LMFDB - Embedded newform 3381.2.a.bf.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3381,2,Mod(1,3381)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3381, 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("3381.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3381 = 3 \cdot 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3381.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:	$26.9974209234$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 15x^{6} + 11x^{5} + 75x^{4} - 35x^{3} - 141x^{2} + 37x + 80 $ x^8 - x^7 - 15x^6 + 11x^5 + 75x^4 - 35x^3 - 141x^2 + 37x + 80
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 483)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$2.51679$ of defining polynomial
Character	$\chi$	$=$	3381.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.51679 q^{2} +1.00000 q^{3} +4.33421 q^{4} +2.41834 q^{5} +2.51679 q^{6} +5.87470 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.51679 q^{2} +1.00000 q^{3} +4.33421 q^{4} +2.41834 q^{5} +2.51679 q^{6} +5.87470 q^{8} +1.00000 q^{9} +6.08644 q^{10} +1.24840 q^{11} +4.33421 q^{12} +2.06826 q^{13} +2.41834 q^{15} +6.11694 q^{16} -3.31028 q^{17} +2.51679 q^{18} -3.61984 q^{19} +10.4816 q^{20} +3.14194 q^{22} -1.00000 q^{23} +5.87470 q^{24} +0.848370 q^{25} +5.20537 q^{26} +1.00000 q^{27} +4.27807 q^{29} +6.08644 q^{30} -7.97744 q^{31} +3.64563 q^{32} +1.24840 q^{33} -8.33126 q^{34} +4.33421 q^{36} +5.09175 q^{37} -9.11035 q^{38} +2.06826 q^{39} +14.2070 q^{40} -0.885683 q^{41} +9.94532 q^{43} +5.41081 q^{44} +2.41834 q^{45} -2.51679 q^{46} -5.69191 q^{47} +6.11694 q^{48} +2.13516 q^{50} -3.31028 q^{51} +8.96427 q^{52} -2.94202 q^{53} +2.51679 q^{54} +3.01905 q^{55} -3.61984 q^{57} +10.7670 q^{58} +2.02444 q^{59} +10.4816 q^{60} -7.38492 q^{61} -20.0775 q^{62} -3.05862 q^{64} +5.00176 q^{65} +3.14194 q^{66} +8.28378 q^{67} -14.3474 q^{68} -1.00000 q^{69} -8.27631 q^{71} +5.87470 q^{72} -11.9873 q^{73} +12.8149 q^{74} +0.848370 q^{75} -15.6891 q^{76} +5.20537 q^{78} -15.2225 q^{79} +14.7928 q^{80} +1.00000 q^{81} -2.22907 q^{82} +15.7586 q^{83} -8.00538 q^{85} +25.0302 q^{86} +4.27807 q^{87} +7.33395 q^{88} -16.2664 q^{89} +6.08644 q^{90} -4.33421 q^{92} -7.97744 q^{93} -14.3253 q^{94} -8.75399 q^{95} +3.64563 q^{96} +16.6972 q^{97} +1.24840 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + 8 q^{3} + 15 q^{4} + 5 q^{5} + q^{6} + 9 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + q^2 + 8 * q^3 + 15 * q^4 + 5 * q^5 + q^6 + 9 * q^8 + 8 * q^9	$ 8 q + q^{2} + 8 q^{3} + 15 q^{4} + 5 q^{5} + q^{6} + 9 q^{8} + 8 q^{9} - 3 q^{10} + 10 q^{11} + 15 q^{12} - 6 q^{13} + 5 q^{15} + 13 q^{16} + 21 q^{17} + q^{18} + 5 q^{19} - q^{20} + 18 q^{22} - 8 q^{23} + 9 q^{24} + 27 q^{25} + 3 q^{26} + 8 q^{27} + 2 q^{29} - 3 q^{30} - 13 q^{31} + 29 q^{32} + 10 q^{33} - 19 q^{34} + 15 q^{36} + 13 q^{37} - 6 q^{38} - 6 q^{39} + 7 q^{40} + 16 q^{41} + 15 q^{43} + 24 q^{44} + 5 q^{45} - q^{46} - q^{47} + 13 q^{48} + 16 q^{50} + 21 q^{51} - 19 q^{52} + 3 q^{53} + q^{54} - 10 q^{55} + 5 q^{57} - 40 q^{58} + 26 q^{59} - q^{60} - 14 q^{61} - 14 q^{62} + 49 q^{64} - 3 q^{65} + 18 q^{66} + 38 q^{67} + 43 q^{68} - 8 q^{69} + 9 q^{71} + 9 q^{72} - 6 q^{73} + 32 q^{74} + 27 q^{75} - 14 q^{76} + 3 q^{78} + 23 q^{79} - 17 q^{80} + 8 q^{81} + 20 q^{82} + 30 q^{83} - 37 q^{85} - 28 q^{86} + 2 q^{87} + 86 q^{88} + 12 q^{89} - 3 q^{90} - 15 q^{92} - 13 q^{93} - 45 q^{94} + 16 q^{95} + 29 q^{96} + 14 q^{97} + 10 q^{99}+O(q^{100}) $ 8 * q + q^2 + 8 * q^3 + 15 * q^4 + 5 * q^5 + q^6 + 9 * q^8 + 8 * q^9 - 3 * q^10 + 10 * q^11 + 15 * q^12 - 6 * q^13 + 5 * q^15 + 13 * q^16 + 21 * q^17 + q^18 + 5 * q^19 - q^20 + 18 * q^22 - 8 * q^23 + 9 * q^24 + 27 * q^25 + 3 * q^26 + 8 * q^27 + 2 * q^29 - 3 * q^30 - 13 * q^31 + 29 * q^32 + 10 * q^33 - 19 * q^34 + 15 * q^36 + 13 * q^37 - 6 * q^38 - 6 * q^39 + 7 * q^40 + 16 * q^41 + 15 * q^43 + 24 * q^44 + 5 * q^45 - q^46 - q^47 + 13 * q^48 + 16 * q^50 + 21 * q^51 - 19 * q^52 + 3 * q^53 + q^54 - 10 * q^55 + 5 * q^57 - 40 * q^58 + 26 * q^59 - q^60 - 14 * q^61 - 14 * q^62 + 49 * q^64 - 3 * q^65 + 18 * q^66 + 38 * q^67 + 43 * q^68 - 8 * q^69 + 9 * q^71 + 9 * q^72 - 6 * q^73 + 32 * q^74 + 27 * q^75 - 14 * q^76 + 3 * q^78 + 23 * q^79 - 17 * q^80 + 8 * q^81 + 20 * q^82 + 30 * q^83 - 37 * q^85 - 28 * q^86 + 2 * q^87 + 86 * q^88 + 12 * q^89 - 3 * q^90 - 15 * q^92 - 13 * q^93 - 45 * q^94 + 16 * q^95 + 29 * q^96 + 14 * q^97 + 10 * 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 $

$2$	2.51679	1.77964	0.889818	−	0.456316i	$-0.150831\pi$
$2$	2.51679	1.77964	0.889818	+	0.456316i	$0.150831\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.33421	2.16710
$5$	2.41834	1.08151	0.540757	−	0.841179i	$-0.318138\pi$
$5$	2.41834	1.08151	0.540757	+	0.841179i	$0.318138\pi$
$6$	2.51679	1.02747
$7$	0	0
$7$	0	0
$8$	5.87470	2.07702
$9$	1.00000	0.333333
$10$	6.08644	1.92470
$11$	1.24840	0.376406	0.188203	−	0.982130i	$-0.439734\pi$
$11$	1.24840	0.376406	0.188203	+	0.982130i	$0.439734\pi$
$12$	4.33421	1.25118
$13$	2.06826	0.573632	0.286816	−	0.957986i	$-0.407403\pi$
$13$	2.06826	0.573632	0.286816	+	0.957986i	$0.407403\pi$
$14$	0	0
$15$	2.41834	0.624413
$16$	6.11694	1.52924
$17$	−3.31028	−0.802860	−0.401430	−	0.915890i	$-0.631487\pi$
$17$	−3.31028	−0.802860	−0.401430	+	0.915890i	$0.631487\pi$
$18$	2.51679	0.593212
$19$	−3.61984	−0.830447	−0.415224	−	0.909719i	$-0.636297\pi$
$19$	−3.61984	−0.830447	−0.415224	+	0.909719i	$0.636297\pi$
$20$	10.4816	2.34375
$21$	0	0
$22$	3.14194	0.669865
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	5.87470	1.19917
$25$	0.848370	0.169674
$26$	5.20537	1.02086
$27$	1.00000	0.192450
$28$	0	0
$29$	4.27807	0.794418	0.397209	−	0.917728i	$-0.369979\pi$
$29$	4.27807	0.794418	0.397209	+	0.917728i	$0.369979\pi$
$30$	6.08644	1.11123
$31$	−7.97744	−1.43279	−0.716395	−	0.697695i	$-0.754209\pi$
$31$	−7.97744	−1.43279	−0.716395	+	0.697695i	$0.754209\pi$
$32$	3.64563	0.644462
$33$	1.24840	0.217318
$34$	−8.33126	−1.42880
$35$	0	0
$36$	4.33421	0.722368
$37$	5.09175	0.837079	0.418540	−	0.908199i	$-0.362542\pi$
$37$	5.09175	0.837079	0.418540	+	0.908199i	$0.362542\pi$
$38$	−9.11035	−1.47789
$39$	2.06826	0.331187
$40$	14.2070	2.24633
$41$	−0.885683	−0.138320	−0.0691602	−	0.997606i	$-0.522032\pi$
$41$	−0.885683	−0.138320	−0.0691602	+	0.997606i	$0.522032\pi$
$42$	0	0
$43$	9.94532	1.51665	0.758324	−	0.651878i	$-0.226019\pi$
$43$	9.94532	1.51665	0.758324	+	0.651878i	$0.226019\pi$
$44$	5.41081	0.815710
$45$	2.41834	0.360505
$46$	−2.51679	−0.371080
$47$	−5.69191	−0.830250	−0.415125	−	0.909764i	$-0.636262\pi$
$47$	−5.69191	−0.830250	−0.415125	+	0.909764i	$0.636262\pi$
$48$	6.11694	0.882904
$49$	0	0
$50$	2.13516	0.301958
$51$	−3.31028	−0.463532
$52$	8.96427	1.24312
$53$	−2.94202	−0.404117	−0.202058	−	0.979373i	$-0.564763\pi$
$53$	−2.94202	−0.404117	−0.202058	+	0.979373i	$0.564763\pi$
$54$	2.51679	0.342491
$55$	3.01905	0.407088
$56$	0	0
$57$	−3.61984	−0.479459
$58$	10.7670	1.41378
$59$	2.02444	0.263560	0.131780	−	0.991279i	$-0.457931\pi$
$59$	2.02444	0.263560	0.131780	+	0.991279i	$0.457931\pi$
$60$	10.4816	1.35317
$61$	−7.38492	−0.945542	−0.472771	−	0.881185i	$-0.656746\pi$
$61$	−7.38492	−0.945542	−0.472771	+	0.881185i	$0.656746\pi$
$62$	−20.0775	−2.54984
$63$	0	0
$64$	−3.05862	−0.382328
$65$	5.00176	0.620392
$66$	3.14194	0.386747
$67$	8.28378	1.01202	0.506012	−	0.862526i	$-0.331119\pi$
$67$	8.28378	1.01202	0.506012	+	0.862526i	$0.331119\pi$
$68$	−14.3474	−1.73988
$69$	−1.00000	−0.120386
$70$	0	0
$71$	−8.27631	−0.982218	−0.491109	−	0.871098i	$-0.663408\pi$
$71$	−8.27631	−0.982218	−0.491109	+	0.871098i	$0.663408\pi$
$72$	5.87470	0.692340
$73$	−11.9873	−1.40301	−0.701504	−	0.712666i	$-0.747488\pi$
$73$	−11.9873	−1.40301	−0.701504	+	0.712666i	$0.747488\pi$
$74$	12.8149	1.48970
$75$	0.848370	0.0979613
$76$	−15.6891	−1.79967
$77$	0	0
$78$	5.20537	0.589392
$79$	−15.2225	−1.71266	−0.856332	−	0.516426i	$-0.827262\pi$
$79$	−15.2225	−1.71266	−0.856332	+	0.516426i	$0.827262\pi$
$80$	14.7928	1.65389
$81$	1.00000	0.111111
$82$	−2.22907	−0.246160
$83$	15.7586	1.72973	0.864866	−	0.502003i	$-0.167403\pi$
$83$	15.7586	1.72973	0.864866	+	0.502003i	$0.167403\pi$
$84$	0	0
$85$	−8.00538	−0.868305
$86$	25.0302	2.69908
$87$	4.27807	0.458658
$88$	7.33395	0.781802
$89$	−16.2664	−1.72424	−0.862119	−	0.506706i	$-0.830863\pi$
$89$	−16.2664	−1.72424	−0.862119	+	0.506706i	$0.830863\pi$
$90$	6.08644	0.641567
$91$	0	0
$92$	−4.33421	−0.451872
$93$	−7.97744	−0.827222
$94$	−14.3253	−1.47754
$95$	−8.75399	−0.898141
$96$	3.64563	0.372080
$97$	16.6972	1.69534	0.847671	−	0.530522i	$-0.178004\pi$
$97$	16.6972	1.69534	0.847671	+	0.530522i	$0.178004\pi$
$98$	0	0
$99$	1.24840	0.125469
$100$	3.67701	0.367701
$101$	−9.05813	−0.901318	−0.450659	−	0.892696i	$-0.648811\pi$
$101$	−9.05813	−0.901318	−0.450659	+	0.892696i	$0.648811\pi$
$102$	−8.33126	−0.824918
$103$	7.70758	0.759450	0.379725	−	0.925099i	$-0.376019\pi$
$103$	7.70758	0.759450	0.379725	+	0.925099i	$0.376019\pi$
$104$	12.1504	1.19145
$105$	0	0
$106$	−7.40442	−0.719181
$107$	14.8187	1.43258	0.716291	−	0.697802i	$-0.245838\pi$
$107$	14.8187	1.43258	0.716291	+	0.697802i	$0.245838\pi$
$108$	4.33421	0.417059
$109$	−4.04929	−0.387852	−0.193926	−	0.981016i	$-0.562122\pi$
$109$	−4.04929	−0.387852	−0.193926	+	0.981016i	$0.562122\pi$
$110$	7.59829	0.724469
$111$	5.09175	0.483288
$112$	0	0
$113$	3.97551	0.373984	0.186992	−	0.982361i	$-0.440126\pi$
$113$	3.97551	0.373984	0.186992	+	0.982361i	$0.440126\pi$
$114$	−9.11035	−0.853262
$115$	−2.41834	−0.225511
$116$	18.5421	1.72159
$117$	2.06826	0.191211
$118$	5.09508	0.469040
$119$	0	0
$120$	14.2070	1.29692
$121$	−9.44151	−0.858319
$122$	−18.5862	−1.68272
$123$	−0.885683	−0.0798593
$124$	−34.5759	−3.10500
$125$	−10.0401	−0.898010
$126$	0	0
$127$	4.89271	0.434158	0.217079	−	0.976154i	$-0.430347\pi$
$127$	4.89271	0.434158	0.217079	+	0.976154i	$0.430347\pi$
$128$	−14.9891	−1.32487
$129$	9.94532	0.875637
$130$	12.5883	1.10407
$131$	−1.52601	−0.133328	−0.0666639	−	0.997775i	$-0.521236\pi$
$131$	−1.52601	−0.133328	−0.0666639	+	0.997775i	$0.521236\pi$
$132$	5.41081	0.470950
$133$	0	0
$134$	20.8485	1.80103
$135$	2.41834	0.208138
$136$	−19.4469	−1.66756
$137$	14.0988	1.20455	0.602273	−	0.798290i	$-0.294262\pi$
$137$	14.0988	1.20455	0.602273	+	0.798290i	$0.294262\pi$
$138$	−2.51679	−0.214243
$139$	2.76556	0.234572	0.117286	−	0.993098i	$-0.462581\pi$
$139$	2.76556	0.234572	0.117286	+	0.993098i	$0.462581\pi$
$140$	0	0
$141$	−5.69191	−0.479345
$142$	−20.8297	−1.74799
$143$	2.58201	0.215918
$144$	6.11694	0.509745
$145$	10.3458	0.859175
$146$	−30.1695	−2.49684
$147$	0	0
$148$	22.0687	1.81404
$149$	−7.03150	−0.576043	−0.288021	−	0.957624i	$-0.592997\pi$
$149$	−7.03150	−0.576043	−0.288021	+	0.957624i	$0.592997\pi$
$150$	2.13516	0.174335
$151$	23.0352	1.87457	0.937287	−	0.348559i	$-0.113329\pi$
$151$	23.0352	1.87457	0.937287	+	0.348559i	$0.113329\pi$
$152$	−21.2654	−1.72486
$153$	−3.31028	−0.267620
$154$	0	0
$155$	−19.2922	−1.54958
$156$	8.96427	0.717716
$157$	−18.2468	−1.45625	−0.728126	−	0.685443i	$-0.759608\pi$
$157$	−18.2468	−1.45625	−0.728126	+	0.685443i	$0.759608\pi$
$158$	−38.3117	−3.04792
$159$	−2.94202	−0.233317
$160$	8.81637	0.696995
$161$	0	0
$162$	2.51679	0.197737
$163$	5.05395	0.395856	0.197928	−	0.980217i	$-0.436579\pi$
$163$	5.05395	0.395856	0.197928	+	0.980217i	$0.436579\pi$
$164$	−3.83873	−0.299755
$165$	3.01905	0.235032
$166$	39.6610	3.07829
$167$	19.3192	1.49497	0.747483	−	0.664281i	$-0.231262\pi$
$167$	19.3192	1.49497	0.747483	+	0.664281i	$0.231262\pi$
$168$	0	0
$169$	−8.72230	−0.670946
$170$	−20.1478	−1.54527
$171$	−3.61984	−0.276816
$172$	43.1051	3.28673
$173$	9.44702	0.718244	0.359122	−	0.933291i	$-0.383076\pi$
$173$	9.44702	0.718244	0.359122	+	0.933291i	$0.383076\pi$
$174$	10.7670	0.816244
$175$	0	0
$176$	7.63636	0.575613
$177$	2.02444	0.152166
$178$	−40.9391	−3.06852
$179$	−16.2651	−1.21571	−0.607854	−	0.794049i	$-0.707969\pi$
$179$	−16.2651	−1.21571	−0.607854	+	0.794049i	$0.707969\pi$
$180$	10.4816	0.781252
$181$	−0.386268	−0.0287110	−0.0143555	−	0.999897i	$-0.504570\pi$
$181$	−0.386268	−0.0287110	−0.0143555	+	0.999897i	$0.504570\pi$
$182$	0	0
$183$	−7.38492	−0.545909
$184$	−5.87470	−0.433089
$185$	12.3136	0.905314
$186$	−20.0775	−1.47215
$187$	−4.13254	−0.302201
$188$	−24.6699	−1.79924
$189$	0	0
$190$	−22.0319	−1.59836
$191$	20.3974	1.47590	0.737950	−	0.674855i	$-0.235794\pi$
$191$	20.3974	1.47590	0.737950	+	0.674855i	$0.235794\pi$
$192$	−3.05862	−0.220737
$193$	25.0195	1.80094	0.900472	−	0.434914i	$-0.143221\pi$
$193$	25.0195	1.80094	0.900472	+	0.434914i	$0.143221\pi$
$194$	42.0232	3.01709
$195$	5.00176	0.358183
$196$	0	0
$197$	−24.5131	−1.74649	−0.873243	−	0.487285i	$-0.837987\pi$
$197$	−24.5131	−1.74649	−0.873243	+	0.487285i	$0.837987\pi$
$198$	3.14194	0.223288
$199$	13.8147	0.979299	0.489650	−	0.871919i	$-0.337125\pi$
$199$	13.8147	0.979299	0.489650	+	0.871919i	$0.337125\pi$
$200$	4.98392	0.352416
$201$	8.28378	0.584293
$202$	−22.7974	−1.60402
$203$	0	0
$204$	−14.3474	−1.00452
$205$	−2.14188	−0.149596
$206$	19.3983	1.35154
$207$	−1.00000	−0.0695048
$208$	12.6514	0.877218
$209$	−4.51899	−0.312585
$210$	0	0
$211$	−11.2182	−0.772296	−0.386148	−	0.922437i	$-0.626195\pi$
$211$	−11.2182	−0.772296	−0.386148	+	0.922437i	$0.626195\pi$
$212$	−12.7513	−0.875763
$213$	−8.27631	−0.567084
$214$	37.2956	2.54947
$215$	24.0512	1.64028
$216$	5.87470	0.399723
$217$	0	0
$218$	−10.1912	−0.690235
$219$	−11.9873	−0.810027
$220$	13.0852	0.882202
$221$	−6.84652	−0.460547
$222$	12.8149	0.860077
$223$	21.3084	1.42691	0.713457	−	0.700699i	$-0.247128\pi$
$223$	21.3084	1.42691	0.713457	+	0.700699i	$0.247128\pi$
$224$	0	0
$225$	0.848370	0.0565580
$226$	10.0055	0.665556
$227$	−4.36100	−0.289450	−0.144725	−	0.989472i	$-0.546230\pi$
$227$	−4.36100	−0.289450	−0.144725	+	0.989472i	$0.546230\pi$
$228$	−15.6891	−1.03904
$229$	10.2262	0.675765	0.337883	−	0.941188i	$-0.390289\pi$
$229$	10.2262	0.675765	0.337883	+	0.941188i	$0.390289\pi$
$230$	−6.08644	−0.401328
$231$	0	0
$232$	25.1324	1.65002
$233$	4.36630	0.286046	0.143023	−	0.989719i	$-0.454318\pi$
$233$	4.36630	0.286046	0.143023	+	0.989719i	$0.454318\pi$
$234$	5.20537	0.340285
$235$	−13.7650	−0.897928
$236$	8.77435	0.571161
$237$	−15.2225	−0.988807
$238$	0	0
$239$	−13.5057	−0.873613	−0.436807	−	0.899555i	$-0.643891\pi$
$239$	−13.5057	−0.873613	−0.436807	+	0.899555i	$0.643891\pi$
$240$	14.7928	0.954874
$241$	−5.20384	−0.335209	−0.167604	−	0.985854i	$-0.553603\pi$
$241$	−5.20384	−0.335209	−0.167604	+	0.985854i	$0.553603\pi$
$242$	−23.7622	−1.52749
$243$	1.00000	0.0641500
$244$	−32.0078	−2.04909
$245$	0	0
$246$	−2.22907	−0.142120
$247$	−7.48676	−0.476371
$248$	−46.8650	−2.97593
$249$	15.7586	0.998661
$250$	−25.2687	−1.59813
$251$	−17.4948	−1.10426	−0.552130	−	0.833758i	$-0.686185\pi$
$251$	−17.4948	−1.10426	−0.552130	+	0.833758i	$0.686185\pi$
$252$	0	0
$253$	−1.24840	−0.0784860
$254$	12.3139	0.772644
$255$	−8.00538	−0.501316
$256$	−31.6072	−1.97545
$257$	18.7532	1.16979	0.584897	−	0.811108i	$-0.301135\pi$
$257$	18.7532	1.16979	0.584897	+	0.811108i	$0.301135\pi$
$258$	25.0302	1.55831
$259$	0	0
$260$	21.6787	1.34445
$261$	4.27807	0.264806
$262$	−3.84063	−0.237275
$263$	0.724893	0.0446988	0.0223494	−	0.999750i	$-0.492885\pi$
$263$	0.724893	0.0446988	0.0223494	+	0.999750i	$0.492885\pi$
$264$	7.33395	0.451373
$265$	−7.11479	−0.437058
$266$	0	0
$267$	−16.2664	−0.995490
$268$	35.9036	2.19316
$269$	11.6787	0.712062	0.356031	−	0.934474i	$-0.384130\pi$
$269$	11.6787	0.712062	0.356031	+	0.934474i	$0.384130\pi$
$270$	6.08644	0.370409
$271$	−13.3613	−0.811639	−0.405820	−	0.913953i	$-0.633014\pi$
$271$	−13.3613	−0.811639	−0.405820	+	0.913953i	$0.633014\pi$
$272$	−20.2488	−1.22776
$273$	0	0
$274$	35.4838	2.14365
$275$	1.05910	0.0638662
$276$	−4.33421	−0.260889
$277$	−20.4944	−1.23139	−0.615696	−	0.787984i	$-0.711125\pi$
$277$	−20.4944	−1.23139	−0.615696	+	0.787984i	$0.711125\pi$
$278$	6.96032	0.417453
$279$	−7.97744	−0.477597
$280$	0	0
$281$	−7.39242	−0.440995	−0.220497	−	0.975388i	$-0.570768\pi$
$281$	−7.39242	−0.440995	−0.220497	+	0.975388i	$0.570768\pi$
$282$	−14.3253	−0.853060
$283$	−5.43725	−0.323211	−0.161605	−	0.986855i	$-0.551667\pi$
$283$	−5.43725	−0.323211	−0.161605	+	0.986855i	$0.551667\pi$
$284$	−35.8713	−2.12857
$285$	−8.75399	−0.518542
$286$	6.49836	0.384256
$287$	0	0
$288$	3.64563	0.214821
$289$	−6.04206	−0.355415
$290$	26.0383	1.52902
$291$	16.6972	0.978806
$292$	−51.9555	−3.04046
$293$	22.0096	1.28582	0.642908	−	0.765943i	$-0.277728\pi$
$293$	22.0096	1.28582	0.642908	+	0.765943i	$0.277728\pi$
$294$	0	0
$295$	4.89579	0.285044
$296$	29.9125	1.73863
$297$	1.24840	0.0724393
$298$	−17.6968	−1.02515
$299$	−2.06826	−0.119611
$300$	3.67701	0.212292
$301$	0	0
$302$	57.9745	3.33606
$303$	−9.05813	−0.520376
$304$	−22.1423	−1.26995
$305$	−17.8592	−1.02262
$306$	−8.33126	−0.476266
$307$	−0.129089	−0.00736751	−0.00368375	−	0.999993i	$-0.501173\pi$
$307$	−0.129089	−0.00736751	−0.00368375	+	0.999993i	$0.501173\pi$
$308$	0	0
$309$	7.70758	0.438469
$310$	−48.5542	−2.75769
$311$	−7.93476	−0.449939	−0.224970	−	0.974366i	$-0.572228\pi$
$311$	−7.93476	−0.449939	−0.224970	+	0.974366i	$0.572228\pi$
$312$	12.1504	0.687881
$313$	−9.68244	−0.547284	−0.273642	−	0.961832i	$-0.588228\pi$
$313$	−9.68244	−0.547284	−0.273642	+	0.961832i	$0.588228\pi$
$314$	−45.9232	−2.59160
$315$	0	0
$316$	−65.9774	−3.71152
$317$	−17.8054	−1.00005	−0.500025	−	0.866011i	$-0.666676\pi$
$317$	−17.8054	−1.00005	−0.500025	+	0.866011i	$0.666676\pi$
$318$	−7.40442	−0.415219
$319$	5.34073	0.299024
$320$	−7.39679	−0.413493
$321$	14.8187	0.827102
$322$	0	0
$323$	11.9827	0.666733
$324$	4.33421	0.240789
$325$	1.75465	0.0973305
$326$	12.7197	0.704479
$327$	−4.04929	−0.223926
$328$	−5.20312	−0.287294
$329$	0	0
$330$	7.59829	0.418272
$331$	23.8177	1.30914	0.654568	−	0.756003i	$-0.272850\pi$
$331$	23.8177	1.30914	0.654568	+	0.756003i	$0.272850\pi$
$332$	68.3011	3.74851
$333$	5.09175	0.279026
$334$	48.6223	2.66049
$335$	20.0330	1.09452
$336$	0	0
$337$	−4.59296	−0.250194	−0.125097	−	0.992144i	$-0.539924\pi$
$337$	−4.59296	−0.250194	−0.125097	+	0.992144i	$0.539924\pi$
$338$	−21.9522	−1.19404
$339$	3.97551	0.215920
$340$	−34.6970	−1.88171
$341$	−9.95900	−0.539310
$342$	−9.11035	−0.492631
$343$	0	0
$344$	58.4258	3.15011
$345$	−2.41834	−0.130199
$346$	23.7761	1.27821
$347$	−31.5083	−1.69145	−0.845726	−	0.533617i	$-0.820832\pi$
$347$	−31.5083	−1.69145	−0.845726	+	0.533617i	$0.820832\pi$
$348$	18.5421	0.993959
$349$	−31.4878	−1.68551	−0.842753	−	0.538300i	$-0.819067\pi$
$349$	−31.4878	−1.68551	−0.842753	+	0.538300i	$0.819067\pi$
$350$	0	0
$351$	2.06826	0.110396
$352$	4.55119	0.242579
$353$	34.9139	1.85828	0.929139	−	0.369731i	$-0.120550\pi$
$353$	34.9139	1.85828	0.929139	+	0.369731i	$0.120550\pi$
$354$	5.09508	0.270801
$355$	−20.0149	−1.06228
$356$	−70.5021	−3.73660
$357$	0	0
$358$	−40.9356	−2.16352
$359$	16.1210	0.850835	0.425417	−	0.904997i	$-0.360127\pi$
$359$	16.1210	0.850835	0.425417	+	0.904997i	$0.360127\pi$
$360$	14.2070	0.748776
$361$	−5.89679	−0.310357
$362$	−0.972153	−0.0510952
$363$	−9.44151	−0.495551
$364$	0	0
$365$	−28.9894	−1.51737
$366$	−18.5862	−0.971519
$367$	−18.0039	−0.939794	−0.469897	−	0.882721i	$-0.655709\pi$
$367$	−18.0039	−0.939794	−0.469897	+	0.882721i	$0.655709\pi$
$368$	−6.11694	−0.318868
$369$	−0.885683	−0.0461068
$370$	30.9907	1.61113
$371$	0	0
$372$	−34.5759	−1.79268
$373$	27.7633	1.43753	0.718765	−	0.695253i	$-0.244708\pi$
$373$	27.7633	1.43753	0.718765	+	0.695253i	$0.244708\pi$
$374$	−10.4007	−0.537808
$375$	−10.0401	−0.518466
$376$	−33.4383	−1.72445
$377$	8.84817	0.455704
$378$	0	0
$379$	8.91763	0.458068	0.229034	−	0.973418i	$-0.426443\pi$
$379$	8.91763	0.458068	0.229034	+	0.973418i	$0.426443\pi$
$380$	−37.9416	−1.94636
$381$	4.89271	0.250661
$382$	51.3358	2.62657
$383$	−1.81386	−0.0926840	−0.0463420	−	0.998926i	$-0.514756\pi$
$383$	−1.81386	−0.0926840	−0.0463420	+	0.998926i	$0.514756\pi$
$384$	−14.9891	−0.764912
$385$	0	0
$386$	62.9687	3.20502
$387$	9.94532	0.505549
$388$	72.3691	3.67398
$389$	−7.92636	−0.401882	−0.200941	−	0.979603i	$-0.564400\pi$
$389$	−7.92636	−0.401882	−0.200941	+	0.979603i	$0.564400\pi$
$390$	12.5883	0.637436
$391$	3.31028	0.167408
$392$	0	0
$393$	−1.52601	−0.0769768
$394$	−61.6942	−3.10811
$395$	−36.8132	−1.85227
$396$	5.41081	0.271903
$397$	17.8488	0.895806	0.447903	−	0.894082i	$-0.352171\pi$
$397$	17.8488	0.895806	0.447903	+	0.894082i	$0.352171\pi$
$398$	34.7687	1.74280
$399$	0	0
$400$	5.18943	0.259471
$401$	−30.9602	−1.54608	−0.773040	−	0.634358i	$-0.781265\pi$
$401$	−30.9602	−1.54608	−0.773040	+	0.634358i	$0.781265\pi$
$402$	20.8485	1.03983
$403$	−16.4994	−0.821894
$404$	−39.2598	−1.95325
$405$	2.41834	0.120168
$406$	0	0
$407$	6.35653	0.315081
$408$	−19.4469	−0.962764
$409$	−1.62618	−0.0804097	−0.0402048	−	0.999191i	$-0.512801\pi$
$409$	−1.62618	−0.0804097	−0.0402048	+	0.999191i	$0.512801\pi$
$410$	−5.39066	−0.266226
$411$	14.0988	0.695445
$412$	33.4062	1.64581
$413$	0	0
$414$	−2.51679	−0.123693
$415$	38.1097	1.87073
$416$	7.54010	0.369684
$417$	2.76556	0.135430
$418$	−11.3733	−0.556287
$419$	7.77197	0.379685	0.189843	−	0.981815i	$-0.439202\pi$
$419$	7.77197	0.379685	0.189843	+	0.981815i	$0.439202\pi$
$420$	0	0
$421$	24.1012	1.17462	0.587311	−	0.809362i	$-0.300187\pi$
$421$	24.1012	1.17462	0.587311	+	0.809362i	$0.300187\pi$
$422$	−28.2339	−1.37441
$423$	−5.69191	−0.276750
$424$	−17.2835	−0.839359
$425$	−2.80834	−0.136225
$426$	−20.8297	−1.00920
$427$	0	0
$428$	64.2275	3.10455
$429$	2.58201	0.124661
$430$	60.5316	2.91909
$431$	−3.61843	−0.174294	−0.0871469	−	0.996195i	$-0.527775\pi$
$431$	−3.61843	−0.174294	−0.0871469	+	0.996195i	$0.527775\pi$
$432$	6.11694	0.294301
$433$	19.6817	0.945840	0.472920	−	0.881105i	$-0.343200\pi$
$433$	19.6817	0.945840	0.472920	+	0.881105i	$0.343200\pi$
$434$	0	0
$435$	10.3458	0.496045
$436$	−17.5505	−0.840515
$437$	3.61984	0.173160
$438$	−30.1695	−1.44155
$439$	32.8609	1.56837	0.784183	−	0.620530i	$-0.213083\pi$
$439$	32.8609	1.56837	0.784183	+	0.620530i	$0.213083\pi$
$440$	17.7360	0.845530
$441$	0	0
$442$	−17.2312	−0.819605
$443$	−17.8084	−0.846103	−0.423051	−	0.906106i	$-0.639041\pi$
$443$	−17.8084	−0.846103	−0.423051	+	0.906106i	$0.639041\pi$
$444$	22.0687	1.04734
$445$	−39.3378	−1.86479
$446$	53.6286	2.53939
$447$	−7.03150	−0.332578
$448$	0	0
$449$	22.1041	1.04316	0.521578	−	0.853204i	$-0.325344\pi$
$449$	22.1041	1.04316	0.521578	+	0.853204i	$0.325344\pi$
$450$	2.13516	0.100653
$451$	−1.10568	−0.0520646
$452$	17.2307	0.810463
$453$	23.0352	1.08229
$454$	−10.9757	−0.515115
$455$	0	0
$456$	−21.2654	−0.995846
$457$	−19.8990	−0.930834	−0.465417	−	0.885092i	$-0.654096\pi$
$457$	−19.8990	−0.930834	−0.465417	+	0.885092i	$0.654096\pi$
$458$	25.7371	1.20262
$459$	−3.31028	−0.154511
$460$	−10.4816	−0.488707
$461$	3.00723	0.140061	0.0700303	−	0.997545i	$-0.477690\pi$
$461$	3.00723	0.140061	0.0700303	+	0.997545i	$0.477690\pi$
$462$	0	0
$463$	−17.9023	−0.831992	−0.415996	−	0.909366i	$-0.636567\pi$
$463$	−17.9023	−0.831992	−0.415996	+	0.909366i	$0.636567\pi$
$464$	26.1687	1.21485
$465$	−19.2922	−0.894652
$466$	10.9890	0.509057
$467$	−7.93823	−0.367337	−0.183669	−	0.982988i	$-0.558797\pi$
$467$	−7.93823	−0.367337	−0.183669	+	0.982988i	$0.558797\pi$
$468$	8.96427	0.414373
$469$	0	0
$470$	−34.6435	−1.59798
$471$	−18.2468	−0.840767
$472$	11.8930	0.547419
$473$	12.4157	0.570875
$474$	−38.3117	−1.75972
$475$	−3.07096	−0.140905
$476$	0	0
$477$	−2.94202	−0.134706
$478$	−33.9910	−1.55471
$479$	25.7465	1.17639	0.588193	−	0.808721i	$-0.299840\pi$
$479$	25.7465	1.17639	0.588193	+	0.808721i	$0.299840\pi$
$480$	8.81637	0.402410
$481$	10.5311	0.480176
$482$	−13.0969	−0.596550
$483$	0	0
$484$	−40.9215	−1.86007
$485$	40.3795	1.83354
$486$	2.51679	0.114164
$487$	−28.3351	−1.28399	−0.641994	−	0.766710i	$-0.721893\pi$
$487$	−28.3351	−1.28399	−0.641994	+	0.766710i	$0.721893\pi$
$488$	−43.3842	−1.96391
$489$	5.05395	0.228547
$490$	0	0
$491$	−10.5092	−0.474272	−0.237136	−	0.971476i	$-0.576209\pi$
$491$	−10.5092	−0.474272	−0.237136	+	0.971476i	$0.576209\pi$
$492$	−3.83873	−0.173063
$493$	−14.1616	−0.637807
$494$	−18.8426	−0.847767
$495$	3.01905	0.135696
$496$	−48.7975	−2.19107
$497$	0	0
$498$	39.6610	1.77725
$499$	−8.22749	−0.368313	−0.184156	−	0.982897i	$-0.558955\pi$
$499$	−8.22749	−0.368313	−0.184156	+	0.982897i	$0.558955\pi$
$500$	−43.5157	−1.94608
$501$	19.3192	0.863119
$502$	−44.0305	−1.96518
$503$	−1.55855	−0.0694922	−0.0347461	−	0.999396i	$-0.511062\pi$
$503$	−1.55855	−0.0694922	−0.0347461	+	0.999396i	$0.511062\pi$
$504$	0	0
$505$	−21.9056	−0.974788
$506$	−3.14194	−0.139676
$507$	−8.72230	−0.387371
$508$	21.2060	0.940866
$509$	−0.347472	−0.0154014	−0.00770071	−	0.999970i	$-0.502451\pi$
$509$	−0.347472	−0.0154014	−0.00770071	+	0.999970i	$0.502451\pi$
$510$	−20.1478	−0.892161
$511$	0	0
$512$	−49.5703	−2.19072
$513$	−3.61984	−0.159820
$514$	47.1978	2.08181
$515$	18.6395	0.821356
$516$	43.1051	1.89760
$517$	−7.10576	−0.312511
$518$	0	0
$519$	9.44702	0.414678
$520$	29.3838	1.28857
$521$	−1.93848	−0.0849261	−0.0424631	−	0.999098i	$-0.513520\pi$
$521$	−1.93848	−0.0849261	−0.0424631	+	0.999098i	$0.513520\pi$
$522$	10.7670	0.471259
$523$	−40.4359	−1.76814	−0.884070	−	0.467354i	$-0.845207\pi$
$523$	−40.4359	−1.76814	−0.884070	+	0.467354i	$0.845207\pi$
$524$	−6.61403	−0.288935
$525$	0	0
$526$	1.82440	0.0795476
$527$	26.4075	1.15033
$528$	7.63636	0.332330
$529$	1.00000	0.0434783
$530$	−17.9064	−0.777805
$531$	2.02444	0.0878533
$532$	0	0
$533$	−1.83182	−0.0793450
$534$	−40.9391	−1.77161
$535$	35.8368	1.54936
$536$	48.6647	2.10199
$537$	−16.2651	−0.701889
$538$	29.3927	1.26721
$539$	0	0
$540$	10.4816	0.451056
$541$	23.4554	1.00843	0.504214	−	0.863579i	$-0.331782\pi$
$541$	23.4554	1.00843	0.504214	+	0.863579i	$0.331782\pi$
$542$	−33.6274	−1.44442
$543$	−0.386268	−0.0165763
$544$	−12.0680	−0.517413
$545$	−9.79256	−0.419467
$546$	0	0
$547$	28.6726	1.22595	0.612976	−	0.790102i	$-0.289972\pi$
$547$	28.6726	1.22595	0.612976	+	0.790102i	$0.289972\pi$
$548$	61.1073	2.61038
$549$	−7.38492	−0.315181
$550$	2.66553	0.113659
$551$	−15.4859	−0.659723
$552$	−5.87470	−0.250044
$553$	0	0
$554$	−51.5801	−2.19143
$555$	12.3136	0.522683
$556$	11.9865	0.508342
$557$	30.1319	1.27673	0.638365	−	0.769733i	$-0.279611\pi$
$557$	30.1319	1.27673	0.638365	+	0.769733i	$0.279611\pi$
$558$	−20.0775	−0.849948
$559$	20.5695	0.869998
$560$	0	0
$561$	−4.13254	−0.174476
$562$	−18.6051	−0.784810
$563$	23.7312	1.00015	0.500074	−	0.865982i	$-0.333306\pi$
$563$	23.7312	1.00015	0.500074	+	0.865982i	$0.333306\pi$
$564$	−24.6699	−1.03879
$565$	9.61413	0.404469
$566$	−13.6844	−0.575197
$567$	0	0
$568$	−48.6208	−2.04009
$569$	−12.8507	−0.538730	−0.269365	−	0.963038i	$-0.586814\pi$
$569$	−12.8507	−0.538730	−0.269365	+	0.963038i	$0.586814\pi$
$570$	−22.0319	−0.922816
$571$	39.0256	1.63317	0.816584	−	0.577226i	$-0.195865\pi$
$571$	39.0256	1.63317	0.816584	+	0.577226i	$0.195865\pi$
$572$	11.1910	0.467917
$573$	20.3974	0.852112
$574$	0	0
$575$	−0.848370	−0.0353795
$576$	−3.05862	−0.127443
$577$	−18.1657	−0.756248	−0.378124	−	0.925755i	$-0.623431\pi$
$577$	−18.1657	−0.756248	−0.378124	+	0.925755i	$0.623431\pi$
$578$	−15.2066	−0.632509
$579$	25.0195	1.03978
$580$	44.8410	1.86192
$581$	0	0
$582$	42.0232	1.74192
$583$	−3.67280	−0.152112
$584$	−70.4218	−2.91407
$585$	5.00176	0.206797
$586$	55.3935	2.28829
$587$	−7.81464	−0.322545	−0.161272	−	0.986910i	$-0.551560\pi$
$587$	−7.81464	−0.322545	−0.161272	+	0.986910i	$0.551560\pi$
$588$	0	0
$589$	28.8770	1.18986
$590$	12.3216	0.507274
$591$	−24.5131	−1.00833
$592$	31.1460	1.28009
$593$	−26.4111	−1.08457	−0.542287	−	0.840194i	$-0.682441\pi$
$593$	−26.4111	−1.08457	−0.542287	+	0.840194i	$0.682441\pi$
$594$	3.14194	0.128916
$595$	0	0
$596$	−30.4760	−1.24834
$597$	13.8147	0.565399
$598$	−5.20537	−0.212863
$599$	35.3946	1.44618	0.723091	−	0.690752i	$-0.242721\pi$
$599$	35.3946	1.44618	0.723091	+	0.690752i	$0.242721\pi$
$600$	4.98392	0.203468
$601$	−25.3306	−1.03326	−0.516629	−	0.856210i	$-0.672813\pi$
$601$	−25.3306	−1.03326	−0.516629	+	0.856210i	$0.672813\pi$
$602$	0	0
$603$	8.28378	0.337341
$604$	99.8391	4.06240
$605$	−22.8328	−0.928284
$606$	−22.7974	−0.926080
$607$	29.9937	1.21741	0.608703	−	0.793398i	$-0.291690\pi$
$607$	29.9937	1.21741	0.608703	+	0.793398i	$0.291690\pi$
$608$	−13.1966	−0.535192
$609$	0	0
$610$	−44.9479	−1.81989
$611$	−11.7723	−0.476258
$612$	−14.3474	−0.579961
$613$	−2.51013	−0.101383	−0.0506916	−	0.998714i	$-0.516143\pi$
$613$	−2.51013	−0.101383	−0.0506916	+	0.998714i	$0.516143\pi$
$614$	−0.324890	−0.0131115
$615$	−2.14188	−0.0863690
$616$	0	0
$617$	10.5953	0.426550	0.213275	−	0.976992i	$-0.431587\pi$
$617$	10.5953	0.426550	0.213275	+	0.976992i	$0.431587\pi$
$618$	19.3983	0.780315
$619$	0.196549	0.00789998	0.00394999	−	0.999992i	$-0.498743\pi$
$619$	0.196549	0.00789998	0.00394999	+	0.999992i	$0.498743\pi$
$620$	−83.6162	−3.35811
$621$	−1.00000	−0.0401286
$622$	−19.9701	−0.800728
$623$	0	0
$624$	12.6514	0.506462
$625$	−28.5221	−1.14088
$626$	−24.3686	−0.973966
$627$	−4.51899	−0.180471
$628$	−79.0853	−3.15585
$629$	−16.8551	−0.672058
$630$	0	0
$631$	18.3191	0.729270	0.364635	−	0.931150i	$-0.381194\pi$
$631$	18.3191	0.729270	0.364635	+	0.931150i	$0.381194\pi$
$632$	−89.4275	−3.55724
$633$	−11.2182	−0.445885
$634$	−44.8124	−1.77973
$635$	11.8322	0.469548
$636$	−12.7513	−0.505622
$637$	0	0
$638$	13.4415	0.532153
$639$	−8.27631	−0.327406
$640$	−36.2489	−1.43286
$641$	21.5375	0.850680	0.425340	−	0.905034i	$-0.360154\pi$
$641$	21.5375	0.850680	0.425340	+	0.905034i	$0.360154\pi$
$642$	37.2956	1.47194
$643$	−14.0708	−0.554897	−0.277449	−	0.960740i	$-0.589489\pi$
$643$	−14.0708	−0.554897	−0.277449	+	0.960740i	$0.589489\pi$
$644$	0	0
$645$	24.0512	0.947014
$646$	30.1578	1.18654
$647$	31.3886	1.23401	0.617006	−	0.786958i	$-0.288345\pi$
$647$	31.3886	1.23401	0.617006	+	0.786958i	$0.288345\pi$
$648$	5.87470	0.230780
$649$	2.52730	0.0992054
$650$	4.41608	0.173213
$651$	0	0
$652$	21.9049	0.857861
$653$	2.45917	0.0962349	0.0481175	−	0.998842i	$-0.484678\pi$
$653$	2.45917	0.0962349	0.0481175	+	0.998842i	$0.484678\pi$
$654$	−10.1912	−0.398507
$655$	−3.69040	−0.144196
$656$	−5.41767	−0.211524
$657$	−11.9873	−0.467669
$658$	0	0
$659$	27.0472	1.05361	0.526805	−	0.849986i	$-0.323390\pi$
$659$	27.0472	1.05361	0.526805	+	0.849986i	$0.323390\pi$
$660$	13.0852	0.509340
$661$	−44.8576	−1.74476	−0.872378	−	0.488831i	$-0.837423\pi$
$661$	−44.8576	−1.74476	−0.872378	+	0.488831i	$0.837423\pi$
$662$	59.9439	2.32979
$663$	−6.84652	−0.265897
$664$	92.5771	3.59269
$665$	0	0
$666$	12.8149	0.496565
$667$	−4.27807	−0.165648
$668$	83.7335	3.23975
$669$	21.3084	0.823830
$670$	50.4187	1.94785
$671$	−9.21930	−0.355907
$672$	0	0
$673$	−40.8475	−1.57456	−0.787279	−	0.616598i	$-0.788511\pi$
$673$	−40.8475	−1.57456	−0.787279	+	0.616598i	$0.788511\pi$
$674$	−11.5595	−0.445255
$675$	0.848370	0.0326538
$676$	−37.8043	−1.45401
$677$	42.5159	1.63402	0.817009	−	0.576625i	$-0.195631\pi$
$677$	42.5159	1.63402	0.817009	+	0.576625i	$0.195631\pi$
$678$	10.0055	0.384259
$679$	0	0
$680$	−47.0292	−1.80349
$681$	−4.36100	−0.167114
$682$	−25.0647	−0.959776
$683$	−6.24357	−0.238903	−0.119452	−	0.992840i	$-0.538114\pi$
$683$	−6.24357	−0.238903	−0.119452	+	0.992840i	$0.538114\pi$
$684$	−15.6891	−0.599888
$685$	34.0958	1.30273
$686$	0	0
$687$	10.2262	0.390153
$688$	60.8349	2.31931
$689$	−6.08485	−0.231814
$690$	−6.08644	−0.231707
$691$	−10.8876	−0.414184	−0.207092	−	0.978321i	$-0.566400\pi$
$691$	−10.8876	−0.414184	−0.207092	+	0.978321i	$0.566400\pi$
$692$	40.9454	1.55651
$693$	0	0
$694$	−79.2995	−3.01017
$695$	6.68807	0.253693
$696$	25.1324	0.952641
$697$	2.93186	0.111052
$698$	−79.2482	−2.99959
$699$	4.36630	0.165149
$700$	0	0
$701$	5.23763	0.197822	0.0989112	−	0.995096i	$-0.468464\pi$
$701$	5.23763	0.197822	0.0989112	+	0.995096i	$0.468464\pi$
$702$	5.20537	0.196464
$703$	−18.4313	−0.695150
$704$	−3.81837	−0.143910
$705$	−13.7650	−0.518419
$706$	87.8707	3.30706
$707$	0	0
$708$	8.77435	0.329760
$709$	−20.9946	−0.788468	−0.394234	−	0.919010i	$-0.628990\pi$
$709$	−20.9946	−0.788468	−0.394234	+	0.919010i	$0.628990\pi$
$710$	−50.3733	−1.89048
$711$	−15.2225	−0.570888
$712$	−95.5604	−3.58128
$713$	7.97744	0.298757
$714$	0	0
$715$	6.24417	0.233519
$716$	−70.4961	−2.63456
$717$	−13.5057	−0.504381
$718$	40.5731	1.51418
$719$	−22.4845	−0.838529	−0.419265	−	0.907864i	$-0.637712\pi$
$719$	−22.4845	−0.838529	−0.419265	+	0.907864i	$0.637712\pi$
$720$	14.7928	0.551297
$721$	0	0
$722$	−14.8410	−0.552323
$723$	−5.20384	−0.193533
$724$	−1.67416	−0.0622198
$725$	3.62939	0.134792
$726$	−23.7622	−0.881900
$727$	−20.7141	−0.768242	−0.384121	−	0.923283i	$-0.625496\pi$
$727$	−20.7141	−0.768242	−0.384121	+	0.923283i	$0.625496\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−72.9600	−2.70037
$731$	−32.9218	−1.21766
$732$	−32.0078	−1.18304
$733$	12.2866	0.453816	0.226908	−	0.973916i	$-0.427138\pi$
$733$	12.2866	0.453816	0.226908	+	0.973916i	$0.427138\pi$
$734$	−45.3119	−1.67249
$735$	0	0
$736$	−3.64563	−0.134380
$737$	10.3414	0.380932
$738$	−2.22907	−0.0820533
$739$	10.9556	0.403009	0.201505	−	0.979488i	$-0.435417\pi$
$739$	10.9556	0.403009	0.201505	+	0.979488i	$0.435417\pi$
$740$	53.3697	1.96191
$741$	−7.48676	−0.275033
$742$	0	0
$743$	−38.8827	−1.42647	−0.713235	−	0.700925i	$-0.752771\pi$
$743$	−38.8827	−1.42647	−0.713235	+	0.700925i	$0.752771\pi$
$744$	−46.8650	−1.71816
$745$	−17.0046	−0.622999
$746$	69.8743	2.55828
$747$	15.7586	0.576577
$748$	−17.9113	−0.654901
$749$	0	0
$750$	−25.2687	−0.922681
$751$	−0.420753	−0.0153535	−0.00767675	−	0.999971i	$-0.502444\pi$
$751$	−0.420753	−0.0153535	−0.00767675	+	0.999971i	$0.502444\pi$
$752$	−34.8171	−1.26965
$753$	−17.4948	−0.637544
$754$	22.2689	0.810987
$755$	55.7068	2.02738
$756$	0	0
$757$	31.5476	1.14662	0.573309	−	0.819339i	$-0.305660\pi$
$757$	31.5476	1.14662	0.573309	+	0.819339i	$0.305660\pi$
$758$	22.4438	0.815194
$759$	−1.24840	−0.0453139
$760$	−51.4271	−1.86546
$761$	−10.9325	−0.396304	−0.198152	−	0.980171i	$-0.563494\pi$
$761$	−10.9325	−0.396304	−0.198152	+	0.980171i	$0.563494\pi$
$762$	12.3139	0.446086
$763$	0	0
$764$	88.4064	3.19843
$765$	−8.00538	−0.289435
$766$	−4.56510	−0.164944
$767$	4.18707	0.151186
$768$	−31.6072	−1.14053
$769$	0.569674	0.0205430	0.0102715	−	0.999947i	$-0.496730\pi$
$769$	0.569674	0.0205430	0.0102715	+	0.999947i	$0.496730\pi$
$770$	0	0
$771$	18.7532	0.675381
$772$	108.440	3.90283
$773$	34.5794	1.24373	0.621867	−	0.783123i	$-0.286374\pi$
$773$	34.5794	1.24373	0.621867	+	0.783123i	$0.286374\pi$
$774$	25.0302	0.899693
$775$	−6.76782	−0.243107
$776$	98.0909	3.52126
$777$	0	0
$778$	−19.9489	−0.715204
$779$	3.20603	0.114868
$780$	21.6787	0.776220
$781$	−10.3321	−0.369712
$782$	8.33126	0.297925
$783$	4.27807	0.152886
$784$	0	0
$785$	−44.1269	−1.57496
$786$	−3.84063	−0.136991
$787$	−11.4846	−0.409382	−0.204691	−	0.978827i	$-0.565619\pi$
$787$	−11.4846	−0.409382	−0.204691	+	0.978827i	$0.565619\pi$
$788$	−106.245	−3.78482
$789$	0.724893	0.0258069
$790$	−92.6508	−3.29637
$791$	0	0
$792$	7.33395	0.260601
$793$	−15.2739	−0.542393
$794$	44.9216	1.59421
$795$	−7.11479	−0.252336
$796$	59.8759	2.12224
$797$	−16.1795	−0.573109	−0.286555	−	0.958064i	$-0.592510\pi$
$797$	−16.1795	−0.573109	−0.286555	+	0.958064i	$0.592510\pi$
$798$	0	0
$799$	18.8418	0.666575
$800$	3.09284	0.109348
$801$	−16.2664	−0.574746
$802$	−77.9202	−2.75146
$803$	−14.9649	−0.528100
$804$	35.9036	1.26622
$805$	0	0
$806$	−41.5255	−1.46267
$807$	11.6787	0.411109
$808$	−53.2138	−1.87205
$809$	−34.2205	−1.20313	−0.601564	−	0.798825i	$-0.705455\pi$
$809$	−34.2205	−1.20313	−0.601564	+	0.798825i	$0.705455\pi$
$810$	6.08644	0.213856
$811$	16.6256	0.583804	0.291902	−	0.956448i	$-0.405712\pi$
$811$	16.6256	0.583804	0.291902	+	0.956448i	$0.405712\pi$
$812$	0	0
$813$	−13.3613	−0.468600
$814$	15.9980	0.560730
$815$	12.2222	0.428124
$816$	−20.2488	−0.708849
$817$	−36.0004	−1.25950
$818$	−4.09276	−0.143100
$819$	0	0
$820$	−9.28336	−0.324189
$821$	−7.62668	−0.266173	−0.133086	−	0.991104i	$-0.542489\pi$
$821$	−7.62668	−0.266173	−0.133086	+	0.991104i	$0.542489\pi$
$822$	35.4838	1.23764
$823$	−31.1450	−1.08565	−0.542823	−	0.839847i	$-0.682644\pi$
$823$	−31.1450	−1.08565	−0.542823	+	0.839847i	$0.682644\pi$
$824$	45.2797	1.57739
$825$	1.05910	0.0368732
$826$	0	0
$827$	−29.5643	−1.02805	−0.514026	−	0.857774i	$-0.671847\pi$
$827$	−29.5643	−1.02805	−0.514026	+	0.857774i	$0.671847\pi$
$828$	−4.33421	−0.150624
$829$	−17.1458	−0.595500	−0.297750	−	0.954644i	$-0.596236\pi$
$829$	−17.1458	−0.595500	−0.297750	+	0.954644i	$0.596236\pi$
$830$	95.9139	3.32922
$831$	−20.4944	−0.710945
$832$	−6.32603	−0.219315
$833$	0	0
$834$	6.96032	0.241016
$835$	46.7204	1.61683
$836$	−19.5862	−0.677404
$837$	−7.97744	−0.275741
$838$	19.5604	0.675702
$839$	9.06553	0.312977	0.156488	−	0.987680i	$-0.449983\pi$
$839$	9.06553	0.312977	0.156488	+	0.987680i	$0.449983\pi$
$840$	0	0
$841$	−10.6981	−0.368899
$842$	60.6576	2.09040
$843$	−7.39242	−0.254608
$844$	−48.6222	−1.67365
$845$	−21.0935	−0.725638
$846$	−14.3253	−0.492514
$847$	0	0
$848$	−17.9961	−0.617990
$849$	−5.43725	−0.186606
$850$	−7.06799	−0.242430
$851$	−5.09175	−0.174543
$852$	−35.8713	−1.22893
$853$	−22.1968	−0.760003	−0.380002	−	0.924986i	$-0.624077\pi$
$853$	−22.1968	−0.760003	−0.380002	+	0.924986i	$0.624077\pi$
$854$	0	0
$855$	−8.75399	−0.299380
$856$	87.0557	2.97550
$857$	16.7067	0.570690	0.285345	−	0.958425i	$-0.407892\pi$
$857$	16.7067	0.570690	0.285345	+	0.958425i	$0.407892\pi$
$858$	6.49836	0.221850
$859$	−28.5743	−0.974941	−0.487471	−	0.873139i	$-0.662080\pi$
$859$	−28.5743	−0.974941	−0.487471	+	0.873139i	$0.662080\pi$
$860$	104.243	3.55465
$861$	0	0
$862$	−9.10682	−0.310180
$863$	−4.43965	−0.151127	−0.0755637	−	0.997141i	$-0.524076\pi$
$863$	−4.43965	−0.151127	−0.0755637	+	0.997141i	$0.524076\pi$
$864$	3.64563	0.124027
$865$	22.8461	0.776791
$866$	49.5345	1.68325
$867$	−6.04206	−0.205199
$868$	0	0
$869$	−19.0037	−0.644656
$870$	26.0383	0.882780
$871$	17.1330	0.580530
$872$	−23.7884	−0.805576
$873$	16.6972	0.565114
$874$	9.11035	0.308162
$875$	0	0
$876$	−51.9555	−1.75541
$877$	9.89313	0.334067	0.167034	−	0.985951i	$-0.446581\pi$
$877$	9.89313	0.334067	0.167034	+	0.985951i	$0.446581\pi$
$878$	82.7038	2.79112
$879$	22.0096	0.742367
$880$	18.4673	0.622533
$881$	19.1692	0.645825	0.322913	−	0.946429i	$-0.395338\pi$
$881$	19.1692	0.645825	0.322913	+	0.946429i	$0.395338\pi$
$882$	0	0
$883$	−21.3067	−0.717026	−0.358513	−	0.933525i	$-0.616716\pi$
$883$	−21.3067	−0.717026	−0.358513	+	0.933525i	$0.616716\pi$
$884$	−29.6742	−0.998052
$885$	4.89579	0.164570
$886$	−44.8199	−1.50575
$887$	6.11328	0.205264	0.102632	−	0.994719i	$-0.467274\pi$
$887$	6.11328	0.205264	0.102632	+	0.994719i	$0.467274\pi$
$888$	29.9125	1.00380
$889$	0	0
$890$	−99.0047	−3.31865
$891$	1.24840	0.0418228
$892$	92.3549	3.09227
$893$	20.6038	0.689479
$894$	−17.6968	−0.591869
$895$	−39.3344	−1.31481
$896$	0	0
$897$	−2.06826	−0.0690572
$898$	55.6312	1.85644
$899$	−34.1281	−1.13823
$900$	3.67701	0.122567
$901$	9.73889	0.324449
$902$	−2.78277	−0.0926560
$903$	0	0
$904$	23.3549	0.776773
$905$	−0.934127	−0.0310514
$906$	57.9745	1.92607
$907$	28.2198	0.937024	0.468512	−	0.883457i	$-0.344790\pi$
$907$	28.2198	0.937024	0.468512	+	0.883457i	$0.344790\pi$
$908$	−18.9015	−0.627268
$909$	−9.05813	−0.300439
$910$	0	0
$911$	37.5458	1.24395	0.621974	−	0.783038i	$-0.286331\pi$
$911$	37.5458	1.24395	0.621974	+	0.783038i	$0.286331\pi$
$912$	−22.1423	−0.733205
$913$	19.6730	0.651081
$914$	−50.0814	−1.65654
$915$	−17.8592	−0.590408
$916$	44.3224	1.46445
$917$	0	0
$918$	−8.33126	−0.274973
$919$	−7.32823	−0.241736	−0.120868	−	0.992669i	$-0.538568\pi$
$919$	−7.32823	−0.241736	−0.120868	+	0.992669i	$0.538568\pi$
$920$	−14.2070	−0.468392
$921$	−0.129089	−0.00425363
$922$	7.56854	0.249257
$923$	−17.1176	−0.563432
$924$	0	0
$925$	4.31969	0.142031
$926$	−45.0564	−1.48064
$927$	7.70758	0.253150
$928$	15.5963	0.511972
$929$	36.8737	1.20979	0.604893	−	0.796307i	$-0.293216\pi$
$929$	36.8737	1.20979	0.604893	+	0.796307i	$0.293216\pi$
$930$	−48.5542	−1.59216
$931$	0	0
$932$	18.9244	0.619891
$933$	−7.93476	−0.259772
$934$	−19.9788	−0.653727
$935$	−9.99388	−0.326835
$936$	12.1504	0.397148
$937$	−4.03995	−0.131980	−0.0659898	−	0.997820i	$-0.521020\pi$
$937$	−4.03995	−0.131980	−0.0659898	+	0.997820i	$0.521020\pi$
$938$	0	0
$939$	−9.68244	−0.315974
$940$	−59.6603	−1.94590
$941$	−26.0649	−0.849691	−0.424846	−	0.905266i	$-0.639672\pi$
$941$	−26.0649	−0.849691	−0.424846	+	0.905266i	$0.639672\pi$
$942$	−45.9232	−1.49626
$943$	0.885683	0.0288418
$944$	12.3834	0.403045
$945$	0	0
$946$	31.2477	1.01595
$947$	37.0439	1.20376	0.601882	−	0.798585i	$-0.294418\pi$
$947$	37.0439	1.20376	0.601882	+	0.798585i	$0.294418\pi$
$948$	−65.9774	−2.14285
$949$	−24.7929	−0.804810
$950$	−7.72895	−0.250760
$951$	−17.8054	−0.577380
$952$	0	0
$953$	−23.2816	−0.754166	−0.377083	−	0.926179i	$-0.623073\pi$
$953$	−23.2816	−0.754166	−0.377083	+	0.926179i	$0.623073\pi$
$954$	−7.40442	−0.239727
$955$	49.3277	1.59621
$956$	−58.5367	−1.89321
$957$	5.34073	0.172641
$958$	64.7983	2.09354
$959$	0	0
$960$	−7.39679	−0.238730
$961$	32.6395	1.05289
$962$	26.5044	0.854538
$963$	14.8187	0.477527
$964$	−22.5545	−0.726432
$965$	60.5057	1.94775
$966$	0	0
$967$	30.3867	0.977170	0.488585	−	0.872516i	$-0.337513\pi$
$967$	30.3867	0.977170	0.488585	+	0.872516i	$0.337513\pi$
$968$	−55.4660	−1.78275
$969$	11.9827	0.384939
$970$	101.626	3.26303
$971$	5.89944	0.189322	0.0946611	−	0.995510i	$-0.469823\pi$
$971$	5.89944	0.189322	0.0946611	+	0.995510i	$0.469823\pi$
$972$	4.33421	0.139020
$973$	0	0
$974$	−71.3135	−2.28503
$975$	1.75465	0.0561938
$976$	−45.1731	−1.44596
$977$	38.6110	1.23528	0.617638	−	0.786463i	$-0.288090\pi$
$977$	38.6110	1.23528	0.617638	+	0.786463i	$0.288090\pi$
$978$	12.7197	0.406731
$979$	−20.3070	−0.649013
$980$	0	0
$981$	−4.04929	−0.129284
$982$	−26.4493	−0.844032
$983$	41.5910	1.32655	0.663274	−	0.748377i	$-0.269166\pi$
$983$	41.5910	1.32655	0.663274	+	0.748377i	$0.269166\pi$
$984$	−5.20312	−0.165869
$985$	−59.2810	−1.88885
$986$	−35.6417	−1.13506
$987$	0	0
$988$	−32.4492	−1.03235
$989$	−9.94532	−0.316243
$990$	7.59829	0.241490
$991$	49.6686	1.57778	0.788888	−	0.614537i	$-0.210657\pi$
$991$	49.6686	1.57778	0.788888	+	0.614537i	$0.210657\pi$
$992$	−29.0828	−0.923378
$993$	23.8177	0.755831
$994$	0	0
$995$	33.4087	1.05913
$996$	68.3011	2.16420
$997$	−35.1240	−1.11239	−0.556194	−	0.831053i	$-0.687739\pi$
$997$	−35.1240	−1.11239	−0.556194	+	0.831053i	$0.687739\pi$
$998$	−20.7068	−0.655463
$999$	5.09175	0.161096

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3381.2.a.bf.1.7		8
7.2	even	3		483.2.i.g.277.2	✓	16
7.4	even	3		483.2.i.g.415.2	yes	16
7.6	odd	2		3381.2.a.be.1.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.i.g.277.2	✓	16	7.2	even	3
483.2.i.g.415.2	yes	16	7.4	even	3
3381.2.a.be.1.7		8	7.6	odd	2
3381.2.a.bf.1.7		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:	\( N \)	\(=\)	\( 3381 = 3 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3381.a (trivial)

\(f(q)\)	\(=\)	\(q+2.51679 q^{2} +1.00000 q^{3} +4.33421 q^{4} +2.41834 q^{5} +2.51679 q^{6} +5.87470 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.51679 q^{2} +1.00000 q^{3} +4.33421 q^{4} +2.41834 q^{5} +2.51679 q^{6} +5.87470 q^{8} +1.00000 q^{9} +6.08644 q^{10} +1.24840 q^{11} +4.33421 q^{12} +2.06826 q^{13} +2.41834 q^{15} +6.11694 q^{16} -3.31028 q^{17} +2.51679 q^{18} -3.61984 q^{19} +10.4816 q^{20} +3.14194 q^{22} -1.00000 q^{23} +5.87470 q^{24} +0.848370 q^{25} +5.20537 q^{26} +1.00000 q^{27} +4.27807 q^{29} +6.08644 q^{30} -7.97744 q^{31} +3.64563 q^{32} +1.24840 q^{33} -8.33126 q^{34} +4.33421 q^{36} +5.09175 q^{37} -9.11035 q^{38} +2.06826 q^{39} +14.2070 q^{40} -0.885683 q^{41} +9.94532 q^{43} +5.41081 q^{44} +2.41834 q^{45} -2.51679 q^{46} -5.69191 q^{47} +6.11694 q^{48} +2.13516 q^{50} -3.31028 q^{51} +8.96427 q^{52} -2.94202 q^{53} +2.51679 q^{54} +3.01905 q^{55} -3.61984 q^{57} +10.7670 q^{58} +2.02444 q^{59} +10.4816 q^{60} -7.38492 q^{61} -20.0775 q^{62} -3.05862 q^{64} +5.00176 q^{65} +3.14194 q^{66} +8.28378 q^{67} -14.3474 q^{68} -1.00000 q^{69} -8.27631 q^{71} +5.87470 q^{72} -11.9873 q^{73} +12.8149 q^{74} +0.848370 q^{75} -15.6891 q^{76} +5.20537 q^{78} -15.2225 q^{79} +14.7928 q^{80} +1.00000 q^{81} -2.22907 q^{82} +15.7586 q^{83} -8.00538 q^{85} +25.0302 q^{86} +4.27807 q^{87} +7.33395 q^{88} -16.2664 q^{89} +6.08644 q^{90} -4.33421 q^{92} -7.97744 q^{93} -14.3253 q^{94} -8.75399 q^{95} +3.64563 q^{96} +16.6972 q^{97} +1.24840 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + 8 q^{3} + 15 q^{4} + 5 q^{5} + q^{6} + 9 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + q^2 + 8 * q^3 + 15 * q^4 + 5 * q^5 + q^6 + 9 * q^8 + 8 * q^9	\( 8 q + q^{2} + 8 q^{3} + 15 q^{4} + 5 q^{5} + q^{6} + 9 q^{8} + 8 q^{9} - 3 q^{10} + 10 q^{11} + 15 q^{12} - 6 q^{13} + 5 q^{15} + 13 q^{16} + 21 q^{17} + q^{18} + 5 q^{19} - q^{20} + 18 q^{22} - 8 q^{23} + 9 q^{24} + 27 q^{25} + 3 q^{26} + 8 q^{27} + 2 q^{29} - 3 q^{30} - 13 q^{31} + 29 q^{32} + 10 q^{33} - 19 q^{34} + 15 q^{36} + 13 q^{37} - 6 q^{38} - 6 q^{39} + 7 q^{40} + 16 q^{41} + 15 q^{43} + 24 q^{44} + 5 q^{45} - q^{46} - q^{47} + 13 q^{48} + 16 q^{50} + 21 q^{51} - 19 q^{52} + 3 q^{53} + q^{54} - 10 q^{55} + 5 q^{57} - 40 q^{58} + 26 q^{59} - q^{60} - 14 q^{61} - 14 q^{62} + 49 q^{64} - 3 q^{65} + 18 q^{66} + 38 q^{67} + 43 q^{68} - 8 q^{69} + 9 q^{71} + 9 q^{72} - 6 q^{73} + 32 q^{74} + 27 q^{75} - 14 q^{76} + 3 q^{78} + 23 q^{79} - 17 q^{80} + 8 q^{81} + 20 q^{82} + 30 q^{83} - 37 q^{85} - 28 q^{86} + 2 q^{87} + 86 q^{88} + 12 q^{89} - 3 q^{90} - 15 q^{92} - 13 q^{93} - 45 q^{94} + 16 q^{95} + 29 q^{96} + 14 q^{97} + 10 q^{99}+O(q^{100}) \) 8 * q + q^2 + 8 * q^3 + 15 * q^4 + 5 * q^5 + q^6 + 9 * q^8 + 8 * q^9 - 3 * q^10 + 10 * q^11 + 15 * q^12 - 6 * q^13 + 5 * q^15 + 13 * q^16 + 21 * q^17 + q^18 + 5 * q^19 - q^20 + 18 * q^22 - 8 * q^23 + 9 * q^24 + 27 * q^25 + 3 * q^26 + 8 * q^27 + 2 * q^29 - 3 * q^30 - 13 * q^31 + 29 * q^32 + 10 * q^33 - 19 * q^34 + 15 * q^36 + 13 * q^37 - 6 * q^38 - 6 * q^39 + 7 * q^40 + 16 * q^41 + 15 * q^43 + 24 * q^44 + 5 * q^45 - q^46 - q^47 + 13 * q^48 + 16 * q^50 + 21 * q^51 - 19 * q^52 + 3 * q^53 + q^54 - 10 * q^55 + 5 * q^57 - 40 * q^58 + 26 * q^59 - q^60 - 14 * q^61 - 14 * q^62 + 49 * q^64 - 3 * q^65 + 18 * q^66 + 38 * q^67 + 43 * q^68 - 8 * q^69 + 9 * q^71 + 9 * q^72 - 6 * q^73 + 32 * q^74 + 27 * q^75 - 14 * q^76 + 3 * q^78 + 23 * q^79 - 17 * q^80 + 8 * q^81 + 20 * q^82 + 30 * q^83 - 37 * q^85 - 28 * q^86 + 2 * q^87 + 86 * q^88 + 12 * q^89 - 3 * q^90 - 15 * q^92 - 13 * q^93 - 45 * q^94 + 16 * q^95 + 29 * q^96 + 14 * q^97 + 10 * q^99

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