LMFDB - Embedded newform 2695.2.a.w.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2695,2,Mod(1,2695)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2695, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2695.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2695 = 5 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2695.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:	$21.5196833447$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 13x^{8} + 24x^{7} + 56x^{6} - 92x^{5} - 86x^{4} + 116x^{3} + 31x^{2} - 22x + 1 $ x^10 - 2x^9 - 13x^8 + 24x^7 + 56x^6 - 92x^5 - 86x^4 + 116x^3 + 31x^2 - 22*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.29554$ of defining polynomial
Character	$\chi$	$=$	2695.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.29554 q^{2} +0.293572 q^{3} +3.26952 q^{4} -1.00000 q^{5} -0.673908 q^{6} -2.91425 q^{8} -2.91382 q^{9} +O(q^{10})$	\(q-2.29554 q^{2} +0.293572 q^{3} +3.26952 q^{4} -1.00000 q^{5} -0.673908 q^{6} -2.91425 q^{8} -2.91382 q^{9} +2.29554 q^{10} -1.00000 q^{11} +0.959841 q^{12} +1.45308 q^{13} -0.293572 q^{15} +0.150739 q^{16} +1.37718 q^{17} +6.68879 q^{18} +3.61374 q^{19} -3.26952 q^{20} +2.29554 q^{22} -5.58209 q^{23} -0.855542 q^{24} +1.00000 q^{25} -3.33562 q^{26} -1.73613 q^{27} +0.104098 q^{29} +0.673908 q^{30} +6.72703 q^{31} +5.48247 q^{32} -0.293572 q^{33} -3.16139 q^{34} -9.52679 q^{36} +0.435179 q^{37} -8.29551 q^{38} +0.426585 q^{39} +2.91425 q^{40} -1.22902 q^{41} +4.44836 q^{43} -3.26952 q^{44} +2.91382 q^{45} +12.8139 q^{46} +0.126494 q^{47} +0.0442527 q^{48} -2.29554 q^{50} +0.404303 q^{51} +4.75089 q^{52} +8.05754 q^{53} +3.98537 q^{54} +1.00000 q^{55} +1.06089 q^{57} -0.238961 q^{58} -11.3961 q^{59} -0.959841 q^{60} -5.32148 q^{61} -15.4422 q^{62} -12.8867 q^{64} -1.45308 q^{65} +0.673908 q^{66} +9.34121 q^{67} +4.50273 q^{68} -1.63875 q^{69} -6.97924 q^{71} +8.49158 q^{72} -14.7242 q^{73} -0.998973 q^{74} +0.293572 q^{75} +11.8152 q^{76} -0.979245 q^{78} -7.63740 q^{79} -0.150739 q^{80} +8.23177 q^{81} +2.82126 q^{82} -8.19774 q^{83} -1.37718 q^{85} -10.2114 q^{86} +0.0305602 q^{87} +2.91425 q^{88} +3.74462 q^{89} -6.68879 q^{90} -18.2508 q^{92} +1.97487 q^{93} -0.290373 q^{94} -3.61374 q^{95} +1.60950 q^{96} +1.39488 q^{97} +2.91382 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{2} + 10 q^{4} - 10 q^{5} - 4 q^{6} + 6 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q + 2 * q^2 + 10 * q^4 - 10 * q^5 - 4 * q^6 + 6 * q^8 + 10 * q^9	$ 10 q + 2 q^{2} + 10 q^{4} - 10 q^{5} - 4 q^{6} + 6 q^{8} + 10 q^{9} - 2 q^{10} - 10 q^{11} - 4 q^{12} - 8 q^{13} + 6 q^{16} - 28 q^{17} - 10 q^{18} - 8 q^{19} - 10 q^{20} - 2 q^{22} - 8 q^{23} - 32 q^{24} + 10 q^{25} - 12 q^{26} - 8 q^{29} + 4 q^{30} + 4 q^{31} + 14 q^{32} - 20 q^{34} - 22 q^{36} + 28 q^{37} - 24 q^{38} - 24 q^{39} - 6 q^{40} - 44 q^{41} + 20 q^{43} - 10 q^{44} - 10 q^{45} - 12 q^{46} - 12 q^{47} - 16 q^{48} + 2 q^{50} - 4 q^{51} - 36 q^{52} + 8 q^{54} + 10 q^{55} + 12 q^{57} - 8 q^{58} - 16 q^{59} + 4 q^{60} - 16 q^{61} - 36 q^{62} - 34 q^{64} + 8 q^{65} + 4 q^{66} + 20 q^{67} - 8 q^{68} - 4 q^{69} - 4 q^{71} + 10 q^{72} - 20 q^{73} - 16 q^{74} - 4 q^{76} + 52 q^{78} - 20 q^{79} - 6 q^{80} + 10 q^{81} + 32 q^{82} - 16 q^{83} + 28 q^{85} - 20 q^{86} - 20 q^{87} - 6 q^{88} - 44 q^{89} + 10 q^{90} - 24 q^{92} + 16 q^{93} - 24 q^{94} + 8 q^{95} + 4 q^{97} - 10 q^{99}+O(q^{100}) $ 10 * q + 2 * q^2 + 10 * q^4 - 10 * q^5 - 4 * q^6 + 6 * q^8 + 10 * q^9 - 2 * q^10 - 10 * q^11 - 4 * q^12 - 8 * q^13 + 6 * q^16 - 28 * q^17 - 10 * q^18 - 8 * q^19 - 10 * q^20 - 2 * q^22 - 8 * q^23 - 32 * q^24 + 10 * q^25 - 12 * q^26 - 8 * q^29 + 4 * q^30 + 4 * q^31 + 14 * q^32 - 20 * q^34 - 22 * q^36 + 28 * q^37 - 24 * q^38 - 24 * q^39 - 6 * q^40 - 44 * q^41 + 20 * q^43 - 10 * q^44 - 10 * q^45 - 12 * q^46 - 12 * q^47 - 16 * q^48 + 2 * q^50 - 4 * q^51 - 36 * q^52 + 8 * q^54 + 10 * q^55 + 12 * q^57 - 8 * q^58 - 16 * q^59 + 4 * q^60 - 16 * q^61 - 36 * q^62 - 34 * q^64 + 8 * q^65 + 4 * q^66 + 20 * q^67 - 8 * q^68 - 4 * q^69 - 4 * q^71 + 10 * q^72 - 20 * q^73 - 16 * q^74 - 4 * q^76 + 52 * q^78 - 20 * q^79 - 6 * q^80 + 10 * q^81 + 32 * q^82 - 16 * q^83 + 28 * q^85 - 20 * q^86 - 20 * q^87 - 6 * q^88 - 44 * q^89 + 10 * q^90 - 24 * q^92 + 16 * q^93 - 24 * q^94 + 8 * q^95 + 4 * q^97 - 10 * 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 $

$2$	−2.29554	−1.62319	−0.811597	−	0.584217i	$-0.801402\pi$
$2$	−2.29554	−1.62319	−0.811597	+	0.584217i	$0.801402\pi$
$3$	0.293572	0.169494	0.0847470	−	0.996403i	$-0.472992\pi$
$3$	0.293572	0.169494	0.0847470	+	0.996403i	$0.472992\pi$
$4$	3.26952	1.63476
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.673908	−0.275122
$7$	0	0
$7$	0	0
$8$	−2.91425	−1.03034
$9$	−2.91382	−0.971272
$10$	2.29554	0.725915
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.959841	0.277082
$13$	1.45308	0.403013	0.201507	−	0.979487i	$-0.435416\pi$
$13$	1.45308	0.403013	0.201507	+	0.979487i	$0.435416\pi$
$14$	0	0
$15$	−0.293572	−0.0758000
$16$	0.150739	0.0376847
$17$	1.37718	0.334016	0.167008	−	0.985956i	$-0.446589\pi$
$17$	1.37718	0.334016	0.167008	+	0.985956i	$0.446589\pi$
$18$	6.68879	1.57656
$19$	3.61374	0.829050	0.414525	−	0.910038i	$-0.363948\pi$
$19$	3.61374	0.829050	0.414525	+	0.910038i	$0.363948\pi$
$20$	−3.26952	−0.731088
$21$	0	0
$22$	2.29554	0.489412
$23$	−5.58209	−1.16395	−0.581973	−	0.813208i	$-0.697719\pi$
$23$	−5.58209	−1.16395	−0.581973	+	0.813208i	$0.697719\pi$
$24$	−0.855542	−0.174637
$25$	1.00000	0.200000
$26$	−3.33562	−0.654169
$27$	−1.73613	−0.334119
$28$	0	0
$29$	0.104098	0.0193304	0.00966522	−	0.999953i	$-0.496923\pi$
$29$	0.104098	0.0193304	0.00966522	+	0.999953i	$0.496923\pi$
$30$	0.673908	0.123038
$31$	6.72703	1.20821	0.604105	−	0.796905i	$-0.293531\pi$
$31$	6.72703	1.20821	0.604105	+	0.796905i	$0.293531\pi$
$32$	5.48247	0.969173
$33$	−0.293572	−0.0511043
$34$	−3.16139	−0.542173
$35$	0	0
$36$	−9.52679	−1.58780
$37$	0.435179	0.0715430	0.0357715	−	0.999360i	$-0.488611\pi$
$37$	0.435179	0.0715430	0.0357715	+	0.999360i	$0.488611\pi$
$38$	−8.29551	−1.34571
$39$	0.426585	0.0683083
$40$	2.91425	0.460783
$41$	−1.22902	−0.191940	−0.0959702	−	0.995384i	$-0.530595\pi$
$41$	−1.22902	−0.191940	−0.0959702	+	0.995384i	$0.530595\pi$
$42$	0	0
$43$	4.44836	0.678368	0.339184	−	0.940720i	$-0.389849\pi$
$43$	4.44836	0.678368	0.339184	+	0.940720i	$0.389849\pi$
$44$	−3.26952	−0.492899
$45$	2.91382	0.434366
$46$	12.8139	1.88931
$47$	0.126494	0.0184511	0.00922555	−	0.999957i	$-0.497063\pi$
$47$	0.126494	0.0184511	0.00922555	+	0.999957i	$0.497063\pi$
$48$	0.0442527	0.00638733
$49$	0	0
$50$	−2.29554	−0.324639
$51$	0.404303	0.0566137
$52$	4.75089	0.658831
$53$	8.05754	1.10679	0.553394	−	0.832920i	$-0.313332\pi$
$53$	8.05754	1.10679	0.553394	+	0.832920i	$0.313332\pi$
$54$	3.98537	0.542340
$55$	1.00000	0.134840
$56$	0	0
$57$	1.06089	0.140519
$58$	−0.238961	−0.0313771
$59$	−11.3961	−1.48365	−0.741826	−	0.670593i	$-0.766040\pi$
$59$	−11.3961	−1.48365	−0.741826	+	0.670593i	$0.766040\pi$
$60$	−0.959841	−0.123915
$61$	−5.32148	−0.681346	−0.340673	−	0.940182i	$-0.610655\pi$
$61$	−5.32148	−0.681346	−0.340673	+	0.940182i	$0.610655\pi$
$62$	−15.4422	−1.96116
$63$	0	0
$64$	−12.8867	−1.61084
$65$	−1.45308	−0.180233
$66$	0.673908	0.0829523
$67$	9.34121	1.14121	0.570605	−	0.821224i	$-0.306709\pi$
$67$	9.34121	1.14121	0.570605	+	0.821224i	$0.306709\pi$
$68$	4.50273	0.546037
$69$	−1.63875	−0.197282
$70$	0	0
$71$	−6.97924	−0.828283	−0.414141	−	0.910213i	$-0.635918\pi$
$71$	−6.97924	−0.828283	−0.414141	+	0.910213i	$0.635918\pi$
$72$	8.49158	1.00074
$73$	−14.7242	−1.72334	−0.861671	−	0.507468i	$-0.830582\pi$
$73$	−14.7242	−1.72334	−0.861671	+	0.507468i	$0.830582\pi$
$74$	−0.998973	−0.116128
$75$	0.293572	0.0338988
$76$	11.8152	1.35530
$77$	0	0
$78$	−0.979245	−0.110878
$79$	−7.63740	−0.859275	−0.429637	−	0.903002i	$-0.641359\pi$
$79$	−7.63740	−0.859275	−0.429637	+	0.903002i	$0.641359\pi$
$80$	−0.150739	−0.0168531
$81$	8.23177	0.914641
$82$	2.82126	0.311557
$83$	−8.19774	−0.899818	−0.449909	−	0.893074i	$-0.648544\pi$
$83$	−8.19774	−0.899818	−0.449909	+	0.893074i	$0.648544\pi$
$84$	0	0
$85$	−1.37718	−0.149377
$86$	−10.2114	−1.10112
$87$	0.0305602	0.00327639
$88$	2.91425	0.310660
$89$	3.74462	0.396929	0.198464	−	0.980108i	$-0.436405\pi$
$89$	3.74462	0.396929	0.198464	+	0.980108i	$0.436405\pi$
$90$	−6.68879	−0.705061
$91$	0	0
$92$	−18.2508	−1.90278
$93$	1.97487	0.204784
$94$	−0.290373	−0.0299497
$95$	−3.61374	−0.370762
$96$	1.60950	0.164269
$97$	1.39488	0.141629	0.0708144	−	0.997490i	$-0.477440\pi$
$97$	1.39488	0.141629	0.0708144	+	0.997490i	$0.477440\pi$
$98$	0	0
$99$	2.91382	0.292849
$100$	3.26952	0.326952
$101$	−6.33566	−0.630422	−0.315211	−	0.949022i	$-0.602075\pi$
$101$	−6.33566	−0.630422	−0.315211	+	0.949022i	$0.602075\pi$
$102$	−0.928095	−0.0918951
$103$	11.4060	1.12386	0.561932	−	0.827184i	$-0.310058\pi$
$103$	11.4060	1.12386	0.561932	+	0.827184i	$0.310058\pi$
$104$	−4.23465	−0.415242
$105$	0	0
$106$	−18.4964	−1.79653
$107$	12.3939	1.19816	0.599080	−	0.800689i	$-0.295533\pi$
$107$	12.3939	1.19816	0.599080	+	0.800689i	$0.295533\pi$
$108$	−5.67632	−0.546204
$109$	−14.7889	−1.41652	−0.708260	−	0.705951i	$-0.750520\pi$
$109$	−14.7889	−1.41652	−0.708260	+	0.705951i	$0.750520\pi$
$110$	−2.29554	−0.218872
$111$	0.127756	0.0121261
$112$	0	0
$113$	9.64437	0.907266	0.453633	−	0.891189i	$-0.350128\pi$
$113$	9.64437	0.907266	0.453633	+	0.891189i	$0.350128\pi$
$114$	−2.43533	−0.228090
$115$	5.58209	0.520533
$116$	0.340350	0.0316007
$117$	−4.23402	−0.391435
$118$	26.1604	2.40826
$119$	0	0
$120$	0.855542	0.0781000
$121$	1.00000	0.0909091
$122$	12.2157	1.10596
$123$	−0.360805	−0.0325327
$124$	21.9942	1.97514
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	0.268275	0.0238055	0.0119028	−	0.999929i	$-0.496211\pi$
$127$	0.268275	0.0238055	0.0119028	+	0.999929i	$0.496211\pi$
$128$	18.6171	1.64554
$129$	1.30591	0.114979
$130$	3.33562	0.292553
$131$	−10.5415	−0.921019	−0.460509	−	0.887655i	$-0.652333\pi$
$131$	−10.5415	−0.921019	−0.460509	+	0.887655i	$0.652333\pi$
$132$	−0.959841	−0.0835434
$133$	0	0
$134$	−21.4432	−1.85241
$135$	1.73613	0.149422
$136$	−4.01345	−0.344151
$137$	−4.98272	−0.425703	−0.212851	−	0.977085i	$-0.568275\pi$
$137$	−4.98272	−0.425703	−0.212851	+	0.977085i	$0.568275\pi$
$138$	3.76182	0.320227
$139$	−5.80701	−0.492544	−0.246272	−	0.969201i	$-0.579206\pi$
$139$	−5.80701	−0.492544	−0.246272	+	0.969201i	$0.579206\pi$
$140$	0	0
$141$	0.0371352	0.00312735
$142$	16.0211	1.34446
$143$	−1.45308	−0.121513
$144$	−0.439225	−0.0366021
$145$	−0.104098	−0.00864484
$146$	33.8001	2.79732
$147$	0	0
$148$	1.42283	0.116956
$149$	−8.28793	−0.678974	−0.339487	−	0.940611i	$-0.610253\pi$
$149$	−8.28793	−0.678974	−0.339487	+	0.940611i	$0.610253\pi$
$150$	−0.673908	−0.0550243
$151$	−2.40230	−0.195496	−0.0977480	−	0.995211i	$-0.531164\pi$
$151$	−2.40230	−0.195496	−0.0977480	+	0.995211i	$0.531164\pi$
$152$	−10.5313	−0.854205
$153$	−4.01286	−0.324420
$154$	0	0
$155$	−6.72703	−0.540328
$156$	1.39473	0.111668
$157$	16.0405	1.28017	0.640085	−	0.768304i	$-0.278899\pi$
$157$	16.0405	1.28017	0.640085	+	0.768304i	$0.278899\pi$
$158$	17.5320	1.39477
$159$	2.36547	0.187594
$160$	−5.48247	−0.433427
$161$	0	0
$162$	−18.8964	−1.48464
$163$	−3.93239	−0.308008	−0.154004	−	0.988070i	$-0.549217\pi$
$163$	−3.93239	−0.308008	−0.154004	+	0.988070i	$0.549217\pi$
$164$	−4.01830	−0.313777
$165$	0.293572	0.0228546
$166$	18.8183	1.46058
$167$	−12.2979	−0.951642	−0.475821	−	0.879542i	$-0.657849\pi$
$167$	−12.2979	−0.951642	−0.475821	+	0.879542i	$0.657849\pi$
$168$	0	0
$169$	−10.8885	−0.837580
$170$	3.16139	0.242467
$171$	−10.5298	−0.805233
$172$	14.5440	1.10897
$173$	−11.3383	−0.862033	−0.431017	−	0.902344i	$-0.641845\pi$
$173$	−11.3383	−0.862033	−0.431017	+	0.902344i	$0.641845\pi$
$174$	−0.0701522	−0.00531822
$175$	0	0
$176$	−0.150739	−0.0113624
$177$	−3.34559	−0.251470
$178$	−8.59594	−0.644293
$179$	−25.3377	−1.89383	−0.946913	−	0.321488i	$-0.895817\pi$
$179$	−25.3377	−1.89383	−0.946913	+	0.321488i	$0.895817\pi$
$180$	9.52679	0.710085
$181$	−3.52411	−0.261945	−0.130972	−	0.991386i	$-0.541810\pi$
$181$	−3.52411	−0.261945	−0.130972	+	0.991386i	$0.541810\pi$
$182$	0	0
$183$	−1.56224	−0.115484
$184$	16.2676	1.19926
$185$	−0.435179	−0.0319950
$186$	−4.53340	−0.332405
$187$	−1.37718	−0.100710
$188$	0.413576	0.0301632
$189$	0	0
$190$	8.29551	0.601819
$191$	10.3942	0.752100	0.376050	−	0.926599i	$-0.377282\pi$
$191$	10.3942	0.752100	0.376050	+	0.926599i	$0.377282\pi$
$192$	−3.78318	−0.273028
$193$	6.33141	0.455745	0.227872	−	0.973691i	$-0.426823\pi$
$193$	6.33141	0.455745	0.227872	+	0.973691i	$0.426823\pi$
$194$	−3.20201	−0.229891
$195$	−0.426585	−0.0305484
$196$	0	0
$197$	25.7530	1.83483	0.917413	−	0.397937i	$-0.130274\pi$
$197$	25.7530	1.83483	0.917413	+	0.397937i	$0.130274\pi$
$198$	−6.68879	−0.475352
$199$	8.00340	0.567346	0.283673	−	0.958921i	$-0.408447\pi$
$199$	8.00340	0.567346	0.283673	+	0.958921i	$0.408447\pi$
$200$	−2.91425	−0.206068
$201$	2.74232	0.193428
$202$	14.5438	1.02330
$203$	0	0
$204$	1.32188	0.0925499
$205$	1.22902	0.0858383
$206$	−26.1829	−1.82425
$207$	16.2652	1.13051
$208$	0.219036	0.0151874
$209$	−3.61374	−0.249968
$210$	0	0
$211$	12.5161	0.861643	0.430821	−	0.902437i	$-0.358224\pi$
$211$	12.5161	0.861643	0.430821	+	0.902437i	$0.358224\pi$
$212$	26.3443	1.80933
$213$	−2.04891	−0.140389
$214$	−28.4507	−1.94485
$215$	−4.44836	−0.303375
$216$	5.05952	0.344257
$217$	0	0
$218$	33.9486	2.29929
$219$	−4.32263	−0.292096
$220$	3.26952	0.220431
$221$	2.00116	0.134613
$222$	−0.293271	−0.0196830
$223$	17.1800	1.15046	0.575229	−	0.817992i	$-0.304913\pi$
$223$	17.1800	1.15046	0.575229	+	0.817992i	$0.304913\pi$
$224$	0	0
$225$	−2.91382	−0.194254
$226$	−22.1391	−1.47267
$227$	−21.9004	−1.45358	−0.726789	−	0.686861i	$-0.758988\pi$
$227$	−21.9004	−1.45358	−0.726789	+	0.686861i	$0.758988\pi$
$228$	3.46862	0.229715
$229$	−12.9430	−0.855296	−0.427648	−	0.903945i	$-0.640658\pi$
$229$	−12.9430	−0.855296	−0.427648	+	0.903945i	$0.640658\pi$
$230$	−12.8139	−0.844926
$231$	0	0
$232$	−0.303366	−0.0199170
$233$	−2.46926	−0.161767	−0.0808833	−	0.996724i	$-0.525774\pi$
$233$	−2.46926	−0.161767	−0.0808833	+	0.996724i	$0.525774\pi$
$234$	9.71938	0.635376
$235$	−0.126494	−0.00825158
$236$	−37.2600	−2.42542
$237$	−2.24213	−0.145642
$238$	0	0
$239$	−15.2734	−0.987957	−0.493978	−	0.869474i	$-0.664458\pi$
$239$	−15.2734	−0.987957	−0.493978	+	0.869474i	$0.664458\pi$
$240$	−0.0442527	−0.00285650
$241$	4.64559	0.299248	0.149624	−	0.988743i	$-0.452194\pi$
$241$	4.64559	0.299248	0.149624	+	0.988743i	$0.452194\pi$
$242$	−2.29554	−0.147563
$243$	7.62501	0.489145
$244$	−17.3987	−1.11384
$245$	0	0
$246$	0.828245	0.0528070
$247$	5.25108	0.334118
$248$	−19.6042	−1.24487
$249$	−2.40663	−0.152514
$250$	2.29554	0.145183
$251$	−25.2788	−1.59558	−0.797791	−	0.602935i	$-0.793998\pi$
$251$	−25.2788	−1.59558	−0.797791	+	0.602935i	$0.793998\pi$
$252$	0	0
$253$	5.58209	0.350943
$254$	−0.615837	−0.0386410
$255$	−0.404303	−0.0253184
$256$	−16.9630	−1.06019
$257$	−30.7280	−1.91676	−0.958378	−	0.285501i	$-0.907840\pi$
$257$	−30.7280	−1.91676	−0.958378	+	0.285501i	$0.907840\pi$
$258$	−2.99778	−0.186634
$259$	0	0
$260$	−4.75089	−0.294638
$261$	−0.303321	−0.0187751
$262$	24.1986	1.49499
$263$	−17.7003	−1.09145	−0.545725	−	0.837965i	$-0.683746\pi$
$263$	−17.7003	−1.09145	−0.545725	+	0.837965i	$0.683746\pi$
$264$	0.855542	0.0526550
$265$	−8.05754	−0.494971
$266$	0	0
$267$	1.09932	0.0672770
$268$	30.5413	1.86561
$269$	−18.4815	−1.12683	−0.563417	−	0.826173i	$-0.690514\pi$
$269$	−18.4815	−1.12683	−0.563417	+	0.826173i	$0.690514\pi$
$270$	−3.98537	−0.242542
$271$	−27.4033	−1.66463	−0.832316	−	0.554302i	$-0.812985\pi$
$271$	−27.4033	−1.66463	−0.832316	+	0.554302i	$0.812985\pi$
$272$	0.207595	0.0125873
$273$	0	0
$274$	11.4381	0.690999
$275$	−1.00000	−0.0603023
$276$	−5.35792	−0.322509
$277$	−9.27239	−0.557124	−0.278562	−	0.960418i	$-0.589858\pi$
$277$	−9.27239	−0.557124	−0.278562	+	0.960418i	$0.589858\pi$
$278$	13.3302	0.799495
$279$	−19.6013	−1.17350
$280$	0	0
$281$	22.8183	1.36122	0.680612	−	0.732644i	$-0.261714\pi$
$281$	22.8183	1.36122	0.680612	+	0.732644i	$0.261714\pi$
$282$	−0.0852456	−0.00507630
$283$	−22.9802	−1.36603	−0.683015	−	0.730404i	$-0.739332\pi$
$283$	−22.9802	−1.36603	−0.683015	+	0.730404i	$0.739332\pi$
$284$	−22.8188	−1.35405
$285$	−1.06089	−0.0628420
$286$	3.33562	0.197239
$287$	0	0
$288$	−15.9749	−0.941330
$289$	−15.1034	−0.888433
$290$	0.238961	0.0140323
$291$	0.409499	0.0240052
$292$	−48.1412	−2.81725
$293$	−7.46806	−0.436289	−0.218144	−	0.975917i	$-0.570000\pi$
$293$	−7.46806	−0.436289	−0.218144	+	0.975917i	$0.570000\pi$
$294$	0	0
$295$	11.3961	0.663509
$296$	−1.26822	−0.0737138
$297$	1.73613	0.100741
$298$	19.0253	1.10211
$299$	−8.11125	−0.469086
$300$	0.959841	0.0554165
$301$	0	0
$302$	5.51458	0.317328
$303$	−1.85997	−0.106853
$304$	0.544732	0.0312425
$305$	5.32148	0.304707
$306$	9.21169	0.526597
$307$	15.3016	0.873311	0.436655	−	0.899629i	$-0.356163\pi$
$307$	15.3016	0.873311	0.436655	+	0.899629i	$0.356163\pi$
$308$	0	0
$309$	3.34847	0.190488
$310$	15.4422	0.877058
$311$	22.5435	1.27833	0.639163	−	0.769072i	$-0.279281\pi$
$311$	22.5435	1.27833	0.639163	+	0.769072i	$0.279281\pi$
$312$	−1.24318	−0.0703809
$313$	−8.51249	−0.481154	−0.240577	−	0.970630i	$-0.577337\pi$
$313$	−8.51249	−0.481154	−0.240577	+	0.970630i	$0.577337\pi$
$314$	−36.8217	−2.07797
$315$	0	0
$316$	−24.9707	−1.40471
$317$	−19.7133	−1.10721	−0.553605	−	0.832779i	$-0.686748\pi$
$317$	−19.7133	−1.10721	−0.553605	+	0.832779i	$0.686748\pi$
$318$	−5.43004	−0.304501
$319$	−0.104098	−0.00582835
$320$	12.8867	0.720390
$321$	3.63849	0.203081
$322$	0	0
$323$	4.97679	0.276916
$324$	26.9140	1.49522
$325$	1.45308	0.0806026
$326$	9.02697	0.499957
$327$	−4.34161	−0.240092
$328$	3.58166	0.197764
$329$	0	0
$330$	−0.673908	−0.0370974
$331$	14.8302	0.815140	0.407570	−	0.913174i	$-0.366376\pi$
$331$	14.8302	0.815140	0.407570	+	0.913174i	$0.366376\pi$
$332$	−26.8027	−1.47099
$333$	−1.26803	−0.0694877
$334$	28.2304	1.54470
$335$	−9.34121	−0.510365
$336$	0	0
$337$	5.99144	0.326374	0.163187	−	0.986595i	$-0.447823\pi$
$337$	5.99144	0.326374	0.163187	+	0.986595i	$0.447823\pi$
$338$	24.9951	1.35956
$339$	2.83132	0.153776
$340$	−4.50273	−0.244195
$341$	−6.72703	−0.364289
$342$	24.1716	1.30705
$343$	0	0
$344$	−12.9636	−0.698951
$345$	1.63875	0.0882272
$346$	26.0275	1.39925
$347$	−11.7269	−0.629535	−0.314767	−	0.949169i	$-0.601926\pi$
$347$	−11.7269	−0.629535	−0.314767	+	0.949169i	$0.601926\pi$
$348$	0.0999172	0.00535612
$349$	−27.8798	−1.49237	−0.746186	−	0.665738i	$-0.768117\pi$
$349$	−27.8798	−1.49237	−0.746186	+	0.665738i	$0.768117\pi$
$350$	0	0
$351$	−2.52275	−0.134654
$352$	−5.48247	−0.292217
$353$	−22.0207	−1.17204	−0.586021	−	0.810296i	$-0.699307\pi$
$353$	−22.0207	−1.17204	−0.586021	+	0.810296i	$0.699307\pi$
$354$	7.67995	0.408185
$355$	6.97924	0.370419
$356$	12.2431	0.648884
$357$	0	0
$358$	58.1638	3.07405
$359$	−17.8613	−0.942682	−0.471341	−	0.881951i	$-0.656230\pi$
$359$	−17.8613	−0.942682	−0.471341	+	0.881951i	$0.656230\pi$
$360$	−8.49158	−0.447546
$361$	−5.94086	−0.312677
$362$	8.08975	0.425188
$363$	0.293572	0.0154085
$364$	0	0
$365$	14.7242	0.770702
$366$	3.58619	0.187453
$367$	−4.37925	−0.228595	−0.114298	−	0.993447i	$-0.536462\pi$
$367$	−4.37925	−0.228595	−0.114298	+	0.993447i	$0.536462\pi$
$368$	−0.841439	−0.0438630
$369$	3.58113	0.186426
$370$	0.998973	0.0519341
$371$	0	0
$372$	6.45688	0.334774
$373$	−7.46212	−0.386374	−0.193187	−	0.981162i	$-0.561882\pi$
$373$	−7.46212	−0.386374	−0.193187	+	0.981162i	$0.561882\pi$
$374$	3.16139	0.163471
$375$	−0.293572	−0.0151600
$376$	−0.368636	−0.0190110
$377$	0.151263	0.00779042
$378$	0	0
$379$	−11.4780	−0.589588	−0.294794	−	0.955561i	$-0.595251\pi$
$379$	−11.4780	−0.589588	−0.294794	+	0.955561i	$0.595251\pi$
$380$	−11.8152	−0.606108
$381$	0.0787580	0.00403489
$382$	−23.8604	−1.22081
$383$	−24.7310	−1.26369	−0.631847	−	0.775093i	$-0.717703\pi$
$383$	−24.7310	−1.26369	−0.631847	+	0.775093i	$0.717703\pi$
$384$	5.46547	0.278908
$385$	0	0
$386$	−14.5340	−0.739763
$387$	−12.9617	−0.658880
$388$	4.56060	0.231529
$389$	−28.4414	−1.44204	−0.721019	−	0.692916i	$-0.756326\pi$
$389$	−28.4414	−1.44204	−0.721019	+	0.692916i	$0.756326\pi$
$390$	0.979245	0.0495860
$391$	−7.68757	−0.388777
$392$	0	0
$393$	−3.09470	−0.156107
$394$	−59.1172	−2.97828
$395$	7.63740	0.384279
$396$	9.52679	0.478739
$397$	−23.1144	−1.16008	−0.580038	−	0.814589i	$-0.696962\pi$
$397$	−23.1144	−1.16008	−0.580038	+	0.814589i	$0.696962\pi$
$398$	−18.3722	−0.920913
$399$	0	0
$400$	0.150739	0.00753695
$401$	2.84597	0.142121	0.0710606	−	0.997472i	$-0.477362\pi$
$401$	2.84597	0.142121	0.0710606	+	0.997472i	$0.477362\pi$
$402$	−6.29512	−0.313972
$403$	9.77494	0.486925
$404$	−20.7146	−1.03059
$405$	−8.23177	−0.409040
$406$	0	0
$407$	−0.435179	−0.0215710
$408$	−1.17824	−0.0583315
$409$	27.0904	1.33953	0.669767	−	0.742571i	$-0.266394\pi$
$409$	27.0904	1.33953	0.669767	+	0.742571i	$0.266394\pi$
$410$	−2.82126	−0.139332
$411$	−1.46279	−0.0721540
$412$	37.2921	1.83725
$413$	0	0
$414$	−37.3375	−1.83504
$415$	8.19774	0.402411
$416$	7.96649	0.390589
$417$	−1.70478	−0.0834833
$418$	8.29551	0.405747
$419$	−7.34341	−0.358749	−0.179375	−	0.983781i	$-0.557407\pi$
$419$	−7.34341	−0.358749	−0.179375	+	0.983781i	$0.557407\pi$
$420$	0	0
$421$	32.3775	1.57798	0.788991	−	0.614404i	$-0.210604\pi$
$421$	32.3775	1.57798	0.788991	+	0.614404i	$0.210604\pi$
$422$	−28.7312	−1.39861
$423$	−0.368581	−0.0179210
$424$	−23.4817	−1.14037
$425$	1.37718	0.0668032
$426$	4.70336	0.227879
$427$	0	0
$428$	40.5220	1.95871
$429$	−0.426585	−0.0205957
$430$	10.2114	0.492437
$431$	35.9538	1.73183	0.865916	−	0.500190i	$-0.166736\pi$
$431$	35.9538	1.73183	0.865916	+	0.500190i	$0.166736\pi$
$432$	−0.261703	−0.0125912
$433$	15.9908	0.768468	0.384234	−	0.923236i	$-0.374466\pi$
$433$	15.9908	0.768468	0.384234	+	0.923236i	$0.374466\pi$
$434$	0	0
$435$	−0.0305602	−0.00146525
$436$	−48.3527	−2.31567
$437$	−20.1723	−0.964970
$438$	9.92278	0.474129
$439$	−17.5823	−0.839157	−0.419578	−	0.907719i	$-0.637822\pi$
$439$	−17.5823	−0.839157	−0.419578	+	0.907719i	$0.637822\pi$
$440$	−2.91425	−0.138931
$441$	0	0
$442$	−4.59376	−0.218503
$443$	4.62095	0.219548	0.109774	−	0.993957i	$-0.464987\pi$
$443$	4.62095	0.219548	0.109774	+	0.993957i	$0.464987\pi$
$444$	0.417703	0.0198233
$445$	−3.74462	−0.177512
$446$	−39.4375	−1.86742
$447$	−2.43311	−0.115082
$448$	0	0
$449$	14.2318	0.671642	0.335821	−	0.941926i	$-0.390986\pi$
$449$	14.2318	0.671642	0.335821	+	0.941926i	$0.390986\pi$
$450$	6.68879	0.315313
$451$	1.22902	0.0578722
$452$	31.5325	1.48316
$453$	−0.705247	−0.0331354
$454$	50.2732	2.35944
$455$	0	0
$456$	−3.09171	−0.144783
$457$	−39.2810	−1.83749	−0.918745	−	0.394852i	$-0.870796\pi$
$457$	−39.2810	−1.83749	−0.918745	+	0.394852i	$0.870796\pi$
$458$	29.7112	1.38831
$459$	−2.39097	−0.111601
$460$	18.2508	0.850947
$461$	−2.04093	−0.0950556	−0.0475278	−	0.998870i	$-0.515134\pi$
$461$	−2.04093	−0.0950556	−0.0475278	+	0.998870i	$0.515134\pi$
$462$	0	0
$463$	17.9813	0.835660	0.417830	−	0.908525i	$-0.362791\pi$
$463$	17.9813	0.835660	0.417830	+	0.908525i	$0.362791\pi$
$464$	0.0156916	0.000728462 0
$465$	−1.97487	−0.0915823
$466$	5.66829	0.262579
$467$	8.06125	0.373030	0.186515	−	0.982452i	$-0.440281\pi$
$467$	8.06125	0.373030	0.186515	+	0.982452i	$0.440281\pi$
$468$	−13.8432	−0.639904
$469$	0	0
$470$	0.290373	0.0133939
$471$	4.70904	0.216981
$472$	33.2112	1.52867
$473$	−4.44836	−0.204536
$474$	5.14690	0.236405
$475$	3.61374	0.165810
$476$	0	0
$477$	−23.4782	−1.07499
$478$	35.0609	1.60365
$479$	−15.0626	−0.688226	−0.344113	−	0.938928i	$-0.611820\pi$
$479$	−15.0626	−0.688226	−0.344113	+	0.938928i	$0.611820\pi$
$480$	−1.60950	−0.0734633
$481$	0.632352	0.0288328
$482$	−10.6641	−0.485739
$483$	0	0
$484$	3.26952	0.148615
$485$	−1.39488	−0.0633383
$486$	−17.5036	−0.793977
$487$	−40.3416	−1.82805	−0.914025	−	0.405657i	$-0.867043\pi$
$487$	−40.3416	−1.82805	−0.914025	+	0.405657i	$0.867043\pi$
$488$	15.5081	0.702020
$489$	−1.15444	−0.0522055
$490$	0	0
$491$	−14.3021	−0.645444	−0.322722	−	0.946494i	$-0.604598\pi$
$491$	−14.3021	−0.645444	−0.322722	+	0.946494i	$0.604598\pi$
$492$	−1.17966	−0.0531833
$493$	0.143361	0.00645668
$494$	−12.0541	−0.542339
$495$	−2.91382	−0.130966
$496$	1.01403	0.0455311
$497$	0	0
$498$	5.52452	0.247560
$499$	24.6179	1.10205	0.551025	−	0.834489i	$-0.314237\pi$
$499$	24.6179	1.10205	0.551025	+	0.834489i	$0.314237\pi$
$500$	−3.26952	−0.146218
$501$	−3.61033	−0.161298
$502$	58.0285	2.58994
$503$	−6.42927	−0.286667	−0.143333	−	0.989674i	$-0.545782\pi$
$503$	−6.42927	−0.286667	−0.143333	+	0.989674i	$0.545782\pi$
$504$	0	0
$505$	6.33566	0.281933
$506$	−12.8139	−0.569649
$507$	−3.19657	−0.141965
$508$	0.877131	0.0389164
$509$	34.7891	1.54200	0.771001	−	0.636834i	$-0.219756\pi$
$509$	34.7891	1.54200	0.771001	+	0.636834i	$0.219756\pi$
$510$	0.928095	0.0410967
$511$	0	0
$512$	1.70500	0.0753512
$513$	−6.27393	−0.277001
$514$	70.5374	3.11127
$515$	−11.4060	−0.502607
$516$	4.26971	0.187964
$517$	−0.126494	−0.00556322
$518$	0	0
$519$	−3.32860	−0.146109
$520$	4.23465	0.185702
$521$	12.8010	0.560821	0.280410	−	0.959880i	$-0.409529\pi$
$521$	12.8010	0.560821	0.280410	+	0.959880i	$0.409529\pi$
$522$	0.696287	0.0304757
$523$	−2.71397	−0.118674	−0.0593368	−	0.998238i	$-0.518899\pi$
$523$	−2.71397	−0.118674	−0.0593368	+	0.998238i	$0.518899\pi$
$524$	−34.4658	−1.50565
$525$	0	0
$526$	40.6319	1.77163
$527$	9.26435	0.403562
$528$	−0.0442527	−0.00192585
$529$	8.15976	0.354772
$530$	18.4964	0.803434
$531$	33.2063	1.44103
$532$	0	0
$533$	−1.78587	−0.0773545
$534$	−2.52353	−0.109204
$535$	−12.3939	−0.535833
$536$	−27.2226	−1.17584
$537$	−7.43844	−0.320992
$538$	42.4250	1.82907
$539$	0	0
$540$	5.67632	0.244270
$541$	18.3714	0.789848	0.394924	−	0.918714i	$-0.370771\pi$
$541$	18.3714	0.789848	0.394924	+	0.918714i	$0.370771\pi$
$542$	62.9055	2.70202
$543$	−1.03458	−0.0443981
$544$	7.55037	0.323719
$545$	14.7889	0.633487
$546$	0	0
$547$	7.58542	0.324329	0.162165	−	0.986764i	$-0.448152\pi$
$547$	7.58542	0.324329	0.162165	+	0.986764i	$0.448152\pi$
$548$	−16.2911	−0.695923
$549$	15.5058	0.661772
$550$	2.29554	0.0978823
$551$	0.376182	0.0160259
$552$	4.77572	0.203268
$553$	0	0
$554$	21.2852	0.904321
$555$	−0.127756	−0.00542296
$556$	−18.9862	−0.805193
$557$	24.4867	1.03754	0.518768	−	0.854915i	$-0.326391\pi$
$557$	24.4867	1.03754	0.518768	+	0.854915i	$0.326391\pi$
$558$	44.9957	1.90482
$559$	6.46384	0.273391
$560$	0	0
$561$	−0.404303	−0.0170697
$562$	−52.3804	−2.20953
$563$	5.29195	0.223029	0.111514	−	0.993763i	$-0.464430\pi$
$563$	5.29195	0.223029	0.111514	+	0.993763i	$0.464430\pi$
$564$	0.121415	0.00511247
$565$	−9.64437	−0.405741
$566$	52.7521	2.21733
$567$	0	0
$568$	20.3392	0.853415
$569$	38.2666	1.60422	0.802111	−	0.597176i	$-0.203710\pi$
$569$	38.2666	1.60422	0.802111	+	0.597176i	$0.203710\pi$
$570$	2.43533	0.102005
$571$	−28.8958	−1.20925	−0.604627	−	0.796509i	$-0.706678\pi$
$571$	−28.8958	−1.20925	−0.604627	+	0.796509i	$0.706678\pi$
$572$	−4.75089	−0.198645
$573$	3.05146	0.127476
$574$	0	0
$575$	−5.58209	−0.232789
$576$	37.5495	1.56456
$577$	−26.4403	−1.10073	−0.550363	−	0.834925i	$-0.685511\pi$
$577$	−26.4403	−1.10073	−0.550363	+	0.834925i	$0.685511\pi$
$578$	34.6704	1.44210
$579$	1.85873	0.0772460
$580$	−0.340350	−0.0141322
$581$	0	0
$582$	−0.940022	−0.0389652
$583$	−8.05754	−0.333709
$584$	42.9101	1.77563
$585$	4.23402	0.175055
$586$	17.1433	0.708182
$587$	29.7315	1.22715	0.613576	−	0.789636i	$-0.289731\pi$
$587$	29.7315	1.22715	0.613576	+	0.789636i	$0.289731\pi$
$588$	0	0
$589$	24.3098	1.00167
$590$	−26.1604	−1.07700
$591$	7.56036	0.310992
$592$	0.0655984	0.00269608
$593$	6.72955	0.276349	0.138175	−	0.990408i	$-0.455876\pi$
$593$	6.72955	0.276349	0.138175	+	0.990408i	$0.455876\pi$
$594$	−3.98537	−0.163522
$595$	0	0
$596$	−27.0976	−1.10996
$597$	2.34957	0.0961617
$598$	18.6197	0.761418
$599$	15.2411	0.622736	0.311368	−	0.950289i	$-0.399213\pi$
$599$	15.2411	0.622736	0.311368	+	0.950289i	$0.399213\pi$
$600$	−0.855542	−0.0349274
$601$	−20.2186	−0.824736	−0.412368	−	0.911017i	$-0.635298\pi$
$601$	−20.2186	−0.824736	−0.412368	+	0.911017i	$0.635298\pi$
$602$	0	0
$603$	−27.2186	−1.10843
$604$	−7.85436	−0.319590
$605$	−1.00000	−0.0406558
$606$	4.26965	0.173443
$607$	40.0956	1.62743	0.813715	−	0.581264i	$-0.197441\pi$
$607$	40.0956	1.62743	0.813715	+	0.581264i	$0.197441\pi$
$608$	19.8122	0.803492
$609$	0	0
$610$	−12.2157	−0.494599
$611$	0.183807	0.00743604
$612$	−13.1201	−0.530350
$613$	−10.0274	−0.405002	−0.202501	−	0.979282i	$-0.564907\pi$
$613$	−10.0274	−0.405002	−0.202501	+	0.979282i	$0.564907\pi$
$614$	−35.1256	−1.41755
$615$	0.360805	0.0145491
$616$	0	0
$617$	−31.1046	−1.25222	−0.626112	−	0.779733i	$-0.715355\pi$
$617$	−31.1046	−1.25222	−0.626112	+	0.779733i	$0.715355\pi$
$618$	−7.68657	−0.309199
$619$	15.6172	0.627710	0.313855	−	0.949471i	$-0.398379\pi$
$619$	15.6172	0.627710	0.313855	+	0.949471i	$0.398379\pi$
$620$	−21.9942	−0.883308
$621$	9.69125	0.388896
$622$	−51.7496	−2.07497
$623$	0	0
$624$	0.0643030	0.00257418
$625$	1.00000	0.0400000
$626$	19.5408	0.781007
$627$	−1.06089	−0.0423680
$628$	52.4448	2.09277
$629$	0.599321	0.0238965
$630$	0	0
$631$	−4.02267	−0.160140	−0.0800699	−	0.996789i	$-0.525514\pi$
$631$	−4.02267	−0.160140	−0.0800699	+	0.996789i	$0.525514\pi$
$632$	22.2573	0.885347
$633$	3.67437	0.146043
$634$	45.2528	1.79722
$635$	−0.268275	−0.0106462
$636$	7.73395	0.306671
$637$	0	0
$638$	0.238961	0.00946054
$639$	20.3362	0.804488
$640$	−18.6171	−0.735906
$641$	27.6129	1.09064	0.545321	−	0.838227i	$-0.316408\pi$
$641$	27.6129	1.09064	0.545321	+	0.838227i	$0.316408\pi$
$642$	−8.35232	−0.329640
$643$	30.9004	1.21859	0.609296	−	0.792942i	$-0.291452\pi$
$643$	30.9004	1.21859	0.609296	+	0.792942i	$0.291452\pi$
$644$	0	0
$645$	−1.30591	−0.0514203
$646$	−11.4244	−0.449488
$647$	−42.4760	−1.66990	−0.834952	−	0.550323i	$-0.814505\pi$
$647$	−42.4760	−1.66990	−0.834952	+	0.550323i	$0.814505\pi$
$648$	−23.9894	−0.942393
$649$	11.3961	0.447338
$650$	−3.33562	−0.130834
$651$	0	0
$652$	−12.8570	−0.503520
$653$	38.7082	1.51477	0.757385	−	0.652969i	$-0.226477\pi$
$653$	38.7082	1.51477	0.757385	+	0.652969i	$0.226477\pi$
$654$	9.96636	0.389716
$655$	10.5415	0.411892
$656$	−0.185261	−0.00723322
$657$	42.9037	1.67383
$658$	0	0
$659$	−14.7649	−0.575160	−0.287580	−	0.957757i	$-0.592851\pi$
$659$	−14.7649	−0.575160	−0.287580	+	0.957757i	$0.592851\pi$
$660$	0.959841	0.0373618
$661$	28.2032	1.09698	0.548489	−	0.836158i	$-0.315203\pi$
$661$	28.2032	1.09698	0.548489	+	0.836158i	$0.315203\pi$
$662$	−34.0433	−1.32313
$663$	0.587486	0.0228161
$664$	23.8902	0.927121
$665$	0	0
$666$	2.91082	0.112792
$667$	−0.581083	−0.0224996
$668$	−40.2084	−1.55571
$669$	5.04357	0.194996
$670$	21.4432	0.828422
$671$	5.32148	0.205434
$672$	0	0
$673$	11.9087	0.459048	0.229524	−	0.973303i	$-0.426283\pi$
$673$	11.9087	0.459048	0.229524	+	0.973303i	$0.426283\pi$
$674$	−13.7536	−0.529769
$675$	−1.73613	−0.0668237
$676$	−35.6004	−1.36924
$677$	−10.1493	−0.390069	−0.195035	−	0.980796i	$-0.562482\pi$
$677$	−10.1493	−0.390069	−0.195035	+	0.980796i	$0.562482\pi$
$678$	−6.49941	−0.249608
$679$	0	0
$680$	4.01345	0.153909
$681$	−6.42933	−0.246373
$682$	15.4422	0.591312
$683$	6.84024	0.261735	0.130867	−	0.991400i	$-0.458224\pi$
$683$	6.84024	0.261735	0.130867	+	0.991400i	$0.458224\pi$
$684$	−34.4274	−1.31636
$685$	4.98272	0.190380
$686$	0	0
$687$	−3.79970	−0.144967
$688$	0.670540	0.0255641
$689$	11.7083	0.446050
$690$	−3.76182	−0.143210
$691$	−25.7899	−0.981094	−0.490547	−	0.871415i	$-0.663203\pi$
$691$	−25.7899	−0.981094	−0.490547	+	0.871415i	$0.663203\pi$
$692$	−37.0708	−1.40922
$693$	0	0
$694$	26.9197	1.02186
$695$	5.80701	0.220272
$696$	−0.0890599	−0.00337581
$697$	−1.69258	−0.0641111
$698$	63.9993	2.42241
$699$	−0.724906	−0.0274184
$700$	0	0
$701$	−25.6370	−0.968298	−0.484149	−	0.874986i	$-0.660871\pi$
$701$	−25.6370	−0.968298	−0.484149	+	0.874986i	$0.660871\pi$
$702$	5.79107	0.218570
$703$	1.57263	0.0593127
$704$	12.8867	0.485687
$705$	−0.0371352	−0.00139859
$706$	50.5495	1.90245
$707$	0	0
$708$	−10.9385	−0.411094
$709$	35.1596	1.32045	0.660223	−	0.751069i	$-0.270462\pi$
$709$	35.1596	1.32045	0.660223	+	0.751069i	$0.270462\pi$
$710$	−16.0211	−0.601263
$711$	22.2540	0.834589
$712$	−10.9128	−0.408973
$713$	−37.5509	−1.40629
$714$	0	0
$715$	1.45308	0.0543423
$716$	−82.8421	−3.09596
$717$	−4.48386	−0.167453
$718$	41.0013	1.53016
$719$	44.8159	1.67135	0.835676	−	0.549222i	$-0.185076\pi$
$719$	44.8159	1.67135	0.835676	+	0.549222i	$0.185076\pi$
$720$	0.439225	0.0163690
$721$	0	0
$722$	13.6375	0.507535
$723$	1.36381	0.0507208
$724$	−11.5222	−0.428217
$725$	0.104098	0.00386609
$726$	−0.673908	−0.0250111
$727$	39.1944	1.45364	0.726819	−	0.686829i	$-0.240998\pi$
$727$	39.1944	1.45364	0.726819	+	0.686829i	$0.240998\pi$
$728$	0	0
$729$	−22.4568	−0.831734
$730$	−33.8001	−1.25100
$731$	6.12620	0.226586
$732$	−5.10778	−0.188789
$733$	−18.2423	−0.673796	−0.336898	−	0.941541i	$-0.609378\pi$
$733$	−18.2423	−0.673796	−0.336898	+	0.941541i	$0.609378\pi$
$734$	10.0528	0.371055
$735$	0	0
$736$	−30.6037	−1.12807
$737$	−9.34121	−0.344088
$738$	−8.22065	−0.302606
$739$	−46.9095	−1.72559	−0.862797	−	0.505550i	$-0.831290\pi$
$739$	−46.9095	−1.72559	−0.862797	+	0.505550i	$0.831290\pi$
$740$	−1.42283	−0.0523042
$741$	1.54157	0.0566310
$742$	0	0
$743$	9.95770	0.365312	0.182656	−	0.983177i	$-0.441530\pi$
$743$	9.95770	0.365312	0.182656	+	0.983177i	$0.441530\pi$
$744$	−5.75526	−0.210998
$745$	8.28793	0.303646
$746$	17.1296	0.627160
$747$	23.8867	0.873968
$748$	−4.50273	−0.164636
$749$	0	0
$750$	0.673908	0.0246076
$751$	8.46961	0.309060	0.154530	−	0.987988i	$-0.450614\pi$
$751$	8.46961	0.309060	0.154530	+	0.987988i	$0.450614\pi$
$752$	0.0190676	0.000695325 0
$753$	−7.42114	−0.270441
$754$	−0.347230	−0.0126454
$755$	2.40230	0.0874285
$756$	0	0
$757$	20.4472	0.743167	0.371584	−	0.928399i	$-0.378815\pi$
$757$	20.4472	0.743167	0.371584	+	0.928399i	$0.378815\pi$
$758$	26.3484	0.957016
$759$	1.63875	0.0594827
$760$	10.5313	0.382012
$761$	−52.8243	−1.91488	−0.957439	−	0.288635i	$-0.906799\pi$
$761$	−52.8243	−1.91488	−0.957439	+	0.288635i	$0.906799\pi$
$762$	−0.180792	−0.00654942
$763$	0	0
$764$	33.9842	1.22951
$765$	4.01286	0.145085
$766$	56.7711	2.05122
$767$	−16.5596	−0.597931
$768$	−4.97985	−0.179695
$769$	−15.4979	−0.558870	−0.279435	−	0.960165i	$-0.590147\pi$
$769$	−15.4979	−0.558870	−0.279435	+	0.960165i	$0.590147\pi$
$770$	0	0
$771$	−9.02087	−0.324879
$772$	20.7007	0.745035
$773$	25.4616	0.915790	0.457895	−	0.889006i	$-0.348604\pi$
$773$	25.4616	0.915790	0.457895	+	0.889006i	$0.348604\pi$
$774$	29.7541	1.06949
$775$	6.72703	0.241642
$776$	−4.06503	−0.145926
$777$	0	0
$778$	65.2885	2.34071
$779$	−4.44136	−0.159128
$780$	−1.39473	−0.0499394
$781$	6.97924	0.249737
$782$	17.6471	0.631061
$783$	−0.180727	−0.00645866
$784$	0	0
$785$	−16.0405	−0.572510
$786$	7.10403	0.253392
$787$	31.9072	1.13737	0.568684	−	0.822556i	$-0.307453\pi$
$787$	31.9072	1.13737	0.568684	+	0.822556i	$0.307453\pi$
$788$	84.2001	2.99950
$789$	−5.19632	−0.184994
$790$	−17.5320	−0.623760
$791$	0	0
$792$	−8.49158	−0.301735
$793$	−7.73256	−0.274591
$794$	53.0600	1.88303
$795$	−2.36547	−0.0838945
$796$	26.1673	0.927475
$797$	28.8682	1.02256	0.511281	−	0.859413i	$-0.329171\pi$
$797$	28.8682	1.02256	0.511281	+	0.859413i	$0.329171\pi$
$798$	0	0
$799$	0.174206	0.00616296
$800$	5.48247	0.193835
$801$	−10.9111	−0.385526
$802$	−6.53306	−0.230690
$803$	14.7242	0.519607
$804$	8.96608	0.316209
$805$	0	0
$806$	−22.4388	−0.790374
$807$	−5.42564	−0.190992
$808$	18.4637	0.649551
$809$	37.4007	1.31494	0.657469	−	0.753482i	$-0.271627\pi$
$809$	37.4007	1.31494	0.657469	+	0.753482i	$0.271627\pi$
$810$	18.8964	0.663951
$811$	28.2722	0.992771	0.496386	−	0.868102i	$-0.334660\pi$
$811$	28.2722	0.992771	0.496386	+	0.868102i	$0.334660\pi$
$812$	0	0
$813$	−8.04484	−0.282145
$814$	0.998973	0.0350140
$815$	3.93239	0.137745
$816$	0.0609441	0.00213347
$817$	16.0752	0.562401
$818$	−62.1872	−2.17433
$819$	0	0
$820$	4.01830	0.140325
$821$	−11.4769	−0.400548	−0.200274	−	0.979740i	$-0.564183\pi$
$821$	−11.4769	−0.400548	−0.200274	+	0.979740i	$0.564183\pi$
$822$	3.35790	0.117120
$823$	−28.5492	−0.995164	−0.497582	−	0.867417i	$-0.665779\pi$
$823$	−28.5492	−0.995164	−0.497582	+	0.867417i	$0.665779\pi$
$824$	−33.2398	−1.15796
$825$	−0.293572	−0.0102209
$826$	0	0
$827$	36.3199	1.26297	0.631483	−	0.775390i	$-0.282446\pi$
$827$	36.3199	1.26297	0.631483	+	0.775390i	$0.282446\pi$
$828$	53.1794	1.84811
$829$	−29.2920	−1.01735	−0.508677	−	0.860957i	$-0.669865\pi$
$829$	−29.2920	−1.01735	−0.508677	+	0.860957i	$0.669865\pi$
$830$	−18.8183	−0.653192
$831$	−2.72212	−0.0944291
$832$	−18.7255	−0.649190
$833$	0	0
$834$	3.91339	0.135510
$835$	12.2979	0.425587
$836$	−11.8152	−0.408638
$837$	−11.6790	−0.403686
$838$	16.8571	0.582320
$839$	3.32507	0.114794	0.0573971	−	0.998351i	$-0.481720\pi$
$839$	3.32507	0.114794	0.0573971	+	0.998351i	$0.481720\pi$
$840$	0	0
$841$	−28.9892	−0.999626
$842$	−74.3240	−2.56137
$843$	6.69881	0.230719
$844$	40.9216	1.40858
$845$	10.8885	0.374577
$846$	0.846095	0.0290893
$847$	0	0
$848$	1.21458	0.0417090
$849$	−6.74634	−0.231534
$850$	−3.16139	−0.108435
$851$	−2.42921	−0.0832722
$852$	−6.69896	−0.229503
$853$	−27.1154	−0.928415	−0.464208	−	0.885726i	$-0.653661\pi$
$853$	−27.1154	−0.928415	−0.464208	+	0.885726i	$0.653661\pi$
$854$	0	0
$855$	10.5298	0.360111
$856$	−36.1188	−1.23451
$857$	−55.1107	−1.88255	−0.941273	−	0.337648i	$-0.890369\pi$
$857$	−55.1107	−1.88255	−0.941273	+	0.337648i	$0.890369\pi$
$858$	0.979245	0.0334309
$859$	−23.9506	−0.817185	−0.408592	−	0.912717i	$-0.633980\pi$
$859$	−23.9506	−0.817185	−0.408592	+	0.912717i	$0.633980\pi$
$860$	−14.5440	−0.495946
$861$	0	0
$862$	−82.5335	−2.81110
$863$	0.309183	0.0105247	0.00526235	−	0.999986i	$-0.498325\pi$
$863$	0.309183	0.0105247	0.00526235	+	0.999986i	$0.498325\pi$
$864$	−9.51829	−0.323819
$865$	11.3383	0.385513
$866$	−36.7075	−1.24737
$867$	−4.43393	−0.150584
$868$	0	0
$869$	7.63740	0.259081
$870$	0.0701522	0.00237838
$871$	13.5736	0.459923
$872$	43.0986	1.45950
$873$	−4.06443	−0.137560
$874$	46.3063	1.56633
$875$	0	0
$876$	−14.1329	−0.477507
$877$	−28.4555	−0.960873	−0.480437	−	0.877029i	$-0.659522\pi$
$877$	−28.4555	−0.960873	−0.480437	+	0.877029i	$0.659522\pi$
$878$	40.3609	1.36212
$879$	−2.19241	−0.0739483
$880$	0.150739	0.00508141
$881$	−37.5430	−1.26486	−0.632428	−	0.774619i	$-0.717941\pi$
$881$	−37.5430	−1.26486	−0.632428	+	0.774619i	$0.717941\pi$
$882$	0	0
$883$	−2.90495	−0.0977592	−0.0488796	−	0.998805i	$-0.515565\pi$
$883$	−2.90495	−0.0977592	−0.0488796	+	0.998805i	$0.515565\pi$
$884$	6.54285	0.220060
$885$	3.34559	0.112461
$886$	−10.6076	−0.356370
$887$	56.7508	1.90550	0.952752	−	0.303749i	$-0.0982385\pi$
$887$	56.7508	1.90550	0.952752	+	0.303749i	$0.0982385\pi$
$888$	−0.372314	−0.0124940
$889$	0	0
$890$	8.59594	0.288137
$891$	−8.23177	−0.275775
$892$	56.1705	1.88073
$893$	0.457118	0.0152969
$894$	5.58530	0.186800
$895$	25.3377	0.846945
$896$	0	0
$897$	−2.38124	−0.0795072
$898$	−32.6698	−1.09021
$899$	0.700268	0.0233552
$900$	−9.52679	−0.317560
$901$	11.0967	0.369685
$902$	−2.82126	−0.0939378
$903$	0	0
$904$	−28.1061	−0.934794
$905$	3.52411	0.117145
$906$	1.61893	0.0537852
$907$	−2.60141	−0.0863784	−0.0431892	−	0.999067i	$-0.513752\pi$
$907$	−2.60141	−0.0863784	−0.0431892	+	0.999067i	$0.513752\pi$
$908$	−71.6037	−2.37625
$909$	18.4610	0.612311
$910$	0	0
$911$	−18.8906	−0.625872	−0.312936	−	0.949774i	$-0.601313\pi$
$911$	−18.8906	−0.625872	−0.312936	+	0.949774i	$0.601313\pi$
$912$	0.159918	0.00529542
$913$	8.19774	0.271305
$914$	90.1714	2.98260
$915$	1.56224	0.0516460
$916$	−42.3174	−1.39821
$917$	0	0
$918$	5.48858	0.181150
$919$	2.85576	0.0942028	0.0471014	−	0.998890i	$-0.485002\pi$
$919$	2.85576	0.0942028	0.0471014	+	0.998890i	$0.485002\pi$
$920$	−16.2676	−0.536327
$921$	4.49214	0.148021
$922$	4.68505	0.154294
$923$	−10.1414	−0.333809
$924$	0	0
$925$	0.435179	0.0143086
$926$	−41.2768	−1.35644
$927$	−33.2349	−1.09158
$928$	0.570712	0.0187345
$929$	4.55208	0.149349	0.0746744	−	0.997208i	$-0.476208\pi$
$929$	4.55208	0.149349	0.0746744	+	0.997208i	$0.476208\pi$
$930$	4.53340	0.148656
$931$	0	0
$932$	−8.07330	−0.264450
$933$	6.61815	0.216668
$934$	−18.5050	−0.605501
$935$	1.37718	0.0450387
$936$	12.3390	0.403312
$937$	−39.5112	−1.29078	−0.645388	−	0.763855i	$-0.723304\pi$
$937$	−39.5112	−1.29078	−0.645388	+	0.763855i	$0.723304\pi$
$938$	0	0
$939$	−2.49903	−0.0815527
$940$	−0.413576	−0.0134894
$941$	35.4567	1.15585	0.577927	−	0.816088i	$-0.303862\pi$
$941$	35.4567	1.15585	0.577927	+	0.816088i	$0.303862\pi$
$942$	−10.8098	−0.352203
$943$	6.86049	0.223408
$944$	−1.71784	−0.0559110
$945$	0	0
$946$	10.2114	0.332001
$947$	8.35366	0.271457	0.135729	−	0.990746i	$-0.456662\pi$
$947$	8.35366	0.271457	0.135729	+	0.990746i	$0.456662\pi$
$948$	−7.33069	−0.238090
$949$	−21.3956	−0.694529
$950$	−8.29551	−0.269142
$951$	−5.78728	−0.187665
$952$	0	0
$953$	−11.3306	−0.367033	−0.183517	−	0.983017i	$-0.558748\pi$
$953$	−11.3306	−0.367033	−0.183517	+	0.983017i	$0.558748\pi$
$954$	53.8952	1.74492
$955$	−10.3942	−0.336350
$956$	−49.9369	−1.61507
$957$	−0.0305602	−0.000987869 0
$958$	34.5768	1.11713
$959$	0	0
$960$	3.78318	0.122102
$961$	14.2529	0.459772
$962$	−1.45159	−0.0468012
$963$	−36.1134	−1.16374
$964$	15.1889	0.489200
$965$	−6.33141	−0.203815
$966$	0	0
$967$	25.7910	0.829383	0.414692	−	0.909962i	$-0.363889\pi$
$967$	25.7910	0.829383	0.414692	+	0.909962i	$0.363889\pi$
$968$	−2.91425	−0.0936675
$969$	1.46105	0.0469356
$970$	3.20201	0.102810
$971$	−25.8433	−0.829349	−0.414675	−	0.909970i	$-0.636105\pi$
$971$	−25.8433	−0.829349	−0.414675	+	0.909970i	$0.636105\pi$
$972$	24.9302	0.799635
$973$	0	0
$974$	92.6058	2.96728
$975$	0.426585	0.0136617
$976$	−0.802154	−0.0256763
$977$	23.7974	0.761345	0.380673	−	0.924710i	$-0.375692\pi$
$977$	23.7974	0.761345	0.380673	+	0.924710i	$0.375692\pi$
$978$	2.65007	0.0847398
$979$	−3.74462	−0.119679
$980$	0	0
$981$	43.0922	1.37583
$982$	32.8311	1.04768
$983$	54.2199	1.72935	0.864674	−	0.502334i	$-0.167525\pi$
$983$	54.2199	1.72935	0.864674	+	0.502334i	$0.167525\pi$
$984$	1.05148	0.0335198
$985$	−25.7530	−0.820559
$986$	−0.329093	−0.0104804
$987$	0	0
$988$	17.1685	0.546203
$989$	−24.8311	−0.789584
$990$	6.68879	0.212584
$991$	−42.1179	−1.33792	−0.668959	−	0.743299i	$-0.733260\pi$
$991$	−42.1179	−1.33792	−0.668959	+	0.743299i	$0.733260\pi$
$992$	36.8807	1.17096
$993$	4.35372	0.138161
$994$	0	0
$995$	−8.00340	−0.253725
$996$	−7.86852	−0.249324
$997$	−20.6025	−0.652487	−0.326244	−	0.945286i	$-0.605783\pi$
$997$	−20.6025	−0.652487	−0.326244	+	0.945286i	$0.605783\pi$
$998$	−56.5116	−1.78884
$999$	−0.755528	−0.0239038

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2695.2.a.w.1.1	✓	10
7.6	odd	2		2695.2.a.x.1.1	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2695.2.a.w.1.1	✓	10	1.1	even	1	trivial
2695.2.a.x.1.1	yes	10	7.6	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:	\( N \)	\(=\)	\( 2695 = 5 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2695.a (trivial)

\(f(q)\)	\(=\)	\(q-2.29554 q^{2} +0.293572 q^{3} +3.26952 q^{4} -1.00000 q^{5} -0.673908 q^{6} -2.91425 q^{8} -2.91382 q^{9} +O(q^{10})\)	\(q-2.29554 q^{2} +0.293572 q^{3} +3.26952 q^{4} -1.00000 q^{5} -0.673908 q^{6} -2.91425 q^{8} -2.91382 q^{9} +2.29554 q^{10} -1.00000 q^{11} +0.959841 q^{12} +1.45308 q^{13} -0.293572 q^{15} +0.150739 q^{16} +1.37718 q^{17} +6.68879 q^{18} +3.61374 q^{19} -3.26952 q^{20} +2.29554 q^{22} -5.58209 q^{23} -0.855542 q^{24} +1.00000 q^{25} -3.33562 q^{26} -1.73613 q^{27} +0.104098 q^{29} +0.673908 q^{30} +6.72703 q^{31} +5.48247 q^{32} -0.293572 q^{33} -3.16139 q^{34} -9.52679 q^{36} +0.435179 q^{37} -8.29551 q^{38} +0.426585 q^{39} +2.91425 q^{40} -1.22902 q^{41} +4.44836 q^{43} -3.26952 q^{44} +2.91382 q^{45} +12.8139 q^{46} +0.126494 q^{47} +0.0442527 q^{48} -2.29554 q^{50} +0.404303 q^{51} +4.75089 q^{52} +8.05754 q^{53} +3.98537 q^{54} +1.00000 q^{55} +1.06089 q^{57} -0.238961 q^{58} -11.3961 q^{59} -0.959841 q^{60} -5.32148 q^{61} -15.4422 q^{62} -12.8867 q^{64} -1.45308 q^{65} +0.673908 q^{66} +9.34121 q^{67} +4.50273 q^{68} -1.63875 q^{69} -6.97924 q^{71} +8.49158 q^{72} -14.7242 q^{73} -0.998973 q^{74} +0.293572 q^{75} +11.8152 q^{76} -0.979245 q^{78} -7.63740 q^{79} -0.150739 q^{80} +8.23177 q^{81} +2.82126 q^{82} -8.19774 q^{83} -1.37718 q^{85} -10.2114 q^{86} +0.0305602 q^{87} +2.91425 q^{88} +3.74462 q^{89} -6.68879 q^{90} -18.2508 q^{92} +1.97487 q^{93} -0.290373 q^{94} -3.61374 q^{95} +1.60950 q^{96} +1.39488 q^{97} +2.91382 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} + 10 q^{4} - 10 q^{5} - 4 q^{6} + 6 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 2 * q^2 + 10 * q^4 - 10 * q^5 - 4 * q^6 + 6 * q^8 + 10 * q^9	\( 10 q + 2 q^{2} + 10 q^{4} - 10 q^{5} - 4 q^{6} + 6 q^{8} + 10 q^{9} - 2 q^{10} - 10 q^{11} - 4 q^{12} - 8 q^{13} + 6 q^{16} - 28 q^{17} - 10 q^{18} - 8 q^{19} - 10 q^{20} - 2 q^{22} - 8 q^{23} - 32 q^{24} + 10 q^{25} - 12 q^{26} - 8 q^{29} + 4 q^{30} + 4 q^{31} + 14 q^{32} - 20 q^{34} - 22 q^{36} + 28 q^{37} - 24 q^{38} - 24 q^{39} - 6 q^{40} - 44 q^{41} + 20 q^{43} - 10 q^{44} - 10 q^{45} - 12 q^{46} - 12 q^{47} - 16 q^{48} + 2 q^{50} - 4 q^{51} - 36 q^{52} + 8 q^{54} + 10 q^{55} + 12 q^{57} - 8 q^{58} - 16 q^{59} + 4 q^{60} - 16 q^{61} - 36 q^{62} - 34 q^{64} + 8 q^{65} + 4 q^{66} + 20 q^{67} - 8 q^{68} - 4 q^{69} - 4 q^{71} + 10 q^{72} - 20 q^{73} - 16 q^{74} - 4 q^{76} + 52 q^{78} - 20 q^{79} - 6 q^{80} + 10 q^{81} + 32 q^{82} - 16 q^{83} + 28 q^{85} - 20 q^{86} - 20 q^{87} - 6 q^{88} - 44 q^{89} + 10 q^{90} - 24 q^{92} + 16 q^{93} - 24 q^{94} + 8 q^{95} + 4 q^{97} - 10 q^{99}+O(q^{100}) \) 10 * q + 2 * q^2 + 10 * q^4 - 10 * q^5 - 4 * q^6 + 6 * q^8 + 10 * q^9 - 2 * q^10 - 10 * q^11 - 4 * q^12 - 8 * q^13 + 6 * q^16 - 28 * q^17 - 10 * q^18 - 8 * q^19 - 10 * q^20 - 2 * q^22 - 8 * q^23 - 32 * q^24 + 10 * q^25 - 12 * q^26 - 8 * q^29 + 4 * q^30 + 4 * q^31 + 14 * q^32 - 20 * q^34 - 22 * q^36 + 28 * q^37 - 24 * q^38 - 24 * q^39 - 6 * q^40 - 44 * q^41 + 20 * q^43 - 10 * q^44 - 10 * q^45 - 12 * q^46 - 12 * q^47 - 16 * q^48 + 2 * q^50 - 4 * q^51 - 36 * q^52 + 8 * q^54 + 10 * q^55 + 12 * q^57 - 8 * q^58 - 16 * q^59 + 4 * q^60 - 16 * q^61 - 36 * q^62 - 34 * q^64 + 8 * q^65 + 4 * q^66 + 20 * q^67 - 8 * q^68 - 4 * q^69 - 4 * q^71 + 10 * q^72 - 20 * q^73 - 16 * q^74 - 4 * q^76 + 52 * q^78 - 20 * q^79 - 6 * q^80 + 10 * q^81 + 32 * q^82 - 16 * q^83 + 28 * q^85 - 20 * q^86 - 20 * q^87 - 6 * q^88 - 44 * q^89 + 10 * q^90 - 24 * q^92 + 16 * q^93 - 24 * q^94 + 8 * q^95 + 4 * q^97 - 10 * q^99

Introduction

L-functions

Modular forms

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Database

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