LMFDB - Embedded newform 6027.2.a.bf.1.11

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			1.11
Root			$-2.44902$ 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)

$f(q)$	$=$	$q+2.44902 q^{2} -1.00000 q^{3} +3.99771 q^{4} -4.01828 q^{5} -2.44902 q^{6} +4.89242 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.44902 q^{2} -1.00000 q^{3} +3.99771 q^{4} -4.01828 q^{5} -2.44902 q^{6} +4.89242 q^{8} +1.00000 q^{9} -9.84085 q^{10} +1.39070 q^{11} -3.99771 q^{12} +3.69638 q^{13} +4.01828 q^{15} +3.98624 q^{16} +0.554845 q^{17} +2.44902 q^{18} -6.06334 q^{19} -16.0639 q^{20} +3.40586 q^{22} -2.40328 q^{23} -4.89242 q^{24} +11.1466 q^{25} +9.05251 q^{26} -1.00000 q^{27} +0.267006 q^{29} +9.84085 q^{30} +1.40981 q^{31} -0.0224689 q^{32} -1.39070 q^{33} +1.35883 q^{34} +3.99771 q^{36} -5.46696 q^{37} -14.8493 q^{38} -3.69638 q^{39} -19.6591 q^{40} +1.00000 q^{41} -3.21046 q^{43} +5.55962 q^{44} -4.01828 q^{45} -5.88568 q^{46} +0.201950 q^{47} -3.98624 q^{48} +27.2982 q^{50} -0.554845 q^{51} +14.7770 q^{52} -6.42142 q^{53} -2.44902 q^{54} -5.58824 q^{55} +6.06334 q^{57} +0.653903 q^{58} +6.58413 q^{59} +16.0639 q^{60} +9.30589 q^{61} +3.45266 q^{62} -8.02750 q^{64} -14.8531 q^{65} -3.40586 q^{66} -13.5912 q^{67} +2.21811 q^{68} +2.40328 q^{69} +12.4476 q^{71} +4.89242 q^{72} -13.5531 q^{73} -13.3887 q^{74} -11.1466 q^{75} -24.2395 q^{76} -9.05251 q^{78} -15.4910 q^{79} -16.0178 q^{80} +1.00000 q^{81} +2.44902 q^{82} -4.93822 q^{83} -2.22952 q^{85} -7.86250 q^{86} -0.267006 q^{87} +6.80391 q^{88} -9.68145 q^{89} -9.84085 q^{90} -9.60759 q^{92} -1.40981 q^{93} +0.494580 q^{94} +24.3642 q^{95} +0.0224689 q^{96} -5.14594 q^{97} +1.39070 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.44902	1.73172	0.865860	−	0.500287i	$-0.166772\pi$
$2$	2.44902	1.73172	0.865860	+	0.500287i	$0.166772\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.99771	1.99885
$5$	−4.01828	−1.79703	−0.898515	−	0.438943i	$-0.855353\pi$
$5$	−4.01828	−1.79703	−0.898515	+	0.438943i	$0.855353\pi$
$6$	−2.44902	−0.999809
$7$	0	0
$7$	0	0
$8$	4.89242	1.72973
$9$	1.00000	0.333333
$10$	−9.84085	−3.11195
$11$	1.39070	0.419313	0.209656	−	0.977775i	$-0.432765\pi$
$11$	1.39070	0.419313	0.209656	+	0.977775i	$0.432765\pi$
$12$	−3.99771	−1.15404
$13$	3.69638	1.02519	0.512596	−	0.858630i	$-0.328684\pi$
$13$	3.69638	1.02519	0.512596	+	0.858630i	$0.328684\pi$
$14$	0	0
$15$	4.01828	1.03752
$16$	3.98624	0.996559
$17$	0.554845	0.134570	0.0672849	−	0.997734i	$-0.478566\pi$
$17$	0.554845	0.134570	0.0672849	+	0.997734i	$0.478566\pi$
$18$	2.44902	0.577240
$19$	−6.06334	−1.39103	−0.695513	−	0.718513i	$-0.744823\pi$
$19$	−6.06334	−1.39103	−0.695513	+	0.718513i	$0.744823\pi$
$20$	−16.0639	−3.59200
$21$	0	0
$22$	3.40586	0.726132
$23$	−2.40328	−0.501118	−0.250559	−	0.968101i	$-0.580614\pi$
$23$	−2.40328	−0.501118	−0.250559	+	0.968101i	$0.580614\pi$
$24$	−4.89242	−0.998661
$25$	11.1466	2.22932
$26$	9.05251	1.77534
$27$	−1.00000	−0.192450
$28$	0	0
$29$	0.267006	0.0495818	0.0247909	−	0.999693i	$-0.492108\pi$
$29$	0.267006	0.0495818	0.0247909	+	0.999693i	$0.492108\pi$
$30$	9.84085	1.79669
$31$	1.40981	0.253210	0.126605	−	0.991953i	$-0.459592\pi$
$31$	1.40981	0.253210	0.126605	+	0.991953i	$0.459592\pi$
$32$	−0.0224689	−0.00397197
$33$	−1.39070	−0.242090
$34$	1.35883	0.233037
$35$	0	0
$36$	3.99771	0.666284
$37$	−5.46696	−0.898762	−0.449381	−	0.893340i	$-0.648355\pi$
$37$	−5.46696	−0.898762	−0.449381	+	0.893340i	$0.648355\pi$
$38$	−14.8493	−2.40887
$39$	−3.69638	−0.591895
$40$	−19.6591	−3.10838
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	−3.21046	−0.489591	−0.244796	−	0.969575i	$-0.578721\pi$
$43$	−3.21046	−0.489591	−0.244796	+	0.969575i	$0.578721\pi$
$44$	5.55962	0.838145
$45$	−4.01828	−0.599010
$46$	−5.88568	−0.867795
$47$	0.201950	0.0294575	0.0147287	−	0.999892i	$-0.495312\pi$
$47$	0.201950	0.0294575	0.0147287	+	0.999892i	$0.495312\pi$
$48$	−3.98624	−0.575364
$49$	0	0
$50$	27.2982	3.86055
$51$	−0.554845	−0.0776939
$52$	14.7770	2.04921
$53$	−6.42142	−0.882050	−0.441025	−	0.897495i	$-0.645385\pi$
$53$	−6.42142	−0.882050	−0.441025	+	0.897495i	$0.645385\pi$
$54$	−2.44902	−0.333270
$55$	−5.58824	−0.753518
$56$	0	0
$57$	6.06334	0.803109
$58$	0.653903	0.0858617
$59$	6.58413	0.857181	0.428591	−	0.903499i	$-0.359010\pi$
$59$	6.58413	0.857181	0.428591	+	0.903499i	$0.359010\pi$
$60$	16.0639	2.07384
$61$	9.30589	1.19150	0.595749	−	0.803171i	$-0.296856\pi$
$61$	9.30589	1.19150	0.595749	+	0.803171i	$0.296856\pi$
$62$	3.45266	0.438488
$63$	0	0
$64$	−8.02750	−1.00344
$65$	−14.8531	−1.84230
$66$	−3.40586	−0.419233
$67$	−13.5912	−1.66043	−0.830217	−	0.557440i	$-0.811784\pi$
$67$	−13.5912	−1.66043	−0.830217	+	0.557440i	$0.811784\pi$
$68$	2.21811	0.268985
$69$	2.40328	0.289320
$70$	0	0
$71$	12.4476	1.47725	0.738627	−	0.674114i	$-0.235475\pi$
$71$	12.4476	1.47725	0.738627	+	0.674114i	$0.235475\pi$
$72$	4.89242	0.576577
$73$	−13.5531	−1.58627	−0.793136	−	0.609044i	$-0.791553\pi$
$73$	−13.5531	−1.58627	−0.793136	+	0.609044i	$0.791553\pi$
$74$	−13.3887	−1.55640
$75$	−11.1466	−1.28710
$76$	−24.2395	−2.78046
$77$	0	0
$78$	−9.05251	−1.02500
$79$	−15.4910	−1.74288	−0.871438	−	0.490506i	$-0.836812\pi$
$79$	−15.4910	−1.74288	−0.871438	+	0.490506i	$0.836812\pi$
$80$	−16.0178	−1.79085
$81$	1.00000	0.111111
$82$	2.44902	0.270449
$83$	−4.93822	−0.542040	−0.271020	−	0.962574i	$-0.587361\pi$
$83$	−4.93822	−0.542040	−0.271020	+	0.962574i	$0.587361\pi$
$84$	0	0
$85$	−2.22952	−0.241826
$86$	−7.86250	−0.847835
$87$	−0.267006	−0.0286261
$88$	6.80391	0.725299
$89$	−9.68145	−1.02623	−0.513116	−	0.858319i	$-0.671509\pi$
$89$	−9.68145	−1.02623	−0.513116	+	0.858319i	$0.671509\pi$
$90$	−9.84085	−1.03732
$91$	0	0
$92$	−9.60759	−1.00166
$93$	−1.40981	−0.146191
$94$	0.494580	0.0510121
$95$	24.3642	2.49972
$96$	0.0224689	0.00229322
$97$	−5.14594	−0.522491	−0.261245	−	0.965272i	$-0.584133\pi$
$97$	−5.14594	−0.522491	−0.261245	+	0.965272i	$0.584133\pi$
$98$	0	0
$99$	1.39070	0.139771
$100$	44.5607	4.45607
$101$	−3.29223	−0.327589	−0.163795	−	0.986494i	$-0.552373\pi$
$101$	−3.29223	−0.327589	−0.163795	+	0.986494i	$0.552373\pi$
$102$	−1.35883	−0.134544
$103$	−15.0405	−1.48198	−0.740990	−	0.671516i	$-0.765644\pi$
$103$	−15.0405	−1.48198	−0.740990	+	0.671516i	$0.765644\pi$
$104$	18.0843	1.77331
$105$	0	0
$106$	−15.7262	−1.52746
$107$	16.8244	1.62648	0.813240	−	0.581929i	$-0.197702\pi$
$107$	16.8244	1.62648	0.813240	+	0.581929i	$0.197702\pi$
$108$	−3.99771	−0.384679
$109$	6.05274	0.579747	0.289874	−	0.957065i	$-0.406387\pi$
$109$	6.05274	0.579747	0.289874	+	0.957065i	$0.406387\pi$
$110$	−13.6857	−1.30488
$111$	5.46696	0.518901
$112$	0	0
$113$	−19.6802	−1.85136	−0.925681	−	0.378306i	$-0.876507\pi$
$113$	−19.6802	−1.85136	−0.925681	+	0.378306i	$0.876507\pi$
$114$	14.8493	1.39076
$115$	9.65704	0.900523
$116$	1.06741	0.0991067
$117$	3.69638	0.341730
$118$	16.1247	1.48440
$119$	0	0
$120$	19.6591	1.79462
$121$	−9.06594	−0.824177
$122$	22.7903	2.06334
$123$	−1.00000	−0.0901670
$124$	5.63602	0.506129
$125$	−24.6987	−2.20912
$126$	0	0
$127$	−14.7424	−1.30818	−0.654088	−	0.756419i	$-0.726947\pi$
$127$	−14.7424	−1.30818	−0.654088	+	0.756419i	$0.726947\pi$
$128$	−19.6146	−1.73370
$129$	3.21046	0.282666
$130$	−36.3755	−3.19035
$131$	6.77980	0.592354	0.296177	−	0.955133i	$-0.404288\pi$
$131$	6.77980	0.592354	0.296177	+	0.955133i	$0.404288\pi$
$132$	−5.55962	−0.483903
$133$	0	0
$134$	−33.2852	−2.87541
$135$	4.01828	0.345838
$136$	2.71454	0.232770
$137$	16.1909	1.38328	0.691641	−	0.722241i	$-0.256888\pi$
$137$	16.1909	1.38328	0.691641	+	0.722241i	$0.256888\pi$
$138$	5.88568	0.501022
$139$	−5.75297	−0.487961	−0.243980	−	0.969780i	$-0.578453\pi$
$139$	−5.75297	−0.487961	−0.243980	+	0.969780i	$0.578453\pi$
$140$	0	0
$141$	−0.201950	−0.0170073
$142$	30.4843	2.55819
$143$	5.14057	0.429876
$144$	3.98624	0.332186
$145$	−1.07291	−0.0890999
$146$	−33.1919	−2.74698
$147$	0	0
$148$	−21.8553	−1.79649
$149$	−16.2438	−1.33074	−0.665371	−	0.746513i	$-0.731727\pi$
$149$	−16.2438	−1.33074	−0.665371	+	0.746513i	$0.731727\pi$
$150$	−27.2982	−2.22889
$151$	13.6120	1.10773	0.553865	−	0.832606i	$-0.313152\pi$
$151$	13.6120	1.10773	0.553865	+	0.832606i	$0.313152\pi$
$152$	−29.6644	−2.40610
$153$	0.554845	0.0448566
$154$	0	0
$155$	−5.66502	−0.455026
$156$	−14.7770	−1.18311
$157$	−23.4345	−1.87028	−0.935139	−	0.354282i	$-0.884725\pi$
$157$	−23.4345	−1.87028	−0.935139	+	0.354282i	$0.884725\pi$
$158$	−37.9378	−3.01817
$159$	6.42142	0.509252
$160$	0.0902863	0.00713776
$161$	0	0
$162$	2.44902	0.192413
$163$	−9.89899	−0.775349	−0.387674	−	0.921796i	$-0.626721\pi$
$163$	−9.89899	−0.775349	−0.387674	+	0.921796i	$0.626721\pi$
$164$	3.99771	0.312168
$165$	5.58824	0.435044
$166$	−12.0938	−0.938661
$167$	−6.20468	−0.480133	−0.240066	−	0.970756i	$-0.577169\pi$
$167$	−6.20468	−0.480133	−0.240066	+	0.970756i	$0.577169\pi$
$168$	0	0
$169$	0.663226	0.0510174
$170$	−5.46015	−0.418774
$171$	−6.06334	−0.463675
$172$	−12.8345	−0.978621
$173$	21.3508	1.62327	0.811636	−	0.584163i	$-0.198577\pi$
$173$	21.3508	1.62327	0.811636	+	0.584163i	$0.198577\pi$
$174$	−0.653903	−0.0495723
$175$	0	0
$176$	5.54367	0.417870
$177$	−6.58413	−0.494894
$178$	−23.7101	−1.77715
$179$	−10.5083	−0.785430	−0.392715	−	0.919660i	$-0.628464\pi$
$179$	−10.5083	−0.785430	−0.392715	+	0.919660i	$0.628464\pi$
$180$	−16.0639	−1.19733
$181$	−16.5010	−1.22651	−0.613253	−	0.789886i	$-0.710139\pi$
$181$	−16.5010	−1.22651	−0.613253	+	0.789886i	$0.710139\pi$
$182$	0	0
$183$	−9.30589	−0.687911
$184$	−11.7578	−0.866800
$185$	21.9678	1.61510
$186$	−3.45266	−0.253161
$187$	0.771625	0.0564268
$188$	0.807337	0.0588811
$189$	0	0
$190$	59.6685	4.32881
$191$	−3.07983	−0.222849	−0.111424	−	0.993773i	$-0.535541\pi$
$191$	−3.07983	−0.222849	−0.111424	+	0.993773i	$0.535541\pi$
$192$	8.02750	0.579335
$193$	15.3568	1.10541	0.552704	−	0.833378i	$-0.313596\pi$
$193$	15.3568	1.10541	0.552704	+	0.833378i	$0.313596\pi$
$194$	−12.6025	−0.904807
$195$	14.8531	1.06365
$196$	0	0
$197$	−17.4582	−1.24384	−0.621921	−	0.783080i	$-0.713647\pi$
$197$	−17.4582	−1.24384	−0.621921	+	0.783080i	$0.713647\pi$
$198$	3.40586	0.242044
$199$	15.1257	1.07224	0.536118	−	0.844143i	$-0.319890\pi$
$199$	15.1257	1.07224	0.536118	+	0.844143i	$0.319890\pi$
$200$	54.5338	3.85612
$201$	13.5912	0.958652
$202$	−8.06274	−0.567292
$203$	0	0
$204$	−2.21811	−0.155299
$205$	−4.01828	−0.280649
$206$	−36.8344	−2.56637
$207$	−2.40328	−0.167039
$208$	14.7346	1.02166
$209$	−8.43231	−0.583275
$210$	0	0
$211$	16.7167	1.15083	0.575414	−	0.817862i	$-0.304841\pi$
$211$	16.7167	1.15083	0.575414	+	0.817862i	$0.304841\pi$
$212$	−25.6710	−1.76309
$213$	−12.4476	−0.852893
$214$	41.2034	2.81661
$215$	12.9005	0.879810
$216$	−4.89242	−0.332887
$217$	0	0
$218$	14.8233	1.00396
$219$	13.5531	0.915835
$220$	−22.3401	−1.50617
$221$	2.05092	0.137960
$222$	13.3887	0.898590
$223$	15.4929	1.03748	0.518739	−	0.854933i	$-0.326402\pi$
$223$	15.4929	1.03748	0.518739	+	0.854933i	$0.326402\pi$
$224$	0	0
$225$	11.1466	0.743105
$226$	−48.1973	−3.20604
$227$	0.382425	0.0253824	0.0126912	−	0.999919i	$-0.495960\pi$
$227$	0.382425	0.0253824	0.0126912	+	0.999919i	$0.495960\pi$
$228$	24.2395	1.60530
$229$	−20.1929	−1.33438	−0.667192	−	0.744886i	$-0.732504\pi$
$229$	−20.1929	−1.33438	−0.667192	+	0.744886i	$0.732504\pi$
$230$	23.6503	1.55945
$231$	0	0
$232$	1.30631	0.0857632
$233$	−8.72635	−0.571682	−0.285841	−	0.958277i	$-0.592273\pi$
$233$	−8.72635	−0.571682	−0.285841	+	0.958277i	$0.592273\pi$
$234$	9.05251	0.591781
$235$	−0.811492	−0.0529359
$236$	26.3214	1.71338
$237$	15.4910	1.00625
$238$	0	0
$239$	12.4387	0.804590	0.402295	−	0.915510i	$-0.368213\pi$
$239$	12.4387	0.804590	0.402295	+	0.915510i	$0.368213\pi$
$240$	16.0178	1.03395
$241$	25.5745	1.64740	0.823699	−	0.567027i	$-0.191907\pi$
$241$	25.5745	1.64740	0.823699	+	0.567027i	$0.191907\pi$
$242$	−22.2027	−1.42724
$243$	−1.00000	−0.0641500
$244$	37.2022	2.38163
$245$	0	0
$246$	−2.44902	−0.156144
$247$	−22.4124	−1.42607
$248$	6.89740	0.437985
$249$	4.93822	0.312947
$250$	−60.4876	−3.82557
$251$	29.3668	1.85362	0.926808	−	0.375534i	$-0.122541\pi$
$251$	29.3668	1.85362	0.926808	+	0.375534i	$0.122541\pi$
$252$	0	0
$253$	−3.34224	−0.210125
$254$	−36.1044	−2.26539
$255$	2.22952	0.139618
$256$	−31.9815	−1.99884
$257$	6.56864	0.409741	0.204870	−	0.978789i	$-0.434323\pi$
$257$	6.56864	0.409741	0.204870	+	0.978789i	$0.434323\pi$
$258$	7.86250	0.489498
$259$	0	0
$260$	−59.3783	−3.68248
$261$	0.267006	0.0165273
$262$	16.6039	1.02579
$263$	13.1447	0.810536	0.405268	−	0.914198i	$-0.367178\pi$
$263$	13.1447	0.810536	0.405268	+	0.914198i	$0.367178\pi$
$264$	−6.80391	−0.418752
$265$	25.8031	1.58507
$266$	0	0
$267$	9.68145	0.592495
$268$	−54.3338	−3.31896
$269$	−11.6648	−0.711214	−0.355607	−	0.934636i	$-0.615726\pi$
$269$	−11.6648	−0.711214	−0.355607	+	0.934636i	$0.615726\pi$
$270$	9.84085	0.598895
$271$	3.36870	0.204634	0.102317	−	0.994752i	$-0.467374\pi$
$271$	3.36870	0.204634	0.102317	+	0.994752i	$0.467374\pi$
$272$	2.21174	0.134107
$273$	0	0
$274$	39.6519	2.39546
$275$	15.5016	0.934780
$276$	9.60759	0.578309
$277$	14.1288	0.848918	0.424459	−	0.905447i	$-0.360464\pi$
$277$	14.1288	0.848918	0.424459	+	0.905447i	$0.360464\pi$
$278$	−14.0891	−0.845011
$279$	1.40981	0.0844033
$280$	0	0
$281$	−14.5035	−0.865207	−0.432603	−	0.901584i	$-0.642405\pi$
$281$	−14.5035	−0.865207	−0.432603	+	0.901584i	$0.642405\pi$
$282$	−0.494580	−0.0294518
$283$	−20.8089	−1.23696	−0.618480	−	0.785800i	$-0.712251\pi$
$283$	−20.8089	−1.23696	−0.618480	+	0.785800i	$0.712251\pi$
$284$	49.7617	2.95281
$285$	−24.3642	−1.44321
$286$	12.5894	0.744425
$287$	0	0
$288$	−0.0224689	−0.00132399
$289$	−16.6921	−0.981891
$290$	−2.62757	−0.154296
$291$	5.14594	0.301660
$292$	−54.1814	−3.17072
$293$	−15.7241	−0.918611	−0.459306	−	0.888278i	$-0.651902\pi$
$293$	−15.7241	−0.918611	−0.459306	+	0.888278i	$0.651902\pi$
$294$	0	0
$295$	−26.4569	−1.54038
$296$	−26.7467	−1.55462
$297$	−1.39070	−0.0806968
$298$	−39.7814	−2.30447
$299$	−8.88342	−0.513742
$300$	−44.5607	−2.57271
$301$	0	0
$302$	33.3361	1.91828
$303$	3.29223	0.189134
$304$	−24.1699	−1.38624
$305$	−37.3937	−2.14116
$306$	1.35883	0.0776790
$307$	−11.4617	−0.654153	−0.327076	−	0.944998i	$-0.606063\pi$
$307$	−11.4617	−0.654153	−0.327076	+	0.944998i	$0.606063\pi$
$308$	0	0
$309$	15.0405	0.855622
$310$	−13.8738	−0.787977
$311$	−0.539450	−0.0305894	−0.0152947	−	0.999883i	$-0.504869\pi$
$311$	−0.539450	−0.0305894	−0.0152947	+	0.999883i	$0.504869\pi$
$312$	−18.0843	−1.02382
$313$	3.30545	0.186835	0.0934174	−	0.995627i	$-0.470221\pi$
$313$	3.30545	0.186835	0.0934174	+	0.995627i	$0.470221\pi$
$314$	−57.3916	−3.23880
$315$	0	0
$316$	−61.9285	−3.48375
$317$	31.3519	1.76090	0.880448	−	0.474143i	$-0.157242\pi$
$317$	31.3519	1.76090	0.880448	+	0.474143i	$0.157242\pi$
$318$	15.7262	0.881882
$319$	0.371326	0.0207903
$320$	32.2567	1.80321
$321$	−16.8244	−0.939048
$322$	0	0
$323$	−3.36422	−0.187190
$324$	3.99771	0.222095
$325$	41.2020	2.28547
$326$	−24.2428	−1.34269
$327$	−6.05274	−0.334717
$328$	4.89242	0.270139
$329$	0	0
$330$	13.6857	0.753373
$331$	−16.3998	−0.901415	−0.450708	−	0.892672i	$-0.648828\pi$
$331$	−16.3998	−0.901415	−0.450708	+	0.892672i	$0.648828\pi$
$332$	−19.7415	−1.08346
$333$	−5.46696	−0.299587
$334$	−15.1954	−0.831455
$335$	54.6134	2.98385
$336$	0	0
$337$	7.79793	0.424780	0.212390	−	0.977185i	$-0.431875\pi$
$337$	7.79793	0.424780	0.212390	+	0.977185i	$0.431875\pi$
$338$	1.62426	0.0883479
$339$	19.6802	1.06888
$340$	−8.91298	−0.483374
$341$	1.96063	0.106174
$342$	−14.8493	−0.802956
$343$	0	0
$344$	−15.7069	−0.846862
$345$	−9.65704	−0.519917
$346$	52.2886	2.81105
$347$	−26.2847	−1.41104	−0.705520	−	0.708690i	$-0.749286\pi$
$347$	−26.2847	−1.41104	−0.705520	+	0.708690i	$0.749286\pi$
$348$	−1.06741	−0.0572193
$349$	10.5647	0.565516	0.282758	−	0.959191i	$-0.408751\pi$
$349$	10.5647	0.565516	0.282758	+	0.959191i	$0.408751\pi$
$350$	0	0
$351$	−3.69638	−0.197298
$352$	−0.0312475	−0.00166550
$353$	32.3260	1.72054	0.860269	−	0.509841i	$-0.170296\pi$
$353$	32.3260	1.72054	0.860269	+	0.509841i	$0.170296\pi$
$354$	−16.1247	−0.857017
$355$	−50.0178	−2.65467
$356$	−38.7036	−2.05129
$357$	0	0
$358$	−25.7352	−1.36015
$359$	9.22531	0.486893	0.243447	−	0.969914i	$-0.421722\pi$
$359$	9.22531	0.486893	0.243447	+	0.969914i	$0.421722\pi$
$360$	−19.6591	−1.03613
$361$	17.7641	0.934954
$362$	−40.4112	−2.12396
$363$	9.06594	0.475839
$364$	0	0
$365$	54.4602	2.85058
$366$	−22.7903	−1.19127
$367$	−26.9727	−1.40796	−0.703982	−	0.710218i	$-0.748596\pi$
$367$	−26.9727	−1.40796	−0.703982	+	0.710218i	$0.748596\pi$
$368$	−9.58003	−0.499393
$369$	1.00000	0.0520579
$370$	53.7995	2.79690
$371$	0	0
$372$	−5.63602	−0.292214
$373$	25.1568	1.30257	0.651284	−	0.758834i	$-0.274231\pi$
$373$	25.1568	1.30257	0.651284	+	0.758834i	$0.274231\pi$
$374$	1.88973	0.0977154
$375$	24.6987	1.27543
$376$	0.988025	0.0509535
$377$	0.986956	0.0508308
$378$	0	0
$379$	26.9410	1.38387	0.691934	−	0.721961i	$-0.256759\pi$
$379$	26.9410	1.38387	0.691934	+	0.721961i	$0.256759\pi$
$380$	97.4009	4.99656
$381$	14.7424	0.755275
$382$	−7.54258	−0.385912
$383$	16.0928	0.822304	0.411152	−	0.911567i	$-0.365127\pi$
$383$	16.0928	0.822304	0.411152	+	0.911567i	$0.365127\pi$
$384$	19.6146	1.00095
$385$	0	0
$386$	37.6092	1.91426
$387$	−3.21046	−0.163197
$388$	−20.5719	−1.04438
$389$	5.77093	0.292598	0.146299	−	0.989240i	$-0.453264\pi$
$389$	5.77093	0.292598	0.146299	+	0.989240i	$0.453264\pi$
$390$	36.3755	1.84195
$391$	−1.33345	−0.0674353
$392$	0	0
$393$	−6.77980	−0.341996
$394$	−42.7554	−2.15399
$395$	62.2472	3.13200
$396$	5.55962	0.279382
$397$	−25.6447	−1.28707	−0.643535	−	0.765416i	$-0.722533\pi$
$397$	−25.6447	−1.28707	−0.643535	+	0.765416i	$0.722533\pi$
$398$	37.0433	1.85681
$399$	0	0
$400$	44.4329	2.22164
$401$	3.96169	0.197837	0.0989186	−	0.995096i	$-0.468462\pi$
$401$	3.96169	0.197837	0.0989186	+	0.995096i	$0.468462\pi$
$402$	33.2852	1.66012
$403$	5.21120	0.259589
$404$	−13.1614	−0.654802
$405$	−4.01828	−0.199670
$406$	0	0
$407$	−7.60292	−0.376863
$408$	−2.71454	−0.134390
$409$	−22.8678	−1.13074	−0.565370	−	0.824837i	$-0.691267\pi$
$409$	−22.8678	−1.13074	−0.565370	+	0.824837i	$0.691267\pi$
$410$	−9.84085	−0.486005
$411$	−16.1909	−0.798638
$412$	−60.1273	−2.96226
$413$	0	0
$414$	−5.88568	−0.289265
$415$	19.8431	0.974062
$416$	−0.0830535	−0.00407203
$417$	5.75297	0.281724
$418$	−20.6509	−1.01007
$419$	16.0852	0.785811	0.392906	−	0.919579i	$-0.371470\pi$
$419$	16.0852	0.785811	0.392906	+	0.919579i	$0.371470\pi$
$420$	0	0
$421$	−2.27709	−0.110979	−0.0554894	−	0.998459i	$-0.517672\pi$
$421$	−2.27709	−0.110979	−0.0554894	+	0.998459i	$0.517672\pi$
$422$	40.9396	1.99291
$423$	0.201950	0.00981915
$424$	−31.4163	−1.52571
$425$	6.18462	0.299998
$426$	−30.4843	−1.47697
$427$	0	0
$428$	67.2591	3.25109
$429$	−5.14057	−0.248189
$430$	31.5937	1.52358
$431$	6.81029	0.328040	0.164020	−	0.986457i	$-0.447554\pi$
$431$	6.81029	0.328040	0.164020	+	0.986457i	$0.447554\pi$
$432$	−3.98624	−0.191788
$433$	2.89923	0.139328	0.0696641	−	0.997571i	$-0.477807\pi$
$433$	2.89923	0.139328	0.0696641	+	0.997571i	$0.477807\pi$
$434$	0	0
$435$	1.07291	0.0514419
$436$	24.1971	1.15883
$437$	14.5719	0.697068
$438$	33.1919	1.58597
$439$	22.6477	1.08092	0.540458	−	0.841371i	$-0.318251\pi$
$439$	22.6477	1.08092	0.540458	+	0.841371i	$0.318251\pi$
$440$	−27.3400	−1.30338
$441$	0	0
$442$	5.02274	0.238908
$443$	−6.92641	−0.329083	−0.164542	−	0.986370i	$-0.552615\pi$
$443$	−6.92641	−0.329083	−0.164542	+	0.986370i	$0.552615\pi$
$444$	21.8553	1.03721
$445$	38.9028	1.84417
$446$	37.9423	1.79662
$447$	16.2438	0.768305
$448$	0	0
$449$	22.3941	1.05684	0.528421	−	0.848982i	$-0.322784\pi$
$449$	22.3941	1.05684	0.528421	+	0.848982i	$0.322784\pi$
$450$	27.2982	1.28685
$451$	1.39070	0.0654857
$452$	−78.6758	−3.70060
$453$	−13.6120	−0.639548
$454$	0.936567	0.0439553
$455$	0	0
$456$	29.6644	1.38916
$457$	−25.3945	−1.18790	−0.593952	−	0.804500i	$-0.702433\pi$
$457$	−25.3945	−1.18790	−0.593952	+	0.804500i	$0.702433\pi$
$458$	−49.4528	−2.31078
$459$	−0.554845	−0.0258980
$460$	38.6060	1.80001
$461$	−21.2080	−0.987756	−0.493878	−	0.869531i	$-0.664421\pi$
$461$	−21.2080	−0.987756	−0.493878	+	0.869531i	$0.664421\pi$
$462$	0	0
$463$	25.7346	1.19599	0.597994	−	0.801501i	$-0.295965\pi$
$463$	25.7346	1.19599	0.597994	+	0.801501i	$0.295965\pi$
$464$	1.06435	0.0494112
$465$	5.66502	0.262709
$466$	−21.3710	−0.989993
$467$	−18.9411	−0.876491	−0.438246	−	0.898855i	$-0.644400\pi$
$467$	−18.9411	−0.876491	−0.438246	+	0.898855i	$0.644400\pi$
$468$	14.7770	0.683069
$469$	0	0
$470$	−1.98736	−0.0916702
$471$	23.4345	1.07981
$472$	32.2124	1.48269
$473$	−4.46480	−0.205292
$474$	37.9378	1.74254
$475$	−67.5855	−3.10104
$476$	0	0
$477$	−6.42142	−0.294017
$478$	30.4626	1.39332
$479$	10.3592	0.473324	0.236662	−	0.971592i	$-0.423947\pi$
$479$	10.3592	0.473324	0.236662	+	0.971592i	$0.423947\pi$
$480$	−0.0902863	−0.00412098
$481$	−20.2080	−0.921403
$482$	62.6325	2.85283
$483$	0	0
$484$	−36.2430	−1.64741
$485$	20.6778	0.938931
$486$	−2.44902	−0.111090
$487$	20.2590	0.918021	0.459011	−	0.888431i	$-0.348204\pi$
$487$	20.2590	0.918021	0.459011	+	0.888431i	$0.348204\pi$
$488$	45.5283	2.06097
$489$	9.89899	0.447648
$490$	0	0
$491$	5.99278	0.270450	0.135225	−	0.990815i	$-0.456824\pi$
$491$	5.99278	0.270450	0.135225	+	0.990815i	$0.456824\pi$
$492$	−3.99771	−0.180230
$493$	0.148147	0.00667221
$494$	−54.8885	−2.46955
$495$	−5.58824	−0.251173
$496$	5.61985	0.252339
$497$	0	0
$498$	12.0938	0.541936
$499$	−12.3751	−0.553985	−0.276993	−	0.960872i	$-0.589338\pi$
$499$	−12.3751	−0.553985	−0.276993	+	0.960872i	$0.589338\pi$
$500$	−98.7380	−4.41570
$501$	6.20468	0.277205
$502$	71.9200	3.20994
$503$	−21.5226	−0.959647	−0.479824	−	0.877365i	$-0.659299\pi$
$503$	−21.5226	−0.959647	−0.479824	+	0.877365i	$0.659299\pi$
$504$	0	0
$505$	13.2291	0.588687
$506$	−8.18523	−0.363878
$507$	−0.663226	−0.0294549
$508$	−58.9357	−2.61485
$509$	12.1120	0.536856	0.268428	−	0.963300i	$-0.413496\pi$
$509$	12.1120	0.536856	0.268428	+	0.963300i	$0.413496\pi$
$510$	5.46015	0.241780
$511$	0	0
$512$	−39.0943	−1.72774
$513$	6.06334	0.267703
$514$	16.0867	0.709556
$515$	60.4368	2.66316
$516$	12.8345	0.565007
$517$	0.280853	0.0123519
$518$	0	0
$519$	−21.3508	−0.937197
$520$	−72.6676	−3.18668
$521$	30.5700	1.33930	0.669649	−	0.742678i	$-0.266445\pi$
$521$	30.5700	1.33930	0.669649	+	0.742678i	$0.266445\pi$
$522$	0.653903	0.0286206
$523$	6.63927	0.290315	0.145158	−	0.989409i	$-0.453631\pi$
$523$	6.63927	0.290315	0.145158	+	0.989409i	$0.453631\pi$
$524$	27.1037	1.18403
$525$	0	0
$526$	32.1916	1.40362
$527$	0.782228	0.0340744
$528$	−5.54367	−0.241257
$529$	−17.2243	−0.748881
$530$	63.1923	2.74490
$531$	6.58413	0.285727
$532$	0	0
$533$	3.69638	0.160108
$534$	23.7101	1.02604
$535$	−67.6053	−2.92283
$536$	−66.4941	−2.87211
$537$	10.5083	0.453468
$538$	−28.5673	−1.23162
$539$	0	0
$540$	16.0639	0.691280
$541$	−25.3354	−1.08925	−0.544627	−	0.838678i	$-0.683329\pi$
$541$	−25.3354	−1.08925	−0.544627	+	0.838678i	$0.683329\pi$
$542$	8.25002	0.354369
$543$	16.5010	0.708124
$544$	−0.0124668	−0.000534508 0
$545$	−24.3216	−1.04182
$546$	0	0
$547$	5.33483	0.228101	0.114050	−	0.993475i	$-0.463617\pi$
$547$	5.33483	0.228101	0.114050	+	0.993475i	$0.463617\pi$
$548$	64.7264	2.76498
$549$	9.30589	0.397166
$550$	37.9637	1.61878
$551$	−1.61895	−0.0689696
$552$	11.7578	0.500447
$553$	0	0
$554$	34.6017	1.47009
$555$	−21.9678	−0.932480
$556$	−22.9987	−0.975361
$557$	1.27434	0.0539954	0.0269977	−	0.999635i	$-0.491405\pi$
$557$	1.27434	0.0539954	0.0269977	+	0.999635i	$0.491405\pi$
$558$	3.45266	0.146163
$559$	−11.8671	−0.501925
$560$	0	0
$561$	−0.771625	−0.0325780
$562$	−35.5194	−1.49830
$563$	−14.3049	−0.602880	−0.301440	−	0.953485i	$-0.597467\pi$
$563$	−14.3049	−0.602880	−0.301440	+	0.953485i	$0.597467\pi$
$564$	−0.807337	−0.0339950
$565$	79.0807	3.32695
$566$	−50.9614	−2.14207
$567$	0	0
$568$	60.8987	2.55525
$569$	21.4436	0.898965	0.449482	−	0.893289i	$-0.351608\pi$
$569$	21.4436	0.898965	0.449482	+	0.893289i	$0.351608\pi$
$570$	−59.6685	−2.49924
$571$	−24.8083	−1.03819	−0.519097	−	0.854715i	$-0.673732\pi$
$571$	−24.8083	−1.03819	−0.519097	+	0.854715i	$0.673732\pi$
$572$	20.5505	0.859259
$573$	3.07983	0.128662
$574$	0	0
$575$	−26.7883	−1.11715
$576$	−8.02750	−0.334479
$577$	17.1309	0.713171	0.356585	−	0.934263i	$-0.383941\pi$
$577$	17.1309	0.713171	0.356585	+	0.934263i	$0.383941\pi$
$578$	−40.8794	−1.70036
$579$	−15.3568	−0.638207
$580$	−4.28916	−0.178098
$581$	0	0
$582$	12.6025	0.522391
$583$	−8.93030	−0.369855
$584$	−66.3076	−2.74383
$585$	−14.8531	−0.614100
$586$	−38.5086	−1.59078
$587$	5.46590	0.225602	0.112801	−	0.993618i	$-0.464018\pi$
$587$	5.46590	0.225602	0.112801	+	0.993618i	$0.464018\pi$
$588$	0	0
$589$	−8.54818	−0.352222
$590$	−64.7935	−2.66751
$591$	17.4582	0.718132
$592$	−21.7926	−0.895669
$593$	8.47567	0.348054	0.174027	−	0.984741i	$-0.444322\pi$
$593$	8.47567	0.348054	0.174027	+	0.984741i	$0.444322\pi$
$594$	−3.40586	−0.139744
$595$	0	0
$596$	−64.9379	−2.65996
$597$	−15.1257	−0.619055
$598$	−21.7557	−0.889656
$599$	26.1128	1.06694	0.533470	−	0.845819i	$-0.320888\pi$
$599$	26.1128	1.06694	0.533470	+	0.845819i	$0.320888\pi$
$600$	−54.5338	−2.22633
$601$	21.7494	0.887176	0.443588	−	0.896231i	$-0.353705\pi$
$601$	21.7494	0.887176	0.443588	+	0.896231i	$0.353705\pi$
$602$	0	0
$603$	−13.5912	−0.553478
$604$	54.4168	2.21419
$605$	36.4295	1.48107
$606$	8.06274	0.327526
$607$	0.442068	0.0179430	0.00897150	−	0.999960i	$-0.497144\pi$
$607$	0.442068	0.0179430	0.00897150	+	0.999960i	$0.497144\pi$
$608$	0.136237	0.00552512
$609$	0	0
$610$	−91.5779	−3.70788
$611$	0.746484	0.0301995
$612$	2.21811	0.0896617
$613$	−9.50989	−0.384101	−0.192051	−	0.981385i	$-0.561514\pi$
$613$	−9.50989	−0.384101	−0.192051	+	0.981385i	$0.561514\pi$
$614$	−28.0699	−1.13281
$615$	4.01828	0.162033
$616$	0	0
$617$	−3.83993	−0.154590	−0.0772949	−	0.997008i	$-0.524628\pi$
$617$	−3.83993	−0.154590	−0.0772949	+	0.997008i	$0.524628\pi$
$618$	36.8344	1.48170
$619$	29.6776	1.19284	0.596422	−	0.802671i	$-0.296588\pi$
$619$	29.6776	1.19284	0.596422	+	0.802671i	$0.296588\pi$
$620$	−22.6471	−0.909529
$621$	2.40328	0.0964402
$622$	−1.32112	−0.0529722
$623$	0	0
$624$	−14.7346	−0.589858
$625$	43.5133	1.74053
$626$	8.09511	0.323546
$627$	8.43231	0.336754
$628$	−93.6843	−3.73841
$629$	−3.03332	−0.120946
$630$	0	0
$631$	3.78576	0.150709	0.0753545	−	0.997157i	$-0.475991\pi$
$631$	3.78576	0.150709	0.0753545	+	0.997157i	$0.475991\pi$
$632$	−75.7886	−3.01471
$633$	−16.7167	−0.664431
$634$	76.7814	3.04938
$635$	59.2390	2.35083
$636$	25.6710	1.01792
$637$	0	0
$638$	0.909386	0.0360029
$639$	12.4476	0.492418
$640$	78.8169	3.11551
$641$	1.34996	0.0533202	0.0266601	−	0.999645i	$-0.491513\pi$
$641$	1.34996	0.0533202	0.0266601	+	0.999645i	$0.491513\pi$
$642$	−41.2034	−1.62617
$643$	32.4546	1.27988	0.639942	−	0.768423i	$-0.278958\pi$
$643$	32.4546	1.27988	0.639942	+	0.768423i	$0.278958\pi$
$644$	0	0
$645$	−12.9005	−0.507959
$646$	−8.23904	−0.324161
$647$	−47.5379	−1.86891	−0.934453	−	0.356086i	$-0.884111\pi$
$647$	−47.5379	−1.86891	−0.934453	+	0.356086i	$0.884111\pi$
$648$	4.89242	0.192192
$649$	9.15658	0.359427
$650$	100.905	3.95780
$651$	0	0
$652$	−39.5732	−1.54981
$653$	44.4581	1.73978	0.869890	−	0.493246i	$-0.164190\pi$
$653$	44.4581	1.73978	0.869890	+	0.493246i	$0.164190\pi$
$654$	−14.8233	−0.579636
$655$	−27.2431	−1.06448
$656$	3.98624	0.155636
$657$	−13.5531	−0.528757
$658$	0	0
$659$	−13.7462	−0.535474	−0.267737	−	0.963492i	$-0.586276\pi$
$659$	−13.7462	−0.535474	−0.267737	+	0.963492i	$0.586276\pi$
$660$	22.3401	0.869588
$661$	−16.5876	−0.645181	−0.322591	−	0.946539i	$-0.604554\pi$
$661$	−16.5876	−0.645181	−0.322591	+	0.946539i	$0.604554\pi$
$662$	−40.1635	−1.56100
$663$	−2.05092	−0.0796511
$664$	−24.1598	−0.937584
$665$	0	0
$666$	−13.3887	−0.518801
$667$	−0.641689	−0.0248463
$668$	−24.8045	−0.959715
$669$	−15.4929	−0.598988
$670$	133.749	5.16719
$671$	12.9417	0.499610
$672$	0	0
$673$	48.9067	1.88522	0.942608	−	0.333902i	$-0.108365\pi$
$673$	48.9067	1.88522	0.942608	+	0.333902i	$0.108365\pi$
$674$	19.0973	0.735600
$675$	−11.1466	−0.429032
$676$	2.65138	0.101976
$677$	15.2741	0.587031	0.293516	−	0.955954i	$-0.405175\pi$
$677$	15.2741	0.587031	0.293516	+	0.955954i	$0.405175\pi$
$678$	48.1973	1.85101
$679$	0	0
$680$	−10.9078	−0.418294
$681$	−0.382425	−0.0146546
$682$	4.80163	0.183864
$683$	−41.2823	−1.57962	−0.789811	−	0.613350i	$-0.789821\pi$
$683$	−41.2823	−1.57962	−0.789811	+	0.613350i	$0.789821\pi$
$684$	−24.2395	−0.926819
$685$	−65.0596	−2.48580
$686$	0	0
$687$	20.1929	0.770407
$688$	−12.7977	−0.487907
$689$	−23.7360	−0.904270
$690$	−23.6503	−0.900351
$691$	−8.24773	−0.313759	−0.156879	−	0.987618i	$-0.550143\pi$
$691$	−8.24773	−0.313759	−0.156879	+	0.987618i	$0.550143\pi$
$692$	85.3543	3.24468
$693$	0	0
$694$	−64.3719	−2.44352
$695$	23.1170	0.876879
$696$	−1.30631	−0.0495154
$697$	0.554845	0.0210163
$698$	25.8732	0.979315
$699$	8.72635	0.330061
$700$	0	0
$701$	−7.14293	−0.269785	−0.134892	−	0.990860i	$-0.543069\pi$
$701$	−7.14293	−0.269785	−0.134892	+	0.990860i	$0.543069\pi$
$702$	−9.05251	−0.341665
$703$	33.1480	1.25020
$704$	−11.1639	−0.420754
$705$	0.811492	0.0305626
$706$	79.1670	2.97949
$707$	0	0
$708$	−26.3214	−0.989220
$709$	−14.0902	−0.529168	−0.264584	−	0.964363i	$-0.585235\pi$
$709$	−14.0902	−0.529168	−0.264584	+	0.964363i	$0.585235\pi$
$710$	−122.495	−4.59714
$711$	−15.4910	−0.580958
$712$	−47.3657	−1.77511
$713$	−3.38817	−0.126888
$714$	0	0
$715$	−20.6562	−0.772500
$716$	−42.0093	−1.56996
$717$	−12.4387	−0.464530
$718$	22.5930	0.843163
$719$	7.77957	0.290129	0.145064	−	0.989422i	$-0.453661\pi$
$719$	7.77957	0.290129	0.145064	+	0.989422i	$0.453661\pi$
$720$	−16.0178	−0.596949
$721$	0	0
$722$	43.5047	1.61908
$723$	−25.5745	−0.951126
$724$	−65.9659	−2.45161
$725$	2.97620	0.110533
$726$	22.2027	0.824019
$727$	9.28850	0.344492	0.172246	−	0.985054i	$-0.444898\pi$
$727$	9.28850	0.344492	0.172246	+	0.985054i	$0.444898\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	133.374	4.93640
$731$	−1.78131	−0.0658842
$732$	−37.2022	−1.37503
$733$	−10.6239	−0.392402	−0.196201	−	0.980564i	$-0.562861\pi$
$733$	−10.6239	−0.392402	−0.196201	+	0.980564i	$0.562861\pi$
$734$	−66.0567	−2.43820
$735$	0	0
$736$	0.0539989	0.00199043
$737$	−18.9014	−0.696241
$738$	2.44902	0.0901497
$739$	−13.4854	−0.496067	−0.248034	−	0.968751i	$-0.579784\pi$
$739$	−13.4854	−0.496067	−0.248034	+	0.968751i	$0.579784\pi$
$740$	87.8206	3.22835
$741$	22.4124	0.823341
$742$	0	0
$743$	−6.89411	−0.252920	−0.126460	−	0.991972i	$-0.540362\pi$
$743$	−6.89411	−0.252920	−0.126460	+	0.991972i	$0.540362\pi$
$744$	−6.89740	−0.252871
$745$	65.2721	2.39138
$746$	61.6095	2.25568
$747$	−4.93822	−0.180680
$748$	3.08473	0.112789
$749$	0	0
$750$	60.4876	2.20869
$751$	15.4385	0.563358	0.281679	−	0.959509i	$-0.409109\pi$
$751$	15.4385	0.563358	0.281679	+	0.959509i	$0.409109\pi$
$752$	0.805021	0.0293561
$753$	−29.3668	−1.07019
$754$	2.41708	0.0880247
$755$	−54.6969	−1.99062
$756$	0	0
$757$	−0.0468098	−0.00170133	−0.000850666	−	1.00000i	$-0.500271\pi$
$757$	−0.0468098	−0.00170133	−0.000850666		1.00000i	$0.500271\pi$
$758$	65.9791	2.39647
$759$	3.34224	0.121316
$760$	119.200	4.32384
$761$	31.4241	1.13912	0.569561	−	0.821949i	$-0.307113\pi$
$761$	31.4241	1.13912	0.569561	+	0.821949i	$0.307113\pi$
$762$	36.1044	1.30792
$763$	0	0
$764$	−12.3123	−0.445442
$765$	−2.22952	−0.0806086
$766$	39.4116	1.42400
$767$	24.3375	0.878775
$768$	31.9815	1.15403
$769$	12.9324	0.466353	0.233176	−	0.972434i	$-0.425088\pi$
$769$	12.9324	0.466353	0.233176	+	0.972434i	$0.425088\pi$
$770$	0	0
$771$	−6.56864	−0.236564
$772$	61.3920	2.20955
$773$	−12.4804	−0.448888	−0.224444	−	0.974487i	$-0.572057\pi$
$773$	−12.4804	−0.448888	−0.224444	+	0.974487i	$0.572057\pi$
$774$	−7.86250	−0.282612
$775$	15.7146	0.564485
$776$	−25.1761	−0.903769
$777$	0	0
$778$	14.1331	0.506698
$779$	−6.06334	−0.217242
$780$	59.3783	2.12608
$781$	17.3109	0.619432
$782$	−3.26564	−0.116779
$783$	−0.267006	−0.00954202
$784$	0	0
$785$	94.1664	3.36094
$786$	−16.6039	−0.592241
$787$	46.0133	1.64020	0.820099	−	0.572221i	$-0.193918\pi$
$787$	46.0133	1.64020	0.820099	+	0.572221i	$0.193918\pi$
$788$	−69.7925	−2.48626
$789$	−13.1447	−0.467963
$790$	152.445	5.42374
$791$	0	0
$792$	6.80391	0.241766
$793$	34.3981	1.22151
$794$	−62.8044	−2.22885
$795$	−25.8031	−0.915141
$796$	60.4682	2.14324
$797$	−54.4612	−1.92911	−0.964557	−	0.263876i	$-0.914999\pi$
$797$	−54.4612	−1.92911	−0.964557	+	0.263876i	$0.914999\pi$
$798$	0	0
$799$	0.112051	0.00396408
$800$	−0.250451	−0.00885478
$801$	−9.68145	−0.342077
$802$	9.70225	0.342598
$803$	−18.8484	−0.665144
$804$	54.3338	1.91620
$805$	0	0
$806$	12.7624	0.449535
$807$	11.6648	0.410620
$808$	−16.1070	−0.566641
$809$	23.1245	0.813014	0.406507	−	0.913648i	$-0.366747\pi$
$809$	23.1245	0.813014	0.406507	+	0.913648i	$0.366747\pi$
$810$	−9.84085	−0.345772
$811$	−6.43373	−0.225919	−0.112959	−	0.993600i	$-0.536033\pi$
$811$	−6.43373	−0.225919	−0.112959	+	0.993600i	$0.536033\pi$
$812$	0	0
$813$	−3.36870	−0.118146
$814$	−18.6197	−0.652620
$815$	39.7769	1.39332
$816$	−2.21174	−0.0774265
$817$	19.4661	0.681034
$818$	−56.0038	−1.95813
$819$	0	0
$820$	−16.0639	−0.560976
$821$	−44.1294	−1.54013	−0.770064	−	0.637967i	$-0.779776\pi$
$821$	−44.1294	−1.54013	−0.770064	+	0.637967i	$0.779776\pi$
$822$	−39.6519	−1.38302
$823$	6.13039	0.213692	0.106846	−	0.994276i	$-0.465925\pi$
$823$	6.13039	0.213692	0.106846	+	0.994276i	$0.465925\pi$
$824$	−73.5843	−2.56343
$825$	−15.5016	−0.539696
$826$	0	0
$827$	9.52187	0.331108	0.165554	−	0.986201i	$-0.447059\pi$
$827$	9.52187	0.331108	0.165554	+	0.986201i	$0.447059\pi$
$828$	−9.60759	−0.333887
$829$	−48.2513	−1.67584	−0.837918	−	0.545796i	$-0.816227\pi$
$829$	−48.2513	−1.67584	−0.837918	+	0.545796i	$0.816227\pi$
$830$	48.5963	1.68680
$831$	−14.1288	−0.490123
$832$	−29.6727	−1.02872
$833$	0	0
$834$	14.0891	0.487867
$835$	24.9322	0.862813
$836$	−33.7099	−1.16588
$837$	−1.40981	−0.0487303
$838$	39.3929	1.36080
$839$	10.5415	0.363935	0.181967	−	0.983305i	$-0.441754\pi$
$839$	10.5415	0.363935	0.181967	+	0.983305i	$0.441754\pi$
$840$	0	0
$841$	−28.9287	−0.997542
$842$	−5.57665	−0.192184
$843$	14.5035	0.499527
$844$	66.8286	2.30033
$845$	−2.66503	−0.0916798
$846$	0.494580	0.0170040
$847$	0	0
$848$	−25.5973	−0.879015
$849$	20.8089	0.714159
$850$	15.1463	0.519513
$851$	13.1386	0.450386
$852$	−49.7617	−1.70481
$853$	−44.3427	−1.51827	−0.759133	−	0.650935i	$-0.774377\pi$
$853$	−44.3427	−1.51827	−0.759133	+	0.650935i	$0.774377\pi$
$854$	0	0
$855$	24.3642	0.833238
$856$	82.3122	2.81337
$857$	14.7010	0.502175	0.251088	−	0.967964i	$-0.419212\pi$
$857$	14.7010	0.502175	0.251088	+	0.967964i	$0.419212\pi$
$858$	−12.5894	−0.429794
$859$	−6.88283	−0.234839	−0.117420	−	0.993082i	$-0.537462\pi$
$859$	−6.88283	−0.234839	−0.117420	+	0.993082i	$0.537462\pi$
$860$	51.5726	1.75861
$861$	0	0
$862$	16.6785	0.568073
$863$	1.22410	0.0416689	0.0208345	−	0.999783i	$-0.493368\pi$
$863$	1.22410	0.0416689	0.0208345	+	0.999783i	$0.493368\pi$
$864$	0.0224689	0.000764407 0
$865$	−85.7936	−2.91707
$866$	7.10028	0.241277
$867$	16.6921	0.566895
$868$	0	0
$869$	−21.5434	−0.730810
$870$	2.62757	0.0890829
$871$	−50.2384	−1.70226
$872$	29.6125	1.00281
$873$	−5.14594	−0.174164
$874$	35.6869	1.20713
$875$	0	0
$876$	54.1814	1.83062
$877$	−9.83549	−0.332121	−0.166060	−	0.986116i	$-0.553105\pi$
$877$	−9.83549	−0.332121	−0.166060	+	0.986116i	$0.553105\pi$
$878$	55.4647	1.87184
$879$	15.7241	0.530360
$880$	−22.2760	−0.750925
$881$	45.2512	1.52455	0.762276	−	0.647252i	$-0.224082\pi$
$881$	45.2512	1.52455	0.762276	+	0.647252i	$0.224082\pi$
$882$	0	0
$883$	42.9341	1.44485	0.722423	−	0.691451i	$-0.243028\pi$
$883$	42.9341	1.44485	0.722423	+	0.691451i	$0.243028\pi$
$884$	8.19897	0.275761
$885$	26.4569	0.889339
$886$	−16.9629	−0.569880
$887$	−50.9963	−1.71229	−0.856143	−	0.516738i	$-0.827146\pi$
$887$	−50.9963	−1.71229	−0.856143	+	0.516738i	$0.827146\pi$
$888$	26.7467	0.897559
$889$	0	0
$890$	95.2737	3.19358
$891$	1.39070	0.0465903
$892$	61.9359	2.07377
$893$	−1.22449	−0.0409761
$894$	39.7814	1.33049
$895$	42.2255	1.41144
$896$	0	0
$897$	8.88342	0.296609
$898$	54.8436	1.83015
$899$	0.376429	0.0125546
$900$	44.5607	1.48536
$901$	−3.56290	−0.118697
$902$	3.40586	0.113403
$903$	0	0
$904$	−96.2840	−3.20236
$905$	66.3055	2.20407
$906$	−33.3361	−1.10752
$907$	23.0929	0.766788	0.383394	−	0.923585i	$-0.374755\pi$
$907$	23.0929	0.766788	0.383394	+	0.923585i	$0.374755\pi$
$908$	1.52882	0.0507358
$909$	−3.29223	−0.109196
$910$	0	0
$911$	−38.5509	−1.27725	−0.638625	−	0.769518i	$-0.720496\pi$
$911$	−38.5509	−1.27725	−0.638625	+	0.769518i	$0.720496\pi$
$912$	24.1699	0.800346
$913$	−6.86760	−0.227284
$914$	−62.1917	−2.05712
$915$	37.3937	1.23620
$916$	−80.7253	−2.66724
$917$	0	0
$918$	−1.35883	−0.0448480
$919$	−39.6514	−1.30798	−0.653990	−	0.756504i	$-0.726906\pi$
$919$	−39.6514	−1.30798	−0.653990	+	0.756504i	$0.726906\pi$
$920$	47.2463	1.55766
$921$	11.4617	0.377675
$922$	−51.9389	−1.71052
$923$	46.0109	1.51447
$924$	0	0
$925$	−60.9379	−2.00362
$926$	63.0246	2.07112
$927$	−15.0405	−0.493993
$928$	−0.00599933	−0.000196938 0
$929$	−49.2994	−1.61746	−0.808731	−	0.588179i	$-0.799845\pi$
$929$	−49.2994	−1.61746	−0.808731	+	0.588179i	$0.799845\pi$
$930$	13.8738	0.454939
$931$	0	0
$932$	−34.8854	−1.14271
$933$	0.539450	0.0176608
$934$	−46.3873	−1.51784
$935$	−3.10061	−0.101401
$936$	18.0843	0.591102
$937$	−29.7098	−0.970577	−0.485288	−	0.874354i	$-0.661285\pi$
$937$	−29.7098	−0.970577	−0.485288	+	0.874354i	$0.661285\pi$
$938$	0	0
$939$	−3.30545	−0.107869
$940$	−3.24411	−0.105811
$941$	−30.0295	−0.978933	−0.489466	−	0.872022i	$-0.662808\pi$
$941$	−30.0295	−0.978933	−0.489466	+	0.872022i	$0.662808\pi$
$942$	57.3916	1.86992
$943$	−2.40328	−0.0782614
$944$	26.2459	0.854232
$945$	0	0
$946$	−10.9344	−0.355508
$947$	−56.0941	−1.82281	−0.911407	−	0.411506i	$-0.865003\pi$
$947$	−56.0941	−1.82281	−0.911407	+	0.411506i	$0.865003\pi$
$948$	61.9285	2.01134
$949$	−50.0975	−1.62623
$950$	−165.518	−5.37012
$951$	−31.3519	−1.01665
$952$	0	0
$953$	−35.0470	−1.13528	−0.567642	−	0.823275i	$-0.692144\pi$
$953$	−35.0470	−1.13528	−0.567642	+	0.823275i	$0.692144\pi$
$954$	−15.7262	−0.509155
$955$	12.3756	0.400466
$956$	49.7261	1.60826
$957$	−0.371326	−0.0120033
$958$	25.3699	0.819664
$959$	0	0
$960$	−32.2567	−1.04108
$961$	−29.0124	−0.935885
$962$	−49.4897	−1.59561
$963$	16.8244	0.542160
$964$	102.239	3.29291
$965$	−61.7080	−1.98645
$966$	0	0
$967$	3.10220	0.0997601	0.0498800	−	0.998755i	$-0.484116\pi$
$967$	3.10220	0.0997601	0.0498800	+	0.998755i	$0.484116\pi$
$968$	−44.3544	−1.42561
$969$	3.36422	0.108074
$970$	50.6404	1.62597
$971$	12.0888	0.387949	0.193975	−	0.981007i	$-0.437862\pi$
$971$	12.0888	0.387949	0.193975	+	0.981007i	$0.437862\pi$
$972$	−3.99771	−0.128226
$973$	0	0
$974$	49.6146	1.58976
$975$	−41.2020	−1.31952
$976$	37.0955	1.18740
$977$	58.8085	1.88145	0.940726	−	0.339167i	$-0.110145\pi$
$977$	58.8085	1.88145	0.940726	+	0.339167i	$0.110145\pi$
$978$	24.2428	0.775200
$979$	−13.4640	−0.430312
$980$	0	0
$981$	6.05274	0.193249
$982$	14.6764	0.468344
$983$	−39.7927	−1.26919	−0.634595	−	0.772845i	$-0.718833\pi$
$983$	−39.7927	−1.26919	−0.634595	+	0.772845i	$0.718833\pi$
$984$	−4.89242	−0.155965
$985$	70.1517	2.23522
$986$	0.362815	0.0115544
$987$	0	0
$988$	−89.5983	−2.85050
$989$	7.71563	0.245343
$990$	−13.6857	−0.434960
$991$	21.0591	0.668965	0.334483	−	0.942402i	$-0.391438\pi$
$991$	21.0591	0.668965	0.334483	+	0.942402i	$0.391438\pi$
$992$	−0.0316769	−0.00100574
$993$	16.3998	0.520432
$994$	0	0
$995$	−60.7795	−1.92684
$996$	19.7415	0.625535
$997$	−14.6394	−0.463633	−0.231816	−	0.972760i	$-0.574467\pi$
$997$	−14.6394	−0.463633	−0.231816	+	0.972760i	$0.574467\pi$
$998$	−30.3069	−0.959347
$999$	5.46696	0.172967

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bf.1.11		12
7.3	odd	6		861.2.i.e.247.2	✓	24
7.5	odd	6		861.2.i.e.739.2	yes	24
7.6	odd	2		6027.2.a.bg.1.11		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.i.e.247.2	✓	24	7.3	odd	6
861.2.i.e.739.2	yes	24	7.5	odd	6
6027.2.a.bf.1.11		12	1.1	even	1	trivial
6027.2.a.bg.1.11		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)

\(f(q)\)	\(=\)	\(q+2.44902 q^{2} -1.00000 q^{3} +3.99771 q^{4} -4.01828 q^{5} -2.44902 q^{6} +4.89242 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.44902 q^{2} -1.00000 q^{3} +3.99771 q^{4} -4.01828 q^{5} -2.44902 q^{6} +4.89242 q^{8} +1.00000 q^{9} -9.84085 q^{10} +1.39070 q^{11} -3.99771 q^{12} +3.69638 q^{13} +4.01828 q^{15} +3.98624 q^{16} +0.554845 q^{17} +2.44902 q^{18} -6.06334 q^{19} -16.0639 q^{20} +3.40586 q^{22} -2.40328 q^{23} -4.89242 q^{24} +11.1466 q^{25} +9.05251 q^{26} -1.00000 q^{27} +0.267006 q^{29} +9.84085 q^{30} +1.40981 q^{31} -0.0224689 q^{32} -1.39070 q^{33} +1.35883 q^{34} +3.99771 q^{36} -5.46696 q^{37} -14.8493 q^{38} -3.69638 q^{39} -19.6591 q^{40} +1.00000 q^{41} -3.21046 q^{43} +5.55962 q^{44} -4.01828 q^{45} -5.88568 q^{46} +0.201950 q^{47} -3.98624 q^{48} +27.2982 q^{50} -0.554845 q^{51} +14.7770 q^{52} -6.42142 q^{53} -2.44902 q^{54} -5.58824 q^{55} +6.06334 q^{57} +0.653903 q^{58} +6.58413 q^{59} +16.0639 q^{60} +9.30589 q^{61} +3.45266 q^{62} -8.02750 q^{64} -14.8531 q^{65} -3.40586 q^{66} -13.5912 q^{67} +2.21811 q^{68} +2.40328 q^{69} +12.4476 q^{71} +4.89242 q^{72} -13.5531 q^{73} -13.3887 q^{74} -11.1466 q^{75} -24.2395 q^{76} -9.05251 q^{78} -15.4910 q^{79} -16.0178 q^{80} +1.00000 q^{81} +2.44902 q^{82} -4.93822 q^{83} -2.22952 q^{85} -7.86250 q^{86} -0.267006 q^{87} +6.80391 q^{88} -9.68145 q^{89} -9.84085 q^{90} -9.60759 q^{92} -1.40981 q^{93} +0.494580 q^{94} +24.3642 q^{95} +0.0224689 q^{96} -5.14594 q^{97} +1.39070 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} - 12 q^{3} + 10 q^{4} - 12 q^{5} + 2 q^{6} + 12 q^{9}+O(q^{10}) \) 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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