LMFDB - Embedded newform 8470.2.a.cu.1.2

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:	6.6.38498000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 12x^{4} + 5x^{3} + 38x^{2} - x - 19 $ x^6 - x^5 - 12x^4 + 5x^3 + 38*x^2 - x - 19
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			1.2
Root			$-1.95171$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.95171 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.95171 q^{6} -1.00000 q^{7} -1.00000 q^{8} +5.71258 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.95171 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.95171 q^{6} -1.00000 q^{7} -1.00000 q^{8} +5.71258 q^{9} +1.00000 q^{10} -2.95171 q^{12} -5.80086 q^{13} +1.00000 q^{14} +2.95171 q^{15} +1.00000 q^{16} +0.469771 q^{17} -5.71258 q^{18} +4.04523 q^{19} -1.00000 q^{20} +2.95171 q^{21} -7.69830 q^{23} +2.95171 q^{24} +1.00000 q^{25} +5.80086 q^{26} -8.00674 q^{27} -1.00000 q^{28} -2.63313 q^{29} -2.95171 q^{30} -3.22145 q^{31} -1.00000 q^{32} -0.469771 q^{34} +1.00000 q^{35} +5.71258 q^{36} -4.56071 q^{37} -4.04523 q^{38} +17.1224 q^{39} +1.00000 q^{40} -1.82473 q^{41} -2.95171 q^{42} +0.790717 q^{43} -5.71258 q^{45} +7.69830 q^{46} -4.28567 q^{47} -2.95171 q^{48} +1.00000 q^{49} -1.00000 q^{50} -1.38663 q^{51} -5.80086 q^{52} +13.9401 q^{53} +8.00674 q^{54} +1.00000 q^{56} -11.9403 q^{57} +2.63313 q^{58} -13.0380 q^{59} +2.95171 q^{60} +6.69651 q^{61} +3.22145 q^{62} -5.71258 q^{63} +1.00000 q^{64} +5.80086 q^{65} -6.73018 q^{67} +0.469771 q^{68} +22.7231 q^{69} -1.00000 q^{70} +11.4855 q^{71} -5.71258 q^{72} -12.2547 q^{73} +4.56071 q^{74} -2.95171 q^{75} +4.04523 q^{76} -17.1224 q^{78} -3.95281 q^{79} -1.00000 q^{80} +6.49582 q^{81} +1.82473 q^{82} +9.44801 q^{83} +2.95171 q^{84} -0.469771 q^{85} -0.790717 q^{86} +7.77222 q^{87} -11.2766 q^{89} +5.71258 q^{90} +5.80086 q^{91} -7.69830 q^{92} +9.50878 q^{93} +4.28567 q^{94} -4.04523 q^{95} +2.95171 q^{96} -16.7510 q^{97} -1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} - 5 q^{3} + 6 q^{4} - 6 q^{5} + 5 q^{6} - 6 q^{7} - 6 q^{8} + 11 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 - 5 * q^3 + 6 * q^4 - 6 * q^5 + 5 * q^6 - 6 * q^7 - 6 * q^8 + 11 * q^9	$ 6 q - 6 q^{2} - 5 q^{3} + 6 q^{4} - 6 q^{5} + 5 q^{6} - 6 q^{7} - 6 q^{8} + 11 q^{9} + 6 q^{10} - 5 q^{12} + 6 q^{14} + 5 q^{15} + 6 q^{16} + 15 q^{17} - 11 q^{18} + 13 q^{19} - 6 q^{20} + 5 q^{21} - 2 q^{23} + 5 q^{24} + 6 q^{25} - 26 q^{27} - 6 q^{28} + 4 q^{29} - 5 q^{30} - 2 q^{31} - 6 q^{32} - 15 q^{34} + 6 q^{35} + 11 q^{36} - 13 q^{38} + 30 q^{39} + 6 q^{40} + 17 q^{41} - 5 q^{42} - 15 q^{43} - 11 q^{45} + 2 q^{46} - 18 q^{47} - 5 q^{48} + 6 q^{49} - 6 q^{50} - 6 q^{51} + 22 q^{53} + 26 q^{54} + 6 q^{56} + 2 q^{57} - 4 q^{58} - 7 q^{59} + 5 q^{60} + 20 q^{61} + 2 q^{62} - 11 q^{63} + 6 q^{64} - 29 q^{67} + 15 q^{68} + 12 q^{69} - 6 q^{70} - 2 q^{71} - 11 q^{72} - q^{73} - 5 q^{75} + 13 q^{76} - 30 q^{78} + 12 q^{79} - 6 q^{80} + 22 q^{81} - 17 q^{82} + 35 q^{83} + 5 q^{84} - 15 q^{85} + 15 q^{86} - 29 q^{89} + 11 q^{90} - 2 q^{92} + 8 q^{93} + 18 q^{94} - 13 q^{95} + 5 q^{96} - 19 q^{97} - 6 q^{98}+O(q^{100}) $ 6 * q - 6 * q^2 - 5 * q^3 + 6 * q^4 - 6 * q^5 + 5 * q^6 - 6 * q^7 - 6 * q^8 + 11 * q^9 + 6 * q^10 - 5 * q^12 + 6 * q^14 + 5 * q^15 + 6 * q^16 + 15 * q^17 - 11 * q^18 + 13 * q^19 - 6 * q^20 + 5 * q^21 - 2 * q^23 + 5 * q^24 + 6 * q^25 - 26 * q^27 - 6 * q^28 + 4 * q^29 - 5 * q^30 - 2 * q^31 - 6 * q^32 - 15 * q^34 + 6 * q^35 + 11 * q^36 - 13 * q^38 + 30 * q^39 + 6 * q^40 + 17 * q^41 - 5 * q^42 - 15 * q^43 - 11 * q^45 + 2 * q^46 - 18 * q^47 - 5 * q^48 + 6 * q^49 - 6 * q^50 - 6 * q^51 + 22 * q^53 + 26 * q^54 + 6 * q^56 + 2 * q^57 - 4 * q^58 - 7 * q^59 + 5 * q^60 + 20 * q^61 + 2 * q^62 - 11 * q^63 + 6 * q^64 - 29 * q^67 + 15 * q^68 + 12 * q^69 - 6 * q^70 - 2 * q^71 - 11 * q^72 - q^73 - 5 * q^75 + 13 * q^76 - 30 * q^78 + 12 * q^79 - 6 * q^80 + 22 * q^81 - 17 * q^82 + 35 * q^83 + 5 * q^84 - 15 * q^85 + 15 * q^86 - 29 * q^89 + 11 * q^90 - 2 * q^92 + 8 * q^93 + 18 * q^94 - 13 * q^95 + 5 * q^96 - 19 * 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
$3$	−2.95171	−1.70417	−0.852085	−	0.523404i	$-0.824662\pi$
$3$	−2.95171	−1.70417	−0.852085	+	0.523404i	$0.824662\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.95171	1.20503
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	5.71258	1.90419
$10$	1.00000	0.316228
$11$	0	0
$11$	0	0
$12$	−2.95171	−0.852085
$13$	−5.80086	−1.60887	−0.804434	−	0.594042i	$-0.797531\pi$
$13$	−5.80086	−1.60887	−0.804434	+	0.594042i	$0.797531\pi$
$14$	1.00000	0.267261
$15$	2.95171	0.762128
$16$	1.00000	0.250000
$17$	0.469771	0.113936	0.0569681	−	0.998376i	$-0.481857\pi$
$17$	0.469771	0.113936	0.0569681	+	0.998376i	$0.481857\pi$
$18$	−5.71258	−1.34647
$19$	4.04523	0.928040	0.464020	−	0.885825i	$-0.346407\pi$
$19$	4.04523	0.928040	0.464020	+	0.885825i	$0.346407\pi$
$20$	−1.00000	−0.223607
$21$	2.95171	0.644115
$22$	0	0
$23$	−7.69830	−1.60521	−0.802603	−	0.596513i	$-0.796552\pi$
$23$	−7.69830	−1.60521	−0.802603	+	0.596513i	$0.796552\pi$
$24$	2.95171	0.602515
$25$	1.00000	0.200000
$26$	5.80086	1.13764
$27$	−8.00674	−1.54090
$28$	−1.00000	−0.188982
$29$	−2.63313	−0.488959	−0.244480	−	0.969654i	$-0.578617\pi$
$29$	−2.63313	−0.488959	−0.244480	+	0.969654i	$0.578617\pi$
$30$	−2.95171	−0.538906
$31$	−3.22145	−0.578589	−0.289295	−	0.957240i	$-0.593421\pi$
$31$	−3.22145	−0.578589	−0.289295	+	0.957240i	$0.593421\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	−0.469771	−0.0805650
$35$	1.00000	0.169031
$36$	5.71258	0.952096
$37$	−4.56071	−0.749776	−0.374888	−	0.927070i	$-0.622319\pi$
$37$	−4.56071	−0.749776	−0.374888	+	0.927070i	$0.622319\pi$
$38$	−4.04523	−0.656223
$39$	17.1224	2.74178
$40$	1.00000	0.158114
$41$	−1.82473	−0.284975	−0.142487	−	0.989797i	$-0.545510\pi$
$41$	−1.82473	−0.284975	−0.142487	+	0.989797i	$0.545510\pi$
$42$	−2.95171	−0.455458
$43$	0.790717	0.120583	0.0602916	−	0.998181i	$-0.480797\pi$
$43$	0.790717	0.120583	0.0602916	+	0.998181i	$0.480797\pi$
$44$	0	0
$45$	−5.71258	−0.851581
$46$	7.69830	1.13505
$47$	−4.28567	−0.625130	−0.312565	−	0.949896i	$-0.601188\pi$
$47$	−4.28567	−0.625130	−0.312565	+	0.949896i	$0.601188\pi$
$48$	−2.95171	−0.426042
$49$	1.00000	0.142857
$50$	−1.00000	−0.141421
$51$	−1.38663	−0.194167
$52$	−5.80086	−0.804434
$53$	13.9401	1.91482	0.957409	−	0.288735i	$-0.0932348\pi$
$53$	13.9401	1.91482	0.957409	+	0.288735i	$0.0932348\pi$
$54$	8.00674	1.08958
$55$	0	0
$56$	1.00000	0.133631
$57$	−11.9403	−1.58154
$58$	2.63313	0.345746
$59$	−13.0380	−1.69741	−0.848703	−	0.528869i	$-0.822616\pi$
$59$	−13.0380	−1.69741	−0.848703	+	0.528869i	$0.822616\pi$
$60$	2.95171	0.381064
$61$	6.69651	0.857400	0.428700	−	0.903447i	$-0.358972\pi$
$61$	6.69651	0.857400	0.428700	+	0.903447i	$0.358972\pi$
$62$	3.22145	0.409124
$63$	−5.71258	−0.719717
$64$	1.00000	0.125000
$65$	5.80086	0.719508
$66$	0	0
$67$	−6.73018	−0.822223	−0.411111	−	0.911585i	$-0.634859\pi$
$67$	−6.73018	−0.822223	−0.411111	+	0.911585i	$0.634859\pi$
$68$	0.469771	0.0569681
$69$	22.7231	2.73554
$70$	−1.00000	−0.119523
$71$	11.4855	1.36308	0.681538	−	0.731783i	$-0.261311\pi$
$71$	11.4855	1.36308	0.681538	+	0.731783i	$0.261311\pi$
$72$	−5.71258	−0.673234
$73$	−12.2547	−1.43430	−0.717152	−	0.696916i	$-0.754555\pi$
$73$	−12.2547	−1.43430	−0.717152	+	0.696916i	$0.754555\pi$
$74$	4.56071	0.530171
$75$	−2.95171	−0.340834
$76$	4.04523	0.464020
$77$	0	0
$78$	−17.1224	−1.93873
$79$	−3.95281	−0.444726	−0.222363	−	0.974964i	$-0.571377\pi$
$79$	−3.95281	−0.444726	−0.222363	+	0.974964i	$0.571377\pi$
$80$	−1.00000	−0.111803
$81$	6.49582	0.721758
$82$	1.82473	0.201508
$83$	9.44801	1.03705	0.518527	−	0.855061i	$-0.326481\pi$
$83$	9.44801	1.03705	0.518527	+	0.855061i	$0.326481\pi$
$84$	2.95171	0.322058
$85$	−0.469771	−0.0509538
$86$	−0.790717	−0.0852652
$87$	7.77222	0.833269
$88$	0	0
$89$	−11.2766	−1.19532	−0.597659	−	0.801751i	$-0.703902\pi$
$89$	−11.2766	−1.19532	−0.597659	+	0.801751i	$0.703902\pi$
$90$	5.71258	0.602159
$91$	5.80086	0.608095
$92$	−7.69830	−0.802603
$93$	9.50878	0.986014
$94$	4.28567	0.442034
$95$	−4.04523	−0.415032
$96$	2.95171	0.301257
$97$	−16.7510	−1.70081	−0.850403	−	0.526131i	$-0.823642\pi$
$97$	−16.7510	−1.70081	−0.850403	+	0.526131i	$0.823642\pi$
$98$	−1.00000	−0.101015
$99$	0	0
$100$	1.00000	0.100000
$101$	8.57037	0.852784	0.426392	−	0.904538i	$-0.359784\pi$
$101$	8.57037	0.852784	0.426392	+	0.904538i	$0.359784\pi$
$102$	1.38663	0.137296
$103$	2.40137	0.236614	0.118307	−	0.992977i	$-0.462253\pi$
$103$	2.40137	0.236614	0.118307	+	0.992977i	$0.462253\pi$
$104$	5.80086	0.568821
$105$	−2.95171	−0.288057
$106$	−13.9401	−1.35398
$107$	−6.06164	−0.586001	−0.293000	−	0.956112i	$-0.594654\pi$
$107$	−6.06164	−0.586001	−0.293000	+	0.956112i	$0.594654\pi$
$108$	−8.00674	−0.770449
$109$	−10.8776	−1.04188	−0.520942	−	0.853592i	$-0.674419\pi$
$109$	−10.8776	−1.04188	−0.520942	+	0.853592i	$0.674419\pi$
$110$	0	0
$111$	13.4619	1.27774
$112$	−1.00000	−0.0944911
$113$	−6.52609	−0.613923	−0.306961	−	0.951722i	$-0.599312\pi$
$113$	−6.52609	−0.613923	−0.306961	+	0.951722i	$0.599312\pi$
$114$	11.9403	1.11832
$115$	7.69830	0.717870
$116$	−2.63313	−0.244480
$117$	−33.1379	−3.06360
$118$	13.0380	1.20025
$119$	−0.469771	−0.0430638
$120$	−2.95171	−0.269453
$121$	0	0
$122$	−6.69651	−0.606274
$123$	5.38607	0.485645
$124$	−3.22145	−0.289295
$125$	−1.00000	−0.0894427
$126$	5.71258	0.508917
$127$	4.04736	0.359145	0.179572	−	0.983745i	$-0.442529\pi$
$127$	4.04736	0.359145	0.179572	+	0.983745i	$0.442529\pi$
$128$	−1.00000	−0.0883883
$129$	−2.33397	−0.205494
$130$	−5.80086	−0.508769
$131$	−9.05921	−0.791507	−0.395753	−	0.918357i	$-0.629516\pi$
$131$	−9.05921	−0.791507	−0.395753	+	0.918357i	$0.629516\pi$
$132$	0	0
$133$	−4.04523	−0.350766
$134$	6.73018	0.581399
$135$	8.00674	0.689110
$136$	−0.469771	−0.0402825
$137$	17.6250	1.50581	0.752905	−	0.658130i	$-0.228652\pi$
$137$	17.6250	1.50581	0.752905	+	0.658130i	$0.228652\pi$
$138$	−22.7231	−1.93432
$139$	−18.6667	−1.58329	−0.791646	−	0.610980i	$-0.790775\pi$
$139$	−18.6667	−1.58329	−0.791646	+	0.610980i	$0.790775\pi$
$140$	1.00000	0.0845154
$141$	12.6501	1.06533
$142$	−11.4855	−0.963840
$143$	0	0
$144$	5.71258	0.476048
$145$	2.63313	0.218669
$146$	12.2547	1.01421
$147$	−2.95171	−0.243453
$148$	−4.56071	−0.374888
$149$	−13.0357	−1.06792	−0.533962	−	0.845508i	$-0.679298\pi$
$149$	−13.0357	−1.06792	−0.533962	+	0.845508i	$0.679298\pi$
$150$	2.95171	0.241006
$151$	9.17018	0.746259	0.373129	−	0.927779i	$-0.378285\pi$
$151$	9.17018	0.746259	0.373129	+	0.927779i	$0.378285\pi$
$152$	−4.04523	−0.328112
$153$	2.68360	0.216956
$154$	0	0
$155$	3.22145	0.258753
$156$	17.1224	1.37089
$157$	9.06306	0.723311	0.361655	−	0.932312i	$-0.382212\pi$
$157$	9.06306	0.723311	0.361655	+	0.932312i	$0.382212\pi$
$158$	3.95281	0.314469
$159$	−41.1471	−3.26317
$160$	1.00000	0.0790569
$161$	7.69830	0.606711
$162$	−6.49582	−0.510360
$163$	−1.69719	−0.132934	−0.0664672	−	0.997789i	$-0.521173\pi$
$163$	−1.69719	−0.132934	−0.0664672	+	0.997789i	$0.521173\pi$
$164$	−1.82473	−0.142487
$165$	0	0
$166$	−9.44801	−0.733308
$167$	−19.8542	−1.53637	−0.768183	−	0.640230i	$-0.778839\pi$
$167$	−19.8542	−1.53637	−0.768183	+	0.640230i	$0.778839\pi$
$168$	−2.95171	−0.227729
$169$	20.6499	1.58846
$170$	0.469771	0.0360298
$171$	23.1087	1.76717
$172$	0.790717	0.0602916
$173$	12.5185	0.951767	0.475884	−	0.879508i	$-0.342128\pi$
$173$	12.5185	0.951767	0.475884	+	0.879508i	$0.342128\pi$
$174$	−7.77222	−0.589210
$175$	−1.00000	−0.0755929
$176$	0	0
$177$	38.4845	2.89267
$178$	11.2766	0.845217
$179$	−16.2877	−1.21740	−0.608698	−	0.793402i	$-0.708308\pi$
$179$	−16.2877	−1.21740	−0.608698	+	0.793402i	$0.708308\pi$
$180$	−5.71258	−0.425790
$181$	−11.8382	−0.879923	−0.439962	−	0.898017i	$-0.645008\pi$
$181$	−11.8382	−0.879923	−0.439962	+	0.898017i	$0.645008\pi$
$182$	−5.80086	−0.429988
$183$	−19.7661	−1.46116
$184$	7.69830	0.567526
$185$	4.56071	0.335310
$186$	−9.50878	−0.697217
$187$	0	0
$188$	−4.28567	−0.312565
$189$	8.00674	0.582405
$190$	4.04523	0.293472
$191$	−27.3346	−1.97787	−0.988933	−	0.148366i	$-0.952599\pi$
$191$	−27.3346	−1.97787	−0.988933	+	0.148366i	$0.952599\pi$
$192$	−2.95171	−0.213021
$193$	−16.8533	−1.21313	−0.606564	−	0.795035i	$-0.707452\pi$
$193$	−16.8533	−1.21313	−0.606564	+	0.795035i	$0.707452\pi$
$194$	16.7510	1.20265
$195$	−17.1224	−1.22616
$196$	1.00000	0.0714286
$197$	4.65860	0.331911	0.165956	−	0.986133i	$-0.446929\pi$
$197$	4.65860	0.331911	0.165956	+	0.986133i	$0.446929\pi$
$198$	0	0
$199$	−12.2080	−0.865404	−0.432702	−	0.901537i	$-0.642440\pi$
$199$	−12.2080	−0.865404	−0.432702	+	0.901537i	$0.642440\pi$
$200$	−1.00000	−0.0707107
$201$	19.8655	1.40121
$202$	−8.57037	−0.603009
$203$	2.63313	0.184809
$204$	−1.38663	−0.0970833
$205$	1.82473	0.127445
$206$	−2.40137	−0.167311
$207$	−43.9771	−3.05662
$208$	−5.80086	−0.402217
$209$	0	0
$210$	2.95171	0.203687
$211$	7.86890	0.541718	0.270859	−	0.962619i	$-0.412692\pi$
$211$	7.86890	0.541718	0.270859	+	0.962619i	$0.412692\pi$
$212$	13.9401	0.957409
$213$	−33.9018	−2.32291
$214$	6.06164	0.414365
$215$	−0.790717	−0.0539265
$216$	8.00674	0.544790
$217$	3.22145	0.218686
$218$	10.8776	0.736723
$219$	36.1723	2.44430
$220$	0	0
$221$	−2.72507	−0.183308
$222$	−13.4619	−0.903502
$223$	−23.8654	−1.59814	−0.799071	−	0.601236i	$-0.794675\pi$
$223$	−23.8654	−1.59814	−0.799071	+	0.601236i	$0.794675\pi$
$224$	1.00000	0.0668153
$225$	5.71258	0.380839
$226$	6.52609	0.434109
$227$	−22.7047	−1.50696	−0.753482	−	0.657469i	$-0.771627\pi$
$227$	−22.7047	−1.50696	−0.753482	+	0.657469i	$0.771627\pi$
$228$	−11.9403	−0.790768
$229$	−15.8703	−1.04874	−0.524371	−	0.851490i	$-0.675699\pi$
$229$	−15.8703	−1.04874	−0.524371	+	0.851490i	$0.675699\pi$
$230$	−7.69830	−0.507611
$231$	0	0
$232$	2.63313	0.172873
$233$	29.2428	1.91576	0.957879	−	0.287171i	$-0.0927147\pi$
$233$	29.2428	1.91576	0.957879	+	0.287171i	$0.0927147\pi$
$234$	33.1379	2.16629
$235$	4.28567	0.279567
$236$	−13.0380	−0.848703
$237$	11.6675	0.757889
$238$	0.469771	0.0304507
$239$	8.72767	0.564546	0.282273	−	0.959334i	$-0.408912\pi$
$239$	8.72767	0.564546	0.282273	+	0.959334i	$0.408912\pi$
$240$	2.95171	0.190532
$241$	9.58858	0.617655	0.308828	−	0.951118i	$-0.400063\pi$
$241$	9.58858	0.617655	0.308828	+	0.951118i	$0.400063\pi$
$242$	0	0
$243$	4.84646	0.310900
$244$	6.69651	0.428700
$245$	−1.00000	−0.0638877
$246$	−5.38607	−0.343403
$247$	−23.4658	−1.49309
$248$	3.22145	0.204562
$249$	−27.8878	−1.76731
$250$	1.00000	0.0632456
$251$	2.70064	0.170463	0.0852315	−	0.996361i	$-0.472837\pi$
$251$	2.70064	0.170463	0.0852315	+	0.996361i	$0.472837\pi$
$252$	−5.71258	−0.359859
$253$	0	0
$254$	−4.04736	−0.253954
$255$	1.38663	0.0868339
$256$	1.00000	0.0625000
$257$	8.92845	0.556941	0.278471	−	0.960445i	$-0.410173\pi$
$257$	8.92845	0.556941	0.278471	+	0.960445i	$0.410173\pi$
$258$	2.33397	0.145306
$259$	4.56071	0.283389
$260$	5.80086	0.359754
$261$	−15.0419	−0.931073
$262$	9.05921	0.559680
$263$	−0.182846	−0.0112748	−0.00563739	−	0.999984i	$-0.501794\pi$
$263$	−0.182846	−0.0112748	−0.00563739	+	0.999984i	$0.501794\pi$
$264$	0	0
$265$	−13.9401	−0.856333
$266$	4.04523	0.248029
$267$	33.2852	2.03702
$268$	−6.73018	−0.411111
$269$	−5.71539	−0.348474	−0.174237	−	0.984704i	$-0.555746\pi$
$269$	−5.71539	−0.348474	−0.174237	+	0.984704i	$0.555746\pi$
$270$	−8.00674	−0.487275
$271$	3.10080	0.188360	0.0941801	−	0.995555i	$-0.469977\pi$
$271$	3.10080	0.188360	0.0941801	+	0.995555i	$0.469977\pi$
$272$	0.469771	0.0284840
$273$	−17.1224	−1.03630
$274$	−17.6250	−1.06477
$275$	0	0
$276$	22.7231	1.36777
$277$	−21.4930	−1.29139	−0.645693	−	0.763597i	$-0.723432\pi$
$277$	−21.4930	−1.29139	−0.645693	+	0.763597i	$0.723432\pi$
$278$	18.6667	1.11956
$279$	−18.4028	−1.10175
$280$	−1.00000	−0.0597614
$281$	11.7569	0.701355	0.350678	−	0.936496i	$-0.385951\pi$
$281$	11.7569	0.701355	0.350678	+	0.936496i	$0.385951\pi$
$282$	−12.6501	−0.753300
$283$	−3.87935	−0.230604	−0.115302	−	0.993331i	$-0.536784\pi$
$283$	−3.87935	−0.230604	−0.115302	+	0.993331i	$0.536784\pi$
$284$	11.4855	0.681538
$285$	11.9403	0.707285
$286$	0	0
$287$	1.82473	0.107710
$288$	−5.71258	−0.336617
$289$	−16.7793	−0.987019
$290$	−2.63313	−0.154623
$291$	49.4441	2.89846
$292$	−12.2547	−0.717152
$293$	30.6082	1.78815	0.894075	−	0.447916i	$-0.147834\pi$
$293$	30.6082	1.78815	0.894075	+	0.447916i	$0.147834\pi$
$294$	2.95171	0.172147
$295$	13.0380	0.759103
$296$	4.56071	0.265086
$297$	0	0
$298$	13.0357	0.755137
$299$	44.6567	2.58257
$300$	−2.95171	−0.170417
$301$	−0.790717	−0.0455762
$302$	−9.17018	−0.527684
$303$	−25.2972	−1.45329
$304$	4.04523	0.232010
$305$	−6.69651	−0.383441
$306$	−2.68360	−0.153411
$307$	2.56751	0.146536	0.0732678	−	0.997312i	$-0.476657\pi$
$307$	2.56751	0.146536	0.0732678	+	0.997312i	$0.476657\pi$
$308$	0	0
$309$	−7.08814	−0.403230
$310$	−3.22145	−0.182966
$311$	−32.5284	−1.84452	−0.922259	−	0.386573i	$-0.873659\pi$
$311$	−32.5284	−1.84452	−0.922259	+	0.386573i	$0.873659\pi$
$312$	−17.1224	−0.969367
$313$	−7.78739	−0.440169	−0.220085	−	0.975481i	$-0.570633\pi$
$313$	−7.78739	−0.440169	−0.220085	+	0.975481i	$0.570633\pi$
$314$	−9.06306	−0.511458
$315$	5.71258	0.321867
$316$	−3.95281	−0.222363
$317$	−17.4682	−0.981111	−0.490556	−	0.871410i	$-0.663206\pi$
$317$	−17.4682	−0.981111	−0.490556	+	0.871410i	$0.663206\pi$
$318$	41.1471	2.30741
$319$	0	0
$320$	−1.00000	−0.0559017
$321$	17.8922	0.998644
$322$	−7.69830	−0.429009
$323$	1.90033	0.105737
$324$	6.49582	0.360879
$325$	−5.80086	−0.321774
$326$	1.69719	0.0939989
$327$	32.1075	1.77555
$328$	1.82473	0.100754
$329$	4.28567	0.236277
$330$	0	0
$331$	−2.01742	−0.110887	−0.0554437	−	0.998462i	$-0.517657\pi$
$331$	−2.01742	−0.110887	−0.0554437	+	0.998462i	$0.517657\pi$
$332$	9.44801	0.518527
$333$	−26.0534	−1.42772
$334$	19.8542	1.08638
$335$	6.73018	0.367709
$336$	2.95171	0.161029
$337$	−23.3327	−1.27102	−0.635508	−	0.772095i	$-0.719209\pi$
$337$	−23.3327	−1.27102	−0.635508	+	0.772095i	$0.719209\pi$
$338$	−20.6499	−1.12321
$339$	19.2631	1.04623
$340$	−0.469771	−0.0254769
$341$	0	0
$342$	−23.1087	−1.24958
$343$	−1.00000	−0.0539949
$344$	−0.790717	−0.0426326
$345$	−22.7231	−1.22337
$346$	−12.5185	−0.673001
$347$	−8.21232	−0.440860	−0.220430	−	0.975403i	$-0.570746\pi$
$347$	−8.21232	−0.440860	−0.220430	+	0.975403i	$0.570746\pi$
$348$	7.77222	0.416635
$349$	17.6030	0.942266	0.471133	−	0.882062i	$-0.343845\pi$
$349$	17.6030	0.942266	0.471133	+	0.882062i	$0.343845\pi$
$350$	1.00000	0.0534522
$351$	46.4460	2.47910
$352$	0	0
$353$	−34.5532	−1.83908	−0.919541	−	0.392994i	$-0.871439\pi$
$353$	−34.5532	−1.83908	−0.919541	+	0.392994i	$0.871439\pi$
$354$	−38.4845	−2.04543
$355$	−11.4855	−0.609586
$356$	−11.2766	−0.597659
$357$	1.38663	0.0733880
$358$	16.2877	0.860829
$359$	8.36302	0.441383	0.220692	−	0.975344i	$-0.429169\pi$
$359$	8.36302	0.441383	0.220692	+	0.975344i	$0.429169\pi$
$360$	5.71258	0.301079
$361$	−2.63610	−0.138742
$362$	11.8382	0.622200
$363$	0	0
$364$	5.80086	0.304048
$365$	12.2547	0.641441
$366$	19.7661	1.03319
$367$	17.2697	0.901470	0.450735	−	0.892658i	$-0.351162\pi$
$367$	17.2697	0.901470	0.450735	+	0.892658i	$0.351162\pi$
$368$	−7.69830	−0.401302
$369$	−10.4239	−0.542647
$370$	−4.56071	−0.237100
$371$	−13.9401	−0.723733
$372$	9.50878	0.493007
$373$	22.9242	1.18697	0.593486	−	0.804844i	$-0.297751\pi$
$373$	22.9242	1.18697	0.593486	+	0.804844i	$0.297751\pi$
$374$	0	0
$375$	2.95171	0.152426
$376$	4.28567	0.221017
$377$	15.2744	0.786671
$378$	−8.00674	−0.411822
$379$	3.81880	0.196159	0.0980793	−	0.995179i	$-0.468730\pi$
$379$	3.81880	0.196159	0.0980793	+	0.995179i	$0.468730\pi$
$380$	−4.04523	−0.207516
$381$	−11.9466	−0.612044
$382$	27.3346	1.39856
$383$	−11.7374	−0.599755	−0.299878	−	0.953978i	$-0.596946\pi$
$383$	−11.7374	−0.599755	−0.299878	+	0.953978i	$0.596946\pi$
$384$	2.95171	0.150629
$385$	0	0
$386$	16.8533	0.857810
$387$	4.51703	0.229614
$388$	−16.7510	−0.850403
$389$	−7.97138	−0.404165	−0.202082	−	0.979369i	$-0.564771\pi$
$389$	−7.97138	−0.404165	−0.202082	+	0.979369i	$0.564771\pi$
$390$	17.1224	0.867028
$391$	−3.61644	−0.182891
$392$	−1.00000	−0.0505076
$393$	26.7401	1.34886
$394$	−4.65860	−0.234697
$395$	3.95281	0.198888
$396$	0	0
$397$	0.554176	0.0278133	0.0139066	−	0.999903i	$-0.495573\pi$
$397$	0.554176	0.0278133	0.0139066	+	0.999903i	$0.495573\pi$
$398$	12.2080	0.611933
$399$	11.9403	0.597765
$400$	1.00000	0.0500000
$401$	−11.8420	−0.591360	−0.295680	−	0.955287i	$-0.595546\pi$
$401$	−11.8420	−0.591360	−0.295680	+	0.955287i	$0.595546\pi$
$402$	−19.8655	−0.990803
$403$	18.6872	0.930874
$404$	8.57037	0.426392
$405$	−6.49582	−0.322780
$406$	−2.63313	−0.130680
$407$	0	0
$408$	1.38663	0.0686482
$409$	8.37786	0.414259	0.207129	−	0.978314i	$-0.433588\pi$
$409$	8.37786	0.414259	0.207129	+	0.978314i	$0.433588\pi$
$410$	−1.82473	−0.0901169
$411$	−52.0240	−2.56615
$412$	2.40137	0.118307
$413$	13.0380	0.641559
$414$	43.9771	2.16136
$415$	−9.44801	−0.463784
$416$	5.80086	0.284410
$417$	55.0987	2.69820
$418$	0	0
$419$	−25.1963	−1.23092	−0.615461	−	0.788167i	$-0.711030\pi$
$419$	−25.1963	−1.23092	−0.615461	+	0.788167i	$0.711030\pi$
$420$	−2.95171	−0.144029
$421$	27.0334	1.31753	0.658764	−	0.752349i	$-0.271079\pi$
$421$	27.0334	1.31753	0.658764	+	0.752349i	$0.271079\pi$
$422$	−7.86890	−0.383052
$423$	−24.4823	−1.19037
$424$	−13.9401	−0.676990
$425$	0.469771	0.0227872
$426$	33.9018	1.64255
$427$	−6.69651	−0.324067
$428$	−6.06164	−0.293000
$429$	0	0
$430$	0.790717	0.0381318
$431$	−16.4280	−0.791310	−0.395655	−	0.918399i	$-0.629482\pi$
$431$	−16.4280	−0.791310	−0.395655	+	0.918399i	$0.629482\pi$
$432$	−8.00674	−0.385224
$433$	−11.4901	−0.552181	−0.276090	−	0.961132i	$-0.589039\pi$
$433$	−11.4901	−0.552181	−0.276090	+	0.961132i	$0.589039\pi$
$434$	−3.22145	−0.154634
$435$	−7.77222	−0.372649
$436$	−10.8776	−0.520942
$437$	−31.1414	−1.48970
$438$	−36.1723	−1.72838
$439$	−36.6689	−1.75011	−0.875056	−	0.484022i	$-0.839176\pi$
$439$	−36.6689	−1.75011	−0.875056	+	0.484022i	$0.839176\pi$
$440$	0	0
$441$	5.71258	0.272028
$442$	2.72507	0.129619
$443$	−11.4883	−0.545824	−0.272912	−	0.962039i	$-0.587987\pi$
$443$	−11.4883	−0.545824	−0.272912	+	0.962039i	$0.587987\pi$
$444$	13.4619	0.638872
$445$	11.2766	0.534562
$446$	23.8654	1.13006
$447$	38.4775	1.81992
$448$	−1.00000	−0.0472456
$449$	−1.18122	−0.0557451	−0.0278725	−	0.999611i	$-0.508873\pi$
$449$	−1.18122	−0.0557451	−0.0278725	+	0.999611i	$0.508873\pi$
$450$	−5.71258	−0.269294
$451$	0	0
$452$	−6.52609	−0.306961
$453$	−27.0677	−1.27175
$454$	22.7047	1.06558
$455$	−5.80086	−0.271948
$456$	11.9403	0.559158
$457$	11.1913	0.523509	0.261754	−	0.965135i	$-0.415699\pi$
$457$	11.1913	0.523509	0.261754	+	0.965135i	$0.415699\pi$
$458$	15.8703	0.741572
$459$	−3.76133	−0.175564
$460$	7.69830	0.358935
$461$	−0.438159	−0.0204071	−0.0102036	−	0.999948i	$-0.503248\pi$
$461$	−0.438159	−0.0204071	−0.0102036	+	0.999948i	$0.503248\pi$
$462$	0	0
$463$	20.1741	0.937570	0.468785	−	0.883312i	$-0.344692\pi$
$463$	20.1741	0.937570	0.468785	+	0.883312i	$0.344692\pi$
$464$	−2.63313	−0.122240
$465$	−9.50878	−0.440959
$466$	−29.2428	−1.35465
$467$	3.27449	0.151525	0.0757627	−	0.997126i	$-0.475861\pi$
$467$	3.27449	0.151525	0.0757627	+	0.997126i	$0.475861\pi$
$468$	−33.1379	−1.53180
$469$	6.73018	0.310771
$470$	−4.28567	−0.197683
$471$	−26.7515	−1.23264
$472$	13.0380	0.600124
$473$	0	0
$474$	−11.6675	−0.535908
$475$	4.04523	0.185608
$476$	−0.469771	−0.0215319
$477$	79.6338	3.64618
$478$	−8.72767	−0.399194
$479$	27.0594	1.23638	0.618188	−	0.786030i	$-0.287867\pi$
$479$	27.0594	1.23638	0.618188	+	0.786030i	$0.287867\pi$
$480$	−2.95171	−0.134726
$481$	26.4560	1.20629
$482$	−9.58858	−0.436748
$483$	−22.7231	−1.03394
$484$	0	0
$485$	16.7510	0.760624
$486$	−4.84646	−0.219840
$487$	25.7086	1.16497	0.582484	−	0.812842i	$-0.302081\pi$
$487$	25.7086	1.16497	0.582484	+	0.812842i	$0.302081\pi$
$488$	−6.69651	−0.303137
$489$	5.00962	0.226543
$490$	1.00000	0.0451754
$491$	29.0080	1.30911	0.654557	−	0.756013i	$-0.272855\pi$
$491$	29.0080	1.30911	0.654557	+	0.756013i	$0.272855\pi$
$492$	5.38607	0.242823
$493$	−1.23697	−0.0557101
$494$	23.4658	1.05578
$495$	0	0
$496$	−3.22145	−0.144647
$497$	−11.4855	−0.515194
$498$	27.8878	1.24968
$499$	22.8099	1.02111	0.510557	−	0.859844i	$-0.329439\pi$
$499$	22.8099	1.02111	0.510557	+	0.859844i	$0.329439\pi$
$500$	−1.00000	−0.0447214
$501$	58.6039	2.61823
$502$	−2.70064	−0.120535
$503$	28.1524	1.25525	0.627626	−	0.778515i	$-0.284027\pi$
$503$	28.1524	1.25525	0.627626	+	0.778515i	$0.284027\pi$
$504$	5.71258	0.254458
$505$	−8.57037	−0.381377
$506$	0	0
$507$	−60.9526	−2.70700
$508$	4.04736	0.179572
$509$	35.7941	1.58655	0.793273	−	0.608866i	$-0.208375\pi$
$509$	35.7941	1.58655	0.793273	+	0.608866i	$0.208375\pi$
$510$	−1.38663	−0.0614008
$511$	12.2547	0.542116
$512$	−1.00000	−0.0441942
$513$	−32.3891	−1.43001
$514$	−8.92845	−0.393817
$515$	−2.40137	−0.105817
$516$	−2.33397	−0.102747
$517$	0	0
$518$	−4.56071	−0.200386
$519$	−36.9511	−1.62197
$520$	−5.80086	−0.254384
$521$	−19.4828	−0.853556	−0.426778	−	0.904356i	$-0.640351\pi$
$521$	−19.4828	−0.853556	−0.426778	+	0.904356i	$0.640351\pi$
$522$	15.0419	0.658368
$523$	25.7545	1.12616	0.563082	−	0.826401i	$-0.309616\pi$
$523$	25.7545	1.12616	0.563082	+	0.826401i	$0.309616\pi$
$524$	−9.05921	−0.395753
$525$	2.95171	0.128823
$526$	0.182846	0.00797248
$527$	−1.51334	−0.0659222
$528$	0	0
$529$	36.2638	1.57669
$530$	13.9401	0.605519
$531$	−74.4808	−3.23219
$532$	−4.04523	−0.175383
$533$	10.5850	0.458487
$534$	−33.2852	−1.44039
$535$	6.06164	0.262067
$536$	6.73018	0.290700
$537$	48.0764	2.07465
$538$	5.71539	0.246408
$539$	0	0
$540$	8.00674	0.344555
$541$	13.1935	0.567234	0.283617	−	0.958938i	$-0.408466\pi$
$541$	13.1935	0.567234	0.283617	+	0.958938i	$0.408466\pi$
$542$	−3.10080	−0.133191
$543$	34.9428	1.49954
$544$	−0.469771	−0.0201413
$545$	10.8776	0.465945
$546$	17.1224	0.732773
$547$	−33.7809	−1.44437	−0.722184	−	0.691701i	$-0.756861\pi$
$547$	−33.7809	−1.44437	−0.722184	+	0.691701i	$0.756861\pi$
$548$	17.6250	0.752905
$549$	38.2543	1.63266
$550$	0	0
$551$	−10.6516	−0.453774
$552$	−22.7231	−0.967161
$553$	3.95281	0.168091
$554$	21.4930	0.913148
$555$	−13.4619	−0.571425
$556$	−18.6667	−0.791646
$557$	25.1981	1.06768	0.533839	−	0.845586i	$-0.320749\pi$
$557$	25.1981	1.06768	0.533839	+	0.845586i	$0.320749\pi$
$558$	18.4028	0.779052
$559$	−4.58684	−0.194003
$560$	1.00000	0.0422577
$561$	0	0
$562$	−11.7569	−0.495933
$563$	−40.9478	−1.72574	−0.862872	−	0.505423i	$-0.831337\pi$
$563$	−40.9478	−1.72574	−0.862872	+	0.505423i	$0.831337\pi$
$564$	12.6501	0.532664
$565$	6.52609	0.274555
$566$	3.87935	0.163061
$567$	−6.49582	−0.272799
$568$	−11.4855	−0.481920
$569$	35.9316	1.50633	0.753167	−	0.657830i	$-0.228525\pi$
$569$	35.9316	1.50633	0.753167	+	0.657830i	$0.228525\pi$
$570$	−11.9403	−0.500126
$571$	−8.88506	−0.371828	−0.185914	−	0.982566i	$-0.559525\pi$
$571$	−8.88506	−0.371828	−0.185914	+	0.982566i	$0.559525\pi$
$572$	0	0
$573$	80.6839	3.37062
$574$	−1.82473	−0.0761627
$575$	−7.69830	−0.321041
$576$	5.71258	0.238024
$577$	−25.1721	−1.04793	−0.523965	−	0.851740i	$-0.675548\pi$
$577$	−25.1721	−1.04793	−0.523965	+	0.851740i	$0.675548\pi$
$578$	16.7793	0.697928
$579$	49.7460	2.06737
$580$	2.63313	0.109335
$581$	−9.44801	−0.391969
$582$	−49.4441	−2.04952
$583$	0	0
$584$	12.2547	0.507103
$585$	33.1379	1.37008
$586$	−30.6082	−1.26441
$587$	37.3063	1.53979	0.769897	−	0.638168i	$-0.220307\pi$
$587$	37.3063	1.53979	0.769897	+	0.638168i	$0.220307\pi$
$588$	−2.95171	−0.121726
$589$	−13.0315	−0.536954
$590$	−13.0380	−0.536767
$591$	−13.7508	−0.565633
$592$	−4.56071	−0.187444
$593$	12.7375	0.523065	0.261533	−	0.965195i	$-0.415772\pi$
$593$	12.7375	0.523065	0.261533	+	0.965195i	$0.415772\pi$
$594$	0	0
$595$	0.469771	0.0192587
$596$	−13.0357	−0.533962
$597$	36.0345	1.47480
$598$	−44.6567	−1.82615
$599$	−6.61890	−0.270441	−0.135220	−	0.990816i	$-0.543174\pi$
$599$	−6.61890	−0.270441	−0.135220	+	0.990816i	$0.543174\pi$
$600$	2.95171	0.120503
$601$	34.5976	1.41126	0.705632	−	0.708578i	$-0.250663\pi$
$601$	34.5976	1.41126	0.705632	+	0.708578i	$0.250663\pi$
$602$	0.790717	0.0322272
$603$	−38.4467	−1.56567
$604$	9.17018	0.373129
$605$	0	0
$606$	25.2972	1.02763
$607$	25.0429	1.01646	0.508230	−	0.861221i	$-0.330300\pi$
$607$	25.0429	1.01646	0.508230	+	0.861221i	$0.330300\pi$
$608$	−4.04523	−0.164056
$609$	−7.77222	−0.314946
$610$	6.69651	0.271134
$611$	24.8606	1.00575
$612$	2.68360	0.108478
$613$	−17.7799	−0.718123	−0.359062	−	0.933314i	$-0.616903\pi$
$613$	−17.7799	−0.718123	−0.359062	+	0.933314i	$0.616903\pi$
$614$	−2.56751	−0.103616
$615$	−5.38607	−0.217187
$616$	0	0
$617$	30.5946	1.23169	0.615847	−	0.787866i	$-0.288814\pi$
$617$	30.5946	1.23169	0.615847	+	0.787866i	$0.288814\pi$
$618$	7.08814	0.285127
$619$	−14.3280	−0.575890	−0.287945	−	0.957647i	$-0.592972\pi$
$619$	−14.3280	−0.575890	−0.287945	+	0.957647i	$0.592972\pi$
$620$	3.22145	0.129376
$621$	61.6383	2.47346
$622$	32.5284	1.30427
$623$	11.2766	0.451788
$624$	17.1224	0.685446
$625$	1.00000	0.0400000
$626$	7.78739	0.311247
$627$	0	0
$628$	9.06306	0.361655
$629$	−2.14249	−0.0854266
$630$	−5.71258	−0.227595
$631$	13.0319	0.518793	0.259397	−	0.965771i	$-0.416476\pi$
$631$	13.0319	0.518793	0.259397	+	0.965771i	$0.416476\pi$
$632$	3.95281	0.157234
$633$	−23.2267	−0.923178
$634$	17.4682	0.693751
$635$	−4.04736	−0.160614
$636$	−41.1471	−1.63159
$637$	−5.80086	−0.229838
$638$	0	0
$639$	65.6117	2.59556
$640$	1.00000	0.0395285
$641$	−26.7435	−1.05630	−0.528152	−	0.849150i	$-0.677115\pi$
$641$	−26.7435	−1.05630	−0.528152	+	0.849150i	$0.677115\pi$
$642$	−17.8922	−0.706148
$643$	7.38192	0.291115	0.145557	−	0.989350i	$-0.453502\pi$
$643$	7.38192	0.291115	0.145557	+	0.989350i	$0.453502\pi$
$644$	7.69830	0.303355
$645$	2.33397	0.0918998
$646$	−1.90033	−0.0747676
$647$	9.10349	0.357895	0.178948	−	0.983859i	$-0.442731\pi$
$647$	9.10349	0.357895	0.178948	+	0.983859i	$0.442731\pi$
$648$	−6.49582	−0.255180
$649$	0	0
$650$	5.80086	0.227528
$651$	−9.50878	−0.372678
$652$	−1.69719	−0.0664672
$653$	36.9634	1.44649	0.723244	−	0.690592i	$-0.242650\pi$
$653$	36.9634	1.44649	0.723244	+	0.690592i	$0.242650\pi$
$654$	−32.1075	−1.25550
$655$	9.05921	0.353973
$656$	−1.82473	−0.0712437
$657$	−70.0060	−2.73119
$658$	−4.28567	−0.167073
$659$	47.4959	1.85018	0.925089	−	0.379750i	$-0.123990\pi$
$659$	47.4959	1.85018	0.925089	+	0.379750i	$0.123990\pi$
$660$	0	0
$661$	23.6252	0.918915	0.459457	−	0.888200i	$-0.348044\pi$
$661$	23.6252	0.918915	0.459457	+	0.888200i	$0.348044\pi$
$662$	2.01742	0.0784092
$663$	8.04362	0.312388
$664$	−9.44801	−0.366654
$665$	4.04523	0.156867
$666$	26.0534	1.00955
$667$	20.2706	0.784881
$668$	−19.8542	−0.768183
$669$	70.4436	2.72351
$670$	−6.73018	−0.260010
$671$	0	0
$672$	−2.95171	−0.113865
$673$	14.0368	0.541081	0.270540	−	0.962709i	$-0.412798\pi$
$673$	14.0368	0.541081	0.270540	+	0.962709i	$0.412798\pi$
$674$	23.3327	0.898744
$675$	−8.00674	−0.308180
$676$	20.6499	0.794229
$677$	42.3578	1.62794	0.813972	−	0.580904i	$-0.197301\pi$
$677$	42.3578	1.62794	0.813972	+	0.580904i	$0.197301\pi$
$678$	−19.2631	−0.739795
$679$	16.7510	0.642845
$680$	0.469771	0.0180149
$681$	67.0176	2.56812
$682$	0	0
$683$	25.5960	0.979402	0.489701	−	0.871890i	$-0.337106\pi$
$683$	25.5960	0.979402	0.489701	+	0.871890i	$0.337106\pi$
$684$	23.1087	0.883583
$685$	−17.6250	−0.673418
$686$	1.00000	0.0381802
$687$	46.8446	1.78723
$688$	0.790717	0.0301458
$689$	−80.8644	−3.08069
$690$	22.7231	0.865055
$691$	45.7118	1.73896	0.869478	−	0.493971i	$-0.164455\pi$
$691$	45.7118	1.73896	0.869478	+	0.493971i	$0.164455\pi$
$692$	12.5185	0.475884
$693$	0	0
$694$	8.21232	0.311735
$695$	18.6667	0.708070
$696$	−7.77222	−0.294605
$697$	−0.857205	−0.0324689
$698$	−17.6030	−0.666282
$699$	−86.3162	−3.26478
$700$	−1.00000	−0.0377964
$701$	37.9328	1.43270	0.716351	−	0.697740i	$-0.245811\pi$
$701$	37.9328	1.43270	0.716351	+	0.697740i	$0.245811\pi$
$702$	−46.4460	−1.75299
$703$	−18.4491	−0.695821
$704$	0	0
$705$	−12.6501	−0.476429
$706$	34.5532	1.30043
$707$	−8.57037	−0.322322
$708$	38.4845	1.44633
$709$	43.8767	1.64782	0.823911	−	0.566718i	$-0.191787\pi$
$709$	43.8767	1.64782	0.823911	+	0.566718i	$0.191787\pi$
$710$	11.4855	0.431042
$711$	−22.5808	−0.846844
$712$	11.2766	0.422609
$713$	24.7997	0.928755
$714$	−1.38663	−0.0518932
$715$	0	0
$716$	−16.2877	−0.608698
$717$	−25.7615	−0.962082
$718$	−8.36302	−0.312105
$719$	−36.3739	−1.35652	−0.678259	−	0.734823i	$-0.737265\pi$
$719$	−36.3739	−1.35652	−0.678259	+	0.734823i	$0.737265\pi$
$720$	−5.71258	−0.212895
$721$	−2.40137	−0.0894316
$722$	2.63610	0.0981056
$723$	−28.3027	−1.05259
$724$	−11.8382	−0.439962
$725$	−2.63313	−0.0977919
$726$	0	0
$727$	0.665574	0.0246848	0.0123424	−	0.999924i	$-0.496071\pi$
$727$	0.665574	0.0246848	0.0123424	+	0.999924i	$0.496071\pi$
$728$	−5.80086	−0.214994
$729$	−33.7928	−1.25158
$730$	−12.2547	−0.453567
$731$	0.371456	0.0137388
$732$	−19.7661	−0.730578
$733$	−18.1648	−0.670932	−0.335466	−	0.942052i	$-0.608894\pi$
$733$	−18.1648	−0.670932	−0.335466	+	0.942052i	$0.608894\pi$
$734$	−17.2697	−0.637435
$735$	2.95171	0.108875
$736$	7.69830	0.283763
$737$	0	0
$738$	10.4239	0.383709
$739$	−23.2301	−0.854533	−0.427267	−	0.904126i	$-0.640523\pi$
$739$	−23.2301	−0.854533	−0.427267	+	0.904126i	$0.640523\pi$
$740$	4.56071	0.167655
$741$	69.2642	2.54448
$742$	13.9401	0.511757
$743$	14.1815	0.520270	0.260135	−	0.965572i	$-0.416233\pi$
$743$	14.1815	0.520270	0.260135	+	0.965572i	$0.416233\pi$
$744$	−9.50878	−0.348609
$745$	13.0357	0.477590
$746$	−22.9242	−0.839316
$747$	53.9725	1.97475
$748$	0	0
$749$	6.06164	0.221487
$750$	−2.95171	−0.107781
$751$	−28.4416	−1.03785	−0.518924	−	0.854820i	$-0.673667\pi$
$751$	−28.4416	−1.03785	−0.518924	+	0.854820i	$0.673667\pi$
$752$	−4.28567	−0.156282
$753$	−7.97150	−0.290498
$754$	−15.2744	−0.556260
$755$	−9.17018	−0.333737
$756$	8.00674	0.291202
$757$	39.1587	1.42325	0.711623	−	0.702561i	$-0.247960\pi$
$757$	39.1587	1.42325	0.711623	+	0.702561i	$0.247960\pi$
$758$	−3.81880	−0.138705
$759$	0	0
$760$	4.04523	0.146736
$761$	13.1808	0.477804	0.238902	−	0.971044i	$-0.423213\pi$
$761$	13.1808	0.477804	0.238902	+	0.971044i	$0.423213\pi$
$762$	11.9466	0.432780
$763$	10.8776	0.393795
$764$	−27.3346	−0.988933
$765$	−2.68360	−0.0970259
$766$	11.7374	0.424091
$767$	75.6317	2.73090
$768$	−2.95171	−0.106511
$769$	−8.58896	−0.309726	−0.154863	−	0.987936i	$-0.549494\pi$
$769$	−8.58896	−0.309726	−0.154863	+	0.987936i	$0.549494\pi$
$770$	0	0
$771$	−26.3542	−0.949122
$772$	−16.8533	−0.606564
$773$	3.31546	0.119249	0.0596244	−	0.998221i	$-0.481010\pi$
$773$	3.31546	0.119249	0.0596244	+	0.998221i	$0.481010\pi$
$774$	−4.51703	−0.162361
$775$	−3.22145	−0.115718
$776$	16.7510	0.601326
$777$	−13.4619	−0.482942
$778$	7.97138	0.285788
$779$	−7.38145	−0.264468
$780$	−17.1224	−0.613082
$781$	0	0
$782$	3.61644	0.129323
$783$	21.0828	0.753436
$784$	1.00000	0.0357143
$785$	−9.06306	−0.323474
$786$	−26.7401	−0.953789
$787$	−20.0844	−0.715933	−0.357966	−	0.933735i	$-0.616530\pi$
$787$	−20.0844	−0.715933	−0.357966	+	0.933735i	$0.616530\pi$
$788$	4.65860	0.165956
$789$	0.539709	0.0192141
$790$	−3.95281	−0.140635
$791$	6.52609	0.232041
$792$	0	0
$793$	−38.8455	−1.37944
$794$	−0.554176	−0.0196670
$795$	41.1471	1.45934
$796$	−12.2080	−0.432702
$797$	−21.2743	−0.753575	−0.376788	−	0.926300i	$-0.622971\pi$
$797$	−21.2743	−0.753575	−0.376788	+	0.926300i	$0.622971\pi$
$798$	−11.9403	−0.422683
$799$	−2.01328	−0.0712249
$800$	−1.00000	−0.0353553
$801$	−64.4185	−2.27611
$802$	11.8420	0.418155
$803$	0	0
$804$	19.8655	0.700603
$805$	−7.69830	−0.271329
$806$	−18.6872	−0.658227
$807$	16.8702	0.593858
$808$	−8.57037	−0.301505
$809$	−5.01561	−0.176339	−0.0881697	−	0.996105i	$-0.528102\pi$
$809$	−5.01561	−0.176339	−0.0881697	+	0.996105i	$0.528102\pi$
$810$	6.49582	0.228240
$811$	−28.0624	−0.985404	−0.492702	−	0.870198i	$-0.663991\pi$
$811$	−28.0624	−0.985404	−0.492702	+	0.870198i	$0.663991\pi$
$812$	2.63313	0.0924046
$813$	−9.15266	−0.320998
$814$	0	0
$815$	1.69719	0.0594501
$816$	−1.38663	−0.0485416
$817$	3.19863	0.111906
$818$	−8.37786	−0.292925
$819$	33.1379	1.15793
$820$	1.82473	0.0637223
$821$	45.4548	1.58638	0.793192	−	0.608972i	$-0.208418\pi$
$821$	45.4548	1.58638	0.793192	+	0.608972i	$0.208418\pi$
$822$	52.0240	1.81455
$823$	−30.4918	−1.06288	−0.531438	−	0.847097i	$-0.678348\pi$
$823$	−30.4918	−1.06288	−0.531438	+	0.847097i	$0.678348\pi$
$824$	−2.40137	−0.0836556
$825$	0	0
$826$	−13.0380	−0.453651
$827$	34.9347	1.21480	0.607399	−	0.794397i	$-0.292213\pi$
$827$	34.9347	1.21480	0.607399	+	0.794397i	$0.292213\pi$
$828$	−43.9771	−1.52831
$829$	−36.8368	−1.27939	−0.639697	−	0.768627i	$-0.720940\pi$
$829$	−36.8368	−1.27939	−0.639697	+	0.768627i	$0.720940\pi$
$830$	9.44801	0.327945
$831$	63.4409	2.20074
$832$	−5.80086	−0.201109
$833$	0.469771	0.0162766
$834$	−55.0987	−1.90791
$835$	19.8542	0.687084
$836$	0	0
$837$	25.7933	0.891547
$838$	25.1963	0.870393
$839$	−12.0264	−0.415198	−0.207599	−	0.978214i	$-0.566565\pi$
$839$	−12.0264	−0.415198	−0.207599	+	0.978214i	$0.566565\pi$
$840$	2.95171	0.101844
$841$	−22.0666	−0.760919
$842$	−27.0334	−0.931633
$843$	−34.7028	−1.19523
$844$	7.86890	0.270859
$845$	−20.6499	−0.710380
$846$	24.4823	0.841717
$847$	0	0
$848$	13.9401	0.478704
$849$	11.4507	0.392988
$850$	−0.469771	−0.0161130
$851$	35.1097	1.20354
$852$	−33.9018	−1.16146
$853$	13.7303	0.470116	0.235058	−	0.971981i	$-0.424472\pi$
$853$	13.7303	0.470116	0.235058	+	0.971981i	$0.424472\pi$
$854$	6.69651	0.229150
$855$	−23.1087	−0.790301
$856$	6.06164	0.207183
$857$	−25.3293	−0.865233	−0.432616	−	0.901578i	$-0.642409\pi$
$857$	−25.3293	−0.865233	−0.432616	+	0.901578i	$0.642409\pi$
$858$	0	0
$859$	−43.9737	−1.50036	−0.750181	−	0.661232i	$-0.770034\pi$
$859$	−43.9737	−1.50036	−0.750181	+	0.661232i	$0.770034\pi$
$860$	−0.790717	−0.0269632
$861$	−5.38607	−0.183557
$862$	16.4280	0.559541
$863$	−15.1797	−0.516723	−0.258361	−	0.966048i	$-0.583183\pi$
$863$	−15.1797	−0.516723	−0.258361	+	0.966048i	$0.583183\pi$
$864$	8.00674	0.272395
$865$	−12.5185	−0.425643
$866$	11.4901	0.390451
$867$	49.5276	1.68205
$868$	3.22145	0.109343
$869$	0	0
$870$	7.77222	0.263503
$871$	39.0408	1.32285
$872$	10.8776	0.368362
$873$	−95.6914	−3.23866
$874$	31.1414	1.05337
$875$	1.00000	0.0338062
$876$	36.1723	1.22215
$877$	42.4873	1.43469	0.717346	−	0.696717i	$-0.245356\pi$
$877$	42.4873	1.43469	0.717346	+	0.696717i	$0.245356\pi$
$878$	36.6689	1.23752
$879$	−90.3465	−3.04731
$880$	0	0
$881$	51.3494	1.73000	0.865002	−	0.501768i	$-0.167317\pi$
$881$	51.3494	1.73000	0.865002	+	0.501768i	$0.167317\pi$
$882$	−5.71258	−0.192353
$883$	−4.89466	−0.164718	−0.0823592	−	0.996603i	$-0.526245\pi$
$883$	−4.89466	−0.164718	−0.0823592	+	0.996603i	$0.526245\pi$
$884$	−2.72507	−0.0916541
$885$	−38.4845	−1.29364
$886$	11.4883	0.385956
$887$	−52.4443	−1.76091	−0.880454	−	0.474131i	$-0.842762\pi$
$887$	−52.4443	−1.76091	−0.880454	+	0.474131i	$0.842762\pi$
$888$	−13.4619	−0.451751
$889$	−4.04736	−0.135744
$890$	−11.2766	−0.377993
$891$	0	0
$892$	−23.8654	−0.799071
$893$	−17.3365	−0.580145
$894$	−38.4775	−1.28688
$895$	16.2877	0.544436
$896$	1.00000	0.0334077
$897$	−131.814	−4.40113
$898$	1.18122	0.0394177
$899$	8.48248	0.282907
$900$	5.71258	0.190419
$901$	6.54865	0.218167
$902$	0	0
$903$	2.33397	0.0776695
$904$	6.52609	0.217054
$905$	11.8382	0.393514
$906$	27.0677	0.899264
$907$	−45.5122	−1.51121	−0.755604	−	0.655028i	$-0.772657\pi$
$907$	−45.5122	−1.51121	−0.755604	+	0.655028i	$0.772657\pi$
$908$	−22.7047	−0.753482
$909$	48.9589	1.62387
$910$	5.80086	0.192297
$911$	29.1249	0.964951	0.482476	−	0.875909i	$-0.339738\pi$
$911$	29.1249	0.964951	0.482476	+	0.875909i	$0.339738\pi$
$912$	−11.9403	−0.395384
$913$	0	0
$914$	−11.1913	−0.370176
$915$	19.7661	0.653449
$916$	−15.8703	−0.524371
$917$	9.05921	0.299161
$918$	3.76133	0.124142
$919$	8.14159	0.268566	0.134283	−	0.990943i	$-0.457127\pi$
$919$	8.14159	0.268566	0.134283	+	0.990943i	$0.457127\pi$
$920$	−7.69830	−0.253805
$921$	−7.57854	−0.249721
$922$	0.438159	0.0144300
$923$	−66.6256	−2.19301
$924$	0	0
$925$	−4.56071	−0.149955
$926$	−20.1741	−0.662962
$927$	13.7180	0.450559
$928$	2.63313	0.0864366
$929$	23.3718	0.766804	0.383402	−	0.923582i	$-0.374752\pi$
$929$	23.3718	0.766804	0.383402	+	0.923582i	$0.374752\pi$
$930$	9.50878	0.311805
$931$	4.04523	0.132577
$932$	29.2428	0.957879
$933$	96.0144	3.14337
$934$	−3.27449	−0.107145
$935$	0	0
$936$	33.1379	1.08314
$937$	−50.8782	−1.66212	−0.831059	−	0.556184i	$-0.812265\pi$
$937$	−50.8782	−1.66212	−0.831059	+	0.556184i	$0.812265\pi$
$938$	−6.73018	−0.219748
$939$	22.9861	0.750123
$940$	4.28567	0.139783
$941$	13.2045	0.430456	0.215228	−	0.976564i	$-0.430951\pi$
$941$	13.2045	0.430456	0.215228	+	0.976564i	$0.430951\pi$
$942$	26.7515	0.871611
$943$	14.0473	0.457443
$944$	−13.0380	−0.424352
$945$	−8.00674	−0.260459
$946$	0	0
$947$	0.766130	0.0248959	0.0124479	−	0.999923i	$-0.496038\pi$
$947$	0.766130	0.0248959	0.0124479	+	0.999923i	$0.496038\pi$
$948$	11.6675	0.378944
$949$	71.0878	2.30761
$950$	−4.04523	−0.131245
$951$	51.5610	1.67198
$952$	0.469771	0.0152254
$953$	7.42412	0.240491	0.120245	−	0.992744i	$-0.461632\pi$
$953$	7.42412	0.240491	0.120245	+	0.992744i	$0.461632\pi$
$954$	−79.6338	−2.57824
$955$	27.3346	0.884528
$956$	8.72767	0.282273
$957$	0	0
$958$	−27.0594	−0.874250
$959$	−17.6250	−0.569142
$960$	2.95171	0.0952660
$961$	−20.6223	−0.665234
$962$	−26.4560	−0.852976
$963$	−34.6276	−1.11586
$964$	9.58858	0.308828
$965$	16.8533	0.542527
$966$	22.7231	0.731105
$967$	−33.2841	−1.07035	−0.535173	−	0.844743i	$-0.679753\pi$
$967$	−33.2841	−1.07035	−0.535173	+	0.844743i	$0.679753\pi$
$968$	0	0
$969$	−5.60922	−0.180194
$970$	−16.7510	−0.537842
$971$	−18.9717	−0.608832	−0.304416	−	0.952539i	$-0.598461\pi$
$971$	−18.9717	−0.608832	−0.304416	+	0.952539i	$0.598461\pi$
$972$	4.84646	0.155450
$973$	18.6667	0.598428
$974$	−25.7086	−0.823757
$975$	17.1224	0.548357
$976$	6.69651	0.214350
$977$	44.7467	1.43157	0.715787	−	0.698319i	$-0.246068\pi$
$977$	44.7467	1.43157	0.715787	+	0.698319i	$0.246068\pi$
$978$	−5.00962	−0.160190
$979$	0	0
$980$	−1.00000	−0.0319438
$981$	−62.1391	−1.98395
$982$	−29.0080	−0.925683
$983$	0.984693	0.0314068	0.0157034	−	0.999877i	$-0.495001\pi$
$983$	0.984693	0.0314068	0.0157034	+	0.999877i	$0.495001\pi$
$984$	−5.38607	−0.171702
$985$	−4.65860	−0.148435
$986$	1.23697	0.0393930
$987$	−12.6501	−0.402656
$988$	−23.4658	−0.746547
$989$	−6.08718	−0.193561
$990$	0	0
$991$	−58.3261	−1.85279	−0.926395	−	0.376554i	$-0.877109\pi$
$991$	−58.3261	−1.85279	−0.926395	+	0.376554i	$0.877109\pi$
$992$	3.22145	0.102281
$993$	5.95483	0.188971
$994$	11.4855	0.364297
$995$	12.2080	0.387021
$996$	−27.8878	−0.883657
$997$	−32.9724	−1.04425	−0.522123	−	0.852870i	$-0.674860\pi$
$997$	−32.9724	−1.04425	−0.522123	+	0.852870i	$0.674860\pi$
$998$	−22.8099	−0.722036
$999$	36.5164	1.15533

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8470.2.a.cu.1.2		6
11.2	odd	10		770.2.n.h.631.1	yes	12
11.6	odd	10		770.2.n.h.421.1	✓	12
11.10	odd	2		8470.2.a.da.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.h.421.1	✓	12	11.6	odd	10
770.2.n.h.631.1	yes	12	11.2	odd	10
8470.2.a.cu.1.2		6	1.1	even	1	trivial
8470.2.a.da.1.2		6	11.10	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.95171 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.95171 q^{6} -1.00000 q^{7} -1.00000 q^{8} +5.71258 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.95171 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.95171 q^{6} -1.00000 q^{7} -1.00000 q^{8} +5.71258 q^{9} +1.00000 q^{10} -2.95171 q^{12} -5.80086 q^{13} +1.00000 q^{14} +2.95171 q^{15} +1.00000 q^{16} +0.469771 q^{17} -5.71258 q^{18} +4.04523 q^{19} -1.00000 q^{20} +2.95171 q^{21} -7.69830 q^{23} +2.95171 q^{24} +1.00000 q^{25} +5.80086 q^{26} -8.00674 q^{27} -1.00000 q^{28} -2.63313 q^{29} -2.95171 q^{30} -3.22145 q^{31} -1.00000 q^{32} -0.469771 q^{34} +1.00000 q^{35} +5.71258 q^{36} -4.56071 q^{37} -4.04523 q^{38} +17.1224 q^{39} +1.00000 q^{40} -1.82473 q^{41} -2.95171 q^{42} +0.790717 q^{43} -5.71258 q^{45} +7.69830 q^{46} -4.28567 q^{47} -2.95171 q^{48} +1.00000 q^{49} -1.00000 q^{50} -1.38663 q^{51} -5.80086 q^{52} +13.9401 q^{53} +8.00674 q^{54} +1.00000 q^{56} -11.9403 q^{57} +2.63313 q^{58} -13.0380 q^{59} +2.95171 q^{60} +6.69651 q^{61} +3.22145 q^{62} -5.71258 q^{63} +1.00000 q^{64} +5.80086 q^{65} -6.73018 q^{67} +0.469771 q^{68} +22.7231 q^{69} -1.00000 q^{70} +11.4855 q^{71} -5.71258 q^{72} -12.2547 q^{73} +4.56071 q^{74} -2.95171 q^{75} +4.04523 q^{76} -17.1224 q^{78} -3.95281 q^{79} -1.00000 q^{80} +6.49582 q^{81} +1.82473 q^{82} +9.44801 q^{83} +2.95171 q^{84} -0.469771 q^{85} -0.790717 q^{86} +7.77222 q^{87} -11.2766 q^{89} +5.71258 q^{90} +5.80086 q^{91} -7.69830 q^{92} +9.50878 q^{93} +4.28567 q^{94} -4.04523 q^{95} +2.95171 q^{96} -16.7510 q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} - 5 q^{3} + 6 q^{4} - 6 q^{5} + 5 q^{6} - 6 q^{7} - 6 q^{8} + 11 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 - 5 * q^3 + 6 * q^4 - 6 * q^5 + 5 * q^6 - 6 * q^7 - 6 * q^8 + 11 * q^9	\( 6 q - 6 q^{2} - 5 q^{3} + 6 q^{4} - 6 q^{5} + 5 q^{6} - 6 q^{7} - 6 q^{8} + 11 q^{9} + 6 q^{10} - 5 q^{12} + 6 q^{14} + 5 q^{15} + 6 q^{16} + 15 q^{17} - 11 q^{18} + 13 q^{19} - 6 q^{20} + 5 q^{21} - 2 q^{23} + 5 q^{24} + 6 q^{25} - 26 q^{27} - 6 q^{28} + 4 q^{29} - 5 q^{30} - 2 q^{31} - 6 q^{32} - 15 q^{34} + 6 q^{35} + 11 q^{36} - 13 q^{38} + 30 q^{39} + 6 q^{40} + 17 q^{41} - 5 q^{42} - 15 q^{43} - 11 q^{45} + 2 q^{46} - 18 q^{47} - 5 q^{48} + 6 q^{49} - 6 q^{50} - 6 q^{51} + 22 q^{53} + 26 q^{54} + 6 q^{56} + 2 q^{57} - 4 q^{58} - 7 q^{59} + 5 q^{60} + 20 q^{61} + 2 q^{62} - 11 q^{63} + 6 q^{64} - 29 q^{67} + 15 q^{68} + 12 q^{69} - 6 q^{70} - 2 q^{71} - 11 q^{72} - q^{73} - 5 q^{75} + 13 q^{76} - 30 q^{78} + 12 q^{79} - 6 q^{80} + 22 q^{81} - 17 q^{82} + 35 q^{83} + 5 q^{84} - 15 q^{85} + 15 q^{86} - 29 q^{89} + 11 q^{90} - 2 q^{92} + 8 q^{93} + 18 q^{94} - 13 q^{95} + 5 q^{96} - 19 q^{97} - 6 q^{98}+O(q^{100}) \) 6 * q - 6 * q^2 - 5 * q^3 + 6 * q^4 - 6 * q^5 + 5 * q^6 - 6 * q^7 - 6 * q^8 + 11 * q^9 + 6 * q^10 - 5 * q^12 + 6 * q^14 + 5 * q^15 + 6 * q^16 + 15 * q^17 - 11 * q^18 + 13 * q^19 - 6 * q^20 + 5 * q^21 - 2 * q^23 + 5 * q^24 + 6 * q^25 - 26 * q^27 - 6 * q^28 + 4 * q^29 - 5 * q^30 - 2 * q^31 - 6 * q^32 - 15 * q^34 + 6 * q^35 + 11 * q^36 - 13 * q^38 + 30 * q^39 + 6 * q^40 + 17 * q^41 - 5 * q^42 - 15 * q^43 - 11 * q^45 + 2 * q^46 - 18 * q^47 - 5 * q^48 + 6 * q^49 - 6 * q^50 - 6 * q^51 + 22 * q^53 + 26 * q^54 + 6 * q^56 + 2 * q^57 - 4 * q^58 - 7 * q^59 + 5 * q^60 + 20 * q^61 + 2 * q^62 - 11 * q^63 + 6 * q^64 - 29 * q^67 + 15 * q^68 + 12 * q^69 - 6 * q^70 - 2 * q^71 - 11 * q^72 - q^73 - 5 * q^75 + 13 * q^76 - 30 * q^78 + 12 * q^79 - 6 * q^80 + 22 * q^81 - 17 * q^82 + 35 * q^83 + 5 * q^84 - 15 * q^85 + 15 * q^86 - 29 * q^89 + 11 * q^90 - 2 * q^92 + 8 * q^93 + 18 * q^94 - 13 * q^95 + 5 * q^96 - 19 * q^97 - 6 * q^98

Introduction

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Database

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