LMFDB - Embedded newform 4598.2.a.ca.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} - 2x^{7} - 10x^{6} + 16x^{5} + 26x^{4} - 32x^{3} - 16x^{2} + 20x - 4 $ x^8 - 2x^7 - 10x^6 + 16x^5 + 26x^4 - 32x^3 - 16x^2 + 20*x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 418)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-1.20254$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +3.01451 q^{3} +1.00000 q^{4} -2.00989 q^{5} +3.01451 q^{6} +2.42872 q^{7} +1.00000 q^{8} +6.08725 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +3.01451 q^{3} +1.00000 q^{4} -2.00989 q^{5} +3.01451 q^{6} +2.42872 q^{7} +1.00000 q^{8} +6.08725 q^{9} -2.00989 q^{10} +3.01451 q^{12} +3.03557 q^{13} +2.42872 q^{14} -6.05881 q^{15} +1.00000 q^{16} -4.31675 q^{17} +6.08725 q^{18} -1.00000 q^{19} -2.00989 q^{20} +7.32140 q^{21} -2.27832 q^{23} +3.01451 q^{24} -0.960362 q^{25} +3.03557 q^{26} +9.30653 q^{27} +2.42872 q^{28} +8.81144 q^{29} -6.05881 q^{30} +9.29488 q^{31} +1.00000 q^{32} -4.31675 q^{34} -4.88145 q^{35} +6.08725 q^{36} +1.06805 q^{37} -1.00000 q^{38} +9.15074 q^{39} -2.00989 q^{40} -5.15603 q^{41} +7.32140 q^{42} +11.9841 q^{43} -12.2347 q^{45} -2.27832 q^{46} -9.00012 q^{47} +3.01451 q^{48} -1.10131 q^{49} -0.960362 q^{50} -13.0129 q^{51} +3.03557 q^{52} +5.09532 q^{53} +9.30653 q^{54} +2.42872 q^{56} -3.01451 q^{57} +8.81144 q^{58} -4.79071 q^{59} -6.05881 q^{60} +9.26197 q^{61} +9.29488 q^{62} +14.7842 q^{63} +1.00000 q^{64} -6.10114 q^{65} +9.19479 q^{67} -4.31675 q^{68} -6.86802 q^{69} -4.88145 q^{70} -10.7608 q^{71} +6.08725 q^{72} +8.93977 q^{73} +1.06805 q^{74} -2.89502 q^{75} -1.00000 q^{76} +9.15074 q^{78} +6.52103 q^{79} -2.00989 q^{80} +9.79285 q^{81} -5.15603 q^{82} -4.09108 q^{83} +7.32140 q^{84} +8.67617 q^{85} +11.9841 q^{86} +26.5621 q^{87} +6.04832 q^{89} -12.2347 q^{90} +7.37255 q^{91} -2.27832 q^{92} +28.0195 q^{93} -9.00012 q^{94} +2.00989 q^{95} +3.01451 q^{96} -9.42693 q^{97} -1.10131 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 8 q^{4} + 2 q^{5} + 8 q^{7} + 8 q^{8} + 20 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 + 8 * q^4 + 2 * q^5 + 8 * q^7 + 8 * q^8 + 20 * q^9	$ 8 q + 8 q^{2} + 8 q^{4} + 2 q^{5} + 8 q^{7} + 8 q^{8} + 20 q^{9} + 2 q^{10} + 18 q^{13} + 8 q^{14} + 10 q^{15} + 8 q^{16} + 4 q^{17} + 20 q^{18} - 8 q^{19} + 2 q^{20} + 14 q^{21} + 12 q^{23} + 18 q^{26} - 24 q^{27} + 8 q^{28} + 14 q^{29} + 10 q^{30} - 2 q^{31} + 8 q^{32} + 4 q^{34} + 40 q^{35} + 20 q^{36} - 22 q^{37} - 8 q^{38} - 4 q^{39} + 2 q^{40} + 8 q^{41} + 14 q^{42} + 28 q^{43} - 28 q^{45} + 12 q^{46} + 6 q^{47} + 32 q^{49} - 12 q^{51} + 18 q^{52} - 24 q^{53} - 24 q^{54} + 8 q^{56} + 14 q^{58} + 46 q^{59} + 10 q^{60} - 24 q^{61} - 2 q^{62} + 30 q^{63} + 8 q^{64} - 16 q^{65} - 22 q^{67} + 4 q^{68} - 38 q^{69} + 40 q^{70} + 8 q^{71} + 20 q^{72} + 16 q^{73} - 22 q^{74} + 6 q^{75} - 8 q^{76} - 4 q^{78} + 4 q^{79} + 2 q^{80} + 28 q^{81} + 8 q^{82} + 12 q^{83} + 14 q^{84} + 48 q^{85} + 28 q^{86} + 42 q^{87} - 28 q^{89} - 28 q^{90} - 12 q^{91} + 12 q^{92} + 22 q^{93} + 6 q^{94} - 2 q^{95} - 22 q^{97} + 32 q^{98}+O(q^{100}) $ 8 * q + 8 * q^2 + 8 * q^4 + 2 * q^5 + 8 * q^7 + 8 * q^8 + 20 * q^9 + 2 * q^10 + 18 * q^13 + 8 * q^14 + 10 * q^15 + 8 * q^16 + 4 * q^17 + 20 * q^18 - 8 * q^19 + 2 * q^20 + 14 * q^21 + 12 * q^23 + 18 * q^26 - 24 * q^27 + 8 * q^28 + 14 * q^29 + 10 * q^30 - 2 * q^31 + 8 * q^32 + 4 * q^34 + 40 * q^35 + 20 * q^36 - 22 * q^37 - 8 * q^38 - 4 * q^39 + 2 * q^40 + 8 * q^41 + 14 * q^42 + 28 * q^43 - 28 * q^45 + 12 * q^46 + 6 * q^47 + 32 * q^49 - 12 * q^51 + 18 * q^52 - 24 * q^53 - 24 * q^54 + 8 * q^56 + 14 * q^58 + 46 * q^59 + 10 * q^60 - 24 * q^61 - 2 * q^62 + 30 * q^63 + 8 * q^64 - 16 * q^65 - 22 * q^67 + 4 * q^68 - 38 * q^69 + 40 * q^70 + 8 * q^71 + 20 * q^72 + 16 * q^73 - 22 * q^74 + 6 * q^75 - 8 * q^76 - 4 * q^78 + 4 * q^79 + 2 * q^80 + 28 * q^81 + 8 * q^82 + 12 * q^83 + 14 * q^84 + 48 * q^85 + 28 * q^86 + 42 * q^87 - 28 * q^89 - 28 * q^90 - 12 * q^91 + 12 * q^92 + 22 * q^93 + 6 * q^94 - 2 * q^95 - 22 * q^97 + 32 * 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
$3$	3.01451	1.74043	0.870213	−	0.492676i	$-0.163981\pi$
$3$	3.01451	1.74043	0.870213	+	0.492676i	$0.163981\pi$
$4$	1.00000	0.500000
$5$	−2.00989	−0.898848	−0.449424	−	0.893319i	$-0.648371\pi$
$5$	−2.00989	−0.898848	−0.449424	+	0.893319i	$0.648371\pi$
$6$	3.01451	1.23067
$7$	2.42872	0.917971	0.458985	−	0.888444i	$-0.348213\pi$
$7$	2.42872	0.917971	0.458985	+	0.888444i	$0.348213\pi$
$8$	1.00000	0.353553
$9$	6.08725	2.02908
$10$	−2.00989	−0.635581
$11$	0	0
$11$	0	0
$12$	3.01451	0.870213
$13$	3.03557	0.841915	0.420957	−	0.907080i	$-0.361694\pi$
$13$	3.03557	0.841915	0.420957	+	0.907080i	$0.361694\pi$
$14$	2.42872	0.649103
$15$	−6.05881	−1.56438
$16$	1.00000	0.250000
$17$	−4.31675	−1.04697	−0.523483	−	0.852036i	$-0.675368\pi$
$17$	−4.31675	−1.04697	−0.523483	+	0.852036i	$0.675368\pi$
$18$	6.08725	1.43478
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−2.00989	−0.449424
$21$	7.32140	1.59766
$22$	0	0
$23$	−2.27832	−0.475064	−0.237532	−	0.971380i	$-0.576338\pi$
$23$	−2.27832	−0.475064	−0.237532	+	0.971380i	$0.576338\pi$
$24$	3.01451	0.615334
$25$	−0.960362	−0.192072
$26$	3.03557	0.595324
$27$	9.30653	1.79104
$28$	2.42872	0.458985
$29$	8.81144	1.63624	0.818121	−	0.575046i	$-0.195016\pi$
$29$	8.81144	1.63624	0.818121	+	0.575046i	$0.195016\pi$
$30$	−6.05881	−1.10618
$31$	9.29488	1.66941	0.834705	−	0.550698i	$-0.185638\pi$
$31$	9.29488	1.66941	0.834705	+	0.550698i	$0.185638\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−4.31675	−0.740316
$35$	−4.88145	−0.825116
$36$	6.08725	1.01454
$37$	1.06805	0.175587	0.0877933	−	0.996139i	$-0.472018\pi$
$37$	1.06805	0.175587	0.0877933	+	0.996139i	$0.472018\pi$
$38$	−1.00000	−0.162221
$39$	9.15074	1.46529
$40$	−2.00989	−0.317791
$41$	−5.15603	−0.805236	−0.402618	−	0.915368i	$-0.631900\pi$
$41$	−5.15603	−0.805236	−0.402618	+	0.915368i	$0.631900\pi$
$42$	7.32140	1.12972
$43$	11.9841	1.82756	0.913779	−	0.406212i	$-0.133151\pi$
$43$	11.9841	1.82756	0.913779	+	0.406212i	$0.133151\pi$
$44$	0	0
$45$	−12.2347	−1.82384
$46$	−2.27832	−0.335921
$47$	−9.00012	−1.31280	−0.656401	−	0.754412i	$-0.727922\pi$
$47$	−9.00012	−1.31280	−0.656401	+	0.754412i	$0.727922\pi$
$48$	3.01451	0.435107
$49$	−1.10131	−0.157330
$50$	−0.960362	−0.135816
$51$	−13.0129	−1.82217
$52$	3.03557	0.420957
$53$	5.09532	0.699896	0.349948	−	0.936769i	$-0.386199\pi$
$53$	5.09532	0.699896	0.349948	+	0.936769i	$0.386199\pi$
$54$	9.30653	1.26646
$55$	0	0
$56$	2.42872	0.324552
$57$	−3.01451	−0.399281
$58$	8.81144	1.15700
$59$	−4.79071	−0.623698	−0.311849	−	0.950132i	$-0.600948\pi$
$59$	−4.79071	−0.623698	−0.311849	+	0.950132i	$0.600948\pi$
$60$	−6.05881	−0.782189
$61$	9.26197	1.18587	0.592937	−	0.805249i	$-0.297968\pi$
$61$	9.26197	1.18587	0.592937	+	0.805249i	$0.297968\pi$
$62$	9.29488	1.18045
$63$	14.7842	1.86264
$64$	1.00000	0.125000
$65$	−6.10114	−0.756753
$66$	0	0
$67$	9.19479	1.12332	0.561661	−	0.827367i	$-0.310162\pi$
$67$	9.19479	1.12332	0.561661	+	0.827367i	$0.310162\pi$
$68$	−4.31675	−0.523483
$69$	−6.86802	−0.826813
$70$	−4.88145	−0.583445
$71$	−10.7608	−1.27707	−0.638535	−	0.769593i	$-0.720459\pi$
$71$	−10.7608	−1.27707	−0.638535	+	0.769593i	$0.720459\pi$
$72$	6.08725	0.717389
$73$	8.93977	1.04632	0.523161	−	0.852234i	$-0.324753\pi$
$73$	8.93977	1.04632	0.523161	+	0.852234i	$0.324753\pi$
$74$	1.06805	0.124158
$75$	−2.89502	−0.334288
$76$	−1.00000	−0.114708
$77$	0	0
$78$	9.15074	1.03612
$79$	6.52103	0.733673	0.366837	−	0.930285i	$-0.380441\pi$
$79$	6.52103	0.733673	0.366837	+	0.930285i	$0.380441\pi$
$80$	−2.00989	−0.224712
$81$	9.79285	1.08809
$82$	−5.15603	−0.569388
$83$	−4.09108	−0.449054	−0.224527	−	0.974468i	$-0.572084\pi$
$83$	−4.09108	−0.449054	−0.224527	+	0.974468i	$0.572084\pi$
$84$	7.32140	0.798830
$85$	8.67617	0.941063
$86$	11.9841	1.29228
$87$	26.5621	2.84776
$88$	0	0
$89$	6.04832	0.641121	0.320560	−	0.947228i	$-0.396129\pi$
$89$	6.04832	0.641121	0.320560	+	0.947228i	$0.396129\pi$
$90$	−12.2347	−1.28965
$91$	7.37255	0.772853
$92$	−2.27832	−0.237532
$93$	28.0195	2.90548
$94$	−9.00012	−0.928291
$95$	2.00989	0.206210
$96$	3.01451	0.307667
$97$	−9.42693	−0.957159	−0.478580	−	0.878044i	$-0.658848\pi$
$97$	−9.42693	−0.957159	−0.478580	+	0.878044i	$0.658848\pi$
$98$	−1.10131	−0.111249
$99$	0	0
$100$	−0.960362	−0.0960362
$101$	−8.78589	−0.874229	−0.437114	−	0.899406i	$-0.643999\pi$
$101$	−8.78589	−0.874229	−0.437114	+	0.899406i	$0.643999\pi$
$102$	−13.0129	−1.28847
$103$	−10.5453	−1.03906	−0.519528	−	0.854454i	$-0.673892\pi$
$103$	−10.5453	−1.03906	−0.519528	+	0.854454i	$0.673892\pi$
$104$	3.03557	0.297662
$105$	−14.7152	−1.43605
$106$	5.09532	0.494901
$107$	−7.69542	−0.743944	−0.371972	−	0.928244i	$-0.621318\pi$
$107$	−7.69542	−0.743944	−0.371972	+	0.928244i	$0.621318\pi$
$108$	9.30653	0.895521
$109$	−14.2327	−1.36324	−0.681622	−	0.731705i	$-0.738725\pi$
$109$	−14.2327	−1.36324	−0.681622	+	0.731705i	$0.738725\pi$
$110$	0	0
$111$	3.21965	0.305596
$112$	2.42872	0.229493
$113$	−9.50553	−0.894205	−0.447103	−	0.894483i	$-0.647544\pi$
$113$	−9.50553	−0.894205	−0.447103	+	0.894483i	$0.647544\pi$
$114$	−3.01451	−0.282334
$115$	4.57917	0.427010
$116$	8.81144	0.818121
$117$	18.4783	1.70831
$118$	−4.79071	−0.441021
$119$	−10.4842	−0.961084
$120$	−6.05881	−0.553091
$121$	0	0
$122$	9.26197	0.838540
$123$	−15.5429	−1.40145
$124$	9.29488	0.834705
$125$	11.9796	1.07149
$126$	14.7842	1.31708
$127$	−10.0590	−0.892593	−0.446296	−	0.894885i	$-0.647257\pi$
$127$	−10.0590	−0.892593	−0.446296	+	0.894885i	$0.647257\pi$
$128$	1.00000	0.0883883
$129$	36.1261	3.18073
$130$	−6.10114	−0.535105
$131$	8.33735	0.728437	0.364219	−	0.931313i	$-0.381336\pi$
$131$	8.33735	0.728437	0.364219	+	0.931313i	$0.381336\pi$
$132$	0	0
$133$	−2.42872	−0.210597
$134$	9.19479	0.794309
$135$	−18.7051	−1.60987
$136$	−4.31675	−0.370158
$137$	−18.8549	−1.61088	−0.805440	−	0.592677i	$-0.798071\pi$
$137$	−18.8549	−1.61088	−0.805440	+	0.592677i	$0.798071\pi$
$138$	−6.86802	−0.584645
$139$	3.62541	0.307503	0.153752	−	0.988110i	$-0.450864\pi$
$139$	3.62541	0.307503	0.153752	+	0.988110i	$0.450864\pi$
$140$	−4.88145	−0.412558
$141$	−27.1309	−2.28483
$142$	−10.7608	−0.903025
$143$	0	0
$144$	6.08725	0.507271
$145$	−17.7100	−1.47073
$146$	8.93977	0.739861
$147$	−3.31990	−0.273821
$148$	1.06805	0.0877933
$149$	5.42145	0.444143	0.222071	−	0.975030i	$-0.428718\pi$
$149$	5.42145	0.444143	0.222071	+	0.975030i	$0.428718\pi$
$150$	−2.89502	−0.236377
$151$	7.67465	0.624554	0.312277	−	0.949991i	$-0.398908\pi$
$151$	7.67465	0.624554	0.312277	+	0.949991i	$0.398908\pi$
$152$	−1.00000	−0.0811107
$153$	−26.2771	−2.12438
$154$	0	0
$155$	−18.6816	−1.50055
$156$	9.15074	0.732645
$157$	−24.0027	−1.91562	−0.957810	−	0.287401i	$-0.907209\pi$
$157$	−24.0027	−1.91562	−0.957810	+	0.287401i	$0.907209\pi$
$158$	6.52103	0.518785
$159$	15.3599	1.21812
$160$	−2.00989	−0.158895
$161$	−5.53342	−0.436095
$162$	9.79285	0.769399
$163$	0.148660	0.0116440	0.00582198	−	0.999983i	$-0.498147\pi$
$163$	0.148660	0.0116440	0.00582198	+	0.999983i	$0.498147\pi$
$164$	−5.15603	−0.402618
$165$	0	0
$166$	−4.09108	−0.317529
$167$	0.501818	0.0388319	0.0194159	−	0.999811i	$-0.493819\pi$
$167$	0.501818	0.0388319	0.0194159	+	0.999811i	$0.493819\pi$
$168$	7.32140	0.564858
$169$	−3.78533	−0.291179
$170$	8.67617	0.665432
$171$	−6.08725	−0.465504
$172$	11.9841	0.913779
$173$	2.46671	0.187540	0.0937701	−	0.995594i	$-0.470108\pi$
$173$	2.46671	0.187540	0.0937701	+	0.995594i	$0.470108\pi$
$174$	26.5621	2.01367
$175$	−2.33245	−0.176317
$176$	0	0
$177$	−14.4416	−1.08550
$178$	6.04832	0.453341
$179$	19.2904	1.44183	0.720915	−	0.693023i	$-0.243722\pi$
$179$	19.2904	1.44183	0.720915	+	0.693023i	$0.243722\pi$
$180$	−12.2347	−0.911918
$181$	−8.54815	−0.635379	−0.317690	−	0.948195i	$-0.602907\pi$
$181$	−8.54815	−0.635379	−0.317690	+	0.948195i	$0.602907\pi$
$182$	7.37255	0.546490
$183$	27.9203	2.06393
$184$	−2.27832	−0.167960
$185$	−2.14666	−0.157826
$186$	28.0195	2.05449
$187$	0	0
$188$	−9.00012	−0.656401
$189$	22.6030	1.64412
$190$	2.00989	0.145812
$191$	−0.999674	−0.0723339	−0.0361669	−	0.999346i	$-0.511515\pi$
$191$	−0.999674	−0.0723339	−0.0361669	+	0.999346i	$0.511515\pi$
$192$	3.01451	0.217553
$193$	5.02121	0.361434	0.180717	−	0.983535i	$-0.442158\pi$
$193$	5.02121	0.361434	0.180717	+	0.983535i	$0.442158\pi$
$194$	−9.42693	−0.676814
$195$	−18.3919	−1.31707
$196$	−1.10131	−0.0786648
$197$	−11.0791	−0.789355	−0.394677	−	0.918820i	$-0.629144\pi$
$197$	−11.0791	−0.789355	−0.394677	+	0.918820i	$0.629144\pi$
$198$	0	0
$199$	−10.4170	−0.738442	−0.369221	−	0.929342i	$-0.620375\pi$
$199$	−10.4170	−0.738442	−0.369221	+	0.929342i	$0.620375\pi$
$200$	−0.960362	−0.0679079
$201$	27.7178	1.95506
$202$	−8.78589	−0.618173
$203$	21.4005	1.50202
$204$	−13.0129	−0.911083
$205$	10.3630	0.723785
$206$	−10.5453	−0.734723
$207$	−13.8687	−0.963943
$208$	3.03557	0.210479
$209$	0	0
$210$	−14.7152	−1.01544
$211$	21.2337	1.46179	0.730894	−	0.682491i	$-0.239104\pi$
$211$	21.2337	1.46179	0.730894	+	0.682491i	$0.239104\pi$
$212$	5.09532	0.349948
$213$	−32.4385	−2.22265
$214$	−7.69542	−0.526048
$215$	−24.0867	−1.64270
$216$	9.30653	0.633229
$217$	22.5747	1.53247
$218$	−14.2327	−0.963959
$219$	26.9490	1.82104
$220$	0	0
$221$	−13.1038	−0.881456
$222$	3.21965	0.216089
$223$	−5.98764	−0.400962	−0.200481	−	0.979698i	$-0.564251\pi$
$223$	−5.98764	−0.400962	−0.200481	+	0.979698i	$0.564251\pi$
$224$	2.42872	0.162276
$225$	−5.84596	−0.389731
$226$	−9.50553	−0.632298
$227$	13.6499	0.905973	0.452987	−	0.891517i	$-0.350359\pi$
$227$	13.6499	0.905973	0.452987	+	0.891517i	$0.350359\pi$
$228$	−3.01451	−0.199641
$229$	−11.3245	−0.748347	−0.374173	−	0.927359i	$-0.622074\pi$
$229$	−11.3245	−0.748347	−0.374173	+	0.927359i	$0.622074\pi$
$230$	4.57917	0.301942
$231$	0	0
$232$	8.81144	0.578499
$233$	7.52089	0.492710	0.246355	−	0.969180i	$-0.420767\pi$
$233$	7.52089	0.492710	0.246355	+	0.969180i	$0.420767\pi$
$234$	18.4783	1.20796
$235$	18.0892	1.18001
$236$	−4.79071	−0.311849
$237$	19.6577	1.27690
$238$	−10.4842	−0.679589
$239$	−0.510794	−0.0330405	−0.0165203	−	0.999864i	$-0.505259\pi$
$239$	−0.510794	−0.0330405	−0.0165203	+	0.999864i	$0.505259\pi$
$240$	−6.05881	−0.391095
$241$	−22.6208	−1.45713	−0.728566	−	0.684975i	$-0.759813\pi$
$241$	−22.6208	−1.45713	−0.728566	+	0.684975i	$0.759813\pi$
$242$	0	0
$243$	1.60101	0.102705
$244$	9.26197	0.592937
$245$	2.21350	0.141415
$246$	−15.5429	−0.990978
$247$	−3.03557	−0.193149
$248$	9.29488	0.590225
$249$	−12.3326	−0.781546
$250$	11.9796	0.757659
$251$	−12.6321	−0.797333	−0.398667	−	0.917096i	$-0.630527\pi$
$251$	−12.6321	−0.797333	−0.398667	+	0.917096i	$0.630527\pi$
$252$	14.7842	0.931319
$253$	0	0
$254$	−10.0590	−0.631158
$255$	26.1544	1.63785
$256$	1.00000	0.0625000
$257$	25.0497	1.56256	0.781278	−	0.624183i	$-0.214568\pi$
$257$	25.0497	1.56256	0.781278	+	0.624183i	$0.214568\pi$
$258$	36.1261	2.24911
$259$	2.59400	0.161183
$260$	−6.10114	−0.378377
$261$	53.6374	3.32007
$262$	8.33735	0.515083
$263$	−1.50368	−0.0927212	−0.0463606	−	0.998925i	$-0.514762\pi$
$263$	−1.50368	−0.0927212	−0.0463606	+	0.998925i	$0.514762\pi$
$264$	0	0
$265$	−10.2410	−0.629100
$266$	−2.42872	−0.148915
$267$	18.2327	1.11582
$268$	9.19479	0.561661
$269$	−10.5493	−0.643201	−0.321601	−	0.946875i	$-0.604221\pi$
$269$	−10.5493	−0.643201	−0.321601	+	0.946875i	$0.604221\pi$
$270$	−18.7051	−1.13835
$271$	1.95259	0.118611	0.0593056	−	0.998240i	$-0.481111\pi$
$271$	1.95259	0.118611	0.0593056	+	0.998240i	$0.481111\pi$
$272$	−4.31675	−0.261741
$273$	22.2246	1.34509
$274$	−18.8549	−1.13906
$275$	0	0
$276$	−6.86802	−0.413407
$277$	32.5196	1.95391	0.976957	−	0.213434i	$-0.0684648\pi$
$277$	32.5196	1.95391	0.976957	+	0.213434i	$0.0684648\pi$
$278$	3.62541	0.217438
$279$	56.5802	3.38737
$280$	−4.88145	−0.291723
$281$	13.9545	0.832454	0.416227	−	0.909261i	$-0.363352\pi$
$281$	13.9545	0.832454	0.416227	+	0.909261i	$0.363352\pi$
$282$	−27.1309	−1.61562
$283$	−22.5828	−1.34241	−0.671205	−	0.741272i	$-0.734223\pi$
$283$	−22.5828	−1.34241	−0.671205	+	0.741272i	$0.734223\pi$
$284$	−10.7608	−0.638535
$285$	6.05881	0.358893
$286$	0	0
$287$	−12.5226	−0.739183
$288$	6.08725	0.358695
$289$	1.63432	0.0961362
$290$	−17.7100	−1.03997
$291$	−28.4175	−1.66586
$292$	8.93977	0.523161
$293$	26.1229	1.52612	0.763058	−	0.646330i	$-0.223697\pi$
$293$	26.1229	1.52612	0.763058	+	0.646330i	$0.223697\pi$
$294$	−3.31990	−0.193620
$295$	9.62879	0.560610
$296$	1.06805	0.0620792
$297$	0	0
$298$	5.42145	0.314056
$299$	−6.91601	−0.399963
$300$	−2.89502	−0.167144
$301$	29.1060	1.67764
$302$	7.67465	0.441626
$303$	−26.4851	−1.52153
$304$	−1.00000	−0.0573539
$305$	−18.6155	−1.06592
$306$	−26.2771	−1.50216
$307$	−17.6119	−1.00516	−0.502581	−	0.864530i	$-0.667616\pi$
$307$	−17.6119	−1.00516	−0.502581	+	0.864530i	$0.667616\pi$
$308$	0	0
$309$	−31.7888	−1.80840
$310$	−18.6816	−1.06105
$311$	−8.78558	−0.498185	−0.249092	−	0.968480i	$-0.580132\pi$
$311$	−8.78558	−0.498185	−0.249092	+	0.968480i	$0.580132\pi$
$312$	9.15074	0.518058
$313$	32.2305	1.82177	0.910886	−	0.412657i	$-0.135399\pi$
$313$	32.2305	1.82177	0.910886	+	0.412657i	$0.135399\pi$
$314$	−24.0027	−1.35455
$315$	−29.7146	−1.67423
$316$	6.52103	0.366837
$317$	0.754060	0.0423522	0.0211761	−	0.999776i	$-0.493259\pi$
$317$	0.754060	0.0423522	0.0211761	+	0.999776i	$0.493259\pi$
$318$	15.3599	0.861339
$319$	0	0
$320$	−2.00989	−0.112356
$321$	−23.1979	−1.29478
$322$	−5.53342	−0.308365
$323$	4.31675	0.240190
$324$	9.79285	0.544047
$325$	−2.91524	−0.161709
$326$	0.148660	0.00823352
$327$	−42.9045	−2.37263
$328$	−5.15603	−0.284694
$329$	−21.8588	−1.20511
$330$	0	0
$331$	6.33131	0.348000	0.174000	−	0.984746i	$-0.444331\pi$
$331$	6.33131	0.348000	0.174000	+	0.984746i	$0.444331\pi$
$332$	−4.09108	−0.224527
$333$	6.50150	0.356280
$334$	0.501818	0.0274583
$335$	−18.4805	−1.00970
$336$	7.32140	0.399415
$337$	9.10922	0.496211	0.248105	−	0.968733i	$-0.420192\pi$
$337$	9.10922	0.496211	0.248105	+	0.968733i	$0.420192\pi$
$338$	−3.78533	−0.205895
$339$	−28.6545	−1.55630
$340$	8.67617	0.470531
$341$	0	0
$342$	−6.08725	−0.329161
$343$	−19.6758	−1.06239
$344$	11.9841	0.646139
$345$	13.8039	0.743179
$346$	2.46671	0.132611
$347$	−0.810769	−0.0435243	−0.0217622	−	0.999763i	$-0.506928\pi$
$347$	−0.810769	−0.0435243	−0.0217622	+	0.999763i	$0.506928\pi$
$348$	26.5621	1.42388
$349$	−25.9076	−1.38680	−0.693401	−	0.720552i	$-0.743889\pi$
$349$	−25.9076	−1.38680	−0.693401	+	0.720552i	$0.743889\pi$
$350$	−2.33245	−0.124675
$351$	28.2506	1.50791
$352$	0	0
$353$	30.9371	1.64662	0.823309	−	0.567594i	$-0.192125\pi$
$353$	30.9371	1.64662	0.823309	+	0.567594i	$0.192125\pi$
$354$	−14.4416	−0.767564
$355$	21.6279	1.14789
$356$	6.04832	0.320560
$357$	−31.6046	−1.67269
$358$	19.2904	1.01953
$359$	−33.8838	−1.78832	−0.894158	−	0.447751i	$-0.852225\pi$
$359$	−33.8838	−1.78832	−0.894158	+	0.447751i	$0.852225\pi$
$360$	−12.2347	−0.644824
$361$	1.00000	0.0526316
$362$	−8.54815	−0.449281
$363$	0	0
$364$	7.37255	0.386427
$365$	−17.9679	−0.940484
$366$	27.9203	1.45942
$367$	−25.7084	−1.34197	−0.670983	−	0.741473i	$-0.734128\pi$
$367$	−25.7084	−1.34197	−0.670983	+	0.741473i	$0.734128\pi$
$368$	−2.27832	−0.118766
$369$	−31.3860	−1.63389
$370$	−2.14666	−0.111600
$371$	12.3751	0.642484
$372$	28.0195	1.45274
$373$	12.1401	0.628589	0.314294	−	0.949326i	$-0.398232\pi$
$373$	12.1401	0.628589	0.314294	+	0.949326i	$0.398232\pi$
$374$	0	0
$375$	36.1127	1.86485
$376$	−9.00012	−0.464146
$377$	26.7477	1.37758
$378$	22.6030	1.16257
$379$	31.9986	1.64366	0.821829	−	0.569734i	$-0.192954\pi$
$379$	31.9986	1.64366	0.821829	+	0.569734i	$0.192954\pi$
$380$	2.00989	0.103105
$381$	−30.3229	−1.55349
$382$	−0.999674	−0.0511478
$383$	−19.5901	−1.00101	−0.500504	−	0.865734i	$-0.666852\pi$
$383$	−19.5901	−1.00101	−0.500504	+	0.865734i	$0.666852\pi$
$384$	3.01451	0.153833
$385$	0	0
$386$	5.02121	0.255573
$387$	72.9502	3.70827
$388$	−9.42693	−0.478580
$389$	−10.9428	−0.554824	−0.277412	−	0.960751i	$-0.589477\pi$
$389$	−10.9428	−0.554824	−0.277412	+	0.960751i	$0.589477\pi$
$390$	−18.3919	−0.931311
$391$	9.83496	0.497375
$392$	−1.10131	−0.0556244
$393$	25.1330	1.26779
$394$	−11.0791	−0.558158
$395$	−13.1065	−0.659460
$396$	0	0
$397$	17.4801	0.877303	0.438651	−	0.898657i	$-0.355456\pi$
$397$	17.4801	0.877303	0.438651	+	0.898657i	$0.355456\pi$
$398$	−10.4170	−0.522157
$399$	−7.32140	−0.366528
$400$	−0.960362	−0.0480181
$401$	16.7907	0.838485	0.419243	−	0.907874i	$-0.362296\pi$
$401$	16.7907	0.838485	0.419243	+	0.907874i	$0.362296\pi$
$402$	27.7178	1.38244
$403$	28.2152	1.40550
$404$	−8.78589	−0.437114
$405$	−19.6825	−0.978031
$406$	21.4005	1.06209
$407$	0	0
$408$	−13.0129	−0.644233
$409$	−7.01163	−0.346703	−0.173351	−	0.984860i	$-0.555460\pi$
$409$	−7.01163	−0.346703	−0.173351	+	0.984860i	$0.555460\pi$
$410$	10.3630	0.511793
$411$	−56.8381	−2.80362
$412$	−10.5453	−0.519528
$413$	−11.6353	−0.572536
$414$	−13.8687	−0.681611
$415$	8.22260	0.403632
$416$	3.03557	0.148831
$417$	10.9288	0.535186
$418$	0	0
$419$	−22.9541	−1.12138	−0.560690	−	0.828026i	$-0.689464\pi$
$419$	−22.9541	−1.12138	−0.560690	+	0.828026i	$0.689464\pi$
$420$	−14.7152	−0.718027
$421$	5.13342	0.250188	0.125094	−	0.992145i	$-0.460077\pi$
$421$	5.13342	0.250188	0.125094	+	0.992145i	$0.460077\pi$
$422$	21.2337	1.03364
$423$	−54.7859	−2.66378
$424$	5.09532	0.247450
$425$	4.14564	0.201093
$426$	−32.4385	−1.57165
$427$	22.4948	1.08860
$428$	−7.69542	−0.371972
$429$	0	0
$430$	−24.0867	−1.16156
$431$	−39.2597	−1.89107	−0.945536	−	0.325518i	$-0.894461\pi$
$431$	−39.2597	−1.89107	−0.945536	+	0.325518i	$0.894461\pi$
$432$	9.30653	0.447761
$433$	−23.8406	−1.14571	−0.572853	−	0.819658i	$-0.694163\pi$
$433$	−23.8406	−1.14571	−0.572853	+	0.819658i	$0.694163\pi$
$434$	22.5747	1.08362
$435$	−53.3868	−2.55970
$436$	−14.2327	−0.681622
$437$	2.27832	0.108987
$438$	26.9490	1.28767
$439$	−20.4659	−0.976783	−0.488391	−	0.872625i	$-0.662416\pi$
$439$	−20.4659	−0.976783	−0.488391	+	0.872625i	$0.662416\pi$
$440$	0	0
$441$	−6.70393	−0.319235
$442$	−13.1038	−0.623283
$443$	20.4954	0.973768	0.486884	−	0.873467i	$-0.338133\pi$
$443$	20.4954	0.973768	0.486884	+	0.873467i	$0.338133\pi$
$444$	3.21965	0.152798
$445$	−12.1564	−0.576270
$446$	−5.98764	−0.283523
$447$	16.3430	0.772998
$448$	2.42872	0.114746
$449$	29.9575	1.41378	0.706891	−	0.707323i	$-0.250097\pi$
$449$	29.9575	1.41378	0.706891	+	0.707323i	$0.250097\pi$
$450$	−5.84596	−0.275581
$451$	0	0
$452$	−9.50553	−0.447103
$453$	23.1353	1.08699
$454$	13.6499	0.640620
$455$	−14.8180	−0.694678
$456$	−3.01451	−0.141167
$457$	−29.4491	−1.37757	−0.688786	−	0.724964i	$-0.741856\pi$
$457$	−29.4491	−1.37757	−0.688786	+	0.724964i	$0.741856\pi$
$458$	−11.3245	−0.529161
$459$	−40.1739	−1.87516
$460$	4.57917	0.213505
$461$	−12.7886	−0.595624	−0.297812	−	0.954624i	$-0.596257\pi$
$461$	−12.7886	−0.595624	−0.297812	+	0.954624i	$0.596257\pi$
$462$	0	0
$463$	−22.8327	−1.06112	−0.530562	−	0.847646i	$-0.678019\pi$
$463$	−22.8327	−1.06112	−0.530562	+	0.847646i	$0.678019\pi$
$464$	8.81144	0.409061
$465$	−56.3159	−2.61159
$466$	7.52089	0.348398
$467$	23.2585	1.07627	0.538137	−	0.842857i	$-0.319128\pi$
$467$	23.2585	1.07627	0.538137	+	0.842857i	$0.319128\pi$
$468$	18.4783	0.854157
$469$	22.3316	1.03118
$470$	18.0892	0.834392
$471$	−72.3562	−3.33400
$472$	−4.79071	−0.220511
$473$	0	0
$474$	19.6577	0.902907
$475$	0.960362	0.0440644
$476$	−10.4842	−0.480542
$477$	31.0165	1.42015
$478$	−0.510794	−0.0233632
$479$	−12.5716	−0.574410	−0.287205	−	0.957869i	$-0.592726\pi$
$479$	−12.5716	−0.574410	−0.287205	+	0.957869i	$0.592726\pi$
$480$	−6.05881	−0.276546
$481$	3.24214	0.147829
$482$	−22.6208	−1.03035
$483$	−16.6805	−0.758990
$484$	0	0
$485$	18.9470	0.860341
$486$	1.60101	0.0726232
$487$	−20.6412	−0.935342	−0.467671	−	0.883903i	$-0.654907\pi$
$487$	−20.6412	−0.935342	−0.467671	+	0.883903i	$0.654907\pi$
$488$	9.26197	0.419270
$489$	0.448137	0.0202654
$490$	2.21350	0.0999958
$491$	−30.2650	−1.36584	−0.682919	−	0.730494i	$-0.739290\pi$
$491$	−30.2650	−1.36584	−0.682919	+	0.730494i	$0.739290\pi$
$492$	−15.5429	−0.700727
$493$	−38.0368	−1.71309
$494$	−3.03557	−0.136577
$495$	0	0
$496$	9.29488	0.417352
$497$	−26.1350	−1.17231
$498$	−12.3326	−0.552636
$499$	−36.2503	−1.62279	−0.811394	−	0.584499i	$-0.801291\pi$
$499$	−36.2503	−1.62279	−0.811394	+	0.584499i	$0.801291\pi$
$500$	11.9796	0.535746
$501$	1.51273	0.0675840
$502$	−12.6321	−0.563800
$503$	14.4032	0.642208	0.321104	−	0.947044i	$-0.395946\pi$
$503$	14.4032	0.642208	0.321104	+	0.947044i	$0.395946\pi$
$504$	14.7842	0.658542
$505$	17.6586	0.785799
$506$	0	0
$507$	−11.4109	−0.506776
$508$	−10.0590	−0.446296
$509$	35.9803	1.59480	0.797400	−	0.603451i	$-0.206208\pi$
$509$	35.9803	1.59480	0.797400	+	0.603451i	$0.206208\pi$
$510$	26.1544	1.15813
$511$	21.7122	0.960492
$512$	1.00000	0.0441942
$513$	−9.30653	−0.410893
$514$	25.0497	1.10489
$515$	21.1948	0.933953
$516$	36.1261	1.59036
$517$	0	0
$518$	2.59400	0.113974
$519$	7.43590	0.326400
$520$	−6.10114	−0.267553
$521$	−24.0468	−1.05351	−0.526756	−	0.850017i	$-0.676592\pi$
$521$	−24.0468	−1.05351	−0.526756	+	0.850017i	$0.676592\pi$
$522$	53.6374	2.34765
$523$	33.7621	1.47631	0.738157	−	0.674629i	$-0.235696\pi$
$523$	33.7621	1.47631	0.738157	+	0.674629i	$0.235696\pi$
$524$	8.33735	0.364219
$525$	−7.03120	−0.306867
$526$	−1.50368	−0.0655638
$527$	−40.1237	−1.74781
$528$	0	0
$529$	−17.8092	−0.774315
$530$	−10.2410	−0.444841
$531$	−29.1623	−1.26553
$532$	−2.42872	−0.105298
$533$	−15.6515	−0.677940
$534$	18.2327	0.789006
$535$	15.4669	0.668693
$536$	9.19479	0.397155
$537$	58.1510	2.50940
$538$	−10.5493	−0.454812
$539$	0	0
$540$	−18.7051	−0.804937
$541$	−8.63940	−0.371437	−0.185718	−	0.982603i	$-0.559461\pi$
$541$	−8.63940	−0.371437	−0.185718	+	0.982603i	$0.559461\pi$
$542$	1.95259	0.0838708
$543$	−25.7685	−1.10583
$544$	−4.31675	−0.185079
$545$	28.6061	1.22535
$546$	22.2246	0.951125
$547$	−19.6355	−0.839552	−0.419776	−	0.907628i	$-0.637891\pi$
$547$	−19.6355	−0.839552	−0.419776	+	0.907628i	$0.637891\pi$
$548$	−18.8549	−0.805440
$549$	56.3799	2.40624
$550$	0	0
$551$	−8.81144	−0.375380
$552$	−6.86802	−0.292323
$553$	15.8378	0.673490
$554$	32.5196	1.38163
$555$	−6.47112	−0.274684
$556$	3.62541	0.153752
$557$	−42.2771	−1.79134	−0.895669	−	0.444722i	$-0.853303\pi$
$557$	−42.2771	−1.79134	−0.895669	+	0.444722i	$0.853303\pi$
$558$	56.5802	2.39523
$559$	36.3785	1.53865
$560$	−4.88145	−0.206279
$561$	0	0
$562$	13.9545	0.588634
$563$	15.9375	0.671688	0.335844	−	0.941918i	$-0.390979\pi$
$563$	15.9375	0.671688	0.335844	+	0.941918i	$0.390979\pi$
$564$	−27.1309	−1.14242
$565$	19.1050	0.803754
$566$	−22.5828	−0.949227
$567$	23.7841	0.998839
$568$	−10.7608	−0.451513
$569$	−21.4299	−0.898387	−0.449193	−	0.893435i	$-0.648289\pi$
$569$	−21.4299	−0.898387	−0.449193	+	0.893435i	$0.648289\pi$
$570$	6.05881	0.253776
$571$	21.2358	0.888691	0.444346	−	0.895855i	$-0.353436\pi$
$571$	21.2358	0.888691	0.444346	+	0.895855i	$0.353436\pi$
$572$	0	0
$573$	−3.01352	−0.125892
$574$	−12.5226	−0.522682
$575$	2.18802	0.0912466
$576$	6.08725	0.253635
$577$	5.86811	0.244292	0.122146	−	0.992512i	$-0.461022\pi$
$577$	5.86811	0.244292	0.122146	+	0.992512i	$0.461022\pi$
$578$	1.63432	0.0679786
$579$	15.1365	0.629050
$580$	−17.7100	−0.735367
$581$	−9.93610	−0.412219
$582$	−28.4175	−1.17794
$583$	0	0
$584$	8.93977	0.369930
$585$	−37.1392	−1.53552
$586$	26.1229	1.07913
$587$	−41.6241	−1.71801	−0.859006	−	0.511966i	$-0.828917\pi$
$587$	−41.6241	−1.71801	−0.859006	+	0.511966i	$0.828917\pi$
$588$	−3.31990	−0.136910
$589$	−9.29488	−0.382989
$590$	9.62879	0.396411
$591$	−33.3981	−1.37381
$592$	1.06805	0.0438967
$593$	−13.4779	−0.553469	−0.276735	−	0.960946i	$-0.589252\pi$
$593$	−13.4779	−0.553469	−0.276735	+	0.960946i	$0.589252\pi$
$594$	0	0
$595$	21.0720	0.863868
$596$	5.42145	0.222071
$597$	−31.4021	−1.28520
$598$	−6.91601	−0.282817
$599$	8.59259	0.351084	0.175542	−	0.984472i	$-0.443832\pi$
$599$	8.59259	0.351084	0.175542	+	0.984472i	$0.443832\pi$
$600$	−2.89502	−0.118189
$601$	8.48908	0.346277	0.173138	−	0.984898i	$-0.444609\pi$
$601$	8.48908	0.346277	0.173138	+	0.984898i	$0.444609\pi$
$602$	29.1060	1.18627
$603$	55.9710	2.27932
$604$	7.67465	0.312277
$605$	0	0
$606$	−26.4851	−1.07588
$607$	−4.75233	−0.192891	−0.0964457	−	0.995338i	$-0.530747\pi$
$607$	−4.75233	−0.192891	−0.0964457	+	0.995338i	$0.530747\pi$
$608$	−1.00000	−0.0405554
$609$	64.5120	2.61416
$610$	−18.6155	−0.753719
$611$	−27.3205	−1.10527
$612$	−26.2771	−1.06219
$613$	29.3790	1.18661	0.593304	−	0.804979i	$-0.297823\pi$
$613$	29.3790	1.18661	0.593304	+	0.804979i	$0.297823\pi$
$614$	−17.6119	−0.710758
$615$	31.2394	1.25969
$616$	0	0
$617$	14.0808	0.566870	0.283435	−	0.958991i	$-0.408526\pi$
$617$	14.0808	0.566870	0.283435	+	0.958991i	$0.408526\pi$
$618$	−31.7888	−1.27873
$619$	−22.3677	−0.899034	−0.449517	−	0.893272i	$-0.648404\pi$
$619$	−22.3677	−0.899034	−0.449517	+	0.893272i	$0.648404\pi$
$620$	−18.6816	−0.750273
$621$	−21.2033	−0.850859
$622$	−8.78558	−0.352270
$623$	14.6897	0.588530
$624$	9.15074	0.366323
$625$	−19.2759	−0.771036
$626$	32.2305	1.28819
$627$	0	0
$628$	−24.0027	−0.957810
$629$	−4.61051	−0.183833
$630$	−29.7146	−1.18386
$631$	−36.4436	−1.45080	−0.725399	−	0.688328i	$-0.758345\pi$
$631$	−36.4436	−1.45080	−0.725399	+	0.688328i	$0.758345\pi$
$632$	6.52103	0.259393
$633$	64.0091	2.54413
$634$	0.754060	0.0299476
$635$	20.2175	0.802305
$636$	15.3599	0.609058
$637$	−3.34309	−0.132458
$638$	0	0
$639$	−65.5036	−2.59128
$640$	−2.00989	−0.0794477
$641$	−15.3418	−0.605964	−0.302982	−	0.952996i	$-0.597982\pi$
$641$	−15.3418	−0.605964	−0.302982	+	0.952996i	$0.597982\pi$
$642$	−23.1979	−0.915547
$643$	−29.2007	−1.15156	−0.575781	−	0.817604i	$-0.695302\pi$
$643$	−29.2007	−1.15156	−0.575781	+	0.817604i	$0.695302\pi$
$644$	−5.53342	−0.218047
$645$	−72.6094	−2.85899
$646$	4.31675	0.169840
$647$	19.9255	0.783350	0.391675	−	0.920104i	$-0.371896\pi$
$647$	19.9255	0.783350	0.391675	+	0.920104i	$0.371896\pi$
$648$	9.79285	0.384699
$649$	0	0
$650$	−2.91524	−0.114345
$651$	68.0515	2.66715
$652$	0.148660	0.00582198
$653$	−3.46955	−0.135774	−0.0678870	−	0.997693i	$-0.521626\pi$
$653$	−3.46955	−0.135774	−0.0678870	+	0.997693i	$0.521626\pi$
$654$	−42.9045	−1.67770
$655$	−16.7571	−0.654754
$656$	−5.15603	−0.201309
$657$	54.4186	2.12307
$658$	−21.8588	−0.852144
$659$	−3.67907	−0.143316	−0.0716582	−	0.997429i	$-0.522829\pi$
$659$	−3.67907	−0.143316	−0.0716582	+	0.997429i	$0.522829\pi$
$660$	0	0
$661$	45.8391	1.78294	0.891468	−	0.453084i	$-0.149676\pi$
$661$	45.8391	1.78294	0.891468	+	0.453084i	$0.149676\pi$
$662$	6.33131	0.246073
$663$	−39.5014	−1.53411
$664$	−4.09108	−0.158765
$665$	4.88145	0.189295
$666$	6.50150	0.251928
$667$	−20.0753	−0.777319
$668$	0.501818	0.0194159
$669$	−18.0498	−0.697845
$670$	−18.4805	−0.713963
$671$	0	0
$672$	7.32140	0.282429
$673$	13.9610	0.538156	0.269078	−	0.963118i	$-0.413281\pi$
$673$	13.9610	0.538156	0.269078	+	0.963118i	$0.413281\pi$
$674$	9.10922	0.350874
$675$	−8.93764	−0.344010
$676$	−3.78533	−0.145590
$677$	−9.42523	−0.362241	−0.181121	−	0.983461i	$-0.557972\pi$
$677$	−9.42523	−0.362241	−0.181121	+	0.983461i	$0.557972\pi$
$678$	−28.6545	−1.10047
$679$	−22.8954	−0.878644
$680$	8.67617	0.332716
$681$	41.1476	1.57678
$682$	0	0
$683$	45.4023	1.73727	0.868635	−	0.495453i	$-0.164998\pi$
$683$	45.4023	1.73727	0.868635	+	0.495453i	$0.164998\pi$
$684$	−6.08725	−0.232752
$685$	37.8961	1.44794
$686$	−19.6758	−0.751227
$687$	−34.1379	−1.30244
$688$	11.9841	0.456889
$689$	15.4672	0.589253
$690$	13.8039	0.525507
$691$	−42.3347	−1.61049	−0.805244	−	0.592944i	$-0.797966\pi$
$691$	−42.3347	−1.61049	−0.805244	+	0.592944i	$0.797966\pi$
$692$	2.46671	0.0937701
$693$	0	0
$694$	−0.810769	−0.0307764
$695$	−7.28665	−0.276399
$696$	26.5621	1.00683
$697$	22.2573	0.843054
$698$	−25.9076	−0.980617
$699$	22.6718	0.857525
$700$	−2.33245	−0.0881585
$701$	−30.8992	−1.16705	−0.583524	−	0.812096i	$-0.698327\pi$
$701$	−30.8992	−1.16705	−0.583524	+	0.812096i	$0.698327\pi$
$702$	28.2506	1.06625
$703$	−1.06805	−0.0402823
$704$	0	0
$705$	54.5300	2.05372
$706$	30.9371	1.16433
$707$	−21.3385	−0.802516
$708$	−14.4416	−0.542750
$709$	13.4148	0.503804	0.251902	−	0.967753i	$-0.418944\pi$
$709$	13.4148	0.503804	0.251902	+	0.967753i	$0.418944\pi$
$710$	21.6279	0.811682
$711$	39.6951	1.48868
$712$	6.04832	0.226670
$713$	−21.1768	−0.793076
$714$	−31.6046	−1.18277
$715$	0	0
$716$	19.2904	0.720915
$717$	−1.53979	−0.0575046
$718$	−33.8838	−1.26453
$719$	40.6614	1.51641	0.758207	−	0.652014i	$-0.226076\pi$
$719$	40.6614	1.51641	0.758207	+	0.652014i	$0.226076\pi$
$720$	−12.2347	−0.455959
$721$	−25.6115	−0.953823
$722$	1.00000	0.0372161
$723$	−68.1905	−2.53603
$724$	−8.54815	−0.317690
$725$	−8.46217	−0.314277
$726$	0	0
$727$	−21.0063	−0.779080	−0.389540	−	0.921010i	$-0.627366\pi$
$727$	−21.0063	−0.779080	−0.389540	+	0.921010i	$0.627366\pi$
$728$	7.37255	0.273245
$729$	−24.5523	−0.909344
$730$	−17.9679	−0.665022
$731$	−51.7323	−1.91339
$732$	27.9203	1.03196
$733$	35.6221	1.31573	0.657867	−	0.753134i	$-0.271459\pi$
$733$	35.6221	1.31573	0.657867	+	0.753134i	$0.271459\pi$
$734$	−25.7084	−0.948913
$735$	6.67261	0.246123
$736$	−2.27832	−0.0839802
$737$	0	0
$738$	−31.3860	−1.15534
$739$	38.8113	1.42770	0.713848	−	0.700300i	$-0.246951\pi$
$739$	38.8113	1.42770	0.713848	+	0.700300i	$0.246951\pi$
$740$	−2.14666	−0.0789128
$741$	−9.15074	−0.336161
$742$	12.3751	0.454305
$743$	−20.4994	−0.752051	−0.376025	−	0.926609i	$-0.622709\pi$
$743$	−20.4994	−0.752051	−0.376025	+	0.926609i	$0.622709\pi$
$744$	28.0195	1.02724
$745$	−10.8965	−0.399217
$746$	12.1401	0.444479
$747$	−24.9034	−0.911168
$748$	0	0
$749$	−18.6900	−0.682919
$750$	36.1127	1.31865
$751$	37.0819	1.35314	0.676568	−	0.736380i	$-0.263466\pi$
$751$	37.0819	1.35314	0.676568	+	0.736380i	$0.263466\pi$
$752$	−9.00012	−0.328200
$753$	−38.0796	−1.38770
$754$	26.7477	0.974094
$755$	−15.4252	−0.561379
$756$	22.6030	0.822062
$757$	1.99625	0.0725549	0.0362774	−	0.999342i	$-0.488450\pi$
$757$	1.99625	0.0725549	0.0362774	+	0.999342i	$0.488450\pi$
$758$	31.9986	1.16224
$759$	0	0
$760$	2.00989	0.0729062
$761$	15.0734	0.546411	0.273205	−	0.961956i	$-0.411916\pi$
$761$	15.0734	0.546411	0.273205	+	0.961956i	$0.411916\pi$
$762$	−30.3229	−1.09848
$763$	−34.5672	−1.25142
$764$	−0.999674	−0.0361669
$765$	52.8140	1.90949
$766$	−19.5901	−0.707820
$767$	−14.5425	−0.525101
$768$	3.01451	0.108777
$769$	−30.4602	−1.09842	−0.549212	−	0.835683i	$-0.685072\pi$
$769$	−30.4602	−1.09842	−0.549212	+	0.835683i	$0.685072\pi$
$770$	0	0
$771$	75.5125	2.71951
$772$	5.02121	0.180717
$773$	−23.3781	−0.840851	−0.420425	−	0.907327i	$-0.638119\pi$
$773$	−23.3781	−0.840851	−0.420425	+	0.907327i	$0.638119\pi$
$774$	72.9502	2.62214
$775$	−8.92645	−0.320648
$776$	−9.42693	−0.338407
$777$	7.81963	0.280528
$778$	−10.9428	−0.392320
$779$	5.15603	0.184734
$780$	−18.3919	−0.658537
$781$	0	0
$782$	9.83496	0.351697
$783$	82.0039	2.93058
$784$	−1.10131	−0.0393324
$785$	48.2426	1.72185
$786$	25.1330	0.896464
$787$	−6.11169	−0.217858	−0.108929	−	0.994050i	$-0.534742\pi$
$787$	−6.11169	−0.217858	−0.108929	+	0.994050i	$0.534742\pi$
$788$	−11.0791	−0.394677
$789$	−4.53287	−0.161374
$790$	−13.1065	−0.466309
$791$	−23.0863	−0.820854
$792$	0	0
$793$	28.1153	0.998405
$794$	17.4801	0.620347
$795$	−30.8716	−1.09490
$796$	−10.4170	−0.369221
$797$	−1.27382	−0.0451210	−0.0225605	−	0.999745i	$-0.507182\pi$
$797$	−1.27382	−0.0451210	−0.0225605	+	0.999745i	$0.507182\pi$
$798$	−7.32140	−0.259175
$799$	38.8512	1.37446
$800$	−0.960362	−0.0339539
$801$	36.8176	1.30089
$802$	16.7907	0.592899
$803$	0	0
$804$	27.7178	0.977530
$805$	11.1215	0.391983
$806$	28.2152	0.993839
$807$	−31.8009	−1.11944
$808$	−8.78589	−0.309086
$809$	−39.4787	−1.38800	−0.693999	−	0.719976i	$-0.744153\pi$
$809$	−39.4787	−1.38800	−0.693999	+	0.719976i	$0.744153\pi$
$810$	−19.6825	−0.691572
$811$	4.05599	0.142425	0.0712125	−	0.997461i	$-0.477313\pi$
$811$	4.05599	0.142425	0.0712125	+	0.997461i	$0.477313\pi$
$812$	21.4005	0.751011
$813$	5.88609	0.206434
$814$	0	0
$815$	−0.298790	−0.0104661
$816$	−13.0129	−0.455541
$817$	−11.9841	−0.419270
$818$	−7.01163	−0.245156
$819$	44.8785	1.56818
$820$	10.3630	0.361892
$821$	5.11544	0.178530	0.0892650	−	0.996008i	$-0.471548\pi$
$821$	5.11544	0.178530	0.0892650	+	0.996008i	$0.471548\pi$
$822$	−56.8381	−1.98246
$823$	−36.6100	−1.27614	−0.638072	−	0.769976i	$-0.720268\pi$
$823$	−36.6100	−1.27614	−0.638072	+	0.769976i	$0.720268\pi$
$824$	−10.5453	−0.367362
$825$	0	0
$826$	−11.6353	−0.404844
$827$	25.8761	0.899800	0.449900	−	0.893079i	$-0.351460\pi$
$827$	25.8761	0.899800	0.449900	+	0.893079i	$0.351460\pi$
$828$	−13.8687	−0.481972
$829$	−32.3503	−1.12357	−0.561785	−	0.827283i	$-0.689885\pi$
$829$	−32.3503	−1.12357	−0.561785	+	0.827283i	$0.689885\pi$
$830$	8.22260	0.285411
$831$	98.0306	3.40064
$832$	3.03557	0.105239
$833$	4.75407	0.164719
$834$	10.9288	0.378434
$835$	−1.00860	−0.0349039
$836$	0	0
$837$	86.5031	2.98998
$838$	−22.9541	−0.792935
$839$	29.3647	1.01378	0.506891	−	0.862010i	$-0.330795\pi$
$839$	29.3647	1.01378	0.506891	+	0.862010i	$0.330795\pi$
$840$	−14.7152	−0.507722
$841$	48.6414	1.67729
$842$	5.13342	0.176909
$843$	42.0659	1.44883
$844$	21.2337	0.730894
$845$	7.60808	0.261726
$846$	−54.7859	−1.88358
$847$	0	0
$848$	5.09532	0.174974
$849$	−68.0761	−2.33636
$850$	4.14564	0.142194
$851$	−2.43337	−0.0834148
$852$	−32.4385	−1.11132
$853$	32.8026	1.12314	0.561570	−	0.827429i	$-0.310197\pi$
$853$	32.8026	1.12314	0.561570	+	0.827429i	$0.310197\pi$
$854$	22.4948	0.769755
$855$	12.2347	0.418417
$856$	−7.69542	−0.263024
$857$	−10.5746	−0.361222	−0.180611	−	0.983555i	$-0.557807\pi$
$857$	−10.5746	−0.361222	−0.180611	+	0.983555i	$0.557807\pi$
$858$	0	0
$859$	31.7422	1.08303	0.541514	−	0.840692i	$-0.317851\pi$
$859$	31.7422	1.08303	0.541514	+	0.840692i	$0.317851\pi$
$860$	−24.0867	−0.821348
$861$	−37.7493	−1.28649
$862$	−39.2597	−1.33719
$863$	−29.2335	−0.995120	−0.497560	−	0.867430i	$-0.665771\pi$
$863$	−29.2335	−0.995120	−0.497560	+	0.867430i	$0.665771\pi$
$864$	9.30653	0.316615
$865$	−4.95780	−0.168570
$866$	−23.8406	−0.810137
$867$	4.92666	0.167318
$868$	22.5747	0.766235
$869$	0	0
$870$	−53.3868	−1.80998
$871$	27.9114	0.945742
$872$	−14.2327	−0.481979
$873$	−57.3840	−1.94216
$874$	2.27832	0.0770655
$875$	29.0952	0.983598
$876$	26.9490	0.910522
$877$	0.282048	0.00952409	0.00476205	−	0.999989i	$-0.498484\pi$
$877$	0.282048	0.00952409	0.00476205	+	0.999989i	$0.498484\pi$
$878$	−20.4659	−0.690690
$879$	78.7476	2.65609
$880$	0	0
$881$	−16.1017	−0.542480	−0.271240	−	0.962512i	$-0.587434\pi$
$881$	−16.1017	−0.542480	−0.271240	+	0.962512i	$0.587434\pi$
$882$	−6.70393	−0.225733
$883$	−22.6230	−0.761326	−0.380663	−	0.924714i	$-0.624304\pi$
$883$	−22.6230	−0.761326	−0.380663	+	0.924714i	$0.624304\pi$
$884$	−13.1038	−0.440728
$885$	29.0260	0.975699
$886$	20.4954	0.688558
$887$	9.68158	0.325076	0.162538	−	0.986702i	$-0.448032\pi$
$887$	9.68158	0.325076	0.162538	+	0.986702i	$0.448032\pi$
$888$	3.21965	0.108044
$889$	−24.4305	−0.819374
$890$	−12.1564	−0.407484
$891$	0	0
$892$	−5.98764	−0.200481
$893$	9.00012	0.301177
$894$	16.3430	0.546592
$895$	−38.7714	−1.29599
$896$	2.42872	0.0811379
$897$	−20.8484	−0.696106
$898$	29.9575	0.999695
$899$	81.9012	2.73156
$900$	−5.84596	−0.194865
$901$	−21.9952	−0.732766
$902$	0	0
$903$	87.7404	2.91982
$904$	−9.50553	−0.316149
$905$	17.1808	0.571109
$906$	23.1353	0.768618
$907$	49.2582	1.63559	0.817796	−	0.575508i	$-0.195196\pi$
$907$	49.2582	1.63559	0.817796	+	0.575508i	$0.195196\pi$
$908$	13.6499	0.452987
$909$	−53.4819	−1.77388
$910$	−14.8180	−0.491211
$911$	46.4531	1.53906	0.769529	−	0.638612i	$-0.220491\pi$
$911$	46.4531	1.53906	0.769529	+	0.638612i	$0.220491\pi$
$912$	−3.01451	−0.0998203
$913$	0	0
$914$	−29.4491	−0.974091
$915$	−56.1165	−1.85516
$916$	−11.3245	−0.374173
$917$	20.2491	0.668684
$918$	−40.1739	−1.32594
$919$	5.90424	0.194763	0.0973814	−	0.995247i	$-0.468953\pi$
$919$	5.90424	0.194763	0.0973814	+	0.995247i	$0.468953\pi$
$920$	4.57917	0.150971
$921$	−53.0911	−1.74941
$922$	−12.7886	−0.421170
$923$	−32.6651	−1.07518
$924$	0	0
$925$	−1.02572	−0.0337254
$926$	−22.8327	−0.750328
$927$	−64.1916	−2.10833
$928$	8.81144	0.289250
$929$	27.7607	0.910799	0.455400	−	0.890287i	$-0.349496\pi$
$929$	27.7607	0.910799	0.455400	+	0.890287i	$0.349496\pi$
$930$	−56.3159	−1.84667
$931$	1.10131	0.0360939
$932$	7.52089	0.246355
$933$	−26.4842	−0.867054
$934$	23.2585	0.761041
$935$	0	0
$936$	18.4783	0.603981
$937$	14.2974	0.467077	0.233539	−	0.972348i	$-0.424969\pi$
$937$	14.2974	0.467077	0.233539	+	0.972348i	$0.424969\pi$
$938$	22.3316	0.729153
$939$	97.1589	3.17066
$940$	18.0892	0.590005
$941$	41.9545	1.36768	0.683839	−	0.729633i	$-0.260309\pi$
$941$	41.9545	1.36768	0.683839	+	0.729633i	$0.260309\pi$
$942$	−72.3562	−2.35749
$943$	11.7471	0.382538
$944$	−4.79071	−0.155924
$945$	−45.4294	−1.47782
$946$	0	0
$947$	20.2850	0.659174	0.329587	−	0.944125i	$-0.393090\pi$
$947$	20.2850	0.659174	0.329587	+	0.944125i	$0.393090\pi$
$948$	19.6577	0.638452
$949$	27.1373	0.880913
$950$	0.960362	0.0311583
$951$	2.27312	0.0737109
$952$	−10.4842	−0.339794
$953$	33.3967	1.08182	0.540912	−	0.841079i	$-0.318079\pi$
$953$	33.3967	1.08182	0.540912	+	0.841079i	$0.318079\pi$
$954$	31.0165	1.00420
$955$	2.00923	0.0650171
$956$	−0.510794	−0.0165203
$957$	0	0
$958$	−12.5716	−0.406169
$959$	−45.7933	−1.47874
$960$	−6.05881	−0.195547
$961$	55.3948	1.78693
$962$	3.24214	0.104531
$963$	−46.8439	−1.50952
$964$	−22.6208	−0.728566
$965$	−10.0920	−0.324874
$966$	−16.6805	−0.536687
$967$	27.7370	0.891963	0.445981	−	0.895042i	$-0.352855\pi$
$967$	27.7370	0.891963	0.445981	+	0.895042i	$0.352855\pi$
$968$	0	0
$969$	13.0129	0.418033
$970$	18.9470	0.608353
$971$	−6.22298	−0.199705	−0.0998524	−	0.995002i	$-0.531837\pi$
$971$	−6.22298	−0.199705	−0.0998524	+	0.995002i	$0.531837\pi$
$972$	1.60101	0.0513524
$973$	8.80511	0.282279
$974$	−20.6412	−0.661387
$975$	−8.78802	−0.281442
$976$	9.26197	0.296468
$977$	26.2137	0.838650	0.419325	−	0.907836i	$-0.362267\pi$
$977$	26.2137	0.838650	0.419325	+	0.907836i	$0.362267\pi$
$978$	0.448137	0.0143298
$979$	0	0
$980$	2.21350	0.0707077
$981$	−86.6379	−2.76613
$982$	−30.2650	−0.965794
$983$	16.2834	0.519360	0.259680	−	0.965695i	$-0.416383\pi$
$983$	16.2834	0.519360	0.259680	+	0.965695i	$0.416383\pi$
$984$	−15.5429	−0.495489
$985$	22.2678	0.709510
$986$	−38.0368	−1.21134
$987$	−65.8934	−2.09741
$988$	−3.03557	−0.0965743
$989$	−27.3037	−0.868206
$990$	0	0
$991$	22.4663	0.713664	0.356832	−	0.934169i	$-0.383857\pi$
$991$	22.4663	0.713664	0.356832	+	0.934169i	$0.383857\pi$
$992$	9.29488	0.295113
$993$	19.0858	0.605669
$994$	−26.1350	−0.828951
$995$	20.9370	0.663747
$996$	−12.3326	−0.390773
$997$	−19.3207	−0.611892	−0.305946	−	0.952049i	$-0.598973\pi$
$997$	−19.3207	−0.611892	−0.305946	+	0.952049i	$0.598973\pi$
$998$	−36.2503	−1.14748
$999$	9.93985	0.314483

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4598.2.a.ca.1.8		8
11.5	even	5		418.2.f.f.267.4	yes	16
11.9	even	5		418.2.f.f.191.4	✓	16
11.10	odd	2		4598.2.a.bx.1.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.f.f.191.4	✓	16	11.9	even	5
418.2.f.f.267.4	yes	16	11.5	even	5
4598.2.a.bx.1.8		8	11.10	odd	2
4598.2.a.ca.1.8		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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +3.01451 q^{3} +1.00000 q^{4} -2.00989 q^{5} +3.01451 q^{6} +2.42872 q^{7} +1.00000 q^{8} +6.08725 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +3.01451 q^{3} +1.00000 q^{4} -2.00989 q^{5} +3.01451 q^{6} +2.42872 q^{7} +1.00000 q^{8} +6.08725 q^{9} -2.00989 q^{10} +3.01451 q^{12} +3.03557 q^{13} +2.42872 q^{14} -6.05881 q^{15} +1.00000 q^{16} -4.31675 q^{17} +6.08725 q^{18} -1.00000 q^{19} -2.00989 q^{20} +7.32140 q^{21} -2.27832 q^{23} +3.01451 q^{24} -0.960362 q^{25} +3.03557 q^{26} +9.30653 q^{27} +2.42872 q^{28} +8.81144 q^{29} -6.05881 q^{30} +9.29488 q^{31} +1.00000 q^{32} -4.31675 q^{34} -4.88145 q^{35} +6.08725 q^{36} +1.06805 q^{37} -1.00000 q^{38} +9.15074 q^{39} -2.00989 q^{40} -5.15603 q^{41} +7.32140 q^{42} +11.9841 q^{43} -12.2347 q^{45} -2.27832 q^{46} -9.00012 q^{47} +3.01451 q^{48} -1.10131 q^{49} -0.960362 q^{50} -13.0129 q^{51} +3.03557 q^{52} +5.09532 q^{53} +9.30653 q^{54} +2.42872 q^{56} -3.01451 q^{57} +8.81144 q^{58} -4.79071 q^{59} -6.05881 q^{60} +9.26197 q^{61} +9.29488 q^{62} +14.7842 q^{63} +1.00000 q^{64} -6.10114 q^{65} +9.19479 q^{67} -4.31675 q^{68} -6.86802 q^{69} -4.88145 q^{70} -10.7608 q^{71} +6.08725 q^{72} +8.93977 q^{73} +1.06805 q^{74} -2.89502 q^{75} -1.00000 q^{76} +9.15074 q^{78} +6.52103 q^{79} -2.00989 q^{80} +9.79285 q^{81} -5.15603 q^{82} -4.09108 q^{83} +7.32140 q^{84} +8.67617 q^{85} +11.9841 q^{86} +26.5621 q^{87} +6.04832 q^{89} -12.2347 q^{90} +7.37255 q^{91} -2.27832 q^{92} +28.0195 q^{93} -9.00012 q^{94} +2.00989 q^{95} +3.01451 q^{96} -9.42693 q^{97} -1.10131 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 8 q^{4} + 2 q^{5} + 8 q^{7} + 8 q^{8} + 20 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 + 8 * q^4 + 2 * q^5 + 8 * q^7 + 8 * q^8 + 20 * q^9	\( 8 q + 8 q^{2} + 8 q^{4} + 2 q^{5} + 8 q^{7} + 8 q^{8} + 20 q^{9} + 2 q^{10} + 18 q^{13} + 8 q^{14} + 10 q^{15} + 8 q^{16} + 4 q^{17} + 20 q^{18} - 8 q^{19} + 2 q^{20} + 14 q^{21} + 12 q^{23} + 18 q^{26} - 24 q^{27} + 8 q^{28} + 14 q^{29} + 10 q^{30} - 2 q^{31} + 8 q^{32} + 4 q^{34} + 40 q^{35} + 20 q^{36} - 22 q^{37} - 8 q^{38} - 4 q^{39} + 2 q^{40} + 8 q^{41} + 14 q^{42} + 28 q^{43} - 28 q^{45} + 12 q^{46} + 6 q^{47} + 32 q^{49} - 12 q^{51} + 18 q^{52} - 24 q^{53} - 24 q^{54} + 8 q^{56} + 14 q^{58} + 46 q^{59} + 10 q^{60} - 24 q^{61} - 2 q^{62} + 30 q^{63} + 8 q^{64} - 16 q^{65} - 22 q^{67} + 4 q^{68} - 38 q^{69} + 40 q^{70} + 8 q^{71} + 20 q^{72} + 16 q^{73} - 22 q^{74} + 6 q^{75} - 8 q^{76} - 4 q^{78} + 4 q^{79} + 2 q^{80} + 28 q^{81} + 8 q^{82} + 12 q^{83} + 14 q^{84} + 48 q^{85} + 28 q^{86} + 42 q^{87} - 28 q^{89} - 28 q^{90} - 12 q^{91} + 12 q^{92} + 22 q^{93} + 6 q^{94} - 2 q^{95} - 22 q^{97} + 32 q^{98}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^4 + 2 * q^5 + 8 * q^7 + 8 * q^8 + 20 * q^9 + 2 * q^10 + 18 * q^13 + 8 * q^14 + 10 * q^15 + 8 * q^16 + 4 * q^17 + 20 * q^18 - 8 * q^19 + 2 * q^20 + 14 * q^21 + 12 * q^23 + 18 * q^26 - 24 * q^27 + 8 * q^28 + 14 * q^29 + 10 * q^30 - 2 * q^31 + 8 * q^32 + 4 * q^34 + 40 * q^35 + 20 * q^36 - 22 * q^37 - 8 * q^38 - 4 * q^39 + 2 * q^40 + 8 * q^41 + 14 * q^42 + 28 * q^43 - 28 * q^45 + 12 * q^46 + 6 * q^47 + 32 * q^49 - 12 * q^51 + 18 * q^52 - 24 * q^53 - 24 * q^54 + 8 * q^56 + 14 * q^58 + 46 * q^59 + 10 * q^60 - 24 * q^61 - 2 * q^62 + 30 * q^63 + 8 * q^64 - 16 * q^65 - 22 * q^67 + 4 * q^68 - 38 * q^69 + 40 * q^70 + 8 * q^71 + 20 * q^72 + 16 * q^73 - 22 * q^74 + 6 * q^75 - 8 * q^76 - 4 * q^78 + 4 * q^79 + 2 * q^80 + 28 * q^81 + 8 * q^82 + 12 * q^83 + 14 * q^84 + 48 * q^85 + 28 * q^86 + 42 * q^87 - 28 * q^89 - 28 * q^90 - 12 * q^91 + 12 * q^92 + 22 * q^93 + 6 * q^94 - 2 * q^95 - 22 * q^97 + 32 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more