LMFDB - Embedded newform 4598.2.a.bx.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:	$1$
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	$-0.651787\pi$
$7$	−2.42872	−0.917971	−0.458985	+	0.888444i	$0.651787\pi$
$8$	−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	$-0.638306\pi$
$13$	−3.03557	−0.841915	−0.420957	+	0.907080i	$0.638306\pi$
$14$	2.42872	0.649103
$15$	−6.05881	−1.56438
$16$	1.00000	0.250000
$17$	4.31675	1.04697	0.523483	−	0.852036i	$-0.324632\pi$
$17$	4.31675	1.04697	0.523483	+	0.852036i	$0.324632\pi$
$18$	−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	$-0.804984\pi$
$29$	−8.81144	−1.63624	−0.818121	+	0.575046i	$0.804984\pi$
$30$	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	$-0.368100\pi$
$41$	5.15603	0.805236	0.402618	+	0.915368i	$0.368100\pi$
$42$	7.32140	1.12972
$43$	−11.9841	−1.82756	−0.913779	−	0.406212i	$-0.866849\pi$
$43$	−11.9841	−1.82756	−0.913779	+	0.406212i	$0.866849\pi$
$44$	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	$-0.702032\pi$
$61$	−9.26197	−1.18587	−0.592937	+	0.805249i	$0.702032\pi$
$62$	−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	$-0.675247\pi$
$73$	−8.93977	−1.04632	−0.523161	+	0.852234i	$0.675247\pi$
$74$	−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	$-0.619559\pi$
$79$	−6.52103	−0.733673	−0.366837	+	0.930285i	$0.619559\pi$
$80$	−2.00989	−0.224712
$81$	9.79285	1.08809
$82$	−5.15603	−0.569388
$83$	4.09108	0.449054	0.224527	−	0.974468i	$-0.427916\pi$
$83$	4.09108	0.449054	0.224527	+	0.974468i	$0.427916\pi$
$84$	−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	$-0.356001\pi$
$101$	8.78589	0.874229	0.437114	+	0.899406i	$0.356001\pi$
$102$	−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	$-0.378682\pi$
$107$	7.69542	0.743944	0.371972	+	0.928244i	$0.378682\pi$
$108$	9.30653	0.895521
$109$	14.2327	1.36324	0.681622	−	0.731705i	$-0.261275\pi$
$109$	14.2327	1.36324	0.681622	+	0.731705i	$0.261275\pi$
$110$	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	$-0.352743\pi$
$127$	10.0590	0.892593	0.446296	+	0.894885i	$0.352743\pi$
$128$	−1.00000	−0.0883883
$129$	−36.1261	−3.18073
$130$	−6.10114	−0.535105
$131$	−8.33735	−0.728437	−0.364219	−	0.931313i	$-0.618664\pi$
$131$	−8.33735	−0.728437	−0.364219	+	0.931313i	$0.618664\pi$
$132$	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	$-0.549136\pi$
$139$	−3.62541	−0.307503	−0.153752	+	0.988110i	$0.549136\pi$
$140$	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	$-0.571282\pi$
$149$	−5.42145	−0.444143	−0.222071	+	0.975030i	$0.571282\pi$
$150$	2.89502	0.236377
$151$	−7.67465	−0.624554	−0.312277	−	0.949991i	$-0.601092\pi$
$151$	−7.67465	−0.624554	−0.312277	+	0.949991i	$0.601092\pi$
$152$	−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	$-0.506181\pi$
$167$	−0.501818	−0.0388319	−0.0194159	+	0.999811i	$0.506181\pi$
$168$	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	$-0.529892\pi$
$173$	−2.46671	−0.187540	−0.0937701	+	0.995594i	$0.529892\pi$
$174$	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	$-0.557842\pi$
$193$	−5.02121	−0.361434	−0.180717	+	0.983535i	$0.557842\pi$
$194$	9.42693	0.676814
$195$	18.3919	1.31707
$196$	−1.10131	−0.0786648
$197$	11.0791	0.789355	0.394677	−	0.918820i	$-0.370856\pi$
$197$	11.0791	0.789355	0.394677	+	0.918820i	$0.370856\pi$
$198$	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	$-0.760896\pi$
$211$	−21.2337	−1.46179	−0.730894	+	0.682491i	$0.760896\pi$
$212$	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	$-0.649641\pi$
$227$	−13.6499	−0.905973	−0.452987	+	0.891517i	$0.649641\pi$
$228$	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	$-0.579233\pi$
$233$	−7.52089	−0.492710	−0.246355	+	0.969180i	$0.579233\pi$
$234$	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	$-0.494741\pi$
$239$	0.510794	0.0330405	0.0165203	+	0.999864i	$0.494741\pi$
$240$	−6.05881	−0.391095
$241$	22.6208	1.45713	0.728566	−	0.684975i	$-0.240187\pi$
$241$	22.6208	1.45713	0.728566	+	0.684975i	$0.240187\pi$
$242$	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	$-0.485238\pi$
$263$	1.50368	0.0927212	0.0463606	+	0.998925i	$0.485238\pi$
$264$	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	$-0.518889\pi$
$271$	−1.95259	−0.118611	−0.0593056	+	0.998240i	$0.518889\pi$
$272$	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	$-0.931535\pi$
$277$	−32.5196	−1.95391	−0.976957	+	0.213434i	$0.931535\pi$
$278$	3.62541	0.217438
$279$	56.5802	3.38737
$280$	−4.88145	−0.291723
$281$	−13.9545	−0.832454	−0.416227	−	0.909261i	$-0.636648\pi$
$281$	−13.9545	−0.832454	−0.416227	+	0.909261i	$0.636648\pi$
$282$	27.1309	1.61562
$283$	22.5828	1.34241	0.671205	−	0.741272i	$-0.265777\pi$
$283$	22.5828	1.34241	0.671205	+	0.741272i	$0.265777\pi$
$284$	−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	$-0.776303\pi$
$293$	−26.1229	−1.52612	−0.763058	+	0.646330i	$0.776303\pi$
$294$	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	$-0.332384\pi$
$307$	17.6119	1.00516	0.502581	+	0.864530i	$0.332384\pi$
$308$	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	$-0.579808\pi$
$337$	−9.10922	−0.496211	−0.248105	+	0.968733i	$0.579808\pi$
$338$	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	$-0.493072\pi$
$347$	0.810769	0.0435243	0.0217622	+	0.999763i	$0.493072\pi$
$348$	−26.5621	−1.42388
$349$	25.9076	1.38680	0.693401	−	0.720552i	$-0.256111\pi$
$349$	25.9076	1.38680	0.693401	+	0.720552i	$0.256111\pi$
$350$	−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	$-0.147775\pi$
$359$	33.8838	1.78832	0.894158	+	0.447751i	$0.147775\pi$
$360$	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	$-0.601768\pi$
$373$	−12.1401	−0.628589	−0.314294	+	0.949326i	$0.601768\pi$
$374$	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	$-0.444540\pi$
$409$	7.01163	0.346703	0.173351	+	0.984860i	$0.444540\pi$
$410$	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	$-0.105539\pi$
$431$	39.2597	1.89107	0.945536	+	0.325518i	$0.105539\pi$
$432$	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	$-0.337584\pi$
$439$	20.4659	0.976783	0.488391	+	0.872625i	$0.337584\pi$
$440$	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	$-0.258144\pi$
$457$	29.4491	1.37757	0.688786	+	0.724964i	$0.258144\pi$
$458$	11.3245	0.529161
$459$	40.1739	1.87516
$460$	4.57917	0.213505
$461$	12.7886	0.595624	0.297812	−	0.954624i	$-0.403743\pi$
$461$	12.7886	0.595624	0.297812	+	0.954624i	$0.403743\pi$
$462$	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	$-0.407274\pi$
$479$	12.5716	0.574410	0.287205	+	0.957869i	$0.407274\pi$
$480$	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	$-0.260710\pi$
$491$	30.2650	1.36584	0.682919	+	0.730494i	$0.260710\pi$
$492$	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	$-0.604054\pi$
$503$	−14.4032	−0.642208	−0.321104	+	0.947044i	$0.604054\pi$
$504$	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	$-0.764304\pi$
$523$	−33.7621	−1.47631	−0.738157	+	0.674629i	$0.764304\pi$
$524$	−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	$-0.440539\pi$
$541$	8.63940	0.371437	0.185718	+	0.982603i	$0.440539\pi$
$542$	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	$-0.362109\pi$
$547$	19.6355	0.839552	0.419776	+	0.907628i	$0.362109\pi$
$548$	−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	$-0.146697\pi$
$557$	42.2771	1.79134	0.895669	+	0.444722i	$0.146697\pi$
$558$	−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	$-0.609021\pi$
$563$	−15.9375	−0.671688	−0.335844	+	0.941918i	$0.609021\pi$
$564$	−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	$-0.351711\pi$
$569$	21.4299	0.898387	0.449193	+	0.893435i	$0.351711\pi$
$570$	6.05881	0.253776
$571$	−21.2358	−0.888691	−0.444346	−	0.895855i	$-0.646564\pi$
$571$	−21.2358	−0.888691	−0.444346	+	0.895855i	$0.646564\pi$
$572$	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	$-0.410748\pi$
$593$	13.4779	0.553469	0.276735	+	0.960946i	$0.410748\pi$
$594$	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	$-0.555391\pi$
$601$	−8.48908	−0.346277	−0.173138	+	0.984898i	$0.555391\pi$
$602$	−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	$-0.469253\pi$
$607$	4.75233	0.192891	0.0964457	+	0.995338i	$0.469253\pi$
$608$	−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	$-0.702177\pi$
$613$	−29.3790	−1.18661	−0.593304	+	0.804979i	$0.702177\pi$
$614$	−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	$-0.477171\pi$
$659$	3.67907	0.143316	0.0716582	+	0.997429i	$0.477171\pi$
$660$	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	$-0.586719\pi$
$673$	−13.9610	−0.538156	−0.269078	+	0.963118i	$0.586719\pi$
$674$	9.10922	0.350874
$675$	−8.93764	−0.344010
$676$	−3.78533	−0.145590
$677$	9.42523	0.362241	0.181121	−	0.983461i	$-0.442028\pi$
$677$	9.42523	0.362241	0.181121	+	0.983461i	$0.442028\pi$
$678$	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	$-0.301673\pi$
$701$	30.8992	1.16705	0.583524	+	0.812096i	$0.301673\pi$
$702$	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	$-0.728541\pi$
$733$	−35.6221	−1.31573	−0.657867	+	0.753134i	$0.728541\pi$
$734$	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	$-0.753049\pi$
$739$	−38.8113	−1.42770	−0.713848	+	0.700300i	$0.753049\pi$
$740$	−2.14666	−0.0789128
$741$	−9.15074	−0.336161
$742$	12.3751	0.454305
$743$	20.4994	0.752051	0.376025	−	0.926609i	$-0.377291\pi$
$743$	20.4994	0.752051	0.376025	+	0.926609i	$0.377291\pi$
$744$	−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	$-0.588084\pi$
$761$	−15.0734	−0.546411	−0.273205	+	0.961956i	$0.588084\pi$
$762$	−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	$-0.314928\pi$
$769$	30.4602	1.09842	0.549212	+	0.835683i	$0.314928\pi$
$770$	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	$-0.465258\pi$
$787$	6.11169	0.217858	0.108929	+	0.994050i	$0.465258\pi$
$788$	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	$-0.255847\pi$
$809$	39.4787	1.38800	0.693999	+	0.719976i	$0.255847\pi$
$810$	19.6825	0.691572
$811$	−4.05599	−0.142425	−0.0712125	−	0.997461i	$-0.522687\pi$
$811$	−4.05599	−0.142425	−0.0712125	+	0.997461i	$0.522687\pi$
$812$	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	$-0.528452\pi$
$821$	−5.11544	−0.178530	−0.0892650	+	0.996008i	$0.528452\pi$
$822$	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	$-0.648540\pi$
$827$	−25.8761	−0.899800	−0.449900	+	0.893079i	$0.648540\pi$
$828$	−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	$-0.689803\pi$
$853$	−32.8026	−1.12314	−0.561570	+	0.827429i	$0.689803\pi$
$854$	−22.4948	−0.769755
$855$	−12.2347	−0.418417
$856$	−7.69542	−0.263024
$857$	10.5746	0.361222	0.180611	−	0.983555i	$-0.442193\pi$
$857$	10.5746	0.361222	0.180611	+	0.983555i	$0.442193\pi$
$858$	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	$-0.501516\pi$
$877$	−0.282048	−0.00952409	−0.00476205	+	0.999989i	$0.501516\pi$
$878$	−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	$-0.551968\pi$
$887$	−9.68158	−0.325076	−0.162538	+	0.986702i	$0.551968\pi$
$888$	−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	$-0.531047\pi$
$919$	−5.90424	−0.194763	−0.0973814	+	0.995247i	$0.531047\pi$
$920$	−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	$-0.575031\pi$
$937$	−14.2974	−0.467077	−0.233539	+	0.972348i	$0.575031\pi$
$938$	22.3316	0.729153
$939$	97.1589	3.17066
$940$	18.0892	0.590005
$941$	−41.9545	−1.36768	−0.683839	−	0.729633i	$-0.739691\pi$
$941$	−41.9545	−1.36768	−0.683839	+	0.729633i	$0.739691\pi$
$942$	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	$-0.681921\pi$
$953$	−33.3967	−1.08182	−0.540912	+	0.841079i	$0.681921\pi$
$954$	−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	$-0.647145\pi$
$967$	−27.7370	−0.891963	−0.445981	+	0.895042i	$0.647145\pi$
$968$	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	$-0.401027\pi$
$997$	19.3207	0.611892	0.305946	+	0.952049i	$0.401027\pi$
$998$	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.bx.1.8		8
11.2	odd	10		418.2.f.f.191.4	✓	16
11.6	odd	10		418.2.f.f.267.4	yes	16
11.10	odd	2		4598.2.a.ca.1.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.f.f.191.4	✓	16	11.2	odd	10
418.2.f.f.267.4	yes	16	11.6	odd	10
4598.2.a.bx.1.8		8	1.1	even	1	trivial
4598.2.a.ca.1.8		8	11.10	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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

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