LMFDB - Embedded newform 3234.2.a.bm.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3234,2,Mod(1,3234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3234, 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("3234.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3234.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:	$25.8236200137$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.4352.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 6x^{2} - 4x + 2 $ x^4 - 6x^2 - 4x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.74912$ of defining polynomial
Character	$\chi$	$=$	3234.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.47363 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.47363 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +2.47363 q^{10} +1.00000 q^{11} +1.00000 q^{12} -3.03127 q^{13} +2.47363 q^{15} +1.00000 q^{16} +6.64167 q^{17} +1.00000 q^{18} -0.557647 q^{19} +2.47363 q^{20} +1.00000 q^{22} -2.66981 q^{23} +1.00000 q^{24} +1.11882 q^{25} -3.03127 q^{26} +1.00000 q^{27} +3.77568 q^{29} +2.47363 q^{30} -2.00666 q^{31} +1.00000 q^{32} +1.00000 q^{33} +6.64167 q^{34} +1.00000 q^{36} -0.158619 q^{37} -0.557647 q^{38} -3.03127 q^{39} +2.47363 q^{40} +5.93207 q^{41} +4.32666 q^{43} +1.00000 q^{44} +2.47363 q^{45} -2.66981 q^{46} +7.38607 q^{47} +1.00000 q^{48} +1.11882 q^{50} +6.64167 q^{51} -3.03127 q^{52} +2.83785 q^{53} +1.00000 q^{54} +2.47363 q^{55} -0.557647 q^{57} +3.77568 q^{58} +1.48881 q^{59} +2.47363 q^{60} -3.19932 q^{61} -2.00666 q^{62} +1.00000 q^{64} -7.49824 q^{65} +1.00000 q^{66} -11.2739 q^{67} +6.64167 q^{68} -2.66981 q^{69} -11.0098 q^{71} +1.00000 q^{72} -3.18323 q^{73} -0.158619 q^{74} +1.11882 q^{75} -0.557647 q^{76} -3.03127 q^{78} -6.95668 q^{79} +2.47363 q^{80} +1.00000 q^{81} +5.93207 q^{82} -4.59744 q^{83} +16.4290 q^{85} +4.32666 q^{86} +3.77568 q^{87} +1.00000 q^{88} +6.62558 q^{89} +2.47363 q^{90} -2.66981 q^{92} -2.00666 q^{93} +7.38607 q^{94} -1.37941 q^{95} +1.00000 q^{96} +1.17656 q^{97} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{5} + 4 q^{6} + 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 4 * q^5 + 4 * q^6 + 4 * q^8 + 4 * q^9	$ 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{5} + 4 q^{6} + 4 q^{8} + 4 q^{9} + 4 q^{10} + 4 q^{11} + 4 q^{12} + 8 q^{13} + 4 q^{15} + 4 q^{16} + 4 q^{17} + 4 q^{18} + 12 q^{19} + 4 q^{20} + 4 q^{22} - 8 q^{23} + 4 q^{24} + 4 q^{25} + 8 q^{26} + 4 q^{27} - 8 q^{29} + 4 q^{30} + 4 q^{31} + 4 q^{32} + 4 q^{33} + 4 q^{34} + 4 q^{36} + 8 q^{37} + 12 q^{38} + 8 q^{39} + 4 q^{40} + 12 q^{41} - 8 q^{43} + 4 q^{44} + 4 q^{45} - 8 q^{46} + 4 q^{47} + 4 q^{48} + 4 q^{50} + 4 q^{51} + 8 q^{52} - 8 q^{53} + 4 q^{54} + 4 q^{55} + 12 q^{57} - 8 q^{58} + 4 q^{60} + 24 q^{61} + 4 q^{62} + 4 q^{64} - 16 q^{65} + 4 q^{66} - 8 q^{67} + 4 q^{68} - 8 q^{69} + 8 q^{71} + 4 q^{72} + 4 q^{73} + 8 q^{74} + 4 q^{75} + 12 q^{76} + 8 q^{78} - 8 q^{79} + 4 q^{80} + 4 q^{81} + 12 q^{82} + 4 q^{83} - 8 q^{85} - 8 q^{86} - 8 q^{87} + 4 q^{88} + 24 q^{89} + 4 q^{90} - 8 q^{92} + 4 q^{93} + 4 q^{94} + 8 q^{95} + 4 q^{96} + 4 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 4 * q^5 + 4 * q^6 + 4 * q^8 + 4 * q^9 + 4 * q^10 + 4 * q^11 + 4 * q^12 + 8 * q^13 + 4 * q^15 + 4 * q^16 + 4 * q^17 + 4 * q^18 + 12 * q^19 + 4 * q^20 + 4 * q^22 - 8 * q^23 + 4 * q^24 + 4 * q^25 + 8 * q^26 + 4 * q^27 - 8 * q^29 + 4 * q^30 + 4 * q^31 + 4 * q^32 + 4 * q^33 + 4 * q^34 + 4 * q^36 + 8 * q^37 + 12 * q^38 + 8 * q^39 + 4 * q^40 + 12 * q^41 - 8 * q^43 + 4 * q^44 + 4 * q^45 - 8 * q^46 + 4 * q^47 + 4 * q^48 + 4 * q^50 + 4 * q^51 + 8 * q^52 - 8 * q^53 + 4 * q^54 + 4 * q^55 + 12 * q^57 - 8 * q^58 + 4 * q^60 + 24 * q^61 + 4 * q^62 + 4 * q^64 - 16 * q^65 + 4 * q^66 - 8 * q^67 + 4 * q^68 - 8 * q^69 + 8 * q^71 + 4 * q^72 + 4 * q^73 + 8 * q^74 + 4 * q^75 + 12 * q^76 + 8 * q^78 - 8 * q^79 + 4 * q^80 + 4 * q^81 + 12 * q^82 + 4 * q^83 - 8 * q^85 - 8 * q^86 - 8 * q^87 + 4 * q^88 + 24 * q^89 + 4 * q^90 - 8 * q^92 + 4 * q^93 + 4 * q^94 + 8 * q^95 + 4 * q^96 + 4 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	2.47363	1.10624	0.553120	−	0.833102i	$-0.313437\pi$
$5$	2.47363	1.10624	0.553120	+	0.833102i	$0.313437\pi$
$6$	1.00000	0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	2.47363	0.782229
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.00000	0.288675
$13$	−3.03127	−0.840724	−0.420362	−	0.907357i	$-0.638097\pi$
$13$	−3.03127	−0.840724	−0.420362	+	0.907357i	$0.638097\pi$
$14$	0	0
$15$	2.47363	0.638687
$16$	1.00000	0.250000
$17$	6.64167	1.61084	0.805421	−	0.592704i	$-0.201939\pi$
$17$	6.64167	1.61084	0.805421	+	0.592704i	$0.201939\pi$
$18$	1.00000	0.235702
$19$	−0.557647	−0.127933	−0.0639665	−	0.997952i	$-0.520375\pi$
$19$	−0.557647	−0.127933	−0.0639665	+	0.997952i	$0.520375\pi$
$20$	2.47363	0.553120
$21$	0	0
$22$	1.00000	0.213201
$23$	−2.66981	−0.556693	−0.278347	−	0.960481i	$-0.589786\pi$
$23$	−2.66981	−0.556693	−0.278347	+	0.960481i	$0.589786\pi$
$24$	1.00000	0.204124
$25$	1.11882	0.223765
$26$	−3.03127	−0.594482
$27$	1.00000	0.192450
$28$	0	0
$29$	3.77568	0.701126	0.350563	−	0.936539i	$-0.385990\pi$
$29$	3.77568	0.701126	0.350563	+	0.936539i	$0.385990\pi$
$30$	2.47363	0.451620
$31$	−2.00666	−0.360407	−0.180204	−	0.983629i	$-0.557676\pi$
$31$	−2.00666	−0.360407	−0.180204	+	0.983629i	$0.557676\pi$
$32$	1.00000	0.176777
$33$	1.00000	0.174078
$34$	6.64167	1.13904
$35$	0	0
$36$	1.00000	0.166667
$37$	−0.158619	−0.0260768	−0.0130384	−	0.999915i	$-0.504150\pi$
$37$	−0.158619	−0.0260768	−0.0130384	+	0.999915i	$0.504150\pi$
$38$	−0.557647	−0.0904623
$39$	−3.03127	−0.485392
$40$	2.47363	0.391115
$41$	5.93207	0.926433	0.463217	−	0.886245i	$-0.346695\pi$
$41$	5.93207	0.926433	0.463217	+	0.886245i	$0.346695\pi$
$42$	0	0
$43$	4.32666	0.659810	0.329905	−	0.944014i	$-0.392983\pi$
$43$	4.32666	0.659810	0.329905	+	0.944014i	$0.392983\pi$
$44$	1.00000	0.150756
$45$	2.47363	0.368746
$46$	−2.66981	−0.393642
$47$	7.38607	1.07737	0.538685	−	0.842507i	$-0.318921\pi$
$47$	7.38607	1.07737	0.538685	+	0.842507i	$0.318921\pi$
$48$	1.00000	0.144338
$49$	0	0
$50$	1.11882	0.158226
$51$	6.64167	0.930020
$52$	−3.03127	−0.420362
$53$	2.83785	0.389809	0.194904	−	0.980822i	$-0.437560\pi$
$53$	2.83785	0.389809	0.194904	+	0.980822i	$0.437560\pi$
$54$	1.00000	0.136083
$55$	2.47363	0.333544
$56$	0	0
$57$	−0.557647	−0.0738622
$58$	3.77568	0.495771
$59$	1.48881	0.193827	0.0969134	−	0.995293i	$-0.469103\pi$
$59$	1.48881	0.193827	0.0969134	+	0.995293i	$0.469103\pi$
$60$	2.47363	0.319344
$61$	−3.19932	−0.409630	−0.204815	−	0.978801i	$-0.565659\pi$
$61$	−3.19932	−0.409630	−0.204815	+	0.978801i	$0.565659\pi$
$62$	−2.00666	−0.254847
$63$	0	0
$64$	1.00000	0.125000
$65$	−7.49824	−0.930042
$66$	1.00000	0.123091
$67$	−11.2739	−1.37733	−0.688664	−	0.725081i	$-0.741802\pi$
$67$	−11.2739	−1.37733	−0.688664	+	0.725081i	$0.741802\pi$
$68$	6.64167	0.805421
$69$	−2.66981	−0.321407
$70$	0	0
$71$	−11.0098	−1.30662	−0.653311	−	0.757089i	$-0.726621\pi$
$71$	−11.0098	−1.30662	−0.653311	+	0.757089i	$0.726621\pi$
$72$	1.00000	0.117851
$73$	−3.18323	−0.372569	−0.186284	−	0.982496i	$-0.559645\pi$
$73$	−3.18323	−0.372569	−0.186284	+	0.982496i	$0.559645\pi$
$74$	−0.158619	−0.0184391
$75$	1.11882	0.129191
$76$	−0.557647	−0.0639665
$77$	0	0
$78$	−3.03127	−0.343224
$79$	−6.95668	−0.782687	−0.391344	−	0.920245i	$-0.627990\pi$
$79$	−6.95668	−0.782687	−0.391344	+	0.920245i	$0.627990\pi$
$80$	2.47363	0.276560
$81$	1.00000	0.111111
$82$	5.93207	0.655087
$83$	−4.59744	−0.504635	−0.252317	−	0.967645i	$-0.581193\pi$
$83$	−4.59744	−0.504635	−0.252317	+	0.967645i	$0.581193\pi$
$84$	0	0
$85$	16.4290	1.78198
$86$	4.32666	0.466556
$87$	3.77568	0.404795
$88$	1.00000	0.106600
$89$	6.62558	0.702310	0.351155	−	0.936317i	$-0.385789\pi$
$89$	6.62558	0.702310	0.351155	+	0.936317i	$0.385789\pi$
$90$	2.47363	0.260743
$91$	0	0
$92$	−2.66981	−0.278347
$93$	−2.00666	−0.208081
$94$	7.38607	0.761815
$95$	−1.37941	−0.141525
$96$	1.00000	0.102062
$97$	1.17656	0.119462	0.0597310	−	0.998215i	$-0.480976\pi$
$97$	1.17656	0.119462	0.0597310	+	0.998215i	$0.480976\pi$
$98$	0	0
$99$	1.00000	0.100504
$100$	1.11882	0.111882
$101$	14.5295	1.44574	0.722870	−	0.690984i	$-0.242823\pi$
$101$	14.5295	1.44574	0.722870	+	0.690984i	$0.242823\pi$
$102$	6.64167	0.657623
$103$	12.2239	1.20446	0.602230	−	0.798323i	$-0.294279\pi$
$103$	12.2239	1.20446	0.602230	+	0.798323i	$0.294279\pi$
$104$	−3.03127	−0.297241
$105$	0	0
$106$	2.83785	0.275636
$107$	−2.81900	−0.272523	−0.136262	−	0.990673i	$-0.543509\pi$
$107$	−2.81900	−0.272523	−0.136262	+	0.990673i	$0.543509\pi$
$108$	1.00000	0.0962250
$109$	−20.5478	−1.96812	−0.984062	−	0.177823i	$-0.943095\pi$
$109$	−20.5478	−1.96812	−0.984062	+	0.177823i	$0.943095\pi$
$110$	2.47363	0.235851
$111$	−0.158619	−0.0150555
$112$	0	0
$113$	11.7194	1.10247	0.551234	−	0.834351i	$-0.314157\pi$
$113$	11.7194	1.10247	0.551234	+	0.834351i	$0.314157\pi$
$114$	−0.557647	−0.0522285
$115$	−6.60411	−0.615836
$116$	3.77568	0.350563
$117$	−3.03127	−0.280241
$118$	1.48881	0.137056
$119$	0	0
$120$	2.47363	0.225810
$121$	1.00000	0.0909091
$122$	−3.19932	−0.289652
$123$	5.93207	0.534876
$124$	−2.00666	−0.180204
$125$	−9.60058	−0.858702
$126$	0	0
$127$	0.0397948	0.00353121	0.00176561	−	0.999998i	$-0.499438\pi$
$127$	0.0397948	0.00353121	0.00176561	+	0.999998i	$0.499438\pi$
$128$	1.00000	0.0883883
$129$	4.32666	0.380941
$130$	−7.49824	−0.657639
$131$	9.60097	0.838841	0.419420	−	0.907792i	$-0.362233\pi$
$131$	9.60097	0.838841	0.419420	+	0.907792i	$0.362233\pi$
$132$	1.00000	0.0870388
$133$	0	0
$134$	−11.2739	−0.973918
$135$	2.47363	0.212896
$136$	6.64167	0.569518
$137$	−18.6667	−1.59480	−0.797400	−	0.603451i	$-0.793792\pi$
$137$	−18.6667	−1.59480	−0.797400	+	0.603451i	$0.793792\pi$
$138$	−2.66981	−0.227269
$139$	8.33333	0.706823	0.353412	−	0.935468i	$-0.385021\pi$
$139$	8.33333	0.706823	0.353412	+	0.935468i	$0.385021\pi$
$140$	0	0
$141$	7.38607	0.622020
$142$	−11.0098	−0.923922
$143$	−3.03127	−0.253488
$144$	1.00000	0.0833333
$145$	9.33962	0.775613
$146$	−3.18323	−0.263446
$147$	0	0
$148$	−0.158619	−0.0130384
$149$	−15.2341	−1.24803	−0.624014	−	0.781413i	$-0.714499\pi$
$149$	−15.2341	−1.24803	−0.624014	+	0.781413i	$0.714499\pi$
$150$	1.11882	0.0913516
$151$	−8.31724	−0.676847	−0.338424	−	0.940994i	$-0.609894\pi$
$151$	−8.31724	−0.676847	−0.338424	+	0.940994i	$0.609894\pi$
$152$	−0.557647	−0.0452312
$153$	6.64167	0.536947
$154$	0	0
$155$	−4.96374	−0.398697
$156$	−3.03127	−0.242696
$157$	−9.13401	−0.728973	−0.364487	−	0.931209i	$-0.618756\pi$
$157$	−9.13401	−0.728973	−0.364487	+	0.931209i	$0.618756\pi$
$158$	−6.95668	−0.553443
$159$	2.83785	0.225056
$160$	2.47363	0.195557
$161$	0	0
$162$	1.00000	0.0785674
$163$	8.33609	0.652933	0.326466	−	0.945209i	$-0.394142\pi$
$163$	8.33609	0.652933	0.326466	+	0.945209i	$0.394142\pi$
$164$	5.93207	0.463217
$165$	2.47363	0.192572
$166$	−4.59744	−0.356831
$167$	−22.1610	−1.71487	−0.857434	−	0.514594i	$-0.827943\pi$
$167$	−22.1610	−1.71487	−0.857434	+	0.514594i	$0.827943\pi$
$168$	0	0
$169$	−3.81138	−0.293183
$170$	16.4290	1.26005
$171$	−0.557647	−0.0426444
$172$	4.32666	0.329905
$173$	20.9656	1.59398	0.796991	−	0.603991i	$-0.206424\pi$
$173$	20.9656	1.59398	0.796991	+	0.603991i	$0.206424\pi$
$174$	3.77568	0.286233
$175$	0	0
$176$	1.00000	0.0753778
$177$	1.48881	0.111906
$178$	6.62558	0.496608
$179$	−12.3759	−0.925017	−0.462508	−	0.886615i	$-0.653050\pi$
$179$	−12.3759	−0.925017	−0.462508	+	0.886615i	$0.653050\pi$
$180$	2.47363	0.184373
$181$	20.5595	1.52817	0.764087	−	0.645113i	$-0.223190\pi$
$181$	20.5595	1.52817	0.764087	+	0.645113i	$0.223190\pi$
$182$	0	0
$183$	−3.19932	−0.236500
$184$	−2.66981	−0.196821
$185$	−0.392364	−0.0288472
$186$	−2.00666	−0.147136
$187$	6.64167	0.485687
$188$	7.38607	0.538685
$189$	0	0
$190$	−1.37941	−0.100073
$191$	−20.3267	−1.47079	−0.735393	−	0.677641i	$-0.763002\pi$
$191$	−20.3267	−1.47079	−0.735393	+	0.677641i	$0.763002\pi$
$192$	1.00000	0.0721688
$193$	−13.0761	−0.941235	−0.470618	−	0.882337i	$-0.655969\pi$
$193$	−13.0761	−0.941235	−0.470618	+	0.882337i	$0.655969\pi$
$194$	1.17656	0.0844724
$195$	−7.49824	−0.536960
$196$	0	0
$197$	−3.80159	−0.270852	−0.135426	−	0.990787i	$-0.543240\pi$
$197$	−3.80159	−0.270852	−0.135426	+	0.990787i	$0.543240\pi$
$198$	1.00000	0.0710669
$199$	−6.87098	−0.487071	−0.243536	−	0.969892i	$-0.578307\pi$
$199$	−6.87098	−0.487071	−0.243536	+	0.969892i	$0.578307\pi$
$200$	1.11882	0.0791128
$201$	−11.2739	−0.795201
$202$	14.5295	1.02229
$203$	0	0
$204$	6.64167	0.465010
$205$	14.6737	1.02486
$206$	12.2239	0.851681
$207$	−2.66981	−0.185564
$208$	−3.03127	−0.210181
$209$	−0.557647	−0.0385733
$210$	0	0
$211$	11.7984	0.812237	0.406119	−	0.913820i	$-0.366882\pi$
$211$	11.7984	0.812237	0.406119	+	0.913820i	$0.366882\pi$
$212$	2.83785	0.194904
$213$	−11.0098	−0.754379
$214$	−2.81900	−0.192703
$215$	10.7025	0.729907
$216$	1.00000	0.0680414
$217$	0	0
$218$	−20.5478	−1.39167
$219$	−3.18323	−0.215103
$220$	2.47363	0.166772
$221$	−20.1327	−1.35427
$222$	−0.158619	−0.0106458
$223$	−21.0031	−1.40647	−0.703237	−	0.710956i	$-0.748263\pi$
$223$	−21.0031	−1.40647	−0.703237	+	0.710956i	$0.748263\pi$
$224$	0	0
$225$	1.11882	0.0745883
$226$	11.7194	0.779563
$227$	−29.4884	−1.95721	−0.978607	−	0.205736i	$-0.934041\pi$
$227$	−29.4884	−1.95721	−0.978607	+	0.205736i	$0.934041\pi$
$228$	−0.557647	−0.0369311
$229$	−17.3254	−1.14489	−0.572446	−	0.819942i	$-0.694005\pi$
$229$	−17.3254	−1.14489	−0.572446	+	0.819942i	$0.694005\pi$
$230$	−6.60411	−0.435462
$231$	0	0
$232$	3.77568	0.247885
$233$	29.4388	1.92860	0.964300	−	0.264812i	$-0.0853100\pi$
$233$	29.4388	1.92860	0.964300	+	0.264812i	$0.0853100\pi$
$234$	−3.03127	−0.198161
$235$	18.2704	1.19183
$236$	1.48881	0.0969134
$237$	−6.95668	−0.451885
$238$	0	0
$239$	24.2047	1.56567	0.782835	−	0.622229i	$-0.213773\pi$
$239$	24.2047	1.56567	0.782835	+	0.622229i	$0.213773\pi$
$240$	2.47363	0.159672
$241$	−15.3083	−0.986096	−0.493048	−	0.870002i	$-0.664117\pi$
$241$	−15.3083	−0.986096	−0.493048	+	0.870002i	$0.664117\pi$
$242$	1.00000	0.0642824
$243$	1.00000	0.0641500
$244$	−3.19932	−0.204815
$245$	0	0
$246$	5.93207	0.378215
$247$	1.69038	0.107556
$248$	−2.00666	−0.127423
$249$	−4.59744	−0.291351
$250$	−9.60058	−0.607194
$251$	7.79453	0.491986	0.245993	−	0.969272i	$-0.420886\pi$
$251$	7.79453	0.491986	0.245993	+	0.969272i	$0.420886\pi$
$252$	0	0
$253$	−2.66981	−0.167849
$254$	0.0397948	0.00249695
$255$	16.4290	1.02882
$256$	1.00000	0.0625000
$257$	14.0973	0.879368	0.439684	−	0.898152i	$-0.355090\pi$
$257$	14.0973	0.879368	0.439684	+	0.898152i	$0.355090\pi$
$258$	4.32666	0.269366
$259$	0	0
$260$	−7.49824	−0.465021
$261$	3.77568	0.233709
$262$	9.60097	0.593150
$263$	4.61353	0.284482	0.142241	−	0.989832i	$-0.454569\pi$
$263$	4.61353	0.284482	0.142241	+	0.989832i	$0.454569\pi$
$264$	1.00000	0.0615457
$265$	7.01978	0.431222
$266$	0	0
$267$	6.62558	0.405479
$268$	−11.2739	−0.688664
$269$	−3.18323	−0.194085	−0.0970424	−	0.995280i	$-0.530938\pi$
$269$	−3.18323	−0.194085	−0.0970424	+	0.995280i	$0.530938\pi$
$270$	2.47363	0.150540
$271$	0.722930	0.0439149	0.0219574	−	0.999759i	$-0.493010\pi$
$271$	0.722930	0.0439149	0.0219574	+	0.999759i	$0.493010\pi$
$272$	6.64167	0.402710
$273$	0	0
$274$	−18.6667	−1.12769
$275$	1.11882	0.0674676
$276$	−2.66981	−0.160704
$277$	1.18490	0.0711938	0.0355969	−	0.999366i	$-0.488667\pi$
$277$	1.18490	0.0711938	0.0355969	+	0.999366i	$0.488667\pi$
$278$	8.33333	0.499800
$279$	−2.00666	−0.120136
$280$	0	0
$281$	2.89097	0.172461	0.0862305	−	0.996275i	$-0.472518\pi$
$281$	2.89097	0.172461	0.0862305	+	0.996275i	$0.472518\pi$
$282$	7.38607	0.439834
$283$	−5.32353	−0.316451	−0.158225	−	0.987403i	$-0.550577\pi$
$283$	−5.32353	−0.316451	−0.158225	+	0.987403i	$0.550577\pi$
$284$	−11.0098	−0.653311
$285$	−1.37941	−0.0817092
$286$	−3.03127	−0.179243
$287$	0	0
$288$	1.00000	0.0589256
$289$	27.1118	1.59481
$290$	9.33962	0.548441
$291$	1.17656	0.0689714
$292$	−3.18323	−0.186284
$293$	10.6413	0.621670	0.310835	−	0.950464i	$-0.399391\pi$
$293$	10.6413	0.621670	0.310835	+	0.950464i	$0.399391\pi$
$294$	0	0
$295$	3.68276	0.214419
$296$	−0.158619	−0.00921955
$297$	1.00000	0.0580259
$298$	−15.2341	−0.882489
$299$	8.09292	0.468025
$300$	1.11882	0.0645954
$301$	0	0
$302$	−8.31724	−0.478603
$303$	14.5295	0.834698
$304$	−0.557647	−0.0319833
$305$	−7.91391	−0.453149
$306$	6.64167	0.379679
$307$	28.9733	1.65359	0.826797	−	0.562500i	$-0.190160\pi$
$307$	28.9733	1.65359	0.826797	+	0.562500i	$0.190160\pi$
$308$	0	0
$309$	12.2239	0.695395
$310$	−4.96374	−0.281921
$311$	2.62019	0.148578	0.0742888	−	0.997237i	$-0.476331\pi$
$311$	2.62019	0.148578	0.0742888	+	0.997237i	$0.476331\pi$
$312$	−3.03127	−0.171612
$313$	−31.7566	−1.79499	−0.897494	−	0.441027i	$-0.854614\pi$
$313$	−31.7566	−1.79499	−0.897494	+	0.441027i	$0.854614\pi$
$314$	−9.13401	−0.515462
$315$	0	0
$316$	−6.95668	−0.391344
$317$	−24.8308	−1.39464	−0.697318	−	0.716762i	$-0.745623\pi$
$317$	−24.8308	−1.39464	−0.697318	+	0.716762i	$0.745623\pi$
$318$	2.83785	0.159139
$319$	3.77568	0.211397
$320$	2.47363	0.138280
$321$	−2.81900	−0.157341
$322$	0	0
$323$	−3.70371	−0.206080
$324$	1.00000	0.0555556
$325$	−3.39146	−0.188124
$326$	8.33609	0.461693
$327$	−20.5478	−1.13630
$328$	5.93207	0.327544
$329$	0	0
$330$	2.47363	0.136169
$331$	21.2669	1.16893	0.584466	−	0.811418i	$-0.301304\pi$
$331$	21.2669	1.16893	0.584466	+	0.811418i	$0.301304\pi$
$332$	−4.59744	−0.252317
$333$	−0.158619	−0.00869228
$334$	−22.1610	−1.21260
$335$	−27.8874	−1.52365
$336$	0	0
$337$	23.3927	1.27428	0.637142	−	0.770747i	$-0.280117\pi$
$337$	23.3927	1.27428	0.637142	+	0.770747i	$0.280117\pi$
$338$	−3.81138	−0.207312
$339$	11.7194	0.636510
$340$	16.4290	0.890988
$341$	−2.00666	−0.108667
$342$	−0.557647	−0.0301541
$343$	0	0
$344$	4.32666	0.233278
$345$	−6.60411	−0.355553
$346$	20.9656	1.12712
$347$	6.60020	0.354317	0.177159	−	0.984182i	$-0.443309\pi$
$347$	6.60020	0.354317	0.177159	+	0.984182i	$0.443309\pi$
$348$	3.77568	0.202398
$349$	5.06164	0.270944	0.135472	−	0.990781i	$-0.456745\pi$
$349$	5.06164	0.270944	0.135472	+	0.990781i	$0.456745\pi$
$350$	0	0
$351$	−3.03127	−0.161797
$352$	1.00000	0.0533002
$353$	−11.5166	−0.612964	−0.306482	−	0.951876i	$-0.599152\pi$
$353$	−11.5166	−0.612964	−0.306482	+	0.951876i	$0.599152\pi$
$354$	1.48881	0.0791294
$355$	−27.2341	−1.44544
$356$	6.62558	0.351155
$357$	0	0
$358$	−12.3759	−0.654086
$359$	−10.5080	−0.554593	−0.277296	−	0.960784i	$-0.589438\pi$
$359$	−10.5080	−0.554593	−0.277296	+	0.960784i	$0.589438\pi$
$360$	2.47363	0.130372
$361$	−18.6890	−0.983633
$362$	20.5595	1.08058
$363$	1.00000	0.0524864
$364$	0	0
$365$	−7.87412	−0.412150
$366$	−3.19932	−0.167231
$367$	10.8976	0.568852	0.284426	−	0.958698i	$-0.408197\pi$
$367$	10.8976	0.568852	0.284426	+	0.958698i	$0.408197\pi$
$368$	−2.66981	−0.139173
$369$	5.93207	0.308811
$370$	−0.392364	−0.0203981
$371$	0	0
$372$	−2.00666	−0.104041
$373$	21.3459	1.10525	0.552624	−	0.833431i	$-0.313627\pi$
$373$	21.3459	1.10525	0.552624	+	0.833431i	$0.313627\pi$
$374$	6.64167	0.343433
$375$	−9.60058	−0.495772
$376$	7.38607	0.380908
$377$	−11.4451	−0.589453
$378$	0	0
$379$	−21.3066	−1.09445	−0.547225	−	0.836986i	$-0.684316\pi$
$379$	−21.3066	−1.09445	−0.547225	+	0.836986i	$0.684316\pi$
$380$	−1.37941	−0.0707623
$381$	0.0397948	0.00203875
$382$	−20.3267	−1.04000
$383$	−34.6202	−1.76901	−0.884505	−	0.466531i	$-0.845503\pi$
$383$	−34.6202	−1.76901	−0.884505	+	0.466531i	$0.845503\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−13.0761	−0.665554
$387$	4.32666	0.219937
$388$	1.17656	0.0597310
$389$	−9.68276	−0.490936	−0.245468	−	0.969405i	$-0.578942\pi$
$389$	−9.68276	−0.490936	−0.245468	+	0.969405i	$0.578942\pi$
$390$	−7.49824	−0.379688
$391$	−17.7320	−0.896745
$392$	0	0
$393$	9.60097	0.484305
$394$	−3.80159	−0.191521
$395$	−17.2082	−0.865839
$396$	1.00000	0.0502519
$397$	−11.8928	−0.596884	−0.298442	−	0.954428i	$-0.596467\pi$
$397$	−11.8928	−0.596884	−0.298442	+	0.954428i	$0.596467\pi$
$398$	−6.87098	−0.344411
$399$	0	0
$400$	1.11882	0.0559412
$401$	33.9804	1.69690	0.848449	−	0.529277i	$-0.177537\pi$
$401$	33.9804	1.69690	0.848449	+	0.529277i	$0.177537\pi$
$402$	−11.2739	−0.562292
$403$	6.08275	0.303003
$404$	14.5295	0.722870
$405$	2.47363	0.122915
$406$	0	0
$407$	−0.158619	−0.00786246
$408$	6.64167	0.328812
$409$	9.51305	0.470390	0.235195	−	0.971948i	$-0.424427\pi$
$409$	9.51305	0.470390	0.235195	+	0.971948i	$0.424427\pi$
$410$	14.6737	0.724683
$411$	−18.6667	−0.920758
$412$	12.2239	0.602230
$413$	0	0
$414$	−2.66981	−0.131214
$415$	−11.3724	−0.558247
$416$	−3.03127	−0.148620
$417$	8.33333	0.408085
$418$	−0.557647	−0.0272754
$419$	−15.9249	−0.777981	−0.388990	−	0.921242i	$-0.627176\pi$
$419$	−15.9249	−0.777981	−0.388990	+	0.921242i	$0.627176\pi$
$420$	0	0
$421$	3.55842	0.173427	0.0867133	−	0.996233i	$-0.472364\pi$
$421$	3.55842	0.173427	0.0867133	+	0.996233i	$0.472364\pi$
$422$	11.7984	0.574339
$423$	7.38607	0.359123
$424$	2.83785	0.137818
$425$	7.43086	0.360450
$426$	−11.0098	−0.533426
$427$	0	0
$428$	−2.81900	−0.136262
$429$	−3.03127	−0.146351
$430$	10.7025	0.516122
$431$	20.2774	0.976730	0.488365	−	0.872639i	$-0.337593\pi$
$431$	20.2774	0.976730	0.488365	+	0.872639i	$0.337593\pi$
$432$	1.00000	0.0481125
$433$	27.7144	1.33187	0.665935	−	0.746010i	$-0.268033\pi$
$433$	27.7144	1.33187	0.665935	+	0.746010i	$0.268033\pi$
$434$	0	0
$435$	9.33962	0.447800
$436$	−20.5478	−0.984062
$437$	1.48881	0.0712195
$438$	−3.18323	−0.152101
$439$	4.85433	0.231685	0.115842	−	0.993268i	$-0.463043\pi$
$439$	4.85433	0.231685	0.115842	+	0.993268i	$0.463043\pi$
$440$	2.47363	0.117925
$441$	0	0
$442$	−20.1327	−0.957615
$443$	−30.5269	−1.45038	−0.725188	−	0.688551i	$-0.758247\pi$
$443$	−30.5269	−1.45038	−0.725188	+	0.688551i	$0.758247\pi$
$444$	−0.158619	−0.00752773
$445$	16.3892	0.776923
$446$	−21.0031	−0.994527
$447$	−15.2341	−0.720549
$448$	0	0
$449$	−30.3986	−1.43460	−0.717300	−	0.696764i	$-0.754622\pi$
$449$	−30.3986	−1.43460	−0.717300	+	0.696764i	$0.754622\pi$
$450$	1.11882	0.0527419
$451$	5.93207	0.279330
$452$	11.7194	0.551234
$453$	−8.31724	−0.390778
$454$	−29.4884	−1.38396
$455$	0	0
$456$	−0.557647	−0.0261142
$457$	11.1020	0.519328	0.259664	−	0.965699i	$-0.416388\pi$
$457$	11.1020	0.519328	0.259664	+	0.965699i	$0.416388\pi$
$458$	−17.3254	−0.809561
$459$	6.64167	0.310007
$460$	−6.60411	−0.307918
$461$	38.1693	1.77772	0.888861	−	0.458177i	$-0.151497\pi$
$461$	38.1693	1.77772	0.888861	+	0.458177i	$0.151497\pi$
$462$	0	0
$463$	−31.4388	−1.46108	−0.730542	−	0.682867i	$-0.760733\pi$
$463$	−31.4388	−1.46108	−0.730542	+	0.682867i	$0.760733\pi$
$464$	3.77568	0.175281
$465$	−4.96374	−0.230188
$466$	29.4388	1.36373
$467$	−11.9204	−0.551611	−0.275805	−	0.961213i	$-0.588945\pi$
$467$	−11.9204	−0.551611	−0.275805	+	0.961213i	$0.588945\pi$
$468$	−3.03127	−0.140121
$469$	0	0
$470$	18.2704	0.842750
$471$	−9.13401	−0.420873
$472$	1.48881	0.0685281
$473$	4.32666	0.198940
$474$	−6.95668	−0.319531
$475$	−0.623909	−0.0286269
$476$	0	0
$477$	2.83785	0.129936
$478$	24.2047	1.10710
$479$	−39.4155	−1.80094	−0.900470	−	0.434918i	$-0.856777\pi$
$479$	−39.4155	−1.80094	−0.900470	+	0.434918i	$0.856777\pi$
$480$	2.47363	0.112905
$481$	0.480818	0.0219234
$482$	−15.3083	−0.697275
$483$	0	0
$484$	1.00000	0.0454545
$485$	2.91038	0.132154
$486$	1.00000	0.0453609
$487$	23.1551	1.04926	0.524629	−	0.851331i	$-0.324204\pi$
$487$	23.1551	1.04926	0.524629	+	0.851331i	$0.324204\pi$
$488$	−3.19932	−0.144826
$489$	8.33609	0.376971
$490$	0	0
$491$	−4.47530	−0.201967	−0.100984	−	0.994888i	$-0.532199\pi$
$491$	−4.47530	−0.201967	−0.100984	+	0.994888i	$0.532199\pi$
$492$	5.93207	0.267438
$493$	25.0768	1.12940
$494$	1.69038	0.0760538
$495$	2.47363	0.111181
$496$	−2.00666	−0.0901019
$497$	0	0
$498$	−4.59744	−0.206016
$499$	−16.7727	−0.750850	−0.375425	−	0.926853i	$-0.622503\pi$
$499$	−16.7727	−0.750850	−0.375425	+	0.926853i	$0.622503\pi$
$500$	−9.60058	−0.429351
$501$	−22.1610	−0.990080
$502$	7.79453	0.347887
$503$	−41.1653	−1.83547	−0.917734	−	0.397195i	$-0.869984\pi$
$503$	−41.1653	−1.83547	−0.917734	+	0.397195i	$0.869984\pi$
$504$	0	0
$505$	35.9406	1.59933
$506$	−2.66981	−0.118687
$507$	−3.81138	−0.169269
$508$	0.0397948	0.00176561
$509$	14.5987	0.647077	0.323538	−	0.946215i	$-0.395128\pi$
$509$	14.5987	0.647077	0.323538	+	0.946215i	$0.395128\pi$
$510$	16.4290	0.727488
$511$	0	0
$512$	1.00000	0.0441942
$513$	−0.557647	−0.0246207
$514$	14.0973	0.621807
$515$	30.2374	1.33242
$516$	4.32666	0.190471
$517$	7.38607	0.324839
$518$	0	0
$519$	20.9656	0.920286
$520$	−7.49824	−0.328819
$521$	17.0054	0.745019	0.372509	−	0.928028i	$-0.378497\pi$
$521$	17.0054	0.745019	0.372509	+	0.928028i	$0.378497\pi$
$522$	3.77568	0.165257
$523$	32.8874	1.43807	0.719033	−	0.694976i	$-0.244585\pi$
$523$	32.8874	1.43807	0.719033	+	0.694976i	$0.244585\pi$
$524$	9.60097	0.419420
$525$	0	0
$526$	4.61353	0.201159
$527$	−13.3276	−0.580559
$528$	1.00000	0.0435194
$529$	−15.8721	−0.690092
$530$	7.01978	0.304920
$531$	1.48881	0.0646089
$532$	0	0
$533$	−17.9817	−0.778874
$534$	6.62558	0.286717
$535$	−6.97316	−0.301476
$536$	−11.2739	−0.486959
$537$	−12.3759	−0.534059
$538$	−3.18323	−0.137239
$539$	0	0
$540$	2.47363	0.106448
$541$	−3.11529	−0.133937	−0.0669685	−	0.997755i	$-0.521333\pi$
$541$	−3.11529	−0.133937	−0.0669685	+	0.997755i	$0.521333\pi$
$542$	0.722930	0.0310525
$543$	20.5595	0.882292
$544$	6.64167	0.284759
$545$	−50.8276	−2.17722
$546$	0	0
$547$	−4.58706	−0.196129	−0.0980643	−	0.995180i	$-0.531265\pi$
$547$	−4.58706	−0.196129	−0.0980643	+	0.995180i	$0.531265\pi$
$548$	−18.6667	−0.797400
$549$	−3.19932	−0.136543
$550$	1.11882	0.0477068
$551$	−2.10550	−0.0896972
$552$	−2.66981	−0.113635
$553$	0	0
$554$	1.18490	0.0503416
$555$	−0.392364	−0.0166549
$556$	8.33333	0.353412
$557$	18.4290	0.780862	0.390431	−	0.920632i	$-0.372326\pi$
$557$	18.4290	0.780862	0.390431	+	0.920632i	$0.372326\pi$
$558$	−2.00666	−0.0849488
$559$	−13.1153	−0.554718
$560$	0	0
$561$	6.64167	0.280411
$562$	2.89097	0.121948
$563$	7.03903	0.296660	0.148330	−	0.988938i	$-0.452610\pi$
$563$	7.03903	0.296660	0.148330	+	0.988938i	$0.452610\pi$
$564$	7.38607	0.311010
$565$	28.9894	1.21959
$566$	−5.32353	−0.223765
$567$	0	0
$568$	−11.0098	−0.461961
$569$	−20.2913	−0.850657	−0.425328	−	0.905039i	$-0.639841\pi$
$569$	−20.2913	−0.850657	−0.425328	+	0.905039i	$0.639841\pi$
$570$	−1.37941	−0.0577772
$571$	10.8517	0.454131	0.227066	−	0.973879i	$-0.427087\pi$
$571$	10.8517	0.454131	0.227066	+	0.973879i	$0.427087\pi$
$572$	−3.03127	−0.126744
$573$	−20.3267	−0.849158
$574$	0	0
$575$	−2.98705	−0.124568
$576$	1.00000	0.0416667
$577$	−15.0944	−0.628387	−0.314194	−	0.949359i	$-0.601734\pi$
$577$	−15.0944	−0.628387	−0.314194	+	0.949359i	$0.601734\pi$
$578$	27.1118	1.12770
$579$	−13.0761	−0.543422
$580$	9.33962	0.387806
$581$	0	0
$582$	1.17656	0.0487702
$583$	2.83785	0.117532
$584$	−3.18323	−0.131723
$585$	−7.49824	−0.310014
$586$	10.6413	0.439587
$587$	8.46197	0.349263	0.174631	−	0.984634i	$-0.444127\pi$
$587$	8.46197	0.349263	0.174631	+	0.984634i	$0.444127\pi$
$588$	0	0
$589$	1.11901	0.0461080
$590$	3.68276	0.151617
$591$	−3.80159	−0.156376
$592$	−0.158619	−0.00651921
$593$	28.2234	1.15900	0.579498	−	0.814974i	$-0.303249\pi$
$593$	28.2234	1.15900	0.579498	+	0.814974i	$0.303249\pi$
$594$	1.00000	0.0410305
$595$	0	0
$596$	−15.2341	−0.624014
$597$	−6.87098	−0.281211
$598$	8.09292	0.330944
$599$	15.4396	0.630845	0.315422	−	0.948951i	$-0.397854\pi$
$599$	15.4396	0.630845	0.315422	+	0.948951i	$0.397854\pi$
$600$	1.11882	0.0456758
$601$	−10.8464	−0.442432	−0.221216	−	0.975225i	$-0.571003\pi$
$601$	−10.8464	−0.442432	−0.221216	+	0.975225i	$0.571003\pi$
$602$	0	0
$603$	−11.2739	−0.459109
$604$	−8.31724	−0.338424
$605$	2.47363	0.100567
$606$	14.5295	0.590221
$607$	−13.9134	−0.564725	−0.282363	−	0.959308i	$-0.591118\pi$
$607$	−13.9134	−0.564725	−0.282363	+	0.959308i	$0.591118\pi$
$608$	−0.557647	−0.0226156
$609$	0	0
$610$	−7.91391	−0.320425
$611$	−22.3892	−0.905770
$612$	6.64167	0.268474
$613$	6.82843	0.275798	0.137899	−	0.990446i	$-0.455965\pi$
$613$	6.82843	0.275798	0.137899	+	0.990446i	$0.455965\pi$
$614$	28.9733	1.16927
$615$	14.6737	0.591701
$616$	0	0
$617$	−32.0688	−1.29104	−0.645521	−	0.763743i	$-0.723360\pi$
$617$	−32.0688	−1.29104	−0.645521	+	0.763743i	$0.723360\pi$
$618$	12.2239	0.491718
$619$	−18.0492	−0.725459	−0.362730	−	0.931894i	$-0.618155\pi$
$619$	−18.0492	−0.725459	−0.362730	+	0.931894i	$0.618155\pi$
$620$	−4.96374	−0.199348
$621$	−2.66981	−0.107136
$622$	2.62019	0.105060
$623$	0	0
$624$	−3.03127	−0.121348
$625$	−29.3424	−1.17369
$626$	−31.7566	−1.26925
$627$	−0.557647	−0.0222703
$628$	−9.13401	−0.364487
$629$	−1.05350	−0.0420056
$630$	0	0
$631$	9.28724	0.369719	0.184860	−	0.982765i	$-0.440817\pi$
$631$	9.28724	0.369719	0.184860	+	0.982765i	$0.440817\pi$
$632$	−6.95668	−0.276722
$633$	11.7984	0.468945
$634$	−24.8308	−0.986157
$635$	0.0984373	0.00390637
$636$	2.83785	0.112528
$637$	0	0
$638$	3.77568	0.149481
$639$	−11.0098	−0.435541
$640$	2.47363	0.0977786
$641$	−15.3700	−0.607078	−0.303539	−	0.952819i	$-0.598168\pi$
$641$	−15.3700	−0.607078	−0.303539	+	0.952819i	$0.598168\pi$
$642$	−2.81900	−0.111257
$643$	−11.3833	−0.448914	−0.224457	−	0.974484i	$-0.572061\pi$
$643$	−11.3833	−0.448914	−0.224457	+	0.974484i	$0.572061\pi$
$644$	0	0
$645$	10.7025	0.421412
$646$	−3.70371	−0.145720
$647$	−20.1464	−0.792038	−0.396019	−	0.918242i	$-0.629609\pi$
$647$	−20.1464	−0.792038	−0.396019	+	0.918242i	$0.629609\pi$
$648$	1.00000	0.0392837
$649$	1.48881	0.0584410
$650$	−3.39146	−0.133024
$651$	0	0
$652$	8.33609	0.326466
$653$	−38.1062	−1.49121	−0.745606	−	0.666387i	$-0.767840\pi$
$653$	−38.1062	−1.49121	−0.745606	+	0.666387i	$0.767840\pi$
$654$	−20.5478	−0.803484
$655$	23.7492	0.927958
$656$	5.93207	0.231608
$657$	−3.18323	−0.124190
$658$	0	0
$659$	21.4653	0.836168	0.418084	−	0.908408i	$-0.362702\pi$
$659$	21.4653	0.836168	0.418084	+	0.908408i	$0.362702\pi$
$660$	2.47363	0.0962858
$661$	6.01166	0.233826	0.116913	−	0.993142i	$-0.462700\pi$
$661$	6.01166	0.233826	0.116913	+	0.993142i	$0.462700\pi$
$662$	21.2669	0.826560
$663$	−20.1327	−0.781890
$664$	−4.59744	−0.178415
$665$	0	0
$666$	−0.158619	−0.00614637
$667$	−10.0803	−0.390312
$668$	−22.1610	−0.857434
$669$	−21.0031	−0.812028
$670$	−27.8874	−1.07739
$671$	−3.19932	−0.123508
$672$	0	0
$673$	0.415116	0.0160015	0.00800077	−	0.999968i	$-0.497453\pi$
$673$	0.415116	0.0160015	0.00800077	+	0.999968i	$0.497453\pi$
$674$	23.3927	0.901055
$675$	1.11882	0.0430636
$676$	−3.81138	−0.146592
$677$	−18.2067	−0.699742	−0.349871	−	0.936798i	$-0.613775\pi$
$677$	−18.2067	−0.699742	−0.349871	+	0.936798i	$0.613775\pi$
$678$	11.7194	0.450081
$679$	0	0
$680$	16.4290	0.630024
$681$	−29.4884	−1.13000
$682$	−2.00666	−0.0768391
$683$	−44.9763	−1.72097	−0.860485	−	0.509476i	$-0.829839\pi$
$683$	−44.9763	−1.72097	−0.860485	+	0.509476i	$0.829839\pi$
$684$	−0.557647	−0.0213222
$685$	−46.1743	−1.76423
$686$	0	0
$687$	−17.3254	−0.661004
$688$	4.32666	0.164952
$689$	−8.60230	−0.327722
$690$	−6.60411	−0.251414
$691$	−30.7910	−1.17134	−0.585672	−	0.810548i	$-0.699169\pi$
$691$	−30.7910	−1.17134	−0.585672	+	0.810548i	$0.699169\pi$
$692$	20.9656	0.796991
$693$	0	0
$694$	6.60020	0.250540
$695$	20.6135	0.781916
$696$	3.77568	0.143117
$697$	39.3988	1.49234
$698$	5.06164	0.191586
$699$	29.4388	1.11348
$700$	0	0
$701$	−7.83376	−0.295877	−0.147939	−	0.988997i	$-0.547264\pi$
$701$	−7.83376	−0.295877	−0.147939	+	0.988997i	$0.547264\pi$
$702$	−3.03127	−0.114408
$703$	0.0884535	0.00333609
$704$	1.00000	0.0376889
$705$	18.2704	0.688102
$706$	−11.5166	−0.433431
$707$	0	0
$708$	1.48881	0.0559530
$709$	44.2507	1.66187	0.830936	−	0.556368i	$-0.187806\pi$
$709$	44.2507	1.66187	0.830936	+	0.556368i	$0.187806\pi$
$710$	−27.2341	−1.02208
$711$	−6.95668	−0.260896
$712$	6.62558	0.248304
$713$	5.35741	0.200636
$714$	0	0
$715$	−7.49824	−0.280418
$716$	−12.3759	−0.462508
$717$	24.2047	0.903940
$718$	−10.5080	−0.392156
$719$	−6.50843	−0.242723	−0.121362	−	0.992608i	$-0.538726\pi$
$719$	−6.50843	−0.242723	−0.121362	+	0.992608i	$0.538726\pi$
$720$	2.47363	0.0921866
$721$	0	0
$722$	−18.6890	−0.695534
$723$	−15.3083	−0.569323
$724$	20.5595	0.764087
$725$	4.22432	0.156887
$726$	1.00000	0.0371135
$727$	18.9110	0.701369	0.350684	−	0.936494i	$-0.385949\pi$
$727$	18.9110	0.701369	0.350684	+	0.936494i	$0.385949\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−7.87412	−0.291434
$731$	28.7363	1.06285
$732$	−3.19932	−0.118250
$733$	−10.2146	−0.377286	−0.188643	−	0.982046i	$-0.560409\pi$
$733$	−10.2146	−0.377286	−0.188643	+	0.982046i	$0.560409\pi$
$734$	10.8976	0.402239
$735$	0	0
$736$	−2.66981	−0.0984104
$737$	−11.2739	−0.415280
$738$	5.93207	0.218362
$739$	7.08939	0.260787	0.130394	−	0.991462i	$-0.458376\pi$
$739$	7.08939	0.260787	0.130394	+	0.991462i	$0.458376\pi$
$740$	−0.392364	−0.0144236
$741$	1.69038	0.0620977
$742$	0	0
$743$	−32.5408	−1.19380	−0.596902	−	0.802314i	$-0.703602\pi$
$743$	−32.5408	−1.19380	−0.596902	+	0.802314i	$0.703602\pi$
$744$	−2.00666	−0.0735679
$745$	−37.6835	−1.38062
$746$	21.3459	0.781528
$747$	−4.59744	−0.168212
$748$	6.64167	0.242843
$749$	0	0
$750$	−9.60058	−0.350563
$751$	−29.0496	−1.06003	−0.530017	−	0.847987i	$-0.677815\pi$
$751$	−29.0496	−1.06003	−0.530017	+	0.847987i	$0.677815\pi$
$752$	7.38607	0.269342
$753$	7.79453	0.284048
$754$	−11.4451	−0.416806
$755$	−20.5737	−0.748755
$756$	0	0
$757$	28.4151	1.03276	0.516382	−	0.856358i	$-0.327278\pi$
$757$	28.4151	1.03276	0.516382	+	0.856358i	$0.327278\pi$
$758$	−21.3066	−0.773892
$759$	−2.66981	−0.0969079
$760$	−1.37941	−0.0500365
$761$	−25.7999	−0.935245	−0.467622	−	0.883928i	$-0.654889\pi$
$761$	−25.7999	−0.935245	−0.467622	+	0.883928i	$0.654889\pi$
$762$	0.0397948	0.00144161
$763$	0	0
$764$	−20.3267	−0.735393
$765$	16.4290	0.593992
$766$	−34.6202	−1.25088
$767$	−4.51299	−0.162955
$768$	1.00000	0.0360844
$769$	27.1932	0.980612	0.490306	−	0.871550i	$-0.336885\pi$
$769$	27.1932	0.980612	0.490306	+	0.871550i	$0.336885\pi$
$770$	0	0
$771$	14.0973	0.507704
$772$	−13.0761	−0.470618
$773$	−24.5032	−0.881319	−0.440660	−	0.897674i	$-0.645255\pi$
$773$	−24.5032	−0.881319	−0.440660	+	0.897674i	$0.645255\pi$
$774$	4.32666	0.155519
$775$	−2.24510	−0.0806465
$776$	1.17656	0.0422362
$777$	0	0
$778$	−9.68276	−0.347144
$779$	−3.30800	−0.118521
$780$	−7.49824	−0.268480
$781$	−11.0098	−0.393962
$782$	−17.7320	−0.634094
$783$	3.77568	0.134932
$784$	0	0
$785$	−22.5941	−0.806419
$786$	9.60097	0.342455
$787$	−52.8741	−1.88476	−0.942379	−	0.334547i	$-0.891417\pi$
$787$	−52.8741	−1.88476	−0.942379	+	0.334547i	$0.891417\pi$
$788$	−3.80159	−0.135426
$789$	4.61353	0.164246
$790$	−17.2082	−0.612241
$791$	0	0
$792$	1.00000	0.0355335
$793$	9.69800	0.344386
$794$	−11.8928	−0.422061
$795$	7.01978	0.248966
$796$	−6.87098	−0.243536
$797$	27.1028	0.960032	0.480016	−	0.877260i	$-0.340631\pi$
$797$	27.1028	0.960032	0.480016	+	0.877260i	$0.340631\pi$
$798$	0	0
$799$	49.0559	1.73547
$800$	1.11882	0.0395564
$801$	6.62558	0.234103
$802$	33.9804	1.19989
$803$	−3.18323	−0.112334
$804$	−11.2739	−0.397600
$805$	0	0
$806$	6.08275	0.214256
$807$	−3.18323	−0.112055
$808$	14.5295	0.511146
$809$	−3.58488	−0.126038	−0.0630189	−	0.998012i	$-0.520073\pi$
$809$	−3.58488	−0.126038	−0.0630189	+	0.998012i	$0.520073\pi$
$810$	2.47363	0.0869143
$811$	50.2933	1.76604	0.883018	−	0.469339i	$-0.155508\pi$
$811$	50.2933	1.76604	0.883018	+	0.469339i	$0.155508\pi$
$812$	0	0
$813$	0.722930	0.0253543
$814$	−0.158619	−0.00555960
$815$	20.6204	0.722300
$816$	6.64167	0.232505
$817$	−2.41275	−0.0844115
$818$	9.51305	0.332616
$819$	0	0
$820$	14.6737	0.512428
$821$	−11.1556	−0.389335	−0.194667	−	0.980869i	$-0.562363\pi$
$821$	−11.1556	−0.389335	−0.194667	+	0.980869i	$0.562363\pi$
$822$	−18.6667	−0.651074
$823$	22.7860	0.794271	0.397136	−	0.917760i	$-0.370004\pi$
$823$	22.7860	0.794271	0.397136	+	0.917760i	$0.370004\pi$
$824$	12.2239	0.425841
$825$	1.11882	0.0389525
$826$	0	0
$827$	17.0490	0.592853	0.296426	−	0.955056i	$-0.404205\pi$
$827$	17.0490	0.592853	0.296426	+	0.955056i	$0.404205\pi$
$828$	−2.66981	−0.0927822
$829$	−11.6952	−0.406190	−0.203095	−	0.979159i	$-0.565100\pi$
$829$	−11.6952	−0.406190	−0.203095	+	0.979159i	$0.565100\pi$
$830$	−11.3724	−0.394740
$831$	1.18490	0.0411037
$832$	−3.03127	−0.105090
$833$	0	0
$834$	8.33333	0.288559
$835$	−54.8180	−1.89705
$836$	−0.557647	−0.0192866
$837$	−2.00666	−0.0693604
$838$	−15.9249	−0.550116
$839$	30.2833	1.04550	0.522748	−	0.852487i	$-0.324907\pi$
$839$	30.2833	1.04550	0.522748	+	0.852487i	$0.324907\pi$
$840$	0	0
$841$	−14.7443	−0.508422
$842$	3.55842	0.122631
$843$	2.89097	0.0995704
$844$	11.7984	0.406119
$845$	−9.42794	−0.324331
$846$	7.38607	0.253938
$847$	0	0
$848$	2.83785	0.0974522
$849$	−5.32353	−0.182703
$850$	7.43086	0.254876
$851$	0.423483	0.0145168
$852$	−11.0098	−0.377189
$853$	−34.7318	−1.18920	−0.594598	−	0.804023i	$-0.702689\pi$
$853$	−34.7318	−1.18920	−0.594598	+	0.804023i	$0.702689\pi$
$854$	0	0
$855$	−1.37941	−0.0471749
$856$	−2.81900	−0.0963515
$857$	21.7344	0.742433	0.371216	−	0.928546i	$-0.378941\pi$
$857$	21.7344	0.742433	0.371216	+	0.928546i	$0.378941\pi$
$858$	−3.03127	−0.103486
$859$	−39.9241	−1.36219	−0.681096	−	0.732194i	$-0.738496\pi$
$859$	−39.9241	−1.36219	−0.681096	+	0.732194i	$0.738496\pi$
$860$	10.7025	0.364954
$861$	0	0
$862$	20.2774	0.690652
$863$	57.8380	1.96883	0.984414	−	0.175866i	$-0.0562726\pi$
$863$	57.8380	1.96883	0.984414	+	0.175866i	$0.0562726\pi$
$864$	1.00000	0.0340207
$865$	51.8610	1.76333
$866$	27.7144	0.941774
$867$	27.1118	0.920764
$868$	0	0
$869$	−6.95668	−0.235989
$870$	9.33962	0.316643
$871$	34.1743	1.15795
$872$	−20.5478	−0.695837
$873$	1.17656	0.0398207
$874$	1.48881	0.0503598
$875$	0	0
$876$	−3.18323	−0.107551
$877$	−38.1717	−1.28897	−0.644484	−	0.764618i	$-0.722928\pi$
$877$	−38.1717	−1.28897	−0.644484	+	0.764618i	$0.722928\pi$
$878$	4.85433	0.163826
$879$	10.6413	0.358921
$880$	2.47363	0.0833859
$881$	−50.5818	−1.70415	−0.852073	−	0.523423i	$-0.824655\pi$
$881$	−50.5818	−1.70415	−0.852073	+	0.523423i	$0.824655\pi$
$882$	0	0
$883$	−45.3333	−1.52559	−0.762794	−	0.646642i	$-0.776173\pi$
$883$	−45.3333	−1.52559	−0.762794	+	0.646642i	$0.776173\pi$
$884$	−20.1327	−0.677136
$885$	3.68276	0.123795
$886$	−30.5269	−1.02557
$887$	−14.6337	−0.491353	−0.245676	−	0.969352i	$-0.579010\pi$
$887$	−14.6337	−0.491353	−0.245676	+	0.969352i	$0.579010\pi$
$888$	−0.158619	−0.00532291
$889$	0	0
$890$	16.3892	0.549368
$891$	1.00000	0.0335013
$892$	−21.0031	−0.703237
$893$	−4.11882	−0.137831
$894$	−15.2341	−0.509505
$895$	−30.6133	−1.02329
$896$	0	0
$897$	8.09292	0.270215
$898$	−30.3986	−1.01442
$899$	−7.57652	−0.252691
$900$	1.11882	0.0372941
$901$	18.8481	0.627920
$902$	5.93207	0.197516
$903$	0	0
$904$	11.7194	0.389781
$905$	50.8565	1.69053
$906$	−8.31724	−0.276322
$907$	51.4597	1.70869	0.854346	−	0.519704i	$-0.173958\pi$
$907$	51.4597	1.70869	0.854346	+	0.519704i	$0.173958\pi$
$908$	−29.4884	−0.978607
$909$	14.5295	0.481913
$910$	0	0
$911$	4.27373	0.141595	0.0707975	−	0.997491i	$-0.477446\pi$
$911$	4.27373	0.141595	0.0707975	+	0.997491i	$0.477446\pi$
$912$	−0.557647	−0.0184655
$913$	−4.59744	−0.152153
$914$	11.1020	0.367220
$915$	−7.91391	−0.261626
$916$	−17.3254	−0.572446
$917$	0	0
$918$	6.64167	0.219208
$919$	46.0992	1.52067	0.760336	−	0.649530i	$-0.225034\pi$
$919$	46.0992	1.52067	0.760336	+	0.649530i	$0.225034\pi$
$920$	−6.60411	−0.217731
$921$	28.9733	0.954703
$922$	38.1693	1.25704
$923$	33.3737	1.09851
$924$	0	0
$925$	−0.177467	−0.00583508
$926$	−31.4388	−1.03314
$927$	12.2239	0.401486
$928$	3.77568	0.123943
$929$	46.3287	1.51999	0.759997	−	0.649926i	$-0.225200\pi$
$929$	46.3287	1.51999	0.759997	+	0.649926i	$0.225200\pi$
$930$	−4.96374	−0.162767
$931$	0	0
$932$	29.4388	0.964300
$933$	2.62019	0.0857813
$934$	−11.9204	−0.390048
$935$	16.4290	0.537286
$936$	−3.03127	−0.0990803
$937$	50.7016	1.65635	0.828175	−	0.560470i	$-0.189379\pi$
$937$	50.7016	1.65635	0.828175	+	0.560470i	$0.189379\pi$
$938$	0	0
$939$	−31.7566	−1.03634
$940$	18.2704	0.595914
$941$	23.8736	0.778257	0.389128	−	0.921184i	$-0.372776\pi$
$941$	23.8736	0.778257	0.389128	+	0.921184i	$0.372776\pi$
$942$	−9.13401	−0.297602
$943$	−15.8375	−0.515739
$944$	1.48881	0.0484567
$945$	0	0
$946$	4.32666	0.140672
$947$	−21.8678	−0.710610	−0.355305	−	0.934751i	$-0.615623\pi$
$947$	−21.8678	−0.710610	−0.355305	+	0.934751i	$0.615623\pi$
$948$	−6.95668	−0.225942
$949$	9.64923	0.313227
$950$	−0.623909	−0.0202423
$951$	−24.8308	−0.805194
$952$	0	0
$953$	4.42292	0.143273	0.0716363	−	0.997431i	$-0.477178\pi$
$953$	4.42292	0.143273	0.0716363	+	0.997431i	$0.477178\pi$
$954$	2.83785	0.0918788
$955$	−50.2806	−1.62704
$956$	24.2047	0.782835
$957$	3.77568	0.122050
$958$	−39.4155	−1.27346
$959$	0	0
$960$	2.47363	0.0798359
$961$	−26.9733	−0.870106
$962$	0.480818	0.0155022
$963$	−2.81900	−0.0908411
$964$	−15.3083	−0.493048
$965$	−32.3453	−1.04123
$966$	0	0
$967$	17.1894	0.552773	0.276386	−	0.961047i	$-0.410863\pi$
$967$	17.1894	0.552773	0.276386	+	0.961047i	$0.410863\pi$
$968$	1.00000	0.0321412
$969$	−3.70371	−0.118980
$970$	2.91038	0.0934467
$971$	−25.4614	−0.817094	−0.408547	−	0.912737i	$-0.633964\pi$
$971$	−25.4614	−0.817094	−0.408547	+	0.912737i	$0.633964\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	23.1551	0.741937
$975$	−3.39146	−0.108614
$976$	−3.19932	−0.102408
$977$	16.9143	0.541136	0.270568	−	0.962701i	$-0.412789\pi$
$977$	16.9143	0.541136	0.270568	+	0.962701i	$0.412789\pi$
$978$	8.33609	0.266559
$979$	6.62558	0.211754
$980$	0	0
$981$	−20.5478	−0.656042
$982$	−4.47530	−0.142812
$983$	20.3763	0.649902	0.324951	−	0.945731i	$-0.394652\pi$
$983$	20.3763	0.649902	0.324951	+	0.945731i	$0.394652\pi$
$984$	5.93207	0.189107
$985$	−9.40370	−0.299627
$986$	25.0768	0.798608
$987$	0	0
$988$	1.69038	0.0537782
$989$	−11.5514	−0.367312
$990$	2.47363	0.0786170
$991$	35.1482	1.11652	0.558260	−	0.829666i	$-0.311469\pi$
$991$	35.1482	1.11652	0.558260	+	0.829666i	$0.311469\pi$
$992$	−2.00666	−0.0637116
$993$	21.2669	0.674883
$994$	0	0
$995$	−16.9962	−0.538817
$996$	−4.59744	−0.145676
$997$	43.8660	1.38925	0.694625	−	0.719372i	$-0.255571\pi$
$997$	43.8660	1.38925	0.694625	+	0.719372i	$0.255571\pi$
$998$	−16.7727	−0.530931
$999$	−0.158619	−0.00501849

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3234.2.a.bm.1.3	yes	4
3.2	odd	2		9702.2.a.dz.1.2		4
7.6	odd	2		3234.2.a.bl.1.2	✓	4
21.20	even	2		9702.2.a.ea.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3234.2.a.bl.1.2	✓	4	7.6	odd	2
3234.2.a.bm.1.3	yes	4	1.1	even	1	trivial
9702.2.a.dz.1.2		4	3.2	odd	2
9702.2.a.ea.1.3		4	21.20	even	2

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:	\( N \)	\(=\)	\( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3234.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.47363 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.47363 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +2.47363 q^{10} +1.00000 q^{11} +1.00000 q^{12} -3.03127 q^{13} +2.47363 q^{15} +1.00000 q^{16} +6.64167 q^{17} +1.00000 q^{18} -0.557647 q^{19} +2.47363 q^{20} +1.00000 q^{22} -2.66981 q^{23} +1.00000 q^{24} +1.11882 q^{25} -3.03127 q^{26} +1.00000 q^{27} +3.77568 q^{29} +2.47363 q^{30} -2.00666 q^{31} +1.00000 q^{32} +1.00000 q^{33} +6.64167 q^{34} +1.00000 q^{36} -0.158619 q^{37} -0.557647 q^{38} -3.03127 q^{39} +2.47363 q^{40} +5.93207 q^{41} +4.32666 q^{43} +1.00000 q^{44} +2.47363 q^{45} -2.66981 q^{46} +7.38607 q^{47} +1.00000 q^{48} +1.11882 q^{50} +6.64167 q^{51} -3.03127 q^{52} +2.83785 q^{53} +1.00000 q^{54} +2.47363 q^{55} -0.557647 q^{57} +3.77568 q^{58} +1.48881 q^{59} +2.47363 q^{60} -3.19932 q^{61} -2.00666 q^{62} +1.00000 q^{64} -7.49824 q^{65} +1.00000 q^{66} -11.2739 q^{67} +6.64167 q^{68} -2.66981 q^{69} -11.0098 q^{71} +1.00000 q^{72} -3.18323 q^{73} -0.158619 q^{74} +1.11882 q^{75} -0.557647 q^{76} -3.03127 q^{78} -6.95668 q^{79} +2.47363 q^{80} +1.00000 q^{81} +5.93207 q^{82} -4.59744 q^{83} +16.4290 q^{85} +4.32666 q^{86} +3.77568 q^{87} +1.00000 q^{88} +6.62558 q^{89} +2.47363 q^{90} -2.66981 q^{92} -2.00666 q^{93} +7.38607 q^{94} -1.37941 q^{95} +1.00000 q^{96} +1.17656 q^{97} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{5} + 4 q^{6} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 4 * q^5 + 4 * q^6 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{5} + 4 q^{6} + 4 q^{8} + 4 q^{9} + 4 q^{10} + 4 q^{11} + 4 q^{12} + 8 q^{13} + 4 q^{15} + 4 q^{16} + 4 q^{17} + 4 q^{18} + 12 q^{19} + 4 q^{20} + 4 q^{22} - 8 q^{23} + 4 q^{24} + 4 q^{25} + 8 q^{26} + 4 q^{27} - 8 q^{29} + 4 q^{30} + 4 q^{31} + 4 q^{32} + 4 q^{33} + 4 q^{34} + 4 q^{36} + 8 q^{37} + 12 q^{38} + 8 q^{39} + 4 q^{40} + 12 q^{41} - 8 q^{43} + 4 q^{44} + 4 q^{45} - 8 q^{46} + 4 q^{47} + 4 q^{48} + 4 q^{50} + 4 q^{51} + 8 q^{52} - 8 q^{53} + 4 q^{54} + 4 q^{55} + 12 q^{57} - 8 q^{58} + 4 q^{60} + 24 q^{61} + 4 q^{62} + 4 q^{64} - 16 q^{65} + 4 q^{66} - 8 q^{67} + 4 q^{68} - 8 q^{69} + 8 q^{71} + 4 q^{72} + 4 q^{73} + 8 q^{74} + 4 q^{75} + 12 q^{76} + 8 q^{78} - 8 q^{79} + 4 q^{80} + 4 q^{81} + 12 q^{82} + 4 q^{83} - 8 q^{85} - 8 q^{86} - 8 q^{87} + 4 q^{88} + 24 q^{89} + 4 q^{90} - 8 q^{92} + 4 q^{93} + 4 q^{94} + 8 q^{95} + 4 q^{96} + 4 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 4 * q^5 + 4 * q^6 + 4 * q^8 + 4 * q^9 + 4 * q^10 + 4 * q^11 + 4 * q^12 + 8 * q^13 + 4 * q^15 + 4 * q^16 + 4 * q^17 + 4 * q^18 + 12 * q^19 + 4 * q^20 + 4 * q^22 - 8 * q^23 + 4 * q^24 + 4 * q^25 + 8 * q^26 + 4 * q^27 - 8 * q^29 + 4 * q^30 + 4 * q^31 + 4 * q^32 + 4 * q^33 + 4 * q^34 + 4 * q^36 + 8 * q^37 + 12 * q^38 + 8 * q^39 + 4 * q^40 + 12 * q^41 - 8 * q^43 + 4 * q^44 + 4 * q^45 - 8 * q^46 + 4 * q^47 + 4 * q^48 + 4 * q^50 + 4 * q^51 + 8 * q^52 - 8 * q^53 + 4 * q^54 + 4 * q^55 + 12 * q^57 - 8 * q^58 + 4 * q^60 + 24 * q^61 + 4 * q^62 + 4 * q^64 - 16 * q^65 + 4 * q^66 - 8 * q^67 + 4 * q^68 - 8 * q^69 + 8 * q^71 + 4 * q^72 + 4 * q^73 + 8 * q^74 + 4 * q^75 + 12 * q^76 + 8 * q^78 - 8 * q^79 + 4 * q^80 + 4 * q^81 + 12 * q^82 + 4 * q^83 - 8 * q^85 - 8 * q^86 - 8 * q^87 + 4 * q^88 + 24 * q^89 + 4 * q^90 - 8 * q^92 + 4 * q^93 + 4 * q^94 + 8 * q^95 + 4 * q^96 + 4 * q^99

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