LMFDB - Embedded newform 6027.2.a.bd.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6027, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6027 = 3 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6027.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.1258372982$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{9} - 11x^{8} + 56x^{7} + 26x^{6} - 266x^{5} + 52x^{4} + 526x^{3} - 255x^{2} - 372x + 239 $ x^10 - 4x^9 - 11x^8 + 56x^7 + 26x^6 - 266x^5 + 52x^4 + 526x^3 - 255x^2 - 372*x + 239
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.49626$ of defining polynomial
Character	$\chi$	$=$	6027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.49626 q^{2} -1.00000 q^{3} +0.238800 q^{4} +0.660548 q^{5} +1.49626 q^{6} +2.63522 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.49626 q^{2} -1.00000 q^{3} +0.238800 q^{4} +0.660548 q^{5} +1.49626 q^{6} +2.63522 q^{8} +1.00000 q^{9} -0.988352 q^{10} +3.09821 q^{11} -0.238800 q^{12} -5.33510 q^{13} -0.660548 q^{15} -4.42057 q^{16} +2.12319 q^{17} -1.49626 q^{18} -6.27752 q^{19} +0.157739 q^{20} -4.63574 q^{22} +4.18993 q^{23} -2.63522 q^{24} -4.56368 q^{25} +7.98271 q^{26} -1.00000 q^{27} +8.89019 q^{29} +0.988352 q^{30} -2.86669 q^{31} +1.34390 q^{32} -3.09821 q^{33} -3.17684 q^{34} +0.238800 q^{36} -3.80939 q^{37} +9.39282 q^{38} +5.33510 q^{39} +1.74069 q^{40} -1.00000 q^{41} +5.14260 q^{43} +0.739853 q^{44} +0.660548 q^{45} -6.26923 q^{46} -8.27146 q^{47} +4.42057 q^{48} +6.82846 q^{50} -2.12319 q^{51} -1.27402 q^{52} -1.81902 q^{53} +1.49626 q^{54} +2.04652 q^{55} +6.27752 q^{57} -13.3021 q^{58} +5.79848 q^{59} -0.157739 q^{60} -3.86770 q^{61} +4.28932 q^{62} +6.83032 q^{64} -3.52409 q^{65} +4.63574 q^{66} +9.83411 q^{67} +0.507017 q^{68} -4.18993 q^{69} +3.39808 q^{71} +2.63522 q^{72} +3.16879 q^{73} +5.69985 q^{74} +4.56368 q^{75} -1.49907 q^{76} -7.98271 q^{78} -4.71484 q^{79} -2.92000 q^{80} +1.00000 q^{81} +1.49626 q^{82} -1.57684 q^{83} +1.40246 q^{85} -7.69468 q^{86} -8.89019 q^{87} +8.16446 q^{88} -3.08183 q^{89} -0.988352 q^{90} +1.00055 q^{92} +2.86669 q^{93} +12.3763 q^{94} -4.14660 q^{95} -1.34390 q^{96} +11.2074 q^{97} +3.09821 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{2} - 10 q^{3} + 18 q^{4} - 6 q^{5} - 4 q^{6} + 12 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q + 4 * q^2 - 10 * q^3 + 18 * q^4 - 6 * q^5 - 4 * q^6 + 12 * q^8 + 10 * q^9	$ 10 q + 4 q^{2} - 10 q^{3} + 18 q^{4} - 6 q^{5} - 4 q^{6} + 12 q^{8} + 10 q^{9} - 2 q^{10} - 2 q^{11} - 18 q^{12} + 6 q^{15} + 14 q^{16} - 8 q^{17} + 4 q^{18} - 6 q^{19} - 20 q^{20} + 2 q^{22} - 12 q^{24} + 10 q^{25} - 16 q^{26} - 10 q^{27} + 16 q^{29} + 2 q^{30} - 2 q^{31} + 38 q^{32} + 2 q^{33} + 4 q^{34} + 18 q^{36} + 24 q^{37} + 26 q^{38} - 40 q^{40} - 10 q^{41} + 8 q^{43} - 8 q^{44} - 6 q^{45} + 4 q^{46} + 8 q^{47} - 14 q^{48} + 44 q^{50} + 8 q^{51} + 30 q^{52} + 24 q^{53} - 4 q^{54} + 6 q^{57} - 14 q^{58} - 6 q^{59} + 20 q^{60} + 14 q^{61} + 2 q^{62} + 86 q^{64} + 28 q^{65} - 2 q^{66} + 26 q^{67} + 6 q^{68} + 14 q^{71} + 12 q^{72} + 36 q^{73} + 18 q^{74} - 10 q^{75} + 32 q^{76} + 16 q^{78} + 20 q^{79} - 70 q^{80} + 10 q^{81} - 4 q^{82} - 40 q^{83} + 24 q^{85} - 36 q^{86} - 16 q^{87} + 14 q^{88} - 2 q^{89} - 2 q^{90} + 8 q^{92} + 2 q^{93} + 54 q^{94} - 24 q^{95} - 38 q^{96} - 16 q^{97} - 2 q^{99}+O(q^{100}) $ 10 * q + 4 * q^2 - 10 * q^3 + 18 * q^4 - 6 * q^5 - 4 * q^6 + 12 * q^8 + 10 * q^9 - 2 * q^10 - 2 * q^11 - 18 * q^12 + 6 * q^15 + 14 * q^16 - 8 * q^17 + 4 * q^18 - 6 * q^19 - 20 * q^20 + 2 * q^22 - 12 * q^24 + 10 * q^25 - 16 * q^26 - 10 * q^27 + 16 * q^29 + 2 * q^30 - 2 * q^31 + 38 * q^32 + 2 * q^33 + 4 * q^34 + 18 * q^36 + 24 * q^37 + 26 * q^38 - 40 * q^40 - 10 * q^41 + 8 * q^43 - 8 * q^44 - 6 * q^45 + 4 * q^46 + 8 * q^47 - 14 * q^48 + 44 * q^50 + 8 * q^51 + 30 * q^52 + 24 * q^53 - 4 * q^54 + 6 * q^57 - 14 * q^58 - 6 * q^59 + 20 * q^60 + 14 * q^61 + 2 * q^62 + 86 * q^64 + 28 * q^65 - 2 * q^66 + 26 * q^67 + 6 * q^68 + 14 * q^71 + 12 * q^72 + 36 * q^73 + 18 * q^74 - 10 * q^75 + 32 * q^76 + 16 * q^78 + 20 * q^79 - 70 * q^80 + 10 * q^81 - 4 * q^82 - 40 * q^83 + 24 * q^85 - 36 * q^86 - 16 * q^87 + 14 * q^88 - 2 * q^89 - 2 * q^90 + 8 * q^92 + 2 * q^93 + 54 * q^94 - 24 * q^95 - 38 * q^96 - 16 * 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 $

$2$	−1.49626	−1.05802	−0.529008	−	0.848617i	$-0.677436\pi$
$2$	−1.49626	−1.05802	−0.529008	+	0.848617i	$0.677436\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.238800	0.119400
$5$	0.660548	0.295406	0.147703	−	0.989032i	$-0.452812\pi$
$5$	0.660548	0.295406	0.147703	+	0.989032i	$0.452812\pi$
$6$	1.49626	0.610846
$7$	0	0
$7$	0	0
$8$	2.63522	0.931690
$9$	1.00000	0.333333
$10$	−0.988352	−0.312544
$11$	3.09821	0.934146	0.467073	−	0.884219i	$-0.345309\pi$
$11$	3.09821	0.934146	0.467073	+	0.884219i	$0.345309\pi$
$12$	−0.238800	−0.0689356
$13$	−5.33510	−1.47969	−0.739846	−	0.672776i	$-0.765102\pi$
$13$	−5.33510	−1.47969	−0.739846	+	0.672776i	$0.765102\pi$
$14$	0	0
$15$	−0.660548	−0.170553
$16$	−4.42057	−1.10514
$17$	2.12319	0.514948	0.257474	−	0.966285i	$-0.417110\pi$
$17$	2.12319	0.514948	0.257474	+	0.966285i	$0.417110\pi$
$18$	−1.49626	−0.352672
$19$	−6.27752	−1.44016	−0.720081	−	0.693890i	$-0.755896\pi$
$19$	−6.27752	−1.44016	−0.720081	+	0.693890i	$0.755896\pi$
$20$	0.157739	0.0352714
$21$	0	0
$22$	−4.63574	−0.988342
$23$	4.18993	0.873660	0.436830	−	0.899544i	$-0.356101\pi$
$23$	4.18993	0.873660	0.436830	+	0.899544i	$0.356101\pi$
$24$	−2.63522	−0.537911
$25$	−4.56368	−0.912735
$26$	7.98271	1.56554
$27$	−1.00000	−0.192450
$28$	0	0
$29$	8.89019	1.65087	0.825434	−	0.564499i	$-0.190931\pi$
$29$	8.89019	1.65087	0.825434	+	0.564499i	$0.190931\pi$
$30$	0.988352	0.180448
$31$	−2.86669	−0.514873	−0.257436	−	0.966295i	$-0.582878\pi$
$31$	−2.86669	−0.514873	−0.257436	+	0.966295i	$0.582878\pi$
$32$	1.34390	0.237571
$33$	−3.09821	−0.539329
$34$	−3.17684	−0.544824
$35$	0	0
$36$	0.238800	0.0398000
$37$	−3.80939	−0.626260	−0.313130	−	0.949710i	$-0.601378\pi$
$37$	−3.80939	−0.626260	−0.313130	+	0.949710i	$0.601378\pi$
$38$	9.39282	1.52372
$39$	5.33510	0.854300
$40$	1.74069	0.275227
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	5.14260	0.784239	0.392120	−	0.919914i	$-0.371742\pi$
$43$	5.14260	0.784239	0.392120	+	0.919914i	$0.371742\pi$
$44$	0.739853	0.111537
$45$	0.660548	0.0984686
$46$	−6.26923	−0.924347
$47$	−8.27146	−1.20652	−0.603258	−	0.797546i	$-0.706131\pi$
$47$	−8.27146	−1.20652	−0.603258	+	0.797546i	$0.706131\pi$
$48$	4.42057	0.638055
$49$	0	0
$50$	6.82846	0.965690
$51$	−2.12319	−0.297305
$52$	−1.27402	−0.176675
$53$	−1.81902	−0.249861	−0.124931	−	0.992165i	$-0.539871\pi$
$53$	−1.81902	−0.249861	−0.124931	+	0.992165i	$0.539871\pi$
$54$	1.49626	0.203615
$55$	2.04652	0.275952
$56$	0	0
$57$	6.27752	0.831478
$58$	−13.3021	−1.74665
$59$	5.79848	0.754897	0.377449	−	0.926031i	$-0.376801\pi$
$59$	5.79848	0.754897	0.377449	+	0.926031i	$0.376801\pi$
$60$	−0.157739	−0.0203640
$61$	−3.86770	−0.495209	−0.247604	−	0.968861i	$-0.579643\pi$
$61$	−3.86770	−0.495209	−0.247604	+	0.968861i	$0.579643\pi$
$62$	4.28932	0.544744
$63$	0	0
$64$	6.83032	0.853790
$65$	−3.52409	−0.437110
$66$	4.63574	0.570620
$67$	9.83411	1.20143	0.600714	−	0.799464i	$-0.294883\pi$
$67$	9.83411	1.20143	0.600714	+	0.799464i	$0.294883\pi$
$68$	0.507017	0.0614848
$69$	−4.18993	−0.504408
$70$	0	0
$71$	3.39808	0.403278	0.201639	−	0.979460i	$-0.435373\pi$
$71$	3.39808	0.403278	0.201639	+	0.979460i	$0.435373\pi$
$72$	2.63522	0.310563
$73$	3.16879	0.370879	0.185440	−	0.982656i	$-0.440629\pi$
$73$	3.16879	0.370879	0.185440	+	0.982656i	$0.440629\pi$
$74$	5.69985	0.662594
$75$	4.56368	0.526968
$76$	−1.49907	−0.171955
$77$	0	0
$78$	−7.98271	−0.903864
$79$	−4.71484	−0.530461	−0.265231	−	0.964185i	$-0.585448\pi$
$79$	−4.71484	−0.530461	−0.265231	+	0.964185i	$0.585448\pi$
$80$	−2.92000	−0.326466
$81$	1.00000	0.111111
$82$	1.49626	0.165234
$83$	−1.57684	−0.173081	−0.0865406	−	0.996248i	$-0.527581\pi$
$83$	−1.57684	−0.173081	−0.0865406	+	0.996248i	$0.527581\pi$
$84$	0	0
$85$	1.40246	0.152119
$86$	−7.69468	−0.829738
$87$	−8.89019	−0.953129
$88$	8.16446	0.870334
$89$	−3.08183	−0.326673	−0.163337	−	0.986570i	$-0.552226\pi$
$89$	−3.08183	−0.326673	−0.163337	+	0.986570i	$0.552226\pi$
$90$	−0.988352	−0.104181
$91$	0	0
$92$	1.00055	0.104315
$93$	2.86669	0.297262
$94$	12.3763	1.27651
$95$	−4.14660	−0.425432
$96$	−1.34390	−0.137162
$97$	11.2074	1.13794	0.568970	−	0.822358i	$-0.307342\pi$
$97$	11.2074	1.13794	0.568970	+	0.822358i	$0.307342\pi$
$98$	0	0
$99$	3.09821	0.311382
$100$	−1.08981	−0.108981
$101$	14.5748	1.45024	0.725122	−	0.688621i	$-0.241784\pi$
$101$	14.5748	1.45024	0.725122	+	0.688621i	$0.241784\pi$
$102$	3.17684	0.314554
$103$	8.79588	0.866684	0.433342	−	0.901230i	$-0.357334\pi$
$103$	8.79588	0.866684	0.433342	+	0.901230i	$0.357334\pi$
$104$	−14.0592	−1.37861
$105$	0	0
$106$	2.72173	0.264357
$107$	10.2572	0.991603	0.495801	−	0.868436i	$-0.334874\pi$
$107$	10.2572	0.991603	0.495801	+	0.868436i	$0.334874\pi$
$108$	−0.238800	−0.0229785
$109$	−10.0836	−0.965834	−0.482917	−	0.875666i	$-0.660423\pi$
$109$	−10.0836	−0.965834	−0.482917	+	0.875666i	$0.660423\pi$
$110$	−3.06212	−0.291962
$111$	3.80939	0.361571
$112$	0	0
$113$	4.56690	0.429618	0.214809	−	0.976656i	$-0.431087\pi$
$113$	4.56690	0.429618	0.214809	+	0.976656i	$0.431087\pi$
$114$	−9.39282	−0.879718
$115$	2.76765	0.258084
$116$	2.12298	0.197113
$117$	−5.33510	−0.493231
$118$	−8.67604	−0.798694
$119$	0	0
$120$	−1.74069	−0.158902
$121$	−1.40109	−0.127372
$122$	5.78710	0.523939
$123$	1.00000	0.0901670
$124$	−0.684566	−0.0614758
$125$	−6.31726	−0.565033
$126$	0	0
$127$	0.538660	0.0477984	0.0238992	−	0.999714i	$-0.492392\pi$
$127$	0.538660	0.0477984	0.0238992	+	0.999714i	$0.492392\pi$
$128$	−12.9078	−1.14089
$129$	−5.14260	−0.452781
$130$	5.27296	0.462469
$131$	−5.01305	−0.437992	−0.218996	−	0.975726i	$-0.570278\pi$
$131$	−5.01305	−0.437992	−0.218996	+	0.975726i	$0.570278\pi$
$132$	−0.739853	−0.0643959
$133$	0	0
$134$	−14.7144	−1.27113
$135$	−0.660548	−0.0568509
$136$	5.59505	0.479772
$137$	−9.78020	−0.835579	−0.417790	−	0.908544i	$-0.637195\pi$
$137$	−9.78020	−0.835579	−0.417790	+	0.908544i	$0.637195\pi$
$138$	6.26923	0.533672
$139$	0.361134	0.0306310	0.0153155	−	0.999883i	$-0.495125\pi$
$139$	0.361134	0.0306310	0.0153155	+	0.999883i	$0.495125\pi$
$140$	0	0
$141$	8.27146	0.696582
$142$	−5.08442	−0.426675
$143$	−16.5293	−1.38225
$144$	−4.42057	−0.368381
$145$	5.87239	0.487676
$146$	−4.74134	−0.392396
$147$	0	0
$148$	−0.909682	−0.0747754
$149$	−15.3031	−1.25368	−0.626841	−	0.779147i	$-0.715652\pi$
$149$	−15.3031	−1.25368	−0.626841	+	0.779147i	$0.715652\pi$
$150$	−6.82846	−0.557541
$151$	−5.10934	−0.415793	−0.207896	−	0.978151i	$-0.566662\pi$
$151$	−5.10934	−0.415793	−0.207896	+	0.978151i	$0.566662\pi$
$152$	−16.5426	−1.34178
$153$	2.12319	0.171649
$154$	0	0
$155$	−1.89359	−0.152096
$156$	1.27402	0.102003
$157$	7.19343	0.574098	0.287049	−	0.957916i	$-0.407326\pi$
$157$	7.19343	0.574098	0.287049	+	0.957916i	$0.407326\pi$
$158$	7.05464	0.561237
$159$	1.81902	0.144257
$160$	0.887713	0.0701798
$161$	0	0
$162$	−1.49626	−0.117557
$163$	−15.4887	−1.21317	−0.606584	−	0.795020i	$-0.707461\pi$
$163$	−15.4887	−1.21317	−0.606584	+	0.795020i	$0.707461\pi$
$164$	−0.238800	−0.0186471
$165$	−2.04652	−0.159321
$166$	2.35937	0.183123
$167$	6.19238	0.479181	0.239591	−	0.970874i	$-0.422987\pi$
$167$	6.19238	0.479181	0.239591	+	0.970874i	$0.422987\pi$
$168$	0	0
$169$	15.4633	1.18949
$170$	−2.09845	−0.160944
$171$	−6.27752	−0.480054
$172$	1.22805	0.0936381
$173$	−8.85743	−0.673418	−0.336709	−	0.941609i	$-0.609314\pi$
$173$	−8.85743	−0.673418	−0.336709	+	0.941609i	$0.609314\pi$
$174$	13.3021	1.00843
$175$	0	0
$176$	−13.6959	−1.03237
$177$	−5.79848	−0.435840
$178$	4.61122	0.345626
$179$	12.4410	0.929881	0.464940	−	0.885342i	$-0.346076\pi$
$179$	12.4410	0.929881	0.464940	+	0.885342i	$0.346076\pi$
$180$	0.157739	0.0117571
$181$	23.2797	1.73036	0.865182	−	0.501459i	$-0.167203\pi$
$181$	23.2797	1.73036	0.865182	+	0.501459i	$0.167203\pi$
$182$	0	0
$183$	3.86770	0.285909
$184$	11.0414	0.813980
$185$	−2.51628	−0.185001
$186$	−4.28932	−0.314508
$187$	6.57808	0.481037
$188$	−1.97522	−0.144058
$189$	0	0
$190$	6.20440	0.450115
$191$	−19.2557	−1.39330	−0.696648	−	0.717413i	$-0.745326\pi$
$191$	−19.2557	−1.39330	−0.696648	+	0.717413i	$0.745326\pi$
$192$	−6.83032	−0.492936
$193$	−1.18650	−0.0854063	−0.0427031	−	0.999088i	$-0.513597\pi$
$193$	−1.18650	−0.0854063	−0.0427031	+	0.999088i	$0.513597\pi$
$194$	−16.7692	−1.20396
$195$	3.52409	0.252365
$196$	0	0
$197$	4.06824	0.289850	0.144925	−	0.989443i	$-0.453706\pi$
$197$	4.06824	0.289850	0.144925	+	0.989443i	$0.453706\pi$
$198$	−4.63574	−0.329447
$199$	−18.4988	−1.31134	−0.655672	−	0.755046i	$-0.727614\pi$
$199$	−18.4988	−1.31134	−0.655672	+	0.755046i	$0.727614\pi$
$200$	−12.0263	−0.850386
$201$	−9.83411	−0.693644
$202$	−21.8077	−1.53438
$203$	0	0
$204$	−0.507017	−0.0354983
$205$	−0.660548	−0.0461346
$206$	−13.1609	−0.916966
$207$	4.18993	0.291220
$208$	23.5842	1.63527
$209$	−19.4491	−1.34532
$210$	0	0
$211$	−12.9411	−0.890900	−0.445450	−	0.895307i	$-0.646956\pi$
$211$	−12.9411	−0.890900	−0.445450	+	0.895307i	$0.646956\pi$
$212$	−0.434381	−0.0298334
$213$	−3.39808	−0.232833
$214$	−15.3475	−1.04913
$215$	3.39693	0.231669
$216$	−2.63522	−0.179304
$217$	0	0
$218$	15.0877	1.02187
$219$	−3.16879	−0.214127
$220$	0.488708	0.0329487
$221$	−11.3274	−0.761964
$222$	−5.69985	−0.382549
$223$	5.68545	0.380726	0.190363	−	0.981714i	$-0.439033\pi$
$223$	5.68545	0.380726	0.190363	+	0.981714i	$0.439033\pi$
$224$	0	0
$225$	−4.56368	−0.304245
$226$	−6.83327	−0.454543
$227$	−9.55024	−0.633872	−0.316936	−	0.948447i	$-0.602654\pi$
$227$	−9.55024	−0.633872	−0.316936	+	0.948447i	$0.602654\pi$
$228$	1.49907	0.0992785
$229$	−5.66080	−0.374076	−0.187038	−	0.982353i	$-0.559889\pi$
$229$	−5.66080	−0.374076	−0.187038	+	0.982353i	$0.559889\pi$
$230$	−4.14112	−0.273058
$231$	0	0
$232$	23.4276	1.53810
$233$	−7.02484	−0.460213	−0.230106	−	0.973165i	$-0.573907\pi$
$233$	−7.02484	−0.460213	−0.230106	+	0.973165i	$0.573907\pi$
$234$	7.98271	0.521846
$235$	−5.46369	−0.356412
$236$	1.38468	0.0901347
$237$	4.71484	0.306262
$238$	0	0
$239$	28.6556	1.85358	0.926789	−	0.375583i	$-0.122557\pi$
$239$	28.6556	1.85358	0.926789	+	0.375583i	$0.122557\pi$
$240$	2.92000	0.188485
$241$	−26.5920	−1.71294	−0.856472	−	0.516193i	$-0.827349\pi$
$241$	−26.5920	−1.71294	−0.856472	+	0.516193i	$0.827349\pi$
$242$	2.09639	0.134761
$243$	−1.00000	−0.0641500
$244$	−0.923608	−0.0591279
$245$	0	0
$246$	−1.49626	−0.0953982
$247$	33.4912	2.13100
$248$	−7.55435	−0.479702
$249$	1.57684	0.0999284
$250$	9.45228	0.597815
$251$	−5.59269	−0.353007	−0.176504	−	0.984300i	$-0.556479\pi$
$251$	−5.59269	−0.353007	−0.176504	+	0.984300i	$0.556479\pi$
$252$	0	0
$253$	12.9813	0.816126
$254$	−0.805977	−0.0505715
$255$	−1.40246	−0.0878258
$256$	5.65274	0.353297
$257$	18.2269	1.13696	0.568482	−	0.822696i	$-0.307531\pi$
$257$	18.2269	1.13696	0.568482	+	0.822696i	$0.307531\pi$
$258$	7.69468	0.479050
$259$	0	0
$260$	−0.841553	−0.0521909
$261$	8.89019	0.550289
$262$	7.50084	0.463403
$263$	20.7807	1.28139	0.640695	−	0.767796i	$-0.278646\pi$
$263$	20.7807	1.28139	0.640695	+	0.767796i	$0.278646\pi$
$264$	−8.16446	−0.502488
$265$	−1.20155	−0.0738105
$266$	0	0
$267$	3.08183	0.188605
$268$	2.34838	0.143450
$269$	7.54533	0.460047	0.230023	−	0.973185i	$-0.426120\pi$
$269$	7.54533	0.460047	0.230023	+	0.973185i	$0.426120\pi$
$270$	0.988352	0.0601492
$271$	31.5336	1.91553	0.957766	−	0.287549i	$-0.0928403\pi$
$271$	31.5336	1.91553	0.957766	+	0.287549i	$0.0928403\pi$
$272$	−9.38570	−0.569092
$273$	0	0
$274$	14.6337	0.884057
$275$	−14.1392	−0.852628
$276$	−1.00055	−0.0602263
$277$	21.1032	1.26797	0.633983	−	0.773347i	$-0.281419\pi$
$277$	21.1032	1.26797	0.633983	+	0.773347i	$0.281419\pi$
$278$	−0.540351	−0.0324081
$279$	−2.86669	−0.171624
$280$	0	0
$281$	28.6757	1.71065	0.855326	−	0.518091i	$-0.173357\pi$
$281$	28.6757	1.71065	0.855326	+	0.518091i	$0.173357\pi$
$282$	−12.3763	−0.736996
$283$	−23.8753	−1.41924	−0.709619	−	0.704586i	$-0.751133\pi$
$283$	−23.8753	−1.41924	−0.709619	+	0.704586i	$0.751133\pi$
$284$	0.811461	0.0481514
$285$	4.14660	0.245624
$286$	24.7321	1.46244
$287$	0	0
$288$	1.34390	0.0791903
$289$	−12.4921	−0.734828
$290$	−8.78664	−0.515969
$291$	−11.2074	−0.656990
$292$	0.756707	0.0442829
$293$	−10.7712	−0.629262	−0.314631	−	0.949214i	$-0.601881\pi$
$293$	−10.7712	−0.629262	−0.314631	+	0.949214i	$0.601881\pi$
$294$	0	0
$295$	3.83017	0.223001
$296$	−10.0386	−0.583480
$297$	−3.09821	−0.179776
$298$	22.8975	1.32642
$299$	−22.3537	−1.29275
$300$	1.08981	0.0629200
$301$	0	0
$302$	7.64492	0.439916
$303$	−14.5748	−0.837298
$304$	27.7503	1.59159
$305$	−2.55480	−0.146288
$306$	−3.17684	−0.181608
$307$	−25.1906	−1.43771	−0.718853	−	0.695163i	$-0.755332\pi$
$307$	−25.1906	−1.43771	−0.718853	+	0.695163i	$0.755332\pi$
$308$	0	0
$309$	−8.79588	−0.500380
$310$	2.83330	0.160921
$311$	11.3282	0.642364	0.321182	−	0.947017i	$-0.395920\pi$
$311$	11.3282	0.642364	0.321182	+	0.947017i	$0.395920\pi$
$312$	14.0592	0.795943
$313$	18.5241	1.04704	0.523522	−	0.852012i	$-0.324618\pi$
$313$	18.5241	1.04704	0.523522	+	0.852012i	$0.324618\pi$
$314$	−10.7633	−0.607406
$315$	0	0
$316$	−1.12590	−0.0633371
$317$	34.5327	1.93955	0.969775	−	0.244001i	$-0.0784602\pi$
$317$	34.5327	1.93955	0.969775	+	0.244001i	$0.0784602\pi$
$318$	−2.72173	−0.152627
$319$	27.5437	1.54215
$320$	4.51175	0.252214
$321$	−10.2572	−0.572502
$322$	0	0
$323$	−13.3283	−0.741609
$324$	0.238800	0.0132667
$325$	24.3477	1.35057
$326$	23.1751	1.28355
$327$	10.0836	0.557625
$328$	−2.63522	−0.145506
$329$	0	0
$330$	3.06212	0.168564
$331$	3.36957	0.185208	0.0926042	−	0.995703i	$-0.470481\pi$
$331$	3.36957	0.185208	0.0926042	+	0.995703i	$0.470481\pi$
$332$	−0.376550	−0.0206659
$333$	−3.80939	−0.208753
$334$	−9.26543	−0.506982
$335$	6.49590	0.354909
$336$	0	0
$337$	8.68320	0.473004	0.236502	−	0.971631i	$-0.423999\pi$
$337$	8.68320	0.473004	0.236502	+	0.971631i	$0.423999\pi$
$338$	−23.1372	−1.25850
$339$	−4.56690	−0.248040
$340$	0.334909	0.0181630
$341$	−8.88161	−0.480966
$342$	9.39282	0.507906
$343$	0	0
$344$	13.5519	0.730668
$345$	−2.76765	−0.149005
$346$	13.2530	0.712487
$347$	4.77708	0.256447	0.128223	−	0.991745i	$-0.459073\pi$
$347$	4.77708	0.256447	0.128223	+	0.991745i	$0.459073\pi$
$348$	−2.12298	−0.113804
$349$	15.0031	0.803096	0.401548	−	0.915838i	$-0.368472\pi$
$349$	15.0031	0.803096	0.401548	+	0.915838i	$0.368472\pi$
$350$	0	0
$351$	5.33510	0.284767
$352$	4.16370	0.221926
$353$	28.9944	1.54322	0.771608	−	0.636098i	$-0.219453\pi$
$353$	28.9944	1.54322	0.771608	+	0.636098i	$0.219453\pi$
$354$	8.67604	0.461126
$355$	2.24459	0.119131
$356$	−0.735941	−0.0390048
$357$	0	0
$358$	−18.6149	−0.983830
$359$	33.6760	1.77735	0.888674	−	0.458539i	$-0.151627\pi$
$359$	33.6760	1.77735	0.888674	+	0.458539i	$0.151627\pi$
$360$	1.74069	0.0917422
$361$	20.4073	1.07407
$362$	−34.8325	−1.83075
$363$	1.40109	0.0735380
$364$	0	0
$365$	2.09314	0.109560
$366$	−5.78710	−0.302497
$367$	−3.87155	−0.202093	−0.101047	−	0.994882i	$-0.532219\pi$
$367$	−3.87155	−0.202093	−0.101047	+	0.994882i	$0.532219\pi$
$368$	−18.5219	−0.965520
$369$	−1.00000	−0.0520579
$370$	3.76502	0.195734
$371$	0	0
$372$	0.684566	0.0354931
$373$	−21.5800	−1.11737	−0.558686	−	0.829379i	$-0.688694\pi$
$373$	−21.5800	−1.11737	−0.558686	+	0.829379i	$0.688694\pi$
$374$	−9.84253	−0.508945
$375$	6.31726	0.326222
$376$	−21.7971	−1.12410
$377$	−47.4301	−2.44277
$378$	0	0
$379$	−37.2302	−1.91239	−0.956194	−	0.292733i	$-0.905435\pi$
$379$	−37.2302	−1.91239	−0.956194	+	0.292733i	$0.905435\pi$
$380$	−0.990209	−0.0507966
$381$	−0.538660	−0.0275964
$382$	28.8116	1.47413
$383$	16.3957	0.837782	0.418891	−	0.908036i	$-0.362419\pi$
$383$	16.3957	0.837782	0.418891	+	0.908036i	$0.362419\pi$
$384$	12.9078	0.658696
$385$	0	0
$386$	1.77532	0.0903613
$387$	5.14260	0.261413
$388$	2.67633	0.135870
$389$	12.0838	0.612675	0.306338	−	0.951923i	$-0.400896\pi$
$389$	12.0838	0.612675	0.306338	+	0.951923i	$0.400896\pi$
$390$	−5.27296	−0.267007
$391$	8.89599	0.449890
$392$	0	0
$393$	5.01305	0.252875
$394$	−6.08715	−0.306666
$395$	−3.11438	−0.156701
$396$	0.739853	0.0371790
$397$	23.2512	1.16694	0.583472	−	0.812133i	$-0.301694\pi$
$397$	23.2512	1.16694	0.583472	+	0.812133i	$0.301694\pi$
$398$	27.6790	1.38742
$399$	0	0
$400$	20.1741	1.00870
$401$	34.5041	1.72305	0.861527	−	0.507712i	$-0.169509\pi$
$401$	34.5041	1.72305	0.861527	+	0.507712i	$0.169509\pi$
$402$	14.7144	0.733888
$403$	15.2941	0.761853
$404$	3.48045	0.173159
$405$	0.660548	0.0328229
$406$	0	0
$407$	−11.8023	−0.585018
$408$	−5.59505	−0.276996
$409$	20.1694	0.997314	0.498657	−	0.866800i	$-0.333827\pi$
$409$	20.1694	0.997314	0.498657	+	0.866800i	$0.333827\pi$
$410$	0.988352	0.0488112
$411$	9.78020	0.482422
$412$	2.10046	0.103482
$413$	0	0
$414$	−6.26923	−0.308116
$415$	−1.04158	−0.0511292
$416$	−7.16987	−0.351532
$417$	−0.361134	−0.0176848
$418$	29.1009	1.42337
$419$	6.16617	0.301237	0.150619	−	0.988592i	$-0.451873\pi$
$419$	6.16617	0.301237	0.150619	+	0.988592i	$0.451873\pi$
$420$	0	0
$421$	−34.3500	−1.67412	−0.837059	−	0.547112i	$-0.815727\pi$
$421$	−34.3500	−1.67412	−0.837059	+	0.547112i	$0.815727\pi$
$422$	19.3632	0.942587
$423$	−8.27146	−0.402172
$424$	−4.79351	−0.232793
$425$	−9.68953	−0.470011
$426$	5.08442	0.246341
$427$	0	0
$428$	2.44942	0.118397
$429$	16.5293	0.798041
$430$	−5.08270	−0.245110
$431$	23.5197	1.13290	0.566452	−	0.824095i	$-0.308316\pi$
$431$	23.5197	1.13290	0.566452	+	0.824095i	$0.308316\pi$
$432$	4.42057	0.212685
$433$	−1.51112	−0.0726197	−0.0363099	−	0.999341i	$-0.511560\pi$
$433$	−1.51112	−0.0726197	−0.0363099	+	0.999341i	$0.511560\pi$
$434$	0	0
$435$	−5.87239	−0.281560
$436$	−2.40796	−0.115321
$437$	−26.3024	−1.25821
$438$	4.74134	0.226550
$439$	−34.0725	−1.62619	−0.813095	−	0.582131i	$-0.802219\pi$
$439$	−34.0725	−1.62619	−0.813095	+	0.582131i	$0.802219\pi$
$440$	5.39301	0.257102
$441$	0	0
$442$	16.9488	0.806171
$443$	8.70107	0.413400	0.206700	−	0.978404i	$-0.433728\pi$
$443$	8.70107	0.413400	0.206700	+	0.978404i	$0.433728\pi$
$444$	0.909682	0.0431716
$445$	−2.03569	−0.0965012
$446$	−8.50693	−0.402815
$447$	15.3031	0.723813
$448$	0	0
$449$	−9.67035	−0.456372	−0.228186	−	0.973618i	$-0.573279\pi$
$449$	−9.67035	−0.456372	−0.228186	+	0.973618i	$0.573279\pi$
$450$	6.82846	0.321897
$451$	−3.09821	−0.145889
$452$	1.09057	0.0512963
$453$	5.10934	0.240058
$454$	14.2897	0.670647
$455$	0	0
$456$	16.5426	0.774680
$457$	27.5623	1.28931	0.644654	−	0.764474i	$-0.277001\pi$
$457$	27.5623	1.28931	0.644654	+	0.764474i	$0.277001\pi$
$458$	8.47004	0.395779
$459$	−2.12319	−0.0991018
$460$	0.660914	0.0308153
$461$	42.2180	1.96629	0.983144	−	0.182834i	$-0.0585271\pi$
$461$	42.2180	1.96629	0.983144	+	0.182834i	$0.0585271\pi$
$462$	0	0
$463$	−6.96482	−0.323683	−0.161841	−	0.986817i	$-0.551743\pi$
$463$	−6.96482	−0.323683	−0.161841	+	0.986817i	$0.551743\pi$
$464$	−39.2998	−1.82445
$465$	1.89359	0.0878129
$466$	10.5110	0.486913
$467$	2.40284	0.111190	0.0555951	−	0.998453i	$-0.482294\pi$
$467$	2.40284	0.111190	0.0555951	+	0.998453i	$0.482294\pi$
$468$	−1.27402	−0.0588917
$469$	0	0
$470$	8.17511	0.377090
$471$	−7.19343	−0.331456
$472$	15.2802	0.703330
$473$	15.9329	0.732594
$474$	−7.05464	−0.324030
$475$	28.6486	1.31449
$476$	0	0
$477$	−1.81902	−0.0832871
$478$	−42.8763	−1.96112
$479$	−2.21831	−0.101357	−0.0506785	−	0.998715i	$-0.516138\pi$
$479$	−2.21831	−0.101357	−0.0506785	+	0.998715i	$0.516138\pi$
$480$	−0.887713	−0.0405184
$481$	20.3235	0.926672
$482$	39.7887	1.81232
$483$	0	0
$484$	−0.334580	−0.0152082
$485$	7.40302	0.336154
$486$	1.49626	0.0678718
$487$	−12.9873	−0.588513	−0.294256	−	0.955726i	$-0.595072\pi$
$487$	−12.9873	−0.588513	−0.294256	+	0.955726i	$0.595072\pi$
$488$	−10.1922	−0.461381
$489$	15.4887	0.700423
$490$	0	0
$491$	16.8996	0.762669	0.381335	−	0.924437i	$-0.375465\pi$
$491$	16.8996	0.762669	0.381335	+	0.924437i	$0.375465\pi$
$492$	0.238800	0.0107659
$493$	18.8755	0.850111
$494$	−50.1117	−2.25463
$495$	2.04652	0.0919840
$496$	12.6724	0.569008
$497$	0	0
$498$	−2.35937	−0.105726
$499$	40.5579	1.81562	0.907811	−	0.419380i	$-0.137753\pi$
$499$	40.5579	1.81562	0.907811	+	0.419380i	$0.137753\pi$
$500$	−1.50856	−0.0674649
$501$	−6.19238	−0.276655
$502$	8.36812	0.373488
$503$	−15.8284	−0.705754	−0.352877	−	0.935670i	$-0.614797\pi$
$503$	−15.8284	−0.705754	−0.352877	+	0.935670i	$0.614797\pi$
$504$	0	0
$505$	9.62733	0.428410
$506$	−19.4234	−0.863475
$507$	−15.4633	−0.686751
$508$	0.128632	0.00570712
$509$	−7.14004	−0.316477	−0.158238	−	0.987401i	$-0.550581\pi$
$509$	−7.14004	−0.316477	−0.158238	+	0.987401i	$0.550581\pi$
$510$	2.09845	0.0929211
$511$	0	0
$512$	17.3575	0.767101
$513$	6.27752	0.277159
$514$	−27.2723	−1.20293
$515$	5.81010	0.256023
$516$	−1.22805	−0.0540620
$517$	−25.6267	−1.12706
$518$	0	0
$519$	8.85743	0.388798
$520$	−9.28674	−0.407251
$521$	−24.2296	−1.06152	−0.530758	−	0.847523i	$-0.678093\pi$
$521$	−24.2296	−1.06152	−0.530758	+	0.847523i	$0.678093\pi$
$522$	−13.3021	−0.582215
$523$	13.5977	0.594585	0.297293	−	0.954786i	$-0.403916\pi$
$523$	13.5977	0.594585	0.297293	+	0.954786i	$0.403916\pi$
$524$	−1.19712	−0.0522963
$525$	0	0
$526$	−31.0933	−1.35573
$527$	−6.08652	−0.265133
$528$	13.6959	0.596036
$529$	−5.44451	−0.236718
$530$	1.79783	0.0780927
$531$	5.79848	0.251632
$532$	0	0
$533$	5.33510	0.231089
$534$	−4.61122	−0.199547
$535$	6.77538	0.292925
$536$	25.9150	1.11936
$537$	−12.4410	−0.536867
$538$	−11.2898	−0.486738
$539$	0	0
$540$	−0.157739	−0.00678799
$541$	11.2955	0.485631	0.242815	−	0.970073i	$-0.421929\pi$
$541$	11.2955	0.485631	0.242815	+	0.970073i	$0.421929\pi$
$542$	−47.1826	−2.02667
$543$	−23.2797	−0.999026
$544$	2.85336	0.122337
$545$	−6.66070	−0.285313
$546$	0	0
$547$	12.3658	0.528722	0.264361	−	0.964424i	$-0.414839\pi$
$547$	12.3658	0.528722	0.264361	+	0.964424i	$0.414839\pi$
$548$	−2.33551	−0.0997681
$549$	−3.86770	−0.165070
$550$	21.1560	0.902095
$551$	−55.8084	−2.37752
$552$	−11.0414	−0.469952
$553$	0	0
$554$	−31.5759	−1.34153
$555$	2.51628	0.106810
$556$	0.0862388	0.00365734
$557$	21.5422	0.912774	0.456387	−	0.889781i	$-0.349143\pi$
$557$	21.5422	0.912774	0.456387	+	0.889781i	$0.349143\pi$
$558$	4.28932	0.181581
$559$	−27.4363	−1.16043
$560$	0	0
$561$	−6.57808	−0.277727
$562$	−42.9064	−1.80990
$563$	46.1175	1.94362	0.971810	−	0.235766i	$-0.0757599\pi$
$563$	46.1175	1.94362	0.971810	+	0.235766i	$0.0757599\pi$
$564$	1.97522	0.0831719
$565$	3.01665	0.126912
$566$	35.7237	1.50158
$567$	0	0
$568$	8.95468	0.375730
$569$	−31.1225	−1.30472	−0.652361	−	0.757908i	$-0.726221\pi$
$569$	−31.1225	−1.30472	−0.652361	+	0.757908i	$0.726221\pi$
$570$	−6.20440	−0.259874
$571$	−13.2293	−0.553630	−0.276815	−	0.960923i	$-0.589279\pi$
$571$	−13.2293	−0.553630	−0.276815	+	0.960923i	$0.589279\pi$
$572$	−3.94719	−0.165040
$573$	19.2557	0.804420
$574$	0	0
$575$	−19.1215	−0.797421
$576$	6.83032	0.284597
$577$	16.6569	0.693435	0.346718	−	0.937970i	$-0.387296\pi$
$577$	16.6569	0.693435	0.346718	+	0.937970i	$0.387296\pi$
$578$	18.6914	0.777461
$579$	1.18650	0.0493093
$580$	1.40233	0.0582285
$581$	0	0
$582$	16.7692	0.695106
$583$	−5.63570	−0.233407
$584$	8.35045	0.345544
$585$	−3.52409	−0.145703
$586$	16.1166	0.665770
$587$	−15.3542	−0.633737	−0.316869	−	0.948469i	$-0.602631\pi$
$587$	−15.3542	−0.633737	−0.316869	+	0.948469i	$0.602631\pi$
$588$	0	0
$589$	17.9957	0.741501
$590$	−5.73094	−0.235939
$591$	−4.06824	−0.167345
$592$	16.8397	0.692107
$593$	−20.2824	−0.832898	−0.416449	−	0.909159i	$-0.636726\pi$
$593$	−20.2824	−0.832898	−0.416449	+	0.909159i	$0.636726\pi$
$594$	4.63574	0.190207
$595$	0	0
$596$	−3.65439	−0.149690
$597$	18.4988	0.757104
$598$	33.4470	1.36775
$599$	−18.2224	−0.744545	−0.372273	−	0.928123i	$-0.621421\pi$
$599$	−18.2224	−0.744545	−0.372273	+	0.928123i	$0.621421\pi$
$600$	12.0263	0.490971
$601$	−20.4858	−0.835635	−0.417818	−	0.908531i	$-0.637205\pi$
$601$	−20.4858	−0.835635	−0.417818	+	0.908531i	$0.637205\pi$
$602$	0	0
$603$	9.83411	0.400476
$604$	−1.22011	−0.0496456
$605$	−0.925485	−0.0376263
$606$	21.8077	0.885876
$607$	36.3234	1.47432	0.737160	−	0.675718i	$-0.236166\pi$
$607$	36.3234	1.47432	0.737160	+	0.675718i	$0.236166\pi$
$608$	−8.43639	−0.342141
$609$	0	0
$610$	3.82265	0.154775
$611$	44.1291	1.78527
$612$	0.507017	0.0204949
$613$	42.9039	1.73287	0.866436	−	0.499289i	$-0.166405\pi$
$613$	42.9039	1.73287	0.866436	+	0.499289i	$0.166405\pi$
$614$	37.6918	1.52112
$615$	0.660548	0.0266358
$616$	0	0
$617$	−25.1745	−1.01349	−0.506744	−	0.862097i	$-0.669151\pi$
$617$	−25.1745	−1.01349	−0.506744	+	0.862097i	$0.669151\pi$
$618$	13.1609	0.529411
$619$	4.05824	0.163114	0.0815571	−	0.996669i	$-0.474011\pi$
$619$	4.05824	0.163114	0.0815571	+	0.996669i	$0.474011\pi$
$620$	−0.452188	−0.0181603
$621$	−4.18993	−0.168136
$622$	−16.9500	−0.679632
$623$	0	0
$624$	−23.5842	−0.944125
$625$	18.6455	0.745821
$626$	−27.7169	−1.10779
$627$	19.4491	0.776722
$628$	1.71779	0.0685473
$629$	−8.08804	−0.322491
$630$	0	0
$631$	−1.73115	−0.0689160	−0.0344580	−	0.999406i	$-0.510970\pi$
$631$	−1.73115	−0.0689160	−0.0344580	+	0.999406i	$0.510970\pi$
$632$	−12.4246	−0.494225
$633$	12.9411	0.514361
$634$	−51.6700	−2.05208
$635$	0.355811	0.0141199
$636$	0.434381	0.0172243
$637$	0	0
$638$	−41.2126	−1.63162
$639$	3.39808	0.134426
$640$	−8.52618	−0.337027
$641$	14.5764	0.575734	0.287867	−	0.957670i	$-0.407054\pi$
$641$	14.5764	0.575734	0.287867	+	0.957670i	$0.407054\pi$
$642$	15.3475	0.605717
$643$	39.9886	1.57700	0.788498	−	0.615038i	$-0.210859\pi$
$643$	39.9886	1.57700	0.788498	+	0.615038i	$0.210859\pi$
$644$	0	0
$645$	−3.39693	−0.133754
$646$	19.9427	0.784635
$647$	−14.3355	−0.563587	−0.281794	−	0.959475i	$-0.590929\pi$
$647$	−14.3355	−0.563587	−0.281794	+	0.959475i	$0.590929\pi$
$648$	2.63522	0.103521
$649$	17.9649	0.705184
$650$	−36.4305	−1.42892
$651$	0	0
$652$	−3.69870	−0.144852
$653$	8.82415	0.345316	0.172658	−	0.984982i	$-0.444764\pi$
$653$	8.82415	0.345316	0.172658	+	0.984982i	$0.444764\pi$
$654$	−15.0877	−0.589976
$655$	−3.31136	−0.129386
$656$	4.42057	0.172594
$657$	3.16879	0.123626
$658$	0	0
$659$	7.61197	0.296520	0.148260	−	0.988948i	$-0.452633\pi$
$659$	7.61197	0.296520	0.148260	+	0.988948i	$0.452633\pi$
$660$	−0.488708	−0.0190229
$661$	19.7403	0.767810	0.383905	−	0.923373i	$-0.374579\pi$
$661$	19.7403	0.767810	0.383905	+	0.923373i	$0.374579\pi$
$662$	−5.04176	−0.195954
$663$	11.3274	0.439920
$664$	−4.15533	−0.161258
$665$	0	0
$666$	5.69985	0.220865
$667$	37.2493	1.44230
$668$	1.47874	0.0572142
$669$	−5.68545	−0.219812
$670$	−9.71956	−0.375499
$671$	−11.9830	−0.462597
$672$	0	0
$673$	30.7096	1.18377	0.591885	−	0.806023i	$-0.298384\pi$
$673$	30.7096	1.18377	0.591885	+	0.806023i	$0.298384\pi$
$674$	−12.9923	−0.500446
$675$	4.56368	0.175656
$676$	3.69265	0.142025
$677$	−20.7467	−0.797361	−0.398681	−	0.917090i	$-0.630532\pi$
$677$	−20.7467	−0.797361	−0.398681	+	0.917090i	$0.630532\pi$
$678$	6.83327	0.262430
$679$	0	0
$680$	3.69580	0.141727
$681$	9.55024	0.365966
$682$	13.2892	0.508871
$683$	45.6216	1.74566	0.872832	−	0.488021i	$-0.162281\pi$
$683$	45.6216	1.74566	0.872832	+	0.488021i	$0.162281\pi$
$684$	−1.49907	−0.0573185
$685$	−6.46029	−0.246835
$686$	0	0
$687$	5.66080	0.215973
$688$	−22.7332	−0.866697
$689$	9.70465	0.369718
$690$	4.14112	0.157650
$691$	45.0379	1.71332	0.856661	−	0.515880i	$-0.172535\pi$
$691$	45.0379	1.71332	0.856661	+	0.515880i	$0.172535\pi$
$692$	−2.11515	−0.0804061
$693$	0	0
$694$	−7.14776	−0.271325
$695$	0.238546	0.00904858
$696$	−23.4276	−0.888020
$697$	−2.12319	−0.0804214
$698$	−22.4485	−0.849689
$699$	7.02484	0.265704
$700$	0	0
$701$	23.4057	0.884019	0.442010	−	0.897010i	$-0.354266\pi$
$701$	23.4057	0.884019	0.442010	+	0.897010i	$0.354266\pi$
$702$	−7.98271	−0.301288
$703$	23.9135	0.901916
$704$	21.1618	0.797564
$705$	5.46369	0.205774
$706$	−43.3832	−1.63275
$707$	0	0
$708$	−1.38468	−0.0520393
$709$	−10.3575	−0.388984	−0.194492	−	0.980904i	$-0.562306\pi$
$709$	−10.3575	−0.388984	−0.194492	+	0.980904i	$0.562306\pi$
$710$	−3.35850	−0.126042
$711$	−4.71484	−0.176820
$712$	−8.12129	−0.304358
$713$	−12.0112	−0.449824
$714$	0	0
$715$	−10.9184	−0.408324
$716$	2.97090	0.111028
$717$	−28.6556	−1.07016
$718$	−50.3880	−1.88047
$719$	−51.6294	−1.92545	−0.962725	−	0.270481i	$-0.912817\pi$
$719$	−51.6294	−1.92545	−0.962725	+	0.270481i	$0.912817\pi$
$720$	−2.92000	−0.108822
$721$	0	0
$722$	−30.5347	−1.13638
$723$	26.5920	0.988969
$724$	5.55918	0.206605
$725$	−40.5720	−1.50680
$726$	−2.09639	−0.0778045
$727$	17.3926	0.645057	0.322528	−	0.946560i	$-0.395467\pi$
$727$	17.3926	0.645057	0.322528	+	0.946560i	$0.395467\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−3.13188	−0.115916
$731$	10.9187	0.403842
$732$	0.923608	0.0341375
$733$	42.4584	1.56824	0.784118	−	0.620612i	$-0.213116\pi$
$733$	42.4584	1.56824	0.784118	+	0.620612i	$0.213116\pi$
$734$	5.79286	0.213818
$735$	0	0
$736$	5.63086	0.207556
$737$	30.4681	1.12231
$738$	1.49626	0.0550782
$739$	−30.5690	−1.12450	−0.562249	−	0.826968i	$-0.690064\pi$
$739$	−30.5690	−1.12450	−0.562249	+	0.826968i	$0.690064\pi$
$740$	−0.600888	−0.0220891
$741$	−33.4912	−1.23033
$742$	0	0
$743$	−14.7084	−0.539599	−0.269799	−	0.962917i	$-0.586957\pi$
$743$	−14.7084	−0.539599	−0.269799	+	0.962917i	$0.586957\pi$
$744$	7.55435	0.276956
$745$	−10.1084	−0.370345
$746$	32.2894	1.18220
$747$	−1.57684	−0.0576937
$748$	1.57084	0.0574358
$749$	0	0
$750$	−9.45228	−0.345149
$751$	20.9598	0.764832	0.382416	−	0.923990i	$-0.375092\pi$
$751$	20.9598	0.764832	0.382416	+	0.923990i	$0.375092\pi$
$752$	36.5646	1.33337
$753$	5.59269	0.203809
$754$	70.9679	2.58450
$755$	−3.37497	−0.122828
$756$	0	0
$757$	−19.4602	−0.707293	−0.353647	−	0.935379i	$-0.615058\pi$
$757$	−19.4602	−0.707293	−0.353647	+	0.935379i	$0.615058\pi$
$758$	55.7062	2.02334
$759$	−12.9813	−0.471191
$760$	−10.9272	−0.396371
$761$	21.6665	0.785411	0.392705	−	0.919664i	$-0.371539\pi$
$761$	21.6665	0.785411	0.392705	+	0.919664i	$0.371539\pi$
$762$	0.805977	0.0291975
$763$	0	0
$764$	−4.59827	−0.166359
$765$	1.40246	0.0507062
$766$	−24.5323	−0.886388
$767$	−30.9355	−1.11702
$768$	−5.65274	−0.203976
$769$	−39.7676	−1.43406	−0.717028	−	0.697044i	$-0.754498\pi$
$769$	−39.7676	−1.43406	−0.717028	+	0.697044i	$0.754498\pi$
$770$	0	0
$771$	−18.2269	−0.656427
$772$	−0.283337	−0.0101975
$773$	23.5136	0.845725	0.422862	−	0.906194i	$-0.361025\pi$
$773$	23.5136	0.845725	0.422862	+	0.906194i	$0.361025\pi$
$774$	−7.69468	−0.276579
$775$	13.0826	0.469943
$776$	29.5339	1.06021
$777$	0	0
$778$	−18.0806	−0.648221
$779$	6.27752	0.224916
$780$	0.841553	0.0301324
$781$	10.5280	0.376720
$782$	−13.3107	−0.475991
$783$	−8.89019	−0.317710
$784$	0	0
$785$	4.75160	0.169592
$786$	−7.50084	−0.267546
$787$	40.3755	1.43923	0.719615	−	0.694373i	$-0.244318\pi$
$787$	40.3755	1.43923	0.719615	+	0.694373i	$0.244318\pi$
$788$	0.971495	0.0346081
$789$	−20.7807	−0.739811
$790$	4.65993	0.165793
$791$	0	0
$792$	8.16446	0.290111
$793$	20.6346	0.732756
$794$	−34.7899	−1.23465
$795$	1.20155	0.0426145
$796$	−4.41751	−0.156574
$797$	7.96493	0.282132	0.141066	−	0.990000i	$-0.454947\pi$
$797$	7.96493	0.282132	0.141066	+	0.990000i	$0.454947\pi$
$798$	0	0
$799$	−17.5618	−0.621293
$800$	−6.13314	−0.216839
$801$	−3.08183	−0.108891
$802$	−51.6272	−1.82302
$803$	9.81759	0.346455
$804$	−2.34838	−0.0828211
$805$	0	0
$806$	−22.8840	−0.806054
$807$	−7.54533	−0.265608
$808$	38.4077	1.35118
$809$	0.841447	0.0295837	0.0147918	−	0.999891i	$-0.495291\pi$
$809$	0.841447	0.0295837	0.0147918	+	0.999891i	$0.495291\pi$
$810$	−0.988352	−0.0347272
$811$	−33.3699	−1.17178	−0.585888	−	0.810392i	$-0.699254\pi$
$811$	−33.3699	−1.17178	−0.585888	+	0.810392i	$0.699254\pi$
$812$	0	0
$813$	−31.5336	−1.10593
$814$	17.6593	0.618959
$815$	−10.2310	−0.358377
$816$	9.38570	0.328565
$817$	−32.2828	−1.12943
$818$	−30.1787	−1.05517
$819$	0	0
$820$	−0.157739	−0.00550847
$821$	15.0078	0.523775	0.261888	−	0.965098i	$-0.415655\pi$
$821$	15.0078	0.523775	0.261888	+	0.965098i	$0.415655\pi$
$822$	−14.6337	−0.510410
$823$	−8.13252	−0.283482	−0.141741	−	0.989904i	$-0.545270\pi$
$823$	−8.13252	−0.283482	−0.141741	+	0.989904i	$0.545270\pi$
$824$	23.1791	0.807480
$825$	14.1392	0.492265
$826$	0	0
$827$	9.36006	0.325481	0.162741	−	0.986669i	$-0.447967\pi$
$827$	9.36006	0.325481	0.162741	+	0.986669i	$0.447967\pi$
$828$	1.00055	0.0347717
$829$	−25.3418	−0.880158	−0.440079	−	0.897959i	$-0.645049\pi$
$829$	−25.3418	−0.880158	−0.440079	+	0.897959i	$0.645049\pi$
$830$	1.55848	0.0540955
$831$	−21.1032	−0.732061
$832$	−36.4405	−1.26335
$833$	0	0
$834$	0.540351	0.0187108
$835$	4.09036	0.141553
$836$	−4.64444	−0.160631
$837$	2.86669	0.0990873
$838$	−9.22621	−0.318714
$839$	10.7462	0.371001	0.185500	−	0.982644i	$-0.440609\pi$
$839$	10.7462	0.371001	0.185500	+	0.982644i	$0.440609\pi$
$840$	0	0
$841$	50.0355	1.72536
$842$	51.3967	1.77125
$843$	−28.6757	−0.987645
$844$	−3.09033	−0.106373
$845$	10.2143	0.351382
$846$	12.3763	0.425505
$847$	0	0
$848$	8.04110	0.276133
$849$	23.8753	0.819397
$850$	14.4981	0.497280
$851$	−15.9611	−0.547138
$852$	−0.811461	−0.0278002
$853$	3.03602	0.103951	0.0519756	−	0.998648i	$-0.483448\pi$
$853$	3.03602	0.103951	0.0519756	+	0.998648i	$0.483448\pi$
$854$	0	0
$855$	−4.14660	−0.141811
$856$	27.0300	0.923866
$857$	−23.2184	−0.793126	−0.396563	−	0.918007i	$-0.629797\pi$
$857$	−23.2184	−0.793126	−0.396563	+	0.918007i	$0.629797\pi$
$858$	−24.7321	−0.844341
$859$	−16.9535	−0.578444	−0.289222	−	0.957262i	$-0.593397\pi$
$859$	−16.9535	−0.578444	−0.289222	+	0.957262i	$0.593397\pi$
$860$	0.811187	0.0276613
$861$	0	0
$862$	−35.1916	−1.19863
$863$	−21.2825	−0.724465	−0.362233	−	0.932088i	$-0.617985\pi$
$863$	−21.2825	−0.724465	−0.362233	+	0.932088i	$0.617985\pi$
$864$	−1.34390	−0.0457205
$865$	−5.85075	−0.198932
$866$	2.26103	0.0768329
$867$	12.4921	0.424253
$868$	0	0
$869$	−14.6076	−0.495528
$870$	8.78664	0.297895
$871$	−52.4660	−1.77774
$872$	−26.5725	−0.899858
$873$	11.2074	0.379313
$874$	39.3552	1.33121
$875$	0	0
$876$	−0.756707	−0.0255668
$877$	8.42693	0.284557	0.142279	−	0.989827i	$-0.454557\pi$
$877$	8.42693	0.284557	0.142279	+	0.989827i	$0.454557\pi$
$878$	50.9813	1.72054
$879$	10.7712	0.363305
$880$	−9.04678	−0.304967
$881$	23.0264	0.775779	0.387889	−	0.921706i	$-0.373204\pi$
$881$	23.0264	0.775779	0.387889	+	0.921706i	$0.373204\pi$
$882$	0	0
$883$	−26.4795	−0.891104	−0.445552	−	0.895256i	$-0.646993\pi$
$883$	−26.4795	−0.891104	−0.445552	+	0.895256i	$0.646993\pi$
$884$	−2.70499	−0.0909785
$885$	−3.83017	−0.128750
$886$	−13.0191	−0.437384
$887$	−30.8122	−1.03457	−0.517287	−	0.855812i	$-0.673058\pi$
$887$	−30.8122	−1.03457	−0.517287	+	0.855812i	$0.673058\pi$
$888$	10.0386	0.336872
$889$	0	0
$890$	3.04593	0.102100
$891$	3.09821	0.103794
$892$	1.35769	0.0454587
$893$	51.9243	1.73758
$894$	−22.8975	−0.765807
$895$	8.21784	0.274692
$896$	0	0
$897$	22.3537	0.746368
$898$	14.4694	0.482849
$899$	−25.4854	−0.849987
$900$	−1.08981	−0.0363269
$901$	−3.86211	−0.128666
$902$	4.63574	0.154353
$903$	0	0
$904$	12.0348	0.400270
$905$	15.3773	0.511159
$906$	−7.64492	−0.253985
$907$	21.5266	0.714780	0.357390	−	0.933955i	$-0.383667\pi$
$907$	21.5266	0.714780	0.357390	+	0.933955i	$0.383667\pi$
$908$	−2.28060	−0.0756843
$909$	14.5748	0.483414
$910$	0	0
$911$	−2.61312	−0.0865766	−0.0432883	−	0.999063i	$-0.513783\pi$
$911$	−2.61312	−0.0865766	−0.0432883	+	0.999063i	$0.513783\pi$
$912$	−27.7503	−0.918903
$913$	−4.88540	−0.161683
$914$	−41.2404	−1.36411
$915$	2.55480	0.0844592
$916$	−1.35180	−0.0446647
$917$	0	0
$918$	3.17684	0.104851
$919$	54.0048	1.78145	0.890727	−	0.454539i	$-0.150196\pi$
$919$	54.0048	1.78145	0.890727	+	0.454539i	$0.150196\pi$
$920$	7.29335	0.240455
$921$	25.1906	0.830059
$922$	−63.1692	−2.08037
$923$	−18.1291	−0.596727
$924$	0	0
$925$	17.3848	0.571610
$926$	10.4212	0.342462
$927$	8.79588	0.288895
$928$	11.9476	0.392198
$929$	−35.0874	−1.15118	−0.575590	−	0.817738i	$-0.695228\pi$
$929$	−35.0874	−1.15118	−0.575590	+	0.817738i	$0.695228\pi$
$930$	−2.83330	−0.0929076
$931$	0	0
$932$	−1.67753	−0.0549494
$933$	−11.3282	−0.370869
$934$	−3.59528	−0.117641
$935$	4.34513	0.142101
$936$	−14.0592	−0.459538
$937$	−3.16012	−0.103236	−0.0516182	−	0.998667i	$-0.516438\pi$
$937$	−3.16012	−0.103236	−0.0516182	+	0.998667i	$0.516438\pi$
$938$	0	0
$939$	−18.5241	−0.604512
$940$	−1.30473	−0.0425556
$941$	25.7018	0.837853	0.418927	−	0.908020i	$-0.362406\pi$
$941$	25.7018	0.837853	0.418927	+	0.908020i	$0.362406\pi$
$942$	10.7633	0.350686
$943$	−4.18993	−0.136443
$944$	−25.6326	−0.834270
$945$	0	0
$946$	−23.8397	−0.775097
$947$	−19.7183	−0.640759	−0.320379	−	0.947289i	$-0.603810\pi$
$947$	−19.7183	−0.640759	−0.320379	+	0.947289i	$0.603810\pi$
$948$	1.12590	0.0365677
$949$	−16.9058	−0.548787
$950$	−42.8658	−1.39075
$951$	−34.5327	−1.11980
$952$	0	0
$953$	−14.0545	−0.455270	−0.227635	−	0.973747i	$-0.573099\pi$
$953$	−14.0545	−0.455270	−0.227635	+	0.973747i	$0.573099\pi$
$954$	2.72173	0.0881192
$955$	−12.7193	−0.411588
$956$	6.84296	0.221317
$957$	−27.5437	−0.890361
$958$	3.31917	0.107237
$959$	0	0
$960$	−4.51175	−0.145616
$961$	−22.7821	−0.734906
$962$	−30.4093	−0.980434
$963$	10.2572	0.330534
$964$	−6.35018	−0.204525
$965$	−0.783741	−0.0252295
$966$	0	0
$967$	28.2664	0.908986	0.454493	−	0.890750i	$-0.349820\pi$
$967$	28.2664	0.908986	0.454493	+	0.890750i	$0.349820\pi$
$968$	−3.69217	−0.118671
$969$	13.3283	0.428168
$970$	−11.0769	−0.355657
$971$	2.37609	0.0762523	0.0381262	−	0.999273i	$-0.487861\pi$
$971$	2.37609	0.0762523	0.0381262	+	0.999273i	$0.487861\pi$
$972$	−0.238800	−0.00765951
$973$	0	0
$974$	19.4325	0.622657
$975$	−24.3477	−0.779750
$976$	17.0975	0.547277
$977$	20.8545	0.667195	0.333598	−	0.942716i	$-0.391737\pi$
$977$	20.8545	0.667195	0.333598	+	0.942716i	$0.391737\pi$
$978$	−23.1751	−0.741059
$979$	−9.54816	−0.305160
$980$	0	0
$981$	−10.0836	−0.321945
$982$	−25.2863	−0.806917
$983$	24.9313	0.795185	0.397593	−	0.917562i	$-0.369846\pi$
$983$	24.9313	0.795185	0.397593	+	0.917562i	$0.369846\pi$
$984$	2.63522	0.0840076
$985$	2.68726	0.0856233
$986$	−28.2427	−0.899432
$987$	0	0
$988$	7.99771	0.254441
$989$	21.5471	0.685159
$990$	−3.06212	−0.0973207
$991$	49.0640	1.55857	0.779285	−	0.626669i	$-0.215582\pi$
$991$	49.0640	1.55857	0.779285	+	0.626669i	$0.215582\pi$
$992$	−3.85256	−0.122319
$993$	−3.36957	−0.106930
$994$	0	0
$995$	−12.2193	−0.387379
$996$	0.376550	0.0119315
$997$	−31.1095	−0.985248	−0.492624	−	0.870242i	$-0.663962\pi$
$997$	−31.1095	−0.985248	−0.492624	+	0.870242i	$0.663962\pi$
$998$	−60.6853	−1.92096
$999$	3.80939	0.120524

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bd.1.3	✓	10
7.6	odd	2		6027.2.a.be.1.3	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6027.2.a.bd.1.3	✓	10	1.1	even	1	trivial
6027.2.a.be.1.3	yes	10	7.6	odd	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:	\( N \)	\(=\)	\( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6027.a (trivial)

\(f(q)\)	\(=\)	\(q-1.49626 q^{2} -1.00000 q^{3} +0.238800 q^{4} +0.660548 q^{5} +1.49626 q^{6} +2.63522 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.49626 q^{2} -1.00000 q^{3} +0.238800 q^{4} +0.660548 q^{5} +1.49626 q^{6} +2.63522 q^{8} +1.00000 q^{9} -0.988352 q^{10} +3.09821 q^{11} -0.238800 q^{12} -5.33510 q^{13} -0.660548 q^{15} -4.42057 q^{16} +2.12319 q^{17} -1.49626 q^{18} -6.27752 q^{19} +0.157739 q^{20} -4.63574 q^{22} +4.18993 q^{23} -2.63522 q^{24} -4.56368 q^{25} +7.98271 q^{26} -1.00000 q^{27} +8.89019 q^{29} +0.988352 q^{30} -2.86669 q^{31} +1.34390 q^{32} -3.09821 q^{33} -3.17684 q^{34} +0.238800 q^{36} -3.80939 q^{37} +9.39282 q^{38} +5.33510 q^{39} +1.74069 q^{40} -1.00000 q^{41} +5.14260 q^{43} +0.739853 q^{44} +0.660548 q^{45} -6.26923 q^{46} -8.27146 q^{47} +4.42057 q^{48} +6.82846 q^{50} -2.12319 q^{51} -1.27402 q^{52} -1.81902 q^{53} +1.49626 q^{54} +2.04652 q^{55} +6.27752 q^{57} -13.3021 q^{58} +5.79848 q^{59} -0.157739 q^{60} -3.86770 q^{61} +4.28932 q^{62} +6.83032 q^{64} -3.52409 q^{65} +4.63574 q^{66} +9.83411 q^{67} +0.507017 q^{68} -4.18993 q^{69} +3.39808 q^{71} +2.63522 q^{72} +3.16879 q^{73} +5.69985 q^{74} +4.56368 q^{75} -1.49907 q^{76} -7.98271 q^{78} -4.71484 q^{79} -2.92000 q^{80} +1.00000 q^{81} +1.49626 q^{82} -1.57684 q^{83} +1.40246 q^{85} -7.69468 q^{86} -8.89019 q^{87} +8.16446 q^{88} -3.08183 q^{89} -0.988352 q^{90} +1.00055 q^{92} +2.86669 q^{93} +12.3763 q^{94} -4.14660 q^{95} -1.34390 q^{96} +11.2074 q^{97} +3.09821 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} - 10 q^{3} + 18 q^{4} - 6 q^{5} - 4 q^{6} + 12 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 4 * q^2 - 10 * q^3 + 18 * q^4 - 6 * q^5 - 4 * q^6 + 12 * q^8 + 10 * q^9	\( 10 q + 4 q^{2} - 10 q^{3} + 18 q^{4} - 6 q^{5} - 4 q^{6} + 12 q^{8} + 10 q^{9} - 2 q^{10} - 2 q^{11} - 18 q^{12} + 6 q^{15} + 14 q^{16} - 8 q^{17} + 4 q^{18} - 6 q^{19} - 20 q^{20} + 2 q^{22} - 12 q^{24} + 10 q^{25} - 16 q^{26} - 10 q^{27} + 16 q^{29} + 2 q^{30} - 2 q^{31} + 38 q^{32} + 2 q^{33} + 4 q^{34} + 18 q^{36} + 24 q^{37} + 26 q^{38} - 40 q^{40} - 10 q^{41} + 8 q^{43} - 8 q^{44} - 6 q^{45} + 4 q^{46} + 8 q^{47} - 14 q^{48} + 44 q^{50} + 8 q^{51} + 30 q^{52} + 24 q^{53} - 4 q^{54} + 6 q^{57} - 14 q^{58} - 6 q^{59} + 20 q^{60} + 14 q^{61} + 2 q^{62} + 86 q^{64} + 28 q^{65} - 2 q^{66} + 26 q^{67} + 6 q^{68} + 14 q^{71} + 12 q^{72} + 36 q^{73} + 18 q^{74} - 10 q^{75} + 32 q^{76} + 16 q^{78} + 20 q^{79} - 70 q^{80} + 10 q^{81} - 4 q^{82} - 40 q^{83} + 24 q^{85} - 36 q^{86} - 16 q^{87} + 14 q^{88} - 2 q^{89} - 2 q^{90} + 8 q^{92} + 2 q^{93} + 54 q^{94} - 24 q^{95} - 38 q^{96} - 16 q^{97} - 2 q^{99}+O(q^{100}) \) 10 * q + 4 * q^2 - 10 * q^3 + 18 * q^4 - 6 * q^5 - 4 * q^6 + 12 * q^8 + 10 * q^9 - 2 * q^10 - 2 * q^11 - 18 * q^12 + 6 * q^15 + 14 * q^16 - 8 * q^17 + 4 * q^18 - 6 * q^19 - 20 * q^20 + 2 * q^22 - 12 * q^24 + 10 * q^25 - 16 * q^26 - 10 * q^27 + 16 * q^29 + 2 * q^30 - 2 * q^31 + 38 * q^32 + 2 * q^33 + 4 * q^34 + 18 * q^36 + 24 * q^37 + 26 * q^38 - 40 * q^40 - 10 * q^41 + 8 * q^43 - 8 * q^44 - 6 * q^45 + 4 * q^46 + 8 * q^47 - 14 * q^48 + 44 * q^50 + 8 * q^51 + 30 * q^52 + 24 * q^53 - 4 * q^54 + 6 * q^57 - 14 * q^58 - 6 * q^59 + 20 * q^60 + 14 * q^61 + 2 * q^62 + 86 * q^64 + 28 * q^65 - 2 * q^66 + 26 * q^67 + 6 * q^68 + 14 * q^71 + 12 * q^72 + 36 * q^73 + 18 * q^74 - 10 * q^75 + 32 * q^76 + 16 * q^78 + 20 * q^79 - 70 * q^80 + 10 * q^81 - 4 * q^82 - 40 * q^83 + 24 * q^85 - 36 * q^86 - 16 * q^87 + 14 * q^88 - 2 * q^89 - 2 * q^90 + 8 * q^92 + 2 * q^93 + 54 * q^94 - 24 * q^95 - 38 * q^96 - 16 * q^97 - 2 * q^99

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