LMFDB - Embedded newform 3381.2.a.ba.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3381,2,Mod(1,3381)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3381, 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("3381.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3381 = 3 \cdot 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3381.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:	$26.9974209234$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.62622704.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 5x^{4} + 13x^{3} + 9x^{2} - 5x - 2 $ x^6 - 3x^5 - 5x^4 + 13x^3 + 9x^2 - 5*x - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.82095$ of defining polynomial
Character	$\chi$	$=$	3381.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.82095 q^{2} -1.00000 q^{3} +5.95777 q^{4} -2.07008 q^{5} +2.82095 q^{6} -11.1647 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.82095 q^{2} -1.00000 q^{3} +5.95777 q^{4} -2.07008 q^{5} +2.82095 q^{6} -11.1647 q^{8} +1.00000 q^{9} +5.83961 q^{10} -2.84078 q^{11} -5.95777 q^{12} -4.70863 q^{13} +2.07008 q^{15} +19.5794 q^{16} +6.62109 q^{17} -2.82095 q^{18} +7.50391 q^{19} -12.3331 q^{20} +8.01371 q^{22} -1.00000 q^{23} +11.1647 q^{24} -0.714752 q^{25} +13.2828 q^{26} -1.00000 q^{27} -0.957621 q^{29} -5.83961 q^{30} -1.85707 q^{31} -32.9033 q^{32} +2.84078 q^{33} -18.6778 q^{34} +5.95777 q^{36} +0.551986 q^{37} -21.1682 q^{38} +4.70863 q^{39} +23.1118 q^{40} -5.78777 q^{41} -4.33885 q^{43} -16.9247 q^{44} -2.07008 q^{45} +2.82095 q^{46} -7.88145 q^{47} -19.5794 q^{48} +2.01628 q^{50} -6.62109 q^{51} -28.0529 q^{52} -0.297011 q^{53} +2.82095 q^{54} +5.88066 q^{55} -7.50391 q^{57} +2.70140 q^{58} +12.8839 q^{59} +12.3331 q^{60} +3.29430 q^{61} +5.23869 q^{62} +53.6598 q^{64} +9.74727 q^{65} -8.01371 q^{66} +1.07620 q^{67} +39.4469 q^{68} +1.00000 q^{69} -10.0810 q^{71} -11.1647 q^{72} +0.394997 q^{73} -1.55712 q^{74} +0.714752 q^{75} +44.7065 q^{76} -13.2828 q^{78} -7.76091 q^{79} -40.5311 q^{80} +1.00000 q^{81} +16.3270 q^{82} -5.59160 q^{83} -13.7062 q^{85} +12.2397 q^{86} +0.957621 q^{87} +31.7164 q^{88} -3.99625 q^{89} +5.83961 q^{90} -5.95777 q^{92} +1.85707 q^{93} +22.2332 q^{94} -15.5337 q^{95} +32.9033 q^{96} -6.17643 q^{97} -2.84078 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 6 q^{3} + 7 q^{4} + 2 q^{5} + 3 q^{6} - 9 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 - 6 * q^3 + 7 * q^4 + 2 * q^5 + 3 * q^6 - 9 * q^8 + 6 * q^9	$ 6 q - 3 q^{2} - 6 q^{3} + 7 q^{4} + 2 q^{5} + 3 q^{6} - 9 q^{8} + 6 q^{9} + 8 q^{10} - 3 q^{11} - 7 q^{12} - 2 q^{15} + 5 q^{16} + 8 q^{17} - 3 q^{18} + 19 q^{19} + 24 q^{22} - 6 q^{23} + 9 q^{24} + 20 q^{26} - 6 q^{27} - 12 q^{29} - 8 q^{30} - 2 q^{31} - 41 q^{32} + 3 q^{33} + 2 q^{34} + 7 q^{36} - 10 q^{37} - 20 q^{38} + 22 q^{40} + 3 q^{41} - 2 q^{43} - 14 q^{44} + 2 q^{45} + 3 q^{46} + 7 q^{47} - 5 q^{48} + 17 q^{50} - 8 q^{51} - 44 q^{52} - 5 q^{53} + 3 q^{54} + 24 q^{55} - 19 q^{57} - 12 q^{58} + 21 q^{59} + 29 q^{61} + 10 q^{62} + 59 q^{64} - 18 q^{65} - 24 q^{66} + 16 q^{67} + 54 q^{68} + 6 q^{69} - 6 q^{71} - 9 q^{72} - 8 q^{73} - 16 q^{74} + 40 q^{76} - 20 q^{78} - 12 q^{79} - 78 q^{80} + 6 q^{81} + 44 q^{82} + 24 q^{83} + 10 q^{85} + 12 q^{86} + 12 q^{87} + 28 q^{88} + 18 q^{89} + 8 q^{90} - 7 q^{92} + 2 q^{93} - 8 q^{94} + 6 q^{95} + 41 q^{96} + 22 q^{97} - 3 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 - 6 * q^3 + 7 * q^4 + 2 * q^5 + 3 * q^6 - 9 * q^8 + 6 * q^9 + 8 * q^10 - 3 * q^11 - 7 * q^12 - 2 * q^15 + 5 * q^16 + 8 * q^17 - 3 * q^18 + 19 * q^19 + 24 * q^22 - 6 * q^23 + 9 * q^24 + 20 * q^26 - 6 * q^27 - 12 * q^29 - 8 * q^30 - 2 * q^31 - 41 * q^32 + 3 * q^33 + 2 * q^34 + 7 * q^36 - 10 * q^37 - 20 * q^38 + 22 * q^40 + 3 * q^41 - 2 * q^43 - 14 * q^44 + 2 * q^45 + 3 * q^46 + 7 * q^47 - 5 * q^48 + 17 * q^50 - 8 * q^51 - 44 * q^52 - 5 * q^53 + 3 * q^54 + 24 * q^55 - 19 * q^57 - 12 * q^58 + 21 * q^59 + 29 * q^61 + 10 * q^62 + 59 * q^64 - 18 * q^65 - 24 * q^66 + 16 * q^67 + 54 * q^68 + 6 * q^69 - 6 * q^71 - 9 * q^72 - 8 * q^73 - 16 * q^74 + 40 * q^76 - 20 * q^78 - 12 * q^79 - 78 * q^80 + 6 * q^81 + 44 * q^82 + 24 * q^83 + 10 * q^85 + 12 * q^86 + 12 * q^87 + 28 * q^88 + 18 * q^89 + 8 * q^90 - 7 * q^92 + 2 * q^93 - 8 * q^94 + 6 * q^95 + 41 * q^96 + 22 * 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 $

$2$	−2.82095	−1.99471	−0.997357	−	0.0726586i	$-0.976852\pi$
$2$	−2.82095	−1.99471	−0.997357	+	0.0726586i	$0.976852\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.95777	2.97888
$5$	−2.07008	−0.925770	−0.462885	−	0.886418i	$-0.653186\pi$
$5$	−2.07008	−0.925770	−0.462885	+	0.886418i	$0.653186\pi$
$6$	2.82095	1.15165
$7$	0	0
$7$	0	0
$8$	−11.1647	−3.94730
$9$	1.00000	0.333333
$10$	5.83961	1.84665
$11$	−2.84078	−0.856529	−0.428264	−	0.903654i	$-0.640875\pi$
$11$	−2.84078	−0.856529	−0.428264	+	0.903654i	$0.640875\pi$
$12$	−5.95777	−1.71986
$13$	−4.70863	−1.30594	−0.652970	−	0.757384i	$-0.726477\pi$
$13$	−4.70863	−1.30594	−0.652970	+	0.757384i	$0.726477\pi$
$14$	0	0
$15$	2.07008	0.534493
$16$	19.5794	4.89486
$17$	6.62109	1.60585	0.802925	−	0.596080i	$-0.203276\pi$
$17$	6.62109	1.60585	0.802925	+	0.596080i	$0.203276\pi$
$18$	−2.82095	−0.664905
$19$	7.50391	1.72151	0.860757	−	0.509015i	$-0.169990\pi$
$19$	7.50391	1.72151	0.860757	+	0.509015i	$0.169990\pi$
$20$	−12.3331	−2.75776
$21$	0	0
$22$	8.01371	1.70853
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	11.1647	2.27898
$25$	−0.714752	−0.142950
$26$	13.2828	2.60498
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−0.957621	−0.177826	−0.0889128	−	0.996039i	$-0.528339\pi$
$29$	−0.957621	−0.177826	−0.0889128	+	0.996039i	$0.528339\pi$
$30$	−5.83961	−1.06616
$31$	−1.85707	−0.333539	−0.166769	−	0.985996i	$-0.553334\pi$
$31$	−1.85707	−0.333539	−0.166769	+	0.985996i	$0.553334\pi$
$32$	−32.9033	−5.81654
$33$	2.84078	0.494517
$34$	−18.6778	−3.20321
$35$	0	0
$36$	5.95777	0.992961
$37$	0.551986	0.0907459	0.0453729	−	0.998970i	$-0.485552\pi$
$37$	0.551986	0.0907459	0.0453729	+	0.998970i	$0.485552\pi$
$38$	−21.1682	−3.43393
$39$	4.70863	0.753985
$40$	23.1118	3.65430
$41$	−5.78777	−0.903897	−0.451949	−	0.892044i	$-0.649271\pi$
$41$	−5.78777	−0.903897	−0.451949	+	0.892044i	$0.649271\pi$
$42$	0	0
$43$	−4.33885	−0.661669	−0.330834	−	0.943689i	$-0.607330\pi$
$43$	−4.33885	−0.661669	−0.330834	+	0.943689i	$0.607330\pi$
$44$	−16.9247	−2.55150
$45$	−2.07008	−0.308590
$46$	2.82095	0.415927
$47$	−7.88145	−1.14963	−0.574814	−	0.818284i	$-0.694925\pi$
$47$	−7.88145	−1.14963	−0.574814	+	0.818284i	$0.694925\pi$
$48$	−19.5794	−2.82605
$49$	0	0
$50$	2.01628	0.285145
$51$	−6.62109	−0.927138
$52$	−28.0529	−3.89024
$53$	−0.297011	−0.0407976	−0.0203988	−	0.999792i	$-0.506494\pi$
$53$	−0.297011	−0.0407976	−0.0203988	+	0.999792i	$0.506494\pi$
$54$	2.82095	0.383883
$55$	5.88066	0.792948
$56$	0	0
$57$	−7.50391	−0.993917
$58$	2.70140	0.354711
$59$	12.8839	1.67735	0.838673	−	0.544636i	$-0.183332\pi$
$59$	12.8839	1.67735	0.838673	+	0.544636i	$0.183332\pi$
$60$	12.3331	1.59219
$61$	3.29430	0.421792	0.210896	−	0.977509i	$-0.432362\pi$
$61$	3.29430	0.421792	0.210896	+	0.977509i	$0.432362\pi$
$62$	5.23869	0.665315
$63$	0	0
$64$	53.6598	6.70747
$65$	9.74727	1.20900
$66$	−8.01371	−0.986420
$67$	1.07620	0.131479	0.0657396	−	0.997837i	$-0.479059\pi$
$67$	1.07620	0.131479	0.0657396	+	0.997837i	$0.479059\pi$
$68$	39.4469	4.78364
$69$	1.00000	0.120386
$70$	0	0
$71$	−10.0810	−1.19640	−0.598198	−	0.801348i	$-0.704116\pi$
$71$	−10.0810	−1.19640	−0.598198	+	0.801348i	$0.704116\pi$
$72$	−11.1647	−1.31577
$73$	0.394997	0.0462309	0.0231155	−	0.999733i	$-0.492641\pi$
$73$	0.394997	0.0462309	0.0231155	+	0.999733i	$0.492641\pi$
$74$	−1.55712	−0.181012
$75$	0.714752	0.0825325
$76$	44.7065	5.12819
$77$	0	0
$78$	−13.2828	−1.50398
$79$	−7.76091	−0.873171	−0.436586	−	0.899663i	$-0.643812\pi$
$79$	−7.76091	−0.873171	−0.436586	+	0.899663i	$0.643812\pi$
$80$	−40.5311	−4.53151
$81$	1.00000	0.111111
$82$	16.3270	1.80302
$83$	−5.59160	−0.613758	−0.306879	−	0.951749i	$-0.599285\pi$
$83$	−5.59160	−0.613758	−0.306879	+	0.951749i	$0.599285\pi$
$84$	0	0
$85$	−13.7062	−1.48665
$86$	12.2397	1.31984
$87$	0.957621	0.102668
$88$	31.7164	3.38098
$89$	−3.99625	−0.423602	−0.211801	−	0.977313i	$-0.567933\pi$
$89$	−3.99625	−0.423602	−0.211801	+	0.977313i	$0.567933\pi$
$90$	5.83961	0.615549
$91$	0	0
$92$	−5.95777	−0.621140
$93$	1.85707	0.192569
$94$	22.2332	2.29318
$95$	−15.5337	−1.59373
$96$	32.9033	3.35818
$97$	−6.17643	−0.627121	−0.313561	−	0.949568i	$-0.601522\pi$
$97$	−6.17643	−0.627121	−0.313561	+	0.949568i	$0.601522\pi$
$98$	0	0
$99$	−2.84078	−0.285510
$100$	−4.25833	−0.425833
$101$	15.6794	1.56015	0.780077	−	0.625683i	$-0.215180\pi$
$101$	15.6794	1.56015	0.780077	+	0.625683i	$0.215180\pi$
$102$	18.6778	1.84937
$103$	8.56062	0.843503	0.421752	−	0.906711i	$-0.361415\pi$
$103$	8.56062	0.843503	0.421752	+	0.906711i	$0.361415\pi$
$104$	52.5703	5.15494
$105$	0	0
$106$	0.837854	0.0813795
$107$	−13.6148	−1.31619	−0.658095	−	0.752934i	$-0.728638\pi$
$107$	−13.6148	−1.31619	−0.658095	+	0.752934i	$0.728638\pi$
$108$	−5.95777	−0.573286
$109$	−19.9760	−1.91336	−0.956678	−	0.291147i	$-0.905963\pi$
$109$	−19.9760	−1.91336	−0.956678	+	0.291147i	$0.905963\pi$
$110$	−16.5891	−1.58170
$111$	−0.551986	−0.0523922
$112$	0	0
$113$	−7.31578	−0.688211	−0.344106	−	0.938931i	$-0.611818\pi$
$113$	−7.31578	−0.688211	−0.344106	+	0.938931i	$0.611818\pi$
$114$	21.1682	1.98258
$115$	2.07008	0.193036
$116$	−5.70528	−0.529722
$117$	−4.70863	−0.435313
$118$	−36.3450	−3.34582
$119$	0	0
$120$	−23.1118	−2.10981
$121$	−2.92995	−0.266359
$122$	−9.29305	−0.841353
$123$	5.78777	0.521865
$124$	−11.0640	−0.993573
$125$	11.8300	1.05811
$126$	0	0
$127$	10.5977	0.940394	0.470197	−	0.882561i	$-0.344183\pi$
$127$	10.5977	0.940394	0.470197	+	0.882561i	$0.344183\pi$
$128$	−85.5650	−7.56295
$129$	4.33885	0.382015
$130$	−27.4966	−2.41161
$131$	4.77955	0.417591	0.208796	−	0.977959i	$-0.433046\pi$
$131$	4.77955	0.417591	0.208796	+	0.977959i	$0.433046\pi$
$132$	16.9247	1.47311
$133$	0	0
$134$	−3.03592	−0.262263
$135$	2.07008	0.178164
$136$	−73.9222	−6.33878
$137$	6.28368	0.536851	0.268425	−	0.963300i	$-0.413497\pi$
$137$	6.28368	0.536851	0.268425	+	0.963300i	$0.413497\pi$
$138$	−2.82095	−0.240135
$139$	5.44598	0.461922	0.230961	−	0.972963i	$-0.425813\pi$
$139$	5.44598	0.461922	0.230961	+	0.972963i	$0.425813\pi$
$140$	0	0
$141$	7.88145	0.663738
$142$	28.4380	2.38647
$143$	13.3762	1.11857
$144$	19.5794	1.63162
$145$	1.98236	0.164626
$146$	−1.11427	−0.0922175
$147$	0	0
$148$	3.28860	0.270321
$149$	16.6160	1.36124	0.680619	−	0.732637i	$-0.261711\pi$
$149$	16.6160	1.36124	0.680619	+	0.732637i	$0.261711\pi$
$150$	−2.01628	−0.164629
$151$	2.18384	0.177719	0.0888594	−	0.996044i	$-0.471678\pi$
$151$	2.18384	0.177719	0.0888594	+	0.996044i	$0.471678\pi$
$152$	−83.7786	−6.79534
$153$	6.62109	0.535283
$154$	0	0
$155$	3.84428	0.308780
$156$	28.0529	2.24603
$157$	−7.70832	−0.615191	−0.307595	−	0.951517i	$-0.599524\pi$
$157$	−7.70832	−0.615191	−0.307595	+	0.951517i	$0.599524\pi$
$158$	21.8932	1.74173
$159$	0.297011	0.0235545
$160$	68.1126	5.38478
$161$	0	0
$162$	−2.82095	−0.221635
$163$	−0.820608	−0.0642750	−0.0321375	−	0.999483i	$-0.510231\pi$
$163$	−0.820608	−0.0642750	−0.0321375	+	0.999483i	$0.510231\pi$
$164$	−34.4822	−2.69260
$165$	−5.88066	−0.457809
$166$	15.7736	1.22427
$167$	−13.4885	−1.04377	−0.521887	−	0.853014i	$-0.674772\pi$
$167$	−13.4885	−1.04377	−0.521887	+	0.853014i	$0.674772\pi$
$168$	0	0
$169$	9.17123	0.705479
$170$	38.6645	2.96544
$171$	7.50391	0.573838
$172$	−25.8499	−1.97103
$173$	8.52112	0.647849	0.323924	−	0.946083i	$-0.394998\pi$
$173$	8.52112	0.647849	0.323924	+	0.946083i	$0.394998\pi$
$174$	−2.70140	−0.204793
$175$	0	0
$176$	−55.6210	−4.19259
$177$	−12.8839	−0.968416
$178$	11.2732	0.844965
$179$	18.0842	1.35167	0.675837	−	0.737051i	$-0.263782\pi$
$179$	18.0842	1.35167	0.675837	+	0.737051i	$0.263782\pi$
$180$	−12.3331	−0.919253
$181$	−13.6374	−1.01366	−0.506831	−	0.862046i	$-0.669183\pi$
$181$	−13.6374	−1.01366	−0.506831	+	0.862046i	$0.669183\pi$
$182$	0	0
$183$	−3.29430	−0.243521
$184$	11.1647	0.823070
$185$	−1.14266	−0.0840098
$186$	−5.23869	−0.384120
$187$	−18.8091	−1.37546
$188$	−46.9558	−3.42460
$189$	0	0
$190$	43.8199	3.17903
$191$	−25.0980	−1.81603	−0.908014	−	0.418940i	$-0.862402\pi$
$191$	−25.0980	−1.81603	−0.908014	+	0.418940i	$0.862402\pi$
$192$	−53.6598	−3.87256
$193$	2.57398	0.185279	0.0926395	−	0.995700i	$-0.470470\pi$
$193$	2.57398	0.185279	0.0926395	+	0.995700i	$0.470470\pi$
$194$	17.4234	1.25093
$195$	−9.74727	−0.698016
$196$	0	0
$197$	9.47671	0.675188	0.337594	−	0.941292i	$-0.390387\pi$
$197$	9.47671	0.675188	0.337594	+	0.941292i	$0.390387\pi$
$198$	8.01371	0.569510
$199$	7.39375	0.524129	0.262065	−	0.965050i	$-0.415597\pi$
$199$	7.39375	0.524129	0.262065	+	0.965050i	$0.415597\pi$
$200$	7.97997	0.564269
$201$	−1.07620	−0.0759095
$202$	−44.2307	−3.11206
$203$	0	0
$204$	−39.4469	−2.76184
$205$	11.9812	0.836801
$206$	−24.1491	−1.68255
$207$	−1.00000	−0.0695048
$208$	−92.1924	−6.39239
$209$	−21.3170	−1.47453
$210$	0	0
$211$	−15.4026	−1.06036	−0.530180	−	0.847885i	$-0.677876\pi$
$211$	−15.4026	−1.06036	−0.530180	+	0.847885i	$0.677876\pi$
$212$	−1.76952	−0.121531
$213$	10.0810	0.690740
$214$	38.4066	2.62542
$215$	8.98179	0.612553
$216$	11.1647	0.759659
$217$	0	0
$218$	56.3514	3.81660
$219$	−0.394997	−0.0266914
$220$	35.0356	2.36210
$221$	−31.1763	−2.09714
$222$	1.55712	0.104507
$223$	−2.29485	−0.153675	−0.0768374	−	0.997044i	$-0.524482\pi$
$223$	−2.29485	−0.153675	−0.0768374	+	0.997044i	$0.524482\pi$
$224$	0	0
$225$	−0.714752	−0.0476502
$226$	20.6375	1.37278
$227$	5.20204	0.345271	0.172636	−	0.984986i	$-0.444772\pi$
$227$	5.20204	0.345271	0.172636	+	0.984986i	$0.444772\pi$
$228$	−44.7065	−2.96076
$229$	10.2842	0.679602	0.339801	−	0.940497i	$-0.389640\pi$
$229$	10.2842	0.679602	0.339801	+	0.940497i	$0.389640\pi$
$230$	−5.83961	−0.385052
$231$	0	0
$232$	10.6915	0.701932
$233$	1.62317	0.106337	0.0531686	−	0.998586i	$-0.483068\pi$
$233$	1.62317	0.106337	0.0531686	+	0.998586i	$0.483068\pi$
$234$	13.2828	0.868325
$235$	16.3153	1.06429
$236$	76.7595	4.99662
$237$	7.76091	0.504126
$238$	0	0
$239$	9.44333	0.610839	0.305419	−	0.952218i	$-0.401203\pi$
$239$	9.44333	0.610839	0.305419	+	0.952218i	$0.401203\pi$
$240$	40.5311	2.61627
$241$	−16.8584	−1.08594	−0.542972	−	0.839751i	$-0.682701\pi$
$241$	−16.8584	−1.08594	−0.542972	+	0.839751i	$0.682701\pi$
$242$	8.26523	0.531309
$243$	−1.00000	−0.0641500
$244$	19.6267	1.25647
$245$	0	0
$246$	−16.3270	−1.04097
$247$	−35.3332	−2.24819
$248$	20.7335	1.31658
$249$	5.59160	0.354353
$250$	−33.3719	−2.11062
$251$	18.0770	1.14101	0.570504	−	0.821295i	$-0.306748\pi$
$251$	18.0770	1.14101	0.570504	+	0.821295i	$0.306748\pi$
$252$	0	0
$253$	2.84078	0.178599
$254$	−29.8956	−1.87582
$255$	13.7062	0.858316
$256$	134.055	8.37844
$257$	15.1805	0.946934	0.473467	−	0.880812i	$-0.343002\pi$
$257$	15.1805	0.946934	0.473467	+	0.880812i	$0.343002\pi$
$258$	−12.2397	−0.762010
$259$	0	0
$260$	58.0719	3.60147
$261$	−0.957621	−0.0592752
$262$	−13.4829	−0.832975
$263$	13.6893	0.844116	0.422058	−	0.906569i	$-0.361308\pi$
$263$	13.6893	0.844116	0.422058	+	0.906569i	$0.361308\pi$
$264$	−31.7164	−1.95201
$265$	0.614838	0.0377692
$266$	0	0
$267$	3.99625	0.244567
$268$	6.41177	0.391661
$269$	30.4655	1.85751	0.928756	−	0.370692i	$-0.120879\pi$
$269$	30.4655	1.85751	0.928756	+	0.370692i	$0.120879\pi$
$270$	−5.83961	−0.355387
$271$	−1.39611	−0.0848076	−0.0424038	−	0.999101i	$-0.513502\pi$
$271$	−1.39611	−0.0848076	−0.0424038	+	0.999101i	$0.513502\pi$
$272$	129.637	7.86041
$273$	0	0
$274$	−17.7259	−1.07086
$275$	2.03046	0.122441
$276$	5.95777	0.358615
$277$	−20.2183	−1.21480	−0.607401	−	0.794395i	$-0.707788\pi$
$277$	−20.2183	−1.21480	−0.607401	+	0.794395i	$0.707788\pi$
$278$	−15.3629	−0.921403
$279$	−1.85707	−0.111180
$280$	0	0
$281$	18.2748	1.09018	0.545092	−	0.838376i	$-0.316495\pi$
$281$	18.2748	1.09018	0.545092	+	0.838376i	$0.316495\pi$
$282$	−22.2332	−1.32397
$283$	13.7137	0.815195	0.407598	−	0.913162i	$-0.366367\pi$
$283$	13.7137	0.815195	0.407598	+	0.913162i	$0.366367\pi$
$284$	−60.0603	−3.56392
$285$	15.5337	0.920138
$286$	−37.7336	−2.23124
$287$	0	0
$288$	−32.9033	−1.93885
$289$	26.8388	1.57875
$290$	−5.59213	−0.328381
$291$	6.17643	0.362069
$292$	2.35330	0.137717
$293$	−7.09687	−0.414604	−0.207302	−	0.978277i	$-0.566468\pi$
$293$	−7.09687	−0.414604	−0.207302	+	0.978277i	$0.566468\pi$
$294$	0	0
$295$	−26.6708	−1.55284
$296$	−6.16273	−0.358202
$297$	2.84078	0.164839
$298$	−46.8730	−2.71528
$299$	4.70863	0.272307
$300$	4.25833	0.245855
$301$	0	0
$302$	−6.16052	−0.354498
$303$	−15.6794	−0.900756
$304$	146.922	8.42658
$305$	−6.81947	−0.390482
$306$	−18.6778	−1.06774
$307$	23.7761	1.35698	0.678488	−	0.734612i	$-0.262636\pi$
$307$	23.7761	1.35698	0.678488	+	0.734612i	$0.262636\pi$
$308$	0	0
$309$	−8.56062	−0.486997
$310$	−10.8445	−0.615928
$311$	−18.1193	−1.02745	−0.513725	−	0.857955i	$-0.671735\pi$
$311$	−18.1193	−1.02745	−0.513725	+	0.857955i	$0.671735\pi$
$312$	−52.5703	−2.97621
$313$	−26.9430	−1.52291	−0.761453	−	0.648220i	$-0.775514\pi$
$313$	−26.9430	−1.52291	−0.761453	+	0.648220i	$0.775514\pi$
$314$	21.7448	1.22713
$315$	0	0
$316$	−46.2377	−2.60107
$317$	−9.06131	−0.508934	−0.254467	−	0.967081i	$-0.581900\pi$
$317$	−9.06131	−0.508934	−0.254467	+	0.967081i	$0.581900\pi$
$318$	−0.837854	−0.0469845
$319$	2.72039	0.152313
$320$	−111.080	−6.20958
$321$	13.6148	0.759903
$322$	0	0
$323$	49.6841	2.76449
$324$	5.95777	0.330987
$325$	3.36551	0.186685
$326$	2.31490	0.128210
$327$	19.9760	1.10468
$328$	64.6185	3.56796
$329$	0	0
$330$	16.5891	0.913198
$331$	9.23856	0.507797	0.253899	−	0.967231i	$-0.418287\pi$
$331$	9.23856	0.507797	0.253899	+	0.967231i	$0.418287\pi$
$332$	−33.3134	−1.82831
$333$	0.551986	0.0302486
$334$	38.0505	2.08203
$335$	−2.22783	−0.121719
$336$	0	0
$337$	19.3474	1.05392	0.526959	−	0.849891i	$-0.323332\pi$
$337$	19.3474	1.05392	0.526959	+	0.849891i	$0.323332\pi$
$338$	−25.8716	−1.40723
$339$	7.31578	0.397339
$340$	−81.6584	−4.42855
$341$	5.27552	0.285686
$342$	−21.1682	−1.14464
$343$	0	0
$344$	48.4418	2.61181
$345$	−2.07008	−0.111450
$346$	−24.0377	−1.29227
$347$	2.17712	0.116874	0.0584369	−	0.998291i	$-0.481388\pi$
$347$	2.17712	0.116874	0.0584369	+	0.998291i	$0.481388\pi$
$348$	5.70528	0.305835
$349$	−16.5377	−0.885244	−0.442622	−	0.896708i	$-0.645952\pi$
$349$	−16.5377	−0.885244	−0.442622	+	0.896708i	$0.645952\pi$
$350$	0	0
$351$	4.70863	0.251328
$352$	93.4712	4.98203
$353$	−14.5097	−0.772272	−0.386136	−	0.922442i	$-0.626190\pi$
$353$	−14.5097	−0.772272	−0.386136	+	0.922442i	$0.626190\pi$
$354$	36.3450	1.93171
$355$	20.8685	1.10759
$356$	−23.8087	−1.26186
$357$	0	0
$358$	−51.0145	−2.69620
$359$	21.2656	1.12236	0.561178	−	0.827695i	$-0.310348\pi$
$359$	21.2656	1.12236	0.561178	+	0.827695i	$0.310348\pi$
$360$	23.1118	1.21810
$361$	37.3087	1.96361
$362$	38.4705	2.02196
$363$	2.92995	0.153782
$364$	0	0
$365$	−0.817678	−0.0427992
$366$	9.29305	0.485756
$367$	24.6766	1.28811	0.644055	−	0.764979i	$-0.277251\pi$
$367$	24.6766	1.28811	0.644055	+	0.764979i	$0.277251\pi$
$368$	−19.5794	−1.02065
$369$	−5.78777	−0.301299
$370$	3.22338	0.167575
$371$	0	0
$372$	11.0640	0.573640
$373$	28.0812	1.45399	0.726995	−	0.686643i	$-0.240916\pi$
$373$	28.0812	1.45399	0.726995	+	0.686643i	$0.240916\pi$
$374$	53.0595	2.74364
$375$	−11.8300	−0.610899
$376$	87.9937	4.53793
$377$	4.50908	0.232230
$378$	0	0
$379$	−24.1463	−1.24031	−0.620157	−	0.784478i	$-0.712931\pi$
$379$	−24.1463	−1.24031	−0.620157	+	0.784478i	$0.712931\pi$
$380$	−92.5463	−4.74752
$381$	−10.5977	−0.542937
$382$	70.8002	3.62245
$383$	−5.29680	−0.270654	−0.135327	−	0.990801i	$-0.543208\pi$
$383$	−5.29680	−0.270654	−0.135327	+	0.990801i	$0.543208\pi$
$384$	85.5650	4.36647
$385$	0	0
$386$	−7.26106	−0.369578
$387$	−4.33885	−0.220556
$388$	−36.7977	−1.86812
$389$	4.00575	0.203099	0.101550	−	0.994830i	$-0.467620\pi$
$389$	4.00575	0.203099	0.101550	+	0.994830i	$0.467620\pi$
$390$	27.4966	1.39234
$391$	−6.62109	−0.334843
$392$	0	0
$393$	−4.77955	−0.241097
$394$	−26.7333	−1.34681
$395$	16.0657	0.808355
$396$	−16.9247	−0.850500
$397$	8.82521	0.442924	0.221462	−	0.975169i	$-0.428917\pi$
$397$	8.82521	0.442924	0.221462	+	0.975169i	$0.428917\pi$
$398$	−20.8574	−1.04549
$399$	0	0
$400$	−13.9945	−0.699723
$401$	16.0103	0.799518	0.399759	−	0.916620i	$-0.369094\pi$
$401$	16.0103	0.799518	0.399759	+	0.916620i	$0.369094\pi$
$402$	3.03592	0.151418
$403$	8.74424	0.435582
$404$	93.4139	4.64752
$405$	−2.07008	−0.102863
$406$	0	0
$407$	−1.56807	−0.0777264
$408$	73.9222	3.65970
$409$	25.5538	1.26355	0.631777	−	0.775150i	$-0.282326\pi$
$409$	25.5538	1.26355	0.631777	+	0.775150i	$0.282326\pi$
$410$	−33.7983	−1.66918
$411$	−6.28368	−0.309951
$412$	51.0022	2.51270
$413$	0	0
$414$	2.82095	0.138642
$415$	11.5751	0.568198
$416$	154.930	7.59605
$417$	−5.44598	−0.266691
$418$	60.1342	2.94126
$419$	22.3951	1.09407	0.547035	−	0.837110i	$-0.315756\pi$
$419$	22.3951	1.09407	0.547035	+	0.837110i	$0.315756\pi$
$420$	0	0
$421$	−23.8071	−1.16029	−0.580143	−	0.814515i	$-0.697003\pi$
$421$	−23.8071	−1.16029	−0.580143	+	0.814515i	$0.697003\pi$
$422$	43.4500	2.11511
$423$	−7.88145	−0.383209
$424$	3.31603	0.161041
$425$	−4.73244	−0.229557
$426$	−28.4380	−1.37783
$427$	0	0
$428$	−81.1137	−3.92078
$429$	−13.3762	−0.645810
$430$	−25.3372	−1.22187
$431$	−22.1311	−1.06602	−0.533010	−	0.846109i	$-0.678939\pi$
$431$	−22.1311	−1.06602	−0.533010	+	0.846109i	$0.678939\pi$
$432$	−19.5794	−0.942016
$433$	9.54698	0.458799	0.229399	−	0.973332i	$-0.426324\pi$
$433$	9.54698	0.458799	0.229399	+	0.973332i	$0.426324\pi$
$434$	0	0
$435$	−1.98236	−0.0950467
$436$	−119.012	−5.69966
$437$	−7.50391	−0.358961
$438$	1.11427	0.0532418
$439$	27.8055	1.32708	0.663541	−	0.748140i	$-0.269053\pi$
$439$	27.8055	1.32708	0.663541	+	0.748140i	$0.269053\pi$
$440$	−65.6556	−3.13001
$441$	0	0
$442$	87.9468	4.18320
$443$	28.4254	1.35053	0.675265	−	0.737575i	$-0.264029\pi$
$443$	28.4254	1.35053	0.675265	+	0.737575i	$0.264029\pi$
$444$	−3.28860	−0.156070
$445$	8.27258	0.392158
$446$	6.47367	0.306537
$447$	−16.6160	−0.785911
$448$	0	0
$449$	27.8119	1.31253	0.656263	−	0.754532i	$-0.272136\pi$
$449$	27.8119	1.31253	0.656263	+	0.754532i	$0.272136\pi$
$450$	2.01628	0.0950484
$451$	16.4418	0.774214
$452$	−43.5857	−2.05010
$453$	−2.18384	−0.102606
$454$	−14.6747	−0.688717
$455$	0	0
$456$	83.7786	3.92329
$457$	−21.7807	−1.01886	−0.509430	−	0.860512i	$-0.670144\pi$
$457$	−21.7807	−1.01886	−0.509430	+	0.860512i	$0.670144\pi$
$458$	−29.0114	−1.35561
$459$	−6.62109	−0.309046
$460$	12.3331	0.575033
$461$	−12.9909	−0.605045	−0.302522	−	0.953142i	$-0.597829\pi$
$461$	−12.9909	−0.605045	−0.302522	+	0.953142i	$0.597829\pi$
$462$	0	0
$463$	−8.17514	−0.379931	−0.189966	−	0.981791i	$-0.560838\pi$
$463$	−8.17514	−0.379931	−0.189966	+	0.981791i	$0.560838\pi$
$464$	−18.7497	−0.870432
$465$	−3.84428	−0.178274
$466$	−4.57888	−0.212112
$467$	3.88621	0.179833	0.0899163	−	0.995949i	$-0.471340\pi$
$467$	3.88621	0.179833	0.0899163	+	0.995949i	$0.471340\pi$
$468$	−28.0529	−1.29675
$469$	0	0
$470$	−46.0245	−2.12295
$471$	7.70832	0.355181
$472$	−143.845	−6.62099
$473$	12.3257	0.566738
$474$	−21.8932	−1.00559
$475$	−5.36344	−0.246091
$476$	0	0
$477$	−0.297011	−0.0135992
$478$	−26.6392	−1.21845
$479$	25.6317	1.17114	0.585570	−	0.810622i	$-0.300871\pi$
$479$	25.6317	1.17114	0.585570	+	0.810622i	$0.300871\pi$
$480$	−68.1126	−3.10890
$481$	−2.59910	−0.118509
$482$	47.5567	2.16615
$483$	0	0
$484$	−17.4559	−0.793451
$485$	12.7857	0.580570
$486$	2.82095	0.127961
$487$	1.66033	0.0752366	0.0376183	−	0.999292i	$-0.488023\pi$
$487$	1.66033	0.0752366	0.0376183	+	0.999292i	$0.488023\pi$
$488$	−36.7797	−1.66494
$489$	0.820608	0.0371092
$490$	0	0
$491$	−3.89339	−0.175706	−0.0878532	−	0.996133i	$-0.528001\pi$
$491$	−3.89339	−0.175706	−0.0878532	+	0.996133i	$0.528001\pi$
$492$	34.4822	1.55458
$493$	−6.34049	−0.285561
$494$	99.6731	4.48451
$495$	5.88066	0.264316
$496$	−36.3603	−1.63263
$497$	0	0
$498$	−15.7736	−0.706833
$499$	17.6290	0.789181	0.394591	−	0.918857i	$-0.370886\pi$
$499$	17.6290	0.789181	0.394591	+	0.918857i	$0.370886\pi$
$500$	70.4805	3.15198
$501$	13.4885	0.602624
$502$	−50.9943	−2.27599
$503$	26.2070	1.16851	0.584256	−	0.811570i	$-0.301387\pi$
$503$	26.2070	1.16851	0.584256	+	0.811570i	$0.301387\pi$
$504$	0	0
$505$	−32.4576	−1.44434
$506$	−8.01371	−0.356253
$507$	−9.17123	−0.407308
$508$	63.1387	2.80132
$509$	9.26932	0.410856	0.205428	−	0.978672i	$-0.434141\pi$
$509$	9.26932	0.410856	0.205428	+	0.978672i	$0.434141\pi$
$510$	−38.6645	−1.71210
$511$	0	0
$512$	−207.033	−9.14965
$513$	−7.50391	−0.331306
$514$	−42.8235	−1.88886
$515$	−17.7212	−0.780890
$516$	25.8499	1.13798
$517$	22.3895	0.984689
$518$	0	0
$519$	−8.52112	−0.374036
$520$	−108.825	−4.77229
$521$	4.91510	0.215334	0.107667	−	0.994187i	$-0.465662\pi$
$521$	4.91510	0.215334	0.107667	+	0.994187i	$0.465662\pi$
$522$	2.70140	0.118237
$523$	37.7702	1.65157	0.825787	−	0.563982i	$-0.190731\pi$
$523$	37.7702	1.65157	0.825787	+	0.563982i	$0.190731\pi$
$524$	28.4755	1.24396
$525$	0	0
$526$	−38.6167	−1.68377
$527$	−12.2958	−0.535613
$528$	55.6210	2.42059
$529$	1.00000	0.0434783
$530$	−1.73443	−0.0753387
$531$	12.8839	0.559115
$532$	0	0
$533$	27.2525	1.18044
$534$	−11.2732	−0.487841
$535$	28.1837	1.21849
$536$	−12.0154	−0.518988
$537$	−18.0842	−0.780389
$538$	−85.9416	−3.70520
$539$	0	0
$540$	12.3331	0.530731
$541$	17.4800	0.751525	0.375762	−	0.926716i	$-0.377381\pi$
$541$	17.4800	0.751525	0.375762	+	0.926716i	$0.377381\pi$
$542$	3.93836	0.169167
$543$	13.6374	0.585238
$544$	−217.856	−9.34049
$545$	41.3521	1.77133
$546$	0	0
$547$	19.5104	0.834206	0.417103	−	0.908859i	$-0.363045\pi$
$547$	19.5104	0.834206	0.417103	+	0.908859i	$0.363045\pi$
$548$	37.4367	1.59922
$549$	3.29430	0.140597
$550$	−5.72782	−0.244235
$551$	−7.18590	−0.306130
$552$	−11.1647	−0.475200
$553$	0	0
$554$	57.0349	2.42318
$555$	1.14266	0.0485031
$556$	32.4459	1.37601
$557$	25.4671	1.07908	0.539538	−	0.841961i	$-0.318599\pi$
$557$	25.4671	1.07908	0.539538	+	0.841961i	$0.318599\pi$
$558$	5.23869	0.221772
$559$	20.4301	0.864100
$560$	0	0
$561$	18.8091	0.794120
$562$	−51.5523	−2.17460
$563$	−7.81196	−0.329235	−0.164618	−	0.986357i	$-0.552639\pi$
$563$	−7.81196	−0.329235	−0.164618	+	0.986357i	$0.552639\pi$
$564$	46.9558	1.97720
$565$	15.1443	0.637125
$566$	−38.6857	−1.62608
$567$	0	0
$568$	112.551	4.72254
$569$	−14.7596	−0.618755	−0.309377	−	0.950939i	$-0.600121\pi$
$569$	−14.7596	−0.618755	−0.309377	+	0.950939i	$0.600121\pi$
$570$	−43.8199	−1.83541
$571$	9.71818	0.406693	0.203347	−	0.979107i	$-0.434818\pi$
$571$	9.71818	0.406693	0.203347	+	0.979107i	$0.434818\pi$
$572$	79.6923	3.33210
$573$	25.0980	1.04848
$574$	0	0
$575$	0.714752	0.0298072
$576$	53.6598	2.23582
$577$	27.5176	1.14557	0.572787	−	0.819705i	$-0.305862\pi$
$577$	27.5176	1.14557	0.572787	+	0.819705i	$0.305862\pi$
$578$	−75.7110	−3.14916
$579$	−2.57398	−0.106971
$580$	11.8104	0.490401
$581$	0	0
$582$	−17.4234	−0.722223
$583$	0.843744	0.0349443
$584$	−4.41001	−0.182488
$585$	9.74727	0.403000
$586$	20.0199	0.827016
$587$	−36.9672	−1.52580	−0.762899	−	0.646517i	$-0.776225\pi$
$587$	−36.9672	−1.52580	−0.762899	+	0.646517i	$0.776225\pi$
$588$	0	0
$589$	−13.9353	−0.574192
$590$	75.2371	3.09746
$591$	−9.47671	−0.389820
$592$	10.8076	0.444188
$593$	−33.0024	−1.35525	−0.677623	−	0.735410i	$-0.736990\pi$
$593$	−33.0024	−1.35525	−0.677623	+	0.735410i	$0.736990\pi$
$594$	−8.01371	−0.328807
$595$	0	0
$596$	98.9944	4.05497
$597$	−7.39375	−0.302606
$598$	−13.2828	−0.543175
$599$	−23.4258	−0.957151	−0.478575	−	0.878047i	$-0.658847\pi$
$599$	−23.4258	−0.957151	−0.478575	+	0.878047i	$0.658847\pi$
$600$	−7.97997	−0.325781
$601$	−30.6497	−1.25023	−0.625113	−	0.780534i	$-0.714947\pi$
$601$	−30.6497	−1.25023	−0.625113	+	0.780534i	$0.714947\pi$
$602$	0	0
$603$	1.07620	0.0438264
$604$	13.0108	0.529403
$605$	6.06523	0.246587
$606$	44.2307	1.79675
$607$	−9.39383	−0.381284	−0.190642	−	0.981660i	$-0.561057\pi$
$607$	−9.39383	−0.381284	−0.190642	+	0.981660i	$0.561057\pi$
$608$	−246.904	−10.0133
$609$	0	0
$610$	19.2374	0.778900
$611$	37.1108	1.50134
$612$	39.4469	1.59455
$613$	−0.472654	−0.0190903	−0.00954515	−	0.999954i	$-0.503038\pi$
$613$	−0.472654	−0.0190903	−0.00954515	+	0.999954i	$0.503038\pi$
$614$	−67.0713	−2.70678
$615$	−11.9812	−0.483127
$616$	0	0
$617$	−28.8393	−1.16103	−0.580513	−	0.814251i	$-0.697148\pi$
$617$	−28.8393	−1.16103	−0.580513	+	0.814251i	$0.697148\pi$
$618$	24.1491	0.971419
$619$	27.3438	1.09904	0.549520	−	0.835481i	$-0.314811\pi$
$619$	27.3438	1.09904	0.549520	+	0.835481i	$0.314811\pi$
$620$	22.9033	0.919820
$621$	1.00000	0.0401286
$622$	51.1136	2.04947
$623$	0	0
$624$	92.1924	3.69065
$625$	−20.9154	−0.836615
$626$	76.0048	3.03776
$627$	21.3170	0.851318
$628$	−45.9244	−1.83258
$629$	3.65475	0.145724
$630$	0	0
$631$	−15.6643	−0.623587	−0.311794	−	0.950150i	$-0.600930\pi$
$631$	−15.6643	−0.623587	−0.311794	+	0.950150i	$0.600930\pi$
$632$	86.6480	3.44667
$633$	15.4026	0.612199
$634$	25.5615	1.01518
$635$	−21.9381	−0.870589
$636$	1.76952	0.0701661
$637$	0	0
$638$	−7.67410	−0.303820
$639$	−10.0810	−0.398799
$640$	177.127	7.00155
$641$	26.9359	1.06391	0.531953	−	0.846774i	$-0.321458\pi$
$641$	26.9359	1.06391	0.531953	+	0.846774i	$0.321458\pi$
$642$	−38.4066	−1.51579
$643$	−41.0603	−1.61926	−0.809629	−	0.586941i	$-0.800332\pi$
$643$	−41.0603	−1.61926	−0.809629	+	0.586941i	$0.800332\pi$
$644$	0	0
$645$	−8.98179	−0.353658
$646$	−140.156	−5.51438
$647$	34.6814	1.36347	0.681733	−	0.731601i	$-0.261227\pi$
$647$	34.6814	1.36347	0.681733	+	0.731601i	$0.261227\pi$
$648$	−11.1647	−0.438589
$649$	−36.6005	−1.43669
$650$	−9.49393	−0.372383
$651$	0	0
$652$	−4.88899	−0.191468
$653$	14.3606	0.561974	0.280987	−	0.959712i	$-0.409338\pi$
$653$	14.3606	0.561974	0.280987	+	0.959712i	$0.409338\pi$
$654$	−56.3514	−2.20351
$655$	−9.89407	−0.386593
$656$	−113.321	−4.42445
$657$	0.394997	0.0154103
$658$	0	0
$659$	35.9004	1.39848	0.699240	−	0.714887i	$-0.253522\pi$
$659$	35.9004	1.39848	0.699240	+	0.714887i	$0.253522\pi$
$660$	−35.0356	−1.36376
$661$	38.3773	1.49270	0.746352	−	0.665551i	$-0.231803\pi$
$661$	38.3773	1.49270	0.746352	+	0.665551i	$0.231803\pi$
$662$	−26.0615	−1.01291
$663$	31.1763	1.21079
$664$	62.4283	2.42269
$665$	0	0
$666$	−1.55712	−0.0603373
$667$	0.957621	0.0370792
$668$	−80.3616	−3.10928
$669$	2.29485	0.0887242
$670$	6.28460	0.242795
$671$	−9.35839	−0.361277
$672$	0	0
$673$	47.1429	1.81723	0.908613	−	0.417640i	$-0.137143\pi$
$673$	47.1429	1.81723	0.908613	+	0.417640i	$0.137143\pi$
$674$	−54.5779	−2.10226
$675$	0.714752	0.0275108
$676$	54.6400	2.10154
$677$	16.9128	0.650011	0.325005	−	0.945712i	$-0.394634\pi$
$677$	16.9128	0.650011	0.325005	+	0.945712i	$0.394634\pi$
$678$	−20.6375	−0.792577
$679$	0	0
$680$	153.025	5.86825
$681$	−5.20204	−0.199342
$682$	−14.8820	−0.569861
$683$	36.9614	1.41429	0.707145	−	0.707069i	$-0.249983\pi$
$683$	36.9614	1.41429	0.707145	+	0.707069i	$0.249983\pi$
$684$	44.7065	1.70940
$685$	−13.0077	−0.497000
$686$	0	0
$687$	−10.2842	−0.392368
$688$	−84.9523	−3.23878
$689$	1.39852	0.0532792
$690$	5.83961	0.222310
$691$	28.7329	1.09305	0.546526	−	0.837442i	$-0.315950\pi$
$691$	28.7329	1.09305	0.546526	+	0.837442i	$0.315950\pi$
$692$	50.7668	1.92987
$693$	0	0
$694$	−6.14154	−0.233130
$695$	−11.2736	−0.427634
$696$	−10.6915	−0.405261
$697$	−38.3213	−1.45152
$698$	46.6521	1.76581
$699$	−1.62317	−0.0613939
$700$	0	0
$701$	−42.4914	−1.60488	−0.802440	−	0.596733i	$-0.796465\pi$
$701$	−42.4914	−1.60488	−0.802440	+	0.596733i	$0.796465\pi$
$702$	−13.2828	−0.501328
$703$	4.14205	0.156220
$704$	−152.436	−5.74514
$705$	−16.3153	−0.614468
$706$	40.9311	1.54046
$707$	0	0
$708$	−76.7595	−2.88480
$709$	−24.0529	−0.903324	−0.451662	−	0.892189i	$-0.649169\pi$
$709$	−24.0529	−0.903324	−0.451662	+	0.892189i	$0.649169\pi$
$710$	−58.8691	−2.20932
$711$	−7.76091	−0.291057
$712$	44.6168	1.67209
$713$	1.85707	0.0695477
$714$	0	0
$715$	−27.6899	−1.03554
$716$	107.741	4.02648
$717$	−9.44333	−0.352668
$718$	−59.9892	−2.23878
$719$	−28.7273	−1.07135	−0.535673	−	0.844425i	$-0.679942\pi$
$719$	−28.7273	−1.07135	−0.535673	+	0.844425i	$0.679942\pi$
$720$	−40.5311	−1.51050
$721$	0	0
$722$	−105.246	−3.91685
$723$	16.8584	0.626970
$724$	−81.2486	−3.01958
$725$	0.684462	0.0254203
$726$	−8.26523	−0.306752
$727$	39.7047	1.47256	0.736282	−	0.676675i	$-0.236580\pi$
$727$	39.7047	1.47256	0.736282	+	0.676675i	$0.236580\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	2.30663	0.0853722
$731$	−28.7279	−1.06254
$732$	−19.6267	−0.725422
$733$	−24.5150	−0.905481	−0.452740	−	0.891642i	$-0.649554\pi$
$733$	−24.5150	−0.905481	−0.452740	+	0.891642i	$0.649554\pi$
$734$	−69.6116	−2.56941
$735$	0	0
$736$	32.9033	1.21283
$737$	−3.05726	−0.112616
$738$	16.3270	0.601005
$739$	27.1793	0.999806	0.499903	−	0.866082i	$-0.333369\pi$
$739$	27.1793	0.999806	0.499903	+	0.866082i	$0.333369\pi$
$740$	−6.80768	−0.250255
$741$	35.3332	1.29800
$742$	0	0
$743$	15.0614	0.552548	0.276274	−	0.961079i	$-0.410900\pi$
$743$	15.0614	0.552548	0.276274	+	0.961079i	$0.410900\pi$
$744$	−20.7335	−0.760128
$745$	−34.3966	−1.26019
$746$	−79.2157	−2.90029
$747$	−5.59160	−0.204586
$748$	−112.060	−4.09732
$749$	0	0
$750$	33.3719	1.21857
$751$	−44.4296	−1.62126	−0.810630	−	0.585559i	$-0.800875\pi$
$751$	−44.4296	−1.62126	−0.810630	+	0.585559i	$0.800875\pi$
$752$	−154.314	−5.62726
$753$	−18.0770	−0.658762
$754$	−12.7199	−0.463232
$755$	−4.52074	−0.164527
$756$	0	0
$757$	−41.0324	−1.49135	−0.745674	−	0.666311i	$-0.767872\pi$
$757$	−41.0324	−1.49135	−0.745674	+	0.666311i	$0.767872\pi$
$758$	68.1156	2.47407
$759$	−2.84078	−0.103114
$760$	173.429	6.29092
$761$	35.7950	1.29757	0.648783	−	0.760973i	$-0.275278\pi$
$761$	35.7950	1.29757	0.648783	+	0.760973i	$0.275278\pi$
$762$	29.8956	1.08300
$763$	0	0
$764$	−149.528	−5.40973
$765$	−13.7062	−0.495549
$766$	14.9420	0.539877
$767$	−60.6657	−2.19051
$768$	−134.055	−4.83730
$769$	23.2391	0.838025	0.419012	−	0.907981i	$-0.362376\pi$
$769$	23.2391	0.838025	0.419012	+	0.907981i	$0.362376\pi$
$770$	0	0
$771$	−15.1805	−0.546713
$772$	15.3352	0.551924
$773$	−14.1080	−0.507429	−0.253715	−	0.967279i	$-0.581652\pi$
$773$	−14.1080	−0.507429	−0.253715	+	0.967279i	$0.581652\pi$
$774$	12.2397	0.439947
$775$	1.32734	0.0476796
$776$	68.9577	2.47544
$777$	0	0
$778$	−11.3000	−0.405125
$779$	−43.4309	−1.55607
$780$	−58.0719	−2.07931
$781$	28.6380	1.02475
$782$	18.6778	0.667916
$783$	0.957621	0.0342226
$784$	0	0
$785$	15.9569	0.569525
$786$	13.4829	0.480919
$787$	−19.7596	−0.704353	−0.352176	−	0.935934i	$-0.614558\pi$
$787$	−19.7596	−0.704353	−0.352176	+	0.935934i	$0.614558\pi$
$788$	56.4600	2.01131
$789$	−13.6893	−0.487351
$790$	−45.3207	−1.61244
$791$	0	0
$792$	31.7164	1.12699
$793$	−15.5116	−0.550834
$794$	−24.8955	−0.883507
$795$	−0.614838	−0.0218060
$796$	44.0502	1.56132
$797$	12.3211	0.436434	0.218217	−	0.975900i	$-0.429976\pi$
$797$	12.3211	0.436434	0.218217	+	0.975900i	$0.429976\pi$
$798$	0	0
$799$	−52.1838	−1.84613
$800$	23.5177	0.831477
$801$	−3.99625	−0.141201
$802$	−45.1644	−1.59481
$803$	−1.12210	−0.0395981
$804$	−6.41177	−0.226126
$805$	0	0
$806$	−24.6671	−0.868861
$807$	−30.4655	−1.07243
$808$	−175.055	−6.15840
$809$	−43.9518	−1.54526	−0.772631	−	0.634855i	$-0.781060\pi$
$809$	−43.9518	−1.54526	−0.772631	+	0.634855i	$0.781060\pi$
$810$	5.83961	0.205183
$811$	39.2083	1.37679	0.688394	−	0.725337i	$-0.258316\pi$
$811$	39.2083	1.37679	0.688394	+	0.725337i	$0.258316\pi$
$812$	0	0
$813$	1.39611	0.0489637
$814$	4.42345	0.155042
$815$	1.69873	0.0595038
$816$	−129.637	−4.53821
$817$	−32.5584	−1.13907
$818$	−72.0860	−2.52043
$819$	0	0
$820$	71.3810	2.49273
$821$	13.1234	0.458008	0.229004	−	0.973425i	$-0.426453\pi$
$821$	13.1234	0.458008	0.229004	+	0.973425i	$0.426453\pi$
$822$	17.7259	0.618263
$823$	46.5927	1.62412	0.812060	−	0.583575i	$-0.198346\pi$
$823$	46.5927	1.62412	0.812060	+	0.583575i	$0.198346\pi$
$824$	−95.5765	−3.32956
$825$	−2.03046	−0.0706915
$826$	0	0
$827$	24.4382	0.849799	0.424900	−	0.905240i	$-0.360309\pi$
$827$	24.4382	0.849799	0.424900	+	0.905240i	$0.360309\pi$
$828$	−5.95777	−0.207047
$829$	−38.3871	−1.33324	−0.666620	−	0.745398i	$-0.732259\pi$
$829$	−38.3871	−1.33324	−0.666620	+	0.745398i	$0.732259\pi$
$830$	−32.6527	−1.13339
$831$	20.2183	0.701366
$832$	−252.664	−8.75956
$833$	0	0
$834$	15.3629	0.531972
$835$	27.9224	0.966295
$836$	−127.002	−4.39244
$837$	1.85707	0.0641896
$838$	−63.1754	−2.18236
$839$	−53.3309	−1.84119	−0.920594	−	0.390522i	$-0.872295\pi$
$839$	−53.3309	−1.84119	−0.920594	+	0.390522i	$0.872295\pi$
$840$	0	0
$841$	−28.0830	−0.968378
$842$	67.1586	2.31444
$843$	−18.2748	−0.629418
$844$	−91.7652	−3.15869
$845$	−18.9852	−0.653111
$846$	22.2332	0.764392
$847$	0	0
$848$	−5.81531	−0.199699
$849$	−13.7137	−0.470653
$850$	13.3500	0.457901
$851$	−0.551986	−0.0189218
$852$	60.0603	2.05763
$853$	55.5710	1.90272	0.951358	−	0.308089i	$-0.0996894\pi$
$853$	55.5710	1.90272	0.951358	+	0.308089i	$0.0996894\pi$
$854$	0	0
$855$	−15.5337	−0.531242
$856$	152.005	5.19541
$857$	−32.5491	−1.11186	−0.555929	−	0.831230i	$-0.687637\pi$
$857$	−32.5491	−1.11186	−0.555929	+	0.831230i	$0.687637\pi$
$858$	37.7336	1.28821
$859$	24.0682	0.821195	0.410598	−	0.911817i	$-0.365320\pi$
$859$	24.0682	0.821195	0.410598	+	0.911817i	$0.365320\pi$
$860$	53.5114	1.82472
$861$	0	0
$862$	62.4308	2.12640
$863$	−3.20736	−0.109180	−0.0545900	−	0.998509i	$-0.517385\pi$
$863$	−3.20736	−0.109180	−0.0545900	+	0.998509i	$0.517385\pi$
$864$	32.9033	1.11939
$865$	−17.6394	−0.599759
$866$	−26.9316	−0.915172
$867$	−26.8388	−0.911494
$868$	0	0
$869$	22.0471	0.747896
$870$	5.59213	0.189591
$871$	−5.06745	−0.171704
$872$	223.026	7.55260
$873$	−6.17643	−0.209040
$874$	21.1682	0.716024
$875$	0	0
$876$	−2.35330	−0.0795107
$877$	−17.8386	−0.602367	−0.301183	−	0.953566i	$-0.597382\pi$
$877$	−17.8386	−0.602367	−0.301183	+	0.953566i	$0.597382\pi$
$878$	−78.4378	−2.64715
$879$	7.09687	0.239372
$880$	115.140	3.88137
$881$	−38.9709	−1.31296	−0.656481	−	0.754342i	$-0.727956\pi$
$881$	−38.9709	−1.31296	−0.656481	+	0.754342i	$0.727956\pi$
$882$	0	0
$883$	34.4782	1.16028	0.580142	−	0.814515i	$-0.302997\pi$
$883$	34.4782	1.16028	0.580142	+	0.814515i	$0.302997\pi$
$884$	−185.741	−6.24714
$885$	26.6708	0.896530
$886$	−80.1866	−2.69392
$887$	−45.3754	−1.52356	−0.761779	−	0.647837i	$-0.775674\pi$
$887$	−45.3754	−1.52356	−0.761779	+	0.647837i	$0.775674\pi$
$888$	6.16273	0.206808
$889$	0	0
$890$	−23.3365	−0.782243
$891$	−2.84078	−0.0951699
$892$	−13.6722	−0.457779
$893$	−59.1417	−1.97910
$894$	46.8730	1.56767
$895$	−37.4357	−1.25134
$896$	0	0
$897$	−4.70863	−0.157217
$898$	−78.4561	−2.61811
$899$	1.77836	0.0593118
$900$	−4.25833	−0.141944
$901$	−1.96654	−0.0655148
$902$	−46.3815	−1.54434
$903$	0	0
$904$	81.6783	2.71658
$905$	28.2306	0.938417
$906$	6.16052	0.204670
$907$	6.61675	0.219706	0.109853	−	0.993948i	$-0.464962\pi$
$907$	6.61675	0.219706	0.109853	+	0.993948i	$0.464962\pi$
$908$	30.9925	1.02852
$909$	15.6794	0.520051
$910$	0	0
$911$	13.0701	0.433031	0.216515	−	0.976279i	$-0.430531\pi$
$911$	13.0701	0.433031	0.216515	+	0.976279i	$0.430531\pi$
$912$	−146.922	−4.86509
$913$	15.8845	0.525701
$914$	61.4424	2.03233
$915$	6.81947	0.225445
$916$	61.2711	2.02446
$917$	0	0
$918$	18.6778	0.616458
$919$	27.9158	0.920858	0.460429	−	0.887696i	$-0.347696\pi$
$919$	27.9158	0.920858	0.460429	+	0.887696i	$0.347696\pi$
$920$	−23.1118	−0.761973
$921$	−23.7761	−0.783450
$922$	36.6466	1.20689
$923$	47.4678	1.56242
$924$	0	0
$925$	−0.394533	−0.0129722
$926$	23.0617	0.757854
$927$	8.56062	0.281168
$928$	31.5089	1.03433
$929$	37.3003	1.22378	0.611892	−	0.790942i	$-0.290409\pi$
$929$	37.3003	1.22378	0.611892	+	0.790942i	$0.290409\pi$
$930$	10.8445	0.355606
$931$	0	0
$932$	9.67046	0.316766
$933$	18.1193	0.593199
$934$	−10.9628	−0.358714
$935$	38.9364	1.27336
$936$	52.5703	1.71831
$937$	41.5345	1.35687	0.678437	−	0.734659i	$-0.262658\pi$
$937$	41.5345	1.35687	0.678437	+	0.734659i	$0.262658\pi$
$938$	0	0
$939$	26.9430	0.879251
$940$	97.2025	3.17040
$941$	−16.9071	−0.551155	−0.275578	−	0.961279i	$-0.588869\pi$
$941$	−16.9071	−0.551155	−0.275578	+	0.961279i	$0.588869\pi$
$942$	−21.7448	−0.708484
$943$	5.78777	0.188476
$944$	252.260	8.21037
$945$	0	0
$946$	−34.7703	−1.13048
$947$	−3.37355	−0.109626	−0.0548128	−	0.998497i	$-0.517456\pi$
$947$	−3.37355	−0.109626	−0.0548128	+	0.998497i	$0.517456\pi$
$948$	46.2377	1.50173
$949$	−1.85990	−0.0603748
$950$	15.1300	0.490882
$951$	9.06131	0.293833
$952$	0	0
$953$	21.0727	0.682611	0.341306	−	0.939952i	$-0.389131\pi$
$953$	21.0727	0.682611	0.341306	+	0.939952i	$0.389131\pi$
$954$	0.837854	0.0271265
$955$	51.9550	1.68122
$956$	56.2612	1.81962
$957$	−2.72039	−0.0879378
$958$	−72.3057	−2.33609
$959$	0	0
$960$	111.080	3.58510
$961$	−27.5513	−0.888752
$962$	7.33193	0.236391
$963$	−13.6148	−0.438730
$964$	−100.438	−3.23490
$965$	−5.32835	−0.171526
$966$	0	0
$967$	−20.3719	−0.655117	−0.327559	−	0.944831i	$-0.606226\pi$
$967$	−20.3719	−0.655117	−0.327559	+	0.944831i	$0.606226\pi$
$968$	32.7119	1.05140
$969$	−49.6841	−1.59608
$970$	−36.0679	−1.15807
$971$	42.5073	1.36413	0.682063	−	0.731294i	$-0.261083\pi$
$971$	42.5073	1.36413	0.682063	+	0.731294i	$0.261083\pi$
$972$	−5.95777	−0.191095
$973$	0	0
$974$	−4.68370	−0.150075
$975$	−3.36551	−0.107782
$976$	64.5005	2.06461
$977$	35.7904	1.14504	0.572519	−	0.819892i	$-0.305966\pi$
$977$	35.7904	1.14504	0.572519	+	0.819892i	$0.305966\pi$
$978$	−2.31490	−0.0740222
$979$	11.3525	0.362827
$980$	0	0
$981$	−19.9760	−0.637785
$982$	10.9831	0.350484
$983$	2.70906	0.0864057	0.0432028	−	0.999066i	$-0.486244\pi$
$983$	2.70906	0.0864057	0.0432028	+	0.999066i	$0.486244\pi$
$984$	−64.6185	−2.05996
$985$	−19.6176	−0.625068
$986$	17.8862	0.569613
$987$	0	0
$988$	−210.507	−6.69711
$989$	4.33885	0.137967
$990$	−16.5891	−0.527235
$991$	−25.5260	−0.810859	−0.405429	−	0.914126i	$-0.632878\pi$
$991$	−25.5260	−0.810859	−0.405429	+	0.914126i	$0.632878\pi$
$992$	61.1036	1.94004
$993$	−9.23856	−0.293177
$994$	0	0
$995$	−15.3057	−0.485223
$996$	33.3134	1.05558
$997$	−5.50502	−0.174346	−0.0871729	−	0.996193i	$-0.527783\pi$
$997$	−5.50502	−0.174346	−0.0871729	+	0.996193i	$0.527783\pi$
$998$	−49.7305	−1.57419
$999$	−0.551986	−0.0174641

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3381.2.a.ba.1.1	✓	6
7.6	odd	2		3381.2.a.bb.1.1	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3381.2.a.ba.1.1	✓	6	1.1	even	1	trivial
3381.2.a.bb.1.1	yes	6	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:	\( N \)	\(=\)	\( 3381 = 3 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3381.a (trivial)

\(f(q)\)	\(=\)	\(q-2.82095 q^{2} -1.00000 q^{3} +5.95777 q^{4} -2.07008 q^{5} +2.82095 q^{6} -11.1647 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.82095 q^{2} -1.00000 q^{3} +5.95777 q^{4} -2.07008 q^{5} +2.82095 q^{6} -11.1647 q^{8} +1.00000 q^{9} +5.83961 q^{10} -2.84078 q^{11} -5.95777 q^{12} -4.70863 q^{13} +2.07008 q^{15} +19.5794 q^{16} +6.62109 q^{17} -2.82095 q^{18} +7.50391 q^{19} -12.3331 q^{20} +8.01371 q^{22} -1.00000 q^{23} +11.1647 q^{24} -0.714752 q^{25} +13.2828 q^{26} -1.00000 q^{27} -0.957621 q^{29} -5.83961 q^{30} -1.85707 q^{31} -32.9033 q^{32} +2.84078 q^{33} -18.6778 q^{34} +5.95777 q^{36} +0.551986 q^{37} -21.1682 q^{38} +4.70863 q^{39} +23.1118 q^{40} -5.78777 q^{41} -4.33885 q^{43} -16.9247 q^{44} -2.07008 q^{45} +2.82095 q^{46} -7.88145 q^{47} -19.5794 q^{48} +2.01628 q^{50} -6.62109 q^{51} -28.0529 q^{52} -0.297011 q^{53} +2.82095 q^{54} +5.88066 q^{55} -7.50391 q^{57} +2.70140 q^{58} +12.8839 q^{59} +12.3331 q^{60} +3.29430 q^{61} +5.23869 q^{62} +53.6598 q^{64} +9.74727 q^{65} -8.01371 q^{66} +1.07620 q^{67} +39.4469 q^{68} +1.00000 q^{69} -10.0810 q^{71} -11.1647 q^{72} +0.394997 q^{73} -1.55712 q^{74} +0.714752 q^{75} +44.7065 q^{76} -13.2828 q^{78} -7.76091 q^{79} -40.5311 q^{80} +1.00000 q^{81} +16.3270 q^{82} -5.59160 q^{83} -13.7062 q^{85} +12.2397 q^{86} +0.957621 q^{87} +31.7164 q^{88} -3.99625 q^{89} +5.83961 q^{90} -5.95777 q^{92} +1.85707 q^{93} +22.2332 q^{94} -15.5337 q^{95} +32.9033 q^{96} -6.17643 q^{97} -2.84078 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 6 q^{3} + 7 q^{4} + 2 q^{5} + 3 q^{6} - 9 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 - 6 * q^3 + 7 * q^4 + 2 * q^5 + 3 * q^6 - 9 * q^8 + 6 * q^9	\( 6 q - 3 q^{2} - 6 q^{3} + 7 q^{4} + 2 q^{5} + 3 q^{6} - 9 q^{8} + 6 q^{9} + 8 q^{10} - 3 q^{11} - 7 q^{12} - 2 q^{15} + 5 q^{16} + 8 q^{17} - 3 q^{18} + 19 q^{19} + 24 q^{22} - 6 q^{23} + 9 q^{24} + 20 q^{26} - 6 q^{27} - 12 q^{29} - 8 q^{30} - 2 q^{31} - 41 q^{32} + 3 q^{33} + 2 q^{34} + 7 q^{36} - 10 q^{37} - 20 q^{38} + 22 q^{40} + 3 q^{41} - 2 q^{43} - 14 q^{44} + 2 q^{45} + 3 q^{46} + 7 q^{47} - 5 q^{48} + 17 q^{50} - 8 q^{51} - 44 q^{52} - 5 q^{53} + 3 q^{54} + 24 q^{55} - 19 q^{57} - 12 q^{58} + 21 q^{59} + 29 q^{61} + 10 q^{62} + 59 q^{64} - 18 q^{65} - 24 q^{66} + 16 q^{67} + 54 q^{68} + 6 q^{69} - 6 q^{71} - 9 q^{72} - 8 q^{73} - 16 q^{74} + 40 q^{76} - 20 q^{78} - 12 q^{79} - 78 q^{80} + 6 q^{81} + 44 q^{82} + 24 q^{83} + 10 q^{85} + 12 q^{86} + 12 q^{87} + 28 q^{88} + 18 q^{89} + 8 q^{90} - 7 q^{92} + 2 q^{93} - 8 q^{94} + 6 q^{95} + 41 q^{96} + 22 q^{97} - 3 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 6 * q^3 + 7 * q^4 + 2 * q^5 + 3 * q^6 - 9 * q^8 + 6 * q^9 + 8 * q^10 - 3 * q^11 - 7 * q^12 - 2 * q^15 + 5 * q^16 + 8 * q^17 - 3 * q^18 + 19 * q^19 + 24 * q^22 - 6 * q^23 + 9 * q^24 + 20 * q^26 - 6 * q^27 - 12 * q^29 - 8 * q^30 - 2 * q^31 - 41 * q^32 + 3 * q^33 + 2 * q^34 + 7 * q^36 - 10 * q^37 - 20 * q^38 + 22 * q^40 + 3 * q^41 - 2 * q^43 - 14 * q^44 + 2 * q^45 + 3 * q^46 + 7 * q^47 - 5 * q^48 + 17 * q^50 - 8 * q^51 - 44 * q^52 - 5 * q^53 + 3 * q^54 + 24 * q^55 - 19 * q^57 - 12 * q^58 + 21 * q^59 + 29 * q^61 + 10 * q^62 + 59 * q^64 - 18 * q^65 - 24 * q^66 + 16 * q^67 + 54 * q^68 + 6 * q^69 - 6 * q^71 - 9 * q^72 - 8 * q^73 - 16 * q^74 + 40 * q^76 - 20 * q^78 - 12 * q^79 - 78 * q^80 + 6 * q^81 + 44 * q^82 + 24 * q^83 + 10 * q^85 + 12 * q^86 + 12 * q^87 + 28 * q^88 + 18 * q^89 + 8 * q^90 - 7 * q^92 + 2 * q^93 - 8 * q^94 + 6 * q^95 + 41 * q^96 + 22 * q^97 - 3 * q^99

Introduction

L-functions

Modular forms

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Database

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