LMFDB - Embedded newform 6027.2.a.t.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6027,2,Mod(1,6027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6027, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6027 = 3 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6027.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:	$48.1258372982$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.785.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 6x + 5 $ x^3 - x^2 - 6*x + 5
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 861)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.38849$ of defining polynomial
Character	$\chi$	$=$	6027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.38849 q^{2} +1.00000 q^{3} +3.70488 q^{4} +1.00000 q^{5} -2.38849 q^{6} -4.07210 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.38849 q^{2} +1.00000 q^{3} +3.70488 q^{4} +1.00000 q^{5} -2.38849 q^{6} -4.07210 q^{8} +1.00000 q^{9} -2.38849 q^{10} +3.09337 q^{11} +3.70488 q^{12} +5.38849 q^{13} +1.00000 q^{15} +2.31639 q^{16} +1.02128 q^{17} -2.38849 q^{18} -0.295117 q^{19} +3.70488 q^{20} -7.38849 q^{22} -5.79826 q^{23} -4.07210 q^{24} -4.00000 q^{25} -12.8704 q^{26} +1.00000 q^{27} +7.48186 q^{29} -2.38849 q^{30} -9.87035 q^{31} +2.61151 q^{32} +3.09337 q^{33} -2.43931 q^{34} +3.70488 q^{36} -1.48186 q^{37} +0.704883 q^{38} +5.38849 q^{39} -4.07210 q^{40} +1.00000 q^{41} +5.36721 q^{43} +11.4606 q^{44} +1.00000 q^{45} +13.8491 q^{46} -4.79826 q^{47} +2.31639 q^{48} +9.55396 q^{50} +1.02128 q^{51} +19.9637 q^{52} +5.68361 q^{53} -2.38849 q^{54} +3.09337 q^{55} -0.295117 q^{57} -17.8704 q^{58} +10.4819 q^{59} +3.70488 q^{60} +9.46059 q^{61} +23.5752 q^{62} -10.8704 q^{64} +5.38849 q^{65} -7.38849 q^{66} -4.31639 q^{67} +3.78371 q^{68} -5.79826 q^{69} +12.3672 q^{71} -4.07210 q^{72} +8.70488 q^{73} +3.53941 q^{74} -4.00000 q^{75} -1.09337 q^{76} -12.8704 q^{78} -3.90663 q^{79} +2.31639 q^{80} +1.00000 q^{81} -2.38849 q^{82} +11.1229 q^{83} +1.02128 q^{85} -12.8195 q^{86} +7.48186 q^{87} -12.5965 q^{88} -10.8704 q^{89} -2.38849 q^{90} -21.4819 q^{92} -9.87035 q^{93} +11.4606 q^{94} -0.295117 q^{95} +2.61151 q^{96} -11.3309 q^{97} +3.09337 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + q^{2} + 3 q^{3} + 7 q^{4} + 3 q^{5} + q^{6} + 3 q^{9}+O(q^{10}) $ 3 * q + q^2 + 3 * q^3 + 7 * q^4 + 3 * q^5 + q^6 + 3 * q^9	$ 3 q + q^{2} + 3 q^{3} + 7 q^{4} + 3 q^{5} + q^{6} + 3 q^{9} + q^{10} - 3 q^{11} + 7 q^{12} + 8 q^{13} + 3 q^{15} + 11 q^{16} + 3 q^{17} + q^{18} - 5 q^{19} + 7 q^{20} - 14 q^{22} - q^{23} - 12 q^{25} - 10 q^{26} + 3 q^{27} + 2 q^{29} + q^{30} - q^{31} + 16 q^{32} - 3 q^{33} + 13 q^{34} + 7 q^{36} + 16 q^{37} - 2 q^{38} + 8 q^{39} + 3 q^{41} + 8 q^{43} + 14 q^{44} + 3 q^{45} + 13 q^{46} + 2 q^{47} + 11 q^{48} - 4 q^{50} + 3 q^{51} + 19 q^{52} + 13 q^{53} + q^{54} - 3 q^{55} - 5 q^{57} - 25 q^{58} + 11 q^{59} + 7 q^{60} + 8 q^{61} + 38 q^{62} - 4 q^{64} + 8 q^{65} - 14 q^{66} - 17 q^{67} + 48 q^{68} - q^{69} + 29 q^{71} + 22 q^{73} + 31 q^{74} - 12 q^{75} + 9 q^{76} - 10 q^{78} - 24 q^{79} + 11 q^{80} + 3 q^{81} + q^{82} + 9 q^{83} + 3 q^{85} - 22 q^{86} + 2 q^{87} - 5 q^{88} - 4 q^{89} + q^{90} - 44 q^{92} - q^{93} + 14 q^{94} - 5 q^{95} + 16 q^{96} + 15 q^{97} - 3 q^{99}+O(q^{100}) $ 3 * q + q^2 + 3 * q^3 + 7 * q^4 + 3 * q^5 + q^6 + 3 * q^9 + q^10 - 3 * q^11 + 7 * q^12 + 8 * q^13 + 3 * q^15 + 11 * q^16 + 3 * q^17 + q^18 - 5 * q^19 + 7 * q^20 - 14 * q^22 - q^23 - 12 * q^25 - 10 * q^26 + 3 * q^27 + 2 * q^29 + q^30 - q^31 + 16 * q^32 - 3 * q^33 + 13 * q^34 + 7 * q^36 + 16 * q^37 - 2 * q^38 + 8 * q^39 + 3 * q^41 + 8 * q^43 + 14 * q^44 + 3 * q^45 + 13 * q^46 + 2 * q^47 + 11 * q^48 - 4 * q^50 + 3 * q^51 + 19 * q^52 + 13 * q^53 + q^54 - 3 * q^55 - 5 * q^57 - 25 * q^58 + 11 * q^59 + 7 * q^60 + 8 * q^61 + 38 * q^62 - 4 * q^64 + 8 * q^65 - 14 * q^66 - 17 * q^67 + 48 * q^68 - q^69 + 29 * q^71 + 22 * q^73 + 31 * q^74 - 12 * q^75 + 9 * q^76 - 10 * q^78 - 24 * q^79 + 11 * q^80 + 3 * q^81 + q^82 + 9 * q^83 + 3 * q^85 - 22 * q^86 + 2 * q^87 - 5 * q^88 - 4 * q^89 + q^90 - 44 * q^92 - q^93 + 14 * q^94 - 5 * q^95 + 16 * q^96 + 15 * q^97 - 3 * 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 $

$2$	−2.38849	−1.68892	−0.844459	−	0.535621i	$-0.820078\pi$
$2$	−2.38849	−1.68892	−0.844459	+	0.535621i	$0.820078\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.70488	1.85244
$5$	1.00000	0.447214	0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.00000	0.447214	0.223607	+	0.974679i	$0.428217\pi$
$6$	−2.38849	−0.975097
$7$	0	0
$7$	0	0
$8$	−4.07210	−1.43970
$9$	1.00000	0.333333
$10$	−2.38849	−0.755307
$11$	3.09337	0.932687	0.466344	−	0.884604i	$-0.345571\pi$
$11$	3.09337	0.932687	0.466344	+	0.884604i	$0.345571\pi$
$12$	3.70488	1.06951
$13$	5.38849	1.49450	0.747249	−	0.664544i	$-0.231374\pi$
$13$	5.38849	1.49450	0.747249	+	0.664544i	$0.231374\pi$
$14$	0	0
$15$	1.00000	0.258199
$16$	2.31639	0.579098
$17$	1.02128	0.247696	0.123848	−	0.992301i	$-0.460476\pi$
$17$	1.02128	0.247696	0.123848	+	0.992301i	$0.460476\pi$
$18$	−2.38849	−0.562972
$19$	−0.295117	−0.0677044	−0.0338522	−	0.999427i	$-0.510778\pi$
$19$	−0.295117	−0.0677044	−0.0338522	+	0.999427i	$0.510778\pi$
$20$	3.70488	0.828437
$21$	0	0
$22$	−7.38849	−1.57523
$23$	−5.79826	−1.20902	−0.604510	−	0.796598i	$-0.706631\pi$
$23$	−5.79826	−1.20902	−0.604510	+	0.796598i	$0.706631\pi$
$24$	−4.07210	−0.831213
$25$	−4.00000	−0.800000
$26$	−12.8704	−2.52408
$27$	1.00000	0.192450
$28$	0	0
$29$	7.48186	1.38935	0.694674	−	0.719325i	$-0.255549\pi$
$29$	7.48186	1.38935	0.694674	+	0.719325i	$0.255549\pi$
$30$	−2.38849	−0.436077
$31$	−9.87035	−1.77277	−0.886384	−	0.462951i	$-0.846791\pi$
$31$	−9.87035	−1.77277	−0.886384	+	0.462951i	$0.846791\pi$
$32$	2.61151	0.461654
$33$	3.09337	0.538487
$34$	−2.43931	−0.418338
$35$	0	0
$36$	3.70488	0.617481
$37$	−1.48186	−0.243617	−0.121808	−	0.992554i	$-0.538869\pi$
$37$	−1.48186	−0.243617	−0.121808	+	0.992554i	$0.538869\pi$
$38$	0.704883	0.114347
$39$	5.38849	0.862849
$40$	−4.07210	−0.643855
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	5.36721	0.818492	0.409246	−	0.912424i	$-0.365792\pi$
$43$	5.36721	0.818492	0.409246	+	0.912424i	$0.365792\pi$
$44$	11.4606	1.72775
$45$	1.00000	0.149071
$46$	13.8491	2.04193
$47$	−4.79826	−0.699898	−0.349949	−	0.936769i	$-0.613801\pi$
$47$	−4.79826	−0.699898	−0.349949	+	0.936769i	$0.613801\pi$
$48$	2.31639	0.334343
$49$	0	0
$50$	9.55396	1.35113
$51$	1.02128	0.143007
$52$	19.9637	2.76847
$53$	5.68361	0.780703	0.390352	−	0.920666i	$-0.372353\pi$
$53$	5.68361	0.780703	0.390352	+	0.920666i	$0.372353\pi$
$54$	−2.38849	−0.325032
$55$	3.09337	0.417110
$56$	0	0
$57$	−0.295117	−0.0390892
$58$	−17.8704	−2.34649
$59$	10.4819	1.36462	0.682311	−	0.731062i	$-0.260975\pi$
$59$	10.4819	1.36462	0.682311	+	0.731062i	$0.260975\pi$
$60$	3.70488	0.478298
$61$	9.46059	1.21130	0.605652	−	0.795730i	$-0.292912\pi$
$61$	9.46059	1.21130	0.605652	+	0.795730i	$0.292912\pi$
$62$	23.5752	2.99406
$63$	0	0
$64$	−10.8704	−1.35879
$65$	5.38849	0.668360
$66$	−7.38849	−0.909460
$67$	−4.31639	−0.527331	−0.263666	−	0.964614i	$-0.584932\pi$
$67$	−4.31639	−0.527331	−0.263666	+	0.964614i	$0.584932\pi$
$68$	3.78371	0.458842
$69$	−5.79826	−0.698028
$70$	0	0
$71$	12.3672	1.46772	0.733859	−	0.679302i	$-0.237717\pi$
$71$	12.3672	1.46772	0.733859	+	0.679302i	$0.237717\pi$
$72$	−4.07210	−0.479901
$73$	8.70488	1.01883	0.509415	−	0.860521i	$-0.329862\pi$
$73$	8.70488	1.01883	0.509415	+	0.860521i	$0.329862\pi$
$74$	3.53941	0.411449
$75$	−4.00000	−0.461880
$76$	−1.09337	−0.125418
$77$	0	0
$78$	−12.8704	−1.45728
$79$	−3.90663	−0.439530	−0.219765	−	0.975553i	$-0.570529\pi$
$79$	−3.90663	−0.439530	−0.219765	+	0.975553i	$0.570529\pi$
$80$	2.31639	0.258981
$81$	1.00000	0.111111
$82$	−2.38849	−0.263765
$83$	11.1229	1.22090	0.610449	−	0.792055i	$-0.290989\pi$
$83$	11.1229	1.22090	0.610449	+	0.792055i	$0.290989\pi$
$84$	0	0
$85$	1.02128	0.110773
$86$	−12.8195	−1.38237
$87$	7.48186	0.802140
$88$	−12.5965	−1.34279
$89$	−10.8704	−1.15226	−0.576128	−	0.817360i	$-0.695437\pi$
$89$	−10.8704	−1.15226	−0.576128	+	0.817360i	$0.695437\pi$
$90$	−2.38849	−0.251769
$91$	0	0
$92$	−21.4819	−2.23964
$93$	−9.87035	−1.02351
$94$	11.4606	1.18207
$95$	−0.295117	−0.0302783
$96$	2.61151	0.266536
$97$	−11.3309	−1.15048	−0.575241	−	0.817984i	$-0.695092\pi$
$97$	−11.3309	−1.15048	−0.575241	+	0.817984i	$0.695092\pi$
$98$	0	0
$99$	3.09337	0.310896
$100$	−14.8195	−1.48195
$101$	−7.48186	−0.744473	−0.372237	−	0.928138i	$-0.621409\pi$
$101$	−7.48186	−0.744473	−0.372237	+	0.928138i	$0.621409\pi$
$102$	−2.43931	−0.241528
$103$	15.2801	1.50559	0.752797	−	0.658252i	$-0.228704\pi$
$103$	15.2801	1.50559	0.752797	+	0.658252i	$0.228704\pi$
$104$	−21.9424	−2.15163
$105$	0	0
$106$	−13.5752	−1.31854
$107$	1.61151	0.155791	0.0778953	−	0.996962i	$-0.475180\pi$
$107$	1.61151	0.155791	0.0778953	+	0.996962i	$0.475180\pi$
$108$	3.70488	0.356503
$109$	10.2080	0.977751	0.488876	−	0.872353i	$-0.337407\pi$
$109$	10.2080	0.977751	0.488876	+	0.872353i	$0.337407\pi$
$110$	−7.38849	−0.704465
$111$	−1.48186	−0.140652
$112$	0	0
$113$	1.61151	0.151598	0.0757991	−	0.997123i	$-0.475849\pi$
$113$	1.61151	0.151598	0.0757991	+	0.997123i	$0.475849\pi$
$114$	0.704883	0.0660184
$115$	−5.79826	−0.540690
$116$	27.7194	2.57368
$117$	5.38849	0.498166
$118$	−25.0358	−2.30473
$119$	0	0
$120$	−4.07210	−0.371730
$121$	−1.43104	−0.130095
$122$	−22.5965	−2.04579
$123$	1.00000	0.0901670
$124$	−36.5685	−3.28395
$125$	−9.00000	−0.804984
$126$	0	0
$127$	−4.43931	−0.393925	−0.196962	−	0.980411i	$-0.563108\pi$
$127$	−4.43931	−0.393925	−0.196962	+	0.980411i	$0.563108\pi$
$128$	20.7407	1.83324
$129$	5.36721	0.472557
$130$	−12.8704	−1.12880
$131$	16.1442	1.41052	0.705262	−	0.708946i	$-0.250829\pi$
$131$	16.1442	1.41052	0.705262	+	0.708946i	$0.250829\pi$
$132$	11.4606	0.997516
$133$	0	0
$134$	10.3097	0.890619
$135$	1.00000	0.0860663
$136$	−4.15874	−0.356609
$137$	17.3309	1.48068	0.740341	−	0.672232i	$-0.234664\pi$
$137$	17.3309	1.48068	0.740341	+	0.672232i	$0.234664\pi$
$138$	13.8491	1.17891
$139$	−18.6261	−1.57984	−0.789921	−	0.613209i	$-0.789878\pi$
$139$	−18.6261	−1.57984	−0.789921	+	0.613209i	$0.789878\pi$
$140$	0	0
$141$	−4.79826	−0.404086
$142$	−29.5390	−2.47885
$143$	16.6686	1.39390
$144$	2.31639	0.193033
$145$	7.48186	0.621335
$146$	−20.7915	−1.72072
$147$	0	0
$148$	−5.49013	−0.451286
$149$	20.6178	1.68908	0.844538	−	0.535496i	$-0.179875\pi$
$149$	20.6178	1.68908	0.844538	+	0.535496i	$0.179875\pi$
$150$	9.55396	0.780077
$151$	−20.5965	−1.67612	−0.838060	−	0.545578i	$-0.816310\pi$
$151$	−20.5965	−1.67612	−0.838060	+	0.545578i	$0.816310\pi$
$152$	1.20174	0.0974743
$153$	1.02128	0.0825653
$154$	0	0
$155$	−9.87035	−0.792806
$156$	19.9637	1.59838
$157$	21.0145	1.67714	0.838572	−	0.544791i	$-0.183391\pi$
$157$	21.0145	1.67714	0.838572	+	0.544791i	$0.183391\pi$
$158$	9.33094	0.742330
$159$	5.68361	0.450739
$160$	2.61151	0.206458
$161$	0	0
$162$	−2.38849	−0.187657
$163$	−12.3885	−0.970341	−0.485171	−	0.874419i	$-0.661243\pi$
$163$	−12.3885	−0.970341	−0.485171	+	0.874419i	$0.661243\pi$
$164$	3.70488	0.289303
$165$	3.09337	0.240819
$166$	−26.5670	−2.06200
$167$	3.23757	0.250530	0.125265	−	0.992123i	$-0.460022\pi$
$167$	3.23757	0.250530	0.125265	+	0.992123i	$0.460022\pi$
$168$	0	0
$169$	16.0358	1.23352
$170$	−2.43931	−0.187086
$171$	−0.295117	−0.0225681
$172$	19.8849	1.51621
$173$	−16.4819	−1.25309	−0.626546	−	0.779384i	$-0.715532\pi$
$173$	−16.4819	−1.25309	−0.626546	+	0.779384i	$0.715532\pi$
$174$	−17.8704	−1.35475
$175$	0	0
$176$	7.16547	0.540118
$177$	10.4819	0.787865
$178$	25.9637	1.94606
$179$	1.68361	0.125839	0.0629193	−	0.998019i	$-0.479959\pi$
$179$	1.68361	0.125839	0.0629193	+	0.998019i	$0.479959\pi$
$180$	3.70488	0.276146
$181$	10.5965	0.787633	0.393816	−	0.919189i	$-0.371155\pi$
$181$	10.5965	0.787633	0.393816	+	0.919189i	$0.371155\pi$
$182$	0	0
$183$	9.46059	0.699347
$184$	23.6111	1.74063
$185$	−1.48186	−0.108949
$186$	23.5752	1.72862
$187$	3.15919	0.231023
$188$	−17.7770	−1.29652
$189$	0	0
$190$	0.704883	0.0511376
$191$	−11.9850	−0.867204	−0.433602	−	0.901104i	$-0.642758\pi$
$191$	−11.9850	−0.867204	−0.433602	+	0.901104i	$0.642758\pi$
$192$	−10.8704	−0.784500
$193$	20.2226	1.45565	0.727826	−	0.685762i	$-0.240531\pi$
$193$	20.2226	1.45565	0.727826	+	0.685762i	$0.240531\pi$
$194$	27.0638	1.94307
$195$	5.38849	0.385878
$196$	0	0
$197$	−4.11465	−0.293157	−0.146578	−	0.989199i	$-0.546826\pi$
$197$	−4.11465	−0.293157	−0.146578	+	0.989199i	$0.546826\pi$
$198$	−7.38849	−0.525077
$199$	−3.45232	−0.244728	−0.122364	−	0.992485i	$-0.539048\pi$
$199$	−3.45232	−0.244728	−0.122364	+	0.992485i	$0.539048\pi$
$200$	16.2884	1.15176
$201$	−4.31639	−0.304455
$202$	17.8704	1.25735
$203$	0	0
$204$	3.78371	0.264913
$205$	1.00000	0.0698430
$206$	−36.4964	−2.54283
$207$	−5.79826	−0.403007
$208$	12.4819	0.865461
$209$	−0.912906	−0.0631470
$210$	0	0
$211$	−5.66233	−0.389811	−0.194905	−	0.980822i	$-0.562440\pi$
$211$	−5.66233	−0.389811	−0.194905	+	0.980822i	$0.562440\pi$
$212$	21.0571	1.44621
$213$	12.3672	0.847387
$214$	−3.84908	−0.263117
$215$	5.36721	0.366041
$216$	−4.07210	−0.277071
$217$	0	0
$218$	−24.3818	−1.65134
$219$	8.70488	0.588222
$220$	11.4606	0.772673
$221$	5.50314	0.370181
$222$	3.53941	0.237550
$223$	0.358947	0.0240369	0.0120184	−	0.999928i	$-0.496174\pi$
$223$	0.358947	0.0240369	0.0120184	+	0.999928i	$0.496174\pi$
$224$	0	0
$225$	−4.00000	−0.266667
$226$	−3.84908	−0.256037
$227$	−7.64733	−0.507571	−0.253786	−	0.967260i	$-0.581676\pi$
$227$	−7.64733	−0.507571	−0.253786	+	0.967260i	$0.581676\pi$
$228$	−1.09337	−0.0724104
$229$	−2.59651	−0.171582	−0.0857912	−	0.996313i	$-0.527342\pi$
$229$	−2.59651	−0.171582	−0.0857912	+	0.996313i	$0.527342\pi$
$230$	13.8491	0.913181
$231$	0	0
$232$	−30.4669	−2.00025
$233$	23.1442	1.51623	0.758113	−	0.652123i	$-0.226121\pi$
$233$	23.1442	1.51623	0.758113	+	0.652123i	$0.226121\pi$
$234$	−12.8704	−0.841361
$235$	−4.79826	−0.313004
$236$	38.8341	2.52788
$237$	−3.90663	−0.253763
$238$	0	0
$239$	7.89163	0.510467	0.255234	−	0.966879i	$-0.417848\pi$
$239$	7.89163	0.510467	0.255234	+	0.966879i	$0.417848\pi$
$240$	2.31639	0.149523
$241$	8.93617	0.575629	0.287815	−	0.957686i	$-0.407071\pi$
$241$	8.93617	0.575629	0.287815	+	0.957686i	$0.407071\pi$
$242$	3.41803	0.219719
$243$	1.00000	0.0641500
$244$	35.0504	2.24387
$245$	0	0
$246$	−2.38849	−0.152285
$247$	−1.59023	−0.101184
$248$	40.1930	2.55226
$249$	11.1229	0.704886
$250$	21.4964	1.35955
$251$	−2.48186	−0.156654	−0.0783269	−	0.996928i	$-0.524958\pi$
$251$	−2.48186	−0.156654	−0.0783269	+	0.996928i	$0.524958\pi$
$252$	0	0
$253$	−17.9362	−1.12764
$254$	10.6032	0.665307
$255$	1.02128	0.0639548
$256$	−27.7983	−1.73739
$257$	9.15720	0.571211	0.285605	−	0.958347i	$-0.407805\pi$
$257$	9.15720	0.571211	0.285605	+	0.958347i	$0.407805\pi$
$258$	−12.8195	−0.798109
$259$	0	0
$260$	19.9637	1.23810
$261$	7.48186	0.463116
$262$	−38.5602	−2.38226
$263$	5.33094	0.328720	0.164360	−	0.986400i	$-0.447444\pi$
$263$	5.33094	0.328720	0.164360	+	0.986400i	$0.447444\pi$
$264$	−12.5965	−0.775262
$265$	5.68361	0.349141
$266$	0	0
$267$	−10.8704	−0.665255
$268$	−15.9917	−0.976851
$269$	10.3885	0.633397	0.316699	−	0.948526i	$-0.397426\pi$
$269$	10.3885	0.633397	0.316699	+	0.948526i	$0.397426\pi$
$270$	−2.38849	−0.145359
$271$	1.53941	0.0935127	0.0467564	−	0.998906i	$-0.485112\pi$
$271$	1.53941	0.0935127	0.0467564	+	0.998906i	$0.485112\pi$
$272$	2.36568	0.143440
$273$	0	0
$274$	−41.3948	−2.50075
$275$	−12.3735	−0.746150
$276$	−21.4819	−1.29306
$277$	1.64778	0.0990058	0.0495029	−	0.998774i	$-0.484236\pi$
$277$	1.64778	0.0990058	0.0495029	+	0.998774i	$0.484236\pi$
$278$	44.4881	2.66822
$279$	−9.87035	−0.590923
$280$	0	0
$281$	6.55396	0.390976	0.195488	−	0.980706i	$-0.437371\pi$
$281$	6.55396	0.390976	0.195488	+	0.980706i	$0.437371\pi$
$282$	11.4606	0.682468
$283$	−15.5114	−0.922057	−0.461029	−	0.887385i	$-0.652519\pi$
$283$	−15.5114	−0.922057	−0.461029	+	0.887385i	$0.652519\pi$
$284$	45.8191	2.71886
$285$	−0.295117	−0.0174812
$286$	−39.8128	−2.35418
$287$	0	0
$288$	2.61151	0.153885
$289$	−15.9570	−0.938647
$290$	−17.8704	−1.04938
$291$	−11.3309	−0.664231
$292$	32.2506	1.88732
$293$	11.6473	0.680444	0.340222	−	0.940345i	$-0.389498\pi$
$293$	11.6473	0.680444	0.340222	+	0.940345i	$0.389498\pi$
$294$	0	0
$295$	10.4819	0.610278
$296$	6.03429	0.350736
$297$	3.09337	0.179496
$298$	−49.2454	−2.85271
$299$	−31.2438	−1.80688
$300$	−14.8195	−0.855606
$301$	0	0
$302$	49.1946	2.83083
$303$	−7.48186	−0.429822
$304$	−0.683606	−0.0392075
$305$	9.46059	0.541712
$306$	−2.43931	−0.139446
$307$	−20.4819	−1.16896	−0.584481	−	0.811408i	$-0.698702\pi$
$307$	−20.4819	−1.16896	−0.584481	+	0.811408i	$0.698702\pi$
$308$	0	0
$309$	15.2801	0.869256
$310$	23.5752	1.33898
$311$	−16.0426	−0.909690	−0.454845	−	0.890571i	$-0.650305\pi$
$311$	−16.0426	−0.909690	−0.454845	+	0.890571i	$0.650305\pi$
$312$	−21.9424	−1.24225
$313$	−3.51814	−0.198857	−0.0994284	−	0.995045i	$-0.531701\pi$
$313$	−3.51814	−0.198857	−0.0994284	+	0.995045i	$0.531701\pi$
$314$	−50.1930	−2.83256
$315$	0	0
$316$	−14.4736	−0.814203
$317$	−8.46732	−0.475572	−0.237786	−	0.971318i	$-0.576422\pi$
$317$	−8.46732	−0.475572	−0.237786	+	0.971318i	$0.576422\pi$
$318$	−13.5752	−0.761261
$319$	23.1442	1.29583
$320$	−10.8704	−0.607671
$321$	1.61151	0.0899457
$322$	0	0
$323$	−0.301396	−0.0167701
$324$	3.70488	0.205827
$325$	−21.5540	−1.19560
$326$	29.5898	1.63883
$327$	10.2080	0.564505
$328$	−4.07210	−0.224844
$329$	0	0
$330$	−7.38849	−0.406723
$331$	19.9720	1.09776	0.548880	−	0.835901i	$-0.315054\pi$
$331$	19.9720	1.09776	0.548880	+	0.835901i	$0.315054\pi$
$332$	41.2091	2.26164
$333$	−1.48186	−0.0812056
$334$	−7.73289	−0.423125
$335$	−4.31639	−0.235830
$336$	0	0
$337$	−26.4373	−1.44013	−0.720066	−	0.693905i	$-0.755889\pi$
$337$	−26.4373	−1.44013	−0.720066	+	0.693905i	$0.755889\pi$
$338$	−38.3014	−2.08332
$339$	1.61151	0.0875252
$340$	3.78371	0.205201
$341$	−30.5327	−1.65344
$342$	0.704883	0.0381157
$343$	0	0
$344$	−21.8558	−1.17839
$345$	−5.79826	−0.312168
$346$	39.3668	2.11637
$347$	−28.3605	−1.52247	−0.761235	−	0.648476i	$-0.775407\pi$
$347$	−28.3605	−1.52247	−0.761235	+	0.648476i	$0.775407\pi$
$348$	27.7194	1.48592
$349$	22.7131	1.21581	0.607903	−	0.794011i	$-0.292011\pi$
$349$	22.7131	1.21581	0.607903	+	0.794011i	$0.292011\pi$
$350$	0	0
$351$	5.38849	0.287616
$352$	8.07838	0.430579
$353$	18.3097	0.974525	0.487262	−	0.873256i	$-0.337995\pi$
$353$	18.3097	0.974525	0.487262	+	0.873256i	$0.337995\pi$
$354$	−25.0358	−1.33064
$355$	12.3672	0.656384
$356$	−40.2734	−2.13449
$357$	0	0
$358$	−4.02128	−0.212531
$359$	22.8916	1.20817	0.604087	−	0.796918i	$-0.293538\pi$
$359$	22.8916	1.20817	0.604087	+	0.796918i	$0.293538\pi$
$360$	−4.07210	−0.214618
$361$	−18.9129	−0.995416
$362$	−25.3097	−1.33025
$363$	−1.43104	−0.0751103
$364$	0	0
$365$	8.70488	0.455634
$366$	−22.5965	−1.18114
$367$	8.69815	0.454040	0.227020	−	0.973890i	$-0.427102\pi$
$367$	8.69815	0.454040	0.227020	+	0.973890i	$0.427102\pi$
$368$	−13.4310	−0.700142
$369$	1.00000	0.0520579
$370$	3.53941	0.184005
$371$	0	0
$372$	−36.5685	−1.89599
$373$	−12.2588	−0.634739	−0.317369	−	0.948302i	$-0.602800\pi$
$373$	−12.2588	−0.634739	−0.317369	+	0.948302i	$0.602800\pi$
$374$	−7.54569	−0.390179
$375$	−9.00000	−0.464758
$376$	19.5390	1.00764
$377$	40.3159	2.07638
$378$	0	0
$379$	−2.26557	−0.116375	−0.0581874	−	0.998306i	$-0.518532\pi$
$379$	−2.26557	−0.116375	−0.0581874	+	0.998306i	$0.518532\pi$
$380$	−1.09337	−0.0560889
$381$	−4.43931	−0.227433
$382$	28.6261	1.46464
$383$	−13.0784	−0.668274	−0.334137	−	0.942525i	$-0.608445\pi$
$383$	−13.0784	−0.668274	−0.334137	+	0.942525i	$0.608445\pi$
$384$	20.7407	1.05842
$385$	0	0
$386$	−48.3014	−2.45848
$387$	5.36721	0.272831
$388$	−41.9798	−2.13120
$389$	−6.51141	−0.330141	−0.165071	−	0.986282i	$-0.552785\pi$
$389$	−6.51141	−0.330141	−0.165071	+	0.986282i	$0.552785\pi$
$390$	−12.8704	−0.651716
$391$	−5.92162	−0.299469
$392$	0	0
$393$	16.1442	0.814367
$394$	9.82780	0.495117
$395$	−3.90663	−0.196564
$396$	11.4606	0.575916
$397$	−25.4601	−1.27781	−0.638904	−	0.769287i	$-0.720612\pi$
$397$	−25.4601	−1.27781	−0.638904	+	0.769287i	$0.720612\pi$
$398$	8.24583	0.413326
$399$	0	0
$400$	−9.26557	−0.463279
$401$	−36.0504	−1.80027	−0.900135	−	0.435612i	$-0.856532\pi$
$401$	−36.0504	−1.80027	−0.900135	+	0.435612i	$0.856532\pi$
$402$	10.3097	0.514199
$403$	−53.1863	−2.64940
$404$	−27.7194	−1.37909
$405$	1.00000	0.0496904
$406$	0	0
$407$	−4.58395	−0.227218
$408$	−4.15874	−0.205888
$409$	−3.25058	−0.160731	−0.0803653	−	0.996765i	$-0.525609\pi$
$409$	−3.25058	−0.160731	−0.0803653	+	0.996765i	$0.525609\pi$
$410$	−2.38849	−0.117959
$411$	17.3309	0.854872
$412$	56.6111	2.78903
$413$	0	0
$414$	13.8491	0.680645
$415$	11.1229	0.546002
$416$	14.0721	0.689941
$417$	−18.6261	−0.912122
$418$	2.18047	0.106650
$419$	22.2163	1.08534	0.542668	−	0.839947i	$-0.317414\pi$
$419$	22.2163	1.08534	0.542668	+	0.839947i	$0.317414\pi$
$420$	0	0
$421$	8.07838	0.393716	0.196858	−	0.980432i	$-0.436926\pi$
$421$	8.07838	0.393716	0.196858	+	0.980432i	$0.436926\pi$
$422$	13.5244	0.658358
$423$	−4.79826	−0.233299
$424$	−23.1442	−1.12398
$425$	−4.08511	−0.198157
$426$	−29.5390	−1.43117
$427$	0	0
$428$	5.97046	0.288593
$429$	16.6686	0.804768
$430$	−12.8195	−0.618213
$431$	−28.0784	−1.35249	−0.676244	−	0.736678i	$-0.736393\pi$
$431$	−28.0784	−1.35249	−0.676244	+	0.736678i	$0.736393\pi$
$432$	2.31639	0.111448
$433$	−0.358947	−0.0172499	−0.00862495	−	0.999963i	$-0.502745\pi$
$433$	−0.358947	−0.0172499	−0.00862495	+	0.999963i	$0.502745\pi$
$434$	0	0
$435$	7.48186	0.358728
$436$	37.8195	1.81123
$437$	1.71116	0.0818560
$438$	−20.7915	−0.993457
$439$	−12.7770	−0.609812	−0.304906	−	0.952382i	$-0.598625\pi$
$439$	−12.7770	−0.609812	−0.304906	+	0.952382i	$0.598625\pi$
$440$	−12.5965	−0.600515
$441$	0	0
$442$	−13.1442	−0.625205
$443$	7.74744	0.368092	0.184046	−	0.982918i	$-0.441080\pi$
$443$	7.74744	0.368092	0.184046	+	0.982918i	$0.441080\pi$
$444$	−5.49013	−0.260550
$445$	−10.8704	−0.515304
$446$	−0.857342	−0.0405963
$447$	20.6178	0.975188
$448$	0	0
$449$	−0.821520	−0.0387699	−0.0193850	−	0.999812i	$-0.506171\pi$
$449$	−0.821520	−0.0387699	−0.0193850	+	0.999812i	$0.506171\pi$
$450$	9.55396	0.450378
$451$	3.09337	0.145661
$452$	5.97046	0.280827
$453$	−20.5965	−0.967709
$454$	18.2656	0.857246
$455$	0	0
$456$	1.20174	0.0562768
$457$	38.0571	1.78024	0.890118	−	0.455730i	$-0.150622\pi$
$457$	38.0571	1.78024	0.890118	+	0.455730i	$0.150622\pi$
$458$	6.20174	0.289788
$459$	1.02128	0.0476691
$460$	−21.4819	−1.00160
$461$	16.4393	0.765655	0.382827	−	0.923820i	$-0.374950\pi$
$461$	16.4393	0.765655	0.382827	+	0.923820i	$0.374950\pi$
$462$	0	0
$463$	40.5898	1.88637	0.943184	−	0.332272i	$-0.107815\pi$
$463$	40.5898	1.88637	0.943184	+	0.332272i	$0.107815\pi$
$464$	17.3309	0.804569
$465$	−9.87035	−0.457727
$466$	−55.2797	−2.56078
$467$	−6.94245	−0.321258	−0.160629	−	0.987015i	$-0.551352\pi$
$467$	−6.94245	−0.321258	−0.160629	+	0.987015i	$0.551352\pi$
$468$	19.9637	0.922824
$469$	0	0
$470$	11.4606	0.528637
$471$	21.0145	0.968299
$472$	−42.6832	−1.96465
$473$	16.6028	0.763397
$474$	9.33094	0.428584
$475$	1.18047	0.0541635
$476$	0	0
$477$	5.68361	0.260234
$478$	−18.8491	−0.862137
$479$	20.8979	0.954850	0.477425	−	0.878673i	$-0.341570\pi$
$479$	20.8979	0.954850	0.477425	+	0.878673i	$0.341570\pi$
$480$	2.61151	0.119199
$481$	−7.98500	−0.364085
$482$	−21.3439	−0.972190
$483$	0	0
$484$	−5.30185	−0.240993
$485$	−11.3309	−0.514511
$486$	−2.38849	−0.108344
$487$	10.0934	0.457374	0.228687	−	0.973500i	$-0.426557\pi$
$487$	10.0934	0.457374	0.228687	+	0.973500i	$0.426557\pi$
$488$	−38.5244	−1.74392
$489$	−12.3885	−0.560227
$490$	0	0
$491$	−25.4669	−1.14930	−0.574652	−	0.818398i	$-0.694862\pi$
$491$	−25.4669	−1.14930	−0.574652	+	0.818398i	$0.694862\pi$
$492$	3.70488	0.167029
$493$	7.64105	0.344136
$494$	3.79826	0.170892
$495$	3.09337	0.139037
$496$	−22.8636	−1.02661
$497$	0	0
$498$	−26.5670	−1.19049
$499$	−24.7344	−1.10726	−0.553632	−	0.832761i	$-0.686759\pi$
$499$	−24.7344	−1.10726	−0.553632	+	0.832761i	$0.686759\pi$
$500$	−33.3439	−1.49119
$501$	3.23757	0.144644
$502$	5.92790	0.264575
$503$	12.1292	0.540814	0.270407	−	0.962746i	$-0.412842\pi$
$503$	12.1292	0.540814	0.270407	+	0.962746i	$0.412842\pi$
$504$	0	0
$505$	−7.48186	−0.332939
$506$	42.8404	1.90449
$507$	16.0358	0.712176
$508$	−16.4471	−0.729723
$509$	27.4180	1.21528	0.607641	−	0.794211i	$-0.292116\pi$
$509$	27.4180	1.21528	0.607641	+	0.794211i	$0.292116\pi$
$510$	−2.43931	−0.108014
$511$	0	0
$512$	24.9144	1.10107
$513$	−0.295117	−0.0130297
$514$	−21.8719	−0.964728
$515$	15.2801	0.673322
$516$	19.8849	0.875384
$517$	−14.8428	−0.652785
$518$	0	0
$519$	−16.4819	−0.723473
$520$	−21.9424	−0.962240
$521$	33.3672	1.46184	0.730922	−	0.682461i	$-0.239090\pi$
$521$	33.3672	1.46184	0.730922	+	0.682461i	$0.239090\pi$
$522$	−17.8704	−0.782164
$523$	8.97674	0.392525	0.196263	−	0.980551i	$-0.437119\pi$
$523$	8.97674	0.392525	0.196263	+	0.980551i	$0.437119\pi$
$524$	59.8123	2.61291
$525$	0	0
$526$	−12.7329	−0.555180
$527$	−10.0804	−0.439107
$528$	7.16547	0.311837
$529$	10.6198	0.461729
$530$	−13.5752	−0.589671
$531$	10.4819	0.454874
$532$	0	0
$533$	5.38849	0.233401
$534$	25.9637	1.12356
$535$	1.61151	0.0696717
$536$	17.5768	0.759201
$537$	1.68361	0.0726530
$538$	−24.8128	−1.06976
$539$	0	0
$540$	3.70488	0.159433
$541$	−41.4113	−1.78041	−0.890205	−	0.455559i	$-0.849439\pi$
$541$	−41.4113	−1.78041	−0.890205	+	0.455559i	$0.849439\pi$
$542$	−3.67687	−0.157935
$543$	10.5965	0.454740
$544$	2.66707	0.114350
$545$	10.2080	0.437264
$546$	0	0
$547$	33.9487	1.45154	0.725771	−	0.687936i	$-0.241483\pi$
$547$	33.9487	1.45154	0.725771	+	0.687936i	$0.241483\pi$
$548$	64.2091	2.74288
$549$	9.46059	0.403768
$550$	29.5540	1.26019
$551$	−2.20802	−0.0940649
$552$	23.6111	1.00495
$553$	0	0
$554$	−3.93572	−0.167213
$555$	−1.48186	−0.0629016
$556$	−69.0074	−2.92656
$557$	−30.2356	−1.28112	−0.640561	−	0.767907i	$-0.721298\pi$
$557$	−30.2356	−1.28112	−0.640561	+	0.767907i	$0.721298\pi$
$558$	23.5752	0.998019
$559$	28.9212	1.22324
$560$	0	0
$561$	3.15919	0.133381
$562$	−15.6541	−0.660327
$563$	32.6406	1.37564	0.687819	−	0.725883i	$-0.258568\pi$
$563$	32.6406	1.37564	0.687819	+	0.725883i	$0.258568\pi$
$564$	−17.7770	−0.748546
$565$	1.61151	0.0677967
$566$	37.0488	1.55728
$567$	0	0
$568$	−50.3605	−2.11308
$569$	−6.88336	−0.288566	−0.144283	−	0.989536i	$-0.546088\pi$
$569$	−6.88336	−0.288566	−0.144283	+	0.989536i	$0.546088\pi$
$570$	0.704883	0.0295243
$571$	46.1225	1.93017	0.965083	−	0.261946i	$-0.0843643\pi$
$571$	46.1225	1.93017	0.965083	+	0.261946i	$0.0843643\pi$
$572$	61.7552	2.58212
$573$	−11.9850	−0.500681
$574$	0	0
$575$	23.1930	0.967216
$576$	−10.8704	−0.452931
$577$	33.3159	1.38696	0.693480	−	0.720476i	$-0.256076\pi$
$577$	33.3159	1.38696	0.693480	+	0.720476i	$0.256076\pi$
$578$	38.1131	1.58530
$579$	20.2226	0.840421
$580$	27.7194	1.15099
$581$	0	0
$582$	27.0638	1.12183
$583$	17.5815	0.728152
$584$	−35.4471	−1.46681
$585$	5.38849	0.222787
$586$	−27.8195	−1.14921
$587$	31.9783	1.31988	0.659942	−	0.751316i	$-0.270581\pi$
$587$	31.9783	1.31988	0.659942	+	0.751316i	$0.270581\pi$
$588$	0	0
$589$	2.91291	0.120024
$590$	−25.0358	−1.03071
$591$	−4.11465	−0.169254
$592$	−3.43258	−0.141078
$593$	17.3589	0.712847	0.356423	−	0.934325i	$-0.383996\pi$
$593$	17.3589	0.712847	0.356423	+	0.934325i	$0.383996\pi$
$594$	−7.38849	−0.303153
$595$	0	0
$596$	76.3865	3.12891
$597$	−3.45232	−0.141294
$598$	74.6256	3.05167
$599$	6.88535	0.281328	0.140664	−	0.990057i	$-0.455076\pi$
$599$	6.88535	0.281328	0.140664	+	0.990057i	$0.455076\pi$
$600$	16.2884	0.664971
$601$	1.41175	0.0575866	0.0287933	−	0.999585i	$-0.490834\pi$
$601$	1.41175	0.0575866	0.0287933	+	0.999585i	$0.490834\pi$
$602$	0	0
$603$	−4.31639	−0.175777
$604$	−76.3077	−3.10492
$605$	−1.43104	−0.0581802
$606$	17.8704	0.725933
$607$	42.3159	1.71755	0.858776	−	0.512352i	$-0.171226\pi$
$607$	42.3159	1.71755	0.858776	+	0.512352i	$0.171226\pi$
$608$	−0.770700	−0.0312560
$609$	0	0
$610$	−22.5965	−0.914906
$611$	−25.8554	−1.04600
$612$	3.78371	0.152947
$613$	−28.3885	−1.14660	−0.573300	−	0.819345i	$-0.694337\pi$
$613$	−28.3885	−1.14660	−0.573300	+	0.819345i	$0.694337\pi$
$614$	48.9207	1.97428
$615$	1.00000	0.0403239
$616$	0	0
$617$	−35.4176	−1.42586	−0.712929	−	0.701236i	$-0.752632\pi$
$617$	−35.4176	−1.42586	−0.712929	+	0.701236i	$0.752632\pi$
$618$	−36.4964	−1.46810
$619$	−42.7833	−1.71960	−0.859802	−	0.510627i	$-0.829413\pi$
$619$	−42.7833	−1.71960	−0.859802	+	0.510627i	$0.829413\pi$
$620$	−36.5685	−1.46863
$621$	−5.79826	−0.232676
$622$	38.3175	1.53639
$623$	0	0
$624$	12.4819	0.499674
$625$	11.0000	0.440000
$626$	8.40303	0.335853
$627$	−0.912906	−0.0364580
$628$	77.8564	3.10681
$629$	−1.51339	−0.0603429
$630$	0	0
$631$	17.2931	0.688429	0.344214	−	0.938891i	$-0.388145\pi$
$631$	17.2931	0.688429	0.344214	+	0.938891i	$0.388145\pi$
$632$	15.9082	0.632793
$633$	−5.66233	−0.225057
$634$	20.2241	0.803202
$635$	−4.43931	−0.176169
$636$	21.0571	0.834968
$637$	0	0
$638$	−55.2797	−2.18854
$639$	12.3672	0.489239
$640$	20.7407	0.819848
$641$	5.09383	0.201194	0.100597	−	0.994927i	$-0.467925\pi$
$641$	5.09383	0.201194	0.100597	+	0.994927i	$0.467925\pi$
$642$	−3.84908	−0.151911
$643$	−17.3522	−0.684305	−0.342152	−	0.939645i	$-0.611156\pi$
$643$	−17.3522	−0.684305	−0.342152	+	0.939645i	$0.611156\pi$
$644$	0	0
$645$	5.36721	0.211334
$646$	0.719881	0.0283233
$647$	2.25256	0.0885574	0.0442787	−	0.999019i	$-0.485901\pi$
$647$	2.25256	0.0885574	0.0442787	+	0.999019i	$0.485901\pi$
$648$	−4.07210	−0.159967
$649$	32.4243	1.27277
$650$	51.4814	2.01927
$651$	0	0
$652$	−45.8979	−1.79750
$653$	48.3309	1.89134	0.945668	−	0.325134i	$-0.105409\pi$
$653$	48.3309	1.89134	0.945668	+	0.325134i	$0.105409\pi$
$654$	−24.3818	−0.953402
$655$	16.1442	0.630806
$656$	2.31639	0.0904400
$657$	8.70488	0.339610
$658$	0	0
$659$	−16.7324	−0.651803	−0.325902	−	0.945404i	$-0.605668\pi$
$659$	−16.7324	−0.651803	−0.325902	+	0.945404i	$0.605668\pi$
$660$	11.4606	0.446103
$661$	−0.150924	−0.00587027	−0.00293514	−	0.999996i	$-0.500934\pi$
$661$	−0.150924	−0.00587027	−0.00293514	+	0.999996i	$0.500934\pi$
$662$	−47.7029	−1.85403
$663$	5.50314	0.213724
$664$	−45.2936	−1.75773
$665$	0	0
$666$	3.53941	0.137150
$667$	−43.3818	−1.67975
$668$	11.9948	0.464093
$669$	0.358947	0.0138777
$670$	10.3097	0.398297
$671$	29.2651	1.12977
$672$	0	0
$673$	−42.6682	−1.64474	−0.822368	−	0.568956i	$-0.807348\pi$
$673$	−42.6682	−1.64474	−0.822368	+	0.568956i	$0.807348\pi$
$674$	63.1453	2.43227
$675$	−4.00000	−0.153960
$676$	59.4108	2.28503
$677$	12.3739	0.475569	0.237785	−	0.971318i	$-0.423579\pi$
$677$	12.3739	0.475569	0.237785	+	0.971318i	$0.423579\pi$
$678$	−3.84908	−0.147823
$679$	0	0
$680$	−4.15874	−0.159480
$681$	−7.64733	−0.293046
$682$	72.9270	2.79252
$683$	−2.99372	−0.114552	−0.0572758	−	0.998358i	$-0.518241\pi$
$683$	−2.99372	−0.114552	−0.0572758	+	0.998358i	$0.518241\pi$
$684$	−1.09337	−0.0418062
$685$	17.3309	0.662181
$686$	0	0
$687$	−2.59651	−0.0990631
$688$	12.4326	0.473988
$689$	30.6261	1.16676
$690$	13.8491	0.527225
$691$	25.6623	0.976241	0.488121	−	0.872776i	$-0.337683\pi$
$691$	25.6623	0.976241	0.488121	+	0.872776i	$0.337683\pi$
$692$	−61.0634	−2.32128
$693$	0	0
$694$	67.7387	2.57133
$695$	−18.6261	−0.706527
$696$	−30.4669	−1.15484
$697$	1.02128	0.0386836
$698$	−54.2501	−2.05340
$699$	23.1442	0.875394
$700$	0	0
$701$	32.0488	1.21047	0.605234	−	0.796048i	$-0.293080\pi$
$701$	32.0488	1.21047	0.605234	+	0.796048i	$0.293080\pi$
$702$	−12.8704	−0.485760
$703$	0.437322	0.0164939
$704$	−33.6261	−1.26733
$705$	−4.79826	−0.180713
$706$	−43.7324	−1.64589
$707$	0	0
$708$	38.8341	1.45947
$709$	−42.2013	−1.58490	−0.792451	−	0.609935i	$-0.791196\pi$
$709$	−42.2013	−1.58490	−0.792451	+	0.609935i	$0.791196\pi$
$710$	−29.5390	−1.10858
$711$	−3.90663	−0.146510
$712$	44.2651	1.65891
$713$	57.2308	2.14331
$714$	0	0
$715$	16.6686	0.623371
$716$	6.23757	0.233109
$717$	7.89163	0.294718
$718$	−54.6764	−2.04051
$719$	−20.8045	−0.775878	−0.387939	−	0.921685i	$-0.626813\pi$
$719$	−20.8045	−0.775878	−0.387939	+	0.921685i	$0.626813\pi$
$720$	2.31639	0.0863269
$721$	0	0
$722$	45.1733	1.68118
$723$	8.93617	0.332340
$724$	39.2588	1.45904
$725$	−29.9275	−1.11148
$726$	3.41803	0.126855
$727$	−1.03627	−0.0384333	−0.0192166	−	0.999815i	$-0.506117\pi$
$727$	−1.03627	−0.0384333	−0.0192166	+	0.999815i	$0.506117\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−20.7915	−0.769529
$731$	5.48141	0.202737
$732$	35.0504	1.29550
$733$	38.0078	1.40385	0.701925	−	0.712251i	$-0.252324\pi$
$733$	38.0078	1.40385	0.701925	+	0.712251i	$0.252324\pi$
$734$	−20.7754	−0.766836
$735$	0	0
$736$	−15.1422	−0.558149
$737$	−13.3522	−0.491835
$738$	−2.38849	−0.0879215
$739$	−0.375479	−0.0138122	−0.00690610	−	0.999976i	$-0.502198\pi$
$739$	−0.375479	−0.0138122	−0.00690610	+	0.999976i	$0.502198\pi$
$740$	−5.49013	−0.201821
$741$	−1.59023	−0.0584187
$742$	0	0
$743$	6.32466	0.232029	0.116015	−	0.993248i	$-0.462988\pi$
$743$	6.32466	0.232029	0.116015	+	0.993248i	$0.462988\pi$
$744$	40.1930	1.47355
$745$	20.6178	0.755377
$746$	29.2801	1.07202
$747$	11.1229	0.406966
$748$	11.7044	0.427956
$749$	0	0
$750$	21.4964	0.784938
$751$	−38.8699	−1.41838	−0.709191	−	0.705016i	$-0.750940\pi$
$751$	−38.8699	−1.41838	−0.709191	+	0.705016i	$0.750940\pi$
$752$	−11.1146	−0.405310
$753$	−2.48186	−0.0904441
$754$	−96.2942	−3.50683
$755$	−20.5965	−0.749584
$756$	0	0
$757$	−34.6261	−1.25851	−0.629253	−	0.777201i	$-0.716639\pi$
$757$	−34.6261	−1.25851	−0.629253	+	0.777201i	$0.716639\pi$
$758$	5.41130	0.196547
$759$	−17.9362	−0.651042
$760$	1.20174	0.0435918
$761$	−48.5327	−1.75931	−0.879654	−	0.475614i	$-0.842226\pi$
$761$	−48.5327	−1.75931	−0.879654	+	0.475614i	$0.842226\pi$
$762$	10.6032	0.384115
$763$	0	0
$764$	−44.4030	−1.60645
$765$	1.02128	0.0369243
$766$	31.2376	1.12866
$767$	56.4814	2.03943
$768$	−27.7983	−1.00308
$769$	−17.1099	−0.616999	−0.308499	−	0.951225i	$-0.599827\pi$
$769$	−17.1099	−0.616999	−0.308499	+	0.951225i	$0.599827\pi$
$770$	0	0
$771$	9.15720	0.329789
$772$	74.9223	2.69651
$773$	−18.0208	−0.648164	−0.324082	−	0.946029i	$-0.605055\pi$
$773$	−18.0208	−0.648164	−0.324082	+	0.946029i	$0.605055\pi$
$774$	−12.8195	−0.460789
$775$	39.4814	1.41821
$776$	46.1407	1.65635
$777$	0	0
$778$	15.5524	0.557581
$779$	−0.295117	−0.0105737
$780$	19.9637	0.714816
$781$	38.2564	1.36892
$782$	14.1437	0.505779
$783$	7.48186	0.267380
$784$	0	0
$785$	21.0145	0.750041
$786$	−38.5602	−1.37540
$787$	−9.89990	−0.352893	−0.176447	−	0.984310i	$-0.556460\pi$
$787$	−9.89990	−0.352893	−0.176447	+	0.984310i	$0.556460\pi$
$788$	−15.2443	−0.543056
$789$	5.33094	0.189786
$790$	9.33094	0.331980
$791$	0	0
$792$	−12.5965	−0.447598
$793$	50.9783	1.81029
$794$	60.8113	2.15811
$795$	5.68361	0.201577
$796$	−12.7904	−0.453345
$797$	−34.2158	−1.21199	−0.605994	−	0.795470i	$-0.707224\pi$
$797$	−34.2158	−1.21199	−0.605994	+	0.795470i	$0.707224\pi$
$798$	0	0
$799$	−4.90035	−0.173362
$800$	−10.4460	−0.369323
$801$	−10.8704	−0.384085
$802$	86.1059	3.04051
$803$	26.9275	0.950249
$804$	−15.9917	−0.563985
$805$	0	0
$806$	127.035	4.47461
$807$	10.3885	0.365692
$808$	30.4669	1.07182
$809$	−36.6686	−1.28920	−0.644600	−	0.764520i	$-0.722976\pi$
$809$	−36.6686	−1.28920	−0.644600	+	0.764520i	$0.722976\pi$
$810$	−2.38849	−0.0839230
$811$	−11.4180	−0.400941	−0.200471	−	0.979700i	$-0.564247\pi$
$811$	−11.4180	−0.400941	−0.200471	+	0.979700i	$0.564247\pi$
$812$	0	0
$813$	1.53941	0.0539896
$814$	10.9487	0.383753
$815$	−12.3885	−0.433950
$816$	2.36568	0.0828153
$817$	−1.58395	−0.0554155
$818$	7.76397	0.271461
$819$	0	0
$820$	3.70488	0.129380
$821$	−38.2584	−1.33523	−0.667614	−	0.744508i	$-0.732684\pi$
$821$	−38.2584	−1.33523	−0.667614	+	0.744508i	$0.732684\pi$
$822$	−41.3948	−1.44381
$823$	−17.0378	−0.593901	−0.296950	−	0.954893i	$-0.595970\pi$
$823$	−17.0378	−0.593901	−0.296950	+	0.954893i	$0.595970\pi$
$824$	−62.2221	−2.16761
$825$	−12.3735	−0.430790
$826$	0	0
$827$	−28.9555	−1.00688	−0.503440	−	0.864030i	$-0.667933\pi$
$827$	−28.9555	−1.00688	−0.503440	+	0.864030i	$0.667933\pi$
$828$	−21.4819	−0.746546
$829$	21.1655	0.735107	0.367554	−	0.930002i	$-0.380195\pi$
$829$	21.1655	0.735107	0.367554	+	0.930002i	$0.380195\pi$
$830$	−26.5670	−0.922153
$831$	1.64778	0.0571610
$832$	−58.5748	−2.03072
$833$	0	0
$834$	44.4881	1.54050
$835$	3.23757	0.112041
$836$	−3.38221	−0.116976
$837$	−9.87035	−0.341169
$838$	−53.0634	−1.83304
$839$	40.4010	1.39480	0.697400	−	0.716683i	$-0.254340\pi$
$839$	40.4010	1.39480	0.697400	+	0.716683i	$0.254340\pi$
$840$	0	0
$841$	26.9783	0.930285
$842$	−19.2951	−0.664954
$843$	6.55396	0.225730
$844$	−20.9783	−0.722102
$845$	16.0358	0.551649
$846$	11.4606	0.394023
$847$	0	0
$848$	13.1655	0.452104
$849$	−15.5114	−0.532350
$850$	9.75724	0.334670
$851$	8.59222	0.294538
$852$	45.8191	1.56974
$853$	22.6411	0.775215	0.387607	−	0.921825i	$-0.373302\pi$
$853$	22.6411	0.775215	0.387607	+	0.921825i	$0.373302\pi$
$854$	0	0
$855$	−0.295117	−0.0100928
$856$	−6.56222	−0.224292
$857$	41.5240	1.41843	0.709216	−	0.704991i	$-0.249049\pi$
$857$	41.5240	1.41843	0.709216	+	0.704991i	$0.249049\pi$
$858$	−39.8128	−1.35919
$859$	25.7262	0.877765	0.438883	−	0.898544i	$-0.355374\pi$
$859$	25.7262	0.877765	0.438883	+	0.898544i	$0.355374\pi$
$860$	19.8849	0.678069
$861$	0	0
$862$	67.0649	2.28424
$863$	−25.6048	−0.871597	−0.435798	−	0.900044i	$-0.643534\pi$
$863$	−25.6048	−0.871597	−0.435798	+	0.900044i	$0.643534\pi$
$864$	2.61151	0.0888454
$865$	−16.4819	−0.560400
$866$	0.857342	0.0291337
$867$	−15.9570	−0.541928
$868$	0	0
$869$	−12.0847	−0.409944
$870$	−17.8704	−0.605862
$871$	−23.2588	−0.788096
$872$	−41.5681	−1.40767
$873$	−11.3309	−0.383494
$874$	−4.08709	−0.138248
$875$	0	0
$876$	32.2506	1.08965
$877$	39.7978	1.34388	0.671938	−	0.740607i	$-0.265462\pi$
$877$	39.7978	1.34388	0.671938	+	0.740607i	$0.265462\pi$
$878$	30.5177	1.02992
$879$	11.6473	0.392855
$880$	7.16547	0.241548
$881$	−21.7750	−0.733618	−0.366809	−	0.930296i	$-0.619550\pi$
$881$	−21.7750	−0.733618	−0.366809	+	0.930296i	$0.619550\pi$
$882$	0	0
$883$	−17.5240	−0.589728	−0.294864	−	0.955539i	$-0.595274\pi$
$883$	−17.5240	−0.589728	−0.294864	+	0.955539i	$0.595274\pi$
$884$	20.3885	0.685739
$885$	10.4819	0.352344
$886$	−18.5047	−0.621677
$887$	24.0338	0.806977	0.403489	−	0.914985i	$-0.367798\pi$
$887$	24.0338	0.806977	0.403489	+	0.914985i	$0.367798\pi$
$888$	6.03429	0.202497
$889$	0	0
$890$	25.9637	0.870306
$891$	3.09337	0.103632
$892$	1.32986	0.0445269
$893$	1.41605	0.0473862
$894$	−49.2454	−1.64701
$895$	1.68361	0.0562768
$896$	0	0
$897$	−31.2438	−1.04320
$898$	1.96219	0.0654792
$899$	−73.8486	−2.46299
$900$	−14.8195	−0.493984
$901$	5.80454	0.193377
$902$	−7.38849	−0.246010
$903$	0	0
$904$	−6.56222	−0.218256
$905$	10.5965	0.352240
$906$	49.1946	1.63438
$907$	11.5622	0.383917	0.191959	−	0.981403i	$-0.438516\pi$
$907$	11.5622	0.383917	0.191959	+	0.981403i	$0.438516\pi$
$908$	−28.3325	−0.940246
$909$	−7.48186	−0.248158
$910$	0	0
$911$	19.0213	0.630203	0.315102	−	0.949058i	$-0.397961\pi$
$911$	19.0213	0.630203	0.315102	+	0.949058i	$0.397961\pi$
$912$	−0.683606	−0.0226365
$913$	34.4073	1.13872
$914$	−90.8990	−3.00667
$915$	9.46059	0.312757
$916$	−9.61978	−0.317846
$917$	0	0
$918$	−2.43931	−0.0805092
$919$	33.7107	1.11201	0.556007	−	0.831178i	$-0.312333\pi$
$919$	33.7107	1.11201	0.556007	+	0.831178i	$0.312333\pi$
$920$	23.6111	0.778434
$921$	−20.4819	−0.674900
$922$	−39.2651	−1.29313
$923$	66.6406	2.19350
$924$	0	0
$925$	5.92745	0.194893
$926$	−96.9483	−3.18592
$927$	15.2801	0.501865
$928$	19.5390	0.641398
$929$	45.3963	1.48940	0.744702	−	0.667397i	$-0.232592\pi$
$929$	45.3963	1.48940	0.744702	+	0.667397i	$0.232592\pi$
$930$	23.5752	0.773062
$931$	0	0
$932$	85.7465	2.80872
$933$	−16.0426	−0.525210
$934$	16.5820	0.542579
$935$	3.15919	0.103317
$936$	−21.9424	−0.717211
$937$	−4.21430	−0.137675	−0.0688376	−	0.997628i	$-0.521929\pi$
$937$	−4.21430	−0.137675	−0.0688376	+	0.997628i	$0.521929\pi$
$938$	0	0
$939$	−3.51814	−0.114810
$940$	−17.7770	−0.579821
$941$	−25.2371	−0.822706	−0.411353	−	0.911476i	$-0.634944\pi$
$941$	−25.2371	−0.822706	−0.411353	+	0.911476i	$0.634944\pi$
$942$	−50.1930	−1.63538
$943$	−5.79826	−0.188817
$944$	24.2801	0.790251
$945$	0	0
$946$	−39.6556	−1.28931
$947$	−6.08664	−0.197789	−0.0988946	−	0.995098i	$-0.531531\pi$
$947$	−6.08664	−0.197789	−0.0988946	+	0.995098i	$0.531531\pi$
$948$	−14.4736	−0.470081
$949$	46.9062	1.52264
$950$	−2.81953	−0.0914777
$951$	−8.46732	−0.274572
$952$	0	0
$953$	53.5768	1.73552	0.867761	−	0.496982i	$-0.165558\pi$
$953$	53.5768	1.73552	0.867761	+	0.496982i	$0.165558\pi$
$954$	−13.5752	−0.439514
$955$	−11.9850	−0.387826
$956$	29.2376	0.945610
$957$	23.1442	0.748145
$958$	−49.9144	−1.61266
$959$	0	0
$960$	−10.8704	−0.350839
$961$	66.4239	2.14271
$962$	19.0721	0.614909
$963$	1.61151	0.0519302
$964$	33.1075	1.06632
$965$	20.2226	0.650987
$966$	0	0
$967$	13.0658	0.420168	0.210084	−	0.977683i	$-0.432626\pi$
$967$	13.0658	0.420168	0.210084	+	0.977683i	$0.432626\pi$
$968$	5.82735	0.187298
$969$	−0.301396	−0.00968223
$970$	27.0638	0.868967
$971$	29.7324	0.954159	0.477080	−	0.878860i	$-0.341695\pi$
$971$	29.7324	0.954159	0.477080	+	0.878860i	$0.341695\pi$
$972$	3.70488	0.118834
$973$	0	0
$974$	−24.1079	−0.772468
$975$	−21.5540	−0.690279
$976$	21.9144	0.701464
$977$	27.1225	0.867724	0.433862	−	0.900979i	$-0.357150\pi$
$977$	27.1225	0.867724	0.433862	+	0.900979i	$0.357150\pi$
$978$	29.5898	0.946177
$979$	−33.6261	−1.07469
$980$	0	0
$981$	10.2080	0.325917
$982$	60.8273	1.94108
$983$	−9.07210	−0.289355	−0.144677	−	0.989479i	$-0.546214\pi$
$983$	−9.07210	−0.289355	−0.144677	+	0.989479i	$0.546214\pi$
$984$	−4.07210	−0.129814
$985$	−4.11465	−0.131104
$986$	−18.2506	−0.581217
$987$	0	0
$988$	−5.89163	−0.187438
$989$	−31.1205	−0.989574
$990$	−7.38849	−0.234822
$991$	−57.7485	−1.83444	−0.917221	−	0.398379i	$-0.869573\pi$
$991$	−57.7485	−1.83444	−0.917221	+	0.398379i	$0.869573\pi$
$992$	−25.7765	−0.818406
$993$	19.9720	0.633792
$994$	0	0
$995$	−3.45232	−0.109446
$996$	41.2091	1.30576
$997$	37.8471	1.19863	0.599315	−	0.800514i	$-0.295440\pi$
$997$	37.8471	1.19863	0.599315	+	0.800514i	$0.295440\pi$
$998$	59.0779	1.87008
$999$	−1.48186	−0.0468841

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.t.1.1		3
7.3	odd	6		861.2.i.b.247.3	✓	6
7.5	odd	6		861.2.i.b.739.3	yes	6
7.6	odd	2		6027.2.a.r.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.i.b.247.3	✓	6	7.3	odd	6
861.2.i.b.739.3	yes	6	7.5	odd	6
6027.2.a.r.1.1		3	7.6	odd	2
6027.2.a.t.1.1		3	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:	\( N \)	\(=\)	\( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.38849 q^{2} +1.00000 q^{3} +3.70488 q^{4} +1.00000 q^{5} -2.38849 q^{6} -4.07210 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.38849 q^{2} +1.00000 q^{3} +3.70488 q^{4} +1.00000 q^{5} -2.38849 q^{6} -4.07210 q^{8} +1.00000 q^{9} -2.38849 q^{10} +3.09337 q^{11} +3.70488 q^{12} +5.38849 q^{13} +1.00000 q^{15} +2.31639 q^{16} +1.02128 q^{17} -2.38849 q^{18} -0.295117 q^{19} +3.70488 q^{20} -7.38849 q^{22} -5.79826 q^{23} -4.07210 q^{24} -4.00000 q^{25} -12.8704 q^{26} +1.00000 q^{27} +7.48186 q^{29} -2.38849 q^{30} -9.87035 q^{31} +2.61151 q^{32} +3.09337 q^{33} -2.43931 q^{34} +3.70488 q^{36} -1.48186 q^{37} +0.704883 q^{38} +5.38849 q^{39} -4.07210 q^{40} +1.00000 q^{41} +5.36721 q^{43} +11.4606 q^{44} +1.00000 q^{45} +13.8491 q^{46} -4.79826 q^{47} +2.31639 q^{48} +9.55396 q^{50} +1.02128 q^{51} +19.9637 q^{52} +5.68361 q^{53} -2.38849 q^{54} +3.09337 q^{55} -0.295117 q^{57} -17.8704 q^{58} +10.4819 q^{59} +3.70488 q^{60} +9.46059 q^{61} +23.5752 q^{62} -10.8704 q^{64} +5.38849 q^{65} -7.38849 q^{66} -4.31639 q^{67} +3.78371 q^{68} -5.79826 q^{69} +12.3672 q^{71} -4.07210 q^{72} +8.70488 q^{73} +3.53941 q^{74} -4.00000 q^{75} -1.09337 q^{76} -12.8704 q^{78} -3.90663 q^{79} +2.31639 q^{80} +1.00000 q^{81} -2.38849 q^{82} +11.1229 q^{83} +1.02128 q^{85} -12.8195 q^{86} +7.48186 q^{87} -12.5965 q^{88} -10.8704 q^{89} -2.38849 q^{90} -21.4819 q^{92} -9.87035 q^{93} +11.4606 q^{94} -0.295117 q^{95} +2.61151 q^{96} -11.3309 q^{97} +3.09337 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + q^{2} + 3 q^{3} + 7 q^{4} + 3 q^{5} + q^{6} + 3 q^{9}+O(q^{10}) \) 3 * q + q^2 + 3 * q^3 + 7 * q^4 + 3 * q^5 + q^6 + 3 * q^9	\( 3 q + q^{2} + 3 q^{3} + 7 q^{4} + 3 q^{5} + q^{6} + 3 q^{9} + q^{10} - 3 q^{11} + 7 q^{12} + 8 q^{13} + 3 q^{15} + 11 q^{16} + 3 q^{17} + q^{18} - 5 q^{19} + 7 q^{20} - 14 q^{22} - q^{23} - 12 q^{25} - 10 q^{26} + 3 q^{27} + 2 q^{29} + q^{30} - q^{31} + 16 q^{32} - 3 q^{33} + 13 q^{34} + 7 q^{36} + 16 q^{37} - 2 q^{38} + 8 q^{39} + 3 q^{41} + 8 q^{43} + 14 q^{44} + 3 q^{45} + 13 q^{46} + 2 q^{47} + 11 q^{48} - 4 q^{50} + 3 q^{51} + 19 q^{52} + 13 q^{53} + q^{54} - 3 q^{55} - 5 q^{57} - 25 q^{58} + 11 q^{59} + 7 q^{60} + 8 q^{61} + 38 q^{62} - 4 q^{64} + 8 q^{65} - 14 q^{66} - 17 q^{67} + 48 q^{68} - q^{69} + 29 q^{71} + 22 q^{73} + 31 q^{74} - 12 q^{75} + 9 q^{76} - 10 q^{78} - 24 q^{79} + 11 q^{80} + 3 q^{81} + q^{82} + 9 q^{83} + 3 q^{85} - 22 q^{86} + 2 q^{87} - 5 q^{88} - 4 q^{89} + q^{90} - 44 q^{92} - q^{93} + 14 q^{94} - 5 q^{95} + 16 q^{96} + 15 q^{97} - 3 q^{99}+O(q^{100}) \) 3 * q + q^2 + 3 * q^3 + 7 * q^4 + 3 * q^5 + q^6 + 3 * q^9 + q^10 - 3 * q^11 + 7 * q^12 + 8 * q^13 + 3 * q^15 + 11 * q^16 + 3 * q^17 + q^18 - 5 * q^19 + 7 * q^20 - 14 * q^22 - q^23 - 12 * q^25 - 10 * q^26 + 3 * q^27 + 2 * q^29 + q^30 - q^31 + 16 * q^32 - 3 * q^33 + 13 * q^34 + 7 * q^36 + 16 * q^37 - 2 * q^38 + 8 * q^39 + 3 * q^41 + 8 * q^43 + 14 * q^44 + 3 * q^45 + 13 * q^46 + 2 * q^47 + 11 * q^48 - 4 * q^50 + 3 * q^51 + 19 * q^52 + 13 * q^53 + q^54 - 3 * q^55 - 5 * q^57 - 25 * q^58 + 11 * q^59 + 7 * q^60 + 8 * q^61 + 38 * q^62 - 4 * q^64 + 8 * q^65 - 14 * q^66 - 17 * q^67 + 48 * q^68 - q^69 + 29 * q^71 + 22 * q^73 + 31 * q^74 - 12 * q^75 + 9 * q^76 - 10 * q^78 - 24 * q^79 + 11 * q^80 + 3 * q^81 + q^82 + 9 * q^83 + 3 * q^85 - 22 * q^86 + 2 * q^87 - 5 * q^88 - 4 * q^89 + q^90 - 44 * q^92 - q^93 + 14 * q^94 - 5 * q^95 + 16 * q^96 + 15 * q^97 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more