LMFDB - Embedded newform 2523.2.a.s.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2523,2,Mod(1,2523)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2523, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2523.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2523 = 3 \cdot 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2523.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:	$20.1462564300$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 2 x^{10} + 38 x^{9} - 30 x^{8} - 90 x^{7} + 55 x^{6} + 90 x^{5} - 30 x^{4} + \cdots + 1 $ x^12 - 6x^11 + 2x^10 + 38x^9 - 30x^8 - 90x^7 + 55x^6 + 90x^5 - 30x^4 - 38x^3 + 2x^2 + 6*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 87)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$2.30214$ of defining polynomial
Character	$\chi$	$=$	2523.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.30214 q^{2} +1.00000 q^{3} -0.304418 q^{4} -0.326108 q^{5} +1.30214 q^{6} -1.10350 q^{7} -3.00069 q^{8} +1.00000 q^{9} -0.424639 q^{10} -0.768140 q^{11} -0.304418 q^{12} +4.81068 q^{13} -1.43692 q^{14} -0.326108 q^{15} -3.29849 q^{16} -5.18289 q^{17} +1.30214 q^{18} -4.18544 q^{19} +0.0992732 q^{20} -1.10350 q^{21} -1.00023 q^{22} -1.41325 q^{23} -3.00069 q^{24} -4.89365 q^{25} +6.26421 q^{26} +1.00000 q^{27} +0.335926 q^{28} -0.424639 q^{30} -4.51575 q^{31} +1.70626 q^{32} -0.768140 q^{33} -6.74888 q^{34} +0.359860 q^{35} -0.304418 q^{36} +1.79176 q^{37} -5.45006 q^{38} +4.81068 q^{39} +0.978547 q^{40} +1.34344 q^{41} -1.43692 q^{42} -7.20917 q^{43} +0.233836 q^{44} -0.326108 q^{45} -1.84026 q^{46} -0.453383 q^{47} -3.29849 q^{48} -5.78229 q^{49} -6.37225 q^{50} -5.18289 q^{51} -1.46446 q^{52} -8.82860 q^{53} +1.30214 q^{54} +0.250496 q^{55} +3.31126 q^{56} -4.18544 q^{57} +3.67450 q^{59} +0.0992732 q^{60} +8.84461 q^{61} -5.88016 q^{62} -1.10350 q^{63} +8.81878 q^{64} -1.56880 q^{65} -1.00023 q^{66} -15.2617 q^{67} +1.57777 q^{68} -1.41325 q^{69} +0.468590 q^{70} +15.0399 q^{71} -3.00069 q^{72} -13.7014 q^{73} +2.33313 q^{74} -4.89365 q^{75} +1.27413 q^{76} +0.847644 q^{77} +6.26421 q^{78} +5.83635 q^{79} +1.07566 q^{80} +1.00000 q^{81} +1.74936 q^{82} +12.7270 q^{83} +0.335926 q^{84} +1.69018 q^{85} -9.38739 q^{86} +2.30495 q^{88} -8.28742 q^{89} -0.424639 q^{90} -5.30860 q^{91} +0.430221 q^{92} -4.51575 q^{93} -0.590370 q^{94} +1.36491 q^{95} +1.70626 q^{96} -1.54591 q^{97} -7.52937 q^{98} -0.768140 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} + 12 q^{3} + 8 q^{4} + 2 q^{5} - 6 q^{6} - 10 q^{7} + 12 q^{9} - 20 q^{10} - 14 q^{11} + 8 q^{12} - 16 q^{13} + 2 q^{15} - 4 q^{16} - 22 q^{17} - 6 q^{18} - 16 q^{19} + 4 q^{20} - 10 q^{21}+ \cdots - 14 q^{99}+O(q^{100}) $ 12 * q - 6 * q^2 + 12 * q^3 + 8 * q^4 + 2 * q^5 - 6 * q^6 - 10 * q^7 + 12 * q^9 - 20 * q^10 - 14 * q^11 + 8 * q^12 - 16 * q^13 + 2 * q^15 - 4 * q^16 - 22 * q^17 - 6 * q^18 - 16 * q^19 + 4 * q^20 - 10 * q^21 + 12 * q^22 + 2 * q^23 - 2 * q^25 + 8 * q^26 + 12 * q^27 - 4 * q^28 - 20 * q^30 - 4 * q^31 - 16 * q^32 - 14 * q^33 - 10 * q^34 - 14 * q^35 + 8 * q^36 - 28 * q^37 + 16 * q^38 - 16 * q^39 - 32 * q^40 + 14 * q^41 - 36 * q^43 - 26 * q^44 + 2 * q^45 - 24 * q^46 - 44 * q^47 - 4 * q^48 - 18 * q^49 - 24 * q^50 - 22 * q^51 - 20 * q^52 - 18 * q^53 - 6 * q^54 - 4 * q^55 + 10 * q^56 - 16 * q^57 + 14 * q^59 + 4 * q^60 - 24 * q^61 + 4 * q^62 - 10 * q^63 - 18 * q^64 + 2 * q^65 + 12 * q^66 - 18 * q^67 - 52 * q^68 + 2 * q^69 + 36 * q^70 + 14 * q^71 - 44 * q^73 + 12 * q^74 - 2 * q^75 - 56 * q^76 - 32 * q^77 + 8 * q^78 - 24 * q^79 + 52 * q^80 + 12 * q^81 + 52 * q^82 + 26 * q^83 - 4 * q^84 - 48 * q^85 + 64 * q^86 - 10 * q^88 - 10 * q^89 - 20 * q^90 - 10 * q^91 + 64 * q^92 - 4 * q^93 - 8 * q^94 + 4 * q^95 - 16 * q^96 - 28 * q^97 - 6 * q^98 - 14 * q^99

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 $

$2$	1.30214	0.920756	0.460378	−	0.887723i	$-0.347714\pi$
$2$	1.30214	0.920756	0.460378	+	0.887723i	$0.347714\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.304418	−0.152209
$5$	−0.326108	−0.145840	−0.0729199	−	0.997338i	$-0.523232\pi$
$5$	−0.326108	−0.145840	−0.0729199	+	0.997338i	$0.523232\pi$
$6$	1.30214	0.531598
$7$	−1.10350	−0.417084	−0.208542	−	0.978013i	$-0.566872\pi$
$7$	−1.10350	−0.417084	−0.208542	+	0.978013i	$0.566872\pi$
$8$	−3.00069	−1.06090
$9$	1.00000	0.333333
$10$	−0.424639	−0.134283
$11$	−0.768140	−0.231603	−0.115802	−	0.993272i	$-0.536944\pi$
$11$	−0.768140	−0.231603	−0.115802	+	0.993272i	$0.536944\pi$
$12$	−0.304418	−0.0878780
$13$	4.81068	1.33424	0.667122	−	0.744949i	$-0.267526\pi$
$13$	4.81068	1.33424	0.667122	+	0.744949i	$0.267526\pi$
$14$	−1.43692	−0.384033
$15$	−0.326108	−0.0842006
$16$	−3.29849	−0.824623
$17$	−5.18289	−1.25704	−0.628518	−	0.777795i	$-0.716338\pi$
$17$	−5.18289	−1.25704	−0.628518	+	0.777795i	$0.716338\pi$
$18$	1.30214	0.306919
$19$	−4.18544	−0.960207	−0.480103	−	0.877212i	$-0.659401\pi$
$19$	−4.18544	−0.960207	−0.480103	+	0.877212i	$0.659401\pi$
$20$	0.0992732	0.0221982
$21$	−1.10350	−0.240804
$22$	−1.00023	−0.213250
$23$	−1.41325	−0.294684	−0.147342	−	0.989086i	$-0.547072\pi$
$23$	−1.41325	−0.294684	−0.147342	+	0.989086i	$0.547072\pi$
$24$	−3.00069	−0.612513
$25$	−4.89365	−0.978731
$26$	6.26421	1.22851
$27$	1.00000	0.192450
$28$	0.335926	0.0634841
$29$	0	0
$29$	0	0
$30$	−0.424639	−0.0775282
$31$	−4.51575	−0.811053	−0.405526	−	0.914083i	$-0.632912\pi$
$31$	−4.51575	−0.811053	−0.405526	+	0.914083i	$0.632912\pi$
$32$	1.70626	0.301627
$33$	−0.768140	−0.133716
$34$	−6.74888	−1.15742
$35$	0.359860	0.0608275
$36$	−0.304418	−0.0507364
$37$	1.79176	0.294564	0.147282	−	0.989095i	$-0.452948\pi$
$37$	1.79176	0.294564	0.147282	+	0.989095i	$0.452948\pi$
$38$	−5.45006	−0.884116
$39$	4.81068	0.770326
$40$	0.978547	0.154722
$41$	1.34344	0.209811	0.104905	−	0.994482i	$-0.466546\pi$
$41$	1.34344	0.209811	0.104905	+	0.994482i	$0.466546\pi$
$42$	−1.43692	−0.221721
$43$	−7.20917	−1.09939	−0.549694	−	0.835366i	$-0.685256\pi$
$43$	−7.20917	−1.09939	−0.549694	+	0.835366i	$0.685256\pi$
$44$	0.233836	0.0352521
$45$	−0.326108	−0.0486132
$46$	−1.84026	−0.271332
$47$	−0.453383	−0.0661327	−0.0330663	−	0.999453i	$-0.510527\pi$
$47$	−0.453383	−0.0661327	−0.0330663	+	0.999453i	$0.510527\pi$
$48$	−3.29849	−0.476096
$49$	−5.78229	−0.826041
$50$	−6.37225	−0.901172
$51$	−5.18289	−0.725750
$52$	−1.46446	−0.203084
$53$	−8.82860	−1.21270	−0.606351	−	0.795197i	$-0.707367\pi$
$53$	−8.82860	−1.21270	−0.606351	+	0.795197i	$0.707367\pi$
$54$	1.30214	0.177199
$55$	0.250496	0.0337769
$56$	3.31126	0.442486
$57$	−4.18544	−0.554376
$58$	0	0
$59$	3.67450	0.478379	0.239190	−	0.970973i	$-0.423118\pi$
$59$	3.67450	0.478379	0.239190	+	0.970973i	$0.423118\pi$
$60$	0.0992732	0.0128161
$61$	8.84461	1.13244	0.566218	−	0.824255i	$-0.308406\pi$
$61$	8.84461	1.13244	0.566218	+	0.824255i	$0.308406\pi$
$62$	−5.88016	−0.746781
$63$	−1.10350	−0.139028
$64$	8.81878	1.10235
$65$	−1.56880	−0.194586
$66$	−1.00023	−0.123120
$67$	−15.2617	−1.86451	−0.932255	−	0.361802i	$-0.882162\pi$
$67$	−15.2617	−1.86451	−0.932255	+	0.361802i	$0.882162\pi$
$68$	1.57777	0.191333
$69$	−1.41325	−0.170136
$70$	0.468590	0.0560072
$71$	15.0399	1.78491	0.892454	−	0.451138i	$-0.148982\pi$
$71$	15.0399	1.78491	0.892454	+	0.451138i	$0.148982\pi$
$72$	−3.00069	−0.353634
$73$	−13.7014	−1.60363	−0.801813	−	0.597575i	$-0.796131\pi$
$73$	−13.7014	−1.60363	−0.801813	+	0.597575i	$0.796131\pi$
$74$	2.33313	0.271221
$75$	−4.89365	−0.565070
$76$	1.27413	0.146152
$77$	0.847644	0.0965980
$78$	6.26421	0.709282
$79$	5.83635	0.656640	0.328320	−	0.944567i	$-0.393518\pi$
$79$	5.83635	0.656640	0.328320	+	0.944567i	$0.393518\pi$
$80$	1.07566	0.120263
$81$	1.00000	0.111111
$82$	1.74936	0.193184
$83$	12.7270	1.39697	0.698484	−	0.715626i	$-0.253858\pi$
$83$	12.7270	1.39697	0.698484	+	0.715626i	$0.253858\pi$
$84$	0.335926	0.0366525
$85$	1.69018	0.183326
$86$	−9.38739	−1.01227
$87$	0	0
$88$	2.30495	0.245708
$89$	−8.28742	−0.878465	−0.439232	−	0.898374i	$-0.644749\pi$
$89$	−8.28742	−0.878465	−0.439232	+	0.898374i	$0.644749\pi$
$90$	−0.424639	−0.0447609
$91$	−5.30860	−0.556492
$92$	0.430221	0.0448536
$93$	−4.51575	−0.468261
$94$	−0.590370	−0.0608920
$95$	1.36491	0.140036
$96$	1.70626	0.174144
$97$	−1.54591	−0.156964	−0.0784819	−	0.996916i	$-0.525007\pi$
$97$	−1.54591	−0.156964	−0.0784819	+	0.996916i	$0.525007\pi$
$98$	−7.52937	−0.760582
$99$	−0.768140	−0.0772010
$100$	1.48972	0.148972
$101$	−16.1622	−1.60820	−0.804099	−	0.594495i	$-0.797352\pi$
$101$	−16.1622	−1.60820	−0.804099	+	0.594495i	$0.797352\pi$
$102$	−6.74888	−0.668239
$103$	−10.9518	−1.07912	−0.539558	−	0.841949i	$-0.681409\pi$
$103$	−10.9518	−1.07912	−0.539558	+	0.841949i	$0.681409\pi$
$104$	−14.4354	−1.41550
$105$	0.359860	0.0351188
$106$	−11.4961	−1.11660
$107$	−12.5095	−1.20934	−0.604669	−	0.796477i	$-0.706695\pi$
$107$	−12.5095	−1.20934	−0.604669	+	0.796477i	$0.706695\pi$
$108$	−0.304418	−0.0292927
$109$	8.80210	0.843089	0.421544	−	0.906808i	$-0.361488\pi$
$109$	8.80210	0.843089	0.421544	+	0.906808i	$0.361488\pi$
$110$	0.326183	0.0311003
$111$	1.79176	0.170066
$112$	3.63989	0.343937
$113$	2.46147	0.231556	0.115778	−	0.993275i	$-0.463064\pi$
$113$	2.46147	0.231556	0.115778	+	0.993275i	$0.463064\pi$
$114$	−5.45006	−0.510444
$115$	0.460873	0.0429766
$116$	0	0
$117$	4.81068	0.444748
$118$	4.78473	0.440470
$119$	5.71933	0.524290
$120$	0.978547	0.0893287
$121$	−10.4100	−0.946360
$122$	11.5170	1.04270
$123$	1.34344	0.121134
$124$	1.37468	0.123450
$125$	3.22640	0.288578
$126$	−1.43692	−0.128011
$127$	15.2655	1.35460	0.677298	−	0.735708i	$-0.263151\pi$
$127$	15.2655	1.35460	0.677298	+	0.735708i	$0.263151\pi$
$128$	8.07081	0.713366
$129$	−7.20917	−0.634732
$130$	−2.04281	−0.179166
$131$	8.74255	0.763840	0.381920	−	0.924195i	$-0.375263\pi$
$131$	8.74255	0.763840	0.381920	+	0.924195i	$0.375263\pi$
$132$	0.233836	0.0203528
$133$	4.61864	0.400487
$134$	−19.8729	−1.71676
$135$	−0.326108	−0.0280669
$136$	15.5522	1.33359
$137$	−23.3003	−1.99068	−0.995341	−	0.0964188i	$-0.969261\pi$
$137$	−23.3003	−1.99068	−0.995341	+	0.0964188i	$0.969261\pi$
$138$	−1.84026	−0.156653
$139$	−13.5292	−1.14753	−0.573765	−	0.819020i	$-0.694518\pi$
$139$	−13.5292	−1.14753	−0.573765	+	0.819020i	$0.694518\pi$
$140$	−0.109548	−0.00925850
$141$	−0.453383	−0.0381817
$142$	19.5841	1.64346
$143$	−3.69528	−0.309015
$144$	−3.29849	−0.274874
$145$	0	0
$146$	−17.8412	−1.47655
$147$	−5.78229	−0.476915
$148$	−0.545445	−0.0448353
$149$	−1.32696	−0.108708	−0.0543542	−	0.998522i	$-0.517310\pi$
$149$	−1.32696	−0.108708	−0.0543542	+	0.998522i	$0.517310\pi$
$150$	−6.37225	−0.520292
$151$	14.3702	1.16943	0.584716	−	0.811238i	$-0.301206\pi$
$151$	14.3702	1.16943	0.584716	+	0.811238i	$0.301206\pi$
$152$	12.5592	1.01869
$153$	−5.18289	−0.419012
$154$	1.10376	0.0889431
$155$	1.47262	0.118284
$156$	−1.46446	−0.117251
$157$	−13.1931	−1.05292	−0.526462	−	0.850199i	$-0.676482\pi$
$157$	−13.1931	−1.05292	−0.526462	+	0.850199i	$0.676482\pi$
$158$	7.59977	0.604605
$159$	−8.82860	−0.700154
$160$	−0.556424	−0.0439892
$161$	1.55953	0.122908
$162$	1.30214	0.102306
$163$	−3.01077	−0.235821	−0.117911	−	0.993024i	$-0.537620\pi$
$163$	−3.01077	−0.235821	−0.117911	+	0.993024i	$0.537620\pi$
$164$	−0.408969	−0.0319351
$165$	0.250496	0.0195011
$166$	16.5724	1.28627
$167$	−1.37455	−0.106366	−0.0531828	−	0.998585i	$-0.516937\pi$
$167$	−1.37455	−0.106366	−0.0531828	+	0.998585i	$0.516937\pi$
$168$	3.31126	0.255469
$169$	10.1427	0.780206
$170$	2.20086	0.168798
$171$	−4.18544	−0.320069
$172$	2.19461	0.167337
$173$	13.2857	1.01009	0.505045	−	0.863093i	$-0.331476\pi$
$173$	13.2857	1.01009	0.505045	+	0.863093i	$0.331476\pi$
$174$	0	0
$175$	5.40015	0.408213
$176$	2.53371	0.190985
$177$	3.67450	0.276192
$178$	−10.7914	−0.808851
$179$	6.15403	0.459974	0.229987	−	0.973194i	$-0.426132\pi$
$179$	6.15403	0.459974	0.229987	+	0.973194i	$0.426132\pi$
$180$	0.0992732	0.00739938
$181$	24.1126	1.79227	0.896136	−	0.443779i	$-0.146362\pi$
$181$	24.1126	1.79227	0.896136	+	0.443779i	$0.146362\pi$
$182$	−6.91256	−0.512393
$183$	8.84461	0.653812
$184$	4.24073	0.312631
$185$	−0.584307	−0.0429591
$186$	−5.88016	−0.431154
$187$	3.98119	0.291133
$188$	0.138018	0.0100660
$189$	−1.10350	−0.0802679
$190$	1.77730	0.128939
$191$	5.15567	0.373051	0.186526	−	0.982450i	$-0.440277\pi$
$191$	5.15567	0.373051	0.186526	+	0.982450i	$0.440277\pi$
$192$	8.81878	0.636441
$193$	2.77395	0.199673	0.0998365	−	0.995004i	$-0.468168\pi$
$193$	2.77395	0.199673	0.0998365	+	0.995004i	$0.468168\pi$
$194$	−2.01300	−0.144525
$195$	−1.56880	−0.112344
$196$	1.76023	0.125731
$197$	24.6895	1.75905	0.879527	−	0.475849i	$-0.157859\pi$
$197$	24.6895	1.75905	0.879527	+	0.475849i	$0.157859\pi$
$198$	−1.00023	−0.0710833
$199$	−5.25719	−0.372672	−0.186336	−	0.982486i	$-0.559661\pi$
$199$	−5.25719	−0.372672	−0.186336	+	0.982486i	$0.559661\pi$
$200$	14.6843	1.03834
$201$	−15.2617	−1.07648
$202$	−21.0455	−1.48076
$203$	0	0
$204$	1.57777	0.110466
$205$	−0.438107	−0.0305988
$206$	−14.2609	−0.993602
$207$	−1.41325	−0.0982279
$208$	−15.8680	−1.10025
$209$	3.21501	0.222387
$210$	0.468590	0.0323358
$211$	24.2023	1.66616	0.833079	−	0.553154i	$-0.186576\pi$
$211$	24.2023	1.66616	0.833079	+	0.553154i	$0.186576\pi$
$212$	2.68759	0.184584
$213$	15.0399	1.03052
$214$	−16.2892	−1.11350
$215$	2.35097	0.160335
$216$	−3.00069	−0.204171
$217$	4.98314	0.338277
$218$	11.4616	0.776279
$219$	−13.7014	−0.925854
$220$	−0.0762557	−0.00514116
$221$	−24.9333	−1.67719
$222$	2.33313	0.156590
$223$	1.21432	0.0813169	0.0406585	−	0.999173i	$-0.487054\pi$
$223$	1.21432	0.0813169	0.0406585	+	0.999173i	$0.487054\pi$
$224$	−1.88286	−0.125804
$225$	−4.89365	−0.326244
$226$	3.20519	0.213206
$227$	15.9762	1.06037	0.530187	−	0.847880i	$-0.322122\pi$
$227$	15.9762	1.06037	0.530187	+	0.847880i	$0.322122\pi$
$228$	1.27413	0.0843811
$229$	−15.3372	−1.01351	−0.506754	−	0.862091i	$-0.669155\pi$
$229$	−15.3372	−1.01351	−0.506754	+	0.862091i	$0.669155\pi$
$230$	0.600123	0.0395710
$231$	0.847644	0.0557709
$232$	0	0
$233$	12.9851	0.850684	0.425342	−	0.905033i	$-0.360154\pi$
$233$	12.9851	0.850684	0.425342	+	0.905033i	$0.360154\pi$
$234$	6.26421	0.409504
$235$	0.147852	0.00964477
$236$	−1.11859	−0.0728137
$237$	5.83635	0.379111
$238$	7.44740	0.482743
$239$	0.255060	0.0164985	0.00824924	−	0.999966i	$-0.497374\pi$
$239$	0.255060	0.0164985	0.00824924	+	0.999966i	$0.497374\pi$
$240$	1.07566	0.0694338
$241$	8.39604	0.540836	0.270418	−	0.962743i	$-0.412838\pi$
$241$	8.39604	0.540836	0.270418	+	0.962743i	$0.412838\pi$
$242$	−13.5553	−0.871366
$243$	1.00000	0.0641500
$244$	−2.69246	−0.172367
$245$	1.88565	0.120470
$246$	1.74936	0.111535
$247$	−20.1348	−1.28115
$248$	13.5504	0.860448
$249$	12.7270	0.806540
$250$	4.20123	0.265709
$251$	18.6458	1.17692	0.588458	−	0.808528i	$-0.299735\pi$
$251$	18.6458	1.17692	0.588458	+	0.808528i	$0.299735\pi$
$252$	0.335926	0.0211614
$253$	1.08558	0.0682497
$254$	19.8779	1.24725
$255$	1.69018	0.105843
$256$	−7.12819	−0.445512
$257$	24.6186	1.53567	0.767834	−	0.640649i	$-0.221335\pi$
$257$	24.6186	1.53567	0.767834	+	0.640649i	$0.221335\pi$
$258$	−9.38739	−0.584433
$259$	−1.97721	−0.122858
$260$	0.477572	0.0296177
$261$	0	0
$262$	11.3841	0.703310
$263$	10.1677	0.626970	0.313485	−	0.949593i	$-0.398503\pi$
$263$	10.1677	0.626970	0.313485	+	0.949593i	$0.398503\pi$
$264$	2.30495	0.141860
$265$	2.87907	0.176860
$266$	6.01414	0.368751
$267$	−8.28742	−0.507182
$268$	4.64594	0.283796
$269$	0.668029	0.0407305	0.0203652	−	0.999793i	$-0.493517\pi$
$269$	0.668029	0.0407305	0.0203652	+	0.999793i	$0.493517\pi$
$270$	−0.424639	−0.0258427
$271$	−9.29114	−0.564396	−0.282198	−	0.959356i	$-0.591064\pi$
$271$	−9.29114	−0.564396	−0.282198	+	0.959356i	$0.591064\pi$
$272$	17.0957	1.03658
$273$	−5.30860	−0.321291
$274$	−30.3404	−1.83293
$275$	3.75901	0.226677
$276$	0.430221	0.0258962
$277$	−14.7432	−0.885833	−0.442917	−	0.896563i	$-0.646056\pi$
$277$	−14.7432	−0.885833	−0.442917	+	0.896563i	$0.646056\pi$
$278$	−17.6169	−1.05659
$279$	−4.51575	−0.270351
$280$	−1.07983	−0.0645320
$281$	−21.5272	−1.28421	−0.642104	−	0.766618i	$-0.721938\pi$
$281$	−21.5272	−1.28421	−0.642104	+	0.766618i	$0.721938\pi$
$282$	−0.590370	−0.0351560
$283$	10.3210	0.613522	0.306761	−	0.951787i	$-0.400755\pi$
$283$	10.3210	0.613522	0.306761	+	0.951787i	$0.400755\pi$
$284$	−4.57843	−0.271680
$285$	1.36491	0.0808500
$286$	−4.81179	−0.284527
$287$	−1.48249	−0.0875088
$288$	1.70626	0.100542
$289$	9.86239	0.580141
$290$	0	0
$291$	−1.54591	−0.0906230
$292$	4.17095	0.244087
$293$	−25.2077	−1.47265	−0.736324	−	0.676630i	$-0.763440\pi$
$293$	−25.2077	−1.47265	−0.736324	+	0.676630i	$0.763440\pi$
$294$	−7.52937	−0.439122
$295$	−1.19828	−0.0697667
$296$	−5.37651	−0.312503
$297$	−0.768140	−0.0445720
$298$	−1.72789	−0.100094
$299$	−6.79872	−0.393180
$300$	1.48972	0.0860089
$301$	7.95533	0.458538
$302$	18.7121	1.07676
$303$	−16.1622	−0.928494
$304$	13.8057	0.791809
$305$	−2.88429	−0.165154
$306$	−6.74888	−0.385808
$307$	17.7845	1.01502	0.507508	−	0.861647i	$-0.330567\pi$
$307$	17.7845	1.01502	0.507508	+	0.861647i	$0.330567\pi$
$308$	−0.258038	−0.0147031
$309$	−10.9518	−0.623028
$310$	1.91757	0.108910
$311$	−8.39849	−0.476234	−0.238117	−	0.971236i	$-0.576530\pi$
$311$	−8.39849	−0.476234	−0.238117	+	0.971236i	$0.576530\pi$
$312$	−14.4354	−0.817241
$313$	−2.10022	−0.118712	−0.0593558	−	0.998237i	$-0.518905\pi$
$313$	−2.10022	−0.118712	−0.0593558	+	0.998237i	$0.518905\pi$
$314$	−17.1793	−0.969486
$315$	0.359860	0.0202758
$316$	−1.77669	−0.0999467
$317$	−5.02786	−0.282393	−0.141196	−	0.989982i	$-0.545095\pi$
$317$	−5.02786	−0.282393	−0.141196	+	0.989982i	$0.545095\pi$
$318$	−11.4961	−0.644670
$319$	0	0
$320$	−2.87587	−0.160766
$321$	−12.5095	−0.698212
$322$	2.03073	0.113168
$323$	21.6927	1.20701
$324$	−0.304418	−0.0169121
$325$	−23.5418	−1.30587
$326$	−3.92045	−0.217134
$327$	8.80210	0.486757
$328$	−4.03126	−0.222589
$329$	0.500309	0.0275829
$330$	0.326183	0.0179558
$331$	−3.80922	−0.209374	−0.104687	−	0.994505i	$-0.533384\pi$
$331$	−3.80922	−0.209374	−0.104687	+	0.994505i	$0.533384\pi$
$332$	−3.87433	−0.212631
$333$	1.79176	0.0981879
$334$	−1.78986	−0.0979368
$335$	4.97695	0.271920
$336$	3.63989	0.198572
$337$	1.51087	0.0823023	0.0411512	−	0.999153i	$-0.486897\pi$
$337$	1.51087	0.0823023	0.0411512	+	0.999153i	$0.486897\pi$
$338$	13.2072	0.718379
$339$	2.46147	0.133689
$340$	−0.514522	−0.0279039
$341$	3.46873	0.187842
$342$	−5.45006	−0.294705
$343$	14.1053	0.761613
$344$	21.6325	1.16634
$345$	0.460873	0.0248126
$346$	17.2999	0.930047
$347$	23.3601	1.25404	0.627019	−	0.779004i	$-0.284275\pi$
$347$	23.3601	1.25404	0.627019	+	0.779004i	$0.284275\pi$
$348$	0	0
$349$	−15.0240	−0.804216	−0.402108	−	0.915592i	$-0.631722\pi$
$349$	−15.0240	−0.804216	−0.402108	+	0.915592i	$0.631722\pi$
$350$	7.03178	0.375865
$351$	4.81068	0.256775
$352$	−1.31065	−0.0698577
$353$	16.0604	0.854808	0.427404	−	0.904061i	$-0.359428\pi$
$353$	16.0604	0.854808	0.427404	+	0.904061i	$0.359428\pi$
$354$	4.78473	0.254306
$355$	−4.90463	−0.260311
$356$	2.52284	0.133710
$357$	5.71933	0.302699
$358$	8.01343	0.423523
$359$	−26.5409	−1.40078	−0.700388	−	0.713762i	$-0.746990\pi$
$359$	−26.5409	−1.40078	−0.700388	+	0.713762i	$0.746990\pi$
$360$	0.978547	0.0515739
$361$	−1.48206	−0.0780030
$362$	31.3981	1.65024
$363$	−10.4100	−0.546381
$364$	1.61603	0.0847032
$365$	4.46812	0.233872
$366$	11.5170	0.602001
$367$	−17.0018	−0.887485	−0.443743	−	0.896154i	$-0.646350\pi$
$367$	−17.0018	−0.887485	−0.443743	+	0.896154i	$0.646350\pi$
$368$	4.66161	0.243003
$369$	1.34344	0.0699369
$370$	−0.760852	−0.0395548
$371$	9.74237	0.505799
$372$	1.37468	0.0712737
$373$	−11.7324	−0.607481	−0.303741	−	0.952755i	$-0.598236\pi$
$373$	−11.7324	−0.607481	−0.303741	+	0.952755i	$0.598236\pi$
$374$	5.18409	0.268063
$375$	3.22640	0.166610
$376$	1.36046	0.0701604
$377$	0	0
$378$	−1.43692	−0.0739071
$379$	−7.71113	−0.396094	−0.198047	−	0.980193i	$-0.563460\pi$
$379$	−7.71113	−0.396094	−0.198047	+	0.980193i	$0.563460\pi$
$380$	−0.415502	−0.0213148
$381$	15.2655	0.782077
$382$	6.71343	0.343489
$383$	−17.6580	−0.902281	−0.451140	−	0.892453i	$-0.648983\pi$
$383$	−17.6580	−0.902281	−0.451140	+	0.892453i	$0.648983\pi$
$384$	8.07081	0.411862
$385$	−0.276423	−0.0140878
$386$	3.61208	0.183850
$387$	−7.20917	−0.366463
$388$	0.470605	0.0238913
$389$	17.4066	0.882550	0.441275	−	0.897372i	$-0.354526\pi$
$389$	17.4066	0.882550	0.441275	+	0.897372i	$0.354526\pi$
$390$	−2.04281	−0.103441
$391$	7.32475	0.370428
$392$	17.3508	0.876349
$393$	8.74255	0.441003
$394$	32.1493	1.61966
$395$	−1.90328	−0.0957642
$396$	0.233836	0.0117507
$397$	8.73479	0.438387	0.219193	−	0.975681i	$-0.429657\pi$
$397$	8.73479	0.438387	0.219193	+	0.975681i	$0.429657\pi$
$398$	−6.84562	−0.343140
$399$	4.61864	0.231221
$400$	16.1417	0.807084
$401$	9.95698	0.497228	0.248614	−	0.968603i	$-0.420025\pi$
$401$	9.95698	0.497228	0.248614	+	0.968603i	$0.420025\pi$
$402$	−19.8729	−0.991171
$403$	−21.7238	−1.08214
$404$	4.92007	0.244783
$405$	−0.326108	−0.0162044
$406$	0	0
$407$	−1.37632	−0.0682218
$408$	15.5522	0.769951
$409$	−20.3896	−1.00820	−0.504101	−	0.863644i	$-0.668176\pi$
$409$	−20.3896	−1.00820	−0.504101	+	0.863644i	$0.668176\pi$
$410$	−0.570479	−0.0281740
$411$	−23.3003	−1.14932
$412$	3.33394	0.164251
$413$	−4.05482	−0.199524
$414$	−1.84026	−0.0904439
$415$	−4.15037	−0.203734
$416$	8.20827	0.402444
$417$	−13.5292	−0.662526
$418$	4.18641	0.204764
$419$	36.4277	1.77961	0.889804	−	0.456342i	$-0.150841\pi$
$419$	36.4277	1.77961	0.889804	+	0.456342i	$0.150841\pi$
$420$	−0.109548	−0.00534540
$421$	19.8525	0.967550	0.483775	−	0.875192i	$-0.339265\pi$
$421$	19.8525	0.967550	0.483775	+	0.875192i	$0.339265\pi$
$422$	31.5150	1.53412
$423$	−0.453383	−0.0220442
$424$	26.4919	1.28656
$425$	25.3633	1.23030
$426$	19.5841	0.948855
$427$	−9.76004	−0.472321
$428$	3.80812	0.184072
$429$	−3.69528	−0.178410
$430$	3.06130	0.147629
$431$	−35.7602	−1.72251	−0.861255	−	0.508174i	$-0.830321\pi$
$431$	−35.7602	−1.72251	−0.861255	+	0.508174i	$0.830321\pi$
$432$	−3.29849	−0.158699
$433$	−37.5454	−1.80432	−0.902159	−	0.431404i	$-0.858018\pi$
$433$	−37.5454	−1.80432	−0.902159	+	0.431404i	$0.858018\pi$
$434$	6.48877	0.311471
$435$	0	0
$436$	−2.67952	−0.128326
$437$	5.91510	0.282957
$438$	−17.8412	−0.852485
$439$	6.89646	0.329150	0.164575	−	0.986365i	$-0.447375\pi$
$439$	6.89646	0.329150	0.164575	+	0.986365i	$0.447375\pi$
$440$	−0.751661	−0.0358340
$441$	−5.78229	−0.275347
$442$	−32.4667	−1.54428
$443$	−13.8273	−0.656955	−0.328477	−	0.944512i	$-0.606535\pi$
$443$	−13.8273	−0.656955	−0.328477	+	0.944512i	$0.606535\pi$
$444$	−0.545445	−0.0258857
$445$	2.70259	0.128115
$446$	1.58122	0.0748730
$447$	−1.32696	−0.0627629
$448$	−9.73154	−0.459772
$449$	−20.0274	−0.945151	−0.472576	−	0.881290i	$-0.656676\pi$
$449$	−20.0274	−0.945151	−0.472576	+	0.881290i	$0.656676\pi$
$450$	−6.37225	−0.300391
$451$	−1.03195	−0.0485928
$452$	−0.749317	−0.0352449
$453$	14.3702	0.675172
$454$	20.8033	0.976346
$455$	1.73117	0.0811587
$456$	12.5592	0.588139
$457$	−24.4578	−1.14409	−0.572045	−	0.820223i	$-0.693850\pi$
$457$	−24.4578	−1.14409	−0.572045	+	0.820223i	$0.693850\pi$
$458$	−19.9712	−0.933193
$459$	−5.18289	−0.241917
$460$	−0.140298	−0.00654144
$461$	−22.2758	−1.03749	−0.518745	−	0.854929i	$-0.673600\pi$
$461$	−22.2758	−1.03749	−0.518745	+	0.854929i	$0.673600\pi$
$462$	1.10376	0.0513513
$463$	27.5102	1.27851	0.639254	−	0.768996i	$-0.279243\pi$
$463$	27.5102	1.27851	0.639254	+	0.768996i	$0.279243\pi$
$464$	0	0
$465$	1.47262	0.0682911
$466$	16.9085	0.783272
$467$	23.7457	1.09882	0.549410	−	0.835553i	$-0.314853\pi$
$467$	23.7457	1.09882	0.549410	+	0.835553i	$0.314853\pi$
$468$	−1.46446	−0.0676947
$469$	16.8413	0.777658
$470$	0.192524	0.00888048
$471$	−13.1931	−0.607906
$472$	−11.0260	−0.507514
$473$	5.53766	0.254622
$474$	7.59977	0.349069
$475$	20.4821	0.939784
$476$	−1.74107	−0.0798018
$477$	−8.82860	−0.404234
$478$	0.332126	0.0151911
$479$	26.1749	1.19596	0.597980	−	0.801511i	$-0.295970\pi$
$479$	26.1749	1.19596	0.597980	+	0.801511i	$0.295970\pi$
$480$	−0.556424	−0.0253972
$481$	8.61959	0.393020
$482$	10.9329	0.497978
$483$	1.55953	0.0709610
$484$	3.16898	0.144045
$485$	0.504134	0.0228915
$486$	1.30214	0.0590665
$487$	−16.3153	−0.739316	−0.369658	−	0.929168i	$-0.620525\pi$
$487$	−16.3153	−0.739316	−0.369658	+	0.929168i	$0.620525\pi$
$488$	−26.5399	−1.20141
$489$	−3.01077	−0.136152
$490$	2.45539	0.110923
$491$	32.9012	1.48481	0.742406	−	0.669950i	$-0.233685\pi$
$491$	32.9012	1.48481	0.742406	+	0.669950i	$0.233685\pi$
$492$	−0.408969	−0.0184378
$493$	0	0
$494$	−26.2185	−1.17963
$495$	0.250496	0.0112590
$496$	14.8952	0.668813
$497$	−16.5966	−0.744457
$498$	16.5724	0.742626
$499$	−22.1639	−0.992193	−0.496097	−	0.868267i	$-0.665234\pi$
$499$	−22.1639	−0.992193	−0.496097	+	0.868267i	$0.665234\pi$
$500$	−0.982174	−0.0439242
$501$	−1.37455	−0.0614102
$502$	24.2796	1.08365
$503$	−39.7760	−1.77352	−0.886762	−	0.462227i	$-0.847050\pi$
$503$	−39.7760	−1.77352	−0.886762	+	0.462227i	$0.847050\pi$
$504$	3.31126	0.147495
$505$	5.27061	0.234539
$506$	1.41358	0.0628413
$507$	10.1427	0.450452
$508$	−4.64711	−0.206182
$509$	−10.1933	−0.451810	−0.225905	−	0.974149i	$-0.572534\pi$
$509$	−10.1933	−0.451810	−0.225905	+	0.974149i	$0.572534\pi$
$510$	2.20086	0.0974558
$511$	15.1195	0.668847
$512$	−25.4236	−1.12357
$513$	−4.18544	−0.184792
$514$	32.0570	1.41397
$515$	3.57147	0.157378
$516$	2.19461	0.0966121
$517$	0.348262	0.0153165
$518$	−2.57461	−0.113122
$519$	13.2857	0.583176
$520$	4.70748	0.206437
$521$	7.09229	0.310719	0.155359	−	0.987858i	$-0.450346\pi$
$521$	7.09229	0.310719	0.155359	+	0.987858i	$0.450346\pi$
$522$	0	0
$523$	10.9937	0.480723	0.240361	−	0.970683i	$-0.422734\pi$
$523$	10.9937	0.480723	0.240361	+	0.970683i	$0.422734\pi$
$524$	−2.66139	−0.116264
$525$	5.40015	0.235682
$526$	13.2399	0.577286
$527$	23.4047	1.01952
$528$	2.53371	0.110265
$529$	−21.0027	−0.913161
$530$	3.74897	0.162845
$531$	3.67450	0.159460
$532$	−1.40600	−0.0609578
$533$	6.46289	0.279939
$534$	−10.7914	−0.466990
$535$	4.07944	0.176370
$536$	45.7955	1.97806
$537$	6.15403	0.265566
$538$	0.869871	0.0375028
$539$	4.44161	0.191314
$540$	0.0992732	0.00427204
$541$	4.82781	0.207564	0.103782	−	0.994600i	$-0.466906\pi$
$541$	4.82781	0.207564	0.103782	+	0.994600i	$0.466906\pi$
$542$	−12.0984	−0.519671
$543$	24.1126	1.03477
$544$	−8.84336	−0.379156
$545$	−2.87043	−0.122956
$546$	−6.91256	−0.295830
$547$	−34.3207	−1.46745	−0.733724	−	0.679448i	$-0.762219\pi$
$547$	−34.3207	−1.46745	−0.733724	+	0.679448i	$0.762219\pi$
$548$	7.09305	0.303000
$549$	8.84461	0.377479
$550$	4.89478	0.208714
$551$	0	0
$552$	4.24073	0.180498
$553$	−6.44041	−0.273874
$554$	−19.1978	−0.815636
$555$	−0.584307	−0.0248024
$556$	4.11853	0.174665
$557$	−13.3893	−0.567325	−0.283662	−	0.958924i	$-0.591550\pi$
$557$	−13.3893	−0.567325	−0.283662	+	0.958924i	$0.591550\pi$
$558$	−5.88016	−0.248927
$559$	−34.6811	−1.46685
$560$	−1.18700	−0.0501597
$561$	3.98119	0.168086
$562$	−28.0316	−1.18244
$563$	−1.89811	−0.0799960	−0.0399980	−	0.999200i	$-0.512735\pi$
$563$	−1.89811	−0.0799960	−0.0399980	+	0.999200i	$0.512735\pi$
$564$	0.138018	0.00581161
$565$	−0.802704	−0.0337700
$566$	13.4395	0.564904
$567$	−1.10350	−0.0463427
$568$	−45.1301	−1.89362
$569$	11.1591	0.467815	0.233908	−	0.972259i	$-0.424849\pi$
$569$	11.1591	0.467815	0.233908	+	0.972259i	$0.424849\pi$
$570$	1.77730	0.0744431
$571$	−13.2107	−0.552849	−0.276425	−	0.961036i	$-0.589150\pi$
$571$	−13.2107	−0.552849	−0.276425	+	0.961036i	$0.589150\pi$
$572$	1.12491	0.0470349
$573$	5.15567	0.215381
$574$	−1.93042	−0.0805742
$575$	6.91598	0.288416
$576$	8.81878	0.367449
$577$	−13.8637	−0.577154	−0.288577	−	0.957457i	$-0.593182\pi$
$577$	−13.8637	−0.577154	−0.288577	+	0.957457i	$0.593182\pi$
$578$	12.8423	0.534168
$579$	2.77395	0.115281
$580$	0	0
$581$	−14.0442	−0.582653
$582$	−2.01300	−0.0834417
$583$	6.78160	0.280865
$584$	41.1136	1.70129
$585$	−1.56880	−0.0648619
$586$	−32.8240	−1.35595
$587$	−27.7891	−1.14698	−0.573489	−	0.819213i	$-0.694411\pi$
$587$	−27.7891	−1.14698	−0.573489	+	0.819213i	$0.694411\pi$
$588$	1.76023	0.0725908
$589$	18.9004	0.778778
$590$	−1.56034	−0.0642381
$591$	24.6895	1.01559
$592$	−5.91011	−0.242904
$593$	−8.07661	−0.331667	−0.165833	−	0.986154i	$-0.553031\pi$
$593$	−8.07661	−0.331667	−0.165833	+	0.986154i	$0.553031\pi$
$594$	−1.00023	−0.0410399
$595$	−1.86512	−0.0764623
$596$	0.403950	0.0165464
$597$	−5.25719	−0.215162
$598$	−8.85292	−0.362023
$599$	−19.2599	−0.786940	−0.393470	−	0.919337i	$-0.628725\pi$
$599$	−19.2599	−0.786940	−0.393470	+	0.919337i	$0.628725\pi$
$600$	14.6843	0.599485
$601$	−22.1275	−0.902600	−0.451300	−	0.892372i	$-0.649040\pi$
$601$	−22.1275	−0.902600	−0.451300	+	0.892372i	$0.649040\pi$
$602$	10.3590	0.422201
$603$	−15.2617	−0.621503
$604$	−4.37456	−0.177998
$605$	3.39477	0.138017
$606$	−21.0455	−0.854916
$607$	−11.8647	−0.481573	−0.240786	−	0.970578i	$-0.577405\pi$
$607$	−11.8647	−0.481573	−0.240786	+	0.970578i	$0.577405\pi$
$608$	−7.14145	−0.289624
$609$	0	0
$610$	−3.75577	−0.152067
$611$	−2.18108	−0.0882371
$612$	1.57777	0.0637775
$613$	33.8315	1.36644	0.683220	−	0.730212i	$-0.260579\pi$
$613$	33.8315	1.36644	0.683220	+	0.730212i	$0.260579\pi$
$614$	23.1580	0.934582
$615$	−0.438107	−0.0176662
$616$	−2.54351	−0.102481
$617$	1.68895	0.0679944	0.0339972	−	0.999422i	$-0.489176\pi$
$617$	1.68895	0.0679944	0.0339972	+	0.999422i	$0.489176\pi$
$618$	−14.2609	−0.573656
$619$	−15.5259	−0.624037	−0.312018	−	0.950076i	$-0.601005\pi$
$619$	−15.5259	−0.624037	−0.312018	+	0.950076i	$0.601005\pi$
$620$	−0.448293	−0.0180039
$621$	−1.41325	−0.0567119
$622$	−10.9360	−0.438495
$623$	9.14518	0.366394
$624$	−15.8680	−0.635229
$625$	23.4161	0.936645
$626$	−2.73479	−0.109304
$627$	3.21501	0.128395
$628$	4.01622	0.160265
$629$	−9.28650	−0.370277
$630$	0.468590	0.0186691
$631$	−18.3607	−0.730929	−0.365465	−	0.930825i	$-0.619090\pi$
$631$	−18.3607	−0.730929	−0.365465	+	0.930825i	$0.619090\pi$
$632$	−17.5130	−0.696632
$633$	24.2023	0.961957
$634$	−6.54700	−0.260014
$635$	−4.97821	−0.197554
$636$	2.68759	0.106570
$637$	−27.8167	−1.10214
$638$	0	0
$639$	15.0399	0.594970
$640$	−2.63195	−0.104037
$641$	5.14969	0.203401	0.101700	−	0.994815i	$-0.467572\pi$
$641$	5.14969	0.203401	0.101700	+	0.994815i	$0.467572\pi$
$642$	−16.2892	−0.642882
$643$	28.2698	1.11485	0.557426	−	0.830227i	$-0.311789\pi$
$643$	28.2698	1.11485	0.557426	+	0.830227i	$0.311789\pi$
$644$	−0.474749	−0.0187077
$645$	2.35097	0.0925692
$646$	28.2471	1.11137
$647$	−28.3512	−1.11460	−0.557301	−	0.830310i	$-0.688163\pi$
$647$	−28.3512	−1.11460	−0.557301	+	0.830310i	$0.688163\pi$
$648$	−3.00069	−0.117878
$649$	−2.82253	−0.110794
$650$	−30.6549	−1.20238
$651$	4.98314	0.195304
$652$	0.916532	0.0358942
$653$	40.3239	1.57800	0.788998	−	0.614396i	$-0.210600\pi$
$653$	40.3239	1.57800	0.788998	+	0.614396i	$0.210600\pi$
$654$	11.4616	0.448185
$655$	−2.85101	−0.111398
$656$	−4.43134	−0.173015
$657$	−13.7014	−0.534542
$658$	0.651474	0.0253971
$659$	49.4421	1.92599	0.962996	−	0.269517i	$-0.0868641\pi$
$659$	49.4421	1.92599	0.962996	+	0.269517i	$0.0868641\pi$
$660$	−0.0762557	−0.00296825
$661$	15.8792	0.617631	0.308815	−	0.951122i	$-0.400067\pi$
$661$	15.8792	0.617631	0.308815	+	0.951122i	$0.400067\pi$
$662$	−4.96016	−0.192782
$663$	−24.9333	−0.968328
$664$	−38.1897	−1.48205
$665$	−1.50617	−0.0584069
$666$	2.33313	0.0904070
$667$	0	0
$668$	0.418437	0.0161898
$669$	1.21432	0.0469483
$670$	6.48071	0.250372
$671$	−6.79390	−0.262276
$672$	−1.88286	−0.0726328
$673$	−11.6979	−0.450923	−0.225461	−	0.974252i	$-0.572389\pi$
$673$	−11.6979	−0.450923	−0.225461	+	0.974252i	$0.572389\pi$
$674$	1.96737	0.0757803
$675$	−4.89365	−0.188357
$676$	−3.08762	−0.118755
$677$	−19.5034	−0.749578	−0.374789	−	0.927110i	$-0.622285\pi$
$677$	−19.5034	−0.749578	−0.374789	+	0.927110i	$0.622285\pi$
$678$	3.20519	0.123095
$679$	1.70592	0.0654671
$680$	−5.07170	−0.194491
$681$	15.9762	0.612208
$682$	4.51679	0.172957
$683$	24.7263	0.946126	0.473063	−	0.881029i	$-0.343148\pi$
$683$	24.7263	0.946126	0.473063	+	0.881029i	$0.343148\pi$
$684$	1.27413	0.0487174
$685$	7.59842	0.290321
$686$	18.3671	0.701259
$687$	−15.3372	−0.585149
$688$	23.7794	0.906581
$689$	−42.4716	−1.61804
$690$	0.600123	0.0228463
$691$	−47.7615	−1.81693	−0.908467	−	0.417956i	$-0.862746\pi$
$691$	−47.7615	−1.81693	−0.908467	+	0.417956i	$0.862746\pi$
$692$	−4.04440	−0.153745
$693$	0.847644	0.0321993
$694$	30.4183	1.15466
$695$	4.41197	0.167355
$696$	0	0
$697$	−6.96293	−0.263740
$698$	−19.5634	−0.740486
$699$	12.9851	0.491143
$700$	−1.64391	−0.0621338
$701$	−8.14298	−0.307556	−0.153778	−	0.988105i	$-0.549144\pi$
$701$	−8.14298	−0.307556	−0.153778	+	0.988105i	$0.549144\pi$
$702$	6.26421	0.236427
$703$	−7.49931	−0.282842
$704$	−6.77406	−0.255307
$705$	0.147852	0.00556841
$706$	20.9130	0.787070
$707$	17.8350	0.670754
$708$	−1.11859	−0.0420390
$709$	−1.77591	−0.0666959	−0.0333479	−	0.999444i	$-0.510617\pi$
$709$	−1.77591	−0.0666959	−0.0333479	+	0.999444i	$0.510617\pi$
$710$	−6.38654	−0.239682
$711$	5.83635	0.218880
$712$	24.8679	0.931966
$713$	6.38190	0.239004
$714$	7.44740	0.278712
$715$	1.20506	0.0450666
$716$	−1.87340	−0.0700122
$717$	0.255060	0.00952540
$718$	−34.5601	−1.28977
$719$	28.0973	1.04785	0.523927	−	0.851763i	$-0.324467\pi$
$719$	28.0973	1.04785	0.523927	+	0.851763i	$0.324467\pi$
$720$	1.07566	0.0400876
$721$	12.0854	0.450082
$722$	−1.92985	−0.0718217
$723$	8.39604	0.312252
$724$	−7.34031	−0.272800
$725$	0	0
$726$	−13.5553	−0.503084
$727$	−47.0198	−1.74387	−0.871934	−	0.489624i	$-0.837134\pi$
$727$	−47.0198	−1.74387	−0.871934	+	0.489624i	$0.837134\pi$
$728$	15.9294	0.590384
$729$	1.00000	0.0370370
$730$	5.81815	0.215339
$731$	37.3644	1.38197
$732$	−2.69246	−0.0995163
$733$	−31.1355	−1.15002	−0.575008	−	0.818148i	$-0.695001\pi$
$733$	−31.1355	−1.15002	−0.575008	+	0.818148i	$0.695001\pi$
$734$	−22.1388	−0.817157
$735$	1.88565	0.0695531
$736$	−2.41138	−0.0888845
$737$	11.7231	0.431826
$738$	1.74936	0.0643948
$739$	−12.6916	−0.466866	−0.233433	−	0.972373i	$-0.574996\pi$
$739$	−12.6916	−0.466866	−0.233433	+	0.972373i	$0.574996\pi$
$740$	0.177874	0.00653877
$741$	−20.1348	−0.739672
$742$	12.6860	0.465717
$743$	13.7277	0.503621	0.251810	−	0.967777i	$-0.418974\pi$
$743$	13.7277	0.503621	0.251810	+	0.967777i	$0.418974\pi$
$744$	13.5504	0.496780
$745$	0.432730	0.0158540
$746$	−15.2773	−0.559342
$747$	12.7270	0.465656
$748$	−1.21195	−0.0443132
$749$	13.8042	0.504396
$750$	4.20123	0.153407
$751$	4.88215	0.178152	0.0890761	−	0.996025i	$-0.471609\pi$
$751$	4.88215	0.178152	0.0890761	+	0.996025i	$0.471609\pi$
$752$	1.49548	0.0545345
$753$	18.6458	0.679492
$754$	0	0
$755$	−4.68624	−0.170550
$756$	0.335926	0.0122175
$757$	−20.3790	−0.740686	−0.370343	−	0.928895i	$-0.620760\pi$
$757$	−20.3790	−0.740686	−0.370343	+	0.928895i	$0.620760\pi$
$758$	−10.0410	−0.364706
$759$	1.08558	0.0394040
$760$	−4.09565	−0.148565
$761$	−35.7484	−1.29588	−0.647940	−	0.761692i	$-0.724369\pi$
$761$	−35.7484	−1.29588	−0.647940	+	0.761692i	$0.724369\pi$
$762$	19.8779	0.720102
$763$	−9.71313	−0.351639
$764$	−1.56948	−0.0567819
$765$	1.69018	0.0611086
$766$	−22.9933	−0.830780
$767$	17.6769	0.638275
$768$	−7.12819	−0.257216
$769$	23.2091	0.836943	0.418471	−	0.908230i	$-0.362566\pi$
$769$	23.2091	0.836943	0.418471	+	0.908230i	$0.362566\pi$
$770$	−0.359943	−0.0129714
$771$	24.6186	0.886618
$772$	−0.844441	−0.0303921
$773$	42.7174	1.53644	0.768220	−	0.640186i	$-0.221143\pi$
$773$	42.7174	1.53644	0.768220	+	0.640186i	$0.221143\pi$
$774$	−9.38739	−0.337423
$775$	22.0985	0.793802
$776$	4.63880	0.166523
$777$	−1.97721	−0.0709320
$778$	22.6659	0.812613
$779$	−5.62291	−0.201462
$780$	0.477572	0.0170998
$781$	−11.5528	−0.413390
$782$	9.53788	0.341074
$783$	0	0
$784$	19.0728	0.681172
$785$	4.30237	0.153558
$786$	11.3841	0.406056
$787$	−14.0075	−0.499313	−0.249657	−	0.968334i	$-0.580318\pi$
$787$	−14.0075	−0.499313	−0.249657	+	0.968334i	$0.580318\pi$
$788$	−7.51594	−0.267744
$789$	10.1677	0.361981
$790$	−2.47834	−0.0881755
$791$	−2.71623	−0.0965782
$792$	2.30495	0.0819028
$793$	42.5486	1.51095
$794$	11.3740	0.403647
$795$	2.87907	0.102110
$796$	1.60038	0.0567241
$797$	−9.17828	−0.325111	−0.162556	−	0.986699i	$-0.551974\pi$
$797$	−9.17828	−0.325111	−0.162556	+	0.986699i	$0.551974\pi$
$798$	6.01414	0.212898
$799$	2.34984	0.0831312
$800$	−8.34984	−0.295211
$801$	−8.28742	−0.292822
$802$	12.9654	0.457825
$803$	10.5246	0.371404
$804$	4.64594	0.163849
$805$	−0.508574	−0.0179249
$806$	−28.2876	−0.996388
$807$	0.668029	0.0235157
$808$	48.4977	1.70614
$809$	11.6633	0.410061	0.205031	−	0.978756i	$-0.434271\pi$
$809$	11.6633	0.410061	0.205031	+	0.978756i	$0.434271\pi$
$810$	−0.424639	−0.0149203
$811$	−10.2506	−0.359946	−0.179973	−	0.983672i	$-0.557601\pi$
$811$	−10.2506	−0.359946	−0.179973	+	0.983672i	$0.557601\pi$
$812$	0	0
$813$	−9.29114	−0.325854
$814$	−1.79217	−0.0628156
$815$	0.981833	0.0343921
$816$	17.0957	0.598471
$817$	30.1736	1.05564
$818$	−26.5503	−0.928308
$819$	−5.30860	−0.185497
$820$	0.133368	0.00465741
$821$	22.8410	0.797157	0.398578	−	0.917134i	$-0.369504\pi$
$821$	22.8410	0.797157	0.398578	+	0.917134i	$0.369504\pi$
$822$	−30.3404	−1.05824
$823$	0.493935	0.0172175	0.00860874	−	0.999963i	$-0.497260\pi$
$823$	0.493935	0.0172175	0.00860874	+	0.999963i	$0.497260\pi$
$824$	32.8630	1.14484
$825$	3.75901	0.130872
$826$	−5.27996	−0.183713
$827$	−52.3490	−1.82035	−0.910177	−	0.414219i	$-0.864055\pi$
$827$	−52.3490	−1.82035	−0.910177	+	0.414219i	$0.864055\pi$
$828$	0.430221	0.0149512
$829$	−39.7417	−1.38029	−0.690143	−	0.723673i	$-0.742452\pi$
$829$	−39.7417	−1.38029	−0.690143	+	0.723673i	$0.742452\pi$
$830$	−5.40438	−0.187589
$831$	−14.7432	−0.511436
$832$	42.4244	1.47080
$833$	29.9690	1.03836
$834$	−17.6169	−0.610025
$835$	0.448250	0.0155123
$836$	−0.978708	−0.0338493
$837$	−4.51575	−0.156087
$838$	47.4341	1.63858
$839$	−31.9102	−1.10166	−0.550831	−	0.834617i	$-0.685689\pi$
$839$	−31.9102	−1.10166	−0.550831	+	0.834617i	$0.685689\pi$
$840$	−1.07983	−0.0372576
$841$	0	0
$842$	25.8508	0.890877
$843$	−21.5272	−0.741438
$844$	−7.36764	−0.253605
$845$	−3.30761	−0.113785
$846$	−0.590370	−0.0202973
$847$	11.4874	0.394712
$848$	29.1211	1.00002
$849$	10.3210	0.354217
$850$	33.0267	1.13281
$851$	−2.53221	−0.0868031
$852$	−4.57843	−0.156854
$853$	12.8451	0.439806	0.219903	−	0.975522i	$-0.429426\pi$
$853$	12.8451	0.439806	0.219903	+	0.975522i	$0.429426\pi$
$854$	−12.7090	−0.434893
$855$	1.36491	0.0466788
$856$	37.5371	1.28299
$857$	9.50092	0.324545	0.162273	−	0.986746i	$-0.448118\pi$
$857$	9.50092	0.324545	0.162273	+	0.986746i	$0.448118\pi$
$858$	−4.81179	−0.164272
$859$	18.5991	0.634594	0.317297	−	0.948326i	$-0.397225\pi$
$859$	18.5991	0.634594	0.317297	+	0.948326i	$0.397225\pi$
$860$	−0.715678	−0.0244044
$861$	−1.48249	−0.0505232
$862$	−46.5650	−1.58601
$863$	48.5996	1.65435	0.827175	−	0.561944i	$-0.189946\pi$
$863$	48.5996	1.65435	0.827175	+	0.561944i	$0.189946\pi$
$864$	1.70626	0.0580481
$865$	−4.33256	−0.147311
$866$	−48.8896	−1.66134
$867$	9.86239	0.334944
$868$	−1.51696	−0.0514889
$869$	−4.48313	−0.152080
$870$	0	0
$871$	−73.4191	−2.48771
$872$	−26.4124	−0.894435
$873$	−1.54591	−0.0523212
$874$	7.70231	0.260535
$875$	−3.56033	−0.120361
$876$	4.17095	0.140923
$877$	12.5576	0.424040	0.212020	−	0.977265i	$-0.431996\pi$
$877$	12.5576	0.424040	0.212020	+	0.977265i	$0.431996\pi$
$878$	8.98019	0.303067
$879$	−25.2077	−0.850233
$880$	−0.826260	−0.0278532
$881$	−14.3595	−0.483783	−0.241892	−	0.970303i	$-0.577768\pi$
$881$	−14.3595	−0.483783	−0.241892	+	0.970303i	$0.577768\pi$
$882$	−7.52937	−0.253527
$883$	−24.7519	−0.832969	−0.416484	−	0.909143i	$-0.636738\pi$
$883$	−24.7519	−0.832969	−0.416484	+	0.909143i	$0.636738\pi$
$884$	7.59015	0.255284
$885$	−1.19828	−0.0402798
$886$	−18.0051	−0.604895
$887$	17.0877	0.573749	0.286875	−	0.957968i	$-0.407384\pi$
$887$	17.0877	0.573749	0.286875	+	0.957968i	$0.407384\pi$
$888$	−5.37651	−0.180424
$889$	−16.8455	−0.564981
$890$	3.51916	0.117963
$891$	−0.768140	−0.0257337
$892$	−0.369662	−0.0123772
$893$	1.89761	0.0635011
$894$	−1.72789	−0.0577893
$895$	−2.00687	−0.0670824
$896$	−8.90615	−0.297534
$897$	−6.79872	−0.227003
$898$	−26.0786	−0.870253
$899$	0	0
$900$	1.48972	0.0496573
$901$	45.7577	1.52441
$902$	−1.34375	−0.0447421
$903$	7.95533	0.264737
$904$	−7.38610	−0.245658
$905$	−7.86329	−0.261385
$906$	18.7121	0.621669
$907$	−5.18557	−0.172184	−0.0860921	−	0.996287i	$-0.527438\pi$
$907$	−5.18557	−0.172184	−0.0860921	+	0.996287i	$0.527438\pi$
$908$	−4.86344	−0.161399
$909$	−16.1622	−0.536066
$910$	2.25424	0.0747273
$911$	−18.0436	−0.597811	−0.298905	−	0.954283i	$-0.596622\pi$
$911$	−18.0436	−0.597811	−0.298905	+	0.954283i	$0.596622\pi$
$912$	13.8057	0.457151
$913$	−9.77611	−0.323542
$914$	−31.8476	−1.05343
$915$	−2.88429	−0.0953518
$916$	4.66891	0.154265
$917$	−9.64741	−0.318586
$918$	−6.74888	−0.222746
$919$	−8.74908	−0.288605	−0.144303	−	0.989534i	$-0.546094\pi$
$919$	−8.74908	−0.288605	−0.144303	+	0.989534i	$0.546094\pi$
$920$	−1.38294	−0.0455940
$921$	17.7845	0.586020
$922$	−29.0064	−0.955274
$923$	72.3522	2.38150
$924$	−0.258038	−0.00848884
$925$	−8.76825	−0.288298
$926$	35.8223	1.17719
$927$	−10.9518	−0.359705
$928$	0	0
$929$	42.8899	1.40717	0.703587	−	0.710609i	$-0.251581\pi$
$929$	42.8899	1.40717	0.703587	+	0.710609i	$0.251581\pi$
$930$	1.91757	0.0628794
$931$	24.2014	0.793170
$932$	−3.95291	−0.129482
$933$	−8.39849	−0.274954
$934$	30.9203	1.01174
$935$	−1.29830	−0.0424588
$936$	−14.4354	−0.471834
$937$	16.6746	0.544736	0.272368	−	0.962193i	$-0.412193\pi$
$937$	16.6746	0.544736	0.272368	+	0.962193i	$0.412193\pi$
$938$	21.9298	0.716033
$939$	−2.10022	−0.0685381
$940$	−0.0450088	−0.00146802
$941$	16.5970	0.541047	0.270523	−	0.962713i	$-0.412803\pi$
$941$	16.5970	0.541047	0.270523	+	0.962713i	$0.412803\pi$
$942$	−17.1793	−0.559733
$943$	−1.89863	−0.0618278
$944$	−12.1203	−0.394483
$945$	0.359860	0.0117063
$946$	7.21083	0.234444
$947$	−45.0452	−1.46377	−0.731886	−	0.681427i	$-0.761360\pi$
$947$	−45.0452	−1.46377	−0.731886	+	0.681427i	$0.761360\pi$
$948$	−1.77669	−0.0577043
$949$	−65.9130	−2.13963
$950$	26.6707	0.865311
$951$	−5.02786	−0.163039
$952$	−17.1619	−0.556221
$953$	19.3815	0.627829	0.313915	−	0.949451i	$-0.398359\pi$
$953$	19.3815	0.627829	0.313915	+	0.949451i	$0.398359\pi$
$954$	−11.4961	−0.372201
$955$	−1.68130	−0.0544057
$956$	−0.0776451	−0.00251122
$957$	0	0
$958$	34.0835	1.10119
$959$	25.7119	0.830282
$960$	−2.87587	−0.0928183
$961$	−10.6080	−0.342194
$962$	11.2240	0.361875
$963$	−12.5095	−0.403113
$964$	−2.55591	−0.0823203
$965$	−0.904605	−0.0291203
$966$	2.03073	0.0653377
$967$	−25.8312	−0.830677	−0.415338	−	0.909667i	$-0.636337\pi$
$967$	−25.8312	−0.830677	−0.415338	+	0.909667i	$0.636337\pi$
$968$	31.2370	1.00400
$969$	21.6927	0.696870
$970$	0.656456	0.0210775
$971$	−28.2138	−0.905424	−0.452712	−	0.891657i	$-0.649543\pi$
$971$	−28.2138	−0.905424	−0.452712	+	0.891657i	$0.649543\pi$
$972$	−0.304418	−0.00976423
$973$	14.9295	0.478616
$974$	−21.2449	−0.680729
$975$	−23.5418	−0.753942
$976$	−29.1739	−0.933833
$977$	28.5608	0.913740	0.456870	−	0.889534i	$-0.348971\pi$
$977$	28.5608	0.913740	0.456870	+	0.889534i	$0.348971\pi$
$978$	−3.92045	−0.125362
$979$	6.36590	0.203455
$980$	−0.574026	−0.0183366
$981$	8.80210	0.281030
$982$	42.8422	1.36715
$983$	22.7065	0.724226	0.362113	−	0.932134i	$-0.382055\pi$
$983$	22.7065	0.724226	0.362113	+	0.932134i	$0.382055\pi$
$984$	−4.03126	−0.128512
$985$	−8.05143	−0.256540
$986$	0	0
$987$	0.500309	0.0159250
$988$	6.12942	0.195003
$989$	10.1884	0.323972
$990$	0.326183	0.0103668
$991$	−46.9070	−1.49005	−0.745026	−	0.667036i	$-0.767563\pi$
$991$	−46.9070	−1.49005	−0.745026	+	0.667036i	$0.767563\pi$
$992$	−7.70504	−0.244635
$993$	−3.80922	−0.120882
$994$	−21.6111	−0.685463
$995$	1.71441	0.0543504
$996$	−3.87433	−0.122763
$997$	−36.3093	−1.14993	−0.574963	−	0.818179i	$-0.694984\pi$
$997$	−36.3093	−1.14993	−0.574963	+	0.818179i	$0.694984\pi$
$998$	−28.8606	−0.913567
$999$	1.79176	0.0566888

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2523.2.a.s.1.10		12
3.2	odd	2		7569.2.a.bt.1.3		12
29.2	odd	28		87.2.i.a.4.3	✓	24
29.15	odd	28		87.2.i.a.22.3	yes	24
29.28	even	2		2523.2.a.v.1.3		12
87.2	even	28		261.2.o.b.91.2		24
87.44	even	28		261.2.o.b.109.2		24
87.86	odd	2		7569.2.a.bn.1.10		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.2.i.a.4.3	✓	24	29.2	odd	28
87.2.i.a.22.3	yes	24	29.15	odd	28
261.2.o.b.91.2		24	87.2	even	28
261.2.o.b.109.2		24	87.44	even	28
2523.2.a.s.1.10		12	1.1	even	1	trivial
2523.2.a.v.1.3		12	29.28	even	2
7569.2.a.bn.1.10		12	87.86	odd	2
7569.2.a.bt.1.3		12	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2523 = 3 \cdot 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2523.a (trivial)

\(f(q)\)	\(=\)	\(q+1.30214 q^{2} +1.00000 q^{3} -0.304418 q^{4} -0.326108 q^{5} +1.30214 q^{6} -1.10350 q^{7} -3.00069 q^{8} +1.00000 q^{9} -0.424639 q^{10} -0.768140 q^{11} -0.304418 q^{12} +4.81068 q^{13} -1.43692 q^{14} -0.326108 q^{15} -3.29849 q^{16} -5.18289 q^{17} +1.30214 q^{18} -4.18544 q^{19} +0.0992732 q^{20} -1.10350 q^{21} -1.00023 q^{22} -1.41325 q^{23} -3.00069 q^{24} -4.89365 q^{25} +6.26421 q^{26} +1.00000 q^{27} +0.335926 q^{28} -0.424639 q^{30} -4.51575 q^{31} +1.70626 q^{32} -0.768140 q^{33} -6.74888 q^{34} +0.359860 q^{35} -0.304418 q^{36} +1.79176 q^{37} -5.45006 q^{38} +4.81068 q^{39} +0.978547 q^{40} +1.34344 q^{41} -1.43692 q^{42} -7.20917 q^{43} +0.233836 q^{44} -0.326108 q^{45} -1.84026 q^{46} -0.453383 q^{47} -3.29849 q^{48} -5.78229 q^{49} -6.37225 q^{50} -5.18289 q^{51} -1.46446 q^{52} -8.82860 q^{53} +1.30214 q^{54} +0.250496 q^{55} +3.31126 q^{56} -4.18544 q^{57} +3.67450 q^{59} +0.0992732 q^{60} +8.84461 q^{61} -5.88016 q^{62} -1.10350 q^{63} +8.81878 q^{64} -1.56880 q^{65} -1.00023 q^{66} -15.2617 q^{67} +1.57777 q^{68} -1.41325 q^{69} +0.468590 q^{70} +15.0399 q^{71} -3.00069 q^{72} -13.7014 q^{73} +2.33313 q^{74} -4.89365 q^{75} +1.27413 q^{76} +0.847644 q^{77} +6.26421 q^{78} +5.83635 q^{79} +1.07566 q^{80} +1.00000 q^{81} +1.74936 q^{82} +12.7270 q^{83} +0.335926 q^{84} +1.69018 q^{85} -9.38739 q^{86} +2.30495 q^{88} -8.28742 q^{89} -0.424639 q^{90} -5.30860 q^{91} +0.430221 q^{92} -4.51575 q^{93} -0.590370 q^{94} +1.36491 q^{95} +1.70626 q^{96} -1.54591 q^{97} -7.52937 q^{98} -0.768140 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} + 12 q^{3} + 8 q^{4} + 2 q^{5} - 6 q^{6} - 10 q^{7} + 12 q^{9} - 20 q^{10} - 14 q^{11} + 8 q^{12} - 16 q^{13} + 2 q^{15} - 4 q^{16} - 22 q^{17} - 6 q^{18} - 16 q^{19} + 4 q^{20} - 10 q^{21}+ \cdots - 14 q^{99}+O(q^{100}) \) 12 * q - 6 * q^2 + 12 * q^3 + 8 * q^4 + 2 * q^5 - 6 * q^6 - 10 * q^7 + 12 * q^9 - 20 * q^10 - 14 * q^11 + 8 * q^12 - 16 * q^13 + 2 * q^15 - 4 * q^16 - 22 * q^17 - 6 * q^18 - 16 * q^19 + 4 * q^20 - 10 * q^21 + 12 * q^22 + 2 * q^23 - 2 * q^25 + 8 * q^26 + 12 * q^27 - 4 * q^28 - 20 * q^30 - 4 * q^31 - 16 * q^32 - 14 * q^33 - 10 * q^34 - 14 * q^35 + 8 * q^36 - 28 * q^37 + 16 * q^38 - 16 * q^39 - 32 * q^40 + 14 * q^41 - 36 * q^43 - 26 * q^44 + 2 * q^45 - 24 * q^46 - 44 * q^47 - 4 * q^48 - 18 * q^49 - 24 * q^50 - 22 * q^51 - 20 * q^52 - 18 * q^53 - 6 * q^54 - 4 * q^55 + 10 * q^56 - 16 * q^57 + 14 * q^59 + 4 * q^60 - 24 * q^61 + 4 * q^62 - 10 * q^63 - 18 * q^64 + 2 * q^65 + 12 * q^66 - 18 * q^67 - 52 * q^68 + 2 * q^69 + 36 * q^70 + 14 * q^71 - 44 * q^73 + 12 * q^74 - 2 * q^75 - 56 * q^76 - 32 * q^77 + 8 * q^78 - 24 * q^79 + 52 * q^80 + 12 * q^81 + 52 * q^82 + 26 * q^83 - 4 * q^84 - 48 * q^85 + 64 * q^86 - 10 * q^88 - 10 * q^89 - 20 * q^90 - 10 * q^91 + 64 * q^92 - 4 * q^93 - 8 * q^94 + 4 * q^95 - 16 * q^96 - 28 * q^97 - 6 * q^98 - 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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