LMFDB - Embedded newform 6027.2.a.bc.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6027,2,Mod(1,6027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6027, 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("6027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6027 = 3 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6027.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:	$48.1258372982$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.8.7457527933.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} - 6x^{6} + 23x^{5} - 4x^{4} - 27x^{3} + 8x^{2} + 8x + 1 $ x^8 - 3x^7 - 6x^6 + 23x^5 - 4x^4 - 27x^3 + 8x^2 + 8*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 861)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.70360$ of defining polynomial
Character	$\chi$	$=$	6027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.23115 q^{2} +1.00000 q^{3} +2.97801 q^{4} -0.893036 q^{5} -2.23115 q^{6} -2.18209 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.23115 q^{2} +1.00000 q^{3} +2.97801 q^{4} -0.893036 q^{5} -2.23115 q^{6} -2.18209 q^{8} +1.00000 q^{9} +1.99249 q^{10} -3.03213 q^{11} +2.97801 q^{12} -1.02235 q^{13} -0.893036 q^{15} -1.08747 q^{16} -0.590534 q^{17} -2.23115 q^{18} -3.50700 q^{19} -2.65947 q^{20} +6.76512 q^{22} -0.556191 q^{23} -2.18209 q^{24} -4.20249 q^{25} +2.28100 q^{26} +1.00000 q^{27} +7.89796 q^{29} +1.99249 q^{30} +1.28393 q^{31} +6.79048 q^{32} -3.03213 q^{33} +1.31757 q^{34} +2.97801 q^{36} -11.5424 q^{37} +7.82463 q^{38} -1.02235 q^{39} +1.94868 q^{40} +1.00000 q^{41} -5.76153 q^{43} -9.02971 q^{44} -0.893036 q^{45} +1.24094 q^{46} +0.229519 q^{47} -1.08747 q^{48} +9.37636 q^{50} -0.590534 q^{51} -3.04456 q^{52} +8.54823 q^{53} -2.23115 q^{54} +2.70780 q^{55} -3.50700 q^{57} -17.6215 q^{58} -10.6811 q^{59} -2.65947 q^{60} -8.09457 q^{61} -2.86464 q^{62} -12.9756 q^{64} +0.912992 q^{65} +6.76512 q^{66} +8.13979 q^{67} -1.75862 q^{68} -0.556191 q^{69} +1.38924 q^{71} -2.18209 q^{72} +10.7543 q^{73} +25.7528 q^{74} -4.20249 q^{75} -10.4439 q^{76} +2.28100 q^{78} +4.67035 q^{79} +0.971148 q^{80} +1.00000 q^{81} -2.23115 q^{82} +3.22689 q^{83} +0.527368 q^{85} +12.8548 q^{86} +7.89796 q^{87} +6.61637 q^{88} +15.9423 q^{89} +1.99249 q^{90} -1.65634 q^{92} +1.28393 q^{93} -0.512091 q^{94} +3.13188 q^{95} +6.79048 q^{96} +5.16775 q^{97} -3.03213 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + 8 q^{3} + 13 q^{4} + 7 q^{5} + q^{6} + 6 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + q^2 + 8 * q^3 + 13 * q^4 + 7 * q^5 + q^6 + 6 * q^8 + 8 * q^9	$ 8 q + q^{2} + 8 q^{3} + 13 q^{4} + 7 q^{5} + q^{6} + 6 q^{8} + 8 q^{9} + 8 q^{10} + 11 q^{11} + 13 q^{12} + 10 q^{13} + 7 q^{15} - 17 q^{16} + 3 q^{17} + q^{18} + 6 q^{19} + 11 q^{20} + 15 q^{22} + 14 q^{23} + 6 q^{24} + 25 q^{25} + 24 q^{26} + 8 q^{27} + 2 q^{29} + 8 q^{30} + 16 q^{31} + 3 q^{32} + 11 q^{33} - 4 q^{34} + 13 q^{36} - 20 q^{37} + 10 q^{38} + 10 q^{39} - 3 q^{40} + 8 q^{41} + 7 q^{43} + 7 q^{45} - 5 q^{46} + 14 q^{47} - 17 q^{48} - 5 q^{50} + 3 q^{51} + 23 q^{52} + 7 q^{53} + q^{54} + 48 q^{55} + 6 q^{57} - 20 q^{58} + 22 q^{59} + 11 q^{60} - 33 q^{62} - 10 q^{64} - 14 q^{65} + 15 q^{66} + 12 q^{67} - 27 q^{68} + 14 q^{69} - 5 q^{71} + 6 q^{72} + 2 q^{73} + 6 q^{74} + 25 q^{75} + 43 q^{76} + 24 q^{78} - 15 q^{79} - 7 q^{80} + 8 q^{81} + q^{82} + 15 q^{83} - 43 q^{85} + 31 q^{86} + 2 q^{87} + 17 q^{88} + 29 q^{89} + 8 q^{90} + 19 q^{92} + 16 q^{93} + 20 q^{94} + 14 q^{95} + 3 q^{96} + 19 q^{97} + 11 q^{99}+O(q^{100}) $ 8 * q + q^2 + 8 * q^3 + 13 * q^4 + 7 * q^5 + q^6 + 6 * q^8 + 8 * q^9 + 8 * q^10 + 11 * q^11 + 13 * q^12 + 10 * q^13 + 7 * q^15 - 17 * q^16 + 3 * q^17 + q^18 + 6 * q^19 + 11 * q^20 + 15 * q^22 + 14 * q^23 + 6 * q^24 + 25 * q^25 + 24 * q^26 + 8 * q^27 + 2 * q^29 + 8 * q^30 + 16 * q^31 + 3 * q^32 + 11 * q^33 - 4 * q^34 + 13 * q^36 - 20 * q^37 + 10 * q^38 + 10 * q^39 - 3 * q^40 + 8 * q^41 + 7 * q^43 + 7 * q^45 - 5 * q^46 + 14 * q^47 - 17 * q^48 - 5 * q^50 + 3 * q^51 + 23 * q^52 + 7 * q^53 + q^54 + 48 * q^55 + 6 * q^57 - 20 * q^58 + 22 * q^59 + 11 * q^60 - 33 * q^62 - 10 * q^64 - 14 * q^65 + 15 * q^66 + 12 * q^67 - 27 * q^68 + 14 * q^69 - 5 * q^71 + 6 * q^72 + 2 * q^73 + 6 * q^74 + 25 * q^75 + 43 * q^76 + 24 * q^78 - 15 * q^79 - 7 * q^80 + 8 * q^81 + q^82 + 15 * q^83 - 43 * q^85 + 31 * q^86 + 2 * q^87 + 17 * q^88 + 29 * q^89 + 8 * q^90 + 19 * q^92 + 16 * q^93 + 20 * q^94 + 14 * q^95 + 3 * q^96 + 19 * q^97 + 11 * q^99

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 $

$2$	−2.23115	−1.57766	−0.788829	−	0.614612i	$-0.789312\pi$
$2$	−2.23115	−1.57766	−0.788829	+	0.614612i	$0.789312\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.97801	1.48901
$5$	−0.893036	−0.399378	−0.199689	−	0.979859i	$-0.563993\pi$
$5$	−0.893036	−0.399378	−0.199689	+	0.979859i	$0.563993\pi$
$6$	−2.23115	−0.910862
$7$	0	0
$7$	0	0
$8$	−2.18209	−0.771485
$9$	1.00000	0.333333
$10$	1.99249	0.630082
$11$	−3.03213	−0.914220	−0.457110	−	0.889410i	$-0.651116\pi$
$11$	−3.03213	−0.914220	−0.457110	+	0.889410i	$0.651116\pi$
$12$	2.97801	0.859678
$13$	−1.02235	−0.283548	−0.141774	−	0.989899i	$-0.545281\pi$
$13$	−1.02235	−0.283548	−0.141774	+	0.989899i	$0.545281\pi$
$14$	0	0
$15$	−0.893036	−0.230581
$16$	−1.08747	−0.271867
$17$	−0.590534	−0.143226	−0.0716128	−	0.997433i	$-0.522815\pi$
$17$	−0.590534	−0.143226	−0.0716128	+	0.997433i	$0.522815\pi$
$18$	−2.23115	−0.525886
$19$	−3.50700	−0.804561	−0.402281	−	0.915516i	$-0.631782\pi$
$19$	−3.50700	−0.804561	−0.402281	+	0.915516i	$0.631782\pi$
$20$	−2.65947	−0.594676
$21$	0	0
$22$	6.76512	1.44233
$23$	−0.556191	−0.115974	−0.0579870	−	0.998317i	$-0.518468\pi$
$23$	−0.556191	−0.115974	−0.0579870	+	0.998317i	$0.518468\pi$
$24$	−2.18209	−0.445417
$25$	−4.20249	−0.840497
$26$	2.28100	0.447342
$27$	1.00000	0.192450
$28$	0	0
$29$	7.89796	1.46661	0.733307	−	0.679898i	$-0.237976\pi$
$29$	7.89796	1.46661	0.733307	+	0.679898i	$0.237976\pi$
$30$	1.99249	0.363778
$31$	1.28393	0.230601	0.115300	−	0.993331i	$-0.463217\pi$
$31$	1.28393	0.230601	0.115300	+	0.993331i	$0.463217\pi$
$32$	6.79048	1.20040
$33$	−3.03213	−0.527825
$34$	1.31757	0.225961
$35$	0	0
$36$	2.97801	0.496335
$37$	−11.5424	−1.89756	−0.948779	−	0.315940i	$-0.897680\pi$
$37$	−11.5424	−1.89756	−0.948779	+	0.315940i	$0.897680\pi$
$38$	7.82463	1.26932
$39$	−1.02235	−0.163706
$40$	1.94868	0.308114
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	−5.76153	−0.878625	−0.439313	−	0.898334i	$-0.644778\pi$
$43$	−5.76153	−0.878625	−0.439313	+	0.898334i	$0.644778\pi$
$44$	−9.02971	−1.36128
$45$	−0.893036	−0.133126
$46$	1.24094	0.182967
$47$	0.229519	0.0334788	0.0167394	−	0.999860i	$-0.494671\pi$
$47$	0.229519	0.0334788	0.0167394	+	0.999860i	$0.494671\pi$
$48$	−1.08747	−0.156962
$49$	0	0
$50$	9.37636	1.32602
$51$	−0.590534	−0.0826913
$52$	−3.04456	−0.422205
$53$	8.54823	1.17419	0.587095	−	0.809518i	$-0.300271\pi$
$53$	8.54823	1.17419	0.587095	+	0.809518i	$0.300271\pi$
$54$	−2.23115	−0.303621
$55$	2.70780	0.365119
$56$	0	0
$57$	−3.50700	−0.464514
$58$	−17.6215	−2.31382
$59$	−10.6811	−1.39056	−0.695282	−	0.718737i	$-0.744721\pi$
$59$	−10.6811	−1.39056	−0.695282	+	0.718737i	$0.744721\pi$
$60$	−2.65947	−0.343336
$61$	−8.09457	−1.03640	−0.518202	−	0.855258i	$-0.673398\pi$
$61$	−8.09457	−1.03640	−0.518202	+	0.855258i	$0.673398\pi$
$62$	−2.86464	−0.363809
$63$	0	0
$64$	−12.9756	−1.62195
$65$	0.912992	0.113243
$66$	6.76512	0.832728
$67$	8.13979	0.994434	0.497217	−	0.867626i	$-0.334355\pi$
$67$	8.13979	0.994434	0.497217	+	0.867626i	$0.334355\pi$
$68$	−1.75862	−0.213264
$69$	−0.556191	−0.0669576
$70$	0	0
$71$	1.38924	0.164873	0.0824363	−	0.996596i	$-0.473730\pi$
$71$	1.38924	0.164873	0.0824363	+	0.996596i	$0.473730\pi$
$72$	−2.18209	−0.257162
$73$	10.7543	1.25869	0.629345	−	0.777126i	$-0.283323\pi$
$73$	10.7543	1.25869	0.629345	+	0.777126i	$0.283323\pi$
$74$	25.7528	2.99370
$75$	−4.20249	−0.485261
$76$	−10.4439	−1.19800
$77$	0	0
$78$	2.28100	0.258273
$79$	4.67035	0.525456	0.262728	−	0.964870i	$-0.415378\pi$
$79$	4.67035	0.525456	0.262728	+	0.964870i	$0.415378\pi$
$80$	0.971148	0.108578
$81$	1.00000	0.111111
$82$	−2.23115	−0.246389
$83$	3.22689	0.354197	0.177099	−	0.984193i	$-0.443329\pi$
$83$	3.22689	0.354197	0.177099	+	0.984193i	$0.443329\pi$
$84$	0	0
$85$	0.527368	0.0572011
$86$	12.8548	1.38617
$87$	7.89796	0.846750
$88$	6.61637	0.705307
$89$	15.9423	1.68989	0.844943	−	0.534857i	$-0.179634\pi$
$89$	15.9423	1.68989	0.844943	+	0.534857i	$0.179634\pi$
$90$	1.99249	0.210027
$91$	0	0
$92$	−1.65634	−0.172686
$93$	1.28393	0.133138
$94$	−0.512091	−0.0528182
$95$	3.13188	0.321324
$96$	6.79048	0.693050
$97$	5.16775	0.524706	0.262353	−	0.964972i	$-0.415502\pi$
$97$	5.16775	0.524706	0.262353	+	0.964972i	$0.415502\pi$
$98$	0	0
$99$	−3.03213	−0.304740
$100$	−12.5151	−1.25151
$101$	10.6304	1.05776	0.528881	−	0.848696i	$-0.322612\pi$
$101$	10.6304	1.05776	0.528881	+	0.848696i	$0.322612\pi$
$102$	1.31757	0.130459
$103$	−3.93822	−0.388044	−0.194022	−	0.980997i	$-0.562153\pi$
$103$	−3.93822	−0.388044	−0.194022	+	0.980997i	$0.562153\pi$
$104$	2.23085	0.218753
$105$	0	0
$106$	−19.0724	−1.85247
$107$	−10.8000	−1.04408	−0.522039	−	0.852922i	$-0.674828\pi$
$107$	−10.8000	−1.04408	−0.522039	+	0.852922i	$0.674828\pi$
$108$	2.97801	0.286559
$109$	−13.7396	−1.31601	−0.658007	−	0.753012i	$-0.728600\pi$
$109$	−13.7396	−1.31601	−0.658007	+	0.753012i	$0.728600\pi$
$110$	−6.04149	−0.576034
$111$	−11.5424	−1.09556
$112$	0	0
$113$	2.87693	0.270638	0.135319	−	0.990802i	$-0.456794\pi$
$113$	2.87693	0.270638	0.135319	+	0.990802i	$0.456794\pi$
$114$	7.82463	0.732844
$115$	0.496699	0.0463174
$116$	23.5202	2.18380
$117$	−1.02235	−0.0945160
$118$	23.8312	2.19384
$119$	0	0
$120$	1.94868	0.177890
$121$	−1.80621	−0.164201
$122$	18.0602	1.63509
$123$	1.00000	0.0901670
$124$	3.82356	0.343366
$125$	8.21815	0.735054
$126$	0	0
$127$	−7.93950	−0.704517	−0.352258	−	0.935903i	$-0.614586\pi$
$127$	−7.93950	−0.704517	−0.352258	+	0.935903i	$0.614586\pi$
$128$	15.3695	1.35849
$129$	−5.76153	−0.507274
$130$	−2.03702	−0.178658
$131$	1.91414	0.167239	0.0836195	−	0.996498i	$-0.473352\pi$
$131$	1.91414	0.167239	0.0836195	+	0.996498i	$0.473352\pi$
$132$	−9.02971	−0.785935
$133$	0	0
$134$	−18.1611	−1.56888
$135$	−0.893036	−0.0768603
$136$	1.28860	0.110496
$137$	10.9420	0.934842	0.467421	−	0.884035i	$-0.345183\pi$
$137$	10.9420	0.934842	0.467421	+	0.884035i	$0.345183\pi$
$138$	1.24094	0.105636
$139$	20.5931	1.74668	0.873341	−	0.487109i	$-0.161949\pi$
$139$	20.5931	1.74668	0.873341	+	0.487109i	$0.161949\pi$
$140$	0	0
$141$	0.229519	0.0193290
$142$	−3.09960	−0.260112
$143$	3.09988	0.259225
$144$	−1.08747	−0.0906223
$145$	−7.05316	−0.585733
$146$	−23.9943	−1.98578
$147$	0	0
$148$	−34.3734	−2.82548
$149$	3.25543	0.266695	0.133347	−	0.991069i	$-0.457427\pi$
$149$	3.25543	0.266695	0.133347	+	0.991069i	$0.457427\pi$
$150$	9.37636	0.765577
$151$	12.0406	0.979852	0.489926	−	0.871764i	$-0.337024\pi$
$151$	12.0406	0.979852	0.489926	+	0.871764i	$0.337024\pi$
$152$	7.65258	0.620706
$153$	−0.590534	−0.0477418
$154$	0	0
$155$	−1.14660	−0.0920969
$156$	−3.04456	−0.243760
$157$	0.580260	0.0463098	0.0231549	−	0.999732i	$-0.492629\pi$
$157$	0.580260	0.0463098	0.0231549	+	0.999732i	$0.492629\pi$
$158$	−10.4202	−0.828990
$159$	8.54823	0.677919
$160$	−6.06414	−0.479412
$161$	0	0
$162$	−2.23115	−0.175295
$163$	11.9654	0.937204	0.468602	−	0.883409i	$-0.344758\pi$
$163$	11.9654	0.937204	0.468602	+	0.883409i	$0.344758\pi$
$164$	2.97801	0.232544
$165$	2.70780	0.210802
$166$	−7.19967	−0.558802
$167$	−16.9933	−1.31498	−0.657490	−	0.753463i	$-0.728382\pi$
$167$	−16.9933	−1.31498	−0.657490	+	0.753463i	$0.728382\pi$
$168$	0	0
$169$	−11.9548	−0.919601
$170$	−1.17664	−0.0902438
$171$	−3.50700	−0.268187
$172$	−17.1579	−1.30828
$173$	3.00321	0.228330	0.114165	−	0.993462i	$-0.463581\pi$
$173$	3.00321	0.228330	0.114165	+	0.993462i	$0.463581\pi$
$174$	−17.6215	−1.33588
$175$	0	0
$176$	3.29734	0.248546
$177$	−10.6811	−0.802843
$178$	−35.5697	−2.66606
$179$	10.3399	0.772844	0.386422	−	0.922322i	$-0.373711\pi$
$179$	10.3399	0.772844	0.386422	+	0.922322i	$0.373711\pi$
$180$	−2.65947	−0.198225
$181$	−9.54059	−0.709146	−0.354573	−	0.935028i	$-0.615374\pi$
$181$	−9.54059	−0.709146	−0.354573	+	0.935028i	$0.615374\pi$
$182$	0	0
$183$	−8.09457	−0.598368
$184$	1.21366	0.0894721
$185$	10.3078	0.757843
$186$	−2.86464	−0.210046
$187$	1.79057	0.130940
$188$	0.683511	0.0498502
$189$	0	0
$190$	−6.98768	−0.506939
$191$	3.85532	0.278961	0.139480	−	0.990225i	$-0.455457\pi$
$191$	3.85532	0.278961	0.139480	+	0.990225i	$0.455457\pi$
$192$	−12.9756	−0.936434
$193$	12.2524	0.881949	0.440975	−	0.897520i	$-0.354633\pi$
$193$	12.2524	0.881949	0.440975	+	0.897520i	$0.354633\pi$
$194$	−11.5300	−0.827806
$195$	0.912992	0.0653807
$196$	0	0
$197$	20.0578	1.42906	0.714529	−	0.699606i	$-0.246641\pi$
$197$	20.0578	1.42906	0.714529	+	0.699606i	$0.246641\pi$
$198$	6.76512	0.480776
$199$	−8.76302	−0.621194	−0.310597	−	0.950542i	$-0.600529\pi$
$199$	−8.76302	−0.621194	−0.310597	+	0.950542i	$0.600529\pi$
$200$	9.17019	0.648431
$201$	8.13979	0.574137
$202$	−23.7179	−1.66879
$203$	0	0
$204$	−1.75862	−0.123128
$205$	−0.893036	−0.0623724
$206$	8.78674	0.612201
$207$	−0.556191	−0.0386580
$208$	1.11177	0.0770873
$209$	10.6337	0.735546
$210$	0	0
$211$	21.8898	1.50696	0.753478	−	0.657473i	$-0.228375\pi$
$211$	21.8898	1.50696	0.753478	+	0.657473i	$0.228375\pi$
$212$	25.4567	1.74838
$213$	1.38924	0.0951892
$214$	24.0964	1.64720
$215$	5.14525	0.350903
$216$	−2.18209	−0.148472
$217$	0	0
$218$	30.6550	2.07622
$219$	10.7543	0.726705
$220$	8.06386	0.543665
$221$	0.603730	0.0406113
$222$	25.7528	1.72841
$223$	19.0053	1.27269	0.636343	−	0.771406i	$-0.280446\pi$
$223$	19.0053	1.27269	0.636343	+	0.771406i	$0.280446\pi$
$224$	0	0
$225$	−4.20249	−0.280166
$226$	−6.41884	−0.426975
$227$	14.7021	0.975814	0.487907	−	0.872896i	$-0.337761\pi$
$227$	14.7021	0.975814	0.487907	+	0.872896i	$0.337761\pi$
$228$	−10.4439	−0.691664
$229$	22.7562	1.50377	0.751886	−	0.659293i	$-0.229144\pi$
$229$	22.7562	1.50377	0.751886	+	0.659293i	$0.229144\pi$
$230$	−1.10821	−0.0730731
$231$	0	0
$232$	−17.2340	−1.13147
$233$	−27.3282	−1.79033	−0.895164	−	0.445737i	$-0.852942\pi$
$233$	−27.3282	−1.79033	−0.895164	+	0.445737i	$0.852942\pi$
$234$	2.28100	0.149114
$235$	−0.204969	−0.0133707
$236$	−31.8085	−2.07056
$237$	4.67035	0.303372
$238$	0	0
$239$	−12.5731	−0.813286	−0.406643	−	0.913587i	$-0.633301\pi$
$239$	−12.5731	−0.813286	−0.406643	+	0.913587i	$0.633301\pi$
$240$	0.971148	0.0626873
$241$	4.30351	0.277214	0.138607	−	0.990347i	$-0.455738\pi$
$241$	4.30351	0.277214	0.138607	+	0.990347i	$0.455738\pi$
$242$	4.02992	0.259053
$243$	1.00000	0.0641500
$244$	−24.1057	−1.54321
$245$	0	0
$246$	−2.23115	−0.142253
$247$	3.58537	0.228132
$248$	−2.80165	−0.177905
$249$	3.22689	0.204496
$250$	−18.3359	−1.15966
$251$	−12.7442	−0.804408	−0.402204	−	0.915550i	$-0.631756\pi$
$251$	−12.7442	−0.804408	−0.402204	+	0.915550i	$0.631756\pi$
$252$	0	0
$253$	1.68644	0.106026
$254$	17.7142	1.11149
$255$	0.527368	0.0330251
$256$	−8.34043	−0.521277
$257$	−15.3531	−0.957701	−0.478850	−	0.877897i	$-0.658946\pi$
$257$	−15.3531	−0.957701	−0.478850	+	0.877897i	$0.658946\pi$
$258$	12.8548	0.800306
$259$	0	0
$260$	2.71890	0.168619
$261$	7.89796	0.488871
$262$	−4.27072	−0.263846
$263$	4.70180	0.289925	0.144963	−	0.989437i	$-0.453694\pi$
$263$	4.70180	0.289925	0.144963	+	0.989437i	$0.453694\pi$
$264$	6.61637	0.407209
$265$	−7.63388	−0.468946
$266$	0	0
$267$	15.9423	0.975656
$268$	24.2404	1.48072
$269$	−17.8058	−1.08564	−0.542818	−	0.839850i	$-0.682643\pi$
$269$	−17.8058	−1.08564	−0.542818	+	0.839850i	$0.682643\pi$
$270$	1.99249	0.121259
$271$	−5.15229	−0.312980	−0.156490	−	0.987680i	$-0.550018\pi$
$271$	−5.15229	−0.312980	−0.156490	+	0.987680i	$0.550018\pi$
$272$	0.642187	0.0389383
$273$	0	0
$274$	−24.4133	−1.47486
$275$	12.7425	0.768400
$276$	−1.65634	−0.0997002
$277$	−8.01369	−0.481496	−0.240748	−	0.970588i	$-0.577393\pi$
$277$	−8.01369	−0.481496	−0.240748	+	0.970588i	$0.577393\pi$
$278$	−45.9462	−2.75567
$279$	1.28393	0.0768670
$280$	0	0
$281$	4.98277	0.297247	0.148624	−	0.988894i	$-0.452516\pi$
$281$	4.98277	0.297247	0.148624	+	0.988894i	$0.452516\pi$
$282$	−0.512091	−0.0304946
$283$	6.83872	0.406520	0.203260	−	0.979125i	$-0.434846\pi$
$283$	6.83872	0.406520	0.203260	+	0.979125i	$0.434846\pi$
$284$	4.13717	0.245496
$285$	3.13188	0.185516
$286$	−6.91629	−0.408969
$287$	0	0
$288$	6.79048	0.400133
$289$	−16.6513	−0.979486
$290$	15.7366	0.924087
$291$	5.16775	0.302939
$292$	32.0263	1.87420
$293$	23.1644	1.35328	0.676639	−	0.736315i	$-0.263436\pi$
$293$	23.1644	1.35328	0.676639	+	0.736315i	$0.263436\pi$
$294$	0	0
$295$	9.53863	0.555361
$296$	25.1865	1.46394
$297$	−3.03213	−0.175942
$298$	−7.26333	−0.420754
$299$	0.568620	0.0328842
$300$	−12.5151	−0.722557
$301$	0	0
$302$	−26.8644	−1.54587
$303$	10.6304	0.610699
$304$	3.81375	0.218734
$305$	7.22875	0.413917
$306$	1.31757	0.0753203
$307$	−16.0121	−0.913857	−0.456929	−	0.889503i	$-0.651051\pi$
$307$	−16.0121	−0.913857	−0.456929	+	0.889503i	$0.651051\pi$
$308$	0	0
$309$	−3.93822	−0.224037
$310$	2.55823	0.145297
$311$	−20.7107	−1.17440	−0.587198	−	0.809443i	$-0.699769\pi$
$311$	−20.7107	−1.17440	−0.587198	+	0.809443i	$0.699769\pi$
$312$	2.23085	0.126297
$313$	18.5447	1.04821	0.524105	−	0.851653i	$-0.324400\pi$
$313$	18.5447	1.04821	0.524105	+	0.851653i	$0.324400\pi$
$314$	−1.29464	−0.0730610
$315$	0	0
$316$	13.9084	0.782407
$317$	20.6683	1.16085	0.580425	−	0.814314i	$-0.302887\pi$
$317$	20.6683	1.16085	0.580425	+	0.814314i	$0.302887\pi$
$318$	−19.0724	−1.06952
$319$	−23.9476	−1.34081
$320$	11.5877	0.647771
$321$	−10.8000	−0.602798
$322$	0	0
$323$	2.07100	0.115234
$324$	2.97801	0.165445
$325$	4.29640	0.238321
$326$	−26.6966	−1.47859
$327$	−13.7396	−0.759801
$328$	−2.18209	−0.120486
$329$	0	0
$330$	−6.04149	−0.332573
$331$	3.75882	0.206603	0.103302	−	0.994650i	$-0.467059\pi$
$331$	3.75882	0.206603	0.103302	+	0.994650i	$0.467059\pi$
$332$	9.60972	0.527402
$333$	−11.5424	−0.632519
$334$	37.9145	2.07459
$335$	−7.26913	−0.397155
$336$	0	0
$337$	−26.8704	−1.46373	−0.731863	−	0.681452i	$-0.761349\pi$
$337$	−26.8704	−1.46373	−0.731863	+	0.681452i	$0.761349\pi$
$338$	26.6729	1.45082
$339$	2.87693	0.156253
$340$	1.57051	0.0851728
$341$	−3.89304	−0.210820
$342$	7.82463	0.423108
$343$	0	0
$344$	12.5722	0.677846
$345$	0.496699	0.0267414
$346$	−6.70059	−0.360226
$347$	−21.4572	−1.15188	−0.575941	−	0.817491i	$-0.695364\pi$
$347$	−21.4572	−1.15188	−0.575941	+	0.817491i	$0.695364\pi$
$348$	23.5202	1.26082
$349$	26.1532	1.39995	0.699974	−	0.714168i	$-0.253195\pi$
$349$	26.1532	1.39995	0.699974	+	0.714168i	$0.253195\pi$
$350$	0	0
$351$	−1.02235	−0.0545688
$352$	−20.5896	−1.09743
$353$	−3.71713	−0.197843	−0.0989216	−	0.995095i	$-0.531539\pi$
$353$	−3.71713	−0.197843	−0.0989216	+	0.995095i	$0.531539\pi$
$354$	23.8312	1.26661
$355$	−1.24064	−0.0658464
$356$	47.4765	2.51625
$357$	0	0
$358$	−23.0699	−1.21928
$359$	13.2589	0.699776	0.349888	−	0.936792i	$-0.386220\pi$
$359$	13.2589	0.699776	0.349888	+	0.936792i	$0.386220\pi$
$360$	1.94868	0.102705
$361$	−6.70095	−0.352681
$362$	21.2864	1.11879
$363$	−1.80621	−0.0948015
$364$	0	0
$365$	−9.60393	−0.502693
$366$	18.0602	0.944021
$367$	−19.4105	−1.01322	−0.506610	−	0.862175i	$-0.669102\pi$
$367$	−19.4105	−1.01322	−0.506610	+	0.862175i	$0.669102\pi$
$368$	0.604840	0.0315295
$369$	1.00000	0.0520579
$370$	−22.9982	−1.19562
$371$	0	0
$372$	3.82356	0.198243
$373$	19.8031	1.02536	0.512682	−	0.858579i	$-0.328652\pi$
$373$	19.8031	1.02536	0.512682	+	0.858579i	$0.328652\pi$
$374$	−3.99503	−0.206578
$375$	8.21815	0.424384
$376$	−0.500831	−0.0258284
$377$	−8.07445	−0.415855
$378$	0	0
$379$	10.4729	0.537955	0.268977	−	0.963147i	$-0.413314\pi$
$379$	10.4729	0.537955	0.268977	+	0.963147i	$0.413314\pi$
$380$	9.32677	0.478453
$381$	−7.93950	−0.406753
$382$	−8.60178	−0.440105
$383$	17.9568	0.917552	0.458776	−	0.888552i	$-0.348288\pi$
$383$	17.9568	0.917552	0.458776	+	0.888552i	$0.348288\pi$
$384$	15.3695	0.784322
$385$	0	0
$386$	−27.3370	−1.39141
$387$	−5.76153	−0.292875
$388$	15.3896	0.781290
$389$	31.2703	1.58547	0.792733	−	0.609569i	$-0.208657\pi$
$389$	31.2703	1.58547	0.792733	+	0.609569i	$0.208657\pi$
$390$	−2.03702	−0.103148
$391$	0.328450	0.0166104
$392$	0	0
$393$	1.91414	0.0965555
$394$	−44.7519	−2.25457
$395$	−4.17079	−0.209855
$396$	−9.02971	−0.453760
$397$	29.4827	1.47969	0.739846	−	0.672776i	$-0.234898\pi$
$397$	29.4827	1.47969	0.739846	+	0.672776i	$0.234898\pi$
$398$	19.5516	0.980032
$399$	0	0
$400$	4.57007	0.228503
$401$	−11.3149	−0.565040	−0.282520	−	0.959261i	$-0.591170\pi$
$401$	−11.3149	−0.565040	−0.282520	+	0.959261i	$0.591170\pi$
$402$	−18.1611	−0.905791
$403$	−1.31262	−0.0653864
$404$	31.6574	1.57501
$405$	−0.893036	−0.0443753
$406$	0	0
$407$	34.9980	1.73479
$408$	1.28860	0.0637951
$409$	18.9256	0.935812	0.467906	−	0.883778i	$-0.345009\pi$
$409$	18.9256	0.935812	0.467906	+	0.883778i	$0.345009\pi$
$410$	1.99249	0.0984023
$411$	10.9420	0.539731
$412$	−11.7281	−0.577800
$413$	0	0
$414$	1.24094	0.0609891
$415$	−2.88173	−0.141459
$416$	−6.94222	−0.340370
$417$	20.5931	1.00845
$418$	−23.7253	−1.16044
$419$	11.2826	0.551193	0.275597	−	0.961273i	$-0.411125\pi$
$419$	11.2826	0.551193	0.275597	+	0.961273i	$0.411125\pi$
$420$	0	0
$421$	1.47063	0.0716742	0.0358371	−	0.999358i	$-0.488590\pi$
$421$	1.47063	0.0716742	0.0358371	+	0.999358i	$0.488590\pi$
$422$	−48.8393	−2.37746
$423$	0.229519	0.0111596
$424$	−18.6530	−0.905870
$425$	2.48171	0.120381
$426$	−3.09960	−0.150176
$427$	0	0
$428$	−32.1626	−1.55464
$429$	3.09988	0.149664
$430$	−11.4798	−0.553606
$431$	−4.90425	−0.236229	−0.118115	−	0.993000i	$-0.537685\pi$
$431$	−4.90425	−0.236229	−0.118115	+	0.993000i	$0.537685\pi$
$432$	−1.08747	−0.0523208
$433$	−9.20606	−0.442415	−0.221207	−	0.975227i	$-0.571000\pi$
$433$	−9.20606	−0.442415	−0.221207	+	0.975227i	$0.571000\pi$
$434$	0	0
$435$	−7.05316	−0.338173
$436$	−40.9166	−1.95955
$437$	1.95056	0.0933081
$438$	−23.9943	−1.14649
$439$	−24.0382	−1.14728	−0.573641	−	0.819107i	$-0.694470\pi$
$439$	−24.0382	−1.14728	−0.573641	+	0.819107i	$0.694470\pi$
$440$	−5.90865	−0.281684
$441$	0	0
$442$	−1.34701	−0.0640708
$443$	−22.3474	−1.06176	−0.530878	−	0.847448i	$-0.678138\pi$
$443$	−22.3474	−1.06176	−0.530878	+	0.847448i	$0.678138\pi$
$444$	−34.3734	−1.63129
$445$	−14.2371	−0.674903
$446$	−42.4035	−2.00786
$447$	3.25543	0.153976
$448$	0	0
$449$	15.0846	0.711886	0.355943	−	0.934508i	$-0.384160\pi$
$449$	15.0846	0.711886	0.355943	+	0.934508i	$0.384160\pi$
$450$	9.37636	0.442006
$451$	−3.03213	−0.142777
$452$	8.56752	0.402982
$453$	12.0406	0.565718
$454$	−32.8026	−1.53950
$455$	0	0
$456$	7.65258	0.358365
$457$	−11.9480	−0.558905	−0.279453	−	0.960160i	$-0.590153\pi$
$457$	−11.9480	−0.558905	−0.279453	+	0.960160i	$0.590153\pi$
$458$	−50.7724	−2.37244
$459$	−0.590534	−0.0275638
$460$	1.47918	0.0689669
$461$	−8.73937	−0.407033	−0.203517	−	0.979071i	$-0.565237\pi$
$461$	−8.73937	−0.407033	−0.203517	+	0.979071i	$0.565237\pi$
$462$	0	0
$463$	−32.3911	−1.50534	−0.752670	−	0.658398i	$-0.771235\pi$
$463$	−32.3911	−1.50534	−0.752670	+	0.658398i	$0.771235\pi$
$464$	−8.58877	−0.398724
$465$	−1.14660	−0.0531722
$466$	60.9731	2.82453
$467$	0.327510	0.0151553	0.00757767	−	0.999971i	$-0.497588\pi$
$467$	0.327510	0.0151553	0.00757767	+	0.999971i	$0.497588\pi$
$468$	−3.04456	−0.140735
$469$	0	0
$470$	0.457316	0.0210944
$471$	0.580260	0.0267370
$472$	23.3072	1.07280
$473$	17.4697	0.803257
$474$	−10.4202	−0.478617
$475$	14.7381	0.676231
$476$	0	0
$477$	8.54823	0.391397
$478$	28.0524	1.28309
$479$	−5.82212	−0.266020	−0.133010	−	0.991115i	$-0.542464\pi$
$479$	−5.82212	−0.266020	−0.133010	+	0.991115i	$0.542464\pi$
$480$	−6.06414	−0.276789
$481$	11.8003	0.538049
$482$	−9.60177	−0.437349
$483$	0	0
$484$	−5.37892	−0.244496
$485$	−4.61499	−0.209556
$486$	−2.23115	−0.101207
$487$	−24.5314	−1.11162	−0.555811	−	0.831309i	$-0.687592\pi$
$487$	−24.5314	−1.11162	−0.555811	+	0.831309i	$0.687592\pi$
$488$	17.6631	0.799570
$489$	11.9654	0.541095
$490$	0	0
$491$	21.0462	0.949801	0.474900	−	0.880040i	$-0.342484\pi$
$491$	21.0462	0.949801	0.474900	+	0.880040i	$0.342484\pi$
$492$	2.97801	0.134259
$493$	−4.66401	−0.210057
$494$	−7.99948	−0.359914
$495$	2.70780	0.121706
$496$	−1.39623	−0.0626928
$497$	0	0
$498$	−7.19967	−0.322625
$499$	21.4488	0.960181	0.480090	−	0.877219i	$-0.340604\pi$
$499$	21.4488	0.960181	0.480090	+	0.877219i	$0.340604\pi$
$500$	24.4738	1.09450
$501$	−16.9933	−0.759204
$502$	28.4342	1.26908
$503$	33.1070	1.47617	0.738084	−	0.674708i	$-0.235731\pi$
$503$	33.1070	1.47617	0.738084	+	0.674708i	$0.235731\pi$
$504$	0	0
$505$	−9.49330	−0.422446
$506$	−3.76270	−0.167272
$507$	−11.9548	−0.530932
$508$	−23.6439	−1.04903
$509$	13.7852	0.611018	0.305509	−	0.952189i	$-0.401173\pi$
$509$	13.7852	0.611018	0.305509	+	0.952189i	$0.401173\pi$
$510$	−1.17664	−0.0521023
$511$	0	0
$512$	−12.1303	−0.536090
$513$	−3.50700	−0.154838
$514$	34.2550	1.51092
$515$	3.51697	0.154976
$516$	−17.1579	−0.755335
$517$	−0.695932	−0.0306070
$518$	0	0
$519$	3.00321	0.131826
$520$	−1.99223	−0.0873651
$521$	27.8521	1.22022	0.610112	−	0.792315i	$-0.291124\pi$
$521$	27.8521	1.22022	0.610112	+	0.792315i	$0.291124\pi$
$522$	−17.6215	−0.771272
$523$	25.6651	1.12226	0.561128	−	0.827729i	$-0.310367\pi$
$523$	25.6651	1.12226	0.561128	+	0.827729i	$0.310367\pi$
$524$	5.70033	0.249020
$525$	0	0
$526$	−10.4904	−0.457403
$527$	−0.758205	−0.0330279
$528$	3.29734	0.143498
$529$	−22.6907	−0.986550
$530$	17.0323	0.739836
$531$	−10.6811	−0.463521
$532$	0	0
$533$	−1.02235	−0.0442827
$534$	−35.5697	−1.53925
$535$	9.64481	0.416981
$536$	−17.7617	−0.767190
$537$	10.3399	0.446202
$538$	39.7273	1.71276
$539$	0	0
$540$	−2.65947	−0.114445
$541$	−24.9672	−1.07342	−0.536711	−	0.843766i	$-0.680333\pi$
$541$	−24.9672	−1.07342	−0.536711	+	0.843766i	$0.680333\pi$
$542$	11.4955	0.493775
$543$	−9.54059	−0.409426
$544$	−4.01001	−0.171928
$545$	12.2699	0.525587
$546$	0	0
$547$	0.176971	0.00756675	0.00378338	−	0.999993i	$-0.498796\pi$
$547$	0.176971	0.00756675	0.00378338	+	0.999993i	$0.498796\pi$
$548$	32.5855	1.39198
$549$	−8.09457	−0.345468
$550$	−28.4303	−1.21227
$551$	−27.6981	−1.17998
$552$	1.21366	0.0516567
$553$	0	0
$554$	17.8797	0.759636
$555$	10.3078	0.437541
$556$	61.3264	2.60082
$557$	28.8231	1.22127	0.610636	−	0.791911i	$-0.290914\pi$
$557$	28.8231	1.22127	0.610636	+	0.791911i	$0.290914\pi$
$558$	−2.86464	−0.121270
$559$	5.89028	0.249132
$560$	0	0
$561$	1.79057	0.0755981
$562$	−11.1173	−0.468954
$563$	28.9563	1.22036	0.610181	−	0.792262i	$-0.291097\pi$
$563$	28.9563	1.22036	0.610181	+	0.792262i	$0.291097\pi$
$564$	0.683511	0.0287810
$565$	−2.56920	−0.108087
$566$	−15.2582	−0.641350
$567$	0	0
$568$	−3.03144	−0.127197
$569$	2.87743	0.120628	0.0603140	−	0.998179i	$-0.480790\pi$
$569$	2.87743	0.120628	0.0603140	+	0.998179i	$0.480790\pi$
$570$	−6.98768	−0.292682
$571$	−23.6968	−0.991680	−0.495840	−	0.868414i	$-0.665140\pi$
$571$	−23.6968	−0.991680	−0.495840	+	0.868414i	$0.665140\pi$
$572$	9.23149	0.385988
$573$	3.85532	0.161058
$574$	0	0
$575$	2.33739	0.0974758
$576$	−12.9756	−0.540650
$577$	25.8656	1.07680	0.538399	−	0.842690i	$-0.319029\pi$
$577$	25.8656	1.07680	0.538399	+	0.842690i	$0.319029\pi$
$578$	37.1514	1.54530
$579$	12.2524	0.509194
$580$	−21.0044	−0.872160
$581$	0	0
$582$	−11.5300	−0.477934
$583$	−25.9193	−1.07347
$584$	−23.4667	−0.971060
$585$	0.912992	0.0377476
$586$	−51.6831	−2.13501
$587$	42.3285	1.74708	0.873542	−	0.486750i	$-0.161818\pi$
$587$	42.3285	1.74708	0.873542	+	0.486750i	$0.161818\pi$
$588$	0	0
$589$	−4.50275	−0.185533
$590$	−21.2821	−0.876170
$591$	20.0578	0.825067
$592$	12.5520	0.515883
$593$	32.3171	1.32711	0.663553	−	0.748129i	$-0.269048\pi$
$593$	32.3171	1.32711	0.663553	+	0.748129i	$0.269048\pi$
$594$	6.76512	0.277576
$595$	0	0
$596$	9.69470	0.397110
$597$	−8.76302	−0.358647
$598$	−1.26868	−0.0518800
$599$	−34.5668	−1.41236	−0.706181	−	0.708032i	$-0.749583\pi$
$599$	−34.5668	−1.41236	−0.706181	+	0.708032i	$0.749583\pi$
$600$	9.17019	0.374372
$601$	21.2165	0.865439	0.432720	−	0.901529i	$-0.357554\pi$
$601$	21.2165	0.865439	0.432720	+	0.901529i	$0.357554\pi$
$602$	0	0
$603$	8.13979	0.331478
$604$	35.8571	1.45900
$605$	1.61301	0.0655783
$606$	−23.7179	−0.963474
$607$	−14.5087	−0.588890	−0.294445	−	0.955668i	$-0.595135\pi$
$607$	−14.5087	−0.588890	−0.294445	+	0.955668i	$0.595135\pi$
$608$	−23.8142	−0.965793
$609$	0	0
$610$	−16.1284	−0.653020
$611$	−0.234648	−0.00949285
$612$	−1.75862	−0.0710879
$613$	−32.3488	−1.30656	−0.653278	−	0.757118i	$-0.726607\pi$
$613$	−32.3488	−1.30656	−0.653278	+	0.757118i	$0.726607\pi$
$614$	35.7253	1.44175
$615$	−0.893036	−0.0360107
$616$	0	0
$617$	0.742674	0.0298989	0.0149495	−	0.999888i	$-0.495241\pi$
$617$	0.742674	0.0298989	0.0149495	+	0.999888i	$0.495241\pi$
$618$	8.78674	0.353455
$619$	26.3539	1.05925	0.529627	−	0.848231i	$-0.322332\pi$
$619$	26.3539	1.05925	0.529627	+	0.848231i	$0.322332\pi$
$620$	−3.41458	−0.137133
$621$	−0.556191	−0.0223192
$622$	46.2086	1.85280
$623$	0	0
$624$	1.11177	0.0445064
$625$	13.6733	0.546933
$626$	−41.3760	−1.65372
$627$	10.6337	0.424668
$628$	1.72802	0.0689556
$629$	6.81618	0.271779
$630$	0	0
$631$	−20.2431	−0.805867	−0.402933	−	0.915229i	$-0.632009\pi$
$631$	−20.2431	−0.805867	−0.402933	+	0.915229i	$0.632009\pi$
$632$	−10.1911	−0.405381
$633$	21.8898	0.870042
$634$	−46.1141	−1.83142
$635$	7.09026	0.281368
$636$	25.4567	1.00943
$637$	0	0
$638$	53.4306	2.11534
$639$	1.38924	0.0549575
$640$	−13.7255	−0.542549
$641$	18.2442	0.720604	0.360302	−	0.932836i	$-0.382674\pi$
$641$	18.2442	0.720604	0.360302	+	0.932836i	$0.382674\pi$
$642$	24.0964	0.951010
$643$	−16.3210	−0.643637	−0.321819	−	0.946801i	$-0.604294\pi$
$643$	−16.3210	−0.643637	−0.321819	+	0.946801i	$0.604294\pi$
$644$	0	0
$645$	5.14525	0.202594
$646$	−4.62071	−0.181799
$647$	47.4111	1.86392	0.931962	−	0.362556i	$-0.118096\pi$
$647$	47.4111	1.86392	0.931962	+	0.362556i	$0.118096\pi$
$648$	−2.18209	−0.0857205
$649$	32.3865	1.27128
$650$	−9.58589	−0.375990
$651$	0	0
$652$	35.6332	1.39550
$653$	−16.4495	−0.643720	−0.321860	−	0.946787i	$-0.604308\pi$
$653$	−16.4495	−0.643720	−0.321860	+	0.946787i	$0.604308\pi$
$654$	30.6550	1.19871
$655$	−1.70940	−0.0667916
$656$	−1.08747	−0.0424585
$657$	10.7543	0.419563
$658$	0	0
$659$	19.4662	0.758297	0.379148	−	0.925336i	$-0.376217\pi$
$659$	19.4662	0.758297	0.379148	+	0.925336i	$0.376217\pi$
$660$	8.06386	0.313885
$661$	29.5252	1.14840	0.574198	−	0.818716i	$-0.305314\pi$
$661$	29.5252	1.14840	0.574198	+	0.818716i	$0.305314\pi$
$662$	−8.38648	−0.325950
$663$	0.603730	0.0234469
$664$	−7.04136	−0.273258
$665$	0	0
$666$	25.7528	0.997900
$667$	−4.39278	−0.170089
$668$	−50.6062	−1.95801
$669$	19.0053	0.734786
$670$	16.2185	0.626575
$671$	24.5438	0.947502
$672$	0	0
$673$	26.0433	1.00390	0.501948	−	0.864898i	$-0.332617\pi$
$673$	26.0433	1.00390	0.501948	+	0.864898i	$0.332617\pi$
$674$	59.9519	2.30926
$675$	−4.20249	−0.161754
$676$	−35.6016	−1.36929
$677$	1.23438	0.0474410	0.0237205	−	0.999719i	$-0.492449\pi$
$677$	1.23438	0.0474410	0.0237205	+	0.999719i	$0.492449\pi$
$678$	−6.41884	−0.246514
$679$	0	0
$680$	−1.15076	−0.0441298
$681$	14.7021	0.563386
$682$	8.68595	0.332602
$683$	−9.24065	−0.353584	−0.176792	−	0.984248i	$-0.556572\pi$
$683$	−9.24065	−0.353584	−0.176792	+	0.984248i	$0.556572\pi$
$684$	−10.4439	−0.399332
$685$	−9.77164	−0.373355
$686$	0	0
$687$	22.7562	0.868203
$688$	6.26548	0.238869
$689$	−8.73926	−0.332939
$690$	−1.10821	−0.0421888
$691$	12.5139	0.476051	0.238026	−	0.971259i	$-0.423500\pi$
$691$	12.5139	0.476051	0.238026	+	0.971259i	$0.423500\pi$
$692$	8.94359	0.339984
$693$	0	0
$694$	47.8741	1.81728
$695$	−18.3904	−0.697586
$696$	−17.2340	−0.653254
$697$	−0.590534	−0.0223681
$698$	−58.3516	−2.20864
$699$	−27.3282	−1.03365
$700$	0	0
$701$	−26.7565	−1.01058	−0.505289	−	0.862950i	$-0.668614\pi$
$701$	−26.7565	−1.01058	−0.505289	+	0.862950i	$0.668614\pi$
$702$	2.28100	0.0860910
$703$	40.4792	1.52670
$704$	39.3437	1.48282
$705$	−0.204969	−0.00771958
$706$	8.29347	0.312129
$707$	0	0
$708$	−31.8085	−1.19544
$709$	25.9800	0.975698	0.487849	−	0.872928i	$-0.337782\pi$
$709$	25.9800	0.975698	0.487849	+	0.872928i	$0.337782\pi$
$710$	2.76805	0.103883
$711$	4.67035	0.175152
$712$	−34.7876	−1.30372
$713$	−0.714112	−0.0267437
$714$	0	0
$715$	−2.76831	−0.103529
$716$	30.7925	1.15077
$717$	−12.5731	−0.469551
$718$	−29.5824	−1.10401
$719$	−23.7887	−0.887169	−0.443585	−	0.896232i	$-0.646293\pi$
$719$	−23.7887	−0.887169	−0.443585	+	0.896232i	$0.646293\pi$
$720$	0.971148	0.0361926
$721$	0	0
$722$	14.9508	0.556411
$723$	4.30351	0.160049
$724$	−28.4120	−1.05592
$725$	−33.1911	−1.23268
$726$	4.02992	0.149564
$727$	−34.9164	−1.29498	−0.647489	−	0.762074i	$-0.724181\pi$
$727$	−34.9164	−1.29498	−0.647489	+	0.762074i	$0.724181\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	21.4278	0.793078
$731$	3.40238	0.125842
$732$	−24.1057	−0.890974
$733$	−1.49359	−0.0551670	−0.0275835	−	0.999620i	$-0.508781\pi$
$733$	−1.49359	−0.0551670	−0.0275835	+	0.999620i	$0.508781\pi$
$734$	43.3077	1.59852
$735$	0	0
$736$	−3.77680	−0.139215
$737$	−24.6809	−0.909132
$738$	−2.23115	−0.0821296
$739$	35.3095	1.29888	0.649440	−	0.760413i	$-0.275003\pi$
$739$	35.3095	1.29888	0.649440	+	0.760413i	$0.275003\pi$
$740$	30.6967	1.12843
$741$	3.58537	0.131712
$742$	0	0
$743$	20.1868	0.740582	0.370291	−	0.928916i	$-0.379258\pi$
$743$	20.1868	0.740582	0.370291	+	0.928916i	$0.379258\pi$
$744$	−2.80165	−0.102714
$745$	−2.90721	−0.106512
$746$	−44.1835	−1.61767
$747$	3.22689	0.118066
$748$	5.33235	0.194970
$749$	0	0
$750$	−18.3359	−0.669532
$751$	43.9665	1.60436	0.802180	−	0.597083i	$-0.203674\pi$
$751$	43.9665	1.60436	0.802180	+	0.597083i	$0.203674\pi$
$752$	−0.249595	−0.00910179
$753$	−12.7442	−0.464425
$754$	18.0153	0.656078
$755$	−10.7527	−0.391331
$756$	0	0
$757$	17.4722	0.635040	0.317520	−	0.948252i	$-0.397150\pi$
$757$	17.4722	0.635040	0.317520	+	0.948252i	$0.397150\pi$
$758$	−23.3665	−0.848709
$759$	1.68644	0.0612140
$760$	−6.83403	−0.247896
$761$	−8.70835	−0.315677	−0.157839	−	0.987465i	$-0.550453\pi$
$761$	−8.70835	−0.315677	−0.157839	+	0.987465i	$0.550453\pi$
$762$	17.7142	0.641717
$763$	0	0
$764$	11.4812	0.415375
$765$	0.527368	0.0190670
$766$	−40.0643	−1.44758
$767$	10.9198	0.394292
$768$	−8.34043	−0.300959
$769$	−18.9265	−0.682507	−0.341253	−	0.939971i	$-0.610851\pi$
$769$	−18.9265	−0.682507	−0.341253	+	0.939971i	$0.610851\pi$
$770$	0	0
$771$	−15.3531	−0.552929
$772$	36.4879	1.31323
$773$	32.6886	1.17573	0.587864	−	0.808960i	$-0.299969\pi$
$773$	32.6886	1.17573	0.587864	+	0.808960i	$0.299969\pi$
$774$	12.8548	0.462057
$775$	−5.39570	−0.193819
$776$	−11.2765	−0.404802
$777$	0	0
$778$	−69.7686	−2.50132
$779$	−3.50700	−0.125651
$780$	2.71890	0.0973523
$781$	−4.21235	−0.150730
$782$	−0.732820	−0.0262056
$783$	7.89796	0.282250
$784$	0	0
$785$	−0.518193	−0.0184951
$786$	−4.27072	−0.152332
$787$	54.7501	1.95163	0.975814	−	0.218601i	$-0.0701494\pi$
$787$	54.7501	1.95163	0.975814	+	0.218601i	$0.0701494\pi$
$788$	59.7323	2.12788
$789$	4.70180	0.167388
$790$	9.30565	0.331080
$791$	0	0
$792$	6.61637	0.235102
$793$	8.27546	0.293870
$794$	−65.7801	−2.33445
$795$	−7.63388	−0.270746
$796$	−26.0964	−0.924962
$797$	44.9819	1.59334	0.796671	−	0.604414i	$-0.206593\pi$
$797$	44.9819	1.59334	0.796671	+	0.604414i	$0.206593\pi$
$798$	0	0
$799$	−0.135539	−0.00479502
$800$	−28.5369	−1.00893
$801$	15.9423	0.563295
$802$	25.2452	0.891439
$803$	−32.6082	−1.15072
$804$	24.2404	0.854893
$805$	0	0
$806$	2.92865	0.103157
$807$	−17.8058	−0.626792
$808$	−23.1964	−0.816046
$809$	11.9297	0.419425	0.209713	−	0.977763i	$-0.432747\pi$
$809$	11.9297	0.419425	0.209713	+	0.977763i	$0.432747\pi$
$810$	1.99249	0.0700091
$811$	6.14692	0.215848	0.107924	−	0.994159i	$-0.465580\pi$
$811$	6.14692	0.215848	0.107924	+	0.994159i	$0.465580\pi$
$812$	0	0
$813$	−5.15229	−0.180699
$814$	−78.0857	−2.73690
$815$	−10.6856	−0.374299
$816$	0.642187	0.0224810
$817$	20.2057	0.706908
$818$	−42.2258	−1.47639
$819$	0	0
$820$	−2.65947	−0.0928728
$821$	28.1002	0.980702	0.490351	−	0.871525i	$-0.336869\pi$
$821$	28.1002	0.980702	0.490351	+	0.871525i	$0.336869\pi$
$822$	−24.4133	−0.851511
$823$	10.2799	0.358334	0.179167	−	0.983819i	$-0.442660\pi$
$823$	10.2799	0.358334	0.179167	+	0.983819i	$0.442660\pi$
$824$	8.59354	0.299370
$825$	12.7425	0.443636
$826$	0	0
$827$	−42.5878	−1.48092	−0.740462	−	0.672098i	$-0.765393\pi$
$827$	−42.5878	−1.48092	−0.740462	+	0.672098i	$0.765393\pi$
$828$	−1.65634	−0.0575620
$829$	−15.6799	−0.544586	−0.272293	−	0.962214i	$-0.587782\pi$
$829$	−15.6799	−0.544586	−0.272293	+	0.962214i	$0.587782\pi$
$830$	6.42956	0.223173
$831$	−8.01369	−0.277992
$832$	13.2656	0.459901
$833$	0	0
$834$	−45.9462	−1.59099
$835$	15.1756	0.525174
$836$	31.6672	1.09523
$837$	1.28393	0.0443792
$838$	−25.1732	−0.869595
$839$	46.4057	1.60210	0.801052	−	0.598595i	$-0.204274\pi$
$839$	46.4057	1.60210	0.801052	+	0.598595i	$0.204274\pi$
$840$	0	0
$841$	33.3777	1.15096
$842$	−3.28119	−0.113077
$843$	4.98277	0.171616
$844$	65.1881	2.24387
$845$	10.6761	0.367268
$846$	−0.512091	−0.0176061
$847$	0	0
$848$	−9.29593	−0.319224
$849$	6.83872	0.234704
$850$	−5.53706	−0.189920
$851$	6.41978	0.220067
$852$	4.13717	0.141737
$853$	23.0031	0.787611	0.393805	−	0.919194i	$-0.371158\pi$
$853$	23.0031	0.787611	0.393805	+	0.919194i	$0.371158\pi$
$854$	0	0
$855$	3.13188	0.107108
$856$	23.5666	0.805489
$857$	−4.92156	−0.168117	−0.0840587	−	0.996461i	$-0.526788\pi$
$857$	−4.92156	−0.168117	−0.0840587	+	0.996461i	$0.526788\pi$
$858$	−6.91629	−0.236118
$859$	7.76979	0.265102	0.132551	−	0.991176i	$-0.457683\pi$
$859$	7.76979	0.265102	0.132551	+	0.991176i	$0.457683\pi$
$860$	15.3226	0.522497
$861$	0	0
$862$	10.9421	0.372689
$863$	−12.3757	−0.421274	−0.210637	−	0.977564i	$-0.567554\pi$
$863$	−12.3757	−0.421274	−0.210637	+	0.977564i	$0.567554\pi$
$864$	6.79048	0.231017
$865$	−2.68197	−0.0911898
$866$	20.5401	0.697980
$867$	−16.6513	−0.565507
$868$	0	0
$869$	−14.1611	−0.480382
$870$	15.7366	0.533522
$871$	−8.32169	−0.281970
$872$	29.9810	1.01528
$873$	5.16775	0.174902
$874$	−4.35199	−0.147208
$875$	0	0
$876$	32.0263	1.08207
$877$	−31.0076	−1.04705	−0.523526	−	0.852010i	$-0.675384\pi$
$877$	−31.0076	−1.04705	−0.523526	+	0.852010i	$0.675384\pi$
$878$	53.6328	1.81002
$879$	23.1644	0.781315
$880$	−2.94464	−0.0992639
$881$	49.0117	1.65125	0.825624	−	0.564221i	$-0.190824\pi$
$881$	49.0117	1.65125	0.825624	+	0.564221i	$0.190824\pi$
$882$	0	0
$883$	52.3902	1.76307	0.881535	−	0.472119i	$-0.156511\pi$
$883$	52.3902	1.76307	0.881535	+	0.472119i	$0.156511\pi$
$884$	1.79792	0.0604705
$885$	9.53863	0.320638
$886$	49.8603	1.67509
$887$	49.6047	1.66556	0.832781	−	0.553603i	$-0.186747\pi$
$887$	49.6047	1.66556	0.832781	+	0.553603i	$0.186747\pi$
$888$	25.1865	0.845204
$889$	0	0
$890$	31.7650	1.06477
$891$	−3.03213	−0.101580
$892$	56.5979	1.89504
$893$	−0.804924	−0.0269358
$894$	−7.26333	−0.242922
$895$	−9.23395	−0.308657
$896$	0	0
$897$	0.568620	0.0189857
$898$	−33.6559	−1.12311
$899$	10.1404	0.338202
$900$	−12.5151	−0.417169
$901$	−5.04802	−0.168174
$902$	6.76512	0.225254
$903$	0	0
$904$	−6.27771	−0.208793
$905$	8.52009	0.283217
$906$	−26.8644	−0.892509
$907$	1.69849	0.0563974	0.0281987	−	0.999602i	$-0.491023\pi$
$907$	1.69849	0.0563974	0.0281987	+	0.999602i	$0.491023\pi$
$908$	43.7831	1.45299
$909$	10.6304	0.352587
$910$	0	0
$911$	−7.66674	−0.254010	−0.127005	−	0.991902i	$-0.540537\pi$
$911$	−7.66674	−0.254010	−0.127005	+	0.991902i	$0.540537\pi$
$912$	3.81375	0.126286
$913$	−9.78434	−0.323814
$914$	26.6578	0.881761
$915$	7.22875	0.238975
$916$	67.7682	2.23913
$917$	0	0
$918$	1.31757	0.0434862
$919$	29.6626	0.978480	0.489240	−	0.872149i	$-0.337274\pi$
$919$	29.6626	0.978480	0.489240	+	0.872149i	$0.337274\pi$
$920$	−1.08384	−0.0357332
$921$	−16.0121	−0.527616
$922$	19.4988	0.642159
$923$	−1.42029	−0.0467493
$924$	0	0
$925$	48.5068	1.59489
$926$	72.2692	2.37491
$927$	−3.93822	−0.129348
$928$	53.6309	1.76052
$929$	−46.0046	−1.50936	−0.754681	−	0.656091i	$-0.772209\pi$
$929$	−46.0046	−1.50936	−0.754681	+	0.656091i	$0.772209\pi$
$930$	2.55823	0.0838875
$931$	0	0
$932$	−81.3836	−2.66581
$933$	−20.7107	−0.678038
$934$	−0.730722	−0.0239100
$935$	−1.59905	−0.0522944
$936$	2.23085	0.0729176
$937$	21.8284	0.713102	0.356551	−	0.934276i	$-0.383953\pi$
$937$	21.8284	0.713102	0.356551	+	0.934276i	$0.383953\pi$
$938$	0	0
$939$	18.5447	0.605185
$940$	−0.610400	−0.0199091
$941$	−27.7442	−0.904435	−0.452217	−	0.891908i	$-0.649367\pi$
$941$	−27.7442	−0.904435	−0.452217	+	0.891908i	$0.649367\pi$
$942$	−1.29464	−0.0421818
$943$	−0.556191	−0.0181121
$944$	11.6154	0.378049
$945$	0	0
$946$	−38.9774	−1.26727
$947$	−12.5298	−0.407163	−0.203581	−	0.979058i	$-0.565258\pi$
$947$	−12.5298	−0.407163	−0.203581	+	0.979058i	$0.565258\pi$
$948$	13.9084	0.451723
$949$	−10.9946	−0.356899
$950$	−32.8829	−1.06686
$951$	20.6683	0.670217
$952$	0	0
$953$	−21.2076	−0.686981	−0.343491	−	0.939156i	$-0.611609\pi$
$953$	−21.2076	−0.686981	−0.343491	+	0.939156i	$0.611609\pi$
$954$	−19.0724	−0.617490
$955$	−3.44294	−0.111411
$956$	−37.4428	−1.21099
$957$	−23.9476	−0.774116
$958$	12.9900	0.419688
$959$	0	0
$960$	11.5877	0.373991
$961$	−29.3515	−0.946823
$962$	−26.3283	−0.848857
$963$	−10.8000	−0.348026
$964$	12.8159	0.412773
$965$	−10.9419	−0.352231
$966$	0	0
$967$	−15.6750	−0.504073	−0.252037	−	0.967718i	$-0.581100\pi$
$967$	−15.6750	−0.504073	−0.252037	+	0.967718i	$0.581100\pi$
$968$	3.94131	0.126679
$969$	2.07100	0.0665302
$970$	10.2967	0.330608
$971$	−32.1713	−1.03243	−0.516214	−	0.856460i	$-0.672659\pi$
$971$	−32.1713	−1.03243	−0.516214	+	0.856460i	$0.672659\pi$
$972$	2.97801	0.0955198
$973$	0	0
$974$	54.7330	1.75376
$975$	4.29640	0.137595
$976$	8.80259	0.281764
$977$	−21.8155	−0.697940	−0.348970	−	0.937134i	$-0.613468\pi$
$977$	−21.8155	−0.697940	−0.348970	+	0.937134i	$0.613468\pi$
$978$	−26.6966	−0.853663
$979$	−48.3392	−1.54493
$980$	0	0
$981$	−13.7396	−0.438671
$982$	−46.9571	−1.49846
$983$	42.4637	1.35438	0.677191	−	0.735808i	$-0.263197\pi$
$983$	42.4637	1.35438	0.677191	+	0.735808i	$0.263197\pi$
$984$	−2.18209	−0.0695624
$985$	−17.9123	−0.570734
$986$	10.4061	0.331397
$987$	0	0
$988$	10.6773	0.339689
$989$	3.20451	0.101898
$990$	−6.04149	−0.192011
$991$	−60.9054	−1.93473	−0.967363	−	0.253396i	$-0.918452\pi$
$991$	−60.9054	−1.93473	−0.967363	+	0.253396i	$0.918452\pi$
$992$	8.71851	0.276813
$993$	3.75882	0.119283
$994$	0	0
$995$	7.82569	0.248091
$996$	9.60972	0.304496
$997$	19.4303	0.615363	0.307681	−	0.951489i	$-0.400447\pi$
$997$	19.4303	0.615363	0.307681	+	0.951489i	$0.400447\pi$
$998$	−47.8554	−1.51484
$999$	−11.5424	−0.365185

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bc.1.1		8
7.3	odd	6		861.2.i.d.247.8	✓	16
7.5	odd	6		861.2.i.d.739.8	yes	16
7.6	odd	2		6027.2.a.bb.1.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.i.d.247.8	✓	16	7.3	odd	6
861.2.i.d.739.8	yes	16	7.5	odd	6
6027.2.a.bb.1.1		8	7.6	odd	2
6027.2.a.bc.1.1		8	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:	\( N \)	\(=\)	\( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.23115 q^{2} +1.00000 q^{3} +2.97801 q^{4} -0.893036 q^{5} -2.23115 q^{6} -2.18209 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.23115 q^{2} +1.00000 q^{3} +2.97801 q^{4} -0.893036 q^{5} -2.23115 q^{6} -2.18209 q^{8} +1.00000 q^{9} +1.99249 q^{10} -3.03213 q^{11} +2.97801 q^{12} -1.02235 q^{13} -0.893036 q^{15} -1.08747 q^{16} -0.590534 q^{17} -2.23115 q^{18} -3.50700 q^{19} -2.65947 q^{20} +6.76512 q^{22} -0.556191 q^{23} -2.18209 q^{24} -4.20249 q^{25} +2.28100 q^{26} +1.00000 q^{27} +7.89796 q^{29} +1.99249 q^{30} +1.28393 q^{31} +6.79048 q^{32} -3.03213 q^{33} +1.31757 q^{34} +2.97801 q^{36} -11.5424 q^{37} +7.82463 q^{38} -1.02235 q^{39} +1.94868 q^{40} +1.00000 q^{41} -5.76153 q^{43} -9.02971 q^{44} -0.893036 q^{45} +1.24094 q^{46} +0.229519 q^{47} -1.08747 q^{48} +9.37636 q^{50} -0.590534 q^{51} -3.04456 q^{52} +8.54823 q^{53} -2.23115 q^{54} +2.70780 q^{55} -3.50700 q^{57} -17.6215 q^{58} -10.6811 q^{59} -2.65947 q^{60} -8.09457 q^{61} -2.86464 q^{62} -12.9756 q^{64} +0.912992 q^{65} +6.76512 q^{66} +8.13979 q^{67} -1.75862 q^{68} -0.556191 q^{69} +1.38924 q^{71} -2.18209 q^{72} +10.7543 q^{73} +25.7528 q^{74} -4.20249 q^{75} -10.4439 q^{76} +2.28100 q^{78} +4.67035 q^{79} +0.971148 q^{80} +1.00000 q^{81} -2.23115 q^{82} +3.22689 q^{83} +0.527368 q^{85} +12.8548 q^{86} +7.89796 q^{87} +6.61637 q^{88} +15.9423 q^{89} +1.99249 q^{90} -1.65634 q^{92} +1.28393 q^{93} -0.512091 q^{94} +3.13188 q^{95} +6.79048 q^{96} +5.16775 q^{97} -3.03213 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + 8 q^{3} + 13 q^{4} + 7 q^{5} + q^{6} + 6 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + q^2 + 8 * q^3 + 13 * q^4 + 7 * q^5 + q^6 + 6 * q^8 + 8 * q^9	\( 8 q + q^{2} + 8 q^{3} + 13 q^{4} + 7 q^{5} + q^{6} + 6 q^{8} + 8 q^{9} + 8 q^{10} + 11 q^{11} + 13 q^{12} + 10 q^{13} + 7 q^{15} - 17 q^{16} + 3 q^{17} + q^{18} + 6 q^{19} + 11 q^{20} + 15 q^{22} + 14 q^{23} + 6 q^{24} + 25 q^{25} + 24 q^{26} + 8 q^{27} + 2 q^{29} + 8 q^{30} + 16 q^{31} + 3 q^{32} + 11 q^{33} - 4 q^{34} + 13 q^{36} - 20 q^{37} + 10 q^{38} + 10 q^{39} - 3 q^{40} + 8 q^{41} + 7 q^{43} + 7 q^{45} - 5 q^{46} + 14 q^{47} - 17 q^{48} - 5 q^{50} + 3 q^{51} + 23 q^{52} + 7 q^{53} + q^{54} + 48 q^{55} + 6 q^{57} - 20 q^{58} + 22 q^{59} + 11 q^{60} - 33 q^{62} - 10 q^{64} - 14 q^{65} + 15 q^{66} + 12 q^{67} - 27 q^{68} + 14 q^{69} - 5 q^{71} + 6 q^{72} + 2 q^{73} + 6 q^{74} + 25 q^{75} + 43 q^{76} + 24 q^{78} - 15 q^{79} - 7 q^{80} + 8 q^{81} + q^{82} + 15 q^{83} - 43 q^{85} + 31 q^{86} + 2 q^{87} + 17 q^{88} + 29 q^{89} + 8 q^{90} + 19 q^{92} + 16 q^{93} + 20 q^{94} + 14 q^{95} + 3 q^{96} + 19 q^{97} + 11 q^{99}+O(q^{100}) \) 8 * q + q^2 + 8 * q^3 + 13 * q^4 + 7 * q^5 + q^6 + 6 * q^8 + 8 * q^9 + 8 * q^10 + 11 * q^11 + 13 * q^12 + 10 * q^13 + 7 * q^15 - 17 * q^16 + 3 * q^17 + q^18 + 6 * q^19 + 11 * q^20 + 15 * q^22 + 14 * q^23 + 6 * q^24 + 25 * q^25 + 24 * q^26 + 8 * q^27 + 2 * q^29 + 8 * q^30 + 16 * q^31 + 3 * q^32 + 11 * q^33 - 4 * q^34 + 13 * q^36 - 20 * q^37 + 10 * q^38 + 10 * q^39 - 3 * q^40 + 8 * q^41 + 7 * q^43 + 7 * q^45 - 5 * q^46 + 14 * q^47 - 17 * q^48 - 5 * q^50 + 3 * q^51 + 23 * q^52 + 7 * q^53 + q^54 + 48 * q^55 + 6 * q^57 - 20 * q^58 + 22 * q^59 + 11 * q^60 - 33 * q^62 - 10 * q^64 - 14 * q^65 + 15 * q^66 + 12 * q^67 - 27 * q^68 + 14 * q^69 - 5 * q^71 + 6 * q^72 + 2 * q^73 + 6 * q^74 + 25 * q^75 + 43 * q^76 + 24 * q^78 - 15 * q^79 - 7 * q^80 + 8 * q^81 + q^82 + 15 * q^83 - 43 * q^85 + 31 * q^86 + 2 * q^87 + 17 * q^88 + 29 * q^89 + 8 * q^90 + 19 * q^92 + 16 * q^93 + 20 * q^94 + 14 * q^95 + 3 * q^96 + 19 * q^97 + 11 * q^99

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