LMFDB - Embedded newform 5054.2.a.s.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5054,2,Mod(1,5054)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5054, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("5054.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5054 = 2 \cdot 7 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5054.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:	$40.3563931816$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{18})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 3x - 1 $ x^3 - 3*x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 266)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.87939$ of defining polynomial
Character	$\chi$	$=$	5054.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.879385 q^{3} +1.00000 q^{4} +0.532089 q^{5} +0.879385 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.22668 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.879385 q^{3} +1.00000 q^{4} +0.532089 q^{5} +0.879385 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.22668 q^{9} -0.532089 q^{10} -2.87939 q^{11} -0.879385 q^{12} +0.347296 q^{13} -1.00000 q^{14} -0.467911 q^{15} +1.00000 q^{16} -4.59627 q^{17} +2.22668 q^{18} +0.532089 q^{20} -0.879385 q^{21} +2.87939 q^{22} +2.45336 q^{23} +0.879385 q^{24} -4.71688 q^{25} -0.347296 q^{26} +4.59627 q^{27} +1.00000 q^{28} +9.41147 q^{29} +0.467911 q^{30} +4.63816 q^{31} -1.00000 q^{32} +2.53209 q^{33} +4.59627 q^{34} +0.532089 q^{35} -2.22668 q^{36} +5.70233 q^{37} -0.305407 q^{39} -0.532089 q^{40} +6.53983 q^{41} +0.879385 q^{42} +1.82295 q^{43} -2.87939 q^{44} -1.18479 q^{45} -2.45336 q^{46} +5.22668 q^{47} -0.879385 q^{48} +1.00000 q^{49} +4.71688 q^{50} +4.04189 q^{51} +0.347296 q^{52} +3.50980 q^{53} -4.59627 q^{54} -1.53209 q^{55} -1.00000 q^{56} -9.41147 q^{58} -8.66044 q^{59} -0.467911 q^{60} -9.06418 q^{61} -4.63816 q^{62} -2.22668 q^{63} +1.00000 q^{64} +0.184793 q^{65} -2.53209 q^{66} -11.7246 q^{67} -4.59627 q^{68} -2.15745 q^{69} -0.532089 q^{70} -13.2344 q^{71} +2.22668 q^{72} -9.92127 q^{73} -5.70233 q^{74} +4.14796 q^{75} -2.87939 q^{77} +0.305407 q^{78} +0.263518 q^{79} +0.532089 q^{80} +2.63816 q^{81} -6.53983 q^{82} +3.95811 q^{83} -0.879385 q^{84} -2.44562 q^{85} -1.82295 q^{86} -8.27631 q^{87} +2.87939 q^{88} +14.6013 q^{89} +1.18479 q^{90} +0.347296 q^{91} +2.45336 q^{92} -4.07873 q^{93} -5.22668 q^{94} +0.879385 q^{96} -10.1284 q^{97} -1.00000 q^{98} +6.41147 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} + 3 q^{7} - 3 q^{8}+O(q^{10}) $ 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 + 3 * q^7 - 3 * q^8	$ 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{10} - 3 q^{11} + 3 q^{12} - 3 q^{14} - 6 q^{15} + 3 q^{16} - 3 q^{20} + 3 q^{21} + 3 q^{22} - 6 q^{23} - 3 q^{24} - 6 q^{25} + 3 q^{28} + 18 q^{29} + 6 q^{30} - 3 q^{31} - 3 q^{32} + 3 q^{33} - 3 q^{35} - 9 q^{37} - 3 q^{39} + 3 q^{40} - 9 q^{41} - 3 q^{42} - 15 q^{43} - 3 q^{44} + 6 q^{46} + 9 q^{47} + 3 q^{48} + 3 q^{49} + 6 q^{50} + 9 q^{51} + 12 q^{53} - 3 q^{56} - 18 q^{58} - 3 q^{59} - 6 q^{60} - 18 q^{61} + 3 q^{62} + 3 q^{64} - 3 q^{65} - 3 q^{66} - 3 q^{67} - 24 q^{69} + 3 q^{70} - 9 q^{71} - 21 q^{73} + 9 q^{74} - 3 q^{75} - 3 q^{77} + 3 q^{78} + 6 q^{79} - 3 q^{80} - 9 q^{81} + 9 q^{82} + 15 q^{83} + 3 q^{84} - 18 q^{85} + 15 q^{86} + 9 q^{87} + 3 q^{88} + 15 q^{89} - 6 q^{92} - 21 q^{93} - 9 q^{94} - 3 q^{96} - 12 q^{97} - 3 q^{98} + 9 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^10 - 3 * q^11 + 3 * q^12 - 3 * q^14 - 6 * q^15 + 3 * q^16 - 3 * q^20 + 3 * q^21 + 3 * q^22 - 6 * q^23 - 3 * q^24 - 6 * q^25 + 3 * q^28 + 18 * q^29 + 6 * q^30 - 3 * q^31 - 3 * q^32 + 3 * q^33 - 3 * q^35 - 9 * q^37 - 3 * q^39 + 3 * q^40 - 9 * q^41 - 3 * q^42 - 15 * q^43 - 3 * q^44 + 6 * q^46 + 9 * q^47 + 3 * q^48 + 3 * q^49 + 6 * q^50 + 9 * q^51 + 12 * q^53 - 3 * q^56 - 18 * q^58 - 3 * q^59 - 6 * q^60 - 18 * q^61 + 3 * q^62 + 3 * q^64 - 3 * q^65 - 3 * q^66 - 3 * q^67 - 24 * q^69 + 3 * q^70 - 9 * q^71 - 21 * q^73 + 9 * q^74 - 3 * q^75 - 3 * q^77 + 3 * q^78 + 6 * q^79 - 3 * q^80 - 9 * q^81 + 9 * q^82 + 15 * q^83 + 3 * q^84 - 18 * q^85 + 15 * q^86 + 9 * q^87 + 3 * q^88 + 15 * q^89 - 6 * q^92 - 21 * q^93 - 9 * q^94 - 3 * q^96 - 12 * q^97 - 3 * q^98 + 9 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−0.879385	−0.507713	−0.253857	−	0.967242i	$-0.581699\pi$
$3$	−0.879385	−0.507713	−0.253857	+	0.967242i	$0.581699\pi$
$4$	1.00000	0.500000
$5$	0.532089	0.237957	0.118979	−	0.992897i	$-0.462038\pi$
$5$	0.532089	0.237957	0.118979	+	0.992897i	$0.462038\pi$
$6$	0.879385	0.359008
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	−2.22668	−0.742227
$10$	−0.532089	−0.168261
$11$	−2.87939	−0.868167	−0.434084	−	0.900873i	$-0.642928\pi$
$11$	−2.87939	−0.868167	−0.434084	+	0.900873i	$0.642928\pi$
$12$	−0.879385	−0.253857
$13$	0.347296	0.0963227	0.0481613	−	0.998840i	$-0.484664\pi$
$13$	0.347296	0.0963227	0.0481613	+	0.998840i	$0.484664\pi$
$14$	−1.00000	−0.267261
$15$	−0.467911	−0.120814
$16$	1.00000	0.250000
$17$	−4.59627	−1.11476	−0.557379	−	0.830258i	$-0.688193\pi$
$17$	−4.59627	−1.11476	−0.557379	+	0.830258i	$0.688193\pi$
$18$	2.22668	0.524834
$19$	0	0
$19$	0	0
$20$	0.532089	0.118979
$21$	−0.879385	−0.191898
$22$	2.87939	0.613887
$23$	2.45336	0.511562	0.255781	−	0.966735i	$-0.417667\pi$
$23$	2.45336	0.511562	0.255781	+	0.966735i	$0.417667\pi$
$24$	0.879385	0.179504
$25$	−4.71688	−0.943376
$26$	−0.347296	−0.0681104
$27$	4.59627	0.884552
$28$	1.00000	0.188982
$29$	9.41147	1.74767	0.873833	−	0.486225i	$-0.161627\pi$
$29$	9.41147	1.74767	0.873833	+	0.486225i	$0.161627\pi$
$30$	0.467911	0.0854285
$31$	4.63816	0.833037	0.416519	−	0.909127i	$-0.363250\pi$
$31$	4.63816	0.833037	0.416519	+	0.909127i	$0.363250\pi$
$32$	−1.00000	−0.176777
$33$	2.53209	0.440780
$34$	4.59627	0.788253
$35$	0.532089	0.0899394
$36$	−2.22668	−0.371114
$37$	5.70233	0.937458	0.468729	−	0.883342i	$-0.344712\pi$
$37$	5.70233	0.937458	0.468729	+	0.883342i	$0.344712\pi$
$38$	0	0
$39$	−0.305407	−0.0489043
$40$	−0.532089	−0.0841306
$41$	6.53983	1.02135	0.510675	−	0.859774i	$-0.329396\pi$
$41$	6.53983	1.02135	0.510675	+	0.859774i	$0.329396\pi$
$42$	0.879385	0.135692
$43$	1.82295	0.277997	0.138999	−	0.990293i	$-0.455612\pi$
$43$	1.82295	0.277997	0.138999	+	0.990293i	$0.455612\pi$
$44$	−2.87939	−0.434084
$45$	−1.18479	−0.176618
$46$	−2.45336	−0.361729
$47$	5.22668	0.762390	0.381195	−	0.924495i	$-0.375513\pi$
$47$	5.22668	0.762390	0.381195	+	0.924495i	$0.375513\pi$
$48$	−0.879385	−0.126928
$49$	1.00000	0.142857
$50$	4.71688	0.667068
$51$	4.04189	0.565978
$52$	0.347296	0.0481613
$53$	3.50980	0.482108	0.241054	−	0.970512i	$-0.422507\pi$
$53$	3.50980	0.482108	0.241054	+	0.970512i	$0.422507\pi$
$54$	−4.59627	−0.625473
$55$	−1.53209	−0.206587
$56$	−1.00000	−0.133631
$57$	0	0
$58$	−9.41147	−1.23579
$59$	−8.66044	−1.12749	−0.563747	−	0.825948i	$-0.690641\pi$
$59$	−8.66044	−1.12749	−0.563747	+	0.825948i	$0.690641\pi$
$60$	−0.467911	−0.0604071
$61$	−9.06418	−1.16055	−0.580275	−	0.814421i	$-0.697055\pi$
$61$	−9.06418	−1.16055	−0.580275	+	0.814421i	$0.697055\pi$
$62$	−4.63816	−0.589046
$63$	−2.22668	−0.280536
$64$	1.00000	0.125000
$65$	0.184793	0.0229207
$66$	−2.53209	−0.311679
$67$	−11.7246	−1.43239	−0.716195	−	0.697900i	$-0.754118\pi$
$67$	−11.7246	−1.43239	−0.716195	+	0.697900i	$0.754118\pi$
$68$	−4.59627	−0.557379
$69$	−2.15745	−0.259727
$70$	−0.532089	−0.0635968
$71$	−13.2344	−1.57064	−0.785318	−	0.619092i	$-0.787501\pi$
$71$	−13.2344	−1.57064	−0.785318	+	0.619092i	$0.787501\pi$
$72$	2.22668	0.262417
$73$	−9.92127	−1.16120	−0.580599	−	0.814190i	$-0.697181\pi$
$73$	−9.92127	−1.16120	−0.580599	+	0.814190i	$0.697181\pi$
$74$	−5.70233	−0.662883
$75$	4.14796	0.478965
$76$	0	0
$77$	−2.87939	−0.328136
$78$	0.305407	0.0345806
$79$	0.263518	0.0296481	0.0148241	−	0.999890i	$-0.495281\pi$
$79$	0.263518	0.0296481	0.0148241	+	0.999890i	$0.495281\pi$
$80$	0.532089	0.0594893
$81$	2.63816	0.293128
$82$	−6.53983	−0.722203
$83$	3.95811	0.434459	0.217230	−	0.976121i	$-0.430298\pi$
$83$	3.95811	0.434459	0.217230	+	0.976121i	$0.430298\pi$
$84$	−0.879385	−0.0959488
$85$	−2.44562	−0.265265
$86$	−1.82295	−0.196574
$87$	−8.27631	−0.887314
$88$	2.87939	0.306943
$89$	14.6013	1.54774	0.773868	−	0.633346i	$-0.218319\pi$
$89$	14.6013	1.54774	0.773868	+	0.633346i	$0.218319\pi$
$90$	1.18479	0.124888
$91$	0.347296	0.0364066
$92$	2.45336	0.255781
$93$	−4.07873	−0.422944
$94$	−5.22668	−0.539091
$95$	0	0
$96$	0.879385	0.0897519
$97$	−10.1284	−1.02838	−0.514189	−	0.857677i	$-0.671907\pi$
$97$	−10.1284	−1.02838	−0.514189	+	0.857677i	$0.671907\pi$
$98$	−1.00000	−0.101015
$99$	6.41147	0.644377
$100$	−4.71688	−0.471688
$101$	11.5817	1.15242	0.576212	−	0.817300i	$-0.304530\pi$
$101$	11.5817	1.15242	0.576212	+	0.817300i	$0.304530\pi$
$102$	−4.04189	−0.400207
$103$	−2.65776	−0.261876	−0.130938	−	0.991391i	$-0.541799\pi$
$103$	−2.65776	−0.261876	−0.130938	+	0.991391i	$0.541799\pi$
$104$	−0.347296	−0.0340552
$105$	−0.467911	−0.0456634
$106$	−3.50980	−0.340902
$107$	11.1702	1.07987	0.539934	−	0.841707i	$-0.318449\pi$
$107$	11.1702	1.07987	0.539934	+	0.841707i	$0.318449\pi$
$108$	4.59627	0.442276
$109$	−17.4243	−1.66894	−0.834471	−	0.551052i	$-0.814227\pi$
$109$	−17.4243	−1.66894	−0.834471	+	0.551052i	$0.814227\pi$
$110$	1.53209	0.146079
$111$	−5.01455	−0.475960
$112$	1.00000	0.0944911
$113$	−3.36959	−0.316984	−0.158492	−	0.987360i	$-0.550663\pi$
$113$	−3.36959	−0.316984	−0.158492	+	0.987360i	$0.550663\pi$
$114$	0	0
$115$	1.30541	0.121730
$116$	9.41147	0.873833
$117$	−0.773318	−0.0714933
$118$	8.66044	0.797259
$119$	−4.59627	−0.421339
$120$	0.467911	0.0427142
$121$	−2.70914	−0.246286
$122$	9.06418	0.820632
$123$	−5.75103	−0.518553
$124$	4.63816	0.416519
$125$	−5.17024	−0.462441
$126$	2.22668	0.198369
$127$	10.1506	0.900724	0.450362	−	0.892846i	$-0.351295\pi$
$127$	10.1506	0.900724	0.450362	+	0.892846i	$0.351295\pi$
$128$	−1.00000	−0.0883883
$129$	−1.60307	−0.141143
$130$	−0.184793	−0.0162074
$131$	−8.74422	−0.763986	−0.381993	−	0.924165i	$-0.624762\pi$
$131$	−8.74422	−0.763986	−0.381993	+	0.924165i	$0.624762\pi$
$132$	2.53209	0.220390
$133$	0	0
$134$	11.7246	1.01285
$135$	2.44562	0.210486
$136$	4.59627	0.394127
$137$	0.504748	0.0431235	0.0215618	−	0.999768i	$-0.493136\pi$
$137$	0.504748	0.0431235	0.0215618	+	0.999768i	$0.493136\pi$
$138$	2.15745	0.183654
$139$	−11.5125	−0.976477	−0.488238	−	0.872710i	$-0.662360\pi$
$139$	−11.5125	−0.976477	−0.488238	+	0.872710i	$0.662360\pi$
$140$	0.532089	0.0449697
$141$	−4.59627	−0.387075
$142$	13.2344	1.11061
$143$	−1.00000	−0.0836242
$144$	−2.22668	−0.185557
$145$	5.00774	0.415870
$146$	9.92127	0.821091
$147$	−0.879385	−0.0725305
$148$	5.70233	0.468729
$149$	2.14290	0.175553	0.0877767	−	0.996140i	$-0.472024\pi$
$149$	2.14290	0.175553	0.0877767	+	0.996140i	$0.472024\pi$
$150$	−4.14796	−0.338679
$151$	4.85710	0.395265	0.197632	−	0.980276i	$-0.436675\pi$
$151$	4.85710	0.395265	0.197632	+	0.980276i	$0.436675\pi$
$152$	0	0
$153$	10.2344	0.827404
$154$	2.87939	0.232027
$155$	2.46791	0.198227
$156$	−0.305407	−0.0244522
$157$	−8.73648	−0.697247	−0.348624	−	0.937263i	$-0.613351\pi$
$157$	−8.73648	−0.697247	−0.348624	+	0.937263i	$0.613351\pi$
$158$	−0.263518	−0.0209644
$159$	−3.08647	−0.244773
$160$	−0.532089	−0.0420653
$161$	2.45336	0.193352
$162$	−2.63816	−0.207273
$163$	−17.6527	−1.38267	−0.691333	−	0.722536i	$-0.742976\pi$
$163$	−17.6527	−1.38267	−0.691333	+	0.722536i	$0.742976\pi$
$164$	6.53983	0.510675
$165$	1.34730	0.104887
$166$	−3.95811	−0.307209
$167$	−11.2490	−0.870471	−0.435236	−	0.900317i	$-0.643335\pi$
$167$	−11.2490	−0.870471	−0.435236	+	0.900317i	$0.643335\pi$
$168$	0.879385	0.0678460
$169$	−12.8794	−0.990722
$170$	2.44562	0.187571
$171$	0	0
$172$	1.82295	0.138999
$173$	−17.7493	−1.34945	−0.674726	−	0.738068i	$-0.735738\pi$
$173$	−17.7493	−1.34945	−0.674726	+	0.738068i	$0.735738\pi$
$174$	8.27631	0.627426
$175$	−4.71688	−0.356563
$176$	−2.87939	−0.217042
$177$	7.61587	0.572444
$178$	−14.6013	−1.09442
$179$	−11.9263	−0.891416	−0.445708	−	0.895179i	$-0.647048\pi$
$179$	−11.9263	−0.891416	−0.445708	+	0.895179i	$0.647048\pi$
$180$	−1.18479	−0.0883092
$181$	−11.9855	−0.890872	−0.445436	−	0.895314i	$-0.646951\pi$
$181$	−11.9855	−0.890872	−0.445436	+	0.895314i	$0.646951\pi$
$182$	−0.347296	−0.0257433
$183$	7.97090	0.589226
$184$	−2.45336	−0.180864
$185$	3.03415	0.223075
$186$	4.07873	0.299067
$187$	13.2344	0.967797
$188$	5.22668	0.381195
$189$	4.59627	0.334329
$190$	0	0
$191$	−7.77332	−0.562458	−0.281229	−	0.959641i	$-0.590742\pi$
$191$	−7.77332	−0.562458	−0.281229	+	0.959641i	$0.590742\pi$
$192$	−0.879385	−0.0634642
$193$	12.6304	0.909157	0.454579	−	0.890707i	$-0.349790\pi$
$193$	12.6304	0.909157	0.454579	+	0.890707i	$0.349790\pi$
$194$	10.1284	0.727174
$195$	−0.162504	−0.0116371
$196$	1.00000	0.0714286
$197$	0.0719186	0.00512399	0.00256199	−	0.999997i	$-0.499184\pi$
$197$	0.0719186	0.00512399	0.00256199	+	0.999997i	$0.499184\pi$
$198$	−6.41147	−0.455644
$199$	0.951304	0.0674361	0.0337181	−	0.999431i	$-0.489265\pi$
$199$	0.951304	0.0674361	0.0337181	+	0.999431i	$0.489265\pi$
$200$	4.71688	0.333534
$201$	10.3105	0.727244
$202$	−11.5817	−0.814887
$203$	9.41147	0.660556
$204$	4.04189	0.282989
$205$	3.47977	0.243038
$206$	2.65776	0.185175
$207$	−5.46286	−0.379695
$208$	0.347296	0.0240807
$209$	0	0
$210$	0.467911	0.0322889
$211$	−10.0865	−0.694381	−0.347190	−	0.937795i	$-0.612864\pi$
$211$	−10.0865	−0.694381	−0.347190	+	0.937795i	$0.612864\pi$
$212$	3.50980	0.241054
$213$	11.6382	0.797433
$214$	−11.1702	−0.763582
$215$	0.969971	0.0661514
$216$	−4.59627	−0.312736
$217$	4.63816	0.314859
$218$	17.4243	1.18012
$219$	8.72462	0.589555
$220$	−1.53209	−0.103293
$221$	−1.59627	−0.107377
$222$	5.01455	0.336554
$223$	−15.2959	−1.02429	−0.512145	−	0.858899i	$-0.671149\pi$
$223$	−15.2959	−1.02429	−0.512145	+	0.858899i	$0.671149\pi$
$224$	−1.00000	−0.0668153
$225$	10.5030	0.700200
$226$	3.36959	0.224141
$227$	17.0942	1.13458	0.567291	−	0.823517i	$-0.307991\pi$
$227$	17.0942	1.13458	0.567291	+	0.823517i	$0.307991\pi$
$228$	0	0
$229$	−9.68685	−0.640125	−0.320063	−	0.947396i	$-0.603704\pi$
$229$	−9.68685	−0.640125	−0.320063	+	0.947396i	$0.603704\pi$
$230$	−1.30541	−0.0860760
$231$	2.53209	0.166599
$232$	−9.41147	−0.617894
$233$	21.3996	1.40194	0.700968	−	0.713193i	$-0.252752\pi$
$233$	21.3996	1.40194	0.700968	+	0.713193i	$0.252752\pi$
$234$	0.773318	0.0505534
$235$	2.78106	0.181416
$236$	−8.66044	−0.563747
$237$	−0.231734	−0.0150527
$238$	4.59627	0.297932
$239$	18.8699	1.22059	0.610296	−	0.792174i	$-0.291051\pi$
$239$	18.8699	1.22059	0.610296	+	0.792174i	$0.291051\pi$
$240$	−0.467911	−0.0302035
$241$	15.9932	1.03021	0.515106	−	0.857126i	$-0.327753\pi$
$241$	15.9932	1.03021	0.515106	+	0.857126i	$0.327753\pi$
$242$	2.70914	0.174150
$243$	−16.1088	−1.03338
$244$	−9.06418	−0.580275
$245$	0.532089	0.0339939
$246$	5.75103	0.366672
$247$	0	0
$248$	−4.63816	−0.294523
$249$	−3.48070	−0.220581
$250$	5.17024	0.326995
$251$	2.93676	0.185366	0.0926832	−	0.995696i	$-0.470456\pi$
$251$	2.93676	0.185366	0.0926832	+	0.995696i	$0.470456\pi$
$252$	−2.22668	−0.140268
$253$	−7.06418	−0.444121
$254$	−10.1506	−0.636908
$255$	2.15064	0.134679
$256$	1.00000	0.0625000
$257$	−19.4020	−1.21026	−0.605131	−	0.796126i	$-0.706879\pi$
$257$	−19.4020	−1.21026	−0.605131	+	0.796126i	$0.706879\pi$
$258$	1.60307	0.0998030
$259$	5.70233	0.354326
$260$	0.184793	0.0114603
$261$	−20.9564	−1.29717
$262$	8.74422	0.540220
$263$	−14.3155	−0.882732	−0.441366	−	0.897327i	$-0.645506\pi$
$263$	−14.3155	−0.882732	−0.441366	+	0.897327i	$0.645506\pi$
$264$	−2.53209	−0.155839
$265$	1.86753	0.114721
$266$	0	0
$267$	−12.8402	−0.785807
$268$	−11.7246	−0.716195
$269$	−0.128356	−0.00782598	−0.00391299	−	0.999992i	$-0.501246\pi$
$269$	−0.128356	−0.00782598	−0.00391299	+	0.999992i	$0.501246\pi$
$270$	−2.44562	−0.148836
$271$	29.6955	1.80387	0.901937	−	0.431867i	$-0.142145\pi$
$271$	29.6955	1.80387	0.901937	+	0.431867i	$0.142145\pi$
$272$	−4.59627	−0.278690
$273$	−0.305407	−0.0184841
$274$	−0.504748	−0.0304929
$275$	13.5817	0.819008
$276$	−2.15745	−0.129863
$277$	−28.7246	−1.72590	−0.862948	−	0.505293i	$-0.831384\pi$
$277$	−28.7246	−1.72590	−0.862948	+	0.505293i	$0.831384\pi$
$278$	11.5125	0.690473
$279$	−10.3277	−0.618303
$280$	−0.532089	−0.0317984
$281$	−20.8229	−1.24219	−0.621096	−	0.783734i	$-0.713312\pi$
$281$	−20.8229	−1.24219	−0.621096	+	0.783734i	$0.713312\pi$
$282$	4.59627	0.273704
$283$	17.0624	1.01426	0.507128	−	0.861871i	$-0.330707\pi$
$283$	17.0624	1.01426	0.507128	+	0.861871i	$0.330707\pi$
$284$	−13.2344	−0.785318
$285$	0	0
$286$	1.00000	0.0591312
$287$	6.53983	0.386034
$288$	2.22668	0.131208
$289$	4.12567	0.242686
$290$	−5.00774	−0.294065
$291$	8.90673	0.522122
$292$	−9.92127	−0.580599
$293$	1.11112	0.0649123	0.0324561	−	0.999473i	$-0.489667\pi$
$293$	1.11112	0.0649123	0.0324561	+	0.999473i	$0.489667\pi$
$294$	0.879385	0.0512868
$295$	−4.60813	−0.268295
$296$	−5.70233	−0.331441
$297$	−13.2344	−0.767939
$298$	−2.14290	−0.124135
$299$	0.852044	0.0492750
$300$	4.14796	0.239482
$301$	1.82295	0.105073
$302$	−4.85710	−0.279494
$303$	−10.1848	−0.585101
$304$	0	0
$305$	−4.82295	−0.276161
$306$	−10.2344	−0.585063
$307$	5.39187	0.307730	0.153865	−	0.988092i	$-0.450828\pi$
$307$	5.39187	0.307730	0.153865	+	0.988092i	$0.450828\pi$
$308$	−2.87939	−0.164068
$309$	2.33719	0.132958
$310$	−2.46791	−0.140168
$311$	−8.29591	−0.470418	−0.235209	−	0.971945i	$-0.575577\pi$
$311$	−8.29591	−0.470418	−0.235209	+	0.971945i	$0.575577\pi$
$312$	0.305407	0.0172903
$313$	−12.1584	−0.687233	−0.343616	−	0.939110i	$-0.611652\pi$
$313$	−12.1584	−0.687233	−0.343616	+	0.939110i	$0.611652\pi$
$314$	8.73648	0.493028
$315$	−1.18479	−0.0667555
$316$	0.263518	0.0148241
$317$	14.3250	0.804573	0.402286	−	0.915514i	$-0.368216\pi$
$317$	14.3250	0.804573	0.402286	+	0.915514i	$0.368216\pi$
$318$	3.08647	0.173080
$319$	−27.0993	−1.51727
$320$	0.532089	0.0297447
$321$	−9.82295	−0.548264
$322$	−2.45336	−0.136721
$323$	0	0
$324$	2.63816	0.146564
$325$	−1.63816	−0.0908685
$326$	17.6527	0.977693
$327$	15.3226	0.847344
$328$	−6.53983	−0.361102
$329$	5.22668	0.288156
$330$	−1.34730	−0.0741662
$331$	19.1607	1.05317	0.526585	−	0.850122i	$-0.323472\pi$
$331$	19.1607	1.05317	0.526585	+	0.850122i	$0.323472\pi$
$332$	3.95811	0.217230
$333$	−12.6973	−0.695807
$334$	11.2490	0.615516
$335$	−6.23854	−0.340848
$336$	−0.879385	−0.0479744
$337$	11.1857	0.609325	0.304663	−	0.952460i	$-0.401456\pi$
$337$	11.1857	0.609325	0.304663	+	0.952460i	$0.401456\pi$
$338$	12.8794	0.700546
$339$	2.96316	0.160937
$340$	−2.44562	−0.132632
$341$	−13.3550	−0.723216
$342$	0	0
$343$	1.00000	0.0539949
$344$	−1.82295	−0.0982868
$345$	−1.14796	−0.0618039
$346$	17.7493	0.954207
$347$	−34.7716	−1.86664	−0.933318	−	0.359052i	$-0.883100\pi$
$347$	−34.7716	−1.86664	−0.933318	+	0.359052i	$0.883100\pi$
$348$	−8.27631	−0.443657
$349$	−34.6810	−1.85643	−0.928215	−	0.372044i	$-0.878657\pi$
$349$	−34.6810	−1.85643	−0.928215	+	0.372044i	$0.878657\pi$
$350$	4.71688	0.252128
$351$	1.59627	0.0852024
$352$	2.87939	0.153472
$353$	−24.1489	−1.28532	−0.642658	−	0.766153i	$-0.722168\pi$
$353$	−24.1489	−1.28532	−0.642658	+	0.766153i	$0.722168\pi$
$354$	−7.61587	−0.404779
$355$	−7.04189	−0.373745
$356$	14.6013	0.773868
$357$	4.04189	0.213919
$358$	11.9263	0.630326
$359$	−8.61350	−0.454603	−0.227302	−	0.973824i	$-0.572990\pi$
$359$	−8.61350	−0.454603	−0.227302	+	0.973824i	$0.572990\pi$
$360$	1.18479	0.0624440
$361$	0	0
$362$	11.9855	0.629941
$363$	2.38238	0.125042
$364$	0.347296	0.0182033
$365$	−5.27900	−0.276315
$366$	−7.97090	−0.416646
$367$	14.2739	0.745094	0.372547	−	0.928013i	$-0.378485\pi$
$367$	14.2739	0.745094	0.372547	+	0.928013i	$0.378485\pi$
$368$	2.45336	0.127890
$369$	−14.5621	−0.758074
$370$	−3.03415	−0.157738
$371$	3.50980	0.182220
$372$	−4.07873	−0.211472
$373$	−6.11112	−0.316422	−0.158211	−	0.987405i	$-0.550573\pi$
$373$	−6.11112	−0.316422	−0.158211	+	0.987405i	$0.550573\pi$
$374$	−13.2344	−0.684336
$375$	4.54664	0.234787
$376$	−5.22668	−0.269546
$377$	3.26857	0.168340
$378$	−4.59627	−0.236406
$379$	28.3773	1.45765	0.728823	−	0.684703i	$-0.240068\pi$
$379$	28.3773	1.45765	0.728823	+	0.684703i	$0.240068\pi$
$380$	0	0
$381$	−8.92633	−0.457310
$382$	7.77332	0.397718
$383$	27.3250	1.39624	0.698121	−	0.715979i	$-0.254020\pi$
$383$	27.3250	1.39624	0.698121	+	0.715979i	$0.254020\pi$
$384$	0.879385	0.0448759
$385$	−1.53209	−0.0780825
$386$	−12.6304	−0.642871
$387$	−4.05913	−0.206337
$388$	−10.1284	−0.514189
$389$	24.1257	1.22322	0.611610	−	0.791159i	$-0.290522\pi$
$389$	24.1257	1.22322	0.611610	+	0.791159i	$0.290522\pi$
$390$	0.162504	0.00822870
$391$	−11.2763	−0.570268
$392$	−1.00000	−0.0505076
$393$	7.68954	0.387886
$394$	−0.0719186	−0.00362320
$395$	0.140215	0.00705499
$396$	6.41147	0.322189
$397$	−16.6391	−0.835092	−0.417546	−	0.908656i	$-0.637110\pi$
$397$	−16.6391	−0.835092	−0.417546	+	0.908656i	$0.637110\pi$
$398$	−0.951304	−0.0476846
$399$	0	0
$400$	−4.71688	−0.235844
$401$	11.2517	0.561881	0.280941	−	0.959725i	$-0.409354\pi$
$401$	11.2517	0.561881	0.280941	+	0.959725i	$0.409354\pi$
$402$	−10.3105	−0.514239
$403$	1.61081	0.0802404
$404$	11.5817	0.576212
$405$	1.40373	0.0697521
$406$	−9.41147	−0.467084
$407$	−16.4192	−0.813870
$408$	−4.04189	−0.200103
$409$	0.389185	0.0192440	0.00962199	−	0.999954i	$-0.496937\pi$
$409$	0.389185	0.0192440	0.00962199	+	0.999954i	$0.496937\pi$
$410$	−3.47977	−0.171854
$411$	−0.443868	−0.0218944
$412$	−2.65776	−0.130938
$413$	−8.66044	−0.426153
$414$	5.46286	0.268485
$415$	2.10607	0.103383
$416$	−0.347296	−0.0170276
$417$	10.1239	0.495770
$418$	0	0
$419$	27.9317	1.36455	0.682277	−	0.731094i	$-0.260990\pi$
$419$	27.9317	1.36455	0.682277	+	0.731094i	$0.260990\pi$
$420$	−0.467911	−0.0228317
$421$	−27.5357	−1.34201	−0.671004	−	0.741454i	$-0.734137\pi$
$421$	−27.5357	−1.34201	−0.671004	+	0.741454i	$0.734137\pi$
$422$	10.0865	0.491002
$423$	−11.6382	−0.565866
$424$	−3.50980	−0.170451
$425$	21.6800	1.05164
$426$	−11.6382	−0.563870
$427$	−9.06418	−0.438646
$428$	11.1702	0.539934
$429$	0.879385	0.0424571
$430$	−0.969971	−0.0467761
$431$	−23.2763	−1.12118	−0.560590	−	0.828093i	$-0.689426\pi$
$431$	−23.2763	−1.12118	−0.560590	+	0.828093i	$0.689426\pi$
$432$	4.59627	0.221138
$433$	−29.2294	−1.40467	−0.702337	−	0.711845i	$-0.747860\pi$
$433$	−29.2294	−1.40467	−0.702337	+	0.711845i	$0.747860\pi$
$434$	−4.63816	−0.222639
$435$	−4.40373	−0.211143
$436$	−17.4243	−0.834471
$437$	0	0
$438$	−8.72462	−0.416879
$439$	−0.313148	−0.0149457	−0.00747287	−	0.999972i	$-0.502379\pi$
$439$	−0.313148	−0.0149457	−0.00747287	+	0.999972i	$0.502379\pi$
$440$	1.53209	0.0730395
$441$	−2.22668	−0.106032
$442$	1.59627	0.0759267
$443$	25.8803	1.22961	0.614806	−	0.788679i	$-0.289234\pi$
$443$	25.8803	1.22961	0.614806	+	0.788679i	$0.289234\pi$
$444$	−5.01455	−0.237980
$445$	7.76920	0.368295
$446$	15.2959	0.724282
$447$	−1.88444	−0.0891308
$448$	1.00000	0.0472456
$449$	−1.93582	−0.0913571	−0.0456785	−	0.998956i	$-0.514545\pi$
$449$	−1.93582	−0.0913571	−0.0456785	+	0.998956i	$0.514545\pi$
$450$	−10.5030	−0.495116
$451$	−18.8307	−0.886703
$452$	−3.36959	−0.158492
$453$	−4.27126	−0.200681
$454$	−17.0942	−0.802271
$455$	0.184793	0.00866321
$456$	0	0
$457$	−32.9864	−1.54304	−0.771519	−	0.636206i	$-0.780503\pi$
$457$	−32.9864	−1.54304	−0.771519	+	0.636206i	$0.780503\pi$
$458$	9.68685	0.452637
$459$	−21.1257	−0.986062
$460$	1.30541	0.0608649
$461$	−2.57667	−0.120007	−0.0600037	−	0.998198i	$-0.519111\pi$
$461$	−2.57667	−0.120007	−0.0600037	+	0.998198i	$0.519111\pi$
$462$	−2.53209	−0.117803
$463$	3.94120	0.183163	0.0915815	−	0.995798i	$-0.470808\pi$
$463$	3.94120	0.183163	0.0915815	+	0.995798i	$0.470808\pi$
$464$	9.41147	0.436917
$465$	−2.17024	−0.100643
$466$	−21.3996	−0.991318
$467$	9.53033	0.441011	0.220506	−	0.975386i	$-0.429229\pi$
$467$	9.53033	0.441011	0.220506	+	0.975386i	$0.429229\pi$
$468$	−0.773318	−0.0357467
$469$	−11.7246	−0.541393
$470$	−2.78106	−0.128281
$471$	7.68273	0.354002
$472$	8.66044	0.398629
$473$	−5.24897	−0.241348
$474$	0.231734	0.0106439
$475$	0	0
$476$	−4.59627	−0.210670
$477$	−7.81521	−0.357834
$478$	−18.8699	−0.863089
$479$	−40.5134	−1.85111	−0.925553	−	0.378619i	$-0.876399\pi$
$479$	−40.5134	−1.85111	−0.925553	+	0.378619i	$0.876399\pi$
$480$	0.467911	0.0213571
$481$	1.98040	0.0902985
$482$	−15.9932	−0.728470
$483$	−2.15745	−0.0981674
$484$	−2.70914	−0.123143
$485$	−5.38919	−0.244710
$486$	16.1088	0.730708
$487$	9.64496	0.437055	0.218527	−	0.975831i	$-0.429875\pi$
$487$	9.64496	0.437055	0.218527	+	0.975831i	$0.429875\pi$
$488$	9.06418	0.410316
$489$	15.5235	0.701998
$490$	−0.532089	−0.0240373
$491$	−8.30129	−0.374632	−0.187316	−	0.982300i	$-0.559979\pi$
$491$	−8.30129	−0.374632	−0.187316	+	0.982300i	$0.559979\pi$
$492$	−5.75103	−0.259276
$493$	−43.2576	−1.94823
$494$	0	0
$495$	3.41147	0.153334
$496$	4.63816	0.208259
$497$	−13.2344	−0.593645
$498$	3.48070	0.155974
$499$	−31.9777	−1.43152	−0.715759	−	0.698347i	$-0.753919\pi$
$499$	−31.9777	−1.43152	−0.715759	+	0.698347i	$0.753919\pi$
$500$	−5.17024	−0.231220
$501$	9.89218	0.441950
$502$	−2.93676	−0.131074
$503$	−41.2490	−1.83920	−0.919600	−	0.392855i	$-0.871487\pi$
$503$	−41.2490	−1.83920	−0.919600	+	0.392855i	$0.871487\pi$
$504$	2.22668	0.0991843
$505$	6.16250	0.274228
$506$	7.06418	0.314041
$507$	11.3259	0.503003
$508$	10.1506	0.450362
$509$	−25.3063	−1.12168	−0.560842	−	0.827923i	$-0.689522\pi$
$509$	−25.3063	−1.12168	−0.560842	+	0.827923i	$0.689522\pi$
$510$	−2.15064	−0.0952321
$511$	−9.92127	−0.438891
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	19.4020	0.855785
$515$	−1.41416	−0.0623154
$516$	−1.60307	−0.0705714
$517$	−15.0496	−0.661882
$518$	−5.70233	−0.250546
$519$	15.6085	0.685135
$520$	−0.184793	−0.00810369
$521$	11.9959	0.525549	0.262775	−	0.964857i	$-0.415362\pi$
$521$	11.9959	0.525549	0.262775	+	0.964857i	$0.415362\pi$
$522$	20.9564	0.917235
$523$	25.8794	1.13163	0.565813	−	0.824533i	$-0.308562\pi$
$523$	25.8794	1.13163	0.565813	+	0.824533i	$0.308562\pi$
$524$	−8.74422	−0.381993
$525$	4.14796	0.181032
$526$	14.3155	0.624186
$527$	−21.3182	−0.928635
$528$	2.53209	0.110195
$529$	−16.9810	−0.738305
$530$	−1.86753	−0.0811201
$531$	19.2841	0.836857
$532$	0	0
$533$	2.27126	0.0983791
$534$	12.8402	0.555649
$535$	5.94356	0.256963
$536$	11.7246	0.506427
$537$	10.4878	0.452584
$538$	0.128356	0.00553380
$539$	−2.87939	−0.124024
$540$	2.44562	0.105243
$541$	−3.22937	−0.138841	−0.0694207	−	0.997587i	$-0.522115\pi$
$541$	−3.22937	−0.138841	−0.0694207	+	0.997587i	$0.522115\pi$
$542$	−29.6955	−1.27553
$543$	10.5398	0.452307
$544$	4.59627	0.197063
$545$	−9.27126	−0.397137
$546$	0.305407	0.0130702
$547$	16.2053	0.692890	0.346445	−	0.938070i	$-0.387389\pi$
$547$	16.2053	0.692890	0.346445	+	0.938070i	$0.387389\pi$
$548$	0.504748	0.0215618
$549$	20.1830	0.861391
$550$	−13.5817	−0.579126
$551$	0	0
$552$	2.15745	0.0918272
$553$	0.263518	0.0112059
$554$	28.7246	1.22039
$555$	−2.66819	−0.113258
$556$	−11.5125	−0.488238
$557$	−13.4757	−0.570982	−0.285491	−	0.958381i	$-0.592157\pi$
$557$	−13.4757	−0.570982	−0.285491	+	0.958381i	$0.592157\pi$
$558$	10.3277	0.437206
$559$	0.633103	0.0267774
$560$	0.532089	0.0224849
$561$	−11.6382	−0.491363
$562$	20.8229	0.878363
$563$	0.573978	0.0241903	0.0120951	−	0.999927i	$-0.496150\pi$
$563$	0.573978	0.0241903	0.0120951	+	0.999927i	$0.496150\pi$
$564$	−4.59627	−0.193538
$565$	−1.79292	−0.0754287
$566$	−17.0624	−0.717187
$567$	2.63816	0.110792
$568$	13.2344	0.555304
$569$	−4.48751	−0.188126	−0.0940631	−	0.995566i	$-0.529986\pi$
$569$	−4.48751	−0.188126	−0.0940631	+	0.995566i	$0.529986\pi$
$570$	0	0
$571$	−33.5648	−1.40464	−0.702322	−	0.711860i	$-0.747853\pi$
$571$	−33.5648	−1.40464	−0.702322	+	0.711860i	$0.747853\pi$
$572$	−1.00000	−0.0418121
$573$	6.83574	0.285567
$574$	−6.53983	−0.272967
$575$	−11.5722	−0.482595
$576$	−2.22668	−0.0927784
$577$	−21.0205	−0.875096	−0.437548	−	0.899195i	$-0.644153\pi$
$577$	−21.0205	−0.875096	−0.437548	+	0.899195i	$0.644153\pi$
$578$	−4.12567	−0.171605
$579$	−11.1070	−0.461591
$580$	5.00774	0.207935
$581$	3.95811	0.164210
$582$	−8.90673	−0.369196
$583$	−10.1061	−0.418551
$584$	9.92127	0.410545
$585$	−0.411474	−0.0170124
$586$	−1.11112	−0.0458999
$587$	42.9290	1.77187	0.885935	−	0.463809i	$-0.153518\pi$
$587$	42.9290	1.77187	0.885935	+	0.463809i	$0.153518\pi$
$588$	−0.879385	−0.0362652
$589$	0	0
$590$	4.60813	0.189714
$591$	−0.0632441	−0.00260152
$592$	5.70233	0.234364
$593$	−34.2540	−1.40664	−0.703322	−	0.710871i	$-0.748301\pi$
$593$	−34.2540	−1.40664	−0.703322	+	0.710871i	$0.748301\pi$
$594$	13.2344	0.543015
$595$	−2.44562	−0.100261
$596$	2.14290	0.0877767
$597$	−0.836563	−0.0342382
$598$	−0.852044	−0.0348427
$599$	−8.30541	−0.339350	−0.169675	−	0.985500i	$-0.554272\pi$
$599$	−8.30541	−0.339350	−0.169675	+	0.985500i	$0.554272\pi$
$600$	−4.14796	−0.169340
$601$	−39.0036	−1.59099	−0.795495	−	0.605960i	$-0.792789\pi$
$601$	−39.0036	−1.59099	−0.795495	+	0.605960i	$0.792789\pi$
$602$	−1.82295	−0.0742978
$603$	26.1070	1.06316
$604$	4.85710	0.197632
$605$	−1.44150	−0.0586055
$606$	10.1848	0.413729
$607$	−30.4424	−1.23562	−0.617810	−	0.786327i	$-0.711980\pi$
$607$	−30.4424	−1.23562	−0.617810	+	0.786327i	$0.711980\pi$
$608$	0	0
$609$	−8.27631	−0.335373
$610$	4.82295	0.195275
$611$	1.81521	0.0734354
$612$	10.2344	0.413702
$613$	14.0401	0.567076	0.283538	−	0.958961i	$-0.408492\pi$
$613$	14.0401	0.567076	0.283538	+	0.958961i	$0.408492\pi$
$614$	−5.39187	−0.217598
$615$	−3.06006	−0.123393
$616$	2.87939	0.116014
$617$	−14.5972	−0.587661	−0.293831	−	0.955858i	$-0.594930\pi$
$617$	−14.5972	−0.587661	−0.293831	+	0.955858i	$0.594930\pi$
$618$	−2.33719	−0.0940156
$619$	−3.05913	−0.122957	−0.0614783	−	0.998108i	$-0.519582\pi$
$619$	−3.05913	−0.122957	−0.0614783	+	0.998108i	$0.519582\pi$
$620$	2.46791	0.0991137
$621$	11.2763	0.452503
$622$	8.29591	0.332636
$623$	14.6013	0.584989
$624$	−0.305407	−0.0122261
$625$	20.8334	0.833335
$626$	12.1584	0.485947
$627$	0	0
$628$	−8.73648	−0.348624
$629$	−26.2094	−1.04504
$630$	1.18479	0.0472033
$631$	2.05913	0.0819725	0.0409862	−	0.999160i	$-0.486950\pi$
$631$	2.05913	0.0819725	0.0409862	+	0.999160i	$0.486950\pi$
$632$	−0.263518	−0.0104822
$633$	8.86989	0.352546
$634$	−14.3250	−0.568919
$635$	5.40104	0.214334
$636$	−3.08647	−0.122386
$637$	0.347296	0.0137604
$638$	27.0993	1.07287
$639$	29.4688	1.16577
$640$	−0.532089	−0.0210327
$641$	2.25671	0.0891347	0.0445674	−	0.999006i	$-0.485809\pi$
$641$	2.25671	0.0891347	0.0445674	+	0.999006i	$0.485809\pi$
$642$	9.82295	0.387681
$643$	32.7202	1.29036	0.645179	−	0.764031i	$-0.276783\pi$
$643$	32.7202	1.29036	0.645179	+	0.764031i	$0.276783\pi$
$644$	2.45336	0.0966761
$645$	−0.852978	−0.0335860
$646$	0	0
$647$	24.0564	0.945756	0.472878	−	0.881128i	$-0.343215\pi$
$647$	24.0564	0.945756	0.472878	+	0.881128i	$0.343215\pi$
$648$	−2.63816	−0.103637
$649$	24.9368	0.978853
$650$	1.63816	0.0642538
$651$	−4.07873	−0.159858
$652$	−17.6527	−0.691333
$653$	31.9617	1.25076	0.625380	−	0.780321i	$-0.284944\pi$
$653$	31.9617	1.25076	0.625380	+	0.780321i	$0.284944\pi$
$654$	−15.3226	−0.599163
$655$	−4.65270	−0.181796
$656$	6.53983	0.255337
$657$	22.0915	0.861872
$658$	−5.22668	−0.203757
$659$	−22.7442	−0.885989	−0.442995	−	0.896524i	$-0.646084\pi$
$659$	−22.7442	−0.885989	−0.442995	+	0.896524i	$0.646084\pi$
$660$	1.34730	0.0524434
$661$	11.5398	0.448847	0.224424	−	0.974492i	$-0.427950\pi$
$661$	11.5398	0.448847	0.224424	+	0.974492i	$0.427950\pi$
$662$	−19.1607	−0.744704
$663$	1.40373	0.0545165
$664$	−3.95811	−0.153604
$665$	0	0
$666$	12.6973	0.492010
$667$	23.0898	0.894039
$668$	−11.2490	−0.435236
$669$	13.4510	0.520046
$670$	6.23854	0.241016
$671$	26.0993	1.00755
$672$	0.879385	0.0339230
$673$	37.1753	1.43300	0.716501	−	0.697586i	$-0.245742\pi$
$673$	37.1753	1.43300	0.716501	+	0.697586i	$0.245742\pi$
$674$	−11.1857	−0.430858
$675$	−21.6800	−0.834465
$676$	−12.8794	−0.495361
$677$	−22.1121	−0.849835	−0.424918	−	0.905232i	$-0.639697\pi$
$677$	−22.1121	−0.849835	−0.424918	+	0.905232i	$0.639697\pi$
$678$	−2.96316	−0.113800
$679$	−10.1284	−0.388691
$680$	2.44562	0.0937853
$681$	−15.0324	−0.576043
$682$	13.3550	0.511391
$683$	−12.7237	−0.486858	−0.243429	−	0.969919i	$-0.578272\pi$
$683$	−12.7237	−0.486858	−0.243429	+	0.969919i	$0.578272\pi$
$684$	0	0
$685$	0.268571	0.0102616
$686$	−1.00000	−0.0381802
$687$	8.51847	0.325000
$688$	1.82295	0.0694993
$689$	1.21894	0.0464379
$690$	1.14796	0.0437019
$691$	23.3173	0.887031	0.443515	−	0.896267i	$-0.353731\pi$
$691$	23.3173	0.887031	0.443515	+	0.896267i	$0.353731\pi$
$692$	−17.7493	−0.674726
$693$	6.41147	0.243552
$694$	34.7716	1.31991
$695$	−6.12567	−0.232360
$696$	8.27631	0.313713
$697$	−30.0588	−1.13856
$698$	34.6810	1.31269
$699$	−18.8185	−0.711781
$700$	−4.71688	−0.178281
$701$	−46.3005	−1.74874	−0.874372	−	0.485256i	$-0.838726\pi$
$701$	−46.3005	−1.74874	−0.874372	+	0.485256i	$0.838726\pi$
$702$	−1.59627	−0.0602472
$703$	0	0
$704$	−2.87939	−0.108521
$705$	−2.44562	−0.0921075
$706$	24.1489	0.908855
$707$	11.5817	0.435575
$708$	7.61587	0.286222
$709$	−32.0155	−1.20237	−0.601183	−	0.799111i	$-0.705304\pi$
$709$	−32.0155	−1.20237	−0.601183	+	0.799111i	$0.705304\pi$
$710$	7.04189	0.264277
$711$	−0.586771	−0.0220056
$712$	−14.6013	−0.547208
$713$	11.3791	0.426150
$714$	−4.04189	−0.151264
$715$	−0.532089	−0.0198990
$716$	−11.9263	−0.445708
$717$	−16.5939	−0.619711
$718$	8.61350	0.321453
$719$	40.0529	1.49372	0.746861	−	0.664980i	$-0.231560\pi$
$719$	40.0529	1.49372	0.746861	+	0.664980i	$0.231560\pi$
$720$	−1.18479	−0.0441546
$721$	−2.65776	−0.0989800
$722$	0	0
$723$	−14.0642	−0.523052
$724$	−11.9855	−0.445436
$725$	−44.3928	−1.64871
$726$	−2.38238	−0.0884184
$727$	−4.60576	−0.170818	−0.0854091	−	0.996346i	$-0.527220\pi$
$727$	−4.60576	−0.170818	−0.0854091	+	0.996346i	$0.527220\pi$
$728$	−0.347296	−0.0128717
$729$	6.25133	0.231531
$730$	5.27900	0.195385
$731$	−8.37876	−0.309899
$732$	7.97090	0.294613
$733$	48.6833	1.79816	0.899080	−	0.437784i	$-0.144237\pi$
$733$	48.6833	1.79816	0.899080	+	0.437784i	$0.144237\pi$
$734$	−14.2739	−0.526861
$735$	−0.467911	−0.0172592
$736$	−2.45336	−0.0904322
$737$	33.7597	1.24355
$738$	14.5621	0.536039
$739$	1.95904	0.0720646	0.0360323	−	0.999351i	$-0.488528\pi$
$739$	1.95904	0.0720646	0.0360323	+	0.999351i	$0.488528\pi$
$740$	3.03415	0.111538
$741$	0	0
$742$	−3.50980	−0.128849
$743$	0.0205340	0.000753320 0	0.000376660	−	1.00000i	$-0.499880\pi$
$743$	0.0205340	0.000753320 0	0.000376660		1.00000i	$0.499880\pi$
$744$	4.07873	0.149533
$745$	1.14022	0.0417742
$746$	6.11112	0.223744
$747$	−8.81345	−0.322467
$748$	13.2344	0.483898
$749$	11.1702	0.408152
$750$	−4.54664	−0.166020
$751$	−38.4861	−1.40438	−0.702189	−	0.711991i	$-0.747794\pi$
$751$	−38.4861	−1.40438	−0.702189	+	0.711991i	$0.747794\pi$
$752$	5.22668	0.190597
$753$	−2.58254	−0.0941130
$754$	−3.26857	−0.119034
$755$	2.58441	0.0940562
$756$	4.59627	0.167165
$757$	−4.21625	−0.153242	−0.0766212	−	0.997060i	$-0.524413\pi$
$757$	−4.21625	−0.153242	−0.0766212	+	0.997060i	$0.524413\pi$
$758$	−28.3773	−1.03071
$759$	6.21213	0.225486
$760$	0	0
$761$	47.2499	1.71281	0.856404	−	0.516307i	$-0.172693\pi$
$761$	47.2499	1.71281	0.856404	+	0.516307i	$0.172693\pi$
$762$	8.92633	0.323367
$763$	−17.4243	−0.630801
$764$	−7.77332	−0.281229
$765$	5.44562	0.196887
$766$	−27.3250	−0.987293
$767$	−3.00774	−0.108603
$768$	−0.879385	−0.0317321
$769$	33.4543	1.20639	0.603196	−	0.797593i	$-0.293894\pi$
$769$	33.4543	1.20639	0.603196	+	0.797593i	$0.293894\pi$
$770$	1.53209	0.0552127
$771$	17.0618	0.614466
$772$	12.6304	0.454579
$773$	−4.68779	−0.168608	−0.0843040	−	0.996440i	$-0.526867\pi$
$773$	−4.68779	−0.168608	−0.0843040	+	0.996440i	$0.526867\pi$
$774$	4.05913	0.145902
$775$	−21.8776	−0.785868
$776$	10.1284	0.363587
$777$	−5.01455	−0.179896
$778$	−24.1257	−0.864947
$779$	0	0
$780$	−0.162504	−0.00581857
$781$	38.1070	1.36358
$782$	11.2763	0.403240
$783$	43.2576	1.54590
$784$	1.00000	0.0357143
$785$	−4.64858	−0.165915
$786$	−7.68954	−0.274277
$787$	39.9077	1.42255	0.711277	−	0.702912i	$-0.248117\pi$
$787$	39.9077	1.42255	0.711277	+	0.702912i	$0.248117\pi$
$788$	0.0719186	0.00256199
$789$	12.5889	0.448175
$790$	−0.140215	−0.00498863
$791$	−3.36959	−0.119809
$792$	−6.41147	−0.227822
$793$	−3.14796	−0.111787
$794$	16.6391	0.590499
$795$	−1.64227	−0.0582455
$796$	0.951304	0.0337181
$797$	−12.5757	−0.445455	−0.222728	−	0.974881i	$-0.571496\pi$
$797$	−12.5757	−0.445455	−0.222728	+	0.974881i	$0.571496\pi$
$798$	0	0
$799$	−24.0232	−0.849881
$800$	4.71688	0.166767
$801$	−32.5125	−1.14877
$802$	−11.2517	−0.397310
$803$	28.5672	1.00811
$804$	10.3105	0.363622
$805$	1.30541	0.0460096
$806$	−1.61081	−0.0567385
$807$	0.112874	0.00397335
$808$	−11.5817	−0.407443
$809$	−46.4074	−1.63160	−0.815798	−	0.578337i	$-0.803702\pi$
$809$	−46.4074	−1.63160	−0.815798	+	0.578337i	$0.803702\pi$
$810$	−1.40373	−0.0493222
$811$	26.3604	0.925639	0.462820	−	0.886452i	$-0.346838\pi$
$811$	26.3604	0.925639	0.462820	+	0.886452i	$0.346838\pi$
$812$	9.41147	0.330278
$813$	−26.1138	−0.915851
$814$	16.4192	0.575493
$815$	−9.39281	−0.329016
$816$	4.04189	0.141494
$817$	0	0
$818$	−0.389185	−0.0136075
$819$	−0.773318	−0.0270219
$820$	3.47977	0.121519
$821$	−50.7478	−1.77111	−0.885556	−	0.464533i	$-0.846222\pi$
$821$	−50.7478	−1.77111	−0.885556	+	0.464533i	$0.846222\pi$
$822$	0.443868	0.0154817
$823$	31.9299	1.11301	0.556504	−	0.830845i	$-0.312142\pi$
$823$	31.9299	1.11301	0.556504	+	0.830845i	$0.312142\pi$
$824$	2.65776	0.0925873
$825$	−11.9436	−0.415821
$826$	8.66044	0.301335
$827$	49.9353	1.73642	0.868211	−	0.496196i	$-0.165270\pi$
$827$	49.9353	1.73642	0.868211	+	0.496196i	$0.165270\pi$
$828$	−5.46286	−0.189847
$829$	−1.63579	−0.0568134	−0.0284067	−	0.999596i	$-0.509043\pi$
$829$	−1.63579	−0.0568134	−0.0284067	+	0.999596i	$0.509043\pi$
$830$	−2.10607	−0.0731026
$831$	25.2600	0.876260
$832$	0.347296	0.0120403
$833$	−4.59627	−0.159251
$834$	−10.1239	−0.350562
$835$	−5.98545	−0.207135
$836$	0	0
$837$	21.3182	0.736865
$838$	−27.9317	−0.964885
$839$	−38.5725	−1.33167	−0.665836	−	0.746098i	$-0.731925\pi$
$839$	−38.5725	−1.33167	−0.665836	+	0.746098i	$0.731925\pi$
$840$	0.467911	0.0161445
$841$	59.5758	2.05434
$842$	27.5357	0.948943
$843$	18.3114	0.630678
$844$	−10.0865	−0.347190
$845$	−6.85298	−0.235750
$846$	11.6382	0.400128
$847$	−2.70914	−0.0930872
$848$	3.50980	0.120527
$849$	−15.0044	−0.514951
$850$	−21.6800	−0.743619
$851$	13.9899	0.479567
$852$	11.6382	0.398717
$853$	48.6391	1.66537	0.832685	−	0.553746i	$-0.186802\pi$
$853$	48.6391	1.66537	0.832685	+	0.553746i	$0.186802\pi$
$854$	9.06418	0.310170
$855$	0	0
$856$	−11.1702	−0.381791
$857$	52.4234	1.79075	0.895375	−	0.445312i	$-0.146907\pi$
$857$	52.4234	1.79075	0.895375	+	0.445312i	$0.146907\pi$
$858$	−0.879385	−0.0300217
$859$	6.81790	0.232624	0.116312	−	0.993213i	$-0.462893\pi$
$859$	6.81790	0.232624	0.116312	+	0.993213i	$0.462893\pi$
$860$	0.969971	0.0330757
$861$	−5.75103	−0.195995
$862$	23.2763	0.792794
$863$	12.0291	0.409475	0.204738	−	0.978817i	$-0.434366\pi$
$863$	12.0291	0.409475	0.204738	+	0.978817i	$0.434366\pi$
$864$	−4.59627	−0.156368
$865$	−9.44419	−0.321112
$866$	29.2294	0.993254
$867$	−3.62805	−0.123215
$868$	4.63816	0.157429
$869$	−0.758770	−0.0257395
$870$	4.40373	0.149301
$871$	−4.07192	−0.137972
$872$	17.4243	0.590060
$873$	22.5526	0.763291
$874$	0	0
$875$	−5.17024	−0.174786
$876$	8.72462	0.294778
$877$	−30.8120	−1.04045	−0.520224	−	0.854030i	$-0.674152\pi$
$877$	−30.8120	−1.04045	−0.520224	+	0.854030i	$0.674152\pi$
$878$	0.313148	0.0105682
$879$	−0.977102	−0.0329568
$880$	−1.53209	−0.0516467
$881$	2.61856	0.0882214	0.0441107	−	0.999027i	$-0.485955\pi$
$881$	2.61856	0.0882214	0.0441107	+	0.999027i	$0.485955\pi$
$882$	2.22668	0.0749763
$883$	−30.6783	−1.03241	−0.516203	−	0.856466i	$-0.672655\pi$
$883$	−30.6783	−1.03241	−0.516203	+	0.856466i	$0.672655\pi$
$884$	−1.59627	−0.0536883
$885$	4.05232	0.136217
$886$	−25.8803	−0.869466
$887$	1.23679	0.0415272	0.0207636	−	0.999784i	$-0.493390\pi$
$887$	1.23679	0.0415272	0.0207636	+	0.999784i	$0.493390\pi$
$888$	5.01455	0.168277
$889$	10.1506	0.340442
$890$	−7.76920	−0.260424
$891$	−7.59627	−0.254485
$892$	−15.2959	−0.512145
$893$	0	0
$894$	1.88444	0.0630250
$895$	−6.34587	−0.212119
$896$	−1.00000	−0.0334077
$897$	−0.749275	−0.0250176
$898$	1.93582	0.0645992
$899$	43.6519	1.45587
$900$	10.5030	0.350100
$901$	−16.1320	−0.537434
$902$	18.8307	0.626993
$903$	−1.60307	−0.0533470
$904$	3.36959	0.112071
$905$	−6.37733	−0.211989
$906$	4.27126	0.141903
$907$	−51.7820	−1.71939	−0.859696	−	0.510805i	$-0.829347\pi$
$907$	−51.7820	−1.71939	−0.859696	+	0.510805i	$0.829347\pi$
$908$	17.0942	0.567291
$909$	−25.7888	−0.855361
$910$	−0.184793	−0.00612581
$911$	35.6878	1.18239	0.591195	−	0.806529i	$-0.298657\pi$
$911$	35.6878	1.18239	0.591195	+	0.806529i	$0.298657\pi$
$912$	0	0
$913$	−11.3969	−0.377183
$914$	32.9864	1.09109
$915$	4.24123	0.140211
$916$	−9.68685	−0.320063
$917$	−8.74422	−0.288760
$918$	21.1257	0.697251
$919$	45.9823	1.51682	0.758408	−	0.651781i	$-0.225978\pi$
$919$	45.9823	1.51682	0.758408	+	0.651781i	$0.225978\pi$
$920$	−1.30541	−0.0430380
$921$	−4.74153	−0.156239
$922$	2.57667	0.0848580
$923$	−4.59627	−0.151288
$924$	2.53209	0.0832996
$925$	−26.8972	−0.884376
$926$	−3.94120	−0.129516
$927$	5.91798	0.194372
$928$	−9.41147	−0.308947
$929$	25.1560	0.825342	0.412671	−	0.910880i	$-0.364596\pi$
$929$	25.1560	0.825342	0.412671	+	0.910880i	$0.364596\pi$
$930$	2.17024	0.0711651
$931$	0	0
$932$	21.3996	0.700968
$933$	7.29530	0.238837
$934$	−9.53033	−0.311842
$935$	7.04189	0.230294
$936$	0.773318	0.0252767
$937$	−22.8503	−0.746486	−0.373243	−	0.927734i	$-0.621754\pi$
$937$	−22.8503	−0.746486	−0.373243	+	0.927734i	$0.621754\pi$
$938$	11.7246	0.382822
$939$	10.6919	0.348917
$940$	2.78106	0.0907081
$941$	44.8557	1.46225	0.731126	−	0.682242i	$-0.238995\pi$
$941$	44.8557	1.46225	0.731126	+	0.682242i	$0.238995\pi$
$942$	−7.68273	−0.250317
$943$	16.0446	0.522483
$944$	−8.66044	−0.281873
$945$	2.44562	0.0795561
$946$	5.24897	0.170659
$947$	−4.15713	−0.135088	−0.0675442	−	0.997716i	$-0.521516\pi$
$947$	−4.15713	−0.135088	−0.0675442	+	0.997716i	$0.521516\pi$
$948$	−0.231734	−0.00752637
$949$	−3.44562	−0.111850
$950$	0	0
$951$	−12.5972	−0.408492
$952$	4.59627	0.148966
$953$	−21.0487	−0.681834	−0.340917	−	0.940093i	$-0.610738\pi$
$953$	−21.0487	−0.681834	−0.340917	+	0.940093i	$0.610738\pi$
$954$	7.81521	0.253027
$955$	−4.13610	−0.133841
$956$	18.8699	0.610296
$957$	23.8307	0.770337
$958$	40.5134	1.30893
$959$	0.504748	0.0162992
$960$	−0.467911	−0.0151018
$961$	−9.48751	−0.306049
$962$	−1.98040	−0.0638506
$963$	−24.8726	−0.801508
$964$	15.9932	0.515106
$965$	6.72050	0.216341
$966$	2.15745	0.0694149
$967$	31.0479	0.998432	0.499216	−	0.866477i	$-0.333621\pi$
$967$	31.0479	0.998432	0.499216	+	0.866477i	$0.333621\pi$
$968$	2.70914	0.0870751
$969$	0	0
$970$	5.38919	0.173036
$971$	−14.0523	−0.450960	−0.225480	−	0.974248i	$-0.572395\pi$
$971$	−14.0523	−0.450960	−0.225480	+	0.974248i	$0.572395\pi$
$972$	−16.1088	−0.516689
$973$	−11.5125	−0.369073
$974$	−9.64496	−0.309045
$975$	1.44057	0.0461352
$976$	−9.06418	−0.290137
$977$	−26.4807	−0.847193	−0.423596	−	0.905851i	$-0.639233\pi$
$977$	−26.4807	−0.847193	−0.423596	+	0.905851i	$0.639233\pi$
$978$	−15.5235	−0.496388
$979$	−42.0428	−1.34369
$980$	0.532089	0.0169970
$981$	38.7983	1.23873
$982$	8.30129	0.264905
$983$	51.0300	1.62761	0.813803	−	0.581141i	$-0.197394\pi$
$983$	51.0300	1.62761	0.813803	+	0.581141i	$0.197394\pi$
$984$	5.75103	0.183336
$985$	0.0382671	0.00121929
$986$	43.2576	1.37760
$987$	−4.59627	−0.146301
$988$	0	0
$989$	4.47235	0.142213
$990$	−3.41147	−0.108424
$991$	−1.38919	−0.0441289	−0.0220645	−	0.999757i	$-0.507024\pi$
$991$	−1.38919	−0.0441289	−0.0220645	+	0.999757i	$0.507024\pi$
$992$	−4.63816	−0.147262
$993$	−16.8497	−0.534708
$994$	13.2344	0.419770
$995$	0.506178	0.0160469
$996$	−3.48070	−0.110290
$997$	28.1242	0.890704	0.445352	−	0.895356i	$-0.353079\pi$
$997$	28.1242	0.890704	0.445352	+	0.895356i	$0.353079\pi$
$998$	31.9777	1.01224
$999$	26.2094	0.829230

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5054.2.a.s.1.1		3
19.2	odd	18		266.2.u.a.99.1	yes	6
19.10	odd	18		266.2.u.a.43.1	✓	6
19.18	odd	2		5054.2.a.t.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
266.2.u.a.43.1	✓	6	19.10	odd	18
266.2.u.a.99.1	yes	6	19.2	odd	18
5054.2.a.s.1.1		3	1.1	even	1	trivial
5054.2.a.t.1.3		3	19.18	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 5054 = 2 \cdot 7 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5054.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.879385 q^{3} +1.00000 q^{4} +0.532089 q^{5} +0.879385 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.22668 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.879385 q^{3} +1.00000 q^{4} +0.532089 q^{5} +0.879385 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.22668 q^{9} -0.532089 q^{10} -2.87939 q^{11} -0.879385 q^{12} +0.347296 q^{13} -1.00000 q^{14} -0.467911 q^{15} +1.00000 q^{16} -4.59627 q^{17} +2.22668 q^{18} +0.532089 q^{20} -0.879385 q^{21} +2.87939 q^{22} +2.45336 q^{23} +0.879385 q^{24} -4.71688 q^{25} -0.347296 q^{26} +4.59627 q^{27} +1.00000 q^{28} +9.41147 q^{29} +0.467911 q^{30} +4.63816 q^{31} -1.00000 q^{32} +2.53209 q^{33} +4.59627 q^{34} +0.532089 q^{35} -2.22668 q^{36} +5.70233 q^{37} -0.305407 q^{39} -0.532089 q^{40} +6.53983 q^{41} +0.879385 q^{42} +1.82295 q^{43} -2.87939 q^{44} -1.18479 q^{45} -2.45336 q^{46} +5.22668 q^{47} -0.879385 q^{48} +1.00000 q^{49} +4.71688 q^{50} +4.04189 q^{51} +0.347296 q^{52} +3.50980 q^{53} -4.59627 q^{54} -1.53209 q^{55} -1.00000 q^{56} -9.41147 q^{58} -8.66044 q^{59} -0.467911 q^{60} -9.06418 q^{61} -4.63816 q^{62} -2.22668 q^{63} +1.00000 q^{64} +0.184793 q^{65} -2.53209 q^{66} -11.7246 q^{67} -4.59627 q^{68} -2.15745 q^{69} -0.532089 q^{70} -13.2344 q^{71} +2.22668 q^{72} -9.92127 q^{73} -5.70233 q^{74} +4.14796 q^{75} -2.87939 q^{77} +0.305407 q^{78} +0.263518 q^{79} +0.532089 q^{80} +2.63816 q^{81} -6.53983 q^{82} +3.95811 q^{83} -0.879385 q^{84} -2.44562 q^{85} -1.82295 q^{86} -8.27631 q^{87} +2.87939 q^{88} +14.6013 q^{89} +1.18479 q^{90} +0.347296 q^{91} +2.45336 q^{92} -4.07873 q^{93} -5.22668 q^{94} +0.879385 q^{96} -10.1284 q^{97} -1.00000 q^{98} +6.41147 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} + 3 q^{7} - 3 q^{8}+O(q^{10}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 + 3 * q^7 - 3 * q^8	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{10} - 3 q^{11} + 3 q^{12} - 3 q^{14} - 6 q^{15} + 3 q^{16} - 3 q^{20} + 3 q^{21} + 3 q^{22} - 6 q^{23} - 3 q^{24} - 6 q^{25} + 3 q^{28} + 18 q^{29} + 6 q^{30} - 3 q^{31} - 3 q^{32} + 3 q^{33} - 3 q^{35} - 9 q^{37} - 3 q^{39} + 3 q^{40} - 9 q^{41} - 3 q^{42} - 15 q^{43} - 3 q^{44} + 6 q^{46} + 9 q^{47} + 3 q^{48} + 3 q^{49} + 6 q^{50} + 9 q^{51} + 12 q^{53} - 3 q^{56} - 18 q^{58} - 3 q^{59} - 6 q^{60} - 18 q^{61} + 3 q^{62} + 3 q^{64} - 3 q^{65} - 3 q^{66} - 3 q^{67} - 24 q^{69} + 3 q^{70} - 9 q^{71} - 21 q^{73} + 9 q^{74} - 3 q^{75} - 3 q^{77} + 3 q^{78} + 6 q^{79} - 3 q^{80} - 9 q^{81} + 9 q^{82} + 15 q^{83} + 3 q^{84} - 18 q^{85} + 15 q^{86} + 9 q^{87} + 3 q^{88} + 15 q^{89} - 6 q^{92} - 21 q^{93} - 9 q^{94} - 3 q^{96} - 12 q^{97} - 3 q^{98} + 9 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^10 - 3 * q^11 + 3 * q^12 - 3 * q^14 - 6 * q^15 + 3 * q^16 - 3 * q^20 + 3 * q^21 + 3 * q^22 - 6 * q^23 - 3 * q^24 - 6 * q^25 + 3 * q^28 + 18 * q^29 + 6 * q^30 - 3 * q^31 - 3 * q^32 + 3 * q^33 - 3 * q^35 - 9 * q^37 - 3 * q^39 + 3 * q^40 - 9 * q^41 - 3 * q^42 - 15 * q^43 - 3 * q^44 + 6 * q^46 + 9 * q^47 + 3 * q^48 + 3 * q^49 + 6 * q^50 + 9 * q^51 + 12 * q^53 - 3 * q^56 - 18 * q^58 - 3 * q^59 - 6 * q^60 - 18 * q^61 + 3 * q^62 + 3 * q^64 - 3 * q^65 - 3 * q^66 - 3 * q^67 - 24 * q^69 + 3 * q^70 - 9 * q^71 - 21 * q^73 + 9 * q^74 - 3 * q^75 - 3 * q^77 + 3 * q^78 + 6 * q^79 - 3 * q^80 - 9 * q^81 + 9 * q^82 + 15 * q^83 + 3 * q^84 - 18 * q^85 + 15 * q^86 + 9 * q^87 + 3 * q^88 + 15 * q^89 - 6 * q^92 - 21 * q^93 - 9 * q^94 - 3 * q^96 - 12 * q^97 - 3 * q^98 + 9 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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