LMFDB - Embedded newform 4641.2.a.i.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [4641,2,Mod(1,4641)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("4641.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4641, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 4641 = 3 \cdot 7 \cdot 13 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4641.a (trivial)

Newform invariants

comment:select newform

sage:traces = [2,-1,-2,-1,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$37.0585715781$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	4641.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.618034 q^{2} -1.00000 q^{3} -1.61803 q^{4} +2.23607 q^{5} -0.618034 q^{6} -1.00000 q^{7} -2.23607 q^{8} +1.00000 q^{9} +1.38197 q^{10} -4.00000 q^{11} +1.61803 q^{12} -1.00000 q^{13} -0.618034 q^{14} -2.23607 q^{15} +1.85410 q^{16} -1.00000 q^{17} +0.618034 q^{18} +6.23607 q^{19} -3.61803 q^{20} +1.00000 q^{21} -2.47214 q^{22} +3.00000 q^{23} +2.23607 q^{24} -0.618034 q^{26} -1.00000 q^{27} +1.61803 q^{28} +8.23607 q^{29} -1.38197 q^{30} +2.47214 q^{31} +5.61803 q^{32} +4.00000 q^{33} -0.618034 q^{34} -2.23607 q^{35} -1.61803 q^{36} -4.47214 q^{37} +3.85410 q^{38} +1.00000 q^{39} -5.00000 q^{40} -4.70820 q^{41} +0.618034 q^{42} -3.76393 q^{43} +6.47214 q^{44} +2.23607 q^{45} +1.85410 q^{46} -4.00000 q^{47} -1.85410 q^{48} +1.00000 q^{49} +1.00000 q^{51} +1.61803 q^{52} +1.52786 q^{53} -0.618034 q^{54} -8.94427 q^{55} +2.23607 q^{56} -6.23607 q^{57} +5.09017 q^{58} +6.00000 q^{59} +3.61803 q^{60} -8.23607 q^{61} +1.52786 q^{62} -1.00000 q^{63} -0.236068 q^{64} -2.23607 q^{65} +2.47214 q^{66} -1.52786 q^{67} +1.61803 q^{68} -3.00000 q^{69} -1.38197 q^{70} -6.47214 q^{71} -2.23607 q^{72} +5.52786 q^{73} -2.76393 q^{74} -10.0902 q^{76} +4.00000 q^{77} +0.618034 q^{78} -6.00000 q^{79} +4.14590 q^{80} +1.00000 q^{81} -2.90983 q^{82} -8.47214 q^{83} -1.61803 q^{84} -2.23607 q^{85} -2.32624 q^{86} -8.23607 q^{87} +8.94427 q^{88} -14.4721 q^{89} +1.38197 q^{90} +1.00000 q^{91} -4.85410 q^{92} -2.47214 q^{93} -2.47214 q^{94} +13.9443 q^{95} -5.61803 q^{96} +10.4721 q^{97} +0.618034 q^{98} -4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - 2 q^{3} - q^{4} + q^{6} - 2 q^{7} + 2 q^{9} + 5 q^{10} - 8 q^{11} + q^{12} - 2 q^{13} + q^{14} - 3 q^{16} - 2 q^{17} - q^{18} + 8 q^{19} - 5 q^{20} + 2 q^{21} + 4 q^{22} + 6 q^{23} + q^{26}+ \cdots - 8 q^{99}+O(q^{100}) $ 2 * q - q^2 - 2 * q^3 - q^4 + q^6 - 2 * q^7 + 2 * q^9 + 5 * q^10 - 8 * q^11 + q^12 - 2 * q^13 + q^14 - 3 * q^16 - 2 * q^17 - q^18 + 8 * q^19 - 5 * q^20 + 2 * q^21 + 4 * q^22 + 6 * q^23 + q^26 - 2 * q^27 + q^28 + 12 * q^29 - 5 * q^30 - 4 * q^31 + 9 * q^32 + 8 * q^33 + q^34 - q^36 + q^38 + 2 * q^39 - 10 * q^40 + 4 * q^41 - q^42 - 12 * q^43 + 4 * q^44 - 3 * q^46 - 8 * q^47 + 3 * q^48 + 2 * q^49 + 2 * q^51 + q^52 + 12 * q^53 + q^54 - 8 * q^57 - q^58 + 12 * q^59 + 5 * q^60 - 12 * q^61 + 12 * q^62 - 2 * q^63 + 4 * q^64 - 4 * q^66 - 12 * q^67 + q^68 - 6 * q^69 - 5 * q^70 - 4 * q^71 + 20 * q^73 - 10 * q^74 - 9 * q^76 + 8 * q^77 - q^78 - 12 * q^79 + 15 * q^80 + 2 * q^81 - 17 * q^82 - 8 * q^83 - q^84 + 11 * q^86 - 12 * q^87 - 20 * q^89 + 5 * q^90 + 2 * q^91 - 3 * q^92 + 4 * q^93 + 4 * q^94 + 10 * q^95 - 9 * q^96 + 12 * q^97 - q^98 - 8 * 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 $

$2$	0.618034	0.437016	0.218508	−	0.975835i	$-0.429881\pi$
$2$	0.618034	0.437016	0.218508	+	0.975835i	$0.429881\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.61803	−0.809017
$5$	2.23607	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$5$	2.23607	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$6$	−0.618034	−0.252311
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−2.23607	−0.790569
$9$	1.00000	0.333333
$10$	1.38197	0.437016
$11$	−4.00000	−1.20605	−0.603023	−	0.797724i	$-0.706037\pi$
$11$	−4.00000	−1.20605	−0.603023	+	0.797724i	$0.706037\pi$
$12$	1.61803	0.467086
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−0.618034	−0.165177
$15$	−2.23607	−0.577350
$16$	1.85410	0.463525
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	0.618034	0.145672
$19$	6.23607	1.43065	0.715326	−	0.698791i	$-0.246278\pi$
$19$	6.23607	1.43065	0.715326	+	0.698791i	$0.246278\pi$
$20$	−3.61803	−0.809017
$21$	1.00000	0.218218
$22$	−2.47214	−0.527061
$23$	3.00000	0.625543	0.312772	−	0.949828i	$-0.398743\pi$
$23$	3.00000	0.625543	0.312772	+	0.949828i	$0.398743\pi$
$24$	2.23607	0.456435
$25$	0	0
$26$	−0.618034	−0.121206
$27$	−1.00000	−0.192450
$28$	1.61803	0.305780
$29$	8.23607	1.52940	0.764700	−	0.644387i	$-0.222887\pi$
$29$	8.23607	1.52940	0.764700	+	0.644387i	$0.222887\pi$
$30$	−1.38197	−0.252311
$31$	2.47214	0.444009	0.222004	−	0.975046i	$-0.428740\pi$
$31$	2.47214	0.444009	0.222004	+	0.975046i	$0.428740\pi$
$32$	5.61803	0.993137
$33$	4.00000	0.696311
$34$	−0.618034	−0.105992
$35$	−2.23607	−0.377964
$36$	−1.61803	−0.269672
$37$	−4.47214	−0.735215	−0.367607	−	0.929981i	$-0.619823\pi$
$37$	−4.47214	−0.735215	−0.367607	+	0.929981i	$0.619823\pi$
$38$	3.85410	0.625218
$39$	1.00000	0.160128
$40$	−5.00000	−0.790569
$41$	−4.70820	−0.735298	−0.367649	−	0.929965i	$-0.619837\pi$
$41$	−4.70820	−0.735298	−0.367649	+	0.929965i	$0.619837\pi$
$42$	0.618034	0.0953647
$43$	−3.76393	−0.573994	−0.286997	−	0.957931i	$-0.592657\pi$
$43$	−3.76393	−0.573994	−0.286997	+	0.957931i	$0.592657\pi$
$44$	6.47214	0.975711
$45$	2.23607	0.333333
$46$	1.85410	0.273372
$47$	−4.00000	−0.583460	−0.291730	−	0.956501i	$-0.594231\pi$
$47$	−4.00000	−0.583460	−0.291730	+	0.956501i	$0.594231\pi$
$48$	−1.85410	−0.267617
$49$	1.00000	0.142857
$50$	0	0
$51$	1.00000	0.140028
$52$	1.61803	0.224381
$53$	1.52786	0.209868	0.104934	−	0.994479i	$-0.466537\pi$
$53$	1.52786	0.209868	0.104934	+	0.994479i	$0.466537\pi$
$54$	−0.618034	−0.0841038
$55$	−8.94427	−1.20605
$56$	2.23607	0.298807
$57$	−6.23607	−0.825987
$58$	5.09017	0.668372
$59$	6.00000	0.781133	0.390567	−	0.920575i	$-0.372279\pi$
$59$	6.00000	0.781133	0.390567	+	0.920575i	$0.372279\pi$
$60$	3.61803	0.467086
$61$	−8.23607	−1.05452	−0.527260	−	0.849704i	$-0.676781\pi$
$61$	−8.23607	−1.05452	−0.527260	+	0.849704i	$0.676781\pi$
$62$	1.52786	0.194039
$63$	−1.00000	−0.125988
$64$	−0.236068	−0.0295085
$65$	−2.23607	−0.277350
$66$	2.47214	0.304299
$67$	−1.52786	−0.186658	−0.0933292	−	0.995635i	$-0.529751\pi$
$67$	−1.52786	−0.186658	−0.0933292	+	0.995635i	$0.529751\pi$
$68$	1.61803	0.196215
$69$	−3.00000	−0.361158
$70$	−1.38197	−0.165177
$71$	−6.47214	−0.768101	−0.384051	−	0.923312i	$-0.625471\pi$
$71$	−6.47214	−0.768101	−0.384051	+	0.923312i	$0.625471\pi$
$72$	−2.23607	−0.263523
$73$	5.52786	0.646988	0.323494	−	0.946230i	$-0.395143\pi$
$73$	5.52786	0.646988	0.323494	+	0.946230i	$0.395143\pi$
$74$	−2.76393	−0.321301
$75$	0	0
$76$	−10.0902	−1.15742
$77$	4.00000	0.455842
$78$	0.618034	0.0699786
$79$	−6.00000	−0.675053	−0.337526	−	0.941316i	$-0.609590\pi$
$79$	−6.00000	−0.675053	−0.337526	+	0.941316i	$0.609590\pi$
$80$	4.14590	0.463525
$81$	1.00000	0.111111
$82$	−2.90983	−0.321337
$83$	−8.47214	−0.929938	−0.464969	−	0.885327i	$-0.653934\pi$
$83$	−8.47214	−0.929938	−0.464969	+	0.885327i	$0.653934\pi$
$84$	−1.61803	−0.176542
$85$	−2.23607	−0.242536
$86$	−2.32624	−0.250845
$87$	−8.23607	−0.882999
$88$	8.94427	0.953463
$89$	−14.4721	−1.53404	−0.767022	−	0.641621i	$-0.778262\pi$
$89$	−14.4721	−1.53404	−0.767022	+	0.641621i	$0.778262\pi$
$90$	1.38197	0.145672
$91$	1.00000	0.104828
$92$	−4.85410	−0.506075
$93$	−2.47214	−0.256349
$94$	−2.47214	−0.254981
$95$	13.9443	1.43065
$96$	−5.61803	−0.573388
$97$	10.4721	1.06328	0.531642	−	0.846969i	$-0.321575\pi$
$97$	10.4721	1.06328	0.531642	+	0.846969i	$0.321575\pi$
$98$	0.618034	0.0624309
$99$	−4.00000	−0.402015
$100$	0	0
$101$	2.52786	0.251532	0.125766	−	0.992060i	$-0.459861\pi$
$101$	2.52786	0.251532	0.125766	+	0.992060i	$0.459861\pi$
$102$	0.618034	0.0611945
$103$	−19.4164	−1.91316	−0.956578	−	0.291477i	$-0.905853\pi$
$103$	−19.4164	−1.91316	−0.956578	+	0.291477i	$0.905853\pi$
$104$	2.23607	0.219265
$105$	2.23607	0.218218
$106$	0.944272	0.0917158
$107$	1.47214	0.142317	0.0711584	−	0.997465i	$-0.477330\pi$
$107$	1.47214	0.142317	0.0711584	+	0.997465i	$0.477330\pi$
$108$	1.61803	0.155695
$109$	−6.70820	−0.642529	−0.321265	−	0.946989i	$-0.604108\pi$
$109$	−6.70820	−0.642529	−0.321265	+	0.946989i	$0.604108\pi$
$110$	−5.52786	−0.527061
$111$	4.47214	0.424476
$112$	−1.85410	−0.175196
$113$	−0.472136	−0.0444148	−0.0222074	−	0.999753i	$-0.507069\pi$
$113$	−0.472136	−0.0444148	−0.0222074	+	0.999753i	$0.507069\pi$
$114$	−3.85410	−0.360970
$115$	6.70820	0.625543
$116$	−13.3262	−1.23731
$117$	−1.00000	−0.0924500
$118$	3.70820	0.341368
$119$	1.00000	0.0916698
$120$	5.00000	0.456435
$121$	5.00000	0.454545
$122$	−5.09017	−0.460842
$123$	4.70820	0.424524
$124$	−4.00000	−0.359211
$125$	−11.1803	−1.00000
$126$	−0.618034	−0.0550588
$127$	5.76393	0.511466	0.255733	−	0.966747i	$-0.417683\pi$
$127$	5.76393	0.511466	0.255733	+	0.966747i	$0.417683\pi$
$128$	−11.3820	−1.00603
$129$	3.76393	0.331396
$130$	−1.38197	−0.121206
$131$	−13.4164	−1.17220	−0.586098	−	0.810240i	$-0.699337\pi$
$131$	−13.4164	−1.17220	−0.586098	+	0.810240i	$0.699337\pi$
$132$	−6.47214	−0.563327
$133$	−6.23607	−0.540736
$134$	−0.944272	−0.0815727
$135$	−2.23607	−0.192450
$136$	2.23607	0.191741
$137$	2.94427	0.251546	0.125773	−	0.992059i	$-0.459859\pi$
$137$	2.94427	0.251546	0.125773	+	0.992059i	$0.459859\pi$
$138$	−1.85410	−0.157832
$139$	−8.41641	−0.713870	−0.356935	−	0.934129i	$-0.616178\pi$
$139$	−8.41641	−0.713870	−0.356935	+	0.934129i	$0.616178\pi$
$140$	3.61803	0.305780
$141$	4.00000	0.336861
$142$	−4.00000	−0.335673
$143$	4.00000	0.334497
$144$	1.85410	0.154508
$145$	18.4164	1.52940
$146$	3.41641	0.282744
$147$	−1.00000	−0.0824786
$148$	7.23607	0.594801
$149$	2.00000	0.163846	0.0819232	−	0.996639i	$-0.473894\pi$
$149$	2.00000	0.163846	0.0819232	+	0.996639i	$0.473894\pi$
$150$	0	0
$151$	−3.52786	−0.287094	−0.143547	−	0.989644i	$-0.545851\pi$
$151$	−3.52786	−0.287094	−0.143547	+	0.989644i	$0.545851\pi$
$152$	−13.9443	−1.13103
$153$	−1.00000	−0.0808452
$154$	2.47214	0.199210
$155$	5.52786	0.444009
$156$	−1.61803	−0.129546
$157$	−2.00000	−0.159617	−0.0798087	−	0.996810i	$-0.525431\pi$
$157$	−2.00000	−0.159617	−0.0798087	+	0.996810i	$0.525431\pi$
$158$	−3.70820	−0.295009
$159$	−1.52786	−0.121168
$160$	12.5623	0.993137
$161$	−3.00000	−0.236433
$162$	0.618034	0.0485573
$163$	0.0557281	0.00436496	0.00218248	−	0.999998i	$-0.499305\pi$
$163$	0.0557281	0.00436496	0.00218248	+	0.999998i	$0.499305\pi$
$164$	7.61803	0.594869
$165$	8.94427	0.696311
$166$	−5.23607	−0.406398
$167$	−13.4721	−1.04251	−0.521253	−	0.853402i	$-0.674535\pi$
$167$	−13.4721	−1.04251	−0.521253	+	0.853402i	$0.674535\pi$
$168$	−2.23607	−0.172516
$169$	1.00000	0.0769231
$170$	−1.38197	−0.105992
$171$	6.23607	0.476884
$172$	6.09017	0.464371
$173$	7.05573	0.536437	0.268219	−	0.963358i	$-0.413565\pi$
$173$	7.05573	0.536437	0.268219	+	0.963358i	$0.413565\pi$
$174$	−5.09017	−0.385885
$175$	0	0
$176$	−7.41641	−0.559033
$177$	−6.00000	−0.450988
$178$	−8.94427	−0.670402
$179$	4.47214	0.334263	0.167132	−	0.985935i	$-0.446550\pi$
$179$	4.47214	0.334263	0.167132	+	0.985935i	$0.446550\pi$
$180$	−3.61803	−0.269672
$181$	−4.47214	−0.332411	−0.166206	−	0.986091i	$-0.553152\pi$
$181$	−4.47214	−0.332411	−0.166206	+	0.986091i	$0.553152\pi$
$182$	0.618034	0.0458117
$183$	8.23607	0.608828
$184$	−6.70820	−0.494535
$185$	−10.0000	−0.735215
$186$	−1.52786	−0.112028
$187$	4.00000	0.292509
$188$	6.47214	0.472029
$189$	1.00000	0.0727393
$190$	8.61803	0.625218
$191$	−11.8885	−0.860225	−0.430112	−	0.902775i	$-0.641526\pi$
$191$	−11.8885	−0.860225	−0.430112	+	0.902775i	$0.641526\pi$
$192$	0.236068	0.0170367
$193$	22.5967	1.62655	0.813275	−	0.581880i	$-0.197683\pi$
$193$	22.5967	1.62655	0.813275	+	0.581880i	$0.197683\pi$
$194$	6.47214	0.464672
$195$	2.23607	0.160128
$196$	−1.61803	−0.115574
$197$	5.41641	0.385903	0.192952	−	0.981208i	$-0.438194\pi$
$197$	5.41641	0.385903	0.192952	+	0.981208i	$0.438194\pi$
$198$	−2.47214	−0.175687
$199$	14.8885	1.05542	0.527710	−	0.849424i	$-0.323051\pi$
$199$	14.8885	1.05542	0.527710	+	0.849424i	$0.323051\pi$
$200$	0	0
$201$	1.52786	0.107767
$202$	1.56231	0.109923
$203$	−8.23607	−0.578059
$204$	−1.61803	−0.113285
$205$	−10.5279	−0.735298
$206$	−12.0000	−0.836080
$207$	3.00000	0.208514
$208$	−1.85410	−0.128559
$209$	−24.9443	−1.72543
$210$	1.38197	0.0953647
$211$	−14.4721	−0.996303	−0.498151	−	0.867090i	$-0.665988\pi$
$211$	−14.4721	−0.996303	−0.498151	+	0.867090i	$0.665988\pi$
$212$	−2.47214	−0.169787
$213$	6.47214	0.443463
$214$	0.909830	0.0621947
$215$	−8.41641	−0.573994
$216$	2.23607	0.152145
$217$	−2.47214	−0.167820
$218$	−4.14590	−0.280796
$219$	−5.52786	−0.373538
$220$	14.4721	0.975711
$221$	1.00000	0.0672673
$222$	2.76393	0.185503
$223$	−1.18034	−0.0790414	−0.0395207	−	0.999219i	$-0.512583\pi$
$223$	−1.18034	−0.0790414	−0.0395207	+	0.999219i	$0.512583\pi$
$224$	−5.61803	−0.375371
$225$	0	0
$226$	−0.291796	−0.0194100
$227$	−23.9443	−1.58924	−0.794619	−	0.607109i	$-0.792329\pi$
$227$	−23.9443	−1.58924	−0.794619	+	0.607109i	$0.792329\pi$
$228$	10.0902	0.668238
$229$	−6.05573	−0.400174	−0.200087	−	0.979778i	$-0.564122\pi$
$229$	−6.05573	−0.400174	−0.200087	+	0.979778i	$0.564122\pi$
$230$	4.14590	0.273372
$231$	−4.00000	−0.263181
$232$	−18.4164	−1.20910
$233$	18.7082	1.22562	0.612808	−	0.790232i	$-0.290040\pi$
$233$	18.7082	1.22562	0.612808	+	0.790232i	$0.290040\pi$
$234$	−0.618034	−0.0404021
$235$	−8.94427	−0.583460
$236$	−9.70820	−0.631950
$237$	6.00000	0.389742
$238$	0.618034	0.0400612
$239$	−13.1803	−0.852565	−0.426283	−	0.904590i	$-0.640177\pi$
$239$	−13.1803	−0.852565	−0.426283	+	0.904590i	$0.640177\pi$
$240$	−4.14590	−0.267617
$241$	−10.0000	−0.644157	−0.322078	−	0.946713i	$-0.604381\pi$
$241$	−10.0000	−0.644157	−0.322078	+	0.946713i	$0.604381\pi$
$242$	3.09017	0.198644
$243$	−1.00000	−0.0641500
$244$	13.3262	0.853125
$245$	2.23607	0.142857
$246$	2.90983	0.185524
$247$	−6.23607	−0.396792
$248$	−5.52786	−0.351020
$249$	8.47214	0.536900
$250$	−6.90983	−0.437016
$251$	−20.2361	−1.27729	−0.638645	−	0.769502i	$-0.720505\pi$
$251$	−20.2361	−1.27729	−0.638645	+	0.769502i	$0.720505\pi$
$252$	1.61803	0.101927
$253$	−12.0000	−0.754434
$254$	3.56231	0.223519
$255$	2.23607	0.140028
$256$	−6.56231	−0.410144
$257$	11.9443	0.745063	0.372532	−	0.928020i	$-0.378490\pi$
$257$	11.9443	0.745063	0.372532	+	0.928020i	$0.378490\pi$
$258$	2.32624	0.144825
$259$	4.47214	0.277885
$260$	3.61803	0.224381
$261$	8.23607	0.509800
$262$	−8.29180	−0.512269
$263$	−10.4721	−0.645740	−0.322870	−	0.946443i	$-0.604648\pi$
$263$	−10.4721	−0.645740	−0.322870	+	0.946443i	$0.604648\pi$
$264$	−8.94427	−0.550482
$265$	3.41641	0.209868
$266$	−3.85410	−0.236310
$267$	14.4721	0.885680
$268$	2.47214	0.151010
$269$	2.47214	0.150729	0.0753644	−	0.997156i	$-0.475988\pi$
$269$	2.47214	0.150729	0.0753644	+	0.997156i	$0.475988\pi$
$270$	−1.38197	−0.0841038
$271$	0.708204	0.0430203	0.0215102	−	0.999769i	$-0.493153\pi$
$271$	0.708204	0.0430203	0.0215102	+	0.999769i	$0.493153\pi$
$272$	−1.85410	−0.112421
$273$	−1.00000	−0.0605228
$274$	1.81966	0.109930
$275$	0	0
$276$	4.85410	0.292183
$277$	−3.05573	−0.183601	−0.0918005	−	0.995777i	$-0.529262\pi$
$277$	−3.05573	−0.183601	−0.0918005	+	0.995777i	$0.529262\pi$
$278$	−5.20163	−0.311973
$279$	2.47214	0.148003
$280$	5.00000	0.298807
$281$	−23.4721	−1.40023	−0.700115	−	0.714030i	$-0.746868\pi$
$281$	−23.4721	−1.40023	−0.700115	+	0.714030i	$0.746868\pi$
$282$	2.47214	0.147214
$283$	14.4164	0.856966	0.428483	−	0.903550i	$-0.359048\pi$
$283$	14.4164	0.856966	0.428483	+	0.903550i	$0.359048\pi$
$284$	10.4721	0.621407
$285$	−13.9443	−0.825987
$286$	2.47214	0.146180
$287$	4.70820	0.277916
$288$	5.61803	0.331046
$289$	1.00000	0.0588235
$290$	11.3820	0.668372
$291$	−10.4721	−0.613887
$292$	−8.94427	−0.523424
$293$	−6.94427	−0.405689	−0.202844	−	0.979211i	$-0.565019\pi$
$293$	−6.94427	−0.405689	−0.202844	+	0.979211i	$0.565019\pi$
$294$	−0.618034	−0.0360445
$295$	13.4164	0.781133
$296$	10.0000	0.581238
$297$	4.00000	0.232104
$298$	1.23607	0.0716035
$299$	−3.00000	−0.173494
$300$	0	0
$301$	3.76393	0.216949
$302$	−2.18034	−0.125464
$303$	−2.52786	−0.145222
$304$	11.5623	0.663144
$305$	−18.4164	−1.05452
$306$	−0.618034	−0.0353307
$307$	−31.6525	−1.80650	−0.903251	−	0.429112i	$-0.858826\pi$
$307$	−31.6525	−1.80650	−0.903251	+	0.429112i	$0.858826\pi$
$308$	−6.47214	−0.368784
$309$	19.4164	1.10456
$310$	3.41641	0.194039
$311$	15.4164	0.874184	0.437092	−	0.899417i	$-0.356008\pi$
$311$	15.4164	0.874184	0.437092	+	0.899417i	$0.356008\pi$
$312$	−2.23607	−0.126592
$313$	12.4721	0.704967	0.352483	−	0.935818i	$-0.385337\pi$
$313$	12.4721	0.704967	0.352483	+	0.935818i	$0.385337\pi$
$314$	−1.23607	−0.0697554
$315$	−2.23607	−0.125988
$316$	9.70820	0.546129
$317$	−13.8885	−0.780058	−0.390029	−	0.920803i	$-0.627535\pi$
$317$	−13.8885	−0.780058	−0.390029	+	0.920803i	$0.627535\pi$
$318$	−0.944272	−0.0529521
$319$	−32.9443	−1.84453
$320$	−0.527864	−0.0295085
$321$	−1.47214	−0.0821666
$322$	−1.85410	−0.103325
$323$	−6.23607	−0.346984
$324$	−1.61803	−0.0898908
$325$	0	0
$326$	0.0344419	0.00190756
$327$	6.70820	0.370965
$328$	10.5279	0.581304
$329$	4.00000	0.220527
$330$	5.52786	0.304299
$331$	−19.4164	−1.06722	−0.533611	−	0.845730i	$-0.679165\pi$
$331$	−19.4164	−1.06722	−0.533611	+	0.845730i	$0.679165\pi$
$332$	13.7082	0.752335
$333$	−4.47214	−0.245072
$334$	−8.32624	−0.455591
$335$	−3.41641	−0.186658
$336$	1.85410	0.101150
$337$	−12.9443	−0.705119	−0.352560	−	0.935789i	$-0.614689\pi$
$337$	−12.9443	−0.705119	−0.352560	+	0.935789i	$0.614689\pi$
$338$	0.618034	0.0336166
$339$	0.472136	0.0256429
$340$	3.61803	0.196215
$341$	−9.88854	−0.535495
$342$	3.85410	0.208406
$343$	−1.00000	−0.0539949
$344$	8.41641	0.453782
$345$	−6.70820	−0.361158
$346$	4.36068	0.234432
$347$	20.0000	1.07366	0.536828	−	0.843692i	$-0.319622\pi$
$347$	20.0000	1.07366	0.536828	+	0.843692i	$0.319622\pi$
$348$	13.3262	0.714361
$349$	−26.8885	−1.43931	−0.719655	−	0.694331i	$-0.755700\pi$
$349$	−26.8885	−1.43931	−0.719655	+	0.694331i	$0.755700\pi$
$350$	0	0
$351$	1.00000	0.0533761
$352$	−22.4721	−1.19777
$353$	17.4164	0.926982	0.463491	−	0.886102i	$-0.346597\pi$
$353$	17.4164	0.926982	0.463491	+	0.886102i	$0.346597\pi$
$354$	−3.70820	−0.197089
$355$	−14.4721	−0.768101
$356$	23.4164	1.24107
$357$	−1.00000	−0.0529256
$358$	2.76393	0.146078
$359$	0.944272	0.0498368	0.0249184	−	0.999689i	$-0.492067\pi$
$359$	0.944272	0.0498368	0.0249184	+	0.999689i	$0.492067\pi$
$360$	−5.00000	−0.263523
$361$	19.8885	1.04677
$362$	−2.76393	−0.145269
$363$	−5.00000	−0.262432
$364$	−1.61803	−0.0848080
$365$	12.3607	0.646988
$366$	5.09017	0.266067
$367$	−18.0557	−0.942501	−0.471251	−	0.881999i	$-0.656197\pi$
$367$	−18.0557	−0.942501	−0.471251	+	0.881999i	$0.656197\pi$
$368$	5.56231	0.289955
$369$	−4.70820	−0.245099
$370$	−6.18034	−0.321301
$371$	−1.52786	−0.0793227
$372$	4.00000	0.207390
$373$	14.4164	0.746453	0.373227	−	0.927740i	$-0.378251\pi$
$373$	14.4164	0.746453	0.373227	+	0.927740i	$0.378251\pi$
$374$	2.47214	0.127831
$375$	11.1803	0.577350
$376$	8.94427	0.461266
$377$	−8.23607	−0.424179
$378$	0.618034	0.0317882
$379$	−12.0557	−0.619261	−0.309631	−	0.950857i	$-0.600205\pi$
$379$	−12.0557	−0.619261	−0.309631	+	0.950857i	$0.600205\pi$
$380$	−22.5623	−1.15742
$381$	−5.76393	−0.295295
$382$	−7.34752	−0.375932
$383$	17.8885	0.914062	0.457031	−	0.889451i	$-0.348913\pi$
$383$	17.8885	0.914062	0.457031	+	0.889451i	$0.348913\pi$
$384$	11.3820	0.580834
$385$	8.94427	0.455842
$386$	13.9656	0.710828
$387$	−3.76393	−0.191331
$388$	−16.9443	−0.860215
$389$	−27.8885	−1.41401	−0.707003	−	0.707211i	$-0.749953\pi$
$389$	−27.8885	−1.41401	−0.707003	+	0.707211i	$0.749953\pi$
$390$	1.38197	0.0699786
$391$	−3.00000	−0.151717
$392$	−2.23607	−0.112938
$393$	13.4164	0.676768
$394$	3.34752	0.168646
$395$	−13.4164	−0.675053
$396$	6.47214	0.325237
$397$	21.4164	1.07486	0.537429	−	0.843309i	$-0.319395\pi$
$397$	21.4164	1.07486	0.537429	+	0.843309i	$0.319395\pi$
$398$	9.20163	0.461236
$399$	6.23607	0.312194
$400$	0	0
$401$	−22.9443	−1.14578	−0.572891	−	0.819631i	$-0.694178\pi$
$401$	−22.9443	−1.14578	−0.572891	+	0.819631i	$0.694178\pi$
$402$	0.944272	0.0470960
$403$	−2.47214	−0.123146
$404$	−4.09017	−0.203494
$405$	2.23607	0.111111
$406$	−5.09017	−0.252621
$407$	17.8885	0.886702
$408$	−2.23607	−0.110702
$409$	8.52786	0.421676	0.210838	−	0.977521i	$-0.432381\pi$
$409$	8.52786	0.421676	0.210838	+	0.977521i	$0.432381\pi$
$410$	−6.50658	−0.321337
$411$	−2.94427	−0.145230
$412$	31.4164	1.54778
$413$	−6.00000	−0.295241
$414$	1.85410	0.0911241
$415$	−18.9443	−0.929938
$416$	−5.61803	−0.275447
$417$	8.41641	0.412153
$418$	−15.4164	−0.754041
$419$	12.0000	0.586238	0.293119	−	0.956076i	$-0.405307\pi$
$419$	12.0000	0.586238	0.293119	+	0.956076i	$0.405307\pi$
$420$	−3.61803	−0.176542
$421$	−15.0557	−0.733771	−0.366886	−	0.930266i	$-0.619576\pi$
$421$	−15.0557	−0.733771	−0.366886	+	0.930266i	$0.619576\pi$
$422$	−8.94427	−0.435400
$423$	−4.00000	−0.194487
$424$	−3.41641	−0.165915
$425$	0	0
$426$	4.00000	0.193801
$427$	8.23607	0.398571
$428$	−2.38197	−0.115137
$429$	−4.00000	−0.193122
$430$	−5.20163	−0.250845
$431$	−22.0000	−1.05970	−0.529851	−	0.848091i	$-0.677752\pi$
$431$	−22.0000	−1.05970	−0.529851	+	0.848091i	$0.677752\pi$
$432$	−1.85410	−0.0892055
$433$	−2.94427	−0.141493	−0.0707463	−	0.997494i	$-0.522538\pi$
$433$	−2.94427	−0.141493	−0.0707463	+	0.997494i	$0.522538\pi$
$434$	−1.52786	−0.0733398
$435$	−18.4164	−0.882999
$436$	10.8541	0.519817
$437$	18.7082	0.894935
$438$	−3.41641	−0.163242
$439$	−37.8885	−1.80832	−0.904161	−	0.427192i	$-0.859503\pi$
$439$	−37.8885	−1.80832	−0.904161	+	0.427192i	$0.859503\pi$
$440$	20.0000	0.953463
$441$	1.00000	0.0476190
$442$	0.618034	0.0293969
$443$	−14.3607	−0.682296	−0.341148	−	0.940010i	$-0.610816\pi$
$443$	−14.3607	−0.682296	−0.341148	+	0.940010i	$0.610816\pi$
$444$	−7.23607	−0.343409
$445$	−32.3607	−1.53404
$446$	−0.729490	−0.0345424
$447$	−2.00000	−0.0945968
$448$	0.236068	0.0111532
$449$	−14.9443	−0.705264	−0.352632	−	0.935762i	$-0.614713\pi$
$449$	−14.9443	−0.705264	−0.352632	+	0.935762i	$0.614713\pi$
$450$	0	0
$451$	18.8328	0.886803
$452$	0.763932	0.0359323
$453$	3.52786	0.165754
$454$	−14.7984	−0.694522
$455$	2.23607	0.104828
$456$	13.9443	0.653000
$457$	24.8328	1.16163	0.580815	−	0.814036i	$-0.302734\pi$
$457$	24.8328	1.16163	0.580815	+	0.814036i	$0.302734\pi$
$458$	−3.74265	−0.174882
$459$	1.00000	0.0466760
$460$	−10.8541	−0.506075
$461$	36.8328	1.71548	0.857738	−	0.514088i	$-0.171869\pi$
$461$	36.8328	1.71548	0.857738	+	0.514088i	$0.171869\pi$
$462$	−2.47214	−0.115014
$463$	−31.4164	−1.46004	−0.730022	−	0.683423i	$-0.760490\pi$
$463$	−31.4164	−1.46004	−0.730022	+	0.683423i	$0.760490\pi$
$464$	15.2705	0.708916
$465$	−5.52786	−0.256349
$466$	11.5623	0.535613
$467$	12.7082	0.588066	0.294033	−	0.955795i	$-0.405003\pi$
$467$	12.7082	0.588066	0.294033	+	0.955795i	$0.405003\pi$
$468$	1.61803	0.0747936
$469$	1.52786	0.0705502
$470$	−5.52786	−0.254981
$471$	2.00000	0.0921551
$472$	−13.4164	−0.617540
$473$	15.0557	0.692263
$474$	3.70820	0.170323
$475$	0	0
$476$	−1.61803	−0.0741625
$477$	1.52786	0.0699561
$478$	−8.14590	−0.372585
$479$	−8.00000	−0.365529	−0.182765	−	0.983157i	$-0.558505\pi$
$479$	−8.00000	−0.365529	−0.182765	+	0.983157i	$0.558505\pi$
$480$	−12.5623	−0.573388
$481$	4.47214	0.203912
$482$	−6.18034	−0.281507
$483$	3.00000	0.136505
$484$	−8.09017	−0.367735
$485$	23.4164	1.06328
$486$	−0.618034	−0.0280346
$487$	−11.3607	−0.514802	−0.257401	−	0.966305i	$-0.582866\pi$
$487$	−11.3607	−0.514802	−0.257401	+	0.966305i	$0.582866\pi$
$488$	18.4164	0.833672
$489$	−0.0557281	−0.00252011
$490$	1.38197	0.0624309
$491$	28.3607	1.27990	0.639950	−	0.768417i	$-0.278955\pi$
$491$	28.3607	1.27990	0.639950	+	0.768417i	$0.278955\pi$
$492$	−7.61803	−0.343447
$493$	−8.23607	−0.370934
$494$	−3.85410	−0.173404
$495$	−8.94427	−0.402015
$496$	4.58359	0.205809
$497$	6.47214	0.290315
$498$	5.23607	0.234634
$499$	−26.8328	−1.20120	−0.600601	−	0.799549i	$-0.705072\pi$
$499$	−26.8328	−1.20120	−0.600601	+	0.799549i	$0.705072\pi$
$500$	18.0902	0.809017
$501$	13.4721	0.601891
$502$	−12.5066	−0.558196
$503$	16.9443	0.755508	0.377754	−	0.925906i	$-0.376697\pi$
$503$	16.9443	0.755508	0.377754	+	0.925906i	$0.376697\pi$
$504$	2.23607	0.0996024
$505$	5.65248	0.251532
$506$	−7.41641	−0.329700
$507$	−1.00000	−0.0444116
$508$	−9.32624	−0.413785
$509$	32.9443	1.46023	0.730115	−	0.683325i	$-0.239467\pi$
$509$	32.9443	1.46023	0.730115	+	0.683325i	$0.239467\pi$
$510$	1.38197	0.0611945
$511$	−5.52786	−0.244538
$512$	18.7082	0.826794
$513$	−6.23607	−0.275329
$514$	7.38197	0.325605
$515$	−43.4164	−1.91316
$516$	−6.09017	−0.268105
$517$	16.0000	0.703679
$518$	2.76393	0.121440
$519$	−7.05573	−0.309712
$520$	5.00000	0.219265
$521$	−37.3050	−1.63436	−0.817180	−	0.576383i	$-0.804464\pi$
$521$	−37.3050	−1.63436	−0.817180	+	0.576383i	$0.804464\pi$
$522$	5.09017	0.222791
$523$	−42.9443	−1.87782	−0.938911	−	0.344160i	$-0.888164\pi$
$523$	−42.9443	−1.87782	−0.938911	+	0.344160i	$0.888164\pi$
$524$	21.7082	0.948327
$525$	0	0
$526$	−6.47214	−0.282199
$527$	−2.47214	−0.107688
$528$	7.41641	0.322758
$529$	−14.0000	−0.608696
$530$	2.11146	0.0917158
$531$	6.00000	0.260378
$532$	10.0902	0.437464
$533$	4.70820	0.203935
$534$	8.94427	0.387056
$535$	3.29180	0.142317
$536$	3.41641	0.147566
$537$	−4.47214	−0.192987
$538$	1.52786	0.0658709
$539$	−4.00000	−0.172292
$540$	3.61803	0.155695
$541$	19.6525	0.844926	0.422463	−	0.906380i	$-0.361166\pi$
$541$	19.6525	0.844926	0.422463	+	0.906380i	$0.361166\pi$
$542$	0.437694	0.0188006
$543$	4.47214	0.191918
$544$	−5.61803	−0.240871
$545$	−15.0000	−0.642529
$546$	−0.618034	−0.0264494
$547$	7.05573	0.301681	0.150841	−	0.988558i	$-0.451802\pi$
$547$	7.05573	0.301681	0.150841	+	0.988558i	$0.451802\pi$
$548$	−4.76393	−0.203505
$549$	−8.23607	−0.351507
$550$	0	0
$551$	51.3607	2.18804
$552$	6.70820	0.285520
$553$	6.00000	0.255146
$554$	−1.88854	−0.0802365
$555$	10.0000	0.424476
$556$	13.6180	0.577533
$557$	−11.9443	−0.506095	−0.253048	−	0.967454i	$-0.581433\pi$
$557$	−11.9443	−0.506095	−0.253048	+	0.967454i	$0.581433\pi$
$558$	1.52786	0.0646796
$559$	3.76393	0.159197
$560$	−4.14590	−0.175196
$561$	−4.00000	−0.168880
$562$	−14.5066	−0.611923
$563$	20.2361	0.852849	0.426424	−	0.904523i	$-0.359773\pi$
$563$	20.2361	0.852849	0.426424	+	0.904523i	$0.359773\pi$
$564$	−6.47214	−0.272526
$565$	−1.05573	−0.0444148
$566$	8.90983	0.374508
$567$	−1.00000	−0.0419961
$568$	14.4721	0.607237
$569$	27.7771	1.16448	0.582238	−	0.813018i	$-0.302177\pi$
$569$	27.7771	1.16448	0.582238	+	0.813018i	$0.302177\pi$
$570$	−8.61803	−0.360970
$571$	−7.52786	−0.315031	−0.157516	−	0.987516i	$-0.550348\pi$
$571$	−7.52786	−0.315031	−0.157516	+	0.987516i	$0.550348\pi$
$572$	−6.47214	−0.270614
$573$	11.8885	0.496651
$574$	2.90983	0.121454
$575$	0	0
$576$	−0.236068	−0.00983617
$577$	38.4164	1.59930	0.799648	−	0.600469i	$-0.205019\pi$
$577$	38.4164	1.59930	0.799648	+	0.600469i	$0.205019\pi$
$578$	0.618034	0.0257068
$579$	−22.5967	−0.939089
$580$	−29.7984	−1.23731
$581$	8.47214	0.351483
$582$	−6.47214	−0.268279
$583$	−6.11146	−0.253111
$584$	−12.3607	−0.511489
$585$	−2.23607	−0.0924500
$586$	−4.29180	−0.177292
$587$	19.3050	0.796801	0.398400	−	0.917212i	$-0.369565\pi$
$587$	19.3050	0.796801	0.398400	+	0.917212i	$0.369565\pi$
$588$	1.61803	0.0667266
$589$	15.4164	0.635222
$590$	8.29180	0.341368
$591$	−5.41641	−0.222801
$592$	−8.29180	−0.340791
$593$	5.41641	0.222425	0.111213	−	0.993797i	$-0.464527\pi$
$593$	5.41641	0.222425	0.111213	+	0.993797i	$0.464527\pi$
$594$	2.47214	0.101433
$595$	2.23607	0.0916698
$596$	−3.23607	−0.132555
$597$	−14.8885	−0.609348
$598$	−1.85410	−0.0758199
$599$	27.7771	1.13494	0.567471	−	0.823394i	$-0.307922\pi$
$599$	27.7771	1.13494	0.567471	+	0.823394i	$0.307922\pi$
$600$	0	0
$601$	46.7082	1.90527	0.952634	−	0.304120i	$-0.0983624\pi$
$601$	46.7082	1.90527	0.952634	+	0.304120i	$0.0983624\pi$
$602$	2.32624	0.0948104
$603$	−1.52786	−0.0622194
$604$	5.70820	0.232264
$605$	11.1803	0.454545
$606$	−1.56231	−0.0634643
$607$	−0.0557281	−0.00226193	−0.00113097	−	0.999999i	$-0.500360\pi$
$607$	−0.0557281	−0.00226193	−0.00113097	+	0.999999i	$0.500360\pi$
$608$	35.0344	1.42083
$609$	8.23607	0.333742
$610$	−11.3820	−0.460842
$611$	4.00000	0.161823
$612$	1.61803	0.0654051
$613$	28.3607	1.14548	0.572739	−	0.819738i	$-0.305881\pi$
$613$	28.3607	1.14548	0.572739	+	0.819738i	$0.305881\pi$
$614$	−19.5623	−0.789470
$615$	10.5279	0.424524
$616$	−8.94427	−0.360375
$617$	−23.0557	−0.928189	−0.464094	−	0.885786i	$-0.653620\pi$
$617$	−23.0557	−0.928189	−0.464094	+	0.885786i	$0.653620\pi$
$618$	12.0000	0.482711
$619$	25.3050	1.01709	0.508546	−	0.861035i	$-0.330183\pi$
$619$	25.3050	1.01709	0.508546	+	0.861035i	$0.330183\pi$
$620$	−8.94427	−0.359211
$621$	−3.00000	−0.120386
$622$	9.52786	0.382033
$623$	14.4721	0.579814
$624$	1.85410	0.0742235
$625$	−25.0000	−1.00000
$626$	7.70820	0.308082
$627$	24.9443	0.996178
$628$	3.23607	0.129133
$629$	4.47214	0.178316
$630$	−1.38197	−0.0550588
$631$	42.3607	1.68635	0.843176	−	0.537638i	$-0.180683\pi$
$631$	42.3607	1.68635	0.843176	+	0.537638i	$0.180683\pi$
$632$	13.4164	0.533676
$633$	14.4721	0.575216
$634$	−8.58359	−0.340898
$635$	12.8885	0.511466
$636$	2.47214	0.0980266
$637$	−1.00000	−0.0396214
$638$	−20.3607	−0.806087
$639$	−6.47214	−0.256034
$640$	−25.4508	−1.00603
$641$	−11.5279	−0.455323	−0.227662	−	0.973740i	$-0.573108\pi$
$641$	−11.5279	−0.455323	−0.227662	+	0.973740i	$0.573108\pi$
$642$	−0.909830	−0.0359081
$643$	−36.3607	−1.43393	−0.716963	−	0.697112i	$-0.754468\pi$
$643$	−36.3607	−1.43393	−0.716963	+	0.697112i	$0.754468\pi$
$644$	4.85410	0.191278
$645$	8.41641	0.331396
$646$	−3.85410	−0.151638
$647$	14.2361	0.559678	0.279839	−	0.960047i	$-0.409719\pi$
$647$	14.2361	0.559678	0.279839	+	0.960047i	$0.409719\pi$
$648$	−2.23607	−0.0878410
$649$	−24.0000	−0.942082
$650$	0	0
$651$	2.47214	0.0968906
$652$	−0.0901699	−0.00353133
$653$	2.81966	0.110342	0.0551709	−	0.998477i	$-0.482430\pi$
$653$	2.81966	0.110342	0.0551709	+	0.998477i	$0.482430\pi$
$654$	4.14590	0.162117
$655$	−30.0000	−1.17220
$656$	−8.72949	−0.340829
$657$	5.52786	0.215663
$658$	2.47214	0.0963739
$659$	−28.8328	−1.12317	−0.561584	−	0.827420i	$-0.689808\pi$
$659$	−28.8328	−1.12317	−0.561584	+	0.827420i	$0.689808\pi$
$660$	−14.4721	−0.563327
$661$	43.9443	1.70923	0.854617	−	0.519259i	$-0.173792\pi$
$661$	43.9443	1.70923	0.854617	+	0.519259i	$0.173792\pi$
$662$	−12.0000	−0.466393
$663$	−1.00000	−0.0388368
$664$	18.9443	0.735180
$665$	−13.9443	−0.540736
$666$	−2.76393	−0.107100
$667$	24.7082	0.956705
$668$	21.7984	0.843404
$669$	1.18034	0.0456346
$670$	−2.11146	−0.0815727
$671$	32.9443	1.27180
$672$	5.61803	0.216720
$673$	−31.3050	−1.20672	−0.603359	−	0.797470i	$-0.706171\pi$
$673$	−31.3050	−1.20672	−0.603359	+	0.797470i	$0.706171\pi$
$674$	−8.00000	−0.308148
$675$	0	0
$676$	−1.61803	−0.0622321
$677$	33.0557	1.27043	0.635217	−	0.772333i	$-0.280910\pi$
$677$	33.0557	1.27043	0.635217	+	0.772333i	$0.280910\pi$
$678$	0.291796	0.0112064
$679$	−10.4721	−0.401884
$680$	5.00000	0.191741
$681$	23.9443	0.917546
$682$	−6.11146	−0.234020
$683$	1.52786	0.0584621	0.0292310	−	0.999573i	$-0.490694\pi$
$683$	1.52786	0.0584621	0.0292310	+	0.999573i	$0.490694\pi$
$684$	−10.0902	−0.385807
$685$	6.58359	0.251546
$686$	−0.618034	−0.0235966
$687$	6.05573	0.231040
$688$	−6.97871	−0.266061
$689$	−1.52786	−0.0582070
$690$	−4.14590	−0.157832
$691$	−47.4164	−1.80381	−0.901903	−	0.431939i	$-0.857829\pi$
$691$	−47.4164	−1.80381	−0.901903	+	0.431939i	$0.857829\pi$
$692$	−11.4164	−0.433987
$693$	4.00000	0.151947
$694$	12.3607	0.469205
$695$	−18.8197	−0.713870
$696$	18.4164	0.698072
$697$	4.70820	0.178336
$698$	−16.6180	−0.629002
$699$	−18.7082	−0.707609
$700$	0	0
$701$	−26.9443	−1.01767	−0.508836	−	0.860864i	$-0.669924\pi$
$701$	−26.9443	−1.01767	−0.508836	+	0.860864i	$0.669924\pi$
$702$	0.618034	0.0233262
$703$	−27.8885	−1.05184
$704$	0.944272	0.0355886
$705$	8.94427	0.336861
$706$	10.7639	0.405106
$707$	−2.52786	−0.0950701
$708$	9.70820	0.364857
$709$	5.41641	0.203417	0.101709	−	0.994814i	$-0.467569\pi$
$709$	5.41641	0.203417	0.101709	+	0.994814i	$0.467569\pi$
$710$	−8.94427	−0.335673
$711$	−6.00000	−0.225018
$712$	32.3607	1.21277
$713$	7.41641	0.277747
$714$	−0.618034	−0.0231293
$715$	8.94427	0.334497
$716$	−7.23607	−0.270425
$717$	13.1803	0.492229
$718$	0.583592	0.0217795
$719$	−2.00000	−0.0745874	−0.0372937	−	0.999304i	$-0.511874\pi$
$719$	−2.00000	−0.0745874	−0.0372937	+	0.999304i	$0.511874\pi$
$720$	4.14590	0.154508
$721$	19.4164	0.723105
$722$	12.2918	0.457453
$723$	10.0000	0.371904
$724$	7.23607	0.268926
$725$	0	0
$726$	−3.09017	−0.114687
$727$	−33.8885	−1.25686	−0.628428	−	0.777868i	$-0.716301\pi$
$727$	−33.8885	−1.25686	−0.628428	+	0.777868i	$0.716301\pi$
$728$	−2.23607	−0.0828742
$729$	1.00000	0.0370370
$730$	7.63932	0.282744
$731$	3.76393	0.139214
$732$	−13.3262	−0.492552
$733$	−41.8328	−1.54513	−0.772565	−	0.634935i	$-0.781027\pi$
$733$	−41.8328	−1.54513	−0.772565	+	0.634935i	$0.781027\pi$
$734$	−11.1591	−0.411888
$735$	−2.23607	−0.0824786
$736$	16.8541	0.621250
$737$	6.11146	0.225118
$738$	−2.90983	−0.107112
$739$	9.41641	0.346388	0.173194	−	0.984888i	$-0.444591\pi$
$739$	9.41641	0.346388	0.173194	+	0.984888i	$0.444591\pi$
$740$	16.1803	0.594801
$741$	6.23607	0.229088
$742$	−0.944272	−0.0346653
$743$	30.2492	1.10974	0.554868	−	0.831938i	$-0.312769\pi$
$743$	30.2492	1.10974	0.554868	+	0.831938i	$0.312769\pi$
$744$	5.52786	0.202661
$745$	4.47214	0.163846
$746$	8.90983	0.326212
$747$	−8.47214	−0.309979
$748$	−6.47214	−0.236645
$749$	−1.47214	−0.0537907
$750$	6.90983	0.252311
$751$	40.8328	1.49001	0.745005	−	0.667059i	$-0.232447\pi$
$751$	40.8328	1.49001	0.745005	+	0.667059i	$0.232447\pi$
$752$	−7.41641	−0.270449
$753$	20.2361	0.737443
$754$	−5.09017	−0.185373
$755$	−7.88854	−0.287094
$756$	−1.61803	−0.0588473
$757$	−39.8885	−1.44977	−0.724887	−	0.688868i	$-0.758108\pi$
$757$	−39.8885	−1.44977	−0.724887	+	0.688868i	$0.758108\pi$
$758$	−7.45085	−0.270627
$759$	12.0000	0.435572
$760$	−31.1803	−1.13103
$761$	47.3050	1.71480	0.857402	−	0.514648i	$-0.172077\pi$
$761$	47.3050	1.71480	0.857402	+	0.514648i	$0.172077\pi$
$762$	−3.56231	−0.129049
$763$	6.70820	0.242853
$764$	19.2361	0.695937
$765$	−2.23607	−0.0808452
$766$	11.0557	0.399460
$767$	−6.00000	−0.216647
$768$	6.56231	0.236797
$769$	−15.8885	−0.572956	−0.286478	−	0.958087i	$-0.592484\pi$
$769$	−15.8885	−0.572956	−0.286478	+	0.958087i	$0.592484\pi$
$770$	5.52786	0.199210
$771$	−11.9443	−0.430162
$772$	−36.5623	−1.31591
$773$	43.7771	1.57455	0.787276	−	0.616601i	$-0.211491\pi$
$773$	43.7771	1.57455	0.787276	+	0.616601i	$0.211491\pi$
$774$	−2.32624	−0.0836149
$775$	0	0
$776$	−23.4164	−0.840600
$777$	−4.47214	−0.160437
$778$	−17.2361	−0.617943
$779$	−29.3607	−1.05196
$780$	−3.61803	−0.129546
$781$	25.8885	0.926365
$782$	−1.85410	−0.0663026
$783$	−8.23607	−0.294333
$784$	1.85410	0.0662179
$785$	−4.47214	−0.159617
$786$	8.29180	0.295759
$787$	13.0557	0.465386	0.232693	−	0.972550i	$-0.425246\pi$
$787$	13.0557	0.465386	0.232693	+	0.972550i	$0.425246\pi$
$788$	−8.76393	−0.312202
$789$	10.4721	0.372818
$790$	−8.29180	−0.295009
$791$	0.472136	0.0167872
$792$	8.94427	0.317821
$793$	8.23607	0.292471
$794$	13.2361	0.469730
$795$	−3.41641	−0.121168
$796$	−24.0902	−0.853853
$797$	38.9443	1.37948	0.689738	−	0.724059i	$-0.257726\pi$
$797$	38.9443	1.37948	0.689738	+	0.724059i	$0.257726\pi$
$798$	3.85410	0.136434
$799$	4.00000	0.141510
$800$	0	0
$801$	−14.4721	−0.511348
$802$	−14.1803	−0.500725
$803$	−22.1115	−0.780296
$804$	−2.47214	−0.0871855
$805$	−6.70820	−0.236433
$806$	−1.52786	−0.0538167
$807$	−2.47214	−0.0870233
$808$	−5.65248	−0.198853
$809$	−19.6525	−0.690944	−0.345472	−	0.938429i	$-0.612281\pi$
$809$	−19.6525	−0.690944	−0.345472	+	0.938429i	$0.612281\pi$
$810$	1.38197	0.0485573
$811$	45.7771	1.60745	0.803725	−	0.595000i	$-0.202848\pi$
$811$	45.7771	1.60745	0.803725	+	0.595000i	$0.202848\pi$
$812$	13.3262	0.467659
$813$	−0.708204	−0.0248378
$814$	11.0557	0.387503
$815$	0.124612	0.00436496
$816$	1.85410	0.0649066
$817$	−23.4721	−0.821186
$818$	5.27051	0.184279
$819$	1.00000	0.0349428
$820$	17.0344	0.594869
$821$	27.7771	0.969427	0.484714	−	0.874673i	$-0.338924\pi$
$821$	27.7771	0.969427	0.484714	+	0.874673i	$0.338924\pi$
$822$	−1.81966	−0.0634679
$823$	−4.47214	−0.155889	−0.0779444	−	0.996958i	$-0.524836\pi$
$823$	−4.47214	−0.155889	−0.0779444	+	0.996958i	$0.524836\pi$
$824$	43.4164	1.51248
$825$	0	0
$826$	−3.70820	−0.129025
$827$	19.0557	0.662633	0.331316	−	0.943520i	$-0.392507\pi$
$827$	19.0557	0.662633	0.331316	+	0.943520i	$0.392507\pi$
$828$	−4.85410	−0.168692
$829$	10.5836	0.367583	0.183792	−	0.982965i	$-0.441163\pi$
$829$	10.5836	0.367583	0.183792	+	0.982965i	$0.441163\pi$
$830$	−11.7082	−0.406398
$831$	3.05573	0.106002
$832$	0.236068	0.00818418
$833$	−1.00000	−0.0346479
$834$	5.20163	0.180118
$835$	−30.1246	−1.04251
$836$	40.3607	1.39590
$837$	−2.47214	−0.0854495
$838$	7.41641	0.256196
$839$	8.52786	0.294415	0.147207	−	0.989106i	$-0.452972\pi$
$839$	8.52786	0.294415	0.147207	+	0.989106i	$0.452972\pi$
$840$	−5.00000	−0.172516
$841$	38.8328	1.33906
$842$	−9.30495	−0.320670
$843$	23.4721	0.808423
$844$	23.4164	0.806026
$845$	2.23607	0.0769231
$846$	−2.47214	−0.0849938
$847$	−5.00000	−0.171802
$848$	2.83282	0.0972793
$849$	−14.4164	−0.494770
$850$	0	0
$851$	−13.4164	−0.459909
$852$	−10.4721	−0.358769
$853$	−16.3607	−0.560179	−0.280090	−	0.959974i	$-0.590364\pi$
$853$	−16.3607	−0.560179	−0.280090	+	0.959974i	$0.590364\pi$
$854$	5.09017	0.174182
$855$	13.9443	0.476884
$856$	−3.29180	−0.112511
$857$	22.0000	0.751506	0.375753	−	0.926720i	$-0.377384\pi$
$857$	22.0000	0.751506	0.375753	+	0.926720i	$0.377384\pi$
$858$	−2.47214	−0.0843973
$859$	−40.8328	−1.39320	−0.696599	−	0.717461i	$-0.745304\pi$
$859$	−40.8328	−1.39320	−0.696599	+	0.717461i	$0.745304\pi$
$860$	13.6180	0.464371
$861$	−4.70820	−0.160455
$862$	−13.5967	−0.463107
$863$	−10.1115	−0.344198	−0.172099	−	0.985080i	$-0.555055\pi$
$863$	−10.1115	−0.344198	−0.172099	+	0.985080i	$0.555055\pi$
$864$	−5.61803	−0.191129
$865$	15.7771	0.536437
$866$	−1.81966	−0.0618346
$867$	−1.00000	−0.0339618
$868$	4.00000	0.135769
$869$	24.0000	0.814144
$870$	−11.3820	−0.385885
$871$	1.52786	0.0517697
$872$	15.0000	0.507964
$873$	10.4721	0.354428
$874$	11.5623	0.391101
$875$	11.1803	0.377964
$876$	8.94427	0.302199
$877$	21.2918	0.718973	0.359486	−	0.933150i	$-0.382952\pi$
$877$	21.2918	0.718973	0.359486	+	0.933150i	$0.382952\pi$
$878$	−23.4164	−0.790265
$879$	6.94427	0.234224
$880$	−16.5836	−0.559033
$881$	39.8885	1.34388	0.671940	−	0.740606i	$-0.265461\pi$
$881$	39.8885	1.34388	0.671940	+	0.740606i	$0.265461\pi$
$882$	0.618034	0.0208103
$883$	−24.2361	−0.815609	−0.407804	−	0.913069i	$-0.633705\pi$
$883$	−24.2361	−0.815609	−0.407804	+	0.913069i	$0.633705\pi$
$884$	−1.61803	−0.0544204
$885$	−13.4164	−0.450988
$886$	−8.87539	−0.298174
$887$	34.4721	1.15746	0.578731	−	0.815519i	$-0.303548\pi$
$887$	34.4721	1.15746	0.578731	+	0.815519i	$0.303548\pi$
$888$	−10.0000	−0.335578
$889$	−5.76393	−0.193316
$890$	−20.0000	−0.670402
$891$	−4.00000	−0.134005
$892$	1.90983	0.0639458
$893$	−24.9443	−0.834728
$894$	−1.23607	−0.0413403
$895$	10.0000	0.334263
$896$	11.3820	0.380245
$897$	3.00000	0.100167
$898$	−9.23607	−0.308212
$899$	20.3607	0.679067
$900$	0	0
$901$	−1.52786	−0.0509005
$902$	11.6393	0.387547
$903$	−3.76393	−0.125256
$904$	1.05573	0.0351130
$905$	−10.0000	−0.332411
$906$	2.18034	0.0724369
$907$	−10.9443	−0.363399	−0.181699	−	0.983354i	$-0.558160\pi$
$907$	−10.9443	−0.363399	−0.181699	+	0.983354i	$0.558160\pi$
$908$	38.7426	1.28572
$909$	2.52786	0.0838440
$910$	1.38197	0.0458117
$911$	25.8885	0.857726	0.428863	−	0.903370i	$-0.358914\pi$
$911$	25.8885	0.857726	0.428863	+	0.903370i	$0.358914\pi$
$912$	−11.5623	−0.382866
$913$	33.8885	1.12155
$914$	15.3475	0.507651
$915$	18.4164	0.608828
$916$	9.79837	0.323747
$917$	13.4164	0.443049
$918$	0.618034	0.0203982
$919$	13.2918	0.438456	0.219228	−	0.975674i	$-0.429646\pi$
$919$	13.2918	0.438456	0.219228	+	0.975674i	$0.429646\pi$
$920$	−15.0000	−0.494535
$921$	31.6525	1.04298
$922$	22.7639	0.749690
$923$	6.47214	0.213033
$924$	6.47214	0.212918
$925$	0	0
$926$	−19.4164	−0.638063
$927$	−19.4164	−0.637719
$928$	46.2705	1.51890
$929$	3.52786	0.115745	0.0578727	−	0.998324i	$-0.481568\pi$
$929$	3.52786	0.115745	0.0578727	+	0.998324i	$0.481568\pi$
$930$	−3.41641	−0.112028
$931$	6.23607	0.204379
$932$	−30.2705	−0.991544
$933$	−15.4164	−0.504711
$934$	7.85410	0.256994
$935$	8.94427	0.292509
$936$	2.23607	0.0730882
$937$	−22.5836	−0.737774	−0.368887	−	0.929474i	$-0.620261\pi$
$937$	−22.5836	−0.737774	−0.368887	+	0.929474i	$0.620261\pi$
$938$	0.944272	0.0308316
$939$	−12.4721	−0.407013
$940$	14.4721	0.472029
$941$	9.29180	0.302904	0.151452	−	0.988465i	$-0.451605\pi$
$941$	9.29180	0.302904	0.151452	+	0.988465i	$0.451605\pi$
$942$	1.23607	0.0402733
$943$	−14.1246	−0.459961
$944$	11.1246	0.362075
$945$	2.23607	0.0727393
$946$	9.30495	0.302530
$947$	1.52786	0.0496489	0.0248245	−	0.999692i	$-0.492097\pi$
$947$	1.52786	0.0496489	0.0248245	+	0.999692i	$0.492097\pi$
$948$	−9.70820	−0.315308
$949$	−5.52786	−0.179442
$950$	0	0
$951$	13.8885	0.450367
$952$	−2.23607	−0.0724714
$953$	−10.4721	−0.339226	−0.169613	−	0.985511i	$-0.554252\pi$
$953$	−10.4721	−0.339226	−0.169613	+	0.985511i	$0.554252\pi$
$954$	0.944272	0.0305719
$955$	−26.5836	−0.860225
$956$	21.3262	0.689740
$957$	32.9443	1.06494
$958$	−4.94427	−0.159742
$959$	−2.94427	−0.0950755
$960$	0.527864	0.0170367
$961$	−24.8885	−0.802856
$962$	2.76393	0.0891127
$963$	1.47214	0.0474389
$964$	16.1803	0.521134
$965$	50.5279	1.62655
$966$	1.85410	0.0596548
$967$	−22.4721	−0.722655	−0.361328	−	0.932439i	$-0.617676\pi$
$967$	−22.4721	−0.722655	−0.361328	+	0.932439i	$0.617676\pi$
$968$	−11.1803	−0.359350
$969$	6.23607	0.200331
$970$	14.4721	0.464672
$971$	10.1246	0.324914	0.162457	−	0.986716i	$-0.448058\pi$
$971$	10.1246	0.324914	0.162457	+	0.986716i	$0.448058\pi$
$972$	1.61803	0.0518985
$973$	8.41641	0.269818
$974$	−7.02129	−0.224977
$975$	0	0
$976$	−15.2705	−0.488797
$977$	32.4164	1.03709	0.518546	−	0.855049i	$-0.326473\pi$
$977$	32.4164	1.03709	0.518546	+	0.855049i	$0.326473\pi$
$978$	−0.0344419	−0.00110133
$979$	57.8885	1.85013
$980$	−3.61803	−0.115574
$981$	−6.70820	−0.214176
$982$	17.5279	0.559337
$983$	−18.3050	−0.583837	−0.291919	−	0.956443i	$-0.594294\pi$
$983$	−18.3050	−0.583837	−0.291919	+	0.956443i	$0.594294\pi$
$984$	−10.5279	−0.335616
$985$	12.1115	0.385903
$986$	−5.09017	−0.162104
$987$	−4.00000	−0.127321
$988$	10.0902	0.321011
$989$	−11.2918	−0.359058
$990$	−5.52786	−0.175687
$991$	−15.8885	−0.504716	−0.252358	−	0.967634i	$-0.581206\pi$
$991$	−15.8885	−0.504716	−0.252358	+	0.967634i	$0.581206\pi$
$992$	13.8885	0.440962
$993$	19.4164	0.616161
$994$	4.00000	0.126872
$995$	33.2918	1.05542
$996$	−13.7082	−0.434361
$997$	48.2492	1.52807	0.764034	−	0.645176i	$-0.223216\pi$
$997$	48.2492	1.52807	0.764034	+	0.645176i	$0.223216\pi$
$998$	−16.5836	−0.524944
$999$	4.47214	0.141492

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4641.2.a.i.1.2	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4641.2.a.i.1.2	✓	2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 4641 = 3 \cdot 7 \cdot 13 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4641.a (trivial)

\(f(q)\)	\(=\)	\(q+0.618034 q^{2} -1.00000 q^{3} -1.61803 q^{4} +2.23607 q^{5} -0.618034 q^{6} -1.00000 q^{7} -2.23607 q^{8} +1.00000 q^{9} +1.38197 q^{10} -4.00000 q^{11} +1.61803 q^{12} -1.00000 q^{13} -0.618034 q^{14} -2.23607 q^{15} +1.85410 q^{16} -1.00000 q^{17} +0.618034 q^{18} +6.23607 q^{19} -3.61803 q^{20} +1.00000 q^{21} -2.47214 q^{22} +3.00000 q^{23} +2.23607 q^{24} -0.618034 q^{26} -1.00000 q^{27} +1.61803 q^{28} +8.23607 q^{29} -1.38197 q^{30} +2.47214 q^{31} +5.61803 q^{32} +4.00000 q^{33} -0.618034 q^{34} -2.23607 q^{35} -1.61803 q^{36} -4.47214 q^{37} +3.85410 q^{38} +1.00000 q^{39} -5.00000 q^{40} -4.70820 q^{41} +0.618034 q^{42} -3.76393 q^{43} +6.47214 q^{44} +2.23607 q^{45} +1.85410 q^{46} -4.00000 q^{47} -1.85410 q^{48} +1.00000 q^{49} +1.00000 q^{51} +1.61803 q^{52} +1.52786 q^{53} -0.618034 q^{54} -8.94427 q^{55} +2.23607 q^{56} -6.23607 q^{57} +5.09017 q^{58} +6.00000 q^{59} +3.61803 q^{60} -8.23607 q^{61} +1.52786 q^{62} -1.00000 q^{63} -0.236068 q^{64} -2.23607 q^{65} +2.47214 q^{66} -1.52786 q^{67} +1.61803 q^{68} -3.00000 q^{69} -1.38197 q^{70} -6.47214 q^{71} -2.23607 q^{72} +5.52786 q^{73} -2.76393 q^{74} -10.0902 q^{76} +4.00000 q^{77} +0.618034 q^{78} -6.00000 q^{79} +4.14590 q^{80} +1.00000 q^{81} -2.90983 q^{82} -8.47214 q^{83} -1.61803 q^{84} -2.23607 q^{85} -2.32624 q^{86} -8.23607 q^{87} +8.94427 q^{88} -14.4721 q^{89} +1.38197 q^{90} +1.00000 q^{91} -4.85410 q^{92} -2.47214 q^{93} -2.47214 q^{94} +13.9443 q^{95} -5.61803 q^{96} +10.4721 q^{97} +0.618034 q^{98} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - 2 q^{3} - q^{4} + q^{6} - 2 q^{7} + 2 q^{9} + 5 q^{10} - 8 q^{11} + q^{12} - 2 q^{13} + q^{14} - 3 q^{16} - 2 q^{17} - q^{18} + 8 q^{19} - 5 q^{20} + 2 q^{21} + 4 q^{22} + 6 q^{23} + q^{26}+ \cdots - 8 q^{99}+O(q^{100}) \) 2 * q - q^2 - 2 * q^3 - q^4 + q^6 - 2 * q^7 + 2 * q^9 + 5 * q^10 - 8 * q^11 + q^12 - 2 * q^13 + q^14 - 3 * q^16 - 2 * q^17 - q^18 + 8 * q^19 - 5 * q^20 + 2 * q^21 + 4 * q^22 + 6 * q^23 + q^26 - 2 * q^27 + q^28 + 12 * q^29 - 5 * q^30 - 4 * q^31 + 9 * q^32 + 8 * q^33 + q^34 - q^36 + q^38 + 2 * q^39 - 10 * q^40 + 4 * q^41 - q^42 - 12 * q^43 + 4 * q^44 - 3 * q^46 - 8 * q^47 + 3 * q^48 + 2 * q^49 + 2 * q^51 + q^52 + 12 * q^53 + q^54 - 8 * q^57 - q^58 + 12 * q^59 + 5 * q^60 - 12 * q^61 + 12 * q^62 - 2 * q^63 + 4 * q^64 - 4 * q^66 - 12 * q^67 + q^68 - 6 * q^69 - 5 * q^70 - 4 * q^71 + 20 * q^73 - 10 * q^74 - 9 * q^76 + 8 * q^77 - q^78 - 12 * q^79 + 15 * q^80 + 2 * q^81 - 17 * q^82 - 8 * q^83 - q^84 + 11 * q^86 - 12 * q^87 - 20 * q^89 + 5 * q^90 + 2 * q^91 - 3 * q^92 + 4 * q^93 + 4 * q^94 + 10 * q^95 - 9 * q^96 + 12 * q^97 - q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more