LMFDB - Embedded newform 8673.2.a.ba.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8673,2,Mod(1,8673)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8673, 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("8673.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8673 = 3 \cdot 7^{2} \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8673.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:	$69.2542536731$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 17 x^{10} + 52 x^{9} + 101 x^{8} - 316 x^{7} - 260 x^{6} + 830 x^{5} + 287 x^{4} + \cdots - 61 $ x^12 - 3x^11 - 17x^10 + 52x^9 + 101x^8 - 316x^7 - 260x^6 + 830x^5 + 287x^4 - 941x^3 - 77x^2 + 360*x - 61
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 1239)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$2.64480$ of defining polynomial
Character	$\chi$	$=$	8673.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.64480 q^{2} +1.00000 q^{3} +4.99498 q^{4} -2.03337 q^{5} +2.64480 q^{6} +7.92115 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.64480 q^{2} +1.00000 q^{3} +4.99498 q^{4} -2.03337 q^{5} +2.64480 q^{6} +7.92115 q^{8} +1.00000 q^{9} -5.37787 q^{10} +4.06390 q^{11} +4.99498 q^{12} +5.39099 q^{13} -2.03337 q^{15} +10.9599 q^{16} +7.35954 q^{17} +2.64480 q^{18} -6.66740 q^{19} -10.1567 q^{20} +10.7482 q^{22} -4.21274 q^{23} +7.92115 q^{24} -0.865395 q^{25} +14.2581 q^{26} +1.00000 q^{27} -1.32709 q^{29} -5.37787 q^{30} +8.65421 q^{31} +13.1445 q^{32} +4.06390 q^{33} +19.4645 q^{34} +4.99498 q^{36} +2.04298 q^{37} -17.6340 q^{38} +5.39099 q^{39} -16.1066 q^{40} -6.72316 q^{41} -0.266764 q^{43} +20.2991 q^{44} -2.03337 q^{45} -11.1419 q^{46} -8.79134 q^{47} +10.9599 q^{48} -2.28880 q^{50} +7.35954 q^{51} +26.9279 q^{52} +4.93647 q^{53} +2.64480 q^{54} -8.26342 q^{55} -6.66740 q^{57} -3.50990 q^{58} +1.00000 q^{59} -10.1567 q^{60} -4.00270 q^{61} +22.8887 q^{62} +12.8448 q^{64} -10.9619 q^{65} +10.7482 q^{66} -0.708528 q^{67} +36.7608 q^{68} -4.21274 q^{69} -8.34927 q^{71} +7.92115 q^{72} +0.827994 q^{73} +5.40327 q^{74} -0.865395 q^{75} -33.3036 q^{76} +14.2581 q^{78} -9.60243 q^{79} -22.2856 q^{80} +1.00000 q^{81} -17.7814 q^{82} +14.1139 q^{83} -14.9647 q^{85} -0.705539 q^{86} -1.32709 q^{87} +32.1907 q^{88} -12.2613 q^{89} -5.37787 q^{90} -21.0426 q^{92} +8.65421 q^{93} -23.2514 q^{94} +13.5573 q^{95} +13.1445 q^{96} +8.69910 q^{97} +4.06390 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} + 12 q^{3} + 19 q^{4} + 4 q^{5} + 3 q^{6} + 12 q^{8} + 12 q^{9}+O(q^{10}) $ 12 * q + 3 * q^2 + 12 * q^3 + 19 * q^4 + 4 * q^5 + 3 * q^6 + 12 * q^8 + 12 * q^9	$ 12 q + 3 q^{2} + 12 q^{3} + 19 q^{4} + 4 q^{5} + 3 q^{6} + 12 q^{8} + 12 q^{9} - 2 q^{10} + 2 q^{11} + 19 q^{12} - 9 q^{13} + 4 q^{15} + 33 q^{16} + 5 q^{17} + 3 q^{18} - 7 q^{19} + 15 q^{20} + 24 q^{22} + q^{23} + 12 q^{24} + 30 q^{25} - 3 q^{26} + 12 q^{27} + 11 q^{29} - 2 q^{30} - 13 q^{31} + 22 q^{32} + 2 q^{33} - 8 q^{34} + 19 q^{36} + 7 q^{37} + 4 q^{38} - 9 q^{39} + 20 q^{40} + 21 q^{43} + 23 q^{44} + 4 q^{45} - 7 q^{46} + 18 q^{47} + 33 q^{48} + 52 q^{50} + 5 q^{51} - 23 q^{52} + 15 q^{53} + 3 q^{54} - 20 q^{55} - 7 q^{57} + 27 q^{58} + 12 q^{59} + 15 q^{60} - 30 q^{61} - q^{62} + 88 q^{64} + q^{65} + 24 q^{66} + 19 q^{67} + 25 q^{68} + q^{69} + 18 q^{71} + 12 q^{72} - 19 q^{73} + 3 q^{74} + 30 q^{75} - 62 q^{76} - 3 q^{78} + 16 q^{79} + 47 q^{80} + 12 q^{81} - 19 q^{82} + 37 q^{83} + 48 q^{85} - 8 q^{86} + 11 q^{87} + 46 q^{88} - 23 q^{89} - 2 q^{90} + 19 q^{92} - 13 q^{93} - 13 q^{94} + 20 q^{95} + 22 q^{96} - 9 q^{97} + 2 q^{99}+O(q^{100}) $ 12 * q + 3 * q^2 + 12 * q^3 + 19 * q^4 + 4 * q^5 + 3 * q^6 + 12 * q^8 + 12 * q^9 - 2 * q^10 + 2 * q^11 + 19 * q^12 - 9 * q^13 + 4 * q^15 + 33 * q^16 + 5 * q^17 + 3 * q^18 - 7 * q^19 + 15 * q^20 + 24 * q^22 + q^23 + 12 * q^24 + 30 * q^25 - 3 * q^26 + 12 * q^27 + 11 * q^29 - 2 * q^30 - 13 * q^31 + 22 * q^32 + 2 * q^33 - 8 * q^34 + 19 * q^36 + 7 * q^37 + 4 * q^38 - 9 * q^39 + 20 * q^40 + 21 * q^43 + 23 * q^44 + 4 * q^45 - 7 * q^46 + 18 * q^47 + 33 * q^48 + 52 * q^50 + 5 * q^51 - 23 * q^52 + 15 * q^53 + 3 * q^54 - 20 * q^55 - 7 * q^57 + 27 * q^58 + 12 * q^59 + 15 * q^60 - 30 * q^61 - q^62 + 88 * q^64 + q^65 + 24 * q^66 + 19 * q^67 + 25 * q^68 + q^69 + 18 * q^71 + 12 * q^72 - 19 * q^73 + 3 * q^74 + 30 * q^75 - 62 * q^76 - 3 * q^78 + 16 * q^79 + 47 * q^80 + 12 * q^81 - 19 * q^82 + 37 * q^83 + 48 * q^85 - 8 * q^86 + 11 * q^87 + 46 * q^88 - 23 * q^89 - 2 * q^90 + 19 * q^92 - 13 * q^93 - 13 * q^94 + 20 * q^95 + 22 * q^96 - 9 * q^97 + 2 * 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 $

$2$	2.64480	1.87016	0.935079	−	0.354439i	$-0.115328\pi$
$2$	2.64480	1.87016	0.935079	+	0.354439i	$0.115328\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.99498	2.49749
$5$	−2.03337	−0.909352	−0.454676	−	0.890657i	$-0.650245\pi$
$5$	−2.03337	−0.909352	−0.454676	+	0.890657i	$0.650245\pi$
$6$	2.64480	1.07974
$7$	0	0
$7$	0	0
$8$	7.92115	2.80055
$9$	1.00000	0.333333
$10$	−5.37787	−1.70063
$11$	4.06390	1.22531	0.612656	−	0.790350i	$-0.290101\pi$
$11$	4.06390	1.22531	0.612656	+	0.790350i	$0.290101\pi$
$12$	4.99498	1.44193
$13$	5.39099	1.49519	0.747596	−	0.664154i	$-0.231208\pi$
$13$	5.39099	1.49519	0.747596	+	0.664154i	$0.231208\pi$
$14$	0	0
$15$	−2.03337	−0.525015
$16$	10.9599	2.73998
$17$	7.35954	1.78495	0.892476	−	0.451095i	$-0.148967\pi$
$17$	7.35954	1.78495	0.892476	+	0.451095i	$0.148967\pi$
$18$	2.64480	0.623386
$19$	−6.66740	−1.52961	−0.764803	−	0.644264i	$-0.777164\pi$
$19$	−6.66740	−1.52961	−0.764803	+	0.644264i	$0.777164\pi$
$20$	−10.1567	−2.27110
$21$	0	0
$22$	10.7482	2.29153
$23$	−4.21274	−0.878416	−0.439208	−	0.898385i	$-0.644741\pi$
$23$	−4.21274	−0.878416	−0.439208	+	0.898385i	$0.644741\pi$
$24$	7.92115	1.61690
$25$	−0.865395	−0.173079
$26$	14.2581	2.79625
$27$	1.00000	0.192450
$28$	0	0
$29$	−1.32709	−0.246435	−0.123217	−	0.992380i	$-0.539321\pi$
$29$	−1.32709	−0.246435	−0.123217	+	0.992380i	$0.539321\pi$
$30$	−5.37787	−0.981860
$31$	8.65421	1.55434	0.777171	−	0.629289i	$-0.216654\pi$
$31$	8.65421	1.55434	0.777171	+	0.629289i	$0.216654\pi$
$32$	13.1445	2.32364
$33$	4.06390	0.707434
$34$	19.4645	3.33814
$35$	0	0
$36$	4.99498	0.832497
$37$	2.04298	0.335863	0.167932	−	0.985799i	$-0.446291\pi$
$37$	2.04298	0.335863	0.167932	+	0.985799i	$0.446291\pi$
$38$	−17.6340	−2.86061
$39$	5.39099	0.863249
$40$	−16.1066	−2.54668
$41$	−6.72316	−1.04998	−0.524990	−	0.851108i	$-0.675931\pi$
$41$	−6.72316	−1.04998	−0.524990	+	0.851108i	$0.675931\pi$
$42$	0	0
$43$	−0.266764	−0.0406812	−0.0203406	−	0.999793i	$-0.506475\pi$
$43$	−0.266764	−0.0406812	−0.0203406	+	0.999793i	$0.506475\pi$
$44$	20.2991	3.06020
$45$	−2.03337	−0.303117
$46$	−11.1419	−1.64278
$47$	−8.79134	−1.28235	−0.641174	−	0.767395i	$-0.721552\pi$
$47$	−8.79134	−1.28235	−0.641174	+	0.767395i	$0.721552\pi$
$48$	10.9599	1.58193
$49$	0	0
$50$	−2.28880	−0.323685
$51$	7.35954	1.03054
$52$	26.9279	3.73423
$53$	4.93647	0.678076	0.339038	−	0.940773i	$-0.389898\pi$
$53$	4.93647	0.678076	0.339038	+	0.940773i	$0.389898\pi$
$54$	2.64480	0.359912
$55$	−8.26342	−1.11424
$56$	0	0
$57$	−6.66740	−0.883119
$58$	−3.50990	−0.460872
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	−10.1567	−1.31122
$61$	−4.00270	−0.512494	−0.256247	−	0.966611i	$-0.582486\pi$
$61$	−4.00270	−0.512494	−0.256247	+	0.966611i	$0.582486\pi$
$62$	22.8887	2.90687
$63$	0	0
$64$	12.8448	1.60560
$65$	−10.9619	−1.35966
$66$	10.7482	1.32301
$67$	−0.708528	−0.0865605	−0.0432802	−	0.999063i	$-0.513781\pi$
$67$	−0.708528	−0.0865605	−0.0432802	+	0.999063i	$0.513781\pi$
$68$	36.7608	4.45790
$69$	−4.21274	−0.507154
$70$	0	0
$71$	−8.34927	−0.990876	−0.495438	−	0.868643i	$-0.664992\pi$
$71$	−8.34927	−0.990876	−0.495438	+	0.868643i	$0.664992\pi$
$72$	7.92115	0.933516
$73$	0.827994	0.0969094	0.0484547	−	0.998825i	$-0.484570\pi$
$73$	0.827994	0.0969094	0.0484547	+	0.998825i	$0.484570\pi$
$74$	5.40327	0.628118
$75$	−0.865395	−0.0999272
$76$	−33.3036	−3.82018
$77$	0	0
$78$	14.2581	1.61441
$79$	−9.60243	−1.08036	−0.540179	−	0.841550i	$-0.681644\pi$
$79$	−9.60243	−1.08036	−0.540179	+	0.841550i	$0.681644\pi$
$80$	−22.2856	−2.49160
$81$	1.00000	0.111111
$82$	−17.7814	−1.96363
$83$	14.1139	1.54920	0.774601	−	0.632450i	$-0.217951\pi$
$83$	14.1139	1.54920	0.774601	+	0.632450i	$0.217951\pi$
$84$	0	0
$85$	−14.9647	−1.62315
$86$	−0.705539	−0.0760802
$87$	−1.32709	−0.142279
$88$	32.1907	3.43154
$89$	−12.2613	−1.29969	−0.649845	−	0.760066i	$-0.725166\pi$
$89$	−12.2613	−1.29969	−0.649845	+	0.760066i	$0.725166\pi$
$90$	−5.37787	−0.566877
$91$	0	0
$92$	−21.0426	−2.19384
$93$	8.65421	0.897400
$94$	−23.2514	−2.39820
$95$	13.5573	1.39095
$96$	13.1445	1.34155
$97$	8.69910	0.883260	0.441630	−	0.897197i	$-0.354400\pi$
$97$	8.69910	0.883260	0.441630	+	0.897197i	$0.354400\pi$
$98$	0	0
$99$	4.06390	0.408437
$100$	−4.32263	−0.432263
$101$	17.3732	1.72870	0.864350	−	0.502890i	$-0.167730\pi$
$101$	17.3732	1.72870	0.864350	+	0.502890i	$0.167730\pi$
$102$	19.4645	1.92728
$103$	−0.550372	−0.0542298	−0.0271149	−	0.999632i	$-0.508632\pi$
$103$	−0.550372	−0.0542298	−0.0271149	+	0.999632i	$0.508632\pi$
$104$	42.7028	4.18736
$105$	0	0
$106$	13.0560	1.26811
$107$	8.51694	0.823364	0.411682	−	0.911328i	$-0.364941\pi$
$107$	8.51694	0.823364	0.411682	+	0.911328i	$0.364941\pi$
$108$	4.99498	0.480643
$109$	7.93981	0.760496	0.380248	−	0.924885i	$-0.375839\pi$
$109$	7.93981	0.760496	0.380248	+	0.924885i	$0.375839\pi$
$110$	−21.8551	−2.08380
$111$	2.04298	0.193911
$112$	0	0
$113$	7.77649	0.731551	0.365775	−	0.930703i	$-0.380804\pi$
$113$	7.77649	0.731551	0.365775	+	0.930703i	$0.380804\pi$
$114$	−17.6340	−1.65157
$115$	8.56606	0.798789
$116$	−6.62881	−0.615469
$117$	5.39099	0.498397
$118$	2.64480	0.243474
$119$	0	0
$120$	−16.1066	−1.47033
$121$	5.51526	0.501387
$122$	−10.5864	−0.958444
$123$	−6.72316	−0.606207
$124$	43.2277	3.88196
$125$	11.9265	1.06674
$126$	0	0
$127$	1.47362	0.130763	0.0653814	−	0.997860i	$-0.479174\pi$
$127$	1.47362	0.130763	0.0653814	+	0.997860i	$0.479174\pi$
$128$	7.68298	0.679086
$129$	−0.266764	−0.0234873
$130$	−28.9920	−2.54277
$131$	−12.5304	−1.09479	−0.547395	−	0.836875i	$-0.684380\pi$
$131$	−12.5304	−1.09479	−0.547395	+	0.836875i	$0.684380\pi$
$132$	20.2991	1.76681
$133$	0	0
$134$	−1.87392	−0.161882
$135$	−2.03337	−0.175005
$136$	58.2960	4.99884
$137$	−6.85079	−0.585302	−0.292651	−	0.956219i	$-0.594537\pi$
$137$	−6.85079	−0.585302	−0.292651	+	0.956219i	$0.594537\pi$
$138$	−11.1419	−0.948458
$139$	0.241386	0.0204741	0.0102370	−	0.999948i	$-0.496741\pi$
$139$	0.241386	0.0204741	0.0102370	+	0.999948i	$0.496741\pi$
$140$	0	0
$141$	−8.79134	−0.740364
$142$	−22.0822	−1.85309
$143$	21.9084	1.83207
$144$	10.9599	0.913325
$145$	2.69847	0.224096
$146$	2.18988	0.181236
$147$	0	0
$148$	10.2046	0.838816
$149$	15.3830	1.26022	0.630111	−	0.776505i	$-0.283009\pi$
$149$	15.3830	1.26022	0.630111	+	0.776505i	$0.283009\pi$
$150$	−2.28880	−0.186880
$151$	−12.3033	−1.00123	−0.500614	−	0.865671i	$-0.666892\pi$
$151$	−12.3033	−1.00123	−0.500614	+	0.865671i	$0.666892\pi$
$152$	−52.8135	−4.28374
$153$	7.35954	0.594984
$154$	0	0
$155$	−17.5972	−1.41344
$156$	26.9279	2.15596
$157$	−13.3888	−1.06855	−0.534273	−	0.845312i	$-0.679415\pi$
$157$	−13.3888	−1.06855	−0.534273	+	0.845312i	$0.679415\pi$
$158$	−25.3965	−2.02044
$159$	4.93647	0.391488
$160$	−26.7277	−2.11301
$161$	0	0
$162$	2.64480	0.207795
$163$	20.7730	1.62707	0.813533	−	0.581519i	$-0.197541\pi$
$163$	20.7730	1.62707	0.813533	+	0.581519i	$0.197541\pi$
$164$	−33.5821	−2.62232
$165$	−8.26342	−0.643306
$166$	37.3285	2.89725
$167$	21.7738	1.68491	0.842454	−	0.538768i	$-0.181110\pi$
$167$	21.7738	1.68491	0.842454	+	0.538768i	$0.181110\pi$
$168$	0	0
$169$	16.0628	1.23560
$170$	−39.5787	−3.03555
$171$	−6.66740	−0.509869
$172$	−1.33248	−0.101601
$173$	13.7699	1.04691	0.523455	−	0.852054i	$-0.324643\pi$
$173$	13.7699	1.04691	0.523455	+	0.852054i	$0.324643\pi$
$174$	−3.50990	−0.266085
$175$	0	0
$176$	44.5399	3.35732
$177$	1.00000	0.0751646
$178$	−32.4286	−2.43063
$179$	8.38278	0.626558	0.313279	−	0.949661i	$-0.398572\pi$
$179$	8.38278	0.626558	0.313279	+	0.949661i	$0.398572\pi$
$180$	−10.1567	−0.757033
$181$	−13.2523	−0.985039	−0.492520	−	0.870301i	$-0.663924\pi$
$181$	−13.2523	−0.985039	−0.492520	+	0.870301i	$0.663924\pi$
$182$	0	0
$183$	−4.00270	−0.295888
$184$	−33.3697	−2.46005
$185$	−4.15413	−0.305418
$186$	22.8887	1.67828
$187$	29.9084	2.18712
$188$	−43.9126	−3.20266
$189$	0	0
$190$	35.8564	2.60130
$191$	−9.11322	−0.659409	−0.329705	−	0.944084i	$-0.606949\pi$
$191$	−9.11322	−0.659409	−0.329705	+	0.944084i	$0.606949\pi$
$192$	12.8448	0.926994
$193$	−23.3040	−1.67746	−0.838728	−	0.544551i	$-0.816700\pi$
$193$	−23.3040	−1.67746	−0.838728	+	0.544551i	$0.816700\pi$
$194$	23.0074	1.65184
$195$	−10.9619	−0.784997
$196$	0	0
$197$	−7.87765	−0.561260	−0.280630	−	0.959816i	$-0.590543\pi$
$197$	−7.87765	−0.561260	−0.280630	+	0.959816i	$0.590543\pi$
$198$	10.7482	0.763842
$199$	11.7559	0.833351	0.416676	−	0.909055i	$-0.363195\pi$
$199$	11.7559	0.833351	0.416676	+	0.909055i	$0.363195\pi$
$200$	−6.85492	−0.484716
$201$	−0.708528	−0.0499757
$202$	45.9488	3.23294
$203$	0	0
$204$	36.7608	2.57377
$205$	13.6707	0.954802
$206$	−1.45563	−0.101418
$207$	−4.21274	−0.292805
$208$	59.0847	4.09679
$209$	−27.0956	−1.87424
$210$	0	0
$211$	14.4236	0.992962	0.496481	−	0.868048i	$-0.334625\pi$
$211$	14.4236	0.992962	0.496481	+	0.868048i	$0.334625\pi$
$212$	24.6576	1.69349
$213$	−8.34927	−0.572082
$214$	22.5256	1.53982
$215$	0.542431	0.0369935
$216$	7.92115	0.538966
$217$	0	0
$218$	20.9992	1.42225
$219$	0.827994	0.0559507
$220$	−41.2756	−2.78280
$221$	39.6752	2.66884
$222$	5.40327	0.362644
$223$	−13.8948	−0.930467	−0.465233	−	0.885188i	$-0.654030\pi$
$223$	−13.8948	−0.930467	−0.465233	+	0.885188i	$0.654030\pi$
$224$	0	0
$225$	−0.865395	−0.0576930
$226$	20.5673	1.36812
$227$	−6.38335	−0.423678	−0.211839	−	0.977305i	$-0.567945\pi$
$227$	−6.38335	−0.423678	−0.211839	+	0.977305i	$0.567945\pi$
$228$	−33.3036	−2.20558
$229$	0.648248	0.0428374	0.0214187	−	0.999771i	$-0.493182\pi$
$229$	0.648248	0.0428374	0.0214187	+	0.999771i	$0.493182\pi$
$230$	22.6556	1.49386
$231$	0	0
$232$	−10.5121	−0.690153
$233$	−27.4916	−1.80104	−0.900518	−	0.434820i	$-0.856812\pi$
$233$	−27.4916	−1.80104	−0.900518	+	0.434820i	$0.856812\pi$
$234$	14.2581	0.932082
$235$	17.8761	1.16611
$236$	4.99498	0.325146
$237$	−9.60243	−0.623745
$238$	0	0
$239$	10.9216	0.706462	0.353231	−	0.935536i	$-0.385083\pi$
$239$	10.9216	0.706462	0.353231	+	0.935536i	$0.385083\pi$
$240$	−22.2856	−1.43853
$241$	−28.4781	−1.83444	−0.917219	−	0.398383i	$-0.869571\pi$
$241$	−28.4781	−1.83444	−0.917219	+	0.398383i	$0.869571\pi$
$242$	14.5868	0.937673
$243$	1.00000	0.0641500
$244$	−19.9934	−1.27995
$245$	0	0
$246$	−17.7814	−1.13370
$247$	−35.9439	−2.28705
$248$	68.5513	4.35301
$249$	14.1139	0.894433
$250$	31.5433	1.99498
$251$	8.23225	0.519615	0.259807	−	0.965660i	$-0.416341\pi$
$251$	8.23225	0.519615	0.259807	+	0.965660i	$0.416341\pi$
$252$	0	0
$253$	−17.1201	−1.07633
$254$	3.89744	0.244547
$255$	−14.9647	−0.937126
$256$	−5.36963	−0.335602
$257$	1.31236	0.0818629	0.0409314	−	0.999162i	$-0.486967\pi$
$257$	1.31236	0.0818629	0.0409314	+	0.999162i	$0.486967\pi$
$258$	−0.705539	−0.0439249
$259$	0	0
$260$	−54.7545	−3.39573
$261$	−1.32709	−0.0821450
$262$	−33.1405	−2.04743
$263$	−20.4356	−1.26011	−0.630055	−	0.776550i	$-0.716968\pi$
$263$	−20.4356	−1.26011	−0.630055	+	0.776550i	$0.716968\pi$
$264$	32.1907	1.98120
$265$	−10.0377	−0.616610
$266$	0	0
$267$	−12.2613	−0.750377
$268$	−3.53909	−0.216184
$269$	−30.1475	−1.83813	−0.919063	−	0.394112i	$-0.871052\pi$
$269$	−30.1475	−1.83813	−0.919063	+	0.394112i	$0.871052\pi$
$270$	−5.37787	−0.327287
$271$	23.0265	1.39876	0.699380	−	0.714750i	$-0.253459\pi$
$271$	23.0265	1.39876	0.699380	+	0.714750i	$0.253459\pi$
$272$	80.6599	4.89072
$273$	0	0
$274$	−18.1190	−1.09461
$275$	−3.51688	−0.212076
$276$	−21.0426	−1.26661
$277$	−6.00541	−0.360830	−0.180415	−	0.983591i	$-0.557744\pi$
$277$	−6.00541	−0.360830	−0.180415	+	0.983591i	$0.557744\pi$
$278$	0.638418	0.0382898
$279$	8.65421	0.518114
$280$	0	0
$281$	−11.8601	−0.707511	−0.353756	−	0.935338i	$-0.615096\pi$
$281$	−11.8601	−0.707511	−0.353756	+	0.935338i	$0.615096\pi$
$282$	−23.2514	−1.38460
$283$	−25.9215	−1.54087	−0.770436	−	0.637517i	$-0.779962\pi$
$283$	−25.9215	−1.54087	−0.770436	+	0.637517i	$0.779962\pi$
$284$	−41.7045	−2.47470
$285$	13.5573	0.803066
$286$	57.9435	3.42627
$287$	0	0
$288$	13.1445	0.774547
$289$	37.1629	2.18605
$290$	7.13693	0.419095
$291$	8.69910	0.509950
$292$	4.13582	0.242030
$293$	−19.0007	−1.11003	−0.555017	−	0.831839i	$-0.687288\pi$
$293$	−19.0007	−1.11003	−0.555017	+	0.831839i	$0.687288\pi$
$294$	0	0
$295$	−2.03337	−0.118388
$296$	16.1827	0.940601
$297$	4.06390	0.235811
$298$	40.6849	2.35681
$299$	−22.7108	−1.31340
$300$	−4.32263	−0.249567
$301$	0	0
$302$	−32.5398	−1.87246
$303$	17.3732	0.998066
$304$	−73.0741	−4.19108
$305$	8.13899	0.466037
$306$	19.4645	1.11271
$307$	10.6306	0.606722	0.303361	−	0.952876i	$-0.401891\pi$
$307$	10.6306	0.606722	0.303361	+	0.952876i	$0.401891\pi$
$308$	0	0
$309$	−0.550372	−0.0313096
$310$	−46.5412	−2.64337
$311$	8.14243	0.461715	0.230857	−	0.972988i	$-0.425847\pi$
$311$	8.14243	0.461715	0.230857	+	0.972988i	$0.425847\pi$
$312$	42.7028	2.41757
$313$	−23.8263	−1.34674	−0.673372	−	0.739303i	$-0.735155\pi$
$313$	−23.8263	−1.34674	−0.673372	+	0.739303i	$0.735155\pi$
$314$	−35.4109	−1.99835
$315$	0	0
$316$	−47.9640	−2.69819
$317$	−12.9362	−0.726568	−0.363284	−	0.931679i	$-0.618344\pi$
$317$	−12.9362	−0.726568	−0.363284	+	0.931679i	$0.618344\pi$
$318$	13.0560	0.732144
$319$	−5.39317	−0.301959
$320$	−26.1183	−1.46006
$321$	8.51694	0.475369
$322$	0	0
$323$	−49.0690	−2.73027
$324$	4.99498	0.277499
$325$	−4.66533	−0.258786
$326$	54.9404	3.04287
$327$	7.93981	0.439073
$328$	−53.2551	−2.94052
$329$	0	0
$330$	−21.8551	−1.20308
$331$	1.48387	0.0815610	0.0407805	−	0.999168i	$-0.487016\pi$
$331$	1.48387	0.0815610	0.0407805	+	0.999168i	$0.487016\pi$
$332$	70.4988	3.86912
$333$	2.04298	0.111954
$334$	57.5874	3.15105
$335$	1.44070	0.0787139
$336$	0	0
$337$	31.0921	1.69369	0.846847	−	0.531837i	$-0.178498\pi$
$337$	31.0921	1.69369	0.846847	+	0.531837i	$0.178498\pi$
$338$	42.4829	2.31076
$339$	7.77649	0.422361
$340$	−74.7484	−4.05380
$341$	35.1698	1.90455
$342$	−17.6340	−0.953536
$343$	0	0
$344$	−2.11308	−0.113930
$345$	8.56606	0.461181
$346$	36.4188	1.95789
$347$	−26.5419	−1.42485	−0.712423	−	0.701751i	$-0.752402\pi$
$347$	−26.5419	−1.42485	−0.712423	+	0.701751i	$0.752402\pi$
$348$	−6.62881	−0.355341
$349$	−10.6157	−0.568245	−0.284123	−	0.958788i	$-0.591702\pi$
$349$	−10.6157	−0.568245	−0.284123	+	0.958788i	$0.591702\pi$
$350$	0	0
$351$	5.39099	0.287750
$352$	53.4179	2.84718
$353$	−31.7751	−1.69122	−0.845609	−	0.533802i	$-0.820763\pi$
$353$	−31.7751	−1.69122	−0.845609	+	0.533802i	$0.820763\pi$
$354$	2.64480	0.140570
$355$	16.9772	0.901055
$356$	−61.2448	−3.24597
$357$	0	0
$358$	22.1708	1.17176
$359$	−14.8047	−0.781362	−0.390681	−	0.920526i	$-0.627761\pi$
$359$	−14.8047	−0.781362	−0.390681	+	0.920526i	$0.627761\pi$
$360$	−16.1066	−0.848895
$361$	25.4542	1.33970
$362$	−35.0499	−1.84218
$363$	5.51526	0.289476
$364$	0	0
$365$	−1.68362	−0.0881247
$366$	−10.5864	−0.553358
$367$	19.9160	1.03961	0.519803	−	0.854286i	$-0.326005\pi$
$367$	19.9160	1.03961	0.519803	+	0.854286i	$0.326005\pi$
$368$	−46.1712	−2.40684
$369$	−6.72316	−0.349994
$370$	−10.9869	−0.571180
$371$	0	0
$372$	43.2277	2.24125
$373$	−10.5659	−0.547081	−0.273541	−	0.961860i	$-0.588195\pi$
$373$	−10.5659	−0.547081	−0.273541	+	0.961860i	$0.588195\pi$
$374$	79.1019	4.09026
$375$	11.9265	0.615884
$376$	−69.6375	−3.59128
$377$	−7.15434	−0.368467
$378$	0	0
$379$	7.29220	0.374575	0.187288	−	0.982305i	$-0.440030\pi$
$379$	7.29220	0.374575	0.187288	+	0.982305i	$0.440030\pi$
$380$	67.7186	3.47389
$381$	1.47362	0.0754959
$382$	−24.1027	−1.23320
$383$	−10.6959	−0.546535	−0.273267	−	0.961938i	$-0.588104\pi$
$383$	−10.6959	−0.546535	−0.273267	+	0.961938i	$0.588104\pi$
$384$	7.68298	0.392070
$385$	0	0
$386$	−61.6344	−3.13711
$387$	−0.266764	−0.0135604
$388$	43.4519	2.20593
$389$	25.0884	1.27203	0.636016	−	0.771676i	$-0.280581\pi$
$389$	25.0884	1.27203	0.636016	+	0.771676i	$0.280581\pi$
$390$	−28.9920	−1.46807
$391$	−31.0038	−1.56793
$392$	0	0
$393$	−12.5304	−0.632077
$394$	−20.8348	−1.04964
$395$	19.5253	0.982426
$396$	20.2991	1.02007
$397$	−17.9925	−0.903018	−0.451509	−	0.892267i	$-0.649114\pi$
$397$	−17.9925	−0.903018	−0.451509	+	0.892267i	$0.649114\pi$
$398$	31.0920	1.55850
$399$	0	0
$400$	−9.48464	−0.474232
$401$	16.3026	0.814111	0.407055	−	0.913403i	$-0.366556\pi$
$401$	16.3026	0.814111	0.407055	+	0.913403i	$0.366556\pi$
$402$	−1.87392	−0.0934625
$403$	46.6548	2.32404
$404$	86.7790	4.31742
$405$	−2.03337	−0.101039
$406$	0	0
$407$	8.30245	0.411537
$408$	58.2960	2.88608
$409$	−28.6075	−1.41455	−0.707275	−	0.706939i	$-0.750076\pi$
$409$	−28.6075	−1.41455	−0.707275	+	0.706939i	$0.750076\pi$
$410$	36.1563	1.78563
$411$	−6.85079	−0.337924
$412$	−2.74910	−0.135439
$413$	0	0
$414$	−11.1419	−0.547592
$415$	−28.6988	−1.40877
$416$	70.8618	3.47429
$417$	0.241386	0.0118207
$418$	−71.6626	−3.50513
$419$	15.5431	0.759331	0.379665	−	0.925124i	$-0.376039\pi$
$419$	15.5431	0.759331	0.379665	+	0.925124i	$0.376039\pi$
$420$	0	0
$421$	21.3258	1.03936	0.519679	−	0.854362i	$-0.326052\pi$
$421$	21.3258	1.03936	0.519679	+	0.854362i	$0.326052\pi$
$422$	38.1476	1.85700
$423$	−8.79134	−0.427450
$424$	39.1025	1.89899
$425$	−6.36891	−0.308938
$426$	−22.0822	−1.06988
$427$	0	0
$428$	42.5420	2.05635
$429$	21.9084	1.05775
$430$	1.43462	0.0691837
$431$	37.8711	1.82419	0.912094	−	0.409981i	$-0.134465\pi$
$431$	37.8711	1.82419	0.912094	+	0.409981i	$0.134465\pi$
$432$	10.9599	0.527309
$433$	−34.4032	−1.65331	−0.826657	−	0.562706i	$-0.809760\pi$
$433$	−34.4032	−1.65331	−0.826657	+	0.562706i	$0.809760\pi$
$434$	0	0
$435$	2.69847	0.129382
$436$	39.6592	1.89933
$437$	28.0880	1.34363
$438$	2.18988	0.104637
$439$	11.7565	0.561106	0.280553	−	0.959839i	$-0.409482\pi$
$439$	11.7565	0.561106	0.280553	+	0.959839i	$0.409482\pi$
$440$	−65.4557	−3.12048
$441$	0	0
$442$	104.933	4.99116
$443$	−30.9452	−1.47025	−0.735125	−	0.677931i	$-0.762877\pi$
$443$	−30.9452	−1.47025	−0.735125	+	0.677931i	$0.762877\pi$
$444$	10.2046	0.484291
$445$	24.9317	1.18188
$446$	−36.7491	−1.74012
$447$	15.3830	0.727589
$448$	0	0
$449$	−38.6124	−1.82223	−0.911115	−	0.412152i	$-0.864777\pi$
$449$	−38.6124	−1.82223	−0.911115	+	0.412152i	$0.864777\pi$
$450$	−2.28880	−0.107895
$451$	−27.3222	−1.28655
$452$	38.8434	1.82704
$453$	−12.3033	−0.578059
$454$	−16.8827	−0.792344
$455$	0	0
$456$	−52.8135	−2.47322
$457$	11.1235	0.520337	0.260168	−	0.965563i	$-0.416222\pi$
$457$	11.1235	0.520337	0.260168	+	0.965563i	$0.416222\pi$
$458$	1.71449	0.0801128
$459$	7.35954	0.343514
$460$	42.7874	1.99497
$461$	10.3138	0.480363	0.240182	−	0.970728i	$-0.422793\pi$
$461$	10.3138	0.480363	0.240182	+	0.970728i	$0.422793\pi$
$462$	0	0
$463$	30.7554	1.42933	0.714663	−	0.699469i	$-0.246580\pi$
$463$	30.7554	1.42933	0.714663	+	0.699469i	$0.246580\pi$
$464$	−14.5448	−0.675226
$465$	−17.5972	−0.816053
$466$	−72.7099	−3.36822
$467$	24.8001	1.14761	0.573805	−	0.818992i	$-0.305467\pi$
$467$	24.8001	1.14761	0.573805	+	0.818992i	$0.305467\pi$
$468$	26.9279	1.24474
$469$	0	0
$470$	47.2787	2.18080
$471$	−13.3888	−0.616925
$472$	7.92115	0.364600
$473$	−1.08410	−0.0498471
$474$	−25.3965	−1.16650
$475$	5.76993	0.264743
$476$	0	0
$477$	4.93647	0.226025
$478$	28.8856	1.32120
$479$	−6.42784	−0.293696	−0.146848	−	0.989159i	$-0.546913\pi$
$479$	−6.42784	−0.293696	−0.146848	+	0.989159i	$0.546913\pi$
$480$	−26.7277	−1.21995
$481$	11.0137	0.502180
$482$	−75.3191	−3.43069
$483$	0	0
$484$	27.5486	1.25221
$485$	−17.6885	−0.803194
$486$	2.64480	0.119971
$487$	−14.5396	−0.658851	−0.329426	−	0.944181i	$-0.606855\pi$
$487$	−14.5396	−0.658851	−0.329426	+	0.944181i	$0.606855\pi$
$488$	−31.7060	−1.43526
$489$	20.7730	0.939387
$490$	0	0
$491$	20.3360	0.917752	0.458876	−	0.888500i	$-0.348252\pi$
$491$	20.3360	0.917752	0.458876	+	0.888500i	$0.348252\pi$
$492$	−33.5821	−1.51400
$493$	−9.76680	−0.439874
$494$	−95.0645	−4.27715
$495$	−8.26342	−0.371413
$496$	94.8493	4.25886
$497$	0	0
$498$	37.3285	1.67273
$499$	−10.0779	−0.451148	−0.225574	−	0.974226i	$-0.572426\pi$
$499$	−10.0779	−0.451148	−0.225574	+	0.974226i	$0.572426\pi$
$500$	59.5729	2.66418
$501$	21.7738	0.972782
$502$	21.7727	0.971762
$503$	−29.4471	−1.31298	−0.656491	−	0.754334i	$-0.727960\pi$
$503$	−29.4471	−1.31298	−0.656491	+	0.754334i	$0.727960\pi$
$504$	0	0
$505$	−35.3263	−1.57200
$506$	−45.2794	−2.01291
$507$	16.0628	0.713373
$508$	7.36071	0.326579
$509$	11.2790	0.499933	0.249966	−	0.968255i	$-0.419580\pi$
$509$	11.2790	0.499933	0.249966	+	0.968255i	$0.419580\pi$
$510$	−39.5787	−1.75257
$511$	0	0
$512$	−29.5676	−1.30671
$513$	−6.66740	−0.294373
$514$	3.47094	0.153097
$515$	1.11911	0.0493140
$516$	−1.33248	−0.0586593
$517$	−35.7271	−1.57128
$518$	0	0
$519$	13.7699	0.604433
$520$	−86.8307	−3.80778
$521$	−4.20621	−0.184278	−0.0921388	−	0.995746i	$-0.529370\pi$
$521$	−4.20621	−0.184278	−0.0921388	+	0.995746i	$0.529370\pi$
$522$	−3.50990	−0.153624
$523$	−39.9164	−1.74542	−0.872712	−	0.488235i	$-0.837641\pi$
$523$	−39.9164	−1.74542	−0.872712	+	0.488235i	$0.837641\pi$
$524$	−62.5893	−2.73423
$525$	0	0
$526$	−54.0480	−2.35661
$527$	63.6911	2.77443
$528$	44.5399	1.93835
$529$	−5.25286	−0.228385
$530$	−26.5477	−1.15316
$531$	1.00000	0.0433963
$532$	0	0
$533$	−36.2445	−1.56992
$534$	−32.4286	−1.40332
$535$	−17.3181	−0.748728
$536$	−5.61235	−0.242417
$537$	8.38278	0.361744
$538$	−79.7342	−3.43758
$539$	0	0
$540$	−10.1567	−0.437073
$541$	−38.5080	−1.65559	−0.827794	−	0.561033i	$-0.810404\pi$
$541$	−38.5080	−1.65559	−0.827794	+	0.561033i	$0.810404\pi$
$542$	60.9006	2.61590
$543$	−13.2523	−0.568713
$544$	96.7375	4.14759
$545$	−16.1446	−0.691559
$546$	0	0
$547$	10.8159	0.462456	0.231228	−	0.972900i	$-0.425726\pi$
$547$	10.8159	0.462456	0.231228	+	0.972900i	$0.425726\pi$
$548$	−34.2196	−1.46179
$549$	−4.00270	−0.170831
$550$	−9.30144	−0.396615
$551$	8.84826	0.376949
$552$	−33.3697	−1.42031
$553$	0	0
$554$	−15.8831	−0.674809
$555$	−4.15413	−0.176333
$556$	1.20572	0.0511339
$557$	31.8018	1.34749	0.673743	−	0.738966i	$-0.264685\pi$
$557$	31.8018	1.34749	0.673743	+	0.738966i	$0.264685\pi$
$558$	22.8887	0.968956
$559$	−1.43812	−0.0608261
$560$	0	0
$561$	29.9084	1.26273
$562$	−31.3675	−1.32316
$563$	10.2356	0.431380	0.215690	−	0.976462i	$-0.430800\pi$
$563$	10.2356	0.431380	0.215690	+	0.976462i	$0.430800\pi$
$564$	−43.9126	−1.84905
$565$	−15.8125	−0.665237
$566$	−68.5572	−2.88168
$567$	0	0
$568$	−66.1357	−2.77499
$569$	−6.27851	−0.263209	−0.131604	−	0.991302i	$-0.542013\pi$
$569$	−6.27851	−0.263209	−0.131604	+	0.991302i	$0.542013\pi$
$570$	35.8564	1.50186
$571$	23.8466	0.997950	0.498975	−	0.866616i	$-0.333710\pi$
$571$	23.8466	0.997950	0.498975	+	0.866616i	$0.333710\pi$
$572$	109.432	4.57559
$573$	−9.11322	−0.380710
$574$	0	0
$575$	3.64568	0.152035
$576$	12.8448	0.535200
$577$	−6.02421	−0.250791	−0.125396	−	0.992107i	$-0.540020\pi$
$577$	−6.02421	−0.250791	−0.125396	+	0.992107i	$0.540020\pi$
$578$	98.2885	4.08826
$579$	−23.3040	−0.968479
$580$	13.4788	0.559678
$581$	0	0
$582$	23.0074	0.953688
$583$	20.0613	0.830855
$584$	6.55866	0.271399
$585$	−10.9619	−0.453218
$586$	−50.2531	−2.07594
$587$	39.1924	1.61764	0.808821	−	0.588055i	$-0.200106\pi$
$587$	39.1924	1.61764	0.808821	+	0.588055i	$0.200106\pi$
$588$	0	0
$589$	−57.7011	−2.37753
$590$	−5.37787	−0.221403
$591$	−7.87765	−0.324043
$592$	22.3908	0.920257
$593$	22.0057	0.903668	0.451834	−	0.892102i	$-0.350770\pi$
$593$	22.0057	0.903668	0.451834	+	0.892102i	$0.350770\pi$
$594$	10.7482	0.441004
$595$	0	0
$596$	76.8377	3.14739
$597$	11.7559	0.481136
$598$	−60.0656	−2.45627
$599$	−28.6299	−1.16979	−0.584893	−	0.811111i	$-0.698863\pi$
$599$	−28.6299	−1.16979	−0.584893	+	0.811111i	$0.698863\pi$
$600$	−6.85492	−0.279851
$601$	−8.59324	−0.350526	−0.175263	−	0.984522i	$-0.556078\pi$
$601$	−8.59324	−0.350526	−0.175263	+	0.984522i	$0.556078\pi$
$602$	0	0
$603$	−0.708528	−0.0288535
$604$	−61.4548	−2.50056
$605$	−11.2146	−0.455937
$606$	45.9488	1.86654
$607$	−8.95847	−0.363613	−0.181807	−	0.983334i	$-0.558194\pi$
$607$	−8.95847	−0.363613	−0.181807	+	0.983334i	$0.558194\pi$
$608$	−87.6396	−3.55426
$609$	0	0
$610$	21.5260	0.871563
$611$	−47.3940	−1.91736
$612$	36.7608	1.48597
$613$	16.6240	0.671438	0.335719	−	0.941962i	$-0.391021\pi$
$613$	16.6240	0.671438	0.335719	+	0.941962i	$0.391021\pi$
$614$	28.1159	1.13467
$615$	13.6707	0.551255
$616$	0	0
$617$	−31.5786	−1.27131	−0.635653	−	0.771975i	$-0.719269\pi$
$617$	−31.5786	−1.27131	−0.635653	+	0.771975i	$0.719269\pi$
$618$	−1.45563	−0.0585539
$619$	33.8720	1.36143	0.680715	−	0.732548i	$-0.261669\pi$
$619$	33.8720	1.36143	0.680715	+	0.732548i	$0.261669\pi$
$620$	−87.8980	−3.53007
$621$	−4.21274	−0.169051
$622$	21.5351	0.863480
$623$	0	0
$624$	59.0847	2.36528
$625$	−19.9241	−0.796965
$626$	−63.0160	−2.51863
$627$	−27.0956	−1.08210
$628$	−66.8771	−2.66869
$629$	15.0354	0.599500
$630$	0	0
$631$	21.0278	0.837103	0.418552	−	0.908193i	$-0.362538\pi$
$631$	21.0278	0.837103	0.418552	+	0.908193i	$0.362538\pi$
$632$	−76.0623	−3.02559
$633$	14.4236	0.573287
$634$	−34.2136	−1.35880
$635$	−2.99642	−0.118909
$636$	24.6576	0.977737
$637$	0	0
$638$	−14.2639	−0.564712
$639$	−8.34927	−0.330292
$640$	−15.6224	−0.617528
$641$	−1.00186	−0.0395713	−0.0197856	−	0.999804i	$-0.506298\pi$
$641$	−1.00186	−0.0395713	−0.0197856	+	0.999804i	$0.506298\pi$
$642$	22.5256	0.889016
$643$	−48.7519	−1.92259	−0.961294	−	0.275526i	$-0.911148\pi$
$643$	−48.7519	−1.92259	−0.961294	+	0.275526i	$0.911148\pi$
$644$	0	0
$645$	0.542431	0.0213582
$646$	−129.778	−5.10604
$647$	−13.2423	−0.520610	−0.260305	−	0.965526i	$-0.583823\pi$
$647$	−13.2423	−0.520610	−0.260305	+	0.965526i	$0.583823\pi$
$648$	7.92115	0.311172
$649$	4.06390	0.159522
$650$	−12.3389	−0.483971
$651$	0	0
$652$	103.761	4.06358
$653$	2.05313	0.0803450	0.0401725	−	0.999193i	$-0.487209\pi$
$653$	2.05313	0.0803450	0.0401725	+	0.999193i	$0.487209\pi$
$654$	20.9992	0.821135
$655$	25.4790	0.995549
$656$	−73.6851	−2.87692
$657$	0.827994	0.0323031
$658$	0	0
$659$	8.28975	0.322923	0.161461	−	0.986879i	$-0.448379\pi$
$659$	8.28975	0.322923	0.161461	+	0.986879i	$0.448379\pi$
$660$	−41.2756	−1.60665
$661$	−7.63712	−0.297050	−0.148525	−	0.988909i	$-0.547452\pi$
$661$	−7.63712	−0.297050	−0.148525	+	0.988909i	$0.547452\pi$
$662$	3.92455	0.152532
$663$	39.6752	1.54086
$664$	111.798	4.33862
$665$	0	0
$666$	5.40327	0.209373
$667$	5.59069	0.216472
$668$	108.760	4.20805
$669$	−13.8948	−0.537205
$670$	3.81037	0.147208
$671$	−16.2666	−0.627964
$672$	0	0
$673$	−14.7905	−0.570130	−0.285065	−	0.958508i	$-0.592015\pi$
$673$	−14.7905	−0.570130	−0.285065	+	0.958508i	$0.592015\pi$
$674$	82.2324	3.16747
$675$	−0.865395	−0.0333091
$676$	80.2333	3.08590
$677$	10.3286	0.396960	0.198480	−	0.980105i	$-0.436400\pi$
$677$	10.3286	0.396960	0.198480	+	0.980105i	$0.436400\pi$
$678$	20.5673	0.789882
$679$	0	0
$680$	−118.538	−4.54571
$681$	−6.38335	−0.244610
$682$	93.0173	3.56182
$683$	9.86135	0.377334	0.188667	−	0.982041i	$-0.439583\pi$
$683$	9.86135	0.377334	0.188667	+	0.982041i	$0.439583\pi$
$684$	−33.3036	−1.27339
$685$	13.9302	0.532246
$686$	0	0
$687$	0.648248	0.0247322
$688$	−2.92371	−0.111465
$689$	26.6125	1.01385
$690$	22.6556	0.862482
$691$	38.3854	1.46025	0.730125	−	0.683313i	$-0.239462\pi$
$691$	38.3854	1.46025	0.730125	+	0.683313i	$0.239462\pi$
$692$	68.7806	2.61465
$693$	0	0
$694$	−70.1982	−2.66469
$695$	−0.490828	−0.0186182
$696$	−10.5121	−0.398460
$697$	−49.4794	−1.87416
$698$	−28.0764	−1.06271
$699$	−27.4916	−1.03983
$700$	0	0
$701$	−14.9102	−0.563151	−0.281575	−	0.959539i	$-0.590857\pi$
$701$	−14.9102	−0.563151	−0.281575	+	0.959539i	$0.590857\pi$
$702$	14.2581	0.538138
$703$	−13.6213	−0.513739
$704$	52.1999	1.96736
$705$	17.8761	0.673252
$706$	−84.0389	−3.16285
$707$	0	0
$708$	4.99498	0.187723
$709$	−17.6490	−0.662821	−0.331411	−	0.943487i	$-0.607525\pi$
$709$	−17.6490	−0.662821	−0.331411	+	0.943487i	$0.607525\pi$
$710$	44.9013	1.68511
$711$	−9.60243	−0.360119
$712$	−97.1232	−3.63985
$713$	−36.4579	−1.36536
$714$	0	0
$715$	−44.5480	−1.66600
$716$	41.8719	1.56482
$717$	10.9216	0.407876
$718$	−39.1555	−1.46127
$719$	10.7701	0.401657	0.200829	−	0.979626i	$-0.435637\pi$
$719$	10.7701	0.401657	0.200829	+	0.979626i	$0.435637\pi$
$720$	−22.2856	−0.830534
$721$	0	0
$722$	67.3214	2.50544
$723$	−28.4781	−1.05911
$724$	−66.1953	−2.46013
$725$	1.14846	0.0426527
$726$	14.5868	0.541366
$727$	−26.5877	−0.986085	−0.493042	−	0.870005i	$-0.664115\pi$
$727$	−26.5877	−0.986085	−0.493042	+	0.870005i	$0.664115\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−4.45285	−0.164807
$731$	−1.96326	−0.0726139
$732$	−19.9934	−0.738979
$733$	−31.9356	−1.17957	−0.589784	−	0.807561i	$-0.700787\pi$
$733$	−31.9356	−1.17957	−0.589784	+	0.807561i	$0.700787\pi$
$734$	52.6739	1.94423
$735$	0	0
$736$	−55.3743	−2.04112
$737$	−2.87939	−0.106064
$738$	−17.7814	−0.654543
$739$	−21.0599	−0.774701	−0.387351	−	0.921932i	$-0.626610\pi$
$739$	−21.0599	−0.774701	−0.387351	+	0.921932i	$0.626610\pi$
$740$	−20.7498	−0.762779
$741$	−35.9439	−1.32043
$742$	0	0
$743$	−5.02600	−0.184386	−0.0921931	−	0.995741i	$-0.529388\pi$
$743$	−5.02600	−0.184386	−0.0921931	+	0.995741i	$0.529388\pi$
$744$	68.5513	2.51321
$745$	−31.2793	−1.14598
$746$	−27.9447	−1.02313
$747$	14.1139	0.516401
$748$	149.392	5.46232
$749$	0	0
$750$	31.5433	1.15180
$751$	19.1693	0.699496	0.349748	−	0.936844i	$-0.386267\pi$
$751$	19.1693	0.699496	0.349748	+	0.936844i	$0.386267\pi$
$752$	−96.3522	−3.51360
$753$	8.23225	0.300000
$754$	−18.9218	−0.689093
$755$	25.0172	0.910469
$756$	0	0
$757$	−26.3018	−0.955956	−0.477978	−	0.878372i	$-0.658630\pi$
$757$	−26.3018	−0.955956	−0.477978	+	0.878372i	$0.658630\pi$
$758$	19.2864	0.700515
$759$	−17.1201	−0.621421
$760$	107.389	3.89542
$761$	−52.7390	−1.91179	−0.955894	−	0.293711i	$-0.905110\pi$
$761$	−52.7390	−1.91179	−0.955894	+	0.293711i	$0.905110\pi$
$762$	3.89744	0.141189
$763$	0	0
$764$	−45.5204	−1.64687
$765$	−14.9647	−0.541050
$766$	−28.2885	−1.02211
$767$	5.39099	0.194657
$768$	−5.36963	−0.193760
$769$	−8.08636	−0.291602	−0.145801	−	0.989314i	$-0.546576\pi$
$769$	−8.08636	−0.291602	−0.145801	+	0.989314i	$0.546576\pi$
$770$	0	0
$771$	1.31236	0.0472635
$772$	−116.403	−4.18943
$773$	5.26853	0.189496	0.0947479	−	0.995501i	$-0.469796\pi$
$773$	5.26853	0.189496	0.0947479	+	0.995501i	$0.469796\pi$
$774$	−0.705539	−0.0253601
$775$	−7.48931	−0.269024
$776$	68.9068	2.47361
$777$	0	0
$778$	66.3539	2.37890
$779$	44.8260	1.60606
$780$	−54.7545	−1.96053
$781$	−33.9306	−1.21413
$782$	−81.9990	−2.93228
$783$	−1.32709	−0.0474264
$784$	0	0
$785$	27.2245	0.971685
$786$	−33.1405	−1.18208
$787$	18.0281	0.642633	0.321316	−	0.946972i	$-0.395875\pi$
$787$	18.0281	0.642633	0.321316	+	0.946972i	$0.395875\pi$
$788$	−39.3488	−1.40174
$789$	−20.4356	−0.727525
$790$	51.6407	1.83729
$791$	0	0
$792$	32.1907	1.14385
$793$	−21.5785	−0.766276
$794$	−47.5866	−1.68879
$795$	−10.0377	−0.356000
$796$	58.7204	2.08129
$797$	9.66054	0.342194	0.171097	−	0.985254i	$-0.445269\pi$
$797$	9.66054	0.342194	0.171097	+	0.985254i	$0.445269\pi$
$798$	0	0
$799$	−64.7003	−2.28893
$800$	−11.3752	−0.402173
$801$	−12.2613	−0.433230
$802$	43.1171	1.52252
$803$	3.36488	0.118744
$804$	−3.53909	−0.124814
$805$	0	0
$806$	123.393	4.34632
$807$	−30.1475	−1.06124
$808$	137.616	4.84131
$809$	41.6587	1.46464	0.732321	−	0.680959i	$-0.238437\pi$
$809$	41.6587	1.46464	0.732321	+	0.680959i	$0.238437\pi$
$810$	−5.37787	−0.188959
$811$	−45.1946	−1.58700	−0.793499	−	0.608572i	$-0.791743\pi$
$811$	−45.1946	−1.58700	−0.793499	+	0.608572i	$0.791743\pi$
$812$	0	0
$813$	23.0265	0.807575
$814$	21.9583	0.769639
$815$	−42.2392	−1.47958
$816$	80.6599	2.82366
$817$	1.77862	0.0622262
$818$	−75.6612	−2.64543
$819$	0	0
$820$	68.2849	2.38461
$821$	16.1829	0.564788	0.282394	−	0.959299i	$-0.408871\pi$
$821$	16.1829	0.564788	0.282394	+	0.959299i	$0.408871\pi$
$822$	−18.1190	−0.631972
$823$	−26.3918	−0.919959	−0.459980	−	0.887930i	$-0.652143\pi$
$823$	−26.3918	−0.919959	−0.459980	+	0.887930i	$0.652143\pi$
$824$	−4.35958	−0.151873
$825$	−3.51688	−0.122442
$826$	0	0
$827$	18.0366	0.627193	0.313597	−	0.949556i	$-0.398466\pi$
$827$	18.0366	0.627193	0.313597	+	0.949556i	$0.398466\pi$
$828$	−21.0426	−0.731279
$829$	−36.0455	−1.25191	−0.625956	−	0.779859i	$-0.715291\pi$
$829$	−36.0455	−1.25191	−0.625956	+	0.779859i	$0.715291\pi$
$830$	−75.9028	−2.63462
$831$	−6.00541	−0.208325
$832$	69.2462	2.40068
$833$	0	0
$834$	0.638418	0.0221066
$835$	−44.2743	−1.53217
$836$	−135.342	−4.68091
$837$	8.65421	0.299133
$838$	41.1085	1.42007
$839$	11.4051	0.393748	0.196874	−	0.980429i	$-0.436921\pi$
$839$	11.4051	0.393748	0.196874	+	0.980429i	$0.436921\pi$
$840$	0	0
$841$	−27.2388	−0.939270
$842$	56.4026	1.94376
$843$	−11.8601	−0.408482
$844$	72.0457	2.47991
$845$	−32.6616	−1.12359
$846$	−23.2514	−0.799398
$847$	0	0
$848$	54.1032	1.85791
$849$	−25.9215	−0.889623
$850$	−16.8445	−0.577762
$851$	−8.60652	−0.295028
$852$	−41.7045	−1.42877
$853$	49.5320	1.69594	0.847971	−	0.530043i	$-0.177824\pi$
$853$	49.5320	1.69594	0.847971	+	0.530043i	$0.177824\pi$
$854$	0	0
$855$	13.5573	0.463650
$856$	67.4639	2.30587
$857$	−7.95227	−0.271644	−0.135822	−	0.990733i	$-0.543368\pi$
$857$	−7.95227	−0.271644	−0.135822	+	0.990733i	$0.543368\pi$
$858$	57.9435	1.97816
$859$	−15.0140	−0.512272	−0.256136	−	0.966641i	$-0.582450\pi$
$859$	−15.0140	−0.512272	−0.256136	+	0.966641i	$0.582450\pi$
$860$	2.70944	0.0923910
$861$	0	0
$862$	100.162	3.41152
$863$	47.2896	1.60976	0.804879	−	0.593440i	$-0.202230\pi$
$863$	47.2896	1.60976	0.804879	+	0.593440i	$0.202230\pi$
$864$	13.1445	0.447185
$865$	−27.9994	−0.952009
$866$	−90.9898	−3.09196
$867$	37.1629	1.26212
$868$	0	0
$869$	−39.0233	−1.32377
$870$	7.13693	0.241965
$871$	−3.81967	−0.129425
$872$	62.8924	2.12981
$873$	8.69910	0.294420
$874$	74.2872	2.51280
$875$	0	0
$876$	4.13582	0.139736
$877$	19.6242	0.662664	0.331332	−	0.943514i	$-0.392502\pi$
$877$	19.6242	0.662664	0.331332	+	0.943514i	$0.392502\pi$
$878$	31.0936	1.04936
$879$	−19.0007	−0.640878
$880$	−90.5663	−3.05299
$881$	31.6995	1.06798	0.533991	−	0.845490i	$-0.320692\pi$
$881$	31.6995	1.06798	0.533991	+	0.845490i	$0.320692\pi$
$882$	0	0
$883$	−14.6384	−0.492623	−0.246312	−	0.969191i	$-0.579219\pi$
$883$	−14.6384	−0.492623	−0.246312	+	0.969191i	$0.579219\pi$
$884$	198.177	6.66542
$885$	−2.03337	−0.0683511
$886$	−81.8440	−2.74960
$887$	39.9120	1.34011	0.670056	−	0.742310i	$-0.266270\pi$
$887$	39.9120	1.34011	0.670056	+	0.742310i	$0.266270\pi$
$888$	16.1827	0.543056
$889$	0	0
$890$	65.9395	2.21030
$891$	4.06390	0.136146
$892$	−69.4045	−2.32383
$893$	58.6154	1.96149
$894$	40.6849	1.36071
$895$	−17.0453	−0.569762
$896$	0	0
$897$	−22.7108	−0.758292
$898$	−102.122	−3.40786
$899$	−11.4849	−0.383044
$900$	−4.32263	−0.144088
$901$	36.3302	1.21033
$902$	−72.2619	−2.40606
$903$	0	0
$904$	61.5987	2.04874
$905$	26.9470	0.895748
$906$	−32.5398	−1.08106
$907$	−38.7293	−1.28599	−0.642993	−	0.765872i	$-0.722308\pi$
$907$	−38.7293	−1.28599	−0.642993	+	0.765872i	$0.722308\pi$
$908$	−31.8847	−1.05813
$909$	17.3732	0.576234
$910$	0	0
$911$	26.0665	0.863623	0.431812	−	0.901964i	$-0.357875\pi$
$911$	26.0665	0.863623	0.431812	+	0.901964i	$0.357875\pi$
$912$	−73.0741	−2.41972
$913$	57.3575	1.89826
$914$	29.4195	0.973112
$915$	8.13899	0.269067
$916$	3.23799	0.106986
$917$	0	0
$918$	19.4645	0.642426
$919$	41.3992	1.36563	0.682816	−	0.730590i	$-0.260755\pi$
$919$	41.3992	1.36563	0.682816	+	0.730590i	$0.260755\pi$
$920$	67.8530	2.23705
$921$	10.6306	0.350291
$922$	27.2781	0.898355
$923$	−45.0108	−1.48155
$924$	0	0
$925$	−1.76798	−0.0581309
$926$	81.3421	2.67307
$927$	−0.550372	−0.0180766
$928$	−17.4440	−0.572626
$929$	30.5845	1.00344	0.501722	−	0.865029i	$-0.332700\pi$
$929$	30.5845	1.00344	0.501722	+	0.865029i	$0.332700\pi$
$930$	−46.5412	−1.52615
$931$	0	0
$932$	−137.320	−4.49807
$933$	8.14243	0.266571
$934$	65.5913	2.14621
$935$	−60.8150	−1.98886
$936$	42.7028	1.39579
$937$	44.9812	1.46947	0.734736	−	0.678353i	$-0.237306\pi$
$937$	44.9812	1.46947	0.734736	+	0.678353i	$0.237306\pi$
$938$	0	0
$939$	−23.8263	−0.777544
$940$	89.2907	2.91234
$941$	11.8998	0.387923	0.193961	−	0.981009i	$-0.437866\pi$
$941$	11.8998	0.387923	0.193961	+	0.981009i	$0.437866\pi$
$942$	−35.4109	−1.15375
$943$	28.3229	0.922320
$944$	10.9599	0.356714
$945$	0	0
$946$	−2.86724	−0.0932219
$947$	−8.95844	−0.291110	−0.145555	−	0.989350i	$-0.546497\pi$
$947$	−8.95844	−0.291110	−0.145555	+	0.989350i	$0.546497\pi$
$948$	−47.9640	−1.55780
$949$	4.46371	0.144898
$950$	15.2603	0.495111
$951$	−12.9362	−0.419484
$952$	0	0
$953$	1.35924	0.0440300	0.0220150	−	0.999758i	$-0.492992\pi$
$953$	1.35924	0.0440300	0.0220150	+	0.999758i	$0.492992\pi$
$954$	13.0560	0.422703
$955$	18.5306	0.599635
$956$	54.5534	1.76438
$957$	−5.39317	−0.174336
$958$	−17.0004	−0.549257
$959$	0	0
$960$	−26.1183	−0.842963
$961$	43.8954	1.41598
$962$	29.1290	0.939156
$963$	8.51694	0.274455
$964$	−142.248	−4.58149
$965$	47.3856	1.52540
$966$	0	0
$967$	29.4339	0.946530	0.473265	−	0.880920i	$-0.343075\pi$
$967$	29.4339	0.946530	0.473265	+	0.880920i	$0.343075\pi$
$968$	43.6872	1.40416
$969$	−49.0690	−1.57632
$970$	−46.7826	−1.50210
$971$	41.8087	1.34171	0.670853	−	0.741590i	$-0.265928\pi$
$971$	41.8087	1.34171	0.670853	+	0.741590i	$0.265928\pi$
$972$	4.99498	0.160214
$973$	0	0
$974$	−38.4543	−1.23216
$975$	−4.66533	−0.149410
$976$	−43.8692	−1.40422
$977$	31.3389	1.00262	0.501310	−	0.865268i	$-0.332852\pi$
$977$	31.3389	1.00262	0.501310	+	0.865268i	$0.332852\pi$
$978$	54.9404	1.75680
$979$	−49.8285	−1.59253
$980$	0	0
$981$	7.93981	0.253499
$982$	53.7848	1.71634
$983$	−7.01563	−0.223764	−0.111882	−	0.993722i	$-0.535688\pi$
$983$	−7.01563	−0.223764	−0.111882	+	0.993722i	$0.535688\pi$
$984$	−53.2551	−1.69771
$985$	16.0182	0.510383
$986$	−25.8313	−0.822635
$987$	0	0
$988$	−179.539	−5.71190
$989$	1.12381	0.0357350
$990$	−21.8551	−0.694601
$991$	−1.21064	−0.0384573	−0.0192287	−	0.999815i	$-0.506121\pi$
$991$	−1.21064	−0.0384573	−0.0192287	+	0.999815i	$0.506121\pi$
$992$	113.755	3.61173
$993$	1.48387	0.0470893
$994$	0	0
$995$	−23.9041	−0.757810
$996$	70.4988	2.23384
$997$	23.0150	0.728893	0.364447	−	0.931224i	$-0.381258\pi$
$997$	23.0150	0.728893	0.364447	+	0.931224i	$0.381258\pi$
$998$	−26.6540	−0.843718
$999$	2.04298	0.0646369

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8673.2.a.ba.1.11		12
7.6	odd	2		1239.2.a.i.1.11	✓	12
21.20	even	2		3717.2.a.q.1.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1239.2.a.i.1.11	✓	12	7.6	odd	2
3717.2.a.q.1.2		12	21.20	even	2
8673.2.a.ba.1.11		12	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:	\( N \)	\(=\)	\( 8673 = 3 \cdot 7^{2} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8673.a (trivial)

\(f(q)\)	\(=\)	\(q+2.64480 q^{2} +1.00000 q^{3} +4.99498 q^{4} -2.03337 q^{5} +2.64480 q^{6} +7.92115 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.64480 q^{2} +1.00000 q^{3} +4.99498 q^{4} -2.03337 q^{5} +2.64480 q^{6} +7.92115 q^{8} +1.00000 q^{9} -5.37787 q^{10} +4.06390 q^{11} +4.99498 q^{12} +5.39099 q^{13} -2.03337 q^{15} +10.9599 q^{16} +7.35954 q^{17} +2.64480 q^{18} -6.66740 q^{19} -10.1567 q^{20} +10.7482 q^{22} -4.21274 q^{23} +7.92115 q^{24} -0.865395 q^{25} +14.2581 q^{26} +1.00000 q^{27} -1.32709 q^{29} -5.37787 q^{30} +8.65421 q^{31} +13.1445 q^{32} +4.06390 q^{33} +19.4645 q^{34} +4.99498 q^{36} +2.04298 q^{37} -17.6340 q^{38} +5.39099 q^{39} -16.1066 q^{40} -6.72316 q^{41} -0.266764 q^{43} +20.2991 q^{44} -2.03337 q^{45} -11.1419 q^{46} -8.79134 q^{47} +10.9599 q^{48} -2.28880 q^{50} +7.35954 q^{51} +26.9279 q^{52} +4.93647 q^{53} +2.64480 q^{54} -8.26342 q^{55} -6.66740 q^{57} -3.50990 q^{58} +1.00000 q^{59} -10.1567 q^{60} -4.00270 q^{61} +22.8887 q^{62} +12.8448 q^{64} -10.9619 q^{65} +10.7482 q^{66} -0.708528 q^{67} +36.7608 q^{68} -4.21274 q^{69} -8.34927 q^{71} +7.92115 q^{72} +0.827994 q^{73} +5.40327 q^{74} -0.865395 q^{75} -33.3036 q^{76} +14.2581 q^{78} -9.60243 q^{79} -22.2856 q^{80} +1.00000 q^{81} -17.7814 q^{82} +14.1139 q^{83} -14.9647 q^{85} -0.705539 q^{86} -1.32709 q^{87} +32.1907 q^{88} -12.2613 q^{89} -5.37787 q^{90} -21.0426 q^{92} +8.65421 q^{93} -23.2514 q^{94} +13.5573 q^{95} +13.1445 q^{96} +8.69910 q^{97} +4.06390 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} + 12 q^{3} + 19 q^{4} + 4 q^{5} + 3 q^{6} + 12 q^{8} + 12 q^{9}+O(q^{10}) \) 12 * q + 3 * q^2 + 12 * q^3 + 19 * q^4 + 4 * q^5 + 3 * q^6 + 12 * q^8 + 12 * q^9	\( 12 q + 3 q^{2} + 12 q^{3} + 19 q^{4} + 4 q^{5} + 3 q^{6} + 12 q^{8} + 12 q^{9} - 2 q^{10} + 2 q^{11} + 19 q^{12} - 9 q^{13} + 4 q^{15} + 33 q^{16} + 5 q^{17} + 3 q^{18} - 7 q^{19} + 15 q^{20} + 24 q^{22} + q^{23} + 12 q^{24} + 30 q^{25} - 3 q^{26} + 12 q^{27} + 11 q^{29} - 2 q^{30} - 13 q^{31} + 22 q^{32} + 2 q^{33} - 8 q^{34} + 19 q^{36} + 7 q^{37} + 4 q^{38} - 9 q^{39} + 20 q^{40} + 21 q^{43} + 23 q^{44} + 4 q^{45} - 7 q^{46} + 18 q^{47} + 33 q^{48} + 52 q^{50} + 5 q^{51} - 23 q^{52} + 15 q^{53} + 3 q^{54} - 20 q^{55} - 7 q^{57} + 27 q^{58} + 12 q^{59} + 15 q^{60} - 30 q^{61} - q^{62} + 88 q^{64} + q^{65} + 24 q^{66} + 19 q^{67} + 25 q^{68} + q^{69} + 18 q^{71} + 12 q^{72} - 19 q^{73} + 3 q^{74} + 30 q^{75} - 62 q^{76} - 3 q^{78} + 16 q^{79} + 47 q^{80} + 12 q^{81} - 19 q^{82} + 37 q^{83} + 48 q^{85} - 8 q^{86} + 11 q^{87} + 46 q^{88} - 23 q^{89} - 2 q^{90} + 19 q^{92} - 13 q^{93} - 13 q^{94} + 20 q^{95} + 22 q^{96} - 9 q^{97} + 2 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + 12 * q^3 + 19 * q^4 + 4 * q^5 + 3 * q^6 + 12 * q^8 + 12 * q^9 - 2 * q^10 + 2 * q^11 + 19 * q^12 - 9 * q^13 + 4 * q^15 + 33 * q^16 + 5 * q^17 + 3 * q^18 - 7 * q^19 + 15 * q^20 + 24 * q^22 + q^23 + 12 * q^24 + 30 * q^25 - 3 * q^26 + 12 * q^27 + 11 * q^29 - 2 * q^30 - 13 * q^31 + 22 * q^32 + 2 * q^33 - 8 * q^34 + 19 * q^36 + 7 * q^37 + 4 * q^38 - 9 * q^39 + 20 * q^40 + 21 * q^43 + 23 * q^44 + 4 * q^45 - 7 * q^46 + 18 * q^47 + 33 * q^48 + 52 * q^50 + 5 * q^51 - 23 * q^52 + 15 * q^53 + 3 * q^54 - 20 * q^55 - 7 * q^57 + 27 * q^58 + 12 * q^59 + 15 * q^60 - 30 * q^61 - q^62 + 88 * q^64 + q^65 + 24 * q^66 + 19 * q^67 + 25 * q^68 + q^69 + 18 * q^71 + 12 * q^72 - 19 * q^73 + 3 * q^74 + 30 * q^75 - 62 * q^76 - 3 * q^78 + 16 * q^79 + 47 * q^80 + 12 * q^81 - 19 * q^82 + 37 * q^83 + 48 * q^85 - 8 * q^86 + 11 * q^87 + 46 * q^88 - 23 * q^89 - 2 * q^90 + 19 * q^92 - 13 * q^93 - 13 * q^94 + 20 * q^95 + 22 * q^96 - 9 * q^97 + 2 * q^99

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