LMFDB - Embedded newform 5070.2.a.bb.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5070,2,Mod(1,5070)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5070, 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("5070.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5070.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:	$40.4841538248$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{17}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4 $ x^2 - x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 390)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.56155$ of defining polynomial
Character	$\chi$	$=$	5070.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -3.56155 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -3.56155 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +4.12311 q^{11} +1.00000 q^{12} +3.56155 q^{14} -1.00000 q^{15} +1.00000 q^{16} +5.12311 q^{17} -1.00000 q^{18} +3.56155 q^{19} -1.00000 q^{20} -3.56155 q^{21} -4.12311 q^{22} -7.68466 q^{23} -1.00000 q^{24} +1.00000 q^{25} +1.00000 q^{27} -3.56155 q^{28} +6.56155 q^{29} +1.00000 q^{30} -5.68466 q^{31} -1.00000 q^{32} +4.12311 q^{33} -5.12311 q^{34} +3.56155 q^{35} +1.00000 q^{36} -4.12311 q^{37} -3.56155 q^{38} +1.00000 q^{40} +4.24621 q^{41} +3.56155 q^{42} +4.56155 q^{43} +4.12311 q^{44} -1.00000 q^{45} +7.68466 q^{46} -7.00000 q^{47} +1.00000 q^{48} +5.68466 q^{49} -1.00000 q^{50} +5.12311 q^{51} +4.43845 q^{53} -1.00000 q^{54} -4.12311 q^{55} +3.56155 q^{56} +3.56155 q^{57} -6.56155 q^{58} -10.5616 q^{59} -1.00000 q^{60} +6.00000 q^{61} +5.68466 q^{62} -3.56155 q^{63} +1.00000 q^{64} -4.12311 q^{66} -14.2462 q^{67} +5.12311 q^{68} -7.68466 q^{69} -3.56155 q^{70} +4.87689 q^{71} -1.00000 q^{72} +15.3693 q^{73} +4.12311 q^{74} +1.00000 q^{75} +3.56155 q^{76} -14.6847 q^{77} +7.43845 q^{79} -1.00000 q^{80} +1.00000 q^{81} -4.24621 q^{82} -1.12311 q^{83} -3.56155 q^{84} -5.12311 q^{85} -4.56155 q^{86} +6.56155 q^{87} -4.12311 q^{88} -1.80776 q^{89} +1.00000 q^{90} -7.68466 q^{92} -5.68466 q^{93} +7.00000 q^{94} -3.56155 q^{95} -1.00000 q^{96} -1.12311 q^{97} -5.68466 q^{98} +4.12311 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - 3 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 - 3 * q^7 - 2 * q^8 + 2 * q^9	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - 3 q^{7} - 2 q^{8} + 2 q^{9} + 2 q^{10} + 2 q^{12} + 3 q^{14} - 2 q^{15} + 2 q^{16} + 2 q^{17} - 2 q^{18} + 3 q^{19} - 2 q^{20} - 3 q^{21} - 3 q^{23} - 2 q^{24} + 2 q^{25} + 2 q^{27} - 3 q^{28} + 9 q^{29} + 2 q^{30} + q^{31} - 2 q^{32} - 2 q^{34} + 3 q^{35} + 2 q^{36} - 3 q^{38} + 2 q^{40} - 8 q^{41} + 3 q^{42} + 5 q^{43} - 2 q^{45} + 3 q^{46} - 14 q^{47} + 2 q^{48} - q^{49} - 2 q^{50} + 2 q^{51} + 13 q^{53} - 2 q^{54} + 3 q^{56} + 3 q^{57} - 9 q^{58} - 17 q^{59} - 2 q^{60} + 12 q^{61} - q^{62} - 3 q^{63} + 2 q^{64} - 12 q^{67} + 2 q^{68} - 3 q^{69} - 3 q^{70} + 18 q^{71} - 2 q^{72} + 6 q^{73} + 2 q^{75} + 3 q^{76} - 17 q^{77} + 19 q^{79} - 2 q^{80} + 2 q^{81} + 8 q^{82} + 6 q^{83} - 3 q^{84} - 2 q^{85} - 5 q^{86} + 9 q^{87} + 17 q^{89} + 2 q^{90} - 3 q^{92} + q^{93} + 14 q^{94} - 3 q^{95} - 2 q^{96} + 6 q^{97} + q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 - 3 * q^7 - 2 * q^8 + 2 * q^9 + 2 * q^10 + 2 * q^12 + 3 * q^14 - 2 * q^15 + 2 * q^16 + 2 * q^17 - 2 * q^18 + 3 * q^19 - 2 * q^20 - 3 * q^21 - 3 * q^23 - 2 * q^24 + 2 * q^25 + 2 * q^27 - 3 * q^28 + 9 * q^29 + 2 * q^30 + q^31 - 2 * q^32 - 2 * q^34 + 3 * q^35 + 2 * q^36 - 3 * q^38 + 2 * q^40 - 8 * q^41 + 3 * q^42 + 5 * q^43 - 2 * q^45 + 3 * q^46 - 14 * q^47 + 2 * q^48 - q^49 - 2 * q^50 + 2 * q^51 + 13 * q^53 - 2 * q^54 + 3 * q^56 + 3 * q^57 - 9 * q^58 - 17 * q^59 - 2 * q^60 + 12 * q^61 - q^62 - 3 * q^63 + 2 * q^64 - 12 * q^67 + 2 * q^68 - 3 * q^69 - 3 * q^70 + 18 * q^71 - 2 * q^72 + 6 * q^73 + 2 * q^75 + 3 * q^76 - 17 * q^77 + 19 * q^79 - 2 * q^80 + 2 * q^81 + 8 * q^82 + 6 * q^83 - 3 * q^84 - 2 * q^85 - 5 * q^86 + 9 * q^87 + 17 * q^89 + 2 * q^90 - 3 * q^92 + q^93 + 14 * q^94 - 3 * q^95 - 2 * q^96 + 6 * q^97 + 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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.00000	−0.408248
$7$	−3.56155	−1.34614	−0.673070	−	0.739579i	$-0.735025\pi$
$7$	−3.56155	−1.34614	−0.673070	+	0.739579i	$0.735025\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	4.12311	1.24316	0.621582	−	0.783349i	$-0.286490\pi$
$11$	4.12311	1.24316	0.621582	+	0.783349i	$0.286490\pi$
$12$	1.00000	0.288675
$13$	0	0
$13$	0	0
$14$	3.56155	0.951865
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	5.12311	1.24254	0.621268	−	0.783598i	$-0.286618\pi$
$17$	5.12311	1.24254	0.621268	+	0.783598i	$0.286618\pi$
$18$	−1.00000	−0.235702
$19$	3.56155	0.817076	0.408538	−	0.912741i	$-0.366039\pi$
$19$	3.56155	0.817076	0.408538	+	0.912741i	$0.366039\pi$
$20$	−1.00000	−0.223607
$21$	−3.56155	−0.777195
$22$	−4.12311	−0.879049
$23$	−7.68466	−1.60236	−0.801181	−	0.598422i	$-0.795795\pi$
$23$	−7.68466	−1.60236	−0.801181	+	0.598422i	$0.795795\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	0	0
$27$	1.00000	0.192450
$28$	−3.56155	−0.673070
$29$	6.56155	1.21845	0.609225	−	0.792998i	$-0.291481\pi$
$29$	6.56155	1.21845	0.609225	+	0.792998i	$0.291481\pi$
$30$	1.00000	0.182574
$31$	−5.68466	−1.02099	−0.510497	−	0.859879i	$-0.670539\pi$
$31$	−5.68466	−1.02099	−0.510497	+	0.859879i	$0.670539\pi$
$32$	−1.00000	−0.176777
$33$	4.12311	0.717741
$34$	−5.12311	−0.878605
$35$	3.56155	0.602012
$36$	1.00000	0.166667
$37$	−4.12311	−0.677834	−0.338917	−	0.940816i	$-0.610061\pi$
$37$	−4.12311	−0.677834	−0.338917	+	0.940816i	$0.610061\pi$
$38$	−3.56155	−0.577760
$39$	0	0
$40$	1.00000	0.158114
$41$	4.24621	0.663147	0.331573	−	0.943429i	$-0.392421\pi$
$41$	4.24621	0.663147	0.331573	+	0.943429i	$0.392421\pi$
$42$	3.56155	0.549560
$43$	4.56155	0.695630	0.347815	−	0.937563i	$-0.386924\pi$
$43$	4.56155	0.695630	0.347815	+	0.937563i	$0.386924\pi$
$44$	4.12311	0.621582
$45$	−1.00000	−0.149071
$46$	7.68466	1.13304
$47$	−7.00000	−1.02105	−0.510527	−	0.859861i	$-0.670550\pi$
$47$	−7.00000	−1.02105	−0.510527	+	0.859861i	$0.670550\pi$
$48$	1.00000	0.144338
$49$	5.68466	0.812094
$50$	−1.00000	−0.141421
$51$	5.12311	0.717378
$52$	0	0
$53$	4.43845	0.609668	0.304834	−	0.952406i	$-0.401399\pi$
$53$	4.43845	0.609668	0.304834	+	0.952406i	$0.401399\pi$
$54$	−1.00000	−0.136083
$55$	−4.12311	−0.555959
$56$	3.56155	0.475933
$57$	3.56155	0.471739
$58$	−6.56155	−0.861574
$59$	−10.5616	−1.37500	−0.687499	−	0.726186i	$-0.741291\pi$
$59$	−10.5616	−1.37500	−0.687499	+	0.726186i	$0.741291\pi$
$60$	−1.00000	−0.129099
$61$	6.00000	0.768221	0.384111	−	0.923287i	$-0.374508\pi$
$61$	6.00000	0.768221	0.384111	+	0.923287i	$0.374508\pi$
$62$	5.68466	0.721952
$63$	−3.56155	−0.448713
$64$	1.00000	0.125000
$65$	0	0
$66$	−4.12311	−0.507519
$67$	−14.2462	−1.74045	−0.870226	−	0.492653i	$-0.836027\pi$
$67$	−14.2462	−1.74045	−0.870226	+	0.492653i	$0.836027\pi$
$68$	5.12311	0.621268
$69$	−7.68466	−0.925124
$70$	−3.56155	−0.425687
$71$	4.87689	0.578781	0.289390	−	0.957211i	$-0.406547\pi$
$71$	4.87689	0.578781	0.289390	+	0.957211i	$0.406547\pi$
$72$	−1.00000	−0.117851
$73$	15.3693	1.79884	0.899421	−	0.437083i	$-0.143988\pi$
$73$	15.3693	1.79884	0.899421	+	0.437083i	$0.143988\pi$
$74$	4.12311	0.479301
$75$	1.00000	0.115470
$76$	3.56155	0.408538
$77$	−14.6847	−1.67347
$78$	0	0
$79$	7.43845	0.836891	0.418445	−	0.908242i	$-0.362575\pi$
$79$	7.43845	0.836891	0.418445	+	0.908242i	$0.362575\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	−4.24621	−0.468916
$83$	−1.12311	−0.123277	−0.0616384	−	0.998099i	$-0.519633\pi$
$83$	−1.12311	−0.123277	−0.0616384	+	0.998099i	$0.519633\pi$
$84$	−3.56155	−0.388597
$85$	−5.12311	−0.555679
$86$	−4.56155	−0.491885
$87$	6.56155	0.703472
$88$	−4.12311	−0.439525
$89$	−1.80776	−0.191623	−0.0958113	−	0.995400i	$-0.530545\pi$
$89$	−1.80776	−0.191623	−0.0958113	+	0.995400i	$0.530545\pi$
$90$	1.00000	0.105409
$91$	0	0
$92$	−7.68466	−0.801181
$93$	−5.68466	−0.589472
$94$	7.00000	0.721995
$95$	−3.56155	−0.365408
$96$	−1.00000	−0.102062
$97$	−1.12311	−0.114034	−0.0570170	−	0.998373i	$-0.518159\pi$
$97$	−1.12311	−0.114034	−0.0570170	+	0.998373i	$0.518159\pi$
$98$	−5.68466	−0.574237
$99$	4.12311	0.414388
$100$	1.00000	0.100000
$101$	−17.1231	−1.70381	−0.851906	−	0.523694i	$-0.824553\pi$
$101$	−17.1231	−1.70381	−0.851906	+	0.523694i	$0.824553\pi$
$102$	−5.12311	−0.507263
$103$	0.438447	0.0432015	0.0216007	−	0.999767i	$-0.493124\pi$
$103$	0.438447	0.0432015	0.0216007	+	0.999767i	$0.493124\pi$
$104$	0	0
$105$	3.56155	0.347572
$106$	−4.43845	−0.431100
$107$	2.00000	0.193347	0.0966736	−	0.995316i	$-0.469180\pi$
$107$	2.00000	0.193347	0.0966736	+	0.995316i	$0.469180\pi$
$108$	1.00000	0.0962250
$109$	20.2462	1.93924	0.969618	−	0.244625i	$-0.0786650\pi$
$109$	20.2462	1.93924	0.969618	+	0.244625i	$0.0786650\pi$
$110$	4.12311	0.393123
$111$	−4.12311	−0.391348
$112$	−3.56155	−0.336535
$113$	−3.68466	−0.346624	−0.173312	−	0.984867i	$-0.555447\pi$
$113$	−3.68466	−0.346624	−0.173312	+	0.984867i	$0.555447\pi$
$114$	−3.56155	−0.333570
$115$	7.68466	0.716598
$116$	6.56155	0.609225
$117$	0	0
$118$	10.5616	0.972270
$119$	−18.2462	−1.67263
$120$	1.00000	0.0912871
$121$	6.00000	0.545455
$122$	−6.00000	−0.543214
$123$	4.24621	0.382868
$124$	−5.68466	−0.510497
$125$	−1.00000	−0.0894427
$126$	3.56155	0.317288
$127$	−4.43845	−0.393849	−0.196924	−	0.980419i	$-0.563095\pi$
$127$	−4.43845	−0.393849	−0.196924	+	0.980419i	$0.563095\pi$
$128$	−1.00000	−0.0883883
$129$	4.56155	0.401622
$130$	0	0
$131$	6.12311	0.534978	0.267489	−	0.963561i	$-0.413806\pi$
$131$	6.12311	0.534978	0.267489	+	0.963561i	$0.413806\pi$
$132$	4.12311	0.358870
$133$	−12.6847	−1.09990
$134$	14.2462	1.23069
$135$	−1.00000	−0.0860663
$136$	−5.12311	−0.439303
$137$	8.80776	0.752498	0.376249	−	0.926519i	$-0.377214\pi$
$137$	8.80776	0.752498	0.376249	+	0.926519i	$0.377214\pi$
$138$	7.68466	0.654162
$139$	8.43845	0.715740	0.357870	−	0.933771i	$-0.383503\pi$
$139$	8.43845	0.715740	0.357870	+	0.933771i	$0.383503\pi$
$140$	3.56155	0.301006
$141$	−7.00000	−0.589506
$142$	−4.87689	−0.409260
$143$	0	0
$144$	1.00000	0.0833333
$145$	−6.56155	−0.544907
$146$	−15.3693	−1.27197
$147$	5.68466	0.468863
$148$	−4.12311	−0.338917
$149$	22.8078	1.86848	0.934242	−	0.356639i	$-0.116077\pi$
$149$	22.8078	1.86848	0.934242	+	0.356639i	$0.116077\pi$
$150$	−1.00000	−0.0816497
$151$	−9.36932	−0.762464	−0.381232	−	0.924479i	$-0.624500\pi$
$151$	−9.36932	−0.762464	−0.381232	+	0.924479i	$0.624500\pi$
$152$	−3.56155	−0.288880
$153$	5.12311	0.414179
$154$	14.6847	1.18332
$155$	5.68466	0.456603
$156$	0	0
$157$	22.1231	1.76562	0.882808	−	0.469734i	$-0.155650\pi$
$157$	22.1231	1.76562	0.882808	+	0.469734i	$0.155650\pi$
$158$	−7.43845	−0.591771
$159$	4.43845	0.351992
$160$	1.00000	0.0790569
$161$	27.3693	2.15700
$162$	−1.00000	−0.0785674
$163$	18.5616	1.45385	0.726927	−	0.686715i	$-0.240948\pi$
$163$	18.5616	1.45385	0.726927	+	0.686715i	$0.240948\pi$
$164$	4.24621	0.331573
$165$	−4.12311	−0.320983
$166$	1.12311	0.0871699
$167$	20.3693	1.57623	0.788113	−	0.615531i	$-0.211058\pi$
$167$	20.3693	1.57623	0.788113	+	0.615531i	$0.211058\pi$
$168$	3.56155	0.274780
$169$	0	0
$170$	5.12311	0.392924
$171$	3.56155	0.272359
$172$	4.56155	0.347815
$173$	−25.1771	−1.91418	−0.957089	−	0.289794i	$-0.906413\pi$
$173$	−25.1771	−1.91418	−0.957089	+	0.289794i	$0.906413\pi$
$174$	−6.56155	−0.497430
$175$	−3.56155	−0.269228
$176$	4.12311	0.310791
$177$	−10.5616	−0.793855
$178$	1.80776	0.135498
$179$	−0.315342	−0.0235697	−0.0117849	−	0.999931i	$-0.503751\pi$
$179$	−0.315342	−0.0235697	−0.0117849	+	0.999931i	$0.503751\pi$
$180$	−1.00000	−0.0745356
$181$	11.1231	0.826774	0.413387	−	0.910555i	$-0.364346\pi$
$181$	11.1231	0.826774	0.413387	+	0.910555i	$0.364346\pi$
$182$	0	0
$183$	6.00000	0.443533
$184$	7.68466	0.566521
$185$	4.12311	0.303137
$186$	5.68466	0.416819
$187$	21.1231	1.54467
$188$	−7.00000	−0.510527
$189$	−3.56155	−0.259065
$190$	3.56155	0.258382
$191$	19.1231	1.38370	0.691850	−	0.722042i	$-0.256796\pi$
$191$	19.1231	1.38370	0.691850	+	0.722042i	$0.256796\pi$
$192$	1.00000	0.0721688
$193$	0	0		−	1.00000i	$-0.5\pi$
$193$	0	0			1.00000i	$0.5\pi$
$194$	1.12311	0.0806343
$195$	0	0
$196$	5.68466	0.406047
$197$	7.80776	0.556280	0.278140	−	0.960541i	$-0.410282\pi$
$197$	7.80776	0.556280	0.278140	+	0.960541i	$0.410282\pi$
$198$	−4.12311	−0.293016
$199$	11.1231	0.788496	0.394248	−	0.919004i	$-0.371005\pi$
$199$	11.1231	0.788496	0.394248	+	0.919004i	$0.371005\pi$
$200$	−1.00000	−0.0707107
$201$	−14.2462	−1.00485
$202$	17.1231	1.20478
$203$	−23.3693	−1.64020
$204$	5.12311	0.358689
$205$	−4.24621	−0.296568
$206$	−0.438447	−0.0305481
$207$	−7.68466	−0.534121
$208$	0	0
$209$	14.6847	1.01576
$210$	−3.56155	−0.245770
$211$	6.93087	0.477141	0.238570	−	0.971125i	$-0.423321\pi$
$211$	6.93087	0.477141	0.238570	+	0.971125i	$0.423321\pi$
$212$	4.43845	0.304834
$213$	4.87689	0.334159
$214$	−2.00000	−0.136717
$215$	−4.56155	−0.311095
$216$	−1.00000	−0.0680414
$217$	20.2462	1.37440
$218$	−20.2462	−1.37125
$219$	15.3693	1.03856
$220$	−4.12311	−0.277980
$221$	0	0
$222$	4.12311	0.276725
$223$	26.3002	1.76119	0.880595	−	0.473869i	$-0.157143\pi$
$223$	26.3002	1.76119	0.880595	+	0.473869i	$0.157143\pi$
$224$	3.56155	0.237966
$225$	1.00000	0.0666667
$226$	3.68466	0.245100
$227$	20.0000	1.32745	0.663723	−	0.747978i	$-0.268975\pi$
$227$	20.0000	1.32745	0.663723	+	0.747978i	$0.268975\pi$
$228$	3.56155	0.235870
$229$	7.75379	0.512385	0.256192	−	0.966626i	$-0.417532\pi$
$229$	7.75379	0.512385	0.256192	+	0.966626i	$0.417532\pi$
$230$	−7.68466	−0.506711
$231$	−14.6847	−0.966180
$232$	−6.56155	−0.430787
$233$	−17.6847	−1.15856	−0.579280	−	0.815128i	$-0.696666\pi$
$233$	−17.6847	−1.15856	−0.579280	+	0.815128i	$0.696666\pi$
$234$	0	0
$235$	7.00000	0.456630
$236$	−10.5616	−0.687499
$237$	7.43845	0.483179
$238$	18.2462	1.18273
$239$	−13.3693	−0.864789	−0.432395	−	0.901684i	$-0.642331\pi$
$239$	−13.3693	−0.864789	−0.432395	+	0.901684i	$0.642331\pi$
$240$	−1.00000	−0.0645497
$241$	19.8769	1.28038	0.640192	−	0.768215i	$-0.278855\pi$
$241$	19.8769	1.28038	0.640192	+	0.768215i	$0.278855\pi$
$242$	−6.00000	−0.385695
$243$	1.00000	0.0641500
$244$	6.00000	0.384111
$245$	−5.68466	−0.363180
$246$	−4.24621	−0.270729
$247$	0	0
$248$	5.68466	0.360976
$249$	−1.12311	−0.0711739
$250$	1.00000	0.0632456
$251$	0.123106	0.00777036	0.00388518	−	0.999992i	$-0.498763\pi$
$251$	0.123106	0.00777036	0.00388518	+	0.999992i	$0.498763\pi$
$252$	−3.56155	−0.224357
$253$	−31.6847	−1.99200
$254$	4.43845	0.278493
$255$	−5.12311	−0.320821
$256$	1.00000	0.0625000
$257$	−1.43845	−0.0897279	−0.0448639	−	0.998993i	$-0.514285\pi$
$257$	−1.43845	−0.0897279	−0.0448639	+	0.998993i	$0.514285\pi$
$258$	−4.56155	−0.283990
$259$	14.6847	0.912460
$260$	0	0
$261$	6.56155	0.406150
$262$	−6.12311	−0.378287
$263$	−13.0000	−0.801614	−0.400807	−	0.916162i	$-0.631270\pi$
$263$	−13.0000	−0.801614	−0.400807	+	0.916162i	$0.631270\pi$
$264$	−4.12311	−0.253760
$265$	−4.43845	−0.272652
$266$	12.6847	0.777746
$267$	−1.80776	−0.110633
$268$	−14.2462	−0.870226
$269$	−3.36932	−0.205431	−0.102715	−	0.994711i	$-0.532753\pi$
$269$	−3.36932	−0.205431	−0.102715	+	0.994711i	$0.532753\pi$
$270$	1.00000	0.0608581
$271$	−32.1771	−1.95462	−0.977309	−	0.211818i	$-0.932062\pi$
$271$	−32.1771	−1.95462	−0.977309	+	0.211818i	$0.932062\pi$
$272$	5.12311	0.310634
$273$	0	0
$274$	−8.80776	−0.532096
$275$	4.12311	0.248633
$276$	−7.68466	−0.462562
$277$	−1.00000	−0.0600842	−0.0300421	−	0.999549i	$-0.509564\pi$
$277$	−1.00000	−0.0600842	−0.0300421	+	0.999549i	$0.509564\pi$
$278$	−8.43845	−0.506104
$279$	−5.68466	−0.340332
$280$	−3.56155	−0.212843
$281$	0.246211	0.0146877	0.00734387	−	0.999973i	$-0.497662\pi$
$281$	0.246211	0.0146877	0.00734387	+	0.999973i	$0.497662\pi$
$282$	7.00000	0.416844
$283$	11.4384	0.679945	0.339973	−	0.940435i	$-0.389582\pi$
$283$	11.4384	0.679945	0.339973	+	0.940435i	$0.389582\pi$
$284$	4.87689	0.289390
$285$	−3.56155	−0.210968
$286$	0	0
$287$	−15.1231	−0.892689
$288$	−1.00000	−0.0589256
$289$	9.24621	0.543895
$290$	6.56155	0.385308
$291$	−1.12311	−0.0658376
$292$	15.3693	0.899421
$293$	24.9309	1.45648	0.728238	−	0.685324i	$-0.240339\pi$
$293$	24.9309	1.45648	0.728238	+	0.685324i	$0.240339\pi$
$294$	−5.68466	−0.331536
$295$	10.5616	0.614917
$296$	4.12311	0.239651
$297$	4.12311	0.239247
$298$	−22.8078	−1.32122
$299$	0	0
$300$	1.00000	0.0577350
$301$	−16.2462	−0.936416
$302$	9.36932	0.539144
$303$	−17.1231	−0.983697
$304$	3.56155	0.204269
$305$	−6.00000	−0.343559
$306$	−5.12311	−0.292868
$307$	15.6155	0.891225	0.445613	−	0.895226i	$-0.352986\pi$
$307$	15.6155	0.891225	0.445613	+	0.895226i	$0.352986\pi$
$308$	−14.6847	−0.836736
$309$	0.438447	0.0249424
$310$	−5.68466	−0.322867
$311$	−18.7386	−1.06257	−0.531285	−	0.847193i	$-0.678291\pi$
$311$	−18.7386	−1.06257	−0.531285	+	0.847193i	$0.678291\pi$
$312$	0	0
$313$	6.63068	0.374788	0.187394	−	0.982285i	$-0.439996\pi$
$313$	6.63068	0.374788	0.187394	+	0.982285i	$0.439996\pi$
$314$	−22.1231	−1.24848
$315$	3.56155	0.200671
$316$	7.43845	0.418445
$317$	4.19224	0.235459	0.117730	−	0.993046i	$-0.462438\pi$
$317$	4.19224	0.235459	0.117730	+	0.993046i	$0.462438\pi$
$318$	−4.43845	−0.248896
$319$	27.0540	1.51473
$320$	−1.00000	−0.0559017
$321$	2.00000	0.111629
$322$	−27.3693	−1.52523
$323$	18.2462	1.01525
$324$	1.00000	0.0555556
$325$	0	0
$326$	−18.5616	−1.02803
$327$	20.2462	1.11962
$328$	−4.24621	−0.234458
$329$	24.9309	1.37448
$330$	4.12311	0.226969
$331$	18.7386	1.02997	0.514984	−	0.857200i	$-0.327798\pi$
$331$	18.7386	1.02997	0.514984	+	0.857200i	$0.327798\pi$
$332$	−1.12311	−0.0616384
$333$	−4.12311	−0.225945
$334$	−20.3693	−1.11456
$335$	14.2462	0.778354
$336$	−3.56155	−0.194299
$337$	−6.00000	−0.326841	−0.163420	−	0.986557i	$-0.552253\pi$
$337$	−6.00000	−0.326841	−0.163420	+	0.986557i	$0.552253\pi$
$338$	0	0
$339$	−3.68466	−0.200123
$340$	−5.12311	−0.277839
$341$	−23.4384	−1.26926
$342$	−3.56155	−0.192587
$343$	4.68466	0.252948
$344$	−4.56155	−0.245942
$345$	7.68466	0.413728
$346$	25.1771	1.35353
$347$	9.12311	0.489754	0.244877	−	0.969554i	$-0.421252\pi$
$347$	9.12311	0.489754	0.244877	+	0.969554i	$0.421252\pi$
$348$	6.56155	0.351736
$349$	24.4924	1.31105	0.655525	−	0.755174i	$-0.272448\pi$
$349$	24.4924	1.31105	0.655525	+	0.755174i	$0.272448\pi$
$350$	3.56155	0.190373
$351$	0	0
$352$	−4.12311	−0.219762
$353$	−31.8617	−1.69583	−0.847915	−	0.530133i	$-0.822142\pi$
$353$	−31.8617	−1.69583	−0.847915	+	0.530133i	$0.822142\pi$
$354$	10.5616	0.561340
$355$	−4.87689	−0.258839
$356$	−1.80776	−0.0958113
$357$	−18.2462	−0.965692
$358$	0.315342	0.0166663
$359$	−4.87689	−0.257393	−0.128696	−	0.991684i	$-0.541079\pi$
$359$	−4.87689	−0.257393	−0.128696	+	0.991684i	$0.541079\pi$
$360$	1.00000	0.0527046
$361$	−6.31534	−0.332386
$362$	−11.1231	−0.584617
$363$	6.00000	0.314918
$364$	0	0
$365$	−15.3693	−0.804467
$366$	−6.00000	−0.313625
$367$	−20.4924	−1.06970	−0.534848	−	0.844948i	$-0.679631\pi$
$367$	−20.4924	−1.06970	−0.534848	+	0.844948i	$0.679631\pi$
$368$	−7.68466	−0.400591
$369$	4.24621	0.221049
$370$	−4.12311	−0.214350
$371$	−15.8078	−0.820698
$372$	−5.68466	−0.294736
$373$	−5.19224	−0.268844	−0.134422	−	0.990924i	$-0.542918\pi$
$373$	−5.19224	−0.268844	−0.134422	+	0.990924i	$0.542918\pi$
$374$	−21.1231	−1.09225
$375$	−1.00000	−0.0516398
$376$	7.00000	0.360997
$377$	0	0
$378$	3.56155	0.183187
$379$	5.31534	0.273031	0.136515	−	0.990638i	$-0.456410\pi$
$379$	5.31534	0.273031	0.136515	+	0.990638i	$0.456410\pi$
$380$	−3.56155	−0.182704
$381$	−4.43845	−0.227389
$382$	−19.1231	−0.978423
$383$	−20.8078	−1.06323	−0.531614	−	0.846987i	$-0.678414\pi$
$383$	−20.8078	−1.06323	−0.531614	+	0.846987i	$0.678414\pi$
$384$	−1.00000	−0.0510310
$385$	14.6847	0.748399
$386$	0	0
$387$	4.56155	0.231877
$388$	−1.12311	−0.0570170
$389$	19.0540	0.966075	0.483037	−	0.875600i	$-0.339533\pi$
$389$	19.0540	0.966075	0.483037	+	0.875600i	$0.339533\pi$
$390$	0	0
$391$	−39.3693	−1.99099
$392$	−5.68466	−0.287119
$393$	6.12311	0.308870
$394$	−7.80776	−0.393349
$395$	−7.43845	−0.374269
$396$	4.12311	0.207194
$397$	11.8769	0.596084	0.298042	−	0.954553i	$-0.403666\pi$
$397$	11.8769	0.596084	0.298042	+	0.954553i	$0.403666\pi$
$398$	−11.1231	−0.557551
$399$	−12.6847	−0.635027
$400$	1.00000	0.0500000
$401$	−12.6847	−0.633442	−0.316721	−	0.948519i	$-0.602582\pi$
$401$	−12.6847	−0.633442	−0.316721	+	0.948519i	$0.602582\pi$
$402$	14.2462	0.710536
$403$	0	0
$404$	−17.1231	−0.851906
$405$	−1.00000	−0.0496904
$406$	23.3693	1.15980
$407$	−17.0000	−0.842659
$408$	−5.12311	−0.253632
$409$	−1.80776	−0.0893882	−0.0446941	−	0.999001i	$-0.514231\pi$
$409$	−1.80776	−0.0893882	−0.0446941	+	0.999001i	$0.514231\pi$
$410$	4.24621	0.209705
$411$	8.80776	0.434455
$412$	0.438447	0.0216007
$413$	37.6155	1.85094
$414$	7.68466	0.377680
$415$	1.12311	0.0551311
$416$	0	0
$417$	8.43845	0.413233
$418$	−14.6847	−0.718250
$419$	−0.492423	−0.0240564	−0.0120282	−	0.999928i	$-0.503829\pi$
$419$	−0.492423	−0.0240564	−0.0120282	+	0.999928i	$0.503829\pi$
$420$	3.56155	0.173786
$421$	−0.492423	−0.0239992	−0.0119996	−	0.999928i	$-0.503820\pi$
$421$	−0.492423	−0.0239992	−0.0119996	+	0.999928i	$0.503820\pi$
$422$	−6.93087	−0.337389
$423$	−7.00000	−0.340352
$424$	−4.43845	−0.215550
$425$	5.12311	0.248507
$426$	−4.87689	−0.236286
$427$	−21.3693	−1.03413
$428$	2.00000	0.0966736
$429$	0	0
$430$	4.56155	0.219978
$431$	−26.7386	−1.28795	−0.643977	−	0.765045i	$-0.722717\pi$
$431$	−26.7386	−1.28795	−0.643977	+	0.765045i	$0.722717\pi$
$432$	1.00000	0.0481125
$433$	30.7386	1.47720	0.738602	−	0.674141i	$-0.235486\pi$
$433$	30.7386	1.47720	0.738602	+	0.674141i	$0.235486\pi$
$434$	−20.2462	−0.971849
$435$	−6.56155	−0.314602
$436$	20.2462	0.969618
$437$	−27.3693	−1.30925
$438$	−15.3693	−0.734374
$439$	16.8769	0.805490	0.402745	−	0.915312i	$-0.368056\pi$
$439$	16.8769	0.805490	0.402745	+	0.915312i	$0.368056\pi$
$440$	4.12311	0.196561
$441$	5.68466	0.270698
$442$	0	0
$443$	−4.87689	−0.231708	−0.115854	−	0.993266i	$-0.536961\pi$
$443$	−4.87689	−0.231708	−0.115854	+	0.993266i	$0.536961\pi$
$444$	−4.12311	−0.195674
$445$	1.80776	0.0856962
$446$	−26.3002	−1.24535
$447$	22.8078	1.07877
$448$	−3.56155	−0.168268
$449$	−25.1771	−1.18818	−0.594090	−	0.804399i	$-0.702488\pi$
$449$	−25.1771	−1.18818	−0.594090	+	0.804399i	$0.702488\pi$
$450$	−1.00000	−0.0471405
$451$	17.5076	0.824400
$452$	−3.68466	−0.173312
$453$	−9.36932	−0.440209
$454$	−20.0000	−0.938647
$455$	0	0
$456$	−3.56155	−0.166785
$457$	−3.75379	−0.175595	−0.0877974	−	0.996138i	$-0.527983\pi$
$457$	−3.75379	−0.175595	−0.0877974	+	0.996138i	$0.527983\pi$
$458$	−7.75379	−0.362311
$459$	5.12311	0.239126
$460$	7.68466	0.358299
$461$	−7.05398	−0.328536	−0.164268	−	0.986416i	$-0.552526\pi$
$461$	−7.05398	−0.328536	−0.164268	+	0.986416i	$0.552526\pi$
$462$	14.6847	0.683192
$463$	−33.6155	−1.56225	−0.781123	−	0.624377i	$-0.785353\pi$
$463$	−33.6155	−1.56225	−0.781123	+	0.624377i	$0.785353\pi$
$464$	6.56155	0.304612
$465$	5.68466	0.263620
$466$	17.6847	0.819226
$467$	39.8617	1.84458	0.922291	−	0.386497i	$-0.126315\pi$
$467$	39.8617	1.84458	0.922291	+	0.386497i	$0.126315\pi$
$468$	0	0
$469$	50.7386	2.34289
$470$	−7.00000	−0.322886
$471$	22.1231	1.01938
$472$	10.5616	0.486135
$473$	18.8078	0.864782
$474$	−7.43845	−0.341659
$475$	3.56155	0.163415
$476$	−18.2462	−0.836314
$477$	4.43845	0.203223
$478$	13.3693	0.611498
$479$	21.7538	0.993956	0.496978	−	0.867763i	$-0.334443\pi$
$479$	21.7538	0.993956	0.496978	+	0.867763i	$0.334443\pi$
$480$	1.00000	0.0456435
$481$	0	0
$482$	−19.8769	−0.905368
$483$	27.3693	1.24535
$484$	6.00000	0.272727
$485$	1.12311	0.0509976
$486$	−1.00000	−0.0453609
$487$	24.0540	1.08999	0.544995	−	0.838439i	$-0.316532\pi$
$487$	24.0540	1.08999	0.544995	+	0.838439i	$0.316532\pi$
$488$	−6.00000	−0.271607
$489$	18.5616	0.839382
$490$	5.68466	0.256807
$491$	−21.5616	−0.973059	−0.486530	−	0.873664i	$-0.661737\pi$
$491$	−21.5616	−0.973059	−0.486530	+	0.873664i	$0.661737\pi$
$492$	4.24621	0.191434
$493$	33.6155	1.51397
$494$	0	0
$495$	−4.12311	−0.185320
$496$	−5.68466	−0.255249
$497$	−17.3693	−0.779120
$498$	1.12311	0.0503276
$499$	−4.00000	−0.179065	−0.0895323	−	0.995984i	$-0.528537\pi$
$499$	−4.00000	−0.179065	−0.0895323	+	0.995984i	$0.528537\pi$
$500$	−1.00000	−0.0447214
$501$	20.3693	0.910034
$502$	−0.123106	−0.00549447
$503$	−5.94602	−0.265120	−0.132560	−	0.991175i	$-0.542320\pi$
$503$	−5.94602	−0.265120	−0.132560	+	0.991175i	$0.542320\pi$
$504$	3.56155	0.158644
$505$	17.1231	0.761968
$506$	31.6847	1.40855
$507$	0	0
$508$	−4.43845	−0.196924
$509$	29.5464	1.30962	0.654811	−	0.755793i	$-0.272748\pi$
$509$	29.5464	1.30962	0.654811	+	0.755793i	$0.272748\pi$
$510$	5.12311	0.226855
$511$	−54.7386	−2.42149
$512$	−1.00000	−0.0441942
$513$	3.56155	0.157246
$514$	1.43845	0.0634472
$515$	−0.438447	−0.0193203
$516$	4.56155	0.200811
$517$	−28.8617	−1.26934
$518$	−14.6847	−0.645207
$519$	−25.1771	−1.10515
$520$	0	0
$521$	−18.6847	−0.818590	−0.409295	−	0.912402i	$-0.634225\pi$
$521$	−18.6847	−0.818590	−0.409295	+	0.912402i	$0.634225\pi$
$522$	−6.56155	−0.287191
$523$	−9.19224	−0.401948	−0.200974	−	0.979597i	$-0.564411\pi$
$523$	−9.19224	−0.401948	−0.200974	+	0.979597i	$0.564411\pi$
$524$	6.12311	0.267489
$525$	−3.56155	−0.155439
$526$	13.0000	0.566827
$527$	−29.1231	−1.26862
$528$	4.12311	0.179435
$529$	36.0540	1.56756
$530$	4.43845	0.192794
$531$	−10.5616	−0.458332
$532$	−12.6847	−0.549950
$533$	0	0
$534$	1.80776	0.0782296
$535$	−2.00000	−0.0864675
$536$	14.2462	0.615343
$537$	−0.315342	−0.0136080
$538$	3.36932	0.145262
$539$	23.4384	1.00957
$540$	−1.00000	−0.0430331
$541$	2.63068	0.113102	0.0565510	−	0.998400i	$-0.481990\pi$
$541$	2.63068	0.113102	0.0565510	+	0.998400i	$0.481990\pi$
$542$	32.1771	1.38212
$543$	11.1231	0.477338
$544$	−5.12311	−0.219651
$545$	−20.2462	−0.867252
$546$	0	0
$547$	35.6155	1.52281	0.761405	−	0.648276i	$-0.224510\pi$
$547$	35.6155	1.52281	0.761405	+	0.648276i	$0.224510\pi$
$548$	8.80776	0.376249
$549$	6.00000	0.256074
$550$	−4.12311	−0.175810
$551$	23.3693	0.995566
$552$	7.68466	0.327081
$553$	−26.4924	−1.12657
$554$	1.00000	0.0424859
$555$	4.12311	0.175016
$556$	8.43845	0.357870
$557$	4.43845	0.188063	0.0940315	−	0.995569i	$-0.470025\pi$
$557$	4.43845	0.188063	0.0940315	+	0.995569i	$0.470025\pi$
$558$	5.68466	0.240651
$559$	0	0
$560$	3.56155	0.150503
$561$	21.1231	0.891818
$562$	−0.246211	−0.0103858
$563$	32.9848	1.39015	0.695073	−	0.718939i	$-0.255372\pi$
$563$	32.9848	1.39015	0.695073	+	0.718939i	$0.255372\pi$
$564$	−7.00000	−0.294753
$565$	3.68466	0.155015
$566$	−11.4384	−0.480794
$567$	−3.56155	−0.149571
$568$	−4.87689	−0.204630
$569$	−19.1771	−0.803945	−0.401973	−	0.915652i	$-0.631675\pi$
$569$	−19.1771	−0.803945	−0.401973	+	0.915652i	$0.631675\pi$
$570$	3.56155	0.149177
$571$	11.3153	0.473532	0.236766	−	0.971567i	$-0.423912\pi$
$571$	11.3153	0.473532	0.236766	+	0.971567i	$0.423912\pi$
$572$	0	0
$573$	19.1231	0.798879
$574$	15.1231	0.631226
$575$	−7.68466	−0.320472
$576$	1.00000	0.0416667
$577$	−8.73863	−0.363794	−0.181897	−	0.983318i	$-0.558224\pi$
$577$	−8.73863	−0.363794	−0.181897	+	0.983318i	$0.558224\pi$
$578$	−9.24621	−0.384592
$579$	0	0
$580$	−6.56155	−0.272454
$581$	4.00000	0.165948
$582$	1.12311	0.0465542
$583$	18.3002	0.757916
$584$	−15.3693	−0.635987
$585$	0	0
$586$	−24.9309	−1.02988
$587$	23.7538	0.980424	0.490212	−	0.871603i	$-0.336919\pi$
$587$	23.7538	0.980424	0.490212	+	0.871603i	$0.336919\pi$
$588$	5.68466	0.234431
$589$	−20.2462	−0.834231
$590$	−10.5616	−0.434812
$591$	7.80776	0.321168
$592$	−4.12311	−0.169459
$593$	12.1771	0.500053	0.250026	−	0.968239i	$-0.419561\pi$
$593$	12.1771	0.500053	0.250026	+	0.968239i	$0.419561\pi$
$594$	−4.12311	−0.169173
$595$	18.2462	0.748022
$596$	22.8078	0.934242
$597$	11.1231	0.455238
$598$	0	0
$599$	−14.0000	−0.572024	−0.286012	−	0.958226i	$-0.592330\pi$
$599$	−14.0000	−0.572024	−0.286012	+	0.958226i	$0.592330\pi$
$600$	−1.00000	−0.0408248
$601$	−35.9848	−1.46785	−0.733926	−	0.679229i	$-0.762314\pi$
$601$	−35.9848	−1.46785	−0.733926	+	0.679229i	$0.762314\pi$
$602$	16.2462	0.662146
$603$	−14.2462	−0.580151
$604$	−9.36932	−0.381232
$605$	−6.00000	−0.243935
$606$	17.1231	0.695579
$607$	−29.4233	−1.19425	−0.597127	−	0.802146i	$-0.703691\pi$
$607$	−29.4233	−1.19425	−0.597127	+	0.802146i	$0.703691\pi$
$608$	−3.56155	−0.144440
$609$	−23.3693	−0.946973
$610$	6.00000	0.242933
$611$	0	0
$612$	5.12311	0.207089
$613$	−28.1231	−1.13588	−0.567941	−	0.823069i	$-0.692260\pi$
$613$	−28.1231	−1.13588	−0.567941	+	0.823069i	$0.692260\pi$
$614$	−15.6155	−0.630191
$615$	−4.24621	−0.171224
$616$	14.6847	0.591662
$617$	41.6847	1.67816	0.839081	−	0.544007i	$-0.183094\pi$
$617$	41.6847	1.67816	0.839081	+	0.544007i	$0.183094\pi$
$618$	−0.438447	−0.0176369
$619$	16.4384	0.660717	0.330358	−	0.943856i	$-0.392830\pi$
$619$	16.4384	0.660717	0.330358	+	0.943856i	$0.392830\pi$
$620$	5.68466	0.228301
$621$	−7.68466	−0.308375
$622$	18.7386	0.751351
$623$	6.43845	0.257951
$624$	0	0
$625$	1.00000	0.0400000
$626$	−6.63068	−0.265015
$627$	14.6847	0.586449
$628$	22.1231	0.882808
$629$	−21.1231	−0.842233
$630$	−3.56155	−0.141896
$631$	30.2462	1.20408	0.602041	−	0.798465i	$-0.294354\pi$
$631$	30.2462	1.20408	0.602041	+	0.798465i	$0.294354\pi$
$632$	−7.43845	−0.295886
$633$	6.93087	0.275477
$634$	−4.19224	−0.166495
$635$	4.43845	0.176134
$636$	4.43845	0.175996
$637$	0	0
$638$	−27.0540	−1.07108
$639$	4.87689	0.192927
$640$	1.00000	0.0395285
$641$	−15.5616	−0.614644	−0.307322	−	0.951606i	$-0.599433\pi$
$641$	−15.5616	−0.614644	−0.307322	+	0.951606i	$0.599433\pi$
$642$	−2.00000	−0.0789337
$643$	−38.2462	−1.50828	−0.754142	−	0.656712i	$-0.771947\pi$
$643$	−38.2462	−1.50828	−0.754142	+	0.656712i	$0.771947\pi$
$644$	27.3693	1.07850
$645$	−4.56155	−0.179611
$646$	−18.2462	−0.717888
$647$	−2.05398	−0.0807501	−0.0403751	−	0.999185i	$-0.512855\pi$
$647$	−2.05398	−0.0807501	−0.0403751	+	0.999185i	$0.512855\pi$
$648$	−1.00000	−0.0392837
$649$	−43.5464	−1.70935
$650$	0	0
$651$	20.2462	0.793512
$652$	18.5616	0.726927
$653$	−40.4384	−1.58248	−0.791239	−	0.611507i	$-0.790564\pi$
$653$	−40.4384	−1.58248	−0.791239	+	0.611507i	$0.790564\pi$
$654$	−20.2462	−0.791690
$655$	−6.12311	−0.239250
$656$	4.24621	0.165787
$657$	15.3693	0.599614
$658$	−24.9309	−0.971906
$659$	31.0540	1.20969	0.604846	−	0.796343i	$-0.293235\pi$
$659$	31.0540	1.20969	0.604846	+	0.796343i	$0.293235\pi$
$660$	−4.12311	−0.160492
$661$	11.6155	0.451792	0.225896	−	0.974151i	$-0.427469\pi$
$661$	11.6155	0.451792	0.225896	+	0.974151i	$0.427469\pi$
$662$	−18.7386	−0.728298
$663$	0	0
$664$	1.12311	0.0435850
$665$	12.6847	0.491890
$666$	4.12311	0.159767
$667$	−50.4233	−1.95240
$668$	20.3693	0.788113
$669$	26.3002	1.01682
$670$	−14.2462	−0.550379
$671$	24.7386	0.955024
$672$	3.56155	0.137390
$673$	42.2462	1.62847	0.814236	−	0.580534i	$-0.197156\pi$
$673$	42.2462	1.62847	0.814236	+	0.580534i	$0.197156\pi$
$674$	6.00000	0.231111
$675$	1.00000	0.0384900
$676$	0	0
$677$	−28.8769	−1.10983	−0.554915	−	0.831907i	$-0.687249\pi$
$677$	−28.8769	−1.10983	−0.554915	+	0.831907i	$0.687249\pi$
$678$	3.68466	0.141508
$679$	4.00000	0.153506
$680$	5.12311	0.196462
$681$	20.0000	0.766402
$682$	23.4384	0.897505
$683$	−8.87689	−0.339665	−0.169832	−	0.985473i	$-0.554323\pi$
$683$	−8.87689	−0.339665	−0.169832	+	0.985473i	$0.554323\pi$
$684$	3.56155	0.136179
$685$	−8.80776	−0.336527
$686$	−4.68466	−0.178861
$687$	7.75379	0.295825
$688$	4.56155	0.173908
$689$	0	0
$690$	−7.68466	−0.292550
$691$	16.4384	0.625348	0.312674	−	0.949860i	$-0.398775\pi$
$691$	16.4384	0.625348	0.312674	+	0.949860i	$0.398775\pi$
$692$	−25.1771	−0.957089
$693$	−14.6847	−0.557824
$694$	−9.12311	−0.346308
$695$	−8.43845	−0.320089
$696$	−6.56155	−0.248715
$697$	21.7538	0.823984
$698$	−24.4924	−0.927052
$699$	−17.6847	−0.668895
$700$	−3.56155	−0.134614
$701$	17.3002	0.653419	0.326710	−	0.945125i	$-0.394060\pi$
$701$	17.3002	0.653419	0.326710	+	0.945125i	$0.394060\pi$
$702$	0	0
$703$	−14.6847	−0.553842
$704$	4.12311	0.155395
$705$	7.00000	0.263635
$706$	31.8617	1.19913
$707$	60.9848	2.29357
$708$	−10.5616	−0.396927
$709$	−17.7538	−0.666758	−0.333379	−	0.942793i	$-0.608189\pi$
$709$	−17.7538	−0.666758	−0.333379	+	0.942793i	$0.608189\pi$
$710$	4.87689	0.183027
$711$	7.43845	0.278964
$712$	1.80776	0.0677488
$713$	43.6847	1.63600
$714$	18.2462	0.682847
$715$	0	0
$716$	−0.315342	−0.0117849
$717$	−13.3693	−0.499286
$718$	4.87689	0.182004
$719$	−20.9848	−0.782603	−0.391301	−	0.920263i	$-0.627975\pi$
$719$	−20.9848	−0.782603	−0.391301	+	0.920263i	$0.627975\pi$
$720$	−1.00000	−0.0372678
$721$	−1.56155	−0.0581553
$722$	6.31534	0.235033
$723$	19.8769	0.739230
$724$	11.1231	0.413387
$725$	6.56155	0.243690
$726$	−6.00000	−0.222681
$727$	−23.4233	−0.868722	−0.434361	−	0.900739i	$-0.643026\pi$
$727$	−23.4233	−0.868722	−0.434361	+	0.900739i	$0.643026\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	15.3693	0.568844
$731$	23.3693	0.864345
$732$	6.00000	0.221766
$733$	−48.9309	−1.80730	−0.903651	−	0.428269i	$-0.859124\pi$
$733$	−48.9309	−1.80730	−0.903651	+	0.428269i	$0.859124\pi$
$734$	20.4924	0.756389
$735$	−5.68466	−0.209682
$736$	7.68466	0.283260
$737$	−58.7386	−2.16367
$738$	−4.24621	−0.156305
$739$	−42.5464	−1.56509	−0.782547	−	0.622591i	$-0.786080\pi$
$739$	−42.5464	−1.56509	−0.782547	+	0.622591i	$0.786080\pi$
$740$	4.12311	0.151568
$741$	0	0
$742$	15.8078	0.580321
$743$	32.1771	1.18046	0.590231	−	0.807234i	$-0.299037\pi$
$743$	32.1771	1.18046	0.590231	+	0.807234i	$0.299037\pi$
$744$	5.68466	0.208410
$745$	−22.8078	−0.835612
$746$	5.19224	0.190101
$747$	−1.12311	−0.0410923
$748$	21.1231	0.772337
$749$	−7.12311	−0.260273
$750$	1.00000	0.0365148
$751$	−3.19224	−0.116486	−0.0582432	−	0.998302i	$-0.518550\pi$
$751$	−3.19224	−0.116486	−0.0582432	+	0.998302i	$0.518550\pi$
$752$	−7.00000	−0.255264
$753$	0.123106	0.00448622
$754$	0	0
$755$	9.36932	0.340984
$756$	−3.56155	−0.129532
$757$	33.4233	1.21479	0.607395	−	0.794400i	$-0.292215\pi$
$757$	33.4233	1.21479	0.607395	+	0.794400i	$0.292215\pi$
$758$	−5.31534	−0.193062
$759$	−31.6847	−1.15008
$760$	3.56155	0.129191
$761$	−10.9309	−0.396244	−0.198122	−	0.980177i	$-0.563484\pi$
$761$	−10.9309	−0.396244	−0.198122	+	0.980177i	$0.563484\pi$
$762$	4.43845	0.160788
$763$	−72.1080	−2.61048
$764$	19.1231	0.691850
$765$	−5.12311	−0.185226
$766$	20.8078	0.751815
$767$	0	0
$768$	1.00000	0.0360844
$769$	45.6847	1.64743	0.823715	−	0.567003i	$-0.191897\pi$
$769$	45.6847	1.64743	0.823715	+	0.567003i	$0.191897\pi$
$770$	−14.6847	−0.529198
$771$	−1.43845	−0.0518044
$772$	0	0
$773$	21.1771	0.761687	0.380843	−	0.924640i	$-0.375634\pi$
$773$	21.1771	0.761687	0.380843	+	0.924640i	$0.375634\pi$
$774$	−4.56155	−0.163962
$775$	−5.68466	−0.204199
$776$	1.12311	0.0403171
$777$	14.6847	0.526809
$778$	−19.0540	−0.683118
$779$	15.1231	0.541841
$780$	0	0
$781$	20.1080	0.719519
$782$	39.3693	1.40784
$783$	6.56155	0.234491
$784$	5.68466	0.203024
$785$	−22.1231	−0.789607
$786$	−6.12311	−0.218404
$787$	−43.6847	−1.55719	−0.778595	−	0.627527i	$-0.784067\pi$
$787$	−43.6847	−1.55719	−0.778595	+	0.627527i	$0.784067\pi$
$788$	7.80776	0.278140
$789$	−13.0000	−0.462812
$790$	7.43845	0.264648
$791$	13.1231	0.466604
$792$	−4.12311	−0.146508
$793$	0	0
$794$	−11.8769	−0.421495
$795$	−4.43845	−0.157415
$796$	11.1231	0.394248
$797$	4.87689	0.172748	0.0863742	−	0.996263i	$-0.472472\pi$
$797$	4.87689	0.172748	0.0863742	+	0.996263i	$0.472472\pi$
$798$	12.6847	0.449032
$799$	−35.8617	−1.26870
$800$	−1.00000	−0.0353553
$801$	−1.80776	−0.0638742
$802$	12.6847	0.447911
$803$	63.3693	2.23625
$804$	−14.2462	−0.502425
$805$	−27.3693	−0.964642
$806$	0	0
$807$	−3.36932	−0.118606
$808$	17.1231	0.602389
$809$	18.4924	0.650159	0.325079	−	0.945687i	$-0.394609\pi$
$809$	18.4924	0.650159	0.325079	+	0.945687i	$0.394609\pi$
$810$	1.00000	0.0351364
$811$	22.5464	0.791711	0.395856	−	0.918313i	$-0.370448\pi$
$811$	22.5464	0.791711	0.395856	+	0.918313i	$0.370448\pi$
$812$	−23.3693	−0.820102
$813$	−32.1771	−1.12850
$814$	17.0000	0.595850
$815$	−18.5616	−0.650183
$816$	5.12311	0.179345
$817$	16.2462	0.568383
$818$	1.80776	0.0632070
$819$	0	0
$820$	−4.24621	−0.148284
$821$	12.5616	0.438401	0.219201	−	0.975680i	$-0.429655\pi$
$821$	12.5616	0.438401	0.219201	+	0.975680i	$0.429655\pi$
$822$	−8.80776	−0.307206
$823$	−32.0540	−1.11733	−0.558666	−	0.829393i	$-0.688687\pi$
$823$	−32.0540	−1.11733	−0.558666	+	0.829393i	$0.688687\pi$
$824$	−0.438447	−0.0152740
$825$	4.12311	0.143548
$826$	−37.6155	−1.30881
$827$	11.7538	0.408719	0.204360	−	0.978896i	$-0.434489\pi$
$827$	11.7538	0.408719	0.204360	+	0.978896i	$0.434489\pi$
$828$	−7.68466	−0.267060
$829$	53.6155	1.86214	0.931072	−	0.364835i	$-0.118875\pi$
$829$	53.6155	1.86214	0.931072	+	0.364835i	$0.118875\pi$
$830$	−1.12311	−0.0389836
$831$	−1.00000	−0.0346896
$832$	0	0
$833$	29.1231	1.00906
$834$	−8.43845	−0.292200
$835$	−20.3693	−0.704909
$836$	14.6847	0.507880
$837$	−5.68466	−0.196491
$838$	0.492423	0.0170105
$839$	12.7386	0.439786	0.219893	−	0.975524i	$-0.429429\pi$
$839$	12.7386	0.439786	0.219893	+	0.975524i	$0.429429\pi$
$840$	−3.56155	−0.122885
$841$	14.0540	0.484620
$842$	0.492423	0.0169700
$843$	0.246211	0.00847997
$844$	6.93087	0.238570
$845$	0	0
$846$	7.00000	0.240665
$847$	−21.3693	−0.734258
$848$	4.43845	0.152417
$849$	11.4384	0.392566
$850$	−5.12311	−0.175721
$851$	31.6847	1.08614
$852$	4.87689	0.167080
$853$	51.3002	1.75648	0.878242	−	0.478216i	$-0.158716\pi$
$853$	51.3002	1.75648	0.878242	+	0.478216i	$0.158716\pi$
$854$	21.3693	0.731243
$855$	−3.56155	−0.121803
$856$	−2.00000	−0.0683586
$857$	−26.8078	−0.915736	−0.457868	−	0.889020i	$-0.651387\pi$
$857$	−26.8078	−0.915736	−0.457868	+	0.889020i	$0.651387\pi$
$858$	0	0
$859$	−46.7926	−1.59654	−0.798272	−	0.602298i	$-0.794252\pi$
$859$	−46.7926	−1.59654	−0.798272	+	0.602298i	$0.794252\pi$
$860$	−4.56155	−0.155548
$861$	−15.1231	−0.515394
$862$	26.7386	0.910721
$863$	−6.56155	−0.223358	−0.111679	−	0.993744i	$-0.535623\pi$
$863$	−6.56155	−0.223358	−0.111679	+	0.993744i	$0.535623\pi$
$864$	−1.00000	−0.0340207
$865$	25.1771	0.856046
$866$	−30.7386	−1.04454
$867$	9.24621	0.314018
$868$	20.2462	0.687201
$869$	30.6695	1.04039
$870$	6.56155	0.222457
$871$	0	0
$872$	−20.2462	−0.685623
$873$	−1.12311	−0.0380114
$874$	27.3693	0.925781
$875$	3.56155	0.120402
$876$	15.3693	0.519281
$877$	−12.5616	−0.424173	−0.212087	−	0.977251i	$-0.568026\pi$
$877$	−12.5616	−0.424173	−0.212087	+	0.977251i	$0.568026\pi$
$878$	−16.8769	−0.569568
$879$	24.9309	0.840897
$880$	−4.12311	−0.138990
$881$	−20.4384	−0.688589	−0.344294	−	0.938862i	$-0.611882\pi$
$881$	−20.4384	−0.688589	−0.344294	+	0.938862i	$0.611882\pi$
$882$	−5.68466	−0.191412
$883$	26.1771	0.880929	0.440464	−	0.897770i	$-0.354814\pi$
$883$	26.1771	0.880929	0.440464	+	0.897770i	$0.354814\pi$
$884$	0	0
$885$	10.5616	0.355023
$886$	4.87689	0.163842
$887$	41.1080	1.38027	0.690135	−	0.723681i	$-0.257551\pi$
$887$	41.1080	1.38027	0.690135	+	0.723681i	$0.257551\pi$
$888$	4.12311	0.138362
$889$	15.8078	0.530175
$890$	−1.80776	−0.0605964
$891$	4.12311	0.138129
$892$	26.3002	0.880595
$893$	−24.9309	−0.834280
$894$	−22.8078	−0.762806
$895$	0.315342	0.0105407
$896$	3.56155	0.118983
$897$	0	0
$898$	25.1771	0.840170
$899$	−37.3002	−1.24403
$900$	1.00000	0.0333333
$901$	22.7386	0.757534
$902$	−17.5076	−0.582939
$903$	−16.2462	−0.540640
$904$	3.68466	0.122550
$905$	−11.1231	−0.369745
$906$	9.36932	0.311275
$907$	40.9157	1.35858	0.679292	−	0.733868i	$-0.262287\pi$
$907$	40.9157	1.35858	0.679292	+	0.733868i	$0.262287\pi$
$908$	20.0000	0.663723
$909$	−17.1231	−0.567938
$910$	0	0
$911$	−43.3693	−1.43689	−0.718445	−	0.695584i	$-0.755146\pi$
$911$	−43.3693	−1.43689	−0.718445	+	0.695584i	$0.755146\pi$
$912$	3.56155	0.117935
$913$	−4.63068	−0.153253
$914$	3.75379	0.124164
$915$	−6.00000	−0.198354
$916$	7.75379	0.256192
$917$	−21.8078	−0.720156
$918$	−5.12311	−0.169088
$919$	41.3693	1.36465	0.682324	−	0.731050i	$-0.260969\pi$
$919$	41.3693	1.36465	0.682324	+	0.731050i	$0.260969\pi$
$920$	−7.68466	−0.253356
$921$	15.6155	0.514549
$922$	7.05398	0.232310
$923$	0	0
$924$	−14.6847	−0.483090
$925$	−4.12311	−0.135567
$926$	33.6155	1.10467
$927$	0.438447	0.0144005
$928$	−6.56155	−0.215394
$929$	16.8769	0.553713	0.276856	−	0.960911i	$-0.410707\pi$
$929$	16.8769	0.553713	0.276856	+	0.960911i	$0.410707\pi$
$930$	−5.68466	−0.186407
$931$	20.2462	0.663543
$932$	−17.6847	−0.579280
$933$	−18.7386	−0.613475
$934$	−39.8617	−1.30432
$935$	−21.1231	−0.690799
$936$	0	0
$937$	−29.2311	−0.954937	−0.477468	−	0.878649i	$-0.658446\pi$
$937$	−29.2311	−0.954937	−0.477468	+	0.878649i	$0.658446\pi$
$938$	−50.7386	−1.65668
$939$	6.63068	0.216384
$940$	7.00000	0.228315
$941$	0.630683	0.0205597	0.0102798	−	0.999947i	$-0.496728\pi$
$941$	0.630683	0.0205597	0.0102798	+	0.999947i	$0.496728\pi$
$942$	−22.1231	−0.720810
$943$	−32.6307	−1.06260
$944$	−10.5616	−0.343749
$945$	3.56155	0.115857
$946$	−18.8078	−0.611493
$947$	−13.8617	−0.450446	−0.225223	−	0.974307i	$-0.572311\pi$
$947$	−13.8617	−0.450446	−0.225223	+	0.974307i	$0.572311\pi$
$948$	7.43845	0.241590
$949$	0	0
$950$	−3.56155	−0.115552
$951$	4.19224	0.135943
$952$	18.2462	0.591363
$953$	5.82292	0.188623	0.0943114	−	0.995543i	$-0.469935\pi$
$953$	5.82292	0.188623	0.0943114	+	0.995543i	$0.469935\pi$
$954$	−4.43845	−0.143700
$955$	−19.1231	−0.618809
$956$	−13.3693	−0.432395
$957$	27.0540	0.874531
$958$	−21.7538	−0.702833
$959$	−31.3693	−1.01297
$960$	−1.00000	−0.0322749
$961$	1.31534	0.0424304
$962$	0	0
$963$	2.00000	0.0644491
$964$	19.8769	0.640192
$965$	0	0
$966$	−27.3693	−0.880593
$967$	−3.31534	−0.106614	−0.0533071	−	0.998578i	$-0.516976\pi$
$967$	−3.31534	−0.106614	−0.0533071	+	0.998578i	$0.516976\pi$
$968$	−6.00000	−0.192847
$969$	18.2462	0.586153
$970$	−1.12311	−0.0360607
$971$	−16.6847	−0.535436	−0.267718	−	0.963497i	$-0.586270\pi$
$971$	−16.6847	−0.535436	−0.267718	+	0.963497i	$0.586270\pi$
$972$	1.00000	0.0320750
$973$	−30.0540	−0.963486
$974$	−24.0540	−0.770739
$975$	0	0
$976$	6.00000	0.192055
$977$	−5.30019	−0.169568	−0.0847840	−	0.996399i	$-0.527020\pi$
$977$	−5.30019	−0.169568	−0.0847840	+	0.996399i	$0.527020\pi$
$978$	−18.5616	−0.593533
$979$	−7.45360	−0.238218
$980$	−5.68466	−0.181590
$981$	20.2462	0.646412
$982$	21.5616	0.688057
$983$	−23.8769	−0.761555	−0.380777	−	0.924667i	$-0.624344\pi$
$983$	−23.8769	−0.761555	−0.380777	+	0.924667i	$0.624344\pi$
$984$	−4.24621	−0.135364
$985$	−7.80776	−0.248776
$986$	−33.6155	−1.07054
$987$	24.9309	0.793558
$988$	0	0
$989$	−35.0540	−1.11465
$990$	4.12311	0.131041
$991$	−12.4233	−0.394639	−0.197319	−	0.980339i	$-0.563224\pi$
$991$	−12.4233	−0.394639	−0.197319	+	0.980339i	$0.563224\pi$
$992$	5.68466	0.180488
$993$	18.7386	0.594653
$994$	17.3693	0.550921
$995$	−11.1231	−0.352626
$996$	−1.12311	−0.0355870
$997$	32.5464	1.03075	0.515377	−	0.856963i	$-0.327652\pi$
$997$	32.5464	1.03075	0.515377	+	0.856963i	$0.327652\pi$
$998$	4.00000	0.126618
$999$	−4.12311	−0.130449

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5070.2.a.bb.1.1		2
13.4	even	6		390.2.i.g.211.1	yes	4
13.5	odd	4		5070.2.b.r.1351.3		4
13.8	odd	4		5070.2.b.r.1351.2		4
13.10	even	6		390.2.i.g.61.1	✓	4
13.12	even	2		5070.2.a.bi.1.2		2
39.17	odd	6		1170.2.i.o.991.1		4
39.23	odd	6		1170.2.i.o.451.1		4
65.4	even	6		1950.2.i.bi.601.2		4
65.17	odd	12		1950.2.z.n.1849.3		8
65.23	odd	12		1950.2.z.n.1699.3		8
65.43	odd	12		1950.2.z.n.1849.2		8
65.49	even	6		1950.2.i.bi.451.2		4
65.62	odd	12		1950.2.z.n.1699.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.i.g.61.1	✓	4	13.10	even	6
390.2.i.g.211.1	yes	4	13.4	even	6
1170.2.i.o.451.1		4	39.23	odd	6
1170.2.i.o.991.1		4	39.17	odd	6
1950.2.i.bi.451.2		4	65.49	even	6
1950.2.i.bi.601.2		4	65.4	even	6
1950.2.z.n.1699.2		8	65.62	odd	12
1950.2.z.n.1699.3		8	65.23	odd	12
1950.2.z.n.1849.2		8	65.43	odd	12
1950.2.z.n.1849.3		8	65.17	odd	12
5070.2.a.bb.1.1		2	1.1	even	1	trivial
5070.2.a.bi.1.2		2	13.12	even	2
5070.2.b.r.1351.2		4	13.8	odd	4
5070.2.b.r.1351.3		4	13.5	odd	4

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:	\( N \)	\(=\)	\( 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5070.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -3.56155 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -3.56155 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +4.12311 q^{11} +1.00000 q^{12} +3.56155 q^{14} -1.00000 q^{15} +1.00000 q^{16} +5.12311 q^{17} -1.00000 q^{18} +3.56155 q^{19} -1.00000 q^{20} -3.56155 q^{21} -4.12311 q^{22} -7.68466 q^{23} -1.00000 q^{24} +1.00000 q^{25} +1.00000 q^{27} -3.56155 q^{28} +6.56155 q^{29} +1.00000 q^{30} -5.68466 q^{31} -1.00000 q^{32} +4.12311 q^{33} -5.12311 q^{34} +3.56155 q^{35} +1.00000 q^{36} -4.12311 q^{37} -3.56155 q^{38} +1.00000 q^{40} +4.24621 q^{41} +3.56155 q^{42} +4.56155 q^{43} +4.12311 q^{44} -1.00000 q^{45} +7.68466 q^{46} -7.00000 q^{47} +1.00000 q^{48} +5.68466 q^{49} -1.00000 q^{50} +5.12311 q^{51} +4.43845 q^{53} -1.00000 q^{54} -4.12311 q^{55} +3.56155 q^{56} +3.56155 q^{57} -6.56155 q^{58} -10.5616 q^{59} -1.00000 q^{60} +6.00000 q^{61} +5.68466 q^{62} -3.56155 q^{63} +1.00000 q^{64} -4.12311 q^{66} -14.2462 q^{67} +5.12311 q^{68} -7.68466 q^{69} -3.56155 q^{70} +4.87689 q^{71} -1.00000 q^{72} +15.3693 q^{73} +4.12311 q^{74} +1.00000 q^{75} +3.56155 q^{76} -14.6847 q^{77} +7.43845 q^{79} -1.00000 q^{80} +1.00000 q^{81} -4.24621 q^{82} -1.12311 q^{83} -3.56155 q^{84} -5.12311 q^{85} -4.56155 q^{86} +6.56155 q^{87} -4.12311 q^{88} -1.80776 q^{89} +1.00000 q^{90} -7.68466 q^{92} -5.68466 q^{93} +7.00000 q^{94} -3.56155 q^{95} -1.00000 q^{96} -1.12311 q^{97} -5.68466 q^{98} +4.12311 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - 3 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 - 3 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - 3 q^{7} - 2 q^{8} + 2 q^{9} + 2 q^{10} + 2 q^{12} + 3 q^{14} - 2 q^{15} + 2 q^{16} + 2 q^{17} - 2 q^{18} + 3 q^{19} - 2 q^{20} - 3 q^{21} - 3 q^{23} - 2 q^{24} + 2 q^{25} + 2 q^{27} - 3 q^{28} + 9 q^{29} + 2 q^{30} + q^{31} - 2 q^{32} - 2 q^{34} + 3 q^{35} + 2 q^{36} - 3 q^{38} + 2 q^{40} - 8 q^{41} + 3 q^{42} + 5 q^{43} - 2 q^{45} + 3 q^{46} - 14 q^{47} + 2 q^{48} - q^{49} - 2 q^{50} + 2 q^{51} + 13 q^{53} - 2 q^{54} + 3 q^{56} + 3 q^{57} - 9 q^{58} - 17 q^{59} - 2 q^{60} + 12 q^{61} - q^{62} - 3 q^{63} + 2 q^{64} - 12 q^{67} + 2 q^{68} - 3 q^{69} - 3 q^{70} + 18 q^{71} - 2 q^{72} + 6 q^{73} + 2 q^{75} + 3 q^{76} - 17 q^{77} + 19 q^{79} - 2 q^{80} + 2 q^{81} + 8 q^{82} + 6 q^{83} - 3 q^{84} - 2 q^{85} - 5 q^{86} + 9 q^{87} + 17 q^{89} + 2 q^{90} - 3 q^{92} + q^{93} + 14 q^{94} - 3 q^{95} - 2 q^{96} + 6 q^{97} + q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 - 3 * q^7 - 2 * q^8 + 2 * q^9 + 2 * q^10 + 2 * q^12 + 3 * q^14 - 2 * q^15 + 2 * q^16 + 2 * q^17 - 2 * q^18 + 3 * q^19 - 2 * q^20 - 3 * q^21 - 3 * q^23 - 2 * q^24 + 2 * q^25 + 2 * q^27 - 3 * q^28 + 9 * q^29 + 2 * q^30 + q^31 - 2 * q^32 - 2 * q^34 + 3 * q^35 + 2 * q^36 - 3 * q^38 + 2 * q^40 - 8 * q^41 + 3 * q^42 + 5 * q^43 - 2 * q^45 + 3 * q^46 - 14 * q^47 + 2 * q^48 - q^49 - 2 * q^50 + 2 * q^51 + 13 * q^53 - 2 * q^54 + 3 * q^56 + 3 * q^57 - 9 * q^58 - 17 * q^59 - 2 * q^60 + 12 * q^61 - q^62 - 3 * q^63 + 2 * q^64 - 12 * q^67 + 2 * q^68 - 3 * q^69 - 3 * q^70 + 18 * q^71 - 2 * q^72 + 6 * q^73 + 2 * q^75 + 3 * q^76 - 17 * q^77 + 19 * q^79 - 2 * q^80 + 2 * q^81 + 8 * q^82 + 6 * q^83 - 3 * q^84 - 2 * q^85 - 5 * q^86 + 9 * q^87 + 17 * q^89 + 2 * q^90 - 3 * q^92 + q^93 + 14 * q^94 - 3 * q^95 - 2 * q^96 + 6 * q^97 + q^98

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