LMFDB - Embedded newform 8470.2.a.cc.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("8470.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$67.6332905120$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
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			1.1
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	8470.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.618034 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.618034 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.61803 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.618034 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.618034 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.61803 q^{9} +1.00000 q^{10} -0.618034 q^{12} +3.38197 q^{13} +1.00000 q^{14} -0.618034 q^{15} +1.00000 q^{16} +2.38197 q^{17} -2.61803 q^{18} -0.763932 q^{19} +1.00000 q^{20} -0.618034 q^{21} -0.472136 q^{23} -0.618034 q^{24} +1.00000 q^{25} +3.38197 q^{26} +3.47214 q^{27} +1.00000 q^{28} +0.854102 q^{29} -0.618034 q^{30} +0.763932 q^{31} +1.00000 q^{32} +2.38197 q^{34} +1.00000 q^{35} -2.61803 q^{36} +9.70820 q^{37} -0.763932 q^{38} -2.09017 q^{39} +1.00000 q^{40} -8.94427 q^{41} -0.618034 q^{42} -1.23607 q^{43} -2.61803 q^{45} -0.472136 q^{46} -1.90983 q^{47} -0.618034 q^{48} +1.00000 q^{49} +1.00000 q^{50} -1.47214 q^{51} +3.38197 q^{52} -2.47214 q^{53} +3.47214 q^{54} +1.00000 q^{56} +0.472136 q^{57} +0.854102 q^{58} +9.23607 q^{59} -0.618034 q^{60} +1.70820 q^{61} +0.763932 q^{62} -2.61803 q^{63} +1.00000 q^{64} +3.38197 q^{65} +3.23607 q^{67} +2.38197 q^{68} +0.291796 q^{69} +1.00000 q^{70} +8.32624 q^{71} -2.61803 q^{72} -11.3262 q^{73} +9.70820 q^{74} -0.618034 q^{75} -0.763932 q^{76} -2.09017 q^{78} +5.85410 q^{79} +1.00000 q^{80} +5.70820 q^{81} -8.94427 q^{82} +11.3820 q^{83} -0.618034 q^{84} +2.38197 q^{85} -1.23607 q^{86} -0.527864 q^{87} +13.7082 q^{89} -2.61803 q^{90} +3.38197 q^{91} -0.472136 q^{92} -0.472136 q^{93} -1.90983 q^{94} -0.763932 q^{95} -0.618034 q^{96} -5.61803 q^{97} +1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + q^{3} + 2 q^{4} + 2 q^{5} + q^{6} + 2 q^{7} + 2 q^{8} - 3 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + q^3 + 2 * q^4 + 2 * q^5 + q^6 + 2 * q^7 + 2 * q^8 - 3 * q^9	$ 2 q + 2 q^{2} + q^{3} + 2 q^{4} + 2 q^{5} + q^{6} + 2 q^{7} + 2 q^{8} - 3 q^{9} + 2 q^{10} + q^{12} + 9 q^{13} + 2 q^{14} + q^{15} + 2 q^{16} + 7 q^{17} - 3 q^{18} - 6 q^{19} + 2 q^{20} + q^{21} + 8 q^{23} + q^{24} + 2 q^{25} + 9 q^{26} - 2 q^{27} + 2 q^{28} - 5 q^{29} + q^{30} + 6 q^{31} + 2 q^{32} + 7 q^{34} + 2 q^{35} - 3 q^{36} + 6 q^{37} - 6 q^{38} + 7 q^{39} + 2 q^{40} + q^{42} + 2 q^{43} - 3 q^{45} + 8 q^{46} - 15 q^{47} + q^{48} + 2 q^{49} + 2 q^{50} + 6 q^{51} + 9 q^{52} + 4 q^{53} - 2 q^{54} + 2 q^{56} - 8 q^{57} - 5 q^{58} + 14 q^{59} + q^{60} - 10 q^{61} + 6 q^{62} - 3 q^{63} + 2 q^{64} + 9 q^{65} + 2 q^{67} + 7 q^{68} + 14 q^{69} + 2 q^{70} + q^{71} - 3 q^{72} - 7 q^{73} + 6 q^{74} + q^{75} - 6 q^{76} + 7 q^{78} + 5 q^{79} + 2 q^{80} - 2 q^{81} + 25 q^{83} + q^{84} + 7 q^{85} + 2 q^{86} - 10 q^{87} + 14 q^{89} - 3 q^{90} + 9 q^{91} + 8 q^{92} + 8 q^{93} - 15 q^{94} - 6 q^{95} + q^{96} - 9 q^{97} + 2 q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 + q^3 + 2 * q^4 + 2 * q^5 + q^6 + 2 * q^7 + 2 * q^8 - 3 * q^9 + 2 * q^10 + q^12 + 9 * q^13 + 2 * q^14 + q^15 + 2 * q^16 + 7 * q^17 - 3 * q^18 - 6 * q^19 + 2 * q^20 + q^21 + 8 * q^23 + q^24 + 2 * q^25 + 9 * q^26 - 2 * q^27 + 2 * q^28 - 5 * q^29 + q^30 + 6 * q^31 + 2 * q^32 + 7 * q^34 + 2 * q^35 - 3 * q^36 + 6 * q^37 - 6 * q^38 + 7 * q^39 + 2 * q^40 + q^42 + 2 * q^43 - 3 * q^45 + 8 * q^46 - 15 * q^47 + q^48 + 2 * q^49 + 2 * q^50 + 6 * q^51 + 9 * q^52 + 4 * q^53 - 2 * q^54 + 2 * q^56 - 8 * q^57 - 5 * q^58 + 14 * q^59 + q^60 - 10 * q^61 + 6 * q^62 - 3 * q^63 + 2 * q^64 + 9 * q^65 + 2 * q^67 + 7 * q^68 + 14 * q^69 + 2 * q^70 + q^71 - 3 * q^72 - 7 * q^73 + 6 * q^74 + q^75 - 6 * q^76 + 7 * q^78 + 5 * q^79 + 2 * q^80 - 2 * q^81 + 25 * q^83 + q^84 + 7 * q^85 + 2 * q^86 - 10 * q^87 + 14 * q^89 - 3 * q^90 + 9 * q^91 + 8 * q^92 + 8 * q^93 - 15 * q^94 - 6 * q^95 + q^96 - 9 * q^97 + 2 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−0.618034	−0.356822	−0.178411	−	0.983956i	$-0.557096\pi$
$3$	−0.618034	−0.356822	−0.178411	+	0.983956i	$0.557096\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.618034	−0.252311
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	−2.61803	−0.872678
$10$	1.00000	0.316228
$11$	0	0
$11$	0	0
$12$	−0.618034	−0.178411
$13$	3.38197	0.937989	0.468994	−	0.883201i	$-0.344616\pi$
$13$	3.38197	0.937989	0.468994	+	0.883201i	$0.344616\pi$
$14$	1.00000	0.267261
$15$	−0.618034	−0.159576
$16$	1.00000	0.250000
$17$	2.38197	0.577712	0.288856	−	0.957373i	$-0.406725\pi$
$17$	2.38197	0.577712	0.288856	+	0.957373i	$0.406725\pi$
$18$	−2.61803	−0.617077
$19$	−0.763932	−0.175258	−0.0876290	−	0.996153i	$-0.527929\pi$
$19$	−0.763932	−0.175258	−0.0876290	+	0.996153i	$0.527929\pi$
$20$	1.00000	0.223607
$21$	−0.618034	−0.134866
$22$	0	0
$23$	−0.472136	−0.0984472	−0.0492236	−	0.998788i	$-0.515675\pi$
$23$	−0.472136	−0.0984472	−0.0492236	+	0.998788i	$0.515675\pi$
$24$	−0.618034	−0.126156
$25$	1.00000	0.200000
$26$	3.38197	0.663258
$27$	3.47214	0.668213
$28$	1.00000	0.188982
$29$	0.854102	0.158603	0.0793014	−	0.996851i	$-0.474731\pi$
$29$	0.854102	0.158603	0.0793014	+	0.996851i	$0.474731\pi$
$30$	−0.618034	−0.112837
$31$	0.763932	0.137206	0.0686031	−	0.997644i	$-0.478146\pi$
$31$	0.763932	0.137206	0.0686031	+	0.997644i	$0.478146\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	2.38197	0.408504
$35$	1.00000	0.169031
$36$	−2.61803	−0.436339
$37$	9.70820	1.59602	0.798009	−	0.602645i	$-0.205886\pi$
$37$	9.70820	1.59602	0.798009	+	0.602645i	$0.205886\pi$
$38$	−0.763932	−0.123926
$39$	−2.09017	−0.334695
$40$	1.00000	0.158114
$41$	−8.94427	−1.39686	−0.698430	−	0.715678i	$-0.746118\pi$
$41$	−8.94427	−1.39686	−0.698430	+	0.715678i	$0.746118\pi$
$42$	−0.618034	−0.0953647
$43$	−1.23607	−0.188499	−0.0942493	−	0.995549i	$-0.530045\pi$
$43$	−1.23607	−0.188499	−0.0942493	+	0.995549i	$0.530045\pi$
$44$	0	0
$45$	−2.61803	−0.390273
$46$	−0.472136	−0.0696126
$47$	−1.90983	−0.278577	−0.139289	−	0.990252i	$-0.544482\pi$
$47$	−1.90983	−0.278577	−0.139289	+	0.990252i	$0.544482\pi$
$48$	−0.618034	−0.0892055
$49$	1.00000	0.142857
$50$	1.00000	0.141421
$51$	−1.47214	−0.206140
$52$	3.38197	0.468994
$53$	−2.47214	−0.339574	−0.169787	−	0.985481i	$-0.554308\pi$
$53$	−2.47214	−0.339574	−0.169787	+	0.985481i	$0.554308\pi$
$54$	3.47214	0.472498
$55$	0	0
$56$	1.00000	0.133631
$57$	0.472136	0.0625359
$58$	0.854102	0.112149
$59$	9.23607	1.20243	0.601217	−	0.799086i	$-0.294683\pi$
$59$	9.23607	1.20243	0.601217	+	0.799086i	$0.294683\pi$
$60$	−0.618034	−0.0797878
$61$	1.70820	0.218713	0.109357	−	0.994003i	$-0.465121\pi$
$61$	1.70820	0.218713	0.109357	+	0.994003i	$0.465121\pi$
$62$	0.763932	0.0970195
$63$	−2.61803	−0.329841
$64$	1.00000	0.125000
$65$	3.38197	0.419481
$66$	0	0
$67$	3.23607	0.395349	0.197674	−	0.980268i	$-0.436661\pi$
$67$	3.23607	0.395349	0.197674	+	0.980268i	$0.436661\pi$
$68$	2.38197	0.288856
$69$	0.291796	0.0351281
$70$	1.00000	0.119523
$71$	8.32624	0.988143	0.494071	−	0.869421i	$-0.335508\pi$
$71$	8.32624	0.988143	0.494071	+	0.869421i	$0.335508\pi$
$72$	−2.61803	−0.308538
$73$	−11.3262	−1.32564	−0.662818	−	0.748781i	$-0.730640\pi$
$73$	−11.3262	−1.32564	−0.662818	+	0.748781i	$0.730640\pi$
$74$	9.70820	1.12856
$75$	−0.618034	−0.0713644
$76$	−0.763932	−0.0876290
$77$	0	0
$78$	−2.09017	−0.236665
$79$	5.85410	0.658638	0.329319	−	0.944219i	$-0.393181\pi$
$79$	5.85410	0.658638	0.329319	+	0.944219i	$0.393181\pi$
$80$	1.00000	0.111803
$81$	5.70820	0.634245
$82$	−8.94427	−0.987730
$83$	11.3820	1.24933	0.624667	−	0.780892i	$-0.285235\pi$
$83$	11.3820	1.24933	0.624667	+	0.780892i	$0.285235\pi$
$84$	−0.618034	−0.0674330
$85$	2.38197	0.258360
$86$	−1.23607	−0.133289
$87$	−0.527864	−0.0565930
$88$	0	0
$89$	13.7082	1.45307	0.726533	−	0.687131i	$-0.241130\pi$
$89$	13.7082	1.45307	0.726533	+	0.687131i	$0.241130\pi$
$90$	−2.61803	−0.275965
$91$	3.38197	0.354526
$92$	−0.472136	−0.0492236
$93$	−0.472136	−0.0489582
$94$	−1.90983	−0.196984
$95$	−0.763932	−0.0783778
$96$	−0.618034	−0.0630778
$97$	−5.61803	−0.570425	−0.285212	−	0.958464i	$-0.592064\pi$
$97$	−5.61803	−0.570425	−0.285212	+	0.958464i	$0.592064\pi$
$98$	1.00000	0.101015
$99$	0	0
$100$	1.00000	0.100000
$101$	−0.763932	−0.0760141	−0.0380070	−	0.999277i	$-0.512101\pi$
$101$	−0.763932	−0.0760141	−0.0380070	+	0.999277i	$0.512101\pi$
$102$	−1.47214	−0.145763
$103$	−16.5623	−1.63193	−0.815966	−	0.578100i	$-0.803795\pi$
$103$	−16.5623	−1.63193	−0.815966	+	0.578100i	$0.803795\pi$
$104$	3.38197	0.331629
$105$	−0.618034	−0.0603139
$106$	−2.47214	−0.240115
$107$	−15.2361	−1.47293	−0.736463	−	0.676478i	$-0.763506\pi$
$107$	−15.2361	−1.47293	−0.736463	+	0.676478i	$0.763506\pi$
$108$	3.47214	0.334106
$109$	12.4721	1.19461	0.597307	−	0.802013i	$-0.296237\pi$
$109$	12.4721	1.19461	0.597307	+	0.802013i	$0.296237\pi$
$110$	0	0
$111$	−6.00000	−0.569495
$112$	1.00000	0.0944911
$113$	−10.4721	−0.985136	−0.492568	−	0.870274i	$-0.663942\pi$
$113$	−10.4721	−0.985136	−0.492568	+	0.870274i	$0.663942\pi$
$114$	0.472136	0.0442196
$115$	−0.472136	−0.0440269
$116$	0.854102	0.0793014
$117$	−8.85410	−0.818562
$118$	9.23607	0.850249
$119$	2.38197	0.218354
$120$	−0.618034	−0.0564185
$121$	0	0
$122$	1.70820	0.154654
$123$	5.52786	0.498431
$124$	0.763932	0.0686031
$125$	1.00000	0.0894427
$126$	−2.61803	−0.233233
$127$	−2.18034	−0.193474	−0.0967369	−	0.995310i	$-0.530841\pi$
$127$	−2.18034	−0.193474	−0.0967369	+	0.995310i	$0.530841\pi$
$128$	1.00000	0.0883883
$129$	0.763932	0.0672605
$130$	3.38197	0.296618
$131$	15.4164	1.34694	0.673469	−	0.739216i	$-0.264804\pi$
$131$	15.4164	1.34694	0.673469	+	0.739216i	$0.264804\pi$
$132$	0	0
$133$	−0.763932	−0.0662413
$134$	3.23607	0.279554
$135$	3.47214	0.298834
$136$	2.38197	0.204252
$137$	−16.0000	−1.36697	−0.683486	−	0.729964i	$-0.739537\pi$
$137$	−16.0000	−1.36697	−0.683486	+	0.729964i	$0.739537\pi$
$138$	0.291796	0.0248393
$139$	−8.94427	−0.758643	−0.379322	−	0.925265i	$-0.623843\pi$
$139$	−8.94427	−0.758643	−0.379322	+	0.925265i	$0.623843\pi$
$140$	1.00000	0.0845154
$141$	1.18034	0.0994026
$142$	8.32624	0.698722
$143$	0	0
$144$	−2.61803	−0.218169
$145$	0.854102	0.0709293
$146$	−11.3262	−0.937366
$147$	−0.618034	−0.0509746
$148$	9.70820	0.798009
$149$	14.1459	1.15888	0.579439	−	0.815016i	$-0.303272\pi$
$149$	14.1459	1.15888	0.579439	+	0.815016i	$0.303272\pi$
$150$	−0.618034	−0.0504623
$151$	23.6180	1.92201	0.961004	−	0.276534i	$-0.0891858\pi$
$151$	23.6180	1.92201	0.961004	+	0.276534i	$0.0891858\pi$
$152$	−0.763932	−0.0619631
$153$	−6.23607	−0.504156
$154$	0	0
$155$	0.763932	0.0613605
$156$	−2.09017	−0.167348
$157$	0.0901699	0.00719634	0.00359817	−	0.999994i	$-0.498855\pi$
$157$	0.0901699	0.00719634	0.00359817	+	0.999994i	$0.498855\pi$
$158$	5.85410	0.465727
$159$	1.52786	0.121168
$160$	1.00000	0.0790569
$161$	−0.472136	−0.0372095
$162$	5.70820	0.448479
$163$	16.6525	1.30432	0.652161	−	0.758080i	$-0.273862\pi$
$163$	16.6525	1.30432	0.652161	+	0.758080i	$0.273862\pi$
$164$	−8.94427	−0.698430
$165$	0	0
$166$	11.3820	0.883412
$167$	20.0000	1.54765	0.773823	−	0.633402i	$-0.218342\pi$
$167$	20.0000	1.54765	0.773823	+	0.633402i	$0.218342\pi$
$168$	−0.618034	−0.0476824
$169$	−1.56231	−0.120177
$170$	2.38197	0.182688
$171$	2.00000	0.152944
$172$	−1.23607	−0.0942493
$173$	22.5066	1.71114	0.855572	−	0.517684i	$-0.173206\pi$
$173$	22.5066	1.71114	0.855572	+	0.517684i	$0.173206\pi$
$174$	−0.527864	−0.0400173
$175$	1.00000	0.0755929
$176$	0	0
$177$	−5.70820	−0.429055
$178$	13.7082	1.02747
$179$	0.562306	0.0420287	0.0210144	−	0.999779i	$-0.493310\pi$
$179$	0.562306	0.0420287	0.0210144	+	0.999779i	$0.493310\pi$
$180$	−2.61803	−0.195137
$181$	0	0		−	1.00000i	$-0.5\pi$
$181$	0	0			1.00000i	$0.5\pi$
$182$	3.38197	0.250688
$183$	−1.05573	−0.0780417
$184$	−0.472136	−0.0348063
$185$	9.70820	0.713761
$186$	−0.472136	−0.0346187
$187$	0	0
$188$	−1.90983	−0.139289
$189$	3.47214	0.252561
$190$	−0.763932	−0.0554215
$191$	−5.85410	−0.423588	−0.211794	−	0.977314i	$-0.567931\pi$
$191$	−5.85410	−0.423588	−0.211794	+	0.977314i	$0.567931\pi$
$192$	−0.618034	−0.0446028
$193$	−4.94427	−0.355896	−0.177948	−	0.984040i	$-0.556946\pi$
$193$	−4.94427	−0.355896	−0.177948	+	0.984040i	$0.556946\pi$
$194$	−5.61803	−0.403351
$195$	−2.09017	−0.149680
$196$	1.00000	0.0714286
$197$	11.4164	0.813385	0.406693	−	0.913565i	$-0.366682\pi$
$197$	11.4164	0.813385	0.406693	+	0.913565i	$0.366682\pi$
$198$	0	0
$199$	6.94427	0.492266	0.246133	−	0.969236i	$-0.420840\pi$
$199$	6.94427	0.492266	0.246133	+	0.969236i	$0.420840\pi$
$200$	1.00000	0.0707107
$201$	−2.00000	−0.141069
$202$	−0.763932	−0.0537501
$203$	0.854102	0.0599462
$204$	−1.47214	−0.103070
$205$	−8.94427	−0.624695
$206$	−16.5623	−1.15395
$207$	1.23607	0.0859127
$208$	3.38197	0.234497
$209$	0	0
$210$	−0.618034	−0.0426484
$211$	−0.326238	−0.0224591	−0.0112296	−	0.999937i	$-0.503575\pi$
$211$	−0.326238	−0.0224591	−0.0112296	+	0.999937i	$0.503575\pi$
$212$	−2.47214	−0.169787
$213$	−5.14590	−0.352591
$214$	−15.2361	−1.04152
$215$	−1.23607	−0.0842991
$216$	3.47214	0.236249
$217$	0.763932	0.0518591
$218$	12.4721	0.844720
$219$	7.00000	0.473016
$220$	0	0
$221$	8.05573	0.541887
$222$	−6.00000	−0.402694
$223$	−9.52786	−0.638033	−0.319016	−	0.947749i	$-0.603353\pi$
$223$	−9.52786	−0.638033	−0.319016	+	0.947749i	$0.603353\pi$
$224$	1.00000	0.0668153
$225$	−2.61803	−0.174536
$226$	−10.4721	−0.696596
$227$	13.8541	0.919529	0.459765	−	0.888041i	$-0.347934\pi$
$227$	13.8541	0.919529	0.459765	+	0.888041i	$0.347934\pi$
$228$	0.472136	0.0312680
$229$	−5.70820	−0.377209	−0.188604	−	0.982053i	$-0.560396\pi$
$229$	−5.70820	−0.377209	−0.188604	+	0.982053i	$0.560396\pi$
$230$	−0.472136	−0.0311317
$231$	0	0
$232$	0.854102	0.0560745
$233$	14.6525	0.959916	0.479958	−	0.877292i	$-0.340652\pi$
$233$	14.6525	0.959916	0.479958	+	0.877292i	$0.340652\pi$
$234$	−8.85410	−0.578811
$235$	−1.90983	−0.124584
$236$	9.23607	0.601217
$237$	−3.61803	−0.235017
$238$	2.38197	0.154400
$239$	2.14590	0.138807	0.0694033	−	0.997589i	$-0.477890\pi$
$239$	2.14590	0.138807	0.0694033	+	0.997589i	$0.477890\pi$
$240$	−0.618034	−0.0398939
$241$	9.70820	0.625360	0.312680	−	0.949858i	$-0.398773\pi$
$241$	9.70820	0.625360	0.312680	+	0.949858i	$0.398773\pi$
$242$	0	0
$243$	−13.9443	−0.894525
$244$	1.70820	0.109357
$245$	1.00000	0.0638877
$246$	5.52786	0.352444
$247$	−2.58359	−0.164390
$248$	0.763932	0.0485097
$249$	−7.03444	−0.445790
$250$	1.00000	0.0632456
$251$	5.23607	0.330498	0.165249	−	0.986252i	$-0.447157\pi$
$251$	5.23607	0.330498	0.165249	+	0.986252i	$0.447157\pi$
$252$	−2.61803	−0.164921
$253$	0	0
$254$	−2.18034	−0.136807
$255$	−1.47214	−0.0921887
$256$	1.00000	0.0625000
$257$	20.2705	1.26444	0.632220	−	0.774789i	$-0.282144\pi$
$257$	20.2705	1.26444	0.632220	+	0.774789i	$0.282144\pi$
$258$	0.763932	0.0475603
$259$	9.70820	0.603238
$260$	3.38197	0.209741
$261$	−2.23607	−0.138409
$262$	15.4164	0.952429
$263$	27.7082	1.70856	0.854281	−	0.519812i	$-0.173998\pi$
$263$	27.7082	1.70856	0.854281	+	0.519812i	$0.173998\pi$
$264$	0	0
$265$	−2.47214	−0.151862
$266$	−0.763932	−0.0468397
$267$	−8.47214	−0.518486
$268$	3.23607	0.197674
$269$	6.29180	0.383618	0.191809	−	0.981432i	$-0.438565\pi$
$269$	6.29180	0.383618	0.191809	+	0.981432i	$0.438565\pi$
$270$	3.47214	0.211307
$271$	−25.1246	−1.52621	−0.763106	−	0.646274i	$-0.776326\pi$
$271$	−25.1246	−1.52621	−0.763106	+	0.646274i	$0.776326\pi$
$272$	2.38197	0.144428
$273$	−2.09017	−0.126503
$274$	−16.0000	−0.966595
$275$	0	0
$276$	0.291796	0.0175641
$277$	−13.4164	−0.806114	−0.403057	−	0.915175i	$-0.632052\pi$
$277$	−13.4164	−0.806114	−0.403057	+	0.915175i	$0.632052\pi$
$278$	−8.94427	−0.536442
$279$	−2.00000	−0.119737
$280$	1.00000	0.0597614
$281$	−26.3607	−1.57255	−0.786273	−	0.617879i	$-0.787992\pi$
$281$	−26.3607	−1.57255	−0.786273	+	0.617879i	$0.787992\pi$
$282$	1.18034	0.0702882
$283$	1.32624	0.0788367	0.0394183	−	0.999223i	$-0.487450\pi$
$283$	1.32624	0.0788367	0.0394183	+	0.999223i	$0.487450\pi$
$284$	8.32624	0.494071
$285$	0.472136	0.0279669
$286$	0	0
$287$	−8.94427	−0.527964
$288$	−2.61803	−0.154269
$289$	−11.3262	−0.666249
$290$	0.854102	0.0501546
$291$	3.47214	0.203540
$292$	−11.3262	−0.662818
$293$	1.41641	0.0827474	0.0413737	−	0.999144i	$-0.486827\pi$
$293$	1.41641	0.0827474	0.0413737	+	0.999144i	$0.486827\pi$
$294$	−0.618034	−0.0360445
$295$	9.23607	0.537745
$296$	9.70820	0.564278
$297$	0	0
$298$	14.1459	0.819450
$299$	−1.59675	−0.0923423
$300$	−0.618034	−0.0356822
$301$	−1.23607	−0.0712458
$302$	23.6180	1.35907
$303$	0.472136	0.0271235
$304$	−0.763932	−0.0438145
$305$	1.70820	0.0978115
$306$	−6.23607	−0.356492
$307$	22.4508	1.28134	0.640669	−	0.767817i	$-0.278657\pi$
$307$	22.4508	1.28134	0.640669	+	0.767817i	$0.278657\pi$
$308$	0	0
$309$	10.2361	0.582310
$310$	0.763932	0.0433884
$311$	−12.1803	−0.690684	−0.345342	−	0.938477i	$-0.612237\pi$
$311$	−12.1803	−0.690684	−0.345342	+	0.938477i	$0.612237\pi$
$312$	−2.09017	−0.118333
$313$	−23.8885	−1.35026	−0.675130	−	0.737699i	$-0.735913\pi$
$313$	−23.8885	−1.35026	−0.675130	+	0.737699i	$0.735913\pi$
$314$	0.0901699	0.00508858
$315$	−2.61803	−0.147510
$316$	5.85410	0.329319
$317$	−17.8885	−1.00472	−0.502360	−	0.864658i	$-0.667535\pi$
$317$	−17.8885	−1.00472	−0.502360	+	0.864658i	$0.667535\pi$
$318$	1.52786	0.0856784
$319$	0	0
$320$	1.00000	0.0559017
$321$	9.41641	0.525573
$322$	−0.472136	−0.0263111
$323$	−1.81966	−0.101249
$324$	5.70820	0.317122
$325$	3.38197	0.187598
$326$	16.6525	0.922295
$327$	−7.70820	−0.426265
$328$	−8.94427	−0.493865
$329$	−1.90983	−0.105292
$330$	0	0
$331$	−8.61803	−0.473690	−0.236845	−	0.971547i	$-0.576113\pi$
$331$	−8.61803	−0.473690	−0.236845	+	0.971547i	$0.576113\pi$
$332$	11.3820	0.624667
$333$	−25.4164	−1.39281
$334$	20.0000	1.09435
$335$	3.23607	0.176805
$336$	−0.618034	−0.0337165
$337$	8.00000	0.435788	0.217894	−	0.975972i	$-0.430081\pi$
$337$	8.00000	0.435788	0.217894	+	0.975972i	$0.430081\pi$
$338$	−1.56231	−0.0849782
$339$	6.47214	0.351518
$340$	2.38197	0.129180
$341$	0	0
$342$	2.00000	0.108148
$343$	1.00000	0.0539949
$344$	−1.23607	−0.0666443
$345$	0.291796	0.0157098
$346$	22.5066	1.20996
$347$	−9.88854	−0.530845	−0.265422	−	0.964132i	$-0.585511\pi$
$347$	−9.88854	−0.530845	−0.265422	+	0.964132i	$0.585511\pi$
$348$	−0.527864	−0.0282965
$349$	−9.05573	−0.484742	−0.242371	−	0.970184i	$-0.577925\pi$
$349$	−9.05573	−0.484742	−0.242371	+	0.970184i	$0.577925\pi$
$350$	1.00000	0.0534522
$351$	11.7426	0.626776
$352$	0	0
$353$	31.4508	1.67396	0.836980	−	0.547234i	$-0.184319\pi$
$353$	31.4508	1.67396	0.836980	+	0.547234i	$0.184319\pi$
$354$	−5.70820	−0.303388
$355$	8.32624	0.441911
$356$	13.7082	0.726533
$357$	−1.47214	−0.0779137
$358$	0.562306	0.0297188
$359$	−28.9787	−1.52944	−0.764719	−	0.644364i	$-0.777122\pi$
$359$	−28.9787	−1.52944	−0.764719	+	0.644364i	$0.777122\pi$
$360$	−2.61803	−0.137983
$361$	−18.4164	−0.969285
$362$	0	0
$363$	0	0
$364$	3.38197	0.177263
$365$	−11.3262	−0.592842
$366$	−1.05573	−0.0551838
$367$	19.6738	1.02696	0.513481	−	0.858101i	$-0.328356\pi$
$367$	19.6738	1.02696	0.513481	+	0.858101i	$0.328356\pi$
$368$	−0.472136	−0.0246118
$369$	23.4164	1.21901
$370$	9.70820	0.504705
$371$	−2.47214	−0.128347
$372$	−0.472136	−0.0244791
$373$	28.6525	1.48357	0.741784	−	0.670638i	$-0.233980\pi$
$373$	28.6525	1.48357	0.741784	+	0.670638i	$0.233980\pi$
$374$	0	0
$375$	−0.618034	−0.0319151
$376$	−1.90983	−0.0984920
$377$	2.88854	0.148768
$378$	3.47214	0.178587
$379$	22.8541	1.17394	0.586968	−	0.809610i	$-0.300321\pi$
$379$	22.8541	1.17394	0.586968	+	0.809610i	$0.300321\pi$
$380$	−0.763932	−0.0391889
$381$	1.34752	0.0690358
$382$	−5.85410	−0.299522
$383$	2.14590	0.109650	0.0548251	−	0.998496i	$-0.482540\pi$
$383$	2.14590	0.109650	0.0548251	+	0.998496i	$0.482540\pi$
$384$	−0.618034	−0.0315389
$385$	0	0
$386$	−4.94427	−0.251657
$387$	3.23607	0.164499
$388$	−5.61803	−0.285212
$389$	13.2705	0.672842	0.336421	−	0.941712i	$-0.390784\pi$
$389$	13.2705	0.672842	0.336421	+	0.941712i	$0.390784\pi$
$390$	−2.09017	−0.105840
$391$	−1.12461	−0.0568741
$392$	1.00000	0.0505076
$393$	−9.52786	−0.480617
$394$	11.4164	0.575150
$395$	5.85410	0.294552
$396$	0	0
$397$	−10.4377	−0.523853	−0.261926	−	0.965088i	$-0.584358\pi$
$397$	−10.4377	−0.523853	−0.261926	+	0.965088i	$0.584358\pi$
$398$	6.94427	0.348085
$399$	0.472136	0.0236364
$400$	1.00000	0.0500000
$401$	−34.3820	−1.71695	−0.858477	−	0.512853i	$-0.828589\pi$
$401$	−34.3820	−1.71695	−0.858477	+	0.512853i	$0.828589\pi$
$402$	−2.00000	−0.0997509
$403$	2.58359	0.128698
$404$	−0.763932	−0.0380070
$405$	5.70820	0.283643
$406$	0.854102	0.0423884
$407$	0	0
$408$	−1.47214	−0.0728816
$409$	0.763932	0.0377740	0.0188870	−	0.999822i	$-0.493988\pi$
$409$	0.763932	0.0377740	0.0188870	+	0.999822i	$0.493988\pi$
$410$	−8.94427	−0.441726
$411$	9.88854	0.487766
$412$	−16.5623	−0.815966
$413$	9.23607	0.454477
$414$	1.23607	0.0607494
$415$	11.3820	0.558719
$416$	3.38197	0.165815
$417$	5.52786	0.270701
$418$	0	0
$419$	−10.9443	−0.534663	−0.267331	−	0.963605i	$-0.586142\pi$
$419$	−10.9443	−0.534663	−0.267331	+	0.963605i	$0.586142\pi$
$420$	−0.618034	−0.0301570
$421$	4.32624	0.210848	0.105424	−	0.994427i	$-0.466380\pi$
$421$	4.32624	0.210848	0.105424	+	0.994427i	$0.466380\pi$
$422$	−0.326238	−0.0158810
$423$	5.00000	0.243108
$424$	−2.47214	−0.120058
$425$	2.38197	0.115542
$426$	−5.14590	−0.249320
$427$	1.70820	0.0826658
$428$	−15.2361	−0.736463
$429$	0	0
$430$	−1.23607	−0.0596085
$431$	4.56231	0.219759	0.109879	−	0.993945i	$-0.464954\pi$
$431$	4.56231	0.219759	0.109879	+	0.993945i	$0.464954\pi$
$432$	3.47214	0.167053
$433$	−7.09017	−0.340732	−0.170366	−	0.985381i	$-0.554495\pi$
$433$	−7.09017	−0.340732	−0.170366	+	0.985381i	$0.554495\pi$
$434$	0.763932	0.0366699
$435$	−0.527864	−0.0253091
$436$	12.4721	0.597307
$437$	0.360680	0.0172537
$438$	7.00000	0.334473
$439$	20.6525	0.985689	0.492844	−	0.870117i	$-0.335957\pi$
$439$	20.6525	0.985689	0.492844	+	0.870117i	$0.335957\pi$
$440$	0	0
$441$	−2.61803	−0.124668
$442$	8.05573	0.383172
$443$	−10.7639	−0.511410	−0.255705	−	0.966755i	$-0.582308\pi$
$443$	−10.7639	−0.511410	−0.255705	+	0.966755i	$0.582308\pi$
$444$	−6.00000	−0.284747
$445$	13.7082	0.649831
$446$	−9.52786	−0.451157
$447$	−8.74265	−0.413513
$448$	1.00000	0.0472456
$449$	18.5066	0.873379	0.436690	−	0.899612i	$-0.356151\pi$
$449$	18.5066	0.873379	0.436690	+	0.899612i	$0.356151\pi$
$450$	−2.61803	−0.123415
$451$	0	0
$452$	−10.4721	−0.492568
$453$	−14.5967	−0.685815
$454$	13.8541	0.650205
$455$	3.38197	0.158549
$456$	0.472136	0.0221098
$457$	−14.0000	−0.654892	−0.327446	−	0.944870i	$-0.606188\pi$
$457$	−14.0000	−0.654892	−0.327446	+	0.944870i	$0.606188\pi$
$458$	−5.70820	−0.266727
$459$	8.27051	0.386034
$460$	−0.472136	−0.0220135
$461$	−15.1246	−0.704423	−0.352212	−	0.935920i	$-0.614570\pi$
$461$	−15.1246	−0.704423	−0.352212	+	0.935920i	$0.614570\pi$
$462$	0	0
$463$	8.18034	0.380173	0.190086	−	0.981767i	$-0.439123\pi$
$463$	8.18034	0.380173	0.190086	+	0.981767i	$0.439123\pi$
$464$	0.854102	0.0396507
$465$	−0.472136	−0.0218948
$466$	14.6525	0.678763
$467$	19.3820	0.896890	0.448445	−	0.893810i	$-0.351978\pi$
$467$	19.3820	0.896890	0.448445	+	0.893810i	$0.351978\pi$
$468$	−8.85410	−0.409281
$469$	3.23607	0.149428
$470$	−1.90983	−0.0880939
$471$	−0.0557281	−0.00256781
$472$	9.23607	0.425124
$473$	0	0
$474$	−3.61803	−0.166182
$475$	−0.763932	−0.0350516
$476$	2.38197	0.109177
$477$	6.47214	0.296339
$478$	2.14590	0.0981511
$479$	5.12461	0.234149	0.117075	−	0.993123i	$-0.462648\pi$
$479$	5.12461	0.234149	0.117075	+	0.993123i	$0.462648\pi$
$480$	−0.618034	−0.0282093
$481$	32.8328	1.49705
$482$	9.70820	0.442197
$483$	0.291796	0.0132772
$484$	0	0
$485$	−5.61803	−0.255102
$486$	−13.9443	−0.632525
$487$	34.1803	1.54886	0.774430	−	0.632660i	$-0.218037\pi$
$487$	34.1803	1.54886	0.774430	+	0.632660i	$0.218037\pi$
$488$	1.70820	0.0773268
$489$	−10.2918	−0.465411
$490$	1.00000	0.0451754
$491$	−16.9443	−0.764684	−0.382342	−	0.924021i	$-0.624882\pi$
$491$	−16.9443	−0.764684	−0.382342	+	0.924021i	$0.624882\pi$
$492$	5.52786	0.249215
$493$	2.03444	0.0916267
$494$	−2.58359	−0.116241
$495$	0	0
$496$	0.763932	0.0343016
$497$	8.32624	0.373483
$498$	−7.03444	−0.315221
$499$	−0.201626	−0.00902602	−0.00451301	−	0.999990i	$-0.501437\pi$
$499$	−0.201626	−0.00902602	−0.00451301	+	0.999990i	$0.501437\pi$
$500$	1.00000	0.0447214
$501$	−12.3607	−0.552234
$502$	5.23607	0.233697
$503$	−20.9787	−0.935395	−0.467697	−	0.883889i	$-0.654916\pi$
$503$	−20.9787	−0.935395	−0.467697	+	0.883889i	$0.654916\pi$
$504$	−2.61803	−0.116617
$505$	−0.763932	−0.0339945
$506$	0	0
$507$	0.965558	0.0428819
$508$	−2.18034	−0.0967369
$509$	15.8885	0.704247	0.352124	−	0.935953i	$-0.385460\pi$
$509$	15.8885	0.704247	0.352124	+	0.935953i	$0.385460\pi$
$510$	−1.47214	−0.0651873
$511$	−11.3262	−0.501043
$512$	1.00000	0.0441942
$513$	−2.65248	−0.117110
$514$	20.2705	0.894094
$515$	−16.5623	−0.729822
$516$	0.763932	0.0336302
$517$	0	0
$518$	9.70820	0.426554
$519$	−13.9098	−0.610574
$520$	3.38197	0.148309
$521$	34.5410	1.51327	0.756635	−	0.653838i	$-0.226842\pi$
$521$	34.5410	1.51327	0.756635	+	0.653838i	$0.226842\pi$
$522$	−2.23607	−0.0978700
$523$	32.7426	1.43174	0.715868	−	0.698236i	$-0.246031\pi$
$523$	32.7426	1.43174	0.715868	+	0.698236i	$0.246031\pi$
$524$	15.4164	0.673469
$525$	−0.618034	−0.0269732
$526$	27.7082	1.20814
$527$	1.81966	0.0792656
$528$	0	0
$529$	−22.7771	−0.990308
$530$	−2.47214	−0.107383
$531$	−24.1803	−1.04934
$532$	−0.763932	−0.0331207
$533$	−30.2492	−1.31024
$534$	−8.47214	−0.366625
$535$	−15.2361	−0.658713
$536$	3.23607	0.139777
$537$	−0.347524	−0.0149968
$538$	6.29180	0.271259
$539$	0	0
$540$	3.47214	0.149417
$541$	3.09017	0.132857	0.0664284	−	0.997791i	$-0.478840\pi$
$541$	3.09017	0.132857	0.0664284	+	0.997791i	$0.478840\pi$
$542$	−25.1246	−1.07919
$543$	0	0
$544$	2.38197	0.102126
$545$	12.4721	0.534248
$546$	−2.09017	−0.0894510
$547$	0.180340	0.00771078	0.00385539	−	0.999993i	$-0.498773\pi$
$547$	0.180340	0.00771078	0.00385539	+	0.999993i	$0.498773\pi$
$548$	−16.0000	−0.683486
$549$	−4.47214	−0.190866
$550$	0	0
$551$	−0.652476	−0.0277964
$552$	0.291796	0.0124197
$553$	5.85410	0.248942
$554$	−13.4164	−0.570009
$555$	−6.00000	−0.254686
$556$	−8.94427	−0.379322
$557$	3.59675	0.152399	0.0761995	−	0.997093i	$-0.475721\pi$
$557$	3.59675	0.152399	0.0761995	+	0.997093i	$0.475721\pi$
$558$	−2.00000	−0.0846668
$559$	−4.18034	−0.176810
$560$	1.00000	0.0422577
$561$	0	0
$562$	−26.3607	−1.11196
$563$	−3.43769	−0.144882	−0.0724408	−	0.997373i	$-0.523079\pi$
$563$	−3.43769	−0.144882	−0.0724408	+	0.997373i	$0.523079\pi$
$564$	1.18034	0.0497013
$565$	−10.4721	−0.440566
$566$	1.32624	0.0557459
$567$	5.70820	0.239722
$568$	8.32624	0.349361
$569$	−5.79837	−0.243080	−0.121540	−	0.992587i	$-0.538783\pi$
$569$	−5.79837	−0.243080	−0.121540	+	0.992587i	$0.538783\pi$
$570$	0.472136	0.0197756
$571$	−37.1459	−1.55451	−0.777254	−	0.629187i	$-0.783388\pi$
$571$	−37.1459	−1.55451	−0.777254	+	0.629187i	$0.783388\pi$
$572$	0	0
$573$	3.61803	0.151146
$574$	−8.94427	−0.373327
$575$	−0.472136	−0.0196894
$576$	−2.61803	−0.109085
$577$	−9.21478	−0.383616	−0.191808	−	0.981432i	$-0.561435\pi$
$577$	−9.21478	−0.383616	−0.191808	+	0.981432i	$0.561435\pi$
$578$	−11.3262	−0.471109
$579$	3.05573	0.126992
$580$	0.854102	0.0354647
$581$	11.3820	0.472204
$582$	3.47214	0.143925
$583$	0	0
$584$	−11.3262	−0.468683
$585$	−8.85410	−0.366072
$586$	1.41641	0.0585113
$587$	−18.5066	−0.763848	−0.381924	−	0.924194i	$-0.624738\pi$
$587$	−18.5066	−0.763848	−0.381924	+	0.924194i	$0.624738\pi$
$588$	−0.618034	−0.0254873
$589$	−0.583592	−0.0240465
$590$	9.23607	0.380243
$591$	−7.05573	−0.290234
$592$	9.70820	0.399005
$593$	−9.79837	−0.402371	−0.201185	−	0.979553i	$-0.564479\pi$
$593$	−9.79837	−0.402371	−0.201185	+	0.979553i	$0.564479\pi$
$594$	0	0
$595$	2.38197	0.0976511
$596$	14.1459	0.579439
$597$	−4.29180	−0.175652
$598$	−1.59675	−0.0652959
$599$	−35.3951	−1.44621	−0.723103	−	0.690741i	$-0.757285\pi$
$599$	−35.3951	−1.44621	−0.723103	+	0.690741i	$0.757285\pi$
$600$	−0.618034	−0.0252311
$601$	−8.00000	−0.326327	−0.163163	−	0.986599i	$-0.552170\pi$
$601$	−8.00000	−0.326327	−0.163163	+	0.986599i	$0.552170\pi$
$602$	−1.23607	−0.0503784
$603$	−8.47214	−0.345012
$604$	23.6180	0.961004
$605$	0	0
$606$	0.472136	0.0191792
$607$	21.6869	0.880245	0.440122	−	0.897938i	$-0.354935\pi$
$607$	21.6869	0.880245	0.440122	+	0.897938i	$0.354935\pi$
$608$	−0.763932	−0.0309815
$609$	−0.527864	−0.0213901
$610$	1.70820	0.0691632
$611$	−6.45898	−0.261302
$612$	−6.23607	−0.252078
$613$	−5.05573	−0.204199	−0.102099	−	0.994774i	$-0.532556\pi$
$613$	−5.05573	−0.204199	−0.102099	+	0.994774i	$0.532556\pi$
$614$	22.4508	0.906043
$615$	5.52786	0.222905
$616$	0	0
$617$	−26.1803	−1.05398	−0.526990	−	0.849871i	$-0.676680\pi$
$617$	−26.1803	−1.05398	−0.526990	+	0.849871i	$0.676680\pi$
$618$	10.2361	0.411755
$619$	27.4164	1.10196	0.550979	−	0.834519i	$-0.314254\pi$
$619$	27.4164	1.10196	0.550979	+	0.834519i	$0.314254\pi$
$620$	0.763932	0.0306802
$621$	−1.63932	−0.0657837
$622$	−12.1803	−0.488387
$623$	13.7082	0.549208
$624$	−2.09017	−0.0836738
$625$	1.00000	0.0400000
$626$	−23.8885	−0.954778
$627$	0	0
$628$	0.0901699	0.00359817
$629$	23.1246	0.922039
$630$	−2.61803	−0.104305
$631$	−46.4508	−1.84918	−0.924590	−	0.380965i	$-0.875592\pi$
$631$	−46.4508	−1.84918	−0.924590	+	0.380965i	$0.875592\pi$
$632$	5.85410	0.232864
$633$	0.201626	0.00801392
$634$	−17.8885	−0.710445
$635$	−2.18034	−0.0865241
$636$	1.52786	0.0605838
$637$	3.38197	0.133998
$638$	0	0
$639$	−21.7984	−0.862330
$640$	1.00000	0.0395285
$641$	−14.7984	−0.584501	−0.292250	−	0.956342i	$-0.594404\pi$
$641$	−14.7984	−0.584501	−0.292250	+	0.956342i	$0.594404\pi$
$642$	9.41641	0.371636
$643$	−21.8541	−0.861842	−0.430921	−	0.902390i	$-0.641811\pi$
$643$	−21.8541	−0.861842	−0.430921	+	0.902390i	$0.641811\pi$
$644$	−0.472136	−0.0186048
$645$	0.763932	0.0300798
$646$	−1.81966	−0.0715936
$647$	0.742646	0.0291964	0.0145982	−	0.999893i	$-0.495353\pi$
$647$	0.742646	0.0291964	0.0145982	+	0.999893i	$0.495353\pi$
$648$	5.70820	0.224239
$649$	0	0
$650$	3.38197	0.132652
$651$	−0.472136	−0.0185045
$652$	16.6525	0.652161
$653$	−27.7082	−1.08431	−0.542153	−	0.840280i	$-0.682391\pi$
$653$	−27.7082	−1.08431	−0.542153	+	0.840280i	$0.682391\pi$
$654$	−7.70820	−0.301415
$655$	15.4164	0.602369
$656$	−8.94427	−0.349215
$657$	29.6525	1.15685
$658$	−1.90983	−0.0744529
$659$	47.7426	1.85979	0.929895	−	0.367826i	$-0.119898\pi$
$659$	47.7426	1.85979	0.929895	+	0.367826i	$0.119898\pi$
$660$	0	0
$661$	−1.05573	−0.0410631	−0.0205315	−	0.999789i	$-0.506536\pi$
$661$	−1.05573	−0.0410631	−0.0205315	+	0.999789i	$0.506536\pi$
$662$	−8.61803	−0.334949
$663$	−4.97871	−0.193357
$664$	11.3820	0.441706
$665$	−0.763932	−0.0296240
$666$	−25.4164	−0.984866
$667$	−0.403252	−0.0156140
$668$	20.0000	0.773823
$669$	5.88854	0.227664
$670$	3.23607	0.125020
$671$	0	0
$672$	−0.618034	−0.0238412
$673$	−31.4164	−1.21101	−0.605507	−	0.795840i	$-0.707030\pi$
$673$	−31.4164	−1.21101	−0.605507	+	0.795840i	$0.707030\pi$
$674$	8.00000	0.308148
$675$	3.47214	0.133643
$676$	−1.56231	−0.0600887
$677$	50.9230	1.95713	0.978565	−	0.205940i	$-0.0660251\pi$
$677$	50.9230	1.95713	0.978565	+	0.205940i	$0.0660251\pi$
$678$	6.47214	0.248561
$679$	−5.61803	−0.215600
$680$	2.38197	0.0913442
$681$	−8.56231	−0.328108
$682$	0	0
$683$	5.59675	0.214154	0.107077	−	0.994251i	$-0.465851\pi$
$683$	5.59675	0.214154	0.107077	+	0.994251i	$0.465851\pi$
$684$	2.00000	0.0764719
$685$	−16.0000	−0.611329
$686$	1.00000	0.0381802
$687$	3.52786	0.134596
$688$	−1.23607	−0.0471246
$689$	−8.36068	−0.318517
$690$	0.291796	0.0111085
$691$	−6.47214	−0.246212	−0.123106	−	0.992394i	$-0.539285\pi$
$691$	−6.47214	−0.246212	−0.123106	+	0.992394i	$0.539285\pi$
$692$	22.5066	0.855572
$693$	0	0
$694$	−9.88854	−0.375364
$695$	−8.94427	−0.339276
$696$	−0.527864	−0.0200086
$697$	−21.3050	−0.806983
$698$	−9.05573	−0.342764
$699$	−9.05573	−0.342519
$700$	1.00000	0.0377964
$701$	48.4721	1.83077	0.915384	−	0.402583i	$-0.131887\pi$
$701$	48.4721	1.83077	0.915384	+	0.402583i	$0.131887\pi$
$702$	11.7426	0.443198
$703$	−7.41641	−0.279715
$704$	0	0
$705$	1.18034	0.0444542
$706$	31.4508	1.18367
$707$	−0.763932	−0.0287306
$708$	−5.70820	−0.214527
$709$	36.0344	1.35330	0.676651	−	0.736304i	$-0.263431\pi$
$709$	36.0344	1.35330	0.676651	+	0.736304i	$0.263431\pi$
$710$	8.32624	0.312478
$711$	−15.3262	−0.574779
$712$	13.7082	0.513737
$713$	−0.360680	−0.0135076
$714$	−1.47214	−0.0550933
$715$	0	0
$716$	0.562306	0.0210144
$717$	−1.32624	−0.0495293
$718$	−28.9787	−1.08148
$719$	12.3607	0.460976	0.230488	−	0.973075i	$-0.425968\pi$
$719$	12.3607	0.460976	0.230488	+	0.973075i	$0.425968\pi$
$720$	−2.61803	−0.0975684
$721$	−16.5623	−0.616813
$722$	−18.4164	−0.685388
$723$	−6.00000	−0.223142
$724$	0	0
$725$	0.854102	0.0317206
$726$	0	0
$727$	23.6738	0.878011	0.439006	−	0.898484i	$-0.355331\pi$
$727$	23.6738	0.878011	0.439006	+	0.898484i	$0.355331\pi$
$728$	3.38197	0.125344
$729$	−8.50658	−0.315058
$730$	−11.3262	−0.419203
$731$	−2.94427	−0.108898
$732$	−1.05573	−0.0390208
$733$	47.7426	1.76341	0.881707	−	0.471797i	$-0.156394\pi$
$733$	47.7426	1.76341	0.881707	+	0.471797i	$0.156394\pi$
$734$	19.6738	0.726172
$735$	−0.618034	−0.0227965
$736$	−0.472136	−0.0174032
$737$	0	0
$738$	23.4164	0.861970
$739$	−20.0000	−0.735712	−0.367856	−	0.929883i	$-0.619908\pi$
$739$	−20.0000	−0.735712	−0.367856	+	0.929883i	$0.619908\pi$
$740$	9.70820	0.356881
$741$	1.59675	0.0586580
$742$	−2.47214	−0.0907550
$743$	21.1246	0.774987	0.387493	−	0.921872i	$-0.373341\pi$
$743$	21.1246	0.774987	0.387493	+	0.921872i	$0.373341\pi$
$744$	−0.472136	−0.0173093
$745$	14.1459	0.518266
$746$	28.6525	1.04904
$747$	−29.7984	−1.09027
$748$	0	0
$749$	−15.2361	−0.556714
$750$	−0.618034	−0.0225674
$751$	18.2705	0.666700	0.333350	−	0.942803i	$-0.391821\pi$
$751$	18.2705	0.666700	0.333350	+	0.942803i	$0.391821\pi$
$752$	−1.90983	−0.0696443
$753$	−3.23607	−0.117929
$754$	2.88854	0.105195
$755$	23.6180	0.859548
$756$	3.47214	0.126280
$757$	18.6525	0.677936	0.338968	−	0.940798i	$-0.389922\pi$
$757$	18.6525	0.677936	0.338968	+	0.940798i	$0.389922\pi$
$758$	22.8541	0.830098
$759$	0	0
$760$	−0.763932	−0.0277107
$761$	45.4164	1.64634	0.823172	−	0.567792i	$-0.192202\pi$
$761$	45.4164	1.64634	0.823172	+	0.567792i	$0.192202\pi$
$762$	1.34752	0.0488156
$763$	12.4721	0.451522
$764$	−5.85410	−0.211794
$765$	−6.23607	−0.225466
$766$	2.14590	0.0775344
$767$	31.2361	1.12787
$768$	−0.618034	−0.0223014
$769$	−8.29180	−0.299010	−0.149505	−	0.988761i	$-0.547768\pi$
$769$	−8.29180	−0.299010	−0.149505	+	0.988761i	$0.547768\pi$
$770$	0	0
$771$	−12.5279	−0.451180
$772$	−4.94427	−0.177948
$773$	1.49342	0.0537147	0.0268573	−	0.999639i	$-0.491450\pi$
$773$	1.49342	0.0537147	0.0268573	+	0.999639i	$0.491450\pi$
$774$	3.23607	0.116318
$775$	0.763932	0.0274412
$776$	−5.61803	−0.201676
$777$	−6.00000	−0.215249
$778$	13.2705	0.475771
$779$	6.83282	0.244811
$780$	−2.09017	−0.0748401
$781$	0	0
$782$	−1.12461	−0.0402160
$783$	2.96556	0.105980
$784$	1.00000	0.0357143
$785$	0.0901699	0.00321830
$786$	−9.52786	−0.339848
$787$	−27.0902	−0.965660	−0.482830	−	0.875714i	$-0.660391\pi$
$787$	−27.0902	−0.965660	−0.482830	+	0.875714i	$0.660391\pi$
$788$	11.4164	0.406693
$789$	−17.1246	−0.609652
$790$	5.85410	0.208280
$791$	−10.4721	−0.372346
$792$	0	0
$793$	5.77709	0.205150
$794$	−10.4377	−0.370420
$795$	1.52786	0.0541878
$796$	6.94427	0.246133
$797$	−48.3262	−1.71180	−0.855902	−	0.517139i	$-0.826997\pi$
$797$	−48.3262	−1.71180	−0.855902	+	0.517139i	$0.826997\pi$
$798$	0.472136	0.0167134
$799$	−4.54915	−0.160937
$800$	1.00000	0.0353553
$801$	−35.8885	−1.26806
$802$	−34.3820	−1.21407
$803$	0	0
$804$	−2.00000	−0.0705346
$805$	−0.472136	−0.0166406
$806$	2.58359	0.0910032
$807$	−3.88854	−0.136883
$808$	−0.763932	−0.0268750
$809$	32.6869	1.14921	0.574605	−	0.818431i	$-0.305156\pi$
$809$	32.6869	1.14921	0.574605	+	0.818431i	$0.305156\pi$
$810$	5.70820	0.200566
$811$	−53.8885	−1.89228	−0.946141	−	0.323754i	$-0.895055\pi$
$811$	−53.8885	−1.89228	−0.946141	+	0.323754i	$0.895055\pi$
$812$	0.854102	0.0299731
$813$	15.5279	0.544586
$814$	0	0
$815$	16.6525	0.583311
$816$	−1.47214	−0.0515351
$817$	0.944272	0.0330359
$818$	0.763932	0.0267103
$819$	−8.85410	−0.309387
$820$	−8.94427	−0.312348
$821$	−37.2148	−1.29880	−0.649402	−	0.760445i	$-0.724981\pi$
$821$	−37.2148	−1.29880	−0.649402	+	0.760445i	$0.724981\pi$
$822$	9.88854	0.344903
$823$	4.36068	0.152004	0.0760019	−	0.997108i	$-0.475785\pi$
$823$	4.36068	0.152004	0.0760019	+	0.997108i	$0.475785\pi$
$824$	−16.5623	−0.576975
$825$	0	0
$826$	9.23607	0.321364
$827$	−15.0557	−0.523539	−0.261769	−	0.965130i	$-0.584306\pi$
$827$	−15.0557	−0.523539	−0.261769	+	0.965130i	$0.584306\pi$
$828$	1.23607	0.0429563
$829$	−5.88854	−0.204518	−0.102259	−	0.994758i	$-0.532607\pi$
$829$	−5.88854	−0.204518	−0.102259	+	0.994758i	$0.532607\pi$
$830$	11.3820	0.395074
$831$	8.29180	0.287639
$832$	3.38197	0.117249
$833$	2.38197	0.0825302
$834$	5.52786	0.191414
$835$	20.0000	0.692129
$836$	0	0
$837$	2.65248	0.0916830
$838$	−10.9443	−0.378064
$839$	44.3607	1.53150	0.765750	−	0.643138i	$-0.222368\pi$
$839$	44.3607	1.53150	0.765750	+	0.643138i	$0.222368\pi$
$840$	−0.618034	−0.0213242
$841$	−28.2705	−0.974845
$842$	4.32624	0.149092
$843$	16.2918	0.561119
$844$	−0.326238	−0.0112296
$845$	−1.56231	−0.0537450
$846$	5.00000	0.171904
$847$	0	0
$848$	−2.47214	−0.0848935
$849$	−0.819660	−0.0281307
$850$	2.38197	0.0817008
$851$	−4.58359	−0.157124
$852$	−5.14590	−0.176296
$853$	−25.2705	−0.865246	−0.432623	−	0.901575i	$-0.642412\pi$
$853$	−25.2705	−0.865246	−0.432623	+	0.901575i	$0.642412\pi$
$854$	1.70820	0.0584535
$855$	2.00000	0.0683986
$856$	−15.2361	−0.520758
$857$	6.58359	0.224891	0.112446	−	0.993658i	$-0.464132\pi$
$857$	6.58359	0.224891	0.112446	+	0.993658i	$0.464132\pi$
$858$	0	0
$859$	28.5836	0.975260	0.487630	−	0.873051i	$-0.337862\pi$
$859$	28.5836	0.975260	0.487630	+	0.873051i	$0.337862\pi$
$860$	−1.23607	−0.0421496
$861$	5.52786	0.188389
$862$	4.56231	0.155393
$863$	0	0		−	1.00000i	$-0.5\pi$
$863$	0	0			1.00000i	$0.5\pi$
$864$	3.47214	0.118124
$865$	22.5066	0.765247
$866$	−7.09017	−0.240934
$867$	7.00000	0.237732
$868$	0.763932	0.0259295
$869$	0	0
$870$	−0.527864	−0.0178963
$871$	10.9443	0.370833
$872$	12.4721	0.422360
$873$	14.7082	0.497797
$874$	0.360680	0.0122002
$875$	1.00000	0.0338062
$876$	7.00000	0.236508
$877$	−40.5410	−1.36897	−0.684486	−	0.729026i	$-0.739974\pi$
$877$	−40.5410	−1.36897	−0.684486	+	0.729026i	$0.739974\pi$
$878$	20.6525	0.696987
$879$	−0.875388	−0.0295261
$880$	0	0
$881$	−47.4853	−1.59982	−0.799910	−	0.600120i	$-0.795120\pi$
$881$	−47.4853	−1.59982	−0.799910	+	0.600120i	$0.795120\pi$
$882$	−2.61803	−0.0881538
$883$	−38.7639	−1.30451	−0.652255	−	0.758000i	$-0.726177\pi$
$883$	−38.7639	−1.30451	−0.652255	+	0.758000i	$0.726177\pi$
$884$	8.05573	0.270943
$885$	−5.70820	−0.191879
$886$	−10.7639	−0.361621
$887$	29.1459	0.978623	0.489312	−	0.872109i	$-0.337248\pi$
$887$	29.1459	0.978623	0.489312	+	0.872109i	$0.337248\pi$
$888$	−6.00000	−0.201347
$889$	−2.18034	−0.0731263
$890$	13.7082	0.459500
$891$	0	0
$892$	−9.52786	−0.319016
$893$	1.45898	0.0488229
$894$	−8.74265	−0.292398
$895$	0.562306	0.0187958
$896$	1.00000	0.0334077
$897$	0.986844	0.0329498
$898$	18.5066	0.617573
$899$	0.652476	0.0217613
$900$	−2.61803	−0.0872678
$901$	−5.88854	−0.196176
$902$	0	0
$903$	0.763932	0.0254221
$904$	−10.4721	−0.348298
$905$	0	0
$906$	−14.5967	−0.484944
$907$	14.3607	0.476839	0.238419	−	0.971162i	$-0.423371\pi$
$907$	14.3607	0.476839	0.238419	+	0.971162i	$0.423371\pi$
$908$	13.8541	0.459765
$909$	2.00000	0.0663358
$910$	3.38197	0.112111
$911$	−38.4508	−1.27393	−0.636967	−	0.770891i	$-0.719811\pi$
$911$	−38.4508	−1.27393	−0.636967	+	0.770891i	$0.719811\pi$
$912$	0.472136	0.0156340
$913$	0	0
$914$	−14.0000	−0.463079
$915$	−1.05573	−0.0349013
$916$	−5.70820	−0.188604
$917$	15.4164	0.509095
$918$	8.27051	0.272967
$919$	14.4934	0.478094	0.239047	−	0.971008i	$-0.423165\pi$
$919$	14.4934	0.478094	0.239047	+	0.971008i	$0.423165\pi$
$920$	−0.472136	−0.0155659
$921$	−13.8754	−0.457210
$922$	−15.1246	−0.498103
$923$	28.1591	0.926867
$924$	0	0
$925$	9.70820	0.319204
$926$	8.18034	0.268823
$927$	43.3607	1.42415
$928$	0.854102	0.0280373
$929$	−43.7771	−1.43628	−0.718140	−	0.695899i	$-0.755006\pi$
$929$	−43.7771	−1.43628	−0.718140	+	0.695899i	$0.755006\pi$
$930$	−0.472136	−0.0154819
$931$	−0.763932	−0.0250369
$932$	14.6525	0.479958
$933$	7.52786	0.246451
$934$	19.3820	0.634197
$935$	0	0
$936$	−8.85410	−0.289405
$937$	36.3951	1.18898	0.594488	−	0.804104i	$-0.297355\pi$
$937$	36.3951	1.18898	0.594488	+	0.804104i	$0.297355\pi$
$938$	3.23607	0.105661
$939$	14.7639	0.481803
$940$	−1.90983	−0.0622918
$941$	11.3475	0.369919	0.184959	−	0.982746i	$-0.440785\pi$
$941$	11.3475	0.369919	0.184959	+	0.982746i	$0.440785\pi$
$942$	−0.0557281	−0.00181572
$943$	4.22291	0.137517
$944$	9.23607	0.300608
$945$	3.47214	0.112949
$946$	0	0
$947$	1.34752	0.0437887	0.0218943	−	0.999760i	$-0.493030\pi$
$947$	1.34752	0.0437887	0.0218943	+	0.999760i	$0.493030\pi$
$948$	−3.61803	−0.117508
$949$	−38.3050	−1.24343
$950$	−0.763932	−0.0247852
$951$	11.0557	0.358507
$952$	2.38197	0.0772000
$953$	29.4164	0.952891	0.476445	−	0.879204i	$-0.341925\pi$
$953$	29.4164	0.952891	0.476445	+	0.879204i	$0.341925\pi$
$954$	6.47214	0.209543
$955$	−5.85410	−0.189434
$956$	2.14590	0.0694033
$957$	0	0
$958$	5.12461	0.165569
$959$	−16.0000	−0.516667
$960$	−0.618034	−0.0199470
$961$	−30.4164	−0.981174
$962$	32.8328	1.05857
$963$	39.8885	1.28539
$964$	9.70820	0.312680
$965$	−4.94427	−0.159162
$966$	0.291796	0.00938838
$967$	−17.7082	−0.569457	−0.284729	−	0.958608i	$-0.591904\pi$
$967$	−17.7082	−0.569457	−0.284729	+	0.958608i	$0.591904\pi$
$968$	0	0
$969$	1.12461	0.0361277
$970$	−5.61803	−0.180384
$971$	−2.36068	−0.0757578	−0.0378789	−	0.999282i	$-0.512060\pi$
$971$	−2.36068	−0.0757578	−0.0378789	+	0.999282i	$0.512060\pi$
$972$	−13.9443	−0.447263
$973$	−8.94427	−0.286740
$974$	34.1803	1.09521
$975$	−2.09017	−0.0669390
$976$	1.70820	0.0546783
$977$	−58.9017	−1.88443	−0.942216	−	0.335006i	$-0.891262\pi$
$977$	−58.9017	−1.88443	−0.942216	+	0.335006i	$0.891262\pi$
$978$	−10.2918	−0.329095
$979$	0	0
$980$	1.00000	0.0319438
$981$	−32.6525	−1.04251
$982$	−16.9443	−0.540713
$983$	−0.965558	−0.0307965	−0.0153983	−	0.999881i	$-0.504902\pi$
$983$	−0.965558	−0.0307965	−0.0153983	+	0.999881i	$0.504902\pi$
$984$	5.52786	0.176222
$985$	11.4164	0.363757
$986$	2.03444	0.0647898
$987$	1.18034	0.0375706
$988$	−2.58359	−0.0821950
$989$	0.583592	0.0185572
$990$	0	0
$991$	−53.9230	−1.71292	−0.856460	−	0.516213i	$-0.827341\pi$
$991$	−53.9230	−1.71292	−0.856460	+	0.516213i	$0.827341\pi$
$992$	0.763932	0.0242549
$993$	5.32624	0.169023
$994$	8.32624	0.264092
$995$	6.94427	0.220148
$996$	−7.03444	−0.222895
$997$	−2.56231	−0.0811490	−0.0405745	−	0.999177i	$-0.512919\pi$
$997$	−2.56231	−0.0811490	−0.0405745	+	0.999177i	$0.512919\pi$
$998$	−0.201626	−0.00638236
$999$	33.7082	1.06648

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8470.2.a.cc.1.1		2
11.5	even	5		770.2.n.a.421.1	✓	4
11.9	even	5		770.2.n.a.631.1	yes	4
11.10	odd	2		8470.2.a.bq.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.a.421.1	✓	4	11.5	even	5
770.2.n.a.631.1	yes	4	11.9	even	5
8470.2.a.bq.1.1		2	11.10	odd	2
8470.2.a.cc.1.1		2	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.618034 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.618034 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.61803 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.618034 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.618034 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.61803 q^{9} +1.00000 q^{10} -0.618034 q^{12} +3.38197 q^{13} +1.00000 q^{14} -0.618034 q^{15} +1.00000 q^{16} +2.38197 q^{17} -2.61803 q^{18} -0.763932 q^{19} +1.00000 q^{20} -0.618034 q^{21} -0.472136 q^{23} -0.618034 q^{24} +1.00000 q^{25} +3.38197 q^{26} +3.47214 q^{27} +1.00000 q^{28} +0.854102 q^{29} -0.618034 q^{30} +0.763932 q^{31} +1.00000 q^{32} +2.38197 q^{34} +1.00000 q^{35} -2.61803 q^{36} +9.70820 q^{37} -0.763932 q^{38} -2.09017 q^{39} +1.00000 q^{40} -8.94427 q^{41} -0.618034 q^{42} -1.23607 q^{43} -2.61803 q^{45} -0.472136 q^{46} -1.90983 q^{47} -0.618034 q^{48} +1.00000 q^{49} +1.00000 q^{50} -1.47214 q^{51} +3.38197 q^{52} -2.47214 q^{53} +3.47214 q^{54} +1.00000 q^{56} +0.472136 q^{57} +0.854102 q^{58} +9.23607 q^{59} -0.618034 q^{60} +1.70820 q^{61} +0.763932 q^{62} -2.61803 q^{63} +1.00000 q^{64} +3.38197 q^{65} +3.23607 q^{67} +2.38197 q^{68} +0.291796 q^{69} +1.00000 q^{70} +8.32624 q^{71} -2.61803 q^{72} -11.3262 q^{73} +9.70820 q^{74} -0.618034 q^{75} -0.763932 q^{76} -2.09017 q^{78} +5.85410 q^{79} +1.00000 q^{80} +5.70820 q^{81} -8.94427 q^{82} +11.3820 q^{83} -0.618034 q^{84} +2.38197 q^{85} -1.23607 q^{86} -0.527864 q^{87} +13.7082 q^{89} -2.61803 q^{90} +3.38197 q^{91} -0.472136 q^{92} -0.472136 q^{93} -1.90983 q^{94} -0.763932 q^{95} -0.618034 q^{96} -5.61803 q^{97} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + q^{3} + 2 q^{4} + 2 q^{5} + q^{6} + 2 q^{7} + 2 q^{8} - 3 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + q^3 + 2 * q^4 + 2 * q^5 + q^6 + 2 * q^7 + 2 * q^8 - 3 * q^9	\( 2 q + 2 q^{2} + q^{3} + 2 q^{4} + 2 q^{5} + q^{6} + 2 q^{7} + 2 q^{8} - 3 q^{9} + 2 q^{10} + q^{12} + 9 q^{13} + 2 q^{14} + q^{15} + 2 q^{16} + 7 q^{17} - 3 q^{18} - 6 q^{19} + 2 q^{20} + q^{21} + 8 q^{23} + q^{24} + 2 q^{25} + 9 q^{26} - 2 q^{27} + 2 q^{28} - 5 q^{29} + q^{30} + 6 q^{31} + 2 q^{32} + 7 q^{34} + 2 q^{35} - 3 q^{36} + 6 q^{37} - 6 q^{38} + 7 q^{39} + 2 q^{40} + q^{42} + 2 q^{43} - 3 q^{45} + 8 q^{46} - 15 q^{47} + q^{48} + 2 q^{49} + 2 q^{50} + 6 q^{51} + 9 q^{52} + 4 q^{53} - 2 q^{54} + 2 q^{56} - 8 q^{57} - 5 q^{58} + 14 q^{59} + q^{60} - 10 q^{61} + 6 q^{62} - 3 q^{63} + 2 q^{64} + 9 q^{65} + 2 q^{67} + 7 q^{68} + 14 q^{69} + 2 q^{70} + q^{71} - 3 q^{72} - 7 q^{73} + 6 q^{74} + q^{75} - 6 q^{76} + 7 q^{78} + 5 q^{79} + 2 q^{80} - 2 q^{81} + 25 q^{83} + q^{84} + 7 q^{85} + 2 q^{86} - 10 q^{87} + 14 q^{89} - 3 q^{90} + 9 q^{91} + 8 q^{92} + 8 q^{93} - 15 q^{94} - 6 q^{95} + q^{96} - 9 q^{97} + 2 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 + q^3 + 2 * q^4 + 2 * q^5 + q^6 + 2 * q^7 + 2 * q^8 - 3 * q^9 + 2 * q^10 + q^12 + 9 * q^13 + 2 * q^14 + q^15 + 2 * q^16 + 7 * q^17 - 3 * q^18 - 6 * q^19 + 2 * q^20 + q^21 + 8 * q^23 + q^24 + 2 * q^25 + 9 * q^26 - 2 * q^27 + 2 * q^28 - 5 * q^29 + q^30 + 6 * q^31 + 2 * q^32 + 7 * q^34 + 2 * q^35 - 3 * q^36 + 6 * q^37 - 6 * q^38 + 7 * q^39 + 2 * q^40 + q^42 + 2 * q^43 - 3 * q^45 + 8 * q^46 - 15 * q^47 + q^48 + 2 * q^49 + 2 * q^50 + 6 * q^51 + 9 * q^52 + 4 * q^53 - 2 * q^54 + 2 * q^56 - 8 * q^57 - 5 * q^58 + 14 * q^59 + q^60 - 10 * q^61 + 6 * q^62 - 3 * q^63 + 2 * q^64 + 9 * q^65 + 2 * q^67 + 7 * q^68 + 14 * q^69 + 2 * q^70 + q^71 - 3 * q^72 - 7 * q^73 + 6 * q^74 + q^75 - 6 * q^76 + 7 * q^78 + 5 * q^79 + 2 * q^80 - 2 * q^81 + 25 * q^83 + q^84 + 7 * q^85 + 2 * q^86 - 10 * q^87 + 14 * q^89 - 3 * q^90 + 9 * q^91 + 8 * q^92 + 8 * q^93 - 15 * q^94 - 6 * q^95 + q^96 - 9 * q^97 + 2 * q^98

Introduction

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