	−0.128414
$527$	−12.2588	−0.534002
$528$	3.32321	0.144624
$529$	−22.8549	−0.993692
$530$	−4.50483	−0.195677
$531$	1.90528	0.0826821
$532$	0	0
$533$	−14.2061	−0.615335
$534$	4.83993	0.209444
$535$	−43.5012	−1.88072
$536$	−7.22494	−0.312070
$537$	−3.45007	−0.148881
$538$	−6.76917	−0.291840
$539$	0	0
$540$	−10.8905	−0.468652
$541$	28.3762	1.21999	0.609994	−	0.792406i	$-0.291172\pi$
$541$	28.3762	1.21999	0.609994	+	0.792406i	$0.291172\pi$
$542$	16.8757	0.724875
$543$	6.82249	0.292781
$544$	−1.53541	−0.0658303
$545$	−22.3220	−0.956167
$546$	0	0
$547$	−19.5396	−0.835455	−0.417727	−	0.908572i	$-0.637173\pi$
$547$	−19.5396	−0.835455	−0.417727	+	0.908572i	$0.637173\pi$
$548$	8.47238	0.361922
$549$	8.48026	0.361929
$550$	55.4389	2.36392
$551$	3.91898	0.166954
$552$	0.196193	0.00835054
$553$	0	0
$554$	26.3155	1.11804
$555$	−14.1840	−0.602077
$556$	−2.40081	−0.101817
$557$	16.2974	0.690543	0.345272	−	0.938503i	$-0.387787\pi$
$557$	16.2974	0.690543	0.345272	+	0.938503i	$0.387787\pi$
$558$	−21.8338	−0.924301
$559$	−32.9501	−1.39364
$560$	0	0
$561$	−5.10250	−0.215428
$562$	0.662563	0.0279485
$563$	−13.8524	−0.583810	−0.291905	−	0.956447i	$-0.594289\pi$
$563$	−13.8524	−0.583810	−0.291905	+	0.956447i	$0.594289\pi$
$564$	4.04789	0.170447
$565$	−12.9339	−0.544132
$566$	−24.9296	−1.04787
$567$	0	0
$568$	−13.2927	−0.557749
$569$	−40.4417	−1.69541	−0.847703	−	0.530472i	$-0.822015\pi$
$569$	−40.4417	−1.69541	−0.847703	+	0.530472i	$0.822015\pi$
$570$	−7.44237	−0.311726
$571$	18.8558	0.789091	0.394546	−	0.918876i	$-0.370902\pi$
$571$	18.8558	0.789091	0.394546	+	0.918876i	$0.370902\pi$
$572$	18.3781	0.768426
$573$	−10.4741	−0.437564
$574$	0	0
$575$	3.27296	0.136492
$576$	−2.73468	−0.113945
$577$	−18.4743	−0.769095	−0.384548	−	0.923105i	$-0.625643\pi$
$577$	−18.4743	−0.769095	−0.384548	+	0.923105i	$0.625643\pi$
$578$	−14.6425	−0.609048
$579$	6.80126	0.282651
$580$	−3.68685	−0.153088
$581$	0	0
$582$	−1.32238	−0.0548146
$583$	−7.88311	−0.326485
$584$	14.9513	0.618688
$585$	−28.7202	−1.18744
$586$	9.98069	0.412299
$587$	29.5731	1.22061	0.610306	−	0.792166i	$-0.291046\pi$
$587$	29.5731	1.22061	0.610306	+	0.792166i	$0.291046\pi$
$588$	0	0
$589$	−31.2893	−1.28925
$590$	−2.56867	−0.105750
$591$	−4.64217	−0.190953
$592$	−7.46896	−0.306972
$593$	35.5469	1.45974	0.729869	−	0.683587i	$-0.239581\pi$
$593$	35.5469	1.45974	0.729869	+	0.683587i	$0.239581\pi$
$594$	−19.0575	−0.781941
$595$	0	0
$596$	−10.3750	−0.424977
$597$	−3.02027	−0.123612
$598$	1.08499	0.0443686
$599$	−1.11873	−0.0457099	−0.0228550	−	0.999739i	$-0.507276\pi$
$599$	−1.11873	−0.0457099	−0.0228550	+	0.999739i	$0.507276\pi$
$600$	4.42611	0.180695
$601$	−5.46816	−0.223051	−0.111525	−	0.993762i	$-0.535574\pi$
$601$	−5.46816	−0.223051	−0.111525	+	0.993762i	$0.535574\pi$
$602$	0	0
$603$	19.7579	0.804605
$604$	6.75687	0.274933
$605$	112.909	4.59039
$606$	−5.16859	−0.209959
$607$	−24.0318	−0.975421	−0.487710	−	0.873006i	$-0.662168\pi$
$607$	−24.0318	−0.975421	−0.487710	+	0.873006i	$0.662168\pi$
$608$	−3.91898	−0.158936
$609$	0	0
$610$	−11.4329	−0.462906
$611$	22.3857	0.905630
$612$	4.19887	0.169729
$613$	11.9080	0.480958	0.240479	−	0.970654i	$-0.422695\pi$
$613$	11.9080	0.480958	0.240479	+	0.970654i	$0.422695\pi$
$614$	−2.78572	−0.112423
$615$	−9.47085	−0.381902
$616$	0	0
$617$	−40.3723	−1.62533	−0.812664	−	0.582733i	$-0.801983\pi$
$617$	−40.3723	−1.62533	−0.812664	+	0.582733i	$0.801983\pi$
$618$	−4.81275	−0.193597
$619$	−25.7432	−1.03471	−0.517353	−	0.855772i	$-0.673082\pi$
$619$	−25.7432	−1.03471	−0.517353	+	0.855772i	$0.673082\pi$
$620$	29.4360	1.18218
$621$	−1.12511	−0.0451489
$622$	15.2581	0.611795
$623$	0	0
$624$	1.46726	0.0587374
$625$	5.87342	0.234937
$626$	34.3024	1.37100
$627$	−13.0236	−0.520112
$628$	−3.89720	−0.155515
$629$	11.4679	0.457257
$630$	0	0
$631$	26.6745	1.06189	0.530947	−	0.847405i	$-0.321836\pi$
$631$	26.6745	1.06189	0.530947	+	0.847405i	$0.321836\pi$
$632$	5.13590	0.204295
$633$	10.8035	0.429401
$634$	−23.5203	−0.934110
$635$	9.73449	0.386301
$636$	−0.629368	−0.0249561
$637$	0	0
$638$	−6.45172	−0.255426
$639$	36.3513	1.43803
$640$	3.68685	0.145736
$641$	23.3821	0.923538	0.461769	−	0.887000i	$-0.347215\pi$
$641$	23.3821	0.923538	0.461769	+	0.887000i	$0.347215\pi$
$642$	−6.07754	−0.239861
$643$	−5.26893	−0.207786	−0.103893	−	0.994588i	$-0.533130\pi$
$643$	−5.26893	−0.207786	−0.103893	+	0.994588i	$0.533130\pi$
$644$	0	0
$645$	−21.9670	−0.864948
$646$	6.01725	0.236745
$647$	10.4615	0.411286	0.205643	−	0.978627i	$-0.434071\pi$
$647$	10.4615	0.411286	0.205643	+	0.978627i	$0.434071\pi$
$648$	6.68254	0.262515
$649$	−4.49497	−0.176443
$650$	24.4774	0.960081
$651$	0	0
$652$	0.389316	0.0152468
$653$	12.6550	0.495229	0.247615	−	0.968859i	$-0.420353\pi$
$653$	12.6550	0.495229	0.247615	+	0.968859i	$0.420353\pi$
$654$	−3.11859	−0.121947
$655$	−39.6590	−1.54961
$656$	−4.98713	−0.194715
$657$	−40.8870	−1.59515
$658$	0	0
$659$	27.0561	1.05396	0.526978	−	0.849879i	$-0.323325\pi$
$659$	27.0561	1.05396	0.526978	+	0.849879i	$0.323325\pi$
$660$	12.2522	0.476916
$661$	−21.1950	−0.824389	−0.412194	−	0.911096i	$-0.635238\pi$
$661$	−21.1950	−0.824389	−0.412194	+	0.911096i	$0.635238\pi$
$662$	−20.9170	−0.812961
$663$	−2.25285	−0.0874934
$664$	12.8154	0.497333
$665$	0	0
$666$	20.4252	0.791462
$667$	−0.380892	−0.0147482
$668$	10.3042	0.398681
$669$	−0.569837	−0.0220312
$670$	−26.6373	−1.02909
$671$	−20.0068	−0.772354
$672$	0	0
$673$	6.95037	0.267917	0.133959	−	0.990987i	$-0.457231\pi$
$673$	6.95037	0.267917	0.133959	+	0.990987i	$0.457231\pi$
$674$	35.1825	1.35518
$675$	−25.3823	−0.976966
$676$	−4.88572	−0.187912
$677$	−45.9370	−1.76550	−0.882752	−	0.469840i	$-0.844312\pi$
$677$	−45.9370	−1.76550	−0.882752	+	0.469840i	$0.844312\pi$
$678$	−1.80699	−0.0693969
$679$	0	0
$680$	−5.66084	−0.217083
$681$	−0.447936	−0.0171650
$682$	51.5108	1.97245
$683$	1.50183	0.0574657	0.0287329	−	0.999587i	$-0.490853\pi$
$683$	1.50183	0.0574657	0.0287329	+	0.999587i	$0.490853\pi$
$684$	10.7172	0.409781
$685$	31.2364	1.19348
$686$	0	0
$687$	−3.60746	−0.137633
$688$	−11.5673	−0.440999
$689$	−3.48055	−0.132598
$690$	0.723336	0.0275369
$691$	−32.0262	−1.21833	−0.609167	−	0.793042i	$-0.708496\pi$
$691$	−32.0262	−1.21833	−0.609167	+	0.793042i	$0.708496\pi$
$692$	23.0407	0.875876
$693$	0	0
$694$	−14.8661	−0.564308
$695$	−8.85144	−0.335754
$696$	−0.515089	−0.0195244
$697$	7.65730	0.290041
$698$	−20.1456	−0.762523
$699$	0.211845	0.00801271
$700$	0	0
$701$	20.1243	0.760083	0.380042	−	0.924969i	$-0.375910\pi$
$701$	20.1243	0.760083	0.380042	+	0.924969i	$0.375910\pi$
$702$	−8.41428	−0.317576
$703$	29.2707	1.10396
$704$	6.45172	0.243158
$705$	14.9240	0.562070
$706$	−9.55582	−0.359638
$707$	0	0
$708$	−0.358868	−0.0134871
$709$	−4.06107	−0.152517	−0.0762584	−	0.997088i	$-0.524297\pi$
$709$	−4.06107	−0.152517	−0.0762584	+	0.997088i	$0.524297\pi$
$710$	−49.0082	−1.83925
$711$	−14.0451	−0.526731
$712$	9.39630	0.352141
$713$	3.04106	0.113889
$714$	0	0
$715$	67.7573	2.53398
$716$	−6.69801	−0.250316
$717$	−6.51152	−0.243177
$718$	12.6878	0.473505
$719$	1.51190	0.0563842	0.0281921	−	0.999603i	$-0.491025\pi$
$719$	1.51190	0.0563842	0.0281921	+	0.999603i	$0.491025\pi$
$720$	−10.0824	−0.375748
$721$	0	0
$722$	−3.64162	−0.135527
$723$	10.7701	0.400544
$724$	13.2453	0.492256
$725$	−8.59290	−0.319132
$726$	15.7744	0.585444
$727$	−28.1717	−1.04483	−0.522414	−	0.852692i	$-0.674969\pi$
$727$	−28.1717	−1.04483	−0.522414	+	0.852692i	$0.674969\pi$
$728$	0	0
$729$	−13.7101	−0.507782
$730$	55.1231	2.04020
$731$	17.7606	0.656898
$732$	−1.59729	−0.0590376
$733$	6.31545	0.233266	0.116633	−	0.993175i	$-0.462790\pi$
$733$	6.31545	0.233266	0.116633	+	0.993175i	$0.462790\pi$
$734$	−33.0253	−1.21899
$735$	0	0
$736$	0.380892	0.0140399
$737$	−46.6133	−1.71702
$738$	13.6382	0.502030
$739$	8.64546	0.318029	0.159014	−	0.987276i	$-0.449168\pi$
$739$	8.64546	0.318029	0.159014	+	0.987276i	$0.449168\pi$
$740$	−27.5370	−1.01228
$741$	−5.75016	−0.211237
$742$	0	0
$743$	18.3123	0.671814	0.335907	−	0.941895i	$-0.390957\pi$
$743$	18.3123	0.671814	0.335907	+	0.941895i	$0.390957\pi$
$744$	4.11250	0.150771
$745$	−38.2511	−1.40141
$746$	−19.9474	−0.730327
$747$	−35.0460	−1.28226
$748$	−9.90604	−0.362201
$749$	0	0
$750$	6.82313	0.249145
$751$	−2.30974	−0.0842835	−0.0421417	−	0.999112i	$-0.513418\pi$
$751$	−2.30974	−0.0842835	−0.0421417	+	0.999112i	$0.513418\pi$
$752$	7.85862	0.286574
$753$	−11.9653	−0.436041
$754$	−2.84856	−0.103738
$755$	24.9116	0.906626
$756$	0	0
$757$	53.8978	1.95895	0.979474	−	0.201573i	$-0.0646052\pi$
$757$	53.8978	1.95895	0.979474	+	0.201573i	$0.0646052\pi$
$758$	27.8725	1.01237
$759$	1.26578	0.0459450
$760$	−14.4487	−0.524109
$761$	−30.9134	−1.12061	−0.560305	−	0.828286i	$-0.689316\pi$
$761$	−30.9134	−1.12061	−0.560305	+	0.828286i	$0.689316\pi$
$762$	1.36000	0.0492677
$763$	0	0
$764$	−20.3346	−0.735681
$765$	15.4806	0.559703
$766$	21.1598	0.764536
$767$	−1.98462	−0.0716604
$768$	0.515089	0.0185867
$769$	8.51208	0.306953	0.153477	−	0.988152i	$-0.450953\pi$
$769$	8.51208	0.306953	0.153477	+	0.988152i	$0.450953\pi$
$770$	0	0
$771$	−7.99148	−0.287806
$772$	13.2040	0.475224
$773$	2.51529	0.0904685	0.0452343	−	0.998976i	$-0.485597\pi$
$773$	2.51529	0.0904685	0.0452343	+	0.998976i	$0.485597\pi$
$774$	31.6329	1.13702
$775$	68.6061	2.46441
$776$	−2.56729	−0.0921604
$777$	0	0
$778$	8.79804	0.315425
$779$	19.5444	0.700252
$780$	5.40958	0.193694
$781$	−85.7606	−3.06876
$782$	−0.584826	−0.0209133
$783$	2.95387	0.105563
$784$	0	0
$785$	−14.3684	−0.512830
$786$	−5.54075	−0.197632
$787$	5.98304	0.213273	0.106636	−	0.994298i	$-0.465992\pi$
$787$	5.98304	0.213273	0.106636	+	0.994298i	$0.465992\pi$
$788$	−9.01237	−0.321052
$789$	−1.51700	−0.0540067
$790$	18.9353	0.673688
$791$	0	0
$792$	−17.6434	−0.626931
$793$	−8.83338	−0.313683
$794$	−7.58413	−0.269151
$795$	−2.32039	−0.0822957
$796$	−5.86360	−0.207830
$797$	−0.207213	−0.00733988	−0.00366994	−	0.999993i	$-0.501168\pi$
$797$	−0.207213	−0.00733988	−0.00366994	+	0.999993i	$0.501168\pi$
$798$	0	0
$799$	−12.0662	−0.426872
$800$	8.59290	0.303805
$801$	−25.6959	−0.907920
$802$	11.8271	0.417629
$803$	96.4613	3.40405
$804$	−3.72149	−0.131247
$805$	0	0
$806$	22.7430	0.801089
$807$	−3.48673	−0.122739
$808$	−10.0344	−0.353007
$809$	31.8360	1.11929	0.559646	−	0.828732i	$-0.310937\pi$
$809$	31.8360	1.11929	0.559646	+	0.828732i	$0.310937\pi$
$810$	24.6376	0.865676
$811$	−19.8976	−0.698699	−0.349350	−	0.936992i	$-0.613597\pi$
$811$	−19.8976	−0.698699	−0.349350	+	0.936992i	$0.613597\pi$
$812$	0	0
$813$	8.69250	0.304859
$814$	−48.1876	−1.68898
$815$	1.43535	0.0502781
$816$	−0.790874	−0.0276861
$817$	45.3319	1.58596
$818$	11.8506	0.414347
$819$	0	0
$820$	−18.3868	−0.642096
$821$	−24.3901	−0.851221	−0.425610	−	0.904907i	$-0.639941\pi$
$821$	−24.3901	−0.851221	−0.425610	+	0.904907i	$0.639941\pi$
$822$	4.36403	0.152213
$823$	−50.1588	−1.74843	−0.874213	−	0.485542i	$-0.838622\pi$
$823$	−50.1588	−1.74843	−0.874213	+	0.485542i	$0.838622\pi$
$824$	−9.34353	−0.325497
$825$	28.5560	0.994192
$826$	0	0
$827$	−12.5847	−0.437612	−0.218806	−	0.975768i	$-0.570216\pi$
$827$	−12.5847	−0.437612	−0.218806	+	0.975768i	$0.570216\pi$
$828$	−1.04162	−0.0361987
$829$	−50.0977	−1.73996	−0.869982	−	0.493083i	$-0.835870\pi$
$829$	−50.0977	−1.73996	−0.869982	+	0.493083i	$0.835870\pi$
$830$	47.2484	1.64002
$831$	13.5548	0.470212
$832$	2.84856	0.0987560
$833$	0	0
$834$	−1.23663	−0.0428210
$835$	37.9900	1.31470
$836$	−25.2841	−0.874470
$837$	−23.5839	−0.815178
$838$	0.933145	0.0322349
$839$	−26.7756	−0.924397	−0.462199	−	0.886776i	$-0.652939\pi$
$839$	−26.7756	−0.924397	−0.462199	+	0.886776i	$0.652939\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	−3.17478	−0.109410
$843$	0.341279	0.0117543
$844$	20.9741	0.721957
$845$	−18.0129	−0.619664
$846$	−21.4908	−0.738870
$847$	0	0
$848$	−1.22186	−0.0419589
$849$	−12.8410	−0.440701
$850$	−13.1936	−0.452538
$851$	−2.84487	−0.0975208
$852$	−6.84692	−0.234572
$853$	−16.8716	−0.577673	−0.288837	−	0.957378i	$-0.593268\pi$
$853$	−16.8716	−0.577673	−0.288837	+	0.957378i	$0.593268\pi$
$854$	0	0
$855$	39.5126	1.35130
$856$	−11.7990	−0.403282
$857$	8.11457	0.277188	0.138594	−	0.990349i	$-0.455742\pi$
$857$	8.11457	0.277188	0.138594	+	0.990349i	$0.455742\pi$
$858$	9.46635	0.323176
$859$	49.5252	1.68978	0.844889	−	0.534942i	$-0.179667\pi$
$859$	49.5252	1.68978	0.844889	+	0.534942i	$0.179667\pi$
$860$	−42.6469	−1.45425
$861$	0	0
$862$	−25.2882	−0.861318
$863$	36.6653	1.24810	0.624051	−	0.781383i	$-0.285486\pi$
$863$	36.6653	1.24810	0.624051	+	0.781383i	$0.285486\pi$
$864$	−2.95387	−0.100493
$865$	84.9477	2.88831
$866$	25.3900	0.862789
$867$	−7.54220	−0.256146
$868$	0	0
$869$	33.1354	1.12404
$870$	−1.89906	−0.0643841
$871$	−20.5807	−0.697349
$872$	−6.05447	−0.205030
$873$	7.02073	0.237616
$874$	−1.49271	−0.0504915
$875$	0	0
$876$	7.70123	0.260200
$877$	2.99441	0.101114	0.0505570	−	0.998721i	$-0.483900\pi$
$877$	2.99441	0.101114	0.0505570	+	0.998721i	$0.483900\pi$
$878$	−9.95941	−0.336114
$879$	5.14095	0.173400
$880$	23.7865	0.801844
$881$	14.1339	0.476183	0.238092	−	0.971243i	$-0.423478\pi$
$881$	14.1339	0.476183	0.238092	+	0.971243i	$0.423478\pi$
$882$	0	0
$883$	−15.9154	−0.535596	−0.267798	−	0.963475i	$-0.586296\pi$
$883$	−15.9154	−0.535596	−0.267798	+	0.963475i	$0.586296\pi$
$884$	−4.37371	−0.147104
$885$	−1.32309	−0.0444753
$886$	−9.69053	−0.325560
$887$	2.14593	0.0720532	0.0360266	−	0.999351i	$-0.488530\pi$
$887$	2.14593	0.0720532	0.0360266	+	0.999351i	$0.488530\pi$
$888$	−3.84718	−0.129103
$889$	0	0
$890$	34.6428	1.16123
$891$	43.1139	1.44437
$892$	−1.10629	−0.0370412
$893$	−30.7978	−1.03061
$894$	−5.34405	−0.178732
$895$	−24.6946	−0.825449
$896$	0	0
$897$	0.558868	0.0186600
$898$	13.7314	0.458223
$899$	−7.98405	−0.266283
$900$	−23.4989	−0.783295
$901$	1.87606	0.0625007
$902$	−32.1755	−1.07133
$903$	0	0
$904$	−3.50810	−0.116678
$905$	48.8334	1.62328
$906$	3.48039	0.115628
$907$	19.4259	0.645025	0.322513	−	0.946565i	$-0.395473\pi$
$907$	19.4259	0.645025	0.322513	+	0.946565i	$0.395473\pi$
$908$	−0.869629	−0.0288596
$909$	27.4408	0.910153
$910$	0	0
$911$	−1.60092	−0.0530408	−0.0265204	−	0.999648i	$-0.508443\pi$
$911$	−1.60092	−0.0530408	−0.0265204	+	0.999648i	$0.508443\pi$
$912$	−2.01862	−0.0668433
$913$	82.6811	2.73634
$914$	12.3389	0.408134
$915$	−5.88899	−0.194684
$916$	−7.00356	−0.231404
$917$	0	0
$918$	4.53541	0.149691
$919$	−50.8625	−1.67780	−0.838899	−	0.544287i	$-0.816800\pi$
$919$	−50.8625	−1.67780	−0.838899	+	0.544287i	$0.816800\pi$
$920$	1.40429	0.0462982
$921$	−1.43490	−0.0472814
$922$	−11.8322	−0.389673
$923$	−37.8650	−1.24634
$924$	0	0
$925$	−64.1800	−2.11023
$926$	−30.3189	−0.996340
$927$	25.5516	0.839225
$928$	−1.00000	−0.0328266
$929$	−27.9717	−0.917723	−0.458861	−	0.888508i	$-0.651743\pi$
$929$	−27.9717	−0.917723	−0.458861	+	0.888508i	$0.651743\pi$
$930$	15.1622	0.497187
$931$	0	0
$932$	0.411278	0.0134719
$933$	7.85930	0.257302
$934$	−8.31097	−0.271943
$935$	−36.5221	−1.19440
$936$	−7.78990	−0.254621
$937$	42.4694	1.38741	0.693707	−	0.720258i	$-0.255976\pi$
$937$	42.4694	1.38741	0.693707	+	0.720258i	$0.255976\pi$
$938$	0	0
$939$	17.6688	0.576599
$940$	28.9736	0.945014
$941$	34.4273	1.12230	0.561149	−	0.827715i	$-0.310360\pi$
$941$	34.4273	1.12230	0.561149	+	0.827715i	$0.310360\pi$
$942$	−2.00740	−0.0654047
$943$	−1.89956	−0.0618581
$944$	−0.696710	−0.0226760
$945$	0	0
$946$	−74.6289	−2.42639
$947$	−28.0358	−0.911040	−0.455520	−	0.890226i	$-0.650547\pi$
$947$	−28.0358	−0.911040	−0.455520	+	0.890226i	$0.650547\pi$
$948$	2.64545	0.0859201
$949$	42.5895	1.38251
$950$	−33.6754	−1.09257
$951$	−12.1150	−0.392857
$952$	0	0
$953$	50.4431	1.63401	0.817007	−	0.576628i	$-0.195632\pi$
$953$	50.4431	1.63401	0.817007	+	0.576628i	$0.195632\pi$
$954$	3.34141	0.108182
$955$	−74.9708	−2.42600
$956$	−12.6415	−0.408857
$957$	−3.32321	−0.107424
$958$	31.3096	1.01157
$959$	0	0
$960$	1.89906	0.0612919
$961$	32.7451	1.05629
$962$	−21.2758	−0.685958
$963$	32.2666	1.03978
$964$	20.9092	0.673439
$965$	48.6814	1.56711
$966$	0	0
$967$	40.9091	1.31555	0.657774	−	0.753215i	$-0.271498\pi$
$967$	40.9091	1.31555	0.657774	+	0.753215i	$0.271498\pi$
$968$	30.6246	0.984313
$969$	3.09942	0.0995676
$970$	−9.46523	−0.303910
$971$	43.1138	1.38359	0.691794	−	0.722095i	$-0.256821\pi$
$971$	43.1138	1.38359	0.691794	+	0.722095i	$0.256821\pi$
$972$	12.3037	0.394642
$973$	0	0
$974$	−21.7094	−0.695615
$975$	12.6080	0.403780
$976$	−3.10100	−0.0992607
$977$	49.1685	1.57304	0.786519	−	0.617566i	$-0.211881\pi$
$977$	49.1685	1.57304	0.786519	+	0.617566i	$0.211881\pi$
$978$	0.200532	0.00641231
$979$	60.6223	1.93750
$980$	0	0
$981$	16.5571	0.528626
$982$	−28.6142	−0.913115
$983$	5.41718	0.172781	0.0863907	−	0.996261i	$-0.472467\pi$
$983$	5.41718	0.172781	0.0863907	+	0.996261i	$0.472467\pi$
$984$	−2.56882	−0.0818908
$985$	−33.2273	−1.05871
$986$	1.53541	0.0488975
$987$	0	0
$988$	−11.1634	−0.355156
$989$	−4.40589	−0.140099
$990$	−65.0487	−2.06738
$991$	6.28876	0.199769	0.0998845	−	0.994999i	$-0.468153\pi$
$991$	6.28876	0.199769	0.0998845	+	0.994999i	$0.468153\pi$
$992$	7.98405	0.253494
$993$	−10.7741	−0.341906
$994$	0	0
$995$	−21.6182	−0.685344
$996$	6.60105	0.209162
$997$	7.11434	0.225313	0.112657	−	0.993634i	$-0.464064\pi$
$997$	7.11434	0.225313	0.112657	+	0.993634i	$0.464064\pi$
$998$	−22.3287	−0.706804
$999$	22.0624	0.698022

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2842.2.a.z.1.3		5
7.2	even	3		406.2.e.a.291.3	yes	10
7.4	even	3		406.2.e.a.233.3	✓	10
7.6	odd	2		2842.2.a.x.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
406.2.e.a.233.3	✓	10	7.4	even	3
406.2.e.a.291.3	yes	10	7.2	even	3
2842.2.a.x.1.3		5	7.6	odd	2
2842.2.a.z.1.3		5	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:	\( N \)	\(=\)	\( 2842 = 2 \cdot 7^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2842.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.515089 q^{3} +1.00000 q^{4} +3.68685 q^{5} +0.515089 q^{6} +1.00000 q^{8} -2.73468 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.515089 q^{3} +1.00000 q^{4} +3.68685 q^{5} +0.515089 q^{6} +1.00000 q^{8} -2.73468 q^{9} +3.68685 q^{10} +6.45172 q^{11} +0.515089 q^{12} +2.84856 q^{13} +1.89906 q^{15} +1.00000 q^{16} -1.53541 q^{17} -2.73468 q^{18} -3.91898 q^{19} +3.68685 q^{20} +6.45172 q^{22} +0.380892 q^{23} +0.515089 q^{24} +8.59290 q^{25} +2.84856 q^{26} -2.95387 q^{27} -1.00000 q^{29} +1.89906 q^{30} +7.98405 q^{31} +1.00000 q^{32} +3.32321 q^{33} -1.53541 q^{34} -2.73468 q^{36} -7.46896 q^{37} -3.91898 q^{38} +1.46726 q^{39} +3.68685 q^{40} -4.98713 q^{41} -11.5673 q^{43} +6.45172 q^{44} -10.0824 q^{45} +0.380892 q^{46} +7.85862 q^{47} +0.515089 q^{48} +8.59290 q^{50} -0.790874 q^{51} +2.84856 q^{52} -1.22186 q^{53} -2.95387 q^{54} +23.7865 q^{55} -2.01862 q^{57} -1.00000 q^{58} -0.696710 q^{59} +1.89906 q^{60} -3.10100 q^{61} +7.98405 q^{62} +1.00000 q^{64} +10.5022 q^{65} +3.32321 q^{66} -7.22494 q^{67} -1.53541 q^{68} +0.196193 q^{69} -13.2927 q^{71} -2.73468 q^{72} +14.9513 q^{73} -7.46896 q^{74} +4.42611 q^{75} -3.91898 q^{76} +1.46726 q^{78} +5.13590 q^{79} +3.68685 q^{80} +6.68254 q^{81} -4.98713 q^{82} +12.8154 q^{83} -5.66084 q^{85} -11.5673 q^{86} -0.515089 q^{87} +6.45172 q^{88} +9.39630 q^{89} -10.0824 q^{90} +0.380892 q^{92} +4.11250 q^{93} +7.85862 q^{94} -14.4487 q^{95} +0.515089 q^{96} -2.56729 q^{97} -17.6434 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} + 3 q^{3} + 5 q^{4} + 7 q^{5} + 3 q^{6} + 5 q^{8} + 8 q^{9}+O(q^{10}) \) 5 * q + 5 * q^2 + 3 * q^3 + 5 * q^4 + 7 * q^5 + 3 * q^6 + 5 * q^8 + 8 * q^9	\( 5 q + 5 q^{2} + 3 q^{3} + 5 q^{4} + 7 q^{5} + 3 q^{6} + 5 q^{8} + 8 q^{9} + 7 q^{10} + 3 q^{12} + 10 q^{13} - 10 q^{15} + 5 q^{16} + 8 q^{17} + 8 q^{18} + 2 q^{19} + 7 q^{20} + q^{23} + 3 q^{24} + 12 q^{25} + 10 q^{26} + 15 q^{27} - 5 q^{29} - 10 q^{30} + 11 q^{31} + 5 q^{32} + 9 q^{33} + 8 q^{34} + 8 q^{36} - 8 q^{37} + 2 q^{38} + 18 q^{39} + 7 q^{40} + 23 q^{41} - 3 q^{43} + 4 q^{45} + q^{46} + 16 q^{47} + 3 q^{48} + 12 q^{50} + 7 q^{51} + 10 q^{52} + 7 q^{53} + 15 q^{54} + 6 q^{55} - 34 q^{57} - 5 q^{58} - 9 q^{59} - 10 q^{60} + 15 q^{61} + 11 q^{62} + 5 q^{64} + 5 q^{65} + 9 q^{66} - 4 q^{67} + 8 q^{68} + 14 q^{69} - 22 q^{71} + 8 q^{72} - 8 q^{74} - 34 q^{75} + 2 q^{76} + 18 q^{78} - 13 q^{79} + 7 q^{80} + 17 q^{81} + 23 q^{82} + 28 q^{83} - 7 q^{85} - 3 q^{86} - 3 q^{87} + 17 q^{89} + 4 q^{90} + q^{92} + 17 q^{93} + 16 q^{94} - 9 q^{95} + 3 q^{96} + 42 q^{97} - 42 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 + 3 * q^3 + 5 * q^4 + 7 * q^5 + 3 * q^6 + 5 * q^8 + 8 * q^9 + 7 * q^10 + 3 * q^12 + 10 * q^13 - 10 * q^15 + 5 * q^16 + 8 * q^17 + 8 * q^18 + 2 * q^19 + 7 * q^20 + q^23 + 3 * q^24 + 12 * q^25 + 10 * q^26 + 15 * q^27 - 5 * q^29 - 10 * q^30 + 11 * q^31 + 5 * q^32 + 9 * q^33 + 8 * q^34 + 8 * q^36 - 8 * q^37 + 2 * q^38 + 18 * q^39 + 7 * q^40 + 23 * q^41 - 3 * q^43 + 4 * q^45 + q^46 + 16 * q^47 + 3 * q^48 + 12 * q^50 + 7 * q^51 + 10 * q^52 + 7 * q^53 + 15 * q^54 + 6 * q^55 - 34 * q^57 - 5 * q^58 - 9 * q^59 - 10 * q^60 + 15 * q^61 + 11 * q^62 + 5 * q^64 + 5 * q^65 + 9 * q^66 - 4 * q^67 + 8 * q^68 + 14 * q^69 - 22 * q^71 + 8 * q^72 - 8 * q^74 - 34 * q^75 + 2 * q^76 + 18 * q^78 - 13 * q^79 + 7 * q^80 + 17 * q^81 + 23 * q^82 + 28 * q^83 - 7 * q^85 - 3 * q^86 - 3 * q^87 + 17 * q^89 + 4 * q^90 + q^92 + 17 * q^93 + 16 * q^94 - 9 * q^95 + 3 * q^96 + 42 * q^97 - 42 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more