LMFDB - Embedded newform 6027.2.a.bf.1.10

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:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} - 15 x^{10} + 30 x^{9} + 74 x^{8} - 149 x^{7} - 140 x^{6} + 278 x^{5} + 126 x^{4} + \cdots + 18 $ x^12 - 2x^11 - 15x^10 + 30x^9 + 74x^8 - 149x^7 - 140x^6 + 278x^5 + 126x^4 - 211x^3 - 64x^2 + 53*x + 18
Coefficient ring:	$\Z[a_1, a_2]$
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			1.10
Root			$-1.09852$ of defining polynomial
Character	$\chi$	$=$	6027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.09852 q^{2} -1.00000 q^{3} -0.793257 q^{4} +3.51189 q^{5} -1.09852 q^{6} -3.06844 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.09852 q^{2} -1.00000 q^{3} -0.793257 q^{4} +3.51189 q^{5} -1.09852 q^{6} -3.06844 q^{8} +1.00000 q^{9} +3.85788 q^{10} -1.19800 q^{11} +0.793257 q^{12} -2.03774 q^{13} -3.51189 q^{15} -1.78423 q^{16} -0.865583 q^{17} +1.09852 q^{18} +3.10472 q^{19} -2.78583 q^{20} -1.31603 q^{22} -0.108732 q^{23} +3.06844 q^{24} +7.33339 q^{25} -2.23850 q^{26} -1.00000 q^{27} -7.73581 q^{29} -3.85788 q^{30} +1.05874 q^{31} +4.17688 q^{32} +1.19800 q^{33} -0.950859 q^{34} -0.793257 q^{36} -11.0129 q^{37} +3.41060 q^{38} +2.03774 q^{39} -10.7760 q^{40} +1.00000 q^{41} -0.138700 q^{43} +0.950325 q^{44} +3.51189 q^{45} -0.119444 q^{46} +0.686936 q^{47} +1.78423 q^{48} +8.05586 q^{50} +0.865583 q^{51} +1.61645 q^{52} +10.0347 q^{53} -1.09852 q^{54} -4.20726 q^{55} -3.10472 q^{57} -8.49793 q^{58} -11.2119 q^{59} +2.78583 q^{60} -5.98402 q^{61} +1.16305 q^{62} +8.15684 q^{64} -7.15632 q^{65} +1.31603 q^{66} -12.7296 q^{67} +0.686630 q^{68} +0.108732 q^{69} +10.3905 q^{71} -3.06844 q^{72} +4.10639 q^{73} -12.0978 q^{74} -7.33339 q^{75} -2.46284 q^{76} +2.23850 q^{78} +1.02066 q^{79} -6.26602 q^{80} +1.00000 q^{81} +1.09852 q^{82} -16.7752 q^{83} -3.03983 q^{85} -0.152365 q^{86} +7.73581 q^{87} +3.67601 q^{88} +7.26262 q^{89} +3.85788 q^{90} +0.0862524 q^{92} -1.05874 q^{93} +0.754612 q^{94} +10.9035 q^{95} -4.17688 q^{96} -16.3003 q^{97} -1.19800 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} - 12 q^{3} + 10 q^{4} - 12 q^{5} + 2 q^{6} + 12 q^{9}+O(q^{10}) $ 12 * q - 2 * q^2 - 12 * q^3 + 10 * q^4 - 12 * q^5 + 2 * q^6 + 12 * q^9	$ 12 q - 2 q^{2} - 12 q^{3} + 10 q^{4} - 12 q^{5} + 2 q^{6} + 12 q^{9} - 11 q^{10} + 10 q^{11} - 10 q^{12} - 15 q^{13} + 12 q^{15} + 14 q^{16} - 8 q^{17} - 2 q^{18} - 2 q^{19} - 16 q^{20} - 7 q^{22} + 5 q^{23} + 20 q^{25} - 12 q^{27} + 20 q^{29} + 11 q^{30} - 10 q^{31} + 3 q^{32} - 10 q^{33} + 23 q^{34} + 10 q^{36} - 17 q^{37} - 6 q^{38} + 15 q^{39} - 39 q^{40} + 12 q^{41} + 12 q^{43} + 20 q^{44} - 12 q^{45} - 36 q^{46} - 34 q^{47} - 14 q^{48} + 59 q^{50} + 8 q^{51} - 26 q^{52} + 6 q^{53} + 2 q^{54} + q^{55} + 2 q^{57} - 11 q^{58} - 27 q^{59} + 16 q^{60} - 22 q^{61} + 45 q^{62} + 26 q^{64} + 7 q^{66} - 26 q^{67} - 33 q^{68} - 5 q^{69} + 50 q^{71} - 21 q^{73} - 35 q^{74} - 20 q^{75} + 24 q^{76} - 10 q^{79} - 22 q^{80} + 12 q^{81} - 2 q^{82} - 8 q^{83} + 8 q^{85} - 17 q^{86} - 20 q^{87} - 46 q^{88} - 11 q^{89} - 11 q^{90} + 63 q^{92} + 10 q^{93} - 10 q^{94} + 35 q^{95} - 3 q^{96} - 32 q^{97} + 10 q^{99}+O(q^{100}) $ 12 * q - 2 * q^2 - 12 * q^3 + 10 * q^4 - 12 * q^5 + 2 * q^6 + 12 * q^9 - 11 * q^10 + 10 * q^11 - 10 * q^12 - 15 * q^13 + 12 * q^15 + 14 * q^16 - 8 * q^17 - 2 * q^18 - 2 * q^19 - 16 * q^20 - 7 * q^22 + 5 * q^23 + 20 * q^25 - 12 * q^27 + 20 * q^29 + 11 * q^30 - 10 * q^31 + 3 * q^32 - 10 * q^33 + 23 * q^34 + 10 * q^36 - 17 * q^37 - 6 * q^38 + 15 * q^39 - 39 * q^40 + 12 * q^41 + 12 * q^43 + 20 * q^44 - 12 * q^45 - 36 * q^46 - 34 * q^47 - 14 * q^48 + 59 * q^50 + 8 * q^51 - 26 * q^52 + 6 * q^53 + 2 * q^54 + q^55 + 2 * q^57 - 11 * q^58 - 27 * q^59 + 16 * q^60 - 22 * q^61 + 45 * q^62 + 26 * q^64 + 7 * q^66 - 26 * q^67 - 33 * q^68 - 5 * q^69 + 50 * q^71 - 21 * q^73 - 35 * q^74 - 20 * q^75 + 24 * q^76 - 10 * q^79 - 22 * q^80 + 12 * q^81 - 2 * q^82 - 8 * q^83 + 8 * q^85 - 17 * q^86 - 20 * q^87 - 46 * q^88 - 11 * q^89 - 11 * q^90 + 63 * q^92 + 10 * q^93 - 10 * q^94 + 35 * q^95 - 3 * q^96 - 32 * 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 $

$2$	1.09852	0.776770	0.388385	−	0.921497i	$-0.373033\pi$
$2$	1.09852	0.776770	0.388385	+	0.921497i	$0.373033\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.793257	−0.396628
$5$	3.51189	1.57057	0.785283	−	0.619137i	$-0.212517\pi$
$5$	3.51189	1.57057	0.785283	+	0.619137i	$0.212517\pi$
$6$	−1.09852	−0.448468
$7$	0	0
$7$	0	0
$8$	−3.06844	−1.08486
$9$	1.00000	0.333333
$10$	3.85788	1.21997
$11$	−1.19800	−0.361212	−0.180606	−	0.983556i	$-0.557806\pi$
$11$	−1.19800	−0.361212	−0.180606	+	0.983556i	$0.557806\pi$
$12$	0.793257	0.228994
$13$	−2.03774	−0.565167	−0.282584	−	0.959243i	$-0.591192\pi$
$13$	−2.03774	−0.565167	−0.282584	+	0.959243i	$0.591192\pi$
$14$	0	0
$15$	−3.51189	−0.906767
$16$	−1.78423	−0.446057
$17$	−0.865583	−0.209935	−0.104967	−	0.994476i	$-0.533474\pi$
$17$	−0.865583	−0.209935	−0.104967	+	0.994476i	$0.533474\pi$
$18$	1.09852	0.258923
$19$	3.10472	0.712272	0.356136	−	0.934434i	$-0.384094\pi$
$19$	3.10472	0.712272	0.356136	+	0.934434i	$0.384094\pi$
$20$	−2.78583	−0.622931
$21$	0	0
$22$	−1.31603	−0.280578
$23$	−0.108732	−0.0226722	−0.0113361	−	0.999936i	$-0.503608\pi$
$23$	−0.108732	−0.0226722	−0.0113361	+	0.999936i	$0.503608\pi$
$24$	3.06844	0.626344
$25$	7.33339	1.46668
$26$	−2.23850	−0.439005
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−7.73581	−1.43650	−0.718252	−	0.695783i	$-0.755057\pi$
$29$	−7.73581	−1.43650	−0.718252	+	0.695783i	$0.755057\pi$
$30$	−3.85788	−0.704349
$31$	1.05874	0.190156	0.0950778	−	0.995470i	$-0.469690\pi$
$31$	1.05874	0.190156	0.0950778	+	0.995470i	$0.469690\pi$
$32$	4.17688	0.738375
$33$	1.19800	0.208546
$34$	−0.950859	−0.163071
$35$	0	0
$36$	−0.793257	−0.132209
$37$	−11.0129	−1.81051	−0.905253	−	0.424874i	$-0.860318\pi$
$37$	−11.0129	−1.81051	−0.905253	+	0.424874i	$0.860318\pi$
$38$	3.41060	0.553272
$39$	2.03774	0.326300
$40$	−10.7760	−1.70384
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	−0.138700	−0.0211516	−0.0105758	−	0.999944i	$-0.503366\pi$
$43$	−0.138700	−0.0211516	−0.0105758	+	0.999944i	$0.503366\pi$
$44$	0.950325	0.143267
$45$	3.51189	0.523522
$46$	−0.119444	−0.0176111
$47$	0.686936	0.100200	0.0501000	−	0.998744i	$-0.484046\pi$
$47$	0.686936	0.100200	0.0501000	+	0.998744i	$0.484046\pi$
$48$	1.78423	0.257531
$49$	0	0
$50$	8.05586	1.13927
$51$	0.865583	0.121206
$52$	1.61645	0.224162
$53$	10.0347	1.37837	0.689187	−	0.724584i	$-0.257968\pi$
$53$	10.0347	1.37837	0.689187	+	0.724584i	$0.257968\pi$
$54$	−1.09852	−0.149489
$55$	−4.20726	−0.567307
$56$	0	0
$57$	−3.10472	−0.411231
$58$	−8.49793	−1.11583
$59$	−11.2119	−1.45966	−0.729830	−	0.683629i	$-0.760401\pi$
$59$	−11.2119	−1.45966	−0.729830	+	0.683629i	$0.760401\pi$
$60$	2.78583	0.359649
$61$	−5.98402	−0.766176	−0.383088	−	0.923712i	$-0.625139\pi$
$61$	−5.98402	−0.766176	−0.383088	+	0.923712i	$0.625139\pi$
$62$	1.16305	0.147707
$63$	0	0
$64$	8.15684	1.01960
$65$	−7.15632	−0.887633
$66$	1.31603	0.161992
$67$	−12.7296	−1.55517	−0.777585	−	0.628778i	$-0.783556\pi$
$67$	−12.7296	−1.55517	−0.777585	+	0.628778i	$0.783556\pi$
$68$	0.686630	0.0832661
$69$	0.108732	0.0130898
$70$	0	0
$71$	10.3905	1.23313	0.616565	−	0.787304i	$-0.288524\pi$
$71$	10.3905	1.23313	0.616565	+	0.787304i	$0.288524\pi$
$72$	−3.06844	−0.361620
$73$	4.10639	0.480617	0.240308	−	0.970697i	$-0.422751\pi$
$73$	4.10639	0.480617	0.240308	+	0.970697i	$0.422751\pi$
$74$	−12.0978	−1.40635
$75$	−7.33339	−0.846786
$76$	−2.46284	−0.282507
$77$	0	0
$78$	2.23850	0.253460
$79$	1.02066	0.114834	0.0574169	−	0.998350i	$-0.481714\pi$
$79$	1.02066	0.114834	0.0574169	+	0.998350i	$0.481714\pi$
$80$	−6.26602	−0.700562
$81$	1.00000	0.111111
$82$	1.09852	0.121311
$83$	−16.7752	−1.84132	−0.920660	−	0.390365i	$-0.872349\pi$
$83$	−16.7752	−1.84132	−0.920660	+	0.390365i	$0.872349\pi$
$84$	0	0
$85$	−3.03983	−0.329716
$86$	−0.152365	−0.0164299
$87$	7.73581	0.829366
$88$	3.67601	0.391864
$89$	7.26262	0.769836	0.384918	−	0.922951i	$-0.374230\pi$
$89$	7.26262	0.769836	0.384918	+	0.922951i	$0.374230\pi$
$90$	3.85788	0.406656
$91$	0	0
$92$	0.0862524	0.00899243
$93$	−1.05874	−0.109786
$94$	0.754612	0.0778323
$95$	10.9035	1.11867
$96$	−4.17688	−0.426301
$97$	−16.3003	−1.65505	−0.827524	−	0.561431i	$-0.810251\pi$
$97$	−16.3003	−1.65505	−0.827524	+	0.561431i	$0.810251\pi$
$98$	0	0
$99$	−1.19800	−0.120404
$100$	−5.81726	−0.581726
$101$	−11.3417	−1.12854	−0.564269	−	0.825591i	$-0.690842\pi$
$101$	−11.3417	−1.12854	−0.564269	+	0.825591i	$0.690842\pi$
$102$	0.950859	0.0941490
$103$	−2.54128	−0.250399	−0.125200	−	0.992132i	$-0.539957\pi$
$103$	−2.54128	−0.250399	−0.125200	+	0.992132i	$0.539957\pi$
$104$	6.25269	0.613127
$105$	0	0
$106$	11.0233	1.07068
$107$	10.5021	1.01528	0.507639	−	0.861570i	$-0.330518\pi$
$107$	10.5021	1.01528	0.507639	+	0.861570i	$0.330518\pi$
$108$	0.793257	0.0763312
$109$	−0.575433	−0.0551165	−0.0275583	−	0.999620i	$-0.508773\pi$
$109$	−0.575433	−0.0551165	−0.0275583	+	0.999620i	$0.508773\pi$
$110$	−4.62175	−0.440667
$111$	11.0129	1.04530
$112$	0	0
$113$	−12.3520	−1.16198	−0.580988	−	0.813912i	$-0.697334\pi$
$113$	−12.3520	−1.16198	−0.580988	+	0.813912i	$0.697334\pi$
$114$	−3.41060	−0.319432
$115$	−0.381855	−0.0356081
$116$	6.13649	0.569758
$117$	−2.03774	−0.188389
$118$	−12.3164	−1.13382
$119$	0	0
$120$	10.7760	0.983714
$121$	−9.56479	−0.869526
$122$	−6.57356	−0.595142
$123$	−1.00000	−0.0901670
$124$	−0.839854	−0.0754211
$125$	8.19460	0.732947
$126$	0	0
$127$	14.6407	1.29915	0.649574	−	0.760298i	$-0.274947\pi$
$127$	14.6407	1.29915	0.649574	+	0.760298i	$0.274947\pi$
$128$	0.606679	0.0536234
$129$	0.138700	0.0122119
$130$	−7.86135	−0.689486
$131$	−19.0331	−1.66293	−0.831463	−	0.555580i	$-0.812496\pi$
$131$	−19.0331	−1.66293	−0.831463	+	0.555580i	$0.812496\pi$
$132$	−0.950325	−0.0827152
$133$	0	0
$134$	−13.9837	−1.20801
$135$	−3.51189	−0.302256
$136$	2.65599	0.227750
$137$	1.74909	0.149435	0.0747173	−	0.997205i	$-0.476195\pi$
$137$	1.74909	0.149435	0.0747173	+	0.997205i	$0.476195\pi$
$138$	0.119444	0.0101678
$139$	8.07467	0.684884	0.342442	−	0.939539i	$-0.388746\pi$
$139$	8.07467	0.684884	0.342442	+	0.939539i	$0.388746\pi$
$140$	0	0
$141$	−0.686936	−0.0578505
$142$	11.4142	0.957858
$143$	2.44122	0.204145
$144$	−1.78423	−0.148686
$145$	−27.1673	−2.25612
$146$	4.51095	0.373329
$147$	0	0
$148$	8.73604	0.718098
$149$	16.3571	1.34003	0.670015	−	0.742348i	$-0.266288\pi$
$149$	16.3571	1.34003	0.670015	+	0.742348i	$0.266288\pi$
$150$	−8.05586	−0.657758
$151$	3.36907	0.274171	0.137085	−	0.990559i	$-0.456227\pi$
$151$	3.36907	0.274171	0.137085	+	0.990559i	$0.456227\pi$
$152$	−9.52667	−0.772715
$153$	−0.865583	−0.0699782
$154$	0	0
$155$	3.71819	0.298652
$156$	−1.61645	−0.129420
$157$	7.38587	0.589456	0.294728	−	0.955581i	$-0.404771\pi$
$157$	7.38587	0.589456	0.294728	+	0.955581i	$0.404771\pi$
$158$	1.12122	0.0891994
$159$	−10.0347	−0.795804
$160$	14.6688	1.15967
$161$	0	0
$162$	1.09852	0.0863078
$163$	2.77829	0.217612	0.108806	−	0.994063i	$-0.465297\pi$
$163$	2.77829	0.217612	0.108806	+	0.994063i	$0.465297\pi$
$164$	−0.793257	−0.0619430
$165$	4.20726	0.327535
$166$	−18.4279	−1.43028
$167$	−15.1850	−1.17505	−0.587526	−	0.809205i	$-0.699898\pi$
$167$	−15.1850	−1.17505	−0.587526	+	0.809205i	$0.699898\pi$
$168$	0	0
$169$	−8.84761	−0.680586
$170$	−3.33931	−0.256114
$171$	3.10472	0.237424
$172$	0.110025	0.00838932
$173$	−13.5167	−1.02766	−0.513828	−	0.857894i	$-0.671773\pi$
$173$	−13.5167	−1.02766	−0.513828	+	0.857894i	$0.671773\pi$
$174$	8.49793	0.644227
$175$	0	0
$176$	2.13751	0.161121
$177$	11.2119	0.842735
$178$	7.97813	0.597986
$179$	−17.9127	−1.33886	−0.669430	−	0.742875i	$-0.733462\pi$
$179$	−17.9127	−1.33886	−0.669430	+	0.742875i	$0.733462\pi$
$180$	−2.78583	−0.207644
$181$	−21.3758	−1.58885	−0.794425	−	0.607363i	$-0.792227\pi$
$181$	−21.3758	−1.58885	−0.794425	+	0.607363i	$0.792227\pi$
$182$	0	0
$183$	5.98402	0.442352
$184$	0.333638	0.0245961
$185$	−38.6760	−2.84352
$186$	−1.16305	−0.0852788
$187$	1.03697	0.0758309
$188$	−0.544917	−0.0397421
$189$	0	0
$190$	11.9776	0.868950
$191$	10.9322	0.791025	0.395513	−	0.918461i	$-0.370567\pi$
$191$	10.9322	0.791025	0.395513	+	0.918461i	$0.370567\pi$
$192$	−8.15684	−0.588669
$193$	12.7101	0.914894	0.457447	−	0.889237i	$-0.348764\pi$
$193$	12.7101	0.914894	0.457447	+	0.889237i	$0.348764\pi$
$194$	−17.9062	−1.28559
$195$	7.15632	0.512475
$196$	0	0
$197$	1.34260	0.0956561	0.0478280	−	0.998856i	$-0.484770\pi$
$197$	1.34260	0.0956561	0.0478280	+	0.998856i	$0.484770\pi$
$198$	−1.31603	−0.0935262
$199$	17.4820	1.23926	0.619632	−	0.784892i	$-0.287282\pi$
$199$	17.4820	1.23926	0.619632	+	0.784892i	$0.287282\pi$
$200$	−22.5021	−1.59114
$201$	12.7296	0.897878
$202$	−12.4590	−0.876615
$203$	0	0
$204$	−0.686630	−0.0480737
$205$	3.51189	0.245281
$206$	−2.79164	−0.194503
$207$	−0.108732	−0.00755739
$208$	3.63580	0.252097
$209$	−3.71947	−0.257281
$210$	0	0
$211$	−13.7763	−0.948400	−0.474200	−	0.880417i	$-0.657263\pi$
$211$	−13.7763	−0.948400	−0.474200	+	0.880417i	$0.657263\pi$
$212$	−7.96011	−0.546702
$213$	−10.3905	−0.711948
$214$	11.5368	0.788638
$215$	−0.487100	−0.0332199
$216$	3.06844	0.208781
$217$	0	0
$218$	−0.632124	−0.0428129
$219$	−4.10639	−0.277484
$220$	3.33744	0.225010
$221$	1.76383	0.118648
$222$	12.0978	0.811954
$223$	17.6305	1.18063	0.590313	−	0.807174i	$-0.299004\pi$
$223$	17.6305	1.18063	0.590313	+	0.807174i	$0.299004\pi$
$224$	0	0
$225$	7.33339	0.488892
$226$	−13.5689	−0.902588
$227$	−11.3661	−0.754392	−0.377196	−	0.926133i	$-0.623112\pi$
$227$	−11.3661	−0.754392	−0.377196	+	0.926133i	$0.623112\pi$
$228$	2.46284	0.163106
$229$	−9.25935	−0.611875	−0.305938	−	0.952052i	$-0.598970\pi$
$229$	−9.25935	−0.611875	−0.305938	+	0.952052i	$0.598970\pi$
$230$	−0.419475	−0.0276593
$231$	0	0
$232$	23.7369	1.55840
$233$	−13.4118	−0.878639	−0.439320	−	0.898331i	$-0.644780\pi$
$233$	−13.4118	−0.878639	−0.439320	+	0.898331i	$0.644780\pi$
$234$	−2.23850	−0.146335
$235$	2.41245	0.157371
$236$	8.89389	0.578943
$237$	−1.02066	−0.0662993
$238$	0	0
$239$	25.5210	1.65082	0.825408	−	0.564537i	$-0.190945\pi$
$239$	25.5210	1.65082	0.825408	+	0.564537i	$0.190945\pi$
$240$	6.26602	0.404470
$241$	15.6464	1.00787	0.503936	−	0.863741i	$-0.331885\pi$
$241$	15.6464	1.00787	0.503936	+	0.863741i	$0.331885\pi$
$242$	−10.5071	−0.675422
$243$	−1.00000	−0.0641500
$244$	4.74687	0.303887
$245$	0	0
$246$	−1.09852	−0.0700390
$247$	−6.32662	−0.402553
$248$	−3.24869	−0.206292
$249$	16.7752	1.06309
$250$	9.00192	0.569331
$251$	−0.155126	−0.00979147	−0.00489573	−	0.999988i	$-0.501558\pi$
$251$	−0.155126	−0.00979147	−0.00489573	+	0.999988i	$0.501558\pi$
$252$	0	0
$253$	0.130261	0.00818946
$254$	16.0830	1.00914
$255$	3.03983	0.190362
$256$	−15.6472	−0.977952
$257$	−3.86845	−0.241307	−0.120654	−	0.992695i	$-0.538499\pi$
$257$	−3.86845	−0.241307	−0.120654	+	0.992695i	$0.538499\pi$
$258$	0.152365	0.00948581
$259$	0	0
$260$	5.67680	0.352060
$261$	−7.73581	−0.478835
$262$	−20.9082	−1.29171
$263$	−15.5289	−0.957554	−0.478777	−	0.877937i	$-0.658920\pi$
$263$	−15.5289	−0.957554	−0.478777	+	0.877937i	$0.658920\pi$
$264$	−3.67601	−0.226243
$265$	35.2408	2.16483
$266$	0	0
$267$	−7.26262	−0.444465
$268$	10.0979	0.616825
$269$	−4.06354	−0.247759	−0.123879	−	0.992297i	$-0.539534\pi$
$269$	−4.06354	−0.247759	−0.123879	+	0.992297i	$0.539534\pi$
$270$	−3.85788	−0.234783
$271$	10.2311	0.621493	0.310747	−	0.950493i	$-0.399421\pi$
$271$	10.2311	0.621493	0.310747	+	0.950493i	$0.399421\pi$
$272$	1.54440	0.0936429
$273$	0	0
$274$	1.92140	0.116076
$275$	−8.78542	−0.529781
$276$	−0.0862524	−0.00519178
$277$	−0.795094	−0.0477725	−0.0238863	−	0.999715i	$-0.507604\pi$
$277$	−0.795094	−0.0477725	−0.0238863	+	0.999715i	$0.507604\pi$
$278$	8.87017	0.531997
$279$	1.05874	0.0633852
$280$	0	0
$281$	7.36091	0.439115	0.219558	−	0.975600i	$-0.429539\pi$
$281$	7.36091	0.439115	0.219558	+	0.975600i	$0.429539\pi$
$282$	−0.754612	−0.0449365
$283$	−11.9803	−0.712158	−0.356079	−	0.934456i	$-0.615887\pi$
$283$	−11.9803	−0.712158	−0.356079	+	0.934456i	$0.615887\pi$
$284$	−8.24237	−0.489095
$285$	−10.9035	−0.645865
$286$	2.68173	0.158574
$287$	0	0
$288$	4.17688	0.246125
$289$	−16.2508	−0.955927
$290$	−29.8438	−1.75249
$291$	16.3003	0.955542
$292$	−3.25742	−0.190626
$293$	−12.7033	−0.742136	−0.371068	−	0.928606i	$-0.621008\pi$
$293$	−12.7033	−0.742136	−0.371068	+	0.928606i	$0.621008\pi$
$294$	0	0
$295$	−39.3748	−2.29249
$296$	33.7924	1.96414
$297$	1.19800	0.0695152
$298$	17.9686	1.04089
$299$	0.221567	0.0128136
$300$	5.81726	0.335860
$301$	0	0
$302$	3.70098	0.212968
$303$	11.3417	0.651562
$304$	−5.53954	−0.317714
$305$	−21.0152	−1.20333
$306$	−0.950859	−0.0543570
$307$	−6.88040	−0.392685	−0.196342	−	0.980535i	$-0.562906\pi$
$307$	−6.88040	−0.392685	−0.196342	+	0.980535i	$0.562906\pi$
$308$	0	0
$309$	2.54128	0.144568
$310$	4.08450	0.231984
$311$	14.2024	0.805347	0.402673	−	0.915344i	$-0.368081\pi$
$311$	14.2024	0.805347	0.402673	+	0.915344i	$0.368081\pi$
$312$	−6.25269	−0.353989
$313$	−1.78226	−0.100739	−0.0503696	−	0.998731i	$-0.516040\pi$
$313$	−1.78226	−0.100739	−0.0503696	+	0.998731i	$0.516040\pi$
$314$	8.11351	0.457872
$315$	0	0
$316$	−0.809649	−0.0455463
$317$	0.753437	0.0423172	0.0211586	−	0.999776i	$-0.493265\pi$
$317$	0.753437	0.0423172	0.0211586	+	0.999776i	$0.493265\pi$
$318$	−11.0233	−0.618157
$319$	9.26753	0.518882
$320$	28.6459	1.60136
$321$	−10.5021	−0.586171
$322$	0	0
$323$	−2.68739	−0.149531
$324$	−0.793257	−0.0440698
$325$	−14.9435	−0.828918
$326$	3.05200	0.169035
$327$	0.575433	0.0318215
$328$	−3.06844	−0.169427
$329$	0	0
$330$	4.62175	0.254419
$331$	−3.09517	−0.170126	−0.0850629	−	0.996376i	$-0.527109\pi$
$331$	−3.09517	−0.170126	−0.0850629	+	0.996376i	$0.527109\pi$
$332$	13.3071	0.730320
$333$	−11.0129	−0.603502
$334$	−16.6810	−0.912745
$335$	−44.7050	−2.44250
$336$	0	0
$337$	3.40333	0.185391	0.0926955	−	0.995695i	$-0.470452\pi$
$337$	3.40333	0.185391	0.0926955	+	0.995695i	$0.470452\pi$
$338$	−9.71927	−0.528659
$339$	12.3520	0.670867
$340$	2.41137	0.130775
$341$	−1.26838	−0.0686864
$342$	3.41060	0.184424
$343$	0	0
$344$	0.425594	0.0229465
$345$	0.381855	0.0205584
$346$	−14.8483	−0.798252
$347$	−28.0829	−1.50757	−0.753785	−	0.657121i	$-0.771774\pi$
$347$	−28.0829	−1.50757	−0.753785	+	0.657121i	$0.771774\pi$
$348$	−6.13649	−0.328950
$349$	−25.1398	−1.34570	−0.672851	−	0.739778i	$-0.734930\pi$
$349$	−25.1398	−1.34570	−0.672851	+	0.739778i	$0.734930\pi$
$350$	0	0
$351$	2.03774	0.108767
$352$	−5.00392	−0.266710
$353$	−13.5603	−0.721742	−0.360871	−	0.932616i	$-0.617520\pi$
$353$	−13.5603	−0.721742	−0.360871	+	0.932616i	$0.617520\pi$
$354$	12.3164	0.654611
$355$	36.4905	1.93671
$356$	−5.76113	−0.305339
$357$	0	0
$358$	−19.6775	−1.03999
$359$	9.00119	0.475065	0.237532	−	0.971380i	$-0.423661\pi$
$359$	9.00119	0.475065	0.237532	+	0.971380i	$0.423661\pi$
$360$	−10.7760	−0.567947
$361$	−9.36070	−0.492668
$362$	−23.4817	−1.23417
$363$	9.56479	0.502021
$364$	0	0
$365$	14.4212	0.754840
$366$	6.57356	0.343606
$367$	−2.90575	−0.151679	−0.0758395	−	0.997120i	$-0.524164\pi$
$367$	−2.90575	−0.151679	−0.0758395	+	0.997120i	$0.524164\pi$
$368$	0.194003	0.0101131
$369$	1.00000	0.0520579
$370$	−42.4863	−2.20876
$371$	0	0
$372$	0.839854	0.0435444
$373$	−3.51537	−0.182019	−0.0910094	−	0.995850i	$-0.529009\pi$
$373$	−3.51537	−0.182019	−0.0910094	+	0.995850i	$0.529009\pi$
$374$	1.13913	0.0589031
$375$	−8.19460	−0.423167
$376$	−2.10783	−0.108703
$377$	15.7636	0.811865
$378$	0	0
$379$	−17.3132	−0.889317	−0.444658	−	0.895700i	$-0.646675\pi$
$379$	−17.3132	−0.889317	−0.444658	+	0.895700i	$0.646675\pi$
$380$	−8.64924	−0.443697
$381$	−14.6407	−0.750064
$382$	12.0092	0.614445
$383$	9.36168	0.478360	0.239180	−	0.970975i	$-0.423121\pi$
$383$	9.36168	0.478360	0.239180	+	0.970975i	$0.423121\pi$
$384$	−0.606679	−0.0309595
$385$	0	0
$386$	13.9623	0.710662
$387$	−0.138700	−0.00705053
$388$	12.9303	0.656439
$389$	−13.0432	−0.661319	−0.330659	−	0.943750i	$-0.607271\pi$
$389$	−13.0432	−0.661319	−0.330659	+	0.943750i	$0.607271\pi$
$390$	7.86135	0.398075
$391$	0.0941165	0.00475968
$392$	0	0
$393$	19.0331	0.960091
$394$	1.47487	0.0743028
$395$	3.58446	0.180354
$396$	0.950325	0.0477556
$397$	9.04266	0.453838	0.226919	−	0.973914i	$-0.427135\pi$
$397$	9.04266	0.453838	0.226919	+	0.973914i	$0.427135\pi$
$398$	19.2043	0.962623
$399$	0	0
$400$	−13.0844	−0.654222
$401$	−4.43511	−0.221479	−0.110739	−	0.993849i	$-0.535322\pi$
$401$	−4.43511	−0.221479	−0.110739	+	0.993849i	$0.535322\pi$
$402$	13.9837	0.697445
$403$	−2.15744	−0.107470
$404$	8.99686	0.447610
$405$	3.51189	0.174507
$406$	0	0
$407$	13.1935	0.653976
$408$	−2.65599	−0.131491
$409$	−32.8900	−1.62631	−0.813153	−	0.582050i	$-0.802251\pi$
$409$	−32.8900	−1.62631	−0.813153	+	0.582050i	$0.802251\pi$
$410$	3.85788	0.190527
$411$	−1.74909	−0.0862761
$412$	2.01588	0.0993155
$413$	0	0
$414$	−0.119444	−0.00587036
$415$	−58.9128	−2.89192
$416$	−8.51140	−0.417306
$417$	−8.07467	−0.395418
$418$	−4.08591	−0.199848
$419$	−29.9086	−1.46113	−0.730565	−	0.682843i	$-0.760743\pi$
$419$	−29.9086	−1.46113	−0.730565	+	0.682843i	$0.760743\pi$
$420$	0	0
$421$	−2.55466	−0.124507	−0.0622533	−	0.998060i	$-0.519829\pi$
$421$	−2.55466	−0.124507	−0.0622533	+	0.998060i	$0.519829\pi$
$422$	−15.1335	−0.736688
$423$	0.686936	0.0334000
$424$	−30.7910	−1.49534
$425$	−6.34765	−0.307906
$426$	−11.4142	−0.553020
$427$	0	0
$428$	−8.33088	−0.402688
$429$	−2.44122	−0.117863
$430$	−0.535088	−0.0258043
$431$	24.8454	1.19676	0.598380	−	0.801213i	$-0.295811\pi$
$431$	24.8454	1.19676	0.598380	+	0.801213i	$0.295811\pi$
$432$	1.78423	0.0858438
$433$	12.9735	0.623468	0.311734	−	0.950169i	$-0.399090\pi$
$433$	12.9735	0.623468	0.311734	+	0.950169i	$0.399090\pi$
$434$	0	0
$435$	27.1673	1.30257
$436$	0.456467	0.0218608
$437$	−0.337583	−0.0161488
$438$	−4.51095	−0.215541
$439$	−19.8149	−0.945714	−0.472857	−	0.881139i	$-0.656777\pi$
$439$	−19.8149	−0.945714	−0.472857	+	0.881139i	$0.656777\pi$
$440$	12.9097	0.615448
$441$	0	0
$442$	1.93760	0.0921624
$443$	−19.7767	−0.939620	−0.469810	−	0.882767i	$-0.655678\pi$
$443$	−19.7767	−0.939620	−0.469810	+	0.882767i	$0.655678\pi$
$444$	−8.73604	−0.414594
$445$	25.5055	1.20908
$446$	19.3674	0.917075
$447$	−16.3571	−0.773666
$448$	0	0
$449$	−8.26604	−0.390098	−0.195049	−	0.980793i	$-0.562487\pi$
$449$	−8.26604	−0.390098	−0.195049	+	0.980793i	$0.562487\pi$
$450$	8.05586	0.379757
$451$	−1.19800	−0.0564118
$452$	9.79829	0.460873
$453$	−3.36907	−0.158293
$454$	−12.4858	−0.585989
$455$	0	0
$456$	9.52667	0.446127
$457$	22.4791	1.05153	0.525763	−	0.850631i	$-0.323780\pi$
$457$	22.4791	1.05153	0.525763	+	0.850631i	$0.323780\pi$
$458$	−10.1716	−0.475286
$459$	0.865583	0.0404019
$460$	0.302909	0.0141232
$461$	22.0791	1.02832	0.514162	−	0.857693i	$-0.328103\pi$
$461$	22.0791	1.02832	0.514162	+	0.857693i	$0.328103\pi$
$462$	0	0
$463$	36.1530	1.68017	0.840087	−	0.542451i	$-0.182504\pi$
$463$	36.1530	1.68017	0.840087	+	0.542451i	$0.182504\pi$
$464$	13.8025	0.640763
$465$	−3.71819	−0.172427
$466$	−14.7332	−0.682501
$467$	22.7272	1.05169	0.525845	−	0.850580i	$-0.323749\pi$
$467$	22.7272	1.05169	0.525845	+	0.850580i	$0.323749\pi$
$468$	1.61645	0.0747205
$469$	0	0
$470$	2.65012	0.122241
$471$	−7.38587	−0.340323
$472$	34.4030	1.58353
$473$	0.166163	0.00764020
$474$	−1.12122	−0.0514993
$475$	22.7681	1.04467
$476$	0	0
$477$	10.0347	0.459458
$478$	28.0353	1.28230
$479$	30.3976	1.38890	0.694450	−	0.719541i	$-0.255648\pi$
$479$	30.3976	1.38890	0.694450	+	0.719541i	$0.255648\pi$
$480$	−14.6688	−0.669534
$481$	22.4414	1.02324
$482$	17.1878	0.782884
$483$	0	0
$484$	7.58733	0.344879
$485$	−57.2450	−2.59936
$486$	−1.09852	−0.0498298
$487$	−25.3134	−1.14706	−0.573530	−	0.819185i	$-0.694426\pi$
$487$	−25.3134	−1.14706	−0.573530	+	0.819185i	$0.694426\pi$
$488$	18.3616	0.831193
$489$	−2.77829	−0.125638
$490$	0	0
$491$	−12.6197	−0.569517	−0.284759	−	0.958599i	$-0.591913\pi$
$491$	−12.6197	−0.569517	−0.284759	+	0.958599i	$0.591913\pi$
$492$	0.793257	0.0357628
$493$	6.69598	0.301572
$494$	−6.94991	−0.312691
$495$	−4.20726	−0.189102
$496$	−1.88904	−0.0848203
$497$	0	0
$498$	18.4279	0.825774
$499$	37.1555	1.66331	0.831655	−	0.555293i	$-0.187394\pi$
$499$	37.1555	1.66331	0.831655	+	0.555293i	$0.187394\pi$
$500$	−6.50042	−0.290708
$501$	15.1850	0.678417
$502$	−0.170409	−0.00760572
$503$	−32.6369	−1.45521	−0.727604	−	0.685997i	$-0.759366\pi$
$503$	−32.6369	−1.45521	−0.727604	+	0.685997i	$0.759366\pi$
$504$	0	0
$505$	−39.8307	−1.77244
$506$	0.143094	0.00636132
$507$	8.84761	0.392936
$508$	−11.6138	−0.515279
$509$	−7.96848	−0.353197	−0.176598	−	0.984283i	$-0.556509\pi$
$509$	−7.96848	−0.353197	−0.176598	+	0.984283i	$0.556509\pi$
$510$	3.33931	0.147867
$511$	0	0
$512$	−18.4021	−0.813267
$513$	−3.10472	−0.137077
$514$	−4.24956	−0.187440
$515$	−8.92468	−0.393269
$516$	−0.110025	−0.00484357
$517$	−0.822952	−0.0361934
$518$	0	0
$519$	13.5167	0.593317
$520$	21.9588	0.962956
$521$	16.8045	0.736219	0.368110	−	0.929782i	$-0.380005\pi$
$521$	16.8045	0.736219	0.368110	+	0.929782i	$0.380005\pi$
$522$	−8.49793	−0.371944
$523$	−32.4862	−1.42052	−0.710262	−	0.703938i	$-0.751423\pi$
$523$	−32.4862	−1.42052	−0.710262	+	0.703938i	$0.751423\pi$
$524$	15.0981	0.659564
$525$	0	0
$526$	−17.0588	−0.743799
$527$	−0.916429	−0.0399203
$528$	−2.13751	−0.0930234
$529$	−22.9882	−0.999486
$530$	38.7127	1.68157
$531$	−11.2119	−0.486553
$532$	0	0
$533$	−2.03774	−0.0882643
$534$	−7.97813	−0.345247
$535$	36.8823	1.59456
$536$	39.0601	1.68714
$537$	17.9127	0.772991
$538$	−4.46388	−0.192451
$539$	0	0
$540$	2.78583	0.119883
$541$	−7.24393	−0.311441	−0.155720	−	0.987801i	$-0.549770\pi$
$541$	−7.24393	−0.311441	−0.155720	+	0.987801i	$0.549770\pi$
$542$	11.2390	0.482757
$543$	21.3758	0.917322
$544$	−3.61544	−0.155011
$545$	−2.02086	−0.0865641
$546$	0	0
$547$	14.8267	0.633945	0.316972	−	0.948435i	$-0.397334\pi$
$547$	14.8267	0.633945	0.316972	+	0.948435i	$0.397334\pi$
$548$	−1.38748	−0.0592700
$549$	−5.98402	−0.255392
$550$	−9.65095	−0.411518
$551$	−24.0175	−1.02318
$552$	−0.333638	−0.0142006
$553$	0	0
$554$	−0.873425	−0.0371083
$555$	38.6760	1.64171
$556$	−6.40529	−0.271645
$557$	−29.5610	−1.25254	−0.626269	−	0.779607i	$-0.715419\pi$
$557$	−29.5610	−1.25254	−0.626269	+	0.779607i	$0.715419\pi$
$558$	1.16305	0.0492357
$559$	0.282635	0.0119542
$560$	0	0
$561$	−1.03697	−0.0437810
$562$	8.08610	0.341092
$563$	17.0509	0.718611	0.359306	−	0.933220i	$-0.383014\pi$
$563$	17.0509	0.718611	0.359306	+	0.933220i	$0.383014\pi$
$564$	0.544917	0.0229451
$565$	−43.3788	−1.82496
$566$	−13.1606	−0.553183
$567$	0	0
$568$	−31.8828	−1.33777
$569$	14.2003	0.595307	0.297653	−	0.954674i	$-0.403796\pi$
$569$	14.2003	0.595307	0.297653	+	0.954674i	$0.403796\pi$
$570$	−11.9776	−0.501688
$571$	43.8411	1.83469	0.917347	−	0.398088i	$-0.130326\pi$
$571$	43.8411	1.83469	0.917347	+	0.398088i	$0.130326\pi$
$572$	−1.93652	−0.0809698
$573$	−10.9322	−0.456699
$574$	0	0
$575$	−0.797373	−0.0332528
$576$	8.15684	0.339868
$577$	38.6961	1.61094	0.805470	−	0.592637i	$-0.201913\pi$
$577$	38.6961	1.61094	0.805470	+	0.592637i	$0.201913\pi$
$578$	−17.8518	−0.742536
$579$	−12.7101	−0.528215
$580$	21.5507	0.894843
$581$	0	0
$582$	17.9062	0.742236
$583$	−12.0216	−0.497885
$584$	−12.6002	−0.521401
$585$	−7.15632	−0.295878
$586$	−13.9548	−0.576469
$587$	14.2148	0.586706	0.293353	−	0.956004i	$-0.405229\pi$
$587$	14.2148	0.586706	0.293353	+	0.956004i	$0.405229\pi$
$588$	0	0
$589$	3.28710	0.135443
$590$	−43.2540	−1.78074
$591$	−1.34260	−0.0552271
$592$	19.6495	0.807589
$593$	−27.5037	−1.12944	−0.564721	−	0.825282i	$-0.691016\pi$
$593$	−27.5037	−1.12944	−0.564721	+	0.825282i	$0.691016\pi$
$594$	1.31603	0.0539973
$595$	0	0
$596$	−12.9754	−0.531494
$597$	−17.4820	−0.715490
$598$	0.243396	0.00995320
$599$	−21.9273	−0.895924	−0.447962	−	0.894053i	$-0.647850\pi$
$599$	−21.9273	−0.895924	−0.447962	+	0.894053i	$0.647850\pi$
$600$	22.5021	0.918644
$601$	31.0737	1.26752	0.633761	−	0.773529i	$-0.281510\pi$
$601$	31.0737	1.26752	0.633761	+	0.773529i	$0.281510\pi$
$602$	0	0
$603$	−12.7296	−0.518390
$604$	−2.67254	−0.108744
$605$	−33.5905	−1.36565
$606$	12.4590	0.506114
$607$	31.3966	1.27435	0.637175	−	0.770719i	$-0.280103\pi$
$607$	31.3966	1.27435	0.637175	+	0.770719i	$0.280103\pi$
$608$	12.9681	0.525924
$609$	0	0
$610$	−23.0856	−0.934710
$611$	−1.39980	−0.0566297
$612$	0.686630	0.0277554
$613$	38.6712	1.56191	0.780957	−	0.624585i	$-0.214732\pi$
$613$	38.6712	1.56191	0.780957	+	0.624585i	$0.214732\pi$
$614$	−7.55824	−0.305026
$615$	−3.51189	−0.141613
$616$	0	0
$617$	−14.1413	−0.569309	−0.284654	−	0.958630i	$-0.591879\pi$
$617$	−14.1413	−0.569309	−0.284654	+	0.958630i	$0.591879\pi$
$618$	2.79164	0.112296
$619$	3.91930	0.157530	0.0787649	−	0.996893i	$-0.474902\pi$
$619$	3.91930	0.157530	0.0787649	+	0.996893i	$0.474902\pi$
$620$	−2.94948	−0.118454
$621$	0.108732	0.00436326
$622$	15.6017	0.625569
$623$	0	0
$624$	−3.63580	−0.145548
$625$	−7.88839	−0.315535
$626$	−1.95784	−0.0782512
$627$	3.71947	0.148541
$628$	−5.85889	−0.233795
$629$	9.53255	0.380088
$630$	0	0
$631$	20.6500	0.822063	0.411032	−	0.911621i	$-0.365169\pi$
$631$	20.6500	0.822063	0.411032	+	0.911621i	$0.365169\pi$
$632$	−3.13185	−0.124578
$633$	13.7763	0.547559
$634$	0.827664	0.0328707
$635$	51.4164	2.04040
$636$	7.96011	0.315639
$637$	0	0
$638$	10.1806	0.403052
$639$	10.3905	0.411043
$640$	2.13059	0.0842190
$641$	30.3221	1.19765	0.598825	−	0.800880i	$-0.295635\pi$
$641$	30.3221	1.19765	0.598825	+	0.800880i	$0.295635\pi$
$642$	−11.5368	−0.455320
$643$	−34.9306	−1.37753	−0.688764	−	0.724986i	$-0.741846\pi$
$643$	−34.9306	−1.37753	−0.688764	+	0.724986i	$0.741846\pi$
$644$	0	0
$645$	0.487100	0.0191795
$646$	−2.95215	−0.116151
$647$	45.0888	1.77262	0.886312	−	0.463089i	$-0.153259\pi$
$647$	45.0888	1.77262	0.886312	+	0.463089i	$0.153259\pi$
$648$	−3.06844	−0.120540
$649$	13.4319	0.527246
$650$	−16.4158	−0.643879
$651$	0	0
$652$	−2.20389	−0.0863112
$653$	−24.6436	−0.964378	−0.482189	−	0.876067i	$-0.660158\pi$
$653$	−24.6436	−0.964378	−0.482189	+	0.876067i	$0.660158\pi$
$654$	0.632124	0.0247180
$655$	−66.8421	−2.61174
$656$	−1.78423	−0.0696625
$657$	4.10639	0.160206
$658$	0	0
$659$	−19.5019	−0.759687	−0.379844	−	0.925051i	$-0.624022\pi$
$659$	−19.5019	−0.759687	−0.379844	+	0.925051i	$0.624022\pi$
$660$	−3.33744	−0.129910
$661$	−42.0714	−1.63639	−0.818193	−	0.574944i	$-0.805024\pi$
$661$	−42.0714	−1.63639	−0.818193	+	0.574944i	$0.805024\pi$
$662$	−3.40010	−0.132149
$663$	−1.76383	−0.0685016
$664$	51.4739	1.99757
$665$	0	0
$666$	−12.0978	−0.468782
$667$	0.841130	0.0325687
$668$	12.0456	0.466059
$669$	−17.6305	−0.681635
$670$	−49.1093	−1.89726
$671$	7.16889	0.276752
$672$	0	0
$673$	−41.3394	−1.59352	−0.796759	−	0.604297i	$-0.793454\pi$
$673$	−41.3394	−1.59352	−0.796759	+	0.604297i	$0.793454\pi$
$674$	3.73862	0.144006
$675$	−7.33339	−0.282262
$676$	7.01843	0.269940
$677$	16.9322	0.650757	0.325379	−	0.945584i	$-0.394508\pi$
$677$	16.9322	0.650757	0.325379	+	0.945584i	$0.394508\pi$
$678$	13.5689	0.521109
$679$	0	0
$680$	9.32756	0.357696
$681$	11.3661	0.435549
$682$	−1.39334	−0.0533536
$683$	48.4457	1.85372	0.926861	−	0.375404i	$-0.122496\pi$
$683$	48.4457	1.85372	0.926861	+	0.375404i	$0.122496\pi$
$684$	−2.46284	−0.0941691
$685$	6.14260	0.234697
$686$	0	0
$687$	9.25935	0.353266
$688$	0.247473	0.00943482
$689$	−20.4481	−0.779012
$690$	0.419475	0.0159691
$691$	35.7511	1.36003	0.680017	−	0.733196i	$-0.261972\pi$
$691$	35.7511	1.36003	0.680017	+	0.733196i	$0.261972\pi$
$692$	10.7222	0.407597
$693$	0	0
$694$	−30.8496	−1.17104
$695$	28.3574	1.07566
$696$	−23.7369	−0.899745
$697$	−0.865583	−0.0327863
$698$	−27.6165	−1.04530
$699$	13.4118	0.507283
$700$	0	0
$701$	40.1227	1.51541	0.757707	−	0.652595i	$-0.226320\pi$
$701$	40.1227	1.51541	0.757707	+	0.652595i	$0.226320\pi$
$702$	2.23850	0.0844866
$703$	−34.1919	−1.28957
$704$	−9.77193	−0.368293
$705$	−2.41245	−0.0908579
$706$	−14.8962	−0.560627
$707$	0	0
$708$	−8.89389	−0.334253
$709$	−7.49353	−0.281425	−0.140713	−	0.990050i	$-0.544939\pi$
$709$	−7.49353	−0.281425	−0.140713	+	0.990050i	$0.544939\pi$
$710$	40.0854	1.50438
$711$	1.02066	0.0382779
$712$	−22.2850	−0.835164
$713$	−0.115119	−0.00431124
$714$	0	0
$715$	8.57330	0.320623
$716$	14.2094	0.531030
$717$	−25.5210	−0.953099
$718$	9.88797	0.369016
$719$	−7.55296	−0.281678	−0.140839	−	0.990033i	$-0.544980\pi$
$719$	−7.55296	−0.281678	−0.140839	+	0.990033i	$0.544980\pi$
$720$	−6.26602	−0.233521
$721$	0	0
$722$	−10.2829	−0.382690
$723$	−15.6464	−0.581895
$724$	16.9565	0.630183
$725$	−56.7297	−2.10689
$726$	10.5071	0.389955
$727$	36.3777	1.34918	0.674588	−	0.738195i	$-0.264321\pi$
$727$	36.3777	1.34918	0.674588	+	0.738195i	$0.264321\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	15.8420	0.586337
$731$	0.120056	0.00444045
$732$	−4.74687	−0.175449
$733$	−48.0400	−1.77440	−0.887199	−	0.461387i	$-0.847352\pi$
$733$	−48.0400	−1.77440	−0.887199	+	0.461387i	$0.847352\pi$
$734$	−3.19202	−0.117820
$735$	0	0
$736$	−0.454160	−0.0167406
$737$	15.2501	0.561746
$738$	1.09852	0.0404370
$739$	38.5615	1.41851	0.709253	−	0.704954i	$-0.249032\pi$
$739$	38.5615	1.41851	0.709253	+	0.704954i	$0.249032\pi$
$740$	30.6800	1.12782
$741$	6.32662	0.232414
$742$	0	0
$743$	12.2227	0.448408	0.224204	−	0.974542i	$-0.428022\pi$
$743$	12.2227	0.448408	0.224204	+	0.974542i	$0.428022\pi$
$744$	3.24869	0.119103
$745$	57.4445	2.10460
$746$	−3.86170	−0.141387
$747$	−16.7752	−0.613774
$748$	−0.822585	−0.0300767
$749$	0	0
$750$	−9.00192	−0.328704
$751$	28.5116	1.04040	0.520202	−	0.854043i	$-0.325857\pi$
$751$	28.5116	1.04040	0.520202	+	0.854043i	$0.325857\pi$
$752$	−1.22565	−0.0446949
$753$	0.155126	0.00565311
$754$	17.3166	0.630633
$755$	11.8318	0.430603
$756$	0	0
$757$	−1.95044	−0.0708900	−0.0354450	−	0.999372i	$-0.511285\pi$
$757$	−1.95044	−0.0708900	−0.0354450	+	0.999372i	$0.511285\pi$
$758$	−19.0188	−0.690795
$759$	−0.130261	−0.00472819
$760$	−33.4566	−1.21360
$761$	−9.52366	−0.345232	−0.172616	−	0.984989i	$-0.555222\pi$
$761$	−9.52366	−0.345232	−0.172616	+	0.984989i	$0.555222\pi$
$762$	−16.0830	−0.582627
$763$	0	0
$764$	−8.67203	−0.313743
$765$	−3.03983	−0.109905
$766$	10.2840	0.371575
$767$	22.8469	0.824952
$768$	15.6472	0.564621
$769$	−39.2269	−1.41456	−0.707279	−	0.706935i	$-0.750077\pi$
$769$	−39.2269	−1.41456	−0.707279	+	0.706935i	$0.750077\pi$
$770$	0	0
$771$	3.86845	0.139319
$772$	−10.0824	−0.362873
$773$	0.0131202	0.000471902 0	0.000235951	−	1.00000i	$-0.499925\pi$
$773$	0.0131202	0.000471902 0	0.000235951		1.00000i	$0.499925\pi$
$774$	−0.152365	−0.00547664
$775$	7.76416	0.278897
$776$	50.0167	1.79549
$777$	0	0
$778$	−14.3283	−0.513693
$779$	3.10472	0.111238
$780$	−5.67680	−0.203262
$781$	−12.4479	−0.445421
$782$	0.103389	0.00369717
$783$	7.73581	0.276455
$784$	0	0
$785$	25.9384	0.925780
$786$	20.9082	0.745770
$787$	21.5852	0.769430	0.384715	−	0.923035i	$-0.374300\pi$
$787$	21.5852	0.769430	0.384715	+	0.923035i	$0.374300\pi$
$788$	−1.06502	−0.0379399
$789$	15.5289	0.552844
$790$	3.93760	0.140093
$791$	0	0
$792$	3.67601	0.130621
$793$	12.1939	0.433018
$794$	9.93352	0.352528
$795$	−35.2408	−1.24986
$796$	−13.8677	−0.491528
$797$	−50.5759	−1.79149	−0.895745	−	0.444569i	$-0.853357\pi$
$797$	−50.5759	−1.79149	−0.895745	+	0.444569i	$0.853357\pi$
$798$	0	0
$799$	−0.594600	−0.0210354
$800$	30.6307	1.08296
$801$	7.26262	0.256612
$802$	−4.87205	−0.172038
$803$	−4.91947	−0.173604
$804$	−10.0979	−0.356124
$805$	0	0
$806$	−2.36999	−0.0834793
$807$	4.06354	0.143043
$808$	34.8013	1.22430
$809$	11.6570	0.409839	0.204920	−	0.978779i	$-0.434307\pi$
$809$	11.6570	0.409839	0.204920	+	0.978779i	$0.434307\pi$
$810$	3.85788	0.135552
$811$	26.2844	0.922971	0.461486	−	0.887148i	$-0.347317\pi$
$811$	26.2844	0.922971	0.461486	+	0.887148i	$0.347317\pi$
$812$	0	0
$813$	−10.2311	−0.358819
$814$	14.4933	0.507989
$815$	9.75704	0.341774
$816$	−1.54440	−0.0540648
$817$	−0.430626	−0.0150657
$818$	−36.1303	−1.26327
$819$	0	0
$820$	−2.78583	−0.0972855
$821$	54.2491	1.89331	0.946654	−	0.322252i	$-0.104440\pi$
$821$	54.2491	1.89331	0.946654	+	0.322252i	$0.104440\pi$
$822$	−1.92140	−0.0670167
$823$	2.29016	0.0798299	0.0399150	−	0.999203i	$-0.487291\pi$
$823$	2.29016	0.0798299	0.0399150	+	0.999203i	$0.487291\pi$
$824$	7.79776	0.271648
$825$	8.78542	0.305869
$826$	0	0
$827$	36.3060	1.26248	0.631242	−	0.775586i	$-0.282546\pi$
$827$	36.3060	1.26248	0.631242	+	0.775586i	$0.282546\pi$
$828$	0.0862524	0.00299748
$829$	−55.1165	−1.91427	−0.957137	−	0.289636i	$-0.906466\pi$
$829$	−55.1165	−1.91427	−0.957137	+	0.289636i	$0.906466\pi$
$830$	−64.7168	−2.24635
$831$	0.795094	0.0275815
$832$	−16.6215	−0.576248
$833$	0	0
$834$	−8.87017	−0.307149
$835$	−53.3282	−1.84550
$836$	2.95050	0.102045
$837$	−1.05874	−0.0365955
$838$	−32.8551	−1.13496
$839$	27.4885	0.949008	0.474504	−	0.880253i	$-0.342627\pi$
$839$	27.4885	0.949008	0.474504	+	0.880253i	$0.342627\pi$
$840$	0	0
$841$	30.8428	1.06354
$842$	−2.80634	−0.0967130
$843$	−7.36091	−0.253523
$844$	10.9281	0.376162
$845$	−31.0719	−1.06890
$846$	0.754612	0.0259441
$847$	0	0
$848$	−17.9042	−0.614834
$849$	11.9803	0.411164
$850$	−6.97301	−0.239172
$851$	1.19745	0.0410481
$852$	8.24237	0.282379
$853$	32.8538	1.12489	0.562446	−	0.826834i	$-0.309860\pi$
$853$	32.8538	1.12489	0.562446	+	0.826834i	$0.309860\pi$
$854$	0	0
$855$	10.9035	0.372890
$856$	−32.2252	−1.10143
$857$	51.7302	1.76707	0.883535	−	0.468365i	$-0.155157\pi$
$857$	51.7302	1.76707	0.883535	+	0.468365i	$0.155157\pi$
$858$	−2.68173	−0.0915526
$859$	13.0146	0.444052	0.222026	−	0.975041i	$-0.428733\pi$
$859$	13.0146	0.444052	0.222026	+	0.975041i	$0.428733\pi$
$860$	0.386395	0.0131760
$861$	0	0
$862$	27.2931	0.929607
$863$	−34.0965	−1.16066	−0.580329	−	0.814382i	$-0.697076\pi$
$863$	−34.0965	−1.16066	−0.580329	+	0.814382i	$0.697076\pi$
$864$	−4.17688	−0.142100
$865$	−47.4692	−1.61400
$866$	14.2517	0.484291
$867$	16.2508	0.551905
$868$	0	0
$869$	−1.22276	−0.0414793
$870$	29.8438	1.01180
$871$	25.9397	0.878932
$872$	1.76569	0.0597937
$873$	−16.3003	−0.551683
$874$	−0.370841	−0.0125439
$875$	0	0
$876$	3.25742	0.110058
$877$	−39.4832	−1.33325	−0.666626	−	0.745393i	$-0.732262\pi$
$877$	−39.4832	−1.33325	−0.666626	+	0.745393i	$0.732262\pi$
$878$	−21.7671	−0.734602
$879$	12.7033	0.428472
$880$	7.50672	0.253051
$881$	11.1305	0.374995	0.187497	−	0.982265i	$-0.439962\pi$
$881$	11.1305	0.374995	0.187497	+	0.982265i	$0.439962\pi$
$882$	0	0
$883$	−30.4354	−1.02423	−0.512116	−	0.858916i	$-0.671138\pi$
$883$	−30.4354	−1.02423	−0.512116	+	0.858916i	$0.671138\pi$
$884$	−1.39917	−0.0470593
$885$	39.3748	1.32357
$886$	−21.7251	−0.729869
$887$	−23.8637	−0.801265	−0.400633	−	0.916239i	$-0.631210\pi$
$887$	−23.8637	−0.801265	−0.400633	+	0.916239i	$0.631210\pi$
$888$	−33.7924	−1.13400
$889$	0	0
$890$	28.0183	0.939176
$891$	−1.19800	−0.0401346
$892$	−13.9855	−0.468270
$893$	2.13275	0.0713696
$894$	−17.9686	−0.600961
$895$	−62.9076	−2.10277
$896$	0	0
$897$	−0.221567	−0.00739792
$898$	−9.08040	−0.303017
$899$	−8.19022	−0.273159
$900$	−5.81726	−0.193909
$901$	−8.68587	−0.289368
$902$	−1.31603	−0.0438190
$903$	0	0
$904$	37.9013	1.26058
$905$	−75.0694	−2.49539
$906$	−3.70098	−0.122957
$907$	49.2003	1.63367	0.816834	−	0.576872i	$-0.195727\pi$
$907$	49.2003	1.63367	0.816834	+	0.576872i	$0.195727\pi$
$908$	9.01621	0.299214
$909$	−11.3417	−0.376179
$910$	0	0
$911$	5.36497	0.177750	0.0888748	−	0.996043i	$-0.471673\pi$
$911$	5.36497	0.177750	0.0888748	+	0.996043i	$0.471673\pi$
$912$	5.53954	0.183432
$913$	20.0968	0.665107
$914$	24.6937	0.816794
$915$	21.0152	0.694743
$916$	7.34505	0.242687
$917$	0	0
$918$	0.950859	0.0313830
$919$	11.9364	0.393744	0.196872	−	0.980429i	$-0.436922\pi$
$919$	11.9364	0.393744	0.196872	+	0.980429i	$0.436922\pi$
$920$	1.17170	0.0386298
$921$	6.88040	0.226717
$922$	24.2543	0.798772
$923$	−21.1732	−0.696925
$924$	0	0
$925$	−80.7616	−2.65543
$926$	39.7148	1.30511
$927$	−2.54128	−0.0834664
$928$	−32.3116	−1.06068
$929$	20.2039	0.662868	0.331434	−	0.943478i	$-0.392468\pi$
$929$	20.2039	0.662868	0.331434	+	0.943478i	$0.392468\pi$
$930$	−4.08450	−0.133936
$931$	0	0
$932$	10.6390	0.348493
$933$	−14.2024	−0.464967
$934$	24.9663	0.816921
$935$	3.64173	0.119097
$936$	6.25269	0.204376
$937$	−41.5754	−1.35821	−0.679104	−	0.734042i	$-0.737632\pi$
$937$	−41.5754	−1.35821	−0.679104	+	0.734042i	$0.737632\pi$
$938$	0	0
$939$	1.78226	0.0581618
$940$	−1.91369	−0.0624177
$941$	9.80199	0.319536	0.159768	−	0.987155i	$-0.448925\pi$
$941$	9.80199	0.319536	0.159768	+	0.987155i	$0.448925\pi$
$942$	−8.11351	−0.264353
$943$	−0.108732	−0.00354080
$944$	20.0045	0.651092
$945$	0	0
$946$	0.182534	0.00593468
$947$	−8.21701	−0.267017	−0.133508	−	0.991048i	$-0.542624\pi$
$947$	−8.21701	−0.267017	−0.133508	+	0.991048i	$0.542624\pi$
$948$	0.809649	0.0262962
$949$	−8.36776	−0.271629
$950$	25.0112	0.811471
$951$	−0.753437	−0.0244319
$952$	0	0
$953$	−12.9420	−0.419232	−0.209616	−	0.977784i	$-0.567221\pi$
$953$	−12.9420	−0.419232	−0.209616	+	0.977784i	$0.567221\pi$
$954$	11.0233	0.356893
$955$	38.3927	1.24236
$956$	−20.2447	−0.654761
$957$	−9.26753	−0.299577
$958$	33.3923	1.07886
$959$	0	0
$960$	−28.6459	−0.924544
$961$	−29.8791	−0.963841
$962$	24.6523	0.794821
$963$	10.5021	0.338426
$964$	−12.4116	−0.399750
$965$	44.6366	1.43690
$966$	0	0
$967$	−23.8640	−0.767415	−0.383707	−	0.923455i	$-0.625353\pi$
$967$	−23.8640	−0.767415	−0.383707	+	0.923455i	$0.625353\pi$
$968$	29.3490	0.943313
$969$	2.68739	0.0863315
$970$	−62.8847	−2.01911
$971$	45.8155	1.47029	0.735145	−	0.677910i	$-0.237114\pi$
$971$	45.8155	1.47029	0.735145	+	0.677910i	$0.237114\pi$
$972$	0.793257	0.0254437
$973$	0	0
$974$	−27.8072	−0.891001
$975$	14.9435	0.478576
$976$	10.6769	0.341758
$977$	32.7341	1.04726	0.523628	−	0.851947i	$-0.324578\pi$
$977$	32.7341	1.04726	0.523628	+	0.851947i	$0.324578\pi$
$978$	−3.05200	−0.0975921
$979$	−8.70065	−0.278074
$980$	0	0
$981$	−0.575433	−0.0183722
$982$	−13.8629	−0.442384
$983$	−26.9962	−0.861044	−0.430522	−	0.902580i	$-0.641671\pi$
$983$	−26.9962	−0.861044	−0.430522	+	0.902580i	$0.641671\pi$
$984$	3.06844	0.0978184
$985$	4.71506	0.150234
$986$	7.35566	0.234252
$987$	0	0
$988$	5.01863	0.159664
$989$	0.0150811	0.000479552 0
$990$	−4.62175	−0.146889
$991$	−6.91400	−0.219630	−0.109815	−	0.993952i	$-0.535026\pi$
$991$	−6.91400	−0.219630	−0.109815	+	0.993952i	$0.535026\pi$
$992$	4.42224	0.140406
$993$	3.09517	0.0982221
$994$	0	0
$995$	61.3948	1.94635
$996$	−13.3071	−0.421651
$997$	−16.6639	−0.527752	−0.263876	−	0.964557i	$-0.585001\pi$
$997$	−16.6639	−0.527752	−0.263876	+	0.964557i	$0.585001\pi$
$998$	40.8160	1.29201
$999$	11.0129	0.348432

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bf.1.10		12
7.3	odd	6		861.2.i.e.247.3	✓	24
7.5	odd	6		861.2.i.e.739.3	yes	24
7.6	odd	2		6027.2.a.bg.1.10		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.i.e.247.3	✓	24	7.3	odd	6
861.2.i.e.739.3	yes	24	7.5	odd	6
6027.2.a.bf.1.10		12	1.1	even	1	trivial
6027.2.a.bg.1.10		12	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.09852 q^{2} -1.00000 q^{3} -0.793257 q^{4} +3.51189 q^{5} -1.09852 q^{6} -3.06844 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.09852 q^{2} -1.00000 q^{3} -0.793257 q^{4} +3.51189 q^{5} -1.09852 q^{6} -3.06844 q^{8} +1.00000 q^{9} +3.85788 q^{10} -1.19800 q^{11} +0.793257 q^{12} -2.03774 q^{13} -3.51189 q^{15} -1.78423 q^{16} -0.865583 q^{17} +1.09852 q^{18} +3.10472 q^{19} -2.78583 q^{20} -1.31603 q^{22} -0.108732 q^{23} +3.06844 q^{24} +7.33339 q^{25} -2.23850 q^{26} -1.00000 q^{27} -7.73581 q^{29} -3.85788 q^{30} +1.05874 q^{31} +4.17688 q^{32} +1.19800 q^{33} -0.950859 q^{34} -0.793257 q^{36} -11.0129 q^{37} +3.41060 q^{38} +2.03774 q^{39} -10.7760 q^{40} +1.00000 q^{41} -0.138700 q^{43} +0.950325 q^{44} +3.51189 q^{45} -0.119444 q^{46} +0.686936 q^{47} +1.78423 q^{48} +8.05586 q^{50} +0.865583 q^{51} +1.61645 q^{52} +10.0347 q^{53} -1.09852 q^{54} -4.20726 q^{55} -3.10472 q^{57} -8.49793 q^{58} -11.2119 q^{59} +2.78583 q^{60} -5.98402 q^{61} +1.16305 q^{62} +8.15684 q^{64} -7.15632 q^{65} +1.31603 q^{66} -12.7296 q^{67} +0.686630 q^{68} +0.108732 q^{69} +10.3905 q^{71} -3.06844 q^{72} +4.10639 q^{73} -12.0978 q^{74} -7.33339 q^{75} -2.46284 q^{76} +2.23850 q^{78} +1.02066 q^{79} -6.26602 q^{80} +1.00000 q^{81} +1.09852 q^{82} -16.7752 q^{83} -3.03983 q^{85} -0.152365 q^{86} +7.73581 q^{87} +3.67601 q^{88} +7.26262 q^{89} +3.85788 q^{90} +0.0862524 q^{92} -1.05874 q^{93} +0.754612 q^{94} +10.9035 q^{95} -4.17688 q^{96} -16.3003 q^{97} -1.19800 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} - 12 q^{3} + 10 q^{4} - 12 q^{5} + 2 q^{6} + 12 q^{9}+O(q^{10}) \) 12 * q - 2 * q^2 - 12 * q^3 + 10 * q^4 - 12 * q^5 + 2 * q^6 + 12 * q^9	\( 12 q - 2 q^{2} - 12 q^{3} + 10 q^{4} - 12 q^{5} + 2 q^{6} + 12 q^{9} - 11 q^{10} + 10 q^{11} - 10 q^{12} - 15 q^{13} + 12 q^{15} + 14 q^{16} - 8 q^{17} - 2 q^{18} - 2 q^{19} - 16 q^{20} - 7 q^{22} + 5 q^{23} + 20 q^{25} - 12 q^{27} + 20 q^{29} + 11 q^{30} - 10 q^{31} + 3 q^{32} - 10 q^{33} + 23 q^{34} + 10 q^{36} - 17 q^{37} - 6 q^{38} + 15 q^{39} - 39 q^{40} + 12 q^{41} + 12 q^{43} + 20 q^{44} - 12 q^{45} - 36 q^{46} - 34 q^{47} - 14 q^{48} + 59 q^{50} + 8 q^{51} - 26 q^{52} + 6 q^{53} + 2 q^{54} + q^{55} + 2 q^{57} - 11 q^{58} - 27 q^{59} + 16 q^{60} - 22 q^{61} + 45 q^{62} + 26 q^{64} + 7 q^{66} - 26 q^{67} - 33 q^{68} - 5 q^{69} + 50 q^{71} - 21 q^{73} - 35 q^{74} - 20 q^{75} + 24 q^{76} - 10 q^{79} - 22 q^{80} + 12 q^{81} - 2 q^{82} - 8 q^{83} + 8 q^{85} - 17 q^{86} - 20 q^{87} - 46 q^{88} - 11 q^{89} - 11 q^{90} + 63 q^{92} + 10 q^{93} - 10 q^{94} + 35 q^{95} - 3 q^{96} - 32 q^{97} + 10 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 - 12 * q^3 + 10 * q^4 - 12 * q^5 + 2 * q^6 + 12 * q^9 - 11 * q^10 + 10 * q^11 - 10 * q^12 - 15 * q^13 + 12 * q^15 + 14 * q^16 - 8 * q^17 - 2 * q^18 - 2 * q^19 - 16 * q^20 - 7 * q^22 + 5 * q^23 + 20 * q^25 - 12 * q^27 + 20 * q^29 + 11 * q^30 - 10 * q^31 + 3 * q^32 - 10 * q^33 + 23 * q^34 + 10 * q^36 - 17 * q^37 - 6 * q^38 + 15 * q^39 - 39 * q^40 + 12 * q^41 + 12 * q^43 + 20 * q^44 - 12 * q^45 - 36 * q^46 - 34 * q^47 - 14 * q^48 + 59 * q^50 + 8 * q^51 - 26 * q^52 + 6 * q^53 + 2 * q^54 + q^55 + 2 * q^57 - 11 * q^58 - 27 * q^59 + 16 * q^60 - 22 * q^61 + 45 * q^62 + 26 * q^64 + 7 * q^66 - 26 * q^67 - 33 * q^68 - 5 * q^69 + 50 * q^71 - 21 * q^73 - 35 * q^74 - 20 * q^75 + 24 * q^76 - 10 * q^79 - 22 * q^80 + 12 * q^81 - 2 * q^82 - 8 * q^83 + 8 * q^85 - 17 * q^86 - 20 * q^87 - 46 * q^88 - 11 * q^89 - 11 * q^90 + 63 * q^92 + 10 * q^93 - 10 * q^94 + 35 * q^95 - 3 * q^96 - 32 * q^97 + 10 * q^99

Introduction

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