LMFDB - Embedded newform 3381.2.a.bb.1.4

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:	$1$
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			1.4
Root			$0.584512$ 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)

$f(q)$	$=$	$q-0.415488 q^{2} +1.00000 q^{3} -1.82737 q^{4} +2.48000 q^{5} -0.415488 q^{6} +1.59023 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.415488 q^{2} +1.00000 q^{3} -1.82737 q^{4} +2.48000 q^{5} -0.415488 q^{6} +1.59023 q^{8} +1.00000 q^{9} -1.03041 q^{10} -1.97936 q^{11} -1.82737 q^{12} -5.89188 q^{13} +2.48000 q^{15} +2.99402 q^{16} +5.84286 q^{17} -0.415488 q^{18} -4.12488 q^{19} -4.53188 q^{20} +0.822402 q^{22} -1.00000 q^{23} +1.59023 q^{24} +1.15041 q^{25} +2.44801 q^{26} +1.00000 q^{27} -6.07143 q^{29} -1.03041 q^{30} -1.49862 q^{31} -4.42443 q^{32} -1.97936 q^{33} -2.42764 q^{34} -1.82737 q^{36} -6.21290 q^{37} +1.71384 q^{38} -5.89188 q^{39} +3.94376 q^{40} +3.52463 q^{41} -11.2694 q^{43} +3.61703 q^{44} +2.48000 q^{45} +0.415488 q^{46} +8.41207 q^{47} +2.99402 q^{48} -0.477981 q^{50} +5.84286 q^{51} +10.7667 q^{52} -1.88774 q^{53} -0.415488 q^{54} -4.90883 q^{55} -4.12488 q^{57} +2.52260 q^{58} +3.95594 q^{59} -4.53188 q^{60} -13.0869 q^{61} +0.622657 q^{62} -4.14974 q^{64} -14.6119 q^{65} +0.822402 q^{66} +10.2215 q^{67} -10.6771 q^{68} -1.00000 q^{69} +8.79143 q^{71} +1.59023 q^{72} -5.75816 q^{73} +2.58139 q^{74} +1.15041 q^{75} +7.53768 q^{76} +2.44801 q^{78} -11.1769 q^{79} +7.42518 q^{80} +1.00000 q^{81} -1.46444 q^{82} -8.82294 q^{83} +14.4903 q^{85} +4.68230 q^{86} -6.07143 q^{87} -3.14764 q^{88} -4.64857 q^{89} -1.03041 q^{90} +1.82737 q^{92} -1.49862 q^{93} -3.49511 q^{94} -10.2297 q^{95} -4.42443 q^{96} -6.85290 q^{97} -1.97936 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.415488	−0.293794	−0.146897	−	0.989152i	$-0.546929\pi$
$2$	−0.415488	−0.293794	−0.146897	+	0.989152i	$0.546929\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.82737	−0.913685
$5$	2.48000	1.10909	0.554545	−	0.832154i	$-0.312892\pi$
$5$	2.48000	1.10909	0.554545	+	0.832154i	$0.312892\pi$
$6$	−0.415488	−0.169622
$7$	0	0
$7$	0	0
$8$	1.59023	0.562230
$9$	1.00000	0.333333
$10$	−1.03041	−0.325844
$11$	−1.97936	−0.596801	−0.298400	−	0.954441i	$-0.596453\pi$
$11$	−1.97936	−0.596801	−0.298400	+	0.954441i	$0.596453\pi$
$12$	−1.82737	−0.527516
$13$	−5.89188	−1.63411	−0.817057	−	0.576556i	$-0.804396\pi$
$13$	−5.89188	−1.63411	−0.817057	+	0.576556i	$0.804396\pi$
$14$	0	0
$15$	2.48000	0.640334
$16$	2.99402	0.748505
$17$	5.84286	1.41710	0.708551	−	0.705660i	$-0.249349\pi$
$17$	5.84286	1.41710	0.708551	+	0.705660i	$0.249349\pi$
$18$	−0.415488	−0.0979314
$19$	−4.12488	−0.946312	−0.473156	−	0.880979i	$-0.656885\pi$
$19$	−4.12488	−0.946312	−0.473156	+	0.880979i	$0.656885\pi$
$20$	−4.53188	−1.01336
$21$	0	0
$22$	0.822402	0.175337
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	1.59023	0.324603
$25$	1.15041	0.230082
$26$	2.44801	0.480094
$27$	1.00000	0.192450
$28$	0	0
$29$	−6.07143	−1.12744	−0.563718	−	0.825967i	$-0.690630\pi$
$29$	−6.07143	−1.12744	−0.563718	+	0.825967i	$0.690630\pi$
$30$	−1.03041	−0.188126
$31$	−1.49862	−0.269160	−0.134580	−	0.990903i	$-0.542968\pi$
$31$	−1.49862	−0.269160	−0.134580	+	0.990903i	$0.542968\pi$
$32$	−4.42443	−0.782136
$33$	−1.97936	−0.344563
$34$	−2.42764	−0.416336
$35$	0	0
$36$	−1.82737	−0.304562
$37$	−6.21290	−1.02139	−0.510697	−	0.859761i	$-0.670613\pi$
$37$	−6.21290	−1.02139	−0.510697	+	0.859761i	$0.670613\pi$
$38$	1.71384	0.278021
$39$	−5.89188	−0.943456
$40$	3.94376	0.623564
$41$	3.52463	0.550454	0.275227	−	0.961379i	$-0.411247\pi$
$41$	3.52463	0.550454	0.275227	+	0.961379i	$0.411247\pi$
$42$	0	0
$43$	−11.2694	−1.71857	−0.859283	−	0.511500i	$-0.829090\pi$
$43$	−11.2694	−1.71857	−0.859283	+	0.511500i	$0.829090\pi$
$44$	3.61703	0.545288
$45$	2.48000	0.369697
$46$	0.415488	0.0612603
$47$	8.41207	1.22703	0.613513	−	0.789684i	$-0.289756\pi$
$47$	8.41207	1.22703	0.613513	+	0.789684i	$0.289756\pi$
$48$	2.99402	0.432150
$49$	0	0
$50$	−0.477981	−0.0675967
$51$	5.84286	0.818164
$52$	10.7667	1.49307
$53$	−1.88774	−0.259300	−0.129650	−	0.991560i	$-0.541385\pi$
$53$	−1.88774	−0.259300	−0.129650	+	0.991560i	$0.541385\pi$
$54$	−0.415488	−0.0565407
$55$	−4.90883	−0.661906
$56$	0	0
$57$	−4.12488	−0.546354
$58$	2.52260	0.331234
$59$	3.95594	0.515020	0.257510	−	0.966276i	$-0.417098\pi$
$59$	3.95594	0.515020	0.257510	+	0.966276i	$0.417098\pi$
$60$	−4.53188	−0.585063
$61$	−13.0869	−1.67561	−0.837804	−	0.545971i	$-0.816161\pi$
$61$	−13.0869	−1.67561	−0.837804	+	0.545971i	$0.816161\pi$
$62$	0.622657	0.0790775
$63$	0	0
$64$	−4.14974	−0.518718
$65$	−14.6119	−1.81238
$66$	0.822402	0.101231
$67$	10.2215	1.24875	0.624376	−	0.781124i	$-0.285353\pi$
$67$	10.2215	1.24875	0.624376	+	0.781124i	$0.285353\pi$
$68$	−10.6771	−1.29478
$69$	−1.00000	−0.120386
$70$	0	0
$71$	8.79143	1.04335	0.521675	−	0.853144i	$-0.325307\pi$
$71$	8.79143	1.04335	0.521675	+	0.853144i	$0.325307\pi$
$72$	1.59023	0.187410
$73$	−5.75816	−0.673942	−0.336971	−	0.941515i	$-0.609402\pi$
$73$	−5.75816	−0.673942	−0.336971	+	0.941515i	$0.609402\pi$
$74$	2.58139	0.300080
$75$	1.15041	0.132838
$76$	7.53768	0.864631
$77$	0	0
$78$	2.44801	0.277182
$79$	−11.1769	−1.25750	−0.628752	−	0.777606i	$-0.716434\pi$
$79$	−11.1769	−1.25750	−0.628752	+	0.777606i	$0.716434\pi$
$80$	7.42518	0.830160
$81$	1.00000	0.111111
$82$	−1.46444	−0.161720
$83$	−8.82294	−0.968444	−0.484222	−	0.874945i	$-0.660897\pi$
$83$	−8.82294	−0.968444	−0.484222	+	0.874945i	$0.660897\pi$
$84$	0	0
$85$	14.4903	1.57169
$86$	4.68230	0.504905
$87$	−6.07143	−0.650925
$88$	−3.14764	−0.335539
$89$	−4.64857	−0.492748	−0.246374	−	0.969175i	$-0.579239\pi$
$89$	−4.64857	−0.492748	−0.246374	+	0.969175i	$0.579239\pi$
$90$	−1.03041	−0.108615
$91$	0	0
$92$	1.82737	0.190516
$93$	−1.49862	−0.155399
$94$	−3.49511	−0.360493
$95$	−10.2297	−1.04955
$96$	−4.42443	−0.451567
$97$	−6.85290	−0.695807	−0.347903	−	0.937530i	$-0.613106\pi$
$97$	−6.85290	−0.695807	−0.347903	+	0.937530i	$0.613106\pi$
$98$	0	0
$99$	−1.97936	−0.198934
$100$	−2.10222	−0.210222
$101$	6.83798	0.680404	0.340202	−	0.940352i	$-0.389505\pi$
$101$	6.83798	0.680404	0.340202	+	0.940352i	$0.389505\pi$
$102$	−2.42764	−0.240372
$103$	2.27732	0.224391	0.112196	−	0.993686i	$-0.464212\pi$
$103$	2.27732	0.224391	0.112196	+	0.993686i	$0.464212\pi$
$104$	−9.36942	−0.918748
$105$	0	0
$106$	0.784331	0.0761810
$107$	−6.94379	−0.671282	−0.335641	−	0.941990i	$-0.608953\pi$
$107$	−6.94379	−0.671282	−0.335641	+	0.941990i	$0.608953\pi$
$108$	−1.82737	−0.175839
$109$	−7.34184	−0.703221	−0.351611	−	0.936146i	$-0.614366\pi$
$109$	−7.34184	−0.703221	−0.351611	+	0.936146i	$0.614366\pi$
$110$	2.03956	0.194464
$111$	−6.21290	−0.589703
$112$	0	0
$113$	17.7260	1.66752	0.833760	−	0.552127i	$-0.186184\pi$
$113$	17.7260	1.66752	0.833760	+	0.552127i	$0.186184\pi$
$114$	1.71384	0.160516
$115$	−2.48000	−0.231261
$116$	11.0947	1.03012
$117$	−5.89188	−0.544705
$118$	−1.64365	−0.151310
$119$	0	0
$120$	3.94376	0.360015
$121$	−7.08212	−0.643829
$122$	5.43745	0.492284
$123$	3.52463	0.317805
$124$	2.73853	0.245927
$125$	−9.54699	−0.853909
$126$	0	0
$127$	−14.2163	−1.26149	−0.630747	−	0.775989i	$-0.717251\pi$
$127$	−14.2163	−1.26149	−0.630747	+	0.775989i	$0.717251\pi$
$128$	10.5730	0.934533
$129$	−11.2694	−0.992215
$130$	6.07106	0.532467
$131$	−13.5969	−1.18796	−0.593982	−	0.804478i	$-0.702445\pi$
$131$	−13.5969	−1.18796	−0.593982	+	0.804478i	$0.702445\pi$
$132$	3.61703	0.314822
$133$	0	0
$134$	−4.24690	−0.366876
$135$	2.48000	0.213445
$136$	9.29146	0.796736
$137$	1.75575	0.150004	0.0750018	−	0.997183i	$-0.476104\pi$
$137$	1.75575	0.150004	0.0750018	+	0.997183i	$0.476104\pi$
$138$	0.415488	0.0353687
$139$	2.93980	0.249351	0.124675	−	0.992198i	$-0.460211\pi$
$139$	2.93980	0.249351	0.124675	+	0.992198i	$0.460211\pi$
$140$	0	0
$141$	8.41207	0.708424
$142$	−3.65273	−0.306530
$143$	11.6622	0.975241
$144$	2.99402	0.249502
$145$	−15.0572	−1.25043
$146$	2.39245	0.198000
$147$	0	0
$148$	11.3533	0.933233
$149$	16.8255	1.37840	0.689201	−	0.724570i	$-0.257962\pi$
$149$	16.8255	1.37840	0.689201	+	0.724570i	$0.257962\pi$
$150$	−0.477981	−0.0390270
$151$	22.2758	1.81278	0.906391	−	0.422440i	$-0.138826\pi$
$151$	22.2758	1.81278	0.906391	+	0.422440i	$0.138826\pi$
$152$	−6.55949	−0.532045
$153$	5.84286	0.472367
$154$	0	0
$155$	−3.71657	−0.298522
$156$	10.7667	0.862022
$157$	16.7300	1.33520	0.667601	−	0.744519i	$-0.267321\pi$
$157$	16.7300	1.33520	0.667601	+	0.744519i	$0.267321\pi$
$158$	4.64389	0.369448
$159$	−1.88774	−0.149707
$160$	−10.9726	−0.867460
$161$	0	0
$162$	−0.415488	−0.0326438
$163$	−13.4753	−1.05547	−0.527733	−	0.849410i	$-0.676958\pi$
$163$	−13.4753	−1.05547	−0.527733	+	0.849410i	$0.676958\pi$
$164$	−6.44079	−0.502942
$165$	−4.90883	−0.382152
$166$	3.66583	0.284523
$167$	−11.1598	−0.863572	−0.431786	−	0.901976i	$-0.642117\pi$
$167$	−11.1598	−0.863572	−0.431786	+	0.901976i	$0.642117\pi$
$168$	0	0
$169$	21.7143	1.67033
$170$	−6.02054	−0.461755
$171$	−4.12488	−0.315437
$172$	20.5934	1.57023
$173$	8.74866	0.665148	0.332574	−	0.943077i	$-0.392083\pi$
$173$	8.74866	0.665148	0.332574	+	0.943077i	$0.392083\pi$
$174$	2.52260	0.191238
$175$	0	0
$176$	−5.92626	−0.446708
$177$	3.95594	0.297347
$178$	1.93142	0.144766
$179$	−11.5624	−0.864214	−0.432107	−	0.901822i	$-0.642230\pi$
$179$	−11.5624	−0.864214	−0.432107	+	0.901822i	$0.642230\pi$
$180$	−4.53188	−0.337786
$181$	12.7965	0.951156	0.475578	−	0.879673i	$-0.342239\pi$
$181$	12.7965	0.951156	0.475578	+	0.879673i	$0.342239\pi$
$182$	0	0
$183$	−13.0869	−0.967413
$184$	−1.59023	−0.117233
$185$	−15.4080	−1.13282
$186$	0.622657	0.0456554
$187$	−11.5651	−0.845727
$188$	−15.3720	−1.12112
$189$	0	0
$190$	4.25032	0.308351
$191$	16.8338	1.21805	0.609025	−	0.793151i	$-0.291561\pi$
$191$	16.8338	1.21805	0.609025	+	0.793151i	$0.291561\pi$
$192$	−4.14974	−0.299482
$193$	7.40988	0.533375	0.266688	−	0.963783i	$-0.414071\pi$
$193$	7.40988	0.533375	0.266688	+	0.963783i	$0.414071\pi$
$194$	2.84730	0.204424
$195$	−14.6119	−1.04638
$196$	0	0
$197$	−17.8299	−1.27033	−0.635165	−	0.772376i	$-0.719068\pi$
$197$	−17.8299	−1.27033	−0.635165	+	0.772376i	$0.719068\pi$
$198$	0.822402	0.0584455
$199$	−5.87642	−0.416568	−0.208284	−	0.978068i	$-0.566788\pi$
$199$	−5.87642	−0.416568	−0.208284	+	0.978068i	$0.566788\pi$
$200$	1.82941	0.129359
$201$	10.2215	0.720967
$202$	−2.84110	−0.199899
$203$	0	0
$204$	−10.6771	−0.747544
$205$	8.74108	0.610503
$206$	−0.946200	−0.0659249
$207$	−1.00000	−0.0695048
$208$	−17.6404	−1.22314
$209$	8.16464	0.564760
$210$	0	0
$211$	−9.40121	−0.647206	−0.323603	−	0.946193i	$-0.604894\pi$
$211$	−9.40121	−0.647206	−0.323603	+	0.946193i	$0.604894\pi$
$212$	3.44959	0.236919
$213$	8.79143	0.602379
$214$	2.88506	0.197219
$215$	−27.9481	−1.90605
$216$	1.59023	0.108201
$217$	0	0
$218$	3.05045	0.206602
$219$	−5.75816	−0.389101
$220$	8.97024	0.604774
$221$	−34.4254	−2.31571
$222$	2.58139	0.173251
$223$	−12.9389	−0.866452	−0.433226	−	0.901285i	$-0.642625\pi$
$223$	−12.9389	−0.866452	−0.433226	+	0.901285i	$0.642625\pi$
$224$	0	0
$225$	1.15041	0.0766940
$226$	−7.36493	−0.489908
$227$	−17.5123	−1.16233	−0.581165	−	0.813786i	$-0.697403\pi$
$227$	−17.5123	−1.16233	−0.581165	+	0.813786i	$0.697403\pi$
$228$	7.53768	0.499195
$229$	−17.2250	−1.13826	−0.569130	−	0.822248i	$-0.692720\pi$
$229$	−17.2250	−1.13826	−0.569130	+	0.822248i	$0.692720\pi$
$230$	1.03041	0.0679433
$231$	0	0
$232$	−9.65494	−0.633878
$233$	−22.8516	−1.49706	−0.748528	−	0.663103i	$-0.769239\pi$
$233$	−22.8516	−1.49706	−0.748528	+	0.663103i	$0.769239\pi$
$234$	2.44801	0.160031
$235$	20.8620	1.36088
$236$	−7.22897	−0.470566
$237$	−11.1769	−0.726021
$238$	0	0
$239$	−18.9393	−1.22508	−0.612542	−	0.790438i	$-0.709853\pi$
$239$	−18.9393	−1.22508	−0.612542	+	0.790438i	$0.709853\pi$
$240$	7.42518	0.479293
$241$	−14.5833	−0.939393	−0.469697	−	0.882828i	$-0.655637\pi$
$241$	−14.5833	−0.939393	−0.469697	+	0.882828i	$0.655637\pi$
$242$	2.94253	0.189153
$243$	1.00000	0.0641500
$244$	23.9146	1.53098
$245$	0	0
$246$	−1.46444	−0.0933692
$247$	24.3033	1.54638
$248$	−2.38314	−0.151329
$249$	−8.82294	−0.559131
$250$	3.96666	0.250874
$251$	−16.3576	−1.03248	−0.516241	−	0.856443i	$-0.672669\pi$
$251$	−16.3576	−1.03248	−0.516241	+	0.856443i	$0.672669\pi$
$252$	0	0
$253$	1.97936	0.124442
$254$	5.90670	0.370620
$255$	14.4903	0.907418
$256$	3.90652	0.244158
$257$	23.3990	1.45959	0.729794	−	0.683667i	$-0.239616\pi$
$257$	23.3990	1.45959	0.729794	+	0.683667i	$0.239616\pi$
$258$	4.68230	0.291507
$259$	0	0
$260$	26.7013	1.65595
$261$	−6.07143	−0.375812
$262$	5.64934	0.349017
$263$	10.3023	0.635266	0.317633	−	0.948214i	$-0.397112\pi$
$263$	10.3023	0.635266	0.317633	+	0.948214i	$0.397112\pi$
$264$	−3.14764	−0.193724
$265$	−4.68159	−0.287588
$266$	0	0
$267$	−4.64857	−0.284488
$268$	−18.6784	−1.14097
$269$	14.9706	0.912776	0.456388	−	0.889781i	$-0.349143\pi$
$269$	14.9706	0.912776	0.456388	+	0.889781i	$0.349143\pi$
$270$	−1.03041	−0.0627088
$271$	−12.3978	−0.753113	−0.376556	−	0.926394i	$-0.622892\pi$
$271$	−12.3978	−0.753113	−0.376556	+	0.926394i	$0.622892\pi$
$272$	17.4936	1.06071
$273$	0	0
$274$	−0.729491	−0.0440702
$275$	−2.27708	−0.137313
$276$	1.82737	0.109995
$277$	22.4377	1.34815	0.674074	−	0.738663i	$-0.264543\pi$
$277$	22.4377	1.34815	0.674074	+	0.738663i	$0.264543\pi$
$278$	−1.22145	−0.0732579
$279$	−1.49862	−0.0897198
$280$	0	0
$281$	14.8428	0.885446	0.442723	−	0.896658i	$-0.354012\pi$
$281$	14.8428	0.885446	0.442723	+	0.896658i	$0.354012\pi$
$282$	−3.49511	−0.208131
$283$	−2.80684	−0.166849	−0.0834247	−	0.996514i	$-0.526586\pi$
$283$	−2.80684	−0.166849	−0.0834247	+	0.996514i	$0.526586\pi$
$284$	−16.0652	−0.953294
$285$	−10.2297	−0.605956
$286$	−4.84550	−0.286520
$287$	0	0
$288$	−4.42443	−0.260712
$289$	17.1390	1.00818
$290$	6.25606	0.367369
$291$	−6.85290	−0.401724
$292$	10.5223	0.615771
$293$	−28.0450	−1.63840	−0.819202	−	0.573505i	$-0.805583\pi$
$293$	−28.0450	−1.63840	−0.819202	+	0.573505i	$0.805583\pi$
$294$	0	0
$295$	9.81074	0.571204
$296$	−9.87992	−0.574259
$297$	−1.97936	−0.114854
$298$	−6.99081	−0.404967
$299$	5.89188	0.340736
$300$	−2.10222	−0.121372
$301$	0	0
$302$	−9.25534	−0.532585
$303$	6.83798	0.392832
$304$	−12.3500	−0.708320
$305$	−32.4556	−1.85840
$306$	−2.42764	−0.138779
$307$	−20.0730	−1.14563	−0.572815	−	0.819685i	$-0.694149\pi$
$307$	−20.0730	−1.14563	−0.572815	+	0.819685i	$0.694149\pi$
$308$	0	0
$309$	2.27732	0.129552
$310$	1.54419	0.0877041
$311$	−18.5865	−1.05394	−0.526971	−	0.849883i	$-0.676672\pi$
$311$	−18.5865	−1.05394	−0.526971	+	0.849883i	$0.676672\pi$
$312$	−9.36942	−0.530439
$313$	9.35719	0.528899	0.264450	−	0.964399i	$-0.414810\pi$
$313$	9.35719	0.528899	0.264450	+	0.964399i	$0.414810\pi$
$314$	−6.95113	−0.392275
$315$	0	0
$316$	20.4244	1.14896
$317$	19.2610	1.08181	0.540903	−	0.841085i	$-0.318083\pi$
$317$	19.2610	1.08181	0.540903	+	0.841085i	$0.318083\pi$
$318$	0.784331	0.0439831
$319$	12.0176	0.672855
$320$	−10.2914	−0.575305
$321$	−6.94379	−0.387565
$322$	0	0
$323$	−24.1011	−1.34102
$324$	−1.82737	−0.101521
$325$	−6.77808	−0.375980
$326$	5.59882	0.310090
$327$	−7.34184	−0.406005
$328$	5.60495	0.309482
$329$	0	0
$330$	2.03956	0.112274
$331$	−22.6604	−1.24553	−0.622763	−	0.782410i	$-0.713990\pi$
$331$	−22.6604	−1.24553	−0.622763	+	0.782410i	$0.713990\pi$
$332$	16.1228	0.884853
$333$	−6.21290	−0.340465
$334$	4.63677	0.253713
$335$	25.3493	1.38498
$336$	0	0
$337$	−10.6004	−0.577443	−0.288722	−	0.957413i	$-0.593230\pi$
$337$	−10.6004	−0.577443	−0.288722	+	0.957413i	$0.593230\pi$
$338$	−9.02203	−0.490734
$339$	17.7260	0.962743
$340$	−26.4791	−1.43603
$341$	2.96631	0.160635
$342$	1.71384	0.0926737
$343$	0	0
$344$	−17.9209	−0.966229
$345$	−2.48000	−0.133519
$346$	−3.63496	−0.195417
$347$	−3.07328	−0.164983	−0.0824913	−	0.996592i	$-0.526288\pi$
$347$	−3.07328	−0.164983	−0.0824913	+	0.996592i	$0.526288\pi$
$348$	11.0947	0.594741
$349$	−22.8486	−1.22306	−0.611528	−	0.791223i	$-0.709445\pi$
$349$	−22.8486	−1.22306	−0.611528	+	0.791223i	$0.709445\pi$
$350$	0	0
$351$	−5.89188	−0.314485
$352$	8.75756	0.466779
$353$	−28.8756	−1.53689	−0.768447	−	0.639913i	$-0.778970\pi$
$353$	−28.8756	−1.53689	−0.768447	+	0.639913i	$0.778970\pi$
$354$	−1.64365	−0.0873588
$355$	21.8028	1.15717
$356$	8.49466	0.450216
$357$	0	0
$358$	4.80404	0.253901
$359$	22.8051	1.20361	0.601803	−	0.798645i	$-0.294449\pi$
$359$	22.8051	1.20361	0.601803	+	0.798645i	$0.294449\pi$
$360$	3.94376	0.207855
$361$	−1.98537	−0.104493
$362$	−5.31679	−0.279444
$363$	−7.08212	−0.371715
$364$	0	0
$365$	−14.2803	−0.747463
$366$	5.43745	0.284220
$367$	−10.3612	−0.540850	−0.270425	−	0.962741i	$-0.587164\pi$
$367$	−10.3612	−0.540850	−0.270425	+	0.962741i	$0.587164\pi$
$368$	−2.99402	−0.156074
$369$	3.52463	0.183485
$370$	6.40184	0.332816
$371$	0	0
$372$	2.73853	0.141986
$373$	10.4271	0.539895	0.269948	−	0.962875i	$-0.412994\pi$
$373$	10.4271	0.539895	0.269948	+	0.962875i	$0.412994\pi$
$374$	4.80518	0.248470
$375$	−9.54699	−0.493005
$376$	13.3771	0.689871
$377$	35.7722	1.84236
$378$	0	0
$379$	2.44753	0.125721	0.0628605	−	0.998022i	$-0.479978\pi$
$379$	2.44753	0.125721	0.0628605	+	0.998022i	$0.479978\pi$
$380$	18.6935	0.958954
$381$	−14.2163	−0.728324
$382$	−6.99424	−0.357856
$383$	10.0860	0.515372	0.257686	−	0.966229i	$-0.417040\pi$
$383$	10.0860	0.515372	0.257686	+	0.966229i	$0.417040\pi$
$384$	10.5730	0.539553
$385$	0	0
$386$	−3.07872	−0.156703
$387$	−11.2694	−0.572856
$388$	12.5228	0.635748
$389$	19.8510	1.00648	0.503242	−	0.864145i	$-0.332140\pi$
$389$	19.8510	1.00648	0.503242	+	0.864145i	$0.332140\pi$
$390$	6.07106	0.307420
$391$	−5.84286	−0.295486
$392$	0	0
$393$	−13.5969	−0.685872
$394$	7.40812	0.373216
$395$	−27.7189	−1.39469
$396$	3.61703	0.181763
$397$	3.33932	0.167596	0.0837979	−	0.996483i	$-0.473295\pi$
$397$	3.33932	0.167596	0.0837979	+	0.996483i	$0.473295\pi$
$398$	2.44158	0.122385
$399$	0	0
$400$	3.44435	0.172217
$401$	−3.55613	−0.177585	−0.0887924	−	0.996050i	$-0.528301\pi$
$401$	−3.55613	−0.177585	−0.0887924	+	0.996050i	$0.528301\pi$
$402$	−4.24690	−0.211816
$403$	8.82968	0.439838
$404$	−12.4955	−0.621675
$405$	2.48000	0.123232
$406$	0	0
$407$	12.2976	0.609569
$408$	9.29146	0.459996
$409$	30.4885	1.50756	0.753779	−	0.657128i	$-0.228229\pi$
$409$	30.4885	1.50756	0.753779	+	0.657128i	$0.228229\pi$
$410$	−3.63181	−0.179362
$411$	1.75575	0.0866046
$412$	−4.16151	−0.205023
$413$	0	0
$414$	0.415488	0.0204201
$415$	−21.8809	−1.07409
$416$	26.0682	1.27810
$417$	2.93980	0.143963
$418$	−3.39231	−0.165923
$419$	7.20827	0.352147	0.176073	−	0.984377i	$-0.443660\pi$
$419$	7.20827	0.352147	0.176073	+	0.984377i	$0.443660\pi$
$420$	0	0
$421$	5.39492	0.262932	0.131466	−	0.991321i	$-0.458032\pi$
$421$	5.39492	0.262932	0.131466	+	0.991321i	$0.458032\pi$
$422$	3.90609	0.190145
$423$	8.41207	0.409009
$424$	−3.00193	−0.145786
$425$	6.72168	0.326049
$426$	−3.65273	−0.176975
$427$	0	0
$428$	12.6889	0.613340
$429$	11.6622	0.563056
$430$	11.6121	0.559985
$431$	−7.21849	−0.347703	−0.173851	−	0.984772i	$-0.555621\pi$
$431$	−7.21849	−0.347703	−0.173851	+	0.984772i	$0.555621\pi$
$432$	2.99402	0.144050
$433$	−26.1933	−1.25877	−0.629385	−	0.777094i	$-0.716693\pi$
$433$	−26.1933	−1.25877	−0.629385	+	0.777094i	$0.716693\pi$
$434$	0	0
$435$	−15.0572	−0.721935
$436$	13.4163	0.642523
$437$	4.12488	0.197320
$438$	2.39245	0.114316
$439$	35.4423	1.69157	0.845786	−	0.533523i	$-0.179132\pi$
$439$	35.4423	1.69157	0.845786	+	0.533523i	$0.179132\pi$
$440$	−7.80614	−0.372143
$441$	0	0
$442$	14.3034	0.680341
$443$	−25.3316	−1.20354	−0.601770	−	0.798669i	$-0.705538\pi$
$443$	−25.3316	−1.20354	−0.601770	+	0.798669i	$0.705538\pi$
$444$	11.3533	0.538802
$445$	−11.5285	−0.546502
$446$	5.37595	0.254559
$447$	16.8255	0.795821
$448$	0	0
$449$	−18.6700	−0.881093	−0.440546	−	0.897730i	$-0.645215\pi$
$449$	−18.6700	−0.881093	−0.440546	+	0.897730i	$0.645215\pi$
$450$	−0.477981	−0.0225322
$451$	−6.97652	−0.328511
$452$	−32.3919	−1.52359
$453$	22.2758	1.04661
$454$	7.27613	0.341486
$455$	0	0
$456$	−6.55949	−0.307176
$457$	28.5186	1.33404	0.667022	−	0.745038i	$-0.267569\pi$
$457$	28.5186	1.33404	0.667022	+	0.745038i	$0.267569\pi$
$458$	7.15678	0.334414
$459$	5.84286	0.272721
$460$	4.53188	0.211300
$461$	27.0865	1.26155	0.630773	−	0.775968i	$-0.282738\pi$
$461$	27.0865	1.26155	0.630773	+	0.775968i	$0.282738\pi$
$462$	0	0
$463$	42.1993	1.96117	0.980584	−	0.196098i	$-0.0628270\pi$
$463$	42.1993	1.96117	0.980584	+	0.196098i	$0.0628270\pi$
$464$	−18.1780	−0.843892
$465$	−3.71657	−0.172352
$466$	9.49455	0.439827
$467$	−17.5413	−0.811713	−0.405857	−	0.913937i	$-0.633027\pi$
$467$	−17.5413	−0.811713	−0.405857	+	0.913937i	$0.633027\pi$
$468$	10.7667	0.497689
$469$	0	0
$470$	−8.66789	−0.399820
$471$	16.7300	0.770879
$472$	6.29084	0.289559
$473$	22.3062	1.02564
$474$	4.64389	0.213301
$475$	−4.74530	−0.217729
$476$	0	0
$477$	−1.88774	−0.0864335
$478$	7.86906	0.359923
$479$	−9.98280	−0.456126	−0.228063	−	0.973646i	$-0.573239\pi$
$479$	−9.98280	−0.456126	−0.228063	+	0.973646i	$0.573239\pi$
$480$	−10.9726	−0.500828
$481$	36.6057	1.66908
$482$	6.05918	0.275988
$483$	0	0
$484$	12.9416	0.588257
$485$	−16.9952	−0.771712
$486$	−0.415488	−0.0188469
$487$	32.7559	1.48431	0.742156	−	0.670227i	$-0.233803\pi$
$487$	32.7559	1.48431	0.742156	+	0.670227i	$0.233803\pi$
$488$	−20.8112	−0.942077
$489$	−13.4753	−0.609374
$490$	0	0
$491$	10.3787	0.468385	0.234193	−	0.972190i	$-0.424755\pi$
$491$	10.3787	0.468385	0.234193	+	0.972190i	$0.424755\pi$
$492$	−6.44079	−0.290373
$493$	−35.4745	−1.59769
$494$	−10.0977	−0.454318
$495$	−4.90883	−0.220635
$496$	−4.48689	−0.201467
$497$	0	0
$498$	3.66583	0.164270
$499$	1.33969	0.0599729	0.0299864	−	0.999550i	$-0.490454\pi$
$499$	1.33969	0.0599729	0.0299864	+	0.999550i	$0.490454\pi$
$500$	17.4459	0.780204
$501$	−11.1598	−0.498584
$502$	6.79638	0.303337
$503$	−8.78510	−0.391708	−0.195854	−	0.980633i	$-0.562748\pi$
$503$	−8.78510	−0.391708	−0.195854	+	0.980633i	$0.562748\pi$
$504$	0	0
$505$	16.9582	0.754630
$506$	−0.822402	−0.0365602
$507$	21.7143	0.964366
$508$	25.9785	1.15261
$509$	9.23642	0.409397	0.204698	−	0.978825i	$-0.434379\pi$
$509$	9.23642	0.409397	0.204698	+	0.978825i	$0.434379\pi$
$510$	−6.02054	−0.266594
$511$	0	0
$512$	−22.7692	−1.00626
$513$	−4.12488	−0.182118
$514$	−9.72199	−0.428819
$515$	5.64776	0.248870
$516$	20.5934	0.906572
$517$	−16.6506	−0.732290
$518$	0	0
$519$	8.74866	0.384023
$520$	−23.2362	−1.01897
$521$	8.08295	0.354120	0.177060	−	0.984200i	$-0.443341\pi$
$521$	8.08295	0.354120	0.177060	+	0.984200i	$0.443341\pi$
$522$	2.52260	0.110411
$523$	−4.62777	−0.202358	−0.101179	−	0.994868i	$-0.532262\pi$
$523$	−4.62777	−0.202358	−0.101179	+	0.994868i	$0.532262\pi$
$524$	24.8465	1.08543
$525$	0	0
$526$	−4.28047	−0.186638
$527$	−8.75621	−0.381426
$528$	−5.92626	−0.257907
$529$	1.00000	0.0434783
$530$	1.94514	0.0844916
$531$	3.95594	0.171673
$532$	0	0
$533$	−20.7667	−0.899505
$534$	1.93142	0.0835809
$535$	−17.2206	−0.744512
$536$	16.2545	0.702085
$537$	−11.5624	−0.498954
$538$	−6.22012	−0.268168
$539$	0	0
$540$	−4.53188	−0.195021
$541$	−24.5121	−1.05386	−0.526929	−	0.849909i	$-0.676657\pi$
$541$	−24.5121	−1.05386	−0.526929	+	0.849909i	$0.676657\pi$
$542$	5.15113	0.221260
$543$	12.7965	0.549150
$544$	−25.8513	−1.10837
$545$	−18.2078	−0.779936
$546$	0	0
$547$	33.4791	1.43146	0.715732	−	0.698375i	$-0.246093\pi$
$547$	33.4791	1.43146	0.715732	+	0.698375i	$0.246093\pi$
$548$	−3.20840	−0.137056
$549$	−13.0869	−0.558536
$550$	0.946099	0.0403418
$551$	25.0439	1.06691
$552$	−1.59023	−0.0676845
$553$	0	0
$554$	−9.32258	−0.396078
$555$	−15.4080	−0.654034
$556$	−5.37211	−0.227828
$557$	−8.86857	−0.375773	−0.187887	−	0.982191i	$-0.560164\pi$
$557$	−8.86857	−0.375773	−0.187887	+	0.982191i	$0.560164\pi$
$558$	0.622657	0.0263592
$559$	66.3980	2.80834
$560$	0	0
$561$	−11.5651	−0.488281
$562$	−6.16700	−0.260139
$563$	−30.7197	−1.29468	−0.647341	−	0.762200i	$-0.724119\pi$
$563$	−30.7197	−1.29468	−0.647341	+	0.762200i	$0.724119\pi$
$564$	−15.3720	−0.647277
$565$	43.9605	1.84943
$566$	1.16621	0.0490194
$567$	0	0
$568$	13.9804	0.586603
$569$	21.9570	0.920484	0.460242	−	0.887793i	$-0.347763\pi$
$569$	21.9570	0.920484	0.460242	+	0.887793i	$0.347763\pi$
$570$	4.25032	0.178026
$571$	34.3455	1.43731	0.718656	−	0.695365i	$-0.244757\pi$
$571$	34.3455	1.43731	0.718656	+	0.695365i	$0.244757\pi$
$572$	−21.3111	−0.891063
$573$	16.8338	0.703242
$574$	0	0
$575$	−1.15041	−0.0479754
$576$	−4.14974	−0.172906
$577$	40.0868	1.66883	0.834417	−	0.551133i	$-0.185804\pi$
$577$	40.0868	1.66883	0.834417	+	0.551133i	$0.185804\pi$
$578$	−7.12104	−0.296196
$579$	7.40988	0.307944
$580$	27.5150	1.14250
$581$	0	0
$582$	2.84730	0.118024
$583$	3.73652	0.154751
$584$	−9.15678	−0.378910
$585$	−14.6119	−0.604127
$586$	11.6523	0.481354
$587$	−26.4668	−1.09240	−0.546201	−	0.837654i	$-0.683926\pi$
$587$	−26.4668	−1.09240	−0.546201	+	0.837654i	$0.683926\pi$
$588$	0	0
$589$	6.18161	0.254709
$590$	−4.07625	−0.167816
$591$	−17.8299	−0.733425
$592$	−18.6016	−0.764519
$593$	42.6481	1.75135	0.875674	−	0.482902i	$-0.160417\pi$
$593$	42.6481	1.75135	0.875674	+	0.482902i	$0.160417\pi$
$594$	0.822402	0.0337436
$595$	0	0
$596$	−30.7465	−1.25942
$597$	−5.87642	−0.240506
$598$	−2.44801	−0.100106
$599$	−11.0506	−0.451516	−0.225758	−	0.974183i	$-0.572486\pi$
$599$	−11.0506	−0.451516	−0.225758	+	0.974183i	$0.572486\pi$
$600$	1.82941	0.0746854
$601$	1.57522	0.0642547	0.0321274	−	0.999484i	$-0.489772\pi$
$601$	1.57522	0.0642547	0.0321274	+	0.999484i	$0.489772\pi$
$602$	0	0
$603$	10.2215	0.416251
$604$	−40.7062	−1.65631
$605$	−17.5637	−0.714064
$606$	−2.84110	−0.115412
$607$	29.9441	1.21539	0.607696	−	0.794170i	$-0.292094\pi$
$607$	29.9441	1.21539	0.607696	+	0.794170i	$0.292094\pi$
$608$	18.2502	0.740145
$609$	0	0
$610$	13.4849	0.545988
$611$	−49.5629	−2.00510
$612$	−10.6771	−0.431595
$613$	12.4684	0.503594	0.251797	−	0.967780i	$-0.418978\pi$
$613$	12.4684	0.503594	0.251797	+	0.967780i	$0.418978\pi$
$614$	8.34011	0.336579
$615$	8.74108	0.352474
$616$	0	0
$617$	3.82651	0.154049	0.0770247	−	0.997029i	$-0.475458\pi$
$617$	3.82651	0.154049	0.0770247	+	0.997029i	$0.475458\pi$
$618$	−0.946200	−0.0380617
$619$	−42.4415	−1.70587	−0.852933	−	0.522020i	$-0.825179\pi$
$619$	−42.4415	−1.70587	−0.852933	+	0.522020i	$0.825179\pi$
$620$	6.79155	0.272755
$621$	−1.00000	−0.0401286
$622$	7.72245	0.309642
$623$	0	0
$624$	−17.6404	−0.706182
$625$	−29.4286	−1.17714
$626$	−3.88780	−0.155388
$627$	8.16464	0.326064
$628$	−30.5720	−1.21995
$629$	−36.3011	−1.44742
$630$	0	0
$631$	−32.2491	−1.28382	−0.641908	−	0.766782i	$-0.721857\pi$
$631$	−32.2491	−1.28382	−0.641908	+	0.766782i	$0.721857\pi$
$632$	−17.7739	−0.707007
$633$	−9.40121	−0.373665
$634$	−8.00271	−0.317828
$635$	−35.2565	−1.39911
$636$	3.44959	0.136785
$637$	0	0
$638$	−4.99315	−0.197681
$639$	8.79143	0.347784
$640$	26.2211	1.03648
$641$	19.9529	0.788093	0.394047	−	0.919090i	$-0.371075\pi$
$641$	19.9529	0.788093	0.394047	+	0.919090i	$0.371075\pi$
$642$	2.88506	0.113864
$643$	14.0794	0.555236	0.277618	−	0.960692i	$-0.410455\pi$
$643$	14.0794	0.555236	0.277618	+	0.960692i	$0.410455\pi$
$644$	0	0
$645$	−27.9481	−1.10046
$646$	10.0137	0.393984
$647$	−21.1391	−0.831062	−0.415531	−	0.909579i	$-0.636404\pi$
$647$	−21.1391	−0.831062	−0.415531	+	0.909579i	$0.636404\pi$
$648$	1.59023	0.0624700
$649$	−7.83025	−0.307364
$650$	2.81621	0.110461
$651$	0	0
$652$	24.6243	0.964364
$653$	34.9079	1.36605	0.683026	−	0.730394i	$-0.260664\pi$
$653$	34.9079	1.36605	0.683026	+	0.730394i	$0.260664\pi$
$654$	3.05045	0.119282
$655$	−33.7203	−1.31756
$656$	10.5528	0.412018
$657$	−5.75816	−0.224647
$658$	0	0
$659$	32.3573	1.26046	0.630231	−	0.776407i	$-0.282960\pi$
$659$	32.3573	1.26046	0.630231	+	0.776407i	$0.282960\pi$
$660$	8.97024	0.349166
$661$	9.20632	0.358084	0.179042	−	0.983841i	$-0.442700\pi$
$661$	9.20632	0.358084	0.179042	+	0.983841i	$0.442700\pi$
$662$	9.41511	0.365928
$663$	−34.4254	−1.33697
$664$	−14.0305	−0.544488
$665$	0	0
$666$	2.58139	0.100027
$667$	6.07143	0.235087
$668$	20.3931	0.789033
$669$	−12.9389	−0.500246
$670$	−10.5323	−0.406899
$671$	25.9038	1.00000
$672$	0	0
$673$	−22.2907	−0.859245	−0.429622	−	0.903009i	$-0.641353\pi$
$673$	−22.2907	−0.859245	−0.429622	+	0.903009i	$0.641353\pi$
$674$	4.40436	0.169650
$675$	1.15041	0.0442793
$676$	−39.6800	−1.52616
$677$	−29.9382	−1.15062	−0.575308	−	0.817937i	$-0.695118\pi$
$677$	−29.9382	−1.15062	−0.575308	+	0.817937i	$0.695118\pi$
$678$	−7.36493	−0.282848
$679$	0	0
$680$	23.0428	0.883653
$681$	−17.5123	−0.671071
$682$	−1.23247	−0.0471935
$683$	6.76599	0.258893	0.129447	−	0.991586i	$-0.458680\pi$
$683$	6.76599	0.258893	0.129447	+	0.991586i	$0.458680\pi$
$684$	7.53768	0.288210
$685$	4.35425	0.166368
$686$	0	0
$687$	−17.2250	−0.657175
$688$	−33.7408	−1.28636
$689$	11.1223	0.423727
$690$	1.03041	0.0392271
$691$	−29.2333	−1.11209	−0.556043	−	0.831153i	$-0.687681\pi$
$691$	−29.2333	−1.11209	−0.556043	+	0.831153i	$0.687681\pi$
$692$	−15.9870	−0.607736
$693$	0	0
$694$	1.27691	0.0484709
$695$	7.29072	0.276553
$696$	−9.65494	−0.365970
$697$	20.5939	0.780049
$698$	9.49330	0.359327
$699$	−22.8516	−0.864326
$700$	0	0
$701$	42.7863	1.61602	0.808009	−	0.589170i	$-0.200545\pi$
$701$	42.7863	1.61602	0.808009	+	0.589170i	$0.200545\pi$
$702$	2.44801	0.0923940
$703$	25.6275	0.966559
$704$	8.21385	0.309571
$705$	20.8620	0.785707
$706$	11.9975	0.451531
$707$	0	0
$708$	−7.22897	−0.271681
$709$	35.4731	1.33222	0.666110	−	0.745853i	$-0.267958\pi$
$709$	35.4731	1.33222	0.666110	+	0.745853i	$0.267958\pi$
$710$	−9.05878	−0.339970
$711$	−11.1769	−0.419168
$712$	−7.39228	−0.277037
$713$	1.49862	0.0561236
$714$	0	0
$715$	28.9222	1.08163
$716$	21.1288	0.789620
$717$	−18.9393	−0.707302
$718$	−9.47523	−0.353612
$719$	2.77965	0.103663	0.0518317	−	0.998656i	$-0.483494\pi$
$719$	2.77965	0.103663	0.0518317	+	0.998656i	$0.483494\pi$
$720$	7.42518	0.276720
$721$	0	0
$722$	0.824896	0.0306994
$723$	−14.5833	−0.542359
$724$	−23.3839	−0.869057
$725$	−6.98463	−0.259403
$726$	2.94253	0.109208
$727$	47.3569	1.75637	0.878185	−	0.478321i	$-0.158754\pi$
$727$	47.3569	1.75637	0.878185	+	0.478321i	$0.158754\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	5.93327	0.219600
$731$	−65.8455	−2.43538
$732$	23.9146	0.883910
$733$	−42.5473	−1.57152	−0.785760	−	0.618531i	$-0.787728\pi$
$733$	−42.5473	−1.57152	−0.785760	+	0.618531i	$0.787728\pi$
$734$	4.30495	0.158899
$735$	0	0
$736$	4.42443	0.163087
$737$	−20.2320	−0.745256
$738$	−1.46444	−0.0539067
$739$	42.1329	1.54988	0.774942	−	0.632033i	$-0.217779\pi$
$739$	42.1329	1.54988	0.774942	+	0.632033i	$0.217779\pi$
$740$	28.1561	1.03504
$741$	24.3033	0.892805
$742$	0	0
$743$	9.84391	0.361138	0.180569	−	0.983562i	$-0.442206\pi$
$743$	9.84391	0.361138	0.180569	+	0.983562i	$0.442206\pi$
$744$	−2.38314	−0.0873701
$745$	41.7274	1.52877
$746$	−4.33234	−0.158618
$747$	−8.82294	−0.322815
$748$	21.1338	0.772728
$749$	0	0
$750$	3.96666	0.144842
$751$	31.4535	1.14776	0.573878	−	0.818941i	$-0.305438\pi$
$751$	31.4535	1.14776	0.573878	+	0.818941i	$0.305438\pi$
$752$	25.1859	0.918436
$753$	−16.3576	−0.596104
$754$	−14.8629	−0.541275
$755$	55.2441	2.01054
$756$	0	0
$757$	4.11964	0.149731	0.0748654	−	0.997194i	$-0.476147\pi$
$757$	4.11964	0.149731	0.0748654	+	0.997194i	$0.476147\pi$
$758$	−1.01692	−0.0369361
$759$	1.97936	0.0718464
$760$	−16.2675	−0.590086
$761$	−6.17226	−0.223744	−0.111872	−	0.993723i	$-0.535685\pi$
$761$	−6.17226	−0.223744	−0.111872	+	0.993723i	$0.535685\pi$
$762$	5.90670	0.213977
$763$	0	0
$764$	−30.7616	−1.11291
$765$	14.4903	0.523898
$766$	−4.19062	−0.151413
$767$	−23.3080	−0.841601
$768$	3.90652	0.140964
$769$	−7.00055	−0.252446	−0.126223	−	0.992002i	$-0.540286\pi$
$769$	−7.00055	−0.252446	−0.126223	+	0.992002i	$0.540286\pi$
$770$	0	0
$771$	23.3990	0.842693
$772$	−13.5406	−0.487337
$773$	5.56909	0.200306	0.100153	−	0.994972i	$-0.468067\pi$
$773$	5.56909	0.200306	0.100153	+	0.994972i	$0.468067\pi$
$774$	4.68230	0.168302
$775$	−1.72402	−0.0619287
$776$	−10.8977	−0.391203
$777$	0	0
$778$	−8.24784	−0.295699
$779$	−14.5387	−0.520901
$780$	26.7013	0.956060
$781$	−17.4014	−0.622672
$782$	2.42764	0.0868121
$783$	−6.07143	−0.216975
$784$	0	0
$785$	41.4905	1.48086
$786$	5.64934	0.201505
$787$	−1.35560	−0.0483219	−0.0241609	−	0.999708i	$-0.507691\pi$
$787$	−1.35560	−0.0483219	−0.0241609	+	0.999708i	$0.507691\pi$
$788$	32.5819	1.16068
$789$	10.3023	0.366771
$790$	11.5168	0.409751
$791$	0	0
$792$	−3.14764	−0.111846
$793$	77.1066	2.73814
$794$	−1.38745	−0.0492387
$795$	−4.68159	−0.166039
$796$	10.7384	0.380612
$797$	42.1281	1.49225	0.746127	−	0.665804i	$-0.231911\pi$
$797$	42.1281	1.49225	0.746127	+	0.665804i	$0.231911\pi$
$798$	0	0
$799$	49.1505	1.73882
$800$	−5.08991	−0.179955
$801$	−4.64857	−0.164249
$802$	1.47753	0.0521734
$803$	11.3975	0.402209
$804$	−18.6784	−0.658737
$805$	0	0
$806$	−3.66862	−0.129222
$807$	14.9706	0.526992
$808$	10.8739	0.382543
$809$	18.5832	0.653349	0.326675	−	0.945137i	$-0.394072\pi$
$809$	18.5832	0.653349	0.326675	+	0.945137i	$0.394072\pi$
$810$	−1.03041	−0.0362049
$811$	10.8617	0.381406	0.190703	−	0.981648i	$-0.438923\pi$
$811$	10.8617	0.381406	0.190703	+	0.981648i	$0.438923\pi$
$812$	0	0
$813$	−12.3978	−0.434810
$814$	−5.10950	−0.179088
$815$	−33.4187	−1.17061
$816$	17.4936	0.612400
$817$	46.4849	1.62630
$818$	−12.6676	−0.442912
$819$	0	0
$820$	−15.9732	−0.557808
$821$	44.2513	1.54438	0.772190	−	0.635391i	$-0.219161\pi$
$821$	44.2513	1.54438	0.772190	+	0.635391i	$0.219161\pi$
$822$	−0.729491	−0.0254439
$823$	24.2056	0.843756	0.421878	−	0.906653i	$-0.361371\pi$
$823$	24.2056	0.843756	0.421878	+	0.906653i	$0.361371\pi$
$824$	3.62146	0.126159
$825$	−2.27708	−0.0792777
$826$	0	0
$827$	−9.95903	−0.346309	−0.173155	−	0.984895i	$-0.555396\pi$
$827$	−9.95903	−0.346309	−0.173155	+	0.984895i	$0.555396\pi$
$828$	1.82737	0.0635055
$829$	−45.0154	−1.56345	−0.781725	−	0.623623i	$-0.785660\pi$
$829$	−45.0154	−1.56345	−0.781725	+	0.623623i	$0.785660\pi$
$830$	9.09126	0.315562
$831$	22.4377	0.778354
$832$	24.4498	0.847645
$833$	0	0
$834$	−1.22145	−0.0422954
$835$	−27.6764	−0.957780
$836$	−14.9198	−0.516013
$837$	−1.49862	−0.0517998
$838$	−2.99495	−0.103459
$839$	−1.34275	−0.0463569	−0.0231785	−	0.999731i	$-0.507379\pi$
$839$	−1.34275	−0.0463569	−0.0231785	+	0.999731i	$0.507379\pi$
$840$	0	0
$841$	7.86224	0.271112
$842$	−2.24152	−0.0772479
$843$	14.8428	0.511213
$844$	17.1795	0.591342
$845$	53.8515	1.85255
$846$	−3.49511	−0.120164
$847$	0	0
$848$	−5.65192	−0.194088
$849$	−2.80684	−0.0963306
$850$	−2.79278	−0.0957914
$851$	6.21290	0.212976
$852$	−16.0652	−0.550384
$853$	25.5552	0.874993	0.437496	−	0.899220i	$-0.355865\pi$
$853$	25.5552	0.874993	0.437496	+	0.899220i	$0.355865\pi$
$854$	0	0
$855$	−10.2297	−0.349849
$856$	−11.0422	−0.377415
$857$	31.5002	1.07603	0.538014	−	0.842936i	$-0.319175\pi$
$857$	31.5002	1.07603	0.538014	+	0.842936i	$0.319175\pi$
$858$	−4.84550	−0.165422
$859$	8.13362	0.277516	0.138758	−	0.990326i	$-0.455689\pi$
$859$	8.13362	0.277516	0.138758	+	0.990326i	$0.455689\pi$
$860$	51.0716	1.74153
$861$	0	0
$862$	2.99920	0.102153
$863$	3.15207	0.107298	0.0536489	−	0.998560i	$-0.482915\pi$
$863$	3.15207	0.107298	0.0536489	+	0.998560i	$0.482915\pi$
$864$	−4.42443	−0.150522
$865$	21.6967	0.737709
$866$	10.8830	0.369819
$867$	17.1390	0.582071
$868$	0	0
$869$	22.1233	0.750480
$870$	6.25606	0.212100
$871$	−60.2238	−2.04060
$872$	−11.6752	−0.395372
$873$	−6.85290	−0.231936
$874$	−1.71384	−0.0579714
$875$	0	0
$876$	10.5223	0.355515
$877$	−18.1050	−0.611362	−0.305681	−	0.952134i	$-0.598884\pi$
$877$	−18.1050	−0.611362	−0.305681	+	0.952134i	$0.598884\pi$
$878$	−14.7259	−0.496974
$879$	−28.0450	−0.945933
$880$	−14.6971	−0.495440
$881$	39.4570	1.32934	0.664670	−	0.747137i	$-0.268572\pi$
$881$	39.4570	1.32934	0.664670	+	0.747137i	$0.268572\pi$
$882$	0	0
$883$	−25.2955	−0.851261	−0.425630	−	0.904897i	$-0.639948\pi$
$883$	−25.2955	−0.851261	−0.425630	+	0.904897i	$0.639948\pi$
$884$	62.9080	2.11583
$885$	9.81074	0.329785
$886$	10.5250	0.353593
$887$	−22.4528	−0.753892	−0.376946	−	0.926235i	$-0.623026\pi$
$887$	−22.4528	−0.753892	−0.376946	+	0.926235i	$0.623026\pi$
$888$	−9.87992	−0.331548
$889$	0	0
$890$	4.78994	0.160559
$891$	−1.97936	−0.0663112
$892$	23.6441	0.791664
$893$	−34.6988	−1.16115
$894$	−6.99081	−0.233808
$895$	−28.6748	−0.958492
$896$	0	0
$897$	5.89188	0.196724
$898$	7.75717	0.258860
$899$	9.09875	0.303460
$900$	−2.10222	−0.0700741
$901$	−11.0298	−0.367455
$902$	2.89866	0.0965148
$903$	0	0
$904$	28.1883	0.937529
$905$	31.7353	1.05492
$906$	−9.25534	−0.307488
$907$	−35.5159	−1.17929	−0.589643	−	0.807664i	$-0.700732\pi$
$907$	−35.5159	−1.17929	−0.589643	+	0.807664i	$0.700732\pi$
$908$	32.0014	1.06200
$909$	6.83798	0.226801
$910$	0	0
$911$	−46.9336	−1.55498	−0.777490	−	0.628896i	$-0.783507\pi$
$911$	−46.9336	−1.55498	−0.777490	+	0.628896i	$0.783507\pi$
$912$	−12.3500	−0.408948
$913$	17.4638	0.577968
$914$	−11.8491	−0.391935
$915$	−32.4556	−1.07295
$916$	31.4764	1.04001
$917$	0	0
$918$	−2.42764	−0.0801239
$919$	−14.4896	−0.477969	−0.238984	−	0.971023i	$-0.576814\pi$
$919$	−14.4896	−0.477969	−0.238984	+	0.971023i	$0.576814\pi$
$920$	−3.94376	−0.130022
$921$	−20.0730	−0.661429
$922$	−11.2541	−0.370635
$923$	−51.7981	−1.70495
$924$	0	0
$925$	−7.14738	−0.235004
$926$	−17.5333	−0.576180
$927$	2.27732	0.0747971
$928$	26.8626	0.881808
$929$	39.4738	1.29509	0.647547	−	0.762025i	$-0.275795\pi$
$929$	39.4738	1.29509	0.647547	+	0.762025i	$0.275795\pi$
$930$	1.54419	0.0506360
$931$	0	0
$932$	41.7583	1.36784
$933$	−18.5865	−0.608494
$934$	7.28819	0.238477
$935$	−28.6816	−0.937988
$936$	−9.36942	−0.306249
$937$	54.8494	1.79185	0.895927	−	0.444202i	$-0.146513\pi$
$937$	54.8494	1.79185	0.895927	+	0.444202i	$0.146513\pi$
$938$	0	0
$939$	9.35719	0.305360
$940$	−38.1225	−1.24342
$941$	47.3393	1.54322	0.771609	−	0.636097i	$-0.219452\pi$
$941$	47.3393	1.54322	0.771609	+	0.636097i	$0.219452\pi$
$942$	−6.95113	−0.226480
$943$	−3.52463	−0.114778
$944$	11.8442	0.385495
$945$	0	0
$946$	−9.26797	−0.301328
$947$	−24.5815	−0.798792	−0.399396	−	0.916779i	$-0.630780\pi$
$947$	−24.5815	−0.798792	−0.399396	+	0.916779i	$0.630780\pi$
$948$	20.4244	0.663354
$949$	33.9264	1.10130
$950$	1.97161	0.0639676
$951$	19.2610	0.624581
$952$	0	0
$953$	−54.6363	−1.76984	−0.884922	−	0.465739i	$-0.845789\pi$
$953$	−54.6363	−1.76984	−0.884922	+	0.465739i	$0.845789\pi$
$954$	0.784331	0.0253937
$955$	41.7478	1.35093
$956$	34.6092	1.11934
$957$	12.0176	0.388473
$958$	4.14773	0.134007
$959$	0	0
$960$	−10.2914	−0.332153
$961$	−28.7541	−0.927553
$962$	−15.2092	−0.490365
$963$	−6.94379	−0.223761
$964$	26.6491	0.858309
$965$	18.3765	0.591561
$966$	0	0
$967$	−30.0485	−0.966293	−0.483147	−	0.875539i	$-0.660506\pi$
$967$	−30.0485	−0.966293	−0.483147	+	0.875539i	$0.660506\pi$
$968$	−11.2622	−0.361980
$969$	−24.1011	−0.774238
$970$	7.06130	0.226725
$971$	−5.36821	−0.172274	−0.0861371	−	0.996283i	$-0.527452\pi$
$971$	−5.36821	−0.172274	−0.0861371	+	0.996283i	$0.527452\pi$
$972$	−1.82737	−0.0586129
$973$	0	0
$974$	−13.6097	−0.436082
$975$	−6.77808	−0.217072
$976$	−39.1825	−1.25420
$977$	−52.0260	−1.66446	−0.832230	−	0.554430i	$-0.812936\pi$
$977$	−52.0260	−1.66446	−0.832230	+	0.554430i	$0.812936\pi$
$978$	5.59882	0.179031
$979$	9.20121	0.294072
$980$	0	0
$981$	−7.34184	−0.234407
$982$	−4.31224	−0.137609
$983$	3.69596	0.117883	0.0589414	−	0.998261i	$-0.481227\pi$
$983$	3.69596	0.117883	0.0589414	+	0.998261i	$0.481227\pi$
$984$	5.60495	0.178679
$985$	−44.2183	−1.40891
$986$	14.7392	0.469392
$987$	0	0
$988$	−44.4111	−1.41291
$989$	11.2694	0.358346
$990$	2.03956	0.0648214
$991$	−22.6998	−0.721082	−0.360541	−	0.932743i	$-0.617408\pi$
$991$	−22.6998	−0.721082	−0.360541	+	0.932743i	$0.617408\pi$
$992$	6.63053	0.210519
$993$	−22.6604	−0.719105
$994$	0	0
$995$	−14.5735	−0.462012
$996$	16.1228	0.510870
$997$	−58.3098	−1.84669	−0.923346	−	0.383970i	$-0.874557\pi$
$997$	−58.3098	−1.84669	−0.923346	+	0.383970i	$0.874557\pi$
$998$	−0.556626	−0.0176197
$999$	−6.21290	−0.196568

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3381.2.a.bb.1.4	yes	6
7.6	odd	2		3381.2.a.ba.1.4	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3381.2.a.ba.1.4	✓	6	7.6	odd	2
3381.2.a.bb.1.4	yes	6	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3381 = 3 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3381.a (trivial)

\(f(q)\)	\(=\)	\(q-0.415488 q^{2} +1.00000 q^{3} -1.82737 q^{4} +2.48000 q^{5} -0.415488 q^{6} +1.59023 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.415488 q^{2} +1.00000 q^{3} -1.82737 q^{4} +2.48000 q^{5} -0.415488 q^{6} +1.59023 q^{8} +1.00000 q^{9} -1.03041 q^{10} -1.97936 q^{11} -1.82737 q^{12} -5.89188 q^{13} +2.48000 q^{15} +2.99402 q^{16} +5.84286 q^{17} -0.415488 q^{18} -4.12488 q^{19} -4.53188 q^{20} +0.822402 q^{22} -1.00000 q^{23} +1.59023 q^{24} +1.15041 q^{25} +2.44801 q^{26} +1.00000 q^{27} -6.07143 q^{29} -1.03041 q^{30} -1.49862 q^{31} -4.42443 q^{32} -1.97936 q^{33} -2.42764 q^{34} -1.82737 q^{36} -6.21290 q^{37} +1.71384 q^{38} -5.89188 q^{39} +3.94376 q^{40} +3.52463 q^{41} -11.2694 q^{43} +3.61703 q^{44} +2.48000 q^{45} +0.415488 q^{46} +8.41207 q^{47} +2.99402 q^{48} -0.477981 q^{50} +5.84286 q^{51} +10.7667 q^{52} -1.88774 q^{53} -0.415488 q^{54} -4.90883 q^{55} -4.12488 q^{57} +2.52260 q^{58} +3.95594 q^{59} -4.53188 q^{60} -13.0869 q^{61} +0.622657 q^{62} -4.14974 q^{64} -14.6119 q^{65} +0.822402 q^{66} +10.2215 q^{67} -10.6771 q^{68} -1.00000 q^{69} +8.79143 q^{71} +1.59023 q^{72} -5.75816 q^{73} +2.58139 q^{74} +1.15041 q^{75} +7.53768 q^{76} +2.44801 q^{78} -11.1769 q^{79} +7.42518 q^{80} +1.00000 q^{81} -1.46444 q^{82} -8.82294 q^{83} +14.4903 q^{85} +4.68230 q^{86} -6.07143 q^{87} -3.14764 q^{88} -4.64857 q^{89} -1.03041 q^{90} +1.82737 q^{92} -1.49862 q^{93} -3.49511 q^{94} -10.2297 q^{95} -4.42443 q^{96} -6.85290 q^{97} -1.97936 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} + 6 q^{3} + 7 q^{4} - 2 q^{5} - 3 q^{6} - 9 q^{8} + 6 q^{9}+O(q^{10}) \) 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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