LMFDB - Embedded newform 7225.2.a.bs.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7225,2,Mod(1,7225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7225, 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("7225.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7225 = 5^{2} \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7225.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:	$57.6919154604$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} - 10 x^{10} + 52 x^{9} + 21 x^{8} - 232 x^{7} + 44 x^{6} + 424 x^{5} - 137 x^{4} + \cdots + 17 $ x^12 - 4x^11 - 10x^10 + 52x^9 + 21x^8 - 232x^7 + 44x^6 + 424x^5 - 137x^4 - 316x^3 + 46x^2 + 92*x + 17
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 85)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$2.73061$ of defining polynomial
Character	$\chi$	$=$	7225.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.73061 q^{2} -1.54691 q^{3} +5.45623 q^{4} -4.22400 q^{6} +1.26445 q^{7} +9.43761 q^{8} -0.607075 q^{9} +O(q^{10})$	\(q+2.73061 q^{2} -1.54691 q^{3} +5.45623 q^{4} -4.22400 q^{6} +1.26445 q^{7} +9.43761 q^{8} -0.607075 q^{9} +0.417956 q^{11} -8.44028 q^{12} +5.66390 q^{13} +3.45273 q^{14} +14.8580 q^{16} -1.65769 q^{18} -0.134144 q^{19} -1.95600 q^{21} +1.14127 q^{22} -6.81922 q^{23} -14.5991 q^{24} +15.4659 q^{26} +5.57981 q^{27} +6.89915 q^{28} +0.329510 q^{29} -0.605659 q^{31} +21.6961 q^{32} -0.646540 q^{33} -3.31234 q^{36} +8.83716 q^{37} -0.366294 q^{38} -8.76154 q^{39} +1.63371 q^{41} -5.34106 q^{42} +1.99751 q^{43} +2.28046 q^{44} -18.6206 q^{46} +5.06253 q^{47} -22.9839 q^{48} -5.40115 q^{49} +30.9036 q^{52} +1.54296 q^{53} +15.2363 q^{54} +11.9334 q^{56} +0.207508 q^{57} +0.899762 q^{58} -1.41104 q^{59} -7.80498 q^{61} -1.65382 q^{62} -0.767619 q^{63} +29.5276 q^{64} -1.76545 q^{66} +12.1014 q^{67} +10.5487 q^{69} +4.82493 q^{71} -5.72934 q^{72} +2.90042 q^{73} +24.1308 q^{74} -0.731919 q^{76} +0.528486 q^{77} -23.9243 q^{78} +4.33770 q^{79} -6.81023 q^{81} +4.46102 q^{82} +4.39202 q^{83} -10.6724 q^{84} +5.45443 q^{86} -0.509721 q^{87} +3.94451 q^{88} +4.98704 q^{89} +7.16175 q^{91} -37.2072 q^{92} +0.936899 q^{93} +13.8238 q^{94} -33.5619 q^{96} +0.635381 q^{97} -14.7484 q^{98} -0.253731 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{2} + 8 q^{3} + 12 q^{4} - 8 q^{6} + 16 q^{7} + 12 q^{8} + 12 q^{9}+O(q^{10}) $ 12 * q + 4 * q^2 + 8 * q^3 + 12 * q^4 - 8 * q^6 + 16 * q^7 + 12 * q^8 + 12 * q^9	$ 12 q + 4 q^{2} + 8 q^{3} + 12 q^{4} - 8 q^{6} + 16 q^{7} + 12 q^{8} + 12 q^{9} - 16 q^{11} + 16 q^{12} + 8 q^{13} + 16 q^{14} + 12 q^{16} - 4 q^{18} + 16 q^{21} + 16 q^{22} + 16 q^{23} + 16 q^{26} + 32 q^{27} + 40 q^{28} - 16 q^{29} - 24 q^{31} + 28 q^{32} + 12 q^{36} + 24 q^{37} + 24 q^{38} - 8 q^{39} - 8 q^{41} + 16 q^{43} - 8 q^{44} - 40 q^{46} + 32 q^{47} - 24 q^{48} + 20 q^{49} + 24 q^{52} - 8 q^{54} + 24 q^{56} + 32 q^{57} - 16 q^{58} + 8 q^{59} - 24 q^{61} + 8 q^{62} + 48 q^{63} + 36 q^{64} + 40 q^{66} + 8 q^{67} + 48 q^{69} + 16 q^{71} - 12 q^{72} + 16 q^{73} + 16 q^{76} - 24 q^{77} - 24 q^{78} - 40 q^{79} + 36 q^{81} - 16 q^{82} + 40 q^{83} + 32 q^{84} - 8 q^{86} + 32 q^{87} + 48 q^{88} + 8 q^{89} - 72 q^{91} - 8 q^{92} - 24 q^{93} - 16 q^{94} - 8 q^{96} + 32 q^{97} + 60 q^{98} - 56 q^{99}+O(q^{100}) $ 12 * q + 4 * q^2 + 8 * q^3 + 12 * q^4 - 8 * q^6 + 16 * q^7 + 12 * q^8 + 12 * q^9 - 16 * q^11 + 16 * q^12 + 8 * q^13 + 16 * q^14 + 12 * q^16 - 4 * q^18 + 16 * q^21 + 16 * q^22 + 16 * q^23 + 16 * q^26 + 32 * q^27 + 40 * q^28 - 16 * q^29 - 24 * q^31 + 28 * q^32 + 12 * q^36 + 24 * q^37 + 24 * q^38 - 8 * q^39 - 8 * q^41 + 16 * q^43 - 8 * q^44 - 40 * q^46 + 32 * q^47 - 24 * q^48 + 20 * q^49 + 24 * q^52 - 8 * q^54 + 24 * q^56 + 32 * q^57 - 16 * q^58 + 8 * q^59 - 24 * q^61 + 8 * q^62 + 48 * q^63 + 36 * q^64 + 40 * q^66 + 8 * q^67 + 48 * q^69 + 16 * q^71 - 12 * q^72 + 16 * q^73 + 16 * q^76 - 24 * q^77 - 24 * q^78 - 40 * q^79 + 36 * q^81 - 16 * q^82 + 40 * q^83 + 32 * q^84 - 8 * q^86 + 32 * q^87 + 48 * q^88 + 8 * q^89 - 72 * q^91 - 8 * q^92 - 24 * q^93 - 16 * q^94 - 8 * q^96 + 32 * q^97 + 60 * q^98 - 56 * 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 $

$2$	2.73061	1.93083	0.965416	−	0.260713i	$-0.0839577\pi$
$2$	2.73061	1.93083	0.965416	+	0.260713i	$0.0839577\pi$
$3$	−1.54691	−0.893108	−0.446554	−	0.894757i	$-0.647349\pi$
$3$	−1.54691	−0.893108	−0.446554	+	0.894757i	$0.647349\pi$
$4$	5.45623	2.72811
$5$	0	0
$5$	0	0
$6$	−4.22400	−1.72444
$7$	1.26445	0.477919	0.238959	−	0.971030i	$-0.423194\pi$
$7$	1.26445	0.477919	0.238959	+	0.971030i	$0.423194\pi$
$8$	9.43761	3.33670
$9$	−0.607075	−0.202358
$10$	0	0
$11$	0.417956	0.126018	0.0630092	−	0.998013i	$-0.479930\pi$
$11$	0.417956	0.126018	0.0630092	+	0.998013i	$0.479930\pi$
$12$	−8.44028	−2.43650
$13$	5.66390	1.57088	0.785442	−	0.618935i	$-0.212436\pi$
$13$	5.66390	1.57088	0.785442	+	0.618935i	$0.212436\pi$
$14$	3.45273	0.922781
$15$	0	0
$16$	14.8580	3.71449
$17$	0	0
$17$	0	0
$18$	−1.65769	−0.390720
$19$	−0.134144	−0.0307747	−0.0153873	−	0.999882i	$-0.504898\pi$
$19$	−0.134144	−0.0307747	−0.0153873	+	0.999882i	$0.504898\pi$
$20$	0	0
$21$	−1.95600	−0.426833
$22$	1.14127	0.243321
$23$	−6.81922	−1.42191	−0.710953	−	0.703239i	$-0.751736\pi$
$23$	−6.81922	−1.42191	−0.710953	+	0.703239i	$0.751736\pi$
$24$	−14.5991	−2.98003
$25$	0	0
$26$	15.4659	3.03311
$27$	5.57981	1.07384
$28$	6.89915	1.30382
$29$	0.329510	0.0611884	0.0305942	−	0.999532i	$-0.490260\pi$
$29$	0.329510	0.0611884	0.0305942	+	0.999532i	$0.490260\pi$
$30$	0	0
$31$	−0.605659	−0.108780	−0.0543898	−	0.998520i	$-0.517321\pi$
$31$	−0.605659	−0.108780	−0.0543898	+	0.998520i	$0.517321\pi$
$32$	21.6961	3.83537
$33$	−0.646540	−0.112548
$34$	0	0
$35$	0	0
$36$	−3.31234	−0.552057
$37$	8.83716	1.45282	0.726410	−	0.687261i	$-0.241187\pi$
$37$	8.83716	1.45282	0.726410	+	0.687261i	$0.241187\pi$
$38$	−0.366294	−0.0594207
$39$	−8.76154	−1.40297
$40$	0	0
$41$	1.63371	0.255143	0.127571	−	0.991829i	$-0.459282\pi$
$41$	1.63371	0.255143	0.127571	+	0.991829i	$0.459282\pi$
$42$	−5.34106	−0.824143
$43$	1.99751	0.304618	0.152309	−	0.988333i	$-0.451329\pi$
$43$	1.99751	0.304618	0.152309	+	0.988333i	$0.451329\pi$
$44$	2.28046	0.343793
$45$	0	0
$46$	−18.6206	−2.74546
$47$	5.06253	0.738445	0.369223	−	0.929341i	$-0.379624\pi$
$47$	5.06253	0.738445	0.369223	+	0.929341i	$0.379624\pi$
$48$	−22.9839	−3.31744
$49$	−5.40115	−0.771594
$50$	0	0
$51$	0	0
$52$	30.9036	4.28555
$53$	1.54296	0.211942	0.105971	−	0.994369i	$-0.466205\pi$
$53$	1.54296	0.211942	0.105971	+	0.994369i	$0.466205\pi$
$54$	15.2363	2.07340
$55$	0	0
$56$	11.9334	1.59467
$57$	0.207508	0.0274851
$58$	0.899762	0.118145
$59$	−1.41104	−0.183702	−0.0918510	−	0.995773i	$-0.529278\pi$
$59$	−1.41104	−0.183702	−0.0918510	+	0.995773i	$0.529278\pi$
$60$	0	0
$61$	−7.80498	−0.999325	−0.499663	−	0.866220i	$-0.666543\pi$
$61$	−7.80498	−0.999325	−0.499663	+	0.866220i	$0.666543\pi$
$62$	−1.65382	−0.210035
$63$	−0.767619	−0.0967109
$64$	29.5276	3.69095
$65$	0	0
$66$	−1.76545	−0.217312
$67$	12.1014	1.47842	0.739209	−	0.673477i	$-0.235200\pi$
$67$	12.1014	1.47842	0.739209	+	0.673477i	$0.235200\pi$
$68$	0	0
$69$	10.5487	1.26992
$70$	0	0
$71$	4.82493	0.572614	0.286307	−	0.958138i	$-0.407572\pi$
$71$	4.82493	0.572614	0.286307	+	0.958138i	$0.407572\pi$
$72$	−5.72934	−0.675209
$73$	2.90042	0.339468	0.169734	−	0.985490i	$-0.445709\pi$
$73$	2.90042	0.339468	0.169734	+	0.985490i	$0.445709\pi$
$74$	24.1308	2.80515
$75$	0	0
$76$	−0.731919	−0.0839568
$77$	0.528486	0.0602266
$78$	−23.9243	−2.70890
$79$	4.33770	0.488029	0.244015	−	0.969772i	$-0.421535\pi$
$79$	4.33770	0.488029	0.244015	+	0.969772i	$0.421535\pi$
$80$	0	0
$81$	−6.81023	−0.756693
$82$	4.46102	0.492638
$83$	4.39202	0.482087	0.241043	−	0.970514i	$-0.422510\pi$
$83$	4.39202	0.482087	0.241043	+	0.970514i	$0.422510\pi$
$84$	−10.6724	−1.16445
$85$	0	0
$86$	5.45443	0.588167
$87$	−0.509721	−0.0546478
$88$	3.94451	0.420486
$89$	4.98704	0.528625	0.264313	−	0.964437i	$-0.414855\pi$
$89$	4.98704	0.528625	0.264313	+	0.964437i	$0.414855\pi$
$90$	0	0
$91$	7.16175	0.750755
$92$	−37.2072	−3.87912
$93$	0.936899	0.0971519
$94$	13.8238	1.42581
$95$	0	0
$96$	−33.5619	−3.42539
$97$	0.635381	0.0645131	0.0322566	−	0.999480i	$-0.489731\pi$
$97$	0.635381	0.0645131	0.0322566	+	0.999480i	$0.489731\pi$
$98$	−14.7484	−1.48982
$99$	−0.253731	−0.0255009
$100$	0	0
$101$	−7.45004	−0.741307	−0.370653	−	0.928771i	$-0.620866\pi$
$101$	−7.45004	−0.741307	−0.370653	+	0.928771i	$0.620866\pi$
$102$	0	0
$103$	−13.5860	−1.33866	−0.669332	−	0.742963i	$-0.733420\pi$
$103$	−13.5860	−1.33866	−0.669332	+	0.742963i	$0.733420\pi$
$104$	53.4537	5.24157
$105$	0	0
$106$	4.21322	0.409224
$107$	9.27421	0.896572	0.448286	−	0.893890i	$-0.352035\pi$
$107$	9.27421	0.896572	0.448286	+	0.893890i	$0.352035\pi$
$108$	30.4447	2.92955
$109$	−15.7066	−1.50442	−0.752209	−	0.658925i	$-0.771012\pi$
$109$	−15.7066	−1.50442	−0.752209	+	0.658925i	$0.771012\pi$
$110$	0	0
$111$	−13.6703	−1.29753
$112$	18.7872	1.77523
$113$	1.24680	0.117289	0.0586447	−	0.998279i	$-0.481322\pi$
$113$	1.24680	0.117289	0.0586447	+	0.998279i	$0.481322\pi$
$114$	0.566623	0.0530691
$115$	0	0
$116$	1.79788	0.166929
$117$	−3.43842	−0.317882
$118$	−3.85301	−0.354698
$119$	0	0
$120$	0	0
$121$	−10.8253	−0.984119
$122$	−21.3124	−1.92953
$123$	−2.52720	−0.227870
$124$	−3.30461	−0.296763
$125$	0	0
$126$	−2.09607	−0.186733
$127$	−17.8153	−1.58085	−0.790427	−	0.612556i	$-0.790141\pi$
$127$	−17.8153	−1.58085	−0.790427	+	0.612556i	$0.790141\pi$
$128$	37.2362	3.29125
$129$	−3.08997	−0.272057
$130$	0	0
$131$	−4.47235	−0.390751	−0.195375	−	0.980729i	$-0.562593\pi$
$131$	−4.47235	−0.390751	−0.195375	+	0.980729i	$0.562593\pi$
$132$	−3.52767	−0.307044
$133$	−0.169619	−0.0147078
$134$	33.0441	2.85458
$135$	0	0
$136$	0	0
$137$	−9.04916	−0.773122	−0.386561	−	0.922264i	$-0.626337\pi$
$137$	−9.04916	−0.773122	−0.386561	+	0.922264i	$0.626337\pi$
$138$	28.8044	2.45199
$139$	−4.70076	−0.398713	−0.199357	−	0.979927i	$-0.563885\pi$
$139$	−4.70076	−0.398713	−0.199357	+	0.979927i	$0.563885\pi$
$140$	0	0
$141$	−7.83126	−0.659511
$142$	13.1750	1.10562
$143$	2.36726	0.197960
$144$	−9.01991	−0.751659
$145$	0	0
$146$	7.91990	0.655456
$147$	8.35509	0.689116
$148$	48.2176	3.96346
$149$	−0.775949	−0.0635683	−0.0317841	−	0.999495i	$-0.510119\pi$
$149$	−0.775949	−0.0635683	−0.0317841	+	0.999495i	$0.510119\pi$
$150$	0	0
$151$	−2.28712	−0.186123	−0.0930617	−	0.995660i	$-0.529665\pi$
$151$	−2.28712	−0.186123	−0.0930617	+	0.995660i	$0.529665\pi$
$152$	−1.26600	−0.102686
$153$	0	0
$154$	1.44309	0.116288
$155$	0	0
$156$	−47.8050	−3.82746
$157$	19.1134	1.52541	0.762707	−	0.646745i	$-0.223870\pi$
$157$	19.1134	1.52541	0.762707	+	0.646745i	$0.223870\pi$
$158$	11.8446	0.942303
$159$	−2.38682	−0.189287
$160$	0	0
$161$	−8.62260	−0.679556
$162$	−18.5961	−1.46105
$163$	18.3295	1.43568	0.717839	−	0.696209i	$-0.245131\pi$
$163$	18.3295	1.43568	0.717839	+	0.696209i	$0.245131\pi$
$164$	8.91389	0.696058
$165$	0	0
$166$	11.9929	0.930829
$167$	20.1484	1.55913	0.779564	−	0.626322i	$-0.215441\pi$
$167$	20.1484	1.55913	0.779564	+	0.626322i	$0.215441\pi$
$168$	−18.4599	−1.42421
$169$	19.0798	1.46768
$170$	0	0
$171$	0.0814353	0.00622751
$172$	10.8989	0.831033
$173$	19.1144	1.45324	0.726619	−	0.687041i	$-0.241091\pi$
$173$	19.1144	1.45324	0.726619	+	0.687041i	$0.241091\pi$
$174$	−1.39185	−0.105516
$175$	0	0
$176$	6.20998	0.468095
$177$	2.18275	0.164066
$178$	13.6177	1.02069
$179$	19.8154	1.48107	0.740535	−	0.672018i	$-0.234572\pi$
$179$	19.8154	1.48107	0.740535	+	0.672018i	$0.234572\pi$
$180$	0	0
$181$	8.86555	0.658971	0.329485	−	0.944161i	$-0.393125\pi$
$181$	8.86555	0.658971	0.329485	+	0.944161i	$0.393125\pi$
$182$	19.5559	1.44958
$183$	12.0736	0.892505
$184$	−64.3572	−4.74447
$185$	0	0
$186$	2.55831	0.187584
$187$	0	0
$188$	27.6223	2.01456
$189$	7.05542	0.513206
$190$	0	0
$191$	10.6081	0.767576	0.383788	−	0.923421i	$-0.374619\pi$
$191$	10.6081	0.767576	0.383788	+	0.923421i	$0.374619\pi$
$192$	−45.6765	−3.29642
$193$	−9.72535	−0.700046	−0.350023	−	0.936741i	$-0.613826\pi$
$193$	−9.72535	−0.700046	−0.350023	+	0.936741i	$0.613826\pi$
$194$	1.73498	0.124564
$195$	0	0
$196$	−29.4699	−2.10500
$197$	−23.7953	−1.69534	−0.847671	−	0.530521i	$-0.821996\pi$
$197$	−23.7953	−1.69534	−0.847671	+	0.530521i	$0.821996\pi$
$198$	−0.692839	−0.0492380
$199$	13.2078	0.936276	0.468138	−	0.883655i	$-0.344925\pi$
$199$	13.2078	0.936276	0.468138	+	0.883655i	$0.344925\pi$
$200$	0	0
$201$	−18.7197	−1.32039
$202$	−20.3431	−1.43134
$203$	0.416650	0.0292431
$204$	0	0
$205$	0	0
$206$	−37.0979	−2.58474
$207$	4.13978	0.287735
$208$	84.1541	5.83504
$209$	−0.0560662	−0.00387818
$210$	0	0
$211$	−19.8864	−1.36904	−0.684518	−	0.728996i	$-0.739987\pi$
$211$	−19.8864	−1.36904	−0.684518	+	0.728996i	$0.739987\pi$
$212$	8.41873	0.578201
$213$	−7.46373	−0.511406
$214$	25.3243	1.73113
$215$	0	0
$216$	52.6601	3.58307
$217$	−0.765828	−0.0519878
$218$	−42.8885	−2.90478
$219$	−4.48668	−0.303182
$220$	0	0
$221$	0	0
$222$	−37.3282	−2.50530
$223$	−6.36311	−0.426106	−0.213053	−	0.977041i	$-0.568341\pi$
$223$	−6.36311	−0.426106	−0.213053	+	0.977041i	$0.568341\pi$
$224$	27.4337	1.83299
$225$	0	0
$226$	3.40453	0.226466
$227$	26.5359	1.76125	0.880625	−	0.473814i	$-0.157123\pi$
$227$	26.5359	1.76125	0.880625	+	0.473814i	$0.157123\pi$
$228$	1.13221	0.0749825
$229$	15.5455	1.02728	0.513639	−	0.858006i	$-0.328297\pi$
$229$	15.5455	1.02728	0.513639	+	0.858006i	$0.328297\pi$
$230$	0	0
$231$	−0.817520	−0.0537889
$232$	3.10978	0.204167
$233$	−3.80274	−0.249126	−0.124563	−	0.992212i	$-0.539753\pi$
$233$	−3.80274	−0.249126	−0.124563	+	0.992212i	$0.539753\pi$
$234$	−9.38897	−0.613776
$235$	0	0
$236$	−7.69897	−0.501160
$237$	−6.71002	−0.435863
$238$	0	0
$239$	−5.80679	−0.375610	−0.187805	−	0.982206i	$-0.560137\pi$
$239$	−5.80679	−0.375610	−0.187805	+	0.982206i	$0.560137\pi$
$240$	0	0
$241$	−8.72796	−0.562218	−0.281109	−	0.959676i	$-0.590702\pi$
$241$	−8.72796	−0.562218	−0.281109	+	0.959676i	$0.590702\pi$
$242$	−29.5597	−1.90017
$243$	−6.20463	−0.398027
$244$	−42.5858	−2.72627
$245$	0	0
$246$	−6.90079	−0.439979
$247$	−0.759777	−0.0483434
$248$	−5.71597	−0.362965
$249$	−6.79405	−0.430556
$250$	0	0
$251$	15.2424	0.962093	0.481047	−	0.876695i	$-0.340257\pi$
$251$	15.2424	0.962093	0.481047	+	0.876695i	$0.340257\pi$
$252$	−4.18830	−0.263838
$253$	−2.85014	−0.179186
$254$	−48.6467	−3.05236
$255$	0	0
$256$	42.6224	2.66390
$257$	−14.5342	−0.906620	−0.453310	−	0.891353i	$-0.649757\pi$
$257$	−14.5342	−0.906620	−0.453310	+	0.891353i	$0.649757\pi$
$258$	−8.43751	−0.525296
$259$	11.1742	0.694331
$260$	0	0
$261$	−0.200037	−0.0123820
$262$	−12.2122	−0.754474
$263$	−19.0283	−1.17333	−0.586666	−	0.809829i	$-0.699560\pi$
$263$	−19.0283	−1.17333	−0.586666	+	0.809829i	$0.699560\pi$
$264$	−6.10179	−0.375539
$265$	0	0
$266$	−0.463162	−0.0283983
$267$	−7.71449	−0.472119
$268$	66.0278	4.03329
$269$	22.6849	1.38312	0.691560	−	0.722319i	$-0.256924\pi$
$269$	22.6849	1.38312	0.691560	+	0.722319i	$0.256924\pi$
$270$	0	0
$271$	−9.96764	−0.605491	−0.302745	−	0.953071i	$-0.597903\pi$
$271$	−9.96764	−0.605491	−0.302745	+	0.953071i	$0.597903\pi$
$272$	0	0
$273$	−11.0786	−0.670506
$274$	−24.7097	−1.49277
$275$	0	0
$276$	57.5562	3.46448
$277$	11.7071	0.703412	0.351706	−	0.936110i	$-0.385602\pi$
$277$	11.7071	0.703412	0.351706	+	0.936110i	$0.385602\pi$
$278$	−12.8359	−0.769848
$279$	0.367681	0.0220125
$280$	0	0
$281$	−1.18521	−0.0707038	−0.0353519	−	0.999375i	$-0.511255\pi$
$281$	−1.18521	−0.0707038	−0.0353519	+	0.999375i	$0.511255\pi$
$282$	−21.3841	−1.27341
$283$	−4.61084	−0.274086	−0.137043	−	0.990565i	$-0.543760\pi$
$283$	−4.61084	−0.274086	−0.137043	+	0.990565i	$0.543760\pi$
$284$	26.3259	1.56216
$285$	0	0
$286$	6.46407	0.382229
$287$	2.06575	0.121937
$288$	−13.1712	−0.776118
$289$	0	0
$290$	0	0
$291$	−0.982876	−0.0576172
$292$	15.8253	0.926108
$293$	3.09527	0.180828	0.0904138	−	0.995904i	$-0.471181\pi$
$293$	3.09527	0.180828	0.0904138	+	0.995904i	$0.471181\pi$
$294$	22.8145	1.33057
$295$	0	0
$296$	83.4017	4.84763
$297$	2.33212	0.135323
$298$	−2.11882	−0.122740
$299$	−38.6234	−2.23365
$300$	0	0
$301$	2.52577	0.145583
$302$	−6.24524	−0.359373
$303$	11.5245	0.662067
$304$	−1.99310	−0.114312
$305$	0	0
$306$	0	0
$307$	−11.8387	−0.675668	−0.337834	−	0.941206i	$-0.609694\pi$
$307$	−11.8387	−0.675668	−0.337834	+	0.941206i	$0.609694\pi$
$308$	2.88354	0.164305
$309$	21.0162	1.19557
$310$	0	0
$311$	23.4500	1.32973	0.664863	−	0.746965i	$-0.268490\pi$
$311$	23.4500	1.32973	0.664863	+	0.746965i	$0.268490\pi$
$312$	−82.6880	−4.68129
$313$	−27.6083	−1.56051	−0.780257	−	0.625459i	$-0.784912\pi$
$313$	−27.6083	−1.56051	−0.780257	+	0.625459i	$0.784912\pi$
$314$	52.1912	2.94532
$315$	0	0
$316$	23.6675	1.33140
$317$	31.8609	1.78949	0.894744	−	0.446580i	$-0.147358\pi$
$317$	31.8609	1.78949	0.894744	+	0.446580i	$0.147358\pi$
$318$	−6.51746	−0.365481
$319$	0.137720	0.00771087
$320$	0	0
$321$	−14.3464	−0.800736
$322$	−23.5449	−1.31211
$323$	0	0
$324$	−37.1582	−2.06434
$325$	0	0
$326$	50.0507	2.77205
$327$	24.2966	1.34361
$328$	15.4183	0.851334
$329$	6.40133	0.352917
$330$	0	0
$331$	−26.0748	−1.43320	−0.716600	−	0.697484i	$-0.754303\pi$
$331$	−26.0748	−1.43320	−0.716600	+	0.697484i	$0.754303\pi$
$332$	23.9639	1.31519
$333$	−5.36482	−0.293990
$334$	55.0174	3.01042
$335$	0	0
$336$	−29.0621	−1.58547
$337$	−16.5187	−0.899833	−0.449917	−	0.893071i	$-0.648546\pi$
$337$	−16.5187	−0.899833	−0.449917	+	0.893071i	$0.648546\pi$
$338$	52.0995	2.83384
$339$	−1.92869	−0.104752
$340$	0	0
$341$	−0.253139	−0.0137082
$342$	0.222368	0.0120243
$343$	−15.6807	−0.846678
$344$	18.8518	1.01642
$345$	0	0
$346$	52.1938	2.80596
$347$	20.3246	1.09108	0.545540	−	0.838085i	$-0.316325\pi$
$347$	20.3246	1.09108	0.545540	+	0.838085i	$0.316325\pi$
$348$	−2.78115	−0.149086
$349$	4.88555	0.261517	0.130759	−	0.991414i	$-0.458259\pi$
$349$	4.88555	0.261517	0.130759	+	0.991414i	$0.458259\pi$
$350$	0	0
$351$	31.6035	1.68687
$352$	9.06802	0.483327
$353$	−22.6733	−1.20678	−0.603389	−	0.797447i	$-0.706183\pi$
$353$	−22.6733	−1.20678	−0.603389	+	0.797447i	$0.706183\pi$
$354$	5.96025	0.316783
$355$	0	0
$356$	27.2104	1.44215
$357$	0	0
$358$	54.1080	2.85970
$359$	13.4808	0.711490	0.355745	−	0.934583i	$-0.384227\pi$
$359$	13.4808	0.711490	0.355745	+	0.934583i	$0.384227\pi$
$360$	0	0
$361$	−18.9820	−0.999053
$362$	24.2083	1.27236
$363$	16.7458	0.878925
$364$	39.0761	2.04815
$365$	0	0
$366$	32.9683	1.72328
$367$	−1.91088	−0.0997470	−0.0498735	−	0.998756i	$-0.515882\pi$
$367$	−1.91088	−0.0997470	−0.0498735	+	0.998756i	$0.515882\pi$
$368$	−101.320	−5.28166
$369$	−0.991785	−0.0516302
$370$	0	0
$371$	1.95100	0.101291
$372$	5.11193	0.265041
$373$	−24.9357	−1.29112	−0.645562	−	0.763708i	$-0.723377\pi$
$373$	−24.9357	−1.29112	−0.645562	+	0.763708i	$0.723377\pi$
$374$	0	0
$375$	0	0
$376$	47.7781	2.46397
$377$	1.86631	0.0961199
$378$	19.2656	0.990916
$379$	−16.6020	−0.852789	−0.426394	−	0.904537i	$-0.640216\pi$
$379$	−16.6020	−0.852789	−0.426394	+	0.904537i	$0.640216\pi$
$380$	0	0
$381$	27.5587	1.41187
$382$	28.9666	1.48206
$383$	20.0900	1.02655	0.513277	−	0.858223i	$-0.328432\pi$
$383$	20.0900	1.02655	0.513277	+	0.858223i	$0.328432\pi$
$384$	−57.6010	−2.93944
$385$	0	0
$386$	−26.5561	−1.35167
$387$	−1.21264	−0.0616420
$388$	3.46678	0.175999
$389$	−22.2783	−1.12955	−0.564777	−	0.825244i	$-0.691038\pi$
$389$	−22.2783	−1.12955	−0.564777	+	0.825244i	$0.691038\pi$
$390$	0	0
$391$	0	0
$392$	−50.9740	−2.57458
$393$	6.91831	0.348983
$394$	−64.9756	−3.27342
$395$	0	0
$396$	−1.38441	−0.0695694
$397$	−26.2699	−1.31845	−0.659223	−	0.751947i	$-0.729115\pi$
$397$	−26.2699	−1.31845	−0.659223	+	0.751947i	$0.729115\pi$
$398$	36.0653	1.80779
$399$	0.262384	0.0131356
$400$	0	0
$401$	−38.1569	−1.90547	−0.952733	−	0.303807i	$-0.901742\pi$
$401$	−38.1569	−1.90547	−0.952733	+	0.303807i	$0.901742\pi$
$402$	−51.1162	−2.54944
$403$	−3.43040	−0.170880
$404$	−40.6491	−2.02237
$405$	0	0
$406$	1.13771	0.0564635
$407$	3.69355	0.183082
$408$	0	0
$409$	−19.0995	−0.944411	−0.472206	−	0.881488i	$-0.656542\pi$
$409$	−19.0995	−0.944411	−0.472206	+	0.881488i	$0.656542\pi$
$410$	0	0
$411$	13.9982	0.690481
$412$	−74.1281	−3.65203
$413$	−1.78420	−0.0877947
$414$	11.3041	0.555567
$415$	0	0
$416$	122.885	6.02492
$417$	7.27164	0.356094
$418$	−0.153095	−0.00748811
$419$	−33.5509	−1.63907	−0.819533	−	0.573032i	$-0.805767\pi$
$419$	−33.5509	−1.63907	−0.819533	+	0.573032i	$0.805767\pi$
$420$	0	0
$421$	−18.9396	−0.923058	−0.461529	−	0.887125i	$-0.652699\pi$
$421$	−18.9396	−0.923058	−0.461529	+	0.887125i	$0.652699\pi$
$422$	−54.3020	−2.64338
$423$	−3.07333	−0.149431
$424$	14.5618	0.707186
$425$	0	0
$426$	−20.3805	−0.987440
$427$	−9.86904	−0.477596
$428$	50.6022	2.44595
$429$	−3.66194	−0.176800
$430$	0	0
$431$	−24.3871	−1.17469	−0.587343	−	0.809338i	$-0.699826\pi$
$431$	−24.3871	−1.17469	−0.587343	+	0.809338i	$0.699826\pi$
$432$	82.9047	3.98876
$433$	−9.69125	−0.465732	−0.232866	−	0.972509i	$-0.574810\pi$
$433$	−9.69125	−0.465732	−0.232866	+	0.972509i	$0.574810\pi$
$434$	−2.09118	−0.100380
$435$	0	0
$436$	−85.6987	−4.10422
$437$	0.914756	0.0437587
$438$	−12.2514	−0.585393
$439$	3.22352	0.153850	0.0769251	−	0.997037i	$-0.475490\pi$
$439$	3.22352	0.153850	0.0769251	+	0.997037i	$0.475490\pi$
$440$	0	0
$441$	3.27891	0.156138
$442$	0	0
$443$	17.5623	0.834412	0.417206	−	0.908812i	$-0.363009\pi$
$443$	17.5623	0.834412	0.417206	+	0.908812i	$0.363009\pi$
$444$	−74.5882	−3.53980
$445$	0	0
$446$	−17.3752	−0.822739
$447$	1.20032	0.0567733
$448$	37.3364	1.76398
$449$	18.5233	0.874169	0.437084	−	0.899421i	$-0.356011\pi$
$449$	18.5233	0.874169	0.437084	+	0.899421i	$0.356011\pi$
$450$	0	0
$451$	0.682819	0.0321527
$452$	6.80284	0.319979
$453$	3.53797	0.166228
$454$	72.4592	3.40068
$455$	0	0
$456$	1.95838	0.0917095
$457$	−14.7077	−0.687997	−0.343998	−	0.938970i	$-0.611781\pi$
$457$	−14.7077	−0.687997	−0.343998	+	0.938970i	$0.611781\pi$
$458$	42.4488	1.98350
$459$	0	0
$460$	0	0
$461$	17.9494	0.835985	0.417992	−	0.908451i	$-0.362734\pi$
$461$	17.9494	0.835985	0.417992	+	0.908451i	$0.362734\pi$
$462$	−2.23233	−0.103857
$463$	−35.5792	−1.65350	−0.826752	−	0.562567i	$-0.809814\pi$
$463$	−35.5792	−1.65350	−0.826752	+	0.562567i	$0.809814\pi$
$464$	4.89584	0.227284
$465$	0	0
$466$	−10.3838	−0.481020
$467$	−29.4411	−1.36237	−0.681185	−	0.732111i	$-0.738535\pi$
$467$	−29.4411	−1.36237	−0.681185	+	0.732111i	$0.738535\pi$
$468$	−18.7608	−0.867217
$469$	15.3016	0.706564
$470$	0	0
$471$	−29.5666	−1.36236
$472$	−13.3169	−0.612959
$473$	0.834873	0.0383875
$474$	−18.3225	−0.841578
$475$	0	0
$476$	0	0
$477$	−0.936692	−0.0428882
$478$	−15.8561	−0.725240
$479$	16.7360	0.764685	0.382343	−	0.924021i	$-0.375117\pi$
$479$	16.7360	0.764685	0.382343	+	0.924021i	$0.375117\pi$
$480$	0	0
$481$	50.0529	2.28221
$482$	−23.8327	−1.08555
$483$	13.3384	0.606917
$484$	−59.0654	−2.68479
$485$	0	0
$486$	−16.9424	−0.768524
$487$	23.4424	1.06228	0.531138	−	0.847285i	$-0.321765\pi$
$487$	23.4424	1.06228	0.531138	+	0.847285i	$0.321765\pi$
$488$	−73.6604	−3.33445
$489$	−28.3541	−1.28222
$490$	0	0
$491$	25.4877	1.15025	0.575123	−	0.818067i	$-0.304954\pi$
$491$	25.4877	1.15025	0.575123	+	0.818067i	$0.304954\pi$
$492$	−13.7890	−0.621655
$493$	0	0
$494$	−2.07465	−0.0933431
$495$	0	0
$496$	−8.99887	−0.404061
$497$	6.10091	0.273663
$498$	−18.5519	−0.831331
$499$	−28.7421	−1.28667	−0.643336	−	0.765584i	$-0.722450\pi$
$499$	−28.7421	−1.28667	−0.643336	+	0.765584i	$0.722450\pi$
$500$	0	0
$501$	−31.1677	−1.39247
$502$	41.6211	1.85764
$503$	0.0102855	0.000458606 0	0.000229303	−	1.00000i	$-0.499927\pi$
$503$	0.0102855	0.000458606 0	0.000229303		1.00000i	$0.499927\pi$
$504$	−7.24449	−0.322695
$505$	0	0
$506$	−7.78261	−0.345979
$507$	−29.5147	−1.31079
$508$	−97.2044	−4.31275
$509$	26.8066	1.18818	0.594091	−	0.804398i	$-0.297512\pi$
$509$	26.8066	1.18818	0.594091	+	0.804398i	$0.297512\pi$
$510$	0	0
$511$	3.66744	0.162238
$512$	41.9126	1.85229
$513$	−0.748497	−0.0330469
$514$	−39.6873	−1.75053
$515$	0	0
$516$	−16.8596	−0.742202
$517$	2.11591	0.0930578
$518$	30.5124	1.34064
$519$	−29.5681	−1.29790
$520$	0	0
$521$	10.1427	0.444359	0.222180	−	0.975006i	$-0.428683\pi$
$521$	10.1427	0.444359	0.222180	+	0.975006i	$0.428683\pi$
$522$	−0.546223	−0.0239075
$523$	16.7568	0.732724	0.366362	−	0.930472i	$-0.380603\pi$
$523$	16.7568	0.732724	0.366362	+	0.930472i	$0.380603\pi$
$524$	−24.4021	−1.06601
$525$	0	0
$526$	−51.9587	−2.26551
$527$	0	0
$528$	−9.60627	−0.418059
$529$	23.5018	1.02182
$530$	0	0
$531$	0.856609	0.0371736
$532$	−0.925478	−0.0401245
$533$	9.25318	0.400800
$534$	−21.0653	−0.911583
$535$	0	0
$536$	114.208	4.93303
$537$	−30.6525	−1.32275
$538$	61.9435	2.67057
$539$	−2.25745	−0.0972351
$540$	0	0
$541$	−18.1364	−0.779745	−0.389873	−	0.920869i	$-0.627481\pi$
$541$	−18.1364	−0.779745	−0.389873	+	0.920869i	$0.627481\pi$
$542$	−27.2177	−1.16910
$543$	−13.7142	−0.588532
$544$	0	0
$545$	0	0
$546$	−30.2512	−1.29463
$547$	22.5759	0.965277	0.482638	−	0.875820i	$-0.339679\pi$
$547$	22.5759	0.965277	0.482638	+	0.875820i	$0.339679\pi$
$548$	−49.3743	−2.10916
$549$	4.73821	0.202222
$550$	0	0
$551$	−0.0442016	−0.00188305
$552$	99.5546	4.23733
$553$	5.48483	0.233239
$554$	31.9676	1.35817
$555$	0	0
$556$	−25.6484	−1.08774
$557$	−5.97545	−0.253188	−0.126594	−	0.991955i	$-0.540405\pi$
$557$	−5.97545	−0.253188	−0.126594	+	0.991955i	$0.540405\pi$
$558$	1.00399	0.0425024
$559$	11.3137	0.478520
$560$	0	0
$561$	0	0
$562$	−3.23635	−0.136517
$563$	3.56804	0.150375	0.0751874	−	0.997169i	$-0.476045\pi$
$563$	3.56804	0.150375	0.0751874	+	0.997169i	$0.476045\pi$
$564$	−42.7292	−1.79922
$565$	0	0
$566$	−12.5904	−0.529214
$567$	−8.61123	−0.361638
$568$	45.5358	1.91064
$569$	−44.1186	−1.84955	−0.924773	−	0.380518i	$-0.875746\pi$
$569$	−44.1186	−1.84955	−0.924773	+	0.380518i	$0.875746\pi$
$570$	0	0
$571$	12.5732	0.526171	0.263085	−	0.964773i	$-0.415260\pi$
$571$	12.5732	0.526171	0.263085	+	0.964773i	$0.415260\pi$
$572$	12.9163	0.540059
$573$	−16.4098	−0.685528
$574$	5.64076	0.235441
$575$	0	0
$576$	−17.9255	−0.746896
$577$	14.5344	0.605075	0.302538	−	0.953137i	$-0.402166\pi$
$577$	14.5344	0.605075	0.302538	+	0.953137i	$0.402166\pi$
$578$	0	0
$579$	15.0442	0.625217
$580$	0	0
$581$	5.55351	0.230398
$582$	−2.68385	−0.111249
$583$	0.644889	0.0267086
$584$	27.3730	1.13270
$585$	0	0
$586$	8.45197	0.349148
$587$	−12.2048	−0.503745	−0.251872	−	0.967760i	$-0.581046\pi$
$587$	−12.2048	−0.503745	−0.251872	+	0.967760i	$0.581046\pi$
$588$	45.5873	1.87999
$589$	0.0812453	0.00334766
$590$	0	0
$591$	36.8091	1.51412
$592$	131.302	5.39649
$593$	11.4292	0.469343	0.234671	−	0.972075i	$-0.424599\pi$
$593$	11.4292	0.469343	0.234671	+	0.972075i	$0.424599\pi$
$594$	6.36810	0.261286
$595$	0	0
$596$	−4.23376	−0.173421
$597$	−20.4312	−0.836195
$598$	−105.465	−4.31280
$599$	−27.2578	−1.11372	−0.556861	−	0.830606i	$-0.687994\pi$
$599$	−27.2578	−1.11372	−0.556861	+	0.830606i	$0.687994\pi$
$600$	0	0
$601$	11.2039	0.457016	0.228508	−	0.973542i	$-0.426615\pi$
$601$	11.2039	0.457016	0.228508	+	0.973542i	$0.426615\pi$
$602$	6.89688	0.281096
$603$	−7.34644	−0.299170
$604$	−12.4791	−0.507766
$605$	0	0
$606$	31.4690	1.27834
$607$	−40.0476	−1.62548	−0.812742	−	0.582624i	$-0.802026\pi$
$607$	−40.0476	−1.62548	−0.812742	+	0.582624i	$0.802026\pi$
$608$	−2.91039	−0.118032
$609$	−0.644519	−0.0261172
$610$	0	0
$611$	28.6737	1.16001
$612$	0	0
$613$	−29.1043	−1.17551	−0.587755	−	0.809039i	$-0.699988\pi$
$613$	−29.1043	−1.17551	−0.587755	+	0.809039i	$0.699988\pi$
$614$	−32.3268	−1.30460
$615$	0	0
$616$	4.98765	0.200958
$617$	−16.4653	−0.662869	−0.331435	−	0.943478i	$-0.607533\pi$
$617$	−16.4653	−0.662869	−0.331435	+	0.943478i	$0.607533\pi$
$618$	57.3871	2.30845
$619$	7.61375	0.306023	0.153011	−	0.988224i	$-0.451103\pi$
$619$	7.61375	0.306023	0.153011	+	0.988224i	$0.451103\pi$
$620$	0	0
$621$	−38.0500	−1.52689
$622$	64.0327	2.56748
$623$	6.30589	0.252640
$624$	−130.179	−5.21132
$625$	0	0
$626$	−75.3875	−3.01309
$627$	0.0867292	0.00346363
$628$	104.287	4.16150
$629$	0	0
$630$	0	0
$631$	−37.1952	−1.48072	−0.740359	−	0.672212i	$-0.765344\pi$
$631$	−37.1952	−1.48072	−0.740359	+	0.672212i	$0.765344\pi$
$632$	40.9375	1.62841
$633$	30.7624	1.22270
$634$	86.9997	3.45520
$635$	0	0
$636$	−13.0230	−0.516396
$637$	−30.5916	−1.21208
$638$	0.376061	0.0148884
$639$	−2.92910	−0.115873
$640$	0	0
$641$	−8.61170	−0.340142	−0.170071	−	0.985432i	$-0.554400\pi$
$641$	−8.61170	−0.340142	−0.170071	+	0.985432i	$0.554400\pi$
$642$	−39.1743	−1.54609
$643$	−19.1230	−0.754136	−0.377068	−	0.926186i	$-0.623068\pi$
$643$	−19.1230	−0.754136	−0.377068	+	0.926186i	$0.623068\pi$
$644$	−47.0469	−1.85391
$645$	0	0
$646$	0	0
$647$	25.5972	1.00633	0.503164	−	0.864191i	$-0.332169\pi$
$647$	25.5972	1.00633	0.503164	+	0.864191i	$0.332169\pi$
$648$	−64.2723	−2.52486
$649$	−0.589754	−0.0231499
$650$	0	0
$651$	1.18467	0.0464307
$652$	100.010	3.91669
$653$	−8.67406	−0.339442	−0.169721	−	0.985492i	$-0.554287\pi$
$653$	−8.67406	−0.339442	−0.169721	+	0.985492i	$0.554287\pi$
$654$	66.3446	2.59428
$655$	0	0
$656$	24.2736	0.947726
$657$	−1.76077	−0.0686942
$658$	17.4795	0.681424
$659$	36.0328	1.40364	0.701819	−	0.712355i	$-0.252372\pi$
$659$	36.0328	1.40364	0.701819	+	0.712355i	$0.252372\pi$
$660$	0	0
$661$	−9.40443	−0.365790	−0.182895	−	0.983132i	$-0.558547\pi$
$661$	−9.40443	−0.365790	−0.182895	+	0.983132i	$0.558547\pi$
$662$	−71.2001	−2.76727
$663$	0	0
$664$	41.4502	1.60858
$665$	0	0
$666$	−14.6492	−0.567646
$667$	−2.24700	−0.0870041
$668$	109.934	4.25348
$669$	9.84315	0.380558
$670$	0	0
$671$	−3.26214	−0.125933
$672$	−42.4375	−1.63706
$673$	−4.55958	−0.175759	−0.0878794	−	0.996131i	$-0.528009\pi$
$673$	−4.55958	−0.175759	−0.0878794	+	0.996131i	$0.528009\pi$
$674$	−45.1062	−1.73743
$675$	0	0
$676$	104.104	4.00399
$677$	−35.6013	−1.36827	−0.684135	−	0.729355i	$-0.739820\pi$
$677$	−35.6013	−1.36827	−0.684135	+	0.729355i	$0.739820\pi$
$678$	−5.26650	−0.202259
$679$	0.803410	0.0308321
$680$	0	0
$681$	−41.0486	−1.57299
$682$	−0.691223	−0.0264683
$683$	−11.9719	−0.458092	−0.229046	−	0.973416i	$-0.573561\pi$
$683$	−11.9719	−0.458092	−0.229046	+	0.973416i	$0.573561\pi$
$684$	0.444329	0.0169894
$685$	0	0
$686$	−42.8179	−1.63479
$687$	−24.0475	−0.917470
$688$	29.6790	1.13150
$689$	8.73917	0.332936
$690$	0	0
$691$	20.7951	0.791082	0.395541	−	0.918448i	$-0.370557\pi$
$691$	20.7951	0.791082	0.395541	+	0.918448i	$0.370557\pi$
$692$	104.292	3.96460
$693$	−0.320831	−0.0121874
$694$	55.4984	2.10669
$695$	0	0
$696$	−4.81055	−0.182343
$697$	0	0
$698$	13.3405	0.504946
$699$	5.88249	0.222496
$700$	0	0
$701$	−13.1645	−0.497215	−0.248607	−	0.968604i	$-0.579973\pi$
$701$	−13.1645	−0.497215	−0.248607	+	0.968604i	$0.579973\pi$
$702$	86.2969	3.25707
$703$	−1.18545	−0.0447101
$704$	12.3413	0.465129
$705$	0	0
$706$	−61.9119	−2.33009
$707$	−9.42024	−0.354284
$708$	11.9096	0.447590
$709$	−20.3126	−0.762854	−0.381427	−	0.924399i	$-0.624567\pi$
$709$	−20.3126	−0.762854	−0.381427	+	0.924399i	$0.624567\pi$
$710$	0	0
$711$	−2.63331	−0.0987568
$712$	47.0657	1.76386
$713$	4.13012	0.154674
$714$	0	0
$715$	0	0
$716$	108.117	4.04053
$717$	8.98257	0.335460
$718$	36.8108	1.37377
$719$	−29.1456	−1.08695	−0.543474	−	0.839426i	$-0.682891\pi$
$719$	−29.1456	−1.08695	−0.543474	+	0.839426i	$0.682891\pi$
$720$	0	0
$721$	−17.1788	−0.639773
$722$	−51.8324	−1.92900
$723$	13.5014	0.502121
$724$	48.3724	1.79775
$725$	0	0
$726$	45.7261	1.69706
$727$	18.9928	0.704402	0.352201	−	0.935924i	$-0.385433\pi$
$727$	18.9928	0.704402	0.352201	+	0.935924i	$0.385433\pi$
$728$	67.5898	2.50505
$729$	30.0287	1.11217
$730$	0	0
$731$	0	0
$732$	65.8762	2.43486
$733$	−32.5640	−1.20278	−0.601390	−	0.798956i	$-0.705386\pi$
$733$	−32.5640	−1.20278	−0.601390	+	0.798956i	$0.705386\pi$
$734$	−5.21786	−0.192595
$735$	0	0
$736$	−147.951	−5.45353
$737$	5.05784	0.186308
$738$	−2.70818	−0.0996894
$739$	30.7452	1.13098	0.565489	−	0.824756i	$-0.308687\pi$
$739$	30.7452	1.13098	0.565489	+	0.824756i	$0.308687\pi$
$740$	0	0
$741$	1.17531	0.0431759
$742$	5.32742	0.195576
$743$	−9.77413	−0.358578	−0.179289	−	0.983796i	$-0.557380\pi$
$743$	−9.77413	−0.358578	−0.179289	+	0.983796i	$0.557380\pi$
$744$	8.84209	0.324167
$745$	0	0
$746$	−68.0898	−2.49294
$747$	−2.66629	−0.0975543
$748$	0	0
$749$	11.7268	0.428489
$750$	0	0
$751$	−12.9774	−0.473551	−0.236776	−	0.971564i	$-0.576091\pi$
$751$	−12.9774	−0.473551	−0.236776	+	0.971564i	$0.576091\pi$
$752$	75.2189	2.74295
$753$	−23.5786	−0.859253
$754$	5.09616	0.185591
$755$	0	0
$756$	38.4960	1.40009
$757$	−35.5081	−1.29057	−0.645283	−	0.763944i	$-0.723260\pi$
$757$	−35.5081	−1.29057	−0.645283	+	0.763944i	$0.723260\pi$
$758$	−45.3337	−1.64659
$759$	4.40890	0.160033
$760$	0	0
$761$	23.6745	0.858200	0.429100	−	0.903257i	$-0.358831\pi$
$761$	23.6745	0.858200	0.429100	+	0.903257i	$0.358831\pi$
$762$	75.2519	2.72609
$763$	−19.8603	−0.718990
$764$	57.8802	2.09403
$765$	0	0
$766$	54.8581	1.98210
$767$	−7.99201	−0.288575
$768$	−65.9329	−2.37915
$769$	5.83645	0.210468	0.105234	−	0.994447i	$-0.466441\pi$
$769$	5.83645	0.210468	0.105234	+	0.994447i	$0.466441\pi$
$770$	0	0
$771$	22.4831	0.809709
$772$	−53.0637	−1.90981
$773$	30.6187	1.10128	0.550639	−	0.834743i	$-0.314384\pi$
$773$	30.6187	1.10128	0.550639	+	0.834743i	$0.314384\pi$
$774$	−3.31125	−0.119020
$775$	0	0
$776$	5.99648	0.215261
$777$	−17.2855	−0.620112
$778$	−60.8333	−2.18098
$779$	−0.219152	−0.00785193
$780$	0	0
$781$	2.01661	0.0721600
$782$	0	0
$783$	1.83860	0.0657063
$784$	−80.2502	−2.86608
$785$	0	0
$786$	18.8912	0.673827
$787$	−37.8438	−1.34898	−0.674492	−	0.738282i	$-0.735637\pi$
$787$	−37.8438	−1.34898	−0.674492	+	0.738282i	$0.735637\pi$
$788$	−129.832	−4.62509
$789$	29.4350	1.04791
$790$	0	0
$791$	1.57653	0.0560548
$792$	−2.39461	−0.0850888
$793$	−44.2067	−1.56982
$794$	−71.7327	−2.54570
$795$	0	0
$796$	72.0647	2.55427
$797$	7.46090	0.264279	0.132139	−	0.991231i	$-0.457815\pi$
$797$	7.46090	0.264279	0.132139	+	0.991231i	$0.457815\pi$
$798$	0.716469	0.0253627
$799$	0	0
$800$	0	0
$801$	−3.02751	−0.106972
$802$	−104.192	−3.67914
$803$	1.21225	0.0427793
$804$	−102.139	−3.60216
$805$	0	0
$806$	−9.36707	−0.329941
$807$	−35.0914	−1.23528
$808$	−70.3106	−2.47352
$809$	37.6824	1.32484	0.662421	−	0.749132i	$-0.269529\pi$
$809$	37.6824	1.32484	0.662421	+	0.749132i	$0.269529\pi$
$810$	0	0
$811$	6.87611	0.241453	0.120726	−	0.992686i	$-0.461478\pi$
$811$	6.87611	0.241453	0.120726	+	0.992686i	$0.461478\pi$
$812$	2.27334	0.0797785
$813$	15.4190	0.540769
$814$	10.0856	0.353501
$815$	0	0
$816$	0	0
$817$	−0.267954	−0.00937452
$818$	−52.1534	−1.82350
$819$	−4.34772	−0.151922
$820$	0	0
$821$	23.5090	0.820471	0.410236	−	0.911980i	$-0.365446\pi$
$821$	23.5090	0.820471	0.410236	+	0.911980i	$0.365446\pi$
$822$	38.2237	1.33320
$823$	−54.8707	−1.91267	−0.956336	−	0.292268i	$-0.905590\pi$
$823$	−54.8707	−1.91267	−0.956336	+	0.292268i	$0.905590\pi$
$824$	−128.219	−4.46672
$825$	0	0
$826$	−4.87195	−0.169517
$827$	17.6179	0.612634	0.306317	−	0.951930i	$-0.400903\pi$
$827$	17.6179	0.612634	0.306317	+	0.951930i	$0.400903\pi$
$828$	22.5876	0.784973
$829$	11.9207	0.414022	0.207011	−	0.978339i	$-0.433626\pi$
$829$	11.9207	0.414022	0.207011	+	0.978339i	$0.433626\pi$
$830$	0	0
$831$	−18.1098	−0.628223
$832$	167.242	5.79806
$833$	0	0
$834$	19.8560	0.687558
$835$	0	0
$836$	−0.305910	−0.0105801
$837$	−3.37946	−0.116811
$838$	−91.6143	−3.16476
$839$	−42.3385	−1.46169	−0.730844	−	0.682545i	$-0.760873\pi$
$839$	−42.3385	−1.46169	−0.730844	+	0.682545i	$0.760873\pi$
$840$	0	0
$841$	−28.8914	−0.996256
$842$	−51.7166	−1.78227
$843$	1.83341	0.0631461
$844$	−108.505	−3.73489
$845$	0	0
$846$	−8.39207	−0.288525
$847$	−13.6881	−0.470329
$848$	22.9252	0.787256
$849$	7.13254	0.244788
$850$	0	0
$851$	−60.2626	−2.06578
$852$	−40.7238	−1.39517
$853$	33.1729	1.13582	0.567909	−	0.823091i	$-0.307753\pi$
$853$	33.1729	1.13582	0.567909	+	0.823091i	$0.307753\pi$
$854$	−26.9485	−0.922159
$855$	0	0
$856$	87.5264	2.99159
$857$	15.3710	0.525062	0.262531	−	0.964924i	$-0.415443\pi$
$857$	15.3710	0.525062	0.262531	+	0.964924i	$0.415443\pi$
$858$	−9.99932	−0.341371
$859$	−42.8054	−1.46050	−0.730250	−	0.683180i	$-0.760596\pi$
$859$	−42.8054	−1.46050	−0.730250	+	0.683180i	$0.760596\pi$
$860$	0	0
$861$	−3.19553	−0.108903
$862$	−66.5917	−2.26812
$863$	−31.3841	−1.06833	−0.534163	−	0.845382i	$-0.679373\pi$
$863$	−31.3841	−1.06833	−0.534163	+	0.845382i	$0.679373\pi$
$864$	121.060	4.11855
$865$	0	0
$866$	−26.4630	−0.899250
$867$	0	0
$868$	−4.17853	−0.141829
$869$	1.81297	0.0615007
$870$	0	0
$871$	68.5410	2.32242
$872$	−148.233	−5.01979
$873$	−0.385724	−0.0130548
$874$	2.49784	0.0844907
$875$	0	0
$876$	−24.4803	−0.827114
$877$	−29.2384	−0.987310	−0.493655	−	0.869658i	$-0.664339\pi$
$877$	−29.2384	−0.987310	−0.493655	+	0.869658i	$0.664339\pi$
$878$	8.80217	0.297059
$879$	−4.78810	−0.161499
$880$	0	0
$881$	−22.9441	−0.773006	−0.386503	−	0.922288i	$-0.626317\pi$
$881$	−22.9441	−0.773006	−0.386503	+	0.922288i	$0.626317\pi$
$882$	8.95341	0.301477
$883$	21.1206	0.710766	0.355383	−	0.934721i	$-0.384351\pi$
$883$	21.1206	0.710766	0.355383	+	0.934721i	$0.384351\pi$
$884$	0	0
$885$	0	0
$886$	47.9559	1.61111
$887$	−17.9732	−0.603482	−0.301741	−	0.953390i	$-0.597568\pi$
$887$	−17.9732	−0.603482	−0.301741	+	0.953390i	$0.597568\pi$
$888$	−129.015	−4.32945
$889$	−22.5267	−0.755520
$890$	0	0
$891$	−2.84638	−0.0953573
$892$	−34.7186	−1.16246
$893$	−0.679106	−0.0227254
$894$	3.27761	0.109620
$895$	0	0
$896$	47.0835	1.57295
$897$	59.7469	1.99489
$898$	50.5799	1.68787
$899$	−0.199570	−0.00665605
$900$	0	0
$901$	0	0
$902$	1.86451	0.0620815
$903$	−3.90713	−0.130021
$904$	11.7668	0.391359
$905$	0	0
$906$	9.66081	0.320959
$907$	55.8990	1.85610	0.928048	−	0.372461i	$-0.121486\pi$
$907$	55.8990	1.85610	0.928048	+	0.372461i	$0.121486\pi$
$908$	144.786	4.80489
$909$	4.52273	0.150010
$910$	0	0
$911$	−0.561306	−0.0185969	−0.00929845	−	0.999957i	$-0.502960\pi$
$911$	−0.561306	−0.0185969	−0.00929845	+	0.999957i	$0.502960\pi$
$912$	3.08315	0.102093
$913$	1.83567	0.0607519
$914$	−40.1610	−1.32841
$915$	0	0
$916$	84.8200	2.80253
$917$	−5.65508	−0.186747
$918$	0	0
$919$	4.29583	0.141706	0.0708531	−	0.997487i	$-0.477428\pi$
$919$	4.29583	0.141706	0.0708531	+	0.997487i	$0.477428\pi$
$920$	0	0
$921$	18.3133	0.603445
$922$	49.0127	1.61415
$923$	27.3280	0.899511
$924$	−4.46058	−0.146742
$925$	0	0
$926$	−97.1528	−3.19264
$927$	8.24769	0.270890
$928$	7.14907	0.234680
$929$	9.55355	0.313442	0.156721	−	0.987643i	$-0.449908\pi$
$929$	9.55355	0.313442	0.156721	+	0.987643i	$0.449908\pi$
$930$	0	0
$931$	0.724531	0.0237455
$932$	−20.7486	−0.679643
$933$	−36.2750	−1.18759
$934$	−80.3921	−2.63051
$935$	0	0
$936$	−32.4504	−1.06068
$937$	55.7449	1.82111	0.910553	−	0.413392i	$-0.135656\pi$
$937$	55.7449	1.82111	0.910553	+	0.413392i	$0.135656\pi$
$938$	41.7828	1.36426
$939$	42.7075	1.39371
$940$	0	0
$941$	29.4430	0.959813	0.479906	−	0.877320i	$-0.340671\pi$
$941$	29.4430	0.959813	0.479906	+	0.877320i	$0.340671\pi$
$942$	−80.7349	−2.63049
$943$	−11.1406	−0.362789
$944$	−20.9652	−0.682360
$945$	0	0
$946$	2.27971	0.0741199
$947$	−31.5924	−1.02662	−0.513308	−	0.858205i	$-0.671580\pi$
$947$	−31.5924	−1.02662	−0.513308	+	0.858205i	$0.671580\pi$
$948$	−36.6114	−1.18908
$949$	16.4277	0.533265
$950$	0	0
$951$	−49.2859	−1.59821
$952$	0	0
$953$	18.4486	0.597610	0.298805	−	0.954314i	$-0.403412\pi$
$953$	18.4486	0.597610	0.298805	+	0.954314i	$0.403412\pi$
$954$	−2.55774	−0.0828099
$955$	0	0
$956$	−31.6832	−1.02471
$957$	−0.213041	−0.00688664
$958$	45.6994	1.47648
$959$	−11.4422	−0.369490
$960$	0	0
$961$	−30.6332	−0.988167
$962$	136.675	4.40657
$963$	−5.63014	−0.181429
$964$	−47.6218	−1.53379
$965$	0	0
$966$	36.4219	1.17185
$967$	38.3638	1.23370	0.616848	−	0.787083i	$-0.288409\pi$
$967$	38.3638	1.23370	0.616848	+	0.787083i	$0.288409\pi$
$968$	−102.165	−3.28371
$969$	0	0
$970$	0	0
$971$	−52.5632	−1.68683	−0.843417	−	0.537260i	$-0.819459\pi$
$971$	−52.5632	−1.68683	−0.843417	+	0.537260i	$0.819459\pi$
$972$	−33.8539	−1.08586
$973$	−5.94390	−0.190553
$974$	64.0120	2.05108
$975$	0	0
$976$	−115.966	−3.71199
$977$	34.3771	1.09982	0.549911	−	0.835224i	$-0.314662\pi$
$977$	34.3771	1.09982	0.549911	+	0.835224i	$0.314662\pi$
$978$	−77.4239	−2.47574
$979$	2.08436	0.0666166
$980$	0	0
$981$	9.53507	0.304431
$982$	69.5971	2.22093
$983$	−28.7282	−0.916288	−0.458144	−	0.888878i	$-0.651486\pi$
$983$	−28.7282	−0.916288	−0.458144	+	0.888878i	$0.651486\pi$
$984$	−23.8507	−0.760333
$985$	0	0
$986$	0	0
$987$	−9.90228	−0.315193
$988$	−4.14552	−0.131886
$989$	−13.6215	−0.433138
$990$	0	0
$991$	−47.8330	−1.51946	−0.759732	−	0.650236i	$-0.774670\pi$
$991$	−47.8330	−1.51946	−0.759732	+	0.650236i	$0.774670\pi$
$992$	−13.1404	−0.417209
$993$	40.3353	1.28000
$994$	16.6592	0.528398
$995$	0	0
$996$	−37.0699	−1.17460
$997$	−7.81193	−0.247406	−0.123703	−	0.992319i	$-0.539477\pi$
$997$	−7.81193	−0.247406	−0.123703	+	0.992319i	$0.539477\pi$
$998$	−78.4833	−2.48435
$999$	49.3097	1.56009

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7225.2.a.bs.1.12		12
5.4	even	2		1445.2.a.p.1.1		12
17.11	odd	16		425.2.m.b.376.6		24
17.14	odd	16		425.2.m.b.26.6		24
17.16	even	2		7225.2.a.bq.1.12		12
85.4	even	4		1445.2.d.j.866.24		24
85.14	odd	16		85.2.l.a.26.1	✓	24
85.28	even	16		425.2.n.c.274.6		24
85.48	even	16		425.2.n.f.349.1		24
85.62	even	16		425.2.n.f.274.1		24
85.64	even	4		1445.2.d.j.866.23		24
85.79	odd	16		85.2.l.a.36.1	yes	24
85.82	even	16		425.2.n.c.349.6		24
85.84	even	2		1445.2.a.q.1.1		12
255.14	even	16		765.2.be.b.451.6		24
255.164	even	16		765.2.be.b.631.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.l.a.26.1	✓	24	85.14	odd	16
85.2.l.a.36.1	yes	24	85.79	odd	16
425.2.m.b.26.6		24	17.14	odd	16
425.2.m.b.376.6		24	17.11	odd	16
425.2.n.c.274.6		24	85.28	even	16
425.2.n.c.349.6		24	85.82	even	16
425.2.n.f.274.1		24	85.62	even	16
425.2.n.f.349.1		24	85.48	even	16
765.2.be.b.451.6		24	255.14	even	16
765.2.be.b.631.6		24	255.164	even	16
1445.2.a.p.1.1		12	5.4	even	2
1445.2.a.q.1.1		12	85.84	even	2
1445.2.d.j.866.23		24	85.64	even	4
1445.2.d.j.866.24		24	85.4	even	4
7225.2.a.bq.1.12		12	17.16	even	2
7225.2.a.bs.1.12		12	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:	\( N \)	\(=\)	\( 7225 = 5^{2} \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7225.a (trivial)

\(f(q)\)	\(=\)	\(q+2.73061 q^{2} -1.54691 q^{3} +5.45623 q^{4} -4.22400 q^{6} +1.26445 q^{7} +9.43761 q^{8} -0.607075 q^{9} +O(q^{10})\)	\(q+2.73061 q^{2} -1.54691 q^{3} +5.45623 q^{4} -4.22400 q^{6} +1.26445 q^{7} +9.43761 q^{8} -0.607075 q^{9} +0.417956 q^{11} -8.44028 q^{12} +5.66390 q^{13} +3.45273 q^{14} +14.8580 q^{16} -1.65769 q^{18} -0.134144 q^{19} -1.95600 q^{21} +1.14127 q^{22} -6.81922 q^{23} -14.5991 q^{24} +15.4659 q^{26} +5.57981 q^{27} +6.89915 q^{28} +0.329510 q^{29} -0.605659 q^{31} +21.6961 q^{32} -0.646540 q^{33} -3.31234 q^{36} +8.83716 q^{37} -0.366294 q^{38} -8.76154 q^{39} +1.63371 q^{41} -5.34106 q^{42} +1.99751 q^{43} +2.28046 q^{44} -18.6206 q^{46} +5.06253 q^{47} -22.9839 q^{48} -5.40115 q^{49} +30.9036 q^{52} +1.54296 q^{53} +15.2363 q^{54} +11.9334 q^{56} +0.207508 q^{57} +0.899762 q^{58} -1.41104 q^{59} -7.80498 q^{61} -1.65382 q^{62} -0.767619 q^{63} +29.5276 q^{64} -1.76545 q^{66} +12.1014 q^{67} +10.5487 q^{69} +4.82493 q^{71} -5.72934 q^{72} +2.90042 q^{73} +24.1308 q^{74} -0.731919 q^{76} +0.528486 q^{77} -23.9243 q^{78} +4.33770 q^{79} -6.81023 q^{81} +4.46102 q^{82} +4.39202 q^{83} -10.6724 q^{84} +5.45443 q^{86} -0.509721 q^{87} +3.94451 q^{88} +4.98704 q^{89} +7.16175 q^{91} -37.2072 q^{92} +0.936899 q^{93} +13.8238 q^{94} -33.5619 q^{96} +0.635381 q^{97} -14.7484 q^{98} -0.253731 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{2} + 8 q^{3} + 12 q^{4} - 8 q^{6} + 16 q^{7} + 12 q^{8} + 12 q^{9}+O(q^{10}) \) 12 * q + 4 * q^2 + 8 * q^3 + 12 * q^4 - 8 * q^6 + 16 * q^7 + 12 * q^8 + 12 * q^9	\( 12 q + 4 q^{2} + 8 q^{3} + 12 q^{4} - 8 q^{6} + 16 q^{7} + 12 q^{8} + 12 q^{9} - 16 q^{11} + 16 q^{12} + 8 q^{13} + 16 q^{14} + 12 q^{16} - 4 q^{18} + 16 q^{21} + 16 q^{22} + 16 q^{23} + 16 q^{26} + 32 q^{27} + 40 q^{28} - 16 q^{29} - 24 q^{31} + 28 q^{32} + 12 q^{36} + 24 q^{37} + 24 q^{38} - 8 q^{39} - 8 q^{41} + 16 q^{43} - 8 q^{44} - 40 q^{46} + 32 q^{47} - 24 q^{48} + 20 q^{49} + 24 q^{52} - 8 q^{54} + 24 q^{56} + 32 q^{57} - 16 q^{58} + 8 q^{59} - 24 q^{61} + 8 q^{62} + 48 q^{63} + 36 q^{64} + 40 q^{66} + 8 q^{67} + 48 q^{69} + 16 q^{71} - 12 q^{72} + 16 q^{73} + 16 q^{76} - 24 q^{77} - 24 q^{78} - 40 q^{79} + 36 q^{81} - 16 q^{82} + 40 q^{83} + 32 q^{84} - 8 q^{86} + 32 q^{87} + 48 q^{88} + 8 q^{89} - 72 q^{91} - 8 q^{92} - 24 q^{93} - 16 q^{94} - 8 q^{96} + 32 q^{97} + 60 q^{98} - 56 q^{99}+O(q^{100}) \) 12 * q + 4 * q^2 + 8 * q^3 + 12 * q^4 - 8 * q^6 + 16 * q^7 + 12 * q^8 + 12 * q^9 - 16 * q^11 + 16 * q^12 + 8 * q^13 + 16 * q^14 + 12 * q^16 - 4 * q^18 + 16 * q^21 + 16 * q^22 + 16 * q^23 + 16 * q^26 + 32 * q^27 + 40 * q^28 - 16 * q^29 - 24 * q^31 + 28 * q^32 + 12 * q^36 + 24 * q^37 + 24 * q^38 - 8 * q^39 - 8 * q^41 + 16 * q^43 - 8 * q^44 - 40 * q^46 + 32 * q^47 - 24 * q^48 + 20 * q^49 + 24 * q^52 - 8 * q^54 + 24 * q^56 + 32 * q^57 - 16 * q^58 + 8 * q^59 - 24 * q^61 + 8 * q^62 + 48 * q^63 + 36 * q^64 + 40 * q^66 + 8 * q^67 + 48 * q^69 + 16 * q^71 - 12 * q^72 + 16 * q^73 + 16 * q^76 - 24 * q^77 - 24 * q^78 - 40 * q^79 + 36 * q^81 - 16 * q^82 + 40 * q^83 + 32 * q^84 - 8 * q^86 + 32 * q^87 + 48 * q^88 + 8 * q^89 - 72 * q^91 - 8 * q^92 - 24 * q^93 - 16 * q^94 - 8 * q^96 + 32 * q^97 + 60 * q^98 - 56 * q^99

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