LMFDB - Embedded newform 6762.2.a.cp.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6762,2,Mod(1,6762)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6762, 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("6762.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6762.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:	$53.9948418468$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.42048.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 13x^{2} + 8x + 34 $ x^4 - 2x^3 - 13x^2 + 8*x + 34
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 966)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.94433$ of defining polynomial
Character	$\chi$	$=$	6762.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.82843 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.82843 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -3.82843 q^{10} +5.27981 q^{11} +1.00000 q^{12} +4.35854 q^{13} -3.82843 q^{15} +1.00000 q^{16} -2.46988 q^{17} +1.00000 q^{18} -1.92127 q^{19} -3.82843 q^{20} +5.27981 q^{22} +1.00000 q^{23} +1.00000 q^{24} +9.65685 q^{25} +4.35854 q^{26} +1.00000 q^{27} -1.35854 q^{29} -3.82843 q^{30} -1.43727 q^{31} +1.00000 q^{32} +5.27981 q^{33} -2.46988 q^{34} +1.00000 q^{36} +6.63836 q^{37} -1.92127 q^{38} +4.35854 q^{39} -3.82843 q^{40} +1.92127 q^{41} -8.21648 q^{43} +5.27981 q^{44} -3.82843 q^{45} +1.00000 q^{46} -6.99690 q^{47} +1.00000 q^{48} +9.65685 q^{50} -2.46988 q^{51} +4.35854 q^{52} -2.88866 q^{53} +1.00000 q^{54} -20.2134 q^{55} -1.92127 q^{57} -1.35854 q^{58} +4.29831 q^{59} -3.82843 q^{60} +11.4342 q^{61} -1.43727 q^{62} +1.00000 q^{64} -16.6864 q^{65} +5.27981 q^{66} +5.33092 q^{67} -2.46988 q^{68} +1.00000 q^{69} +7.64146 q^{71} +1.00000 q^{72} -0.437273 q^{73} +6.63836 q^{74} +9.65685 q^{75} -1.92127 q^{76} +4.35854 q^{78} +1.35854 q^{79} -3.82843 q^{80} +1.00000 q^{81} +1.92127 q^{82} -4.37704 q^{83} +9.45577 q^{85} -8.21648 q^{86} -1.35854 q^{87} +5.27981 q^{88} -12.2952 q^{89} -3.82843 q^{90} +1.00000 q^{92} -1.43727 q^{93} -6.99690 q^{94} +7.35544 q^{95} +1.00000 q^{96} +0.298311 q^{97} +5.27981 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^5 + 4 * q^6 + 4 * q^8 + 4 * q^9	$ 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{8} + 4 q^{9} - 4 q^{10} + 6 q^{11} + 4 q^{12} + 6 q^{13} - 4 q^{15} + 4 q^{16} - 10 q^{17} + 4 q^{18} - 4 q^{19} - 4 q^{20} + 6 q^{22} + 4 q^{23} + 4 q^{24} + 16 q^{25} + 6 q^{26} + 4 q^{27} + 6 q^{29} - 4 q^{30} + 2 q^{31} + 4 q^{32} + 6 q^{33} - 10 q^{34} + 4 q^{36} - 4 q^{38} + 6 q^{39} - 4 q^{40} + 4 q^{41} + 20 q^{43} + 6 q^{44} - 4 q^{45} + 4 q^{46} + 10 q^{47} + 4 q^{48} + 16 q^{50} - 10 q^{51} + 6 q^{52} + 4 q^{54} + 10 q^{55} - 4 q^{57} + 6 q^{58} + 6 q^{59} - 4 q^{60} + 2 q^{62} + 4 q^{64} - 14 q^{65} + 6 q^{66} + 18 q^{67} - 10 q^{68} + 4 q^{69} + 42 q^{71} + 4 q^{72} + 6 q^{73} + 16 q^{75} - 4 q^{76} + 6 q^{78} - 6 q^{79} - 4 q^{80} + 4 q^{81} + 4 q^{82} - 10 q^{83} + 34 q^{85} + 20 q^{86} + 6 q^{87} + 6 q^{88} - 4 q^{90} + 4 q^{92} + 2 q^{93} + 10 q^{94} - 20 q^{95} + 4 q^{96} - 10 q^{97} + 6 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^5 + 4 * q^6 + 4 * q^8 + 4 * q^9 - 4 * q^10 + 6 * q^11 + 4 * q^12 + 6 * q^13 - 4 * q^15 + 4 * q^16 - 10 * q^17 + 4 * q^18 - 4 * q^19 - 4 * q^20 + 6 * q^22 + 4 * q^23 + 4 * q^24 + 16 * q^25 + 6 * q^26 + 4 * q^27 + 6 * q^29 - 4 * q^30 + 2 * q^31 + 4 * q^32 + 6 * q^33 - 10 * q^34 + 4 * q^36 - 4 * q^38 + 6 * q^39 - 4 * q^40 + 4 * q^41 + 20 * q^43 + 6 * q^44 - 4 * q^45 + 4 * q^46 + 10 * q^47 + 4 * q^48 + 16 * q^50 - 10 * q^51 + 6 * q^52 + 4 * q^54 + 10 * q^55 - 4 * q^57 + 6 * q^58 + 6 * q^59 - 4 * q^60 + 2 * q^62 + 4 * q^64 - 14 * q^65 + 6 * q^66 + 18 * q^67 - 10 * q^68 + 4 * q^69 + 42 * q^71 + 4 * q^72 + 6 * q^73 + 16 * q^75 - 4 * q^76 + 6 * q^78 - 6 * q^79 - 4 * q^80 + 4 * q^81 + 4 * q^82 - 10 * q^83 + 34 * q^85 + 20 * q^86 + 6 * q^87 + 6 * q^88 - 4 * q^90 + 4 * q^92 + 2 * q^93 + 10 * q^94 - 20 * q^95 + 4 * q^96 - 10 * q^97 + 6 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−3.82843	−1.71212	−0.856062	−	0.516873i	$-0.827096\pi$
$5$	−3.82843	−1.71212	−0.856062	+	0.516873i	$0.827096\pi$
$6$	1.00000	0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−3.82843	−1.21065
$11$	5.27981	1.59192	0.795962	−	0.605347i	$-0.206966\pi$
$11$	5.27981	1.59192	0.795962	+	0.605347i	$0.206966\pi$
$12$	1.00000	0.288675
$13$	4.35854	1.20884	0.604421	−	0.796665i	$-0.293404\pi$
$13$	4.35854	1.20884	0.604421	+	0.796665i	$0.293404\pi$
$14$	0	0
$15$	−3.82843	−0.988496
$16$	1.00000	0.250000
$17$	−2.46988	−0.599035	−0.299517	−	0.954091i	$-0.596826\pi$
$17$	−2.46988	−0.599035	−0.299517	+	0.954091i	$0.596826\pi$
$18$	1.00000	0.235702
$19$	−1.92127	−0.440770	−0.220385	−	0.975413i	$-0.570731\pi$
$19$	−1.92127	−0.440770	−0.220385	+	0.975413i	$0.570731\pi$
$20$	−3.82843	−0.856062
$21$	0	0
$22$	5.27981	1.12566
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	1.00000	0.204124
$25$	9.65685	1.93137
$26$	4.35854	0.854781
$27$	1.00000	0.192450
$28$	0	0
$29$	−1.35854	−0.252275	−0.126138	−	0.992013i	$-0.540258\pi$
$29$	−1.35854	−0.252275	−0.126138	+	0.992013i	$0.540258\pi$
$30$	−3.82843	−0.698972
$31$	−1.43727	−0.258142	−0.129071	−	0.991635i	$-0.541199\pi$
$31$	−1.43727	−0.258142	−0.129071	+	0.991635i	$0.541199\pi$
$32$	1.00000	0.176777
$33$	5.27981	0.919098
$34$	−2.46988	−0.423582
$35$	0	0
$36$	1.00000	0.166667
$37$	6.63836	1.09134	0.545670	−	0.838000i	$-0.316275\pi$
$37$	6.63836	1.09134	0.545670	+	0.838000i	$0.316275\pi$
$38$	−1.92127	−0.311671
$39$	4.35854	0.697926
$40$	−3.82843	−0.605327
$41$	1.92127	0.300052	0.150026	−	0.988682i	$-0.452064\pi$
$41$	1.92127	0.300052	0.150026	+	0.988682i	$0.452064\pi$
$42$	0	0
$43$	−8.21648	−1.25300	−0.626501	−	0.779421i	$-0.715514\pi$
$43$	−8.21648	−1.25300	−0.626501	+	0.779421i	$0.715514\pi$
$44$	5.27981	0.795962
$45$	−3.82843	−0.570708
$46$	1.00000	0.147442
$47$	−6.99690	−1.02060	−0.510301	−	0.859996i	$-0.670466\pi$
$47$	−6.99690	−1.02060	−0.510301	+	0.859996i	$0.670466\pi$
$48$	1.00000	0.144338
$49$	0	0
$50$	9.65685	1.36569
$51$	−2.46988	−0.345853
$52$	4.35854	0.604421
$53$	−2.88866	−0.396788	−0.198394	−	0.980122i	$-0.563573\pi$
$53$	−2.88866	−0.396788	−0.198394	+	0.980122i	$0.563573\pi$
$54$	1.00000	0.136083
$55$	−20.2134	−2.72557
$56$	0	0
$57$	−1.92127	−0.254479
$58$	−1.35854	−0.178385
$59$	4.29831	0.559592	0.279796	−	0.960059i	$-0.409733\pi$
$59$	4.29831	0.559592	0.279796	+	0.960059i	$0.409733\pi$
$60$	−3.82843	−0.494248
$61$	11.4342	1.46400	0.731998	−	0.681307i	$-0.238588\pi$
$61$	11.4342	1.46400	0.731998	+	0.681307i	$0.238588\pi$
$62$	−1.43727	−0.182534
$63$	0	0
$64$	1.00000	0.125000
$65$	−16.6864	−2.06969
$66$	5.27981	0.649900
$67$	5.33092	0.651276	0.325638	−	0.945495i	$-0.394421\pi$
$67$	5.33092	0.651276	0.325638	+	0.945495i	$0.394421\pi$
$68$	−2.46988	−0.299517
$69$	1.00000	0.120386
$70$	0	0
$71$	7.64146	0.906874	0.453437	−	0.891288i	$-0.350198\pi$
$71$	7.64146	0.906874	0.453437	+	0.891288i	$0.350198\pi$
$72$	1.00000	0.117851
$73$	−0.437273	−0.0511789	−0.0255895	−	0.999673i	$-0.508146\pi$
$73$	−0.437273	−0.0511789	−0.0255895	+	0.999673i	$0.508146\pi$
$74$	6.63836	0.771693
$75$	9.65685	1.11508
$76$	−1.92127	−0.220385
$77$	0	0
$78$	4.35854	0.493508
$79$	1.35854	0.152848	0.0764240	−	0.997075i	$-0.475650\pi$
$79$	1.35854	0.152848	0.0764240	+	0.997075i	$0.475650\pi$
$80$	−3.82843	−0.428031
$81$	1.00000	0.111111
$82$	1.92127	0.212169
$83$	−4.37704	−0.480443	−0.240221	−	0.970718i	$-0.577220\pi$
$83$	−4.37704	−0.480443	−0.240221	+	0.970718i	$0.577220\pi$
$84$	0	0
$85$	9.45577	1.02562
$86$	−8.21648	−0.886006
$87$	−1.35854	−0.145651
$88$	5.27981	0.562830
$89$	−12.2952	−1.30329	−0.651645	−	0.758524i	$-0.725921\pi$
$89$	−12.2952	−1.30329	−0.651645	+	0.758524i	$0.725921\pi$
$90$	−3.82843	−0.403552
$91$	0	0
$92$	1.00000	0.104257
$93$	−1.43727	−0.149038
$94$	−6.99690	−0.721675
$95$	7.35544	0.754653
$96$	1.00000	0.102062
$97$	0.298311	0.0302889	0.0151444	−	0.999885i	$-0.495179\pi$
$97$	0.298311	0.0302889	0.0151444	+	0.999885i	$0.495179\pi$
$98$	0	0
$99$	5.27981	0.530641
$100$	9.65685	0.965685
$101$	18.0590	1.79694	0.898470	−	0.439035i	$-0.144680\pi$
$101$	18.0590	1.79694	0.898470	+	0.439035i	$0.144680\pi$
$102$	−2.46988	−0.244555
$103$	−0.669078	−0.0659263	−0.0329631	−	0.999457i	$-0.510494\pi$
$103$	−0.669078	−0.0659263	−0.0329631	+	0.999457i	$0.510494\pi$
$104$	4.35854	0.427390
$105$	0	0
$106$	−2.88866	−0.280571
$107$	−18.4361	−1.78228	−0.891141	−	0.453727i	$-0.850094\pi$
$107$	−18.4361	−1.78228	−0.891141	+	0.453727i	$0.850094\pi$
$108$	1.00000	0.0962250
$109$	16.5314	1.58342	0.791710	−	0.610896i	$-0.209191\pi$
$109$	16.5314	1.58342	0.791710	+	0.610896i	$0.209191\pi$
$110$	−20.2134	−1.92727
$111$	6.63836	0.630085
$112$	0	0
$113$	19.7466	1.85760	0.928802	−	0.370577i	$-0.120840\pi$
$113$	19.7466	1.85760	0.928802	+	0.370577i	$0.120840\pi$
$114$	−1.92127	−0.179943
$115$	−3.82843	−0.357003
$116$	−1.35854	−0.126138
$117$	4.35854	0.402947
$118$	4.29831	0.395692
$119$	0	0
$120$	−3.82843	−0.349486
$121$	16.8764	1.53422
$122$	11.4342	1.03520
$123$	1.92127	0.173235
$124$	−1.43727	−0.129071
$125$	−17.8284	−1.59462
$126$	0	0
$127$	18.9367	1.68036	0.840179	−	0.542310i	$-0.182450\pi$
$127$	18.9367	1.68036	0.840179	+	0.542310i	$0.182450\pi$
$128$	1.00000	0.0883883
$129$	−8.21648	−0.723421
$130$	−16.6864	−1.46349
$131$	16.3554	1.42898	0.714491	−	0.699645i	$-0.246658\pi$
$131$	16.3554	1.42898	0.714491	+	0.699645i	$0.246658\pi$
$132$	5.27981	0.459549
$133$	0	0
$134$	5.33092	0.460521
$135$	−3.82843	−0.329499
$136$	−2.46988	−0.211791
$137$	−5.10824	−0.436426	−0.218213	−	0.975901i	$-0.570023\pi$
$137$	−5.10824	−0.436426	−0.218213	+	0.975901i	$0.570023\pi$
$138$	1.00000	0.0851257
$139$	9.31371	0.789978	0.394989	−	0.918686i	$-0.370748\pi$
$139$	9.31371	0.789978	0.394989	+	0.918686i	$0.370748\pi$
$140$	0	0
$141$	−6.99690	−0.589245
$142$	7.64146	0.641257
$143$	23.0123	1.92439
$144$	1.00000	0.0833333
$145$	5.20108	0.431927
$146$	−0.437273	−0.0361890
$147$	0	0
$148$	6.63836	0.545670
$149$	2.23370	0.182991	0.0914957	−	0.995805i	$-0.470835\pi$
$149$	2.23370	0.182991	0.0914957	+	0.995805i	$0.470835\pi$
$150$	9.65685	0.788479
$151$	−22.2134	−1.80770	−0.903850	−	0.427850i	$-0.859271\pi$
$151$	−22.2134	−1.80770	−0.903850	+	0.427850i	$0.859271\pi$
$152$	−1.92127	−0.155836
$153$	−2.46988	−0.199678
$154$	0	0
$155$	5.50249	0.441971
$156$	4.35854	0.348963
$157$	10.5731	0.843828	0.421914	−	0.906636i	$-0.361358\pi$
$157$	10.5731	0.843828	0.421914	+	0.906636i	$0.361358\pi$
$158$	1.35854	0.108080
$159$	−2.88866	−0.229086
$160$	−3.82843	−0.302664
$161$	0	0
$162$	1.00000	0.0785674
$163$	19.7294	1.54532	0.772662	−	0.634817i	$-0.218925\pi$
$163$	19.7294	1.54532	0.772662	+	0.634817i	$0.218925\pi$
$164$	1.92127	0.150026
$165$	−20.2134	−1.57361
$166$	−4.37704	−0.339724
$167$	10.6907	0.827275	0.413637	−	0.910442i	$-0.364258\pi$
$167$	10.6907	0.827275	0.413637	+	0.910442i	$0.364258\pi$
$168$	0	0
$169$	5.99690	0.461300
$170$	9.45577	0.725224
$171$	−1.92127	−0.146923
$172$	−8.21648	−0.626501
$173$	22.0308	1.67497	0.837485	−	0.546460i	$-0.184025\pi$
$173$	22.0308	1.67497	0.837485	+	0.546460i	$0.184025\pi$
$174$	−1.35854	−0.102991
$175$	0	0
$176$	5.27981	0.397981
$177$	4.29831	0.323081
$178$	−12.2952	−0.921565
$179$	−16.9969	−1.27041	−0.635204	−	0.772344i	$-0.719084\pi$
$179$	−16.9969	−1.27041	−0.635204	+	0.772344i	$0.719084\pi$
$180$	−3.82843	−0.285354
$181$	−12.4022	−0.921846	−0.460923	−	0.887440i	$-0.652482\pi$
$181$	−12.4022	−0.921846	−0.460923	+	0.887440i	$0.652482\pi$
$182$	0	0
$183$	11.4342	0.845238
$184$	1.00000	0.0737210
$185$	−25.4145	−1.86851
$186$	−1.43727	−0.105386
$187$	−13.0405	−0.953618
$188$	−6.99690	−0.510301
$189$	0	0
$190$	7.35544	0.533620
$191$	−16.6384	−1.20391	−0.601955	−	0.798530i	$-0.705611\pi$
$191$	−16.6384	−1.20391	−0.601955	+	0.798530i	$0.705611\pi$
$192$	1.00000	0.0721688
$193$	25.2165	1.81512	0.907561	−	0.419920i	$-0.137942\pi$
$193$	25.2165	1.81512	0.907561	+	0.419920i	$0.137942\pi$
$194$	0.298311	0.0214175
$195$	−16.6864	−1.19494
$196$	0	0
$197$	13.6199	0.970375	0.485187	−	0.874410i	$-0.338751\pi$
$197$	13.6199	0.970375	0.485187	+	0.874410i	$0.338751\pi$
$198$	5.27981	0.375220
$199$	−0.902774	−0.0639959	−0.0319980	−	0.999488i	$-0.510187\pi$
$199$	−0.902774	−0.0639959	−0.0319980	+	0.999488i	$0.510187\pi$
$200$	9.65685	0.682843
$201$	5.33092	0.376014
$202$	18.0590	1.27063
$203$	0	0
$204$	−2.46988	−0.172926
$205$	−7.35544	−0.513727
$206$	−0.669078	−0.0466169
$207$	1.00000	0.0695048
$208$	4.35854	0.302211
$209$	−10.1440	−0.701672
$210$	0	0
$211$	−22.8131	−1.57052	−0.785259	−	0.619167i	$-0.787470\pi$
$211$	−22.8131	−1.57052	−0.785259	+	0.619167i	$0.787470\pi$
$212$	−2.88866	−0.198394
$213$	7.64146	0.523584
$214$	−18.4361	−1.26026
$215$	31.4562	2.14530
$216$	1.00000	0.0680414
$217$	0	0
$218$	16.5314	1.11965
$219$	−0.437273	−0.0295482
$220$	−20.2134	−1.36279
$221$	−10.7651	−0.724139
$222$	6.63836	0.445537
$223$	−0.942867	−0.0631390	−0.0315695	−	0.999502i	$-0.510051\pi$
$223$	−0.942867	−0.0631390	−0.0315695	+	0.999502i	$0.510051\pi$
$224$	0	0
$225$	9.65685	0.643790
$226$	19.7466	1.31352
$227$	15.3106	1.01620	0.508100	−	0.861298i	$-0.330348\pi$
$227$	15.3106	1.01620	0.508100	+	0.861298i	$0.330348\pi$
$228$	−1.92127	−0.127239
$229$	−6.07873	−0.401694	−0.200847	−	0.979623i	$-0.564369\pi$
$229$	−6.07873	−0.401694	−0.200847	+	0.979623i	$0.564369\pi$
$230$	−3.82843	−0.252439
$231$	0	0
$232$	−1.35854	−0.0891927
$233$	−7.57812	−0.496459	−0.248230	−	0.968701i	$-0.579849\pi$
$233$	−7.57812	−0.496459	−0.248230	+	0.968701i	$0.579849\pi$
$234$	4.35854	0.284927
$235$	26.7871	1.74740
$236$	4.29831	0.279796
$237$	1.35854	0.0882469
$238$	0	0
$239$	−16.4330	−1.06296	−0.531480	−	0.847071i	$-0.678364\pi$
$239$	−16.4330	−1.06296	−0.531480	+	0.847071i	$0.678364\pi$
$240$	−3.82843	−0.247124
$241$	−13.2319	−0.852340	−0.426170	−	0.904643i	$-0.640138\pi$
$241$	−13.2319	−0.852340	−0.426170	+	0.904643i	$0.640138\pi$
$242$	16.8764	1.08486
$243$	1.00000	0.0641500
$244$	11.4342	0.731998
$245$	0	0
$246$	1.92127	0.122496
$247$	−8.37394	−0.532821
$248$	−1.43727	−0.0912669
$249$	−4.37704	−0.277384
$250$	−17.8284	−1.12757
$251$	9.87644	0.623395	0.311698	−	0.950181i	$-0.399102\pi$
$251$	9.87644	0.623395	0.311698	+	0.950181i	$0.399102\pi$
$252$	0	0
$253$	5.27981	0.331939
$254$	18.9367	1.18819
$255$	9.45577	0.592143
$256$	1.00000	0.0625000
$257$	−21.3554	−1.33212	−0.666058	−	0.745900i	$-0.732020\pi$
$257$	−21.3554	−1.33212	−0.666058	+	0.745900i	$0.732020\pi$
$258$	−8.21648	−0.511536
$259$	0	0
$260$	−16.6864	−1.03484
$261$	−1.35854	−0.0840917
$262$	16.3554	1.01044
$263$	8.68009	0.535237	0.267619	−	0.963525i	$-0.413763\pi$
$263$	8.68009	0.535237	0.267619	+	0.963525i	$0.413763\pi$
$264$	5.27981	0.324950
$265$	11.0590	0.679350
$266$	0	0
$267$	−12.2952	−0.752455
$268$	5.33092	0.325638
$269$	−26.0142	−1.58611	−0.793057	−	0.609148i	$-0.791512\pi$
$269$	−26.0142	−1.58611	−0.793057	+	0.609148i	$0.791512\pi$
$270$	−3.82843	−0.232991
$271$	1.43727	0.0873081	0.0436541	−	0.999047i	$-0.486100\pi$
$271$	1.43727	0.0873081	0.0436541	+	0.999047i	$0.486100\pi$
$272$	−2.46988	−0.149759
$273$	0	0
$274$	−5.10824	−0.308600
$275$	50.9864	3.07460
$276$	1.00000	0.0601929
$277$	18.0289	1.08325	0.541626	−	0.840620i	$-0.317809\pi$
$277$	18.0289	1.08325	0.541626	+	0.840620i	$0.317809\pi$
$278$	9.31371	0.558599
$279$	−1.43727	−0.0860473
$280$	0	0
$281$	24.9643	1.48924	0.744622	−	0.667486i	$-0.232630\pi$
$281$	24.9643	1.48924	0.744622	+	0.667486i	$0.232630\pi$
$282$	−6.99690	−0.416659
$283$	2.73430	0.162537	0.0812686	−	0.996692i	$-0.474103\pi$
$283$	2.73430	0.162537	0.0812686	+	0.996692i	$0.474103\pi$
$284$	7.64146	0.453437
$285$	7.35544	0.435699
$286$	23.0123	1.36075
$287$	0	0
$288$	1.00000	0.0589256
$289$	−10.8997	−0.641157
$290$	5.20108	0.305418
$291$	0.298311	0.0174873
$292$	−0.437273	−0.0255895
$293$	−14.5147	−0.847959	−0.423979	−	0.905672i	$-0.639367\pi$
$293$	−14.5147	−0.847959	−0.423979	+	0.905672i	$0.639367\pi$
$294$	0	0
$295$	−16.4558	−0.958092
$296$	6.63836	0.385847
$297$	5.27981	0.306366
$298$	2.23370	0.129394
$299$	4.35854	0.252061
$300$	9.65685	0.557539
$301$	0	0
$302$	−22.2134	−1.27824
$303$	18.0590	1.03746
$304$	−1.92127	−0.110192
$305$	−43.7749	−2.50654
$306$	−2.46988	−0.141194
$307$	31.9521	1.82360	0.911800	−	0.410634i	$-0.134693\pi$
$307$	31.9521	1.82360	0.911800	+	0.410634i	$0.134693\pi$
$308$	0	0
$309$	−0.669078	−0.0380625
$310$	5.50249	0.312521
$311$	31.0142	1.75865	0.879327	−	0.476219i	$-0.157993\pi$
$311$	31.0142	1.75865	0.879327	+	0.476219i	$0.157993\pi$
$312$	4.35854	0.246754
$313$	−6.57623	−0.371711	−0.185855	−	0.982577i	$-0.559506\pi$
$313$	−6.57623	−0.371711	−0.185855	+	0.982577i	$0.559506\pi$
$314$	10.5731	0.596677
$315$	0	0
$316$	1.35854	0.0764240
$317$	−28.0142	−1.57343	−0.786717	−	0.617314i	$-0.788221\pi$
$317$	−28.0142	−1.57343	−0.786717	+	0.617314i	$0.788221\pi$
$318$	−2.88866	−0.161988
$319$	−7.17286	−0.401603
$320$	−3.82843	−0.214016
$321$	−18.4361	−1.02900
$322$	0	0
$323$	4.74531	0.264036
$324$	1.00000	0.0555556
$325$	42.0898	2.33472
$326$	19.7294	1.09271
$327$	16.5314	0.914189
$328$	1.92127	0.106084
$329$	0	0
$330$	−20.2134	−1.11271
$331$	24.8266	1.36459	0.682297	−	0.731075i	$-0.260981\pi$
$331$	24.8266	1.36459	0.682297	+	0.731075i	$0.260981\pi$
$332$	−4.37704	−0.240221
$333$	6.63836	0.363780
$334$	10.6907	0.584972
$335$	−20.4090	−1.11507
$336$	0	0
$337$	17.4176	0.948795	0.474398	−	0.880311i	$-0.342666\pi$
$337$	17.4176	0.948795	0.474398	+	0.880311i	$0.342666\pi$
$338$	5.99690	0.326188
$339$	19.7466	1.07249
$340$	9.45577	0.512811
$341$	−7.58853	−0.410942
$342$	−1.92127	−0.103890
$343$	0	0
$344$	−8.21648	−0.443003
$345$	−3.82843	−0.206116
$346$	22.0308	1.18438
$347$	−9.87145	−0.529927	−0.264964	−	0.964258i	$-0.585360\pi$
$347$	−9.87145	−0.529927	−0.264964	+	0.964258i	$0.585360\pi$
$348$	−1.35854	−0.0728256
$349$	33.9170	1.81553	0.907767	−	0.419475i	$-0.137786\pi$
$349$	33.9170	1.81553	0.907767	+	0.419475i	$0.137786\pi$
$350$	0	0
$351$	4.35854	0.232642
$352$	5.27981	0.281415
$353$	−7.35544	−0.391491	−0.195745	−	0.980655i	$-0.562713\pi$
$353$	−7.35544	−0.391491	−0.195745	+	0.980655i	$0.562713\pi$
$354$	4.29831	0.228453
$355$	−29.2548	−1.55268
$356$	−12.2952	−0.651645
$357$	0	0
$358$	−16.9969	−0.898314
$359$	15.1932	0.801869	0.400934	−	0.916107i	$-0.368686\pi$
$359$	15.1932	0.801869	0.400934	+	0.916107i	$0.368686\pi$
$360$	−3.82843	−0.201776
$361$	−15.3087	−0.805722
$362$	−12.4022	−0.651844
$363$	16.8764	0.885783
$364$	0	0
$365$	1.67407	0.0876247
$366$	11.4342	0.597674
$367$	8.34632	0.435674	0.217837	−	0.975985i	$-0.430100\pi$
$367$	8.34632	0.435674	0.217837	+	0.975985i	$0.430100\pi$
$368$	1.00000	0.0521286
$369$	1.92127	0.100017
$370$	−25.4145	−1.32124
$371$	0	0
$372$	−1.43727	−0.0745191
$373$	20.5596	1.06454	0.532269	−	0.846576i	$-0.321340\pi$
$373$	20.5596	1.06454	0.532269	+	0.846576i	$0.321340\pi$
$374$	−13.0405	−0.674310
$375$	−17.8284	−0.920656
$376$	−6.99690	−0.360838
$377$	−5.92127	−0.304961
$378$	0	0
$379$	−1.45139	−0.0745527	−0.0372764	−	0.999305i	$-0.511868\pi$
$379$	−1.45139	−0.0745527	−0.0372764	+	0.999305i	$0.511868\pi$
$380$	7.35544	0.377326
$381$	18.9367	0.970155
$382$	−16.6384	−0.851292
$383$	−29.4145	−1.50301	−0.751505	−	0.659728i	$-0.770672\pi$
$383$	−29.4145	−1.50301	−0.751505	+	0.659728i	$0.770672\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	25.2165	1.28349
$387$	−8.21648	−0.417667
$388$	0.298311	0.0151444
$389$	22.1513	1.12311	0.561557	−	0.827438i	$-0.310203\pi$
$389$	22.1513	1.12311	0.561557	+	0.827438i	$0.310203\pi$
$390$	−16.6864	−0.844947
$391$	−2.46988	−0.124907
$392$	0	0
$393$	16.3554	0.825023
$394$	13.6199	0.686159
$395$	−5.20108	−0.261695
$396$	5.27981	0.265321
$397$	−20.8567	−1.04677	−0.523385	−	0.852097i	$-0.675331\pi$
$397$	−20.8567	−1.04677	−0.523385	+	0.852097i	$0.675331\pi$
$398$	−0.902774	−0.0452520
$399$	0	0
$400$	9.65685	0.482843
$401$	−15.0430	−0.751213	−0.375606	−	0.926779i	$-0.622565\pi$
$401$	−15.0430	−0.751213	−0.375606	+	0.926779i	$0.622565\pi$
$402$	5.33092	0.265882
$403$	−6.26442	−0.312053
$404$	18.0590	0.898470
$405$	−3.82843	−0.190236
$406$	0	0
$407$	35.0493	1.73733
$408$	−2.46988	−0.122277
$409$	−19.0960	−0.944237	−0.472119	−	0.881535i	$-0.656511\pi$
$409$	−19.0960	−0.944237	−0.472119	+	0.881535i	$0.656511\pi$
$410$	−7.35544	−0.363259
$411$	−5.10824	−0.251971
$412$	−0.669078	−0.0329631
$413$	0	0
$414$	1.00000	0.0491473
$415$	16.7572	0.822578
$416$	4.35854	0.213695
$417$	9.31371	0.456094
$418$	−10.1440	−0.496157
$419$	−20.2165	−0.987640	−0.493820	−	0.869564i	$-0.664400\pi$
$419$	−20.2165	−0.987640	−0.493820	+	0.869564i	$0.664400\pi$
$420$	0	0
$421$	8.59662	0.418974	0.209487	−	0.977811i	$-0.432821\pi$
$421$	8.59662	0.418974	0.209487	+	0.977811i	$0.432821\pi$
$422$	−22.8131	−1.11052
$423$	−6.99690	−0.340201
$424$	−2.88866	−0.140286
$425$	−23.8513	−1.15696
$426$	7.64146	0.370230
$427$	0	0
$428$	−18.4361	−0.891141
$429$	23.0123	1.11104
$430$	31.4562	1.51695
$431$	36.0616	1.73703	0.868513	−	0.495667i	$-0.165076\pi$
$431$	36.0616	1.73703	0.868513	+	0.495667i	$0.165076\pi$
$432$	1.00000	0.0481125
$433$	7.56462	0.363532	0.181766	−	0.983342i	$-0.441819\pi$
$433$	7.56462	0.363532	0.181766	+	0.983342i	$0.441819\pi$
$434$	0	0
$435$	5.20108	0.249373
$436$	16.5314	0.791710
$437$	−1.92127	−0.0919068
$438$	−0.437273	−0.0208937
$439$	35.1470	1.67747	0.838736	−	0.544538i	$-0.183295\pi$
$439$	35.1470	1.67747	0.838736	+	0.544538i	$0.183295\pi$
$440$	−20.2134	−0.963635
$441$	0	0
$442$	−10.7651	−0.512043
$443$	−6.35544	−0.301956	−0.150978	−	0.988537i	$-0.548242\pi$
$443$	−6.35544	−0.301956	−0.150978	+	0.988537i	$0.548242\pi$
$444$	6.63836	0.315043
$445$	47.0713	2.23139
$446$	−0.942867	−0.0446460
$447$	2.23370	0.105650
$448$	0	0
$449$	−4.36043	−0.205782	−0.102891	−	0.994693i	$-0.532809\pi$
$449$	−4.36043	−0.205782	−0.102891	+	0.994693i	$0.532809\pi$
$450$	9.65685	0.455228
$451$	10.1440	0.477660
$452$	19.7466	0.928802
$453$	−22.2134	−1.04368
$454$	15.3106	0.718563
$455$	0	0
$456$	−1.92127	−0.0899717
$457$	−33.8567	−1.58375	−0.791876	−	0.610683i	$-0.790895\pi$
$457$	−33.8567	−1.58375	−0.791876	+	0.610683i	$0.790895\pi$
$458$	−6.07873	−0.284040
$459$	−2.46988	−0.115284
$460$	−3.82843	−0.178501
$461$	−17.6851	−0.823676	−0.411838	−	0.911257i	$-0.635113\pi$
$461$	−17.6851	−0.823676	−0.411838	+	0.911257i	$0.635113\pi$
$462$	0	0
$463$	35.5954	1.65426	0.827130	−	0.562011i	$-0.189972\pi$
$463$	35.5954	1.65426	0.827130	+	0.562011i	$0.189972\pi$
$464$	−1.35854	−0.0630688
$465$	5.50249	0.255172
$466$	−7.57812	−0.351050
$467$	−14.4022	−0.666453	−0.333226	−	0.942847i	$-0.608137\pi$
$467$	−14.4022	−0.666453	−0.333226	+	0.942847i	$0.608137\pi$
$468$	4.35854	0.201474
$469$	0	0
$470$	26.7871	1.23560
$471$	10.5731	0.487184
$472$	4.29831	0.197846
$473$	−43.3815	−1.99468
$474$	1.35854	0.0624000
$475$	−18.5534	−0.851290
$476$	0	0
$477$	−2.88866	−0.132263
$478$	−16.4330	−0.751626
$479$	−38.3542	−1.75245	−0.876225	−	0.481902i	$-0.839946\pi$
$479$	−38.3542	−1.75245	−0.876225	+	0.481902i	$0.839946\pi$
$480$	−3.82843	−0.174743
$481$	28.9336	1.31926
$482$	−13.2319	−0.602696
$483$	0	0
$484$	16.8764	0.767111
$485$	−1.14206	−0.0518583
$486$	1.00000	0.0453609
$487$	20.2504	0.917632	0.458816	−	0.888531i	$-0.348274\pi$
$487$	20.2504	0.917632	0.458816	+	0.888531i	$0.348274\pi$
$488$	11.4342	0.517601
$489$	19.7294	0.892194
$490$	0	0
$491$	−26.6459	−1.20251	−0.601257	−	0.799056i	$-0.705333\pi$
$491$	−26.6459	−1.20251	−0.601257	+	0.799056i	$0.705333\pi$
$492$	1.92127	0.0866176
$493$	3.35544	0.151122
$494$	−8.37394	−0.376761
$495$	−20.2134	−0.908524
$496$	−1.43727	−0.0645355
$497$	0	0
$498$	−4.37704	−0.196140
$499$	−13.0602	−0.584656	−0.292328	−	0.956318i	$-0.594430\pi$
$499$	−13.0602	−0.584656	−0.292328	+	0.956318i	$0.594430\pi$
$500$	−17.8284	−0.797311
$501$	10.6907	0.477627
$502$	9.87644	0.440807
$503$	−11.1525	−0.497264	−0.248632	−	0.968598i	$-0.579981\pi$
$503$	−11.1525	−0.497264	−0.248632	+	0.968598i	$0.579981\pi$
$504$	0	0
$505$	−69.1377	−3.07659
$506$	5.27981	0.234716
$507$	5.99690	0.266332
$508$	18.9367	0.840179
$509$	−11.8874	−0.526899	−0.263449	−	0.964673i	$-0.584860\pi$
$509$	−11.8874	−0.526899	−0.263449	+	0.964673i	$0.584860\pi$
$510$	9.45577	0.418709
$511$	0	0
$512$	1.00000	0.0441942
$513$	−1.92127	−0.0848262
$514$	−21.3554	−0.941948
$515$	2.56152	0.112874
$516$	−8.21648	−0.361710
$517$	−36.9423	−1.62472
$518$	0	0
$519$	22.0308	0.967045
$520$	−16.6864	−0.731746
$521$	25.4452	1.11477	0.557387	−	0.830253i	$-0.311804\pi$
$521$	25.4452	1.11477	0.557387	+	0.830253i	$0.311804\pi$
$522$	−1.35854	−0.0594618
$523$	−24.5424	−1.07316	−0.536582	−	0.843848i	$-0.680285\pi$
$523$	−24.5424	−1.07316	−0.536582	+	0.843848i	$0.680285\pi$
$524$	16.3554	0.714491
$525$	0	0
$526$	8.68009	0.378470
$527$	3.54990	0.154636
$528$	5.27981	0.229774
$529$	1.00000	0.0434783
$530$	11.0590	0.480373
$531$	4.29831	0.186531
$532$	0	0
$533$	8.37394	0.362716
$534$	−12.2952	−0.532066
$535$	70.5811	3.05149
$536$	5.33092	0.230261
$537$	−16.9969	−0.733470
$538$	−26.0142	−1.12155
$539$	0	0
$540$	−3.82843	−0.164749
$541$	−29.9909	−1.28941	−0.644706	−	0.764431i	$-0.723020\pi$
$541$	−29.9909	−1.28941	−0.644706	+	0.764431i	$0.723020\pi$
$542$	1.43727	0.0617362
$543$	−12.4022	−0.532228
$544$	−2.46988	−0.105895
$545$	−63.2893	−2.71101
$546$	0	0
$547$	−35.6986	−1.52636	−0.763181	−	0.646185i	$-0.776363\pi$
$547$	−35.6986	−1.52636	−0.763181	+	0.646185i	$0.776363\pi$
$548$	−5.10824	−0.218213
$549$	11.4342	0.487999
$550$	50.9864	2.17407
$551$	2.61013	0.111195
$552$	1.00000	0.0425628
$553$	0	0
$554$	18.0289	0.765975
$555$	−25.4145	−1.07878
$556$	9.31371	0.394989
$557$	−34.3426	−1.45514	−0.727572	−	0.686032i	$-0.759351\pi$
$557$	−34.3426	−1.45514	−0.727572	+	0.686032i	$0.759351\pi$
$558$	−1.43727	−0.0608446
$559$	−35.8119	−1.51468
$560$	0	0
$561$	−13.0405	−0.550571
$562$	24.9643	1.05306
$563$	−32.4078	−1.36583	−0.682914	−	0.730499i	$-0.739288\pi$
$563$	−32.4078	−1.36583	−0.682914	+	0.730499i	$0.739288\pi$
$564$	−6.99690	−0.294623
$565$	−75.5984	−3.18045
$566$	2.73430	0.114931
$567$	0	0
$568$	7.64146	0.320628
$569$	−19.4884	−0.816995	−0.408498	−	0.912759i	$-0.633947\pi$
$569$	−19.4884	−0.816995	−0.408498	+	0.912759i	$0.633947\pi$
$570$	7.35544	0.308086
$571$	−9.13173	−0.382151	−0.191075	−	0.981575i	$-0.561198\pi$
$571$	−9.13173	−0.382151	−0.191075	+	0.981575i	$0.561198\pi$
$572$	23.0123	0.962193
$573$	−16.6384	−0.695077
$574$	0	0
$575$	9.65685	0.402719
$576$	1.00000	0.0416667
$577$	34.9957	1.45689	0.728445	−	0.685104i	$-0.240243\pi$
$577$	34.9957	1.45689	0.728445	+	0.685104i	$0.240243\pi$
$578$	−10.8997	−0.453367
$579$	25.2165	1.04796
$580$	5.20108	0.215963
$581$	0	0
$582$	0.298311	0.0123654
$583$	−15.2516	−0.631656
$584$	−0.437273	−0.0180945
$585$	−16.6864	−0.689896
$586$	−14.5147	−0.599597
$587$	−3.60136	−0.148644	−0.0743221	−	0.997234i	$-0.523679\pi$
$587$	−3.60136	−0.148644	−0.0743221	+	0.997234i	$0.523679\pi$
$588$	0	0
$589$	2.76139	0.113781
$590$	−16.4558	−0.677473
$591$	13.6199	0.560246
$592$	6.63836	0.272835
$593$	7.65066	0.314175	0.157087	−	0.987585i	$-0.449790\pi$
$593$	7.65066	0.314175	0.157087	+	0.987585i	$0.449790\pi$
$594$	5.27981	0.216633
$595$	0	0
$596$	2.23370	0.0914957
$597$	−0.902774	−0.0369481
$598$	4.35854	0.178234
$599$	−19.7030	−0.805045	−0.402522	−	0.915410i	$-0.631866\pi$
$599$	−19.7030	−0.805045	−0.402522	+	0.915410i	$0.631866\pi$
$600$	9.65685	0.394239
$601$	−22.3094	−0.910019	−0.455010	−	0.890486i	$-0.650364\pi$
$601$	−22.3094	−0.910019	−0.455010	+	0.890486i	$0.650364\pi$
$602$	0	0
$603$	5.33092	0.217092
$604$	−22.2134	−0.903850
$605$	−64.6102	−2.62678
$606$	18.0590	0.733598
$607$	4.21958	0.171268	0.0856338	−	0.996327i	$-0.472709\pi$
$607$	4.21958	0.171268	0.0856338	+	0.996327i	$0.472709\pi$
$608$	−1.92127	−0.0779178
$609$	0	0
$610$	−43.7749	−1.77239
$611$	−30.4963	−1.23375
$612$	−2.46988	−0.0998391
$613$	−9.33816	−0.377165	−0.188582	−	0.982057i	$-0.560389\pi$
$613$	−9.33816	−0.377165	−0.188582	+	0.982057i	$0.560389\pi$
$614$	31.9521	1.28948
$615$	−7.35544	−0.296600
$616$	0	0
$617$	1.89055	0.0761107	0.0380553	−	0.999276i	$-0.487884\pi$
$617$	1.89055	0.0761107	0.0380553	+	0.999276i	$0.487884\pi$
$618$	−0.669078	−0.0269143
$619$	−15.3665	−0.617630	−0.308815	−	0.951122i	$-0.599932\pi$
$619$	−15.3665	−0.617630	−0.308815	+	0.951122i	$0.599932\pi$
$620$	5.50249	0.220985
$621$	1.00000	0.0401286
$622$	31.0142	1.24356
$623$	0	0
$624$	4.35854	0.174481
$625$	19.9706	0.798823
$626$	−6.57623	−0.262839
$627$	−10.1440	−0.405110
$628$	10.5731	0.421914
$629$	−16.3960	−0.653750
$630$	0	0
$631$	−1.49622	−0.0595636	−0.0297818	−	0.999556i	$-0.509481\pi$
$631$	−1.49622	−0.0595636	−0.0297818	+	0.999556i	$0.509481\pi$
$632$	1.35854	0.0540400
$633$	−22.8131	−0.906739
$634$	−28.0142	−1.11259
$635$	−72.4977	−2.87698
$636$	−2.88866	−0.114543
$637$	0	0
$638$	−7.17286	−0.283976
$639$	7.64146	0.302291
$640$	−3.82843	−0.151332
$641$	−1.33566	−0.0527555	−0.0263778	−	0.999652i	$-0.508397\pi$
$641$	−1.33566	−0.0527555	−0.0263778	+	0.999652i	$0.508397\pi$
$642$	−18.4361	−0.727613
$643$	−17.5167	−0.690791	−0.345395	−	0.938457i	$-0.612255\pi$
$643$	−17.5167	−0.690791	−0.345395	+	0.938457i	$0.612255\pi$
$644$	0	0
$645$	31.4562	1.23859
$646$	4.74531	0.186702
$647$	22.1612	0.871248	0.435624	−	0.900129i	$-0.356528\pi$
$647$	22.1612	0.871248	0.435624	+	0.900129i	$0.356528\pi$
$648$	1.00000	0.0392837
$649$	22.6943	0.890828
$650$	42.0898	1.65090
$651$	0	0
$652$	19.7294	0.772662
$653$	−9.17286	−0.358962	−0.179481	−	0.983761i	$-0.557442\pi$
$653$	−9.17286	−0.358962	−0.179481	+	0.983761i	$0.557442\pi$
$654$	16.5314	0.646429
$655$	−62.6156	−2.44659
$656$	1.92127	0.0750130
$657$	−0.437273	−0.0170596
$658$	0	0
$659$	−23.3419	−0.909273	−0.454636	−	0.890677i	$-0.650231\pi$
$659$	−23.3419	−0.909273	−0.454636	+	0.890677i	$0.650231\pi$
$660$	−20.2134	−0.786805
$661$	−35.9632	−1.39880	−0.699402	−	0.714728i	$-0.746550\pi$
$661$	−35.9632	−1.39880	−0.699402	+	0.714728i	$0.746550\pi$
$662$	24.8266	0.964914
$663$	−10.7651	−0.418082
$664$	−4.37704	−0.169862
$665$	0	0
$666$	6.63836	0.257231
$667$	−1.35854	−0.0526030
$668$	10.6907	0.413637
$669$	−0.942867	−0.0364533
$670$	−20.4090	−0.788470
$671$	60.3703	2.33057
$672$	0	0
$673$	22.9957	0.886419	0.443209	−	0.896418i	$-0.353840\pi$
$673$	22.9957	0.886419	0.443209	+	0.896418i	$0.353840\pi$
$674$	17.4176	0.670900
$675$	9.65685	0.371692
$676$	5.99690	0.230650
$677$	13.3648	0.513652	0.256826	−	0.966458i	$-0.417323\pi$
$677$	13.3648	0.513652	0.256826	+	0.966458i	$0.417323\pi$
$678$	19.7466	0.758364
$679$	0	0
$680$	9.45577	0.362612
$681$	15.3106	0.586704
$682$	−7.58853	−0.290580
$683$	−11.1660	−0.427254	−0.213627	−	0.976915i	$-0.568528\pi$
$683$	−11.1660	−0.427254	−0.213627	+	0.976915i	$0.568528\pi$
$684$	−1.92127	−0.0734616
$685$	19.5565	0.747217
$686$	0	0
$687$	−6.07873	−0.231918
$688$	−8.21648	−0.313250
$689$	−12.5903	−0.479654
$690$	−3.82843	−0.145746
$691$	43.9829	1.67319	0.836593	−	0.547824i	$-0.184544\pi$
$691$	43.9829	1.67319	0.836593	+	0.547824i	$0.184544\pi$
$692$	22.0308	0.837485
$693$	0	0
$694$	−9.87145	−0.374715
$695$	−35.6569	−1.35254
$696$	−1.35854	−0.0514955
$697$	−4.74531	−0.179742
$698$	33.9170	1.28378
$699$	−7.57812	−0.286631
$700$	0	0
$701$	−2.86043	−0.108037	−0.0540185	−	0.998540i	$-0.517203\pi$
$701$	−2.86043	−0.108037	−0.0540185	+	0.998540i	$0.517203\pi$
$702$	4.35854	0.164503
$703$	−12.7541	−0.481029
$704$	5.27981	0.198990
$705$	26.7871	1.00886
$706$	−7.35544	−0.276826
$707$	0	0
$708$	4.29831	0.161540
$709$	−34.5795	−1.29866	−0.649330	−	0.760507i	$-0.724951\pi$
$709$	−34.5795	−1.29866	−0.649330	+	0.760507i	$0.724951\pi$
$710$	−29.2548	−1.09791
$711$	1.35854	0.0509494
$712$	−12.2952	−0.460783
$713$	−1.43727	−0.0538263
$714$	0	0
$715$	−88.1009	−3.29479
$716$	−16.9969	−0.635204
$717$	−16.4330	−0.613700
$718$	15.1932	0.567007
$719$	23.3991	0.872638	0.436319	−	0.899792i	$-0.356282\pi$
$719$	23.3991	0.872638	0.436319	+	0.899792i	$0.356282\pi$
$720$	−3.82843	−0.142677
$721$	0	0
$722$	−15.3087	−0.569732
$723$	−13.2319	−0.492099
$724$	−12.4022	−0.460923
$725$	−13.1193	−0.487237
$726$	16.8764	0.626343
$727$	0.604463	0.0224183	0.0112091	−	0.999937i	$-0.496432\pi$
$727$	0.604463	0.0224183	0.0112091	+	0.999937i	$0.496432\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	1.67407	0.0619600
$731$	20.2938	0.750592
$732$	11.4342	0.422619
$733$	20.2670	0.748578	0.374289	−	0.927312i	$-0.377887\pi$
$733$	20.2670	0.748578	0.374289	+	0.927312i	$0.377887\pi$
$734$	8.34632	0.308068
$735$	0	0
$736$	1.00000	0.0368605
$737$	28.1463	1.03678
$738$	1.92127	0.0707229
$739$	−20.8376	−0.766522	−0.383261	−	0.923640i	$-0.625199\pi$
$739$	−20.8376	−0.766522	−0.383261	+	0.923640i	$0.625199\pi$
$740$	−25.4145	−0.934254
$741$	−8.37394	−0.307624
$742$	0	0
$743$	−29.3222	−1.07573	−0.537864	−	0.843032i	$-0.680769\pi$
$743$	−29.3222	−1.07573	−0.537864	+	0.843032i	$0.680769\pi$
$744$	−1.43727	−0.0526930
$745$	−8.55154	−0.313304
$746$	20.5596	0.752741
$747$	−4.37704	−0.160148
$748$	−13.0405	−0.476809
$749$	0	0
$750$	−17.8284	−0.651002
$751$	3.60325	0.131485	0.0657423	−	0.997837i	$-0.479058\pi$
$751$	3.60325	0.131485	0.0657423	+	0.997837i	$0.479058\pi$
$752$	−6.99690	−0.255151
$753$	9.87644	0.359917
$754$	−5.92127	−0.215640
$755$	85.0423	3.09501
$756$	0	0
$757$	51.0161	1.85421	0.927105	−	0.374801i	$-0.122289\pi$
$757$	51.0161	1.85421	0.927105	+	0.374801i	$0.122289\pi$
$758$	−1.45139	−0.0527167
$759$	5.27981	0.191645
$760$	7.35544	0.266810
$761$	38.8524	1.40840	0.704200	−	0.710002i	$-0.251306\pi$
$761$	38.8524	1.40840	0.704200	+	0.710002i	$0.251306\pi$
$762$	18.9367	0.686003
$763$	0	0
$764$	−16.6384	−0.601955
$765$	9.45577	0.341874
$766$	−29.4145	−1.06279
$767$	18.7344	0.676459
$768$	1.00000	0.0360844
$769$	−23.4176	−0.844459	−0.422230	−	0.906489i	$-0.638752\pi$
$769$	−23.4176	−0.844459	−0.422230	+	0.906489i	$0.638752\pi$
$770$	0	0
$771$	−21.3554	−0.769098
$772$	25.2165	0.907561
$773$	26.1685	0.941215	0.470607	−	0.882343i	$-0.344035\pi$
$773$	26.1685	0.941215	0.470607	+	0.882343i	$0.344035\pi$
$774$	−8.21648	−0.295335
$775$	−13.8795	−0.498568
$776$	0.298311	0.0107087
$777$	0	0
$778$	22.1513	0.794161
$779$	−3.69128	−0.132254
$780$	−16.6864	−0.597468
$781$	40.3455	1.44367
$782$	−2.46988	−0.0883229
$783$	−1.35854	−0.0485504
$784$	0	0
$785$	−40.4785	−1.44474
$786$	16.3554	0.583379
$787$	−12.4872	−0.445120	−0.222560	−	0.974919i	$-0.571441\pi$
$787$	−12.4872	−0.445120	−0.222560	+	0.974919i	$0.571441\pi$
$788$	13.6199	0.485187
$789$	8.68009	0.309019
$790$	−5.20108	−0.185046
$791$	0	0
$792$	5.27981	0.187610
$793$	49.8363	1.76974
$794$	−20.8567	−0.740178
$795$	11.0590	0.392223
$796$	−0.902774	−0.0319980
$797$	−15.2626	−0.540629	−0.270315	−	0.962772i	$-0.587128\pi$
$797$	−15.2626	−0.540629	−0.270315	+	0.962772i	$0.587128\pi$
$798$	0	0
$799$	17.2815	0.611377
$800$	9.65685	0.341421
$801$	−12.2952	−0.434430
$802$	−15.0430	−0.531187
$803$	−2.30872	−0.0814729
$804$	5.33092	0.188007
$805$	0	0
$806$	−6.26442	−0.220655
$807$	−26.0142	−0.915743
$808$	18.0590	0.635314
$809$	−21.3492	−0.750600	−0.375300	−	0.926903i	$-0.622460\pi$
$809$	−21.3492	−0.750600	−0.375300	+	0.926903i	$0.622460\pi$
$810$	−3.82843	−0.134517
$811$	2.14869	0.0754508	0.0377254	−	0.999288i	$-0.487989\pi$
$811$	2.14869	0.0754508	0.0377254	+	0.999288i	$0.487989\pi$
$812$	0	0
$813$	1.43727	0.0504074
$814$	35.0493	1.22848
$815$	−75.5325	−2.64579
$816$	−2.46988	−0.0864632
$817$	15.7861	0.552285
$818$	−19.0960	−0.667677
$819$	0	0
$820$	−7.35544	−0.256863
$821$	23.5688	0.822558	0.411279	−	0.911510i	$-0.365082\pi$
$821$	23.5688	0.822558	0.411279	+	0.911510i	$0.365082\pi$
$822$	−5.10824	−0.178170
$823$	−19.0948	−0.665603	−0.332802	−	0.942997i	$-0.607994\pi$
$823$	−19.0948	−0.665603	−0.332802	+	0.942997i	$0.607994\pi$
$824$	−0.669078	−0.0233084
$825$	50.9864	1.77512
$826$	0	0
$827$	−13.2428	−0.460498	−0.230249	−	0.973132i	$-0.573954\pi$
$827$	−13.2428	−0.460498	−0.230249	+	0.973132i	$0.573954\pi$
$828$	1.00000	0.0347524
$829$	17.6218	0.612029	0.306014	−	0.952027i	$-0.401004\pi$
$829$	17.6218	0.612029	0.306014	+	0.952027i	$0.401004\pi$
$830$	16.7572	0.581650
$831$	18.0289	0.625416
$832$	4.35854	0.151105
$833$	0	0
$834$	9.31371	0.322507
$835$	−40.9288	−1.41640
$836$	−10.1440	−0.350836
$837$	−1.43727	−0.0496794
$838$	−20.2165	−0.698367
$839$	−5.89682	−0.203581	−0.101790	−	0.994806i	$-0.532457\pi$
$839$	−5.89682	−0.203581	−0.101790	+	0.994806i	$0.532457\pi$
$840$	0	0
$841$	−27.1544	−0.936357
$842$	8.59662	0.296259
$843$	24.9643	0.859816
$844$	−22.8131	−0.785259
$845$	−22.9587	−0.789803
$846$	−6.99690	−0.240558
$847$	0	0
$848$	−2.88866	−0.0991970
$849$	2.73430	0.0938409
$850$	−23.8513	−0.818093
$851$	6.63836	0.227560
$852$	7.64146	0.261792
$853$	26.1575	0.895614	0.447807	−	0.894130i	$-0.352205\pi$
$853$	26.1575	0.895614	0.447807	+	0.894130i	$0.352205\pi$
$854$	0	0
$855$	7.35544	0.251551
$856$	−18.4361	−0.630132
$857$	−26.3825	−0.901208	−0.450604	−	0.892724i	$-0.648791\pi$
$857$	−26.3825	−0.901208	−0.450604	+	0.892724i	$0.648791\pi$
$858$	23.0123	0.785627
$859$	40.4565	1.38036	0.690178	−	0.723640i	$-0.257532\pi$
$859$	40.4565	1.38036	0.690178	+	0.723640i	$0.257532\pi$
$860$	31.4562	1.07265
$861$	0	0
$862$	36.0616	1.22826
$863$	−20.2501	−0.689322	−0.344661	−	0.938727i	$-0.612006\pi$
$863$	−20.2501	−0.689322	−0.344661	+	0.938727i	$0.612006\pi$
$864$	1.00000	0.0340207
$865$	−84.3433	−2.86776
$866$	7.56462	0.257056
$867$	−10.8997	−0.370172
$868$	0	0
$869$	7.17286	0.243322
$870$	5.20108	0.176333
$871$	23.2351	0.787290
$872$	16.5314	0.559824
$873$	0.298311	0.0100963
$874$	−1.92127	−0.0649879
$875$	0	0
$876$	−0.437273	−0.0147741
$877$	−9.88873	−0.333919	−0.166959	−	0.985964i	$-0.553395\pi$
$877$	−9.88873	−0.333919	−0.166959	+	0.985964i	$0.553395\pi$
$878$	35.1470	1.18615
$879$	−14.5147	−0.489569
$880$	−20.2134	−0.681393
$881$	4.39115	0.147942	0.0739709	−	0.997260i	$-0.476433\pi$
$881$	4.39115	0.147942	0.0739709	+	0.997260i	$0.476433\pi$
$882$	0	0
$883$	−6.05428	−0.203743	−0.101871	−	0.994798i	$-0.532483\pi$
$883$	−6.05428	−0.203743	−0.101871	+	0.994798i	$0.532483\pi$
$884$	−10.7651	−0.362069
$885$	−16.4558	−0.553155
$886$	−6.35544	−0.213515
$887$	−44.4946	−1.49398	−0.746990	−	0.664835i	$-0.768502\pi$
$887$	−44.4946	−1.49398	−0.746990	+	0.664835i	$0.768502\pi$
$888$	6.63836	0.222769
$889$	0	0
$890$	47.0713	1.57783
$891$	5.27981	0.176880
$892$	−0.942867	−0.0315695
$893$	13.4429	0.449851
$894$	2.23370	0.0747059
$895$	65.0714	2.17510
$896$	0	0
$897$	4.35854	0.145528
$898$	−4.36043	−0.145510
$899$	1.95260	0.0651228
$900$	9.65685	0.321895
$901$	7.13465	0.237690
$902$	10.1440	0.337757
$903$	0	0
$904$	19.7466	0.656762
$905$	47.4808	1.57832
$906$	−22.2134	−0.737990
$907$	−20.0063	−0.664297	−0.332149	−	0.943227i	$-0.607774\pi$
$907$	−20.0063	−0.664297	−0.332149	+	0.943227i	$0.607774\pi$
$908$	15.3106	0.508100
$909$	18.0590	0.598980
$910$	0	0
$911$	36.4085	1.20627	0.603134	−	0.797640i	$-0.293918\pi$
$911$	36.4085	1.20627	0.603134	+	0.797640i	$0.293918\pi$
$912$	−1.92127	−0.0636196
$913$	−23.1100	−0.764828
$914$	−33.8567	−1.11988
$915$	−43.7749	−1.44715
$916$	−6.07873	−0.200847
$917$	0	0
$918$	−2.46988	−0.0815183
$919$	−33.7883	−1.11457	−0.557287	−	0.830320i	$-0.688158\pi$
$919$	−33.7883	−1.11457	−0.557287	+	0.830320i	$0.688158\pi$
$920$	−3.82843	−0.126220
$921$	31.9521	1.05286
$922$	−17.6851	−0.582427
$923$	33.3056	1.09627
$924$	0	0
$925$	64.1056	2.10778
$926$	35.5954	1.16974
$927$	−0.669078	−0.0219754
$928$	−1.35854	−0.0445964
$929$	−28.8610	−0.946900	−0.473450	−	0.880821i	$-0.656992\pi$
$929$	−28.8610	−0.946900	−0.473450	+	0.880821i	$0.656992\pi$
$930$	5.50249	0.180434
$931$	0	0
$932$	−7.57812	−0.248230
$933$	31.0142	1.01536
$934$	−14.4022	−0.471253
$935$	49.9247	1.63271
$936$	4.35854	0.142463
$937$	15.6710	0.511951	0.255975	−	0.966683i	$-0.417603\pi$
$937$	15.6710	0.511951	0.255975	+	0.966683i	$0.417603\pi$
$938$	0	0
$939$	−6.57623	−0.214607
$940$	26.7871	0.873700
$941$	21.7460	0.708899	0.354450	−	0.935075i	$-0.384668\pi$
$941$	21.7460	0.708899	0.354450	+	0.935075i	$0.384668\pi$
$942$	10.5731	0.344491
$943$	1.92127	0.0625652
$944$	4.29831	0.139898
$945$	0	0
$946$	−43.3815	−1.41045
$947$	24.3784	0.792192	0.396096	−	0.918209i	$-0.370365\pi$
$947$	24.3784	0.792192	0.396096	+	0.918209i	$0.370365\pi$
$948$	1.35854	0.0441234
$949$	−1.90587	−0.0618673
$950$	−18.5534	−0.601953
$951$	−28.0142	−0.908422
$952$	0	0
$953$	41.2178	1.33518	0.667588	−	0.744531i	$-0.267327\pi$
$953$	41.2178	1.33518	0.667588	+	0.744531i	$0.267327\pi$
$954$	−2.88866	−0.0935238
$955$	63.6987	2.06124
$956$	−16.4330	−0.531480
$957$	−7.17286	−0.231866
$958$	−38.3542	−1.23917
$959$	0	0
$960$	−3.82843	−0.123562
$961$	−28.9342	−0.933363
$962$	28.9336	0.932856
$963$	−18.4361	−0.594094
$964$	−13.2319	−0.426170
$965$	−96.5395	−3.10772
$966$	0	0
$967$	36.7730	1.18254	0.591270	−	0.806474i	$-0.298627\pi$
$967$	36.7730	1.18254	0.591270	+	0.806474i	$0.298627\pi$
$968$	16.8764	0.542429
$969$	4.74531	0.152441
$970$	−1.14206	−0.0366694
$971$	15.9661	0.512377	0.256188	−	0.966627i	$-0.417533\pi$
$971$	15.9661	0.512377	0.256188	+	0.966627i	$0.417533\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	20.2504	0.648864
$975$	42.0898	1.34795
$976$	11.4342	0.365999
$977$	18.0392	0.577127	0.288563	−	0.957461i	$-0.406822\pi$
$977$	18.0392	0.577127	0.288563	+	0.957461i	$0.406822\pi$
$978$	19.7294	0.630876
$979$	−64.9164	−2.07474
$980$	0	0
$981$	16.5314	0.527807
$982$	−26.6459	−0.850305
$983$	−14.0417	−0.447862	−0.223931	−	0.974605i	$-0.571889\pi$
$983$	−14.0417	−0.447862	−0.223931	+	0.974605i	$0.571889\pi$
$984$	1.92127	0.0612479
$985$	−52.1426	−1.66140
$986$	3.35544	0.106859
$987$	0	0
$988$	−8.37394	−0.266411
$989$	−8.21648	−0.261269
$990$	−20.2134	−0.642423
$991$	14.1581	0.449748	0.224874	−	0.974388i	$-0.427803\pi$
$991$	14.1581	0.449748	0.224874	+	0.974388i	$0.427803\pi$
$992$	−1.43727	−0.0456335
$993$	24.8266	0.787849
$994$	0	0
$995$	3.45620	0.109569
$996$	−4.37704	−0.138692
$997$	−25.1735	−0.797254	−0.398627	−	0.917113i	$-0.630513\pi$
$997$	−25.1735	−0.797254	−0.398627	+	0.917113i	$0.630513\pi$
$998$	−13.0602	−0.413414
$999$	6.63836	0.210028

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6762.2.a.cp.1.2		4
7.2	even	3		966.2.i.l.277.3	✓	8
7.4	even	3		966.2.i.l.415.3	yes	8
7.6	odd	2		6762.2.a.cm.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.i.l.277.3	✓	8	7.2	even	3
966.2.i.l.415.3	yes	8	7.4	even	3
6762.2.a.cm.1.4		4	7.6	odd	2
6762.2.a.cp.1.2		4	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:	\( N \)	\(=\)	\( 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6762.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.82843 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.82843 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -3.82843 q^{10} +5.27981 q^{11} +1.00000 q^{12} +4.35854 q^{13} -3.82843 q^{15} +1.00000 q^{16} -2.46988 q^{17} +1.00000 q^{18} -1.92127 q^{19} -3.82843 q^{20} +5.27981 q^{22} +1.00000 q^{23} +1.00000 q^{24} +9.65685 q^{25} +4.35854 q^{26} +1.00000 q^{27} -1.35854 q^{29} -3.82843 q^{30} -1.43727 q^{31} +1.00000 q^{32} +5.27981 q^{33} -2.46988 q^{34} +1.00000 q^{36} +6.63836 q^{37} -1.92127 q^{38} +4.35854 q^{39} -3.82843 q^{40} +1.92127 q^{41} -8.21648 q^{43} +5.27981 q^{44} -3.82843 q^{45} +1.00000 q^{46} -6.99690 q^{47} +1.00000 q^{48} +9.65685 q^{50} -2.46988 q^{51} +4.35854 q^{52} -2.88866 q^{53} +1.00000 q^{54} -20.2134 q^{55} -1.92127 q^{57} -1.35854 q^{58} +4.29831 q^{59} -3.82843 q^{60} +11.4342 q^{61} -1.43727 q^{62} +1.00000 q^{64} -16.6864 q^{65} +5.27981 q^{66} +5.33092 q^{67} -2.46988 q^{68} +1.00000 q^{69} +7.64146 q^{71} +1.00000 q^{72} -0.437273 q^{73} +6.63836 q^{74} +9.65685 q^{75} -1.92127 q^{76} +4.35854 q^{78} +1.35854 q^{79} -3.82843 q^{80} +1.00000 q^{81} +1.92127 q^{82} -4.37704 q^{83} +9.45577 q^{85} -8.21648 q^{86} -1.35854 q^{87} +5.27981 q^{88} -12.2952 q^{89} -3.82843 q^{90} +1.00000 q^{92} -1.43727 q^{93} -6.99690 q^{94} +7.35544 q^{95} +1.00000 q^{96} +0.298311 q^{97} +5.27981 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^5 + 4 * q^6 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{8} + 4 q^{9} - 4 q^{10} + 6 q^{11} + 4 q^{12} + 6 q^{13} - 4 q^{15} + 4 q^{16} - 10 q^{17} + 4 q^{18} - 4 q^{19} - 4 q^{20} + 6 q^{22} + 4 q^{23} + 4 q^{24} + 16 q^{25} + 6 q^{26} + 4 q^{27} + 6 q^{29} - 4 q^{30} + 2 q^{31} + 4 q^{32} + 6 q^{33} - 10 q^{34} + 4 q^{36} - 4 q^{38} + 6 q^{39} - 4 q^{40} + 4 q^{41} + 20 q^{43} + 6 q^{44} - 4 q^{45} + 4 q^{46} + 10 q^{47} + 4 q^{48} + 16 q^{50} - 10 q^{51} + 6 q^{52} + 4 q^{54} + 10 q^{55} - 4 q^{57} + 6 q^{58} + 6 q^{59} - 4 q^{60} + 2 q^{62} + 4 q^{64} - 14 q^{65} + 6 q^{66} + 18 q^{67} - 10 q^{68} + 4 q^{69} + 42 q^{71} + 4 q^{72} + 6 q^{73} + 16 q^{75} - 4 q^{76} + 6 q^{78} - 6 q^{79} - 4 q^{80} + 4 q^{81} + 4 q^{82} - 10 q^{83} + 34 q^{85} + 20 q^{86} + 6 q^{87} + 6 q^{88} - 4 q^{90} + 4 q^{92} + 2 q^{93} + 10 q^{94} - 20 q^{95} + 4 q^{96} - 10 q^{97} + 6 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^5 + 4 * q^6 + 4 * q^8 + 4 * q^9 - 4 * q^10 + 6 * q^11 + 4 * q^12 + 6 * q^13 - 4 * q^15 + 4 * q^16 - 10 * q^17 + 4 * q^18 - 4 * q^19 - 4 * q^20 + 6 * q^22 + 4 * q^23 + 4 * q^24 + 16 * q^25 + 6 * q^26 + 4 * q^27 + 6 * q^29 - 4 * q^30 + 2 * q^31 + 4 * q^32 + 6 * q^33 - 10 * q^34 + 4 * q^36 - 4 * q^38 + 6 * q^39 - 4 * q^40 + 4 * q^41 + 20 * q^43 + 6 * q^44 - 4 * q^45 + 4 * q^46 + 10 * q^47 + 4 * q^48 + 16 * q^50 - 10 * q^51 + 6 * q^52 + 4 * q^54 + 10 * q^55 - 4 * q^57 + 6 * q^58 + 6 * q^59 - 4 * q^60 + 2 * q^62 + 4 * q^64 - 14 * q^65 + 6 * q^66 + 18 * q^67 - 10 * q^68 + 4 * q^69 + 42 * q^71 + 4 * q^72 + 6 * q^73 + 16 * q^75 - 4 * q^76 + 6 * q^78 - 6 * q^79 - 4 * q^80 + 4 * q^81 + 4 * q^82 - 10 * q^83 + 34 * q^85 + 20 * q^86 + 6 * q^87 + 6 * q^88 - 4 * q^90 + 4 * q^92 + 2 * q^93 + 10 * q^94 - 20 * q^95 + 4 * q^96 - 10 * q^97 + 6 * q^99

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