LMFDB - Embedded newform 5415.2.a.z.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5415,2,Mod(1,5415)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5415, 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("5415.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5415 = 3 \cdot 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5415.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:	$43.2389926945$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.8797896.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 8x^{3} + 5x^{2} + 13x - 4 $ x^5 - x^4 - 8x^3 + 5x^2 + 13*x - 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 285)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.64661$ of defining polynomial
Character	$\chi$	$=$	5415.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.64661 q^{2} +1.00000 q^{3} +0.711327 q^{4} +1.00000 q^{5} +1.64661 q^{6} +4.47988 q^{7} -2.12194 q^{8} +1.00000 q^{9} +1.64661 q^{10} -3.44134 q^{11} +0.711327 q^{12} -2.47988 q^{13} +7.37662 q^{14} +1.00000 q^{15} -4.91667 q^{16} +7.62799 q^{17} +1.64661 q^{18} +0.711327 q^{20} +4.47988 q^{21} -5.66654 q^{22} +3.87057 q^{23} -2.12194 q^{24} +1.00000 q^{25} -4.08340 q^{26} +1.00000 q^{27} +3.18666 q^{28} +8.73456 q^{29} +1.64661 q^{30} +0.422654 q^{31} -3.85195 q^{32} -3.44134 q^{33} +12.5603 q^{34} +4.47988 q^{35} +0.711327 q^{36} -3.90253 q^{37} -2.47988 q^{39} -2.12194 q^{40} -5.29322 q^{41} +7.37662 q^{42} +2.47988 q^{43} -2.44791 q^{44} +1.00000 q^{45} +6.37332 q^{46} -0.677330 q^{47} -4.91667 q^{48} +13.0693 q^{49} +1.64661 q^{50} +7.62799 q^{51} -1.76401 q^{52} -11.4986 q^{53} +1.64661 q^{54} -3.44134 q^{55} -9.50605 q^{56} +14.3824 q^{58} +8.53053 q^{59} +0.711327 q^{60} +8.20233 q^{61} +0.695946 q^{62} +4.47988 q^{63} +3.49067 q^{64} -2.47988 q^{65} -5.66654 q^{66} +9.63457 q^{67} +5.42600 q^{68} +3.87057 q^{69} +7.37662 q^{70} +3.85189 q^{71} -2.12194 q^{72} +16.7852 q^{73} -6.42595 q^{74} +1.00000 q^{75} -15.4168 q^{77} -4.08340 q^{78} -12.1252 q^{79} -4.91667 q^{80} +1.00000 q^{81} -8.71588 q^{82} -2.03855 q^{83} +3.18666 q^{84} +7.62799 q^{85} +4.08340 q^{86} +8.73456 q^{87} +7.30232 q^{88} +3.14511 q^{89} +1.64661 q^{90} -11.1096 q^{91} +2.75324 q^{92} +0.422654 q^{93} -1.11530 q^{94} -3.85195 q^{96} -2.00000 q^{97} +21.5201 q^{98} -3.44134 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + q^{2} + 5 q^{3} + 7 q^{4} + 5 q^{5} + q^{6} + 2 q^{7} + 6 q^{8} + 5 q^{9} + q^{10} + 5 q^{11} + 7 q^{12} + 8 q^{13} + 4 q^{14} + 5 q^{15} + 7 q^{16} + 10 q^{17} + q^{18} + 7 q^{20} + 2 q^{21}+ \cdots + 5 q^{99}+O(q^{100}) $ 5 * q + q^2 + 5 * q^3 + 7 * q^4 + 5 * q^5 + q^6 + 2 * q^7 + 6 * q^8 + 5 * q^9 + q^10 + 5 * q^11 + 7 * q^12 + 8 * q^13 + 4 * q^14 + 5 * q^15 + 7 * q^16 + 10 * q^17 + q^18 + 7 * q^20 + 2 * q^21 - 2 * q^22 - 2 * q^23 + 6 * q^24 + 5 * q^25 - 2 * q^26 + 5 * q^27 + 10 * q^28 + 7 * q^29 + q^30 + 9 * q^31 + 23 * q^32 + 5 * q^33 - 25 * q^34 + 2 * q^35 + 7 * q^36 - 6 * q^37 + 8 * q^39 + 6 * q^40 - 12 * q^41 + 4 * q^42 - 8 * q^43 + 16 * q^44 + 5 * q^45 + 20 * q^46 + 6 * q^47 + 7 * q^48 + 15 * q^49 + q^50 + 10 * q^51 + 4 * q^52 - 8 * q^53 + q^54 + 5 * q^55 - 36 * q^56 + 38 * q^58 + q^59 + 7 * q^60 + 7 * q^61 + 15 * q^62 + 2 * q^63 + 14 * q^64 + 8 * q^65 - 2 * q^66 + 14 * q^67 - q^68 - 2 * q^69 + 4 * q^70 + 27 * q^71 + 6 * q^72 + 26 * q^73 - 18 * q^74 + 5 * q^75 + 14 * q^77 - 2 * q^78 - 23 * q^79 + 7 * q^80 + 5 * q^81 - 36 * q^82 - 12 * q^83 + 10 * q^84 + 10 * q^85 + 2 * q^86 + 7 * q^87 + 9 * q^89 + q^90 - 46 * q^91 - 52 * q^92 + 9 * q^93 - 45 * q^94 + 23 * q^96 - 10 * q^97 - 21 * q^98 + 5 * q^99

Coefficient data

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

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

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

$2$	1.64661	1.16433	0.582165	−	0.813071i	$-0.302206\pi$
$2$	1.64661	1.16433	0.582165	+	0.813071i	$0.302206\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.711327	0.355663
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.64661	0.672226
$7$	4.47988	1.69324	0.846618	−	0.532201i	$-0.178635\pi$
$7$	4.47988	1.69324	0.846618	+	0.532201i	$0.178635\pi$
$8$	−2.12194	−0.750220
$9$	1.00000	0.333333
$10$	1.64661	0.520704
$11$	−3.44134	−1.03760	−0.518801	−	0.854895i	$-0.673621\pi$
$11$	−3.44134	−1.03760	−0.518801	+	0.854895i	$0.673621\pi$
$12$	0.711327	0.205342
$13$	−2.47988	−0.687795	−0.343898	−	0.939007i	$-0.611747\pi$
$13$	−2.47988	−0.687795	−0.343898	+	0.939007i	$0.611747\pi$
$14$	7.37662	1.97148
$15$	1.00000	0.258199
$16$	−4.91667	−1.22917
$17$	7.62799	1.85006	0.925030	−	0.379894i	$-0.124039\pi$
$17$	7.62799	1.85006	0.925030	+	0.379894i	$0.124039\pi$
$18$	1.64661	0.388110
$19$	0	0
$19$	0	0
$20$	0.711327	0.159058
$21$	4.47988	0.977590
$22$	−5.66654	−1.20811
$23$	3.87057	0.807069	0.403535	−	0.914964i	$-0.367782\pi$
$23$	3.87057	0.807069	0.403535	+	0.914964i	$0.367782\pi$
$24$	−2.12194	−0.433140
$25$	1.00000	0.200000
$26$	−4.08340	−0.800820
$27$	1.00000	0.192450
$28$	3.18666	0.602222
$29$	8.73456	1.62197	0.810983	−	0.585069i	$-0.198933\pi$
$29$	8.73456	1.62197	0.810983	+	0.585069i	$0.198933\pi$
$30$	1.64661	0.300629
$31$	0.422654	0.0759108	0.0379554	−	0.999279i	$-0.487916\pi$
$31$	0.422654	0.0759108	0.0379554	+	0.999279i	$0.487916\pi$
$32$	−3.85195	−0.680935
$33$	−3.44134	−0.599060
$34$	12.5603	2.15408
$35$	4.47988	0.757238
$36$	0.711327	0.118554
$37$	−3.90253	−0.641573	−0.320786	−	0.947152i	$-0.603947\pi$
$37$	−3.90253	−0.641573	−0.320786	+	0.947152i	$0.603947\pi$
$38$	0	0
$39$	−2.47988	−0.397099
$40$	−2.12194	−0.335509
$41$	−5.29322	−0.826662	−0.413331	−	0.910581i	$-0.635635\pi$
$41$	−5.29322	−0.826662	−0.413331	+	0.910581i	$0.635635\pi$
$42$	7.37662	1.13824
$43$	2.47988	0.378178	0.189089	−	0.981960i	$-0.439446\pi$
$43$	2.47988	0.378178	0.189089	+	0.981960i	$0.439446\pi$
$44$	−2.44791	−0.369037
$45$	1.00000	0.149071
$46$	6.37332	0.939695
$47$	−0.677330	−0.0987987	−0.0493994	−	0.998779i	$-0.515731\pi$
$47$	−0.677330	−0.0987987	−0.0493994	+	0.998779i	$0.515731\pi$
$48$	−4.91667	−0.709660
$49$	13.0693	1.86705
$50$	1.64661	0.232866
$51$	7.62799	1.06813
$52$	−1.76401	−0.244624
$53$	−11.4986	−1.57945	−0.789725	−	0.613462i	$-0.789777\pi$
$53$	−11.4986	−1.57945	−0.789725	+	0.613462i	$0.789777\pi$
$54$	1.64661	0.224075
$55$	−3.44134	−0.464030
$56$	−9.50605	−1.27030
$57$	0	0
$58$	14.3824	1.88850
$59$	8.53053	1.11058	0.555290	−	0.831657i	$-0.312607\pi$
$59$	8.53053	1.11058	0.555290	+	0.831657i	$0.312607\pi$
$60$	0.711327	0.0918319
$61$	8.20233	1.05020	0.525101	−	0.851040i	$-0.324028\pi$
$61$	8.20233	1.05020	0.525101	+	0.851040i	$0.324028\pi$
$62$	0.695946	0.0883852
$63$	4.47988	0.564412
$64$	3.49067	0.436334
$65$	−2.47988	−0.307591
$66$	−5.66654	−0.697503
$67$	9.63457	1.17705	0.588525	−	0.808479i	$-0.299709\pi$
$67$	9.63457	1.17705	0.588525	+	0.808479i	$0.299709\pi$
$68$	5.42600	0.657999
$69$	3.87057	0.465962
$70$	7.37662	0.881675
$71$	3.85189	0.457135	0.228567	−	0.973528i	$-0.426596\pi$
$71$	3.85189	0.457135	0.228567	+	0.973528i	$0.426596\pi$
$72$	−2.12194	−0.250073
$73$	16.7852	1.96456	0.982280	−	0.187420i	$-0.0600126\pi$
$73$	16.7852	1.96456	0.982280	+	0.187420i	$0.0600126\pi$
$74$	−6.42595	−0.747002
$75$	1.00000	0.115470
$76$	0	0
$77$	−15.4168	−1.75690
$78$	−4.08340	−0.462354
$79$	−12.1252	−1.36420	−0.682098	−	0.731261i	$-0.738932\pi$
$79$	−12.1252	−1.36420	−0.682098	+	0.731261i	$0.738932\pi$
$80$	−4.91667	−0.549700
$81$	1.00000	0.111111
$82$	−8.71588	−0.962507
$83$	−2.03855	−0.223759	−0.111880	−	0.993722i	$-0.535687\pi$
$83$	−2.03855	−0.223759	−0.111880	+	0.993722i	$0.535687\pi$
$84$	3.18666	0.347693
$85$	7.62799	0.827372
$86$	4.08340	0.440324
$87$	8.73456	0.936443
$88$	7.30232	0.778430
$89$	3.14511	0.333381	0.166690	−	0.986009i	$-0.446692\pi$
$89$	3.14511	0.333381	0.166690	+	0.986009i	$0.446692\pi$
$90$	1.64661	0.173568
$91$	−11.1096	−1.16460
$92$	2.75324	0.287045
$93$	0.422654	0.0438271
$94$	−1.11530	−0.115034
$95$	0	0
$96$	−3.85195	−0.393138
$97$	−2.00000	−0.203069	−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000	−0.203069	−0.101535	+	0.994832i	$0.532375\pi$
$98$	21.5201	2.17386
$99$	−3.44134	−0.345867
$100$	0.711327	0.0711327
$101$	−2.01868	−0.200866	−0.100433	−	0.994944i	$-0.532023\pi$
$101$	−2.01868	−0.200866	−0.100433	+	0.994944i	$0.532023\pi$
$102$	12.5603	1.24366
$103$	−6.48898	−0.639378	−0.319689	−	0.947523i	$-0.603578\pi$
$103$	−6.48898	−0.639378	−0.319689	+	0.947523i	$0.603578\pi$
$104$	5.26217	0.515998
$105$	4.47988	0.437192
$106$	−18.9337	−1.83900
$107$	−3.96145	−0.382968	−0.191484	−	0.981496i	$-0.561330\pi$
$107$	−3.96145	−0.382968	−0.191484	+	0.981496i	$0.561330\pi$
$108$	0.711327	0.0684475
$109$	2.96803	0.284286	0.142143	−	0.989846i	$-0.454601\pi$
$109$	2.96803	0.284286	0.142143	+	0.989846i	$0.454601\pi$
$110$	−5.66654	−0.540283
$111$	−3.90253	−0.370412
$112$	−22.0261	−2.08127
$113$	8.71719	0.820044	0.410022	−	0.912076i	$-0.365521\pi$
$113$	8.71719	0.820044	0.410022	+	0.912076i	$0.365521\pi$
$114$	0	0
$115$	3.87057	0.360932
$116$	6.21312	0.576874
$117$	−2.47988	−0.229265
$118$	14.0465	1.29308
$119$	34.1725	3.13259
$120$	−2.12194	−0.193706
$121$	0.842790	0.0766172
$122$	13.5061	1.22278
$123$	−5.29322	−0.477274
$124$	0.300645	0.0269987
$125$	1.00000	0.0894427
$126$	7.37662	0.657161
$127$	4.57735	0.406174	0.203087	−	0.979161i	$-0.434903\pi$
$127$	4.57735	0.406174	0.203087	+	0.979161i	$0.434903\pi$
$128$	13.4517	1.18897
$129$	2.47988	0.218341
$130$	−4.08340	−0.358138
$131$	−20.6728	−1.80619	−0.903094	−	0.429443i	$-0.858710\pi$
$131$	−20.6728	−1.80619	−0.903094	+	0.429443i	$0.858710\pi$
$132$	−2.44791	−0.213064
$133$	0	0
$134$	15.8644	1.37047
$135$	1.00000	0.0860663
$136$	−16.1862	−1.38795
$137$	17.6280	1.50606	0.753031	−	0.657985i	$-0.228591\pi$
$137$	17.6280	1.50606	0.753031	+	0.657985i	$0.228591\pi$
$138$	6.37332	0.542533
$139$	11.7346	0.995312	0.497656	−	0.867374i	$-0.334194\pi$
$139$	11.7346	0.995312	0.497656	+	0.867374i	$0.334194\pi$
$140$	3.18666	0.269322
$141$	−0.677330	−0.0570415
$142$	6.34256	0.532256
$143$	8.53410	0.713657
$144$	−4.91667	−0.409722
$145$	8.73456	0.725365
$146$	27.6387	2.28739
$147$	13.0693	1.07794
$148$	−2.77598	−0.228184
$149$	−21.5649	−1.76666	−0.883332	−	0.468748i	$-0.844705\pi$
$149$	−21.5649	−1.76666	−0.883332	+	0.468748i	$0.844705\pi$
$150$	1.64661	0.134445
$151$	−18.3102	−1.49006	−0.745032	−	0.667029i	$-0.767566\pi$
$151$	−18.3102	−1.49006	−0.745032	+	0.667029i	$0.767566\pi$
$152$	0	0
$153$	7.62799	0.616687
$154$	−25.3854	−2.04562
$155$	0.422654	0.0339484
$156$	−1.76401	−0.141233
$157$	−11.4305	−0.912257	−0.456128	−	0.889914i	$-0.650764\pi$
$157$	−11.4305	−0.912257	−0.456128	+	0.889914i	$0.650764\pi$
$158$	−19.9656	−1.58837
$159$	−11.4986	−0.911895
$160$	−3.85195	−0.304524
$161$	17.3397	1.36656
$162$	1.64661	0.129370
$163$	−8.19876	−0.642177	−0.321088	−	0.947049i	$-0.604049\pi$
$163$	−8.19876	−0.642177	−0.321088	+	0.947049i	$0.604049\pi$
$164$	−3.76521	−0.294014
$165$	−3.44134	−0.267908
$166$	−3.35669	−0.260530
$167$	8.84413	0.684379	0.342189	−	0.939631i	$-0.388832\pi$
$167$	8.84413	0.684379	0.342189	+	0.939631i	$0.388832\pi$
$168$	−9.50605	−0.733408
$169$	−6.85019	−0.526938
$170$	12.5603	0.963334
$171$	0	0
$172$	1.76401	0.134504
$173$	−17.5462	−1.33401	−0.667007	−	0.745052i	$-0.732425\pi$
$173$	−17.5462	−1.33401	−0.667007	+	0.745052i	$0.732425\pi$
$174$	14.3824	1.09033
$175$	4.47988	0.338647
$176$	16.9199	1.27539
$177$	8.53053	0.641194
$178$	5.17877	0.388165
$179$	−4.30890	−0.322062	−0.161031	−	0.986949i	$-0.551482\pi$
$179$	−4.30890	−0.322062	−0.161031	+	0.986949i	$0.551482\pi$
$180$	0.711327	0.0530192
$181$	−6.34387	−0.471536	−0.235768	−	0.971809i	$-0.575761\pi$
$181$	−6.34387	−0.471536	−0.235768	+	0.971809i	$0.575761\pi$
$182$	−18.2931	−1.35598
$183$	8.20233	0.606334
$184$	−8.21312	−0.605480
$185$	−3.90253	−0.286920
$186$	0.695946	0.0510292
$187$	−26.2505	−1.91963
$188$	−0.481803	−0.0351391
$189$	4.47988	0.325863
$190$	0	0
$191$	0.845796	0.0611997	0.0305998	−	0.999532i	$-0.490258\pi$
$191$	0.845796	0.0611997	0.0305998	+	0.999532i	$0.490258\pi$
$192$	3.49067	0.251917
$193$	13.1808	0.948773	0.474387	−	0.880317i	$-0.342670\pi$
$193$	13.1808	0.948773	0.474387	+	0.880317i	$0.342670\pi$
$194$	−3.29322	−0.236440
$195$	−2.47988	−0.177588
$196$	9.29656	0.664040
$197$	6.91212	0.492468	0.246234	−	0.969210i	$-0.420807\pi$
$197$	6.91212	0.492468	0.246234	+	0.969210i	$0.420807\pi$
$198$	−5.66654	−0.402703
$199$	−13.3812	−0.948570	−0.474285	−	0.880371i	$-0.657293\pi$
$199$	−13.3812	−0.948570	−0.474285	+	0.880371i	$0.657293\pi$
$200$	−2.12194	−0.150044
$201$	9.63457	0.679570
$202$	−3.32398	−0.233875
$203$	39.1298	2.74637
$204$	5.42600	0.379896
$205$	−5.29322	−0.369695
$206$	−10.6848	−0.744447
$207$	3.87057	0.269023
$208$	12.1927	0.845415
$209$	0	0
$210$	7.37662	0.509035
$211$	14.7502	1.01545	0.507724	−	0.861520i	$-0.330487\pi$
$211$	14.7502	1.01545	0.507724	+	0.861520i	$0.330487\pi$
$212$	−8.17924	−0.561752
$213$	3.85189	0.263927
$214$	−6.52297	−0.445901
$215$	2.47988	0.169126
$216$	−2.12194	−0.144380
$217$	1.89344	0.128535
$218$	4.88720	0.331003
$219$	16.7852	1.13424
$220$	−2.44791	−0.165038
$221$	−18.9165	−1.27246
$222$	−6.42595	−0.431282
$223$	2.28834	0.153238	0.0766192	−	0.997060i	$-0.475587\pi$
$223$	2.28834	0.153238	0.0766192	+	0.997060i	$0.475587\pi$
$224$	−17.2563	−1.15298
$225$	1.00000	0.0666667
$226$	14.3538	0.954802
$227$	4.19493	0.278427	0.139214	−	0.990262i	$-0.455543\pi$
$227$	4.19493	0.278427	0.139214	+	0.990262i	$0.455543\pi$
$228$	0	0
$229$	−26.2742	−1.73625	−0.868123	−	0.496348i	$-0.834674\pi$
$229$	−26.2742	−1.73625	−0.868123	+	0.496348i	$0.834674\pi$
$230$	6.37332	0.420244
$231$	−15.4168	−1.01435
$232$	−18.5342	−1.21683
$233$	−5.56250	−0.364411	−0.182206	−	0.983260i	$-0.558324\pi$
$233$	−5.56250	−0.364411	−0.182206	+	0.983260i	$0.558324\pi$
$234$	−4.08340	−0.266940
$235$	−0.677330	−0.0441841
$236$	6.06799	0.394993
$237$	−12.1252	−0.787619
$238$	56.2688	3.64737
$239$	−6.84901	−0.443026	−0.221513	−	0.975157i	$-0.571099\pi$
$239$	−6.84901	−0.443026	−0.221513	+	0.975157i	$0.571099\pi$
$240$	−4.91667	−0.317370
$241$	−14.8424	−0.956085	−0.478043	−	0.878337i	$-0.658654\pi$
$241$	−14.8424	−0.956085	−0.478043	+	0.878337i	$0.658654\pi$
$242$	1.38775	0.0892077
$243$	1.00000	0.0641500
$244$	5.83454	0.373518
$245$	13.0693	0.834969
$246$	−8.71588	−0.555704
$247$	0	0
$248$	−0.896847	−0.0569498
$249$	−2.03855	−0.129188
$250$	1.64661	0.104141
$251$	−4.80255	−0.303134	−0.151567	−	0.988447i	$-0.548432\pi$
$251$	−4.80255	−0.303134	−0.151567	+	0.988447i	$0.548432\pi$
$252$	3.18666	0.200741
$253$	−13.3199	−0.837416
$254$	7.53711	0.472920
$255$	7.62799	0.477684
$256$	15.1683	0.948021
$257$	−3.49725	−0.218152	−0.109076	−	0.994033i	$-0.534789\pi$
$257$	−3.49725	−0.218152	−0.109076	+	0.994033i	$0.534789\pi$
$258$	4.08340	0.254221
$259$	−17.4829	−1.08633
$260$	−1.76401	−0.109399
$261$	8.73456	0.540655
$262$	−34.0400	−2.10300
$263$	−5.23242	−0.322645	−0.161322	−	0.986902i	$-0.551576\pi$
$263$	−5.23242	−0.322645	−0.161322	+	0.986902i	$0.551576\pi$
$264$	7.30232	0.449427
$265$	−11.4986	−0.706351
$266$	0	0
$267$	3.14511	0.192477
$268$	6.85333	0.418634
$269$	15.8983	0.969339	0.484670	−	0.874697i	$-0.338940\pi$
$269$	15.8983	0.969339	0.484670	+	0.874697i	$0.338940\pi$
$270$	1.64661	0.100210
$271$	9.99579	0.607201	0.303600	−	0.952799i	$-0.401811\pi$
$271$	9.99579	0.607201	0.303600	+	0.952799i	$0.401811\pi$
$272$	−37.5043	−2.27403
$273$	−11.1096	−0.672382
$274$	29.0264	1.75355
$275$	−3.44134	−0.207520
$276$	2.75324	0.165725
$277$	4.08619	0.245515	0.122758	−	0.992437i	$-0.460826\pi$
$277$	4.08619	0.245515	0.122758	+	0.992437i	$0.460826\pi$
$278$	19.3222	1.15887
$279$	0.422654	0.0253036
$280$	−9.50605	−0.568095
$281$	11.6384	0.694289	0.347144	−	0.937812i	$-0.387151\pi$
$281$	11.6384	0.694289	0.347144	+	0.937812i	$0.387151\pi$
$282$	−1.11530	−0.0664151
$283$	4.35821	0.259069	0.129534	−	0.991575i	$-0.458652\pi$
$283$	4.35821	0.259069	0.129534	+	0.991575i	$0.458652\pi$
$284$	2.73995	0.162586
$285$	0	0
$286$	14.0523	0.830932
$287$	−23.7130	−1.39973
$288$	−3.85195	−0.226978
$289$	41.1863	2.42272
$290$	14.3824	0.844564
$291$	−2.00000	−0.117242
$292$	11.9398	0.698722
$293$	7.20233	0.420765	0.210382	−	0.977619i	$-0.432529\pi$
$293$	7.20233	0.420765	0.210382	+	0.977619i	$0.432529\pi$
$294$	21.5201	1.25508
$295$	8.53053	0.496667
$296$	8.28096	0.481321
$297$	−3.44134	−0.199687
$298$	−35.5090	−2.05698
$299$	−9.59855	−0.555098
$300$	0.711327	0.0410685
$301$	11.1096	0.640345
$302$	−30.1498	−1.73493
$303$	−2.01868	−0.115970
$304$	0	0
$305$	8.20233	0.469664
$306$	12.5603	0.718027
$307$	−16.2811	−0.929213	−0.464606	−	0.885517i	$-0.653804\pi$
$307$	−16.2811	−0.929213	−0.464606	+	0.885517i	$0.653804\pi$
$308$	−10.9664	−0.624867
$309$	−6.48898	−0.369145
$310$	0.695946	0.0395271
$311$	−4.07709	−0.231191	−0.115595	−	0.993296i	$-0.536878\pi$
$311$	−4.07709	−0.231191	−0.115595	+	0.993296i	$0.536878\pi$
$312$	5.26217	0.297911
$313$	−21.5553	−1.21838	−0.609189	−	0.793025i	$-0.708505\pi$
$313$	−21.5553	−1.21838	−0.609189	+	0.793025i	$0.708505\pi$
$314$	−18.8217	−1.06217
$315$	4.47988	0.252413
$316$	−8.62501	−0.485195
$317$	14.2668	0.801302	0.400651	−	0.916231i	$-0.368784\pi$
$317$	14.2668	0.801302	0.400651	+	0.916231i	$0.368784\pi$
$318$	−18.9337	−1.06175
$319$	−30.0585	−1.68296
$320$	3.49067	0.195134
$321$	−3.96145	−0.221107
$322$	28.5517	1.59112
$323$	0	0
$324$	0.711327	0.0395182
$325$	−2.47988	−0.137559
$326$	−13.5002	−0.747705
$327$	2.96803	0.164133
$328$	11.2319	0.620179
$329$	−3.03436	−0.167290
$330$	−5.66654	−0.311933
$331$	−23.9646	−1.31722	−0.658608	−	0.752486i	$-0.728854\pi$
$331$	−23.9646	−1.31722	−0.658608	+	0.752486i	$0.728854\pi$
$332$	−1.45007	−0.0795830
$333$	−3.90253	−0.213858
$334$	14.5628	0.796843
$335$	9.63457	0.526393
$336$	−22.0261	−1.20162
$337$	−32.6408	−1.77806	−0.889029	−	0.457851i	$-0.848619\pi$
$337$	−32.6408	−1.77806	−0.889029	+	0.457851i	$0.848619\pi$
$338$	−11.2796	−0.613529
$339$	8.71719	0.473453
$340$	5.42600	0.294266
$341$	−1.45449	−0.0787652
$342$	0	0
$343$	27.1899	1.46812
$344$	−5.26217	−0.283717
$345$	3.87057	0.208384
$346$	−28.8918	−1.55323
$347$	16.8291	0.903436	0.451718	−	0.892161i	$-0.350811\pi$
$347$	16.8291	0.903436	0.451718	+	0.892161i	$0.350811\pi$
$348$	6.21312	0.333058
$349$	2.46947	0.132188	0.0660939	−	0.997813i	$-0.478946\pi$
$349$	2.46947	0.132188	0.0660939	+	0.997813i	$0.478946\pi$
$350$	7.37662	0.394297
$351$	−2.47988	−0.132366
$352$	13.2559	0.706540
$353$	27.7653	1.47780	0.738900	−	0.673815i	$-0.235346\pi$
$353$	27.7653	1.47780	0.738900	+	0.673815i	$0.235346\pi$
$354$	14.0465	0.746561
$355$	3.85189	0.204437
$356$	2.23720	0.118571
$357$	34.1725	1.80860
$358$	−7.09508	−0.374986
$359$	−20.0490	−1.05814	−0.529072	−	0.848577i	$-0.677460\pi$
$359$	−20.0490	−1.05814	−0.529072	+	0.848577i	$0.677460\pi$
$360$	−2.12194	−0.111836
$361$	0	0
$362$	−10.4459	−0.549023
$363$	0.842790	0.0442350
$364$	−7.90253	−0.414205
$365$	16.7852	0.878578
$366$	13.5061	0.705973
$367$	−6.67481	−0.348422	−0.174211	−	0.984708i	$-0.555738\pi$
$367$	−6.67481	−0.348422	−0.174211	+	0.984708i	$0.555738\pi$
$368$	−19.0303	−0.992023
$369$	−5.29322	−0.275554
$370$	−6.42595	−0.334069
$371$	−51.5122	−2.67438
$372$	0.300645	0.0155877
$373$	12.4380	0.644014	0.322007	−	0.946737i	$-0.395643\pi$
$373$	12.4380	0.644014	0.322007	+	0.946737i	$0.395643\pi$
$374$	−43.2243	−2.23508
$375$	1.00000	0.0516398
$376$	1.43726	0.0741208
$377$	−21.6607	−1.11558
$378$	7.37662	0.379412
$379$	−21.3994	−1.09921	−0.549607	−	0.835423i	$-0.685223\pi$
$379$	−21.3994	−1.09921	−0.549607	+	0.835423i	$0.685223\pi$
$380$	0	0
$381$	4.57735	0.234505
$382$	1.39270	0.0712566
$383$	−10.7081	−0.547158	−0.273579	−	0.961850i	$-0.588207\pi$
$383$	−10.7081	−0.547158	−0.273579	+	0.961850i	$0.588207\pi$
$384$	13.4517	0.686453
$385$	−15.4168	−0.785711
$386$	21.7036	1.10468
$387$	2.47988	0.126059
$388$	−1.42265	−0.0722243
$389$	−3.50933	−0.177930	−0.0889650	−	0.996035i	$-0.528356\pi$
$389$	−3.50933	−0.177930	−0.0889650	+	0.996035i	$0.528356\pi$
$390$	−4.08340	−0.206771
$391$	29.5247	1.49313
$392$	−27.7324	−1.40070
$393$	−20.6728	−1.04280
$394$	11.3816	0.573395
$395$	−12.1252	−0.610087
$396$	−2.44791	−0.123012
$397$	31.1990	1.56583	0.782916	−	0.622128i	$-0.213732\pi$
$397$	31.1990	1.56583	0.782916	+	0.622128i	$0.213732\pi$
$398$	−22.0337	−1.10445
$399$	0	0
$400$	−4.91667	−0.245833
$401$	19.7532	0.986429	0.493214	−	0.869908i	$-0.335822\pi$
$401$	19.7532	0.986429	0.493214	+	0.869908i	$0.335822\pi$
$402$	15.8644	0.791244
$403$	−1.04813	−0.0522111
$404$	−1.43594	−0.0714408
$405$	1.00000	0.0496904
$406$	64.4315	3.19768
$407$	13.4299	0.665697
$408$	−16.1862	−0.801335
$409$	2.13902	0.105768	0.0528838	−	0.998601i	$-0.483159\pi$
$409$	2.13902	0.105768	0.0528838	+	0.998601i	$0.483159\pi$
$410$	−8.71588	−0.430446
$411$	17.6280	0.869525
$412$	−4.61578	−0.227403
$413$	38.2158	1.88047
$414$	6.37332	0.313232
$415$	−2.03855	−0.100068
$416$	9.55238	0.468344
$417$	11.7346	0.574644
$418$	0	0
$419$	−5.70341	−0.278630	−0.139315	−	0.990248i	$-0.544490\pi$
$419$	−5.70341	−0.278630	−0.139315	+	0.990248i	$0.544490\pi$
$420$	3.18666	0.155493
$421$	−39.0530	−1.90333	−0.951664	−	0.307140i	$-0.900628\pi$
$421$	−39.0530	−1.90333	−0.951664	+	0.307140i	$0.900628\pi$
$422$	24.2879	1.18232
$423$	−0.677330	−0.0329329
$424$	24.3993	1.18493
$425$	7.62799	0.370012
$426$	6.34256	0.307298
$427$	36.7455	1.77824
$428$	−2.81789	−0.136208
$429$	8.53410	0.412030
$430$	4.08340	0.196919
$431$	−1.73756	−0.0836955	−0.0418477	−	0.999124i	$-0.513324\pi$
$431$	−1.73756	−0.0836955	−0.0418477	+	0.999124i	$0.513324\pi$
$432$	−4.91667	−0.236553
$433$	−23.6312	−1.13564	−0.567821	−	0.823152i	$-0.692213\pi$
$433$	−23.6312	−1.13564	−0.567821	+	0.823152i	$0.692213\pi$
$434$	3.11775	0.149657
$435$	8.73456	0.418790
$436$	2.11124	0.101110
$437$	0	0
$438$	27.6387	1.32063
$439$	3.16929	0.151262	0.0756310	−	0.997136i	$-0.475903\pi$
$439$	3.16929	0.151262	0.0756310	+	0.997136i	$0.475903\pi$
$440$	7.30232	0.348124
$441$	13.0693	0.622349
$442$	−31.1481	−1.48157
$443$	23.1833	1.10147	0.550736	−	0.834680i	$-0.314347\pi$
$443$	23.1833	1.10147	0.550736	+	0.834680i	$0.314347\pi$
$444$	−2.77598	−0.131742
$445$	3.14511	0.149092
$446$	3.76800	0.178420
$447$	−21.5649	−1.01998
$448$	15.6378	0.738816
$449$	−13.2505	−0.625328	−0.312664	−	0.949864i	$-0.601221\pi$
$449$	−13.2505	−0.625328	−0.312664	+	0.949864i	$0.601221\pi$
$450$	1.64661	0.0776220
$451$	18.2158	0.857746
$452$	6.20077	0.291660
$453$	−18.3102	−0.860289
$454$	6.90742	0.324181
$455$	−11.1096	−0.520825
$456$	0	0
$457$	4.13077	0.193229	0.0966146	−	0.995322i	$-0.469199\pi$
$457$	4.13077	0.193229	0.0966146	+	0.995322i	$0.469199\pi$
$458$	−43.2633	−2.02156
$459$	7.62799	0.356044
$460$	2.75324	0.128370
$461$	21.8585	1.01805	0.509026	−	0.860751i	$-0.330006\pi$
$461$	21.8585	1.01805	0.509026	+	0.860751i	$0.330006\pi$
$462$	−25.3854	−1.18104
$463$	30.9461	1.43819	0.719094	−	0.694913i	$-0.244557\pi$
$463$	30.9461	1.43819	0.719094	+	0.694913i	$0.244557\pi$
$464$	−42.9449	−1.99367
$465$	0.422654	0.0196001
$466$	−9.15926	−0.424295
$467$	0.394259	0.0182441	0.00912207	−	0.999958i	$-0.497096\pi$
$467$	0.394259	0.0182441	0.00912207	+	0.999958i	$0.497096\pi$
$468$	−1.76401	−0.0815412
$469$	43.1617	1.99302
$470$	−1.11530	−0.0514449
$471$	−11.4305	−0.526692
$472$	−18.1013	−0.833180
$473$	−8.53410	−0.392398
$474$	−19.9656	−0.917048
$475$	0	0
$476$	24.3078	1.11415
$477$	−11.4986	−0.526483
$478$	−11.2777	−0.515828
$479$	−7.04238	−0.321774	−0.160887	−	0.986973i	$-0.551436\pi$
$479$	−7.04238	−0.321774	−0.160887	+	0.986973i	$0.551436\pi$
$480$	−3.85195	−0.175817
$481$	9.67782	0.441271
$482$	−24.4397	−1.11320
$483$	17.3397	0.788983
$484$	0.599499	0.0272499
$485$	−2.00000	−0.0908153
$486$	1.64661	0.0746918
$487$	−0.689174	−0.0312295	−0.0156147	−	0.999878i	$-0.504971\pi$
$487$	−0.689174	−0.0312295	−0.0156147	+	0.999878i	$0.504971\pi$
$488$	−17.4049	−0.787882
$489$	−8.19876	−0.370761
$490$	21.5201	0.972179
$491$	9.09472	0.410439	0.205219	−	0.978716i	$-0.434209\pi$
$491$	9.09472	0.410439	0.205219	+	0.978716i	$0.434209\pi$
$492$	−3.76521	−0.169749
$493$	66.6272	3.00074
$494$	0	0
$495$	−3.44134	−0.154677
$496$	−2.07805	−0.0933071
$497$	17.2560	0.774037
$498$	−3.35669	−0.150417
$499$	−23.0808	−1.03324	−0.516619	−	0.856215i	$-0.672810\pi$
$499$	−23.0808	−1.03324	−0.516619	+	0.856215i	$0.672810\pi$
$500$	0.711327	0.0318115
$501$	8.84413	0.395126
$502$	−7.90793	−0.352948
$503$	−21.1965	−0.945103	−0.472552	−	0.881303i	$-0.656667\pi$
$503$	−21.1965	−0.945103	−0.472552	+	0.881303i	$0.656667\pi$
$504$	−9.50605	−0.423433
$505$	−2.01868	−0.0898302
$506$	−21.9327	−0.975029
$507$	−6.85019	−0.304228
$508$	3.25599	0.144461
$509$	−18.2530	−0.809049	−0.404525	−	0.914527i	$-0.632563\pi$
$509$	−18.2530	−0.809049	−0.404525	+	0.914527i	$0.632563\pi$
$510$	12.5603	0.556181
$511$	75.1957	3.32646
$512$	−1.92701	−0.0851627
$513$	0	0
$514$	−5.75861	−0.254001
$515$	−6.48898	−0.285938
$516$	1.76401	0.0776560
$517$	2.33092	0.102514
$518$	−28.7875	−1.26485
$519$	−17.5462	−0.770193
$520$	5.26217	0.230761
$521$	34.4874	1.51092	0.755461	−	0.655194i	$-0.227413\pi$
$521$	34.4874	1.51092	0.755461	+	0.655194i	$0.227413\pi$
$522$	14.3824	0.629501
$523$	−16.1399	−0.705747	−0.352874	−	0.935671i	$-0.614795\pi$
$523$	−16.1399	−0.705747	−0.352874	+	0.935671i	$0.614795\pi$
$524$	−14.7051	−0.642395
$525$	4.47988	0.195518
$526$	−8.61576	−0.375665
$527$	3.22400	0.140440
$528$	16.9199	0.736344
$529$	−8.01871	−0.348639
$530$	−18.9337	−0.822425
$531$	8.53053	0.370193
$532$	0	0
$533$	13.1266	0.568574
$534$	5.17877	0.224107
$535$	−3.96145	−0.171269
$536$	−20.4440	−0.883047
$537$	−4.30890	−0.185943
$538$	26.1784	1.12863
$539$	−44.9759	−1.93725
$540$	0.711327	0.0306106
$541$	16.9327	0.727993	0.363996	−	0.931400i	$-0.381412\pi$
$541$	16.9327	0.727993	0.363996	+	0.931400i	$0.381412\pi$
$542$	16.4592	0.706982
$543$	−6.34387	−0.272242
$544$	−29.3827	−1.25977
$545$	2.96803	0.127137
$546$	−18.2931	−0.782874
$547$	29.3743	1.25595	0.627977	−	0.778232i	$-0.283883\pi$
$547$	29.3743	1.25595	0.627977	+	0.778232i	$0.283883\pi$
$548$	12.5393	0.535651
$549$	8.20233	0.350067
$550$	−5.66654	−0.241622
$551$	0	0
$552$	−8.21312	−0.349574
$553$	−54.3196	−2.30991
$554$	6.72836	0.285861
$555$	−3.90253	−0.165653
$556$	8.34710	0.353996
$557$	8.58644	0.363819	0.181910	−	0.983315i	$-0.441772\pi$
$557$	8.58644	0.363819	0.181910	+	0.983315i	$0.441772\pi$
$558$	0.695946	0.0294617
$559$	−6.14981	−0.260109
$560$	−22.0261	−0.930772
$561$	−26.2505	−1.10830
$562$	19.1639	0.808381
$563$	−2.59685	−0.109444	−0.0547221	−	0.998502i	$-0.517427\pi$
$563$	−2.59685	−0.109444	−0.0547221	+	0.998502i	$0.517427\pi$
$564$	−0.481803	−0.0202876
$565$	8.71719	0.366735
$566$	7.17627	0.301641
$567$	4.47988	0.188137
$568$	−8.17348	−0.342952
$569$	33.8768	1.42019	0.710094	−	0.704107i	$-0.248652\pi$
$569$	33.8768	1.42019	0.710094	+	0.704107i	$0.248652\pi$
$570$	0	0
$571$	−10.6731	−0.446657	−0.223329	−	0.974743i	$-0.571692\pi$
$571$	−10.6731	−0.446657	−0.223329	+	0.974743i	$0.571692\pi$
$572$	6.07053	0.253822
$573$	0.845796	0.0353336
$574$	−39.0461	−1.62975
$575$	3.87057	0.161414
$576$	3.49067	0.145445
$577$	−11.6607	−0.485440	−0.242720	−	0.970096i	$-0.578040\pi$
$577$	−11.6607	−0.485440	−0.242720	+	0.970096i	$0.578040\pi$
$578$	67.8178	2.82085
$579$	13.1808	0.547774
$580$	6.21312	0.257986
$581$	−9.13244	−0.378877
$582$	−3.29322	−0.136508
$583$	39.5704	1.63884
$584$	−35.6172	−1.47385
$585$	−2.47988	−0.102530
$586$	11.8594	0.489909
$587$	40.2725	1.66222	0.831112	−	0.556105i	$-0.187705\pi$
$587$	40.2725	1.66222	0.831112	+	0.556105i	$0.187705\pi$
$588$	9.29656	0.383384
$589$	0	0
$590$	14.0465	0.578284
$591$	6.91212	0.284327
$592$	19.1875	0.788600
$593$	−14.1026	−0.579125	−0.289562	−	0.957159i	$-0.593510\pi$
$593$	−14.1026	−0.579125	−0.289562	+	0.957159i	$0.593510\pi$
$594$	−5.66654	−0.232501
$595$	34.1725	1.40094
$596$	−15.3397	−0.628338
$597$	−13.3812	−0.547657
$598$	−15.8051	−0.646317
$599$	10.4871	0.428491	0.214246	−	0.976780i	$-0.431271\pi$
$599$	10.4871	0.428491	0.214246	+	0.976780i	$0.431271\pi$
$600$	−2.12194	−0.0866280
$601$	−21.0718	−0.859539	−0.429769	−	0.902939i	$-0.641405\pi$
$601$	−21.0718	−0.859539	−0.429769	+	0.902939i	$0.641405\pi$
$602$	18.2931	0.745573
$603$	9.63457	0.392350
$604$	−13.0245	−0.529961
$605$	0.842790	0.0342643
$606$	−3.32398	−0.135028
$607$	22.2759	0.904149	0.452074	−	0.891980i	$-0.350684\pi$
$607$	22.2759	0.904149	0.452074	+	0.891980i	$0.350684\pi$
$608$	0	0
$609$	39.1298	1.58562
$610$	13.5061	0.546844
$611$	1.67970	0.0679533
$612$	5.42600	0.219333
$613$	−17.8953	−0.722785	−0.361393	−	0.932414i	$-0.617699\pi$
$613$	−17.8953	−0.722785	−0.361393	+	0.932414i	$0.617699\pi$
$614$	−26.8087	−1.08191
$615$	−5.29322	−0.213443
$616$	32.7135	1.31806
$617$	17.6312	0.709806	0.354903	−	0.934903i	$-0.384514\pi$
$617$	17.6312	0.709806	0.354903	+	0.934903i	$0.384514\pi$
$618$	−10.6848	−0.429806
$619$	−49.2003	−1.97753	−0.988763	−	0.149490i	$-0.952237\pi$
$619$	−49.2003	−1.97753	−0.988763	+	0.149490i	$0.952237\pi$
$620$	0.300645	0.0120742
$621$	3.87057	0.155321
$622$	−6.71338	−0.269182
$623$	14.0897	0.564492
$624$	12.1927	0.488101
$625$	1.00000	0.0400000
$626$	−35.4932	−1.41859
$627$	0	0
$628$	−8.13085	−0.324456
$629$	−29.7685	−1.18695
$630$	7.37662	0.293892
$631$	−33.3185	−1.32639	−0.663194	−	0.748448i	$-0.730800\pi$
$631$	−33.3185	−1.32639	−0.663194	+	0.748448i	$0.730800\pi$
$632$	25.7291	1.02345
$633$	14.7502	0.586269
$634$	23.4918	0.932980
$635$	4.57735	0.181646
$636$	−8.17924	−0.324328
$637$	−32.4104	−1.28415
$638$	−49.4947	−1.95951
$639$	3.85189	0.152378
$640$	13.4517	0.531724
$641$	−13.2222	−0.522245	−0.261123	−	0.965306i	$-0.584093\pi$
$641$	−13.2222	−0.522245	−0.261123	+	0.965306i	$0.584093\pi$
$642$	−6.52297	−0.257441
$643$	−1.90253	−0.0750286	−0.0375143	−	0.999296i	$-0.511944\pi$
$643$	−1.90253	−0.0750286	−0.0375143	+	0.999296i	$0.511944\pi$
$644$	12.3342	0.486035
$645$	2.47988	0.0976452
$646$	0	0
$647$	27.2141	1.06989	0.534947	−	0.844885i	$-0.320331\pi$
$647$	27.2141	1.06989	0.534947	+	0.844885i	$0.320331\pi$
$648$	−2.12194	−0.0833578
$649$	−29.3564	−1.15234
$650$	−4.08340	−0.160164
$651$	1.89344	0.0742097
$652$	−5.83200	−0.228399
$653$	−43.6980	−1.71004	−0.855018	−	0.518599i	$-0.826454\pi$
$653$	−43.6980	−1.71004	−0.855018	+	0.518599i	$0.826454\pi$
$654$	4.88720	0.191104
$655$	−20.6728	−0.807752
$656$	26.0250	1.01611
$657$	16.7852	0.654853
$658$	−4.99640	−0.194780
$659$	6.87344	0.267751	0.133876	−	0.990998i	$-0.457258\pi$
$659$	6.87344	0.267751	0.133876	+	0.990998i	$0.457258\pi$
$660$	−2.44791	−0.0952849
$661$	−37.2982	−1.45073	−0.725367	−	0.688363i	$-0.758330\pi$
$661$	−37.2982	−1.45073	−0.725367	+	0.688363i	$0.758330\pi$
$662$	−39.4604	−1.53367
$663$	−18.9165	−0.734657
$664$	4.32568	0.167869
$665$	0	0
$666$	−6.42595	−0.249001
$667$	33.8077	1.30904
$668$	6.29106	0.243409
$669$	2.28834	0.0884722
$670$	15.8644	0.612895
$671$	−28.2270	−1.08969
$672$	−17.2563	−0.665676
$673$	−50.6185	−1.95120	−0.975601	−	0.219553i	$-0.929540\pi$
$673$	−50.6185	−1.95120	−0.975601	+	0.219553i	$0.929540\pi$
$674$	−53.7467	−2.07024
$675$	1.00000	0.0384900
$676$	−4.87273	−0.187413
$677$	−33.8725	−1.30182	−0.650912	−	0.759153i	$-0.725613\pi$
$677$	−33.8725	−1.30182	−0.650912	+	0.759153i	$0.725613\pi$
$678$	14.3538	0.551255
$679$	−8.95976	−0.343844
$680$	−16.1862	−0.620711
$681$	4.19493	0.160750
$682$	−2.39498	−0.0917087
$683$	−47.0846	−1.80164	−0.900822	−	0.434190i	$-0.857035\pi$
$683$	−47.0846	−1.80164	−0.900822	+	0.434190i	$0.857035\pi$
$684$	0	0
$685$	17.6280	0.673531
$686$	44.7711	1.70937
$687$	−26.2742	−1.00242
$688$	−12.1927	−0.464844
$689$	28.5151	1.08634
$690$	6.37332	0.242628
$691$	3.91269	0.148846	0.0744228	−	0.997227i	$-0.476289\pi$
$691$	3.91269	0.148846	0.0744228	+	0.997227i	$0.476289\pi$
$692$	−12.4811	−0.474460
$693$	−15.4168	−0.585635
$694$	27.7111	1.05190
$695$	11.7346	0.445117
$696$	−18.5342	−0.702538
$697$	−40.3767	−1.52938
$698$	4.06626	0.153910
$699$	−5.56250	−0.210393
$700$	3.18666	0.120444
$701$	13.2070	0.498823	0.249411	−	0.968398i	$-0.419763\pi$
$701$	13.2070	0.498823	0.249411	+	0.968398i	$0.419763\pi$
$702$	−4.08340	−0.154118
$703$	0	0
$704$	−12.0126	−0.452741
$705$	−0.677330	−0.0255097
$706$	45.7187	1.72065
$707$	−9.04345	−0.340114
$708$	6.06799	0.228049
$709$	−17.9971	−0.675896	−0.337948	−	0.941165i	$-0.609733\pi$
$709$	−17.9971	−0.675896	−0.337948	+	0.941165i	$0.609733\pi$
$710$	6.34256	0.238032
$711$	−12.1252	−0.454732
$712$	−6.67374	−0.250109
$713$	1.63591	0.0612653
$714$	56.2688	2.10581
$715$	8.53410	0.319157
$716$	−3.06503	−0.114546
$717$	−6.84901	−0.255781
$718$	−33.0128	−1.23203
$719$	−12.4782	−0.465358	−0.232679	−	0.972554i	$-0.574749\pi$
$719$	−12.4782	−0.465358	−0.232679	+	0.972554i	$0.574749\pi$
$720$	−4.91667	−0.183233
$721$	−29.0698	−1.08262
$722$	0	0
$723$	−14.8424	−0.551996
$724$	−4.51256	−0.167708
$725$	8.73456	0.324393
$726$	1.38775	0.0515041
$727$	−43.4131	−1.61010	−0.805051	−	0.593206i	$-0.797862\pi$
$727$	−43.4131	−1.61010	−0.805051	+	0.593206i	$0.797862\pi$
$728$	23.5739	0.873706
$729$	1.00000	0.0370370
$730$	27.6387	1.02295
$731$	18.9165	0.699653
$732$	5.83454	0.215651
$733$	−28.5740	−1.05540	−0.527702	−	0.849430i	$-0.676946\pi$
$733$	−28.5740	−1.05540	−0.527702	+	0.849430i	$0.676946\pi$
$734$	−10.9908	−0.405678
$735$	13.0693	0.482070
$736$	−14.9092	−0.549562
$737$	−33.1558	−1.22131
$738$	−8.71588	−0.320836
$739$	−9.23538	−0.339729	−0.169864	−	0.985467i	$-0.554333\pi$
$739$	−9.23538	−0.339729	−0.169864	+	0.985467i	$0.554333\pi$
$740$	−2.77598	−0.102047
$741$	0	0
$742$	−84.8205	−3.11386
$743$	5.03749	0.184808	0.0924038	−	0.995722i	$-0.470545\pi$
$743$	5.03749	0.184808	0.0924038	+	0.995722i	$0.470545\pi$
$744$	−0.896847	−0.0328800
$745$	−21.5649	−0.790076
$746$	20.4805	0.749844
$747$	−2.03855	−0.0745865
$748$	−18.6727	−0.682741
$749$	−17.7468	−0.648456
$750$	1.64661	0.0601257
$751$	−12.8273	−0.468076	−0.234038	−	0.972227i	$-0.575194\pi$
$751$	−12.8273	−0.468076	−0.234038	+	0.972227i	$0.575194\pi$
$752$	3.33021	0.121440
$753$	−4.80255	−0.175015
$754$	−35.6667	−1.29890
$755$	−18.3102	−0.666377
$756$	3.18666	0.115898
$757$	25.8851	0.940809	0.470404	−	0.882451i	$-0.344108\pi$
$757$	25.8851	0.940809	0.470404	+	0.882451i	$0.344108\pi$
$758$	−35.2365	−1.27985
$759$	−13.3199	−0.483483
$760$	0	0
$761$	−28.9722	−1.05024	−0.525121	−	0.851028i	$-0.675980\pi$
$761$	−28.9722	−1.05024	−0.525121	+	0.851028i	$0.675980\pi$
$762$	7.53711	0.273041
$763$	13.2964	0.481363
$764$	0.601637	0.0217665
$765$	7.62799	0.275791
$766$	−17.6321	−0.637072
$767$	−21.1547	−0.763852
$768$	15.1683	0.547340
$769$	5.45380	0.196669	0.0983345	−	0.995153i	$-0.468649\pi$
$769$	5.45380	0.196669	0.0983345	+	0.995153i	$0.468649\pi$
$770$	−25.3854	−0.914827
$771$	−3.49725	−0.125950
$772$	9.37584	0.337444
$773$	47.0119	1.69090	0.845451	−	0.534053i	$-0.179332\pi$
$773$	47.0119	1.69090	0.845451	+	0.534053i	$0.179332\pi$
$774$	4.08340	0.146775
$775$	0.422654	0.0151822
$776$	4.24389	0.152347
$777$	−17.4829	−0.627195
$778$	−5.77850	−0.207169
$779$	0	0
$780$	−1.76401	−0.0631615
$781$	−13.2556	−0.474324
$782$	48.6156	1.73849
$783$	8.73456	0.312148
$784$	−64.2576	−2.29491
$785$	−11.4305	−0.407974
$786$	−34.0400	−1.21417
$787$	−3.86923	−0.137923	−0.0689616	−	0.997619i	$-0.521969\pi$
$787$	−3.86923	−0.137923	−0.0689616	+	0.997619i	$0.521969\pi$
$788$	4.91678	0.175153
$789$	−5.23242	−0.186279
$790$	−19.9656	−0.710343
$791$	39.0520	1.38853
$792$	7.30232	0.259477
$793$	−20.3408	−0.722323
$794$	51.3726	1.82314
$795$	−11.4986	−0.407812
$796$	−9.51843	−0.337372
$797$	12.6814	0.449198	0.224599	−	0.974451i	$-0.427893\pi$
$797$	12.6814	0.449198	0.224599	+	0.974451i	$0.427893\pi$
$798$	0	0
$799$	−5.16667	−0.182784
$800$	−3.85195	−0.136187
$801$	3.14511	0.111127
$802$	32.5259	1.14853
$803$	−57.7635	−2.03843
$804$	6.85333	0.241698
$805$	17.3397	0.611143
$806$	−1.72586	−0.0607909
$807$	15.8983	0.559648
$808$	4.28353	0.150694
$809$	33.2439	1.16879	0.584397	−	0.811468i	$-0.301331\pi$
$809$	33.2439	1.16879	0.584397	+	0.811468i	$0.301331\pi$
$810$	1.64661	0.0578560
$811$	2.86530	0.100614	0.0503072	−	0.998734i	$-0.483980\pi$
$811$	2.86530	0.100614	0.0503072	+	0.998734i	$0.483980\pi$
$812$	27.8341	0.976784
$813$	9.99579	0.350568
$814$	22.1139	0.775091
$815$	−8.19876	−0.287190
$816$	−37.5043	−1.31291
$817$	0	0
$818$	3.52213	0.123148
$819$	−11.1096	−0.388200
$820$	−3.76521	−0.131487
$821$	−14.3770	−0.501762	−0.250881	−	0.968018i	$-0.580720\pi$
$821$	−14.3770	−0.501762	−0.250881	+	0.968018i	$0.580720\pi$
$822$	29.0264	1.01241
$823$	56.7277	1.97740	0.988702	−	0.149893i	$-0.0478931\pi$
$823$	56.7277	1.97740	0.988702	+	0.149893i	$0.0478931\pi$
$824$	13.7692	0.479674
$825$	−3.44134	−0.119812
$826$	62.9265	2.18949
$827$	−20.1954	−0.702263	−0.351131	−	0.936326i	$-0.614203\pi$
$827$	−20.1954	−0.702263	−0.351131	+	0.936326i	$0.614203\pi$
$828$	2.75324	0.0956817
$829$	−38.0954	−1.32311	−0.661554	−	0.749898i	$-0.730103\pi$
$829$	−38.0954	−1.32311	−0.661554	+	0.749898i	$0.730103\pi$
$830$	−3.35669	−0.116512
$831$	4.08619	0.141748
$832$	−8.65645	−0.300108
$833$	99.6928	3.45415
$834$	19.3222	0.669075
$835$	8.84413	0.306064
$836$	0	0
$837$	0.422654	0.0146090
$838$	−9.39130	−0.324417
$839$	−38.2640	−1.32102	−0.660511	−	0.750817i	$-0.729660\pi$
$839$	−38.2640	−1.32102	−0.660511	+	0.750817i	$0.729660\pi$
$840$	−9.50605	−0.327990
$841$	47.2925	1.63078
$842$	−64.3052	−2.21610
$843$	11.6384	0.400848
$844$	10.4922	0.361158
$845$	−6.85019	−0.235654
$846$	−1.11530	−0.0383448
$847$	3.77560	0.129731
$848$	56.5346	1.94141
$849$	4.35821	0.149573
$850$	12.5603	0.430816
$851$	−15.1050	−0.517794
$852$	2.73995	0.0938691
$853$	3.43393	0.117576	0.0587878	−	0.998271i	$-0.481276\pi$
$853$	3.43393	0.117576	0.0587878	+	0.998271i	$0.481276\pi$
$854$	60.5055	2.07046
$855$	0	0
$856$	8.40598	0.287311
$857$	27.3260	0.933439	0.466719	−	0.884405i	$-0.345436\pi$
$857$	27.3260	0.933439	0.466719	+	0.884405i	$0.345436\pi$
$858$	14.0523	0.479739
$859$	−44.1207	−1.50538	−0.752689	−	0.658376i	$-0.771244\pi$
$859$	−44.1207	−1.50538	−0.752689	+	0.658376i	$0.771244\pi$
$860$	1.76401	0.0601521
$861$	−23.7130	−0.808137
$862$	−2.86109	−0.0974491
$863$	41.3721	1.40832	0.704161	−	0.710040i	$-0.251323\pi$
$863$	41.3721	1.40832	0.704161	+	0.710040i	$0.251323\pi$
$864$	−3.85195	−0.131046
$865$	−17.5462	−0.596589
$866$	−38.9114	−1.32226
$867$	41.1863	1.39876
$868$	1.34685	0.0457152
$869$	41.7270	1.41549
$870$	14.3824	0.487610
$871$	−23.8926	−0.809570
$872$	−6.29800	−0.213277
$873$	−2.00000	−0.0676897
$874$	0	0
$875$	4.47988	0.151448
$876$	11.9398	0.403407
$877$	−56.6303	−1.91227	−0.956134	−	0.292929i	$-0.905370\pi$
$877$	−56.6303	−1.91227	−0.956134	+	0.292929i	$0.905370\pi$
$878$	5.21859	0.176119
$879$	7.20233	0.242929
$880$	16.9199	0.570370
$881$	−1.34253	−0.0452311	−0.0226156	−	0.999744i	$-0.507199\pi$
$881$	−1.34253	−0.0452311	−0.0226156	+	0.999744i	$0.507199\pi$
$882$	21.5201	0.724619
$883$	26.6839	0.897985	0.448993	−	0.893536i	$-0.351783\pi$
$883$	26.6839	0.897985	0.448993	+	0.893536i	$0.351783\pi$
$884$	−13.4558	−0.452568
$885$	8.53053	0.286751
$886$	38.1739	1.28248
$887$	−27.7758	−0.932618	−0.466309	−	0.884622i	$-0.654417\pi$
$887$	−27.7758	−0.932618	−0.466309	+	0.884622i	$0.654417\pi$
$888$	8.28096	0.277891
$889$	20.5060	0.687748
$890$	5.17877	0.173593
$891$	−3.44134	−0.115289
$892$	1.62776	0.0545013
$893$	0	0
$894$	−35.5090	−1.18760
$895$	−4.30890	−0.144031
$896$	60.2619	2.01321
$897$	−9.59855	−0.320486
$898$	−21.8184	−0.728088
$899$	3.69169	0.123125
$900$	0.711327	0.0237109
$901$	−87.7110	−2.92208
$902$	29.9942	0.998699
$903$	11.1096	0.369703
$904$	−18.4974	−0.615214
$905$	−6.34387	−0.210877
$906$	−30.1498	−1.00166
$907$	−7.39198	−0.245447	−0.122723	−	0.992441i	$-0.539163\pi$
$907$	−7.39198	−0.245447	−0.122723	+	0.992441i	$0.539163\pi$
$908$	2.98397	0.0990264
$909$	−2.01868	−0.0669554
$910$	−18.2931	−0.606412
$911$	−13.3084	−0.440926	−0.220463	−	0.975395i	$-0.570757\pi$
$911$	−13.3084	−0.440926	−0.220463	+	0.975395i	$0.570757\pi$
$912$	0	0
$913$	7.01532	0.232173
$914$	6.80177	0.224982
$915$	8.20233	0.271161
$916$	−18.6895	−0.617519
$917$	−92.6115	−3.05830
$918$	12.5603	0.414553
$919$	−27.8298	−0.918022	−0.459011	−	0.888431i	$-0.651796\pi$
$919$	−27.8298	−0.918022	−0.459011	+	0.888431i	$0.651796\pi$
$920$	−8.21312	−0.270779
$921$	−16.2811	−0.536481
$922$	35.9924	1.18535
$923$	−9.55222	−0.314415
$924$	−10.9664	−0.360767
$925$	−3.90253	−0.128315
$926$	50.9562	1.67452
$927$	−6.48898	−0.213126
$928$	−33.6451	−1.10445
$929$	6.34215	0.208079	0.104040	−	0.994573i	$-0.466823\pi$
$929$	6.34215	0.208079	0.104040	+	0.994573i	$0.466823\pi$
$930$	0.695946	0.0228210
$931$	0	0
$932$	−3.95675	−0.129608
$933$	−4.07709	−0.133478
$934$	0.649192	0.0212422
$935$	−26.2505	−0.858483
$936$	5.26217	0.171999
$937$	−43.9739	−1.43656	−0.718282	−	0.695752i	$-0.755071\pi$
$937$	−43.9739	−1.43656	−0.718282	+	0.695752i	$0.755071\pi$
$938$	71.0706	2.32054
$939$	−21.5553	−0.703431
$940$	−0.481803	−0.0157147
$941$	−15.9457	−0.519813	−0.259907	−	0.965634i	$-0.583692\pi$
$941$	−15.9457	−0.519813	−0.259907	+	0.965634i	$0.583692\pi$
$942$	−18.8217	−0.613243
$943$	−20.4878	−0.667174
$944$	−41.9418	−1.36509
$945$	4.47988	0.145731
$946$	−14.0523	−0.456881
$947$	−3.10574	−0.100923	−0.0504615	−	0.998726i	$-0.516069\pi$
$947$	−3.10574	−0.100923	−0.0504615	+	0.998726i	$0.516069\pi$
$948$	−8.62501	−0.280127
$949$	−41.6253	−1.35121
$950$	0	0
$951$	14.2668	0.462632
$952$	−72.5121	−2.35013
$953$	20.5256	0.664891	0.332445	−	0.943122i	$-0.392126\pi$
$953$	20.5256	0.664891	0.332445	+	0.943122i	$0.392126\pi$
$954$	−18.9337	−0.613000
$955$	0.845796	0.0273693
$956$	−4.87188	−0.157568
$957$	−30.0585	−0.971655
$958$	−11.5961	−0.374651
$959$	78.9713	2.55012
$960$	3.49067	0.112661
$961$	−30.8214	−0.994238
$962$	15.9356	0.513784
$963$	−3.96145	−0.127656
$964$	−10.5578	−0.340044
$965$	13.1808	0.424304
$966$	28.5517	0.918636
$967$	24.8226	0.798240	0.399120	−	0.916899i	$-0.369316\pi$
$967$	24.8226	0.798240	0.399120	+	0.916899i	$0.369316\pi$
$968$	−1.78835	−0.0574798
$969$	0	0
$970$	−3.29322	−0.105739
$971$	36.5997	1.17454	0.587271	−	0.809391i	$-0.300202\pi$
$971$	36.5997	1.17454	0.587271	+	0.809391i	$0.300202\pi$
$972$	0.711327	0.0228158
$973$	52.5694	1.68530
$974$	−1.13480	−0.0363614
$975$	−2.47988	−0.0794197
$976$	−40.3282	−1.29087
$977$	−31.6228	−1.01170	−0.505851	−	0.862621i	$-0.668822\pi$
$977$	−31.6228	−1.01170	−0.505851	+	0.862621i	$0.668822\pi$
$978$	−13.5002	−0.431688
$979$	−10.8234	−0.345916
$980$	9.29656	0.296968
$981$	2.96803	0.0947620
$982$	14.9755	0.477886
$983$	−45.7608	−1.45954	−0.729771	−	0.683692i	$-0.760373\pi$
$983$	−45.7608	−1.45954	−0.729771	+	0.683692i	$0.760373\pi$
$984$	11.2319	0.358060
$985$	6.91212	0.220238
$986$	109.709	3.49385
$987$	−3.03436	−0.0965846
$988$	0	0
$989$	9.59855	0.305216
$990$	−5.66654	−0.180094
$991$	−26.4112	−0.838981	−0.419490	−	0.907760i	$-0.637791\pi$
$991$	−26.4112	−0.838981	−0.419490	+	0.907760i	$0.637791\pi$
$992$	−1.62804	−0.0516904
$993$	−23.9646	−0.760495
$994$	28.4139	0.901234
$995$	−13.3812	−0.424214
$996$	−1.45007	−0.0459473
$997$	−41.1562	−1.30343	−0.651714	−	0.758465i	$-0.725950\pi$
$997$	−41.1562	−1.30343	−0.651714	+	0.758465i	$0.725950\pi$
$998$	−38.0051	−1.20303
$999$	−3.90253	−0.123471

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5415.2.a.z.1.4		5
19.8	odd	6		285.2.i.f.121.4	yes	10
19.12	odd	6		285.2.i.f.106.4	✓	10
19.18	odd	2		5415.2.a.y.1.2		5
57.8	even	6		855.2.k.i.406.2		10
57.50	even	6		855.2.k.i.676.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.2.i.f.106.4	✓	10	19.12	odd	6
285.2.i.f.121.4	yes	10	19.8	odd	6
855.2.k.i.406.2		10	57.8	even	6
855.2.k.i.676.2		10	57.50	even	6
5415.2.a.y.1.2		5	19.18	odd	2
5415.2.a.z.1.4		5	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 5415 = 3 \cdot 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5415.a (trivial)

\(f(q)\)	\(=\)	\(q+1.64661 q^{2} +1.00000 q^{3} +0.711327 q^{4} +1.00000 q^{5} +1.64661 q^{6} +4.47988 q^{7} -2.12194 q^{8} +1.00000 q^{9} +1.64661 q^{10} -3.44134 q^{11} +0.711327 q^{12} -2.47988 q^{13} +7.37662 q^{14} +1.00000 q^{15} -4.91667 q^{16} +7.62799 q^{17} +1.64661 q^{18} +0.711327 q^{20} +4.47988 q^{21} -5.66654 q^{22} +3.87057 q^{23} -2.12194 q^{24} +1.00000 q^{25} -4.08340 q^{26} +1.00000 q^{27} +3.18666 q^{28} +8.73456 q^{29} +1.64661 q^{30} +0.422654 q^{31} -3.85195 q^{32} -3.44134 q^{33} +12.5603 q^{34} +4.47988 q^{35} +0.711327 q^{36} -3.90253 q^{37} -2.47988 q^{39} -2.12194 q^{40} -5.29322 q^{41} +7.37662 q^{42} +2.47988 q^{43} -2.44791 q^{44} +1.00000 q^{45} +6.37332 q^{46} -0.677330 q^{47} -4.91667 q^{48} +13.0693 q^{49} +1.64661 q^{50} +7.62799 q^{51} -1.76401 q^{52} -11.4986 q^{53} +1.64661 q^{54} -3.44134 q^{55} -9.50605 q^{56} +14.3824 q^{58} +8.53053 q^{59} +0.711327 q^{60} +8.20233 q^{61} +0.695946 q^{62} +4.47988 q^{63} +3.49067 q^{64} -2.47988 q^{65} -5.66654 q^{66} +9.63457 q^{67} +5.42600 q^{68} +3.87057 q^{69} +7.37662 q^{70} +3.85189 q^{71} -2.12194 q^{72} +16.7852 q^{73} -6.42595 q^{74} +1.00000 q^{75} -15.4168 q^{77} -4.08340 q^{78} -12.1252 q^{79} -4.91667 q^{80} +1.00000 q^{81} -8.71588 q^{82} -2.03855 q^{83} +3.18666 q^{84} +7.62799 q^{85} +4.08340 q^{86} +8.73456 q^{87} +7.30232 q^{88} +3.14511 q^{89} +1.64661 q^{90} -11.1096 q^{91} +2.75324 q^{92} +0.422654 q^{93} -1.11530 q^{94} -3.85195 q^{96} -2.00000 q^{97} +21.5201 q^{98} -3.44134 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + q^{2} + 5 q^{3} + 7 q^{4} + 5 q^{5} + q^{6} + 2 q^{7} + 6 q^{8} + 5 q^{9} + q^{10} + 5 q^{11} + 7 q^{12} + 8 q^{13} + 4 q^{14} + 5 q^{15} + 7 q^{16} + 10 q^{17} + q^{18} + 7 q^{20} + 2 q^{21}+ \cdots + 5 q^{99}+O(q^{100}) \) 5 * q + q^2 + 5 * q^3 + 7 * q^4 + 5 * q^5 + q^6 + 2 * q^7 + 6 * q^8 + 5 * q^9 + q^10 + 5 * q^11 + 7 * q^12 + 8 * q^13 + 4 * q^14 + 5 * q^15 + 7 * q^16 + 10 * q^17 + q^18 + 7 * q^20 + 2 * q^21 - 2 * q^22 - 2 * q^23 + 6 * q^24 + 5 * q^25 - 2 * q^26 + 5 * q^27 + 10 * q^28 + 7 * q^29 + q^30 + 9 * q^31 + 23 * q^32 + 5 * q^33 - 25 * q^34 + 2 * q^35 + 7 * q^36 - 6 * q^37 + 8 * q^39 + 6 * q^40 - 12 * q^41 + 4 * q^42 - 8 * q^43 + 16 * q^44 + 5 * q^45 + 20 * q^46 + 6 * q^47 + 7 * q^48 + 15 * q^49 + q^50 + 10 * q^51 + 4 * q^52 - 8 * q^53 + q^54 + 5 * q^55 - 36 * q^56 + 38 * q^58 + q^59 + 7 * q^60 + 7 * q^61 + 15 * q^62 + 2 * q^63 + 14 * q^64 + 8 * q^65 - 2 * q^66 + 14 * q^67 - q^68 - 2 * q^69 + 4 * q^70 + 27 * q^71 + 6 * q^72 + 26 * q^73 - 18 * q^74 + 5 * q^75 + 14 * q^77 - 2 * q^78 - 23 * q^79 + 7 * q^80 + 5 * q^81 - 36 * q^82 - 12 * q^83 + 10 * q^84 + 10 * q^85 + 2 * q^86 + 7 * q^87 + 9 * q^89 + q^90 - 46 * q^91 - 52 * q^92 + 9 * q^93 - 45 * q^94 + 23 * q^96 - 10 * q^97 - 21 * q^98 + 5 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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