LMFDB - Embedded newform 1849.2.a.q.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1849,2,Mod(1,1849)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1849, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1849.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1849 = 43^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1849.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:	$14.7643393337$
Analytic rank:	$1$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 27 x^{18} + 300 x^{16} - 1775 x^{14} + 6037 x^{12} - 11859 x^{10} + 12809 x^{8} - 6823 x^{6} + \cdots + 1 $ x^20 - 27x^18 + 300x^16 - 1775x^14 + 6037x^12 - 11859x^10 + 12809x^8 - 6823x^6 + 1500x^4 - 75*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-2.02007$ of defining polynomial
Character	$\chi$	$=$	1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.02007 q^{2} +0.200809 q^{3} +2.08069 q^{4} +1.28791 q^{5} -0.405649 q^{6} -0.549923 q^{7} -0.163010 q^{8} -2.95968 q^{9} +O(q^{10})$	\(q-2.02007 q^{2} +0.200809 q^{3} +2.08069 q^{4} +1.28791 q^{5} -0.405649 q^{6} -0.549923 q^{7} -0.163010 q^{8} -2.95968 q^{9} -2.60166 q^{10} +3.56633 q^{11} +0.417822 q^{12} -5.49952 q^{13} +1.11088 q^{14} +0.258623 q^{15} -3.83210 q^{16} -0.626393 q^{17} +5.97876 q^{18} +7.30193 q^{19} +2.67974 q^{20} -0.110429 q^{21} -7.20424 q^{22} +4.76787 q^{23} -0.0327338 q^{24} -3.34130 q^{25} +11.1094 q^{26} -1.19676 q^{27} -1.14422 q^{28} -4.81806 q^{29} -0.522437 q^{30} -6.95392 q^{31} +8.06714 q^{32} +0.716151 q^{33} +1.26536 q^{34} -0.708249 q^{35} -6.15818 q^{36} -2.95138 q^{37} -14.7504 q^{38} -1.10435 q^{39} -0.209941 q^{40} -3.93552 q^{41} +0.223076 q^{42} +7.42044 q^{44} -3.81178 q^{45} -9.63145 q^{46} +6.32880 q^{47} -0.769520 q^{48} -6.69758 q^{49} +6.74967 q^{50} -0.125785 q^{51} -11.4428 q^{52} -9.94942 q^{53} +2.41754 q^{54} +4.59309 q^{55} +0.0896427 q^{56} +1.46629 q^{57} +9.73283 q^{58} +1.19617 q^{59} +0.538116 q^{60} +5.31347 q^{61} +14.0474 q^{62} +1.62759 q^{63} -8.63201 q^{64} -7.08286 q^{65} -1.44668 q^{66} +11.6204 q^{67} -1.30333 q^{68} +0.957431 q^{69} +1.43071 q^{70} -15.0459 q^{71} +0.482456 q^{72} +11.9716 q^{73} +5.96201 q^{74} -0.670963 q^{75} +15.1931 q^{76} -1.96121 q^{77} +2.23087 q^{78} -2.90001 q^{79} -4.93538 q^{80} +8.63871 q^{81} +7.95004 q^{82} -4.69871 q^{83} -0.229770 q^{84} -0.806735 q^{85} -0.967509 q^{87} -0.581346 q^{88} -9.56444 q^{89} +7.70008 q^{90} +3.02431 q^{91} +9.92048 q^{92} -1.39641 q^{93} -12.7846 q^{94} +9.40419 q^{95} +1.61995 q^{96} -14.1645 q^{97} +13.5296 q^{98} -10.5552 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 14 q^{4} - 32 q^{6} - 6 q^{9}+O(q^{10}) $ 20 * q + 14 * q^4 - 32 * q^6 - 6 * q^9	$ 20 q + 14 q^{4} - 32 q^{6} - 6 q^{9} + 12 q^{10} - 20 q^{11} + 6 q^{13} - 34 q^{14} - 34 q^{15} + 14 q^{16} - 8 q^{17} + 12 q^{21} - 46 q^{23} + 2 q^{24} + 20 q^{25} - 38 q^{31} - 76 q^{35} - 46 q^{36} - 68 q^{38} - 64 q^{40} - 56 q^{41} - 58 q^{44} - 24 q^{47} - 20 q^{49} - 20 q^{52} - 42 q^{53} + 66 q^{54} - 46 q^{56} + 2 q^{57} + 12 q^{58} - 90 q^{59} + 18 q^{60} - 28 q^{64} + 76 q^{66} - 62 q^{67} - 54 q^{68} + 24 q^{74} - 36 q^{78} - 10 q^{79} - 48 q^{81} - 68 q^{83} + 70 q^{84} - 12 q^{87} + 58 q^{90} - 8 q^{92} - 42 q^{95} - 22 q^{96} - 44 q^{97} - 38 q^{99}+O(q^{100}) $ 20 * q + 14 * q^4 - 32 * q^6 - 6 * q^9 + 12 * q^10 - 20 * q^11 + 6 * q^13 - 34 * q^14 - 34 * q^15 + 14 * q^16 - 8 * q^17 + 12 * q^21 - 46 * q^23 + 2 * q^24 + 20 * q^25 - 38 * q^31 - 76 * q^35 - 46 * q^36 - 68 * q^38 - 64 * q^40 - 56 * q^41 - 58 * q^44 - 24 * q^47 - 20 * q^49 - 20 * q^52 - 42 * q^53 + 66 * q^54 - 46 * q^56 + 2 * q^57 + 12 * q^58 - 90 * q^59 + 18 * q^60 - 28 * q^64 + 76 * q^66 - 62 * q^67 - 54 * q^68 + 24 * q^74 - 36 * q^78 - 10 * q^79 - 48 * q^81 - 68 * q^83 + 70 * q^84 - 12 * q^87 + 58 * q^90 - 8 * q^92 - 42 * q^95 - 22 * q^96 - 44 * q^97 - 38 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.02007	−1.42841	−0.714204	−	0.699938i	$-0.753211\pi$
$2$	−2.02007	−1.42841	−0.714204	+	0.699938i	$0.753211\pi$
$3$	0.200809	0.115937	0.0579686	−	0.998318i	$-0.481538\pi$
$3$	0.200809	0.115937	0.0579686	+	0.998318i	$0.481538\pi$
$4$	2.08069	1.04035
$5$	1.28791	0.575969	0.287984	−	0.957635i	$-0.407015\pi$
$5$	1.28791	0.575969	0.287984	+	0.957635i	$0.407015\pi$
$6$	−0.405649	−0.165605
$7$	−0.549923	−0.207851	−0.103926	−	0.994585i	$-0.533140\pi$
$7$	−0.549923	−0.207851	−0.103926	+	0.994585i	$0.533140\pi$
$8$	−0.163010	−0.0576326
$9$	−2.95968	−0.986559
$10$	−2.60166	−0.822718
$11$	3.56633	1.07529	0.537644	−	0.843172i	$-0.319314\pi$
$11$	3.56633	1.07529	0.537644	+	0.843172i	$0.319314\pi$
$12$	0.417822	0.120615
$13$	−5.49952	−1.52529	−0.762646	−	0.646816i	$-0.776100\pi$
$13$	−5.49952	−1.52529	−0.762646	+	0.646816i	$0.776100\pi$
$14$	1.11088	0.296896
$15$	0.258623	0.0667762
$16$	−3.83210	−0.958025
$17$	−0.626393	−0.151923	−0.0759613	−	0.997111i	$-0.524203\pi$
$17$	−0.626393	−0.151923	−0.0759613	+	0.997111i	$0.524203\pi$
$18$	5.97876	1.40921
$19$	7.30193	1.67518	0.837588	−	0.546302i	$-0.183965\pi$
$19$	7.30193	1.67518	0.837588	+	0.546302i	$0.183965\pi$
$20$	2.67974	0.599208
$21$	−0.110429	−0.0240977
$22$	−7.20424	−1.53595
$23$	4.76787	0.994170	0.497085	−	0.867702i	$-0.334404\pi$
$23$	4.76787	0.994170	0.497085	+	0.867702i	$0.334404\pi$
$24$	−0.0327338	−0.00668176
$25$	−3.34130	−0.668260
$26$	11.1094	2.17874
$27$	−1.19676	−0.230316
$28$	−1.14422	−0.216238
$29$	−4.81806	−0.894691	−0.447345	−	0.894361i	$-0.647631\pi$
$29$	−4.81806	−0.894691	−0.447345	+	0.894361i	$0.647631\pi$
$30$	−0.522437	−0.0953836
$31$	−6.95392	−1.24896	−0.624480	−	0.781041i	$-0.714689\pi$
$31$	−6.95392	−1.24896	−0.624480	+	0.781041i	$0.714689\pi$
$32$	8.06714	1.42608
$33$	0.716151	0.124666
$34$	1.26536	0.217007
$35$	−0.708249	−0.119716
$36$	−6.15818	−1.02636
$37$	−2.95138	−0.485205	−0.242602	−	0.970126i	$-0.578001\pi$
$37$	−2.95138	−0.485205	−0.242602	+	0.970126i	$0.578001\pi$
$38$	−14.7504	−2.39284
$39$	−1.10435	−0.176838
$40$	−0.209941	−0.0331946
$41$	−3.93552	−0.614625	−0.307312	−	0.951609i	$-0.599430\pi$
$41$	−3.93552	−0.614625	−0.307312	+	0.951609i	$0.599430\pi$
$42$	0.223076	0.0344213
$43$	0	0
$43$	0	0
$44$	7.42044	1.11867
$45$	−3.81178	−0.568227
$46$	−9.63145	−1.42008
$47$	6.32880	0.923150	0.461575	−	0.887101i	$-0.347285\pi$
$47$	6.32880	0.923150	0.461575	+	0.887101i	$0.347285\pi$
$48$	−0.769520	−0.111071
$49$	−6.69758	−0.956798
$50$	6.74967	0.954548
$51$	−0.125785	−0.0176135
$52$	−11.4428	−1.58683
$53$	−9.94942	−1.36666	−0.683329	−	0.730111i	$-0.739469\pi$
$53$	−9.94942	−1.36666	−0.683329	+	0.730111i	$0.739469\pi$
$54$	2.41754	0.328985
$55$	4.59309	0.619333
$56$	0.0896427	0.0119790
$57$	1.46629	0.194215
$58$	9.73283	1.27798
$59$	1.19617	0.155728	0.0778641	−	0.996964i	$-0.475190\pi$
$59$	1.19617	0.155728	0.0778641	+	0.996964i	$0.475190\pi$
$60$	0.538116	0.0694704
$61$	5.31347	0.680320	0.340160	−	0.940367i	$-0.389519\pi$
$61$	5.31347	0.680320	0.340160	+	0.940367i	$0.389519\pi$
$62$	14.0474	1.78402
$63$	1.62759	0.205057
$64$	−8.63201	−1.07900
$65$	−7.08286	−0.878521
$66$	−1.44668	−0.178074
$67$	11.6204	1.41966	0.709832	−	0.704371i	$-0.248771\pi$
$67$	11.6204	1.41966	0.709832	+	0.704371i	$0.248771\pi$
$68$	−1.30333	−0.158052
$69$	0.957431	0.115261
$70$	1.43071	0.171003
$71$	−15.0459	−1.78562	−0.892809	−	0.450435i	$-0.851269\pi$
$71$	−15.0459	−1.78562	−0.892809	+	0.450435i	$0.851269\pi$
$72$	0.482456	0.0568579
$73$	11.9716	1.40117	0.700584	−	0.713570i	$-0.252923\pi$
$73$	11.9716	1.40117	0.700584	+	0.713570i	$0.252923\pi$
$74$	5.96201	0.693070
$75$	−0.670963	−0.0774762
$76$	15.1931	1.74277
$77$	−1.96121	−0.223500
$78$	2.23087	0.252597
$79$	−2.90001	−0.326277	−0.163138	−	0.986603i	$-0.552162\pi$
$79$	−2.90001	−0.326277	−0.163138	+	0.986603i	$0.552162\pi$
$80$	−4.93538	−0.551792
$81$	8.63871	0.959856
$82$	7.95004	0.877935
$83$	−4.69871	−0.515751	−0.257875	−	0.966178i	$-0.583022\pi$
$83$	−4.69871	−0.515751	−0.257875	+	0.966178i	$0.583022\pi$
$84$	−0.229770	−0.0250700
$85$	−0.806735	−0.0875027
$86$	0	0
$87$	−0.967509	−0.103728
$88$	−0.581346	−0.0619717
$89$	−9.56444	−1.01383	−0.506914	−	0.861996i	$-0.669214\pi$
$89$	−9.56444	−1.01383	−0.506914	+	0.861996i	$0.669214\pi$
$90$	7.70008	0.811659
$91$	3.02431	0.317034
$92$	9.92048	1.03428
$93$	−1.39641	−0.144801
$94$	−12.7846	−1.31863
$95$	9.40419	0.964850
$96$	1.61995	0.165336
$97$	−14.1645	−1.43819	−0.719095	−	0.694911i	$-0.755444\pi$
$97$	−14.1645	−1.43819	−0.719095	+	0.694911i	$0.755444\pi$
$98$	13.5296	1.36670
$99$	−10.5552	−1.06084
$100$	−6.95223	−0.695223
$101$	−1.21990	−0.121385	−0.0606924	−	0.998157i	$-0.519331\pi$
$101$	−1.21990	−0.121385	−0.0606924	+	0.998157i	$0.519331\pi$
$102$	0.254096	0.0251592
$103$	11.5281	1.13590	0.567949	−	0.823064i	$-0.307737\pi$
$103$	11.5281	1.13590	0.567949	+	0.823064i	$0.307737\pi$
$104$	0.896475	0.0879066
$105$	−0.142223	−0.0138795
$106$	20.0986	1.95214
$107$	−1.92282	−0.185886	−0.0929430	−	0.995671i	$-0.529627\pi$
$107$	−1.92282	−0.185886	−0.0929430	+	0.995671i	$0.529627\pi$
$108$	−2.49009	−0.239609
$109$	−13.0726	−1.25213	−0.626066	−	0.779770i	$-0.715336\pi$
$109$	−13.0726	−1.25213	−0.626066	+	0.779770i	$0.715336\pi$
$110$	−9.27838	−0.884659
$111$	−0.592665	−0.0562532
$112$	2.10736	0.199127
$113$	3.37440	0.317436	0.158718	−	0.987324i	$-0.449264\pi$
$113$	3.37440	0.317436	0.158718	+	0.987324i	$0.449264\pi$
$114$	−2.96202	−0.277418
$115$	6.14057	0.572611
$116$	−10.0249	−0.930789
$117$	16.2768	1.50479
$118$	−2.41635	−0.222443
$119$	0.344468	0.0315773
$120$	−0.0421580	−0.00384848
$121$	1.71870	0.156245
$122$	−10.7336	−0.971775
$123$	−0.790288	−0.0712578
$124$	−14.4690	−1.29935
$125$	−10.7428	−0.960866
$126$	−3.28786	−0.292906
$127$	−5.18400	−0.460006	−0.230003	−	0.973190i	$-0.573874\pi$
$127$	−5.18400	−0.460006	−0.230003	+	0.973190i	$0.573874\pi$
$128$	1.30302	0.115171
$129$	0	0
$130$	14.3079	1.25489
$131$	9.86435	0.861852	0.430926	−	0.902387i	$-0.358187\pi$
$131$	9.86435	0.861852	0.430926	+	0.902387i	$0.358187\pi$
$132$	1.49009	0.129696
$133$	−4.01550	−0.348188
$134$	−23.4742	−2.02786
$135$	−1.54131	−0.132655
$136$	0.102108	0.00875570
$137$	6.70993	0.573268	0.286634	−	0.958040i	$-0.407464\pi$
$137$	6.70993	0.573268	0.286634	+	0.958040i	$0.407464\pi$
$138$	−1.93408	−0.164640
$139$	7.56409	0.641578	0.320789	−	0.947151i	$-0.396052\pi$
$139$	7.56409	0.641578	0.320789	+	0.947151i	$0.396052\pi$
$140$	−1.47365	−0.124546
$141$	1.27088	0.107027
$142$	30.3938	2.55059
$143$	−19.6131	−1.64013
$144$	11.3418	0.945147
$145$	−6.20520	−0.515314
$146$	−24.1835	−2.00144
$147$	−1.34494	−0.110928
$148$	−6.14093	−0.504781
$149$	−21.8344	−1.78874	−0.894371	−	0.447326i	$-0.852376\pi$
$149$	−21.8344	−1.78874	−0.894371	+	0.447326i	$0.852376\pi$
$150$	1.35539	0.110668
$151$	1.17507	0.0956262	0.0478131	−	0.998856i	$-0.484775\pi$
$151$	1.17507	0.0956262	0.0478131	+	0.998856i	$0.484775\pi$
$152$	−1.19028	−0.0965448
$153$	1.85392	0.149881
$154$	3.96178	0.319249
$155$	−8.95599	−0.719362
$156$	−2.29782	−0.183973
$157$	−2.57534	−0.205535	−0.102767	−	0.994705i	$-0.532770\pi$
$157$	−2.57534	−0.205535	−0.102767	+	0.994705i	$0.532770\pi$
$158$	5.85823	0.466056
$159$	−1.99793	−0.158446
$160$	10.3897	0.821379
$161$	−2.62196	−0.206639
$162$	−17.4508	−1.37107
$163$	−6.68876	−0.523904	−0.261952	−	0.965081i	$-0.584366\pi$
$163$	−6.68876	−0.523904	−0.261952	+	0.965081i	$0.584366\pi$
$164$	−8.18861	−0.639423
$165$	0.922334	0.0718036
$166$	9.49174	0.736702
$167$	12.2826	0.950459	0.475229	−	0.879862i	$-0.342365\pi$
$167$	12.2826	0.950459	0.475229	+	0.879862i	$0.342365\pi$
$168$	0.0180011	0.00138881
$169$	17.2447	1.32652
$170$	1.62966	0.124989
$171$	−21.6113	−1.65266
$172$	0	0
$173$	−17.0844	−1.29891	−0.649453	−	0.760402i	$-0.725002\pi$
$173$	−17.0844	−1.29891	−0.649453	+	0.760402i	$0.725002\pi$
$174$	1.95444	0.148166
$175$	1.83746	0.138899
$176$	−13.6665	−1.03015
$177$	0.240202	0.0180547
$178$	19.3209	1.44816
$179$	−23.7043	−1.77174	−0.885872	−	0.463929i	$-0.846439\pi$
$179$	−23.7043	−1.77174	−0.885872	+	0.463929i	$0.846439\pi$
$180$	−7.93116	−0.591153
$181$	7.08332	0.526499	0.263250	−	0.964728i	$-0.415206\pi$
$181$	7.08332	0.526499	0.263250	+	0.964728i	$0.415206\pi$
$182$	−6.10933	−0.452854
$183$	1.06699	0.0788744
$184$	−0.777209	−0.0572966
$185$	−3.80110	−0.279463
$186$	2.82085	0.206835
$187$	−2.23392	−0.163361
$188$	13.1683	0.960397
$189$	0.658124	0.0478715
$190$	−18.9972	−1.37820
$191$	0.521942	0.0377664	0.0188832	−	0.999822i	$-0.493989\pi$
$191$	0.521942	0.0377664	0.0188832	+	0.999822i	$0.493989\pi$
$192$	−1.73339	−0.125096
$193$	−18.1930	−1.30956	−0.654782	−	0.755818i	$-0.727239\pi$
$193$	−18.1930	−1.30956	−0.654782	+	0.755818i	$0.727239\pi$
$194$	28.6134	2.05432
$195$	−1.42230	−0.101853
$196$	−13.9356	−0.995402
$197$	−21.8912	−1.55968	−0.779840	−	0.625979i	$-0.784700\pi$
$197$	−21.8912	−1.55968	−0.779840	+	0.625979i	$0.784700\pi$
$198$	21.3222	1.51530
$199$	−11.3066	−0.801503	−0.400751	−	0.916187i	$-0.631251\pi$
$199$	−11.3066	−0.801503	−0.400751	+	0.916187i	$0.631251\pi$
$200$	0.544664	0.0385136
$201$	2.33349	0.164592
$202$	2.46429	0.173387
$203$	2.64956	0.185963
$204$	−0.261721	−0.0183241
$205$	−5.06858	−0.354005
$206$	−23.2876	−1.62253
$207$	−14.1114	−0.980807
$208$	21.0747	1.46127
$209$	26.0411	1.80130
$210$	0.287300	0.0198256
$211$	−6.31942	−0.435047	−0.217523	−	0.976055i	$-0.569798\pi$
$211$	−6.31942	−0.435047	−0.217523	+	0.976055i	$0.569798\pi$
$212$	−20.7017	−1.42180
$213$	−3.02135	−0.207019
$214$	3.88424	0.265521
$215$	0	0
$216$	0.195083	0.0132737
$217$	3.82412	0.259598
$218$	26.4077	1.78855
$219$	2.40400	0.162447
$220$	9.55683	0.644321
$221$	3.44486	0.231727
$222$	1.19723	0.0803525
$223$	−3.72657	−0.249549	−0.124775	−	0.992185i	$-0.539821\pi$
$223$	−3.72657	−0.249549	−0.124775	+	0.992185i	$0.539821\pi$
$224$	−4.43630	−0.296413
$225$	9.88916	0.659278
$226$	−6.81653	−0.453429
$227$	−21.0115	−1.39458	−0.697292	−	0.716787i	$-0.745612\pi$
$227$	−21.0115	−1.39458	−0.697292	+	0.716787i	$0.745612\pi$
$228$	3.05091	0.202051
$229$	−12.5361	−0.828408	−0.414204	−	0.910184i	$-0.635940\pi$
$229$	−12.5361	−0.828408	−0.414204	+	0.910184i	$0.635940\pi$
$230$	−12.4044	−0.817921
$231$	−0.393828	−0.0259120
$232$	0.785390	0.0515634
$233$	5.45808	0.357571	0.178785	−	0.983888i	$-0.442783\pi$
$233$	5.45808	0.357571	0.178785	+	0.983888i	$0.442783\pi$
$234$	−32.8803	−2.14945
$235$	8.15089	0.531705
$236$	2.48887	0.162011
$237$	−0.582348	−0.0378276
$238$	−0.695850	−0.0451053
$239$	−4.16829	−0.269624	−0.134812	−	0.990871i	$-0.543043\pi$
$239$	−4.16829	−0.269624	−0.134812	+	0.990871i	$0.543043\pi$
$240$	−0.991069	−0.0639732
$241$	−19.2791	−1.24188	−0.620938	−	0.783859i	$-0.713248\pi$
$241$	−19.2791	−1.24188	−0.620938	+	0.783859i	$0.713248\pi$
$242$	−3.47190	−0.223182
$243$	5.32500	0.341599
$244$	11.0557	0.707770
$245$	−8.62585	−0.551086
$246$	1.59644	0.101785
$247$	−40.1571	−2.55514
$248$	1.13356	0.0719808
$249$	−0.943544	−0.0597946
$250$	21.7012	1.37251
$251$	1.67352	0.105631	0.0528157	−	0.998604i	$-0.483180\pi$
$251$	1.67352	0.105631	0.0528157	+	0.998604i	$0.483180\pi$
$252$	3.38653	0.213331
$253$	17.0038	1.06902
$254$	10.4721	0.657076
$255$	−0.162000	−0.0101448
$256$	14.6318	0.914490
$257$	4.30169	0.268332	0.134166	−	0.990959i	$-0.457164\pi$
$257$	4.30169	0.268332	0.134166	+	0.990959i	$0.457164\pi$
$258$	0	0
$259$	1.62303	0.100850
$260$	−14.7373	−0.913967
$261$	14.2599	0.882665
$262$	−19.9267	−1.23108
$263$	3.65913	0.225631	0.112816	−	0.993616i	$-0.464013\pi$
$263$	3.65913	0.225631	0.112816	+	0.993616i	$0.464013\pi$
$264$	−0.116739	−0.00718482
$265$	−12.8139	−0.787152
$266$	8.11160	0.497354
$267$	−1.92063	−0.117540
$268$	24.1786	1.47694
$269$	13.2027	0.804981	0.402490	−	0.915424i	$-0.368145\pi$
$269$	13.2027	0.804981	0.402490	+	0.915424i	$0.368145\pi$
$270$	3.11356	0.189485
$271$	−8.70124	−0.528563	−0.264281	−	0.964446i	$-0.585135\pi$
$271$	−8.70124	−0.528563	−0.264281	+	0.964446i	$0.585135\pi$
$272$	2.40040	0.145546
$273$	0.607309	0.0367560
$274$	−13.5546	−0.818860
$275$	−11.9162	−0.718572
$276$	1.99212	0.119912
$277$	6.41923	0.385694	0.192847	−	0.981229i	$-0.438228\pi$
$277$	6.41923	0.385694	0.192847	+	0.981229i	$0.438228\pi$
$278$	−15.2800	−0.916434
$279$	20.5813	1.23217
$280$	0.115451	0.00689954
$281$	−14.9721	−0.893159	−0.446579	−	0.894744i	$-0.647358\pi$
$281$	−14.9721	−0.893159	−0.446579	+	0.894744i	$0.647358\pi$
$282$	−2.56727	−0.152879
$283$	9.50215	0.564844	0.282422	−	0.959290i	$-0.408862\pi$
$283$	9.50215	0.564844	0.282422	+	0.959290i	$0.408862\pi$
$284$	−31.3059	−1.85766
$285$	1.88845	0.111862
$286$	39.6199	2.34277
$287$	2.16423	0.127751
$288$	−23.8761	−1.40691
$289$	−16.6076	−0.976920
$290$	12.5350	0.736078
$291$	−2.84437	−0.166740
$292$	24.9092	1.45770
$293$	−13.0333	−0.761416	−0.380708	−	0.924695i	$-0.624320\pi$
$293$	−13.0333	−0.761416	−0.380708	+	0.924695i	$0.624320\pi$
$294$	2.71687	0.158451
$295$	1.54055	0.0896945
$296$	0.481104	0.0279636
$297$	−4.26803	−0.247656
$298$	44.1070	2.55505
$299$	−26.2210	−1.51640
$300$	−1.39607	−0.0806021
$301$	0	0
$302$	−2.37374	−0.136593
$303$	−0.244967	−0.0140730
$304$	−27.9817	−1.60486
$305$	6.84325	0.391843
$306$	−3.74505	−0.214091
$307$	−16.0133	−0.913928	−0.456964	−	0.889485i	$-0.651063\pi$
$307$	−16.0133	−0.913928	−0.456964	+	0.889485i	$0.651063\pi$
$308$	−4.08067	−0.232518
$309$	2.31495	0.131693
$310$	18.0917	1.02754
$311$	−12.9781	−0.735919	−0.367959	−	0.929842i	$-0.619943\pi$
$311$	−12.9781	−0.735919	−0.367959	+	0.929842i	$0.619943\pi$
$312$	0.180020	0.0101916
$313$	1.71595	0.0969910	0.0484955	−	0.998823i	$-0.484557\pi$
$313$	1.71595	0.0969910	0.0484955	+	0.998823i	$0.484557\pi$
$314$	5.20238	0.293587
$315$	2.09619	0.118107
$316$	−6.03404	−0.339441
$317$	−4.74852	−0.266704	−0.133352	−	0.991069i	$-0.542574\pi$
$317$	−4.74852	−0.266704	−0.133352	+	0.991069i	$0.542574\pi$
$318$	4.03597	0.226326
$319$	−17.1828	−0.962051
$320$	−11.1172	−0.621471
$321$	−0.386120	−0.0215511
$322$	5.29655	0.295165
$323$	−4.57388	−0.254497
$324$	17.9745	0.998584
$325$	18.3756	1.01929
$326$	13.5118	0.748348
$327$	−2.62510	−0.145169
$328$	0.641527	0.0354224
$329$	−3.48035	−0.191878
$330$	−1.86318	−0.102565
$331$	28.1768	1.54874	0.774368	−	0.632736i	$-0.218068\pi$
$331$	28.1768	1.54874	0.774368	+	0.632736i	$0.218068\pi$
$332$	−9.77658	−0.536560
$333$	8.73514	0.478683
$334$	−24.8118	−1.35764
$335$	14.9660	0.817682
$336$	0.423177	0.0230862
$337$	9.98109	0.543705	0.271852	−	0.962339i	$-0.412364\pi$
$337$	9.98109	0.543705	0.271852	+	0.962339i	$0.412364\pi$
$338$	−34.8356	−1.89481
$339$	0.677609	0.0368027
$340$	−1.67857	−0.0910332
$341$	−24.8000	−1.34299
$342$	43.6565	2.36067
$343$	7.53262	0.406723
$344$	0	0
$345$	1.23308	0.0663868
$346$	34.5118	1.85537
$347$	27.2177	1.46112	0.730560	−	0.682848i	$-0.239259\pi$
$347$	27.2177	1.46112	0.730560	+	0.682848i	$0.239259\pi$
$348$	−2.01309	−0.107913
$349$	23.2068	1.24223	0.621116	−	0.783719i	$-0.286680\pi$
$349$	23.2068	1.24223	0.621116	+	0.783719i	$0.286680\pi$
$350$	−3.71180	−0.198404
$351$	6.58159	0.351299
$352$	28.7701	1.53345
$353$	26.6495	1.41841	0.709205	−	0.705003i	$-0.249054\pi$
$353$	26.6495	1.41841	0.709205	+	0.705003i	$0.249054\pi$
$354$	−0.485225	−0.0257894
$355$	−19.3777	−1.02846
$356$	−19.9007	−1.05473
$357$	0.0691723	0.00366098
$358$	47.8845	2.53077
$359$	−18.1730	−0.959132	−0.479566	−	0.877506i	$-0.659206\pi$
$359$	−18.1730	−0.959132	−0.479566	+	0.877506i	$0.659206\pi$
$360$	0.621357	0.0327484
$361$	34.3181	1.80622
$362$	−14.3088	−0.752056
$363$	0.345130	0.0181146
$364$	6.29267	0.329826
$365$	15.4183	0.807029
$366$	−2.15540	−0.112665
$367$	20.6596	1.07842	0.539211	−	0.842171i	$-0.318723\pi$
$367$	20.6596	1.07842	0.539211	+	0.842171i	$0.318723\pi$
$368$	−18.2709	−0.952439
$369$	11.6479	0.606363
$370$	7.67851	0.399187
$371$	5.47141	0.284062
$372$	−2.90550	−0.150643
$373$	−8.07752	−0.418238	−0.209119	−	0.977890i	$-0.567060\pi$
$373$	−8.07752	−0.418238	−0.209119	+	0.977890i	$0.567060\pi$
$374$	4.51269	0.233346
$375$	−2.15725	−0.111400
$376$	−1.03165	−0.0532035
$377$	26.4970	1.36467
$378$	−1.32946	−0.0683799
$379$	24.0079	1.23320	0.616601	−	0.787276i	$-0.288509\pi$
$379$	24.0079	1.23320	0.616601	+	0.787276i	$0.288509\pi$
$380$	19.5673	1.00378
$381$	−1.04099	−0.0533318
$382$	−1.05436	−0.0539458
$383$	17.7574	0.907362	0.453681	−	0.891164i	$-0.350111\pi$
$383$	17.7574	0.907362	0.453681	+	0.891164i	$0.350111\pi$
$384$	0.261657	0.0133526
$385$	−2.52585	−0.128729
$386$	36.7513	1.87059
$387$	0	0
$388$	−29.4721	−1.49622
$389$	−18.2584	−0.925738	−0.462869	−	0.886427i	$-0.653180\pi$
$389$	−18.2584	−0.925738	−0.462869	+	0.886427i	$0.653180\pi$
$390$	2.87316	0.145488
$391$	−2.98656	−0.151037
$392$	1.09177	0.0551428
$393$	1.98085	0.0999206
$394$	44.2217	2.22786
$395$	−3.73494	−0.187925
$396$	−21.9621	−1.10364
$397$	1.57362	0.0789776	0.0394888	−	0.999220i	$-0.487427\pi$
$397$	1.57362	0.0789776	0.0394888	+	0.999220i	$0.487427\pi$
$398$	22.8401	1.14487
$399$	−0.806348	−0.0403679
$400$	12.8042	0.640210
$401$	19.1723	0.957417	0.478709	−	0.877974i	$-0.341105\pi$
$401$	19.1723	0.957417	0.478709	+	0.877974i	$0.341105\pi$
$402$	−4.71382	−0.235104
$403$	38.2432	1.90503
$404$	−2.53825	−0.126282
$405$	11.1258	0.552847
$406$	−5.35230	−0.265630
$407$	−10.5256	−0.521735
$408$	0.0205042	0.00101511
$409$	20.0489	0.991356	0.495678	−	0.868506i	$-0.334920\pi$
$409$	20.0489	0.991356	0.495678	+	0.868506i	$0.334920\pi$
$410$	10.2389	0.505663
$411$	1.34741	0.0664631
$412$	23.9865	1.18173
$413$	−0.657802	−0.0323683
$414$	28.5060	1.40099
$415$	−6.05149	−0.297056
$416$	−44.3654	−2.17519
$417$	1.51894	0.0743827
$418$	−52.6049	−2.57299
$419$	36.4072	1.77861	0.889303	−	0.457318i	$-0.151190\pi$
$419$	36.4072	1.77861	0.889303	+	0.457318i	$0.151190\pi$
$420$	−0.295922	−0.0144395
$421$	7.95451	0.387679	0.193840	−	0.981033i	$-0.437906\pi$
$421$	7.95451	0.387679	0.193840	+	0.981033i	$0.437906\pi$
$422$	12.7657	0.621424
$423$	−18.7312	−0.910741
$424$	1.62185	0.0787641
$425$	2.09297	0.101524
$426$	6.10335	0.295708
$427$	−2.92200	−0.141405
$428$	−4.00080	−0.193386
$429$	−3.93849	−0.190152
$430$	0	0
$431$	−23.3883	−1.12657	−0.563287	−	0.826262i	$-0.690463\pi$
$431$	−23.3883	−1.12657	−0.563287	+	0.826262i	$0.690463\pi$
$432$	4.58609	0.220648
$433$	−27.4473	−1.31903	−0.659516	−	0.751690i	$-0.729239\pi$
$433$	−27.4473	−1.31903	−0.659516	+	0.751690i	$0.729239\pi$
$434$	−7.72500	−0.370812
$435$	−1.24606	−0.0597440
$436$	−27.2002	−1.30265
$437$	34.8146	1.66541
$438$	−4.85626	−0.232041
$439$	−31.9495	−1.52487	−0.762433	−	0.647068i	$-0.775995\pi$
$439$	−31.9495	−1.52487	−0.762433	+	0.647068i	$0.775995\pi$
$440$	−0.748718	−0.0356937
$441$	19.8227	0.943937
$442$	−6.95887	−0.331000
$443$	−23.2163	−1.10304	−0.551520	−	0.834161i	$-0.685952\pi$
$443$	−23.2163	−1.10304	−0.551520	+	0.834161i	$0.685952\pi$
$444$	−1.23315	−0.0585229
$445$	−12.3181	−0.583934
$446$	7.52794	0.356458
$447$	−4.38454	−0.207382
$448$	4.74694	0.224272
$449$	−6.93380	−0.327226	−0.163613	−	0.986525i	$-0.552315\pi$
$449$	−6.93380	−0.327226	−0.163613	+	0.986525i	$0.552315\pi$
$450$	−19.9768	−0.941717
$451$	−14.0354	−0.660899
$452$	7.02109	0.330244
$453$	0.235965	0.0110866
$454$	42.4448	1.99203
$455$	3.89503	0.182602
$456$	−0.239020	−0.0111931
$457$	5.09847	0.238497	0.119248	−	0.992864i	$-0.461952\pi$
$457$	5.09847	0.238497	0.119248	+	0.992864i	$0.461952\pi$
$458$	25.3238	1.18330
$459$	0.749640	0.0349902
$460$	12.7766	0.595714
$461$	3.21538	0.149755	0.0748775	−	0.997193i	$-0.476143\pi$
$461$	3.21538	0.149755	0.0748775	+	0.997193i	$0.476143\pi$
$462$	0.795561	0.0370128
$463$	40.5745	1.88566	0.942829	−	0.333276i	$-0.108154\pi$
$463$	40.5745	1.88566	0.942829	+	0.333276i	$0.108154\pi$
$464$	18.4633	0.857136
$465$	−1.79844	−0.0834008
$466$	−11.0257	−0.510757
$467$	−35.8995	−1.66123	−0.830616	−	0.556846i	$-0.812011\pi$
$467$	−35.8995	−1.66123	−0.830616	+	0.556846i	$0.812011\pi$
$468$	33.8671	1.56551
$469$	−6.39035	−0.295079
$470$	−16.4654	−0.759492
$471$	−0.517152	−0.0238291
$472$	−0.194987	−0.00897502
$473$	0	0
$474$	1.17639	0.0540332
$475$	−24.3979	−1.11945
$476$	0.716733	0.0328514
$477$	29.4471	1.34829
$478$	8.42025	0.385133
$479$	−25.0204	−1.14321	−0.571606	−	0.820528i	$-0.693679\pi$
$479$	−25.0204	−1.14321	−0.571606	+	0.820528i	$0.693679\pi$
$480$	2.08635	0.0952283
$481$	16.2312	0.740079
$482$	38.9452	1.77391
$483$	−0.526513	−0.0239572
$484$	3.57609	0.162549
$485$	−18.2426	−0.828353
$486$	−10.7569	−0.487942
$487$	21.4793	0.973319	0.486659	−	0.873592i	$-0.338215\pi$
$487$	21.4793	0.973319	0.486659	+	0.873592i	$0.338215\pi$
$488$	−0.866147	−0.0392086
$489$	−1.34316	−0.0607399
$490$	17.4249	0.787175
$491$	10.2408	0.462161	0.231081	−	0.972935i	$-0.425774\pi$
$491$	10.2408	0.462161	0.231081	+	0.972935i	$0.425774\pi$
$492$	−1.64435	−0.0741329
$493$	3.01800	0.135924
$494$	81.1203	3.64977
$495$	−13.5941	−0.611008
$496$	26.6481	1.19653
$497$	8.27408	0.371143
$498$	1.90603	0.0854111
$499$	−30.9246	−1.38437	−0.692187	−	0.721718i	$-0.743353\pi$
$499$	−30.9246	−1.38437	−0.692187	+	0.721718i	$0.743353\pi$
$500$	−22.3525	−0.999634
$501$	2.46646	0.110193
$502$	−3.38063	−0.150885
$503$	9.62808	0.429295	0.214647	−	0.976692i	$-0.431140\pi$
$503$	9.62808	0.429295	0.214647	+	0.976692i	$0.431140\pi$
$504$	−0.265313	−0.0118180
$505$	−1.57112	−0.0699139
$506$	−34.3489	−1.52699
$507$	3.46290	0.153793
$508$	−10.7863	−0.478566
$509$	−2.97449	−0.131842	−0.0659210	−	0.997825i	$-0.520999\pi$
$509$	−2.97449	−0.131842	−0.0659210	+	0.997825i	$0.520999\pi$
$510$	0.327251	0.0144909
$511$	−6.58345	−0.291235
$512$	−32.1634	−1.42144
$513$	−8.73863	−0.385820
$514$	−8.68973	−0.383288
$515$	14.8471	0.654242
$516$	0	0
$517$	22.5706	0.992652
$518$	−3.27865	−0.144055
$519$	−3.43071	−0.150591
$520$	1.15457	0.0506315
$521$	16.0472	0.703042	0.351521	−	0.936180i	$-0.385665\pi$
$521$	16.0472	0.703042	0.351521	+	0.936180i	$0.385665\pi$
$522$	−28.8060	−1.26080
$523$	6.76310	0.295730	0.147865	−	0.989008i	$-0.452760\pi$
$523$	6.76310	0.295730	0.147865	+	0.989008i	$0.452760\pi$
$524$	20.5247	0.896625
$525$	0.368978	0.0161035
$526$	−7.39170	−0.322294
$527$	4.35589	0.189745
$528$	−2.74436	−0.119433
$529$	−0.267413	−0.0116266
$530$	25.8850	1.12437
$531$	−3.54028	−0.153635
$532$	−8.35502	−0.362236
$533$	21.6435	0.937483
$534$	3.87980	0.167896
$535$	−2.47641	−0.107065
$536$	−1.89424	−0.0818189
$537$	−4.76004	−0.205411
$538$	−26.6703	−1.14984
$539$	−23.8858	−1.02883
$540$	−3.20699	−0.138007
$541$	9.37273	0.402965	0.201483	−	0.979492i	$-0.435424\pi$
$541$	9.37273	0.402965	0.201483	+	0.979492i	$0.435424\pi$
$542$	17.5771	0.755003
$543$	1.42240	0.0610408
$544$	−5.05320	−0.216654
$545$	−16.8363	−0.721189
$546$	−1.22681	−0.0525026
$547$	−16.9960	−0.726697	−0.363348	−	0.931653i	$-0.618367\pi$
$547$	−16.9960	−0.726697	−0.363348	+	0.931653i	$0.618367\pi$
$548$	13.9613	0.596398
$549$	−15.7262	−0.671176
$550$	24.0715	1.02641
$551$	−35.1811	−1.49877
$552$	−0.156071	−0.00664280
$553$	1.59478	0.0678170
$554$	−12.9673	−0.550928
$555$	−0.763296	−0.0324001
$556$	15.7386	0.667464
$557$	18.6725	0.791179	0.395590	−	0.918427i	$-0.370540\pi$
$557$	18.6725	0.791179	0.395590	+	0.918427i	$0.370540\pi$
$558$	−41.5758	−1.76004
$559$	0	0
$560$	2.71408	0.114691
$561$	−0.448592	−0.0189396
$562$	30.2447	1.27579
$563$	−0.254085	−0.0107084	−0.00535420	−	0.999986i	$-0.501704\pi$
$563$	−0.254085	−0.0107084	−0.00535420	+	0.999986i	$0.501704\pi$
$564$	2.64431	0.111346
$565$	4.34590	0.182833
$566$	−19.1950	−0.806828
$567$	−4.75062	−0.199507
$568$	2.45262	0.102910
$569$	−2.71166	−0.113679	−0.0568394	−	0.998383i	$-0.518102\pi$
$569$	−2.71166	−0.113679	−0.0568394	+	0.998383i	$0.518102\pi$
$570$	−3.81480	−0.159784
$571$	−0.174166	−0.00728863	−0.00364431	−	0.999993i	$-0.501160\pi$
$571$	−0.174166	−0.00728863	−0.00364431	+	0.999993i	$0.501160\pi$
$572$	−40.8089	−1.70630
$573$	0.104811	0.00437852
$574$	−4.37191	−0.182480
$575$	−15.9309	−0.664364
$576$	25.5480	1.06450
$577$	38.8908	1.61905	0.809523	−	0.587088i	$-0.199726\pi$
$577$	38.8908	1.61905	0.809523	+	0.587088i	$0.199726\pi$
$578$	33.5486	1.39544
$579$	−3.65333	−0.151827
$580$	−12.9111	−0.536105
$581$	2.58393	0.107199
$582$	5.74583	0.238172
$583$	−35.4829	−1.46955
$584$	−1.95148	−0.0807530
$585$	20.9630	0.866712
$586$	26.3283	1.08761
$587$	17.3695	0.716915	0.358457	−	0.933546i	$-0.383303\pi$
$587$	17.3695	0.716915	0.358457	+	0.933546i	$0.383303\pi$
$588$	−2.79840	−0.115404
$589$	−50.7770	−2.09223
$590$	−3.11203	−0.128120
$591$	−4.39594	−0.180825
$592$	11.3100	0.464838
$593$	−10.3765	−0.426110	−0.213055	−	0.977040i	$-0.568341\pi$
$593$	−10.3765	−0.426110	−0.213055	+	0.977040i	$0.568341\pi$
$594$	8.62173	0.353754
$595$	0.443642	0.0181875
$596$	−45.4307	−1.86091
$597$	−2.27046	−0.0929239
$598$	52.9683	2.16604
$599$	6.16827	0.252029	0.126014	−	0.992028i	$-0.459781\pi$
$599$	6.16827	0.252029	0.126014	+	0.992028i	$0.459781\pi$
$600$	0.109373	0.00446515
$601$	46.3073	1.88891	0.944457	−	0.328634i	$-0.106588\pi$
$601$	46.3073	1.88891	0.944457	+	0.328634i	$0.106588\pi$
$602$	0	0
$603$	−34.3928	−1.40058
$604$	2.44497	0.0994844
$605$	2.21352	0.0899924
$606$	0.494852	0.0201020
$607$	2.46505	0.100053	0.0500266	−	0.998748i	$-0.484069\pi$
$607$	2.46505	0.100053	0.0500266	+	0.998748i	$0.484069\pi$
$608$	58.9057	2.38894
$609$	0.532055	0.0215600
$610$	−13.8239	−0.559712
$611$	−34.8054	−1.40807
$612$	3.85744	0.155928
$613$	4.62638	0.186858	0.0934290	−	0.995626i	$-0.470217\pi$
$613$	4.62638	0.186858	0.0934290	+	0.995626i	$0.470217\pi$
$614$	32.3481	1.30546
$615$	−1.01782	−0.0410423
$616$	0.319695	0.0128809
$617$	19.8040	0.797279	0.398639	−	0.917108i	$-0.369483\pi$
$617$	19.8040	0.797279	0.398639	+	0.917108i	$0.369483\pi$
$618$	−4.67637	−0.188111
$619$	−28.2731	−1.13639	−0.568196	−	0.822894i	$-0.692358\pi$
$619$	−28.2731	−1.13639	−0.568196	+	0.822894i	$0.692358\pi$
$620$	−18.6347	−0.748387
$621$	−5.70598	−0.228973
$622$	26.2166	1.05119
$623$	5.25971	0.210726
$624$	4.23199	0.169415
$625$	2.87079	0.114831
$626$	−3.46634	−0.138543
$627$	5.22928	0.208837
$628$	−5.35850	−0.213827
$629$	1.84873	0.0737136
$630$	−4.23445	−0.168704
$631$	42.2655	1.68256	0.841282	−	0.540596i	$-0.181801\pi$
$631$	42.2655	1.68256	0.841282	+	0.540596i	$0.181801\pi$
$632$	0.472730	0.0188042
$633$	−1.26900	−0.0504381
$634$	9.59236	0.380961
$635$	−6.67650	−0.264949
$636$	−4.15709	−0.164839
$637$	36.8335	1.45940
$638$	34.7105	1.37420
$639$	44.5309	1.76162
$640$	1.67816	0.0663351
$641$	18.7180	0.739316	0.369658	−	0.929168i	$-0.379475\pi$
$641$	18.7180	0.739316	0.369658	+	0.929168i	$0.379475\pi$
$642$	0.779990	0.0307837
$643$	30.5819	1.20603	0.603017	−	0.797728i	$-0.293965\pi$
$643$	30.5819	1.20603	0.603017	+	0.797728i	$0.293965\pi$
$644$	−5.45550	−0.214977
$645$	0	0
$646$	9.23956	0.363526
$647$	−21.5301	−0.846436	−0.423218	−	0.906028i	$-0.639100\pi$
$647$	−21.5301	−0.846436	−0.423218	+	0.906028i	$0.639100\pi$
$648$	−1.40819	−0.0553190
$649$	4.26594	0.167453
$650$	−37.1200	−1.45596
$651$	0.767917	0.0300971
$652$	−13.9173	−0.545042
$653$	4.91398	0.192299	0.0961494	−	0.995367i	$-0.469347\pi$
$653$	4.91398	0.192299	0.0961494	+	0.995367i	$0.469347\pi$
$654$	5.30290	0.207360
$655$	12.7043	0.496400
$656$	15.0813	0.588826
$657$	−35.4320	−1.38233
$658$	7.03056	0.274080
$659$	−15.5219	−0.604647	−0.302323	−	0.953205i	$-0.597762\pi$
$659$	−15.5219	−0.604647	−0.302323	+	0.953205i	$0.597762\pi$
$660$	1.91910	0.0747007
$661$	2.87875	0.111970	0.0559851	−	0.998432i	$-0.482170\pi$
$661$	2.87875	0.111970	0.0559851	+	0.998432i	$0.482170\pi$
$662$	−56.9191	−2.21222
$663$	0.691759	0.0268657
$664$	0.765935	0.0297241
$665$	−5.17158	−0.200545
$666$	−17.6456	−0.683754
$667$	−22.9719	−0.889474
$668$	25.5564	0.988807
$669$	−0.748328	−0.0289320
$670$	−30.2325	−1.16798
$671$	18.9496	0.731541
$672$	−0.890850	−0.0343653
$673$	28.2287	1.08814	0.544068	−	0.839041i	$-0.316883\pi$
$673$	28.2287	1.08814	0.544068	+	0.839041i	$0.316883\pi$
$674$	−20.1625	−0.776632
$675$	3.99872	0.153911
$676$	35.8810	1.38004
$677$	−27.8532	−1.07049	−0.535243	−	0.844698i	$-0.679780\pi$
$677$	−27.8532	−1.07049	−0.535243	+	0.844698i	$0.679780\pi$
$678$	−1.36882	−0.0525692
$679$	7.78940	0.298930
$680$	0.131506	0.00504301
$681$	−4.21930	−0.161684
$682$	50.0977	1.91834
$683$	−7.48209	−0.286294	−0.143147	−	0.989701i	$-0.545722\pi$
$683$	−7.48209	−0.286294	−0.143147	+	0.989701i	$0.545722\pi$
$684$	−44.9666	−1.71934
$685$	8.64176	0.330185
$686$	−15.2164	−0.580966
$687$	−2.51736	−0.0960433
$688$	0	0
$689$	54.7171	2.08455
$690$	−2.49091	−0.0948274
$691$	19.9615	0.759372	0.379686	−	0.925115i	$-0.376032\pi$
$691$	19.9615	0.759372	0.379686	+	0.925115i	$0.376032\pi$
$692$	−35.5475	−1.35131
$693$	5.80453	0.220496
$694$	−54.9816	−2.08707
$695$	9.74183	0.369529
$696$	0.157713	0.00597811
$697$	2.46518	0.0933754
$698$	−46.8794	−1.77441
$699$	1.09603	0.0414558
$700$	3.82319	0.144503
$701$	30.8816	1.16638	0.583190	−	0.812336i	$-0.301804\pi$
$701$	30.8816	1.16638	0.583190	+	0.812336i	$0.301804\pi$
$702$	−13.2953	−0.501798
$703$	−21.5508	−0.812804
$704$	−30.7846	−1.16024
$705$	1.63677	0.0616444
$706$	−53.8339	−2.02607
$707$	0.670852	0.0252300
$708$	0.499787	0.0187831
$709$	−34.9629	−1.31306	−0.656530	−	0.754300i	$-0.727977\pi$
$709$	−34.9629	−1.31306	−0.656530	+	0.754300i	$0.727977\pi$
$710$	39.1443	1.46906
$711$	8.58309	0.321891
$712$	1.55910	0.0584296
$713$	−33.1554	−1.24168
$714$	−0.139733	−0.00522938
$715$	−25.2598	−0.944664
$716$	−49.3215	−1.84323
$717$	−0.837031	−0.0312595
$718$	36.7107	1.37003
$719$	−7.40695	−0.276233	−0.138116	−	0.990416i	$-0.544105\pi$
$719$	−7.40695	−0.276233	−0.138116	+	0.990416i	$0.544105\pi$
$720$	14.6071	0.544375
$721$	−6.33957	−0.236098
$722$	−69.3251	−2.58001
$723$	−3.87142	−0.143980
$724$	14.7382	0.547742
$725$	16.0986	0.597886
$726$	−0.697188	−0.0258751
$727$	−28.1082	−1.04247	−0.521237	−	0.853412i	$-0.674529\pi$
$727$	−28.1082	−1.04247	−0.521237	+	0.853412i	$0.674529\pi$
$728$	−0.492992	−0.0182715
$729$	−24.8468	−0.920252
$730$	−31.1460	−1.15277
$731$	0	0
$732$	2.22009	0.0820568
$733$	27.9573	1.03263	0.516313	−	0.856400i	$-0.327304\pi$
$733$	27.9573	1.03263	0.516313	+	0.856400i	$0.327304\pi$
$734$	−41.7339	−1.54043
$735$	−1.73215	−0.0638913
$736$	38.4631	1.41777
$737$	41.4423	1.52655
$738$	−23.5295	−0.866134
$739$	−41.7793	−1.53688	−0.768439	−	0.639923i	$-0.778966\pi$
$739$	−41.7793	−1.53688	−0.768439	+	0.639923i	$0.778966\pi$
$740$	−7.90894	−0.290738
$741$	−8.06391	−0.296235
$742$	−11.0527	−0.405756
$743$	47.3420	1.73681	0.868405	−	0.495855i	$-0.165145\pi$
$743$	47.3420	1.73681	0.868405	+	0.495855i	$0.165145\pi$
$744$	0.227628	0.00834525
$745$	−28.1206	−1.03026
$746$	16.3172	0.597415
$747$	13.9067	0.508818
$748$	−4.64811	−0.169952
$749$	1.05740	0.0386367
$750$	4.35781	0.159125
$751$	2.32905	0.0849881	0.0424941	−	0.999097i	$-0.486470\pi$
$751$	2.32905	0.0849881	0.0424941	+	0.999097i	$0.486470\pi$
$752$	−24.2526	−0.884400
$753$	0.336057	0.0122466
$754$	−53.5259	−1.94930
$755$	1.51338	0.0550777
$756$	1.36935	0.0498030
$757$	8.75617	0.318248	0.159124	−	0.987259i	$-0.449133\pi$
$757$	8.75617	0.318248	0.159124	+	0.987259i	$0.449133\pi$
$758$	−48.4976	−1.76151
$759$	3.41451	0.123939
$760$	−1.53297	−0.0556068
$761$	−26.2597	−0.951914	−0.475957	−	0.879469i	$-0.657898\pi$
$761$	−26.2597	−0.951914	−0.475957	+	0.879469i	$0.657898\pi$
$762$	2.10288	0.0761795
$763$	7.18894	0.260257
$764$	1.08600	0.0392901
$765$	2.38767	0.0863265
$766$	−35.8713	−1.29608
$767$	−6.57837	−0.237531
$768$	2.93820	0.106023
$769$	−19.5899	−0.706432	−0.353216	−	0.935542i	$-0.614912\pi$
$769$	−19.5899	−0.706432	−0.353216	+	0.935542i	$0.614912\pi$
$770$	5.10240	0.183878
$771$	0.863819	0.0311097
$772$	−37.8542	−1.36240
$773$	−18.2397	−0.656036	−0.328018	−	0.944671i	$-0.606381\pi$
$773$	−18.2397	−0.656036	−0.328018	+	0.944671i	$0.606381\pi$
$774$	0	0
$775$	23.2351	0.834630
$776$	2.30896	0.0828867
$777$	0.325920	0.0116923
$778$	36.8833	1.32233
$779$	−28.7369	−1.02961
$780$	−2.95938	−0.105963
$781$	−53.6586	−1.92005
$782$	6.03307	0.215742
$783$	5.76604	0.206061
$784$	25.6658	0.916636
$785$	−3.31680	−0.118382
$786$	−4.00146	−0.142727
$787$	23.5647	0.839989	0.419995	−	0.907527i	$-0.362032\pi$
$787$	23.5647	0.839989	0.419995	+	0.907527i	$0.362032\pi$
$788$	−45.5488	−1.62261
$789$	0.734785	0.0261591
$790$	7.54485	0.268434
$791$	−1.85566	−0.0659796
$792$	1.72060	0.0611387
$793$	−29.2216	−1.03769
$794$	−3.17882	−0.112812
$795$	−2.57315	−0.0912602
$796$	−23.5256	−0.833841
$797$	−33.0266	−1.16986	−0.584931	−	0.811083i	$-0.698878\pi$
$797$	−33.0266	−1.16986	−0.584931	+	0.811083i	$0.698878\pi$
$798$	1.62888	0.0576618
$799$	−3.96431	−0.140247
$800$	−26.9547	−0.952994
$801$	28.3076	1.00020
$802$	−38.7294	−1.36758
$803$	42.6946	1.50666
$804$	4.85528	0.171233
$805$	−3.37684	−0.119018
$806$	−77.2541	−2.72116
$807$	2.65121	0.0933271
$808$	0.198856	0.00699573
$809$	7.82261	0.275028	0.137514	−	0.990500i	$-0.456089\pi$
$809$	7.82261	0.275028	0.137514	+	0.990500i	$0.456089\pi$
$810$	−22.4750	−0.789691
$811$	−1.48937	−0.0522990	−0.0261495	−	0.999658i	$-0.508325\pi$
$811$	−1.48937	−0.0522990	−0.0261495	+	0.999658i	$0.508325\pi$
$812$	5.51293	0.193466
$813$	−1.74729	−0.0612801
$814$	21.2625	0.745250
$815$	−8.61448	−0.301752
$816$	0.482022	0.0168741
$817$	0	0
$818$	−40.5003	−1.41606
$819$	−8.95099	−0.312773
$820$	−10.5462	−0.368288
$821$	−22.3680	−0.780649	−0.390324	−	0.920677i	$-0.627637\pi$
$821$	−22.3680	−0.780649	−0.390324	+	0.920677i	$0.627637\pi$
$822$	−2.72188	−0.0949363
$823$	39.6776	1.38308	0.691538	−	0.722340i	$-0.256934\pi$
$823$	39.6776	1.38308	0.691538	+	0.722340i	$0.256934\pi$
$824$	−1.87919	−0.0654648
$825$	−2.39288	−0.0833092
$826$	1.32881	0.0462351
$827$	51.2404	1.78180	0.890901	−	0.454198i	$-0.150074\pi$
$827$	51.2404	1.78180	0.890901	+	0.454198i	$0.150074\pi$
$828$	−29.3614	−1.02038
$829$	−3.09946	−0.107649	−0.0538244	−	0.998550i	$-0.517141\pi$
$829$	−3.09946	−0.107649	−0.0538244	+	0.998550i	$0.517141\pi$
$830$	12.2245	0.424317
$831$	1.28904	0.0447163
$832$	47.4719	1.64579
$833$	4.19532	0.145359
$834$	−3.06836	−0.106249
$835$	15.8189	0.547434
$836$	54.1835	1.87398
$837$	8.32215	0.287655
$838$	−73.5451	−2.54057
$839$	49.1146	1.69562	0.847811	−	0.530298i	$-0.177920\pi$
$839$	49.1146	1.69562	0.847811	+	0.530298i	$0.177920\pi$
$840$	0.0231837	0.000799913 0
$841$	−5.78633	−0.199529
$842$	−16.0687	−0.553764
$843$	−3.00653	−0.103550
$844$	−13.1488	−0.452600
$845$	22.2096	0.764033
$846$	37.8384	1.30091
$847$	−0.945152	−0.0324758
$848$	38.1272	1.30929
$849$	1.90812	0.0654864
$850$	−4.22795	−0.145017
$851$	−14.0718	−0.482376
$852$	−6.28651	−0.215372
$853$	−39.5129	−1.35290	−0.676448	−	0.736491i	$-0.736481\pi$
$853$	−39.5129	−1.35290	−0.676448	+	0.736491i	$0.736481\pi$
$854$	5.90265	0.201985
$855$	−27.8334	−0.951881
$856$	0.313438	0.0107131
$857$	−29.0474	−0.992239	−0.496119	−	0.868254i	$-0.665242\pi$
$857$	−29.0474	−0.992239	−0.496119	+	0.868254i	$0.665242\pi$
$858$	7.95603	0.271614
$859$	−11.6957	−0.399053	−0.199526	−	0.979892i	$-0.563940\pi$
$859$	−11.6957	−0.399053	−0.199526	+	0.979892i	$0.563940\pi$
$860$	0	0
$861$	0.434597	0.0148110
$862$	47.2460	1.60921
$863$	46.2967	1.57596	0.787979	−	0.615703i	$-0.211128\pi$
$863$	46.2967	1.57596	0.787979	+	0.615703i	$0.211128\pi$
$864$	−9.65440	−0.328449
$865$	−22.0031	−0.748129
$866$	55.4455	1.88412
$867$	−3.33496	−0.113261
$868$	7.95682	0.270072
$869$	−10.3424	−0.350841
$870$	2.51713	0.0853388
$871$	−63.9069	−2.16540
$872$	2.13097	0.0721636
$873$	41.9224	1.41886
$874$	−70.3281	−2.37888
$875$	5.90771	0.199717
$876$	5.00199	0.169002
$877$	12.3365	0.416573	0.208287	−	0.978068i	$-0.433211\pi$
$877$	12.3365	0.416573	0.208287	+	0.978068i	$0.433211\pi$
$878$	64.5403	2.17813
$879$	−2.61721	−0.0882763
$880$	−17.6012	−0.593336
$881$	27.4405	0.924494	0.462247	−	0.886751i	$-0.347043\pi$
$881$	27.4405	0.924494	0.462247	+	0.886751i	$0.347043\pi$
$882$	−40.0433	−1.34833
$883$	6.81153	0.229226	0.114613	−	0.993410i	$-0.463437\pi$
$883$	6.81153	0.229226	0.114613	+	0.993410i	$0.463437\pi$
$884$	7.16771	0.241076
$885$	0.309357	0.0103989
$886$	46.8987	1.57559
$887$	−9.36281	−0.314373	−0.157186	−	0.987569i	$-0.550242\pi$
$887$	−9.36281	−0.314373	−0.157186	+	0.987569i	$0.550242\pi$
$888$	0.0966101	0.00324202
$889$	2.85080	0.0956128
$890$	24.8834	0.834095
$891$	30.8085	1.03212
$892$	−7.75385	−0.259618
$893$	46.2124	1.54644
$894$	8.85709	0.296225
$895$	−30.5289	−1.02047
$896$	−0.716558	−0.0239385
$897$	−5.26541	−0.175807
$898$	14.0068	0.467412
$899$	33.5044	1.11743
$900$	20.5763	0.685878
$901$	6.23225	0.207626
$902$	28.3524	0.944033
$903$	0	0
$904$	−0.550059	−0.0182947
$905$	9.12265	0.303247
$906$	−0.476667	−0.0158362
$907$	−27.5571	−0.915017	−0.457509	−	0.889205i	$-0.651258\pi$
$907$	−27.5571	−0.915017	−0.457509	+	0.889205i	$0.651258\pi$
$908$	−43.7186	−1.45085
$909$	3.61052	0.119753
$910$	−7.86824	−0.260830
$911$	−8.68659	−0.287800	−0.143900	−	0.989592i	$-0.545964\pi$
$911$	−8.68659	−0.287800	−0.143900	+	0.989592i	$0.545964\pi$
$912$	−5.61898	−0.186063
$913$	−16.7571	−0.554581
$914$	−10.2993	−0.340670
$915$	1.37419	0.0454292
$916$	−26.0838	−0.861832
$917$	−5.42463	−0.179137
$918$	−1.51433	−0.0499803
$919$	5.22712	0.172427	0.0862134	−	0.996277i	$-0.472523\pi$
$919$	5.22712	0.172427	0.0862134	+	0.996277i	$0.472523\pi$
$920$	−1.00097	−0.0330010
$921$	−3.21562	−0.105958
$922$	−6.49530	−0.213911
$923$	82.7452	2.72359
$924$	−0.819435	−0.0269574
$925$	9.86146	0.324243
$926$	−81.9635	−2.69349
$927$	−34.1195	−1.12063
$928$	−38.8679	−1.27590
$929$	−29.9481	−0.982565	−0.491282	−	0.871000i	$-0.663472\pi$
$929$	−29.9481	−0.982565	−0.491282	+	0.871000i	$0.663472\pi$
$930$	3.63299	0.119130
$931$	−48.9053	−1.60281
$932$	11.3566	0.371998
$933$	−2.60611	−0.0853203
$934$	72.5196	2.37291
$935$	−2.87708	−0.0940906
$936$	−2.65328	−0.0867250
$937$	−15.4887	−0.505995	−0.252998	−	0.967467i	$-0.581416\pi$
$937$	−15.4887	−0.505995	−0.252998	+	0.967467i	$0.581416\pi$
$938$	12.9090	0.421493
$939$	0.344578	0.0112449
$940$	16.9595	0.553158
$941$	−17.0977	−0.557370	−0.278685	−	0.960383i	$-0.589899\pi$
$941$	−17.0977	−0.557370	−0.278685	+	0.960383i	$0.589899\pi$
$942$	1.04468	0.0340377
$943$	−18.7640	−0.611041
$944$	−4.58384	−0.149191
$945$	0.847601	0.0275725
$946$	0	0
$947$	40.9855	1.33185	0.665924	−	0.746019i	$-0.268037\pi$
$947$	40.9855	1.33185	0.665924	+	0.746019i	$0.268037\pi$
$948$	−1.21169	−0.0393538
$949$	−65.8380	−2.13719
$950$	49.2856	1.59904
$951$	−0.953546	−0.0309208
$952$	−0.0561516	−0.00181988
$953$	−15.6529	−0.507047	−0.253524	−	0.967329i	$-0.581590\pi$
$953$	−15.6529	−0.507047	−0.253524	+	0.967329i	$0.581590\pi$
$954$	−59.4852	−1.92590
$955$	0.672211	0.0217522
$956$	−8.67294	−0.280503
$957$	−3.45046	−0.111537
$958$	50.5431	1.63297
$959$	−3.68994	−0.119155
$960$	−2.23244	−0.0720516
$961$	17.3570	0.559902
$962$	−32.7882	−1.05713
$963$	5.69092	0.183387
$964$	−40.1140	−1.29198
$965$	−23.4309	−0.754268
$966$	1.06360	0.0342206
$967$	23.9490	0.770148	0.385074	−	0.922886i	$-0.374176\pi$
$967$	23.9490	0.770148	0.385074	+	0.922886i	$0.374176\pi$
$968$	−0.280164	−0.00900483
$969$	−0.918476	−0.0295057
$970$	36.8513	1.18323
$971$	50.1850	1.61051	0.805257	−	0.592926i	$-0.202028\pi$
$971$	50.1850	1.61051	0.805257	+	0.592926i	$0.202028\pi$
$972$	11.0797	0.355382
$973$	−4.15967	−0.133353
$974$	−43.3897	−1.39030
$975$	3.68998	0.118174
$976$	−20.3617	−0.651764
$977$	54.8891	1.75606	0.878029	−	0.478607i	$-0.158858\pi$
$977$	54.8891	1.75606	0.878029	+	0.478607i	$0.158858\pi$
$978$	2.71329	0.0867613
$979$	−34.1099	−1.09016
$980$	−17.9478	−0.573321
$981$	38.6908	1.23530
$982$	−20.6872	−0.660155
$983$	−39.0349	−1.24502	−0.622510	−	0.782612i	$-0.713887\pi$
$983$	−39.0349	−1.24502	−0.622510	+	0.782612i	$0.713887\pi$
$984$	0.128824	0.00410677
$985$	−28.1937	−0.898327
$986$	−6.09658	−0.194155
$987$	−0.698886	−0.0222458
$988$	−83.5547	−2.65823
$989$	0	0
$990$	27.4610	0.872768
$991$	11.0281	0.350318	0.175159	−	0.984540i	$-0.443956\pi$
$991$	11.0281	0.350318	0.175159	+	0.984540i	$0.443956\pi$
$992$	−56.0982	−1.78112
$993$	5.65815	0.179556
$994$	−16.7142	−0.530143
$995$	−14.5618	−0.461641
$996$	−1.96323	−0.0622072
$997$	−28.7779	−0.911404	−0.455702	−	0.890132i	$-0.650612\pi$
$997$	−28.7779	−0.911404	−0.455702	+	0.890132i	$0.650612\pi$
$998$	62.4699	1.97745
$999$	3.53209	0.111750

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.2.a.q.1.3	✓	20
43.42	odd	2	inner	1849.2.a.q.1.18	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.2.a.q.1.3	✓	20	1.1	even	1	trivial
1849.2.a.q.1.18	yes	20	43.42	odd	2	inner

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:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q-2.02007 q^{2} +0.200809 q^{3} +2.08069 q^{4} +1.28791 q^{5} -0.405649 q^{6} -0.549923 q^{7} -0.163010 q^{8} -2.95968 q^{9} +O(q^{10})\)	\(q-2.02007 q^{2} +0.200809 q^{3} +2.08069 q^{4} +1.28791 q^{5} -0.405649 q^{6} -0.549923 q^{7} -0.163010 q^{8} -2.95968 q^{9} -2.60166 q^{10} +3.56633 q^{11} +0.417822 q^{12} -5.49952 q^{13} +1.11088 q^{14} +0.258623 q^{15} -3.83210 q^{16} -0.626393 q^{17} +5.97876 q^{18} +7.30193 q^{19} +2.67974 q^{20} -0.110429 q^{21} -7.20424 q^{22} +4.76787 q^{23} -0.0327338 q^{24} -3.34130 q^{25} +11.1094 q^{26} -1.19676 q^{27} -1.14422 q^{28} -4.81806 q^{29} -0.522437 q^{30} -6.95392 q^{31} +8.06714 q^{32} +0.716151 q^{33} +1.26536 q^{34} -0.708249 q^{35} -6.15818 q^{36} -2.95138 q^{37} -14.7504 q^{38} -1.10435 q^{39} -0.209941 q^{40} -3.93552 q^{41} +0.223076 q^{42} +7.42044 q^{44} -3.81178 q^{45} -9.63145 q^{46} +6.32880 q^{47} -0.769520 q^{48} -6.69758 q^{49} +6.74967 q^{50} -0.125785 q^{51} -11.4428 q^{52} -9.94942 q^{53} +2.41754 q^{54} +4.59309 q^{55} +0.0896427 q^{56} +1.46629 q^{57} +9.73283 q^{58} +1.19617 q^{59} +0.538116 q^{60} +5.31347 q^{61} +14.0474 q^{62} +1.62759 q^{63} -8.63201 q^{64} -7.08286 q^{65} -1.44668 q^{66} +11.6204 q^{67} -1.30333 q^{68} +0.957431 q^{69} +1.43071 q^{70} -15.0459 q^{71} +0.482456 q^{72} +11.9716 q^{73} +5.96201 q^{74} -0.670963 q^{75} +15.1931 q^{76} -1.96121 q^{77} +2.23087 q^{78} -2.90001 q^{79} -4.93538 q^{80} +8.63871 q^{81} +7.95004 q^{82} -4.69871 q^{83} -0.229770 q^{84} -0.806735 q^{85} -0.967509 q^{87} -0.581346 q^{88} -9.56444 q^{89} +7.70008 q^{90} +3.02431 q^{91} +9.92048 q^{92} -1.39641 q^{93} -12.7846 q^{94} +9.40419 q^{95} +1.61995 q^{96} -14.1645 q^{97} +13.5296 q^{98} -10.5552 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 14 q^{4} - 32 q^{6} - 6 q^{9}+O(q^{10}) \) 20 * q + 14 * q^4 - 32 * q^6 - 6 * q^9	\( 20 q + 14 q^{4} - 32 q^{6} - 6 q^{9} + 12 q^{10} - 20 q^{11} + 6 q^{13} - 34 q^{14} - 34 q^{15} + 14 q^{16} - 8 q^{17} + 12 q^{21} - 46 q^{23} + 2 q^{24} + 20 q^{25} - 38 q^{31} - 76 q^{35} - 46 q^{36} - 68 q^{38} - 64 q^{40} - 56 q^{41} - 58 q^{44} - 24 q^{47} - 20 q^{49} - 20 q^{52} - 42 q^{53} + 66 q^{54} - 46 q^{56} + 2 q^{57} + 12 q^{58} - 90 q^{59} + 18 q^{60} - 28 q^{64} + 76 q^{66} - 62 q^{67} - 54 q^{68} + 24 q^{74} - 36 q^{78} - 10 q^{79} - 48 q^{81} - 68 q^{83} + 70 q^{84} - 12 q^{87} + 58 q^{90} - 8 q^{92} - 42 q^{95} - 22 q^{96} - 44 q^{97} - 38 q^{99}+O(q^{100}) \) 20 * q + 14 * q^4 - 32 * q^6 - 6 * q^9 + 12 * q^10 - 20 * q^11 + 6 * q^13 - 34 * q^14 - 34 * q^15 + 14 * q^16 - 8 * q^17 + 12 * q^21 - 46 * q^23 + 2 * q^24 + 20 * q^25 - 38 * q^31 - 76 * q^35 - 46 * q^36 - 68 * q^38 - 64 * q^40 - 56 * q^41 - 58 * q^44 - 24 * q^47 - 20 * q^49 - 20 * q^52 - 42 * q^53 + 66 * q^54 - 46 * q^56 + 2 * q^57 + 12 * q^58 - 90 * q^59 + 18 * q^60 - 28 * q^64 + 76 * q^66 - 62 * q^67 - 54 * q^68 + 24 * q^74 - 36 * q^78 - 10 * q^79 - 48 * q^81 - 68 * q^83 + 70 * q^84 - 12 * q^87 + 58 * q^90 - 8 * q^92 - 42 * q^95 - 22 * q^96 - 44 * q^97 - 38 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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