LMFDB - Embedded newform 1666.2.a.ba.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1666,2,Mod(1,1666)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1666, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1666.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1666 = 2 \cdot 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1666.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:	$13.3030769767$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.23949216.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 13x^{3} - 2x^{2} + 24x - 4 $ x^5 - 13x^3 - 2x^2 + 24*x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 238)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.26770$ of defining polynomial
Character	$\chi$	$=$	1666.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.26770 q^{3} +1.00000 q^{4} +2.80049 q^{5} +1.26770 q^{6} +1.00000 q^{8} -1.39293 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.26770 q^{3} +1.00000 q^{4} +2.80049 q^{5} +1.26770 q^{6} +1.00000 q^{8} -1.39293 q^{9} +2.80049 q^{10} +0.732296 q^{11} +1.26770 q^{12} +1.37814 q^{13} +3.55019 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.39293 q^{18} -2.37814 q^{19} +2.80049 q^{20} +0.732296 q^{22} +8.57156 q^{23} +1.26770 q^{24} +2.84273 q^{25} +1.37814 q^{26} -5.56893 q^{27} -4.61576 q^{29} +3.55019 q^{30} +3.01478 q^{31} +1.00000 q^{32} +0.928334 q^{33} +1.00000 q^{34} -1.39293 q^{36} -0.800488 q^{37} -2.37814 q^{38} +1.74708 q^{39} +2.80049 q^{40} -0.985218 q^{41} +11.5293 q^{43} +0.732296 q^{44} -3.90087 q^{45} +8.57156 q^{46} -9.15117 q^{47} +1.26770 q^{48} +2.84273 q^{50} +1.26770 q^{51} +1.37814 q^{52} +11.7730 q^{53} -5.56893 q^{54} +2.05078 q^{55} -3.01478 q^{57} -4.61576 q^{58} -4.74346 q^{59} +3.55019 q^{60} -10.0856 q^{61} +3.01478 q^{62} +1.00000 q^{64} +3.85947 q^{65} +0.928334 q^{66} -3.97912 q^{67} +1.00000 q^{68} +10.8662 q^{69} -7.83926 q^{71} -1.39293 q^{72} +4.98522 q^{73} -0.800488 q^{74} +3.60375 q^{75} -2.37814 q^{76} +1.74708 q^{78} -8.86868 q^{79} +2.80049 q^{80} -2.88098 q^{81} -0.985218 q^{82} -4.84469 q^{83} +2.80049 q^{85} +11.5293 q^{86} -5.85142 q^{87} +0.732296 q^{88} -16.9370 q^{89} -3.90087 q^{90} +8.57156 q^{92} +3.82185 q^{93} -9.15117 q^{94} -6.65996 q^{95} +1.26770 q^{96} -1.77107 q^{97} -1.02003 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 5 q^{2} + 5 q^{4} + q^{5} + 5 q^{8} + 11 q^{9}+O(q^{10}) $ 5 * q + 5 * q^2 + 5 * q^4 + q^5 + 5 * q^8 + 11 * q^9	$ 5 q + 5 q^{2} + 5 q^{4} + q^{5} + 5 q^{8} + 11 q^{9} + q^{10} + 10 q^{11} - 2 q^{13} - 4 q^{15} + 5 q^{16} + 5 q^{17} + 11 q^{18} - 3 q^{19} + q^{20} + 10 q^{22} + 3 q^{23} + 18 q^{25} - 2 q^{26} + 6 q^{27} + 12 q^{29} - 4 q^{30} + 6 q^{31} + 5 q^{32} - 26 q^{33} + 5 q^{34} + 11 q^{36} + 9 q^{37} - 3 q^{38} + 6 q^{39} + q^{40} - 14 q^{41} + q^{43} + 10 q^{44} + 37 q^{45} + 3 q^{46} + 2 q^{47} + 18 q^{50} - 2 q^{52} + 20 q^{53} + 6 q^{54} + 6 q^{55} - 6 q^{57} + 12 q^{58} - 3 q^{59} - 4 q^{60} - 16 q^{61} + 6 q^{62} + 5 q^{64} + 2 q^{65} - 26 q^{66} + 15 q^{67} + 5 q^{68} - 4 q^{69} + 7 q^{71} + 11 q^{72} + 34 q^{73} + 9 q^{74} - 46 q^{75} - 3 q^{76} + 6 q^{78} - 12 q^{79} + q^{80} + 53 q^{81} - 14 q^{82} - 16 q^{83} + q^{85} + q^{86} + 20 q^{87} + 10 q^{88} - q^{89} + 37 q^{90} + 3 q^{92} - 12 q^{93} + 2 q^{94} - 3 q^{95} + 18 q^{97} + 16 q^{99}+O(q^{100}) $ 5 * q + 5 * q^2 + 5 * q^4 + q^5 + 5 * q^8 + 11 * q^9 + q^10 + 10 * q^11 - 2 * q^13 - 4 * q^15 + 5 * q^16 + 5 * q^17 + 11 * q^18 - 3 * q^19 + q^20 + 10 * q^22 + 3 * q^23 + 18 * q^25 - 2 * q^26 + 6 * q^27 + 12 * q^29 - 4 * q^30 + 6 * q^31 + 5 * q^32 - 26 * q^33 + 5 * q^34 + 11 * q^36 + 9 * q^37 - 3 * q^38 + 6 * q^39 + q^40 - 14 * q^41 + q^43 + 10 * q^44 + 37 * q^45 + 3 * q^46 + 2 * q^47 + 18 * q^50 - 2 * q^52 + 20 * q^53 + 6 * q^54 + 6 * q^55 - 6 * q^57 + 12 * q^58 - 3 * q^59 - 4 * q^60 - 16 * q^61 + 6 * q^62 + 5 * q^64 + 2 * q^65 - 26 * q^66 + 15 * q^67 + 5 * q^68 - 4 * q^69 + 7 * q^71 + 11 * q^72 + 34 * q^73 + 9 * q^74 - 46 * q^75 - 3 * q^76 + 6 * q^78 - 12 * q^79 + q^80 + 53 * q^81 - 14 * q^82 - 16 * q^83 + q^85 + q^86 + 20 * q^87 + 10 * q^88 - q^89 + 37 * q^90 + 3 * q^92 - 12 * q^93 + 2 * q^94 - 3 * q^95 + 18 * q^97 + 16 * 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
$3$	1.26770	0.731910	0.365955	−	0.930633i	$-0.380742\pi$
$3$	1.26770	0.731910	0.365955	+	0.930633i	$0.380742\pi$
$4$	1.00000	0.500000
$5$	2.80049	1.25242	0.626208	−	0.779656i	$-0.284606\pi$
$5$	2.80049	1.25242	0.626208	+	0.779656i	$0.284606\pi$
$6$	1.26770	0.517538
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	−1.39293	−0.464308
$10$	2.80049	0.885592
$11$	0.732296	0.220795	0.110398	−	0.993887i	$-0.464788\pi$
$11$	0.732296	0.220795	0.110398	+	0.993887i	$0.464788\pi$
$12$	1.26770	0.365955
$13$	1.37814	0.382228	0.191114	−	0.981568i	$-0.438790\pi$
$13$	1.37814	0.382228	0.191114	+	0.981568i	$0.438790\pi$
$14$	0	0
$15$	3.55019	0.916655
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.39293	−0.328316
$19$	−2.37814	−0.545583	−0.272792	−	0.962073i	$-0.587947\pi$
$19$	−2.37814	−0.545583	−0.272792	+	0.962073i	$0.587947\pi$
$20$	2.80049	0.626208
$21$	0	0
$22$	0.732296	0.156126
$23$	8.57156	1.78729	0.893647	−	0.448772i	$-0.148138\pi$
$23$	8.57156	1.78729	0.893647	+	0.448772i	$0.148138\pi$
$24$	1.26770	0.258769
$25$	2.84273	0.568547
$26$	1.37814	0.270276
$27$	−5.56893	−1.07174
$28$	0	0
$29$	−4.61576	−0.857125	−0.428562	−	0.903512i	$-0.640980\pi$
$29$	−4.61576	−0.857125	−0.428562	+	0.903512i	$0.640980\pi$
$30$	3.55019	0.648173
$31$	3.01478	0.541471	0.270735	−	0.962654i	$-0.412733\pi$
$31$	3.01478	0.541471	0.270735	+	0.962654i	$0.412733\pi$
$32$	1.00000	0.176777
$33$	0.928334	0.161602
$34$	1.00000	0.171499
$35$	0	0
$36$	−1.39293	−0.232154
$37$	−0.800488	−0.131599	−0.0657997	−	0.997833i	$-0.520960\pi$
$37$	−0.800488	−0.131599	−0.0657997	+	0.997833i	$0.520960\pi$
$38$	−2.37814	−0.385786
$39$	1.74708	0.279756
$40$	2.80049	0.442796
$41$	−0.985218	−0.153865	−0.0769326	−	0.997036i	$-0.524513\pi$
$41$	−0.985218	−0.153865	−0.0769326	+	0.997036i	$0.524513\pi$
$42$	0	0
$43$	11.5293	1.75820	0.879102	−	0.476634i	$-0.158143\pi$
$43$	11.5293	1.75820	0.879102	+	0.476634i	$0.158143\pi$
$44$	0.732296	0.110398
$45$	−3.90087	−0.581508
$46$	8.57156	1.26381
$47$	−9.15117	−1.33484	−0.667418	−	0.744684i	$-0.732600\pi$
$47$	−9.15117	−1.33484	−0.667418	+	0.744684i	$0.732600\pi$
$48$	1.26770	0.182977
$49$	0	0
$50$	2.84273	0.402023
$51$	1.26770	0.177514
$52$	1.37814	0.191114
$53$	11.7730	1.61715	0.808575	−	0.588394i	$-0.200239\pi$
$53$	11.7730	1.61715	0.808575	+	0.588394i	$0.200239\pi$
$54$	−5.56893	−0.757836
$55$	2.05078	0.276528
$56$	0	0
$57$	−3.01478	−0.399318
$58$	−4.61576	−0.606079
$59$	−4.74346	−0.617546	−0.308773	−	0.951136i	$-0.599918\pi$
$59$	−4.74346	−0.617546	−0.308773	+	0.951136i	$0.599918\pi$
$60$	3.55019	0.458328
$61$	−10.0856	−1.29133	−0.645664	−	0.763621i	$-0.723419\pi$
$61$	−10.0856	−1.29133	−0.645664	+	0.763621i	$0.723419\pi$
$62$	3.01478	0.382878
$63$	0	0
$64$	1.00000	0.125000
$65$	3.85947	0.478709
$66$	0.928334	0.114270
$67$	−3.97912	−0.486127	−0.243063	−	0.970010i	$-0.578152\pi$
$67$	−3.97912	−0.486127	−0.243063	+	0.970010i	$0.578152\pi$
$68$	1.00000	0.121268
$69$	10.8662	1.30814
$70$	0	0
$71$	−7.83926	−0.930349	−0.465175	−	0.885219i	$-0.654008\pi$
$71$	−7.83926	−0.930349	−0.465175	+	0.885219i	$0.654008\pi$
$72$	−1.39293	−0.164158
$73$	4.98522	0.583476	0.291738	−	0.956498i	$-0.405767\pi$
$73$	4.98522	0.583476	0.291738	+	0.956498i	$0.405767\pi$
$74$	−0.800488	−0.0930549
$75$	3.60375	0.416125
$76$	−2.37814	−0.272792
$77$	0	0
$78$	1.74708	0.197818
$79$	−8.86868	−0.997805	−0.498902	−	0.866658i	$-0.666263\pi$
$79$	−8.86868	−0.997805	−0.498902	+	0.866658i	$0.666263\pi$
$80$	2.80049	0.313104
$81$	−2.88098	−0.320109
$82$	−0.985218	−0.108799
$83$	−4.84469	−0.531774	−0.265887	−	0.964004i	$-0.585665\pi$
$83$	−4.84469	−0.531774	−0.265887	+	0.964004i	$0.585665\pi$
$84$	0	0
$85$	2.80049	0.303756
$86$	11.5293	1.24324
$87$	−5.85142	−0.627338
$88$	0.732296	0.0780630
$89$	−16.9370	−1.79532	−0.897660	−	0.440688i	$-0.854734\pi$
$89$	−16.9370	−1.79532	−0.897660	+	0.440688i	$0.854734\pi$
$90$	−3.90087	−0.411188
$91$	0	0
$92$	8.57156	0.893647
$93$	3.82185	0.396308
$94$	−9.15117	−0.943871
$95$	−6.65996	−0.683298
$96$	1.26770	0.129385
$97$	−1.77107	−0.179825	−0.0899124	−	0.995950i	$-0.528659\pi$
$97$	−1.77107	−0.179825	−0.0899124	+	0.995950i	$0.528659\pi$
$98$	0	0
$99$	−1.02003	−0.102517
$100$	2.84273	0.284273
$101$	9.63054	0.958275	0.479137	−	0.877740i	$-0.340950\pi$
$101$	9.63054	0.958275	0.479137	+	0.877740i	$0.340950\pi$
$102$	1.26770	0.125521
$103$	−0.764341	−0.0753127	−0.0376564	−	0.999291i	$-0.511989\pi$
$103$	−0.764341	−0.0753127	−0.0376564	+	0.999291i	$0.511989\pi$
$104$	1.37814	0.135138
$105$	0	0
$106$	11.7730	1.14350
$107$	−9.65453	−0.933339	−0.466669	−	0.884432i	$-0.654546\pi$
$107$	−9.65453	−0.933339	−0.466669	+	0.884432i	$0.654546\pi$
$108$	−5.56893	−0.535871
$109$	15.4162	1.47661	0.738304	−	0.674468i	$-0.235627\pi$
$109$	15.4162	1.47661	0.738304	+	0.674468i	$0.235627\pi$
$110$	2.05078	0.195535
$111$	−1.01478	−0.0963189
$112$	0	0
$113$	−5.60098	−0.526896	−0.263448	−	0.964674i	$-0.584860\pi$
$113$	−5.60098	−0.526896	−0.263448	+	0.964674i	$0.584860\pi$
$114$	−3.01478	−0.282360
$115$	24.0045	2.23844
$116$	−4.61576	−0.428562
$117$	−1.91965	−0.177472
$118$	−4.74346	−0.436671
$119$	0	0
$120$	3.55019	0.324087
$121$	−10.4637	−0.951249
$122$	−10.0856	−0.913107
$123$	−1.24896	−0.112615
$124$	3.01478	0.270735
$125$	−6.04140	−0.540359
$126$	0	0
$127$	10.7521	0.954099	0.477049	−	0.878877i	$-0.341706\pi$
$127$	10.7521	0.954099	0.477049	+	0.878877i	$0.341706\pi$
$128$	1.00000	0.0883883
$129$	14.6158	1.28685
$130$	3.85947	0.338498
$131$	−19.4576	−1.70002	−0.850011	−	0.526765i	$-0.823405\pi$
$131$	−19.4576	−1.70002	−0.850011	+	0.526765i	$0.823405\pi$
$132$	0.928334	0.0808011
$133$	0	0
$134$	−3.97912	−0.343744
$135$	−15.5957	−1.34227
$136$	1.00000	0.0857493
$137$	10.2072	0.872060	0.436030	−	0.899932i	$-0.356384\pi$
$137$	10.2072	0.872060	0.436030	+	0.899932i	$0.356384\pi$
$138$	10.8662	0.924992
$139$	−6.63975	−0.563176	−0.281588	−	0.959535i	$-0.590861\pi$
$139$	−6.63975	−0.563176	−0.281588	+	0.959535i	$0.590861\pi$
$140$	0	0
$141$	−11.6010	−0.976978
$142$	−7.83926	−0.657856
$143$	1.00921	0.0843942
$144$	−1.39293	−0.116077
$145$	−12.9264	−1.07348
$146$	4.98522	0.412580
$147$	0	0
$148$	−0.800488	−0.0657997
$149$	11.5441	0.945729	0.472864	−	0.881135i	$-0.343220\pi$
$149$	11.5441	0.945729	0.472864	+	0.881135i	$0.343220\pi$
$150$	3.60375	0.294245
$151$	−14.8662	−1.20979	−0.604897	−	0.796304i	$-0.706786\pi$
$151$	−14.8662	−1.20979	−0.604897	+	0.796304i	$0.706786\pi$
$152$	−2.37814	−0.192893
$153$	−1.39293	−0.112611
$154$	0	0
$155$	8.44286	0.678147
$156$	1.74708	0.139878
$157$	−3.15727	−0.251977	−0.125989	−	0.992032i	$-0.540210\pi$
$157$	−3.15727	−0.251977	−0.125989	+	0.992032i	$0.540210\pi$
$158$	−8.86868	−0.705554
$159$	14.9247	1.18361
$160$	2.80049	0.221398
$161$	0	0
$162$	−2.88098	−0.226351
$163$	−4.98522	−0.390472	−0.195236	−	0.980756i	$-0.562547\pi$
$163$	−4.98522	−0.390472	−0.195236	+	0.980756i	$0.562547\pi$
$164$	−0.985218	−0.0769326
$165$	2.59979	0.202393
$166$	−4.84469	−0.376021
$167$	17.3895	1.34564	0.672818	−	0.739808i	$-0.265084\pi$
$167$	17.3895	1.34564	0.672818	+	0.739808i	$0.265084\pi$
$168$	0	0
$169$	−11.1007	−0.853902
$170$	2.80049	0.214788
$171$	3.31258	0.253319
$172$	11.5293	0.879102
$173$	22.4282	1.70519	0.852593	−	0.522575i	$-0.175029\pi$
$173$	22.4282	1.70519	0.852593	+	0.522575i	$0.175029\pi$
$174$	−5.85142	−0.443595
$175$	0	0
$176$	0.732296	0.0551989
$177$	−6.01331	−0.451988
$178$	−16.9370	−1.26948
$179$	14.1451	1.05725	0.528626	−	0.848855i	$-0.322707\pi$
$179$	14.1451	1.05725	0.528626	+	0.848855i	$0.322707\pi$
$180$	−3.90087	−0.290754
$181$	9.50074	0.706184	0.353092	−	0.935589i	$-0.385130\pi$
$181$	9.50074	0.706184	0.353092	+	0.935589i	$0.385130\pi$
$182$	0	0
$183$	−12.7856	−0.945136
$184$	8.57156	0.631904
$185$	−2.24176	−0.164817
$186$	3.82185	0.280232
$187$	0.732296	0.0535508
$188$	−9.15117	−0.667418
$189$	0	0
$190$	−6.65996	−0.483164
$191$	7.14592	0.517060	0.258530	−	0.966003i	$-0.416762\pi$
$191$	7.14592	0.517060	0.258530	+	0.966003i	$0.416762\pi$
$192$	1.26770	0.0914887
$193$	15.8567	1.14139	0.570694	−	0.821163i	$-0.306674\pi$
$193$	15.8567	1.14139	0.570694	+	0.821163i	$0.306674\pi$
$194$	−1.77107	−0.127155
$195$	4.89267	0.350371
$196$	0	0
$197$	0.669353	0.0476895	0.0238447	−	0.999716i	$-0.492409\pi$
$197$	0.669353	0.0476895	0.0238447	+	0.999716i	$0.492409\pi$
$198$	−1.02003	−0.0724906
$199$	−8.49678	−0.602321	−0.301160	−	0.953573i	$-0.597374\pi$
$199$	−8.49678	−0.602321	−0.301160	+	0.953573i	$0.597374\pi$
$200$	2.84273	0.201012
$201$	−5.04435	−0.355801
$202$	9.63054	0.677603
$203$	0	0
$204$	1.26770	0.0887571
$205$	−2.75909	−0.192703
$206$	−0.764341	−0.0532541
$207$	−11.9395	−0.829855
$208$	1.37814	0.0955570
$209$	−1.74150	−0.120462
$210$	0	0
$211$	−21.4872	−1.47924	−0.739620	−	0.673024i	$-0.764995\pi$
$211$	−21.4872	−1.47924	−0.739620	+	0.673024i	$0.764995\pi$
$212$	11.7730	0.808575
$213$	−9.93787	−0.680931
$214$	−9.65453	−0.659970
$215$	32.2877	2.20200
$216$	−5.56893	−0.378918
$217$	0	0
$218$	15.4162	1.04412
$219$	6.31978	0.427051
$220$	2.05078	0.138264
$221$	1.37814	0.0927039
$222$	−1.01478	−0.0681077
$223$	19.3732	1.29732	0.648661	−	0.761077i	$-0.275329\pi$
$223$	19.3732	1.29732	0.648661	+	0.761077i	$0.275329\pi$
$224$	0	0
$225$	−3.95972	−0.263981
$226$	−5.60098	−0.372571
$227$	−13.2636	−0.880334	−0.440167	−	0.897916i	$-0.645081\pi$
$227$	−13.2636	−0.880334	−0.440167	+	0.897916i	$0.645081\pi$
$228$	−3.01478	−0.199659
$229$	10.0734	0.665669	0.332835	−	0.942985i	$-0.391995\pi$
$229$	10.0734	0.665669	0.332835	+	0.942985i	$0.391995\pi$
$230$	24.0045	1.58281
$231$	0	0
$232$	−4.61576	−0.303039
$233$	−21.1898	−1.38819	−0.694094	−	0.719885i	$-0.744195\pi$
$233$	−21.1898	−1.38819	−0.694094	+	0.719885i	$0.744195\pi$
$234$	−1.91965	−0.125491
$235$	−25.6277	−1.67177
$236$	−4.74346	−0.308773
$237$	−11.2429	−0.730303
$238$	0	0
$239$	13.3425	0.863053	0.431527	−	0.902100i	$-0.357975\pi$
$239$	13.3425	0.863053	0.431527	+	0.902100i	$0.357975\pi$
$240$	3.55019	0.229164
$241$	24.8325	1.59960	0.799801	−	0.600266i	$-0.204938\pi$
$241$	24.8325	1.59960	0.799801	+	0.600266i	$0.204938\pi$
$242$	−10.4637	−0.672635
$243$	13.0546	0.837450
$244$	−10.0856	−0.645664
$245$	0	0
$246$	−1.24896	−0.0796311
$247$	−3.27742	−0.208537
$248$	3.01478	0.191439
$249$	−6.14164	−0.389210
$250$	−6.04140	−0.382092
$251$	−29.0534	−1.83383	−0.916916	−	0.399080i	$-0.869330\pi$
$251$	−29.0534	−1.83383	−0.916916	+	0.399080i	$0.869330\pi$
$252$	0	0
$253$	6.27691	0.394626
$254$	10.7521	0.674650
$255$	3.55019	0.222322
$256$	1.00000	0.0625000
$257$	1.39377	0.0869412	0.0434706	−	0.999055i	$-0.486159\pi$
$257$	1.39377	0.0869412	0.0434706	+	0.999055i	$0.486159\pi$
$258$	14.6158	0.909937
$259$	0	0
$260$	3.85947	0.239354
$261$	6.42941	0.397970
$262$	−19.4576	−1.20210
$263$	−27.5084	−1.69624	−0.848121	−	0.529802i	$-0.822266\pi$
$263$	−27.5084	−1.69624	−0.848121	+	0.529802i	$0.822266\pi$
$264$	0.928334	0.0571350
$265$	32.9702	2.02534
$266$	0	0
$267$	−21.4711	−1.31401
$268$	−3.97912	−0.243063
$269$	−27.6302	−1.68464	−0.842321	−	0.538976i	$-0.818811\pi$
$269$	−27.6302	−1.68464	−0.842321	+	0.538976i	$0.818811\pi$
$270$	−15.5957	−0.949126
$271$	−20.9170	−1.27062	−0.635308	−	0.772259i	$-0.719127\pi$
$271$	−20.9170	−1.27062	−0.635308	+	0.772259i	$0.719127\pi$
$272$	1.00000	0.0606339
$273$	0	0
$274$	10.2072	0.616640
$275$	2.08172	0.125533
$276$	10.8662	0.654068
$277$	7.37204	0.442943	0.221472	−	0.975167i	$-0.428914\pi$
$277$	7.37204	0.442943	0.221472	+	0.975167i	$0.428914\pi$
$278$	−6.63975	−0.398226
$279$	−4.19937	−0.251410
$280$	0	0
$281$	15.9303	0.950321	0.475161	−	0.879899i	$-0.342390\pi$
$281$	15.9303	0.950321	0.475161	+	0.879899i	$0.342390\pi$
$282$	−11.6010	−0.690828
$283$	0.116537	0.00692739	0.00346370	−	0.999994i	$-0.498897\pi$
$283$	0.116537	0.00692739	0.00346370	+	0.999994i	$0.498897\pi$
$284$	−7.83926	−0.465175
$285$	−8.44286	−0.500112
$286$	1.00921	0.0596757
$287$	0	0
$288$	−1.39293	−0.0820789
$289$	1.00000	0.0588235
$290$	−12.9264	−0.759063
$291$	−2.24519	−0.131615
$292$	4.98522	0.291738
$293$	−15.2296	−0.889720	−0.444860	−	0.895600i	$-0.646747\pi$
$293$	−15.2296	−0.889720	−0.444860	+	0.895600i	$0.646747\pi$
$294$	0	0
$295$	−13.2840	−0.773425
$296$	−0.800488	−0.0465274
$297$	−4.07810	−0.236636
$298$	11.5441	0.668731
$299$	11.8128	0.683154
$300$	3.60375	0.208062
$301$	0	0
$302$	−14.8662	−0.855454
$303$	12.2087	0.701370
$304$	−2.37814	−0.136396
$305$	−28.2446	−1.61728
$306$	−1.39293	−0.0796282
$307$	3.85079	0.219776	0.109888	−	0.993944i	$-0.464951\pi$
$307$	3.85079	0.219776	0.109888	+	0.993944i	$0.464951\pi$
$308$	0	0
$309$	−0.968958	−0.0551221
$310$	8.44286	0.479522
$311$	−20.6759	−1.17242	−0.586211	−	0.810158i	$-0.699381\pi$
$311$	−20.6759	−1.17242	−0.586211	+	0.810158i	$0.699381\pi$
$312$	1.74708	0.0989088
$313$	−13.9451	−0.788222	−0.394111	−	0.919063i	$-0.628947\pi$
$313$	−13.9451	−0.788222	−0.394111	+	0.919063i	$0.628947\pi$
$314$	−3.15727	−0.178175
$315$	0	0
$316$	−8.86868	−0.498902
$317$	−12.2609	−0.688643	−0.344321	−	0.938852i	$-0.611891\pi$
$317$	−12.2609	−0.688643	−0.344321	+	0.938852i	$0.611891\pi$
$318$	14.9247	0.836937
$319$	−3.38010	−0.189249
$320$	2.80049	0.156552
$321$	−12.2391	−0.683120
$322$	0	0
$323$	−2.37814	−0.132323
$324$	−2.88098	−0.160055
$325$	3.91769	0.217315
$326$	−4.98522	−0.276106
$327$	19.5432	1.08074
$328$	−0.985218	−0.0543995
$329$	0	0
$330$	2.59979	0.143114
$331$	−5.61380	−0.308562	−0.154281	−	0.988027i	$-0.549306\pi$
$331$	−5.61380	−0.308562	−0.154281	+	0.988027i	$0.549306\pi$
$332$	−4.84469	−0.265887
$333$	1.11502	0.0611027
$334$	17.3895	0.951508
$335$	−11.1435	−0.608833
$336$	0	0
$337$	33.4027	1.81956	0.909781	−	0.415089i	$-0.136249\pi$
$337$	33.4027	1.81956	0.909781	+	0.415089i	$0.136249\pi$
$338$	−11.1007	−0.603800
$339$	−7.10038	−0.385640
$340$	2.80049	0.151878
$341$	2.20771	0.119554
$342$	3.31258	0.179124
$343$	0	0
$344$	11.5293	0.621619
$345$	30.4307	1.63833
$346$	22.4282	1.20575
$347$	5.40441	0.290124	0.145062	−	0.989423i	$-0.453662\pi$
$347$	5.40441	0.290124	0.145062	+	0.989423i	$0.453662\pi$
$348$	−5.85142	−0.313669
$349$	−31.0882	−1.66411	−0.832056	−	0.554691i	$-0.812836\pi$
$349$	−31.0882	−1.66411	−0.832056	+	0.554691i	$0.812836\pi$
$350$	0	0
$351$	−7.67478	−0.409650
$352$	0.732296	0.0390315
$353$	21.6690	1.15332	0.576662	−	0.816983i	$-0.304355\pi$
$353$	21.6690	1.15332	0.576662	+	0.816983i	$0.304355\pi$
$354$	−6.01331	−0.319604
$355$	−21.9538	−1.16518
$356$	−16.9370	−0.897660
$357$	0	0
$358$	14.1451	0.747590
$359$	14.7267	0.777247	0.388623	−	0.921397i	$-0.372951\pi$
$359$	14.7267	0.777247	0.388623	+	0.921397i	$0.372951\pi$
$360$	−3.90087	−0.205594
$361$	−13.3444	−0.702339
$362$	9.50074	0.499348
$363$	−13.2649	−0.696228
$364$	0	0
$365$	13.9610	0.730754
$366$	−12.7856	−0.668312
$367$	25.1003	1.31023	0.655114	−	0.755530i	$-0.272621\pi$
$367$	25.1003	1.31023	0.655114	+	0.755530i	$0.272621\pi$
$368$	8.57156	0.446823
$369$	1.37233	0.0714409
$370$	−2.24176	−0.116543
$371$	0	0
$372$	3.82185	0.198154
$373$	−20.1060	−1.04105	−0.520524	−	0.853847i	$-0.674263\pi$
$373$	−20.1060	−1.04105	−0.520524	+	0.853847i	$0.674263\pi$
$374$	0.732296	0.0378661
$375$	−7.65871	−0.395494
$376$	−9.15117	−0.471935
$377$	−6.36118	−0.327617
$378$	0	0
$379$	−27.1445	−1.39432	−0.697161	−	0.716915i	$-0.745554\pi$
$379$	−27.1445	−1.39432	−0.697161	+	0.716915i	$0.745554\pi$
$380$	−6.65996	−0.341649
$381$	13.6305	0.698314
$382$	7.14592	0.365617
$383$	21.9878	1.12352	0.561762	−	0.827299i	$-0.310124\pi$
$383$	21.9878	1.12352	0.561762	+	0.827299i	$0.310124\pi$
$384$	1.26770	0.0646923
$385$	0	0
$386$	15.8567	0.807083
$387$	−16.0595	−0.816349
$388$	−1.77107	−0.0899124
$389$	10.8358	0.549396	0.274698	−	0.961531i	$-0.411422\pi$
$389$	10.8358	0.549396	0.274698	+	0.961531i	$0.411422\pi$
$390$	4.89267	0.247750
$391$	8.57156	0.433482
$392$	0	0
$393$	−24.6665	−1.24426
$394$	0.669353	0.0337215
$395$	−24.8366	−1.24967
$396$	−1.02003	−0.0512586
$397$	21.4458	1.07633	0.538167	−	0.842838i	$-0.319117\pi$
$397$	21.4458	1.07633	0.538167	+	0.842838i	$0.319117\pi$
$398$	−8.49678	−0.425905
$399$	0	0
$400$	2.84273	0.142137
$401$	10.7859	0.538620	0.269310	−	0.963054i	$-0.413204\pi$
$401$	10.7859	0.538620	0.269310	+	0.963054i	$0.413204\pi$
$402$	−5.04435	−0.251589
$403$	4.15480	0.206965
$404$	9.63054	0.479137
$405$	−8.06816	−0.400910
$406$	0	0
$407$	−0.586194	−0.0290566
$408$	1.26770	0.0627607
$409$	−7.58963	−0.375283	−0.187641	−	0.982238i	$-0.560084\pi$
$409$	−7.58963	−0.375283	−0.187641	+	0.982238i	$0.560084\pi$
$410$	−2.75909	−0.136262
$411$	12.9397	0.638269
$412$	−0.764341	−0.0376564
$413$	0	0
$414$	−11.9395	−0.586796
$415$	−13.5675	−0.666002
$416$	1.37814	0.0675690
$417$	−8.41724	−0.412194
$418$	−1.74150	−0.0851797
$419$	4.86868	0.237851	0.118925	−	0.992903i	$-0.462055\pi$
$419$	4.86868	0.237851	0.118925	+	0.992903i	$0.462055\pi$
$420$	0	0
$421$	−3.61037	−0.175959	−0.0879793	−	0.996122i	$-0.528041\pi$
$421$	−3.61037	−0.175959	−0.0879793	+	0.996122i	$0.528041\pi$
$422$	−21.4872	−1.04598
$423$	12.7469	0.619775
$424$	11.7730	0.571749
$425$	2.84273	0.137893
$426$	−9.93787	−0.481491
$427$	0	0
$428$	−9.65453	−0.466669
$429$	1.27938	0.0617689
$430$	32.2877	1.55705
$431$	15.4430	0.743865	0.371933	−	0.928260i	$-0.378695\pi$
$431$	15.4430	0.743865	0.371933	+	0.928260i	$0.378695\pi$
$432$	−5.56893	−0.267935
$433$	−13.5282	−0.650124	−0.325062	−	0.945693i	$-0.605385\pi$
$433$	−13.5282	−0.650124	−0.325062	+	0.945693i	$0.605385\pi$
$434$	0	0
$435$	−16.3868	−0.785688
$436$	15.4162	0.738304
$437$	−20.3844	−0.975117
$438$	6.31978	0.301971
$439$	13.9704	0.666771	0.333385	−	0.942791i	$-0.391809\pi$
$439$	13.9704	0.666771	0.333385	+	0.942791i	$0.391809\pi$
$440$	2.05078	0.0977673
$441$	0	0
$442$	1.37814	0.0655516
$443$	11.9311	0.566866	0.283433	−	0.958992i	$-0.408527\pi$
$443$	11.9311	0.566866	0.283433	+	0.958992i	$0.408527\pi$
$444$	−1.01478	−0.0481594
$445$	−47.4319	−2.24849
$446$	19.3732	0.917345
$447$	14.6345	0.692188
$448$	0	0
$449$	6.62796	0.312793	0.156396	−	0.987694i	$-0.450012\pi$
$449$	6.62796	0.312793	0.156396	+	0.987694i	$0.450012\pi$
$450$	−3.95972	−0.186663
$451$	−0.721470	−0.0339727
$452$	−5.60098	−0.263448
$453$	−18.8459	−0.885460
$454$	−13.2636	−0.622490
$455$	0	0
$456$	−3.01478	−0.141180
$457$	35.4193	1.65685	0.828423	−	0.560103i	$-0.189239\pi$
$457$	35.4193	1.65685	0.828423	+	0.560103i	$0.189239\pi$
$458$	10.0734	0.470699
$459$	−5.56893	−0.259935
$460$	24.0045	1.11922
$461$	5.18683	0.241575	0.120787	−	0.992678i	$-0.461458\pi$
$461$	5.18683	0.241575	0.120787	+	0.992678i	$0.461458\pi$
$462$	0	0
$463$	−39.8136	−1.85029	−0.925147	−	0.379610i	$-0.876058\pi$
$463$	−39.8136	−1.85029	−0.925147	+	0.379610i	$0.876058\pi$
$464$	−4.61576	−0.214281
$465$	10.7031	0.496342
$466$	−21.1898	−0.981596
$467$	−2.69268	−0.124602	−0.0623011	−	0.998057i	$-0.519844\pi$
$467$	−2.69268	−0.124602	−0.0623011	+	0.998057i	$0.519844\pi$
$468$	−1.91965	−0.0887359
$469$	0	0
$470$	−25.6277	−1.18212
$471$	−4.00248	−0.184425
$472$	−4.74346	−0.218335
$473$	8.44286	0.388203
$474$	−11.2429	−0.516402
$475$	−6.76043	−0.310190
$476$	0	0
$477$	−16.3989	−0.750856
$478$	13.3425	0.610271
$479$	−21.9009	−1.00068	−0.500338	−	0.865830i	$-0.666791\pi$
$479$	−21.9009	−1.00068	−0.500338	+	0.865830i	$0.666791\pi$
$480$	3.55019	0.162043
$481$	−1.10319	−0.0503010
$482$	24.8325	1.13109
$483$	0	0
$484$	−10.4637	−0.475625
$485$	−4.95986	−0.225215
$486$	13.0546	0.592167
$487$	−10.7389	−0.486625	−0.243313	−	0.969948i	$-0.578234\pi$
$487$	−10.7389	−0.486625	−0.243313	+	0.969948i	$0.578234\pi$
$488$	−10.0856	−0.456554
$489$	−6.31978	−0.285790
$490$	0	0
$491$	23.5081	1.06091	0.530453	−	0.847715i	$-0.322022\pi$
$491$	23.5081	1.06091	0.530453	+	0.847715i	$0.322022\pi$
$492$	−1.24896	−0.0563077
$493$	−4.61576	−0.207883
$494$	−3.27742	−0.147458
$495$	−2.85659	−0.128394
$496$	3.01478	0.135368
$497$	0	0
$498$	−6.14164	−0.275213
$499$	33.2982	1.49063	0.745317	−	0.666710i	$-0.232298\pi$
$499$	33.2982	1.49063	0.745317	+	0.666710i	$0.232298\pi$
$500$	−6.04140	−0.270180
$501$	22.0447	0.984884
$502$	−29.0534	−1.29672
$503$	6.24634	0.278511	0.139255	−	0.990257i	$-0.455529\pi$
$503$	6.24634	0.278511	0.139255	+	0.990257i	$0.455529\pi$
$504$	0	0
$505$	26.9702	1.20016
$506$	6.27691	0.279043
$507$	−14.0724	−0.624979
$508$	10.7521	0.477049
$509$	−18.2759	−0.810063	−0.405032	−	0.914303i	$-0.632740\pi$
$509$	−18.2759	−0.810063	−0.405032	+	0.914303i	$0.632740\pi$
$510$	3.55019	0.157205
$511$	0	0
$512$	1.00000	0.0441942
$513$	13.2437	0.584724
$514$	1.39377	0.0614767
$515$	−2.14053	−0.0943229
$516$	14.6158	0.643423
$517$	−6.70136	−0.294725
$518$	0	0
$519$	28.4324	1.24804
$520$	3.85947	0.169249
$521$	33.1178	1.45092	0.725458	−	0.688267i	$-0.241628\pi$
$521$	33.1178	1.45092	0.725458	+	0.688267i	$0.241628\pi$
$522$	6.42941	0.281408
$523$	16.1607	0.706658	0.353329	−	0.935499i	$-0.385050\pi$
$523$	16.1607	0.706658	0.353329	+	0.935499i	$0.385050\pi$
$524$	−19.4576	−0.850011
$525$	0	0
$526$	−27.5084	−1.19942
$527$	3.01478	0.131326
$528$	0.928334	0.0404006
$529$	50.4716	2.19442
$530$	32.9702	1.43213
$531$	6.60729	0.286732
$532$	0	0
$533$	−1.35777	−0.0588116
$534$	−21.4711	−0.929147
$535$	−27.0374	−1.16893
$536$	−3.97912	−0.171872
$537$	17.9318	0.773813
$538$	−27.6302	−1.19122
$539$	0	0
$540$	−15.5957	−0.671133
$541$	−21.4607	−0.922669	−0.461335	−	0.887226i	$-0.652629\pi$
$541$	−21.4607	−0.922669	−0.461335	+	0.887226i	$0.652629\pi$
$542$	−20.9170	−0.898461
$543$	12.0441	0.516863
$544$	1.00000	0.0428746
$545$	43.1730	1.84933
$546$	0	0
$547$	−19.2016	−0.821002	−0.410501	−	0.911860i	$-0.634646\pi$
$547$	−19.2016	−0.821002	−0.410501	+	0.911860i	$0.634646\pi$
$548$	10.2072	0.436030
$549$	14.0485	0.599575
$550$	2.08172	0.0887649
$551$	10.9769	0.467633
$552$	10.8662	0.462496
$553$	0	0
$554$	7.37204	0.313208
$555$	−2.84189	−0.120631
$556$	−6.63975	−0.281588
$557$	40.4103	1.71224	0.856120	−	0.516778i	$-0.172869\pi$
$557$	40.4103	1.71224	0.856120	+	0.516778i	$0.172869\pi$
$558$	−4.19937	−0.177773
$559$	15.8890	0.672035
$560$	0	0
$561$	0.928334	0.0391943
$562$	15.9303	0.671979
$563$	28.1757	1.18747	0.593733	−	0.804662i	$-0.297654\pi$
$563$	28.1757	1.18747	0.593733	+	0.804662i	$0.297654\pi$
$564$	−11.6010	−0.488489
$565$	−15.6855	−0.659893
$566$	0.116537	0.00489841
$567$	0	0
$568$	−7.83926	−0.328928
$569$	8.52897	0.357553	0.178777	−	0.983890i	$-0.442786\pi$
$569$	8.52897	0.357553	0.178777	+	0.983890i	$0.442786\pi$
$570$	−8.44286	−0.353633
$571$	34.3462	1.43734	0.718671	−	0.695350i	$-0.244751\pi$
$571$	34.3462	1.43734	0.718671	+	0.695350i	$0.244751\pi$
$572$	1.00921	0.0421971
$573$	9.05891	0.378441
$574$	0	0
$575$	24.3667	1.01616
$576$	−1.39293	−0.0580386
$577$	−32.7798	−1.36464	−0.682319	−	0.731054i	$-0.739029\pi$
$577$	−32.7798	−1.36464	−0.682319	+	0.731054i	$0.739029\pi$
$578$	1.00000	0.0415945
$579$	20.1016	0.835393
$580$	−12.9264	−0.536739
$581$	0	0
$582$	−2.24519	−0.0930662
$583$	8.62133	0.357059
$584$	4.98522	0.206290
$585$	−5.37596	−0.222268
$586$	−15.2296	−0.629127
$587$	−10.2092	−0.421377	−0.210689	−	0.977553i	$-0.567571\pi$
$587$	−10.2092	−0.421377	−0.210689	+	0.977553i	$0.567571\pi$
$588$	0	0
$589$	−7.16958	−0.295418
$590$	−13.2840	−0.546894
$591$	0.848542	0.0349044
$592$	−0.800488	−0.0328999
$593$	−4.26971	−0.175336	−0.0876679	−	0.996150i	$-0.527941\pi$
$593$	−4.26971	−0.175336	−0.0876679	+	0.996150i	$0.527941\pi$
$594$	−4.07810	−0.167327
$595$	0	0
$596$	11.5441	0.472864
$597$	−10.7714	−0.440844
$598$	11.8128	0.483063
$599$	−14.5996	−0.596525	−0.298263	−	0.954484i	$-0.596407\pi$
$599$	−14.5996	−0.596525	−0.298263	+	0.954484i	$0.596407\pi$
$600$	3.60375	0.147122
$601$	−11.2639	−0.459464	−0.229732	−	0.973254i	$-0.573785\pi$
$601$	−11.2639	−0.459464	−0.229732	+	0.973254i	$0.573785\pi$
$602$	0	0
$603$	5.54262	0.225713
$604$	−14.8662	−0.604897
$605$	−29.3036	−1.19136
$606$	12.2087	0.495944
$607$	−43.6114	−1.77013	−0.885067	−	0.465464i	$-0.845887\pi$
$607$	−43.6114	−1.77013	−0.885067	+	0.465464i	$0.845887\pi$
$608$	−2.37814	−0.0964464
$609$	0	0
$610$	−28.2446	−1.14359
$611$	−12.6116	−0.510211
$612$	−1.39293	−0.0563057
$613$	−18.6281	−0.752381	−0.376190	−	0.926542i	$-0.622766\pi$
$613$	−18.6281	−0.752381	−0.376190	+	0.926542i	$0.622766\pi$
$614$	3.85079	0.155405
$615$	−3.49771	−0.141041
$616$	0	0
$617$	41.8312	1.68406	0.842030	−	0.539431i	$-0.181361\pi$
$617$	41.8312	1.68406	0.842030	+	0.539431i	$0.181361\pi$
$618$	−0.968958	−0.0389772
$619$	0.905192	0.0363827	0.0181914	−	0.999835i	$-0.494209\pi$
$619$	0.905192	0.0363827	0.0181914	+	0.999835i	$0.494209\pi$
$620$	8.44286	0.339074
$621$	−47.7344	−1.91552
$622$	−20.6759	−0.829028
$623$	0	0
$624$	1.74708	0.0699391
$625$	−31.1325	−1.24530
$626$	−13.9451	−0.557357
$627$	−2.20771	−0.0881675
$628$	−3.15727	−0.125989
$629$	−0.800488	−0.0319176
$630$	0	0
$631$	−17.8851	−0.711996	−0.355998	−	0.934487i	$-0.615859\pi$
$631$	−17.8851	−0.711996	−0.355998	+	0.934487i	$0.615859\pi$
$632$	−8.86868	−0.352777
$633$	−27.2394	−1.08267
$634$	−12.2609	−0.486944
$635$	30.1113	1.19493
$636$	14.9247	0.591803
$637$	0	0
$638$	−3.38010	−0.133819
$639$	10.9195	0.431969
$640$	2.80049	0.110699
$641$	−5.54214	−0.218901	−0.109451	−	0.993992i	$-0.534909\pi$
$641$	−5.54214	−0.218901	−0.109451	+	0.993992i	$0.534909\pi$
$642$	−12.2391	−0.483038
$643$	−2.99982	−0.118301	−0.0591506	−	0.998249i	$-0.518839\pi$
$643$	−2.99982	−0.118301	−0.0591506	+	0.998249i	$0.518839\pi$
$644$	0	0
$645$	40.9313	1.61167
$646$	−2.37814	−0.0935668
$647$	16.3451	0.642591	0.321295	−	0.946979i	$-0.395882\pi$
$647$	16.3451	0.642591	0.321295	+	0.946979i	$0.395882\pi$
$648$	−2.88098	−0.113176
$649$	−3.47361	−0.136351
$650$	3.91769	0.153665
$651$	0	0
$652$	−4.98522	−0.195236
$653$	3.98618	0.155991	0.0779957	−	0.996954i	$-0.475148\pi$
$653$	3.98618	0.155991	0.0779957	+	0.996954i	$0.475148\pi$
$654$	19.5432	0.764201
$655$	−54.4909	−2.12914
$656$	−0.985218	−0.0384663
$657$	−6.94404	−0.270913
$658$	0	0
$659$	−19.1049	−0.744222	−0.372111	−	0.928188i	$-0.621366\pi$
$659$	−19.1049	−0.744222	−0.372111	+	0.928188i	$0.621366\pi$
$660$	2.59979	0.101197
$661$	−6.67460	−0.259612	−0.129806	−	0.991539i	$-0.541435\pi$
$661$	−6.67460	−0.259612	−0.129806	+	0.991539i	$0.541435\pi$
$662$	−5.61380	−0.218187
$663$	1.74708	0.0678509
$664$	−4.84469	−0.188010
$665$	0	0
$666$	1.11502	0.0432062
$667$	−39.5642	−1.53193
$668$	17.3895	0.672818
$669$	24.5594	0.949523
$670$	−11.1435	−0.430510
$671$	−7.38564	−0.285119
$672$	0	0
$673$	50.9884	1.96546	0.982729	−	0.185049i	$-0.0592444\pi$
$673$	50.9884	1.96546	0.982729	+	0.185049i	$0.0592444\pi$
$674$	33.4027	1.28662
$675$	−15.8310	−0.609335
$676$	−11.1007	−0.426951
$677$	−20.5996	−0.791709	−0.395854	−	0.918313i	$-0.629552\pi$
$677$	−20.5996	−0.791709	−0.395854	+	0.918313i	$0.629552\pi$
$678$	−7.10038	−0.272689
$679$	0	0
$680$	2.80049	0.107394
$681$	−16.8143	−0.644325
$682$	2.20771	0.0845376
$683$	0.271986	0.0104072	0.00520362	−	0.999986i	$-0.498344\pi$
$683$	0.271986	0.0104072	0.00520362	+	0.999986i	$0.498344\pi$
$684$	3.31258	0.126659
$685$	28.5852	1.09218
$686$	0	0
$687$	12.7701	0.487210
$688$	11.5293	0.439551
$689$	16.2249	0.618120
$690$	30.4307	1.15848
$691$	15.9412	0.606430	0.303215	−	0.952922i	$-0.401940\pi$
$691$	15.9412	0.606430	0.303215	+	0.952922i	$0.401940\pi$
$692$	22.4282	0.852593
$693$	0	0
$694$	5.40441	0.205149
$695$	−18.5945	−0.705331
$696$	−5.85142	−0.221797
$697$	−0.985218	−0.0373178
$698$	−31.0882	−1.17671
$699$	−26.8623	−1.01603
$700$	0	0
$701$	10.5658	0.399066	0.199533	−	0.979891i	$-0.436058\pi$
$701$	10.5658	0.399066	0.199533	+	0.979891i	$0.436058\pi$
$702$	−7.67478	−0.289666
$703$	1.90368	0.0717985
$704$	0.732296	0.0275994
$705$	−32.4884	−1.22358
$706$	21.6690	0.815523
$707$	0	0
$708$	−6.01331	−0.225994
$709$	41.8267	1.57084	0.785418	−	0.618966i	$-0.212448\pi$
$709$	41.8267	1.57084	0.785418	+	0.618966i	$0.212448\pi$
$710$	−21.9538	−0.823910
$711$	12.3534	0.463289
$712$	−16.9370	−0.634742
$713$	25.8414	0.967767
$714$	0	0
$715$	2.82627	0.105697
$716$	14.1451	0.528626
$717$	16.9143	0.631677
$718$	14.7267	0.549596
$719$	2.23170	0.0832284	0.0416142	−	0.999134i	$-0.486750\pi$
$719$	2.23170	0.0832284	0.0416142	+	0.999134i	$0.486750\pi$
$720$	−3.90087	−0.145377
$721$	0	0
$722$	−13.3444	−0.496628
$723$	31.4803	1.17076
$724$	9.50074	0.353092
$725$	−13.1214	−0.487316
$726$	−13.2649	−0.492308
$727$	−16.7737	−0.622100	−0.311050	−	0.950393i	$-0.600681\pi$
$727$	−16.7737	−0.622100	−0.311050	+	0.950393i	$0.600681\pi$
$728$	0	0
$729$	25.1923	0.933047
$730$	13.9610	0.516721
$731$	11.5293	0.426427
$732$	−12.7856	−0.472568
$733$	31.1291	1.14978	0.574890	−	0.818231i	$-0.305045\pi$
$733$	31.1291	1.14978	0.574890	+	0.818231i	$0.305045\pi$
$734$	25.1003	0.926471
$735$	0	0
$736$	8.57156	0.315952
$737$	−2.91389	−0.107335
$738$	1.37233	0.0505163
$739$	18.2591	0.671673	0.335836	−	0.941920i	$-0.390981\pi$
$739$	18.2591	0.671673	0.335836	+	0.941920i	$0.390981\pi$
$740$	−2.24176	−0.0824086
$741$	−4.15480	−0.152630
$742$	0	0
$743$	38.8433	1.42502	0.712512	−	0.701660i	$-0.247558\pi$
$743$	38.8433	1.42502	0.712512	+	0.701660i	$0.247558\pi$
$744$	3.82185	0.140116
$745$	32.3291	1.18445
$746$	−20.1060	−0.736132
$747$	6.74829	0.246907
$748$	0.732296	0.0267754
$749$	0	0
$750$	−7.65871	−0.279656
$751$	−2.89551	−0.105659	−0.0528294	−	0.998604i	$-0.516824\pi$
$751$	−2.89551	−0.105659	−0.0528294	+	0.998604i	$0.516824\pi$
$752$	−9.15117	−0.333709
$753$	−36.8311	−1.34220
$754$	−6.36118	−0.231660
$755$	−41.6326	−1.51517
$756$	0	0
$757$	29.9942	1.09016	0.545079	−	0.838385i	$-0.316500\pi$
$757$	29.9942	1.09016	0.545079	+	0.838385i	$0.316500\pi$
$758$	−27.1445	−0.985934
$759$	7.95727	0.288831
$760$	−6.65996	−0.241582
$761$	38.1532	1.38305	0.691527	−	0.722351i	$-0.256938\pi$
$761$	38.1532	1.38305	0.691527	+	0.722351i	$0.256938\pi$
$762$	13.6305	0.493782
$763$	0	0
$764$	7.14592	0.258530
$765$	−3.90087	−0.141036
$766$	21.9878	0.794452
$767$	−6.53717	−0.236043
$768$	1.26770	0.0457443
$769$	−4.29169	−0.154762	−0.0773812	−	0.997002i	$-0.524656\pi$
$769$	−4.29169	−0.154762	−0.0773812	+	0.997002i	$0.524656\pi$
$770$	0	0
$771$	1.76689	0.0636331
$772$	15.8567	0.570694
$773$	−31.3204	−1.12652	−0.563258	−	0.826281i	$-0.690452\pi$
$773$	−31.3204	−1.12652	−0.563258	+	0.826281i	$0.690452\pi$
$774$	−16.0595	−0.577246
$775$	8.57022	0.307852
$776$	−1.77107	−0.0635776
$777$	0	0
$778$	10.8358	0.388482
$779$	2.34299	0.0839463
$780$	4.89267	0.175186
$781$	−5.74066	−0.205417
$782$	8.57156	0.306518
$783$	25.7048	0.918616
$784$	0	0
$785$	−8.84189	−0.315580
$786$	−24.6665	−0.879826
$787$	−33.3894	−1.19020	−0.595102	−	0.803650i	$-0.702888\pi$
$787$	−33.3894	−1.19020	−0.595102	+	0.803650i	$0.702888\pi$
$788$	0.669353	0.0238447
$789$	−34.8726	−1.24150
$790$	−24.8366	−0.883648
$791$	0	0
$792$	−1.02003	−0.0362453
$793$	−13.8994	−0.493582
$794$	21.4458	0.761083
$795$	41.7965	1.48237
$796$	−8.49678	−0.301160
$797$	54.3175	1.92402	0.962012	−	0.273009i	$-0.0880188\pi$
$797$	54.3175	1.92402	0.962012	+	0.273009i	$0.0880188\pi$
$798$	0	0
$799$	−9.15117	−0.323745
$800$	2.84273	0.100506
$801$	23.5920	0.833582
$802$	10.7859	0.380862
$803$	3.65065	0.128829
$804$	−5.04435	−0.177900
$805$	0	0
$806$	4.15480	0.146347
$807$	−35.0269	−1.23301
$808$	9.63054	0.338801
$809$	31.2744	1.09955	0.549774	−	0.835313i	$-0.314714\pi$
$809$	31.2744	1.09955	0.549774	+	0.835313i	$0.314714\pi$
$810$	−8.06816	−0.283486
$811$	−1.84768	−0.0648808	−0.0324404	−	0.999474i	$-0.510328\pi$
$811$	−1.84768	−0.0648808	−0.0324404	+	0.999474i	$0.510328\pi$
$812$	0	0
$813$	−26.5166	−0.929976
$814$	−0.586194	−0.0205461
$815$	−13.9610	−0.489034
$816$	1.26770	0.0443785
$817$	−27.4183	−0.959247
$818$	−7.58963	−0.265365
$819$	0	0
$820$	−2.75909	−0.0963516
$821$	−3.77631	−0.131794	−0.0658971	−	0.997826i	$-0.520991\pi$
$821$	−3.77631	−0.131794	−0.0658971	+	0.997826i	$0.520991\pi$
$822$	12.9397	0.451324
$823$	−8.47660	−0.295476	−0.147738	−	0.989027i	$-0.547199\pi$
$823$	−8.47660	−0.295476	−0.147738	+	0.989027i	$0.547199\pi$
$824$	−0.764341	−0.0266271
$825$	2.63901	0.0918784
$826$	0	0
$827$	44.1521	1.53532	0.767659	−	0.640858i	$-0.221421\pi$
$827$	44.1521	1.53532	0.767659	+	0.640858i	$0.221421\pi$
$828$	−11.9395	−0.414928
$829$	−43.6213	−1.51503	−0.757515	−	0.652818i	$-0.773587\pi$
$829$	−43.6213	−1.51503	−0.757515	+	0.652818i	$0.773587\pi$
$830$	−13.5675	−0.470935
$831$	9.34557	0.324194
$832$	1.37814	0.0477785
$833$	0	0
$834$	−8.41724	−0.291465
$835$	48.6990	1.68530
$836$	−1.74150	−0.0602312
$837$	−16.7891	−0.580317
$838$	4.86868	0.168186
$839$	43.8793	1.51488	0.757441	−	0.652904i	$-0.226450\pi$
$839$	43.8793	1.51488	0.757441	+	0.652904i	$0.226450\pi$
$840$	0	0
$841$	−7.69477	−0.265337
$842$	−3.61037	−0.124422
$843$	20.1949	0.695549
$844$	−21.4872	−0.739620
$845$	−31.0874	−1.06944
$846$	12.7469	0.438247
$847$	0	0
$848$	11.7730	0.404287
$849$	0.147734	0.00507022
$850$	2.84273	0.0975050
$851$	−6.86143	−0.235207
$852$	−9.93787	−0.340466
$853$	41.2287	1.41164	0.705822	−	0.708389i	$-0.250578\pi$
$853$	41.2287	1.41164	0.705822	+	0.708389i	$0.250578\pi$
$854$	0	0
$855$	9.27683	0.317261
$856$	−9.65453	−0.329985
$857$	2.17091	0.0741569	0.0370784	−	0.999312i	$-0.488195\pi$
$857$	2.17091	0.0741569	0.0370784	+	0.999312i	$0.488195\pi$
$858$	1.27938	0.0436772
$859$	−36.5778	−1.24802	−0.624009	−	0.781417i	$-0.714497\pi$
$859$	−36.5778	−1.24802	−0.624009	+	0.781417i	$0.714497\pi$
$860$	32.2877	1.10100
$861$	0	0
$862$	15.4430	0.525992
$863$	−17.5231	−0.596492	−0.298246	−	0.954489i	$-0.596402\pi$
$863$	−17.5231	−0.596492	−0.298246	+	0.954489i	$0.596402\pi$
$864$	−5.56893	−0.189459
$865$	62.8100	2.13560
$866$	−13.5282	−0.459707
$867$	1.26770	0.0430535
$868$	0	0
$869$	−6.49450	−0.220311
$870$	−16.3868	−0.555565
$871$	−5.48380	−0.185811
$872$	15.4162	0.522060
$873$	2.46697	0.0834941
$874$	−20.3844	−0.689512
$875$	0	0
$876$	6.31978	0.213526
$877$	8.38765	0.283231	0.141615	−	0.989922i	$-0.454770\pi$
$877$	8.38765	0.283231	0.141615	+	0.989922i	$0.454770\pi$
$878$	13.9704	0.471478
$879$	−19.3066	−0.651195
$880$	2.05078	0.0691319
$881$	51.8191	1.74583	0.872915	−	0.487872i	$-0.162227\pi$
$881$	51.8191	1.74583	0.872915	+	0.487872i	$0.162227\pi$
$882$	0	0
$883$	−4.84889	−0.163178	−0.0815891	−	0.996666i	$-0.526000\pi$
$883$	−4.84889	−0.163178	−0.0815891	+	0.996666i	$0.526000\pi$
$884$	1.37814	0.0463520
$885$	−16.8402	−0.566077
$886$	11.9311	0.400834
$887$	52.0088	1.74628	0.873142	−	0.487467i	$-0.162079\pi$
$887$	52.0088	1.74628	0.873142	+	0.487467i	$0.162079\pi$
$888$	−1.01478	−0.0340539
$889$	0	0
$890$	−47.4319	−1.58992
$891$	−2.10973	−0.0706786
$892$	19.3732	0.648661
$893$	21.7628	0.728264
$894$	14.6345	0.489451
$895$	39.6131	1.32412
$896$	0	0
$897$	14.9752	0.500007
$898$	6.62796	0.221178
$899$	−13.9155	−0.464108
$900$	−3.95972	−0.131991
$901$	11.7730	0.392216
$902$	−0.721470	−0.0240223
$903$	0	0
$904$	−5.60098	−0.186286
$905$	26.6067	0.884437
$906$	−18.8459	−0.626115
$907$	−2.33190	−0.0774295	−0.0387147	−	0.999250i	$-0.512326\pi$
$907$	−2.33190	−0.0774295	−0.0387147	+	0.999250i	$0.512326\pi$
$908$	−13.2636	−0.440167
$909$	−13.4146	−0.444935
$910$	0	0
$911$	−48.9490	−1.62175	−0.810876	−	0.585218i	$-0.801009\pi$
$911$	−48.9490	−1.62175	−0.810876	+	0.585218i	$0.801009\pi$
$912$	−3.01478	−0.0998294
$913$	−3.54775	−0.117413
$914$	35.4193	1.17157
$915$	−35.8058	−1.18370
$916$	10.0734	0.332835
$917$	0	0
$918$	−5.56893	−0.183802
$919$	−26.6506	−0.879121	−0.439561	−	0.898213i	$-0.644866\pi$
$919$	−26.6506	−0.879121	−0.439561	+	0.898213i	$0.644866\pi$
$920$	24.0045	0.791406
$921$	4.88166	0.160856
$922$	5.18683	0.170819
$923$	−10.8036	−0.355606
$924$	0	0
$925$	−2.27557	−0.0748204
$926$	−39.8136	−1.30836
$927$	1.06467	0.0349683
$928$	−4.61576	−0.151520
$929$	7.06661	0.231848	0.115924	−	0.993258i	$-0.463017\pi$
$929$	7.06661	0.231848	0.115924	+	0.993258i	$0.463017\pi$
$930$	10.7031	0.350967
$931$	0	0
$932$	−21.1898	−0.694094
$933$	−26.2109	−0.858107
$934$	−2.69268	−0.0881070
$935$	2.05078	0.0670678
$936$	−1.91965	−0.0627457
$937$	34.7304	1.13459	0.567297	−	0.823513i	$-0.307989\pi$
$937$	34.7304	1.13459	0.567297	+	0.823513i	$0.307989\pi$
$938$	0	0
$939$	−17.6782	−0.576907
$940$	−25.6277	−0.835885
$941$	36.2021	1.18015	0.590077	−	0.807347i	$-0.299097\pi$
$941$	36.2021	1.18015	0.590077	+	0.807347i	$0.299097\pi$
$942$	−4.00248	−0.130408
$943$	−8.44485	−0.275002
$944$	−4.74346	−0.154386
$945$	0	0
$946$	8.44286	0.274501
$947$	46.7519	1.51923	0.759616	−	0.650372i	$-0.225387\pi$
$947$	46.7519	1.51923	0.759616	+	0.650372i	$0.225387\pi$
$948$	−11.2429	−0.365151
$949$	6.87034	0.223021
$950$	−6.76043	−0.219337
$951$	−15.5432	−0.504024
$952$	0	0
$953$	22.5949	0.731921	0.365960	−	0.930630i	$-0.380741\pi$
$953$	22.5949	0.731921	0.365960	+	0.930630i	$0.380741\pi$
$954$	−16.3989	−0.530935
$955$	20.0121	0.647575
$956$	13.3425	0.431527
$957$	−4.28497	−0.138513
$958$	−21.9009	−0.707585
$959$	0	0
$960$	3.55019	0.114582
$961$	−21.9111	−0.706809
$962$	−1.10319	−0.0355682
$963$	13.4480	0.433357
$964$	24.8325	0.799801
$965$	44.4064	1.42949
$966$	0	0
$967$	22.3492	0.718702	0.359351	−	0.933202i	$-0.382998\pi$
$967$	22.3492	0.718702	0.359351	+	0.933202i	$0.382998\pi$
$968$	−10.4637	−0.336317
$969$	−3.01478	−0.0968488
$970$	−4.95986	−0.159251
$971$	10.2205	0.327993	0.163996	−	0.986461i	$-0.447561\pi$
$971$	10.2205	0.327993	0.163996	+	0.986461i	$0.447561\pi$
$972$	13.0546	0.418725
$973$	0	0
$974$	−10.7389	−0.344096
$975$	4.96648	0.159055
$976$	−10.0856	−0.322832
$977$	−19.7196	−0.630885	−0.315443	−	0.948945i	$-0.602153\pi$
$977$	−19.7196	−0.630885	−0.315443	+	0.948945i	$0.602153\pi$
$978$	−6.31978	−0.202084
$979$	−12.4029	−0.396398
$980$	0	0
$981$	−21.4737	−0.685602
$982$	23.5081	0.750173
$983$	−26.9598	−0.859883	−0.429941	−	0.902857i	$-0.641466\pi$
$983$	−26.9598	−0.859883	−0.429941	+	0.902857i	$0.641466\pi$
$984$	−1.24896	−0.0398155
$985$	1.87452	0.0597271
$986$	−4.61576	−0.146996
$987$	0	0
$988$	−3.27742	−0.104269
$989$	98.8241	3.14242
$990$	−2.85659	−0.0907884
$991$	12.0306	0.382166	0.191083	−	0.981574i	$-0.438800\pi$
$991$	12.0306	0.382166	0.191083	+	0.981574i	$0.438800\pi$
$992$	3.01478	0.0957194
$993$	−7.11664	−0.225840
$994$	0	0
$995$	−23.7951	−0.754356
$996$	−6.14164	−0.194605
$997$	36.6075	1.15937	0.579685	−	0.814841i	$-0.303176\pi$
$997$	36.6075	1.15937	0.579685	+	0.814841i	$0.303176\pi$
$998$	33.2982	1.05404
$999$	4.45786	0.141041

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1666.2.a.ba.1.4		5
7.3	odd	6		238.2.e.f.205.4	yes	10
7.5	odd	6		238.2.e.f.137.4	✓	10
7.6	odd	2		1666.2.a.z.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
238.2.e.f.137.4	✓	10	7.5	odd	6
238.2.e.f.205.4	yes	10	7.3	odd	6
1666.2.a.z.1.2		5	7.6	odd	2
1666.2.a.ba.1.4		5	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:	\( N \)	\(=\)	\( 1666 = 2 \cdot 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1666.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.26770 q^{3} +1.00000 q^{4} +2.80049 q^{5} +1.26770 q^{6} +1.00000 q^{8} -1.39293 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.26770 q^{3} +1.00000 q^{4} +2.80049 q^{5} +1.26770 q^{6} +1.00000 q^{8} -1.39293 q^{9} +2.80049 q^{10} +0.732296 q^{11} +1.26770 q^{12} +1.37814 q^{13} +3.55019 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.39293 q^{18} -2.37814 q^{19} +2.80049 q^{20} +0.732296 q^{22} +8.57156 q^{23} +1.26770 q^{24} +2.84273 q^{25} +1.37814 q^{26} -5.56893 q^{27} -4.61576 q^{29} +3.55019 q^{30} +3.01478 q^{31} +1.00000 q^{32} +0.928334 q^{33} +1.00000 q^{34} -1.39293 q^{36} -0.800488 q^{37} -2.37814 q^{38} +1.74708 q^{39} +2.80049 q^{40} -0.985218 q^{41} +11.5293 q^{43} +0.732296 q^{44} -3.90087 q^{45} +8.57156 q^{46} -9.15117 q^{47} +1.26770 q^{48} +2.84273 q^{50} +1.26770 q^{51} +1.37814 q^{52} +11.7730 q^{53} -5.56893 q^{54} +2.05078 q^{55} -3.01478 q^{57} -4.61576 q^{58} -4.74346 q^{59} +3.55019 q^{60} -10.0856 q^{61} +3.01478 q^{62} +1.00000 q^{64} +3.85947 q^{65} +0.928334 q^{66} -3.97912 q^{67} +1.00000 q^{68} +10.8662 q^{69} -7.83926 q^{71} -1.39293 q^{72} +4.98522 q^{73} -0.800488 q^{74} +3.60375 q^{75} -2.37814 q^{76} +1.74708 q^{78} -8.86868 q^{79} +2.80049 q^{80} -2.88098 q^{81} -0.985218 q^{82} -4.84469 q^{83} +2.80049 q^{85} +11.5293 q^{86} -5.85142 q^{87} +0.732296 q^{88} -16.9370 q^{89} -3.90087 q^{90} +8.57156 q^{92} +3.82185 q^{93} -9.15117 q^{94} -6.65996 q^{95} +1.26770 q^{96} -1.77107 q^{97} -1.02003 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} + 5 q^{4} + q^{5} + 5 q^{8} + 11 q^{9}+O(q^{10}) \) 5 * q + 5 * q^2 + 5 * q^4 + q^5 + 5 * q^8 + 11 * q^9	\( 5 q + 5 q^{2} + 5 q^{4} + q^{5} + 5 q^{8} + 11 q^{9} + q^{10} + 10 q^{11} - 2 q^{13} - 4 q^{15} + 5 q^{16} + 5 q^{17} + 11 q^{18} - 3 q^{19} + q^{20} + 10 q^{22} + 3 q^{23} + 18 q^{25} - 2 q^{26} + 6 q^{27} + 12 q^{29} - 4 q^{30} + 6 q^{31} + 5 q^{32} - 26 q^{33} + 5 q^{34} + 11 q^{36} + 9 q^{37} - 3 q^{38} + 6 q^{39} + q^{40} - 14 q^{41} + q^{43} + 10 q^{44} + 37 q^{45} + 3 q^{46} + 2 q^{47} + 18 q^{50} - 2 q^{52} + 20 q^{53} + 6 q^{54} + 6 q^{55} - 6 q^{57} + 12 q^{58} - 3 q^{59} - 4 q^{60} - 16 q^{61} + 6 q^{62} + 5 q^{64} + 2 q^{65} - 26 q^{66} + 15 q^{67} + 5 q^{68} - 4 q^{69} + 7 q^{71} + 11 q^{72} + 34 q^{73} + 9 q^{74} - 46 q^{75} - 3 q^{76} + 6 q^{78} - 12 q^{79} + q^{80} + 53 q^{81} - 14 q^{82} - 16 q^{83} + q^{85} + q^{86} + 20 q^{87} + 10 q^{88} - q^{89} + 37 q^{90} + 3 q^{92} - 12 q^{93} + 2 q^{94} - 3 q^{95} + 18 q^{97} + 16 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 + 5 * q^4 + q^5 + 5 * q^8 + 11 * q^9 + q^10 + 10 * q^11 - 2 * q^13 - 4 * q^15 + 5 * q^16 + 5 * q^17 + 11 * q^18 - 3 * q^19 + q^20 + 10 * q^22 + 3 * q^23 + 18 * q^25 - 2 * q^26 + 6 * q^27 + 12 * q^29 - 4 * q^30 + 6 * q^31 + 5 * q^32 - 26 * q^33 + 5 * q^34 + 11 * q^36 + 9 * q^37 - 3 * q^38 + 6 * q^39 + q^40 - 14 * q^41 + q^43 + 10 * q^44 + 37 * q^45 + 3 * q^46 + 2 * q^47 + 18 * q^50 - 2 * q^52 + 20 * q^53 + 6 * q^54 + 6 * q^55 - 6 * q^57 + 12 * q^58 - 3 * q^59 - 4 * q^60 - 16 * q^61 + 6 * q^62 + 5 * q^64 + 2 * q^65 - 26 * q^66 + 15 * q^67 + 5 * q^68 - 4 * q^69 + 7 * q^71 + 11 * q^72 + 34 * q^73 + 9 * q^74 - 46 * q^75 - 3 * q^76 + 6 * q^78 - 12 * q^79 + q^80 + 53 * q^81 - 14 * q^82 - 16 * q^83 + q^85 + q^86 + 20 * q^87 + 10 * q^88 - q^89 + 37 * q^90 + 3 * q^92 - 12 * q^93 + 2 * q^94 - 3 * q^95 + 18 * q^97 + 16 * q^99

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