LMFDB - Embedded newform 8470.2.a.cl.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8470,2,Mod(1,8470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8470, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8470.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8470.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:	$67.6332905120$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.892.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 8x + 10 $ x^3 - x^2 - 8*x + 10
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 770)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-2.91729$ of defining polynomial
Character	$\chi$	$=$	8470.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.406728 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.406728 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.83457 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.406728 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.406728 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.83457 q^{9} -1.00000 q^{10} -0.406728 q^{12} +0.813457 q^{13} +1.00000 q^{14} +0.406728 q^{15} +1.00000 q^{16} -3.83457 q^{17} -2.83457 q^{18} -5.42784 q^{19} -1.00000 q^{20} -0.406728 q^{21} -5.42784 q^{23} -0.406728 q^{24} +1.00000 q^{25} +0.813457 q^{26} +2.37309 q^{27} +1.00000 q^{28} -6.61439 q^{29} +0.406728 q^{30} +6.00000 q^{31} +1.00000 q^{32} -3.83457 q^{34} -1.00000 q^{35} -2.83457 q^{36} +8.24130 q^{37} -5.42784 q^{38} -0.330856 q^{39} -1.00000 q^{40} +5.59327 q^{41} -0.406728 q^{42} +3.02112 q^{43} +2.83457 q^{45} -5.42784 q^{46} -5.02112 q^{47} -0.406728 q^{48} +1.00000 q^{49} +1.00000 q^{50} +1.55963 q^{51} +0.813457 q^{52} +6.61439 q^{53} +2.37309 q^{54} +1.00000 q^{56} +2.20766 q^{57} -6.61439 q^{58} +10.6480 q^{59} +0.406728 q^{60} -0.978885 q^{61} +6.00000 q^{62} -2.83457 q^{63} +1.00000 q^{64} -0.813457 q^{65} +8.00000 q^{67} -3.83457 q^{68} +2.20766 q^{69} -1.00000 q^{70} +14.8557 q^{71} -2.83457 q^{72} +6.20766 q^{73} +8.24130 q^{74} -0.406728 q^{75} -5.42784 q^{76} -0.330856 q^{78} -17.0970 q^{79} -1.00000 q^{80} +7.53851 q^{81} +5.59327 q^{82} +8.81346 q^{83} -0.406728 q^{84} +3.83457 q^{85} +3.02112 q^{86} +2.69026 q^{87} -1.18654 q^{89} +2.83457 q^{90} +0.813457 q^{91} -5.42784 q^{92} -2.44037 q^{93} -5.02112 q^{94} +5.42784 q^{95} -0.406728 q^{96} -3.42784 q^{97} +1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + 3 q^{4} - 3 q^{5} + 3 q^{7} + 3 q^{8} + 11 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 + 3 * q^4 - 3 * q^5 + 3 * q^7 + 3 * q^8 + 11 * q^9	$ 3 q + 3 q^{2} + 3 q^{4} - 3 q^{5} + 3 q^{7} + 3 q^{8} + 11 q^{9} - 3 q^{10} + 3 q^{14} + 3 q^{16} + 8 q^{17} + 11 q^{18} + 2 q^{19} - 3 q^{20} + 2 q^{23} + 3 q^{25} + 12 q^{27} + 3 q^{28} - 4 q^{29} + 18 q^{31} + 3 q^{32} + 8 q^{34} - 3 q^{35} + 11 q^{36} + 4 q^{37} + 2 q^{38} - 40 q^{39} - 3 q^{40} + 18 q^{41} - 8 q^{43} - 11 q^{45} + 2 q^{46} + 2 q^{47} + 3 q^{49} + 3 q^{50} + 12 q^{51} + 4 q^{53} + 12 q^{54} + 3 q^{56} - 8 q^{57} - 4 q^{58} + 10 q^{59} - 20 q^{61} + 18 q^{62} + 11 q^{63} + 3 q^{64} + 24 q^{67} + 8 q^{68} - 8 q^{69} - 3 q^{70} + 8 q^{71} + 11 q^{72} + 4 q^{73} + 4 q^{74} + 2 q^{76} - 40 q^{78} + 6 q^{79} - 3 q^{80} + 47 q^{81} + 18 q^{82} + 24 q^{83} - 8 q^{85} - 8 q^{86} - 48 q^{87} - 6 q^{89} - 11 q^{90} + 2 q^{92} + 2 q^{94} - 2 q^{95} + 8 q^{97} + 3 q^{98}+O(q^{100}) $ 3 * q + 3 * q^2 + 3 * q^4 - 3 * q^5 + 3 * q^7 + 3 * q^8 + 11 * q^9 - 3 * q^10 + 3 * q^14 + 3 * q^16 + 8 * q^17 + 11 * q^18 + 2 * q^19 - 3 * q^20 + 2 * q^23 + 3 * q^25 + 12 * q^27 + 3 * q^28 - 4 * q^29 + 18 * q^31 + 3 * q^32 + 8 * q^34 - 3 * q^35 + 11 * q^36 + 4 * q^37 + 2 * q^38 - 40 * q^39 - 3 * q^40 + 18 * q^41 - 8 * q^43 - 11 * q^45 + 2 * q^46 + 2 * q^47 + 3 * q^49 + 3 * q^50 + 12 * q^51 + 4 * q^53 + 12 * q^54 + 3 * q^56 - 8 * q^57 - 4 * q^58 + 10 * q^59 - 20 * q^61 + 18 * q^62 + 11 * q^63 + 3 * q^64 + 24 * q^67 + 8 * q^68 - 8 * q^69 - 3 * q^70 + 8 * q^71 + 11 * q^72 + 4 * q^73 + 4 * q^74 + 2 * q^76 - 40 * q^78 + 6 * q^79 - 3 * q^80 + 47 * q^81 + 18 * q^82 + 24 * q^83 - 8 * q^85 - 8 * q^86 - 48 * q^87 - 6 * q^89 - 11 * q^90 + 2 * q^92 + 2 * q^94 - 2 * q^95 + 8 * q^97 + 3 * 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
$3$	−0.406728	−0.234825	−0.117412	−	0.993083i	$-0.537460\pi$
$3$	−0.406728	−0.234825	−0.117412	+	0.993083i	$0.537460\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.406728	−0.166046
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	−2.83457	−0.944857
$10$	−1.00000	−0.316228
$11$	0	0
$11$	0	0
$12$	−0.406728	−0.117412
$13$	0.813457	0.225612	0.112806	−	0.993617i	$-0.464016\pi$
$13$	0.813457	0.225612	0.112806	+	0.993617i	$0.464016\pi$
$14$	1.00000	0.267261
$15$	0.406728	0.105017
$16$	1.00000	0.250000
$17$	−3.83457	−0.930020	−0.465010	−	0.885305i	$-0.653949\pi$
$17$	−3.83457	−0.930020	−0.465010	+	0.885305i	$0.653949\pi$
$18$	−2.83457	−0.668115
$19$	−5.42784	−1.24523	−0.622616	−	0.782527i	$-0.713930\pi$
$19$	−5.42784	−1.24523	−0.622616	+	0.782527i	$0.713930\pi$
$20$	−1.00000	−0.223607
$21$	−0.406728	−0.0887554
$22$	0	0
$23$	−5.42784	−1.13178	−0.565892	−	0.824480i	$-0.691468\pi$
$23$	−5.42784	−1.13178	−0.565892	+	0.824480i	$0.691468\pi$
$24$	−0.406728	−0.0830231
$25$	1.00000	0.200000
$26$	0.813457	0.159532
$27$	2.37309	0.456701
$28$	1.00000	0.188982
$29$	−6.61439	−1.22826	−0.614130	−	0.789205i	$-0.710493\pi$
$29$	−6.61439	−1.22826	−0.614130	+	0.789205i	$0.710493\pi$
$30$	0.406728	0.0742581
$31$	6.00000	1.07763	0.538816	−	0.842424i	$-0.318872\pi$
$31$	6.00000	1.07763	0.538816	+	0.842424i	$0.318872\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−3.83457	−0.657624
$35$	−1.00000	−0.169031
$36$	−2.83457	−0.472429
$37$	8.24130	1.35486	0.677431	−	0.735587i	$-0.263093\pi$
$37$	8.24130	1.35486	0.677431	+	0.735587i	$0.263093\pi$
$38$	−5.42784	−0.880512
$39$	−0.330856	−0.0529794
$40$	−1.00000	−0.158114
$41$	5.59327	0.873522	0.436761	−	0.899578i	$-0.356125\pi$
$41$	5.59327	0.873522	0.436761	+	0.899578i	$0.356125\pi$
$42$	−0.406728	−0.0627596
$43$	3.02112	0.460716	0.230358	−	0.973106i	$-0.426010\pi$
$43$	3.02112	0.460716	0.230358	+	0.973106i	$0.426010\pi$
$44$	0	0
$45$	2.83457	0.422553
$46$	−5.42784	−0.800292
$47$	−5.02112	−0.732405	−0.366202	−	0.930535i	$-0.619342\pi$
$47$	−5.02112	−0.732405	−0.366202	+	0.930535i	$0.619342\pi$
$48$	−0.406728	−0.0587062
$49$	1.00000	0.142857
$50$	1.00000	0.141421
$51$	1.55963	0.218392
$52$	0.813457	0.112806
$53$	6.61439	0.908556	0.454278	−	0.890860i	$-0.349897\pi$
$53$	6.61439	0.908556	0.454278	+	0.890860i	$0.349897\pi$
$54$	2.37309	0.322936
$55$	0	0
$56$	1.00000	0.133631
$57$	2.20766	0.292411
$58$	−6.61439	−0.868512
$59$	10.6480	1.38626	0.693128	−	0.720815i	$-0.256232\pi$
$59$	10.6480	1.38626	0.693128	+	0.720815i	$0.256232\pi$
$60$	0.406728	0.0525084
$61$	−0.978885	−0.125333	−0.0626667	−	0.998035i	$-0.519961\pi$
$61$	−0.978885	−0.125333	−0.0626667	+	0.998035i	$0.519961\pi$
$62$	6.00000	0.762001
$63$	−2.83457	−0.357123
$64$	1.00000	0.125000
$65$	−0.813457	−0.100897
$66$	0	0
$67$	8.00000	0.977356	0.488678	−	0.872464i	$-0.337479\pi$
$67$	8.00000	0.977356	0.488678	+	0.872464i	$0.337479\pi$
$68$	−3.83457	−0.465010
$69$	2.20766	0.265771
$70$	−1.00000	−0.119523
$71$	14.8557	1.76305	0.881523	−	0.472141i	$-0.156519\pi$
$71$	14.8557	1.76305	0.881523	+	0.472141i	$0.156519\pi$
$72$	−2.83457	−0.334058
$73$	6.20766	0.726551	0.363276	−	0.931682i	$-0.381658\pi$
$73$	6.20766	0.726551	0.363276	+	0.931682i	$0.381658\pi$
$74$	8.24130	0.958032
$75$	−0.406728	−0.0469650
$76$	−5.42784	−0.622616
$77$	0	0
$78$	−0.330856	−0.0374621
$79$	−17.0970	−1.92356	−0.961781	−	0.273821i	$-0.911712\pi$
$79$	−17.0970	−1.92356	−0.961781	+	0.273821i	$0.911712\pi$
$80$	−1.00000	−0.111803
$81$	7.53851	0.837613
$82$	5.59327	0.617674
$83$	8.81346	0.967403	0.483701	−	0.875233i	$-0.339292\pi$
$83$	8.81346	0.967403	0.483701	+	0.875233i	$0.339292\pi$
$84$	−0.406728	−0.0443777
$85$	3.83457	0.415918
$86$	3.02112	0.325775
$87$	2.69026	0.288426
$88$	0	0
$89$	−1.18654	−0.125773	−0.0628867	−	0.998021i	$-0.520031\pi$
$89$	−1.18654	−0.125773	−0.0628867	+	0.998021i	$0.520031\pi$
$90$	2.83457	0.298790
$91$	0.813457	0.0852734
$92$	−5.42784	−0.565892
$93$	−2.44037	−0.253055
$94$	−5.02112	−0.517888
$95$	5.42784	0.556885
$96$	−0.406728	−0.0415115
$97$	−3.42784	−0.348045	−0.174022	−	0.984742i	$-0.555677\pi$
$97$	−3.42784	−0.348045	−0.174022	+	0.984742i	$0.555677\pi$
$98$	1.00000	0.101015
$99$	0	0
$100$	1.00000	0.100000
$101$	18.6903	1.85975	0.929875	−	0.367875i	$-0.119915\pi$
$101$	18.6903	1.85975	0.929875	+	0.367875i	$0.119915\pi$
$102$	1.55963	0.154426
$103$	15.4615	1.52347	0.761733	−	0.647891i	$-0.224349\pi$
$103$	15.4615	1.52347	0.761733	+	0.647891i	$0.224349\pi$
$104$	0.813457	0.0797660
$105$	0.406728	0.0396926
$106$	6.61439	0.642446
$107$	11.0211	1.06545	0.532726	−	0.846288i	$-0.321168\pi$
$107$	11.0211	1.06545	0.532726	+	0.846288i	$0.321168\pi$
$108$	2.37309	0.228350
$109$	−16.2413	−1.55563	−0.777817	−	0.628491i	$-0.783673\pi$
$109$	−16.2413	−1.55563	−0.777817	+	0.628491i	$0.783673\pi$
$110$	0	0
$111$	−3.35197	−0.318155
$112$	1.00000	0.0944911
$113$	−14.0000	−1.31701	−0.658505	−	0.752577i	$-0.728811\pi$
$113$	−14.0000	−1.31701	−0.658505	+	0.752577i	$0.728811\pi$
$114$	2.20766	0.206766
$115$	5.42784	0.506149
$116$	−6.61439	−0.614130
$117$	−2.30580	−0.213171
$118$	10.6480	0.980231
$119$	−3.83457	−0.351515
$120$	0.406728	0.0371291
$121$	0	0
$122$	−0.978885	−0.0886241
$123$	−2.27494	−0.205125
$124$	6.00000	0.538816
$125$	−1.00000	−0.0894427
$126$	−2.83457	−0.252524
$127$	−17.2961	−1.53478	−0.767388	−	0.641182i	$-0.778444\pi$
$127$	−17.2961	−1.53478	−0.767388	+	0.641182i	$0.778444\pi$
$128$	1.00000	0.0883883
$129$	−1.22877	−0.108187
$130$	−0.813457	−0.0713449
$131$	−9.42784	−0.823715	−0.411857	−	0.911248i	$-0.635120\pi$
$131$	−9.42784	−0.823715	−0.411857	+	0.911248i	$0.635120\pi$
$132$	0	0
$133$	−5.42784	−0.470654
$134$	8.00000	0.691095
$135$	−2.37309	−0.204243
$136$	−3.83457	−0.328812
$137$	13.6691	1.16783	0.583917	−	0.811813i	$-0.301519\pi$
$137$	13.6691	1.16783	0.583917	+	0.811813i	$0.301519\pi$
$138$	2.20766	0.187928
$139$	11.8682	1.00665	0.503324	−	0.864098i	$-0.332110\pi$
$139$	11.8682	1.00665	0.503324	+	0.864098i	$0.332110\pi$
$140$	−1.00000	−0.0845154
$141$	2.04223	0.171987
$142$	14.8557	1.24666
$143$	0	0
$144$	−2.83457	−0.236214
$145$	6.61439	0.549295
$146$	6.20766	0.513749
$147$	−0.406728	−0.0335464
$148$	8.24130	0.677431
$149$	22.2835	1.82554	0.912769	−	0.408476i	$-0.133940\pi$
$149$	22.2835	1.82554	0.912769	+	0.408476i	$0.133940\pi$
$150$	−0.406728	−0.0332092
$151$	3.05476	0.248593	0.124296	−	0.992245i	$-0.460333\pi$
$151$	3.05476	0.248593	0.124296	+	0.992245i	$0.460333\pi$
$152$	−5.42784	−0.440256
$153$	10.8694	0.878737
$154$	0	0
$155$	−6.00000	−0.481932
$156$	−0.330856	−0.0264897
$157$	4.85569	0.387526	0.193763	−	0.981048i	$-0.437931\pi$
$157$	4.85569	0.387526	0.193763	+	0.981048i	$0.437931\pi$
$158$	−17.0970	−1.36016
$159$	−2.69026	−0.213351
$160$	−1.00000	−0.0790569
$161$	−5.42784	−0.427774
$162$	7.53851	0.592282
$163$	−8.00000	−0.626608	−0.313304	−	0.949653i	$-0.601436\pi$
$163$	−8.00000	−0.626608	−0.313304	+	0.949653i	$0.601436\pi$
$164$	5.59327	0.436761
$165$	0	0
$166$	8.81346	0.684057
$167$	−8.00000	−0.619059	−0.309529	−	0.950890i	$-0.600171\pi$
$167$	−8.00000	−0.619059	−0.309529	+	0.950890i	$0.600171\pi$
$168$	−0.406728	−0.0313798
$169$	−12.3383	−0.949099
$170$	3.83457	0.294098
$171$	15.3856	1.17657
$172$	3.02112	0.230358
$173$	19.0211	1.44615	0.723074	−	0.690770i	$-0.242728\pi$
$173$	19.0211	1.44615	0.723074	+	0.690770i	$0.242728\pi$
$174$	2.69026	0.203948
$175$	1.00000	0.0755929
$176$	0	0
$177$	−4.33086	−0.325527
$178$	−1.18654	−0.0889352
$179$	4.64803	0.347410	0.173705	−	0.984798i	$-0.444426\pi$
$179$	4.64803	0.347410	0.173705	+	0.984798i	$0.444426\pi$
$180$	2.83457	0.211277
$181$	−25.3383	−1.88338	−0.941690	−	0.336482i	$-0.890763\pi$
$181$	−25.3383	−1.88338	−0.941690	+	0.336482i	$0.890763\pi$
$182$	0.813457	0.0602974
$183$	0.398140	0.0294314
$184$	−5.42784	−0.400146
$185$	−8.24130	−0.605912
$186$	−2.44037	−0.178937
$187$	0	0
$188$	−5.02112	−0.366202
$189$	2.37309	0.172617
$190$	5.42784	0.393777
$191$	15.6691	1.13378	0.566890	−	0.823794i	$-0.308147\pi$
$191$	15.6691	1.13378	0.566890	+	0.823794i	$0.308147\pi$
$192$	−0.406728	−0.0293531
$193$	2.16543	0.155871	0.0779355	−	0.996958i	$-0.475167\pi$
$193$	2.16543	0.155871	0.0779355	+	0.996958i	$0.475167\pi$
$194$	−3.42784	−0.246105
$195$	0.330856	0.0236931
$196$	1.00000	0.0714286
$197$	−2.81346	−0.200451	−0.100225	−	0.994965i	$-0.531956\pi$
$197$	−2.81346	−0.200451	−0.100225	+	0.994965i	$0.531956\pi$
$198$	0	0
$199$	−13.0211	−0.923042	−0.461521	−	0.887129i	$-0.652696\pi$
$199$	−13.0211	−0.923042	−0.461521	+	0.887129i	$0.652696\pi$
$200$	1.00000	0.0707107
$201$	−3.25383	−0.229507
$202$	18.6903	1.31504
$203$	−6.61439	−0.464239
$204$	1.55963	0.109196
$205$	−5.59327	−0.390651
$206$	15.4615	1.07725
$207$	15.3856	1.06937
$208$	0.813457	0.0564031
$209$	0	0
$210$	0.406728	0.0280669
$211$	−19.6691	−1.35408	−0.677040	−	0.735946i	$-0.736738\pi$
$211$	−19.6691	−1.35408	−0.677040	+	0.735946i	$0.736738\pi$
$212$	6.61439	0.454278
$213$	−6.04223	−0.414007
$214$	11.0211	0.753388
$215$	−3.02112	−0.206038
$216$	2.37309	0.161468
$217$	6.00000	0.407307
$218$	−16.2413	−1.10000
$219$	−2.52483	−0.170612
$220$	0	0
$221$	−3.11926	−0.209824
$222$	−3.35197	−0.224970
$223$	−3.79234	−0.253954	−0.126977	−	0.991906i	$-0.540527\pi$
$223$	−3.79234	−0.253954	−0.126977	+	0.991906i	$0.540527\pi$
$224$	1.00000	0.0668153
$225$	−2.83457	−0.188971
$226$	−14.0000	−0.931266
$227$	14.0422	0.932016	0.466008	−	0.884781i	$-0.345692\pi$
$227$	14.0422	0.932016	0.466008	+	0.884781i	$0.345692\pi$
$228$	2.20766	0.146206
$229$	1.83457	0.121232	0.0606160	−	0.998161i	$-0.480694\pi$
$229$	1.83457	0.121232	0.0606160	+	0.998161i	$0.480694\pi$
$230$	5.42784	0.357901
$231$	0	0
$232$	−6.61439	−0.434256
$233$	8.04223	0.526864	0.263432	−	0.964678i	$-0.415146\pi$
$233$	8.04223	0.526864	0.263432	+	0.964678i	$0.415146\pi$
$234$	−2.30580	−0.150735
$235$	5.02112	0.327541
$236$	10.6480	0.693128
$237$	6.95383	0.451700
$238$	−3.83457	−0.248558
$239$	15.4701	1.00068	0.500338	−	0.865830i	$-0.333209\pi$
$239$	15.4701	1.00068	0.500338	+	0.865830i	$0.333209\pi$
$240$	0.406728	0.0262542
$241$	−11.6355	−0.749509	−0.374754	−	0.927124i	$-0.622273\pi$
$241$	−11.6355	−0.749509	−0.374754	+	0.927124i	$0.622273\pi$
$242$	0	0
$243$	−10.1854	−0.653393
$244$	−0.978885	−0.0626667
$245$	−1.00000	−0.0638877
$246$	−2.27494	−0.145045
$247$	−4.41532	−0.280940
$248$	6.00000	0.381000
$249$	−3.58468	−0.227170
$250$	−1.00000	−0.0632456
$251$	5.35197	0.337813	0.168907	−	0.985632i	$-0.445976\pi$
$251$	5.35197	0.337813	0.168907	+	0.985632i	$0.445976\pi$
$252$	−2.83457	−0.178561
$253$	0	0
$254$	−17.2961	−1.08525
$255$	−1.55963	−0.0976678
$256$	1.00000	0.0625000
$257$	12.7239	0.793695	0.396848	−	0.917885i	$-0.370104\pi$
$257$	12.7239	0.793695	0.396848	+	0.917885i	$0.370104\pi$
$258$	−1.22877	−0.0765001
$259$	8.24130	0.512089
$260$	−0.813457	−0.0504485
$261$	18.7490	1.16053
$262$	−9.42784	−0.582454
$263$	1.62691	0.100320	0.0501599	−	0.998741i	$-0.484027\pi$
$263$	1.62691	0.100320	0.0501599	+	0.998741i	$0.484027\pi$
$264$	0	0
$265$	−6.61439	−0.406319
$266$	−5.42784	−0.332802
$267$	0.482601	0.0295347
$268$	8.00000	0.488678
$269$	23.8768	1.45579	0.727897	−	0.685686i	$-0.240498\pi$
$269$	23.8768	1.45579	0.727897	+	0.685686i	$0.240498\pi$
$270$	−2.37309	−0.144421
$271$	−2.44037	−0.148242	−0.0741210	−	0.997249i	$-0.523615\pi$
$271$	−2.44037	−0.148242	−0.0741210	+	0.997249i	$0.523615\pi$
$272$	−3.83457	−0.232505
$273$	−0.330856	−0.0200243
$274$	13.6691	0.825783
$275$	0	0
$276$	2.20766	0.132885
$277$	−22.0000	−1.32185	−0.660926	−	0.750451i	$-0.729836\pi$
$277$	−22.0000	−1.32185	−0.660926	+	0.750451i	$0.729836\pi$
$278$	11.8682	0.711808
$279$	−17.0074	−1.01821
$280$	−1.00000	−0.0597614
$281$	20.8557	1.24415	0.622073	−	0.782959i	$-0.286291\pi$
$281$	20.8557	1.24415	0.622073	+	0.782959i	$0.286291\pi$
$282$	2.04223	0.121613
$283$	−0.330856	−0.0196673	−0.00983367	−	0.999952i	$-0.503130\pi$
$283$	−0.330856	−0.0196673	−0.00983367	+	0.999952i	$0.503130\pi$
$284$	14.8557	0.881523
$285$	−2.20766	−0.130770
$286$	0	0
$287$	5.59327	0.330160
$288$	−2.83457	−0.167029
$289$	−2.29606	−0.135062
$290$	6.61439	0.388410
$291$	1.39420	0.0817295
$292$	6.20766	0.363276
$293$	3.18654	0.186160	0.0930799	−	0.995659i	$-0.470329\pi$
$293$	3.18654	0.186160	0.0930799	+	0.995659i	$0.470329\pi$
$294$	−0.406728	−0.0237209
$295$	−10.6480	−0.619952
$296$	8.24130	0.479016
$297$	0	0
$298$	22.2835	1.29085
$299$	−4.41532	−0.255344
$300$	−0.406728	−0.0234825
$301$	3.02112	0.174134
$302$	3.05476	0.175782
$303$	−7.60186	−0.436715
$304$	−5.42784	−0.311308
$305$	0.978885	0.0560508
$306$	10.8694	0.621361
$307$	−20.4826	−1.16900	−0.584502	−	0.811392i	$-0.698710\pi$
$307$	−20.4826	−1.16900	−0.584502	+	0.811392i	$0.698710\pi$
$308$	0	0
$309$	−6.28863	−0.357747
$310$	−6.00000	−0.340777
$311$	3.62691	0.205663	0.102832	−	0.994699i	$-0.467210\pi$
$311$	3.62691	0.205663	0.102832	+	0.994699i	$0.467210\pi$
$312$	−0.330856	−0.0187310
$313$	20.7239	1.17138	0.585692	−	0.810534i	$-0.300823\pi$
$313$	20.7239	1.17138	0.585692	+	0.810534i	$0.300823\pi$
$314$	4.85569	0.274022
$315$	2.83457	0.159710
$316$	−17.0970	−0.961781
$317$	−1.80093	−0.101150	−0.0505751	−	0.998720i	$-0.516105\pi$
$317$	−1.80093	−0.101150	−0.0505751	+	0.998720i	$0.516105\pi$
$318$	−2.69026	−0.150862
$319$	0	0
$320$	−1.00000	−0.0559017
$321$	−4.48260	−0.250194
$322$	−5.42784	−0.302482
$323$	20.8135	1.15809
$324$	7.53851	0.418806
$325$	0.813457	0.0451225
$326$	−8.00000	−0.443079
$327$	6.60580	0.365301
$328$	5.59327	0.308837
$329$	−5.02112	−0.276823
$330$	0	0
$331$	−3.02112	−0.166056	−0.0830278	−	0.996547i	$-0.526459\pi$
$331$	−3.02112	−0.166056	−0.0830278	+	0.996547i	$0.526459\pi$
$332$	8.81346	0.483701
$333$	−23.3606	−1.28015
$334$	−8.00000	−0.437741
$335$	−8.00000	−0.437087
$336$	−0.406728	−0.0221889
$337$	9.66914	0.526712	0.263356	−	0.964699i	$-0.415171\pi$
$337$	9.66914	0.526712	0.263356	+	0.964699i	$0.415171\pi$
$338$	−12.3383	−0.671114
$339$	5.69420	0.309266
$340$	3.83457	0.207959
$341$	0	0
$342$	15.3856	0.831959
$343$	1.00000	0.0539949
$344$	3.02112	0.162888
$345$	−2.20766	−0.118856
$346$	19.0211	1.02258
$347$	−9.39420	−0.504307	−0.252154	−	0.967687i	$-0.581139\pi$
$347$	−9.39420	−0.504307	−0.252154	+	0.967687i	$0.581139\pi$
$348$	2.69026	0.144213
$349$	18.2077	0.974634	0.487317	−	0.873225i	$-0.337976\pi$
$349$	18.2077	0.974634	0.487317	+	0.873225i	$0.337976\pi$
$350$	1.00000	0.0534522
$351$	1.93040	0.103037
$352$	0	0
$353$	12.7239	0.677225	0.338612	−	0.940926i	$-0.390042\pi$
$353$	12.7239	0.677225	0.338612	+	0.940926i	$0.390042\pi$
$354$	−4.33086	−0.230182
$355$	−14.8557	−0.788458
$356$	−1.18654	−0.0628867
$357$	1.55963	0.0825443
$358$	4.64803	0.245656
$359$	−29.8432	−1.57506	−0.787531	−	0.616275i	$-0.788641\pi$
$359$	−29.8432	−1.57506	−0.787531	+	0.616275i	$0.788641\pi$
$360$	2.83457	0.149395
$361$	10.4615	0.550605
$362$	−25.3383	−1.33175
$363$	0	0
$364$	0.813457	0.0426367
$365$	−6.20766	−0.324924
$366$	0.398140	0.0208111
$367$	15.4615	0.807083	0.403541	−	0.914961i	$-0.367779\pi$
$367$	15.4615	0.807083	0.403541	+	0.914961i	$0.367779\pi$
$368$	−5.42784	−0.282946
$369$	−15.8545	−0.825354
$370$	−8.24130	−0.428445
$371$	6.61439	0.343402
$372$	−2.44037	−0.126527
$373$	8.10951	0.419895	0.209947	−	0.977713i	$-0.432671\pi$
$373$	8.10951	0.419895	0.209947	+	0.977713i	$0.432671\pi$
$374$	0	0
$375$	0.406728	0.0210034
$376$	−5.02112	−0.258944
$377$	−5.38052	−0.277111
$378$	2.37309	0.122058
$379$	22.0422	1.13223	0.566117	−	0.824325i	$-0.308445\pi$
$379$	22.0422	1.13223	0.566117	+	0.824325i	$0.308445\pi$
$380$	5.42784	0.278442
$381$	7.03480	0.360404
$382$	15.6691	0.801703
$383$	38.2499	1.95448	0.977239	−	0.212141i	$-0.0680437\pi$
$383$	38.2499	1.95448	0.977239	+	0.212141i	$0.0680437\pi$
$384$	−0.406728	−0.0207558
$385$	0	0
$386$	2.16543	0.110217
$387$	−8.56357	−0.435311
$388$	−3.42784	−0.174022
$389$	16.8557	0.854617	0.427309	−	0.904106i	$-0.359462\pi$
$389$	16.8557	0.854617	0.427309	+	0.904106i	$0.359462\pi$
$390$	0.330856	0.0167535
$391$	20.8135	1.05258
$392$	1.00000	0.0505076
$393$	3.83457	0.193429
$394$	−2.81346	−0.141740
$395$	17.0970	0.860243
$396$	0	0
$397$	−4.44037	−0.222856	−0.111428	−	0.993773i	$-0.535542\pi$
$397$	−4.44037	−0.222856	−0.111428	+	0.993773i	$0.535542\pi$
$398$	−13.0211	−0.652690
$399$	2.20766	0.110521
$400$	1.00000	0.0500000
$401$	−3.46149	−0.172858	−0.0864292	−	0.996258i	$-0.527546\pi$
$401$	−3.46149	−0.172858	−0.0864292	+	0.996258i	$0.527546\pi$
$402$	−3.25383	−0.162286
$403$	4.88074	0.243127
$404$	18.6903	0.929875
$405$	−7.53851	−0.374592
$406$	−6.61439	−0.328267
$407$	0	0
$408$	1.55963	0.0772132
$409$	17.2624	0.853572	0.426786	−	0.904353i	$-0.359646\pi$
$409$	17.2624	0.853572	0.426786	+	0.904353i	$0.359646\pi$
$410$	−5.59327	−0.276232
$411$	−5.55963	−0.274236
$412$	15.4615	0.761733
$413$	10.6480	0.523955
$414$	15.3856	0.756162
$415$	−8.81346	−0.432636
$416$	0.813457	0.0398830
$417$	−4.82714	−0.236386
$418$	0	0
$419$	9.02112	0.440710	0.220355	−	0.975420i	$-0.429278\pi$
$419$	9.02112	0.440710	0.220355	+	0.975420i	$0.429278\pi$
$420$	0.406728	0.0198463
$421$	31.7114	1.54552	0.772759	−	0.634700i	$-0.218876\pi$
$421$	31.7114	1.54552	0.772759	+	0.634700i	$0.218876\pi$
$422$	−19.6691	−0.957479
$423$	14.2327	0.692018
$424$	6.61439	0.321223
$425$	−3.83457	−0.186004
$426$	−6.04223	−0.292747
$427$	−0.978885	−0.0473716
$428$	11.0211	0.532726
$429$	0	0
$430$	−3.02112	−0.145691
$431$	3.05476	0.147142	0.0735712	−	0.997290i	$-0.476560\pi$
$431$	3.05476	0.147142	0.0735712	+	0.997290i	$0.476560\pi$
$432$	2.37309	0.114175
$433$	27.9104	1.34129	0.670645	−	0.741778i	$-0.266017\pi$
$433$	27.9104	1.34129	0.670645	+	0.741778i	$0.266017\pi$
$434$	6.00000	0.288009
$435$	−2.69026	−0.128988
$436$	−16.2413	−0.777817
$437$	29.4615	1.40933
$438$	−2.52483	−0.120641
$439$	14.8557	0.709023	0.354512	−	0.935052i	$-0.384647\pi$
$439$	14.8557	0.709023	0.354512	+	0.935052i	$0.384647\pi$
$440$	0	0
$441$	−2.83457	−0.134980
$442$	−3.11926	−0.148368
$443$	0.746173	0.0354517	0.0177259	−	0.999843i	$-0.494357\pi$
$443$	0.746173	0.0354517	0.0177259	+	0.999843i	$0.494357\pi$
$444$	−3.35197	−0.159078
$445$	1.18654	0.0562475
$446$	−3.79234	−0.179573
$447$	−9.06335	−0.428682
$448$	1.00000	0.0472456
$449$	9.83457	0.464122	0.232061	−	0.972701i	$-0.425453\pi$
$449$	9.83457	0.464122	0.232061	+	0.972701i	$0.425453\pi$
$450$	−2.83457	−0.133623
$451$	0	0
$452$	−14.0000	−0.658505
$453$	−1.24246	−0.0583757
$454$	14.0422	0.659035
$455$	−0.813457	−0.0381354
$456$	2.20766	0.103383
$457$	−11.2961	−0.528407	−0.264204	−	0.964467i	$-0.585109\pi$
$457$	−11.2961	−0.528407	−0.264204	+	0.964467i	$0.585109\pi$
$458$	1.83457	0.0857239
$459$	−9.09977	−0.424741
$460$	5.42784	0.253075
$461$	7.41926	0.345549	0.172775	−	0.984961i	$-0.444727\pi$
$461$	7.41926	0.345549	0.172775	+	0.984961i	$0.444727\pi$
$462$	0	0
$463$	−10.1740	−0.472827	−0.236413	−	0.971653i	$-0.575972\pi$
$463$	−10.1740	−0.472827	−0.236413	+	0.971653i	$0.575972\pi$
$464$	−6.61439	−0.307065
$465$	2.44037	0.113169
$466$	8.04223	0.372549
$467$	−32.4912	−1.50351	−0.751756	−	0.659441i	$-0.770793\pi$
$467$	−32.4912	−1.50351	−0.751756	+	0.659441i	$0.770793\pi$
$468$	−2.30580	−0.106586
$469$	8.00000	0.369406
$470$	5.02112	0.231607
$471$	−1.97495	−0.0910007
$472$	10.6480	0.490115
$473$	0	0
$474$	6.95383	0.319400
$475$	−5.42784	−0.249047
$476$	−3.83457	−0.175757
$477$	−18.7490	−0.858456
$478$	15.4701	0.707585
$479$	11.6691	0.533177	0.266588	−	0.963810i	$-0.414104\pi$
$479$	11.6691	0.533177	0.266588	+	0.963810i	$0.414104\pi$
$480$	0.406728	0.0185645
$481$	6.70394	0.305673
$482$	−11.6355	−0.529983
$483$	2.20766	0.100452
$484$	0	0
$485$	3.42784	0.155650
$486$	−10.1854	−0.462019
$487$	−5.49513	−0.249008	−0.124504	−	0.992219i	$-0.539734\pi$
$487$	−5.49513	−0.249008	−0.124504	+	0.992219i	$0.539734\pi$
$488$	−0.978885	−0.0443120
$489$	3.25383	0.147143
$490$	−1.00000	−0.0451754
$491$	13.2961	0.600043	0.300021	−	0.953932i	$-0.403006\pi$
$491$	13.2961	0.600043	0.300021	+	0.953932i	$0.403006\pi$
$492$	−2.27494	−0.102562
$493$	25.3633	1.14231
$494$	−4.41532	−0.198654
$495$	0	0
$496$	6.00000	0.269408
$497$	14.8557	0.666369
$498$	−3.58468	−0.160634
$499$	−24.6480	−1.10340	−0.551699	−	0.834044i	$-0.686020\pi$
$499$	−24.6480	−1.10340	−0.551699	+	0.834044i	$0.686020\pi$
$500$	−1.00000	−0.0447214
$501$	3.25383	0.145370
$502$	5.35197	0.238870
$503$	−38.9230	−1.73549	−0.867745	−	0.497010i	$-0.834431\pi$
$503$	−38.9230	−1.73549	−0.867745	+	0.497010i	$0.834431\pi$
$504$	−2.83457	−0.126262
$505$	−18.6903	−0.831706
$506$	0	0
$507$	5.01833	0.222872
$508$	−17.2961	−0.767388
$509$	−39.0497	−1.73085	−0.865423	−	0.501042i	$-0.832950\pi$
$509$	−39.0497	−1.73085	−0.865423	+	0.501042i	$0.832950\pi$
$510$	−1.55963	−0.0690616
$511$	6.20766	0.274611
$512$	1.00000	0.0441942
$513$	−12.8807	−0.568699
$514$	12.7239	0.561227
$515$	−15.4615	−0.681314
$516$	−1.22877	−0.0540937
$517$	0	0
$518$	8.24130	0.362102
$519$	−7.73643	−0.339592
$520$	−0.813457	−0.0356724
$521$	−33.2710	−1.45763	−0.728815	−	0.684711i	$-0.759928\pi$
$521$	−33.2710	−1.45763	−0.728815	+	0.684711i	$0.759928\pi$
$522$	18.7490	0.820619
$523$	40.2362	1.75941	0.879703	−	0.475523i	$-0.157741\pi$
$523$	40.2362	1.75941	0.879703	+	0.475523i	$0.157741\pi$
$524$	−9.42784	−0.411857
$525$	−0.406728	−0.0177511
$526$	1.62691	0.0709368
$527$	−23.0074	−1.00222
$528$	0	0
$529$	6.46149	0.280934
$530$	−6.61439	−0.287311
$531$	−30.1826	−1.30981
$532$	−5.42784	−0.235327
$533$	4.54989	0.197077
$534$	0.482601	0.0208842
$535$	−11.0211	−0.476484
$536$	8.00000	0.345547
$537$	−1.89049	−0.0815805
$538$	23.8768	1.02940
$539$	0	0
$540$	−2.37309	−0.102121
$541$	−26.2835	−1.13002	−0.565009	−	0.825085i	$-0.691127\pi$
$541$	−26.2835	−1.13002	−0.565009	+	0.825085i	$0.691127\pi$
$542$	−2.44037	−0.104823
$543$	10.3058	0.442264
$544$	−3.83457	−0.164406
$545$	16.2413	0.695701
$546$	−0.330856	−0.0141593
$547$	−13.6269	−0.582645	−0.291322	−	0.956625i	$-0.594095\pi$
$547$	−13.6269	−0.582645	−0.291322	+	0.956625i	$0.594095\pi$
$548$	13.6691	0.583917
$549$	2.77472	0.118422
$550$	0	0
$551$	35.9019	1.52947
$552$	2.20766	0.0939642
$553$	−17.0970	−0.727038
$554$	−22.0000	−0.934690
$555$	3.35197	0.142283
$556$	11.8682	0.503324
$557$	−14.8979	−0.631245	−0.315623	−	0.948885i	$-0.602213\pi$
$557$	−14.8979	−0.631245	−0.315623	+	0.948885i	$0.602213\pi$
$558$	−17.0074	−0.719982
$559$	2.45755	0.103943
$560$	−1.00000	−0.0422577
$561$	0	0
$562$	20.8557	0.879744
$563$	−39.7536	−1.67541	−0.837707	−	0.546119i	$-0.816104\pi$
$563$	−39.7536	−1.67541	−0.837707	+	0.546119i	$0.816104\pi$
$564$	2.04223	0.0859934
$565$	14.0000	0.588984
$566$	−0.330856	−0.0139069
$567$	7.53851	0.316588
$568$	14.8557	0.623331
$569$	−8.78840	−0.368429	−0.184215	−	0.982886i	$-0.558974\pi$
$569$	−8.78840	−0.368429	−0.184215	+	0.982886i	$0.558974\pi$
$570$	−2.20766	−0.0924686
$571$	5.22877	0.218817	0.109409	−	0.993997i	$-0.465104\pi$
$571$	5.22877	0.218817	0.109409	+	0.993997i	$0.465104\pi$
$572$	0	0
$573$	−6.37309	−0.266239
$574$	5.59327	0.233459
$575$	−5.42784	−0.226357
$576$	−2.83457	−0.118107
$577$	5.80093	0.241496	0.120748	−	0.992683i	$-0.461471\pi$
$577$	5.80093	0.241496	0.120748	+	0.992683i	$0.461471\pi$
$578$	−2.29606	−0.0955034
$579$	−0.880741	−0.0366024
$580$	6.61439	0.274647
$581$	8.81346	0.365644
$582$	1.39420	0.0577915
$583$	0	0
$584$	6.20766	0.256875
$585$	2.30580	0.0953332
$586$	3.18654	0.131635
$587$	25.3046	1.04443	0.522217	−	0.852812i	$-0.325105\pi$
$587$	25.3046	1.04443	0.522217	+	0.852812i	$0.325105\pi$
$588$	−0.406728	−0.0167732
$589$	−32.5671	−1.34190
$590$	−10.6480	−0.438372
$591$	1.14431	0.0470707
$592$	8.24130	0.338715
$593$	23.1729	0.951595	0.475798	−	0.879555i	$-0.342159\pi$
$593$	23.1729	0.951595	0.475798	+	0.879555i	$0.342159\pi$
$594$	0	0
$595$	3.83457	0.157202
$596$	22.2835	0.912769
$597$	5.29606	0.216753
$598$	−4.41532	−0.180556
$599$	−8.48260	−0.346590	−0.173295	−	0.984870i	$-0.555441\pi$
$599$	−8.48260	−0.346590	−0.173295	+	0.984870i	$0.555441\pi$
$600$	−0.406728	−0.0166046
$601$	32.4490	1.32362	0.661810	−	0.749671i	$-0.269788\pi$
$601$	32.4490	1.32362	0.661810	+	0.749671i	$0.269788\pi$
$602$	3.02112	0.123131
$603$	−22.6766	−0.923462
$604$	3.05476	0.124296
$605$	0	0
$606$	−7.60186	−0.308804
$607$	33.9441	1.37775	0.688874	−	0.724881i	$-0.258105\pi$
$607$	33.9441	1.37775	0.688874	+	0.724881i	$0.258105\pi$
$608$	−5.42784	−0.220128
$609$	2.69026	0.109015
$610$	0.978885	0.0396339
$611$	−4.08446	−0.165240
$612$	10.8694	0.439368
$613$	−8.77123	−0.354267	−0.177133	−	0.984187i	$-0.556682\pi$
$613$	−8.77123	−0.354267	−0.177133	+	0.984187i	$0.556682\pi$
$614$	−20.4826	−0.826610
$615$	2.27494	0.0917345
$616$	0	0
$617$	−32.1095	−1.29268	−0.646340	−	0.763049i	$-0.723701\pi$
$617$	−32.1095	−1.29268	−0.646340	+	0.763049i	$0.723701\pi$
$618$	−6.28863	−0.252966
$619$	−28.2749	−1.13647	−0.568233	−	0.822868i	$-0.692373\pi$
$619$	−28.2749	−1.13647	−0.568233	+	0.822868i	$0.692373\pi$
$620$	−6.00000	−0.240966
$621$	−12.8807	−0.516886
$622$	3.62691	0.145426
$623$	−1.18654	−0.0475378
$624$	−0.330856	−0.0132448
$625$	1.00000	0.0400000
$626$	20.7239	0.828294
$627$	0	0
$628$	4.85569	0.193763
$629$	−31.6019	−1.26005
$630$	2.83457	0.112932
$631$	34.9230	1.39026	0.695131	−	0.718883i	$-0.255346\pi$
$631$	34.9230	1.39026	0.695131	+	0.718883i	$0.255346\pi$
$632$	−17.0970	−0.680082
$633$	8.00000	0.317971
$634$	−1.80093	−0.0715241
$635$	17.2961	0.686373
$636$	−2.69026	−0.106676
$637$	0.813457	0.0322303
$638$	0	0
$639$	−42.1095	−1.66583
$640$	−1.00000	−0.0395285
$641$	−5.25383	−0.207514	−0.103757	−	0.994603i	$-0.533086\pi$
$641$	−5.25383	−0.207514	−0.103757	+	0.994603i	$0.533086\pi$
$642$	−4.48260	−0.176914
$643$	−3.17796	−0.125326	−0.0626632	−	0.998035i	$-0.519959\pi$
$643$	−3.17796	−0.125326	−0.0626632	+	0.998035i	$0.519959\pi$
$644$	−5.42784	−0.213887
$645$	1.22877	0.0483829
$646$	20.8135	0.818895
$647$	37.9190	1.49075	0.745375	−	0.666645i	$-0.232270\pi$
$647$	37.9190	1.49075	0.745375	+	0.666645i	$0.232270\pi$
$648$	7.53851	0.296141
$649$	0	0
$650$	0.813457	0.0319064
$651$	−2.44037	−0.0956457
$652$	−8.00000	−0.313304
$653$	29.5374	1.15589	0.577943	−	0.816077i	$-0.303856\pi$
$653$	29.5374	1.15589	0.577943	+	0.816077i	$0.303856\pi$
$654$	6.60580	0.258307
$655$	9.42784	0.368376
$656$	5.59327	0.218381
$657$	−17.5961	−0.686487
$658$	−5.02112	−0.195743
$659$	−15.1865	−0.591584	−0.295792	−	0.955252i	$-0.595583\pi$
$659$	−15.1865	−0.591584	−0.295792	+	0.955252i	$0.595583\pi$
$660$	0	0
$661$	−44.6766	−1.73772	−0.868859	−	0.495060i	$-0.835146\pi$
$661$	−44.6766	−1.73772	−0.868859	+	0.495060i	$0.835146\pi$
$662$	−3.02112	−0.117419
$663$	1.26869	0.0492719
$664$	8.81346	0.342028
$665$	5.42784	0.210483
$666$	−23.3606	−0.905203
$667$	35.9019	1.39013
$668$	−8.00000	−0.309529
$669$	1.54245	0.0596347
$670$	−8.00000	−0.309067
$671$	0	0
$672$	−0.406728	−0.0156899
$673$	−38.0000	−1.46479	−0.732396	−	0.680879i	$-0.761598\pi$
$673$	−38.0000	−1.46479	−0.732396	+	0.680879i	$0.761598\pi$
$674$	9.66914	0.372442
$675$	2.37309	0.0913401
$676$	−12.3383	−0.474550
$677$	48.7325	1.87294	0.936471	−	0.350745i	$-0.114072\pi$
$677$	48.7325	1.87294	0.936471	+	0.350745i	$0.114072\pi$
$678$	5.69420	0.218684
$679$	−3.42784	−0.131549
$680$	3.83457	0.147049
$681$	−5.71137	−0.218860
$682$	0	0
$683$	−0.482601	−0.0184662	−0.00923310	−	0.999957i	$-0.502939\pi$
$683$	−0.482601	−0.0184662	−0.00923310	+	0.999957i	$0.502939\pi$
$684$	15.3856	0.588284
$685$	−13.6691	−0.522271
$686$	1.00000	0.0381802
$687$	−0.746173	−0.0284683
$688$	3.02112	0.115179
$689$	5.38052	0.204981
$690$	−2.20766	−0.0840441
$691$	−25.5037	−0.970207	−0.485104	−	0.874457i	$-0.661218\pi$
$691$	−25.5037	−0.970207	−0.485104	+	0.874457i	$0.661218\pi$
$692$	19.0211	0.723074
$693$	0	0
$694$	−9.39420	−0.356599
$695$	−11.8682	−0.450187
$696$	2.69026	0.101974
$697$	−21.4478	−0.812393
$698$	18.2077	0.689170
$699$	−3.27100	−0.123721
$700$	1.00000	0.0377964
$701$	−33.8682	−1.27918	−0.639592	−	0.768714i	$-0.720897\pi$
$701$	−33.8682	−1.27918	−0.639592	+	0.768714i	$0.720897\pi$
$702$	1.93040	0.0728584
$703$	−44.7325	−1.68712
$704$	0	0
$705$	−2.04223	−0.0769148
$706$	12.7239	0.478870
$707$	18.6903	0.702920
$708$	−4.33086	−0.162764
$709$	−15.9749	−0.599952	−0.299976	−	0.953947i	$-0.596979\pi$
$709$	−15.9749	−0.599952	−0.299976	+	0.953947i	$0.596979\pi$
$710$	−14.8557	−0.557524
$711$	48.4626	1.81749
$712$	−1.18654	−0.0444676
$713$	−32.5671	−1.21965
$714$	1.55963	0.0583677
$715$	0	0
$716$	4.64803	0.173705
$717$	−6.29212	−0.234983
$718$	−29.8432	−1.11374
$719$	−13.4364	−0.501094	−0.250547	−	0.968104i	$-0.580611\pi$
$719$	−13.4364	−0.501094	−0.250547	+	0.968104i	$0.580611\pi$
$720$	2.83457	0.105638
$721$	15.4615	0.575816
$722$	10.4615	0.389336
$723$	4.73249	0.176003
$724$	−25.3383	−0.941690
$725$	−6.61439	−0.245652
$726$	0	0
$727$	6.64803	0.246562	0.123281	−	0.992372i	$-0.460658\pi$
$727$	6.64803	0.246562	0.123281	+	0.992372i	$0.460658\pi$
$728$	0.813457	0.0301487
$729$	−18.4729	−0.684180
$730$	−6.20766	−0.229756
$731$	−11.5847	−0.428475
$732$	0.398140	0.0147157
$733$	−38.0285	−1.40462	−0.702308	−	0.711873i	$-0.747847\pi$
$733$	−38.0285	−1.40462	−0.702308	+	0.711873i	$0.747847\pi$
$734$	15.4615	0.570694
$735$	0.406728	0.0150024
$736$	−5.42784	−0.200073
$737$	0	0
$738$	−15.8545	−0.583613
$739$	52.6343	1.93619	0.968093	−	0.250592i	$-0.0806252\pi$
$739$	52.6343	1.93619	0.968093	+	0.250592i	$0.0806252\pi$
$740$	−8.24130	−0.302956
$741$	1.79583	0.0659716
$742$	6.61439	0.242822
$743$	−28.0845	−1.03032	−0.515159	−	0.857094i	$-0.672267\pi$
$743$	−28.0845	−1.03032	−0.515159	+	0.857094i	$0.672267\pi$
$744$	−2.44037	−0.0894683
$745$	−22.2835	−0.816405
$746$	8.10951	0.296910
$747$	−24.9824	−0.914057
$748$	0	0
$749$	11.0211	0.402703
$750$	0.406728	0.0148516
$751$	48.4826	1.76916	0.884578	−	0.466393i	$-0.154447\pi$
$751$	48.4826	1.76916	0.884578	+	0.466393i	$0.154447\pi$
$752$	−5.02112	−0.183101
$753$	−2.17680	−0.0793270
$754$	−5.38052	−0.195947
$755$	−3.05476	−0.111174
$756$	2.37309	0.0863083
$757$	−11.8260	−0.429823	−0.214911	−	0.976634i	$-0.568946\pi$
$757$	−11.8260	−0.429823	−0.214911	+	0.976634i	$0.568946\pi$
$758$	22.0422	0.800610
$759$	0	0
$760$	5.42784	0.196889
$761$	19.5510	0.708725	0.354362	−	0.935108i	$-0.384698\pi$
$761$	19.5510	0.708725	0.354362	+	0.935108i	$0.384698\pi$
$762$	7.03480	0.254844
$763$	−16.2413	−0.587975
$764$	15.6691	0.566890
$765$	−10.8694	−0.392983
$766$	38.2499	1.38202
$767$	8.66171	0.312756
$768$	−0.406728	−0.0146765
$769$	−6.07587	−0.219102	−0.109551	−	0.993981i	$-0.534941\pi$
$769$	−6.07587	−0.219102	−0.109551	+	0.993981i	$0.534941\pi$
$770$	0	0
$771$	−5.17517	−0.186379
$772$	2.16543	0.0779355
$773$	−2.33086	−0.0838351	−0.0419175	−	0.999121i	$-0.513347\pi$
$773$	−2.33086	−0.0838351	−0.0419175	+	0.999121i	$0.513347\pi$
$774$	−8.56357	−0.307811
$775$	6.00000	0.215526
$776$	−3.42784	−0.123052
$777$	−3.35197	−0.120251
$778$	16.8557	0.604306
$779$	−30.3594	−1.08774
$780$	0.330856	0.0118465
$781$	0	0
$782$	20.8135	0.744288
$783$	−15.6965	−0.560948
$784$	1.00000	0.0357143
$785$	−4.85569	−0.173307
$786$	3.83457	0.136775
$787$	17.3805	0.619549	0.309774	−	0.950810i	$-0.399747\pi$
$787$	17.3805	0.619549	0.309774	+	0.950810i	$0.399747\pi$
$788$	−2.81346	−0.100225
$789$	−0.661712	−0.0235576
$790$	17.0970	0.608284
$791$	−14.0000	−0.497783
$792$	0	0
$793$	−0.796281	−0.0282768
$794$	−4.44037	−0.157583
$795$	2.69026	0.0954137
$796$	−13.0211	−0.461521
$797$	−15.6942	−0.555917	−0.277959	−	0.960593i	$-0.589658\pi$
$797$	−15.6942	−0.555917	−0.277959	+	0.960593i	$0.589658\pi$
$798$	2.20766	0.0781503
$799$	19.2538	0.681151
$800$	1.00000	0.0353553
$801$	3.36334	0.118838
$802$	−3.46149	−0.122229
$803$	0	0
$804$	−3.25383	−0.114754
$805$	5.42784	0.191306
$806$	4.88074	0.171917
$807$	−9.71137	−0.341857
$808$	18.6903	0.657521
$809$	−23.1443	−0.813711	−0.406855	−	0.913493i	$-0.633375\pi$
$809$	−23.1443	−0.813711	−0.406855	+	0.913493i	$0.633375\pi$
$810$	−7.53851	−0.264876
$811$	27.6218	0.969933	0.484967	−	0.874533i	$-0.338832\pi$
$811$	27.6218	0.969933	0.484967	+	0.874533i	$0.338832\pi$
$812$	−6.61439	−0.232119
$813$	0.992568	0.0348109
$814$	0	0
$815$	8.00000	0.280228
$816$	1.55963	0.0545980
$817$	−16.3981	−0.573698
$818$	17.2624	0.603566
$819$	−2.30580	−0.0805712
$820$	−5.59327	−0.195326
$821$	39.5123	1.37899	0.689494	−	0.724291i	$-0.257833\pi$
$821$	39.5123	1.37899	0.689494	+	0.724291i	$0.257833\pi$
$822$	−5.55963	−0.193914
$823$	13.5123	0.471009	0.235505	−	0.971873i	$-0.424326\pi$
$823$	13.5123	0.471009	0.235505	+	0.971873i	$0.424326\pi$
$824$	15.4615	0.538626
$825$	0	0
$826$	10.6480	0.370492
$827$	−12.0000	−0.417281	−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000	−0.417281	−0.208640	+	0.977992i	$0.566904\pi$
$828$	15.3856	0.534687
$829$	13.8346	0.480495	0.240247	−	0.970712i	$-0.422771\pi$
$829$	13.8346	0.480495	0.240247	+	0.970712i	$0.422771\pi$
$830$	−8.81346	−0.305920
$831$	8.94803	0.310404
$832$	0.813457	0.0282015
$833$	−3.83457	−0.132860
$834$	−4.82714	−0.167150
$835$	8.00000	0.276851
$836$	0	0
$837$	14.2385	0.492155
$838$	9.02112	0.311629
$839$	44.0422	1.52051	0.760253	−	0.649627i	$-0.225075\pi$
$839$	44.0422	1.52051	0.760253	+	0.649627i	$0.225075\pi$
$840$	0.406728	0.0140335
$841$	14.7501	0.508625
$842$	31.7114	1.09285
$843$	−8.48260	−0.292156
$844$	−19.6691	−0.677040
$845$	12.3383	0.424450
$846$	14.2327	0.489331
$847$	0	0
$848$	6.61439	0.227139
$849$	0.134569	0.00461838
$850$	−3.83457	−0.131525
$851$	−44.7325	−1.53341
$852$	−6.04223	−0.207003
$853$	29.8095	1.02066	0.510329	−	0.859979i	$-0.329524\pi$
$853$	29.8095	1.02066	0.510329	+	0.859979i	$0.329524\pi$
$854$	−0.978885	−0.0334968
$855$	−15.3856	−0.526177
$856$	11.0211	0.376694
$857$	−42.7575	−1.46057	−0.730285	−	0.683143i	$-0.760613\pi$
$857$	−42.7575	−1.46057	−0.730285	+	0.683143i	$0.760613\pi$
$858$	0	0
$859$	6.31717	0.215539	0.107770	−	0.994176i	$-0.465629\pi$
$859$	6.31717	0.215539	0.107770	+	0.994176i	$0.465629\pi$
$860$	−3.02112	−0.103019
$861$	−2.27494	−0.0775298
$862$	3.05476	0.104045
$863$	−48.3680	−1.64647	−0.823233	−	0.567704i	$-0.807832\pi$
$863$	−48.3680	−1.64647	−0.823233	+	0.567704i	$0.807832\pi$
$864$	2.37309	0.0807340
$865$	−19.0211	−0.646737
$866$	27.9104	0.948436
$867$	0.933872	0.0317160
$868$	6.00000	0.203653
$869$	0	0
$870$	−2.69026	−0.0912083
$871$	6.50765	0.220503
$872$	−16.2413	−0.550000
$873$	9.71647	0.328853
$874$	29.4615	0.996550
$875$	−1.00000	−0.0338062
$876$	−2.52483	−0.0853061
$877$	24.1940	0.816972	0.408486	−	0.912764i	$-0.366057\pi$
$877$	24.1940	0.816972	0.408486	+	0.912764i	$0.366057\pi$
$878$	14.8557	0.501355
$879$	−1.29606	−0.0437149
$880$	0	0
$881$	12.3731	0.416860	0.208430	−	0.978037i	$-0.433165\pi$
$881$	12.3731	0.416860	0.208430	+	0.978037i	$0.433165\pi$
$882$	−2.83457	−0.0954450
$883$	−14.5248	−0.488799	−0.244400	−	0.969675i	$-0.578591\pi$
$883$	−14.5248	−0.488799	−0.244400	+	0.969675i	$0.578591\pi$
$884$	−3.11926	−0.104912
$885$	4.33086	0.145580
$886$	0.746173	0.0250682
$887$	25.3805	0.852194	0.426097	−	0.904677i	$-0.359888\pi$
$887$	25.3805	0.852194	0.426097	+	0.904677i	$0.359888\pi$
$888$	−3.35197	−0.112485
$889$	−17.2961	−0.580091
$890$	1.18654	0.0397730
$891$	0	0
$892$	−3.79234	−0.126977
$893$	27.2538	0.912015
$894$	−9.06335	−0.303124
$895$	−4.64803	−0.155366
$896$	1.00000	0.0334077
$897$	1.79583	0.0599612
$898$	9.83457	0.328184
$899$	−39.6863	−1.32361
$900$	−2.83457	−0.0944857
$901$	−25.3633	−0.844975
$902$	0	0
$903$	−1.22877	−0.0408910
$904$	−14.0000	−0.465633
$905$	25.3383	0.842273
$906$	−1.24246	−0.0412779
$907$	−7.93272	−0.263402	−0.131701	−	0.991290i	$-0.542044\pi$
$907$	−7.93272	−0.263402	−0.131701	+	0.991290i	$0.542044\pi$
$908$	14.0422	0.466008
$909$	−52.9789	−1.75720
$910$	−0.813457	−0.0269658
$911$	43.7364	1.44905	0.724526	−	0.689247i	$-0.242059\pi$
$911$	43.7364	1.44905	0.724526	+	0.689247i	$0.242059\pi$
$912$	2.20766	0.0731029
$913$	0	0
$914$	−11.2961	−0.373640
$915$	−0.398140	−0.0131621
$916$	1.83457	0.0606160
$917$	−9.42784	−0.311335
$918$	−9.09977	−0.300337
$919$	32.7661	1.08085	0.540427	−	0.841391i	$-0.318263\pi$
$919$	32.7661	1.08085	0.540427	+	0.841391i	$0.318263\pi$
$920$	5.42784	0.178951
$921$	8.33086	0.274511
$922$	7.41926	0.244340
$923$	12.0845	0.397765
$924$	0	0
$925$	8.24130	0.270972
$926$	−10.1740	−0.334339
$927$	−43.8267	−1.43946
$928$	−6.61439	−0.217128
$929$	59.4478	1.95042	0.975210	−	0.221283i	$-0.0710246\pi$
$929$	59.4478	1.95042	0.975210	+	0.221283i	$0.0710246\pi$
$930$	2.44037	0.0800229
$931$	−5.42784	−0.177890
$932$	8.04223	0.263432
$933$	−1.47517	−0.0482949
$934$	−32.4912	−1.06314
$935$	0	0
$936$	−2.30580	−0.0753675
$937$	−53.2824	−1.74066	−0.870330	−	0.492470i	$-0.836094\pi$
$937$	−53.2824	−1.74066	−0.870330	+	0.492470i	$0.836094\pi$
$938$	8.00000	0.261209
$939$	−8.42900	−0.275070
$940$	5.02112	0.163771
$941$	5.72506	0.186632	0.0933158	−	0.995637i	$-0.470253\pi$
$941$	5.72506	0.186632	0.0933158	+	0.995637i	$0.470253\pi$
$942$	−1.97495	−0.0643472
$943$	−30.3594	−0.988638
$944$	10.6480	0.346564
$945$	−2.37309	−0.0771965
$946$	0	0
$947$	−27.4056	−0.890561	−0.445281	−	0.895391i	$-0.646896\pi$
$947$	−27.4056	−0.890561	−0.445281	+	0.895391i	$0.646896\pi$
$948$	6.95383	0.225850
$949$	5.04966	0.163919
$950$	−5.42784	−0.176102
$951$	0.732489	0.0237526
$952$	−3.83457	−0.124279
$953$	10.7998	0.349839	0.174919	−	0.984583i	$-0.444033\pi$
$953$	10.7998	0.349839	0.174919	+	0.984583i	$0.444033\pi$
$954$	−18.7490	−0.607020
$955$	−15.6691	−0.507042
$956$	15.4701	0.500338
$957$	0	0
$958$	11.6691	0.377013
$959$	13.6691	0.441400
$960$	0.406728	0.0131271
$961$	5.00000	0.161290
$962$	6.70394	0.216144
$963$	−31.2401	−1.00670
$964$	−11.6355	−0.374754
$965$	−2.16543	−0.0697076
$966$	2.20766	0.0710302
$967$	−11.2538	−0.361899	−0.180949	−	0.983492i	$-0.557917\pi$
$967$	−11.2538	−0.361899	−0.180949	+	0.983492i	$0.557917\pi$
$968$	0	0
$969$	−8.46542	−0.271949
$970$	3.42784	0.110061
$971$	33.2401	1.06673	0.533363	−	0.845886i	$-0.320928\pi$
$971$	33.2401	1.06673	0.533363	+	0.845886i	$0.320928\pi$
$972$	−10.1854	−0.326696
$973$	11.8682	0.380477
$974$	−5.49513	−0.176075
$975$	−0.330856	−0.0105959
$976$	−0.978885	−0.0313333
$977$	−2.74617	−0.0878578	−0.0439289	−	0.999035i	$-0.513988\pi$
$977$	−2.74617	−0.0878578	−0.0439289	+	0.999035i	$0.513988\pi$
$978$	3.25383	0.104046
$979$	0	0
$980$	−1.00000	−0.0319438
$981$	46.0371	1.46985
$982$	13.2961	0.424294
$983$	39.4615	1.25863	0.629313	−	0.777152i	$-0.283336\pi$
$983$	39.4615	1.25863	0.629313	+	0.777152i	$0.283336\pi$
$984$	−2.27494	−0.0725225
$985$	2.81346	0.0896442
$986$	25.3633	0.807733
$987$	2.04223	0.0650049
$988$	−4.41532	−0.140470
$989$	−16.3981	−0.521431
$990$	0	0
$991$	20.9652	0.665982	0.332991	−	0.942930i	$-0.391942\pi$
$991$	20.9652	0.665982	0.332991	+	0.942930i	$0.391942\pi$
$992$	6.00000	0.190500
$993$	1.22877	0.0389939
$994$	14.8557	0.471194
$995$	13.0211	0.412797
$996$	−3.58468	−0.113585
$997$	−21.9441	−0.694976	−0.347488	−	0.937684i	$-0.612965\pi$
$997$	−21.9441	−0.694976	−0.347488	+	0.937684i	$0.612965\pi$
$998$	−24.6480	−0.780220
$999$	19.5573	0.618766

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8470.2.a.cl.1.2		3
11.10	odd	2		770.2.a.l.1.2	✓	3
33.32	even	2		6930.2.a.cl.1.2		3
44.43	even	2		6160.2.a.bi.1.2		3
55.32	even	4		3850.2.c.z.1849.2		6
55.43	even	4		3850.2.c.z.1849.5		6
55.54	odd	2		3850.2.a.bu.1.2		3
77.76	even	2		5390.2.a.bz.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.a.l.1.2	✓	3	11.10	odd	2
3850.2.a.bu.1.2		3	55.54	odd	2
3850.2.c.z.1849.2		6	55.32	even	4
3850.2.c.z.1849.5		6	55.43	even	4
5390.2.a.bz.1.2		3	77.76	even	2
6160.2.a.bi.1.2		3	44.43	even	2
6930.2.a.cl.1.2		3	33.32	even	2
8470.2.a.cl.1.2		3	1.1	even	1	trivial

Overview	Random
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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:	\( N \)	\(=\)	\( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8470.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.406728 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.406728 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.83457 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.406728 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.406728 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.83457 q^{9} -1.00000 q^{10} -0.406728 q^{12} +0.813457 q^{13} +1.00000 q^{14} +0.406728 q^{15} +1.00000 q^{16} -3.83457 q^{17} -2.83457 q^{18} -5.42784 q^{19} -1.00000 q^{20} -0.406728 q^{21} -5.42784 q^{23} -0.406728 q^{24} +1.00000 q^{25} +0.813457 q^{26} +2.37309 q^{27} +1.00000 q^{28} -6.61439 q^{29} +0.406728 q^{30} +6.00000 q^{31} +1.00000 q^{32} -3.83457 q^{34} -1.00000 q^{35} -2.83457 q^{36} +8.24130 q^{37} -5.42784 q^{38} -0.330856 q^{39} -1.00000 q^{40} +5.59327 q^{41} -0.406728 q^{42} +3.02112 q^{43} +2.83457 q^{45} -5.42784 q^{46} -5.02112 q^{47} -0.406728 q^{48} +1.00000 q^{49} +1.00000 q^{50} +1.55963 q^{51} +0.813457 q^{52} +6.61439 q^{53} +2.37309 q^{54} +1.00000 q^{56} +2.20766 q^{57} -6.61439 q^{58} +10.6480 q^{59} +0.406728 q^{60} -0.978885 q^{61} +6.00000 q^{62} -2.83457 q^{63} +1.00000 q^{64} -0.813457 q^{65} +8.00000 q^{67} -3.83457 q^{68} +2.20766 q^{69} -1.00000 q^{70} +14.8557 q^{71} -2.83457 q^{72} +6.20766 q^{73} +8.24130 q^{74} -0.406728 q^{75} -5.42784 q^{76} -0.330856 q^{78} -17.0970 q^{79} -1.00000 q^{80} +7.53851 q^{81} +5.59327 q^{82} +8.81346 q^{83} -0.406728 q^{84} +3.83457 q^{85} +3.02112 q^{86} +2.69026 q^{87} -1.18654 q^{89} +2.83457 q^{90} +0.813457 q^{91} -5.42784 q^{92} -2.44037 q^{93} -5.02112 q^{94} +5.42784 q^{95} -0.406728 q^{96} -3.42784 q^{97} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 3 q^{4} - 3 q^{5} + 3 q^{7} + 3 q^{8} + 11 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 + 3 * q^4 - 3 * q^5 + 3 * q^7 + 3 * q^8 + 11 * q^9	\( 3 q + 3 q^{2} + 3 q^{4} - 3 q^{5} + 3 q^{7} + 3 q^{8} + 11 q^{9} - 3 q^{10} + 3 q^{14} + 3 q^{16} + 8 q^{17} + 11 q^{18} + 2 q^{19} - 3 q^{20} + 2 q^{23} + 3 q^{25} + 12 q^{27} + 3 q^{28} - 4 q^{29} + 18 q^{31} + 3 q^{32} + 8 q^{34} - 3 q^{35} + 11 q^{36} + 4 q^{37} + 2 q^{38} - 40 q^{39} - 3 q^{40} + 18 q^{41} - 8 q^{43} - 11 q^{45} + 2 q^{46} + 2 q^{47} + 3 q^{49} + 3 q^{50} + 12 q^{51} + 4 q^{53} + 12 q^{54} + 3 q^{56} - 8 q^{57} - 4 q^{58} + 10 q^{59} - 20 q^{61} + 18 q^{62} + 11 q^{63} + 3 q^{64} + 24 q^{67} + 8 q^{68} - 8 q^{69} - 3 q^{70} + 8 q^{71} + 11 q^{72} + 4 q^{73} + 4 q^{74} + 2 q^{76} - 40 q^{78} + 6 q^{79} - 3 q^{80} + 47 q^{81} + 18 q^{82} + 24 q^{83} - 8 q^{85} - 8 q^{86} - 48 q^{87} - 6 q^{89} - 11 q^{90} + 2 q^{92} + 2 q^{94} - 2 q^{95} + 8 q^{97} + 3 q^{98}+O(q^{100}) \) 3 * q + 3 * q^2 + 3 * q^4 - 3 * q^5 + 3 * q^7 + 3 * q^8 + 11 * q^9 - 3 * q^10 + 3 * q^14 + 3 * q^16 + 8 * q^17 + 11 * q^18 + 2 * q^19 - 3 * q^20 + 2 * q^23 + 3 * q^25 + 12 * q^27 + 3 * q^28 - 4 * q^29 + 18 * q^31 + 3 * q^32 + 8 * q^34 - 3 * q^35 + 11 * q^36 + 4 * q^37 + 2 * q^38 - 40 * q^39 - 3 * q^40 + 18 * q^41 - 8 * q^43 - 11 * q^45 + 2 * q^46 + 2 * q^47 + 3 * q^49 + 3 * q^50 + 12 * q^51 + 4 * q^53 + 12 * q^54 + 3 * q^56 - 8 * q^57 - 4 * q^58 + 10 * q^59 - 20 * q^61 + 18 * q^62 + 11 * q^63 + 3 * q^64 + 24 * q^67 + 8 * q^68 - 8 * q^69 - 3 * q^70 + 8 * q^71 + 11 * q^72 + 4 * q^73 + 4 * q^74 + 2 * q^76 - 40 * q^78 + 6 * q^79 - 3 * q^80 + 47 * q^81 + 18 * q^82 + 24 * q^83 - 8 * q^85 - 8 * q^86 - 48 * q^87 - 6 * q^89 - 11 * q^90 + 2 * q^92 + 2 * q^94 - 2 * q^95 + 8 * q^97 + 3 * q^98

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