LMFDB - Embedded newform 8470.2.a.bo.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:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 770)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.41421$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +2.82843 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.82843 q^{6} +1.00000 q^{7} -1.00000 q^{8} +5.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.82843 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.82843 q^{6} +1.00000 q^{7} -1.00000 q^{8} +5.00000 q^{9} +1.00000 q^{10} +2.82843 q^{12} -2.00000 q^{13} -1.00000 q^{14} -2.82843 q^{15} +1.00000 q^{16} -7.65685 q^{17} -5.00000 q^{18} +2.82843 q^{19} -1.00000 q^{20} +2.82843 q^{21} -2.82843 q^{23} -2.82843 q^{24} +1.00000 q^{25} +2.00000 q^{26} +5.65685 q^{27} +1.00000 q^{28} -3.17157 q^{29} +2.82843 q^{30} -5.65685 q^{31} -1.00000 q^{32} +7.65685 q^{34} -1.00000 q^{35} +5.00000 q^{36} +3.17157 q^{37} -2.82843 q^{38} -5.65685 q^{39} +1.00000 q^{40} +0.828427 q^{41} -2.82843 q^{42} +9.65685 q^{43} -5.00000 q^{45} +2.82843 q^{46} -8.00000 q^{47} +2.82843 q^{48} +1.00000 q^{49} -1.00000 q^{50} -21.6569 q^{51} -2.00000 q^{52} -10.4853 q^{53} -5.65685 q^{54} -1.00000 q^{56} +8.00000 q^{57} +3.17157 q^{58} -8.00000 q^{59} -2.82843 q^{60} +9.31371 q^{61} +5.65685 q^{62} +5.00000 q^{63} +1.00000 q^{64} +2.00000 q^{65} +15.3137 q^{67} -7.65685 q^{68} -8.00000 q^{69} +1.00000 q^{70} -5.65685 q^{71} -5.00000 q^{72} -7.65685 q^{73} -3.17157 q^{74} +2.82843 q^{75} +2.82843 q^{76} +5.65685 q^{78} +5.17157 q^{79} -1.00000 q^{80} +1.00000 q^{81} -0.828427 q^{82} +2.34315 q^{83} +2.82843 q^{84} +7.65685 q^{85} -9.65685 q^{86} -8.97056 q^{87} -11.6569 q^{89} +5.00000 q^{90} -2.00000 q^{91} -2.82843 q^{92} -16.0000 q^{93} +8.00000 q^{94} -2.82843 q^{95} -2.82843 q^{96} -0.828427 q^{97} -1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{4} - 2 q^{5} + 2 q^{7} - 2 q^{8} + 10 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^4 - 2 * q^5 + 2 * q^7 - 2 * q^8 + 10 * q^9	$ 2 q - 2 q^{2} + 2 q^{4} - 2 q^{5} + 2 q^{7} - 2 q^{8} + 10 q^{9} + 2 q^{10} - 4 q^{13} - 2 q^{14} + 2 q^{16} - 4 q^{17} - 10 q^{18} - 2 q^{20} + 2 q^{25} + 4 q^{26} + 2 q^{28} - 12 q^{29} - 2 q^{32} + 4 q^{34} - 2 q^{35} + 10 q^{36} + 12 q^{37} + 2 q^{40} - 4 q^{41} + 8 q^{43} - 10 q^{45} - 16 q^{47} + 2 q^{49} - 2 q^{50} - 32 q^{51} - 4 q^{52} - 4 q^{53} - 2 q^{56} + 16 q^{57} + 12 q^{58} - 16 q^{59} - 4 q^{61} + 10 q^{63} + 2 q^{64} + 4 q^{65} + 8 q^{67} - 4 q^{68} - 16 q^{69} + 2 q^{70} - 10 q^{72} - 4 q^{73} - 12 q^{74} + 16 q^{79} - 2 q^{80} + 2 q^{81} + 4 q^{82} + 16 q^{83} + 4 q^{85} - 8 q^{86} + 16 q^{87} - 12 q^{89} + 10 q^{90} - 4 q^{91} - 32 q^{93} + 16 q^{94} + 4 q^{97} - 2 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^4 - 2 * q^5 + 2 * q^7 - 2 * q^8 + 10 * q^9 + 2 * q^10 - 4 * q^13 - 2 * q^14 + 2 * q^16 - 4 * q^17 - 10 * q^18 - 2 * q^20 + 2 * q^25 + 4 * q^26 + 2 * q^28 - 12 * q^29 - 2 * q^32 + 4 * q^34 - 2 * q^35 + 10 * q^36 + 12 * q^37 + 2 * q^40 - 4 * q^41 + 8 * q^43 - 10 * q^45 - 16 * q^47 + 2 * q^49 - 2 * q^50 - 32 * q^51 - 4 * q^52 - 4 * q^53 - 2 * q^56 + 16 * q^57 + 12 * q^58 - 16 * q^59 - 4 * q^61 + 10 * q^63 + 2 * q^64 + 4 * q^65 + 8 * q^67 - 4 * q^68 - 16 * q^69 + 2 * q^70 - 10 * q^72 - 4 * q^73 - 12 * q^74 + 16 * q^79 - 2 * q^80 + 2 * q^81 + 4 * q^82 + 16 * q^83 + 4 * q^85 - 8 * q^86 + 16 * q^87 - 12 * q^89 + 10 * q^90 - 4 * q^91 - 32 * q^93 + 16 * q^94 + 4 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	2.82843	1.63299	0.816497	−	0.577350i	$-0.195913\pi$
$3$	2.82843	1.63299	0.816497	+	0.577350i	$0.195913\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.82843	−1.15470
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	5.00000	1.66667
$10$	1.00000	0.316228
$11$	0	0
$11$	0	0
$12$	2.82843	0.816497
$13$	−2.00000	−0.554700	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000	−0.554700	−0.277350	+	0.960769i	$0.589456\pi$
$14$	−1.00000	−0.267261
$15$	−2.82843	−0.730297
$16$	1.00000	0.250000
$17$	−7.65685	−1.85706	−0.928530	−	0.371257i	$-0.878927\pi$
$17$	−7.65685	−1.85706	−0.928530	+	0.371257i	$0.878927\pi$
$18$	−5.00000	−1.17851
$19$	2.82843	0.648886	0.324443	−	0.945905i	$-0.394823\pi$
$19$	2.82843	0.648886	0.324443	+	0.945905i	$0.394823\pi$
$20$	−1.00000	−0.223607
$21$	2.82843	0.617213
$22$	0	0
$23$	−2.82843	−0.589768	−0.294884	−	0.955533i	$-0.595281\pi$
$23$	−2.82843	−0.589768	−0.294884	+	0.955533i	$0.595281\pi$
$24$	−2.82843	−0.577350
$25$	1.00000	0.200000
$26$	2.00000	0.392232
$27$	5.65685	1.08866
$28$	1.00000	0.188982
$29$	−3.17157	−0.588946	−0.294473	−	0.955660i	$-0.595144\pi$
$29$	−3.17157	−0.588946	−0.294473	+	0.955660i	$0.595144\pi$
$30$	2.82843	0.516398
$31$	−5.65685	−1.01600	−0.508001	−	0.861357i	$-0.669615\pi$
$31$	−5.65685	−1.01600	−0.508001	+	0.861357i	$0.669615\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	7.65685	1.31314
$35$	−1.00000	−0.169031
$36$	5.00000	0.833333
$37$	3.17157	0.521403	0.260702	−	0.965419i	$-0.416046\pi$
$37$	3.17157	0.521403	0.260702	+	0.965419i	$0.416046\pi$
$38$	−2.82843	−0.458831
$39$	−5.65685	−0.905822
$40$	1.00000	0.158114
$41$	0.828427	0.129379	0.0646893	−	0.997905i	$-0.479394\pi$
$41$	0.828427	0.129379	0.0646893	+	0.997905i	$0.479394\pi$
$42$	−2.82843	−0.436436
$43$	9.65685	1.47266	0.736328	−	0.676625i	$-0.236558\pi$
$43$	9.65685	1.47266	0.736328	+	0.676625i	$0.236558\pi$
$44$	0	0
$45$	−5.00000	−0.745356
$46$	2.82843	0.417029
$47$	−8.00000	−1.16692	−0.583460	−	0.812142i	$-0.698301\pi$
$47$	−8.00000	−1.16692	−0.583460	+	0.812142i	$0.698301\pi$
$48$	2.82843	0.408248
$49$	1.00000	0.142857
$50$	−1.00000	−0.141421
$51$	−21.6569	−3.03257
$52$	−2.00000	−0.277350
$53$	−10.4853	−1.44026	−0.720132	−	0.693837i	$-0.755919\pi$
$53$	−10.4853	−1.44026	−0.720132	+	0.693837i	$0.755919\pi$
$54$	−5.65685	−0.769800
$55$	0	0
$56$	−1.00000	−0.133631
$57$	8.00000	1.05963
$58$	3.17157	0.416448
$59$	−8.00000	−1.04151	−0.520756	−	0.853706i	$-0.674350\pi$
$59$	−8.00000	−1.04151	−0.520756	+	0.853706i	$0.674350\pi$
$60$	−2.82843	−0.365148
$61$	9.31371	1.19250	0.596249	−	0.802799i	$-0.296657\pi$
$61$	9.31371	1.19250	0.596249	+	0.802799i	$0.296657\pi$
$62$	5.65685	0.718421
$63$	5.00000	0.629941
$64$	1.00000	0.125000
$65$	2.00000	0.248069
$66$	0	0
$67$	15.3137	1.87087	0.935434	−	0.353502i	$-0.115009\pi$
$67$	15.3137	1.87087	0.935434	+	0.353502i	$0.115009\pi$
$68$	−7.65685	−0.928530
$69$	−8.00000	−0.963087
$70$	1.00000	0.119523
$71$	−5.65685	−0.671345	−0.335673	−	0.941979i	$-0.608964\pi$
$71$	−5.65685	−0.671345	−0.335673	+	0.941979i	$0.608964\pi$
$72$	−5.00000	−0.589256
$73$	−7.65685	−0.896167	−0.448084	−	0.893992i	$-0.647893\pi$
$73$	−7.65685	−0.896167	−0.448084	+	0.893992i	$0.647893\pi$
$74$	−3.17157	−0.368688
$75$	2.82843	0.326599
$76$	2.82843	0.324443
$77$	0	0
$78$	5.65685	0.640513
$79$	5.17157	0.581847	0.290924	−	0.956746i	$-0.406037\pi$
$79$	5.17157	0.581847	0.290924	+	0.956746i	$0.406037\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	−0.828427	−0.0914845
$83$	2.34315	0.257194	0.128597	−	0.991697i	$-0.458953\pi$
$83$	2.34315	0.257194	0.128597	+	0.991697i	$0.458953\pi$
$84$	2.82843	0.308607
$85$	7.65685	0.830502
$86$	−9.65685	−1.04133
$87$	−8.97056	−0.961745
$88$	0	0
$89$	−11.6569	−1.23562	−0.617812	−	0.786326i	$-0.711981\pi$
$89$	−11.6569	−1.23562	−0.617812	+	0.786326i	$0.711981\pi$
$90$	5.00000	0.527046
$91$	−2.00000	−0.209657
$92$	−2.82843	−0.294884
$93$	−16.0000	−1.65912
$94$	8.00000	0.825137
$95$	−2.82843	−0.290191
$96$	−2.82843	−0.288675
$97$	−0.828427	−0.0841140	−0.0420570	−	0.999115i	$-0.513391\pi$
$97$	−0.828427	−0.0841140	−0.0420570	+	0.999115i	$0.513391\pi$
$98$	−1.00000	−0.101015
$99$	0	0
$100$	1.00000	0.100000
$101$	−10.0000	−0.995037	−0.497519	−	0.867453i	$-0.665755\pi$
$101$	−10.0000	−0.995037	−0.497519	+	0.867453i	$0.665755\pi$
$102$	21.6569	2.14435
$103$	−5.65685	−0.557386	−0.278693	−	0.960380i	$-0.589901\pi$
$103$	−5.65685	−0.557386	−0.278693	+	0.960380i	$0.589901\pi$
$104$	2.00000	0.196116
$105$	−2.82843	−0.276026
$106$	10.4853	1.01842
$107$	1.65685	0.160174	0.0800871	−	0.996788i	$-0.474480\pi$
$107$	1.65685	0.160174	0.0800871	+	0.996788i	$0.474480\pi$
$108$	5.65685	0.544331
$109$	−14.4853	−1.38744	−0.693719	−	0.720246i	$-0.744029\pi$
$109$	−14.4853	−1.38744	−0.693719	+	0.720246i	$0.744029\pi$
$110$	0	0
$111$	8.97056	0.851448
$112$	1.00000	0.0944911
$113$	2.00000	0.188144	0.0940721	−	0.995565i	$-0.470012\pi$
$113$	2.00000	0.188144	0.0940721	+	0.995565i	$0.470012\pi$
$114$	−8.00000	−0.749269
$115$	2.82843	0.263752
$116$	−3.17157	−0.294473
$117$	−10.0000	−0.924500
$118$	8.00000	0.736460
$119$	−7.65685	−0.701903
$120$	2.82843	0.258199
$121$	0	0
$122$	−9.31371	−0.843224
$123$	2.34315	0.211274
$124$	−5.65685	−0.508001
$125$	−1.00000	−0.0894427
$126$	−5.00000	−0.445435
$127$	−19.3137	−1.71381	−0.856907	−	0.515471i	$-0.827617\pi$
$127$	−19.3137	−1.71381	−0.856907	+	0.515471i	$0.827617\pi$
$128$	−1.00000	−0.0883883
$129$	27.3137	2.40484
$130$	−2.00000	−0.175412
$131$	−18.8284	−1.64505	−0.822524	−	0.568731i	$-0.807435\pi$
$131$	−18.8284	−1.64505	−0.822524	+	0.568731i	$0.807435\pi$
$132$	0	0
$133$	2.82843	0.245256
$134$	−15.3137	−1.32290
$135$	−5.65685	−0.486864
$136$	7.65685	0.656570
$137$	5.31371	0.453981	0.226990	−	0.973897i	$-0.427111\pi$
$137$	5.31371	0.453981	0.226990	+	0.973897i	$0.427111\pi$
$138$	8.00000	0.681005
$139$	−18.8284	−1.59701	−0.798503	−	0.601991i	$-0.794374\pi$
$139$	−18.8284	−1.59701	−0.798503	+	0.601991i	$0.794374\pi$
$140$	−1.00000	−0.0845154
$141$	−22.6274	−1.90557
$142$	5.65685	0.474713
$143$	0	0
$144$	5.00000	0.416667
$145$	3.17157	0.263385
$146$	7.65685	0.633686
$147$	2.82843	0.233285
$148$	3.17157	0.260702
$149$	1.51472	0.124091	0.0620453	−	0.998073i	$-0.480238\pi$
$149$	1.51472	0.124091	0.0620453	+	0.998073i	$0.480238\pi$
$150$	−2.82843	−0.230940
$151$	−10.8284	−0.881205	−0.440602	−	0.897702i	$-0.645235\pi$
$151$	−10.8284	−0.881205	−0.440602	+	0.897702i	$0.645235\pi$
$152$	−2.82843	−0.229416
$153$	−38.2843	−3.09510
$154$	0	0
$155$	5.65685	0.454369
$156$	−5.65685	−0.452911
$157$	15.6569	1.24955	0.624777	−	0.780804i	$-0.285190\pi$
$157$	15.6569	1.24955	0.624777	+	0.780804i	$0.285190\pi$
$158$	−5.17157	−0.411428
$159$	−29.6569	−2.35194
$160$	1.00000	0.0790569
$161$	−2.82843	−0.222911
$162$	−1.00000	−0.0785674
$163$	12.0000	0.939913	0.469956	−	0.882690i	$-0.344270\pi$
$163$	12.0000	0.939913	0.469956	+	0.882690i	$0.344270\pi$
$164$	0.828427	0.0646893
$165$	0	0
$166$	−2.34315	−0.181863
$167$	16.0000	1.23812	0.619059	−	0.785345i	$-0.287514\pi$
$167$	16.0000	1.23812	0.619059	+	0.785345i	$0.287514\pi$
$168$	−2.82843	−0.218218
$169$	−9.00000	−0.692308
$170$	−7.65685	−0.587254
$171$	14.1421	1.08148
$172$	9.65685	0.736328
$173$	1.31371	0.0998794	0.0499397	−	0.998752i	$-0.484097\pi$
$173$	1.31371	0.0998794	0.0499397	+	0.998752i	$0.484097\pi$
$174$	8.97056	0.680057
$175$	1.00000	0.0755929
$176$	0	0
$177$	−22.6274	−1.70078
$178$	11.6569	0.873718
$179$	6.34315	0.474109	0.237054	−	0.971496i	$-0.423818\pi$
$179$	6.34315	0.474109	0.237054	+	0.971496i	$0.423818\pi$
$180$	−5.00000	−0.372678
$181$	−14.0000	−1.04061	−0.520306	−	0.853980i	$-0.674182\pi$
$181$	−14.0000	−1.04061	−0.520306	+	0.853980i	$0.674182\pi$
$182$	2.00000	0.148250
$183$	26.3431	1.94734
$184$	2.82843	0.208514
$185$	−3.17157	−0.233179
$186$	16.0000	1.17318
$187$	0	0
$188$	−8.00000	−0.583460
$189$	5.65685	0.411476
$190$	2.82843	0.205196
$191$	19.3137	1.39749	0.698745	−	0.715370i	$-0.253742\pi$
$191$	19.3137	1.39749	0.698745	+	0.715370i	$0.253742\pi$
$192$	2.82843	0.204124
$193$	−21.3137	−1.53419	−0.767097	−	0.641531i	$-0.778300\pi$
$193$	−21.3137	−1.53419	−0.767097	+	0.641531i	$0.778300\pi$
$194$	0.828427	0.0594776
$195$	5.65685	0.405096
$196$	1.00000	0.0714286
$197$	12.3431	0.879413	0.439706	−	0.898142i	$-0.355083\pi$
$197$	12.3431	0.879413	0.439706	+	0.898142i	$0.355083\pi$
$198$	0	0
$199$	−11.3137	−0.802008	−0.401004	−	0.916076i	$-0.631339\pi$
$199$	−11.3137	−0.802008	−0.401004	+	0.916076i	$0.631339\pi$
$200$	−1.00000	−0.0707107
$201$	43.3137	3.05511
$202$	10.0000	0.703598
$203$	−3.17157	−0.222601
$204$	−21.6569	−1.51628
$205$	−0.828427	−0.0578599
$206$	5.65685	0.394132
$207$	−14.1421	−0.982946
$208$	−2.00000	−0.138675
$209$	0	0
$210$	2.82843	0.195180
$211$	−15.3137	−1.05424	−0.527120	−	0.849791i	$-0.676728\pi$
$211$	−15.3137	−1.05424	−0.527120	+	0.849791i	$0.676728\pi$
$212$	−10.4853	−0.720132
$213$	−16.0000	−1.09630
$214$	−1.65685	−0.113260
$215$	−9.65685	−0.658592
$216$	−5.65685	−0.384900
$217$	−5.65685	−0.384012
$218$	14.4853	0.981067
$219$	−21.6569	−1.46343
$220$	0	0
$221$	15.3137	1.03011
$222$	−8.97056	−0.602065
$223$	−28.2843	−1.89405	−0.947027	−	0.321153i	$-0.895930\pi$
$223$	−28.2843	−1.89405	−0.947027	+	0.321153i	$0.895930\pi$
$224$	−1.00000	−0.0668153
$225$	5.00000	0.333333
$226$	−2.00000	−0.133038
$227$	24.0000	1.59294	0.796468	−	0.604681i	$-0.206699\pi$
$227$	24.0000	1.59294	0.796468	+	0.604681i	$0.206699\pi$
$228$	8.00000	0.529813
$229$	−1.31371	−0.0868123	−0.0434062	−	0.999058i	$-0.513821\pi$
$229$	−1.31371	−0.0868123	−0.0434062	+	0.999058i	$0.513821\pi$
$230$	−2.82843	−0.186501
$231$	0	0
$232$	3.17157	0.208224
$233$	6.00000	0.393073	0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000	0.393073	0.196537	+	0.980497i	$0.437031\pi$
$234$	10.0000	0.653720
$235$	8.00000	0.521862
$236$	−8.00000	−0.520756
$237$	14.6274	0.950153
$238$	7.65685	0.496320
$239$	7.51472	0.486087	0.243043	−	0.970015i	$-0.421854\pi$
$239$	7.51472	0.486087	0.243043	+	0.970015i	$0.421854\pi$
$240$	−2.82843	−0.182574
$241$	8.82843	0.568689	0.284344	−	0.958722i	$-0.408224\pi$
$241$	8.82843	0.568689	0.284344	+	0.958722i	$0.408224\pi$
$242$	0	0
$243$	−14.1421	−0.907218
$244$	9.31371	0.596249
$245$	−1.00000	−0.0638877
$246$	−2.34315	−0.149394
$247$	−5.65685	−0.359937
$248$	5.65685	0.359211
$249$	6.62742	0.419995
$250$	1.00000	0.0632456
$251$	−11.3137	−0.714115	−0.357057	−	0.934082i	$-0.616220\pi$
$251$	−11.3137	−0.714115	−0.357057	+	0.934082i	$0.616220\pi$
$252$	5.00000	0.314970
$253$	0	0
$254$	19.3137	1.21185
$255$	21.6569	1.35620
$256$	1.00000	0.0625000
$257$	23.1716	1.44540	0.722702	−	0.691160i	$-0.242900\pi$
$257$	23.1716	1.44540	0.722702	+	0.691160i	$0.242900\pi$
$258$	−27.3137	−1.70048
$259$	3.17157	0.197072
$260$	2.00000	0.124035
$261$	−15.8579	−0.981577
$262$	18.8284	1.16322
$263$	14.6274	0.901965	0.450983	−	0.892533i	$-0.351074\pi$
$263$	14.6274	0.901965	0.450983	+	0.892533i	$0.351074\pi$
$264$	0	0
$265$	10.4853	0.644106
$266$	−2.82843	−0.173422
$267$	−32.9706	−2.01777
$268$	15.3137	0.935434
$269$	2.00000	0.121942	0.0609711	−	0.998140i	$-0.480580\pi$
$269$	2.00000	0.121942	0.0609711	+	0.998140i	$0.480580\pi$
$270$	5.65685	0.344265
$271$	−16.9706	−1.03089	−0.515444	−	0.856923i	$-0.672373\pi$
$271$	−16.9706	−1.03089	−0.515444	+	0.856923i	$0.672373\pi$
$272$	−7.65685	−0.464265
$273$	−5.65685	−0.342368
$274$	−5.31371	−0.321013
$275$	0	0
$276$	−8.00000	−0.481543
$277$	13.3137	0.799943	0.399972	−	0.916528i	$-0.369020\pi$
$277$	13.3137	0.799943	0.399972	+	0.916528i	$0.369020\pi$
$278$	18.8284	1.12925
$279$	−28.2843	−1.69334
$280$	1.00000	0.0597614
$281$	6.97056	0.415829	0.207914	−	0.978147i	$-0.433332\pi$
$281$	6.97056	0.415829	0.207914	+	0.978147i	$0.433332\pi$
$282$	22.6274	1.34744
$283$	22.6274	1.34506	0.672530	−	0.740070i	$-0.265208\pi$
$283$	22.6274	1.34506	0.672530	+	0.740070i	$0.265208\pi$
$284$	−5.65685	−0.335673
$285$	−8.00000	−0.473879
$286$	0	0
$287$	0.828427	0.0489005
$288$	−5.00000	−0.294628
$289$	41.6274	2.44867
$290$	−3.17157	−0.186241
$291$	−2.34315	−0.137358
$292$	−7.65685	−0.448084
$293$	−2.00000	−0.116841	−0.0584206	−	0.998292i	$-0.518606\pi$
$293$	−2.00000	−0.116841	−0.0584206	+	0.998292i	$0.518606\pi$
$294$	−2.82843	−0.164957
$295$	8.00000	0.465778
$296$	−3.17157	−0.184344
$297$	0	0
$298$	−1.51472	−0.0877453
$299$	5.65685	0.327144
$300$	2.82843	0.163299
$301$	9.65685	0.556612
$302$	10.8284	0.623106
$303$	−28.2843	−1.62489
$304$	2.82843	0.162221
$305$	−9.31371	−0.533301
$306$	38.2843	2.18857
$307$	8.97056	0.511977	0.255989	−	0.966680i	$-0.417599\pi$
$307$	8.97056	0.511977	0.255989	+	0.966680i	$0.417599\pi$
$308$	0	0
$309$	−16.0000	−0.910208
$310$	−5.65685	−0.321288
$311$	0.970563	0.0550356	0.0275178	−	0.999621i	$-0.491240\pi$
$311$	0.970563	0.0550356	0.0275178	+	0.999621i	$0.491240\pi$
$312$	5.65685	0.320256
$313$	−8.82843	−0.499012	−0.249506	−	0.968373i	$-0.580268\pi$
$313$	−8.82843	−0.499012	−0.249506	+	0.968373i	$0.580268\pi$
$314$	−15.6569	−0.883567
$315$	−5.00000	−0.281718
$316$	5.17157	0.290924
$317$	3.17157	0.178133	0.0890666	−	0.996026i	$-0.471612\pi$
$317$	3.17157	0.178133	0.0890666	+	0.996026i	$0.471612\pi$
$318$	29.6569	1.66307
$319$	0	0
$320$	−1.00000	−0.0559017
$321$	4.68629	0.261563
$322$	2.82843	0.157622
$323$	−21.6569	−1.20502
$324$	1.00000	0.0555556
$325$	−2.00000	−0.110940
$326$	−12.0000	−0.664619
$327$	−40.9706	−2.26568
$328$	−0.828427	−0.0457422
$329$	−8.00000	−0.441054
$330$	0	0
$331$	28.9706	1.59237	0.796183	−	0.605056i	$-0.206849\pi$
$331$	28.9706	1.59237	0.796183	+	0.605056i	$0.206849\pi$
$332$	2.34315	0.128597
$333$	15.8579	0.869006
$334$	−16.0000	−0.875481
$335$	−15.3137	−0.836677
$336$	2.82843	0.154303
$337$	−29.3137	−1.59682	−0.798410	−	0.602115i	$-0.794325\pi$
$337$	−29.3137	−1.59682	−0.798410	+	0.602115i	$0.794325\pi$
$338$	9.00000	0.489535
$339$	5.65685	0.307238
$340$	7.65685	0.415251
$341$	0	0
$342$	−14.1421	−0.764719
$343$	1.00000	0.0539949
$344$	−9.65685	−0.520663
$345$	8.00000	0.430706
$346$	−1.31371	−0.0706254
$347$	−28.9706	−1.55522	−0.777611	−	0.628746i	$-0.783568\pi$
$347$	−28.9706	−1.55522	−0.777611	+	0.628746i	$0.783568\pi$
$348$	−8.97056	−0.480873
$349$	−26.9706	−1.44370	−0.721851	−	0.692049i	$-0.756708\pi$
$349$	−26.9706	−1.44370	−0.721851	+	0.692049i	$0.756708\pi$
$350$	−1.00000	−0.0534522
$351$	−11.3137	−0.603881
$352$	0	0
$353$	−24.8284	−1.32148	−0.660742	−	0.750613i	$-0.729758\pi$
$353$	−24.8284	−1.32148	−0.660742	+	0.750613i	$0.729758\pi$
$354$	22.6274	1.20263
$355$	5.65685	0.300235
$356$	−11.6569	−0.617812
$357$	−21.6569	−1.14620
$358$	−6.34315	−0.335246
$359$	−33.4558	−1.76573	−0.882866	−	0.469625i	$-0.844389\pi$
$359$	−33.4558	−1.76573	−0.882866	+	0.469625i	$0.844389\pi$
$360$	5.00000	0.263523
$361$	−11.0000	−0.578947
$362$	14.0000	0.735824
$363$	0	0
$364$	−2.00000	−0.104828
$365$	7.65685	0.400778
$366$	−26.3431	−1.37698
$367$	28.2843	1.47643	0.738213	−	0.674567i	$-0.235670\pi$
$367$	28.2843	1.47643	0.738213	+	0.674567i	$0.235670\pi$
$368$	−2.82843	−0.147442
$369$	4.14214	0.215631
$370$	3.17157	0.164882
$371$	−10.4853	−0.544369
$372$	−16.0000	−0.829561
$373$	−3.65685	−0.189345	−0.0946724	−	0.995508i	$-0.530180\pi$
$373$	−3.65685	−0.189345	−0.0946724	+	0.995508i	$0.530180\pi$
$374$	0	0
$375$	−2.82843	−0.146059
$376$	8.00000	0.412568
$377$	6.34315	0.326689
$378$	−5.65685	−0.290957
$379$	4.00000	0.205466	0.102733	−	0.994709i	$-0.467241\pi$
$379$	4.00000	0.205466	0.102733	+	0.994709i	$0.467241\pi$
$380$	−2.82843	−0.145095
$381$	−54.6274	−2.79865
$382$	−19.3137	−0.988175
$383$	−29.6569	−1.51539	−0.757697	−	0.652606i	$-0.773676\pi$
$383$	−29.6569	−1.51539	−0.757697	+	0.652606i	$0.773676\pi$
$384$	−2.82843	−0.144338
$385$	0	0
$386$	21.3137	1.08484
$387$	48.2843	2.45443
$388$	−0.828427	−0.0420570
$389$	30.9706	1.57027	0.785135	−	0.619325i	$-0.212594\pi$
$389$	30.9706	1.57027	0.785135	+	0.619325i	$0.212594\pi$
$390$	−5.65685	−0.286446
$391$	21.6569	1.09523
$392$	−1.00000	−0.0505076
$393$	−53.2548	−2.68635
$394$	−12.3431	−0.621839
$395$	−5.17157	−0.260210
$396$	0	0
$397$	−22.9706	−1.15286	−0.576430	−	0.817147i	$-0.695555\pi$
$397$	−22.9706	−1.15286	−0.576430	+	0.817147i	$0.695555\pi$
$398$	11.3137	0.567105
$399$	8.00000	0.400501
$400$	1.00000	0.0500000
$401$	10.0000	0.499376	0.249688	−	0.968326i	$-0.419672\pi$
$401$	10.0000	0.499376	0.249688	+	0.968326i	$0.419672\pi$
$402$	−43.3137	−2.16029
$403$	11.3137	0.563576
$404$	−10.0000	−0.497519
$405$	−1.00000	−0.0496904
$406$	3.17157	0.157403
$407$	0	0
$408$	21.6569	1.07217
$409$	12.1421	0.600390	0.300195	−	0.953878i	$-0.402948\pi$
$409$	12.1421	0.600390	0.300195	+	0.953878i	$0.402948\pi$
$410$	0.828427	0.0409131
$411$	15.0294	0.741347
$412$	−5.65685	−0.278693
$413$	−8.00000	−0.393654
$414$	14.1421	0.695048
$415$	−2.34315	−0.115021
$416$	2.00000	0.0980581
$417$	−53.2548	−2.60790
$418$	0	0
$419$	−30.6274	−1.49625	−0.748124	−	0.663559i	$-0.769045\pi$
$419$	−30.6274	−1.49625	−0.748124	+	0.663559i	$0.769045\pi$
$420$	−2.82843	−0.138013
$421$	28.6274	1.39521	0.697607	−	0.716480i	$-0.254248\pi$
$421$	28.6274	1.39521	0.697607	+	0.716480i	$0.254248\pi$
$422$	15.3137	0.745460
$423$	−40.0000	−1.94487
$424$	10.4853	0.509210
$425$	−7.65685	−0.371412
$426$	16.0000	0.775203
$427$	9.31371	0.450722
$428$	1.65685	0.0800871
$429$	0	0
$430$	9.65685	0.465695
$431$	19.7990	0.953684	0.476842	−	0.878989i	$-0.341781\pi$
$431$	19.7990	0.953684	0.476842	+	0.878989i	$0.341781\pi$
$432$	5.65685	0.272166
$433$	20.8284	1.00095	0.500475	−	0.865751i	$-0.333159\pi$
$433$	20.8284	1.00095	0.500475	+	0.865751i	$0.333159\pi$
$434$	5.65685	0.271538
$435$	8.97056	0.430106
$436$	−14.4853	−0.693719
$437$	−8.00000	−0.382692
$438$	21.6569	1.03480
$439$	−24.9706	−1.19178	−0.595890	−	0.803066i	$-0.703201\pi$
$439$	−24.9706	−1.19178	−0.595890	+	0.803066i	$0.703201\pi$
$440$	0	0
$441$	5.00000	0.238095
$442$	−15.3137	−0.728399
$443$	−8.68629	−0.412698	−0.206349	−	0.978478i	$-0.566158\pi$
$443$	−8.68629	−0.412698	−0.206349	+	0.978478i	$0.566158\pi$
$444$	8.97056	0.425724
$445$	11.6569	0.552588
$446$	28.2843	1.33930
$447$	4.28427	0.202639
$448$	1.00000	0.0472456
$449$	−6.00000	−0.283158	−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000	−0.283158	−0.141579	+	0.989927i	$0.545218\pi$
$450$	−5.00000	−0.235702
$451$	0	0
$452$	2.00000	0.0940721
$453$	−30.6274	−1.43900
$454$	−24.0000	−1.12638
$455$	2.00000	0.0937614
$456$	−8.00000	−0.374634
$457$	22.0000	1.02912	0.514558	−	0.857455i	$-0.327956\pi$
$457$	22.0000	1.02912	0.514558	+	0.857455i	$0.327956\pi$
$458$	1.31371	0.0613856
$459$	−43.3137	−2.02171
$460$	2.82843	0.131876
$461$	11.6569	0.542914	0.271457	−	0.962451i	$-0.412495\pi$
$461$	11.6569	0.542914	0.271457	+	0.962451i	$0.412495\pi$
$462$	0	0
$463$	−9.45584	−0.439450	−0.219725	−	0.975562i	$-0.570516\pi$
$463$	−9.45584	−0.439450	−0.219725	+	0.975562i	$0.570516\pi$
$464$	−3.17157	−0.147237
$465$	16.0000	0.741982
$466$	−6.00000	−0.277945
$467$	11.7990	0.545992	0.272996	−	0.962015i	$-0.411985\pi$
$467$	11.7990	0.545992	0.272996	+	0.962015i	$0.411985\pi$
$468$	−10.0000	−0.462250
$469$	15.3137	0.707121
$470$	−8.00000	−0.369012
$471$	44.2843	2.04051
$472$	8.00000	0.368230
$473$	0	0
$474$	−14.6274	−0.671860
$475$	2.82843	0.129777
$476$	−7.65685	−0.350951
$477$	−52.4264	−2.40044
$478$	−7.51472	−0.343715
$479$	−35.3137	−1.61352	−0.806762	−	0.590876i	$-0.798782\pi$
$479$	−35.3137	−1.61352	−0.806762	+	0.590876i	$0.798782\pi$
$480$	2.82843	0.129099
$481$	−6.34315	−0.289223
$482$	−8.82843	−0.402124
$483$	−8.00000	−0.364013
$484$	0	0
$485$	0.828427	0.0376169
$486$	14.1421	0.641500
$487$	−36.7696	−1.66619	−0.833094	−	0.553132i	$-0.813433\pi$
$487$	−36.7696	−1.66619	−0.833094	+	0.553132i	$0.813433\pi$
$488$	−9.31371	−0.421612
$489$	33.9411	1.53487
$490$	1.00000	0.0451754
$491$	8.68629	0.392007	0.196003	−	0.980603i	$-0.437204\pi$
$491$	8.68629	0.392007	0.196003	+	0.980603i	$0.437204\pi$
$492$	2.34315	0.105637
$493$	24.2843	1.09371
$494$	5.65685	0.254514
$495$	0	0
$496$	−5.65685	−0.254000
$497$	−5.65685	−0.253745
$498$	−6.62742	−0.296982
$499$	28.9706	1.29690	0.648450	−	0.761257i	$-0.275417\pi$
$499$	28.9706	1.29690	0.648450	+	0.761257i	$0.275417\pi$
$500$	−1.00000	−0.0447214
$501$	45.2548	2.02184
$502$	11.3137	0.504956
$503$	3.31371	0.147751	0.0738755	−	0.997267i	$-0.476463\pi$
$503$	3.31371	0.147751	0.0738755	+	0.997267i	$0.476463\pi$
$504$	−5.00000	−0.222718
$505$	10.0000	0.444994
$506$	0	0
$507$	−25.4558	−1.13053
$508$	−19.3137	−0.856907
$509$	−10.6863	−0.473662	−0.236831	−	0.971551i	$-0.576109\pi$
$509$	−10.6863	−0.473662	−0.236831	+	0.971551i	$0.576109\pi$
$510$	−21.6569	−0.958982
$511$	−7.65685	−0.338719
$512$	−1.00000	−0.0441942
$513$	16.0000	0.706417
$514$	−23.1716	−1.02205
$515$	5.65685	0.249271
$516$	27.3137	1.20242
$517$	0	0
$518$	−3.17157	−0.139351
$519$	3.71573	0.163102
$520$	−2.00000	−0.0877058
$521$	41.5980	1.82244	0.911220	−	0.411919i	$-0.135141\pi$
$521$	41.5980	1.82244	0.911220	+	0.411919i	$0.135141\pi$
$522$	15.8579	0.694080
$523$	10.3431	0.452274	0.226137	−	0.974095i	$-0.427390\pi$
$523$	10.3431	0.452274	0.226137	+	0.974095i	$0.427390\pi$
$524$	−18.8284	−0.822524
$525$	2.82843	0.123443
$526$	−14.6274	−0.637786
$527$	43.3137	1.88677
$528$	0	0
$529$	−15.0000	−0.652174
$530$	−10.4853	−0.455452
$531$	−40.0000	−1.73585
$532$	2.82843	0.122628
$533$	−1.65685	−0.0717663
$534$	32.9706	1.42678
$535$	−1.65685	−0.0716321
$536$	−15.3137	−0.661451
$537$	17.9411	0.774217
$538$	−2.00000	−0.0862261
$539$	0	0
$540$	−5.65685	−0.243432
$541$	33.1127	1.42363	0.711813	−	0.702369i	$-0.247874\pi$
$541$	33.1127	1.42363	0.711813	+	0.702369i	$0.247874\pi$
$542$	16.9706	0.728948
$543$	−39.5980	−1.69931
$544$	7.65685	0.328285
$545$	14.4853	0.620481
$546$	5.65685	0.242091
$547$	−23.3137	−0.996822	−0.498411	−	0.866941i	$-0.666083\pi$
$547$	−23.3137	−0.996822	−0.498411	+	0.866941i	$0.666083\pi$
$548$	5.31371	0.226990
$549$	46.5685	1.98750
$550$	0	0
$551$	−8.97056	−0.382159
$552$	8.00000	0.340503
$553$	5.17157	0.219918
$554$	−13.3137	−0.565645
$555$	−8.97056	−0.380779
$556$	−18.8284	−0.798503
$557$	26.9706	1.14278	0.571390	−	0.820679i	$-0.306404\pi$
$557$	26.9706	1.14278	0.571390	+	0.820679i	$0.306404\pi$
$558$	28.2843	1.19737
$559$	−19.3137	−0.816883
$560$	−1.00000	−0.0422577
$561$	0	0
$562$	−6.97056	−0.294035
$563$	22.6274	0.953632	0.476816	−	0.879003i	$-0.341791\pi$
$563$	22.6274	0.953632	0.476816	+	0.879003i	$0.341791\pi$
$564$	−22.6274	−0.952786
$565$	−2.00000	−0.0841406
$566$	−22.6274	−0.951101
$567$	1.00000	0.0419961
$568$	5.65685	0.237356
$569$	−16.6274	−0.697058	−0.348529	−	0.937298i	$-0.613319\pi$
$569$	−16.6274	−0.697058	−0.348529	+	0.937298i	$0.613319\pi$
$570$	8.00000	0.335083
$571$	35.5980	1.48973	0.744865	−	0.667216i	$-0.232514\pi$
$571$	35.5980	1.48973	0.744865	+	0.667216i	$0.232514\pi$
$572$	0	0
$573$	54.6274	2.28209
$574$	−0.828427	−0.0345779
$575$	−2.82843	−0.117954
$576$	5.00000	0.208333
$577$	25.1127	1.04546	0.522728	−	0.852500i	$-0.324914\pi$
$577$	25.1127	1.04546	0.522728	+	0.852500i	$0.324914\pi$
$578$	−41.6274	−1.73147
$579$	−60.2843	−2.50533
$580$	3.17157	0.131692
$581$	2.34315	0.0972101
$582$	2.34315	0.0971265
$583$	0	0
$584$	7.65685	0.316843
$585$	10.0000	0.413449
$586$	2.00000	0.0826192
$587$	−38.1421	−1.57429	−0.787147	−	0.616765i	$-0.788443\pi$
$587$	−38.1421	−1.57429	−0.787147	+	0.616765i	$0.788443\pi$
$588$	2.82843	0.116642
$589$	−16.0000	−0.659269
$590$	−8.00000	−0.329355
$591$	34.9117	1.43607
$592$	3.17157	0.130351
$593$	−20.3431	−0.835393	−0.417696	−	0.908587i	$-0.637162\pi$
$593$	−20.3431	−0.835393	−0.417696	+	0.908587i	$0.637162\pi$
$594$	0	0
$595$	7.65685	0.313900
$596$	1.51472	0.0620453
$597$	−32.0000	−1.30967
$598$	−5.65685	−0.231326
$599$	21.6569	0.884875	0.442438	−	0.896799i	$-0.354114\pi$
$599$	21.6569	0.884875	0.442438	+	0.896799i	$0.354114\pi$
$600$	−2.82843	−0.115470
$601$	−12.8284	−0.523282	−0.261641	−	0.965165i	$-0.584264\pi$
$601$	−12.8284	−0.523282	−0.261641	+	0.965165i	$0.584264\pi$
$602$	−9.65685	−0.393584
$603$	76.5685	3.11811
$604$	−10.8284	−0.440602
$605$	0	0
$606$	28.2843	1.14897
$607$	−29.6569	−1.20373	−0.601867	−	0.798596i	$-0.705576\pi$
$607$	−29.6569	−1.20373	−0.601867	+	0.798596i	$0.705576\pi$
$608$	−2.82843	−0.114708
$609$	−8.97056	−0.363506
$610$	9.31371	0.377101
$611$	16.0000	0.647291
$612$	−38.2843	−1.54755
$613$	−22.9706	−0.927772	−0.463886	−	0.885895i	$-0.653545\pi$
$613$	−22.9706	−0.927772	−0.463886	+	0.885895i	$0.653545\pi$
$614$	−8.97056	−0.362022
$615$	−2.34315	−0.0944848
$616$	0	0
$617$	−32.3431	−1.30209	−0.651043	−	0.759041i	$-0.725668\pi$
$617$	−32.3431	−1.30209	−0.651043	+	0.759041i	$0.725668\pi$
$618$	16.0000	0.643614
$619$	40.0000	1.60774	0.803868	−	0.594808i	$-0.202772\pi$
$619$	40.0000	1.60774	0.803868	+	0.594808i	$0.202772\pi$
$620$	5.65685	0.227185
$621$	−16.0000	−0.642058
$622$	−0.970563	−0.0389160
$623$	−11.6569	−0.467022
$624$	−5.65685	−0.226455
$625$	1.00000	0.0400000
$626$	8.82843	0.352855
$627$	0	0
$628$	15.6569	0.624777
$629$	−24.2843	−0.968277
$630$	5.00000	0.199205
$631$	−22.6274	−0.900783	−0.450392	−	0.892831i	$-0.648716\pi$
$631$	−22.6274	−0.900783	−0.450392	+	0.892831i	$0.648716\pi$
$632$	−5.17157	−0.205714
$633$	−43.3137	−1.72157
$634$	−3.17157	−0.125959
$635$	19.3137	0.766441
$636$	−29.6569	−1.17597
$637$	−2.00000	−0.0792429
$638$	0	0
$639$	−28.2843	−1.11891
$640$	1.00000	0.0395285
$641$	−30.0000	−1.18493	−0.592464	−	0.805597i	$-0.701845\pi$
$641$	−30.0000	−1.18493	−0.592464	+	0.805597i	$0.701845\pi$
$642$	−4.68629	−0.184953
$643$	14.1421	0.557711	0.278856	−	0.960333i	$-0.410045\pi$
$643$	14.1421	0.557711	0.278856	+	0.960333i	$0.410045\pi$
$644$	−2.82843	−0.111456
$645$	−27.3137	−1.07548
$646$	21.6569	0.852078
$647$	12.2843	0.482945	0.241472	−	0.970408i	$-0.422370\pi$
$647$	12.2843	0.482945	0.241472	+	0.970408i	$0.422370\pi$
$648$	−1.00000	−0.0392837
$649$	0	0
$650$	2.00000	0.0784465
$651$	−16.0000	−0.627089
$652$	12.0000	0.469956
$653$	7.45584	0.291770	0.145885	−	0.989302i	$-0.453397\pi$
$653$	7.45584	0.291770	0.145885	+	0.989302i	$0.453397\pi$
$654$	40.9706	1.60208
$655$	18.8284	0.735688
$656$	0.828427	0.0323446
$657$	−38.2843	−1.49361
$658$	8.00000	0.311872
$659$	9.65685	0.376178	0.188089	−	0.982152i	$-0.439771\pi$
$659$	9.65685	0.376178	0.188089	+	0.982152i	$0.439771\pi$
$660$	0	0
$661$	−6.00000	−0.233373	−0.116686	−	0.993169i	$-0.537227\pi$
$661$	−6.00000	−0.233373	−0.116686	+	0.993169i	$0.537227\pi$
$662$	−28.9706	−1.12597
$663$	43.3137	1.68217
$664$	−2.34315	−0.0909317
$665$	−2.82843	−0.109682
$666$	−15.8579	−0.614480
$667$	8.97056	0.347342
$668$	16.0000	0.619059
$669$	−80.0000	−3.09298
$670$	15.3137	0.591620
$671$	0	0
$672$	−2.82843	−0.109109
$673$	36.6274	1.41188	0.705942	−	0.708270i	$-0.250524\pi$
$673$	36.6274	1.41188	0.705942	+	0.708270i	$0.250524\pi$
$674$	29.3137	1.12912
$675$	5.65685	0.217732
$676$	−9.00000	−0.346154
$677$	14.0000	0.538064	0.269032	−	0.963131i	$-0.413296\pi$
$677$	14.0000	0.538064	0.269032	+	0.963131i	$0.413296\pi$
$678$	−5.65685	−0.217250
$679$	−0.828427	−0.0317921
$680$	−7.65685	−0.293627
$681$	67.8823	2.60125
$682$	0	0
$683$	22.3431	0.854937	0.427468	−	0.904030i	$-0.359406\pi$
$683$	22.3431	0.854937	0.427468	+	0.904030i	$0.359406\pi$
$684$	14.1421	0.540738
$685$	−5.31371	−0.203026
$686$	−1.00000	−0.0381802
$687$	−3.71573	−0.141764
$688$	9.65685	0.368164
$689$	20.9706	0.798915
$690$	−8.00000	−0.304555
$691$	0.970563	0.0369219	0.0184610	−	0.999830i	$-0.494123\pi$
$691$	0.970563	0.0369219	0.0184610	+	0.999830i	$0.494123\pi$
$692$	1.31371	0.0499397
$693$	0	0
$694$	28.9706	1.09971
$695$	18.8284	0.714203
$696$	8.97056	0.340028
$697$	−6.34315	−0.240264
$698$	26.9706	1.02085
$699$	16.9706	0.641886
$700$	1.00000	0.0377964
$701$	−40.8284	−1.54207	−0.771034	−	0.636794i	$-0.780260\pi$
$701$	−40.8284	−1.54207	−0.771034	+	0.636794i	$0.780260\pi$
$702$	11.3137	0.427008
$703$	8.97056	0.338331
$704$	0	0
$705$	22.6274	0.852198
$706$	24.8284	0.934430
$707$	−10.0000	−0.376089
$708$	−22.6274	−0.850390
$709$	26.2843	0.987127	0.493563	−	0.869710i	$-0.335694\pi$
$709$	26.2843	0.987127	0.493563	+	0.869710i	$0.335694\pi$
$710$	−5.65685	−0.212298
$711$	25.8579	0.969746
$712$	11.6569	0.436859
$713$	16.0000	0.599205
$714$	21.6569	0.810487
$715$	0	0
$716$	6.34315	0.237054
$717$	21.2548	0.793776
$718$	33.4558	1.24856
$719$	−8.00000	−0.298350	−0.149175	−	0.988811i	$-0.547662\pi$
$719$	−8.00000	−0.298350	−0.149175	+	0.988811i	$0.547662\pi$
$720$	−5.00000	−0.186339
$721$	−5.65685	−0.210672
$722$	11.0000	0.409378
$723$	24.9706	0.928665
$724$	−14.0000	−0.520306
$725$	−3.17157	−0.117789
$726$	0	0
$727$	4.68629	0.173805	0.0869025	−	0.996217i	$-0.472303\pi$
$727$	4.68629	0.173805	0.0869025	+	0.996217i	$0.472303\pi$
$728$	2.00000	0.0741249
$729$	−43.0000	−1.59259
$730$	−7.65685	−0.283393
$731$	−73.9411	−2.73481
$732$	26.3431	0.973671
$733$	46.0000	1.69905	0.849524	−	0.527549i	$-0.176889\pi$
$733$	46.0000	1.69905	0.849524	+	0.527549i	$0.176889\pi$
$734$	−28.2843	−1.04399
$735$	−2.82843	−0.104328
$736$	2.82843	0.104257
$737$	0	0
$738$	−4.14214	−0.152474
$739$	−41.2548	−1.51758	−0.758792	−	0.651333i	$-0.774210\pi$
$739$	−41.2548	−1.51758	−0.758792	+	0.651333i	$0.774210\pi$
$740$	−3.17157	−0.116589
$741$	−16.0000	−0.587775
$742$	10.4853	0.384927
$743$	16.0000	0.586983	0.293492	−	0.955962i	$-0.405183\pi$
$743$	16.0000	0.586983	0.293492	+	0.955962i	$0.405183\pi$
$744$	16.0000	0.586588
$745$	−1.51472	−0.0554950
$746$	3.65685	0.133887
$747$	11.7157	0.428656
$748$	0	0
$749$	1.65685	0.0605401
$750$	2.82843	0.103280
$751$	39.5980	1.44495	0.722475	−	0.691397i	$-0.243004\pi$
$751$	39.5980	1.44495	0.722475	+	0.691397i	$0.243004\pi$
$752$	−8.00000	−0.291730
$753$	−32.0000	−1.16614
$754$	−6.34315	−0.231004
$755$	10.8284	0.394087
$756$	5.65685	0.205738
$757$	−25.1127	−0.912737	−0.456368	−	0.889791i	$-0.650850\pi$
$757$	−25.1127	−0.912737	−0.456368	+	0.889791i	$0.650850\pi$
$758$	−4.00000	−0.145287
$759$	0	0
$760$	2.82843	0.102598
$761$	7.45584	0.270274	0.135137	−	0.990827i	$-0.456853\pi$
$761$	7.45584	0.270274	0.135137	+	0.990827i	$0.456853\pi$
$762$	54.6274	1.97894
$763$	−14.4853	−0.524402
$764$	19.3137	0.698745
$765$	38.2843	1.38417
$766$	29.6569	1.07155
$767$	16.0000	0.577727
$768$	2.82843	0.102062
$769$	14.4853	0.522353	0.261176	−	0.965291i	$-0.415890\pi$
$769$	14.4853	0.522353	0.261176	+	0.965291i	$0.415890\pi$
$770$	0	0
$771$	65.5391	2.36033
$772$	−21.3137	−0.767097
$773$	−10.6863	−0.384359	−0.192180	−	0.981360i	$-0.561556\pi$
$773$	−10.6863	−0.384359	−0.192180	+	0.981360i	$0.561556\pi$
$774$	−48.2843	−1.73554
$775$	−5.65685	−0.203200
$776$	0.828427	0.0297388
$777$	8.97056	0.321817
$778$	−30.9706	−1.11035
$779$	2.34315	0.0839519
$780$	5.65685	0.202548
$781$	0	0
$782$	−21.6569	−0.774448
$783$	−17.9411	−0.641164
$784$	1.00000	0.0357143
$785$	−15.6569	−0.558817
$786$	53.2548	1.89954
$787$	−30.6274	−1.09175	−0.545875	−	0.837867i	$-0.683803\pi$
$787$	−30.6274	−1.09175	−0.545875	+	0.837867i	$0.683803\pi$
$788$	12.3431	0.439706
$789$	41.3726	1.47290
$790$	5.17157	0.183996
$791$	2.00000	0.0711118
$792$	0	0
$793$	−18.6274	−0.661479
$794$	22.9706	0.815195
$795$	29.6569	1.05182
$796$	−11.3137	−0.401004
$797$	6.28427	0.222600	0.111300	−	0.993787i	$-0.464499\pi$
$797$	6.28427	0.222600	0.111300	+	0.993787i	$0.464499\pi$
$798$	−8.00000	−0.283197
$799$	61.2548	2.16704
$800$	−1.00000	−0.0353553
$801$	−58.2843	−2.05937
$802$	−10.0000	−0.353112
$803$	0	0
$804$	43.3137	1.52756
$805$	2.82843	0.0996890
$806$	−11.3137	−0.398508
$807$	5.65685	0.199131
$808$	10.0000	0.351799
$809$	−22.2843	−0.783473	−0.391737	−	0.920077i	$-0.628126\pi$
$809$	−22.2843	−0.783473	−0.391737	+	0.920077i	$0.628126\pi$
$810$	1.00000	0.0351364
$811$	−22.1421	−0.777516	−0.388758	−	0.921340i	$-0.627096\pi$
$811$	−22.1421	−0.777516	−0.388758	+	0.921340i	$0.627096\pi$
$812$	−3.17157	−0.111300
$813$	−48.0000	−1.68343
$814$	0	0
$815$	−12.0000	−0.420342
$816$	−21.6569	−0.758142
$817$	27.3137	0.955586
$818$	−12.1421	−0.424540
$819$	−10.0000	−0.349428
$820$	−0.828427	−0.0289299
$821$	29.7990	1.03999	0.519996	−	0.854169i	$-0.325933\pi$
$821$	29.7990	1.03999	0.519996	+	0.854169i	$0.325933\pi$
$822$	−15.0294	−0.524212
$823$	21.1716	0.737995	0.368997	−	0.929430i	$-0.379701\pi$
$823$	21.1716	0.737995	0.368997	+	0.929430i	$0.379701\pi$
$824$	5.65685	0.197066
$825$	0	0
$826$	8.00000	0.278356
$827$	49.2548	1.71276	0.856379	−	0.516347i	$-0.172709\pi$
$827$	49.2548	1.71276	0.856379	+	0.516347i	$0.172709\pi$
$828$	−14.1421	−0.491473
$829$	39.2548	1.36338	0.681688	−	0.731643i	$-0.261246\pi$
$829$	39.2548	1.36338	0.681688	+	0.731643i	$0.261246\pi$
$830$	2.34315	0.0813318
$831$	37.6569	1.30630
$832$	−2.00000	−0.0693375
$833$	−7.65685	−0.265294
$834$	53.2548	1.84406
$835$	−16.0000	−0.553703
$836$	0	0
$837$	−32.0000	−1.10608
$838$	30.6274	1.05801
$839$	−34.3431	−1.18566	−0.592829	−	0.805329i	$-0.701989\pi$
$839$	−34.3431	−1.18566	−0.592829	+	0.805329i	$0.701989\pi$
$840$	2.82843	0.0975900
$841$	−18.9411	−0.653142
$842$	−28.6274	−0.986566
$843$	19.7157	0.679046
$844$	−15.3137	−0.527120
$845$	9.00000	0.309609
$846$	40.0000	1.37523
$847$	0	0
$848$	−10.4853	−0.360066
$849$	64.0000	2.19647
$850$	7.65685	0.262628
$851$	−8.97056	−0.307507
$852$	−16.0000	−0.548151
$853$	25.3137	0.866725	0.433362	−	0.901220i	$-0.357327\pi$
$853$	25.3137	0.866725	0.433362	+	0.901220i	$0.357327\pi$
$854$	−9.31371	−0.318709
$855$	−14.1421	−0.483651
$856$	−1.65685	−0.0566301
$857$	6.97056	0.238110	0.119055	−	0.992888i	$-0.462014\pi$
$857$	6.97056	0.238110	0.119055	+	0.992888i	$0.462014\pi$
$858$	0	0
$859$	4.68629	0.159894	0.0799471	−	0.996799i	$-0.474525\pi$
$859$	4.68629	0.159894	0.0799471	+	0.996799i	$0.474525\pi$
$860$	−9.65685	−0.329296
$861$	2.34315	0.0798542
$862$	−19.7990	−0.674356
$863$	−36.7696	−1.25165	−0.625825	−	0.779963i	$-0.715238\pi$
$863$	−36.7696	−1.25165	−0.625825	+	0.779963i	$0.715238\pi$
$864$	−5.65685	−0.192450
$865$	−1.31371	−0.0446674
$866$	−20.8284	−0.707779
$867$	117.740	3.99866
$868$	−5.65685	−0.192006
$869$	0	0
$870$	−8.97056	−0.304131
$871$	−30.6274	−1.03777
$872$	14.4853	0.490534
$873$	−4.14214	−0.140190
$874$	8.00000	0.270604
$875$	−1.00000	−0.0338062
$876$	−21.6569	−0.731717
$877$	2.97056	0.100309	0.0501544	−	0.998741i	$-0.484029\pi$
$877$	2.97056	0.100309	0.0501544	+	0.998741i	$0.484029\pi$
$878$	24.9706	0.842716
$879$	−5.65685	−0.190801
$880$	0	0
$881$	−2.68629	−0.0905035	−0.0452517	−	0.998976i	$-0.514409\pi$
$881$	−2.68629	−0.0905035	−0.0452517	+	0.998976i	$0.514409\pi$
$882$	−5.00000	−0.168359
$883$	41.6569	1.40186	0.700932	−	0.713228i	$-0.252767\pi$
$883$	41.6569	1.40186	0.700932	+	0.713228i	$0.252767\pi$
$884$	15.3137	0.515056
$885$	22.6274	0.760612
$886$	8.68629	0.291822
$887$	22.6274	0.759754	0.379877	−	0.925037i	$-0.375966\pi$
$887$	22.6274	0.759754	0.379877	+	0.925037i	$0.375966\pi$
$888$	−8.97056	−0.301032
$889$	−19.3137	−0.647761
$890$	−11.6569	−0.390739
$891$	0	0
$892$	−28.2843	−0.947027
$893$	−22.6274	−0.757198
$894$	−4.28427	−0.143287
$895$	−6.34315	−0.212028
$896$	−1.00000	−0.0334077
$897$	16.0000	0.534224
$898$	6.00000	0.200223
$899$	17.9411	0.598370
$900$	5.00000	0.166667
$901$	80.2843	2.67466
$902$	0	0
$903$	27.3137	0.908943
$904$	−2.00000	−0.0665190
$905$	14.0000	0.465376
$906$	30.6274	1.01753
$907$	17.6569	0.586286	0.293143	−	0.956069i	$-0.405299\pi$
$907$	17.6569	0.586286	0.293143	+	0.956069i	$0.405299\pi$
$908$	24.0000	0.796468
$909$	−50.0000	−1.65840
$910$	−2.00000	−0.0662994
$911$	−21.6569	−0.717524	−0.358762	−	0.933429i	$-0.616801\pi$
$911$	−21.6569	−0.717524	−0.358762	+	0.933429i	$0.616801\pi$
$912$	8.00000	0.264906
$913$	0	0
$914$	−22.0000	−0.727695
$915$	−26.3431	−0.870878
$916$	−1.31371	−0.0434062
$917$	−18.8284	−0.621769
$918$	43.3137	1.42957
$919$	−20.7696	−0.685124	−0.342562	−	0.939495i	$-0.611295\pi$
$919$	−20.7696	−0.685124	−0.342562	+	0.939495i	$0.611295\pi$
$920$	−2.82843	−0.0932505
$921$	25.3726	0.836055
$922$	−11.6569	−0.383898
$923$	11.3137	0.372395
$924$	0	0
$925$	3.17157	0.104281
$926$	9.45584	0.310738
$927$	−28.2843	−0.928977
$928$	3.17157	0.104112
$929$	−38.9706	−1.27858	−0.639291	−	0.768965i	$-0.720772\pi$
$929$	−38.9706	−1.27858	−0.639291	+	0.768965i	$0.720772\pi$
$930$	−16.0000	−0.524661
$931$	2.82843	0.0926980
$932$	6.00000	0.196537
$933$	2.74517	0.0898727
$934$	−11.7990	−0.386075
$935$	0	0
$936$	10.0000	0.326860
$937$	−24.6274	−0.804543	−0.402271	−	0.915520i	$-0.631779\pi$
$937$	−24.6274	−0.804543	−0.402271	+	0.915520i	$0.631779\pi$
$938$	−15.3137	−0.500010
$939$	−24.9706	−0.814884
$940$	8.00000	0.260931
$941$	−13.3137	−0.434014	−0.217007	−	0.976170i	$-0.569630\pi$
$941$	−13.3137	−0.434014	−0.217007	+	0.976170i	$0.569630\pi$
$942$	−44.2843	−1.44286
$943$	−2.34315	−0.0763033
$944$	−8.00000	−0.260378
$945$	−5.65685	−0.184017
$946$	0	0
$947$	35.5980	1.15678	0.578389	−	0.815761i	$-0.303681\pi$
$947$	35.5980	1.15678	0.578389	+	0.815761i	$0.303681\pi$
$948$	14.6274	0.475076
$949$	15.3137	0.497104
$950$	−2.82843	−0.0917663
$951$	8.97056	0.290890
$952$	7.65685	0.248160
$953$	43.2548	1.40116	0.700581	−	0.713573i	$-0.252924\pi$
$953$	43.2548	1.40116	0.700581	+	0.713573i	$0.252924\pi$
$954$	52.4264	1.69737
$955$	−19.3137	−0.624977
$956$	7.51472	0.243043
$957$	0	0
$958$	35.3137	1.14093
$959$	5.31371	0.171589
$960$	−2.82843	−0.0912871
$961$	1.00000	0.0322581
$962$	6.34315	0.204511
$963$	8.28427	0.266957
$964$	8.82843	0.284344
$965$	21.3137	0.686113
$966$	8.00000	0.257396
$967$	−59.3137	−1.90740	−0.953700	−	0.300759i	$-0.902760\pi$
$967$	−59.3137	−1.90740	−0.953700	+	0.300759i	$0.902760\pi$
$968$	0	0
$969$	−61.2548	−1.96779
$970$	−0.828427	−0.0265992
$971$	−41.9411	−1.34595	−0.672977	−	0.739663i	$-0.734985\pi$
$971$	−41.9411	−1.34595	−0.672977	+	0.739663i	$0.734985\pi$
$972$	−14.1421	−0.453609
$973$	−18.8284	−0.603612
$974$	36.7696	1.17817
$975$	−5.65685	−0.181164
$976$	9.31371	0.298125
$977$	−20.6274	−0.659930	−0.329965	−	0.943993i	$-0.607037\pi$
$977$	−20.6274	−0.659930	−0.329965	+	0.943993i	$0.607037\pi$
$978$	−33.9411	−1.08532
$979$	0	0
$980$	−1.00000	−0.0319438
$981$	−72.4264	−2.31240
$982$	−8.68629	−0.277191
$983$	39.5980	1.26298	0.631490	−	0.775384i	$-0.282444\pi$
$983$	39.5980	1.26298	0.631490	+	0.775384i	$0.282444\pi$
$984$	−2.34315	−0.0746968
$985$	−12.3431	−0.393285
$986$	−24.2843	−0.773369
$987$	−22.6274	−0.720239
$988$	−5.65685	−0.179969
$989$	−27.3137	−0.868525
$990$	0	0
$991$	−40.0000	−1.27064	−0.635321	−	0.772248i	$-0.719132\pi$
$991$	−40.0000	−1.27064	−0.635321	+	0.772248i	$0.719132\pi$
$992$	5.65685	0.179605
$993$	81.9411	2.60032
$994$	5.65685	0.179425
$995$	11.3137	0.358669
$996$	6.62742	0.209998
$997$	−42.0000	−1.33015	−0.665077	−	0.746775i	$-0.731601\pi$
$997$	−42.0000	−1.33015	−0.665077	+	0.746775i	$0.731601\pi$
$998$	−28.9706	−0.917047
$999$	17.9411	0.567632

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8470.2.a.bo.1.2		2
11.10	odd	2		770.2.a.i.1.2	✓	2
33.32	even	2		6930.2.a.br.1.1		2
44.43	even	2		6160.2.a.ba.1.1		2
55.32	even	4		3850.2.c.u.1849.3		4
55.43	even	4		3850.2.c.u.1849.2		4
55.54	odd	2		3850.2.a.bi.1.1		2
77.76	even	2		5390.2.a.bt.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.a.i.1.2	✓	2	11.10	odd	2
3850.2.a.bi.1.1		2	55.54	odd	2
3850.2.c.u.1849.2		4	55.43	even	4
3850.2.c.u.1849.3		4	55.32	even	4
5390.2.a.bt.1.1		2	77.76	even	2
6160.2.a.ba.1.1		2	44.43	even	2
6930.2.a.br.1.1		2	33.32	even	2
8470.2.a.bo.1.2		2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.82843 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.82843 q^{6} +1.00000 q^{7} -1.00000 q^{8} +5.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.82843 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.82843 q^{6} +1.00000 q^{7} -1.00000 q^{8} +5.00000 q^{9} +1.00000 q^{10} +2.82843 q^{12} -2.00000 q^{13} -1.00000 q^{14} -2.82843 q^{15} +1.00000 q^{16} -7.65685 q^{17} -5.00000 q^{18} +2.82843 q^{19} -1.00000 q^{20} +2.82843 q^{21} -2.82843 q^{23} -2.82843 q^{24} +1.00000 q^{25} +2.00000 q^{26} +5.65685 q^{27} +1.00000 q^{28} -3.17157 q^{29} +2.82843 q^{30} -5.65685 q^{31} -1.00000 q^{32} +7.65685 q^{34} -1.00000 q^{35} +5.00000 q^{36} +3.17157 q^{37} -2.82843 q^{38} -5.65685 q^{39} +1.00000 q^{40} +0.828427 q^{41} -2.82843 q^{42} +9.65685 q^{43} -5.00000 q^{45} +2.82843 q^{46} -8.00000 q^{47} +2.82843 q^{48} +1.00000 q^{49} -1.00000 q^{50} -21.6569 q^{51} -2.00000 q^{52} -10.4853 q^{53} -5.65685 q^{54} -1.00000 q^{56} +8.00000 q^{57} +3.17157 q^{58} -8.00000 q^{59} -2.82843 q^{60} +9.31371 q^{61} +5.65685 q^{62} +5.00000 q^{63} +1.00000 q^{64} +2.00000 q^{65} +15.3137 q^{67} -7.65685 q^{68} -8.00000 q^{69} +1.00000 q^{70} -5.65685 q^{71} -5.00000 q^{72} -7.65685 q^{73} -3.17157 q^{74} +2.82843 q^{75} +2.82843 q^{76} +5.65685 q^{78} +5.17157 q^{79} -1.00000 q^{80} +1.00000 q^{81} -0.828427 q^{82} +2.34315 q^{83} +2.82843 q^{84} +7.65685 q^{85} -9.65685 q^{86} -8.97056 q^{87} -11.6569 q^{89} +5.00000 q^{90} -2.00000 q^{91} -2.82843 q^{92} -16.0000 q^{93} +8.00000 q^{94} -2.82843 q^{95} -2.82843 q^{96} -0.828427 q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{4} - 2 q^{5} + 2 q^{7} - 2 q^{8} + 10 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^4 - 2 * q^5 + 2 * q^7 - 2 * q^8 + 10 * q^9	\( 2 q - 2 q^{2} + 2 q^{4} - 2 q^{5} + 2 q^{7} - 2 q^{8} + 10 q^{9} + 2 q^{10} - 4 q^{13} - 2 q^{14} + 2 q^{16} - 4 q^{17} - 10 q^{18} - 2 q^{20} + 2 q^{25} + 4 q^{26} + 2 q^{28} - 12 q^{29} - 2 q^{32} + 4 q^{34} - 2 q^{35} + 10 q^{36} + 12 q^{37} + 2 q^{40} - 4 q^{41} + 8 q^{43} - 10 q^{45} - 16 q^{47} + 2 q^{49} - 2 q^{50} - 32 q^{51} - 4 q^{52} - 4 q^{53} - 2 q^{56} + 16 q^{57} + 12 q^{58} - 16 q^{59} - 4 q^{61} + 10 q^{63} + 2 q^{64} + 4 q^{65} + 8 q^{67} - 4 q^{68} - 16 q^{69} + 2 q^{70} - 10 q^{72} - 4 q^{73} - 12 q^{74} + 16 q^{79} - 2 q^{80} + 2 q^{81} + 4 q^{82} + 16 q^{83} + 4 q^{85} - 8 q^{86} + 16 q^{87} - 12 q^{89} + 10 q^{90} - 4 q^{91} - 32 q^{93} + 16 q^{94} + 4 q^{97} - 2 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^4 - 2 * q^5 + 2 * q^7 - 2 * q^8 + 10 * q^9 + 2 * q^10 - 4 * q^13 - 2 * q^14 + 2 * q^16 - 4 * q^17 - 10 * q^18 - 2 * q^20 + 2 * q^25 + 4 * q^26 + 2 * q^28 - 12 * q^29 - 2 * q^32 + 4 * q^34 - 2 * q^35 + 10 * q^36 + 12 * q^37 + 2 * q^40 - 4 * q^41 + 8 * q^43 - 10 * q^45 - 16 * q^47 + 2 * q^49 - 2 * q^50 - 32 * q^51 - 4 * q^52 - 4 * q^53 - 2 * q^56 + 16 * q^57 + 12 * q^58 - 16 * q^59 - 4 * q^61 + 10 * q^63 + 2 * q^64 + 4 * q^65 + 8 * q^67 - 4 * q^68 - 16 * q^69 + 2 * q^70 - 10 * q^72 - 4 * q^73 - 12 * q^74 + 16 * q^79 - 2 * q^80 + 2 * q^81 + 4 * q^82 + 16 * q^83 + 4 * q^85 - 8 * q^86 + 16 * q^87 - 12 * q^89 + 10 * q^90 - 4 * q^91 - 32 * q^93 + 16 * q^94 + 4 * q^97 - 2 * q^98

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