LMFDB - Embedded newform 4598.2.a.cb.1.8

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:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 16x^{6} - 4x^{5} + 75x^{4} + 32x^{3} - 90x^{2} - 28x - 2 $ x^8 - 16x^6 - 4x^5 + 75x^4 + 32x^3 - 90x^2 - 28x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-2.75320$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +3.37860 q^{3} +1.00000 q^{4} -4.17017 q^{5} +3.37860 q^{6} -3.60700 q^{7} +1.00000 q^{8} +8.41492 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +3.37860 q^{3} +1.00000 q^{4} -4.17017 q^{5} +3.37860 q^{6} -3.60700 q^{7} +1.00000 q^{8} +8.41492 q^{9} -4.17017 q^{10} +3.37860 q^{12} -0.669426 q^{13} -3.60700 q^{14} -14.0893 q^{15} +1.00000 q^{16} +4.10493 q^{17} +8.41492 q^{18} -1.00000 q^{19} -4.17017 q^{20} -12.1866 q^{21} +6.35872 q^{23} +3.37860 q^{24} +12.3903 q^{25} -0.669426 q^{26} +18.2948 q^{27} -3.60700 q^{28} +3.27213 q^{29} -14.0893 q^{30} -1.55576 q^{31} +1.00000 q^{32} +4.10493 q^{34} +15.0418 q^{35} +8.41492 q^{36} +3.51430 q^{37} -1.00000 q^{38} -2.26172 q^{39} -4.17017 q^{40} +7.30933 q^{41} -12.1866 q^{42} -6.04669 q^{43} -35.0916 q^{45} +6.35872 q^{46} +0.862845 q^{47} +3.37860 q^{48} +6.01048 q^{49} +12.3903 q^{50} +13.8689 q^{51} -0.669426 q^{52} +6.79423 q^{53} +18.2948 q^{54} -3.60700 q^{56} -3.37860 q^{57} +3.27213 q^{58} -9.41317 q^{59} -14.0893 q^{60} -4.40660 q^{61} -1.55576 q^{62} -30.3526 q^{63} +1.00000 q^{64} +2.79162 q^{65} +1.80340 q^{67} +4.10493 q^{68} +21.4836 q^{69} +15.0418 q^{70} +11.9933 q^{71} +8.41492 q^{72} +9.91252 q^{73} +3.51430 q^{74} +41.8618 q^{75} -1.00000 q^{76} -2.26172 q^{78} +1.04552 q^{79} -4.17017 q^{80} +36.5661 q^{81} +7.30933 q^{82} +0.503831 q^{83} -12.1866 q^{84} -17.1183 q^{85} -6.04669 q^{86} +11.0552 q^{87} +8.23674 q^{89} -35.0916 q^{90} +2.41462 q^{91} +6.35872 q^{92} -5.25629 q^{93} +0.862845 q^{94} +4.17017 q^{95} +3.37860 q^{96} +0.809369 q^{97} +6.01048 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 8 q^{6} + 4 q^{7} + 8 q^{8} + 22 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 8 * q^6 + 4 * q^7 + 8 * q^8 + 22 * q^9	$ 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 8 q^{6} + 4 q^{7} + 8 q^{8} + 22 q^{9} + 8 q^{12} - 12 q^{13} + 4 q^{14} + 4 q^{15} + 8 q^{16} - 4 q^{17} + 22 q^{18} - 8 q^{19} - 20 q^{21} + 14 q^{23} + 8 q^{24} + 36 q^{25} - 12 q^{26} + 32 q^{27} + 4 q^{28} - 2 q^{29} + 4 q^{30} + 8 q^{32} - 4 q^{34} + 36 q^{35} + 22 q^{36} + 24 q^{37} - 8 q^{38} + 16 q^{39} + 8 q^{41} - 20 q^{42} + 8 q^{43} + 16 q^{45} + 14 q^{46} - 16 q^{47} + 8 q^{48} + 34 q^{49} + 36 q^{50} + 18 q^{51} - 12 q^{52} + 36 q^{53} + 32 q^{54} + 4 q^{56} - 8 q^{57} - 2 q^{58} - 24 q^{59} + 4 q^{60} + 12 q^{61} + 24 q^{63} + 8 q^{64} + 16 q^{65} + 16 q^{67} - 4 q^{68} + 4 q^{69} + 36 q^{70} + 4 q^{71} + 22 q^{72} - 20 q^{73} + 24 q^{74} + 40 q^{75} - 8 q^{76} + 16 q^{78} - 12 q^{79} + 40 q^{81} + 8 q^{82} + 20 q^{83} - 20 q^{84} + 12 q^{85} + 8 q^{86} - 36 q^{87} + 8 q^{89} + 16 q^{90} - 24 q^{91} + 14 q^{92} + 12 q^{93} - 16 q^{94} + 8 q^{96} + 4 q^{97} + 34 q^{98}+O(q^{100}) $ 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 8 * q^6 + 4 * q^7 + 8 * q^8 + 22 * q^9 + 8 * q^12 - 12 * q^13 + 4 * q^14 + 4 * q^15 + 8 * q^16 - 4 * q^17 + 22 * q^18 - 8 * q^19 - 20 * q^21 + 14 * q^23 + 8 * q^24 + 36 * q^25 - 12 * q^26 + 32 * q^27 + 4 * q^28 - 2 * q^29 + 4 * q^30 + 8 * q^32 - 4 * q^34 + 36 * q^35 + 22 * q^36 + 24 * q^37 - 8 * q^38 + 16 * q^39 + 8 * q^41 - 20 * q^42 + 8 * q^43 + 16 * q^45 + 14 * q^46 - 16 * q^47 + 8 * q^48 + 34 * q^49 + 36 * q^50 + 18 * q^51 - 12 * q^52 + 36 * q^53 + 32 * q^54 + 4 * q^56 - 8 * q^57 - 2 * q^58 - 24 * q^59 + 4 * q^60 + 12 * q^61 + 24 * q^63 + 8 * q^64 + 16 * q^65 + 16 * q^67 - 4 * q^68 + 4 * q^69 + 36 * q^70 + 4 * q^71 + 22 * q^72 - 20 * q^73 + 24 * q^74 + 40 * q^75 - 8 * q^76 + 16 * q^78 - 12 * q^79 + 40 * q^81 + 8 * q^82 + 20 * q^83 - 20 * q^84 + 12 * q^85 + 8 * q^86 - 36 * q^87 + 8 * q^89 + 16 * q^90 - 24 * q^91 + 14 * q^92 + 12 * q^93 - 16 * q^94 + 8 * q^96 + 4 * q^97 + 34 * q^98

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
$3$	3.37860	1.95063	0.975317	−	0.220810i	$-0.0708701\pi$
$3$	3.37860	1.95063	0.975317	+	0.220810i	$0.0708701\pi$
$4$	1.00000	0.500000
$5$	−4.17017	−1.86496	−0.932478	−	0.361228i	$-0.882358\pi$
$5$	−4.17017	−1.86496	−0.932478	+	0.361228i	$0.882358\pi$
$6$	3.37860	1.37931
$7$	−3.60700	−1.36332	−0.681660	−	0.731669i	$-0.738742\pi$
$7$	−3.60700	−1.36332	−0.681660	+	0.731669i	$0.738742\pi$
$8$	1.00000	0.353553
$9$	8.41492	2.80497
$10$	−4.17017	−1.31872
$11$	0	0
$11$	0	0
$12$	3.37860	0.975317
$13$	−0.669426	−0.185665	−0.0928326	−	0.995682i	$-0.529592\pi$
$13$	−0.669426	−0.185665	−0.0928326	+	0.995682i	$0.529592\pi$
$14$	−3.60700	−0.964012
$15$	−14.0893	−3.63784
$16$	1.00000	0.250000
$17$	4.10493	0.995592	0.497796	−	0.867294i	$-0.334143\pi$
$17$	4.10493	0.995592	0.497796	+	0.867294i	$0.334143\pi$
$18$	8.41492	1.98341
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−4.17017	−0.932478
$21$	−12.1866	−2.65934
$22$	0	0
$23$	6.35872	1.32589	0.662943	−	0.748670i	$-0.269307\pi$
$23$	6.35872	1.32589	0.662943	+	0.748670i	$0.269307\pi$
$24$	3.37860	0.689653
$25$	12.3903	2.47806
$26$	−0.669426	−0.131285
$27$	18.2948	3.52084
$28$	−3.60700	−0.681660
$29$	3.27213	0.607619	0.303809	−	0.952733i	$-0.401741\pi$
$29$	3.27213	0.607619	0.303809	+	0.952733i	$0.401741\pi$
$30$	−14.0893	−2.57234
$31$	−1.55576	−0.279423	−0.139712	−	0.990192i	$-0.544618\pi$
$31$	−1.55576	−0.279423	−0.139712	+	0.990192i	$0.544618\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	4.10493	0.703990
$35$	15.0418	2.54253
$36$	8.41492	1.40249
$37$	3.51430	0.577747	0.288873	−	0.957367i	$-0.406719\pi$
$37$	3.51430	0.577747	0.288873	+	0.957367i	$0.406719\pi$
$38$	−1.00000	−0.162221
$39$	−2.26172	−0.362165
$40$	−4.17017	−0.659361
$41$	7.30933	1.14153	0.570763	−	0.821115i	$-0.306648\pi$
$41$	7.30933	1.14153	0.570763	+	0.821115i	$0.306648\pi$
$42$	−12.1866	−1.88044
$43$	−6.04669	−0.922112	−0.461056	−	0.887371i	$-0.652529\pi$
$43$	−6.04669	−0.922112	−0.461056	+	0.887371i	$0.652529\pi$
$44$	0	0
$45$	−35.0916	−5.23115
$46$	6.35872	0.937543
$47$	0.862845	0.125859	0.0629294	−	0.998018i	$-0.479956\pi$
$47$	0.862845	0.125859	0.0629294	+	0.998018i	$0.479956\pi$
$48$	3.37860	0.487658
$49$	6.01048	0.858640
$50$	12.3903	1.75225
$51$	13.8689	1.94204
$52$	−0.669426	−0.0928326
$53$	6.79423	0.933260	0.466630	−	0.884453i	$-0.345468\pi$
$53$	6.79423	0.933260	0.466630	+	0.884453i	$0.345468\pi$
$54$	18.2948	2.48961
$55$	0	0
$56$	−3.60700	−0.482006
$57$	−3.37860	−0.447506
$58$	3.27213	0.429651
$59$	−9.41317	−1.22549	−0.612745	−	0.790280i	$-0.709935\pi$
$59$	−9.41317	−1.22549	−0.612745	+	0.790280i	$0.709935\pi$
$60$	−14.0893	−1.81892
$61$	−4.40660	−0.564207	−0.282103	−	0.959384i	$-0.591032\pi$
$61$	−4.40660	−0.564207	−0.282103	+	0.959384i	$0.591032\pi$
$62$	−1.55576	−0.197582
$63$	−30.3526	−3.82407
$64$	1.00000	0.125000
$65$	2.79162	0.346257
$66$	0	0
$67$	1.80340	0.220320	0.110160	−	0.993914i	$-0.464864\pi$
$67$	1.80340	0.220320	0.110160	+	0.993914i	$0.464864\pi$
$68$	4.10493	0.497796
$69$	21.4836	2.58632
$70$	15.0418	1.79784
$71$	11.9933	1.42334	0.711669	−	0.702514i	$-0.247939\pi$
$71$	11.9933	1.42334	0.711669	+	0.702514i	$0.247939\pi$
$72$	8.41492	0.991707
$73$	9.91252	1.16017	0.580087	−	0.814555i	$-0.303019\pi$
$73$	9.91252	1.16017	0.580087	+	0.814555i	$0.303019\pi$
$74$	3.51430	0.408529
$75$	41.8618	4.83378
$76$	−1.00000	−0.114708
$77$	0	0
$78$	−2.26172	−0.256089
$79$	1.04552	0.117630	0.0588152	−	0.998269i	$-0.481268\pi$
$79$	1.04552	0.117630	0.0588152	+	0.998269i	$0.481268\pi$
$80$	−4.17017	−0.466239
$81$	36.5661	4.06290
$82$	7.30933	0.807180
$83$	0.503831	0.0553026	0.0276513	−	0.999618i	$-0.491197\pi$
$83$	0.503831	0.0553026	0.0276513	+	0.999618i	$0.491197\pi$
$84$	−12.1866	−1.32967
$85$	−17.1183	−1.85674
$86$	−6.04669	−0.652032
$87$	11.0552	1.18524
$88$	0	0
$89$	8.23674	0.873093	0.436546	−	0.899682i	$-0.356201\pi$
$89$	8.23674	0.873093	0.436546	+	0.899682i	$0.356201\pi$
$90$	−35.0916	−3.69898
$91$	2.41462	0.253121
$92$	6.35872	0.662943
$93$	−5.25629	−0.545052
$94$	0.862845	0.0889957
$95$	4.17017	0.427850
$96$	3.37860	0.344827
$97$	0.809369	0.0821790	0.0410895	−	0.999155i	$-0.486917\pi$
$97$	0.809369	0.0821790	0.0410895	+	0.999155i	$0.486917\pi$
$98$	6.01048	0.607150
$99$	0	0
$100$	12.3903	1.23903
$101$	−12.0493	−1.19895	−0.599475	−	0.800393i	$-0.704624\pi$
$101$	−12.0493	−1.19895	−0.599475	+	0.800393i	$0.704624\pi$
$102$	13.8689	1.37323
$103$	5.64096	0.555820	0.277910	−	0.960607i	$-0.410358\pi$
$103$	5.64096	0.555820	0.277910	+	0.960607i	$0.410358\pi$
$104$	−0.669426	−0.0656426
$105$	50.8202	4.95954
$106$	6.79423	0.659914
$107$	15.1059	1.46034	0.730172	−	0.683264i	$-0.239440\pi$
$107$	15.1059	1.46034	0.730172	+	0.683264i	$0.239440\pi$
$108$	18.2948	1.76042
$109$	−11.6030	−1.11137	−0.555685	−	0.831393i	$-0.687544\pi$
$109$	−11.6030	−1.11137	−0.555685	+	0.831393i	$0.687544\pi$
$110$	0	0
$111$	11.8734	1.12697
$112$	−3.60700	−0.340830
$113$	−6.03660	−0.567876	−0.283938	−	0.958843i	$-0.591641\pi$
$113$	−6.03660	−0.567876	−0.283938	+	0.958843i	$0.591641\pi$
$114$	−3.37860	−0.316435
$115$	−26.5169	−2.47272
$116$	3.27213	0.303809
$117$	−5.63316	−0.520786
$118$	−9.41317	−0.866553
$119$	−14.8065	−1.35731
$120$	−14.0893	−1.28617
$121$	0	0
$122$	−4.40660	−0.398954
$123$	24.6953	2.22670
$124$	−1.55576	−0.139712
$125$	−30.8187	−2.75651
$126$	−30.3526	−2.70403
$127$	−7.06535	−0.626949	−0.313474	−	0.949597i	$-0.601493\pi$
$127$	−7.06535	−0.626949	−0.313474	+	0.949597i	$0.601493\pi$
$128$	1.00000	0.0883883
$129$	−20.4293	−1.79870
$130$	2.79162	0.244841
$131$	−3.26224	−0.285023	−0.142512	−	0.989793i	$-0.545518\pi$
$131$	−3.26224	−0.285023	−0.142512	+	0.989793i	$0.545518\pi$
$132$	0	0
$133$	3.60700	0.312767
$134$	1.80340	0.155790
$135$	−76.2924	−6.56621
$136$	4.10493	0.351995
$137$	1.25379	0.107118	0.0535592	−	0.998565i	$-0.482943\pi$
$137$	1.25379	0.107118	0.0535592	+	0.998565i	$0.482943\pi$
$138$	21.4836	1.82880
$139$	1.52427	0.129287	0.0646433	−	0.997908i	$-0.479409\pi$
$139$	1.52427	0.129287	0.0646433	+	0.997908i	$0.479409\pi$
$140$	15.0418	1.27127
$141$	2.91521	0.245505
$142$	11.9933	1.00645
$143$	0	0
$144$	8.41492	0.701243
$145$	−13.6453	−1.13318
$146$	9.91252	0.820366
$147$	20.3070	1.67489
$148$	3.51430	0.288873
$149$	−15.6872	−1.28515	−0.642575	−	0.766223i	$-0.722134\pi$
$149$	−15.6872	−1.28515	−0.642575	+	0.766223i	$0.722134\pi$
$150$	41.8618	3.41800
$151$	18.9865	1.54510	0.772548	−	0.634957i	$-0.218982\pi$
$151$	18.9865	1.54510	0.772548	+	0.634957i	$0.218982\pi$
$152$	−1.00000	−0.0811107
$153$	34.5427	2.79261
$154$	0	0
$155$	6.48779	0.521112
$156$	−2.26172	−0.181082
$157$	−8.89570	−0.709954	−0.354977	−	0.934875i	$-0.615511\pi$
$157$	−8.89570	−0.709954	−0.354977	+	0.934875i	$0.615511\pi$
$158$	1.04552	0.0831772
$159$	22.9550	1.82045
$160$	−4.17017	−0.329681
$161$	−22.9359	−1.80761
$162$	36.5661	2.87290
$163$	−4.84499	−0.379489	−0.189744	−	0.981834i	$-0.560766\pi$
$163$	−4.84499	−0.379489	−0.189744	+	0.981834i	$0.560766\pi$
$164$	7.30933	0.570763
$165$	0	0
$166$	0.503831	0.0391049
$167$	−4.61536	−0.357148	−0.178574	−	0.983927i	$-0.557148\pi$
$167$	−4.61536	−0.357148	−0.178574	+	0.983927i	$0.557148\pi$
$168$	−12.1866	−0.940218
$169$	−12.5519	−0.965528
$170$	−17.1183	−1.31291
$171$	−8.41492	−0.643505
$172$	−6.04669	−0.461056
$173$	−9.33836	−0.709982	−0.354991	−	0.934870i	$-0.615516\pi$
$173$	−9.33836	−0.709982	−0.354991	+	0.934870i	$0.615516\pi$
$174$	11.0552	0.838092
$175$	−44.6918	−3.37839
$176$	0	0
$177$	−31.8033	−2.39048
$178$	8.23674	0.617370
$179$	16.7881	1.25480	0.627401	−	0.778696i	$-0.284119\pi$
$179$	16.7881	1.25480	0.627401	+	0.778696i	$0.284119\pi$
$180$	−35.0916	−2.61557
$181$	17.5877	1.30729	0.653643	−	0.756803i	$-0.273240\pi$
$181$	17.5877	1.30729	0.653643	+	0.756803i	$0.273240\pi$
$182$	2.41462	0.178984
$183$	−14.8881	−1.10056
$184$	6.35872	0.468771
$185$	−14.6552	−1.07747
$186$	−5.25629	−0.385410
$187$	0	0
$188$	0.862845	0.0629294
$189$	−65.9895	−4.80003
$190$	4.17017	0.302536
$191$	−2.76249	−0.199887	−0.0999435	−	0.994993i	$-0.531866\pi$
$191$	−2.76249	−0.199887	−0.0999435	+	0.994993i	$0.531866\pi$
$192$	3.37860	0.243829
$193$	21.4775	1.54598	0.772991	−	0.634417i	$-0.218760\pi$
$193$	21.4775	1.54598	0.772991	+	0.634417i	$0.218760\pi$
$194$	0.809369	0.0581093
$195$	9.43175	0.675421
$196$	6.01048	0.429320
$197$	−18.9032	−1.34680	−0.673399	−	0.739280i	$-0.735166\pi$
$197$	−18.9032	−1.34680	−0.673399	+	0.739280i	$0.735166\pi$
$198$	0	0
$199$	7.76283	0.550292	0.275146	−	0.961402i	$-0.411274\pi$
$199$	7.76283	0.550292	0.275146	+	0.961402i	$0.411274\pi$
$200$	12.3903	0.876126
$201$	6.09296	0.429764
$202$	−12.0493	−0.847786
$203$	−11.8026	−0.828378
$204$	13.8689	0.971018
$205$	−30.4811	−2.12889
$206$	5.64096	0.393024
$207$	53.5081	3.71907
$208$	−0.669426	−0.0464163
$209$	0	0
$210$	50.8202	3.50693
$211$	−6.88377	−0.473898	−0.236949	−	0.971522i	$-0.576147\pi$
$211$	−6.88377	−0.473898	−0.236949	+	0.971522i	$0.576147\pi$
$212$	6.79423	0.466630
$213$	40.5204	2.77641
$214$	15.1059	1.03262
$215$	25.2157	1.71970
$216$	18.2948	1.24480
$217$	5.61164	0.380943
$218$	−11.6030	−0.785857
$219$	33.4904	2.26307
$220$	0	0
$221$	−2.74795	−0.184847
$222$	11.8734	0.796890
$223$	14.5212	0.972409	0.486204	−	0.873845i	$-0.338381\pi$
$223$	14.5212	0.972409	0.486204	+	0.873845i	$0.338381\pi$
$224$	−3.60700	−0.241003
$225$	104.263	6.95088
$226$	−6.03660	−0.401549
$227$	−18.1073	−1.20182	−0.600912	−	0.799315i	$-0.705196\pi$
$227$	−18.1073	−1.20182	−0.600912	+	0.799315i	$0.705196\pi$
$228$	−3.37860	−0.223753
$229$	−25.3580	−1.67570	−0.837850	−	0.545900i	$-0.816188\pi$
$229$	−25.3580	−1.67570	−0.837850	+	0.545900i	$0.816188\pi$
$230$	−26.5169	−1.74848
$231$	0	0
$232$	3.27213	0.214826
$233$	−21.9886	−1.44052	−0.720261	−	0.693704i	$-0.755978\pi$
$233$	−21.9886	−1.44052	−0.720261	+	0.693704i	$0.755978\pi$
$234$	−5.63316	−0.368251
$235$	−3.59821	−0.234721
$236$	−9.41317	−0.612745
$237$	3.53240	0.229454
$238$	−14.8065	−0.959764
$239$	15.2971	0.989488	0.494744	−	0.869039i	$-0.335262\pi$
$239$	15.2971	0.989488	0.494744	+	0.869039i	$0.335262\pi$
$240$	−14.0893	−0.909461
$241$	16.0409	1.03328	0.516642	−	0.856201i	$-0.327182\pi$
$241$	16.0409	1.03328	0.516642	+	0.856201i	$0.327182\pi$
$242$	0	0
$243$	68.6575	4.40438
$244$	−4.40660	−0.282103
$245$	−25.0647	−1.60133
$246$	24.6953	1.57451
$247$	0.669426	0.0425945
$248$	−1.55576	−0.0987910
$249$	1.70224	0.107875
$250$	−30.8187	−1.94915
$251$	−6.91197	−0.436279	−0.218140	−	0.975918i	$-0.569999\pi$
$251$	−6.91197	−0.436279	−0.218140	+	0.975918i	$0.569999\pi$
$252$	−30.3526	−1.91204
$253$	0	0
$254$	−7.06535	−0.443320
$255$	−57.8357	−3.62181
$256$	1.00000	0.0625000
$257$	−24.7512	−1.54394	−0.771968	−	0.635661i	$-0.780727\pi$
$257$	−24.7512	−1.54394	−0.771968	+	0.635661i	$0.780727\pi$
$258$	−20.4293	−1.27187
$259$	−12.6761	−0.787654
$260$	2.79162	0.173129
$261$	27.5347	1.70435
$262$	−3.26224	−0.201542
$263$	16.8155	1.03689	0.518444	−	0.855112i	$-0.326512\pi$
$263$	16.8155	1.03689	0.518444	+	0.855112i	$0.326512\pi$
$264$	0	0
$265$	−28.3331	−1.74049
$266$	3.60700	0.221160
$267$	27.8286	1.70308
$268$	1.80340	0.110160
$269$	17.8288	1.08704	0.543521	−	0.839395i	$-0.317091\pi$
$269$	17.8288	1.08704	0.543521	+	0.839395i	$0.317091\pi$
$270$	−76.2924	−4.64301
$271$	−30.2063	−1.83490	−0.917450	−	0.397850i	$-0.869756\pi$
$271$	−30.2063	−1.83490	−0.917450	+	0.397850i	$0.869756\pi$
$272$	4.10493	0.248898
$273$	8.15803	0.493747
$274$	1.25379	0.0757441
$275$	0	0
$276$	21.4836	1.29316
$277$	32.7642	1.96861	0.984306	−	0.176473i	$-0.0564688\pi$
$277$	32.7642	1.96861	0.984306	+	0.176473i	$0.0564688\pi$
$278$	1.52427	0.0914194
$279$	−13.0916	−0.783774
$280$	15.0418	0.898920
$281$	−9.70846	−0.579158	−0.289579	−	0.957154i	$-0.593515\pi$
$281$	−9.70846	−0.579158	−0.289579	+	0.957154i	$0.593515\pi$
$282$	2.91521	0.173598
$283$	14.5739	0.866326	0.433163	−	0.901316i	$-0.357397\pi$
$283$	14.5739	0.866326	0.433163	+	0.901316i	$0.357397\pi$
$284$	11.9933	0.711669
$285$	14.0893	0.834579
$286$	0	0
$287$	−26.3648	−1.55626
$288$	8.41492	0.495854
$289$	−0.149526	−0.00879562
$290$	−13.6453	−0.801281
$291$	2.73453	0.160301
$292$	9.91252	0.580087
$293$	−10.5241	−0.614824	−0.307412	−	0.951576i	$-0.599463\pi$
$293$	−10.5241	−0.614824	−0.307412	+	0.951576i	$0.599463\pi$
$294$	20.3070	1.18433
$295$	39.2545	2.28549
$296$	3.51430	0.204264
$297$	0	0
$298$	−15.6872	−0.908738
$299$	−4.25669	−0.246171
$300$	41.8618	2.41689
$301$	21.8104	1.25713
$302$	18.9865	1.09255
$303$	−40.7097	−2.33871
$304$	−1.00000	−0.0573539
$305$	18.3762	1.05222
$306$	34.5427	1.97467
$307$	−21.4131	−1.22211	−0.611054	−	0.791589i	$-0.709254\pi$
$307$	−21.4131	−1.22211	−0.611054	+	0.791589i	$0.709254\pi$
$308$	0	0
$309$	19.0585	1.08420
$310$	6.48779	0.368482
$311$	8.91440	0.505489	0.252745	−	0.967533i	$-0.418667\pi$
$311$	8.91440	0.505489	0.252745	+	0.967533i	$0.418667\pi$
$312$	−2.26172	−0.128045
$313$	−29.2280	−1.65206	−0.826031	−	0.563624i	$-0.809407\pi$
$313$	−29.2280	−1.65206	−0.826031	+	0.563624i	$0.809407\pi$
$314$	−8.89570	−0.502014
$315$	126.576	7.13173
$316$	1.04552	0.0588152
$317$	−3.86251	−0.216940	−0.108470	−	0.994100i	$-0.534595\pi$
$317$	−3.86251	−0.216940	−0.108470	+	0.994100i	$0.534595\pi$
$318$	22.9550	1.28725
$319$	0	0
$320$	−4.17017	−0.233119
$321$	51.0368	2.84860
$322$	−22.9359	−1.27817
$323$	−4.10493	−0.228405
$324$	36.5661	2.03145
$325$	−8.29438	−0.460089
$326$	−4.84499	−0.268339
$327$	−39.2020	−2.16788
$328$	7.30933	0.403590
$329$	−3.11229	−0.171586
$330$	0	0
$331$	30.7968	1.69275	0.846373	−	0.532590i	$-0.178781\pi$
$331$	30.7968	1.69275	0.846373	+	0.532590i	$0.178781\pi$
$332$	0.503831	0.0276513
$333$	29.5725	1.62056
$334$	−4.61536	−0.252542
$335$	−7.52048	−0.410888
$336$	−12.1866	−0.664834
$337$	−16.0941	−0.876704	−0.438352	−	0.898803i	$-0.644438\pi$
$337$	−16.0941	−0.876704	−0.438352	+	0.898803i	$0.644438\pi$
$338$	−12.5519	−0.682732
$339$	−20.3953	−1.10772
$340$	−17.1183	−0.928368
$341$	0	0
$342$	−8.41492	−0.455027
$343$	3.56920	0.192719
$344$	−6.04669	−0.326016
$345$	−89.5900	−4.82337
$346$	−9.33836	−0.502033
$347$	−31.7933	−1.70676	−0.853378	−	0.521292i	$-0.825450\pi$
$347$	−31.7933	−1.70676	−0.853378	+	0.521292i	$0.825450\pi$
$348$	11.0552	0.592621
$349$	11.5331	0.617350	0.308675	−	0.951168i	$-0.400114\pi$
$349$	11.5331	0.617350	0.308675	+	0.951168i	$0.400114\pi$
$350$	−44.6918	−2.38888
$351$	−12.2470	−0.653697
$352$	0	0
$353$	−3.56825	−0.189919	−0.0949593	−	0.995481i	$-0.530272\pi$
$353$	−3.56825	−0.189919	−0.0949593	+	0.995481i	$0.530272\pi$
$354$	−31.8033	−1.69033
$355$	−50.0139	−2.65446
$356$	8.23674	0.436546
$357$	−50.0252	−2.64762
$358$	16.7881	0.887279
$359$	21.8282	1.15205	0.576025	−	0.817432i	$-0.304603\pi$
$359$	21.8282	1.15205	0.576025	+	0.817432i	$0.304603\pi$
$360$	−35.0916	−1.84949
$361$	1.00000	0.0526316
$362$	17.5877	0.924391
$363$	0	0
$364$	2.41462	0.126561
$365$	−41.3369	−2.16367
$366$	−14.8881	−0.778214
$367$	7.86931	0.410774	0.205387	−	0.978681i	$-0.434155\pi$
$367$	7.86931	0.410774	0.205387	+	0.978681i	$0.434155\pi$
$368$	6.35872	0.331471
$369$	61.5074	3.20195
$370$	−14.6552	−0.761888
$371$	−24.5068	−1.27233
$372$	−5.25629	−0.272526
$373$	−2.90718	−0.150528	−0.0752639	−	0.997164i	$-0.523980\pi$
$373$	−2.90718	−0.150528	−0.0752639	+	0.997164i	$0.523980\pi$
$374$	0	0
$375$	−104.124	−5.37695
$376$	0.862845	0.0444978
$377$	−2.19045	−0.112814
$378$	−65.9895	−3.39413
$379$	4.89402	0.251389	0.125694	−	0.992069i	$-0.459884\pi$
$379$	4.89402	0.251389	0.125694	+	0.992069i	$0.459884\pi$
$380$	4.17017	0.213925
$381$	−23.8710	−1.22295
$382$	−2.76249	−0.141341
$383$	−12.3879	−0.632994	−0.316497	−	0.948593i	$-0.602507\pi$
$383$	−12.3879	−0.632994	−0.316497	+	0.948593i	$0.602507\pi$
$384$	3.37860	0.172413
$385$	0	0
$386$	21.4775	1.09317
$387$	−50.8824	−2.58650
$388$	0.809369	0.0410895
$389$	−13.7527	−0.697291	−0.348645	−	0.937255i	$-0.613358\pi$
$389$	−13.7527	−0.697291	−0.348645	+	0.937255i	$0.613358\pi$
$390$	9.43175	0.477595
$391$	26.1021	1.32004
$392$	6.01048	0.303575
$393$	−11.0218	−0.555975
$394$	−18.9032	−0.952330
$395$	−4.36000	−0.219375
$396$	0	0
$397$	10.0289	0.503338	0.251669	−	0.967813i	$-0.419021\pi$
$397$	10.0289	0.503338	0.251669	+	0.967813i	$0.419021\pi$
$398$	7.76283	0.389115
$399$	12.1866	0.610094
$400$	12.3903	0.619515
$401$	22.2869	1.11296	0.556479	−	0.830862i	$-0.312152\pi$
$401$	22.2869	1.11296	0.556479	+	0.830862i	$0.312152\pi$
$402$	6.09296	0.303889
$403$	1.04147	0.0518792
$404$	−12.0493	−0.599475
$405$	−152.487	−7.57712
$406$	−11.8026	−0.585752
$407$	0	0
$408$	13.8689	0.686613
$409$	5.88120	0.290807	0.145403	−	0.989372i	$-0.453552\pi$
$409$	5.88120	0.290807	0.145403	+	0.989372i	$0.453552\pi$
$410$	−30.4811	−1.50536
$411$	4.23604	0.208949
$412$	5.64096	0.277910
$413$	33.9534	1.67074
$414$	53.5081	2.62978
$415$	−2.10106	−0.103137
$416$	−0.669426	−0.0328213
$417$	5.14988	0.252191
$418$	0	0
$419$	3.24502	0.158530	0.0792648	−	0.996854i	$-0.474743\pi$
$419$	3.24502	0.158530	0.0792648	+	0.996854i	$0.474743\pi$
$420$	50.8202	2.47977
$421$	−19.2545	−0.938405	−0.469203	−	0.883091i	$-0.655459\pi$
$421$	−19.2545	−0.938405	−0.469203	+	0.883091i	$0.655459\pi$
$422$	−6.88377	−0.335097
$423$	7.26077	0.353031
$424$	6.79423	0.329957
$425$	50.8613	2.46714
$426$	40.5204	1.96322
$427$	15.8946	0.769194
$428$	15.1059	0.730172
$429$	0	0
$430$	25.2157	1.21601
$431$	−23.7828	−1.14558	−0.572789	−	0.819703i	$-0.694139\pi$
$431$	−23.7828	−1.14558	−0.572789	+	0.819703i	$0.694139\pi$
$432$	18.2948	0.880210
$433$	−17.1402	−0.823707	−0.411853	−	0.911250i	$-0.635118\pi$
$433$	−17.1402	−0.823707	−0.411853	+	0.911250i	$0.635118\pi$
$434$	5.61164	0.269367
$435$	−46.1020	−2.21042
$436$	−11.6030	−0.555685
$437$	−6.35872	−0.304179
$438$	33.4904	1.60023
$439$	−0.144467	−0.00689503	−0.00344752	−	0.999994i	$-0.501097\pi$
$439$	−0.144467	−0.00689503	−0.00344752	+	0.999994i	$0.501097\pi$
$440$	0	0
$441$	50.5777	2.40846
$442$	−2.74795	−0.130707
$443$	−19.6940	−0.935692	−0.467846	−	0.883810i	$-0.654970\pi$
$443$	−19.6940	−0.935692	−0.467846	+	0.883810i	$0.654970\pi$
$444$	11.8734	0.563486
$445$	−34.3486	−1.62828
$446$	14.5212	0.687597
$447$	−53.0009	−2.50686
$448$	−3.60700	−0.170415
$449$	−30.0122	−1.41636	−0.708182	−	0.706030i	$-0.750484\pi$
$449$	−30.0122	−1.41636	−0.708182	+	0.706030i	$0.750484\pi$
$450$	104.263	4.91502
$451$	0	0
$452$	−6.03660	−0.283938
$453$	64.1476	3.01392
$454$	−18.1073	−0.849817
$455$	−10.0694	−0.472060
$456$	−3.37860	−0.158217
$457$	0.810437	0.0379106	0.0189553	−	0.999820i	$-0.493966\pi$
$457$	0.810437	0.0379106	0.0189553	+	0.999820i	$0.493966\pi$
$458$	−25.3580	−1.18490
$459$	75.0990	3.50532
$460$	−26.5169	−1.23636
$461$	29.4451	1.37139	0.685697	−	0.727888i	$-0.259498\pi$
$461$	29.4451	1.37139	0.685697	+	0.727888i	$0.259498\pi$
$462$	0	0
$463$	24.9830	1.16106	0.580529	−	0.814239i	$-0.302846\pi$
$463$	24.9830	1.16106	0.580529	+	0.814239i	$0.302846\pi$
$464$	3.27213	0.151905
$465$	21.9196	1.01650
$466$	−21.9886	−1.01860
$467$	−21.6826	−1.00335	−0.501676	−	0.865056i	$-0.667283\pi$
$467$	−21.6826	−1.00335	−0.501676	+	0.865056i	$0.667283\pi$
$468$	−5.63316	−0.260393
$469$	−6.50487	−0.300367
$470$	−3.59821	−0.165973
$471$	−30.0550	−1.38486
$472$	−9.41317	−0.433276
$473$	0	0
$474$	3.53240	0.162248
$475$	−12.3903	−0.568506
$476$	−14.8065	−0.678655
$477$	57.1729	2.61777
$478$	15.2971	0.699674
$479$	30.8590	1.40998	0.704992	−	0.709215i	$-0.250951\pi$
$479$	30.8590	1.40998	0.704992	+	0.709215i	$0.250951\pi$
$480$	−14.0893	−0.643086
$481$	−2.35256	−0.107268
$482$	16.0409	0.730643
$483$	−77.4913	−3.52598
$484$	0	0
$485$	−3.37520	−0.153260
$486$	68.6575	3.11437
$487$	−5.68001	−0.257386	−0.128693	−	0.991685i	$-0.541078\pi$
$487$	−5.68001	−0.257386	−0.128693	+	0.991685i	$0.541078\pi$
$488$	−4.40660	−0.199477
$489$	−16.3693	−0.740244
$490$	−25.0647	−1.13231
$491$	29.9204	1.35029	0.675145	−	0.737685i	$-0.264081\pi$
$491$	29.9204	1.35029	0.675145	+	0.737685i	$0.264081\pi$
$492$	24.6953	1.11335
$493$	13.4319	0.604941
$494$	0.669426	0.0301189
$495$	0	0
$496$	−1.55576	−0.0698558
$497$	−43.2598	−1.94047
$498$	1.70224	0.0762793
$499$	−2.89019	−0.129383	−0.0646913	−	0.997905i	$-0.520606\pi$
$499$	−2.89019	−0.129383	−0.0646913	+	0.997905i	$0.520606\pi$
$500$	−30.8187	−1.37826
$501$	−15.5935	−0.696664
$502$	−6.91197	−0.308496
$503$	−27.9653	−1.24691	−0.623456	−	0.781858i	$-0.714272\pi$
$503$	−27.9653	−1.24691	−0.623456	+	0.781858i	$0.714272\pi$
$504$	−30.3526	−1.35201
$505$	50.2476	2.23599
$506$	0	0
$507$	−42.4077	−1.88339
$508$	−7.06535	−0.313474
$509$	−34.7436	−1.53998	−0.769992	−	0.638054i	$-0.779740\pi$
$509$	−34.7436	−1.53998	−0.769992	+	0.638054i	$0.779740\pi$
$510$	−57.8357	−2.56101
$511$	−35.7545	−1.58169
$512$	1.00000	0.0441942
$513$	−18.2948	−0.807736
$514$	−24.7512	−1.09173
$515$	−23.5237	−1.03658
$516$	−20.4293	−0.899351
$517$	0	0
$518$	−12.6761	−0.556955
$519$	−31.5506	−1.38492
$520$	2.79162	0.122420
$521$	26.9219	1.17947	0.589734	−	0.807597i	$-0.299232\pi$
$521$	26.9219	1.17947	0.589734	+	0.807597i	$0.299232\pi$
$522$	27.5347	1.20516
$523$	−2.23979	−0.0979394	−0.0489697	−	0.998800i	$-0.515594\pi$
$523$	−2.23979	−0.0979394	−0.0489697	+	0.998800i	$0.515594\pi$
$524$	−3.26224	−0.142512
$525$	−150.996	−6.58999
$526$	16.8155	0.733190
$527$	−6.38630	−0.278192
$528$	0	0
$529$	17.4334	0.757973
$530$	−28.3331	−1.23071
$531$	−79.2110	−3.43747
$532$	3.60700	0.156383
$533$	−4.89305	−0.211942
$534$	27.8286	1.20426
$535$	−62.9942	−2.72348
$536$	1.80340	0.0778950
$537$	56.7203	2.44766
$538$	17.8288	0.768655
$539$	0	0
$540$	−76.2924	−3.28310
$541$	−9.52299	−0.409425	−0.204713	−	0.978822i	$-0.565626\pi$
$541$	−9.52299	−0.409425	−0.204713	+	0.978822i	$0.565626\pi$
$542$	−30.2063	−1.29747
$543$	59.4219	2.55004
$544$	4.10493	0.175998
$545$	48.3866	2.07265
$546$	8.15803	0.349132
$547$	−17.0265	−0.727999	−0.364000	−	0.931399i	$-0.618589\pi$
$547$	−17.0265	−0.727999	−0.364000	+	0.931399i	$0.618589\pi$
$548$	1.25379	0.0535592
$549$	−37.0811	−1.58258
$550$	0	0
$551$	−3.27213	−0.139397
$552$	21.4836	0.914401
$553$	−3.77120	−0.160368
$554$	32.7642	1.39202
$555$	−49.5140	−2.10175
$556$	1.52427	0.0646433
$557$	−14.4105	−0.610593	−0.305296	−	0.952257i	$-0.598756\pi$
$557$	−14.4105	−0.610593	−0.305296	+	0.952257i	$0.598756\pi$
$558$	−13.0916	−0.554212
$559$	4.04781	0.171204
$560$	15.0418	0.635633
$561$	0	0
$562$	−9.70846	−0.409527
$563$	−14.3589	−0.605156	−0.302578	−	0.953125i	$-0.597847\pi$
$563$	−14.3589	−0.605156	−0.302578	+	0.953125i	$0.597847\pi$
$564$	2.91521	0.122752
$565$	25.1736	1.05906
$566$	14.5739	0.612585
$567$	−131.894	−5.53902
$568$	11.9933	0.503226
$569$	27.8880	1.16912	0.584562	−	0.811349i	$-0.301266\pi$
$569$	27.8880	1.16912	0.584562	+	0.811349i	$0.301266\pi$
$570$	14.0893	0.590136
$571$	−40.1622	−1.68073	−0.840367	−	0.542018i	$-0.817660\pi$
$571$	−40.1622	−1.68073	−0.840367	+	0.542018i	$0.817660\pi$
$572$	0	0
$573$	−9.33335	−0.389906
$574$	−26.3648	−1.10044
$575$	78.7864	3.28562
$576$	8.41492	0.350621
$577$	3.68171	0.153271	0.0766357	−	0.997059i	$-0.475582\pi$
$577$	3.68171	0.153271	0.0766357	+	0.997059i	$0.475582\pi$
$578$	−0.149526	−0.00621944
$579$	72.5637	3.01564
$580$	−13.6453	−0.566591
$581$	−1.81732	−0.0753952
$582$	2.73453	0.113350
$583$	0	0
$584$	9.91252	0.410183
$585$	23.4912	0.971242
$586$	−10.5241	−0.434746
$587$	−44.1246	−1.82122	−0.910608	−	0.413272i	$-0.864386\pi$
$587$	−44.1246	−1.82122	−0.910608	+	0.413272i	$0.864386\pi$
$588$	20.3070	0.837446
$589$	1.55576	0.0641041
$590$	39.2545	1.61608
$591$	−63.8663	−2.62711
$592$	3.51430	0.144437
$593$	−2.42622	−0.0996330	−0.0498165	−	0.998758i	$-0.515864\pi$
$593$	−2.42622	−0.0996330	−0.0498165	+	0.998758i	$0.515864\pi$
$594$	0	0
$595$	61.7456	2.53132
$596$	−15.6872	−0.642575
$597$	26.2275	1.07342
$598$	−4.25669	−0.174069
$599$	30.0748	1.22882	0.614412	−	0.788986i	$-0.289393\pi$
$599$	30.0748	1.22882	0.614412	+	0.788986i	$0.289393\pi$
$600$	41.8618	1.70900
$601$	43.6023	1.77858	0.889288	−	0.457348i	$-0.151201\pi$
$601$	43.6023	1.77858	0.889288	+	0.457348i	$0.151201\pi$
$602$	21.8104	0.888927
$603$	15.1755	0.617992
$604$	18.9865	0.772548
$605$	0	0
$606$	−40.7097	−1.65372
$607$	−3.95907	−0.160694	−0.0803468	−	0.996767i	$-0.525603\pi$
$607$	−3.95907	−0.160694	−0.0803468	+	0.996767i	$0.525603\pi$
$608$	−1.00000	−0.0405554
$609$	−39.8761	−1.61586
$610$	18.3762	0.744032
$611$	−0.577611	−0.0233676
$612$	34.5427	1.39630
$613$	33.3417	1.34666	0.673329	−	0.739343i	$-0.264864\pi$
$613$	33.3417	1.34666	0.673329	+	0.739343i	$0.264864\pi$
$614$	−21.4131	−0.864161
$615$	−102.983	−4.15269
$616$	0	0
$617$	−46.8084	−1.88443	−0.942217	−	0.335004i	$-0.891262\pi$
$617$	−46.8084	−1.88443	−0.942217	+	0.335004i	$0.891262\pi$
$618$	19.0585	0.766646
$619$	−3.44952	−0.138648	−0.0693239	−	0.997594i	$-0.522084\pi$
$619$	−3.44952	−0.138648	−0.0693239	+	0.997594i	$0.522084\pi$
$620$	6.48779	0.260556
$621$	116.332	4.66823
$622$	8.91440	0.357435
$623$	−29.7100	−1.19030
$624$	−2.26172	−0.0905412
$625$	66.5679	2.66271
$626$	−29.2280	−1.16818
$627$	0	0
$628$	−8.89570	−0.354977
$629$	14.4260	0.575200
$630$	126.576	5.04289
$631$	−3.45479	−0.137533	−0.0687665	−	0.997633i	$-0.521906\pi$
$631$	−3.45479	−0.137533	−0.0687665	+	0.997633i	$0.521906\pi$
$632$	1.04552	0.0415886
$633$	−23.2575	−0.924402
$634$	−3.86251	−0.153400
$635$	29.4637	1.16923
$636$	22.9550	0.910224
$637$	−4.02357	−0.159420
$638$	0	0
$639$	100.922	3.99243
$640$	−4.17017	−0.164840
$641$	4.16142	0.164366	0.0821831	−	0.996617i	$-0.473811\pi$
$641$	4.16142	0.164366	0.0821831	+	0.996617i	$0.473811\pi$
$642$	51.0368	2.01426
$643$	−27.0695	−1.06752	−0.533759	−	0.845637i	$-0.679221\pi$
$643$	−27.0695	−1.06752	−0.533759	+	0.845637i	$0.679221\pi$
$644$	−22.9359	−0.903803
$645$	85.1937	3.35450
$646$	−4.10493	−0.161506
$647$	−4.31680	−0.169711	−0.0848554	−	0.996393i	$-0.527043\pi$
$647$	−4.31680	−0.169711	−0.0848554	+	0.996393i	$0.527043\pi$
$648$	36.5661	1.43645
$649$	0	0
$650$	−8.29438	−0.325332
$651$	18.9595	0.743080
$652$	−4.84499	−0.189744
$653$	−5.85277	−0.229037	−0.114518	−	0.993421i	$-0.536532\pi$
$653$	−5.85277	−0.229037	−0.114518	+	0.993421i	$0.536532\pi$
$654$	−39.2020	−1.53292
$655$	13.6041	0.531555
$656$	7.30933	0.285381
$657$	83.4131	3.25425
$658$	−3.11229	−0.121330
$659$	16.4116	0.639307	0.319653	−	0.947535i	$-0.396434\pi$
$659$	16.4116	0.639307	0.319653	+	0.947535i	$0.396434\pi$
$660$	0	0
$661$	−25.8425	−1.00516	−0.502578	−	0.864532i	$-0.667615\pi$
$661$	−25.8425	−1.00516	−0.502578	+	0.864532i	$0.667615\pi$
$662$	30.7968	1.19695
$663$	−9.28421	−0.360569
$664$	0.503831	0.0195524
$665$	−15.0418	−0.583296
$666$	29.5725	1.14591
$667$	20.8066	0.805633
$668$	−4.61536	−0.178574
$669$	49.0611	1.89681
$670$	−7.52048	−0.290541
$671$	0	0
$672$	−12.1866	−0.470109
$673$	4.23989	0.163436	0.0817178	−	0.996656i	$-0.473959\pi$
$673$	4.23989	0.163436	0.0817178	+	0.996656i	$0.473959\pi$
$674$	−16.0941	−0.619923
$675$	226.678	8.72484
$676$	−12.5519	−0.482764
$677$	49.7388	1.91162	0.955809	−	0.293988i	$-0.0949826\pi$
$677$	49.7388	1.91162	0.955809	+	0.293988i	$0.0949826\pi$
$678$	−20.3953	−0.783275
$679$	−2.91940	−0.112036
$680$	−17.1183	−0.656455
$681$	−61.1772	−2.34432
$682$	0	0
$683$	38.4329	1.47059	0.735297	−	0.677745i	$-0.237043\pi$
$683$	38.4329	1.47059	0.735297	+	0.677745i	$0.237043\pi$
$684$	−8.41492	−0.321752
$685$	−5.22851	−0.199771
$686$	3.56920	0.136273
$687$	−85.6743	−3.26868
$688$	−6.04669	−0.230528
$689$	−4.54823	−0.173274
$690$	−89.5900	−3.41063
$691$	26.5880	1.01145	0.505727	−	0.862693i	$-0.331224\pi$
$691$	26.5880	1.01145	0.505727	+	0.862693i	$0.331224\pi$
$692$	−9.33836	−0.354991
$693$	0	0
$694$	−31.7933	−1.20686
$695$	−6.35644	−0.241114
$696$	11.0552	0.419046
$697$	30.0043	1.13649
$698$	11.5331	0.436532
$699$	−74.2906	−2.80993
$700$	−44.6918	−1.68919
$701$	−14.6368	−0.552826	−0.276413	−	0.961039i	$-0.589146\pi$
$701$	−14.6368	−0.552826	−0.276413	+	0.961039i	$0.589146\pi$
$702$	−12.2470	−0.462234
$703$	−3.51430	−0.132544
$704$	0	0
$705$	−12.1569	−0.457855
$706$	−3.56825	−0.134293
$707$	43.4619	1.63455
$708$	−31.8033	−1.19524
$709$	14.7490	0.553911	0.276956	−	0.960883i	$-0.410674\pi$
$709$	14.7490	0.553911	0.276956	+	0.960883i	$0.410674\pi$
$710$	−50.0139	−1.87699
$711$	8.79798	0.329950
$712$	8.23674	0.308685
$713$	−9.89266	−0.370483
$714$	−50.0252	−1.87215
$715$	0	0
$716$	16.7881	0.627401
$717$	51.6828	1.93013
$718$	21.8282	0.814622
$719$	8.82348	0.329060	0.164530	−	0.986372i	$-0.447389\pi$
$719$	8.82348	0.329060	0.164530	+	0.986372i	$0.447389\pi$
$720$	−35.0916	−1.30779
$721$	−20.3470	−0.757760
$722$	1.00000	0.0372161
$723$	54.1957	2.01556
$724$	17.5877	0.653643
$725$	40.5426	1.50571
$726$	0	0
$727$	0.938013	0.0347890	0.0173945	−	0.999849i	$-0.494463\pi$
$727$	0.938013	0.0347890	0.0173945	+	0.999849i	$0.494463\pi$
$728$	2.41462	0.0894918
$729$	122.268	4.52844
$730$	−41.3369	−1.52995
$731$	−24.8213	−0.918048
$732$	−14.8881	−0.550280
$733$	2.58558	0.0955007	0.0477504	−	0.998859i	$-0.484795\pi$
$733$	2.58558	0.0955007	0.0477504	+	0.998859i	$0.484795\pi$
$734$	7.86931	0.290461
$735$	−84.6835	−3.12360
$736$	6.35872	0.234386
$737$	0	0
$738$	61.5074	2.26412
$739$	−1.56553	−0.0575888	−0.0287944	−	0.999585i	$-0.509167\pi$
$739$	−1.56553	−0.0575888	−0.0287944	+	0.999585i	$0.509167\pi$
$740$	−14.6552	−0.538736
$741$	2.26172	0.0830863
$742$	−24.5068	−0.899674
$743$	35.3325	1.29623	0.648113	−	0.761545i	$-0.275559\pi$
$743$	35.3325	1.29623	0.648113	+	0.761545i	$0.275559\pi$
$744$	−5.25629	−0.192705
$745$	65.4184	2.39675
$746$	−2.90718	−0.106439
$747$	4.23970	0.155122
$748$	0	0
$749$	−54.4871	−1.99092
$750$	−104.124	−3.80208
$751$	−11.3947	−0.415799	−0.207900	−	0.978150i	$-0.566663\pi$
$751$	−11.3947	−0.415799	−0.207900	+	0.978150i	$0.566663\pi$
$752$	0.862845	0.0314647
$753$	−23.3527	−0.851021
$754$	−2.19045	−0.0797713
$755$	−79.1767	−2.88153
$756$	−65.9895	−2.40001
$757$	−6.68211	−0.242865	−0.121433	−	0.992600i	$-0.538749\pi$
$757$	−6.68211	−0.242865	−0.121433	+	0.992600i	$0.538749\pi$
$758$	4.89402	0.177759
$759$	0	0
$760$	4.17017	0.151268
$761$	2.33169	0.0845239	0.0422619	−	0.999107i	$-0.486544\pi$
$761$	2.33169	0.0845239	0.0422619	+	0.999107i	$0.486544\pi$
$762$	−23.8710	−0.864754
$763$	41.8522	1.51515
$764$	−2.76249	−0.0999435
$765$	−144.049	−5.20809
$766$	−12.3879	−0.447594
$767$	6.30142	0.227531
$768$	3.37860	0.121915
$769$	28.8994	1.04214	0.521070	−	0.853514i	$-0.325533\pi$
$769$	28.8994	1.04214	0.521070	+	0.853514i	$0.325533\pi$
$770$	0	0
$771$	−83.6242	−3.01165
$772$	21.4775	0.772991
$773$	−25.5506	−0.918991	−0.459495	−	0.888180i	$-0.651970\pi$
$773$	−25.5506	−0.918991	−0.459495	+	0.888180i	$0.651970\pi$
$774$	−50.8824	−1.82893
$775$	−19.2763	−0.692427
$776$	0.809369	0.0290546
$777$	−42.8274	−1.53642
$778$	−13.7527	−0.493059
$779$	−7.30933	−0.261884
$780$	9.43175	0.337711
$781$	0	0
$782$	26.1021	0.933411
$783$	59.8630	2.13933
$784$	6.01048	0.214660
$785$	37.0966	1.32403
$786$	−11.0218	−0.393134
$787$	10.5042	0.374436	0.187218	−	0.982318i	$-0.440053\pi$
$787$	10.5042	0.374436	0.187218	+	0.982318i	$0.440053\pi$
$788$	−18.9032	−0.673399
$789$	56.8128	2.02259
$790$	−4.36000	−0.155122
$791$	21.7741	0.774196
$792$	0	0
$793$	2.94989	0.104754
$794$	10.0289	0.355914
$795$	−95.7261	−3.39505
$796$	7.76283	0.275146
$797$	−6.50041	−0.230256	−0.115128	−	0.993351i	$-0.536728\pi$
$797$	−6.50041	−0.230256	−0.115128	+	0.993351i	$0.536728\pi$
$798$	12.1866	0.431401
$799$	3.54192	0.125304
$800$	12.3903	0.438063
$801$	69.3115	2.44900
$802$	22.2869	0.786979
$803$	0	0
$804$	6.09296	0.214882
$805$	95.6467	3.37110
$806$	1.04147	0.0366841
$807$	60.2364	2.12042
$808$	−12.0493	−0.423893
$809$	−30.5543	−1.07423	−0.537116	−	0.843509i	$-0.680486\pi$
$809$	−30.5543	−1.07423	−0.537116	+	0.843509i	$0.680486\pi$
$810$	−152.487	−5.35783
$811$	5.81000	0.204017	0.102008	−	0.994784i	$-0.467473\pi$
$811$	5.81000	0.204017	0.102008	+	0.994784i	$0.467473\pi$
$812$	−11.8026	−0.414189
$813$	−102.055	−3.57922
$814$	0	0
$815$	20.2044	0.707730
$816$	13.8689	0.485509
$817$	6.04669	0.211547
$818$	5.88120	0.205631
$819$	20.3188	0.709997
$820$	−30.4811	−1.06445
$821$	−43.0690	−1.50312	−0.751559	−	0.659666i	$-0.770698\pi$
$821$	−43.0690	−1.50312	−0.751559	+	0.659666i	$0.770698\pi$
$822$	4.23604	0.147749
$823$	−20.6760	−0.720722	−0.360361	−	0.932813i	$-0.617346\pi$
$823$	−20.6760	−0.720722	−0.360361	+	0.932813i	$0.617346\pi$
$824$	5.64096	0.196512
$825$	0	0
$826$	33.9534	1.18139
$827$	35.8535	1.24675	0.623374	−	0.781924i	$-0.285761\pi$
$827$	35.8535	1.24675	0.623374	+	0.781924i	$0.285761\pi$
$828$	53.5081	1.85954
$829$	10.6519	0.369956	0.184978	−	0.982743i	$-0.440779\pi$
$829$	10.6519	0.369956	0.184978	+	0.982743i	$0.440779\pi$
$830$	−2.10106	−0.0729288
$831$	110.697	3.84004
$832$	−0.669426	−0.0232082
$833$	24.6726	0.854856
$834$	5.14988	0.178326
$835$	19.2468	0.666064
$836$	0	0
$837$	−28.4624	−0.983804
$838$	3.24502	0.112097
$839$	−46.8329	−1.61685	−0.808425	−	0.588599i	$-0.799680\pi$
$839$	−46.8329	−1.61685	−0.808425	+	0.588599i	$0.799680\pi$
$840$	50.8202	1.75346
$841$	−18.2932	−0.630799
$842$	−19.2545	−0.663553
$843$	−32.8010	−1.12973
$844$	−6.88377	−0.236949
$845$	52.3434	1.80067
$846$	7.26077	0.249630
$847$	0	0
$848$	6.79423	0.233315
$849$	49.2392	1.68988
$850$	50.8613	1.74453
$851$	22.3464	0.766026
$852$	40.5204	1.38821
$853$	35.3351	1.20985	0.604926	−	0.796282i	$-0.293203\pi$
$853$	35.3351	1.20985	0.604926	+	0.796282i	$0.293203\pi$
$854$	15.8946	0.543902
$855$	35.0916	1.20011
$856$	15.1059	0.516309
$857$	−4.94229	−0.168826	−0.0844128	−	0.996431i	$-0.526901\pi$
$857$	−4.94229	−0.168826	−0.0844128	+	0.996431i	$0.526901\pi$
$858$	0	0
$859$	10.1131	0.345054	0.172527	−	0.985005i	$-0.444807\pi$
$859$	10.1131	0.345054	0.172527	+	0.985005i	$0.444807\pi$
$860$	25.2157	0.859849
$861$	−89.0760	−3.03570
$862$	−23.7828	−0.810046
$863$	12.9844	0.441995	0.220998	−	0.975274i	$-0.429069\pi$
$863$	12.9844	0.441995	0.220998	+	0.975274i	$0.429069\pi$
$864$	18.2948	0.622402
$865$	38.9425	1.32409
$866$	−17.1402	−0.582449
$867$	−0.505186	−0.0171570
$868$	5.61164	0.190471
$869$	0	0
$870$	−46.1020	−1.56300
$871$	−1.20724	−0.0409058
$872$	−11.6030	−0.392929
$873$	6.81077	0.230510
$874$	−6.35872	−0.215087
$875$	111.163	3.75801
$876$	33.4904	1.13154
$877$	44.8363	1.51401	0.757007	−	0.653407i	$-0.226661\pi$
$877$	44.8363	1.51401	0.757007	+	0.653407i	$0.226661\pi$
$878$	−0.144467	−0.00487552
$879$	−35.5567	−1.19930
$880$	0	0
$881$	−21.0954	−0.710722	−0.355361	−	0.934729i	$-0.615642\pi$
$881$	−21.0954	−0.710722	−0.355361	+	0.934729i	$0.615642\pi$
$882$	50.5777	1.70304
$883$	53.8142	1.81099	0.905496	−	0.424355i	$-0.139499\pi$
$883$	53.8142	1.81099	0.905496	+	0.424355i	$0.139499\pi$
$884$	−2.74795	−0.0924235
$885$	132.625	4.45814
$886$	−19.6940	−0.661634
$887$	−28.4930	−0.956701	−0.478351	−	0.878169i	$-0.658765\pi$
$887$	−28.4930	−0.956701	−0.478351	+	0.878169i	$0.658765\pi$
$888$	11.8734	0.398445
$889$	25.4848	0.854731
$890$	−34.3486	−1.15137
$891$	0	0
$892$	14.5212	0.486204
$893$	−0.862845	−0.0288740
$894$	−53.0009	−1.77261
$895$	−70.0092	−2.34015
$896$	−3.60700	−0.120502
$897$	−14.3816	−0.480189
$898$	−30.0122	−1.00152
$899$	−5.09065	−0.169783
$900$	104.263	3.47544
$901$	27.8899	0.929146
$902$	0	0
$903$	73.6887	2.45221
$904$	−6.03660	−0.200774
$905$	−73.3438	−2.43803
$906$	64.1476	2.13116
$907$	−19.0581	−0.632815	−0.316408	−	0.948623i	$-0.602477\pi$
$907$	−19.0581	−0.632815	−0.316408	+	0.948623i	$0.602477\pi$
$908$	−18.1073	−0.600912
$909$	−101.394	−3.36302
$910$	−10.0694	−0.333796
$911$	−8.41671	−0.278858	−0.139429	−	0.990232i	$-0.544527\pi$
$911$	−8.41671	−0.278858	−0.139429	+	0.990232i	$0.544527\pi$
$912$	−3.37860	−0.111877
$913$	0	0
$914$	0.810437	0.0268069
$915$	62.0859	2.05250
$916$	−25.3580	−0.837850
$917$	11.7669	0.388577
$918$	75.0990	2.47864
$919$	−10.5289	−0.347315	−0.173658	−	0.984806i	$-0.555559\pi$
$919$	−10.5289	−0.347315	−0.173658	+	0.984806i	$0.555559\pi$
$920$	−26.5169	−0.874238
$921$	−72.3461	−2.38388
$922$	29.4451	0.969721
$923$	−8.02860	−0.264265
$924$	0	0
$925$	43.5432	1.43169
$926$	24.9830	0.820992
$927$	47.4682	1.55906
$928$	3.27213	0.107413
$929$	−19.5004	−0.639787	−0.319893	−	0.947454i	$-0.603647\pi$
$929$	−19.5004	−0.639787	−0.319893	+	0.947454i	$0.603647\pi$
$930$	21.9196	0.718773
$931$	−6.01048	−0.196986
$932$	−21.9886	−0.720261
$933$	30.1182	0.986024
$934$	−21.6826	−0.709477
$935$	0	0
$936$	−5.63316	−0.184126
$937$	46.4018	1.51588	0.757941	−	0.652323i	$-0.226206\pi$
$937$	46.4018	1.51588	0.757941	+	0.652323i	$0.226206\pi$
$938$	−6.50487	−0.212392
$939$	−98.7495	−3.22257
$940$	−3.59821	−0.117361
$941$	−17.4235	−0.567991	−0.283996	−	0.958826i	$-0.591660\pi$
$941$	−17.4235	−0.567991	−0.283996	+	0.958826i	$0.591660\pi$
$942$	−30.0550	−0.979245
$943$	46.4780	1.51353
$944$	−9.41317	−0.306373
$945$	275.187	8.95184
$946$	0	0
$947$	−18.8103	−0.611254	−0.305627	−	0.952151i	$-0.598866\pi$
$947$	−18.8103	−0.611254	−0.305627	+	0.952151i	$0.598866\pi$
$948$	3.53240	0.114727
$949$	−6.63570	−0.215404
$950$	−12.3903	−0.401994
$951$	−13.0499	−0.423171
$952$	−14.8065	−0.479882
$953$	54.4674	1.76437	0.882187	−	0.470900i	$-0.156071\pi$
$953$	54.4674	1.76437	0.882187	+	0.470900i	$0.156071\pi$
$954$	57.1729	1.85104
$955$	11.5201	0.372780
$956$	15.2971	0.494744
$957$	0	0
$958$	30.8590	0.997009
$959$	−4.52242	−0.146037
$960$	−14.0893	−0.454731
$961$	−28.5796	−0.921923
$962$	−2.35256	−0.0758496
$963$	127.115	4.09622
$964$	16.0409	0.516642
$965$	−89.5646	−2.88319
$966$	−77.4913	−2.49324
$967$	51.7050	1.66272	0.831361	−	0.555733i	$-0.187562\pi$
$967$	51.7050	1.66272	0.831361	+	0.555733i	$0.187562\pi$
$968$	0	0
$969$	−13.8689	−0.445534
$970$	−3.37520	−0.108371
$971$	41.0651	1.31784	0.658920	−	0.752213i	$-0.271013\pi$
$971$	41.0651	1.31784	0.658920	+	0.752213i	$0.271013\pi$
$972$	68.6575	2.20219
$973$	−5.49803	−0.176259
$974$	−5.68001	−0.181999
$975$	−28.0234	−0.897466
$976$	−4.40660	−0.141052
$977$	−15.0675	−0.482052	−0.241026	−	0.970519i	$-0.577484\pi$
$977$	−15.0675	−0.482052	−0.241026	+	0.970519i	$0.577484\pi$
$978$	−16.3693	−0.523431
$979$	0	0
$980$	−25.0647	−0.800663
$981$	−97.6386	−3.11736
$982$	29.9204	0.954799
$983$	−24.2754	−0.774263	−0.387132	−	0.922024i	$-0.626534\pi$
$983$	−24.2754	−0.774263	−0.387132	+	0.922024i	$0.626534\pi$
$984$	24.6953	0.787257
$985$	78.8295	2.51172
$986$	13.4319	0.427758
$987$	−10.5152	−0.334701
$988$	0.669426	0.0212973
$989$	−38.4492	−1.22261
$990$	0	0
$991$	−18.0803	−0.574339	−0.287169	−	0.957880i	$-0.592714\pi$
$991$	−18.0803	−0.574339	−0.287169	+	0.957880i	$0.592714\pi$
$992$	−1.55576	−0.0493955
$993$	104.050	3.30193
$994$	−43.2598	−1.37212
$995$	−32.3723	−1.02627
$996$	1.70224	0.0539376
$997$	17.0357	0.539527	0.269764	−	0.962927i	$-0.413054\pi$
$997$	17.0357	0.539527	0.269764	+	0.962927i	$0.413054\pi$
$998$	−2.89019	−0.0914873
$999$	64.2934	2.03415

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4598.2.a.cb.1.8	yes	8
11.10	odd	2		4598.2.a.by.1.8	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4598.2.a.by.1.8	✓	8	11.10	odd	2
4598.2.a.cb.1.8	yes	8	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4598 = 2 \cdot 11^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4598.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +3.37860 q^{3} +1.00000 q^{4} -4.17017 q^{5} +3.37860 q^{6} -3.60700 q^{7} +1.00000 q^{8} +8.41492 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +3.37860 q^{3} +1.00000 q^{4} -4.17017 q^{5} +3.37860 q^{6} -3.60700 q^{7} +1.00000 q^{8} +8.41492 q^{9} -4.17017 q^{10} +3.37860 q^{12} -0.669426 q^{13} -3.60700 q^{14} -14.0893 q^{15} +1.00000 q^{16} +4.10493 q^{17} +8.41492 q^{18} -1.00000 q^{19} -4.17017 q^{20} -12.1866 q^{21} +6.35872 q^{23} +3.37860 q^{24} +12.3903 q^{25} -0.669426 q^{26} +18.2948 q^{27} -3.60700 q^{28} +3.27213 q^{29} -14.0893 q^{30} -1.55576 q^{31} +1.00000 q^{32} +4.10493 q^{34} +15.0418 q^{35} +8.41492 q^{36} +3.51430 q^{37} -1.00000 q^{38} -2.26172 q^{39} -4.17017 q^{40} +7.30933 q^{41} -12.1866 q^{42} -6.04669 q^{43} -35.0916 q^{45} +6.35872 q^{46} +0.862845 q^{47} +3.37860 q^{48} +6.01048 q^{49} +12.3903 q^{50} +13.8689 q^{51} -0.669426 q^{52} +6.79423 q^{53} +18.2948 q^{54} -3.60700 q^{56} -3.37860 q^{57} +3.27213 q^{58} -9.41317 q^{59} -14.0893 q^{60} -4.40660 q^{61} -1.55576 q^{62} -30.3526 q^{63} +1.00000 q^{64} +2.79162 q^{65} +1.80340 q^{67} +4.10493 q^{68} +21.4836 q^{69} +15.0418 q^{70} +11.9933 q^{71} +8.41492 q^{72} +9.91252 q^{73} +3.51430 q^{74} +41.8618 q^{75} -1.00000 q^{76} -2.26172 q^{78} +1.04552 q^{79} -4.17017 q^{80} +36.5661 q^{81} +7.30933 q^{82} +0.503831 q^{83} -12.1866 q^{84} -17.1183 q^{85} -6.04669 q^{86} +11.0552 q^{87} +8.23674 q^{89} -35.0916 q^{90} +2.41462 q^{91} +6.35872 q^{92} -5.25629 q^{93} +0.862845 q^{94} +4.17017 q^{95} +3.37860 q^{96} +0.809369 q^{97} +6.01048 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 8 q^{6} + 4 q^{7} + 8 q^{8} + 22 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 8 * q^6 + 4 * q^7 + 8 * q^8 + 22 * q^9	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 8 q^{6} + 4 q^{7} + 8 q^{8} + 22 q^{9} + 8 q^{12} - 12 q^{13} + 4 q^{14} + 4 q^{15} + 8 q^{16} - 4 q^{17} + 22 q^{18} - 8 q^{19} - 20 q^{21} + 14 q^{23} + 8 q^{24} + 36 q^{25} - 12 q^{26} + 32 q^{27} + 4 q^{28} - 2 q^{29} + 4 q^{30} + 8 q^{32} - 4 q^{34} + 36 q^{35} + 22 q^{36} + 24 q^{37} - 8 q^{38} + 16 q^{39} + 8 q^{41} - 20 q^{42} + 8 q^{43} + 16 q^{45} + 14 q^{46} - 16 q^{47} + 8 q^{48} + 34 q^{49} + 36 q^{50} + 18 q^{51} - 12 q^{52} + 36 q^{53} + 32 q^{54} + 4 q^{56} - 8 q^{57} - 2 q^{58} - 24 q^{59} + 4 q^{60} + 12 q^{61} + 24 q^{63} + 8 q^{64} + 16 q^{65} + 16 q^{67} - 4 q^{68} + 4 q^{69} + 36 q^{70} + 4 q^{71} + 22 q^{72} - 20 q^{73} + 24 q^{74} + 40 q^{75} - 8 q^{76} + 16 q^{78} - 12 q^{79} + 40 q^{81} + 8 q^{82} + 20 q^{83} - 20 q^{84} + 12 q^{85} + 8 q^{86} - 36 q^{87} + 8 q^{89} + 16 q^{90} - 24 q^{91} + 14 q^{92} + 12 q^{93} - 16 q^{94} + 8 q^{96} + 4 q^{97} + 34 q^{98}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 8 * q^6 + 4 * q^7 + 8 * q^8 + 22 * q^9 + 8 * q^12 - 12 * q^13 + 4 * q^14 + 4 * q^15 + 8 * q^16 - 4 * q^17 + 22 * q^18 - 8 * q^19 - 20 * q^21 + 14 * q^23 + 8 * q^24 + 36 * q^25 - 12 * q^26 + 32 * q^27 + 4 * q^28 - 2 * q^29 + 4 * q^30 + 8 * q^32 - 4 * q^34 + 36 * q^35 + 22 * q^36 + 24 * q^37 - 8 * q^38 + 16 * q^39 + 8 * q^41 - 20 * q^42 + 8 * q^43 + 16 * q^45 + 14 * q^46 - 16 * q^47 + 8 * q^48 + 34 * q^49 + 36 * q^50 + 18 * q^51 - 12 * q^52 + 36 * q^53 + 32 * q^54 + 4 * q^56 - 8 * q^57 - 2 * q^58 - 24 * q^59 + 4 * q^60 + 12 * q^61 + 24 * q^63 + 8 * q^64 + 16 * q^65 + 16 * q^67 - 4 * q^68 + 4 * q^69 + 36 * q^70 + 4 * q^71 + 22 * q^72 - 20 * q^73 + 24 * q^74 + 40 * q^75 - 8 * q^76 + 16 * q^78 - 12 * q^79 + 40 * q^81 + 8 * q^82 + 20 * q^83 - 20 * q^84 + 12 * q^85 + 8 * q^86 - 36 * q^87 + 8 * q^89 + 16 * q^90 - 24 * q^91 + 14 * q^92 + 12 * q^93 - 16 * q^94 + 8 * q^96 + 4 * q^97 + 34 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more