LMFDB - Embedded newform 5225.2.a.u.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5225,2,Mod(1,5225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5225, 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("5225.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5225 = 5^{2} \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5225.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:	$41.7218350561$
Analytic rank:	$0$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - x^{14} - 21 x^{13} + 21 x^{12} + 168 x^{11} - 165 x^{10} - 645 x^{9} + 606 x^{8} + 1239 x^{7} + \cdots - 5 $ x^15 - x^14 - 21x^13 + 21x^12 + 168x^11 - 165x^10 - 645x^9 + 606x^8 + 1239x^7 - 1055x^6 - 1160x^5 + 793x^4 + 485x^3 - 171x^2 - 93*x - 5
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			1.7
Root			$0.814490$ of defining polynomial
Character	$\chi$	$=$	5225.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.814490 q^{2} +2.50015 q^{3} -1.33661 q^{4} -2.03634 q^{6} +4.83914 q^{7} +2.71763 q^{8} +3.25073 q^{9} +O(q^{10})$	\(q-0.814490 q^{2} +2.50015 q^{3} -1.33661 q^{4} -2.03634 q^{6} +4.83914 q^{7} +2.71763 q^{8} +3.25073 q^{9} -1.00000 q^{11} -3.34171 q^{12} +4.12188 q^{13} -3.94143 q^{14} +0.459728 q^{16} -2.02683 q^{17} -2.64769 q^{18} +1.00000 q^{19} +12.0985 q^{21} +0.814490 q^{22} -6.38724 q^{23} +6.79448 q^{24} -3.35723 q^{26} +0.626858 q^{27} -6.46802 q^{28} +7.42993 q^{29} -4.40903 q^{31} -5.80971 q^{32} -2.50015 q^{33} +1.65083 q^{34} -4.34494 q^{36} -1.77785 q^{37} -0.814490 q^{38} +10.3053 q^{39} +9.92201 q^{41} -9.85414 q^{42} +9.89030 q^{43} +1.33661 q^{44} +5.20234 q^{46} -0.145235 q^{47} +1.14939 q^{48} +16.4172 q^{49} -5.06736 q^{51} -5.50933 q^{52} +12.9926 q^{53} -0.510570 q^{54} +13.1510 q^{56} +2.50015 q^{57} -6.05160 q^{58} +1.17115 q^{59} +2.03091 q^{61} +3.59111 q^{62} +15.7307 q^{63} +3.81249 q^{64} +2.03634 q^{66} -7.84101 q^{67} +2.70907 q^{68} -15.9690 q^{69} -11.1719 q^{71} +8.83428 q^{72} +3.27201 q^{73} +1.44804 q^{74} -1.33661 q^{76} -4.83914 q^{77} -8.39357 q^{78} +11.3472 q^{79} -8.18495 q^{81} -8.08137 q^{82} -2.37099 q^{83} -16.1710 q^{84} -8.05555 q^{86} +18.5759 q^{87} -2.71763 q^{88} -9.26921 q^{89} +19.9463 q^{91} +8.53722 q^{92} -11.0232 q^{93} +0.118292 q^{94} -14.5251 q^{96} -8.29514 q^{97} -13.3717 q^{98} -3.25073 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - q^{2} + 4 q^{3} + 13 q^{4} - q^{6} + 17 q^{7} + 3 q^{8} + 15 q^{9}+O(q^{10}) $ 15 * q - q^2 + 4 * q^3 + 13 * q^4 - q^6 + 17 * q^7 + 3 * q^8 + 15 * q^9	$ 15 q - q^{2} + 4 q^{3} + 13 q^{4} - q^{6} + 17 q^{7} + 3 q^{8} + 15 q^{9} - 15 q^{11} + 9 q^{12} + 3 q^{13} - 11 q^{14} + 13 q^{16} + q^{17} - 10 q^{18} + 15 q^{19} + 16 q^{21} + q^{22} + 18 q^{23} - 27 q^{24} + 15 q^{26} + 31 q^{27} + 34 q^{28} + 11 q^{29} - 2 q^{31} + 10 q^{32} - 4 q^{33} - 13 q^{34} + 8 q^{36} + 27 q^{37} - q^{38} + 4 q^{39} + 6 q^{41} + 2 q^{42} + 38 q^{43} - 13 q^{44} - 9 q^{46} + 14 q^{47} + 32 q^{48} + 28 q^{49} - 32 q^{51} + 16 q^{52} + 11 q^{53} - 11 q^{54} + 2 q^{56} + 4 q^{57} - 6 q^{58} + 13 q^{59} + 8 q^{61} + 7 q^{62} + 49 q^{63} + 9 q^{64} + q^{66} + 31 q^{67} - 26 q^{68} + 39 q^{69} - 3 q^{71} - 18 q^{72} + 18 q^{73} + 7 q^{74} + 13 q^{76} - 17 q^{77} + 18 q^{78} + 10 q^{79} + 31 q^{81} + 58 q^{82} + 16 q^{83} + 112 q^{84} - 63 q^{86} + 67 q^{87} - 3 q^{88} - 7 q^{89} - 50 q^{91} + 98 q^{92} + 26 q^{93} + 22 q^{94} - 37 q^{96} + 24 q^{97} - 46 q^{98} - 15 q^{99}+O(q^{100}) $ 15 * q - q^2 + 4 * q^3 + 13 * q^4 - q^6 + 17 * q^7 + 3 * q^8 + 15 * q^9 - 15 * q^11 + 9 * q^12 + 3 * q^13 - 11 * q^14 + 13 * q^16 + q^17 - 10 * q^18 + 15 * q^19 + 16 * q^21 + q^22 + 18 * q^23 - 27 * q^24 + 15 * q^26 + 31 * q^27 + 34 * q^28 + 11 * q^29 - 2 * q^31 + 10 * q^32 - 4 * q^33 - 13 * q^34 + 8 * q^36 + 27 * q^37 - q^38 + 4 * q^39 + 6 * q^41 + 2 * q^42 + 38 * q^43 - 13 * q^44 - 9 * q^46 + 14 * q^47 + 32 * q^48 + 28 * q^49 - 32 * q^51 + 16 * q^52 + 11 * q^53 - 11 * q^54 + 2 * q^56 + 4 * q^57 - 6 * q^58 + 13 * q^59 + 8 * q^61 + 7 * q^62 + 49 * q^63 + 9 * q^64 + q^66 + 31 * q^67 - 26 * q^68 + 39 * q^69 - 3 * q^71 - 18 * q^72 + 18 * q^73 + 7 * q^74 + 13 * q^76 - 17 * q^77 + 18 * q^78 + 10 * q^79 + 31 * q^81 + 58 * q^82 + 16 * q^83 + 112 * q^84 - 63 * q^86 + 67 * q^87 - 3 * q^88 - 7 * q^89 - 50 * q^91 + 98 * q^92 + 26 * q^93 + 22 * q^94 - 37 * q^96 + 24 * q^97 - 46 * q^98 - 15 * 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 $

$2$	−0.814490	−0.575931	−0.287966	−	0.957641i	$-0.592979\pi$
$2$	−0.814490	−0.575931	−0.287966	+	0.957641i	$0.592979\pi$
$3$	2.50015	1.44346	0.721730	−	0.692175i	$-0.243347\pi$
$3$	2.50015	1.44346	0.721730	+	0.692175i	$0.243347\pi$
$4$	−1.33661	−0.668303
$5$	0	0
$5$	0	0
$6$	−2.03634	−0.831334
$7$	4.83914	1.82902	0.914511	−	0.404562i	$-0.132576\pi$
$7$	4.83914	1.82902	0.914511	+	0.404562i	$0.132576\pi$
$8$	2.71763	0.960828
$9$	3.25073	1.08358
$10$	0	0
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−3.34171	−0.964669
$13$	4.12188	1.14320	0.571602	−	0.820531i	$-0.306322\pi$
$13$	4.12188	1.14320	0.571602	+	0.820531i	$0.306322\pi$
$14$	−3.94143	−1.05339
$15$	0	0
$16$	0.459728	0.114932
$17$	−2.02683	−0.491578	−0.245789	−	0.969323i	$-0.579047\pi$
$17$	−2.02683	−0.491578	−0.245789	+	0.969323i	$0.579047\pi$
$18$	−2.64769	−0.624065
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0	0
$21$	12.0985	2.64012
$22$	0.814490	0.173650
$23$	−6.38724	−1.33183	−0.665915	−	0.746027i	$-0.731959\pi$
$23$	−6.38724	−1.33183	−0.665915	+	0.746027i	$0.731959\pi$
$24$	6.79448	1.38692
$25$	0	0
$26$	−3.35723	−0.658407
$27$	0.626858	0.120639
$28$	−6.46802	−1.22234
$29$	7.42993	1.37970	0.689851	−	0.723951i	$-0.257676\pi$
$29$	7.42993	1.37970	0.689851	+	0.723951i	$0.257676\pi$
$30$	0	0
$31$	−4.40903	−0.791885	−0.395943	−	0.918275i	$-0.629582\pi$
$31$	−4.40903	−0.791885	−0.395943	+	0.918275i	$0.629582\pi$
$32$	−5.80971	−1.02702
$33$	−2.50015	−0.435220
$34$	1.65083	0.283115
$35$	0	0
$36$	−4.34494	−0.724157
$37$	−1.77785	−0.292277	−0.146139	−	0.989264i	$-0.546685\pi$
$37$	−1.77785	−0.292277	−0.146139	+	0.989264i	$0.546685\pi$
$38$	−0.814490	−0.132128
$39$	10.3053	1.65017
$40$	0	0
$41$	9.92201	1.54956	0.774778	−	0.632233i	$-0.217861\pi$
$41$	9.92201	1.54956	0.774778	+	0.632233i	$0.217861\pi$
$42$	−9.85414	−1.52053
$43$	9.89030	1.50826	0.754129	−	0.656727i	$-0.228059\pi$
$43$	9.89030	1.50826	0.754129	+	0.656727i	$0.228059\pi$
$44$	1.33661	0.201501
$45$	0	0
$46$	5.20234	0.767043
$47$	−0.145235	−0.0211847	−0.0105923	−	0.999944i	$-0.503372\pi$
$47$	−0.145235	−0.0211847	−0.0105923	+	0.999944i	$0.503372\pi$
$48$	1.14939	0.165900
$49$	16.4172	2.34532
$50$	0	0
$51$	−5.06736	−0.709573
$52$	−5.50933	−0.764007
$53$	12.9926	1.78467	0.892333	−	0.451378i	$-0.149067\pi$
$53$	12.9926	1.78467	0.892333	+	0.451378i	$0.149067\pi$
$54$	−0.510570	−0.0694797
$55$	0	0
$56$	13.1510	1.75737
$57$	2.50015	0.331152
$58$	−6.05160	−0.794614
$59$	1.17115	0.152471	0.0762354	−	0.997090i	$-0.475710\pi$
$59$	1.17115	0.152471	0.0762354	+	0.997090i	$0.475710\pi$
$60$	0	0
$61$	2.03091	0.260032	0.130016	−	0.991512i	$-0.458497\pi$
$61$	2.03091	0.260032	0.130016	+	0.991512i	$0.458497\pi$
$62$	3.59111	0.456071
$63$	15.7307	1.98188
$64$	3.81249	0.476561
$65$	0	0
$66$	2.03634	0.250657
$67$	−7.84101	−0.957932	−0.478966	−	0.877833i	$-0.658988\pi$
$67$	−7.84101	−0.957932	−0.478966	+	0.877833i	$0.658988\pi$
$68$	2.70907	0.328523
$69$	−15.9690	−1.92244
$70$	0	0
$71$	−11.1719	−1.32586	−0.662928	−	0.748683i	$-0.730686\pi$
$71$	−11.1719	−1.32586	−0.662928	+	0.748683i	$0.730686\pi$
$72$	8.83428	1.04113
$73$	3.27201	0.382959	0.191480	−	0.981497i	$-0.438671\pi$
$73$	3.27201	0.382959	0.191480	+	0.981497i	$0.438671\pi$
$74$	1.44804	0.168332
$75$	0	0
$76$	−1.33661	−0.153319
$77$	−4.83914	−0.551471
$78$	−8.39357	−0.950385
$79$	11.3472	1.27666	0.638331	−	0.769762i	$-0.279625\pi$
$79$	11.3472	1.27666	0.638331	+	0.769762i	$0.279625\pi$
$80$	0	0
$81$	−8.18495	−0.909439
$82$	−8.08137	−0.892438
$83$	−2.37099	−0.260250	−0.130125	−	0.991498i	$-0.541538\pi$
$83$	−2.37099	−0.260250	−0.130125	+	0.991498i	$0.541538\pi$
$84$	−16.1710	−1.76440
$85$	0	0
$86$	−8.05555	−0.868653
$87$	18.5759	1.99155
$88$	−2.71763	−0.289701
$89$	−9.26921	−0.982534	−0.491267	−	0.871009i	$-0.663466\pi$
$89$	−9.26921	−0.982534	−0.491267	+	0.871009i	$0.663466\pi$
$90$	0	0
$91$	19.9463	2.09095
$92$	8.53722	0.890067
$93$	−11.0232	−1.14305
$94$	0.118292	0.0122009
$95$	0	0
$96$	−14.5251	−1.48246
$97$	−8.29514	−0.842244	−0.421122	−	0.907004i	$-0.638364\pi$
$97$	−8.29514	−0.842244	−0.421122	+	0.907004i	$0.638364\pi$
$98$	−13.3717	−1.35074
$99$	−3.25073	−0.326711
$100$	0	0
$101$	4.99870	0.497389	0.248695	−	0.968582i	$-0.419998\pi$
$101$	4.99870	0.497389	0.248695	+	0.968582i	$0.419998\pi$
$102$	4.12732	0.408665
$103$	17.6185	1.73600	0.867999	−	0.496565i	$-0.165406\pi$
$103$	17.6185	1.73600	0.867999	+	0.496565i	$0.165406\pi$
$104$	11.2018	1.09842
$105$	0	0
$106$	−10.5823	−1.02784
$107$	4.68661	0.453072	0.226536	−	0.974003i	$-0.427260\pi$
$107$	4.68661	0.453072	0.226536	+	0.974003i	$0.427260\pi$
$108$	−0.837862	−0.0806233
$109$	−5.02273	−0.481090	−0.240545	−	0.970638i	$-0.577326\pi$
$109$	−5.02273	−0.481090	−0.240545	+	0.970638i	$0.577326\pi$
$110$	0	0
$111$	−4.44489	−0.421890
$112$	2.22469	0.210213
$113$	−17.8589	−1.68002	−0.840011	−	0.542569i	$-0.817452\pi$
$113$	−17.8589	−1.68002	−0.840011	+	0.542569i	$0.817452\pi$
$114$	−2.03634	−0.190721
$115$	0	0
$116$	−9.93089	−0.922060
$117$	13.3991	1.23875
$118$	−0.953891	−0.0878128
$119$	−9.80809	−0.899106
$120$	0	0
$121$	1.00000	0.0909091
$122$	−1.65416	−0.149760
$123$	24.8065	2.23672
$124$	5.89314	0.529219
$125$	0	0
$126$	−12.8125	−1.14143
$127$	−5.52662	−0.490409	−0.245204	−	0.969471i	$-0.578855\pi$
$127$	−5.52662	−0.490409	−0.245204	+	0.969471i	$0.578855\pi$
$128$	8.51418	0.752554
$129$	24.7272	2.17711
$130$	0	0
$131$	−4.31319	−0.376846	−0.188423	−	0.982088i	$-0.560338\pi$
$131$	−4.31319	−0.376846	−0.188423	+	0.982088i	$0.560338\pi$
$132$	3.34171	0.290859
$133$	4.83914	0.419606
$134$	6.38643	0.551703
$135$	0	0
$136$	−5.50817	−0.472322
$137$	−10.9200	−0.932958	−0.466479	−	0.884532i	$-0.654478\pi$
$137$	−10.9200	−0.932958	−0.466479	+	0.884532i	$0.654478\pi$
$138$	13.0066	1.10720
$139$	16.1839	1.37270	0.686352	−	0.727270i	$-0.259211\pi$
$139$	16.1839	1.37270	0.686352	+	0.727270i	$0.259211\pi$
$140$	0	0
$141$	−0.363108	−0.0305792
$142$	9.09936	0.763602
$143$	−4.12188	−0.344689
$144$	1.49445	0.124538
$145$	0	0
$146$	−2.66502	−0.220558
$147$	41.0455	3.38537
$148$	2.37629	0.195330
$149$	−14.5778	−1.19426	−0.597129	−	0.802145i	$-0.703692\pi$
$149$	−14.5778	−1.19426	−0.597129	+	0.802145i	$0.703692\pi$
$150$	0	0
$151$	−22.0082	−1.79100	−0.895501	−	0.445060i	$-0.853182\pi$
$151$	−22.0082	−1.79100	−0.895501	+	0.445060i	$0.853182\pi$
$152$	2.71763	0.220429
$153$	−6.58867	−0.532662
$154$	3.94143	0.317609
$155$	0	0
$156$	−13.7741	−1.10281
$157$	−18.5410	−1.47974	−0.739868	−	0.672752i	$-0.765112\pi$
$157$	−18.5410	−1.47974	−0.739868	+	0.672752i	$0.765112\pi$
$158$	−9.24220	−0.735270
$159$	32.4833	2.57609
$160$	0	0
$161$	−30.9087	−2.43595
$162$	6.66656	0.523774
$163$	−3.79670	−0.297381	−0.148690	−	0.988884i	$-0.547506\pi$
$163$	−3.79670	−0.297381	−0.148690	+	0.988884i	$0.547506\pi$
$164$	−13.2618	−1.03557
$165$	0	0
$166$	1.93114	0.149886
$167$	18.4689	1.42917	0.714583	−	0.699550i	$-0.246616\pi$
$167$	18.4689	1.42917	0.714583	+	0.699550i	$0.246616\pi$
$168$	32.8794	2.53670
$169$	3.98992	0.306917
$170$	0	0
$171$	3.25073	0.248589
$172$	−13.2194	−1.00797
$173$	−3.71022	−0.282082	−0.141041	−	0.990004i	$-0.545045\pi$
$173$	−3.71022	−0.282082	−0.141041	+	0.990004i	$0.545045\pi$
$174$	−15.1299	−1.14699
$175$	0	0
$176$	−0.459728	−0.0346533
$177$	2.92805	0.220086
$178$	7.54968	0.565872
$179$	18.6382	1.39308	0.696542	−	0.717516i	$-0.254721\pi$
$179$	18.6382	1.39308	0.696542	+	0.717516i	$0.254721\pi$
$180$	0	0
$181$	8.27637	0.615178	0.307589	−	0.951519i	$-0.400478\pi$
$181$	8.27637	0.615178	0.307589	+	0.951519i	$0.400478\pi$
$182$	−16.2461	−1.20424
$183$	5.07758	0.375346
$184$	−17.3582	−1.27966
$185$	0	0
$186$	8.97830	0.658321
$187$	2.02683	0.148216
$188$	0.194122	0.0141578
$189$	3.03345	0.220651
$190$	0	0
$191$	−20.9577	−1.51645	−0.758223	−	0.651996i	$-0.773932\pi$
$191$	−20.9577	−1.51645	−0.758223	+	0.651996i	$0.773932\pi$
$192$	9.53179	0.687897
$193$	−1.14465	−0.0823936	−0.0411968	−	0.999151i	$-0.513117\pi$
$193$	−1.14465	−0.0823936	−0.0411968	+	0.999151i	$0.513117\pi$
$194$	6.75631	0.485075
$195$	0	0
$196$	−21.9434	−1.56738
$197$	−0.139556	−0.00994294	−0.00497147	−	0.999988i	$-0.501582\pi$
$197$	−0.139556	−0.00994294	−0.00497147	+	0.999988i	$0.501582\pi$
$198$	2.64769	0.188163
$199$	10.3017	0.730266	0.365133	−	0.930955i	$-0.381023\pi$
$199$	10.3017	0.730266	0.365133	+	0.930955i	$0.381023\pi$
$200$	0	0
$201$	−19.6037	−1.38274
$202$	−4.07139	−0.286462
$203$	35.9544	2.52351
$204$	6.77307	0.474210
$205$	0	0
$206$	−14.3501	−0.999816
$207$	−20.7632	−1.44314
$208$	1.89495	0.131391
$209$	−1.00000	−0.0691714
$210$	0	0
$211$	27.3988	1.88621	0.943107	−	0.332490i	$-0.107889\pi$
$211$	27.3988	1.88621	0.943107	+	0.332490i	$0.107889\pi$
$212$	−17.3659	−1.19270
$213$	−27.9313	−1.91382
$214$	−3.81720	−0.260938
$215$	0	0
$216$	1.70357	0.115913
$217$	−21.3359	−1.44837
$218$	4.09096	0.277075
$219$	8.18050	0.552787
$220$	0	0
$221$	−8.35435	−0.561974
$222$	3.62032	0.242980
$223$	13.3605	0.894688	0.447344	−	0.894362i	$-0.352370\pi$
$223$	13.3605	0.894688	0.447344	+	0.894362i	$0.352370\pi$
$224$	−28.1140	−1.87844
$225$	0	0
$226$	14.5459	0.967577
$227$	−22.2383	−1.47601	−0.738005	−	0.674795i	$-0.764232\pi$
$227$	−22.2383	−1.47601	−0.738005	+	0.674795i	$0.764232\pi$
$228$	−3.34171	−0.221310
$229$	14.3077	0.945481	0.472740	−	0.881202i	$-0.343265\pi$
$229$	14.3077	0.945481	0.472740	+	0.881202i	$0.343265\pi$
$230$	0	0
$231$	−12.0985	−0.796026
$232$	20.1918	1.32566
$233$	−0.655778	−0.0429615	−0.0214807	−	0.999769i	$-0.506838\pi$
$233$	−0.655778	−0.0429615	−0.0214807	+	0.999769i	$0.506838\pi$
$234$	−10.9135	−0.713435
$235$	0	0
$236$	−1.56537	−0.101897
$237$	28.3697	1.84281
$238$	7.98859	0.517824
$239$	−1.24483	−0.0805216	−0.0402608	−	0.999189i	$-0.512819\pi$
$239$	−1.24483	−0.0805216	−0.0402608	+	0.999189i	$0.512819\pi$
$240$	0	0
$241$	26.2028	1.68787	0.843935	−	0.536446i	$-0.180233\pi$
$241$	26.2028	1.68787	0.843935	+	0.536446i	$0.180233\pi$
$242$	−0.814490	−0.0523574
$243$	−22.3441	−1.43338
$244$	−2.71453	−0.173780
$245$	0	0
$246$	−20.2046	−1.28820
$247$	4.12188	0.262269
$248$	−11.9821	−0.760865
$249$	−5.92781	−0.375660
$250$	0	0
$251$	6.42911	0.405802	0.202901	−	0.979199i	$-0.434963\pi$
$251$	6.42911	0.405802	0.202901	+	0.979199i	$0.434963\pi$
$252$	−21.0258	−1.32450
$253$	6.38724	0.401562
$254$	4.50138	0.282442
$255$	0	0
$256$	−14.5597	−0.909981
$257$	20.6502	1.28813	0.644064	−	0.764972i	$-0.277247\pi$
$257$	20.6502	1.28813	0.644064	+	0.764972i	$0.277247\pi$
$258$	−20.1401	−1.25387
$259$	−8.60327	−0.534581
$260$	0	0
$261$	24.1527	1.49501
$262$	3.51305	0.217037
$263$	6.43749	0.396953	0.198476	−	0.980106i	$-0.436401\pi$
$263$	6.43749	0.396953	0.198476	+	0.980106i	$0.436401\pi$
$264$	−6.79448	−0.418171
$265$	0	0
$266$	−3.94143	−0.241664
$267$	−23.1744	−1.41825
$268$	10.4803	0.640189
$269$	−3.76698	−0.229677	−0.114838	−	0.993384i	$-0.536635\pi$
$269$	−3.76698	−0.229677	−0.114838	+	0.993384i	$0.536635\pi$
$270$	0	0
$271$	−7.83339	−0.475845	−0.237922	−	0.971284i	$-0.576466\pi$
$271$	−7.83339	−0.475845	−0.237922	+	0.971284i	$0.576466\pi$
$272$	−0.931790	−0.0564981
$273$	49.8688	3.01820
$274$	8.89422	0.537320
$275$	0	0
$276$	21.3443	1.28478
$277$	30.7008	1.84463	0.922315	−	0.386439i	$-0.126295\pi$
$277$	30.7008	1.84463	0.922315	+	0.386439i	$0.126295\pi$
$278$	−13.1817	−0.790583
$279$	−14.3326	−0.858068
$280$	0	0
$281$	25.8170	1.54011	0.770057	−	0.637975i	$-0.220228\pi$
$281$	25.8170	1.54011	0.770057	+	0.637975i	$0.220228\pi$
$282$	0.295748	0.0176115
$283$	8.25782	0.490876	0.245438	−	0.969412i	$-0.421068\pi$
$283$	8.25782	0.490876	0.245438	+	0.969412i	$0.421068\pi$
$284$	14.9324	0.886073
$285$	0	0
$286$	3.35723	0.198517
$287$	48.0139	2.83417
$288$	−18.8858	−1.11286
$289$	−12.8920	−0.758351
$290$	0	0
$291$	−20.7391	−1.21575
$292$	−4.37339	−0.255933
$293$	−12.2486	−0.715574	−0.357787	−	0.933803i	$-0.616469\pi$
$293$	−12.2486	−0.715574	−0.357787	+	0.933803i	$0.616469\pi$
$294$	−33.4311	−1.94974
$295$	0	0
$296$	−4.83155	−0.280828
$297$	−0.626858	−0.0363740
$298$	11.8735	0.687811
$299$	−26.3274	−1.52256
$300$	0	0
$301$	47.8605	2.75863
$302$	17.9255	1.03149
$303$	12.4975	0.717961
$304$	0.459728	0.0263672
$305$	0	0
$306$	5.36640	0.306777
$307$	−1.13694	−0.0648885	−0.0324443	−	0.999474i	$-0.510329\pi$
$307$	−1.13694	−0.0648885	−0.0324443	+	0.999474i	$0.510329\pi$
$308$	6.46802	0.368550
$309$	44.0487	2.50584
$310$	0	0
$311$	−5.71535	−0.324088	−0.162044	−	0.986784i	$-0.551809\pi$
$311$	−5.71535	−0.324088	−0.162044	+	0.986784i	$0.551809\pi$
$312$	28.0060	1.58553
$313$	9.16694	0.518146	0.259073	−	0.965858i	$-0.416583\pi$
$313$	9.16694	0.518146	0.259073	+	0.965858i	$0.416583\pi$
$314$	15.1015	0.852226
$315$	0	0
$316$	−15.1668	−0.853197
$317$	8.67039	0.486977	0.243489	−	0.969904i	$-0.421708\pi$
$317$	8.67039	0.486977	0.243489	+	0.969904i	$0.421708\pi$
$318$	−26.4573	−1.48365
$319$	−7.42993	−0.415996
$320$	0	0
$321$	11.7172	0.653991
$322$	25.1748	1.40294
$323$	−2.02683	−0.112776
$324$	10.9401	0.607781
$325$	0	0
$326$	3.09238	0.171271
$327$	−12.5575	−0.694434
$328$	26.9644	1.48886
$329$	−0.702810	−0.0387472
$330$	0	0
$331$	−17.6479	−0.970019	−0.485009	−	0.874509i	$-0.661184\pi$
$331$	−17.6479	−0.970019	−0.485009	+	0.874509i	$0.661184\pi$
$332$	3.16908	0.173926
$333$	−5.77932	−0.316705
$334$	−15.0427	−0.823102
$335$	0	0
$336$	5.56204	0.303434
$337$	23.9468	1.30447	0.652233	−	0.758019i	$-0.273832\pi$
$337$	23.9468	1.30447	0.652233	+	0.758019i	$0.273832\pi$
$338$	−3.24975	−0.176763
$339$	−44.6498	−2.42504
$340$	0	0
$341$	4.40903	0.238762
$342$	−2.64769	−0.143170
$343$	45.5712	2.46062
$344$	26.8782	1.44918
$345$	0	0
$346$	3.02193	0.162460
$347$	4.75858	0.255454	0.127727	−	0.991809i	$-0.459232\pi$
$347$	4.75858	0.255454	0.127727	+	0.991809i	$0.459232\pi$
$348$	−24.8287	−1.33096
$349$	−21.1755	−1.13350	−0.566748	−	0.823891i	$-0.691799\pi$
$349$	−21.1755	−1.13350	−0.566748	+	0.823891i	$0.691799\pi$
$350$	0	0
$351$	2.58384	0.137915
$352$	5.80971	0.309658
$353$	−25.7740	−1.37181	−0.685905	−	0.727691i	$-0.740594\pi$
$353$	−25.7740	−1.37181	−0.685905	+	0.727691i	$0.740594\pi$
$354$	−2.38487	−0.126754
$355$	0	0
$356$	12.3893	0.656631
$357$	−24.5217	−1.29782
$358$	−15.1806	−0.802321
$359$	−14.4460	−0.762432	−0.381216	−	0.924486i	$-0.624495\pi$
$359$	−14.4460	−0.762432	−0.381216	+	0.924486i	$0.624495\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	−6.74102	−0.354300
$363$	2.50015	0.131224
$364$	−26.6604	−1.39739
$365$	0	0
$366$	−4.13564	−0.216173
$367$	19.6353	1.02496	0.512478	−	0.858700i	$-0.328728\pi$
$367$	19.6353	1.02496	0.512478	+	0.858700i	$0.328728\pi$
$368$	−2.93639	−0.153070
$369$	32.2537	1.67906
$370$	0	0
$371$	62.8728	3.26419
$372$	14.7337	0.763907
$373$	2.25454	0.116735	0.0583677	−	0.998295i	$-0.481410\pi$
$373$	2.25454	0.116735	0.0583677	+	0.998295i	$0.481410\pi$
$374$	−1.65083	−0.0853624
$375$	0	0
$376$	−0.394694	−0.0203548
$377$	30.6253	1.57728
$378$	−2.47071	−0.127080
$379$	17.2791	0.887570	0.443785	−	0.896133i	$-0.353635\pi$
$379$	17.2791	0.887570	0.443785	+	0.896133i	$0.353635\pi$
$380$	0	0
$381$	−13.8174	−0.707885
$382$	17.0698	0.873369
$383$	16.9020	0.863649	0.431825	−	0.901958i	$-0.357870\pi$
$383$	16.9020	0.863649	0.431825	+	0.901958i	$0.357870\pi$
$384$	21.2867	1.08628
$385$	0	0
$386$	0.932304	0.0474530
$387$	32.1507	1.63431
$388$	11.0873	0.562874
$389$	−6.06683	−0.307600	−0.153800	−	0.988102i	$-0.549151\pi$
$389$	−6.06683	−0.307600	−0.153800	+	0.988102i	$0.549151\pi$
$390$	0	0
$391$	12.9458	0.654699
$392$	44.6160	2.25345
$393$	−10.7836	−0.543961
$394$	0.113667	0.00572645
$395$	0	0
$396$	4.34494	0.218342
$397$	−23.1083	−1.15977	−0.579887	−	0.814697i	$-0.696903\pi$
$397$	−23.1083	−1.15977	−0.579887	+	0.814697i	$0.696903\pi$
$398$	−8.39061	−0.420583
$399$	12.0985	0.605685
$400$	0	0
$401$	−27.5387	−1.37522	−0.687608	−	0.726082i	$-0.741339\pi$
$401$	−27.5387	−1.37522	−0.687608	+	0.726082i	$0.741339\pi$
$402$	15.9670	0.796361
$403$	−18.1735	−0.905287
$404$	−6.68129	−0.332407
$405$	0	0
$406$	−29.2845	−1.45337
$407$	1.77785	0.0881249
$408$	−13.7712	−0.681778
$409$	22.0368	1.08965	0.544824	−	0.838551i	$-0.316597\pi$
$409$	22.0368	1.08965	0.544824	+	0.838551i	$0.316597\pi$
$410$	0	0
$411$	−27.3016	−1.34669
$412$	−23.5489	−1.16017
$413$	5.66736	0.278872
$414$	16.9114	0.831150
$415$	0	0
$416$	−23.9469	−1.17410
$417$	40.4622	1.98144
$418$	0.814490	0.0398380
$419$	−6.24131	−0.304908	−0.152454	−	0.988311i	$-0.548718\pi$
$419$	−6.24131	−0.304908	−0.152454	+	0.988311i	$0.548718\pi$
$420$	0	0
$421$	−14.9972	−0.730918	−0.365459	−	0.930827i	$-0.619088\pi$
$421$	−14.9972	−0.730918	−0.365459	+	0.930827i	$0.619088\pi$
$422$	−22.3161	−1.08633
$423$	−0.472119	−0.0229552
$424$	35.3090	1.71476
$425$	0	0
$426$	22.7497	1.10223
$427$	9.82787	0.475604
$428$	−6.26416	−0.302789
$429$	−10.3053	−0.497545
$430$	0	0
$431$	21.4445	1.03295	0.516473	−	0.856303i	$-0.327245\pi$
$431$	21.4445	1.03295	0.516473	+	0.856303i	$0.327245\pi$
$432$	0.288184	0.0138653
$433$	−10.6928	−0.513861	−0.256931	−	0.966430i	$-0.582711\pi$
$433$	−10.6928	−0.513861	−0.256931	+	0.966430i	$0.582711\pi$
$434$	17.3779	0.834164
$435$	0	0
$436$	6.71341	0.321514
$437$	−6.38724	−0.305543
$438$	−6.66293	−0.318367
$439$	−36.6563	−1.74951	−0.874755	−	0.484565i	$-0.838978\pi$
$439$	−36.6563	−1.74951	−0.874755	+	0.484565i	$0.838978\pi$
$440$	0	0
$441$	53.3680	2.54133
$442$	6.80453	0.323659
$443$	21.8919	1.04012	0.520058	−	0.854131i	$-0.325910\pi$
$443$	21.8919	1.04012	0.520058	+	0.854131i	$0.325910\pi$
$444$	5.94107	0.281951
$445$	0	0
$446$	−10.8820	−0.515279
$447$	−36.4466	−1.72386
$448$	18.4492	0.871641
$449$	−26.2989	−1.24112	−0.620561	−	0.784158i	$-0.713095\pi$
$449$	−26.2989	−1.24112	−0.620561	+	0.784158i	$0.713095\pi$
$450$	0	0
$451$	−9.92201	−0.467209
$452$	23.8703	1.12276
$453$	−55.0237	−2.58524
$454$	18.1129	0.850081
$455$	0	0
$456$	6.79448	0.318180
$457$	−33.5722	−1.57044	−0.785221	−	0.619215i	$-0.787451\pi$
$457$	−33.5722	−1.57044	−0.785221	+	0.619215i	$0.787451\pi$
$458$	−11.6535	−0.544532
$459$	−1.27053	−0.0593034
$460$	0	0
$461$	−3.64687	−0.169852	−0.0849258	−	0.996387i	$-0.527065\pi$
$461$	−3.64687	−0.169852	−0.0849258	+	0.996387i	$0.527065\pi$
$462$	9.85414	0.458456
$463$	−14.8684	−0.690991	−0.345495	−	0.938420i	$-0.612289\pi$
$463$	−14.8684	−0.690991	−0.345495	+	0.938420i	$0.612289\pi$
$464$	3.41575	0.158572
$465$	0	0
$466$	0.534125	0.0247429
$467$	27.8778	1.29003	0.645015	−	0.764170i	$-0.276851\pi$
$467$	27.8778	1.29003	0.645015	+	0.764170i	$0.276851\pi$
$468$	−17.9094	−0.827860
$469$	−37.9437	−1.75208
$470$	0	0
$471$	−46.3553	−2.13594
$472$	3.18276	0.146498
$473$	−9.89030	−0.454757
$474$	−23.1068	−1.06133
$475$	0	0
$476$	13.1096	0.600876
$477$	42.2353	1.93382
$478$	1.01390	0.0463749
$479$	−2.90602	−0.132779	−0.0663897	−	0.997794i	$-0.521148\pi$
$479$	−2.90602	−0.132779	−0.0663897	+	0.997794i	$0.521148\pi$
$480$	0	0
$481$	−7.32810	−0.334133
$482$	−21.3419	−0.972097
$483$	−77.2762	−3.51619
$484$	−1.33661	−0.0607548
$485$	0	0
$486$	18.1991	0.825527
$487$	−17.6547	−0.800010	−0.400005	−	0.916513i	$-0.630992\pi$
$487$	−17.6547	−0.800010	−0.400005	+	0.916513i	$0.630992\pi$
$488$	5.51928	0.249846
$489$	−9.49231	−0.429257
$490$	0	0
$491$	27.3096	1.23247	0.616233	−	0.787564i	$-0.288658\pi$
$491$	27.3096	1.23247	0.616233	+	0.787564i	$0.288658\pi$
$492$	−33.1565	−1.49481
$493$	−15.0592	−0.678231
$494$	−3.35723	−0.151049
$495$	0	0
$496$	−2.02696	−0.0910130
$497$	−54.0621	−2.42502
$498$	4.82814	0.216354
$499$	−19.0909	−0.854627	−0.427314	−	0.904104i	$-0.640540\pi$
$499$	−19.0909	−0.854627	−0.427314	+	0.904104i	$0.640540\pi$
$500$	0	0
$501$	46.1749	2.06294
$502$	−5.23644	−0.233714
$503$	−39.8092	−1.77500	−0.887501	−	0.460805i	$-0.847561\pi$
$503$	−39.8092	−1.77500	−0.887501	+	0.460805i	$0.847561\pi$
$504$	42.7503	1.90425
$505$	0	0
$506$	−5.20234	−0.231272
$507$	9.97538	0.443022
$508$	7.38692	0.327742
$509$	−9.96761	−0.441806	−0.220903	−	0.975296i	$-0.570900\pi$
$509$	−9.96761	−0.441806	−0.220903	+	0.975296i	$0.570900\pi$
$510$	0	0
$511$	15.8337	0.700441
$512$	−5.16963	−0.228468
$513$	0.626858	0.0276765
$514$	−16.8194	−0.741873
$515$	0	0
$516$	−33.0505	−1.45497
$517$	0.145235	0.00638742
$518$	7.00728	0.307882
$519$	−9.27608	−0.407175
$520$	0	0
$521$	24.1830	1.05948	0.529738	−	0.848162i	$-0.322290\pi$
$521$	24.1830	1.05948	0.529738	+	0.848162i	$0.322290\pi$
$522$	−19.6721	−0.861025
$523$	−12.1479	−0.531189	−0.265594	−	0.964085i	$-0.585568\pi$
$523$	−12.1479	−0.531189	−0.265594	+	0.964085i	$0.585568\pi$
$524$	5.76504	0.251847
$525$	0	0
$526$	−5.24327	−0.228618
$527$	8.93634	0.389273
$528$	−1.14939	−0.0500207
$529$	17.7968	0.773773
$530$	0	0
$531$	3.80709	0.165214
$532$	−6.46802	−0.280424
$533$	40.8973	1.77146
$534$	18.8753	0.816814
$535$	0	0
$536$	−21.3090	−0.920408
$537$	46.5982	2.01086
$538$	3.06817	0.132278
$539$	−16.4172	−0.707140
$540$	0	0
$541$	−17.1167	−0.735905	−0.367952	−	0.929845i	$-0.619941\pi$
$541$	−17.1167	−0.735905	−0.367952	+	0.929845i	$0.619941\pi$
$542$	6.38022	0.274054
$543$	20.6921	0.887984
$544$	11.7753	0.504861
$545$	0	0
$546$	−40.6176	−1.73827
$547$	−27.0558	−1.15682	−0.578411	−	0.815746i	$-0.696327\pi$
$547$	−27.0558	−1.15682	−0.578411	+	0.815746i	$0.696327\pi$
$548$	14.5957	0.623499
$549$	6.60195	0.281764
$550$	0	0
$551$	7.42993	0.316526
$552$	−43.3979	−1.84714
$553$	54.9107	2.33504
$554$	−25.0055	−1.06238
$555$	0	0
$556$	−21.6316	−0.917382
$557$	−32.5288	−1.37829	−0.689144	−	0.724624i	$-0.742013\pi$
$557$	−32.5288	−1.37829	−0.689144	+	0.724624i	$0.742013\pi$
$558$	11.6737	0.494188
$559$	40.7667	1.72425
$560$	0	0
$561$	5.06736	0.213944
$562$	−21.0277	−0.887000
$563$	3.59287	0.151421	0.0757107	−	0.997130i	$-0.475877\pi$
$563$	3.59287	0.151421	0.0757107	+	0.997130i	$0.475877\pi$
$564$	0.485332	0.0204362
$565$	0	0
$566$	−6.72591	−0.282711
$567$	−39.6081	−1.66338
$568$	−30.3610	−1.27392
$569$	−32.6119	−1.36716	−0.683582	−	0.729874i	$-0.739579\pi$
$569$	−32.6119	−1.36716	−0.683582	+	0.729874i	$0.739579\pi$
$570$	0	0
$571$	35.9109	1.50283	0.751413	−	0.659832i	$-0.229373\pi$
$571$	35.9109	1.50283	0.751413	+	0.659832i	$0.229373\pi$
$572$	5.50933	0.230357
$573$	−52.3973	−2.18893
$574$	−39.1069	−1.63229
$575$	0	0
$576$	12.3934	0.516391
$577$	−34.5334	−1.43764	−0.718822	−	0.695194i	$-0.755318\pi$
$577$	−34.5334	−1.43764	−0.718822	+	0.695194i	$0.755318\pi$
$578$	10.5004	0.436758
$579$	−2.86179	−0.118932
$580$	0	0
$581$	−11.4735	−0.476002
$582$	16.8918	0.700186
$583$	−12.9926	−0.538097
$584$	8.89211	0.367958
$585$	0	0
$586$	9.97640	0.412121
$587$	37.3612	1.54206	0.771031	−	0.636798i	$-0.219741\pi$
$587$	37.3612	1.54206	0.771031	+	0.636798i	$0.219741\pi$
$588$	−54.8616	−2.26246
$589$	−4.40903	−0.181671
$590$	0	0
$591$	−0.348910	−0.0143522
$592$	−0.817330	−0.0335920
$593$	8.14523	0.334484	0.167242	−	0.985916i	$-0.446514\pi$
$593$	8.14523	0.334484	0.167242	+	0.985916i	$0.446514\pi$
$594$	0.510570	0.0209489
$595$	0	0
$596$	19.4847	0.798126
$597$	25.7557	1.05411
$598$	21.4434	0.876887
$599$	−27.7885	−1.13541	−0.567704	−	0.823233i	$-0.692168\pi$
$599$	−27.7885	−1.13541	−0.567704	+	0.823233i	$0.692168\pi$
$600$	0	0
$601$	3.66613	0.149544	0.0747722	−	0.997201i	$-0.476177\pi$
$601$	3.66613	0.149544	0.0747722	+	0.997201i	$0.476177\pi$
$602$	−38.9819	−1.58878
$603$	−25.4890	−1.03799
$604$	29.4163	1.19693
$605$	0	0
$606$	−10.1791	−0.413496
$607$	−20.5553	−0.834315	−0.417158	−	0.908834i	$-0.636974\pi$
$607$	−20.5553	−0.834315	−0.417158	+	0.908834i	$0.636974\pi$
$608$	−5.80971	−0.235615
$609$	89.8913	3.64258
$610$	0	0
$611$	−0.598640	−0.0242184
$612$	8.80645	0.355980
$613$	−18.0377	−0.728534	−0.364267	−	0.931295i	$-0.618680\pi$
$613$	−18.0377	−0.728534	−0.364267	+	0.931295i	$0.618680\pi$
$614$	0.926025	0.0373713
$615$	0	0
$616$	−13.1510	−0.529868
$617$	−1.78298	−0.0717801	−0.0358901	−	0.999356i	$-0.511427\pi$
$617$	−1.78298	−0.0717801	−0.0358901	+	0.999356i	$0.511427\pi$
$618$	−35.8772	−1.44319
$619$	23.1501	0.930479	0.465240	−	0.885185i	$-0.345968\pi$
$619$	23.1501	0.930479	0.465240	+	0.885185i	$0.345968\pi$
$620$	0	0
$621$	−4.00389	−0.160671
$622$	4.65510	0.186652
$623$	−44.8550	−1.79708
$624$	4.73764	0.189658
$625$	0	0
$626$	−7.46638	−0.298417
$627$	−2.50015	−0.0998462
$628$	24.7821	0.988912
$629$	3.60340	0.143677
$630$	0	0
$631$	16.4227	0.653778	0.326889	−	0.945063i	$-0.394000\pi$
$631$	16.4227	0.653778	0.326889	+	0.945063i	$0.394000\pi$
$632$	30.8376	1.22665
$633$	68.5011	2.72267
$634$	−7.06194	−0.280466
$635$	0	0
$636$	−43.4174	−1.72161
$637$	67.6699	2.68118
$638$	6.05160	0.239585
$639$	−36.3167	−1.43667
$640$	0	0
$641$	−16.3288	−0.644947	−0.322474	−	0.946578i	$-0.604514\pi$
$641$	−16.3288	−0.644947	−0.322474	+	0.946578i	$0.604514\pi$
$642$	−9.54356	−0.376654
$643$	25.4635	1.00418	0.502091	−	0.864815i	$-0.332564\pi$
$643$	25.4635	1.00418	0.502091	+	0.864815i	$0.332564\pi$
$644$	41.3128	1.62795
$645$	0	0
$646$	1.65083	0.0649511
$647$	−4.22559	−0.166125	−0.0830625	−	0.996544i	$-0.526470\pi$
$647$	−4.22559	−0.166125	−0.0830625	+	0.996544i	$0.526470\pi$
$648$	−22.2437	−0.873814
$649$	−1.17115	−0.0459717
$650$	0	0
$651$	−53.3428	−2.09067
$652$	5.07470	0.198741
$653$	6.29198	0.246224	0.123112	−	0.992393i	$-0.460713\pi$
$653$	6.29198	0.246224	0.123112	+	0.992393i	$0.460713\pi$
$654$	10.2280	0.399946
$655$	0	0
$656$	4.56143	0.178094
$657$	10.6364	0.414966
$658$	0.572432	0.0223157
$659$	−32.2776	−1.25736	−0.628678	−	0.777666i	$-0.716404\pi$
$659$	−32.2776	−1.25736	−0.628678	+	0.777666i	$0.716404\pi$
$660$	0	0
$661$	41.5732	1.61701	0.808505	−	0.588489i	$-0.200277\pi$
$661$	41.5732	1.61701	0.808505	+	0.588489i	$0.200277\pi$
$662$	14.3741	0.558664
$663$	−20.8871	−0.811187
$664$	−6.44347	−0.250055
$665$	0	0
$666$	4.70720	0.182400
$667$	−47.4567	−1.83753
$668$	−24.6856	−0.955116
$669$	33.4033	1.29145
$670$	0	0
$671$	−2.03091	−0.0784026
$672$	−70.2890	−2.71146
$673$	16.4972	0.635921	0.317960	−	0.948104i	$-0.397002\pi$
$673$	16.4972	0.635921	0.317960	+	0.948104i	$0.397002\pi$
$674$	−19.5044	−0.751283
$675$	0	0
$676$	−5.33295	−0.205113
$677$	34.3832	1.32145	0.660726	−	0.750627i	$-0.270248\pi$
$677$	34.3832	1.32145	0.660726	+	0.750627i	$0.270248\pi$
$678$	36.3668	1.39666
$679$	−40.1413	−1.54048
$680$	0	0
$681$	−55.5991	−2.13056
$682$	−3.59111	−0.137511
$683$	26.1835	1.00188	0.500941	−	0.865481i	$-0.332987\pi$
$683$	26.1835	1.00188	0.500941	+	0.865481i	$0.332987\pi$
$684$	−4.34494	−0.166133
$685$	0	0
$686$	−37.1173	−1.41715
$687$	35.7714	1.36476
$688$	4.54685	0.173347
$689$	53.5538	2.04024
$690$	0	0
$691$	−45.2927	−1.72301	−0.861507	−	0.507745i	$-0.830479\pi$
$691$	−45.2927	−1.72301	−0.861507	+	0.507745i	$0.830479\pi$
$692$	4.95910	0.188517
$693$	−15.7307	−0.597560
$694$	−3.87582	−0.147124
$695$	0	0
$696$	50.4825	1.91353
$697$	−20.1102	−0.761728
$698$	17.2472	0.652816
$699$	−1.63954	−0.0620132
$700$	0	0
$701$	−12.7781	−0.482624	−0.241312	−	0.970448i	$-0.577578\pi$
$701$	−12.7781	−0.482624	−0.241312	+	0.970448i	$0.577578\pi$
$702$	−2.10451	−0.0794295
$703$	−1.77785	−0.0670530
$704$	−3.81249	−0.143689
$705$	0	0
$706$	20.9926	0.790069
$707$	24.1894	0.909736
$708$	−3.91365	−0.147084
$709$	−16.4621	−0.618247	−0.309124	−	0.951022i	$-0.600036\pi$
$709$	−16.4621	−0.618247	−0.309124	+	0.951022i	$0.600036\pi$
$710$	0	0
$711$	36.8867	1.38336
$712$	−25.1903	−0.944047
$713$	28.1615	1.05466
$714$	19.9726	0.747458
$715$	0	0
$716$	−24.9119	−0.931003
$717$	−3.11227	−0.116230
$718$	11.7661	0.439109
$719$	6.34240	0.236532	0.118266	−	0.992982i	$-0.462266\pi$
$719$	6.34240	0.236532	0.118266	+	0.992982i	$0.462266\pi$
$720$	0	0
$721$	85.2581	3.17518
$722$	−0.814490	−0.0303122
$723$	65.5108	2.43637
$724$	−11.0622	−0.411125
$725$	0	0
$726$	−2.03634	−0.0755758
$727$	−23.3638	−0.866517	−0.433258	−	0.901270i	$-0.642636\pi$
$727$	−23.3638	−0.866517	−0.433258	+	0.901270i	$0.642636\pi$
$728$	54.2068	2.00904
$729$	−31.3088	−1.15958
$730$	0	0
$731$	−20.0459	−0.741426
$732$	−6.78672	−0.250845
$733$	−1.38798	−0.0512661	−0.0256331	−	0.999671i	$-0.508160\pi$
$733$	−1.38798	−0.0512661	−0.0256331	+	0.999671i	$0.508160\pi$
$734$	−15.9928	−0.590304
$735$	0	0
$736$	37.1080	1.36782
$737$	7.84101	0.288827
$738$	−26.2704	−0.967025
$739$	3.75342	0.138072	0.0690360	−	0.997614i	$-0.478008\pi$
$739$	3.75342	0.138072	0.0690360	+	0.997614i	$0.478008\pi$
$740$	0	0
$741$	10.3053	0.378575
$742$	−51.2092	−1.87995
$743$	−6.00085	−0.220150	−0.110075	−	0.993923i	$-0.535109\pi$
$743$	−6.00085	−0.220150	−0.110075	+	0.993923i	$0.535109\pi$
$744$	−29.9570	−1.09828
$745$	0	0
$746$	−1.83630	−0.0672316
$747$	−7.70743	−0.282000
$748$	−2.70907	−0.0990534
$749$	22.6792	0.828678
$750$	0	0
$751$	−29.4168	−1.07343	−0.536717	−	0.843763i	$-0.680336\pi$
$751$	−29.4168	−1.07343	−0.536717	+	0.843763i	$0.680336\pi$
$752$	−0.0667685	−0.00243480
$753$	16.0737	0.585758
$754$	−24.9440	−0.908407
$755$	0	0
$756$	−4.05453	−0.147462
$757$	11.1487	0.405207	0.202604	−	0.979261i	$-0.435060\pi$
$757$	11.1487	0.405207	0.202604	+	0.979261i	$0.435060\pi$
$758$	−14.0737	−0.511179
$759$	15.9690	0.579639
$760$	0	0
$761$	−19.0044	−0.688909	−0.344454	−	0.938803i	$-0.611936\pi$
$761$	−19.0044	−0.688909	−0.344454	+	0.938803i	$0.611936\pi$
$762$	11.2541	0.407693
$763$	−24.3057	−0.879924
$764$	28.0122	1.01345
$765$	0	0
$766$	−13.7665	−0.497403
$767$	4.82735	0.174305
$768$	−36.4014	−1.31352
$769$	−12.9925	−0.468521	−0.234261	−	0.972174i	$-0.575267\pi$
$769$	−12.9925	−0.468521	−0.234261	+	0.972174i	$0.575267\pi$
$770$	0	0
$771$	51.6286	1.85936
$772$	1.52994	0.0550639
$773$	−8.76741	−0.315342	−0.157671	−	0.987492i	$-0.550398\pi$
$773$	−8.76741	−0.315342	−0.157671	+	0.987492i	$0.550398\pi$
$774$	−26.1864	−0.941251
$775$	0	0
$776$	−22.5431	−0.809252
$777$	−21.5094	−0.771646
$778$	4.94137	0.177157
$779$	9.92201	0.355493
$780$	0	0
$781$	11.1719	0.399760
$782$	−10.5442	−0.377061
$783$	4.65751	0.166446
$784$	7.54747	0.269552
$785$	0	0
$786$	8.78314	0.313284
$787$	42.7634	1.52435	0.762175	−	0.647371i	$-0.224132\pi$
$787$	42.7634	1.52435	0.762175	+	0.647371i	$0.224132\pi$
$788$	0.186531	0.00664489
$789$	16.0947	0.572986
$790$	0	0
$791$	−86.4215	−3.07280
$792$	−8.83428	−0.313913
$793$	8.37119	0.297270
$794$	18.8215	0.667950
$795$	0	0
$796$	−13.7693	−0.488039
$797$	−19.2140	−0.680593	−0.340297	−	0.940318i	$-0.610527\pi$
$797$	−19.2140	−0.680593	−0.340297	+	0.940318i	$0.610527\pi$
$798$	−9.85414	−0.348833
$799$	0.294366	0.0104139
$800$	0	0
$801$	−30.1317	−1.06465
$802$	22.4300	0.792030
$803$	−3.27201	−0.115467
$804$	26.2024	0.924087
$805$	0	0
$806$	14.8021	0.521383
$807$	−9.41800	−0.331529
$808$	13.5846	0.477906
$809$	−51.4141	−1.80762	−0.903812	−	0.427930i	$-0.859243\pi$
$809$	−51.4141	−1.80762	−0.903812	+	0.427930i	$0.859243\pi$
$810$	0	0
$811$	−38.7105	−1.35931	−0.679654	−	0.733533i	$-0.737870\pi$
$811$	−38.7105	−1.35931	−0.679654	+	0.733533i	$0.737870\pi$
$812$	−48.0569	−1.68647
$813$	−19.5846	−0.686863
$814$	−1.44804	−0.0507539
$815$	0	0
$816$	−2.32961	−0.0815527
$817$	9.89030	0.346018
$818$	−17.9487	−0.627562
$819$	64.8402	2.26570
$820$	0	0
$821$	27.2774	0.951986	0.475993	−	0.879449i	$-0.342089\pi$
$821$	27.2774	0.951986	0.475993	+	0.879449i	$0.342089\pi$
$822$	22.2369	0.775599
$823$	−29.7389	−1.03663	−0.518316	−	0.855189i	$-0.673441\pi$
$823$	−29.7389	−1.03663	−0.518316	+	0.855189i	$0.673441\pi$
$824$	47.8805	1.66800
$825$	0	0
$826$	−4.61601	−0.160611
$827$	7.43328	0.258481	0.129240	−	0.991613i	$-0.458746\pi$
$827$	7.43328	0.258481	0.129240	+	0.991613i	$0.458746\pi$
$828$	27.7522	0.964455
$829$	19.8954	0.690996	0.345498	−	0.938419i	$-0.387710\pi$
$829$	19.8954	0.690996	0.345498	+	0.938419i	$0.387710\pi$
$830$	0	0
$831$	76.7564	2.66265
$832$	15.7146	0.544807
$833$	−33.2749	−1.15291
$834$	−32.9561	−1.14117
$835$	0	0
$836$	1.33661	0.0462275
$837$	−2.76384	−0.0955321
$838$	5.08349	0.175606
$839$	33.5693	1.15894	0.579471	−	0.814993i	$-0.303259\pi$
$839$	33.5693	1.15894	0.579471	+	0.814993i	$0.303259\pi$
$840$	0	0
$841$	26.2038	0.903580
$842$	12.2151	0.420959
$843$	64.5463	2.22309
$844$	−36.6214	−1.26056
$845$	0	0
$846$	0.384536	0.0132206
$847$	4.83914	0.166275
$848$	5.97305	0.205115
$849$	20.6457	0.708560
$850$	0	0
$851$	11.3556	0.389264
$852$	37.3331	1.27901
$853$	2.86820	0.0982052	0.0491026	−	0.998794i	$-0.484364\pi$
$853$	2.86820	0.0982052	0.0491026	+	0.998794i	$0.484364\pi$
$854$	−8.00470	−0.273915
$855$	0	0
$856$	12.7365	0.435324
$857$	−38.0209	−1.29877	−0.649385	−	0.760460i	$-0.724974\pi$
$857$	−38.0209	−1.29877	−0.649385	+	0.760460i	$0.724974\pi$
$858$	8.39357	0.286552
$859$	−14.8502	−0.506681	−0.253341	−	0.967377i	$-0.581529\pi$
$859$	−14.8502	−0.506681	−0.253341	+	0.967377i	$0.581529\pi$
$860$	0	0
$861$	120.042	4.09101
$862$	−17.4664	−0.594906
$863$	−15.6023	−0.531109	−0.265554	−	0.964096i	$-0.585555\pi$
$863$	−15.6023	−0.531109	−0.265554	+	0.964096i	$0.585555\pi$
$864$	−3.64186	−0.123899
$865$	0	0
$866$	8.70914	0.295949
$867$	−32.2318	−1.09465
$868$	28.5177	0.967953
$869$	−11.3472	−0.384928
$870$	0	0
$871$	−32.3197	−1.09511
$872$	−13.6499	−0.462245
$873$	−26.9653	−0.912635
$874$	5.20234	0.175972
$875$	0	0
$876$	−10.9341	−0.369429
$877$	−37.4675	−1.26519	−0.632594	−	0.774484i	$-0.718010\pi$
$877$	−37.4675	−1.26519	−0.632594	+	0.774484i	$0.718010\pi$
$878$	29.8562	1.00760
$879$	−30.6234	−1.03290
$880$	0	0
$881$	−43.7824	−1.47507	−0.737533	−	0.675311i	$-0.764009\pi$
$881$	−43.7824	−1.47507	−0.737533	+	0.675311i	$0.764009\pi$
$882$	−43.4677	−1.46363
$883$	56.9866	1.91775	0.958876	−	0.283825i	$-0.0916035\pi$
$883$	56.9866	1.91775	0.958876	+	0.283825i	$0.0916035\pi$
$884$	11.1665	0.375569
$885$	0	0
$886$	−17.8307	−0.599036
$887$	41.5001	1.39344	0.696718	−	0.717345i	$-0.254643\pi$
$887$	41.5001	1.39344	0.696718	+	0.717345i	$0.254643\pi$
$888$	−12.0796	−0.405364
$889$	−26.7441	−0.896968
$890$	0	0
$891$	8.18495	0.274206
$892$	−17.8578	−0.597923
$893$	−0.145235	−0.00486009
$894$	29.6854	0.992827
$895$	0	0
$896$	41.2013	1.37644
$897$	−65.8224	−2.19775
$898$	21.4202	0.714801
$899$	−32.7588	−1.09257
$900$	0	0
$901$	−26.3337	−0.877302
$902$	8.08137	0.269080
$903$	119.658	3.98198
$904$	−48.5339	−1.61421
$905$	0	0
$906$	44.8163	1.48892
$907$	11.8437	0.393263	0.196632	−	0.980477i	$-0.437000\pi$
$907$	11.8437	0.393263	0.196632	+	0.980477i	$0.437000\pi$
$908$	29.7239	0.986423
$909$	16.2494	0.538959
$910$	0	0
$911$	−23.4751	−0.777765	−0.388882	−	0.921287i	$-0.627139\pi$
$911$	−23.4751	−0.777765	−0.388882	+	0.921287i	$0.627139\pi$
$912$	1.14939	0.0380600
$913$	2.37099	0.0784682
$914$	27.3442	0.904467
$915$	0	0
$916$	−19.1238	−0.631868
$917$	−20.8721	−0.689258
$918$	1.03484	0.0341547
$919$	16.6026	0.547668	0.273834	−	0.961777i	$-0.411708\pi$
$919$	16.6026	0.547668	0.273834	+	0.961777i	$0.411708\pi$
$920$	0	0
$921$	−2.84251	−0.0936640
$922$	2.97034	0.0978229
$923$	−46.0491	−1.51572
$924$	16.1710	0.531986
$925$	0	0
$926$	12.1101	0.397963
$927$	57.2728	1.88109
$928$	−43.1657	−1.41698
$929$	24.2704	0.796287	0.398144	−	0.917323i	$-0.369655\pi$
$929$	24.2704	0.796287	0.398144	+	0.917323i	$0.369655\pi$
$930$	0	0
$931$	16.4172	0.538053
$932$	0.876518	0.0287113
$933$	−14.2892	−0.467808
$934$	−22.7062	−0.742969
$935$	0	0
$936$	36.4139	1.19023
$937$	4.73959	0.154836	0.0774179	−	0.996999i	$-0.475332\pi$
$937$	4.73959	0.154836	0.0774179	+	0.996999i	$0.475332\pi$
$938$	30.9048	1.00908
$939$	22.9187	0.747923
$940$	0	0
$941$	−17.3884	−0.566846	−0.283423	−	0.958995i	$-0.591470\pi$
$941$	−17.3884	−0.566846	−0.283423	+	0.958995i	$0.591470\pi$
$942$	37.7559	1.23015
$943$	−63.3742	−2.06375
$944$	0.538412	0.0175238
$945$	0	0
$946$	8.05555	0.261909
$947$	−36.0870	−1.17267	−0.586335	−	0.810069i	$-0.699430\pi$
$947$	−36.0870	−1.17267	−0.586335	+	0.810069i	$0.699430\pi$
$948$	−37.9191	−1.23156
$949$	13.4868	0.437801
$950$	0	0
$951$	21.6772	0.702932
$952$	−26.6548	−0.863887
$953$	2.22478	0.0720676	0.0360338	−	0.999351i	$-0.488528\pi$
$953$	2.22478	0.0720676	0.0360338	+	0.999351i	$0.488528\pi$
$954$	−34.4002	−1.11375
$955$	0	0
$956$	1.66385	0.0538128
$957$	−18.5759	−0.600474
$958$	2.36692	0.0764718
$959$	−52.8433	−1.70640
$960$	0	0
$961$	−11.5605	−0.372918
$962$	5.96866	0.192437
$963$	15.2349	0.490938
$964$	−35.0228	−1.12801
$965$	0	0
$966$	62.9407	2.02508
$967$	11.2409	0.361484	0.180742	−	0.983531i	$-0.442150\pi$
$967$	11.2409	0.361484	0.180742	+	0.983531i	$0.442150\pi$
$968$	2.71763	0.0873480
$969$	−5.06736	−0.162787
$970$	0	0
$971$	−41.8105	−1.34176	−0.670881	−	0.741565i	$-0.734084\pi$
$971$	−41.8105	−1.34176	−0.670881	+	0.741565i	$0.734084\pi$
$972$	29.8653	0.957930
$973$	78.3163	2.51070
$974$	14.3796	0.460751
$975$	0	0
$976$	0.933669	0.0298860
$977$	−6.49730	−0.207867	−0.103934	−	0.994584i	$-0.533143\pi$
$977$	−6.49730	−0.207867	−0.103934	+	0.994584i	$0.533143\pi$
$978$	7.73139	0.247223
$979$	9.26921	0.296245
$980$	0	0
$981$	−16.3275	−0.521298
$982$	−22.2434	−0.709816
$983$	−49.7817	−1.58779	−0.793895	−	0.608055i	$-0.791950\pi$
$983$	−49.7817	−1.58779	−0.793895	+	0.608055i	$0.791950\pi$
$984$	67.4148	2.14911
$985$	0	0
$986$	12.2656	0.390615
$987$	−1.75713	−0.0559300
$988$	−5.50933	−0.175275
$989$	−63.1717	−2.00874
$990$	0	0
$991$	3.05414	0.0970179	0.0485090	−	0.998823i	$-0.484553\pi$
$991$	3.05414	0.0970179	0.0485090	+	0.998823i	$0.484553\pi$
$992$	25.6152	0.813283
$993$	−44.1224	−1.40018
$994$	44.0331	1.39664
$995$	0	0
$996$	7.92315	0.251055
$997$	14.2020	0.449783	0.224892	−	0.974384i	$-0.427797\pi$
$997$	14.2020	0.449783	0.224892	+	0.974384i	$0.427797\pi$
$998$	15.5494	0.492207
$999$	−1.11446	−0.0352600

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5225.2.a.u.1.7	✓	15
5.4	even	2		5225.2.a.v.1.9	yes	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5225.2.a.u.1.7	✓	15	1.1	even	1	trivial
5225.2.a.v.1.9	yes	15	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:	\( N \)	\(=\)	\( 5225 = 5^{2} \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5225.a (trivial)

\(f(q)\)	\(=\)	\(q-0.814490 q^{2} +2.50015 q^{3} -1.33661 q^{4} -2.03634 q^{6} +4.83914 q^{7} +2.71763 q^{8} +3.25073 q^{9} +O(q^{10})\)	\(q-0.814490 q^{2} +2.50015 q^{3} -1.33661 q^{4} -2.03634 q^{6} +4.83914 q^{7} +2.71763 q^{8} +3.25073 q^{9} -1.00000 q^{11} -3.34171 q^{12} +4.12188 q^{13} -3.94143 q^{14} +0.459728 q^{16} -2.02683 q^{17} -2.64769 q^{18} +1.00000 q^{19} +12.0985 q^{21} +0.814490 q^{22} -6.38724 q^{23} +6.79448 q^{24} -3.35723 q^{26} +0.626858 q^{27} -6.46802 q^{28} +7.42993 q^{29} -4.40903 q^{31} -5.80971 q^{32} -2.50015 q^{33} +1.65083 q^{34} -4.34494 q^{36} -1.77785 q^{37} -0.814490 q^{38} +10.3053 q^{39} +9.92201 q^{41} -9.85414 q^{42} +9.89030 q^{43} +1.33661 q^{44} +5.20234 q^{46} -0.145235 q^{47} +1.14939 q^{48} +16.4172 q^{49} -5.06736 q^{51} -5.50933 q^{52} +12.9926 q^{53} -0.510570 q^{54} +13.1510 q^{56} +2.50015 q^{57} -6.05160 q^{58} +1.17115 q^{59} +2.03091 q^{61} +3.59111 q^{62} +15.7307 q^{63} +3.81249 q^{64} +2.03634 q^{66} -7.84101 q^{67} +2.70907 q^{68} -15.9690 q^{69} -11.1719 q^{71} +8.83428 q^{72} +3.27201 q^{73} +1.44804 q^{74} -1.33661 q^{76} -4.83914 q^{77} -8.39357 q^{78} +11.3472 q^{79} -8.18495 q^{81} -8.08137 q^{82} -2.37099 q^{83} -16.1710 q^{84} -8.05555 q^{86} +18.5759 q^{87} -2.71763 q^{88} -9.26921 q^{89} +19.9463 q^{91} +8.53722 q^{92} -11.0232 q^{93} +0.118292 q^{94} -14.5251 q^{96} -8.29514 q^{97} -13.3717 q^{98} -3.25073 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - q^{2} + 4 q^{3} + 13 q^{4} - q^{6} + 17 q^{7} + 3 q^{8} + 15 q^{9}+O(q^{10}) \) 15 * q - q^2 + 4 * q^3 + 13 * q^4 - q^6 + 17 * q^7 + 3 * q^8 + 15 * q^9	\( 15 q - q^{2} + 4 q^{3} + 13 q^{4} - q^{6} + 17 q^{7} + 3 q^{8} + 15 q^{9} - 15 q^{11} + 9 q^{12} + 3 q^{13} - 11 q^{14} + 13 q^{16} + q^{17} - 10 q^{18} + 15 q^{19} + 16 q^{21} + q^{22} + 18 q^{23} - 27 q^{24} + 15 q^{26} + 31 q^{27} + 34 q^{28} + 11 q^{29} - 2 q^{31} + 10 q^{32} - 4 q^{33} - 13 q^{34} + 8 q^{36} + 27 q^{37} - q^{38} + 4 q^{39} + 6 q^{41} + 2 q^{42} + 38 q^{43} - 13 q^{44} - 9 q^{46} + 14 q^{47} + 32 q^{48} + 28 q^{49} - 32 q^{51} + 16 q^{52} + 11 q^{53} - 11 q^{54} + 2 q^{56} + 4 q^{57} - 6 q^{58} + 13 q^{59} + 8 q^{61} + 7 q^{62} + 49 q^{63} + 9 q^{64} + q^{66} + 31 q^{67} - 26 q^{68} + 39 q^{69} - 3 q^{71} - 18 q^{72} + 18 q^{73} + 7 q^{74} + 13 q^{76} - 17 q^{77} + 18 q^{78} + 10 q^{79} + 31 q^{81} + 58 q^{82} + 16 q^{83} + 112 q^{84} - 63 q^{86} + 67 q^{87} - 3 q^{88} - 7 q^{89} - 50 q^{91} + 98 q^{92} + 26 q^{93} + 22 q^{94} - 37 q^{96} + 24 q^{97} - 46 q^{98} - 15 q^{99}+O(q^{100}) \) 15 * q - q^2 + 4 * q^3 + 13 * q^4 - q^6 + 17 * q^7 + 3 * q^8 + 15 * q^9 - 15 * q^11 + 9 * q^12 + 3 * q^13 - 11 * q^14 + 13 * q^16 + q^17 - 10 * q^18 + 15 * q^19 + 16 * q^21 + q^22 + 18 * q^23 - 27 * q^24 + 15 * q^26 + 31 * q^27 + 34 * q^28 + 11 * q^29 - 2 * q^31 + 10 * q^32 - 4 * q^33 - 13 * q^34 + 8 * q^36 + 27 * q^37 - q^38 + 4 * q^39 + 6 * q^41 + 2 * q^42 + 38 * q^43 - 13 * q^44 - 9 * q^46 + 14 * q^47 + 32 * q^48 + 28 * q^49 - 32 * q^51 + 16 * q^52 + 11 * q^53 - 11 * q^54 + 2 * q^56 + 4 * q^57 - 6 * q^58 + 13 * q^59 + 8 * q^61 + 7 * q^62 + 49 * q^63 + 9 * q^64 + q^66 + 31 * q^67 - 26 * q^68 + 39 * q^69 - 3 * q^71 - 18 * q^72 + 18 * q^73 + 7 * q^74 + 13 * q^76 - 17 * q^77 + 18 * q^78 + 10 * q^79 + 31 * q^81 + 58 * q^82 + 16 * q^83 + 112 * q^84 - 63 * q^86 + 67 * q^87 - 3 * q^88 - 7 * q^89 - 50 * q^91 + 98 * q^92 + 26 * q^93 + 22 * q^94 - 37 * q^96 + 24 * q^97 - 46 * q^98 - 15 * q^99

Introduction

L-functions

Modular forms

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Database

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