LMFDB - Embedded newform 8670.2.a.cj.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8670,2,Mod(1,8670)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8670, 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("8670.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8670 = 2 \cdot 3 \cdot 5 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8670.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:	$69.2302985525$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.8.20417871872.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 12x^{6} - 8x^{5} + 38x^{4} + 40x^{3} - 20x^{2} - 24x + 2 $ x^8 - 12x^6 - 8x^5 + 38x^4 + 40x^3 - 20x^2 - 24x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 510)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.92677$ of defining polynomial
Character	$\chi$	$=$	8670.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -4.93134 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -4.93134 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +1.32869 q^{11} -1.00000 q^{12} -1.89404 q^{13} +4.93134 q^{14} +1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{18} +2.79135 q^{19} -1.00000 q^{20} +4.93134 q^{21} -1.32869 q^{22} -8.15133 q^{23} +1.00000 q^{24} +1.00000 q^{25} +1.89404 q^{26} -1.00000 q^{27} -4.93134 q^{28} +4.87244 q^{29} -1.00000 q^{30} -7.68100 q^{31} -1.00000 q^{32} -1.32869 q^{33} +4.93134 q^{35} +1.00000 q^{36} -7.69552 q^{37} -2.79135 q^{38} +1.89404 q^{39} +1.00000 q^{40} -1.44724 q^{41} -4.93134 q^{42} +2.60613 q^{43} +1.32869 q^{44} -1.00000 q^{45} +8.15133 q^{46} -9.27246 q^{47} -1.00000 q^{48} +17.3181 q^{49} -1.00000 q^{50} -1.89404 q^{52} -2.63814 q^{53} +1.00000 q^{54} -1.32869 q^{55} +4.93134 q^{56} -2.79135 q^{57} -4.87244 q^{58} -5.34546 q^{59} +1.00000 q^{60} +8.70880 q^{61} +7.68100 q^{62} -4.93134 q^{63} +1.00000 q^{64} +1.89404 q^{65} +1.32869 q^{66} -8.76374 q^{67} +8.15133 q^{69} -4.93134 q^{70} -12.7470 q^{71} -1.00000 q^{72} +8.44174 q^{73} +7.69552 q^{74} -1.00000 q^{75} +2.79135 q^{76} -6.55222 q^{77} -1.89404 q^{78} -6.31617 q^{79} -1.00000 q^{80} +1.00000 q^{81} +1.44724 q^{82} +10.4660 q^{83} +4.93134 q^{84} -2.60613 q^{86} -4.87244 q^{87} -1.32869 q^{88} -11.3043 q^{89} +1.00000 q^{90} +9.34018 q^{91} -8.15133 q^{92} +7.68100 q^{93} +9.27246 q^{94} -2.79135 q^{95} +1.00000 q^{96} -0.224146 q^{97} -17.3181 q^{98} +1.32869 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} - 8 q^{3} + 8 q^{4} - 8 q^{5} + 8 q^{6} - 8 q^{7} - 8 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 - 8 * q^5 + 8 * q^6 - 8 * q^7 - 8 * q^8 + 8 * q^9	$ 8 q - 8 q^{2} - 8 q^{3} + 8 q^{4} - 8 q^{5} + 8 q^{6} - 8 q^{7} - 8 q^{8} + 8 q^{9} + 8 q^{10} + 8 q^{11} - 8 q^{12} + 8 q^{14} + 8 q^{15} + 8 q^{16} - 8 q^{18} - 8 q^{20} + 8 q^{21} - 8 q^{22} + 8 q^{24} + 8 q^{25} - 8 q^{27} - 8 q^{28} + 8 q^{29} - 8 q^{30} - 8 q^{31} - 8 q^{32} - 8 q^{33} + 8 q^{35} + 8 q^{36} - 32 q^{37} + 8 q^{40} + 8 q^{41} - 8 q^{42} - 8 q^{43} + 8 q^{44} - 8 q^{45} - 8 q^{48} + 40 q^{49} - 8 q^{50} + 16 q^{53} + 8 q^{54} - 8 q^{55} + 8 q^{56} - 8 q^{58} + 32 q^{59} + 8 q^{60} - 8 q^{61} + 8 q^{62} - 8 q^{63} + 8 q^{64} + 8 q^{66} - 8 q^{67} - 8 q^{70} + 24 q^{71} - 8 q^{72} - 40 q^{73} + 32 q^{74} - 8 q^{75} + 16 q^{77} - 24 q^{79} - 8 q^{80} + 8 q^{81} - 8 q^{82} - 16 q^{83} + 8 q^{84} + 8 q^{86} - 8 q^{87} - 8 q^{88} + 48 q^{89} + 8 q^{90} - 24 q^{91} + 8 q^{93} + 8 q^{96} - 24 q^{97} - 40 q^{98} + 8 q^{99}+O(q^{100}) $ 8 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 - 8 * q^5 + 8 * q^6 - 8 * q^7 - 8 * q^8 + 8 * q^9 + 8 * q^10 + 8 * q^11 - 8 * q^12 + 8 * q^14 + 8 * q^15 + 8 * q^16 - 8 * q^18 - 8 * q^20 + 8 * q^21 - 8 * q^22 + 8 * q^24 + 8 * q^25 - 8 * q^27 - 8 * q^28 + 8 * q^29 - 8 * q^30 - 8 * q^31 - 8 * q^32 - 8 * q^33 + 8 * q^35 + 8 * q^36 - 32 * q^37 + 8 * q^40 + 8 * q^41 - 8 * q^42 - 8 * q^43 + 8 * q^44 - 8 * q^45 - 8 * q^48 + 40 * q^49 - 8 * q^50 + 16 * q^53 + 8 * q^54 - 8 * q^55 + 8 * q^56 - 8 * q^58 + 32 * q^59 + 8 * q^60 - 8 * q^61 + 8 * q^62 - 8 * q^63 + 8 * q^64 + 8 * q^66 - 8 * q^67 - 8 * q^70 + 24 * q^71 - 8 * q^72 - 40 * q^73 + 32 * q^74 - 8 * q^75 + 16 * q^77 - 24 * q^79 - 8 * q^80 + 8 * q^81 - 8 * q^82 - 16 * q^83 + 8 * q^84 + 8 * q^86 - 8 * q^87 - 8 * q^88 + 48 * q^89 + 8 * q^90 - 24 * q^91 + 8 * q^93 + 8 * q^96 - 24 * q^97 - 40 * q^98 + 8 * q^99

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
$7$	−4.93134	−1.86387	−0.931936	−	0.362624i	$-0.881881\pi$
$7$	−4.93134	−1.86387	−0.931936	+	0.362624i	$0.881881\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	1.32869	0.400615	0.200308	−	0.979733i	$-0.435806\pi$
$11$	1.32869	0.400615	0.200308	+	0.979733i	$0.435806\pi$
$12$	−1.00000	−0.288675
$13$	−1.89404	−0.525313	−0.262657	−	0.964889i	$-0.584599\pi$
$13$	−1.89404	−0.525313	−0.262657	+	0.964889i	$0.584599\pi$
$14$	4.93134	1.31796
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	0	0
$17$	0	0
$18$	−1.00000	−0.235702
$19$	2.79135	0.640379	0.320190	−	0.947353i	$-0.396253\pi$
$19$	2.79135	0.640379	0.320190	+	0.947353i	$0.396253\pi$
$20$	−1.00000	−0.223607
$21$	4.93134	1.07611
$22$	−1.32869	−0.283278
$23$	−8.15133	−1.69967	−0.849835	−	0.527050i	$-0.823298\pi$
$23$	−8.15133	−1.69967	−0.849835	+	0.527050i	$0.823298\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	1.89404	0.371453
$27$	−1.00000	−0.192450
$28$	−4.93134	−0.931936
$29$	4.87244	0.904790	0.452395	−	0.891818i	$-0.350570\pi$
$29$	4.87244	0.904790	0.452395	+	0.891818i	$0.350570\pi$
$30$	−1.00000	−0.182574
$31$	−7.68100	−1.37955	−0.689774	−	0.724025i	$-0.742290\pi$
$31$	−7.68100	−1.37955	−0.689774	+	0.724025i	$0.742290\pi$
$32$	−1.00000	−0.176777
$33$	−1.32869	−0.231295
$34$	0	0
$35$	4.93134	0.833549
$36$	1.00000	0.166667
$37$	−7.69552	−1.26514	−0.632568	−	0.774505i	$-0.717999\pi$
$37$	−7.69552	−1.26514	−0.632568	+	0.774505i	$0.717999\pi$
$38$	−2.79135	−0.452817
$39$	1.89404	0.303290
$40$	1.00000	0.158114
$41$	−1.44724	−0.226021	−0.113011	−	0.993594i	$-0.536049\pi$
$41$	−1.44724	−0.226021	−0.113011	+	0.993594i	$0.536049\pi$
$42$	−4.93134	−0.760922
$43$	2.60613	0.397431	0.198716	−	0.980057i	$-0.436323\pi$
$43$	2.60613	0.397431	0.198716	+	0.980057i	$0.436323\pi$
$44$	1.32869	0.200308
$45$	−1.00000	−0.149071
$46$	8.15133	1.20185
$47$	−9.27246	−1.35253	−0.676264	−	0.736659i	$-0.736402\pi$
$47$	−9.27246	−1.35253	−0.676264	+	0.736659i	$0.736402\pi$
$48$	−1.00000	−0.144338
$49$	17.3181	2.47402
$50$	−1.00000	−0.141421
$51$	0	0
$52$	−1.89404	−0.262657
$53$	−2.63814	−0.362376	−0.181188	−	0.983448i	$-0.557994\pi$
$53$	−2.63814	−0.362376	−0.181188	+	0.983448i	$0.557994\pi$
$54$	1.00000	0.136083
$55$	−1.32869	−0.179161
$56$	4.93134	0.658978
$57$	−2.79135	−0.369723
$58$	−4.87244	−0.639783
$59$	−5.34546	−0.695920	−0.347960	−	0.937509i	$-0.613125\pi$
$59$	−5.34546	−0.695920	−0.347960	+	0.937509i	$0.613125\pi$
$60$	1.00000	0.129099
$61$	8.70880	1.11505	0.557524	−	0.830161i	$-0.311752\pi$
$61$	8.70880	1.11505	0.557524	+	0.830161i	$0.311752\pi$
$62$	7.68100	0.975488
$63$	−4.93134	−0.621290
$64$	1.00000	0.125000
$65$	1.89404	0.234927
$66$	1.32869	0.163550
$67$	−8.76374	−1.07066	−0.535331	−	0.844643i	$-0.679813\pi$
$67$	−8.76374	−1.07066	−0.535331	+	0.844643i	$0.679813\pi$
$68$	0	0
$69$	8.15133	0.981304
$70$	−4.93134	−0.589408
$71$	−12.7470	−1.51279	−0.756395	−	0.654115i	$-0.773041\pi$
$71$	−12.7470	−1.51279	−0.756395	+	0.654115i	$0.773041\pi$
$72$	−1.00000	−0.117851
$73$	8.44174	0.988031	0.494015	−	0.869453i	$-0.335529\pi$
$73$	8.44174	0.988031	0.494015	+	0.869453i	$0.335529\pi$
$74$	7.69552	0.894586
$75$	−1.00000	−0.115470
$76$	2.79135	0.320190
$77$	−6.55222	−0.746695
$78$	−1.89404	−0.214458
$79$	−6.31617	−0.710624	−0.355312	−	0.934748i	$-0.615625\pi$
$79$	−6.31617	−0.710624	−0.355312	+	0.934748i	$0.615625\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	1.44724	0.159821
$83$	10.4660	1.14880	0.574398	−	0.818576i	$-0.305236\pi$
$83$	10.4660	1.14880	0.574398	+	0.818576i	$0.305236\pi$
$84$	4.93134	0.538053
$85$	0	0
$86$	−2.60613	−0.281026
$87$	−4.87244	−0.522381
$88$	−1.32869	−0.141639
$89$	−11.3043	−1.19826	−0.599128	−	0.800653i	$-0.704486\pi$
$89$	−11.3043	−1.19826	−0.599128	+	0.800653i	$0.704486\pi$
$90$	1.00000	0.105409
$91$	9.34018	0.979116
$92$	−8.15133	−0.849835
$93$	7.68100	0.796482
$94$	9.27246	0.956382
$95$	−2.79135	−0.286386
$96$	1.00000	0.102062
$97$	−0.224146	−0.0227586	−0.0113793	−	0.999935i	$-0.503622\pi$
$97$	−0.224146	−0.0227586	−0.0113793	+	0.999935i	$0.503622\pi$
$98$	−17.3181	−1.74939
$99$	1.32869	0.133538
$100$	1.00000	0.100000
$101$	1.47066	0.146336	0.0731680	−	0.997320i	$-0.476689\pi$
$101$	1.47066	0.146336	0.0731680	+	0.997320i	$0.476689\pi$
$102$	0	0
$103$	−10.7734	−1.06153	−0.530767	−	0.847518i	$-0.678096\pi$
$103$	−10.7734	−1.06153	−0.530767	+	0.847518i	$0.678096\pi$
$104$	1.89404	0.185726
$105$	−4.93134	−0.481249
$106$	2.63814	0.256238
$107$	−7.31058	−0.706741	−0.353370	−	0.935484i	$-0.614964\pi$
$107$	−7.31058	−0.706741	−0.353370	+	0.935484i	$0.614964\pi$
$108$	−1.00000	−0.0962250
$109$	−14.6697	−1.40510	−0.702552	−	0.711632i	$-0.747956\pi$
$109$	−14.6697	−1.40510	−0.702552	+	0.711632i	$0.747956\pi$
$110$	1.32869	0.126686
$111$	7.69552	0.730426
$112$	−4.93134	−0.465968
$113$	4.19452	0.394587	0.197294	−	0.980344i	$-0.436785\pi$
$113$	4.19452	0.394587	0.197294	+	0.980344i	$0.436785\pi$
$114$	2.79135	0.261434
$115$	8.15133	0.760115
$116$	4.87244	0.452395
$117$	−1.89404	−0.175104
$118$	5.34546	0.492090
$119$	0	0
$120$	−1.00000	−0.0912871
$121$	−9.23458	−0.839508
$122$	−8.70880	−0.788457
$123$	1.44724	0.130493
$124$	−7.68100	−0.689774
$125$	−1.00000	−0.0894427
$126$	4.93134	0.439319
$127$	12.5302	1.11187	0.555937	−	0.831225i	$-0.312360\pi$
$127$	12.5302	1.11187	0.555937	+	0.831225i	$0.312360\pi$
$128$	−1.00000	−0.0883883
$129$	−2.60613	−0.229457
$130$	−1.89404	−0.166119
$131$	−1.76934	−0.154588	−0.0772938	−	0.997008i	$-0.524628\pi$
$131$	−1.76934	−0.154588	−0.0772938	+	0.997008i	$0.524628\pi$
$132$	−1.32869	−0.115648
$133$	−13.7651	−1.19358
$134$	8.76374	0.757072
$135$	1.00000	0.0860663
$136$	0	0
$137$	−20.3147	−1.73560	−0.867802	−	0.496910i	$-0.834468\pi$
$137$	−20.3147	−1.73560	−0.867802	+	0.496910i	$0.834468\pi$
$138$	−8.15133	−0.693887
$139$	−8.86841	−0.752209	−0.376104	−	0.926577i	$-0.622737\pi$
$139$	−8.86841	−0.752209	−0.376104	+	0.926577i	$0.622737\pi$
$140$	4.93134	0.416774
$141$	9.27246	0.780882
$142$	12.7470	1.06970
$143$	−2.51660	−0.210448
$144$	1.00000	0.0833333
$145$	−4.87244	−0.404634
$146$	−8.44174	−0.698643
$147$	−17.3181	−1.42837
$148$	−7.69552	−0.632568
$149$	11.7197	0.960116	0.480058	−	0.877237i	$-0.340616\pi$
$149$	11.7197	0.960116	0.480058	+	0.877237i	$0.340616\pi$
$150$	1.00000	0.0816497
$151$	−10.7897	−0.878054	−0.439027	−	0.898474i	$-0.644677\pi$
$151$	−10.7897	−0.878054	−0.439027	+	0.898474i	$0.644677\pi$
$152$	−2.79135	−0.226408
$153$	0	0
$154$	6.55222	0.527993
$155$	7.68100	0.616953
$156$	1.89404	0.151645
$157$	1.36867	0.109232	0.0546160	−	0.998507i	$-0.482607\pi$
$157$	1.36867	0.109232	0.0546160	+	0.998507i	$0.482607\pi$
$158$	6.31617	0.502487
$159$	2.63814	0.209218
$160$	1.00000	0.0790569
$161$	40.1970	3.16796
$162$	−1.00000	−0.0785674
$163$	−23.3711	−1.83057	−0.915284	−	0.402810i	$-0.868033\pi$
$163$	−23.3711	−1.83057	−0.915284	+	0.402810i	$0.868033\pi$
$164$	−1.44724	−0.113011
$165$	1.32869	0.103438
$166$	−10.4660	−0.812322
$167$	5.64492	0.436817	0.218409	−	0.975857i	$-0.429913\pi$
$167$	5.64492	0.436817	0.218409	+	0.975857i	$0.429913\pi$
$168$	−4.93134	−0.380461
$169$	−9.41260	−0.724046
$170$	0	0
$171$	2.79135	0.213460
$172$	2.60613	0.198716
$173$	2.94823	0.224150	0.112075	−	0.993700i	$-0.464250\pi$
$173$	2.94823	0.224150	0.112075	+	0.993700i	$0.464250\pi$
$174$	4.87244	0.369379
$175$	−4.93134	−0.372774
$176$	1.32869	0.100154
$177$	5.34546	0.401789
$178$	11.3043	0.847295
$179$	19.0596	1.42458	0.712290	−	0.701885i	$-0.247658\pi$
$179$	19.0596	1.42458	0.712290	+	0.701885i	$0.247658\pi$
$180$	−1.00000	−0.0745356
$181$	−12.9755	−0.964461	−0.482230	−	0.876044i	$-0.660173\pi$
$181$	−12.9755	−0.964461	−0.482230	+	0.876044i	$0.660173\pi$
$182$	−9.34018	−0.692340
$183$	−8.70880	−0.643773
$184$	8.15133	0.600924
$185$	7.69552	0.565786
$186$	−7.68100	−0.563198
$187$	0	0
$188$	−9.27246	−0.676264
$189$	4.93134	0.358702
$190$	2.79135	0.202506
$191$	−14.5352	−1.05173	−0.525865	−	0.850568i	$-0.676258\pi$
$191$	−14.5352	−1.05173	−0.525865	+	0.850568i	$0.676258\pi$
$192$	−1.00000	−0.0721688
$193$	−8.83005	−0.635601	−0.317800	−	0.948158i	$-0.602944\pi$
$193$	−8.83005	−0.635601	−0.317800	+	0.948158i	$0.602944\pi$
$194$	0.224146	0.0160927
$195$	−1.89404	−0.135635
$196$	17.3181	1.23701
$197$	9.91812	0.706637	0.353318	−	0.935503i	$-0.385053\pi$
$197$	9.91812	0.706637	0.353318	+	0.935503i	$0.385053\pi$
$198$	−1.32869	−0.0944259
$199$	−21.4302	−1.51914	−0.759572	−	0.650423i	$-0.774592\pi$
$199$	−21.4302	−1.51914	−0.759572	+	0.650423i	$0.774592\pi$
$200$	−1.00000	−0.0707107
$201$	8.76374	0.618147
$202$	−1.47066	−0.103475
$203$	−24.0277	−1.68641
$204$	0	0
$205$	1.44724	0.101080
$206$	10.7734	0.750618
$207$	−8.15133	−0.566556
$208$	−1.89404	−0.131328
$209$	3.70884	0.256546
$210$	4.93134	0.340295
$211$	21.3583	1.47036	0.735182	−	0.677870i	$-0.237097\pi$
$211$	21.3583	1.47036	0.735182	+	0.677870i	$0.237097\pi$
$212$	−2.63814	−0.181188
$213$	12.7470	0.873410
$214$	7.31058	0.499741
$215$	−2.60613	−0.177737
$216$	1.00000	0.0680414
$217$	37.8776	2.57130
$218$	14.6697	0.993559
$219$	−8.44174	−0.570440
$220$	−1.32869	−0.0895803
$221$	0	0
$222$	−7.69552	−0.516489
$223$	15.2409	1.02061	0.510304	−	0.859994i	$-0.329533\pi$
$223$	15.2409	1.02061	0.510304	+	0.859994i	$0.329533\pi$
$224$	4.93134	0.329489
$225$	1.00000	0.0666667
$226$	−4.19452	−0.279015
$227$	−2.92118	−0.193886	−0.0969428	−	0.995290i	$-0.530906\pi$
$227$	−2.92118	−0.193886	−0.0969428	+	0.995290i	$0.530906\pi$
$228$	−2.79135	−0.184862
$229$	−26.3171	−1.73908	−0.869540	−	0.493862i	$-0.835585\pi$
$229$	−26.3171	−1.73908	−0.869540	+	0.493862i	$0.835585\pi$
$230$	−8.15133	−0.537483
$231$	6.55222	0.431105
$232$	−4.87244	−0.319892
$233$	23.5368	1.54194	0.770972	−	0.636869i	$-0.219771\pi$
$233$	23.5368	1.54194	0.770972	+	0.636869i	$0.219771\pi$
$234$	1.89404	0.123818
$235$	9.27246	0.604869
$236$	−5.34546	−0.347960
$237$	6.31617	0.410279
$238$	0	0
$239$	23.3112	1.50788	0.753938	−	0.656945i	$-0.228152\pi$
$239$	23.3112	1.50788	0.753938	+	0.656945i	$0.228152\pi$
$240$	1.00000	0.0645497
$241$	−14.2474	−0.917754	−0.458877	−	0.888500i	$-0.651748\pi$
$241$	−14.2474	−0.917754	−0.458877	+	0.888500i	$0.651748\pi$
$242$	9.23458	0.593621
$243$	−1.00000	−0.0641500
$244$	8.70880	0.557524
$245$	−17.3181	−1.10641
$246$	−1.44724	−0.0922727
$247$	−5.28694	−0.336400
$248$	7.68100	0.487744
$249$	−10.4660	−0.663258
$250$	1.00000	0.0632456
$251$	−0.439583	−0.0277462	−0.0138731	−	0.999904i	$-0.504416\pi$
$251$	−0.439583	−0.0277462	−0.0138731	+	0.999904i	$0.504416\pi$
$252$	−4.93134	−0.310645
$253$	−10.8306	−0.680913
$254$	−12.5302	−0.786213
$255$	0	0
$256$	1.00000	0.0625000
$257$	13.3887	0.835165	0.417582	−	0.908639i	$-0.362878\pi$
$257$	13.3887	0.835165	0.417582	+	0.908639i	$0.362878\pi$
$258$	2.60613	0.162251
$259$	37.9492	2.35805
$260$	1.89404	0.117464
$261$	4.87244	0.301597
$262$	1.76934	0.109310
$263$	20.7852	1.28167	0.640835	−	0.767679i	$-0.278588\pi$
$263$	20.7852	1.28167	0.640835	+	0.767679i	$0.278588\pi$
$264$	1.32869	0.0817752
$265$	2.63814	0.162059
$266$	13.7651	0.843992
$267$	11.3043	0.691814
$268$	−8.76374	−0.535331
$269$	14.9797	0.913328	0.456664	−	0.889639i	$-0.349044\pi$
$269$	14.9797	0.913328	0.456664	+	0.889639i	$0.349044\pi$
$270$	−1.00000	−0.0608581
$271$	−16.0733	−0.976383	−0.488192	−	0.872736i	$-0.662343\pi$
$271$	−16.0733	−0.976383	−0.488192	+	0.872736i	$0.662343\pi$
$272$	0	0
$273$	−9.34018	−0.565293
$274$	20.3147	1.22726
$275$	1.32869	0.0801230
$276$	8.15133	0.490652
$277$	24.0723	1.44637	0.723184	−	0.690656i	$-0.242678\pi$
$277$	24.0723	1.44637	0.723184	+	0.690656i	$0.242678\pi$
$278$	8.86841	0.531892
$279$	−7.68100	−0.459849
$280$	−4.93134	−0.294704
$281$	−24.0773	−1.43633	−0.718165	−	0.695873i	$-0.755018\pi$
$281$	−24.0773	−1.43633	−0.718165	+	0.695873i	$0.755018\pi$
$282$	−9.27246	−0.552167
$283$	13.1937	0.784282	0.392141	−	0.919905i	$-0.371735\pi$
$283$	13.1937	0.784282	0.392141	+	0.919905i	$0.371735\pi$
$284$	−12.7470	−0.756395
$285$	2.79135	0.165345
$286$	2.51660	0.148810
$287$	7.13684	0.421274
$288$	−1.00000	−0.0589256
$289$	0	0
$290$	4.87244	0.286120
$291$	0.224146	0.0131397
$292$	8.44174	0.494015
$293$	−17.6260	−1.02972	−0.514860	−	0.857274i	$-0.672156\pi$
$293$	−17.6260	−1.02972	−0.514860	+	0.857274i	$0.672156\pi$
$294$	17.3181	1.01001
$295$	5.34546	0.311225
$296$	7.69552	0.447293
$297$	−1.32869	−0.0770984
$298$	−11.7197	−0.678905
$299$	15.4390	0.892859
$300$	−1.00000	−0.0577350
$301$	−12.8517	−0.740761
$302$	10.7897	0.620878
$303$	−1.47066	−0.0844871
$304$	2.79135	0.160095
$305$	−8.70880	−0.498664
$306$	0	0
$307$	18.5418	1.05824	0.529118	−	0.848548i	$-0.322523\pi$
$307$	18.5418	1.05824	0.529118	+	0.848548i	$0.322523\pi$
$308$	−6.55222	−0.373348
$309$	10.7734	0.612877
$310$	−7.68100	−0.436251
$311$	−4.62634	−0.262336	−0.131168	−	0.991360i	$-0.541873\pi$
$311$	−4.62634	−0.262336	−0.131168	+	0.991360i	$0.541873\pi$
$312$	−1.89404	−0.107229
$313$	−5.84120	−0.330164	−0.165082	−	0.986280i	$-0.552789\pi$
$313$	−5.84120	−0.330164	−0.165082	+	0.986280i	$0.552789\pi$
$314$	−1.36867	−0.0772387
$315$	4.93134	0.277850
$316$	−6.31617	−0.355312
$317$	21.8811	1.22896	0.614482	−	0.788931i	$-0.289365\pi$
$317$	21.8811	1.22896	0.614482	+	0.788931i	$0.289365\pi$
$318$	−2.63814	−0.147939
$319$	6.47397	0.362473
$320$	−1.00000	−0.0559017
$321$	7.31058	0.408037
$322$	−40.1970	−2.24009
$323$	0	0
$324$	1.00000	0.0555556
$325$	−1.89404	−0.105063
$326$	23.3711	1.29441
$327$	14.6697	0.811238
$328$	1.44724	0.0799105
$329$	45.7257	2.52094
$330$	−1.32869	−0.0731420
$331$	26.2339	1.44195	0.720973	−	0.692964i	$-0.243695\pi$
$331$	26.2339	1.44195	0.720973	+	0.692964i	$0.243695\pi$
$332$	10.4660	0.574398
$333$	−7.69552	−0.421712
$334$	−5.64492	−0.308876
$335$	8.76374	0.478814
$336$	4.93134	0.269027
$337$	−1.25491	−0.0683592	−0.0341796	−	0.999416i	$-0.510882\pi$
$337$	−1.25491	−0.0683592	−0.0341796	+	0.999416i	$0.510882\pi$
$338$	9.41260	0.511978
$339$	−4.19452	−0.227815
$340$	0	0
$341$	−10.2057	−0.552668
$342$	−2.79135	−0.150939
$343$	−50.8821	−2.74738
$344$	−2.60613	−0.140513
$345$	−8.15133	−0.438853
$346$	−2.94823	−0.158498
$347$	18.1147	0.972450	0.486225	−	0.873834i	$-0.338374\pi$
$347$	18.1147	0.972450	0.486225	+	0.873834i	$0.338374\pi$
$348$	−4.87244	−0.261190
$349$	−12.3586	−0.661543	−0.330771	−	0.943711i	$-0.607309\pi$
$349$	−12.3586	−0.661543	−0.330771	+	0.943711i	$0.607309\pi$
$350$	4.93134	0.263591
$351$	1.89404	0.101097
$352$	−1.32869	−0.0708194
$353$	−0.614015	−0.0326807	−0.0163404	−	0.999866i	$-0.505202\pi$
$353$	−0.614015	−0.0326807	−0.0163404	+	0.999866i	$0.505202\pi$
$354$	−5.34546	−0.284108
$355$	12.7470	0.676540
$356$	−11.3043	−0.599128
$357$	0	0
$358$	−19.0596	−1.00733
$359$	−23.1409	−1.22133	−0.610664	−	0.791889i	$-0.709098\pi$
$359$	−23.1409	−1.22133	−0.610664	+	0.791889i	$0.709098\pi$
$360$	1.00000	0.0527046
$361$	−11.2084	−0.589914
$362$	12.9755	0.681977
$363$	9.23458	0.484690
$364$	9.34018	0.489558
$365$	−8.44174	−0.441861
$366$	8.70880	0.455216
$367$	−28.2056	−1.47232	−0.736160	−	0.676808i	$-0.763363\pi$
$367$	−28.2056	−1.47232	−0.736160	+	0.676808i	$0.763363\pi$
$368$	−8.15133	−0.424917
$369$	−1.44724	−0.0753404
$370$	−7.69552	−0.400071
$371$	13.0095	0.675422
$372$	7.68100	0.398241
$373$	17.4045	0.901173	0.450587	−	0.892733i	$-0.351215\pi$
$373$	17.4045	0.901173	0.450587	+	0.892733i	$0.351215\pi$
$374$	0	0
$375$	1.00000	0.0516398
$376$	9.27246	0.478191
$377$	−9.22862	−0.475298
$378$	−4.93134	−0.253641
$379$	30.2548	1.55408	0.777042	−	0.629448i	$-0.216719\pi$
$379$	30.2548	1.55408	0.777042	+	0.629448i	$0.216719\pi$
$380$	−2.79135	−0.143193
$381$	−12.5302	−0.641941
$382$	14.5352	0.743685
$383$	21.8149	1.11469	0.557345	−	0.830281i	$-0.311820\pi$
$383$	21.8149	1.11469	0.557345	+	0.830281i	$0.311820\pi$
$384$	1.00000	0.0510310
$385$	6.55222	0.333932
$386$	8.83005	0.449438
$387$	2.60613	0.132477
$388$	−0.224146	−0.0113793
$389$	13.2560	0.672106	0.336053	−	0.941843i	$-0.390908\pi$
$389$	13.2560	0.672106	0.336053	+	0.941843i	$0.390908\pi$
$390$	1.89404	0.0959086
$391$	0	0
$392$	−17.3181	−0.874697
$393$	1.76934	0.0892512
$394$	−9.91812	−0.499667
$395$	6.31617	0.317801
$396$	1.32869	0.0667692
$397$	2.72734	0.136881	0.0684406	−	0.997655i	$-0.478198\pi$
$397$	2.72734	0.136881	0.0684406	+	0.997655i	$0.478198\pi$
$398$	21.4302	1.07420
$399$	13.7651	0.689116
$400$	1.00000	0.0500000
$401$	−22.8351	−1.14033	−0.570166	−	0.821530i	$-0.693121\pi$
$401$	−22.8351	−1.14033	−0.570166	+	0.821530i	$0.693121\pi$
$402$	−8.76374	−0.437096
$403$	14.5481	0.724695
$404$	1.47066	0.0731680
$405$	−1.00000	−0.0496904
$406$	24.0277	1.19247
$407$	−10.2250	−0.506832
$408$	0	0
$409$	−13.6810	−0.676481	−0.338241	−	0.941060i	$-0.609832\pi$
$409$	−13.6810	−0.676481	−0.338241	+	0.941060i	$0.609832\pi$
$410$	−1.44724	−0.0714741
$411$	20.3147	1.00205
$412$	−10.7734	−0.530767
$413$	26.3603	1.29710
$414$	8.15133	0.400616
$415$	−10.4660	−0.513758
$416$	1.89404	0.0928632
$417$	8.86841	0.434288
$418$	−3.70884	−0.181405
$419$	24.2669	1.18552	0.592758	−	0.805380i	$-0.298039\pi$
$419$	24.2669	1.18552	0.592758	+	0.805380i	$0.298039\pi$
$420$	−4.93134	−0.240625
$421$	28.5394	1.39092	0.695462	−	0.718563i	$-0.255200\pi$
$421$	28.5394	1.39092	0.695462	+	0.718563i	$0.255200\pi$
$422$	−21.3583	−1.03970
$423$	−9.27246	−0.450843
$424$	2.63814	0.128119
$425$	0	0
$426$	−12.7470	−0.617594
$427$	−42.9460	−2.07830
$428$	−7.31058	−0.353370
$429$	2.51660	0.121502
$430$	2.60613	0.125679
$431$	−4.16955	−0.200840	−0.100420	−	0.994945i	$-0.532019\pi$
$431$	−4.16955	−0.200840	−0.100420	+	0.994945i	$0.532019\pi$
$432$	−1.00000	−0.0481125
$433$	−32.7958	−1.57607	−0.788034	−	0.615632i	$-0.788901\pi$
$433$	−32.7958	−1.57607	−0.788034	+	0.615632i	$0.788901\pi$
$434$	−37.8776	−1.81818
$435$	4.87244	0.233616
$436$	−14.6697	−0.702552
$437$	−22.7532	−1.08843
$438$	8.44174	0.403362
$439$	1.61438	0.0770503	0.0385252	−	0.999258i	$-0.487734\pi$
$439$	1.61438	0.0770503	0.0385252	+	0.999258i	$0.487734\pi$
$440$	1.32869	0.0633428
$441$	17.3181	0.824672
$442$	0	0
$443$	−23.7190	−1.12693	−0.563463	−	0.826142i	$-0.690531\pi$
$443$	−23.7190	−1.12693	−0.563463	+	0.826142i	$0.690531\pi$
$444$	7.69552	0.365213
$445$	11.3043	0.535877
$446$	−15.2409	−0.721679
$447$	−11.7197	−0.554323
$448$	−4.93134	−0.232984
$449$	7.02327	0.331449	0.165724	−	0.986172i	$-0.447004\pi$
$449$	7.02327	0.331449	0.165724	+	0.986172i	$0.447004\pi$
$450$	−1.00000	−0.0471405
$451$	−1.92293	−0.0905475
$452$	4.19452	0.197294
$453$	10.7897	0.506945
$454$	2.92118	0.137098
$455$	−9.34018	−0.437874
$456$	2.79135	0.130717
$457$	−4.81359	−0.225170	−0.112585	−	0.993642i	$-0.535913\pi$
$457$	−4.81359	−0.225170	−0.112585	+	0.993642i	$0.535913\pi$
$458$	26.3171	1.22972
$459$	0	0
$460$	8.15133	0.380058
$461$	18.5660	0.864705	0.432352	−	0.901705i	$-0.357684\pi$
$461$	18.5660	0.864705	0.432352	+	0.901705i	$0.357684\pi$
$462$	−6.55222	−0.304837
$463$	−6.17640	−0.287042	−0.143521	−	0.989647i	$-0.545842\pi$
$463$	−6.17640	−0.287042	−0.143521	+	0.989647i	$0.545842\pi$
$464$	4.87244	0.226198
$465$	−7.68100	−0.356198
$466$	−23.5368	−1.09032
$467$	39.1112	1.80985	0.904925	−	0.425571i	$-0.139927\pi$
$467$	39.1112	1.80985	0.904925	+	0.425571i	$0.139927\pi$
$468$	−1.89404	−0.0875522
$469$	43.2170	1.99557
$470$	−9.27246	−0.427707
$471$	−1.36867	−0.0630652
$472$	5.34546	0.246045
$473$	3.46274	0.159217
$474$	−6.31617	−0.290111
$475$	2.79135	0.128076
$476$	0	0
$477$	−2.63814	−0.120792
$478$	−23.3112	−1.06623
$479$	−18.2613	−0.834379	−0.417190	−	0.908819i	$-0.636985\pi$
$479$	−18.2613	−0.834379	−0.417190	+	0.908819i	$0.636985\pi$
$480$	−1.00000	−0.0456435
$481$	14.5757	0.664592
$482$	14.2474	0.648950
$483$	−40.1970	−1.82903
$484$	−9.23458	−0.419754
$485$	0.224146	0.0101779
$486$	1.00000	0.0453609
$487$	−4.83641	−0.219159	−0.109579	−	0.993978i	$-0.534950\pi$
$487$	−4.83641	−0.219159	−0.109579	+	0.993978i	$0.534950\pi$
$488$	−8.70880	−0.394229
$489$	23.3711	1.05688
$490$	17.3181	0.782353
$491$	−8.43164	−0.380514	−0.190257	−	0.981734i	$-0.560932\pi$
$491$	−8.43164	−0.380514	−0.190257	+	0.981734i	$0.560932\pi$
$492$	1.44724	0.0652467
$493$	0	0
$494$	5.28694	0.237871
$495$	−1.32869	−0.0597202
$496$	−7.68100	−0.344887
$497$	62.8598	2.81965
$498$	10.4660	0.468994
$499$	−8.49143	−0.380129	−0.190064	−	0.981772i	$-0.560870\pi$
$499$	−8.49143	−0.380129	−0.190064	+	0.981772i	$0.560870\pi$
$500$	−1.00000	−0.0447214
$501$	−5.64492	−0.252197
$502$	0.439583	0.0196195
$503$	−35.2796	−1.57304	−0.786519	−	0.617566i	$-0.788119\pi$
$503$	−35.2796	−1.57304	−0.786519	+	0.617566i	$0.788119\pi$
$504$	4.93134	0.219659
$505$	−1.47066	−0.0654434
$506$	10.8306	0.481478
$507$	9.41260	0.418028
$508$	12.5302	0.555937
$509$	26.9992	1.19672	0.598359	−	0.801228i	$-0.295820\pi$
$509$	26.9992	1.19672	0.598359	+	0.801228i	$0.295820\pi$
$510$	0	0
$511$	−41.6291	−1.84156
$512$	−1.00000	−0.0441942
$513$	−2.79135	−0.123241
$514$	−13.3887	−0.590551
$515$	10.7734	0.474732
$516$	−2.60613	−0.114729
$517$	−12.3202	−0.541843
$518$	−37.9492	−1.66739
$519$	−2.94823	−0.129413
$520$	−1.89404	−0.0830593
$521$	−3.39983	−0.148949	−0.0744746	−	0.997223i	$-0.523728\pi$
$521$	−3.39983	−0.148949	−0.0744746	+	0.997223i	$0.523728\pi$
$522$	−4.87244	−0.213261
$523$	23.2646	1.01729	0.508645	−	0.860977i	$-0.330147\pi$
$523$	23.2646	1.01729	0.508645	+	0.860977i	$0.330147\pi$
$524$	−1.76934	−0.0772938
$525$	4.93134	0.215221
$526$	−20.7852	−0.906277
$527$	0	0
$528$	−1.32869	−0.0578238
$529$	43.4441	1.88888
$530$	−2.63814	−0.114593
$531$	−5.34546	−0.231973
$532$	−13.7651	−0.596792
$533$	2.74114	0.118732
$534$	−11.3043	−0.489186
$535$	7.31058	0.316064
$536$	8.76374	0.378536
$537$	−19.0596	−0.822482
$538$	−14.9797	−0.645820
$539$	23.0104	0.991128
$540$	1.00000	0.0430331
$541$	31.1105	1.33754	0.668772	−	0.743468i	$-0.266820\pi$
$541$	31.1105	1.33754	0.668772	+	0.743468i	$0.266820\pi$
$542$	16.0733	0.690407
$543$	12.9755	0.556832
$544$	0	0
$545$	14.6697	0.628382
$546$	9.34018	0.399723
$547$	37.7351	1.61344	0.806718	−	0.590937i	$-0.201242\pi$
$547$	37.7351	1.61344	0.806718	+	0.590937i	$0.201242\pi$
$548$	−20.3147	−0.867802
$549$	8.70880	0.371682
$550$	−1.32869	−0.0566555
$551$	13.6007	0.579409
$552$	−8.15133	−0.346944
$553$	31.1472	1.32451
$554$	−24.0723	−1.02274
$555$	−7.69552	−0.326657
$556$	−8.86841	−0.376104
$557$	−16.2578	−0.688865	−0.344433	−	0.938811i	$-0.611929\pi$
$557$	−16.2578	−0.688865	−0.344433	+	0.938811i	$0.611929\pi$
$558$	7.68100	0.325163
$559$	−4.93613	−0.208776
$560$	4.93134	0.208387
$561$	0	0
$562$	24.0773	1.01564
$563$	−30.5751	−1.28858	−0.644292	−	0.764779i	$-0.722848\pi$
$563$	−30.5751	−1.28858	−0.644292	+	0.764779i	$0.722848\pi$
$564$	9.27246	0.390441
$565$	−4.19452	−0.176465
$566$	−13.1937	−0.554571
$567$	−4.93134	−0.207097
$568$	12.7470	0.534852
$569$	11.4269	0.479039	0.239519	−	0.970892i	$-0.423010\pi$
$569$	11.4269	0.479039	0.239519	+	0.970892i	$0.423010\pi$
$570$	−2.79135	−0.116917
$571$	1.61954	0.0677756	0.0338878	−	0.999426i	$-0.489211\pi$
$571$	1.61954	0.0677756	0.0338878	+	0.999426i	$0.489211\pi$
$572$	−2.51660	−0.105224
$573$	14.5352	0.607216
$574$	−7.13684	−0.297886
$575$	−8.15133	−0.339934
$576$	1.00000	0.0416667
$577$	34.9547	1.45518	0.727592	−	0.686010i	$-0.240639\pi$
$577$	34.9547	1.45518	0.727592	+	0.686010i	$0.240639\pi$
$578$	0	0
$579$	8.83005	0.366964
$580$	−4.87244	−0.202317
$581$	−51.6116	−2.14121
$582$	−0.224146	−0.00929114
$583$	−3.50527	−0.145173
$584$	−8.44174	−0.349322
$585$	1.89404	0.0783091
$586$	17.6260	0.728122
$587$	−1.76505	−0.0728513	−0.0364257	−	0.999336i	$-0.511597\pi$
$587$	−1.76505	−0.0728513	−0.0364257	+	0.999336i	$0.511597\pi$
$588$	−17.3181	−0.714187
$589$	−21.4403	−0.883434
$590$	−5.34546	−0.220069
$591$	−9.91812	−0.407977
$592$	−7.69552	−0.316284
$593$	30.4123	1.24888	0.624442	−	0.781071i	$-0.285326\pi$
$593$	30.4123	1.24888	0.624442	+	0.781071i	$0.285326\pi$
$594$	1.32869	0.0545168
$595$	0	0
$596$	11.7197	0.480058
$597$	21.4302	0.877078
$598$	−15.4390	−0.631347
$599$	33.7283	1.37810	0.689051	−	0.724713i	$-0.258028\pi$
$599$	33.7283	1.37810	0.689051	+	0.724713i	$0.258028\pi$
$600$	1.00000	0.0408248
$601$	−17.9643	−0.732781	−0.366390	−	0.930461i	$-0.619407\pi$
$601$	−17.9643	−0.732781	−0.366390	+	0.930461i	$0.619407\pi$
$602$	12.8517	0.523797
$603$	−8.76374	−0.356887
$604$	−10.7897	−0.439027
$605$	9.23458	0.375439
$606$	1.47066	0.0597414
$607$	−14.1184	−0.573046	−0.286523	−	0.958073i	$-0.592500\pi$
$607$	−14.1184	−0.573046	−0.286523	+	0.958073i	$0.592500\pi$
$608$	−2.79135	−0.113204
$609$	24.0277	0.973651
$610$	8.70880	0.352609
$611$	17.5625	0.710501
$612$	0	0
$613$	−21.2784	−0.859428	−0.429714	−	0.902965i	$-0.641386\pi$
$613$	−21.2784	−0.859428	−0.429714	+	0.902965i	$0.641386\pi$
$614$	−18.5418	−0.748286
$615$	−1.44724	−0.0583584
$616$	6.55222	0.263997
$617$	42.4038	1.70711	0.853556	−	0.521001i	$-0.174441\pi$
$617$	42.4038	1.70711	0.853556	+	0.521001i	$0.174441\pi$
$618$	−10.7734	−0.433369
$619$	−37.3978	−1.50314	−0.751572	−	0.659651i	$-0.770704\pi$
$619$	−37.3978	−1.50314	−0.751572	+	0.659651i	$0.770704\pi$
$620$	7.68100	0.308476
$621$	8.15133	0.327101
$622$	4.62634	0.185499
$623$	55.7455	2.23340
$624$	1.89404	0.0758224
$625$	1.00000	0.0400000
$626$	5.84120	0.233461
$627$	−3.70884	−0.148117
$628$	1.36867	0.0546160
$629$	0	0
$630$	−4.93134	−0.196469
$631$	−7.40376	−0.294739	−0.147370	−	0.989082i	$-0.547081\pi$
$631$	−7.40376	−0.294739	−0.147370	+	0.989082i	$0.547081\pi$
$632$	6.31617	0.251244
$633$	−21.3583	−0.848915
$634$	−21.8811	−0.869009
$635$	−12.5302	−0.497245
$636$	2.63814	0.104609
$637$	−32.8013	−1.29963
$638$	−6.47397	−0.256307
$639$	−12.7470	−0.504263
$640$	1.00000	0.0395285
$641$	23.6370	0.933604	0.466802	−	0.884362i	$-0.345406\pi$
$641$	23.6370	0.933604	0.466802	+	0.884362i	$0.345406\pi$
$642$	−7.31058	−0.288526
$643$	−38.3173	−1.51109	−0.755543	−	0.655099i	$-0.772627\pi$
$643$	−38.3173	−1.51109	−0.755543	+	0.655099i	$0.772627\pi$
$644$	40.1970	1.58398
$645$	2.60613	0.102616
$646$	0	0
$647$	−9.13227	−0.359026	−0.179513	−	0.983756i	$-0.557452\pi$
$647$	−9.13227	−0.359026	−0.179513	+	0.983756i	$0.557452\pi$
$648$	−1.00000	−0.0392837
$649$	−7.10246	−0.278796
$650$	1.89404	0.0742905
$651$	−37.8776	−1.48454
$652$	−23.3711	−0.915284
$653$	−29.0909	−1.13841	−0.569207	−	0.822195i	$-0.692750\pi$
$653$	−29.0909	−1.13841	−0.569207	+	0.822195i	$0.692750\pi$
$654$	−14.6697	−0.573632
$655$	1.76934	0.0691337
$656$	−1.44724	−0.0565053
$657$	8.44174	0.329344
$658$	−45.7257	−1.78257
$659$	−18.8829	−0.735575	−0.367787	−	0.929910i	$-0.619885\pi$
$659$	−18.8829	−0.735575	−0.367787	+	0.929910i	$0.619885\pi$
$660$	1.32869	0.0517192
$661$	−3.56052	−0.138488	−0.0692441	−	0.997600i	$-0.522059\pi$
$661$	−3.56052	−0.138488	−0.0692441	+	0.997600i	$0.522059\pi$
$662$	−26.2339	−1.01961
$663$	0	0
$664$	−10.4660	−0.406161
$665$	13.7651	0.533787
$666$	7.69552	0.298195
$667$	−39.7169	−1.53784
$668$	5.64492	0.218409
$669$	−15.2409	−0.589248
$670$	−8.76374	−0.338573
$671$	11.5713	0.446705
$672$	−4.93134	−0.190231
$673$	−3.79811	−0.146406	−0.0732032	−	0.997317i	$-0.523322\pi$
$673$	−3.79811	−0.146406	−0.0732032	+	0.997317i	$0.523322\pi$
$674$	1.25491	0.0483373
$675$	−1.00000	−0.0384900
$676$	−9.41260	−0.362023
$677$	6.66867	0.256298	0.128149	−	0.991755i	$-0.459096\pi$
$677$	6.66867	0.256298	0.128149	+	0.991755i	$0.459096\pi$
$678$	4.19452	0.161090
$679$	1.10534	0.0424190
$680$	0	0
$681$	2.92118	0.111940
$682$	10.2057	0.390795
$683$	−10.1533	−0.388505	−0.194252	−	0.980952i	$-0.562228\pi$
$683$	−10.1533	−0.388505	−0.194252	+	0.980952i	$0.562228\pi$
$684$	2.79135	0.106730
$685$	20.3147	0.776186
$686$	50.8821	1.94269
$687$	26.3171	1.00406
$688$	2.60613	0.0993579
$689$	4.99675	0.190361
$690$	8.15133	0.310316
$691$	13.1495	0.500232	0.250116	−	0.968216i	$-0.419531\pi$
$691$	13.1495	0.500232	0.250116	+	0.968216i	$0.419531\pi$
$692$	2.94823	0.112075
$693$	−6.55222	−0.248898
$694$	−18.1147	−0.687626
$695$	8.86841	0.336398
$696$	4.87244	0.184690
$697$	0	0
$698$	12.3586	0.467781
$699$	−23.5368	−0.890242
$700$	−4.93134	−0.186387
$701$	14.6027	0.551537	0.275768	−	0.961224i	$-0.411068\pi$
$701$	14.6027	0.551537	0.275768	+	0.961224i	$0.411068\pi$
$702$	−1.89404	−0.0714861
$703$	−21.4809	−0.810167
$704$	1.32869	0.0500769
$705$	−9.27246	−0.349221
$706$	0.614015	0.0231088
$707$	−7.25231	−0.272751
$708$	5.34546	0.200895
$709$	33.2497	1.24872	0.624359	−	0.781137i	$-0.285360\pi$
$709$	33.2497	1.24872	0.624359	+	0.781137i	$0.285360\pi$
$710$	−12.7470	−0.478386
$711$	−6.31617	−0.236875
$712$	11.3043	0.423648
$713$	62.6103	2.34478
$714$	0	0
$715$	2.51660	0.0941154
$716$	19.0596	0.712290
$717$	−23.3112	−0.870573
$718$	23.1409	0.863610
$719$	35.7139	1.33190	0.665951	−	0.745995i	$-0.268026\pi$
$719$	35.7139	1.33190	0.665951	+	0.745995i	$0.268026\pi$
$720$	−1.00000	−0.0372678
$721$	53.1273	1.97856
$722$	11.2084	0.417132
$723$	14.2474	0.529865
$724$	−12.9755	−0.482230
$725$	4.87244	0.180958
$726$	−9.23458	−0.342728
$727$	28.4381	1.05471	0.527355	−	0.849645i	$-0.323184\pi$
$727$	28.4381	1.05471	0.527355	+	0.849645i	$0.323184\pi$
$728$	−9.34018	−0.346170
$729$	1.00000	0.0370370
$730$	8.44174	0.312443
$731$	0	0
$732$	−8.70880	−0.321886
$733$	16.8091	0.620859	0.310429	−	0.950596i	$-0.399527\pi$
$733$	16.8091	0.620859	0.310429	+	0.950596i	$0.399527\pi$
$734$	28.2056	1.04109
$735$	17.3181	0.638788
$736$	8.15133	0.300462
$737$	−11.6443	−0.428923
$738$	1.44724	0.0532737
$739$	−19.7802	−0.727626	−0.363813	−	0.931472i	$-0.618525\pi$
$739$	−19.7802	−0.727626	−0.363813	+	0.931472i	$0.618525\pi$
$740$	7.69552	0.282893
$741$	5.28694	0.194221
$742$	−13.0095	−0.477595
$743$	−2.74307	−0.100633	−0.0503167	−	0.998733i	$-0.516023\pi$
$743$	−2.74307	−0.100633	−0.0503167	+	0.998733i	$0.516023\pi$
$744$	−7.68100	−0.281599
$745$	−11.7197	−0.429377
$746$	−17.4045	−0.637226
$747$	10.4660	0.382932
$748$	0	0
$749$	36.0510	1.31727
$750$	−1.00000	−0.0365148
$751$	−8.70754	−0.317743	−0.158871	−	0.987299i	$-0.550785\pi$
$751$	−8.70754	−0.317743	−0.158871	+	0.987299i	$0.550785\pi$
$752$	−9.27246	−0.338132
$753$	0.439583	0.0160193
$754$	9.22862	0.336087
$755$	10.7897	0.392678
$756$	4.93134	0.179351
$757$	−23.5143	−0.854641	−0.427320	−	0.904100i	$-0.640542\pi$
$757$	−23.5143	−0.854641	−0.427320	+	0.904100i	$0.640542\pi$
$758$	−30.2548	−1.09890
$759$	10.8306	0.393125
$760$	2.79135	0.101253
$761$	3.30068	0.119649	0.0598247	−	0.998209i	$-0.480946\pi$
$761$	3.30068	0.119649	0.0598247	+	0.998209i	$0.480946\pi$
$762$	12.5302	0.453920
$763$	72.3414	2.61893
$764$	−14.5352	−0.525865
$765$	0	0
$766$	−21.8149	−0.788205
$767$	10.1245	0.365576
$768$	−1.00000	−0.0360844
$769$	−10.4541	−0.376986	−0.188493	−	0.982075i	$-0.560360\pi$
$769$	−10.4541	−0.376986	−0.188493	+	0.982075i	$0.560360\pi$
$770$	−6.55222	−0.236126
$771$	−13.3887	−0.482183
$772$	−8.83005	−0.317800
$773$	24.0109	0.863613	0.431807	−	0.901966i	$-0.357876\pi$
$773$	24.0109	0.863613	0.431807	+	0.901966i	$0.357876\pi$
$774$	−2.60613	−0.0936755
$775$	−7.68100	−0.275910
$776$	0.224146	0.00804637
$777$	−37.9492	−1.36142
$778$	−13.2560	−0.475251
$779$	−4.03975	−0.144739
$780$	−1.89404	−0.0678177
$781$	−16.9368	−0.606046
$782$	0	0
$783$	−4.87244	−0.174127
$784$	17.3181	0.618504
$785$	−1.36867	−0.0488501
$786$	−1.76934	−0.0631102
$787$	38.2587	1.36377	0.681887	−	0.731458i	$-0.261160\pi$
$787$	38.2587	1.36377	0.681887	+	0.731458i	$0.261160\pi$
$788$	9.91812	0.353318
$789$	−20.7852	−0.739972
$790$	−6.31617	−0.224719
$791$	−20.6846	−0.735460
$792$	−1.32869	−0.0472129
$793$	−16.4948	−0.585749
$794$	−2.72734	−0.0967897
$795$	−2.63814	−0.0935651
$796$	−21.4302	−0.759572
$797$	1.65715	0.0586993	0.0293496	−	0.999569i	$-0.490656\pi$
$797$	1.65715	0.0586993	0.0293496	+	0.999569i	$0.490656\pi$
$798$	−13.7651	−0.487279
$799$	0	0
$800$	−1.00000	−0.0353553
$801$	−11.3043	−0.399419
$802$	22.8351	0.806336
$803$	11.2165	0.395820
$804$	8.76374	0.309073
$805$	−40.1970	−1.41676
$806$	−14.5481	−0.512437
$807$	−14.9797	−0.527310
$808$	−1.47066	−0.0517376
$809$	2.12785	0.0748111	0.0374056	−	0.999300i	$-0.488091\pi$
$809$	2.12785	0.0748111	0.0374056	+	0.999300i	$0.488091\pi$
$810$	1.00000	0.0351364
$811$	−0.973128	−0.0341712	−0.0170856	−	0.999854i	$-0.505439\pi$
$811$	−0.973128	−0.0341712	−0.0170856	+	0.999854i	$0.505439\pi$
$812$	−24.0277	−0.843206
$813$	16.0733	0.563715
$814$	10.2250	0.358385
$815$	23.3711	0.818655
$816$	0	0
$817$	7.27462	0.254507
$818$	13.6810	0.478344
$819$	9.34018	0.326372
$820$	1.44724	0.0505399
$821$	−7.30416	−0.254917	−0.127459	−	0.991844i	$-0.540682\pi$
$821$	−7.30416	−0.254917	−0.127459	+	0.991844i	$0.540682\pi$
$822$	−20.3147	−0.708558
$823$	−45.3496	−1.58079	−0.790393	−	0.612600i	$-0.790124\pi$
$823$	−45.3496	−1.58079	−0.790393	+	0.612600i	$0.790124\pi$
$824$	10.7734	0.375309
$825$	−1.32869	−0.0462590
$826$	−26.3603	−0.917192
$827$	43.0898	1.49838	0.749190	−	0.662355i	$-0.230443\pi$
$827$	43.0898	1.49838	0.749190	+	0.662355i	$0.230443\pi$
$828$	−8.15133	−0.283278
$829$	−14.4564	−0.502092	−0.251046	−	0.967975i	$-0.580775\pi$
$829$	−14.4564	−0.502092	−0.251046	+	0.967975i	$0.580775\pi$
$830$	10.4660	0.363281
$831$	−24.0723	−0.835061
$832$	−1.89404	−0.0656642
$833$	0	0
$834$	−8.86841	−0.307088
$835$	−5.64492	−0.195351
$836$	3.70884	0.128273
$837$	7.68100	0.265494
$838$	−24.2669	−0.838287
$839$	39.6347	1.36834	0.684171	−	0.729321i	$-0.260164\pi$
$839$	39.6347	1.36834	0.684171	+	0.729321i	$0.260164\pi$
$840$	4.93134	0.170147
$841$	−5.25929	−0.181355
$842$	−28.5394	−0.983531
$843$	24.0773	0.829266
$844$	21.3583	0.735182
$845$	9.41260	0.323803
$846$	9.27246	0.318794
$847$	45.5389	1.56473
$848$	−2.63814	−0.0905940
$849$	−13.1937	−0.452805
$850$	0	0
$851$	62.7287	2.15031
$852$	12.7470	0.436705
$853$	15.5727	0.533197	0.266599	−	0.963808i	$-0.414100\pi$
$853$	15.5727	0.533197	0.266599	+	0.963808i	$0.414100\pi$
$854$	42.9460	1.46958
$855$	−2.79135	−0.0954621
$856$	7.31058	0.249871
$857$	27.1129	0.926159	0.463080	−	0.886317i	$-0.346744\pi$
$857$	27.1129	0.926159	0.463080	+	0.886317i	$0.346744\pi$
$858$	−2.51660	−0.0859152
$859$	−48.0534	−1.63956	−0.819781	−	0.572678i	$-0.805905\pi$
$859$	−48.0534	−1.63956	−0.819781	+	0.572678i	$0.805905\pi$
$860$	−2.60613	−0.0888684
$861$	−7.13684	−0.243223
$862$	4.16955	0.142016
$863$	−11.4851	−0.390959	−0.195479	−	0.980708i	$-0.562626\pi$
$863$	−11.4851	−0.390959	−0.195479	+	0.980708i	$0.562626\pi$
$864$	1.00000	0.0340207
$865$	−2.94823	−0.100243
$866$	32.7958	1.11445
$867$	0	0
$868$	37.8776	1.28565
$869$	−8.39223	−0.284687
$870$	−4.87244	−0.165191
$871$	16.5989	0.562433
$872$	14.6697	0.496780
$873$	−0.224146	−0.00758619
$874$	22.7532	0.769638
$875$	4.93134	0.166710
$876$	−8.44174	−0.285220
$877$	−9.37236	−0.316482	−0.158241	−	0.987401i	$-0.550582\pi$
$877$	−9.37236	−0.316482	−0.158241	+	0.987401i	$0.550582\pi$
$878$	−1.61438	−0.0544828
$879$	17.6260	0.594509
$880$	−1.32869	−0.0447901
$881$	3.38434	0.114021	0.0570106	−	0.998374i	$-0.481843\pi$
$881$	3.38434	0.114021	0.0570106	+	0.998374i	$0.481843\pi$
$882$	−17.3181	−0.583131
$883$	15.0218	0.505525	0.252762	−	0.967528i	$-0.418661\pi$
$883$	15.0218	0.505525	0.252762	+	0.967528i	$0.418661\pi$
$884$	0	0
$885$	−5.34546	−0.179686
$886$	23.7190	0.796856
$887$	−10.2286	−0.343444	−0.171722	−	0.985145i	$-0.554933\pi$
$887$	−10.2286	−0.343444	−0.171722	+	0.985145i	$0.554933\pi$
$888$	−7.69552	−0.258245
$889$	−61.7906	−2.07239
$890$	−11.3043	−0.378922
$891$	1.32869	0.0445128
$892$	15.2409	0.510304
$893$	−25.8827	−0.866131
$894$	11.7197	0.391966
$895$	−19.0596	−0.637092
$896$	4.93134	0.164745
$897$	−15.4390	−0.515492
$898$	−7.02327	−0.234370
$899$	−37.4252	−1.24820
$900$	1.00000	0.0333333
$901$	0	0
$902$	1.92293	0.0640267
$903$	12.8517	0.427679
$904$	−4.19452	−0.139508
$905$	12.9755	0.431320
$906$	−10.7897	−0.358464
$907$	15.8960	0.527817	0.263909	−	0.964548i	$-0.414988\pi$
$907$	15.8960	0.527817	0.263909	+	0.964548i	$0.414988\pi$
$908$	−2.92118	−0.0969428
$909$	1.47066	0.0487786
$910$	9.34018	0.309624
$911$	33.7302	1.11753	0.558766	−	0.829325i	$-0.311275\pi$
$911$	33.7302	1.11753	0.558766	+	0.829325i	$0.311275\pi$
$912$	−2.79135	−0.0924308
$913$	13.9061	0.460225
$914$	4.81359	0.159219
$915$	8.70880	0.287904
$916$	−26.3171	−0.869540
$917$	8.72520	0.288132
$918$	0	0
$919$	−55.8801	−1.84331	−0.921657	−	0.388006i	$-0.873164\pi$
$919$	−55.8801	−1.84331	−0.921657	+	0.388006i	$0.873164\pi$
$920$	−8.15133	−0.268741
$921$	−18.5418	−0.610973
$922$	−18.5660	−0.611439
$923$	24.1434	0.794689
$924$	6.55222	0.215552
$925$	−7.69552	−0.253027
$926$	6.17640	0.202969
$927$	−10.7734	−0.353845
$928$	−4.87244	−0.159946
$929$	−6.78894	−0.222738	−0.111369	−	0.993779i	$-0.535524\pi$
$929$	−6.78894	−0.222738	−0.111369	+	0.993779i	$0.535524\pi$
$930$	7.68100	0.251870
$931$	48.3409	1.58431
$932$	23.5368	0.770972
$933$	4.62634	0.151460
$934$	−39.1112	−1.27976
$935$	0	0
$936$	1.89404	0.0619088
$937$	−33.2143	−1.08506	−0.542532	−	0.840035i	$-0.682534\pi$
$937$	−33.2143	−1.08506	−0.542532	+	0.840035i	$0.682534\pi$
$938$	−43.2170	−1.41108
$939$	5.84120	0.190621
$940$	9.27246	0.302434
$941$	55.6185	1.81311	0.906556	−	0.422086i	$-0.138702\pi$
$941$	55.6185	1.81311	0.906556	+	0.422086i	$0.138702\pi$
$942$	1.36867	0.0445938
$943$	11.7969	0.384161
$944$	−5.34546	−0.173980
$945$	−4.93134	−0.160416
$946$	−3.46274	−0.112583
$947$	29.9065	0.971832	0.485916	−	0.874006i	$-0.338486\pi$
$947$	29.9065	0.971832	0.485916	+	0.874006i	$0.338486\pi$
$948$	6.31617	0.205140
$949$	−15.9890	−0.519026
$950$	−2.79135	−0.0905633
$951$	−21.8811	−0.709543
$952$	0	0
$953$	54.5344	1.76654	0.883272	−	0.468861i	$-0.155335\pi$
$953$	54.5344	1.76654	0.883272	+	0.468861i	$0.155335\pi$
$954$	2.63814	0.0854128
$955$	14.5352	0.470348
$956$	23.3112	0.753938
$957$	−6.47397	−0.209274
$958$	18.2613	0.589995
$959$	100.179	3.23494
$960$	1.00000	0.0322749
$961$	27.9977	0.903153
$962$	−14.5757	−0.469938
$963$	−7.31058	−0.235580
$964$	−14.2474	−0.458877
$965$	8.83005	0.284249
$966$	40.1970	1.29332
$967$	12.0874	0.388704	0.194352	−	0.980932i	$-0.437740\pi$
$967$	12.0874	0.388704	0.194352	+	0.980932i	$0.437740\pi$
$968$	9.23458	0.296811
$969$	0	0
$970$	−0.224146	−0.00719689
$971$	0.877636	0.0281647	0.0140823	−	0.999901i	$-0.495517\pi$
$971$	0.877636	0.0281647	0.0140823	+	0.999901i	$0.495517\pi$
$972$	−1.00000	−0.0320750
$973$	43.7331	1.40202
$974$	4.83641	0.154969
$975$	1.89404	0.0606580
$976$	8.70880	0.278762
$977$	−23.7530	−0.759926	−0.379963	−	0.925002i	$-0.624063\pi$
$977$	−23.7530	−0.759926	−0.379963	+	0.925002i	$0.624063\pi$
$978$	−23.3711	−0.747326
$979$	−15.0199	−0.480040
$980$	−17.3181	−0.553207
$981$	−14.6697	−0.468368
$982$	8.43164	0.269064
$983$	−46.8979	−1.49581	−0.747905	−	0.663805i	$-0.768940\pi$
$983$	−46.8979	−1.49581	−0.747905	+	0.663805i	$0.768940\pi$
$984$	−1.44724	−0.0461364
$985$	−9.91812	−0.316017
$986$	0	0
$987$	−45.7257	−1.45546
$988$	−5.28694	−0.168200
$989$	−21.2434	−0.675502
$990$	1.32869	0.0422285
$991$	−40.1550	−1.27557	−0.637783	−	0.770216i	$-0.720148\pi$
$991$	−40.1550	−1.27557	−0.637783	+	0.770216i	$0.720148\pi$
$992$	7.68100	0.243872
$993$	−26.2339	−0.832507
$994$	−62.8598	−1.99379
$995$	21.4302	0.679382
$996$	−10.4660	−0.331629
$997$	55.5257	1.75852	0.879259	−	0.476345i	$-0.158039\pi$
$997$	55.5257	1.75852	0.879259	+	0.476345i	$0.158039\pi$
$998$	8.49143	0.268792
$999$	7.69552	0.243475

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8670.2.a.cj.1.1		8
17.11	odd	16		510.2.u.c.121.3	✓	16
17.14	odd	16		510.2.u.c.451.3	yes	16
17.16	even	2		8670.2.a.ck.1.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
510.2.u.c.121.3	✓	16	17.11	odd	16
510.2.u.c.451.3	yes	16	17.14	odd	16
8670.2.a.cj.1.1		8	1.1	even	1	trivial
8670.2.a.ck.1.8		8	17.16	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8670 = 2 \cdot 3 \cdot 5 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8670.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -4.93134 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -4.93134 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +1.32869 q^{11} -1.00000 q^{12} -1.89404 q^{13} +4.93134 q^{14} +1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{18} +2.79135 q^{19} -1.00000 q^{20} +4.93134 q^{21} -1.32869 q^{22} -8.15133 q^{23} +1.00000 q^{24} +1.00000 q^{25} +1.89404 q^{26} -1.00000 q^{27} -4.93134 q^{28} +4.87244 q^{29} -1.00000 q^{30} -7.68100 q^{31} -1.00000 q^{32} -1.32869 q^{33} +4.93134 q^{35} +1.00000 q^{36} -7.69552 q^{37} -2.79135 q^{38} +1.89404 q^{39} +1.00000 q^{40} -1.44724 q^{41} -4.93134 q^{42} +2.60613 q^{43} +1.32869 q^{44} -1.00000 q^{45} +8.15133 q^{46} -9.27246 q^{47} -1.00000 q^{48} +17.3181 q^{49} -1.00000 q^{50} -1.89404 q^{52} -2.63814 q^{53} +1.00000 q^{54} -1.32869 q^{55} +4.93134 q^{56} -2.79135 q^{57} -4.87244 q^{58} -5.34546 q^{59} +1.00000 q^{60} +8.70880 q^{61} +7.68100 q^{62} -4.93134 q^{63} +1.00000 q^{64} +1.89404 q^{65} +1.32869 q^{66} -8.76374 q^{67} +8.15133 q^{69} -4.93134 q^{70} -12.7470 q^{71} -1.00000 q^{72} +8.44174 q^{73} +7.69552 q^{74} -1.00000 q^{75} +2.79135 q^{76} -6.55222 q^{77} -1.89404 q^{78} -6.31617 q^{79} -1.00000 q^{80} +1.00000 q^{81} +1.44724 q^{82} +10.4660 q^{83} +4.93134 q^{84} -2.60613 q^{86} -4.87244 q^{87} -1.32869 q^{88} -11.3043 q^{89} +1.00000 q^{90} +9.34018 q^{91} -8.15133 q^{92} +7.68100 q^{93} +9.27246 q^{94} -2.79135 q^{95} +1.00000 q^{96} -0.224146 q^{97} -17.3181 q^{98} +1.32869 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} - 8 q^{3} + 8 q^{4} - 8 q^{5} + 8 q^{6} - 8 q^{7} - 8 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 - 8 * q^5 + 8 * q^6 - 8 * q^7 - 8 * q^8 + 8 * q^9	\( 8 q - 8 q^{2} - 8 q^{3} + 8 q^{4} - 8 q^{5} + 8 q^{6} - 8 q^{7} - 8 q^{8} + 8 q^{9} + 8 q^{10} + 8 q^{11} - 8 q^{12} + 8 q^{14} + 8 q^{15} + 8 q^{16} - 8 q^{18} - 8 q^{20} + 8 q^{21} - 8 q^{22} + 8 q^{24} + 8 q^{25} - 8 q^{27} - 8 q^{28} + 8 q^{29} - 8 q^{30} - 8 q^{31} - 8 q^{32} - 8 q^{33} + 8 q^{35} + 8 q^{36} - 32 q^{37} + 8 q^{40} + 8 q^{41} - 8 q^{42} - 8 q^{43} + 8 q^{44} - 8 q^{45} - 8 q^{48} + 40 q^{49} - 8 q^{50} + 16 q^{53} + 8 q^{54} - 8 q^{55} + 8 q^{56} - 8 q^{58} + 32 q^{59} + 8 q^{60} - 8 q^{61} + 8 q^{62} - 8 q^{63} + 8 q^{64} + 8 q^{66} - 8 q^{67} - 8 q^{70} + 24 q^{71} - 8 q^{72} - 40 q^{73} + 32 q^{74} - 8 q^{75} + 16 q^{77} - 24 q^{79} - 8 q^{80} + 8 q^{81} - 8 q^{82} - 16 q^{83} + 8 q^{84} + 8 q^{86} - 8 q^{87} - 8 q^{88} + 48 q^{89} + 8 q^{90} - 24 q^{91} + 8 q^{93} + 8 q^{96} - 24 q^{97} - 40 q^{98} + 8 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 - 8 * q^5 + 8 * q^6 - 8 * q^7 - 8 * q^8 + 8 * q^9 + 8 * q^10 + 8 * q^11 - 8 * q^12 + 8 * q^14 + 8 * q^15 + 8 * q^16 - 8 * q^18 - 8 * q^20 + 8 * q^21 - 8 * q^22 + 8 * q^24 + 8 * q^25 - 8 * q^27 - 8 * q^28 + 8 * q^29 - 8 * q^30 - 8 * q^31 - 8 * q^32 - 8 * q^33 + 8 * q^35 + 8 * q^36 - 32 * q^37 + 8 * q^40 + 8 * q^41 - 8 * q^42 - 8 * q^43 + 8 * q^44 - 8 * q^45 - 8 * q^48 + 40 * q^49 - 8 * q^50 + 16 * q^53 + 8 * q^54 - 8 * q^55 + 8 * q^56 - 8 * q^58 + 32 * q^59 + 8 * q^60 - 8 * q^61 + 8 * q^62 - 8 * q^63 + 8 * q^64 + 8 * q^66 - 8 * q^67 - 8 * q^70 + 24 * q^71 - 8 * q^72 - 40 * q^73 + 32 * q^74 - 8 * q^75 + 16 * q^77 - 24 * q^79 - 8 * q^80 + 8 * q^81 - 8 * q^82 - 16 * q^83 + 8 * q^84 + 8 * q^86 - 8 * q^87 - 8 * q^88 + 48 * q^89 + 8 * q^90 - 24 * q^91 + 8 * q^93 + 8 * q^96 - 24 * q^97 - 40 * q^98 + 8 * q^99

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