LMFDB - Embedded newform 6762.2.a.ca.1.1

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:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 966)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.41421$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -3.00000 q^{11} -1.00000 q^{12} -1.41421 q^{13} -1.00000 q^{15} +1.00000 q^{16} +1.41421 q^{17} +1.00000 q^{18} +3.41421 q^{19} +1.00000 q^{20} -3.00000 q^{22} -1.00000 q^{23} -1.00000 q^{24} -4.00000 q^{25} -1.41421 q^{26} -1.00000 q^{27} -0.757359 q^{29} -1.00000 q^{30} -4.65685 q^{31} +1.00000 q^{32} +3.00000 q^{33} +1.41421 q^{34} +1.00000 q^{36} -9.07107 q^{37} +3.41421 q^{38} +1.41421 q^{39} +1.00000 q^{40} -1.75736 q^{41} -7.65685 q^{43} -3.00000 q^{44} +1.00000 q^{45} -1.00000 q^{46} +9.31371 q^{47} -1.00000 q^{48} -4.00000 q^{50} -1.41421 q^{51} -1.41421 q^{52} -2.17157 q^{53} -1.00000 q^{54} -3.00000 q^{55} -3.41421 q^{57} -0.757359 q^{58} +0.757359 q^{59} -1.00000 q^{60} +6.00000 q^{61} -4.65685 q^{62} +1.00000 q^{64} -1.41421 q^{65} +3.00000 q^{66} -4.34315 q^{67} +1.41421 q^{68} +1.00000 q^{69} +5.89949 q^{71} +1.00000 q^{72} -5.65685 q^{73} -9.07107 q^{74} +4.00000 q^{75} +3.41421 q^{76} +1.41421 q^{78} -0.414214 q^{79} +1.00000 q^{80} +1.00000 q^{81} -1.75736 q^{82} -12.3137 q^{83} +1.41421 q^{85} -7.65685 q^{86} +0.757359 q^{87} -3.00000 q^{88} -14.7279 q^{89} +1.00000 q^{90} -1.00000 q^{92} +4.65685 q^{93} +9.31371 q^{94} +3.41421 q^{95} -1.00000 q^{96} +3.58579 q^{97} -3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{8} + 2 q^{9} + 2 q^{10} - 6 q^{11} - 2 q^{12} - 2 q^{15} + 2 q^{16} + 2 q^{18} + 4 q^{19} + 2 q^{20} - 6 q^{22} - 2 q^{23} - 2 q^{24} - 8 q^{25} - 2 q^{27} - 10 q^{29} - 2 q^{30} + 2 q^{31} + 2 q^{32} + 6 q^{33} + 2 q^{36} - 4 q^{37} + 4 q^{38} + 2 q^{40} - 12 q^{41} - 4 q^{43} - 6 q^{44} + 2 q^{45} - 2 q^{46} - 4 q^{47} - 2 q^{48} - 8 q^{50} - 10 q^{53} - 2 q^{54} - 6 q^{55} - 4 q^{57} - 10 q^{58} + 10 q^{59} - 2 q^{60} + 12 q^{61} + 2 q^{62} + 2 q^{64} + 6 q^{66} - 20 q^{67} + 2 q^{69} - 8 q^{71} + 2 q^{72} - 4 q^{74} + 8 q^{75} + 4 q^{76} + 2 q^{79} + 2 q^{80} + 2 q^{81} - 12 q^{82} - 2 q^{83} - 4 q^{86} + 10 q^{87} - 6 q^{88} - 4 q^{89} + 2 q^{90} - 2 q^{92} - 2 q^{93} - 4 q^{94} + 4 q^{95} - 2 q^{96} + 10 q^{97} - 6 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^8 + 2 * q^9 + 2 * q^10 - 6 * q^11 - 2 * q^12 - 2 * q^15 + 2 * q^16 + 2 * q^18 + 4 * q^19 + 2 * q^20 - 6 * q^22 - 2 * q^23 - 2 * q^24 - 8 * q^25 - 2 * q^27 - 10 * q^29 - 2 * q^30 + 2 * q^31 + 2 * q^32 + 6 * q^33 + 2 * q^36 - 4 * q^37 + 4 * q^38 + 2 * q^40 - 12 * q^41 - 4 * q^43 - 6 * q^44 + 2 * q^45 - 2 * q^46 - 4 * q^47 - 2 * q^48 - 8 * q^50 - 10 * q^53 - 2 * q^54 - 6 * q^55 - 4 * q^57 - 10 * q^58 + 10 * q^59 - 2 * q^60 + 12 * q^61 + 2 * q^62 + 2 * q^64 + 6 * q^66 - 20 * q^67 + 2 * q^69 - 8 * q^71 + 2 * q^72 - 4 * q^74 + 8 * q^75 + 4 * q^76 + 2 * q^79 + 2 * q^80 + 2 * q^81 - 12 * q^82 - 2 * q^83 - 4 * q^86 + 10 * q^87 - 6 * q^88 - 4 * q^89 + 2 * q^90 - 2 * q^92 - 2 * q^93 - 4 * q^94 + 4 * q^95 - 2 * 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
$5$	1.00000	0.447214	0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.00000	0.447214	0.223607	+	0.974679i	$0.428217\pi$
$6$	−1.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	−3.00000	−0.904534	−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000	−0.904534	−0.452267	+	0.891883i	$0.649385\pi$
$12$	−1.00000	−0.288675
$13$	−1.41421	−0.392232	−0.196116	−	0.980581i	$-0.562833\pi$
$13$	−1.41421	−0.392232	−0.196116	+	0.980581i	$0.562833\pi$
$14$	0	0
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	1.41421	0.342997	0.171499	−	0.985184i	$-0.445139\pi$
$17$	1.41421	0.342997	0.171499	+	0.985184i	$0.445139\pi$
$18$	1.00000	0.235702
$19$	3.41421	0.783274	0.391637	−	0.920120i	$-0.371909\pi$
$19$	3.41421	0.783274	0.391637	+	0.920120i	$0.371909\pi$
$20$	1.00000	0.223607
$21$	0	0
$22$	−3.00000	−0.639602
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−1.00000	−0.204124
$25$	−4.00000	−0.800000
$26$	−1.41421	−0.277350
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−0.757359	−0.140638	−0.0703190	−	0.997525i	$-0.522402\pi$
$29$	−0.757359	−0.140638	−0.0703190	+	0.997525i	$0.522402\pi$
$30$	−1.00000	−0.182574
$31$	−4.65685	−0.836396	−0.418198	−	0.908356i	$-0.637338\pi$
$31$	−4.65685	−0.836396	−0.418198	+	0.908356i	$0.637338\pi$
$32$	1.00000	0.176777
$33$	3.00000	0.522233
$34$	1.41421	0.242536
$35$	0	0
$36$	1.00000	0.166667
$37$	−9.07107	−1.49127	−0.745637	−	0.666352i	$-0.767855\pi$
$37$	−9.07107	−1.49127	−0.745637	+	0.666352i	$0.767855\pi$
$38$	3.41421	0.553859
$39$	1.41421	0.226455
$40$	1.00000	0.158114
$41$	−1.75736	−0.274453	−0.137227	−	0.990540i	$-0.543819\pi$
$41$	−1.75736	−0.274453	−0.137227	+	0.990540i	$0.543819\pi$
$42$	0	0
$43$	−7.65685	−1.16766	−0.583830	−	0.811876i	$-0.698446\pi$
$43$	−7.65685	−1.16766	−0.583830	+	0.811876i	$0.698446\pi$
$44$	−3.00000	−0.452267
$45$	1.00000	0.149071
$46$	−1.00000	−0.147442
$47$	9.31371	1.35854	0.679272	−	0.733887i	$-0.262296\pi$
$47$	9.31371	1.35854	0.679272	+	0.733887i	$0.262296\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	−4.00000	−0.565685
$51$	−1.41421	−0.198030
$52$	−1.41421	−0.196116
$53$	−2.17157	−0.298288	−0.149144	−	0.988815i	$-0.547652\pi$
$53$	−2.17157	−0.298288	−0.149144	+	0.988815i	$0.547652\pi$
$54$	−1.00000	−0.136083
$55$	−3.00000	−0.404520
$56$	0	0
$57$	−3.41421	−0.452224
$58$	−0.757359	−0.0994461
$59$	0.757359	0.0985998	0.0492999	−	0.998784i	$-0.484301\pi$
$59$	0.757359	0.0985998	0.0492999	+	0.998784i	$0.484301\pi$
$60$	−1.00000	−0.129099
$61$	6.00000	0.768221	0.384111	−	0.923287i	$-0.374508\pi$
$61$	6.00000	0.768221	0.384111	+	0.923287i	$0.374508\pi$
$62$	−4.65685	−0.591421
$63$	0	0
$64$	1.00000	0.125000
$65$	−1.41421	−0.175412
$66$	3.00000	0.369274
$67$	−4.34315	−0.530600	−0.265300	−	0.964166i	$-0.585471\pi$
$67$	−4.34315	−0.530600	−0.265300	+	0.964166i	$0.585471\pi$
$68$	1.41421	0.171499
$69$	1.00000	0.120386
$70$	0	0
$71$	5.89949	0.700141	0.350071	−	0.936723i	$-0.386158\pi$
$71$	5.89949	0.700141	0.350071	+	0.936723i	$0.386158\pi$
$72$	1.00000	0.117851
$73$	−5.65685	−0.662085	−0.331042	−	0.943616i	$-0.607400\pi$
$73$	−5.65685	−0.662085	−0.331042	+	0.943616i	$0.607400\pi$
$74$	−9.07107	−1.05449
$75$	4.00000	0.461880
$76$	3.41421	0.391637
$77$	0	0
$78$	1.41421	0.160128
$79$	−0.414214	−0.0466027	−0.0233013	−	0.999728i	$-0.507418\pi$
$79$	−0.414214	−0.0466027	−0.0233013	+	0.999728i	$0.507418\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	−1.75736	−0.194068
$83$	−12.3137	−1.35161	−0.675803	−	0.737083i	$-0.736203\pi$
$83$	−12.3137	−1.35161	−0.675803	+	0.737083i	$0.736203\pi$
$84$	0	0
$85$	1.41421	0.153393
$86$	−7.65685	−0.825660
$87$	0.757359	0.0811974
$88$	−3.00000	−0.319801
$89$	−14.7279	−1.56116	−0.780578	−	0.625058i	$-0.785075\pi$
$89$	−14.7279	−1.56116	−0.780578	+	0.625058i	$0.785075\pi$
$90$	1.00000	0.105409
$91$	0	0
$92$	−1.00000	−0.104257
$93$	4.65685	0.482893
$94$	9.31371	0.960636
$95$	3.41421	0.350291
$96$	−1.00000	−0.102062
$97$	3.58579	0.364081	0.182041	−	0.983291i	$-0.441730\pi$
$97$	3.58579	0.364081	0.182041	+	0.983291i	$0.441730\pi$
$98$	0	0
$99$	−3.00000	−0.301511
$100$	−4.00000	−0.400000
$101$	4.48528	0.446302	0.223151	−	0.974784i	$-0.428366\pi$
$101$	4.48528	0.446302	0.223151	+	0.974784i	$0.428366\pi$
$102$	−1.41421	−0.140028
$103$	13.6569	1.34565	0.672825	−	0.739802i	$-0.265081\pi$
$103$	13.6569	1.34565	0.672825	+	0.739802i	$0.265081\pi$
$104$	−1.41421	−0.138675
$105$	0	0
$106$	−2.17157	−0.210922
$107$	−7.48528	−0.723629	−0.361815	−	0.932250i	$-0.617843\pi$
$107$	−7.48528	−0.723629	−0.361815	+	0.932250i	$0.617843\pi$
$108$	−1.00000	−0.0962250
$109$	5.31371	0.508961	0.254480	−	0.967078i	$-0.418096\pi$
$109$	5.31371	0.508961	0.254480	+	0.967078i	$0.418096\pi$
$110$	−3.00000	−0.286039
$111$	9.07107	0.860988
$112$	0	0
$113$	−17.4142	−1.63819	−0.819096	−	0.573657i	$-0.805524\pi$
$113$	−17.4142	−1.63819	−0.819096	+	0.573657i	$0.805524\pi$
$114$	−3.41421	−0.319770
$115$	−1.00000	−0.0932505
$116$	−0.757359	−0.0703190
$117$	−1.41421	−0.130744
$118$	0.757359	0.0697206
$119$	0	0
$120$	−1.00000	−0.0912871
$121$	−2.00000	−0.181818
$122$	6.00000	0.543214
$123$	1.75736	0.158456
$124$	−4.65685	−0.418198
$125$	−9.00000	−0.804984
$126$	0	0
$127$	−5.82843	−0.517189	−0.258595	−	0.965986i	$-0.583259\pi$
$127$	−5.82843	−0.517189	−0.258595	+	0.965986i	$0.583259\pi$
$128$	1.00000	0.0883883
$129$	7.65685	0.674148
$130$	−1.41421	−0.124035
$131$	1.24264	0.108570	0.0542850	−	0.998525i	$-0.482712\pi$
$131$	1.24264	0.108570	0.0542850	+	0.998525i	$0.482712\pi$
$132$	3.00000	0.261116
$133$	0	0
$134$	−4.34315	−0.375191
$135$	−1.00000	−0.0860663
$136$	1.41421	0.121268
$137$	−18.9706	−1.62076	−0.810382	−	0.585901i	$-0.800741\pi$
$137$	−18.9706	−1.62076	−0.810382	+	0.585901i	$0.800741\pi$
$138$	1.00000	0.0851257
$139$	5.31371	0.450703	0.225351	−	0.974278i	$-0.427647\pi$
$139$	5.31371	0.450703	0.225351	+	0.974278i	$0.427647\pi$
$140$	0	0
$141$	−9.31371	−0.784356
$142$	5.89949	0.495075
$143$	4.24264	0.354787
$144$	1.00000	0.0833333
$145$	−0.757359	−0.0628953
$146$	−5.65685	−0.468165
$147$	0	0
$148$	−9.07107	−0.745637
$149$	13.6569	1.11881	0.559407	−	0.828893i	$-0.311029\pi$
$149$	13.6569	1.11881	0.559407	+	0.828893i	$0.311029\pi$
$150$	4.00000	0.326599
$151$	−1.34315	−0.109304	−0.0546518	−	0.998505i	$-0.517405\pi$
$151$	−1.34315	−0.109304	−0.0546518	+	0.998505i	$0.517405\pi$
$152$	3.41421	0.276929
$153$	1.41421	0.114332
$154$	0	0
$155$	−4.65685	−0.374048
$156$	1.41421	0.113228
$157$	3.89949	0.311214	0.155607	−	0.987819i	$-0.450267\pi$
$157$	3.89949	0.311214	0.155607	+	0.987819i	$0.450267\pi$
$158$	−0.414214	−0.0329531
$159$	2.17157	0.172217
$160$	1.00000	0.0790569
$161$	0	0
$162$	1.00000	0.0785674
$163$	−1.41421	−0.110770	−0.0553849	−	0.998465i	$-0.517639\pi$
$163$	−1.41421	−0.110770	−0.0553849	+	0.998465i	$0.517639\pi$
$164$	−1.75736	−0.137227
$165$	3.00000	0.233550
$166$	−12.3137	−0.955729
$167$	−18.4853	−1.43043	−0.715217	−	0.698902i	$-0.753672\pi$
$167$	−18.4853	−1.43043	−0.715217	+	0.698902i	$0.753672\pi$
$168$	0	0
$169$	−11.0000	−0.846154
$170$	1.41421	0.108465
$171$	3.41421	0.261091
$172$	−7.65685	−0.583830
$173$	−4.82843	−0.367099	−0.183549	−	0.983011i	$-0.558759\pi$
$173$	−4.82843	−0.367099	−0.183549	+	0.983011i	$0.558759\pi$
$174$	0.757359	0.0574153
$175$	0	0
$176$	−3.00000	−0.226134
$177$	−0.757359	−0.0569266
$178$	−14.7279	−1.10390
$179$	16.0000	1.19590	0.597948	−	0.801535i	$-0.295983\pi$
$179$	16.0000	1.19590	0.597948	+	0.801535i	$0.295983\pi$
$180$	1.00000	0.0745356
$181$	12.4853	0.928024	0.464012	−	0.885829i	$-0.346410\pi$
$181$	12.4853	0.928024	0.464012	+	0.885829i	$0.346410\pi$
$182$	0	0
$183$	−6.00000	−0.443533
$184$	−1.00000	−0.0737210
$185$	−9.07107	−0.666918
$186$	4.65685	0.341457
$187$	−4.24264	−0.310253
$188$	9.31371	0.679272
$189$	0	0
$190$	3.41421	0.247693
$191$	1.41421	0.102329	0.0511645	−	0.998690i	$-0.483707\pi$
$191$	1.41421	0.102329	0.0511645	+	0.998690i	$0.483707\pi$
$192$	−1.00000	−0.0721688
$193$	−19.6274	−1.41281	−0.706406	−	0.707807i	$-0.749685\pi$
$193$	−19.6274	−1.41281	−0.706406	+	0.707807i	$0.749685\pi$
$194$	3.58579	0.257444
$195$	1.41421	0.101274
$196$	0	0
$197$	−3.17157	−0.225965	−0.112983	−	0.993597i	$-0.536040\pi$
$197$	−3.17157	−0.225965	−0.112983	+	0.993597i	$0.536040\pi$
$198$	−3.00000	−0.213201
$199$	−5.31371	−0.376679	−0.188339	−	0.982104i	$-0.560310\pi$
$199$	−5.31371	−0.376679	−0.188339	+	0.982104i	$0.560310\pi$
$200$	−4.00000	−0.282843
$201$	4.34315	0.306342
$202$	4.48528	0.315583
$203$	0	0
$204$	−1.41421	−0.0990148
$205$	−1.75736	−0.122739
$206$	13.6569	0.951518
$207$	−1.00000	−0.0695048
$208$	−1.41421	−0.0980581
$209$	−10.2426	−0.708498
$210$	0	0
$211$	4.82843	0.332403	0.166201	−	0.986092i	$-0.446850\pi$
$211$	4.82843	0.332403	0.166201	+	0.986092i	$0.446850\pi$
$212$	−2.17157	−0.149144
$213$	−5.89949	−0.404227
$214$	−7.48528	−0.511683
$215$	−7.65685	−0.522193
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	5.31371	0.359890
$219$	5.65685	0.382255
$220$	−3.00000	−0.202260
$221$	−2.00000	−0.134535
$222$	9.07107	0.608810
$223$	10.1716	0.681139	0.340569	−	0.940219i	$-0.389380\pi$
$223$	10.1716	0.681139	0.340569	+	0.940219i	$0.389380\pi$
$224$	0	0
$225$	−4.00000	−0.266667
$226$	−17.4142	−1.15838
$227$	7.82843	0.519591	0.259795	−	0.965664i	$-0.416345\pi$
$227$	7.82843	0.519591	0.259795	+	0.965664i	$0.416345\pi$
$228$	−3.41421	−0.226112
$229$	−22.7279	−1.50190	−0.750952	−	0.660357i	$-0.770405\pi$
$229$	−22.7279	−1.50190	−0.750952	+	0.660357i	$0.770405\pi$
$230$	−1.00000	−0.0659380
$231$	0	0
$232$	−0.757359	−0.0497231
$233$	15.2132	0.996650	0.498325	−	0.866990i	$-0.333949\pi$
$233$	15.2132	0.996650	0.498325	+	0.866990i	$0.333949\pi$
$234$	−1.41421	−0.0924500
$235$	9.31371	0.607559
$236$	0.757359	0.0492999
$237$	0.414214	0.0269061
$238$	0	0
$239$	−23.3137	−1.50804	−0.754019	−	0.656852i	$-0.771887\pi$
$239$	−23.3137	−1.50804	−0.754019	+	0.656852i	$0.771887\pi$
$240$	−1.00000	−0.0645497
$241$	9.92893	0.639579	0.319789	−	0.947489i	$-0.396388\pi$
$241$	9.92893	0.639579	0.319789	+	0.947489i	$0.396388\pi$
$242$	−2.00000	−0.128565
$243$	−1.00000	−0.0641500
$244$	6.00000	0.384111
$245$	0	0
$246$	1.75736	0.112045
$247$	−4.82843	−0.307225
$248$	−4.65685	−0.295711
$249$	12.3137	0.780350
$250$	−9.00000	−0.569210
$251$	−25.8284	−1.63028	−0.815138	−	0.579267i	$-0.803339\pi$
$251$	−25.8284	−1.63028	−0.815138	+	0.579267i	$0.803339\pi$
$252$	0	0
$253$	3.00000	0.188608
$254$	−5.82843	−0.365708
$255$	−1.41421	−0.0885615
$256$	1.00000	0.0625000
$257$	1.41421	0.0882162	0.0441081	−	0.999027i	$-0.485955\pi$
$257$	1.41421	0.0882162	0.0441081	+	0.999027i	$0.485955\pi$
$258$	7.65685	0.476695
$259$	0	0
$260$	−1.41421	−0.0877058
$261$	−0.757359	−0.0468794
$262$	1.24264	0.0767706
$263$	10.9706	0.676474	0.338237	−	0.941061i	$-0.390169\pi$
$263$	10.9706	0.676474	0.338237	+	0.941061i	$0.390169\pi$
$264$	3.00000	0.184637
$265$	−2.17157	−0.133399
$266$	0	0
$267$	14.7279	0.901334
$268$	−4.34315	−0.265300
$269$	−1.58579	−0.0966871	−0.0483436	−	0.998831i	$-0.515394\pi$
$269$	−1.58579	−0.0966871	−0.0483436	+	0.998831i	$0.515394\pi$
$270$	−1.00000	−0.0608581
$271$	7.00000	0.425220	0.212610	−	0.977137i	$-0.431804\pi$
$271$	7.00000	0.425220	0.212610	+	0.977137i	$0.431804\pi$
$272$	1.41421	0.0857493
$273$	0	0
$274$	−18.9706	−1.14605
$275$	12.0000	0.723627
$276$	1.00000	0.0601929
$277$	−2.82843	−0.169944	−0.0849719	−	0.996383i	$-0.527080\pi$
$277$	−2.82843	−0.169944	−0.0849719	+	0.996383i	$0.527080\pi$
$278$	5.31371	0.318695
$279$	−4.65685	−0.278799
$280$	0	0
$281$	−26.7279	−1.59445	−0.797227	−	0.603680i	$-0.793701\pi$
$281$	−26.7279	−1.59445	−0.797227	+	0.603680i	$0.793701\pi$
$282$	−9.31371	−0.554623
$283$	24.1421	1.43510	0.717551	−	0.696506i	$-0.245263\pi$
$283$	24.1421	1.43510	0.717551	+	0.696506i	$0.245263\pi$
$284$	5.89949	0.350071
$285$	−3.41421	−0.202241
$286$	4.24264	0.250873
$287$	0	0
$288$	1.00000	0.0589256
$289$	−15.0000	−0.882353
$290$	−0.757359	−0.0444737
$291$	−3.58579	−0.210203
$292$	−5.65685	−0.331042
$293$	21.6274	1.26349	0.631744	−	0.775177i	$-0.282340\pi$
$293$	21.6274	1.26349	0.631744	+	0.775177i	$0.282340\pi$
$294$	0	0
$295$	0.757359	0.0440952
$296$	−9.07107	−0.527245
$297$	3.00000	0.174078
$298$	13.6569	0.791120
$299$	1.41421	0.0817861
$300$	4.00000	0.230940
$301$	0	0
$302$	−1.34315	−0.0772894
$303$	−4.48528	−0.257673
$304$	3.41421	0.195819
$305$	6.00000	0.343559
$306$	1.41421	0.0808452
$307$	−25.8995	−1.47816	−0.739081	−	0.673616i	$-0.764740\pi$
$307$	−25.8995	−1.47816	−0.739081	+	0.673616i	$0.764740\pi$
$308$	0	0
$309$	−13.6569	−0.776911
$310$	−4.65685	−0.264492
$311$	−3.41421	−0.193602	−0.0968011	−	0.995304i	$-0.530861\pi$
$311$	−3.41421	−0.193602	−0.0968011	+	0.995304i	$0.530861\pi$
$312$	1.41421	0.0800641
$313$	−16.7574	−0.947182	−0.473591	−	0.880745i	$-0.657042\pi$
$313$	−16.7574	−0.947182	−0.473591	+	0.880745i	$0.657042\pi$
$314$	3.89949	0.220061
$315$	0	0
$316$	−0.414214	−0.0233013
$317$	9.92893	0.557664	0.278832	−	0.960340i	$-0.410053\pi$
$317$	9.92893	0.557664	0.278832	+	0.960340i	$0.410053\pi$
$318$	2.17157	0.121776
$319$	2.27208	0.127212
$320$	1.00000	0.0559017
$321$	7.48528	0.417788
$322$	0	0
$323$	4.82843	0.268661
$324$	1.00000	0.0555556
$325$	5.65685	0.313786
$326$	−1.41421	−0.0783260
$327$	−5.31371	−0.293849
$328$	−1.75736	−0.0970339
$329$	0	0
$330$	3.00000	0.165145
$331$	25.8995	1.42356	0.711782	−	0.702400i	$-0.247888\pi$
$331$	25.8995	1.42356	0.711782	+	0.702400i	$0.247888\pi$
$332$	−12.3137	−0.675803
$333$	−9.07107	−0.497091
$334$	−18.4853	−1.01147
$335$	−4.34315	−0.237291
$336$	0	0
$337$	−13.9289	−0.758757	−0.379379	−	0.925242i	$-0.623862\pi$
$337$	−13.9289	−0.758757	−0.379379	+	0.925242i	$0.623862\pi$
$338$	−11.0000	−0.598321
$339$	17.4142	0.945810
$340$	1.41421	0.0766965
$341$	13.9706	0.756548
$342$	3.41421	0.184620
$343$	0	0
$344$	−7.65685	−0.412830
$345$	1.00000	0.0538382
$346$	−4.82843	−0.259578
$347$	−14.6274	−0.785241	−0.392620	−	0.919701i	$-0.628431\pi$
$347$	−14.6274	−0.785241	−0.392620	+	0.919701i	$0.628431\pi$
$348$	0.757359	0.0405987
$349$	−26.0416	−1.39398	−0.696988	−	0.717083i	$-0.745477\pi$
$349$	−26.0416	−1.39398	−0.696988	+	0.717083i	$0.745477\pi$
$350$	0	0
$351$	1.41421	0.0754851
$352$	−3.00000	−0.159901
$353$	22.7279	1.20969	0.604843	−	0.796345i	$-0.293236\pi$
$353$	22.7279	1.20969	0.604843	+	0.796345i	$0.293236\pi$
$354$	−0.757359	−0.0402532
$355$	5.89949	0.313113
$356$	−14.7279	−0.780578
$357$	0	0
$358$	16.0000	0.845626
$359$	2.00000	0.105556	0.0527780	−	0.998606i	$-0.483192\pi$
$359$	2.00000	0.105556	0.0527780	+	0.998606i	$0.483192\pi$
$360$	1.00000	0.0527046
$361$	−7.34315	−0.386481
$362$	12.4853	0.656212
$363$	2.00000	0.104973
$364$	0	0
$365$	−5.65685	−0.296093
$366$	−6.00000	−0.313625
$367$	34.6985	1.81125	0.905623	−	0.424084i	$-0.139404\pi$
$367$	34.6985	1.81125	0.905623	+	0.424084i	$0.139404\pi$
$368$	−1.00000	−0.0521286
$369$	−1.75736	−0.0914845
$370$	−9.07107	−0.471582
$371$	0	0
$372$	4.65685	0.241447
$373$	−14.3431	−0.742660	−0.371330	−	0.928501i	$-0.621098\pi$
$373$	−14.3431	−0.742660	−0.371330	+	0.928501i	$0.621098\pi$
$374$	−4.24264	−0.219382
$375$	9.00000	0.464758
$376$	9.31371	0.480318
$377$	1.07107	0.0551628
$378$	0	0
$379$	28.9706	1.48812	0.744059	−	0.668114i	$-0.232898\pi$
$379$	28.9706	1.48812	0.744059	+	0.668114i	$0.232898\pi$
$380$	3.41421	0.175145
$381$	5.82843	0.298599
$382$	1.41421	0.0723575
$383$	1.27208	0.0650001	0.0325001	−	0.999472i	$-0.489653\pi$
$383$	1.27208	0.0650001	0.0325001	+	0.999472i	$0.489653\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−19.6274	−0.999009
$387$	−7.65685	−0.389220
$388$	3.58579	0.182041
$389$	−1.17157	−0.0594011	−0.0297006	−	0.999559i	$-0.509455\pi$
$389$	−1.17157	−0.0594011	−0.0297006	+	0.999559i	$0.509455\pi$
$390$	1.41421	0.0716115
$391$	−1.41421	−0.0715199
$392$	0	0
$393$	−1.24264	−0.0626829
$394$	−3.17157	−0.159782
$395$	−0.414214	−0.0208413
$396$	−3.00000	−0.150756
$397$	−0.443651	−0.0222662	−0.0111331	−	0.999938i	$-0.503544\pi$
$397$	−0.443651	−0.0222662	−0.0111331	+	0.999938i	$0.503544\pi$
$398$	−5.31371	−0.266352
$399$	0	0
$400$	−4.00000	−0.200000
$401$	−0.485281	−0.0242338	−0.0121169	−	0.999927i	$-0.503857\pi$
$401$	−0.485281	−0.0242338	−0.0121169	+	0.999927i	$0.503857\pi$
$402$	4.34315	0.216616
$403$	6.58579	0.328061
$404$	4.48528	0.223151
$405$	1.00000	0.0496904
$406$	0	0
$407$	27.2132	1.34891
$408$	−1.41421	−0.0700140
$409$	13.3431	0.659776	0.329888	−	0.944020i	$-0.392989\pi$
$409$	13.3431	0.659776	0.329888	+	0.944020i	$0.392989\pi$
$410$	−1.75736	−0.0867898
$411$	18.9706	0.935749
$412$	13.6569	0.672825
$413$	0	0
$414$	−1.00000	−0.0491473
$415$	−12.3137	−0.604456
$416$	−1.41421	−0.0693375
$417$	−5.31371	−0.260213
$418$	−10.2426	−0.500984
$419$	6.00000	0.293119	0.146560	−	0.989202i	$-0.453180\pi$
$419$	6.00000	0.293119	0.146560	+	0.989202i	$0.453180\pi$
$420$	0	0
$421$	31.4558	1.53306	0.766532	−	0.642206i	$-0.221981\pi$
$421$	31.4558	1.53306	0.766532	+	0.642206i	$0.221981\pi$
$422$	4.82843	0.235044
$423$	9.31371	0.452848
$424$	−2.17157	−0.105461
$425$	−5.65685	−0.274398
$426$	−5.89949	−0.285831
$427$	0	0
$428$	−7.48528	−0.361815
$429$	−4.24264	−0.204837
$430$	−7.65685	−0.369246
$431$	6.34315	0.305539	0.152769	−	0.988262i	$-0.451181\pi$
$431$	6.34315	0.305539	0.152769	+	0.988262i	$0.451181\pi$
$432$	−1.00000	−0.0481125
$433$	−30.0000	−1.44171	−0.720854	−	0.693087i	$-0.756250\pi$
$433$	−30.0000	−1.44171	−0.720854	+	0.693087i	$0.756250\pi$
$434$	0	0
$435$	0.757359	0.0363126
$436$	5.31371	0.254480
$437$	−3.41421	−0.163324
$438$	5.65685	0.270295
$439$	−11.1421	−0.531785	−0.265893	−	0.964003i	$-0.585667\pi$
$439$	−11.1421	−0.531785	−0.265893	+	0.964003i	$0.585667\pi$
$440$	−3.00000	−0.143019
$441$	0	0
$442$	−2.00000	−0.0951303
$443$	10.2721	0.488041	0.244021	−	0.969770i	$-0.421534\pi$
$443$	10.2721	0.488041	0.244021	+	0.969770i	$0.421534\pi$
$444$	9.07107	0.430494
$445$	−14.7279	−0.698170
$446$	10.1716	0.481638
$447$	−13.6569	−0.645947
$448$	0	0
$449$	−1.75736	−0.0829349	−0.0414675	−	0.999140i	$-0.513203\pi$
$449$	−1.75736	−0.0829349	−0.0414675	+	0.999140i	$0.513203\pi$
$450$	−4.00000	−0.188562
$451$	5.27208	0.248252
$452$	−17.4142	−0.819096
$453$	1.34315	0.0631065
$454$	7.82843	0.367406
$455$	0	0
$456$	−3.41421	−0.159885
$457$	20.2132	0.945534	0.472767	−	0.881188i	$-0.343255\pi$
$457$	20.2132	0.945534	0.472767	+	0.881188i	$0.343255\pi$
$458$	−22.7279	−1.06201
$459$	−1.41421	−0.0660098
$460$	−1.00000	−0.0466252
$461$	−30.9706	−1.44244	−0.721221	−	0.692705i	$-0.756419\pi$
$461$	−30.9706	−1.44244	−0.721221	+	0.692705i	$0.756419\pi$
$462$	0	0
$463$	−13.7990	−0.641293	−0.320647	−	0.947199i	$-0.603900\pi$
$463$	−13.7990	−0.641293	−0.320647	+	0.947199i	$0.603900\pi$
$464$	−0.757359	−0.0351595
$465$	4.65685	0.215956
$466$	15.2132	0.704738
$467$	−28.8284	−1.33402	−0.667010	−	0.745049i	$-0.732426\pi$
$467$	−28.8284	−1.33402	−0.667010	+	0.745049i	$0.732426\pi$
$468$	−1.41421	−0.0653720
$469$	0	0
$470$	9.31371	0.429609
$471$	−3.89949	−0.179679
$472$	0.757359	0.0348603
$473$	22.9706	1.05619
$474$	0.414214	0.0190255
$475$	−13.6569	−0.626619
$476$	0	0
$477$	−2.17157	−0.0994295
$478$	−23.3137	−1.06634
$479$	−30.5269	−1.39481	−0.697405	−	0.716677i	$-0.745662\pi$
$479$	−30.5269	−1.39481	−0.697405	+	0.716677i	$0.745662\pi$
$480$	−1.00000	−0.0456435
$481$	12.8284	0.584926
$482$	9.92893	0.452250
$483$	0	0
$484$	−2.00000	−0.0909091
$485$	3.58579	0.162822
$486$	−1.00000	−0.0453609
$487$	−29.4853	−1.33611	−0.668053	−	0.744114i	$-0.732872\pi$
$487$	−29.4853	−1.33611	−0.668053	+	0.744114i	$0.732872\pi$
$488$	6.00000	0.271607
$489$	1.41421	0.0639529
$490$	0	0
$491$	−9.10051	−0.410700	−0.205350	−	0.978689i	$-0.565833\pi$
$491$	−9.10051	−0.410700	−0.205350	+	0.978689i	$0.565833\pi$
$492$	1.75736	0.0792279
$493$	−1.07107	−0.0482385
$494$	−4.82843	−0.217241
$495$	−3.00000	−0.134840
$496$	−4.65685	−0.209099
$497$	0	0
$498$	12.3137	0.551790
$499$	−13.7990	−0.617728	−0.308864	−	0.951106i	$-0.599949\pi$
$499$	−13.7990	−0.617728	−0.308864	+	0.951106i	$0.599949\pi$
$500$	−9.00000	−0.402492
$501$	18.4853	0.825861
$502$	−25.8284	−1.15278
$503$	6.82843	0.304465	0.152232	−	0.988345i	$-0.451354\pi$
$503$	6.82843	0.304465	0.152232	+	0.988345i	$0.451354\pi$
$504$	0	0
$505$	4.48528	0.199592
$506$	3.00000	0.133366
$507$	11.0000	0.488527
$508$	−5.82843	−0.258595
$509$	−41.7279	−1.84956	−0.924779	−	0.380505i	$-0.875750\pi$
$509$	−41.7279	−1.84956	−0.924779	+	0.380505i	$0.875750\pi$
$510$	−1.41421	−0.0626224
$511$	0	0
$512$	1.00000	0.0441942
$513$	−3.41421	−0.150741
$514$	1.41421	0.0623783
$515$	13.6569	0.601793
$516$	7.65685	0.337074
$517$	−27.9411	−1.22885
$518$	0	0
$519$	4.82843	0.211944
$520$	−1.41421	−0.0620174
$521$	−26.0000	−1.13908	−0.569540	−	0.821963i	$-0.692879\pi$
$521$	−26.0000	−1.13908	−0.569540	+	0.821963i	$0.692879\pi$
$522$	−0.757359	−0.0331487
$523$	16.2843	0.712061	0.356031	−	0.934474i	$-0.384130\pi$
$523$	16.2843	0.712061	0.356031	+	0.934474i	$0.384130\pi$
$524$	1.24264	0.0542850
$525$	0	0
$526$	10.9706	0.478339
$527$	−6.58579	−0.286881
$528$	3.00000	0.130558
$529$	1.00000	0.0434783
$530$	−2.17157	−0.0943271
$531$	0.757359	0.0328666
$532$	0	0
$533$	2.48528	0.107649
$534$	14.7279	0.637340
$535$	−7.48528	−0.323617
$536$	−4.34315	−0.187595
$537$	−16.0000	−0.690451
$538$	−1.58579	−0.0683681
$539$	0	0
$540$	−1.00000	−0.0430331
$541$	−39.6985	−1.70677	−0.853386	−	0.521280i	$-0.825455\pi$
$541$	−39.6985	−1.70677	−0.853386	+	0.521280i	$0.825455\pi$
$542$	7.00000	0.300676
$543$	−12.4853	−0.535795
$544$	1.41421	0.0606339
$545$	5.31371	0.227614
$546$	0	0
$547$	24.2426	1.03654	0.518270	−	0.855217i	$-0.326576\pi$
$547$	24.2426	1.03654	0.518270	+	0.855217i	$0.326576\pi$
$548$	−18.9706	−0.810382
$549$	6.00000	0.256074
$550$	12.0000	0.511682
$551$	−2.58579	−0.110158
$552$	1.00000	0.0425628
$553$	0	0
$554$	−2.82843	−0.120168
$555$	9.07107	0.385045
$556$	5.31371	0.225351
$557$	−40.3137	−1.70815	−0.854073	−	0.520153i	$-0.825875\pi$
$557$	−40.3137	−1.70815	−0.854073	+	0.520153i	$0.825875\pi$
$558$	−4.65685	−0.197140
$559$	10.8284	0.457994
$560$	0	0
$561$	4.24264	0.179124
$562$	−26.7279	−1.12745
$563$	13.1421	0.553875	0.276937	−	0.960888i	$-0.410681\pi$
$563$	13.1421	0.553875	0.276937	+	0.960888i	$0.410681\pi$
$564$	−9.31371	−0.392178
$565$	−17.4142	−0.732621
$566$	24.1421	1.01477
$567$	0	0
$568$	5.89949	0.247537
$569$	−5.85786	−0.245574	−0.122787	−	0.992433i	$-0.539183\pi$
$569$	−5.85786	−0.245574	−0.122787	+	0.992433i	$0.539183\pi$
$570$	−3.41421	−0.143006
$571$	40.5269	1.69600	0.847999	−	0.529997i	$-0.177807\pi$
$571$	40.5269	1.69600	0.847999	+	0.529997i	$0.177807\pi$
$572$	4.24264	0.177394
$573$	−1.41421	−0.0590796
$574$	0	0
$575$	4.00000	0.166812
$576$	1.00000	0.0416667
$577$	7.62742	0.317534	0.158767	−	0.987316i	$-0.449248\pi$
$577$	7.62742	0.317534	0.158767	+	0.987316i	$0.449248\pi$
$578$	−15.0000	−0.623918
$579$	19.6274	0.815688
$580$	−0.757359	−0.0314476
$581$	0	0
$582$	−3.58579	−0.148636
$583$	6.51472	0.269812
$584$	−5.65685	−0.234082
$585$	−1.41421	−0.0584705
$586$	21.6274	0.893420
$587$	2.41421	0.0996453	0.0498226	−	0.998758i	$-0.484134\pi$
$587$	2.41421	0.0996453	0.0498226	+	0.998758i	$0.484134\pi$
$588$	0	0
$589$	−15.8995	−0.655127
$590$	0.757359	0.0311800
$591$	3.17157	0.130461
$592$	−9.07107	−0.372819
$593$	−8.97056	−0.368377	−0.184188	−	0.982891i	$-0.558966\pi$
$593$	−8.97056	−0.368377	−0.184188	+	0.982891i	$0.558966\pi$
$594$	3.00000	0.123091
$595$	0	0
$596$	13.6569	0.559407
$597$	5.31371	0.217476
$598$	1.41421	0.0578315
$599$	−0.928932	−0.0379551	−0.0189776	−	0.999820i	$-0.506041\pi$
$599$	−0.928932	−0.0379551	−0.0189776	+	0.999820i	$0.506041\pi$
$600$	4.00000	0.163299
$601$	40.9411	1.67002	0.835012	−	0.550232i	$-0.185461\pi$
$601$	40.9411	1.67002	0.835012	+	0.550232i	$0.185461\pi$
$602$	0	0
$603$	−4.34315	−0.176867
$604$	−1.34315	−0.0546518
$605$	−2.00000	−0.0813116
$606$	−4.48528	−0.182202
$607$	−19.2843	−0.782724	−0.391362	−	0.920237i	$-0.627996\pi$
$607$	−19.2843	−0.782724	−0.391362	+	0.920237i	$0.627996\pi$
$608$	3.41421	0.138465
$609$	0	0
$610$	6.00000	0.242933
$611$	−13.1716	−0.532865
$612$	1.41421	0.0571662
$613$	−16.0000	−0.646234	−0.323117	−	0.946359i	$-0.604731\pi$
$613$	−16.0000	−0.646234	−0.323117	+	0.946359i	$0.604731\pi$
$614$	−25.8995	−1.04522
$615$	1.75736	0.0708636
$616$	0	0
$617$	−31.9411	−1.28590	−0.642951	−	0.765908i	$-0.722290\pi$
$617$	−31.9411	−1.28590	−0.642951	+	0.765908i	$0.722290\pi$
$618$	−13.6569	−0.549359
$619$	−9.89949	−0.397894	−0.198947	−	0.980010i	$-0.563752\pi$
$619$	−9.89949	−0.397894	−0.198947	+	0.980010i	$0.563752\pi$
$620$	−4.65685	−0.187024
$621$	1.00000	0.0401286
$622$	−3.41421	−0.136897
$623$	0	0
$624$	1.41421	0.0566139
$625$	11.0000	0.440000
$626$	−16.7574	−0.669759
$627$	10.2426	0.409052
$628$	3.89949	0.155607
$629$	−12.8284	−0.511503
$630$	0	0
$631$	2.41421	0.0961083	0.0480542	−	0.998845i	$-0.484698\pi$
$631$	2.41421	0.0961083	0.0480542	+	0.998845i	$0.484698\pi$
$632$	−0.414214	−0.0164765
$633$	−4.82843	−0.191913
$634$	9.92893	0.394328
$635$	−5.82843	−0.231294
$636$	2.17157	0.0861085
$637$	0	0
$638$	2.27208	0.0899524
$639$	5.89949	0.233380
$640$	1.00000	0.0395285
$641$	39.6985	1.56800	0.783998	−	0.620763i	$-0.213177\pi$
$641$	39.6985	1.56800	0.783998	+	0.620763i	$0.213177\pi$
$642$	7.48528	0.295420
$643$	10.5858	0.417463	0.208731	−	0.977973i	$-0.433067\pi$
$643$	10.5858	0.417463	0.208731	+	0.977973i	$0.433067\pi$
$644$	0	0
$645$	7.65685	0.301488
$646$	4.82843	0.189972
$647$	0.828427	0.0325688	0.0162844	−	0.999867i	$-0.494816\pi$
$647$	0.828427	0.0325688	0.0162844	+	0.999867i	$0.494816\pi$
$648$	1.00000	0.0392837
$649$	−2.27208	−0.0891869
$650$	5.65685	0.221880
$651$	0	0
$652$	−1.41421	−0.0553849
$653$	45.7279	1.78947	0.894736	−	0.446596i	$-0.147364\pi$
$653$	45.7279	1.78947	0.894736	+	0.446596i	$0.147364\pi$
$654$	−5.31371	−0.207782
$655$	1.24264	0.0485540
$656$	−1.75736	−0.0686134
$657$	−5.65685	−0.220695
$658$	0	0
$659$	−43.9411	−1.71170	−0.855852	−	0.517221i	$-0.826966\pi$
$659$	−43.9411	−1.71170	−0.855852	+	0.517221i	$0.826966\pi$
$660$	3.00000	0.116775
$661$	−10.9706	−0.426705	−0.213353	−	0.976975i	$-0.568438\pi$
$661$	−10.9706	−0.426705	−0.213353	+	0.976975i	$0.568438\pi$
$662$	25.8995	1.00661
$663$	2.00000	0.0776736
$664$	−12.3137	−0.477865
$665$	0	0
$666$	−9.07107	−0.351497
$667$	0.757359	0.0293251
$668$	−18.4853	−0.715217
$669$	−10.1716	−0.393256
$670$	−4.34315	−0.167790
$671$	−18.0000	−0.694882
$672$	0	0
$673$	10.0294	0.386606	0.193303	−	0.981139i	$-0.438080\pi$
$673$	10.0294	0.386606	0.193303	+	0.981139i	$0.438080\pi$
$674$	−13.9289	−0.536522
$675$	4.00000	0.153960
$676$	−11.0000	−0.423077
$677$	42.6569	1.63944	0.819718	−	0.572767i	$-0.194130\pi$
$677$	42.6569	1.63944	0.819718	+	0.572767i	$0.194130\pi$
$678$	17.4142	0.668789
$679$	0	0
$680$	1.41421	0.0542326
$681$	−7.82843	−0.299986
$682$	13.9706	0.534960
$683$	−7.04163	−0.269441	−0.134720	−	0.990884i	$-0.543014\pi$
$683$	−7.04163	−0.269441	−0.134720	+	0.990884i	$0.543014\pi$
$684$	3.41421	0.130546
$685$	−18.9706	−0.724828
$686$	0	0
$687$	22.7279	0.867124
$688$	−7.65685	−0.291915
$689$	3.07107	0.116998
$690$	1.00000	0.0380693
$691$	46.5858	1.77221	0.886103	−	0.463488i	$-0.153402\pi$
$691$	46.5858	1.77221	0.886103	+	0.463488i	$0.153402\pi$
$692$	−4.82843	−0.183549
$693$	0	0
$694$	−14.6274	−0.555249
$695$	5.31371	0.201560
$696$	0.757359	0.0287076
$697$	−2.48528	−0.0941367
$698$	−26.0416	−0.985690
$699$	−15.2132	−0.575416
$700$	0	0
$701$	0.514719	0.0194407	0.00972033	−	0.999953i	$-0.496906\pi$
$701$	0.514719	0.0194407	0.00972033	+	0.999953i	$0.496906\pi$
$702$	1.41421	0.0533761
$703$	−30.9706	−1.16808
$704$	−3.00000	−0.113067
$705$	−9.31371	−0.350775
$706$	22.7279	0.855377
$707$	0	0
$708$	−0.757359	−0.0284633
$709$	−6.58579	−0.247334	−0.123667	−	0.992324i	$-0.539466\pi$
$709$	−6.58579	−0.247334	−0.123667	+	0.992324i	$0.539466\pi$
$710$	5.89949	0.221404
$711$	−0.414214	−0.0155342
$712$	−14.7279	−0.551952
$713$	4.65685	0.174401
$714$	0	0
$715$	4.24264	0.158666
$716$	16.0000	0.597948
$717$	23.3137	0.870666
$718$	2.00000	0.0746393
$719$	0.142136	0.00530076	0.00265038	−	0.999996i	$-0.499156\pi$
$719$	0.142136	0.00530076	0.00265038	+	0.999996i	$0.499156\pi$
$720$	1.00000	0.0372678
$721$	0	0
$722$	−7.34315	−0.273284
$723$	−9.92893	−0.369261
$724$	12.4853	0.464012
$725$	3.02944	0.112510
$726$	2.00000	0.0742270
$727$	5.44365	0.201894	0.100947	−	0.994892i	$-0.467813\pi$
$727$	5.44365	0.201894	0.100947	+	0.994892i	$0.467813\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−5.65685	−0.209370
$731$	−10.8284	−0.400504
$732$	−6.00000	−0.221766
$733$	−15.5563	−0.574587	−0.287293	−	0.957843i	$-0.592755\pi$
$733$	−15.5563	−0.574587	−0.287293	+	0.957843i	$0.592755\pi$
$734$	34.6985	1.28074
$735$	0	0
$736$	−1.00000	−0.0368605
$737$	13.0294	0.479945
$738$	−1.75736	−0.0646893
$739$	20.8284	0.766186	0.383093	−	0.923710i	$-0.374859\pi$
$739$	20.8284	0.766186	0.383093	+	0.923710i	$0.374859\pi$
$740$	−9.07107	−0.333459
$741$	4.82843	0.177377
$742$	0	0
$743$	−6.24264	−0.229020	−0.114510	−	0.993422i	$-0.536530\pi$
$743$	−6.24264	−0.229020	−0.114510	+	0.993422i	$0.536530\pi$
$744$	4.65685	0.170729
$745$	13.6569	0.500348
$746$	−14.3431	−0.525140
$747$	−12.3137	−0.450535
$748$	−4.24264	−0.155126
$749$	0	0
$750$	9.00000	0.328634
$751$	35.5269	1.29640	0.648198	−	0.761472i	$-0.275523\pi$
$751$	35.5269	1.29640	0.648198	+	0.761472i	$0.275523\pi$
$752$	9.31371	0.339636
$753$	25.8284	0.941240
$754$	1.07107	0.0390060
$755$	−1.34315	−0.0488821
$756$	0	0
$757$	39.0711	1.42006	0.710031	−	0.704170i	$-0.248681\pi$
$757$	39.0711	1.42006	0.710031	+	0.704170i	$0.248681\pi$
$758$	28.9706	1.05226
$759$	−3.00000	−0.108893
$760$	3.41421	0.123847
$761$	−4.58579	−0.166235	−0.0831173	−	0.996540i	$-0.526488\pi$
$761$	−4.58579	−0.166235	−0.0831173	+	0.996540i	$0.526488\pi$
$762$	5.82843	0.211142
$763$	0	0
$764$	1.41421	0.0511645
$765$	1.41421	0.0511310
$766$	1.27208	0.0459620
$767$	−1.07107	−0.0386740
$768$	−1.00000	−0.0360844
$769$	42.0122	1.51500	0.757499	−	0.652836i	$-0.226421\pi$
$769$	42.0122	1.51500	0.757499	+	0.652836i	$0.226421\pi$
$770$	0	0
$771$	−1.41421	−0.0509317
$772$	−19.6274	−0.706406
$773$	−22.8284	−0.821081	−0.410541	−	0.911842i	$-0.634660\pi$
$773$	−22.8284	−0.821081	−0.410541	+	0.911842i	$0.634660\pi$
$774$	−7.65685	−0.275220
$775$	18.6274	0.669117
$776$	3.58579	0.128722
$777$	0	0
$778$	−1.17157	−0.0420029
$779$	−6.00000	−0.214972
$780$	1.41421	0.0506370
$781$	−17.6985	−0.633302
$782$	−1.41421	−0.0505722
$783$	0.757359	0.0270658
$784$	0	0
$785$	3.89949	0.139179
$786$	−1.24264	−0.0443235
$787$	−23.4558	−0.836111	−0.418055	−	0.908422i	$-0.637288\pi$
$787$	−23.4558	−0.836111	−0.418055	+	0.908422i	$0.637288\pi$
$788$	−3.17157	−0.112983
$789$	−10.9706	−0.390562
$790$	−0.414214	−0.0147371
$791$	0	0
$792$	−3.00000	−0.106600
$793$	−8.48528	−0.301321
$794$	−0.443651	−0.0157446
$795$	2.17157	0.0770178
$796$	−5.31371	−0.188339
$797$	3.97056	0.140645	0.0703223	−	0.997524i	$-0.477597\pi$
$797$	3.97056	0.140645	0.0703223	+	0.997524i	$0.477597\pi$
$798$	0	0
$799$	13.1716	0.465977
$800$	−4.00000	−0.141421
$801$	−14.7279	−0.520386
$802$	−0.485281	−0.0171359
$803$	16.9706	0.598878
$804$	4.34315	0.153171
$805$	0	0
$806$	6.58579	0.231974
$807$	1.58579	0.0558223
$808$	4.48528	0.157792
$809$	50.5269	1.77643	0.888216	−	0.459426i	$-0.151945\pi$
$809$	50.5269	1.77643	0.888216	+	0.459426i	$0.151945\pi$
$810$	1.00000	0.0351364
$811$	42.2843	1.48480	0.742401	−	0.669956i	$-0.233687\pi$
$811$	42.2843	1.48480	0.742401	+	0.669956i	$0.233687\pi$
$812$	0	0
$813$	−7.00000	−0.245501
$814$	27.2132	0.953822
$815$	−1.41421	−0.0495377
$816$	−1.41421	−0.0495074
$817$	−26.1421	−0.914598
$818$	13.3431	0.466532
$819$	0	0
$820$	−1.75736	−0.0613696
$821$	14.7574	0.515035	0.257518	−	0.966274i	$-0.417095\pi$
$821$	14.7574	0.515035	0.257518	+	0.966274i	$0.417095\pi$
$822$	18.9706	0.661674
$823$	46.6274	1.62533	0.812665	−	0.582731i	$-0.198016\pi$
$823$	46.6274	1.62533	0.812665	+	0.582731i	$0.198016\pi$
$824$	13.6569	0.475759
$825$	−12.0000	−0.417786
$826$	0	0
$827$	20.7990	0.723252	0.361626	−	0.932323i	$-0.382222\pi$
$827$	20.7990	0.723252	0.361626	+	0.932323i	$0.382222\pi$
$828$	−1.00000	−0.0347524
$829$	27.5147	0.955626	0.477813	−	0.878462i	$-0.341430\pi$
$829$	27.5147	0.955626	0.477813	+	0.878462i	$0.341430\pi$
$830$	−12.3137	−0.427415
$831$	2.82843	0.0981170
$832$	−1.41421	−0.0490290
$833$	0	0
$834$	−5.31371	−0.183999
$835$	−18.4853	−0.639710
$836$	−10.2426	−0.354249
$837$	4.65685	0.160964
$838$	6.00000	0.207267
$839$	17.6985	0.611020	0.305510	−	0.952189i	$-0.401173\pi$
$839$	17.6985	0.611020	0.305510	+	0.952189i	$0.401173\pi$
$840$	0	0
$841$	−28.4264	−0.980221
$842$	31.4558	1.08404
$843$	26.7279	0.920559
$844$	4.82843	0.166201
$845$	−11.0000	−0.378412
$846$	9.31371	0.320212
$847$	0	0
$848$	−2.17157	−0.0745721
$849$	−24.1421	−0.828556
$850$	−5.65685	−0.194029
$851$	9.07107	0.310952
$852$	−5.89949	−0.202113
$853$	28.1421	0.963568	0.481784	−	0.876290i	$-0.339989\pi$
$853$	28.1421	0.963568	0.481784	+	0.876290i	$0.339989\pi$
$854$	0	0
$855$	3.41421	0.116764
$856$	−7.48528	−0.255842
$857$	−26.8701	−0.917864	−0.458932	−	0.888471i	$-0.651768\pi$
$857$	−26.8701	−0.917864	−0.458932	+	0.888471i	$0.651768\pi$
$858$	−4.24264	−0.144841
$859$	−19.4142	−0.662404	−0.331202	−	0.943560i	$-0.607454\pi$
$859$	−19.4142	−0.662404	−0.331202	+	0.943560i	$0.607454\pi$
$860$	−7.65685	−0.261097
$861$	0	0
$862$	6.34315	0.216048
$863$	38.8701	1.32315	0.661576	−	0.749878i	$-0.269888\pi$
$863$	38.8701	1.32315	0.661576	+	0.749878i	$0.269888\pi$
$864$	−1.00000	−0.0340207
$865$	−4.82843	−0.164171
$866$	−30.0000	−1.01944
$867$	15.0000	0.509427
$868$	0	0
$869$	1.24264	0.0421537
$870$	0.757359	0.0256769
$871$	6.14214	0.208118
$872$	5.31371	0.179945
$873$	3.58579	0.121360
$874$	−3.41421	−0.115487
$875$	0	0
$876$	5.65685	0.191127
$877$	37.8995	1.27978	0.639888	−	0.768469i	$-0.278981\pi$
$877$	37.8995	1.27978	0.639888	+	0.768469i	$0.278981\pi$
$878$	−11.1421	−0.376029
$879$	−21.6274	−0.729475
$880$	−3.00000	−0.101130
$881$	−8.14214	−0.274316	−0.137158	−	0.990549i	$-0.543797\pi$
$881$	−8.14214	−0.274316	−0.137158	+	0.990549i	$0.543797\pi$
$882$	0	0
$883$	53.6985	1.80710	0.903549	−	0.428485i	$-0.140952\pi$
$883$	53.6985	1.80710	0.903549	+	0.428485i	$0.140952\pi$
$884$	−2.00000	−0.0672673
$885$	−0.757359	−0.0254584
$886$	10.2721	0.345097
$887$	45.6569	1.53301	0.766504	−	0.642240i	$-0.221995\pi$
$887$	45.6569	1.53301	0.766504	+	0.642240i	$0.221995\pi$
$888$	9.07107	0.304405
$889$	0	0
$890$	−14.7279	−0.493681
$891$	−3.00000	−0.100504
$892$	10.1716	0.340569
$893$	31.7990	1.06411
$894$	−13.6569	−0.456754
$895$	16.0000	0.534821
$896$	0	0
$897$	−1.41421	−0.0472192
$898$	−1.75736	−0.0586438
$899$	3.52691	0.117629
$900$	−4.00000	−0.133333
$901$	−3.07107	−0.102312
$902$	5.27208	0.175541
$903$	0	0
$904$	−17.4142	−0.579188
$905$	12.4853	0.415025
$906$	1.34315	0.0446230
$907$	−25.0711	−0.832471	−0.416236	−	0.909257i	$-0.636651\pi$
$907$	−25.0711	−0.832471	−0.416236	+	0.909257i	$0.636651\pi$
$908$	7.82843	0.259795
$909$	4.48528	0.148767
$910$	0	0
$911$	−4.34315	−0.143895	−0.0719474	−	0.997408i	$-0.522921\pi$
$911$	−4.34315	−0.143895	−0.0719474	+	0.997408i	$0.522921\pi$
$912$	−3.41421	−0.113056
$913$	36.9411	1.22257
$914$	20.2132	0.668593
$915$	−6.00000	−0.198354
$916$	−22.7279	−0.750952
$917$	0	0
$918$	−1.41421	−0.0466760
$919$	36.2843	1.19691	0.598454	−	0.801157i	$-0.295782\pi$
$919$	36.2843	1.19691	0.598454	+	0.801157i	$0.295782\pi$
$920$	−1.00000	−0.0329690
$921$	25.8995	0.853417
$922$	−30.9706	−1.01996
$923$	−8.34315	−0.274618
$924$	0	0
$925$	36.2843	1.19302
$926$	−13.7990	−0.453463
$927$	13.6569	0.448550
$928$	−0.757359	−0.0248615
$929$	−0.727922	−0.0238823	−0.0119412	−	0.999929i	$-0.503801\pi$
$929$	−0.727922	−0.0238823	−0.0119412	+	0.999929i	$0.503801\pi$
$930$	4.65685	0.152704
$931$	0	0
$932$	15.2132	0.498325
$933$	3.41421	0.111776
$934$	−28.8284	−0.943295
$935$	−4.24264	−0.138749
$936$	−1.41421	−0.0462250
$937$	−47.1838	−1.54143	−0.770713	−	0.637182i	$-0.780100\pi$
$937$	−47.1838	−1.54143	−0.770713	+	0.637182i	$0.780100\pi$
$938$	0	0
$939$	16.7574	0.546856
$940$	9.31371	0.303780
$941$	−35.4853	−1.15679	−0.578394	−	0.815758i	$-0.696320\pi$
$941$	−35.4853	−1.15679	−0.578394	+	0.815758i	$0.696320\pi$
$942$	−3.89949	−0.127052
$943$	1.75736	0.0572275
$944$	0.757359	0.0246499
$945$	0	0
$946$	22.9706	0.746837
$947$	−6.28427	−0.204211	−0.102106	−	0.994774i	$-0.532558\pi$
$947$	−6.28427	−0.204211	−0.102106	+	0.994774i	$0.532558\pi$
$948$	0.414214	0.0134530
$949$	8.00000	0.259691
$950$	−13.6569	−0.443087
$951$	−9.92893	−0.321968
$952$	0	0
$953$	−37.7990	−1.22443	−0.612215	−	0.790692i	$-0.709721\pi$
$953$	−37.7990	−1.22443	−0.612215	+	0.790692i	$0.709721\pi$
$954$	−2.17157	−0.0703073
$955$	1.41421	0.0457629
$956$	−23.3137	−0.754019
$957$	−2.27208	−0.0734458
$958$	−30.5269	−0.986280
$959$	0	0
$960$	−1.00000	−0.0322749
$961$	−9.31371	−0.300442
$962$	12.8284	0.413605
$963$	−7.48528	−0.241210
$964$	9.92893	0.319789
$965$	−19.6274	−0.631829
$966$	0	0
$967$	−35.9706	−1.15674	−0.578368	−	0.815776i	$-0.696310\pi$
$967$	−35.9706	−1.15674	−0.578368	+	0.815776i	$0.696310\pi$
$968$	−2.00000	−0.0642824
$969$	−4.82843	−0.155111
$970$	3.58579	0.115133
$971$	−3.97056	−0.127421	−0.0637107	−	0.997968i	$-0.520293\pi$
$971$	−3.97056	−0.127421	−0.0637107	+	0.997968i	$0.520293\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	−29.4853	−0.944769
$975$	−5.65685	−0.181164
$976$	6.00000	0.192055
$977$	34.9706	1.11881	0.559404	−	0.828895i	$-0.311030\pi$
$977$	34.9706	1.11881	0.559404	+	0.828895i	$0.311030\pi$
$978$	1.41421	0.0452216
$979$	44.1838	1.41212
$980$	0	0
$981$	5.31371	0.169654
$982$	−9.10051	−0.290409
$983$	−6.58579	−0.210054	−0.105027	−	0.994469i	$-0.533493\pi$
$983$	−6.58579	−0.210054	−0.105027	+	0.994469i	$0.533493\pi$
$984$	1.75736	0.0560226
$985$	−3.17157	−0.101055
$986$	−1.07107	−0.0341097
$987$	0	0
$988$	−4.82843	−0.153613
$989$	7.65685	0.243474
$990$	−3.00000	−0.0953463
$991$	−35.7696	−1.13626	−0.568129	−	0.822940i	$-0.692332\pi$
$991$	−35.7696	−1.13626	−0.568129	+	0.822940i	$0.692332\pi$
$992$	−4.65685	−0.147855
$993$	−25.8995	−0.821896
$994$	0	0
$995$	−5.31371	−0.168456
$996$	12.3137	0.390175
$997$	44.8701	1.42105	0.710524	−	0.703672i	$-0.248458\pi$
$997$	44.8701	1.42105	0.710524	+	0.703672i	$0.248458\pi$
$998$	−13.7990	−0.436799
$999$	9.07107	0.286996

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6762.2.a.ca.1.1		2
7.3	odd	6		966.2.i.h.415.2	yes	4
7.5	odd	6		966.2.i.h.277.2	✓	4
7.6	odd	2		6762.2.a.cc.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.i.h.277.2	✓	4	7.5	odd	6
966.2.i.h.415.2	yes	4	7.3	odd	6
6762.2.a.ca.1.1		2	1.1	even	1	trivial
6762.2.a.cc.1.2		2	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6762.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -3.00000 q^{11} -1.00000 q^{12} -1.41421 q^{13} -1.00000 q^{15} +1.00000 q^{16} +1.41421 q^{17} +1.00000 q^{18} +3.41421 q^{19} +1.00000 q^{20} -3.00000 q^{22} -1.00000 q^{23} -1.00000 q^{24} -4.00000 q^{25} -1.41421 q^{26} -1.00000 q^{27} -0.757359 q^{29} -1.00000 q^{30} -4.65685 q^{31} +1.00000 q^{32} +3.00000 q^{33} +1.41421 q^{34} +1.00000 q^{36} -9.07107 q^{37} +3.41421 q^{38} +1.41421 q^{39} +1.00000 q^{40} -1.75736 q^{41} -7.65685 q^{43} -3.00000 q^{44} +1.00000 q^{45} -1.00000 q^{46} +9.31371 q^{47} -1.00000 q^{48} -4.00000 q^{50} -1.41421 q^{51} -1.41421 q^{52} -2.17157 q^{53} -1.00000 q^{54} -3.00000 q^{55} -3.41421 q^{57} -0.757359 q^{58} +0.757359 q^{59} -1.00000 q^{60} +6.00000 q^{61} -4.65685 q^{62} +1.00000 q^{64} -1.41421 q^{65} +3.00000 q^{66} -4.34315 q^{67} +1.41421 q^{68} +1.00000 q^{69} +5.89949 q^{71} +1.00000 q^{72} -5.65685 q^{73} -9.07107 q^{74} +4.00000 q^{75} +3.41421 q^{76} +1.41421 q^{78} -0.414214 q^{79} +1.00000 q^{80} +1.00000 q^{81} -1.75736 q^{82} -12.3137 q^{83} +1.41421 q^{85} -7.65685 q^{86} +0.757359 q^{87} -3.00000 q^{88} -14.7279 q^{89} +1.00000 q^{90} -1.00000 q^{92} +4.65685 q^{93} +9.31371 q^{94} +3.41421 q^{95} -1.00000 q^{96} +3.58579 q^{97} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{8} + 2 q^{9} + 2 q^{10} - 6 q^{11} - 2 q^{12} - 2 q^{15} + 2 q^{16} + 2 q^{18} + 4 q^{19} + 2 q^{20} - 6 q^{22} - 2 q^{23} - 2 q^{24} - 8 q^{25} - 2 q^{27} - 10 q^{29} - 2 q^{30} + 2 q^{31} + 2 q^{32} + 6 q^{33} + 2 q^{36} - 4 q^{37} + 4 q^{38} + 2 q^{40} - 12 q^{41} - 4 q^{43} - 6 q^{44} + 2 q^{45} - 2 q^{46} - 4 q^{47} - 2 q^{48} - 8 q^{50} - 10 q^{53} - 2 q^{54} - 6 q^{55} - 4 q^{57} - 10 q^{58} + 10 q^{59} - 2 q^{60} + 12 q^{61} + 2 q^{62} + 2 q^{64} + 6 q^{66} - 20 q^{67} + 2 q^{69} - 8 q^{71} + 2 q^{72} - 4 q^{74} + 8 q^{75} + 4 q^{76} + 2 q^{79} + 2 q^{80} + 2 q^{81} - 12 q^{82} - 2 q^{83} - 4 q^{86} + 10 q^{87} - 6 q^{88} - 4 q^{89} + 2 q^{90} - 2 q^{92} - 2 q^{93} - 4 q^{94} + 4 q^{95} - 2 q^{96} + 10 q^{97} - 6 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^8 + 2 * q^9 + 2 * q^10 - 6 * q^11 - 2 * q^12 - 2 * q^15 + 2 * q^16 + 2 * q^18 + 4 * q^19 + 2 * q^20 - 6 * q^22 - 2 * q^23 - 2 * q^24 - 8 * q^25 - 2 * q^27 - 10 * q^29 - 2 * q^30 + 2 * q^31 + 2 * q^32 + 6 * q^33 + 2 * q^36 - 4 * q^37 + 4 * q^38 + 2 * q^40 - 12 * q^41 - 4 * q^43 - 6 * q^44 + 2 * q^45 - 2 * q^46 - 4 * q^47 - 2 * q^48 - 8 * q^50 - 10 * q^53 - 2 * q^54 - 6 * q^55 - 4 * q^57 - 10 * q^58 + 10 * q^59 - 2 * q^60 + 12 * q^61 + 2 * q^62 + 2 * q^64 + 6 * q^66 - 20 * q^67 + 2 * q^69 - 8 * q^71 + 2 * q^72 - 4 * q^74 + 8 * q^75 + 4 * q^76 + 2 * q^79 + 2 * q^80 + 2 * q^81 - 12 * q^82 - 2 * q^83 - 4 * q^86 + 10 * q^87 - 6 * q^88 - 4 * q^89 + 2 * q^90 - 2 * q^92 - 2 * q^93 - 4 * q^94 + 4 * q^95 - 2 * q^96 + 10 * q^97 - 6 * q^99

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