LMFDB - Embedded newform 7381.2.a.n.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7381,2,Mod(1,7381)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7381, 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("7381.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7381 = 11^{2} \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7381.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:	$58.9375817319$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	7381.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.69917 q^{2} -3.03253 q^{3} +0.887194 q^{4} -2.24383 q^{5} +5.15280 q^{6} -4.06792 q^{7} +1.89085 q^{8} +6.19625 q^{9} +O(q^{10})$	\(q-1.69917 q^{2} -3.03253 q^{3} +0.887194 q^{4} -2.24383 q^{5} +5.15280 q^{6} -4.06792 q^{7} +1.89085 q^{8} +6.19625 q^{9} +3.81265 q^{10} -2.69044 q^{12} -0.345273 q^{13} +6.91210 q^{14} +6.80447 q^{15} -4.98727 q^{16} +4.31305 q^{17} -10.5285 q^{18} -3.41511 q^{19} -1.99071 q^{20} +12.3361 q^{21} +5.21746 q^{23} -5.73407 q^{24} +0.0347544 q^{25} +0.586679 q^{26} -9.69274 q^{27} -3.60903 q^{28} -5.26357 q^{29} -11.5620 q^{30} -3.84549 q^{31} +4.69255 q^{32} -7.32862 q^{34} +9.12769 q^{35} +5.49728 q^{36} -6.55064 q^{37} +5.80287 q^{38} +1.04705 q^{39} -4.24274 q^{40} -0.807276 q^{41} -20.9612 q^{42} -12.0954 q^{43} -13.9033 q^{45} -8.86537 q^{46} -1.91695 q^{47} +15.1241 q^{48} +9.54794 q^{49} -0.0590537 q^{50} -13.0795 q^{51} -0.306324 q^{52} +5.09494 q^{53} +16.4697 q^{54} -7.69183 q^{56} +10.3564 q^{57} +8.94373 q^{58} -6.80265 q^{59} +6.03689 q^{60} +1.00000 q^{61} +6.53415 q^{62} -25.2058 q^{63} +2.00110 q^{64} +0.774732 q^{65} -9.92804 q^{67} +3.82651 q^{68} -15.8221 q^{69} -15.5095 q^{70} -5.17396 q^{71} +11.7162 q^{72} +13.2805 q^{73} +11.1307 q^{74} -0.105394 q^{75} -3.02987 q^{76} -1.77912 q^{78} +11.4450 q^{79} +11.1906 q^{80} +10.8048 q^{81} +1.37170 q^{82} +7.61720 q^{83} +10.9445 q^{84} -9.67772 q^{85} +20.5522 q^{86} +15.9620 q^{87} +14.5492 q^{89} +23.6242 q^{90} +1.40454 q^{91} +4.62890 q^{92} +11.6616 q^{93} +3.25724 q^{94} +7.66292 q^{95} -14.2303 q^{96} +2.58164 q^{97} -16.2236 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 5 q^{2} - q^{3} + 25 q^{4} - q^{5} - 4 q^{7} - 21 q^{8} + 24 q^{9}+O(q^{10}) $ 25 * q - 5 * q^2 - q^3 + 25 * q^4 - q^5 - 4 * q^7 - 21 * q^8 + 24 * q^9	$ 25 q - 5 q^{2} - q^{3} + 25 q^{4} - q^{5} - 4 q^{7} - 21 q^{8} + 24 q^{9} - q^{12} - 4 q^{13} - q^{14} - 2 q^{15} + 21 q^{16} - 10 q^{17} - 40 q^{18} - 17 q^{19} - 6 q^{20} - 15 q^{21} - 4 q^{23} + 9 q^{24} + 40 q^{25} - 18 q^{26} + 8 q^{27} + 29 q^{28} - 35 q^{29} + 6 q^{30} - 12 q^{31} - 47 q^{32} - 45 q^{35} + 41 q^{36} - 14 q^{37} - 13 q^{38} - 20 q^{39} - 69 q^{40} - 24 q^{41} - 32 q^{42} - 24 q^{43} - 16 q^{45} - 10 q^{46} + 22 q^{47} - 54 q^{48} + 23 q^{49} - 26 q^{50} - 76 q^{51} - q^{52} - 27 q^{53} - 13 q^{54} - 9 q^{56} - 4 q^{57} + 76 q^{58} - 21 q^{59} + 28 q^{60} + 25 q^{61} - 25 q^{62} - 4 q^{63} + 5 q^{64} - 20 q^{65} + 13 q^{67} + 34 q^{68} - 7 q^{69} - 41 q^{70} - 24 q^{71} - 54 q^{72} - 39 q^{73} - 56 q^{74} + 7 q^{75} - 42 q^{76} + 30 q^{78} - 5 q^{79} + 92 q^{80} + 9 q^{81} - 9 q^{82} - 51 q^{83} - 125 q^{84} - 5 q^{85} - 10 q^{86} - 3 q^{87} + 17 q^{89} + 104 q^{90} + 8 q^{91} - 23 q^{92} - 36 q^{93} + 29 q^{94} - 81 q^{95} + 48 q^{96} - 15 q^{97} - 25 q^{98}+O(q^{100}) $ 25 * q - 5 * q^2 - q^3 + 25 * q^4 - q^5 - 4 * q^7 - 21 * q^8 + 24 * q^9 - q^12 - 4 * q^13 - q^14 - 2 * q^15 + 21 * q^16 - 10 * q^17 - 40 * q^18 - 17 * q^19 - 6 * q^20 - 15 * q^21 - 4 * q^23 + 9 * q^24 + 40 * q^25 - 18 * q^26 + 8 * q^27 + 29 * q^28 - 35 * q^29 + 6 * q^30 - 12 * q^31 - 47 * q^32 - 45 * q^35 + 41 * q^36 - 14 * q^37 - 13 * q^38 - 20 * q^39 - 69 * q^40 - 24 * q^41 - 32 * q^42 - 24 * q^43 - 16 * q^45 - 10 * q^46 + 22 * q^47 - 54 * q^48 + 23 * q^49 - 26 * q^50 - 76 * q^51 - q^52 - 27 * q^53 - 13 * q^54 - 9 * q^56 - 4 * q^57 + 76 * q^58 - 21 * q^59 + 28 * q^60 + 25 * q^61 - 25 * q^62 - 4 * q^63 + 5 * q^64 - 20 * q^65 + 13 * q^67 + 34 * q^68 - 7 * q^69 - 41 * q^70 - 24 * q^71 - 54 * q^72 - 39 * q^73 - 56 * q^74 + 7 * q^75 - 42 * q^76 + 30 * q^78 - 5 * q^79 + 92 * q^80 + 9 * q^81 - 9 * q^82 - 51 * q^83 - 125 * q^84 - 5 * q^85 - 10 * q^86 - 3 * q^87 + 17 * q^89 + 104 * q^90 + 8 * q^91 - 23 * q^92 - 36 * q^93 + 29 * q^94 - 81 * q^95 + 48 * q^96 - 15 * q^97 - 25 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.69917	−1.20150	−0.600749	−	0.799438i	$-0.705131\pi$
$2$	−1.69917	−1.20150	−0.600749	+	0.799438i	$0.705131\pi$
$3$	−3.03253	−1.75083	−0.875417	−	0.483369i	$-0.839413\pi$
$3$	−3.03253	−1.75083	−0.875417	+	0.483369i	$0.839413\pi$
$4$	0.887194	0.443597
$5$	−2.24383	−1.00347	−0.501735	−	0.865022i	$-0.667305\pi$
$5$	−2.24383	−1.00347	−0.501735	+	0.865022i	$0.667305\pi$
$6$	5.15280	2.10362
$7$	−4.06792	−1.53753	−0.768764	−	0.639533i	$-0.779128\pi$
$7$	−4.06792	−1.53753	−0.768764	+	0.639533i	$0.779128\pi$
$8$	1.89085	0.668517
$9$	6.19625	2.06542
$10$	3.81265	1.20567
$11$	0	0
$11$	0	0
$12$	−2.69044	−0.776664
$13$	−0.345273	−0.0957615	−0.0478807	−	0.998853i	$-0.515247\pi$
$13$	−0.345273	−0.0957615	−0.0478807	+	0.998853i	$0.515247\pi$
$14$	6.91210	1.84734
$15$	6.80447	1.75691
$16$	−4.98727	−1.24682
$17$	4.31305	1.04607	0.523034	−	0.852312i	$-0.324800\pi$
$17$	4.31305	1.04607	0.523034	+	0.852312i	$0.324800\pi$
$18$	−10.5285	−2.48160
$19$	−3.41511	−0.783480	−0.391740	−	0.920076i	$-0.628127\pi$
$19$	−3.41511	−0.783480	−0.391740	+	0.920076i	$0.628127\pi$
$20$	−1.99071	−0.445136
$21$	12.3361	2.69195
$22$	0	0
$23$	5.21746	1.08792	0.543958	−	0.839113i	$-0.316925\pi$
$23$	5.21746	1.08792	0.543958	+	0.839113i	$0.316925\pi$
$24$	−5.73407	−1.17046
$25$	0.0347544	0.00695087
$26$	0.586679	0.115057
$27$	−9.69274	−1.86537
$28$	−3.60903	−0.682042
$29$	−5.26357	−0.977421	−0.488710	−	0.872446i	$-0.662533\pi$
$29$	−5.26357	−0.977421	−0.488710	+	0.872446i	$0.662533\pi$
$30$	−11.5620	−2.11092
$31$	−3.84549	−0.690670	−0.345335	−	0.938480i	$-0.612235\pi$
$31$	−3.84549	−0.690670	−0.345335	+	0.938480i	$0.612235\pi$
$32$	4.69255	0.829533
$33$	0	0
$34$	−7.32862	−1.25685
$35$	9.12769	1.54286
$36$	5.49728	0.916213
$37$	−6.55064	−1.07692	−0.538459	−	0.842651i	$-0.680993\pi$
$37$	−6.55064	−1.07692	−0.538459	+	0.842651i	$0.680993\pi$
$38$	5.80287	0.941350
$39$	1.04705	0.167662
$40$	−4.24274	−0.670836
$41$	−0.807276	−0.126075	−0.0630377	−	0.998011i	$-0.520079\pi$
$41$	−0.807276	−0.126075	−0.0630377	+	0.998011i	$0.520079\pi$
$42$	−20.9612	−3.23438
$43$	−12.0954	−1.84453	−0.922264	−	0.386560i	$-0.873663\pi$
$43$	−12.0954	−1.84453	−0.922264	+	0.386560i	$0.873663\pi$
$44$	0	0
$45$	−13.9033	−2.07258
$46$	−8.86537	−1.30713
$47$	−1.91695	−0.279616	−0.139808	−	0.990179i	$-0.544649\pi$
$47$	−1.91695	−0.279616	−0.139808	+	0.990179i	$0.544649\pi$
$48$	15.1241	2.18297
$49$	9.54794	1.36399
$50$	−0.0590537	−0.00835146
$51$	−13.0795	−1.83149
$52$	−0.306324	−0.0424795
$53$	5.09494	0.699845	0.349922	−	0.936779i	$-0.386208\pi$
$53$	5.09494	0.699845	0.349922	+	0.936779i	$0.386208\pi$
$54$	16.4697	2.24124
$55$	0	0
$56$	−7.69183	−1.02786
$57$	10.3564	1.37174
$58$	8.94373	1.17437
$59$	−6.80265	−0.885629	−0.442815	−	0.896613i	$-0.646020\pi$
$59$	−6.80265	−0.885629	−0.442815	+	0.896613i	$0.646020\pi$
$60$	6.03689	0.779359
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	6.53415	0.829838
$63$	−25.2058	−3.17564
$64$	2.00110	0.250137
$65$	0.774732	0.0960937
$66$	0	0
$67$	−9.92804	−1.21290	−0.606452	−	0.795120i	$-0.707408\pi$
$67$	−9.92804	−1.21290	−0.606452	+	0.795120i	$0.707408\pi$
$68$	3.82651	0.464032
$69$	−15.8221	−1.90476
$70$	−15.5095	−1.85375
$71$	−5.17396	−0.614036	−0.307018	−	0.951704i	$-0.599331\pi$
$71$	−5.17396	−0.614036	−0.307018	+	0.951704i	$0.599331\pi$
$72$	11.7162	1.38077
$73$	13.2805	1.55437	0.777183	−	0.629274i	$-0.216648\pi$
$73$	13.2805	1.55437	0.777183	+	0.629274i	$0.216648\pi$
$74$	11.1307	1.29392
$75$	−0.105394	−0.0121698
$76$	−3.02987	−0.347549
$77$	0	0
$78$	−1.77912	−0.201446
$79$	11.4450	1.28766	0.643831	−	0.765168i	$-0.277344\pi$
$79$	11.4450	1.28766	0.643831	+	0.765168i	$0.277344\pi$
$80$	11.1906	1.25114
$81$	10.8048	1.20053
$82$	1.37170	0.151479
$83$	7.61720	0.836096	0.418048	−	0.908425i	$-0.362714\pi$
$83$	7.61720	0.836096	0.418048	+	0.908425i	$0.362714\pi$
$84$	10.9445	1.19414
$85$	−9.67772	−1.04970
$86$	20.5522	2.21620
$87$	15.9620	1.71130
$88$	0	0
$89$	14.5492	1.54221	0.771106	−	0.636707i	$-0.219704\pi$
$89$	14.5492	1.54221	0.771106	+	0.636707i	$0.219704\pi$
$90$	23.6242	2.49020
$91$	1.40454	0.147236
$92$	4.62890	0.482596
$93$	11.6616	1.20925
$94$	3.25724	0.335959
$95$	7.66292	0.786199
$96$	−14.2303	−1.45237
$97$	2.58164	0.262126	0.131063	−	0.991374i	$-0.458161\pi$
$97$	2.58164	0.262126	0.131063	+	0.991374i	$0.458161\pi$
$98$	−16.2236	−1.63883
$99$	0	0
$100$	0.0308339	0.00308339
$101$	−6.06287	−0.603279	−0.301639	−	0.953422i	$-0.597534\pi$
$101$	−6.06287	−0.603279	−0.301639	+	0.953422i	$0.597534\pi$
$102$	22.2243	2.20053
$103$	−18.1557	−1.78893	−0.894467	−	0.447134i	$-0.852445\pi$
$103$	−18.1557	−1.78893	−0.894467	+	0.447134i	$0.852445\pi$
$104$	−0.652860	−0.0640182
$105$	−27.6800	−2.70129
$106$	−8.65720	−0.840862
$107$	−3.80288	−0.367638	−0.183819	−	0.982960i	$-0.558846\pi$
$107$	−3.80288	−0.367638	−0.183819	+	0.982960i	$0.558846\pi$
$108$	−8.59934	−0.827472
$109$	−16.2495	−1.55642	−0.778210	−	0.628004i	$-0.783872\pi$
$109$	−16.2495	−1.55642	−0.778210	+	0.628004i	$0.783872\pi$
$110$	0	0
$111$	19.8650	1.88551
$112$	20.2878	1.91702
$113$	11.1544	1.04931	0.524657	−	0.851314i	$-0.324194\pi$
$113$	11.1544	1.04931	0.524657	+	0.851314i	$0.324194\pi$
$114$	−17.5974	−1.64815
$115$	−11.7071	−1.09169
$116$	−4.66981	−0.433581
$117$	−2.13940	−0.197787
$118$	11.5589	1.06408
$119$	−17.5451	−1.60836
$120$	12.8663	1.17452
$121$	0	0
$122$	−1.69917	−0.153836
$123$	2.44809	0.220737
$124$	−3.41169	−0.306379
$125$	11.1411	0.996494
$126$	42.8291	3.81552
$127$	11.9209	1.05781	0.528905	−	0.848681i	$-0.322603\pi$
$127$	11.9209	1.05781	0.528905	+	0.848681i	$0.322603\pi$
$128$	−12.7853	−1.13007
$129$	36.6796	3.22946
$130$	−1.31641	−0.115456
$131$	−3.39651	−0.296755	−0.148377	−	0.988931i	$-0.547405\pi$
$131$	−3.39651	−0.296755	−0.148377	+	0.988931i	$0.547405\pi$
$132$	0	0
$133$	13.8924	1.20462
$134$	16.8695	1.45730
$135$	21.7488	1.87184
$136$	8.15533	0.699314
$137$	16.1570	1.38038	0.690191	−	0.723627i	$-0.257526\pi$
$137$	16.1570	1.38038	0.690191	+	0.723627i	$0.257526\pi$
$138$	26.8845	2.28856
$139$	−11.7331	−0.995189	−0.497594	−	0.867410i	$-0.665783\pi$
$139$	−11.7331	−0.995189	−0.497594	+	0.867410i	$0.665783\pi$
$140$	8.09803	0.684409
$141$	5.81322	0.489562
$142$	8.79146	0.737763
$143$	0	0
$144$	−30.9024	−2.57520
$145$	11.8105	0.980812
$146$	−22.5659	−1.86757
$147$	−28.9544	−2.38812
$148$	−5.81169	−0.477718
$149$	4.56742	0.374177	0.187089	−	0.982343i	$-0.440095\pi$
$149$	4.56742	0.374177	0.187089	+	0.982343i	$0.440095\pi$
$150$	0.179082	0.0146220
$151$	3.38980	0.275858	0.137929	−	0.990442i	$-0.455955\pi$
$151$	3.38980	0.275858	0.137929	+	0.990442i	$0.455955\pi$
$152$	−6.45747	−0.523770
$153$	26.7247	2.16057
$154$	0	0
$155$	8.62860	0.693066
$156$	0.928937	0.0743745
$157$	8.88436	0.709049	0.354525	−	0.935047i	$-0.384643\pi$
$157$	8.88436	0.709049	0.354525	+	0.935047i	$0.384643\pi$
$158$	−19.4470	−1.54712
$159$	−15.4506	−1.22531
$160$	−10.5293	−0.832411
$161$	−21.2242	−1.67270
$162$	−18.3592	−1.44244
$163$	18.1224	1.41946	0.709730	−	0.704474i	$-0.248817\pi$
$163$	18.1224	1.41946	0.709730	+	0.704474i	$0.248817\pi$
$164$	−0.716210	−0.0559266
$165$	0	0
$166$	−12.9429	−1.00457
$167$	12.4331	0.962103	0.481051	−	0.876692i	$-0.340255\pi$
$167$	12.4331	0.962103	0.481051	+	0.876692i	$0.340255\pi$
$168$	23.3257	1.79962
$169$	−12.8808	−0.990830
$170$	16.4441	1.26121
$171$	−21.1609	−1.61821
$172$	−10.7309	−0.818227
$173$	−19.5664	−1.48760	−0.743802	−	0.668400i	$-0.766979\pi$
$173$	−19.5664	−1.48760	−0.743802	+	0.668400i	$0.766979\pi$
$174$	−27.1221	−2.05612
$175$	−0.141378	−0.0106872
$176$	0	0
$177$	20.6293	1.55059
$178$	−24.7216	−1.85296
$179$	17.2239	1.28737	0.643686	−	0.765290i	$-0.277404\pi$
$179$	17.2239	1.28737	0.643686	+	0.765290i	$0.277404\pi$
$180$	−12.3349	−0.919392
$181$	−19.0081	−1.41286	−0.706429	−	0.707784i	$-0.749695\pi$
$181$	−19.0081	−1.41286	−0.706429	+	0.707784i	$0.749695\pi$
$182$	−2.38656	−0.176904
$183$	−3.03253	−0.224171
$184$	9.86544	0.727290
$185$	14.6985	1.08066
$186$	−19.8150	−1.45291
$187$	0	0
$188$	−1.70071	−0.124037
$189$	39.4293	2.86806
$190$	−13.0206	−0.944616
$191$	3.78035	0.273537	0.136768	−	0.990603i	$-0.456328\pi$
$191$	3.78035	0.273537	0.136768	+	0.990603i	$0.456328\pi$
$192$	−6.06839	−0.437948
$193$	−4.58479	−0.330020	−0.165010	−	0.986292i	$-0.552766\pi$
$193$	−4.58479	−0.330020	−0.165010	+	0.986292i	$0.552766\pi$
$194$	−4.38666	−0.314944
$195$	−2.34940	−0.168244
$196$	8.47087	0.605062
$197$	21.7343	1.54850	0.774252	−	0.632877i	$-0.218126\pi$
$197$	21.7343	1.54850	0.774252	+	0.632877i	$0.218126\pi$
$198$	0	0
$199$	15.0074	1.06385	0.531924	−	0.846792i	$-0.321469\pi$
$199$	15.0074	1.06385	0.531924	+	0.846792i	$0.321469\pi$
$200$	0.0657153	0.00464678
$201$	30.1071	2.12359
$202$	10.3019	0.724838
$203$	21.4118	1.50281
$204$	−11.6040	−0.812443
$205$	1.81139	0.126513
$206$	30.8497	2.14940
$207$	32.3287	2.24700
$208$	1.72197	0.119397
$209$	0	0
$210$	47.0332	3.24560
$211$	−12.3631	−0.851114	−0.425557	−	0.904932i	$-0.639922\pi$
$211$	−12.3631	−0.851114	−0.425557	+	0.904932i	$0.639922\pi$
$212$	4.52020	0.310449
$213$	15.6902	1.07507
$214$	6.46175	0.441716
$215$	27.1399	1.85093
$216$	−18.3275	−1.24703
$217$	15.6431	1.06192
$218$	27.6107	1.87003
$219$	−40.2736	−2.72144
$220$	0	0
$221$	−1.48918	−0.100173
$222$	−33.7542	−2.26543
$223$	21.6990	1.45307	0.726536	−	0.687128i	$-0.241129\pi$
$223$	21.6990	1.45307	0.726536	+	0.687128i	$0.241129\pi$
$224$	−19.0889	−1.27543
$225$	0.215347	0.0143565
$226$	−18.9532	−1.26075
$227$	−10.5734	−0.701780	−0.350890	−	0.936417i	$-0.614121\pi$
$227$	−10.5734	−0.701780	−0.350890	+	0.936417i	$0.614121\pi$
$228$	9.18817	0.608501
$229$	15.9875	1.05648	0.528242	−	0.849094i	$-0.322851\pi$
$229$	15.9875	1.05648	0.528242	+	0.849094i	$0.322851\pi$
$230$	19.8924	1.31166
$231$	0	0
$232$	−9.95263	−0.653422
$233$	12.0898	0.792031	0.396016	−	0.918244i	$-0.370393\pi$
$233$	12.0898	0.792031	0.396016	+	0.918244i	$0.370393\pi$
$234$	3.63521	0.237641
$235$	4.30131	0.280587
$236$	−6.03527	−0.392862
$237$	−34.7073	−2.25448
$238$	29.8122	1.93244
$239$	−27.9233	−1.80621	−0.903103	−	0.429423i	$-0.858717\pi$
$239$	−27.9233	−1.80621	−0.903103	+	0.429423i	$0.858717\pi$
$240$	−33.9358	−2.19055
$241$	−17.1219	−1.10292	−0.551458	−	0.834203i	$-0.685928\pi$
$241$	−17.1219	−1.10292	−0.551458	+	0.834203i	$0.685928\pi$
$242$	0	0
$243$	−3.68768	−0.236565
$244$	0.887194	0.0567968
$245$	−21.4239	−1.36872
$246$	−4.15973	−0.265215
$247$	1.17915	0.0750272
$248$	−7.27124	−0.461724
$249$	−23.0994	−1.46386
$250$	−18.9308	−1.19729
$251$	17.6075	1.11137	0.555687	−	0.831392i	$-0.312455\pi$
$251$	17.6075	1.11137	0.555687	+	0.831392i	$0.312455\pi$
$252$	−22.3625	−1.40870
$253$	0	0
$254$	−20.2557	−1.27096
$255$	29.3480	1.83784
$256$	17.7223	1.10764
$257$	18.7490	1.16953	0.584765	−	0.811203i	$-0.301187\pi$
$257$	18.7490	1.16953	0.584765	+	0.811203i	$0.301187\pi$
$258$	−62.3251	−3.88019
$259$	26.6475	1.65579
$260$	0.687338	0.0426269
$261$	−32.6144	−2.01878
$262$	5.77127	0.356550
$263$	14.5047	0.894396	0.447198	−	0.894435i	$-0.352422\pi$
$263$	14.5047	0.894396	0.447198	+	0.894435i	$0.352422\pi$
$264$	0	0
$265$	−11.4322	−0.702273
$266$	−23.6056	−1.44735
$267$	−44.1209	−2.70016
$268$	−8.80810	−0.538040
$269$	6.86326	0.418460	0.209230	−	0.977866i	$-0.432904\pi$
$269$	6.86326	0.418460	0.209230	+	0.977866i	$0.432904\pi$
$270$	−36.9551	−2.24901
$271$	30.9042	1.87730	0.938649	−	0.344873i	$-0.112078\pi$
$271$	30.9042	1.87730	0.938649	+	0.344873i	$0.112078\pi$
$272$	−21.5103	−1.30426
$273$	−4.25932	−0.257786
$274$	−27.4535	−1.65853
$275$	0	0
$276$	−14.0373	−0.844945
$277$	−13.1291	−0.788852	−0.394426	−	0.918928i	$-0.629057\pi$
$277$	−13.1291	−0.788852	−0.394426	+	0.918928i	$0.629057\pi$
$278$	19.9366	1.19572
$279$	−23.8276	−1.42652
$280$	17.2591	1.03143
$281$	−32.0655	−1.91287	−0.956434	−	0.291949i	$-0.905696\pi$
$281$	−32.0655	−1.91287	−0.956434	+	0.291949i	$0.905696\pi$
$282$	−9.87768	−0.588207
$283$	−8.44535	−0.502024	−0.251012	−	0.967984i	$-0.580763\pi$
$283$	−8.44535	−0.502024	−0.251012	+	0.967984i	$0.580763\pi$
$284$	−4.59030	−0.272384
$285$	−23.2380	−1.37650
$286$	0	0
$287$	3.28393	0.193844
$288$	29.0762	1.71333
$289$	1.60236	0.0942566
$290$	−20.0682	−1.17844
$291$	−7.82892	−0.458939
$292$	11.7824	0.689512
$293$	8.09847	0.473118	0.236559	−	0.971617i	$-0.423980\pi$
$293$	8.09847	0.473118	0.236559	+	0.971617i	$0.423980\pi$
$294$	49.1986	2.86932
$295$	15.2640	0.888702
$296$	−12.3863	−0.719939
$297$	0	0
$298$	−7.76084	−0.449573
$299$	−1.80145	−0.104180
$300$	−0.0935047	−0.00539849
$301$	49.2030	2.83601
$302$	−5.75986	−0.331443
$303$	18.3859	1.05624
$304$	17.0321	0.976858
$305$	−2.24383	−0.128481
$306$	−45.4100	−2.59592
$307$	−14.5881	−0.832588	−0.416294	−	0.909230i	$-0.636671\pi$
$307$	−14.5881	−0.832588	−0.416294	+	0.909230i	$0.636671\pi$
$308$	0	0
$309$	55.0577	3.13213
$310$	−14.6615	−0.832717
$311$	−24.9713	−1.41599	−0.707997	−	0.706215i	$-0.750401\pi$
$311$	−24.9713	−1.41599	−0.707997	+	0.706215i	$0.750401\pi$
$312$	1.97982	0.112085
$313$	13.8124	0.780722	0.390361	−	0.920662i	$-0.372350\pi$
$313$	13.8124	0.780722	0.390361	+	0.920662i	$0.372350\pi$
$314$	−15.0961	−0.851921
$315$	56.5575	3.18665
$316$	10.1539	0.571202
$317$	23.9479	1.34505	0.672525	−	0.740074i	$-0.265210\pi$
$317$	23.9479	1.34505	0.672525	+	0.740074i	$0.265210\pi$
$318$	26.2532	1.47221
$319$	0	0
$320$	−4.49011	−0.251005
$321$	11.5324	0.643673
$322$	36.0636	2.00975
$323$	−14.7295	−0.819573
$324$	9.58595	0.532553
$325$	−0.0119997	−0.000665626 0
$326$	−30.7932	−1.70548
$327$	49.2771	2.72503
$328$	−1.52644	−0.0842835
$329$	7.79801	0.429918
$330$	0	0
$331$	17.8555	0.981428	0.490714	−	0.871321i	$-0.336736\pi$
$331$	17.8555	0.981428	0.490714	+	0.871321i	$0.336736\pi$
$332$	6.75793	0.370890
$333$	−40.5894	−2.22429
$334$	−21.1260	−1.15596
$335$	22.2768	1.21711
$336$	−61.5235	−3.35638
$337$	2.15258	0.117258	0.0586291	−	0.998280i	$-0.481327\pi$
$337$	2.15258	0.117258	0.0586291	+	0.998280i	$0.481327\pi$
$338$	21.8867	1.19048
$339$	−33.8260	−1.83717
$340$	−8.58602	−0.465642
$341$	0	0
$342$	35.9561	1.94428
$343$	−10.3648	−0.559646
$344$	−22.8706	−1.23310
$345$	35.5021	1.91137
$346$	33.2467	1.78735
$347$	5.46006	0.293112	0.146556	−	0.989202i	$-0.453181\pi$
$347$	5.46006	0.293112	0.146556	+	0.989202i	$0.453181\pi$
$348$	14.1613	0.759128
$349$	33.1504	1.77450	0.887249	−	0.461291i	$-0.152614\pi$
$349$	33.1504	1.77450	0.887249	+	0.461291i	$0.152614\pi$
$350$	0.240226	0.0128406
$351$	3.34664	0.178631
$352$	0	0
$353$	−9.04520	−0.481428	−0.240714	−	0.970596i	$-0.577382\pi$
$353$	−9.04520	−0.481428	−0.240714	+	0.970596i	$0.577382\pi$
$354$	−35.0527	−1.86303
$355$	11.6095	0.616166
$356$	12.9080	0.684120
$357$	53.2061	2.81597
$358$	−29.2663	−1.54677
$359$	−20.2868	−1.07069	−0.535347	−	0.844632i	$-0.679819\pi$
$359$	−20.2868	−1.07069	−0.535347	+	0.844632i	$0.679819\pi$
$360$	−26.2891	−1.38556
$361$	−7.33701	−0.386159
$362$	32.2980	1.69755
$363$	0	0
$364$	1.24610	0.0653134
$365$	−29.7992	−1.55976
$366$	5.15280	0.269341
$367$	33.6040	1.75411	0.877057	−	0.480386i	$-0.159503\pi$
$367$	33.6040	1.75411	0.877057	+	0.480386i	$0.159503\pi$
$368$	−26.0209	−1.35643
$369$	−5.00209	−0.260398
$370$	−24.9753	−1.29840
$371$	−20.7258	−1.07603
$372$	10.3461	0.536418
$373$	−19.3749	−1.00319	−0.501597	−	0.865101i	$-0.667254\pi$
$373$	−19.3749	−1.00319	−0.501597	+	0.865101i	$0.667254\pi$
$374$	0	0
$375$	−33.7859	−1.74470
$376$	−3.62468	−0.186928
$377$	1.81737	0.0935992
$378$	−66.9972	−3.44596
$379$	22.4411	1.15272	0.576360	−	0.817196i	$-0.304473\pi$
$379$	22.4411	1.15272	0.576360	+	0.817196i	$0.304473\pi$
$380$	6.79849	0.348755
$381$	−36.1506	−1.85205
$382$	−6.42348	−0.328654
$383$	5.28812	0.270210	0.135105	−	0.990831i	$-0.456863\pi$
$383$	5.28812	0.270210	0.135105	+	0.990831i	$0.456863\pi$
$384$	38.7718	1.97857
$385$	0	0
$386$	7.79035	0.396518
$387$	−74.9461	−3.80972
$388$	2.29042	0.116278
$389$	9.17792	0.465339	0.232670	−	0.972556i	$-0.425254\pi$
$389$	9.17792	0.465339	0.232670	+	0.972556i	$0.425254\pi$
$390$	3.99204	0.202145
$391$	22.5031	1.13803
$392$	18.0537	0.911851
$393$	10.3000	0.519568
$394$	−36.9304	−1.86052
$395$	−25.6805	−1.29213
$396$	0	0
$397$	10.4480	0.524368	0.262184	−	0.965018i	$-0.415557\pi$
$397$	10.4480	0.524368	0.262184	+	0.965018i	$0.415557\pi$
$398$	−25.5002	−1.27821
$399$	−42.1291	−2.10909
$400$	−0.173330	−0.00866648
$401$	−1.21791	−0.0608198	−0.0304099	−	0.999538i	$-0.509681\pi$
$401$	−1.21791	−0.0608198	−0.0304099	+	0.999538i	$0.509681\pi$
$402$	−51.1572	−2.55149
$403$	1.32774	0.0661395
$404$	−5.37894	−0.267613
$405$	−24.2441	−1.20470
$406$	−36.3823	−1.80562
$407$	0	0
$408$	−24.7313	−1.22438
$409$	39.5439	1.95532	0.977659	−	0.210197i	$-0.0674104\pi$
$409$	39.5439	1.95532	0.977659	+	0.210197i	$0.0674104\pi$
$410$	−3.07786	−0.152005
$411$	−48.9965	−2.41682
$412$	−16.1076	−0.793565
$413$	27.6726	1.36168
$414$	−54.9321	−2.69977
$415$	−17.0917	−0.838997
$416$	−1.62021	−0.0794373
$417$	35.5810	1.74241
$418$	0	0
$419$	−8.56920	−0.418633	−0.209316	−	0.977848i	$-0.567124\pi$
$419$	−8.56920	−0.418633	−0.209316	+	0.977848i	$0.567124\pi$
$420$	−24.5576	−1.19829
$421$	9.76812	0.476069	0.238034	−	0.971257i	$-0.423497\pi$
$421$	9.76812	0.476069	0.238034	+	0.971257i	$0.423497\pi$
$422$	21.0071	1.02261
$423$	−11.8779	−0.577525
$424$	9.63379	0.467858
$425$	0.149897	0.00727108
$426$	−26.6604	−1.29170
$427$	−4.06792	−0.196860
$428$	−3.37389	−0.163083
$429$	0	0
$430$	−46.1155	−2.22389
$431$	−16.1426	−0.777561	−0.388781	−	0.921330i	$-0.627104\pi$
$431$	−16.1426	−0.777561	−0.388781	+	0.921330i	$0.627104\pi$
$432$	48.3404	2.32578
$433$	−27.8164	−1.33677	−0.668386	−	0.743814i	$-0.733015\pi$
$433$	−27.8164	−1.33677	−0.668386	+	0.743814i	$0.733015\pi$
$434$	−26.5804	−1.27590
$435$	−35.8158	−1.71724
$436$	−14.4165	−0.690423
$437$	−17.8182	−0.852360
$438$	68.4319	3.26980
$439$	−7.76951	−0.370819	−0.185409	−	0.982661i	$-0.559361\pi$
$439$	−7.76951	−0.370819	−0.185409	+	0.982661i	$0.559361\pi$
$440$	0	0
$441$	59.1614	2.81721
$442$	2.53037	0.120358
$443$	0.0619506	0.00294336	0.00147168	−	0.999999i	$-0.499532\pi$
$443$	0.0619506	0.00294336	0.00147168	+	0.999999i	$0.499532\pi$
$444$	17.6241	0.836404
$445$	−32.6459	−1.54756
$446$	−36.8704	−1.74586
$447$	−13.8508	−0.655122
$448$	−8.14029	−0.384592
$449$	−18.1849	−0.858200	−0.429100	−	0.903257i	$-0.641169\pi$
$449$	−18.1849	−0.858200	−0.429100	+	0.903257i	$0.641169\pi$
$450$	−0.365912	−0.0172493
$451$	0	0
$452$	9.89608	0.465472
$453$	−10.2797	−0.482982
$454$	17.9660	0.843187
$455$	−3.15155	−0.147747
$456$	19.5825	0.917034
$457$	−10.5852	−0.495155	−0.247578	−	0.968868i	$-0.579635\pi$
$457$	−10.5852	−0.495155	−0.247578	+	0.968868i	$0.579635\pi$
$458$	−27.1656	−1.26936
$459$	−41.8052	−1.95130
$460$	−10.3864	−0.484270
$461$	38.0468	1.77202	0.886009	−	0.463668i	$-0.153467\pi$
$461$	38.0468	1.77202	0.886009	+	0.463668i	$0.153467\pi$
$462$	0	0
$463$	−38.7405	−1.80042	−0.900212	−	0.435452i	$-0.856589\pi$
$463$	−38.7405	−1.80042	−0.900212	+	0.435452i	$0.856589\pi$
$464$	26.2509	1.21867
$465$	−26.1665	−1.21344
$466$	−20.5427	−0.951624
$467$	−12.2973	−0.569051	−0.284525	−	0.958669i	$-0.591836\pi$
$467$	−12.2973	−0.569051	−0.284525	+	0.958669i	$0.591836\pi$
$468$	−1.89806	−0.0877379
$469$	40.3864	1.86487
$470$	−7.30868	−0.337124
$471$	−26.9421	−1.24143
$472$	−12.8628	−0.592058
$473$	0	0
$474$	58.9737	2.70875
$475$	−0.118690	−0.00544587
$476$	−15.5659	−0.713462
$477$	31.5696	1.44547
$478$	47.4465	2.17015
$479$	−24.2880	−1.10975	−0.554875	−	0.831934i	$-0.687234\pi$
$479$	−24.2880	−1.10975	−0.554875	+	0.831934i	$0.687234\pi$
$480$	31.9303	1.45741
$481$	2.26176	0.103127
$482$	29.0930	1.32515
$483$	64.3630	2.92862
$484$	0	0
$485$	−5.79276	−0.263036
$486$	6.26600	0.284232
$487$	22.1739	1.00479	0.502397	−	0.864637i	$-0.332452\pi$
$487$	22.1739	1.00479	0.502397	+	0.864637i	$0.332452\pi$
$488$	1.89085	0.0855948
$489$	−54.9569	−2.48524
$490$	36.4030	1.64452
$491$	−26.6662	−1.20343	−0.601714	−	0.798712i	$-0.705515\pi$
$491$	−26.6662	−1.20343	−0.601714	+	0.798712i	$0.705515\pi$
$492$	2.17193	0.0979182
$493$	−22.7020	−1.02245
$494$	−2.00357	−0.0901450
$495$	0	0
$496$	19.1785	0.861140
$497$	21.0472	0.944097
$498$	39.2499	1.75883
$499$	16.5110	0.739133	0.369567	−	0.929204i	$-0.379506\pi$
$499$	16.5110	0.739133	0.369567	+	0.929204i	$0.379506\pi$
$500$	9.88436	0.442042
$501$	−37.7038	−1.68448
$502$	−29.9182	−1.33531
$503$	31.5177	1.40530	0.702651	−	0.711534i	$-0.251999\pi$
$503$	31.5177	1.40530	0.702651	+	0.711534i	$0.251999\pi$
$504$	−47.6605	−2.12297
$505$	13.6040	0.605372
$506$	0	0
$507$	39.0614	1.73478
$508$	10.5762	0.469241
$509$	−0.491920	−0.0218039	−0.0109020	−	0.999941i	$-0.503470\pi$
$509$	−0.491920	−0.0218039	−0.0109020	+	0.999941i	$0.503470\pi$
$510$	−49.8674	−2.20817
$511$	−54.0240	−2.38988
$512$	−4.54262	−0.200757
$513$	33.1018	1.46148
$514$	−31.8578	−1.40519
$515$	40.7382	1.79514
$516$	32.5420	1.43258
$517$	0	0
$518$	−45.2787	−1.98943
$519$	59.3357	2.60455
$520$	1.46490	0.0642403
$521$	−15.3580	−0.672848	−0.336424	−	0.941711i	$-0.609217\pi$
$521$	−15.3580	−0.672848	−0.336424	+	0.941711i	$0.609217\pi$
$522$	55.4176	2.42556
$523$	16.2168	0.709112	0.354556	−	0.935035i	$-0.384632\pi$
$523$	16.2168	0.709112	0.354556	+	0.935035i	$0.384632\pi$
$524$	−3.01336	−0.131639
$525$	0.428733	0.0187114
$526$	−24.6460	−1.07461
$527$	−16.5858	−0.722487
$528$	0	0
$529$	4.22188	0.183560
$530$	19.4252	0.843779
$531$	−42.1509	−1.82919
$532$	12.3252	0.534367
$533$	0.278731	0.0120732
$534$	74.9691	3.24423
$535$	8.53300	0.368914
$536$	−18.7725	−0.810847
$537$	−52.2319	−2.25397
$538$	−11.6619	−0.502779
$539$	0	0
$540$	19.2954	0.830343
$541$	34.1254	1.46716	0.733582	−	0.679601i	$-0.237847\pi$
$541$	34.1254	1.46716	0.733582	+	0.679601i	$0.237847\pi$
$542$	−52.5117	−2.25557
$543$	57.6426	2.47368
$544$	20.2392	0.867747
$545$	36.4610	1.56182
$546$	7.23732	0.309729
$547$	−11.2920	−0.482812	−0.241406	−	0.970424i	$-0.577609\pi$
$547$	−11.2920	−0.482812	−0.241406	+	0.970424i	$0.577609\pi$
$548$	14.3344	0.612333
$549$	6.19625	0.264450
$550$	0	0
$551$	17.9757	0.765790
$552$	−29.9173	−1.27336
$553$	−46.5572	−1.97981
$554$	22.3087	0.947804
$555$	−44.5737	−1.89205
$556$	−10.4095	−0.441463
$557$	−7.78546	−0.329880	−0.164940	−	0.986304i	$-0.552743\pi$
$557$	−7.78546	−0.329880	−0.164940	+	0.986304i	$0.552743\pi$
$558$	40.4873	1.71396
$559$	4.17621	0.176635
$560$	−45.5223	−1.92367
$561$	0	0
$562$	54.4849	2.29831
$563$	−19.4881	−0.821324	−0.410662	−	0.911788i	$-0.634702\pi$
$563$	−19.4881	−0.821324	−0.410662	+	0.911788i	$0.634702\pi$
$564$	5.15746	0.217168
$565$	−25.0284	−1.05295
$566$	14.3501	0.603181
$567$	−43.9530	−1.84585
$568$	−9.78319	−0.410493
$569$	−19.9819	−0.837685	−0.418843	−	0.908059i	$-0.637564\pi$
$569$	−19.9819	−0.837685	−0.418843	+	0.908059i	$0.637564\pi$
$570$	39.4855	1.65386
$571$	−1.50450	−0.0629614	−0.0314807	−	0.999504i	$-0.510022\pi$
$571$	−1.50450	−0.0629614	−0.0314807	+	0.999504i	$0.510022\pi$
$572$	0	0
$573$	−11.4640	−0.478917
$574$	−5.57997	−0.232903
$575$	0.181329	0.00756196
$576$	12.3993	0.516637
$577$	−17.7987	−0.740969	−0.370484	−	0.928839i	$-0.620808\pi$
$577$	−17.7987	−0.740969	−0.370484	+	0.928839i	$0.620808\pi$
$578$	−2.72269	−0.113249
$579$	13.9035	0.577810
$580$	10.4782	0.435085
$581$	−30.9861	−1.28552
$582$	13.3027	0.551414
$583$	0	0
$584$	25.1115	1.03912
$585$	4.80044	0.198474
$586$	−13.7607	−0.568450
$587$	16.3009	0.672811	0.336405	−	0.941717i	$-0.390789\pi$
$587$	16.3009	0.672811	0.336405	+	0.941717i	$0.390789\pi$
$588$	−25.6882	−1.05936
$589$	13.1328	0.541126
$590$	−25.9361	−1.06777
$591$	−65.9100	−2.71117
$592$	32.6698	1.34272
$593$	−27.2202	−1.11780	−0.558900	−	0.829235i	$-0.688777\pi$
$593$	−27.2202	−1.11780	−0.558900	+	0.829235i	$0.688777\pi$
$594$	0	0
$595$	39.3682	1.61394
$596$	4.05218	0.165984
$597$	−45.5105	−1.86262
$598$	3.06097	0.125173
$599$	17.8581	0.729661	0.364831	−	0.931074i	$-0.381127\pi$
$599$	17.8581	0.729661	0.364831	+	0.931074i	$0.381127\pi$
$600$	−0.199284	−0.00813573
$601$	−2.94974	−0.120323	−0.0601613	−	0.998189i	$-0.519162\pi$
$601$	−2.94974	−0.120323	−0.0601613	+	0.998189i	$0.519162\pi$
$602$	−83.6045	−3.40746
$603$	−61.5167	−2.50515
$604$	3.00741	0.122370
$605$	0	0
$606$	−31.2408	−1.26907
$607$	31.3937	1.27423	0.637115	−	0.770769i	$-0.280128\pi$
$607$	31.3937	1.27423	0.637115	+	0.770769i	$0.280128\pi$
$608$	−16.0256	−0.649923
$609$	−64.9319	−2.63117
$610$	3.81265	0.154370
$611$	0.661872	0.0267765
$612$	23.7100	0.958420
$613$	46.6464	1.88403	0.942015	−	0.335570i	$-0.108929\pi$
$613$	46.6464	1.88403	0.942015	+	0.335570i	$0.108929\pi$
$614$	24.7878	1.00035
$615$	−5.49309	−0.221503
$616$	0	0
$617$	39.1805	1.57735	0.788673	−	0.614813i	$-0.210769\pi$
$617$	39.1805	1.57735	0.788673	+	0.614813i	$0.210769\pi$
$618$	−93.5527	−3.76324
$619$	−5.13363	−0.206338	−0.103169	−	0.994664i	$-0.532898\pi$
$619$	−5.13363	−0.206338	−0.103169	+	0.994664i	$0.532898\pi$
$620$	7.65524	0.307442
$621$	−50.5715	−2.02936
$622$	42.4307	1.70131
$623$	−59.1849	−2.37119
$624$	−5.22193	−0.209045
$625$	−25.1726	−1.00690
$626$	−23.4696	−0.938035
$627$	0	0
$628$	7.88215	0.314532
$629$	−28.2532	−1.12653
$630$	−96.1011	−3.82876
$631$	40.3125	1.60482	0.802408	−	0.596776i	$-0.203552\pi$
$631$	40.3125	1.60482	0.802408	+	0.596776i	$0.203552\pi$
$632$	21.6408	0.860823
$633$	37.4916	1.49016
$634$	−40.6917	−1.61607
$635$	−26.7485	−1.06148
$636$	−13.7077	−0.543544
$637$	−3.29664	−0.130618
$638$	0	0
$639$	−32.0592	−1.26824
$640$	28.6880	1.13399
$641$	13.8058	0.545294	0.272647	−	0.962114i	$-0.412101\pi$
$641$	13.8058	0.545294	0.272647	+	0.962114i	$0.412101\pi$
$642$	−19.5955	−0.773372
$643$	2.37542	0.0936773	0.0468387	−	0.998902i	$-0.485085\pi$
$643$	2.37542	0.0936773	0.0468387	+	0.998902i	$0.485085\pi$
$644$	−18.8300	−0.742005
$645$	−82.3027	−3.24067
$646$	25.0280	0.984715
$647$	−8.74734	−0.343894	−0.171947	−	0.985106i	$-0.555006\pi$
$647$	−8.74734	−0.343894	−0.171947	+	0.985106i	$0.555006\pi$
$648$	20.4303	0.802577
$649$	0	0
$650$	0.0203896	0.000799748 0
$651$	−47.4382	−1.85925
$652$	16.0781	0.629668
$653$	44.5109	1.74185	0.870923	−	0.491419i	$-0.163522\pi$
$653$	44.5109	1.74185	0.870923	+	0.491419i	$0.163522\pi$
$654$	−83.7305	−3.27412
$655$	7.62118	0.297784
$656$	4.02611	0.157193
$657$	82.2894	3.21042
$658$	−13.2502	−0.516545
$659$	−15.1164	−0.588853	−0.294426	−	0.955674i	$-0.595129\pi$
$659$	−15.1164	−0.588853	−0.294426	+	0.955674i	$0.595129\pi$
$660$	0	0
$661$	17.7521	0.690475	0.345238	−	0.938515i	$-0.387798\pi$
$661$	17.7521	0.690475	0.345238	+	0.938515i	$0.387798\pi$
$662$	−30.3396	−1.17918
$663$	4.51598	0.175386
$664$	14.4030	0.558944
$665$	−31.1721	−1.20880
$666$	68.9685	2.67248
$667$	−27.4625	−1.06335
$668$	11.0306	0.426786
$669$	−65.8029	−2.54409
$670$	−37.8522	−1.46236
$671$	0	0
$672$	57.8877	2.23306
$673$	−40.1259	−1.54674	−0.773371	−	0.633954i	$-0.781431\pi$
$673$	−40.1259	−1.54674	−0.773371	+	0.633954i	$0.781431\pi$
$674$	−3.65760	−0.140886
$675$	−0.336865	−0.0129659
$676$	−11.4278	−0.439529
$677$	−1.94787	−0.0748626	−0.0374313	−	0.999299i	$-0.511918\pi$
$677$	−1.94787	−0.0748626	−0.0374313	+	0.999299i	$0.511918\pi$
$678$	57.4762	2.20736
$679$	−10.5019	−0.403026
$680$	−18.2991	−0.701740
$681$	32.0641	1.22870
$682$	0	0
$683$	−44.0655	−1.68612	−0.843060	−	0.537820i	$-0.819248\pi$
$683$	−44.0655	−1.68612	−0.843060	+	0.537820i	$0.819248\pi$
$684$	−18.7738	−0.717835
$685$	−36.2534	−1.38517
$686$	17.6116	0.672414
$687$	−48.4826	−1.84973
$688$	60.3230	2.29979
$689$	−1.75915	−0.0670181
$690$	−60.3242	−2.29650
$691$	18.6369	0.708983	0.354491	−	0.935059i	$-0.384654\pi$
$691$	18.6369	0.708983	0.354491	+	0.935059i	$0.384654\pi$
$692$	−17.3592	−0.659896
$693$	0	0
$694$	−9.27760	−0.352173
$695$	26.3270	0.998642
$696$	30.1817	1.14403
$697$	−3.48182	−0.131883
$698$	−56.3282	−2.13206
$699$	−36.6628	−1.38672
$700$	−0.125430	−0.00474079
$701$	39.8453	1.50494	0.752468	−	0.658629i	$-0.228863\pi$
$701$	39.8453	1.50494	0.752468	+	0.658629i	$0.228863\pi$
$702$	−5.68653	−0.214624
$703$	22.3712	0.843745
$704$	0	0
$705$	−13.0439	−0.491260
$706$	15.3694	0.578434
$707$	24.6633	0.927557
$708$	18.3021	0.687837
$709$	17.5499	0.659099	0.329550	−	0.944138i	$-0.393103\pi$
$709$	17.5499	0.659099	0.329550	+	0.944138i	$0.393103\pi$
$710$	−19.7265	−0.740322
$711$	70.9160	2.65956
$712$	27.5104	1.03099
$713$	−20.0637	−0.751390
$714$	−90.4065	−3.38338
$715$	0	0
$716$	15.2809	0.571074
$717$	84.6782	3.16237
$718$	34.4707	1.28644
$719$	29.7999	1.11135	0.555675	−	0.831400i	$-0.312460\pi$
$719$	29.7999	1.11135	0.555675	+	0.831400i	$0.312460\pi$
$720$	69.3396	2.58414
$721$	73.8558	2.75054
$722$	12.4669	0.463969
$723$	51.9226	1.93102
$724$	−16.8638	−0.626739
$725$	−0.182932	−0.00679393
$726$	0	0
$727$	14.2132	0.527140	0.263570	−	0.964640i	$-0.415100\pi$
$727$	14.2132	0.527140	0.263570	+	0.964640i	$0.415100\pi$
$728$	2.65578	0.0984297
$729$	−21.2314	−0.786348
$730$	50.6340	1.87405
$731$	−52.1679	−1.92950
$732$	−2.69044	−0.0994417
$733$	1.47585	0.0545119	0.0272559	−	0.999628i	$-0.491323\pi$
$733$	1.47585	0.0545119	0.0272559	+	0.999628i	$0.491323\pi$
$734$	−57.0991	−2.10757
$735$	64.9687	2.39641
$736$	24.4832	0.902462
$737$	0	0
$738$	8.49942	0.312868
$739$	−11.8246	−0.434976	−0.217488	−	0.976063i	$-0.569786\pi$
$739$	−11.8246	−0.434976	−0.217488	+	0.976063i	$0.569786\pi$
$740$	13.0404	0.479375
$741$	−3.57580	−0.131360
$742$	35.2168	1.29285
$743$	−32.3540	−1.18695	−0.593477	−	0.804851i	$-0.702245\pi$
$743$	−32.3540	−1.18695	−0.593477	+	0.804851i	$0.702245\pi$
$744$	22.0503	0.808403
$745$	−10.2485	−0.375475
$746$	32.9213	1.20534
$747$	47.1981	1.72689
$748$	0	0
$749$	15.4698	0.565254
$750$	57.4081	2.09625
$751$	−25.0347	−0.913531	−0.456765	−	0.889587i	$-0.650992\pi$
$751$	−25.0347	−0.913531	−0.456765	+	0.889587i	$0.650992\pi$
$752$	9.56037	0.348631
$753$	−53.3952	−1.94583
$754$	−3.08803	−0.112459
$755$	−7.60613	−0.276815
$756$	34.9814	1.27226
$757$	−19.5063	−0.708968	−0.354484	−	0.935062i	$-0.615343\pi$
$757$	−19.5063	−0.708968	−0.354484	+	0.935062i	$0.615343\pi$
$758$	−38.1313	−1.38499
$759$	0	0
$760$	14.4894	0.525587
$761$	−24.9609	−0.904833	−0.452416	−	0.891807i	$-0.649438\pi$
$761$	−24.9609	−0.904833	−0.452416	+	0.891807i	$0.649438\pi$
$762$	61.4261	2.22523
$763$	66.1016	2.39304
$764$	3.35391	0.121340
$765$	−59.9656	−2.16806
$766$	−8.98544	−0.324657
$767$	2.34877	0.0848092
$768$	−53.7434	−1.93930
$769$	−48.4831	−1.74834	−0.874172	−	0.485616i	$-0.838595\pi$
$769$	−48.4831	−1.74834	−0.874172	+	0.485616i	$0.838595\pi$
$770$	0	0
$771$	−56.8569	−2.04765
$772$	−4.06759	−0.146396
$773$	47.6596	1.71420	0.857099	−	0.515152i	$-0.172264\pi$
$773$	47.6596	1.71420	0.857099	+	0.515152i	$0.172264\pi$
$774$	127.346	4.57737
$775$	−0.133647	−0.00480076
$776$	4.88150	0.175236
$777$	−80.8093	−2.89902
$778$	−15.5949	−0.559104
$779$	2.75694	0.0987775
$780$	−2.08437	−0.0746326
$781$	0	0
$782$	−38.2368	−1.36734
$783$	51.0185	1.82325
$784$	−47.6182	−1.70065
$785$	−19.9350	−0.711509
$786$	−17.5016	−0.624260
$787$	−23.5799	−0.840533	−0.420267	−	0.907401i	$-0.638063\pi$
$787$	−23.5799	−0.840533	−0.420267	+	0.907401i	$0.638063\pi$
$788$	19.2825	0.686912
$789$	−43.9859	−1.56594
$790$	43.6357	1.55249
$791$	−45.3750	−1.61335
$792$	0	0
$793$	−0.345273	−0.0122610
$794$	−17.7529	−0.630027
$795$	34.6684	1.22956
$796$	13.3145	0.471920
$797$	−16.1572	−0.572318	−0.286159	−	0.958182i	$-0.592378\pi$
$797$	−16.1572	−0.572318	−0.286159	+	0.958182i	$0.592378\pi$
$798$	71.5847	2.53407
$799$	−8.26791	−0.292498
$800$	0.163086	0.00576598
$801$	90.1505	3.18531
$802$	2.06945	0.0730748
$803$	0	0
$804$	26.7108	0.942019
$805$	47.6234	1.67850
$806$	−2.25606	−0.0794665
$807$	−20.8130	−0.732654
$808$	−11.4640	−0.403302
$809$	18.8265	0.661905	0.330952	−	0.943647i	$-0.392630\pi$
$809$	18.8265	0.661905	0.330952	+	0.943647i	$0.392630\pi$
$810$	41.1949	1.44744
$811$	−29.8136	−1.04690	−0.523448	−	0.852057i	$-0.675355\pi$
$811$	−29.8136	−1.04690	−0.523448	+	0.852057i	$0.675355\pi$
$812$	18.9964	0.666642
$813$	−93.7181	−3.28684
$814$	0	0
$815$	−40.6636	−1.42438
$816$	65.2308	2.28354
$817$	41.3071	1.44515
$818$	−67.1919	−2.34931
$819$	8.70289	0.304104
$820$	1.60705	0.0561207
$821$	−20.0393	−0.699375	−0.349688	−	0.936866i	$-0.613712\pi$
$821$	−20.0393	−0.699375	−0.349688	+	0.936866i	$0.613712\pi$
$822$	83.2536	2.90380
$823$	−42.3084	−1.47478	−0.737389	−	0.675468i	$-0.763942\pi$
$823$	−42.3084	−1.47478	−0.737389	+	0.675468i	$0.763942\pi$
$824$	−34.3297	−1.19593
$825$	0	0
$826$	−47.0206	−1.63605
$827$	−20.8088	−0.723593	−0.361796	−	0.932257i	$-0.617836\pi$
$827$	−20.8088	−0.723593	−0.361796	+	0.932257i	$0.617836\pi$
$828$	28.6818	0.996762
$829$	−19.1426	−0.664851	−0.332426	−	0.943129i	$-0.607867\pi$
$829$	−19.1426	−0.664851	−0.332426	+	0.943129i	$0.607867\pi$
$830$	29.0417	1.00805
$831$	39.8145	1.38115
$832$	−0.690924	−0.0239535
$833$	41.1807	1.42683
$834$	−60.4584	−2.09350
$835$	−27.8977	−0.965441
$836$	0	0
$837$	37.2733	1.28835
$838$	14.5606	0.502986
$839$	−37.2577	−1.28628	−0.643139	−	0.765749i	$-0.722368\pi$
$839$	−37.2577	−1.28628	−0.643139	+	0.765749i	$0.722368\pi$
$840$	−52.3388	−1.80586
$841$	−1.29481	−0.0446487
$842$	−16.5977	−0.571996
$843$	97.2397	3.34911
$844$	−10.9685	−0.377551
$845$	28.9022	0.994267
$846$	20.1827	0.693895
$847$	0	0
$848$	−25.4099	−0.872579
$849$	25.6108	0.878961
$850$	−0.254701	−0.00873619
$851$	−34.1777	−1.17160
$852$	13.9202	0.476900
$853$	34.8079	1.19180	0.595899	−	0.803059i	$-0.296796\pi$
$853$	34.8079	1.19180	0.595899	+	0.803059i	$0.296796\pi$
$854$	6.91210	0.236527
$855$	47.4814	1.62383
$856$	−7.19068	−0.245772
$857$	19.1380	0.653740	0.326870	−	0.945069i	$-0.394006\pi$
$857$	19.1380	0.653740	0.326870	+	0.945069i	$0.394006\pi$
$858$	0	0
$859$	−10.9139	−0.372377	−0.186189	−	0.982514i	$-0.559614\pi$
$859$	−10.9139	−0.372377	−0.186189	+	0.982514i	$0.559614\pi$
$860$	24.0784	0.821066
$861$	−9.95863	−0.339389
$862$	27.4291	0.934238
$863$	32.7665	1.11539	0.557693	−	0.830047i	$-0.311687\pi$
$863$	32.7665	1.11539	0.557693	+	0.830047i	$0.311687\pi$
$864$	−45.4836	−1.54739
$865$	43.9035	1.49276
$866$	47.2650	1.60613
$867$	−4.85922	−0.165028
$868$	13.8785	0.471066
$869$	0	0
$870$	60.8574	2.06326
$871$	3.42788	0.116149
$872$	−30.7254	−1.04049
$873$	15.9965	0.541400
$874$	30.2762	1.02411
$875$	−45.3212	−1.53214
$876$	−35.7305	−1.20722
$877$	50.7742	1.71452	0.857261	−	0.514882i	$-0.172164\pi$
$877$	50.7742	1.71452	0.857261	+	0.514882i	$0.172164\pi$
$878$	13.2018	0.445538
$879$	−24.5589	−0.828351
$880$	0	0
$881$	28.7934	0.970073	0.485037	−	0.874494i	$-0.338806\pi$
$881$	28.7934	0.970073	0.485037	+	0.874494i	$0.338806\pi$
$882$	−100.526	−3.38487
$883$	14.1943	0.477677	0.238839	−	0.971059i	$-0.423233\pi$
$883$	14.1943	0.477677	0.238839	+	0.971059i	$0.423233\pi$
$884$	−1.32119	−0.0444364
$885$	−46.2884	−1.55597
$886$	−0.105265	−0.00353644
$887$	−3.85777	−0.129531	−0.0647657	−	0.997900i	$-0.520630\pi$
$887$	−3.85777	−0.129531	−0.0647657	+	0.997900i	$0.520630\pi$
$888$	37.5618	1.26049
$889$	−48.4933	−1.62641
$890$	55.4710	1.85939
$891$	0	0
$892$	19.2512	0.644578
$893$	6.54661	0.219074
$894$	23.5350	0.787128
$895$	−38.6473	−1.29184
$896$	52.0095	1.73752
$897$	5.46295	0.182403
$898$	30.8994	1.03113
$899$	20.2410	0.675075
$900$	0.191054	0.00636848
$901$	21.9747	0.732084
$902$	0	0
$903$	−149.210	−4.96539
$904$	21.0912	0.701484
$905$	42.6508	1.41776
$906$	17.4670	0.580301
$907$	−48.8273	−1.62128	−0.810642	−	0.585542i	$-0.800882\pi$
$907$	−48.8273	−1.62128	−0.810642	+	0.585542i	$0.800882\pi$
$908$	−9.38064	−0.311307
$909$	−37.5671	−1.24602
$910$	5.35503	0.177517
$911$	−17.7352	−0.587592	−0.293796	−	0.955868i	$-0.594919\pi$
$911$	−17.7352	−0.587592	−0.293796	+	0.955868i	$0.594919\pi$
$912$	−51.6504	−1.71032
$913$	0	0
$914$	17.9861	0.594928
$915$	6.80447	0.224949
$916$	14.1840	0.468653
$917$	13.8167	0.456268
$918$	71.0344	2.34448
$919$	0.368225	0.0121466	0.00607331	−	0.999982i	$-0.498067\pi$
$919$	0.368225	0.0121466	0.00607331	+	0.999982i	$0.498067\pi$
$920$	−22.1363	−0.729813
$921$	44.2390	1.45772
$922$	−64.6482	−2.12908
$923$	1.78643	0.0588010
$924$	0	0
$925$	−0.227663	−0.00748552
$926$	65.8269	2.16321
$927$	−112.497	−3.69490
$928$	−24.6996	−0.810803
$929$	−19.1822	−0.629348	−0.314674	−	0.949200i	$-0.601895\pi$
$929$	−19.1822	−0.629348	−0.314674	+	0.949200i	$0.601895\pi$
$930$	44.4615	1.45795
$931$	−32.6073	−1.06866
$932$	10.7260	0.351343
$933$	75.7264	2.47917
$934$	20.8952	0.683713
$935$	0	0
$936$	−4.04529	−0.132224
$937$	29.7824	0.972949	0.486475	−	0.873695i	$-0.338283\pi$
$937$	29.7824	0.972949	0.486475	+	0.873695i	$0.338283\pi$
$938$	−68.6236	−2.24064
$939$	−41.8865	−1.36691
$940$	3.81610	0.124467
$941$	−21.2059	−0.691293	−0.345647	−	0.938365i	$-0.612340\pi$
$941$	−21.2059	−0.691293	−0.345647	+	0.938365i	$0.612340\pi$
$942$	45.7793	1.49157
$943$	−4.21193	−0.137159
$944$	33.9267	1.10422
$945$	−88.4724	−2.87801
$946$	0	0
$947$	−15.8475	−0.514974	−0.257487	−	0.966282i	$-0.582894\pi$
$947$	−15.8475	−0.514974	−0.257487	+	0.966282i	$0.582894\pi$
$948$	−30.7921	−1.00008
$949$	−4.58540	−0.148848
$950$	0.201675	0.00654320
$951$	−72.6229	−2.35496
$952$	−33.1752	−1.07521
$953$	34.8354	1.12843	0.564214	−	0.825628i	$-0.309179\pi$
$953$	34.8354	1.12843	0.564214	+	0.825628i	$0.309179\pi$
$954$	−53.6422	−1.73673
$955$	−8.48246	−0.274486
$956$	−24.7734	−0.801228
$957$	0	0
$958$	41.2696	1.33336
$959$	−65.7252	−2.12238
$960$	13.6164	0.439467
$961$	−16.2122	−0.522976
$962$	−3.84312	−0.123907
$963$	−23.5636	−0.759326
$964$	−15.1904	−0.489250
$965$	10.2875	0.331165
$966$	−109.364	−3.51873
$967$	−8.94712	−0.287720	−0.143860	−	0.989598i	$-0.545952\pi$
$967$	−8.94712	−0.287720	−0.143860	+	0.989598i	$0.545952\pi$
$968$	0	0
$969$	44.6678	1.43494
$970$	9.84290	0.316037
$971$	47.1121	1.51190	0.755949	−	0.654630i	$-0.227176\pi$
$971$	47.1121	1.51190	0.755949	+	0.654630i	$0.227176\pi$
$972$	−3.27168	−0.104939
$973$	47.7293	1.53013
$974$	−37.6773	−1.20726
$975$	0.0363896	0.00116540
$976$	−4.98727	−0.159639
$977$	1.09601	0.0350645	0.0175322	−	0.999846i	$-0.494419\pi$
$977$	1.09601	0.0350645	0.0175322	+	0.999846i	$0.494419\pi$
$978$	93.3813	2.98601
$979$	0	0
$980$	−19.0072	−0.607161
$981$	−100.686	−3.21466
$982$	45.3105	1.44592
$983$	−28.2262	−0.900275	−0.450138	−	0.892959i	$-0.648625\pi$
$983$	−28.2262	−0.900275	−0.450138	+	0.892959i	$0.648625\pi$
$984$	4.62898	0.147566
$985$	−48.7680	−1.55388
$986$	38.5747	1.22847
$987$	−23.6477	−0.752715
$988$	1.04613	0.0332818
$989$	−63.1072	−2.00669
$990$	0	0
$991$	−42.1215	−1.33803	−0.669017	−	0.743247i	$-0.733285\pi$
$991$	−42.1215	−1.33803	−0.669017	+	0.743247i	$0.733285\pi$
$992$	−18.0451	−0.572933
$993$	−54.1474	−1.71832
$994$	−35.7629	−1.13433
$995$	−33.6741	−1.06754
$996$	−20.4936	−0.649366
$997$	3.72926	0.118107	0.0590534	−	0.998255i	$-0.481192\pi$
$997$	3.72926	0.118107	0.0590534	+	0.998255i	$0.481192\pi$
$998$	−28.0551	−0.888067
$999$	63.4937	2.00885

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7381.2.a.n.1.8	✓	25
11.10	odd	2		7381.2.a.o.1.18	yes	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7381.2.a.n.1.8	✓	25	1.1	even	1	trivial
7381.2.a.o.1.18	yes	25	11.10	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 7381 = 11^{2} \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7381.a (trivial)

\(f(q)\)	\(=\)	\(q-1.69917 q^{2} -3.03253 q^{3} +0.887194 q^{4} -2.24383 q^{5} +5.15280 q^{6} -4.06792 q^{7} +1.89085 q^{8} +6.19625 q^{9} +O(q^{10})\)	\(q-1.69917 q^{2} -3.03253 q^{3} +0.887194 q^{4} -2.24383 q^{5} +5.15280 q^{6} -4.06792 q^{7} +1.89085 q^{8} +6.19625 q^{9} +3.81265 q^{10} -2.69044 q^{12} -0.345273 q^{13} +6.91210 q^{14} +6.80447 q^{15} -4.98727 q^{16} +4.31305 q^{17} -10.5285 q^{18} -3.41511 q^{19} -1.99071 q^{20} +12.3361 q^{21} +5.21746 q^{23} -5.73407 q^{24} +0.0347544 q^{25} +0.586679 q^{26} -9.69274 q^{27} -3.60903 q^{28} -5.26357 q^{29} -11.5620 q^{30} -3.84549 q^{31} +4.69255 q^{32} -7.32862 q^{34} +9.12769 q^{35} +5.49728 q^{36} -6.55064 q^{37} +5.80287 q^{38} +1.04705 q^{39} -4.24274 q^{40} -0.807276 q^{41} -20.9612 q^{42} -12.0954 q^{43} -13.9033 q^{45} -8.86537 q^{46} -1.91695 q^{47} +15.1241 q^{48} +9.54794 q^{49} -0.0590537 q^{50} -13.0795 q^{51} -0.306324 q^{52} +5.09494 q^{53} +16.4697 q^{54} -7.69183 q^{56} +10.3564 q^{57} +8.94373 q^{58} -6.80265 q^{59} +6.03689 q^{60} +1.00000 q^{61} +6.53415 q^{62} -25.2058 q^{63} +2.00110 q^{64} +0.774732 q^{65} -9.92804 q^{67} +3.82651 q^{68} -15.8221 q^{69} -15.5095 q^{70} -5.17396 q^{71} +11.7162 q^{72} +13.2805 q^{73} +11.1307 q^{74} -0.105394 q^{75} -3.02987 q^{76} -1.77912 q^{78} +11.4450 q^{79} +11.1906 q^{80} +10.8048 q^{81} +1.37170 q^{82} +7.61720 q^{83} +10.9445 q^{84} -9.67772 q^{85} +20.5522 q^{86} +15.9620 q^{87} +14.5492 q^{89} +23.6242 q^{90} +1.40454 q^{91} +4.62890 q^{92} +11.6616 q^{93} +3.25724 q^{94} +7.66292 q^{95} -14.2303 q^{96} +2.58164 q^{97} -16.2236 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 5 q^{2} - q^{3} + 25 q^{4} - q^{5} - 4 q^{7} - 21 q^{8} + 24 q^{9}+O(q^{10}) \) 25 * q - 5 * q^2 - q^3 + 25 * q^4 - q^5 - 4 * q^7 - 21 * q^8 + 24 * q^9	\( 25 q - 5 q^{2} - q^{3} + 25 q^{4} - q^{5} - 4 q^{7} - 21 q^{8} + 24 q^{9} - q^{12} - 4 q^{13} - q^{14} - 2 q^{15} + 21 q^{16} - 10 q^{17} - 40 q^{18} - 17 q^{19} - 6 q^{20} - 15 q^{21} - 4 q^{23} + 9 q^{24} + 40 q^{25} - 18 q^{26} + 8 q^{27} + 29 q^{28} - 35 q^{29} + 6 q^{30} - 12 q^{31} - 47 q^{32} - 45 q^{35} + 41 q^{36} - 14 q^{37} - 13 q^{38} - 20 q^{39} - 69 q^{40} - 24 q^{41} - 32 q^{42} - 24 q^{43} - 16 q^{45} - 10 q^{46} + 22 q^{47} - 54 q^{48} + 23 q^{49} - 26 q^{50} - 76 q^{51} - q^{52} - 27 q^{53} - 13 q^{54} - 9 q^{56} - 4 q^{57} + 76 q^{58} - 21 q^{59} + 28 q^{60} + 25 q^{61} - 25 q^{62} - 4 q^{63} + 5 q^{64} - 20 q^{65} + 13 q^{67} + 34 q^{68} - 7 q^{69} - 41 q^{70} - 24 q^{71} - 54 q^{72} - 39 q^{73} - 56 q^{74} + 7 q^{75} - 42 q^{76} + 30 q^{78} - 5 q^{79} + 92 q^{80} + 9 q^{81} - 9 q^{82} - 51 q^{83} - 125 q^{84} - 5 q^{85} - 10 q^{86} - 3 q^{87} + 17 q^{89} + 104 q^{90} + 8 q^{91} - 23 q^{92} - 36 q^{93} + 29 q^{94} - 81 q^{95} + 48 q^{96} - 15 q^{97} - 25 q^{98}+O(q^{100}) \) 25 * q - 5 * q^2 - q^3 + 25 * q^4 - q^5 - 4 * q^7 - 21 * q^8 + 24 * q^9 - q^12 - 4 * q^13 - q^14 - 2 * q^15 + 21 * q^16 - 10 * q^17 - 40 * q^18 - 17 * q^19 - 6 * q^20 - 15 * q^21 - 4 * q^23 + 9 * q^24 + 40 * q^25 - 18 * q^26 + 8 * q^27 + 29 * q^28 - 35 * q^29 + 6 * q^30 - 12 * q^31 - 47 * q^32 - 45 * q^35 + 41 * q^36 - 14 * q^37 - 13 * q^38 - 20 * q^39 - 69 * q^40 - 24 * q^41 - 32 * q^42 - 24 * q^43 - 16 * q^45 - 10 * q^46 + 22 * q^47 - 54 * q^48 + 23 * q^49 - 26 * q^50 - 76 * q^51 - q^52 - 27 * q^53 - 13 * q^54 - 9 * q^56 - 4 * q^57 + 76 * q^58 - 21 * q^59 + 28 * q^60 + 25 * q^61 - 25 * q^62 - 4 * q^63 + 5 * q^64 - 20 * q^65 + 13 * q^67 + 34 * q^68 - 7 * q^69 - 41 * q^70 - 24 * q^71 - 54 * q^72 - 39 * q^73 - 56 * q^74 + 7 * q^75 - 42 * q^76 + 30 * q^78 - 5 * q^79 + 92 * q^80 + 9 * q^81 - 9 * q^82 - 51 * q^83 - 125 * q^84 - 5 * q^85 - 10 * q^86 - 3 * q^87 + 17 * q^89 + 104 * q^90 + 8 * q^91 - 23 * q^92 - 36 * q^93 + 29 * q^94 - 81 * q^95 + 48 * q^96 - 15 * q^97 - 25 * q^98

Introduction

L-functions

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Database

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