LMFDB - Embedded newform 8470.2.a.cw.1.5

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:	$6$
Coefficient field:	6.6.19898000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 10x^{4} + 7x^{3} + 24x^{2} - 15x - 5 $ x^6 - x^5 - 10x^4 + 7x^3 + 24x^2 - 15x - 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			1.5
Root			$-2.05906$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +2.05906 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.05906 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.23973 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.05906 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.05906 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.23973 q^{9} -1.00000 q^{10} +2.05906 q^{12} -2.27257 q^{13} -1.00000 q^{14} +2.05906 q^{15} +1.00000 q^{16} -7.44890 q^{17} -1.23973 q^{18} -0.851836 q^{19} +1.00000 q^{20} +2.05906 q^{21} +0.651398 q^{23} -2.05906 q^{24} +1.00000 q^{25} +2.27257 q^{26} -3.62450 q^{27} +1.00000 q^{28} +2.36641 q^{29} -2.05906 q^{30} -0.145026 q^{31} -1.00000 q^{32} +7.44890 q^{34} +1.00000 q^{35} +1.23973 q^{36} +2.32711 q^{37} +0.851836 q^{38} -4.67936 q^{39} -1.00000 q^{40} +4.64211 q^{41} -2.05906 q^{42} -11.7588 q^{43} +1.23973 q^{45} -0.651398 q^{46} -5.27536 q^{47} +2.05906 q^{48} +1.00000 q^{49} -1.00000 q^{50} -15.3377 q^{51} -2.27257 q^{52} -0.962643 q^{53} +3.62450 q^{54} -1.00000 q^{56} -1.75398 q^{57} -2.36641 q^{58} +1.04296 q^{59} +2.05906 q^{60} -3.58885 q^{61} +0.145026 q^{62} +1.23973 q^{63} +1.00000 q^{64} -2.27257 q^{65} -0.430333 q^{67} -7.44890 q^{68} +1.34127 q^{69} -1.00000 q^{70} +10.6384 q^{71} -1.23973 q^{72} -1.16253 q^{73} -2.32711 q^{74} +2.05906 q^{75} -0.851836 q^{76} +4.67936 q^{78} +10.7068 q^{79} +1.00000 q^{80} -11.1823 q^{81} -4.64211 q^{82} +1.08367 q^{83} +2.05906 q^{84} -7.44890 q^{85} +11.7588 q^{86} +4.87258 q^{87} +3.73563 q^{89} -1.23973 q^{90} -2.27257 q^{91} +0.651398 q^{92} -0.298618 q^{93} +5.27536 q^{94} -0.851836 q^{95} -2.05906 q^{96} -1.47983 q^{97} -1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} - q^{3} + 6 q^{4} + 6 q^{5} + q^{6} + 6 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 - q^3 + 6 * q^4 + 6 * q^5 + q^6 + 6 * q^7 - 6 * q^8 + 3 * q^9	$ 6 q - 6 q^{2} - q^{3} + 6 q^{4} + 6 q^{5} + q^{6} + 6 q^{7} - 6 q^{8} + 3 q^{9} - 6 q^{10} - q^{12} - 9 q^{13} - 6 q^{14} - q^{15} + 6 q^{16} - 9 q^{17} - 3 q^{18} - 12 q^{19} + 6 q^{20} - q^{21} + 4 q^{23} + q^{24} + 6 q^{25} + 9 q^{26} - 4 q^{27} + 6 q^{28} - 15 q^{29} + q^{30} + 8 q^{31} - 6 q^{32} + 9 q^{34} + 6 q^{35} + 3 q^{36} - 4 q^{37} + 12 q^{38} + 19 q^{39} - 6 q^{40} - 4 q^{41} + q^{42} - 30 q^{43} + 3 q^{45} - 4 q^{46} - 7 q^{47} - q^{48} + 6 q^{49} - 6 q^{50} - 16 q^{51} - 9 q^{52} - 6 q^{53} + 4 q^{54} - 6 q^{56} + 14 q^{57} + 15 q^{58} + 4 q^{59} - q^{60} + 14 q^{61} - 8 q^{62} + 3 q^{63} + 6 q^{64} - 9 q^{65} + 18 q^{67} - 9 q^{68} - 10 q^{69} - 6 q^{70} + 23 q^{71} - 3 q^{72} - 23 q^{73} + 4 q^{74} - q^{75} - 12 q^{76} - 19 q^{78} - 21 q^{79} + 6 q^{80} - 18 q^{81} + 4 q^{82} - 25 q^{83} - q^{84} - 9 q^{85} + 30 q^{86} - 14 q^{87} - 18 q^{89} - 3 q^{90} - 9 q^{91} + 4 q^{92} - 24 q^{93} + 7 q^{94} - 12 q^{95} + q^{96} + 7 q^{97} - 6 q^{98}+O(q^{100}) $ 6 * q - 6 * q^2 - q^3 + 6 * q^4 + 6 * q^5 + q^6 + 6 * q^7 - 6 * q^8 + 3 * q^9 - 6 * q^10 - q^12 - 9 * q^13 - 6 * q^14 - q^15 + 6 * q^16 - 9 * q^17 - 3 * q^18 - 12 * q^19 + 6 * q^20 - q^21 + 4 * q^23 + q^24 + 6 * q^25 + 9 * q^26 - 4 * q^27 + 6 * q^28 - 15 * q^29 + q^30 + 8 * q^31 - 6 * q^32 + 9 * q^34 + 6 * q^35 + 3 * q^36 - 4 * q^37 + 12 * q^38 + 19 * q^39 - 6 * q^40 - 4 * q^41 + q^42 - 30 * q^43 + 3 * q^45 - 4 * q^46 - 7 * q^47 - q^48 + 6 * q^49 - 6 * q^50 - 16 * q^51 - 9 * q^52 - 6 * q^53 + 4 * q^54 - 6 * q^56 + 14 * q^57 + 15 * q^58 + 4 * q^59 - q^60 + 14 * q^61 - 8 * q^62 + 3 * q^63 + 6 * q^64 - 9 * q^65 + 18 * q^67 - 9 * q^68 - 10 * q^69 - 6 * q^70 + 23 * q^71 - 3 * q^72 - 23 * q^73 + 4 * q^74 - q^75 - 12 * q^76 - 19 * q^78 - 21 * q^79 + 6 * q^80 - 18 * q^81 + 4 * q^82 - 25 * q^83 - q^84 - 9 * q^85 + 30 * q^86 - 14 * q^87 - 18 * q^89 - 3 * q^90 - 9 * q^91 + 4 * q^92 - 24 * q^93 + 7 * q^94 - 12 * q^95 + q^96 + 7 * q^97 - 6 * 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
$3$	2.05906	1.18880	0.594400	−	0.804170i	$-0.297390\pi$
$3$	2.05906	1.18880	0.594400	+	0.804170i	$0.297390\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.05906	−0.840608
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	1.23973	0.413245
$10$	−1.00000	−0.316228
$11$	0	0
$11$	0	0
$12$	2.05906	0.594400
$13$	−2.27257	−0.630298	−0.315149	−	0.949042i	$-0.602054\pi$
$13$	−2.27257	−0.630298	−0.315149	+	0.949042i	$0.602054\pi$
$14$	−1.00000	−0.267261
$15$	2.05906	0.531647
$16$	1.00000	0.250000
$17$	−7.44890	−1.80662	−0.903312	−	0.428985i	$-0.858871\pi$
$17$	−7.44890	−1.80662	−0.903312	+	0.428985i	$0.858871\pi$
$18$	−1.23973	−0.292208
$19$	−0.851836	−0.195425	−0.0977123	−	0.995215i	$-0.531152\pi$
$19$	−0.851836	−0.195425	−0.0977123	+	0.995215i	$0.531152\pi$
$20$	1.00000	0.223607
$21$	2.05906	0.449324
$22$	0	0
$23$	0.651398	0.135826	0.0679130	−	0.997691i	$-0.478366\pi$
$23$	0.651398	0.135826	0.0679130	+	0.997691i	$0.478366\pi$
$24$	−2.05906	−0.420304
$25$	1.00000	0.200000
$26$	2.27257	0.445688
$27$	−3.62450	−0.697534
$28$	1.00000	0.188982
$29$	2.36641	0.439431	0.219715	−	0.975564i	$-0.429487\pi$
$29$	2.36641	0.439431	0.219715	+	0.975564i	$0.429487\pi$
$30$	−2.05906	−0.375931
$31$	−0.145026	−0.0260475	−0.0130237	−	0.999915i	$-0.504146\pi$
$31$	−0.145026	−0.0260475	−0.0130237	+	0.999915i	$0.504146\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	7.44890	1.27748
$35$	1.00000	0.169031
$36$	1.23973	0.206622
$37$	2.32711	0.382574	0.191287	−	0.981534i	$-0.438734\pi$
$37$	2.32711	0.382574	0.191287	+	0.981534i	$0.438734\pi$
$38$	0.851836	0.138186
$39$	−4.67936	−0.749298
$40$	−1.00000	−0.158114
$41$	4.64211	0.724976	0.362488	−	0.931988i	$-0.381927\pi$
$41$	4.64211	0.724976	0.362488	+	0.931988i	$0.381927\pi$
$42$	−2.05906	−0.317720
$43$	−11.7588	−1.79320	−0.896602	−	0.442837i	$-0.853972\pi$
$43$	−11.7588	−1.79320	−0.896602	+	0.442837i	$0.853972\pi$
$44$	0	0
$45$	1.23973	0.184809
$46$	−0.651398	−0.0960434
$47$	−5.27536	−0.769491	−0.384746	−	0.923023i	$-0.625711\pi$
$47$	−5.27536	−0.769491	−0.384746	+	0.923023i	$0.625711\pi$
$48$	2.05906	0.297200
$49$	1.00000	0.142857
$50$	−1.00000	−0.141421
$51$	−15.3377	−2.14771
$52$	−2.27257	−0.315149
$53$	−0.962643	−0.132229	−0.0661146	−	0.997812i	$-0.521060\pi$
$53$	−0.962643	−0.132229	−0.0661146	+	0.997812i	$0.521060\pi$
$54$	3.62450	0.493231
$55$	0	0
$56$	−1.00000	−0.133631
$57$	−1.75398	−0.232321
$58$	−2.36641	−0.310724
$59$	1.04296	0.135782	0.0678911	−	0.997693i	$-0.478373\pi$
$59$	1.04296	0.135782	0.0678911	+	0.997693i	$0.478373\pi$
$60$	2.05906	0.265824
$61$	−3.58885	−0.459505	−0.229752	−	0.973249i	$-0.573792\pi$
$61$	−3.58885	−0.459505	−0.229752	+	0.973249i	$0.573792\pi$
$62$	0.145026	0.0184183
$63$	1.23973	0.156192
$64$	1.00000	0.125000
$65$	−2.27257	−0.281878
$66$	0	0
$67$	−0.430333	−0.0525735	−0.0262868	−	0.999654i	$-0.508368\pi$
$67$	−0.430333	−0.0525735	−0.0262868	+	0.999654i	$0.508368\pi$
$68$	−7.44890	−0.903312
$69$	1.34127	0.161470
$70$	−1.00000	−0.119523
$71$	10.6384	1.26255	0.631276	−	0.775558i	$-0.282532\pi$
$71$	10.6384	1.26255	0.631276	+	0.775558i	$0.282532\pi$
$72$	−1.23973	−0.146104
$73$	−1.16253	−0.136063	−0.0680316	−	0.997683i	$-0.521672\pi$
$73$	−1.16253	−0.136063	−0.0680316	+	0.997683i	$0.521672\pi$
$74$	−2.32711	−0.270521
$75$	2.05906	0.237760
$76$	−0.851836	−0.0977123
$77$	0	0
$78$	4.67936	0.529833
$79$	10.7068	1.20461	0.602303	−	0.798268i	$-0.294250\pi$
$79$	10.7068	1.20461	0.602303	+	0.798268i	$0.294250\pi$
$80$	1.00000	0.111803
$81$	−11.1823	−1.24247
$82$	−4.64211	−0.512636
$83$	1.08367	0.118948	0.0594741	−	0.998230i	$-0.481058\pi$
$83$	1.08367	0.118948	0.0594741	+	0.998230i	$0.481058\pi$
$84$	2.05906	0.224662
$85$	−7.44890	−0.807947
$86$	11.7588	1.26799
$87$	4.87258	0.522395
$88$	0	0
$89$	3.73563	0.395976	0.197988	−	0.980204i	$-0.436559\pi$
$89$	3.73563	0.395976	0.197988	+	0.980204i	$0.436559\pi$
$90$	−1.23973	−0.130679
$91$	−2.27257	−0.238230
$92$	0.651398	0.0679130
$93$	−0.298618	−0.0309652
$94$	5.27536	0.544112
$95$	−0.851836	−0.0873965
$96$	−2.05906	−0.210152
$97$	−1.47983	−0.150254	−0.0751270	−	0.997174i	$-0.523936\pi$
$97$	−1.47983	−0.150254	−0.0751270	+	0.997174i	$0.523936\pi$
$98$	−1.00000	−0.101015
$99$	0	0
$100$	1.00000	0.100000
$101$	−13.9523	−1.38830	−0.694151	−	0.719830i	$-0.744220\pi$
$101$	−13.9523	−1.38830	−0.694151	+	0.719830i	$0.744220\pi$
$102$	15.3377	1.51866
$103$	−1.40558	−0.138496	−0.0692481	−	0.997599i	$-0.522060\pi$
$103$	−1.40558	−0.138496	−0.0692481	+	0.997599i	$0.522060\pi$
$104$	2.27257	0.222844
$105$	2.05906	0.200944
$106$	0.962643	0.0935001
$107$	−18.9282	−1.82985	−0.914927	−	0.403618i	$-0.867752\pi$
$107$	−18.9282	−1.82985	−0.914927	+	0.403618i	$0.867752\pi$
$108$	−3.62450	−0.348767
$109$	−10.8423	−1.03850	−0.519252	−	0.854621i	$-0.673789\pi$
$109$	−10.8423	−1.03850	−0.519252	+	0.854621i	$0.673789\pi$
$110$	0	0
$111$	4.79166	0.454804
$112$	1.00000	0.0944911
$113$	−17.1609	−1.61436	−0.807179	−	0.590307i	$-0.799007\pi$
$113$	−17.1609	−1.61436	−0.807179	+	0.590307i	$0.799007\pi$
$114$	1.75398	0.164276
$115$	0.651398	0.0607432
$116$	2.36641	0.219715
$117$	−2.81738	−0.260467
$118$	−1.04296	−0.0960125
$119$	−7.44890	−0.682839
$120$	−2.05906	−0.187966
$121$	0	0
$122$	3.58885	0.324919
$123$	9.55840	0.861852
$124$	−0.145026	−0.0130237
$125$	1.00000	0.0894427
$126$	−1.23973	−0.110444
$127$	11.1188	0.986631	0.493316	−	0.869850i	$-0.335785\pi$
$127$	11.1188	0.986631	0.493316	+	0.869850i	$0.335785\pi$
$128$	−1.00000	−0.0883883
$129$	−24.2121	−2.13176
$130$	2.27257	0.199318
$131$	−10.9162	−0.953749	−0.476874	−	0.878971i	$-0.658230\pi$
$131$	−10.9162	−0.953749	−0.476874	+	0.878971i	$0.658230\pi$
$132$	0	0
$133$	−0.851836	−0.0738635
$134$	0.430333	0.0371751
$135$	−3.62450	−0.311947
$136$	7.44890	0.638738
$137$	−4.81357	−0.411251	−0.205626	−	0.978631i	$-0.565923\pi$
$137$	−4.81357	−0.411251	−0.205626	+	0.978631i	$0.565923\pi$
$138$	−1.34127	−0.114176
$139$	−10.1432	−0.860336	−0.430168	−	0.902749i	$-0.641546\pi$
$139$	−10.1432	−0.860336	−0.430168	+	0.902749i	$0.641546\pi$
$140$	1.00000	0.0845154
$141$	−10.8623	−0.914771
$142$	−10.6384	−0.892759
$143$	0	0
$144$	1.23973	0.103311
$145$	2.36641	0.196519
$146$	1.16253	0.0962113
$147$	2.05906	0.169829
$148$	2.32711	0.191287
$149$	1.88432	0.154370	0.0771848	−	0.997017i	$-0.475407\pi$
$149$	1.88432	0.154370	0.0771848	+	0.997017i	$0.475407\pi$
$150$	−2.05906	−0.168122
$151$	14.3826	1.17044	0.585218	−	0.810876i	$-0.301009\pi$
$151$	14.3826	1.17044	0.585218	+	0.810876i	$0.301009\pi$
$152$	0.851836	0.0690930
$153$	−9.23466	−0.746578
$154$	0	0
$155$	−0.145026	−0.0116488
$156$	−4.67936	−0.374649
$157$	−12.6590	−1.01030	−0.505150	−	0.863031i	$-0.668563\pi$
$157$	−12.6590	−1.01030	−0.505150	+	0.863031i	$0.668563\pi$
$158$	−10.7068	−0.851784
$159$	−1.98214	−0.157194
$160$	−1.00000	−0.0790569
$161$	0.651398	0.0513374
$162$	11.1823	0.878561
$163$	−8.95282	−0.701239	−0.350620	−	0.936518i	$-0.614029\pi$
$163$	−8.95282	−0.701239	−0.350620	+	0.936518i	$0.614029\pi$
$164$	4.64211	0.362488
$165$	0	0
$166$	−1.08367	−0.0841091
$167$	6.36465	0.492511	0.246256	−	0.969205i	$-0.420800\pi$
$167$	6.36465	0.492511	0.246256	+	0.969205i	$0.420800\pi$
$168$	−2.05906	−0.158860
$169$	−7.83543	−0.602725
$170$	7.44890	0.571305
$171$	−1.05605	−0.0807582
$172$	−11.7588	−0.896602
$173$	−24.4230	−1.85684	−0.928421	−	0.371529i	$-0.878834\pi$
$173$	−24.4230	−1.85684	−0.928421	+	0.371529i	$0.878834\pi$
$174$	−4.87258	−0.369389
$175$	1.00000	0.0755929
$176$	0	0
$177$	2.14753	0.161418
$178$	−3.73563	−0.279997
$179$	5.80767	0.434086	0.217043	−	0.976162i	$-0.430359\pi$
$179$	5.80767	0.434086	0.217043	+	0.976162i	$0.430359\pi$
$180$	1.23973	0.0924044
$181$	−12.8812	−0.957450	−0.478725	−	0.877965i	$-0.658901\pi$
$181$	−12.8812	−0.957450	−0.478725	+	0.877965i	$0.658901\pi$
$182$	2.27257	0.168454
$183$	−7.38966	−0.546259
$184$	−0.651398	−0.0480217
$185$	2.32711	0.171093
$186$	0.298618	0.0218957
$187$	0	0
$188$	−5.27536	−0.384746
$189$	−3.62450	−0.263643
$190$	0.851836	0.0617987
$191$	−5.65871	−0.409450	−0.204725	−	0.978820i	$-0.565630\pi$
$191$	−5.65871	−0.409450	−0.204725	+	0.978820i	$0.565630\pi$
$192$	2.05906	0.148600
$193$	13.7878	0.992470	0.496235	−	0.868188i	$-0.334715\pi$
$193$	13.7878	0.992470	0.496235	+	0.868188i	$0.334715\pi$
$194$	1.47983	0.106246
$195$	−4.67936	−0.335096
$196$	1.00000	0.0714286
$197$	2.82825	0.201504	0.100752	−	0.994912i	$-0.467875\pi$
$197$	2.82825	0.201504	0.100752	+	0.994912i	$0.467875\pi$
$198$	0	0
$199$	−0.513194	−0.0363793	−0.0181897	−	0.999835i	$-0.505790\pi$
$199$	−0.513194	−0.0363793	−0.0181897	+	0.999835i	$0.505790\pi$
$200$	−1.00000	−0.0707107
$201$	−0.886082	−0.0624994
$202$	13.9523	0.981677
$203$	2.36641	0.166089
$204$	−15.3377	−1.07386
$205$	4.64211	0.324219
$206$	1.40558	0.0979316
$207$	0.807561	0.0561294
$208$	−2.27257	−0.157574
$209$	0	0
$210$	−2.05906	−0.142089
$211$	−20.4146	−1.40540	−0.702698	−	0.711488i	$-0.748021\pi$
$211$	−20.4146	−1.40540	−0.702698	+	0.711488i	$0.748021\pi$
$212$	−0.962643	−0.0661146
$213$	21.9052	1.50092
$214$	18.9282	1.29390
$215$	−11.7588	−0.801945
$216$	3.62450	0.246616
$217$	−0.145026	−0.00984502
$218$	10.8423	0.734333
$219$	−2.39371	−0.161752
$220$	0	0
$221$	16.9281	1.13871
$222$	−4.79166	−0.321595
$223$	15.3296	1.02654	0.513272	−	0.858226i	$-0.328433\pi$
$223$	15.3296	1.02654	0.513272	+	0.858226i	$0.328433\pi$
$224$	−1.00000	−0.0668153
$225$	1.23973	0.0826490
$226$	17.1609	1.14152
$227$	−28.8027	−1.91170	−0.955850	−	0.293856i	$-0.905061\pi$
$227$	−28.8027	−1.91170	−0.955850	+	0.293856i	$0.905061\pi$
$228$	−1.75398	−0.116160
$229$	7.06918	0.467145	0.233572	−	0.972339i	$-0.424958\pi$
$229$	7.06918	0.467145	0.233572	+	0.972339i	$0.424958\pi$
$230$	−0.651398	−0.0429519
$231$	0	0
$232$	−2.36641	−0.155362
$233$	25.1088	1.64493	0.822466	−	0.568814i	$-0.192598\pi$
$233$	25.1088	1.64493	0.822466	+	0.568814i	$0.192598\pi$
$234$	2.81738	0.184178
$235$	−5.27536	−0.344127
$236$	1.04296	0.0678911
$237$	22.0459	1.43203
$238$	7.44890	0.482840
$239$	9.09178	0.588098	0.294049	−	0.955790i	$-0.404997\pi$
$239$	9.09178	0.588098	0.294049	+	0.955790i	$0.404997\pi$
$240$	2.05906	0.132912
$241$	11.8409	0.762739	0.381370	−	0.924423i	$-0.375452\pi$
$241$	11.8409	0.762739	0.381370	+	0.924423i	$0.375452\pi$
$242$	0	0
$243$	−12.1515	−0.779518
$244$	−3.58885	−0.229752
$245$	1.00000	0.0638877
$246$	−9.55840	−0.609421
$247$	1.93586	0.123176
$248$	0.145026	0.00920917
$249$	2.23134	0.141406
$250$	−1.00000	−0.0632456
$251$	−12.2824	−0.775260	−0.387630	−	0.921815i	$-0.626706\pi$
$251$	−12.2824	−0.775260	−0.387630	+	0.921815i	$0.626706\pi$
$252$	1.23973	0.0780959
$253$	0	0
$254$	−11.1188	−0.697654
$255$	−15.3377	−0.960487
$256$	1.00000	0.0625000
$257$	−23.8811	−1.48966	−0.744830	−	0.667254i	$-0.767469\pi$
$257$	−23.8811	−1.48966	−0.744830	+	0.667254i	$0.767469\pi$
$258$	24.2121	1.50738
$259$	2.32711	0.144600
$260$	−2.27257	−0.140939
$261$	2.93372	0.181592
$262$	10.9162	0.674402
$263$	−10.5902	−0.653019	−0.326509	−	0.945194i	$-0.605872\pi$
$263$	−10.5902	−0.653019	−0.326509	+	0.945194i	$0.605872\pi$
$264$	0	0
$265$	−0.962643	−0.0591347
$266$	0.851836	0.0522294
$267$	7.69189	0.470736
$268$	−0.430333	−0.0262868
$269$	16.5719	1.01041	0.505203	−	0.863001i	$-0.331418\pi$
$269$	16.5719	1.01041	0.505203	+	0.863001i	$0.331418\pi$
$270$	3.62450	0.220580
$271$	−29.4244	−1.78740	−0.893702	−	0.448661i	$-0.851901\pi$
$271$	−29.4244	−1.78740	−0.893702	+	0.448661i	$0.851901\pi$
$272$	−7.44890	−0.451656
$273$	−4.67936	−0.283208
$274$	4.81357	0.290799
$275$	0	0
$276$	1.34127	0.0807349
$277$	29.6933	1.78410	0.892049	−	0.451939i	$-0.149267\pi$
$277$	29.6933	1.78410	0.892049	+	0.451939i	$0.149267\pi$
$278$	10.1432	0.608349
$279$	−0.179794	−0.0107640
$280$	−1.00000	−0.0597614
$281$	−23.8076	−1.42024	−0.710121	−	0.704080i	$-0.751360\pi$
$281$	−23.8076	−1.42024	−0.710121	+	0.704080i	$0.751360\pi$
$282$	10.8623	0.646841
$283$	−17.5036	−1.04048	−0.520241	−	0.854019i	$-0.674158\pi$
$283$	−17.5036	−1.04048	−0.520241	+	0.854019i	$0.674158\pi$
$284$	10.6384	0.631276
$285$	−1.75398	−0.103897
$286$	0	0
$287$	4.64211	0.274015
$288$	−1.23973	−0.0730521
$289$	38.4861	2.26389
$290$	−2.36641	−0.138960
$291$	−3.04706	−0.178622
$292$	−1.16253	−0.0680316
$293$	23.1174	1.35053	0.675267	−	0.737573i	$-0.264028\pi$
$293$	23.1174	1.35053	0.675267	+	0.737573i	$0.264028\pi$
$294$	−2.05906	−0.120087
$295$	1.04296	0.0607237
$296$	−2.32711	−0.135261
$297$	0	0
$298$	−1.88432	−0.109156
$299$	−1.48035	−0.0856107
$300$	2.05906	0.118880
$301$	−11.7588	−0.677768
$302$	−14.3826	−0.827623
$303$	−28.7285	−1.65041
$304$	−0.851836	−0.0488561
$305$	−3.58885	−0.205497
$306$	9.23466	0.527910
$307$	−17.1933	−0.981271	−0.490635	−	0.871365i	$-0.663235\pi$
$307$	−17.1933	−0.981271	−0.490635	+	0.871365i	$0.663235\pi$
$308$	0	0
$309$	−2.89418	−0.164644
$310$	0.145026	0.00823693
$311$	−13.9706	−0.792200	−0.396100	−	0.918207i	$-0.629637\pi$
$311$	−13.9706	−0.792200	−0.396100	+	0.918207i	$0.629637\pi$
$312$	4.67936	0.264917
$313$	10.4793	0.592327	0.296163	−	0.955137i	$-0.404293\pi$
$313$	10.4793	0.592327	0.296163	+	0.955137i	$0.404293\pi$
$314$	12.6590	0.714390
$315$	1.23973	0.0698511
$316$	10.7068	0.602303
$317$	−32.2756	−1.81278	−0.906390	−	0.422442i	$-0.861173\pi$
$317$	−32.2756	−1.81278	−0.906390	+	0.422442i	$0.861173\pi$
$318$	1.98214	0.111153
$319$	0	0
$320$	1.00000	0.0559017
$321$	−38.9743	−2.17533
$322$	−0.651398	−0.0363010
$323$	6.34524	0.353059
$324$	−11.1823	−0.621237
$325$	−2.27257	−0.126060
$326$	8.95282	0.495851
$327$	−22.3250	−1.23457
$328$	−4.64211	−0.256318
$329$	−5.27536	−0.290840
$330$	0	0
$331$	27.1275	1.49106	0.745532	−	0.666470i	$-0.232196\pi$
$331$	27.1275	1.49106	0.745532	+	0.666470i	$0.232196\pi$
$332$	1.08367	0.0594741
$333$	2.88500	0.158097
$334$	−6.36465	−0.348258
$335$	−0.430333	−0.0235116
$336$	2.05906	0.112331
$337$	25.8297	1.40703	0.703517	−	0.710678i	$-0.251612\pi$
$337$	25.8297	1.40703	0.703517	+	0.710678i	$0.251612\pi$
$338$	7.83543	0.426191
$339$	−35.3353	−1.91915
$340$	−7.44890	−0.403973
$341$	0	0
$342$	1.05605	0.0571047
$343$	1.00000	0.0539949
$344$	11.7588	0.633993
$345$	1.34127	0.0722115
$346$	24.4230	1.31299
$347$	6.20850	0.333290	0.166645	−	0.986017i	$-0.446707\pi$
$347$	6.20850	0.333290	0.166645	+	0.986017i	$0.446707\pi$
$348$	4.87258	0.261198
$349$	−10.3551	−0.554295	−0.277148	−	0.960827i	$-0.589389\pi$
$349$	−10.3551	−0.554295	−0.277148	+	0.960827i	$0.589389\pi$
$350$	−1.00000	−0.0534522
$351$	8.23692	0.439654
$352$	0	0
$353$	27.4798	1.46260	0.731300	−	0.682055i	$-0.238914\pi$
$353$	27.4798	1.46260	0.731300	+	0.682055i	$0.238914\pi$
$354$	−2.14753	−0.114140
$355$	10.6384	0.564630
$356$	3.73563	0.197988
$357$	−15.3377	−0.811759
$358$	−5.80767	−0.306945
$359$	0.0307419	0.00162250	0.000811248	−	1.00000i	$-0.499742\pi$
$359$	0.0307419	0.00162250	0.000811248		1.00000i	$0.499742\pi$
$360$	−1.23973	−0.0653397
$361$	−18.2744	−0.961809
$362$	12.8812	0.677019
$363$	0	0
$364$	−2.27257	−0.119115
$365$	−1.16253	−0.0608493
$366$	7.38966	0.386264
$367$	−10.2929	−0.537285	−0.268643	−	0.963240i	$-0.586575\pi$
$367$	−10.2929	−0.537285	−0.268643	+	0.963240i	$0.586575\pi$
$368$	0.651398	0.0339565
$369$	5.75499	0.299593
$370$	−2.32711	−0.120981
$371$	−0.962643	−0.0499779
$372$	−0.298618	−0.0154826
$373$	−12.2144	−0.632438	−0.316219	−	0.948686i	$-0.602413\pi$
$373$	−12.2144	−0.632438	−0.316219	+	0.948686i	$0.602413\pi$
$374$	0	0
$375$	2.05906	0.106329
$376$	5.27536	0.272056
$377$	−5.37782	−0.276972
$378$	3.62450	0.186424
$379$	0.699608	0.0359364	0.0179682	−	0.999839i	$-0.494280\pi$
$379$	0.699608	0.0359364	0.0179682	+	0.999839i	$0.494280\pi$
$380$	−0.851836	−0.0436983
$381$	22.8942	1.17291
$382$	5.65871	0.289525
$383$	−37.4527	−1.91374	−0.956871	−	0.290513i	$-0.906174\pi$
$383$	−37.4527	−1.91374	−0.956871	+	0.290513i	$0.906174\pi$
$384$	−2.05906	−0.105076
$385$	0	0
$386$	−13.7878	−0.701783
$387$	−14.5778	−0.741032
$388$	−1.47983	−0.0751270
$389$	−8.64880	−0.438512	−0.219256	−	0.975667i	$-0.570363\pi$
$389$	−8.64880	−0.438512	−0.219256	+	0.975667i	$0.570363\pi$
$390$	4.67936	0.236949
$391$	−4.85220	−0.245386
$392$	−1.00000	−0.0505076
$393$	−22.4770	−1.13382
$394$	−2.82825	−0.142485
$395$	10.7068	0.538716
$396$	0	0
$397$	9.10554	0.456994	0.228497	−	0.973545i	$-0.426619\pi$
$397$	9.10554	0.456994	0.228497	+	0.973545i	$0.426619\pi$
$398$	0.513194	0.0257241
$399$	−1.75398	−0.0878090
$400$	1.00000	0.0500000
$401$	19.2528	0.961437	0.480718	−	0.876875i	$-0.340376\pi$
$401$	19.2528	0.961437	0.480718	+	0.876875i	$0.340376\pi$
$402$	0.886082	0.0441938
$403$	0.329582	0.0164177
$404$	−13.9523	−0.694151
$405$	−11.1823	−0.555651
$406$	−2.36641	−0.117443
$407$	0	0
$408$	15.3377	0.759331
$409$	26.7614	1.32327	0.661634	−	0.749827i	$-0.269863\pi$
$409$	26.7614	1.32327	0.661634	+	0.749827i	$0.269863\pi$
$410$	−4.64211	−0.229258
$411$	−9.91144	−0.488895
$412$	−1.40558	−0.0692481
$413$	1.04296	0.0513209
$414$	−0.807561	−0.0396894
$415$	1.08367	0.0531953
$416$	2.27257	0.111422
$417$	−20.8855	−1.02277
$418$	0	0
$419$	−24.4437	−1.19415	−0.597075	−	0.802185i	$-0.703671\pi$
$419$	−24.4437	−1.19415	−0.597075	+	0.802185i	$0.703671\pi$
$420$	2.05906	0.100472
$421$	−7.85402	−0.382781	−0.191391	−	0.981514i	$-0.561300\pi$
$421$	−7.85402	−0.382781	−0.191391	+	0.981514i	$0.561300\pi$
$422$	20.4146	0.993765
$423$	−6.54005	−0.317988
$424$	0.962643	0.0467501
$425$	−7.44890	−0.361325
$426$	−21.9052	−1.06131
$427$	−3.58885	−0.173677
$428$	−18.9282	−0.914927
$429$	0	0
$430$	11.7588	0.567061
$431$	−23.8170	−1.14722	−0.573612	−	0.819127i	$-0.694458\pi$
$431$	−23.8170	−1.14722	−0.573612	+	0.819127i	$0.694458\pi$
$432$	−3.62450	−0.174384
$433$	15.4390	0.741952	0.370976	−	0.928642i	$-0.379023\pi$
$433$	15.4390	0.741952	0.370976	+	0.928642i	$0.379023\pi$
$434$	0.145026	0.00696148
$435$	4.87258	0.233622
$436$	−10.8423	−0.519252
$437$	−0.554884	−0.0265437
$438$	2.39371	0.114376
$439$	29.0621	1.38706	0.693530	−	0.720428i	$-0.256054\pi$
$439$	29.0621	1.38706	0.693530	+	0.720428i	$0.256054\pi$
$440$	0	0
$441$	1.23973	0.0590350
$442$	−16.9281	−0.805190
$443$	34.7126	1.64924	0.824622	−	0.565685i	$-0.191388\pi$
$443$	34.7126	1.64924	0.824622	+	0.565685i	$0.191388\pi$
$444$	4.79166	0.227402
$445$	3.73563	0.177086
$446$	−15.3296	−0.725877
$447$	3.87993	0.183515
$448$	1.00000	0.0472456
$449$	−30.7259	−1.45005	−0.725024	−	0.688724i	$-0.758171\pi$
$449$	−30.7259	−1.45005	−0.725024	+	0.688724i	$0.758171\pi$
$450$	−1.23973	−0.0584416
$451$	0	0
$452$	−17.1609	−0.807179
$453$	29.6146	1.39141
$454$	28.8027	1.35178
$455$	−2.27257	−0.106540
$456$	1.75398	0.0821378
$457$	20.4932	0.958633	0.479317	−	0.877642i	$-0.340885\pi$
$457$	20.4932	0.958633	0.479317	+	0.877642i	$0.340885\pi$
$458$	−7.06918	−0.330321
$459$	26.9985	1.26018
$460$	0.651398	0.0303716
$461$	17.5629	0.817988	0.408994	−	0.912537i	$-0.365880\pi$
$461$	17.5629	0.817988	0.408994	+	0.912537i	$0.365880\pi$
$462$	0	0
$463$	13.6361	0.633721	0.316861	−	0.948472i	$-0.397371\pi$
$463$	13.6361	0.633721	0.316861	+	0.948472i	$0.397371\pi$
$464$	2.36641	0.109858
$465$	−0.298618	−0.0138481
$466$	−25.1088	−1.16314
$467$	−30.7210	−1.42160	−0.710799	−	0.703395i	$-0.751666\pi$
$467$	−30.7210	−1.42160	−0.710799	+	0.703395i	$0.751666\pi$
$468$	−2.81738	−0.130234
$469$	−0.430333	−0.0198709
$470$	5.27536	0.243334
$471$	−26.0657	−1.20105
$472$	−1.04296	−0.0480063
$473$	0	0
$474$	−22.0459	−1.01260
$475$	−0.851836	−0.0390849
$476$	−7.44890	−0.341420
$477$	−1.19342	−0.0546430
$478$	−9.09178	−0.415848
$479$	34.6829	1.58470	0.792352	−	0.610064i	$-0.208856\pi$
$479$	34.6829	1.58470	0.792352	+	0.610064i	$0.208856\pi$
$480$	−2.05906	−0.0939829
$481$	−5.28852	−0.241136
$482$	−11.8409	−0.539338
$483$	1.34127	0.0610298
$484$	0	0
$485$	−1.47983	−0.0671956
$486$	12.1515	0.551202
$487$	35.5251	1.60980	0.804899	−	0.593412i	$-0.202220\pi$
$487$	35.5251	1.60980	0.804899	+	0.593412i	$0.202220\pi$
$488$	3.58885	0.162460
$489$	−18.4344	−0.833633
$490$	−1.00000	−0.0451754
$491$	26.0609	1.17611	0.588055	−	0.808821i	$-0.299894\pi$
$491$	26.0609	1.17611	0.588055	+	0.808821i	$0.299894\pi$
$492$	9.55840	0.430926
$493$	−17.6271	−0.793886
$494$	−1.93586	−0.0870983
$495$	0	0
$496$	−0.145026	−0.00651187
$497$	10.6384	0.477200
$498$	−2.23134	−0.0999889
$499$	13.6585	0.611439	0.305719	−	0.952122i	$-0.401103\pi$
$499$	13.6585	0.611439	0.305719	+	0.952122i	$0.401103\pi$
$500$	1.00000	0.0447214
$501$	13.1052	0.585497
$502$	12.2824	0.548191
$503$	33.6925	1.50227	0.751136	−	0.660147i	$-0.229506\pi$
$503$	33.6925	1.50227	0.751136	+	0.660147i	$0.229506\pi$
$504$	−1.23973	−0.0552222
$505$	−13.9523	−0.620867
$506$	0	0
$507$	−16.1336	−0.716519
$508$	11.1188	0.493316
$509$	25.0801	1.11166	0.555829	−	0.831297i	$-0.312401\pi$
$509$	25.0801	1.11166	0.555829	+	0.831297i	$0.312401\pi$
$510$	15.3377	0.679167
$511$	−1.16253	−0.0514271
$512$	−1.00000	−0.0441942
$513$	3.08748	0.136315
$514$	23.8811	1.05335
$515$	−1.40558	−0.0619374
$516$	−24.2121	−1.06588
$517$	0	0
$518$	−2.32711	−0.102247
$519$	−50.2884	−2.20741
$520$	2.27257	0.0996588
$521$	−23.2513	−1.01866	−0.509330	−	0.860572i	$-0.670107\pi$
$521$	−23.2513	−1.01866	−0.509330	+	0.860572i	$0.670107\pi$
$522$	−2.93372	−0.128405
$523$	0.198677	0.00868753	0.00434376	−	0.999991i	$-0.498617\pi$
$523$	0.198677	0.00868753	0.00434376	+	0.999991i	$0.498617\pi$
$524$	−10.9162	−0.476874
$525$	2.05906	0.0898648
$526$	10.5902	0.461754
$527$	1.08029	0.0470580
$528$	0	0
$529$	−22.5757	−0.981551
$530$	0.962643	0.0418145
$531$	1.29300	0.0561113
$532$	−0.851836	−0.0369318
$533$	−10.5495	−0.456951
$534$	−7.69189	−0.332861
$535$	−18.9282	−0.818336
$536$	0.430333	0.0185876
$537$	11.9584	0.516041
$538$	−16.5719	−0.714465
$539$	0	0
$540$	−3.62450	−0.155973
$541$	32.5444	1.39919	0.699597	−	0.714538i	$-0.253363\pi$
$541$	32.5444	1.39919	0.699597	+	0.714538i	$0.253363\pi$
$542$	29.4244	1.26389
$543$	−26.5231	−1.13822
$544$	7.44890	0.319369
$545$	−10.8423	−0.464433
$546$	4.67936	0.200258
$547$	−24.7703	−1.05910	−0.529550	−	0.848279i	$-0.677639\pi$
$547$	−24.7703	−1.05910	−0.529550	+	0.848279i	$0.677639\pi$
$548$	−4.81357	−0.205626
$549$	−4.44922	−0.189888
$550$	0	0
$551$	−2.01579	−0.0858755
$552$	−1.34127	−0.0570882
$553$	10.7068	0.455298
$554$	−29.6933	−1.26155
$555$	4.79166	0.203395
$556$	−10.1432	−0.430168
$557$	37.3936	1.58442	0.792208	−	0.610251i	$-0.208931\pi$
$557$	37.3936	1.58442	0.792208	+	0.610251i	$0.208931\pi$
$558$	0.179794	0.00761128
$559$	26.7228	1.13025
$560$	1.00000	0.0422577
$561$	0	0
$562$	23.8076	1.00426
$563$	17.2949	0.728894	0.364447	−	0.931224i	$-0.381258\pi$
$563$	17.2949	0.728894	0.364447	+	0.931224i	$0.381258\pi$
$564$	−10.8623	−0.457385
$565$	−17.1609	−0.721963
$566$	17.5036	0.735732
$567$	−11.1823	−0.469611
$568$	−10.6384	−0.446379
$569$	38.4117	1.61030	0.805152	−	0.593068i	$-0.202084\pi$
$569$	38.4117	1.61030	0.805152	+	0.593068i	$0.202084\pi$
$570$	1.75398	0.0734662
$571$	−5.08249	−0.212696	−0.106348	−	0.994329i	$-0.533916\pi$
$571$	−5.08249	−0.212696	−0.106348	+	0.994329i	$0.533916\pi$
$572$	0	0
$573$	−11.6516	−0.486754
$574$	−4.64211	−0.193758
$575$	0.651398	0.0271652
$576$	1.23973	0.0516556
$577$	41.3365	1.72086	0.860430	−	0.509568i	$-0.170195\pi$
$577$	41.3365	1.72086	0.860430	+	0.509568i	$0.170195\pi$
$578$	−38.4861	−1.60081
$579$	28.3900	1.17985
$580$	2.36641	0.0982597
$581$	1.08367	0.0449582
$582$	3.04706	0.126305
$583$	0	0
$584$	1.16253	0.0481056
$585$	−2.81738	−0.116484
$586$	−23.1174	−0.954972
$587$	−6.92122	−0.285669	−0.142835	−	0.989747i	$-0.545622\pi$
$587$	−6.92122	−0.285669	−0.142835	+	0.989747i	$0.545622\pi$
$588$	2.05906	0.0849143
$589$	0.123538	0.00509032
$590$	−1.04296	−0.0429381
$591$	5.82354	0.239548
$592$	2.32711	0.0956436
$593$	22.7439	0.933979	0.466989	−	0.884263i	$-0.345339\pi$
$593$	22.7439	0.933979	0.466989	+	0.884263i	$0.345339\pi$
$594$	0	0
$595$	−7.44890	−0.305375
$596$	1.88432	0.0771848
$597$	−1.05670	−0.0432477
$598$	1.48035	0.0605359
$599$	4.13028	0.168759	0.0843794	−	0.996434i	$-0.473109\pi$
$599$	4.13028	0.168759	0.0843794	+	0.996434i	$0.473109\pi$
$600$	−2.05906	−0.0840608
$601$	3.87084	0.157895	0.0789474	−	0.996879i	$-0.474844\pi$
$601$	3.87084	0.157895	0.0789474	+	0.996879i	$0.474844\pi$
$602$	11.7588	0.479254
$603$	−0.533499	−0.0217257
$604$	14.3826	0.585218
$605$	0	0
$606$	28.7285	1.16702
$607$	29.7726	1.20843	0.604216	−	0.796820i	$-0.293486\pi$
$607$	29.7726	1.20843	0.604216	+	0.796820i	$0.293486\pi$
$608$	0.851836	0.0345465
$609$	4.87258	0.197447
$610$	3.58885	0.145308
$611$	11.9886	0.485008
$612$	−9.23466	−0.373289
$613$	−26.1253	−1.05519	−0.527595	−	0.849496i	$-0.676906\pi$
$613$	−26.1253	−1.05519	−0.527595	+	0.849496i	$0.676906\pi$
$614$	17.1933	0.693863
$615$	9.55840	0.385432
$616$	0	0
$617$	13.3021	0.535524	0.267762	−	0.963485i	$-0.413716\pi$
$617$	13.3021	0.535524	0.267762	+	0.963485i	$0.413716\pi$
$618$	2.89418	0.116421
$619$	−9.29198	−0.373476	−0.186738	−	0.982410i	$-0.559792\pi$
$619$	−9.29198	−0.373476	−0.186738	+	0.982410i	$0.559792\pi$
$620$	−0.145026	−0.00582439
$621$	−2.36099	−0.0947432
$622$	13.9706	0.560170
$623$	3.73563	0.149665
$624$	−4.67936	−0.187324
$625$	1.00000	0.0400000
$626$	−10.4793	−0.418838
$627$	0	0
$628$	−12.6590	−0.505150
$629$	−17.3344	−0.691168
$630$	−1.23973	−0.0493922
$631$	−29.7104	−1.18275	−0.591376	−	0.806396i	$-0.701415\pi$
$631$	−29.7104	−1.18275	−0.591376	+	0.806396i	$0.701415\pi$
$632$	−10.7068	−0.425892
$633$	−42.0348	−1.67073
$634$	32.2756	1.28183
$635$	11.1188	0.441235
$636$	−1.98214	−0.0785970
$637$	−2.27257	−0.0900425
$638$	0	0
$639$	13.1889	0.521743
$640$	−1.00000	−0.0395285
$641$	−17.1408	−0.677020	−0.338510	−	0.940963i	$-0.609923\pi$
$641$	−17.1408	−0.677020	−0.338510	+	0.940963i	$0.609923\pi$
$642$	38.9743	1.53819
$643$	−25.7316	−1.01476	−0.507378	−	0.861724i	$-0.669385\pi$
$643$	−25.7316	−1.01476	−0.507378	+	0.861724i	$0.669385\pi$
$644$	0.651398	0.0256687
$645$	−24.2121	−0.953352
$646$	−6.34524	−0.249650
$647$	−21.6382	−0.850686	−0.425343	−	0.905032i	$-0.639847\pi$
$647$	−21.6382	−0.850686	−0.425343	+	0.905032i	$0.639847\pi$
$648$	11.1823	0.439281
$649$	0	0
$650$	2.27257	0.0891375
$651$	−0.298618	−0.0117038
$652$	−8.95282	−0.350620
$653$	38.5661	1.50921	0.754604	−	0.656181i	$-0.227829\pi$
$653$	38.5661	1.50921	0.754604	+	0.656181i	$0.227829\pi$
$654$	22.3250	0.872975
$655$	−10.9162	−0.426529
$656$	4.64211	0.181244
$657$	−1.44122	−0.0562274
$658$	5.27536	0.205655
$659$	−41.3104	−1.60923	−0.804613	−	0.593799i	$-0.797627\pi$
$659$	−41.3104	−1.60923	−0.804613	+	0.593799i	$0.797627\pi$
$660$	0	0
$661$	−17.6230	−0.685456	−0.342728	−	0.939435i	$-0.611351\pi$
$661$	−17.6230	−0.685456	−0.342728	+	0.939435i	$0.611351\pi$
$662$	−27.1275	−1.05434
$663$	34.8561	1.35370
$664$	−1.08367	−0.0420546
$665$	−0.851836	−0.0330328
$666$	−2.88500	−0.111791
$667$	1.54147	0.0596861
$668$	6.36465	0.246256
$669$	31.5645	1.22036
$670$	0.430333	0.0166252
$671$	0	0
$672$	−2.05906	−0.0794300
$673$	−23.9060	−0.921508	−0.460754	−	0.887528i	$-0.652421\pi$
$673$	−23.9060	−0.921508	−0.460754	+	0.887528i	$0.652421\pi$
$674$	−25.8297	−0.994923
$675$	−3.62450	−0.139507
$676$	−7.83543	−0.301363
$677$	−4.64307	−0.178448	−0.0892238	−	0.996012i	$-0.528439\pi$
$677$	−4.64307	−0.178448	−0.0892238	+	0.996012i	$0.528439\pi$
$678$	35.3353	1.35704
$679$	−1.47983	−0.0567906
$680$	7.44890	0.285652
$681$	−59.3064	−2.27263
$682$	0	0
$683$	−25.5818	−0.978859	−0.489430	−	0.872043i	$-0.662795\pi$
$683$	−25.5818	−0.978859	−0.489430	+	0.872043i	$0.662795\pi$
$684$	−1.05605	−0.0403791
$685$	−4.81357	−0.183917
$686$	−1.00000	−0.0381802
$687$	14.5559	0.555341
$688$	−11.7588	−0.448301
$689$	2.18767	0.0833437
$690$	−1.34127	−0.0510612
$691$	22.5390	0.857424	0.428712	−	0.903441i	$-0.358967\pi$
$691$	22.5390	0.857424	0.428712	+	0.903441i	$0.358967\pi$
$692$	−24.4230	−0.928421
$693$	0	0
$694$	−6.20850	−0.235671
$695$	−10.1432	−0.384754
$696$	−4.87258	−0.184695
$697$	−34.5786	−1.30976
$698$	10.3551	0.391946
$699$	51.7006	1.95550
$700$	1.00000	0.0377964
$701$	34.9336	1.31942	0.659711	−	0.751519i	$-0.270679\pi$
$701$	34.9336	1.31942	0.659711	+	0.751519i	$0.270679\pi$
$702$	−8.23692	−0.310882
$703$	−1.98232	−0.0747645
$704$	0	0
$705$	−10.8623	−0.409098
$706$	−27.4798	−1.03422
$707$	−13.9523	−0.524729
$708$	2.14753	0.0807089
$709$	−2.18225	−0.0819563	−0.0409781	−	0.999160i	$-0.513047\pi$
$709$	−2.18225	−0.0819563	−0.0409781	+	0.999160i	$0.513047\pi$
$710$	−10.6384	−0.399254
$711$	13.2735	0.497797
$712$	−3.73563	−0.139999
$713$	−0.0944698	−0.00353792
$714$	15.3377	0.574001
$715$	0	0
$716$	5.80767	0.217043
$717$	18.7205	0.699131
$718$	−0.0307419	−0.00114728
$719$	23.1198	0.862224	0.431112	−	0.902299i	$-0.358121\pi$
$719$	23.1198	0.862224	0.431112	+	0.902299i	$0.358121\pi$
$720$	1.23973	0.0462022
$721$	−1.40558	−0.0523466
$722$	18.2744	0.680102
$723$	24.3811	0.906745
$724$	−12.8812	−0.478725
$725$	2.36641	0.0878861
$726$	0	0
$727$	−48.6753	−1.80527	−0.902633	−	0.430410i	$-0.858369\pi$
$727$	−48.6753	−1.80527	−0.902633	+	0.430410i	$0.858369\pi$
$728$	2.27257	0.0842270
$729$	8.52614	0.315783
$730$	1.16253	0.0430270
$731$	87.5903	3.23964
$732$	−7.38966	−0.273130
$733$	21.8686	0.807735	0.403867	−	0.914818i	$-0.367666\pi$
$733$	21.8686	0.807735	0.403867	+	0.914818i	$0.367666\pi$
$734$	10.2929	0.379918
$735$	2.05906	0.0759496
$736$	−0.651398	−0.0240109
$737$	0	0
$738$	−5.75499	−0.211844
$739$	−0.178113	−0.00655200	−0.00327600	−	0.999995i	$-0.501043\pi$
$739$	−0.178113	−0.00655200	−0.00327600	+	0.999995i	$0.501043\pi$
$740$	2.32711	0.0855463
$741$	3.98605	0.146431
$742$	0.962643	0.0353397
$743$	−37.0632	−1.35972	−0.679859	−	0.733343i	$-0.737959\pi$
$743$	−37.0632	−1.35972	−0.679859	+	0.733343i	$0.737959\pi$
$744$	0.298618	0.0109479
$745$	1.88432	0.0690362
$746$	12.2144	0.447201
$747$	1.34346	0.0491548
$748$	0	0
$749$	−18.9282	−0.691620
$750$	−2.05906	−0.0751863
$751$	−26.4258	−0.964291	−0.482146	−	0.876091i	$-0.660142\pi$
$751$	−26.4258	−0.964291	−0.482146	+	0.876091i	$0.660142\pi$
$752$	−5.27536	−0.192373
$753$	−25.2903	−0.921628
$754$	5.37782	0.195849
$755$	14.3826	0.523435
$756$	−3.62450	−0.131822
$757$	9.40549	0.341848	0.170924	−	0.985284i	$-0.445325\pi$
$757$	9.40549	0.341848	0.170924	+	0.985284i	$0.445325\pi$
$758$	−0.699608	−0.0254109
$759$	0	0
$760$	0.851836	0.0308993
$761$	−22.7380	−0.824253	−0.412127	−	0.911127i	$-0.635214\pi$
$761$	−22.7380	−0.824253	−0.412127	+	0.911127i	$0.635214\pi$
$762$	−22.8942	−0.829371
$763$	−10.8423	−0.392517
$764$	−5.65871	−0.204725
$765$	−9.23466	−0.333880
$766$	37.4527	1.35322
$767$	−2.37021	−0.0855832
$768$	2.05906	0.0743000
$769$	13.3469	0.481300	0.240650	−	0.970612i	$-0.422639\pi$
$769$	13.3469	0.481300	0.240650	+	0.970612i	$0.422639\pi$
$770$	0	0
$771$	−49.1726	−1.77091
$772$	13.7878	0.496235
$773$	−2.14317	−0.0770845	−0.0385422	−	0.999257i	$-0.512271\pi$
$773$	−2.14317	−0.0770845	−0.0385422	+	0.999257i	$0.512271\pi$
$774$	14.5778	0.523989
$775$	−0.145026	−0.00520949
$776$	1.47983	0.0531228
$777$	4.79166	0.171900
$778$	8.64880	0.310074
$779$	−3.95432	−0.141678
$780$	−4.67936	−0.167548
$781$	0	0
$782$	4.85220	0.173514
$783$	−8.57703	−0.306518
$784$	1.00000	0.0357143
$785$	−12.6590	−0.451820
$786$	22.4770	0.801729
$787$	39.7496	1.41692	0.708461	−	0.705750i	$-0.249390\pi$
$787$	39.7496	1.41692	0.708461	+	0.705750i	$0.249390\pi$
$788$	2.82825	0.100752
$789$	−21.8058	−0.776308
$790$	−10.7068	−0.380930
$791$	−17.1609	−0.610170
$792$	0	0
$793$	8.15591	0.289625
$794$	−9.10554	−0.323144
$795$	−1.98214	−0.0702993
$796$	−0.513194	−0.0181897
$797$	−45.8902	−1.62551	−0.812757	−	0.582603i	$-0.802034\pi$
$797$	−45.8902	−1.62551	−0.812757	+	0.582603i	$0.802034\pi$
$798$	1.75398	0.0620903
$799$	39.2957	1.39018
$800$	−1.00000	−0.0353553
$801$	4.63119	0.163635
$802$	−19.2528	−0.679838
$803$	0	0
$804$	−0.886082	−0.0312497
$805$	0.651398	0.0229588
$806$	−0.329582	−0.0116090
$807$	34.1225	1.20117
$808$	13.9523	0.490839
$809$	3.54263	0.124552	0.0622761	−	0.998059i	$-0.480164\pi$
$809$	3.54263	0.124552	0.0622761	+	0.998059i	$0.480164\pi$
$810$	11.1823	0.392905
$811$	31.0933	1.09183	0.545916	−	0.837840i	$-0.316182\pi$
$811$	31.0933	1.09183	0.545916	+	0.837840i	$0.316182\pi$
$812$	2.36641	0.0830446
$813$	−60.5866	−2.12487
$814$	0	0
$815$	−8.95282	−0.313604
$816$	−15.3377	−0.536928
$817$	10.0166	0.350436
$818$	−26.7614	−0.935692
$819$	−2.81738	−0.0984473
$820$	4.64211	0.162110
$821$	−12.0289	−0.419812	−0.209906	−	0.977722i	$-0.567316\pi$
$821$	−12.0289	−0.419812	−0.209906	+	0.977722i	$0.567316\pi$
$822$	9.91144	0.345701
$823$	8.79883	0.306708	0.153354	−	0.988171i	$-0.450993\pi$
$823$	8.79883	0.306708	0.153354	+	0.988171i	$0.450993\pi$
$824$	1.40558	0.0489658
$825$	0	0
$826$	−1.04296	−0.0362893
$827$	−27.7899	−0.966349	−0.483175	−	0.875524i	$-0.660516\pi$
$827$	−27.7899	−0.966349	−0.483175	+	0.875524i	$0.660516\pi$
$828$	0.807561	0.0280647
$829$	−13.8407	−0.480708	−0.240354	−	0.970685i	$-0.577263\pi$
$829$	−13.8407	−0.480708	−0.240354	+	0.970685i	$0.577263\pi$
$830$	−1.08367	−0.0376148
$831$	61.1403	2.12094
$832$	−2.27257	−0.0787872
$833$	−7.44890	−0.258089
$834$	20.8855	0.723205
$835$	6.36465	0.220258
$836$	0	0
$837$	0.525647	0.0181690
$838$	24.4437	0.844392
$839$	34.3543	1.18604	0.593022	−	0.805187i	$-0.297935\pi$
$839$	34.3543	1.18604	0.593022	+	0.805187i	$0.297935\pi$
$840$	−2.05906	−0.0710444
$841$	−23.4001	−0.806901
$842$	7.85402	0.270667
$843$	−49.0213	−1.68838
$844$	−20.4146	−0.702698
$845$	−7.83543	−0.269547
$846$	6.54005	0.224852
$847$	0	0
$848$	−0.962643	−0.0330573
$849$	−36.0410	−1.23693
$850$	7.44890	0.255495
$851$	1.51588	0.0519635
$852$	21.9052	0.750460
$853$	−40.0952	−1.37283	−0.686416	−	0.727209i	$-0.740817\pi$
$853$	−40.0952	−1.37283	−0.686416	+	0.727209i	$0.740817\pi$
$854$	3.58885	0.122808
$855$	−1.05605	−0.0361162
$856$	18.9282	0.646951
$857$	26.0287	0.889123	0.444562	−	0.895748i	$-0.353359\pi$
$857$	26.0287	0.889123	0.444562	+	0.895748i	$0.353359\pi$
$858$	0	0
$859$	29.9861	1.02311	0.511556	−	0.859250i	$-0.329069\pi$
$859$	29.9861	1.02311	0.511556	+	0.859250i	$0.329069\pi$
$860$	−11.7588	−0.400973
$861$	9.55840	0.325749
$862$	23.8170	0.811210
$863$	28.1310	0.957590	0.478795	−	0.877927i	$-0.341074\pi$
$863$	28.1310	0.957590	0.478795	+	0.877927i	$0.341074\pi$
$864$	3.62450	0.123308
$865$	−24.4230	−0.830405
$866$	−15.4390	−0.524639
$867$	79.2453	2.69131
$868$	−0.145026	−0.00492251
$869$	0	0
$870$	−4.87258	−0.165196
$871$	0.977962	0.0331370
$872$	10.8423	0.367166
$873$	−1.83460	−0.0620917
$874$	0.554884	0.0187692
$875$	1.00000	0.0338062
$876$	−2.39371	−0.0808760
$877$	−15.9142	−0.537383	−0.268691	−	0.963226i	$-0.586591\pi$
$877$	−15.9142	−0.537383	−0.268691	+	0.963226i	$0.586591\pi$
$878$	−29.0621	−0.980800
$879$	47.6002	1.60551
$880$	0	0
$881$	42.3031	1.42523	0.712614	−	0.701556i	$-0.247511\pi$
$881$	42.3031	1.42523	0.712614	+	0.701556i	$0.247511\pi$
$882$	−1.23973	−0.0417440
$883$	−38.5685	−1.29793	−0.648967	−	0.760817i	$-0.724799\pi$
$883$	−38.5685	−1.29793	−0.648967	+	0.760817i	$0.724799\pi$
$884$	16.9281	0.569355
$885$	2.14753	0.0721883
$886$	−34.7126	−1.16619
$887$	11.4973	0.386041	0.193021	−	0.981195i	$-0.438172\pi$
$887$	11.4973	0.386041	0.193021	+	0.981195i	$0.438172\pi$
$888$	−4.79166	−0.160798
$889$	11.1188	0.372912
$890$	−3.73563	−0.125219
$891$	0	0
$892$	15.3296	0.513272
$893$	4.49375	0.150377
$894$	−3.87993	−0.129764
$895$	5.80767	0.194129
$896$	−1.00000	−0.0334077
$897$	−3.04813	−0.101774
$898$	30.7259	1.02534
$899$	−0.343191	−0.0114461
$900$	1.23973	0.0413245
$901$	7.17063	0.238888
$902$	0	0
$903$	−24.2121	−0.805730
$904$	17.1609	0.570762
$905$	−12.8812	−0.428185
$906$	−29.6146	−0.983878
$907$	35.9537	1.19382	0.596911	−	0.802308i	$-0.296395\pi$
$907$	35.9537	1.19382	0.596911	+	0.802308i	$0.296395\pi$
$908$	−28.8027	−0.955850
$909$	−17.2971	−0.573708
$910$	2.27257	0.0753350
$911$	13.3132	0.441086	0.220543	−	0.975377i	$-0.429217\pi$
$911$	13.3132	0.441086	0.220543	+	0.975377i	$0.429217\pi$
$912$	−1.75398	−0.0580802
$913$	0	0
$914$	−20.4932	−0.677856
$915$	−7.38966	−0.244295
$916$	7.06918	0.233572
$917$	−10.9162	−0.360483
$918$	−26.9985	−0.891083
$919$	57.6449	1.90153	0.950764	−	0.309915i	$-0.100301\pi$
$919$	57.6449	1.90153	0.950764	+	0.309915i	$0.100301\pi$
$920$	−0.651398	−0.0214760
$921$	−35.4020	−1.16653
$922$	−17.5629	−0.578405
$923$	−24.1766	−0.795783
$924$	0	0
$925$	2.32711	0.0765149
$926$	−13.6361	−0.448109
$927$	−1.74255	−0.0572328
$928$	−2.36641	−0.0776811
$929$	0.549043	0.0180135	0.00900675	−	0.999959i	$-0.497133\pi$
$929$	0.549043	0.0180135	0.00900675	+	0.999959i	$0.497133\pi$
$930$	0.298618	0.00979206
$931$	−0.851836	−0.0279178
$932$	25.1088	0.822466
$933$	−28.7663	−0.941767
$934$	30.7210	1.00522
$935$	0	0
$936$	2.81738	0.0920891
$937$	56.7821	1.85499	0.927495	−	0.373835i	$-0.121957\pi$
$937$	56.7821	1.85499	0.927495	+	0.373835i	$0.121957\pi$
$938$	0.430333	0.0140509
$939$	21.5776	0.704158
$940$	−5.27536	−0.172063
$941$	−29.2904	−0.954840	−0.477420	−	0.878675i	$-0.658428\pi$
$941$	−29.2904	−0.954840	−0.477420	+	0.878675i	$0.658428\pi$
$942$	26.0657	0.849267
$943$	3.02386	0.0984706
$944$	1.04296	0.0339456
$945$	−3.62450	−0.117905
$946$	0	0
$947$	24.8536	0.807632	0.403816	−	0.914840i	$-0.367684\pi$
$947$	24.8536	0.807632	0.403816	+	0.914840i	$0.367684\pi$
$948$	22.0459	0.716017
$949$	2.64192	0.0857603
$950$	0.851836	0.0276372
$951$	−66.4575	−2.15503
$952$	7.44890	0.241420
$953$	−43.8496	−1.42043	−0.710214	−	0.703986i	$-0.751402\pi$
$953$	−43.8496	−1.42043	−0.710214	+	0.703986i	$0.751402\pi$
$954$	1.19342	0.0386384
$955$	−5.65871	−0.183111
$956$	9.09178	0.294049
$957$	0	0
$958$	−34.6829	−1.12056
$959$	−4.81357	−0.155438
$960$	2.05906	0.0664559
$961$	−30.9790	−0.999322
$962$	5.28852	0.170509
$963$	−23.4659	−0.756178
$964$	11.8409	0.381370
$965$	13.7878	0.443846
$966$	−1.34127	−0.0431546
$967$	40.0914	1.28925	0.644627	−	0.764497i	$-0.277013\pi$
$967$	40.0914	1.28925	0.644627	+	0.764497i	$0.277013\pi$
$968$	0	0
$969$	13.0652	0.419716
$970$	1.47983	0.0475145
$971$	−51.9047	−1.66570	−0.832850	−	0.553498i	$-0.813292\pi$
$971$	−51.9047	−1.66570	−0.832850	+	0.553498i	$0.813292\pi$
$972$	−12.1515	−0.389759
$973$	−10.1432	−0.325176
$974$	−35.5251	−1.13830
$975$	−4.67936	−0.149860
$976$	−3.58885	−0.114876
$977$	−16.3448	−0.522918	−0.261459	−	0.965215i	$-0.584204\pi$
$977$	−16.3448	−0.522918	−0.261459	+	0.965215i	$0.584204\pi$
$978$	18.4344	0.589467
$979$	0	0
$980$	1.00000	0.0319438
$981$	−13.4416	−0.429156
$982$	−26.0609	−0.831636
$983$	−39.4682	−1.25884	−0.629420	−	0.777065i	$-0.716708\pi$
$983$	−39.4682	−1.25884	−0.629420	+	0.777065i	$0.716708\pi$
$984$	−9.55840	−0.304711
$985$	2.82825	0.0901155
$986$	17.6271	0.561362
$987$	−10.8623	−0.345751
$988$	1.93586	0.0615878
$989$	−7.65968	−0.243564
$990$	0	0
$991$	20.8327	0.661771	0.330886	−	0.943671i	$-0.392653\pi$
$991$	20.8327	0.661771	0.330886	+	0.943671i	$0.392653\pi$
$992$	0.145026	0.00460459
$993$	55.8572	1.77258
$994$	−10.6384	−0.337431
$995$	−0.513194	−0.0162693
$996$	2.23134	0.0707028
$997$	1.23042	0.0389678	0.0194839	−	0.999810i	$-0.493798\pi$
$997$	1.23042	0.0389678	0.0194839	+	0.999810i	$0.493798\pi$
$998$	−13.6585	−0.432353
$999$	−8.43460	−0.266859

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8470.2.a.cw.1.5		6
11.5	even	5		770.2.n.j.421.3	✓	12
11.9	even	5		770.2.n.j.631.3	yes	12
11.10	odd	2		8470.2.a.dc.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.j.421.3	✓	12	11.5	even	5
770.2.n.j.631.3	yes	12	11.9	even	5
8470.2.a.cw.1.5		6	1.1	even	1	trivial
8470.2.a.dc.1.5		6	11.10	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.05906 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.05906 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.23973 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.05906 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.05906 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.23973 q^{9} -1.00000 q^{10} +2.05906 q^{12} -2.27257 q^{13} -1.00000 q^{14} +2.05906 q^{15} +1.00000 q^{16} -7.44890 q^{17} -1.23973 q^{18} -0.851836 q^{19} +1.00000 q^{20} +2.05906 q^{21} +0.651398 q^{23} -2.05906 q^{24} +1.00000 q^{25} +2.27257 q^{26} -3.62450 q^{27} +1.00000 q^{28} +2.36641 q^{29} -2.05906 q^{30} -0.145026 q^{31} -1.00000 q^{32} +7.44890 q^{34} +1.00000 q^{35} +1.23973 q^{36} +2.32711 q^{37} +0.851836 q^{38} -4.67936 q^{39} -1.00000 q^{40} +4.64211 q^{41} -2.05906 q^{42} -11.7588 q^{43} +1.23973 q^{45} -0.651398 q^{46} -5.27536 q^{47} +2.05906 q^{48} +1.00000 q^{49} -1.00000 q^{50} -15.3377 q^{51} -2.27257 q^{52} -0.962643 q^{53} +3.62450 q^{54} -1.00000 q^{56} -1.75398 q^{57} -2.36641 q^{58} +1.04296 q^{59} +2.05906 q^{60} -3.58885 q^{61} +0.145026 q^{62} +1.23973 q^{63} +1.00000 q^{64} -2.27257 q^{65} -0.430333 q^{67} -7.44890 q^{68} +1.34127 q^{69} -1.00000 q^{70} +10.6384 q^{71} -1.23973 q^{72} -1.16253 q^{73} -2.32711 q^{74} +2.05906 q^{75} -0.851836 q^{76} +4.67936 q^{78} +10.7068 q^{79} +1.00000 q^{80} -11.1823 q^{81} -4.64211 q^{82} +1.08367 q^{83} +2.05906 q^{84} -7.44890 q^{85} +11.7588 q^{86} +4.87258 q^{87} +3.73563 q^{89} -1.23973 q^{90} -2.27257 q^{91} +0.651398 q^{92} -0.298618 q^{93} +5.27536 q^{94} -0.851836 q^{95} -2.05906 q^{96} -1.47983 q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} - q^{3} + 6 q^{4} + 6 q^{5} + q^{6} + 6 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 - q^3 + 6 * q^4 + 6 * q^5 + q^6 + 6 * q^7 - 6 * q^8 + 3 * q^9	\( 6 q - 6 q^{2} - q^{3} + 6 q^{4} + 6 q^{5} + q^{6} + 6 q^{7} - 6 q^{8} + 3 q^{9} - 6 q^{10} - q^{12} - 9 q^{13} - 6 q^{14} - q^{15} + 6 q^{16} - 9 q^{17} - 3 q^{18} - 12 q^{19} + 6 q^{20} - q^{21} + 4 q^{23} + q^{24} + 6 q^{25} + 9 q^{26} - 4 q^{27} + 6 q^{28} - 15 q^{29} + q^{30} + 8 q^{31} - 6 q^{32} + 9 q^{34} + 6 q^{35} + 3 q^{36} - 4 q^{37} + 12 q^{38} + 19 q^{39} - 6 q^{40} - 4 q^{41} + q^{42} - 30 q^{43} + 3 q^{45} - 4 q^{46} - 7 q^{47} - q^{48} + 6 q^{49} - 6 q^{50} - 16 q^{51} - 9 q^{52} - 6 q^{53} + 4 q^{54} - 6 q^{56} + 14 q^{57} + 15 q^{58} + 4 q^{59} - q^{60} + 14 q^{61} - 8 q^{62} + 3 q^{63} + 6 q^{64} - 9 q^{65} + 18 q^{67} - 9 q^{68} - 10 q^{69} - 6 q^{70} + 23 q^{71} - 3 q^{72} - 23 q^{73} + 4 q^{74} - q^{75} - 12 q^{76} - 19 q^{78} - 21 q^{79} + 6 q^{80} - 18 q^{81} + 4 q^{82} - 25 q^{83} - q^{84} - 9 q^{85} + 30 q^{86} - 14 q^{87} - 18 q^{89} - 3 q^{90} - 9 q^{91} + 4 q^{92} - 24 q^{93} + 7 q^{94} - 12 q^{95} + q^{96} + 7 q^{97} - 6 q^{98}+O(q^{100}) \) 6 * q - 6 * q^2 - q^3 + 6 * q^4 + 6 * q^5 + q^6 + 6 * q^7 - 6 * q^8 + 3 * q^9 - 6 * q^10 - q^12 - 9 * q^13 - 6 * q^14 - q^15 + 6 * q^16 - 9 * q^17 - 3 * q^18 - 12 * q^19 + 6 * q^20 - q^21 + 4 * q^23 + q^24 + 6 * q^25 + 9 * q^26 - 4 * q^27 + 6 * q^28 - 15 * q^29 + q^30 + 8 * q^31 - 6 * q^32 + 9 * q^34 + 6 * q^35 + 3 * q^36 - 4 * q^37 + 12 * q^38 + 19 * q^39 - 6 * q^40 - 4 * q^41 + q^42 - 30 * q^43 + 3 * q^45 - 4 * q^46 - 7 * q^47 - q^48 + 6 * q^49 - 6 * q^50 - 16 * q^51 - 9 * q^52 - 6 * q^53 + 4 * q^54 - 6 * q^56 + 14 * q^57 + 15 * q^58 + 4 * q^59 - q^60 + 14 * q^61 - 8 * q^62 + 3 * q^63 + 6 * q^64 - 9 * q^65 + 18 * q^67 - 9 * q^68 - 10 * q^69 - 6 * q^70 + 23 * q^71 - 3 * q^72 - 23 * q^73 + 4 * q^74 - q^75 - 12 * q^76 - 19 * q^78 - 21 * q^79 + 6 * q^80 - 18 * q^81 + 4 * q^82 - 25 * q^83 - q^84 - 9 * q^85 + 30 * q^86 - 14 * q^87 - 18 * q^89 - 3 * q^90 - 9 * q^91 + 4 * q^92 - 24 * q^93 + 7 * q^94 - 12 * q^95 + q^96 + 7 * q^97 - 6 * q^98

Introduction

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