LMFDB - Embedded newform 8673.2.a.s.1.3

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:	$1$
Dimension:	$3$
Coefficient field:	3.3.229.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 4x - 1 $ x^3 - 4*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 177)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.11491$ 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)

$f(q)$	$=$	$q+2.11491 q^{2} +1.00000 q^{3} +2.47283 q^{4} +0.357926 q^{5} +2.11491 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.11491 q^{2} +1.00000 q^{3} +2.47283 q^{4} +0.357926 q^{5} +2.11491 q^{6} +1.00000 q^{8} +1.00000 q^{9} +0.756981 q^{10} -4.58774 q^{11} +2.47283 q^{12} +2.58774 q^{13} +0.357926 q^{15} -2.83076 q^{16} -2.18869 q^{17} +2.11491 q^{18} -0.527166 q^{19} +0.885092 q^{20} -9.70265 q^{22} -5.70265 q^{23} +1.00000 q^{24} -4.87189 q^{25} +5.47283 q^{26} +1.00000 q^{27} +2.06058 q^{29} +0.756981 q^{30} -5.83076 q^{31} -7.98680 q^{32} -4.58774 q^{33} -4.62887 q^{34} +2.47283 q^{36} -7.70265 q^{37} -1.11491 q^{38} +2.58774 q^{39} +0.357926 q^{40} -2.39905 q^{41} +7.15604 q^{43} -11.3447 q^{44} +0.357926 q^{45} -12.0606 q^{46} -8.77643 q^{47} -2.83076 q^{48} -10.3036 q^{50} -2.18869 q^{51} +6.39905 q^{52} -8.10170 q^{53} +2.11491 q^{54} -1.64207 q^{55} -0.527166 q^{57} +4.35793 q^{58} -1.00000 q^{59} +0.885092 q^{60} -9.00624 q^{61} -12.3315 q^{62} -11.2298 q^{64} +0.926221 q^{65} -9.70265 q^{66} +14.4791 q^{67} -5.41226 q^{68} -5.70265 q^{69} +4.12811 q^{71} +1.00000 q^{72} +11.2361 q^{73} -16.2904 q^{74} -4.87189 q^{75} -1.30359 q^{76} +5.47283 q^{78} -3.87189 q^{79} -1.01320 q^{80} +1.00000 q^{81} -5.07378 q^{82} +0.737534 q^{83} -0.783389 q^{85} +15.1344 q^{86} +2.06058 q^{87} -4.58774 q^{88} +8.54661 q^{89} +0.756981 q^{90} -14.1017 q^{92} -5.83076 q^{93} -18.5613 q^{94} -0.188687 q^{95} -7.98680 q^{96} +4.10170 q^{97} -4.58774 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{3} + 2 q^{4} + 2 q^{5} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 3 * q^3 + 2 * q^4 + 2 * q^5 + 3 * q^8 + 3 * q^9	$ 3 q + 3 q^{3} + 2 q^{4} + 2 q^{5} + 3 q^{8} + 3 q^{9} - 5 q^{10} - 2 q^{11} + 2 q^{12} - 4 q^{13} + 2 q^{15} - 4 q^{16} - 3 q^{17} - 7 q^{19} + 9 q^{20} - 11 q^{22} + q^{23} + 3 q^{24} - q^{25} + 11 q^{26} + 3 q^{27} - 11 q^{29} - 5 q^{30} - 13 q^{31} - 4 q^{32} - 2 q^{33} + 7 q^{34} + 2 q^{36} - 5 q^{37} + 3 q^{38} - 4 q^{39} + 2 q^{40} + q^{41} + 6 q^{43} - 15 q^{44} + 2 q^{45} - 19 q^{46} - 11 q^{47} - 4 q^{48} - 21 q^{50} - 3 q^{51} + 11 q^{52} + 2 q^{53} - 4 q^{55} - 7 q^{57} + 14 q^{58} - 3 q^{59} + 9 q^{60} + q^{61} + 2 q^{62} - 21 q^{64} - 11 q^{66} + 10 q^{67} - 28 q^{68} + q^{69} + 26 q^{71} + 3 q^{72} - 7 q^{73} - 19 q^{74} - q^{75} + 6 q^{76} + 11 q^{78} + 2 q^{79} - 23 q^{80} + 3 q^{81} - 18 q^{82} + 3 q^{83} - 35 q^{85} + 31 q^{86} - 11 q^{87} - 2 q^{88} + 23 q^{89} - 5 q^{90} - 16 q^{92} - 13 q^{93} - 4 q^{94} + 3 q^{95} - 4 q^{96} - 14 q^{97} - 2 q^{99}+O(q^{100}) $ 3 * q + 3 * q^3 + 2 * q^4 + 2 * q^5 + 3 * q^8 + 3 * q^9 - 5 * q^10 - 2 * q^11 + 2 * q^12 - 4 * q^13 + 2 * q^15 - 4 * q^16 - 3 * q^17 - 7 * q^19 + 9 * q^20 - 11 * q^22 + q^23 + 3 * q^24 - q^25 + 11 * q^26 + 3 * q^27 - 11 * q^29 - 5 * q^30 - 13 * q^31 - 4 * q^32 - 2 * q^33 + 7 * q^34 + 2 * q^36 - 5 * q^37 + 3 * q^38 - 4 * q^39 + 2 * q^40 + q^41 + 6 * q^43 - 15 * q^44 + 2 * q^45 - 19 * q^46 - 11 * q^47 - 4 * q^48 - 21 * q^50 - 3 * q^51 + 11 * q^52 + 2 * q^53 - 4 * q^55 - 7 * q^57 + 14 * q^58 - 3 * q^59 + 9 * q^60 + q^61 + 2 * q^62 - 21 * q^64 - 11 * q^66 + 10 * q^67 - 28 * q^68 + q^69 + 26 * q^71 + 3 * q^72 - 7 * q^73 - 19 * q^74 - q^75 + 6 * q^76 + 11 * q^78 + 2 * q^79 - 23 * q^80 + 3 * q^81 - 18 * q^82 + 3 * q^83 - 35 * q^85 + 31 * q^86 - 11 * q^87 - 2 * q^88 + 23 * q^89 - 5 * q^90 - 16 * q^92 - 13 * q^93 - 4 * q^94 + 3 * q^95 - 4 * q^96 - 14 * 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 $

$2$	2.11491	1.49547	0.747733	−	0.664000i	$-0.231142\pi$
$2$	2.11491	1.49547	0.747733	+	0.664000i	$0.231142\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.47283	1.23642
$5$	0.357926	0.160070	0.0800348	−	0.996792i	$-0.474497\pi$
$5$	0.357926	0.160070	0.0800348	+	0.996792i	$0.474497\pi$
$6$	2.11491	0.863407
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0.756981	0.239378
$11$	−4.58774	−1.38326	−0.691628	−	0.722254i	$-0.743106\pi$
$11$	−4.58774	−1.38326	−0.691628	+	0.722254i	$0.743106\pi$
$12$	2.47283	0.713846
$13$	2.58774	0.717710	0.358855	−	0.933393i	$-0.383167\pi$
$13$	2.58774	0.717710	0.358855	+	0.933393i	$0.383167\pi$
$14$	0	0
$15$	0.357926	0.0924162
$16$	−2.83076	−0.707690
$17$	−2.18869	−0.530834	−0.265417	−	0.964134i	$-0.585510\pi$
$17$	−2.18869	−0.530834	−0.265417	+	0.964134i	$0.585510\pi$
$18$	2.11491	0.498488
$19$	−0.527166	−0.120940	−0.0604701	−	0.998170i	$-0.519260\pi$
$19$	−0.527166	−0.120940	−0.0604701	+	0.998170i	$0.519260\pi$
$20$	0.885092	0.197913
$21$	0	0
$22$	−9.70265	−2.06861
$23$	−5.70265	−1.18908	−0.594542	−	0.804064i	$-0.702667\pi$
$23$	−5.70265	−1.18908	−0.594542	+	0.804064i	$0.702667\pi$
$24$	1.00000	0.204124
$25$	−4.87189	−0.974378
$26$	5.47283	1.07331
$27$	1.00000	0.192450
$28$	0	0
$29$	2.06058	0.382639	0.191320	−	0.981528i	$-0.438723\pi$
$29$	2.06058	0.382639	0.191320	+	0.981528i	$0.438723\pi$
$30$	0.756981	0.138205
$31$	−5.83076	−1.04724	−0.523618	−	0.851953i	$-0.675418\pi$
$31$	−5.83076	−1.04724	−0.523618	+	0.851953i	$0.675418\pi$
$32$	−7.98680	−1.41188
$33$	−4.58774	−0.798623
$34$	−4.62887	−0.793845
$35$	0	0
$36$	2.47283	0.412139
$37$	−7.70265	−1.26631	−0.633154	−	0.774026i	$-0.718240\pi$
$37$	−7.70265	−1.26631	−0.633154	+	0.774026i	$0.718240\pi$
$38$	−1.11491	−0.180862
$39$	2.58774	0.414370
$40$	0.357926	0.0565931
$41$	−2.39905	−0.374669	−0.187335	−	0.982296i	$-0.559985\pi$
$41$	−2.39905	−0.374669	−0.187335	+	0.982296i	$0.559985\pi$
$42$	0	0
$43$	7.15604	1.09129	0.545643	−	0.838018i	$-0.316286\pi$
$43$	7.15604	1.09129	0.545643	+	0.838018i	$0.316286\pi$
$44$	−11.3447	−1.71028
$45$	0.357926	0.0533565
$46$	−12.0606	−1.77823
$47$	−8.77643	−1.28017	−0.640087	−	0.768303i	$-0.721102\pi$
$47$	−8.77643	−1.28017	−0.640087	+	0.768303i	$0.721102\pi$
$48$	−2.83076	−0.408585
$49$	0	0
$50$	−10.3036	−1.45715
$51$	−2.18869	−0.306477
$52$	6.39905	0.887389
$53$	−8.10170	−1.11285	−0.556427	−	0.830896i	$-0.687828\pi$
$53$	−8.10170	−1.11285	−0.556427	+	0.830896i	$0.687828\pi$
$54$	2.11491	0.287802
$55$	−1.64207	−0.221417
$56$	0	0
$57$	−0.527166	−0.0698249
$58$	4.35793	0.572224
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	0.885092	0.114265
$61$	−9.00624	−1.15313	−0.576566	−	0.817051i	$-0.695607\pi$
$61$	−9.00624	−1.15313	−0.576566	+	0.817051i	$0.695607\pi$
$62$	−12.3315	−1.56610
$63$	0	0
$64$	−11.2298	−1.40373
$65$	0.926221	0.114884
$66$	−9.70265	−1.19431
$67$	14.4791	1.76890	0.884450	−	0.466634i	$-0.154534\pi$
$67$	14.4791	1.76890	0.884450	+	0.466634i	$0.154534\pi$
$68$	−5.41226	−0.656333
$69$	−5.70265	−0.686518
$70$	0	0
$71$	4.12811	0.489917	0.244958	−	0.969534i	$-0.421226\pi$
$71$	4.12811	0.489917	0.244958	+	0.969534i	$0.421226\pi$
$72$	1.00000	0.117851
$73$	11.2361	1.31508	0.657541	−	0.753419i	$-0.271597\pi$
$73$	11.2361	1.31508	0.657541	+	0.753419i	$0.271597\pi$
$74$	−16.2904	−1.89372
$75$	−4.87189	−0.562557
$76$	−1.30359	−0.149533
$77$	0	0
$78$	5.47283	0.619676
$79$	−3.87189	−0.435622	−0.217811	−	0.975991i	$-0.569892\pi$
$79$	−3.87189	−0.435622	−0.217811	+	0.975991i	$0.569892\pi$
$80$	−1.01320	−0.113280
$81$	1.00000	0.111111
$82$	−5.07378	−0.560305
$83$	0.737534	0.0809549	0.0404775	−	0.999180i	$-0.487112\pi$
$83$	0.737534	0.0809549	0.0404775	+	0.999180i	$0.487112\pi$
$84$	0	0
$85$	−0.783389	−0.0849704
$86$	15.1344	1.63198
$87$	2.06058	0.220917
$88$	−4.58774	−0.489055
$89$	8.54661	0.905939	0.452970	−	0.891526i	$-0.350365\pi$
$89$	8.54661	0.905939	0.452970	+	0.891526i	$0.350365\pi$
$90$	0.756981	0.0797928
$91$	0	0
$92$	−14.1017	−1.47020
$93$	−5.83076	−0.604622
$94$	−18.5613	−1.91446
$95$	−0.188687	−0.0193588
$96$	−7.98680	−0.815149
$97$	4.10170	0.416465	0.208232	−	0.978079i	$-0.433229\pi$
$97$	4.10170	0.416465	0.208232	+	0.978079i	$0.433229\pi$
$98$	0	0
$99$	−4.58774	−0.461085
$100$	−12.0474	−1.20474
$101$	8.22982	0.818897	0.409449	−	0.912333i	$-0.365721\pi$
$101$	8.22982	0.818897	0.409449	+	0.912333i	$0.365721\pi$
$102$	−4.62887	−0.458326
$103$	−4.79811	−0.472772	−0.236386	−	0.971659i	$-0.575963\pi$
$103$	−4.79811	−0.472772	−0.236386	+	0.971659i	$0.575963\pi$
$104$	2.58774	0.253749
$105$	0	0
$106$	−17.1344	−1.66424
$107$	14.0411	1.35741	0.678704	−	0.734412i	$-0.262542\pi$
$107$	14.0411	1.35741	0.678704	+	0.734412i	$0.262542\pi$
$108$	2.47283	0.237949
$109$	−9.81131	−0.939753	−0.469877	−	0.882732i	$-0.655702\pi$
$109$	−9.81131	−0.939753	−0.469877	+	0.882732i	$0.655702\pi$
$110$	−3.47283	−0.331122
$111$	−7.70265	−0.731103
$112$	0	0
$113$	13.2772	1.24901	0.624506	−	0.781020i	$-0.285300\pi$
$113$	13.2772	1.24901	0.624506	+	0.781020i	$0.285300\pi$
$114$	−1.11491	−0.104421
$115$	−2.04113	−0.190336
$116$	5.09546	0.473102
$117$	2.58774	0.239237
$118$	−2.11491	−0.194693
$119$	0	0
$120$	0.357926	0.0326741
$121$	10.0474	0.913397
$122$	−19.0474	−1.72447
$123$	−2.39905	−0.216315
$124$	−14.4185	−1.29482
$125$	−3.53341	−0.316038
$126$	0	0
$127$	−0.587741	−0.0521536	−0.0260768	−	0.999660i	$-0.508301\pi$
$127$	−0.587741	−0.0521536	−0.0260768	+	0.999660i	$0.508301\pi$
$128$	−7.77643	−0.687346
$129$	7.15604	0.630054
$130$	1.95887	0.171804
$131$	8.08226	0.706150	0.353075	−	0.935595i	$-0.385136\pi$
$131$	8.08226	0.706150	0.353075	+	0.935595i	$0.385136\pi$
$132$	−11.3447	−0.987431
$133$	0	0
$134$	30.6219	2.64533
$135$	0.357926	0.0308054
$136$	−2.18869	−0.187678
$137$	8.10170	0.692175	0.346088	−	0.938202i	$-0.387510\pi$
$137$	8.10170	0.692175	0.346088	+	0.938202i	$0.387510\pi$
$138$	−12.0606	−1.02666
$139$	−4.96511	−0.421136	−0.210568	−	0.977579i	$-0.567531\pi$
$139$	−4.96511	−0.421136	−0.210568	+	0.977579i	$0.567531\pi$
$140$	0	0
$141$	−8.77643	−0.739109
$142$	8.73057	0.732653
$143$	−11.8719	−0.992777
$144$	−2.83076	−0.235897
$145$	0.737534	0.0612489
$146$	23.7632	1.96666
$147$	0	0
$148$	−19.0474	−1.56568
$149$	−21.9325	−1.79678	−0.898389	−	0.439201i	$-0.855262\pi$
$149$	−21.9325	−1.79678	−0.898389	+	0.439201i	$0.855262\pi$
$150$	−10.3036	−0.841285
$151$	1.49228	0.121440	0.0607200	−	0.998155i	$-0.480660\pi$
$151$	1.49228	0.121440	0.0607200	+	0.998155i	$0.480660\pi$
$152$	−0.527166	−0.0427588
$153$	−2.18869	−0.176945
$154$	0	0
$155$	−2.08698	−0.167630
$156$	6.39905	0.512334
$157$	18.7089	1.49313	0.746566	−	0.665311i	$-0.231701\pi$
$157$	18.7089	1.49313	0.746566	+	0.665311i	$0.231701\pi$
$158$	−8.18869	−0.651457
$159$	−8.10170	−0.642507
$160$	−2.85868	−0.225999
$161$	0	0
$162$	2.11491	0.166163
$163$	3.34472	0.261979	0.130989	−	0.991384i	$-0.458185\pi$
$163$	3.34472	0.261979	0.130989	+	0.991384i	$0.458185\pi$
$164$	−5.93246	−0.463248
$165$	−1.64207	−0.127835
$166$	1.55982	0.121065
$167$	−16.3991	−1.26900	−0.634498	−	0.772924i	$-0.718793\pi$
$167$	−16.3991	−1.26900	−0.634498	+	0.772924i	$0.718793\pi$
$168$	0	0
$169$	−6.30359	−0.484892
$170$	−1.65679	−0.127070
$171$	−0.527166	−0.0403134
$172$	17.6957	1.34928
$173$	−25.2097	−1.91665	−0.958327	−	0.285673i	$-0.907783\pi$
$173$	−25.2097	−1.91665	−0.958327	+	0.285673i	$0.907783\pi$
$174$	4.35793	0.330374
$175$	0	0
$176$	12.9868	0.978917
$177$	−1.00000	−0.0751646
$178$	18.0753	1.35480
$179$	−15.0738	−1.12667	−0.563334	−	0.826230i	$-0.690481\pi$
$179$	−15.0738	−1.12667	−0.563334	+	0.826230i	$0.690481\pi$
$180$	0.885092	0.0659709
$181$	−14.7764	−1.09832	−0.549162	−	0.835716i	$-0.685053\pi$
$181$	−14.7764	−1.09832	−0.549162	+	0.835716i	$0.685053\pi$
$182$	0	0
$183$	−9.00624	−0.665761
$184$	−5.70265	−0.420405
$185$	−2.75698	−0.202697
$186$	−12.3315	−0.904191
$187$	10.0411	0.734280
$188$	−21.7026	−1.58283
$189$	0	0
$190$	−0.399055	−0.0289505
$191$	−19.9930	−1.44665	−0.723323	−	0.690510i	$-0.757386\pi$
$191$	−19.9930	−1.44665	−0.723323	+	0.690510i	$0.757386\pi$
$192$	−11.2298	−0.810442
$193$	5.28415	0.380361	0.190181	−	0.981749i	$-0.439093\pi$
$193$	5.28415	0.380361	0.190181	+	0.981749i	$0.439093\pi$
$194$	8.67472	0.622809
$195$	0.926221	0.0663281
$196$	0	0
$197$	6.12115	0.436114	0.218057	−	0.975936i	$-0.430028\pi$
$197$	6.12115	0.436114	0.218057	+	0.975936i	$0.430028\pi$
$198$	−9.70265	−0.689537
$199$	18.7500	1.32915	0.664577	−	0.747220i	$-0.268612\pi$
$199$	18.7500	1.32915	0.664577	+	0.747220i	$0.268612\pi$
$200$	−4.87189	−0.344495
$201$	14.4791	1.02128
$202$	17.4053	1.22463
$203$	0	0
$204$	−5.41226	−0.378934
$205$	−0.858685	−0.0599732
$206$	−10.1476	−0.707014
$207$	−5.70265	−0.396362
$208$	−7.32528	−0.507916
$209$	2.41850	0.167291
$210$	0	0
$211$	5.32528	0.366607	0.183304	−	0.983056i	$-0.441321\pi$
$211$	5.32528	0.366607	0.183304	+	0.983056i	$0.441321\pi$
$212$	−20.0342	−1.37595
$213$	4.12811	0.282854
$214$	29.6957	2.02996
$215$	2.56133	0.174682
$216$	1.00000	0.0680414
$217$	0	0
$218$	−20.7500	−1.40537
$219$	11.2361	0.759262
$220$	−4.06058	−0.273764
$221$	−5.66376	−0.380985
$222$	−16.2904	−1.09334
$223$	11.0279	0.738484	0.369242	−	0.929333i	$-0.379617\pi$
$223$	11.0279	0.738484	0.369242	+	0.929333i	$0.379617\pi$
$224$	0	0
$225$	−4.87189	−0.324793
$226$	28.0800	1.86786
$227$	11.1344	0.739013	0.369507	−	0.929228i	$-0.379527\pi$
$227$	11.1344	0.739013	0.369507	+	0.929228i	$0.379527\pi$
$228$	−1.30359	−0.0863326
$229$	−25.4270	−1.68026	−0.840131	−	0.542383i	$-0.817522\pi$
$229$	−25.4270	−1.68026	−0.840131	+	0.542383i	$0.817522\pi$
$230$	−4.31680	−0.284641
$231$	0	0
$232$	2.06058	0.135283
$233$	−10.1212	−0.663059	−0.331529	−	0.943445i	$-0.607565\pi$
$233$	−10.1212	−0.663059	−0.331529	+	0.943445i	$0.607565\pi$
$234$	5.47283	0.357770
$235$	−3.14132	−0.204917
$236$	−2.47283	−0.160968
$237$	−3.87189	−0.251506
$238$	0	0
$239$	10.9387	0.707566	0.353783	−	0.935328i	$-0.384895\pi$
$239$	10.9387	0.707566	0.353783	+	0.935328i	$0.384895\pi$
$240$	−1.01320	−0.0654020
$241$	10.2034	0.657259	0.328630	−	0.944459i	$-0.393413\pi$
$241$	10.2034	0.657259	0.328630	+	0.944459i	$0.393413\pi$
$242$	21.2493	1.36595
$243$	1.00000	0.0641500
$244$	−22.2709	−1.42575
$245$	0	0
$246$	−5.07378	−0.323492
$247$	−1.36417	−0.0868000
$248$	−5.83076	−0.370254
$249$	0.737534	0.0467393
$250$	−7.47283	−0.472624
$251$	−12.2104	−0.770712	−0.385356	−	0.922768i	$-0.625921\pi$
$251$	−12.2104	−0.770712	−0.385356	+	0.922768i	$0.625921\pi$
$252$	0	0
$253$	26.1623	1.64481
$254$	−1.24302	−0.0779939
$255$	−0.783389	−0.0490577
$256$	6.01320	0.375825
$257$	9.52645	0.594244	0.297122	−	0.954840i	$-0.403973\pi$
$257$	9.52645	0.594244	0.297122	+	0.954840i	$0.403973\pi$
$258$	15.1344	0.942224
$259$	0	0
$260$	2.29039	0.142044
$261$	2.06058	0.127546
$262$	17.0932	1.05602
$263$	−16.0995	−0.992736	−0.496368	−	0.868112i	$-0.665333\pi$
$263$	−16.0995	−0.992736	−0.496368	+	0.868112i	$0.665333\pi$
$264$	−4.58774	−0.282356
$265$	−2.89981	−0.178134
$266$	0	0
$267$	8.54661	0.523044
$268$	35.8044	2.18710
$269$	−28.3051	−1.72579	−0.862897	−	0.505381i	$-0.831352\pi$
$269$	−28.3051	−1.72579	−0.862897	+	0.505381i	$0.831352\pi$
$270$	0.756981	0.0460684
$271$	−1.38585	−0.0841845	−0.0420922	−	0.999114i	$-0.513402\pi$
$271$	−1.38585	−0.0841845	−0.0420922	+	0.999114i	$0.513402\pi$
$272$	6.19565	0.375666
$273$	0	0
$274$	17.1344	1.03512
$275$	22.3510	1.34781
$276$	−14.1017	−0.848823
$277$	−1.15604	−0.0694595	−0.0347297	−	0.999397i	$-0.511057\pi$
$277$	−1.15604	−0.0694595	−0.0347297	+	0.999397i	$0.511057\pi$
$278$	−10.5008	−0.629794
$279$	−5.83076	−0.349078
$280$	0	0
$281$	−19.5140	−1.16411	−0.582053	−	0.813151i	$-0.697750\pi$
$281$	−19.5140	−1.16411	−0.582053	+	0.813151i	$0.697750\pi$
$282$	−18.5613	−1.10531
$283$	2.04113	0.121332	0.0606662	−	0.998158i	$-0.480677\pi$
$283$	2.04113	0.121332	0.0606662	+	0.998158i	$0.480677\pi$
$284$	10.2081	0.605741
$285$	−0.188687	−0.0111768
$286$	−25.1079	−1.48466
$287$	0	0
$288$	−7.98680	−0.470626
$289$	−12.2097	−0.718215
$290$	1.55982	0.0915956
$291$	4.10170	0.240446
$292$	27.7849	1.62599
$293$	2.73057	0.159522	0.0797609	−	0.996814i	$-0.474584\pi$
$293$	2.73057	0.159522	0.0797609	+	0.996814i	$0.474584\pi$
$294$	0	0
$295$	−0.357926	−0.0208393
$296$	−7.70265	−0.447707
$297$	−4.58774	−0.266208
$298$	−46.3851	−2.68702
$299$	−14.7570	−0.853418
$300$	−12.0474	−0.695555
$301$	0	0
$302$	3.15604	0.181609
$303$	8.22982	0.472791
$304$	1.49228	0.0855882
$305$	−3.22357	−0.184581
$306$	−4.62887	−0.264615
$307$	28.2423	1.61187	0.805937	−	0.592002i	$-0.201662\pi$
$307$	28.2423	1.61187	0.805937	+	0.592002i	$0.201662\pi$
$308$	0	0
$309$	−4.79811	−0.272955
$310$	−4.41378	−0.250686
$311$	−20.5272	−1.16399	−0.581994	−	0.813193i	$-0.697727\pi$
$311$	−20.5272	−1.16399	−0.581994	+	0.813193i	$0.697727\pi$
$312$	2.58774	0.146502
$313$	6.86565	0.388069	0.194035	−	0.980995i	$-0.437843\pi$
$313$	6.86565	0.388069	0.194035	+	0.980995i	$0.437843\pi$
$314$	39.5676	2.23293
$315$	0	0
$316$	−9.57454	−0.538610
$317$	28.6002	1.60635	0.803174	−	0.595744i	$-0.203143\pi$
$317$	28.6002	1.60635	0.803174	+	0.595744i	$0.203143\pi$
$318$	−17.1344	−0.960847
$319$	−9.45339	−0.529288
$320$	−4.01945	−0.224694
$321$	14.0411	0.783699
$322$	0	0
$323$	1.15380	0.0641992
$324$	2.47283	0.137380
$325$	−12.6072	−0.699321
$326$	7.07378	0.391780
$327$	−9.81131	−0.542567
$328$	−2.39905	−0.132466
$329$	0	0
$330$	−3.47283	−0.191173
$331$	21.2966	1.17057	0.585284	−	0.810828i	$-0.300983\pi$
$331$	21.2966	1.17057	0.585284	+	0.810828i	$0.300983\pi$
$332$	1.82380	0.100094
$333$	−7.70265	−0.422103
$334$	−34.6825	−1.89774
$335$	5.18244	0.283147
$336$	0	0
$337$	−11.3253	−0.616927	−0.308464	−	0.951236i	$-0.599815\pi$
$337$	−11.3253	−0.616927	−0.308464	+	0.951236i	$0.599815\pi$
$338$	−13.3315	−0.725139
$339$	13.2772	0.721118
$340$	−1.93719	−0.105059
$341$	26.7500	1.44859
$342$	−1.11491	−0.0602873
$343$	0	0
$344$	7.15604	0.385828
$345$	−2.04113	−0.109891
$346$	−53.3161	−2.86629
$347$	2.58998	0.139037	0.0695186	−	0.997581i	$-0.477854\pi$
$347$	2.58998	0.139037	0.0695186	+	0.997581i	$0.477854\pi$
$348$	5.09546	0.273145
$349$	26.0319	1.39346	0.696729	−	0.717335i	$-0.254638\pi$
$349$	26.0319	1.39346	0.696729	+	0.717335i	$0.254638\pi$
$350$	0	0
$351$	2.58774	0.138123
$352$	36.6414	1.95299
$353$	−13.9325	−0.741550	−0.370775	−	0.928723i	$-0.620908\pi$
$353$	−13.9325	−0.741550	−0.370775	+	0.928723i	$0.620908\pi$
$354$	−2.11491	−0.112406
$355$	1.47756	0.0784207
$356$	21.1344	1.12012
$357$	0	0
$358$	−31.8796	−1.68489
$359$	−5.89134	−0.310933	−0.155466	−	0.987841i	$-0.549688\pi$
$359$	−5.89134	−0.310933	−0.155466	+	0.987841i	$0.549688\pi$
$360$	0.357926	0.0188644
$361$	−18.7221	−0.985373
$362$	−31.2508	−1.64250
$363$	10.0474	0.527350
$364$	0	0
$365$	4.02168	0.210504
$366$	−19.0474	−0.995622
$367$	0.926221	0.0483483	0.0241742	−	0.999708i	$-0.492304\pi$
$367$	0.926221	0.0483483	0.0241742	+	0.999708i	$0.492304\pi$
$368$	16.1428	0.841503
$369$	−2.39905	−0.124890
$370$	−5.83076	−0.303127
$371$	0	0
$372$	−14.4185	−0.747564
$373$	10.1498	0.525536	0.262768	−	0.964859i	$-0.415365\pi$
$373$	10.1498	0.525536	0.262768	+	0.964859i	$0.415365\pi$
$374$	21.2361	1.09809
$375$	−3.53341	−0.182464
$376$	−8.77643	−0.452610
$377$	5.33224	0.274624
$378$	0	0
$379$	−28.0753	−1.44213	−0.721066	−	0.692867i	$-0.756347\pi$
$379$	−28.0753	−1.44213	−0.721066	+	0.692867i	$0.756347\pi$
$380$	−0.466591	−0.0239356
$381$	−0.587741	−0.0301109
$382$	−42.2834	−2.16341
$383$	−34.8176	−1.77909	−0.889547	−	0.456844i	$-0.848980\pi$
$383$	−34.8176	−1.77909	−0.889547	+	0.456844i	$0.848980\pi$
$384$	−7.77643	−0.396839
$385$	0	0
$386$	11.1755	0.568817
$387$	7.15604	0.363762
$388$	10.1428	0.514924
$389$	1.78267	0.0903850	0.0451925	−	0.998978i	$-0.485610\pi$
$389$	1.78267	0.0903850	0.0451925	+	0.998978i	$0.485610\pi$
$390$	1.95887	0.0991913
$391$	12.4813	0.631207
$392$	0	0
$393$	8.08226	0.407696
$394$	12.9457	0.652193
$395$	−1.38585	−0.0697297
$396$	−11.3447	−0.570094
$397$	−0.817557	−0.0410320	−0.0205160	−	0.999790i	$-0.506531\pi$
$397$	−0.817557	−0.0410320	−0.0205160	+	0.999790i	$0.506531\pi$
$398$	39.6546	1.98770
$399$	0	0
$400$	13.7911	0.689557
$401$	−5.35168	−0.267250	−0.133625	−	0.991032i	$-0.542662\pi$
$401$	−5.35168	−0.267250	−0.133625	+	0.991032i	$0.542662\pi$
$402$	30.6219	1.52728
$403$	−15.0885	−0.751612
$404$	20.3510	1.01250
$405$	0.357926	0.0177855
$406$	0	0
$407$	35.3378	1.75163
$408$	−2.18869	−0.108356
$409$	38.4068	1.89909	0.949547	−	0.313624i	$-0.101543\pi$
$409$	38.4068	1.89909	0.949547	+	0.313624i	$0.101543\pi$
$410$	−1.81604	−0.0896878
$411$	8.10170	0.399628
$412$	−11.8649	−0.584543
$413$	0	0
$414$	−12.0606	−0.592745
$415$	0.263983	0.0129584
$416$	−20.6678	−1.01332
$417$	−4.96511	−0.243143
$418$	5.11491	0.250178
$419$	−8.71585	−0.425797	−0.212899	−	0.977074i	$-0.568290\pi$
$419$	−8.71585	−0.425797	−0.212899	+	0.977074i	$0.568290\pi$
$420$	0	0
$421$	−0.357926	−0.0174443	−0.00872213	−	0.999962i	$-0.502776\pi$
$421$	−0.357926	−0.0174443	−0.00872213	+	0.999962i	$0.502776\pi$
$422$	11.2625	0.548248
$423$	−8.77643	−0.426725
$424$	−8.10170	−0.393454
$425$	10.6630	0.517233
$426$	8.73057	0.422998
$427$	0	0
$428$	34.7214	1.67832
$429$	−11.8719	−0.573180
$430$	5.41698	0.261230
$431$	−13.2361	−0.637558	−0.318779	−	0.947829i	$-0.603273\pi$
$431$	−13.2361	−0.637558	−0.318779	+	0.947829i	$0.603273\pi$
$432$	−2.83076	−0.136195
$433$	27.4031	1.31691	0.658454	−	0.752621i	$-0.271211\pi$
$433$	27.4031	1.31691	0.658454	+	0.752621i	$0.271211\pi$
$434$	0	0
$435$	0.737534	0.0353621
$436$	−24.2617	−1.16193
$437$	3.00624	0.143808
$438$	23.7632	1.13545
$439$	−32.5955	−1.55570	−0.777849	−	0.628451i	$-0.783689\pi$
$439$	−32.5955	−1.55570	−0.777849	+	0.628451i	$0.783689\pi$
$440$	−1.64207	−0.0782828
$441$	0	0
$442$	−11.9783	−0.569751
$443$	−30.8392	−1.46522	−0.732608	−	0.680651i	$-0.761697\pi$
$443$	−30.8392	−1.46522	−0.732608	+	0.680651i	$0.761697\pi$
$444$	−19.0474	−0.903948
$445$	3.05906	0.145013
$446$	23.3230	1.10438
$447$	−21.9325	−1.03737
$448$	0	0
$449$	35.0863	1.65582	0.827912	−	0.560859i	$-0.189529\pi$
$449$	35.0863	1.65582	0.827912	+	0.560859i	$0.189529\pi$
$450$	−10.3036	−0.485716
$451$	11.0062	0.518264
$452$	32.8323	1.54430
$453$	1.49228	0.0701135
$454$	23.5481	1.10517
$455$	0	0
$456$	−0.527166	−0.0246868
$457$	10.6414	0.497782	0.248891	−	0.968532i	$-0.419934\pi$
$457$	10.6414	0.497782	0.248891	+	0.968532i	$0.419934\pi$
$458$	−53.7757	−2.51277
$459$	−2.18869	−0.102159
$460$	−5.04737	−0.235335
$461$	28.4046	1.32293	0.661467	−	0.749975i	$-0.269934\pi$
$461$	28.4046	1.32293	0.661467	+	0.749975i	$0.269934\pi$
$462$	0	0
$463$	−9.58150	−0.445290	−0.222645	−	0.974900i	$-0.571469\pi$
$463$	−9.58150	−0.445290	−0.222645	+	0.974900i	$0.571469\pi$
$464$	−5.83299	−0.270790
$465$	−2.08698	−0.0967815
$466$	−21.4053	−0.991581
$467$	−26.1336	−1.20932	−0.604660	−	0.796484i	$-0.706691\pi$
$467$	−26.1336	−1.20932	−0.604660	+	0.796484i	$0.706691\pi$
$468$	6.39905	0.295796
$469$	0	0
$470$	−6.64359	−0.306446
$471$	18.7089	0.862060
$472$	−1.00000	−0.0460287
$473$	−32.8300	−1.50953
$474$	−8.18869	−0.376119
$475$	2.56829	0.117841
$476$	0	0
$477$	−8.10170	−0.370952
$478$	23.1344	1.05814
$479$	18.5397	0.847098	0.423549	−	0.905873i	$-0.360784\pi$
$479$	18.5397	0.847098	0.423549	+	0.905873i	$0.360784\pi$
$480$	−2.85868	−0.130481
$481$	−19.9325	−0.908842
$482$	21.5793	0.982909
$483$	0	0
$484$	24.8455	1.12934
$485$	1.46811	0.0666633
$486$	2.11491	0.0959342
$487$	−21.5676	−0.977320	−0.488660	−	0.872474i	$-0.662514\pi$
$487$	−21.5676	−0.977320	−0.488660	+	0.872474i	$0.662514\pi$
$488$	−9.00624	−0.407693
$489$	3.34472	0.151254
$490$	0	0
$491$	−11.4659	−0.517448	−0.258724	−	0.965951i	$-0.583302\pi$
$491$	−11.4659	−0.517448	−0.258724	+	0.965951i	$0.583302\pi$
$492$	−5.93246	−0.267456
$493$	−4.50995	−0.203118
$494$	−2.88509	−0.129806
$495$	−1.64207	−0.0738057
$496$	16.5055	0.741118
$497$	0	0
$498$	1.55982	0.0698971
$499$	−17.4681	−0.781980	−0.390990	−	0.920395i	$-0.627867\pi$
$499$	−17.4681	−0.781980	−0.390990	+	0.920395i	$0.627867\pi$
$500$	−8.73753	−0.390754
$501$	−16.3991	−0.732656
$502$	−25.8238	−1.15257
$503$	−0.655277	−0.0292174	−0.0146087	−	0.999893i	$-0.504650\pi$
$503$	−0.655277	−0.0292174	−0.0146087	+	0.999893i	$0.504650\pi$
$504$	0	0
$505$	2.94567	0.131080
$506$	55.3308	2.45975
$507$	−6.30359	−0.279952
$508$	−1.45339	−0.0644836
$509$	15.8168	0.701069	0.350535	−	0.936550i	$-0.386000\pi$
$509$	15.8168	0.701069	0.350535	+	0.936550i	$0.386000\pi$
$510$	−1.65679	−0.0733641
$511$	0	0
$512$	28.2702	1.24938
$513$	−0.527166	−0.0232750
$514$	20.1476	0.888671
$515$	−1.71737	−0.0756764
$516$	17.6957	0.779009
$517$	40.2640	1.77081
$518$	0	0
$519$	−25.2097	−1.10658
$520$	0.926221	0.0406175
$521$	12.2470	0.536552	0.268276	−	0.963342i	$-0.413546\pi$
$521$	12.2470	0.536552	0.268276	+	0.963342i	$0.413546\pi$
$522$	4.35793	0.190741
$523$	2.23678	0.0978074	0.0489037	−	0.998803i	$-0.484427\pi$
$523$	2.23678	0.0978074	0.0489037	+	0.998803i	$0.484427\pi$
$524$	19.9861	0.873096
$525$	0	0
$526$	−34.0489	−1.48460
$527$	12.7617	0.555909
$528$	12.9868	0.565178
$529$	9.52021	0.413922
$530$	−6.13284	−0.266393
$531$	−1.00000	−0.0433963
$532$	0	0
$533$	−6.20813	−0.268904
$534$	18.0753	0.782195
$535$	5.02569	0.217280
$536$	14.4791	0.625401
$537$	−15.0738	−0.650482
$538$	−59.8627	−2.58086
$539$	0	0
$540$	0.885092	0.0380883
$541$	−11.0863	−0.476636	−0.238318	−	0.971187i	$-0.576596\pi$
$541$	−11.0863	−0.476636	−0.238318	+	0.971187i	$0.576596\pi$
$542$	−2.93095	−0.125895
$543$	−14.7764	−0.634117
$544$	17.4806	0.749474
$545$	−3.51173	−0.150426
$546$	0	0
$547$	12.1887	0.521151	0.260575	−	0.965454i	$-0.416088\pi$
$547$	12.1887	0.521151	0.260575	+	0.965454i	$0.416088\pi$
$548$	20.0342	0.855817
$549$	−9.00624	−0.384377
$550$	47.2702	2.01561
$551$	−1.08627	−0.0462765
$552$	−5.70265	−0.242721
$553$	0	0
$554$	−2.44491	−0.103874
$555$	−2.75698	−0.117027
$556$	−12.2779	−0.520699
$557$	−8.56829	−0.363050	−0.181525	−	0.983386i	$-0.558103\pi$
$557$	−8.56829	−0.363050	−0.181525	+	0.983386i	$0.558103\pi$
$558$	−12.3315	−0.522035
$559$	18.5180	0.783227
$560$	0	0
$561$	10.0411	0.423937
$562$	−41.2702	−1.74088
$563$	−9.98055	−0.420630	−0.210315	−	0.977634i	$-0.567449\pi$
$563$	−9.98055	−0.420630	−0.210315	+	0.977634i	$0.567449\pi$
$564$	−21.7026	−0.913846
$565$	4.75226	0.199929
$566$	4.31680	0.181449
$567$	0	0
$568$	4.12811	0.173212
$569$	46.1428	1.93441	0.967204	−	0.254001i	$-0.0817465\pi$
$569$	46.1428	1.93441	0.967204	+	0.254001i	$0.0817465\pi$
$570$	−0.399055	−0.0167146
$571$	−21.1824	−0.886458	−0.443229	−	0.896409i	$-0.646167\pi$
$571$	−21.1824	−0.886458	−0.443229	+	0.896409i	$0.646167\pi$
$572$	−29.3572	−1.22749
$573$	−19.9930	−0.835221
$574$	0	0
$575$	27.7827	1.15862
$576$	−11.2298	−0.467909
$577$	−40.8859	−1.70210	−0.851051	−	0.525083i	$-0.824034\pi$
$577$	−40.8859	−1.70210	−0.851051	+	0.525083i	$0.824034\pi$
$578$	−25.8223	−1.07407
$579$	5.28415	0.219602
$580$	1.82380	0.0757292
$581$	0	0
$582$	8.67472	0.359579
$583$	37.1685	1.53936
$584$	11.2361	0.464951
$585$	0.926221	0.0382945
$586$	5.77491	0.238559
$587$	4.21037	0.173780	0.0868902	−	0.996218i	$-0.472307\pi$
$587$	4.21037	0.173780	0.0868902	+	0.996218i	$0.472307\pi$
$588$	0	0
$589$	3.07378	0.126653
$590$	−0.756981	−0.0311644
$591$	6.12115	0.251790
$592$	21.8044	0.896153
$593$	22.5202	0.924794	0.462397	−	0.886673i	$-0.346990\pi$
$593$	22.5202	0.924794	0.462397	+	0.886673i	$0.346990\pi$
$594$	−9.70265	−0.398105
$595$	0	0
$596$	−54.2353	−2.22157
$597$	18.7500	0.767387
$598$	−31.2097	−1.27626
$599$	−16.7981	−0.686352	−0.343176	−	0.939271i	$-0.611503\pi$
$599$	−16.7981	−0.686352	−0.343176	+	0.939271i	$0.611503\pi$
$600$	−4.87189	−0.198894
$601$	17.0955	0.697338	0.348669	−	0.937246i	$-0.386634\pi$
$601$	17.0955	0.697338	0.348669	+	0.937246i	$0.386634\pi$
$602$	0	0
$603$	14.4791	0.589634
$604$	3.69016	0.150151
$605$	3.59622	0.146207
$606$	17.4053	0.707042
$607$	7.53341	0.305772	0.152886	−	0.988244i	$-0.451143\pi$
$607$	7.53341	0.305772	0.152886	+	0.988244i	$0.451143\pi$
$608$	4.21037	0.170753
$609$	0	0
$610$	−6.81756	−0.276035
$611$	−22.7111	−0.918794
$612$	−5.41226	−0.218778
$613$	15.1321	0.611181	0.305590	−	0.952163i	$-0.401146\pi$
$613$	15.1321	0.611181	0.305590	+	0.952163i	$0.401146\pi$
$614$	59.7299	2.41050
$615$	−0.858685	−0.0346255
$616$	0	0
$617$	15.8672	0.638788	0.319394	−	0.947622i	$-0.396521\pi$
$617$	15.8672	0.638788	0.319394	+	0.947622i	$0.396521\pi$
$618$	−10.1476	−0.408195
$619$	−11.0210	−0.442970	−0.221485	−	0.975164i	$-0.571090\pi$
$619$	−11.0210	−0.442970	−0.221485	+	0.975164i	$0.571090\pi$
$620$	−5.16076	−0.207261
$621$	−5.70265	−0.228839
$622$	−43.4131	−1.74071
$623$	0	0
$624$	−7.32528	−0.293246
$625$	23.0947	0.923790
$626$	14.5202	0.580344
$627$	2.41850	0.0965857
$628$	46.2640	1.84613
$629$	16.8587	0.672200
$630$	0	0
$631$	−23.1560	−0.921827	−0.460914	−	0.887445i	$-0.652478\pi$
$631$	−23.1560	−0.921827	−0.460914	+	0.887445i	$0.652478\pi$
$632$	−3.87189	−0.154015
$633$	5.32528	0.211661
$634$	60.4868	2.40224
$635$	−0.210368	−0.00834821
$636$	−20.0342	−0.794406
$637$	0	0
$638$	−19.9930	−0.791532
$639$	4.12811	0.163306
$640$	−2.78339	−0.110023
$641$	39.5459	1.56197	0.780984	−	0.624550i	$-0.214718\pi$
$641$	39.5459	1.56197	0.780984	+	0.624550i	$0.214718\pi$
$642$	29.6957	1.17200
$643$	−18.6219	−0.734376	−0.367188	−	0.930147i	$-0.619680\pi$
$643$	−18.6219	−0.734376	−0.367188	+	0.930147i	$0.619680\pi$
$644$	0	0
$645$	2.56133	0.100852
$646$	2.44018	0.0960077
$647$	−7.24525	−0.284840	−0.142420	−	0.989806i	$-0.545488\pi$
$647$	−7.24525	−0.284840	−0.142420	+	0.989806i	$0.545488\pi$
$648$	1.00000	0.0392837
$649$	4.58774	0.180085
$650$	−26.6630	−1.04581
$651$	0	0
$652$	8.27094	0.323915
$653$	31.3183	1.22558	0.612790	−	0.790246i	$-0.290047\pi$
$653$	31.3183	1.22558	0.612790	+	0.790246i	$0.290047\pi$
$654$	−20.7500	−0.811390
$655$	2.89285	0.113033
$656$	6.79115	0.265150
$657$	11.2361	0.438360
$658$	0	0
$659$	8.13587	0.316929	0.158464	−	0.987365i	$-0.449346\pi$
$659$	8.13587	0.316929	0.158464	+	0.987365i	$0.449346\pi$
$660$	−4.06058	−0.158058
$661$	9.47979	0.368721	0.184361	−	0.982859i	$-0.440979\pi$
$661$	9.47979	0.368721	0.184361	+	0.982859i	$0.440979\pi$
$662$	45.0404	1.75055
$663$	−5.66376	−0.219962
$664$	0.737534	0.0286219
$665$	0	0
$666$	−16.2904	−0.631240
$667$	−11.7507	−0.454990
$668$	−40.5521	−1.56901
$669$	11.0279	0.426364
$670$	10.9604	0.423437
$671$	41.3183	1.59508
$672$	0	0
$673$	11.4317	0.440660	0.220330	−	0.975425i	$-0.429287\pi$
$673$	11.4317	0.440660	0.220330	+	0.975425i	$0.429287\pi$
$674$	−23.9519	−0.922593
$675$	−4.87189	−0.187519
$676$	−15.5877	−0.599529
$677$	6.83700	0.262767	0.131384	−	0.991332i	$-0.458058\pi$
$677$	6.83700	0.262767	0.131384	+	0.991332i	$0.458058\pi$
$678$	28.0800	1.07841
$679$	0	0
$680$	−0.783389	−0.0300416
$681$	11.1344	0.426669
$682$	56.5738	2.16632
$683$	−34.6002	−1.32394	−0.661970	−	0.749530i	$-0.730280\pi$
$683$	−34.6002	−1.32394	−0.661970	+	0.749530i	$0.730280\pi$
$684$	−1.30359	−0.0498442
$685$	2.89981	0.110796
$686$	0	0
$687$	−25.4270	−0.970100
$688$	−20.2570	−0.772292
$689$	−20.9651	−0.798707
$690$	−4.31680	−0.164338
$691$	42.8929	1.63172	0.815861	−	0.578249i	$-0.196264\pi$
$691$	42.8929	1.63172	0.815861	+	0.578249i	$0.196264\pi$
$692$	−62.3393	−2.36978
$693$	0	0
$694$	5.47756	0.207925
$695$	−1.77715	−0.0674110
$696$	2.06058	0.0781059
$697$	5.25078	0.198887
$698$	55.0551	2.08387
$699$	−10.1212	−0.382817
$700$	0	0
$701$	8.83228	0.333591	0.166795	−	0.985992i	$-0.446658\pi$
$701$	8.83228	0.333591	0.166795	+	0.985992i	$0.446658\pi$
$702$	5.47283	0.206559
$703$	4.06058	0.153148
$704$	51.5195	1.94171
$705$	−3.14132	−0.118309
$706$	−29.4659	−1.10896
$707$	0	0
$708$	−2.47283	−0.0929348
$709$	22.7981	0.856201	0.428100	−	0.903731i	$-0.359183\pi$
$709$	22.7981	0.856201	0.428100	+	0.903731i	$0.359183\pi$
$710$	3.12490	0.117276
$711$	−3.87189	−0.145207
$712$	8.54661	0.320298
$713$	33.2508	1.24525
$714$	0	0
$715$	−4.24926	−0.158913
$716$	−37.2750	−1.39303
$717$	10.9387	0.408514
$718$	−12.4596	−0.464989
$719$	−21.6887	−0.808853	−0.404427	−	0.914570i	$-0.632529\pi$
$719$	−21.6887	−0.808853	−0.404427	+	0.914570i	$0.632529\pi$
$720$	−1.01320	−0.0377599
$721$	0	0
$722$	−39.5955	−1.47359
$723$	10.2034	0.379469
$724$	−36.5397	−1.35799
$725$	−10.0389	−0.372835
$726$	21.2493	0.788634
$727$	−47.7438	−1.77072	−0.885359	−	0.464907i	$-0.846088\pi$
$727$	−47.7438	−1.77072	−0.885359	+	0.464907i	$0.846088\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	8.50548	0.314802
$731$	−15.6623	−0.579292
$732$	−22.2709	−0.823158
$733$	−37.3983	−1.38134	−0.690670	−	0.723170i	$-0.742684\pi$
$733$	−37.3983	−1.38134	−0.690670	+	0.723170i	$0.742684\pi$
$734$	1.95887	0.0723033
$735$	0	0
$736$	45.5459	1.67884
$737$	−66.4263	−2.44684
$738$	−5.07378	−0.186768
$739$	−13.9450	−0.512973	−0.256487	−	0.966548i	$-0.582565\pi$
$739$	−13.9450	−0.512973	−0.256487	+	0.966548i	$0.582565\pi$
$740$	−6.81756	−0.250618
$741$	−1.36417	−0.0501140
$742$	0	0
$743$	47.4200	1.73967	0.869836	−	0.493341i	$-0.164225\pi$
$743$	47.4200	1.73967	0.869836	+	0.493341i	$0.164225\pi$
$744$	−5.83076	−0.213766
$745$	−7.85021	−0.287609
$746$	21.4659	0.785921
$747$	0.737534	0.0269850
$748$	24.8300	0.907876
$749$	0	0
$750$	−7.47283	−0.272869
$751$	46.8929	1.71114	0.855572	−	0.517683i	$-0.173205\pi$
$751$	46.8929	1.71114	0.855572	+	0.517683i	$0.173205\pi$
$752$	24.8440	0.905966
$753$	−12.2104	−0.444971
$754$	11.2772	0.410691
$755$	0.534127	0.0194389
$756$	0	0
$757$	−21.7151	−0.789250	−0.394625	−	0.918842i	$-0.629125\pi$
$757$	−21.7151	−0.789250	−0.394625	+	0.918842i	$0.629125\pi$
$758$	−59.3767	−2.15666
$759$	26.1623	0.949631
$760$	−0.188687	−0.00684438
$761$	36.6002	1.32676	0.663379	−	0.748284i	$-0.269122\pi$
$761$	36.6002	1.32676	0.663379	+	0.748284i	$0.269122\pi$
$762$	−1.24302	−0.0450298
$763$	0	0
$764$	−49.4395	−1.78866
$765$	−0.783389	−0.0283235
$766$	−73.6359	−2.66057
$767$	−2.58774	−0.0934379
$768$	6.01320	0.216983
$769$	−11.9200	−0.429845	−0.214923	−	0.976631i	$-0.568950\pi$
$769$	−11.9200	−0.429845	−0.214923	+	0.976631i	$0.568950\pi$
$770$	0	0
$771$	9.52645	0.343087
$772$	13.0668	0.470285
$773$	−20.3076	−0.730414	−0.365207	−	0.930926i	$-0.619002\pi$
$773$	−20.3076	−0.730414	−0.365207	+	0.930926i	$0.619002\pi$
$774$	15.1344	0.543993
$775$	28.4068	1.02040
$776$	4.10170	0.147243
$777$	0	0
$778$	3.77018	0.135168
$779$	1.26470	0.0453126
$780$	2.29039	0.0820091
$781$	−18.9387	−0.677680
$782$	26.3968	0.943948
$783$	2.06058	0.0736390
$784$	0	0
$785$	6.69641	0.239005
$786$	17.0932	0.609695
$787$	−18.2687	−0.651209	−0.325605	−	0.945506i	$-0.605568\pi$
$787$	−18.2687	−0.651209	−0.325605	+	0.945506i	$0.605568\pi$
$788$	15.1366	0.539219
$789$	−16.0995	−0.573156
$790$	−2.93095	−0.104278
$791$	0	0
$792$	−4.58774	−0.163018
$793$	−23.3058	−0.827614
$794$	−1.72906	−0.0613619
$795$	−2.89981	−0.102846
$796$	46.3657	1.64339
$797$	21.3664	0.756837	0.378418	−	0.925635i	$-0.376468\pi$
$797$	21.3664	0.756837	0.378418	+	0.925635i	$0.376468\pi$
$798$	0	0
$799$	19.2089	0.679560
$800$	38.9108	1.37570
$801$	8.54661	0.301980
$802$	−11.3183	−0.399664
$803$	−51.5481	−1.81909
$804$	35.8044	1.26272
$805$	0	0
$806$	−31.9108	−1.12401
$807$	−28.3051	−0.996387
$808$	8.22982	0.289524
$809$	−23.7460	−0.834865	−0.417433	−	0.908708i	$-0.637070\pi$
$809$	−23.7460	−0.834865	−0.417433	+	0.908708i	$0.637070\pi$
$810$	0.756981	0.0265976
$811$	−15.3664	−0.539587	−0.269794	−	0.962918i	$-0.586956\pi$
$811$	−15.3664	−0.539587	−0.269794	+	0.962918i	$0.586956\pi$
$812$	0	0
$813$	−1.38585	−0.0486039
$814$	74.7361	2.61950
$815$	1.19716	0.0419348
$816$	6.19565	0.216891
$817$	−3.77242	−0.131980
$818$	81.2269	2.84003
$819$	0	0
$820$	−2.12339	−0.0741518
$821$	−29.6009	−1.03308	−0.516540	−	0.856263i	$-0.672780\pi$
$821$	−29.6009	−1.03308	−0.516540	+	0.856263i	$0.672780\pi$
$822$	17.1344	0.597629
$823$	−19.6546	−0.685115	−0.342557	−	0.939497i	$-0.611293\pi$
$823$	−19.6546	−0.685115	−0.342557	+	0.939497i	$0.611293\pi$
$824$	−4.79811	−0.167150
$825$	22.3510	0.778161
$826$	0	0
$827$	−13.1296	−0.456562	−0.228281	−	0.973595i	$-0.573310\pi$
$827$	−13.1296	−0.456562	−0.228281	+	0.973595i	$0.573310\pi$
$828$	−14.1017	−0.490068
$829$	3.69569	0.128357	0.0641783	−	0.997938i	$-0.479557\pi$
$829$	3.69569	0.128357	0.0641783	+	0.997938i	$0.479557\pi$
$830$	0.558300	0.0193789
$831$	−1.15604	−0.0401024
$832$	−29.0599	−1.00747
$833$	0	0
$834$	−10.5008	−0.363612
$835$	−5.86965	−0.203128
$836$	5.98055	0.206842
$837$	−5.83076	−0.201541
$838$	−18.4332	−0.636765
$839$	−20.7911	−0.717790	−0.358895	−	0.933378i	$-0.616846\pi$
$839$	−20.7911	−0.717790	−0.358895	+	0.933378i	$0.616846\pi$
$840$	0	0
$841$	−24.7540	−0.853587
$842$	−0.756981	−0.0260873
$843$	−19.5140	−0.672097
$844$	13.1685	0.453279
$845$	−2.25622	−0.0776164
$846$	−18.5613	−0.638152
$847$	0	0
$848$	22.9340	0.787556
$849$	2.04113	0.0700513
$850$	22.5513	0.773505
$851$	43.9255	1.50575
$852$	10.2081	0.349725
$853$	−17.5162	−0.599743	−0.299872	−	0.953980i	$-0.596944\pi$
$853$	−17.5162	−0.599743	−0.299872	+	0.953980i	$0.596944\pi$
$854$	0	0
$855$	−0.188687	−0.00645295
$856$	14.0411	0.479916
$857$	−16.0628	−0.548695	−0.274348	−	0.961631i	$-0.588462\pi$
$857$	−16.0628	−0.548695	−0.274348	+	0.961631i	$0.588462\pi$
$858$	−25.1079	−0.857171
$859$	5.39281	0.184000	0.0920002	−	0.995759i	$-0.470674\pi$
$859$	5.39281	0.184000	0.0920002	+	0.995759i	$0.470674\pi$
$860$	6.33375	0.215979
$861$	0	0
$862$	−27.9930	−0.953447
$863$	7.55509	0.257178	0.128589	−	0.991698i	$-0.458955\pi$
$863$	7.55509	0.257178	0.128589	+	0.991698i	$0.458955\pi$
$864$	−7.98680	−0.271716
$865$	−9.02320	−0.306798
$866$	57.9549	1.96939
$867$	−12.2097	−0.414661
$868$	0	0
$869$	17.7632	0.602576
$870$	1.55982	0.0528827
$871$	37.4681	1.26956
$872$	−9.81131	−0.332253
$873$	4.10170	0.138822
$874$	6.35793	0.215060
$875$	0	0
$876$	27.7849	0.938765
$877$	21.0807	0.711846	0.355923	−	0.934515i	$-0.384167\pi$
$877$	21.0807	0.711846	0.355923	+	0.934515i	$0.384167\pi$
$878$	−68.9365	−2.32649
$879$	2.73057	0.0921000
$880$	4.64832	0.156695
$881$	−8.90677	−0.300077	−0.150038	−	0.988680i	$-0.547940\pi$
$881$	−8.90677	−0.300077	−0.150038	+	0.988680i	$0.547940\pi$
$882$	0	0
$883$	7.94719	0.267444	0.133722	−	0.991019i	$-0.457307\pi$
$883$	7.94719	0.267444	0.133722	+	0.991019i	$0.457307\pi$
$884$	−14.0055	−0.471057
$885$	−0.357926	−0.0120316
$886$	−65.2221	−2.19118
$887$	13.1685	0.442156	0.221078	−	0.975256i	$-0.429043\pi$
$887$	13.1685	0.442156	0.221078	+	0.975256i	$0.429043\pi$
$888$	−7.70265	−0.258484
$889$	0	0
$890$	6.46963	0.216862
$891$	−4.58774	−0.153695
$892$	27.2702	0.913075
$893$	4.62664	0.154824
$894$	−46.3851	−1.55135
$895$	−5.39530	−0.180345
$896$	0	0
$897$	−14.7570	−0.492721
$898$	74.2042	2.47623
$899$	−12.0147	−0.400713
$900$	−12.0474	−0.401579
$901$	17.7321	0.590742
$902$	23.2772	0.775046
$903$	0	0
$904$	13.2772	0.441593
$905$	−5.28887	−0.175808
$906$	3.15604	0.104852
$907$	−23.9497	−0.795236	−0.397618	−	0.917551i	$-0.630163\pi$
$907$	−23.9497	−0.795236	−0.397618	+	0.917551i	$0.630163\pi$
$908$	27.5334	0.913728
$909$	8.22982	0.272966
$910$	0	0
$911$	−46.8184	−1.55116	−0.775581	−	0.631248i	$-0.782543\pi$
$911$	−46.8184	−1.55116	−0.775581	+	0.631248i	$0.782543\pi$
$912$	1.49228	0.0494144
$913$	−3.38362	−0.111981
$914$	22.5055	0.744415
$915$	−3.22357	−0.106568
$916$	−62.8767	−2.07750
$917$	0	0
$918$	−4.62887	−0.152775
$919$	30.6506	1.01107	0.505534	−	0.862807i	$-0.331295\pi$
$919$	30.6506	1.01107	0.505534	+	0.862807i	$0.331295\pi$
$920$	−2.04113	−0.0672940
$921$	28.2423	0.930615
$922$	60.0731	1.97840
$923$	10.6825	0.351618
$924$	0	0
$925$	37.5264	1.23386
$926$	−20.2640	−0.665916
$927$	−4.79811	−0.157591
$928$	−16.4574	−0.540240
$929$	−7.52092	−0.246753	−0.123377	−	0.992360i	$-0.539372\pi$
$929$	−7.52092	−0.246753	−0.123377	+	0.992360i	$0.539372\pi$
$930$	−4.41378	−0.144733
$931$	0	0
$932$	−25.0279	−0.819817
$933$	−20.5272	−0.672029
$934$	−55.2702	−1.80850
$935$	3.59398	0.117536
$936$	2.58774	0.0845830
$937$	31.6421	1.03370	0.516851	−	0.856076i	$-0.327104\pi$
$937$	31.6421	1.03370	0.516851	+	0.856076i	$0.327104\pi$
$938$	0	0
$939$	6.86565	0.224052
$940$	−7.76795	−0.253363
$941$	11.1824	0.364537	0.182269	−	0.983249i	$-0.441656\pi$
$941$	11.1824	0.364537	0.182269	+	0.983249i	$0.441656\pi$
$942$	39.5676	1.28918
$943$	13.6810	0.445514
$944$	2.83076	0.0921334
$945$	0	0
$946$	−69.4325	−2.25745
$947$	−30.6149	−0.994852	−0.497426	−	0.867506i	$-0.665721\pi$
$947$	−30.6149	−0.994852	−0.497426	+	0.867506i	$0.665721\pi$
$948$	−9.57454	−0.310967
$949$	29.0760	0.943847
$950$	5.43171	0.176228
$951$	28.6002	0.927426
$952$	0	0
$953$	3.17548	0.102864	0.0514320	−	0.998676i	$-0.483621\pi$
$953$	3.17548	0.102864	0.0514320	+	0.998676i	$0.483621\pi$
$954$	−17.1344	−0.554745
$955$	−7.15604	−0.231564
$956$	27.0496	0.874847
$957$	−9.45339	−0.305585
$958$	39.2097	1.26681
$959$	0	0
$960$	−4.01945	−0.129727
$961$	2.99777	0.0967021
$962$	−42.1553	−1.35914
$963$	14.0411	0.452469
$964$	25.2313	0.812646
$965$	1.89134	0.0608842
$966$	0	0
$967$	40.5566	1.30421	0.652106	−	0.758128i	$-0.273886\pi$
$967$	40.5566	1.30421	0.652106	+	0.758128i	$0.273886\pi$
$968$	10.0474	0.322935
$969$	1.15380	0.0370654
$970$	3.10491	0.0996927
$971$	4.23205	0.135813	0.0679065	−	0.997692i	$-0.478368\pi$
$971$	4.23205	0.135813	0.0679065	+	0.997692i	$0.478368\pi$
$972$	2.47283	0.0793162
$973$	0	0
$974$	−45.6134	−1.46155
$975$	−12.6072	−0.403753
$976$	25.4945	0.816060
$977$	26.5055	0.847986	0.423993	−	0.905666i	$-0.360628\pi$
$977$	26.5055	0.847986	0.423993	+	0.905666i	$0.360628\pi$
$978$	7.07378	0.226195
$979$	−39.2097	−1.25315
$980$	0	0
$981$	−9.81131	−0.313251
$982$	−24.2493	−0.773825
$983$	−2.27567	−0.0725826	−0.0362913	−	0.999341i	$-0.511554\pi$
$983$	−2.27567	−0.0725826	−0.0362913	+	0.999341i	$0.511554\pi$
$984$	−2.39905	−0.0764791
$985$	2.19092	0.0698086
$986$	−9.53814	−0.303756
$987$	0	0
$988$	−3.37336	−0.107321
$989$	−40.8084	−1.29763
$990$	−3.47283	−0.110374
$991$	43.9185	1.39512	0.697559	−	0.716527i	$-0.254269\pi$
$991$	43.9185	1.39512	0.697559	+	0.716527i	$0.254269\pi$
$992$	46.5691	1.47857
$993$	21.2966	0.675828
$994$	0	0
$995$	6.71113	0.212757
$996$	1.82380	0.0577893
$997$	−2.81532	−0.0891621	−0.0445811	−	0.999006i	$-0.514195\pi$
$997$	−2.81532	−0.0891621	−0.0445811	+	0.999006i	$0.514195\pi$
$998$	−36.9434	−1.16942
$999$	−7.70265	−0.243701

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8673.2.a.s.1.3		3
7.6	odd	2		177.2.a.d.1.3	✓	3
21.20	even	2		531.2.a.d.1.1		3
28.27	even	2		2832.2.a.t.1.2		3
35.34	odd	2		4425.2.a.w.1.1		3
84.83	odd	2		8496.2.a.bl.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.2.a.d.1.3	✓	3	7.6	odd	2
531.2.a.d.1.1		3	21.20	even	2
2832.2.a.t.1.2		3	28.27	even	2
4425.2.a.w.1.1		3	35.34	odd	2
8496.2.a.bl.1.2		3	84.83	odd	2
8673.2.a.s.1.3		3	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)

\(f(q)\)	\(=\)	\(q+2.11491 q^{2} +1.00000 q^{3} +2.47283 q^{4} +0.357926 q^{5} +2.11491 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.11491 q^{2} +1.00000 q^{3} +2.47283 q^{4} +0.357926 q^{5} +2.11491 q^{6} +1.00000 q^{8} +1.00000 q^{9} +0.756981 q^{10} -4.58774 q^{11} +2.47283 q^{12} +2.58774 q^{13} +0.357926 q^{15} -2.83076 q^{16} -2.18869 q^{17} +2.11491 q^{18} -0.527166 q^{19} +0.885092 q^{20} -9.70265 q^{22} -5.70265 q^{23} +1.00000 q^{24} -4.87189 q^{25} +5.47283 q^{26} +1.00000 q^{27} +2.06058 q^{29} +0.756981 q^{30} -5.83076 q^{31} -7.98680 q^{32} -4.58774 q^{33} -4.62887 q^{34} +2.47283 q^{36} -7.70265 q^{37} -1.11491 q^{38} +2.58774 q^{39} +0.357926 q^{40} -2.39905 q^{41} +7.15604 q^{43} -11.3447 q^{44} +0.357926 q^{45} -12.0606 q^{46} -8.77643 q^{47} -2.83076 q^{48} -10.3036 q^{50} -2.18869 q^{51} +6.39905 q^{52} -8.10170 q^{53} +2.11491 q^{54} -1.64207 q^{55} -0.527166 q^{57} +4.35793 q^{58} -1.00000 q^{59} +0.885092 q^{60} -9.00624 q^{61} -12.3315 q^{62} -11.2298 q^{64} +0.926221 q^{65} -9.70265 q^{66} +14.4791 q^{67} -5.41226 q^{68} -5.70265 q^{69} +4.12811 q^{71} +1.00000 q^{72} +11.2361 q^{73} -16.2904 q^{74} -4.87189 q^{75} -1.30359 q^{76} +5.47283 q^{78} -3.87189 q^{79} -1.01320 q^{80} +1.00000 q^{81} -5.07378 q^{82} +0.737534 q^{83} -0.783389 q^{85} +15.1344 q^{86} +2.06058 q^{87} -4.58774 q^{88} +8.54661 q^{89} +0.756981 q^{90} -14.1017 q^{92} -5.83076 q^{93} -18.5613 q^{94} -0.188687 q^{95} -7.98680 q^{96} +4.10170 q^{97} -4.58774 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{3} + 2 q^{4} + 2 q^{5} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^3 + 2 * q^4 + 2 * q^5 + 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{3} + 2 q^{4} + 2 q^{5} + 3 q^{8} + 3 q^{9} - 5 q^{10} - 2 q^{11} + 2 q^{12} - 4 q^{13} + 2 q^{15} - 4 q^{16} - 3 q^{17} - 7 q^{19} + 9 q^{20} - 11 q^{22} + q^{23} + 3 q^{24} - q^{25} + 11 q^{26} + 3 q^{27} - 11 q^{29} - 5 q^{30} - 13 q^{31} - 4 q^{32} - 2 q^{33} + 7 q^{34} + 2 q^{36} - 5 q^{37} + 3 q^{38} - 4 q^{39} + 2 q^{40} + q^{41} + 6 q^{43} - 15 q^{44} + 2 q^{45} - 19 q^{46} - 11 q^{47} - 4 q^{48} - 21 q^{50} - 3 q^{51} + 11 q^{52} + 2 q^{53} - 4 q^{55} - 7 q^{57} + 14 q^{58} - 3 q^{59} + 9 q^{60} + q^{61} + 2 q^{62} - 21 q^{64} - 11 q^{66} + 10 q^{67} - 28 q^{68} + q^{69} + 26 q^{71} + 3 q^{72} - 7 q^{73} - 19 q^{74} - q^{75} + 6 q^{76} + 11 q^{78} + 2 q^{79} - 23 q^{80} + 3 q^{81} - 18 q^{82} + 3 q^{83} - 35 q^{85} + 31 q^{86} - 11 q^{87} - 2 q^{88} + 23 q^{89} - 5 q^{90} - 16 q^{92} - 13 q^{93} - 4 q^{94} + 3 q^{95} - 4 q^{96} - 14 q^{97} - 2 q^{99}+O(q^{100}) \) 3 * q + 3 * q^3 + 2 * q^4 + 2 * q^5 + 3 * q^8 + 3 * q^9 - 5 * q^10 - 2 * q^11 + 2 * q^12 - 4 * q^13 + 2 * q^15 - 4 * q^16 - 3 * q^17 - 7 * q^19 + 9 * q^20 - 11 * q^22 + q^23 + 3 * q^24 - q^25 + 11 * q^26 + 3 * q^27 - 11 * q^29 - 5 * q^30 - 13 * q^31 - 4 * q^32 - 2 * q^33 + 7 * q^34 + 2 * q^36 - 5 * q^37 + 3 * q^38 - 4 * q^39 + 2 * q^40 + q^41 + 6 * q^43 - 15 * q^44 + 2 * q^45 - 19 * q^46 - 11 * q^47 - 4 * q^48 - 21 * q^50 - 3 * q^51 + 11 * q^52 + 2 * q^53 - 4 * q^55 - 7 * q^57 + 14 * q^58 - 3 * q^59 + 9 * q^60 + q^61 + 2 * q^62 - 21 * q^64 - 11 * q^66 + 10 * q^67 - 28 * q^68 + q^69 + 26 * q^71 + 3 * q^72 - 7 * q^73 - 19 * q^74 - q^75 + 6 * q^76 + 11 * q^78 + 2 * q^79 - 23 * q^80 + 3 * q^81 - 18 * q^82 + 3 * q^83 - 35 * q^85 + 31 * q^86 - 11 * q^87 - 2 * q^88 + 23 * q^89 - 5 * q^90 - 16 * q^92 - 13 * q^93 - 4 * q^94 + 3 * q^95 - 4 * q^96 - 14 * q^97 - 2 * q^99

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