LMFDB - Embedded newform 8470.2.a.dc.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("8470.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$67.6332905120$
Analytic rank:	$0$
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			1.6
Root			$-2.18328$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +2.18328 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.18328 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.76673 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.18328 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.18328 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.76673 q^{9} +1.00000 q^{10} +2.18328 q^{12} -2.53263 q^{13} -1.00000 q^{14} +2.18328 q^{15} +1.00000 q^{16} +5.73813 q^{17} +1.76673 q^{18} +2.24060 q^{19} +1.00000 q^{20} -2.18328 q^{21} -2.51489 q^{23} +2.18328 q^{24} +1.00000 q^{25} -2.53263 q^{26} -2.69257 q^{27} -1.00000 q^{28} +8.62000 q^{29} +2.18328 q^{30} +1.84089 q^{31} +1.00000 q^{32} +5.73813 q^{34} -1.00000 q^{35} +1.76673 q^{36} -4.63124 q^{37} +2.24060 q^{38} -5.52945 q^{39} +1.00000 q^{40} +10.5523 q^{41} -2.18328 q^{42} +2.18804 q^{43} +1.76673 q^{45} -2.51489 q^{46} +3.22482 q^{47} +2.18328 q^{48} +1.00000 q^{49} +1.00000 q^{50} +12.5280 q^{51} -2.53263 q^{52} -4.01746 q^{53} -2.69257 q^{54} -1.00000 q^{56} +4.89187 q^{57} +8.62000 q^{58} +2.01405 q^{59} +2.18328 q^{60} +0.268235 q^{61} +1.84089 q^{62} -1.76673 q^{63} +1.00000 q^{64} -2.53263 q^{65} +3.86233 q^{67} +5.73813 q^{68} -5.49071 q^{69} -1.00000 q^{70} -9.55514 q^{71} +1.76673 q^{72} +11.4258 q^{73} -4.63124 q^{74} +2.18328 q^{75} +2.24060 q^{76} -5.52945 q^{78} +11.7534 q^{79} +1.00000 q^{80} -11.1789 q^{81} +10.5523 q^{82} +7.34851 q^{83} -2.18328 q^{84} +5.73813 q^{85} +2.18804 q^{86} +18.8199 q^{87} -2.65397 q^{89} +1.76673 q^{90} +2.53263 q^{91} -2.51489 q^{92} +4.01919 q^{93} +3.22482 q^{94} +2.24060 q^{95} +2.18328 q^{96} +16.5045 q^{97} +1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	2.18328	1.26052	0.630260	−	0.776384i	$-0.282948\pi$
$3$	2.18328	1.26052	0.630260	+	0.776384i	$0.282948\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.18328	0.891322
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	1.76673	0.588911
$10$	1.00000	0.316228
$11$	0	0
$11$	0	0
$12$	2.18328	0.630260
$13$	−2.53263	−0.702425	−0.351212	−	0.936296i	$-0.614231\pi$
$13$	−2.53263	−0.702425	−0.351212	+	0.936296i	$0.614231\pi$
$14$	−1.00000	−0.267261
$15$	2.18328	0.563722
$16$	1.00000	0.250000
$17$	5.73813	1.39170	0.695850	−	0.718187i	$-0.255028\pi$
$17$	5.73813	1.39170	0.695850	+	0.718187i	$0.255028\pi$
$18$	1.76673	0.416423
$19$	2.24060	0.514029	0.257014	−	0.966408i	$-0.417261\pi$
$19$	2.24060	0.514029	0.257014	+	0.966408i	$0.417261\pi$
$20$	1.00000	0.223607
$21$	−2.18328	−0.476432
$22$	0	0
$23$	−2.51489	−0.524390	−0.262195	−	0.965015i	$-0.584446\pi$
$23$	−2.51489	−0.524390	−0.262195	+	0.965015i	$0.584446\pi$
$24$	2.18328	0.445661
$25$	1.00000	0.200000
$26$	−2.53263	−0.496689
$27$	−2.69257	−0.518186
$28$	−1.00000	−0.188982
$29$	8.62000	1.60069	0.800347	−	0.599537i	$-0.204649\pi$
$29$	8.62000	1.60069	0.800347	+	0.599537i	$0.204649\pi$
$30$	2.18328	0.398611
$31$	1.84089	0.330634	0.165317	−	0.986240i	$-0.447135\pi$
$31$	1.84089	0.330634	0.165317	+	0.986240i	$0.447135\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	5.73813	0.984080
$35$	−1.00000	−0.169031
$36$	1.76673	0.294455
$37$	−4.63124	−0.761372	−0.380686	−	0.924704i	$-0.624312\pi$
$37$	−4.63124	−0.761372	−0.380686	+	0.924704i	$0.624312\pi$
$38$	2.24060	0.363473
$39$	−5.52945	−0.885421
$40$	1.00000	0.158114
$41$	10.5523	1.64800	0.823999	−	0.566591i	$-0.191738\pi$
$41$	10.5523	1.64800	0.823999	+	0.566591i	$0.191738\pi$
$42$	−2.18328	−0.336888
$43$	2.18804	0.333672	0.166836	−	0.985985i	$-0.446645\pi$
$43$	2.18804	0.333672	0.166836	+	0.985985i	$0.446645\pi$
$44$	0	0
$45$	1.76673	0.263369
$46$	−2.51489	−0.370800
$47$	3.22482	0.470389	0.235194	−	0.971948i	$-0.424427\pi$
$47$	3.22482	0.470389	0.235194	+	0.971948i	$0.424427\pi$
$48$	2.18328	0.315130
$49$	1.00000	0.142857
$50$	1.00000	0.141421
$51$	12.5280	1.75427
$52$	−2.53263	−0.351212
$53$	−4.01746	−0.551841	−0.275920	−	0.961180i	$-0.588983\pi$
$53$	−4.01746	−0.551841	−0.275920	+	0.961180i	$0.588983\pi$
$54$	−2.69257	−0.366413
$55$	0	0
$56$	−1.00000	−0.133631
$57$	4.89187	0.647944
$58$	8.62000	1.13186
$59$	2.01405	0.262207	0.131103	−	0.991369i	$-0.458148\pi$
$59$	2.01405	0.262207	0.131103	+	0.991369i	$0.458148\pi$
$60$	2.18328	0.281861
$61$	0.268235	0.0343440	0.0171720	−	0.999853i	$-0.494534\pi$
$61$	0.268235	0.0343440	0.0171720	+	0.999853i	$0.494534\pi$
$62$	1.84089	0.233793
$63$	−1.76673	−0.222587
$64$	1.00000	0.125000
$65$	−2.53263	−0.314134
$66$	0	0
$67$	3.86233	0.471859	0.235929	−	0.971770i	$-0.424187\pi$
$67$	3.86233	0.471859	0.235929	+	0.971770i	$0.424187\pi$
$68$	5.73813	0.695850
$69$	−5.49071	−0.661004
$70$	−1.00000	−0.119523
$71$	−9.55514	−1.13399	−0.566993	−	0.823723i	$-0.691893\pi$
$71$	−9.55514	−1.13399	−0.566993	+	0.823723i	$0.691893\pi$
$72$	1.76673	0.208211
$73$	11.4258	1.33729	0.668647	−	0.743580i	$-0.266874\pi$
$73$	11.4258	1.33729	0.668647	+	0.743580i	$0.266874\pi$
$74$	−4.63124	−0.538371
$75$	2.18328	0.252104
$76$	2.24060	0.257014
$77$	0	0
$78$	−5.52945	−0.626087
$79$	11.7534	1.32236	0.661182	−	0.750225i	$-0.270055\pi$
$79$	11.7534	1.32236	0.661182	+	0.750225i	$0.270055\pi$
$80$	1.00000	0.111803
$81$	−11.1789	−1.24209
$82$	10.5523	1.16531
$83$	7.34851	0.806604	0.403302	−	0.915067i	$-0.367862\pi$
$83$	7.34851	0.806604	0.403302	+	0.915067i	$0.367862\pi$
$84$	−2.18328	−0.238216
$85$	5.73813	0.622387
$86$	2.18804	0.235942
$87$	18.8199	2.01771
$88$	0	0
$89$	−2.65397	−0.281321	−0.140660	−	0.990058i	$-0.544923\pi$
$89$	−2.65397	−0.281321	−0.140660	+	0.990058i	$0.544923\pi$
$90$	1.76673	0.186230
$91$	2.53263	0.265492
$92$	−2.51489	−0.262195
$93$	4.01919	0.416771
$94$	3.22482	0.332615
$95$	2.24060	0.229881
$96$	2.18328	0.222831
$97$	16.5045	1.67578	0.837891	−	0.545838i	$-0.183789\pi$
$97$	16.5045	1.67578	0.837891	+	0.545838i	$0.183789\pi$
$98$	1.00000	0.101015
$99$	0	0
$100$	1.00000	0.100000
$101$	−16.0478	−1.59682	−0.798408	−	0.602116i	$-0.794324\pi$
$101$	−16.0478	−1.59682	−0.798408	+	0.602116i	$0.794324\pi$
$102$	12.5280	1.24045
$103$	−12.9029	−1.27136	−0.635680	−	0.771953i	$-0.719280\pi$
$103$	−12.9029	−1.27136	−0.635680	+	0.771953i	$0.719280\pi$
$104$	−2.53263	−0.248345
$105$	−2.18328	−0.213067
$106$	−4.01746	−0.390210
$107$	6.74567	0.652129	0.326064	−	0.945348i	$-0.394277\pi$
$107$	6.74567	0.652129	0.326064	+	0.945348i	$0.394277\pi$
$108$	−2.69257	−0.259093
$109$	−18.6864	−1.78983	−0.894916	−	0.446235i	$-0.852765\pi$
$109$	−18.6864	−1.78983	−0.894916	+	0.446235i	$0.852765\pi$
$110$	0	0
$111$	−10.1113	−0.959725
$112$	−1.00000	−0.0944911
$113$	7.56433	0.711593	0.355796	−	0.934564i	$-0.384210\pi$
$113$	7.56433	0.711593	0.355796	+	0.934564i	$0.384210\pi$
$114$	4.89187	0.458165
$115$	−2.51489	−0.234514
$116$	8.62000	0.800347
$117$	−4.47448	−0.413666
$118$	2.01405	0.185408
$119$	−5.73813	−0.526013
$120$	2.18328	0.199306
$121$	0	0
$122$	0.268235	0.0242849
$123$	23.0388	2.07733
$124$	1.84089	0.165317
$125$	1.00000	0.0894427
$126$	−1.76673	−0.157393
$127$	10.7426	0.953249	0.476625	−	0.879107i	$-0.341860\pi$
$127$	10.7426	0.953249	0.476625	+	0.879107i	$0.341860\pi$
$128$	1.00000	0.0883883
$129$	4.77710	0.420601
$130$	−2.53263	−0.222126
$131$	17.0221	1.48723	0.743613	−	0.668610i	$-0.233110\pi$
$131$	17.0221	1.48723	0.743613	+	0.668610i	$0.233110\pi$
$132$	0	0
$133$	−2.24060	−0.194285
$134$	3.86233	0.333654
$135$	−2.69257	−0.231740
$136$	5.73813	0.492040
$137$	−12.4777	−1.06604	−0.533019	−	0.846103i	$-0.678943\pi$
$137$	−12.4777	−1.06604	−0.533019	+	0.846103i	$0.678943\pi$
$138$	−5.49071	−0.467401
$139$	−17.3812	−1.47426	−0.737129	−	0.675752i	$-0.763819\pi$
$139$	−17.3812	−1.47426	−0.737129	+	0.675752i	$0.763819\pi$
$140$	−1.00000	−0.0845154
$141$	7.04070	0.592934
$142$	−9.55514	−0.801849
$143$	0	0
$144$	1.76673	0.147228
$145$	8.62000	0.715852
$146$	11.4258	0.945610
$147$	2.18328	0.180074
$148$	−4.63124	−0.380686
$149$	1.49206	0.122235	0.0611173	−	0.998131i	$-0.480534\pi$
$149$	1.49206	0.122235	0.0611173	+	0.998131i	$0.480534\pi$
$150$	2.18328	0.178264
$151$	7.99555	0.650668	0.325334	−	0.945599i	$-0.394523\pi$
$151$	7.99555	0.650668	0.325334	+	0.945599i	$0.394523\pi$
$152$	2.24060	0.181737
$153$	10.1377	0.819587
$154$	0	0
$155$	1.84089	0.147864
$156$	−5.52945	−0.442710
$157$	2.05173	0.163746	0.0818729	−	0.996643i	$-0.473910\pi$
$157$	2.05173	0.163746	0.0818729	+	0.996643i	$0.473910\pi$
$158$	11.7534	0.935053
$159$	−8.77126	−0.695606
$160$	1.00000	0.0790569
$161$	2.51489	0.198201
$162$	−11.1789	−0.878294
$163$	20.6976	1.62116	0.810579	−	0.585629i	$-0.199152\pi$
$163$	20.6976	1.62116	0.810579	+	0.585629i	$0.199152\pi$
$164$	10.5523	0.823999
$165$	0	0
$166$	7.34851	0.570355
$167$	−1.32050	−0.102183	−0.0510917	−	0.998694i	$-0.516270\pi$
$167$	−1.32050	−0.102183	−0.0510917	+	0.998694i	$0.516270\pi$
$168$	−2.18328	−0.168444
$169$	−6.58579	−0.506599
$170$	5.73813	0.440094
$171$	3.95854	0.302717
$172$	2.18804	0.166836
$173$	−15.7029	−1.19387	−0.596933	−	0.802291i	$-0.703614\pi$
$173$	−15.7029	−1.19387	−0.596933	+	0.802291i	$0.703614\pi$
$174$	18.8199	1.42673
$175$	−1.00000	−0.0755929
$176$	0	0
$177$	4.39724	0.330517
$178$	−2.65397	−0.198924
$179$	4.65497	0.347929	0.173964	−	0.984752i	$-0.444342\pi$
$179$	4.65497	0.347929	0.173964	+	0.984752i	$0.444342\pi$
$180$	1.76673	0.131684
$181$	−5.90450	−0.438878	−0.219439	−	0.975626i	$-0.570423\pi$
$181$	−5.90450	−0.438878	−0.219439	+	0.975626i	$0.570423\pi$
$182$	2.53263	0.187731
$183$	0.585633	0.0432913
$184$	−2.51489	−0.185400
$185$	−4.63124	−0.340496
$186$	4.01919	0.294701
$187$	0	0
$188$	3.22482	0.235194
$189$	2.69257	0.195856
$190$	2.24060	0.162550
$191$	−5.93400	−0.429369	−0.214685	−	0.976683i	$-0.568872\pi$
$191$	−5.93400	−0.429369	−0.214685	+	0.976683i	$0.568872\pi$
$192$	2.18328	0.157565
$193$	−10.8377	−0.780113	−0.390056	−	0.920791i	$-0.627544\pi$
$193$	−10.8377	−0.780113	−0.390056	+	0.920791i	$0.627544\pi$
$194$	16.5045	1.18496
$195$	−5.52945	−0.395972
$196$	1.00000	0.0714286
$197$	−12.0176	−0.856216	−0.428108	−	0.903728i	$-0.640820\pi$
$197$	−12.0176	−0.856216	−0.428108	+	0.903728i	$0.640820\pi$
$198$	0	0
$199$	18.4014	1.30444	0.652220	−	0.758030i	$-0.273838\pi$
$199$	18.4014	1.30444	0.652220	+	0.758030i	$0.273838\pi$
$200$	1.00000	0.0707107
$201$	8.43256	0.594787
$202$	−16.0478	−1.12912
$203$	−8.62000	−0.605005
$204$	12.5280	0.877133
$205$	10.5523	0.737007
$206$	−12.9029	−0.898987
$207$	−4.44313	−0.308819
$208$	−2.53263	−0.175606
$209$	0	0
$210$	−2.18328	−0.150661
$211$	−20.0422	−1.37976	−0.689880	−	0.723924i	$-0.742337\pi$
$211$	−20.0422	−1.37976	−0.689880	+	0.723924i	$0.742337\pi$
$212$	−4.01746	−0.275920
$213$	−20.8616	−1.42941
$214$	6.74567	0.461125
$215$	2.18804	0.149223
$216$	−2.69257	−0.183206
$217$	−1.84089	−0.124968
$218$	−18.6864	−1.26560
$219$	24.9459	1.68569
$220$	0	0
$221$	−14.5325	−0.977565
$222$	−10.1113	−0.678628
$223$	11.8000	0.790185	0.395092	−	0.918641i	$-0.370713\pi$
$223$	11.8000	0.790185	0.395092	+	0.918641i	$0.370713\pi$
$224$	−1.00000	−0.0668153
$225$	1.76673	0.117782
$226$	7.56433	0.503172
$227$	−0.990121	−0.0657166	−0.0328583	−	0.999460i	$-0.510461\pi$
$227$	−0.990121	−0.0657166	−0.0328583	+	0.999460i	$0.510461\pi$
$228$	4.89187	0.323972
$229$	18.3559	1.21299	0.606495	−	0.795087i	$-0.292575\pi$
$229$	18.3559	1.21299	0.606495	+	0.795087i	$0.292575\pi$
$230$	−2.51489	−0.165827
$231$	0	0
$232$	8.62000	0.565931
$233$	17.3650	1.13762	0.568809	−	0.822470i	$-0.307404\pi$
$233$	17.3650	1.13762	0.568809	+	0.822470i	$0.307404\pi$
$234$	−4.47448	−0.292506
$235$	3.22482	0.210364
$236$	2.01405	0.131103
$237$	25.6611	1.66687
$238$	−5.73813	−0.371947
$239$	−8.92113	−0.577060	−0.288530	−	0.957471i	$-0.593166\pi$
$239$	−8.92113	−0.577060	−0.288530	+	0.957471i	$0.593166\pi$
$240$	2.18328	0.140930
$241$	0.896696	0.0577613	0.0288806	−	0.999583i	$-0.490806\pi$
$241$	0.896696	0.0577613	0.0288806	+	0.999583i	$0.490806\pi$
$242$	0	0
$243$	−16.3289	−1.04750
$244$	0.268235	0.0171720
$245$	1.00000	0.0638877
$246$	23.0388	1.46890
$247$	−5.67461	−0.361067
$248$	1.84089	0.116897
$249$	16.0439	1.01674
$250$	1.00000	0.0632456
$251$	−22.4978	−1.42005	−0.710026	−	0.704176i	$-0.751317\pi$
$251$	−22.4978	−1.42005	−0.710026	+	0.704176i	$0.751317\pi$
$252$	−1.76673	−0.111294
$253$	0	0
$254$	10.7426	0.674049
$255$	12.5280	0.784531
$256$	1.00000	0.0625000
$257$	−24.9449	−1.55602	−0.778009	−	0.628254i	$-0.783770\pi$
$257$	−24.9449	−1.55602	−0.778009	+	0.628254i	$0.783770\pi$
$258$	4.77710	0.297410
$259$	4.63124	0.287772
$260$	−2.53263	−0.157067
$261$	15.2292	0.942666
$262$	17.0221	1.05163
$263$	−6.25594	−0.385758	−0.192879	−	0.981223i	$-0.561782\pi$
$263$	−6.25594	−0.385758	−0.192879	+	0.981223i	$0.561782\pi$
$264$	0	0
$265$	−4.01746	−0.246791
$266$	−2.24060	−0.137380
$267$	−5.79438	−0.354610
$268$	3.86233	0.235929
$269$	−13.0673	−0.796727	−0.398364	−	0.917228i	$-0.630422\pi$
$269$	−13.0673	−0.796727	−0.398364	+	0.917228i	$0.630422\pi$
$270$	−2.69257	−0.163865
$271$	24.3157	1.47707	0.738535	−	0.674215i	$-0.235518\pi$
$271$	24.3157	1.47707	0.738535	+	0.674215i	$0.235518\pi$
$272$	5.73813	0.347925
$273$	5.52945	0.334658
$274$	−12.4777	−0.753803
$275$	0	0
$276$	−5.49071	−0.330502
$277$	13.4094	0.805696	0.402848	−	0.915267i	$-0.368020\pi$
$277$	13.4094	0.805696	0.402848	+	0.915267i	$0.368020\pi$
$278$	−17.3812	−1.04246
$279$	3.25236	0.194714
$280$	−1.00000	−0.0597614
$281$	−12.7398	−0.759993	−0.379997	−	0.924988i	$-0.624075\pi$
$281$	−12.7398	−0.759993	−0.379997	+	0.924988i	$0.624075\pi$
$282$	7.04070	0.419268
$283$	13.7495	0.817325	0.408662	−	0.912686i	$-0.365995\pi$
$283$	13.7495	0.817325	0.408662	+	0.912686i	$0.365995\pi$
$284$	−9.55514	−0.566993
$285$	4.89187	0.289769
$286$	0	0
$287$	−10.5523	−0.622885
$288$	1.76673	0.104106
$289$	15.9261	0.936828
$290$	8.62000	0.506184
$291$	36.0341	2.11236
$292$	11.4258	0.668647
$293$	−16.6376	−0.971982	−0.485991	−	0.873964i	$-0.661541\pi$
$293$	−16.6376	−0.971982	−0.485991	+	0.873964i	$0.661541\pi$
$294$	2.18328	0.127332
$295$	2.01405	0.117262
$296$	−4.63124	−0.269186
$297$	0	0
$298$	1.49206	0.0864329
$299$	6.36928	0.368345
$300$	2.18328	0.126052
$301$	−2.18804	−0.126116
$302$	7.99555	0.460092
$303$	−35.0369	−2.01282
$304$	2.24060	0.128507
$305$	0.268235	0.0153591
$306$	10.1377	0.579536
$307$	−5.56226	−0.317455	−0.158728	−	0.987322i	$-0.550739\pi$
$307$	−5.56226	−0.317455	−0.158728	+	0.987322i	$0.550739\pi$
$308$	0	0
$309$	−28.1707	−1.60258
$310$	1.84089	0.104556
$311$	17.9179	1.01603	0.508014	−	0.861349i	$-0.330380\pi$
$311$	17.9179	1.01603	0.508014	+	0.861349i	$0.330380\pi$
$312$	−5.52945	−0.313043
$313$	5.15478	0.291365	0.145683	−	0.989331i	$-0.453462\pi$
$313$	5.15478	0.291365	0.145683	+	0.989331i	$0.453462\pi$
$314$	2.05173	0.115786
$315$	−1.76673	−0.0995441
$316$	11.7534	0.661182
$317$	28.4614	1.59855	0.799275	−	0.600965i	$-0.205217\pi$
$317$	28.4614	1.59855	0.799275	+	0.600965i	$0.205217\pi$
$318$	−8.77126	−0.491868
$319$	0	0
$320$	1.00000	0.0559017
$321$	14.7277	0.822021
$322$	2.51489	0.140149
$323$	12.8568	0.715374
$324$	−11.1789	−0.621047
$325$	−2.53263	−0.140485
$326$	20.6976	1.14633
$327$	−40.7977	−2.25612
$328$	10.5523	0.582655
$329$	−3.22482	−0.177790
$330$	0	0
$331$	−24.8572	−1.36627	−0.683136	−	0.730291i	$-0.739385\pi$
$331$	−24.8572	−1.36627	−0.683136	+	0.730291i	$0.739385\pi$
$332$	7.34851	0.403302
$333$	−8.18217	−0.448380
$334$	−1.32050	−0.0722546
$335$	3.86233	0.211022
$336$	−2.18328	−0.119108
$337$	15.6474	0.852369	0.426184	−	0.904636i	$-0.359858\pi$
$337$	15.6474	0.852369	0.426184	+	0.904636i	$0.359858\pi$
$338$	−6.58579	−0.358220
$339$	16.5151	0.896977
$340$	5.73813	0.311194
$341$	0	0
$342$	3.95854	0.214053
$343$	−1.00000	−0.0539949
$344$	2.18804	0.117971
$345$	−5.49071	−0.295610
$346$	−15.7029	−0.844191
$347$	−14.6646	−0.787239	−0.393620	−	0.919273i	$-0.628777\pi$
$347$	−14.6646	−0.787239	−0.393620	+	0.919273i	$0.628777\pi$
$348$	18.8199	1.00885
$349$	−26.9763	−1.44401	−0.722004	−	0.691889i	$-0.756779\pi$
$349$	−26.9763	−1.44401	−0.722004	+	0.691889i	$0.756779\pi$
$350$	−1.00000	−0.0534522
$351$	6.81929	0.363987
$352$	0	0
$353$	4.77463	0.254128	0.127064	−	0.991895i	$-0.459445\pi$
$353$	4.77463	0.254128	0.127064	+	0.991895i	$0.459445\pi$
$354$	4.39724	0.233711
$355$	−9.55514	−0.507134
$356$	−2.65397	−0.140660
$357$	−12.5280	−0.663050
$358$	4.65497	0.246023
$359$	−34.0982	−1.79963	−0.899816	−	0.436269i	$-0.856300\pi$
$359$	−34.0982	−1.79963	−0.899816	+	0.436269i	$0.856300\pi$
$360$	1.76673	0.0931150
$361$	−13.9797	−0.735774
$362$	−5.90450	−0.310334
$363$	0	0
$364$	2.53263	0.132746
$365$	11.4258	0.598056
$366$	0.585633	0.0306115
$367$	−9.98965	−0.521455	−0.260728	−	0.965412i	$-0.583962\pi$
$367$	−9.98965	−0.521455	−0.260728	+	0.965412i	$0.583962\pi$
$368$	−2.51489	−0.131098
$369$	18.6432	0.970524
$370$	−4.63124	−0.240767
$371$	4.01746	0.208576
$372$	4.01919	0.208385
$373$	0.510916	0.0264542	0.0132271	−	0.999913i	$-0.495790\pi$
$373$	0.510916	0.0264542	0.0132271	+	0.999913i	$0.495790\pi$
$374$	0	0
$375$	2.18328	0.112744
$376$	3.22482	0.166307
$377$	−21.8313	−1.12437
$378$	2.69257	0.138491
$379$	5.31376	0.272949	0.136475	−	0.990644i	$-0.456423\pi$
$379$	5.31376	0.272949	0.136475	+	0.990644i	$0.456423\pi$
$380$	2.24060	0.114940
$381$	23.4541	1.20159
$382$	−5.93400	−0.303610
$383$	23.5202	1.20183	0.600914	−	0.799314i	$-0.294803\pi$
$383$	23.5202	1.20183	0.600914	+	0.799314i	$0.294803\pi$
$384$	2.18328	0.111415
$385$	0	0
$386$	−10.8377	−0.551623
$387$	3.86567	0.196503
$388$	16.5045	0.837891
$389$	9.18397	0.465646	0.232823	−	0.972519i	$-0.425204\pi$
$389$	9.18397	0.465646	0.232823	+	0.972519i	$0.425204\pi$
$390$	−5.52945	−0.279995
$391$	−14.4307	−0.729794
$392$	1.00000	0.0505076
$393$	37.1641	1.87468
$394$	−12.0176	−0.605436
$395$	11.7534	0.591380
$396$	0	0
$397$	−31.5709	−1.58450	−0.792248	−	0.610199i	$-0.791089\pi$
$397$	−31.5709	−1.58450	−0.792248	+	0.610199i	$0.791089\pi$
$398$	18.4014	0.922378
$399$	−4.89187	−0.244900
$400$	1.00000	0.0500000
$401$	−10.6804	−0.533354	−0.266677	−	0.963786i	$-0.585926\pi$
$401$	−10.6804	−0.533354	−0.266677	+	0.963786i	$0.585926\pi$
$402$	8.43256	0.420578
$403$	−4.66229	−0.232245
$404$	−16.0478	−0.798408
$405$	−11.1789	−0.555482
$406$	−8.62000	−0.427803
$407$	0	0
$408$	12.5280	0.620227
$409$	23.5770	1.16581	0.582903	−	0.812542i	$-0.301917\pi$
$409$	23.5770	1.16581	0.582903	+	0.812542i	$0.301917\pi$
$410$	10.5523	0.521143
$411$	−27.2423	−1.34376
$412$	−12.9029	−0.635680
$413$	−2.01405	−0.0991048
$414$	−4.44313	−0.218368
$415$	7.34851	0.360724
$416$	−2.53263	−0.124172
$417$	−37.9482	−1.85833
$418$	0	0
$419$	−15.9235	−0.777915	−0.388958	−	0.921256i	$-0.627165\pi$
$419$	−15.9235	−0.777915	−0.388958	+	0.921256i	$0.627165\pi$
$420$	−2.18328	−0.106533
$421$	−39.8602	−1.94267	−0.971333	−	0.237722i	$-0.923599\pi$
$421$	−39.8602	−1.94267	−0.971333	+	0.237722i	$0.923599\pi$
$422$	−20.0422	−0.975638
$423$	5.69740	0.277017
$424$	−4.01746	−0.195105
$425$	5.73813	0.278340
$426$	−20.8616	−1.01075
$427$	−0.268235	−0.0129808
$428$	6.74567	0.326064
$429$	0	0
$430$	2.18804	0.105516
$431$	17.5909	0.847325	0.423662	−	0.905820i	$-0.360744\pi$
$431$	17.5909	0.847325	0.423662	+	0.905820i	$0.360744\pi$
$432$	−2.69257	−0.129547
$433$	20.5443	0.987296	0.493648	−	0.869662i	$-0.335663\pi$
$433$	20.5443	0.987296	0.493648	+	0.869662i	$0.335663\pi$
$434$	−1.84089	−0.0883656
$435$	18.8199	0.902346
$436$	−18.6864	−0.894916
$437$	−5.63485	−0.269552
$438$	24.9459	1.19196
$439$	−22.4200	−1.07005	−0.535023	−	0.844837i	$-0.679697\pi$
$439$	−22.4200	−1.07005	−0.535023	+	0.844837i	$0.679697\pi$
$440$	0	0
$441$	1.76673	0.0841301
$442$	−14.5325	−0.691243
$443$	7.63516	0.362757	0.181379	−	0.983413i	$-0.441944\pi$
$443$	7.63516	0.362757	0.181379	+	0.983413i	$0.441944\pi$
$444$	−10.1113	−0.479862
$445$	−2.65397	−0.125810
$446$	11.8000	0.558745
$447$	3.25760	0.154079
$448$	−1.00000	−0.0472456
$449$	−0.652470	−0.0307920	−0.0153960	−	0.999881i	$-0.504901\pi$
$449$	−0.652470	−0.0307920	−0.0153960	+	0.999881i	$0.504901\pi$
$450$	1.76673	0.0832846
$451$	0	0
$452$	7.56433	0.355796
$453$	17.4566	0.820181
$454$	−0.990121	−0.0464687
$455$	2.53263	0.118731
$456$	4.89187	0.229083
$457$	−30.5691	−1.42996	−0.714981	−	0.699144i	$-0.753565\pi$
$457$	−30.5691	−1.42996	−0.714981	+	0.699144i	$0.753565\pi$
$458$	18.3559	0.857714
$459$	−15.4503	−0.721160
$460$	−2.51489	−0.117257
$461$	3.55735	0.165682	0.0828412	−	0.996563i	$-0.473601\pi$
$461$	3.55735	0.165682	0.0828412	+	0.996563i	$0.473601\pi$
$462$	0	0
$463$	6.57677	0.305648	0.152824	−	0.988253i	$-0.451163\pi$
$463$	6.57677	0.305648	0.152824	+	0.988253i	$0.451163\pi$
$464$	8.62000	0.400173
$465$	4.01919	0.186385
$466$	17.3650	0.804418
$467$	−18.3935	−0.851150	−0.425575	−	0.904923i	$-0.639928\pi$
$467$	−18.3935	−0.851150	−0.425575	+	0.904923i	$0.639928\pi$
$468$	−4.47448	−0.206833
$469$	−3.86233	−0.178346
$470$	3.22482	0.148750
$471$	4.47951	0.206405
$472$	2.01405	0.0927040
$473$	0	0
$474$	25.6611	1.17865
$475$	2.24060	0.102806
$476$	−5.73813	−0.263007
$477$	−7.09778	−0.324985
$478$	−8.92113	−0.408043
$479$	−33.1011	−1.51243	−0.756213	−	0.654325i	$-0.772953\pi$
$479$	−33.1011	−1.51243	−0.756213	+	0.654325i	$0.772953\pi$
$480$	2.18328	0.0996529
$481$	11.7292	0.534807
$482$	0.896696	0.0408434
$483$	5.49071	0.249836
$484$	0	0
$485$	16.5045	0.749432
$486$	−16.3289	−0.740694
$487$	−15.5981	−0.706819	−0.353410	−	0.935469i	$-0.614978\pi$
$487$	−15.5981	−0.706819	−0.353410	+	0.935469i	$0.614978\pi$
$488$	0.268235	0.0121424
$489$	45.1887	2.04350
$490$	1.00000	0.0451754
$491$	41.6636	1.88025	0.940127	−	0.340825i	$-0.110706\pi$
$491$	41.6636	1.88025	0.940127	+	0.340825i	$0.110706\pi$
$492$	23.0388	1.03867
$493$	49.4626	2.22768
$494$	−5.67461	−0.255313
$495$	0	0
$496$	1.84089	0.0826585
$497$	9.55514	0.428606
$498$	16.0439	0.718944
$499$	−2.45110	−0.109726	−0.0548631	−	0.998494i	$-0.517472\pi$
$499$	−2.45110	−0.109726	−0.0548631	+	0.998494i	$0.517472\pi$
$500$	1.00000	0.0447214
$501$	−2.88303	−0.128804
$502$	−22.4978	−1.00413
$503$	6.68855	0.298228	0.149114	−	0.988820i	$-0.452358\pi$
$503$	6.68855	0.298228	0.149114	+	0.988820i	$0.452358\pi$
$504$	−1.76673	−0.0786965
$505$	−16.0478	−0.714118
$506$	0	0
$507$	−14.3787	−0.638579
$508$	10.7426	0.476625
$509$	−14.0762	−0.623917	−0.311959	−	0.950096i	$-0.600985\pi$
$509$	−14.0762	−0.623917	−0.311959	+	0.950096i	$0.600985\pi$
$510$	12.5280	0.554747
$511$	−11.4258	−0.505450
$512$	1.00000	0.0441942
$513$	−6.03298	−0.266363
$514$	−24.9449	−1.10027
$515$	−12.9029	−0.568570
$516$	4.77710	0.210300
$517$	0	0
$518$	4.63124	0.203485
$519$	−34.2838	−1.50489
$520$	−2.53263	−0.111063
$521$	41.6989	1.82686	0.913431	−	0.406993i	$-0.133423\pi$
$521$	41.6989	1.82686	0.913431	+	0.406993i	$0.133423\pi$
$522$	15.2292	0.666565
$523$	−10.6960	−0.467703	−0.233851	−	0.972272i	$-0.575133\pi$
$523$	−10.6960	−0.467703	−0.233851	+	0.972272i	$0.575133\pi$
$524$	17.0221	0.743613
$525$	−2.18328	−0.0952864
$526$	−6.25594	−0.272772
$527$	10.5633	0.460143
$528$	0	0
$529$	−16.6753	−0.725015
$530$	−4.01746	−0.174507
$531$	3.55828	0.154416
$532$	−2.24060	−0.0971423
$533$	−26.7252	−1.15759
$534$	−5.79438	−0.250747
$535$	6.74567	0.291641
$536$	3.86233	0.166827
$537$	10.1631	0.438571
$538$	−13.0673	−0.563371
$539$	0	0
$540$	−2.69257	−0.115870
$541$	−9.64911	−0.414847	−0.207424	−	0.978251i	$-0.566508\pi$
$541$	−9.64911	−0.414847	−0.207424	+	0.978251i	$0.566508\pi$
$542$	24.3157	1.04445
$543$	−12.8912	−0.553215
$544$	5.73813	0.246020
$545$	−18.6864	−0.800437
$546$	5.52945	0.236639
$547$	−14.8545	−0.635133	−0.317567	−	0.948236i	$-0.602866\pi$
$547$	−14.8545	−0.635133	−0.317567	+	0.948236i	$0.602866\pi$
$548$	−12.4777	−0.533019
$549$	0.473900	0.0202255
$550$	0	0
$551$	19.3140	0.822803
$552$	−5.49071	−0.233700
$553$	−11.7534	−0.499807
$554$	13.4094	0.569713
$555$	−10.1113	−0.429202
$556$	−17.3812	−0.737129
$557$	−39.9349	−1.69210	−0.846048	−	0.533106i	$-0.821025\pi$
$557$	−39.9349	−1.69210	−0.846048	+	0.533106i	$0.821025\pi$
$558$	3.25236	0.137683
$559$	−5.54148	−0.234380
$560$	−1.00000	−0.0422577
$561$	0	0
$562$	−12.7398	−0.537396
$563$	−4.06409	−0.171281	−0.0856405	−	0.996326i	$-0.527294\pi$
$563$	−4.06409	−0.171281	−0.0856405	+	0.996326i	$0.527294\pi$
$564$	7.04070	0.296467
$565$	7.56433	0.318234
$566$	13.7495	0.577936
$567$	11.1789	0.469468
$568$	−9.55514	−0.400925
$569$	−31.8994	−1.33729	−0.668647	−	0.743580i	$-0.733126\pi$
$569$	−31.8994	−1.33729	−0.668647	+	0.743580i	$0.733126\pi$
$570$	4.89187	0.204898
$571$	−20.3883	−0.853222	−0.426611	−	0.904435i	$-0.640293\pi$
$571$	−20.3883	−0.853222	−0.426611	+	0.904435i	$0.640293\pi$
$572$	0	0
$573$	−12.9556	−0.541229
$574$	−10.5523	−0.440446
$575$	−2.51489	−0.104878
$576$	1.76673	0.0736139
$577$	−26.0450	−1.08427	−0.542134	−	0.840292i	$-0.682383\pi$
$577$	−26.0450	−1.08427	−0.542134	+	0.840292i	$0.682383\pi$
$578$	15.9261	0.662438
$579$	−23.6617	−0.983348
$580$	8.62000	0.357926
$581$	−7.34851	−0.304867
$582$	36.0341	1.49366
$583$	0	0
$584$	11.4258	0.472805
$585$	−4.47448	−0.184997
$586$	−16.6376	−0.687295
$587$	−38.9847	−1.60907	−0.804536	−	0.593904i	$-0.797586\pi$
$587$	−38.9847	−1.60907	−0.804536	+	0.593904i	$0.797586\pi$
$588$	2.18328	0.0900371
$589$	4.12470	0.169955
$590$	2.01405	0.0829170
$591$	−26.2378	−1.07928
$592$	−4.63124	−0.190343
$593$	0.526179	0.0216076	0.0108038	−	0.999942i	$-0.496561\pi$
$593$	0.526179	0.0216076	0.0108038	+	0.999942i	$0.496561\pi$
$594$	0	0
$595$	−5.73813	−0.235240
$596$	1.49206	0.0611173
$597$	40.1755	1.64427
$598$	6.36928	0.260459
$599$	−12.3903	−0.506256	−0.253128	−	0.967433i	$-0.581459\pi$
$599$	−12.3903	−0.506256	−0.253128	+	0.967433i	$0.581459\pi$
$600$	2.18328	0.0891322
$601$	−26.8732	−1.09618	−0.548091	−	0.836418i	$-0.684645\pi$
$601$	−26.8732	−1.09618	−0.548091	+	0.836418i	$0.684645\pi$
$602$	−2.18804	−0.0891777
$603$	6.82370	0.277883
$604$	7.99555	0.325334
$605$	0	0
$606$	−35.0369	−1.42328
$607$	36.1325	1.46657	0.733286	−	0.679920i	$-0.237986\pi$
$607$	36.1325	1.46657	0.733286	+	0.679920i	$0.237986\pi$
$608$	2.24060	0.0908683
$609$	−18.8199	−0.762621
$610$	0.268235	0.0108605
$611$	−8.16728	−0.330413
$612$	10.1377	0.409794
$613$	33.2590	1.34332	0.671659	−	0.740860i	$-0.265582\pi$
$613$	33.2590	1.34332	0.671659	+	0.740860i	$0.265582\pi$
$614$	−5.56226	−0.224475
$615$	23.0388	0.929012
$616$	0	0
$617$	−27.1415	−1.09267	−0.546337	−	0.837565i	$-0.683978\pi$
$617$	−27.1415	−1.09267	−0.546337	+	0.837565i	$0.683978\pi$
$618$	−28.1707	−1.13319
$619$	2.93234	0.117861	0.0589303	−	0.998262i	$-0.481231\pi$
$619$	2.93234	0.117861	0.0589303	+	0.998262i	$0.481231\pi$
$620$	1.84089	0.0739320
$621$	6.77152	0.271732
$622$	17.9179	0.718441
$623$	2.65397	0.106329
$624$	−5.52945	−0.221355
$625$	1.00000	0.0400000
$626$	5.15478	0.206026
$627$	0	0
$628$	2.05173	0.0818729
$629$	−26.5747	−1.05960
$630$	−1.76673	−0.0703883
$631$	−7.10213	−0.282731	−0.141366	−	0.989957i	$-0.545149\pi$
$631$	−7.10213	−0.282731	−0.141366	+	0.989957i	$0.545149\pi$
$632$	11.7534	0.467527
$633$	−43.7578	−1.73922
$634$	28.4614	1.13035
$635$	10.7426	0.426306
$636$	−8.77126	−0.347803
$637$	−2.53263	−0.100346
$638$	0	0
$639$	−16.8814	−0.667817
$640$	1.00000	0.0395285
$641$	1.60982	0.0635842	0.0317921	−	0.999495i	$-0.489879\pi$
$641$	1.60982	0.0635842	0.0317921	+	0.999495i	$0.489879\pi$
$642$	14.7277	0.581257
$643$	−17.9131	−0.706422	−0.353211	−	0.935544i	$-0.614910\pi$
$643$	−17.9131	−0.706422	−0.353211	+	0.935544i	$0.614910\pi$
$644$	2.51489	0.0991004
$645$	4.77710	0.188098
$646$	12.8568	0.505846
$647$	−5.38711	−0.211789	−0.105895	−	0.994377i	$-0.533771\pi$
$647$	−5.38711	−0.211789	−0.105895	+	0.994377i	$0.533771\pi$
$648$	−11.1789	−0.439147
$649$	0	0
$650$	−2.53263	−0.0993379
$651$	−4.01919	−0.157524
$652$	20.6976	0.810579
$653$	48.6527	1.90393	0.951963	−	0.306212i	$-0.0990616\pi$
$653$	48.6527	1.90393	0.951963	+	0.306212i	$0.0990616\pi$
$654$	−40.7977	−1.59532
$655$	17.0221	0.665108
$656$	10.5523	0.411999
$657$	20.1864	0.787547
$658$	−3.22482	−0.125717
$659$	29.0793	1.13277	0.566385	−	0.824141i	$-0.308342\pi$
$659$	29.0793	1.13277	0.566385	+	0.824141i	$0.308342\pi$
$660$	0	0
$661$	−13.9160	−0.541270	−0.270635	−	0.962682i	$-0.587234\pi$
$661$	−13.9160	−0.541270	−0.270635	+	0.962682i	$0.587234\pi$
$662$	−24.8572	−0.966101
$663$	−31.7287	−1.23224
$664$	7.34851	0.285177
$665$	−2.24060	−0.0868867
$666$	−8.18217	−0.317053
$667$	−21.6783	−0.839388
$668$	−1.32050	−0.0510917
$669$	25.7627	0.996043
$670$	3.86233	0.149215
$671$	0	0
$672$	−2.18328	−0.0842220
$673$	32.6201	1.25741	0.628707	−	0.777642i	$-0.283585\pi$
$673$	32.6201	1.25741	0.628707	+	0.777642i	$0.283585\pi$
$674$	15.6474	0.602716
$675$	−2.69257	−0.103637
$676$	−6.58579	−0.253300
$677$	−37.5887	−1.44465	−0.722325	−	0.691554i	$-0.756926\pi$
$677$	−37.5887	−1.44465	−0.722325	+	0.691554i	$0.756926\pi$
$678$	16.5151	0.634258
$679$	−16.5045	−0.633386
$680$	5.73813	0.220047
$681$	−2.16172	−0.0828372
$682$	0	0
$683$	−17.5199	−0.670380	−0.335190	−	0.942151i	$-0.608800\pi$
$683$	−17.5199	−0.670380	−0.335190	+	0.942151i	$0.608800\pi$
$684$	3.95854	0.151359
$685$	−12.4777	−0.476747
$686$	−1.00000	−0.0381802
$687$	40.0761	1.52900
$688$	2.18804	0.0834181
$689$	10.1747	0.387627
$690$	−5.49071	−0.209028
$691$	7.14352	0.271752	0.135876	−	0.990726i	$-0.456615\pi$
$691$	7.14352	0.271752	0.135876	+	0.990726i	$0.456615\pi$
$692$	−15.7029	−0.596933
$693$	0	0
$694$	−14.6646	−0.556662
$695$	−17.3812	−0.659308
$696$	18.8199	0.713367
$697$	60.5506	2.29352
$698$	−26.9763	−1.02107
$699$	37.9127	1.43399
$700$	−1.00000	−0.0377964
$701$	38.7733	1.46445	0.732224	−	0.681064i	$-0.238482\pi$
$701$	38.7733	1.46445	0.732224	+	0.681064i	$0.238482\pi$
$702$	6.81929	0.257378
$703$	−10.3768	−0.391367
$704$	0	0
$705$	7.04070	0.265168
$706$	4.77463	0.179696
$707$	16.0478	0.603540
$708$	4.39724	0.165258
$709$	30.3511	1.13986	0.569930	−	0.821693i	$-0.306970\pi$
$709$	30.3511	1.13986	0.569930	+	0.821693i	$0.306970\pi$
$710$	−9.55514	−0.358598
$711$	20.7652	0.778755
$712$	−2.65397	−0.0994618
$713$	−4.62963	−0.173381
$714$	−12.5280	−0.468847
$715$	0	0
$716$	4.65497	0.173964
$717$	−19.4774	−0.727396
$718$	−34.0982	−1.27253
$719$	36.0357	1.34391	0.671953	−	0.740594i	$-0.265456\pi$
$719$	36.0357	1.34391	0.671953	+	0.740594i	$0.265456\pi$
$720$	1.76673	0.0658422
$721$	12.9029	0.480529
$722$	−13.9797	−0.520271
$723$	1.95774	0.0728092
$724$	−5.90450	−0.219439
$725$	8.62000	0.320139
$726$	0	0
$727$	31.1833	1.15653	0.578263	−	0.815850i	$-0.303731\pi$
$727$	31.1833	1.15653	0.578263	+	0.815850i	$0.303731\pi$
$728$	2.53263	0.0938655
$729$	−2.11408	−0.0782992
$730$	11.4258	0.422890
$731$	12.5552	0.464372
$732$	0.585633	0.0216456
$733$	26.0329	0.961548	0.480774	−	0.876844i	$-0.340356\pi$
$733$	26.0329	0.961548	0.480774	+	0.876844i	$0.340356\pi$
$734$	−9.98965	−0.368725
$735$	2.18328	0.0805317
$736$	−2.51489	−0.0927000
$737$	0	0
$738$	18.6432	0.686264
$739$	−22.4140	−0.824514	−0.412257	−	0.911068i	$-0.635259\pi$
$739$	−22.4140	−0.824514	−0.412257	+	0.911068i	$0.635259\pi$
$740$	−4.63124	−0.170248
$741$	−12.3893	−0.455132
$742$	4.01746	0.147486
$743$	44.3080	1.62550	0.812752	−	0.582610i	$-0.197969\pi$
$743$	44.3080	1.62550	0.812752	+	0.582610i	$0.197969\pi$
$744$	4.01919	0.147351
$745$	1.49206	0.0546650
$746$	0.510916	0.0187060
$747$	12.9828	0.475018
$748$	0	0
$749$	−6.74567	−0.246482
$750$	2.18328	0.0797223
$751$	39.3682	1.43657	0.718283	−	0.695751i	$-0.244928\pi$
$751$	39.3682	1.43657	0.718283	+	0.695751i	$0.244928\pi$
$752$	3.22482	0.117597
$753$	−49.1192	−1.79000
$754$	−21.8313	−0.795048
$755$	7.99555	0.290988
$756$	2.69257	0.0979280
$757$	−33.4097	−1.21430	−0.607149	−	0.794588i	$-0.707687\pi$
$757$	−33.4097	−1.21430	−0.607149	+	0.794588i	$0.707687\pi$
$758$	5.31376	0.193004
$759$	0	0
$760$	2.24060	0.0812751
$761$	−38.9480	−1.41186	−0.705932	−	0.708279i	$-0.749472\pi$
$761$	−38.9480	−1.41186	−0.705932	+	0.708279i	$0.749472\pi$
$762$	23.4541	0.849652
$763$	18.6864	0.676493
$764$	−5.93400	−0.214685
$765$	10.1377	0.366531
$766$	23.5202	0.849821
$767$	−5.10083	−0.184180
$768$	2.18328	0.0787825
$769$	0.875099	0.0315569	0.0157784	−	0.999876i	$-0.494977\pi$
$769$	0.875099	0.0315569	0.0157784	+	0.999876i	$0.494977\pi$
$770$	0	0
$771$	−54.4617	−1.96139
$772$	−10.8377	−0.390056
$773$	−22.9131	−0.824125	−0.412063	−	0.911155i	$-0.635192\pi$
$773$	−22.9131	−0.824125	−0.412063	+	0.911155i	$0.635192\pi$
$774$	3.86567	0.138949
$775$	1.84089	0.0661268
$776$	16.5045	0.592478
$777$	10.1113	0.362742
$778$	9.18397	0.329261
$779$	23.6436	0.847118
$780$	−5.52945	−0.197986
$781$	0	0
$782$	−14.4307	−0.516042
$783$	−23.2100	−0.829457
$784$	1.00000	0.0357143
$785$	2.05173	0.0732293
$786$	37.1641	1.32560
$787$	33.4092	1.19091	0.595455	−	0.803388i	$-0.296972\pi$
$787$	33.4092	1.19091	0.595455	+	0.803388i	$0.296972\pi$
$788$	−12.0176	−0.428108
$789$	−13.6585	−0.486255
$790$	11.7534	0.418168
$791$	−7.56433	−0.268957
$792$	0	0
$793$	−0.679340	−0.0241241
$794$	−31.5709	−1.12041
$795$	−8.77126	−0.311085
$796$	18.4014	0.652220
$797$	−3.43820	−0.121787	−0.0608936	−	0.998144i	$-0.519395\pi$
$797$	−3.43820	−0.121787	−0.0608936	+	0.998144i	$0.519395\pi$
$798$	−4.89187	−0.173170
$799$	18.5044	0.654640
$800$	1.00000	0.0353553
$801$	−4.68886	−0.165673
$802$	−10.6804	−0.377138
$803$	0	0
$804$	8.43256	0.297394
$805$	2.51489	0.0886381
$806$	−4.66229	−0.164222
$807$	−28.5296	−1.00429
$808$	−16.0478	−0.564560
$809$	35.3314	1.24219	0.621093	−	0.783737i	$-0.286689\pi$
$809$	35.3314	1.24219	0.621093	+	0.783737i	$0.286689\pi$
$810$	−11.1789	−0.392785
$811$	−48.6796	−1.70937	−0.854686	−	0.519145i	$-0.826251\pi$
$811$	−48.6796	−1.70937	−0.854686	+	0.519145i	$0.826251\pi$
$812$	−8.62000	−0.302503
$813$	53.0880	1.86188
$814$	0	0
$815$	20.6976	0.725004
$816$	12.5280	0.438566
$817$	4.90251	0.171517
$818$	23.5770	0.824349
$819$	4.47448	0.156351
$820$	10.5523	0.368504
$821$	−17.1917	−0.599995	−0.299997	−	0.953940i	$-0.596986\pi$
$821$	−17.1917	−0.599995	−0.299997	+	0.953940i	$0.596986\pi$
$822$	−27.2423	−0.950184
$823$	−45.8799	−1.59927	−0.799636	−	0.600485i	$-0.794974\pi$
$823$	−45.8799	−1.59927	−0.799636	+	0.600485i	$0.794974\pi$
$824$	−12.9029	−0.449494
$825$	0	0
$826$	−2.01405	−0.0700777
$827$	27.9645	0.972420	0.486210	−	0.873842i	$-0.338379\pi$
$827$	27.9645	0.972420	0.486210	+	0.873842i	$0.338379\pi$
$828$	−4.44313	−0.154410
$829$	−18.8815	−0.655782	−0.327891	−	0.944715i	$-0.606338\pi$
$829$	−18.8815	−0.655782	−0.327891	+	0.944715i	$0.606338\pi$
$830$	7.34851	0.255070
$831$	29.2766	1.01560
$832$	−2.53263	−0.0878031
$833$	5.73813	0.198814
$834$	−37.9482	−1.31404
$835$	−1.32050	−0.0456978
$836$	0	0
$837$	−4.95674	−0.171330
$838$	−15.9235	−0.550069
$839$	−19.7116	−0.680521	−0.340261	−	0.940331i	$-0.610515\pi$
$839$	−19.7116	−0.680521	−0.340261	+	0.940331i	$0.610515\pi$
$840$	−2.18328	−0.0753305
$841$	45.3044	1.56222
$842$	−39.8602	−1.37367
$843$	−27.8146	−0.957987
$844$	−20.0422	−0.689880
$845$	−6.58579	−0.226558
$846$	5.69740	0.195881
$847$	0	0
$848$	−4.01746	−0.137960
$849$	30.0191	1.03025
$850$	5.73813	0.196816
$851$	11.6471	0.399256
$852$	−20.8616	−0.714706
$853$	30.8936	1.05778	0.528888	−	0.848692i	$-0.322609\pi$
$853$	30.8936	1.05778	0.528888	+	0.848692i	$0.322609\pi$
$854$	−0.268235	−0.00917881
$855$	3.95854	0.135379
$856$	6.74567	0.230562
$857$	−24.2847	−0.829550	−0.414775	−	0.909924i	$-0.636140\pi$
$857$	−24.2847	−0.829550	−0.414775	+	0.909924i	$0.636140\pi$
$858$	0	0
$859$	22.0877	0.753621	0.376811	−	0.926290i	$-0.377021\pi$
$859$	22.0877	0.753621	0.376811	+	0.926290i	$0.377021\pi$
$860$	2.18804	0.0746114
$861$	−23.0388	−0.785159
$862$	17.5909	0.599149
$863$	−14.1052	−0.480146	−0.240073	−	0.970755i	$-0.577171\pi$
$863$	−14.1052	−0.480146	−0.240073	+	0.970755i	$0.577171\pi$
$864$	−2.69257	−0.0916032
$865$	−15.7029	−0.533913
$866$	20.5443	0.698124
$867$	34.7712	1.18089
$868$	−1.84089	−0.0624839
$869$	0	0
$870$	18.8199	0.638055
$871$	−9.78185	−0.331445
$872$	−18.6864	−0.632801
$873$	29.1591	0.986886
$874$	−5.63485	−0.190602
$875$	−1.00000	−0.0338062
$876$	24.9459	0.842843
$877$	−55.9227	−1.88838	−0.944188	−	0.329406i	$-0.893151\pi$
$877$	−55.9227	−1.88838	−0.944188	+	0.329406i	$0.893151\pi$
$878$	−22.4200	−0.756637
$879$	−36.3247	−1.22520
$880$	0	0
$881$	−46.2057	−1.55671	−0.778354	−	0.627826i	$-0.783945\pi$
$881$	−46.2057	−1.55671	−0.778354	+	0.627826i	$0.783945\pi$
$882$	1.76673	0.0594890
$883$	−14.1307	−0.475536	−0.237768	−	0.971322i	$-0.576416\pi$
$883$	−14.1307	−0.475536	−0.237768	+	0.971322i	$0.576416\pi$
$884$	−14.5325	−0.488782
$885$	4.39724	0.147812
$886$	7.63516	0.256508
$887$	37.6208	1.26318	0.631591	−	0.775302i	$-0.282402\pi$
$887$	37.6208	1.26318	0.631591	+	0.775302i	$0.282402\pi$
$888$	−10.1113	−0.339314
$889$	−10.7426	−0.360294
$890$	−2.65397	−0.0889614
$891$	0	0
$892$	11.8000	0.395092
$893$	7.22553	0.241793
$894$	3.25760	0.108950
$895$	4.65497	0.155598
$896$	−1.00000	−0.0334077
$897$	13.9059	0.464306
$898$	−0.652470	−0.0217732
$899$	15.8685	0.529243
$900$	1.76673	0.0588911
$901$	−23.0527	−0.767997
$902$	0	0
$903$	−4.77710	−0.158972
$904$	7.56433	0.251586
$905$	−5.90450	−0.196272
$906$	17.4566	0.579955
$907$	−2.97518	−0.0987893	−0.0493947	−	0.998779i	$-0.515729\pi$
$907$	−2.97518	−0.0987893	−0.0493947	+	0.998779i	$0.515729\pi$
$908$	−0.990121	−0.0328583
$909$	−28.3522	−0.940383
$910$	2.53263	0.0839558
$911$	−53.8707	−1.78481	−0.892407	−	0.451231i	$-0.850985\pi$
$911$	−53.8707	−1.78481	−0.892407	+	0.451231i	$0.850985\pi$
$912$	4.89187	0.161986
$913$	0	0
$914$	−30.5691	−1.01114
$915$	0.585633	0.0193604
$916$	18.3559	0.606495
$917$	−17.0221	−0.562119
$918$	−15.4503	−0.509937
$919$	16.9667	0.559678	0.279839	−	0.960047i	$-0.409719\pi$
$919$	16.9667	0.559678	0.279839	+	0.960047i	$0.409719\pi$
$920$	−2.51489	−0.0829134
$921$	−12.1440	−0.400159
$922$	3.55735	0.117155
$923$	24.1996	0.796540
$924$	0	0
$925$	−4.63124	−0.152274
$926$	6.57677	0.216126
$927$	−22.7960	−0.748718
$928$	8.62000	0.282965
$929$	32.3876	1.06260	0.531301	−	0.847183i	$-0.321703\pi$
$929$	32.3876	1.06260	0.531301	+	0.847183i	$0.321703\pi$
$930$	4.01919	0.131794
$931$	2.24060	0.0734327
$932$	17.3650	0.568809
$933$	39.1198	1.28072
$934$	−18.3935	−0.601854
$935$	0	0
$936$	−4.47448	−0.146253
$937$	24.1450	0.788784	0.394392	−	0.918942i	$-0.370955\pi$
$937$	24.1450	0.788784	0.394392	+	0.918942i	$0.370955\pi$
$938$	−3.86233	−0.126110
$939$	11.2543	0.367272
$940$	3.22482	0.105182
$941$	−40.6046	−1.32367	−0.661836	−	0.749648i	$-0.730223\pi$
$941$	−40.6046	−1.32367	−0.661836	+	0.749648i	$0.730223\pi$
$942$	4.47951	0.145950
$943$	−26.5379	−0.864194
$944$	2.01405	0.0655516
$945$	2.69257	0.0875894
$946$	0	0
$947$	0.111103	0.00361036	0.00180518	−	0.999998i	$-0.499425\pi$
$947$	0.111103	0.00361036	0.00180518	+	0.999998i	$0.499425\pi$
$948$	25.6611	0.833434
$949$	−28.9374	−0.939349
$950$	2.24060	0.0726946
$951$	62.1393	2.01500
$952$	−5.73813	−0.185974
$953$	7.70395	0.249555	0.124778	−	0.992185i	$-0.460178\pi$
$953$	7.70395	0.249555	0.124778	+	0.992185i	$0.460178\pi$
$954$	−7.09778	−0.229799
$955$	−5.93400	−0.192020
$956$	−8.92113	−0.288530
$957$	0	0
$958$	−33.1011	−1.06945
$959$	12.4777	0.402925
$960$	2.18328	0.0704652
$961$	−27.6111	−0.890681
$962$	11.7292	0.378165
$963$	11.9178	0.384046
$964$	0.896696	0.0288806
$965$	−10.8377	−0.348877
$966$	5.49071	0.176661
$967$	−41.8250	−1.34500	−0.672501	−	0.740096i	$-0.734780\pi$
$967$	−41.8250	−1.34500	−0.672501	+	0.740096i	$0.734780\pi$
$968$	0	0
$969$	28.0701	0.901743
$970$	16.5045	0.529929
$971$	37.2897	1.19668	0.598342	−	0.801241i	$-0.295826\pi$
$971$	37.2897	1.19668	0.598342	+	0.801241i	$0.295826\pi$
$972$	−16.3289	−0.523750
$973$	17.3812	0.557217
$974$	−15.5981	−0.499797
$975$	−5.52945	−0.177084
$976$	0.268235	0.00858599
$977$	2.41139	0.0771471	0.0385736	−	0.999256i	$-0.487719\pi$
$977$	2.41139	0.0771471	0.0385736	+	0.999256i	$0.487719\pi$
$978$	45.1887	1.44498
$979$	0	0
$980$	1.00000	0.0319438
$981$	−33.0139	−1.05405
$982$	41.6636	1.32954
$983$	−40.4385	−1.28979	−0.644894	−	0.764272i	$-0.723098\pi$
$983$	−40.4385	−1.28979	−0.644894	+	0.764272i	$0.723098\pi$
$984$	23.0388	0.734449
$985$	−12.0176	−0.382911
$986$	49.4626	1.57521
$987$	−7.04070	−0.224108
$988$	−5.67461	−0.180533
$989$	−5.50266	−0.174974
$990$	0	0
$991$	26.7075	0.848392	0.424196	−	0.905570i	$-0.360557\pi$
$991$	26.7075	0.848392	0.424196	+	0.905570i	$0.360557\pi$
$992$	1.84089	0.0584484
$993$	−54.2702	−1.72221
$994$	9.55514	0.303071
$995$	18.4014	0.583363
$996$	16.0439	0.508370
$997$	27.3325	0.865630	0.432815	−	0.901483i	$-0.357520\pi$
$997$	27.3325	0.865630	0.432815	+	0.901483i	$0.357520\pi$
$998$	−2.45110	−0.0775881
$999$	12.4700	0.394532

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8470.2.a.dc.1.6		6
11.7	odd	10		770.2.n.j.71.1	✓	12
11.8	odd	10		770.2.n.j.141.1	yes	12
11.10	odd	2		8470.2.a.cw.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.j.71.1	✓	12	11.7	odd	10
770.2.n.j.141.1	yes	12	11.8	odd	10
8470.2.a.cw.1.6		6	11.10	odd	2
8470.2.a.dc.1.6		6	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.18328 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.18328 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.76673 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.18328 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.18328 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.76673 q^{9} +1.00000 q^{10} +2.18328 q^{12} -2.53263 q^{13} -1.00000 q^{14} +2.18328 q^{15} +1.00000 q^{16} +5.73813 q^{17} +1.76673 q^{18} +2.24060 q^{19} +1.00000 q^{20} -2.18328 q^{21} -2.51489 q^{23} +2.18328 q^{24} +1.00000 q^{25} -2.53263 q^{26} -2.69257 q^{27} -1.00000 q^{28} +8.62000 q^{29} +2.18328 q^{30} +1.84089 q^{31} +1.00000 q^{32} +5.73813 q^{34} -1.00000 q^{35} +1.76673 q^{36} -4.63124 q^{37} +2.24060 q^{38} -5.52945 q^{39} +1.00000 q^{40} +10.5523 q^{41} -2.18328 q^{42} +2.18804 q^{43} +1.76673 q^{45} -2.51489 q^{46} +3.22482 q^{47} +2.18328 q^{48} +1.00000 q^{49} +1.00000 q^{50} +12.5280 q^{51} -2.53263 q^{52} -4.01746 q^{53} -2.69257 q^{54} -1.00000 q^{56} +4.89187 q^{57} +8.62000 q^{58} +2.01405 q^{59} +2.18328 q^{60} +0.268235 q^{61} +1.84089 q^{62} -1.76673 q^{63} +1.00000 q^{64} -2.53263 q^{65} +3.86233 q^{67} +5.73813 q^{68} -5.49071 q^{69} -1.00000 q^{70} -9.55514 q^{71} +1.76673 q^{72} +11.4258 q^{73} -4.63124 q^{74} +2.18328 q^{75} +2.24060 q^{76} -5.52945 q^{78} +11.7534 q^{79} +1.00000 q^{80} -11.1789 q^{81} +10.5523 q^{82} +7.34851 q^{83} -2.18328 q^{84} +5.73813 q^{85} +2.18804 q^{86} +18.8199 q^{87} -2.65397 q^{89} +1.76673 q^{90} +2.53263 q^{91} -2.51489 q^{92} +4.01919 q^{93} +3.22482 q^{94} +2.24060 q^{95} +2.18328 q^{96} +16.5045 q^{97} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} - q^{3} + 6 q^{4} + 6 q^{5} - q^{6} - 6 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) 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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