LMFDB - Embedded newform 6027.2.a.bg.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("6027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.1258372982$
Analytic rank:	$0$
Dimension:	$12$
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			1.1
Root			$2.71780$ 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)

$f(q)$	$=$	$q-2.71780 q^{2} +1.00000 q^{3} +5.38643 q^{4} +0.137890 q^{5} -2.71780 q^{6} -9.20364 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.71780 q^{2} +1.00000 q^{3} +5.38643 q^{4} +0.137890 q^{5} -2.71780 q^{6} -9.20364 q^{8} +1.00000 q^{9} -0.374758 q^{10} +5.69547 q^{11} +5.38643 q^{12} +2.94856 q^{13} +0.137890 q^{15} +14.2408 q^{16} +2.25728 q^{17} -2.71780 q^{18} -2.05134 q^{19} +0.742737 q^{20} -15.4791 q^{22} +8.70330 q^{23} -9.20364 q^{24} -4.98099 q^{25} -8.01360 q^{26} +1.00000 q^{27} +1.76086 q^{29} -0.374758 q^{30} +5.49304 q^{31} -20.2963 q^{32} +5.69547 q^{33} -6.13482 q^{34} +5.38643 q^{36} -4.72721 q^{37} +5.57512 q^{38} +2.94856 q^{39} -1.26909 q^{40} -1.00000 q^{41} -1.02193 q^{43} +30.6782 q^{44} +0.137890 q^{45} -23.6538 q^{46} +8.56787 q^{47} +14.2408 q^{48} +13.5373 q^{50} +2.25728 q^{51} +15.8822 q^{52} +13.1785 q^{53} -2.71780 q^{54} +0.785350 q^{55} -2.05134 q^{57} -4.78567 q^{58} +14.6044 q^{59} +0.742737 q^{60} -11.2219 q^{61} -14.9290 q^{62} +26.6797 q^{64} +0.406578 q^{65} -15.4791 q^{66} -3.37054 q^{67} +12.1587 q^{68} +8.70330 q^{69} -5.43268 q^{71} -9.20364 q^{72} +10.5185 q^{73} +12.8476 q^{74} -4.98099 q^{75} -11.0494 q^{76} -8.01360 q^{78} -8.16244 q^{79} +1.96366 q^{80} +1.00000 q^{81} +2.71780 q^{82} -7.37479 q^{83} +0.311256 q^{85} +2.77739 q^{86} +1.76086 q^{87} -52.4190 q^{88} -0.423214 q^{89} -0.374758 q^{90} +46.8797 q^{92} +5.49304 q^{93} -23.2857 q^{94} -0.282859 q^{95} -20.2963 q^{96} +5.89236 q^{97} +5.69547 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.71780	−1.92177	−0.960887	−	0.276941i	$-0.910679\pi$
$2$	−2.71780	−1.92177	−0.960887	+	0.276941i	$0.910679\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.38643	2.69322
$5$	0.137890	0.0616664	0.0308332	−	0.999525i	$-0.490184\pi$
$5$	0.137890	0.0616664	0.0308332	+	0.999525i	$0.490184\pi$
$6$	−2.71780	−1.10954
$7$	0	0
$7$	0	0
$8$	−9.20364	−3.25398
$9$	1.00000	0.333333
$10$	−0.374758	−0.118509
$11$	5.69547	1.71725	0.858624	−	0.512606i	$-0.171320\pi$
$11$	5.69547	1.71725	0.858624	+	0.512606i	$0.171320\pi$
$12$	5.38643	1.55493
$13$	2.94856	0.817784	0.408892	−	0.912583i	$-0.365915\pi$
$13$	2.94856	0.817784	0.408892	+	0.912583i	$0.365915\pi$
$14$	0	0
$15$	0.137890	0.0356031
$16$	14.2408	3.56019
$17$	2.25728	0.547470	0.273735	−	0.961805i	$-0.411741\pi$
$17$	2.25728	0.547470	0.273735	+	0.961805i	$0.411741\pi$
$18$	−2.71780	−0.640591
$19$	−2.05134	−0.470609	−0.235304	−	0.971922i	$-0.575609\pi$
$19$	−2.05134	−0.470609	−0.235304	+	0.971922i	$0.575609\pi$
$20$	0.742737	0.166081
$21$	0	0
$22$	−15.4791	−3.30016
$23$	8.70330	1.81476	0.907382	−	0.420308i	$-0.138078\pi$
$23$	8.70330	1.81476	0.907382	+	0.420308i	$0.138078\pi$
$24$	−9.20364	−1.87868
$25$	−4.98099	−0.996197
$26$	−8.01360	−1.57160
$27$	1.00000	0.192450
$28$	0	0
$29$	1.76086	0.326984	0.163492	−	0.986545i	$-0.447724\pi$
$29$	1.76086	0.326984	0.163492	+	0.986545i	$0.447724\pi$
$30$	−0.374758	−0.0684212
$31$	5.49304	0.986579	0.493289	−	0.869865i	$-0.335794\pi$
$31$	5.49304	0.986579	0.493289	+	0.869865i	$0.335794\pi$
$32$	−20.2963	−3.58791
$33$	5.69547	0.991454
$34$	−6.13482	−1.05211
$35$	0	0
$36$	5.38643	0.897738
$37$	−4.72721	−0.777148	−0.388574	−	0.921417i	$-0.627032\pi$
$37$	−4.72721	−0.777148	−0.388574	+	0.921417i	$0.627032\pi$
$38$	5.57512	0.904403
$39$	2.94856	0.472148
$40$	−1.26909	−0.200661
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	−1.02193	−0.155843	−0.0779213	−	0.996960i	$-0.524828\pi$
$43$	−1.02193	−0.155843	−0.0779213	+	0.996960i	$0.524828\pi$
$44$	30.6782	4.62492
$45$	0.137890	0.0205555
$46$	−23.6538	−3.48756
$47$	8.56787	1.24975	0.624876	−	0.780724i	$-0.285150\pi$
$47$	8.56787	1.24975	0.624876	+	0.780724i	$0.285150\pi$
$48$	14.2408	2.05548
$49$	0	0
$50$	13.5373	1.91447
$51$	2.25728	0.316082
$52$	15.8822	2.20247
$53$	13.1785	1.81020	0.905101	−	0.425197i	$-0.139795\pi$
$53$	13.1785	1.81020	0.905101	+	0.425197i	$0.139795\pi$
$54$	−2.71780	−0.369846
$55$	0.785350	0.105897
$56$	0	0
$57$	−2.05134	−0.271706
$58$	−4.78567	−0.628389
$59$	14.6044	1.90134	0.950668	−	0.310212i	$-0.100400\pi$
$59$	14.6044	1.90134	0.950668	+	0.310212i	$0.100400\pi$
$60$	0.742737	0.0958869
$61$	−11.2219	−1.43682	−0.718408	−	0.695622i	$-0.755129\pi$
$61$	−11.2219	−1.43682	−0.718408	+	0.695622i	$0.755129\pi$
$62$	−14.9290	−1.89598
$63$	0	0
$64$	26.6797	3.33496
$65$	0.406578	0.0504298
$66$	−15.4791	−1.90535
$67$	−3.37054	−0.411777	−0.205889	−	0.978575i	$-0.566008\pi$
$67$	−3.37054	−0.411777	−0.205889	+	0.978575i	$0.566008\pi$
$68$	12.1587	1.47445
$69$	8.70330	1.04775
$70$	0	0
$71$	−5.43268	−0.644741	−0.322370	−	0.946614i	$-0.604480\pi$
$71$	−5.43268	−0.644741	−0.322370	+	0.946614i	$0.604480\pi$
$72$	−9.20364	−1.08466
$73$	10.5185	1.23110	0.615550	−	0.788098i	$-0.288934\pi$
$73$	10.5185	1.23110	0.615550	+	0.788098i	$0.288934\pi$
$74$	12.8476	1.49350
$75$	−4.98099	−0.575155
$76$	−11.0494	−1.26745
$77$	0	0
$78$	−8.01360	−0.907362
$79$	−8.16244	−0.918347	−0.459173	−	0.888347i	$-0.651854\pi$
$79$	−8.16244	−0.918347	−0.459173	+	0.888347i	$0.651854\pi$
$80$	1.96366	0.219544
$81$	1.00000	0.111111
$82$	2.71780	0.300131
$83$	−7.37479	−0.809488	−0.404744	−	0.914430i	$-0.632639\pi$
$83$	−7.37479	−0.809488	−0.404744	+	0.914430i	$0.632639\pi$
$84$	0	0
$85$	0.311256	0.0337605
$86$	2.77739	0.299494
$87$	1.76086	0.188784
$88$	−52.4190	−5.58789
$89$	−0.423214	−0.0448606	−0.0224303	−	0.999748i	$-0.507140\pi$
$89$	−0.423214	−0.0448606	−0.0224303	+	0.999748i	$0.507140\pi$
$90$	−0.374758	−0.0395030
$91$	0	0
$92$	46.8797	4.88755
$93$	5.49304	0.569601
$94$	−23.2857	−2.40174
$95$	−0.282859	−0.0290207
$96$	−20.2963	−2.07148
$97$	5.89236	0.598279	0.299139	−	0.954209i	$-0.403300\pi$
$97$	5.89236	0.598279	0.299139	+	0.954209i	$0.403300\pi$
$98$	0	0
$99$	5.69547	0.572416
$100$	−26.8297	−2.68297
$101$	−9.55449	−0.950707	−0.475354	−	0.879795i	$-0.657680\pi$
$101$	−9.55449	−0.950707	−0.475354	+	0.879795i	$0.657680\pi$
$102$	−6.13482	−0.607438
$103$	8.30815	0.818626	0.409313	−	0.912394i	$-0.365768\pi$
$103$	8.30815	0.818626	0.409313	+	0.912394i	$0.365768\pi$
$104$	−27.1375	−2.66105
$105$	0	0
$106$	−35.8164	−3.47880
$107$	−0.0814347	−0.00787259	−0.00393629	−	0.999992i	$-0.501253\pi$
$107$	−0.0814347	−0.00787259	−0.00393629	+	0.999992i	$0.501253\pi$
$108$	5.38643	0.518310
$109$	−2.56804	−0.245974	−0.122987	−	0.992408i	$-0.539247\pi$
$109$	−2.56804	−0.245974	−0.122987	+	0.992408i	$0.539247\pi$
$110$	−2.13442	−0.203509
$111$	−4.72721	−0.448687
$112$	0	0
$113$	−7.58629	−0.713658	−0.356829	−	0.934170i	$-0.616142\pi$
$113$	−7.58629	−0.713658	−0.356829	+	0.934170i	$0.616142\pi$
$114$	5.57512	0.522158
$115$	1.20010	0.111910
$116$	9.48476	0.880638
$117$	2.94856	0.272595
$118$	−39.6919	−3.65394
$119$	0	0
$120$	−1.26909	−0.115852
$121$	21.4383	1.94894
$122$	30.4988	2.76123
$123$	−1.00000	−0.0901670
$124$	29.5879	2.65707
$125$	−1.37628	−0.123098
$126$	0	0
$127$	−6.43273	−0.570812	−0.285406	−	0.958407i	$-0.592129\pi$
$127$	−6.43273	−0.570812	−0.285406	+	0.958407i	$0.592129\pi$
$128$	−31.9174	−2.82113
$129$	−1.02193	−0.0899757
$130$	−1.10500	−0.0969147
$131$	−17.2068	−1.50336	−0.751681	−	0.659527i	$-0.770757\pi$
$131$	−17.2068	−1.50336	−0.751681	+	0.659527i	$0.770757\pi$
$132$	30.6782	2.67020
$133$	0	0
$134$	9.16045	0.791342
$135$	0.137890	0.0118677
$136$	−20.7751	−1.78145
$137$	−13.6477	−1.16600	−0.583002	−	0.812470i	$-0.698122\pi$
$137$	−13.6477	−1.16600	−0.583002	+	0.812470i	$0.698122\pi$
$138$	−23.6538	−2.01355
$139$	19.8373	1.68258	0.841290	−	0.540584i	$-0.181797\pi$
$139$	19.8373	1.68258	0.841290	+	0.540584i	$0.181797\pi$
$140$	0	0
$141$	8.56787	0.721545
$142$	14.7649	1.23905
$143$	16.7934	1.40434
$144$	14.2408	1.18673
$145$	0.242806	0.0201639
$146$	−28.5872	−2.36589
$147$	0	0
$148$	−25.4628	−2.09303
$149$	−11.5612	−0.947132	−0.473566	−	0.880758i	$-0.657034\pi$
$149$	−11.5612	−0.947132	−0.473566	+	0.880758i	$0.657034\pi$
$150$	13.5373	1.10532
$151$	−9.37905	−0.763256	−0.381628	−	0.924316i	$-0.624636\pi$
$151$	−9.37905	−0.763256	−0.381628	+	0.924316i	$0.624636\pi$
$152$	18.8797	1.53135
$153$	2.25728	0.182490
$154$	0	0
$155$	0.757437	0.0608388
$156$	15.8822	1.27160
$157$	3.90097	0.311331	0.155666	−	0.987810i	$-0.450248\pi$
$157$	3.90097	0.311331	0.155666	+	0.987810i	$0.450248\pi$
$158$	22.1839	1.76485
$159$	13.1785	1.04512
$160$	−2.79866	−0.221254
$161$	0	0
$162$	−2.71780	−0.213530
$163$	10.3720	0.812400	0.406200	−	0.913784i	$-0.366854\pi$
$163$	10.3720	0.812400	0.406200	+	0.913784i	$0.366854\pi$
$164$	−5.38643	−0.420610
$165$	0.785350	0.0611394
$166$	20.0432	1.55565
$167$	25.5160	1.97448	0.987242	−	0.159226i	$-0.0508998\pi$
$167$	25.5160	1.97448	0.987242	+	0.159226i	$0.0508998\pi$
$168$	0	0
$169$	−4.30598	−0.331229
$170$	−0.845932	−0.0648800
$171$	−2.05134	−0.156870
$172$	−5.50454	−0.419717
$173$	−15.7882	−1.20035	−0.600176	−	0.799868i	$-0.704903\pi$
$173$	−15.7882	−1.20035	−0.600176	+	0.799868i	$0.704903\pi$
$174$	−4.78567	−0.362801
$175$	0	0
$176$	81.1079	6.11374
$177$	14.6044	1.09774
$178$	1.15021	0.0862119
$179$	5.92947	0.443190	0.221595	−	0.975139i	$-0.428874\pi$
$179$	5.92947	0.443190	0.221595	+	0.975139i	$0.428874\pi$
$180$	0.742737	0.0553603
$181$	1.42300	0.105771	0.0528854	−	0.998601i	$-0.483158\pi$
$181$	1.42300	0.105771	0.0528854	+	0.998601i	$0.483158\pi$
$182$	0	0
$183$	−11.2219	−0.829546
$184$	−80.1020	−5.90520
$185$	−0.651836	−0.0479240
$186$	−14.9290	−1.09465
$187$	12.8562	0.940141
$188$	46.1502	3.36585
$189$	0	0
$190$	0.768755	0.0557713
$191$	−8.64650	−0.625638	−0.312819	−	0.949813i	$-0.601273\pi$
$191$	−8.64650	−0.625638	−0.312819	+	0.949813i	$0.601273\pi$
$192$	26.6797	1.92544
$193$	−2.63703	−0.189817	−0.0949086	−	0.995486i	$-0.530256\pi$
$193$	−2.63703	−0.189817	−0.0949086	+	0.995486i	$0.530256\pi$
$194$	−16.0143	−1.14976
$195$	0.406578	0.0291157
$196$	0	0
$197$	4.19645	0.298985	0.149492	−	0.988763i	$-0.452236\pi$
$197$	4.19645	0.298985	0.149492	+	0.988763i	$0.452236\pi$
$198$	−15.4791	−1.10005
$199$	−7.64107	−0.541661	−0.270831	−	0.962627i	$-0.587298\pi$
$199$	−7.64107	−0.541661	−0.270831	+	0.962627i	$0.587298\pi$
$200$	45.8432	3.24160
$201$	−3.37054	−0.237740
$202$	25.9672	1.82704
$203$	0	0
$204$	12.1587	0.851276
$205$	−0.137890	−0.00963068
$206$	−22.5799	−1.57321
$207$	8.70330	0.604921
$208$	41.9898	2.91147
$209$	−11.6833	−0.808152
$210$	0	0
$211$	17.1760	1.18244	0.591221	−	0.806510i	$-0.298646\pi$
$211$	17.1760	1.18244	0.591221	+	0.806510i	$0.298646\pi$
$212$	70.9849	4.87526
$213$	−5.43268	−0.372241
$214$	0.221323	0.0151293
$215$	−0.140914	−0.00961025
$216$	−9.20364	−0.626228
$217$	0	0
$218$	6.97943	0.472706
$219$	10.5185	0.710776
$220$	4.23023	0.285202
$221$	6.65572	0.447712
$222$	12.8476	0.862275
$223$	−6.84499	−0.458374	−0.229187	−	0.973382i	$-0.573607\pi$
$223$	−6.84499	−0.458374	−0.229187	+	0.973382i	$0.573607\pi$
$224$	0	0
$225$	−4.98099	−0.332066
$226$	20.6180	1.37149
$227$	26.9142	1.78636	0.893178	−	0.449704i	$-0.148471\pi$
$227$	26.9142	1.78636	0.893178	+	0.449704i	$0.148471\pi$
$228$	−11.0494	−0.731763
$229$	−20.6619	−1.36538	−0.682688	−	0.730710i	$-0.739189\pi$
$229$	−20.6619	−1.36538	−0.682688	+	0.730710i	$0.739189\pi$
$230$	−3.26163	−0.215066
$231$	0	0
$232$	−16.2063	−1.06400
$233$	7.60211	0.498031	0.249015	−	0.968500i	$-0.419893\pi$
$233$	7.60211	0.498031	0.249015	+	0.968500i	$0.419893\pi$
$234$	−8.01360	−0.523866
$235$	1.18143	0.0770677
$236$	78.6658	5.12070
$237$	−8.16244	−0.530208
$238$	0	0
$239$	20.6224	1.33395	0.666975	−	0.745080i	$-0.267589\pi$
$239$	20.6224	1.33395	0.666975	+	0.745080i	$0.267589\pi$
$240$	1.96366	0.126754
$241$	−1.59647	−0.102838	−0.0514190	−	0.998677i	$-0.516374\pi$
$241$	−1.59647	−0.102838	−0.0514190	+	0.998677i	$0.516374\pi$
$242$	−58.2651	−3.74542
$243$	1.00000	0.0641500
$244$	−60.4459	−3.86965
$245$	0	0
$246$	2.71780	0.173281
$247$	−6.04849	−0.384856
$248$	−50.5559	−3.21030
$249$	−7.37479	−0.467358
$250$	3.74046	0.236567
$251$	−17.9220	−1.13122	−0.565612	−	0.824671i	$-0.691360\pi$
$251$	−17.9220	−1.13122	−0.565612	+	0.824671i	$0.691360\pi$
$252$	0	0
$253$	49.5693	3.11640
$254$	17.4829	1.09697
$255$	0.311256	0.0194916
$256$	33.3858	2.08661
$257$	−14.0708	−0.877711	−0.438855	−	0.898558i	$-0.644616\pi$
$257$	−14.0708	−0.877711	−0.438855	+	0.898558i	$0.644616\pi$
$258$	2.77739	0.172913
$259$	0	0
$260$	2.19001	0.135818
$261$	1.76086	0.108995
$262$	46.7645	2.88912
$263$	−5.30298	−0.326996	−0.163498	−	0.986544i	$-0.552278\pi$
$263$	−5.30298	−0.326996	−0.163498	+	0.986544i	$0.552278\pi$
$264$	−52.4190	−3.22617
$265$	1.81718	0.111629
$266$	0	0
$267$	−0.423214	−0.0259003
$268$	−18.1552	−1.10900
$269$	9.79232	0.597048	0.298524	−	0.954402i	$-0.403506\pi$
$269$	9.79232	0.597048	0.298524	+	0.954402i	$0.403506\pi$
$270$	−0.374758	−0.0228071
$271$	−0.343237	−0.0208501	−0.0104251	−	0.999946i	$-0.503318\pi$
$271$	−0.343237	−0.0208501	−0.0104251	+	0.999946i	$0.503318\pi$
$272$	32.1454	1.94910
$273$	0	0
$274$	37.0918	2.24080
$275$	−28.3690	−1.71072
$276$	46.8797	2.82183
$277$	−19.0973	−1.14744	−0.573722	−	0.819050i	$-0.694501\pi$
$277$	−19.0973	−1.14744	−0.573722	+	0.819050i	$0.694501\pi$
$278$	−53.9139	−3.23354
$279$	5.49304	0.328860
$280$	0	0
$281$	−31.1488	−1.85818	−0.929090	−	0.369854i	$-0.879408\pi$
$281$	−31.1488	−1.85818	−0.929090	+	0.369854i	$0.879408\pi$
$282$	−23.2857	−1.38665
$283$	5.23598	0.311247	0.155623	−	0.987816i	$-0.450261\pi$
$283$	5.23598	0.311247	0.155623	+	0.987816i	$0.450261\pi$
$284$	−29.2628	−1.73643
$285$	−0.282859	−0.0167551
$286$	−45.6412	−2.69882
$287$	0	0
$288$	−20.2963	−1.19597
$289$	−11.9047	−0.700277
$290$	−0.659897	−0.0387505
$291$	5.89236	0.345416
$292$	56.6573	3.31562
$293$	12.6426	0.738591	0.369295	−	0.929312i	$-0.379599\pi$
$293$	12.6426	0.738591	0.369295	+	0.929312i	$0.379599\pi$
$294$	0	0
$295$	2.01381	0.117249
$296$	43.5075	2.52882
$297$	5.69547	0.330485
$298$	31.4211	1.82017
$299$	25.6622	1.48408
$300$	−26.8297	−1.54902
$301$	0	0
$302$	25.4904	1.46681
$303$	−9.55449	−0.548891
$304$	−29.2126	−1.67546
$305$	−1.54739	−0.0886032
$306$	−6.13482	−0.350704
$307$	−23.5963	−1.34671	−0.673356	−	0.739318i	$-0.735148\pi$
$307$	−23.5963	−1.34671	−0.673356	+	0.739318i	$0.735148\pi$
$308$	0	0
$309$	8.30815	0.472634
$310$	−2.05856	−0.116918
$311$	−20.9484	−1.18787	−0.593937	−	0.804512i	$-0.702427\pi$
$311$	−20.9484	−1.18787	−0.593937	+	0.804512i	$0.702427\pi$
$312$	−27.1375	−1.53636
$313$	−22.3034	−1.26066	−0.630331	−	0.776326i	$-0.717081\pi$
$313$	−22.3034	−1.26066	−0.630331	+	0.776326i	$0.717081\pi$
$314$	−10.6020	−0.598308
$315$	0	0
$316$	−43.9664	−2.47330
$317$	6.32615	0.355312	0.177656	−	0.984093i	$-0.443149\pi$
$317$	6.32615	0.355312	0.177656	+	0.984093i	$0.443149\pi$
$318$	−35.8164	−2.00849
$319$	10.0289	0.561512
$320$	3.67887	0.205655
$321$	−0.0814347	−0.00454524
$322$	0	0
$323$	−4.63043	−0.257644
$324$	5.38643	0.299246
$325$	−14.6868	−0.814674
$326$	−28.1891	−1.56125
$327$	−2.56804	−0.142013
$328$	9.20364	0.508186
$329$	0	0
$330$	−2.13442	−0.117496
$331$	14.6780	0.806778	0.403389	−	0.915029i	$-0.367832\pi$
$331$	14.6780	0.806778	0.403389	+	0.915029i	$0.367832\pi$
$332$	−39.7238	−2.18013
$333$	−4.72721	−0.259049
$334$	−69.3473	−3.79451
$335$	−0.464765	−0.0253928
$336$	0	0
$337$	4.23367	0.230623	0.115311	−	0.993329i	$-0.463213\pi$
$337$	4.23367	0.230623	0.115311	+	0.993329i	$0.463213\pi$
$338$	11.7028	0.636547
$339$	−7.58629	−0.412031
$340$	1.67656	0.0909243
$341$	31.2854	1.69420
$342$	5.57512	0.301468
$343$	0	0
$344$	9.40545	0.507108
$345$	1.20010	0.0646112
$346$	42.9090	2.30680
$347$	25.0094	1.34258	0.671288	−	0.741196i	$-0.265741\pi$
$347$	25.0094	1.34258	0.671288	+	0.741196i	$0.265741\pi$
$348$	9.48476	0.508437
$349$	−1.66313	−0.0890251	−0.0445125	−	0.999009i	$-0.514173\pi$
$349$	−1.66313	−0.0890251	−0.0445125	+	0.999009i	$0.514173\pi$
$350$	0	0
$351$	2.94856	0.157383
$352$	−115.597	−6.16133
$353$	−13.5535	−0.721382	−0.360691	−	0.932685i	$-0.617459\pi$
$353$	−13.5535	−0.721382	−0.360691	+	0.932685i	$0.617459\pi$
$354$	−39.6919	−2.10960
$355$	−0.749114	−0.0397588
$356$	−2.27961	−0.120819
$357$	0	0
$358$	−16.1151	−0.851710
$359$	−5.71263	−0.301501	−0.150751	−	0.988572i	$-0.548169\pi$
$359$	−5.71263	−0.301501	−0.150751	+	0.988572i	$0.548169\pi$
$360$	−1.26909	−0.0668870
$361$	−14.7920	−0.778528
$362$	−3.86743	−0.203268
$363$	21.4383	1.12522
$364$	0	0
$365$	1.45040	0.0759175
$366$	30.4988	1.59420
$367$	5.89895	0.307923	0.153961	−	0.988077i	$-0.450797\pi$
$367$	5.89895	0.307923	0.153961	+	0.988077i	$0.450797\pi$
$368$	123.942	6.46091
$369$	−1.00000	−0.0520579
$370$	1.77156	0.0920990
$371$	0	0
$372$	29.5879	1.53406
$373$	2.82924	0.146492	0.0732462	−	0.997314i	$-0.476664\pi$
$373$	2.82924	0.146492	0.0732462	+	0.997314i	$0.476664\pi$
$374$	−34.9407	−1.80674
$375$	−1.37628	−0.0710709
$376$	−78.8555	−4.06666
$377$	5.19201	0.267402
$378$	0	0
$379$	−26.3304	−1.35250	−0.676250	−	0.736672i	$-0.736396\pi$
$379$	−26.3304	−1.35250	−0.676250	+	0.736672i	$0.736396\pi$
$380$	−1.52360	−0.0781591
$381$	−6.43273	−0.329559
$382$	23.4994	1.20234
$383$	−1.93965	−0.0991112	−0.0495556	−	0.998771i	$-0.515781\pi$
$383$	−1.93965	−0.0991112	−0.0495556	+	0.998771i	$0.515781\pi$
$384$	−31.9174	−1.62878
$385$	0	0
$386$	7.16691	0.364786
$387$	−1.02193	−0.0519475
$388$	31.7388	1.61129
$389$	−0.270900	−0.0137352	−0.00686759	−	0.999976i	$-0.502186\pi$
$389$	−0.270900	−0.0137352	−0.00686759	+	0.999976i	$0.502186\pi$
$390$	−1.10500	−0.0559537
$391$	19.6457	0.993528
$392$	0	0
$393$	−17.2068	−0.867967
$394$	−11.4051	−0.574581
$395$	−1.12552	−0.0566311
$396$	30.6782	1.54164
$397$	−5.18192	−0.260073	−0.130037	−	0.991509i	$-0.541509\pi$
$397$	−5.18192	−0.260073	−0.130037	+	0.991509i	$0.541509\pi$
$398$	20.7669	1.04095
$399$	0	0
$400$	−70.9331	−3.54666
$401$	38.8896	1.94205	0.971026	−	0.238975i	$-0.0768114\pi$
$401$	38.8896	1.94205	0.971026	+	0.238975i	$0.0768114\pi$
$402$	9.16045	0.456882
$403$	16.1966	0.806809
$404$	−51.4646	−2.56046
$405$	0.137890	0.00685182
$406$	0	0
$407$	−26.9237	−1.33456
$408$	−20.7751	−1.02852
$409$	−13.7995	−0.682340	−0.341170	−	0.940002i	$-0.610823\pi$
$409$	−13.7995	−0.682340	−0.341170	+	0.940002i	$0.610823\pi$
$410$	0.374758	0.0185080
$411$	−13.6477	−0.673193
$412$	44.7513	2.20474
$413$	0	0
$414$	−23.6538	−1.16252
$415$	−1.01691	−0.0499182
$416$	−59.8449	−2.93414
$417$	19.8373	0.971438
$418$	31.7529	1.55309
$419$	30.3487	1.48263	0.741316	−	0.671156i	$-0.234202\pi$
$419$	30.3487	1.48263	0.741316	+	0.671156i	$0.234202\pi$
$420$	0	0
$421$	1.76934	0.0862323	0.0431162	−	0.999070i	$-0.486271\pi$
$421$	1.76934	0.0862323	0.0431162	+	0.999070i	$0.486271\pi$
$422$	−46.6808	−2.27239
$423$	8.56787	0.416584
$424$	−121.290	−5.89035
$425$	−11.2435	−0.545388
$426$	14.7649	0.715363
$427$	0	0
$428$	−0.438642	−0.0212026
$429$	16.7934	0.810795
$430$	0.382976	0.0184687
$431$	11.1640	0.537749	0.268874	−	0.963175i	$-0.413348\pi$
$431$	11.1640	0.537749	0.268874	+	0.963175i	$0.413348\pi$
$432$	14.2408	0.685160
$433$	25.5146	1.22615	0.613077	−	0.790023i	$-0.289932\pi$
$433$	25.5146	1.22615	0.613077	+	0.790023i	$0.289932\pi$
$434$	0	0
$435$	0.242806	0.0116416
$436$	−13.8326	−0.662461
$437$	−17.8534	−0.854043
$438$	−28.5872	−1.36595
$439$	−26.6425	−1.27158	−0.635788	−	0.771863i	$-0.719325\pi$
$439$	−26.6425	−1.27158	−0.635788	+	0.771863i	$0.719325\pi$
$440$	−7.22807	−0.344585
$441$	0	0
$442$	−18.0889	−0.860402
$443$	−37.8063	−1.79623	−0.898116	−	0.439759i	$-0.855064\pi$
$443$	−37.8063	−1.79623	−0.898116	+	0.439759i	$0.855064\pi$
$444$	−25.4628	−1.20841
$445$	−0.0583571	−0.00276639
$446$	18.6033	0.880892
$447$	−11.5612	−0.546827
$448$	0	0
$449$	4.85848	0.229286	0.114643	−	0.993407i	$-0.463428\pi$
$449$	4.85848	0.229286	0.114643	+	0.993407i	$0.463428\pi$
$450$	13.5373	0.638155
$451$	−5.69547	−0.268189
$452$	−40.8630	−1.92203
$453$	−9.37905	−0.440666
$454$	−73.1473	−3.43297
$455$	0	0
$456$	18.8797	0.884125
$457$	13.4224	0.627873	0.313936	−	0.949444i	$-0.398352\pi$
$457$	13.4224	0.627873	0.313936	+	0.949444i	$0.398352\pi$
$458$	56.1548	2.62394
$459$	2.25728	0.105361
$460$	6.46426	0.301398
$461$	−5.34164	−0.248785	−0.124393	−	0.992233i	$-0.539698\pi$
$461$	−5.34164	−0.248785	−0.124393	+	0.992233i	$0.539698\pi$
$462$	0	0
$463$	−9.82708	−0.456703	−0.228351	−	0.973579i	$-0.573334\pi$
$463$	−9.82708	−0.456703	−0.228351	+	0.973579i	$0.573334\pi$
$464$	25.0760	1.16413
$465$	0.757437	0.0351253
$466$	−20.6610	−0.957103
$467$	−4.55513	−0.210786	−0.105393	−	0.994431i	$-0.533610\pi$
$467$	−4.55513	−0.210786	−0.105393	+	0.994431i	$0.533610\pi$
$468$	15.8822	0.734156
$469$	0	0
$470$	−3.21088	−0.148107
$471$	3.90097	0.179747
$472$	−134.414	−6.18690
$473$	−5.82036	−0.267620
$474$	22.1839	1.01894
$475$	10.2177	0.468819
$476$	0	0
$477$	13.1785	0.603400
$478$	−56.0474	−2.56355
$479$	−6.08067	−0.277833	−0.138917	−	0.990304i	$-0.544362\pi$
$479$	−6.08067	−0.277833	−0.138917	+	0.990304i	$0.544362\pi$
$480$	−2.79866	−0.127741
$481$	−13.9385	−0.635540
$482$	4.33889	0.197631
$483$	0	0
$484$	115.476	5.24892
$485$	0.812500	0.0368937
$486$	−2.71780	−0.123282
$487$	−5.55456	−0.251701	−0.125851	−	0.992049i	$-0.540166\pi$
$487$	−5.55456	−0.251701	−0.125851	+	0.992049i	$0.540166\pi$
$488$	103.282	4.67536
$489$	10.3720	0.469039
$490$	0	0
$491$	−34.9842	−1.57881	−0.789407	−	0.613871i	$-0.789612\pi$
$491$	−34.9842	−1.57881	−0.789407	+	0.613871i	$0.789612\pi$
$492$	−5.38643	−0.242839
$493$	3.97475	0.179014
$494$	16.4386	0.739607
$495$	0.785350	0.0352988
$496$	78.2251	3.51241
$497$	0	0
$498$	20.0432	0.898157
$499$	22.0788	0.988382	0.494191	−	0.869353i	$-0.335464\pi$
$499$	22.0788	0.988382	0.494191	+	0.869353i	$0.335464\pi$
$500$	−7.41324	−0.331530
$501$	25.5160	1.13997
$502$	48.7083	2.17396
$503$	17.2173	0.767683	0.383842	−	0.923399i	$-0.374601\pi$
$503$	17.2173	0.767683	0.383842	+	0.923399i	$0.374601\pi$
$504$	0	0
$505$	−1.31747	−0.0586267
$506$	−134.720	−5.98901
$507$	−4.30598	−0.191235
$508$	−34.6495	−1.53732
$509$	25.8858	1.14737	0.573684	−	0.819077i	$-0.305514\pi$
$509$	25.8858	1.14737	0.573684	+	0.819077i	$0.305514\pi$
$510$	−0.845932	−0.0374585
$511$	0	0
$512$	−26.9010	−1.18887
$513$	−2.05134	−0.0905687
$514$	38.2415	1.68676
$515$	1.14561	0.0504818
$516$	−5.50454	−0.242324
$517$	48.7980	2.14613
$518$	0	0
$519$	−15.7882	−0.693023
$520$	−3.74200	−0.164098
$521$	19.1420	0.838626	0.419313	−	0.907842i	$-0.362271\pi$
$521$	19.1420	0.838626	0.419313	+	0.907842i	$0.362271\pi$
$522$	−4.78567	−0.209463
$523$	31.5611	1.38007	0.690035	−	0.723776i	$-0.257595\pi$
$523$	31.5611	1.38007	0.690035	+	0.723776i	$0.257595\pi$
$524$	−92.6831	−4.04888
$525$	0	0
$526$	14.4124	0.628412
$527$	12.3993	0.540122
$528$	81.1079	3.52977
$529$	52.7474	2.29337
$530$	−4.93874	−0.214525
$531$	14.6044	0.633778
$532$	0	0
$533$	−2.94856	−0.127716
$534$	1.15021	0.0497744
$535$	−0.0112291	−0.000485474 0
$536$	31.0212	1.33991
$537$	5.92947	0.255876
$538$	−26.6136	−1.14739
$539$	0	0
$540$	0.742737	0.0319623
$541$	−1.60963	−0.0692034	−0.0346017	−	0.999401i	$-0.511016\pi$
$541$	−1.60963	−0.0692034	−0.0346017	+	0.999401i	$0.511016\pi$
$542$	0.932848	0.0400692
$543$	1.42300	0.0610668
$544$	−45.8143	−1.96427
$545$	−0.354108	−0.0151683
$546$	0	0
$547$	−10.6856	−0.456881	−0.228441	−	0.973558i	$-0.573363\pi$
$547$	−10.6856	−0.456881	−0.228441	+	0.973558i	$0.573363\pi$
$548$	−73.5126	−3.14030
$549$	−11.2219	−0.478938
$550$	77.1014	3.28761
$551$	−3.61212	−0.153881
$552$	−80.1020	−3.40937
$553$	0	0
$554$	51.9026	2.20513
$555$	−0.651836	−0.0276689
$556$	106.852	4.53155
$557$	−27.6662	−1.17225	−0.586127	−	0.810219i	$-0.699348\pi$
$557$	−27.6662	−1.17225	−0.586127	+	0.810219i	$0.699348\pi$
$558$	−14.9290	−0.631994
$559$	−3.01322	−0.127446
$560$	0	0
$561$	12.8562	0.542791
$562$	84.6561	3.57100
$563$	−21.7715	−0.917561	−0.458781	−	0.888550i	$-0.651714\pi$
$563$	−21.7715	−0.917561	−0.458781	+	0.888550i	$0.651714\pi$
$564$	46.1502	1.94327
$565$	−1.04608	−0.0440087
$566$	−14.2303	−0.598146
$567$	0	0
$568$	50.0004	2.09797
$569$	−25.9417	−1.08753	−0.543767	−	0.839236i	$-0.683002\pi$
$569$	−25.9417	−1.08753	−0.543767	+	0.839236i	$0.683002\pi$
$570$	0.768755	0.0321996
$571$	−21.3734	−0.894449	−0.447225	−	0.894422i	$-0.647588\pi$
$571$	−21.3734	−0.894449	−0.447225	+	0.894422i	$0.647588\pi$
$572$	90.4567	3.78219
$573$	−8.64650	−0.361213
$574$	0	0
$575$	−43.3510	−1.80786
$576$	26.6797	1.11165
$577$	20.9358	0.871569	0.435785	−	0.900051i	$-0.356471\pi$
$577$	20.9358	0.871569	0.435785	+	0.900051i	$0.356471\pi$
$578$	32.3546	1.34577
$579$	−2.63703	−0.109591
$580$	1.30786	0.0543058
$581$	0	0
$582$	−16.0143	−0.663812
$583$	75.0575	3.10856
$584$	−96.8086	−4.00597
$585$	0.406578	0.0168099
$586$	−34.3601	−1.41940
$587$	−1.95535	−0.0807059	−0.0403529	−	0.999185i	$-0.512848\pi$
$587$	−1.95535	−0.0807059	−0.0403529	+	0.999185i	$0.512848\pi$
$588$	0	0
$589$	−11.2681	−0.464292
$590$	−5.47313	−0.225325
$591$	4.19645	0.172619
$592$	−67.3191	−2.76680
$593$	43.5096	1.78672	0.893362	−	0.449338i	$-0.148340\pi$
$593$	43.5096	1.78672	0.893362	+	0.449338i	$0.148340\pi$
$594$	−15.4791	−0.635117
$595$	0	0
$596$	−62.2737	−2.55083
$597$	−7.64107	−0.312728
$598$	−69.7448	−2.85208
$599$	31.8233	1.30026	0.650132	−	0.759822i	$-0.274714\pi$
$599$	31.8233	1.30026	0.650132	+	0.759822i	$0.274714\pi$
$600$	45.8432	1.87154
$601$	19.4908	0.795045	0.397523	−	0.917592i	$-0.369870\pi$
$601$	19.4908	0.795045	0.397523	+	0.917592i	$0.369870\pi$
$602$	0	0
$603$	−3.37054	−0.137259
$604$	−50.5196	−2.05561
$605$	2.95614	0.120184
$606$	25.9672	1.05484
$607$	−11.0817	−0.449792	−0.224896	−	0.974383i	$-0.572204\pi$
$607$	−11.0817	−0.449792	−0.224896	+	0.974383i	$0.572204\pi$
$608$	41.6345	1.68850
$609$	0	0
$610$	4.20549	0.170275
$611$	25.2629	1.02203
$612$	12.1587	0.491485
$613$	10.2471	0.413877	0.206938	−	0.978354i	$-0.433650\pi$
$613$	10.2471	0.413877	0.206938	+	0.978354i	$0.433650\pi$
$614$	64.1300	2.58808
$615$	−0.137890	−0.00556027
$616$	0	0
$617$	2.77276	0.111627	0.0558136	−	0.998441i	$-0.482225\pi$
$617$	2.77276	0.111627	0.0558136	+	0.998441i	$0.482225\pi$
$618$	−22.5799	−0.908296
$619$	22.6056	0.908596	0.454298	−	0.890850i	$-0.349890\pi$
$619$	22.6056	0.908596	0.454298	+	0.890850i	$0.349890\pi$
$620$	4.07988	0.163852
$621$	8.70330	0.349251
$622$	56.9335	2.28282
$623$	0	0
$624$	41.9898	1.68094
$625$	24.7152	0.988606
$626$	60.6162	2.42271
$627$	−11.6833	−0.466587
$628$	21.0123	0.838482
$629$	−10.6706	−0.425465
$630$	0	0
$631$	−41.3439	−1.64588	−0.822938	−	0.568132i	$-0.807666\pi$
$631$	−41.3439	−1.64588	−0.822938	+	0.568132i	$0.807666\pi$
$632$	75.1242	2.98828
$633$	17.1760	0.682683
$634$	−17.1932	−0.682829
$635$	−0.887011	−0.0352000
$636$	70.9849	2.81473
$637$	0	0
$638$	−27.2566	−1.07910
$639$	−5.43268	−0.214914
$640$	−4.40110	−0.173969
$641$	−13.9450	−0.550796	−0.275398	−	0.961330i	$-0.588810\pi$
$641$	−13.9450	−0.550796	−0.275398	+	0.961330i	$0.588810\pi$
$642$	0.221323	0.00873493
$643$	44.4950	1.75471	0.877356	−	0.479839i	$-0.159305\pi$
$643$	44.4950	1.75471	0.877356	+	0.479839i	$0.159305\pi$
$644$	0	0
$645$	−0.140914	−0.00554848
$646$	12.5846	0.495134
$647$	43.3120	1.70277	0.851385	−	0.524541i	$-0.175763\pi$
$647$	43.3120	1.70277	0.851385	+	0.524541i	$0.175763\pi$
$648$	−9.20364	−0.361553
$649$	83.1791	3.26506
$650$	39.9156	1.56562
$651$	0	0
$652$	55.8682	2.18797
$653$	−20.5501	−0.804186	−0.402093	−	0.915599i	$-0.631717\pi$
$653$	−20.5501	−0.804186	−0.402093	+	0.915599i	$0.631717\pi$
$654$	6.97943	0.272917
$655$	−2.37265	−0.0927070
$656$	−14.2408	−0.556009
$657$	10.5185	0.410366
$658$	0	0
$659$	−0.961502	−0.0374548	−0.0187274	−	0.999825i	$-0.505961\pi$
$659$	−0.961502	−0.0374548	−0.0187274	+	0.999825i	$0.505961\pi$
$660$	4.23023	0.164662
$661$	36.3619	1.41431	0.707157	−	0.707057i	$-0.249977\pi$
$661$	36.3619	1.41431	0.707157	+	0.707057i	$0.249977\pi$
$662$	−39.8919	−1.55044
$663$	6.65572	0.258487
$664$	67.8749	2.63406
$665$	0	0
$666$	12.8476	0.497834
$667$	15.3253	0.593398
$668$	137.440	5.31771
$669$	−6.84499	−0.264643
$670$	1.26314	0.0487992
$671$	−63.9139	−2.46737
$672$	0	0
$673$	6.94798	0.267825	0.133912	−	0.990993i	$-0.457246\pi$
$673$	6.94798	0.267825	0.133912	+	0.990993i	$0.457246\pi$
$674$	−11.5063	−0.443205
$675$	−4.98099	−0.191718
$676$	−23.1938	−0.892071
$677$	−1.47043	−0.0565132	−0.0282566	−	0.999601i	$-0.508996\pi$
$677$	−1.47043	−0.0565132	−0.0282566	+	0.999601i	$0.508996\pi$
$678$	20.6180	0.791830
$679$	0	0
$680$	−2.86469	−0.109856
$681$	26.9142	1.03135
$682$	−85.0275	−3.25587
$683$	−2.66016	−0.101788	−0.0508942	−	0.998704i	$-0.516207\pi$
$683$	−2.66016	−0.101788	−0.0508942	+	0.998704i	$0.516207\pi$
$684$	−11.0494	−0.422483
$685$	−1.88189	−0.0719033
$686$	0	0
$687$	−20.6619	−0.788300
$688$	−14.5530	−0.554830
$689$	38.8575	1.48035
$690$	−3.26163	−0.124168
$691$	38.5799	1.46765	0.733824	−	0.679340i	$-0.237734\pi$
$691$	38.5799	1.46765	0.733824	+	0.679340i	$0.237734\pi$
$692$	−85.0418	−3.23281
$693$	0	0
$694$	−67.9706	−2.58013
$695$	2.73537	0.103759
$696$	−16.2063	−0.614300
$697$	−2.25728	−0.0855004
$698$	4.52004	0.171086
$699$	7.60211	0.287538
$700$	0	0
$701$	−9.29163	−0.350940	−0.175470	−	0.984485i	$-0.556145\pi$
$701$	−9.29163	−0.350940	−0.175470	+	0.984485i	$0.556145\pi$
$702$	−8.01360	−0.302454
$703$	9.69709	0.365733
$704$	151.953	5.72695
$705$	1.18143	0.0444951
$706$	36.8358	1.38633
$707$	0	0
$708$	78.6658	2.95644
$709$	−42.7815	−1.60669	−0.803346	−	0.595513i	$-0.796949\pi$
$709$	−42.7815	−1.60669	−0.803346	+	0.595513i	$0.796949\pi$
$710$	2.03594	0.0764075
$711$	−8.16244	−0.306116
$712$	3.89511	0.145975
$713$	47.8075	1.79041
$714$	0	0
$715$	2.31565	0.0866005
$716$	31.9387	1.19361
$717$	20.6224	0.770156
$718$	15.5258	0.579417
$719$	19.1569	0.714433	0.357216	−	0.934022i	$-0.383726\pi$
$719$	19.1569	0.714433	0.357216	+	0.934022i	$0.383726\pi$
$720$	1.96366	0.0731815
$721$	0	0
$722$	40.2017	1.49615
$723$	−1.59647	−0.0593735
$724$	7.66490	0.284864
$725$	−8.77083	−0.325740
$726$	−58.2651	−2.16242
$727$	13.6120	0.504840	0.252420	−	0.967618i	$-0.418774\pi$
$727$	13.6120	0.504840	0.252420	+	0.967618i	$0.418774\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−3.94190	−0.145896
$731$	−2.30677	−0.0853191
$732$	−60.4459	−2.23415
$733$	41.2165	1.52236	0.761182	−	0.648538i	$-0.224619\pi$
$733$	41.2165	1.52236	0.761182	+	0.648538i	$0.224619\pi$
$734$	−16.0322	−0.591758
$735$	0	0
$736$	−176.645	−6.51121
$737$	−19.1968	−0.707123
$738$	2.71780	0.100044
$739$	11.8394	0.435520	0.217760	−	0.976002i	$-0.430125\pi$
$739$	11.8394	0.435520	0.217760	+	0.976002i	$0.430125\pi$
$740$	−3.51107	−0.129070
$741$	−6.04849	−0.222197
$742$	0	0
$743$	26.7175	0.980172	0.490086	−	0.871674i	$-0.336965\pi$
$743$	26.7175	0.980172	0.490086	+	0.871674i	$0.336965\pi$
$744$	−50.5559	−1.85347
$745$	−1.59418	−0.0584063
$746$	−7.68930	−0.281525
$747$	−7.37479	−0.269829
$748$	69.2492	2.53200
$749$	0	0
$750$	3.74046	0.136582
$751$	−36.0271	−1.31465	−0.657323	−	0.753609i	$-0.728311\pi$
$751$	−36.0271	−1.31465	−0.657323	+	0.753609i	$0.728311\pi$
$752$	122.013	4.44936
$753$	−17.9220	−0.653113
$754$	−14.1108	−0.513887
$755$	−1.29328	−0.0470673
$756$	0	0
$757$	−5.03844	−0.183125	−0.0915626	−	0.995799i	$-0.529186\pi$
$757$	−5.03844	−0.183125	−0.0915626	+	0.995799i	$0.529186\pi$
$758$	71.5606	2.59920
$759$	49.5693	1.79925
$760$	2.60333	0.0944329
$761$	−23.9622	−0.868631	−0.434315	−	0.900761i	$-0.643010\pi$
$761$	−23.9622	−0.868631	−0.434315	+	0.900761i	$0.643010\pi$
$762$	17.4829	0.633337
$763$	0	0
$764$	−46.5738	−1.68498
$765$	0.311256	0.0112535
$766$	5.27157	0.190469
$767$	43.0621	1.55488
$768$	33.3858	1.20471
$769$	34.3157	1.23746	0.618728	−	0.785605i	$-0.287648\pi$
$769$	34.3157	1.23746	0.618728	+	0.785605i	$0.287648\pi$
$770$	0	0
$771$	−14.0708	−0.506746
$772$	−14.2042	−0.511219
$773$	−4.39789	−0.158181	−0.0790905	−	0.996867i	$-0.525202\pi$
$773$	−4.39789	−0.158181	−0.0790905	+	0.996867i	$0.525202\pi$
$774$	2.77739	0.0998314
$775$	−27.3607	−0.982827
$776$	−54.2312	−1.94679
$777$	0	0
$778$	0.736252	0.0263959
$779$	2.05134	0.0734967
$780$	2.19001	0.0784148
$781$	−30.9417	−1.10718
$782$	−53.3932	−1.90934
$783$	1.76086	0.0629281
$784$	0	0
$785$	0.537906	0.0191987
$786$	46.7645	1.66804
$787$	−22.9544	−0.818235	−0.409118	−	0.912482i	$-0.634163\pi$
$787$	−22.9544	−0.818235	−0.409118	+	0.912482i	$0.634163\pi$
$788$	22.6039	0.805231
$789$	−5.30298	−0.188791
$790$	3.05894	0.108832
$791$	0	0
$792$	−52.4190	−1.86263
$793$	−33.0884	−1.17500
$794$	14.0834	0.499802
$795$	1.81718	0.0644488
$796$	−41.1581	−1.45881
$797$	47.4393	1.68039	0.840194	−	0.542286i	$-0.182441\pi$
$797$	47.4393	1.68039	0.840194	+	0.542286i	$0.182441\pi$
$798$	0	0
$799$	19.3400	0.684201
$800$	101.096	3.57427
$801$	−0.423214	−0.0149535
$802$	−105.694	−3.73218
$803$	59.9079	2.11410
$804$	−18.1552	−0.640284
$805$	0	0
$806$	−44.0190	−1.55050
$807$	9.79232	0.344706
$808$	87.9360	3.09358
$809$	−25.6569	−0.902050	−0.451025	−	0.892511i	$-0.648941\pi$
$809$	−25.6569	−0.902050	−0.451025	+	0.892511i	$0.648941\pi$
$810$	−0.374758	−0.0131677
$811$	−23.8794	−0.838517	−0.419259	−	0.907867i	$-0.637710\pi$
$811$	−23.8794	−0.838517	−0.419259	+	0.907867i	$0.637710\pi$
$812$	0	0
$813$	−0.343237	−0.0120378
$814$	73.1731	2.56472
$815$	1.43020	0.0500978
$816$	32.1454	1.12531
$817$	2.09632	0.0733408
$818$	37.5042	1.31130
$819$	0	0
$820$	−0.742737	−0.0259375
$821$	27.8160	0.970785	0.485392	−	0.874296i	$-0.338677\pi$
$821$	27.8160	0.970785	0.485392	+	0.874296i	$0.338677\pi$
$822$	37.0918	1.29373
$823$	−23.6498	−0.824379	−0.412189	−	0.911098i	$-0.635236\pi$
$823$	−23.6498	−0.824379	−0.412189	+	0.911098i	$0.635236\pi$
$824$	−76.4652	−2.66379
$825$	−28.3690	−0.987683
$826$	0	0
$827$	36.1847	1.25827	0.629133	−	0.777298i	$-0.283410\pi$
$827$	36.1847	1.25827	0.629133	+	0.777298i	$0.283410\pi$
$828$	46.8797	1.62918
$829$	12.6265	0.438536	0.219268	−	0.975665i	$-0.429633\pi$
$829$	12.6265	0.438536	0.219268	+	0.975665i	$0.429633\pi$
$830$	2.76376	0.0959315
$831$	−19.0973	−0.662477
$832$	78.6667	2.72728
$833$	0	0
$834$	−53.9139	−1.86688
$835$	3.51840	0.121759
$836$	−62.9314	−2.17653
$837$	5.49304	0.189867
$838$	−82.4817	−2.84928
$839$	−16.1686	−0.558203	−0.279101	−	0.960262i	$-0.590037\pi$
$839$	−16.1686	−0.558203	−0.279101	+	0.960262i	$0.590037\pi$
$840$	0	0
$841$	−25.8994	−0.893082
$842$	−4.80871	−0.165719
$843$	−31.1488	−1.07282
$844$	92.5171	3.18457
$845$	−0.593752	−0.0204257
$846$	−23.2857	−0.800580
$847$	0	0
$848$	187.672	6.44467
$849$	5.23598	0.179698
$850$	30.5575	1.04811
$851$	−41.1423	−1.41034
$852$	−29.2628	−1.00253
$853$	−50.6273	−1.73345	−0.866723	−	0.498789i	$-0.833778\pi$
$853$	−50.6273	−1.73345	−0.866723	+	0.498789i	$0.833778\pi$
$854$	0	0
$855$	−0.282859	−0.00967358
$856$	0.749495	0.0256172
$857$	−30.1494	−1.02988	−0.514942	−	0.857225i	$-0.672187\pi$
$857$	−30.1494	−1.02988	−0.514942	+	0.857225i	$0.672187\pi$
$858$	−45.6412	−1.55817
$859$	−47.7413	−1.62891	−0.814457	−	0.580224i	$-0.802965\pi$
$859$	−47.7413	−1.62891	−0.814457	+	0.580224i	$0.802965\pi$
$860$	−0.759023	−0.0258825
$861$	0	0
$862$	−30.3414	−1.03343
$863$	37.2766	1.26891	0.634456	−	0.772959i	$-0.281224\pi$
$863$	37.2766	1.26891	0.634456	+	0.772959i	$0.281224\pi$
$864$	−20.2963	−0.690494
$865$	−2.17703	−0.0740214
$866$	−69.3436	−2.35639
$867$	−11.9047	−0.404305
$868$	0	0
$869$	−46.4889	−1.57703
$870$	−0.659897	−0.0223726
$871$	−9.93825	−0.336745
$872$	23.6353	0.800394
$873$	5.89236	0.199426
$874$	48.5219	1.64128
$875$	0	0
$876$	56.6573	1.91427
$877$	30.9833	1.04623	0.523117	−	0.852261i	$-0.324769\pi$
$877$	30.9833	1.04623	0.523117	+	0.852261i	$0.324769\pi$
$878$	72.4089	2.44368
$879$	12.6426	0.426425
$880$	11.1840	0.377012
$881$	−4.67015	−0.157341	−0.0786706	−	0.996901i	$-0.525068\pi$
$881$	−4.67015	−0.157341	−0.0786706	+	0.996901i	$0.525068\pi$
$882$	0	0
$883$	−7.14696	−0.240514	−0.120257	−	0.992743i	$-0.538372\pi$
$883$	−7.14696	−0.240514	−0.120257	+	0.992743i	$0.538372\pi$
$884$	35.8506	1.20579
$885$	2.01381	0.0676935
$886$	102.750	3.45195
$887$	2.44189	0.0819907	0.0409954	−	0.999159i	$-0.486947\pi$
$887$	2.44189	0.0819907	0.0409954	+	0.999159i	$0.486947\pi$
$888$	43.5075	1.46002
$889$	0	0
$890$	0.158603	0.00531638
$891$	5.69547	0.190805
$892$	−36.8701	−1.23450
$893$	−17.5756	−0.588144
$894$	31.4211	1.05088
$895$	0.817617	0.0273299
$896$	0	0
$897$	25.6622	0.856837
$898$	−13.2044	−0.440636
$899$	9.67248	0.322595
$900$	−26.8297	−0.894325
$901$	29.7474	0.991030
$902$	15.4791	0.515399
$903$	0	0
$904$	69.8214	2.32223
$905$	0.196218	0.00652251
$906$	25.4904	0.846861
$907$	42.4848	1.41068	0.705342	−	0.708867i	$-0.250793\pi$
$907$	42.4848	1.41068	0.705342	+	0.708867i	$0.250793\pi$
$908$	144.971	4.81104
$909$	−9.55449	−0.316902
$910$	0	0
$911$	42.7700	1.41703	0.708516	−	0.705694i	$-0.249365\pi$
$911$	42.7700	1.41703	0.708516	+	0.705694i	$0.249365\pi$
$912$	−29.2126	−0.967326
$913$	−42.0029	−1.39009
$914$	−36.4793	−1.20663
$915$	−1.54739	−0.0511551
$916$	−111.294	−3.67725
$917$	0	0
$918$	−6.13482	−0.202479
$919$	−54.5475	−1.79936	−0.899679	−	0.436553i	$-0.856199\pi$
$919$	−54.5475	−1.79936	−0.899679	+	0.436553i	$0.856199\pi$
$920$	−11.0453	−0.364152
$921$	−23.5963	−0.777524
$922$	14.5175	0.478109
$923$	−16.0186	−0.527259
$924$	0	0
$925$	23.5462	0.774193
$926$	26.7080	0.877680
$927$	8.30815	0.272875
$928$	−35.7390	−1.17319
$929$	22.7948	0.747875	0.373937	−	0.927454i	$-0.378008\pi$
$929$	22.7948	0.747875	0.373937	+	0.927454i	$0.378008\pi$
$930$	−2.05856	−0.0675029
$931$	0	0
$932$	40.9483	1.34130
$933$	−20.9484	−0.685819
$934$	12.3799	0.405084
$935$	1.77275	0.0579751
$936$	−27.1375	−0.887017
$937$	−19.9171	−0.650664	−0.325332	−	0.945600i	$-0.605476\pi$
$937$	−19.9171	−0.650664	−0.325332	+	0.945600i	$0.605476\pi$
$938$	0	0
$939$	−22.3034	−0.727844
$940$	6.36367	0.207560
$941$	29.0778	0.947910	0.473955	−	0.880549i	$-0.342826\pi$
$941$	29.0778	0.947910	0.473955	+	0.880549i	$0.342826\pi$
$942$	−10.6020	−0.345433
$943$	−8.70330	−0.283418
$944$	207.978	6.76912
$945$	0	0
$946$	15.8186	0.514306
$947$	−53.2914	−1.73174	−0.865869	−	0.500270i	$-0.833234\pi$
$947$	−53.2914	−1.73174	−0.865869	+	0.500270i	$0.833234\pi$
$948$	−43.9664	−1.42796
$949$	31.0145	1.00677
$950$	−27.7696	−0.900964
$951$	6.32615	0.205139
$952$	0	0
$953$	−9.58803	−0.310587	−0.155293	−	0.987868i	$-0.549632\pi$
$953$	−9.58803	−0.310587	−0.155293	+	0.987868i	$0.549632\pi$
$954$	−35.8164	−1.15960
$955$	−1.19227	−0.0385809
$956$	111.081	3.59261
$957$	10.0289	0.324189
$958$	16.5260	0.533932
$959$	0	0
$960$	3.67887	0.118735
$961$	−0.826538	−0.0266625
$962$	37.8820	1.22136
$963$	−0.0814347	−0.00262420
$964$	−8.59929	−0.276965
$965$	−0.363620	−0.0117054
$966$	0	0
$967$	−11.8877	−0.382284	−0.191142	−	0.981562i	$-0.561219\pi$
$967$	−11.8877	−0.382284	−0.191142	+	0.981562i	$0.561219\pi$
$968$	−197.311	−6.34181
$969$	−4.63043	−0.148751
$970$	−2.20821	−0.0709014
$971$	11.8513	0.380328	0.190164	−	0.981752i	$-0.439098\pi$
$971$	11.8513	0.380328	0.190164	+	0.981752i	$0.439098\pi$
$972$	5.38643	0.172770
$973$	0	0
$974$	15.0962	0.483713
$975$	−14.6868	−0.470353
$976$	−159.808	−5.11534
$977$	−37.8545	−1.21107	−0.605537	−	0.795817i	$-0.707042\pi$
$977$	−37.8545	−1.21107	−0.605537	+	0.795817i	$0.707042\pi$
$978$	−28.1891	−0.901387
$979$	−2.41040	−0.0770367
$980$	0	0
$981$	−2.56804	−0.0819913
$982$	95.0799	3.03412
$983$	−14.0245	−0.447313	−0.223656	−	0.974668i	$-0.571799\pi$
$983$	−14.0245	−0.447313	−0.223656	+	0.974668i	$0.571799\pi$
$984$	9.20364	0.293401
$985$	0.578650	0.0184373
$986$	−10.8026	−0.344024
$987$	0	0
$988$	−32.5798	−1.03650
$989$	−8.89414	−0.282817
$990$	−2.13442	−0.0678364
$991$	0.801775	0.0254692	0.0127346	−	0.999919i	$-0.495946\pi$
$991$	0.801775	0.0254692	0.0127346	+	0.999919i	$0.495946\pi$
$992$	−111.488	−3.53976
$993$	14.6780	0.465793
$994$	0	0
$995$	−1.05363	−0.0334023
$996$	−39.7238	−1.25870
$997$	6.90057	0.218543	0.109272	−	0.994012i	$-0.465148\pi$
$997$	6.90057	0.218543	0.109272	+	0.994012i	$0.465148\pi$
$998$	−60.0057	−1.89945
$999$	−4.72721	−0.149562

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bg.1.1		12
7.2	even	3		861.2.i.e.739.12	yes	24
7.4	even	3		861.2.i.e.247.12	✓	24
7.6	odd	2		6027.2.a.bf.1.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.i.e.247.12	✓	24	7.4	even	3
861.2.i.e.739.12	yes	24	7.2	even	3
6027.2.a.bf.1.1		12	7.6	odd	2
6027.2.a.bg.1.1		12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.71780 q^{2} +1.00000 q^{3} +5.38643 q^{4} +0.137890 q^{5} -2.71780 q^{6} -9.20364 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.71780 q^{2} +1.00000 q^{3} +5.38643 q^{4} +0.137890 q^{5} -2.71780 q^{6} -9.20364 q^{8} +1.00000 q^{9} -0.374758 q^{10} +5.69547 q^{11} +5.38643 q^{12} +2.94856 q^{13} +0.137890 q^{15} +14.2408 q^{16} +2.25728 q^{17} -2.71780 q^{18} -2.05134 q^{19} +0.742737 q^{20} -15.4791 q^{22} +8.70330 q^{23} -9.20364 q^{24} -4.98099 q^{25} -8.01360 q^{26} +1.00000 q^{27} +1.76086 q^{29} -0.374758 q^{30} +5.49304 q^{31} -20.2963 q^{32} +5.69547 q^{33} -6.13482 q^{34} +5.38643 q^{36} -4.72721 q^{37} +5.57512 q^{38} +2.94856 q^{39} -1.26909 q^{40} -1.00000 q^{41} -1.02193 q^{43} +30.6782 q^{44} +0.137890 q^{45} -23.6538 q^{46} +8.56787 q^{47} +14.2408 q^{48} +13.5373 q^{50} +2.25728 q^{51} +15.8822 q^{52} +13.1785 q^{53} -2.71780 q^{54} +0.785350 q^{55} -2.05134 q^{57} -4.78567 q^{58} +14.6044 q^{59} +0.742737 q^{60} -11.2219 q^{61} -14.9290 q^{62} +26.6797 q^{64} +0.406578 q^{65} -15.4791 q^{66} -3.37054 q^{67} +12.1587 q^{68} +8.70330 q^{69} -5.43268 q^{71} -9.20364 q^{72} +10.5185 q^{73} +12.8476 q^{74} -4.98099 q^{75} -11.0494 q^{76} -8.01360 q^{78} -8.16244 q^{79} +1.96366 q^{80} +1.00000 q^{81} +2.71780 q^{82} -7.37479 q^{83} +0.311256 q^{85} +2.77739 q^{86} +1.76086 q^{87} -52.4190 q^{88} -0.423214 q^{89} -0.374758 q^{90} +46.8797 q^{92} +5.49304 q^{93} -23.2857 q^{94} -0.282859 q^{95} -20.2963 q^{96} +5.89236 q^{97} +5.69547 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} + 12 q^{3} + 10 q^{4} + 12 q^{5} - 2 q^{6} + 12 q^{9}+O(q^{10}) \) 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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