LMFDB - Embedded newform 8470.2.a.dg.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8470.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$67.6332905120$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 16x^{6} + 69x^{4} - 10x^{3} - 70x^{2} + 10x + 5 $ x^8 - 16x^6 + 69x^4 - 10x^3 - 70x^2 + 10*x + 5
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 770)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$1.22201$ of defining polynomial
Character	$\chi$	$=$	8470.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.22201 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.22201 q^{6} +1.00000 q^{7} -1.00000 q^{8} -1.50670 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.22201 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.22201 q^{6} +1.00000 q^{7} -1.00000 q^{8} -1.50670 q^{9} +1.00000 q^{10} +1.22201 q^{12} -3.47816 q^{13} -1.00000 q^{14} -1.22201 q^{15} +1.00000 q^{16} +0.138127 q^{17} +1.50670 q^{18} -0.515316 q^{19} -1.00000 q^{20} +1.22201 q^{21} +1.51048 q^{23} -1.22201 q^{24} +1.00000 q^{25} +3.47816 q^{26} -5.50722 q^{27} +1.00000 q^{28} -9.24062 q^{29} +1.22201 q^{30} +10.2626 q^{31} -1.00000 q^{32} -0.138127 q^{34} -1.00000 q^{35} -1.50670 q^{36} +1.66859 q^{37} +0.515316 q^{38} -4.25033 q^{39} +1.00000 q^{40} +12.1868 q^{41} -1.22201 q^{42} +10.6660 q^{43} +1.50670 q^{45} -1.51048 q^{46} -1.80692 q^{47} +1.22201 q^{48} +1.00000 q^{49} -1.00000 q^{50} +0.168791 q^{51} -3.47816 q^{52} +1.39105 q^{53} +5.50722 q^{54} -1.00000 q^{56} -0.629719 q^{57} +9.24062 q^{58} +9.30512 q^{59} -1.22201 q^{60} -13.5218 q^{61} -10.2626 q^{62} -1.50670 q^{63} +1.00000 q^{64} +3.47816 q^{65} -1.84979 q^{67} +0.138127 q^{68} +1.84582 q^{69} +1.00000 q^{70} -6.39213 q^{71} +1.50670 q^{72} +11.0649 q^{73} -1.66859 q^{74} +1.22201 q^{75} -0.515316 q^{76} +4.25033 q^{78} -9.98676 q^{79} -1.00000 q^{80} -2.20974 q^{81} -12.1868 q^{82} -2.20436 q^{83} +1.22201 q^{84} -0.138127 q^{85} -10.6660 q^{86} -11.2921 q^{87} +1.74164 q^{89} -1.50670 q^{90} -3.47816 q^{91} +1.51048 q^{92} +12.5410 q^{93} +1.80692 q^{94} +0.515316 q^{95} -1.22201 q^{96} -4.41074 q^{97} -1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 8 q^{4} - 8 q^{5} + 8 q^{7} - 8 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 + 8 * q^4 - 8 * q^5 + 8 * q^7 - 8 * q^8 + 8 * q^9	$ 8 q - 8 q^{2} + 8 q^{4} - 8 q^{5} + 8 q^{7} - 8 q^{8} + 8 q^{9} + 8 q^{10} + q^{13} - 8 q^{14} + 8 q^{16} - 6 q^{17} - 8 q^{18} - 5 q^{19} - 8 q^{20} + 10 q^{23} + 8 q^{25} - q^{26} + 8 q^{28} - 3 q^{29} - 8 q^{31} - 8 q^{32} + 6 q^{34} - 8 q^{35} + 8 q^{36} - 6 q^{37} + 5 q^{38} - 35 q^{39} + 8 q^{40} - 11 q^{41} + 5 q^{43} - 8 q^{45} - 10 q^{46} - 15 q^{47} + 8 q^{49} - 8 q^{50} + 6 q^{51} + q^{52} - 16 q^{53} - 8 q^{56} - 38 q^{57} + 3 q^{58} - 9 q^{59} - 32 q^{61} + 8 q^{62} + 8 q^{63} + 8 q^{64} - q^{65} + 33 q^{67} - 6 q^{68} - 22 q^{69} + 8 q^{70} + 11 q^{71} - 8 q^{72} + 34 q^{73} + 6 q^{74} - 5 q^{76} + 35 q^{78} - 31 q^{79} - 8 q^{80} + 20 q^{81} + 11 q^{82} - 50 q^{83} + 6 q^{85} - 5 q^{86} + 12 q^{87} + q^{89} + 8 q^{90} + q^{91} + 10 q^{92} + 26 q^{93} + 15 q^{94} + 5 q^{95} - 4 q^{97} - 8 q^{98}+O(q^{100}) $ 8 * q - 8 * q^2 + 8 * q^4 - 8 * q^5 + 8 * q^7 - 8 * q^8 + 8 * q^9 + 8 * q^10 + q^13 - 8 * q^14 + 8 * q^16 - 6 * q^17 - 8 * q^18 - 5 * q^19 - 8 * q^20 + 10 * q^23 + 8 * q^25 - q^26 + 8 * q^28 - 3 * q^29 - 8 * q^31 - 8 * q^32 + 6 * q^34 - 8 * q^35 + 8 * q^36 - 6 * q^37 + 5 * q^38 - 35 * q^39 + 8 * q^40 - 11 * q^41 + 5 * q^43 - 8 * q^45 - 10 * q^46 - 15 * q^47 + 8 * q^49 - 8 * q^50 + 6 * q^51 + q^52 - 16 * q^53 - 8 * q^56 - 38 * q^57 + 3 * q^58 - 9 * q^59 - 32 * q^61 + 8 * q^62 + 8 * q^63 + 8 * q^64 - q^65 + 33 * q^67 - 6 * q^68 - 22 * q^69 + 8 * q^70 + 11 * q^71 - 8 * q^72 + 34 * q^73 + 6 * q^74 - 5 * q^76 + 35 * q^78 - 31 * q^79 - 8 * q^80 + 20 * q^81 + 11 * q^82 - 50 * q^83 + 6 * q^85 - 5 * q^86 + 12 * q^87 + q^89 + 8 * q^90 + q^91 + 10 * q^92 + 26 * q^93 + 15 * q^94 + 5 * q^95 - 4 * q^97 - 8 * 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
$3$	1.22201	0.705525	0.352763	−	0.935713i	$-0.385242\pi$
$3$	1.22201	0.705525	0.352763	+	0.935713i	$0.385242\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.22201	−0.498882
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	−1.50670	−0.502234
$10$	1.00000	0.316228
$11$	0	0
$11$	0	0
$12$	1.22201	0.352763
$13$	−3.47816	−0.964669	−0.482334	−	0.875987i	$-0.660211\pi$
$13$	−3.47816	−0.964669	−0.482334	+	0.875987i	$0.660211\pi$
$14$	−1.00000	−0.267261
$15$	−1.22201	−0.315520
$16$	1.00000	0.250000
$17$	0.138127	0.0335006	0.0167503	−	0.999860i	$-0.494668\pi$
$17$	0.138127	0.0335006	0.0167503	+	0.999860i	$0.494668\pi$
$18$	1.50670	0.355133
$19$	−0.515316	−0.118222	−0.0591108	−	0.998251i	$-0.518827\pi$
$19$	−0.515316	−0.118222	−0.0591108	+	0.998251i	$0.518827\pi$
$20$	−1.00000	−0.223607
$21$	1.22201	0.266663
$22$	0	0
$23$	1.51048	0.314957	0.157479	−	0.987522i	$-0.449663\pi$
$23$	1.51048	0.314957	0.157479	+	0.987522i	$0.449663\pi$
$24$	−1.22201	−0.249441
$25$	1.00000	0.200000
$26$	3.47816	0.682124
$27$	−5.50722	−1.05986
$28$	1.00000	0.188982
$29$	−9.24062	−1.71594	−0.857970	−	0.513699i	$-0.828275\pi$
$29$	−9.24062	−1.71594	−0.857970	+	0.513699i	$0.828275\pi$
$30$	1.22201	0.223107
$31$	10.2626	1.84322	0.921612	−	0.388112i	$-0.126873\pi$
$31$	10.2626	1.84322	0.921612	+	0.388112i	$0.126873\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	−0.138127	−0.0236885
$35$	−1.00000	−0.169031
$36$	−1.50670	−0.251117
$37$	1.66859	0.274315	0.137157	−	0.990549i	$-0.456203\pi$
$37$	1.66859	0.274315	0.137157	+	0.990549i	$0.456203\pi$
$38$	0.515316	0.0835952
$39$	−4.25033	−0.680598
$40$	1.00000	0.158114
$41$	12.1868	1.90326	0.951628	−	0.307251i	$-0.0994092\pi$
$41$	12.1868	1.90326	0.951628	+	0.307251i	$0.0994092\pi$
$42$	−1.22201	−0.188560
$43$	10.6660	1.62655	0.813277	−	0.581877i	$-0.197682\pi$
$43$	10.6660	1.62655	0.813277	+	0.581877i	$0.197682\pi$
$44$	0	0
$45$	1.50670	0.224606
$46$	−1.51048	−0.222708
$47$	−1.80692	−0.263567	−0.131783	−	0.991279i	$-0.542070\pi$
$47$	−1.80692	−0.263567	−0.131783	+	0.991279i	$0.542070\pi$
$48$	1.22201	0.176381
$49$	1.00000	0.142857
$50$	−1.00000	−0.141421
$51$	0.168791	0.0236355
$52$	−3.47816	−0.482334
$53$	1.39105	0.191075	0.0955376	−	0.995426i	$-0.469543\pi$
$53$	1.39105	0.191075	0.0955376	+	0.995426i	$0.469543\pi$
$54$	5.50722	0.749437
$55$	0	0
$56$	−1.00000	−0.133631
$57$	−0.629719	−0.0834083
$58$	9.24062	1.21335
$59$	9.30512	1.21142	0.605712	−	0.795684i	$-0.292889\pi$
$59$	9.30512	1.21142	0.605712	+	0.795684i	$0.292889\pi$
$60$	−1.22201	−0.157760
$61$	−13.5218	−1.73129	−0.865646	−	0.500656i	$-0.833092\pi$
$61$	−13.5218	−1.73129	−0.865646	+	0.500656i	$0.833092\pi$
$62$	−10.2626	−1.30336
$63$	−1.50670	−0.189827
$64$	1.00000	0.125000
$65$	3.47816	0.431413
$66$	0	0
$67$	−1.84979	−0.225988	−0.112994	−	0.993596i	$-0.536044\pi$
$67$	−1.84979	−0.225988	−0.112994	+	0.993596i	$0.536044\pi$
$68$	0.138127	0.0167503
$69$	1.84582	0.222210
$70$	1.00000	0.119523
$71$	−6.39213	−0.758606	−0.379303	−	0.925272i	$-0.623836\pi$
$71$	−6.39213	−0.758606	−0.379303	+	0.925272i	$0.623836\pi$
$72$	1.50670	0.177567
$73$	11.0649	1.29505	0.647525	−	0.762044i	$-0.275804\pi$
$73$	11.0649	1.29505	0.647525	+	0.762044i	$0.275804\pi$
$74$	−1.66859	−0.193970
$75$	1.22201	0.141105
$76$	−0.515316	−0.0591108
$77$	0	0
$78$	4.25033	0.481256
$79$	−9.98676	−1.12360	−0.561799	−	0.827274i	$-0.689891\pi$
$79$	−9.98676	−1.12360	−0.561799	+	0.827274i	$0.689891\pi$
$80$	−1.00000	−0.111803
$81$	−2.20974	−0.245527
$82$	−12.1868	−1.34581
$83$	−2.20436	−0.241960	−0.120980	−	0.992655i	$-0.538604\pi$
$83$	−2.20436	−0.241960	−0.120980	+	0.992655i	$0.538604\pi$
$84$	1.22201	0.133332
$85$	−0.138127	−0.0149819
$86$	−10.6660	−1.15015
$87$	−11.2921	−1.21064
$88$	0	0
$89$	1.74164	0.184614	0.0923069	−	0.995731i	$-0.470576\pi$
$89$	1.74164	0.184614	0.0923069	+	0.995731i	$0.470576\pi$
$90$	−1.50670	−0.158820
$91$	−3.47816	−0.364610
$92$	1.51048	0.157479
$93$	12.5410	1.30044
$94$	1.80692	0.186370
$95$	0.515316	0.0528703
$96$	−1.22201	−0.124720
$97$	−4.41074	−0.447843	−0.223921	−	0.974607i	$-0.571886\pi$
$97$	−4.41074	−0.447843	−0.223921	+	0.974607i	$0.571886\pi$
$98$	−1.00000	−0.101015
$99$	0	0
$100$	1.00000	0.100000
$101$	−12.5813	−1.25188	−0.625942	−	0.779870i	$-0.715285\pi$
$101$	−12.5813	−1.25188	−0.625942	+	0.779870i	$0.715285\pi$
$102$	−0.168791	−0.0167128
$103$	−2.98471	−0.294092	−0.147046	−	0.989130i	$-0.546976\pi$
$103$	−2.98471	−0.294092	−0.147046	+	0.989130i	$0.546976\pi$
$104$	3.47816	0.341062
$105$	−1.22201	−0.119256
$106$	−1.39105	−0.135111
$107$	−13.2777	−1.28360	−0.641800	−	0.766872i	$-0.721812\pi$
$107$	−13.2777	−1.28360	−0.641800	+	0.766872i	$0.721812\pi$
$108$	−5.50722	−0.529932
$109$	−0.502741	−0.0481539	−0.0240769	−	0.999710i	$-0.507665\pi$
$109$	−0.502741	−0.0481539	−0.0240769	+	0.999710i	$0.507665\pi$
$110$	0	0
$111$	2.03903	0.193536
$112$	1.00000	0.0944911
$113$	−8.91196	−0.838367	−0.419183	−	0.907902i	$-0.637684\pi$
$113$	−8.91196	−0.838367	−0.419183	+	0.907902i	$0.637684\pi$
$114$	0.629719	0.0589786
$115$	−1.51048	−0.140853
$116$	−9.24062	−0.857970
$117$	5.24056	0.484489
$118$	−9.30512	−0.856605
$119$	0.138127	0.0126620
$120$	1.22201	0.111553
$121$	0	0
$122$	13.5218	1.22421
$123$	14.8923	1.34280
$124$	10.2626	0.921612
$125$	−1.00000	−0.0894427
$126$	1.50670	0.134228
$127$	−12.6728	−1.12452	−0.562262	−	0.826959i	$-0.690069\pi$
$127$	−12.6728	−1.12452	−0.562262	+	0.826959i	$0.690069\pi$
$128$	−1.00000	−0.0883883
$129$	13.0339	1.14757
$130$	−3.47816	−0.305055
$131$	−15.1497	−1.32364	−0.661818	−	0.749664i	$-0.730215\pi$
$131$	−15.1497	−1.32364	−0.661818	+	0.749664i	$0.730215\pi$
$132$	0	0
$133$	−0.515316	−0.0446835
$134$	1.84979	0.159798
$135$	5.50722	0.473986
$136$	−0.138127	−0.0118443
$137$	21.8856	1.86981	0.934904	−	0.354900i	$-0.115485\pi$
$137$	21.8856	1.86981	0.934904	+	0.354900i	$0.115485\pi$
$138$	−1.84582	−0.157126
$139$	−2.47370	−0.209816	−0.104908	−	0.994482i	$-0.533455\pi$
$139$	−2.47370	−0.209816	−0.104908	+	0.994482i	$0.533455\pi$
$140$	−1.00000	−0.0845154
$141$	−2.20807	−0.185953
$142$	6.39213	0.536416
$143$	0	0
$144$	−1.50670	−0.125559
$145$	9.24062	0.767392
$146$	−11.0649	−0.915738
$147$	1.22201	0.100789
$148$	1.66859	0.137157
$149$	−17.1038	−1.40120	−0.700598	−	0.713556i	$-0.747083\pi$
$149$	−17.1038	−1.40120	−0.700598	+	0.713556i	$0.747083\pi$
$150$	−1.22201	−0.0997763
$151$	−3.21272	−0.261447	−0.130724	−	0.991419i	$-0.541730\pi$
$151$	−3.21272	−0.261447	−0.130724	+	0.991419i	$0.541730\pi$
$152$	0.515316	0.0417976
$153$	−0.208116	−0.0168252
$154$	0	0
$155$	−10.2626	−0.824315
$156$	−4.25033	−0.340299
$157$	2.74824	0.219333	0.109667	−	0.993968i	$-0.465022\pi$
$157$	2.74824	0.219333	0.109667	+	0.993968i	$0.465022\pi$
$158$	9.98676	0.794504
$159$	1.69987	0.134808
$160$	1.00000	0.0790569
$161$	1.51048	0.119043
$162$	2.20974	0.173614
$163$	−12.5201	−0.980649	−0.490325	−	0.871540i	$-0.663122\pi$
$163$	−12.5201	−0.980649	−0.490325	+	0.871540i	$0.663122\pi$
$164$	12.1868	0.951628
$165$	0	0
$166$	2.20436	0.171091
$167$	−17.0335	−1.31809	−0.659047	−	0.752102i	$-0.729040\pi$
$167$	−17.0335	−1.31809	−0.659047	+	0.752102i	$0.729040\pi$
$168$	−1.22201	−0.0942798
$169$	−0.902388	−0.0694145
$170$	0.138127	0.0105938
$171$	0.776427	0.0593749
$172$	10.6660	0.813277
$173$	−9.38603	−0.713607	−0.356803	−	0.934179i	$-0.616133\pi$
$173$	−9.38603	−0.713607	−0.356803	+	0.934179i	$0.616133\pi$
$174$	11.2921	0.856051
$175$	1.00000	0.0755929
$176$	0	0
$177$	11.3709	0.854690
$178$	−1.74164	−0.130542
$179$	−11.1233	−0.831397	−0.415698	−	0.909503i	$-0.636463\pi$
$179$	−11.1233	−0.831397	−0.415698	+	0.909503i	$0.636463\pi$
$180$	1.50670	0.112303
$181$	9.57646	0.711813	0.355906	−	0.934522i	$-0.384172\pi$
$181$	9.57646	0.711813	0.355906	+	0.934522i	$0.384172\pi$
$182$	3.47816	0.257819
$183$	−16.5237	−1.22147
$184$	−1.51048	−0.111354
$185$	−1.66859	−0.122677
$186$	−12.5410	−0.919551
$187$	0	0
$188$	−1.80692	−0.131783
$189$	−5.50722	−0.400591
$190$	−0.515316	−0.0373849
$191$	9.79900	0.709031	0.354515	−	0.935050i	$-0.384646\pi$
$191$	9.79900	0.709031	0.354515	+	0.935050i	$0.384646\pi$
$192$	1.22201	0.0881907
$193$	−14.4512	−1.04022	−0.520111	−	0.854099i	$-0.674109\pi$
$193$	−14.4512	−1.04022	−0.520111	+	0.854099i	$0.674109\pi$
$194$	4.41074	0.316673
$195$	4.25033	0.304373
$196$	1.00000	0.0714286
$197$	−22.6950	−1.61695	−0.808476	−	0.588530i	$-0.799707\pi$
$197$	−22.6950	−1.61695	−0.808476	+	0.588530i	$0.799707\pi$
$198$	0	0
$199$	9.43893	0.669108	0.334554	−	0.942377i	$-0.391414\pi$
$199$	9.43893	0.669108	0.334554	+	0.942377i	$0.391414\pi$
$200$	−1.00000	−0.0707107
$201$	−2.26045	−0.159440
$202$	12.5813	0.885215
$203$	−9.24062	−0.648565
$204$	0.168791	0.0118178
$205$	−12.1868	−0.851162
$206$	2.98471	0.207954
$207$	−2.27585	−0.158182
$208$	−3.47816	−0.241167
$209$	0	0
$210$	1.22201	0.0843264
$211$	−11.1500	−0.767595	−0.383797	−	0.923417i	$-0.625384\pi$
$211$	−11.1500	−0.767595	−0.383797	+	0.923417i	$0.625384\pi$
$212$	1.39105	0.0955376
$213$	−7.81122	−0.535216
$214$	13.2777	0.907642
$215$	−10.6660	−0.727417
$216$	5.50722	0.374719
$217$	10.2626	0.696673
$218$	0.502741	0.0340499
$219$	13.5214	0.913690
$220$	0	0
$221$	−0.480427	−0.0323170
$222$	−2.03903	−0.136851
$223$	−3.97800	−0.266387	−0.133193	−	0.991090i	$-0.542523\pi$
$223$	−3.97800	−0.266387	−0.133193	+	0.991090i	$0.542523\pi$
$224$	−1.00000	−0.0668153
$225$	−1.50670	−0.100447
$226$	8.91196	0.592815
$227$	−21.7347	−1.44258	−0.721292	−	0.692631i	$-0.756452\pi$
$227$	−21.7347	−1.44258	−0.721292	+	0.692631i	$0.756452\pi$
$228$	−0.629719	−0.0417041
$229$	1.64618	0.108783	0.0543913	−	0.998520i	$-0.482678\pi$
$229$	1.64618	0.108783	0.0543913	+	0.998520i	$0.482678\pi$
$230$	1.51048	0.0995982
$231$	0	0
$232$	9.24062	0.606677
$233$	1.11650	0.0731441	0.0365720	−	0.999331i	$-0.488356\pi$
$233$	1.11650	0.0731441	0.0365720	+	0.999331i	$0.488356\pi$
$234$	−5.24056	−0.342586
$235$	1.80692	0.117871
$236$	9.30512	0.605712
$237$	−12.2039	−0.792727
$238$	−0.138127	−0.00895342
$239$	−17.3118	−1.11981	−0.559903	−	0.828558i	$-0.689161\pi$
$239$	−17.3118	−1.11981	−0.559903	+	0.828558i	$0.689161\pi$
$240$	−1.22201	−0.0788801
$241$	23.7524	1.53003	0.765015	−	0.644013i	$-0.222732\pi$
$241$	23.7524	1.53003	0.765015	+	0.644013i	$0.222732\pi$
$242$	0	0
$243$	13.8213	0.886639
$244$	−13.5218	−0.865646
$245$	−1.00000	−0.0638877
$246$	−14.8923	−0.949500
$247$	1.79235	0.114045
$248$	−10.2626	−0.651678
$249$	−2.69374	−0.170709
$250$	1.00000	0.0632456
$251$	12.1255	0.765357	0.382679	−	0.923881i	$-0.375002\pi$
$251$	12.1255	0.765357	0.382679	+	0.923881i	$0.375002\pi$
$252$	−1.50670	−0.0949133
$253$	0	0
$254$	12.6728	0.795159
$255$	−0.168791	−0.0105701
$256$	1.00000	0.0625000
$257$	−28.6094	−1.78461	−0.892304	−	0.451435i	$-0.850912\pi$
$257$	−28.6094	−1.78461	−0.892304	+	0.451435i	$0.850912\pi$
$258$	−13.0339	−0.811458
$259$	1.66859	0.103681
$260$	3.47816	0.215706
$261$	13.9229	0.861804
$262$	15.1497	0.935953
$263$	30.4738	1.87910	0.939549	−	0.342415i	$-0.111245\pi$
$263$	30.4738	1.87910	0.939549	+	0.342415i	$0.111245\pi$
$264$	0	0
$265$	−1.39105	−0.0854514
$266$	0.515316	0.0315960
$267$	2.12830	0.130250
$268$	−1.84979	−0.112994
$269$	−31.0485	−1.89306	−0.946531	−	0.322613i	$-0.895439\pi$
$269$	−31.0485	−1.89306	−0.946531	+	0.322613i	$0.895439\pi$
$270$	−5.50722	−0.335158
$271$	−8.50957	−0.516920	−0.258460	−	0.966022i	$-0.583215\pi$
$271$	−8.50957	−0.516920	−0.258460	+	0.966022i	$0.583215\pi$
$272$	0.138127	0.00837515
$273$	−4.25033	−0.257242
$274$	−21.8856	−1.32215
$275$	0	0
$276$	1.84582	0.111105
$277$	14.6394	0.879598	0.439799	−	0.898096i	$-0.355050\pi$
$277$	14.6394	0.879598	0.439799	+	0.898096i	$0.355050\pi$
$278$	2.47370	0.148363
$279$	−15.4627	−0.925730
$280$	1.00000	0.0597614
$281$	8.91851	0.532034	0.266017	−	0.963968i	$-0.414292\pi$
$281$	8.91851	0.532034	0.266017	+	0.963968i	$0.414292\pi$
$282$	2.20807	0.131489
$283$	−19.7163	−1.17201	−0.586005	−	0.810307i	$-0.699300\pi$
$283$	−19.7163	−1.17201	−0.586005	+	0.810307i	$0.699300\pi$
$284$	−6.39213	−0.379303
$285$	0.629719	0.0373013
$286$	0	0
$287$	12.1868	0.719363
$288$	1.50670	0.0887833
$289$	−16.9809	−0.998878
$290$	−9.24062	−0.542628
$291$	−5.38995	−0.315964
$292$	11.0649	0.647525
$293$	−6.92872	−0.404780	−0.202390	−	0.979305i	$-0.564871\pi$
$293$	−6.92872	−0.404780	−0.202390	+	0.979305i	$0.564871\pi$
$294$	−1.22201	−0.0712688
$295$	−9.30512	−0.541765
$296$	−1.66859	−0.0969850
$297$	0	0
$298$	17.1038	0.990795
$299$	−5.25370	−0.303829
$300$	1.22201	0.0705525
$301$	10.6660	0.614779
$302$	3.21272	0.184871
$303$	−15.3744	−0.883235
$304$	−0.515316	−0.0295554
$305$	13.5218	0.774257
$306$	0.208116	0.0118972
$307$	20.6340	1.17764	0.588821	−	0.808263i	$-0.299592\pi$
$307$	20.6340	1.17764	0.588821	+	0.808263i	$0.299592\pi$
$308$	0	0
$309$	−3.64733	−0.207489
$310$	10.2626	0.582879
$311$	−20.2359	−1.14748	−0.573738	−	0.819039i	$-0.694507\pi$
$311$	−20.2359	−1.14748	−0.573738	+	0.819039i	$0.694507\pi$
$312$	4.25033	0.240628
$313$	−4.40784	−0.249146	−0.124573	−	0.992210i	$-0.539756\pi$
$313$	−4.40784	−0.249146	−0.124573	+	0.992210i	$0.539756\pi$
$314$	−2.74824	−0.155092
$315$	1.50670	0.0848931
$316$	−9.98676	−0.561799
$317$	25.9982	1.46020	0.730101	−	0.683339i	$-0.239473\pi$
$317$	25.9982	1.46020	0.730101	+	0.683339i	$0.239473\pi$
$318$	−1.69987	−0.0953239
$319$	0	0
$320$	−1.00000	−0.0559017
$321$	−16.2254	−0.905612
$322$	−1.51048	−0.0841759
$323$	−0.0711788	−0.00396049
$324$	−2.20974	−0.122763
$325$	−3.47816	−0.192934
$326$	12.5201	0.693424
$327$	−0.614353	−0.0339738
$328$	−12.1868	−0.672903
$329$	−1.80692	−0.0996188
$330$	0	0
$331$	−19.8219	−1.08951	−0.544755	−	0.838595i	$-0.683377\pi$
$331$	−19.8219	−1.08951	−0.544755	+	0.838595i	$0.683377\pi$
$332$	−2.20436	−0.120980
$333$	−2.51407	−0.137770
$334$	17.0335	0.932033
$335$	1.84979	0.101065
$336$	1.22201	0.0666659
$337$	−30.3840	−1.65512	−0.827560	−	0.561377i	$-0.810272\pi$
$337$	−30.3840	−1.65512	−0.827560	+	0.561377i	$0.810272\pi$
$338$	0.902388	0.0490834
$339$	−10.8905	−0.591489
$340$	−0.138127	−0.00749096
$341$	0	0
$342$	−0.776427	−0.0419844
$343$	1.00000	0.0539949
$344$	−10.6660	−0.575074
$345$	−1.84582	−0.0993755
$346$	9.38603	0.504596
$347$	16.6544	0.894057	0.447028	−	0.894520i	$-0.352482\pi$
$347$	16.6544	0.894057	0.447028	+	0.894520i	$0.352482\pi$
$348$	−11.2921	−0.605320
$349$	1.70386	0.0912057	0.0456028	−	0.998960i	$-0.485479\pi$
$349$	1.70386	0.0912057	0.0456028	+	0.998960i	$0.485479\pi$
$350$	−1.00000	−0.0534522
$351$	19.1550	1.02242
$352$	0	0
$353$	10.7417	0.571724	0.285862	−	0.958271i	$-0.407720\pi$
$353$	10.7417	0.571724	0.285862	+	0.958271i	$0.407720\pi$
$354$	−11.3709	−0.604357
$355$	6.39213	0.339259
$356$	1.74164	0.0923069
$357$	0.168791	0.00893339
$358$	11.1233	0.587886
$359$	16.2804	0.859246	0.429623	−	0.903008i	$-0.358646\pi$
$359$	16.2804	0.859246	0.429623	+	0.903008i	$0.358646\pi$
$360$	−1.50670	−0.0794102
$361$	−18.7344	−0.986024
$362$	−9.57646	−0.503328
$363$	0	0
$364$	−3.47816	−0.182305
$365$	−11.0649	−0.579164
$366$	16.5237	0.863710
$367$	−21.0947	−1.10114	−0.550568	−	0.834790i	$-0.685589\pi$
$367$	−21.0947	−1.10114	−0.550568	+	0.834790i	$0.685589\pi$
$368$	1.51048	0.0787393
$369$	−18.3619	−0.955881
$370$	1.66859	0.0867460
$371$	1.39105	0.0722196
$372$	12.5410	0.650221
$373$	13.9335	0.721449	0.360725	−	0.932672i	$-0.382529\pi$
$373$	13.9335	0.721449	0.360725	+	0.932672i	$0.382529\pi$
$374$	0	0
$375$	−1.22201	−0.0631041
$376$	1.80692	0.0931849
$377$	32.1404	1.65531
$378$	5.50722	0.283261
$379$	22.1451	1.13752	0.568759	−	0.822505i	$-0.307424\pi$
$379$	22.1451	1.13752	0.568759	+	0.822505i	$0.307424\pi$
$380$	0.515316	0.0264351
$381$	−15.4862	−0.793381
$382$	−9.79900	−0.501360
$383$	−22.5171	−1.15057	−0.575284	−	0.817954i	$-0.695108\pi$
$383$	−22.5171	−1.15057	−0.575284	+	0.817954i	$0.695108\pi$
$384$	−1.22201	−0.0623602
$385$	0	0
$386$	14.4512	0.735548
$387$	−16.0705	−0.816911
$388$	−4.41074	−0.223921
$389$	−20.8343	−1.05634	−0.528171	−	0.849138i	$-0.677122\pi$
$389$	−20.8343	−1.05634	−0.528171	+	0.849138i	$0.677122\pi$
$390$	−4.25033	−0.215224
$391$	0.208638	0.0105513
$392$	−1.00000	−0.0505076
$393$	−18.5130	−0.933859
$394$	22.6950	1.14336
$395$	9.98676	0.502488
$396$	0	0
$397$	19.0865	0.957924	0.478962	−	0.877836i	$-0.341013\pi$
$397$	19.0865	0.957924	0.478962	+	0.877836i	$0.341013\pi$
$398$	−9.43893	−0.473131
$399$	−0.629719	−0.0315254
$400$	1.00000	0.0500000
$401$	30.1895	1.50759	0.753795	−	0.657110i	$-0.228221\pi$
$401$	30.1895	1.50759	0.753795	+	0.657110i	$0.228221\pi$
$402$	2.26045	0.112741
$403$	−35.6951	−1.77810
$404$	−12.5813	−0.625942
$405$	2.20974	0.109803
$406$	9.24062	0.458604
$407$	0	0
$408$	−0.168791	−0.00835642
$409$	29.4582	1.45662	0.728308	−	0.685250i	$-0.240307\pi$
$409$	29.4582	1.45662	0.728308	+	0.685250i	$0.240307\pi$
$410$	12.1868	0.601863
$411$	26.7443	1.31920
$412$	−2.98471	−0.147046
$413$	9.30512	0.457875
$414$	2.27585	0.111852
$415$	2.20436	0.108208
$416$	3.47816	0.170531
$417$	−3.02287	−0.148031
$418$	0	0
$419$	−20.4867	−1.00084	−0.500419	−	0.865783i	$-0.666821\pi$
$419$	−20.4867	−1.00084	−0.500419	+	0.865783i	$0.666821\pi$
$420$	−1.22201	−0.0596278
$421$	−2.61302	−0.127351	−0.0636755	−	0.997971i	$-0.520282\pi$
$421$	−2.61302	−0.127351	−0.0636755	+	0.997971i	$0.520282\pi$
$422$	11.1500	0.542772
$423$	2.72249	0.132372
$424$	−1.39105	−0.0675553
$425$	0.138127	0.00670012
$426$	7.81122	0.378455
$427$	−13.5218	−0.654367
$428$	−13.2777	−0.641800
$429$	0	0
$430$	10.6660	0.514361
$431$	9.87795	0.475804	0.237902	−	0.971289i	$-0.423540\pi$
$431$	9.87795	0.475804	0.237902	+	0.971289i	$0.423540\pi$
$432$	−5.50722	−0.264966
$433$	19.5259	0.938356	0.469178	−	0.883104i	$-0.344550\pi$
$433$	19.5259	0.938356	0.469178	+	0.883104i	$0.344550\pi$
$434$	−10.2626	−0.492623
$435$	11.2921	0.541414
$436$	−0.502741	−0.0240769
$437$	−0.778375	−0.0372347
$438$	−13.5214	−0.646077
$439$	−3.38579	−0.161595	−0.0807974	−	0.996731i	$-0.525747\pi$
$439$	−3.38579	−0.161595	−0.0807974	+	0.996731i	$0.525747\pi$
$440$	0	0
$441$	−1.50670	−0.0717477
$442$	0.480427	0.0228516
$443$	−19.3485	−0.919276	−0.459638	−	0.888106i	$-0.652021\pi$
$443$	−19.3485	−0.919276	−0.459638	+	0.888106i	$0.652021\pi$
$444$	2.03903	0.0967680
$445$	−1.74164	−0.0825618
$446$	3.97800	0.188364
$447$	−20.9009	−0.988579
$448$	1.00000	0.0472456
$449$	33.1331	1.56365	0.781824	−	0.623500i	$-0.214290\pi$
$449$	33.1331	1.56365	0.781824	+	0.623500i	$0.214290\pi$
$450$	1.50670	0.0710266
$451$	0	0
$452$	−8.91196	−0.419183
$453$	−3.92596	−0.184458
$454$	21.7347	1.02006
$455$	3.47816	0.163059
$456$	0.629719	0.0294893
$457$	12.6845	0.593358	0.296679	−	0.954977i	$-0.404121\pi$
$457$	12.6845	0.593358	0.296679	+	0.954977i	$0.404121\pi$
$458$	−1.64618	−0.0769210
$459$	−0.760693	−0.0355061
$460$	−1.51048	−0.0704266
$461$	−19.4617	−0.906421	−0.453211	−	0.891403i	$-0.649721\pi$
$461$	−19.4617	−0.906421	−0.453211	+	0.891403i	$0.649721\pi$
$462$	0	0
$463$	29.6401	1.37749	0.688746	−	0.725003i	$-0.258162\pi$
$463$	29.6401	1.37749	0.688746	+	0.725003i	$0.258162\pi$
$464$	−9.24062	−0.428985
$465$	−12.5410	−0.581575
$466$	−1.11650	−0.0517207
$467$	26.8009	1.24020	0.620099	−	0.784523i	$-0.287092\pi$
$467$	26.8009	1.24020	0.620099	+	0.784523i	$0.287092\pi$
$468$	5.24056	0.242245
$469$	−1.84979	−0.0854154
$470$	−1.80692	−0.0833471
$471$	3.35836	0.154745
$472$	−9.30512	−0.428303
$473$	0	0
$474$	12.2039	0.560542
$475$	−0.515316	−0.0236443
$476$	0.138127	0.00633102
$477$	−2.09590	−0.0959645
$478$	17.3118	0.791822
$479$	−13.3413	−0.609581	−0.304791	−	0.952419i	$-0.598587\pi$
$479$	−13.3413	−0.609581	−0.304791	+	0.952419i	$0.598587\pi$
$480$	1.22201	0.0557767
$481$	−5.80363	−0.264623
$482$	−23.7524	−1.08189
$483$	1.84582	0.0839876
$484$	0	0
$485$	4.41074	0.200281
$486$	−13.8213	−0.626948
$487$	−13.3718	−0.605932	−0.302966	−	0.953001i	$-0.597977\pi$
$487$	−13.3718	−0.605932	−0.302966	+	0.953001i	$0.597977\pi$
$488$	13.5218	0.612104
$489$	−15.2996	−0.691873
$490$	1.00000	0.0451754
$491$	−25.9713	−1.17207	−0.586033	−	0.810287i	$-0.699311\pi$
$491$	−25.9713	−1.17207	−0.586033	+	0.810287i	$0.699311\pi$
$492$	14.8923	0.671398
$493$	−1.27638	−0.0574851
$494$	−1.79235	−0.0806417
$495$	0	0
$496$	10.2626	0.460806
$497$	−6.39213	−0.286726
$498$	2.69374	0.120709
$499$	−22.5866	−1.01111	−0.505557	−	0.862793i	$-0.668713\pi$
$499$	−22.5866	−1.01111	−0.505557	+	0.862793i	$0.668713\pi$
$500$	−1.00000	−0.0447214
$501$	−20.8151	−0.929948
$502$	−12.1255	−0.541189
$503$	28.7933	1.28383	0.641916	−	0.766775i	$-0.278140\pi$
$503$	28.7933	1.28383	0.641916	+	0.766775i	$0.278140\pi$
$504$	1.50670	0.0671139
$505$	12.5813	0.559859
$506$	0	0
$507$	−1.10272	−0.0489737
$508$	−12.6728	−0.562262
$509$	−23.9556	−1.06182	−0.530908	−	0.847430i	$-0.678149\pi$
$509$	−23.9556	−1.06182	−0.530908	+	0.847430i	$0.678149\pi$
$510$	0.168791	0.00747421
$511$	11.0649	0.489483
$512$	−1.00000	−0.0441942
$513$	2.83795	0.125299
$514$	28.6094	1.26191
$515$	2.98471	0.131522
$516$	13.0339	0.573787
$517$	0	0
$518$	−1.66859	−0.0733137
$519$	−11.4698	−0.503468
$520$	−3.47816	−0.152528
$521$	−15.7907	−0.691804	−0.345902	−	0.938271i	$-0.612427\pi$
$521$	−15.7907	−0.691804	−0.345902	+	0.938271i	$0.612427\pi$
$522$	−13.9229	−0.609387
$523$	22.1852	0.970091	0.485045	−	0.874489i	$-0.338803\pi$
$523$	22.1852	0.970091	0.485045	+	0.874489i	$0.338803\pi$
$524$	−15.1497	−0.661818
$525$	1.22201	0.0533327
$526$	−30.4738	−1.32872
$527$	1.41754	0.0617492
$528$	0	0
$529$	−20.7184	−0.900802
$530$	1.39105	0.0604233
$531$	−14.0200	−0.608418
$532$	−0.515316	−0.0223418
$533$	−42.3876	−1.83601
$534$	−2.12830	−0.0921005
$535$	13.2777	0.574044
$536$	1.84979	0.0798988
$537$	−13.5928	−0.586571
$538$	31.0485	1.33860
$539$	0	0
$540$	5.50722	0.236993
$541$	18.9510	0.814768	0.407384	−	0.913257i	$-0.366441\pi$
$541$	18.9510	0.814768	0.407384	+	0.913257i	$0.366441\pi$
$542$	8.50957	0.365517
$543$	11.7025	0.502202
$544$	−0.138127	−0.00592213
$545$	0.502741	0.0215351
$546$	4.25033	0.181897
$547$	31.6057	1.35136	0.675681	−	0.737194i	$-0.263850\pi$
$547$	31.6057	1.35136	0.675681	+	0.737194i	$0.263850\pi$
$548$	21.8856	0.934904
$549$	20.3734	0.869514
$550$	0	0
$551$	4.76184	0.202861
$552$	−1.84582	−0.0785632
$553$	−9.98676	−0.424680
$554$	−14.6394	−0.621970
$555$	−2.03903	−0.0865520
$556$	−2.47370	−0.104908
$557$	15.7384	0.666857	0.333429	−	0.942775i	$-0.391794\pi$
$557$	15.7384	0.666857	0.333429	+	0.942775i	$0.391794\pi$
$558$	15.4627	0.654590
$559$	−37.0982	−1.56909
$560$	−1.00000	−0.0422577
$561$	0	0
$562$	−8.91851	−0.376205
$563$	−1.64956	−0.0695206	−0.0347603	−	0.999396i	$-0.511067\pi$
$563$	−1.64956	−0.0695206	−0.0347603	+	0.999396i	$0.511067\pi$
$564$	−2.20807	−0.0929765
$565$	8.91196	0.374929
$566$	19.7163	0.828736
$567$	−2.20974	−0.0928004
$568$	6.39213	0.268208
$569$	35.6665	1.49522	0.747608	−	0.664141i	$-0.231202\pi$
$569$	35.6665	1.49522	0.747608	+	0.664141i	$0.231202\pi$
$570$	−0.629719	−0.0263760
$571$	−29.5199	−1.23537	−0.617684	−	0.786427i	$-0.711929\pi$
$571$	−29.5199	−1.23537	−0.617684	+	0.786427i	$0.711929\pi$
$572$	0	0
$573$	11.9744	0.500239
$574$	−12.1868	−0.508667
$575$	1.51048	0.0629915
$576$	−1.50670	−0.0627793
$577$	−31.1204	−1.29556	−0.647780	−	0.761827i	$-0.724302\pi$
$577$	−31.1204	−1.29556	−0.647780	+	0.761827i	$0.724302\pi$
$578$	16.9809	0.706313
$579$	−17.6595	−0.733903
$580$	9.24062	0.383696
$581$	−2.20436	−0.0914521
$582$	5.38995	0.223420
$583$	0	0
$584$	−11.0649	−0.457869
$585$	−5.24056	−0.216670
$586$	6.92872	0.286223
$587$	−36.5570	−1.50887	−0.754435	−	0.656374i	$-0.772089\pi$
$587$	−36.5570	−1.50887	−0.754435	+	0.656374i	$0.772089\pi$
$588$	1.22201	0.0503947
$589$	−5.28850	−0.217909
$590$	9.30512	0.383086
$591$	−27.7334	−1.14080
$592$	1.66859	0.0685787
$593$	4.49251	0.184485	0.0922427	−	0.995737i	$-0.470596\pi$
$593$	4.49251	0.184485	0.0922427	+	0.995737i	$0.470596\pi$
$594$	0	0
$595$	−0.138127	−0.00566264
$596$	−17.1038	−0.700598
$597$	11.5344	0.472073
$598$	5.25370	0.214840
$599$	−5.04343	−0.206069	−0.103035	−	0.994678i	$-0.532855\pi$
$599$	−5.04343	−0.206069	−0.103035	+	0.994678i	$0.532855\pi$
$600$	−1.22201	−0.0498882
$601$	27.5263	1.12282	0.561410	−	0.827538i	$-0.310259\pi$
$601$	27.5263	1.12282	0.561410	+	0.827538i	$0.310259\pi$
$602$	−10.6660	−0.434715
$603$	2.78708	0.113499
$604$	−3.21272	−0.130724
$605$	0	0
$606$	15.3744	0.624542
$607$	3.44128	0.139677	0.0698387	−	0.997558i	$-0.477752\pi$
$607$	3.44128	0.139677	0.0698387	+	0.997558i	$0.477752\pi$
$608$	0.515316	0.0208988
$609$	−11.2921	−0.457579
$610$	−13.5218	−0.547483
$611$	6.28477	0.254254
$612$	−0.208116	−0.00841258
$613$	11.1154	0.448949	0.224474	−	0.974480i	$-0.427934\pi$
$613$	11.1154	0.448949	0.224474	+	0.974480i	$0.427934\pi$
$614$	−20.6340	−0.832719
$615$	−14.8923	−0.600517
$616$	0	0
$617$	−10.7522	−0.432869	−0.216434	−	0.976297i	$-0.569443\pi$
$617$	−10.7522	−0.432869	−0.216434	+	0.976297i	$0.569443\pi$
$618$	3.64733	0.146717
$619$	10.1391	0.407523	0.203761	−	0.979021i	$-0.434683\pi$
$619$	10.1391	0.407523	0.203761	+	0.979021i	$0.434683\pi$
$620$	−10.2626	−0.412158
$621$	−8.31855	−0.333812
$622$	20.2359	0.811388
$623$	1.74164	0.0697775
$624$	−4.25033	−0.170150
$625$	1.00000	0.0400000
$626$	4.40784	0.176173
$627$	0	0
$628$	2.74824	0.109667
$629$	0.230477	0.00918972
$630$	−1.50670	−0.0600285
$631$	−2.60248	−0.103603	−0.0518015	−	0.998657i	$-0.516496\pi$
$631$	−2.60248	−0.103603	−0.0518015	+	0.998657i	$0.516496\pi$
$632$	9.98676	0.397252
$633$	−13.6253	−0.541558
$634$	−25.9982	−1.03252
$635$	12.6728	0.502903
$636$	1.69987	0.0674042
$637$	−3.47816	−0.137810
$638$	0	0
$639$	9.63104	0.380998
$640$	1.00000	0.0395285
$641$	−12.1917	−0.481543	−0.240771	−	0.970582i	$-0.577400\pi$
$641$	−12.1917	−0.481543	−0.240771	+	0.970582i	$0.577400\pi$
$642$	16.2254	0.640365
$643$	−12.1108	−0.477603	−0.238802	−	0.971068i	$-0.576755\pi$
$643$	−12.1108	−0.477603	−0.238802	+	0.971068i	$0.576755\pi$
$644$	1.51048	0.0595213
$645$	−13.0339	−0.513211
$646$	0.0711788	0.00280049
$647$	−4.91915	−0.193392	−0.0966959	−	0.995314i	$-0.530827\pi$
$647$	−4.91915	−0.193392	−0.0966959	+	0.995314i	$0.530827\pi$
$648$	2.20974	0.0868068
$649$	0	0
$650$	3.47816	0.136425
$651$	12.5410	0.491521
$652$	−12.5201	−0.490325
$653$	−13.2506	−0.518537	−0.259268	−	0.965805i	$-0.583481\pi$
$653$	−13.2506	−0.518537	−0.259268	+	0.965805i	$0.583481\pi$
$654$	0.614353	0.0240231
$655$	15.1497	0.591948
$656$	12.1868	0.475814
$657$	−16.6715	−0.650418
$658$	1.80692	0.0704412
$659$	−30.5268	−1.18916	−0.594579	−	0.804038i	$-0.702681\pi$
$659$	−30.5268	−1.18916	−0.594579	+	0.804038i	$0.702681\pi$
$660$	0	0
$661$	−2.30028	−0.0894707	−0.0447353	−	0.998999i	$-0.514244\pi$
$661$	−2.30028	−0.0894707	−0.0447353	+	0.998999i	$0.514244\pi$
$662$	19.8219	0.770400
$663$	−0.587084	−0.0228005
$664$	2.20436	0.0855456
$665$	0.515316	0.0199831
$666$	2.51407	0.0974183
$667$	−13.9578	−0.540448
$668$	−17.0335	−0.659047
$669$	−4.86114	−0.187943
$670$	−1.84979	−0.0714636
$671$	0	0
$672$	−1.22201	−0.0471399
$673$	24.9976	0.963588	0.481794	−	0.876284i	$-0.339985\pi$
$673$	24.9976	0.963588	0.481794	+	0.876284i	$0.339985\pi$
$674$	30.3840	1.17035
$675$	−5.50722	−0.211973
$676$	−0.902388	−0.0347072
$677$	−16.6035	−0.638123	−0.319062	−	0.947734i	$-0.603368\pi$
$677$	−16.6035	−0.638123	−0.319062	+	0.947734i	$0.603368\pi$
$678$	10.8905	0.418246
$679$	−4.41074	−0.169269
$680$	0.138127	0.00529691
$681$	−26.5600	−1.01778
$682$	0	0
$683$	13.6055	0.520598	0.260299	−	0.965528i	$-0.416179\pi$
$683$	13.6055	0.520598	0.260299	+	0.965528i	$0.416179\pi$
$684$	0.776427	0.0296874
$685$	−21.8856	−0.836204
$686$	−1.00000	−0.0381802
$687$	2.01164	0.0767489
$688$	10.6660	0.406638
$689$	−4.83829	−0.184324
$690$	1.84582	0.0702691
$691$	−28.3703	−1.07926	−0.539629	−	0.841903i	$-0.681436\pi$
$691$	−28.3703	−1.07926	−0.539629	+	0.841903i	$0.681436\pi$
$692$	−9.38603	−0.356803
$693$	0	0
$694$	−16.6544	−0.632194
$695$	2.47370	0.0938328
$696$	11.2921	0.428026
$697$	1.68332	0.0637603
$698$	−1.70386	−0.0644922
$699$	1.36436	0.0516050
$700$	1.00000	0.0377964
$701$	−21.8649	−0.825826	−0.412913	−	0.910770i	$-0.635489\pi$
$701$	−21.8649	−0.825826	−0.412913	+	0.910770i	$0.635489\pi$
$702$	−19.1550	−0.722958
$703$	−0.859852	−0.0324299
$704$	0	0
$705$	2.20807	0.0831607
$706$	−10.7417	−0.404270
$707$	−12.5813	−0.473167
$708$	11.3709	0.427345
$709$	37.6438	1.41374	0.706872	−	0.707342i	$-0.250106\pi$
$709$	37.6438	1.41374	0.706872	+	0.707342i	$0.250106\pi$
$710$	−6.39213	−0.239892
$711$	15.0471	0.564309
$712$	−1.74164	−0.0652709
$713$	15.5015	0.580537
$714$	−0.168791	−0.00631686
$715$	0	0
$716$	−11.1233	−0.415698
$717$	−21.1551	−0.790051
$718$	−16.2804	−0.607579
$719$	8.91960	0.332645	0.166322	−	0.986071i	$-0.446811\pi$
$719$	8.91960	0.332645	0.166322	+	0.986071i	$0.446811\pi$
$720$	1.50670	0.0561515
$721$	−2.98471	−0.111156
$722$	18.7344	0.697224
$723$	29.0256	1.07947
$724$	9.57646	0.355906
$725$	−9.24062	−0.343188
$726$	0	0
$727$	−21.9240	−0.813116	−0.406558	−	0.913625i	$-0.633271\pi$
$727$	−21.9240	−0.813116	−0.406558	+	0.913625i	$0.633271\pi$
$728$	3.47816	0.128909
$729$	23.5190	0.871073
$730$	11.0649	0.409531
$731$	1.47326	0.0544905
$732$	−16.5237	−0.610735
$733$	29.9606	1.10662	0.553310	−	0.832975i	$-0.313364\pi$
$733$	29.9606	1.10662	0.553310	+	0.832975i	$0.313364\pi$
$734$	21.0947	0.778621
$735$	−1.22201	−0.0450744
$736$	−1.51048	−0.0556771
$737$	0	0
$738$	18.3619	0.675910
$739$	−25.1030	−0.923428	−0.461714	−	0.887029i	$-0.652765\pi$
$739$	−25.1030	−0.923428	−0.461714	+	0.887029i	$0.652765\pi$
$740$	−1.66859	−0.0613387
$741$	2.19026	0.0804613
$742$	−1.39105	−0.0510670
$743$	36.8689	1.35259	0.676294	−	0.736632i	$-0.263585\pi$
$743$	36.8689	1.35259	0.676294	+	0.736632i	$0.263585\pi$
$744$	−12.5410	−0.459776
$745$	17.1038	0.626634
$746$	−13.9335	−0.510142
$747$	3.32131	0.121520
$748$	0	0
$749$	−13.2777	−0.485155
$750$	1.22201	0.0446213
$751$	30.4227	1.11014	0.555070	−	0.831803i	$-0.312691\pi$
$751$	30.4227	1.11014	0.555070	+	0.831803i	$0.312691\pi$
$752$	−1.80692	−0.0658917
$753$	14.8175	0.539979
$754$	−32.1404	−1.17048
$755$	3.21272	0.116923
$756$	−5.50722	−0.200295
$757$	−12.0400	−0.437601	−0.218801	−	0.975770i	$-0.570214\pi$
$757$	−12.0400	−0.437601	−0.218801	+	0.975770i	$0.570214\pi$
$758$	−22.1451	−0.804346
$759$	0	0
$760$	−0.515316	−0.0186925
$761$	11.4432	0.414817	0.207408	−	0.978254i	$-0.433497\pi$
$761$	11.4432	0.414817	0.207408	+	0.978254i	$0.433497\pi$
$762$	15.4862	0.561005
$763$	−0.502741	−0.0182005
$764$	9.79900	0.354515
$765$	0.208116	0.00752444
$766$	22.5171	0.813574
$767$	−32.3647	−1.16862
$768$	1.22201	0.0440953
$769$	−3.36501	−0.121346	−0.0606728	−	0.998158i	$-0.519325\pi$
$769$	−3.36501	−0.121346	−0.0606728	+	0.998158i	$0.519325\pi$
$770$	0	0
$771$	−34.9609	−1.25909
$772$	−14.4512	−0.520111
$773$	−3.19918	−0.115067	−0.0575333	−	0.998344i	$-0.518324\pi$
$773$	−3.19918	−0.115067	−0.0575333	+	0.998344i	$0.518324\pi$
$774$	16.0705	0.577643
$775$	10.2626	0.368645
$776$	4.41074	0.158336
$777$	2.03903	0.0731498
$778$	20.8343	0.746946
$779$	−6.28004	−0.225006
$780$	4.25033	0.152186
$781$	0	0
$782$	−0.208638	−0.00746087
$783$	50.8901	1.81866
$784$	1.00000	0.0357143
$785$	−2.74824	−0.0980889
$786$	18.5130	0.660338
$787$	5.27916	0.188182	0.0940908	−	0.995564i	$-0.470006\pi$
$787$	5.27916	0.188182	0.0940908	+	0.995564i	$0.470006\pi$
$788$	−22.6950	−0.808476
$789$	37.2392	1.32575
$790$	−9.98676	−0.355313
$791$	−8.91196	−0.316873
$792$	0	0
$793$	47.0311	1.67012
$794$	−19.0865	−0.677355
$795$	−1.69987	−0.0602881
$796$	9.43893	0.334554
$797$	41.1536	1.45773	0.728867	−	0.684655i	$-0.240047\pi$
$797$	41.1536	1.45773	0.728867	+	0.684655i	$0.240047\pi$
$798$	0.629719	0.0222918
$799$	−0.249584	−0.00882964
$800$	−1.00000	−0.0353553
$801$	−2.62414	−0.0927194
$802$	−30.1895	−1.06603
$803$	0	0
$804$	−2.26045	−0.0797201
$805$	−1.51048	−0.0532375
$806$	35.6951	1.25731
$807$	−37.9415	−1.33560
$808$	12.5813	0.442608
$809$	11.2803	0.396596	0.198298	−	0.980142i	$-0.436459\pi$
$809$	11.2803	0.396596	0.198298	+	0.980142i	$0.436459\pi$
$810$	−2.20974	−0.0776424
$811$	37.0216	1.30000	0.650002	−	0.759933i	$-0.274768\pi$
$811$	37.0216	1.30000	0.650002	+	0.759933i	$0.274768\pi$
$812$	−9.24062	−0.324282
$813$	−10.3987	−0.364700
$814$	0	0
$815$	12.5201	0.438560
$816$	0.168791	0.00590888
$817$	−5.49637	−0.192294
$818$	−29.4582	−1.02998
$819$	5.24056	0.183120
$820$	−12.1868	−0.425581
$821$	−49.7341	−1.73573	−0.867866	−	0.496799i	$-0.834509\pi$
$821$	−49.7341	−1.73573	−0.867866	+	0.496799i	$0.834509\pi$
$822$	−26.7443	−0.932813
$823$	34.5639	1.20482	0.602410	−	0.798187i	$-0.294207\pi$
$823$	34.5639	1.20482	0.602410	+	0.798187i	$0.294207\pi$
$824$	2.98471	0.103977
$825$	0	0
$826$	−9.30512	−0.323766
$827$	25.6050	0.890374	0.445187	−	0.895438i	$-0.353137\pi$
$827$	25.6050	0.890374	0.445187	+	0.895438i	$0.353137\pi$
$828$	−2.27585	−0.0790911
$829$	−12.0869	−0.419797	−0.209898	−	0.977723i	$-0.567313\pi$
$829$	−12.0869	−0.419797	−0.209898	+	0.977723i	$0.567313\pi$
$830$	−2.20436	−0.0765143
$831$	17.8895	0.620579
$832$	−3.47816	−0.120584
$833$	0.138127	0.00478580
$834$	3.02287	0.104674
$835$	17.0335	0.589469
$836$	0	0
$837$	−56.5186	−1.95357
$838$	20.4867	0.707700
$839$	−9.12559	−0.315050	−0.157525	−	0.987515i	$-0.550352\pi$
$839$	−9.12559	−0.315050	−0.157525	+	0.987515i	$0.550352\pi$
$840$	1.22201	0.0421632
$841$	56.3891	1.94445
$842$	2.61302	0.0900507
$843$	10.8985	0.375363
$844$	−11.1500	−0.383797
$845$	0.902388	0.0310431
$846$	−2.72249	−0.0936013
$847$	0	0
$848$	1.39105	0.0477688
$849$	−24.0934	−0.826883
$850$	−0.138127	−0.00473770
$851$	2.52038	0.0863975
$852$	−7.81122	−0.267608
$853$	−4.18612	−0.143330	−0.0716650	−	0.997429i	$-0.522831\pi$
$853$	−4.18612	−0.143330	−0.0716650	+	0.997429i	$0.522831\pi$
$854$	13.5218	0.462707
$855$	−0.776427	−0.0265533
$856$	13.2777	0.453821
$857$	23.8579	0.814971	0.407485	−	0.913212i	$-0.366406\pi$
$857$	23.8579	0.814971	0.407485	+	0.913212i	$0.366406\pi$
$858$	0	0
$859$	−11.8765	−0.405221	−0.202610	−	0.979259i	$-0.564943\pi$
$859$	−11.8765	−0.405221	−0.202610	+	0.979259i	$0.564943\pi$
$860$	−10.6660	−0.363708
$861$	14.8923	0.507529
$862$	−9.87795	−0.336444
$863$	16.8809	0.574633	0.287316	−	0.957836i	$-0.407237\pi$
$863$	16.8809	0.574633	0.287316	+	0.957836i	$0.407237\pi$
$864$	5.50722	0.187359
$865$	9.38603	0.319135
$866$	−19.5259	−0.663518
$867$	−20.7508	−0.704733
$868$	10.2626	0.348337
$869$	0	0
$870$	−11.2921	−0.382838
$871$	6.43387	0.218003
$872$	0.502741	0.0170250
$873$	6.64567	0.224922
$874$	0.778375	0.0263289
$875$	−1.00000	−0.0338062
$876$	13.5214	0.456845
$877$	8.83200	0.298236	0.149118	−	0.988819i	$-0.452357\pi$
$877$	8.83200	0.298236	0.149118	+	0.988819i	$0.452357\pi$
$878$	3.38579	0.114265
$879$	−8.46693	−0.285582
$880$	0	0
$881$	−9.23255	−0.311052	−0.155526	−	0.987832i	$-0.549707\pi$
$881$	−9.23255	−0.311052	−0.155526	+	0.987832i	$0.549707\pi$
$882$	1.50670	0.0507333
$883$	−36.8709	−1.24080	−0.620402	−	0.784284i	$-0.713031\pi$
$883$	−36.8709	−1.24080	−0.620402	+	0.784284i	$0.713031\pi$
$884$	−0.480427	−0.0161585
$885$	−11.3709	−0.382229
$886$	19.3485	0.650026
$887$	30.1184	1.01128	0.505638	−	0.862746i	$-0.331257\pi$
$887$	30.1184	1.01128	0.505638	+	0.862746i	$0.331257\pi$
$888$	−2.03903	−0.0684253
$889$	−12.6728	−0.425030
$890$	1.74164	0.0583800
$891$	0	0
$892$	−3.97800	−0.133193
$893$	0.931135	0.0311593
$894$	20.9009	0.699031
$895$	11.1233	0.371812
$896$	−1.00000	−0.0334077
$897$	−6.42005	−0.214359
$898$	−33.1331	−1.10567
$899$	−94.8332	−3.16286
$900$	−1.50670	−0.0502234
$901$	0.192141	0.00640114
$902$	0	0
$903$	13.0339	0.433742
$904$	8.91196	0.296407
$905$	−9.57646	−0.318332
$906$	3.92596	0.130431
$907$	−49.5891	−1.64658	−0.823290	−	0.567621i	$-0.807864\pi$
$907$	−49.5891	−1.64658	−0.823290	+	0.567621i	$0.807864\pi$
$908$	−21.7347	−0.721292
$909$	18.9562	0.628738
$910$	−3.47816	−0.115300
$911$	−51.5703	−1.70860	−0.854301	−	0.519779i	$-0.826014\pi$
$911$	−51.5703	−1.70860	−0.854301	+	0.519779i	$0.826014\pi$
$912$	−0.629719	−0.0208521
$913$	0	0
$914$	−12.6845	−0.419567
$915$	16.5237	0.546258
$916$	1.64618	0.0543913
$917$	−15.1497	−0.500288
$918$	0.760693	0.0251066
$919$	−29.1350	−0.961075	−0.480537	−	0.876974i	$-0.659558\pi$
$919$	−29.1350	−0.961075	−0.480537	+	0.876974i	$0.659558\pi$
$920$	1.51048	0.0497991
$921$	25.2148	0.830856
$922$	19.4617	0.640937
$923$	22.2329	0.731804
$924$	0	0
$925$	1.66859	0.0548630
$926$	−29.6401	−0.974034
$927$	4.49706	0.147703
$928$	9.24062	0.303338
$929$	−45.0244	−1.47720	−0.738602	−	0.674142i	$-0.764513\pi$
$929$	−45.0244	−1.47720	−0.738602	+	0.674142i	$0.764513\pi$
$930$	12.5410	0.411236
$931$	−0.515316	−0.0168888
$932$	1.11650	0.0365720
$933$	−24.7284	−0.809573
$934$	−26.8009	−0.876953
$935$	0	0
$936$	−5.24056	−0.171293
$937$	6.89838	0.225360	0.112680	−	0.993631i	$-0.464056\pi$
$937$	6.89838	0.225360	0.112680	+	0.993631i	$0.464056\pi$
$938$	1.84979	0.0603978
$939$	−5.38641	−0.175779
$940$	1.80692	0.0589353
$941$	6.88982	0.224602	0.112301	−	0.993674i	$-0.464178\pi$
$941$	6.88982	0.224602	0.112301	+	0.993674i	$0.464178\pi$
$942$	−3.35836	−0.109421
$943$	18.4079	0.599445
$944$	9.30512	0.302856
$945$	5.50722	0.179150
$946$	0	0
$947$	34.2294	1.11231	0.556154	−	0.831079i	$-0.312277\pi$
$947$	34.2294	1.11231	0.556154	+	0.831079i	$0.312277\pi$
$948$	−12.2039	−0.396363
$949$	−38.4856	−1.24929
$950$	0.515316	0.0167190
$951$	31.7699	1.03021
$952$	−0.138127	−0.00447671
$953$	−57.9062	−1.87577	−0.937883	−	0.346951i	$-0.887217\pi$
$953$	−57.9062	−1.87577	−0.937883	+	0.346951i	$0.887217\pi$
$954$	2.09590	0.0678571
$955$	−9.79900	−0.317088
$956$	−17.3118	−0.559903
$957$	0	0
$958$	13.3413	0.431039
$959$	21.8856	0.706721
$960$	−1.22201	−0.0394401
$961$	74.3218	2.39748
$962$	5.80363	0.187117
$963$	20.0055	0.644668
$964$	23.7524	0.765015
$965$	14.4512	0.465202
$966$	−1.84582	−0.0593882
$967$	−39.7063	−1.27687	−0.638435	−	0.769676i	$-0.720418\pi$
$967$	−39.7063	−1.27687	−0.638435	+	0.769676i	$0.720418\pi$
$968$	0	0
$969$	−0.0869809	−0.00279423
$970$	−4.41074	−0.141620
$971$	−7.63191	−0.244920	−0.122460	−	0.992473i	$-0.539078\pi$
$971$	−7.63191	−0.244920	−0.122460	+	0.992473i	$0.539078\pi$
$972$	13.8213	0.443319
$973$	−2.47370	−0.0793032
$974$	13.3718	0.428459
$975$	−4.25033	−0.136120
$976$	−13.5218	−0.432823
$977$	14.9297	0.477643	0.238821	−	0.971063i	$-0.423239\pi$
$977$	14.9297	0.477643	0.238821	+	0.971063i	$0.423239\pi$
$978$	15.2996	0.489228
$979$	0	0
$980$	−1.00000	−0.0319438
$981$	0.757481	0.0241845
$982$	25.9713	0.828776
$983$	1.28851	0.0410971	0.0205485	−	0.999789i	$-0.493459\pi$
$983$	1.28851	0.0410971	0.0205485	+	0.999789i	$0.493459\pi$
$984$	−14.8923	−0.474750
$985$	22.6950	0.723122
$986$	1.27638	0.0406481
$987$	−2.20807	−0.0702836
$988$	1.79235	0.0570223
$989$	16.1108	0.512295
$990$	0	0
$991$	30.8872	0.981163	0.490582	−	0.871395i	$-0.336784\pi$
$991$	30.8872	0.981163	0.490582	+	0.871395i	$0.336784\pi$
$992$	−10.2626	−0.325839
$993$	−24.2225	−0.768677
$994$	6.39213	0.202746
$995$	−9.43893	−0.299234
$996$	−2.69374	−0.0853543
$997$	44.9211	1.42266	0.711332	−	0.702856i	$-0.248092\pi$
$997$	44.9211	1.42266	0.711332	+	0.702856i	$0.248092\pi$
$998$	22.5866	0.714966
$999$	−9.18930	−0.290736

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8470.2.a.dg.1.6		8
11.7	odd	10		770.2.n.k.71.2	✓	16
11.8	odd	10		770.2.n.k.141.2	yes	16
11.10	odd	2		8470.2.a.dh.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.k.71.2	✓	16	11.7	odd	10
770.2.n.k.141.2	yes	16	11.8	odd	10
8470.2.a.dg.1.6		8	1.1	even	1	trivial
8470.2.a.dh.1.6		8	11.10	odd	2

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Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.22201 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.22201 q^{6} +1.00000 q^{7} -1.00000 q^{8} -1.50670 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.22201 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.22201 q^{6} +1.00000 q^{7} -1.00000 q^{8} -1.50670 q^{9} +1.00000 q^{10} +1.22201 q^{12} -3.47816 q^{13} -1.00000 q^{14} -1.22201 q^{15} +1.00000 q^{16} +0.138127 q^{17} +1.50670 q^{18} -0.515316 q^{19} -1.00000 q^{20} +1.22201 q^{21} +1.51048 q^{23} -1.22201 q^{24} +1.00000 q^{25} +3.47816 q^{26} -5.50722 q^{27} +1.00000 q^{28} -9.24062 q^{29} +1.22201 q^{30} +10.2626 q^{31} -1.00000 q^{32} -0.138127 q^{34} -1.00000 q^{35} -1.50670 q^{36} +1.66859 q^{37} +0.515316 q^{38} -4.25033 q^{39} +1.00000 q^{40} +12.1868 q^{41} -1.22201 q^{42} +10.6660 q^{43} +1.50670 q^{45} -1.51048 q^{46} -1.80692 q^{47} +1.22201 q^{48} +1.00000 q^{49} -1.00000 q^{50} +0.168791 q^{51} -3.47816 q^{52} +1.39105 q^{53} +5.50722 q^{54} -1.00000 q^{56} -0.629719 q^{57} +9.24062 q^{58} +9.30512 q^{59} -1.22201 q^{60} -13.5218 q^{61} -10.2626 q^{62} -1.50670 q^{63} +1.00000 q^{64} +3.47816 q^{65} -1.84979 q^{67} +0.138127 q^{68} +1.84582 q^{69} +1.00000 q^{70} -6.39213 q^{71} +1.50670 q^{72} +11.0649 q^{73} -1.66859 q^{74} +1.22201 q^{75} -0.515316 q^{76} +4.25033 q^{78} -9.98676 q^{79} -1.00000 q^{80} -2.20974 q^{81} -12.1868 q^{82} -2.20436 q^{83} +1.22201 q^{84} -0.138127 q^{85} -10.6660 q^{86} -11.2921 q^{87} +1.74164 q^{89} -1.50670 q^{90} -3.47816 q^{91} +1.51048 q^{92} +12.5410 q^{93} +1.80692 q^{94} +0.515316 q^{95} -1.22201 q^{96} -4.41074 q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 8 q^{4} - 8 q^{5} + 8 q^{7} - 8 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 + 8 * q^4 - 8 * q^5 + 8 * q^7 - 8 * q^8 + 8 * q^9	\( 8 q - 8 q^{2} + 8 q^{4} - 8 q^{5} + 8 q^{7} - 8 q^{8} + 8 q^{9} + 8 q^{10} + q^{13} - 8 q^{14} + 8 q^{16} - 6 q^{17} - 8 q^{18} - 5 q^{19} - 8 q^{20} + 10 q^{23} + 8 q^{25} - q^{26} + 8 q^{28} - 3 q^{29} - 8 q^{31} - 8 q^{32} + 6 q^{34} - 8 q^{35} + 8 q^{36} - 6 q^{37} + 5 q^{38} - 35 q^{39} + 8 q^{40} - 11 q^{41} + 5 q^{43} - 8 q^{45} - 10 q^{46} - 15 q^{47} + 8 q^{49} - 8 q^{50} + 6 q^{51} + q^{52} - 16 q^{53} - 8 q^{56} - 38 q^{57} + 3 q^{58} - 9 q^{59} - 32 q^{61} + 8 q^{62} + 8 q^{63} + 8 q^{64} - q^{65} + 33 q^{67} - 6 q^{68} - 22 q^{69} + 8 q^{70} + 11 q^{71} - 8 q^{72} + 34 q^{73} + 6 q^{74} - 5 q^{76} + 35 q^{78} - 31 q^{79} - 8 q^{80} + 20 q^{81} + 11 q^{82} - 50 q^{83} + 6 q^{85} - 5 q^{86} + 12 q^{87} + q^{89} + 8 q^{90} + q^{91} + 10 q^{92} + 26 q^{93} + 15 q^{94} + 5 q^{95} - 4 q^{97} - 8 q^{98}+O(q^{100}) \) 8 * q - 8 * q^2 + 8 * q^4 - 8 * q^5 + 8 * q^7 - 8 * q^8 + 8 * q^9 + 8 * q^10 + q^13 - 8 * q^14 + 8 * q^16 - 6 * q^17 - 8 * q^18 - 5 * q^19 - 8 * q^20 + 10 * q^23 + 8 * q^25 - q^26 + 8 * q^28 - 3 * q^29 - 8 * q^31 - 8 * q^32 + 6 * q^34 - 8 * q^35 + 8 * q^36 - 6 * q^37 + 5 * q^38 - 35 * q^39 + 8 * q^40 - 11 * q^41 + 5 * q^43 - 8 * q^45 - 10 * q^46 - 15 * q^47 + 8 * q^49 - 8 * q^50 + 6 * q^51 + q^52 - 16 * q^53 - 8 * q^56 - 38 * q^57 + 3 * q^58 - 9 * q^59 - 32 * q^61 + 8 * q^62 + 8 * q^63 + 8 * q^64 - q^65 + 33 * q^67 - 6 * q^68 - 22 * q^69 + 8 * q^70 + 11 * q^71 - 8 * q^72 + 34 * q^73 + 6 * q^74 - 5 * q^76 + 35 * q^78 - 31 * q^79 - 8 * q^80 + 20 * q^81 + 11 * q^82 - 50 * q^83 + 6 * q^85 - 5 * q^86 + 12 * q^87 + q^89 + 8 * q^90 + q^91 + 10 * q^92 + 26 * q^93 + 15 * q^94 + 5 * q^95 - 4 * q^97 - 8 * q^98

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