LMFDB - Embedded newform 5054.2.a.be.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5054,2,Mod(1,5054)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5054, 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("5054.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5054 = 2 \cdot 7 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5054.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:	$40.3563931816$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.36538000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 13x^{4} - 4x^{3} + 41x^{2} + 16x - 16 $ x^6 - 13x^4 - 4x^3 + 41x^2 + 16x - 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-2.52231$ of defining polynomial
Character	$\chi$	$=$	5054.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.52231 q^{3} +1.00000 q^{4} +1.42123 q^{5} +2.52231 q^{6} +1.00000 q^{7} +1.00000 q^{8} +3.36207 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.52231 q^{3} +1.00000 q^{4} +1.42123 q^{5} +2.52231 q^{6} +1.00000 q^{7} +1.00000 q^{8} +3.36207 q^{9} +1.42123 q^{10} +1.22272 q^{11} +2.52231 q^{12} +2.87837 q^{13} +1.00000 q^{14} +3.58479 q^{15} +1.00000 q^{16} +3.92300 q^{17} +3.36207 q^{18} +1.42123 q^{20} +2.52231 q^{21} +1.22272 q^{22} -3.82191 q^{23} +2.52231 q^{24} -2.98011 q^{25} +2.87837 q^{26} +0.913260 q^{27} +1.00000 q^{28} -1.85516 q^{29} +3.58479 q^{30} -4.99711 q^{31} +1.00000 q^{32} +3.08408 q^{33} +3.92300 q^{34} +1.42123 q^{35} +3.36207 q^{36} -0.841807 q^{37} +7.26015 q^{39} +1.42123 q^{40} +7.37747 q^{41} +2.52231 q^{42} -4.80751 q^{43} +1.22272 q^{44} +4.77828 q^{45} -3.82191 q^{46} +6.55168 q^{47} +2.52231 q^{48} +1.00000 q^{49} -2.98011 q^{50} +9.89504 q^{51} +2.87837 q^{52} +3.68427 q^{53} +0.913260 q^{54} +1.73776 q^{55} +1.00000 q^{56} -1.85516 q^{58} +11.3276 q^{59} +3.58479 q^{60} -13.9313 q^{61} -4.99711 q^{62} +3.36207 q^{63} +1.00000 q^{64} +4.09082 q^{65} +3.08408 q^{66} -9.35356 q^{67} +3.92300 q^{68} -9.64007 q^{69} +1.42123 q^{70} +9.04463 q^{71} +3.36207 q^{72} -4.26204 q^{73} -0.841807 q^{74} -7.51677 q^{75} +1.22272 q^{77} +7.26015 q^{78} -1.87884 q^{79} +1.42123 q^{80} -7.78269 q^{81} +7.37747 q^{82} -3.84190 q^{83} +2.52231 q^{84} +5.57548 q^{85} -4.80751 q^{86} -4.67929 q^{87} +1.22272 q^{88} +18.4510 q^{89} +4.77828 q^{90} +2.87837 q^{91} -3.82191 q^{92} -12.6043 q^{93} +6.55168 q^{94} +2.52231 q^{96} -17.7866 q^{97} +1.00000 q^{98} +4.11086 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 6 q^{4} - q^{5} + 6 q^{7} + 6 q^{8} + 8 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 + 6 * q^4 - q^5 + 6 * q^7 + 6 * q^8 + 8 * q^9	$ 6 q + 6 q^{2} + 6 q^{4} - q^{5} + 6 q^{7} + 6 q^{8} + 8 q^{9} - q^{10} + 4 q^{11} + 15 q^{13} + 6 q^{14} + 6 q^{15} + 6 q^{16} - 9 q^{17} + 8 q^{18} - q^{20} + 4 q^{22} + 4 q^{23} + q^{25} + 15 q^{26} - 12 q^{27} + 6 q^{28} + 7 q^{29} + 6 q^{30} + 4 q^{31} + 6 q^{32} + 28 q^{33} - 9 q^{34} - q^{35} + 8 q^{36} + 3 q^{37} - 8 q^{39} - q^{40} + 11 q^{41} - 10 q^{43} + 4 q^{44} + 19 q^{45} + 4 q^{46} + 12 q^{47} + 6 q^{49} + q^{50} + 44 q^{51} + 15 q^{52} - 5 q^{53} - 12 q^{54} - 8 q^{55} + 6 q^{56} + 7 q^{58} + 4 q^{59} + 6 q^{60} - 21 q^{61} + 4 q^{62} + 8 q^{63} + 6 q^{64} - 20 q^{65} + 28 q^{66} + 14 q^{67} - 9 q^{68} - 24 q^{69} - q^{70} + 24 q^{71} + 8 q^{72} - 21 q^{73} + 3 q^{74} + 12 q^{75} + 4 q^{77} - 8 q^{78} + 58 q^{79} - q^{80} - 6 q^{81} + 11 q^{82} + 20 q^{83} - 4 q^{85} - 10 q^{86} - 8 q^{87} + 4 q^{88} + 7 q^{89} + 19 q^{90} + 15 q^{91} + 4 q^{92} - 22 q^{93} + 12 q^{94} + 7 q^{97} + 6 q^{98} - 26 q^{99}+O(q^{100}) $ 6 * q + 6 * q^2 + 6 * q^4 - q^5 + 6 * q^7 + 6 * q^8 + 8 * q^9 - q^10 + 4 * q^11 + 15 * q^13 + 6 * q^14 + 6 * q^15 + 6 * q^16 - 9 * q^17 + 8 * q^18 - q^20 + 4 * q^22 + 4 * q^23 + q^25 + 15 * q^26 - 12 * q^27 + 6 * q^28 + 7 * q^29 + 6 * q^30 + 4 * q^31 + 6 * q^32 + 28 * q^33 - 9 * q^34 - q^35 + 8 * q^36 + 3 * q^37 - 8 * q^39 - q^40 + 11 * q^41 - 10 * q^43 + 4 * q^44 + 19 * q^45 + 4 * q^46 + 12 * q^47 + 6 * q^49 + q^50 + 44 * q^51 + 15 * q^52 - 5 * q^53 - 12 * q^54 - 8 * q^55 + 6 * q^56 + 7 * q^58 + 4 * q^59 + 6 * q^60 - 21 * q^61 + 4 * q^62 + 8 * q^63 + 6 * q^64 - 20 * q^65 + 28 * q^66 + 14 * q^67 - 9 * q^68 - 24 * q^69 - q^70 + 24 * q^71 + 8 * q^72 - 21 * q^73 + 3 * q^74 + 12 * q^75 + 4 * q^77 - 8 * q^78 + 58 * q^79 - q^80 - 6 * q^81 + 11 * q^82 + 20 * q^83 - 4 * q^85 - 10 * q^86 - 8 * q^87 + 4 * q^88 + 7 * q^89 + 19 * q^90 + 15 * q^91 + 4 * q^92 - 22 * q^93 + 12 * q^94 + 7 * q^97 + 6 * q^98 - 26 * 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
$3$	2.52231	1.45626	0.728130	−	0.685440i	$-0.240390\pi$
$3$	2.52231	1.45626	0.728130	+	0.685440i	$0.240390\pi$
$4$	1.00000	0.500000
$5$	1.42123	0.635593	0.317797	−	0.948159i	$-0.397057\pi$
$5$	1.42123	0.635593	0.317797	+	0.948159i	$0.397057\pi$
$6$	2.52231	1.02973
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	3.36207	1.12069
$10$	1.42123	0.449432
$11$	1.22272	0.368663	0.184331	−	0.982864i	$-0.440988\pi$
$11$	1.22272	0.368663	0.184331	+	0.982864i	$0.440988\pi$
$12$	2.52231	0.728130
$13$	2.87837	0.798316	0.399158	−	0.916882i	$-0.369303\pi$
$13$	2.87837	0.798316	0.399158	+	0.916882i	$0.369303\pi$
$14$	1.00000	0.267261
$15$	3.58479	0.925588
$16$	1.00000	0.250000
$17$	3.92300	0.951467	0.475733	−	0.879590i	$-0.342183\pi$
$17$	3.92300	0.951467	0.475733	+	0.879590i	$0.342183\pi$
$18$	3.36207	0.792448
$19$	0	0
$19$	0	0
$20$	1.42123	0.317797
$21$	2.52231	0.550414
$22$	1.22272	0.260684
$23$	−3.82191	−0.796924	−0.398462	−	0.917185i	$-0.630456\pi$
$23$	−3.82191	−0.796924	−0.398462	+	0.917185i	$0.630456\pi$
$24$	2.52231	0.514865
$25$	−2.98011	−0.596021
$26$	2.87837	0.564494
$27$	0.913260	0.175757
$28$	1.00000	0.188982
$29$	−1.85516	−0.344494	−0.172247	−	0.985054i	$-0.555103\pi$
$29$	−1.85516	−0.344494	−0.172247	+	0.985054i	$0.555103\pi$
$30$	3.58479	0.654490
$31$	−4.99711	−0.897508	−0.448754	−	0.893655i	$-0.648132\pi$
$31$	−4.99711	−0.897508	−0.448754	+	0.893655i	$0.648132\pi$
$32$	1.00000	0.176777
$33$	3.08408	0.536869
$34$	3.92300	0.672789
$35$	1.42123	0.240232
$36$	3.36207	0.560345
$37$	−0.841807	−0.138392	−0.0691961	−	0.997603i	$-0.522043\pi$
$37$	−0.841807	−0.138392	−0.0691961	+	0.997603i	$0.522043\pi$
$38$	0	0
$39$	7.26015	1.16255
$40$	1.42123	0.224716
$41$	7.37747	1.15217	0.576084	−	0.817391i	$-0.304580\pi$
$41$	7.37747	1.15217	0.576084	+	0.817391i	$0.304580\pi$
$42$	2.52231	0.389202
$43$	−4.80751	−0.733138	−0.366569	−	0.930391i	$-0.619468\pi$
$43$	−4.80751	−0.733138	−0.366569	+	0.930391i	$0.619468\pi$
$44$	1.22272	0.184331
$45$	4.77828	0.712303
$46$	−3.82191	−0.563510
$47$	6.55168	0.955661	0.477830	−	0.878452i	$-0.341423\pi$
$47$	6.55168	0.955661	0.477830	+	0.878452i	$0.341423\pi$
$48$	2.52231	0.364065
$49$	1.00000	0.142857
$50$	−2.98011	−0.421451
$51$	9.89504	1.38558
$52$	2.87837	0.399158
$53$	3.68427	0.506073	0.253036	−	0.967457i	$-0.418571\pi$
$53$	3.68427	0.506073	0.253036	+	0.967457i	$0.418571\pi$
$54$	0.913260	0.124279
$55$	1.73776	0.234320
$56$	1.00000	0.133631
$57$	0	0
$58$	−1.85516	−0.243594
$59$	11.3276	1.47473	0.737367	−	0.675492i	$-0.236069\pi$
$59$	11.3276	1.47473	0.737367	+	0.675492i	$0.236069\pi$
$60$	3.58479	0.462794
$61$	−13.9313	−1.78372	−0.891859	−	0.452314i	$-0.850599\pi$
$61$	−13.9313	−1.78372	−0.891859	+	0.452314i	$0.850599\pi$
$62$	−4.99711	−0.634634
$63$	3.36207	0.423581
$64$	1.00000	0.125000
$65$	4.09082	0.507404
$66$	3.08408	0.379624
$67$	−9.35356	−1.14272	−0.571360	−	0.820700i	$-0.693584\pi$
$67$	−9.35356	−1.14272	−0.571360	+	0.820700i	$0.693584\pi$
$68$	3.92300	0.475733
$69$	−9.64007	−1.16053
$70$	1.42123	0.169869
$71$	9.04463	1.07340	0.536700	−	0.843773i	$-0.319671\pi$
$71$	9.04463	1.07340	0.536700	+	0.843773i	$0.319671\pi$
$72$	3.36207	0.396224
$73$	−4.26204	−0.498834	−0.249417	−	0.968396i	$-0.580239\pi$
$73$	−4.26204	−0.498834	−0.249417	+	0.968396i	$0.580239\pi$
$74$	−0.841807	−0.0978581
$75$	−7.51677	−0.867961
$76$	0	0
$77$	1.22272	0.139342
$78$	7.26015	0.822050
$79$	−1.87884	−0.211386	−0.105693	−	0.994399i	$-0.533706\pi$
$79$	−1.87884	−0.211386	−0.105693	+	0.994399i	$0.533706\pi$
$80$	1.42123	0.158898
$81$	−7.78269	−0.864743
$82$	7.37747	0.814706
$83$	−3.84190	−0.421703	−0.210851	−	0.977518i	$-0.567624\pi$
$83$	−3.84190	−0.421703	−0.210851	+	0.977518i	$0.567624\pi$
$84$	2.52231	0.275207
$85$	5.57548	0.604746
$86$	−4.80751	−0.518407
$87$	−4.67929	−0.501673
$88$	1.22272	0.130342
$89$	18.4510	1.95580	0.977901	−	0.209068i	$-0.0670429\pi$
$89$	18.4510	1.95580	0.977901	+	0.209068i	$0.0670429\pi$
$90$	4.77828	0.503675
$91$	2.87837	0.301735
$92$	−3.82191	−0.398462
$93$	−12.6043	−1.30700
$94$	6.55168	0.675754
$95$	0	0
$96$	2.52231	0.257433
$97$	−17.7866	−1.80596	−0.902978	−	0.429686i	$-0.858624\pi$
$97$	−17.7866	−1.80596	−0.902978	+	0.429686i	$0.858624\pi$
$98$	1.00000	0.101015
$99$	4.11086	0.413157
$100$	−2.98011	−0.298011
$101$	9.40739	0.936070	0.468035	−	0.883710i	$-0.344962\pi$
$101$	9.40739	0.936070	0.468035	+	0.883710i	$0.344962\pi$
$102$	9.89504	0.979755
$103$	−2.62267	−0.258420	−0.129210	−	0.991617i	$-0.541244\pi$
$103$	−2.62267	−0.258420	−0.129210	+	0.991617i	$0.541244\pi$
$104$	2.87837	0.282247
$105$	3.58479	0.349840
$106$	3.68427	0.357848
$107$	−19.3222	−1.86795	−0.933973	−	0.357345i	$-0.883682\pi$
$107$	−19.3222	−1.86795	−0.933973	+	0.357345i	$0.883682\pi$
$108$	0.913260	0.0878785
$109$	−10.4840	−1.00419	−0.502093	−	0.864814i	$-0.667437\pi$
$109$	−10.4840	−1.00419	−0.502093	+	0.864814i	$0.667437\pi$
$110$	1.73776	0.165689
$111$	−2.12330	−0.201535
$112$	1.00000	0.0944911
$113$	−17.9428	−1.68792	−0.843958	−	0.536409i	$-0.819781\pi$
$113$	−17.9428	−1.68792	−0.843958	+	0.536409i	$0.819781\pi$
$114$	0	0
$115$	−5.43182	−0.506519
$116$	−1.85516	−0.172247
$117$	9.67728	0.894665
$118$	11.3276	1.04279
$119$	3.92300	0.359621
$120$	3.58479	0.327245
$121$	−9.50496	−0.864088
$122$	−13.9313	−1.26128
$123$	18.6083	1.67785
$124$	−4.99711	−0.448754
$125$	−11.3416	−1.01442
$126$	3.36207	0.299517
$127$	11.3031	1.00298	0.501492	−	0.865162i	$-0.332785\pi$
$127$	11.3031	1.00298	0.501492	+	0.865162i	$0.332785\pi$
$128$	1.00000	0.0883883
$129$	−12.1260	−1.06764
$130$	4.09082	0.358789
$131$	−2.59653	−0.226860	−0.113430	−	0.993546i	$-0.536184\pi$
$131$	−2.59653	−0.226860	−0.113430	+	0.993546i	$0.536184\pi$
$132$	3.08408	0.268434
$133$	0	0
$134$	−9.35356	−0.808025
$135$	1.29795	0.111710
$136$	3.92300	0.336394
$137$	−16.9885	−1.45142	−0.725712	−	0.687999i	$-0.758490\pi$
$137$	−16.9885	−1.45142	−0.725712	+	0.687999i	$0.758490\pi$
$138$	−9.64007	−0.820617
$139$	20.1303	1.70743	0.853716	−	0.520739i	$-0.174344\pi$
$139$	20.1303	1.70743	0.853716	+	0.520739i	$0.174344\pi$
$140$	1.42123	0.120116
$141$	16.5254	1.39169
$142$	9.04463	0.759008
$143$	3.51943	0.294309
$144$	3.36207	0.280173
$145$	−2.63661	−0.218958
$146$	−4.26204	−0.352729
$147$	2.52231	0.208037
$148$	−0.841807	−0.0691961
$149$	3.63751	0.297996	0.148998	−	0.988837i	$-0.452395\pi$
$149$	3.63751	0.297996	0.148998	+	0.988837i	$0.452395\pi$
$150$	−7.51677	−0.613741
$151$	18.5627	1.51061	0.755306	−	0.655372i	$-0.227488\pi$
$151$	18.5627	1.51061	0.755306	+	0.655372i	$0.227488\pi$
$152$	0	0
$153$	13.1894	1.06630
$154$	1.22272	0.0985293
$155$	−7.10205	−0.570450
$156$	7.26015	0.581277
$157$	7.84878	0.626401	0.313200	−	0.949687i	$-0.398599\pi$
$157$	7.84878	0.626401	0.313200	+	0.949687i	$0.398599\pi$
$158$	−1.87884	−0.149472
$159$	9.29288	0.736973
$160$	1.42123	0.112358
$161$	−3.82191	−0.301209
$162$	−7.78269	−0.611466
$163$	18.1480	1.42146	0.710730	−	0.703465i	$-0.248365\pi$
$163$	18.1480	1.42146	0.710730	+	0.703465i	$0.248365\pi$
$164$	7.37747	0.576084
$165$	4.38318	0.341230
$166$	−3.84190	−0.298189
$167$	−19.2481	−1.48946	−0.744732	−	0.667364i	$-0.767422\pi$
$167$	−19.2481	−1.48946	−0.744732	+	0.667364i	$0.767422\pi$
$168$	2.52231	0.194601
$169$	−4.71500	−0.362692
$170$	5.57548	0.427620
$171$	0	0
$172$	−4.80751	−0.366569
$173$	−2.63060	−0.200000	−0.100000	−	0.994987i	$-0.531884\pi$
$173$	−2.63060	−0.200000	−0.100000	+	0.994987i	$0.531884\pi$
$174$	−4.67929	−0.354736
$175$	−2.98011	−0.225275
$176$	1.22272	0.0921657
$177$	28.5719	2.14760
$178$	18.4510	1.38296
$179$	12.4273	0.928861	0.464430	−	0.885610i	$-0.346259\pi$
$179$	12.4273	0.928861	0.464430	+	0.885610i	$0.346259\pi$
$180$	4.77828	0.356152
$181$	21.4062	1.59111	0.795554	−	0.605882i	$-0.207180\pi$
$181$	21.4062	1.59111	0.795554	+	0.605882i	$0.207180\pi$
$182$	2.87837	0.213359
$183$	−35.1391	−2.59755
$184$	−3.82191	−0.281755
$185$	−1.19640	−0.0879611
$186$	−12.6043	−0.924192
$187$	4.79672	0.350771
$188$	6.55168	0.477830
$189$	0.913260	0.0664299
$190$	0	0
$191$	−9.62706	−0.696589	−0.348295	−	0.937385i	$-0.613239\pi$
$191$	−9.62706	−0.696589	−0.348295	+	0.937385i	$0.613239\pi$
$192$	2.52231	0.182032
$193$	18.0674	1.30052	0.650258	−	0.759713i	$-0.274661\pi$
$193$	18.0674	1.30052	0.650258	+	0.759713i	$0.274661\pi$
$194$	−17.7866	−1.27700
$195$	10.3183	0.738912
$196$	1.00000	0.0714286
$197$	12.8396	0.914781	0.457390	−	0.889266i	$-0.348784\pi$
$197$	12.8396	0.914781	0.457390	+	0.889266i	$0.348784\pi$
$198$	4.11086	0.292146
$199$	−5.67539	−0.402318	−0.201159	−	0.979559i	$-0.564471\pi$
$199$	−5.67539	−0.402318	−0.201159	+	0.979559i	$0.564471\pi$
$200$	−2.98011	−0.210725
$201$	−23.5926	−1.66410
$202$	9.40739	0.661902
$203$	−1.85516	−0.130207
$204$	9.89504	0.692791
$205$	10.4851	0.732310
$206$	−2.62267	−0.182730
$207$	−12.8495	−0.893105
$208$	2.87837	0.199579
$209$	0	0
$210$	3.58479	0.247374
$211$	1.91154	0.131596	0.0657979	−	0.997833i	$-0.479041\pi$
$211$	1.91154	0.131596	0.0657979	+	0.997833i	$0.479041\pi$
$212$	3.68427	0.253036
$213$	22.8134	1.56315
$214$	−19.3222	−1.32084
$215$	−6.83257	−0.465977
$216$	0.913260	0.0621394
$217$	−4.99711	−0.339226
$218$	−10.4840	−0.710067
$219$	−10.7502	−0.726432
$220$	1.73776	0.117160
$221$	11.2918	0.759571
$222$	−2.12330	−0.142507
$223$	2.67452	0.179099	0.0895494	−	0.995982i	$-0.471457\pi$
$223$	2.67452	0.179099	0.0895494	+	0.995982i	$0.471457\pi$
$224$	1.00000	0.0668153
$225$	−10.0193	−0.667955
$226$	−17.9428	−1.19354
$227$	−2.75727	−0.183006	−0.0915032	−	0.995805i	$-0.529167\pi$
$227$	−2.75727	−0.183006	−0.0915032	+	0.995805i	$0.529167\pi$
$228$	0	0
$229$	−15.4798	−1.02293	−0.511467	−	0.859303i	$-0.670898\pi$
$229$	−15.4798	−1.02293	−0.511467	+	0.859303i	$0.670898\pi$
$230$	−5.43182	−0.358163
$231$	3.08408	0.202917
$232$	−1.85516	−0.121797
$233$	−1.91201	−0.125260	−0.0626298	−	0.998037i	$-0.519949\pi$
$233$	−1.91201	−0.125260	−0.0626298	+	0.998037i	$0.519949\pi$
$234$	9.67728	0.632624
$235$	9.31144	0.607412
$236$	11.3276	0.737367
$237$	−4.73902	−0.307832
$238$	3.92300	0.254290
$239$	3.61595	0.233896	0.116948	−	0.993138i	$-0.462689\pi$
$239$	3.61595	0.233896	0.116948	+	0.993138i	$0.462689\pi$
$240$	3.58479	0.231397
$241$	0.285715	0.0184045	0.00920226	−	0.999958i	$-0.497071\pi$
$241$	0.285715	0.0184045	0.00920226	+	0.999958i	$0.497071\pi$
$242$	−9.50496	−0.611002
$243$	−22.3702	−1.43505
$244$	−13.9313	−0.891859
$245$	1.42123	0.0907990
$246$	18.6083	1.18642
$247$	0	0
$248$	−4.99711	−0.317317
$249$	−9.69047	−0.614109
$250$	−11.3416	−0.717303
$251$	17.4569	1.10187	0.550935	−	0.834548i	$-0.314271\pi$
$251$	17.4569	1.10187	0.550935	+	0.834548i	$0.314271\pi$
$252$	3.36207	0.211791
$253$	−4.67312	−0.293796
$254$	11.3031	0.709217
$255$	14.0631	0.880667
$256$	1.00000	0.0625000
$257$	6.07436	0.378908	0.189454	−	0.981890i	$-0.439328\pi$
$257$	6.07436	0.378908	0.189454	+	0.981890i	$0.439328\pi$
$258$	−12.1260	−0.754934
$259$	−0.841807	−0.0523073
$260$	4.09082	0.253702
$261$	−6.23717	−0.386071
$262$	−2.59653	−0.160414
$263$	−17.9415	−1.10632	−0.553161	−	0.833074i	$-0.686579\pi$
$263$	−17.9415	−1.10632	−0.553161	+	0.833074i	$0.686579\pi$
$264$	3.08408	0.189812
$265$	5.23619	0.321657
$266$	0	0
$267$	46.5392	2.84816
$268$	−9.35356	−0.571360
$269$	−1.68138	−0.102516	−0.0512578	−	0.998685i	$-0.516323\pi$
$269$	−1.68138	−0.102516	−0.0512578	+	0.998685i	$0.516323\pi$
$270$	1.29795	0.0789908
$271$	7.95578	0.483279	0.241640	−	0.970366i	$-0.422315\pi$
$271$	7.95578	0.483279	0.241640	+	0.970366i	$0.422315\pi$
$272$	3.92300	0.237867
$273$	7.26015	0.439404
$274$	−16.9885	−1.02631
$275$	−3.64383	−0.219731
$276$	−9.64007	−0.580264
$277$	−30.0011	−1.80259	−0.901295	−	0.433205i	$-0.857382\pi$
$277$	−30.0011	−1.80259	−0.901295	+	0.433205i	$0.857382\pi$
$278$	20.1303	1.20734
$279$	−16.8007	−1.00583
$280$	1.42123	0.0849347
$281$	−10.4565	−0.623780	−0.311890	−	0.950118i	$-0.600962\pi$
$281$	−10.4565	−0.623780	−0.311890	+	0.950118i	$0.600962\pi$
$282$	16.5254	0.984073
$283$	−8.05939	−0.479081	−0.239541	−	0.970886i	$-0.576997\pi$
$283$	−8.05939	−0.479081	−0.239541	+	0.970886i	$0.576997\pi$
$284$	9.04463	0.536700
$285$	0	0
$286$	3.51943	0.208108
$287$	7.37747	0.435478
$288$	3.36207	0.198112
$289$	−1.61009	−0.0947110
$290$	−2.63661	−0.154827
$291$	−44.8634	−2.62994
$292$	−4.26204	−0.249417
$293$	−8.05923	−0.470825	−0.235413	−	0.971895i	$-0.575644\pi$
$293$	−8.05923	−0.470825	−0.235413	+	0.971895i	$0.575644\pi$
$294$	2.52231	0.147104
$295$	16.0992	0.937331
$296$	−0.841807	−0.0489290
$297$	1.11666	0.0647951
$298$	3.63751	0.210715
$299$	−11.0009	−0.636197
$300$	−7.51677	−0.433981
$301$	−4.80751	−0.277100
$302$	18.5627	1.06816
$303$	23.7284	1.36316
$304$	0	0
$305$	−19.7995	−1.13372
$306$	13.1894	0.753988
$307$	−14.3712	−0.820207	−0.410103	−	0.912039i	$-0.634507\pi$
$307$	−14.3712	−0.820207	−0.410103	+	0.912039i	$0.634507\pi$
$308$	1.22272	0.0696708
$309$	−6.61521	−0.376326
$310$	−7.10205	−0.403369
$311$	28.8765	1.63744	0.818719	−	0.574195i	$-0.194685\pi$
$311$	28.8765	1.63744	0.818719	+	0.574195i	$0.194685\pi$
$312$	7.26015	0.411025
$313$	−4.12543	−0.233183	−0.116592	−	0.993180i	$-0.537197\pi$
$313$	−4.12543	−0.233183	−0.116592	+	0.993180i	$0.537197\pi$
$314$	7.84878	0.442932
$315$	4.77828	0.269225
$316$	−1.87884	−0.105693
$317$	6.54790	0.367767	0.183883	−	0.982948i	$-0.441133\pi$
$317$	6.54790	0.367767	0.183883	+	0.982948i	$0.441133\pi$
$318$	9.29288	0.521119
$319$	−2.26833	−0.127002
$320$	1.42123	0.0794492
$321$	−48.7366	−2.72021
$322$	−3.82191	−0.212987
$323$	0	0
$324$	−7.78269	−0.432372
$325$	−8.57784	−0.475813
$326$	18.1480	1.00512
$327$	−26.4440	−1.46236
$328$	7.37747	0.407353
$329$	6.55168	0.361206
$330$	4.38318	0.241286
$331$	18.3461	1.00839	0.504195	−	0.863590i	$-0.331789\pi$
$331$	18.3461	1.00839	0.504195	+	0.863590i	$0.331789\pi$
$332$	−3.84190	−0.210851
$333$	−2.83022	−0.155095
$334$	−19.2481	−1.05321
$335$	−13.2936	−0.726305
$336$	2.52231	0.137604
$337$	28.3353	1.54352	0.771762	−	0.635911i	$-0.219376\pi$
$337$	28.3353	1.54352	0.771762	+	0.635911i	$0.219376\pi$
$338$	−4.71500	−0.256462
$339$	−45.2574	−2.45804
$340$	5.57548	0.302373
$341$	−6.11006	−0.330878
$342$	0	0
$343$	1.00000	0.0539949
$344$	−4.80751	−0.259203
$345$	−13.7008	−0.737624
$346$	−2.63060	−0.141422
$347$	−15.9023	−0.853682	−0.426841	−	0.904327i	$-0.640374\pi$
$347$	−15.9023	−0.853682	−0.426841	+	0.904327i	$0.640374\pi$
$348$	−4.67929	−0.250836
$349$	−3.46506	−0.185480	−0.0927402	−	0.995690i	$-0.529563\pi$
$349$	−3.46506	−0.185480	−0.0927402	+	0.995690i	$0.529563\pi$
$350$	−2.98011	−0.159293
$351$	2.62870	0.140310
$352$	1.22272	0.0651710
$353$	−8.76647	−0.466592	−0.233296	−	0.972406i	$-0.574951\pi$
$353$	−8.76647	−0.466592	−0.233296	+	0.972406i	$0.574951\pi$
$354$	28.5719	1.51858
$355$	12.8545	0.682246
$356$	18.4510	0.977901
$357$	9.89504	0.523701
$358$	12.4273	0.656804
$359$	11.2383	0.593136	0.296568	−	0.955012i	$-0.404158\pi$
$359$	11.2383	0.593136	0.296568	+	0.955012i	$0.404158\pi$
$360$	4.77828	0.251837
$361$	0	0
$362$	21.4062	1.12508
$363$	−23.9745	−1.25834
$364$	2.87837	0.150867
$365$	−6.05734	−0.317056
$366$	−35.1391	−1.83675
$367$	5.92259	0.309156	0.154578	−	0.987981i	$-0.450598\pi$
$367$	5.92259	0.309156	0.154578	+	0.987981i	$0.450598\pi$
$368$	−3.82191	−0.199231
$369$	24.8036	1.29122
$370$	−1.19640	−0.0621979
$371$	3.68427	0.191278
$372$	−12.6043	−0.653502
$373$	22.7567	1.17829	0.589147	−	0.808026i	$-0.299464\pi$
$373$	22.7567	1.17829	0.589147	+	0.808026i	$0.299464\pi$
$374$	4.79672	0.248032
$375$	−28.6070	−1.47726
$376$	6.55168	0.337877
$377$	−5.33983	−0.275015
$378$	0.913260	0.0469730
$379$	7.09293	0.364340	0.182170	−	0.983267i	$-0.441688\pi$
$379$	7.09293	0.364340	0.182170	+	0.983267i	$0.441688\pi$
$380$	0	0
$381$	28.5099	1.46060
$382$	−9.62706	−0.492563
$383$	20.1267	1.02842	0.514212	−	0.857663i	$-0.328084\pi$
$383$	20.1267	1.02842	0.514212	+	0.857663i	$0.328084\pi$
$384$	2.52231	0.128716
$385$	1.73776	0.0885645
$386$	18.0674	0.919604
$387$	−16.1632	−0.821621
$388$	−17.7866	−0.902978
$389$	−30.2580	−1.53414	−0.767070	−	0.641564i	$-0.778286\pi$
$389$	−30.2580	−1.53414	−0.767070	+	0.641564i	$0.778286\pi$
$390$	10.3183	0.522490
$391$	−14.9934	−0.758247
$392$	1.00000	0.0505076
$393$	−6.54927	−0.330367
$394$	12.8396	0.646848
$395$	−2.67026	−0.134355
$396$	4.11086	0.206579
$397$	2.90935	0.146016	0.0730081	−	0.997331i	$-0.476740\pi$
$397$	2.90935	0.146016	0.0730081	+	0.997331i	$0.476740\pi$
$398$	−5.67539	−0.284482
$399$	0	0
$400$	−2.98011	−0.149005
$401$	−28.7840	−1.43741	−0.718703	−	0.695317i	$-0.755264\pi$
$401$	−28.7840	−1.43741	−0.718703	+	0.695317i	$0.755264\pi$
$402$	−23.5926	−1.17669
$403$	−14.3835	−0.716495
$404$	9.40739	0.468035
$405$	−11.0610	−0.549625
$406$	−1.85516	−0.0920699
$407$	−1.02929	−0.0510201
$408$	9.89504	0.489877
$409$	25.6553	1.26857	0.634285	−	0.773099i	$-0.281294\pi$
$409$	25.6553	1.26857	0.634285	+	0.773099i	$0.281294\pi$
$410$	10.4851	0.517821
$411$	−42.8503	−2.11365
$412$	−2.62267	−0.129210
$413$	11.3276	0.557397
$414$	−12.8495	−0.631521
$415$	−5.46022	−0.268032
$416$	2.87837	0.141124
$417$	50.7750	2.48646
$418$	0	0
$419$	1.06546	0.0520512	0.0260256	−	0.999661i	$-0.491715\pi$
$419$	1.06546	0.0520512	0.0260256	+	0.999661i	$0.491715\pi$
$420$	3.58479	0.174920
$421$	5.48941	0.267538	0.133769	−	0.991013i	$-0.457292\pi$
$421$	5.48941	0.267538	0.133769	+	0.991013i	$0.457292\pi$
$422$	1.91154	0.0930523
$423$	22.0272	1.07100
$424$	3.68427	0.178924
$425$	−11.6909	−0.567094
$426$	22.8134	1.10531
$427$	−13.9313	−0.674182
$428$	−19.3222	−0.933973
$429$	8.87711	0.428591
$430$	−6.83257	−0.329496
$431$	22.2378	1.07116	0.535578	−	0.844486i	$-0.320094\pi$
$431$	22.2378	1.07116	0.535578	+	0.844486i	$0.320094\pi$
$432$	0.913260	0.0439392
$433$	12.8888	0.619396	0.309698	−	0.950835i	$-0.399772\pi$
$433$	12.8888	0.619396	0.309698	+	0.950835i	$0.399772\pi$
$434$	−4.99711	−0.239869
$435$	−6.65035	−0.318860
$436$	−10.4840	−0.502093
$437$	0	0
$438$	−10.7502	−0.513665
$439$	−17.0046	−0.811587	−0.405793	−	0.913965i	$-0.633005\pi$
$439$	−17.0046	−0.811587	−0.405793	+	0.913965i	$0.633005\pi$
$440$	1.73776	0.0828445
$441$	3.36207	0.160099
$442$	11.2918	0.537098
$443$	2.51156	0.119328	0.0596638	−	0.998219i	$-0.480997\pi$
$443$	2.51156	0.119328	0.0596638	+	0.998219i	$0.480997\pi$
$444$	−2.12330	−0.100767
$445$	26.2231	1.24309
$446$	2.67452	0.126642
$447$	9.17495	0.433960
$448$	1.00000	0.0472456
$449$	11.7883	0.556326	0.278163	−	0.960534i	$-0.410274\pi$
$449$	11.7883	0.556326	0.278163	+	0.960534i	$0.410274\pi$
$450$	−10.0193	−0.472316
$451$	9.02056	0.424762
$452$	−17.9428	−0.843958
$453$	46.8210	2.19984
$454$	−2.75727	−0.129405
$455$	4.09082	0.191781
$456$	0	0
$457$	−27.4286	−1.28306	−0.641528	−	0.767100i	$-0.721699\pi$
$457$	−27.4286	−1.28306	−0.641528	+	0.767100i	$0.721699\pi$
$458$	−15.4798	−0.723323
$459$	3.58272	0.167227
$460$	−5.43182	−0.253260
$461$	21.1906	0.986944	0.493472	−	0.869762i	$-0.335728\pi$
$461$	21.1906	0.986944	0.493472	+	0.869762i	$0.335728\pi$
$462$	3.08408	0.143484
$463$	−21.9687	−1.02097	−0.510487	−	0.859886i	$-0.670535\pi$
$463$	−21.9687	−1.02097	−0.510487	+	0.859886i	$0.670535\pi$
$464$	−1.85516	−0.0861235
$465$	−17.9136	−0.830723
$466$	−1.91201	−0.0885719
$467$	−5.91139	−0.273547	−0.136773	−	0.990602i	$-0.543673\pi$
$467$	−5.91139	−0.273547	−0.136773	+	0.990602i	$0.543673\pi$
$468$	9.67728	0.447332
$469$	−9.35356	−0.431907
$470$	9.31144	0.429505
$471$	19.7971	0.912202
$472$	11.3276	0.521397
$473$	−5.87822	−0.270281
$474$	−4.73902	−0.217670
$475$	0	0
$476$	3.92300	0.179810
$477$	12.3868	0.567151
$478$	3.61595	0.165390
$479$	25.5707	1.16836	0.584178	−	0.811626i	$-0.301417\pi$
$479$	25.5707	1.16836	0.584178	+	0.811626i	$0.301417\pi$
$480$	3.58479	0.163622
$481$	−2.42303	−0.110481
$482$	0.285715	0.0130140
$483$	−9.64007	−0.438638
$484$	−9.50496	−0.432044
$485$	−25.2789	−1.14785
$486$	−22.3702	−1.01473
$487$	33.0894	1.49942	0.749711	−	0.661765i	$-0.230192\pi$
$487$	33.0894	1.49942	0.749711	+	0.661765i	$0.230192\pi$
$488$	−13.9313	−0.630639
$489$	45.7749	2.07001
$490$	1.42123	0.0642046
$491$	−38.7050	−1.74673	−0.873367	−	0.487062i	$-0.838068\pi$
$491$	−38.7050	−1.74673	−0.873367	+	0.487062i	$0.838068\pi$
$492$	18.6083	0.838927
$493$	−7.27778	−0.327775
$494$	0	0
$495$	5.84248	0.262600
$496$	−4.99711	−0.224377
$497$	9.04463	0.405707
$498$	−9.69047	−0.434240
$499$	−34.0924	−1.52618	−0.763092	−	0.646290i	$-0.776320\pi$
$499$	−34.0924	−1.52618	−0.763092	+	0.646290i	$0.776320\pi$
$500$	−11.3416	−0.507210
$501$	−48.5498	−2.16904
$502$	17.4569	0.779140
$503$	−38.6263	−1.72226	−0.861130	−	0.508385i	$-0.830243\pi$
$503$	−38.6263	−1.72226	−0.861130	+	0.508385i	$0.830243\pi$
$504$	3.36207	0.149759
$505$	13.3701	0.594960
$506$	−4.67312	−0.207745
$507$	−11.8927	−0.528174
$508$	11.3031	0.501492
$509$	6.60339	0.292690	0.146345	−	0.989234i	$-0.453249\pi$
$509$	6.60339	0.292690	0.146345	+	0.989234i	$0.453249\pi$
$510$	14.0631	0.622725
$511$	−4.26204	−0.188542
$512$	1.00000	0.0441942
$513$	0	0
$514$	6.07436	0.267929
$515$	−3.72742	−0.164250
$516$	−12.1260	−0.533819
$517$	8.01085	0.352317
$518$	−0.841807	−0.0369869
$519$	−6.63519	−0.291252
$520$	4.09082	0.179394
$521$	27.1001	1.18728	0.593639	−	0.804731i	$-0.297691\pi$
$521$	27.1001	1.18728	0.593639	+	0.804731i	$0.297691\pi$
$522$	−6.23717	−0.272994
$523$	−16.7594	−0.732838	−0.366419	−	0.930450i	$-0.619416\pi$
$523$	−16.7594	−0.732838	−0.366419	+	0.930450i	$0.619416\pi$
$524$	−2.59653	−0.113430
$525$	−7.51677	−0.328059
$526$	−17.9415	−0.782288
$527$	−19.6037	−0.853949
$528$	3.08408	0.134217
$529$	−8.39298	−0.364912
$530$	5.23619	0.227446
$531$	38.0844	1.65272
$532$	0	0
$533$	21.2351	0.919794
$534$	46.5392	2.01395
$535$	−27.4613	−1.18725
$536$	−9.35356	−0.404012
$537$	31.3456	1.35266
$538$	−1.68138	−0.0724895
$539$	1.22272	0.0526661
$540$	1.29795	0.0558550
$541$	−5.43274	−0.233572	−0.116786	−	0.993157i	$-0.537259\pi$
$541$	−5.43274	−0.233572	−0.116786	+	0.993157i	$0.537259\pi$
$542$	7.95578	0.341730
$543$	53.9931	2.31707
$544$	3.92300	0.168197
$545$	−14.9002	−0.638254
$546$	7.26015	0.310706
$547$	8.21665	0.351318	0.175659	−	0.984451i	$-0.443794\pi$
$547$	8.21665	0.351318	0.175659	+	0.984451i	$0.443794\pi$
$548$	−16.9885	−0.725712
$549$	−46.8380	−1.99900
$550$	−3.64383	−0.155373
$551$	0	0
$552$	−9.64007	−0.410309
$553$	−1.87884	−0.0798963
$554$	−30.0011	−1.27462
$555$	−3.01770	−0.128094
$556$	20.1303	0.853716
$557$	−7.40318	−0.313683	−0.156841	−	0.987624i	$-0.550131\pi$
$557$	−7.40318	−0.313683	−0.156841	+	0.987624i	$0.550131\pi$
$558$	−16.8007	−0.711229
$559$	−13.8378	−0.585275
$560$	1.42123	0.0600579
$561$	12.0988	0.510813
$562$	−10.4565	−0.441079
$563$	10.0619	0.424061	0.212030	−	0.977263i	$-0.431992\pi$
$563$	10.0619	0.424061	0.212030	+	0.977263i	$0.431992\pi$
$564$	16.5254	0.695845
$565$	−25.5008	−1.07283
$566$	−8.05939	−0.338762
$567$	−7.78269	−0.326842
$568$	9.04463	0.379504
$569$	1.54777	0.0648857	0.0324429	−	0.999474i	$-0.489671\pi$
$569$	1.54777	0.0648857	0.0324429	+	0.999474i	$0.489671\pi$
$570$	0	0
$571$	−35.8448	−1.50006	−0.750028	−	0.661406i	$-0.769960\pi$
$571$	−35.8448	−1.50006	−0.750028	+	0.661406i	$0.769960\pi$
$572$	3.51943	0.147155
$573$	−24.2825	−1.01441
$574$	7.37747	0.307930
$575$	11.3897	0.474984
$576$	3.36207	0.140086
$577$	−9.67971	−0.402972	−0.201486	−	0.979491i	$-0.564577\pi$
$577$	−9.67971	−0.402972	−0.201486	+	0.979491i	$0.564577\pi$
$578$	−1.61009	−0.0669708
$579$	45.5715	1.89389
$580$	−2.63661	−0.109479
$581$	−3.84190	−0.159389
$582$	−44.8634	−1.85965
$583$	4.50481	0.186570
$584$	−4.26204	−0.176365
$585$	13.7536	0.568643
$586$	−8.05923	−0.332924
$587$	30.1678	1.24516	0.622578	−	0.782558i	$-0.286085\pi$
$587$	30.1678	1.24516	0.622578	+	0.782558i	$0.286085\pi$
$588$	2.52231	0.104019
$589$	0	0
$590$	16.0992	0.662793
$591$	32.3854	1.33216
$592$	−0.841807	−0.0345980
$593$	−29.6496	−1.21756	−0.608782	−	0.793337i	$-0.708342\pi$
$593$	−29.6496	−1.21756	−0.608782	+	0.793337i	$0.708342\pi$
$594$	1.11666	0.0458170
$595$	5.57548	0.228572
$596$	3.63751	0.148998
$597$	−14.3151	−0.585879
$598$	−11.0009	−0.449859
$599$	−31.6080	−1.29147	−0.645733	−	0.763563i	$-0.723448\pi$
$599$	−31.6080	−1.29147	−0.645733	+	0.763563i	$0.723448\pi$
$600$	−7.51677	−0.306871
$601$	−22.8515	−0.932132	−0.466066	−	0.884750i	$-0.654329\pi$
$601$	−22.8515	−0.932132	−0.466066	+	0.884750i	$0.654329\pi$
$602$	−4.80751	−0.195939
$603$	−31.4474	−1.28064
$604$	18.5627	0.755306
$605$	−13.5087	−0.549208
$606$	23.7284	0.963900
$607$	−2.70015	−0.109596	−0.0547978	−	0.998497i	$-0.517451\pi$
$607$	−2.70015	−0.109596	−0.0547978	+	0.998497i	$0.517451\pi$
$608$	0	0
$609$	−4.67929	−0.189615
$610$	−19.7995	−0.801660
$611$	18.8582	0.762919
$612$	13.1894	0.533150
$613$	−45.9337	−1.85525	−0.927623	−	0.373517i	$-0.878152\pi$
$613$	−45.9337	−1.85525	−0.927623	+	0.373517i	$0.878152\pi$
$614$	−14.3712	−0.579974
$615$	26.4467	1.06643
$616$	1.22272	0.0492647
$617$	26.5890	1.07043	0.535217	−	0.844715i	$-0.320230\pi$
$617$	26.5890	1.07043	0.535217	+	0.844715i	$0.320230\pi$
$618$	−6.61521	−0.266103
$619$	30.5279	1.22702	0.613510	−	0.789687i	$-0.289757\pi$
$619$	30.5279	1.22702	0.613510	+	0.789687i	$0.289757\pi$
$620$	−7.10205	−0.285225
$621$	−3.49040	−0.140065
$622$	28.8765	1.15784
$623$	18.4510	0.739224
$624$	7.26015	0.290639
$625$	−1.21844	−0.0487375
$626$	−4.12543	−0.164886
$627$	0	0
$628$	7.84878	0.313200
$629$	−3.30241	−0.131676
$630$	4.77828	0.190371
$631$	6.96559	0.277296	0.138648	−	0.990342i	$-0.455724\pi$
$631$	6.96559	0.277296	0.138648	+	0.990342i	$0.455724\pi$
$632$	−1.87884	−0.0747361
$633$	4.82150	0.191638
$634$	6.54790	0.260050
$635$	16.0642	0.637490
$636$	9.29288	0.368487
$637$	2.87837	0.114045
$638$	−2.26833	−0.0898042
$639$	30.4087	1.20295
$640$	1.42123	0.0561790
$641$	−28.6345	−1.13099	−0.565497	−	0.824751i	$-0.691316\pi$
$641$	−28.6345	−1.13099	−0.565497	+	0.824751i	$0.691316\pi$
$642$	−48.7366	−1.92348
$643$	35.5025	1.40008	0.700040	−	0.714104i	$-0.253165\pi$
$643$	35.5025	1.40008	0.700040	+	0.714104i	$0.253165\pi$
$644$	−3.82191	−0.150604
$645$	−17.2339	−0.678584
$646$	0	0
$647$	−30.9592	−1.21713	−0.608567	−	0.793503i	$-0.708255\pi$
$647$	−30.9592	−1.21713	−0.608567	+	0.793503i	$0.708255\pi$
$648$	−7.78269	−0.305733
$649$	13.8505	0.543680
$650$	−8.57784	−0.336451
$651$	−12.6043	−0.494001
$652$	18.1480	0.710730
$653$	4.34571	0.170061	0.0850305	−	0.996378i	$-0.472901\pi$
$653$	4.34571	0.170061	0.0850305	+	0.996378i	$0.472901\pi$
$654$	−26.4440	−1.03404
$655$	−3.69027	−0.144191
$656$	7.37747	0.288042
$657$	−14.3293	−0.559039
$658$	6.55168	0.255411
$659$	2.04990	0.0798528	0.0399264	−	0.999203i	$-0.487288\pi$
$659$	2.04990	0.0798528	0.0399264	+	0.999203i	$0.487288\pi$
$660$	4.38318	0.170615
$661$	45.2457	1.75986	0.879928	−	0.475108i	$-0.157591\pi$
$661$	45.2457	1.75986	0.879928	+	0.475108i	$0.157591\pi$
$662$	18.3461	0.713040
$663$	28.4816	1.10613
$664$	−3.84190	−0.149095
$665$	0	0
$666$	−2.83022	−0.109669
$667$	7.09025	0.274536
$668$	−19.2481	−0.744732
$669$	6.74597	0.260814
$670$	−13.2936	−0.513575
$671$	−17.0340	−0.657591
$672$	2.52231	0.0973004
$673$	−22.8180	−0.879569	−0.439784	−	0.898103i	$-0.644945\pi$
$673$	−22.8180	−0.879569	−0.439784	+	0.898103i	$0.644945\pi$
$674$	28.3353	1.09144
$675$	−2.72161	−0.104755
$676$	−4.71500	−0.181346
$677$	−37.7097	−1.44930	−0.724652	−	0.689115i	$-0.757999\pi$
$677$	−37.7097	−1.44930	−0.724652	+	0.689115i	$0.757999\pi$
$678$	−45.2574	−1.73810
$679$	−17.7866	−0.682587
$680$	5.57548	0.213810
$681$	−6.95470	−0.266505
$682$	−6.11006	−0.233966
$683$	6.67991	0.255600	0.127800	−	0.991800i	$-0.459208\pi$
$683$	6.67991	0.255600	0.127800	+	0.991800i	$0.459208\pi$
$684$	0	0
$685$	−24.1445	−0.922515
$686$	1.00000	0.0381802
$687$	−39.0449	−1.48966
$688$	−4.80751	−0.183284
$689$	10.6047	0.404006
$690$	−13.7008	−0.521579
$691$	−9.27273	−0.352751	−0.176376	−	0.984323i	$-0.556437\pi$
$691$	−9.27273	−0.352751	−0.176376	+	0.984323i	$0.556437\pi$
$692$	−2.63060	−0.100000
$693$	4.11086	0.156159
$694$	−15.9023	−0.603645
$695$	28.6098	1.08523
$696$	−4.67929	−0.177368
$697$	28.9418	1.09625
$698$	−3.46506	−0.131155
$699$	−4.82268	−0.182411
$700$	−2.98011	−0.112637
$701$	7.55523	0.285357	0.142679	−	0.989769i	$-0.454428\pi$
$701$	7.55523	0.285357	0.142679	+	0.989769i	$0.454428\pi$
$702$	2.62870	0.0992138
$703$	0	0
$704$	1.22272	0.0460829
$705$	23.4864	0.884549
$706$	−8.76647	−0.329931
$707$	9.40739	0.353801
$708$	28.5719	1.07380
$709$	47.6195	1.78839	0.894193	−	0.447681i	$-0.147750\pi$
$709$	47.6195	1.78839	0.894193	+	0.447681i	$0.147750\pi$
$710$	12.8545	0.482421
$711$	−6.31679	−0.236898
$712$	18.4510	0.691481
$713$	19.0985	0.715246
$714$	9.89504	0.370312
$715$	5.00192	0.187061
$716$	12.4273	0.464430
$717$	9.12056	0.340614
$718$	11.2383	0.419410
$719$	−45.0257	−1.67918	−0.839588	−	0.543224i	$-0.817203\pi$
$719$	−45.0257	−1.67918	−0.839588	+	0.543224i	$0.817203\pi$
$720$	4.77828	0.178076
$721$	−2.62267	−0.0976734
$722$	0	0
$723$	0.720663	0.0268018
$724$	21.4062	0.795554
$725$	5.52857	0.205326
$726$	−23.9745	−0.889778
$727$	20.7456	0.769413	0.384707	−	0.923039i	$-0.374303\pi$
$727$	20.7456	0.769413	0.384707	+	0.923039i	$0.374303\pi$
$728$	2.87837	0.106679
$729$	−33.0765	−1.22506
$730$	−6.05734	−0.224192
$731$	−18.8598	−0.697556
$732$	−35.1391	−1.29878
$733$	−20.4921	−0.756892	−0.378446	−	0.925623i	$-0.623542\pi$
$733$	−20.4921	−0.756892	−0.378446	+	0.925623i	$0.623542\pi$
$734$	5.92259	0.218607
$735$	3.58479	0.132227
$736$	−3.82191	−0.140878
$737$	−11.4368	−0.421278
$738$	24.8036	0.913033
$739$	−18.8930	−0.694989	−0.347495	−	0.937682i	$-0.612968\pi$
$739$	−18.8930	−0.694989	−0.347495	+	0.937682i	$0.612968\pi$
$740$	−1.19640	−0.0439806
$741$	0	0
$742$	3.68427	0.135254
$743$	38.6114	1.41651	0.708257	−	0.705955i	$-0.249482\pi$
$743$	38.6114	1.41651	0.708257	+	0.705955i	$0.249482\pi$
$744$	−12.6043	−0.462096
$745$	5.16974	0.189405
$746$	22.7567	0.833180
$747$	−12.9167	−0.472599
$748$	4.79672	0.175385
$749$	−19.3222	−0.706017
$750$	−28.6070	−1.04458
$751$	4.43470	0.161825	0.0809123	−	0.996721i	$-0.474217\pi$
$751$	4.43470	0.161825	0.0809123	+	0.996721i	$0.474217\pi$
$752$	6.55168	0.238915
$753$	44.0318	1.60461
$754$	−5.33983	−0.194465
$755$	26.3819	0.960135
$756$	0.913260	0.0332149
$757$	38.7770	1.40937	0.704687	−	0.709518i	$-0.251087\pi$
$757$	38.7770	1.40937	0.704687	+	0.709518i	$0.251087\pi$
$758$	7.09293	0.257627
$759$	−11.7871	−0.427844
$760$	0	0
$761$	−23.0453	−0.835391	−0.417695	−	0.908587i	$-0.637162\pi$
$761$	−23.0453	−0.835391	−0.417695	+	0.908587i	$0.637162\pi$
$762$	28.5099	1.03280
$763$	−10.4840	−0.379547
$764$	−9.62706	−0.348295
$765$	18.7452	0.677733
$766$	20.1267	0.727206
$767$	32.6051	1.17730
$768$	2.52231	0.0910162
$769$	−53.1943	−1.91824	−0.959118	−	0.283007i	$-0.908668\pi$
$769$	−53.1943	−1.91824	−0.959118	+	0.283007i	$0.908668\pi$
$770$	1.73776	0.0626246
$771$	15.3215	0.551789
$772$	18.0674	0.650258
$773$	−27.8717	−1.00248	−0.501238	−	0.865310i	$-0.667122\pi$
$773$	−27.8717	−1.00248	−0.501238	+	0.865310i	$0.667122\pi$
$774$	−16.1632	−0.580974
$775$	14.8919	0.534934
$776$	−17.7866	−0.638502
$777$	−2.12330	−0.0761730
$778$	−30.2580	−1.08480
$779$	0	0
$780$	10.3183	0.369456
$781$	11.0590	0.395723
$782$	−14.9934	−0.536161
$783$	−1.69424	−0.0605472
$784$	1.00000	0.0357143
$785$	11.1549	0.398136
$786$	−6.54927	−0.233605
$787$	−24.7006	−0.880483	−0.440241	−	0.897879i	$-0.645107\pi$
$787$	−24.7006	−0.880483	−0.440241	+	0.897879i	$0.645107\pi$
$788$	12.8396	0.457390
$789$	−45.2542	−1.61109
$790$	−2.67026	−0.0950036
$791$	−17.9428	−0.637972
$792$	4.11086	0.146073
$793$	−40.0993	−1.42397
$794$	2.90935	0.103249
$795$	13.2073	0.468415
$796$	−5.67539	−0.201159
$797$	−53.0008	−1.87738	−0.938692	−	0.344758i	$-0.887961\pi$
$797$	−53.0008	−1.87738	−0.938692	+	0.344758i	$0.887961\pi$
$798$	0	0
$799$	25.7022	0.909280
$800$	−2.98011	−0.105363
$801$	62.0336	2.19185
$802$	−28.7840	−1.01640
$803$	−5.21127	−0.183902
$804$	−23.5926	−0.832048
$805$	−5.43182	−0.191446
$806$	−14.3835	−0.506638
$807$	−4.24097	−0.149289
$808$	9.40739	0.330951
$809$	24.5013	0.861419	0.430710	−	0.902491i	$-0.358263\pi$
$809$	24.5013	0.861419	0.430710	+	0.902491i	$0.358263\pi$
$810$	−11.0610	−0.388643
$811$	32.5875	1.14430	0.572151	−	0.820148i	$-0.306109\pi$
$811$	32.5875	1.14430	0.572151	+	0.820148i	$0.306109\pi$
$812$	−1.85516	−0.0651033
$813$	20.0670	0.703780
$814$	−1.02929	−0.0360766
$815$	25.7925	0.903471
$816$	9.89504	0.346396
$817$	0	0
$818$	25.6553	0.897015
$819$	9.67728	0.338152
$820$	10.4851	0.366155
$821$	32.4658	1.13307	0.566533	−	0.824039i	$-0.308285\pi$
$821$	32.4658	1.13307	0.566533	+	0.824039i	$0.308285\pi$
$822$	−42.8503	−1.49458
$823$	−23.3268	−0.813122	−0.406561	−	0.913624i	$-0.633272\pi$
$823$	−23.3268	−0.813122	−0.406561	+	0.913624i	$0.633272\pi$
$824$	−2.62267	−0.0913651
$825$	−9.19088	−0.319985
$826$	11.3276	0.394139
$827$	37.5495	1.30572	0.652862	−	0.757477i	$-0.273568\pi$
$827$	37.5495	1.30572	0.652862	+	0.757477i	$0.273568\pi$
$828$	−12.8495	−0.446553
$829$	50.5787	1.75667	0.878336	−	0.478044i	$-0.158654\pi$
$829$	50.5787	1.75667	0.878336	+	0.478044i	$0.158654\pi$
$830$	−5.46022	−0.189527
$831$	−75.6722	−2.62504
$832$	2.87837	0.0997895
$833$	3.92300	0.135924
$834$	50.7750	1.75819
$835$	−27.3560	−0.946693
$836$	0	0
$837$	−4.56366	−0.157743
$838$	1.06546	0.0368058
$839$	−18.9843	−0.655412	−0.327706	−	0.944780i	$-0.606276\pi$
$839$	−18.9843	−0.655412	−0.327706	+	0.944780i	$0.606276\pi$
$840$	3.58479	0.123687
$841$	−25.5584	−0.881324
$842$	5.48941	0.189178
$843$	−26.3745	−0.908386
$844$	1.91154	0.0657979
$845$	−6.70109	−0.230525
$846$	22.0272	0.757312
$847$	−9.50496	−0.326594
$848$	3.68427	0.126518
$849$	−20.3283	−0.697666
$850$	−11.6909	−0.400996
$851$	3.21731	0.110288
$852$	22.8134	0.781574
$853$	−34.5054	−1.18144	−0.590722	−	0.806875i	$-0.701157\pi$
$853$	−34.5054	−1.18144	−0.590722	+	0.806875i	$0.701157\pi$
$854$	−13.9313	−0.476718
$855$	0	0
$856$	−19.3222	−0.660418
$857$	18.5707	0.634363	0.317181	−	0.948365i	$-0.397264\pi$
$857$	18.5707	0.634363	0.317181	+	0.948365i	$0.397264\pi$
$858$	8.87711	0.303059
$859$	−19.8310	−0.676624	−0.338312	−	0.941034i	$-0.609856\pi$
$859$	−19.8310	−0.676624	−0.338312	+	0.941034i	$0.609856\pi$
$860$	−6.83257	−0.232989
$861$	18.6083	0.634169
$862$	22.2378	0.757422
$863$	−48.3278	−1.64510	−0.822549	−	0.568694i	$-0.807449\pi$
$863$	−48.3278	−1.64510	−0.822549	+	0.568694i	$0.807449\pi$
$864$	0.913260	0.0310697
$865$	−3.73868	−0.127119
$866$	12.8888	0.437979
$867$	−4.06115	−0.137924
$868$	−4.99711	−0.169613
$869$	−2.29729	−0.0779301
$870$	−6.65035	−0.225468
$871$	−26.9230	−0.912251
$872$	−10.4840	−0.355034
$873$	−59.7999	−2.02392
$874$	0	0
$875$	−11.3416	−0.383415
$876$	−10.7502	−0.363216
$877$	46.2497	1.56174	0.780871	−	0.624692i	$-0.214776\pi$
$877$	46.2497	1.56174	0.780871	+	0.624692i	$0.214776\pi$
$878$	−17.0046	−0.573878
$879$	−20.3279	−0.685644
$880$	1.73776	0.0585799
$881$	−9.15551	−0.308457	−0.154228	−	0.988035i	$-0.549289\pi$
$881$	−9.15551	−0.308457	−0.154228	+	0.988035i	$0.549289\pi$
$882$	3.36207	0.113207
$883$	45.5264	1.53208	0.766042	−	0.642790i	$-0.222223\pi$
$883$	45.5264	1.53208	0.766042	+	0.642790i	$0.222223\pi$
$884$	11.2918	0.379785
$885$	40.6072	1.36500
$886$	2.51156	0.0843774
$887$	8.12938	0.272958	0.136479	−	0.990643i	$-0.456421\pi$
$887$	8.12938	0.272958	0.136479	+	0.990643i	$0.456421\pi$
$888$	−2.12330	−0.0712533
$889$	11.3031	0.379092
$890$	26.2231	0.879001
$891$	−9.51602	−0.318799
$892$	2.67452	0.0895494
$893$	0	0
$894$	9.17495	0.306856
$895$	17.6621	0.590378
$896$	1.00000	0.0334077
$897$	−27.7477	−0.926468
$898$	11.7883	0.393382
$899$	9.27044	0.309186
$900$	−10.0193	−0.333978
$901$	14.4534	0.481512
$902$	9.02056	0.300352
$903$	−12.1260	−0.403529
$904$	−17.9428	−0.596769
$905$	30.4231	1.01130
$906$	46.8210	1.55552
$907$	16.9768	0.563706	0.281853	−	0.959458i	$-0.409051\pi$
$907$	16.9768	0.563706	0.281853	+	0.959458i	$0.409051\pi$
$908$	−2.75727	−0.0915032
$909$	31.6283	1.04905
$910$	4.09082	0.135609
$911$	−40.6971	−1.34836	−0.674178	−	0.738569i	$-0.735502\pi$
$911$	−40.6971	−1.34836	−0.674178	+	0.738569i	$0.735502\pi$
$912$	0	0
$913$	−4.69755	−0.155466
$914$	−27.4286	−0.907257
$915$	−49.9407	−1.65099
$916$	−15.4798	−0.511467
$917$	−2.59653	−0.0857451
$918$	3.58272	0.118247
$919$	37.2379	1.22837	0.614183	−	0.789164i	$-0.289486\pi$
$919$	37.2379	1.22837	0.614183	+	0.789164i	$0.289486\pi$
$920$	−5.43182	−0.179082
$921$	−36.2487	−1.19443
$922$	21.1906	0.697875
$923$	26.0338	0.856912
$924$	3.08408	0.101459
$925$	2.50867	0.0824847
$926$	−21.9687	−0.721937
$927$	−8.81761	−0.289608
$928$	−1.85516	−0.0608985
$929$	58.4574	1.91793	0.958963	−	0.283532i	$-0.0915064\pi$
$929$	58.4574	1.91793	0.958963	+	0.283532i	$0.0915064\pi$
$930$	−17.9136	−0.587410
$931$	0	0
$932$	−1.91201	−0.0626298
$933$	72.8357	2.38453
$934$	−5.91139	−0.193427
$935$	6.81723	0.222947
$936$	9.67728	0.316312
$937$	17.8662	0.583664	0.291832	−	0.956470i	$-0.405735\pi$
$937$	17.8662	0.583664	0.291832	+	0.956470i	$0.405735\pi$
$938$	−9.35356	−0.305405
$939$	−10.4056	−0.339575
$940$	9.31144	0.303706
$941$	−21.3224	−0.695089	−0.347545	−	0.937663i	$-0.612985\pi$
$941$	−21.3224	−0.695089	−0.347545	+	0.937663i	$0.612985\pi$
$942$	19.7971	0.645024
$943$	−28.1961	−0.918190
$944$	11.3276	0.368684
$945$	1.29795	0.0422224
$946$	−5.87822	−0.191117
$947$	−35.0239	−1.13812	−0.569061	−	0.822295i	$-0.692693\pi$
$947$	−35.0239	−1.13812	−0.569061	+	0.822295i	$0.692693\pi$
$948$	−4.73902	−0.153916
$949$	−12.2677	−0.398227
$950$	0	0
$951$	16.5159	0.535564
$952$	3.92300	0.127145
$953$	2.15394	0.0697729	0.0348865	−	0.999391i	$-0.488893\pi$
$953$	2.15394	0.0697729	0.0348865	+	0.999391i	$0.488893\pi$
$954$	12.3868	0.401036
$955$	−13.6823	−0.442748
$956$	3.61595	0.116948
$957$	−5.72145	−0.184948
$958$	25.5707	0.826152
$959$	−16.9885	−0.548587
$960$	3.58479	0.115699
$961$	−6.02885	−0.194479
$962$	−2.42303	−0.0781216
$963$	−64.9625	−2.09339
$964$	0.285715	0.00920226
$965$	25.6779	0.826599
$966$	−9.64007	−0.310164
$967$	50.8485	1.63518	0.817589	−	0.575802i	$-0.195310\pi$
$967$	50.8485	1.63518	0.817589	+	0.575802i	$0.195310\pi$
$968$	−9.50496	−0.305501
$969$	0	0
$970$	−25.2789	−0.811655
$971$	−52.9962	−1.70073	−0.850364	−	0.526195i	$-0.823618\pi$
$971$	−52.9962	−1.70073	−0.850364	+	0.526195i	$0.823618\pi$
$972$	−22.3702	−0.717523
$973$	20.1303	0.645348
$974$	33.0894	1.06025
$975$	−21.6360	−0.692907
$976$	−13.9313	−0.445929
$977$	15.8968	0.508583	0.254291	−	0.967128i	$-0.418158\pi$
$977$	15.8968	0.508583	0.254291	+	0.967128i	$0.418158\pi$
$978$	45.7749	1.46372
$979$	22.5604	0.721032
$980$	1.42123	0.0453995
$981$	−35.2480	−1.12538
$982$	−38.7050	−1.23513
$983$	23.6553	0.754487	0.377244	−	0.926114i	$-0.376872\pi$
$983$	23.6553	0.754487	0.377244	+	0.926114i	$0.376872\pi$
$984$	18.6083	0.593211
$985$	18.2480	0.581429
$986$	−7.27778	−0.231772
$987$	16.5254	0.526009
$988$	0	0
$989$	18.3739	0.584255
$990$	5.84248	0.185686
$991$	39.8094	1.26459	0.632293	−	0.774729i	$-0.282114\pi$
$991$	39.8094	1.26459	0.632293	+	0.774729i	$0.282114\pi$
$992$	−4.99711	−0.158659
$993$	46.2745	1.46848
$994$	9.04463	0.286878
$995$	−8.06603	−0.255710
$996$	−9.69047	−0.307054
$997$	26.5487	0.840805	0.420403	−	0.907338i	$-0.361889\pi$
$997$	26.5487	0.840805	0.420403	+	0.907338i	$0.361889\pi$
$998$	−34.0924	−1.07918
$999$	−0.768788	−0.0243234

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5054.2.a.be.1.6	yes	6
19.18	odd	2		5054.2.a.z.1.1	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5054.2.a.z.1.1	✓	6	19.18	odd	2
5054.2.a.be.1.6	yes	6	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:	\( N \)	\(=\)	\( 5054 = 2 \cdot 7 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5054.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.52231 q^{3} +1.00000 q^{4} +1.42123 q^{5} +2.52231 q^{6} +1.00000 q^{7} +1.00000 q^{8} +3.36207 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.52231 q^{3} +1.00000 q^{4} +1.42123 q^{5} +2.52231 q^{6} +1.00000 q^{7} +1.00000 q^{8} +3.36207 q^{9} +1.42123 q^{10} +1.22272 q^{11} +2.52231 q^{12} +2.87837 q^{13} +1.00000 q^{14} +3.58479 q^{15} +1.00000 q^{16} +3.92300 q^{17} +3.36207 q^{18} +1.42123 q^{20} +2.52231 q^{21} +1.22272 q^{22} -3.82191 q^{23} +2.52231 q^{24} -2.98011 q^{25} +2.87837 q^{26} +0.913260 q^{27} +1.00000 q^{28} -1.85516 q^{29} +3.58479 q^{30} -4.99711 q^{31} +1.00000 q^{32} +3.08408 q^{33} +3.92300 q^{34} +1.42123 q^{35} +3.36207 q^{36} -0.841807 q^{37} +7.26015 q^{39} +1.42123 q^{40} +7.37747 q^{41} +2.52231 q^{42} -4.80751 q^{43} +1.22272 q^{44} +4.77828 q^{45} -3.82191 q^{46} +6.55168 q^{47} +2.52231 q^{48} +1.00000 q^{49} -2.98011 q^{50} +9.89504 q^{51} +2.87837 q^{52} +3.68427 q^{53} +0.913260 q^{54} +1.73776 q^{55} +1.00000 q^{56} -1.85516 q^{58} +11.3276 q^{59} +3.58479 q^{60} -13.9313 q^{61} -4.99711 q^{62} +3.36207 q^{63} +1.00000 q^{64} +4.09082 q^{65} +3.08408 q^{66} -9.35356 q^{67} +3.92300 q^{68} -9.64007 q^{69} +1.42123 q^{70} +9.04463 q^{71} +3.36207 q^{72} -4.26204 q^{73} -0.841807 q^{74} -7.51677 q^{75} +1.22272 q^{77} +7.26015 q^{78} -1.87884 q^{79} +1.42123 q^{80} -7.78269 q^{81} +7.37747 q^{82} -3.84190 q^{83} +2.52231 q^{84} +5.57548 q^{85} -4.80751 q^{86} -4.67929 q^{87} +1.22272 q^{88} +18.4510 q^{89} +4.77828 q^{90} +2.87837 q^{91} -3.82191 q^{92} -12.6043 q^{93} +6.55168 q^{94} +2.52231 q^{96} -17.7866 q^{97} +1.00000 q^{98} +4.11086 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 6 q^{4} - q^{5} + 6 q^{7} + 6 q^{8} + 8 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 + 6 * q^4 - q^5 + 6 * q^7 + 6 * q^8 + 8 * q^9	\( 6 q + 6 q^{2} + 6 q^{4} - q^{5} + 6 q^{7} + 6 q^{8} + 8 q^{9} - q^{10} + 4 q^{11} + 15 q^{13} + 6 q^{14} + 6 q^{15} + 6 q^{16} - 9 q^{17} + 8 q^{18} - q^{20} + 4 q^{22} + 4 q^{23} + q^{25} + 15 q^{26} - 12 q^{27} + 6 q^{28} + 7 q^{29} + 6 q^{30} + 4 q^{31} + 6 q^{32} + 28 q^{33} - 9 q^{34} - q^{35} + 8 q^{36} + 3 q^{37} - 8 q^{39} - q^{40} + 11 q^{41} - 10 q^{43} + 4 q^{44} + 19 q^{45} + 4 q^{46} + 12 q^{47} + 6 q^{49} + q^{50} + 44 q^{51} + 15 q^{52} - 5 q^{53} - 12 q^{54} - 8 q^{55} + 6 q^{56} + 7 q^{58} + 4 q^{59} + 6 q^{60} - 21 q^{61} + 4 q^{62} + 8 q^{63} + 6 q^{64} - 20 q^{65} + 28 q^{66} + 14 q^{67} - 9 q^{68} - 24 q^{69} - q^{70} + 24 q^{71} + 8 q^{72} - 21 q^{73} + 3 q^{74} + 12 q^{75} + 4 q^{77} - 8 q^{78} + 58 q^{79} - q^{80} - 6 q^{81} + 11 q^{82} + 20 q^{83} - 4 q^{85} - 10 q^{86} - 8 q^{87} + 4 q^{88} + 7 q^{89} + 19 q^{90} + 15 q^{91} + 4 q^{92} - 22 q^{93} + 12 q^{94} + 7 q^{97} + 6 q^{98} - 26 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 6 * q^4 - q^5 + 6 * q^7 + 6 * q^8 + 8 * q^9 - q^10 + 4 * q^11 + 15 * q^13 + 6 * q^14 + 6 * q^15 + 6 * q^16 - 9 * q^17 + 8 * q^18 - q^20 + 4 * q^22 + 4 * q^23 + q^25 + 15 * q^26 - 12 * q^27 + 6 * q^28 + 7 * q^29 + 6 * q^30 + 4 * q^31 + 6 * q^32 + 28 * q^33 - 9 * q^34 - q^35 + 8 * q^36 + 3 * q^37 - 8 * q^39 - q^40 + 11 * q^41 - 10 * q^43 + 4 * q^44 + 19 * q^45 + 4 * q^46 + 12 * q^47 + 6 * q^49 + q^50 + 44 * q^51 + 15 * q^52 - 5 * q^53 - 12 * q^54 - 8 * q^55 + 6 * q^56 + 7 * q^58 + 4 * q^59 + 6 * q^60 - 21 * q^61 + 4 * q^62 + 8 * q^63 + 6 * q^64 - 20 * q^65 + 28 * q^66 + 14 * q^67 - 9 * q^68 - 24 * q^69 - q^70 + 24 * q^71 + 8 * q^72 - 21 * q^73 + 3 * q^74 + 12 * q^75 + 4 * q^77 - 8 * q^78 + 58 * q^79 - q^80 - 6 * q^81 + 11 * q^82 + 20 * q^83 - 4 * q^85 - 10 * q^86 - 8 * q^87 + 4 * q^88 + 7 * q^89 + 19 * q^90 + 15 * q^91 + 4 * q^92 - 22 * q^93 + 12 * q^94 + 7 * q^97 + 6 * q^98 - 26 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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