LMFDB - Embedded newform 4598.2.a.w.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4598,2,Mod(1,4598)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4598, 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("4598.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4598 = 2 \cdot 11^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4598.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:	$36.7152148494$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.73205$ of defining polynomial
Character	$\chi$	$=$	4598.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.732051 q^{5} +1.00000 q^{6} +0.267949 q^{7} -1.00000 q^{8} -2.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.732051 q^{5} +1.00000 q^{6} +0.267949 q^{7} -1.00000 q^{8} -2.00000 q^{9} +0.732051 q^{10} -1.00000 q^{12} -3.46410 q^{13} -0.267949 q^{14} +0.732051 q^{15} +1.00000 q^{16} -7.46410 q^{17} +2.00000 q^{18} +1.00000 q^{19} -0.732051 q^{20} -0.267949 q^{21} -1.00000 q^{23} +1.00000 q^{24} -4.46410 q^{25} +3.46410 q^{26} +5.00000 q^{27} +0.267949 q^{28} +1.73205 q^{29} -0.732051 q^{30} -1.46410 q^{31} -1.00000 q^{32} +7.46410 q^{34} -0.196152 q^{35} -2.00000 q^{36} -6.46410 q^{37} -1.00000 q^{38} +3.46410 q^{39} +0.732051 q^{40} -10.7321 q^{41} +0.267949 q^{42} +4.92820 q^{43} +1.46410 q^{45} +1.00000 q^{46} +12.4641 q^{47} -1.00000 q^{48} -6.92820 q^{49} +4.46410 q^{50} +7.46410 q^{51} -3.46410 q^{52} -9.92820 q^{53} -5.00000 q^{54} -0.267949 q^{56} -1.00000 q^{57} -1.73205 q^{58} -9.39230 q^{59} +0.732051 q^{60} +1.26795 q^{61} +1.46410 q^{62} -0.535898 q^{63} +1.00000 q^{64} +2.53590 q^{65} +14.0000 q^{67} -7.46410 q^{68} +1.00000 q^{69} +0.196152 q^{70} +14.1962 q^{71} +2.00000 q^{72} +2.00000 q^{73} +6.46410 q^{74} +4.46410 q^{75} +1.00000 q^{76} -3.46410 q^{78} -2.19615 q^{79} -0.732051 q^{80} +1.00000 q^{81} +10.7321 q^{82} -3.80385 q^{83} -0.267949 q^{84} +5.46410 q^{85} -4.92820 q^{86} -1.73205 q^{87} +12.1962 q^{89} -1.46410 q^{90} -0.928203 q^{91} -1.00000 q^{92} +1.46410 q^{93} -12.4641 q^{94} -0.732051 q^{95} +1.00000 q^{96} +13.4641 q^{97} +6.92820 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} + 4 q^{7} - 2 q^{8} - 4 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 + 4 * q^7 - 2 * q^8 - 4 * q^9	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} + 4 q^{7} - 2 q^{8} - 4 q^{9} - 2 q^{10} - 2 q^{12} - 4 q^{14} - 2 q^{15} + 2 q^{16} - 8 q^{17} + 4 q^{18} + 2 q^{19} + 2 q^{20} - 4 q^{21} - 2 q^{23} + 2 q^{24} - 2 q^{25} + 10 q^{27} + 4 q^{28} + 2 q^{30} + 4 q^{31} - 2 q^{32} + 8 q^{34} + 10 q^{35} - 4 q^{36} - 6 q^{37} - 2 q^{38} - 2 q^{40} - 18 q^{41} + 4 q^{42} - 4 q^{43} - 4 q^{45} + 2 q^{46} + 18 q^{47} - 2 q^{48} + 2 q^{50} + 8 q^{51} - 6 q^{53} - 10 q^{54} - 4 q^{56} - 2 q^{57} + 2 q^{59} - 2 q^{60} + 6 q^{61} - 4 q^{62} - 8 q^{63} + 2 q^{64} + 12 q^{65} + 28 q^{67} - 8 q^{68} + 2 q^{69} - 10 q^{70} + 18 q^{71} + 4 q^{72} + 4 q^{73} + 6 q^{74} + 2 q^{75} + 2 q^{76} + 6 q^{79} + 2 q^{80} + 2 q^{81} + 18 q^{82} - 18 q^{83} - 4 q^{84} + 4 q^{85} + 4 q^{86} + 14 q^{89} + 4 q^{90} + 12 q^{91} - 2 q^{92} - 4 q^{93} - 18 q^{94} + 2 q^{95} + 2 q^{96} + 20 q^{97}+O(q^{100}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 + 4 * q^7 - 2 * q^8 - 4 * q^9 - 2 * q^10 - 2 * q^12 - 4 * q^14 - 2 * q^15 + 2 * q^16 - 8 * q^17 + 4 * q^18 + 2 * q^19 + 2 * q^20 - 4 * q^21 - 2 * q^23 + 2 * q^24 - 2 * q^25 + 10 * q^27 + 4 * q^28 + 2 * q^30 + 4 * q^31 - 2 * q^32 + 8 * q^34 + 10 * q^35 - 4 * q^36 - 6 * q^37 - 2 * q^38 - 2 * q^40 - 18 * q^41 + 4 * q^42 - 4 * q^43 - 4 * q^45 + 2 * q^46 + 18 * q^47 - 2 * q^48 + 2 * q^50 + 8 * q^51 - 6 * q^53 - 10 * q^54 - 4 * q^56 - 2 * q^57 + 2 * q^59 - 2 * q^60 + 6 * q^61 - 4 * q^62 - 8 * q^63 + 2 * q^64 + 12 * q^65 + 28 * q^67 - 8 * q^68 + 2 * q^69 - 10 * q^70 + 18 * q^71 + 4 * q^72 + 4 * q^73 + 6 * q^74 + 2 * q^75 + 2 * q^76 + 6 * q^79 + 2 * q^80 + 2 * q^81 + 18 * q^82 - 18 * q^83 - 4 * q^84 + 4 * q^85 + 4 * q^86 + 14 * q^89 + 4 * q^90 + 12 * q^91 - 2 * q^92 - 4 * q^93 - 18 * q^94 + 2 * q^95 + 2 * q^96 + 20 * q^97

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350	−0.288675	−	0.957427i	$-0.593215\pi$
$3$	−1.00000	−0.577350	−0.288675	+	0.957427i	$0.593215\pi$
$4$	1.00000	0.500000
$5$	−0.732051	−0.327383	−0.163692	−	0.986512i	$-0.552340\pi$
$5$	−0.732051	−0.327383	−0.163692	+	0.986512i	$0.552340\pi$
$6$	1.00000	0.408248
$7$	0.267949	0.101275	0.0506376	−	0.998717i	$-0.483875\pi$
$7$	0.267949	0.101275	0.0506376	+	0.998717i	$0.483875\pi$
$8$	−1.00000	−0.353553
$9$	−2.00000	−0.666667
$10$	0.732051	0.231495
$11$	0	0
$11$	0	0
$12$	−1.00000	−0.288675
$13$	−3.46410	−0.960769	−0.480384	−	0.877058i	$-0.659503\pi$
$13$	−3.46410	−0.960769	−0.480384	+	0.877058i	$0.659503\pi$
$14$	−0.267949	−0.0716124
$15$	0.732051	0.189015
$16$	1.00000	0.250000
$17$	−7.46410	−1.81031	−0.905155	−	0.425081i	$-0.860246\pi$
$17$	−7.46410	−1.81031	−0.905155	+	0.425081i	$0.860246\pi$
$18$	2.00000	0.471405
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−0.732051	−0.163692
$21$	−0.267949	−0.0584713
$22$	0	0
$23$	−1.00000	−0.208514	−0.104257	−	0.994550i	$-0.533247\pi$
$23$	−1.00000	−0.208514	−0.104257	+	0.994550i	$0.533247\pi$
$24$	1.00000	0.204124
$25$	−4.46410	−0.892820
$26$	3.46410	0.679366
$27$	5.00000	0.962250
$28$	0.267949	0.0506376
$29$	1.73205	0.321634	0.160817	−	0.986984i	$-0.448587\pi$
$29$	1.73205	0.321634	0.160817	+	0.986984i	$0.448587\pi$
$30$	−0.732051	−0.133654
$31$	−1.46410	−0.262960	−0.131480	−	0.991319i	$-0.541973\pi$
$31$	−1.46410	−0.262960	−0.131480	+	0.991319i	$0.541973\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	7.46410	1.28008
$35$	−0.196152	−0.0331558
$36$	−2.00000	−0.333333
$37$	−6.46410	−1.06269	−0.531346	−	0.847155i	$-0.678314\pi$
$37$	−6.46410	−1.06269	−0.531346	+	0.847155i	$0.678314\pi$
$38$	−1.00000	−0.162221
$39$	3.46410	0.554700
$40$	0.732051	0.115747
$41$	−10.7321	−1.67606	−0.838032	−	0.545621i	$-0.816294\pi$
$41$	−10.7321	−1.67606	−0.838032	+	0.545621i	$0.816294\pi$
$42$	0.267949	0.0413455
$43$	4.92820	0.751544	0.375772	−	0.926712i	$-0.377378\pi$
$43$	4.92820	0.751544	0.375772	+	0.926712i	$0.377378\pi$
$44$	0	0
$45$	1.46410	0.218255
$46$	1.00000	0.147442
$47$	12.4641	1.81808	0.909038	−	0.416713i	$-0.136818\pi$
$47$	12.4641	1.81808	0.909038	+	0.416713i	$0.136818\pi$
$48$	−1.00000	−0.144338
$49$	−6.92820	−0.989743
$50$	4.46410	0.631319
$51$	7.46410	1.04518
$52$	−3.46410	−0.480384
$53$	−9.92820	−1.36374	−0.681872	−	0.731472i	$-0.738834\pi$
$53$	−9.92820	−1.36374	−0.681872	+	0.731472i	$0.738834\pi$
$54$	−5.00000	−0.680414
$55$	0	0
$56$	−0.267949	−0.0358062
$57$	−1.00000	−0.132453
$58$	−1.73205	−0.227429
$59$	−9.39230	−1.22277	−0.611387	−	0.791332i	$-0.709388\pi$
$59$	−9.39230	−1.22277	−0.611387	+	0.791332i	$0.709388\pi$
$60$	0.732051	0.0945074
$61$	1.26795	0.162344	0.0811721	−	0.996700i	$-0.474134\pi$
$61$	1.26795	0.162344	0.0811721	+	0.996700i	$0.474134\pi$
$62$	1.46410	0.185941
$63$	−0.535898	−0.0675169
$64$	1.00000	0.125000
$65$	2.53590	0.314539
$66$	0	0
$67$	14.0000	1.71037	0.855186	−	0.518321i	$-0.173443\pi$
$67$	14.0000	1.71037	0.855186	+	0.518321i	$0.173443\pi$
$68$	−7.46410	−0.905155
$69$	1.00000	0.120386
$70$	0.196152	0.0234447
$71$	14.1962	1.68477	0.842387	−	0.538874i	$-0.181150\pi$
$71$	14.1962	1.68477	0.842387	+	0.538874i	$0.181150\pi$
$72$	2.00000	0.235702
$73$	2.00000	0.234082	0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000	0.234082	0.117041	+	0.993127i	$0.462659\pi$
$74$	6.46410	0.751437
$75$	4.46410	0.515470
$76$	1.00000	0.114708
$77$	0	0
$78$	−3.46410	−0.392232
$79$	−2.19615	−0.247086	−0.123543	−	0.992339i	$-0.539426\pi$
$79$	−2.19615	−0.247086	−0.123543	+	0.992339i	$0.539426\pi$
$80$	−0.732051	−0.0818458
$81$	1.00000	0.111111
$82$	10.7321	1.18516
$83$	−3.80385	−0.417527	−0.208763	−	0.977966i	$-0.566944\pi$
$83$	−3.80385	−0.417527	−0.208763	+	0.977966i	$0.566944\pi$
$84$	−0.267949	−0.0292357
$85$	5.46410	0.592665
$86$	−4.92820	−0.531422
$87$	−1.73205	−0.185695
$88$	0	0
$89$	12.1962	1.29279	0.646395	−	0.763003i	$-0.276276\pi$
$89$	12.1962	1.29279	0.646395	+	0.763003i	$0.276276\pi$
$90$	−1.46410	−0.154330
$91$	−0.928203	−0.0973021
$92$	−1.00000	−0.104257
$93$	1.46410	0.151820
$94$	−12.4641	−1.28557
$95$	−0.732051	−0.0751068
$96$	1.00000	0.102062
$97$	13.4641	1.36707	0.683536	−	0.729917i	$-0.260441\pi$
$97$	13.4641	1.36707	0.683536	+	0.729917i	$0.260441\pi$
$98$	6.92820	0.699854
$99$	0	0
$100$	−4.46410	−0.446410
$101$	−16.5885	−1.65061	−0.825307	−	0.564685i	$-0.808998\pi$
$101$	−16.5885	−1.65061	−0.825307	+	0.564685i	$0.808998\pi$
$102$	−7.46410	−0.739056
$103$	−2.73205	−0.269197	−0.134598	−	0.990900i	$-0.542974\pi$
$103$	−2.73205	−0.269197	−0.134598	+	0.990900i	$0.542974\pi$
$104$	3.46410	0.339683
$105$	0.196152	0.0191425
$106$	9.92820	0.964312
$107$	−2.80385	−0.271058	−0.135529	−	0.990773i	$-0.543273\pi$
$107$	−2.80385	−0.271058	−0.135529	+	0.990773i	$0.543273\pi$
$108$	5.00000	0.481125
$109$	−6.12436	−0.586607	−0.293303	−	0.956019i	$-0.594755\pi$
$109$	−6.12436	−0.586607	−0.293303	+	0.956019i	$0.594755\pi$
$110$	0	0
$111$	6.46410	0.613545
$112$	0.267949	0.0253188
$113$	−4.73205	−0.445154	−0.222577	−	0.974915i	$-0.571447\pi$
$113$	−4.73205	−0.445154	−0.222577	+	0.974915i	$0.571447\pi$
$114$	1.00000	0.0936586
$115$	0.732051	0.0682641
$116$	1.73205	0.160817
$117$	6.92820	0.640513
$118$	9.39230	0.864632
$119$	−2.00000	−0.183340
$120$	−0.732051	−0.0668268
$121$	0	0
$122$	−1.26795	−0.114795
$123$	10.7321	0.967676
$124$	−1.46410	−0.131480
$125$	6.92820	0.619677
$126$	0.535898	0.0477416
$127$	4.00000	0.354943	0.177471	−	0.984126i	$-0.443208\pi$
$127$	4.00000	0.354943	0.177471	+	0.984126i	$0.443208\pi$
$128$	−1.00000	−0.0883883
$129$	−4.92820	−0.433904
$130$	−2.53590	−0.222413
$131$	−20.9282	−1.82851	−0.914253	−	0.405144i	$-0.867221\pi$
$131$	−20.9282	−1.82851	−0.914253	+	0.405144i	$0.867221\pi$
$132$	0	0
$133$	0.267949	0.0232341
$134$	−14.0000	−1.20942
$135$	−3.66025	−0.315025
$136$	7.46410	0.640041
$137$	9.46410	0.808573	0.404286	−	0.914632i	$-0.367520\pi$
$137$	9.46410	0.808573	0.404286	+	0.914632i	$0.367520\pi$
$138$	−1.00000	−0.0851257
$139$	−6.53590	−0.554368	−0.277184	−	0.960817i	$-0.589401\pi$
$139$	−6.53590	−0.554368	−0.277184	+	0.960817i	$0.589401\pi$
$140$	−0.196152	−0.0165779
$141$	−12.4641	−1.04967
$142$	−14.1962	−1.19131
$143$	0	0
$144$	−2.00000	−0.166667
$145$	−1.26795	−0.105297
$146$	−2.00000	−0.165521
$147$	6.92820	0.571429
$148$	−6.46410	−0.531346
$149$	11.3205	0.927412	0.463706	−	0.885989i	$-0.346519\pi$
$149$	11.3205	0.927412	0.463706	+	0.885989i	$0.346519\pi$
$150$	−4.46410	−0.364492
$151$	−20.7321	−1.68715	−0.843575	−	0.537011i	$-0.819553\pi$
$151$	−20.7321	−1.68715	−0.843575	+	0.537011i	$0.819553\pi$
$152$	−1.00000	−0.0811107
$153$	14.9282	1.20687
$154$	0	0
$155$	1.07180	0.0860888
$156$	3.46410	0.277350
$157$	−5.26795	−0.420428	−0.210214	−	0.977655i	$-0.567416\pi$
$157$	−5.26795	−0.420428	−0.210214	+	0.977655i	$0.567416\pi$
$158$	2.19615	0.174717
$159$	9.92820	0.787358
$160$	0.732051	0.0578737
$161$	−0.267949	−0.0211174
$162$	−1.00000	−0.0785674
$163$	17.3205	1.35665	0.678323	−	0.734763i	$-0.262707\pi$
$163$	17.3205	1.35665	0.678323	+	0.734763i	$0.262707\pi$
$164$	−10.7321	−0.838032
$165$	0	0
$166$	3.80385	0.295236
$167$	−3.46410	−0.268060	−0.134030	−	0.990977i	$-0.542792\pi$
$167$	−3.46410	−0.268060	−0.134030	+	0.990977i	$0.542792\pi$
$168$	0.267949	0.0206727
$169$	−1.00000	−0.0769231
$170$	−5.46410	−0.419077
$171$	−2.00000	−0.152944
$172$	4.92820	0.375772
$173$	−4.12436	−0.313569	−0.156784	−	0.987633i	$-0.550113\pi$
$173$	−4.12436	−0.313569	−0.156784	+	0.987633i	$0.550113\pi$
$174$	1.73205	0.131306
$175$	−1.19615	−0.0904206
$176$	0	0
$177$	9.39230	0.705969
$178$	−12.1962	−0.914140
$179$	−2.07180	−0.154853	−0.0774267	−	0.996998i	$-0.524670\pi$
$179$	−2.07180	−0.154853	−0.0774267	+	0.996998i	$0.524670\pi$
$180$	1.46410	0.109128
$181$	24.3923	1.81307	0.906533	−	0.422135i	$-0.138719\pi$
$181$	24.3923	1.81307	0.906533	+	0.422135i	$0.138719\pi$
$182$	0.928203	0.0688030
$183$	−1.26795	−0.0937295
$184$	1.00000	0.0737210
$185$	4.73205	0.347907
$186$	−1.46410	−0.107353
$187$	0	0
$188$	12.4641	0.909038
$189$	1.33975	0.0974522
$190$	0.732051	0.0531085
$191$	−17.3923	−1.25846	−0.629232	−	0.777218i	$-0.716630\pi$
$191$	−17.3923	−1.25846	−0.629232	+	0.777218i	$0.716630\pi$
$192$	−1.00000	−0.0721688
$193$	12.5359	0.902354	0.451177	−	0.892435i	$-0.351004\pi$
$193$	12.5359	0.902354	0.451177	+	0.892435i	$0.351004\pi$
$194$	−13.4641	−0.966666
$195$	−2.53590	−0.181599
$196$	−6.92820	−0.494872
$197$	5.07180	0.361351	0.180675	−	0.983543i	$-0.442172\pi$
$197$	5.07180	0.361351	0.180675	+	0.983543i	$0.442172\pi$
$198$	0	0
$199$	16.9282	1.20001	0.600004	−	0.799997i	$-0.295166\pi$
$199$	16.9282	1.20001	0.600004	+	0.799997i	$0.295166\pi$
$200$	4.46410	0.315660
$201$	−14.0000	−0.987484
$202$	16.5885	1.16716
$203$	0.464102	0.0325735
$204$	7.46410	0.522592
$205$	7.85641	0.548715
$206$	2.73205	0.190351
$207$	2.00000	0.139010
$208$	−3.46410	−0.240192
$209$	0	0
$210$	−0.196152	−0.0135358
$211$	−4.12436	−0.283932	−0.141966	−	0.989872i	$-0.545342\pi$
$211$	−4.12436	−0.283932	−0.141966	+	0.989872i	$0.545342\pi$
$212$	−9.92820	−0.681872
$213$	−14.1962	−0.972704
$214$	2.80385	0.191667
$215$	−3.60770	−0.246043
$216$	−5.00000	−0.340207
$217$	−0.392305	−0.0266314
$218$	6.12436	0.414794
$219$	−2.00000	−0.135147
$220$	0	0
$221$	25.8564	1.73929
$222$	−6.46410	−0.433842
$223$	13.1244	0.878872	0.439436	−	0.898274i	$-0.355178\pi$
$223$	13.1244	0.878872	0.439436	+	0.898274i	$0.355178\pi$
$224$	−0.267949	−0.0179031
$225$	8.92820	0.595214
$226$	4.73205	0.314771
$227$	8.39230	0.557017	0.278508	−	0.960434i	$-0.410160\pi$
$227$	8.39230	0.557017	0.278508	+	0.960434i	$0.410160\pi$
$228$	−1.00000	−0.0662266
$229$	−12.3923	−0.818907	−0.409453	−	0.912331i	$-0.634281\pi$
$229$	−12.3923	−0.818907	−0.409453	+	0.912331i	$0.634281\pi$
$230$	−0.732051	−0.0482700
$231$	0	0
$232$	−1.73205	−0.113715
$233$	−8.26795	−0.541651	−0.270826	−	0.962628i	$-0.587297\pi$
$233$	−8.26795	−0.541651	−0.270826	+	0.962628i	$0.587297\pi$
$234$	−6.92820	−0.452911
$235$	−9.12436	−0.595207
$236$	−9.39230	−0.611387
$237$	2.19615	0.142655
$238$	2.00000	0.129641
$239$	−14.1244	−0.913629	−0.456814	−	0.889562i	$-0.651010\pi$
$239$	−14.1244	−0.913629	−0.456814	+	0.889562i	$0.651010\pi$
$240$	0.732051	0.0472537
$241$	11.2679	0.725832	0.362916	−	0.931822i	$-0.381781\pi$
$241$	11.2679	0.725832	0.362916	+	0.931822i	$0.381781\pi$
$242$	0	0
$243$	−16.0000	−1.02640
$244$	1.26795	0.0811721
$245$	5.07180	0.324025
$246$	−10.7321	−0.684251
$247$	−3.46410	−0.220416
$248$	1.46410	0.0929705
$249$	3.80385	0.241059
$250$	−6.92820	−0.438178
$251$	8.53590	0.538781	0.269391	−	0.963031i	$-0.413178\pi$
$251$	8.53590	0.538781	0.269391	+	0.963031i	$0.413178\pi$
$252$	−0.535898	−0.0337584
$253$	0	0
$254$	−4.00000	−0.250982
$255$	−5.46410	−0.342175
$256$	1.00000	0.0625000
$257$	−3.32051	−0.207128	−0.103564	−	0.994623i	$-0.533025\pi$
$257$	−3.32051	−0.207128	−0.103564	+	0.994623i	$0.533025\pi$
$258$	4.92820	0.306817
$259$	−1.73205	−0.107624
$260$	2.53590	0.157270
$261$	−3.46410	−0.214423
$262$	20.9282	1.29295
$263$	24.7846	1.52828	0.764142	−	0.645048i	$-0.223163\pi$
$263$	24.7846	1.52828	0.764142	+	0.645048i	$0.223163\pi$
$264$	0	0
$265$	7.26795	0.446467
$266$	−0.267949	−0.0164290
$267$	−12.1962	−0.746392
$268$	14.0000	0.855186
$269$	−29.7846	−1.81600	−0.908000	−	0.418970i	$-0.862391\pi$
$269$	−29.7846	−1.81600	−0.908000	+	0.418970i	$0.862391\pi$
$270$	3.66025	0.222756
$271$	−7.32051	−0.444689	−0.222345	−	0.974968i	$-0.571371\pi$
$271$	−7.32051	−0.444689	−0.222345	+	0.974968i	$0.571371\pi$
$272$	−7.46410	−0.452578
$273$	0.928203	0.0561774
$274$	−9.46410	−0.571747
$275$	0	0
$276$	1.00000	0.0601929
$277$	15.1244	0.908734	0.454367	−	0.890814i	$-0.349865\pi$
$277$	15.1244	0.908734	0.454367	+	0.890814i	$0.349865\pi$
$278$	6.53590	0.391997
$279$	2.92820	0.175307
$280$	0.196152	0.0117223
$281$	16.0526	0.957615	0.478808	−	0.877920i	$-0.341069\pi$
$281$	16.0526	0.957615	0.478808	+	0.877920i	$0.341069\pi$
$282$	12.4641	0.742226
$283$	21.4641	1.27591	0.637954	−	0.770074i	$-0.279781\pi$
$283$	21.4641	1.27591	0.637954	+	0.770074i	$0.279781\pi$
$284$	14.1962	0.842387
$285$	0.732051	0.0433629
$286$	0	0
$287$	−2.87564	−0.169744
$288$	2.00000	0.117851
$289$	38.7128	2.27722
$290$	1.26795	0.0744565
$291$	−13.4641	−0.789280
$292$	2.00000	0.117041
$293$	12.1244	0.708312	0.354156	−	0.935186i	$-0.384768\pi$
$293$	12.1244	0.708312	0.354156	+	0.935186i	$0.384768\pi$
$294$	−6.92820	−0.404061
$295$	6.87564	0.400315
$296$	6.46410	0.375718
$297$	0	0
$298$	−11.3205	−0.655779
$299$	3.46410	0.200334
$300$	4.46410	0.257735
$301$	1.32051	0.0761128
$302$	20.7321	1.19300
$303$	16.5885	0.952982
$304$	1.00000	0.0573539
$305$	−0.928203	−0.0531488
$306$	−14.9282	−0.853389
$307$	15.5885	0.889680	0.444840	−	0.895610i	$-0.353260\pi$
$307$	15.5885	0.889680	0.444840	+	0.895610i	$0.353260\pi$
$308$	0	0
$309$	2.73205	0.155421
$310$	−1.07180	−0.0608740
$311$	−1.60770	−0.0911640	−0.0455820	−	0.998961i	$-0.514514\pi$
$311$	−1.60770	−0.0911640	−0.0455820	+	0.998961i	$0.514514\pi$
$312$	−3.46410	−0.196116
$313$	13.5359	0.765094	0.382547	−	0.923936i	$-0.375047\pi$
$313$	13.5359	0.765094	0.382547	+	0.923936i	$0.375047\pi$
$314$	5.26795	0.297288
$315$	0.392305	0.0221039
$316$	−2.19615	−0.123543
$317$	−20.7846	−1.16738	−0.583690	−	0.811977i	$-0.698392\pi$
$317$	−20.7846	−1.16738	−0.583690	+	0.811977i	$0.698392\pi$
$318$	−9.92820	−0.556746
$319$	0	0
$320$	−0.732051	−0.0409229
$321$	2.80385	0.156496
$322$	0.267949	0.0149322
$323$	−7.46410	−0.415314
$324$	1.00000	0.0555556
$325$	15.4641	0.857794
$326$	−17.3205	−0.959294
$327$	6.12436	0.338678
$328$	10.7321	0.592578
$329$	3.33975	0.184126
$330$	0	0
$331$	21.7846	1.19739	0.598695	−	0.800977i	$-0.295686\pi$
$331$	21.7846	1.19739	0.598695	+	0.800977i	$0.295686\pi$
$332$	−3.80385	−0.208763
$333$	12.9282	0.708461
$334$	3.46410	0.189547
$335$	−10.2487	−0.559947
$336$	−0.267949	−0.0146178
$337$	−24.1962	−1.31805	−0.659024	−	0.752122i	$-0.729031\pi$
$337$	−24.1962	−1.31805	−0.659024	+	0.752122i	$0.729031\pi$
$338$	1.00000	0.0543928
$339$	4.73205	0.257010
$340$	5.46410	0.296333
$341$	0	0
$342$	2.00000	0.108148
$343$	−3.73205	−0.201512
$344$	−4.92820	−0.265711
$345$	−0.732051	−0.0394123
$346$	4.12436	0.221727
$347$	10.0526	0.539650	0.269825	−	0.962909i	$-0.413034\pi$
$347$	10.0526	0.539650	0.269825	+	0.962909i	$0.413034\pi$
$348$	−1.73205	−0.0928477
$349$	−14.7846	−0.791402	−0.395701	−	0.918379i	$-0.629498\pi$
$349$	−14.7846	−0.791402	−0.395701	+	0.918379i	$0.629498\pi$
$350$	1.19615	0.0639370
$351$	−17.3205	−0.924500
$352$	0	0
$353$	−6.46410	−0.344049	−0.172025	−	0.985093i	$-0.555031\pi$
$353$	−6.46410	−0.344049	−0.172025	+	0.985093i	$0.555031\pi$
$354$	−9.39230	−0.499195
$355$	−10.3923	−0.551566
$356$	12.1962	0.646395
$357$	2.00000	0.105851
$358$	2.07180	0.109498
$359$	28.3923	1.49849	0.749244	−	0.662294i	$-0.230417\pi$
$359$	28.3923	1.49849	0.749244	+	0.662294i	$0.230417\pi$
$360$	−1.46410	−0.0771649
$361$	1.00000	0.0526316
$362$	−24.3923	−1.28203
$363$	0	0
$364$	−0.928203	−0.0486511
$365$	−1.46410	−0.0766346
$366$	1.26795	0.0662768
$367$	−22.8564	−1.19309	−0.596547	−	0.802578i	$-0.703461\pi$
$367$	−22.8564	−1.19309	−0.596547	+	0.802578i	$0.703461\pi$
$368$	−1.00000	−0.0521286
$369$	21.4641	1.11738
$370$	−4.73205	−0.246008
$371$	−2.66025	−0.138114
$372$	1.46410	0.0759101
$373$	−16.8038	−0.870070	−0.435035	−	0.900413i	$-0.643264\pi$
$373$	−16.8038	−0.870070	−0.435035	+	0.900413i	$0.643264\pi$
$374$	0	0
$375$	−6.92820	−0.357771
$376$	−12.4641	−0.642787
$377$	−6.00000	−0.309016
$378$	−1.33975	−0.0689091
$379$	23.9282	1.22911	0.614555	−	0.788874i	$-0.289336\pi$
$379$	23.9282	1.22911	0.614555	+	0.788874i	$0.289336\pi$
$380$	−0.732051	−0.0375534
$381$	−4.00000	−0.204926
$382$	17.3923	0.889868
$383$	33.4641	1.70994	0.854968	−	0.518681i	$-0.173577\pi$
$383$	33.4641	1.70994	0.854968	+	0.518681i	$0.173577\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−12.5359	−0.638060
$387$	−9.85641	−0.501029
$388$	13.4641	0.683536
$389$	−0.588457	−0.0298360	−0.0149180	−	0.999889i	$-0.504749\pi$
$389$	−0.588457	−0.0298360	−0.0149180	+	0.999889i	$0.504749\pi$
$390$	2.53590	0.128410
$391$	7.46410	0.377476
$392$	6.92820	0.349927
$393$	20.9282	1.05569
$394$	−5.07180	−0.255513
$395$	1.60770	0.0808919
$396$	0	0
$397$	5.60770	0.281442	0.140721	−	0.990049i	$-0.455058\pi$
$397$	5.60770	0.281442	0.140721	+	0.990049i	$0.455058\pi$
$398$	−16.9282	−0.848534
$399$	−0.267949	−0.0134142
$400$	−4.46410	−0.223205
$401$	−16.0526	−0.801627	−0.400813	−	0.916160i	$-0.631272\pi$
$401$	−16.0526	−0.801627	−0.400813	+	0.916160i	$0.631272\pi$
$402$	14.0000	0.698257
$403$	5.07180	0.252644
$404$	−16.5885	−0.825307
$405$	−0.732051	−0.0363759
$406$	−0.464102	−0.0230330
$407$	0	0
$408$	−7.46410	−0.369528
$409$	13.4641	0.665757	0.332878	−	0.942970i	$-0.391980\pi$
$409$	13.4641	0.665757	0.332878	+	0.942970i	$0.391980\pi$
$410$	−7.85641	−0.388000
$411$	−9.46410	−0.466830
$412$	−2.73205	−0.134598
$413$	−2.51666	−0.123837
$414$	−2.00000	−0.0982946
$415$	2.78461	0.136691
$416$	3.46410	0.169842
$417$	6.53590	0.320064
$418$	0	0
$419$	−32.4449	−1.58504	−0.792518	−	0.609849i	$-0.791230\pi$
$419$	−32.4449	−1.58504	−0.792518	+	0.609849i	$0.791230\pi$
$420$	0.196152	0.00957126
$421$	−1.67949	−0.0818534	−0.0409267	−	0.999162i	$-0.513031\pi$
$421$	−1.67949	−0.0818534	−0.0409267	+	0.999162i	$0.513031\pi$
$422$	4.12436	0.200770
$423$	−24.9282	−1.21205
$424$	9.92820	0.482156
$425$	33.3205	1.61628
$426$	14.1962	0.687806
$427$	0.339746	0.0164415
$428$	−2.80385	−0.135529
$429$	0	0
$430$	3.60770	0.173979
$431$	23.6603	1.13967	0.569837	−	0.821758i	$-0.307006\pi$
$431$	23.6603	1.13967	0.569837	+	0.821758i	$0.307006\pi$
$432$	5.00000	0.240563
$433$	18.7846	0.902731	0.451365	−	0.892339i	$-0.350937\pi$
$433$	18.7846	0.902731	0.451365	+	0.892339i	$0.350937\pi$
$434$	0.392305	0.0188312
$435$	1.26795	0.0607935
$436$	−6.12436	−0.293303
$437$	−1.00000	−0.0478365
$438$	2.00000	0.0955637
$439$	17.4641	0.833516	0.416758	−	0.909017i	$-0.363166\pi$
$439$	17.4641	0.833516	0.416758	+	0.909017i	$0.363166\pi$
$440$	0	0
$441$	13.8564	0.659829
$442$	−25.8564	−1.22986
$443$	18.0000	0.855206	0.427603	−	0.903967i	$-0.359358\pi$
$443$	18.0000	0.855206	0.427603	+	0.903967i	$0.359358\pi$
$444$	6.46410	0.306773
$445$	−8.92820	−0.423237
$446$	−13.1244	−0.621456
$447$	−11.3205	−0.535442
$448$	0.267949	0.0126594
$449$	27.8564	1.31463	0.657313	−	0.753618i	$-0.271693\pi$
$449$	27.8564	1.31463	0.657313	+	0.753618i	$0.271693\pi$
$450$	−8.92820	−0.420880
$451$	0	0
$452$	−4.73205	−0.222577
$453$	20.7321	0.974077
$454$	−8.39230	−0.393870
$455$	0.679492	0.0318551
$456$	1.00000	0.0468293
$457$	−25.4449	−1.19026	−0.595130	−	0.803629i	$-0.702900\pi$
$457$	−25.4449	−1.19026	−0.595130	+	0.803629i	$0.702900\pi$
$458$	12.3923	0.579054
$459$	−37.3205	−1.74197
$460$	0.732051	0.0341320
$461$	−28.1962	−1.31323	−0.656613	−	0.754228i	$-0.728011\pi$
$461$	−28.1962	−1.31323	−0.656613	+	0.754228i	$0.728011\pi$
$462$	0	0
$463$	26.0000	1.20832	0.604161	−	0.796862i	$-0.293508\pi$
$463$	26.0000	1.20832	0.604161	+	0.796862i	$0.293508\pi$
$464$	1.73205	0.0804084
$465$	−1.07180	−0.0497034
$466$	8.26795	0.383005
$467$	33.7128	1.56004	0.780021	−	0.625753i	$-0.215208\pi$
$467$	33.7128	1.56004	0.780021	+	0.625753i	$0.215208\pi$
$468$	6.92820	0.320256
$469$	3.75129	0.173218
$470$	9.12436	0.420875
$471$	5.26795	0.242734
$472$	9.39230	0.432316
$473$	0	0
$474$	−2.19615	−0.100873
$475$	−4.46410	−0.204827
$476$	−2.00000	−0.0916698
$477$	19.8564	0.909162
$478$	14.1244	0.646033
$479$	−31.7321	−1.44987	−0.724937	−	0.688815i	$-0.758131\pi$
$479$	−31.7321	−1.44987	−0.724937	+	0.688815i	$0.758131\pi$
$480$	−0.732051	−0.0334134
$481$	22.3923	1.02100
$482$	−11.2679	−0.513241
$483$	0.267949	0.0121921
$484$	0	0
$485$	−9.85641	−0.447556
$486$	16.0000	0.725775
$487$	27.1769	1.23150	0.615752	−	0.787940i	$-0.288852\pi$
$487$	27.1769	1.23150	0.615752	+	0.787940i	$0.288852\pi$
$488$	−1.26795	−0.0573974
$489$	−17.3205	−0.783260
$490$	−5.07180	−0.229120
$491$	3.60770	0.162813	0.0814065	−	0.996681i	$-0.474059\pi$
$491$	3.60770	0.162813	0.0814065	+	0.996681i	$0.474059\pi$
$492$	10.7321	0.483838
$493$	−12.9282	−0.582257
$494$	3.46410	0.155857
$495$	0	0
$496$	−1.46410	−0.0657401
$497$	3.80385	0.170626
$498$	−3.80385	−0.170454
$499$	21.2679	0.952084	0.476042	−	0.879423i	$-0.342071\pi$
$499$	21.2679	0.952084	0.476042	+	0.879423i	$0.342071\pi$
$500$	6.92820	0.309839
$501$	3.46410	0.154765
$502$	−8.53590	−0.380976
$503$	−0.660254	−0.0294393	−0.0147196	−	0.999892i	$-0.504686\pi$
$503$	−0.660254	−0.0294393	−0.0147196	+	0.999892i	$0.504686\pi$
$504$	0.535898	0.0238708
$505$	12.1436	0.540383
$506$	0	0
$507$	1.00000	0.0444116
$508$	4.00000	0.177471
$509$	33.9282	1.50384	0.751921	−	0.659254i	$-0.229128\pi$
$509$	33.9282	1.50384	0.751921	+	0.659254i	$0.229128\pi$
$510$	5.46410	0.241954
$511$	0.535898	0.0237067
$512$	−1.00000	−0.0441942
$513$	5.00000	0.220755
$514$	3.32051	0.146461
$515$	2.00000	0.0881305
$516$	−4.92820	−0.216952
$517$	0	0
$518$	1.73205	0.0761019
$519$	4.12436	0.181039
$520$	−2.53590	−0.111207
$521$	−17.3205	−0.758825	−0.379413	−	0.925228i	$-0.623874\pi$
$521$	−17.3205	−0.758825	−0.379413	+	0.925228i	$0.623874\pi$
$522$	3.46410	0.151620
$523$	9.33975	0.408399	0.204199	−	0.978929i	$-0.434541\pi$
$523$	9.33975	0.408399	0.204199	+	0.978929i	$0.434541\pi$
$524$	−20.9282	−0.914253
$525$	1.19615	0.0522044
$526$	−24.7846	−1.08066
$527$	10.9282	0.476040
$528$	0	0
$529$	−22.0000	−0.956522
$530$	−7.26795	−0.315700
$531$	18.7846	0.815183
$532$	0.267949	0.0116171
$533$	37.1769	1.61031
$534$	12.1962	0.527779
$535$	2.05256	0.0887399
$536$	−14.0000	−0.604708
$537$	2.07180	0.0894046
$538$	29.7846	1.28411
$539$	0	0
$540$	−3.66025	−0.157512
$541$	27.1769	1.16843	0.584213	−	0.811600i	$-0.301403\pi$
$541$	27.1769	1.16843	0.584213	+	0.811600i	$0.301403\pi$
$542$	7.32051	0.314443
$543$	−24.3923	−1.04677
$544$	7.46410	0.320021
$545$	4.48334	0.192045
$546$	−0.928203	−0.0397234
$547$	−4.80385	−0.205398	−0.102699	−	0.994712i	$-0.532748\pi$
$547$	−4.80385	−0.205398	−0.102699	+	0.994712i	$0.532748\pi$
$548$	9.46410	0.404286
$549$	−2.53590	−0.108230
$550$	0	0
$551$	1.73205	0.0737878
$552$	−1.00000	−0.0425628
$553$	−0.588457	−0.0250237
$554$	−15.1244	−0.642572
$555$	−4.73205	−0.200864
$556$	−6.53590	−0.277184
$557$	23.1769	0.982037	0.491019	−	0.871149i	$-0.336625\pi$
$557$	23.1769	0.982037	0.491019	+	0.871149i	$0.336625\pi$
$558$	−2.92820	−0.123961
$559$	−17.0718	−0.722060
$560$	−0.196152	−0.00828895
$561$	0	0
$562$	−16.0526	−0.677136
$563$	−24.6603	−1.03931	−0.519653	−	0.854377i	$-0.673939\pi$
$563$	−24.6603	−1.03931	−0.519653	+	0.854377i	$0.673939\pi$
$564$	−12.4641	−0.524833
$565$	3.46410	0.145736
$566$	−21.4641	−0.902203
$567$	0.267949	0.0112528
$568$	−14.1962	−0.595657
$569$	39.7128	1.66485	0.832424	−	0.554139i	$-0.186953\pi$
$569$	39.7128	1.66485	0.832424	+	0.554139i	$0.186953\pi$
$570$	−0.732051	−0.0306622
$571$	22.9808	0.961715	0.480857	−	0.876799i	$-0.340325\pi$
$571$	22.9808	0.961715	0.480857	+	0.876799i	$0.340325\pi$
$572$	0	0
$573$	17.3923	0.726574
$574$	2.87564	0.120027
$575$	4.46410	0.186166
$576$	−2.00000	−0.0833333
$577$	−33.1769	−1.38117	−0.690587	−	0.723250i	$-0.742648\pi$
$577$	−33.1769	−1.38117	−0.690587	+	0.723250i	$0.742648\pi$
$578$	−38.7128	−1.61024
$579$	−12.5359	−0.520974
$580$	−1.26795	−0.0526487
$581$	−1.01924	−0.0422851
$582$	13.4641	0.558105
$583$	0	0
$584$	−2.00000	−0.0827606
$585$	−5.07180	−0.209693
$586$	−12.1244	−0.500853
$587$	−31.3731	−1.29491	−0.647453	−	0.762106i	$-0.724166\pi$
$587$	−31.3731	−1.29491	−0.647453	+	0.762106i	$0.724166\pi$
$588$	6.92820	0.285714
$589$	−1.46410	−0.0603273
$590$	−6.87564	−0.283066
$591$	−5.07180	−0.208626
$592$	−6.46410	−0.265673
$593$	−1.87564	−0.0770235	−0.0385117	−	0.999258i	$-0.512262\pi$
$593$	−1.87564	−0.0770235	−0.0385117	+	0.999258i	$0.512262\pi$
$594$	0	0
$595$	1.46410	0.0600223
$596$	11.3205	0.463706
$597$	−16.9282	−0.692825
$598$	−3.46410	−0.141658
$599$	−19.6077	−0.801149	−0.400574	−	0.916264i	$-0.631189\pi$
$599$	−19.6077	−0.801149	−0.400574	+	0.916264i	$0.631189\pi$
$600$	−4.46410	−0.182246
$601$	−18.7846	−0.766240	−0.383120	−	0.923699i	$-0.625150\pi$
$601$	−18.7846	−0.766240	−0.383120	+	0.923699i	$0.625150\pi$
$602$	−1.32051	−0.0538199
$603$	−28.0000	−1.14025
$604$	−20.7321	−0.843575
$605$	0	0
$606$	−16.5885	−0.673860
$607$	3.26795	0.132642	0.0663210	−	0.997798i	$-0.478874\pi$
$607$	3.26795	0.132642	0.0663210	+	0.997798i	$0.478874\pi$
$608$	−1.00000	−0.0405554
$609$	−0.464102	−0.0188063
$610$	0.928203	0.0375819
$611$	−43.1769	−1.74675
$612$	14.9282	0.603437
$613$	22.1962	0.896494	0.448247	−	0.893910i	$-0.352048\pi$
$613$	22.1962	0.896494	0.448247	+	0.893910i	$0.352048\pi$
$614$	−15.5885	−0.629099
$615$	−7.85641	−0.316801
$616$	0	0
$617$	−1.92820	−0.0776265	−0.0388133	−	0.999246i	$-0.512358\pi$
$617$	−1.92820	−0.0776265	−0.0388133	+	0.999246i	$0.512358\pi$
$618$	−2.73205	−0.109899
$619$	34.3923	1.38234	0.691172	−	0.722691i	$-0.257095\pi$
$619$	34.3923	1.38234	0.691172	+	0.722691i	$0.257095\pi$
$620$	1.07180	0.0430444
$621$	−5.00000	−0.200643
$622$	1.60770	0.0644627
$623$	3.26795	0.130928
$624$	3.46410	0.138675
$625$	17.2487	0.689948
$626$	−13.5359	−0.541003
$627$	0	0
$628$	−5.26795	−0.210214
$629$	48.2487	1.92380
$630$	−0.392305	−0.0156298
$631$	−21.2487	−0.845898	−0.422949	−	0.906154i	$-0.639005\pi$
$631$	−21.2487	−0.845898	−0.422949	+	0.906154i	$0.639005\pi$
$632$	2.19615	0.0873583
$633$	4.12436	0.163928
$634$	20.7846	0.825462
$635$	−2.92820	−0.116202
$636$	9.92820	0.393679
$637$	24.0000	0.950915
$638$	0	0
$639$	−28.3923	−1.12318
$640$	0.732051	0.0289368
$641$	−33.8038	−1.33517	−0.667586	−	0.744533i	$-0.732672\pi$
$641$	−33.8038	−1.33517	−0.667586	+	0.744533i	$0.732672\pi$
$642$	−2.80385	−0.110659
$643$	−17.7128	−0.698525	−0.349263	−	0.937025i	$-0.613568\pi$
$643$	−17.7128	−0.698525	−0.349263	+	0.937025i	$0.613568\pi$
$644$	−0.267949	−0.0105587
$645$	3.60770	0.142053
$646$	7.46410	0.293671
$647$	−3.14359	−0.123587	−0.0617937	−	0.998089i	$-0.519682\pi$
$647$	−3.14359	−0.123587	−0.0617937	+	0.998089i	$0.519682\pi$
$648$	−1.00000	−0.0392837
$649$	0	0
$650$	−15.4641	−0.606552
$651$	0.392305	0.0153756
$652$	17.3205	0.678323
$653$	−2.67949	−0.104857	−0.0524283	−	0.998625i	$-0.516696\pi$
$653$	−2.67949	−0.104857	−0.0524283	+	0.998625i	$0.516696\pi$
$654$	−6.12436	−0.239481
$655$	15.3205	0.598622
$656$	−10.7321	−0.419016
$657$	−4.00000	−0.156055
$658$	−3.33975	−0.130197
$659$	17.3205	0.674711	0.337356	−	0.941377i	$-0.390468\pi$
$659$	17.3205	0.674711	0.337356	+	0.941377i	$0.390468\pi$
$660$	0	0
$661$	19.2487	0.748688	0.374344	−	0.927290i	$-0.377868\pi$
$661$	19.2487	0.748688	0.374344	+	0.927290i	$0.377868\pi$
$662$	−21.7846	−0.846683
$663$	−25.8564	−1.00418
$664$	3.80385	0.147618
$665$	−0.196152	−0.00760646
$666$	−12.9282	−0.500958
$667$	−1.73205	−0.0670653
$668$	−3.46410	−0.134030
$669$	−13.1244	−0.507417
$670$	10.2487	0.395942
$671$	0	0
$672$	0.267949	0.0103364
$673$	−14.5885	−0.562344	−0.281172	−	0.959657i	$-0.590723\pi$
$673$	−14.5885	−0.562344	−0.281172	+	0.959657i	$0.590723\pi$
$674$	24.1962	0.932001
$675$	−22.3205	−0.859117
$676$	−1.00000	−0.0384615
$677$	36.6603	1.40897	0.704484	−	0.709720i	$-0.251178\pi$
$677$	36.6603	1.40897	0.704484	+	0.709720i	$0.251178\pi$
$678$	−4.73205	−0.181733
$679$	3.60770	0.138451
$680$	−5.46410	−0.209539
$681$	−8.39230	−0.321594
$682$	0	0
$683$	−22.7846	−0.871829	−0.435914	−	0.899988i	$-0.643575\pi$
$683$	−22.7846	−0.871829	−0.435914	+	0.899988i	$0.643575\pi$
$684$	−2.00000	−0.0764719
$685$	−6.92820	−0.264713
$686$	3.73205	0.142490
$687$	12.3923	0.472796
$688$	4.92820	0.187886
$689$	34.3923	1.31024
$690$	0.732051	0.0278687
$691$	28.0526	1.06717	0.533585	−	0.845747i	$-0.320845\pi$
$691$	28.0526	1.06717	0.533585	+	0.845747i	$0.320845\pi$
$692$	−4.12436	−0.156784
$693$	0	0
$694$	−10.0526	−0.381590
$695$	4.78461	0.181491
$696$	1.73205	0.0656532
$697$	80.1051	3.03420
$698$	14.7846	0.559606
$699$	8.26795	0.312723
$700$	−1.19615	−0.0452103
$701$	−9.46410	−0.357454	−0.178727	−	0.983899i	$-0.557198\pi$
$701$	−9.46410	−0.357454	−0.178727	+	0.983899i	$0.557198\pi$
$702$	17.3205	0.653720
$703$	−6.46410	−0.243798
$704$	0	0
$705$	9.12436	0.343643
$706$	6.46410	0.243280
$707$	−4.44486	−0.167166
$708$	9.39230	0.352984
$709$	9.85641	0.370165	0.185083	−	0.982723i	$-0.440745\pi$
$709$	9.85641	0.370165	0.185083	+	0.982723i	$0.440745\pi$
$710$	10.3923	0.390016
$711$	4.39230	0.164724
$712$	−12.1962	−0.457070
$713$	1.46410	0.0548310
$714$	−2.00000	−0.0748481
$715$	0	0
$716$	−2.07180	−0.0774267
$717$	14.1244	0.527484
$718$	−28.3923	−1.05959
$719$	−16.0000	−0.596699	−0.298350	−	0.954457i	$-0.596436\pi$
$719$	−16.0000	−0.596699	−0.298350	+	0.954457i	$0.596436\pi$
$720$	1.46410	0.0545638
$721$	−0.732051	−0.0272630
$722$	−1.00000	−0.0372161
$723$	−11.2679	−0.419060
$724$	24.3923	0.906533
$725$	−7.73205	−0.287161
$726$	0	0
$727$	−28.3205	−1.05035	−0.525175	−	0.850994i	$-0.676000\pi$
$727$	−28.3205	−1.05035	−0.525175	+	0.850994i	$0.676000\pi$
$728$	0.928203	0.0344015
$729$	13.0000	0.481481
$730$	1.46410	0.0541888
$731$	−36.7846	−1.36053
$732$	−1.26795	−0.0468648
$733$	5.07180	0.187331	0.0936655	−	0.995604i	$-0.470142\pi$
$733$	5.07180	0.187331	0.0936655	+	0.995604i	$0.470142\pi$
$734$	22.8564	0.843645
$735$	−5.07180	−0.187076
$736$	1.00000	0.0368605
$737$	0	0
$738$	−21.4641	−0.790104
$739$	−31.6603	−1.16464	−0.582321	−	0.812959i	$-0.697855\pi$
$739$	−31.6603	−1.16464	−0.582321	+	0.812959i	$0.697855\pi$
$740$	4.73205	0.173954
$741$	3.46410	0.127257
$742$	2.66025	0.0976610
$743$	−12.5359	−0.459898	−0.229949	−	0.973203i	$-0.573856\pi$
$743$	−12.5359	−0.459898	−0.229949	+	0.973203i	$0.573856\pi$
$744$	−1.46410	−0.0536766
$745$	−8.28719	−0.303619
$746$	16.8038	0.615233
$747$	7.60770	0.278351
$748$	0	0
$749$	−0.751289	−0.0274515
$750$	6.92820	0.252982
$751$	−12.0000	−0.437886	−0.218943	−	0.975738i	$-0.570261\pi$
$751$	−12.0000	−0.437886	−0.218943	+	0.975738i	$0.570261\pi$
$752$	12.4641	0.454519
$753$	−8.53590	−0.311065
$754$	6.00000	0.218507
$755$	15.1769	0.552344
$756$	1.33975	0.0487261
$757$	−21.3731	−0.776817	−0.388409	−	0.921487i	$-0.626975\pi$
$757$	−21.3731	−0.776817	−0.388409	+	0.921487i	$0.626975\pi$
$758$	−23.9282	−0.869111
$759$	0	0
$760$	0.732051	0.0265543
$761$	−48.7654	−1.76774	−0.883872	−	0.467729i	$-0.845072\pi$
$761$	−48.7654	−1.76774	−0.883872	+	0.467729i	$0.845072\pi$
$762$	4.00000	0.144905
$763$	−1.64102	−0.0594088
$764$	−17.3923	−0.629232
$765$	−10.9282	−0.395110
$766$	−33.4641	−1.20911
$767$	32.5359	1.17480
$768$	−1.00000	−0.0360844
$769$	27.5885	0.994865	0.497433	−	0.867503i	$-0.334276\pi$
$769$	27.5885	0.994865	0.497433	+	0.867503i	$0.334276\pi$
$770$	0	0
$771$	3.32051	0.119585
$772$	12.5359	0.451177
$773$	6.60770	0.237662	0.118831	−	0.992914i	$-0.462085\pi$
$773$	6.60770	0.237662	0.118831	+	0.992914i	$0.462085\pi$
$774$	9.85641	0.354281
$775$	6.53590	0.234776
$776$	−13.4641	−0.483333
$777$	1.73205	0.0621370
$778$	0.588457	0.0210972
$779$	−10.7321	−0.384516
$780$	−2.53590	−0.0907997
$781$	0	0
$782$	−7.46410	−0.266916
$783$	8.66025	0.309492
$784$	−6.92820	−0.247436
$785$	3.85641	0.137641
$786$	−20.9282	−0.746484
$787$	−13.0526	−0.465273	−0.232637	−	0.972564i	$-0.574735\pi$
$787$	−13.0526	−0.465273	−0.232637	+	0.972564i	$0.574735\pi$
$788$	5.07180	0.180675
$789$	−24.7846	−0.882355
$790$	−1.60770	−0.0571992
$791$	−1.26795	−0.0450831
$792$	0	0
$793$	−4.39230	−0.155975
$794$	−5.60770	−0.199010
$795$	−7.26795	−0.257768
$796$	16.9282	0.600004
$797$	11.6077	0.411166	0.205583	−	0.978640i	$-0.434091\pi$
$797$	11.6077	0.411166	0.205583	+	0.978640i	$0.434091\pi$
$798$	0.267949	0.00948530
$799$	−93.0333	−3.29128
$800$	4.46410	0.157830
$801$	−24.3923	−0.861860
$802$	16.0526	0.566836
$803$	0	0
$804$	−14.0000	−0.493742
$805$	0.196152	0.00691346
$806$	−5.07180	−0.178646
$807$	29.7846	1.04847
$808$	16.5885	0.583580
$809$	−19.1962	−0.674901	−0.337450	−	0.941343i	$-0.609565\pi$
$809$	−19.1962	−0.674901	−0.337450	+	0.941343i	$0.609565\pi$
$810$	0.732051	0.0257216
$811$	46.7654	1.64215	0.821077	−	0.570817i	$-0.193374\pi$
$811$	46.7654	1.64215	0.821077	+	0.570817i	$0.193374\pi$
$812$	0.464102	0.0162868
$813$	7.32051	0.256741
$814$	0	0
$815$	−12.6795	−0.444143
$816$	7.46410	0.261296
$817$	4.92820	0.172416
$818$	−13.4641	−0.470761
$819$	1.85641	0.0648681
$820$	7.85641	0.274358
$821$	−42.0526	−1.46764	−0.733822	−	0.679342i	$-0.762265\pi$
$821$	−42.0526	−1.46764	−0.733822	+	0.679342i	$0.762265\pi$
$822$	9.46410	0.330098
$823$	−21.5359	−0.750694	−0.375347	−	0.926884i	$-0.622476\pi$
$823$	−21.5359	−0.750694	−0.375347	+	0.926884i	$0.622476\pi$
$824$	2.73205	0.0951755
$825$	0	0
$826$	2.51666	0.0875658
$827$	21.3205	0.741387	0.370693	−	0.928755i	$-0.379120\pi$
$827$	21.3205	0.741387	0.370693	+	0.928755i	$0.379120\pi$
$828$	2.00000	0.0695048
$829$	18.6410	0.647429	0.323715	−	0.946155i	$-0.395068\pi$
$829$	18.6410	0.647429	0.323715	+	0.946155i	$0.395068\pi$
$830$	−2.78461	−0.0966552
$831$	−15.1244	−0.524658
$832$	−3.46410	−0.120096
$833$	51.7128	1.79174
$834$	−6.53590	−0.226320
$835$	2.53590	0.0877584
$836$	0	0
$837$	−7.32051	−0.253034
$838$	32.4449	1.12079
$839$	14.9808	0.517193	0.258597	−	0.965985i	$-0.416740\pi$
$839$	14.9808	0.517193	0.258597	+	0.965985i	$0.416740\pi$
$840$	−0.196152	−0.00676790
$841$	−26.0000	−0.896552
$842$	1.67949	0.0578791
$843$	−16.0526	−0.552879
$844$	−4.12436	−0.141966
$845$	0.732051	0.0251833
$846$	24.9282	0.857049
$847$	0	0
$848$	−9.92820	−0.340936
$849$	−21.4641	−0.736646
$850$	−33.3205	−1.14288
$851$	6.46410	0.221587
$852$	−14.1962	−0.486352
$853$	−54.1051	−1.85252	−0.926262	−	0.376880i	$-0.876997\pi$
$853$	−54.1051	−1.85252	−0.926262	+	0.376880i	$0.876997\pi$
$854$	−0.339746	−0.0116259
$855$	1.46410	0.0500712
$856$	2.80385	0.0958335
$857$	−16.5359	−0.564856	−0.282428	−	0.959289i	$-0.591140\pi$
$857$	−16.5359	−0.564856	−0.282428	+	0.959289i	$0.591140\pi$
$858$	0	0
$859$	−19.9474	−0.680598	−0.340299	−	0.940317i	$-0.610528\pi$
$859$	−19.9474	−0.680598	−0.340299	+	0.940317i	$0.610528\pi$
$860$	−3.60770	−0.123021
$861$	2.87564	0.0980017
$862$	−23.6603	−0.805871
$863$	−42.9282	−1.46129	−0.730647	−	0.682756i	$-0.760781\pi$
$863$	−42.9282	−1.46129	−0.730647	+	0.682756i	$0.760781\pi$
$864$	−5.00000	−0.170103
$865$	3.01924	0.102657
$866$	−18.7846	−0.638327
$867$	−38.7128	−1.31476
$868$	−0.392305	−0.0133157
$869$	0	0
$870$	−1.26795	−0.0429875
$871$	−48.4974	−1.64327
$872$	6.12436	0.207397
$873$	−26.9282	−0.911382
$874$	1.00000	0.0338255
$875$	1.85641	0.0627580
$876$	−2.00000	−0.0675737
$877$	37.8564	1.27832	0.639160	−	0.769074i	$-0.279282\pi$
$877$	37.8564	1.27832	0.639160	+	0.769074i	$0.279282\pi$
$878$	−17.4641	−0.589385
$879$	−12.1244	−0.408944
$880$	0	0
$881$	−13.5359	−0.456036	−0.228018	−	0.973657i	$-0.573225\pi$
$881$	−13.5359	−0.456036	−0.228018	+	0.973657i	$0.573225\pi$
$882$	−13.8564	−0.466569
$883$	−24.5885	−0.827467	−0.413734	−	0.910398i	$-0.635776\pi$
$883$	−24.5885	−0.827467	−0.413734	+	0.910398i	$0.635776\pi$
$884$	25.8564	0.869645
$885$	−6.87564	−0.231122
$886$	−18.0000	−0.604722
$887$	29.6603	0.995894	0.497947	−	0.867208i	$-0.334087\pi$
$887$	29.6603	0.995894	0.497947	+	0.867208i	$0.334087\pi$
$888$	−6.46410	−0.216921
$889$	1.07180	0.0359469
$890$	8.92820	0.299274
$891$	0	0
$892$	13.1244	0.439436
$893$	12.4641	0.417095
$894$	11.3205	0.378614
$895$	1.51666	0.0506964
$896$	−0.267949	−0.00895155
$897$	−3.46410	−0.115663
$898$	−27.8564	−0.929580
$899$	−2.53590	−0.0845769
$900$	8.92820	0.297607
$901$	74.1051	2.46880
$902$	0	0
$903$	−1.32051	−0.0439438
$904$	4.73205	0.157386
$905$	−17.8564	−0.593567
$906$	−20.7321	−0.688776
$907$	29.2487	0.971188	0.485594	−	0.874185i	$-0.338603\pi$
$907$	29.2487	0.971188	0.485594	+	0.874185i	$0.338603\pi$
$908$	8.39230	0.278508
$909$	33.1769	1.10041
$910$	−0.679492	−0.0225249
$911$	4.58846	0.152022	0.0760112	−	0.997107i	$-0.475782\pi$
$911$	4.58846	0.152022	0.0760112	+	0.997107i	$0.475782\pi$
$912$	−1.00000	−0.0331133
$913$	0	0
$914$	25.4449	0.841641
$915$	0.928203	0.0306855
$916$	−12.3923	−0.409453
$917$	−5.60770	−0.185182
$918$	37.3205	1.23176
$919$	−54.1051	−1.78476	−0.892382	−	0.451282i	$-0.850967\pi$
$919$	−54.1051	−1.78476	−0.892382	+	0.451282i	$0.850967\pi$
$920$	−0.732051	−0.0241350
$921$	−15.5885	−0.513657
$922$	28.1962	0.928591
$923$	−49.1769	−1.61868
$924$	0	0
$925$	28.8564	0.948793
$926$	−26.0000	−0.854413
$927$	5.46410	0.179465
$928$	−1.73205	−0.0568574
$929$	−58.0333	−1.90401	−0.952006	−	0.306080i	$-0.900982\pi$
$929$	−58.0333	−1.90401	−0.952006	+	0.306080i	$0.900982\pi$
$930$	1.07180	0.0351456
$931$	−6.92820	−0.227063
$932$	−8.26795	−0.270826
$933$	1.60770	0.0526336
$934$	−33.7128	−1.10312
$935$	0	0
$936$	−6.92820	−0.226455
$937$	29.8756	0.975995	0.487997	−	0.872845i	$-0.337728\pi$
$937$	29.8756	0.975995	0.487997	+	0.872845i	$0.337728\pi$
$938$	−3.75129	−0.122484
$939$	−13.5359	−0.441727
$940$	−9.12436	−0.297604
$941$	24.2487	0.790485	0.395243	−	0.918577i	$-0.370660\pi$
$941$	24.2487	0.790485	0.395243	+	0.918577i	$0.370660\pi$
$942$	−5.26795	−0.171639
$943$	10.7321	0.349484
$944$	−9.39230	−0.305693
$945$	−0.980762	−0.0319042
$946$	0	0
$947$	23.7128	0.770563	0.385281	−	0.922799i	$-0.374104\pi$
$947$	23.7128	0.770563	0.385281	+	0.922799i	$0.374104\pi$
$948$	2.19615	0.0713277
$949$	−6.92820	−0.224899
$950$	4.46410	0.144835
$951$	20.7846	0.673987
$952$	2.00000	0.0648204
$953$	−14.9808	−0.485274	−0.242637	−	0.970117i	$-0.578012\pi$
$953$	−14.9808	−0.485274	−0.242637	+	0.970117i	$0.578012\pi$
$954$	−19.8564	−0.642875
$955$	12.7321	0.411999
$956$	−14.1244	−0.456814
$957$	0	0
$958$	31.7321	1.02522
$959$	2.53590	0.0818884
$960$	0.732051	0.0236268
$961$	−28.8564	−0.930852
$962$	−22.3923	−0.721957
$963$	5.60770	0.180705
$964$	11.2679	0.362916
$965$	−9.17691	−0.295415
$966$	−0.267949	−0.00862112
$967$	8.51666	0.273877	0.136939	−	0.990580i	$-0.456274\pi$
$967$	8.51666	0.273877	0.136939	+	0.990580i	$0.456274\pi$
$968$	0	0
$969$	7.46410	0.239781
$970$	9.85641	0.316470
$971$	20.4641	0.656724	0.328362	−	0.944552i	$-0.393503\pi$
$971$	20.4641	0.656724	0.328362	+	0.944552i	$0.393503\pi$
$972$	−16.0000	−0.513200
$973$	−1.75129	−0.0561437
$974$	−27.1769	−0.870805
$975$	−15.4641	−0.495248
$976$	1.26795	0.0405861
$977$	−20.5359	−0.657002	−0.328501	−	0.944504i	$-0.606543\pi$
$977$	−20.5359	−0.657002	−0.328501	+	0.944504i	$0.606543\pi$
$978$	17.3205	0.553849
$979$	0	0
$980$	5.07180	0.162013
$981$	12.2487	0.391071
$982$	−3.60770	−0.115126
$983$	10.9808	0.350232	0.175116	−	0.984548i	$-0.443970\pi$
$983$	10.9808	0.350232	0.175116	+	0.984548i	$0.443970\pi$
$984$	−10.7321	−0.342125
$985$	−3.71281	−0.118300
$986$	12.9282	0.411718
$987$	−3.33975	−0.106305
$988$	−3.46410	−0.110208
$989$	−4.92820	−0.156708
$990$	0	0
$991$	−16.0526	−0.509926	−0.254963	−	0.966951i	$-0.582063\pi$
$991$	−16.0526	−0.509926	−0.254963	+	0.966951i	$0.582063\pi$
$992$	1.46410	0.0464853
$993$	−21.7846	−0.691314
$994$	−3.80385	−0.120651
$995$	−12.3923	−0.392862
$996$	3.80385	0.120530
$997$	10.3397	0.327463	0.163732	−	0.986505i	$-0.447647\pi$
$997$	10.3397	0.327463	0.163732	+	0.986505i	$0.447647\pi$
$998$	−21.2679	−0.673225
$999$	−32.3205	−1.02258

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4598.2.a.w.1.1	✓	2
11.10	odd	2		4598.2.a.bf.1.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4598.2.a.w.1.1	✓	2	1.1	even	1	trivial
4598.2.a.bf.1.1	yes	2	11.10	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:	\( N \)	\(=\)	\( 4598 = 2 \cdot 11^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4598.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.732051 q^{5} +1.00000 q^{6} +0.267949 q^{7} -1.00000 q^{8} -2.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.732051 q^{5} +1.00000 q^{6} +0.267949 q^{7} -1.00000 q^{8} -2.00000 q^{9} +0.732051 q^{10} -1.00000 q^{12} -3.46410 q^{13} -0.267949 q^{14} +0.732051 q^{15} +1.00000 q^{16} -7.46410 q^{17} +2.00000 q^{18} +1.00000 q^{19} -0.732051 q^{20} -0.267949 q^{21} -1.00000 q^{23} +1.00000 q^{24} -4.46410 q^{25} +3.46410 q^{26} +5.00000 q^{27} +0.267949 q^{28} +1.73205 q^{29} -0.732051 q^{30} -1.46410 q^{31} -1.00000 q^{32} +7.46410 q^{34} -0.196152 q^{35} -2.00000 q^{36} -6.46410 q^{37} -1.00000 q^{38} +3.46410 q^{39} +0.732051 q^{40} -10.7321 q^{41} +0.267949 q^{42} +4.92820 q^{43} +1.46410 q^{45} +1.00000 q^{46} +12.4641 q^{47} -1.00000 q^{48} -6.92820 q^{49} +4.46410 q^{50} +7.46410 q^{51} -3.46410 q^{52} -9.92820 q^{53} -5.00000 q^{54} -0.267949 q^{56} -1.00000 q^{57} -1.73205 q^{58} -9.39230 q^{59} +0.732051 q^{60} +1.26795 q^{61} +1.46410 q^{62} -0.535898 q^{63} +1.00000 q^{64} +2.53590 q^{65} +14.0000 q^{67} -7.46410 q^{68} +1.00000 q^{69} +0.196152 q^{70} +14.1962 q^{71} +2.00000 q^{72} +2.00000 q^{73} +6.46410 q^{74} +4.46410 q^{75} +1.00000 q^{76} -3.46410 q^{78} -2.19615 q^{79} -0.732051 q^{80} +1.00000 q^{81} +10.7321 q^{82} -3.80385 q^{83} -0.267949 q^{84} +5.46410 q^{85} -4.92820 q^{86} -1.73205 q^{87} +12.1962 q^{89} -1.46410 q^{90} -0.928203 q^{91} -1.00000 q^{92} +1.46410 q^{93} -12.4641 q^{94} -0.732051 q^{95} +1.00000 q^{96} +13.4641 q^{97} +6.92820 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} + 4 q^{7} - 2 q^{8} - 4 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 + 4 * q^7 - 2 * q^8 - 4 * q^9	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} + 4 q^{7} - 2 q^{8} - 4 q^{9} - 2 q^{10} - 2 q^{12} - 4 q^{14} - 2 q^{15} + 2 q^{16} - 8 q^{17} + 4 q^{18} + 2 q^{19} + 2 q^{20} - 4 q^{21} - 2 q^{23} + 2 q^{24} - 2 q^{25} + 10 q^{27} + 4 q^{28} + 2 q^{30} + 4 q^{31} - 2 q^{32} + 8 q^{34} + 10 q^{35} - 4 q^{36} - 6 q^{37} - 2 q^{38} - 2 q^{40} - 18 q^{41} + 4 q^{42} - 4 q^{43} - 4 q^{45} + 2 q^{46} + 18 q^{47} - 2 q^{48} + 2 q^{50} + 8 q^{51} - 6 q^{53} - 10 q^{54} - 4 q^{56} - 2 q^{57} + 2 q^{59} - 2 q^{60} + 6 q^{61} - 4 q^{62} - 8 q^{63} + 2 q^{64} + 12 q^{65} + 28 q^{67} - 8 q^{68} + 2 q^{69} - 10 q^{70} + 18 q^{71} + 4 q^{72} + 4 q^{73} + 6 q^{74} + 2 q^{75} + 2 q^{76} + 6 q^{79} + 2 q^{80} + 2 q^{81} + 18 q^{82} - 18 q^{83} - 4 q^{84} + 4 q^{85} + 4 q^{86} + 14 q^{89} + 4 q^{90} + 12 q^{91} - 2 q^{92} - 4 q^{93} - 18 q^{94} + 2 q^{95} + 2 q^{96} + 20 q^{97}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 + 4 * q^7 - 2 * q^8 - 4 * q^9 - 2 * q^10 - 2 * q^12 - 4 * q^14 - 2 * q^15 + 2 * q^16 - 8 * q^17 + 4 * q^18 + 2 * q^19 + 2 * q^20 - 4 * q^21 - 2 * q^23 + 2 * q^24 - 2 * q^25 + 10 * q^27 + 4 * q^28 + 2 * q^30 + 4 * q^31 - 2 * q^32 + 8 * q^34 + 10 * q^35 - 4 * q^36 - 6 * q^37 - 2 * q^38 - 2 * q^40 - 18 * q^41 + 4 * q^42 - 4 * q^43 - 4 * q^45 + 2 * q^46 + 18 * q^47 - 2 * q^48 + 2 * q^50 + 8 * q^51 - 6 * q^53 - 10 * q^54 - 4 * q^56 - 2 * q^57 + 2 * q^59 - 2 * q^60 + 6 * q^61 - 4 * q^62 - 8 * q^63 + 2 * q^64 + 12 * q^65 + 28 * q^67 - 8 * q^68 + 2 * q^69 - 10 * q^70 + 18 * q^71 + 4 * q^72 + 4 * q^73 + 6 * q^74 + 2 * q^75 + 2 * q^76 + 6 * q^79 + 2 * q^80 + 2 * q^81 + 18 * q^82 - 18 * q^83 - 4 * q^84 + 4 * q^85 + 4 * q^86 + 14 * q^89 + 4 * q^90 + 12 * q^91 - 2 * q^92 - 4 * q^93 - 18 * q^94 + 2 * q^95 + 2 * q^96 + 20 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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