LMFDB - Embedded newform 6025.2.a.l.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6025,2,Mod(1,6025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6025, 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("6025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6025 = 5^{2} \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6025.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:	$48.1098672178$
Analytic rank:	$1$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	6025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.17490 q^{2} +0.995168 q^{3} +2.73018 q^{4} -2.16439 q^{6} +3.57474 q^{7} -1.58807 q^{8} -2.00964 q^{9} +O(q^{10})$	\(q-2.17490 q^{2} +0.995168 q^{3} +2.73018 q^{4} -2.16439 q^{6} +3.57474 q^{7} -1.58807 q^{8} -2.00964 q^{9} -2.14280 q^{11} +2.71699 q^{12} +1.64478 q^{13} -7.77470 q^{14} -2.00648 q^{16} +0.660538 q^{17} +4.37076 q^{18} +4.16594 q^{19} +3.55747 q^{21} +4.66037 q^{22} -0.236291 q^{23} -1.58039 q^{24} -3.57724 q^{26} -4.98544 q^{27} +9.75969 q^{28} -6.17856 q^{29} -0.0561187 q^{31} +7.54002 q^{32} -2.13245 q^{33} -1.43660 q^{34} -5.48668 q^{36} -10.8833 q^{37} -9.06049 q^{38} +1.63684 q^{39} +9.65875 q^{41} -7.73714 q^{42} -11.8970 q^{43} -5.85023 q^{44} +0.513910 q^{46} -10.6445 q^{47} -1.99678 q^{48} +5.77878 q^{49} +0.657347 q^{51} +4.49056 q^{52} +0.824478 q^{53} +10.8428 q^{54} -5.67693 q^{56} +4.14581 q^{57} +13.4377 q^{58} +0.481563 q^{59} +15.0106 q^{61} +0.122053 q^{62} -7.18394 q^{63} -12.3858 q^{64} +4.63785 q^{66} -1.76662 q^{67} +1.80339 q^{68} -0.235150 q^{69} -11.6191 q^{71} +3.19144 q^{72} +10.5925 q^{73} +23.6701 q^{74} +11.3738 q^{76} -7.65995 q^{77} -3.55995 q^{78} -12.4857 q^{79} +1.06757 q^{81} -21.0068 q^{82} -7.30251 q^{83} +9.71254 q^{84} +25.8747 q^{86} -6.14871 q^{87} +3.40291 q^{88} +8.65772 q^{89} +5.87968 q^{91} -0.645118 q^{92} -0.0558476 q^{93} +23.1506 q^{94} +7.50359 q^{96} -2.57045 q^{97} -12.5683 q^{98} +4.30625 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 11 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 16 q^{7} - 33 q^{8} + 38 q^{9}+O(q^{10}) $ 40 * q - 11 * q^2 - 8 * q^3 + 41 * q^4 + 3 * q^6 - 16 * q^7 - 33 * q^8 + 38 * q^9	$ 40 q - 11 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 16 q^{7} - 33 q^{8} + 38 q^{9} + q^{11} - 14 q^{12} - 9 q^{13} - q^{14} + 43 q^{16} - 12 q^{17} - 42 q^{18} + 2 q^{21} - 5 q^{22} - 77 q^{23} - 2 q^{24} + 2 q^{26} - 38 q^{27} - 42 q^{28} + 2 q^{29} + q^{31} - 72 q^{32} - 20 q^{33} + 5 q^{34} + 32 q^{36} - 28 q^{37} - 23 q^{38} - 2 q^{39} - 2 q^{41} - 37 q^{42} - 31 q^{43} + 3 q^{44} + 14 q^{46} - 96 q^{47} - 13 q^{48} + 40 q^{49} - 10 q^{51} - 42 q^{52} - 54 q^{53} + 4 q^{54} - 15 q^{56} - 37 q^{57} - 27 q^{58} + q^{59} + 5 q^{61} - 39 q^{62} - 70 q^{63} + 65 q^{64} - 52 q^{66} - 34 q^{67} - 52 q^{68} + 21 q^{69} - 9 q^{71} - 70 q^{72} - 25 q^{73} + 22 q^{74} - 47 q^{76} - 54 q^{77} - 58 q^{78} + 13 q^{79} + 12 q^{81} + 5 q^{82} - 63 q^{83} + 95 q^{84} - 18 q^{86} - 47 q^{87} - 13 q^{88} + 19 q^{89} - 31 q^{91} - 137 q^{92} - 52 q^{93} + 120 q^{94} - 49 q^{96} - 36 q^{97} - 64 q^{98} + 16 q^{99}+O(q^{100}) $ 40 * q - 11 * q^2 - 8 * q^3 + 41 * q^4 + 3 * q^6 - 16 * q^7 - 33 * q^8 + 38 * q^9 + q^11 - 14 * q^12 - 9 * q^13 - q^14 + 43 * q^16 - 12 * q^17 - 42 * q^18 + 2 * q^21 - 5 * q^22 - 77 * q^23 - 2 * q^24 + 2 * q^26 - 38 * q^27 - 42 * q^28 + 2 * q^29 + q^31 - 72 * q^32 - 20 * q^33 + 5 * q^34 + 32 * q^36 - 28 * q^37 - 23 * q^38 - 2 * q^39 - 2 * q^41 - 37 * q^42 - 31 * q^43 + 3 * q^44 + 14 * q^46 - 96 * q^47 - 13 * q^48 + 40 * q^49 - 10 * q^51 - 42 * q^52 - 54 * q^53 + 4 * q^54 - 15 * q^56 - 37 * q^57 - 27 * q^58 + q^59 + 5 * q^61 - 39 * q^62 - 70 * q^63 + 65 * q^64 - 52 * q^66 - 34 * q^67 - 52 * q^68 + 21 * q^69 - 9 * q^71 - 70 * q^72 - 25 * q^73 + 22 * q^74 - 47 * q^76 - 54 * q^77 - 58 * q^78 + 13 * q^79 + 12 * q^81 + 5 * q^82 - 63 * q^83 + 95 * q^84 - 18 * q^86 - 47 * q^87 - 13 * q^88 + 19 * q^89 - 31 * q^91 - 137 * q^92 - 52 * q^93 + 120 * q^94 - 49 * q^96 - 36 * q^97 - 64 * q^98 + 16 * 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 $

$2$	−2.17490	−1.53788	−0.768942	−	0.639318i	$-0.779217\pi$
$2$	−2.17490	−1.53788	−0.768942	+	0.639318i	$0.779217\pi$
$3$	0.995168	0.574561	0.287280	−	0.957847i	$-0.407249\pi$
$3$	0.995168	0.574561	0.287280	+	0.957847i	$0.407249\pi$
$4$	2.73018	1.36509
$5$	0	0
$5$	0	0
$6$	−2.16439	−0.883608
$7$	3.57474	1.35113	0.675563	−	0.737302i	$-0.263901\pi$
$7$	3.57474	1.35113	0.675563	+	0.737302i	$0.263901\pi$
$8$	−1.58807	−0.561467
$9$	−2.00964	−0.669880
$10$	0	0
$11$	−2.14280	−0.646078	−0.323039	−	0.946386i	$-0.604705\pi$
$11$	−2.14280	−0.646078	−0.323039	+	0.946386i	$0.604705\pi$
$12$	2.71699	0.784327
$13$	1.64478	0.456181	0.228091	−	0.973640i	$-0.426752\pi$
$13$	1.64478	0.456181	0.228091	+	0.973640i	$0.426752\pi$
$14$	−7.77470	−2.07788
$15$	0	0
$16$	−2.00648	−0.501619
$17$	0.660538	0.160204	0.0801020	−	0.996787i	$-0.474475\pi$
$17$	0.660538	0.160204	0.0801020	+	0.996787i	$0.474475\pi$
$18$	4.37076	1.03020
$19$	4.16594	0.955732	0.477866	−	0.878433i	$-0.341410\pi$
$19$	4.16594	0.955732	0.477866	+	0.878433i	$0.341410\pi$
$20$	0	0
$21$	3.55747	0.776304
$22$	4.66037	0.993594
$23$	−0.236291	−0.0492702	−0.0246351	−	0.999697i	$-0.507842\pi$
$23$	−0.236291	−0.0492702	−0.0246351	+	0.999697i	$0.507842\pi$
$24$	−1.58039	−0.322597
$25$	0	0
$26$	−3.57724	−0.701554
$27$	−4.98544	−0.959448
$28$	9.75969	1.84441
$29$	−6.17856	−1.14733	−0.573665	−	0.819090i	$-0.694479\pi$
$29$	−6.17856	−1.14733	−0.573665	+	0.819090i	$0.694479\pi$
$30$	0	0
$31$	−0.0561187	−0.0100792	−0.00503961	−	0.999987i	$-0.501604\pi$
$31$	−0.0561187	−0.0100792	−0.00503961	+	0.999987i	$0.501604\pi$
$32$	7.54002	1.33290
$33$	−2.13245	−0.371211
$34$	−1.43660	−0.246375
$35$	0	0
$36$	−5.48668	−0.914446
$37$	−10.8833	−1.78920	−0.894602	−	0.446865i	$-0.852541\pi$
$37$	−10.8833	−1.78920	−0.894602	+	0.446865i	$0.852541\pi$
$38$	−9.06049	−1.46981
$39$	1.63684	0.262104
$40$	0	0
$41$	9.65875	1.50844	0.754221	−	0.656620i	$-0.228014\pi$
$41$	9.65875	1.50844	0.754221	+	0.656620i	$0.228014\pi$
$42$	−7.73714	−1.19387
$43$	−11.8970	−1.81427	−0.907137	−	0.420836i	$-0.861737\pi$
$43$	−11.8970	−1.81427	−0.907137	+	0.420836i	$0.861737\pi$
$44$	−5.85023	−0.881955
$45$	0	0
$46$	0.513910	0.0757718
$47$	−10.6445	−1.55265	−0.776327	−	0.630331i	$-0.782919\pi$
$47$	−10.6445	−1.55265	−0.776327	+	0.630331i	$0.782919\pi$
$48$	−1.99678	−0.288211
$49$	5.77878	0.825541
$50$	0	0
$51$	0.657347	0.0920470
$52$	4.49056	0.622728
$53$	0.824478	0.113251	0.0566254	−	0.998395i	$-0.481966\pi$
$53$	0.824478	0.113251	0.0566254	+	0.998395i	$0.481966\pi$
$54$	10.8428	1.47552
$55$	0	0
$56$	−5.67693	−0.758612
$57$	4.14581	0.549126
$58$	13.4377	1.76446
$59$	0.481563	0.0626942	0.0313471	−	0.999509i	$-0.490020\pi$
$59$	0.481563	0.0626942	0.0313471	+	0.999509i	$0.490020\pi$
$60$	0	0
$61$	15.0106	1.92191	0.960955	−	0.276704i	$-0.0892421\pi$
$61$	15.0106	1.92191	0.960955	+	0.276704i	$0.0892421\pi$
$62$	0.122053	0.0155007
$63$	−7.18394	−0.905092
$64$	−12.3858	−1.54823
$65$	0	0
$66$	4.63785	0.570880
$67$	−1.76662	−0.215826	−0.107913	−	0.994160i	$-0.534417\pi$
$67$	−1.76662	−0.215826	−0.107913	+	0.994160i	$0.534417\pi$
$68$	1.80339	0.218693
$69$	−0.235150	−0.0283087
$70$	0	0
$71$	−11.6191	−1.37893	−0.689465	−	0.724319i	$-0.742154\pi$
$71$	−11.6191	−1.37893	−0.689465	+	0.724319i	$0.742154\pi$
$72$	3.19144	0.376115
$73$	10.5925	1.23976	0.619882	−	0.784695i	$-0.287181\pi$
$73$	10.5925	1.23976	0.619882	+	0.784695i	$0.287181\pi$
$74$	23.6701	2.75159
$75$	0	0
$76$	11.3738	1.30466
$77$	−7.65995	−0.872933
$78$	−3.55995	−0.403085
$79$	−12.4857	−1.40476	−0.702378	−	0.711804i	$-0.747878\pi$
$79$	−12.4857	−1.40476	−0.702378	+	0.711804i	$0.747878\pi$
$80$	0	0
$81$	1.06757	0.118619
$82$	−21.0068	−2.31981
$83$	−7.30251	−0.801555	−0.400777	−	0.916175i	$-0.631260\pi$
$83$	−7.30251	−0.801555	−0.400777	+	0.916175i	$0.631260\pi$
$84$	9.71254	1.05972
$85$	0	0
$86$	25.8747	2.79014
$87$	−6.14871	−0.659211
$88$	3.40291	0.362751
$89$	8.65772	0.917717	0.458858	−	0.888509i	$-0.348259\pi$
$89$	8.65772	0.917717	0.458858	+	0.888509i	$0.348259\pi$
$90$	0	0
$91$	5.87968	0.616358
$92$	−0.645118	−0.0672582
$93$	−0.0558476	−0.00579113
$94$	23.1506	2.38780
$95$	0	0
$96$	7.50359	0.765831
$97$	−2.57045	−0.260990	−0.130495	−	0.991449i	$-0.541657\pi$
$97$	−2.57045	−0.260990	−0.130495	+	0.991449i	$0.541657\pi$
$98$	−12.5683	−1.26959
$99$	4.30625	0.432795
$100$	0	0
$101$	−15.3863	−1.53099	−0.765497	−	0.643439i	$-0.777507\pi$
$101$	−15.3863	−1.53099	−0.765497	+	0.643439i	$0.777507\pi$
$102$	−1.42966	−0.141558
$103$	13.0326	1.28414	0.642070	−	0.766646i	$-0.278076\pi$
$103$	13.0326	1.28414	0.642070	+	0.766646i	$0.278076\pi$
$104$	−2.61203	−0.256131
$105$	0	0
$106$	−1.79315	−0.174167
$107$	−9.27514	−0.896662	−0.448331	−	0.893868i	$-0.647981\pi$
$107$	−9.27514	−0.896662	−0.448331	+	0.893868i	$0.647981\pi$
$108$	−13.6111	−1.30973
$109$	1.70201	0.163023	0.0815117	−	0.996672i	$-0.474025\pi$
$109$	1.70201	0.163023	0.0815117	+	0.996672i	$0.474025\pi$
$110$	0	0
$111$	−10.8307	−1.02801
$112$	−7.17264	−0.677750
$113$	−10.1146	−0.951503	−0.475752	−	0.879580i	$-0.657824\pi$
$113$	−10.1146	−0.951503	−0.475752	+	0.879580i	$0.657824\pi$
$114$	−9.01671	−0.844493
$115$	0	0
$116$	−16.8686	−1.56621
$117$	−3.30542	−0.305587
$118$	−1.04735	−0.0964165
$119$	2.36125	0.216456
$120$	0	0
$121$	−6.40842	−0.582583
$122$	−32.6465	−2.95568
$123$	9.61208	0.866692
$124$	−0.153214	−0.0137590
$125$	0	0
$126$	15.6243	1.39193
$127$	−14.5083	−1.28740	−0.643700	−	0.765278i	$-0.722601\pi$
$127$	−14.5083	−1.28740	−0.643700	+	0.765278i	$0.722601\pi$
$128$	11.8578	1.04809
$129$	−11.8395	−1.04241
$130$	0	0
$131$	−10.7901	−0.942740	−0.471370	−	0.881936i	$-0.656240\pi$
$131$	−10.7901	−0.942740	−0.471370	+	0.881936i	$0.656240\pi$
$132$	−5.82196	−0.506737
$133$	14.8922	1.29131
$134$	3.84221	0.331916
$135$	0	0
$136$	−1.04898	−0.0899492
$137$	−2.13394	−0.182315	−0.0911574	−	0.995836i	$-0.529057\pi$
$137$	−2.13394	−0.182315	−0.0911574	+	0.995836i	$0.529057\pi$
$138$	0.511427	0.0435355
$139$	2.33824	0.198327	0.0991636	−	0.995071i	$-0.468383\pi$
$139$	2.33824	0.198327	0.0991636	+	0.995071i	$0.468383\pi$
$140$	0	0
$141$	−10.5930	−0.892094
$142$	25.2703	2.12064
$143$	−3.52444	−0.294729
$144$	4.03229	0.336025
$145$	0	0
$146$	−23.0377	−1.90661
$147$	5.75086	0.474323
$148$	−29.7134	−2.44242
$149$	−11.6752	−0.956473	−0.478237	−	0.878231i	$-0.658724\pi$
$149$	−11.6752	−0.956473	−0.478237	+	0.878231i	$0.658724\pi$
$150$	0	0
$151$	−12.2124	−0.993828	−0.496914	−	0.867800i	$-0.665534\pi$
$151$	−12.2124	−0.993828	−0.496914	+	0.867800i	$0.665534\pi$
$152$	−6.61579	−0.536612
$153$	−1.32744	−0.107317
$154$	16.6596	1.34247
$155$	0	0
$156$	4.46886	0.357795
$157$	9.76433	0.779279	0.389639	−	0.920968i	$-0.372600\pi$
$157$	9.76433	0.779279	0.389639	+	0.920968i	$0.372600\pi$
$158$	27.1552	2.16035
$159$	0.820494	0.0650694
$160$	0	0
$161$	−0.844681	−0.0665702
$162$	−2.32186	−0.182422
$163$	23.3726	1.83069	0.915343	−	0.402674i	$-0.131919\pi$
$163$	23.3726	1.83069	0.915343	+	0.402674i	$0.131919\pi$
$164$	26.3701	2.05916
$165$	0	0
$166$	15.8822	1.23270
$167$	−20.0872	−1.55439	−0.777197	−	0.629257i	$-0.783359\pi$
$167$	−20.0872	−1.55439	−0.777197	+	0.629257i	$0.783359\pi$
$168$	−5.64950	−0.435869
$169$	−10.2947	−0.791899
$170$	0	0
$171$	−8.37204	−0.640226
$172$	−32.4809	−2.47665
$173$	−15.7577	−1.19803	−0.599017	−	0.800736i	$-0.704442\pi$
$173$	−15.7577	−1.19803	−0.599017	+	0.800736i	$0.704442\pi$
$174$	13.3728	1.01379
$175$	0	0
$176$	4.29947	0.324085
$177$	0.479237	0.0360216
$178$	−18.8297	−1.41134
$179$	19.0820	1.42626	0.713130	−	0.701032i	$-0.247277\pi$
$179$	19.0820	1.42626	0.713130	+	0.701032i	$0.247277\pi$
$180$	0	0
$181$	19.0266	1.41424	0.707119	−	0.707094i	$-0.249994\pi$
$181$	19.0266	1.41424	0.707119	+	0.707094i	$0.249994\pi$
$182$	−12.7877	−0.947888
$183$	14.9381	1.10425
$184$	0.375247	0.0276636
$185$	0	0
$186$	0.121463	0.00890609
$187$	−1.41540	−0.103504
$188$	−29.0613	−2.11951
$189$	−17.8216	−1.29633
$190$	0	0
$191$	−16.5103	−1.19465	−0.597323	−	0.802001i	$-0.703769\pi$
$191$	−16.5103	−1.19465	−0.597323	+	0.802001i	$0.703769\pi$
$192$	−12.3260	−0.889550
$193$	16.9004	1.21652	0.608258	−	0.793740i	$-0.291869\pi$
$193$	16.9004	1.21652	0.608258	+	0.793740i	$0.291869\pi$
$194$	5.59047	0.401372
$195$	0	0
$196$	15.7771	1.12694
$197$	−20.2646	−1.44379	−0.721897	−	0.692001i	$-0.756729\pi$
$197$	−20.2646	−1.44379	−0.721897	+	0.692001i	$0.756729\pi$
$198$	−9.36566	−0.665588
$199$	15.3572	1.08864	0.544321	−	0.838877i	$-0.316787\pi$
$199$	15.3572	1.08864	0.544321	+	0.838877i	$0.316787\pi$
$200$	0	0
$201$	−1.75808	−0.124005
$202$	33.4636	2.35449
$203$	−22.0868	−1.55019
$204$	1.79468	0.125652
$205$	0	0
$206$	−28.3446	−1.97486
$207$	0.474861	0.0330051
$208$	−3.30022	−0.228829
$209$	−8.92677	−0.617477
$210$	0	0
$211$	3.96591	0.273025	0.136512	−	0.990638i	$-0.456411\pi$
$211$	3.96591	0.273025	0.136512	+	0.990638i	$0.456411\pi$
$212$	2.25097	0.154597
$213$	−11.5629	−0.792279
$214$	20.1725	1.37896
$215$	0	0
$216$	7.91721	0.538698
$217$	−0.200610	−0.0136183
$218$	−3.70171	−0.250711
$219$	10.5414	0.712319
$220$	0	0
$221$	1.08644	0.0730821
$222$	23.5557	1.58095
$223$	1.06015	0.0709926	0.0354963	−	0.999370i	$-0.488699\pi$
$223$	1.06015	0.0709926	0.0354963	+	0.999370i	$0.488699\pi$
$224$	26.9536	1.80091
$225$	0	0
$226$	21.9983	1.46330
$227$	−0.472126	−0.0313361	−0.0156681	−	0.999877i	$-0.504987\pi$
$227$	−0.472126	−0.0313361	−0.0156681	+	0.999877i	$0.504987\pi$
$228$	11.3188	0.749607
$229$	19.8682	1.31293	0.656464	−	0.754358i	$-0.272052\pi$
$229$	19.8682	1.31293	0.656464	+	0.754358i	$0.272052\pi$
$230$	0	0
$231$	−7.62294	−0.501553
$232$	9.81197	0.644188
$233$	28.8434	1.88959	0.944797	−	0.327655i	$-0.106258\pi$
$233$	28.8434	1.88959	0.944797	+	0.327655i	$0.106258\pi$
$234$	7.18896	0.469957
$235$	0	0
$236$	1.31475	0.0855832
$237$	−12.4254	−0.807117
$238$	−5.13549	−0.332884
$239$	30.0843	1.94599	0.972995	−	0.230825i	$-0.0741426\pi$
$239$	30.0843	1.94599	0.972995	+	0.230825i	$0.0741426\pi$
$240$	0	0
$241$	−1.00000	−0.0644157
$241$	−1.00000	−0.0644157
$242$	13.9376	0.895946
$243$	16.0187	1.02760
$244$	40.9816	2.62358
$245$	0	0
$246$	−20.9053	−1.33287
$247$	6.85207	0.435987
$248$	0.0891203	0.00565915
$249$	−7.26723	−0.460542
$250$	0	0
$251$	−0.493643	−0.0311585	−0.0155792	−	0.999879i	$-0.504959\pi$
$251$	−0.493643	−0.0311585	−0.0155792	+	0.999879i	$0.504959\pi$
$252$	−19.6135	−1.23553
$253$	0.506325	0.0318324
$254$	31.5540	1.97987
$255$	0	0
$256$	−1.01797	−0.0636232
$257$	−0.629762	−0.0392835	−0.0196417	−	0.999807i	$-0.506253\pi$
$257$	−0.629762	−0.0392835	−0.0196417	+	0.999807i	$0.506253\pi$
$258$	25.7497	1.60311
$259$	−38.9050	−2.41744
$260$	0	0
$261$	12.4167	0.768573
$262$	23.4675	1.44983
$263$	−20.2647	−1.24958	−0.624789	−	0.780794i	$-0.714815\pi$
$263$	−20.2647	−1.24958	−0.624789	+	0.780794i	$0.714815\pi$
$264$	3.38647	0.208423
$265$	0	0
$266$	−32.3889	−1.98589
$267$	8.61589	0.527284
$268$	−4.82318	−0.294622
$269$	−4.53269	−0.276363	−0.138181	−	0.990407i	$-0.544126\pi$
$269$	−4.53269	−0.276363	−0.138181	+	0.990407i	$0.544126\pi$
$270$	0	0
$271$	−19.6497	−1.19364	−0.596818	−	0.802377i	$-0.703568\pi$
$271$	−19.6497	−1.19364	−0.596818	+	0.802377i	$0.703568\pi$
$272$	−1.32535	−0.0803614
$273$	5.85127	0.354135
$274$	4.64110	0.280379
$275$	0	0
$276$	−0.642001	−0.0386439
$277$	−20.6266	−1.23933	−0.619665	−	0.784866i	$-0.712732\pi$
$277$	−20.6266	−1.23933	−0.619665	+	0.784866i	$0.712732\pi$
$278$	−5.08544	−0.305004
$279$	0.112778	0.00675187
$280$	0	0
$281$	7.79009	0.464718	0.232359	−	0.972630i	$-0.425356\pi$
$281$	7.79009	0.464718	0.232359	+	0.972630i	$0.425356\pi$
$282$	23.0387	1.37194
$283$	12.2038	0.725442	0.362721	−	0.931898i	$-0.381848\pi$
$283$	12.2038	0.725442	0.362721	+	0.931898i	$0.381848\pi$
$284$	−31.7222	−1.88236
$285$	0	0
$286$	7.66530	0.453259
$287$	34.5275	2.03810
$288$	−15.1527	−0.892882
$289$	−16.5637	−0.974335
$290$	0	0
$291$	−2.55803	−0.149955
$292$	28.9195	1.69239
$293$	0.941948	0.0550292	0.0275146	−	0.999621i	$-0.491241\pi$
$293$	0.941948	0.0550292	0.0275146	+	0.999621i	$0.491241\pi$
$294$	−12.5075	−0.729455
$295$	0	0
$296$	17.2834	1.00458
$297$	10.6828	0.619878
$298$	25.3925	1.47095
$299$	−0.388648	−0.0224761
$300$	0	0
$301$	−42.5287	−2.45131
$302$	26.5606	1.52839
$303$	−15.3120	−0.879650
$304$	−8.35886	−0.479413
$305$	0	0
$306$	2.88705	0.165042
$307$	11.0615	0.631314	0.315657	−	0.948873i	$-0.397775\pi$
$307$	11.0615	0.631314	0.315657	+	0.948873i	$0.397775\pi$
$308$	−20.9131	−1.19163
$309$	12.9696	0.737817
$310$	0	0
$311$	8.89176	0.504205	0.252103	−	0.967700i	$-0.418878\pi$
$311$	8.89176	0.504205	0.252103	+	0.967700i	$0.418878\pi$
$312$	−2.59941	−0.147163
$313$	−27.4866	−1.55364	−0.776818	−	0.629725i	$-0.783167\pi$
$313$	−27.4866	−1.55364	−0.776818	+	0.629725i	$0.783167\pi$
$314$	−21.2364	−1.19844
$315$	0	0
$316$	−34.0883	−1.91762
$317$	−10.6883	−0.600318	−0.300159	−	0.953889i	$-0.597040\pi$
$317$	−10.6883	−0.600318	−0.300159	+	0.953889i	$0.597040\pi$
$318$	−1.78449	−0.100069
$319$	13.2394	0.741265
$320$	0	0
$321$	−9.23033	−0.515187
$322$	1.83709	0.102377
$323$	2.75176	0.153112
$324$	2.91466	0.161926
$325$	0	0
$326$	−50.8331	−2.81539
$327$	1.69379	0.0936669
$328$	−15.3387	−0.846940
$329$	−38.0512	−2.09783
$330$	0	0
$331$	32.7774	1.80161	0.900805	−	0.434224i	$-0.142977\pi$
$331$	32.7774	1.80161	0.900805	+	0.434224i	$0.142977\pi$
$332$	−19.9372	−1.09419
$333$	21.8715	1.19855
$334$	43.6876	2.39048
$335$	0	0
$336$	−7.13798	−0.389409
$337$	−18.1201	−0.987064	−0.493532	−	0.869728i	$-0.664294\pi$
$337$	−18.1201	−0.987064	−0.493532	+	0.869728i	$0.664294\pi$
$338$	22.3899	1.21785
$339$	−10.0658	−0.546697
$340$	0	0
$341$	0.120251	0.00651196
$342$	18.2083	0.984593
$343$	−4.36553	−0.235717
$344$	18.8932	1.01865
$345$	0	0
$346$	34.2713	1.84244
$347$	11.6120	0.623366	0.311683	−	0.950186i	$-0.399107\pi$
$347$	11.6120	0.623366	0.311683	+	0.950186i	$0.399107\pi$
$348$	−16.7871	−0.899882
$349$	−0.628561	−0.0336461	−0.0168230	−	0.999858i	$-0.505355\pi$
$349$	−0.628561	−0.0336461	−0.0168230	+	0.999858i	$0.505355\pi$
$350$	0	0
$351$	−8.19997	−0.437682
$352$	−16.1567	−0.861157
$353$	10.6295	0.565753	0.282876	−	0.959156i	$-0.408711\pi$
$353$	10.6295	0.565753	0.282876	+	0.959156i	$0.408711\pi$
$354$	−1.04229	−0.0553971
$355$	0	0
$356$	23.6371	1.25277
$357$	2.34985	0.124367
$358$	−41.5015	−2.19342
$359$	1.54110	0.0813361	0.0406680	−	0.999173i	$-0.487051\pi$
$359$	1.54110	0.0813361	0.0406680	+	0.999173i	$0.487051\pi$
$360$	0	0
$361$	−1.64495	−0.0865766
$362$	−41.3810	−2.17494
$363$	−6.37745	−0.334729
$364$	16.0526	0.841384
$365$	0	0
$366$	−32.4888	−1.69822
$367$	−33.3459	−1.74064	−0.870320	−	0.492487i	$-0.836088\pi$
$367$	−33.3459	−1.74064	−0.870320	+	0.492487i	$0.836088\pi$
$368$	0.474113	0.0247149
$369$	−19.4106	−1.01048
$370$	0	0
$371$	2.94730	0.153016
$372$	−0.152474	−0.00790541
$373$	−30.4228	−1.57523	−0.787617	−	0.616165i	$-0.788685\pi$
$373$	−30.4228	−1.57523	−0.787617	+	0.616165i	$0.788685\pi$
$374$	3.07835	0.159178
$375$	0	0
$376$	16.9041	0.871763
$377$	−10.1624	−0.523390
$378$	38.7603	1.99361
$379$	24.9206	1.28008	0.640042	−	0.768340i	$-0.278917\pi$
$379$	24.9206	1.28008	0.640042	+	0.768340i	$0.278917\pi$
$380$	0	0
$381$	−14.4382	−0.739689
$382$	35.9083	1.83723
$383$	−3.42197	−0.174854	−0.0874272	−	0.996171i	$-0.527865\pi$
$383$	−3.42197	−0.174854	−0.0874272	+	0.996171i	$0.527865\pi$
$384$	11.8005	0.602194
$385$	0	0
$386$	−36.7566	−1.87086
$387$	23.9087	1.21535
$388$	−7.01780	−0.356275
$389$	0.0531094	0.00269276	0.00134638	−	0.999999i	$-0.499571\pi$
$389$	0.0531094	0.00269276	0.00134638	+	0.999999i	$0.499571\pi$
$390$	0	0
$391$	−0.156080	−0.00789328
$392$	−9.17710	−0.463514
$393$	−10.7380	−0.541661
$394$	44.0734	2.22039
$395$	0	0
$396$	11.7568	0.590804
$397$	2.75259	0.138149	0.0690744	−	0.997612i	$-0.477995\pi$
$397$	2.75259	0.138149	0.0690744	+	0.997612i	$0.477995\pi$
$398$	−33.4003	−1.67421
$399$	14.8202	0.741938
$400$	0	0
$401$	15.3416	0.766123	0.383062	−	0.923723i	$-0.374870\pi$
$401$	15.3416	0.766123	0.383062	+	0.923723i	$0.374870\pi$
$402$	3.82364	0.190706
$403$	−0.0923032	−0.00459795
$404$	−42.0074	−2.08995
$405$	0	0
$406$	48.0365	2.38401
$407$	23.3207	1.15596
$408$	−1.04391	−0.0516813
$409$	−37.6394	−1.86115	−0.930573	−	0.366106i	$-0.880691\pi$
$409$	−37.6394	−1.86115	−0.930573	+	0.366106i	$0.880691\pi$
$410$	0	0
$411$	−2.12363	−0.104751
$412$	35.5814	1.75297
$413$	1.72147	0.0847078
$414$	−1.03277	−0.0507580
$415$	0	0
$416$	12.4017	0.608043
$417$	2.32695	0.113951
$418$	19.4148	0.949609
$419$	−27.4474	−1.34089	−0.670447	−	0.741958i	$-0.733898\pi$
$419$	−27.4474	−1.34089	−0.670447	+	0.741958i	$0.733898\pi$
$420$	0	0
$421$	18.9065	0.921448	0.460724	−	0.887543i	$-0.347590\pi$
$421$	18.9065	0.921448	0.460724	+	0.887543i	$0.347590\pi$
$422$	−8.62545	−0.419880
$423$	21.3915	1.04009
$424$	−1.30933	−0.0635865
$425$	0	0
$426$	25.1482	1.21843
$427$	53.6590	2.59674
$428$	−25.3228	−1.22402
$429$	−3.50741	−0.169339
$430$	0	0
$431$	35.3247	1.70153	0.850766	−	0.525545i	$-0.176139\pi$
$431$	35.3247	1.70153	0.850766	+	0.525545i	$0.176139\pi$
$432$	10.0032	0.481277
$433$	4.12878	0.198417	0.0992083	−	0.995067i	$-0.468369\pi$
$433$	4.12878	0.198417	0.0992083	+	0.995067i	$0.468369\pi$
$434$	0.436306	0.0209434
$435$	0	0
$436$	4.64681	0.222542
$437$	−0.984376	−0.0470891
$438$	−22.9264	−1.09547
$439$	0.720721	0.0343981	0.0171991	−	0.999852i	$-0.494525\pi$
$439$	0.720721	0.0343981	0.0171991	+	0.999852i	$0.494525\pi$
$440$	0	0
$441$	−11.6133	−0.553013
$442$	−2.36290	−0.112392
$443$	−5.08399	−0.241547	−0.120774	−	0.992680i	$-0.538538\pi$
$443$	−5.08399	−0.241547	−0.120774	+	0.992680i	$0.538538\pi$
$444$	−29.5698	−1.40332
$445$	0	0
$446$	−2.30571	−0.109178
$447$	−11.6188	−0.549552
$448$	−44.2761	−2.09185
$449$	11.4515	0.540427	0.270214	−	0.962800i	$-0.412906\pi$
$449$	11.4515	0.540427	0.270214	+	0.962800i	$0.412906\pi$
$450$	0	0
$451$	−20.6967	−0.974572
$452$	−27.6147	−1.29889
$453$	−12.1534	−0.571015
$454$	1.02683	0.0481913
$455$	0	0
$456$	−6.58383	−0.308316
$457$	28.6494	1.34016	0.670082	−	0.742287i	$-0.266259\pi$
$457$	28.6494	1.34016	0.670082	+	0.742287i	$0.266259\pi$
$458$	−43.2113	−2.01913
$459$	−3.29307	−0.153707
$460$	0	0
$461$	20.4489	0.952401	0.476201	−	0.879337i	$-0.342014\pi$
$461$	20.4489	0.952401	0.476201	+	0.879337i	$0.342014\pi$
$462$	16.5791	0.771331
$463$	22.5059	1.04594	0.522969	−	0.852352i	$-0.324824\pi$
$463$	22.5059	1.04594	0.522969	+	0.852352i	$0.324824\pi$
$464$	12.3971	0.575523
$465$	0	0
$466$	−62.7315	−2.90598
$467$	−29.8571	−1.38162	−0.690810	−	0.723036i	$-0.742746\pi$
$467$	−29.8571	−1.38162	−0.690810	+	0.723036i	$0.742746\pi$
$468$	−9.02440	−0.417153
$469$	−6.31519	−0.291609
$470$	0	0
$471$	9.71715	0.447743
$472$	−0.764755	−0.0352007
$473$	25.4928	1.17216
$474$	27.0240	1.24125
$475$	0	0
$476$	6.44665	0.295482
$477$	−1.65690	−0.0758644
$478$	−65.4302	−2.99271
$479$	−27.7402	−1.26748	−0.633742	−	0.773545i	$-0.718482\pi$
$479$	−27.7402	−1.26748	−0.633742	+	0.773545i	$0.718482\pi$
$480$	0	0
$481$	−17.9007	−0.816201
$482$	2.17490	0.0990639
$483$	−0.840600	−0.0382486
$484$	−17.4961	−0.795279
$485$	0	0
$486$	−34.8391	−1.58033
$487$	−26.9173	−1.21974	−0.609870	−	0.792502i	$-0.708778\pi$
$487$	−26.9173	−1.21974	−0.609870	+	0.792502i	$0.708778\pi$
$488$	−23.8378	−1.07909
$489$	23.2597	1.05184
$490$	0	0
$491$	37.3841	1.68712	0.843561	−	0.537033i	$-0.180455\pi$
$491$	37.3841	1.68712	0.843561	+	0.537033i	$0.180455\pi$
$492$	26.2427	1.18311
$493$	−4.08118	−0.183807
$494$	−14.9026	−0.670498
$495$	0	0
$496$	0.112601	0.00505593
$497$	−41.5352	−1.86311
$498$	15.8055	0.708261
$499$	−7.31755	−0.327578	−0.163789	−	0.986495i	$-0.552372\pi$
$499$	−7.31755	−0.327578	−0.163789	+	0.986495i	$0.552372\pi$
$500$	0	0
$501$	−19.9902	−0.893094
$502$	1.07362	0.0479181
$503$	−13.8428	−0.617220	−0.308610	−	0.951189i	$-0.599864\pi$
$503$	−13.8428	−0.617220	−0.308610	+	0.951189i	$0.599864\pi$
$504$	11.4086	0.508179
$505$	0	0
$506$	−1.10120	−0.0489545
$507$	−10.2449	−0.454994
$508$	−39.6102	−1.75742
$509$	16.3327	0.723935	0.361967	−	0.932191i	$-0.382105\pi$
$509$	16.3327	0.723935	0.361967	+	0.932191i	$0.382105\pi$
$510$	0	0
$511$	37.8656	1.67508
$512$	−21.5017	−0.950250
$513$	−20.7690	−0.916975
$514$	1.36967	0.0604134
$515$	0	0
$516$	−32.3240	−1.42298
$517$	22.8089	1.00314
$518$	84.6144	3.71774
$519$	−15.6815	−0.688343
$520$	0	0
$521$	−19.4267	−0.851097	−0.425549	−	0.904936i	$-0.639919\pi$
$521$	−19.4267	−0.851097	−0.425549	+	0.904936i	$0.639919\pi$
$522$	−27.0050	−1.18198
$523$	9.84831	0.430637	0.215318	−	0.976544i	$-0.430921\pi$
$523$	9.84831	0.430637	0.215318	+	0.976544i	$0.430921\pi$
$524$	−29.4591	−1.28692
$525$	0	0
$526$	44.0737	1.92171
$527$	−0.0370686	−0.00161473
$528$	4.27870	0.186207
$529$	−22.9442	−0.997572
$530$	0	0
$531$	−0.967769	−0.0419976
$532$	40.6583	1.76276
$533$	15.8866	0.688123
$534$	−18.7387	−0.810902
$535$	0	0
$536$	2.80550	0.121179
$537$	18.9899	0.819473
$538$	9.85813	0.425014
$539$	−12.3828	−0.533364
$540$	0	0
$541$	6.30937	0.271261	0.135631	−	0.990759i	$-0.456694\pi$
$541$	6.30937	0.271261	0.135631	+	0.990759i	$0.456694\pi$
$542$	42.7361	1.83567
$543$	18.9347	0.812566
$544$	4.98047	0.213536
$545$	0	0
$546$	−12.7259	−0.544619
$547$	−25.9302	−1.10870	−0.554348	−	0.832285i	$-0.687032\pi$
$547$	−25.9302	−1.10870	−0.554348	+	0.832285i	$0.687032\pi$
$548$	−5.82604	−0.248876
$549$	−30.1659	−1.28745
$550$	0	0
$551$	−25.7395	−1.09654
$552$	0.373434	0.0158944
$553$	−44.6333	−1.89800
$554$	44.8607	1.90595
$555$	0	0
$556$	6.38382	0.270734
$557$	16.0326	0.679325	0.339663	−	0.940547i	$-0.389687\pi$
$557$	16.0326	0.679325	0.339663	+	0.940547i	$0.389687\pi$
$558$	−0.245282	−0.0103836
$559$	−19.5680	−0.827637
$560$	0	0
$561$	−1.40856	−0.0594695
$562$	−16.9426	−0.714683
$563$	−39.7361	−1.67468	−0.837340	−	0.546683i	$-0.815890\pi$
$563$	−39.7361	−1.67468	−0.837340	+	0.546683i	$0.815890\pi$
$564$	−28.9209	−1.21779
$565$	0	0
$566$	−26.5421	−1.11565
$567$	3.81629	0.160269
$568$	18.4519	0.774223
$569$	8.62464	0.361564	0.180782	−	0.983523i	$-0.442137\pi$
$569$	8.62464	0.361564	0.180782	+	0.983523i	$0.442137\pi$
$570$	0	0
$571$	35.2994	1.47724	0.738618	−	0.674124i	$-0.235479\pi$
$571$	35.2994	1.47724	0.738618	+	0.674124i	$0.235479\pi$
$572$	−9.62236	−0.402331
$573$	−16.4306	−0.686396
$574$	−75.0939	−3.13436
$575$	0	0
$576$	24.8910	1.03713
$577$	20.8857	0.869481	0.434741	−	0.900556i	$-0.356840\pi$
$577$	20.8857	0.869481	0.434741	+	0.900556i	$0.356840\pi$
$578$	36.0243	1.49841
$579$	16.8187	0.698962
$580$	0	0
$581$	−26.1046	−1.08300
$582$	5.56346	0.230613
$583$	−1.76669	−0.0731688
$584$	−16.8217	−0.696086
$585$	0	0
$586$	−2.04864	−0.0846285
$587$	−20.0720	−0.828460	−0.414230	−	0.910172i	$-0.635949\pi$
$587$	−20.0720	−0.828460	−0.414230	+	0.910172i	$0.635949\pi$
$588$	15.7009	0.647494
$589$	−0.233787	−0.00963303
$590$	0	0
$591$	−20.1667	−0.829547
$592$	21.8371	0.897498
$593$	29.9449	1.22969	0.614845	−	0.788648i	$-0.289219\pi$
$593$	29.9449	1.22969	0.614845	+	0.788648i	$0.289219\pi$
$594$	−23.2340	−0.953301
$595$	0	0
$596$	−31.8755	−1.30567
$597$	15.2830	0.625491
$598$	0.845271	0.0345657
$599$	−16.8384	−0.687998	−0.343999	−	0.938970i	$-0.611782\pi$
$599$	−16.8384	−0.687998	−0.343999	+	0.938970i	$0.611782\pi$
$600$	0	0
$601$	12.0027	0.489599	0.244799	−	0.969574i	$-0.421278\pi$
$601$	12.0027	0.489599	0.244799	+	0.969574i	$0.421278\pi$
$602$	92.4955	3.76983
$603$	3.55026	0.144578
$604$	−33.3420	−1.35667
$605$	0	0
$606$	33.3020	1.35280
$607$	−49.0077	−1.98916	−0.994580	−	0.103973i	$-0.966844\pi$
$607$	−49.0077	−1.98916	−0.994580	+	0.103973i	$0.966844\pi$
$608$	31.4112	1.27389
$609$	−21.9801	−0.890677
$610$	0	0
$611$	−17.5078	−0.708291
$612$	−3.62416	−0.146498
$613$	14.6513	0.591760	0.295880	−	0.955225i	$-0.404387\pi$
$613$	14.6513	0.591760	0.295880	+	0.955225i	$0.404387\pi$
$614$	−24.0577	−0.970888
$615$	0	0
$616$	12.1645	0.490123
$617$	−36.8232	−1.48245	−0.741224	−	0.671258i	$-0.765754\pi$
$617$	−36.8232	−1.48245	−0.741224	+	0.671258i	$0.765754\pi$
$618$	−28.2076	−1.13468
$619$	45.4722	1.82768	0.913841	−	0.406072i	$-0.133102\pi$
$619$	45.4722	1.82768	0.913841	+	0.406072i	$0.133102\pi$
$620$	0	0
$621$	1.17802	0.0472721
$622$	−19.3387	−0.775410
$623$	30.9491	1.23995
$624$	−3.28428	−0.131476
$625$	0	0
$626$	59.7806	2.38931
$627$	−8.88364	−0.354778
$628$	26.6584	1.06379
$629$	−7.18883	−0.286638
$630$	0	0
$631$	−20.2437	−0.805890	−0.402945	−	0.915224i	$-0.632013\pi$
$631$	−20.2437	−0.805890	−0.402945	+	0.915224i	$0.632013\pi$
$632$	19.8282	0.788723
$633$	3.94675	0.156869
$634$	23.2461	0.923219
$635$	0	0
$636$	2.24010	0.0888256
$637$	9.50485	0.376596
$638$	−28.7944	−1.13998
$639$	23.3502	0.923718
$640$	0	0
$641$	−41.7882	−1.65054	−0.825268	−	0.564741i	$-0.808976\pi$
$641$	−41.7882	−1.65054	−0.825268	+	0.564741i	$0.808976\pi$
$642$	20.0750	0.792298
$643$	−40.3083	−1.58961	−0.794803	−	0.606868i	$-0.792426\pi$
$643$	−40.3083	−1.58961	−0.794803	+	0.606868i	$0.792426\pi$
$644$	−2.30613	−0.0908743
$645$	0	0
$646$	−5.98480	−0.235469
$647$	−44.8702	−1.76403	−0.882014	−	0.471223i	$-0.843813\pi$
$647$	−44.8702	−1.76403	−0.882014	+	0.471223i	$0.843813\pi$
$648$	−1.69538	−0.0666006
$649$	−1.03189	−0.0405053
$650$	0	0
$651$	−0.199641	−0.00782454
$652$	63.8115	2.49905
$653$	2.92608	0.114507	0.0572533	−	0.998360i	$-0.481766\pi$
$653$	2.92608	0.114507	0.0572533	+	0.998360i	$0.481766\pi$
$654$	−3.68382	−0.144049
$655$	0	0
$656$	−19.3800	−0.756664
$657$	−21.2872	−0.830492
$658$	82.7574	3.22622
$659$	−21.9078	−0.853406	−0.426703	−	0.904392i	$-0.640325\pi$
$659$	−21.9078	−0.853406	−0.426703	+	0.904392i	$0.640325\pi$
$660$	0	0
$661$	25.9734	1.01025	0.505125	−	0.863046i	$-0.331446\pi$
$661$	25.9734	1.01025	0.505125	+	0.863046i	$0.331446\pi$
$662$	−71.2875	−2.77067
$663$	1.08119	0.0419901
$664$	11.5969	0.450046
$665$	0	0
$666$	−47.5683	−1.84323
$667$	1.45994	0.0565291
$668$	−54.8417	−2.12189
$669$	1.05502	0.0407896
$670$	0	0
$671$	−32.1647	−1.24170
$672$	26.8234	1.03473
$673$	−19.5900	−0.755138	−0.377569	−	0.925981i	$-0.623240\pi$
$673$	−19.5900	−0.755138	−0.377569	+	0.925981i	$0.623240\pi$
$674$	39.4094	1.51799
$675$	0	0
$676$	−28.1063	−1.08101
$677$	21.7156	0.834596	0.417298	−	0.908770i	$-0.362977\pi$
$677$	21.7156	0.834596	0.417298	+	0.908770i	$0.362977\pi$
$678$	21.8920	0.840756
$679$	−9.18871	−0.352630
$680$	0	0
$681$	−0.469845	−0.0180045
$682$	−0.261534	−0.0100147
$683$	−9.02292	−0.345252	−0.172626	−	0.984987i	$-0.555225\pi$
$683$	−9.02292	−0.345252	−0.172626	+	0.984987i	$0.555225\pi$
$684$	−22.8572	−0.873966
$685$	0	0
$686$	9.49459	0.362505
$687$	19.7722	0.754356
$688$	23.8710	0.910074
$689$	1.35609	0.0516628
$690$	0	0
$691$	−25.0698	−0.953700	−0.476850	−	0.878985i	$-0.658221\pi$
$691$	−25.0698	−0.953700	−0.476850	+	0.878985i	$0.658221\pi$
$692$	−43.0213	−1.63542
$693$	15.3937	0.584760
$694$	−25.2550	−0.958666
$695$	0	0
$696$	9.76457	0.370125
$697$	6.37997	0.241659
$698$	1.36706	0.0517438
$699$	28.7041	1.08569
$700$	0	0
$701$	−18.1409	−0.685172	−0.342586	−	0.939486i	$-0.611303\pi$
$701$	−18.1409	−0.685172	−0.342586	+	0.939486i	$0.611303\pi$
$702$	17.8341	0.673104
$703$	−45.3391	−1.71000
$704$	26.5403	1.00027
$705$	0	0
$706$	−23.1181	−0.870062
$707$	−55.0021	−2.06857
$708$	1.30840	0.0491728
$709$	−20.2193	−0.759352	−0.379676	−	0.925120i	$-0.623965\pi$
$709$	−20.2193	−0.759352	−0.379676	+	0.925120i	$0.623965\pi$
$710$	0	0
$711$	25.0918	0.941017
$712$	−13.7490	−0.515267
$713$	0.0132604	0.000496605 0
$714$	−5.11067	−0.191262
$715$	0	0
$716$	52.0974	1.94697
$717$	29.9389	1.11809
$718$	−3.35173	−0.125086
$719$	1.41119	0.0526286	0.0263143	−	0.999654i	$-0.491623\pi$
$719$	1.41119	0.0526286	0.0263143	+	0.999654i	$0.491623\pi$
$720$	0	0
$721$	46.5882	1.73504
$722$	3.57761	0.133145
$723$	−0.995168	−0.0370107
$724$	51.9461	1.93056
$725$	0	0
$726$	13.8703	0.514775
$727$	16.0736	0.596135	0.298068	−	0.954545i	$-0.403658\pi$
$727$	16.0736	0.596135	0.298068	+	0.954545i	$0.403658\pi$
$728$	−9.33733	−0.346065
$729$	12.7386	0.471800
$730$	0	0
$731$	−7.85841	−0.290654
$732$	40.7836	1.50741
$733$	−21.5338	−0.795369	−0.397684	−	0.917522i	$-0.630186\pi$
$733$	−21.5338	−0.795369	−0.397684	+	0.917522i	$0.630186\pi$
$734$	72.5238	2.67690
$735$	0	0
$736$	−1.78164	−0.0656722
$737$	3.78550	0.139441
$738$	42.2161	1.55400
$739$	−19.5469	−0.719043	−0.359522	−	0.933137i	$-0.617060\pi$
$739$	−19.5469	−0.719043	−0.359522	+	0.933137i	$0.617060\pi$
$740$	0	0
$741$	6.81897	0.250501
$742$	−6.41007	−0.235321
$743$	−17.2158	−0.631588	−0.315794	−	0.948828i	$-0.602271\pi$
$743$	−17.2158	−0.631588	−0.315794	+	0.948828i	$0.602271\pi$
$744$	0.0886898	0.00325152
$745$	0	0
$746$	66.1665	2.42253
$747$	14.6754	0.536946
$748$	−3.86430	−0.141293
$749$	−33.1562	−1.21150
$750$	0	0
$751$	0.294980	0.0107640	0.00538199	−	0.999986i	$-0.498287\pi$
$751$	0.294980	0.0107640	0.00538199	+	0.999986i	$0.498287\pi$
$752$	21.3578	0.778840
$753$	−0.491258	−0.0179024
$754$	22.1022	0.804914
$755$	0	0
$756$	−48.6563	−1.76961
$757$	−5.06019	−0.183916	−0.0919579	−	0.995763i	$-0.529313\pi$
$757$	−5.06019	−0.183916	−0.0919579	+	0.995763i	$0.529313\pi$
$758$	−54.1997	−1.96862
$759$	0.503878	0.0182896
$760$	0	0
$761$	−22.1767	−0.803903	−0.401952	−	0.915661i	$-0.631668\pi$
$761$	−22.1767	−0.803903	−0.401952	+	0.915661i	$0.631668\pi$
$762$	31.4015	1.13756
$763$	6.08426	0.220265
$764$	−45.0762	−1.63080
$765$	0	0
$766$	7.44243	0.268906
$767$	0.792068	0.0285999
$768$	−1.01305	−0.0365554
$769$	24.1094	0.869409	0.434704	−	0.900573i	$-0.356853\pi$
$769$	24.1094	0.869409	0.434704	+	0.900573i	$0.356853\pi$
$770$	0	0
$771$	−0.626719	−0.0225707
$772$	46.1411	1.66065
$773$	1.32362	0.0476074	0.0238037	−	0.999717i	$-0.492422\pi$
$773$	1.32362	0.0476074	0.0238037	+	0.999717i	$0.492422\pi$
$774$	−51.9989	−1.86906
$775$	0	0
$776$	4.08205	0.146537
$777$	−38.7170	−1.38897
$778$	−0.115508	−0.00414115
$779$	40.2378	1.44167
$780$	0	0
$781$	24.8973	0.890897
$782$	0.339457	0.0121390
$783$	30.8028	1.10080
$784$	−11.5950	−0.414107
$785$	0	0
$786$	23.3541	0.833013
$787$	−21.2362	−0.756988	−0.378494	−	0.925604i	$-0.623558\pi$
$787$	−21.2362	−0.756988	−0.378494	+	0.925604i	$0.623558\pi$
$788$	−55.3260	−1.97091
$789$	−20.1668	−0.717958
$790$	0	0
$791$	−36.1572	−1.28560
$792$	−6.83862	−0.243000
$793$	24.6892	0.876739
$794$	−5.98661	−0.212457
$795$	0	0
$796$	41.9279	1.48610
$797$	−20.0623	−0.710644	−0.355322	−	0.934744i	$-0.615629\pi$
$797$	−20.0623	−0.710644	−0.355322	+	0.934744i	$0.615629\pi$
$798$	−32.2324	−1.14102
$799$	−7.03107	−0.248741
$800$	0	0
$801$	−17.3989	−0.614760
$802$	−33.3664	−1.17821
$803$	−22.6977	−0.800984
$804$	−4.79987	−0.169279
$805$	0	0
$806$	0.200750	0.00707112
$807$	−4.51079	−0.158787
$808$	24.4345	0.859603
$809$	−16.7286	−0.588145	−0.294072	−	0.955783i	$-0.595011\pi$
$809$	−16.7286	−0.588145	−0.294072	+	0.955783i	$0.595011\pi$
$810$	0	0
$811$	8.27147	0.290451	0.145225	−	0.989399i	$-0.453609\pi$
$811$	8.27147	0.290451	0.145225	+	0.989399i	$0.453609\pi$
$812$	−60.3009	−2.11615
$813$	−19.5548	−0.685816
$814$	−50.7202	−1.77774
$815$	0	0
$816$	−1.31895	−0.0461725
$817$	−49.5621	−1.73396
$818$	81.8618	2.86223
$819$	−11.8160	−0.412886
$820$	0	0
$821$	44.3275	1.54704	0.773521	−	0.633771i	$-0.218494\pi$
$821$	44.3275	1.54704	0.773521	+	0.633771i	$0.218494\pi$
$822$	4.61868	0.161095
$823$	−44.8565	−1.56360	−0.781800	−	0.623529i	$-0.785698\pi$
$823$	−44.8565	−1.56360	−0.781800	+	0.623529i	$0.785698\pi$
$824$	−20.6967	−0.721002
$825$	0	0
$826$	−3.74401	−0.130271
$827$	48.8334	1.69810	0.849052	−	0.528309i	$-0.177174\pi$
$827$	48.8334	1.69810	0.849052	+	0.528309i	$0.177174\pi$
$828$	1.29646	0.0450549
$829$	−37.5847	−1.30537	−0.652685	−	0.757630i	$-0.726357\pi$
$829$	−37.5847	−1.30537	−0.652685	+	0.757630i	$0.726357\pi$
$830$	0	0
$831$	−20.5269	−0.712070
$832$	−20.3720	−0.706272
$833$	3.81711	0.132255
$834$	−5.06087	−0.175244
$835$	0	0
$836$	−24.3717	−0.842912
$837$	0.279776	0.00967048
$838$	59.6953	2.06214
$839$	12.6371	0.436283	0.218141	−	0.975917i	$-0.430001\pi$
$839$	12.6371	0.436283	0.218141	+	0.975917i	$0.430001\pi$
$840$	0	0
$841$	9.17463	0.316367
$842$	−41.1198	−1.41708
$843$	7.75245	0.267009
$844$	10.8277	0.372703
$845$	0	0
$846$	−46.5244	−1.59954
$847$	−22.9084	−0.787143
$848$	−1.65429	−0.0568087
$849$	12.1449	0.416811
$850$	0	0
$851$	2.57163	0.0881543
$852$	−31.5689	−1.08153
$853$	−6.32445	−0.216545	−0.108273	−	0.994121i	$-0.534532\pi$
$853$	−6.32445	−0.216545	−0.108273	+	0.994121i	$0.534532\pi$
$854$	−116.703	−3.99349
$855$	0	0
$856$	14.7296	0.503446
$857$	20.0524	0.684978	0.342489	−	0.939522i	$-0.388730\pi$
$857$	20.0524	0.684978	0.342489	+	0.939522i	$0.388730\pi$
$858$	7.62826	0.260425
$859$	−20.6809	−0.705623	−0.352812	−	0.935694i	$-0.614774\pi$
$859$	−20.6809	−0.705623	−0.352812	+	0.935694i	$0.614774\pi$
$860$	0	0
$861$	34.3607	1.17101
$862$	−76.8276	−2.61676
$863$	−9.35107	−0.318314	−0.159157	−	0.987253i	$-0.550878\pi$
$863$	−9.35107	−0.318314	−0.159157	+	0.987253i	$0.550878\pi$
$864$	−37.5903	−1.27885
$865$	0	0
$866$	−8.97968	−0.305142
$867$	−16.4837	−0.559814
$868$	−0.547702	−0.0185902
$869$	26.7544	0.907582
$870$	0	0
$871$	−2.90570	−0.0984559
$872$	−2.70291	−0.0915322
$873$	5.16568	0.174832
$874$	2.14092	0.0724176
$875$	0	0
$876$	28.7798	0.972380
$877$	34.8026	1.17520	0.587600	−	0.809151i	$-0.300073\pi$
$877$	34.8026	1.17520	0.587600	+	0.809151i	$0.300073\pi$
$878$	−1.56749	−0.0529003
$879$	0.937397	0.0316176
$880$	0	0
$881$	−52.5693	−1.77110	−0.885552	−	0.464541i	$-0.846220\pi$
$881$	−52.5693	−1.77110	−0.885552	+	0.464541i	$0.846220\pi$
$882$	25.2577	0.850470
$883$	−5.46583	−0.183940	−0.0919700	−	0.995762i	$-0.529316\pi$
$883$	−5.46583	−0.183940	−0.0919700	+	0.995762i	$0.529316\pi$
$884$	2.96619	0.0997636
$885$	0	0
$886$	11.0572	0.371472
$887$	4.29456	0.144197	0.0720986	−	0.997398i	$-0.477030\pi$
$887$	4.29456	0.144197	0.0720986	+	0.997398i	$0.477030\pi$
$888$	17.1999	0.577191
$889$	−51.8633	−1.73944
$890$	0	0
$891$	−2.28759	−0.0766371
$892$	2.89439	0.0969113
$893$	−44.3441	−1.48392
$894$	25.2698	0.845148
$895$	0	0
$896$	42.3887	1.41611
$897$	−0.386771	−0.0129139
$898$	−24.9057	−0.831115
$899$	0.346733	0.0115642
$900$	0	0
$901$	0.544599	0.0181432
$902$	45.0133	1.49878
$903$	−42.3232	−1.40843
$904$	16.0627	0.534237
$905$	0	0
$906$	26.4323	0.878155
$907$	−15.4572	−0.513249	−0.256625	−	0.966511i	$-0.582610\pi$
$907$	−15.4572	−0.513249	−0.256625	+	0.966511i	$0.582610\pi$
$908$	−1.28899	−0.0427766
$909$	30.9209	1.02558
$910$	0	0
$911$	53.1696	1.76159	0.880793	−	0.473502i	$-0.157010\pi$
$911$	53.1696	1.76159	0.880793	+	0.473502i	$0.157010\pi$
$912$	−8.31847	−0.275452
$913$	15.6478	0.517867
$914$	−62.3096	−2.06102
$915$	0	0
$916$	54.2437	1.79226
$917$	−38.5720	−1.27376
$918$	7.16209	0.236384
$919$	−23.4129	−0.772321	−0.386160	−	0.922432i	$-0.626199\pi$
$919$	−23.4129	−0.772321	−0.386160	+	0.922432i	$0.626199\pi$
$920$	0	0
$921$	11.0081	0.362728
$922$	−44.4743	−1.46468
$923$	−19.1109	−0.629042
$924$	−20.8120	−0.684665
$925$	0	0
$926$	−48.9480	−1.60853
$927$	−26.1908	−0.860220
$928$	−46.5865	−1.52928
$929$	−54.3893	−1.78445	−0.892227	−	0.451587i	$-0.850858\pi$
$929$	−54.3893	−1.78445	−0.892227	+	0.451587i	$0.850858\pi$
$930$	0	0
$931$	24.0741	0.788995
$932$	78.7477	2.57947
$933$	8.84880	0.289697
$934$	64.9361	2.12477
$935$	0	0
$936$	5.24924	0.171577
$937$	37.2899	1.21821	0.609105	−	0.793090i	$-0.291529\pi$
$937$	37.2899	1.21821	0.609105	+	0.793090i	$0.291529\pi$
$938$	13.7349	0.448460
$939$	−27.3538	−0.892658
$940$	0	0
$941$	−20.4028	−0.665112	−0.332556	−	0.943083i	$-0.607911\pi$
$941$	−20.4028	−0.665112	−0.332556	+	0.943083i	$0.607911\pi$
$942$	−21.1338	−0.688577
$943$	−2.28228	−0.0743212
$944$	−0.966245	−0.0314486
$945$	0	0
$946$	−55.4443	−1.80265
$947$	40.1120	1.30347	0.651733	−	0.758449i	$-0.274042\pi$
$947$	40.1120	1.30347	0.651733	+	0.758449i	$0.274042\pi$
$948$	−33.9236	−1.10179
$949$	17.4224	0.565557
$950$	0	0
$951$	−10.6367	−0.344919
$952$	−3.74983	−0.121533
$953$	−21.9176	−0.709982	−0.354991	−	0.934870i	$-0.615516\pi$
$953$	−21.9176	−0.709982	−0.354991	+	0.934870i	$0.615516\pi$
$954$	3.60359	0.116671
$955$	0	0
$956$	82.1355	2.65645
$957$	13.1754	0.425902
$958$	60.3321	1.94924
$959$	−7.62829	−0.246330
$960$	0	0
$961$	−30.9969	−0.999898
$962$	38.9321	1.25522
$963$	18.6397	0.600656
$964$	−2.73018	−0.0879332
$965$	0	0
$966$	1.82822	0.0588220
$967$	−31.4765	−1.01222	−0.506109	−	0.862470i	$-0.668917\pi$
$967$	−31.4765	−1.01222	−0.506109	+	0.862470i	$0.668917\pi$
$968$	10.1770	0.327101
$969$	2.73847	0.0879722
$970$	0	0
$971$	−15.0675	−0.483539	−0.241769	−	0.970334i	$-0.577728\pi$
$971$	−15.0675	−0.483539	−0.241769	+	0.970334i	$0.577728\pi$
$972$	43.7340	1.40277
$973$	8.35862	0.267965
$974$	58.5424	1.87582
$975$	0	0
$976$	−30.1184	−0.964067
$977$	−29.5053	−0.943959	−0.471979	−	0.881610i	$-0.656460\pi$
$977$	−29.5053	−0.943959	−0.471979	+	0.881610i	$0.656460\pi$
$978$	−50.5875	−1.61761
$979$	−18.5518	−0.592917
$980$	0	0
$981$	−3.42044	−0.109206
$982$	−81.3067	−2.59460
$983$	54.1116	1.72589	0.862946	−	0.505295i	$-0.168616\pi$
$983$	54.1116	1.72589	0.862946	+	0.505295i	$0.168616\pi$
$984$	−15.2646	−0.486619
$985$	0	0
$986$	8.87614	0.282674
$987$	−37.8673	−1.20533
$988$	18.7074	0.595161
$989$	2.81116	0.0893895
$990$	0	0
$991$	−37.3910	−1.18777	−0.593883	−	0.804552i	$-0.702406\pi$
$991$	−37.3910	−1.18777	−0.593883	+	0.804552i	$0.702406\pi$
$992$	−0.423136	−0.0134346
$993$	32.6191	1.03513
$994$	90.3348	2.86525
$995$	0	0
$996$	−19.8408	−0.628681
$997$	44.7165	1.41618	0.708092	−	0.706120i	$-0.249556\pi$
$997$	44.7165	1.41618	0.708092	+	0.706120i	$0.249556\pi$
$998$	15.9149	0.503778
$999$	54.2580	1.71665

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.l.1.8	✓	40
5.4	even	2		6025.2.a.o.1.33	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6025.2.a.l.1.8	✓	40	1.1	even	1	trivial
6025.2.a.o.1.33	yes	40	5.4	even	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:	\( N \)	\(=\)	\( 6025 = 5^{2} \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6025.a (trivial)

\(f(q)\)	\(=\)	\(q-2.17490 q^{2} +0.995168 q^{3} +2.73018 q^{4} -2.16439 q^{6} +3.57474 q^{7} -1.58807 q^{8} -2.00964 q^{9} +O(q^{10})\)	\(q-2.17490 q^{2} +0.995168 q^{3} +2.73018 q^{4} -2.16439 q^{6} +3.57474 q^{7} -1.58807 q^{8} -2.00964 q^{9} -2.14280 q^{11} +2.71699 q^{12} +1.64478 q^{13} -7.77470 q^{14} -2.00648 q^{16} +0.660538 q^{17} +4.37076 q^{18} +4.16594 q^{19} +3.55747 q^{21} +4.66037 q^{22} -0.236291 q^{23} -1.58039 q^{24} -3.57724 q^{26} -4.98544 q^{27} +9.75969 q^{28} -6.17856 q^{29} -0.0561187 q^{31} +7.54002 q^{32} -2.13245 q^{33} -1.43660 q^{34} -5.48668 q^{36} -10.8833 q^{37} -9.06049 q^{38} +1.63684 q^{39} +9.65875 q^{41} -7.73714 q^{42} -11.8970 q^{43} -5.85023 q^{44} +0.513910 q^{46} -10.6445 q^{47} -1.99678 q^{48} +5.77878 q^{49} +0.657347 q^{51} +4.49056 q^{52} +0.824478 q^{53} +10.8428 q^{54} -5.67693 q^{56} +4.14581 q^{57} +13.4377 q^{58} +0.481563 q^{59} +15.0106 q^{61} +0.122053 q^{62} -7.18394 q^{63} -12.3858 q^{64} +4.63785 q^{66} -1.76662 q^{67} +1.80339 q^{68} -0.235150 q^{69} -11.6191 q^{71} +3.19144 q^{72} +10.5925 q^{73} +23.6701 q^{74} +11.3738 q^{76} -7.65995 q^{77} -3.55995 q^{78} -12.4857 q^{79} +1.06757 q^{81} -21.0068 q^{82} -7.30251 q^{83} +9.71254 q^{84} +25.8747 q^{86} -6.14871 q^{87} +3.40291 q^{88} +8.65772 q^{89} +5.87968 q^{91} -0.645118 q^{92} -0.0558476 q^{93} +23.1506 q^{94} +7.50359 q^{96} -2.57045 q^{97} -12.5683 q^{98} +4.30625 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 11 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 16 q^{7} - 33 q^{8} + 38 q^{9}+O(q^{10}) \) 40 * q - 11 * q^2 - 8 * q^3 + 41 * q^4 + 3 * q^6 - 16 * q^7 - 33 * q^8 + 38 * q^9	\( 40 q - 11 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 16 q^{7} - 33 q^{8} + 38 q^{9} + q^{11} - 14 q^{12} - 9 q^{13} - q^{14} + 43 q^{16} - 12 q^{17} - 42 q^{18} + 2 q^{21} - 5 q^{22} - 77 q^{23} - 2 q^{24} + 2 q^{26} - 38 q^{27} - 42 q^{28} + 2 q^{29} + q^{31} - 72 q^{32} - 20 q^{33} + 5 q^{34} + 32 q^{36} - 28 q^{37} - 23 q^{38} - 2 q^{39} - 2 q^{41} - 37 q^{42} - 31 q^{43} + 3 q^{44} + 14 q^{46} - 96 q^{47} - 13 q^{48} + 40 q^{49} - 10 q^{51} - 42 q^{52} - 54 q^{53} + 4 q^{54} - 15 q^{56} - 37 q^{57} - 27 q^{58} + q^{59} + 5 q^{61} - 39 q^{62} - 70 q^{63} + 65 q^{64} - 52 q^{66} - 34 q^{67} - 52 q^{68} + 21 q^{69} - 9 q^{71} - 70 q^{72} - 25 q^{73} + 22 q^{74} - 47 q^{76} - 54 q^{77} - 58 q^{78} + 13 q^{79} + 12 q^{81} + 5 q^{82} - 63 q^{83} + 95 q^{84} - 18 q^{86} - 47 q^{87} - 13 q^{88} + 19 q^{89} - 31 q^{91} - 137 q^{92} - 52 q^{93} + 120 q^{94} - 49 q^{96} - 36 q^{97} - 64 q^{98} + 16 q^{99}+O(q^{100}) \) 40 * q - 11 * q^2 - 8 * q^3 + 41 * q^4 + 3 * q^6 - 16 * q^7 - 33 * q^8 + 38 * q^9 + q^11 - 14 * q^12 - 9 * q^13 - q^14 + 43 * q^16 - 12 * q^17 - 42 * q^18 + 2 * q^21 - 5 * q^22 - 77 * q^23 - 2 * q^24 + 2 * q^26 - 38 * q^27 - 42 * q^28 + 2 * q^29 + q^31 - 72 * q^32 - 20 * q^33 + 5 * q^34 + 32 * q^36 - 28 * q^37 - 23 * q^38 - 2 * q^39 - 2 * q^41 - 37 * q^42 - 31 * q^43 + 3 * q^44 + 14 * q^46 - 96 * q^47 - 13 * q^48 + 40 * q^49 - 10 * q^51 - 42 * q^52 - 54 * q^53 + 4 * q^54 - 15 * q^56 - 37 * q^57 - 27 * q^58 + q^59 + 5 * q^61 - 39 * q^62 - 70 * q^63 + 65 * q^64 - 52 * q^66 - 34 * q^67 - 52 * q^68 + 21 * q^69 - 9 * q^71 - 70 * q^72 - 25 * q^73 + 22 * q^74 - 47 * q^76 - 54 * q^77 - 58 * q^78 + 13 * q^79 + 12 * q^81 + 5 * q^82 - 63 * q^83 + 95 * q^84 - 18 * q^86 - 47 * q^87 - 13 * q^88 + 19 * q^89 - 31 * q^91 - 137 * q^92 - 52 * q^93 + 120 * q^94 - 49 * q^96 - 36 * q^97 - 64 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

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Database

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