LMFDB - Embedded newform 6027.2.a.bj.1.13

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:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} - 19 x^{12} + 36 x^{11} + 134 x^{10} - 237 x^{9} - 438 x^{8} + 716 x^{7} + 662 x^{6} + \cdots + 16 $ x^14 - 2x^13 - 19x^12 + 36x^11 + 134x^10 - 237x^9 - 438x^8 + 716x^7 + 662x^6 - 1007x^5 - 384x^4 + 579x^3 + 44x^2 - 112*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 861)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Root			$-2.13271$ 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)

$f(q)$	$=$	$q+2.13271 q^{2} -1.00000 q^{3} +2.54845 q^{4} +0.889988 q^{5} -2.13271 q^{6} +1.16968 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.13271 q^{2} -1.00000 q^{3} +2.54845 q^{4} +0.889988 q^{5} -2.13271 q^{6} +1.16968 q^{8} +1.00000 q^{9} +1.89809 q^{10} +3.41733 q^{11} -2.54845 q^{12} +6.24747 q^{13} -0.889988 q^{15} -2.60231 q^{16} +7.99996 q^{17} +2.13271 q^{18} -0.0729909 q^{19} +2.26809 q^{20} +7.28817 q^{22} +1.57406 q^{23} -1.16968 q^{24} -4.20792 q^{25} +13.3240 q^{26} -1.00000 q^{27} -0.756839 q^{29} -1.89809 q^{30} +2.56122 q^{31} -7.88933 q^{32} -3.41733 q^{33} +17.0616 q^{34} +2.54845 q^{36} -11.1697 q^{37} -0.155668 q^{38} -6.24747 q^{39} +1.04100 q^{40} +1.00000 q^{41} -6.17260 q^{43} +8.70889 q^{44} +0.889988 q^{45} +3.35702 q^{46} +1.59757 q^{47} +2.60231 q^{48} -8.97427 q^{50} -7.99996 q^{51} +15.9214 q^{52} +9.15967 q^{53} -2.13271 q^{54} +3.04138 q^{55} +0.0729909 q^{57} -1.61412 q^{58} -0.919674 q^{59} -2.26809 q^{60} -8.51853 q^{61} +5.46234 q^{62} -11.6210 q^{64} +5.56017 q^{65} -7.28817 q^{66} +2.41279 q^{67} +20.3875 q^{68} -1.57406 q^{69} +8.88392 q^{71} +1.16968 q^{72} +3.64101 q^{73} -23.8216 q^{74} +4.20792 q^{75} -0.186014 q^{76} -13.3240 q^{78} +11.7568 q^{79} -2.31602 q^{80} +1.00000 q^{81} +2.13271 q^{82} +4.03102 q^{83} +7.11987 q^{85} -13.1644 q^{86} +0.756839 q^{87} +3.99719 q^{88} -8.44697 q^{89} +1.89809 q^{90} +4.01141 q^{92} -2.56122 q^{93} +3.40716 q^{94} -0.0649610 q^{95} +7.88933 q^{96} -9.05668 q^{97} +3.41733 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{2} - 14 q^{3} + 14 q^{4} + 10 q^{5} + 2 q^{6} - 6 q^{8} + 14 q^{9}+O(q^{10}) $ 14 * q - 2 * q^2 - 14 * q^3 + 14 * q^4 + 10 * q^5 + 2 * q^6 - 6 * q^8 + 14 * q^9	$ 14 q - 2 q^{2} - 14 q^{3} + 14 q^{4} + 10 q^{5} + 2 q^{6} - 6 q^{8} + 14 q^{9} + 3 q^{10} - 16 q^{11} - 14 q^{12} + 21 q^{13} - 10 q^{15} + 22 q^{16} + 12 q^{17} - 2 q^{18} + 2 q^{19} + 40 q^{20} + q^{22} - 7 q^{23} + 6 q^{24} + 22 q^{25} + 2 q^{26} - 14 q^{27} - 16 q^{29} - 3 q^{30} + 8 q^{31} - 19 q^{32} + 16 q^{33} + 33 q^{34} + 14 q^{36} + q^{37} + 32 q^{38} - 21 q^{39} - 13 q^{40} + 14 q^{41} + 14 q^{43} - 36 q^{44} + 10 q^{45} - 12 q^{46} + 12 q^{47} - 22 q^{48} - q^{50} - 12 q^{51} + 60 q^{52} - 20 q^{53} + 2 q^{54} - 11 q^{55} - 2 q^{57} + 21 q^{58} + 25 q^{59} - 40 q^{60} + 26 q^{61} - 33 q^{62} + 42 q^{64} - 8 q^{65} - q^{66} - 22 q^{67} + 15 q^{68} + 7 q^{69} - 36 q^{71} - 6 q^{72} + 31 q^{73} - 65 q^{74} - 22 q^{75} - 2 q^{76} - 2 q^{78} + 12 q^{79} + 112 q^{80} + 14 q^{81} - 2 q^{82} + 20 q^{83} + 40 q^{85} - 9 q^{86} + 16 q^{87} - 54 q^{88} + 39 q^{89} + 3 q^{90} + 63 q^{92} - 8 q^{93} + 14 q^{94} - 55 q^{95} + 19 q^{96} + 18 q^{97} - 16 q^{99}+O(q^{100}) $ 14 * q - 2 * q^2 - 14 * q^3 + 14 * q^4 + 10 * q^5 + 2 * q^6 - 6 * q^8 + 14 * q^9 + 3 * q^10 - 16 * q^11 - 14 * q^12 + 21 * q^13 - 10 * q^15 + 22 * q^16 + 12 * q^17 - 2 * q^18 + 2 * q^19 + 40 * q^20 + q^22 - 7 * q^23 + 6 * q^24 + 22 * q^25 + 2 * q^26 - 14 * q^27 - 16 * q^29 - 3 * q^30 + 8 * q^31 - 19 * q^32 + 16 * q^33 + 33 * q^34 + 14 * q^36 + q^37 + 32 * q^38 - 21 * q^39 - 13 * q^40 + 14 * q^41 + 14 * q^43 - 36 * q^44 + 10 * q^45 - 12 * q^46 + 12 * q^47 - 22 * q^48 - q^50 - 12 * q^51 + 60 * q^52 - 20 * q^53 + 2 * q^54 - 11 * q^55 - 2 * q^57 + 21 * q^58 + 25 * q^59 - 40 * q^60 + 26 * q^61 - 33 * q^62 + 42 * q^64 - 8 * q^65 - q^66 - 22 * q^67 + 15 * q^68 + 7 * q^69 - 36 * q^71 - 6 * q^72 + 31 * q^73 - 65 * q^74 - 22 * q^75 - 2 * q^76 - 2 * q^78 + 12 * q^79 + 112 * q^80 + 14 * q^81 - 2 * q^82 + 20 * q^83 + 40 * q^85 - 9 * q^86 + 16 * q^87 - 54 * q^88 + 39 * q^89 + 3 * q^90 + 63 * q^92 - 8 * q^93 + 14 * q^94 - 55 * q^95 + 19 * q^96 + 18 * q^97 - 16 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.13271	1.50805	0.754027	−	0.656844i	$-0.228109\pi$
$2$	2.13271	1.50805	0.754027	+	0.656844i	$0.228109\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.54845	1.27422
$5$	0.889988	0.398015	0.199007	−	0.979998i	$-0.436228\pi$
$5$	0.889988	0.398015	0.199007	+	0.979998i	$0.436228\pi$
$6$	−2.13271	−0.870675
$7$	0	0
$7$	0	0
$8$	1.16968	0.413545
$9$	1.00000	0.333333
$10$	1.89809	0.600227
$11$	3.41733	1.03036	0.515182	−	0.857081i	$-0.327724\pi$
$11$	3.41733	1.03036	0.515182	+	0.857081i	$0.327724\pi$
$12$	−2.54845	−0.735674
$13$	6.24747	1.73274	0.866368	−	0.499406i	$-0.166448\pi$
$13$	6.24747	1.73274	0.866368	+	0.499406i	$0.166448\pi$
$14$	0	0
$15$	−0.889988	−0.229794
$16$	−2.60231	−0.650577
$17$	7.99996	1.94027	0.970137	−	0.242556i	$-0.0779857\pi$
$17$	7.99996	1.94027	0.970137	+	0.242556i	$0.0779857\pi$
$18$	2.13271	0.502684
$19$	−0.0729909	−0.0167453	−0.00837263	−	0.999965i	$-0.502665\pi$
$19$	−0.0729909	−0.0167453	−0.00837263	+	0.999965i	$0.502665\pi$
$20$	2.26809	0.507160
$21$	0	0
$22$	7.28817	1.55384
$23$	1.57406	0.328215	0.164107	−	0.986443i	$-0.447526\pi$
$23$	1.57406	0.328215	0.164107	+	0.986443i	$0.447526\pi$
$24$	−1.16968	−0.238760
$25$	−4.20792	−0.841584
$26$	13.3240	2.61306
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−0.756839	−0.140541	−0.0702707	−	0.997528i	$-0.522386\pi$
$29$	−0.756839	−0.140541	−0.0702707	+	0.997528i	$0.522386\pi$
$30$	−1.89809	−0.346541
$31$	2.56122	0.460009	0.230004	−	0.973190i	$-0.426126\pi$
$31$	2.56122	0.460009	0.230004	+	0.973190i	$0.426126\pi$
$32$	−7.88933	−1.39465
$33$	−3.41733	−0.594881
$34$	17.0616	2.92604
$35$	0	0
$36$	2.54845	0.424741
$37$	−11.1697	−1.83628	−0.918140	−	0.396257i	$-0.870309\pi$
$37$	−11.1697	−1.83628	−0.918140	+	0.396257i	$0.870309\pi$
$38$	−0.155668	−0.0252527
$39$	−6.24747	−1.00040
$40$	1.04100	0.164597
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	−6.17260	−0.941312	−0.470656	−	0.882317i	$-0.655983\pi$
$43$	−6.17260	−0.941312	−0.470656	+	0.882317i	$0.655983\pi$
$44$	8.70889	1.31291
$45$	0.889988	0.132672
$46$	3.35702	0.494965
$47$	1.59757	0.233030	0.116515	−	0.993189i	$-0.462828\pi$
$47$	1.59757	0.233030	0.116515	+	0.993189i	$0.462828\pi$
$48$	2.60231	0.375611
$49$	0	0
$50$	−8.97427	−1.26915
$51$	−7.99996	−1.12022
$52$	15.9214	2.20789
$53$	9.15967	1.25818	0.629088	−	0.777334i	$-0.283428\pi$
$53$	9.15967	1.25818	0.629088	+	0.777334i	$0.283428\pi$
$54$	−2.13271	−0.290225
$55$	3.04138	0.410100
$56$	0	0
$57$	0.0729909	0.00966788
$58$	−1.61412	−0.211944
$59$	−0.919674	−0.119731	−0.0598657	−	0.998206i	$-0.519067\pi$
$59$	−0.919674	−0.119731	−0.0598657	+	0.998206i	$0.519067\pi$
$60$	−2.26809	−0.292809
$61$	−8.51853	−1.09069	−0.545343	−	0.838213i	$-0.683601\pi$
$61$	−8.51853	−1.09069	−0.545343	+	0.838213i	$0.683601\pi$
$62$	5.46234	0.693717
$63$	0	0
$64$	−11.6210	−1.45263
$65$	5.56017	0.689655
$66$	−7.28817	−0.897112
$67$	2.41279	0.294770	0.147385	−	0.989079i	$-0.452914\pi$
$67$	2.41279	0.294770	0.147385	+	0.989079i	$0.452914\pi$
$68$	20.3875	2.47235
$69$	−1.57406	−0.189495
$70$	0	0
$71$	8.88392	1.05433	0.527163	−	0.849764i	$-0.323256\pi$
$71$	8.88392	1.05433	0.527163	+	0.849764i	$0.323256\pi$
$72$	1.16968	0.137848
$73$	3.64101	0.426148	0.213074	−	0.977036i	$-0.431652\pi$
$73$	3.64101	0.426148	0.213074	+	0.977036i	$0.431652\pi$
$74$	−23.8216	−2.76921
$75$	4.20792	0.485889
$76$	−0.186014	−0.0213372
$77$	0	0
$78$	−13.3240	−1.50865
$79$	11.7568	1.32274	0.661371	−	0.750059i	$-0.269975\pi$
$79$	11.7568	1.32274	0.661371	+	0.750059i	$0.269975\pi$
$80$	−2.31602	−0.258939
$81$	1.00000	0.111111
$82$	2.13271	0.235518
$83$	4.03102	0.442462	0.221231	−	0.975221i	$-0.428992\pi$
$83$	4.03102	0.442462	0.221231	+	0.975221i	$0.428992\pi$
$84$	0	0
$85$	7.11987	0.772258
$86$	−13.1644	−1.41955
$87$	0.756839	0.0811417
$88$	3.99719	0.426101
$89$	−8.44697	−0.895377	−0.447688	−	0.894190i	$-0.647753\pi$
$89$	−8.44697	−0.895377	−0.447688	+	0.894190i	$0.647753\pi$
$90$	1.89809	0.200076
$91$	0	0
$92$	4.01141	0.418219
$93$	−2.56122	−0.265586
$94$	3.40716	0.351421
$95$	−0.0649610	−0.00666486
$96$	7.88933	0.805201
$97$	−9.05668	−0.919567	−0.459783	−	0.888031i	$-0.652073\pi$
$97$	−9.05668	−0.919567	−0.459783	+	0.888031i	$0.652073\pi$
$98$	0	0
$99$	3.41733	0.343455
$100$	−10.7237	−1.07237
$101$	10.8514	1.07976	0.539879	−	0.841742i	$-0.318470\pi$
$101$	10.8514	1.07976	0.539879	+	0.841742i	$0.318470\pi$
$102$	−17.0616	−1.68935
$103$	−3.12953	−0.308362	−0.154181	−	0.988043i	$-0.549274\pi$
$103$	−3.12953	−0.308362	−0.154181	+	0.988043i	$0.549274\pi$
$104$	7.30755	0.716564
$105$	0	0
$106$	19.5349	1.89740
$107$	3.35731	0.324564	0.162282	−	0.986744i	$-0.448115\pi$
$107$	3.35731	0.324564	0.162282	+	0.986744i	$0.448115\pi$
$108$	−2.54845	−0.245225
$109$	0.403889	0.0386856	0.0193428	−	0.999813i	$-0.493843\pi$
$109$	0.403889	0.0386856	0.0193428	+	0.999813i	$0.493843\pi$
$110$	6.48638	0.618453
$111$	11.1697	1.06018
$112$	0	0
$113$	5.43878	0.511637	0.255818	−	0.966725i	$-0.417655\pi$
$113$	5.43878	0.511637	0.255818	+	0.966725i	$0.417655\pi$
$114$	0.155668	0.0145797
$115$	1.40090	0.130634
$116$	−1.92877	−0.179081
$117$	6.24747	0.577579
$118$	−1.96140	−0.180561
$119$	0	0
$120$	−1.04100	−0.0950301
$121$	0.678140	0.0616491
$122$	−18.1675	−1.64481
$123$	−1.00000	−0.0901670
$124$	6.52713	0.586154
$125$	−8.19494	−0.732978
$126$	0	0
$127$	−5.15902	−0.457789	−0.228895	−	0.973451i	$-0.573511\pi$
$127$	−5.15902	−0.457789	−0.228895	+	0.973451i	$0.573511\pi$
$128$	−9.00561	−0.795991
$129$	6.17260	0.543467
$130$	11.8582	1.04004
$131$	11.9242	1.04182	0.520911	−	0.853611i	$-0.325592\pi$
$131$	11.9242	1.04182	0.520911	+	0.853611i	$0.325592\pi$
$132$	−8.70889	−0.758011
$133$	0	0
$134$	5.14579	0.444528
$135$	−0.889988	−0.0765980
$136$	9.35740	0.802390
$137$	4.57666	0.391010	0.195505	−	0.980703i	$-0.437365\pi$
$137$	4.57666	0.391010	0.195505	+	0.980703i	$0.437365\pi$
$138$	−3.35702	−0.285768
$139$	14.6408	1.24181	0.620906	−	0.783885i	$-0.286765\pi$
$139$	14.6408	1.24181	0.620906	+	0.783885i	$0.286765\pi$
$140$	0	0
$141$	−1.59757	−0.134540
$142$	18.9468	1.58998
$143$	21.3497	1.78535
$144$	−2.60231	−0.216859
$145$	−0.673578	−0.0559376
$146$	7.76522	0.642654
$147$	0	0
$148$	−28.4653	−2.33983
$149$	2.31277	0.189470	0.0947348	−	0.995503i	$-0.469800\pi$
$149$	2.31277	0.189470	0.0947348	+	0.995503i	$0.469800\pi$
$150$	8.97427	0.732746
$151$	1.08733	0.0884857	0.0442428	−	0.999021i	$-0.485912\pi$
$151$	1.08733	0.0884857	0.0442428	+	0.999021i	$0.485912\pi$
$152$	−0.0853761	−0.00692491
$153$	7.99996	0.646758
$154$	0	0
$155$	2.27945	0.183090
$156$	−15.9214	−1.27473
$157$	24.5214	1.95702	0.978512	−	0.206192i	$-0.0661072\pi$
$157$	24.5214	1.95702	0.978512	+	0.206192i	$0.0661072\pi$
$158$	25.0738	1.99477
$159$	−9.15967	−0.726409
$160$	−7.02141	−0.555091
$161$	0	0
$162$	2.13271	0.167561
$163$	−20.7325	−1.62390	−0.811948	−	0.583730i	$-0.801593\pi$
$163$	−20.7325	−1.62390	−0.811948	+	0.583730i	$0.801593\pi$
$164$	2.54845	0.199000
$165$	−3.04138	−0.236771
$166$	8.59700	0.667257
$167$	−9.83140	−0.760776	−0.380388	−	0.924827i	$-0.624210\pi$
$167$	−9.83140	−0.760776	−0.380388	+	0.924827i	$0.624210\pi$
$168$	0	0
$169$	26.0309	2.00238
$170$	15.1846	1.16461
$171$	−0.0729909	−0.00558175
$172$	−15.7305	−1.19944
$173$	19.3348	1.47000	0.734998	−	0.678070i	$-0.237183\pi$
$173$	19.3348	1.47000	0.734998	+	0.678070i	$0.237183\pi$
$174$	1.61412	0.122366
$175$	0	0
$176$	−8.89294	−0.670331
$177$	0.919674	0.0691269
$178$	−18.0149	−1.35028
$179$	16.3998	1.22578	0.612888	−	0.790170i	$-0.290008\pi$
$179$	16.3998	1.22578	0.612888	+	0.790170i	$0.290008\pi$
$180$	2.26809	0.169053
$181$	16.4233	1.22073	0.610366	−	0.792119i	$-0.291022\pi$
$181$	16.4233	1.22073	0.610366	+	0.792119i	$0.291022\pi$
$182$	0	0
$183$	8.51853	0.629708
$184$	1.84115	0.135731
$185$	−9.94086	−0.730866
$186$	−5.46234	−0.400518
$187$	27.3385	1.99919
$188$	4.07133	0.296932
$189$	0	0
$190$	−0.138543	−0.0100510
$191$	−25.9485	−1.87757	−0.938785	−	0.344503i	$-0.888047\pi$
$191$	−25.9485	−1.87757	−0.938785	+	0.344503i	$0.888047\pi$
$192$	11.6210	0.838675
$193$	26.2201	1.88737	0.943683	−	0.330850i	$-0.107335\pi$
$193$	26.2201	1.88737	0.943683	+	0.330850i	$0.107335\pi$
$194$	−19.3153	−1.38676
$195$	−5.56017	−0.398172
$196$	0	0
$197$	5.03749	0.358906	0.179453	−	0.983767i	$-0.442567\pi$
$197$	5.03749	0.358906	0.179453	+	0.983767i	$0.442567\pi$
$198$	7.28817	0.517948
$199$	−2.53705	−0.179847	−0.0899234	−	0.995949i	$-0.528662\pi$
$199$	−2.53705	−0.179847	−0.0899234	+	0.995949i	$0.528662\pi$
$200$	−4.92193	−0.348033
$201$	−2.41279	−0.170185
$202$	23.1430	1.62833
$203$	0	0
$204$	−20.3875	−1.42741
$205$	0.889988	0.0621595
$206$	−6.67438	−0.465026
$207$	1.57406	0.109405
$208$	−16.2578	−1.12728
$209$	−0.249434	−0.0172537
$210$	0	0
$211$	−23.1162	−1.59139	−0.795693	−	0.605700i	$-0.792893\pi$
$211$	−23.1162	−1.59139	−0.795693	+	0.605700i	$0.792893\pi$
$212$	23.3429	1.60320
$213$	−8.88392	−0.608716
$214$	7.16017	0.489459
$215$	−5.49354	−0.374656
$216$	−1.16968	−0.0795867
$217$	0	0
$218$	0.861378	0.0583399
$219$	−3.64101	−0.246037
$220$	7.75081	0.522559
$221$	49.9795	3.36198
$222$	23.8216	1.59880
$223$	−0.239630	−0.0160468	−0.00802341	−	0.999968i	$-0.502554\pi$
$223$	−0.239630	−0.0160468	−0.00802341	+	0.999968i	$0.502554\pi$
$224$	0	0
$225$	−4.20792	−0.280528
$226$	11.5993	0.771576
$227$	−3.70162	−0.245685	−0.122843	−	0.992426i	$-0.539201\pi$
$227$	−3.70162	−0.245685	−0.122843	+	0.992426i	$0.539201\pi$
$228$	0.186014	0.0123190
$229$	6.25848	0.413572	0.206786	−	0.978386i	$-0.433700\pi$
$229$	6.25848	0.413572	0.206786	+	0.978386i	$0.433700\pi$
$230$	2.98770	0.197003
$231$	0	0
$232$	−0.885260	−0.0581202
$233$	−25.6456	−1.68010	−0.840050	−	0.542509i	$-0.817474\pi$
$233$	−25.6456	−1.68010	−0.840050	+	0.542509i	$0.817474\pi$
$234$	13.3240	0.871020
$235$	1.42182	0.0927493
$236$	−2.34374	−0.152565
$237$	−11.7568	−0.763686
$238$	0	0
$239$	−17.7843	−1.15037	−0.575185	−	0.818023i	$-0.695070\pi$
$239$	−17.7843	−1.15037	−0.575185	+	0.818023i	$0.695070\pi$
$240$	2.31602	0.149499
$241$	−7.64067	−0.492179	−0.246089	−	0.969247i	$-0.579146\pi$
$241$	−7.64067	−0.492179	−0.246089	+	0.969247i	$0.579146\pi$
$242$	1.44627	0.0929700
$243$	−1.00000	−0.0641500
$244$	−21.7090	−1.38978
$245$	0	0
$246$	−2.13271	−0.135977
$247$	−0.456008	−0.0290151
$248$	2.99581	0.190234
$249$	−4.03102	−0.255456
$250$	−17.4774	−1.10537
$251$	2.01280	0.127047	0.0635235	−	0.997980i	$-0.479766\pi$
$251$	2.01280	0.127047	0.0635235	+	0.997980i	$0.479766\pi$
$252$	0	0
$253$	5.37909	0.338180
$254$	−11.0027	−0.690370
$255$	−7.11987	−0.445863
$256$	4.03570	0.252231
$257$	6.23662	0.389030	0.194515	−	0.980900i	$-0.437687\pi$
$257$	6.23662	0.389030	0.194515	+	0.980900i	$0.437687\pi$
$258$	13.1644	0.819577
$259$	0	0
$260$	14.1698	0.878775
$261$	−0.756839	−0.0468472
$262$	25.4309	1.57112
$263$	−8.13880	−0.501860	−0.250930	−	0.968005i	$-0.580736\pi$
$263$	−8.13880	−0.501860	−0.250930	+	0.968005i	$0.580736\pi$
$264$	−3.99719	−0.246010
$265$	8.15199	0.500773
$266$	0	0
$267$	8.44697	0.516946
$268$	6.14888	0.375603
$269$	−25.6694	−1.56509	−0.782544	−	0.622595i	$-0.786079\pi$
$269$	−25.6694	−1.56509	−0.782544	+	0.622595i	$0.786079\pi$
$270$	−1.89809	−0.115514
$271$	−30.0299	−1.82419	−0.912093	−	0.409983i	$-0.865535\pi$
$271$	−30.0299	−1.82419	−0.912093	+	0.409983i	$0.865535\pi$
$272$	−20.8184	−1.26230
$273$	0	0
$274$	9.76068	0.589664
$275$	−14.3799	−0.867138
$276$	−4.01141	−0.241459
$277$	−10.2884	−0.618169	−0.309085	−	0.951035i	$-0.600023\pi$
$277$	−10.2884	−0.618169	−0.309085	+	0.951035i	$0.600023\pi$
$278$	31.2245	1.87272
$279$	2.56122	0.153336
$280$	0	0
$281$	11.9838	0.714894	0.357447	−	0.933933i	$-0.383647\pi$
$281$	11.9838	0.714894	0.357447	+	0.933933i	$0.383647\pi$
$282$	−3.40716	−0.202893
$283$	−15.2539	−0.906752	−0.453376	−	0.891319i	$-0.649781\pi$
$283$	−15.2539	−0.906752	−0.453376	+	0.891319i	$0.649781\pi$
$284$	22.6402	1.34345
$285$	0.0649610	0.00384796
$286$	45.5326	2.69240
$287$	0	0
$288$	−7.88933	−0.464883
$289$	46.9993	2.76467
$290$	−1.43655	−0.0843569
$291$	9.05668	0.530912
$292$	9.27893	0.543008
$293$	−29.2216	−1.70714	−0.853571	−	0.520976i	$-0.825568\pi$
$293$	−29.2216	−1.70714	−0.853571	+	0.520976i	$0.825568\pi$
$294$	0	0
$295$	−0.818499	−0.0476548
$296$	−13.0649	−0.759384
$297$	−3.41733	−0.198294
$298$	4.93247	0.285730
$299$	9.83390	0.568709
$300$	10.7237	0.619131
$301$	0	0
$302$	2.31896	0.133441
$303$	−10.8514	−0.623399
$304$	0.189945	0.0108941
$305$	−7.58139	−0.434109
$306$	17.0616	0.975346
$307$	−27.7393	−1.58317	−0.791584	−	0.611061i	$-0.790743\pi$
$307$	−27.7393	−1.58317	−0.791584	+	0.611061i	$0.790743\pi$
$308$	0	0
$309$	3.12953	0.178033
$310$	4.86141	0.276110
$311$	−13.6882	−0.776187	−0.388093	−	0.921620i	$-0.626866\pi$
$311$	−13.6882	−0.776187	−0.388093	+	0.921620i	$0.626866\pi$
$312$	−7.30755	−0.413708
$313$	21.4280	1.21118	0.605590	−	0.795777i	$-0.292937\pi$
$313$	21.4280	1.21118	0.605590	+	0.795777i	$0.292937\pi$
$314$	52.2971	2.95129
$315$	0	0
$316$	29.9616	1.68547
$317$	−27.6310	−1.55191	−0.775956	−	0.630786i	$-0.782732\pi$
$317$	−27.6310	−1.55191	−0.775956	+	0.630786i	$0.782732\pi$
$318$	−19.5349	−1.09546
$319$	−2.58637	−0.144809
$320$	−10.3426	−0.578168
$321$	−3.35731	−0.187387
$322$	0	0
$323$	−0.583924	−0.0324904
$324$	2.54845	0.141580
$325$	−26.2889	−1.45824
$326$	−44.2164	−2.44892
$327$	−0.403889	−0.0223351
$328$	1.16968	0.0645848
$329$	0	0
$330$	−6.48638	−0.357064
$331$	−17.5293	−0.963498	−0.481749	−	0.876309i	$-0.659998\pi$
$331$	−17.5293	−0.963498	−0.481749	+	0.876309i	$0.659998\pi$
$332$	10.2729	0.563796
$333$	−11.1697	−0.612093
$334$	−20.9675	−1.14729
$335$	2.14736	0.117323
$336$	0	0
$337$	13.3142	0.725272	0.362636	−	0.931931i	$-0.381877\pi$
$337$	13.3142	0.725272	0.362636	+	0.931931i	$0.381877\pi$
$338$	55.5163	3.01969
$339$	−5.43878	−0.295394
$340$	18.1446	0.984030
$341$	8.75253	0.473976
$342$	−0.155668	−0.00841758
$343$	0	0
$344$	−7.21997	−0.389275
$345$	−1.40090	−0.0754217
$346$	41.2354	2.21683
$347$	−3.91557	−0.210199	−0.105099	−	0.994462i	$-0.533516\pi$
$347$	−3.91557	−0.210199	−0.105099	+	0.994462i	$0.533516\pi$
$348$	1.92877	0.103393
$349$	−20.1583	−1.07905	−0.539524	−	0.841970i	$-0.681396\pi$
$349$	−20.1583	−1.07905	−0.539524	+	0.841970i	$0.681396\pi$
$350$	0	0
$351$	−6.24747	−0.333465
$352$	−26.9604	−1.43700
$353$	20.7285	1.10327	0.551633	−	0.834087i	$-0.314005\pi$
$353$	20.7285	1.10327	0.551633	+	0.834087i	$0.314005\pi$
$354$	1.96140	0.104247
$355$	7.90658	0.419638
$356$	−21.5267	−1.14091
$357$	0	0
$358$	34.9759	1.84854
$359$	−34.7155	−1.83221	−0.916107	−	0.400934i	$-0.868686\pi$
$359$	−34.7155	−1.83221	−0.916107	+	0.400934i	$0.868686\pi$
$360$	1.04100	0.0548656
$361$	−18.9947	−0.999720
$362$	35.0261	1.84093
$363$	−0.678140	−0.0355931
$364$	0	0
$365$	3.24046	0.169613
$366$	18.1675	0.949633
$367$	−22.9795	−1.19952	−0.599761	−	0.800179i	$-0.704738\pi$
$367$	−22.9795	−1.19952	−0.599761	+	0.800179i	$0.704738\pi$
$368$	−4.09619	−0.213529
$369$	1.00000	0.0520579
$370$	−21.2010	−1.10219
$371$	0	0
$372$	−6.52713	−0.338416
$373$	9.55192	0.494580	0.247290	−	0.968942i	$-0.420460\pi$
$373$	9.55192	0.494580	0.247290	+	0.968942i	$0.420460\pi$
$374$	58.3051	3.01488
$375$	8.19494	0.423185
$376$	1.86865	0.0963683
$377$	−4.72833	−0.243521
$378$	0	0
$379$	−16.6032	−0.852847	−0.426423	−	0.904524i	$-0.640227\pi$
$379$	−16.6032	−0.852847	−0.426423	+	0.904524i	$0.640227\pi$
$380$	−0.165550	−0.00849253
$381$	5.15902	0.264305
$382$	−55.3407	−2.83148
$383$	37.5062	1.91648	0.958239	−	0.285969i	$-0.0923153\pi$
$383$	37.5062	1.91648	0.958239	+	0.285969i	$0.0923153\pi$
$384$	9.00561	0.459566
$385$	0	0
$386$	55.9199	2.84625
$387$	−6.17260	−0.313771
$388$	−23.0805	−1.17173
$389$	−1.49006	−0.0755488	−0.0377744	−	0.999286i	$-0.512027\pi$
$389$	−1.49006	−0.0755488	−0.0377744	+	0.999286i	$0.512027\pi$
$390$	−11.8582	−0.600465
$391$	12.5924	0.636826
$392$	0	0
$393$	−11.9242	−0.601496
$394$	10.7435	0.541250
$395$	10.4634	0.526471
$396$	8.70889	0.437638
$397$	6.71173	0.336852	0.168426	−	0.985714i	$-0.446132\pi$
$397$	6.71173	0.336852	0.168426	+	0.985714i	$0.446132\pi$
$398$	−5.41079	−0.271218
$399$	0	0
$400$	10.9503	0.547515
$401$	−3.68773	−0.184157	−0.0920783	−	0.995752i	$-0.529351\pi$
$401$	−3.68773	−0.184157	−0.0920783	+	0.995752i	$0.529351\pi$
$402$	−5.14579	−0.256648
$403$	16.0011	0.797074
$404$	27.6543	1.37585
$405$	0.889988	0.0442239
$406$	0	0
$407$	−38.1704	−1.89204
$408$	−9.35740	−0.463260
$409$	−6.90268	−0.341316	−0.170658	−	0.985330i	$-0.554589\pi$
$409$	−6.90268	−0.341316	−0.170658	+	0.985330i	$0.554589\pi$
$410$	1.89809	0.0937398
$411$	−4.57666	−0.225750
$412$	−7.97544	−0.392922
$413$	0	0
$414$	3.35702	0.164988
$415$	3.58756	0.176107
$416$	−49.2883	−2.41656
$417$	−14.6408	−0.716961
$418$	−0.531970	−0.0260195
$419$	7.45445	0.364174	0.182087	−	0.983282i	$-0.441715\pi$
$419$	7.45445	0.364174	0.182087	+	0.983282i	$0.441715\pi$
$420$	0	0
$421$	7.74992	0.377708	0.188854	−	0.982005i	$-0.439523\pi$
$421$	7.74992	0.377708	0.188854	+	0.982005i	$0.439523\pi$
$422$	−49.3002	−2.39989
$423$	1.59757	0.0776766
$424$	10.7139	0.520312
$425$	−33.6632	−1.63290
$426$	−18.9468	−0.917976
$427$	0	0
$428$	8.55594	0.413567
$429$	−21.3497	−1.03077
$430$	−11.7161	−0.565001
$431$	8.87444	0.427467	0.213733	−	0.976892i	$-0.431438\pi$
$431$	8.87444	0.427467	0.213733	+	0.976892i	$0.431438\pi$
$432$	2.60231	0.125204
$433$	−15.3304	−0.736734	−0.368367	−	0.929681i	$-0.620083\pi$
$433$	−15.3304	−0.736734	−0.368367	+	0.929681i	$0.620083\pi$
$434$	0	0
$435$	0.673578	0.0322956
$436$	1.02929	0.0492941
$437$	−0.114892	−0.00549604
$438$	−7.76522	−0.371037
$439$	27.4686	1.31100	0.655501	−	0.755194i	$-0.272457\pi$
$439$	27.4686	1.31100	0.655501	+	0.755194i	$0.272457\pi$
$440$	3.55745	0.169595
$441$	0	0
$442$	106.592	5.07005
$443$	−1.87494	−0.0890811	−0.0445406	−	0.999008i	$-0.514182\pi$
$443$	−1.87494	−0.0890811	−0.0445406	+	0.999008i	$0.514182\pi$
$444$	28.4653	1.35090
$445$	−7.51770	−0.356373
$446$	−0.511062	−0.0241995
$447$	−2.31277	−0.109390
$448$	0	0
$449$	29.4978	1.39209	0.696043	−	0.718001i	$-0.254942\pi$
$449$	29.4978	1.39209	0.696043	+	0.718001i	$0.254942\pi$
$450$	−8.97427	−0.423051
$451$	3.41733	0.160916
$452$	13.8604	0.651940
$453$	−1.08733	−0.0510872
$454$	−7.89449	−0.370507
$455$	0	0
$456$	0.0853761	0.00399810
$457$	30.2742	1.41617	0.708084	−	0.706129i	$-0.249560\pi$
$457$	30.2742	1.41617	0.708084	+	0.706129i	$0.249560\pi$
$458$	13.3475	0.623689
$459$	−7.99996	−0.373406
$460$	3.57011	0.166457
$461$	23.7455	1.10594	0.552968	−	0.833202i	$-0.313495\pi$
$461$	23.7455	1.10594	0.552968	+	0.833202i	$0.313495\pi$
$462$	0	0
$463$	−21.6384	−1.00562	−0.502811	−	0.864396i	$-0.667701\pi$
$463$	−21.6384	−1.00562	−0.502811	+	0.864396i	$0.667701\pi$
$464$	1.96953	0.0914330
$465$	−2.27945	−0.105707
$466$	−54.6946	−2.53368
$467$	4.37189	0.202307	0.101153	−	0.994871i	$-0.467747\pi$
$467$	4.37189	0.202307	0.101153	+	0.994871i	$0.467747\pi$
$468$	15.9214	0.735965
$469$	0	0
$470$	3.03233	0.139871
$471$	−24.5214	−1.12989
$472$	−1.07572	−0.0495142
$473$	−21.0938	−0.969894
$474$	−25.0738	−1.15168
$475$	0.307140	0.0140925
$476$	0	0
$477$	9.15967	0.419392
$478$	−37.9287	−1.73482
$479$	16.5420	0.755824	0.377912	−	0.925842i	$-0.376642\pi$
$479$	16.5420	0.755824	0.377912	+	0.925842i	$0.376642\pi$
$480$	7.02141	0.320482
$481$	−69.7821	−3.18179
$482$	−16.2953	−0.742232
$483$	0	0
$484$	1.72820	0.0785547
$485$	−8.06034	−0.366001
$486$	−2.13271	−0.0967417
$487$	−21.6708	−0.981998	−0.490999	−	0.871160i	$-0.663368\pi$
$487$	−21.6708	−0.981998	−0.490999	+	0.871160i	$0.663368\pi$
$488$	−9.96396	−0.451047
$489$	20.7325	0.937557
$490$	0	0
$491$	2.65513	0.119824	0.0599121	−	0.998204i	$-0.480918\pi$
$491$	2.65513	0.119824	0.0599121	+	0.998204i	$0.480918\pi$
$492$	−2.54845	−0.114893
$493$	−6.05468	−0.272689
$494$	−0.972533	−0.0437563
$495$	3.04138	0.136700
$496$	−6.66508	−0.299271
$497$	0	0
$498$	−8.59700	−0.385241
$499$	−3.67247	−0.164402	−0.0822012	−	0.996616i	$-0.526195\pi$
$499$	−3.67247	−0.164402	−0.0822012	+	0.996616i	$0.526195\pi$
$500$	−20.8844	−0.933978
$501$	9.83140	0.439234
$502$	4.29272	0.191594
$503$	−23.5718	−1.05101	−0.525506	−	0.850790i	$-0.676124\pi$
$503$	−23.5718	−1.05101	−0.525506	+	0.850790i	$0.676124\pi$
$504$	0	0
$505$	9.65766	0.429760
$506$	11.4720	0.509994
$507$	−26.0309	−1.15607
$508$	−13.1475	−0.583326
$509$	34.8559	1.54496	0.772481	−	0.635037i	$-0.219015\pi$
$509$	34.8559	1.54496	0.772481	+	0.635037i	$0.219015\pi$
$510$	−15.1846	−0.672386
$511$	0	0
$512$	26.6182	1.17637
$513$	0.0729909	0.00322263
$514$	13.3009	0.586677
$515$	−2.78524	−0.122733
$516$	15.7305	0.692498
$517$	5.45943	0.240105
$518$	0	0
$519$	−19.3348	−0.848702
$520$	6.50363	0.285203
$521$	−39.0969	−1.71287	−0.856434	−	0.516257i	$-0.827325\pi$
$521$	−39.0969	−1.71287	−0.856434	+	0.516257i	$0.827325\pi$
$522$	−1.61412	−0.0706480
$523$	10.0083	0.437632	0.218816	−	0.975766i	$-0.429781\pi$
$523$	10.0083	0.437632	0.218816	+	0.975766i	$0.429781\pi$
$524$	30.3882	1.32752
$525$	0	0
$526$	−17.3577	−0.756831
$527$	20.4896	0.892543
$528$	8.89294	0.387016
$529$	−20.5223	−0.892275
$530$	17.3858	0.755192
$531$	−0.919674	−0.0399104
$532$	0	0
$533$	6.24747	0.270608
$534$	18.0149	0.779582
$535$	2.98797	0.129181
$536$	2.82220	0.121900
$537$	−16.3998	−0.707702
$538$	−54.7453	−2.36024
$539$	0	0
$540$	−2.26809	−0.0976030
$541$	22.2218	0.955390	0.477695	−	0.878526i	$-0.341472\pi$
$541$	22.2218	0.955390	0.477695	+	0.878526i	$0.341472\pi$
$542$	−64.0450	−2.75097
$543$	−16.4233	−0.704790
$544$	−63.1143	−2.70600
$545$	0.359457	0.0153974
$546$	0	0
$547$	26.4397	1.13048	0.565240	−	0.824927i	$-0.308784\pi$
$547$	26.4397	1.13048	0.565240	+	0.824927i	$0.308784\pi$
$548$	11.6634	0.498235
$549$	−8.51853	−0.363562
$550$	−30.6680	−1.30769
$551$	0.0552424	0.00235340
$552$	−1.84115	−0.0783645
$553$	0	0
$554$	−21.9421	−0.932232
$555$	9.94086	0.421966
$556$	37.3112	1.58235
$557$	25.7136	1.08952	0.544759	−	0.838593i	$-0.316621\pi$
$557$	25.7136	1.08952	0.544759	+	0.838593i	$0.316621\pi$
$558$	5.46234	0.231239
$559$	−38.5631	−1.63105
$560$	0	0
$561$	−27.3385	−1.15423
$562$	25.5580	1.07810
$563$	−31.4548	−1.32566	−0.662830	−	0.748770i	$-0.730645\pi$
$563$	−31.4548	−1.32566	−0.662830	+	0.748770i	$0.730645\pi$
$564$	−4.07133	−0.171434
$565$	4.84045	0.203639
$566$	−32.5322	−1.36743
$567$	0	0
$568$	10.3913	0.436011
$569$	−26.4186	−1.10752	−0.553762	−	0.832675i	$-0.686808\pi$
$569$	−26.4186	−1.10752	−0.553762	+	0.832675i	$0.686808\pi$
$570$	0.138543	0.00580293
$571$	4.76235	0.199298	0.0996491	−	0.995023i	$-0.468228\pi$
$571$	4.76235	0.199298	0.0996491	+	0.995023i	$0.468228\pi$
$572$	54.4085	2.27493
$573$	25.9485	1.08402
$574$	0	0
$575$	−6.62353	−0.276220
$576$	−11.6210	−0.484209
$577$	7.27641	0.302921	0.151460	−	0.988463i	$-0.451602\pi$
$577$	7.27641	0.302921	0.151460	+	0.988463i	$0.451602\pi$
$578$	100.236	4.16926
$579$	−26.2201	−1.08967
$580$	−1.71658	−0.0712770
$581$	0	0
$582$	19.3153	0.800644
$583$	31.3016	1.29638
$584$	4.25882	0.176231
$585$	5.56017	0.229885
$586$	−62.3211	−2.57446
$587$	−1.48111	−0.0611320	−0.0305660	−	0.999533i	$-0.509731\pi$
$587$	−1.48111	−0.0611320	−0.0305660	+	0.999533i	$0.509731\pi$
$588$	0	0
$589$	−0.186946	−0.00770296
$590$	−1.74562	−0.0718660
$591$	−5.03749	−0.207215
$592$	29.0669	1.19464
$593$	−0.770893	−0.0316568	−0.0158284	−	0.999875i	$-0.505039\pi$
$593$	−0.770893	−0.0316568	−0.0158284	+	0.999875i	$0.505039\pi$
$594$	−7.28817	−0.299037
$595$	0	0
$596$	5.89398	0.241427
$597$	2.53705	0.103835
$598$	20.9729	0.857644
$599$	2.95056	0.120557	0.0602783	−	0.998182i	$-0.480801\pi$
$599$	2.95056	0.120557	0.0602783	+	0.998182i	$0.480801\pi$
$600$	4.92193	0.200937
$601$	14.1523	0.577285	0.288642	−	0.957437i	$-0.406796\pi$
$601$	14.1523	0.577285	0.288642	+	0.957437i	$0.406796\pi$
$602$	0	0
$603$	2.41279	0.0982565
$604$	2.77100	0.112751
$605$	0.603536	0.0245372
$606$	−23.1430	−0.940119
$607$	39.5171	1.60395	0.801975	−	0.597358i	$-0.203783\pi$
$607$	39.5171	1.60395	0.801975	+	0.597358i	$0.203783\pi$
$608$	0.575849	0.0233538
$609$	0	0
$610$	−16.1689	−0.654660
$611$	9.98078	0.403779
$612$	20.3875	0.824115
$613$	41.8648	1.69091	0.845453	−	0.534050i	$-0.179331\pi$
$613$	41.8648	1.69091	0.845453	+	0.534050i	$0.179331\pi$
$614$	−59.1599	−2.38750
$615$	−0.889988	−0.0358878
$616$	0	0
$617$	24.9542	1.00462	0.502310	−	0.864688i	$-0.332484\pi$
$617$	24.9542	1.00462	0.502310	+	0.864688i	$0.332484\pi$
$618$	6.67438	0.268483
$619$	5.05747	0.203277	0.101638	−	0.994821i	$-0.467592\pi$
$619$	5.05747	0.203277	0.101638	+	0.994821i	$0.467592\pi$
$620$	5.80907	0.233298
$621$	−1.57406	−0.0631649
$622$	−29.1929	−1.17053
$623$	0	0
$624$	16.2578	0.650834
$625$	13.7462	0.549848
$626$	45.6996	1.82652
$627$	0.249434	0.00996143
$628$	62.4916	2.49369
$629$	−89.3568	−3.56289
$630$	0	0
$631$	−16.8805	−0.672000	−0.336000	−	0.941862i	$-0.609074\pi$
$631$	−16.8805	−0.672000	−0.336000	+	0.941862i	$0.609074\pi$
$632$	13.7517	0.547013
$633$	23.1162	0.918787
$634$	−58.9289	−2.34037
$635$	−4.59147	−0.182207
$636$	−23.3429	−0.925608
$637$	0	0
$638$	−5.51597	−0.218379
$639$	8.88392	0.351442
$640$	−8.01489	−0.316816
$641$	−32.4571	−1.28198	−0.640990	−	0.767549i	$-0.721476\pi$
$641$	−32.4571	−1.28198	−0.640990	+	0.767549i	$0.721476\pi$
$642$	−7.16017	−0.282590
$643$	32.8318	1.29476	0.647381	−	0.762167i	$-0.275864\pi$
$643$	32.8318	1.29476	0.647381	+	0.762167i	$0.275864\pi$
$644$	0	0
$645$	5.49354	0.216308
$646$	−1.24534	−0.0489973
$647$	−7.44564	−0.292718	−0.146359	−	0.989232i	$-0.546755\pi$
$647$	−7.44564	−0.292718	−0.146359	+	0.989232i	$0.546755\pi$
$648$	1.16968	0.0459494
$649$	−3.14283	−0.123367
$650$	−56.0665	−2.19911
$651$	0	0
$652$	−52.8357	−2.06921
$653$	−14.6003	−0.571353	−0.285676	−	0.958326i	$-0.592218\pi$
$653$	−14.6003	−0.571353	−0.285676	+	0.958326i	$0.592218\pi$
$654$	−0.861378	−0.0336826
$655$	10.6124	0.414661
$656$	−2.60231	−0.101603
$657$	3.64101	0.142049
$658$	0	0
$659$	7.79447	0.303629	0.151815	−	0.988409i	$-0.451488\pi$
$659$	7.79447	0.303629	0.151815	+	0.988409i	$0.451488\pi$
$660$	−7.75081	−0.301700
$661$	13.7123	0.533345	0.266673	−	0.963787i	$-0.414076\pi$
$661$	13.7123	0.533345	0.266673	+	0.963787i	$0.414076\pi$
$662$	−37.3849	−1.45301
$663$	−49.9795	−1.94104
$664$	4.71501	0.182978
$665$	0	0
$666$	−23.8216	−0.923069
$667$	−1.19131	−0.0461278
$668$	−25.0548	−0.969400
$669$	0.239630	0.00926464
$670$	4.57969	0.176929
$671$	−29.1106	−1.12380
$672$	0	0
$673$	−31.7957	−1.22563	−0.612817	−	0.790225i	$-0.709964\pi$
$673$	−31.7957	−1.22563	−0.612817	+	0.790225i	$0.709964\pi$
$674$	28.3953	1.09375
$675$	4.20792	0.161963
$676$	66.3384	2.55148
$677$	−15.6921	−0.603095	−0.301547	−	0.953451i	$-0.597503\pi$
$677$	−15.6921	−0.603095	−0.301547	+	0.953451i	$0.597503\pi$
$678$	−11.5993	−0.445469
$679$	0	0
$680$	8.32798	0.319363
$681$	3.70162	0.141847
$682$	18.6666	0.714781
$683$	−45.4953	−1.74083	−0.870415	−	0.492320i	$-0.836149\pi$
$683$	−45.4953	−1.74083	−0.870415	+	0.492320i	$0.836149\pi$
$684$	−0.186014	−0.00711241
$685$	4.07317	0.155628
$686$	0	0
$687$	−6.25848	−0.238776
$688$	16.0630	0.612396
$689$	57.2247	2.18009
$690$	−2.98770	−0.113740
$691$	−33.1928	−1.26271	−0.631356	−	0.775493i	$-0.717501\pi$
$691$	−33.1928	−1.26271	−0.631356	+	0.775493i	$0.717501\pi$
$692$	49.2737	1.87310
$693$	0	0
$694$	−8.35077	−0.316991
$695$	13.0301	0.494260
$696$	0.885260	0.0335557
$697$	7.99996	0.303020
$698$	−42.9918	−1.62726
$699$	25.6456	0.970006
$700$	0	0
$701$	17.9370	0.677470	0.338735	−	0.940882i	$-0.390001\pi$
$701$	17.9370	0.677470	0.338735	+	0.940882i	$0.390001\pi$
$702$	−13.3240	−0.502883
$703$	0.815283	0.0307490
$704$	−39.7129	−1.49674
$705$	−1.42182	−0.0535488
$706$	44.2078	1.66378
$707$	0	0
$708$	2.34374	0.0880832
$709$	−19.7437	−0.741492	−0.370746	−	0.928734i	$-0.620898\pi$
$709$	−19.7437	−0.741492	−0.370746	+	0.928734i	$0.620898\pi$
$710$	16.8624	0.632836
$711$	11.7568	0.440914
$712$	−9.88026	−0.370278
$713$	4.03152	0.150981
$714$	0	0
$715$	19.0009	0.710595
$716$	41.7940	1.56191
$717$	17.7843	0.664167
$718$	−74.0381	−2.76308
$719$	42.0245	1.56725	0.783625	−	0.621234i	$-0.213368\pi$
$719$	42.0245	1.56725	0.783625	+	0.621234i	$0.213368\pi$
$720$	−2.31602	−0.0863131
$721$	0	0
$722$	−40.5101	−1.50763
$723$	7.64067	0.284160
$724$	41.8539	1.55549
$725$	3.18472	0.118277
$726$	−1.44627	−0.0536763
$727$	−32.6634	−1.21142	−0.605709	−	0.795686i	$-0.707110\pi$
$727$	−32.6634	−1.21142	−0.605709	+	0.795686i	$0.707110\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	6.91095	0.255786
$731$	−49.3805	−1.82640
$732$	21.7090	0.802389
$733$	−36.1097	−1.33374	−0.666870	−	0.745174i	$-0.732366\pi$
$733$	−36.1097	−1.33374	−0.666870	+	0.745174i	$0.732366\pi$
$734$	−49.0087	−1.80894
$735$	0	0
$736$	−12.4183	−0.457744
$737$	8.24531	0.303720
$738$	2.13271	0.0785061
$739$	26.6713	0.981118	0.490559	−	0.871408i	$-0.336793\pi$
$739$	26.6713	0.981118	0.490559	+	0.871408i	$0.336793\pi$
$740$	−25.3338	−0.931288
$741$	0.456008	0.0167519
$742$	0	0
$743$	−32.0519	−1.17587	−0.587935	−	0.808908i	$-0.700059\pi$
$743$	−32.0519	−1.17587	−0.587935	+	0.808908i	$0.700059\pi$
$744$	−2.99581	−0.109832
$745$	2.05834	0.0754117
$746$	20.3715	0.745853
$747$	4.03102	0.147487
$748$	69.6707	2.54741
$749$	0	0
$750$	17.4774	0.638185
$751$	11.2233	0.409545	0.204772	−	0.978810i	$-0.434355\pi$
$751$	11.2233	0.409545	0.204772	+	0.978810i	$0.434355\pi$
$752$	−4.15737	−0.151604
$753$	−2.01280	−0.0733506
$754$	−10.0842	−0.367243
$755$	0.967711	0.0352186
$756$	0	0
$757$	−11.3051	−0.410890	−0.205445	−	0.978669i	$-0.565864\pi$
$757$	−11.3051	−0.410890	−0.205445	+	0.978669i	$0.565864\pi$
$758$	−35.4097	−1.28614
$759$	−5.37909	−0.195248
$760$	−0.0759837	−0.00275622
$761$	−14.9745	−0.542826	−0.271413	−	0.962463i	$-0.587491\pi$
$761$	−14.9745	−0.542826	−0.271413	+	0.962463i	$0.587491\pi$
$762$	11.0027	0.398586
$763$	0	0
$764$	−66.1285	−2.39245
$765$	7.11987	0.257419
$766$	79.9898	2.89015
$767$	−5.74563	−0.207463
$768$	−4.03570	−0.145626
$769$	29.8781	1.07743	0.538716	−	0.842487i	$-0.318910\pi$
$769$	29.8781	1.07743	0.538716	+	0.842487i	$0.318910\pi$
$770$	0	0
$771$	−6.23662	−0.224606
$772$	66.8207	2.40493
$773$	−6.39402	−0.229977	−0.114989	−	0.993367i	$-0.536683\pi$
$773$	−6.39402	−0.229977	−0.114989	+	0.993367i	$0.536683\pi$
$774$	−13.1644	−0.473183
$775$	−10.7774	−0.387136
$776$	−10.5934	−0.380282
$777$	0	0
$778$	−3.17786	−0.113932
$779$	−0.0729909	−0.00261517
$780$	−14.1698	−0.507361
$781$	30.3593	1.08634
$782$	26.8560	0.960368
$783$	0.756839	0.0270472
$784$	0	0
$785$	21.8238	0.778924
$786$	−25.4309	−0.907089
$787$	−40.7910	−1.45404	−0.727021	−	0.686615i	$-0.759096\pi$
$787$	−40.7910	−1.45404	−0.727021	+	0.686615i	$0.759096\pi$
$788$	12.8378	0.457327
$789$	8.13880	0.289749
$790$	22.3154	0.793947
$791$	0	0
$792$	3.99719	0.142034
$793$	−53.2193	−1.88987
$794$	14.3142	0.507991
$795$	−8.15199	−0.289121
$796$	−6.46554	−0.229165
$797$	33.0669	1.17129	0.585645	−	0.810567i	$-0.300841\pi$
$797$	33.0669	1.17129	0.585645	+	0.810567i	$0.300841\pi$
$798$	0	0
$799$	12.7805	0.452142
$800$	33.1977	1.17371
$801$	−8.44697	−0.298459
$802$	−7.86486	−0.277718
$803$	12.4425	0.439088
$804$	−6.14888	−0.216854
$805$	0	0
$806$	34.1258	1.20203
$807$	25.6694	0.903604
$808$	12.6927	0.446529
$809$	9.54220	0.335486	0.167743	−	0.985831i	$-0.446352\pi$
$809$	9.54220	0.335486	0.167743	+	0.985831i	$0.446352\pi$
$810$	1.89809	0.0666919
$811$	−2.64941	−0.0930333	−0.0465166	−	0.998918i	$-0.514812\pi$
$811$	−2.64941	−0.0930333	−0.0465166	+	0.998918i	$0.514812\pi$
$812$	0	0
$813$	30.0299	1.05319
$814$	−81.4063	−2.85329
$815$	−18.4517	−0.646334
$816$	20.8184	0.728788
$817$	0.450543	0.0157625
$818$	−14.7214	−0.514722
$819$	0	0
$820$	2.26809	0.0792051
$821$	39.2366	1.36937	0.684683	−	0.728841i	$-0.259941\pi$
$821$	39.2366	1.36937	0.684683	+	0.728841i	$0.259941\pi$
$822$	−9.76068	−0.340443
$823$	−46.2425	−1.61191	−0.805956	−	0.591976i	$-0.798348\pi$
$823$	−46.2425	−1.61191	−0.805956	+	0.591976i	$0.798348\pi$
$824$	−3.66055	−0.127521
$825$	14.3799	0.500642
$826$	0	0
$827$	19.5022	0.678158	0.339079	−	0.940758i	$-0.389885\pi$
$827$	19.5022	0.678158	0.339079	+	0.940758i	$0.389885\pi$
$828$	4.01141	0.139406
$829$	8.56705	0.297546	0.148773	−	0.988871i	$-0.452468\pi$
$829$	8.56705	0.297546	0.148773	+	0.988871i	$0.452468\pi$
$830$	7.65123	0.265578
$831$	10.2884	0.356900
$832$	−72.6020	−2.51702
$833$	0	0
$834$	−31.2245	−1.08121
$835$	−8.74983	−0.302800
$836$	−0.635670	−0.0219851
$837$	−2.56122	−0.0885287
$838$	15.8982	0.549193
$839$	43.6287	1.50623	0.753115	−	0.657888i	$-0.228550\pi$
$839$	43.6287	1.50623	0.753115	+	0.657888i	$0.228550\pi$
$840$	0	0
$841$	−28.4272	−0.980248
$842$	16.5283	0.569603
$843$	−11.9838	−0.412744
$844$	−58.9105	−2.02778
$845$	23.1672	0.796975
$846$	3.40716	0.117140
$847$	0	0
$848$	−23.8363	−0.818541
$849$	15.2539	0.523514
$850$	−71.7938	−2.46251
$851$	−17.5817	−0.602694
$852$	−22.6402	−0.775641
$853$	−3.06449	−0.104926	−0.0524630	−	0.998623i	$-0.516707\pi$
$853$	−3.06449	−0.104926	−0.0524630	+	0.998623i	$0.516707\pi$
$854$	0	0
$855$	−0.0649610	−0.00222162
$856$	3.92699	0.134222
$857$	−10.5860	−0.361610	−0.180805	−	0.983519i	$-0.557870\pi$
$857$	−10.5860	−0.361610	−0.180805	+	0.983519i	$0.557870\pi$
$858$	−45.5326	−1.55446
$859$	−7.65853	−0.261306	−0.130653	−	0.991428i	$-0.541707\pi$
$859$	−7.65853	−0.261306	−0.130653	+	0.991428i	$0.541707\pi$
$860$	−14.0000	−0.477396
$861$	0	0
$862$	18.9266	0.644642
$863$	4.80094	0.163426	0.0817129	−	0.996656i	$-0.473961\pi$
$863$	4.80094	0.163426	0.0817129	+	0.996656i	$0.473961\pi$
$864$	7.88933	0.268400
$865$	17.2077	0.585080
$866$	−32.6954	−1.11103
$867$	−46.9993	−1.59618
$868$	0	0
$869$	40.1768	1.36291
$870$	1.43655	0.0487035
$871$	15.0739	0.510758
$872$	0.472422	0.0159982
$873$	−9.05668	−0.306522
$874$	−0.245032	−0.00828832
$875$	0	0
$876$	−9.27893	−0.313506
$877$	−52.0697	−1.75827	−0.879135	−	0.476573i	$-0.841879\pi$
$877$	−52.0697	−1.75827	−0.879135	+	0.476573i	$0.841879\pi$
$878$	58.5824	1.97706
$879$	29.2216	0.985619
$880$	−7.91461	−0.266802
$881$	−17.6360	−0.594171	−0.297085	−	0.954851i	$-0.596015\pi$
$881$	−17.6360	−0.594171	−0.297085	+	0.954851i	$0.596015\pi$
$882$	0	0
$883$	12.2941	0.413731	0.206866	−	0.978369i	$-0.433674\pi$
$883$	12.2941	0.413731	0.206866	+	0.978369i	$0.433674\pi$
$884$	127.370	4.28392
$885$	0.818499	0.0275135
$886$	−3.99870	−0.134339
$887$	−41.9487	−1.40850	−0.704251	−	0.709952i	$-0.748717\pi$
$887$	−41.9487	−1.40850	−0.704251	+	0.709952i	$0.748717\pi$
$888$	13.0649	0.438430
$889$	0	0
$890$	−16.0331	−0.537430
$891$	3.41733	0.114485
$892$	−0.610685	−0.0204473
$893$	−0.116608	−0.00390215
$894$	−4.93247	−0.164966
$895$	14.5956	0.487877
$896$	0	0
$897$	−9.83390	−0.328344
$898$	62.9101	2.09934
$899$	−1.93843	−0.0646503
$900$	−10.7237	−0.357456
$901$	73.2769	2.44121
$902$	7.28817	0.242670
$903$	0	0
$904$	6.36163	0.211585
$905$	14.6165	0.485870
$906$	−2.31896	−0.0770422
$907$	−0.531208	−0.0176385	−0.00881923	−	0.999961i	$-0.502807\pi$
$907$	−0.531208	−0.0176385	−0.00881923	+	0.999961i	$0.502807\pi$
$908$	−9.43340	−0.313058
$909$	10.8514	0.359920
$910$	0	0
$911$	−19.0477	−0.631078	−0.315539	−	0.948913i	$-0.602185\pi$
$911$	−19.0477	−0.631078	−0.315539	+	0.948913i	$0.602185\pi$
$912$	−0.189945	−0.00628970
$913$	13.7753	0.455897
$914$	64.5661	2.13566
$915$	7.58139	0.250633
$916$	15.9494	0.526984
$917$	0	0
$918$	−17.0616	−0.563116
$919$	9.06567	0.299049	0.149524	−	0.988758i	$-0.452226\pi$
$919$	9.06567	0.299049	0.149524	+	0.988758i	$0.452226\pi$
$920$	1.63860	0.0540231
$921$	27.7393	0.914042
$922$	50.6422	1.66781
$923$	55.5020	1.82687
$924$	0	0
$925$	47.0010	1.54538
$926$	−46.1484	−1.51653
$927$	−3.12953	−0.102787
$928$	5.97095	0.196006
$929$	−9.91561	−0.325321	−0.162660	−	0.986682i	$-0.552007\pi$
$929$	−9.91561	−0.325321	−0.162660	+	0.986682i	$0.552007\pi$
$930$	−4.86141	−0.159412
$931$	0	0
$932$	−65.3565	−2.14082
$933$	13.6882	0.448131
$934$	9.32397	0.305090
$935$	24.3309	0.795707
$936$	7.30755	0.238855
$937$	22.9798	0.750718	0.375359	−	0.926879i	$-0.377519\pi$
$937$	22.9798	0.750718	0.375359	+	0.926879i	$0.377519\pi$
$938$	0	0
$939$	−21.4280	−0.699275
$940$	3.62344	0.118183
$941$	13.1179	0.427630	0.213815	−	0.976874i	$-0.431411\pi$
$941$	13.1179	0.427630	0.213815	+	0.976874i	$0.431411\pi$
$942$	−52.2971	−1.70393
$943$	1.57406	0.0512585
$944$	2.39327	0.0778944
$945$	0	0
$946$	−44.9869	−1.46265
$947$	−27.6733	−0.899262	−0.449631	−	0.893214i	$-0.648445\pi$
$947$	−27.6733	−0.899262	−0.449631	+	0.893214i	$0.648445\pi$
$948$	−29.9616	−0.973107
$949$	22.7471	0.738403
$950$	0.655040	0.0212523
$951$	27.6310	0.895997
$952$	0	0
$953$	−14.5017	−0.469757	−0.234878	−	0.972025i	$-0.575469\pi$
$953$	−14.5017	−0.469757	−0.234878	+	0.972025i	$0.575469\pi$
$954$	19.5349	0.632466
$955$	−23.0939	−0.747301
$956$	−45.3224	−1.46583
$957$	2.58637	0.0836054
$958$	35.2793	1.13982
$959$	0	0
$960$	10.3426	0.333805
$961$	−24.4402	−0.788392
$962$	−148.825	−4.79831
$963$	3.35731	0.108188
$964$	−19.4719	−0.627146
$965$	23.3356	0.751200
$966$	0	0
$967$	−4.81409	−0.154811	−0.0774054	−	0.997000i	$-0.524664\pi$
$967$	−4.81409	−0.154811	−0.0774054	+	0.997000i	$0.524664\pi$
$968$	0.793207	0.0254946
$969$	0.583924	0.0187583
$970$	−17.1904	−0.551949
$971$	−56.7999	−1.82279	−0.911397	−	0.411527i	$-0.864995\pi$
$971$	−56.7999	−1.82279	−0.911397	+	0.411527i	$0.864995\pi$
$972$	−2.54845	−0.0817415
$973$	0	0
$974$	−46.2175	−1.48090
$975$	26.2889	0.841917
$976$	22.1678	0.709575
$977$	26.0244	0.832595	0.416297	−	0.909229i	$-0.363328\pi$
$977$	26.0244	0.832595	0.416297	+	0.909229i	$0.363328\pi$
$978$	44.2164	1.41389
$979$	−28.8661	−0.922564
$980$	0	0
$981$	0.403889	0.0128952
$982$	5.66261	0.180701
$983$	59.1340	1.88608	0.943041	−	0.332677i	$-0.107952\pi$
$983$	59.1340	1.88608	0.943041	+	0.332677i	$0.107952\pi$
$984$	−1.16968	−0.0372881
$985$	4.48331	0.142850
$986$	−12.9129	−0.411230
$987$	0	0
$988$	−1.16211	−0.0369718
$989$	−9.71604	−0.308952
$990$	6.48638	0.206151
$991$	41.2982	1.31188	0.655941	−	0.754812i	$-0.272272\pi$
$991$	41.2982	1.31188	0.655941	+	0.754812i	$0.272272\pi$
$992$	−20.2063	−0.641550
$993$	17.5293	0.556276
$994$	0	0
$995$	−2.25794	−0.0715817
$996$	−10.2729	−0.325508
$997$	−12.4930	−0.395657	−0.197828	−	0.980237i	$-0.563389\pi$
$997$	−12.4930	−0.395657	−0.197828	+	0.980237i	$0.563389\pi$
$998$	−7.83231	−0.247927
$999$	11.1697	0.353392

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bj.1.13		14
7.2	even	3		861.2.i.g.739.2	yes	28
7.4	even	3		861.2.i.g.247.2	✓	28
7.6	odd	2		6027.2.a.bk.1.13		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.i.g.247.2	✓	28	7.4	even	3
861.2.i.g.739.2	yes	28	7.2	even	3
6027.2.a.bj.1.13		14	1.1	even	1	trivial
6027.2.a.bk.1.13		14	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)

\(f(q)\)	\(=\)	\(q+2.13271 q^{2} -1.00000 q^{3} +2.54845 q^{4} +0.889988 q^{5} -2.13271 q^{6} +1.16968 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.13271 q^{2} -1.00000 q^{3} +2.54845 q^{4} +0.889988 q^{5} -2.13271 q^{6} +1.16968 q^{8} +1.00000 q^{9} +1.89809 q^{10} +3.41733 q^{11} -2.54845 q^{12} +6.24747 q^{13} -0.889988 q^{15} -2.60231 q^{16} +7.99996 q^{17} +2.13271 q^{18} -0.0729909 q^{19} +2.26809 q^{20} +7.28817 q^{22} +1.57406 q^{23} -1.16968 q^{24} -4.20792 q^{25} +13.3240 q^{26} -1.00000 q^{27} -0.756839 q^{29} -1.89809 q^{30} +2.56122 q^{31} -7.88933 q^{32} -3.41733 q^{33} +17.0616 q^{34} +2.54845 q^{36} -11.1697 q^{37} -0.155668 q^{38} -6.24747 q^{39} +1.04100 q^{40} +1.00000 q^{41} -6.17260 q^{43} +8.70889 q^{44} +0.889988 q^{45} +3.35702 q^{46} +1.59757 q^{47} +2.60231 q^{48} -8.97427 q^{50} -7.99996 q^{51} +15.9214 q^{52} +9.15967 q^{53} -2.13271 q^{54} +3.04138 q^{55} +0.0729909 q^{57} -1.61412 q^{58} -0.919674 q^{59} -2.26809 q^{60} -8.51853 q^{61} +5.46234 q^{62} -11.6210 q^{64} +5.56017 q^{65} -7.28817 q^{66} +2.41279 q^{67} +20.3875 q^{68} -1.57406 q^{69} +8.88392 q^{71} +1.16968 q^{72} +3.64101 q^{73} -23.8216 q^{74} +4.20792 q^{75} -0.186014 q^{76} -13.3240 q^{78} +11.7568 q^{79} -2.31602 q^{80} +1.00000 q^{81} +2.13271 q^{82} +4.03102 q^{83} +7.11987 q^{85} -13.1644 q^{86} +0.756839 q^{87} +3.99719 q^{88} -8.44697 q^{89} +1.89809 q^{90} +4.01141 q^{92} -2.56122 q^{93} +3.40716 q^{94} -0.0649610 q^{95} +7.88933 q^{96} -9.05668 q^{97} +3.41733 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{2} - 14 q^{3} + 14 q^{4} + 10 q^{5} + 2 q^{6} - 6 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q - 2 * q^2 - 14 * q^3 + 14 * q^4 + 10 * q^5 + 2 * q^6 - 6 * q^8 + 14 * q^9	\( 14 q - 2 q^{2} - 14 q^{3} + 14 q^{4} + 10 q^{5} + 2 q^{6} - 6 q^{8} + 14 q^{9} + 3 q^{10} - 16 q^{11} - 14 q^{12} + 21 q^{13} - 10 q^{15} + 22 q^{16} + 12 q^{17} - 2 q^{18} + 2 q^{19} + 40 q^{20} + q^{22} - 7 q^{23} + 6 q^{24} + 22 q^{25} + 2 q^{26} - 14 q^{27} - 16 q^{29} - 3 q^{30} + 8 q^{31} - 19 q^{32} + 16 q^{33} + 33 q^{34} + 14 q^{36} + q^{37} + 32 q^{38} - 21 q^{39} - 13 q^{40} + 14 q^{41} + 14 q^{43} - 36 q^{44} + 10 q^{45} - 12 q^{46} + 12 q^{47} - 22 q^{48} - q^{50} - 12 q^{51} + 60 q^{52} - 20 q^{53} + 2 q^{54} - 11 q^{55} - 2 q^{57} + 21 q^{58} + 25 q^{59} - 40 q^{60} + 26 q^{61} - 33 q^{62} + 42 q^{64} - 8 q^{65} - q^{66} - 22 q^{67} + 15 q^{68} + 7 q^{69} - 36 q^{71} - 6 q^{72} + 31 q^{73} - 65 q^{74} - 22 q^{75} - 2 q^{76} - 2 q^{78} + 12 q^{79} + 112 q^{80} + 14 q^{81} - 2 q^{82} + 20 q^{83} + 40 q^{85} - 9 q^{86} + 16 q^{87} - 54 q^{88} + 39 q^{89} + 3 q^{90} + 63 q^{92} - 8 q^{93} + 14 q^{94} - 55 q^{95} + 19 q^{96} + 18 q^{97} - 16 q^{99}+O(q^{100}) \) 14 * q - 2 * q^2 - 14 * q^3 + 14 * q^4 + 10 * q^5 + 2 * q^6 - 6 * q^8 + 14 * q^9 + 3 * q^10 - 16 * q^11 - 14 * q^12 + 21 * q^13 - 10 * q^15 + 22 * q^16 + 12 * q^17 - 2 * q^18 + 2 * q^19 + 40 * q^20 + q^22 - 7 * q^23 + 6 * q^24 + 22 * q^25 + 2 * q^26 - 14 * q^27 - 16 * q^29 - 3 * q^30 + 8 * q^31 - 19 * q^32 + 16 * q^33 + 33 * q^34 + 14 * q^36 + q^37 + 32 * q^38 - 21 * q^39 - 13 * q^40 + 14 * q^41 + 14 * q^43 - 36 * q^44 + 10 * q^45 - 12 * q^46 + 12 * q^47 - 22 * q^48 - q^50 - 12 * q^51 + 60 * q^52 - 20 * q^53 + 2 * q^54 - 11 * q^55 - 2 * q^57 + 21 * q^58 + 25 * q^59 - 40 * q^60 + 26 * q^61 - 33 * q^62 + 42 * q^64 - 8 * q^65 - q^66 - 22 * q^67 + 15 * q^68 + 7 * q^69 - 36 * q^71 - 6 * q^72 + 31 * q^73 - 65 * q^74 - 22 * q^75 - 2 * q^76 - 2 * q^78 + 12 * q^79 + 112 * q^80 + 14 * q^81 - 2 * q^82 + 20 * q^83 + 40 * q^85 - 9 * q^86 + 16 * q^87 - 54 * q^88 + 39 * q^89 + 3 * q^90 + 63 * q^92 - 8 * q^93 + 14 * q^94 - 55 * q^95 + 19 * q^96 + 18 * q^97 - 16 * q^99

Introduction

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