LMFDB - Embedded newform 6762.2.a.cp.1.3

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			1.3
Root			$4.18558$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.82843 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.82843 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +1.82843 q^{10} +1.68049 q^{11} +1.00000 q^{12} +3.77137 q^{13} +1.82843 q^{15} +1.00000 q^{16} +2.59980 q^{17} +1.00000 q^{18} +1.09088 q^{19} +1.82843 q^{20} +1.68049 q^{22} +1.00000 q^{23} +1.00000 q^{24} -1.65685 q^{25} +3.77137 q^{26} +1.00000 q^{27} -0.771369 q^{29} +1.82843 q^{30} -3.86225 q^{31} +1.00000 q^{32} +1.68049 q^{33} +2.59980 q^{34} +1.00000 q^{36} +2.45186 q^{37} +1.09088 q^{38} +3.77137 q^{39} +1.82843 q^{40} -1.09088 q^{41} +10.2959 q^{43} +1.68049 q^{44} +1.82843 q^{45} +1.00000 q^{46} -2.22323 q^{47} +1.00000 q^{48} -1.65685 q^{50} +2.59980 q^{51} +3.77137 q^{52} -7.37117 q^{53} +1.00000 q^{54} +3.07265 q^{55} +1.09088 q^{57} -0.771369 q^{58} -6.42822 q^{59} +1.82843 q^{60} +9.08548 q^{61} -3.86225 q^{62} +1.00000 q^{64} +6.89567 q^{65} +1.68049 q^{66} -12.8903 q^{67} +2.59980 q^{68} +1.00000 q^{69} +8.22863 q^{71} +1.00000 q^{72} -2.86225 q^{73} +2.45186 q^{74} -1.65685 q^{75} +1.09088 q^{76} +3.77137 q^{78} +0.771369 q^{79} +1.82843 q^{80} +1.00000 q^{81} -1.09088 q^{82} +3.33734 q^{83} +4.75354 q^{85} +10.2959 q^{86} -0.771369 q^{87} +1.68049 q^{88} +3.20500 q^{89} +1.82843 q^{90} +1.00000 q^{92} -3.86225 q^{93} -2.22323 q^{94} +1.99460 q^{95} +1.00000 q^{96} -10.4282 q^{97} +1.68049 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	1.82843	0.817697	0.408849	−	0.912602i	$-0.365930\pi$
$5$	1.82843	0.817697	0.408849	+	0.912602i	$0.365930\pi$
$6$	1.00000	0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.82843	0.578199
$11$	1.68049	0.506686	0.253343	−	0.967376i	$-0.418470\pi$
$11$	1.68049	0.506686	0.253343	+	0.967376i	$0.418470\pi$
$12$	1.00000	0.288675
$13$	3.77137	1.04599	0.522995	−	0.852336i	$-0.324815\pi$
$13$	3.77137	1.04599	0.522995	+	0.852336i	$0.324815\pi$
$14$	0	0
$15$	1.82843	0.472098
$16$	1.00000	0.250000
$17$	2.59980	0.630543	0.315272	−	0.949001i	$-0.397904\pi$
$17$	2.59980	0.630543	0.315272	+	0.949001i	$0.397904\pi$
$18$	1.00000	0.235702
$19$	1.09088	0.250265	0.125133	−	0.992140i	$-0.460064\pi$
$19$	1.09088	0.250265	0.125133	+	0.992140i	$0.460064\pi$
$20$	1.82843	0.408849
$21$	0	0
$22$	1.68049	0.358281
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	1.00000	0.204124
$25$	−1.65685	−0.331371
$26$	3.77137	0.739626
$27$	1.00000	0.192450
$28$	0	0
$29$	−0.771369	−0.143240	−0.0716199	−	0.997432i	$-0.522817\pi$
$29$	−0.771369	−0.143240	−0.0716199	+	0.997432i	$0.522817\pi$
$30$	1.82843	0.333824
$31$	−3.86225	−0.693681	−0.346840	−	0.937924i	$-0.612745\pi$
$31$	−3.86225	−0.693681	−0.346840	+	0.937924i	$0.612745\pi$
$32$	1.00000	0.176777
$33$	1.68049	0.292535
$34$	2.59980	0.445861
$35$	0	0
$36$	1.00000	0.166667
$37$	2.45186	0.403083	0.201541	−	0.979480i	$-0.435405\pi$
$37$	2.45186	0.403083	0.201541	+	0.979480i	$0.435405\pi$
$38$	1.09088	0.176964
$39$	3.77137	0.603902
$40$	1.82843	0.289100
$41$	−1.09088	−0.170367	−0.0851835	−	0.996365i	$-0.527148\pi$
$41$	−1.09088	−0.170367	−0.0851835	+	0.996365i	$0.527148\pi$
$42$	0	0
$43$	10.2959	1.57011	0.785053	−	0.619428i	$-0.212636\pi$
$43$	10.2959	1.57011	0.785053	+	0.619428i	$0.212636\pi$
$44$	1.68049	0.253343
$45$	1.82843	0.272566
$46$	1.00000	0.147442
$47$	−2.22323	−0.324291	−0.162146	−	0.986767i	$-0.551841\pi$
$47$	−2.22323	−0.324291	−0.162146	+	0.986767i	$0.551841\pi$
$48$	1.00000	0.144338
$49$	0	0
$50$	−1.65685	−0.234315
$51$	2.59980	0.364044
$52$	3.77137	0.522995
$53$	−7.37117	−1.01251	−0.506254	−	0.862385i	$-0.668970\pi$
$53$	−7.37117	−1.01251	−0.506254	+	0.862385i	$0.668970\pi$
$54$	1.00000	0.136083
$55$	3.07265	0.414316
$56$	0	0
$57$	1.09088	0.144491
$58$	−0.771369	−0.101286
$59$	−6.42822	−0.836883	−0.418442	−	0.908244i	$-0.637424\pi$
$59$	−6.42822	−0.836883	−0.418442	+	0.908244i	$0.637424\pi$
$60$	1.82843	0.236049
$61$	9.08548	1.16328	0.581638	−	0.813448i	$-0.302412\pi$
$61$	9.08548	1.16328	0.581638	+	0.813448i	$0.302412\pi$
$62$	−3.86225	−0.490506
$63$	0	0
$64$	1.00000	0.125000
$65$	6.89567	0.855303
$66$	1.68049	0.206854
$67$	−12.8903	−1.57480	−0.787399	−	0.616444i	$-0.788573\pi$
$67$	−12.8903	−1.57480	−0.787399	+	0.616444i	$0.788573\pi$
$68$	2.59980	0.315272
$69$	1.00000	0.120386
$70$	0	0
$71$	8.22863	0.976559	0.488279	−	0.872687i	$-0.337625\pi$
$71$	8.22863	0.976559	0.488279	+	0.872687i	$0.337625\pi$
$72$	1.00000	0.117851
$73$	−2.86225	−0.335001	−0.167501	−	0.985872i	$-0.553570\pi$
$73$	−2.86225	−0.335001	−0.167501	+	0.985872i	$0.553570\pi$
$74$	2.45186	0.285023
$75$	−1.65685	−0.191317
$76$	1.09088	0.125133
$77$	0	0
$78$	3.77137	0.427023
$79$	0.771369	0.0867858	0.0433929	−	0.999058i	$-0.486183\pi$
$79$	0.771369	0.0867858	0.0433929	+	0.999058i	$0.486183\pi$
$80$	1.82843	0.204424
$81$	1.00000	0.111111
$82$	−1.09088	−0.120468
$83$	3.33734	0.366321	0.183160	−	0.983083i	$-0.441367\pi$
$83$	3.33734	0.366321	0.183160	+	0.983083i	$0.441367\pi$
$84$	0	0
$85$	4.75354	0.515594
$86$	10.2959	1.11023
$87$	−0.771369	−0.0826995
$88$	1.68049	0.179141
$89$	3.20500	0.339729	0.169864	−	0.985467i	$-0.445667\pi$
$89$	3.20500	0.339729	0.169864	+	0.985467i	$0.445667\pi$
$90$	1.82843	0.192733
$91$	0	0
$92$	1.00000	0.104257
$93$	−3.86225	−0.400497
$94$	−2.22323	−0.229308
$95$	1.99460	0.204641
$96$	1.00000	0.102062
$97$	−10.4282	−1.05883	−0.529413	−	0.848364i	$-0.677588\pi$
$97$	−10.4282	−1.05883	−0.529413	+	0.848364i	$0.677588\pi$
$98$	0	0
$99$	1.68049	0.168895
$100$	−1.65685	−0.165685
$101$	−6.47764	−0.644549	−0.322275	−	0.946646i	$-0.604447\pi$
$101$	−6.47764	−0.644549	−0.322275	+	0.946646i	$0.604447\pi$
$102$	2.59980	0.257418
$103$	−18.8903	−1.86131	−0.930657	−	0.365893i	$-0.880764\pi$
$103$	−18.8903	−1.86131	−0.930657	+	0.365893i	$0.880764\pi$
$104$	3.77137	0.369813
$105$	0	0
$106$	−7.37117	−0.715951
$107$	13.8150	1.33554	0.667772	−	0.744366i	$-0.267248\pi$
$107$	13.8150	1.33554	0.667772	+	0.744366i	$0.267248\pi$
$108$	1.00000	0.0962250
$109$	10.0676	0.964306	0.482153	−	0.876087i	$-0.339855\pi$
$109$	10.0676	0.964306	0.482153	+	0.876087i	$0.339855\pi$
$110$	3.07265	0.292966
$111$	2.45186	0.232720
$112$	0	0
$113$	6.30392	0.593023	0.296511	−	0.955029i	$-0.404177\pi$
$113$	6.30392	0.593023	0.296511	+	0.955029i	$0.404177\pi$
$114$	1.09088	0.102170
$115$	1.82843	0.170502
$116$	−0.771369	−0.0716199
$117$	3.77137	0.348663
$118$	−6.42822	−0.591766
$119$	0	0
$120$	1.82843	0.166912
$121$	−8.17596	−0.743269
$122$	9.08548	0.822560
$123$	−1.09088	−0.0983614
$124$	−3.86225	−0.346840
$125$	−12.1716	−1.08866
$126$	0	0
$127$	4.02363	0.357040	0.178520	−	0.983936i	$-0.442869\pi$
$127$	4.02363	0.357040	0.178520	+	0.983936i	$0.442869\pi$
$128$	1.00000	0.0883883
$129$	10.2959	0.906501
$130$	6.89567	0.604791
$131$	10.9946	0.960602	0.480301	−	0.877104i	$-0.340527\pi$
$131$	10.9946	0.960602	0.480301	+	0.877104i	$0.340527\pi$
$132$	1.68049	0.146268
$133$	0	0
$134$	−12.8903	−1.11355
$135$	1.82843	0.157366
$136$	2.59980	0.222931
$137$	4.14794	0.354382	0.177191	−	0.984176i	$-0.443299\pi$
$137$	4.14794	0.354382	0.177191	+	0.984176i	$0.443299\pi$
$138$	1.00000	0.0851257
$139$	−13.3137	−1.12925	−0.564627	−	0.825346i	$-0.690980\pi$
$139$	−13.3137	−1.12925	−0.564627	+	0.825346i	$0.690980\pi$
$140$	0	0
$141$	−2.22323	−0.187229
$142$	8.22863	0.690531
$143$	6.33774	0.529989
$144$	1.00000	0.0833333
$145$	−1.41039	−0.117127
$146$	−2.86225	−0.236882
$147$	0	0
$148$	2.45186	0.201541
$149$	−11.8724	−0.972628	−0.486314	−	0.873784i	$-0.661659\pi$
$149$	−11.8724	−0.972628	−0.486314	+	0.873784i	$0.661659\pi$
$150$	−1.65685	−0.135282
$151$	1.07265	0.0872911	0.0436455	−	0.999047i	$-0.486103\pi$
$151$	1.07265	0.0872911	0.0436455	+	0.999047i	$0.486103\pi$
$152$	1.09088	0.0884821
$153$	2.59980	0.210181
$154$	0	0
$155$	−7.06184	−0.567221
$156$	3.77137	0.301951
$157$	21.3760	1.70599	0.852993	−	0.521922i	$-0.174785\pi$
$157$	21.3760	1.70599	0.852993	+	0.521922i	$0.174785\pi$
$158$	0.771369	0.0613669
$159$	−7.37117	−0.584571
$160$	1.82843	0.144550
$161$	0	0
$162$	1.00000	0.0785674
$163$	1.88048	0.147291	0.0736453	−	0.997284i	$-0.476537\pi$
$163$	1.88048	0.147291	0.0736453	+	0.997284i	$0.476537\pi$
$164$	−1.09088	−0.0851835
$165$	3.07265	0.239206
$166$	3.33734	0.259028
$167$	−19.6511	−1.52064	−0.760322	−	0.649546i	$-0.774959\pi$
$167$	−19.6511	−1.52064	−0.760322	+	0.649546i	$0.774959\pi$
$168$	0	0
$169$	1.22323	0.0940944
$170$	4.75354	0.364580
$171$	1.09088	0.0834218
$172$	10.2959	0.785053
$173$	−1.77097	−0.134644	−0.0673222	−	0.997731i	$-0.521446\pi$
$173$	−1.77097	−0.134644	−0.0673222	+	0.997731i	$0.521446\pi$
$174$	−0.771369	−0.0584774
$175$	0	0
$176$	1.68049	0.126672
$177$	−6.42822	−0.483175
$178$	3.20500	0.240225
$179$	−12.2232	−0.913607	−0.456803	−	0.889568i	$-0.651006\pi$
$179$	−12.2232	−0.913607	−0.456803	+	0.889568i	$0.651006\pi$
$180$	1.82843	0.136283
$181$	0.820785	0.0610085	0.0305043	−	0.999535i	$-0.490289\pi$
$181$	0.820785	0.0610085	0.0305043	+	0.999535i	$0.490289\pi$
$182$	0	0
$183$	9.08548	0.671618
$184$	1.00000	0.0737210
$185$	4.48304	0.329600
$186$	−3.86225	−0.283194
$187$	4.36893	0.319488
$188$	−2.22323	−0.162146
$189$	0	0
$190$	1.99460	0.144703
$191$	−12.4519	−0.900985	−0.450492	−	0.892780i	$-0.648752\pi$
$191$	−12.4519	−0.900985	−0.450492	+	0.892780i	$0.648752\pi$
$192$	1.00000	0.0721688
$193$	6.70412	0.482573	0.241287	−	0.970454i	$-0.422431\pi$
$193$	6.70412	0.482573	0.241287	+	0.970454i	$0.422431\pi$
$194$	−10.4282	−0.748703
$195$	6.89567	0.493809
$196$	0	0
$197$	16.5606	1.17989	0.589946	−	0.807443i	$-0.299149\pi$
$197$	16.5606	1.17989	0.589946	+	0.807443i	$0.299149\pi$
$198$	1.68049	0.119427
$199$	−5.01783	−0.355705	−0.177852	−	0.984057i	$-0.556915\pi$
$199$	−5.01783	−0.355705	−0.177852	+	0.984057i	$0.556915\pi$
$200$	−1.65685	−0.117157
$201$	−12.8903	−0.909210
$202$	−6.47764	−0.455765
$203$	0	0
$204$	2.59980	0.182022
$205$	−1.99460	−0.139309
$206$	−18.8903	−1.31615
$207$	1.00000	0.0695048
$208$	3.77137	0.261497
$209$	1.83321	0.126806
$210$	0	0
$211$	17.1523	1.18081	0.590407	−	0.807105i	$-0.298967\pi$
$211$	17.1523	1.18081	0.590407	+	0.807105i	$0.298967\pi$
$212$	−7.37117	−0.506254
$213$	8.22863	0.563816
$214$	13.8150	0.944373
$215$	18.8253	1.28387
$216$	1.00000	0.0680414
$217$	0	0
$218$	10.0676	0.681867
$219$	−2.86225	−0.193413
$220$	3.07265	0.207158
$221$	9.80479	0.659542
$222$	2.45186	0.164558
$223$	4.42282	0.296174	0.148087	−	0.988974i	$-0.452688\pi$
$223$	4.42282	0.296174	0.148087	+	0.988974i	$0.452688\pi$
$224$	0	0
$225$	−1.65685	−0.110457
$226$	6.30392	0.419330
$227$	−12.0905	−0.802473	−0.401237	−	0.915974i	$-0.631420\pi$
$227$	−12.0905	−0.802473	−0.401237	+	0.915974i	$0.631420\pi$
$228$	1.09088	0.0722454
$229$	−9.09088	−0.600742	−0.300371	−	0.953822i	$-0.597111\pi$
$229$	−9.09088	−0.600742	−0.300371	+	0.953822i	$0.597111\pi$
$230$	1.82843	0.120563
$231$	0	0
$232$	−0.771369	−0.0506429
$233$	6.74774	0.442059	0.221029	−	0.975267i	$-0.429058\pi$
$233$	6.74774	0.442059	0.221029	+	0.975267i	$0.429058\pi$
$234$	3.77137	0.246542
$235$	−4.06501	−0.265172
$236$	−6.42822	−0.418442
$237$	0.771369	0.0501058
$238$	0	0
$239$	20.5918	1.33197	0.665985	−	0.745965i	$-0.268011\pi$
$239$	20.5918	1.33197	0.665985	+	0.745965i	$0.268011\pi$
$240$	1.82843	0.118024
$241$	17.1814	1.10675	0.553374	−	0.832933i	$-0.313340\pi$
$241$	17.1814	1.10675	0.553374	+	0.832933i	$0.313340\pi$
$242$	−8.17596	−0.525571
$243$	1.00000	0.0641500
$244$	9.08548	0.581638
$245$	0	0
$246$	−1.09088	−0.0695520
$247$	4.11412	0.261775
$248$	−3.86225	−0.245253
$249$	3.33734	0.211495
$250$	−12.1716	−0.769798
$251$	−15.1760	−0.957898	−0.478949	−	0.877843i	$-0.658982\pi$
$251$	−15.1760	−0.957898	−0.478949	+	0.877843i	$0.658982\pi$
$252$	0	0
$253$	1.68049	0.105651
$254$	4.02363	0.252465
$255$	4.75354	0.297678
$256$	1.00000	0.0625000
$257$	−15.9946	−0.997716	−0.498858	−	0.866684i	$-0.666247\pi$
$257$	−15.9946	−0.997716	−0.498858	+	0.866684i	$0.666247\pi$
$258$	10.2959	0.640993
$259$	0	0
$260$	6.89567	0.427652
$261$	−0.771369	−0.0477466
$262$	10.9946	0.679248
$263$	21.7602	1.34179	0.670895	−	0.741553i	$-0.265910\pi$
$263$	21.7602	1.34179	0.670895	+	0.741553i	$0.265910\pi$
$264$	1.68049	0.103427
$265$	−13.4776	−0.827925
$266$	0	0
$267$	3.20500	0.196143
$268$	−12.8903	−0.787399
$269$	20.5627	1.25373	0.626866	−	0.779127i	$-0.284338\pi$
$269$	20.5627	1.25373	0.626866	+	0.779127i	$0.284338\pi$
$270$	1.82843	0.111275
$271$	3.86225	0.234615	0.117308	−	0.993096i	$-0.462574\pi$
$271$	3.86225	0.234615	0.117308	+	0.993096i	$0.462574\pi$
$272$	2.59980	0.157636
$273$	0	0
$274$	4.14794	0.250586
$275$	−2.78432	−0.167901
$276$	1.00000	0.0601929
$277$	24.1295	1.44980	0.724900	−	0.688854i	$-0.241886\pi$
$277$	24.1295	1.44980	0.724900	+	0.688854i	$0.241886\pi$
$278$	−13.3137	−0.798503
$279$	−3.86225	−0.231227
$280$	0	0
$281$	27.6853	1.65156	0.825782	−	0.563989i	$-0.190734\pi$
$281$	27.6853	1.65156	0.825782	+	0.563989i	$0.190734\pi$
$282$	−2.22323	−0.132391
$283$	5.96618	0.354652	0.177326	−	0.984152i	$-0.443255\pi$
$283$	5.96618	0.354652	0.177326	+	0.984152i	$0.443255\pi$
$284$	8.22863	0.488279
$285$	1.99460	0.118150
$286$	6.33774	0.374759
$287$	0	0
$288$	1.00000	0.0589256
$289$	−10.2411	−0.602415
$290$	−1.41039	−0.0828211
$291$	−10.4282	−0.611313
$292$	−2.86225	−0.167501
$293$	−31.4853	−1.83939	−0.919695	−	0.392634i	$-0.871564\pi$
$293$	−31.4853	−1.83939	−0.919695	+	0.392634i	$0.871564\pi$
$294$	0	0
$295$	−11.7535	−0.684317
$296$	2.45186	0.142511
$297$	1.68049	0.0975118
$298$	−11.8724	−0.687752
$299$	3.77137	0.218104
$300$	−1.65685	−0.0956585
$301$	0	0
$302$	1.07265	0.0617241
$303$	−6.47764	−0.372131
$304$	1.09088	0.0625663
$305$	16.6121	0.951208
$306$	2.59980	0.148620
$307$	5.13815	0.293250	0.146625	−	0.989192i	$-0.453159\pi$
$307$	5.13815	0.293250	0.146625	+	0.989192i	$0.453159\pi$
$308$	0	0
$309$	−18.8903	−1.07463
$310$	−7.06184	−0.401086
$311$	−15.5627	−0.882481	−0.441240	−	0.897389i	$-0.645461\pi$
$311$	−15.5627	−0.882481	−0.441240	+	0.897389i	$0.645461\pi$
$312$	3.77137	0.213512
$313$	−22.1527	−1.25215	−0.626073	−	0.779764i	$-0.715339\pi$
$313$	−22.1527	−1.25215	−0.626073	+	0.779764i	$0.715339\pi$
$314$	21.3760	1.20631
$315$	0	0
$316$	0.771369	0.0433929
$317$	18.5627	1.04259	0.521293	−	0.853378i	$-0.325450\pi$
$317$	18.5627	1.04259	0.521293	+	0.853378i	$0.325450\pi$
$318$	−7.37117	−0.413354
$319$	−1.29628	−0.0725776
$320$	1.82843	0.102212
$321$	13.8150	0.771077
$322$	0	0
$323$	2.83607	0.157803
$324$	1.00000	0.0555556
$325$	−6.24861	−0.346610
$326$	1.88048	0.104150
$327$	10.0676	0.556742
$328$	−1.09088	−0.0602338
$329$	0	0
$330$	3.07265	0.169144
$331$	2.86265	0.157345	0.0786727	−	0.996900i	$-0.474932\pi$
$331$	2.86265	0.157345	0.0786727	+	0.996900i	$0.474932\pi$
$332$	3.33734	0.183160
$333$	2.45186	0.134361
$334$	−19.6511	−1.07526
$335$	−23.5689	−1.28771
$336$	0	0
$337$	−7.70627	−0.419787	−0.209894	−	0.977724i	$-0.567312\pi$
$337$	−7.70627	−0.419787	−0.209894	+	0.977724i	$0.567312\pi$
$338$	1.22323	0.0665348
$339$	6.30392	0.342382
$340$	4.75354	0.257797
$341$	−6.49047	−0.351478
$342$	1.09088	0.0589881
$343$	0	0
$344$	10.2959	0.555117
$345$	1.82843	0.0984392
$346$	−1.77097	−0.0952079
$347$	−9.94773	−0.534022	−0.267011	−	0.963693i	$-0.586036\pi$
$347$	−9.94773	−0.534022	−0.267011	+	0.963693i	$0.586036\pi$
$348$	−0.771369	−0.0413497
$349$	−8.54489	−0.457397	−0.228699	−	0.973497i	$-0.573447\pi$
$349$	−8.54489	−0.457397	−0.228699	+	0.973497i	$0.573447\pi$
$350$	0	0
$351$	3.77137	0.201301
$352$	1.68049	0.0895703
$353$	−1.99460	−0.106162	−0.0530808	−	0.998590i	$-0.516904\pi$
$353$	−1.99460	−0.106162	−0.0530808	+	0.998590i	$0.516904\pi$
$354$	−6.42822	−0.341656
$355$	15.0455	0.798530
$356$	3.20500	0.169864
$357$	0	0
$358$	−12.2232	−0.646018
$359$	−27.7129	−1.46263	−0.731315	−	0.682040i	$-0.761093\pi$
$359$	−27.7129	−1.46263	−0.731315	+	0.682040i	$0.761093\pi$
$360$	1.82843	0.0963666
$361$	−17.8100	−0.937367
$362$	0.820785	0.0431395
$363$	−8.17596	−0.429127
$364$	0	0
$365$	−5.23342	−0.273930
$366$	9.08548	0.474906
$367$	−21.7758	−1.13669	−0.568343	−	0.822792i	$-0.692415\pi$
$367$	−21.7758	−1.13669	−0.568343	+	0.822792i	$0.692415\pi$
$368$	1.00000	0.0521286
$369$	−1.09088	−0.0567890
$370$	4.48304	0.233062
$371$	0	0
$372$	−3.86225	−0.200248
$373$	13.3610	0.691805	0.345903	−	0.938270i	$-0.387573\pi$
$373$	13.3610	0.691805	0.345903	+	0.938270i	$0.387573\pi$
$374$	4.36893	0.225912
$375$	−12.1716	−0.628537
$376$	−2.22323	−0.114654
$377$	−2.90912	−0.149827
$378$	0	0
$379$	−3.50892	−0.180241	−0.0901204	−	0.995931i	$-0.528725\pi$
$379$	−3.50892	−0.180241	−0.0901204	+	0.995931i	$0.528725\pi$
$380$	1.99460	0.102321
$381$	4.02363	0.206137
$382$	−12.4519	−0.637092
$383$	0.483043	0.0246824	0.0123412	−	0.999924i	$-0.496072\pi$
$383$	0.483043	0.0246824	0.0123412	+	0.999924i	$0.496072\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	6.70412	0.341231
$387$	10.2959	0.523369
$388$	−10.4282	−0.529413
$389$	18.6282	0.944488	0.472244	−	0.881468i	$-0.343444\pi$
$389$	18.6282	0.944488	0.472244	+	0.881468i	$0.343444\pi$
$390$	6.89567	0.349176
$391$	2.59980	0.131477
$392$	0	0
$393$	10.9946	0.554604
$394$	16.5606	0.834309
$395$	1.41039	0.0709646
$396$	1.68049	0.0844477
$397$	31.7445	1.59321	0.796605	−	0.604500i	$-0.206627\pi$
$397$	31.7445	1.59321	0.796605	+	0.604500i	$0.206627\pi$
$398$	−5.01783	−0.251521
$399$	0	0
$400$	−1.65685	−0.0828427
$401$	−20.7762	−1.03751	−0.518756	−	0.854922i	$-0.673605\pi$
$401$	−20.7762	−1.03751	−0.518756	+	0.854922i	$0.673605\pi$
$402$	−12.8903	−0.642908
$403$	−14.5660	−0.725583
$404$	−6.47764	−0.322275
$405$	1.82843	0.0908553
$406$	0	0
$407$	4.12032	0.204237
$408$	2.59980	0.128709
$409$	19.6951	0.973858	0.486929	−	0.873441i	$-0.338117\pi$
$409$	19.6951	0.973858	0.486929	+	0.873441i	$0.338117\pi$
$410$	−1.99460	−0.0985061
$411$	4.14794	0.204603
$412$	−18.8903	−0.930657
$413$	0	0
$414$	1.00000	0.0491473
$415$	6.10209	0.299540
$416$	3.77137	0.184907
$417$	−13.3137	−0.651975
$418$	1.83321	0.0896654
$419$	−1.70412	−0.0832518	−0.0416259	−	0.999133i	$-0.513254\pi$
$419$	−1.70412	−0.0832518	−0.0416259	+	0.999133i	$0.513254\pi$
$420$	0	0
$421$	−12.8564	−0.626585	−0.313292	−	0.949657i	$-0.601432\pi$
$421$	−12.8564	−0.626585	−0.313292	+	0.949657i	$0.601432\pi$
$422$	17.1523	0.834962
$423$	−2.22323	−0.108097
$424$	−7.37117	−0.357975
$425$	−4.30748	−0.208944
$426$	8.22863	0.398678
$427$	0	0
$428$	13.8150	0.667772
$429$	6.33774	0.305989
$430$	18.8253	0.907835
$431$	−11.5419	−0.555956	−0.277978	−	0.960587i	$-0.589664\pi$
$431$	−11.5419	−0.555956	−0.277978	+	0.960587i	$0.589664\pi$
$432$	1.00000	0.0481125
$433$	−24.7627	−1.19002	−0.595010	−	0.803718i	$-0.702852\pi$
$433$	−24.7627	−1.19002	−0.595010	+	0.803718i	$0.702852\pi$
$434$	0	0
$435$	−1.41039	−0.0676232
$436$	10.0676	0.482153
$437$	1.09088	0.0521839
$438$	−2.86225	−0.136764
$439$	−7.82579	−0.373505	−0.186752	−	0.982407i	$-0.559796\pi$
$439$	−7.82579	−0.373505	−0.186752	+	0.982407i	$0.559796\pi$
$440$	3.07265	0.146483
$441$	0	0
$442$	9.80479	0.466366
$443$	−0.994597	−0.0472547	−0.0236274	−	0.999721i	$-0.507522\pi$
$443$	−0.994597	−0.0472547	−0.0236274	+	0.999721i	$0.507522\pi$
$444$	2.45186	0.116360
$445$	5.86010	0.277796
$446$	4.42282	0.209427
$447$	−11.8724	−0.561547
$448$	0	0
$449$	26.1291	1.23311	0.616554	−	0.787313i	$-0.288528\pi$
$449$	26.1291	1.23311	0.616554	+	0.787313i	$0.288528\pi$
$450$	−1.65685	−0.0781049
$451$	−1.83321	−0.0863226
$452$	6.30392	0.296511
$453$	1.07265	0.0503975
$454$	−12.0905	−0.567434
$455$	0	0
$456$	1.09088	0.0510852
$457$	18.7445	0.876830	0.438415	−	0.898773i	$-0.355540\pi$
$457$	18.7445	0.876830	0.438415	+	0.898773i	$0.355540\pi$
$458$	−9.09088	−0.424789
$459$	2.59980	0.121348
$460$	1.82843	0.0852509
$461$	−5.63648	−0.262517	−0.131258	−	0.991348i	$-0.541902\pi$
$461$	−5.63648	−0.262517	−0.131258	+	0.991348i	$0.541902\pi$
$462$	0	0
$463$	−20.5337	−0.954281	−0.477141	−	0.878827i	$-0.658327\pi$
$463$	−20.5337	−0.954281	−0.477141	+	0.878827i	$0.658327\pi$
$464$	−0.771369	−0.0358099
$465$	−7.06184	−0.327485
$466$	6.74774	0.312583
$467$	−1.17921	−0.0545675	−0.0272838	−	0.999628i	$-0.508686\pi$
$467$	−1.17921	−0.0545675	−0.0272838	+	0.999628i	$0.508686\pi$
$468$	3.77137	0.174332
$469$	0	0
$470$	−4.06501	−0.187505
$471$	21.3760	0.984952
$472$	−6.42822	−0.295883
$473$	17.3021	0.795552
$474$	0.771369	0.0354302
$475$	−1.80743	−0.0829306
$476$	0	0
$477$	−7.37117	−0.337503
$478$	20.5918	0.941845
$479$	1.68264	0.0768816	0.0384408	−	0.999261i	$-0.487761\pi$
$479$	1.68264	0.0768816	0.0384408	+	0.999261i	$0.487761\pi$
$480$	1.82843	0.0834559
$481$	9.24686	0.421621
$482$	17.1814	0.782590
$483$	0	0
$484$	−8.17596	−0.371634
$485$	−19.0672	−0.865799
$486$	1.00000	0.0453609
$487$	−17.2901	−0.783488	−0.391744	−	0.920074i	$-0.628128\pi$
$487$	−17.2901	−0.783488	−0.391744	+	0.920074i	$0.628128\pi$
$488$	9.08548	0.411280
$489$	1.88048	0.0850383
$490$	0	0
$491$	25.7361	1.16146	0.580728	−	0.814098i	$-0.302768\pi$
$491$	25.7361	1.16146	0.580728	+	0.814098i	$0.302768\pi$
$492$	−1.09088	−0.0491807
$493$	−2.00540	−0.0903188
$494$	4.11412	0.185103
$495$	3.07265	0.138105
$496$	−3.86225	−0.173420
$497$	0	0
$498$	3.33734	0.149550
$499$	−23.1996	−1.03856	−0.519278	−	0.854605i	$-0.673799\pi$
$499$	−23.1996	−1.03856	−0.519278	+	0.854605i	$0.673799\pi$
$500$	−12.1716	−0.544329
$501$	−19.6511	−0.877944
$502$	−15.1760	−0.677336
$503$	−42.3054	−1.88631	−0.943153	−	0.332358i	$-0.892156\pi$
$503$	−42.3054	−1.88631	−0.943153	+	0.332358i	$0.892156\pi$
$504$	0	0
$505$	−11.8439	−0.527046
$506$	1.68049	0.0747068
$507$	1.22323	0.0543254
$508$	4.02363	0.178520
$509$	−27.9033	−1.23679	−0.618396	−	0.785866i	$-0.712217\pi$
$509$	−27.9033	−1.23679	−0.618396	+	0.785866i	$0.712217\pi$
$510$	4.75354	0.210490
$511$	0	0
$512$	1.00000	0.0441942
$513$	1.09088	0.0481636
$514$	−15.9946	−0.705491
$515$	−34.5395	−1.52199
$516$	10.2959	0.453251
$517$	−3.73611	−0.164314
$518$	0	0
$519$	−1.77097	−0.0777369
$520$	6.89567	0.302395
$521$	17.9554	0.786639	0.393320	−	0.919402i	$-0.371327\pi$
$521$	17.9554	0.786639	0.393320	+	0.919402i	$0.371327\pi$
$522$	−0.771369	−0.0337619
$523$	−12.9375	−0.565719	−0.282860	−	0.959161i	$-0.591283\pi$
$523$	−12.9375	−0.565719	−0.282860	+	0.959161i	$0.591283\pi$
$524$	10.9946	0.480301
$525$	0	0
$526$	21.7602	0.948788
$527$	−10.0411	−0.437396
$528$	1.68049	0.0731339
$529$	1.00000	0.0434783
$530$	−13.4776	−0.585431
$531$	−6.42822	−0.278961
$532$	0	0
$533$	−4.11412	−0.178202
$534$	3.20500	0.138694
$535$	25.2597	1.09207
$536$	−12.8903	−0.556775
$537$	−12.2232	−0.527471
$538$	20.5627	0.886522
$539$	0	0
$540$	1.82843	0.0786830
$541$	40.9797	1.76186	0.880928	−	0.473250i	$-0.156919\pi$
$541$	40.9797	1.76186	0.880928	+	0.473250i	$0.156919\pi$
$542$	3.86225	0.165898
$543$	0.820785	0.0352233
$544$	2.59980	0.111465
$545$	18.4080	0.788510
$546$	0	0
$547$	−41.6515	−1.78089	−0.890444	−	0.455093i	$-0.849606\pi$
$547$	−41.6515	−1.78089	−0.890444	+	0.455093i	$0.849606\pi$
$548$	4.14794	0.177191
$549$	9.08548	0.387759
$550$	−2.78432	−0.118724
$551$	−0.841472	−0.0358479
$552$	1.00000	0.0425628
$553$	0	0
$554$	24.1295	1.02516
$555$	4.48304	0.190295
$556$	−13.3137	−0.564627
$557$	−17.8158	−0.754879	−0.377439	−	0.926034i	$-0.623195\pi$
$557$	−17.8158	−0.754879	−0.377439	+	0.926034i	$0.623195\pi$
$558$	−3.86225	−0.163502
$559$	38.8296	1.64232
$560$	0	0
$561$	4.36893	0.184456
$562$	27.6853	1.16783
$563$	−0.891688	−0.0375802	−0.0187901	−	0.999823i	$-0.505981\pi$
$563$	−0.891688	−0.0375802	−0.0187901	+	0.999823i	$0.505981\pi$
$564$	−2.22323	−0.0936147
$565$	11.5263	0.484913
$566$	5.96618	0.250777
$567$	0	0
$568$	8.22863	0.345266
$569$	−7.29149	−0.305675	−0.152838	−	0.988251i	$-0.548841\pi$
$569$	−7.29149	−0.305675	−0.152838	+	0.988251i	$0.548841\pi$
$570$	1.99460	0.0835445
$571$	32.3803	1.35507	0.677537	−	0.735488i	$-0.263047\pi$
$571$	32.3803	1.35507	0.677537	+	0.735488i	$0.263047\pi$
$572$	6.33774	0.264994
$573$	−12.4519	−0.520184
$574$	0	0
$575$	−1.65685	−0.0690956
$576$	1.00000	0.0416667
$577$	−4.45401	−0.185423	−0.0927113	−	0.995693i	$-0.529553\pi$
$577$	−4.45401	−0.185423	−0.0927113	+	0.995693i	$0.529553\pi$
$578$	−10.2411	−0.425972
$579$	6.70412	0.278614
$580$	−1.41039	−0.0585634
$581$	0	0
$582$	−10.4282	−0.432264
$583$	−12.3872	−0.513024
$584$	−2.86225	−0.118441
$585$	6.89567	0.285101
$586$	−31.4853	−1.30064
$587$	−13.6693	−0.564192	−0.282096	−	0.959386i	$-0.591030\pi$
$587$	−13.6693	−0.564192	−0.282096	+	0.959386i	$0.591030\pi$
$588$	0	0
$589$	−4.21326	−0.173604
$590$	−11.7535	−0.483886
$591$	16.5606	0.681211
$592$	2.45186	0.100771
$593$	−13.2104	−0.542486	−0.271243	−	0.962511i	$-0.587435\pi$
$593$	−13.2104	−0.542486	−0.271243	+	0.962511i	$0.587435\pi$
$594$	1.68049	0.0689513
$595$	0	0
$596$	−11.8724	−0.486314
$597$	−5.01783	−0.205366
$598$	3.77137	0.154223
$599$	27.3133	1.11599	0.557996	−	0.829844i	$-0.311571\pi$
$599$	27.3133	1.11599	0.557996	+	0.829844i	$0.311571\pi$
$600$	−1.65685	−0.0676408
$601$	39.7677	1.62216	0.811079	−	0.584936i	$-0.198880\pi$
$601$	39.7677	1.62216	0.811079	+	0.584936i	$0.198880\pi$
$602$	0	0
$603$	−12.8903	−0.524932
$604$	1.07265	0.0436455
$605$	−14.9491	−0.607769
$606$	−6.47764	−0.263136
$607$	−9.51910	−0.386369	−0.193184	−	0.981162i	$-0.561882\pi$
$607$	−9.51910	−0.386369	−0.193184	+	0.981162i	$0.561882\pi$
$608$	1.09088	0.0442411
$609$	0	0
$610$	16.6121	0.672606
$611$	−8.38461	−0.339205
$612$	2.59980	0.105091
$613$	−45.7805	−1.84906	−0.924529	−	0.381111i	$-0.875542\pi$
$613$	−45.7805	−1.84906	−0.924529	+	0.381111i	$0.875542\pi$
$614$	5.13815	0.207359
$615$	−1.99460	−0.0804299
$616$	0	0
$617$	−23.5293	−0.947254	−0.473627	−	0.880726i	$-0.657055\pi$
$617$	−23.5293	−0.947254	−0.473627	+	0.880726i	$0.657055\pi$
$618$	−18.8903	−0.759878
$619$	−4.86449	−0.195520	−0.0977602	−	0.995210i	$-0.531168\pi$
$619$	−4.86449	−0.195520	−0.0977602	+	0.995210i	$0.531168\pi$
$620$	−7.06184	−0.283610
$621$	1.00000	0.0401286
$622$	−15.5627	−0.624008
$623$	0	0
$624$	3.77137	0.150976
$625$	−13.9706	−0.558823
$626$	−22.1527	−0.885401
$627$	1.83321	0.0732115
$628$	21.3760	0.852993
$629$	6.37433	0.254161
$630$	0	0
$631$	−25.5940	−1.01888	−0.509440	−	0.860506i	$-0.670148\pi$
$631$	−25.5940	−1.01888	−0.509440	+	0.860506i	$0.670148\pi$
$632$	0.771369	0.0306834
$633$	17.1523	0.681744
$634$	18.5627	0.737220
$635$	7.35692	0.291951
$636$	−7.37117	−0.292286
$637$	0	0
$638$	−1.29628	−0.0513201
$639$	8.22863	0.325520
$640$	1.82843	0.0722749
$641$	−14.6355	−0.578066	−0.289033	−	0.957319i	$-0.593334\pi$
$641$	−14.6355	−0.578066	−0.289033	+	0.957319i	$0.593334\pi$
$642$	13.8150	0.545234
$643$	41.6246	1.64151	0.820756	−	0.571279i	$-0.193552\pi$
$643$	41.6246	1.64151	0.820756	+	0.571279i	$0.193552\pi$
$644$	0	0
$645$	18.8253	0.741244
$646$	2.83607	0.111584
$647$	−31.6192	−1.24308	−0.621539	−	0.783383i	$-0.713492\pi$
$647$	−31.6192	−1.24308	−0.621539	+	0.783383i	$0.713492\pi$
$648$	1.00000	0.0392837
$649$	−10.8026	−0.424037
$650$	−6.24861	−0.245091
$651$	0	0
$652$	1.88048	0.0736453
$653$	−3.29628	−0.128993	−0.0644966	−	0.997918i	$-0.520544\pi$
$653$	−3.29628	−0.128993	−0.0644966	+	0.997918i	$0.520544\pi$
$654$	10.0676	0.393676
$655$	20.1028	0.785482
$656$	−1.09088	−0.0425917
$657$	−2.86225	−0.111667
$658$	0	0
$659$	0.0203785	0.000793834 0	0.000396917	−	1.00000i	$-0.499874\pi$
$659$	0.0203785	0.000793834 0	0.000396917		1.00000i	$0.499874\pi$
$660$	3.07265	0.119603
$661$	42.2013	1.64144	0.820721	−	0.571329i	$-0.193572\pi$
$661$	42.2013	1.64144	0.820721	+	0.571329i	$0.193572\pi$
$662$	2.86265	0.111260
$663$	9.80479	0.380787
$664$	3.33734	0.129514
$665$	0	0
$666$	2.45186	0.0950076
$667$	−0.771369	−0.0298675
$668$	−19.6511	−0.760322
$669$	4.42282	0.170996
$670$	−23.5689	−0.910547
$671$	15.2680	0.589416
$672$	0	0
$673$	−16.4540	−0.634255	−0.317128	−	0.948383i	$-0.602718\pi$
$673$	−16.4540	−0.634255	−0.317128	+	0.948383i	$0.602718\pi$
$674$	−7.70627	−0.296834
$675$	−1.65685	−0.0637723
$676$	1.22323	0.0470472
$677$	−23.8845	−0.917955	−0.458977	−	0.888448i	$-0.651784\pi$
$677$	−23.8845	−0.917955	−0.458977	+	0.888448i	$0.651784\pi$
$678$	6.30392	0.242101
$679$	0	0
$680$	4.75354	0.182290
$681$	−12.0905	−0.463308
$682$	−6.49047	−0.248533
$683$	11.0934	0.424478	0.212239	−	0.977218i	$-0.431924\pi$
$683$	11.0934	0.424478	0.212239	+	0.977218i	$0.431924\pi$
$684$	1.09088	0.0417109
$685$	7.58420	0.289778
$686$	0	0
$687$	−9.09088	−0.346839
$688$	10.2959	0.392527
$689$	−27.7994	−1.05907
$690$	1.82843	0.0696070
$691$	−6.63282	−0.252324	−0.126162	−	0.992010i	$-0.540266\pi$
$691$	−6.63282	−0.252324	−0.126162	+	0.992010i	$0.540266\pi$
$692$	−1.77097	−0.0673222
$693$	0	0
$694$	−9.94773	−0.377611
$695$	−24.3431	−0.923388
$696$	−0.771369	−0.0292387
$697$	−2.83607	−0.107424
$698$	−8.54489	−0.323429
$699$	6.74774	0.255223
$700$	0	0
$701$	−8.07784	−0.305096	−0.152548	−	0.988296i	$-0.548748\pi$
$701$	−8.07784	−0.305096	−0.152548	+	0.988296i	$0.548748\pi$
$702$	3.77137	0.142341
$703$	2.67469	0.100878
$704$	1.68049	0.0633358
$705$	−4.06501	−0.153097
$706$	−1.99460	−0.0750676
$707$	0	0
$708$	−6.42822	−0.241587
$709$	37.4893	1.40794	0.703970	−	0.710230i	$-0.251409\pi$
$709$	37.4893	1.40794	0.703970	+	0.710230i	$0.251409\pi$
$710$	15.0455	0.564646
$711$	0.771369	0.0289286
$712$	3.20500	0.120112
$713$	−3.86225	−0.144642
$714$	0	0
$715$	11.5881	0.433370
$716$	−12.2232	−0.456803
$717$	20.5918	0.769013
$718$	−27.7129	−1.03424
$719$	5.40244	0.201477	0.100739	−	0.994913i	$-0.467879\pi$
$719$	5.40244	0.201477	0.100739	+	0.994913i	$0.467879\pi$
$720$	1.82843	0.0681415
$721$	0	0
$722$	−17.8100	−0.662819
$723$	17.1814	0.638982
$724$	0.820785	0.0305043
$725$	1.27805	0.0474655
$726$	−8.17596	−0.303438
$727$	15.4461	0.572862	0.286431	−	0.958101i	$-0.407531\pi$
$727$	15.4461	0.572862	0.286431	+	0.958101i	$0.407531\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−5.23342	−0.193697
$731$	26.7672	0.990020
$732$	9.08548	0.335809
$733$	5.50167	0.203209	0.101604	−	0.994825i	$-0.467602\pi$
$733$	5.50167	0.203209	0.101604	+	0.994825i	$0.467602\pi$
$734$	−21.7758	−0.803758
$735$	0	0
$736$	1.00000	0.0368605
$737$	−21.6619	−0.797928
$738$	−1.09088	−0.0401559
$739$	−39.9419	−1.46929	−0.734644	−	0.678453i	$-0.762651\pi$
$739$	−39.9419	−1.46929	−0.734644	+	0.678453i	$0.762651\pi$
$740$	4.48304	0.164800
$741$	4.11412	0.151136
$742$	0	0
$743$	21.5889	0.792020	0.396010	−	0.918246i	$-0.370395\pi$
$743$	21.5889	0.792020	0.396010	+	0.918246i	$0.370395\pi$
$744$	−3.86225	−0.141597
$745$	−21.7079	−0.795316
$746$	13.3610	0.489180
$747$	3.33734	0.122107
$748$	4.36893	0.159744
$749$	0	0
$750$	−12.1716	−0.444443
$751$	−16.2312	−0.592284	−0.296142	−	0.955144i	$-0.595700\pi$
$751$	−16.2312	−0.592284	−0.296142	+	0.955144i	$0.595700\pi$
$752$	−2.22323	−0.0810728
$753$	−15.1760	−0.553043
$754$	−2.90912	−0.105944
$755$	1.96126	0.0713777
$756$	0	0
$757$	−25.4632	−0.925475	−0.462737	−	0.886495i	$-0.653133\pi$
$757$	−25.4632	−0.925475	−0.462737	+	0.886495i	$0.653133\pi$
$758$	−3.50892	−0.127450
$759$	1.68049	0.0609979
$760$	1.99460	0.0723516
$761$	−53.1985	−1.92844	−0.964222	−	0.265097i	$-0.914596\pi$
$761$	−53.1985	−1.92844	−0.964222	+	0.265097i	$0.914596\pi$
$762$	4.02363	0.145761
$763$	0	0
$764$	−12.4519	−0.450492
$765$	4.75354	0.171865
$766$	0.483043	0.0174531
$767$	−24.2432	−0.875371
$768$	1.00000	0.0360844
$769$	1.70627	0.0615297	0.0307648	−	0.999527i	$-0.490206\pi$
$769$	1.70627	0.0615297	0.0307648	+	0.999527i	$0.490206\pi$
$770$	0	0
$771$	−15.9946	−0.576031
$772$	6.70412	0.241287
$773$	27.0517	0.972980	0.486490	−	0.873686i	$-0.338277\pi$
$773$	27.0517	0.972980	0.486490	+	0.873686i	$0.338277\pi$
$774$	10.2959	0.370078
$775$	6.39919	0.229866
$776$	−10.4282	−0.374351
$777$	0	0
$778$	18.6282	0.667854
$779$	−1.19002	−0.0426369
$780$	6.89567	0.246905
$781$	13.8281	0.494809
$782$	2.59980	0.0929685
$783$	−0.771369	−0.0275665
$784$	0	0
$785$	39.0844	1.39498
$786$	10.9946	0.392164
$787$	34.3857	1.22572	0.612860	−	0.790192i	$-0.290019\pi$
$787$	34.3857	1.22572	0.612860	+	0.790192i	$0.290019\pi$
$788$	16.5606	0.589946
$789$	21.7602	0.774682
$790$	1.41039	0.0501795
$791$	0	0
$792$	1.68049	0.0597136
$793$	34.2647	1.21677
$794$	31.7445	1.12657
$795$	−13.4776	−0.478003
$796$	−5.01783	−0.177852
$797$	−7.25705	−0.257058	−0.128529	−	0.991706i	$-0.541026\pi$
$797$	−7.25705	−0.257058	−0.128529	+	0.991706i	$0.541026\pi$
$798$	0	0
$799$	−5.77994	−0.204480
$800$	−1.65685	−0.0585786
$801$	3.20500	0.113243
$802$	−20.7762	−0.733632
$803$	−4.80998	−0.169740
$804$	−12.8903	−0.454605
$805$	0	0
$806$	−14.5660	−0.513065
$807$	20.5627	0.723842
$808$	−6.47764	−0.227883
$809$	−6.44105	−0.226455	−0.113228	−	0.993569i	$-0.536119\pi$
$809$	−6.44105	−0.226455	−0.113228	+	0.993569i	$0.536119\pi$
$810$	1.82843	0.0642444
$811$	21.6925	0.761727	0.380864	−	0.924631i	$-0.375627\pi$
$811$	21.6925	0.761727	0.380864	+	0.924631i	$0.375627\pi$
$812$	0	0
$813$	3.86225	0.135455
$814$	4.12032	0.144417
$815$	3.43832	0.120439
$816$	2.59980	0.0910111
$817$	11.2316	0.392943
$818$	19.6951	0.688622
$819$	0	0
$820$	−1.99460	−0.0696543
$821$	−5.07805	−0.177225	−0.0886127	−	0.996066i	$-0.528243\pi$
$821$	−5.07805	−0.177225	−0.0886127	+	0.996066i	$0.528243\pi$
$822$	4.14794	0.144676
$823$	54.3723	1.89530	0.947650	−	0.319312i	$-0.103452\pi$
$823$	54.3723	1.89530	0.947650	+	0.319312i	$0.103452\pi$
$824$	−18.8903	−0.658074
$825$	−2.78432	−0.0969377
$826$	0	0
$827$	−23.8979	−0.831012	−0.415506	−	0.909590i	$-0.636395\pi$
$827$	−23.8979	−0.831012	−0.415506	+	0.909590i	$0.636395\pi$
$828$	1.00000	0.0347524
$829$	−9.33989	−0.324388	−0.162194	−	0.986759i	$-0.551857\pi$
$829$	−9.33989	−0.324388	−0.162194	+	0.986759i	$0.551857\pi$
$830$	6.10209	0.211807
$831$	24.1295	0.837043
$832$	3.77137	0.130749
$833$	0	0
$834$	−13.3137	−0.461016
$835$	−35.9305	−1.24343
$836$	1.83321	0.0634030
$837$	−3.86225	−0.133499
$838$	−1.70412	−0.0588679
$839$	56.1851	1.93973	0.969863	−	0.243651i	$-0.0783450\pi$
$839$	56.1851	1.93973	0.969863	+	0.243651i	$0.0783450\pi$
$840$	0	0
$841$	−28.4050	−0.979482
$842$	−12.8564	−0.443062
$843$	27.6853	0.953531
$844$	17.1523	0.590407
$845$	2.23658	0.0769407
$846$	−2.22323	−0.0764361
$847$	0	0
$848$	−7.37117	−0.253127
$849$	5.96618	0.204759
$850$	−4.30748	−0.147745
$851$	2.45186	0.0840486
$852$	8.22863	0.281908
$853$	32.1818	1.10188	0.550941	−	0.834544i	$-0.314269\pi$
$853$	32.1818	1.10188	0.550941	+	0.834544i	$0.314269\pi$
$854$	0	0
$855$	1.99460	0.0682138
$856$	13.8150	0.472186
$857$	14.3893	0.491529	0.245765	−	0.969330i	$-0.420961\pi$
$857$	14.3893	0.491529	0.245765	+	0.969330i	$0.420961\pi$
$858$	6.33774	0.216367
$859$	−28.8242	−0.983467	−0.491734	−	0.870746i	$-0.663637\pi$
$859$	−28.8242	−0.983467	−0.491734	+	0.870746i	$0.663637\pi$
$860$	18.8253	0.641936
$861$	0	0
$862$	−11.5419	−0.393120
$863$	−39.3593	−1.33981	−0.669904	−	0.742448i	$-0.733665\pi$
$863$	−39.3593	−1.33981	−0.669904	+	0.742448i	$0.733665\pi$
$864$	1.00000	0.0340207
$865$	−3.23809	−0.110098
$866$	−24.7627	−0.841471
$867$	−10.2411	−0.347805
$868$	0	0
$869$	1.29628	0.0439732
$870$	−1.41039	−0.0478168
$871$	−48.6140	−1.64722
$872$	10.0676	0.340934
$873$	−10.4282	−0.352942
$874$	1.09088	0.0368996
$875$	0	0
$876$	−2.86225	−0.0967065
$877$	31.8382	1.07510	0.537550	−	0.843232i	$-0.319350\pi$
$877$	31.8382	1.07510	0.537550	+	0.843232i	$0.319350\pi$
$878$	−7.82579	−0.264108
$879$	−31.4853	−1.06197
$880$	3.07265	0.103579
$881$	−3.69068	−0.124342	−0.0621710	−	0.998066i	$-0.519802\pi$
$881$	−3.69068	−0.124342	−0.0621710	+	0.998066i	$0.519802\pi$
$882$	0	0
$883$	50.0034	1.68275	0.841374	−	0.540454i	$-0.181747\pi$
$883$	50.0034	1.68275	0.841374	+	0.540454i	$0.181747\pi$
$884$	9.80479	0.329771
$885$	−11.7535	−0.395091
$886$	−0.994597	−0.0334141
$887$	40.1337	1.34756	0.673779	−	0.738933i	$-0.264670\pi$
$887$	40.1337	1.34756	0.673779	+	0.738933i	$0.264670\pi$
$888$	2.45186	0.0822790
$889$	0	0
$890$	5.86010	0.196431
$891$	1.68049	0.0562985
$892$	4.42282	0.148087
$893$	−2.42528	−0.0811588
$894$	−11.8724	−0.397074
$895$	−22.3493	−0.747054
$896$	0	0
$897$	3.77137	0.125922
$898$	26.1291	0.871939
$899$	2.97922	0.0993626
$900$	−1.65685	−0.0552285
$901$	−19.1635	−0.638430
$902$	−1.83321	−0.0610393
$903$	0	0
$904$	6.30392	0.209665
$905$	1.50075	0.0498865
$906$	1.07265	0.0356364
$907$	16.6558	0.553048	0.276524	−	0.961007i	$-0.410817\pi$
$907$	16.6558	0.553048	0.276524	+	0.961007i	$0.410817\pi$
$908$	−12.0905	−0.401237
$909$	−6.47764	−0.214850
$910$	0	0
$911$	−59.6860	−1.97749	−0.988743	−	0.149625i	$-0.952193\pi$
$911$	−59.6860	−1.97749	−0.988743	+	0.149625i	$0.952193\pi$
$912$	1.09088	0.0361227
$913$	5.60837	0.185610
$914$	18.7445	0.620012
$915$	16.6121	0.549180
$916$	−9.09088	−0.300371
$917$	0	0
$918$	2.59980	0.0858061
$919$	−37.6122	−1.24071	−0.620356	−	0.784320i	$-0.713012\pi$
$919$	−37.6122	−1.24071	−0.620356	+	0.784320i	$0.713012\pi$
$920$	1.82843	0.0602815
$921$	5.13815	0.169308
$922$	−5.63648	−0.185627
$923$	31.0332	1.02147
$924$	0	0
$925$	−4.06237	−0.133570
$926$	−20.5337	−0.674779
$927$	−18.8903	−0.620438
$928$	−0.771369	−0.0253214
$929$	−15.7095	−0.515413	−0.257706	−	0.966223i	$-0.582967\pi$
$929$	−15.7095	−0.515413	−0.257706	+	0.966223i	$0.582967\pi$
$930$	−7.06184	−0.231567
$931$	0	0
$932$	6.74774	0.221029
$933$	−15.5627	−0.509501
$934$	−1.17921	−0.0385851
$935$	7.98827	0.261244
$936$	3.77137	0.123271
$937$	−42.2196	−1.37925	−0.689627	−	0.724165i	$-0.742225\pi$
$937$	−42.2196	−1.37925	−0.689627	+	0.724165i	$0.742225\pi$
$938$	0	0
$939$	−22.1527	−0.722927
$940$	−4.06501	−0.132586
$941$	26.6722	0.869490	0.434745	−	0.900554i	$-0.356839\pi$
$941$	26.6722	0.869490	0.434745	+	0.900554i	$0.356839\pi$
$942$	21.3760	0.696466
$943$	−1.09088	−0.0355240
$944$	−6.42822	−0.209221
$945$	0	0
$946$	17.3021	0.562540
$947$	−41.0789	−1.33488	−0.667442	−	0.744662i	$-0.732611\pi$
$947$	−41.0789	−1.33488	−0.667442	+	0.744662i	$0.732611\pi$
$948$	0.771369	0.0250529
$949$	−10.7946	−0.350408
$950$	−1.80743	−0.0586408
$951$	18.5627	0.601937
$952$	0	0
$953$	−35.0374	−1.13497	−0.567487	−	0.823383i	$-0.692084\pi$
$953$	−35.0374	−1.13497	−0.567487	+	0.823383i	$0.692084\pi$
$954$	−7.37117	−0.238650
$955$	−22.7673	−0.736733
$956$	20.5918	0.665985
$957$	−1.29628	−0.0419027
$958$	1.68264	0.0543635
$959$	0	0
$960$	1.82843	0.0590122
$961$	−16.0830	−0.518807
$962$	9.24686	0.298131
$963$	13.8150	0.445182
$964$	17.1814	0.553374
$965$	12.2580	0.394599
$966$	0	0
$967$	6.28833	0.202219	0.101109	−	0.994875i	$-0.467761\pi$
$967$	6.28833	0.202219	0.101109	+	0.994875i	$0.467761\pi$
$968$	−8.17596	−0.262785
$969$	2.83607	0.0911077
$970$	−19.0672	−0.612212
$971$	34.9942	1.12302	0.561509	−	0.827471i	$-0.310221\pi$
$971$	34.9942	1.12302	0.561509	+	0.827471i	$0.310221\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	−17.2901	−0.554010
$975$	−6.24861	−0.200116
$976$	9.08548	0.290819
$977$	12.1632	0.389136	0.194568	−	0.980889i	$-0.437670\pi$
$977$	12.1632	0.389136	0.194568	+	0.980889i	$0.437670\pi$
$978$	1.88048	0.0601312
$979$	5.38596	0.172136
$980$	0	0
$981$	10.0676	0.321435
$982$	25.7361	0.821273
$983$	−31.3083	−0.998580	−0.499290	−	0.866435i	$-0.666406\pi$
$983$	−31.3083	−0.998580	−0.499290	+	0.866435i	$0.666406\pi$
$984$	−1.09088	−0.0347760
$985$	30.2798	0.964794
$986$	−2.00540	−0.0638651
$987$	0	0
$988$	4.11412	0.130887
$989$	10.2959	0.327390
$990$	3.07265	0.0976552
$991$	−44.3959	−1.41028	−0.705142	−	0.709067i	$-0.749117\pi$
$991$	−44.3959	−1.41028	−0.705142	+	0.709067i	$0.749117\pi$
$992$	−3.86225	−0.122627
$993$	2.86265	0.0908435
$994$	0	0
$995$	−9.17474	−0.290859
$996$	3.33734	0.105748
$997$	45.2814	1.43408	0.717038	−	0.697034i	$-0.245497\pi$
$997$	45.2814	1.43408	0.717038	+	0.697034i	$0.245497\pi$
$998$	−23.1996	−0.734370
$999$	2.45186	0.0775733

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6762.2.a.cp.1.3		4
7.2	even	3		966.2.i.l.277.2	✓	8
7.4	even	3		966.2.i.l.415.2	yes	8
7.6	odd	2		6762.2.a.cm.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.i.l.277.2	✓	8	7.2	even	3
966.2.i.l.415.2	yes	8	7.4	even	3
6762.2.a.cm.1.1		4	7.6	odd	2
6762.2.a.cp.1.3		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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.82843 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.82843 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +1.82843 q^{10} +1.68049 q^{11} +1.00000 q^{12} +3.77137 q^{13} +1.82843 q^{15} +1.00000 q^{16} +2.59980 q^{17} +1.00000 q^{18} +1.09088 q^{19} +1.82843 q^{20} +1.68049 q^{22} +1.00000 q^{23} +1.00000 q^{24} -1.65685 q^{25} +3.77137 q^{26} +1.00000 q^{27} -0.771369 q^{29} +1.82843 q^{30} -3.86225 q^{31} +1.00000 q^{32} +1.68049 q^{33} +2.59980 q^{34} +1.00000 q^{36} +2.45186 q^{37} +1.09088 q^{38} +3.77137 q^{39} +1.82843 q^{40} -1.09088 q^{41} +10.2959 q^{43} +1.68049 q^{44} +1.82843 q^{45} +1.00000 q^{46} -2.22323 q^{47} +1.00000 q^{48} -1.65685 q^{50} +2.59980 q^{51} +3.77137 q^{52} -7.37117 q^{53} +1.00000 q^{54} +3.07265 q^{55} +1.09088 q^{57} -0.771369 q^{58} -6.42822 q^{59} +1.82843 q^{60} +9.08548 q^{61} -3.86225 q^{62} +1.00000 q^{64} +6.89567 q^{65} +1.68049 q^{66} -12.8903 q^{67} +2.59980 q^{68} +1.00000 q^{69} +8.22863 q^{71} +1.00000 q^{72} -2.86225 q^{73} +2.45186 q^{74} -1.65685 q^{75} +1.09088 q^{76} +3.77137 q^{78} +0.771369 q^{79} +1.82843 q^{80} +1.00000 q^{81} -1.09088 q^{82} +3.33734 q^{83} +4.75354 q^{85} +10.2959 q^{86} -0.771369 q^{87} +1.68049 q^{88} +3.20500 q^{89} +1.82843 q^{90} +1.00000 q^{92} -3.86225 q^{93} -2.22323 q^{94} +1.99460 q^{95} +1.00000 q^{96} -10.4282 q^{97} +1.68049 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 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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