LMFDB - Embedded newform 4018.2.a.bo.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4018,2,Mod(1,4018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4018, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("4018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4018 = 2 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4018.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:	$32.0838915322$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.52046292.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 10x^{4} + 9x^{3} + 24x^{2} - 18x + 1 $ x^6 - x^5 - 10x^4 + 9x^3 + 24x^2 - 18x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 574)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-2.43859$ of defining polynomial
Character	$\chi$	$=$	4018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.30861 q^{3} +1.00000 q^{4} -0.374437 q^{5} -2.30861 q^{6} -1.00000 q^{8} +2.32969 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.30861 q^{3} +1.00000 q^{4} -0.374437 q^{5} -2.30861 q^{6} -1.00000 q^{8} +2.32969 q^{9} +0.374437 q^{10} +2.34222 q^{11} +2.30861 q^{12} +0.133679 q^{13} -0.864429 q^{15} +1.00000 q^{16} +1.70413 q^{17} -2.32969 q^{18} +0.725210 q^{19} -0.374437 q^{20} -2.34222 q^{22} +0.678862 q^{23} -2.30861 q^{24} -4.85980 q^{25} -0.133679 q^{26} -1.54748 q^{27} +2.81673 q^{29} +0.864429 q^{30} +2.53866 q^{31} -1.00000 q^{32} +5.40728 q^{33} -1.70413 q^{34} +2.32969 q^{36} +9.14872 q^{37} -0.725210 q^{38} +0.308613 q^{39} +0.374437 q^{40} +1.00000 q^{41} +6.66821 q^{43} +2.34222 q^{44} -0.872322 q^{45} -0.678862 q^{46} -3.99629 q^{47} +2.30861 q^{48} +4.85980 q^{50} +3.93418 q^{51} +0.133679 q^{52} -1.22541 q^{53} +1.54748 q^{54} -0.877012 q^{55} +1.67423 q^{57} -2.81673 q^{58} +13.6176 q^{59} -0.864429 q^{60} +1.22171 q^{61} -2.53866 q^{62} +1.00000 q^{64} -0.0500543 q^{65} -5.40728 q^{66} +0.682971 q^{67} +1.70413 q^{68} +1.56723 q^{69} +8.12528 q^{71} -2.32969 q^{72} +2.89686 q^{73} -9.14872 q^{74} -11.2194 q^{75} +0.725210 q^{76} -0.308613 q^{78} -13.0919 q^{79} -0.374437 q^{80} -10.5616 q^{81} -1.00000 q^{82} +1.52221 q^{83} -0.638089 q^{85} -6.66821 q^{86} +6.50274 q^{87} -2.34222 q^{88} -8.52779 q^{89} +0.872322 q^{90} +0.678862 q^{92} +5.86078 q^{93} +3.99629 q^{94} -0.271545 q^{95} -2.30861 q^{96} +1.74259 q^{97} +5.45665 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + q^{3} + 6 q^{4} - q^{6} - 6 q^{8} + 5 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 + q^3 + 6 * q^4 - q^6 - 6 * q^8 + 5 * q^9	$ 6 q - 6 q^{2} + q^{3} + 6 q^{4} - q^{6} - 6 q^{8} + 5 q^{9} + q^{11} + q^{12} + 4 q^{13} + 2 q^{15} + 6 q^{16} - q^{17} - 5 q^{18} - 3 q^{19} - q^{22} + 21 q^{23} - q^{24} - 4 q^{26} + 13 q^{27} + 5 q^{29} - 2 q^{30} + 3 q^{31} - 6 q^{32} - 19 q^{33} + q^{34} + 5 q^{36} - 2 q^{37} + 3 q^{38} - 11 q^{39} + 6 q^{41} + 12 q^{43} + q^{44} + 28 q^{45} - 21 q^{46} - 18 q^{47} + q^{48} + 13 q^{51} + 4 q^{52} + 14 q^{53} - 13 q^{54} - 7 q^{55} + 5 q^{57} - 5 q^{58} + 16 q^{59} + 2 q^{60} - 20 q^{61} - 3 q^{62} + 6 q^{64} + 18 q^{65} + 19 q^{66} - 13 q^{67} - q^{68} + 15 q^{69} + 11 q^{71} - 5 q^{72} + q^{73} + 2 q^{74} - 23 q^{75} - 3 q^{76} + 11 q^{78} + 19 q^{79} - 6 q^{81} - 6 q^{82} + 15 q^{83} - 2 q^{85} - 12 q^{86} + 10 q^{87} - q^{88} - 14 q^{89} - 28 q^{90} + 21 q^{92} + 35 q^{93} + 18 q^{94} + 24 q^{95} - q^{96} + q^{97} + 10 q^{99}+O(q^{100}) $ 6 * q - 6 * q^2 + q^3 + 6 * q^4 - q^6 - 6 * q^8 + 5 * q^9 + q^11 + q^12 + 4 * q^13 + 2 * q^15 + 6 * q^16 - q^17 - 5 * q^18 - 3 * q^19 - q^22 + 21 * q^23 - q^24 - 4 * q^26 + 13 * q^27 + 5 * q^29 - 2 * q^30 + 3 * q^31 - 6 * q^32 - 19 * q^33 + q^34 + 5 * q^36 - 2 * q^37 + 3 * q^38 - 11 * q^39 + 6 * q^41 + 12 * q^43 + q^44 + 28 * q^45 - 21 * q^46 - 18 * q^47 + q^48 + 13 * q^51 + 4 * q^52 + 14 * q^53 - 13 * q^54 - 7 * q^55 + 5 * q^57 - 5 * q^58 + 16 * q^59 + 2 * q^60 - 20 * q^61 - 3 * q^62 + 6 * q^64 + 18 * q^65 + 19 * q^66 - 13 * q^67 - q^68 + 15 * q^69 + 11 * q^71 - 5 * q^72 + q^73 + 2 * q^74 - 23 * q^75 - 3 * q^76 + 11 * q^78 + 19 * q^79 - 6 * q^81 - 6 * q^82 + 15 * q^83 - 2 * q^85 - 12 * q^86 + 10 * q^87 - q^88 - 14 * q^89 - 28 * q^90 + 21 * q^92 + 35 * q^93 + 18 * q^94 + 24 * q^95 - q^96 + q^97 + 10 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	2.30861	1.33288	0.666439	−	0.745559i	$-0.267818\pi$
$3$	2.30861	1.33288	0.666439	+	0.745559i	$0.267818\pi$
$4$	1.00000	0.500000
$5$	−0.374437	−0.167453	−0.0837266	−	0.996489i	$-0.526682\pi$
$5$	−0.374437	−0.167453	−0.0837266	+	0.996489i	$0.526682\pi$
$6$	−2.30861	−0.942487
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	2.32969	0.776564
$10$	0.374437	0.118407
$11$	2.34222	0.706205	0.353103	−	0.935585i	$-0.385127\pi$
$11$	2.34222	0.706205	0.353103	+	0.935585i	$0.385127\pi$
$12$	2.30861	0.666439
$13$	0.133679	0.0370759	0.0185379	−	0.999828i	$-0.494099\pi$
$13$	0.133679	0.0370759	0.0185379	+	0.999828i	$0.494099\pi$
$14$	0	0
$15$	−0.864429	−0.223195
$16$	1.00000	0.250000
$17$	1.70413	0.413312	0.206656	−	0.978414i	$-0.433742\pi$
$17$	1.70413	0.413312	0.206656	+	0.978414i	$0.433742\pi$
$18$	−2.32969	−0.549114
$19$	0.725210	0.166375	0.0831873	−	0.996534i	$-0.473490\pi$
$19$	0.725210	0.166375	0.0831873	+	0.996534i	$0.473490\pi$
$20$	−0.374437	−0.0837266
$21$	0	0
$22$	−2.34222	−0.499363
$23$	0.678862	0.141553	0.0707763	−	0.997492i	$-0.477452\pi$
$23$	0.678862	0.141553	0.0707763	+	0.997492i	$0.477452\pi$
$24$	−2.30861	−0.471244
$25$	−4.85980	−0.971959
$26$	−0.133679	−0.0262166
$27$	−1.54748	−0.297812
$28$	0	0
$29$	2.81673	0.523053	0.261527	−	0.965196i	$-0.415774\pi$
$29$	2.81673	0.523053	0.261527	+	0.965196i	$0.415774\pi$
$30$	0.864429	0.157822
$31$	2.53866	0.455957	0.227978	−	0.973666i	$-0.426788\pi$
$31$	2.53866	0.455957	0.227978	+	0.973666i	$0.426788\pi$
$32$	−1.00000	−0.176777
$33$	5.40728	0.941286
$34$	−1.70413	−0.292256
$35$	0	0
$36$	2.32969	0.388282
$37$	9.14872	1.50404	0.752020	−	0.659140i	$-0.229080\pi$
$37$	9.14872	1.50404	0.752020	+	0.659140i	$0.229080\pi$
$38$	−0.725210	−0.117645
$39$	0.308613	0.0494176
$40$	0.374437	0.0592036
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	6.66821	1.01689	0.508446	−	0.861094i	$-0.330220\pi$
$43$	6.66821	1.01689	0.508446	+	0.861094i	$0.330220\pi$
$44$	2.34222	0.353103
$45$	−0.872322	−0.130038
$46$	−0.678862	−0.100093
$47$	−3.99629	−0.582919	−0.291460	−	0.956583i	$-0.594141\pi$
$47$	−3.99629	−0.582919	−0.291460	+	0.956583i	$0.594141\pi$
$48$	2.30861	0.333220
$49$	0	0
$50$	4.85980	0.687279
$51$	3.93418	0.550895
$52$	0.133679	0.0185379
$53$	−1.22541	−0.168324	−0.0841618	−	0.996452i	$-0.526821\pi$
$53$	−1.22541	−0.168324	−0.0841618	+	0.996452i	$0.526821\pi$
$54$	1.54748	0.210585
$55$	−0.877012	−0.118256
$56$	0	0
$57$	1.67423	0.221757
$58$	−2.81673	−0.369855
$59$	13.6176	1.77286	0.886432	−	0.462859i	$-0.153176\pi$
$59$	13.6176	1.77286	0.886432	+	0.462859i	$0.153176\pi$
$60$	−0.864429	−0.111597
$61$	1.22171	0.156424	0.0782119	−	0.996937i	$-0.475079\pi$
$61$	1.22171	0.156424	0.0782119	+	0.996937i	$0.475079\pi$
$62$	−2.53866	−0.322410
$63$	0	0
$64$	1.00000	0.125000
$65$	−0.0500543	−0.00620847
$66$	−5.40728	−0.665590
$67$	0.682971	0.0834382	0.0417191	−	0.999129i	$-0.486717\pi$
$67$	0.682971	0.0834382	0.0417191	+	0.999129i	$0.486717\pi$
$68$	1.70413	0.206656
$69$	1.56723	0.188672
$70$	0	0
$71$	8.12528	0.964294	0.482147	−	0.876090i	$-0.339857\pi$
$71$	8.12528	0.964294	0.482147	+	0.876090i	$0.339857\pi$
$72$	−2.32969	−0.274557
$73$	2.89686	0.339052	0.169526	−	0.985526i	$-0.445776\pi$
$73$	2.89686	0.339052	0.169526	+	0.985526i	$0.445776\pi$
$74$	−9.14872	−1.06352
$75$	−11.2194	−1.29550
$76$	0.725210	0.0831873
$77$	0	0
$78$	−0.308613	−0.0349435
$79$	−13.0919	−1.47296	−0.736479	−	0.676461i	$-0.763513\pi$
$79$	−13.0919	−1.47296	−0.736479	+	0.676461i	$0.763513\pi$
$80$	−0.374437	−0.0418633
$81$	−10.5616	−1.17351
$82$	−1.00000	−0.110432
$83$	1.52221	0.167084	0.0835422	−	0.996504i	$-0.473377\pi$
$83$	1.52221	0.167084	0.0835422	+	0.996504i	$0.473377\pi$
$84$	0	0
$85$	−0.638089	−0.0692104
$86$	−6.66821	−0.719051
$87$	6.50274	0.697166
$88$	−2.34222	−0.249681
$89$	−8.52779	−0.903943	−0.451972	−	0.892032i	$-0.649279\pi$
$89$	−8.52779	−0.903943	−0.451972	+	0.892032i	$0.649279\pi$
$90$	0.872322	0.0919509
$91$	0	0
$92$	0.678862	0.0707763
$93$	5.86078	0.607735
$94$	3.99629	0.412186
$95$	−0.271545	−0.0278600
$96$	−2.30861	−0.235622
$97$	1.74259	0.176933	0.0884664	−	0.996079i	$-0.471803\pi$
$97$	1.74259	0.176933	0.0884664	+	0.996079i	$0.471803\pi$
$98$	0	0
$99$	5.45665	0.548414
$100$	−4.85980	−0.485980
$101$	16.3793	1.62980	0.814901	−	0.579600i	$-0.196791\pi$
$101$	16.3793	1.62980	0.814901	+	0.579600i	$0.196791\pi$
$102$	−3.93418	−0.389541
$103$	−0.328088	−0.0323275	−0.0161637	−	0.999869i	$-0.505145\pi$
$103$	−0.328088	−0.0323275	−0.0161637	+	0.999869i	$0.505145\pi$
$104$	−0.133679	−0.0131083
$105$	0	0
$106$	1.22541	0.119023
$107$	1.47989	0.143066	0.0715332	−	0.997438i	$-0.477211\pi$
$107$	1.47989	0.143066	0.0715332	+	0.997438i	$0.477211\pi$
$108$	−1.54748	−0.148906
$109$	10.0351	0.961192	0.480596	−	0.876942i	$-0.340420\pi$
$109$	10.0351	0.961192	0.480596	+	0.876942i	$0.340420\pi$
$110$	0.877012	0.0836198
$111$	21.1208	2.00470
$112$	0	0
$113$	0.994747	0.0935779	0.0467890	−	0.998905i	$-0.485101\pi$
$113$	0.994747	0.0935779	0.0467890	+	0.998905i	$0.485101\pi$
$114$	−1.67423	−0.156806
$115$	−0.254191	−0.0237034
$116$	2.81673	0.261527
$117$	0.311431	0.0287918
$118$	−13.6176	−1.25360
$119$	0	0
$120$	0.864429	0.0789112
$121$	−5.51401	−0.501274
$122$	−1.22171	−0.110608
$123$	2.30861	0.208161
$124$	2.53866	0.227978
$125$	3.69187	0.330211
$126$	0	0
$127$	15.3765	1.36445	0.682223	−	0.731144i	$-0.261013\pi$
$127$	15.3765	1.36445	0.682223	+	0.731144i	$0.261013\pi$
$128$	−1.00000	−0.0883883
$129$	15.3943	1.35539
$130$	0.0500543	0.00439005
$131$	−12.0702	−1.05458	−0.527288	−	0.849687i	$-0.676791\pi$
$131$	−12.0702	−1.05458	−0.527288	+	0.849687i	$0.676791\pi$
$132$	5.40728	0.470643
$133$	0	0
$134$	−0.682971	−0.0589997
$135$	0.579433	0.0498696
$136$	−1.70413	−0.146128
$137$	6.61995	0.565580	0.282790	−	0.959182i	$-0.408740\pi$
$137$	6.61995	0.565580	0.282790	+	0.959182i	$0.408740\pi$
$138$	−1.56723	−0.133411
$139$	0.730250	0.0619390	0.0309695	−	0.999520i	$-0.490141\pi$
$139$	0.730250	0.0619390	0.0309695	+	0.999520i	$0.490141\pi$
$140$	0	0
$141$	−9.22590	−0.776961
$142$	−8.12528	−0.681859
$143$	0.313105	0.0261832
$144$	2.32969	0.194141
$145$	−1.05469	−0.0875869
$146$	−2.89686	−0.239746
$147$	0	0
$148$	9.14872	0.752020
$149$	3.39341	0.277999	0.138999	−	0.990292i	$-0.455611\pi$
$149$	3.39341	0.277999	0.138999	+	0.990292i	$0.455611\pi$
$150$	11.2194	0.916059
$151$	−15.9780	−1.30027	−0.650135	−	0.759819i	$-0.725288\pi$
$151$	−15.9780	−1.30027	−0.650135	+	0.759819i	$0.725288\pi$
$152$	−0.725210	−0.0588223
$153$	3.97010	0.320964
$154$	0	0
$155$	−0.950567	−0.0763514
$156$	0.308613	0.0247088
$157$	−9.31987	−0.743806	−0.371903	−	0.928272i	$-0.621295\pi$
$157$	−9.31987	−0.743806	−0.371903	+	0.928272i	$0.621295\pi$
$158$	13.0919	1.04154
$159$	−2.82901	−0.224355
$160$	0.374437	0.0296018
$161$	0	0
$162$	10.5616	0.829798
$163$	20.0824	1.57297	0.786487	−	0.617607i	$-0.211898\pi$
$163$	20.0824	1.57297	0.786487	+	0.617607i	$0.211898\pi$
$164$	1.00000	0.0780869
$165$	−2.02468	−0.157621
$166$	−1.52221	−0.118146
$167$	−2.04253	−0.158056	−0.0790278	−	0.996872i	$-0.525182\pi$
$167$	−2.04253	−0.158056	−0.0790278	+	0.996872i	$0.525182\pi$
$168$	0	0
$169$	−12.9821	−0.998625
$170$	0.638089	0.0489392
$171$	1.68952	0.129201
$172$	6.66821	0.508446
$173$	9.56918	0.727531	0.363766	−	0.931491i	$-0.381491\pi$
$173$	9.56918	0.727531	0.363766	+	0.931491i	$0.381491\pi$
$174$	−6.50274	−0.492971
$175$	0	0
$176$	2.34222	0.176551
$177$	31.4378	2.36301
$178$	8.52779	0.639185
$179$	9.97650	0.745678	0.372839	−	0.927896i	$-0.378384\pi$
$179$	9.97650	0.745678	0.372839	+	0.927896i	$0.378384\pi$
$180$	−0.872322	−0.0650191
$181$	24.3936	1.81316	0.906581	−	0.422032i	$-0.138683\pi$
$181$	24.3936	1.81316	0.906581	+	0.422032i	$0.138683\pi$
$182$	0	0
$183$	2.82045	0.208494
$184$	−0.678862	−0.0500464
$185$	−3.42561	−0.251856
$186$	−5.86078	−0.429733
$187$	3.99144	0.291883
$188$	−3.99629	−0.291460
$189$	0	0
$190$	0.271545	0.0197000
$191$	4.44946	0.321952	0.160976	−	0.986958i	$-0.448536\pi$
$191$	4.44946	0.321952	0.160976	+	0.986958i	$0.448536\pi$
$192$	2.30861	0.166610
$193$	−11.2662	−0.810956	−0.405478	−	0.914105i	$-0.632895\pi$
$193$	−11.2662	−0.810956	−0.405478	+	0.914105i	$0.632895\pi$
$194$	−1.74259	−0.125110
$195$	−0.115556	−0.00827513
$196$	0	0
$197$	5.60076	0.399037	0.199519	−	0.979894i	$-0.436062\pi$
$197$	5.60076	0.399037	0.199519	+	0.979894i	$0.436062\pi$
$198$	−5.45665	−0.387787
$199$	−5.73582	−0.406601	−0.203301	−	0.979116i	$-0.565167\pi$
$199$	−5.73582	−0.406601	−0.203301	+	0.979116i	$0.565167\pi$
$200$	4.85980	0.343640
$201$	1.57672	0.111213
$202$	−16.3793	−1.15244
$203$	0	0
$204$	3.93418	0.275447
$205$	−0.374437	−0.0261518
$206$	0.328088	0.0228590
$207$	1.58154	0.109925
$208$	0.133679	0.00926897
$209$	1.69860	0.117495
$210$	0	0
$211$	7.41074	0.510176	0.255088	−	0.966918i	$-0.417896\pi$
$211$	7.41074	0.510176	0.255088	+	0.966918i	$0.417896\pi$
$212$	−1.22541	−0.0841618
$213$	18.7581	1.28529
$214$	−1.47989	−0.101163
$215$	−2.49682	−0.170282
$216$	1.54748	0.105293
$217$	0	0
$218$	−10.0351	−0.679665
$219$	6.68774	0.451916
$220$	−0.877012	−0.0591282
$221$	0.227806	0.0153239
$222$	−21.1208	−1.41754
$223$	−1.69048	−0.113203	−0.0566015	−	0.998397i	$-0.518026\pi$
$223$	−1.69048	−0.113203	−0.0566015	+	0.998397i	$0.518026\pi$
$224$	0	0
$225$	−11.3218	−0.754789
$226$	−0.994747	−0.0661696
$227$	−7.85873	−0.521602	−0.260801	−	0.965393i	$-0.583987\pi$
$227$	−7.85873	−0.521602	−0.260801	+	0.965393i	$0.583987\pi$
$228$	1.67423	0.110879
$229$	16.2972	1.07695	0.538475	−	0.842642i	$-0.319001\pi$
$229$	16.2972	1.07695	0.538475	+	0.842642i	$0.319001\pi$
$230$	0.254191	0.0167608
$231$	0	0
$232$	−2.81673	−0.184927
$233$	9.03314	0.591781	0.295890	−	0.955222i	$-0.404384\pi$
$233$	9.03314	0.591781	0.295890	+	0.955222i	$0.404384\pi$
$234$	−0.311431	−0.0203589
$235$	1.49636	0.0976117
$236$	13.6176	0.886432
$237$	−30.2242	−1.96327
$238$	0	0
$239$	−1.20554	−0.0779796	−0.0389898	−	0.999240i	$-0.512414\pi$
$239$	−1.20554	−0.0779796	−0.0389898	+	0.999240i	$0.512414\pi$
$240$	−0.864429	−0.0557987
$241$	−17.6334	−1.13587	−0.567933	−	0.823075i	$-0.692257\pi$
$241$	−17.6334	−1.13587	−0.567933	+	0.823075i	$0.692257\pi$
$242$	5.51401	0.354454
$243$	−19.7402	−1.26634
$244$	1.22171	0.0782119
$245$	0	0
$246$	−2.30861	−0.147192
$247$	0.0969453	0.00616848
$248$	−2.53866	−0.161205
$249$	3.51419	0.222703
$250$	−3.69187	−0.233494
$251$	−7.98132	−0.503776	−0.251888	−	0.967756i	$-0.581052\pi$
$251$	−7.98132	−0.503776	−0.251888	+	0.967756i	$0.581052\pi$
$252$	0	0
$253$	1.59004	0.0999652
$254$	−15.3765	−0.964809
$255$	−1.47310	−0.0922491
$256$	1.00000	0.0625000
$257$	−12.3379	−0.769616	−0.384808	−	0.922997i	$-0.625732\pi$
$257$	−12.3379	−0.769616	−0.384808	+	0.922997i	$0.625732\pi$
$258$	−15.3943	−0.958408
$259$	0	0
$260$	−0.0500543	−0.00310423
$261$	6.56211	0.406185
$262$	12.0702	0.745698
$263$	24.8075	1.52969	0.764847	−	0.644212i	$-0.222815\pi$
$263$	24.8075	1.52969	0.764847	+	0.644212i	$0.222815\pi$
$264$	−5.40728	−0.332795
$265$	0.458840	0.0281863
$266$	0	0
$267$	−19.6874	−1.20485
$268$	0.682971	0.0417191
$269$	0.0721853	0.00440122	0.00220061	−	0.999998i	$-0.499300\pi$
$269$	0.0721853	0.00440122	0.00220061	+	0.999998i	$0.499300\pi$
$270$	−0.579433	−0.0352631
$271$	−21.7890	−1.32359	−0.661793	−	0.749687i	$-0.730204\pi$
$271$	−21.7890	−1.32359	−0.661793	+	0.749687i	$0.730204\pi$
$272$	1.70413	0.103328
$273$	0	0
$274$	−6.61995	−0.399926
$275$	−11.3827	−0.686403
$276$	1.56723	0.0943361
$277$	−6.50956	−0.391122	−0.195561	−	0.980692i	$-0.562653\pi$
$277$	−6.50956	−0.391122	−0.195561	+	0.980692i	$0.562653\pi$
$278$	−0.730250	−0.0437975
$279$	5.91430	0.354080
$280$	0	0
$281$	28.2833	1.68724	0.843621	−	0.536939i	$-0.180419\pi$
$281$	28.2833	1.68724	0.843621	+	0.536939i	$0.180419\pi$
$282$	9.22590	0.549394
$283$	−21.3545	−1.26939	−0.634696	−	0.772762i	$-0.718875\pi$
$283$	−21.3545	−1.26939	−0.634696	+	0.772762i	$0.718875\pi$
$284$	8.12528	0.482147
$285$	−0.626893	−0.0371339
$286$	−0.313105	−0.0185143
$287$	0	0
$288$	−2.32969	−0.137278
$289$	−14.0959	−0.829173
$290$	1.05469	0.0619333
$291$	4.02295	0.235830
$292$	2.89686	0.169526
$293$	−7.82803	−0.457319	−0.228659	−	0.973507i	$-0.573434\pi$
$293$	−7.82803	−0.457319	−0.228659	+	0.973507i	$0.573434\pi$
$294$	0	0
$295$	−5.09894	−0.296872
$296$	−9.14872	−0.531758
$297$	−3.62453	−0.210317
$298$	−3.39341	−0.196575
$299$	0.0907495	0.00524818
$300$	−11.2194	−0.647752
$301$	0	0
$302$	15.9780	0.919430
$303$	37.8135	2.17233
$304$	0.725210	0.0415937
$305$	−0.457452	−0.0261936
$306$	−3.97010	−0.226956
$307$	−23.9521	−1.36702	−0.683510	−	0.729941i	$-0.739547\pi$
$307$	−23.9521	−1.36702	−0.683510	+	0.729941i	$0.739547\pi$
$308$	0	0
$309$	−0.757428	−0.0430886
$310$	0.950567	0.0539886
$311$	−14.4749	−0.820797	−0.410399	−	0.911906i	$-0.634610\pi$
$311$	−14.4749	−0.820797	−0.410399	+	0.911906i	$0.634610\pi$
$312$	−0.308613	−0.0174718
$313$	14.2889	0.807655	0.403828	−	0.914835i	$-0.367680\pi$
$313$	14.2889	0.807655	0.403828	+	0.914835i	$0.367680\pi$
$314$	9.31987	0.525951
$315$	0	0
$316$	−13.0919	−0.736479
$317$	2.19881	0.123498	0.0617488	−	0.998092i	$-0.480332\pi$
$317$	2.19881	0.123498	0.0617488	+	0.998092i	$0.480332\pi$
$318$	2.82901	0.158643
$319$	6.59739	0.369383
$320$	−0.374437	−0.0209316
$321$	3.41649	0.190690
$322$	0	0
$323$	1.23585	0.0687647
$324$	−10.5616	−0.586756
$325$	−0.649652	−0.0360362
$326$	−20.0824	−1.11226
$327$	23.1672	1.28115
$328$	−1.00000	−0.0552158
$329$	0	0
$330$	2.02468	0.111455
$331$	22.2134	1.22096	0.610478	−	0.792033i	$-0.290977\pi$
$331$	22.2134	1.22096	0.610478	+	0.792033i	$0.290977\pi$
$332$	1.52221	0.0835422
$333$	21.3137	1.16798
$334$	2.04253	0.111762
$335$	−0.255729	−0.0139720
$336$	0	0
$337$	14.8724	0.810149	0.405075	−	0.914284i	$-0.367246\pi$
$337$	14.8724	0.810149	0.405075	+	0.914284i	$0.367246\pi$
$338$	12.9821	0.706135
$339$	2.29649	0.124728
$340$	−0.638089	−0.0346052
$341$	5.94609	0.321999
$342$	−1.68952	−0.0913587
$343$	0	0
$344$	−6.66821	−0.359526
$345$	−0.586828	−0.0315938
$346$	−9.56918	−0.514442
$347$	5.22478	0.280481	0.140240	−	0.990117i	$-0.455212\pi$
$347$	5.22478	0.280481	0.140240	+	0.990117i	$0.455212\pi$
$348$	6.50274	0.348583
$349$	−23.4754	−1.25661	−0.628305	−	0.777967i	$-0.716251\pi$
$349$	−23.4754	−1.25661	−0.628305	+	0.777967i	$0.716251\pi$
$350$	0	0
$351$	−0.206865	−0.0110417
$352$	−2.34222	−0.124841
$353$	−5.25312	−0.279595	−0.139798	−	0.990180i	$-0.544645\pi$
$353$	−5.25312	−0.279595	−0.139798	+	0.990180i	$0.544645\pi$
$354$	−31.4378	−1.67090
$355$	−3.04240	−0.161474
$356$	−8.52779	−0.451972
$357$	0	0
$358$	−9.97650	−0.527274
$359$	10.0526	0.530557	0.265278	−	0.964172i	$-0.414536\pi$
$359$	10.0526	0.530557	0.265278	+	0.964172i	$0.414536\pi$
$360$	0.872322	0.0459754
$361$	−18.4741	−0.972319
$362$	−24.3936	−1.28210
$363$	−12.7297	−0.668137
$364$	0	0
$365$	−1.08469	−0.0567754
$366$	−2.82045	−0.147427
$367$	4.93946	0.257837	0.128919	−	0.991655i	$-0.458849\pi$
$367$	4.93946	0.257837	0.128919	+	0.991655i	$0.458849\pi$
$368$	0.678862	0.0353881
$369$	2.32969	0.121279
$370$	3.42561	0.178089
$371$	0	0
$372$	5.86078	0.303867
$373$	−19.0600	−0.986889	−0.493444	−	0.869777i	$-0.664262\pi$
$373$	−19.0600	−0.986889	−0.493444	+	0.869777i	$0.664262\pi$
$374$	−3.99144	−0.206393
$375$	8.52310	0.440131
$376$	3.99629	0.206093
$377$	0.376537	0.0193927
$378$	0	0
$379$	−20.8915	−1.07312	−0.536562	−	0.843861i	$-0.680277\pi$
$379$	−20.8915	−1.07312	−0.536562	+	0.843861i	$0.680277\pi$
$380$	−0.271545	−0.0139300
$381$	35.4984	1.81864
$382$	−4.44946	−0.227654
$383$	−36.0739	−1.84329	−0.921645	−	0.388034i	$-0.873154\pi$
$383$	−36.0739	−1.84329	−0.921645	+	0.388034i	$0.873154\pi$
$384$	−2.30861	−0.117811
$385$	0	0
$386$	11.2662	0.573433
$387$	15.5349	0.789682
$388$	1.74259	0.0884664
$389$	35.0407	1.77663	0.888317	−	0.459230i	$-0.151875\pi$
$389$	35.0407	1.77663	0.888317	+	0.459230i	$0.151875\pi$
$390$	0.115556	0.00585140
$391$	1.15687	0.0585054
$392$	0	0
$393$	−27.8654	−1.40562
$394$	−5.60076	−0.282162
$395$	4.90210	0.246651
$396$	5.45665	0.274207
$397$	21.3240	1.07022	0.535111	−	0.844782i	$-0.320270\pi$
$397$	21.3240	1.07022	0.535111	+	0.844782i	$0.320270\pi$
$398$	5.73582	0.287511
$399$	0	0
$400$	−4.85980	−0.242990
$401$	2.72976	0.136318	0.0681590	−	0.997674i	$-0.478287\pi$
$401$	2.72976	0.136318	0.0681590	+	0.997674i	$0.478287\pi$
$402$	−1.57672	−0.0786395
$403$	0.339365	0.0169050
$404$	16.3793	0.814901
$405$	3.95465	0.196508
$406$	0	0
$407$	21.4283	1.06216
$408$	−3.93418	−0.194771
$409$	−20.4532	−1.01135	−0.505673	−	0.862725i	$-0.668756\pi$
$409$	−20.4532	−1.01135	−0.505673	+	0.862725i	$0.668756\pi$
$410$	0.374437	0.0184921
$411$	15.2829	0.753850
$412$	−0.328088	−0.0161637
$413$	0	0
$414$	−1.58154	−0.0777285
$415$	−0.569971	−0.0279788
$416$	−0.133679	−0.00655415
$417$	1.68587	0.0825572
$418$	−1.69860	−0.0830813
$419$	−7.57172	−0.369903	−0.184951	−	0.982748i	$-0.559213\pi$
$419$	−7.57172	−0.369903	−0.184951	+	0.982748i	$0.559213\pi$
$420$	0	0
$421$	12.0012	0.584903	0.292451	−	0.956280i	$-0.405529\pi$
$421$	12.0012	0.584903	0.292451	+	0.956280i	$0.405529\pi$
$422$	−7.41074	−0.360749
$423$	−9.31014	−0.452674
$424$	1.22541	0.0595114
$425$	−8.28173	−0.401723
$426$	−18.7581	−0.908835
$427$	0	0
$428$	1.47989	0.0715332
$429$	0.722839	0.0348990
$430$	2.49682	0.120407
$431$	13.7132	0.660543	0.330271	−	0.943886i	$-0.392860\pi$
$431$	13.7132	0.660543	0.330271	+	0.943886i	$0.392860\pi$
$432$	−1.54748	−0.0744531
$433$	−23.7704	−1.14233	−0.571167	−	0.820834i	$-0.693509\pi$
$433$	−23.7704	−1.14233	−0.571167	+	0.820834i	$0.693509\pi$
$434$	0	0
$435$	−2.43486	−0.116743
$436$	10.0351	0.480596
$437$	0.492318	0.0235508
$438$	−6.68774	−0.319553
$439$	−19.3393	−0.923014	−0.461507	−	0.887137i	$-0.652691\pi$
$439$	−19.3393	−0.923014	−0.461507	+	0.887137i	$0.652691\pi$
$440$	0.877012	0.0418099
$441$	0	0
$442$	−0.227806	−0.0108356
$443$	32.4468	1.54159	0.770797	−	0.637080i	$-0.219858\pi$
$443$	32.4468	1.54159	0.770797	+	0.637080i	$0.219858\pi$
$444$	21.1208	1.00235
$445$	3.19311	0.151368
$446$	1.69048	0.0800466
$447$	7.83406	0.370539
$448$	0	0
$449$	10.8167	0.510472	0.255236	−	0.966879i	$-0.417847\pi$
$449$	10.8167	0.510472	0.255236	+	0.966879i	$0.417847\pi$
$450$	11.3218	0.533717
$451$	2.34222	0.110291
$452$	0.994747	0.0467890
$453$	−36.8870	−1.73310
$454$	7.85873	0.368829
$455$	0	0
$456$	−1.67423	−0.0784030
$457$	−14.6183	−0.683816	−0.341908	−	0.939733i	$-0.611073\pi$
$457$	−14.6183	−0.683816	−0.341908	+	0.939733i	$0.611073\pi$
$458$	−16.2972	−0.761519
$459$	−2.63710	−0.123089
$460$	−0.254191	−0.0118517
$461$	21.3560	0.994650	0.497325	−	0.867564i	$-0.334316\pi$
$461$	21.3560	0.994650	0.497325	+	0.867564i	$0.334316\pi$
$462$	0	0
$463$	17.3519	0.806412	0.403206	−	0.915109i	$-0.367896\pi$
$463$	17.3519	0.806412	0.403206	+	0.915109i	$0.367896\pi$
$464$	2.81673	0.130763
$465$	−2.19449	−0.101767
$466$	−9.03314	−0.418452
$467$	−10.3452	−0.478720	−0.239360	−	0.970931i	$-0.576938\pi$
$467$	−10.3452	−0.478720	−0.239360	+	0.970931i	$0.576938\pi$
$468$	0.311431	0.0143959
$469$	0	0
$470$	−1.49636	−0.0690219
$471$	−21.5160	−0.991403
$472$	−13.6176	−0.626802
$473$	15.6184	0.718135
$474$	30.2242	1.38824
$475$	−3.52438	−0.161709
$476$	0	0
$477$	−2.85484	−0.130714
$478$	1.20554	0.0551399
$479$	−37.8835	−1.73094	−0.865471	−	0.500959i	$-0.832981\pi$
$479$	−37.8835	−1.73094	−0.865471	+	0.500959i	$0.832981\pi$
$480$	0.864429	0.0394556
$481$	1.22299	0.0557636
$482$	17.6334	0.803179
$483$	0	0
$484$	−5.51401	−0.250637
$485$	−0.652488	−0.0296279
$486$	19.7402	0.895435
$487$	−18.9378	−0.858152	−0.429076	−	0.903268i	$-0.641161\pi$
$487$	−18.9378	−0.858152	−0.429076	+	0.903268i	$0.641161\pi$
$488$	−1.22171	−0.0553042
$489$	46.3625	2.09658
$490$	0	0
$491$	21.3032	0.961398	0.480699	−	0.876886i	$-0.340383\pi$
$491$	21.3032	0.961398	0.480699	+	0.876886i	$0.340383\pi$
$492$	2.30861	0.104080
$493$	4.80007	0.216184
$494$	−0.0969453	−0.00436178
$495$	−2.04317	−0.0918336
$496$	2.53866	0.113989
$497$	0	0
$498$	−3.51419	−0.157475
$499$	−27.3251	−1.22324	−0.611621	−	0.791151i	$-0.709482\pi$
$499$	−27.3251	−1.22324	−0.611621	+	0.791151i	$0.709482\pi$
$500$	3.69187	0.165105
$501$	−4.71541	−0.210669
$502$	7.98132	0.356224
$503$	32.9508	1.46920	0.734601	−	0.678500i	$-0.237370\pi$
$503$	32.9508	1.46920	0.734601	+	0.678500i	$0.237370\pi$
$504$	0	0
$505$	−6.13301	−0.272915
$506$	−1.59004	−0.0706860
$507$	−29.9707	−1.33105
$508$	15.3765	0.682223
$509$	−5.72873	−0.253921	−0.126961	−	0.991908i	$-0.540522\pi$
$509$	−5.72873	−0.253921	−0.126961	+	0.991908i	$0.540522\pi$
$510$	1.47310	0.0652299
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	−1.12225	−0.0495484
$514$	12.3379	0.544201
$515$	0.122848	0.00541334
$516$	15.3943	0.677697
$517$	−9.36019	−0.411661
$518$	0	0
$519$	22.0915	0.969711
$520$	0.0500543	0.00219503
$521$	−26.4083	−1.15697	−0.578484	−	0.815694i	$-0.696356\pi$
$521$	−26.4083	−1.15697	−0.578484	+	0.815694i	$0.696356\pi$
$522$	−6.56211	−0.287216
$523$	−4.18053	−0.182802	−0.0914008	−	0.995814i	$-0.529134\pi$
$523$	−4.18053	−0.182802	−0.0914008	+	0.995814i	$0.529134\pi$
$524$	−12.0702	−0.527288
$525$	0	0
$526$	−24.8075	−1.08166
$527$	4.32621	0.188452
$528$	5.40728	0.235321
$529$	−22.5391	−0.979963
$530$	−0.458840	−0.0199307
$531$	31.7249	1.37674
$532$	0	0
$533$	0.133679	0.00579028
$534$	19.6874	0.851955
$535$	−0.554125	−0.0239569
$536$	−0.682971	−0.0294999
$537$	23.0319	0.993899
$538$	−0.0721853	−0.00311213
$539$	0	0
$540$	0.579433	0.0249348
$541$	−20.2919	−0.872419	−0.436209	−	0.899845i	$-0.643679\pi$
$541$	−20.2919	−0.872419	−0.436209	+	0.899845i	$0.643679\pi$
$542$	21.7890	0.935917
$543$	56.3154	2.41672
$544$	−1.70413	−0.0730640
$545$	−3.75752	−0.160955
$546$	0	0
$547$	25.4553	1.08839	0.544195	−	0.838959i	$-0.316835\pi$
$547$	25.4553	1.08839	0.544195	+	0.838959i	$0.316835\pi$
$548$	6.61995	0.282790
$549$	2.84621	0.121473
$550$	11.3827	0.485360
$551$	2.04272	0.0870228
$552$	−1.56723	−0.0667057
$553$	0	0
$554$	6.50956	0.276565
$555$	−7.90842	−0.335694
$556$	0.730250	0.0309695
$557$	−3.05327	−0.129371	−0.0646855	−	0.997906i	$-0.520604\pi$
$557$	−3.05327	−0.129371	−0.0646855	+	0.997906i	$0.520604\pi$
$558$	−5.91430	−0.250372
$559$	0.891399	0.0377021
$560$	0	0
$561$	9.21470	0.389045
$562$	−28.2833	−1.19306
$563$	41.3768	1.74382	0.871912	−	0.489663i	$-0.162880\pi$
$563$	41.3768	1.74382	0.871912	+	0.489663i	$0.162880\pi$
$564$	−9.22590	−0.388480
$565$	−0.372470	−0.0156699
$566$	21.3545	0.897596
$567$	0	0
$568$	−8.12528	−0.340929
$569$	−3.02824	−0.126950	−0.0634752	−	0.997983i	$-0.520218\pi$
$569$	−3.02824	−0.126950	−0.0634752	+	0.997983i	$0.520218\pi$
$570$	0.626893	0.0262577
$571$	−9.63737	−0.403311	−0.201656	−	0.979456i	$-0.564632\pi$
$571$	−9.63737	−0.403311	−0.201656	+	0.979456i	$0.564632\pi$
$572$	0.313105	0.0130916
$573$	10.2721	0.429122
$574$	0	0
$575$	−3.29913	−0.137583
$576$	2.32969	0.0970706
$577$	−26.5826	−1.10665	−0.553323	−	0.832967i	$-0.686641\pi$
$577$	−26.5826	−1.10665	−0.553323	+	0.832967i	$0.686641\pi$
$578$	14.0959	0.586314
$579$	−26.0092	−1.08091
$580$	−1.05469	−0.0437935
$581$	0	0
$582$	−4.02295	−0.166757
$583$	−2.87019	−0.118871
$584$	−2.89686	−0.119873
$585$	−0.116611	−0.00482128
$586$	7.82803	0.323373
$587$	−35.2886	−1.45652	−0.728259	−	0.685302i	$-0.759670\pi$
$587$	−35.2886	−1.45652	−0.728259	+	0.685302i	$0.759670\pi$
$588$	0	0
$589$	1.84106	0.0758596
$590$	5.09894	0.209920
$591$	12.9300	0.531868
$592$	9.14872	0.376010
$593$	26.0103	1.06812	0.534058	−	0.845448i	$-0.320666\pi$
$593$	26.0103	1.06812	0.534058	+	0.845448i	$0.320666\pi$
$594$	3.62453	0.148716
$595$	0	0
$596$	3.39341	0.138999
$597$	−13.2418	−0.541950
$598$	−0.0907495	−0.00371102
$599$	38.6365	1.57865	0.789323	−	0.613978i	$-0.210432\pi$
$599$	38.6365	1.57865	0.789323	+	0.613978i	$0.210432\pi$
$600$	11.2194	0.458030
$601$	36.0703	1.47134	0.735669	−	0.677341i	$-0.236868\pi$
$601$	36.0703	1.47134	0.735669	+	0.677341i	$0.236868\pi$
$602$	0	0
$603$	1.59111	0.0647952
$604$	−15.9780	−0.650135
$605$	2.06465	0.0839399
$606$	−37.8135	−1.53607
$607$	24.7841	1.00596	0.502978	−	0.864299i	$-0.332238\pi$
$607$	24.7841	1.00596	0.502978	+	0.864299i	$0.332238\pi$
$608$	−0.725210	−0.0294112
$609$	0	0
$610$	0.457452	0.0185217
$611$	−0.534220	−0.0216122
$612$	3.97010	0.160482
$613$	34.6013	1.39753	0.698766	−	0.715350i	$-0.253733\pi$
$613$	34.6013	1.39753	0.698766	+	0.715350i	$0.253733\pi$
$614$	23.9521	0.966629
$615$	−0.864429	−0.0348571
$616$	0	0
$617$	41.4565	1.66897	0.834487	−	0.551027i	$-0.185764\pi$
$617$	41.4565	1.66897	0.834487	+	0.551027i	$0.185764\pi$
$618$	0.757428	0.0304682
$619$	−25.1330	−1.01018	−0.505091	−	0.863066i	$-0.668541\pi$
$619$	−25.1330	−1.01018	−0.505091	+	0.863066i	$0.668541\pi$
$620$	−0.950567	−0.0381757
$621$	−1.05052	−0.0421561
$622$	14.4749	0.580391
$623$	0	0
$624$	0.308613	0.0123544
$625$	22.9166	0.916665
$626$	−14.2889	−0.571098
$627$	3.92141	0.156606
$628$	−9.31987	−0.371903
$629$	15.5906	0.621638
$630$	0	0
$631$	−35.3032	−1.40540	−0.702699	−	0.711487i	$-0.748022\pi$
$631$	−35.3032	−1.40540	−0.702699	+	0.711487i	$0.748022\pi$
$632$	13.0919	0.520769
$633$	17.1085	0.680003
$634$	−2.19881	−0.0873260
$635$	−5.75753	−0.228481
$636$	−2.82901	−0.112177
$637$	0	0
$638$	−6.59739	−0.261193
$639$	18.9294	0.748836
$640$	0.374437	0.0148009
$641$	−34.9140	−1.37902	−0.689509	−	0.724277i	$-0.742174\pi$
$641$	−34.9140	−1.37902	−0.689509	+	0.724277i	$0.742174\pi$
$642$	−3.41649	−0.134838
$643$	28.9500	1.14168	0.570838	−	0.821063i	$-0.306618\pi$
$643$	28.9500	1.14168	0.570838	+	0.821063i	$0.306618\pi$
$644$	0	0
$645$	−5.76419	−0.226965
$646$	−1.23585	−0.0486240
$647$	14.7297	0.579085	0.289542	−	0.957165i	$-0.406497\pi$
$647$	14.7297	0.579085	0.289542	+	0.957165i	$0.406497\pi$
$648$	10.5616	0.414899
$649$	31.8955	1.25201
$650$	0.649652	0.0254815
$651$	0	0
$652$	20.0824	0.786487
$653$	−37.6229	−1.47230	−0.736149	−	0.676820i	$-0.763358\pi$
$653$	−37.6229	−1.47230	−0.736149	+	0.676820i	$0.763358\pi$
$654$	−23.1672	−0.905911
$655$	4.51951	0.176592
$656$	1.00000	0.0390434
$657$	6.74881	0.263296
$658$	0	0
$659$	−15.2994	−0.595979	−0.297989	−	0.954569i	$-0.596316\pi$
$659$	−15.2994	−0.595979	−0.297989	+	0.954569i	$0.596316\pi$
$660$	−2.02468	−0.0788106
$661$	−26.3758	−1.02590	−0.512949	−	0.858419i	$-0.671447\pi$
$661$	−26.3758	−1.02590	−0.512949	+	0.858419i	$0.671447\pi$
$662$	−22.2134	−0.863346
$663$	0.525916	0.0204249
$664$	−1.52221	−0.0590732
$665$	0	0
$666$	−21.3137	−0.825889
$667$	1.91217	0.0740395
$668$	−2.04253	−0.0790278
$669$	−3.90267	−0.150886
$670$	0.255729	0.00987969
$671$	2.86151	0.110467
$672$	0	0
$673$	11.4518	0.441433	0.220717	−	0.975338i	$-0.429160\pi$
$673$	11.4518	0.441433	0.220717	+	0.975338i	$0.429160\pi$
$674$	−14.8724	−0.572862
$675$	7.52043	0.289462
$676$	−12.9821	−0.499313
$677$	32.1448	1.23543	0.617713	−	0.786404i	$-0.288059\pi$
$677$	32.1448	1.23543	0.617713	+	0.786404i	$0.288059\pi$
$678$	−2.29649	−0.0881960
$679$	0	0
$680$	0.638089	0.0244696
$681$	−18.1428	−0.695232
$682$	−5.94609	−0.227688
$683$	−26.2292	−1.00363	−0.501815	−	0.864975i	$-0.667334\pi$
$683$	−26.2292	−1.00363	−0.501815	+	0.864975i	$0.667334\pi$
$684$	1.68952	0.0646003
$685$	−2.47875	−0.0947082
$686$	0	0
$687$	37.6239	1.43544
$688$	6.66821	0.254223
$689$	−0.163812	−0.00624074
$690$	0.586828	0.0223402
$691$	20.2617	0.770791	0.385396	−	0.922751i	$-0.374065\pi$
$691$	20.2617	0.770791	0.385396	+	0.922751i	$0.374065\pi$
$692$	9.56918	0.363766
$693$	0	0
$694$	−5.22478	−0.198330
$695$	−0.273432	−0.0103719
$696$	−6.50274	−0.246486
$697$	1.70413	0.0645485
$698$	23.4754	0.888557
$699$	20.8540	0.788772
$700$	0	0
$701$	0.932833	0.0352326	0.0176163	−	0.999845i	$-0.494392\pi$
$701$	0.932833	0.0352326	0.0176163	+	0.999845i	$0.494392\pi$
$702$	0.206865	0.00780763
$703$	6.63475	0.250234
$704$	2.34222	0.0882757
$705$	3.45451	0.130104
$706$	5.25312	0.197704
$707$	0	0
$708$	31.4378	1.18151
$709$	−52.6076	−1.97572	−0.987860	−	0.155346i	$-0.950351\pi$
$709$	−52.6076	−1.97572	−0.987860	+	0.155346i	$0.950351\pi$
$710$	3.04240	0.114179
$711$	−30.5002	−1.14385
$712$	8.52779	0.319592
$713$	1.72340	0.0645418
$714$	0	0
$715$	−0.117238	−0.00438445
$716$	9.97650	0.372839
$717$	−2.78312	−0.103937
$718$	−10.0526	−0.375160
$719$	−2.08372	−0.0777098	−0.0388549	−	0.999245i	$-0.512371\pi$
$719$	−2.08372	−0.0777098	−0.0388549	+	0.999245i	$0.512371\pi$
$720$	−0.872322	−0.0325095
$721$	0	0
$722$	18.4741	0.687534
$723$	−40.7087	−1.51397
$724$	24.3936	0.906581
$725$	−13.6887	−0.508387
$726$	12.7297	0.472444
$727$	−40.7427	−1.51106	−0.755532	−	0.655112i	$-0.772621\pi$
$727$	−40.7427	−1.51106	−0.755532	+	0.655112i	$0.772621\pi$
$728$	0	0
$729$	−13.8877	−0.514360
$730$	1.08469	0.0401463
$731$	11.3635	0.420294
$732$	2.82045	0.104247
$733$	−2.54040	−0.0938320	−0.0469160	−	0.998899i	$-0.514939\pi$
$733$	−2.54040	−0.0938320	−0.0469160	+	0.998899i	$0.514939\pi$
$734$	−4.93946	−0.182319
$735$	0	0
$736$	−0.678862	−0.0250232
$737$	1.59967	0.0589245
$738$	−2.32969	−0.0857572
$739$	−0.495193	−0.0182160	−0.00910798	−	0.999959i	$-0.502899\pi$
$739$	−0.495193	−0.0182160	−0.00910798	+	0.999959i	$0.502899\pi$
$740$	−3.42561	−0.125928
$741$	0.223809	0.00822184
$742$	0	0
$743$	−27.8689	−1.02241	−0.511205	−	0.859459i	$-0.670801\pi$
$743$	−27.8689	−1.02241	−0.511205	+	0.859459i	$0.670801\pi$
$744$	−5.86078	−0.214867
$745$	−1.27062	−0.0465518
$746$	19.0600	0.697836
$747$	3.54628	0.129752
$748$	3.99144	0.145942
$749$	0	0
$750$	−8.52310	−0.311219
$751$	−17.3440	−0.632893	−0.316446	−	0.948610i	$-0.602490\pi$
$751$	−17.3440	−0.632893	−0.316446	+	0.948610i	$0.602490\pi$
$752$	−3.99629	−0.145730
$753$	−18.4258	−0.671473
$754$	−0.376537	−0.0137127
$755$	5.98274	0.217734
$756$	0	0
$757$	0.664377	0.0241472	0.0120736	−	0.999927i	$-0.496157\pi$
$757$	0.664377	0.0241472	0.0120736	+	0.999927i	$0.496157\pi$
$758$	20.8915	0.758813
$759$	3.67079	0.133241
$760$	0.271545	0.00984998
$761$	34.3582	1.24548	0.622742	−	0.782427i	$-0.286019\pi$
$761$	34.3582	1.24548	0.622742	+	0.782427i	$0.286019\pi$
$762$	−35.4984	−1.28597
$763$	0	0
$764$	4.44946	0.160976
$765$	−1.48655	−0.0537464
$766$	36.0739	1.30340
$767$	1.82039	0.0657305
$768$	2.30861	0.0833049
$769$	−14.2112	−0.512468	−0.256234	−	0.966615i	$-0.582482\pi$
$769$	−14.2112	−0.512468	−0.256234	+	0.966615i	$0.582482\pi$
$770$	0	0
$771$	−28.4834	−1.02580
$772$	−11.2662	−0.405478
$773$	−50.5040	−1.81650	−0.908252	−	0.418423i	$-0.862583\pi$
$773$	−50.5040	−1.81650	−0.908252	+	0.418423i	$0.862583\pi$
$774$	−15.5349	−0.558390
$775$	−12.3374	−0.443171
$776$	−1.74259	−0.0625552
$777$	0	0
$778$	−35.0407	−1.25627
$779$	0.725210	0.0259834
$780$	−0.115556	−0.00413757
$781$	19.0312	0.680989
$782$	−1.15687	−0.0413696
$783$	−4.35883	−0.155772
$784$	0	0
$785$	3.48970	0.124553
$786$	27.8654	0.993924
$787$	−26.3396	−0.938906	−0.469453	−	0.882957i	$-0.655549\pi$
$787$	−26.3396	−0.938906	−0.469453	+	0.882957i	$0.655549\pi$
$788$	5.60076	0.199519
$789$	57.2708	2.03890
$790$	−4.90210	−0.174409
$791$	0	0
$792$	−5.45665	−0.193894
$793$	0.163317	0.00579955
$794$	−21.3240	−0.756761
$795$	1.05928	0.0375689
$796$	−5.73582	−0.203301
$797$	−11.4534	−0.405700	−0.202850	−	0.979210i	$-0.565020\pi$
$797$	−11.4534	−0.405700	−0.202850	+	0.979210i	$0.565020\pi$
$798$	0	0
$799$	−6.81020	−0.240928
$800$	4.85980	0.171820
$801$	−19.8671	−0.701970
$802$	−2.72976	−0.0963913
$803$	6.78509	0.239441
$804$	1.57672	0.0556065
$805$	0	0
$806$	−0.339365	−0.0119536
$807$	0.166648	0.00586629
$808$	−16.3793	−0.576222
$809$	16.2845	0.572532	0.286266	−	0.958150i	$-0.407586\pi$
$809$	16.2845	0.572532	0.286266	+	0.958150i	$0.407586\pi$
$810$	−3.95465	−0.138952
$811$	−23.4547	−0.823607	−0.411804	−	0.911273i	$-0.635101\pi$
$811$	−23.4547	−0.823607	−0.411804	+	0.911273i	$0.635101\pi$
$812$	0	0
$813$	−50.3023	−1.76418
$814$	−21.4283	−0.751061
$815$	−7.51958	−0.263399
$816$	3.93418	0.137724
$817$	4.83585	0.169185
$818$	20.4532	0.715130
$819$	0	0
$820$	−0.374437	−0.0130759
$821$	32.6342	1.13894	0.569470	−	0.822012i	$-0.307148\pi$
$821$	32.6342	1.13894	0.569470	+	0.822012i	$0.307148\pi$
$822$	−15.2829	−0.533052
$823$	8.23017	0.286886	0.143443	−	0.989659i	$-0.454183\pi$
$823$	8.23017	0.286886	0.143443	+	0.989659i	$0.454183\pi$
$824$	0.328088	0.0114295
$825$	−26.2783	−0.914892
$826$	0	0
$827$	−51.3662	−1.78618	−0.893089	−	0.449879i	$-0.851467\pi$
$827$	−51.3662	−1.78618	−0.893089	+	0.449879i	$0.851467\pi$
$828$	1.58154	0.0549623
$829$	42.0898	1.46184	0.730920	−	0.682463i	$-0.239091\pi$
$829$	42.0898	1.46184	0.730920	+	0.682463i	$0.239091\pi$
$830$	0.569971	0.0197840
$831$	−15.0281	−0.521318
$832$	0.133679	0.00463448
$833$	0	0
$834$	−1.68587	−0.0583767
$835$	0.764798	0.0264669
$836$	1.69860	0.0587474
$837$	−3.92852	−0.135790
$838$	7.57172	0.261561
$839$	−10.2124	−0.352572	−0.176286	−	0.984339i	$-0.556408\pi$
$839$	−10.2124	−0.352572	−0.176286	+	0.984339i	$0.556408\pi$
$840$	0	0
$841$	−21.0660	−0.726415
$842$	−12.0012	−0.413589
$843$	65.2953	2.24889
$844$	7.41074	0.255088
$845$	4.86098	0.167223
$846$	9.31014	0.320089
$847$	0	0
$848$	−1.22541	−0.0420809
$849$	−49.2993	−1.69195
$850$	8.28173	0.284061
$851$	6.21072	0.212901
$852$	18.7581	0.642643
$853$	32.3872	1.10892	0.554459	−	0.832211i	$-0.312925\pi$
$853$	32.3872	1.10892	0.554459	+	0.832211i	$0.312925\pi$
$854$	0	0
$855$	−0.632617	−0.0216351
$856$	−1.47989	−0.0505816
$857$	−55.8370	−1.90735	−0.953677	−	0.300831i	$-0.902736\pi$
$857$	−55.8370	−1.90735	−0.953677	+	0.300831i	$0.902736\pi$
$858$	−0.722839	−0.0246773
$859$	7.27325	0.248160	0.124080	−	0.992272i	$-0.460402\pi$
$859$	7.27325	0.248160	0.124080	+	0.992272i	$0.460402\pi$
$860$	−2.49682	−0.0851409
$861$	0	0
$862$	−13.7132	−0.467074
$863$	13.0836	0.445369	0.222685	−	0.974891i	$-0.428518\pi$
$863$	13.0836	0.445369	0.222685	+	0.974891i	$0.428518\pi$
$864$	1.54748	0.0526463
$865$	−3.58305	−0.121827
$866$	23.7704	0.807753
$867$	−32.5421	−1.10519
$868$	0	0
$869$	−30.6642	−1.04021
$870$	2.43486	0.0825496
$871$	0.0912989	0.00309354
$872$	−10.0351	−0.339833
$873$	4.05969	0.137400
$874$	−0.492318	−0.0166529
$875$	0	0
$876$	6.68774	0.225958
$877$	43.5882	1.47187	0.735935	−	0.677052i	$-0.236743\pi$
$877$	43.5882	1.47187	0.735935	+	0.677052i	$0.236743\pi$
$878$	19.3393	0.652669
$879$	−18.0719	−0.609550
$880$	−0.877012	−0.0295641
$881$	−21.2788	−0.716901	−0.358451	−	0.933549i	$-0.616695\pi$
$881$	−21.2788	−0.716901	−0.358451	+	0.933549i	$0.616695\pi$
$882$	0	0
$883$	−18.1393	−0.610435	−0.305218	−	0.952283i	$-0.598729\pi$
$883$	−18.1393	−0.610435	−0.305218	+	0.952283i	$0.598729\pi$
$884$	0.227806	0.00766195
$885$	−11.7715	−0.395694
$886$	−32.4468	−1.09007
$887$	−45.6323	−1.53218	−0.766092	−	0.642731i	$-0.777801\pi$
$887$	−45.6323	−1.53218	−0.766092	+	0.642731i	$0.777801\pi$
$888$	−21.1208	−0.708769
$889$	0	0
$890$	−3.19311	−0.107033
$891$	−24.7376	−0.828741
$892$	−1.69048	−0.0566015
$893$	−2.89815	−0.0969830
$894$	−7.83406	−0.262010
$895$	−3.73557	−0.124866
$896$	0	0
$897$	0.209506	0.00699519
$898$	−10.8167	−0.360958
$899$	7.15071	0.238490
$900$	−11.3218	−0.377395
$901$	−2.08827	−0.0695702
$902$	−2.34222	−0.0779873
$903$	0	0
$904$	−0.994747	−0.0330848
$905$	−9.13385	−0.303620
$906$	36.8870	1.22549
$907$	−39.6445	−1.31637	−0.658187	−	0.752855i	$-0.728676\pi$
$907$	−39.6445	−1.31637	−0.658187	+	0.752855i	$0.728676\pi$
$908$	−7.85873	−0.260801
$909$	38.1588	1.26565
$910$	0	0
$911$	−23.2850	−0.771468	−0.385734	−	0.922610i	$-0.626052\pi$
$911$	−23.2850	−0.771468	−0.385734	+	0.922610i	$0.626052\pi$
$912$	1.67423	0.0554393
$913$	3.56535	0.117996
$914$	14.6183	0.483531
$915$	−1.05608	−0.0349129
$916$	16.2972	0.538475
$917$	0	0
$918$	2.63710	0.0870374
$919$	39.5032	1.30309	0.651544	−	0.758610i	$-0.274121\pi$
$919$	39.5032	1.30309	0.651544	+	0.758610i	$0.274121\pi$
$920$	0.254191	0.00838042
$921$	−55.2962	−1.82207
$922$	−21.3560	−0.703323
$923$	1.08618	0.0357520
$924$	0	0
$925$	−44.4609	−1.46187
$926$	−17.3519	−0.570220
$927$	−0.764345	−0.0251044
$928$	−2.81673	−0.0924636
$929$	−41.4690	−1.36055	−0.680277	−	0.732955i	$-0.738141\pi$
$929$	−41.4690	−1.36055	−0.680277	+	0.732955i	$0.738141\pi$
$930$	2.19449	0.0719602
$931$	0	0
$932$	9.03314	0.295890
$933$	−33.4170	−1.09402
$934$	10.3452	0.338506
$935$	−1.49454	−0.0488768
$936$	−0.311431	−0.0101794
$937$	−32.0902	−1.04834	−0.524170	−	0.851613i	$-0.675625\pi$
$937$	−32.0902	−1.04834	−0.524170	+	0.851613i	$0.675625\pi$
$938$	0	0
$939$	32.9875	1.07651
$940$	1.49636	0.0488058
$941$	17.0335	0.555275	0.277638	−	0.960686i	$-0.410449\pi$
$941$	17.0335	0.555275	0.277638	+	0.960686i	$0.410449\pi$
$942$	21.5160	0.701028
$943$	0.678862	0.0221068
$944$	13.6176	0.443216
$945$	0	0
$946$	−15.6184	−0.507798
$947$	−26.5551	−0.862923	−0.431462	−	0.902131i	$-0.642002\pi$
$947$	−26.5551	−0.862923	−0.431462	+	0.902131i	$0.642002\pi$
$948$	−30.2242	−0.981636
$949$	0.387250	0.0125707
$950$	3.52438	0.114346
$951$	5.07621	0.164607
$952$	0	0
$953$	−34.2798	−1.11043	−0.555215	−	0.831707i	$-0.687364\pi$
$953$	−34.2798	−1.11043	−0.555215	+	0.831707i	$0.687364\pi$
$954$	2.85484	0.0924289
$955$	−1.66604	−0.0539118
$956$	−1.20554	−0.0389898
$957$	15.2308	0.492343
$958$	37.8835	1.22396
$959$	0	0
$960$	−0.864429	−0.0278993
$961$	−24.5552	−0.792104
$962$	−1.22299	−0.0394308
$963$	3.44769	0.111100
$964$	−17.6334	−0.567933
$965$	4.21847	0.135797
$966$	0	0
$967$	−46.5935	−1.49835	−0.749173	−	0.662375i	$-0.769549\pi$
$967$	−46.5935	−1.49835	−0.749173	+	0.662375i	$0.769549\pi$
$968$	5.51401	0.177227
$969$	2.85311	0.0916550
$970$	0.652488	0.0209501
$971$	−2.67921	−0.0859800	−0.0429900	−	0.999076i	$-0.513688\pi$
$971$	−2.67921	−0.0859800	−0.0429900	+	0.999076i	$0.513688\pi$
$972$	−19.7402	−0.633168
$973$	0	0
$974$	18.9378	0.606805
$975$	−1.49980	−0.0480319
$976$	1.22171	0.0391059
$977$	−47.8723	−1.53157	−0.765786	−	0.643096i	$-0.777650\pi$
$977$	−47.8723	−1.53157	−0.765786	+	0.643096i	$0.777650\pi$
$978$	−46.3625	−1.48251
$979$	−19.9739	−0.638370
$980$	0	0
$981$	23.3788	0.746427
$982$	−21.3032	−0.679811
$983$	−13.1498	−0.419414	−0.209707	−	0.977764i	$-0.567251\pi$
$983$	−13.1498	−0.419414	−0.209707	+	0.977764i	$0.567251\pi$
$984$	−2.30861	−0.0735959
$985$	−2.09713	−0.0668201
$986$	−4.80007	−0.152865
$987$	0	0
$988$	0.0969453	0.00308424
$989$	4.52679	0.143944
$990$	2.04317	0.0649362
$991$	54.2881	1.72452	0.862260	−	0.506467i	$-0.169049\pi$
$991$	54.2881	1.72452	0.862260	+	0.506467i	$0.169049\pi$
$992$	−2.53866	−0.0806025
$993$	51.2820	1.62739
$994$	0	0
$995$	2.14770	0.0680867
$996$	3.51419	0.111352
$997$	8.22418	0.260462	0.130231	−	0.991484i	$-0.458428\pi$
$997$	8.22418	0.260462	0.130231	+	0.991484i	$0.458428\pi$
$998$	27.3251	0.864962
$999$	−14.1574	−0.447922

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4018.2.a.bo.1.5		6
7.2	even	3		574.2.e.g.165.2	✓	12
7.4	even	3		574.2.e.g.247.2	yes	12
7.6	odd	2		4018.2.a.bn.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
574.2.e.g.165.2	✓	12	7.2	even	3
574.2.e.g.247.2	yes	12	7.4	even	3
4018.2.a.bn.1.2		6	7.6	odd	2
4018.2.a.bo.1.5		6	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4018 = 2 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.30861 q^{3} +1.00000 q^{4} -0.374437 q^{5} -2.30861 q^{6} -1.00000 q^{8} +2.32969 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.30861 q^{3} +1.00000 q^{4} -0.374437 q^{5} -2.30861 q^{6} -1.00000 q^{8} +2.32969 q^{9} +0.374437 q^{10} +2.34222 q^{11} +2.30861 q^{12} +0.133679 q^{13} -0.864429 q^{15} +1.00000 q^{16} +1.70413 q^{17} -2.32969 q^{18} +0.725210 q^{19} -0.374437 q^{20} -2.34222 q^{22} +0.678862 q^{23} -2.30861 q^{24} -4.85980 q^{25} -0.133679 q^{26} -1.54748 q^{27} +2.81673 q^{29} +0.864429 q^{30} +2.53866 q^{31} -1.00000 q^{32} +5.40728 q^{33} -1.70413 q^{34} +2.32969 q^{36} +9.14872 q^{37} -0.725210 q^{38} +0.308613 q^{39} +0.374437 q^{40} +1.00000 q^{41} +6.66821 q^{43} +2.34222 q^{44} -0.872322 q^{45} -0.678862 q^{46} -3.99629 q^{47} +2.30861 q^{48} +4.85980 q^{50} +3.93418 q^{51} +0.133679 q^{52} -1.22541 q^{53} +1.54748 q^{54} -0.877012 q^{55} +1.67423 q^{57} -2.81673 q^{58} +13.6176 q^{59} -0.864429 q^{60} +1.22171 q^{61} -2.53866 q^{62} +1.00000 q^{64} -0.0500543 q^{65} -5.40728 q^{66} +0.682971 q^{67} +1.70413 q^{68} +1.56723 q^{69} +8.12528 q^{71} -2.32969 q^{72} +2.89686 q^{73} -9.14872 q^{74} -11.2194 q^{75} +0.725210 q^{76} -0.308613 q^{78} -13.0919 q^{79} -0.374437 q^{80} -10.5616 q^{81} -1.00000 q^{82} +1.52221 q^{83} -0.638089 q^{85} -6.66821 q^{86} +6.50274 q^{87} -2.34222 q^{88} -8.52779 q^{89} +0.872322 q^{90} +0.678862 q^{92} +5.86078 q^{93} +3.99629 q^{94} -0.271545 q^{95} -2.30861 q^{96} +1.74259 q^{97} +5.45665 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + q^{3} + 6 q^{4} - q^{6} - 6 q^{8} + 5 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 + q^3 + 6 * q^4 - q^6 - 6 * q^8 + 5 * q^9	\( 6 q - 6 q^{2} + q^{3} + 6 q^{4} - q^{6} - 6 q^{8} + 5 q^{9} + q^{11} + q^{12} + 4 q^{13} + 2 q^{15} + 6 q^{16} - q^{17} - 5 q^{18} - 3 q^{19} - q^{22} + 21 q^{23} - q^{24} - 4 q^{26} + 13 q^{27} + 5 q^{29} - 2 q^{30} + 3 q^{31} - 6 q^{32} - 19 q^{33} + q^{34} + 5 q^{36} - 2 q^{37} + 3 q^{38} - 11 q^{39} + 6 q^{41} + 12 q^{43} + q^{44} + 28 q^{45} - 21 q^{46} - 18 q^{47} + q^{48} + 13 q^{51} + 4 q^{52} + 14 q^{53} - 13 q^{54} - 7 q^{55} + 5 q^{57} - 5 q^{58} + 16 q^{59} + 2 q^{60} - 20 q^{61} - 3 q^{62} + 6 q^{64} + 18 q^{65} + 19 q^{66} - 13 q^{67} - q^{68} + 15 q^{69} + 11 q^{71} - 5 q^{72} + q^{73} + 2 q^{74} - 23 q^{75} - 3 q^{76} + 11 q^{78} + 19 q^{79} - 6 q^{81} - 6 q^{82} + 15 q^{83} - 2 q^{85} - 12 q^{86} + 10 q^{87} - q^{88} - 14 q^{89} - 28 q^{90} + 21 q^{92} + 35 q^{93} + 18 q^{94} + 24 q^{95} - q^{96} + q^{97} + 10 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + q^3 + 6 * q^4 - q^6 - 6 * q^8 + 5 * q^9 + q^11 + q^12 + 4 * q^13 + 2 * q^15 + 6 * q^16 - q^17 - 5 * q^18 - 3 * q^19 - q^22 + 21 * q^23 - q^24 - 4 * q^26 + 13 * q^27 + 5 * q^29 - 2 * q^30 + 3 * q^31 - 6 * q^32 - 19 * q^33 + q^34 + 5 * q^36 - 2 * q^37 + 3 * q^38 - 11 * q^39 + 6 * q^41 + 12 * q^43 + q^44 + 28 * q^45 - 21 * q^46 - 18 * q^47 + q^48 + 13 * q^51 + 4 * q^52 + 14 * q^53 - 13 * q^54 - 7 * q^55 + 5 * q^57 - 5 * q^58 + 16 * q^59 + 2 * q^60 - 20 * q^61 - 3 * q^62 + 6 * q^64 + 18 * q^65 + 19 * q^66 - 13 * q^67 - q^68 + 15 * q^69 + 11 * q^71 - 5 * q^72 + q^73 + 2 * q^74 - 23 * q^75 - 3 * q^76 + 11 * q^78 + 19 * q^79 - 6 * q^81 - 6 * q^82 + 15 * q^83 - 2 * q^85 - 12 * q^86 + 10 * q^87 - q^88 - 14 * q^89 - 28 * q^90 + 21 * q^92 + 35 * q^93 + 18 * q^94 + 24 * q^95 - q^96 + q^97 + 10 * q^99

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