LMFDB - Embedded newform 2225.2.a.l.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2225,2,Mod(1,2225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2225, 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("2225.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2225 = 5^{2} \cdot 89 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2225.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:	$17.7667144497$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 11x^{6} + 9x^{5} + 34x^{4} - 19x^{3} - 27x^{2} + 11x - 1 $ x^8 - x^7 - 11x^6 + 9x^5 + 34x^4 - 19x^3 - 27x^2 + 11x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 445)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-2.50065$ of defining polynomial
Character	$\chi$	$=$	2225.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.50065 q^{2} -1.23408 q^{3} +4.25326 q^{4} -3.08600 q^{6} +4.89614 q^{7} +5.63461 q^{8} -1.47705 q^{9} +O(q^{10})$	\(q+2.50065 q^{2} -1.23408 q^{3} +4.25326 q^{4} -3.08600 q^{6} +4.89614 q^{7} +5.63461 q^{8} -1.47705 q^{9} +5.13396 q^{11} -5.24885 q^{12} -0.293733 q^{13} +12.2435 q^{14} +5.58369 q^{16} -4.78896 q^{17} -3.69359 q^{18} +4.79227 q^{19} -6.04222 q^{21} +12.8382 q^{22} -5.18988 q^{23} -6.95355 q^{24} -0.734525 q^{26} +5.52503 q^{27} +20.8246 q^{28} +8.87657 q^{29} -6.58148 q^{31} +2.69363 q^{32} -6.33571 q^{33} -11.9755 q^{34} -6.28228 q^{36} -0.840228 q^{37} +11.9838 q^{38} +0.362490 q^{39} -2.51195 q^{41} -15.1095 q^{42} -9.39183 q^{43} +21.8361 q^{44} -12.9781 q^{46} -8.06738 q^{47} -6.89071 q^{48} +16.9722 q^{49} +5.90996 q^{51} -1.24932 q^{52} +11.4348 q^{53} +13.8162 q^{54} +27.5879 q^{56} -5.91403 q^{57} +22.1972 q^{58} +1.04378 q^{59} +6.77868 q^{61} -16.4580 q^{62} -7.23185 q^{63} -4.43155 q^{64} -15.8434 q^{66} +14.0551 q^{67} -20.3687 q^{68} +6.40471 q^{69} +2.08800 q^{71} -8.32261 q^{72} -6.37951 q^{73} -2.10112 q^{74} +20.3827 q^{76} +25.1366 q^{77} +0.906461 q^{78} +0.566895 q^{79} -2.38717 q^{81} -6.28152 q^{82} -6.12572 q^{83} -25.6991 q^{84} -23.4857 q^{86} -10.9544 q^{87} +28.9279 q^{88} +1.00000 q^{89} -1.43816 q^{91} -22.0739 q^{92} +8.12206 q^{93} -20.1737 q^{94} -3.32415 q^{96} +3.68712 q^{97} +42.4416 q^{98} -7.58312 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} - 6 q^{3} + 7 q^{4} + 6 q^{6} + 6 q^{7} - 3 q^{8} + 12 q^{9}+O(q^{10}) $ 8 * q - q^2 - 6 * q^3 + 7 * q^4 + 6 * q^6 + 6 * q^7 - 3 * q^8 + 12 * q^9	$ 8 q - q^{2} - 6 q^{3} + 7 q^{4} + 6 q^{6} + 6 q^{7} - 3 q^{8} + 12 q^{9} + 14 q^{11} - 17 q^{12} + 7 q^{13} + 15 q^{14} + 9 q^{16} - 17 q^{17} + q^{18} + 17 q^{19} - 2 q^{22} + q^{23} + 8 q^{24} + 3 q^{26} - 21 q^{27} + 29 q^{28} + 10 q^{29} + q^{31} - 2 q^{32} - 10 q^{33} - 16 q^{34} - 17 q^{36} + 11 q^{37} + 30 q^{38} - 5 q^{39} + 15 q^{41} - 14 q^{42} + 5 q^{43} + 7 q^{44} - 12 q^{46} - 12 q^{47} - 3 q^{48} + 4 q^{49} + 35 q^{51} + 14 q^{52} + q^{53} - 29 q^{54} + 3 q^{56} - 15 q^{57} + 37 q^{58} + 26 q^{59} + 13 q^{61} - 22 q^{62} + 16 q^{63} - 15 q^{64} + 4 q^{66} + 25 q^{67} - 23 q^{68} - 5 q^{69} + 28 q^{71} - 22 q^{72} + 17 q^{73} - 5 q^{74} + 8 q^{76} + 56 q^{78} - 7 q^{79} + 24 q^{81} - 5 q^{82} - 44 q^{83} - 57 q^{84} - 13 q^{86} + 12 q^{87} + 66 q^{88} + 8 q^{89} + 27 q^{91} - 15 q^{92} + 38 q^{93} - 27 q^{94} - 20 q^{96} - q^{97} + 34 q^{98} + q^{99}+O(q^{100}) $ 8 * q - q^2 - 6 * q^3 + 7 * q^4 + 6 * q^6 + 6 * q^7 - 3 * q^8 + 12 * q^9 + 14 * q^11 - 17 * q^12 + 7 * q^13 + 15 * q^14 + 9 * q^16 - 17 * q^17 + q^18 + 17 * q^19 - 2 * q^22 + q^23 + 8 * q^24 + 3 * q^26 - 21 * q^27 + 29 * q^28 + 10 * q^29 + q^31 - 2 * q^32 - 10 * q^33 - 16 * q^34 - 17 * q^36 + 11 * q^37 + 30 * q^38 - 5 * q^39 + 15 * q^41 - 14 * q^42 + 5 * q^43 + 7 * q^44 - 12 * q^46 - 12 * q^47 - 3 * q^48 + 4 * q^49 + 35 * q^51 + 14 * q^52 + q^53 - 29 * q^54 + 3 * q^56 - 15 * q^57 + 37 * q^58 + 26 * q^59 + 13 * q^61 - 22 * q^62 + 16 * q^63 - 15 * q^64 + 4 * q^66 + 25 * q^67 - 23 * q^68 - 5 * q^69 + 28 * q^71 - 22 * q^72 + 17 * q^73 - 5 * q^74 + 8 * q^76 + 56 * q^78 - 7 * q^79 + 24 * q^81 - 5 * q^82 - 44 * q^83 - 57 * q^84 - 13 * q^86 + 12 * q^87 + 66 * q^88 + 8 * q^89 + 27 * q^91 - 15 * q^92 + 38 * q^93 - 27 * q^94 - 20 * q^96 - q^97 + 34 * q^98 + 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 $

$2$	2.50065	1.76823	0.884114	−	0.467272i	$-0.154763\pi$
$2$	2.50065	1.76823	0.884114	+	0.467272i	$0.154763\pi$
$3$	−1.23408	−0.712495	−0.356248	−	0.934392i	$-0.615944\pi$
$3$	−1.23408	−0.712495	−0.356248	+	0.934392i	$0.615944\pi$
$4$	4.25326	2.12663
$5$	0	0
$5$	0	0
$6$	−3.08600	−1.25985
$7$	4.89614	1.85057	0.925284	−	0.379275i	$-0.123827\pi$
$7$	4.89614	1.85057	0.925284	+	0.379275i	$0.123827\pi$
$8$	5.63461	1.99214
$9$	−1.47705	−0.492350
$10$	0	0
$11$	5.13396	1.54795	0.773974	−	0.633218i	$-0.218266\pi$
$11$	5.13396	1.54795	0.773974	+	0.633218i	$0.218266\pi$
$12$	−5.24885	−1.51521
$13$	−0.293733	−0.0814670	−0.0407335	−	0.999170i	$-0.512969\pi$
$13$	−0.293733	−0.0814670	−0.0407335	+	0.999170i	$0.512969\pi$
$14$	12.2435	3.27223
$15$	0	0
$16$	5.58369	1.39592
$17$	−4.78896	−1.16149	−0.580747	−	0.814084i	$-0.697240\pi$
$17$	−4.78896	−1.16149	−0.580747	+	0.814084i	$0.697240\pi$
$18$	−3.69359	−0.870587
$19$	4.79227	1.09942	0.549711	−	0.835355i	$-0.314738\pi$
$19$	4.79227	1.09942	0.549711	+	0.835355i	$0.314738\pi$
$20$	0	0
$21$	−6.04222	−1.31852
$22$	12.8382	2.73712
$23$	−5.18988	−1.08216	−0.541082	−	0.840970i	$-0.681985\pi$
$23$	−5.18988	−1.08216	−0.541082	+	0.840970i	$0.681985\pi$
$24$	−6.95355	−1.41939
$25$	0	0
$26$	−0.734525	−0.144052
$27$	5.52503	1.06329
$28$	20.8246	3.93547
$29$	8.87657	1.64834	0.824169	−	0.566344i	$-0.191643\pi$
$29$	8.87657	1.64834	0.824169	+	0.566344i	$0.191643\pi$
$30$	0	0
$31$	−6.58148	−1.18207	−0.591034	−	0.806646i	$-0.701280\pi$
$31$	−6.58148	−1.18207	−0.591034	+	0.806646i	$0.701280\pi$
$32$	2.69363	0.476171
$33$	−6.33571	−1.10291
$34$	−11.9755	−2.05379
$35$	0	0
$36$	−6.28228	−1.04705
$37$	−0.840228	−0.138133	−0.0690663	−	0.997612i	$-0.522002\pi$
$37$	−0.840228	−0.138133	−0.0690663	+	0.997612i	$0.522002\pi$
$38$	11.9838	1.94403
$39$	0.362490	0.0580449
$40$	0	0
$41$	−2.51195	−0.392301	−0.196150	−	0.980574i	$-0.562844\pi$
$41$	−2.51195	−0.392301	−0.196150	+	0.980574i	$0.562844\pi$
$42$	−15.1095	−2.33145
$43$	−9.39183	−1.43224	−0.716120	−	0.697977i	$-0.754084\pi$
$43$	−9.39183	−1.43224	−0.716120	+	0.697977i	$0.754084\pi$
$44$	21.8361	3.29191
$45$	0	0
$46$	−12.9781	−1.91351
$47$	−8.06738	−1.17675	−0.588374	−	0.808589i	$-0.700232\pi$
$47$	−8.06738	−1.17675	−0.588374	+	0.808589i	$0.700232\pi$
$48$	−6.89071	−0.994588
$49$	16.9722	2.42460
$50$	0	0
$51$	5.90996	0.827559
$52$	−1.24932	−0.173250
$53$	11.4348	1.57070	0.785348	−	0.619055i	$-0.212484\pi$
$53$	11.4348	1.57070	0.785348	+	0.619055i	$0.212484\pi$
$54$	13.8162	1.88014
$55$	0	0
$56$	27.5879	3.68658
$57$	−5.91403	−0.783333
$58$	22.1972	2.91464
$59$	1.04378	0.135888	0.0679441	−	0.997689i	$-0.478356\pi$
$59$	1.04378	0.135888	0.0679441	+	0.997689i	$0.478356\pi$
$60$	0	0
$61$	6.77868	0.867921	0.433961	−	0.900932i	$-0.357116\pi$
$61$	6.77868	0.867921	0.433961	+	0.900932i	$0.357116\pi$
$62$	−16.4580	−2.09017
$63$	−7.23185	−0.911128
$64$	−4.43155	−0.553943
$65$	0	0
$66$	−15.8434	−1.95019
$67$	14.0551	1.71710	0.858551	−	0.512727i	$-0.171365\pi$
$67$	14.0551	1.71710	0.858551	+	0.512727i	$0.171365\pi$
$68$	−20.3687	−2.47007
$69$	6.40471	0.771037
$70$	0	0
$71$	2.08800	0.247800	0.123900	−	0.992295i	$-0.460460\pi$
$71$	2.08800	0.247800	0.123900	+	0.992295i	$0.460460\pi$
$72$	−8.32261	−0.980829
$73$	−6.37951	−0.746665	−0.373332	−	0.927698i	$-0.621785\pi$
$73$	−6.37951	−0.746665	−0.373332	+	0.927698i	$0.621785\pi$
$74$	−2.10112	−0.244250
$75$	0	0
$76$	20.3827	2.33806
$77$	25.1366	2.86458
$78$	0.906461	0.102637
$79$	0.566895	0.0637807	0.0318903	−	0.999491i	$-0.489847\pi$
$79$	0.566895	0.0637807	0.0318903	+	0.999491i	$0.489847\pi$
$80$	0	0
$81$	−2.38717	−0.265241
$82$	−6.28152	−0.693677
$83$	−6.12572	−0.672385	−0.336192	−	0.941793i	$-0.609139\pi$
$83$	−6.12572	−0.672385	−0.336192	+	0.941793i	$0.609139\pi$
$84$	−25.6991	−2.80400
$85$	0	0
$86$	−23.4857	−2.53253
$87$	−10.9544	−1.17443
$88$	28.9279	3.08372
$89$	1.00000	0.106000
$89$	1.00000	0.106000
$90$	0	0
$91$	−1.43816	−0.150760
$92$	−22.0739	−2.30136
$93$	8.12206	0.842219
$94$	−20.1737	−2.08076
$95$	0	0
$96$	−3.32415	−0.339270
$97$	3.68712	0.374370	0.187185	−	0.982325i	$-0.440064\pi$
$97$	3.68712	0.374370	0.187185	+	0.982325i	$0.440064\pi$
$98$	42.4416	4.28725
$99$	−7.58312	−0.762132
$100$	0	0
$101$	−6.79147	−0.675777	−0.337888	−	0.941186i	$-0.609713\pi$
$101$	−6.79147	−0.675777	−0.337888	+	0.941186i	$0.609713\pi$
$102$	14.7787	1.46331
$103$	−10.1620	−1.00129	−0.500646	−	0.865652i	$-0.666904\pi$
$103$	−10.1620	−1.00129	−0.500646	+	0.865652i	$0.666904\pi$
$104$	−1.65507	−0.162293
$105$	0	0
$106$	28.5945	2.77735
$107$	−7.95873	−0.769399	−0.384700	−	0.923042i	$-0.625695\pi$
$107$	−7.95873	−0.769399	−0.384700	+	0.923042i	$0.625695\pi$
$108$	23.4994	2.26123
$109$	−3.91220	−0.374721	−0.187360	−	0.982291i	$-0.559993\pi$
$109$	−3.91220	−0.374721	−0.187360	+	0.982291i	$0.559993\pi$
$110$	0	0
$111$	1.03691	0.0984188
$112$	27.3385	2.58325
$113$	8.18970	0.770423	0.385211	−	0.922828i	$-0.374129\pi$
$113$	8.18970	0.770423	0.385211	+	0.922828i	$0.374129\pi$
$114$	−14.7889	−1.38511
$115$	0	0
$116$	37.7543	3.50540
$117$	0.433859	0.0401103
$118$	2.61012	0.240281
$119$	−23.4475	−2.14942
$120$	0	0
$121$	15.3576	1.39614
$122$	16.9511	1.53468
$123$	3.09995	0.279513
$124$	−27.9927	−2.51382
$125$	0	0
$126$	−18.0843	−1.61108
$127$	2.03100	0.180222	0.0901110	−	0.995932i	$-0.471278\pi$
$127$	2.03100	0.180222	0.0901110	+	0.995932i	$0.471278\pi$
$128$	−16.4690	−1.45567
$129$	11.5903	1.02046
$130$	0	0
$131$	9.71902	0.849155	0.424578	−	0.905392i	$-0.360423\pi$
$131$	9.71902	0.849155	0.424578	+	0.905392i	$0.360423\pi$
$132$	−26.9474	−2.34547
$133$	23.4636	2.03455
$134$	35.1469	3.03623
$135$	0	0
$136$	−26.9840	−2.31386
$137$	−21.4520	−1.83277	−0.916386	−	0.400296i	$-0.868907\pi$
$137$	−21.4520	−1.83277	−0.916386	+	0.400296i	$0.868907\pi$
$138$	16.0160	1.36337
$139$	−0.595475	−0.0505075	−0.0252538	−	0.999681i	$-0.508039\pi$
$139$	−0.595475	−0.0505075	−0.0252538	+	0.999681i	$0.508039\pi$
$140$	0	0
$141$	9.95578	0.838428
$142$	5.22136	0.438166
$143$	−1.50802	−0.126107
$144$	−8.24739	−0.687283
$145$	0	0
$146$	−15.9529	−1.32027
$147$	−20.9450	−1.72752
$148$	−3.57371	−0.293757
$149$	−16.4598	−1.34844	−0.674220	−	0.738531i	$-0.735520\pi$
$149$	−16.4598	−1.34844	−0.674220	+	0.738531i	$0.735520\pi$
$150$	0	0
$151$	1.01236	0.0823849	0.0411924	−	0.999151i	$-0.486884\pi$
$151$	1.01236	0.0823849	0.0411924	+	0.999151i	$0.486884\pi$
$152$	27.0026	2.19020
$153$	7.07354	0.571862
$154$	62.8579	5.06523
$155$	0	0
$156$	1.54176	0.123440
$157$	3.66401	0.292420	0.146210	−	0.989254i	$-0.453293\pi$
$157$	3.66401	0.292420	0.146210	+	0.989254i	$0.453293\pi$
$158$	1.41761	0.112779
$159$	−14.1115	−1.11911
$160$	0	0
$161$	−25.4104	−2.00262
$162$	−5.96947	−0.469006
$163$	0.396340	0.0310437	0.0155219	−	0.999880i	$-0.495059\pi$
$163$	0.396340	0.0310437	0.0155219	+	0.999880i	$0.495059\pi$
$164$	−10.6840	−0.834279
$165$	0	0
$166$	−15.3183	−1.18893
$167$	8.91272	0.689687	0.344843	−	0.938660i	$-0.387932\pi$
$167$	8.91272	0.689687	0.344843	+	0.938660i	$0.387932\pi$
$168$	−34.0456	−2.62667
$169$	−12.9137	−0.993363
$170$	0	0
$171$	−7.07842	−0.541300
$172$	−39.9459	−3.04584
$173$	−20.4096	−1.55171	−0.775855	−	0.630911i	$-0.782681\pi$
$173$	−20.4096	−1.55171	−0.775855	+	0.630911i	$0.782681\pi$
$174$	−27.3931	−2.07666
$175$	0	0
$176$	28.6664	2.16081
$177$	−1.28810	−0.0968197
$178$	2.50065	0.187432
$179$	−3.85954	−0.288476	−0.144238	−	0.989543i	$-0.546073\pi$
$179$	−3.85954	−0.288476	−0.144238	+	0.989543i	$0.546073\pi$
$180$	0	0
$181$	−4.85674	−0.360998	−0.180499	−	0.983575i	$-0.557771\pi$
$181$	−4.85674	−0.360998	−0.180499	+	0.983575i	$0.557771\pi$
$182$	−3.59634	−0.266578
$183$	−8.36542	−0.618390
$184$	−29.2429	−2.15582
$185$	0	0
$186$	20.3104	1.48923
$187$	−24.5864	−1.79793
$188$	−34.3126	−2.50251
$189$	27.0513	1.96770
$190$	0	0
$191$	7.44680	0.538831	0.269416	−	0.963024i	$-0.413169\pi$
$191$	7.44680	0.538831	0.269416	+	0.963024i	$0.413169\pi$
$192$	5.46887	0.394682
$193$	7.68593	0.553245	0.276623	−	0.960979i	$-0.410785\pi$
$193$	7.68593	0.553245	0.276623	+	0.960979i	$0.410785\pi$
$194$	9.22021	0.661972
$195$	0	0
$196$	72.1872	5.15623
$197$	26.9802	1.92226	0.961131	−	0.276092i	$-0.0890395\pi$
$197$	26.9802	1.92226	0.961131	+	0.276092i	$0.0890395\pi$
$198$	−18.9627	−1.34762
$199$	5.24242	0.371625	0.185813	−	0.982585i	$-0.440508\pi$
$199$	5.24242	0.371625	0.185813	+	0.982585i	$0.440508\pi$
$200$	0	0
$201$	−17.3451	−1.22343
$202$	−16.9831	−1.19493
$203$	43.4609	3.05036
$204$	25.1366	1.75991
$205$	0	0
$206$	−25.4116	−1.77051
$207$	7.66571	0.532804
$208$	−1.64012	−0.113722
$209$	24.6033	1.70185
$210$	0	0
$211$	−0.509470	−0.0350734	−0.0175367	−	0.999846i	$-0.505582\pi$
$211$	−0.509470	−0.0350734	−0.0175367	+	0.999846i	$0.505582\pi$
$212$	48.6353	3.34029
$213$	−2.57675	−0.176556
$214$	−19.9020	−1.36047
$215$	0	0
$216$	31.1314	2.11822
$217$	−32.2239	−2.18750
$218$	−9.78305	−0.662592
$219$	7.87281	0.531995
$220$	0	0
$221$	1.40668	0.0946235
$222$	2.59294	0.174027
$223$	−11.1310	−0.745384	−0.372692	−	0.927955i	$-0.621565\pi$
$223$	−11.1310	−0.745384	−0.372692	+	0.927955i	$0.621565\pi$
$224$	13.1884	0.881186
$225$	0	0
$226$	20.4796	1.36228
$227$	1.50278	0.0997427	0.0498713	−	0.998756i	$-0.484119\pi$
$227$	1.50278	0.0997427	0.0498713	+	0.998756i	$0.484119\pi$
$228$	−25.1539	−1.66586
$229$	−8.07817	−0.533820	−0.266910	−	0.963721i	$-0.586003\pi$
$229$	−8.07817	−0.533820	−0.266910	+	0.963721i	$0.586003\pi$
$230$	0	0
$231$	−31.0205	−2.04100
$232$	50.0160	3.28371
$233$	−9.45410	−0.619359	−0.309679	−	0.950841i	$-0.600222\pi$
$233$	−9.45410	−0.619359	−0.309679	+	0.950841i	$0.600222\pi$
$234$	1.08493	0.0709241
$235$	0	0
$236$	4.43945	0.288984
$237$	−0.699593	−0.0454434
$238$	−58.6339	−3.80067
$239$	−9.38903	−0.607326	−0.303663	−	0.952780i	$-0.598210\pi$
$239$	−9.38903	−0.607326	−0.303663	+	0.952780i	$0.598210\pi$
$240$	0	0
$241$	−1.14337	−0.0736510	−0.0368255	−	0.999322i	$-0.511725\pi$
$241$	−1.14337	−0.0736510	−0.0368255	+	0.999322i	$0.511725\pi$
$242$	38.4039	2.46870
$243$	−13.6291	−0.874310
$244$	28.8315	1.84575
$245$	0	0
$246$	7.75188	0.494242
$247$	−1.40765	−0.0895665
$248$	−37.0841	−2.35484
$249$	7.55962	0.479071
$250$	0	0
$251$	−16.7613	−1.05796	−0.528981	−	0.848634i	$-0.677426\pi$
$251$	−16.7613	−1.05796	−0.528981	+	0.848634i	$0.677426\pi$
$252$	−30.7589	−1.93763
$253$	−26.6446	−1.67513
$254$	5.07882	0.318674
$255$	0	0
$256$	−32.3202	−2.02001
$257$	−17.2697	−1.07725	−0.538626	−	0.842545i	$-0.681056\pi$
$257$	−17.2697	−1.07725	−0.538626	+	0.842545i	$0.681056\pi$
$258$	28.9832	1.80441
$259$	−4.11387	−0.255624
$260$	0	0
$261$	−13.1111	−0.811560
$262$	24.3039	1.50150
$263$	−27.3161	−1.68438	−0.842192	−	0.539177i	$-0.818735\pi$
$263$	−27.3161	−1.68438	−0.842192	+	0.539177i	$0.818735\pi$
$264$	−35.6993	−2.19714
$265$	0	0
$266$	58.6743	3.59755
$267$	−1.23408	−0.0755244
$268$	59.7799	3.65164
$269$	−8.56066	−0.521953	−0.260976	−	0.965345i	$-0.584044\pi$
$269$	−8.56066	−0.521953	−0.260976	+	0.965345i	$0.584044\pi$
$270$	0	0
$271$	−6.04443	−0.367173	−0.183587	−	0.983004i	$-0.558771\pi$
$271$	−6.04443	−0.367173	−0.183587	+	0.983004i	$0.558771\pi$
$272$	−26.7401	−1.62136
$273$	1.77480	0.107416
$274$	−53.6441	−3.24076
$275$	0	0
$276$	27.2409	1.63971
$277$	−1.06300	−0.0638694	−0.0319347	−	0.999490i	$-0.510167\pi$
$277$	−1.06300	−0.0638694	−0.0319347	+	0.999490i	$0.510167\pi$
$278$	−1.48908	−0.0893088
$279$	9.72118	0.581992
$280$	0	0
$281$	−0.545199	−0.0325239	−0.0162619	−	0.999868i	$-0.505177\pi$
$281$	−0.545199	−0.0325239	−0.0162619	+	0.999868i	$0.505177\pi$
$282$	24.8959	1.48253
$283$	−14.1051	−0.838461	−0.419230	−	0.907880i	$-0.637700\pi$
$283$	−14.1051	−0.838461	−0.419230	+	0.907880i	$0.637700\pi$
$284$	8.88079	0.526978
$285$	0	0
$286$	−3.77102	−0.222985
$287$	−12.2989	−0.725980
$288$	−3.97863	−0.234443
$289$	5.93418	0.349069
$290$	0	0
$291$	−4.55020	−0.266737
$292$	−27.1337	−1.58788
$293$	17.0930	0.998586	0.499293	−	0.866433i	$-0.333593\pi$
$293$	17.0930	0.998586	0.499293	+	0.866433i	$0.333593\pi$
$294$	−52.3762	−3.05464
$295$	0	0
$296$	−4.73436	−0.275179
$297$	28.3653	1.64592
$298$	−41.1602	−2.38435
$299$	1.52444	0.0881606
$300$	0	0
$301$	−45.9837	−2.65046
$302$	2.53157	0.145675
$303$	8.38121	0.481488
$304$	26.7585	1.53471
$305$	0	0
$306$	17.6885	1.01118
$307$	0.280920	0.0160329	0.00801646	−	0.999968i	$-0.497448\pi$
$307$	0.280920	0.0160329	0.00801646	+	0.999968i	$0.497448\pi$
$308$	106.912	6.09190
$309$	12.5407	0.713416
$310$	0	0
$311$	−12.9003	−0.731507	−0.365753	−	0.930712i	$-0.619189\pi$
$311$	−12.9003	−0.731507	−0.365753	+	0.930712i	$0.619189\pi$
$312$	2.04249	0.115633
$313$	3.04911	0.172346	0.0861729	−	0.996280i	$-0.472536\pi$
$313$	3.04911	0.172346	0.0861729	+	0.996280i	$0.472536\pi$
$314$	9.16241	0.517065
$315$	0	0
$316$	2.41115	0.135638
$317$	−1.96859	−0.110567	−0.0552835	−	0.998471i	$-0.517606\pi$
$317$	−1.96859	−0.110567	−0.0552835	+	0.998471i	$0.517606\pi$
$318$	−35.2879	−1.97885
$319$	45.5720	2.55154
$320$	0	0
$321$	9.82169	0.548193
$322$	−63.5425	−3.54108
$323$	−22.9500	−1.27697
$324$	−10.1532	−0.564069
$325$	0	0
$326$	0.991107	0.0548923
$327$	4.82796	0.266987
$328$	−14.1539	−0.781517
$329$	−39.4990	−2.17765
$330$	0	0
$331$	19.6542	1.08029	0.540147	−	0.841571i	$-0.318369\pi$
$331$	19.6542	1.08029	0.540147	+	0.841571i	$0.318369\pi$
$332$	−26.0543	−1.42991
$333$	1.24106	0.0680096
$334$	22.2876	1.21952
$335$	0	0
$336$	−33.7379	−1.84055
$337$	19.5743	1.06628	0.533140	−	0.846027i	$-0.321012\pi$
$337$	19.5743	1.06628	0.533140	+	0.846027i	$0.321012\pi$
$338$	−32.2927	−1.75649
$339$	−10.1067	−0.548922
$340$	0	0
$341$	−33.7891	−1.82978
$342$	−17.7007	−0.957142
$343$	48.8254	2.63632
$344$	−52.9193	−2.85322
$345$	0	0
$346$	−51.0372	−2.74378
$347$	−13.2711	−0.712431	−0.356215	−	0.934404i	$-0.615933\pi$
$347$	−13.2711	−0.712431	−0.356215	+	0.934404i	$0.615933\pi$
$348$	−46.5918	−2.49758
$349$	25.7299	1.37729	0.688646	−	0.725097i	$-0.258205\pi$
$349$	25.7299	1.37729	0.688646	+	0.725097i	$0.258205\pi$
$350$	0	0
$351$	−1.62289	−0.0866233
$352$	13.8290	0.737088
$353$	−33.4472	−1.78022	−0.890108	−	0.455750i	$-0.849371\pi$
$353$	−33.4472	−1.78022	−0.890108	+	0.455750i	$0.849371\pi$
$354$	−3.22110	−0.171199
$355$	0	0
$356$	4.25326	0.225422
$357$	28.9360	1.53145
$358$	−9.65137	−0.510091
$359$	2.49760	0.131818	0.0659090	−	0.997826i	$-0.479005\pi$
$359$	2.49760	0.131818	0.0659090	+	0.997826i	$0.479005\pi$
$360$	0	0
$361$	3.96581	0.208727
$362$	−12.1450	−0.638327
$363$	−18.9524	−0.994744
$364$	−6.11687	−0.320611
$365$	0	0
$366$	−20.9190	−1.09345
$367$	31.2573	1.63162	0.815810	−	0.578320i	$-0.196292\pi$
$367$	31.2573	1.63162	0.815810	+	0.578320i	$0.196292\pi$
$368$	−28.9786	−1.51062
$369$	3.71028	0.193150
$370$	0	0
$371$	55.9866	2.90668
$372$	34.5452	1.79109
$373$	35.2179	1.82351	0.911757	−	0.410730i	$-0.134726\pi$
$373$	35.2179	1.82351	0.911757	+	0.410730i	$0.134726\pi$
$374$	−61.4819	−3.17915
$375$	0	0
$376$	−45.4566	−2.34424
$377$	−2.60735	−0.134285
$378$	67.6460	3.47933
$379$	−3.50658	−0.180121	−0.0900605	−	0.995936i	$-0.528706\pi$
$379$	−3.50658	−0.180121	−0.0900605	+	0.995936i	$0.528706\pi$
$380$	0	0
$381$	−2.50641	−0.128407
$382$	18.6218	0.952776
$383$	−21.9576	−1.12198	−0.560991	−	0.827822i	$-0.689580\pi$
$383$	−21.9576	−1.12198	−0.560991	+	0.827822i	$0.689580\pi$
$384$	20.3240	1.03716
$385$	0	0
$386$	19.2198	0.978263
$387$	13.8722	0.705164
$388$	15.6823	0.796147
$389$	−13.3115	−0.674918	−0.337459	−	0.941340i	$-0.609567\pi$
$389$	−13.3115	−0.674918	−0.337459	+	0.941340i	$0.609567\pi$
$390$	0	0
$391$	24.8541	1.25693
$392$	95.6318	4.83014
$393$	−11.9940	−0.605019
$394$	67.4682	3.39900
$395$	0	0
$396$	−32.2530	−1.62077
$397$	−17.8358	−0.895155	−0.447578	−	0.894245i	$-0.647713\pi$
$397$	−17.8358	−0.895155	−0.447578	+	0.894245i	$0.647713\pi$
$398$	13.1095	0.657118
$399$	−28.9559	−1.44961
$400$	0	0
$401$	−3.19387	−0.159494	−0.0797471	−	0.996815i	$-0.525411\pi$
$401$	−3.19387	−0.159494	−0.0797471	+	0.996815i	$0.525411\pi$
$402$	−43.3740	−2.16330
$403$	1.93320	0.0962996
$404$	−28.8859	−1.43713
$405$	0	0
$406$	108.681	5.39373
$407$	−4.31370	−0.213822
$408$	33.3003	1.64861
$409$	−24.5244	−1.21266	−0.606328	−	0.795215i	$-0.707358\pi$
$409$	−24.5244	−1.21266	−0.606328	+	0.795215i	$0.707358\pi$
$410$	0	0
$411$	26.4735	1.30584
$412$	−43.2216	−2.12938
$413$	5.11048	0.251470
$414$	19.1693	0.942118
$415$	0	0
$416$	−0.791209	−0.0387922
$417$	0.734863	0.0359864
$418$	61.5243	3.00925
$419$	4.89589	0.239180	0.119590	−	0.992823i	$-0.461842\pi$
$419$	4.89589	0.239180	0.119590	+	0.992823i	$0.461842\pi$
$420$	0	0
$421$	4.48965	0.218812	0.109406	−	0.993997i	$-0.465105\pi$
$421$	4.48965	0.218812	0.109406	+	0.993997i	$0.465105\pi$
$422$	−1.27401	−0.0620177
$423$	11.9159	0.579372
$424$	64.4309	3.12904
$425$	0	0
$426$	−6.44356	−0.312192
$427$	33.1894	1.60615
$428$	−33.8505	−1.63623
$429$	1.86101	0.0898504
$430$	0	0
$431$	35.8073	1.72477	0.862387	−	0.506249i	$-0.168968\pi$
$431$	35.8073	1.72477	0.862387	+	0.506249i	$0.168968\pi$
$432$	30.8500	1.48427
$433$	18.7569	0.901399	0.450700	−	0.892676i	$-0.351175\pi$
$433$	18.7569	0.901399	0.450700	+	0.892676i	$0.351175\pi$
$434$	−80.5807	−3.86800
$435$	0	0
$436$	−16.6396	−0.796892
$437$	−24.8713	−1.18975
$438$	19.6871	0.940688
$439$	31.4002	1.49865	0.749325	−	0.662202i	$-0.230378\pi$
$439$	31.4002	1.49865	0.749325	+	0.662202i	$0.230378\pi$
$440$	0	0
$441$	−25.0688	−1.19375
$442$	3.51761	0.167316
$443$	25.6079	1.21667	0.608334	−	0.793681i	$-0.291838\pi$
$443$	25.6079	1.21667	0.608334	+	0.793681i	$0.291838\pi$
$444$	4.41023	0.209300
$445$	0	0
$446$	−27.8347	−1.31801
$447$	20.3127	0.960757
$448$	−21.6975	−1.02511
$449$	−21.3542	−1.00777	−0.503883	−	0.863772i	$-0.668096\pi$
$449$	−21.3542	−1.00777	−0.503883	+	0.863772i	$0.668096\pi$
$450$	0	0
$451$	−12.8963	−0.607261
$452$	34.8329	1.63840
$453$	−1.24933	−0.0586988
$454$	3.75792	0.176368
$455$	0	0
$456$	−33.3233	−1.56051
$457$	27.2671	1.27550	0.637750	−	0.770243i	$-0.279865\pi$
$457$	27.2671	1.27550	0.637750	+	0.770243i	$0.279865\pi$
$458$	−20.2007	−0.943916
$459$	−26.4592	−1.23501
$460$	0	0
$461$	−18.9331	−0.881801	−0.440900	−	0.897556i	$-0.645341\pi$
$461$	−18.9331	−0.881801	−0.440900	+	0.897556i	$0.645341\pi$
$462$	−77.5715	−3.60895
$463$	−30.1659	−1.40193	−0.700965	−	0.713196i	$-0.747247\pi$
$463$	−30.1659	−1.40193	−0.700965	+	0.713196i	$0.747247\pi$
$464$	49.5640	2.30095
$465$	0	0
$466$	−23.6414	−1.09517
$467$	−34.1721	−1.58130	−0.790649	−	0.612270i	$-0.790257\pi$
$467$	−34.1721	−1.58130	−0.790649	+	0.612270i	$0.790257\pi$
$468$	1.84532	0.0852997
$469$	68.8157	3.17762
$470$	0	0
$471$	−4.52168	−0.208348
$472$	5.88128	0.270708
$473$	−48.2173	−2.21703
$474$	−1.74944	−0.0803544
$475$	0	0
$476$	−99.7281	−4.57103
$477$	−16.8898	−0.773333
$478$	−23.4787	−1.07389
$479$	19.0555	0.870666	0.435333	−	0.900269i	$-0.356631\pi$
$479$	19.0555	0.870666	0.435333	+	0.900269i	$0.356631\pi$
$480$	0	0
$481$	0.246803	0.0112532
$482$	−2.85917	−0.130232
$483$	31.3584	1.42686
$484$	65.3196	2.96907
$485$	0	0
$486$	−34.0817	−1.54598
$487$	−25.7093	−1.16500	−0.582501	−	0.812830i	$-0.697926\pi$
$487$	−25.7093	−1.16500	−0.582501	+	0.812830i	$0.697926\pi$
$488$	38.1952	1.72902
$489$	−0.489114	−0.0221185
$490$	0	0
$491$	21.1649	0.955158	0.477579	−	0.878589i	$-0.341514\pi$
$491$	21.1649	0.955158	0.477579	+	0.878589i	$0.341514\pi$
$492$	13.1849	0.594420
$493$	−42.5096	−1.91454
$494$	−3.52004	−0.158374
$495$	0	0
$496$	−36.7489	−1.65008
$497$	10.2231	0.458570
$498$	18.9040	0.847107
$499$	25.0315	1.12056	0.560281	−	0.828302i	$-0.310693\pi$
$499$	25.0315	1.12056	0.560281	+	0.828302i	$0.310693\pi$
$500$	0	0
$501$	−10.9990	−0.491399
$502$	−41.9141	−1.87072
$503$	−5.82665	−0.259797	−0.129899	−	0.991527i	$-0.541465\pi$
$503$	−5.82665	−0.259797	−0.129899	+	0.991527i	$0.541465\pi$
$504$	−40.7487	−1.81509
$505$	0	0
$506$	−66.6289	−2.96202
$507$	15.9365	0.707767
$508$	8.63836	0.383265
$509$	−13.7961	−0.611503	−0.305752	−	0.952111i	$-0.598908\pi$
$509$	−13.7961	−0.611503	−0.305752	+	0.952111i	$0.598908\pi$
$510$	0	0
$511$	−31.2350	−1.38175
$512$	−47.8834	−2.11617
$513$	26.4774	1.16901
$514$	−43.1854	−1.90483
$515$	0	0
$516$	49.2963	2.17015
$517$	−41.4176	−1.82154
$518$	−10.2874	−0.452001
$519$	25.1870	1.10559
$520$	0	0
$521$	34.4027	1.50721	0.753604	−	0.657329i	$-0.228314\pi$
$521$	34.4027	1.50721	0.753604	+	0.657329i	$0.228314\pi$
$522$	−32.7864	−1.43502
$523$	25.0955	1.09735	0.548674	−	0.836036i	$-0.315133\pi$
$523$	25.0955	1.09735	0.548674	+	0.836036i	$0.315133\pi$
$524$	41.3375	1.80584
$525$	0	0
$526$	−68.3081	−2.97838
$527$	31.5185	1.37297
$528$	−35.3766	−1.53957
$529$	3.93481	0.171079
$530$	0	0
$531$	−1.54171	−0.0669046
$532$	99.7968	4.32674
$533$	0.737844	0.0319596
$534$	−3.08600	−0.133544
$535$	0	0
$536$	79.1950	3.42070
$537$	4.76298	0.205538
$538$	−21.4072	−0.922931
$539$	87.1347	3.75316
$540$	0	0
$541$	16.2525	0.698750	0.349375	−	0.936983i	$-0.386394\pi$
$541$	16.2525	0.698750	0.349375	+	0.936983i	$0.386394\pi$
$542$	−15.1150	−0.649246
$543$	5.99359	0.257210
$544$	−12.8997	−0.553070
$545$	0	0
$546$	4.43816	0.189936
$547$	−17.3751	−0.742905	−0.371452	−	0.928452i	$-0.621140\pi$
$547$	−17.3751	−0.742905	−0.371452	+	0.928452i	$0.621140\pi$
$548$	−91.2411	−3.89762
$549$	−10.0125	−0.427321
$550$	0	0
$551$	42.5389	1.81222
$552$	36.0881	1.53601
$553$	2.77560	0.118030
$554$	−2.65819	−0.112936
$555$	0	0
$556$	−2.53271	−0.107411
$557$	43.3855	1.83830	0.919152	−	0.393904i	$-0.128876\pi$
$557$	43.3855	1.83830	0.919152	+	0.393904i	$0.128876\pi$
$558$	24.3093	1.02909
$559$	2.75869	0.116680
$560$	0	0
$561$	30.3415	1.28102
$562$	−1.36335	−0.0575096
$563$	−14.5950	−0.615108	−0.307554	−	0.951531i	$-0.599510\pi$
$563$	−14.5950	−0.615108	−0.307554	+	0.951531i	$0.599510\pi$
$564$	42.3445	1.78302
$565$	0	0
$566$	−35.2719	−1.48259
$567$	−11.6879	−0.490846
$568$	11.7651	0.493651
$569$	−25.4644	−1.06752	−0.533762	−	0.845635i	$-0.679222\pi$
$569$	−25.4644	−1.06752	−0.533762	+	0.845635i	$0.679222\pi$
$570$	0	0
$571$	3.34046	0.139794	0.0698969	−	0.997554i	$-0.477733\pi$
$571$	3.34046	0.139794	0.0698969	+	0.997554i	$0.477733\pi$
$572$	−6.41398	−0.268182
$573$	−9.18993	−0.383915
$574$	−30.7552	−1.28370
$575$	0	0
$576$	6.54562	0.272734
$577$	28.9214	1.20401	0.602007	−	0.798491i	$-0.294368\pi$
$577$	28.9214	1.20401	0.602007	+	0.798491i	$0.294368\pi$
$578$	14.8393	0.617234
$579$	−9.48503	−0.394185
$580$	0	0
$581$	−29.9924	−1.24429
$582$	−11.3785	−0.471652
$583$	58.7060	2.43135
$584$	−35.9460	−1.48746
$585$	0	0
$586$	42.7437	1.76573
$587$	−16.5407	−0.682706	−0.341353	−	0.939935i	$-0.610885\pi$
$587$	−16.5407	−0.682706	−0.341353	+	0.939935i	$0.610885\pi$
$588$	−89.0846	−3.67379
$589$	−31.5402	−1.29959
$590$	0	0
$591$	−33.2957	−1.36960
$592$	−4.69157	−0.192822
$593$	27.0667	1.11150	0.555748	−	0.831351i	$-0.312432\pi$
$593$	27.0667	1.11150	0.555748	+	0.831351i	$0.312432\pi$
$594$	70.9317	2.91036
$595$	0	0
$596$	−70.0078	−2.86763
$597$	−6.46955	−0.264781
$598$	3.81209	0.155888
$599$	7.11352	0.290651	0.145325	−	0.989384i	$-0.453577\pi$
$599$	7.11352	0.290651	0.145325	+	0.989384i	$0.453577\pi$
$600$	0	0
$601$	−42.8950	−1.74972	−0.874861	−	0.484374i	$-0.839047\pi$
$601$	−42.8950	−1.74972	−0.874861	+	0.484374i	$0.839047\pi$
$602$	−114.989	−4.68661
$603$	−20.7601	−0.845416
$604$	4.30584	0.175202
$605$	0	0
$606$	20.9585	0.851380
$607$	27.9087	1.13278	0.566390	−	0.824137i	$-0.308340\pi$
$607$	27.9087	1.13278	0.566390	+	0.824137i	$0.308340\pi$
$608$	12.9086	0.523512
$609$	−53.6342	−2.17337
$610$	0	0
$611$	2.36966	0.0958662
$612$	30.0856	1.21614
$613$	−11.2291	−0.453538	−0.226769	−	0.973949i	$-0.572816\pi$
$613$	−11.2291	−0.453538	−0.226769	+	0.973949i	$0.572816\pi$
$614$	0.702482	0.0283499
$615$	0	0
$616$	141.635	5.70664
$617$	29.7394	1.19726	0.598631	−	0.801025i	$-0.295712\pi$
$617$	29.7394	1.19726	0.598631	+	0.801025i	$0.295712\pi$
$618$	31.3600	1.26148
$619$	−47.0184	−1.88983	−0.944915	−	0.327315i	$-0.893856\pi$
$619$	−47.0184	−1.88983	−0.944915	+	0.327315i	$0.893856\pi$
$620$	0	0
$621$	−28.6742	−1.15066
$622$	−32.2591	−1.29347
$623$	4.89614	0.196160
$624$	2.02403	0.0810261
$625$	0	0
$626$	7.62476	0.304747
$627$	−30.3624	−1.21256
$628$	15.5840	0.621869
$629$	4.02382	0.160440
$630$	0	0
$631$	−4.61993	−0.183917	−0.0919583	−	0.995763i	$-0.529313\pi$
$631$	−4.61993	−0.183917	−0.0919583	+	0.995763i	$0.529313\pi$
$632$	3.19423	0.127060
$633$	0.628726	0.0249896
$634$	−4.92276	−0.195508
$635$	0	0
$636$	−60.0198	−2.37994
$637$	−4.98531	−0.197525
$638$	113.960	4.51170
$639$	−3.08408	−0.122004
$640$	0	0
$641$	−0.763355	−0.0301507	−0.0150754	−	0.999886i	$-0.504799\pi$
$641$	−0.763355	−0.0301507	−0.0150754	+	0.999886i	$0.504799\pi$
$642$	24.5606	0.969331
$643$	24.5483	0.968091	0.484046	−	0.875043i	$-0.339167\pi$
$643$	24.5483	0.968091	0.484046	+	0.875043i	$0.339167\pi$
$644$	−108.077	−4.25882
$645$	0	0
$646$	−57.3899	−2.25798
$647$	20.9739	0.824567	0.412284	−	0.911056i	$-0.364731\pi$
$647$	20.9739	0.824567	0.412284	+	0.911056i	$0.364731\pi$
$648$	−13.4508	−0.528396
$649$	5.35871	0.210348
$650$	0	0
$651$	39.7668	1.55858
$652$	1.68573	0.0660185
$653$	0.521815	0.0204202	0.0102101	−	0.999948i	$-0.496750\pi$
$653$	0.521815	0.0204202	0.0102101	+	0.999948i	$0.496750\pi$
$654$	12.0730	0.472093
$655$	0	0
$656$	−14.0260	−0.547621
$657$	9.42285	0.367621
$658$	−98.7733	−3.85059
$659$	1.63679	0.0637603	0.0318802	−	0.999492i	$-0.489851\pi$
$659$	1.63679	0.0637603	0.0318802	+	0.999492i	$0.489851\pi$
$660$	0	0
$661$	25.0711	0.975151	0.487576	−	0.873081i	$-0.337881\pi$
$661$	25.0711	0.975151	0.487576	+	0.873081i	$0.337881\pi$
$662$	49.1484	1.91021
$663$	−1.73595	−0.0674188
$664$	−34.5161	−1.33948
$665$	0	0
$666$	3.10346	0.120256
$667$	−46.0683	−1.78377
$668$	37.9081	1.46671
$669$	13.7365	0.531083
$670$	0	0
$671$	34.8015	1.34350
$672$	−16.2755	−0.627841
$673$	33.2875	1.28314	0.641569	−	0.767065i	$-0.278284\pi$
$673$	33.2875	1.28314	0.641569	+	0.767065i	$0.278284\pi$
$674$	48.9485	1.88542
$675$	0	0
$676$	−54.9254	−2.11251
$677$	−17.5066	−0.672834	−0.336417	−	0.941713i	$-0.609215\pi$
$677$	−17.5066	−0.672834	−0.336417	+	0.941713i	$0.609215\pi$
$678$	−25.2734	−0.970620
$679$	18.0527	0.692798
$680$	0	0
$681$	−1.85454	−0.0710662
$682$	−84.4947	−3.23547
$683$	46.2972	1.77151	0.885757	−	0.464150i	$-0.153640\pi$
$683$	46.2972	1.77151	0.885757	+	0.464150i	$0.153640\pi$
$684$	−30.1064	−1.15115
$685$	0	0
$686$	122.095	4.66162
$687$	9.96909	0.380345
$688$	−52.4410	−1.99930
$689$	−3.35879	−0.127960
$690$	0	0
$691$	4.46210	0.169746	0.0848732	−	0.996392i	$-0.472951\pi$
$691$	4.46210	0.169746	0.0848732	+	0.996392i	$0.472951\pi$
$692$	−86.8071	−3.29991
$693$	−37.1280	−1.41038
$694$	−33.1864	−1.25974
$695$	0	0
$696$	−61.7237	−2.33963
$697$	12.0296	0.455655
$698$	64.3416	2.43537
$699$	11.6671	0.441290
$700$	0	0
$701$	−5.13544	−0.193963	−0.0969815	−	0.995286i	$-0.530919\pi$
$701$	−5.13544	−0.193963	−0.0969815	+	0.995286i	$0.530919\pi$
$702$	−4.05827	−0.153170
$703$	−4.02659	−0.151866
$704$	−22.7514	−0.857475
$705$	0	0
$706$	−83.6398	−3.14783
$707$	−33.2520	−1.25057
$708$	−5.47863	−0.205900
$709$	4.95502	0.186090	0.0930449	−	0.995662i	$-0.470340\pi$
$709$	4.95502	0.186090	0.0930449	+	0.995662i	$0.470340\pi$
$710$	0	0
$711$	−0.837333	−0.0314024
$712$	5.63461	0.211166
$713$	34.1571	1.27919
$714$	72.3588	2.70796
$715$	0	0
$716$	−16.4156	−0.613481
$717$	11.5868	0.432717
$718$	6.24562	0.233084
$719$	−32.2241	−1.20176	−0.600878	−	0.799341i	$-0.705182\pi$
$719$	−32.2241	−1.20176	−0.600878	+	0.799341i	$0.705182\pi$
$720$	0	0
$721$	−49.7546	−1.85296
$722$	9.91712	0.369077
$723$	1.41101	0.0524760
$724$	−20.6570	−0.767710
$725$	0	0
$726$	−47.3934	−1.75893
$727$	31.3167	1.16147	0.580735	−	0.814093i	$-0.302765\pi$
$727$	31.3167	1.16147	0.580735	+	0.814093i	$0.302765\pi$
$728$	−8.10348	−0.300335
$729$	23.9809	0.888183
$730$	0	0
$731$	44.9771	1.66354
$732$	−35.5803	−1.31509
$733$	1.84406	0.0681118	0.0340559	−	0.999420i	$-0.489158\pi$
$733$	1.84406	0.0681118	0.0340559	+	0.999420i	$0.489158\pi$
$734$	78.1637	2.88508
$735$	0	0
$736$	−13.9796	−0.515295
$737$	72.1583	2.65799
$738$	9.27812	0.341532
$739$	23.1432	0.851338	0.425669	−	0.904879i	$-0.360039\pi$
$739$	23.1432	0.851338	0.425669	+	0.904879i	$0.360039\pi$
$740$	0	0
$741$	1.73715	0.0638158
$742$	140.003	5.13967
$743$	2.13174	0.0782059	0.0391029	−	0.999235i	$-0.487550\pi$
$743$	2.13174	0.0782059	0.0391029	+	0.999235i	$0.487550\pi$
$744$	45.7647	1.67781
$745$	0	0
$746$	88.0677	3.22439
$747$	9.04800	0.331049
$748$	−104.572	−3.82354
$749$	−38.9671	−1.42383
$750$	0	0
$751$	9.83764	0.358981	0.179490	−	0.983760i	$-0.442555\pi$
$751$	9.83764	0.358981	0.179490	+	0.983760i	$0.442555\pi$
$752$	−45.0457	−1.64265
$753$	20.6847	0.753793
$754$	−6.52006	−0.237447
$755$	0	0
$756$	115.056	4.18456
$757$	38.2109	1.38880	0.694400	−	0.719590i	$-0.255670\pi$
$757$	38.2109	1.38880	0.694400	+	0.719590i	$0.255670\pi$
$758$	−8.76874	−0.318495
$759$	32.8815	1.19352
$760$	0	0
$761$	−5.67543	−0.205734	−0.102867	−	0.994695i	$-0.532802\pi$
$761$	−5.67543	−0.205734	−0.102867	+	0.994695i	$0.532802\pi$
$762$	−6.26766	−0.227053
$763$	−19.1547	−0.693446
$764$	31.6731	1.14589
$765$	0	0
$766$	−54.9083	−1.98392
$767$	−0.306592	−0.0110704
$768$	39.8856	1.43925
$769$	19.1784	0.691590	0.345795	−	0.938310i	$-0.387609\pi$
$769$	19.1784	0.691590	0.345795	+	0.938310i	$0.387609\pi$
$770$	0	0
$771$	21.3121	0.767537
$772$	32.6902	1.17655
$773$	−26.8742	−0.966598	−0.483299	−	0.875455i	$-0.660562\pi$
$773$	−26.8742	−0.966598	−0.483299	+	0.875455i	$0.660562\pi$
$774$	34.6896	1.24689
$775$	0	0
$776$	20.7755	0.745797
$777$	5.07684	0.182131
$778$	−33.2873	−1.19341
$779$	−12.0379	−0.431304
$780$	0	0
$781$	10.7197	0.383581
$782$	62.1515	2.22253
$783$	49.0433	1.75267
$784$	94.7675	3.38455
$785$	0	0
$786$	−29.9929	−1.06981
$787$	−11.4331	−0.407546	−0.203773	−	0.979018i	$-0.565320\pi$
$787$	−11.4331	−0.407546	−0.203773	+	0.979018i	$0.565320\pi$
$788$	114.754	4.08794
$789$	33.7102	1.20012
$790$	0	0
$791$	40.0980	1.42572
$792$	−42.7280	−1.51827
$793$	−1.99113	−0.0707069
$794$	−44.6012	−1.58284
$795$	0	0
$796$	22.2974	0.790309
$797$	38.2874	1.35621	0.678105	−	0.734965i	$-0.262801\pi$
$797$	38.2874	1.35621	0.678105	+	0.734965i	$0.262801\pi$
$798$	−72.4087	−2.56324
$799$	38.6344	1.36679
$800$	0	0
$801$	−1.47705	−0.0521890
$802$	−7.98676	−0.282022
$803$	−32.7521	−1.15580
$804$	−73.7731	−2.60178
$805$	0	0
$806$	4.83426	0.170280
$807$	10.5645	0.371889
$808$	−38.2673	−1.34624
$809$	−4.98203	−0.175159	−0.0875794	−	0.996158i	$-0.527913\pi$
$809$	−4.98203	−0.175159	−0.0875794	+	0.996158i	$0.527913\pi$
$810$	0	0
$811$	2.56566	0.0900924	0.0450462	−	0.998985i	$-0.485656\pi$
$811$	2.56566	0.0900924	0.0450462	+	0.998985i	$0.485656\pi$
$812$	184.851	6.48699
$813$	7.45930	0.261609
$814$	−10.7871	−0.378086
$815$	0	0
$816$	32.9993	1.15521
$817$	−45.0082	−1.57464
$818$	−61.3271	−2.14425
$819$	2.12424	0.0742268
$820$	0	0
$821$	7.39548	0.258104	0.129052	−	0.991638i	$-0.458807\pi$
$821$	7.39548	0.258104	0.129052	+	0.991638i	$0.458807\pi$
$822$	66.2010	2.30902
$823$	−14.2404	−0.496389	−0.248195	−	0.968710i	$-0.579837\pi$
$823$	−14.2404	−0.496389	−0.248195	+	0.968710i	$0.579837\pi$
$824$	−57.2590	−1.99471
$825$	0	0
$826$	12.7795	0.444657
$827$	22.1225	0.769273	0.384637	−	0.923068i	$-0.374327\pi$
$827$	22.1225	0.769273	0.384637	+	0.923068i	$0.374327\pi$
$828$	32.6042	1.13308
$829$	43.2604	1.50250	0.751248	−	0.660021i	$-0.229452\pi$
$829$	43.2604	1.50250	0.751248	+	0.660021i	$0.229452\pi$
$830$	0	0
$831$	1.31182	0.0455067
$832$	1.30169	0.0451281
$833$	−81.2793	−2.81616
$834$	1.83764	0.0636321
$835$	0	0
$836$	104.644	3.61920
$837$	−36.3629	−1.25689
$838$	12.2429	0.422925
$839$	−6.71522	−0.231835	−0.115917	−	0.993259i	$-0.536981\pi$
$839$	−6.71522	−0.231835	−0.115917	+	0.993259i	$0.536981\pi$
$840$	0	0
$841$	49.7935	1.71702
$842$	11.2271	0.386910
$843$	0.672818	0.0231731
$844$	−2.16691	−0.0745880
$845$	0	0
$846$	29.7976	1.02446
$847$	75.1928	2.58365
$848$	63.8486	2.19257
$849$	17.4068	0.597399
$850$	0	0
$851$	4.36068	0.149482
$852$	−10.9596	−0.375470
$853$	3.93209	0.134632	0.0673160	−	0.997732i	$-0.478556\pi$
$853$	3.93209	0.134632	0.0673160	+	0.997732i	$0.478556\pi$
$854$	82.9951	2.84003
$855$	0	0
$856$	−44.8443	−1.53275
$857$	4.62748	0.158072	0.0790358	−	0.996872i	$-0.474816\pi$
$857$	4.62748	0.158072	0.0790358	+	0.996872i	$0.474816\pi$
$858$	4.65374	0.158876
$859$	−19.7777	−0.674805	−0.337403	−	0.941360i	$-0.609548\pi$
$859$	−19.7777	−0.674805	−0.337403	+	0.941360i	$0.609548\pi$
$860$	0	0
$861$	15.1778	0.517257
$862$	89.5415	3.04979
$863$	−8.03916	−0.273656	−0.136828	−	0.990595i	$-0.543691\pi$
$863$	−8.03916	−0.273656	−0.136828	+	0.990595i	$0.543691\pi$
$864$	14.8824	0.506309
$865$	0	0
$866$	46.9045	1.59388
$867$	−7.32324	−0.248710
$868$	−137.056	−4.65200
$869$	2.91042	0.0987292
$870$	0	0
$871$	−4.12845	−0.139887
$872$	−22.0437	−0.746495
$873$	−5.44607	−0.184321
$874$	−62.1944	−2.10376
$875$	0	0
$876$	33.4851	1.13136
$877$	−55.5811	−1.87684	−0.938420	−	0.345496i	$-0.887711\pi$
$877$	−55.5811	−1.87684	−0.938420	+	0.345496i	$0.887711\pi$
$878$	78.5210	2.64996
$879$	−21.0941	−0.711488
$880$	0	0
$881$	44.8890	1.51235	0.756174	−	0.654370i	$-0.227066\pi$
$881$	44.8890	1.51235	0.756174	+	0.654370i	$0.227066\pi$
$882$	−62.6884	−2.11083
$883$	13.5457	0.455848	0.227924	−	0.973679i	$-0.426806\pi$
$883$	13.5457	0.455848	0.227924	+	0.973679i	$0.426806\pi$
$884$	5.98297	0.201229
$885$	0	0
$886$	64.0364	2.15135
$887$	−36.1333	−1.21324	−0.606619	−	0.794992i	$-0.707475\pi$
$887$	−36.1333	−1.21324	−0.606619	+	0.794992i	$0.707475\pi$
$888$	5.84257	0.196064
$889$	9.94406	0.333513
$890$	0	0
$891$	−12.2556	−0.410579
$892$	−47.3429	−1.58516
$893$	−38.6610	−1.29374
$894$	50.7950	1.69884
$895$	0	0
$896$	−80.6346	−2.69381
$897$	−1.88128	−0.0628141
$898$	−53.3994	−1.78196
$899$	−58.4210	−1.94845
$900$	0	0
$901$	−54.7610	−1.82435
$902$	−32.2491	−1.07378
$903$	56.7475	1.88844
$904$	46.1458	1.53479
$905$	0	0
$906$	−3.12415	−0.103793
$907$	41.6649	1.38346	0.691730	−	0.722156i	$-0.256849\pi$
$907$	41.6649	1.38346	0.691730	+	0.722156i	$0.256849\pi$
$908$	6.39169	0.212116
$909$	10.0314	0.332719
$910$	0	0
$911$	−55.3548	−1.83399	−0.916993	−	0.398903i	$-0.869391\pi$
$911$	−55.3548	−1.83399	−0.916993	+	0.398903i	$0.869391\pi$
$912$	−33.0221	−1.09347
$913$	−31.4492	−1.04082
$914$	68.1855	2.25537
$915$	0	0
$916$	−34.3585	−1.13524
$917$	47.5857	1.57142
$918$	−66.1652	−2.18378
$919$	9.44714	0.311633	0.155816	−	0.987786i	$-0.450199\pi$
$919$	9.44714	0.311633	0.155816	+	0.987786i	$0.450199\pi$
$920$	0	0
$921$	−0.346677	−0.0114234
$922$	−47.3450	−1.55922
$923$	−0.613315	−0.0201875
$924$	−131.938	−4.34045
$925$	0	0
$926$	−75.4345	−2.47893
$927$	15.0098	0.492987
$928$	23.9102	0.784890
$929$	−23.0801	−0.757234	−0.378617	−	0.925553i	$-0.623600\pi$
$929$	−23.0801	−0.757234	−0.378617	+	0.925553i	$0.623600\pi$
$930$	0	0
$931$	81.3353	2.66566
$932$	−40.2107	−1.31715
$933$	15.9199	0.521195
$934$	−85.4526	−2.79609
$935$	0	0
$936$	2.44463	0.0799052
$937$	−31.4855	−1.02859	−0.514293	−	0.857615i	$-0.671946\pi$
$937$	−31.4855	−1.02859	−0.514293	+	0.857615i	$0.671946\pi$
$938$	172.084	5.61875
$939$	−3.76284	−0.122796
$940$	0	0
$941$	16.7640	0.546492	0.273246	−	0.961944i	$-0.411903\pi$
$941$	16.7640	0.546492	0.273246	+	0.961944i	$0.411903\pi$
$942$	−11.3071	−0.368406
$943$	13.0367	0.424534
$944$	5.82812	0.189689
$945$	0	0
$946$	−120.575	−3.92022
$947$	59.7924	1.94299	0.971497	−	0.237053i	$-0.0761816\pi$
$947$	59.7924	1.94299	0.971497	+	0.237053i	$0.0761816\pi$
$948$	−2.97555	−0.0966413
$949$	1.87387	0.0608285
$950$	0	0
$951$	2.42939	0.0787785
$952$	−132.117	−4.28195
$953$	−17.8565	−0.578428	−0.289214	−	0.957264i	$-0.593394\pi$
$953$	−17.8565	−0.578428	−0.289214	+	0.957264i	$0.593394\pi$
$954$	−42.2356	−1.36743
$955$	0	0
$956$	−39.9340	−1.29156
$957$	−56.2394	−1.81796
$958$	47.6511	1.53954
$959$	−105.032	−3.39167
$960$	0	0
$961$	12.3159	0.397287
$962$	0.617168	0.0198983
$963$	11.7554	0.378814
$964$	−4.86305	−0.156628
$965$	0	0
$966$	78.4164	2.52301
$967$	31.9918	1.02879	0.514393	−	0.857554i	$-0.328017\pi$
$967$	31.9918	1.02879	0.514393	+	0.857554i	$0.328017\pi$
$968$	86.5339	2.78130
$969$	28.3221	0.909836
$970$	0	0
$971$	13.8839	0.445555	0.222778	−	0.974869i	$-0.428488\pi$
$971$	13.8839	0.445555	0.222778	+	0.974869i	$0.428488\pi$
$972$	−57.9683	−1.85933
$973$	−2.91553	−0.0934676
$974$	−64.2901	−2.05999
$975$	0	0
$976$	37.8500	1.21155
$977$	−5.04704	−0.161469	−0.0807346	−	0.996736i	$-0.525727\pi$
$977$	−5.04704	−0.161469	−0.0807346	+	0.996736i	$0.525727\pi$
$978$	−1.22310	−0.0391105
$979$	5.13396	0.164082
$980$	0	0
$981$	5.77852	0.184494
$982$	52.9260	1.68894
$983$	26.6803	0.850971	0.425485	−	0.904965i	$-0.360103\pi$
$983$	26.6803	0.850971	0.425485	+	0.904965i	$0.360103\pi$
$984$	17.4670	0.556827
$985$	0	0
$986$	−106.302	−3.38533
$987$	48.7449	1.55157
$988$	−5.98709	−0.190475
$989$	48.7424	1.54992
$990$	0	0
$991$	−37.2339	−1.18277	−0.591386	−	0.806388i	$-0.701419\pi$
$991$	−37.2339	−1.18277	−0.591386	+	0.806388i	$0.701419\pi$
$992$	−17.7281	−0.562867
$993$	−24.2549	−0.769705
$994$	25.5645	0.810857
$995$	0	0
$996$	32.1530	1.01881
$997$	15.6534	0.495748	0.247874	−	0.968792i	$-0.420268\pi$
$997$	15.6534	0.495748	0.247874	+	0.968792i	$0.420268\pi$
$998$	62.5950	1.98141
$999$	−4.64228	−0.146875

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2225.2.a.l.1.8		8
5.4	even	2		445.2.a.g.1.1	✓	8
15.14	odd	2		4005.2.a.p.1.8		8
20.19	odd	2		7120.2.a.bk.1.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
445.2.a.g.1.1	✓	8	5.4	even	2
2225.2.a.l.1.8		8	1.1	even	1	trivial
4005.2.a.p.1.8		8	15.14	odd	2
7120.2.a.bk.1.4		8	20.19	odd	2

Overview	Random
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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:	\( N \)	\(=\)	\( 2225 = 5^{2} \cdot 89 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2225.a (trivial)

\(f(q)\)	\(=\)	\(q+2.50065 q^{2} -1.23408 q^{3} +4.25326 q^{4} -3.08600 q^{6} +4.89614 q^{7} +5.63461 q^{8} -1.47705 q^{9} +O(q^{10})\)	\(q+2.50065 q^{2} -1.23408 q^{3} +4.25326 q^{4} -3.08600 q^{6} +4.89614 q^{7} +5.63461 q^{8} -1.47705 q^{9} +5.13396 q^{11} -5.24885 q^{12} -0.293733 q^{13} +12.2435 q^{14} +5.58369 q^{16} -4.78896 q^{17} -3.69359 q^{18} +4.79227 q^{19} -6.04222 q^{21} +12.8382 q^{22} -5.18988 q^{23} -6.95355 q^{24} -0.734525 q^{26} +5.52503 q^{27} +20.8246 q^{28} +8.87657 q^{29} -6.58148 q^{31} +2.69363 q^{32} -6.33571 q^{33} -11.9755 q^{34} -6.28228 q^{36} -0.840228 q^{37} +11.9838 q^{38} +0.362490 q^{39} -2.51195 q^{41} -15.1095 q^{42} -9.39183 q^{43} +21.8361 q^{44} -12.9781 q^{46} -8.06738 q^{47} -6.89071 q^{48} +16.9722 q^{49} +5.90996 q^{51} -1.24932 q^{52} +11.4348 q^{53} +13.8162 q^{54} +27.5879 q^{56} -5.91403 q^{57} +22.1972 q^{58} +1.04378 q^{59} +6.77868 q^{61} -16.4580 q^{62} -7.23185 q^{63} -4.43155 q^{64} -15.8434 q^{66} +14.0551 q^{67} -20.3687 q^{68} +6.40471 q^{69} +2.08800 q^{71} -8.32261 q^{72} -6.37951 q^{73} -2.10112 q^{74} +20.3827 q^{76} +25.1366 q^{77} +0.906461 q^{78} +0.566895 q^{79} -2.38717 q^{81} -6.28152 q^{82} -6.12572 q^{83} -25.6991 q^{84} -23.4857 q^{86} -10.9544 q^{87} +28.9279 q^{88} +1.00000 q^{89} -1.43816 q^{91} -22.0739 q^{92} +8.12206 q^{93} -20.1737 q^{94} -3.32415 q^{96} +3.68712 q^{97} +42.4416 q^{98} -7.58312 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} - 6 q^{3} + 7 q^{4} + 6 q^{6} + 6 q^{7} - 3 q^{8} + 12 q^{9}+O(q^{10}) \) 8 * q - q^2 - 6 * q^3 + 7 * q^4 + 6 * q^6 + 6 * q^7 - 3 * q^8 + 12 * q^9	\( 8 q - q^{2} - 6 q^{3} + 7 q^{4} + 6 q^{6} + 6 q^{7} - 3 q^{8} + 12 q^{9} + 14 q^{11} - 17 q^{12} + 7 q^{13} + 15 q^{14} + 9 q^{16} - 17 q^{17} + q^{18} + 17 q^{19} - 2 q^{22} + q^{23} + 8 q^{24} + 3 q^{26} - 21 q^{27} + 29 q^{28} + 10 q^{29} + q^{31} - 2 q^{32} - 10 q^{33} - 16 q^{34} - 17 q^{36} + 11 q^{37} + 30 q^{38} - 5 q^{39} + 15 q^{41} - 14 q^{42} + 5 q^{43} + 7 q^{44} - 12 q^{46} - 12 q^{47} - 3 q^{48} + 4 q^{49} + 35 q^{51} + 14 q^{52} + q^{53} - 29 q^{54} + 3 q^{56} - 15 q^{57} + 37 q^{58} + 26 q^{59} + 13 q^{61} - 22 q^{62} + 16 q^{63} - 15 q^{64} + 4 q^{66} + 25 q^{67} - 23 q^{68} - 5 q^{69} + 28 q^{71} - 22 q^{72} + 17 q^{73} - 5 q^{74} + 8 q^{76} + 56 q^{78} - 7 q^{79} + 24 q^{81} - 5 q^{82} - 44 q^{83} - 57 q^{84} - 13 q^{86} + 12 q^{87} + 66 q^{88} + 8 q^{89} + 27 q^{91} - 15 q^{92} + 38 q^{93} - 27 q^{94} - 20 q^{96} - q^{97} + 34 q^{98} + q^{99}+O(q^{100}) \) 8 * q - q^2 - 6 * q^3 + 7 * q^4 + 6 * q^6 + 6 * q^7 - 3 * q^8 + 12 * q^9 + 14 * q^11 - 17 * q^12 + 7 * q^13 + 15 * q^14 + 9 * q^16 - 17 * q^17 + q^18 + 17 * q^19 - 2 * q^22 + q^23 + 8 * q^24 + 3 * q^26 - 21 * q^27 + 29 * q^28 + 10 * q^29 + q^31 - 2 * q^32 - 10 * q^33 - 16 * q^34 - 17 * q^36 + 11 * q^37 + 30 * q^38 - 5 * q^39 + 15 * q^41 - 14 * q^42 + 5 * q^43 + 7 * q^44 - 12 * q^46 - 12 * q^47 - 3 * q^48 + 4 * q^49 + 35 * q^51 + 14 * q^52 + q^53 - 29 * q^54 + 3 * q^56 - 15 * q^57 + 37 * q^58 + 26 * q^59 + 13 * q^61 - 22 * q^62 + 16 * q^63 - 15 * q^64 + 4 * q^66 + 25 * q^67 - 23 * q^68 - 5 * q^69 + 28 * q^71 - 22 * q^72 + 17 * q^73 - 5 * q^74 + 8 * q^76 + 56 * q^78 - 7 * q^79 + 24 * q^81 - 5 * q^82 - 44 * q^83 - 57 * q^84 - 13 * q^86 + 12 * q^87 + 66 * q^88 + 8 * q^89 + 27 * q^91 - 15 * q^92 + 38 * q^93 - 27 * q^94 - 20 * q^96 - q^97 + 34 * q^98 + q^99

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