LMFDB - Embedded newform 6713.2.a.k.1.38

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6713,2,Mod(1,6713)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6713, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6713.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6713 = 7^{2} \cdot 137 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6713.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:	$53.6035748769$
Analytic rank:	$1$
Dimension:	$45$
Twist minimal:	no (minimal twist has level 959)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.38
Character	$\chi$	$=$	6713.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.92886 q^{2} +2.29737 q^{3} +1.72049 q^{4} -1.09188 q^{5} +4.43130 q^{6} -0.539134 q^{8} +2.27792 q^{9} +O(q^{10})$	\(q+1.92886 q^{2} +2.29737 q^{3} +1.72049 q^{4} -1.09188 q^{5} +4.43130 q^{6} -0.539134 q^{8} +2.27792 q^{9} -2.10607 q^{10} -0.0928769 q^{11} +3.95261 q^{12} -5.52150 q^{13} -2.50845 q^{15} -4.48089 q^{16} +1.48098 q^{17} +4.39378 q^{18} +0.762544 q^{19} -1.87856 q^{20} -0.179146 q^{22} -5.36773 q^{23} -1.23859 q^{24} -3.80781 q^{25} -10.6502 q^{26} -1.65889 q^{27} -1.44696 q^{29} -4.83843 q^{30} -7.19415 q^{31} -7.56474 q^{32} -0.213373 q^{33} +2.85660 q^{34} +3.91913 q^{36} +3.36621 q^{37} +1.47084 q^{38} -12.6849 q^{39} +0.588668 q^{40} -5.80988 q^{41} +10.7384 q^{43} -0.159794 q^{44} -2.48720 q^{45} -10.3536 q^{46} +9.80224 q^{47} -10.2943 q^{48} -7.34472 q^{50} +3.40236 q^{51} -9.49968 q^{52} -0.405891 q^{53} -3.19977 q^{54} +0.101410 q^{55} +1.75185 q^{57} -2.79098 q^{58} -10.3079 q^{59} -4.31576 q^{60} -8.76468 q^{61} -13.8765 q^{62} -5.62951 q^{64} +6.02879 q^{65} -0.411566 q^{66} +1.52684 q^{67} +2.54801 q^{68} -12.3317 q^{69} -4.98542 q^{71} -1.22810 q^{72} +10.3229 q^{73} +6.49294 q^{74} -8.74795 q^{75} +1.31195 q^{76} -24.4674 q^{78} +9.66300 q^{79} +4.89258 q^{80} -10.6448 q^{81} -11.2064 q^{82} -11.7043 q^{83} -1.61705 q^{85} +20.7129 q^{86} -3.32420 q^{87} +0.0500732 q^{88} +10.5625 q^{89} -4.79746 q^{90} -9.23512 q^{92} -16.5276 q^{93} +18.9071 q^{94} -0.832603 q^{95} -17.3790 q^{96} -12.5772 q^{97} -0.211566 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 45 q - 11 q^{3} + 44 q^{4} - 4 q^{5} - 10 q^{6} - 3 q^{8} + 44 q^{9}+O(q^{10}) $ 45 * q - 11 * q^3 + 44 * q^4 - 4 * q^5 - 10 * q^6 - 3 * q^8 + 44 * q^9	$ 45 q - 11 q^{3} + 44 q^{4} - 4 q^{5} - 10 q^{6} - 3 q^{8} + 44 q^{9} - 25 q^{10} - 33 q^{12} - 36 q^{13} + 38 q^{16} - 18 q^{17} - 5 q^{18} - 43 q^{19} - 10 q^{20} - q^{23} - 20 q^{24} + 43 q^{25} - 2 q^{26} - 53 q^{27} - 4 q^{29} - 12 q^{30} - 59 q^{31} - 11 q^{32} - 37 q^{33} - 48 q^{34} + 14 q^{36} - 39 q^{38} + 16 q^{39} - 56 q^{40} - 15 q^{41} - q^{43} - 2 q^{44} - 28 q^{45} + 31 q^{46} - 58 q^{47} - 12 q^{48} - 74 q^{50} - 5 q^{51} - 115 q^{52} + 10 q^{53} - 39 q^{54} - 81 q^{55} - 18 q^{57} - 11 q^{58} - 41 q^{59} + 90 q^{60} - 40 q^{61} + 29 q^{62} + 15 q^{64} - 9 q^{65} - 42 q^{66} - 56 q^{68} - 5 q^{69} - 42 q^{71} - 11 q^{72} - 67 q^{73} + 39 q^{74} - 40 q^{75} - 68 q^{76} - 78 q^{78} - 9 q^{79} - 14 q^{80} + 73 q^{81} - 34 q^{82} - 48 q^{83} + 6 q^{85} - 13 q^{86} - 135 q^{87} + 47 q^{88} - 17 q^{89} + 44 q^{90} - 61 q^{92} - q^{93} - 28 q^{94} + 47 q^{95} - 50 q^{96} - 81 q^{97} - 35 q^{99}+O(q^{100}) $ 45 * q - 11 * q^3 + 44 * q^4 - 4 * q^5 - 10 * q^6 - 3 * q^8 + 44 * q^9 - 25 * q^10 - 33 * q^12 - 36 * q^13 + 38 * q^16 - 18 * q^17 - 5 * q^18 - 43 * q^19 - 10 * q^20 - q^23 - 20 * q^24 + 43 * q^25 - 2 * q^26 - 53 * q^27 - 4 * q^29 - 12 * q^30 - 59 * q^31 - 11 * q^32 - 37 * q^33 - 48 * q^34 + 14 * q^36 - 39 * q^38 + 16 * q^39 - 56 * q^40 - 15 * q^41 - q^43 - 2 * q^44 - 28 * q^45 + 31 * q^46 - 58 * q^47 - 12 * q^48 - 74 * q^50 - 5 * q^51 - 115 * q^52 + 10 * q^53 - 39 * q^54 - 81 * q^55 - 18 * q^57 - 11 * q^58 - 41 * q^59 + 90 * q^60 - 40 * q^61 + 29 * q^62 + 15 * q^64 - 9 * q^65 - 42 * q^66 - 56 * q^68 - 5 * q^69 - 42 * q^71 - 11 * q^72 - 67 * q^73 + 39 * q^74 - 40 * q^75 - 68 * q^76 - 78 * q^78 - 9 * q^79 - 14 * q^80 + 73 * q^81 - 34 * q^82 - 48 * q^83 + 6 * q^85 - 13 * q^86 - 135 * q^87 + 47 * q^88 - 17 * q^89 + 44 * q^90 - 61 * q^92 - q^93 - 28 * q^94 + 47 * q^95 - 50 * q^96 - 81 * q^97 - 35 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.92886	1.36391	0.681954	−	0.731395i	$-0.261130\pi$
$2$	1.92886	1.36391	0.681954	+	0.731395i	$0.261130\pi$
$3$	2.29737	1.32639	0.663194	−	0.748447i	$-0.269200\pi$
$3$	2.29737	1.32639	0.663194	+	0.748447i	$0.269200\pi$
$4$	1.72049	0.860245
$5$	−1.09188	−0.488302	−0.244151	−	0.969737i	$-0.578509\pi$
$5$	−1.09188	−0.488302	−0.244151	+	0.969737i	$0.578509\pi$
$6$	4.43130	1.80907
$7$	0	0
$7$	0	0
$8$	−0.539134	−0.190613
$9$	2.27792	0.759306
$10$	−2.10607	−0.665999
$11$	−0.0928769	−0.0280034	−0.0140017	−	0.999902i	$-0.504457\pi$
$11$	−0.0928769	−0.0280034	−0.0140017	+	0.999902i	$0.504457\pi$
$12$	3.95261	1.14102
$13$	−5.52150	−1.53139	−0.765694	−	0.643205i	$-0.777604\pi$
$13$	−5.52150	−1.53139	−0.765694	+	0.643205i	$0.777604\pi$
$14$	0	0
$15$	−2.50845	−0.647678
$16$	−4.48089	−1.12022
$17$	1.48098	0.359190	0.179595	−	0.983741i	$-0.442521\pi$
$17$	1.48098	0.359190	0.179595	+	0.983741i	$0.442521\pi$
$18$	4.39378	1.03562
$19$	0.762544	0.174939	0.0874697	−	0.996167i	$-0.472122\pi$
$19$	0.762544	0.174939	0.0874697	+	0.996167i	$0.472122\pi$
$20$	−1.87856	−0.420059
$21$	0	0
$22$	−0.179146	−0.0381941
$23$	−5.36773	−1.11925	−0.559624	−	0.828746i	$-0.689055\pi$
$23$	−5.36773	−1.11925	−0.559624	+	0.828746i	$0.689055\pi$
$24$	−1.23859	−0.252827
$25$	−3.80781	−0.761561
$26$	−10.6502	−2.08867
$27$	−1.65889	−0.319254
$28$	0	0
$29$	−1.44696	−0.268693	−0.134347	−	0.990934i	$-0.542894\pi$
$29$	−1.44696	−0.268693	−0.134347	+	0.990934i	$0.542894\pi$
$30$	−4.83843	−0.883373
$31$	−7.19415	−1.29211	−0.646054	−	0.763292i	$-0.723582\pi$
$31$	−7.19415	−1.29211	−0.646054	+	0.763292i	$0.723582\pi$
$32$	−7.56474	−1.33727
$33$	−0.213373	−0.0371434
$34$	2.85660	0.489903
$35$	0	0
$36$	3.91913	0.653189
$37$	3.36621	0.553401	0.276701	−	0.960956i	$-0.410759\pi$
$37$	3.36621	0.553401	0.276701	+	0.960956i	$0.410759\pi$
$38$	1.47084	0.238601
$39$	−12.6849	−2.03121
$40$	0.588668	0.0930766
$41$	−5.80988	−0.907351	−0.453676	−	0.891167i	$-0.649888\pi$
$41$	−5.80988	−0.907351	−0.453676	+	0.891167i	$0.649888\pi$
$42$	0	0
$43$	10.7384	1.63759	0.818797	−	0.574084i	$-0.194642\pi$
$43$	10.7384	1.63759	0.818797	+	0.574084i	$0.194642\pi$
$44$	−0.159794	−0.0240898
$45$	−2.48720	−0.370770
$46$	−10.3536	−1.52655
$47$	9.80224	1.42980	0.714902	−	0.699225i	$-0.246471\pi$
$47$	9.80224	1.42980	0.714902	+	0.699225i	$0.246471\pi$
$48$	−10.2943	−1.48585
$49$	0	0
$50$	−7.34472	−1.03870
$51$	3.40236	0.476426
$52$	−9.49968	−1.31737
$53$	−0.405891	−0.0557534	−0.0278767	−	0.999611i	$-0.508875\pi$
$53$	−0.405891	−0.0557534	−0.0278767	+	0.999611i	$0.508875\pi$
$54$	−3.19977	−0.435433
$55$	0.101410	0.0136741
$56$	0	0
$57$	1.75185	0.232038
$58$	−2.79098	−0.366473
$59$	−10.3079	−1.34197	−0.670984	−	0.741472i	$-0.734128\pi$
$59$	−10.3079	−1.34197	−0.670984	+	0.741472i	$0.734128\pi$
$60$	−4.31576	−0.557162
$61$	−8.76468	−1.12220	−0.561101	−	0.827747i	$-0.689622\pi$
$61$	−8.76468	−1.12220	−0.561101	+	0.827747i	$0.689622\pi$
$62$	−13.8765	−1.76232
$63$	0	0
$64$	−5.62951	−0.703688
$65$	6.02879	0.747779
$66$	−0.411566	−0.0506602
$67$	1.52684	0.186533	0.0932666	−	0.995641i	$-0.470269\pi$
$67$	1.52684	0.186533	0.0932666	+	0.995641i	$0.470269\pi$
$68$	2.54801	0.308992
$69$	−12.3317	−1.48456
$70$	0	0
$71$	−4.98542	−0.591660	−0.295830	−	0.955241i	$-0.595596\pi$
$71$	−4.98542	−0.591660	−0.295830	+	0.955241i	$0.595596\pi$
$72$	−1.22810	−0.144733
$73$	10.3229	1.20820	0.604102	−	0.796907i	$-0.293532\pi$
$73$	10.3229	1.20820	0.604102	+	0.796907i	$0.293532\pi$
$74$	6.49294	0.754789
$75$	−8.74795	−1.01013
$76$	1.31195	0.150491
$77$	0	0
$78$	−24.4674	−2.77039
$79$	9.66300	1.08717	0.543586	−	0.839353i	$-0.317066\pi$
$79$	9.66300	1.08717	0.543586	+	0.839353i	$0.317066\pi$
$80$	4.89258	0.547007
$81$	−10.6448	−1.18276
$82$	−11.2064	−1.23754
$83$	−11.7043	−1.28471	−0.642356	−	0.766406i	$-0.722043\pi$
$83$	−11.7043	−1.28471	−0.642356	+	0.766406i	$0.722043\pi$
$84$	0	0
$85$	−1.61705	−0.175393
$86$	20.7129	2.23353
$87$	−3.32420	−0.356392
$88$	0.0500732	0.00533782
$89$	10.5625	1.11963	0.559814	−	0.828619i	$-0.310873\pi$
$89$	10.5625	1.11963	0.559814	+	0.828619i	$0.310873\pi$
$90$	−4.79746	−0.505697
$91$	0	0
$92$	−9.23512	−0.962828
$93$	−16.5276	−1.71384
$94$	18.9071	1.95012
$95$	−0.832603	−0.0854233
$96$	−17.3790	−1.77374
$97$	−12.5772	−1.27703	−0.638513	−	0.769611i	$-0.720450\pi$
$97$	−12.5772	−1.27703	−0.638513	+	0.769611i	$0.720450\pi$
$98$	0	0
$99$	−0.211566	−0.0212632
$100$	−6.55129	−0.655129
$101$	12.9792	1.29148	0.645739	−	0.763558i	$-0.276549\pi$
$101$	12.9792	1.29148	0.645739	+	0.763558i	$0.276549\pi$
$102$	6.56267	0.649801
$103$	−2.12573	−0.209454	−0.104727	−	0.994501i	$-0.533397\pi$
$103$	−2.12573	−0.209454	−0.104727	+	0.994501i	$0.533397\pi$
$104$	2.97683	0.291902
$105$	0	0
$106$	−0.782905	−0.0760424
$107$	2.27186	0.219629	0.109815	−	0.993952i	$-0.464974\pi$
$107$	2.27186	0.219629	0.109815	+	0.993952i	$0.464974\pi$
$108$	−2.85411	−0.274637
$109$	−12.6892	−1.21541	−0.607704	−	0.794164i	$-0.707909\pi$
$109$	−12.6892	−1.21541	−0.607704	+	0.794164i	$0.707909\pi$
$110$	0.195606	0.0186503
$111$	7.73343	0.734025
$112$	0	0
$113$	−6.75715	−0.635659	−0.317830	−	0.948148i	$-0.602954\pi$
$113$	−6.75715	−0.635659	−0.317830	+	0.948148i	$0.602954\pi$
$114$	3.37906	0.316478
$115$	5.86089	0.546531
$116$	−2.48948	−0.231142
$117$	−12.5775	−1.16279
$118$	−19.8824	−1.83032
$119$	0	0
$120$	1.35239	0.123456
$121$	−10.9914	−0.999216
$122$	−16.9058	−1.53058
$123$	−13.3475	−1.20350
$124$	−12.3775	−1.11153
$125$	9.61703	0.860174
$126$	0	0
$127$	16.9966	1.50821	0.754103	−	0.656757i	$-0.228072\pi$
$127$	16.9966	1.50821	0.754103	+	0.656757i	$0.228072\pi$
$128$	4.27096	0.377503
$129$	24.6701	2.17208
$130$	11.6287	1.01990
$131$	−1.70546	−0.149007	−0.0745033	−	0.997221i	$-0.523737\pi$
$131$	−1.70546	−0.149007	−0.0745033	+	0.997221i	$0.523737\pi$
$132$	−0.367106	−0.0319525
$133$	0	0
$134$	2.94506	0.254414
$135$	1.81131	0.155892
$136$	−0.798447	−0.0684663
$137$	−1.00000	−0.0854358
$137$	−1.00000	−0.0854358
$138$	−23.7860	−2.02480
$139$	−12.3348	−1.04622	−0.523112	−	0.852264i	$-0.675229\pi$
$139$	−12.3348	−1.04622	−0.523112	+	0.852264i	$0.675229\pi$
$140$	0	0
$141$	22.5194	1.89647
$142$	−9.61616	−0.806970
$143$	0.512820	0.0428841
$144$	−10.2071	−0.850592
$145$	1.57990	0.131204
$146$	19.9114	1.64788
$147$	0	0
$148$	5.79153	0.476061
$149$	13.4660	1.10318	0.551589	−	0.834116i	$-0.314022\pi$
$149$	13.4660	1.10318	0.551589	+	0.834116i	$0.314022\pi$
$150$	−16.8735	−1.37772
$151$	1.73078	0.140849	0.0704246	−	0.997517i	$-0.477565\pi$
$151$	1.73078	0.140849	0.0704246	+	0.997517i	$0.477565\pi$
$152$	−0.411114	−0.0333457
$153$	3.37355	0.272735
$154$	0	0
$155$	7.85512	0.630938
$156$	−21.8243	−1.74734
$157$	−2.88497	−0.230246	−0.115123	−	0.993351i	$-0.536726\pi$
$157$	−2.88497	−0.230246	−0.115123	+	0.993351i	$0.536726\pi$
$158$	18.6385	1.48280
$159$	−0.932482	−0.0739506
$160$	8.25975	0.652991
$161$	0	0
$162$	−20.5324	−1.61318
$163$	14.7113	1.15227	0.576137	−	0.817353i	$-0.304559\pi$
$163$	14.7113	1.15227	0.576137	+	0.817353i	$0.304559\pi$
$164$	−9.99585	−0.780545
$165$	0.232977	0.0181372
$166$	−22.5759	−1.75223
$167$	1.01831	0.0787989	0.0393994	−	0.999224i	$-0.487456\pi$
$167$	1.01831	0.0787989	0.0393994	+	0.999224i	$0.487456\pi$
$168$	0	0
$169$	17.4869	1.34515
$170$	−3.11905	−0.239220
$171$	1.73701	0.132833
$172$	18.4753	1.40873
$173$	−8.49169	−0.645612	−0.322806	−	0.946465i	$-0.604626\pi$
$173$	−8.49169	−0.645612	−0.322806	+	0.946465i	$0.604626\pi$
$174$	−6.41191	−0.486086
$175$	0	0
$176$	0.416172	0.0313701
$177$	−23.6810	−1.77997
$178$	20.3736	1.52707
$179$	21.8147	1.63051	0.815254	−	0.579104i	$-0.196597\pi$
$179$	21.8147	1.63051	0.815254	+	0.579104i	$0.196597\pi$
$180$	−4.27921	−0.318953
$181$	−5.56506	−0.413648	−0.206824	−	0.978378i	$-0.566313\pi$
$181$	−5.56506	−0.413648	−0.206824	+	0.978378i	$0.566313\pi$
$182$	0	0
$183$	−20.1357	−1.48848
$184$	2.89393	0.213343
$185$	−3.67548	−0.270227
$186$	−31.8794	−2.33751
$187$	−0.137549	−0.0100586
$188$	16.8647	1.22998
$189$	0	0
$190$	−1.60597	−0.116509
$191$	5.06463	0.366464	0.183232	−	0.983070i	$-0.441344\pi$
$191$	5.06463	0.366464	0.183232	+	0.983070i	$0.441344\pi$
$192$	−12.9331	−0.933364
$193$	19.1208	1.37634	0.688171	−	0.725548i	$-0.258414\pi$
$193$	19.1208	1.37634	0.688171	+	0.725548i	$0.258414\pi$
$194$	−24.2597	−1.74175
$195$	13.8504	0.991846
$196$	0	0
$197$	1.14288	0.0814265	0.0407133	−	0.999171i	$-0.487037\pi$
$197$	1.14288	0.0814265	0.0407133	+	0.999171i	$0.487037\pi$
$198$	−0.408081	−0.0290010
$199$	−26.1023	−1.85034	−0.925171	−	0.379551i	$-0.876078\pi$
$199$	−26.1023	−1.85034	−0.925171	+	0.379551i	$0.876078\pi$
$200$	2.05292	0.145163
$201$	3.50772	0.247415
$202$	25.0350	1.76146
$203$	0	0
$204$	5.85373	0.409843
$205$	6.34367	0.443061
$206$	−4.10023	−0.285676
$207$	−12.2272	−0.849852
$208$	24.7412	1.71550
$209$	−0.0708227	−0.00489891
$210$	0	0
$211$	13.6521	0.939851	0.469926	−	0.882706i	$-0.344281\pi$
$211$	13.6521	0.939851	0.469926	+	0.882706i	$0.344281\pi$
$212$	−0.698331	−0.0479616
$213$	−11.4534	−0.784771
$214$	4.38210	0.299554
$215$	−11.7250	−0.799640
$216$	0.894366	0.0608539
$217$	0	0
$218$	−24.4757	−1.65770
$219$	23.7155	1.60255
$220$	0.174475	0.0117631
$221$	−8.17722	−0.550060
$222$	14.9167	1.00114
$223$	−11.6557	−0.780521	−0.390261	−	0.920704i	$-0.627615\pi$
$223$	−11.6557	−0.780521	−0.390261	+	0.920704i	$0.627615\pi$
$224$	0	0
$225$	−8.67387	−0.578258
$226$	−13.0336	−0.866981
$227$	−25.3759	−1.68426	−0.842129	−	0.539276i	$-0.818698\pi$
$227$	−25.3759	−1.68426	−0.842129	+	0.539276i	$0.818698\pi$
$228$	3.01403	0.199609
$229$	−28.0348	−1.85259	−0.926294	−	0.376801i	$-0.877024\pi$
$229$	−28.0348	−1.85259	−0.926294	+	0.376801i	$0.877024\pi$
$230$	11.3048	0.745418
$231$	0	0
$232$	0.780105	0.0512164
$233$	11.2332	0.735913	0.367956	−	0.929843i	$-0.380058\pi$
$233$	11.2332	0.735913	0.367956	+	0.929843i	$0.380058\pi$
$234$	−24.2602	−1.58594
$235$	−10.7028	−0.698175
$236$	−17.7346	−1.15442
$237$	22.1995	1.44201
$238$	0	0
$239$	−11.1649	−0.722197	−0.361099	−	0.932528i	$-0.617598\pi$
$239$	−11.1649	−0.722197	−0.361099	+	0.932528i	$0.617598\pi$
$240$	11.2401	0.725544
$241$	−12.0903	−0.778802	−0.389401	−	0.921068i	$-0.627318\pi$
$241$	−12.0903	−0.778802	−0.389401	+	0.921068i	$0.627318\pi$
$242$	−21.2008	−1.36284
$243$	−19.4785	−1.24955
$244$	−15.0795	−0.965369
$245$	0	0
$246$	−25.7454	−1.64146
$247$	−4.21038	−0.267900
$248$	3.87861	0.246292
$249$	−26.8891	−1.70403
$250$	18.5499	1.17320
$251$	−9.17226	−0.578948	−0.289474	−	0.957186i	$-0.593480\pi$
$251$	−9.17226	−0.578948	−0.289474	+	0.957186i	$0.593480\pi$
$252$	0	0
$253$	0.498538	0.0313428
$254$	32.7840	2.05705
$255$	−3.71496	−0.232640
$256$	19.4971	1.21857
$257$	17.6073	1.09831	0.549156	−	0.835720i	$-0.314949\pi$
$257$	17.6073	1.09831	0.549156	+	0.835720i	$0.314949\pi$
$258$	47.5852	2.96252
$259$	0	0
$260$	10.3725	0.643273
$261$	−3.29605	−0.204020
$262$	−3.28958	−0.203231
$263$	−4.79339	−0.295573	−0.147787	−	0.989019i	$-0.547215\pi$
$263$	−4.79339	−0.295573	−0.147787	+	0.989019i	$0.547215\pi$
$264$	0.115037	0.00708002
$265$	0.443182	0.0272245
$266$	0	0
$267$	24.2661	1.48506
$268$	2.62691	0.160464
$269$	10.7542	0.655696	0.327848	−	0.944731i	$-0.393677\pi$
$269$	10.7542	0.655696	0.327848	+	0.944731i	$0.393677\pi$
$270$	3.49375	0.212623
$271$	−16.0132	−0.972735	−0.486367	−	0.873754i	$-0.661678\pi$
$271$	−16.0132	−0.972735	−0.486367	+	0.873754i	$0.661678\pi$
$272$	−6.63611	−0.402373
$273$	0	0
$274$	−1.92886	−0.116527
$275$	0.353657	0.0213263
$276$	−21.2165	−1.27708
$277$	11.3295	0.680723	0.340361	−	0.940295i	$-0.389451\pi$
$277$	11.3295	0.680723	0.340361	+	0.940295i	$0.389451\pi$
$278$	−23.7920	−1.42695
$279$	−16.3877	−0.981104
$280$	0	0
$281$	−28.0552	−1.67363	−0.836815	−	0.547486i	$-0.815585\pi$
$281$	−28.0552	−1.67363	−0.836815	+	0.547486i	$0.815585\pi$
$282$	43.4367	2.58662
$283$	6.16696	0.366588	0.183294	−	0.983058i	$-0.441324\pi$
$283$	6.16696	0.366588	0.183294	+	0.983058i	$0.441324\pi$
$284$	−8.57736	−0.508973
$285$	−1.91280	−0.113304
$286$	0.989156	0.0584900
$287$	0	0
$288$	−17.2318	−1.01540
$289$	−14.8067	−0.870982
$290$	3.04740	0.178950
$291$	−28.8946	−1.69383
$292$	17.7605	1.03935
$293$	−11.9097	−0.695772	−0.347886	−	0.937537i	$-0.613100\pi$
$293$	−11.9097	−0.695772	−0.347886	+	0.937537i	$0.613100\pi$
$294$	0	0
$295$	11.2549	0.655286
$296$	−1.81484	−0.105485
$297$	0.154073	0.00894021
$298$	25.9740	1.50463
$299$	29.6379	1.71400
$300$	−15.0508	−0.868956
$301$	0	0
$302$	3.33843	0.192105
$303$	29.8180	1.71300
$304$	−3.41688	−0.195971
$305$	9.56994	0.547973
$306$	6.50709	0.371986
$307$	21.9454	1.25249	0.626246	−	0.779626i	$-0.284591\pi$
$307$	21.9454	1.25249	0.626246	+	0.779626i	$0.284591\pi$
$308$	0	0
$309$	−4.88359	−0.277818
$310$	15.1514	0.860542
$311$	−17.6949	−1.00339	−0.501693	−	0.865046i	$-0.667289\pi$
$311$	−17.6949	−1.00339	−0.501693	+	0.865046i	$0.667289\pi$
$312$	6.83888	0.387175
$313$	22.3103	1.26105	0.630526	−	0.776168i	$-0.282839\pi$
$313$	22.3103	1.26105	0.630526	+	0.776168i	$0.282839\pi$
$314$	−5.56470	−0.314034
$315$	0	0
$316$	16.6251	0.935235
$317$	−13.7637	−0.773049	−0.386524	−	0.922279i	$-0.626324\pi$
$317$	−13.7637	−0.773049	−0.386524	+	0.922279i	$0.626324\pi$
$318$	−1.79862	−0.100862
$319$	0.134389	0.00752434
$320$	6.14672	0.343612
$321$	5.21931	0.291314
$322$	0	0
$323$	1.12931	0.0628366
$324$	−18.3144	−1.01746
$325$	21.0248	1.16625
$326$	28.3759	1.57160
$327$	−29.1519	−1.61210
$328$	3.13231	0.172953
$329$	0	0
$330$	0.449379	0.0247375
$331$	−4.45220	−0.244715	−0.122357	−	0.992486i	$-0.539045\pi$
$331$	−4.45220	−0.244715	−0.122357	+	0.992486i	$0.539045\pi$
$332$	−20.1371	−1.10517
$333$	7.66795	0.420201
$334$	1.96417	0.107474
$335$	−1.66712	−0.0910845
$336$	0	0
$337$	9.43535	0.513976	0.256988	−	0.966415i	$-0.417270\pi$
$337$	9.43535	0.513976	0.256988	+	0.966415i	$0.417270\pi$
$338$	33.7298	1.83466
$339$	−15.5237	−0.843131
$340$	−2.78211	−0.150881
$341$	0.668170	0.0361835
$342$	3.35045	0.181171
$343$	0	0
$344$	−5.78945	−0.312146
$345$	13.4647	0.724912
$346$	−16.3793	−0.880555
$347$	29.1989	1.56748	0.783739	−	0.621090i	$-0.213310\pi$
$347$	29.1989	1.56748	0.783739	+	0.621090i	$0.213310\pi$
$348$	−5.71926	−0.306584
$349$	−1.51188	−0.0809293	−0.0404647	−	0.999181i	$-0.512884\pi$
$349$	−1.51188	−0.0809293	−0.0404647	+	0.999181i	$0.512884\pi$
$350$	0	0
$351$	9.15957	0.488902
$352$	0.702589	0.0374481
$353$	13.4177	0.714149	0.357075	−	0.934076i	$-0.383774\pi$
$353$	13.4177	0.714149	0.357075	+	0.934076i	$0.383774\pi$
$354$	−45.6772	−2.42772
$355$	5.44346	0.288909
$356$	18.1728	0.963154
$357$	0	0
$358$	42.0775	2.22386
$359$	−12.6190	−0.666006	−0.333003	−	0.942926i	$-0.608062\pi$
$359$	−12.6190	−0.666006	−0.333003	+	0.942926i	$0.608062\pi$
$360$	1.34094	0.0706736
$361$	−18.4185	−0.969396
$362$	−10.7342	−0.564177
$363$	−25.2513	−1.32535
$364$	0	0
$365$	−11.2713	−0.589968
$366$	−38.8389	−2.03014
$367$	24.3425	1.27067	0.635334	−	0.772237i	$-0.280862\pi$
$367$	24.3425	1.27067	0.635334	+	0.772237i	$0.280862\pi$
$368$	24.0522	1.25381
$369$	−13.2344	−0.688957
$370$	−7.08948	−0.368565
$371$	0	0
$372$	−28.4356	−1.47432
$373$	5.16273	0.267316	0.133658	−	0.991028i	$-0.457328\pi$
$373$	5.16273	0.267316	0.133658	+	0.991028i	$0.457328\pi$
$374$	−0.265312	−0.0137190
$375$	22.0939	1.14092
$376$	−5.28472	−0.272539
$377$	7.98938	0.411474
$378$	0	0
$379$	−17.4509	−0.896391	−0.448195	−	0.893936i	$-0.647933\pi$
$379$	−17.4509	−0.896391	−0.448195	+	0.893936i	$0.647933\pi$
$380$	−1.43249	−0.0734850
$381$	39.0475	2.00047
$382$	9.76894	0.499823
$383$	−2.87438	−0.146874	−0.0734370	−	0.997300i	$-0.523397\pi$
$383$	−2.87438	−0.146874	−0.0734370	+	0.997300i	$0.523397\pi$
$384$	9.81197	0.500715
$385$	0	0
$386$	36.8812	1.87720
$387$	24.4612	1.24343
$388$	−21.6390	−1.09856
$389$	28.3223	1.43600	0.717998	−	0.696045i	$-0.245059\pi$
$389$	28.3223	1.43600	0.717998	+	0.696045i	$0.245059\pi$
$390$	26.7154	1.35279
$391$	−7.94950	−0.402023
$392$	0	0
$393$	−3.91807	−0.197640
$394$	2.20444	0.111058
$395$	−10.5508	−0.530868
$396$	−0.363997	−0.0182915
$397$	−18.0673	−0.906774	−0.453387	−	0.891314i	$-0.649784\pi$
$397$	−18.0673	−0.906774	−0.453387	+	0.891314i	$0.649784\pi$
$398$	−50.3476	−2.52370
$399$	0	0
$400$	17.0624	0.853119
$401$	−0.245407	−0.0122550	−0.00612751	−	0.999981i	$-0.501950\pi$
$401$	−0.245407	−0.0122550	−0.00612751	+	0.999981i	$0.501950\pi$
$402$	6.76589	0.337452
$403$	39.7225	1.97872
$404$	22.3306	1.11099
$405$	11.6229	0.577544
$406$	0	0
$407$	−0.312643	−0.0154971
$408$	−1.83433	−0.0908129
$409$	29.0796	1.43790	0.718948	−	0.695064i	$-0.244624\pi$
$409$	29.0796	1.43790	0.718948	+	0.695064i	$0.244624\pi$
$410$	12.2360	0.604295
$411$	−2.29737	−0.113321
$412$	−3.65730	−0.180182
$413$	0	0
$414$	−23.5846	−1.15912
$415$	12.7796	0.627327
$416$	41.7687	2.04788
$417$	−28.3376	−1.38770
$418$	−0.136607	−0.00668166
$419$	14.6653	0.716448	0.358224	−	0.933636i	$-0.383382\pi$
$419$	14.6653	0.716448	0.358224	+	0.933636i	$0.383382\pi$
$420$	0	0
$421$	−9.45353	−0.460737	−0.230368	−	0.973103i	$-0.573993\pi$
$421$	−9.45353	−0.460737	−0.230368	+	0.973103i	$0.573993\pi$
$422$	26.3330	1.28187
$423$	22.3287	1.08566
$424$	0.218830	0.0106273
$425$	−5.63928	−0.273545
$426$	−22.0919	−1.07036
$427$	0	0
$428$	3.90872	0.188935
$429$	1.17814	0.0568810
$430$	−22.6159	−1.09063
$431$	−24.0203	−1.15702	−0.578508	−	0.815676i	$-0.696365\pi$
$431$	−24.0203	−1.15702	−0.578508	+	0.815676i	$0.696365\pi$
$432$	7.43332	0.357636
$433$	−30.3434	−1.45821	−0.729104	−	0.684402i	$-0.760063\pi$
$433$	−30.3434	−1.45821	−0.729104	+	0.684402i	$0.760063\pi$
$434$	0	0
$435$	3.62962	0.174027
$436$	−21.8317	−1.04555
$437$	−4.09313	−0.195801
$438$	45.7439	2.18573
$439$	22.9494	1.09532	0.547658	−	0.836702i	$-0.315520\pi$
$439$	22.9494	1.09532	0.547658	+	0.836702i	$0.315520\pi$
$440$	−0.0546737	−0.00260647
$441$	0	0
$442$	−15.7727	−0.750231
$443$	−14.0744	−0.668693	−0.334347	−	0.942450i	$-0.608516\pi$
$443$	−14.0744	−0.668693	−0.334347	+	0.942450i	$0.608516\pi$
$444$	13.3053	0.631441
$445$	−11.5330	−0.546716
$446$	−22.4821	−1.06456
$447$	30.9364	1.46324
$448$	0	0
$449$	−30.2652	−1.42830	−0.714151	−	0.699992i	$-0.753187\pi$
$449$	−30.2652	−1.42830	−0.714151	+	0.699992i	$0.753187\pi$
$450$	−16.7307	−0.788691
$451$	0.539604	0.0254090
$452$	−11.6256	−0.546823
$453$	3.97625	0.186821
$454$	−48.9465	−2.29717
$455$	0	0
$456$	−0.944481	−0.0442294
$457$	25.6042	1.19771	0.598857	−	0.800856i	$-0.295622\pi$
$457$	25.6042	1.19771	0.598857	+	0.800856i	$0.295622\pi$
$458$	−54.0750	−2.52676
$459$	−2.45679	−0.114673
$460$	10.0836	0.470151
$461$	−37.3845	−1.74117	−0.870586	−	0.492016i	$-0.836260\pi$
$461$	−37.3845	−1.74117	−0.870586	+	0.492016i	$0.836260\pi$
$462$	0	0
$463$	−14.4887	−0.673346	−0.336673	−	0.941622i	$-0.609302\pi$
$463$	−14.4887	−0.673346	−0.336673	+	0.941622i	$0.609302\pi$
$464$	6.48367	0.300997
$465$	18.0461	0.836869
$466$	21.6673	1.00372
$467$	15.2102	0.703843	0.351922	−	0.936030i	$-0.385528\pi$
$467$	15.2102	0.703843	0.351922	+	0.936030i	$0.385528\pi$
$468$	−21.6395	−1.00029
$469$	0	0
$470$	−20.6442	−0.952247
$471$	−6.62785	−0.305395
$472$	5.55732	0.255796
$473$	−0.997351	−0.0458583
$474$	42.8197	1.96677
$475$	−2.90362	−0.133227
$476$	0	0
$477$	−0.924585	−0.0423338
$478$	−21.5355	−0.985010
$479$	24.1582	1.10382	0.551908	−	0.833905i	$-0.313900\pi$
$479$	24.1582	1.10382	0.551908	+	0.833905i	$0.313900\pi$
$480$	18.9757	0.866119
$481$	−18.5865	−0.847472
$482$	−23.3204	−1.06221
$483$	0	0
$484$	−18.9106	−0.859571
$485$	13.7328	0.623574
$486$	−37.5712	−1.70427
$487$	−21.2094	−0.961089	−0.480545	−	0.876970i	$-0.659561\pi$
$487$	−21.2094	−0.961089	−0.480545	+	0.876970i	$0.659561\pi$
$488$	4.72534	0.213906
$489$	33.7972	1.52836
$490$	0	0
$491$	−15.0104	−0.677410	−0.338705	−	0.940893i	$-0.609989\pi$
$491$	−15.0104	−0.677410	−0.338705	+	0.940893i	$0.609989\pi$
$492$	−22.9642	−1.03531
$493$	−2.14292	−0.0965121
$494$	−8.12122	−0.365391
$495$	0.231004	0.0103828
$496$	32.2362	1.44745
$497$	0	0
$498$	−51.8652	−2.32414
$499$	16.5400	0.740431	0.370216	−	0.928946i	$-0.379284\pi$
$499$	16.5400	0.740431	0.370216	+	0.928946i	$0.379284\pi$
$500$	16.5460	0.739960
$501$	2.33943	0.104518
$502$	−17.6920	−0.789632
$503$	−11.0462	−0.492527	−0.246264	−	0.969203i	$-0.579203\pi$
$503$	−11.0462	−0.492527	−0.246264	+	0.969203i	$0.579203\pi$
$504$	0	0
$505$	−14.1717	−0.630631
$506$	0.961609	0.0427487
$507$	40.1739	1.78419
$508$	29.2425	1.29743
$509$	−41.4806	−1.83859	−0.919297	−	0.393565i	$-0.871242\pi$
$509$	−41.4806	−1.83859	−0.919297	+	0.393565i	$0.871242\pi$
$510$	−7.16562	−0.317299
$511$	0	0
$512$	29.0652	1.28451
$513$	−1.26498	−0.0558501
$514$	33.9619	1.49800
$515$	2.32103	0.102277
$516$	42.4447	1.86852
$517$	−0.910402	−0.0400394
$518$	0	0
$519$	−19.5086	−0.856332
$520$	−3.25033	−0.142536
$521$	−12.3926	−0.542931	−0.271466	−	0.962448i	$-0.587508\pi$
$521$	−12.3926	−0.542931	−0.271466	+	0.962448i	$0.587508\pi$
$522$	−6.35761	−0.278265
$523$	−24.9733	−1.09201	−0.546004	−	0.837783i	$-0.683852\pi$
$523$	−24.9733	−1.09201	−0.546004	+	0.837783i	$0.683852\pi$
$524$	−2.93422	−0.128182
$525$	0	0
$526$	−9.24577	−0.403135
$527$	−10.6544	−0.464112
$528$	0.956101	0.0416090
$529$	5.81250	0.252717
$530$	0.854835	0.0371317
$531$	−23.4804	−1.01896
$532$	0	0
$533$	32.0793	1.38951
$534$	46.8058	2.02549
$535$	−2.48059	−0.107245
$536$	−0.823172	−0.0355556
$537$	50.1165	2.16269
$538$	20.7433	0.894309
$539$	0	0
$540$	3.11633	0.134106
$541$	2.47732	0.106508	0.0532542	−	0.998581i	$-0.483041\pi$
$541$	2.47732	0.106508	0.0532542	+	0.998581i	$0.483041\pi$
$542$	−30.8872	−1.32672
$543$	−12.7850	−0.548657
$544$	−11.2032	−0.480334
$545$	13.8551	0.593486
$546$	0	0
$547$	−1.67277	−0.0715225	−0.0357612	−	0.999360i	$-0.511386\pi$
$547$	−1.67277	−0.0715225	−0.0357612	+	0.999360i	$0.511386\pi$
$548$	−1.72049	−0.0734957
$549$	−19.9652	−0.852094
$550$	0.682155	0.0290872
$551$	−1.10337	−0.0470051
$552$	6.64843	0.282976
$553$	0	0
$554$	21.8530	0.928443
$555$	−8.44395	−0.358426
$556$	−21.2219	−0.900008
$557$	0.916098	0.0388163	0.0194082	−	0.999812i	$-0.493822\pi$
$557$	0.916098	0.0388163	0.0194082	+	0.999812i	$0.493822\pi$
$558$	−31.6095	−1.33814
$559$	−59.2921	−2.50779
$560$	0	0
$561$	−0.316001	−0.0133416
$562$	−54.1144	−2.28268
$563$	1.88965	0.0796394	0.0398197	−	0.999207i	$-0.487322\pi$
$563$	1.88965	0.0796394	0.0398197	+	0.999207i	$0.487322\pi$
$564$	38.7444	1.63143
$565$	7.37797	0.310394
$566$	11.8952	0.499992
$567$	0	0
$568$	2.68781	0.112778
$569$	−4.29192	−0.179927	−0.0899633	−	0.995945i	$-0.528675\pi$
$569$	−4.29192	−0.179927	−0.0899633	+	0.995945i	$0.528675\pi$
$570$	−3.68952	−0.154537
$571$	15.8294	0.662439	0.331219	−	0.943554i	$-0.392540\pi$
$571$	15.8294	0.662439	0.331219	+	0.943554i	$0.392540\pi$
$572$	0.882301	0.0368909
$573$	11.6353	0.486073
$574$	0	0
$575$	20.4393	0.852376
$576$	−12.8236	−0.534315
$577$	−26.6285	−1.10856	−0.554279	−	0.832331i	$-0.687006\pi$
$577$	−26.6285	−1.10856	−0.554279	+	0.832331i	$0.687006\pi$
$578$	−28.5600	−1.18794
$579$	43.9275	1.82556
$580$	2.71820	0.112867
$581$	0	0
$582$	−55.7336	−2.31023
$583$	0.0376979	0.00156129
$584$	−5.56543	−0.230299
$585$	13.7331	0.567793
$586$	−22.9721	−0.948970
$587$	−18.1406	−0.748742	−0.374371	−	0.927279i	$-0.622141\pi$
$587$	−18.1406	−0.748742	−0.374371	+	0.927279i	$0.622141\pi$
$588$	0	0
$589$	−5.48585	−0.226041
$590$	21.7091	0.893749
$591$	2.62561	0.108003
$592$	−15.0836	−0.619933
$593$	26.5153	1.08885	0.544426	−	0.838809i	$-0.316748\pi$
$593$	26.5153	1.08885	0.544426	+	0.838809i	$0.316748\pi$
$594$	0.297185	0.0121936
$595$	0	0
$596$	23.1681	0.949004
$597$	−59.9666	−2.45427
$598$	57.1672	2.33774
$599$	−22.7847	−0.930956	−0.465478	−	0.885059i	$-0.654118\pi$
$599$	−22.7847	−0.930956	−0.465478	+	0.885059i	$0.654118\pi$
$600$	4.71632	0.192543
$601$	1.27019	0.0518123	0.0259061	−	0.999664i	$-0.491753\pi$
$601$	1.27019	0.0518123	0.0259061	+	0.999664i	$0.491753\pi$
$602$	0	0
$603$	3.47802	0.141636
$604$	2.97780	0.121165
$605$	12.0012	0.487919
$606$	57.5147	2.33638
$607$	37.8796	1.53749	0.768743	−	0.639558i	$-0.220882\pi$
$607$	37.8796	1.53749	0.768743	+	0.639558i	$0.220882\pi$
$608$	−5.76844	−0.233941
$609$	0	0
$610$	18.4590	0.747385
$611$	−54.1230	−2.18958
$612$	5.80416	0.234619
$613$	−28.3610	−1.14549	−0.572746	−	0.819733i	$-0.694122\pi$
$613$	−28.3610	−1.14549	−0.572746	+	0.819733i	$0.694122\pi$
$614$	42.3296	1.70828
$615$	14.5738	0.587671
$616$	0	0
$617$	−6.44088	−0.259300	−0.129650	−	0.991560i	$-0.541385\pi$
$617$	−6.44088	−0.259300	−0.129650	+	0.991560i	$0.541385\pi$
$618$	−9.41975	−0.378918
$619$	4.58503	0.184288	0.0921441	−	0.995746i	$-0.470628\pi$
$619$	4.58503	0.184288	0.0921441	+	0.995746i	$0.470628\pi$
$620$	13.5147	0.542762
$621$	8.90448	0.357325
$622$	−34.1309	−1.36853
$623$	0	0
$624$	56.8398	2.27541
$625$	8.53842	0.341537
$626$	43.0334	1.71996
$627$	−0.162706	−0.00649786
$628$	−4.96357	−0.198068
$629$	4.98529	0.198776
$630$	0	0
$631$	47.0342	1.87240	0.936201	−	0.351464i	$-0.114316\pi$
$631$	47.0342	1.87240	0.936201	+	0.351464i	$0.114316\pi$
$632$	−5.20966	−0.207229
$633$	31.3640	1.24661
$634$	−26.5483	−1.05437
$635$	−18.5582	−0.736459
$636$	−1.60433	−0.0636156
$637$	0	0
$638$	0.259217	0.0102625
$639$	−11.3564	−0.449251
$640$	−4.66335	−0.184335
$641$	2.25607	0.0891092	0.0445546	−	0.999007i	$-0.485813\pi$
$641$	2.25607	0.0891092	0.0445546	+	0.999007i	$0.485813\pi$
$642$	10.0673	0.397325
$643$	34.8323	1.37365	0.686826	−	0.726822i	$-0.259003\pi$
$643$	34.8323	1.37365	0.686826	+	0.726822i	$0.259003\pi$
$644$	0	0
$645$	−26.9367	−1.06063
$646$	2.17828	0.0857033
$647$	−14.8599	−0.584201	−0.292101	−	0.956388i	$-0.594354\pi$
$647$	−14.8599	−0.584201	−0.292101	+	0.956388i	$0.594354\pi$
$648$	5.73900	0.225449
$649$	0.957362	0.0375797
$650$	40.5538	1.59065
$651$	0	0
$652$	25.3106	0.991238
$653$	29.3773	1.14962	0.574812	−	0.818285i	$-0.305075\pi$
$653$	29.3773	1.14962	0.574812	+	0.818285i	$0.305075\pi$
$654$	−56.2298	−2.19876
$655$	1.86215	0.0727602
$656$	26.0335	1.01644
$657$	23.5147	0.917396
$658$	0	0
$659$	−17.1556	−0.668288	−0.334144	−	0.942522i	$-0.608447\pi$
$659$	−17.1556	−0.668288	−0.334144	+	0.942522i	$0.608447\pi$
$660$	0.400834	0.0156024
$661$	−26.6730	−1.03746	−0.518729	−	0.854939i	$-0.673595\pi$
$661$	−26.6730	−1.03746	−0.518729	+	0.854939i	$0.673595\pi$
$662$	−8.58765	−0.333769
$663$	−18.7861	−0.729593
$664$	6.31018	0.244883
$665$	0	0
$666$	14.7904	0.573115
$667$	7.76688	0.300735
$668$	1.75199	0.0677864
$669$	−26.7774	−1.03527
$670$	−3.21564	−0.124231
$671$	0.814036	0.0314255
$672$	0	0
$673$	32.0325	1.23476	0.617382	−	0.786664i	$-0.288193\pi$
$673$	32.0325	1.23476	0.617382	+	0.786664i	$0.288193\pi$
$674$	18.1994	0.701016
$675$	6.31674	0.243132
$676$	30.0861	1.15716
$677$	23.7374	0.912303	0.456151	−	0.889902i	$-0.349228\pi$
$677$	23.7374	0.912303	0.456151	+	0.889902i	$0.349228\pi$
$678$	−29.9430	−1.14995
$679$	0	0
$680$	0.871805	0.0334322
$681$	−58.2979	−2.23398
$682$	1.28881	0.0493509
$683$	2.76441	0.105777	0.0528886	−	0.998600i	$-0.483157\pi$
$683$	2.76441	0.105777	0.0528886	+	0.998600i	$0.483157\pi$
$684$	2.98851	0.114269
$685$	1.09188	0.0417184
$686$	0	0
$687$	−64.4063	−2.45725
$688$	−48.1177	−1.83447
$689$	2.24112	0.0853800
$690$	25.9714	0.988714
$691$	47.2507	1.79750	0.898752	−	0.438458i	$-0.144475\pi$
$691$	47.2507	1.79750	0.898752	+	0.438458i	$0.144475\pi$
$692$	−14.6099	−0.555384
$693$	0	0
$694$	56.3205	2.13790
$695$	13.4681	0.510873
$696$	1.79219	0.0679328
$697$	−8.60432	−0.325912
$698$	−2.91621	−0.110380
$699$	25.8069	0.976106
$700$	0	0
$701$	−40.7327	−1.53845	−0.769227	−	0.638976i	$-0.779358\pi$
$701$	−40.7327	−1.53845	−0.769227	+	0.638976i	$0.779358\pi$
$702$	17.6675	0.666817
$703$	2.56688	0.0968118
$704$	0.522851	0.0197057
$705$	−24.5884	−0.926052
$706$	25.8807	0.974034
$707$	0	0
$708$	−40.7429	−1.53121
$709$	4.62971	0.173872	0.0869362	−	0.996214i	$-0.472292\pi$
$709$	4.62971	0.173872	0.0869362	+	0.996214i	$0.472292\pi$
$710$	10.4997	0.394045
$711$	22.0115	0.825496
$712$	−5.69463	−0.213415
$713$	38.6162	1.44619
$714$	0	0
$715$	−0.559935	−0.0209404
$716$	37.5320	1.40264
$717$	−25.6499	−0.957914
$718$	−24.3403	−0.908371
$719$	20.4501	0.762661	0.381331	−	0.924439i	$-0.375466\pi$
$719$	20.4501	0.762661	0.381331	+	0.924439i	$0.375466\pi$
$720$	11.1449	0.415346
$721$	0	0
$722$	−35.5267	−1.32217
$723$	−27.7758	−1.03299
$724$	−9.57463	−0.355838
$725$	5.50974	0.204627
$726$	−48.7061	−1.80765
$727$	5.98752	0.222065	0.111032	−	0.993817i	$-0.464584\pi$
$727$	5.98752	0.222065	0.111032	+	0.993817i	$0.464584\pi$
$728$	0	0
$729$	−12.8148	−0.474622
$730$	−21.7408	−0.804663
$731$	15.9034	0.588208
$732$	−34.6433	−1.28045
$733$	−0.722356	−0.0266808	−0.0133404	−	0.999911i	$-0.504247\pi$
$733$	−0.722356	−0.0266808	−0.0133404	+	0.999911i	$0.504247\pi$
$734$	46.9532	1.73307
$735$	0	0
$736$	40.6054	1.49674
$737$	−0.141808	−0.00522357
$738$	−25.5273	−0.939674
$739$	39.2349	1.44328	0.721640	−	0.692268i	$-0.243388\pi$
$739$	39.2349	1.44328	0.721640	+	0.692268i	$0.243388\pi$
$740$	−6.32363	−0.232461
$741$	−9.67281	−0.355340
$742$	0	0
$743$	−15.7573	−0.578081	−0.289041	−	0.957317i	$-0.593336\pi$
$743$	−15.7573	−0.578081	−0.289041	+	0.957317i	$0.593336\pi$
$744$	8.91062	0.326679
$745$	−14.7032	−0.538684
$746$	9.95816	0.364594
$747$	−26.6614	−0.975489
$748$	−0.236651	−0.00865283
$749$	0	0
$750$	42.6160	1.55612
$751$	31.5460	1.15113	0.575565	−	0.817756i	$-0.304782\pi$
$751$	31.5460	1.15113	0.575565	+	0.817756i	$0.304782\pi$
$752$	−43.9228	−1.60170
$753$	−21.0721	−0.767910
$754$	15.4104	0.561212
$755$	−1.88980	−0.0687769
$756$	0	0
$757$	−49.4085	−1.79578	−0.897891	−	0.440218i	$-0.854901\pi$
$757$	−49.4085	−1.79578	−0.897891	+	0.440218i	$0.854901\pi$
$758$	−33.6602	−1.22259
$759$	1.14533	0.0415727
$760$	0.448885	0.0162828
$761$	−1.39665	−0.0506284	−0.0253142	−	0.999680i	$-0.508059\pi$
$761$	−1.39665	−0.0506284	−0.0253142	+	0.999680i	$0.508059\pi$
$762$	75.3171	2.72845
$763$	0	0
$764$	8.71364	0.315248
$765$	−3.68350	−0.133177
$766$	−5.54427	−0.200323
$767$	56.9148	2.05507
$768$	44.7920	1.61629
$769$	4.95291	0.178607	0.0893033	−	0.996004i	$-0.471536\pi$
$769$	4.95291	0.178607	0.0893033	+	0.996004i	$0.471536\pi$
$770$	0	0
$771$	40.4504	1.45679
$772$	32.8971	1.18399
$773$	48.8648	1.75754	0.878772	−	0.477243i	$-0.158364\pi$
$773$	48.8648	1.75754	0.878772	+	0.477243i	$0.158364\pi$
$774$	47.1822	1.69593
$775$	27.3939	0.984019
$776$	6.78083	0.243418
$777$	0	0
$778$	54.6296	1.95857
$779$	−4.43029	−0.158732
$780$	23.8294	0.853230
$781$	0.463030	0.0165685
$782$	−15.3334	−0.548323
$783$	2.40035	0.0857815
$784$	0	0
$785$	3.15003	0.112429
$786$	−7.55740	−0.269563
$787$	17.4733	0.622856	0.311428	−	0.950270i	$-0.399193\pi$
$787$	17.4733	0.622856	0.311428	+	0.950270i	$0.399193\pi$
$788$	1.96631	0.0700468
$789$	−11.0122	−0.392045
$790$	−20.3510	−0.724055
$791$	0	0
$792$	0.114062	0.00405303
$793$	48.3941	1.71853
$794$	−34.8493	−1.23676
$795$	1.01815	0.0361102
$796$	−44.9087	−1.59175
$797$	−6.38717	−0.226245	−0.113123	−	0.993581i	$-0.536085\pi$
$797$	−6.38717	−0.226245	−0.113123	+	0.993581i	$0.536085\pi$
$798$	0	0
$799$	14.5169	0.513571
$800$	28.8051	1.01841
$801$	24.0606	0.850139
$802$	−0.473354	−0.0167147
$803$	−0.958759	−0.0338339
$804$	6.03500	0.212838
$805$	0	0
$806$	76.6190	2.69879
$807$	24.7064	0.869707
$808$	−6.99753	−0.246172
$809$	−54.0959	−1.90191	−0.950956	−	0.309328i	$-0.899896\pi$
$809$	−54.0959	−1.90191	−0.950956	+	0.309328i	$0.899896\pi$
$810$	22.4188	0.787717
$811$	−3.57360	−0.125486	−0.0627430	−	0.998030i	$-0.519985\pi$
$811$	−3.57360	−0.125486	−0.0627430	+	0.998030i	$0.519985\pi$
$812$	0	0
$813$	−36.7883	−1.29022
$814$	−0.603044	−0.0211367
$815$	−16.0629	−0.562658
$816$	−15.2456	−0.533703
$817$	8.18851	0.286480
$818$	56.0905	1.96116
$819$	0	0
$820$	10.9142	0.381141
$821$	21.3809	0.746200	0.373100	−	0.927791i	$-0.378295\pi$
$821$	21.3809	0.746200	0.373100	+	0.927791i	$0.378295\pi$
$822$	−4.43130	−0.154559
$823$	−42.6542	−1.48683	−0.743416	−	0.668829i	$-0.766796\pi$
$823$	−42.6542	−1.48683	−0.743416	+	0.668829i	$0.766796\pi$
$824$	1.14605	0.0399247
$825$	0.812483	0.0282870
$826$	0	0
$827$	−24.2213	−0.842257	−0.421129	−	0.907001i	$-0.638366\pi$
$827$	−24.2213	−0.842257	−0.421129	+	0.907001i	$0.638366\pi$
$828$	−21.0368	−0.731081
$829$	−14.6958	−0.510406	−0.255203	−	0.966887i	$-0.582142\pi$
$829$	−14.6958	−0.510406	−0.255203	+	0.966887i	$0.582142\pi$
$830$	24.6501	0.855617
$831$	26.0280	0.902903
$832$	31.0833	1.07762
$833$	0	0
$834$	−54.6592	−1.89269
$835$	−1.11186	−0.0384776
$836$	−0.121850	−0.00421426
$837$	11.9343	0.412510
$838$	28.2873	0.977170
$839$	−0.165133	−0.00570103	−0.00285052	−	0.999996i	$-0.500907\pi$
$839$	−0.165133	−0.00570103	−0.00285052	+	0.999996i	$0.500907\pi$
$840$	0	0
$841$	−26.9063	−0.927804
$842$	−18.2345	−0.628403
$843$	−64.4531	−2.21988
$844$	23.4883	0.808502
$845$	−19.0935	−0.656838
$846$	43.0688	1.48074
$847$	0	0
$848$	1.81875	0.0624562
$849$	14.1678	0.486238
$850$	−10.8774	−0.373091
$851$	−18.0689	−0.619394
$852$	−19.7054	−0.675096
$853$	−20.7532	−0.710575	−0.355288	−	0.934757i	$-0.615617\pi$
$853$	−20.7532	−0.710575	−0.355288	+	0.934757i	$0.615617\pi$
$854$	0	0
$855$	−1.89660	−0.0648624
$856$	−1.22484	−0.0418641
$857$	33.9252	1.15886	0.579431	−	0.815022i	$-0.303275\pi$
$857$	33.9252	1.15886	0.579431	+	0.815022i	$0.303275\pi$
$858$	2.27246	0.0775805
$859$	−3.75554	−0.128137	−0.0640687	−	0.997945i	$-0.520408\pi$
$859$	−3.75554	−0.128137	−0.0640687	+	0.997945i	$0.520408\pi$
$860$	−20.1728	−0.687886
$861$	0	0
$862$	−46.3317	−1.57806
$863$	33.6984	1.14711	0.573554	−	0.819168i	$-0.305564\pi$
$863$	33.6984	1.14711	0.573554	+	0.819168i	$0.305564\pi$
$864$	12.5491	0.426929
$865$	9.27188	0.315253
$866$	−58.5280	−1.98886
$867$	−34.0165	−1.15526
$868$	0	0
$869$	−0.897470	−0.0304446
$870$	7.00101	0.237357
$871$	−8.43044	−0.285655
$872$	6.84120	0.231672
$873$	−28.6499	−0.969653
$874$	−7.89506	−0.267054
$875$	0	0
$876$	40.8024	1.37858
$877$	−8.18652	−0.276439	−0.138220	−	0.990402i	$-0.544138\pi$
$877$	−8.18652	−0.276439	−0.138220	+	0.990402i	$0.544138\pi$
$878$	44.2661	1.49391
$879$	−27.3610	−0.922864
$880$	−0.454408	−0.0153181
$881$	10.9583	0.369195	0.184597	−	0.982814i	$-0.440902\pi$
$881$	10.9583	0.369195	0.184597	+	0.982814i	$0.440902\pi$
$882$	0	0
$883$	−5.13051	−0.172655	−0.0863276	−	0.996267i	$-0.527513\pi$
$883$	−5.13051	−0.172655	−0.0863276	+	0.996267i	$0.527513\pi$
$884$	−14.0688	−0.473186
$885$	25.8567	0.869163
$886$	−27.1474	−0.912036
$887$	−51.7535	−1.73771	−0.868857	−	0.495063i	$-0.835145\pi$
$887$	−51.7535	−1.73771	−0.868857	+	0.495063i	$0.835145\pi$
$888$	−4.16936	−0.139915
$889$	0	0
$890$	−22.2455	−0.745670
$891$	0.988661	0.0331214
$892$	−20.0535	−0.671439
$893$	7.47463	0.250129
$894$	59.6719	1.99573
$895$	−23.8190	−0.796180
$896$	0	0
$897$	68.0892	2.27343
$898$	−58.3772	−1.94807
$899$	10.4096	0.347181
$900$	−14.9233	−0.497444
$901$	−0.601116	−0.0200261
$902$	1.04082	0.0346555
$903$	0	0
$904$	3.64301	0.121165
$905$	6.07636	0.201985
$906$	7.66962	0.254806
$907$	5.24883	0.174285	0.0871423	−	0.996196i	$-0.472227\pi$
$907$	5.24883	0.174285	0.0871423	+	0.996196i	$0.472227\pi$
$908$	−43.6590	−1.44887
$909$	29.5655	0.980627
$910$	0	0
$911$	34.8795	1.15561	0.577805	−	0.816175i	$-0.303910\pi$
$911$	34.8795	1.15561	0.577805	+	0.816175i	$0.303910\pi$
$912$	−7.84984	−0.259934
$913$	1.08706	0.0359764
$914$	49.3868	1.63357
$915$	21.9857	0.726825
$916$	−48.2335	−1.59368
$917$	0	0
$918$	−4.73879	−0.156403
$919$	−43.1979	−1.42497	−0.712484	−	0.701689i	$-0.752430\pi$
$919$	−43.1979	−1.42497	−0.712484	+	0.701689i	$0.752430\pi$
$920$	−3.15981	−0.104176
$921$	50.4168	1.66129
$922$	−72.1095	−2.37480
$923$	27.5270	0.906061
$924$	0	0
$925$	−12.8179	−0.421449
$926$	−27.9466	−0.918382
$927$	−4.84223	−0.159040
$928$	10.9459	0.359315
$929$	57.4511	1.88491	0.942454	−	0.334335i	$-0.108512\pi$
$929$	57.4511	1.88491	0.942454	+	0.334335i	$0.108512\pi$
$930$	34.8084	1.14141
$931$	0	0
$932$	19.3266	0.633065
$933$	−40.6518	−1.33088
$934$	29.3383	0.959977
$935$	0.150186	0.00491162
$936$	6.78097	0.221643
$937$	−45.4822	−1.48584	−0.742920	−	0.669380i	$-0.766560\pi$
$937$	−45.4822	−1.48584	−0.742920	+	0.669380i	$0.766560\pi$
$938$	0	0
$939$	51.2550	1.67264
$940$	−18.4141	−0.600602
$941$	0.888552	0.0289660	0.0144830	−	0.999895i	$-0.495390\pi$
$941$	0.888552	0.0289660	0.0144830	+	0.999895i	$0.495390\pi$
$942$	−12.7842	−0.416531
$943$	31.1859	1.01555
$944$	46.1884	1.50330
$945$	0	0
$946$	−1.92375	−0.0625464
$947$	2.30399	0.0748697	0.0374349	−	0.999299i	$-0.488081\pi$
$947$	2.30399	0.0748697	0.0374349	+	0.999299i	$0.488081\pi$
$948$	38.1940	1.24048
$949$	−56.9979	−1.85023
$950$	−5.60067	−0.181710
$951$	−31.6204	−1.02536
$952$	0	0
$953$	−18.3900	−0.595712	−0.297856	−	0.954611i	$-0.596271\pi$
$953$	−18.3900	−0.595712	−0.297856	+	0.954611i	$0.596271\pi$
$954$	−1.78339	−0.0577395
$955$	−5.52994	−0.178945
$956$	−19.2091	−0.621267
$957$	0.308742	0.00998020
$958$	46.5977	1.50550
$959$	0	0
$960$	14.1213	0.455763
$961$	20.7558	0.669541
$962$	−35.8507	−1.15587
$963$	5.17511	0.166766
$964$	−20.8012	−0.669960
$965$	−20.8775	−0.672071
$966$	0	0
$967$	−42.2737	−1.35943	−0.679716	−	0.733476i	$-0.737897\pi$
$967$	−42.2737	−1.35943	−0.679716	+	0.733476i	$0.737897\pi$
$968$	5.92583	0.190463
$969$	2.59445	0.0833457
$970$	26.4886	0.850498
$971$	−50.0697	−1.60681	−0.803406	−	0.595432i	$-0.796981\pi$
$971$	−50.0697	−1.60681	−0.803406	+	0.595432i	$0.796981\pi$
$972$	−33.5125	−1.07492
$973$	0	0
$974$	−40.9099	−1.31084
$975$	48.3018	1.54689
$976$	39.2736	1.25712
$977$	54.1319	1.73183	0.865916	−	0.500190i	$-0.166736\pi$
$977$	54.1319	1.73183	0.865916	+	0.500190i	$0.166736\pi$
$978$	65.1900	2.08455
$979$	−0.981017	−0.0313534
$980$	0	0
$981$	−28.9050	−0.922866
$982$	−28.9529	−0.923925
$983$	−8.44047	−0.269209	−0.134605	−	0.990899i	$-0.542976\pi$
$983$	−8.44047	−0.269209	−0.134605	+	0.990899i	$0.542976\pi$
$984$	7.19608	0.229403
$985$	−1.24788	−0.0397607
$986$	−4.13338	−0.131634
$987$	0	0
$988$	−7.24392	−0.230460
$989$	−57.6409	−1.83287
$990$	0.445573	0.0141613
$991$	−50.2828	−1.59729	−0.798643	−	0.601805i	$-0.794448\pi$
$991$	−50.2828	−1.59729	−0.798643	+	0.601805i	$0.794448\pi$
$992$	54.4218	1.72789
$993$	−10.2284	−0.324587
$994$	0	0
$995$	28.5005	0.903525
$996$	−46.2624	−1.46588
$997$	−38.8807	−1.23136	−0.615682	−	0.787995i	$-0.711119\pi$
$997$	−38.8807	−1.23136	−0.615682	+	0.787995i	$0.711119\pi$
$998$	31.9033	1.00988
$999$	−5.58418	−0.176676

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6713.2.a.k.1.38		45
7.2	even	3		959.2.e.b.823.8	yes	90
7.4	even	3		959.2.e.b.275.8	✓	90
7.6	odd	2		6713.2.a.l.1.38		45

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
959.2.e.b.275.8	✓	90	7.4	even	3
959.2.e.b.823.8	yes	90	7.2	even	3
6713.2.a.k.1.38		45	1.1	even	1	trivial
6713.2.a.l.1.38		45	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6713 = 7^{2} \cdot 137 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6713.a (trivial)

\(f(q)\)	\(=\)	\(q+1.92886 q^{2} +2.29737 q^{3} +1.72049 q^{4} -1.09188 q^{5} +4.43130 q^{6} -0.539134 q^{8} +2.27792 q^{9} +O(q^{10})\)	\(q+1.92886 q^{2} +2.29737 q^{3} +1.72049 q^{4} -1.09188 q^{5} +4.43130 q^{6} -0.539134 q^{8} +2.27792 q^{9} -2.10607 q^{10} -0.0928769 q^{11} +3.95261 q^{12} -5.52150 q^{13} -2.50845 q^{15} -4.48089 q^{16} +1.48098 q^{17} +4.39378 q^{18} +0.762544 q^{19} -1.87856 q^{20} -0.179146 q^{22} -5.36773 q^{23} -1.23859 q^{24} -3.80781 q^{25} -10.6502 q^{26} -1.65889 q^{27} -1.44696 q^{29} -4.83843 q^{30} -7.19415 q^{31} -7.56474 q^{32} -0.213373 q^{33} +2.85660 q^{34} +3.91913 q^{36} +3.36621 q^{37} +1.47084 q^{38} -12.6849 q^{39} +0.588668 q^{40} -5.80988 q^{41} +10.7384 q^{43} -0.159794 q^{44} -2.48720 q^{45} -10.3536 q^{46} +9.80224 q^{47} -10.2943 q^{48} -7.34472 q^{50} +3.40236 q^{51} -9.49968 q^{52} -0.405891 q^{53} -3.19977 q^{54} +0.101410 q^{55} +1.75185 q^{57} -2.79098 q^{58} -10.3079 q^{59} -4.31576 q^{60} -8.76468 q^{61} -13.8765 q^{62} -5.62951 q^{64} +6.02879 q^{65} -0.411566 q^{66} +1.52684 q^{67} +2.54801 q^{68} -12.3317 q^{69} -4.98542 q^{71} -1.22810 q^{72} +10.3229 q^{73} +6.49294 q^{74} -8.74795 q^{75} +1.31195 q^{76} -24.4674 q^{78} +9.66300 q^{79} +4.89258 q^{80} -10.6448 q^{81} -11.2064 q^{82} -11.7043 q^{83} -1.61705 q^{85} +20.7129 q^{86} -3.32420 q^{87} +0.0500732 q^{88} +10.5625 q^{89} -4.79746 q^{90} -9.23512 q^{92} -16.5276 q^{93} +18.9071 q^{94} -0.832603 q^{95} -17.3790 q^{96} -12.5772 q^{97} -0.211566 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 45 q - 11 q^{3} + 44 q^{4} - 4 q^{5} - 10 q^{6} - 3 q^{8} + 44 q^{9}+O(q^{10}) \) 45 * q - 11 * q^3 + 44 * q^4 - 4 * q^5 - 10 * q^6 - 3 * q^8 + 44 * q^9	\( 45 q - 11 q^{3} + 44 q^{4} - 4 q^{5} - 10 q^{6} - 3 q^{8} + 44 q^{9} - 25 q^{10} - 33 q^{12} - 36 q^{13} + 38 q^{16} - 18 q^{17} - 5 q^{18} - 43 q^{19} - 10 q^{20} - q^{23} - 20 q^{24} + 43 q^{25} - 2 q^{26} - 53 q^{27} - 4 q^{29} - 12 q^{30} - 59 q^{31} - 11 q^{32} - 37 q^{33} - 48 q^{34} + 14 q^{36} - 39 q^{38} + 16 q^{39} - 56 q^{40} - 15 q^{41} - q^{43} - 2 q^{44} - 28 q^{45} + 31 q^{46} - 58 q^{47} - 12 q^{48} - 74 q^{50} - 5 q^{51} - 115 q^{52} + 10 q^{53} - 39 q^{54} - 81 q^{55} - 18 q^{57} - 11 q^{58} - 41 q^{59} + 90 q^{60} - 40 q^{61} + 29 q^{62} + 15 q^{64} - 9 q^{65} - 42 q^{66} - 56 q^{68} - 5 q^{69} - 42 q^{71} - 11 q^{72} - 67 q^{73} + 39 q^{74} - 40 q^{75} - 68 q^{76} - 78 q^{78} - 9 q^{79} - 14 q^{80} + 73 q^{81} - 34 q^{82} - 48 q^{83} + 6 q^{85} - 13 q^{86} - 135 q^{87} + 47 q^{88} - 17 q^{89} + 44 q^{90} - 61 q^{92} - q^{93} - 28 q^{94} + 47 q^{95} - 50 q^{96} - 81 q^{97} - 35 q^{99}+O(q^{100}) \) 45 * q - 11 * q^3 + 44 * q^4 - 4 * q^5 - 10 * q^6 - 3 * q^8 + 44 * q^9 - 25 * q^10 - 33 * q^12 - 36 * q^13 + 38 * q^16 - 18 * q^17 - 5 * q^18 - 43 * q^19 - 10 * q^20 - q^23 - 20 * q^24 + 43 * q^25 - 2 * q^26 - 53 * q^27 - 4 * q^29 - 12 * q^30 - 59 * q^31 - 11 * q^32 - 37 * q^33 - 48 * q^34 + 14 * q^36 - 39 * q^38 + 16 * q^39 - 56 * q^40 - 15 * q^41 - q^43 - 2 * q^44 - 28 * q^45 + 31 * q^46 - 58 * q^47 - 12 * q^48 - 74 * q^50 - 5 * q^51 - 115 * q^52 + 10 * q^53 - 39 * q^54 - 81 * q^55 - 18 * q^57 - 11 * q^58 - 41 * q^59 + 90 * q^60 - 40 * q^61 + 29 * q^62 + 15 * q^64 - 9 * q^65 - 42 * q^66 - 56 * q^68 - 5 * q^69 - 42 * q^71 - 11 * q^72 - 67 * q^73 + 39 * q^74 - 40 * q^75 - 68 * q^76 - 78 * q^78 - 9 * q^79 - 14 * q^80 + 73 * q^81 - 34 * q^82 - 48 * q^83 + 6 * q^85 - 13 * q^86 - 135 * q^87 + 47 * q^88 - 17 * q^89 + 44 * q^90 - 61 * q^92 - q^93 - 28 * q^94 + 47 * q^95 - 50 * q^96 - 81 * q^97 - 35 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more