LMFDB - Embedded newform 1875.2.a.o.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1875,2,Mod(1,1875)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1875, 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("1875.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1875 = 3 \cdot 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1875.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:	$14.9719503790$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.8.13366265625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 12x^{6} + 10x^{5} + 41x^{4} - 20x^{3} - 48x^{2} + 8x + 16 $ x^8 - x^7 - 12x^6 + 10x^5 + 41x^4 - 20x^3 - 48x^2 + 8x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$2.59716$ of defining polynomial
Character	$\chi$	$=$	1875.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.59716 q^{2} +1.00000 q^{3} +4.74525 q^{4} +2.59716 q^{6} +3.28414 q^{7} +7.12986 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.59716 q^{2} +1.00000 q^{3} +4.74525 q^{4} +2.59716 q^{6} +3.28414 q^{7} +7.12986 q^{8} +1.00000 q^{9} +4.30834 q^{11} +4.74525 q^{12} -3.46120 q^{13} +8.52943 q^{14} +9.02691 q^{16} -5.44757 q^{17} +2.59716 q^{18} -7.63427 q^{19} +3.28414 q^{21} +11.1895 q^{22} -5.04986 q^{23} +7.12986 q^{24} -8.98929 q^{26} +1.00000 q^{27} +15.5841 q^{28} -3.12329 q^{29} -2.06658 q^{31} +9.18462 q^{32} +4.30834 q^{33} -14.1482 q^{34} +4.74525 q^{36} -1.89142 q^{37} -19.8274 q^{38} -3.46120 q^{39} +3.89896 q^{41} +8.52943 q^{42} -3.20815 q^{43} +20.4442 q^{44} -13.1153 q^{46} +6.28577 q^{47} +9.02691 q^{48} +3.78555 q^{49} -5.44757 q^{51} -16.4243 q^{52} -2.51480 q^{53} +2.59716 q^{54} +23.4154 q^{56} -7.63427 q^{57} -8.11170 q^{58} +7.72948 q^{59} -2.95661 q^{61} -5.36725 q^{62} +3.28414 q^{63} +5.80013 q^{64} +11.1895 q^{66} +12.9952 q^{67} -25.8501 q^{68} -5.04986 q^{69} -4.72665 q^{71} +7.12986 q^{72} -1.64933 q^{73} -4.91232 q^{74} -36.2265 q^{76} +14.1492 q^{77} -8.98929 q^{78} +13.7349 q^{79} +1.00000 q^{81} +10.1262 q^{82} -5.01687 q^{83} +15.5841 q^{84} -8.33208 q^{86} -3.12329 q^{87} +30.7179 q^{88} -9.00209 q^{89} -11.3670 q^{91} -23.9628 q^{92} -2.06658 q^{93} +16.3252 q^{94} +9.18462 q^{96} +2.57278 q^{97} +9.83169 q^{98} +4.30834 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + 8 q^{3} + 9 q^{4} + q^{6} + 12 q^{7} + 3 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + q^2 + 8 * q^3 + 9 * q^4 + q^6 + 12 * q^7 + 3 * q^8 + 8 * q^9	$ 8 q + q^{2} + 8 q^{3} + 9 q^{4} + q^{6} + 12 q^{7} + 3 q^{8} + 8 q^{9} + 12 q^{11} + 9 q^{12} + 14 q^{13} + 16 q^{14} + 15 q^{16} - q^{17} + q^{18} + 16 q^{19} + 12 q^{21} + 18 q^{22} - 4 q^{23} + 3 q^{24} - 34 q^{26} + 8 q^{27} - 21 q^{28} + 2 q^{29} + 13 q^{31} - 18 q^{32} + 12 q^{33} - 37 q^{34} + 9 q^{36} - 8 q^{37} - 24 q^{38} + 14 q^{39} - 12 q^{41} + 16 q^{42} + 20 q^{43} + 47 q^{44} + 33 q^{46} - 15 q^{47} + 15 q^{48} + 30 q^{49} - q^{51} - q^{52} - 4 q^{53} + q^{54} + 60 q^{56} + 16 q^{57} + 2 q^{58} + 14 q^{59} + 10 q^{61} + 4 q^{62} + 12 q^{63} + 41 q^{64} + 18 q^{66} + 19 q^{67} - 33 q^{68} - 4 q^{69} + 21 q^{71} + 3 q^{72} - 19 q^{73} - 9 q^{74} - q^{76} - 11 q^{77} - 34 q^{78} + 10 q^{79} + 8 q^{81} + 24 q^{82} - 27 q^{83} - 21 q^{84} + 42 q^{86} + 2 q^{87} + 53 q^{88} - 9 q^{89} - 12 q^{91} - 63 q^{92} + 13 q^{93} + 14 q^{94} - 18 q^{96} + 24 q^{97} - 24 q^{98} + 12 q^{99}+O(q^{100}) $ 8 * q + q^2 + 8 * q^3 + 9 * q^4 + q^6 + 12 * q^7 + 3 * q^8 + 8 * q^9 + 12 * q^11 + 9 * q^12 + 14 * q^13 + 16 * q^14 + 15 * q^16 - q^17 + q^18 + 16 * q^19 + 12 * q^21 + 18 * q^22 - 4 * q^23 + 3 * q^24 - 34 * q^26 + 8 * q^27 - 21 * q^28 + 2 * q^29 + 13 * q^31 - 18 * q^32 + 12 * q^33 - 37 * q^34 + 9 * q^36 - 8 * q^37 - 24 * q^38 + 14 * q^39 - 12 * q^41 + 16 * q^42 + 20 * q^43 + 47 * q^44 + 33 * q^46 - 15 * q^47 + 15 * q^48 + 30 * q^49 - q^51 - q^52 - 4 * q^53 + q^54 + 60 * q^56 + 16 * q^57 + 2 * q^58 + 14 * q^59 + 10 * q^61 + 4 * q^62 + 12 * q^63 + 41 * q^64 + 18 * q^66 + 19 * q^67 - 33 * q^68 - 4 * q^69 + 21 * q^71 + 3 * q^72 - 19 * q^73 - 9 * q^74 - q^76 - 11 * q^77 - 34 * q^78 + 10 * q^79 + 8 * q^81 + 24 * q^82 - 27 * q^83 - 21 * q^84 + 42 * q^86 + 2 * q^87 + 53 * q^88 - 9 * q^89 - 12 * q^91 - 63 * q^92 + 13 * q^93 + 14 * q^94 - 18 * q^96 + 24 * q^97 - 24 * q^98 + 12 * 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 $

$2$	2.59716	1.83647	0.918235	−	0.396035i	$-0.129614\pi$
$2$	2.59716	1.83647	0.918235	+	0.396035i	$0.129614\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.74525	2.37263
$5$	0	0
$5$	0	0
$6$	2.59716	1.06029
$7$	3.28414	1.24129	0.620643	−	0.784093i	$-0.286871\pi$
$7$	3.28414	1.24129	0.620643	+	0.784093i	$0.286871\pi$
$8$	7.12986	2.52079
$9$	1.00000	0.333333
$10$	0	0
$11$	4.30834	1.29901	0.649507	−	0.760356i	$-0.274975\pi$
$11$	4.30834	1.29901	0.649507	+	0.760356i	$0.274975\pi$
$12$	4.74525	1.36984
$13$	−3.46120	−0.959964	−0.479982	−	0.877278i	$-0.659357\pi$
$13$	−3.46120	−0.959964	−0.479982	+	0.877278i	$0.659357\pi$
$14$	8.52943	2.27959
$15$	0	0
$16$	9.02691	2.25673
$17$	−5.44757	−1.32123	−0.660615	−	0.750725i	$-0.729705\pi$
$17$	−5.44757	−1.32123	−0.660615	+	0.750725i	$0.729705\pi$
$18$	2.59716	0.612157
$19$	−7.63427	−1.75142	−0.875711	−	0.482835i	$-0.839607\pi$
$19$	−7.63427	−1.75142	−0.875711	+	0.482835i	$0.839607\pi$
$20$	0	0
$21$	3.28414	0.716657
$22$	11.1895	2.38560
$23$	−5.04986	−1.05297	−0.526484	−	0.850185i	$-0.676490\pi$
$23$	−5.04986	−1.05297	−0.526484	+	0.850185i	$0.676490\pi$
$24$	7.12986	1.45538
$25$	0	0
$26$	−8.98929	−1.76295
$27$	1.00000	0.192450
$28$	15.5841	2.94511
$29$	−3.12329	−0.579981	−0.289990	−	0.957030i	$-0.593652\pi$
$29$	−3.12329	−0.579981	−0.289990	+	0.957030i	$0.593652\pi$
$30$	0	0
$31$	−2.06658	−0.371169	−0.185584	−	0.982628i	$-0.559418\pi$
$31$	−2.06658	−0.371169	−0.185584	+	0.982628i	$0.559418\pi$
$32$	9.18462	1.62363
$33$	4.30834	0.749986
$34$	−14.1482	−2.42640
$35$	0	0
$36$	4.74525	0.790875
$37$	−1.89142	−0.310947	−0.155474	−	0.987840i	$-0.549690\pi$
$37$	−1.89142	−0.310947	−0.155474	+	0.987840i	$0.549690\pi$
$38$	−19.8274	−3.21644
$39$	−3.46120	−0.554235
$40$	0	0
$41$	3.89896	0.608915	0.304457	−	0.952526i	$-0.401525\pi$
$41$	3.89896	0.608915	0.304457	+	0.952526i	$0.401525\pi$
$42$	8.52943	1.31612
$43$	−3.20815	−0.489238	−0.244619	−	0.969619i	$-0.578663\pi$
$43$	−3.20815	−0.489238	−0.244619	+	0.969619i	$0.578663\pi$
$44$	20.4442	3.08207
$45$	0	0
$46$	−13.1153	−1.93375
$47$	6.28577	0.916874	0.458437	−	0.888727i	$-0.348409\pi$
$47$	6.28577	0.916874	0.458437	+	0.888727i	$0.348409\pi$
$48$	9.02691	1.30292
$49$	3.78555	0.540793
$50$	0	0
$51$	−5.44757	−0.762813
$52$	−16.4243	−2.27763
$53$	−2.51480	−0.345434	−0.172717	−	0.984971i	$-0.555255\pi$
$53$	−2.51480	−0.345434	−0.172717	+	0.984971i	$0.555255\pi$
$54$	2.59716	0.353429
$55$	0	0
$56$	23.4154	3.12902
$57$	−7.63427	−1.01118
$58$	−8.11170	−1.06512
$59$	7.72948	1.00629	0.503146	−	0.864201i	$-0.332176\pi$
$59$	7.72948	1.00629	0.503146	+	0.864201i	$0.332176\pi$
$60$	0	0
$61$	−2.95661	−0.378555	−0.189278	−	0.981924i	$-0.560615\pi$
$61$	−2.95661	−0.378555	−0.189278	+	0.981924i	$0.560615\pi$
$62$	−5.36725	−0.681641
$63$	3.28414	0.413762
$64$	5.80013	0.725016
$65$	0	0
$66$	11.1895	1.37733
$67$	12.9952	1.58762	0.793811	−	0.608165i	$-0.208094\pi$
$67$	12.9952	1.58762	0.793811	+	0.608165i	$0.208094\pi$
$68$	−25.8501	−3.13479
$69$	−5.04986	−0.607931
$70$	0	0
$71$	−4.72665	−0.560950	−0.280475	−	0.959861i	$-0.590492\pi$
$71$	−4.72665	−0.560950	−0.280475	+	0.959861i	$0.590492\pi$
$72$	7.12986	0.840262
$73$	−1.64933	−0.193040	−0.0965198	−	0.995331i	$-0.530771\pi$
$73$	−1.64933	−0.193040	−0.0965198	+	0.995331i	$0.530771\pi$
$74$	−4.91232	−0.571046
$75$	0	0
$76$	−36.2265	−4.15547
$77$	14.1492	1.61245
$78$	−8.98929	−1.01784
$79$	13.7349	1.54530	0.772648	−	0.634835i	$-0.218932\pi$
$79$	13.7349	1.54530	0.772648	+	0.634835i	$0.218932\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	10.1262	1.11825
$83$	−5.01687	−0.550673	−0.275336	−	0.961348i	$-0.588789\pi$
$83$	−5.01687	−0.550673	−0.275336	+	0.961348i	$0.588789\pi$
$84$	15.5841	1.70036
$85$	0	0
$86$	−8.33208	−0.898472
$87$	−3.12329	−0.334852
$88$	30.7179	3.27454
$89$	−9.00209	−0.954220	−0.477110	−	0.878844i	$-0.658316\pi$
$89$	−9.00209	−0.954220	−0.477110	+	0.878844i	$0.658316\pi$
$90$	0	0
$91$	−11.3670	−1.19159
$92$	−23.9628	−2.49830
$93$	−2.06658	−0.214294
$94$	16.3252	1.68381
$95$	0	0
$96$	9.18462	0.937401
$97$	2.57278	0.261226	0.130613	−	0.991433i	$-0.458305\pi$
$97$	2.57278	0.261226	0.130613	+	0.991433i	$0.458305\pi$
$98$	9.83169	0.993150
$99$	4.30834	0.433005
$100$	0	0
$101$	7.87863	0.783953	0.391976	−	0.919975i	$-0.371791\pi$
$101$	7.87863	0.783953	0.391976	+	0.919975i	$0.371791\pi$
$102$	−14.1482	−1.40088
$103$	12.4046	1.22226	0.611131	−	0.791530i	$-0.290715\pi$
$103$	12.4046	1.22226	0.611131	+	0.791530i	$0.290715\pi$
$104$	−24.6779	−2.41986
$105$	0	0
$106$	−6.53134	−0.634380
$107$	8.52094	0.823750	0.411875	−	0.911240i	$-0.364874\pi$
$107$	8.52094	0.823750	0.411875	+	0.911240i	$0.364874\pi$
$108$	4.74525	0.456612
$109$	17.5139	1.67752	0.838762	−	0.544499i	$-0.183280\pi$
$109$	17.5139	1.67752	0.838762	+	0.544499i	$0.183280\pi$
$110$	0	0
$111$	−1.89142	−0.179526
$112$	29.6456	2.80125
$113$	4.17711	0.392949	0.196475	−	0.980509i	$-0.437051\pi$
$113$	4.17711	0.392949	0.196475	+	0.980509i	$0.437051\pi$
$114$	−19.8274	−1.85701
$115$	0	0
$116$	−14.8208	−1.37608
$117$	−3.46120	−0.319988
$118$	20.0747	1.84803
$119$	−17.8906	−1.64003
$120$	0	0
$121$	7.56181	0.687438
$122$	−7.67880	−0.695206
$123$	3.89896	0.351557
$124$	−9.80645	−0.880645
$125$	0	0
$126$	8.52943	0.759862
$127$	10.2112	0.906097	0.453049	−	0.891486i	$-0.350336\pi$
$127$	10.2112	0.906097	0.453049	+	0.891486i	$0.350336\pi$
$128$	−3.30537	−0.292156
$129$	−3.20815	−0.282462
$130$	0	0
$131$	−4.91686	−0.429588	−0.214794	−	0.976659i	$-0.568908\pi$
$131$	−4.91686	−0.429588	−0.214794	+	0.976659i	$0.568908\pi$
$132$	20.4442	1.77944
$133$	−25.0720	−2.17402
$134$	33.7508	2.91562
$135$	0	0
$136$	−38.8404	−3.33054
$137$	−12.3817	−1.05784	−0.528919	−	0.848672i	$-0.677403\pi$
$137$	−12.3817	−1.05784	−0.528919	+	0.848672i	$0.677403\pi$
$138$	−13.1153	−1.11645
$139$	13.2420	1.12317	0.561584	−	0.827420i	$-0.310192\pi$
$139$	13.2420	1.12317	0.561584	+	0.827420i	$0.310192\pi$
$140$	0	0
$141$	6.28577	0.529357
$142$	−12.2759	−1.03017
$143$	−14.9120	−1.24701
$144$	9.02691	0.752242
$145$	0	0
$146$	−4.28358	−0.354512
$147$	3.78555	0.312227
$148$	−8.97526	−0.737762
$149$	5.20686	0.426563	0.213281	−	0.976991i	$-0.431585\pi$
$149$	5.20686	0.426563	0.213281	+	0.976991i	$0.431585\pi$
$150$	0	0
$151$	7.78162	0.633259	0.316630	−	0.948549i	$-0.397449\pi$
$151$	7.78162	0.633259	0.316630	+	0.948549i	$0.397449\pi$
$152$	−54.4313	−4.41496
$153$	−5.44757	−0.440410
$154$	36.7477	2.96122
$155$	0	0
$156$	−16.4243	−1.31499
$157$	−16.4474	−1.31264	−0.656322	−	0.754481i	$-0.727889\pi$
$157$	−16.4474	−1.31264	−0.656322	+	0.754481i	$0.727889\pi$
$158$	35.6717	2.83789
$159$	−2.51480	−0.199436
$160$	0	0
$161$	−16.5844	−1.30704
$162$	2.59716	0.204052
$163$	7.81342	0.611994	0.305997	−	0.952032i	$-0.401010\pi$
$163$	7.81342	0.611994	0.305997	+	0.952032i	$0.401010\pi$
$164$	18.5015	1.44473
$165$	0	0
$166$	−13.0296	−1.01129
$167$	−2.77030	−0.214372	−0.107186	−	0.994239i	$-0.534184\pi$
$167$	−2.77030	−0.214372	−0.107186	+	0.994239i	$0.534184\pi$
$168$	23.4154	1.80654
$169$	−1.02011	−0.0784700
$170$	0	0
$171$	−7.63427	−0.583807
$172$	−15.2235	−1.16078
$173$	−16.9573	−1.28924	−0.644620	−	0.764503i	$-0.722985\pi$
$173$	−16.9573	−1.28924	−0.644620	+	0.764503i	$0.722985\pi$
$174$	−8.11170	−0.614946
$175$	0	0
$176$	38.8910	2.93152
$177$	7.72948	0.580983
$178$	−23.3799	−1.75240
$179$	1.56173	0.116729	0.0583645	−	0.998295i	$-0.481411\pi$
$179$	1.56173	0.116729	0.0583645	+	0.998295i	$0.481411\pi$
$180$	0	0
$181$	1.55277	0.115416	0.0577081	−	0.998333i	$-0.481621\pi$
$181$	1.55277	0.115416	0.0577081	+	0.998333i	$0.481621\pi$
$182$	−29.5221	−2.18832
$183$	−2.95661	−0.218559
$184$	−36.0048	−2.65431
$185$	0	0
$186$	−5.36725	−0.393546
$187$	−23.4700	−1.71630
$188$	29.8276	2.17540
$189$	3.28414	0.238886
$190$	0	0
$191$	26.5640	1.92211	0.961054	−	0.276362i	$-0.0891290\pi$
$191$	26.5640	1.92211	0.961054	+	0.276362i	$0.0891290\pi$
$192$	5.80013	0.418588
$193$	−13.7642	−0.990772	−0.495386	−	0.868673i	$-0.664973\pi$
$193$	−13.7642	−0.990772	−0.495386	+	0.868673i	$0.664973\pi$
$194$	6.68192	0.479734
$195$	0	0
$196$	17.9634	1.28310
$197$	6.25851	0.445901	0.222950	−	0.974830i	$-0.428431\pi$
$197$	6.25851	0.445901	0.222950	+	0.974830i	$0.428431\pi$
$198$	11.1895	0.795201
$199$	3.35009	0.237482	0.118741	−	0.992925i	$-0.462114\pi$
$199$	3.35009	0.237482	0.118741	+	0.992925i	$0.462114\pi$
$200$	0	0
$201$	12.9952	0.916614
$202$	20.4621	1.43971
$203$	−10.2573	−0.719923
$204$	−25.8501	−1.80987
$205$	0	0
$206$	32.2168	2.24465
$207$	−5.04986	−0.350989
$208$	−31.2439	−2.16638
$209$	−32.8911	−2.27512
$210$	0	0
$211$	24.0984	1.65900	0.829502	−	0.558504i	$-0.188624\pi$
$211$	24.0984	1.65900	0.829502	+	0.558504i	$0.188624\pi$
$212$	−11.9333	−0.819586
$213$	−4.72665	−0.323865
$214$	22.1303	1.51279
$215$	0	0
$216$	7.12986	0.485126
$217$	−6.78693	−0.460727
$218$	45.4863	3.08072
$219$	−1.64933	−0.111452
$220$	0	0
$221$	18.8551	1.26833
$222$	−4.91232	−0.329693
$223$	−18.2697	−1.22343	−0.611714	−	0.791079i	$-0.709520\pi$
$223$	−18.2697	−1.22343	−0.611714	+	0.791079i	$0.709520\pi$
$224$	30.1635	2.01539
$225$	0	0
$226$	10.8486	0.721640
$227$	−17.9602	−1.19206	−0.596031	−	0.802962i	$-0.703256\pi$
$227$	−17.9602	−1.19206	−0.596031	+	0.802962i	$0.703256\pi$
$228$	−36.2265	−2.39916
$229$	6.00658	0.396926	0.198463	−	0.980108i	$-0.436405\pi$
$229$	6.00658	0.396926	0.198463	+	0.980108i	$0.436405\pi$
$230$	0	0
$231$	14.1492	0.930948
$232$	−22.2687	−1.46201
$233$	−20.8526	−1.36610	−0.683049	−	0.730373i	$-0.739346\pi$
$233$	−20.8526	−1.36610	−0.683049	+	0.730373i	$0.739346\pi$
$234$	−8.98929	−0.587648
$235$	0	0
$236$	36.6783	2.38755
$237$	13.7349	0.892177
$238$	−46.4647	−3.01186
$239$	−27.8722	−1.80290	−0.901452	−	0.432880i	$-0.857497\pi$
$239$	−27.8722	−1.80290	−0.901452	+	0.432880i	$0.857497\pi$
$240$	0	0
$241$	−18.7159	−1.20560	−0.602798	−	0.797894i	$-0.705947\pi$
$241$	−18.7159	−1.20560	−0.602798	+	0.797894i	$0.705947\pi$
$242$	19.6393	1.26246
$243$	1.00000	0.0641500
$244$	−14.0299	−0.898170
$245$	0	0
$246$	10.1262	0.645624
$247$	26.4237	1.68130
$248$	−14.7344	−0.935638
$249$	−5.01687	−0.317931
$250$	0	0
$251$	11.0995	0.700594	0.350297	−	0.936639i	$-0.386081\pi$
$251$	11.0995	0.700594	0.350297	+	0.936639i	$0.386081\pi$
$252$	15.5841	0.981703
$253$	−21.7565	−1.36782
$254$	26.5201	1.66402
$255$	0	0
$256$	−20.1848	−1.26155
$257$	−17.8844	−1.11560	−0.557800	−	0.829975i	$-0.688354\pi$
$257$	−17.8844	−1.11560	−0.557800	+	0.829975i	$0.688354\pi$
$258$	−8.33208	−0.518733
$259$	−6.21168	−0.385975
$260$	0	0
$261$	−3.12329	−0.193327
$262$	−12.7699	−0.788927
$263$	−18.1341	−1.11819	−0.559097	−	0.829102i	$-0.688852\pi$
$263$	−18.1341	−1.11819	−0.559097	+	0.829102i	$0.688852\pi$
$264$	30.7179	1.89056
$265$	0	0
$266$	−65.1160	−3.99252
$267$	−9.00209	−0.550919
$268$	61.6657	3.76683
$269$	−22.2963	−1.35943	−0.679714	−	0.733477i	$-0.737896\pi$
$269$	−22.2963	−1.35943	−0.679714	+	0.733477i	$0.737896\pi$
$270$	0	0
$271$	16.8621	1.02430	0.512149	−	0.858896i	$-0.328849\pi$
$271$	16.8621	1.02430	0.512149	+	0.858896i	$0.328849\pi$
$272$	−49.1747	−2.98166
$273$	−11.3670	−0.687965
$274$	−32.1572	−1.94269
$275$	0	0
$276$	−23.9628	−1.44239
$277$	−18.6929	−1.12315	−0.561575	−	0.827426i	$-0.689804\pi$
$277$	−18.6929	−1.12315	−0.561575	+	0.827426i	$0.689804\pi$
$278$	34.3915	2.06266
$279$	−2.06658	−0.123723
$280$	0	0
$281$	25.9852	1.55015	0.775075	−	0.631870i	$-0.217712\pi$
$281$	25.9852	1.55015	0.775075	+	0.631870i	$0.217712\pi$
$282$	16.3252	0.972150
$283$	16.9219	1.00591	0.502953	−	0.864314i	$-0.332247\pi$
$283$	16.9219	1.00591	0.502953	+	0.864314i	$0.332247\pi$
$284$	−22.4291	−1.33092
$285$	0	0
$286$	−38.7289	−2.29009
$287$	12.8047	0.755838
$288$	9.18462	0.541209
$289$	12.6760	0.745650
$290$	0	0
$291$	2.57278	0.150819
$292$	−7.82649	−0.458011
$293$	1.05979	0.0619134	0.0309567	−	0.999521i	$-0.490145\pi$
$293$	1.05979	0.0619134	0.0309567	+	0.999521i	$0.490145\pi$
$294$	9.83169	0.573396
$295$	0	0
$296$	−13.4856	−0.783832
$297$	4.30834	0.249995
$298$	13.5231	0.783370
$299$	17.4786	1.01081
$300$	0	0
$301$	−10.5360	−0.607285
$302$	20.2101	1.16296
$303$	7.87863	0.452615
$304$	−68.9139	−3.95248
$305$	0	0
$306$	−14.1482	−0.808800
$307$	29.7239	1.69643	0.848215	−	0.529652i	$-0.177677\pi$
$307$	29.7239	1.69643	0.848215	+	0.529652i	$0.177677\pi$
$308$	67.1414	3.82574
$309$	12.4046	0.705673
$310$	0	0
$311$	5.08513	0.288351	0.144176	−	0.989552i	$-0.453947\pi$
$311$	5.08513	0.288351	0.144176	+	0.989552i	$0.453947\pi$
$312$	−24.6779	−1.39711
$313$	25.9388	1.46615	0.733074	−	0.680149i	$-0.238085\pi$
$313$	25.9388	1.46615	0.733074	+	0.680149i	$0.238085\pi$
$314$	−42.7165	−2.41063
$315$	0	0
$316$	65.1755	3.66641
$317$	19.7727	1.11054	0.555271	−	0.831669i	$-0.312614\pi$
$317$	19.7727	1.11054	0.555271	+	0.831669i	$0.312614\pi$
$318$	−6.53134	−0.366259
$319$	−13.4562	−0.753403
$320$	0	0
$321$	8.52094	0.475592
$322$	−43.0724	−2.40033
$323$	41.5883	2.31403
$324$	4.74525	0.263625
$325$	0	0
$326$	20.2927	1.12391
$327$	17.5139	0.968519
$328$	27.7990	1.53494
$329$	20.6433	1.13810
$330$	0	0
$331$	−23.9589	−1.31690	−0.658449	−	0.752625i	$-0.728787\pi$
$331$	−23.9589	−1.31690	−0.658449	+	0.752625i	$0.728787\pi$
$332$	−23.8063	−1.30654
$333$	−1.89142	−0.103649
$334$	−7.19492	−0.393689
$335$	0	0
$336$	29.6456	1.61730
$337$	−27.6779	−1.50771	−0.753857	−	0.657039i	$-0.771809\pi$
$337$	−27.6779	−1.50771	−0.753857	+	0.657039i	$0.771809\pi$
$338$	−2.64939	−0.144108
$339$	4.17711	0.226869
$340$	0	0
$341$	−8.90354	−0.482154
$342$	−19.8274	−1.07215
$343$	−10.5567	−0.570008
$344$	−22.8737	−1.23327
$345$	0	0
$346$	−44.0409	−2.36765
$347$	−13.4880	−0.724075	−0.362037	−	0.932164i	$-0.617919\pi$
$347$	−13.4880	−0.724075	−0.362037	+	0.932164i	$0.617919\pi$
$348$	−14.8208	−0.794479
$349$	19.1678	1.02603	0.513015	−	0.858379i	$-0.328528\pi$
$349$	19.1678	1.02603	0.513015	+	0.858379i	$0.328528\pi$
$350$	0	0
$351$	−3.46120	−0.184745
$352$	39.5705	2.10911
$353$	7.61950	0.405545	0.202773	−	0.979226i	$-0.435005\pi$
$353$	7.61950	0.405545	0.202773	+	0.979226i	$0.435005\pi$
$354$	20.0747	1.06696
$355$	0	0
$356$	−42.7172	−2.26401
$357$	−17.8906	−0.946869
$358$	4.05606	0.214369
$359$	31.2943	1.65165	0.825826	−	0.563925i	$-0.190709\pi$
$359$	31.2943	1.65165	0.825826	+	0.563925i	$0.190709\pi$
$360$	0	0
$361$	39.2821	2.06748
$362$	4.03279	0.211959
$363$	7.56181	0.396892
$364$	−53.9395	−2.82720
$365$	0	0
$366$	−7.67880	−0.401377
$367$	−6.35079	−0.331508	−0.165754	−	0.986167i	$-0.553006\pi$
$367$	−6.35079	−0.331508	−0.165754	+	0.986167i	$0.553006\pi$
$368$	−45.5846	−2.37626
$369$	3.89896	0.202972
$370$	0	0
$371$	−8.25894	−0.428783
$372$	−9.80645	−0.508441
$373$	11.1710	0.578410	0.289205	−	0.957267i	$-0.406609\pi$
$373$	11.1710	0.578410	0.289205	+	0.957267i	$0.406609\pi$
$374$	−60.9554	−3.15193
$375$	0	0
$376$	44.8167	2.31124
$377$	10.8103	0.556761
$378$	8.52943	0.438707
$379$	−20.7113	−1.06387	−0.531933	−	0.846787i	$-0.678534\pi$
$379$	−20.7113	−1.06387	−0.531933	+	0.846787i	$0.678534\pi$
$380$	0	0
$381$	10.2112	0.523135
$382$	68.9911	3.52989
$383$	−12.5869	−0.643158	−0.321579	−	0.946883i	$-0.604214\pi$
$383$	−12.5869	−0.643158	−0.321579	+	0.946883i	$0.604214\pi$
$384$	−3.30537	−0.168676
$385$	0	0
$386$	−35.7480	−1.81952
$387$	−3.20815	−0.163079
$388$	12.2085	0.619792
$389$	10.8301	0.549110	0.274555	−	0.961571i	$-0.411469\pi$
$389$	10.8301	0.549110	0.274555	+	0.961571i	$0.411469\pi$
$390$	0	0
$391$	27.5095	1.39121
$392$	26.9905	1.36322
$393$	−4.91686	−0.248023
$394$	16.2544	0.818884
$395$	0	0
$396$	20.4442	1.02736
$397$	−4.90704	−0.246277	−0.123139	−	0.992389i	$-0.539296\pi$
$397$	−4.90704	−0.246277	−0.123139	+	0.992389i	$0.539296\pi$
$398$	8.70072	0.436128
$399$	−25.0720	−1.25517
$400$	0	0
$401$	−27.5223	−1.37440	−0.687198	−	0.726470i	$-0.741160\pi$
$401$	−27.5223	−1.37440	−0.687198	+	0.726470i	$0.741160\pi$
$402$	33.7508	1.68333
$403$	7.15285	0.356309
$404$	37.3861	1.86003
$405$	0	0
$406$	−26.6399	−1.32212
$407$	−8.14888	−0.403925
$408$	−38.8404	−1.92289
$409$	19.7665	0.977390	0.488695	−	0.872455i	$-0.337473\pi$
$409$	19.7665	0.977390	0.488695	+	0.872455i	$0.337473\pi$
$410$	0	0
$411$	−12.3817	−0.610743
$412$	58.8630	2.89997
$413$	25.3847	1.24910
$414$	−13.1153	−0.644582
$415$	0	0
$416$	−31.7898	−1.55862
$417$	13.2420	0.648461
$418$	−85.4234	−4.17820
$419$	−6.67948	−0.326314	−0.163157	−	0.986600i	$-0.552168\pi$
$419$	−6.67948	−0.326314	−0.163157	+	0.986600i	$0.552168\pi$
$420$	0	0
$421$	5.65996	0.275849	0.137925	−	0.990443i	$-0.455957\pi$
$421$	5.65996	0.275849	0.137925	+	0.990443i	$0.455957\pi$
$422$	62.5875	3.04671
$423$	6.28577	0.305625
$424$	−17.9302	−0.870766
$425$	0	0
$426$	−12.2759	−0.594768
$427$	−9.70991	−0.469896
$428$	40.4340	1.95445
$429$	−14.9120	−0.719959
$430$	0	0
$431$	6.41717	0.309104	0.154552	−	0.987985i	$-0.450607\pi$
$431$	6.41717	0.309104	0.154552	+	0.987985i	$0.450607\pi$
$432$	9.02691	0.434307
$433$	−1.10506	−0.0531059	−0.0265530	−	0.999647i	$-0.508453\pi$
$433$	−1.10506	−0.0531059	−0.0265530	+	0.999647i	$0.508453\pi$
$434$	−17.6268	−0.846112
$435$	0	0
$436$	83.1077	3.98014
$437$	38.5520	1.84419
$438$	−4.28358	−0.204677
$439$	−5.11313	−0.244036	−0.122018	−	0.992528i	$-0.538937\pi$
$439$	−5.11313	−0.244036	−0.122018	+	0.992528i	$0.538937\pi$
$440$	0	0
$441$	3.78555	0.180264
$442$	48.9698	2.32926
$443$	−17.9079	−0.850829	−0.425414	−	0.904999i	$-0.639872\pi$
$443$	−17.9079	−0.850829	−0.425414	+	0.904999i	$0.639872\pi$
$444$	−8.97526	−0.425947
$445$	0	0
$446$	−47.4493	−2.24679
$447$	5.20686	0.246276
$448$	19.0484	0.899953
$449$	27.3710	1.29172	0.645859	−	0.763457i	$-0.276499\pi$
$449$	27.3710	1.29172	0.645859	+	0.763457i	$0.276499\pi$
$450$	0	0
$451$	16.7980	0.790989
$452$	19.8214	0.932322
$453$	7.78162	0.365612
$454$	−46.6456	−2.18919
$455$	0	0
$456$	−54.4313	−2.54898
$457$	8.92806	0.417637	0.208819	−	0.977954i	$-0.433038\pi$
$457$	8.92806	0.417637	0.208819	+	0.977954i	$0.433038\pi$
$458$	15.6001	0.728943
$459$	−5.44757	−0.254271
$460$	0	0
$461$	1.81204	0.0843952	0.0421976	−	0.999109i	$-0.486564\pi$
$461$	1.81204	0.0843952	0.0421976	+	0.999109i	$0.486564\pi$
$462$	36.7477	1.70966
$463$	2.72192	0.126498	0.0632492	−	0.997998i	$-0.479854\pi$
$463$	2.72192	0.126498	0.0632492	+	0.997998i	$0.479854\pi$
$464$	−28.1937	−1.30886
$465$	0	0
$466$	−54.1575	−2.50880
$467$	−40.2261	−1.86144	−0.930721	−	0.365729i	$-0.880820\pi$
$467$	−40.2261	−1.86144	−0.930721	+	0.365729i	$0.880820\pi$
$468$	−16.4243	−0.759211
$469$	42.6781	1.97069
$470$	0	0
$471$	−16.4474	−0.757855
$472$	55.1101	2.53665
$473$	−13.8218	−0.635527
$474$	35.6717	1.63846
$475$	0	0
$476$	−84.8953	−3.89117
$477$	−2.51480	−0.115145
$478$	−72.3886	−3.31098
$479$	−27.9457	−1.27687	−0.638435	−	0.769676i	$-0.720418\pi$
$479$	−27.9457	−1.27687	−0.638435	+	0.769676i	$0.720418\pi$
$480$	0	0
$481$	6.54657	0.298498
$482$	−48.6082	−2.21404
$483$	−16.5844	−0.754617
$484$	35.8827	1.63103
$485$	0	0
$486$	2.59716	0.117810
$487$	−25.8089	−1.16951	−0.584756	−	0.811209i	$-0.698810\pi$
$487$	−25.8089	−1.16951	−0.584756	+	0.811209i	$0.698810\pi$
$488$	−21.0802	−0.954257
$489$	7.81342	0.353335
$490$	0	0
$491$	23.7044	1.06976	0.534882	−	0.844927i	$-0.320356\pi$
$491$	23.7044	1.06976	0.534882	+	0.844927i	$0.320356\pi$
$492$	18.5015	0.834113
$493$	17.0144	0.766288
$494$	68.6267	3.08766
$495$	0	0
$496$	−18.6548	−0.837627
$497$	−15.5230	−0.696300
$498$	−13.0296	−0.583871
$499$	8.95752	0.400994	0.200497	−	0.979694i	$-0.435744\pi$
$499$	8.95752	0.400994	0.200497	+	0.979694i	$0.435744\pi$
$500$	0	0
$501$	−2.77030	−0.123768
$502$	28.8272	1.28662
$503$	10.1655	0.453256	0.226628	−	0.973981i	$-0.427230\pi$
$503$	10.1655	0.453256	0.226628	+	0.973981i	$0.427230\pi$
$504$	23.4154	1.04301
$505$	0	0
$506$	−56.5052	−2.51196
$507$	−1.02011	−0.0453047
$508$	48.4547	2.14983
$509$	−6.54473	−0.290090	−0.145045	−	0.989425i	$-0.546333\pi$
$509$	−6.54473	−0.290090	−0.145045	+	0.989425i	$0.546333\pi$
$510$	0	0
$511$	−5.41663	−0.239618
$512$	−45.8125	−2.02465
$513$	−7.63427	−0.337061
$514$	−46.4488	−2.04877
$515$	0	0
$516$	−15.2235	−0.670176
$517$	27.0813	1.19103
$518$	−16.1327	−0.708832
$519$	−16.9573	−0.744343
$520$	0	0
$521$	−25.6022	−1.12165	−0.560827	−	0.827933i	$-0.689517\pi$
$521$	−25.6022	−1.12165	−0.560827	+	0.827933i	$0.689517\pi$
$522$	−8.11170	−0.355039
$523$	5.02210	0.219601	0.109801	−	0.993954i	$-0.464979\pi$
$523$	5.02210	0.219601	0.109801	+	0.993954i	$0.464979\pi$
$524$	−23.3318	−1.01925
$525$	0	0
$526$	−47.0971	−2.05353
$527$	11.2579	0.490400
$528$	38.8910	1.69251
$529$	2.50105	0.108741
$530$	0	0
$531$	7.72948	0.335431
$532$	−118.973	−5.15813
$533$	−13.4951	−0.584536
$534$	−23.3799	−1.01175
$535$	0	0
$536$	92.6543	4.00206
$537$	1.56173	0.0673935
$538$	−57.9071	−2.49655
$539$	16.3094	0.702498
$540$	0	0
$541$	−7.99099	−0.343560	−0.171780	−	0.985135i	$-0.554952\pi$
$541$	−7.99099	−0.343560	−0.171780	+	0.985135i	$0.554952\pi$
$542$	43.7936	1.88109
$543$	1.55277	0.0666356
$544$	−50.0339	−2.14518
$545$	0	0
$546$	−29.5221	−1.26343
$547$	−21.9399	−0.938084	−0.469042	−	0.883176i	$-0.655401\pi$
$547$	−21.9399	−0.938084	−0.469042	+	0.883176i	$0.655401\pi$
$548$	−58.7542	−2.50986
$549$	−2.95661	−0.126185
$550$	0	0
$551$	23.8441	1.01579
$552$	−36.0048	−1.53247
$553$	45.1072	1.91815
$554$	−48.5486	−2.06263
$555$	0	0
$556$	62.8364	2.66486
$557$	32.6366	1.38286	0.691429	−	0.722444i	$-0.256981\pi$
$557$	32.6366	1.38286	0.691429	+	0.722444i	$0.256981\pi$
$558$	−5.36725	−0.227214
$559$	11.1040	0.469651
$560$	0	0
$561$	−23.4700	−0.990905
$562$	67.4879	2.84680
$563$	−5.25771	−0.221586	−0.110793	−	0.993843i	$-0.535339\pi$
$563$	−5.25771	−0.221586	−0.110793	+	0.993843i	$0.535339\pi$
$564$	29.8276	1.25597
$565$	0	0
$566$	43.9490	1.84732
$567$	3.28414	0.137921
$568$	−33.7004	−1.41404
$569$	15.1931	0.636926	0.318463	−	0.947935i	$-0.396833\pi$
$569$	15.1931	0.636926	0.318463	+	0.947935i	$0.396833\pi$
$570$	0	0
$571$	−8.29434	−0.347107	−0.173554	−	0.984824i	$-0.555525\pi$
$571$	−8.29434	−0.347107	−0.173554	+	0.984824i	$0.555525\pi$
$572$	−70.7613	−2.95868
$573$	26.5640	1.10973
$574$	33.2559	1.38807
$575$	0	0
$576$	5.80013	0.241672
$577$	2.69155	0.112051	0.0560253	−	0.998429i	$-0.482157\pi$
$577$	2.69155	0.112051	0.0560253	+	0.998429i	$0.482157\pi$
$578$	32.9218	1.36936
$579$	−13.7642	−0.572022
$580$	0	0
$581$	−16.4761	−0.683543
$582$	6.68192	0.276975
$583$	−10.8346	−0.448724
$584$	−11.7595	−0.486612
$585$	0	0
$586$	2.75244	0.113702
$587$	27.2841	1.12613	0.563067	−	0.826411i	$-0.309621\pi$
$587$	27.2841	1.12613	0.563067	+	0.826411i	$0.309621\pi$
$588$	17.9634	0.740798
$589$	15.7768	0.650074
$590$	0	0
$591$	6.25851	0.257441
$592$	−17.0737	−0.701723
$593$	−3.04738	−0.125141	−0.0625704	−	0.998041i	$-0.519930\pi$
$593$	−3.04738	−0.125141	−0.0625704	+	0.998041i	$0.519930\pi$
$594$	11.1895	0.459109
$595$	0	0
$596$	24.7079	1.01207
$597$	3.35009	0.137110
$598$	45.3946	1.85632
$599$	−21.1104	−0.862549	−0.431274	−	0.902221i	$-0.641936\pi$
$599$	−21.1104	−0.862549	−0.431274	+	0.902221i	$0.641936\pi$
$600$	0	0
$601$	1.78443	0.0727884	0.0363942	−	0.999338i	$-0.488413\pi$
$601$	1.78443	0.0727884	0.0363942	+	0.999338i	$0.488413\pi$
$602$	−27.3637	−1.11526
$603$	12.9952	0.529207
$604$	36.9258	1.50249
$605$	0	0
$606$	20.4621	0.831215
$607$	43.9927	1.78561	0.892805	−	0.450444i	$-0.148734\pi$
$607$	43.9927	1.78561	0.892805	+	0.450444i	$0.148734\pi$
$608$	−70.1179	−2.84366
$609$	−10.2573	−0.415648
$610$	0	0
$611$	−21.7563	−0.880166
$612$	−25.8501	−1.04493
$613$	−37.9419	−1.53246	−0.766230	−	0.642567i	$-0.777870\pi$
$613$	−37.9419	−1.53246	−0.766230	+	0.642567i	$0.777870\pi$
$614$	77.1977	3.11544
$615$	0	0
$616$	100.882	4.06464
$617$	−7.92668	−0.319116	−0.159558	−	0.987189i	$-0.551007\pi$
$617$	−7.92668	−0.319116	−0.159558	+	0.987189i	$0.551007\pi$
$618$	32.2168	1.29595
$619$	−7.83411	−0.314880	−0.157440	−	0.987529i	$-0.550324\pi$
$619$	−7.83411	−0.314880	−0.157440	+	0.987529i	$0.550324\pi$
$620$	0	0
$621$	−5.04986	−0.202644
$622$	13.2069	0.529548
$623$	−29.5641	−1.18446
$624$	−31.2439	−1.25076
$625$	0	0
$626$	67.3673	2.69254
$627$	−32.8911	−1.31354
$628$	−78.0469	−3.11441
$629$	10.3036	0.410833
$630$	0	0
$631$	19.0248	0.757366	0.378683	−	0.925526i	$-0.376377\pi$
$631$	19.0248	0.757366	0.378683	+	0.925526i	$0.376377\pi$
$632$	97.9279	3.89536
$633$	24.0984	0.957826
$634$	51.3528	2.03948
$635$	0	0
$636$	−11.9333	−0.473188
$637$	−13.1025	−0.519141
$638$	−34.9480	−1.38360
$639$	−4.72665	−0.186983
$640$	0	0
$641$	−32.5783	−1.28677	−0.643383	−	0.765545i	$-0.722470\pi$
$641$	−32.5783	−1.28677	−0.643383	+	0.765545i	$0.722470\pi$
$642$	22.1303	0.873411
$643$	40.0025	1.57755	0.788773	−	0.614684i	$-0.210717\pi$
$643$	40.0025	1.57755	0.788773	+	0.614684i	$0.210717\pi$
$644$	−78.6972	−3.10111
$645$	0	0
$646$	108.011	4.24965
$647$	−20.0199	−0.787063	−0.393532	−	0.919311i	$-0.628747\pi$
$647$	−20.0199	−0.787063	−0.393532	+	0.919311i	$0.628747\pi$
$648$	7.12986	0.280087
$649$	33.3012	1.30719
$650$	0	0
$651$	−6.78693	−0.266001
$652$	37.0766	1.45203
$653$	−10.3332	−0.404369	−0.202185	−	0.979347i	$-0.564804\pi$
$653$	−10.3332	−0.404369	−0.202185	+	0.979347i	$0.564804\pi$
$654$	45.4863	1.77866
$655$	0	0
$656$	35.1955	1.37415
$657$	−1.64933	−0.0643466
$658$	53.6141	2.09009
$659$	−47.2403	−1.84022	−0.920111	−	0.391657i	$-0.871902\pi$
$659$	−47.2403	−1.84022	−0.920111	+	0.391657i	$0.871902\pi$
$660$	0	0
$661$	51.3528	1.99739	0.998696	−	0.0510604i	$-0.0162601\pi$
$661$	51.3528	1.99739	0.998696	+	0.0510604i	$0.0162601\pi$
$662$	−62.2250	−2.41844
$663$	18.8551	0.732272
$664$	−35.7696	−1.38813
$665$	0	0
$666$	−4.91232	−0.190349
$667$	15.7722	0.610701
$668$	−13.1458	−0.508625
$669$	−18.2697	−0.706346
$670$	0	0
$671$	−12.7381	−0.491749
$672$	30.1635	1.16358
$673$	40.5790	1.56420	0.782102	−	0.623150i	$-0.214147\pi$
$673$	40.5790	1.56420	0.782102	+	0.623150i	$0.214147\pi$
$674$	−71.8841	−2.76887
$675$	0	0
$676$	−4.84068	−0.186180
$677$	9.21482	0.354154	0.177077	−	0.984197i	$-0.443336\pi$
$677$	9.21482	0.354154	0.177077	+	0.984197i	$0.443336\pi$
$678$	10.8486	0.416639
$679$	8.44935	0.324256
$680$	0	0
$681$	−17.9602	−0.688237
$682$	−23.1239	−0.885461
$683$	13.3281	0.509987	0.254994	−	0.966943i	$-0.417927\pi$
$683$	13.3281	0.509987	0.254994	+	0.966943i	$0.417927\pi$
$684$	−36.2265	−1.38516
$685$	0	0
$686$	−27.4174	−1.04680
$687$	6.00658	0.229165
$688$	−28.9597	−1.10408
$689$	8.70421	0.331604
$690$	0	0
$691$	−32.5862	−1.23964	−0.619819	−	0.784745i	$-0.712794\pi$
$691$	−32.5862	−1.23964	−0.619819	+	0.784745i	$0.712794\pi$
$692$	−80.4667	−3.05889
$693$	14.1492	0.537483
$694$	−35.0306	−1.32974
$695$	0	0
$696$	−22.2687	−0.844091
$697$	−21.2398	−0.804516
$698$	49.7820	1.88428
$699$	−20.8526	−0.788717
$700$	0	0
$701$	−33.5547	−1.26734	−0.633672	−	0.773602i	$-0.718453\pi$
$701$	−33.5547	−1.26734	−0.633672	+	0.773602i	$0.718453\pi$
$702$	−8.98929	−0.339279
$703$	14.4396	0.544600
$704$	24.9889	0.941806
$705$	0	0
$706$	19.7891	0.744772
$707$	25.8745	0.973110
$708$	36.6783	1.37846
$709$	12.4731	0.468436	0.234218	−	0.972184i	$-0.424747\pi$
$709$	12.4731	0.468436	0.234218	+	0.972184i	$0.424747\pi$
$710$	0	0
$711$	13.7349	0.515098
$712$	−64.1837	−2.40539
$713$	10.4359	0.390829
$714$	−46.4647	−1.73890
$715$	0	0
$716$	7.41079	0.276954
$717$	−27.8722	−1.04091
$718$	81.2765	3.03321
$719$	−7.53586	−0.281040	−0.140520	−	0.990078i	$-0.544877\pi$
$719$	−7.53586	−0.281040	−0.140520	+	0.990078i	$0.544877\pi$
$720$	0	0
$721$	40.7384	1.51718
$722$	102.022	3.79687
$723$	−18.7159	−0.696051
$724$	7.36827	0.273839
$725$	0	0
$726$	19.6393	0.728881
$727$	−42.8265	−1.58835	−0.794173	−	0.607691i	$-0.792096\pi$
$727$	−42.8265	−1.58835	−0.794173	+	0.607691i	$0.792096\pi$
$728$	−81.0455	−3.00375
$729$	1.00000	0.0370370
$730$	0	0
$731$	17.4766	0.646396
$732$	−14.0299	−0.518559
$733$	48.4170	1.78832	0.894161	−	0.447745i	$-0.147773\pi$
$733$	48.4170	1.78832	0.894161	+	0.447745i	$0.147773\pi$
$734$	−16.4940	−0.608806
$735$	0	0
$736$	−46.3810	−1.70963
$737$	55.9880	2.06234
$738$	10.1262	0.372751
$739$	31.1926	1.14744	0.573720	−	0.819052i	$-0.305500\pi$
$739$	31.1926	1.14744	0.573720	+	0.819052i	$0.305500\pi$
$740$	0	0
$741$	26.4237	0.970700
$742$	−21.4498	−0.787447
$743$	45.9840	1.68699	0.843495	−	0.537137i	$-0.180494\pi$
$743$	45.9840	1.68699	0.843495	+	0.537137i	$0.180494\pi$
$744$	−14.7344	−0.540191
$745$	0	0
$746$	29.0128	1.06223
$747$	−5.01687	−0.183558
$748$	−111.371	−4.07213
$749$	27.9839	1.02251
$750$	0	0
$751$	2.51488	0.0917695	0.0458847	−	0.998947i	$-0.485389\pi$
$751$	2.51488	0.0917695	0.0458847	+	0.998947i	$0.485389\pi$
$752$	56.7411	2.06913
$753$	11.0995	0.404488
$754$	28.0762	1.02247
$755$	0	0
$756$	15.5841	0.566786
$757$	−39.6597	−1.44146	−0.720728	−	0.693218i	$-0.756192\pi$
$757$	−39.6597	−1.44146	−0.720728	+	0.693218i	$0.756192\pi$
$758$	−53.7905	−1.95376
$759$	−21.7565	−0.789711
$760$	0	0
$761$	17.2752	0.626225	0.313113	−	0.949716i	$-0.398628\pi$
$761$	17.2752	0.626225	0.313113	+	0.949716i	$0.398628\pi$
$762$	26.5201	0.960723
$763$	57.5179	2.08229
$764$	126.053	4.56044
$765$	0	0
$766$	−32.6901	−1.18114
$767$	−26.7533	−0.966004
$768$	−20.1848	−0.728357
$769$	−4.50943	−0.162614	−0.0813071	−	0.996689i	$-0.525909\pi$
$769$	−4.50943	−0.162614	−0.0813071	+	0.996689i	$0.525909\pi$
$770$	0	0
$771$	−17.8844	−0.644092
$772$	−65.3148	−2.35073
$773$	−33.6503	−1.21032	−0.605159	−	0.796105i	$-0.706890\pi$
$773$	−33.6503	−1.21032	−0.605159	+	0.796105i	$0.706890\pi$
$774$	−8.33208	−0.299491
$775$	0	0
$776$	18.3436	0.658495
$777$	−6.21168	−0.222843
$778$	28.1276	1.00842
$779$	−29.7657	−1.06647
$780$	0	0
$781$	−20.3640	−0.728682
$782$	71.4465	2.55492
$783$	−3.12329	−0.111617
$784$	34.1718	1.22042
$785$	0	0
$786$	−12.7699	−0.455487
$787$	36.8366	1.31308	0.656542	−	0.754289i	$-0.272018\pi$
$787$	36.8366	1.31308	0.656542	+	0.754289i	$0.272018\pi$
$788$	29.6982	1.05796
$789$	−18.1341	−0.645589
$790$	0	0
$791$	13.7182	0.487763
$792$	30.7179	1.09151
$793$	10.2334	0.363399
$794$	−12.7444	−0.452281
$795$	0	0
$796$	15.8970	0.563455
$797$	−40.4962	−1.43445	−0.717224	−	0.696843i	$-0.754588\pi$
$797$	−40.4962	−1.43445	−0.717224	+	0.696843i	$0.754588\pi$
$798$	−65.1160	−2.30508
$799$	−34.2422	−1.21140
$800$	0	0
$801$	−9.00209	−0.318073
$802$	−71.4798	−2.52404
$803$	−7.10589	−0.250761
$804$	61.6657	2.17478
$805$	0	0
$806$	18.5771	0.654350
$807$	−22.2963	−0.784866
$808$	56.1735	1.97618
$809$	−11.9110	−0.418767	−0.209384	−	0.977834i	$-0.567146\pi$
$809$	−11.9110	−0.418767	−0.209384	+	0.977834i	$0.567146\pi$
$810$	0	0
$811$	−42.2433	−1.48336	−0.741681	−	0.670752i	$-0.765971\pi$
$811$	−42.2433	−1.48336	−0.741681	+	0.670752i	$0.765971\pi$
$812$	−48.6736	−1.70811
$813$	16.8621	0.591379
$814$	−21.1640	−0.741796
$815$	0	0
$816$	−49.1747	−1.72146
$817$	24.4919	0.856863
$818$	51.3368	1.79495
$819$	−11.3670	−0.397197
$820$	0	0
$821$	44.5710	1.55554	0.777769	−	0.628551i	$-0.216352\pi$
$821$	44.5710	1.55554	0.777769	+	0.628551i	$0.216352\pi$
$822$	−32.1572	−1.12161
$823$	12.3125	0.429186	0.214593	−	0.976704i	$-0.431157\pi$
$823$	12.3125	0.429186	0.214593	+	0.976704i	$0.431157\pi$
$824$	88.4431	3.08106
$825$	0	0
$826$	65.9281	2.29393
$827$	−24.7421	−0.860367	−0.430183	−	0.902742i	$-0.641551\pi$
$827$	−24.7421	−0.860367	−0.430183	+	0.902742i	$0.641551\pi$
$828$	−23.9628	−0.832766
$829$	−53.7221	−1.86584	−0.932922	−	0.360077i	$-0.882750\pi$
$829$	−53.7221	−1.86584	−0.932922	+	0.360077i	$0.882750\pi$
$830$	0	0
$831$	−18.6929	−0.648451
$832$	−20.0754	−0.695989
$833$	−20.6221	−0.714512
$834$	34.3915	1.19088
$835$	0	0
$836$	−156.076	−5.39801
$837$	−2.06658	−0.0714315
$838$	−17.3477	−0.599266
$839$	−45.7865	−1.58073	−0.790363	−	0.612639i	$-0.790108\pi$
$839$	−45.7865	−1.58073	−0.790363	+	0.612639i	$0.790108\pi$
$840$	0	0
$841$	−19.2450	−0.663622
$842$	14.6998	0.506589
$843$	25.9852	0.894979
$844$	114.353	3.93620
$845$	0	0
$846$	16.3252	0.561271
$847$	24.8340	0.853307
$848$	−22.7009	−0.779550
$849$	16.9219	0.580760
$850$	0	0
$851$	9.55139	0.327418
$852$	−22.4291	−0.768410
$853$	−20.3074	−0.695311	−0.347655	−	0.937622i	$-0.613022\pi$
$853$	−20.3074	−0.695311	−0.347655	+	0.937622i	$0.613022\pi$
$854$	−25.2182	−0.862950
$855$	0	0
$856$	60.7531	2.07650
$857$	−47.4031	−1.61926	−0.809630	−	0.586941i	$-0.800332\pi$
$857$	−47.4031	−1.61926	−0.809630	+	0.586941i	$0.800332\pi$
$858$	−38.7289	−1.32218
$859$	−5.37538	−0.183406	−0.0917028	−	0.995786i	$-0.529231\pi$
$859$	−5.37538	−0.183406	−0.0917028	+	0.995786i	$0.529231\pi$
$860$	0	0
$861$	12.8047	0.436383
$862$	16.6664	0.567661
$863$	−15.0679	−0.512916	−0.256458	−	0.966555i	$-0.582556\pi$
$863$	−15.0679	−0.512916	−0.256458	+	0.966555i	$0.582556\pi$
$864$	9.18462	0.312467
$865$	0	0
$866$	−2.87003	−0.0975275
$867$	12.6760	0.430501
$868$	−32.2057	−1.09313
$869$	59.1746	2.00736
$870$	0	0
$871$	−44.9791	−1.52406
$872$	124.871	4.22868
$873$	2.57278	0.0870753
$874$	100.126	3.38680
$875$	0	0
$876$	−7.82649	−0.264433
$877$	6.43572	0.217319	0.108659	−	0.994079i	$-0.465344\pi$
$877$	6.43572	0.217319	0.108659	+	0.994079i	$0.465344\pi$
$878$	−13.2796	−0.448165
$879$	1.05979	0.0357457
$880$	0	0
$881$	46.2411	1.55790	0.778950	−	0.627085i	$-0.215752\pi$
$881$	46.2411	1.55790	0.778950	+	0.627085i	$0.215752\pi$
$882$	9.83169	0.331050
$883$	−12.8545	−0.432590	−0.216295	−	0.976328i	$-0.569397\pi$
$883$	−12.8545	−0.432590	−0.216295	+	0.976328i	$0.569397\pi$
$884$	89.4723	3.00928
$885$	0	0
$886$	−46.5097	−1.56252
$887$	−33.5617	−1.12689	−0.563446	−	0.826153i	$-0.690525\pi$
$887$	−33.5617	−1.12689	−0.563446	+	0.826153i	$0.690525\pi$
$888$	−13.4856	−0.452546
$889$	33.5350	1.12473
$890$	0	0
$891$	4.30834	0.144335
$892$	−86.6942	−2.90274
$893$	−47.9873	−1.60583
$894$	13.5231	0.452279
$895$	0	0
$896$	−10.8553	−0.362649
$897$	17.4786	0.583592
$898$	71.0870	2.37220
$899$	6.45454	0.215271
$900$	0	0
$901$	13.6995	0.456398
$902$	43.6272	1.45263
$903$	−10.5360	−0.350616
$904$	29.7822	0.990542
$905$	0	0
$906$	20.2101	0.671437
$907$	5.73678	0.190487	0.0952433	−	0.995454i	$-0.469637\pi$
$907$	5.73678	0.190487	0.0952433	+	0.995454i	$0.469637\pi$
$908$	−85.2257	−2.82831
$909$	7.87863	0.261318
$910$	0	0
$911$	4.08321	0.135283	0.0676413	−	0.997710i	$-0.478453\pi$
$911$	4.08321	0.135283	0.0676413	+	0.997710i	$0.478453\pi$
$912$	−68.9139	−2.28197
$913$	−21.6144	−0.715332
$914$	23.1876	0.766978
$915$	0	0
$916$	28.5027	0.941757
$917$	−16.1476	−0.533242
$918$	−14.1482	−0.466961
$919$	34.1894	1.12780	0.563902	−	0.825842i	$-0.309300\pi$
$919$	34.1894	1.12780	0.563902	+	0.825842i	$0.309300\pi$
$920$	0	0
$921$	29.7239	0.979434
$922$	4.70617	0.154989
$923$	16.3599	0.538492
$924$	67.1414	2.20879
$925$	0	0
$926$	7.06927	0.232311
$927$	12.4046	0.407421
$928$	−28.6863	−0.941672
$929$	−23.9398	−0.785438	−0.392719	−	0.919659i	$-0.628465\pi$
$929$	−23.9398	−0.785438	−0.392719	+	0.919659i	$0.628465\pi$
$930$	0	0
$931$	−28.8999	−0.947157
$932$	−98.9507	−3.24124
$933$	5.08513	0.166480
$934$	−104.474	−3.41849
$935$	0	0
$936$	−24.6779	−0.806621
$937$	21.4640	0.701199	0.350600	−	0.936525i	$-0.385978\pi$
$937$	21.4640	0.701199	0.350600	+	0.936525i	$0.385978\pi$
$938$	110.842	3.61912
$939$	25.9388	0.846481
$940$	0	0
$941$	−1.78646	−0.0582371	−0.0291185	−	0.999576i	$-0.509270\pi$
$941$	−1.78646	−0.0582371	−0.0291185	+	0.999576i	$0.509270\pi$
$942$	−42.7165	−1.39178
$943$	−19.6892	−0.641167
$944$	69.7733	2.27093
$945$	0	0
$946$	−35.8975	−1.16713
$947$	−45.4097	−1.47562	−0.737809	−	0.675009i	$-0.764140\pi$
$947$	−45.4097	−1.47562	−0.737809	+	0.675009i	$0.764140\pi$
$948$	65.1755	2.11680
$949$	5.70866	0.185311
$950$	0	0
$951$	19.7727	0.641172
$952$	−127.557	−4.13416
$953$	1.00850	0.0326686	0.0163343	−	0.999867i	$-0.494800\pi$
$953$	1.00850	0.0326686	0.0163343	+	0.999867i	$0.494800\pi$
$954$	−6.53134	−0.211460
$955$	0	0
$956$	−132.261	−4.27761
$957$	−13.4562	−0.434978
$958$	−72.5794	−2.34493
$959$	−40.6631	−1.31308
$960$	0	0
$961$	−26.7292	−0.862234
$962$	17.0025	0.548183
$963$	8.52094	0.274583
$964$	−88.8115	−2.86043
$965$	0	0
$966$	−43.0724	−1.38583
$967$	21.4625	0.690188	0.345094	−	0.938568i	$-0.387847\pi$
$967$	21.4625	0.690188	0.345094	+	0.938568i	$0.387847\pi$
$968$	53.9147	1.73288
$969$	41.5883	1.33601
$970$	0	0
$971$	47.3619	1.51992	0.759958	−	0.649972i	$-0.225219\pi$
$971$	47.3619	1.51992	0.759958	+	0.649972i	$0.225219\pi$
$972$	4.74525	0.152204
$973$	43.4884	1.39417
$974$	−67.0298	−2.14777
$975$	0	0
$976$	−26.6891	−0.854296
$977$	6.29459	0.201382	0.100691	−	0.994918i	$-0.467895\pi$
$977$	6.29459	0.201382	0.100691	+	0.994918i	$0.467895\pi$
$978$	20.2927	0.648889
$979$	−38.7841	−1.23955
$980$	0	0
$981$	17.5139	0.559174
$982$	61.5641	1.96459
$983$	−7.80790	−0.249033	−0.124517	−	0.992218i	$-0.539738\pi$
$983$	−7.80790	−0.249033	−0.124517	+	0.992218i	$0.539738\pi$
$984$	27.7990	0.886200
$985$	0	0
$986$	44.1891	1.40727
$987$	20.6433	0.657084
$988$	125.387	3.98910
$989$	16.2007	0.515152
$990$	0	0
$991$	−21.0569	−0.668896	−0.334448	−	0.942414i	$-0.608550\pi$
$991$	−21.0569	−0.668896	−0.334448	+	0.942414i	$0.608550\pi$
$992$	−18.9808	−0.602640
$993$	−23.9589	−0.760311
$994$	−40.3156	−1.27873
$995$	0	0
$996$	−23.8063	−0.754332
$997$	29.3042	0.928072	0.464036	−	0.885816i	$-0.346401\pi$
$997$	29.3042	0.928072	0.464036	+	0.885816i	$0.346401\pi$
$998$	23.2641	0.736413
$999$	−1.89142	−0.0598418

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1875.2.a.o.1.8	yes	8
3.2	odd	2		5625.2.a.u.1.1		8
5.2	odd	4		1875.2.b.g.1249.15		16
5.3	odd	4		1875.2.b.g.1249.2		16
5.4	even	2		1875.2.a.n.1.1	✓	8
15.14	odd	2		5625.2.a.bc.1.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1875.2.a.n.1.1	✓	8	5.4	even	2
1875.2.a.o.1.8	yes	8	1.1	even	1	trivial
1875.2.b.g.1249.2		16	5.3	odd	4
1875.2.b.g.1249.15		16	5.2	odd	4
5625.2.a.u.1.1		8	3.2	odd	2
5625.2.a.bc.1.8		8	15.14	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:	\( N \)	\(=\)	\( 1875 = 3 \cdot 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1875.a (trivial)

\(f(q)\)	\(=\)	\(q+2.59716 q^{2} +1.00000 q^{3} +4.74525 q^{4} +2.59716 q^{6} +3.28414 q^{7} +7.12986 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.59716 q^{2} +1.00000 q^{3} +4.74525 q^{4} +2.59716 q^{6} +3.28414 q^{7} +7.12986 q^{8} +1.00000 q^{9} +4.30834 q^{11} +4.74525 q^{12} -3.46120 q^{13} +8.52943 q^{14} +9.02691 q^{16} -5.44757 q^{17} +2.59716 q^{18} -7.63427 q^{19} +3.28414 q^{21} +11.1895 q^{22} -5.04986 q^{23} +7.12986 q^{24} -8.98929 q^{26} +1.00000 q^{27} +15.5841 q^{28} -3.12329 q^{29} -2.06658 q^{31} +9.18462 q^{32} +4.30834 q^{33} -14.1482 q^{34} +4.74525 q^{36} -1.89142 q^{37} -19.8274 q^{38} -3.46120 q^{39} +3.89896 q^{41} +8.52943 q^{42} -3.20815 q^{43} +20.4442 q^{44} -13.1153 q^{46} +6.28577 q^{47} +9.02691 q^{48} +3.78555 q^{49} -5.44757 q^{51} -16.4243 q^{52} -2.51480 q^{53} +2.59716 q^{54} +23.4154 q^{56} -7.63427 q^{57} -8.11170 q^{58} +7.72948 q^{59} -2.95661 q^{61} -5.36725 q^{62} +3.28414 q^{63} +5.80013 q^{64} +11.1895 q^{66} +12.9952 q^{67} -25.8501 q^{68} -5.04986 q^{69} -4.72665 q^{71} +7.12986 q^{72} -1.64933 q^{73} -4.91232 q^{74} -36.2265 q^{76} +14.1492 q^{77} -8.98929 q^{78} +13.7349 q^{79} +1.00000 q^{81} +10.1262 q^{82} -5.01687 q^{83} +15.5841 q^{84} -8.33208 q^{86} -3.12329 q^{87} +30.7179 q^{88} -9.00209 q^{89} -11.3670 q^{91} -23.9628 q^{92} -2.06658 q^{93} +16.3252 q^{94} +9.18462 q^{96} +2.57278 q^{97} +9.83169 q^{98} +4.30834 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + 8 q^{3} + 9 q^{4} + q^{6} + 12 q^{7} + 3 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + q^2 + 8 * q^3 + 9 * q^4 + q^6 + 12 * q^7 + 3 * q^8 + 8 * q^9	\( 8 q + q^{2} + 8 q^{3} + 9 q^{4} + q^{6} + 12 q^{7} + 3 q^{8} + 8 q^{9} + 12 q^{11} + 9 q^{12} + 14 q^{13} + 16 q^{14} + 15 q^{16} - q^{17} + q^{18} + 16 q^{19} + 12 q^{21} + 18 q^{22} - 4 q^{23} + 3 q^{24} - 34 q^{26} + 8 q^{27} - 21 q^{28} + 2 q^{29} + 13 q^{31} - 18 q^{32} + 12 q^{33} - 37 q^{34} + 9 q^{36} - 8 q^{37} - 24 q^{38} + 14 q^{39} - 12 q^{41} + 16 q^{42} + 20 q^{43} + 47 q^{44} + 33 q^{46} - 15 q^{47} + 15 q^{48} + 30 q^{49} - q^{51} - q^{52} - 4 q^{53} + q^{54} + 60 q^{56} + 16 q^{57} + 2 q^{58} + 14 q^{59} + 10 q^{61} + 4 q^{62} + 12 q^{63} + 41 q^{64} + 18 q^{66} + 19 q^{67} - 33 q^{68} - 4 q^{69} + 21 q^{71} + 3 q^{72} - 19 q^{73} - 9 q^{74} - q^{76} - 11 q^{77} - 34 q^{78} + 10 q^{79} + 8 q^{81} + 24 q^{82} - 27 q^{83} - 21 q^{84} + 42 q^{86} + 2 q^{87} + 53 q^{88} - 9 q^{89} - 12 q^{91} - 63 q^{92} + 13 q^{93} + 14 q^{94} - 18 q^{96} + 24 q^{97} - 24 q^{98} + 12 q^{99}+O(q^{100}) \) 8 * q + q^2 + 8 * q^3 + 9 * q^4 + q^6 + 12 * q^7 + 3 * q^8 + 8 * q^9 + 12 * q^11 + 9 * q^12 + 14 * q^13 + 16 * q^14 + 15 * q^16 - q^17 + q^18 + 16 * q^19 + 12 * q^21 + 18 * q^22 - 4 * q^23 + 3 * q^24 - 34 * q^26 + 8 * q^27 - 21 * q^28 + 2 * q^29 + 13 * q^31 - 18 * q^32 + 12 * q^33 - 37 * q^34 + 9 * q^36 - 8 * q^37 - 24 * q^38 + 14 * q^39 - 12 * q^41 + 16 * q^42 + 20 * q^43 + 47 * q^44 + 33 * q^46 - 15 * q^47 + 15 * q^48 + 30 * q^49 - q^51 - q^52 - 4 * q^53 + q^54 + 60 * q^56 + 16 * q^57 + 2 * q^58 + 14 * q^59 + 10 * q^61 + 4 * q^62 + 12 * q^63 + 41 * q^64 + 18 * q^66 + 19 * q^67 - 33 * q^68 - 4 * q^69 + 21 * q^71 + 3 * q^72 - 19 * q^73 - 9 * q^74 - q^76 - 11 * q^77 - 34 * q^78 + 10 * q^79 + 8 * q^81 + 24 * q^82 - 27 * q^83 - 21 * q^84 + 42 * q^86 + 2 * q^87 + 53 * q^88 - 9 * q^89 - 12 * q^91 - 63 * q^92 + 13 * q^93 + 14 * q^94 - 18 * q^96 + 24 * q^97 - 24 * q^98 + 12 * q^99

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