LMFDB - Embedded newform 6027.2.a.bl.1.5

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:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} - 14 x^{14} + 68 x^{13} + 64 x^{12} - 456 x^{11} - 54 x^{10} + 1532 x^{9} - 400 x^{8} + \cdots - 49 $ x^16 - 4x^15 - 14x^14 + 68x^13 + 64x^12 - 456x^11 - 54x^10 + 1532x^9 - 400x^8 - 2708x^7 + 1218x^6 + 2424x^5 - 1276x^4 - 960x^3 + 500x^2 + 112*x - 49
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$1.63508$ of defining polynomial
Character	$\chi$	$=$	6027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.63508 q^{2} -1.00000 q^{3} +0.673497 q^{4} -1.18651 q^{5} +1.63508 q^{6} +2.16894 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.63508 q^{2} -1.00000 q^{3} +0.673497 q^{4} -1.18651 q^{5} +1.63508 q^{6} +2.16894 q^{8} +1.00000 q^{9} +1.94005 q^{10} +6.03827 q^{11} -0.673497 q^{12} +6.76120 q^{13} +1.18651 q^{15} -4.89340 q^{16} -2.16841 q^{17} -1.63508 q^{18} +0.190732 q^{19} -0.799112 q^{20} -9.87308 q^{22} +1.56671 q^{23} -2.16894 q^{24} -3.59219 q^{25} -11.0551 q^{26} -1.00000 q^{27} -1.86469 q^{29} -1.94005 q^{30} +4.59985 q^{31} +3.66322 q^{32} -6.03827 q^{33} +3.54554 q^{34} +0.673497 q^{36} -9.75991 q^{37} -0.311862 q^{38} -6.76120 q^{39} -2.57348 q^{40} -1.00000 q^{41} -3.27874 q^{43} +4.06676 q^{44} -1.18651 q^{45} -2.56169 q^{46} -7.29761 q^{47} +4.89340 q^{48} +5.87353 q^{50} +2.16841 q^{51} +4.55365 q^{52} -8.09108 q^{53} +1.63508 q^{54} -7.16449 q^{55} -0.190732 q^{57} +3.04892 q^{58} +6.53265 q^{59} +0.799112 q^{60} +2.90591 q^{61} -7.52114 q^{62} +3.79712 q^{64} -8.02225 q^{65} +9.87308 q^{66} -10.5427 q^{67} -1.46042 q^{68} -1.56671 q^{69} -15.0801 q^{71} +2.16894 q^{72} -1.12356 q^{73} +15.9583 q^{74} +3.59219 q^{75} +0.128457 q^{76} +11.0551 q^{78} -13.1347 q^{79} +5.80607 q^{80} +1.00000 q^{81} +1.63508 q^{82} +6.13893 q^{83} +2.57285 q^{85} +5.36102 q^{86} +1.86469 q^{87} +13.0967 q^{88} -8.62339 q^{89} +1.94005 q^{90} +1.05517 q^{92} -4.59985 q^{93} +11.9322 q^{94} -0.226306 q^{95} -3.66322 q^{96} +6.82744 q^{97} +6.03827 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} - 16 q^{3} + 12 q^{4} + 12 q^{5} + 4 q^{6} - 12 q^{8} + 16 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 - 16 * q^3 + 12 * q^4 + 12 * q^5 + 4 * q^6 - 12 * q^8 + 16 * q^9	$ 16 q - 4 q^{2} - 16 q^{3} + 12 q^{4} + 12 q^{5} + 4 q^{6} - 12 q^{8} + 16 q^{9} + 4 q^{10} - 4 q^{11} - 12 q^{12} - 12 q^{15} + 8 q^{17} - 4 q^{18} - 4 q^{19} + 20 q^{20} - 16 q^{22} - 12 q^{23} + 12 q^{24} - 8 q^{25} + 8 q^{26} - 16 q^{27} - 16 q^{29} - 4 q^{30} + 4 q^{31} - 48 q^{32} + 4 q^{33} - 16 q^{34} + 12 q^{36} - 48 q^{37} + 4 q^{38} - 56 q^{40} - 16 q^{41} - 16 q^{43} + 12 q^{45} - 4 q^{46} + 36 q^{47} - 8 q^{50} - 8 q^{51} - 60 q^{53} + 4 q^{54} - 8 q^{55} + 4 q^{57} - 36 q^{58} + 36 q^{59} - 20 q^{60} + 4 q^{61} + 12 q^{62} + 52 q^{64} - 36 q^{65} + 16 q^{66} - 52 q^{67} + 8 q^{68} + 12 q^{69} - 12 q^{71} - 12 q^{72} + 16 q^{73} + 4 q^{74} + 8 q^{75} - 16 q^{76} - 8 q^{78} - 36 q^{79} + 68 q^{80} + 16 q^{81} + 4 q^{82} + 32 q^{83} - 28 q^{85} - 8 q^{86} + 16 q^{87} - 36 q^{88} + 12 q^{89} + 4 q^{90} - 36 q^{92} - 4 q^{93} - 24 q^{94} - 20 q^{95} + 48 q^{96} - 48 q^{97} - 4 q^{99}+O(q^{100}) $ 16 * q - 4 * q^2 - 16 * q^3 + 12 * q^4 + 12 * q^5 + 4 * q^6 - 12 * q^8 + 16 * q^9 + 4 * q^10 - 4 * q^11 - 12 * q^12 - 12 * q^15 + 8 * q^17 - 4 * q^18 - 4 * q^19 + 20 * q^20 - 16 * q^22 - 12 * q^23 + 12 * q^24 - 8 * q^25 + 8 * q^26 - 16 * q^27 - 16 * q^29 - 4 * q^30 + 4 * q^31 - 48 * q^32 + 4 * q^33 - 16 * q^34 + 12 * q^36 - 48 * q^37 + 4 * q^38 - 56 * q^40 - 16 * q^41 - 16 * q^43 + 12 * q^45 - 4 * q^46 + 36 * q^47 - 8 * q^50 - 8 * q^51 - 60 * q^53 + 4 * q^54 - 8 * q^55 + 4 * q^57 - 36 * q^58 + 36 * q^59 - 20 * q^60 + 4 * q^61 + 12 * q^62 + 52 * q^64 - 36 * q^65 + 16 * q^66 - 52 * q^67 + 8 * q^68 + 12 * q^69 - 12 * q^71 - 12 * q^72 + 16 * q^73 + 4 * q^74 + 8 * q^75 - 16 * q^76 - 8 * q^78 - 36 * q^79 + 68 * q^80 + 16 * q^81 + 4 * q^82 + 32 * q^83 - 28 * q^85 - 8 * q^86 + 16 * q^87 - 36 * q^88 + 12 * q^89 + 4 * q^90 - 36 * q^92 - 4 * q^93 - 24 * q^94 - 20 * q^95 + 48 * q^96 - 48 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.63508	−1.15618	−0.578089	−	0.815974i	$-0.696201\pi$
$2$	−1.63508	−1.15618	−0.578089	+	0.815974i	$0.696201\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.673497	0.336748
$5$	−1.18651	−0.530624	−0.265312	−	0.964163i	$-0.585475\pi$
$5$	−1.18651	−0.530624	−0.265312	+	0.964163i	$0.585475\pi$
$6$	1.63508	0.667520
$7$	0	0
$7$	0	0
$8$	2.16894	0.766837
$9$	1.00000	0.333333
$10$	1.94005	0.613496
$11$	6.03827	1.82061	0.910304	−	0.413940i	$-0.135848\pi$
$11$	6.03827	1.82061	0.910304	+	0.413940i	$0.135848\pi$
$12$	−0.673497	−0.194422
$13$	6.76120	1.87522	0.937610	−	0.347690i	$-0.113034\pi$
$13$	6.76120	1.87522	0.937610	+	0.347690i	$0.113034\pi$
$14$	0	0
$15$	1.18651	0.306356
$16$	−4.89340	−1.22335
$17$	−2.16841	−0.525917	−0.262959	−	0.964807i	$-0.584698\pi$
$17$	−2.16841	−0.525917	−0.262959	+	0.964807i	$0.584698\pi$
$18$	−1.63508	−0.385393
$19$	0.190732	0.0437569	0.0218784	−	0.999761i	$-0.493035\pi$
$19$	0.190732	0.0437569	0.0218784	+	0.999761i	$0.493035\pi$
$20$	−0.799112	−0.178687
$21$	0	0
$22$	−9.87308	−2.10495
$23$	1.56671	0.326681	0.163340	−	0.986570i	$-0.447773\pi$
$23$	1.56671	0.326681	0.163340	+	0.986570i	$0.447773\pi$
$24$	−2.16894	−0.442734
$25$	−3.59219	−0.718438
$26$	−11.0551	−2.16809
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−1.86469	−0.346264	−0.173132	−	0.984899i	$-0.555389\pi$
$29$	−1.86469	−0.346264	−0.173132	+	0.984899i	$0.555389\pi$
$30$	−1.94005	−0.354202
$31$	4.59985	0.826158	0.413079	−	0.910695i	$-0.364453\pi$
$31$	4.59985	0.826158	0.413079	+	0.910695i	$0.364453\pi$
$32$	3.66322	0.647572
$33$	−6.03827	−1.05113
$34$	3.54554	0.608054
$35$	0	0
$36$	0.673497	0.112249
$37$	−9.75991	−1.60452	−0.802259	−	0.596976i	$-0.796369\pi$
$37$	−9.75991	−1.60452	−0.802259	+	0.596976i	$0.796369\pi$
$38$	−0.311862	−0.0505907
$39$	−6.76120	−1.08266
$40$	−2.57348	−0.406903
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	−3.27874	−0.500003	−0.250002	−	0.968245i	$-0.580431\pi$
$43$	−3.27874	−0.500003	−0.250002	+	0.968245i	$0.580431\pi$
$44$	4.06676	0.613087
$45$	−1.18651	−0.176875
$46$	−2.56169	−0.377701
$47$	−7.29761	−1.06447	−0.532233	−	0.846598i	$-0.678647\pi$
$47$	−7.29761	−1.06447	−0.532233	+	0.846598i	$0.678647\pi$
$48$	4.89340	0.706301
$49$	0	0
$50$	5.87353	0.830642
$51$	2.16841	0.303639
$52$	4.55365	0.631477
$53$	−8.09108	−1.11140	−0.555698	−	0.831384i	$-0.687549\pi$
$53$	−8.09108	−1.11140	−0.555698	+	0.831384i	$0.687549\pi$
$54$	1.63508	0.222507
$55$	−7.16449	−0.966059
$56$	0	0
$57$	−0.190732	−0.0252630
$58$	3.04892	0.400343
$59$	6.53265	0.850478	0.425239	−	0.905081i	$-0.360190\pi$
$59$	6.53265	0.850478	0.425239	+	0.905081i	$0.360190\pi$
$60$	0.799112	0.103165
$61$	2.90591	0.372063	0.186032	−	0.982544i	$-0.440437\pi$
$61$	2.90591	0.372063	0.186032	+	0.982544i	$0.440437\pi$
$62$	−7.52114	−0.955186
$63$	0	0
$64$	3.79712	0.474640
$65$	−8.02225	−0.995037
$66$	9.87308	1.21529
$67$	−10.5427	−1.28800	−0.643999	−	0.765027i	$-0.722726\pi$
$67$	−10.5427	−1.28800	−0.643999	+	0.765027i	$0.722726\pi$
$68$	−1.46042	−0.177102
$69$	−1.56671	−0.188609
$70$	0	0
$71$	−15.0801	−1.78968	−0.894841	−	0.446384i	$-0.852712\pi$
$71$	−15.0801	−1.78968	−0.894841	+	0.446384i	$0.852712\pi$
$72$	2.16894	0.255612
$73$	−1.12356	−0.131503	−0.0657516	−	0.997836i	$-0.520944\pi$
$73$	−1.12356	−0.131503	−0.0657516	+	0.997836i	$0.520944\pi$
$74$	15.9583	1.85511
$75$	3.59219	0.414790
$76$	0.128457	0.0147351
$77$	0	0
$78$	11.0551	1.25175
$79$	−13.1347	−1.47776	−0.738882	−	0.673834i	$-0.764646\pi$
$79$	−13.1347	−1.47776	−0.738882	+	0.673834i	$0.764646\pi$
$80$	5.80607	0.649139
$81$	1.00000	0.111111
$82$	1.63508	0.180565
$83$	6.13893	0.673835	0.336918	−	0.941534i	$-0.390616\pi$
$83$	6.13893	0.673835	0.336918	+	0.941534i	$0.390616\pi$
$84$	0	0
$85$	2.57285	0.279065
$86$	5.36102	0.578093
$87$	1.86469	0.199916
$88$	13.0967	1.39611
$89$	−8.62339	−0.914077	−0.457039	−	0.889447i	$-0.651090\pi$
$89$	−8.62339	−0.914077	−0.457039	+	0.889447i	$0.651090\pi$
$90$	1.94005	0.204499
$91$	0	0
$92$	1.05517	0.110009
$93$	−4.59985	−0.476983
$94$	11.9322	1.23071
$95$	−0.226306	−0.0232185
$96$	−3.66322	−0.373876
$97$	6.82744	0.693221	0.346611	−	0.938009i	$-0.387333\pi$
$97$	6.82744	0.693221	0.346611	+	0.938009i	$0.387333\pi$
$98$	0	0
$99$	6.03827	0.606869
$100$	−2.41933	−0.241933
$101$	6.63595	0.660302	0.330151	−	0.943928i	$-0.392900\pi$
$101$	6.63595	0.660302	0.330151	+	0.943928i	$0.392900\pi$
$102$	−3.54554	−0.351060
$103$	−12.2443	−1.20647	−0.603233	−	0.797565i	$-0.706121\pi$
$103$	−12.2443	−1.20647	−0.603233	+	0.797565i	$0.706121\pi$
$104$	14.6647	1.43799
$105$	0	0
$106$	13.2296	1.28497
$107$	6.76869	0.654354	0.327177	−	0.944963i	$-0.393903\pi$
$107$	6.76869	0.654354	0.327177	+	0.944963i	$0.393903\pi$
$108$	−0.673497	−0.0648073
$109$	−9.13962	−0.875417	−0.437709	−	0.899117i	$-0.644210\pi$
$109$	−9.13962	−0.875417	−0.437709	+	0.899117i	$0.644210\pi$
$110$	11.7145	1.11694
$111$	9.75991	0.926369
$112$	0	0
$113$	3.30804	0.311194	0.155597	−	0.987821i	$-0.450270\pi$
$113$	3.30804	0.311194	0.155597	+	0.987821i	$0.450270\pi$
$114$	0.311862	0.0292086
$115$	−1.85892	−0.173345
$116$	−1.25586	−0.116604
$117$	6.76120	0.625073
$118$	−10.6814	−0.983305
$119$	0	0
$120$	2.57348	0.234925
$121$	25.4608	2.31461
$122$	−4.75140	−0.430171
$123$	1.00000	0.0901670
$124$	3.09799	0.278207
$125$	10.1947	0.911845
$126$	0	0
$127$	−15.8127	−1.40315	−0.701573	−	0.712597i	$-0.747519\pi$
$127$	−15.8127	−1.40315	−0.701573	+	0.712597i	$0.747519\pi$
$128$	−13.5350	−1.19634
$129$	3.27874	0.288677
$130$	13.1170	1.15044
$131$	1.88985	0.165117	0.0825584	−	0.996586i	$-0.473691\pi$
$131$	1.88985	0.165117	0.0825584	+	0.996586i	$0.473691\pi$
$132$	−4.06676	−0.353966
$133$	0	0
$134$	17.2382	1.48915
$135$	1.18651	0.102119
$136$	−4.70317	−0.403293
$137$	−0.0721484	−0.00616405	−0.00308203	−	0.999995i	$-0.500981\pi$
$137$	−0.0721484	−0.00616405	−0.00308203	+	0.999995i	$0.500981\pi$
$138$	2.56169	0.218066
$139$	−12.1969	−1.03453	−0.517266	−	0.855825i	$-0.673050\pi$
$139$	−12.1969	−1.03453	−0.517266	+	0.855825i	$0.673050\pi$
$140$	0	0
$141$	7.29761	0.614569
$142$	24.6573	2.06919
$143$	40.8260	3.41404
$144$	−4.89340	−0.407783
$145$	2.21248	0.183736
$146$	1.83712	0.152041
$147$	0	0
$148$	−6.57326	−0.540319
$149$	22.1052	1.81093	0.905465	−	0.424421i	$-0.139522\pi$
$149$	22.1052	1.81093	0.905465	+	0.424421i	$0.139522\pi$
$150$	−5.87353	−0.479571
$151$	−21.6238	−1.75972	−0.879859	−	0.475234i	$-0.842363\pi$
$151$	−21.6238	−1.75972	−0.879859	+	0.475234i	$0.842363\pi$
$152$	0.413686	0.0335544
$153$	−2.16841	−0.175306
$154$	0	0
$155$	−5.45778	−0.438380
$156$	−4.55365	−0.364583
$157$	2.96167	0.236367	0.118183	−	0.992992i	$-0.462293\pi$
$157$	2.96167	0.236367	0.118183	+	0.992992i	$0.462293\pi$
$158$	21.4763	1.70856
$159$	8.09108	0.641665
$160$	−4.34646	−0.343618
$161$	0	0
$162$	−1.63508	−0.128464
$163$	−10.6953	−0.837720	−0.418860	−	0.908051i	$-0.637570\pi$
$163$	−10.6953	−0.837720	−0.418860	+	0.908051i	$0.637570\pi$
$164$	−0.673497	−0.0525913
$165$	7.16449	0.557754
$166$	−10.0377	−0.779074
$167$	−4.18953	−0.324196	−0.162098	−	0.986775i	$-0.551826\pi$
$167$	−4.18953	−0.324196	−0.162098	+	0.986775i	$0.551826\pi$
$168$	0	0
$169$	32.7138	2.51645
$170$	−4.20682	−0.322649
$171$	0.190732	0.0145856
$172$	−2.20822	−0.168375
$173$	−8.24573	−0.626911	−0.313455	−	0.949603i	$-0.601487\pi$
$173$	−8.24573	−0.626911	−0.313455	+	0.949603i	$0.601487\pi$
$174$	−3.04892	−0.231138
$175$	0	0
$176$	−29.5477	−2.22724
$177$	−6.53265	−0.491024
$178$	14.1000	1.05684
$179$	−0.0995296	−0.00743919	−0.00371959	−	0.999993i	$-0.501184\pi$
$179$	−0.0995296	−0.00743919	−0.00371959	+	0.999993i	$0.501184\pi$
$180$	−0.799112	−0.0595623
$181$	0.598347	0.0444748	0.0222374	−	0.999753i	$-0.492921\pi$
$181$	0.598347	0.0444748	0.0222374	+	0.999753i	$0.492921\pi$
$182$	0	0
$183$	−2.90591	−0.214811
$184$	3.39810	0.250511
$185$	11.5802	0.851397
$186$	7.52114	0.551477
$187$	−13.0935	−0.957490
$188$	−4.91492	−0.358457
$189$	0	0
$190$	0.370028	0.0268447
$191$	6.09259	0.440844	0.220422	−	0.975405i	$-0.429256\pi$
$191$	6.09259	0.440844	0.220422	+	0.975405i	$0.429256\pi$
$192$	−3.79712	−0.274033
$193$	8.47368	0.609949	0.304974	−	0.952361i	$-0.401352\pi$
$193$	8.47368	0.609949	0.304974	+	0.952361i	$0.401352\pi$
$194$	−11.1634	−0.801487
$195$	8.02225	0.574485
$196$	0	0
$197$	−3.03721	−0.216392	−0.108196	−	0.994130i	$-0.534507\pi$
$197$	−3.03721	−0.216392	−0.108196	+	0.994130i	$0.534507\pi$
$198$	−9.87308	−0.701649
$199$	−10.6476	−0.754790	−0.377395	−	0.926052i	$-0.623180\pi$
$199$	−10.6476	−0.754790	−0.377395	+	0.926052i	$0.623180\pi$
$200$	−7.79125	−0.550925
$201$	10.5427	0.743626
$202$	−10.8503	−0.763427
$203$	0	0
$204$	1.46042	0.102250
$205$	1.18651	0.0828696
$206$	20.0204	1.39489
$207$	1.56671	0.108894
$208$	−33.0852	−2.29405
$209$	1.15169	0.0796641
$210$	0	0
$211$	1.16029	0.0798776	0.0399388	−	0.999202i	$-0.487284\pi$
$211$	1.16029	0.0798776	0.0399388	+	0.999202i	$0.487284\pi$
$212$	−5.44932	−0.374261
$213$	15.0801	1.03327
$214$	−11.0674	−0.756550
$215$	3.89027	0.265314
$216$	−2.16894	−0.147578
$217$	0	0
$218$	14.9440	1.01214
$219$	1.12356	0.0759234
$220$	−4.82526	−0.325319
$221$	−14.6611	−0.986211
$222$	−15.9583	−1.07105
$223$	1.73694	0.116314	0.0581571	−	0.998307i	$-0.481478\pi$
$223$	1.73694	0.116314	0.0581571	+	0.998307i	$0.481478\pi$
$224$	0	0
$225$	−3.59219	−0.239479
$226$	−5.40892	−0.359796
$227$	−2.94864	−0.195708	−0.0978541	−	0.995201i	$-0.531198\pi$
$227$	−2.94864	−0.195708	−0.0978541	+	0.995201i	$0.531198\pi$
$228$	−0.128457	−0.00850729
$229$	−25.2145	−1.66622	−0.833110	−	0.553108i	$-0.813442\pi$
$229$	−25.2145	−1.66622	−0.833110	+	0.553108i	$0.813442\pi$
$230$	3.03948	0.200418
$231$	0	0
$232$	−4.04440	−0.265528
$233$	−0.291334	−0.0190859	−0.00954297	−	0.999954i	$-0.503038\pi$
$233$	−0.291334	−0.0190859	−0.00954297	+	0.999954i	$0.503038\pi$
$234$	−11.0551	−0.722696
$235$	8.65870	0.564831
$236$	4.39972	0.286397
$237$	13.1347	0.853188
$238$	0	0
$239$	−24.8353	−1.60646	−0.803232	−	0.595667i	$-0.796888\pi$
$239$	−24.8353	−1.60646	−0.803232	+	0.595667i	$0.796888\pi$
$240$	−5.80607	−0.374780
$241$	−7.18194	−0.462630	−0.231315	−	0.972879i	$-0.574303\pi$
$241$	−7.18194	−0.462630	−0.231315	+	0.972879i	$0.574303\pi$
$242$	−41.6304	−2.67611
$243$	−1.00000	−0.0641500
$244$	1.95712	0.125292
$245$	0	0
$246$	−1.63508	−0.104249
$247$	1.28958	0.0820537
$248$	9.97682	0.633529
$249$	−6.13893	−0.389039
$250$	−16.6692	−1.05426
$251$	5.47716	0.345715	0.172858	−	0.984947i	$-0.444700\pi$
$251$	5.47716	0.345715	0.172858	+	0.984947i	$0.444700\pi$
$252$	0	0
$253$	9.46020	0.594758
$254$	25.8550	1.62229
$255$	−2.57285	−0.161118
$256$	14.5367	0.908543
$257$	−22.7771	−1.42080	−0.710399	−	0.703800i	$-0.751485\pi$
$257$	−22.7771	−1.42080	−0.710399	+	0.703800i	$0.751485\pi$
$258$	−5.36102	−0.333762
$259$	0	0
$260$	−5.40296	−0.335077
$261$	−1.86469	−0.115421
$262$	−3.09006	−0.190905
$263$	30.4246	1.87606	0.938032	−	0.346549i	$-0.112647\pi$
$263$	30.4246	1.87606	0.938032	+	0.346549i	$0.112647\pi$
$264$	−13.0967	−0.806044
$265$	9.60017	0.589734
$266$	0	0
$267$	8.62339	0.527743
$268$	−7.10048	−0.433731
$269$	8.54145	0.520781	0.260391	−	0.965503i	$-0.416149\pi$
$269$	8.54145	0.520781	0.260391	+	0.965503i	$0.416149\pi$
$270$	−1.94005	−0.118067
$271$	−14.8801	−0.903902	−0.451951	−	0.892043i	$-0.649272\pi$
$271$	−14.8801	−0.903902	−0.451951	+	0.892043i	$0.649272\pi$
$272$	10.6109	0.643381
$273$	0	0
$274$	0.117969	0.00712674
$275$	−21.6906	−1.30799
$276$	−1.05517	−0.0635139
$277$	−17.9250	−1.07701	−0.538504	−	0.842623i	$-0.681010\pi$
$277$	−17.9250	−1.07701	−0.538504	+	0.842623i	$0.681010\pi$
$278$	19.9430	1.19610
$279$	4.59985	0.275386
$280$	0	0
$281$	8.08764	0.482468	0.241234	−	0.970467i	$-0.422448\pi$
$281$	8.08764	0.482468	0.241234	+	0.970467i	$0.422448\pi$
$282$	−11.9322	−0.710552
$283$	27.1588	1.61443	0.807213	−	0.590261i	$-0.200975\pi$
$283$	27.1588	1.61443	0.807213	+	0.590261i	$0.200975\pi$
$284$	−10.1564	−0.602673
$285$	0.226306	0.0134052
$286$	−66.7539	−3.94724
$287$	0	0
$288$	3.66322	0.215857
$289$	−12.2980	−0.723411
$290$	−3.61758	−0.212432
$291$	−6.82744	−0.400231
$292$	−0.756716	−0.0442835
$293$	−18.4774	−1.07946	−0.539730	−	0.841838i	$-0.681473\pi$
$293$	−18.4774	−1.07946	−0.539730	+	0.841838i	$0.681473\pi$
$294$	0	0
$295$	−7.75107	−0.451285
$296$	−21.1687	−1.23040
$297$	−6.03827	−0.350376
$298$	−36.1439	−2.09376
$299$	10.5928	0.612598
$300$	2.41933	0.139680
$301$	0	0
$302$	35.3567	2.03455
$303$	−6.63595	−0.381226
$304$	−0.933326	−0.0535299
$305$	−3.44789	−0.197426
$306$	3.54554	0.202685
$307$	25.7014	1.46686	0.733429	−	0.679766i	$-0.237919\pi$
$307$	25.7014	1.46686	0.733429	+	0.679766i	$0.237919\pi$
$308$	0	0
$309$	12.2443	0.696553
$310$	8.92393	0.506845
$311$	−12.2010	−0.691855	−0.345928	−	0.938261i	$-0.612436\pi$
$311$	−12.2010	−0.691855	−0.345928	+	0.938261i	$0.612436\pi$
$312$	−14.6647	−0.830223
$313$	−13.5275	−0.764617	−0.382309	−	0.924035i	$-0.624871\pi$
$313$	−13.5275	−0.764617	−0.382309	+	0.924035i	$0.624871\pi$
$314$	−4.84257	−0.273282
$315$	0	0
$316$	−8.84615	−0.497635
$317$	−25.3356	−1.42299	−0.711495	−	0.702691i	$-0.751982\pi$
$317$	−25.3356	−1.42299	−0.711495	+	0.702691i	$0.751982\pi$
$318$	−13.2296	−0.741879
$319$	−11.2595	−0.630411
$320$	−4.50533	−0.251855
$321$	−6.76869	−0.377791
$322$	0	0
$323$	−0.413585	−0.0230125
$324$	0.673497	0.0374165
$325$	−24.2875	−1.34723
$326$	17.4877	0.968554
$327$	9.13962	0.505422
$328$	−2.16894	−0.119760
$329$	0	0
$330$	−11.7145	−0.644864
$331$	−14.6290	−0.804083	−0.402041	−	0.915621i	$-0.631699\pi$
$331$	−14.6290	−0.804083	−0.402041	+	0.915621i	$0.631699\pi$
$332$	4.13455	0.226913
$333$	−9.75991	−0.534840
$334$	6.85023	0.374828
$335$	12.5091	0.683443
$336$	0	0
$337$	−22.0068	−1.19879	−0.599394	−	0.800454i	$-0.704592\pi$
$337$	−22.0068	−1.19879	−0.599394	+	0.800454i	$0.704592\pi$
$338$	−53.4898	−2.90946
$339$	−3.30804	−0.179668
$340$	1.73281	0.0939746
$341$	27.7752	1.50411
$342$	−0.311862	−0.0168636
$343$	0	0
$344$	−7.11140	−0.383421
$345$	1.85892	0.100081
$346$	13.4824	0.724821
$347$	−1.86868	−0.100316	−0.0501579	−	0.998741i	$-0.515972\pi$
$347$	−1.86868	−0.100316	−0.0501579	+	0.998741i	$0.515972\pi$
$348$	1.25586	0.0673212
$349$	22.4885	1.20378	0.601891	−	0.798579i	$-0.294414\pi$
$349$	22.4885	1.20378	0.601891	+	0.798579i	$0.294414\pi$
$350$	0	0
$351$	−6.76120	−0.360886
$352$	22.1195	1.17898
$353$	17.1123	0.910797	0.455398	−	0.890288i	$-0.349497\pi$
$353$	17.1123	0.910797	0.455398	+	0.890288i	$0.349497\pi$
$354$	10.6814	0.567711
$355$	17.8928	0.949649
$356$	−5.80782	−0.307814
$357$	0	0
$358$	0.162739	0.00860103
$359$	13.8490	0.730922	0.365461	−	0.930827i	$-0.380911\pi$
$359$	13.8490	0.730922	0.365461	+	0.930827i	$0.380911\pi$
$360$	−2.57348	−0.135634
$361$	−18.9636	−0.998085
$362$	−0.978348	−0.0514208
$363$	−25.4608	−1.33634
$364$	0	0
$365$	1.33312	0.0697788
$366$	4.75140	0.248359
$367$	−27.1366	−1.41652	−0.708260	−	0.705952i	$-0.750519\pi$
$367$	−27.1366	−1.41652	−0.708260	+	0.705952i	$0.750519\pi$
$368$	−7.66651	−0.399645
$369$	−1.00000	−0.0520579
$370$	−18.9347	−0.984366
$371$	0	0
$372$	−3.09799	−0.160623
$373$	−12.9137	−0.668647	−0.334324	−	0.942458i	$-0.608508\pi$
$373$	−12.9137	−0.668647	−0.334324	+	0.942458i	$0.608508\pi$
$374$	21.4089	1.10703
$375$	−10.1947	−0.526454
$376$	−15.8281	−0.816272
$377$	−12.6075	−0.649321
$378$	0	0
$379$	15.2859	0.785185	0.392592	−	0.919713i	$-0.371578\pi$
$379$	15.2859	0.785185	0.392592	+	0.919713i	$0.371578\pi$
$380$	−0.152416	−0.00781878
$381$	15.8127	0.810107
$382$	−9.96189	−0.509695
$383$	31.5671	1.61301	0.806503	−	0.591231i	$-0.201358\pi$
$383$	31.5671	1.61301	0.806503	+	0.591231i	$0.201358\pi$
$384$	13.5350	0.690708
$385$	0	0
$386$	−13.8552	−0.705210
$387$	−3.27874	−0.166668
$388$	4.59826	0.233441
$389$	10.7554	0.545320	0.272660	−	0.962110i	$-0.412097\pi$
$389$	10.7554	0.545320	0.272660	+	0.962110i	$0.412097\pi$
$390$	−13.1170	−0.664207
$391$	−3.39727	−0.171807
$392$	0	0
$393$	−1.88985	−0.0953303
$394$	4.96610	0.250188
$395$	15.5844	0.784138
$396$	4.06676	0.204362
$397$	30.7767	1.54464	0.772320	−	0.635233i	$-0.219096\pi$
$397$	30.7767	1.54464	0.772320	+	0.635233i	$0.219096\pi$
$398$	17.4097	0.872672
$399$	0	0
$400$	17.5780	0.878900
$401$	19.3013	0.963863	0.481931	−	0.876209i	$-0.339935\pi$
$401$	19.3013	0.963863	0.481931	+	0.876209i	$0.339935\pi$
$402$	−17.2382	−0.859764
$403$	31.1005	1.54923
$404$	4.46929	0.222356
$405$	−1.18651	−0.0589583
$406$	0	0
$407$	−58.9330	−2.92120
$408$	4.70317	0.232841
$409$	−32.8122	−1.62246	−0.811229	−	0.584729i	$-0.801201\pi$
$409$	−32.8122	−1.62246	−0.811229	+	0.584729i	$0.801201\pi$
$410$	−1.94005	−0.0958120
$411$	0.0721484	0.00355882
$412$	−8.24649	−0.406275
$413$	0	0
$414$	−2.56169	−0.125900
$415$	−7.28392	−0.357553
$416$	24.7678	1.21434
$417$	12.1969	0.597287
$418$	−1.88311	−0.0921059
$419$	−12.5559	−0.613398	−0.306699	−	0.951807i	$-0.599225\pi$
$419$	−12.5559	−0.613398	−0.306699	+	0.951807i	$0.599225\pi$
$420$	0	0
$421$	3.98056	0.194001	0.0970004	−	0.995284i	$-0.469075\pi$
$421$	3.98056	0.194001	0.0970004	+	0.995284i	$0.469075\pi$
$422$	−1.89717	−0.0923528
$423$	−7.29761	−0.354822
$424$	−17.5491	−0.852260
$425$	7.78935	0.377839
$426$	−24.6573	−1.19465
$427$	0	0
$428$	4.55869	0.220353
$429$	−40.8260	−1.97110
$430$	−6.36091	−0.306750
$431$	15.1697	0.730698	0.365349	−	0.930871i	$-0.380950\pi$
$431$	15.1697	0.730698	0.365349	+	0.930871i	$0.380950\pi$
$432$	4.89340	0.235434
$433$	−23.7096	−1.13941	−0.569706	−	0.821849i	$-0.692943\pi$
$433$	−23.7096	−1.13941	−0.569706	+	0.821849i	$0.692943\pi$
$434$	0	0
$435$	−2.21248	−0.106080
$436$	−6.15551	−0.294795
$437$	0.298821	0.0142945
$438$	−1.83712	−0.0877809
$439$	26.8746	1.28265	0.641327	−	0.767267i	$-0.278384\pi$
$439$	26.8746	1.28265	0.641327	+	0.767267i	$0.278384\pi$
$440$	−15.5394	−0.740810
$441$	0	0
$442$	23.9721	1.14024
$443$	34.7765	1.65228	0.826142	−	0.563462i	$-0.190531\pi$
$443$	34.7765	1.65228	0.826142	+	0.563462i	$0.190531\pi$
$444$	6.57326	0.311953
$445$	10.2318	0.485032
$446$	−2.84004	−0.134480
$447$	−22.1052	−1.04554
$448$	0	0
$449$	31.7289	1.49738	0.748690	−	0.662921i	$-0.230683\pi$
$449$	31.7289	1.49738	0.748690	+	0.662921i	$0.230683\pi$
$450$	5.87353	0.276881
$451$	−6.03827	−0.284331
$452$	2.22795	0.104794
$453$	21.6238	1.01597
$454$	4.82127	0.226274
$455$	0	0
$456$	−0.413686	−0.0193726
$457$	0.596013	0.0278803	0.0139401	−	0.999903i	$-0.495563\pi$
$457$	0.596013	0.0278803	0.0139401	+	0.999903i	$0.495563\pi$
$458$	41.2278	1.92645
$459$	2.16841	0.101213
$460$	−1.25197	−0.0583736
$461$	2.14488	0.0998972	0.0499486	−	0.998752i	$-0.484094\pi$
$461$	2.14488	0.0998972	0.0499486	+	0.998752i	$0.484094\pi$
$462$	0	0
$463$	21.6912	1.00807	0.504037	−	0.863682i	$-0.331847\pi$
$463$	21.6912	1.00807	0.504037	+	0.863682i	$0.331847\pi$
$464$	9.12466	0.423602
$465$	5.45778	0.253099
$466$	0.476356	0.0220667
$467$	36.2250	1.67629	0.838147	−	0.545444i	$-0.183639\pi$
$467$	36.2250	1.67629	0.838147	+	0.545444i	$0.183639\pi$
$468$	4.55365	0.210492
$469$	0	0
$470$	−14.1577	−0.653046
$471$	−2.96167	−0.136466
$472$	14.1689	0.652178
$473$	−19.7979	−0.910310
$474$	−21.4763	−0.986437
$475$	−0.685144	−0.0314366
$476$	0	0
$477$	−8.09108	−0.370465
$478$	40.6078	1.85736
$479$	−33.6997	−1.53978	−0.769888	−	0.638179i	$-0.779688\pi$
$479$	−33.6997	−1.53978	−0.769888	+	0.638179i	$0.779688\pi$
$480$	4.34646	0.198388
$481$	−65.9887	−3.00882
$482$	11.7431	0.534882
$483$	0	0
$484$	17.1477	0.779442
$485$	−8.10084	−0.367840
$486$	1.63508	0.0741689
$487$	−16.0359	−0.726658	−0.363329	−	0.931661i	$-0.618360\pi$
$487$	−16.0359	−0.726658	−0.363329	+	0.931661i	$0.618360\pi$
$488$	6.30274	0.285312
$489$	10.6953	0.483658
$490$	0	0
$491$	9.67196	0.436490	0.218245	−	0.975894i	$-0.429967\pi$
$491$	9.67196	0.436490	0.218245	+	0.975894i	$0.429967\pi$
$492$	0.673497	0.0303636
$493$	4.04342	0.182106
$494$	−2.10856	−0.0948687
$495$	−7.16449	−0.322020
$496$	−22.5089	−1.01068
$497$	0	0
$498$	10.0377	0.449799
$499$	−7.79437	−0.348924	−0.174462	−	0.984664i	$-0.555819\pi$
$499$	−7.79437	−0.348924	−0.174462	+	0.984664i	$0.555819\pi$
$500$	6.86612	0.307062
$501$	4.18953	0.187175
$502$	−8.95561	−0.399709
$503$	31.0481	1.38437	0.692184	−	0.721721i	$-0.256649\pi$
$503$	31.0481	1.38437	0.692184	+	0.721721i	$0.256649\pi$
$504$	0	0
$505$	−7.87364	−0.350372
$506$	−15.4682	−0.687646
$507$	−32.7138	−1.45287
$508$	−10.6498	−0.472507
$509$	−2.77977	−0.123211	−0.0616056	−	0.998101i	$-0.519622\pi$
$509$	−2.77977	−0.123211	−0.0616056	+	0.998101i	$0.519622\pi$
$510$	4.20682	0.186281
$511$	0	0
$512$	3.30140	0.145902
$513$	−0.190732	−0.00842101
$514$	37.2425	1.64269
$515$	14.5280	0.640180
$516$	2.20822	0.0972116
$517$	−44.0650	−1.93797
$518$	0	0
$519$	8.24573	0.361947
$520$	−17.3998	−0.763031
$521$	9.59805	0.420498	0.210249	−	0.977648i	$-0.432572\pi$
$521$	9.59805	0.420498	0.210249	+	0.977648i	$0.432572\pi$
$522$	3.04892	0.133448
$523$	18.8288	0.823324	0.411662	−	0.911337i	$-0.364948\pi$
$523$	18.8288	0.823324	0.411662	+	0.911337i	$0.364948\pi$
$524$	1.27281	0.0556028
$525$	0	0
$526$	−49.7468	−2.16906
$527$	−9.97438	−0.434491
$528$	29.5477	1.28590
$529$	−20.5454	−0.893280
$530$	−15.6971	−0.681837
$531$	6.53265	0.283493
$532$	0	0
$533$	−6.76120	−0.292860
$534$	−14.1000	−0.610165
$535$	−8.03113	−0.347216
$536$	−22.8665	−0.987684
$537$	0.0995296	0.00429502
$538$	−13.9660	−0.602116
$539$	0	0
$540$	0.799112	0.0343883
$541$	42.8223	1.84108	0.920538	−	0.390653i	$-0.127751\pi$
$541$	42.8223	1.84108	0.920538	+	0.390653i	$0.127751\pi$
$542$	24.3302	1.04507
$543$	−0.598347	−0.0256775
$544$	−7.94338	−0.340570
$545$	10.8443	0.464518
$546$	0	0
$547$	−37.0730	−1.58513	−0.792564	−	0.609789i	$-0.791254\pi$
$547$	−37.0730	−1.58513	−0.792564	+	0.609789i	$0.791254\pi$
$548$	−0.0485917	−0.00207573
$549$	2.90591	0.124021
$550$	35.4660	1.51227
$551$	−0.355655	−0.0151514
$552$	−3.39810	−0.144633
$553$	0	0
$554$	29.3088	1.24521
$555$	−11.5802	−0.491554
$556$	−8.21461	−0.348377
$557$	−15.5614	−0.659359	−0.329679	−	0.944093i	$-0.606941\pi$
$557$	−15.5614	−0.659359	−0.329679	+	0.944093i	$0.606941\pi$
$558$	−7.52114	−0.318395
$559$	−22.1682	−0.937616
$560$	0	0
$561$	13.0935	0.552807
$562$	−13.2240	−0.557819
$563$	−29.6009	−1.24753	−0.623765	−	0.781612i	$-0.714398\pi$
$563$	−29.6009	−1.24753	−0.623765	+	0.781612i	$0.714398\pi$
$564$	4.91492	0.206955
$565$	−3.92503	−0.165127
$566$	−44.4070	−1.86656
$567$	0	0
$568$	−32.7080	−1.37240
$569$	−3.87808	−0.162577	−0.0812887	−	0.996691i	$-0.525904\pi$
$569$	−3.87808	−0.162577	−0.0812887	+	0.996691i	$0.525904\pi$
$570$	−0.370028	−0.0154988
$571$	8.99096	0.376260	0.188130	−	0.982144i	$-0.439757\pi$
$571$	8.99096	0.376260	0.188130	+	0.982144i	$0.439757\pi$
$572$	27.4962	1.14967
$573$	−6.09259	−0.254522
$574$	0	0
$575$	−5.62790	−0.234700
$576$	3.79712	0.158213
$577$	2.57684	0.107275	0.0536376	−	0.998560i	$-0.482918\pi$
$577$	2.57684	0.107275	0.0536376	+	0.998560i	$0.482918\pi$
$578$	20.1082	0.836392
$579$	−8.47368	−0.352154
$580$	1.49010	0.0618728
$581$	0	0
$582$	11.1634	0.462739
$583$	−48.8562	−2.02342
$584$	−2.43694	−0.100841
$585$	−8.02225	−0.331679
$586$	30.2120	1.24805
$587$	0.220807	0.00911369	0.00455684	−	0.999990i	$-0.498550\pi$
$587$	0.220807	0.00911369	0.00455684	+	0.999990i	$0.498550\pi$
$588$	0	0
$589$	0.877338	0.0361501
$590$	12.6736	0.521765
$591$	3.03721	0.124934
$592$	47.7591	1.96289
$593$	−39.2367	−1.61126	−0.805630	−	0.592420i	$-0.798173\pi$
$593$	−39.2367	−1.61126	−0.805630	+	0.592420i	$0.798173\pi$
$594$	9.87308	0.405097
$595$	0	0
$596$	14.8878	0.609828
$597$	10.6476	0.435778
$598$	−17.3201	−0.708273
$599$	−15.9137	−0.650216	−0.325108	−	0.945677i	$-0.605401\pi$
$599$	−15.9137	−0.650216	−0.325108	+	0.945677i	$0.605401\pi$
$600$	7.79125	0.318077
$601$	17.8588	0.728474	0.364237	−	0.931306i	$-0.381330\pi$
$601$	17.8588	0.728474	0.364237	+	0.931306i	$0.381330\pi$
$602$	0	0
$603$	−10.5427	−0.429333
$604$	−14.5635	−0.592582
$605$	−30.2095	−1.22819
$606$	10.8503	0.440765
$607$	−21.8339	−0.886209	−0.443105	−	0.896470i	$-0.646123\pi$
$607$	−21.8339	−0.886209	−0.443105	+	0.896470i	$0.646123\pi$
$608$	0.698693	0.0283357
$609$	0	0
$610$	5.63759	0.228259
$611$	−49.3406	−1.99611
$612$	−1.46042	−0.0590340
$613$	−43.8002	−1.76907	−0.884537	−	0.466470i	$-0.845526\pi$
$613$	−43.8002	−1.76907	−0.884537	+	0.466470i	$0.845526\pi$
$614$	−42.0240	−1.69595
$615$	−1.18651	−0.0478448
$616$	0	0
$617$	−43.8427	−1.76504	−0.882521	−	0.470274i	$-0.844155\pi$
$617$	−43.8427	−1.76504	−0.882521	+	0.470274i	$0.844155\pi$
$618$	−20.0204	−0.805340
$619$	15.8048	0.635250	0.317625	−	0.948216i	$-0.397115\pi$
$619$	15.8048	0.635250	0.317625	+	0.948216i	$0.397115\pi$
$620$	−3.67580	−0.147624
$621$	−1.56671	−0.0628698
$622$	19.9496	0.799908
$623$	0	0
$624$	33.0852	1.32447
$625$	5.86476	0.234591
$626$	22.1185	0.884034
$627$	−1.15169	−0.0459941
$628$	1.99467	0.0795961
$629$	21.1635	0.843844
$630$	0	0
$631$	9.99857	0.398037	0.199018	−	0.979996i	$-0.436225\pi$
$631$	9.99857	0.398037	0.199018	+	0.979996i	$0.436225\pi$
$632$	−28.4883	−1.13321
$633$	−1.16029	−0.0461174
$634$	41.4258	1.64523
$635$	18.7619	0.744544
$636$	5.44932	0.216080
$637$	0	0
$638$	18.4102	0.728867
$639$	−15.0801	−0.596561
$640$	16.0595	0.634807
$641$	15.8669	0.626706	0.313353	−	0.949637i	$-0.398548\pi$
$641$	15.8669	0.626706	0.313353	+	0.949637i	$0.398548\pi$
$642$	11.0674	0.436794
$643$	−13.4252	−0.529439	−0.264720	−	0.964325i	$-0.585279\pi$
$643$	−13.4252	−0.529439	−0.264720	+	0.964325i	$0.585279\pi$
$644$	0	0
$645$	−3.89027	−0.153179
$646$	0.676246	0.0266066
$647$	−10.4724	−0.411713	−0.205857	−	0.978582i	$-0.565998\pi$
$647$	−10.4724	−0.411713	−0.205857	+	0.978582i	$0.565998\pi$
$648$	2.16894	0.0852041
$649$	39.4459	1.54839
$650$	39.7121	1.55764
$651$	0	0
$652$	−7.20325	−0.282101
$653$	−31.6074	−1.23689	−0.618447	−	0.785826i	$-0.712238\pi$
$653$	−31.6074	−1.23689	−0.618447	+	0.785826i	$0.712238\pi$
$654$	−14.9440	−0.584358
$655$	−2.24233	−0.0876150
$656$	4.89340	0.191055
$657$	−1.12356	−0.0438344
$658$	0	0
$659$	−47.0497	−1.83280	−0.916398	−	0.400269i	$-0.868917\pi$
$659$	−47.0497	−1.83280	−0.916398	+	0.400269i	$0.868917\pi$
$660$	4.82526	0.187823
$661$	−8.28359	−0.322194	−0.161097	−	0.986939i	$-0.551503\pi$
$661$	−8.28359	−0.322194	−0.161097	+	0.986939i	$0.551503\pi$
$662$	23.9196	0.929663
$663$	14.6611	0.569389
$664$	13.3150	0.516722
$665$	0	0
$666$	15.9583	0.618370
$667$	−2.92142	−0.113118
$668$	−2.82164	−0.109172
$669$	−1.73694	−0.0671540
$670$	−20.4534	−0.790182
$671$	17.5467	0.677381
$672$	0	0
$673$	−36.5082	−1.40729	−0.703643	−	0.710554i	$-0.748445\pi$
$673$	−36.5082	−1.40729	−0.703643	+	0.710554i	$0.748445\pi$
$674$	35.9830	1.38601
$675$	3.59219	0.138263
$676$	22.0327	0.847410
$677$	25.6242	0.984817	0.492408	−	0.870364i	$-0.336117\pi$
$677$	25.6242	0.984817	0.492408	+	0.870364i	$0.336117\pi$
$678$	5.40892	0.207728
$679$	0	0
$680$	5.58036	0.213997
$681$	2.94864	0.112992
$682$	−45.4147	−1.73902
$683$	1.57119	0.0601199	0.0300599	−	0.999548i	$-0.490430\pi$
$683$	1.57119	0.0601199	0.0300599	+	0.999548i	$0.490430\pi$
$684$	0.128457	0.00491168
$685$	0.0856049	0.00327080
$686$	0	0
$687$	25.2145	0.961992
$688$	16.0442	0.611679
$689$	−54.7054	−2.08411
$690$	−3.03948	−0.115711
$691$	51.8594	1.97283	0.986413	−	0.164285i	$-0.0525317\pi$
$691$	51.8594	1.97283	0.986413	+	0.164285i	$0.0525317\pi$
$692$	−5.55347	−0.211111
$693$	0	0
$694$	3.05544	0.115983
$695$	14.4718	0.548948
$696$	4.04440	0.153303
$697$	2.16841	0.0821345
$698$	−36.7706	−1.39179
$699$	0.291334	0.0110193
$700$	0	0
$701$	−18.2912	−0.690850	−0.345425	−	0.938446i	$-0.612265\pi$
$701$	−18.2912	−0.690850	−0.345425	+	0.938446i	$0.612265\pi$
$702$	11.0551	0.417249
$703$	−1.86152	−0.0702087
$704$	22.9280	0.864133
$705$	−8.65870	−0.326106
$706$	−27.9801	−1.05304
$707$	0	0
$708$	−4.39972	−0.165351
$709$	26.7300	1.00387	0.501934	−	0.864906i	$-0.332622\pi$
$709$	26.7300	1.00387	0.501934	+	0.864906i	$0.332622\pi$
$710$	−29.2562	−1.09796
$711$	−13.1347	−0.492588
$712$	−18.7036	−0.700948
$713$	7.20662	0.269890
$714$	0	0
$715$	−48.4405	−1.81157
$716$	−0.0670328	−0.00250513
$717$	24.8353	0.927492
$718$	−22.6443	−0.845076
$719$	26.6398	0.993497	0.496748	−	0.867895i	$-0.334527\pi$
$719$	26.6398	0.993497	0.496748	+	0.867895i	$0.334527\pi$
$720$	5.80607	0.216380
$721$	0	0
$722$	31.0071	1.15396
$723$	7.18194	0.267099
$724$	0.402985	0.0149768
$725$	6.69831	0.248769
$726$	41.6304	1.54505
$727$	−10.5021	−0.389503	−0.194751	−	0.980853i	$-0.562390\pi$
$727$	−10.5021	−0.389503	−0.194751	+	0.980853i	$0.562390\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−2.17976	−0.0806767
$731$	7.10967	0.262961
$732$	−1.95712	−0.0723372
$733$	47.4356	1.75207	0.876037	−	0.482244i	$-0.160178\pi$
$733$	47.4356	1.75207	0.876037	+	0.482244i	$0.160178\pi$
$734$	44.3706	1.63775
$735$	0	0
$736$	5.73919	0.211549
$737$	−63.6598	−2.34494
$738$	1.63508	0.0601882
$739$	1.56904	0.0577181	0.0288591	−	0.999583i	$-0.490813\pi$
$739$	1.56904	0.0577181	0.0288591	+	0.999583i	$0.490813\pi$
$740$	7.79926	0.286706
$741$	−1.28958	−0.0473737
$742$	0	0
$743$	−27.4416	−1.00674	−0.503368	−	0.864072i	$-0.667906\pi$
$743$	−27.4416	−1.00674	−0.503368	+	0.864072i	$0.667906\pi$
$744$	−9.97682	−0.365768
$745$	−26.2281	−0.960924
$746$	21.1150	0.773075
$747$	6.13893	0.224612
$748$	−8.81841	−0.322433
$749$	0	0
$750$	16.6692	0.608675
$751$	6.36454	0.232245	0.116123	−	0.993235i	$-0.462953\pi$
$751$	6.36454	0.232245	0.116123	+	0.993235i	$0.462953\pi$
$752$	35.7101	1.30221
$753$	−5.47716	−0.199599
$754$	20.6144	0.750731
$755$	25.6569	0.933750
$756$	0	0
$757$	−52.1059	−1.89382	−0.946911	−	0.321495i	$-0.895815\pi$
$757$	−52.1059	−1.89382	−0.946911	+	0.321495i	$0.895815\pi$
$758$	−24.9937	−0.907814
$759$	−9.46020	−0.343384
$760$	−0.490844	−0.0178048
$761$	10.4650	0.379355	0.189677	−	0.981846i	$-0.439256\pi$
$761$	10.4650	0.379355	0.189677	+	0.981846i	$0.439256\pi$
$762$	−25.8550	−0.936628
$763$	0	0
$764$	4.10334	0.148454
$765$	2.57285	0.0930215
$766$	−51.6149	−1.86492
$767$	44.1685	1.59483
$768$	−14.5367	−0.524548
$769$	−53.8129	−1.94054	−0.970272	−	0.242019i	$-0.922190\pi$
$769$	−53.8129	−1.94054	−0.970272	+	0.242019i	$0.922190\pi$
$770$	0	0
$771$	22.7771	0.820298
$772$	5.70700	0.205399
$773$	−41.3159	−1.48603	−0.743015	−	0.669274i	$-0.766605\pi$
$773$	−41.3159	−1.48603	−0.743015	+	0.669274i	$0.766605\pi$
$774$	5.36102	0.192698
$775$	−16.5235	−0.593543
$776$	14.8083	0.531588
$777$	0	0
$778$	−17.5860	−0.630488
$779$	−0.190732	−0.00683367
$780$	5.40296	0.193457
$781$	−91.0580	−3.25831
$782$	5.55481	0.198640
$783$	1.86469	0.0666385
$784$	0	0
$785$	−3.51405	−0.125422
$786$	3.09006	0.110219
$787$	43.4359	1.54832	0.774161	−	0.632989i	$-0.218172\pi$
$787$	43.4359	1.54832	0.774161	+	0.632989i	$0.218172\pi$
$788$	−2.04555	−0.0728698
$789$	−30.4246	−1.08315
$790$	−25.4818	−0.906604
$791$	0	0
$792$	13.0967	0.465370
$793$	19.6474	0.697700
$794$	−50.3225	−1.78588
$795$	−9.60017	−0.340483
$796$	−7.17114	−0.254174
$797$	20.4671	0.724983	0.362492	−	0.931987i	$-0.381926\pi$
$797$	20.4671	0.724983	0.362492	+	0.931987i	$0.381926\pi$
$798$	0	0
$799$	15.8242	0.559821
$800$	−13.1590	−0.465240
$801$	−8.62339	−0.304692
$802$	−31.5593	−1.11440
$803$	−6.78438	−0.239416
$804$	7.10048	0.250415
$805$	0	0
$806$	−50.8519	−1.79118
$807$	−8.54145	−0.300673
$808$	14.3930	0.506344
$809$	17.9052	0.629515	0.314757	−	0.949172i	$-0.398077\pi$
$809$	17.9052	0.629515	0.314757	+	0.949172i	$0.398077\pi$
$810$	1.94005	0.0681663
$811$	−28.0013	−0.983259	−0.491629	−	0.870805i	$-0.663599\pi$
$811$	−28.0013	−0.983259	−0.491629	+	0.870805i	$0.663599\pi$
$812$	0	0
$813$	14.8801	0.521868
$814$	96.3603	3.37743
$815$	12.6901	0.444515
$816$	−10.6109	−0.371456
$817$	−0.625360	−0.0218786
$818$	53.6506	1.87585
$819$	0	0
$820$	0.799112	0.0279062
$821$	20.8566	0.727901	0.363950	−	0.931418i	$-0.381428\pi$
$821$	20.8566	0.727901	0.363950	+	0.931418i	$0.381428\pi$
$822$	−0.117969	−0.00411463
$823$	−2.92738	−0.102042	−0.0510209	−	0.998698i	$-0.516248\pi$
$823$	−2.92738	−0.102042	−0.0510209	+	0.998698i	$0.516248\pi$
$824$	−26.5572	−0.925162
$825$	21.6906	0.755170
$826$	0	0
$827$	31.8673	1.10814	0.554068	−	0.832471i	$-0.313075\pi$
$827$	31.8673	1.10814	0.554068	+	0.832471i	$0.313075\pi$
$828$	1.05517	0.0366697
$829$	31.9250	1.10880	0.554401	−	0.832250i	$-0.312948\pi$
$829$	31.9250	1.10880	0.554401	+	0.832250i	$0.312948\pi$
$830$	11.9098	0.413396
$831$	17.9250	0.621811
$832$	25.6731	0.890054
$833$	0	0
$834$	−19.9430	−0.690571
$835$	4.97093	0.172026
$836$	0.775660	0.0268268
$837$	−4.59985	−0.158994
$838$	20.5300	0.709198
$839$	49.2274	1.69952	0.849760	−	0.527170i	$-0.176747\pi$
$839$	49.2274	1.69952	0.849760	+	0.527170i	$0.176747\pi$
$840$	0	0
$841$	−25.5229	−0.880101
$842$	−6.50855	−0.224300
$843$	−8.08764	−0.278553
$844$	0.781451	0.0268987
$845$	−38.8153	−1.33529
$846$	11.9322	0.410237
$847$	0	0
$848$	39.5929	1.35962
$849$	−27.1588	−0.932089
$850$	−12.7362	−0.436849
$851$	−15.2909	−0.524165
$852$	10.1564	0.347953
$853$	−17.9981	−0.616242	−0.308121	−	0.951347i	$-0.599700\pi$
$853$	−17.9981	−0.616242	−0.308121	+	0.951347i	$0.599700\pi$
$854$	0	0
$855$	−0.226306	−0.00773949
$856$	14.6809	0.501783
$857$	−42.5590	−1.45379	−0.726894	−	0.686749i	$-0.759037\pi$
$857$	−42.5590	−1.45379	−0.726894	+	0.686749i	$0.759037\pi$
$858$	66.7539	2.27894
$859$	9.46509	0.322945	0.161472	−	0.986877i	$-0.448376\pi$
$859$	9.46509	0.322945	0.161472	+	0.986877i	$0.448376\pi$
$860$	2.62008	0.0893441
$861$	0	0
$862$	−24.8037	−0.844818
$863$	35.0039	1.19155	0.595773	−	0.803153i	$-0.296846\pi$
$863$	35.0039	1.19155	0.595773	+	0.803153i	$0.296846\pi$
$864$	−3.66322	−0.124625
$865$	9.78365	0.332654
$866$	38.7672	1.31736
$867$	12.2980	0.417661
$868$	0	0
$869$	−79.3107	−2.69043
$870$	3.61758	0.122647
$871$	−71.2814	−2.41528
$872$	−19.8233	−0.671302
$873$	6.82744	0.231074
$874$	−0.488597	−0.0165270
$875$	0	0
$876$	0.756716	0.0255671
$877$	31.0315	1.04786	0.523929	−	0.851762i	$-0.324466\pi$
$877$	31.0315	1.04786	0.523929	+	0.851762i	$0.324466\pi$
$878$	−43.9422	−1.48298
$879$	18.4774	0.623226
$880$	35.0587	1.18183
$881$	5.51668	0.185862	0.0929309	−	0.995673i	$-0.470376\pi$
$881$	5.51668	0.185862	0.0929309	+	0.995673i	$0.470376\pi$
$882$	0	0
$883$	13.3820	0.450341	0.225170	−	0.974319i	$-0.427706\pi$
$883$	13.3820	0.450341	0.225170	+	0.974319i	$0.427706\pi$
$884$	−9.87419	−0.332105
$885$	7.75107	0.260549
$886$	−56.8625	−1.91033
$887$	−39.4172	−1.32350	−0.661750	−	0.749725i	$-0.730186\pi$
$887$	−39.4172	−1.32350	−0.661750	+	0.749725i	$0.730186\pi$
$888$	21.1687	0.710374
$889$	0	0
$890$	−16.7298	−0.560783
$891$	6.03827	0.202290
$892$	1.16982	0.0391686
$893$	−1.39189	−0.0465777
$894$	36.1439	1.20883
$895$	0.118093	0.00394741
$896$	0	0
$897$	−10.5928	−0.353684
$898$	−51.8794	−1.73124
$899$	−8.57729	−0.286069
$900$	−2.41933	−0.0806442
$901$	17.5448	0.584503
$902$	9.87308	0.328738
$903$	0	0
$904$	7.17495	0.238635
$905$	−0.709947	−0.0235994
$906$	−35.3567	−1.17465
$907$	−37.2578	−1.23712	−0.618562	−	0.785736i	$-0.712285\pi$
$907$	−37.2578	−1.23712	−0.618562	+	0.785736i	$0.712285\pi$
$908$	−1.98590	−0.0659044
$909$	6.63595	0.220101
$910$	0	0
$911$	−14.0722	−0.466233	−0.233116	−	0.972449i	$-0.574892\pi$
$911$	−14.0722	−0.466233	−0.233116	+	0.972449i	$0.574892\pi$
$912$	0.933326	0.0309055
$913$	37.0686	1.22679
$914$	−0.974530	−0.0322346
$915$	3.44789	0.113984
$916$	−16.9819	−0.561097
$917$	0	0
$918$	−3.54554	−0.117020
$919$	33.2871	1.09804	0.549020	−	0.835809i	$-0.315001\pi$
$919$	33.2871	1.09804	0.549020	+	0.835809i	$0.315001\pi$
$920$	−4.03188	−0.132927
$921$	−25.7014	−0.846891
$922$	−3.50706	−0.115499
$923$	−101.960	−3.35605
$924$	0	0
$925$	35.0594	1.15275
$926$	−35.4669	−1.16551
$927$	−12.2443	−0.402155
$928$	−6.83077	−0.224231
$929$	49.8856	1.63669	0.818346	−	0.574726i	$-0.194891\pi$
$929$	49.8856	1.63669	0.818346	+	0.574726i	$0.194891\pi$
$930$	−8.92393	−0.292627
$931$	0	0
$932$	−0.196213	−0.00642716
$933$	12.2010	0.399443
$934$	−59.2309	−1.93810
$935$	15.5356	0.508067
$936$	14.6647	0.479329
$937$	10.0550	0.328481	0.164241	−	0.986420i	$-0.447483\pi$
$937$	10.0550	0.328481	0.164241	+	0.986420i	$0.447483\pi$
$938$	0	0
$939$	13.5275	0.441452
$940$	5.83161	0.190206
$941$	0.902873	0.0294328	0.0147164	−	0.999892i	$-0.495315\pi$
$941$	0.902873	0.0294328	0.0147164	+	0.999892i	$0.495315\pi$
$942$	4.84257	0.157779
$943$	−1.56671	−0.0510190
$944$	−31.9668	−1.04043
$945$	0	0
$946$	32.3713	1.05248
$947$	8.29979	0.269707	0.134853	−	0.990866i	$-0.456944\pi$
$947$	8.29979	0.269707	0.134853	+	0.990866i	$0.456944\pi$
$948$	8.84615	0.287310
$949$	−7.59663	−0.246597
$950$	1.12027	0.0363463
$951$	25.3356	0.821564
$952$	0	0
$953$	15.6761	0.507799	0.253899	−	0.967231i	$-0.418287\pi$
$953$	15.6761	0.507799	0.253899	+	0.967231i	$0.418287\pi$
$954$	13.2296	0.428324
$955$	−7.22893	−0.233923
$956$	−16.7265	−0.540974
$957$	11.2595	0.363968
$958$	55.1017	1.78026
$959$	0	0
$960$	4.50533	0.145409
$961$	−9.84135	−0.317463
$962$	107.897	3.47874
$963$	6.76869	0.218118
$964$	−4.83701	−0.155790
$965$	−10.0541	−0.323654
$966$	0	0
$967$	−15.4670	−0.497385	−0.248693	−	0.968582i	$-0.580001\pi$
$967$	−15.4670	−0.497385	−0.248693	+	0.968582i	$0.580001\pi$
$968$	55.2229	1.77493
$969$	0.413585	0.0132863
$970$	13.2455	0.425289
$971$	23.3623	0.749731	0.374865	−	0.927079i	$-0.377689\pi$
$971$	23.3623	0.749731	0.374865	+	0.927079i	$0.377689\pi$
$972$	−0.673497	−0.0216024
$973$	0	0
$974$	26.2201	0.840146
$975$	24.2875	0.777823
$976$	−14.2197	−0.455163
$977$	−46.8664	−1.49939	−0.749695	−	0.661784i	$-0.769800\pi$
$977$	−46.8664	−1.49939	−0.749695	+	0.661784i	$0.769800\pi$
$978$	−17.4877	−0.559195
$979$	−52.0704	−1.66418
$980$	0	0
$981$	−9.13962	−0.291806
$982$	−15.8145	−0.504660
$983$	32.4502	1.03500	0.517501	−	0.855683i	$-0.326863\pi$
$983$	32.4502	1.03500	0.517501	+	0.855683i	$0.326863\pi$
$984$	2.16894	0.0691434
$985$	3.60369	0.114823
$986$	−6.61132	−0.210547
$987$	0	0
$988$	0.868525	0.0276315
$989$	−5.13683	−0.163342
$990$	11.7145	0.372312
$991$	−43.7943	−1.39117	−0.695586	−	0.718443i	$-0.744855\pi$
$991$	−43.7943	−1.39117	−0.695586	+	0.718443i	$0.744855\pi$
$992$	16.8503	0.534997
$993$	14.6290	0.464238
$994$	0	0
$995$	12.6335	0.400510
$996$	−4.13455	−0.131008
$997$	−13.6442	−0.432116	−0.216058	−	0.976381i	$-0.569320\pi$
$997$	−13.6442	−0.432116	−0.216058	+	0.976381i	$0.569320\pi$
$998$	12.7445	0.403419
$999$	9.75991	0.308790

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bl.1.5	✓	16
7.6	odd	2		6027.2.a.bm.1.5	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6027.2.a.bl.1.5	✓	16	1.1	even	1	trivial
6027.2.a.bm.1.5	yes	16	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.63508 q^{2} -1.00000 q^{3} +0.673497 q^{4} -1.18651 q^{5} +1.63508 q^{6} +2.16894 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.63508 q^{2} -1.00000 q^{3} +0.673497 q^{4} -1.18651 q^{5} +1.63508 q^{6} +2.16894 q^{8} +1.00000 q^{9} +1.94005 q^{10} +6.03827 q^{11} -0.673497 q^{12} +6.76120 q^{13} +1.18651 q^{15} -4.89340 q^{16} -2.16841 q^{17} -1.63508 q^{18} +0.190732 q^{19} -0.799112 q^{20} -9.87308 q^{22} +1.56671 q^{23} -2.16894 q^{24} -3.59219 q^{25} -11.0551 q^{26} -1.00000 q^{27} -1.86469 q^{29} -1.94005 q^{30} +4.59985 q^{31} +3.66322 q^{32} -6.03827 q^{33} +3.54554 q^{34} +0.673497 q^{36} -9.75991 q^{37} -0.311862 q^{38} -6.76120 q^{39} -2.57348 q^{40} -1.00000 q^{41} -3.27874 q^{43} +4.06676 q^{44} -1.18651 q^{45} -2.56169 q^{46} -7.29761 q^{47} +4.89340 q^{48} +5.87353 q^{50} +2.16841 q^{51} +4.55365 q^{52} -8.09108 q^{53} +1.63508 q^{54} -7.16449 q^{55} -0.190732 q^{57} +3.04892 q^{58} +6.53265 q^{59} +0.799112 q^{60} +2.90591 q^{61} -7.52114 q^{62} +3.79712 q^{64} -8.02225 q^{65} +9.87308 q^{66} -10.5427 q^{67} -1.46042 q^{68} -1.56671 q^{69} -15.0801 q^{71} +2.16894 q^{72} -1.12356 q^{73} +15.9583 q^{74} +3.59219 q^{75} +0.128457 q^{76} +11.0551 q^{78} -13.1347 q^{79} +5.80607 q^{80} +1.00000 q^{81} +1.63508 q^{82} +6.13893 q^{83} +2.57285 q^{85} +5.36102 q^{86} +1.86469 q^{87} +13.0967 q^{88} -8.62339 q^{89} +1.94005 q^{90} +1.05517 q^{92} -4.59985 q^{93} +11.9322 q^{94} -0.226306 q^{95} -3.66322 q^{96} +6.82744 q^{97} +6.03827 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 16 q^{3} + 12 q^{4} + 12 q^{5} + 4 q^{6} - 12 q^{8} + 16 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 - 16 * q^3 + 12 * q^4 + 12 * q^5 + 4 * q^6 - 12 * q^8 + 16 * q^9	\( 16 q - 4 q^{2} - 16 q^{3} + 12 q^{4} + 12 q^{5} + 4 q^{6} - 12 q^{8} + 16 q^{9} + 4 q^{10} - 4 q^{11} - 12 q^{12} - 12 q^{15} + 8 q^{17} - 4 q^{18} - 4 q^{19} + 20 q^{20} - 16 q^{22} - 12 q^{23} + 12 q^{24} - 8 q^{25} + 8 q^{26} - 16 q^{27} - 16 q^{29} - 4 q^{30} + 4 q^{31} - 48 q^{32} + 4 q^{33} - 16 q^{34} + 12 q^{36} - 48 q^{37} + 4 q^{38} - 56 q^{40} - 16 q^{41} - 16 q^{43} + 12 q^{45} - 4 q^{46} + 36 q^{47} - 8 q^{50} - 8 q^{51} - 60 q^{53} + 4 q^{54} - 8 q^{55} + 4 q^{57} - 36 q^{58} + 36 q^{59} - 20 q^{60} + 4 q^{61} + 12 q^{62} + 52 q^{64} - 36 q^{65} + 16 q^{66} - 52 q^{67} + 8 q^{68} + 12 q^{69} - 12 q^{71} - 12 q^{72} + 16 q^{73} + 4 q^{74} + 8 q^{75} - 16 q^{76} - 8 q^{78} - 36 q^{79} + 68 q^{80} + 16 q^{81} + 4 q^{82} + 32 q^{83} - 28 q^{85} - 8 q^{86} + 16 q^{87} - 36 q^{88} + 12 q^{89} + 4 q^{90} - 36 q^{92} - 4 q^{93} - 24 q^{94} - 20 q^{95} + 48 q^{96} - 48 q^{97} - 4 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 16 * q^3 + 12 * q^4 + 12 * q^5 + 4 * q^6 - 12 * q^8 + 16 * q^9 + 4 * q^10 - 4 * q^11 - 12 * q^12 - 12 * q^15 + 8 * q^17 - 4 * q^18 - 4 * q^19 + 20 * q^20 - 16 * q^22 - 12 * q^23 + 12 * q^24 - 8 * q^25 + 8 * q^26 - 16 * q^27 - 16 * q^29 - 4 * q^30 + 4 * q^31 - 48 * q^32 + 4 * q^33 - 16 * q^34 + 12 * q^36 - 48 * q^37 + 4 * q^38 - 56 * q^40 - 16 * q^41 - 16 * q^43 + 12 * q^45 - 4 * q^46 + 36 * q^47 - 8 * q^50 - 8 * q^51 - 60 * q^53 + 4 * q^54 - 8 * q^55 + 4 * q^57 - 36 * q^58 + 36 * q^59 - 20 * q^60 + 4 * q^61 + 12 * q^62 + 52 * q^64 - 36 * q^65 + 16 * q^66 - 52 * q^67 + 8 * q^68 + 12 * q^69 - 12 * q^71 - 12 * q^72 + 16 * q^73 + 4 * q^74 + 8 * q^75 - 16 * q^76 - 8 * q^78 - 36 * q^79 + 68 * q^80 + 16 * q^81 + 4 * q^82 + 32 * q^83 - 28 * q^85 - 8 * q^86 + 16 * q^87 - 36 * q^88 + 12 * q^89 + 4 * q^90 - 36 * q^92 - 4 * q^93 - 24 * q^94 - 20 * q^95 + 48 * q^96 - 48 * q^97 - 4 * q^99

Introduction

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