LMFDB - Embedded newform 5054.2.a.bk.1.8

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:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 3x^{8} - 15x^{7} + 40x^{6} + 81x^{5} - 162x^{4} - 205x^{3} + 204x^{2} + 210x + 1 $ x^9 - 3x^8 - 15x^7 + 40x^6 + 81x^5 - 162x^4 - 205x^3 + 204x^2 + 210x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
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			1.8
Root			$2.67565$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +2.67565 q^{3} +1.00000 q^{4} -2.78796 q^{5} +2.67565 q^{6} -1.00000 q^{7} +1.00000 q^{8} +4.15909 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.67565 q^{3} +1.00000 q^{4} -2.78796 q^{5} +2.67565 q^{6} -1.00000 q^{7} +1.00000 q^{8} +4.15909 q^{9} -2.78796 q^{10} -4.75235 q^{11} +2.67565 q^{12} +0.615323 q^{13} -1.00000 q^{14} -7.45959 q^{15} +1.00000 q^{16} +7.22327 q^{17} +4.15909 q^{18} -2.78796 q^{20} -2.67565 q^{21} -4.75235 q^{22} +3.07588 q^{23} +2.67565 q^{24} +2.77270 q^{25} +0.615323 q^{26} +3.10131 q^{27} -1.00000 q^{28} +0.676828 q^{29} -7.45959 q^{30} +2.93521 q^{31} +1.00000 q^{32} -12.7156 q^{33} +7.22327 q^{34} +2.78796 q^{35} +4.15909 q^{36} +7.74177 q^{37} +1.64639 q^{39} -2.78796 q^{40} +11.2334 q^{41} -2.67565 q^{42} +4.14105 q^{43} -4.75235 q^{44} -11.5954 q^{45} +3.07588 q^{46} -4.03763 q^{47} +2.67565 q^{48} +1.00000 q^{49} +2.77270 q^{50} +19.3269 q^{51} +0.615323 q^{52} +11.9204 q^{53} +3.10131 q^{54} +13.2494 q^{55} -1.00000 q^{56} +0.676828 q^{58} +7.48688 q^{59} -7.45959 q^{60} +12.2615 q^{61} +2.93521 q^{62} -4.15909 q^{63} +1.00000 q^{64} -1.71549 q^{65} -12.7156 q^{66} +3.56514 q^{67} +7.22327 q^{68} +8.22997 q^{69} +2.78796 q^{70} -0.372488 q^{71} +4.15909 q^{72} -8.38290 q^{73} +7.74177 q^{74} +7.41878 q^{75} +4.75235 q^{77} +1.64639 q^{78} +6.66242 q^{79} -2.78796 q^{80} -4.17925 q^{81} +11.2334 q^{82} -17.1808 q^{83} -2.67565 q^{84} -20.1382 q^{85} +4.14105 q^{86} +1.81095 q^{87} -4.75235 q^{88} -12.0919 q^{89} -11.5954 q^{90} -0.615323 q^{91} +3.07588 q^{92} +7.85358 q^{93} -4.03763 q^{94} +2.67565 q^{96} -11.2046 q^{97} +1.00000 q^{98} -19.7654 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 9 q^{2} + 3 q^{3} + 9 q^{4} + 3 q^{5} + 3 q^{6} - 9 q^{7} + 9 q^{8} + 12 q^{9}+O(q^{10}) $ 9 * q + 9 * q^2 + 3 * q^3 + 9 * q^4 + 3 * q^5 + 3 * q^6 - 9 * q^7 + 9 * q^8 + 12 * q^9	\( 9 q + 9 q^{2} + 3 q^{3} + 9 q^{4} + 3 q^{5} + 3 q^{6} - 9 q^{7} + 9 q^{8} + 12 q^{9} + 3 q^{10} - 3 q^{11} + 3 q^{12} + 12 q^{13} - 9 q^{14} - 6 q^{15} + 9 q^{16} + 12 q^{17} + 12 q^{18} + 3 q^{20} - 3 q^{21} - 3 q^{22} + 6 q^{23} + 3 q^{24} + 12 q^{26} + 24 q^{27} - 9 q^{28} - 6 q^{29} - 6 q^{30} + 9 q^{31} + 9 q^{32} - 3 q^{33} + 12 q^{34} - 3 q^{35} + 12 q^{36} + 9 q^{37} + 33 q^{39} + 3 q^{40} + 3 q^{41} - 3 q^{42} + 21 q^{43} - 3 q^{44} + 18 q^{45} + 6 q^{46} + 21 q^{47} + 3 q^{48} + 9 q^{49} + 39 q^{51} + 12 q^{52} + 24 q^{54} + 24 q^{55} - 9 q^{56} - 6 q^{58} - 9 q^{59} - 6 q^{60} + 6 q^{61} + 9 q^{62} - 12 q^{63} + 9 q^{64} - 3 q^{65} - 3 q^{66} + 27 q^{67} + 12 q^{68} + 6 q^{69} - 3 q^{70} + 9 q^{71} + 12 q^{72} + 51 q^{73} + 9 q^{74} - 3 q^{75} + 3 q^{77} + 33 q^{78} + 24 q^{79} + 3 q^{80} - 3 q^{81} + 3 q^{82} + 9 q^{83} - 3 q^{84} + 6 q^{85} + 21 q^{86} - 3 q^{87} - 3 q^{88} + 9 q^{89} + 18 q^{90} - 12 q^{91} + 6 q^{92} + 3 q^{93} + 21 q^{94} + 3 q^{96} - 12 q^{97} + 9 q^{98} - 15 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 + 3 * q^3 + 9 * q^4 + 3 * q^5 + 3 * q^6 - 9 * q^7 + 9 * q^8 + 12 * q^9 + 3 * q^10 - 3 * q^11 + 3 * q^12 + 12 * q^13 - 9 * q^14 - 6 * q^15 + 9 * q^16 + 12 * q^17 + 12 * q^18 + 3 * q^20 - 3 * q^21 - 3 * q^22 + 6 * q^23 + 3 * q^24 + 12 * q^26 + 24 * q^27 - 9 * q^28 - 6 * q^29 - 6 * q^30 + 9 * q^31 + 9 * q^32 - 3 * q^33 + 12 * q^34 - 3 * q^35 + 12 * q^36 + 9 * q^37 + 33 * q^39 + 3 * q^40 + 3 * q^41 - 3 * q^42 + 21 * q^43 - 3 * q^44 + 18 * q^45 + 6 * q^46 + 21 * q^47 + 3 * q^48 + 9 * q^49 + 39 * q^51 + 12 * q^52 + 24 * q^54 + 24 * q^55 - 9 * q^56 - 6 * q^58 - 9 * q^59 - 6 * q^60 + 6 * q^61 + 9 * q^62 - 12 * q^63 + 9 * q^64 - 3 * q^65 - 3 * q^66 + 27 * q^67 + 12 * q^68 + 6 * q^69 - 3 * q^70 + 9 * q^71 + 12 * q^72 + 51 * q^73 + 9 * q^74 - 3 * q^75 + 3 * q^77 + 33 * q^78 + 24 * q^79 + 3 * q^80 - 3 * q^81 + 3 * q^82 + 9 * q^83 - 3 * q^84 + 6 * q^85 + 21 * q^86 - 3 * q^87 - 3 * q^88 + 9 * q^89 + 18 * q^90 - 12 * q^91 + 6 * q^92 + 3 * q^93 + 21 * q^94 + 3 * q^96 - 12 * q^97 + 9 * q^98 - 15 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	2.67565	1.54479	0.772393	−	0.635145i	$-0.219060\pi$
$3$	2.67565	1.54479	0.772393	+	0.635145i	$0.219060\pi$
$4$	1.00000	0.500000
$5$	−2.78796	−1.24681	−0.623406	−	0.781898i	$-0.714252\pi$
$5$	−2.78796	−1.24681	−0.623406	+	0.781898i	$0.714252\pi$
$6$	2.67565	1.09233
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	4.15909	1.38636
$10$	−2.78796	−0.881629
$11$	−4.75235	−1.43289	−0.716444	−	0.697645i	$-0.754231\pi$
$11$	−4.75235	−1.43289	−0.716444	+	0.697645i	$0.754231\pi$
$12$	2.67565	0.772393
$13$	0.615323	0.170660	0.0853299	−	0.996353i	$-0.472806\pi$
$13$	0.615323	0.170660	0.0853299	+	0.996353i	$0.472806\pi$
$14$	−1.00000	−0.267261
$15$	−7.45959	−1.92606
$16$	1.00000	0.250000
$17$	7.22327	1.75190	0.875950	−	0.482403i	$-0.160236\pi$
$17$	7.22327	1.75190	0.875950	+	0.482403i	$0.160236\pi$
$18$	4.15909	0.980306
$19$	0	0
$19$	0	0
$20$	−2.78796	−0.623406
$21$	−2.67565	−0.583874
$22$	−4.75235	−1.01320
$23$	3.07588	0.641366	0.320683	−	0.947187i	$-0.396088\pi$
$23$	3.07588	0.641366	0.320683	+	0.947187i	$0.396088\pi$
$24$	2.67565	0.546164
$25$	2.77270	0.554541
$26$	0.615323	0.120675
$27$	3.10131	0.596848
$28$	−1.00000	−0.188982
$29$	0.676828	0.125684	0.0628419	−	0.998023i	$-0.479984\pi$
$29$	0.676828	0.125684	0.0628419	+	0.998023i	$0.479984\pi$
$30$	−7.45959	−1.36193
$31$	2.93521	0.527179	0.263589	−	0.964635i	$-0.415094\pi$
$31$	2.93521	0.527179	0.263589	+	0.964635i	$0.415094\pi$
$32$	1.00000	0.176777
$33$	−12.7156	−2.21350
$34$	7.22327	1.23878
$35$	2.78796	0.471251
$36$	4.15909	0.693181
$37$	7.74177	1.27274	0.636369	−	0.771385i	$-0.280435\pi$
$37$	7.74177	1.27274	0.636369	+	0.771385i	$0.280435\pi$
$38$	0	0
$39$	1.64639	0.263633
$40$	−2.78796	−0.440815
$41$	11.2334	1.75436	0.877178	−	0.480166i	$-0.159424\pi$
$41$	11.2334	1.75436	0.877178	+	0.480166i	$0.159424\pi$
$42$	−2.67565	−0.412861
$43$	4.14105	0.631505	0.315752	−	0.948842i	$-0.397743\pi$
$43$	4.14105	0.631505	0.315752	+	0.948842i	$0.397743\pi$
$44$	−4.75235	−0.716444
$45$	−11.5954	−1.72853
$46$	3.07588	0.453514
$47$	−4.03763	−0.588949	−0.294475	−	0.955659i	$-0.595145\pi$
$47$	−4.03763	−0.588949	−0.294475	+	0.955659i	$0.595145\pi$
$48$	2.67565	0.386196
$49$	1.00000	0.142857
$50$	2.77270	0.392120
$51$	19.3269	2.70631
$52$	0.615323	0.0853299
$53$	11.9204	1.63739	0.818694	−	0.574230i	$-0.194698\pi$
$53$	11.9204	1.63739	0.818694	+	0.574230i	$0.194698\pi$
$54$	3.10131	0.422035
$55$	13.2494	1.78654
$56$	−1.00000	−0.133631
$57$	0	0
$58$	0.676828	0.0888718
$59$	7.48688	0.974708	0.487354	−	0.873204i	$-0.337962\pi$
$59$	7.48688	0.974708	0.487354	+	0.873204i	$0.337962\pi$
$60$	−7.45959	−0.963029
$61$	12.2615	1.56992	0.784959	−	0.619548i	$-0.212684\pi$
$61$	12.2615	1.56992	0.784959	+	0.619548i	$0.212684\pi$
$62$	2.93521	0.372772
$63$	−4.15909	−0.523996
$64$	1.00000	0.125000
$65$	−1.71549	−0.212781
$66$	−12.7156	−1.56518
$67$	3.56514	0.435551	0.217776	−	0.975999i	$-0.430120\pi$
$67$	3.56514	0.435551	0.217776	+	0.975999i	$0.430120\pi$
$68$	7.22327	0.875950
$69$	8.22997	0.990772
$70$	2.78796	0.333225
$71$	−0.372488	−0.0442062	−0.0221031	−	0.999756i	$-0.507036\pi$
$71$	−0.372488	−0.0442062	−0.0221031	+	0.999756i	$0.507036\pi$
$72$	4.15909	0.490153
$73$	−8.38290	−0.981144	−0.490572	−	0.871401i	$-0.663212\pi$
$73$	−8.38290	−0.981144	−0.490572	+	0.871401i	$0.663212\pi$
$74$	7.74177	0.899962
$75$	7.41878	0.856647
$76$	0	0
$77$	4.75235	0.541581
$78$	1.64639	0.186417
$79$	6.66242	0.749580	0.374790	−	0.927110i	$-0.377715\pi$
$79$	6.66242	0.749580	0.374790	+	0.927110i	$0.377715\pi$
$80$	−2.78796	−0.311703
$81$	−4.17925	−0.464361
$82$	11.2334	1.24052
$83$	−17.1808	−1.88583	−0.942916	−	0.333029i	$-0.891929\pi$
$83$	−17.1808	−1.88583	−0.942916	+	0.333029i	$0.891929\pi$
$84$	−2.67565	−0.291937
$85$	−20.1382	−2.18429
$86$	4.14105	0.446541
$87$	1.81095	0.194154
$88$	−4.75235	−0.506602
$89$	−12.0919	−1.28174	−0.640868	−	0.767651i	$-0.721425\pi$
$89$	−12.0919	−1.28174	−0.640868	+	0.767651i	$0.721425\pi$
$90$	−11.5954	−1.22226
$91$	−0.615323	−0.0645033
$92$	3.07588	0.320683
$93$	7.85358	0.814378
$94$	−4.03763	−0.416450
$95$	0	0
$96$	2.67565	0.273082
$97$	−11.2046	−1.13766	−0.568829	−	0.822456i	$-0.692603\pi$
$97$	−11.2046	−1.13766	−0.568829	+	0.822456i	$0.692603\pi$
$98$	1.00000	0.101015
$99$	−19.7654	−1.98650
$100$	2.77270	0.277270
$101$	5.20034	0.517453	0.258727	−	0.965951i	$-0.416697\pi$
$101$	5.20034	0.517453	0.258727	+	0.965951i	$0.416697\pi$
$102$	19.3269	1.91365
$103$	5.82979	0.574426	0.287213	−	0.957867i	$-0.407271\pi$
$103$	5.82979	0.574426	0.287213	+	0.957867i	$0.407271\pi$
$104$	0.615323	0.0603373
$105$	7.45959	0.727981
$106$	11.9204	1.15781
$107$	10.6072	1.02543	0.512717	−	0.858558i	$-0.328639\pi$
$107$	10.6072	1.02543	0.512717	+	0.858558i	$0.328639\pi$
$108$	3.10131	0.298424
$109$	−5.91402	−0.566460	−0.283230	−	0.959052i	$-0.591406\pi$
$109$	−5.91402	−0.566460	−0.283230	+	0.959052i	$0.591406\pi$
$110$	13.2494	1.26328
$111$	20.7142	1.96611
$112$	−1.00000	−0.0944911
$113$	0.0281582	0.00264890	0.00132445	−	0.999999i	$-0.499578\pi$
$113$	0.0281582	0.00264890	0.00132445	+	0.999999i	$0.499578\pi$
$114$	0	0
$115$	−8.57543	−0.799663
$116$	0.676828	0.0628419
$117$	2.55918	0.236596
$118$	7.48688	0.689223
$119$	−7.22327	−0.662156
$120$	−7.45959	−0.680964
$121$	11.5848	1.05317
$122$	12.2615	1.11010
$123$	30.0565	2.71010
$124$	2.93521	0.263589
$125$	6.20961	0.555404
$126$	−4.15909	−0.370521
$127$	4.61129	0.409185	0.204593	−	0.978847i	$-0.434413\pi$
$127$	4.61129	0.409185	0.204593	+	0.978847i	$0.434413\pi$
$128$	1.00000	0.0883883
$129$	11.0800	0.975540
$130$	−1.71549	−0.150459
$131$	−7.64595	−0.668030	−0.334015	−	0.942568i	$-0.608404\pi$
$131$	−7.64595	−0.668030	−0.334015	+	0.942568i	$0.608404\pi$
$132$	−12.7156	−1.10675
$133$	0	0
$134$	3.56514	0.307981
$135$	−8.64632	−0.744157
$136$	7.22327	0.619390
$137$	−18.4237	−1.57404	−0.787020	−	0.616928i	$-0.788377\pi$
$137$	−18.4237	−1.57404	−0.787020	+	0.616928i	$0.788377\pi$
$138$	8.22997	0.700582
$139$	−0.918748	−0.0779272	−0.0389636	−	0.999241i	$-0.512406\pi$
$139$	−0.918748	−0.0779272	−0.0389636	+	0.999241i	$0.512406\pi$
$140$	2.78796	0.235625
$141$	−10.8033	−0.909800
$142$	−0.372488	−0.0312585
$143$	−2.92423	−0.244536
$144$	4.15909	0.346591
$145$	−1.88697	−0.156704
$146$	−8.38290	−0.693774
$147$	2.67565	0.220684
$148$	7.74177	0.636369
$149$	−10.5117	−0.861151	−0.430576	−	0.902554i	$-0.641689\pi$
$149$	−10.5117	−0.861151	−0.430576	+	0.902554i	$0.641689\pi$
$150$	7.41878	0.605741
$151$	18.6362	1.51659	0.758294	−	0.651913i	$-0.226033\pi$
$151$	18.6362	1.51659	0.758294	+	0.651913i	$0.226033\pi$
$152$	0	0
$153$	30.0422	2.42877
$154$	4.75235	0.382955
$155$	−8.18323	−0.657293
$156$	1.64639	0.131816
$157$	−15.9868	−1.27588	−0.637942	−	0.770084i	$-0.720214\pi$
$157$	−15.9868	−1.27588	−0.637942	+	0.770084i	$0.720214\pi$
$158$	6.66242	0.530033
$159$	31.8947	2.52941
$160$	−2.78796	−0.220407
$161$	−3.07588	−0.242413
$162$	−4.17925	−0.328353
$163$	−2.09713	−0.164260	−0.0821298	−	0.996622i	$-0.526172\pi$
$163$	−2.09713	−0.164260	−0.0821298	+	0.996622i	$0.526172\pi$
$164$	11.2334	0.877178
$165$	35.4506	2.75982
$166$	−17.1808	−1.33349
$167$	−6.38945	−0.494431	−0.247215	−	0.968961i	$-0.579516\pi$
$167$	−6.38945	−0.494431	−0.247215	+	0.968961i	$0.579516\pi$
$168$	−2.67565	−0.206431
$169$	−12.6214	−0.970875
$170$	−20.1382	−1.54453
$171$	0	0
$172$	4.14105	0.315752
$173$	−23.7146	−1.80299	−0.901493	−	0.432793i	$-0.857528\pi$
$173$	−23.7146	−1.80299	−0.901493	+	0.432793i	$0.857528\pi$
$174$	1.81095	0.137288
$175$	−2.77270	−0.209597
$176$	−4.75235	−0.358222
$177$	20.0322	1.50572
$178$	−12.0919	−0.906324
$179$	13.9786	1.04481	0.522404	−	0.852698i	$-0.325035\pi$
$179$	13.9786	1.04481	0.522404	+	0.852698i	$0.325035\pi$
$180$	−11.5954	−0.864267
$181$	−9.94297	−0.739055	−0.369528	−	0.929220i	$-0.620481\pi$
$181$	−9.94297	−0.739055	−0.369528	+	0.929220i	$0.620481\pi$
$182$	−0.615323	−0.0456107
$183$	32.8073	2.42519
$184$	3.07588	0.226757
$185$	−21.5837	−1.58687
$186$	7.85358	0.575852
$187$	−34.3275	−2.51028
$188$	−4.03763	−0.294475
$189$	−3.10131	−0.225587
$190$	0	0
$191$	−12.2899	−0.889263	−0.444632	−	0.895714i	$-0.646665\pi$
$191$	−12.2899	−0.889263	−0.444632	+	0.895714i	$0.646665\pi$
$192$	2.67565	0.193098
$193$	−10.5006	−0.755848	−0.377924	−	0.925837i	$-0.623362\pi$
$193$	−10.5006	−0.755848	−0.377924	+	0.925837i	$0.623362\pi$
$194$	−11.2046	−0.804446
$195$	−4.59005	−0.328701
$196$	1.00000	0.0714286
$197$	−12.4623	−0.887901	−0.443951	−	0.896051i	$-0.646423\pi$
$197$	−12.4623	−0.887901	−0.443951	+	0.896051i	$0.646423\pi$
$198$	−19.7654	−1.40467
$199$	10.7924	0.765051	0.382525	−	0.923945i	$-0.375054\pi$
$199$	10.7924	0.765051	0.382525	+	0.923945i	$0.375054\pi$
$200$	2.77270	0.196060
$201$	9.53906	0.672833
$202$	5.20034	0.365895
$203$	−0.676828	−0.0475040
$204$	19.3269	1.35315
$205$	−31.3181	−2.18735
$206$	5.82979	0.406181
$207$	12.7929	0.889165
$208$	0.615323	0.0426649
$209$	0	0
$210$	7.45959	0.514761
$211$	−1.38335	−0.0952338	−0.0476169	−	0.998866i	$-0.515163\pi$
$211$	−1.38335	−0.0952338	−0.0476169	+	0.998866i	$0.515163\pi$
$212$	11.9204	0.818694
$213$	−0.996647	−0.0682891
$214$	10.6072	0.725091
$215$	−11.5451	−0.787368
$216$	3.10131	0.211017
$217$	−2.93521	−0.199255
$218$	−5.91402	−0.400548
$219$	−22.4297	−1.51566
$220$	13.2494	0.893271
$221$	4.44464	0.298979
$222$	20.7142	1.39025
$223$	13.4281	0.899215	0.449608	−	0.893226i	$-0.351564\pi$
$223$	13.4281	0.899215	0.449608	+	0.893226i	$0.351564\pi$
$224$	−1.00000	−0.0668153
$225$	11.5319	0.768795
$226$	0.0281582	0.00187306
$227$	20.6046	1.36758	0.683789	−	0.729680i	$-0.260331\pi$
$227$	20.6046	1.36758	0.683789	+	0.729680i	$0.260331\pi$
$228$	0	0
$229$	12.0038	0.793237	0.396618	−	0.917984i	$-0.370184\pi$
$229$	12.0038	0.793237	0.396618	+	0.917984i	$0.370184\pi$
$230$	−8.57543	−0.565447
$231$	12.7156	0.836626
$232$	0.676828	0.0444359
$233$	−4.63426	−0.303600	−0.151800	−	0.988411i	$-0.548507\pi$
$233$	−4.63426	−0.303600	−0.151800	+	0.988411i	$0.548507\pi$
$234$	2.55918	0.167299
$235$	11.2567	0.734309
$236$	7.48688	0.487354
$237$	17.8263	1.15794
$238$	−7.22327	−0.468215
$239$	27.3654	1.77012	0.885060	−	0.465477i	$-0.154117\pi$
$239$	27.3654	1.77012	0.885060	+	0.465477i	$0.154117\pi$
$240$	−7.45959	−0.481514
$241$	−0.649735	−0.0418531	−0.0209266	−	0.999781i	$-0.506662\pi$
$241$	−0.649735	−0.0418531	−0.0209266	+	0.999781i	$0.506662\pi$
$242$	11.5848	0.744702
$243$	−20.4861	−1.31419
$244$	12.2615	0.784959
$245$	−2.78796	−0.178116
$246$	30.0565	1.91633
$247$	0	0
$248$	2.93521	0.186386
$249$	−45.9696	−2.91321
$250$	6.20961	0.392730
$251$	6.03119	0.380685	0.190343	−	0.981718i	$-0.439040\pi$
$251$	6.03119	0.380685	0.190343	+	0.981718i	$0.439040\pi$
$252$	−4.15909	−0.261998
$253$	−14.6177	−0.919005
$254$	4.61129	0.289338
$255$	−53.8826	−3.37426
$256$	1.00000	0.0625000
$257$	11.8913	0.741759	0.370879	−	0.928681i	$-0.379056\pi$
$257$	11.8913	0.741759	0.370879	+	0.928681i	$0.379056\pi$
$258$	11.0800	0.689811
$259$	−7.74177	−0.481050
$260$	−1.71549	−0.106390
$261$	2.81499	0.174243
$262$	−7.64595	−0.472369
$263$	−3.43553	−0.211844	−0.105922	−	0.994374i	$-0.533779\pi$
$263$	−3.43553	−0.211844	−0.105922	+	0.994374i	$0.533779\pi$
$264$	−12.7156	−0.782592
$265$	−33.2335	−2.04152
$266$	0	0
$267$	−32.3536	−1.98001
$268$	3.56514	0.217776
$269$	22.7522	1.38722	0.693612	−	0.720349i	$-0.256018\pi$
$269$	22.7522	1.38722	0.693612	+	0.720349i	$0.256018\pi$
$270$	−8.64632	−0.526198
$271$	28.1967	1.71282	0.856412	−	0.516293i	$-0.172688\pi$
$271$	28.1967	1.71282	0.856412	+	0.516293i	$0.172688\pi$
$272$	7.22327	0.437975
$273$	−1.64639	−0.0996438
$274$	−18.4237	−1.11301
$275$	−13.1769	−0.794595
$276$	8.22997	0.495386
$277$	−14.0129	−0.841953	−0.420977	−	0.907072i	$-0.638313\pi$
$277$	−14.0129	−0.841953	−0.420977	+	0.907072i	$0.638313\pi$
$278$	−0.918748	−0.0551029
$279$	12.2078	0.730861
$280$	2.78796	0.166612
$281$	−27.4551	−1.63783	−0.818917	−	0.573912i	$-0.805425\pi$
$281$	−27.4551	−1.63783	−0.818917	+	0.573912i	$0.805425\pi$
$282$	−10.8033	−0.643326
$283$	3.89300	0.231415	0.115707	−	0.993283i	$-0.463086\pi$
$283$	3.89300	0.231415	0.115707	+	0.993283i	$0.463086\pi$
$284$	−0.372488	−0.0221031
$285$	0	0
$286$	−2.92423	−0.172913
$287$	−11.2334	−0.663084
$288$	4.15909	0.245077
$289$	35.1756	2.06915
$290$	−1.88697	−0.110806
$291$	−29.9796	−1.75744
$292$	−8.38290	−0.490572
$293$	9.63006	0.562594	0.281297	−	0.959621i	$-0.409235\pi$
$293$	9.63006	0.562594	0.281297	+	0.959621i	$0.409235\pi$
$294$	2.67565	0.156047
$295$	−20.8731	−1.21528
$296$	7.74177	0.449981
$297$	−14.7385	−0.855216
$298$	−10.5117	−0.608926
$299$	1.89266	0.109455
$300$	7.41878	0.428323
$301$	−4.14105	−0.238686
$302$	18.6362	1.07239
$303$	13.9143	0.799354
$304$	0	0
$305$	−34.1844	−1.95739
$306$	30.0422	1.71740
$307$	11.2087	0.639712	0.319856	−	0.947466i	$-0.396366\pi$
$307$	11.2087	0.639712	0.319856	+	0.947466i	$0.396366\pi$
$308$	4.75235	0.270790
$309$	15.5985	0.887366
$310$	−8.18323	−0.464776
$311$	−16.1665	−0.916720	−0.458360	−	0.888767i	$-0.651563\pi$
$311$	−16.1665	−0.916720	−0.458360	+	0.888767i	$0.651563\pi$
$312$	1.64639	0.0932083
$313$	23.8380	1.34741	0.673703	−	0.739003i	$-0.264703\pi$
$313$	23.8380	1.34741	0.673703	+	0.739003i	$0.264703\pi$
$314$	−15.9868	−0.902186
$315$	11.5954	0.653324
$316$	6.66242	0.374790
$317$	22.6665	1.27308	0.636538	−	0.771245i	$-0.280366\pi$
$317$	22.6665	1.27308	0.636538	+	0.771245i	$0.280366\pi$
$318$	31.8947	1.78857
$319$	−3.21652	−0.180091
$320$	−2.78796	−0.155852
$321$	28.3810	1.58407
$322$	−3.07588	−0.171412
$323$	0	0
$324$	−4.17925	−0.232181
$325$	1.70611	0.0946378
$326$	−2.09713	−0.116149
$327$	−15.8238	−0.875059
$328$	11.2334	0.620258
$329$	4.03763	0.222602
$330$	35.4506	1.95149
$331$	5.56883	0.306090	0.153045	−	0.988219i	$-0.451092\pi$
$331$	5.56883	0.306090	0.153045	+	0.988219i	$0.451092\pi$
$332$	−17.1808	−0.942916
$333$	32.1987	1.76448
$334$	−6.38945	−0.349615
$335$	−9.93946	−0.543051
$336$	−2.67565	−0.145969
$337$	−26.9956	−1.47054	−0.735272	−	0.677772i	$-0.762946\pi$
$337$	−26.9956	−1.47054	−0.735272	+	0.677772i	$0.762946\pi$
$338$	−12.6214	−0.686512
$339$	0.0753414	0.00409199
$340$	−20.1382	−1.09214
$341$	−13.9491	−0.755388
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	4.14105	0.223271
$345$	−22.9448	−1.23531
$346$	−23.7146	−1.27490
$347$	9.27421	0.497865	0.248933	−	0.968521i	$-0.419920\pi$
$347$	9.27421	0.497865	0.248933	+	0.968521i	$0.419920\pi$
$348$	1.81095	0.0970772
$349$	30.4033	1.62745	0.813727	−	0.581247i	$-0.197435\pi$
$349$	30.4033	1.62745	0.813727	+	0.581247i	$0.197435\pi$
$350$	−2.77270	−0.148207
$351$	1.90831	0.101858
$352$	−4.75235	−0.253301
$353$	7.95467	0.423385	0.211692	−	0.977336i	$-0.432103\pi$
$353$	7.95467	0.423385	0.211692	+	0.977336i	$0.432103\pi$
$354$	20.0322	1.06470
$355$	1.03848	0.0551168
$356$	−12.0919	−0.640868
$357$	−19.3269	−1.02289
$358$	13.9786	0.738791
$359$	−23.3547	−1.23262	−0.616308	−	0.787505i	$-0.711372\pi$
$359$	−23.3547	−1.23262	−0.616308	+	0.787505i	$0.711372\pi$
$360$	−11.5954	−0.611129
$361$	0	0
$362$	−9.94297	−0.522591
$363$	30.9969	1.62692
$364$	−0.615323	−0.0322517
$365$	23.3712	1.22330
$366$	32.8073	1.71487
$367$	13.5912	0.709453	0.354727	−	0.934970i	$-0.384574\pi$
$367$	13.5912	0.709453	0.354727	+	0.934970i	$0.384574\pi$
$368$	3.07588	0.160341
$369$	46.7205	2.43217
$370$	−21.5837	−1.12208
$371$	−11.9204	−0.618875
$372$	7.85358	0.407189
$373$	−9.89636	−0.512414	−0.256207	−	0.966622i	$-0.582473\pi$
$373$	−9.89636	−0.512414	−0.256207	+	0.966622i	$0.582473\pi$
$374$	−34.3275	−1.77503
$375$	16.6147	0.857980
$376$	−4.03763	−0.208225
$377$	0.416467	0.0214492
$378$	−3.10131	−0.159514
$379$	−18.7384	−0.962527	−0.481264	−	0.876576i	$-0.659822\pi$
$379$	−18.7384	−0.962527	−0.481264	+	0.876576i	$0.659822\pi$
$380$	0	0
$381$	12.3382	0.632104
$382$	−12.2899	−0.628804
$383$	−8.23732	−0.420907	−0.210454	−	0.977604i	$-0.567494\pi$
$383$	−8.23732	−0.420907	−0.210454	+	0.977604i	$0.567494\pi$
$384$	2.67565	0.136541
$385$	−13.2494	−0.675249
$386$	−10.5006	−0.534466
$387$	17.2230	0.875495
$388$	−11.2046	−0.568829
$389$	−35.1493	−1.78214	−0.891070	−	0.453866i	$-0.850044\pi$
$389$	−35.1493	−1.78214	−0.891070	+	0.453866i	$0.850044\pi$
$390$	−4.59005	−0.232426
$391$	22.2179	1.12361
$392$	1.00000	0.0505076
$393$	−20.4579	−1.03196
$394$	−12.4623	−0.627841
$395$	−18.5745	−0.934586
$396$	−19.7654	−0.993251
$397$	12.2995	0.617294	0.308647	−	0.951177i	$-0.400124\pi$
$397$	12.2995	0.617294	0.308647	+	0.951177i	$0.400124\pi$
$398$	10.7924	0.540973
$399$	0	0
$400$	2.77270	0.138635
$401$	−11.0861	−0.553613	−0.276807	−	0.960926i	$-0.589276\pi$
$401$	−11.0861	−0.553613	−0.276807	+	0.960926i	$0.589276\pi$
$402$	9.53906	0.475765
$403$	1.80610	0.0899682
$404$	5.20034	0.258727
$405$	11.6516	0.578971
$406$	−0.676828	−0.0335904
$407$	−36.7916	−1.82369
$408$	19.3269	0.956825
$409$	−27.5519	−1.36235	−0.681177	−	0.732118i	$-0.738532\pi$
$409$	−27.5519	−1.36235	−0.681177	+	0.732118i	$0.738532\pi$
$410$	−31.3181	−1.54669
$411$	−49.2952	−2.43155
$412$	5.82979	0.287213
$413$	−7.48688	−0.368405
$414$	12.7929	0.628735
$415$	47.8992	2.35128
$416$	0.615323	0.0301687
$417$	−2.45825	−0.120381
$418$	0	0
$419$	31.8705	1.55698	0.778488	−	0.627660i	$-0.215987\pi$
$419$	31.8705	1.55698	0.778488	+	0.627660i	$0.215987\pi$
$420$	7.45959	0.363991
$421$	6.03813	0.294280	0.147140	−	0.989116i	$-0.452993\pi$
$421$	6.03813	0.294280	0.147140	+	0.989116i	$0.452993\pi$
$422$	−1.38335	−0.0673404
$423$	−16.7929	−0.816497
$424$	11.9204	0.578904
$425$	20.0280	0.971500
$426$	−0.996647	−0.0482877
$427$	−12.2615	−0.593373
$428$	10.6072	0.512717
$429$	−7.82421	−0.377756
$430$	−11.5451	−0.556753
$431$	−18.3947	−0.886039	−0.443020	−	0.896512i	$-0.646093\pi$
$431$	−18.3947	−0.886039	−0.443020	+	0.896512i	$0.646093\pi$
$432$	3.10131	0.149212
$433$	15.0672	0.724085	0.362042	−	0.932162i	$-0.382080\pi$
$433$	15.0672	0.724085	0.362042	+	0.932162i	$0.382080\pi$
$434$	−2.93521	−0.140894
$435$	−5.04886	−0.242074
$436$	−5.91402	−0.283230
$437$	0	0
$438$	−22.4297	−1.07173
$439$	14.4522	0.689766	0.344883	−	0.938646i	$-0.387919\pi$
$439$	14.4522	0.689766	0.344883	+	0.938646i	$0.387919\pi$
$440$	13.2494	0.631638
$441$	4.15909	0.198052
$442$	4.44464	0.211410
$443$	17.8600	0.848554	0.424277	−	0.905532i	$-0.360528\pi$
$443$	17.8600	0.848554	0.424277	+	0.905532i	$0.360528\pi$
$444$	20.7142	0.983054
$445$	33.7116	1.59808
$446$	13.4281	0.635841
$447$	−28.1256	−1.33029
$448$	−1.00000	−0.0472456
$449$	−29.8637	−1.40935	−0.704676	−	0.709529i	$-0.748908\pi$
$449$	−29.8637	−1.40935	−0.704676	+	0.709529i	$0.748908\pi$
$450$	11.5319	0.543620
$451$	−53.3848	−2.51379
$452$	0.0281582	0.00132445
$453$	49.8638	2.34280
$454$	20.6046	0.967024
$455$	1.71549	0.0804235
$456$	0	0
$457$	−11.7730	−0.550720	−0.275360	−	0.961341i	$-0.588797\pi$
$457$	−11.7730	−0.550720	−0.275360	+	0.961341i	$0.588797\pi$
$458$	12.0038	0.560903
$459$	22.4016	1.04562
$460$	−8.57543	−0.399831
$461$	−32.4227	−1.51008	−0.755039	−	0.655680i	$-0.772382\pi$
$461$	−32.4227	−1.51008	−0.755039	+	0.655680i	$0.772382\pi$
$462$	12.7156	0.591584
$463$	7.40154	0.343979	0.171989	−	0.985099i	$-0.444981\pi$
$463$	7.40154	0.343979	0.171989	+	0.985099i	$0.444981\pi$
$464$	0.676828	0.0314209
$465$	−21.8954	−1.01538
$466$	−4.63426	−0.214678
$467$	8.17380	0.378239	0.189119	−	0.981954i	$-0.439437\pi$
$467$	8.17380	0.378239	0.189119	+	0.981954i	$0.439437\pi$
$468$	2.55918	0.118298
$469$	−3.56514	−0.164623
$470$	11.2567	0.519235
$471$	−42.7750	−1.97097
$472$	7.48688	0.344611
$473$	−19.6797	−0.904876
$474$	17.8263	0.818788
$475$	0	0
$476$	−7.22327	−0.331078
$477$	49.5779	2.27001
$478$	27.3654	1.25166
$479$	−15.2272	−0.695749	−0.347874	−	0.937541i	$-0.613096\pi$
$479$	−15.2272	−0.695749	−0.347874	+	0.937541i	$0.613096\pi$
$480$	−7.45959	−0.340482
$481$	4.76368	0.217205
$482$	−0.649735	−0.0295946
$483$	−8.22997	−0.374477
$484$	11.5848	0.526584
$485$	31.2380	1.41845
$486$	−20.4861	−0.929270
$487$	−1.78125	−0.0807162	−0.0403581	−	0.999185i	$-0.512850\pi$
$487$	−1.78125	−0.0807162	−0.0403581	+	0.999185i	$0.512850\pi$
$488$	12.2615	0.555050
$489$	−5.61117	−0.253746
$490$	−2.78796	−0.125947
$491$	−34.0418	−1.53628	−0.768142	−	0.640279i	$-0.778819\pi$
$491$	−34.0418	−1.53628	−0.768142	+	0.640279i	$0.778819\pi$
$492$	30.0565	1.35505
$493$	4.88891	0.220185
$494$	0	0
$495$	55.1052	2.47680
$496$	2.93521	0.131795
$497$	0.372488	0.0167084
$498$	−45.9696	−2.05995
$499$	20.0504	0.897580	0.448790	−	0.893637i	$-0.351855\pi$
$499$	20.0504	0.897580	0.448790	+	0.893637i	$0.351855\pi$
$500$	6.20961	0.277702
$501$	−17.0959	−0.763789
$502$	6.03119	0.269185
$503$	−29.1438	−1.29946	−0.649729	−	0.760166i	$-0.725118\pi$
$503$	−29.1438	−1.29946	−0.649729	+	0.760166i	$0.725118\pi$
$504$	−4.15909	−0.185261
$505$	−14.4983	−0.645167
$506$	−14.6177	−0.649835
$507$	−33.7704	−1.49979
$508$	4.61129	0.204593
$509$	33.5897	1.48884	0.744418	−	0.667714i	$-0.232727\pi$
$509$	33.5897	1.48884	0.744418	+	0.667714i	$0.232727\pi$
$510$	−53.8826	−2.38596
$511$	8.38290	0.370838
$512$	1.00000	0.0441942
$513$	0	0
$514$	11.8913	0.524503
$515$	−16.2532	−0.716202
$516$	11.0800	0.487770
$517$	19.1882	0.843898
$518$	−7.74177	−0.340154
$519$	−63.4519	−2.78523
$520$	−1.71549	−0.0752293
$521$	−22.7684	−0.997501	−0.498751	−	0.866745i	$-0.666208\pi$
$521$	−22.7684	−0.997501	−0.498751	+	0.866745i	$0.666208\pi$
$522$	2.81499	0.123209
$523$	8.30310	0.363069	0.181535	−	0.983385i	$-0.441894\pi$
$523$	8.30310	0.363069	0.181535	+	0.983385i	$0.441894\pi$
$524$	−7.64595	−0.334015
$525$	−7.41878	−0.323782
$526$	−3.43553	−0.149796
$527$	21.2018	0.923564
$528$	−12.7156	−0.553376
$529$	−13.5390	−0.588650
$530$	−33.2335	−1.44357
$531$	31.1386	1.35130
$532$	0	0
$533$	6.91214	0.299398
$534$	−32.3536	−1.40008
$535$	−29.5723	−1.27852
$536$	3.56514	0.153991
$537$	37.4018	1.61401
$538$	22.7522	0.980916
$539$	−4.75235	−0.204698
$540$	−8.64632	−0.372078
$541$	20.6152	0.886316	0.443158	−	0.896444i	$-0.353858\pi$
$541$	20.6152	0.886316	0.443158	+	0.896444i	$0.353858\pi$
$542$	28.1967	1.21115
$543$	−26.6039	−1.14168
$544$	7.22327	0.309695
$545$	16.4880	0.706269
$546$	−1.64639	−0.0704588
$547$	28.8070	1.23170	0.615850	−	0.787863i	$-0.288813\pi$
$547$	28.8070	1.23170	0.615850	+	0.787863i	$0.288813\pi$
$548$	−18.4237	−0.787020
$549$	50.9965	2.17648
$550$	−13.1769	−0.561863
$551$	0	0
$552$	8.22997	0.350291
$553$	−6.66242	−0.283315
$554$	−14.0129	−0.595351
$555$	−57.7504	−2.45137
$556$	−0.918748	−0.0389636
$557$	−9.59228	−0.406438	−0.203219	−	0.979133i	$-0.565140\pi$
$557$	−9.59228	−0.406438	−0.203219	+	0.979133i	$0.565140\pi$
$558$	12.2078	0.516797
$559$	2.54808	0.107772
$560$	2.78796	0.117813
$561$	−91.8483	−3.87784
$562$	−27.4551	−1.15812
$563$	6.87717	0.289838	0.144919	−	0.989444i	$-0.453708\pi$
$563$	6.87717	0.289838	0.144919	+	0.989444i	$0.453708\pi$
$564$	−10.8033	−0.454900
$565$	−0.0785039	−0.00330268
$566$	3.89300	0.163635
$567$	4.17925	0.175512
$568$	−0.372488	−0.0156293
$569$	0.390852	0.0163854	0.00819268	−	0.999966i	$-0.497392\pi$
$569$	0.390852	0.0163854	0.00819268	+	0.999966i	$0.497392\pi$
$570$	0	0
$571$	−40.2112	−1.68279	−0.841394	−	0.540423i	$-0.818264\pi$
$571$	−40.2112	−1.68279	−0.841394	+	0.540423i	$0.818264\pi$
$572$	−2.92423	−0.122268
$573$	−32.8833	−1.37372
$574$	−11.2334	−0.468871
$575$	8.52851	0.355663
$576$	4.15909	0.173295
$577$	10.3470	0.430752	0.215376	−	0.976531i	$-0.430902\pi$
$577$	10.3470	0.430752	0.215376	+	0.976531i	$0.430902\pi$
$578$	35.1756	1.46311
$579$	−28.0959	−1.16762
$580$	−1.88697	−0.0783520
$581$	17.1808	0.712778
$582$	−29.9796	−1.24270
$583$	−56.6498	−2.34619
$584$	−8.38290	−0.346887
$585$	−7.13489	−0.294991
$586$	9.63006	0.397814
$587$	−10.1416	−0.418588	−0.209294	−	0.977853i	$-0.567117\pi$
$587$	−10.1416	−0.418588	−0.209294	+	0.977853i	$0.567117\pi$
$588$	2.67565	0.110342
$589$	0	0
$590$	−20.8731	−0.859332
$591$	−33.3447	−1.37162
$592$	7.74177	0.318185
$593$	−14.6177	−0.600277	−0.300139	−	0.953896i	$-0.597033\pi$
$593$	−14.6177	−0.600277	−0.300139	+	0.953896i	$0.597033\pi$
$594$	−14.7385	−0.604729
$595$	20.1382	0.825584
$596$	−10.5117	−0.430576
$597$	28.8766	1.18184
$598$	1.89266	0.0773966
$599$	26.2808	1.07380	0.536902	−	0.843645i	$-0.319595\pi$
$599$	26.2808	1.07380	0.536902	+	0.843645i	$0.319595\pi$
$600$	7.41878	0.302870
$601$	19.0761	0.778132	0.389066	−	0.921210i	$-0.372798\pi$
$601$	19.0761	0.778132	0.389066	+	0.921210i	$0.372798\pi$
$602$	−4.14105	−0.168777
$603$	14.8277	0.603832
$604$	18.6362	0.758294
$605$	−32.2980	−1.31310
$606$	13.9143	0.565229
$607$	11.8663	0.481637	0.240818	−	0.970570i	$-0.422584\pi$
$607$	11.8663	0.481637	0.240818	+	0.970570i	$0.422584\pi$
$608$	0	0
$609$	−1.81095	−0.0733835
$610$	−34.1844	−1.38409
$611$	−2.48445	−0.100510
$612$	30.0422	1.21438
$613$	12.0680	0.487423	0.243712	−	0.969848i	$-0.421635\pi$
$613$	12.0680	0.487423	0.243712	+	0.969848i	$0.421635\pi$
$614$	11.2087	0.452344
$615$	−83.7962	−3.37899
$616$	4.75235	0.191478
$617$	−2.53298	−0.101974	−0.0509869	−	0.998699i	$-0.516237\pi$
$617$	−2.53298	−0.101974	−0.0509869	+	0.998699i	$0.516237\pi$
$618$	15.5985	0.627462
$619$	2.46877	0.0992284	0.0496142	−	0.998768i	$-0.484201\pi$
$619$	2.46877	0.0992284	0.0496142	+	0.998768i	$0.484201\pi$
$620$	−8.18323	−0.328647
$621$	9.53927	0.382798
$622$	−16.1665	−0.648219
$623$	12.0919	0.484451
$624$	1.64639	0.0659082
$625$	−31.1756	−1.24703
$626$	23.8380	0.952759
$627$	0	0
$628$	−15.9868	−0.637942
$629$	55.9208	2.22971
$630$	11.5954	0.461970
$631$	14.1776	0.564403	0.282201	−	0.959355i	$-0.408935\pi$
$631$	14.1776	0.564403	0.282201	+	0.959355i	$0.408935\pi$
$632$	6.66242	0.265017
$633$	−3.70136	−0.147116
$634$	22.6665	0.900201
$635$	−12.8561	−0.510177
$636$	31.8947	1.26471
$637$	0.615323	0.0243800
$638$	−3.21652	−0.127343
$639$	−1.54921	−0.0612858
$640$	−2.78796	−0.110204
$641$	−39.7199	−1.56884	−0.784421	−	0.620228i	$-0.787040\pi$
$641$	−39.7199	−1.56884	−0.784421	+	0.620228i	$0.787040\pi$
$642$	28.3810	1.12011
$643$	0.663060	0.0261485	0.0130743	−	0.999915i	$-0.495838\pi$
$643$	0.663060	0.0261485	0.0130743	+	0.999915i	$0.495838\pi$
$644$	−3.07588	−0.121207
$645$	−30.8906	−1.21631
$646$	0	0
$647$	−15.1612	−0.596049	−0.298024	−	0.954558i	$-0.596328\pi$
$647$	−15.1612	−0.596049	−0.298024	+	0.954558i	$0.596328\pi$
$648$	−4.17925	−0.164176
$649$	−35.5803	−1.39665
$650$	1.70611	0.0669190
$651$	−7.85358	−0.307806
$652$	−2.09713	−0.0821298
$653$	10.1648	0.397779	0.198889	−	0.980022i	$-0.436267\pi$
$653$	10.1648	0.397779	0.198889	+	0.980022i	$0.436267\pi$
$654$	−15.8238	−0.618760
$655$	21.3166	0.832908
$656$	11.2334	0.438589
$657$	−34.8652	−1.36022
$658$	4.03763	0.157403
$659$	−37.1233	−1.44612	−0.723058	−	0.690787i	$-0.757264\pi$
$659$	−37.1233	−1.44612	−0.723058	+	0.690787i	$0.757264\pi$
$660$	35.4506	1.37991
$661$	−24.4293	−0.950188	−0.475094	−	0.879935i	$-0.657586\pi$
$661$	−24.4293	−0.950188	−0.475094	+	0.879935i	$0.657586\pi$
$662$	5.56883	0.216439
$663$	11.8923	0.461858
$664$	−17.1808	−0.666743
$665$	0	0
$666$	32.1987	1.24767
$667$	2.08184	0.0806092
$668$	−6.38945	−0.247215
$669$	35.9290	1.38909
$670$	−9.93946	−0.383995
$671$	−58.2707	−2.24952
$672$	−2.67565	−0.103215
$673$	5.14190	0.198206	0.0991029	−	0.995077i	$-0.468403\pi$
$673$	5.14190	0.198206	0.0991029	+	0.995077i	$0.468403\pi$
$674$	−26.9956	−1.03983
$675$	8.59902	0.330976
$676$	−12.6214	−0.485438
$677$	−14.2553	−0.547874	−0.273937	−	0.961748i	$-0.588326\pi$
$677$	−14.2553	−0.547874	−0.273937	+	0.961748i	$0.588326\pi$
$678$	0.0753414	0.00289347
$679$	11.2046	0.429994
$680$	−20.1382	−0.772263
$681$	55.1307	2.11261
$682$	−13.9491	−0.534140
$683$	−0.582100	−0.0222734	−0.0111367	−	0.999938i	$-0.503545\pi$
$683$	−0.582100	−0.0222734	−0.0111367	+	0.999938i	$0.503545\pi$
$684$	0	0
$685$	51.3644	1.96253
$686$	−1.00000	−0.0381802
$687$	32.1181	1.22538
$688$	4.14105	0.157876
$689$	7.33487	0.279436
$690$	−22.9448	−0.873494
$691$	14.8327	0.564264	0.282132	−	0.959376i	$-0.408958\pi$
$691$	14.8327	0.564264	0.282132	+	0.959376i	$0.408958\pi$
$692$	−23.7146	−0.901493
$693$	19.7654	0.750827
$694$	9.27421	0.352044
$695$	2.56143	0.0971606
$696$	1.81095	0.0686440
$697$	81.1415	3.07345
$698$	30.4033	1.15078
$699$	−12.3996	−0.468997
$700$	−2.77270	−0.104798
$701$	31.7188	1.19800	0.599001	−	0.800749i	$-0.295565\pi$
$701$	31.7188	1.19800	0.599001	+	0.800749i	$0.295565\pi$
$702$	1.90831	0.0720244
$703$	0	0
$704$	−4.75235	−0.179111
$705$	30.1191	1.13435
$706$	7.95467	0.299378
$707$	−5.20034	−0.195579
$708$	20.0322	0.752858
$709$	−2.78091	−0.104439	−0.0522196	−	0.998636i	$-0.516630\pi$
$709$	−2.78091	−0.104439	−0.0522196	+	0.998636i	$0.516630\pi$
$710$	1.03848	0.0389735
$711$	27.7096	1.03919
$712$	−12.0919	−0.453162
$713$	9.02835	0.338114
$714$	−19.3269	−0.723291
$715$	8.15262	0.304891
$716$	13.9786	0.522404
$717$	73.2201	2.73446
$718$	−23.3547	−0.871591
$719$	26.8534	1.00146	0.500731	−	0.865603i	$-0.333064\pi$
$719$	26.8534	1.00146	0.500731	+	0.865603i	$0.333064\pi$
$720$	−11.5954	−0.432134
$721$	−5.82979	−0.217113
$722$	0	0
$723$	−1.73846	−0.0646541
$724$	−9.94297	−0.369528
$725$	1.87664	0.0696968
$726$	30.9969	1.15040
$727$	−25.1657	−0.933344	−0.466672	−	0.884430i	$-0.654547\pi$
$727$	−25.1657	−0.933344	−0.466672	+	0.884430i	$0.654547\pi$
$728$	−0.615323	−0.0228054
$729$	−42.2759	−1.56577
$730$	23.3712	0.865006
$731$	29.9119	1.10633
$732$	32.8073	1.21259
$733$	17.9918	0.664544	0.332272	−	0.943184i	$-0.392185\pi$
$733$	17.9918	0.664544	0.332272	+	0.943184i	$0.392185\pi$
$734$	13.5912	0.501659
$735$	−7.45959	−0.275151
$736$	3.07588	0.113379
$737$	−16.9428	−0.624096
$738$	46.7205	1.71981
$739$	−24.6582	−0.907067	−0.453534	−	0.891239i	$-0.649837\pi$
$739$	−24.6582	−0.907067	−0.453534	+	0.891239i	$0.649837\pi$
$740$	−21.5837	−0.793433
$741$	0	0
$742$	−11.9204	−0.437610
$743$	41.9224	1.53799	0.768993	−	0.639258i	$-0.220758\pi$
$743$	41.9224	1.53799	0.768993	+	0.639258i	$0.220758\pi$
$744$	7.85358	0.287926
$745$	29.3061	1.07369
$746$	−9.89636	−0.362331
$747$	−71.4563	−2.61445
$748$	−34.3275	−1.25514
$749$	−10.6072	−0.387577
$750$	16.6147	0.606684
$751$	−16.0539	−0.585814	−0.292907	−	0.956141i	$-0.594623\pi$
$751$	−16.0539	−0.585814	−0.292907	+	0.956141i	$0.594623\pi$
$752$	−4.03763	−0.147237
$753$	16.1373	0.588077
$754$	0.416467	0.0151668
$755$	−51.9568	−1.89090
$756$	−3.10131	−0.112794
$757$	−0.213215	−0.00774945	−0.00387472	−	0.999992i	$-0.501233\pi$
$757$	−0.213215	−0.00774945	−0.00387472	+	0.999992i	$0.501233\pi$
$758$	−18.7384	−0.680610
$759$	−39.1117	−1.41967
$760$	0	0
$761$	18.6668	0.676669	0.338335	−	0.941026i	$-0.390136\pi$
$761$	18.6668	0.676669	0.338335	+	0.941026i	$0.390136\pi$
$762$	12.3382	0.446965
$763$	5.91402	0.214102
$764$	−12.2899	−0.444632
$765$	−83.7564	−3.02822
$766$	−8.23732	−0.297626
$767$	4.60684	0.166344
$768$	2.67565	0.0965491
$769$	−17.2811	−0.623174	−0.311587	−	0.950218i	$-0.600861\pi$
$769$	−17.2811	−0.623174	−0.311587	+	0.950218i	$0.600861\pi$
$770$	−13.2494	−0.477473
$771$	31.8169	1.14586
$772$	−10.5006	−0.377924
$773$	−18.5891	−0.668602	−0.334301	−	0.942466i	$-0.608500\pi$
$773$	−18.5891	−0.668602	−0.334301	+	0.942466i	$0.608500\pi$
$774$	17.2230	0.619068
$775$	8.13846	0.292342
$776$	−11.2046	−0.402223
$777$	−20.7142	−0.743119
$778$	−35.1493	−1.26016
$779$	0	0
$780$	−4.59005	−0.164350
$781$	1.77019	0.0633425
$782$	22.2179	0.794511
$783$	2.09905	0.0750140
$784$	1.00000	0.0357143
$785$	44.5705	1.59079
$786$	−20.4579	−0.729708
$787$	35.1915	1.25444	0.627221	−	0.778841i	$-0.284192\pi$
$787$	35.1915	1.25444	0.627221	+	0.778841i	$0.284192\pi$
$788$	−12.4623	−0.443951
$789$	−9.19228	−0.327254
$790$	−18.5745	−0.660852
$791$	−0.0281582	−0.00100119
$792$	−19.7654	−0.702335
$793$	7.54475	0.267922
$794$	12.2995	0.436493
$795$	−88.9210	−3.15370
$796$	10.7924	0.382525
$797$	−28.7272	−1.01757	−0.508785	−	0.860894i	$-0.669905\pi$
$797$	−28.7272	−1.01757	−0.508785	+	0.860894i	$0.669905\pi$
$798$	0	0
$799$	−29.1649	−1.03178
$800$	2.77270	0.0980299
$801$	−50.2912	−1.77695
$802$	−11.0861	−0.391464
$803$	39.8385	1.40587
$804$	9.53906	0.336417
$805$	8.57543	0.302244
$806$	1.80610	0.0636171
$807$	60.8768	2.14296
$808$	5.20034	0.182947
$809$	−23.0924	−0.811886	−0.405943	−	0.913898i	$-0.633057\pi$
$809$	−23.0924	−0.811886	−0.405943	+	0.913898i	$0.633057\pi$
$810$	11.6516	0.409394
$811$	−38.2097	−1.34172	−0.670862	−	0.741583i	$-0.734076\pi$
$811$	−38.2097	−1.34172	−0.670862	+	0.741583i	$0.734076\pi$
$812$	−0.676828	−0.0237520
$813$	75.4443	2.64595
$814$	−36.7916	−1.28954
$815$	5.84670	0.204801
$816$	19.3269	0.676577
$817$	0	0
$818$	−27.5519	−0.963330
$819$	−2.55918	−0.0894250
$820$	−31.3181	−1.09368
$821$	15.1488	0.528697	0.264348	−	0.964427i	$-0.414843\pi$
$821$	15.1488	0.528697	0.264348	+	0.964427i	$0.414843\pi$
$822$	−49.2952	−1.71937
$823$	11.9946	0.418105	0.209052	−	0.977904i	$-0.432962\pi$
$823$	11.9946	0.418105	0.209052	+	0.977904i	$0.432962\pi$
$824$	5.82979	0.203090
$825$	−35.2566	−1.22748
$826$	−7.48688	−0.260502
$827$	22.1125	0.768927	0.384463	−	0.923140i	$-0.374386\pi$
$827$	22.1125	0.768927	0.384463	+	0.923140i	$0.374386\pi$
$828$	12.7929	0.444583
$829$	12.2835	0.426623	0.213312	−	0.976984i	$-0.431575\pi$
$829$	12.2835	0.426623	0.213312	+	0.976984i	$0.431575\pi$
$830$	47.8992	1.66261
$831$	−37.4936	−1.30064
$832$	0.615323	0.0213325
$833$	7.22327	0.250271
$834$	−2.45825	−0.0851221
$835$	17.8135	0.616462
$836$	0	0
$837$	9.10299	0.314645
$838$	31.8705	1.10095
$839$	−46.4488	−1.60359	−0.801796	−	0.597598i	$-0.796122\pi$
$839$	−46.4488	−1.60359	−0.801796	+	0.597598i	$0.796122\pi$
$840$	7.45959	0.257380
$841$	−28.5419	−0.984204
$842$	6.03813	0.208088
$843$	−73.4602	−2.53010
$844$	−1.38335	−0.0476169
$845$	35.1879	1.21050
$846$	−16.7929	−0.577351
$847$	−11.5848	−0.398060
$848$	11.9204	0.409347
$849$	10.4163	0.357486
$850$	20.0280	0.686954
$851$	23.8128	0.816291
$852$	−0.996647	−0.0341446
$853$	−15.0868	−0.516564	−0.258282	−	0.966070i	$-0.583156\pi$
$853$	−15.0868	−0.516564	−0.258282	+	0.966070i	$0.583156\pi$
$854$	−12.2615	−0.419578
$855$	0	0
$856$	10.6072	0.362545
$857$	−25.8864	−0.884264	−0.442132	−	0.896950i	$-0.645778\pi$
$857$	−25.8864	−0.884264	−0.442132	+	0.896950i	$0.645778\pi$
$858$	−7.82421	−0.267114
$859$	28.5497	0.974104	0.487052	−	0.873373i	$-0.338072\pi$
$859$	28.5497	0.974104	0.487052	+	0.873373i	$0.338072\pi$
$860$	−11.5451	−0.393684
$861$	−30.0565	−1.02432
$862$	−18.3947	−0.626524
$863$	−5.86478	−0.199639	−0.0998197	−	0.995006i	$-0.531827\pi$
$863$	−5.86478	−0.199639	−0.0998197	+	0.995006i	$0.531827\pi$
$864$	3.10131	0.105509
$865$	66.1152	2.24799
$866$	15.0672	0.512005
$867$	94.1174	3.19640
$868$	−2.93521	−0.0996274
$869$	−31.6621	−1.07406
$870$	−5.04886	−0.171172
$871$	2.19371	0.0743311
$872$	−5.91402	−0.200274
$873$	−46.6010	−1.57721
$874$	0	0
$875$	−6.20961	−0.209923
$876$	−22.4297	−0.757829
$877$	34.3941	1.16141	0.580703	−	0.814116i	$-0.302778\pi$
$877$	34.3941	1.16141	0.580703	+	0.814116i	$0.302778\pi$
$878$	14.4522	0.487738
$879$	25.7667	0.869088
$880$	13.2494	0.446636
$881$	57.0050	1.92055	0.960273	−	0.279063i	$-0.0900238\pi$
$881$	57.0050	1.92055	0.960273	+	0.279063i	$0.0900238\pi$
$882$	4.15909	0.140044
$883$	−4.04401	−0.136092	−0.0680459	−	0.997682i	$-0.521676\pi$
$883$	−4.04401	−0.136092	−0.0680459	+	0.997682i	$0.521676\pi$
$884$	4.44464	0.149489
$885$	−55.8490	−1.87734
$886$	17.8600	0.600019
$887$	−35.8147	−1.20254	−0.601270	−	0.799046i	$-0.705338\pi$
$887$	−35.8147	−1.20254	−0.601270	+	0.799046i	$0.705338\pi$
$888$	20.7142	0.695124
$889$	−4.61129	−0.154658
$890$	33.7116	1.13002
$891$	19.8613	0.665377
$892$	13.4281	0.449608
$893$	0	0
$894$	−28.1256	−0.940660
$895$	−38.9717	−1.30268
$896$	−1.00000	−0.0334077
$897$	5.06409	0.169085
$898$	−29.8637	−0.996563
$899$	1.98663	0.0662578
$900$	11.5319	0.384397
$901$	86.1040	2.86854
$902$	−53.3848	−1.77752
$903$	−11.0800	−0.368719
$904$	0.0281582	0.000936528 0
$905$	27.7206	0.921463
$906$	49.8638	1.65661
$907$	18.2070	0.604554	0.302277	−	0.953220i	$-0.402253\pi$
$907$	18.2070	0.604554	0.302277	+	0.953220i	$0.402253\pi$
$908$	20.6046	0.683789
$909$	21.6287	0.717378
$910$	1.71549	0.0568680
$911$	25.5938	0.847960	0.423980	−	0.905672i	$-0.360633\pi$
$911$	25.5938	0.847960	0.423980	+	0.905672i	$0.360633\pi$
$912$	0	0
$913$	81.6490	2.70219
$914$	−11.7730	−0.389418
$915$	−91.4654	−3.02375
$916$	12.0038	0.396618
$917$	7.64595	0.252492
$918$	22.4016	0.739363
$919$	17.2492	0.568998	0.284499	−	0.958676i	$-0.408173\pi$
$919$	17.2492	0.568998	0.284499	+	0.958676i	$0.408173\pi$
$920$	−8.57543	−0.282723
$921$	29.9904	0.988217
$922$	−32.4227	−1.06779
$923$	−0.229200	−0.00754422
$924$	12.7156	0.418313
$925$	21.4656	0.705785
$926$	7.40154	0.243230
$927$	24.2466	0.796363
$928$	0.676828	0.0222180
$929$	−7.96975	−0.261479	−0.130739	−	0.991417i	$-0.541735\pi$
$929$	−7.96975	−0.261479	−0.130739	+	0.991417i	$0.541735\pi$
$930$	−21.8954	−0.717980
$931$	0	0
$932$	−4.63426	−0.151800
$933$	−43.2559	−1.41614
$934$	8.17380	0.267455
$935$	95.7036	3.12984
$936$	2.55918	0.0836494
$937$	54.3500	1.77554	0.887769	−	0.460290i	$-0.152255\pi$
$937$	54.3500	1.77554	0.887769	+	0.460290i	$0.152255\pi$
$938$	−3.56514	−0.116406
$939$	63.7822	2.08145
$940$	11.2567	0.367155
$941$	−22.6296	−0.737704	−0.368852	−	0.929488i	$-0.620249\pi$
$941$	−22.6296	−0.737704	−0.368852	+	0.929488i	$0.620249\pi$
$942$	−42.7750	−1.39368
$943$	34.5525	1.12518
$944$	7.48688	0.243677
$945$	8.64632	0.281265
$946$	−19.6797	−0.639844
$947$	−40.1770	−1.30558	−0.652789	−	0.757540i	$-0.726401\pi$
$947$	−40.1770	−1.30558	−0.652789	+	0.757540i	$0.726401\pi$
$948$	17.8263	0.578970
$949$	−5.15819	−0.167442
$950$	0	0
$951$	60.6475	1.96663
$952$	−7.22327	−0.234107
$953$	−20.3315	−0.658603	−0.329302	−	0.944225i	$-0.606813\pi$
$953$	−20.3315	−0.658603	−0.329302	+	0.944225i	$0.606813\pi$
$954$	49.5779	1.60514
$955$	34.2636	1.10874
$956$	27.3654	0.885060
$957$	−8.60628	−0.278202
$958$	−15.2272	−0.491969
$959$	18.4237	0.594931
$960$	−7.45959	−0.240757
$961$	−22.3846	−0.722082
$962$	4.76368	0.153587
$963$	44.1161	1.42162
$964$	−0.649735	−0.0209266
$965$	29.2752	0.942401
$966$	−8.22997	−0.264795
$967$	−46.6150	−1.49904	−0.749519	−	0.661982i	$-0.769715\pi$
$967$	−46.6150	−1.49904	−0.749519	+	0.661982i	$0.769715\pi$
$968$	11.5848	0.372351
$969$	0	0
$970$	31.2380	1.00299
$971$	14.2804	0.458279	0.229140	−	0.973394i	$-0.426409\pi$
$971$	14.2804	0.458279	0.229140	+	0.973394i	$0.426409\pi$
$972$	−20.4861	−0.657093
$973$	0.918748	0.0294537
$974$	−1.78125	−0.0570750
$975$	4.56494	0.146195
$976$	12.2615	0.392480
$977$	−30.5842	−0.978477	−0.489238	−	0.872150i	$-0.662725\pi$
$977$	−30.5842	−0.978477	−0.489238	+	0.872150i	$0.662725\pi$
$978$	−5.61117	−0.179426
$979$	57.4648	1.83658
$980$	−2.78796	−0.0890580
$981$	−24.5969	−0.785319
$982$	−34.0418	−1.08632
$983$	26.3155	0.839333	0.419666	−	0.907678i	$-0.362147\pi$
$983$	26.3155	0.839333	0.419666	+	0.907678i	$0.362147\pi$
$984$	30.0565	0.958166
$985$	34.7443	1.10705
$986$	4.88891	0.155694
$987$	10.8033	0.343872
$988$	0	0
$989$	12.7374	0.405026
$990$	55.1052	1.75136
$991$	−50.0639	−1.59033	−0.795166	−	0.606392i	$-0.792616\pi$
$991$	−50.0639	−1.59033	−0.795166	+	0.606392i	$0.792616\pi$
$992$	2.93521	0.0931929
$993$	14.9002	0.472844
$994$	0.372488	0.0118146
$995$	−30.0887	−0.953875
$996$	−45.9696	−1.45660
$997$	−3.93121	−0.124503	−0.0622513	−	0.998061i	$-0.519828\pi$
$997$	−3.93121	−0.124503	−0.0622513	+	0.998061i	$0.519828\pi$
$998$	20.0504	0.634685
$999$	24.0096	0.759631

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5054.2.a.bk.1.8		9
19.9	even	9		266.2.u.c.43.3	✓	18
19.17	even	9		266.2.u.c.99.3	yes	18
19.18	odd	2		5054.2.a.bj.1.2		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
266.2.u.c.43.3	✓	18	19.9	even	9
266.2.u.c.99.3	yes	18	19.17	even	9
5054.2.a.bj.1.2		9	19.18	odd	2
5054.2.a.bk.1.8		9	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.67565 q^{3} +1.00000 q^{4} -2.78796 q^{5} +2.67565 q^{6} -1.00000 q^{7} +1.00000 q^{8} +4.15909 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.67565 q^{3} +1.00000 q^{4} -2.78796 q^{5} +2.67565 q^{6} -1.00000 q^{7} +1.00000 q^{8} +4.15909 q^{9} -2.78796 q^{10} -4.75235 q^{11} +2.67565 q^{12} +0.615323 q^{13} -1.00000 q^{14} -7.45959 q^{15} +1.00000 q^{16} +7.22327 q^{17} +4.15909 q^{18} -2.78796 q^{20} -2.67565 q^{21} -4.75235 q^{22} +3.07588 q^{23} +2.67565 q^{24} +2.77270 q^{25} +0.615323 q^{26} +3.10131 q^{27} -1.00000 q^{28} +0.676828 q^{29} -7.45959 q^{30} +2.93521 q^{31} +1.00000 q^{32} -12.7156 q^{33} +7.22327 q^{34} +2.78796 q^{35} +4.15909 q^{36} +7.74177 q^{37} +1.64639 q^{39} -2.78796 q^{40} +11.2334 q^{41} -2.67565 q^{42} +4.14105 q^{43} -4.75235 q^{44} -11.5954 q^{45} +3.07588 q^{46} -4.03763 q^{47} +2.67565 q^{48} +1.00000 q^{49} +2.77270 q^{50} +19.3269 q^{51} +0.615323 q^{52} +11.9204 q^{53} +3.10131 q^{54} +13.2494 q^{55} -1.00000 q^{56} +0.676828 q^{58} +7.48688 q^{59} -7.45959 q^{60} +12.2615 q^{61} +2.93521 q^{62} -4.15909 q^{63} +1.00000 q^{64} -1.71549 q^{65} -12.7156 q^{66} +3.56514 q^{67} +7.22327 q^{68} +8.22997 q^{69} +2.78796 q^{70} -0.372488 q^{71} +4.15909 q^{72} -8.38290 q^{73} +7.74177 q^{74} +7.41878 q^{75} +4.75235 q^{77} +1.64639 q^{78} +6.66242 q^{79} -2.78796 q^{80} -4.17925 q^{81} +11.2334 q^{82} -17.1808 q^{83} -2.67565 q^{84} -20.1382 q^{85} +4.14105 q^{86} +1.81095 q^{87} -4.75235 q^{88} -12.0919 q^{89} -11.5954 q^{90} -0.615323 q^{91} +3.07588 q^{92} +7.85358 q^{93} -4.03763 q^{94} +2.67565 q^{96} -11.2046 q^{97} +1.00000 q^{98} -19.7654 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} + 3 q^{3} + 9 q^{4} + 3 q^{5} + 3 q^{6} - 9 q^{7} + 9 q^{8} + 12 q^{9}+O(q^{10}) \) 9 * q + 9 * q^2 + 3 * q^3 + 9 * q^4 + 3 * q^5 + 3 * q^6 - 9 * q^7 + 9 * q^8 + 12 * q^9	\( 9 q + 9 q^{2} + 3 q^{3} + 9 q^{4} + 3 q^{5} + 3 q^{6} - 9 q^{7} + 9 q^{8} + 12 q^{9} + 3 q^{10} - 3 q^{11} + 3 q^{12} + 12 q^{13} - 9 q^{14} - 6 q^{15} + 9 q^{16} + 12 q^{17} + 12 q^{18} + 3 q^{20} - 3 q^{21} - 3 q^{22} + 6 q^{23} + 3 q^{24} + 12 q^{26} + 24 q^{27} - 9 q^{28} - 6 q^{29} - 6 q^{30} + 9 q^{31} + 9 q^{32} - 3 q^{33} + 12 q^{34} - 3 q^{35} + 12 q^{36} + 9 q^{37} + 33 q^{39} + 3 q^{40} + 3 q^{41} - 3 q^{42} + 21 q^{43} - 3 q^{44} + 18 q^{45} + 6 q^{46} + 21 q^{47} + 3 q^{48} + 9 q^{49} + 39 q^{51} + 12 q^{52} + 24 q^{54} + 24 q^{55} - 9 q^{56} - 6 q^{58} - 9 q^{59} - 6 q^{60} + 6 q^{61} + 9 q^{62} - 12 q^{63} + 9 q^{64} - 3 q^{65} - 3 q^{66} + 27 q^{67} + 12 q^{68} + 6 q^{69} - 3 q^{70} + 9 q^{71} + 12 q^{72} + 51 q^{73} + 9 q^{74} - 3 q^{75} + 3 q^{77} + 33 q^{78} + 24 q^{79} + 3 q^{80} - 3 q^{81} + 3 q^{82} + 9 q^{83} - 3 q^{84} + 6 q^{85} + 21 q^{86} - 3 q^{87} - 3 q^{88} + 9 q^{89} + 18 q^{90} - 12 q^{91} + 6 q^{92} + 3 q^{93} + 21 q^{94} + 3 q^{96} - 12 q^{97} + 9 q^{98} - 15 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 + 3 * q^3 + 9 * q^4 + 3 * q^5 + 3 * q^6 - 9 * q^7 + 9 * q^8 + 12 * q^9 + 3 * q^10 - 3 * q^11 + 3 * q^12 + 12 * q^13 - 9 * q^14 - 6 * q^15 + 9 * q^16 + 12 * q^17 + 12 * q^18 + 3 * q^20 - 3 * q^21 - 3 * q^22 + 6 * q^23 + 3 * q^24 + 12 * q^26 + 24 * q^27 - 9 * q^28 - 6 * q^29 - 6 * q^30 + 9 * q^31 + 9 * q^32 - 3 * q^33 + 12 * q^34 - 3 * q^35 + 12 * q^36 + 9 * q^37 + 33 * q^39 + 3 * q^40 + 3 * q^41 - 3 * q^42 + 21 * q^43 - 3 * q^44 + 18 * q^45 + 6 * q^46 + 21 * q^47 + 3 * q^48 + 9 * q^49 + 39 * q^51 + 12 * q^52 + 24 * q^54 + 24 * q^55 - 9 * q^56 - 6 * q^58 - 9 * q^59 - 6 * q^60 + 6 * q^61 + 9 * q^62 - 12 * q^63 + 9 * q^64 - 3 * q^65 - 3 * q^66 + 27 * q^67 + 12 * q^68 + 6 * q^69 - 3 * q^70 + 9 * q^71 + 12 * q^72 + 51 * q^73 + 9 * q^74 - 3 * q^75 + 3 * q^77 + 33 * q^78 + 24 * q^79 + 3 * q^80 - 3 * q^81 + 3 * q^82 + 9 * q^83 - 3 * q^84 + 6 * q^85 + 21 * q^86 - 3 * q^87 - 3 * q^88 + 9 * q^89 + 18 * q^90 - 12 * q^91 + 6 * q^92 + 3 * q^93 + 21 * q^94 + 3 * q^96 - 12 * q^97 + 9 * q^98 - 15 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more