LMFDB - Embedded newform 3822.2.a.ca.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3822,2,Mod(1,3822)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3822, 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("3822.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3822.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:	$30.5188236525$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.31808.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 11x^{2} + 12x + 28 $ x^4 - 2x^3 - 11x^2 + 12*x + 28
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.51304$ of defining polynomial
Character	$\chi$	$=$	3822.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.51304 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.51304 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -3.51304 q^{10} +3.45515 q^{11} +1.00000 q^{12} +1.00000 q^{13} -3.51304 q^{15} +1.00000 q^{16} -1.45515 q^{17} +1.00000 q^{18} -3.51304 q^{19} -3.51304 q^{20} +3.45515 q^{22} +5.51304 q^{23} +1.00000 q^{24} +7.34147 q^{25} +1.00000 q^{26} +1.00000 q^{27} -0.869364 q^{29} -3.51304 q^{30} +4.96819 q^{31} +1.00000 q^{32} +3.45515 q^{33} -1.45515 q^{34} +1.00000 q^{36} -5.75568 q^{37} -3.51304 q^{38} +1.00000 q^{39} -3.51304 q^{40} +3.55398 q^{41} -4.42334 q^{43} +3.45515 q^{44} -3.51304 q^{45} +5.51304 q^{46} -2.72555 q^{47} +1.00000 q^{48} +7.34147 q^{50} -1.45515 q^{51} +1.00000 q^{52} +10.3824 q^{53} +1.00000 q^{54} -12.1381 q^{55} -3.51304 q^{57} -0.869364 q^{58} +4.96819 q^{59} -3.51304 q^{60} +11.3097 q^{61} +4.96819 q^{62} +1.00000 q^{64} -3.51304 q^{65} +3.45515 q^{66} +14.4403 q^{67} -1.45515 q^{68} +5.51304 q^{69} +11.0840 q^{71} +1.00000 q^{72} -0.486957 q^{73} -5.75568 q^{74} +7.34147 q^{75} -3.51304 q^{76} +1.00000 q^{78} -8.62505 q^{79} -3.51304 q^{80} +1.00000 q^{81} +3.55398 q^{82} +1.36923 q^{83} +5.11200 q^{85} -4.42334 q^{86} -0.869364 q^{87} +3.45515 q^{88} +1.33234 q^{89} -3.51304 q^{90} +5.51304 q^{92} +4.96819 q^{93} -2.72555 q^{94} +12.3415 q^{95} +1.00000 q^{96} +2.08187 q^{97} +3.45515 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - 2 q^{5} + 4 q^{6} + 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 - 2 * q^5 + 4 * q^6 + 4 * q^8 + 4 * q^9	$ 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - 2 q^{5} + 4 q^{6} + 4 q^{8} + 4 q^{9} - 2 q^{10} + 6 q^{11} + 4 q^{12} + 4 q^{13} - 2 q^{15} + 4 q^{16} + 2 q^{17} + 4 q^{18} - 2 q^{19} - 2 q^{20} + 6 q^{22} + 10 q^{23} + 4 q^{24} + 6 q^{25} + 4 q^{26} + 4 q^{27} + 10 q^{29} - 2 q^{30} + 4 q^{32} + 6 q^{33} + 2 q^{34} + 4 q^{36} + 6 q^{37} - 2 q^{38} + 4 q^{39} - 2 q^{40} + 10 q^{43} + 6 q^{44} - 2 q^{45} + 10 q^{46} - 8 q^{47} + 4 q^{48} + 6 q^{50} + 2 q^{51} + 4 q^{52} + 16 q^{53} + 4 q^{54} + 6 q^{55} - 2 q^{57} + 10 q^{58} - 2 q^{60} + 2 q^{61} + 4 q^{64} - 2 q^{65} + 6 q^{66} + 28 q^{67} + 2 q^{68} + 10 q^{69} + 16 q^{71} + 4 q^{72} - 14 q^{73} + 6 q^{74} + 6 q^{75} - 2 q^{76} + 4 q^{78} + 8 q^{79} - 2 q^{80} + 4 q^{81} + 4 q^{83} - 10 q^{85} + 10 q^{86} + 10 q^{87} + 6 q^{88} + 4 q^{89} - 2 q^{90} + 10 q^{92} - 8 q^{94} + 26 q^{95} + 4 q^{96} + 4 q^{97} + 6 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 - 2 * q^5 + 4 * q^6 + 4 * q^8 + 4 * q^9 - 2 * q^10 + 6 * q^11 + 4 * q^12 + 4 * q^13 - 2 * q^15 + 4 * q^16 + 2 * q^17 + 4 * q^18 - 2 * q^19 - 2 * q^20 + 6 * q^22 + 10 * q^23 + 4 * q^24 + 6 * q^25 + 4 * q^26 + 4 * q^27 + 10 * q^29 - 2 * q^30 + 4 * q^32 + 6 * q^33 + 2 * q^34 + 4 * q^36 + 6 * q^37 - 2 * q^38 + 4 * q^39 - 2 * q^40 + 10 * q^43 + 6 * q^44 - 2 * q^45 + 10 * q^46 - 8 * q^47 + 4 * q^48 + 6 * q^50 + 2 * q^51 + 4 * q^52 + 16 * q^53 + 4 * q^54 + 6 * q^55 - 2 * q^57 + 10 * q^58 - 2 * q^60 + 2 * q^61 + 4 * q^64 - 2 * q^65 + 6 * q^66 + 28 * q^67 + 2 * q^68 + 10 * q^69 + 16 * q^71 + 4 * q^72 - 14 * q^73 + 6 * q^74 + 6 * q^75 - 2 * q^76 + 4 * q^78 + 8 * q^79 - 2 * q^80 + 4 * q^81 + 4 * q^83 - 10 * q^85 + 10 * q^86 + 10 * q^87 + 6 * q^88 + 4 * q^89 - 2 * q^90 + 10 * q^92 - 8 * q^94 + 26 * q^95 + 4 * q^96 + 4 * q^97 + 6 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−3.51304	−1.57108	−0.785540	−	0.618811i	$-0.787615\pi$
$5$	−3.51304	−1.57108	−0.785540	+	0.618811i	$0.787615\pi$
$6$	1.00000	0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−3.51304	−1.11092
$11$	3.45515	1.04177	0.520883	−	0.853628i	$-0.325603\pi$
$11$	3.45515	1.04177	0.520883	+	0.853628i	$0.325603\pi$
$12$	1.00000	0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0	0
$15$	−3.51304	−0.907064
$16$	1.00000	0.250000
$17$	−1.45515	−0.352926	−0.176463	−	0.984307i	$-0.556466\pi$
$17$	−1.45515	−0.352926	−0.176463	+	0.984307i	$0.556466\pi$
$18$	1.00000	0.235702
$19$	−3.51304	−0.805947	−0.402974	−	0.915212i	$-0.632023\pi$
$19$	−3.51304	−0.805947	−0.402974	+	0.915212i	$0.632023\pi$
$20$	−3.51304	−0.785540
$21$	0	0
$22$	3.45515	0.736640
$23$	5.51304	1.14955	0.574774	−	0.818312i	$-0.305090\pi$
$23$	5.51304	1.14955	0.574774	+	0.818312i	$0.305090\pi$
$24$	1.00000	0.204124
$25$	7.34147	1.46829
$26$	1.00000	0.196116
$27$	1.00000	0.192450
$28$	0	0
$29$	−0.869364	−0.161437	−0.0807184	−	0.996737i	$-0.525721\pi$
$29$	−0.869364	−0.161437	−0.0807184	+	0.996737i	$0.525721\pi$
$30$	−3.51304	−0.641391
$31$	4.96819	0.892314	0.446157	−	0.894955i	$-0.352792\pi$
$31$	4.96819	0.892314	0.446157	+	0.894955i	$0.352792\pi$
$32$	1.00000	0.176777
$33$	3.45515	0.601464
$34$	−1.45515	−0.249556
$35$	0	0
$36$	1.00000	0.166667
$37$	−5.75568	−0.946229	−0.473114	−	0.881001i	$-0.656870\pi$
$37$	−5.75568	−0.946229	−0.473114	+	0.881001i	$0.656870\pi$
$38$	−3.51304	−0.569891
$39$	1.00000	0.160128
$40$	−3.51304	−0.555461
$41$	3.55398	0.555038	0.277519	−	0.960720i	$-0.410488\pi$
$41$	3.55398	0.555038	0.277519	+	0.960720i	$0.410488\pi$
$42$	0	0
$43$	−4.42334	−0.674553	−0.337277	−	0.941406i	$-0.609506\pi$
$43$	−4.42334	−0.674553	−0.337277	+	0.941406i	$0.609506\pi$
$44$	3.45515	0.520883
$45$	−3.51304	−0.523694
$46$	5.51304	0.812854
$47$	−2.72555	−0.397563	−0.198781	−	0.980044i	$-0.563698\pi$
$47$	−2.72555	−0.397563	−0.198781	+	0.980044i	$0.563698\pi$
$48$	1.00000	0.144338
$49$	0	0
$50$	7.34147	1.03824
$51$	−1.45515	−0.203762
$52$	1.00000	0.138675
$53$	10.3824	1.42613	0.713067	−	0.701096i	$-0.247306\pi$
$53$	10.3824	1.42613	0.713067	+	0.701096i	$0.247306\pi$
$54$	1.00000	0.136083
$55$	−12.1381	−1.63670
$56$	0	0
$57$	−3.51304	−0.465314
$58$	−0.869364	−0.114153
$59$	4.96819	0.646804	0.323402	−	0.946262i	$-0.395173\pi$
$59$	4.96819	0.646804	0.323402	+	0.946262i	$0.395173\pi$
$60$	−3.51304	−0.453532
$61$	11.3097	1.44805	0.724027	−	0.689772i	$-0.242289\pi$
$61$	11.3097	1.44805	0.724027	+	0.689772i	$0.242289\pi$
$62$	4.96819	0.630961
$63$	0	0
$64$	1.00000	0.125000
$65$	−3.51304	−0.435739
$66$	3.45515	0.425300
$67$	14.4403	1.76416	0.882082	−	0.471097i	$-0.156142\pi$
$67$	14.4403	1.76416	0.882082	+	0.471097i	$0.156142\pi$
$68$	−1.45515	−0.176463
$69$	5.51304	0.663692
$70$	0	0
$71$	11.0840	1.31543	0.657713	−	0.753269i	$-0.271524\pi$
$71$	11.0840	1.31543	0.657713	+	0.753269i	$0.271524\pi$
$72$	1.00000	0.117851
$73$	−0.486957	−0.0569940	−0.0284970	−	0.999594i	$-0.509072\pi$
$73$	−0.486957	−0.0569940	−0.0284970	+	0.999594i	$0.509072\pi$
$74$	−5.75568	−0.669085
$75$	7.34147	0.847720
$76$	−3.51304	−0.402974
$77$	0	0
$78$	1.00000	0.113228
$79$	−8.62505	−0.970394	−0.485197	−	0.874405i	$-0.661252\pi$
$79$	−8.62505	−0.970394	−0.485197	+	0.874405i	$0.661252\pi$
$80$	−3.51304	−0.392770
$81$	1.00000	0.111111
$82$	3.55398	0.392471
$83$	1.36923	0.150293	0.0751463	−	0.997173i	$-0.476058\pi$
$83$	1.36923	0.150293	0.0751463	+	0.997173i	$0.476058\pi$
$84$	0	0
$85$	5.11200	0.554475
$86$	−4.42334	−0.476981
$87$	−0.869364	−0.0932056
$88$	3.45515	0.368320
$89$	1.33234	0.141228	0.0706139	−	0.997504i	$-0.477504\pi$
$89$	1.33234	0.141228	0.0706139	+	0.997504i	$0.477504\pi$
$90$	−3.51304	−0.370307
$91$	0	0
$92$	5.51304	0.574774
$93$	4.96819	0.515178
$94$	−2.72555	−0.281119
$95$	12.3415	1.26621
$96$	1.00000	0.102062
$97$	2.08187	0.211382	0.105691	−	0.994399i	$-0.466295\pi$
$97$	2.08187	0.211382	0.105691	+	0.994399i	$0.466295\pi$
$98$	0	0
$99$	3.45515	0.347256
$100$	7.34147	0.734147
$101$	−0.770534	−0.0766710	−0.0383355	−	0.999265i	$-0.512206\pi$
$101$	−0.770534	−0.0766710	−0.0383355	+	0.999265i	$0.512206\pi$
$102$	−1.45515	−0.144081
$103$	16.4386	1.61975	0.809873	−	0.586605i	$-0.199536\pi$
$103$	16.4386	1.61975	0.809873	+	0.586605i	$0.199536\pi$
$104$	1.00000	0.0980581
$105$	0	0
$106$	10.3824	1.00843
$107$	10.3584	1.00139	0.500693	−	0.865625i	$-0.333078\pi$
$107$	10.3584	1.00139	0.500693	+	0.865625i	$0.333078\pi$
$108$	1.00000	0.0962250
$109$	−1.46806	−0.140615	−0.0703074	−	0.997525i	$-0.522398\pi$
$109$	−1.46806	−0.140615	−0.0703074	+	0.997525i	$0.522398\pi$
$110$	−12.1381	−1.15732
$111$	−5.75568	−0.546305
$112$	0	0
$113$	0.0239800	0.00225585	0.00112792	−	0.999999i	$-0.499641\pi$
$113$	0.0239800	0.00225585	0.00112792	+	0.999999i	$0.499641\pi$
$114$	−3.51304	−0.329027
$115$	−19.3676	−1.80603
$116$	−0.869364	−0.0807184
$117$	1.00000	0.0924500
$118$	4.96819	0.457359
$119$	0	0
$120$	−3.51304	−0.320695
$121$	0.938061	0.0852783
$122$	11.3097	1.02393
$123$	3.55398	0.320452
$124$	4.96819	0.446157
$125$	−8.22568	−0.735728
$126$	0	0
$127$	−9.16585	−0.813338	−0.406669	−	0.913576i	$-0.633310\pi$
$127$	−9.16585	−0.813338	−0.406669	+	0.913576i	$0.633310\pi$
$128$	1.00000	0.0883883
$129$	−4.42334	−0.389454
$130$	−3.51304	−0.308114
$131$	−2.90625	−0.253921	−0.126960	−	0.991908i	$-0.540522\pi$
$131$	−2.90625	−0.253921	−0.126960	+	0.991908i	$0.540522\pi$
$132$	3.45515	0.300732
$133$	0	0
$134$	14.4403	1.24745
$135$	−3.51304	−0.302355
$136$	−1.45515	−0.124778
$137$	−13.0484	−1.11480	−0.557400	−	0.830244i	$-0.688201\pi$
$137$	−13.0484	−1.11480	−0.557400	+	0.830244i	$0.688201\pi$
$138$	5.51304	0.469301
$139$	−16.6490	−1.41215	−0.706076	−	0.708136i	$-0.749536\pi$
$139$	−16.6490	−1.41215	−0.706076	+	0.708136i	$0.749536\pi$
$140$	0	0
$141$	−2.72555	−0.229533
$142$	11.0840	0.930147
$143$	3.45515	0.288934
$144$	1.00000	0.0833333
$145$	3.05411	0.253630
$146$	−0.486957	−0.0403009
$147$	0	0
$148$	−5.75568	−0.473114
$149$	17.6751	1.44800	0.724001	−	0.689799i	$-0.242301\pi$
$149$	17.6751	1.44800	0.724001	+	0.689799i	$0.242301\pi$
$150$	7.34147	0.599429
$151$	7.25749	0.590606	0.295303	−	0.955404i	$-0.404579\pi$
$151$	7.25749	0.590606	0.295303	+	0.955404i	$0.404579\pi$
$152$	−3.51304	−0.284945
$153$	−1.45515	−0.117642
$154$	0	0
$155$	−17.4535	−1.40190
$156$	1.00000	0.0800641
$157$	21.4437	1.71139	0.855697	−	0.517477i	$-0.173129\pi$
$157$	21.4437	1.71139	0.855697	+	0.517477i	$0.173129\pi$
$158$	−8.62505	−0.686172
$159$	10.3824	0.823378
$160$	−3.51304	−0.277730
$161$	0	0
$162$	1.00000	0.0785674
$163$	−22.2708	−1.74439	−0.872193	−	0.489162i	$-0.837303\pi$
$163$	−22.2708	−1.74439	−0.872193	+	0.489162i	$0.837303\pi$
$164$	3.55398	0.277519
$165$	−12.1381	−0.944949
$166$	1.36923	0.106273
$167$	−11.1909	−0.865978	−0.432989	−	0.901399i	$-0.642541\pi$
$167$	−11.1909	−0.865978	−0.432989	+	0.901399i	$0.642541\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	5.11200	0.392073
$171$	−3.51304	−0.268649
$172$	−4.42334	−0.337277
$173$	22.7591	1.73034	0.865171	−	0.501477i	$-0.167210\pi$
$173$	22.7591	1.73034	0.865171	+	0.501477i	$0.167210\pi$
$174$	−0.869364	−0.0659063
$175$	0	0
$176$	3.45515	0.260442
$177$	4.96819	0.373432
$178$	1.33234	0.0998632
$179$	−5.15294	−0.385149	−0.192574	−	0.981282i	$-0.561684\pi$
$179$	−5.15294	−0.385149	−0.192574	+	0.981282i	$0.561684\pi$
$180$	−3.51304	−0.261847
$181$	17.3056	1.28632	0.643158	−	0.765733i	$-0.277624\pi$
$181$	17.3056	1.28632	0.643158	+	0.765733i	$0.277624\pi$
$182$	0	0
$183$	11.3097	0.836034
$184$	5.51304	0.406427
$185$	20.2200	1.48660
$186$	4.96819	0.364286
$187$	−5.02776	−0.367666
$188$	−2.72555	−0.198781
$189$	0	0
$190$	12.3415	0.895344
$191$	25.3120	1.83151	0.915757	−	0.401732i	$-0.131592\pi$
$191$	25.3120	1.83151	0.915757	+	0.401732i	$0.131592\pi$
$192$	1.00000	0.0721688
$193$	−13.0204	−0.937226	−0.468613	−	0.883403i	$-0.655246\pi$
$193$	−13.0204	−0.937226	−0.468613	+	0.883403i	$0.655246\pi$
$194$	2.08187	0.149470
$195$	−3.51304	−0.251574
$196$	0	0
$197$	18.1919	1.29612	0.648061	−	0.761588i	$-0.275580\pi$
$197$	18.1919	1.29612	0.648061	+	0.761588i	$0.275580\pi$
$198$	3.45515	0.245547
$199$	−15.9194	−1.12850	−0.564249	−	0.825605i	$-0.690834\pi$
$199$	−15.9194	−1.12850	−0.564249	+	0.825605i	$0.690834\pi$
$200$	7.34147	0.519120
$201$	14.4403	1.01854
$202$	−0.770534	−0.0542146
$203$	0	0
$204$	−1.45515	−0.101881
$205$	−12.4853	−0.872010
$206$	16.4386	1.14533
$207$	5.51304	0.383183
$208$	1.00000	0.0693375
$209$	−12.1381	−0.839609
$210$	0	0
$211$	8.42334	0.579887	0.289943	−	0.957044i	$-0.406364\pi$
$211$	8.42334	0.579887	0.289943	+	0.957044i	$0.406364\pi$
$212$	10.3824	0.713067
$213$	11.0840	0.759462
$214$	10.3584	0.708087
$215$	15.5394	1.05978
$216$	1.00000	0.0680414
$217$	0	0
$218$	−1.46806	−0.0994296
$219$	−0.486957	−0.0329055
$220$	−12.1381	−0.818350
$221$	−1.45515	−0.0978840
$222$	−5.75568	−0.386296
$223$	−19.2318	−1.28786	−0.643929	−	0.765085i	$-0.722697\pi$
$223$	−19.2318	−1.28786	−0.643929	+	0.765085i	$0.722697\pi$
$224$	0	0
$225$	7.34147	0.489431
$226$	0.0239800	0.00159513
$227$	8.77053	0.582121	0.291060	−	0.956705i	$-0.405992\pi$
$227$	8.77053	0.582121	0.291060	+	0.956705i	$0.405992\pi$
$228$	−3.51304	−0.232657
$229$	−26.9865	−1.78331	−0.891657	−	0.452711i	$-0.850457\pi$
$229$	−26.9865	−1.78331	−0.891657	+	0.452711i	$0.850457\pi$
$230$	−19.3676	−1.27706
$231$	0	0
$232$	−0.869364	−0.0570765
$233$	23.5635	1.54370	0.771849	−	0.635805i	$-0.219332\pi$
$233$	23.5635	1.54370	0.771849	+	0.635805i	$0.219332\pi$
$234$	1.00000	0.0653720
$235$	9.57498	0.624603
$236$	4.96819	0.323402
$237$	−8.62505	−0.560257
$238$	0	0
$239$	−23.9388	−1.54847	−0.774235	−	0.632899i	$-0.781865\pi$
$239$	−23.9388	−1.54847	−0.774235	+	0.632899i	$0.781865\pi$
$240$	−3.51304	−0.226766
$241$	−12.9442	−0.833810	−0.416905	−	0.908950i	$-0.636885\pi$
$241$	−12.9442	−0.833810	−0.416905	+	0.908950i	$0.636885\pi$
$242$	0.938061	0.0603009
$243$	1.00000	0.0641500
$244$	11.3097	0.724027
$245$	0	0
$246$	3.55398	0.226593
$247$	−3.51304	−0.223530
$248$	4.96819	0.315481
$249$	1.36923	0.0867715
$250$	−8.22568	−0.520238
$251$	3.73468	0.235731	0.117865	−	0.993030i	$-0.462395\pi$
$251$	3.73468	0.235731	0.117865	+	0.993030i	$0.462395\pi$
$252$	0	0
$253$	19.0484	1.19756
$254$	−9.16585	−0.575117
$255$	5.11200	0.320126
$256$	1.00000	0.0625000
$257$	6.56715	0.409648	0.204824	−	0.978799i	$-0.434338\pi$
$257$	6.56715	0.409648	0.204824	+	0.978799i	$0.434338\pi$
$258$	−4.42334	−0.275385
$259$	0	0
$260$	−3.51304	−0.217870
$261$	−0.869364	−0.0538123
$262$	−2.90625	−0.179549
$263$	26.2159	1.61654	0.808271	−	0.588810i	$-0.200403\pi$
$263$	26.2159	1.61654	0.808271	+	0.588810i	$0.200403\pi$
$264$	3.45515	0.212650
$265$	−36.4738	−2.24057
$266$	0	0
$267$	1.33234	0.0815379
$268$	14.4403	0.882082
$269$	−12.1919	−0.743356	−0.371678	−	0.928362i	$-0.621217\pi$
$269$	−12.1919	−0.743356	−0.371678	+	0.928362i	$0.621217\pi$
$270$	−3.51304	−0.213797
$271$	9.25582	0.562251	0.281125	−	0.959671i	$-0.409292\pi$
$271$	9.25582	0.562251	0.281125	+	0.959671i	$0.409292\pi$
$272$	−1.45515	−0.0882314
$273$	0	0
$274$	−13.0484	−0.788282
$275$	25.3659	1.52962
$276$	5.51304	0.331846
$277$	26.8830	1.61524	0.807621	−	0.589703i	$-0.200755\pi$
$277$	26.8830	1.61524	0.807621	+	0.589703i	$0.200755\pi$
$278$	−16.6490	−0.998542
$279$	4.96819	0.297438
$280$	0	0
$281$	−20.6829	−1.23384	−0.616920	−	0.787026i	$-0.711620\pi$
$281$	−20.6829	−1.23384	−0.616920	+	0.787026i	$0.711620\pi$
$282$	−2.72555	−0.162304
$283$	−4.40676	−0.261955	−0.130977	−	0.991385i	$-0.541812\pi$
$283$	−4.40676	−0.261955	−0.130977	+	0.991385i	$0.541812\pi$
$284$	11.0840	0.657713
$285$	12.3415	0.731046
$286$	3.45515	0.204307
$287$	0	0
$288$	1.00000	0.0589256
$289$	−14.8825	−0.875443
$290$	3.05411	0.179344
$291$	2.08187	0.122042
$292$	−0.486957	−0.0284970
$293$	−17.5114	−1.02302	−0.511512	−	0.859276i	$-0.670915\pi$
$293$	−17.5114	−1.02302	−0.511512	+	0.859276i	$0.670915\pi$
$294$	0	0
$295$	−17.4535	−1.01618
$296$	−5.75568	−0.334542
$297$	3.45515	0.200488
$298$	17.6751	1.02389
$299$	5.51304	0.318827
$300$	7.34147	0.423860
$301$	0	0
$302$	7.25749	0.417622
$303$	−0.770534	−0.0442660
$304$	−3.51304	−0.201487
$305$	−39.7313	−2.27501
$306$	−1.45515	−0.0831854
$307$	−26.3398	−1.50329	−0.751646	−	0.659567i	$-0.770740\pi$
$307$	−26.3398	−1.50329	−0.751646	+	0.659567i	$0.770740\pi$
$308$	0	0
$309$	16.4386	0.935161
$310$	−17.4535	−0.991291
$311$	−13.7273	−0.778403	−0.389201	−	0.921153i	$-0.627249\pi$
$311$	−13.7273	−0.778403	−0.389201	+	0.921153i	$0.627249\pi$
$312$	1.00000	0.0566139
$313$	−18.2609	−1.03217	−0.516084	−	0.856538i	$-0.672611\pi$
$313$	−18.2609	−1.03217	−0.516084	+	0.856538i	$0.672611\pi$
$314$	21.4437	1.21014
$315$	0	0
$316$	−8.62505	−0.485197
$317$	−28.8146	−1.61839	−0.809195	−	0.587540i	$-0.800096\pi$
$317$	−28.8146	−1.61839	−0.809195	+	0.587540i	$0.800096\pi$
$318$	10.3824	0.582216
$319$	−3.00378	−0.168179
$320$	−3.51304	−0.196385
$321$	10.3584	0.578151
$322$	0	0
$323$	5.11200	0.284440
$324$	1.00000	0.0555556
$325$	7.34147	0.407231
$326$	−22.2708	−1.23347
$327$	−1.46806	−0.0811839
$328$	3.55398	0.196236
$329$	0	0
$330$	−12.1381	−0.668180
$331$	−30.1973	−1.65979	−0.829896	−	0.557917i	$-0.811601\pi$
$331$	−30.1973	−1.65979	−0.829896	+	0.557917i	$0.811601\pi$
$332$	1.36923	0.0751463
$333$	−5.75568	−0.315410
$334$	−11.1909	−0.612339
$335$	−50.7294	−2.77164
$336$	0	0
$337$	−21.7188	−1.18310	−0.591549	−	0.806269i	$-0.701483\pi$
$337$	−21.7188	−1.18310	−0.591549	+	0.806269i	$0.701483\pi$
$338$	1.00000	0.0543928
$339$	0.0239800	0.00130241
$340$	5.11200	0.277237
$341$	17.1659	0.929583
$342$	−3.51304	−0.189964
$343$	0	0
$344$	−4.42334	−0.238491
$345$	−19.3676	−1.04271
$346$	22.7591	1.22354
$347$	6.11876	0.328472	0.164236	−	0.986421i	$-0.447484\pi$
$347$	6.11876	0.328472	0.164236	+	0.986421i	$0.447484\pi$
$348$	−0.869364	−0.0466028
$349$	22.9385	1.22787	0.613935	−	0.789357i	$-0.289586\pi$
$349$	22.9385	1.22787	0.613935	+	0.789357i	$0.289586\pi$
$350$	0	0
$351$	1.00000	0.0533761
$352$	3.45515	0.184160
$353$	−9.45645	−0.503316	−0.251658	−	0.967816i	$-0.580976\pi$
$353$	−9.45645	−0.503316	−0.251658	+	0.967816i	$0.580976\pi$
$354$	4.96819	0.264056
$355$	−38.9385	−2.06664
$356$	1.33234	0.0706139
$357$	0	0
$358$	−5.15294	−0.272341
$359$	−28.4136	−1.49961	−0.749806	−	0.661658i	$-0.769853\pi$
$359$	−28.4136	−1.49961	−0.749806	+	0.661658i	$0.769853\pi$
$360$	−3.51304	−0.185154
$361$	−6.65853	−0.350449
$362$	17.3056	0.909563
$363$	0.938061	0.0492355
$364$	0	0
$365$	1.71070	0.0895422
$366$	11.3097	0.591166
$367$	−23.9676	−1.25110	−0.625548	−	0.780186i	$-0.715125\pi$
$367$	−23.9676	−1.25110	−0.625548	+	0.780186i	$0.715125\pi$
$368$	5.51304	0.287387
$369$	3.55398	0.185013
$370$	20.2200	1.05119
$371$	0	0
$372$	4.96819	0.257589
$373$	−14.1580	−0.733075	−0.366537	−	0.930403i	$-0.619457\pi$
$373$	−14.1580	−0.733075	−0.366537	+	0.930403i	$0.619457\pi$
$374$	−5.02776	−0.259979
$375$	−8.22568	−0.424773
$376$	−2.72555	−0.140560
$377$	−0.869364	−0.0447745
$378$	0	0
$379$	10.4742	0.538024	0.269012	−	0.963137i	$-0.413303\pi$
$379$	10.4742	0.538024	0.269012	+	0.963137i	$0.413303\pi$
$380$	12.3415	0.633104
$381$	−9.16585	−0.469581
$382$	25.3120	1.29508
$383$	−10.5784	−0.540530	−0.270265	−	0.962786i	$-0.587111\pi$
$383$	−10.5784	−0.540530	−0.270265	+	0.962786i	$0.587111\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−13.0204	−0.662719
$387$	−4.42334	−0.224851
$388$	2.08187	0.105691
$389$	2.98347	0.151268	0.0756341	−	0.997136i	$-0.475902\pi$
$389$	2.98347	0.151268	0.0756341	+	0.997136i	$0.475902\pi$
$390$	−3.51304	−0.177890
$391$	−8.02230	−0.405705
$392$	0	0
$393$	−2.90625	−0.146601
$394$	18.1919	0.916497
$395$	30.3002	1.52457
$396$	3.45515	0.173628
$397$	6.86234	0.344411	0.172205	−	0.985061i	$-0.444911\pi$
$397$	6.86234	0.344411	0.172205	+	0.985061i	$0.444911\pi$
$398$	−15.9194	−0.797969
$399$	0	0
$400$	7.34147	0.367073
$401$	−16.2795	−0.812961	−0.406481	−	0.913659i	$-0.633244\pi$
$401$	−16.2795	−0.812961	−0.406481	+	0.913659i	$0.633244\pi$
$402$	14.4403	0.720217
$403$	4.96819	0.247483
$404$	−0.770534	−0.0383355
$405$	−3.51304	−0.174565
$406$	0	0
$407$	−19.8867	−0.985750
$408$	−1.45515	−0.0720407
$409$	30.5837	1.51227	0.756134	−	0.654417i	$-0.227086\pi$
$409$	30.5837	1.51227	0.756134	+	0.654417i	$0.227086\pi$
$410$	−12.4853	−0.616604
$411$	−13.0484	−0.643630
$412$	16.4386	0.809873
$413$	0	0
$414$	5.51304	0.270951
$415$	−4.81017	−0.236122
$416$	1.00000	0.0490290
$417$	−16.6490	−0.815306
$418$	−12.1381	−0.593693
$419$	37.4776	1.83090	0.915451	−	0.402430i	$-0.131834\pi$
$419$	37.4776	1.83090	0.915451	+	0.402430i	$0.131834\pi$
$420$	0	0
$421$	−14.3905	−0.701350	−0.350675	−	0.936497i	$-0.614048\pi$
$421$	−14.3905	−0.701350	−0.350675	+	0.936497i	$0.614048\pi$
$422$	8.42334	0.410042
$423$	−2.72555	−0.132521
$424$	10.3824	0.504214
$425$	−10.6829	−0.518199
$426$	11.0840	0.537021
$427$	0	0
$428$	10.3584	0.500693
$429$	3.45515	0.166816
$430$	15.5394	0.749376
$431$	18.0441	0.869153	0.434576	−	0.900635i	$-0.356898\pi$
$431$	18.0441	0.869153	0.434576	+	0.900635i	$0.356898\pi$
$432$	1.00000	0.0481125
$433$	34.6247	1.66396	0.831978	−	0.554809i	$-0.187209\pi$
$433$	34.6247	1.66396	0.831978	+	0.554809i	$0.187209\pi$
$434$	0	0
$435$	3.05411	0.146433
$436$	−1.46806	−0.0703074
$437$	−19.3676	−0.926476
$438$	−0.486957	−0.0232677
$439$	−30.5022	−1.45579	−0.727896	−	0.685687i	$-0.759502\pi$
$439$	−30.5022	−1.45579	−0.727896	+	0.685687i	$0.759502\pi$
$440$	−12.1381	−0.578661
$441$	0	0
$442$	−1.45515	−0.0692144
$443$	−19.8377	−0.942519	−0.471259	−	0.881995i	$-0.656200\pi$
$443$	−19.8377	−0.942519	−0.471259	+	0.881995i	$0.656200\pi$
$444$	−5.75568	−0.273153
$445$	−4.68057	−0.221880
$446$	−19.2318	−0.910654
$447$	17.6751	0.836004
$448$	0	0
$449$	−21.5628	−1.01761	−0.508807	−	0.860881i	$-0.669913\pi$
$449$	−21.5628	−1.01761	−0.508807	+	0.860881i	$0.669913\pi$
$450$	7.34147	0.346080
$451$	12.2795	0.578221
$452$	0.0239800	0.00112792
$453$	7.25749	0.340987
$454$	8.77053	0.411622
$455$	0	0
$456$	−3.51304	−0.164513
$457$	33.0089	1.54409	0.772046	−	0.635567i	$-0.219233\pi$
$457$	33.0089	1.54409	0.772046	+	0.635567i	$0.219233\pi$
$458$	−26.9865	−1.26099
$459$	−1.45515	−0.0679206
$460$	−19.3676	−0.903017
$461$	24.2859	1.13111	0.565555	−	0.824711i	$-0.308662\pi$
$461$	24.2859	1.13111	0.565555	+	0.824711i	$0.308662\pi$
$462$	0	0
$463$	−9.70498	−0.451029	−0.225514	−	0.974240i	$-0.572406\pi$
$463$	−9.70498	−0.451029	−0.225514	+	0.974240i	$0.572406\pi$
$464$	−0.869364	−0.0403592
$465$	−17.4535	−0.809385
$466$	23.5635	1.09156
$467$	12.1678	0.563058	0.281529	−	0.959553i	$-0.409158\pi$
$467$	12.1678	0.563058	0.281529	+	0.959553i	$0.409158\pi$
$468$	1.00000	0.0462250
$469$	0	0
$470$	9.57498	0.441661
$471$	21.4437	0.988074
$472$	4.96819	0.228680
$473$	−15.2833	−0.702727
$474$	−8.62505	−0.396162
$475$	−25.7909	−1.18337
$476$	0	0
$477$	10.3824	0.475378
$478$	−23.9388	−1.09493
$479$	26.9033	1.22924	0.614621	−	0.788823i	$-0.289309\pi$
$479$	26.9033	1.22924	0.614621	+	0.788823i	$0.289309\pi$
$480$	−3.51304	−0.160348
$481$	−5.75568	−0.262437
$482$	−12.9442	−0.589593
$483$	0	0
$484$	0.938061	0.0426392
$485$	−7.31371	−0.332098
$486$	1.00000	0.0453609
$487$	−2.86234	−0.129705	−0.0648525	−	0.997895i	$-0.520658\pi$
$487$	−2.86234	−0.129705	−0.0648525	+	0.997895i	$0.520658\pi$
$488$	11.3097	0.511964
$489$	−22.2708	−1.00712
$490$	0	0
$491$	5.75973	0.259933	0.129966	−	0.991518i	$-0.458513\pi$
$491$	5.75973	0.259933	0.129966	+	0.991518i	$0.458513\pi$
$492$	3.55398	0.160226
$493$	1.26505	0.0569752
$494$	−3.51304	−0.158059
$495$	−12.1381	−0.545567
$496$	4.96819	0.223078
$497$	0	0
$498$	1.36923	0.0613567
$499$	−24.4586	−1.09492	−0.547458	−	0.836833i	$-0.684404\pi$
$499$	−24.4586	−1.09492	−0.547458	+	0.836833i	$0.684404\pi$
$500$	−8.22568	−0.367864
$501$	−11.1909	−0.499973
$502$	3.73468	0.166687
$503$	−12.0282	−0.536311	−0.268155	−	0.963376i	$-0.586414\pi$
$503$	−12.0282	−0.536311	−0.268155	+	0.963376i	$0.586414\pi$
$504$	0	0
$505$	2.70692	0.120456
$506$	19.0484	0.846804
$507$	1.00000	0.0444116
$508$	−9.16585	−0.406669
$509$	35.9788	1.59473	0.797366	−	0.603496i	$-0.206226\pi$
$509$	35.9788	1.59473	0.797366	+	0.603496i	$0.206226\pi$
$510$	5.11200	0.226363
$511$	0	0
$512$	1.00000	0.0441942
$513$	−3.51304	−0.155105
$514$	6.56715	0.289665
$515$	−57.7496	−2.54475
$516$	−4.42334	−0.194727
$517$	−9.41719	−0.414168
$518$	0	0
$519$	22.7591	0.999013
$520$	−3.51304	−0.154057
$521$	6.45489	0.282794	0.141397	−	0.989953i	$-0.454841\pi$
$521$	6.45489	0.282794	0.141397	+	0.989953i	$0.454841\pi$
$522$	−0.869364	−0.0380510
$523$	−2.00993	−0.0878882	−0.0439441	−	0.999034i	$-0.513992\pi$
$523$	−2.00993	−0.0878882	−0.0439441	+	0.999034i	$0.513992\pi$
$524$	−2.90625	−0.126960
$525$	0	0
$526$	26.2159	1.14307
$527$	−7.22947	−0.314920
$528$	3.45515	0.150366
$529$	7.39364	0.321463
$530$	−36.4738	−1.58432
$531$	4.96819	0.215601
$532$	0	0
$533$	3.55398	0.153940
$534$	1.33234	0.0576560
$535$	−36.3896	−1.57326
$536$	14.4403	0.623726
$537$	−5.15294	−0.222366
$538$	−12.1919	−0.525632
$539$	0	0
$540$	−3.51304	−0.151177
$541$	13.6318	0.586077	0.293039	−	0.956101i	$-0.405334\pi$
$541$	13.6318	0.586077	0.293039	+	0.956101i	$0.405334\pi$
$542$	9.25582	0.397571
$543$	17.3056	0.742655
$544$	−1.45515	−0.0623890
$545$	5.15736	0.220917
$546$	0	0
$547$	−15.5114	−0.663218	−0.331609	−	0.943417i	$-0.607591\pi$
$547$	−15.5114	−0.663218	−0.331609	+	0.943417i	$0.607591\pi$
$548$	−13.0484	−0.557400
$549$	11.3097	0.482685
$550$	25.3659	1.08160
$551$	3.05411	0.130110
$552$	5.51304	0.234651
$553$	0	0
$554$	26.8830	1.14215
$555$	20.2200	0.858290
$556$	−16.6490	−0.706076
$557$	−7.52702	−0.318930	−0.159465	−	0.987204i	$-0.550977\pi$
$557$	−7.52702	−0.318930	−0.159465	+	0.987204i	$0.550977\pi$
$558$	4.96819	0.210320
$559$	−4.42334	−0.187087
$560$	0	0
$561$	−5.02776	−0.212272
$562$	−20.6829	−0.872457
$563$	−20.1300	−0.848378	−0.424189	−	0.905574i	$-0.639441\pi$
$563$	−20.1300	−0.848378	−0.424189	+	0.905574i	$0.639441\pi$
$564$	−2.72555	−0.114766
$565$	−0.0842428	−0.00354412
$566$	−4.40676	−0.185230
$567$	0	0
$568$	11.0840	0.465073
$569$	−1.55672	−0.0652612	−0.0326306	−	0.999467i	$-0.510388\pi$
$569$	−1.55672	−0.0652612	−0.0326306	+	0.999467i	$0.510388\pi$
$570$	12.3415	0.516927
$571$	17.6535	0.738776	0.369388	−	0.929275i	$-0.379567\pi$
$571$	17.6535	0.738776	0.369388	+	0.929275i	$0.379567\pi$
$572$	3.45515	0.144467
$573$	25.3120	1.05743
$574$	0	0
$575$	40.4738	1.68788
$576$	1.00000	0.0416667
$577$	5.07405	0.211235	0.105618	−	0.994407i	$-0.466318\pi$
$577$	5.07405	0.211235	0.105618	+	0.994407i	$0.466318\pi$
$578$	−14.8825	−0.619032
$579$	−13.0204	−0.541108
$580$	3.05411	0.126815
$581$	0	0
$582$	2.08187	0.0862964
$583$	35.8728	1.48570
$584$	−0.486957	−0.0201504
$585$	−3.51304	−0.145246
$586$	−17.5114	−0.723388
$587$	−7.96609	−0.328796	−0.164398	−	0.986394i	$-0.552568\pi$
$587$	−7.96609	−0.328796	−0.164398	+	0.986394i	$0.552568\pi$
$588$	0	0
$589$	−17.4535	−0.719158
$590$	−17.4535	−0.718548
$591$	18.1919	0.748316
$592$	−5.75568	−0.236557
$593$	−6.98919	−0.287012	−0.143506	−	0.989649i	$-0.545838\pi$
$593$	−6.98919	−0.287012	−0.143506	+	0.989649i	$0.545838\pi$
$594$	3.45515	0.141767
$595$	0	0
$596$	17.6751	0.724001
$597$	−15.9194	−0.651539
$598$	5.51304	0.225445
$599$	−14.1060	−0.576356	−0.288178	−	0.957577i	$-0.593050\pi$
$599$	−14.1060	−0.576356	−0.288178	+	0.957577i	$0.593050\pi$
$600$	7.34147	0.299714
$601$	15.5282	0.633407	0.316703	−	0.948525i	$-0.397424\pi$
$601$	15.5282	0.633407	0.316703	+	0.948525i	$0.397424\pi$
$602$	0	0
$603$	14.4403	0.588054
$604$	7.25749	0.295303
$605$	−3.29545	−0.133979
$606$	−0.770534	−0.0313008
$607$	−0.777558	−0.0315601	−0.0157800	−	0.999875i	$-0.505023\pi$
$607$	−0.777558	−0.0315601	−0.0157800	+	0.999875i	$0.505023\pi$
$608$	−3.51304	−0.142473
$609$	0	0
$610$	−39.7313	−1.60867
$611$	−2.72555	−0.110264
$612$	−1.45515	−0.0588210
$613$	9.89729	0.399748	0.199874	−	0.979822i	$-0.435947\pi$
$613$	9.89729	0.399748	0.199874	+	0.979822i	$0.435947\pi$
$614$	−26.3398	−1.06299
$615$	−12.4853	−0.503455
$616$	0	0
$617$	−42.7973	−1.72295	−0.861477	−	0.507797i	$-0.830460\pi$
$617$	−42.7973	−1.72295	−0.861477	+	0.507797i	$0.830460\pi$
$618$	16.4386	0.661258
$619$	8.05050	0.323577	0.161788	−	0.986825i	$-0.448274\pi$
$619$	8.05050	0.323577	0.161788	+	0.986825i	$0.448274\pi$
$620$	−17.4535	−0.700948
$621$	5.51304	0.221231
$622$	−13.7273	−0.550414
$623$	0	0
$624$	1.00000	0.0400320
$625$	−7.81017	−0.312407
$626$	−18.2609	−0.729852
$627$	−12.1381	−0.484749
$628$	21.4437	0.855697
$629$	8.37538	0.333948
$630$	0	0
$631$	−1.31301	−0.0522703	−0.0261351	−	0.999658i	$-0.508320\pi$
$631$	−1.31301	−0.0522703	−0.0261351	+	0.999658i	$0.508320\pi$
$632$	−8.62505	−0.343086
$633$	8.42334	0.334798
$634$	−28.8146	−1.14437
$635$	32.2000	1.27782
$636$	10.3824	0.411689
$637$	0	0
$638$	−3.00378	−0.118921
$639$	11.0840	0.438475
$640$	−3.51304	−0.138865
$641$	−15.0420	−0.594122	−0.297061	−	0.954858i	$-0.596007\pi$
$641$	−15.0420	−0.594122	−0.297061	+	0.954858i	$0.596007\pi$
$642$	10.3584	0.408814
$643$	1.54696	0.0610060	0.0305030	−	0.999535i	$-0.490289\pi$
$643$	1.54696	0.0610060	0.0305030	+	0.999535i	$0.490289\pi$
$644$	0	0
$645$	15.5394	0.611863
$646$	5.11200	0.201129
$647$	−19.8363	−0.779844	−0.389922	−	0.920848i	$-0.627498\pi$
$647$	−19.8363	−0.779844	−0.389922	+	0.920848i	$0.627498\pi$
$648$	1.00000	0.0392837
$649$	17.1659	0.673819
$650$	7.34147	0.287956
$651$	0	0
$652$	−22.2708	−0.872193
$653$	−38.5114	−1.50707	−0.753534	−	0.657409i	$-0.771653\pi$
$653$	−38.5114	−1.50707	−0.753534	+	0.657409i	$0.771653\pi$
$654$	−1.46806	−0.0574057
$655$	10.2098	0.398930
$656$	3.55398	0.138760
$657$	−0.486957	−0.0189980
$658$	0	0
$659$	−23.2894	−0.907224	−0.453612	−	0.891199i	$-0.649865\pi$
$659$	−23.2894	−0.907224	−0.453612	+	0.891199i	$0.649865\pi$
$660$	−12.1381	−0.472475
$661$	−31.9411	−1.24237	−0.621183	−	0.783666i	$-0.713348\pi$
$661$	−31.9411	−1.24237	−0.621183	+	0.783666i	$0.713348\pi$
$662$	−30.1973	−1.17365
$663$	−1.45515	−0.0565133
$664$	1.36923	0.0531365
$665$	0	0
$666$	−5.75568	−0.223028
$667$	−4.79284	−0.185579
$668$	−11.1909	−0.432989
$669$	−19.2318	−0.743546
$670$	−50.7294	−1.95985
$671$	39.0766	1.50853
$672$	0	0
$673$	48.3267	1.86286	0.931428	−	0.363925i	$-0.118564\pi$
$673$	48.3267	1.86286	0.931428	+	0.363925i	$0.118564\pi$
$674$	−21.7188	−0.836577
$675$	7.34147	0.282573
$676$	1.00000	0.0384615
$677$	37.9330	1.45788	0.728942	−	0.684575i	$-0.240012\pi$
$677$	37.9330	1.45788	0.728942	+	0.684575i	$0.240012\pi$
$678$	0.0239800	0.000920946 0
$679$	0	0
$680$	5.11200	0.196036
$681$	8.77053	0.336088
$682$	17.1659	0.657314
$683$	−16.3438	−0.625380	−0.312690	−	0.949855i	$-0.601230\pi$
$683$	−16.3438	−0.625380	−0.312690	+	0.949855i	$0.601230\pi$
$684$	−3.51304	−0.134325
$685$	45.8396	1.75144
$686$	0	0
$687$	−26.9865	−1.02960
$688$	−4.42334	−0.168638
$689$	10.3824	0.395538
$690$	−19.3676	−0.737310
$691$	40.3805	1.53615	0.768074	−	0.640361i	$-0.221215\pi$
$691$	40.3805	1.53615	0.768074	+	0.640361i	$0.221215\pi$
$692$	22.7591	0.865171
$693$	0	0
$694$	6.11876	0.232265
$695$	58.4887	2.21860
$696$	−0.869364	−0.0329531
$697$	−5.17157	−0.195887
$698$	22.9385	0.868235
$699$	23.5635	0.891255
$700$	0	0
$701$	−47.6325	−1.79905	−0.899527	−	0.436864i	$-0.856089\pi$
$701$	−47.6325	−1.79905	−0.899527	+	0.436864i	$0.856089\pi$
$702$	1.00000	0.0377426
$703$	20.2200	0.762610
$704$	3.45515	0.130221
$705$	9.57498	0.360615
$706$	−9.45645	−0.355898
$707$	0	0
$708$	4.96819	0.186716
$709$	−4.66582	−0.175228	−0.0876142	−	0.996154i	$-0.527924\pi$
$709$	−4.66582	−0.175228	−0.0876142	+	0.996154i	$0.527924\pi$
$710$	−38.9385	−1.46134
$711$	−8.62505	−0.323465
$712$	1.33234	0.0499316
$713$	27.3899	1.02576
$714$	0	0
$715$	−12.1381	−0.453939
$716$	−5.15294	−0.192574
$717$	−23.9388	−0.894009
$718$	−28.4136	−1.06039
$719$	−40.2446	−1.50087	−0.750436	−	0.660943i	$-0.770156\pi$
$719$	−40.2446	−1.50087	−0.750436	+	0.660943i	$0.770156\pi$
$720$	−3.51304	−0.130923
$721$	0	0
$722$	−6.65853	−0.247805
$723$	−12.9442	−0.481400
$724$	17.3056	0.643158
$725$	−6.38241	−0.237037
$726$	0.938061	0.0348147
$727$	30.7737	1.14133	0.570666	−	0.821182i	$-0.306685\pi$
$727$	30.7737	1.14133	0.570666	+	0.821182i	$0.306685\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	1.71070	0.0633159
$731$	6.43663	0.238067
$732$	11.3097	0.418017
$733$	−32.8707	−1.21411	−0.607053	−	0.794661i	$-0.707648\pi$
$733$	−32.8707	−1.21411	−0.607053	+	0.794661i	$0.707648\pi$
$734$	−23.9676	−0.884659
$735$	0	0
$736$	5.51304	0.203213
$737$	49.8934	1.83785
$738$	3.55398	0.130824
$739$	−11.8599	−0.436272	−0.218136	−	0.975918i	$-0.569998\pi$
$739$	−11.8599	−0.436272	−0.218136	+	0.975918i	$0.569998\pi$
$740$	20.2200	0.743301
$741$	−3.51304	−0.129055
$742$	0	0
$743$	36.1604	1.32660	0.663298	−	0.748355i	$-0.269156\pi$
$743$	36.1604	1.32660	0.663298	+	0.748355i	$0.269156\pi$
$744$	4.96819	0.182143
$745$	−62.0934	−2.27493
$746$	−14.1580	−0.518362
$747$	1.36923	0.0500976
$748$	−5.02776	−0.183833
$749$	0	0
$750$	−8.22568	−0.300360
$751$	−34.8194	−1.27058	−0.635288	−	0.772275i	$-0.719119\pi$
$751$	−34.8194	−1.27058	−0.635288	+	0.772275i	$0.719119\pi$
$752$	−2.72555	−0.0993907
$753$	3.73468	0.136099
$754$	−0.869364	−0.0316604
$755$	−25.4959	−0.927890
$756$	0	0
$757$	25.5056	0.927018	0.463509	−	0.886092i	$-0.346590\pi$
$757$	25.5056	0.927018	0.463509	+	0.886092i	$0.346590\pi$
$758$	10.4742	0.380441
$759$	19.0484	0.691413
$760$	12.3415	0.447672
$761$	12.2823	0.445232	0.222616	−	0.974906i	$-0.428540\pi$
$761$	12.2823	0.445232	0.222616	+	0.974906i	$0.428540\pi$
$762$	−9.16585	−0.332044
$763$	0	0
$764$	25.3120	0.915757
$765$	5.11200	0.184825
$766$	−10.5784	−0.382213
$767$	4.96819	0.179391
$768$	1.00000	0.0360844
$769$	−33.5652	−1.21039	−0.605196	−	0.796076i	$-0.706905\pi$
$769$	−33.5652	−1.21039	−0.605196	+	0.796076i	$0.706905\pi$
$770$	0	0
$771$	6.56715	0.236510
$772$	−13.0204	−0.468613
$773$	12.5947	0.452998	0.226499	−	0.974011i	$-0.427272\pi$
$773$	12.5947	0.452998	0.226499	+	0.974011i	$0.427272\pi$
$774$	−4.42334	−0.158994
$775$	36.4738	1.31018
$776$	2.08187	0.0747349
$777$	0	0
$778$	2.98347	0.106963
$779$	−12.4853	−0.447332
$780$	−3.51304	−0.125787
$781$	38.2968	1.37037
$782$	−8.02230	−0.286877
$783$	−0.869364	−0.0310685
$784$	0	0
$785$	−75.3327	−2.68874
$786$	−2.90625	−0.103663
$787$	20.2740	0.722689	0.361345	−	0.932432i	$-0.382318\pi$
$787$	20.2740	0.722689	0.361345	+	0.932432i	$0.382318\pi$
$788$	18.1919	0.648061
$789$	26.2159	0.933311
$790$	30.3002	1.07803
$791$	0	0
$792$	3.45515	0.122773
$793$	11.3097	0.401618
$794$	6.86234	0.243535
$795$	−36.4738	−1.29359
$796$	−15.9194	−0.564249
$797$	48.9831	1.73507	0.867535	−	0.497376i	$-0.165703\pi$
$797$	48.9831	1.73507	0.867535	+	0.497376i	$0.165703\pi$
$798$	0	0
$799$	3.96609	0.140310
$800$	7.34147	0.259560
$801$	1.33234	0.0470759
$802$	−16.2795	−0.574850
$803$	−1.68251	−0.0593745
$804$	14.4403	0.509270
$805$	0	0
$806$	4.96819	0.174997
$807$	−12.1919	−0.429177
$808$	−0.770534	−0.0271073
$809$	23.6478	0.831412	0.415706	−	0.909499i	$-0.363535\pi$
$809$	23.6478	0.831412	0.415706	+	0.909499i	$0.363535\pi$
$810$	−3.51304	−0.123436
$811$	5.05411	0.177474	0.0887369	−	0.996055i	$-0.471717\pi$
$811$	5.05411	0.177474	0.0887369	+	0.996055i	$0.471717\pi$
$812$	0	0
$813$	9.25582	0.324616
$814$	−19.8867	−0.697030
$815$	78.2384	2.74057
$816$	−1.45515	−0.0509404
$817$	15.5394	0.543655
$818$	30.5837	1.06934
$819$	0	0
$820$	−12.4853	−0.436005
$821$	5.47485	0.191074	0.0955368	−	0.995426i	$-0.469543\pi$
$821$	5.47485	0.191074	0.0955368	+	0.995426i	$0.469543\pi$
$822$	−13.0484	−0.455115
$823$	16.6811	0.581467	0.290733	−	0.956804i	$-0.406101\pi$
$823$	16.6811	0.581467	0.290733	+	0.956804i	$0.406101\pi$
$824$	16.4386	0.572667
$825$	25.3659	0.883127
$826$	0	0
$827$	35.6461	1.23954	0.619768	−	0.784785i	$-0.287227\pi$
$827$	35.6461	1.23954	0.619768	+	0.784785i	$0.287227\pi$
$828$	5.51304	0.191591
$829$	−22.3472	−0.776150	−0.388075	−	0.921628i	$-0.626860\pi$
$829$	−22.3472	−0.776150	−0.388075	+	0.921628i	$0.626860\pi$
$830$	−4.81017	−0.166963
$831$	26.8830	0.932560
$832$	1.00000	0.0346688
$833$	0	0
$834$	−16.6490	−0.576509
$835$	39.3141	1.36052
$836$	−12.1381	−0.419805
$837$	4.96819	0.171726
$838$	37.4776	1.29464
$839$	35.5162	1.22615	0.613077	−	0.790023i	$-0.289931\pi$
$839$	35.5162	1.22615	0.613077	+	0.790023i	$0.289931\pi$
$840$	0	0
$841$	−28.2442	−0.973938
$842$	−14.3905	−0.495929
$843$	−20.6829	−0.712358
$844$	8.42334	0.289943
$845$	−3.51304	−0.120852
$846$	−2.72555	−0.0937064
$847$	0	0
$848$	10.3824	0.356533
$849$	−4.40676	−0.151240
$850$	−10.6829	−0.366422
$851$	−31.7313	−1.08774
$852$	11.0840	0.379731
$853$	33.8694	1.15967	0.579833	−	0.814735i	$-0.303118\pi$
$853$	33.8694	1.15967	0.579833	+	0.814735i	$0.303118\pi$
$854$	0	0
$855$	12.3415	0.422069
$856$	10.3584	0.354044
$857$	−17.5338	−0.598944	−0.299472	−	0.954105i	$-0.596811\pi$
$857$	−17.5338	−0.598944	−0.299472	+	0.954105i	$0.596811\pi$
$858$	3.45515	0.117957
$859$	−21.4931	−0.733335	−0.366668	−	0.930352i	$-0.619501\pi$
$859$	−21.4931	−0.733335	−0.366668	+	0.930352i	$0.619501\pi$
$860$	15.5394	0.529889
$861$	0	0
$862$	18.0441	0.614584
$863$	34.4738	1.17350	0.586752	−	0.809767i	$-0.300407\pi$
$863$	34.4738	1.17350	0.586752	+	0.809767i	$0.300407\pi$
$864$	1.00000	0.0340207
$865$	−79.9537	−2.71851
$866$	34.6247	1.17659
$867$	−14.8825	−0.505438
$868$	0	0
$869$	−29.8008	−1.01092
$870$	3.05411	0.103544
$871$	14.4403	0.489291
$872$	−1.46806	−0.0497148
$873$	2.08187	0.0704607
$874$	−19.3676	−0.655117
$875$	0	0
$876$	−0.486957	−0.0164528
$877$	−24.4231	−0.824711	−0.412355	−	0.911023i	$-0.635294\pi$
$877$	−24.4231	−0.824711	−0.412355	+	0.911023i	$0.635294\pi$
$878$	−30.5022	−1.02940
$879$	−17.5114	−0.590644
$880$	−12.1381	−0.409175
$881$	−31.5331	−1.06238	−0.531189	−	0.847253i	$-0.678255\pi$
$881$	−31.5331	−1.06238	−0.531189	+	0.847253i	$0.678255\pi$
$882$	0	0
$883$	−9.23351	−0.310732	−0.155366	−	0.987857i	$-0.549656\pi$
$883$	−9.23351	−0.310732	−0.155366	+	0.987857i	$0.549656\pi$
$884$	−1.45515	−0.0489420
$885$	−17.4535	−0.586692
$886$	−19.8377	−0.666461
$887$	56.7534	1.90559	0.952796	−	0.303612i	$-0.0981926\pi$
$887$	56.7534	1.90559	0.952796	+	0.303612i	$0.0981926\pi$
$888$	−5.75568	−0.193148
$889$	0	0
$890$	−4.68057	−0.156893
$891$	3.45515	0.115752
$892$	−19.2318	−0.643929
$893$	9.57498	0.320415
$894$	17.6751	0.591144
$895$	18.1025	0.605100
$896$	0	0
$897$	5.51304	0.184075
$898$	−21.5628	−0.719561
$899$	−4.31917	−0.144052
$900$	7.34147	0.244716
$901$	−15.1080	−0.503319
$902$	12.2795	0.408864
$903$	0	0
$904$	0.0239800	0.000797563 0
$905$	−60.7954	−2.02091
$906$	7.25749	0.241114
$907$	32.6715	1.08484	0.542420	−	0.840108i	$-0.317508\pi$
$907$	32.6715	1.08484	0.542420	+	0.840108i	$0.317508\pi$
$908$	8.77053	0.291060
$909$	−0.770534	−0.0255570
$910$	0	0
$911$	−39.2904	−1.30175	−0.650875	−	0.759185i	$-0.725598\pi$
$911$	−39.2904	−1.30175	−0.650875	+	0.759185i	$0.725598\pi$
$912$	−3.51304	−0.116328
$913$	4.73090	0.156570
$914$	33.0089	1.09184
$915$	−39.7313	−1.31348
$916$	−26.9865	−0.891657
$917$	0	0
$918$	−1.45515	−0.0480271
$919$	9.40367	0.310199	0.155099	−	0.987899i	$-0.450430\pi$
$919$	9.40367	0.310199	0.155099	+	0.987899i	$0.450430\pi$
$920$	−19.3676	−0.638529
$921$	−26.3398	−0.867926
$922$	24.2859	0.799815
$923$	11.0840	0.364834
$924$	0	0
$925$	−42.2552	−1.38934
$926$	−9.70498	−0.318925
$927$	16.4386	0.539915
$928$	−0.869364	−0.0285383
$929$	−39.1778	−1.28538	−0.642691	−	0.766126i	$-0.722182\pi$
$929$	−39.1778	−1.28538	−0.642691	+	0.766126i	$0.722182\pi$
$930$	−17.4535	−0.572322
$931$	0	0
$932$	23.5635	0.771849
$933$	−13.7273	−0.449411
$934$	12.1678	0.398142
$935$	17.6627	0.577633
$936$	1.00000	0.0326860
$937$	31.3026	1.02261	0.511306	−	0.859399i	$-0.329162\pi$
$937$	31.3026	1.02261	0.511306	+	0.859399i	$0.329162\pi$
$938$	0	0
$939$	−18.2609	−0.595922
$940$	9.57498	0.312301
$941$	−11.3401	−0.369675	−0.184838	−	0.982769i	$-0.559176\pi$
$941$	−11.3401	−0.369675	−0.184838	+	0.982769i	$0.559176\pi$
$942$	21.4437	0.698674
$943$	19.5932	0.638044
$944$	4.96819	0.161701
$945$	0	0
$946$	−15.2833	−0.496903
$947$	3.38137	0.109880	0.0549399	−	0.998490i	$-0.482503\pi$
$947$	3.38137	0.109880	0.0549399	+	0.998490i	$0.482503\pi$
$948$	−8.62505	−0.280129
$949$	−0.486957	−0.0158073
$950$	−25.7909	−0.836767
$951$	−28.8146	−0.934378
$952$	0	0
$953$	48.5294	1.57202	0.786010	−	0.618214i	$-0.212143\pi$
$953$	48.5294	1.57202	0.786010	+	0.618214i	$0.212143\pi$
$954$	10.3824	0.336143
$955$	−88.9223	−2.87746
$956$	−23.9388	−0.774235
$957$	−3.00378	−0.0970985
$958$	26.9033	0.869205
$959$	0	0
$960$	−3.51304	−0.113383
$961$	−6.31706	−0.203776
$962$	−5.75568	−0.185571
$963$	10.3584	0.333796
$964$	−12.9442	−0.416905
$965$	45.7411	1.47246
$966$	0	0
$967$	−33.1507	−1.06605	−0.533027	−	0.846098i	$-0.678945\pi$
$967$	−33.1507	−1.06605	−0.533027	+	0.846098i	$0.678945\pi$
$968$	0.938061	0.0301504
$969$	5.11200	0.164221
$970$	−7.31371	−0.234829
$971$	20.1455	0.646499	0.323250	−	0.946314i	$-0.395225\pi$
$971$	20.1455	0.646499	0.323250	+	0.946314i	$0.395225\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	−2.86234	−0.0917153
$975$	7.34147	0.235115
$976$	11.3097	0.362013
$977$	5.95869	0.190635	0.0953177	−	0.995447i	$-0.469613\pi$
$977$	5.95869	0.190635	0.0953177	+	0.995447i	$0.469613\pi$
$978$	−22.2708	−0.712143
$979$	4.60344	0.147126
$980$	0	0
$981$	−1.46806	−0.0468716
$982$	5.75973	0.183800
$983$	29.7682	0.949459	0.474729	−	0.880132i	$-0.342546\pi$
$983$	29.7682	0.949459	0.474729	+	0.880132i	$0.342546\pi$
$984$	3.55398	0.113297
$985$	−63.9091	−2.03631
$986$	1.26505	0.0402875
$987$	0	0
$988$	−3.51304	−0.111765
$989$	−24.3861	−0.775432
$990$	−12.1381	−0.385774
$991$	50.1829	1.59411	0.797056	−	0.603906i	$-0.206390\pi$
$991$	50.1829	1.59411	0.797056	+	0.603906i	$0.206390\pi$
$992$	4.96819	0.157740
$993$	−30.1973	−0.958282
$994$	0	0
$995$	55.9256	1.77296
$996$	1.36923	0.0433858
$997$	−35.6081	−1.12772	−0.563861	−	0.825870i	$-0.690685\pi$
$997$	−35.6081	−1.12772	−0.563861	+	0.825870i	$0.690685\pi$
$998$	−24.4586	−0.774222
$999$	−5.75568	−0.182102

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3822.2.a.ca.1.1	yes	4
7.6	odd	2		3822.2.a.bz.1.4	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3822.2.a.bz.1.4	✓	4	7.6	odd	2
3822.2.a.ca.1.1	yes	4	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:	\( N \)	\(=\)	\( 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3822.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.51304 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.51304 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -3.51304 q^{10} +3.45515 q^{11} +1.00000 q^{12} +1.00000 q^{13} -3.51304 q^{15} +1.00000 q^{16} -1.45515 q^{17} +1.00000 q^{18} -3.51304 q^{19} -3.51304 q^{20} +3.45515 q^{22} +5.51304 q^{23} +1.00000 q^{24} +7.34147 q^{25} +1.00000 q^{26} +1.00000 q^{27} -0.869364 q^{29} -3.51304 q^{30} +4.96819 q^{31} +1.00000 q^{32} +3.45515 q^{33} -1.45515 q^{34} +1.00000 q^{36} -5.75568 q^{37} -3.51304 q^{38} +1.00000 q^{39} -3.51304 q^{40} +3.55398 q^{41} -4.42334 q^{43} +3.45515 q^{44} -3.51304 q^{45} +5.51304 q^{46} -2.72555 q^{47} +1.00000 q^{48} +7.34147 q^{50} -1.45515 q^{51} +1.00000 q^{52} +10.3824 q^{53} +1.00000 q^{54} -12.1381 q^{55} -3.51304 q^{57} -0.869364 q^{58} +4.96819 q^{59} -3.51304 q^{60} +11.3097 q^{61} +4.96819 q^{62} +1.00000 q^{64} -3.51304 q^{65} +3.45515 q^{66} +14.4403 q^{67} -1.45515 q^{68} +5.51304 q^{69} +11.0840 q^{71} +1.00000 q^{72} -0.486957 q^{73} -5.75568 q^{74} +7.34147 q^{75} -3.51304 q^{76} +1.00000 q^{78} -8.62505 q^{79} -3.51304 q^{80} +1.00000 q^{81} +3.55398 q^{82} +1.36923 q^{83} +5.11200 q^{85} -4.42334 q^{86} -0.869364 q^{87} +3.45515 q^{88} +1.33234 q^{89} -3.51304 q^{90} +5.51304 q^{92} +4.96819 q^{93} -2.72555 q^{94} +12.3415 q^{95} +1.00000 q^{96} +2.08187 q^{97} +3.45515 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - 2 q^{5} + 4 q^{6} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 - 2 * q^5 + 4 * q^6 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - 2 q^{5} + 4 q^{6} + 4 q^{8} + 4 q^{9} - 2 q^{10} + 6 q^{11} + 4 q^{12} + 4 q^{13} - 2 q^{15} + 4 q^{16} + 2 q^{17} + 4 q^{18} - 2 q^{19} - 2 q^{20} + 6 q^{22} + 10 q^{23} + 4 q^{24} + 6 q^{25} + 4 q^{26} + 4 q^{27} + 10 q^{29} - 2 q^{30} + 4 q^{32} + 6 q^{33} + 2 q^{34} + 4 q^{36} + 6 q^{37} - 2 q^{38} + 4 q^{39} - 2 q^{40} + 10 q^{43} + 6 q^{44} - 2 q^{45} + 10 q^{46} - 8 q^{47} + 4 q^{48} + 6 q^{50} + 2 q^{51} + 4 q^{52} + 16 q^{53} + 4 q^{54} + 6 q^{55} - 2 q^{57} + 10 q^{58} - 2 q^{60} + 2 q^{61} + 4 q^{64} - 2 q^{65} + 6 q^{66} + 28 q^{67} + 2 q^{68} + 10 q^{69} + 16 q^{71} + 4 q^{72} - 14 q^{73} + 6 q^{74} + 6 q^{75} - 2 q^{76} + 4 q^{78} + 8 q^{79} - 2 q^{80} + 4 q^{81} + 4 q^{83} - 10 q^{85} + 10 q^{86} + 10 q^{87} + 6 q^{88} + 4 q^{89} - 2 q^{90} + 10 q^{92} - 8 q^{94} + 26 q^{95} + 4 q^{96} + 4 q^{97} + 6 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 - 2 * q^5 + 4 * q^6 + 4 * q^8 + 4 * q^9 - 2 * q^10 + 6 * q^11 + 4 * q^12 + 4 * q^13 - 2 * q^15 + 4 * q^16 + 2 * q^17 + 4 * q^18 - 2 * q^19 - 2 * q^20 + 6 * q^22 + 10 * q^23 + 4 * q^24 + 6 * q^25 + 4 * q^26 + 4 * q^27 + 10 * q^29 - 2 * q^30 + 4 * q^32 + 6 * q^33 + 2 * q^34 + 4 * q^36 + 6 * q^37 - 2 * q^38 + 4 * q^39 - 2 * q^40 + 10 * q^43 + 6 * q^44 - 2 * q^45 + 10 * q^46 - 8 * q^47 + 4 * q^48 + 6 * q^50 + 2 * q^51 + 4 * q^52 + 16 * q^53 + 4 * q^54 + 6 * q^55 - 2 * q^57 + 10 * q^58 - 2 * q^60 + 2 * q^61 + 4 * q^64 - 2 * q^65 + 6 * q^66 + 28 * q^67 + 2 * q^68 + 10 * q^69 + 16 * q^71 + 4 * q^72 - 14 * q^73 + 6 * q^74 + 6 * q^75 - 2 * q^76 + 4 * q^78 + 8 * q^79 - 2 * q^80 + 4 * q^81 + 4 * q^83 - 10 * q^85 + 10 * q^86 + 10 * q^87 + 6 * q^88 + 4 * q^89 - 2 * q^90 + 10 * q^92 - 8 * q^94 + 26 * q^95 + 4 * q^96 + 4 * q^97 + 6 * q^99

Introduction

L-functions

Modular forms

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Database

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