LMFDB - Embedded newform 7581.2.a.l.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [7581,2,Mod(1,7581)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("7581.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7581, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 7581 = 3 \cdot 7 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7581.a (trivial)

Newform invariants

comment:select newform

sage:traces = [3,-1,-3,9,0,1,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	yes
Analytic conductor:	$60.5345897723$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.404.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 5x - 1 $ x^3 - x^2 - 5*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 399)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.210756$ of defining polynomial
Character	$\chi$	$=$	7581.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.74483 q^{2} -1.00000 q^{3} +5.53407 q^{4} -2.53407 q^{5} -2.74483 q^{6} -1.00000 q^{7} +9.70041 q^{8} +1.00000 q^{9} -6.95558 q^{10} +2.42151 q^{11} -5.53407 q^{12} +0.421512 q^{13} -2.74483 q^{14} +2.53407 q^{15} +15.5578 q^{16} +6.53407 q^{17} +2.74483 q^{18} -14.0237 q^{20} +1.00000 q^{21} +6.64663 q^{22} -1.57849 q^{23} -9.70041 q^{24} +1.42151 q^{25} +1.15698 q^{26} -1.00000 q^{27} -5.53407 q^{28} -6.02372 q^{29} +6.95558 q^{30} -3.48965 q^{31} +23.3026 q^{32} -2.42151 q^{33} +17.9349 q^{34} +2.53407 q^{35} +5.53407 q^{36} +2.84302 q^{37} -0.421512 q^{39} -24.5815 q^{40} -8.42151 q^{41} +2.74483 q^{42} +11.4897 q^{43} +13.4008 q^{44} -2.53407 q^{45} -4.33268 q^{46} +8.02372 q^{47} -15.5578 q^{48} +1.00000 q^{49} +3.90180 q^{50} -6.53407 q^{51} +2.33268 q^{52} +10.8667 q^{53} -2.74483 q^{54} -6.13628 q^{55} -9.70041 q^{56} -16.5341 q^{58} -14.1363 q^{59} +14.0237 q^{60} +6.84302 q^{61} -9.57849 q^{62} -1.00000 q^{63} +32.8461 q^{64} -1.06814 q^{65} -6.64663 q^{66} +9.91116 q^{67} +36.1600 q^{68} +1.57849 q^{69} +6.95558 q^{70} +13.3771 q^{71} +9.70041 q^{72} +7.06814 q^{73} +7.80361 q^{74} -1.42151 q^{75} -2.42151 q^{77} -1.15698 q^{78} -14.1363 q^{79} -39.4245 q^{80} +1.00000 q^{81} -23.1156 q^{82} +2.11256 q^{83} +5.53407 q^{84} -16.5578 q^{85} +31.5371 q^{86} +6.02372 q^{87} +23.4897 q^{88} +9.71477 q^{89} -6.95558 q^{90} -0.421512 q^{91} -8.73546 q^{92} +3.48965 q^{93} +22.0237 q^{94} -23.3026 q^{96} +4.97930 q^{97} +2.74483 q^{98} +2.42151 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - q^{2} - 3 q^{3} + 9 q^{4} + q^{6} - 3 q^{7} + 9 q^{8} + 3 q^{9} - 10 q^{10} + 4 q^{11} - 9 q^{12} - 2 q^{13} + q^{14} + 13 q^{16} + 12 q^{17} - q^{18} - 16 q^{20} + 3 q^{21} + 8 q^{22} - 8 q^{23}+ \cdots + 4 q^{99}+O(q^{100}) $ 3 * q - q^2 - 3 * q^3 + 9 * q^4 + q^6 - 3 * q^7 + 9 * q^8 + 3 * q^9 - 10 * q^10 + 4 * q^11 - 9 * q^12 - 2 * q^13 + q^14 + 13 * q^16 + 12 * q^17 - q^18 - 16 * q^20 + 3 * q^21 + 8 * q^22 - 8 * q^23 - 9 * q^24 + q^25 + 10 * q^26 - 3 * q^27 - 9 * q^28 + 8 * q^29 + 10 * q^30 + 8 * q^31 + 27 * q^32 - 4 * q^33 + 6 * q^34 + 9 * q^36 + 2 * q^37 + 2 * q^39 - 14 * q^40 - 22 * q^41 - q^42 + 16 * q^43 + 12 * q^46 - 2 * q^47 - 13 * q^48 + 3 * q^49 + 9 * q^50 - 12 * q^51 - 18 * q^52 + q^54 + 12 * q^55 - 9 * q^56 - 42 * q^58 - 12 * q^59 + 16 * q^60 + 14 * q^61 - 32 * q^62 - 3 * q^63 + 29 * q^64 + 12 * q^65 - 8 * q^66 + 8 * q^67 + 52 * q^68 + 8 * q^69 + 10 * q^70 + 26 * q^71 + 9 * q^72 + 6 * q^73 + 18 * q^74 - q^75 - 4 * q^77 - 10 * q^78 - 12 * q^79 - 52 * q^80 + 3 * q^81 - 2 * q^82 + 2 * q^83 + 9 * q^84 - 16 * q^85 + 24 * q^86 - 8 * q^87 + 52 * q^88 + 2 * q^89 - 10 * q^90 + 2 * q^91 - 36 * q^92 - 8 * q^93 + 40 * q^94 - 27 * q^96 - 22 * q^97 - q^98 + 4 * q^99

Coefficient data

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

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

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

$2$	2.74483	1.94089	0.970443	−	0.241332i	$-0.0775843\pi$
$2$	2.74483	1.94089	0.970443	+	0.241332i	$0.0775843\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.53407	2.76704
$5$	−2.53407	−1.13327	−0.566635	−	0.823969i	$-0.691755\pi$
$5$	−2.53407	−1.13327	−0.566635	+	0.823969i	$0.691755\pi$
$6$	−2.74483	−1.12057
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	9.70041	3.42961
$9$	1.00000	0.333333
$10$	−6.95558	−2.19955
$11$	2.42151	0.730113	0.365057	−	0.930985i	$-0.381050\pi$
$11$	2.42151	0.730113	0.365057	+	0.930985i	$0.381050\pi$
$12$	−5.53407	−1.59755
$13$	0.421512	0.116906	0.0584532	−	0.998290i	$-0.481383\pi$
$13$	0.421512	0.116906	0.0584532	+	0.998290i	$0.481383\pi$
$14$	−2.74483	−0.733586
$15$	2.53407	0.654294
$16$	15.5578	3.88945
$17$	6.53407	1.58474	0.792372	−	0.610038i	$-0.208846\pi$
$17$	6.53407	1.58474	0.792372	+	0.610038i	$0.208846\pi$
$18$	2.74483	0.646962
$19$	0	0
$19$	0	0
$20$	−14.0237	−3.13580
$21$	1.00000	0.218218
$22$	6.64663	1.41707
$23$	−1.57849	−0.329138	−0.164569	−	0.986366i	$-0.552623\pi$
$23$	−1.57849	−0.329138	−0.164569	+	0.986366i	$0.552623\pi$
$24$	−9.70041	−1.98009
$25$	1.42151	0.284302
$26$	1.15698	0.226902
$27$	−1.00000	−0.192450
$28$	−5.53407	−1.04584
$29$	−6.02372	−1.11858	−0.559289	−	0.828973i	$-0.688926\pi$
$29$	−6.02372	−1.11858	−0.559289	+	0.828973i	$0.688926\pi$
$30$	6.95558	1.26991
$31$	−3.48965	−0.626760	−0.313380	−	0.949628i	$-0.601461\pi$
$31$	−3.48965	−0.626760	−0.313380	+	0.949628i	$0.601461\pi$
$32$	23.3026	4.11936
$33$	−2.42151	−0.421531
$34$	17.9349	3.07581
$35$	2.53407	0.428336
$36$	5.53407	0.922345
$37$	2.84302	0.467390	0.233695	−	0.972310i	$-0.424918\pi$
$37$	2.84302	0.467390	0.233695	+	0.972310i	$0.424918\pi$
$38$	0	0
$39$	−0.421512	−0.0674959
$40$	−24.5815	−3.88668
$41$	−8.42151	−1.31522	−0.657610	−	0.753359i	$-0.728432\pi$
$41$	−8.42151	−1.31522	−0.657610	+	0.753359i	$0.728432\pi$
$42$	2.74483	0.423536
$43$	11.4897	1.75216	0.876078	−	0.482170i	$-0.160151\pi$
$43$	11.4897	1.75216	0.876078	+	0.482170i	$0.160151\pi$
$44$	13.4008	2.02025
$45$	−2.53407	−0.377757
$46$	−4.33268	−0.638818
$47$	8.02372	1.17038	0.585190	−	0.810896i	$-0.301020\pi$
$47$	8.02372	1.17038	0.585190	+	0.810896i	$0.301020\pi$
$48$	−15.5578	−2.24557
$49$	1.00000	0.142857
$50$	3.90180	0.551798
$51$	−6.53407	−0.914953
$52$	2.33268	0.323484
$53$	10.8667	1.49266	0.746331	−	0.665575i	$-0.231814\pi$
$53$	10.8667	1.49266	0.746331	+	0.665575i	$0.231814\pi$
$54$	−2.74483	−0.373524
$55$	−6.13628	−0.827416
$56$	−9.70041	−1.29627
$57$	0	0
$58$	−16.5341	−2.17103
$59$	−14.1363	−1.84039	−0.920194	−	0.391464i	$-0.871969\pi$
$59$	−14.1363	−1.84039	−0.920194	+	0.391464i	$0.871969\pi$
$60$	14.0237	1.81045
$61$	6.84302	0.876159	0.438080	−	0.898936i	$-0.355659\pi$
$61$	6.84302	0.876159	0.438080	+	0.898936i	$0.355659\pi$
$62$	−9.57849	−1.21647
$63$	−1.00000	−0.125988
$64$	32.8461	4.10576
$65$	−1.06814	−0.132487
$66$	−6.64663	−0.818143
$67$	9.91116	1.21084	0.605421	−	0.795906i	$-0.293005\pi$
$67$	9.91116	1.21084	0.605421	+	0.795906i	$0.293005\pi$
$68$	36.1600	4.38504
$69$	1.57849	0.190028
$70$	6.95558	0.831351
$71$	13.3771	1.58757	0.793784	−	0.608199i	$-0.208108\pi$
$71$	13.3771	1.58757	0.793784	+	0.608199i	$0.208108\pi$
$72$	9.70041	1.14320
$73$	7.06814	0.827263	0.413632	−	0.910444i	$-0.364260\pi$
$73$	7.06814	0.827263	0.413632	+	0.910444i	$0.364260\pi$
$74$	7.80361	0.907151
$75$	−1.42151	−0.164142
$76$	0	0
$77$	−2.42151	−0.275957
$78$	−1.15698	−0.131002
$79$	−14.1363	−1.59046	−0.795228	−	0.606311i	$-0.792649\pi$
$79$	−14.1363	−1.59046	−0.795228	+	0.606311i	$0.792649\pi$
$80$	−39.4245	−4.40780
$81$	1.00000	0.111111
$82$	−23.1156	−2.55269
$83$	2.11256	0.231883	0.115942	−	0.993256i	$-0.463011\pi$
$83$	2.11256	0.231883	0.115942	+	0.993256i	$0.463011\pi$
$84$	5.53407	0.603817
$85$	−16.5578	−1.79594
$86$	31.5371	3.40073
$87$	6.02372	0.645811
$88$	23.4897	2.50401
$89$	9.71477	1.02976	0.514882	−	0.857261i	$-0.327836\pi$
$89$	9.71477	1.02976	0.514882	+	0.857261i	$0.327836\pi$
$90$	−6.95558	−0.733183
$91$	−0.421512	−0.0441864
$92$	−8.73546	−0.910735
$93$	3.48965	0.361860
$94$	22.0237	2.27157
$95$	0	0
$96$	−23.3026	−2.37831
$97$	4.97930	0.505572	0.252786	−	0.967522i	$-0.418653\pi$
$97$	4.97930	0.505572	0.252786	+	0.967522i	$0.418653\pi$
$98$	2.74483	0.277269
$99$	2.42151	0.243371
$100$	7.86675	0.786675
$101$	−1.69105	−0.168265	−0.0841327	−	0.996455i	$-0.526812\pi$
$101$	−1.69105	−0.168265	−0.0841327	+	0.996455i	$0.526812\pi$
$102$	−17.9349	−1.77582
$103$	−3.15698	−0.311066	−0.155533	−	0.987831i	$-0.549710\pi$
$103$	−3.15698	−0.311066	−0.155533	+	0.987831i	$0.549710\pi$
$104$	4.08884	0.400943
$105$	−2.53407	−0.247300
$106$	29.8273	2.89709
$107$	16.5341	1.59841	0.799204	−	0.601059i	$-0.205254\pi$
$107$	16.5341	1.59841	0.799204	+	0.601059i	$0.205254\pi$
$108$	−5.53407	−0.532516
$109$	−1.77488	−0.170003	−0.0850015	−	0.996381i	$-0.527090\pi$
$109$	−1.77488	−0.170003	−0.0850015	+	0.996381i	$0.527090\pi$
$110$	−16.8430	−1.60592
$111$	−2.84302	−0.269848
$112$	−15.5578	−1.47007
$113$	−10.0237	−0.942952	−0.471476	−	0.881879i	$-0.656279\pi$
$113$	−10.0237	−0.942952	−0.471476	+	0.881879i	$0.656279\pi$
$114$	0	0
$115$	4.00000	0.373002
$116$	−33.3357	−3.09514
$117$	0.421512	0.0389688
$118$	−38.8016	−3.57198
$119$	−6.53407	−0.598977
$120$	24.5815	2.24398
$121$	−5.13628	−0.466935
$122$	18.7829	1.70052
$123$	8.42151	0.759342
$124$	−19.3120	−1.73427
$125$	9.06814	0.811079
$126$	−2.74483	−0.244529
$127$	−2.08884	−0.185354	−0.0926771	−	0.995696i	$-0.529542\pi$
$127$	−2.08884	−0.185354	−0.0926771	+	0.995696i	$0.529542\pi$
$128$	43.5515	3.84944
$129$	−11.4897	−1.01161
$130$	−2.93186	−0.257141
$131$	−13.9349	−1.21750	−0.608748	−	0.793363i	$-0.708328\pi$
$131$	−13.9349	−1.21750	−0.608748	+	0.793363i	$0.708328\pi$
$132$	−13.4008	−1.16639
$133$	0	0
$134$	27.2044	2.35010
$135$	2.53407	0.218098
$136$	63.3831	5.43506
$137$	16.9793	1.45064	0.725320	−	0.688412i	$-0.241692\pi$
$137$	16.9793	1.45064	0.725320	+	0.688412i	$0.241692\pi$
$138$	4.33268	0.368822
$139$	−1.06814	−0.0905985	−0.0452992	−	0.998973i	$-0.514424\pi$
$139$	−1.06814	−0.0905985	−0.0452992	+	0.998973i	$0.514424\pi$
$140$	14.0237	1.18522
$141$	−8.02372	−0.675719
$142$	36.7178	3.08129
$143$	1.02070	0.0853549
$144$	15.5578	1.29648
$145$	15.2645	1.26765
$146$	19.4008	1.60562
$147$	−1.00000	−0.0824786
$148$	15.7335	1.29329
$149$	14.0474	1.15081	0.575406	−	0.817868i	$-0.304844\pi$
$149$	14.0474	1.15081	0.575406	+	0.817868i	$0.304844\pi$
$150$	−3.90180	−0.318581
$151$	14.7542	1.20068	0.600339	−	0.799745i	$-0.295032\pi$
$151$	14.7542	1.20068	0.600339	+	0.799745i	$0.295032\pi$
$152$	0	0
$153$	6.53407	0.528248
$154$	−6.64663	−0.535601
$155$	8.84302	0.710289
$156$	−2.33268	−0.186764
$157$	−16.1363	−1.28782	−0.643908	−	0.765103i	$-0.722688\pi$
$157$	−16.1363	−1.28782	−0.643908	+	0.765103i	$0.722688\pi$
$158$	−38.8016	−3.08689
$159$	−10.8667	−0.861789
$160$	−59.0505	−4.66835
$161$	1.57849	0.124402
$162$	2.74483	0.215654
$163$	−6.64663	−0.520604	−0.260302	−	0.965527i	$-0.583822\pi$
$163$	−6.64663	−0.520604	−0.260302	+	0.965527i	$0.583822\pi$
$164$	−46.6052	−3.63926
$165$	6.13628	0.477709
$166$	5.79861	0.450059
$167$	14.3614	1.11132	0.555659	−	0.831410i	$-0.312466\pi$
$167$	14.3614	1.11132	0.555659	+	0.831410i	$0.312466\pi$
$168$	9.70041	0.748403
$169$	−12.8223	−0.986333
$170$	−45.4483	−3.48572
$171$	0	0
$172$	63.5845	4.84828
$173$	5.71477	0.434486	0.217243	−	0.976118i	$-0.430294\pi$
$173$	5.71477	0.434486	0.217243	+	0.976118i	$0.430294\pi$
$174$	16.5341	1.25344
$175$	−1.42151	−0.107456
$176$	37.6734	2.83974
$177$	14.1363	1.06255
$178$	26.6654	1.99865
$179$	9.60221	0.717703	0.358851	−	0.933395i	$-0.383168\pi$
$179$	9.60221	0.717703	0.358851	+	0.933395i	$0.383168\pi$
$180$	−14.0237	−1.04527
$181$	0.979304	0.0727911	0.0363956	−	0.999337i	$-0.488412\pi$
$181$	0.979304	0.0727911	0.0363956	+	0.999337i	$0.488412\pi$
$182$	−1.15698	−0.0857608
$183$	−6.84302	−0.505851
$184$	−15.3120	−1.12881
$185$	−7.20442	−0.529680
$186$	9.57849	0.702329
$187$	15.8223	1.15704
$188$	44.4038	3.23848
$189$	1.00000	0.0727393
$190$	0	0
$191$	−11.7148	−0.847651	−0.423825	−	0.905744i	$-0.639313\pi$
$191$	−11.7148	−0.847651	−0.423825	+	0.905744i	$0.639313\pi$
$192$	−32.8461	−2.37046
$193$	−17.8223	−1.28288	−0.641440	−	0.767174i	$-0.721663\pi$
$193$	−17.8223	−1.28288	−0.641440	+	0.767174i	$0.721663\pi$
$194$	13.6673	0.981257
$195$	1.06814	0.0764911
$196$	5.53407	0.395291
$197$	−19.1156	−1.36193	−0.680965	−	0.732316i	$-0.738439\pi$
$197$	−19.1156	−1.36193	−0.680965	+	0.732316i	$0.738439\pi$
$198$	6.64663	0.472355
$199$	16.0474	1.13757	0.568787	−	0.822485i	$-0.307413\pi$
$199$	16.0474	1.13757	0.568787	+	0.822485i	$0.307413\pi$
$200$	13.7892	0.975047
$201$	−9.91116	−0.699080
$202$	−4.64163	−0.326584
$203$	6.02372	0.422782
$204$	−36.1600	−2.53171
$205$	21.3407	1.49050
$206$	−8.66535	−0.603744
$207$	−1.57849	−0.109713
$208$	6.55779	0.454701
$209$	0	0
$210$	−6.95558	−0.479981
$211$	9.29326	0.639774	0.319887	−	0.947456i	$-0.396355\pi$
$211$	9.29326	0.639774	0.319887	+	0.947456i	$0.396355\pi$
$212$	60.1373	4.13025
$213$	−13.3771	−0.916583
$214$	45.3831	3.10233
$215$	−29.1156	−1.98567
$216$	−9.70041	−0.660029
$217$	3.48965	0.236893
$218$	−4.87175	−0.329956
$219$	−7.06814	−0.477621
$220$	−33.9586	−2.28949
$221$	2.75419	0.185267
$222$	−7.80361	−0.523744
$223$	8.33268	0.557997	0.278999	−	0.960292i	$-0.409998\pi$
$223$	8.33268	0.557997	0.278999	+	0.960292i	$0.409998\pi$
$224$	−23.3026	−1.55697
$225$	1.42151	0.0947675
$226$	−27.5134	−1.83016
$227$	−16.8905	−1.12106	−0.560530	−	0.828134i	$-0.689403\pi$
$227$	−16.8905	−1.12106	−0.560530	+	0.828134i	$0.689403\pi$
$228$	0	0
$229$	6.04744	0.399626	0.199813	−	0.979834i	$-0.435966\pi$
$229$	6.04744	0.399626	0.199813	+	0.979834i	$0.435966\pi$
$230$	10.9793	0.723954
$231$	2.42151	0.159324
$232$	−58.4326	−3.83629
$233$	21.2044	1.38915	0.694574	−	0.719421i	$-0.255593\pi$
$233$	21.2044	1.38915	0.694574	+	0.719421i	$0.255593\pi$
$234$	1.15698	0.0756339
$235$	−20.3327	−1.32636
$236$	−78.2312	−5.09242
$237$	14.1363	0.918250
$238$	−17.9349	−1.16255
$239$	−5.80361	−0.375404	−0.187702	−	0.982226i	$-0.560104\pi$
$239$	−5.80361	−0.375404	−0.187702	+	0.982226i	$0.560104\pi$
$240$	39.4245	2.54484
$241$	12.9793	0.836070	0.418035	−	0.908431i	$-0.362719\pi$
$241$	12.9793	0.836070	0.418035	+	0.908431i	$0.362719\pi$
$242$	−14.0982	−0.906266
$243$	−1.00000	−0.0641500
$244$	37.8698	2.42436
$245$	−2.53407	−0.161896
$246$	23.1156	1.47380
$247$	0	0
$248$	−33.8510	−2.14954
$249$	−2.11256	−0.133878
$250$	24.8905	1.57421
$251$	10.3377	0.652508	0.326254	−	0.945282i	$-0.394213\pi$
$251$	10.3377	0.652508	0.326254	+	0.945282i	$0.394213\pi$
$252$	−5.53407	−0.348614
$253$	−3.82233	−0.240308
$254$	−5.73349	−0.359751
$255$	16.5578	1.03689
$256$	53.8491	3.36557
$257$	15.1757	0.946634	0.473317	−	0.880892i	$-0.343056\pi$
$257$	15.1757	0.946634	0.473317	+	0.880892i	$0.343056\pi$
$258$	−31.5371	−1.96341
$259$	−2.84302	−0.176657
$260$	−5.91116	−0.366595
$261$	−6.02372	−0.372859
$262$	−38.2488	−2.36302
$263$	−8.51035	−0.524771	−0.262385	−	0.964963i	$-0.584509\pi$
$263$	−8.51035	−0.524771	−0.262385	+	0.964963i	$0.584509\pi$
$264$	−23.4897	−1.44569
$265$	−27.5371	−1.69159
$266$	0	0
$267$	−9.71477	−0.594534
$268$	54.8491	3.35044
$269$	−15.1757	−0.925279	−0.462639	−	0.886547i	$-0.653098\pi$
$269$	−15.1757	−0.925279	−0.462639	+	0.886547i	$0.653098\pi$
$270$	6.95558	0.423303
$271$	0.843024	0.0512100	0.0256050	−	0.999672i	$-0.491849\pi$
$271$	0.843024	0.0512100	0.0256050	+	0.999672i	$0.491849\pi$
$272$	101.656	6.16378
$273$	0.421512	0.0255111
$274$	46.6052	2.81553
$275$	3.44221	0.207573
$276$	8.73546	0.525813
$277$	10.5578	0.634356	0.317178	−	0.948366i	$-0.397265\pi$
$277$	10.5578	0.634356	0.317178	+	0.948366i	$0.397265\pi$
$278$	−2.93186	−0.175841
$279$	−3.48965	−0.208920
$280$	24.5815	1.46903
$281$	−15.0444	−0.897475	−0.448737	−	0.893664i	$-0.648126\pi$
$281$	−15.0444	−0.897475	−0.448737	+	0.893664i	$0.648126\pi$
$282$	−22.0237	−1.31149
$283$	1.24581	0.0740559	0.0370279	−	0.999314i	$-0.488211\pi$
$283$	1.24581	0.0740559	0.0370279	+	0.999314i	$0.488211\pi$
$284$	74.0298	4.39286
$285$	0	0
$286$	2.80163	0.165664
$287$	8.42151	0.497106
$288$	23.3026	1.37312
$289$	25.6941	1.51142
$290$	41.8985	2.46036
$291$	−4.97930	−0.291892
$292$	39.1156	2.28907
$293$	−20.4215	−1.19304	−0.596519	−	0.802599i	$-0.703450\pi$
$293$	−20.4215	−1.19304	−0.596519	+	0.802599i	$0.703450\pi$
$294$	−2.74483	−0.160082
$295$	35.8223	2.08566
$296$	27.5785	1.60297
$297$	−2.42151	−0.140510
$298$	38.5578	2.23359
$299$	−0.665351	−0.0384783
$300$	−7.86675	−0.454187
$301$	−11.4897	−0.662253
$302$	40.4977	2.33038
$303$	1.69105	0.0971481
$304$	0	0
$305$	−17.3407	−0.992926
$306$	17.9349	1.02527
$307$	2.64663	0.151051	0.0755255	−	0.997144i	$-0.475937\pi$
$307$	2.64663	0.151051	0.0755255	+	0.997144i	$0.475937\pi$
$308$	−13.4008	−0.763582
$309$	3.15698	0.179594
$310$	24.2726	1.37859
$311$	−5.09186	−0.288733	−0.144367	−	0.989524i	$-0.546114\pi$
$311$	−5.09186	−0.288733	−0.144367	+	0.989524i	$0.546114\pi$
$312$	−4.08884	−0.231485
$313$	19.9586	1.12813	0.564064	−	0.825731i	$-0.309237\pi$
$313$	19.9586	1.12813	0.564064	+	0.825731i	$0.309237\pi$
$314$	−44.2913	−2.49950
$315$	2.53407	0.142779
$316$	−78.2312	−4.40085
$317$	6.81930	0.383010	0.191505	−	0.981492i	$-0.438663\pi$
$317$	6.81930	0.383010	0.191505	+	0.981492i	$0.438663\pi$
$318$	−29.8273	−1.67263
$319$	−14.5865	−0.816688
$320$	−83.2342	−4.65293
$321$	−16.5341	−0.922842
$322$	4.33268	0.241451
$323$	0	0
$324$	5.53407	0.307448
$325$	0.599184	0.0332367
$326$	−18.2438	−1.01043
$327$	1.77488	0.0981513
$328$	−81.6921	−4.51069
$329$	−8.02372	−0.442362
$330$	16.8430	0.927178
$331$	5.91116	0.324907	0.162453	−	0.986716i	$-0.448059\pi$
$331$	5.91116	0.324907	0.162453	+	0.986716i	$0.448059\pi$
$332$	11.6910	0.641630
$333$	2.84302	0.155797
$334$	39.4195	2.15694
$335$	−25.1156	−1.37221
$336$	15.5578	0.848747
$337$	−4.08884	−0.222733	−0.111367	−	0.993779i	$-0.535523\pi$
$337$	−4.08884	−0.222733	−0.111367	+	0.993779i	$0.535523\pi$
$338$	−35.1951	−1.91436
$339$	10.0237	0.544414
$340$	−91.6320	−4.96944
$341$	−8.45023	−0.457606
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	111.454	6.00921
$345$	−4.00000	−0.215353
$346$	15.6860	0.843287
$347$	−17.3534	−0.931578	−0.465789	−	0.884896i	$-0.654229\pi$
$347$	−17.3534	−0.931578	−0.465789	+	0.884896i	$0.654229\pi$
$348$	33.3357	1.78698
$349$	−4.70674	−0.251946	−0.125973	−	0.992034i	$-0.540205\pi$
$349$	−4.70674	−0.251946	−0.125973	+	0.992034i	$0.540205\pi$
$350$	−3.90180	−0.208560
$351$	−0.421512	−0.0224986
$352$	56.4276	3.00760
$353$	20.6704	1.10017	0.550086	−	0.835108i	$-0.314595\pi$
$353$	20.6704	1.10017	0.550086	+	0.835108i	$0.314595\pi$
$354$	38.8016	2.06228
$355$	−33.8985	−1.79915
$356$	53.7622	2.84939
$357$	6.53407	0.345820
$358$	26.3564	1.39298
$359$	8.10756	0.427901	0.213950	−	0.976845i	$-0.431367\pi$
$359$	8.10756	0.427901	0.213950	+	0.976845i	$0.431367\pi$
$360$	−24.5815	−1.29556
$361$	0	0
$362$	2.68802	0.141279
$363$	5.13628	0.269585
$364$	−2.33268	−0.122265
$365$	−17.9112	−0.937513
$366$	−18.7829	−0.981798
$367$	28.8905	1.50807	0.754035	−	0.656834i	$-0.228105\pi$
$367$	28.8905	1.50807	0.754035	+	0.656834i	$0.228105\pi$
$368$	−24.5578	−1.28016
$369$	−8.42151	−0.438406
$370$	−19.7749	−1.02805
$371$	−10.8667	−0.564173
$372$	19.3120	1.00128
$373$	−11.9586	−0.619193	−0.309597	−	0.950868i	$-0.600194\pi$
$373$	−11.9586	−0.619193	−0.309597	+	0.950868i	$0.600194\pi$
$374$	43.4295	2.24569
$375$	−9.06814	−0.468277
$376$	77.8334	4.01395
$377$	−2.53907	−0.130769
$378$	2.74483	0.141179
$379$	15.3821	0.790125	0.395063	−	0.918654i	$-0.370723\pi$
$379$	15.3821	0.790125	0.395063	+	0.918654i	$0.370723\pi$
$380$	0	0
$381$	2.08884	0.107014
$382$	−32.1550	−1.64519
$383$	0.617907	0.0315736	0.0157868	−	0.999875i	$-0.494975\pi$
$383$	0.617907	0.0315736	0.0157868	+	0.999875i	$0.494975\pi$
$384$	−43.5515	−2.22248
$385$	6.13628	0.312734
$386$	−48.9192	−2.48992
$387$	11.4897	0.584052
$388$	27.5558	1.39893
$389$	−11.0681	−0.561177	−0.280588	−	0.959828i	$-0.590530\pi$
$389$	−11.0681	−0.561177	−0.280588	+	0.959828i	$0.590530\pi$
$390$	2.93186	0.148460
$391$	−10.3140	−0.521599
$392$	9.70041	0.489945
$393$	13.9349	0.702922
$394$	−52.4690	−2.64335
$395$	35.8223	1.80242
$396$	13.4008	0.673416
$397$	−10.4502	−0.524482	−0.262241	−	0.965002i	$-0.584462\pi$
$397$	−10.4502	−0.524482	−0.262241	+	0.965002i	$0.584462\pi$
$398$	44.0474	2.20790
$399$	0	0
$400$	22.1156	1.10578
$401$	−3.26953	−0.163273	−0.0816364	−	0.996662i	$-0.526015\pi$
$401$	−3.26953	−0.163273	−0.0816364	+	0.996662i	$0.526015\pi$
$402$	−27.2044	−1.35683
$403$	−1.47093	−0.0732722
$404$	−9.35837	−0.465596
$405$	−2.53407	−0.125919
$406$	16.5341	0.820572
$407$	6.88441	0.341248
$408$	−63.3831	−3.13793
$409$	−7.40082	−0.365947	−0.182973	−	0.983118i	$-0.558572\pi$
$409$	−7.40082	−0.365947	−0.182973	+	0.983118i	$0.558572\pi$
$410$	58.5765	2.89289
$411$	−16.9793	−0.837527
$412$	−17.4709	−0.860731
$413$	14.1363	0.695601
$414$	−4.33268	−0.212939
$415$	−5.35337	−0.262787
$416$	9.82233	0.481579
$417$	1.06814	0.0523071
$418$	0	0
$419$	−31.8461	−1.55578	−0.777891	−	0.628400i	$-0.783710\pi$
$419$	−31.8461	−1.55578	−0.777891	+	0.628400i	$0.783710\pi$
$420$	−14.0237	−0.684288
$421$	−40.0061	−1.94978	−0.974888	−	0.222696i	$-0.928514\pi$
$421$	−40.0061	−1.94978	−0.974888	+	0.222696i	$0.928514\pi$
$422$	25.5084	1.24173
$423$	8.02372	0.390127
$424$	105.412	5.11925
$425$	9.28826	0.450547
$426$	−36.7178	−1.77898
$427$	−6.84302	−0.331157
$428$	91.5007	4.42285
$429$	−1.02070	−0.0492797
$430$	−79.9172	−3.85395
$431$	−3.91616	−0.188635	−0.0943175	−	0.995542i	$-0.530067\pi$
$431$	−3.91616	−0.188635	−0.0943175	+	0.995542i	$0.530067\pi$
$432$	−15.5578	−0.748525
$433$	−18.0000	−0.865025	−0.432512	−	0.901628i	$-0.642373\pi$
$433$	−18.0000	−0.865025	−0.432512	+	0.901628i	$0.642373\pi$
$434$	9.57849	0.459782
$435$	−15.2645	−0.731878
$436$	−9.82233	−0.470404
$437$	0	0
$438$	−19.4008	−0.927007
$439$	−17.4483	−0.832760	−0.416380	−	0.909191i	$-0.636701\pi$
$439$	−17.4483	−0.832760	−0.416380	+	0.909191i	$0.636701\pi$
$440$	−59.5244	−2.83772
$441$	1.00000	0.0476190
$442$	7.55977	0.359581
$443$	−3.03942	−0.144407	−0.0722036	−	0.997390i	$-0.523003\pi$
$443$	−3.03942	−0.144407	−0.0722036	+	0.997390i	$0.523003\pi$
$444$	−15.7335	−0.746678
$445$	−24.6179	−1.16700
$446$	22.8717	1.08301
$447$	−14.0474	−0.664421
$448$	−32.8461	−1.55183
$449$	−35.9349	−1.69587	−0.847936	−	0.530099i	$-0.822155\pi$
$449$	−35.9349	−1.69587	−0.847936	+	0.530099i	$0.822155\pi$
$450$	3.90180	0.183933
$451$	−20.3928	−0.960259
$452$	−55.4720	−2.60918
$453$	−14.7542	−0.693212
$454$	−46.3614	−2.17585
$455$	1.06814	0.0500752
$456$	0	0
$457$	−24.4215	−1.14239	−0.571195	−	0.820814i	$-0.693520\pi$
$457$	−24.4215	−1.14239	−0.571195	+	0.820814i	$0.693520\pi$
$458$	16.5992	0.775629
$459$	−6.53407	−0.304984
$460$	22.1363	1.03211
$461$	10.1313	0.471861	0.235930	−	0.971770i	$-0.424186\pi$
$461$	10.1313	0.471861	0.235930	+	0.971770i	$0.424186\pi$
$462$	6.64663	0.309229
$463$	−5.86372	−0.272510	−0.136255	−	0.990674i	$-0.543507\pi$
$463$	−5.86372	−0.272510	−0.136255	+	0.990674i	$0.543507\pi$
$464$	−93.7158	−4.35065
$465$	−8.84302	−0.410085
$466$	58.2024	2.69618
$467$	−14.9556	−0.692062	−0.346031	−	0.938223i	$-0.612471\pi$
$467$	−14.9556	−0.692062	−0.346031	+	0.938223i	$0.612471\pi$
$468$	2.33268	0.107828
$469$	−9.91116	−0.457655
$470$	−55.8097	−2.57431
$471$	16.1363	0.743521
$472$	−137.128	−6.31181
$473$	27.8223	1.27927
$474$	38.8016	1.78222
$475$	0	0
$476$	−36.1600	−1.65739
$477$	10.8667	0.497554
$478$	−15.9299	−0.728616
$479$	−33.7098	−1.54024	−0.770119	−	0.637900i	$-0.779803\pi$
$479$	−33.7098	−1.54024	−0.770119	+	0.637900i	$0.779803\pi$
$480$	59.0505	2.69527
$481$	1.19837	0.0546409
$482$	35.6259	1.62272
$483$	−1.57849	−0.0718237
$484$	−28.4245	−1.29202
$485$	−12.6179	−0.572950
$486$	−2.74483	−0.124508
$487$	−21.5084	−0.974637	−0.487319	−	0.873224i	$-0.662025\pi$
$487$	−21.5084	−0.974637	−0.487319	+	0.873224i	$0.662025\pi$
$488$	66.3801	3.00489
$489$	6.64663	0.300571
$490$	−6.95558	−0.314221
$491$	−17.3534	−0.783147	−0.391573	−	0.920147i	$-0.628069\pi$
$491$	−17.3534	−0.783147	−0.391573	+	0.920147i	$0.628069\pi$
$492$	46.6052	2.10113
$493$	−39.3594	−1.77266
$494$	0	0
$495$	−6.13628	−0.275805
$496$	−54.2913	−2.43775
$497$	−13.3771	−0.600045
$498$	−5.79861	−0.259842
$499$	−32.9379	−1.47450	−0.737252	−	0.675618i	$-0.763877\pi$
$499$	−32.9379	−1.47450	−0.737252	+	0.675618i	$0.763877\pi$
$500$	50.1837	2.24428
$501$	−14.3614	−0.641620
$502$	28.3751	1.26644
$503$	−38.2074	−1.70359	−0.851793	−	0.523879i	$-0.824485\pi$
$503$	−38.2074	−1.70359	−0.851793	+	0.523879i	$0.824485\pi$
$504$	−9.70041	−0.432091
$505$	4.28523	0.190690
$506$	−10.4916	−0.466410
$507$	12.8223	0.569460
$508$	−11.5598	−0.512882
$509$	8.82430	0.391130	0.195565	−	0.980691i	$-0.437346\pi$
$509$	8.82430	0.391130	0.195565	+	0.980691i	$0.437346\pi$
$510$	45.4483	2.01248
$511$	−7.06814	−0.312676
$512$	60.7034	2.68274
$513$	0	0
$514$	41.6547	1.83731
$515$	8.00000	0.352522
$516$	−63.5845	−2.79915
$517$	19.4295	0.854510
$518$	−7.80361	−0.342871
$519$	−5.71477	−0.250851
$520$	−10.3614	−0.454377
$521$	24.2913	1.06422	0.532110	−	0.846675i	$-0.321399\pi$
$521$	24.2913	1.06422	0.532110	+	0.846675i	$0.321399\pi$
$522$	−16.5341	−0.723677
$523$	−19.0969	−0.835047	−0.417524	−	0.908666i	$-0.637102\pi$
$523$	−19.0969	−0.835047	−0.417524	+	0.908666i	$0.637102\pi$
$524$	−77.1166	−3.36886
$525$	1.42151	0.0620399
$526$	−23.3594	−1.01852
$527$	−22.8016	−0.993255
$528$	−37.6734	−1.63952
$529$	−20.5084	−0.891668
$530$	−75.5845	−3.28318
$531$	−14.1363	−0.613462
$532$	0	0
$533$	−3.54977	−0.153757
$534$	−26.6654	−1.15392
$535$	−41.8985	−1.81143
$536$	96.1423	4.15272
$537$	−9.60221	−0.414366
$538$	−41.6547	−1.79586
$539$	2.42151	0.104302
$540$	14.0237	0.603485
$541$	−36.2312	−1.55770	−0.778850	−	0.627210i	$-0.784197\pi$
$541$	−36.2312	−1.55770	−0.778850	+	0.627210i	$0.784197\pi$
$542$	2.31395	0.0993928
$543$	−0.979304	−0.0420260
$544$	152.261	6.52813
$545$	4.49768	0.192659
$546$	1.15698	0.0495140
$547$	29.9586	1.28094	0.640469	−	0.767984i	$-0.278740\pi$
$547$	29.9586	1.28094	0.640469	+	0.767984i	$0.278740\pi$
$548$	93.9647	4.01397
$549$	6.84302	0.292053
$550$	9.44826	0.402875
$551$	0	0
$552$	15.3120	0.651721
$553$	14.1363	0.601136
$554$	28.9793	1.23121
$555$	7.20442	0.305811
$556$	−5.91116	−0.250689
$557$	−14.4402	−0.611852	−0.305926	−	0.952055i	$-0.598966\pi$
$557$	−14.4402	−0.611852	−0.305926	+	0.952055i	$0.598966\pi$
$558$	−9.57849	−0.405490
$559$	4.84302	0.204838
$560$	39.4245	1.66599
$561$	−15.8223	−0.668019
$562$	−41.2943	−1.74190
$563$	17.9112	0.754866	0.377433	−	0.926037i	$-0.376807\pi$
$563$	17.9112	0.754866	0.377433	+	0.926037i	$0.376807\pi$
$564$	−44.4038	−1.86974
$565$	25.4008	1.06862
$566$	3.41954	0.143734
$567$	−1.00000	−0.0419961
$568$	129.763	5.44475
$569$	8.50535	0.356563	0.178281	−	0.983980i	$-0.442946\pi$
$569$	8.50535	0.356563	0.178281	+	0.983980i	$0.442946\pi$
$570$	0	0
$571$	−6.80163	−0.284639	−0.142320	−	0.989821i	$-0.545456\pi$
$571$	−6.80163	−0.284639	−0.142320	+	0.989821i	$0.545456\pi$
$572$	5.64860	0.236180
$573$	11.7148	0.489391
$574$	23.1156	0.964826
$575$	−2.24384	−0.0935746
$576$	32.8461	1.36859
$577$	−14.2726	−0.594175	−0.297087	−	0.954850i	$-0.596015\pi$
$577$	−14.2726	−0.594175	−0.297087	+	0.954850i	$0.596015\pi$
$578$	70.5258	2.93348
$579$	17.8223	0.740671
$580$	84.4750	3.50763
$581$	−2.11256	−0.0876437
$582$	−13.6673	−0.566529
$583$	26.3140	1.08981
$584$	68.5638	2.83719
$585$	−1.06814	−0.0441622
$586$	−56.0535	−2.31555
$587$	40.2963	1.66321	0.831603	−	0.555371i	$-0.187424\pi$
$587$	40.2963	1.66321	0.831603	+	0.555371i	$0.187424\pi$
$588$	−5.53407	−0.228221
$589$	0	0
$590$	98.3261	4.04802
$591$	19.1156	0.786310
$592$	44.2312	1.81789
$593$	26.1313	1.07308	0.536542	−	0.843874i	$-0.319730\pi$
$593$	26.1313	1.07308	0.536542	+	0.843874i	$0.319730\pi$
$594$	−6.64663	−0.272714
$595$	16.5578	0.678803
$596$	77.7395	3.18434
$597$	−16.0474	−0.656778
$598$	−1.82627	−0.0746819
$599$	−3.06314	−0.125157	−0.0625783	−	0.998040i	$-0.519932\pi$
$599$	−3.06314	−0.125157	−0.0625783	+	0.998040i	$0.519932\pi$
$600$	−13.7892	−0.562944
$601$	−28.1363	−1.14770	−0.573851	−	0.818959i	$-0.694551\pi$
$601$	−28.1363	−1.14770	−0.573851	+	0.818959i	$0.694551\pi$
$602$	−31.5371	−1.28536
$603$	9.91116	0.403614
$604$	81.6507	3.32232
$605$	13.0157	0.529163
$606$	4.64163	0.188553
$607$	−28.8430	−1.17070	−0.585351	−	0.810780i	$-0.699043\pi$
$607$	−28.8430	−1.17070	−0.585351	+	0.810780i	$0.699043\pi$
$608$	0	0
$609$	−6.02372	−0.244094
$610$	−47.5972	−1.92715
$611$	3.38209	0.136825
$612$	36.1600	1.46168
$613$	22.2852	0.900092	0.450046	−	0.893005i	$-0.351408\pi$
$613$	22.2852	0.900092	0.450046	+	0.893005i	$0.351408\pi$
$614$	7.26454	0.293173
$615$	−21.3407	−0.860540
$616$	−23.4897	−0.946425
$617$	4.13628	0.166520	0.0832602	−	0.996528i	$-0.473467\pi$
$617$	4.13628	0.166520	0.0832602	+	0.996528i	$0.473467\pi$
$618$	8.66535	0.348572
$619$	−9.06814	−0.364479	−0.182240	−	0.983254i	$-0.558335\pi$
$619$	−9.06814	−0.364479	−0.182240	+	0.983254i	$0.558335\pi$
$620$	48.9379	1.96539
$621$	1.57849	0.0633426
$622$	−13.9763	−0.560398
$623$	−9.71477	−0.389214
$624$	−6.55779	−0.262522
$625$	−30.0869	−1.20347
$626$	54.7829	2.18957
$627$	0	0
$628$	−89.2993	−3.56343
$629$	18.5765	0.740694
$630$	6.95558	0.277117
$631$	−41.6259	−1.65710	−0.828551	−	0.559913i	$-0.810834\pi$
$631$	−41.6259	−1.65710	−0.828551	+	0.559913i	$0.810834\pi$
$632$	−137.128	−5.45465
$633$	−9.29326	−0.369374
$634$	18.7178	0.743379
$635$	5.29326	0.210057
$636$	−60.1373	−2.38460
$637$	0.421512	0.0167009
$638$	−40.0374	−1.58510
$639$	13.3771	0.529190
$640$	−110.362	−4.36246
$641$	−3.09186	−0.122121	−0.0610606	−	0.998134i	$-0.519448\pi$
$641$	−3.09186	−0.122121	−0.0610606	+	0.998134i	$0.519448\pi$
$642$	−45.3831	−1.79113
$643$	2.93186	0.115621	0.0578106	−	0.998328i	$-0.481588\pi$
$643$	2.93186	0.115621	0.0578106	+	0.998328i	$0.481588\pi$
$644$	8.73546	0.344226
$645$	29.1156	1.14643
$646$	0	0
$647$	−5.93489	−0.233324	−0.116662	−	0.993172i	$-0.537219\pi$
$647$	−5.93489	−0.233324	−0.116662	+	0.993172i	$0.537219\pi$
$648$	9.70041	0.381068
$649$	−34.2312	−1.34369
$650$	1.64466	0.0645087
$651$	−3.48965	−0.136770
$652$	−36.7829	−1.44053
$653$	1.82233	0.0713132	0.0356566	−	0.999364i	$-0.488648\pi$
$653$	1.82233	0.0713132	0.0356566	+	0.999364i	$0.488648\pi$
$654$	4.87175	0.190500
$655$	35.3120	1.37975
$656$	−131.020	−5.11548
$657$	7.06814	0.275754
$658$	−22.0237	−0.858574
$659$	−10.3978	−0.405040	−0.202520	−	0.979278i	$-0.564913\pi$
$659$	−10.3978	−0.405040	−0.202520	+	0.979278i	$0.564913\pi$
$660$	33.9586	1.32184
$661$	−23.2231	−0.903276	−0.451638	−	0.892201i	$-0.649160\pi$
$661$	−23.2231	−0.903276	−0.451638	+	0.892201i	$0.649160\pi$
$662$	16.2251	0.630607
$663$	−2.75419	−0.106964
$664$	20.4927	0.795270
$665$	0	0
$666$	7.80361	0.302384
$667$	9.50837	0.368166
$668$	79.4770	3.07506
$669$	−8.33268	−0.322160
$670$	−68.9379	−2.66330
$671$	16.5705	0.639696
$672$	23.3026	0.898918
$673$	−13.5498	−0.522305	−0.261153	−	0.965298i	$-0.584103\pi$
$673$	−13.5498	−0.522305	−0.261153	+	0.965298i	$0.584103\pi$
$674$	−11.2231	−0.432299
$675$	−1.42151	−0.0547140
$676$	−70.9597	−2.72922
$677$	12.6466	0.486049	0.243025	−	0.970020i	$-0.421860\pi$
$677$	12.6466	0.486049	0.243025	+	0.970020i	$0.421860\pi$
$678$	27.5134	1.05664
$679$	−4.97930	−0.191088
$680$	−160.617	−6.15939
$681$	16.8905	0.647244
$682$	−23.1944	−0.888160
$683$	13.7799	0.527273	0.263636	−	0.964622i	$-0.415078\pi$
$683$	13.7799	0.527273	0.263636	+	0.964622i	$0.415078\pi$
$684$	0	0
$685$	−43.0267	−1.64397
$686$	−2.74483	−0.104798
$687$	−6.04744	−0.230724
$688$	178.754	6.81492
$689$	4.58046	0.174502
$690$	−10.9793	−0.417975
$691$	1.11559	0.0424389	0.0212194	−	0.999775i	$-0.493245\pi$
$691$	1.11559	0.0424389	0.0212194	+	0.999775i	$0.493245\pi$
$692$	31.6259	1.20224
$693$	−2.42151	−0.0919856
$694$	−47.6320	−1.80809
$695$	2.70674	0.102673
$696$	58.4326	2.21488
$697$	−55.0267	−2.08429
$698$	−12.9192	−0.488999
$699$	−21.2044	−0.802025
$700$	−7.86675	−0.297335
$701$	16.7067	0.631005	0.315502	−	0.948925i	$-0.397827\pi$
$701$	16.7067	0.631005	0.315502	+	0.948925i	$0.397827\pi$
$702$	−1.15698	−0.0436673
$703$	0	0
$704$	79.5371	2.99767
$705$	20.3327	0.765773
$706$	56.7365	2.13531
$707$	1.69105	0.0635984
$708$	78.2312	2.94011
$709$	−25.1443	−0.944314	−0.472157	−	0.881514i	$-0.656525\pi$
$709$	−25.1443	−0.944314	−0.472157	+	0.881514i	$0.656525\pi$
$710$	−93.0455	−3.49193
$711$	−14.1363	−0.530152
$712$	94.2372	3.53169
$713$	5.50837	0.206290
$714$	17.9349	0.671196
$715$	−2.58651	−0.0967302
$716$	53.1393	1.98591
$717$	5.80361	0.216740
$718$	22.2538	0.830506
$719$	32.2488	1.20268	0.601339	−	0.798994i	$-0.294634\pi$
$719$	32.2488	1.20268	0.601339	+	0.798994i	$0.294634\pi$
$720$	−39.4245	−1.46927
$721$	3.15698	0.117572
$722$	0	0
$723$	−12.9793	−0.482706
$724$	5.41954	0.201416
$725$	−8.56279	−0.318014
$726$	14.0982	0.523233
$727$	−30.2312	−1.12121	−0.560606	−	0.828083i	$-0.689432\pi$
$727$	−30.2312	−1.12121	−0.560606	+	0.828083i	$0.689432\pi$
$728$	−4.08884	−0.151542
$729$	1.00000	0.0370370
$730$	−49.1630	−1.81961
$731$	75.0742	2.77672
$732$	−37.8698	−1.39971
$733$	25.0267	0.924384	0.462192	−	0.886780i	$-0.347063\pi$
$733$	25.0267	0.924384	0.462192	+	0.886780i	$0.347063\pi$
$734$	79.2993	2.92699
$735$	2.53407	0.0934706
$736$	−36.7829	−1.35584
$737$	24.0000	0.884051
$738$	−23.1156	−0.850896
$739$	5.53104	0.203463	0.101731	−	0.994812i	$-0.467562\pi$
$739$	5.53104	0.203463	0.101731	+	0.994812i	$0.467562\pi$
$740$	−39.8698	−1.46564
$741$	0	0
$742$	−29.8273	−1.09500
$743$	−21.6971	−0.795989	−0.397995	−	0.917388i	$-0.630294\pi$
$743$	−21.6971	−0.795989	−0.397995	+	0.917388i	$0.630294\pi$
$744$	33.8510	1.24104
$745$	−35.5972	−1.30418
$746$	−32.8243	−1.20178
$747$	2.11256	0.0772945
$748$	87.5619	3.20158
$749$	−16.5341	−0.604142
$750$	−24.8905	−0.908871
$751$	48.9854	1.78750	0.893751	−	0.448564i	$-0.148065\pi$
$751$	48.9854	1.78750	0.893751	+	0.448564i	$0.148065\pi$
$752$	124.831	4.55213
$753$	−10.3377	−0.376726
$754$	−6.96931	−0.253807
$755$	−37.3881	−1.36069
$756$	5.53407	0.201272
$757$	−4.04139	−0.146887	−0.0734434	−	0.997299i	$-0.523399\pi$
$757$	−4.04139	−0.146887	−0.0734434	+	0.997299i	$0.523399\pi$
$758$	42.2212	1.53354
$759$	3.82233	0.138742
$760$	0	0
$761$	−36.9429	−1.33918	−0.669590	−	0.742731i	$-0.733530\pi$
$761$	−36.9429	−1.33918	−0.669590	+	0.742731i	$0.733530\pi$
$762$	5.73349	0.207702
$763$	1.77488	0.0642551
$764$	−64.8304	−2.34548
$765$	−16.5578	−0.598648
$766$	1.69605	0.0612806
$767$	−5.95861	−0.215153
$768$	−53.8491	−1.94311
$769$	24.1363	0.870377	0.435188	−	0.900339i	$-0.356682\pi$
$769$	24.1363	0.870377	0.435188	+	0.900339i	$0.356682\pi$
$770$	16.8430	0.606980
$771$	−15.1757	−0.546539
$772$	−98.6300	−3.54977
$773$	25.5371	0.918506	0.459253	−	0.888306i	$-0.348117\pi$
$773$	25.5371	0.918506	0.459253	+	0.888306i	$0.348117\pi$
$774$	31.5371	1.13358
$775$	−4.96058	−0.178189
$776$	48.3013	1.73392
$777$	2.84302	0.101993
$778$	−30.3801	−1.08918
$779$	0	0
$780$	5.91116	0.211654
$781$	32.3928	1.15911
$782$	−28.3100	−1.01236
$783$	6.02372	0.215270
$784$	15.5578	0.555635
$785$	40.8905	1.45944
$786$	38.2488	1.36429
$787$	19.0969	0.680730	0.340365	−	0.940293i	$-0.389449\pi$
$787$	19.0969	0.680730	0.340365	+	0.940293i	$0.389449\pi$
$788$	−105.787	−3.76851
$789$	8.51035	0.302976
$790$	98.3261	3.49828
$791$	10.0237	0.356403
$792$	23.4897	0.834668
$793$	2.88441	0.102429
$794$	−28.6841	−1.01796
$795$	27.5371	0.976640
$796$	88.8077	3.14770
$797$	−8.02872	−0.284392	−0.142196	−	0.989839i	$-0.545416\pi$
$797$	−8.02872	−0.284392	−0.142196	+	0.989839i	$0.545416\pi$
$798$	0	0
$799$	52.4276	1.85475
$800$	33.1249	1.17114
$801$	9.71477	0.343254
$802$	−8.97430	−0.316894
$803$	17.1156	0.603996
$804$	−54.8491	−1.93438
$805$	−4.00000	−0.140981
$806$	−4.03745	−0.142213
$807$	15.1757	0.534210
$808$	−16.4038	−0.577085
$809$	−29.0742	−1.02219	−0.511097	−	0.859523i	$-0.670761\pi$
$809$	−29.0742	−1.02219	−0.511097	+	0.859523i	$0.670761\pi$
$810$	−6.95558	−0.244394
$811$	−4.66535	−0.163823	−0.0819113	−	0.996640i	$-0.526102\pi$
$811$	−4.66535	−0.163823	−0.0819113	+	0.996640i	$0.526102\pi$
$812$	33.3357	1.16985
$813$	−0.843024	−0.0295661
$814$	18.8965	0.662323
$815$	16.8430	0.589985
$816$	−101.656	−3.55866
$817$	0	0
$818$	−20.3140	−0.710261
$819$	−0.421512	−0.0147288
$820$	118.101	4.12426
$821$	−17.5972	−0.614147	−0.307073	−	0.951686i	$-0.599350\pi$
$821$	−17.5972	−0.614147	−0.307073	+	0.951686i	$0.599350\pi$
$822$	−46.6052	−1.62554
$823$	−7.93989	−0.276767	−0.138384	−	0.990379i	$-0.544191\pi$
$823$	−7.93989	−0.276767	−0.138384	+	0.990379i	$0.544191\pi$
$824$	−30.6240	−1.06684
$825$	−3.44221	−0.119842
$826$	38.8016	1.35008
$827$	31.7859	1.10531	0.552653	−	0.833412i	$-0.313616\pi$
$827$	31.7859	1.10531	0.552653	+	0.833412i	$0.313616\pi$
$828$	−8.73546	−0.303578
$829$	48.9793	1.70112	0.850561	−	0.525877i	$-0.176263\pi$
$829$	48.9793	1.70112	0.850561	+	0.525877i	$0.176263\pi$
$830$	−14.6941	−0.510039
$831$	−10.5578	−0.366246
$832$	13.8450	0.479989
$833$	6.53407	0.226392
$834$	2.93186	0.101522
$835$	−36.3928	−1.25942
$836$	0	0
$837$	3.48965	0.120620
$838$	−87.4119	−3.01959
$839$	−36.2726	−1.25227	−0.626134	−	0.779716i	$-0.715364\pi$
$839$	−36.2726	−1.25227	−0.626134	+	0.779716i	$0.715364\pi$
$840$	−24.5815	−0.848143
$841$	7.28523	0.251215
$842$	−109.810	−3.78429
$843$	15.0444	0.518157
$844$	51.4295	1.77028
$845$	32.4927	1.11778
$846$	22.0237	0.757191
$847$	5.13628	0.176485
$848$	169.063	5.80563
$849$	−1.24581	−0.0427562
$850$	25.4947	0.874459
$851$	−4.48768	−0.153836
$852$	−74.0298	−2.53622
$853$	−34.6654	−1.18692	−0.593460	−	0.804864i	$-0.702238\pi$
$853$	−34.6654	−1.18692	−0.593460	+	0.804864i	$0.702238\pi$
$854$	−18.7829	−0.642738
$855$	0	0
$856$	160.387	5.48192
$857$	4.87175	0.166416	0.0832078	−	0.996532i	$-0.473483\pi$
$857$	4.87175	0.166416	0.0832078	+	0.996532i	$0.473483\pi$
$858$	−2.80163	−0.0956461
$859$	−37.1156	−1.26637	−0.633184	−	0.774002i	$-0.718252\pi$
$859$	−37.1156	−1.26637	−0.633184	+	0.774002i	$0.718252\pi$
$860$	−161.128	−5.49441
$861$	−8.42151	−0.287004
$862$	−10.7492	−0.366119
$863$	29.1520	0.992345	0.496172	−	0.868224i	$-0.334738\pi$
$863$	29.1520	0.992345	0.496172	+	0.868224i	$0.334738\pi$
$864$	−23.3026	−0.792771
$865$	−14.4816	−0.492390
$866$	−49.4069	−1.67891
$867$	−25.6941	−0.872616
$868$	19.3120	0.655491
$869$	−34.2312	−1.16121
$870$	−41.8985	−1.42049
$871$	4.17767	0.141555
$872$	−17.2171	−0.583044
$873$	4.97930	0.168524
$874$	0	0
$875$	−9.06814	−0.306559
$876$	−39.1156	−1.32159
$877$	−14.4502	−0.487950	−0.243975	−	0.969782i	$-0.578451\pi$
$877$	−14.4502	−0.487950	−0.243975	+	0.969782i	$0.578451\pi$
$878$	−47.8924	−1.61629
$879$	20.4215	0.688800
$880$	−95.4670	−3.21819
$881$	10.5341	0.354902	0.177451	−	0.984130i	$-0.443215\pi$
$881$	10.5341	0.354902	0.177451	+	0.984130i	$0.443215\pi$
$882$	2.74483	0.0924231
$883$	−5.11559	−0.172153	−0.0860766	−	0.996289i	$-0.527433\pi$
$883$	−5.11559	−0.172153	−0.0860766	+	0.996289i	$0.527433\pi$
$884$	15.2419	0.512639
$885$	−35.8223	−1.20415
$886$	−8.34267	−0.280278
$887$	0.617907	0.0207473	0.0103736	−	0.999946i	$-0.496698\pi$
$887$	0.617907	0.0207473	0.0103736	+	0.999946i	$0.496698\pi$
$888$	−27.5785	−0.925473
$889$	2.08884	0.0700573
$890$	−67.5719	−2.26501
$891$	2.42151	0.0811237
$892$	46.1136	1.54400
$893$	0	0
$894$	−38.5578	−1.28957
$895$	−24.3327	−0.813352
$896$	−43.5515	−1.45495
$897$	0.665351	0.0222154
$898$	−98.6350	−3.29149
$899$	21.0207	0.701079
$900$	7.86675	0.262225
$901$	71.0041	2.36549
$902$	−55.9747	−1.86375
$903$	11.4897	0.382352
$904$	−97.2342	−3.23396
$905$	−2.48163	−0.0824920
$906$	−40.4977	−1.34545
$907$	8.27256	0.274686	0.137343	−	0.990524i	$-0.456144\pi$
$907$	8.27256	0.274686	0.137343	+	0.990524i	$0.456144\pi$
$908$	−93.4730	−3.10201
$909$	−1.69105	−0.0560885
$910$	2.93186	0.0971902
$911$	5.77988	0.191496	0.0957480	−	0.995406i	$-0.469476\pi$
$911$	5.77988	0.191496	0.0957480	+	0.995406i	$0.469476\pi$
$912$	0	0
$913$	5.11559	0.169301
$914$	−67.0328	−2.21725
$915$	17.3407	0.573266
$916$	33.4670	1.10578
$917$	13.9349	0.460170
$918$	−17.9349	−0.591939
$919$	4.62791	0.152661	0.0763303	−	0.997083i	$-0.475680\pi$
$919$	4.62791	0.152661	0.0763303	+	0.997083i	$0.475680\pi$
$920$	38.8016	1.27925
$921$	−2.64663	−0.0872094
$922$	27.8086	0.915828
$923$	5.63860	0.185597
$924$	13.4008	0.440854
$925$	4.04139	0.132880
$926$	−16.0949	−0.528911
$927$	−3.15698	−0.103689
$928$	−140.369	−4.60782
$929$	−29.9536	−0.982746	−0.491373	−	0.870949i	$-0.663505\pi$
$929$	−29.9536	−0.982746	−0.491373	+	0.870949i	$0.663505\pi$
$930$	−24.2726	−0.795929
$931$	0	0
$932$	117.347	3.84382
$933$	5.09186	0.166700
$934$	−41.0505	−1.34321
$935$	−40.0949	−1.31124
$936$	4.08884	0.133648
$937$	4.58651	0.149835	0.0749174	−	0.997190i	$-0.476131\pi$
$937$	4.58651	0.149835	0.0749174	+	0.997190i	$0.476131\pi$
$938$	−27.2044	−0.888256
$939$	−19.9586	−0.651325
$940$	−112.522	−3.67008
$941$	−7.41082	−0.241586	−0.120793	−	0.992678i	$-0.538544\pi$
$941$	−7.41082	−0.241586	−0.120793	+	0.992678i	$0.538544\pi$
$942$	44.2913	1.44309
$943$	13.2933	0.432888
$944$	−219.929	−7.15809
$945$	−2.53407	−0.0824333
$946$	76.3675	2.48292
$947$	59.6320	1.93778	0.968890	−	0.247493i	$-0.0796068\pi$
$947$	59.6320	1.93778	0.968890	+	0.247493i	$0.0796068\pi$
$948$	78.2312	2.54083
$949$	2.97930	0.0967123
$950$	0	0
$951$	−6.81930	−0.221131
$952$	−63.3831	−2.05426
$953$	−25.7986	−0.835699	−0.417849	−	0.908516i	$-0.637216\pi$
$953$	−25.7986	−0.835699	−0.417849	+	0.908516i	$0.637216\pi$
$954$	29.8273	0.965695
$955$	29.6860	0.960618
$956$	−32.1176	−1.03876
$957$	14.5865	0.471515
$958$	−92.5275	−2.98943
$959$	−16.9793	−0.548290
$960$	83.2342	2.68637
$961$	−18.8223	−0.607172
$962$	3.28931	0.106052
$963$	16.5341	0.532803
$964$	71.8284	2.31344
$965$	45.1630	1.45385
$966$	−4.33268	−0.139402
$967$	55.5845	1.78748	0.893739	−	0.448587i	$-0.148073\pi$
$967$	55.5845	1.78748	0.893739	+	0.448587i	$0.148073\pi$
$968$	−49.8240	−1.60140
$969$	0	0
$970$	−34.6340	−1.11203
$971$	48.4877	1.55604	0.778022	−	0.628237i	$-0.216223\pi$
$971$	48.4877	1.55604	0.778022	+	0.628237i	$0.216223\pi$
$972$	−5.53407	−0.177505
$973$	1.06814	0.0342430
$974$	−59.0367	−1.89166
$975$	−0.599184	−0.0191892
$976$	106.462	3.40778
$977$	−53.0505	−1.69723	−0.848617	−	0.529007i	$-0.822565\pi$
$977$	−53.0505	−1.69723	−0.848617	+	0.529007i	$0.822565\pi$
$978$	18.2438	0.583374
$979$	23.5244	0.751844
$980$	−14.0237	−0.447971
$981$	−1.77488	−0.0566677
$982$	−47.6320	−1.52000
$983$	−12.1777	−0.388407	−0.194204	−	0.980961i	$-0.562212\pi$
$983$	−12.1777	−0.388407	−0.194204	+	0.980961i	$0.562212\pi$
$984$	81.6921	2.60425
$985$	48.4402	1.54343
$986$	−108.035	−3.44053
$987$	8.02372	0.255398
$988$	0	0
$989$	−18.1363	−0.576700
$990$	−16.8430	−0.535306
$991$	2.04139	0.0648469	0.0324235	−	0.999474i	$-0.489677\pi$
$991$	2.04139	0.0648469	0.0324235	+	0.999474i	$0.489677\pi$
$992$	−81.3180	−2.58185
$993$	−5.91116	−0.187585
$994$	−36.7178	−1.16462
$995$	−40.6654	−1.28918
$996$	−11.6910	−0.370445
$997$	−45.6447	−1.44558	−0.722790	−	0.691067i	$-0.757141\pi$
$997$	−45.6447	−1.44558	−0.722790	+	0.691067i	$0.757141\pi$
$998$	−90.4088	−2.86184
$999$	−2.84302	−0.0899493

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7581.2.a.l.1.3		3
19.18	odd	2		399.2.a.e.1.1	✓	3
57.56	even	2		1197.2.a.m.1.3		3
76.75	even	2		6384.2.a.bu.1.1		3
95.94	odd	2		9975.2.a.x.1.3		3
133.132	even	2		2793.2.a.w.1.1		3
399.398	odd	2		8379.2.a.bq.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
399.2.a.e.1.1	✓	3	19.18	odd	2
1197.2.a.m.1.3		3	57.56	even	2
2793.2.a.w.1.1		3	133.132	even	2
6384.2.a.bu.1.1		3	76.75	even	2
7581.2.a.l.1.3		3	1.1	even	1	trivial
8379.2.a.bq.1.3		3	399.398	odd	2
9975.2.a.x.1.3		3	95.94	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 7581 = 3 \cdot 7 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7581.a (trivial)

\(f(q)\)	\(=\)	\(q+2.74483 q^{2} -1.00000 q^{3} +5.53407 q^{4} -2.53407 q^{5} -2.74483 q^{6} -1.00000 q^{7} +9.70041 q^{8} +1.00000 q^{9} -6.95558 q^{10} +2.42151 q^{11} -5.53407 q^{12} +0.421512 q^{13} -2.74483 q^{14} +2.53407 q^{15} +15.5578 q^{16} +6.53407 q^{17} +2.74483 q^{18} -14.0237 q^{20} +1.00000 q^{21} +6.64663 q^{22} -1.57849 q^{23} -9.70041 q^{24} +1.42151 q^{25} +1.15698 q^{26} -1.00000 q^{27} -5.53407 q^{28} -6.02372 q^{29} +6.95558 q^{30} -3.48965 q^{31} +23.3026 q^{32} -2.42151 q^{33} +17.9349 q^{34} +2.53407 q^{35} +5.53407 q^{36} +2.84302 q^{37} -0.421512 q^{39} -24.5815 q^{40} -8.42151 q^{41} +2.74483 q^{42} +11.4897 q^{43} +13.4008 q^{44} -2.53407 q^{45} -4.33268 q^{46} +8.02372 q^{47} -15.5578 q^{48} +1.00000 q^{49} +3.90180 q^{50} -6.53407 q^{51} +2.33268 q^{52} +10.8667 q^{53} -2.74483 q^{54} -6.13628 q^{55} -9.70041 q^{56} -16.5341 q^{58} -14.1363 q^{59} +14.0237 q^{60} +6.84302 q^{61} -9.57849 q^{62} -1.00000 q^{63} +32.8461 q^{64} -1.06814 q^{65} -6.64663 q^{66} +9.91116 q^{67} +36.1600 q^{68} +1.57849 q^{69} +6.95558 q^{70} +13.3771 q^{71} +9.70041 q^{72} +7.06814 q^{73} +7.80361 q^{74} -1.42151 q^{75} -2.42151 q^{77} -1.15698 q^{78} -14.1363 q^{79} -39.4245 q^{80} +1.00000 q^{81} -23.1156 q^{82} +2.11256 q^{83} +5.53407 q^{84} -16.5578 q^{85} +31.5371 q^{86} +6.02372 q^{87} +23.4897 q^{88} +9.71477 q^{89} -6.95558 q^{90} -0.421512 q^{91} -8.73546 q^{92} +3.48965 q^{93} +22.0237 q^{94} -23.3026 q^{96} +4.97930 q^{97} +2.74483 q^{98} +2.42151 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - q^{2} - 3 q^{3} + 9 q^{4} + q^{6} - 3 q^{7} + 9 q^{8} + 3 q^{9} - 10 q^{10} + 4 q^{11} - 9 q^{12} - 2 q^{13} + q^{14} + 13 q^{16} + 12 q^{17} - q^{18} - 16 q^{20} + 3 q^{21} + 8 q^{22} - 8 q^{23}+ \cdots + 4 q^{99}+O(q^{100}) \) 3 * q - q^2 - 3 * q^3 + 9 * q^4 + q^6 - 3 * q^7 + 9 * q^8 + 3 * q^9 - 10 * q^10 + 4 * q^11 - 9 * q^12 - 2 * q^13 + q^14 + 13 * q^16 + 12 * q^17 - q^18 - 16 * q^20 + 3 * q^21 + 8 * q^22 - 8 * q^23 - 9 * q^24 + q^25 + 10 * q^26 - 3 * q^27 - 9 * q^28 + 8 * q^29 + 10 * q^30 + 8 * q^31 + 27 * q^32 - 4 * q^33 + 6 * q^34 + 9 * q^36 + 2 * q^37 + 2 * q^39 - 14 * q^40 - 22 * q^41 - q^42 + 16 * q^43 + 12 * q^46 - 2 * q^47 - 13 * q^48 + 3 * q^49 + 9 * q^50 - 12 * q^51 - 18 * q^52 + q^54 + 12 * q^55 - 9 * q^56 - 42 * q^58 - 12 * q^59 + 16 * q^60 + 14 * q^61 - 32 * q^62 - 3 * q^63 + 29 * q^64 + 12 * q^65 - 8 * q^66 + 8 * q^67 + 52 * q^68 + 8 * q^69 + 10 * q^70 + 26 * q^71 + 9 * q^72 + 6 * q^73 + 18 * q^74 - q^75 - 4 * q^77 - 10 * q^78 - 12 * q^79 - 52 * q^80 + 3 * q^81 - 2 * q^82 + 2 * q^83 + 9 * q^84 - 16 * q^85 + 24 * q^86 - 8 * q^87 + 52 * q^88 + 2 * q^89 - 10 * q^90 + 2 * q^91 - 36 * q^92 - 8 * q^93 + 40 * q^94 - 27 * q^96 - 22 * q^97 - q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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