LMFDB - Embedded newform 1875.2.a.l.1.1

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:	$6$
Coefficient field:	6.6.46840000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 11x^{4} + 8x^{3} + 31x^{2} - 15x - 9 $ x^6 - x^5 - 11x^4 + 8x^3 + 31x^2 - 15x - 9
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			1.1
Root			$-2.38719$ 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)

$f(q)$	$=$	$q-2.38719 q^{2} -1.00000 q^{3} +3.69868 q^{4} +2.38719 q^{6} -3.31671 q^{7} -4.05506 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.38719 q^{2} -1.00000 q^{3} +3.69868 q^{4} +2.38719 q^{6} -3.31671 q^{7} -4.05506 q^{8} +1.00000 q^{9} -4.36655 q^{11} -3.69868 q^{12} -5.85502 q^{13} +7.91762 q^{14} +2.28286 q^{16} -0.407830 q^{17} -2.38719 q^{18} -6.64447 q^{19} +3.31671 q^{21} +10.4238 q^{22} -4.61860 q^{23} +4.05506 q^{24} +13.9771 q^{26} -1.00000 q^{27} -12.2674 q^{28} +3.30132 q^{29} -8.77495 q^{31} +2.66052 q^{32} +4.36655 q^{33} +0.973567 q^{34} +3.69868 q^{36} -3.09911 q^{37} +15.8616 q^{38} +5.85502 q^{39} +2.89349 q^{41} -7.91762 q^{42} -1.33270 q^{43} -16.1505 q^{44} +11.0255 q^{46} +11.0609 q^{47} -2.28286 q^{48} +4.00057 q^{49} +0.407830 q^{51} -21.6558 q^{52} -2.70021 q^{53} +2.38719 q^{54} +13.4495 q^{56} +6.64447 q^{57} -7.88089 q^{58} -5.80518 q^{59} +11.2366 q^{61} +20.9475 q^{62} -3.31671 q^{63} -10.9169 q^{64} -10.4238 q^{66} +0.0418484 q^{67} -1.50843 q^{68} +4.61860 q^{69} -16.2062 q^{71} -4.05506 q^{72} -5.35799 q^{73} +7.39817 q^{74} -24.5757 q^{76} +14.4826 q^{77} -13.9771 q^{78} -3.55370 q^{79} +1.00000 q^{81} -6.90732 q^{82} -4.98952 q^{83} +12.2674 q^{84} +3.18140 q^{86} -3.30132 q^{87} +17.7066 q^{88} -1.94025 q^{89} +19.4194 q^{91} -17.0827 q^{92} +8.77495 q^{93} -26.4044 q^{94} -2.66052 q^{96} -5.99258 q^{97} -9.55012 q^{98} -4.36655 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} - 6 q^{3} + 11 q^{4} - q^{6} - 2 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q + q^2 - 6 * q^3 + 11 * q^4 - q^6 - 2 * q^7 + 6 * q^8 + 6 * q^9	$ 6 q + q^{2} - 6 q^{3} + 11 q^{4} - q^{6} - 2 q^{7} + 6 q^{8} + 6 q^{9} - 11 q^{12} - 4 q^{14} + 17 q^{16} + 2 q^{17} + q^{18} - 2 q^{19} + 2 q^{21} + 9 q^{22} - q^{23} - 6 q^{24} + 37 q^{26} - 6 q^{27} - 44 q^{28} + 31 q^{29} - 2 q^{31} + 33 q^{32} + 37 q^{34} + 11 q^{36} - 22 q^{37} + 27 q^{38} + 33 q^{41} + 4 q^{42} - 3 q^{43} - 11 q^{44} - 12 q^{46} - 6 q^{47} - 17 q^{48} + 4 q^{49} - 2 q^{51} - 33 q^{52} + 14 q^{53} - q^{54} - 30 q^{56} + 2 q^{57} - q^{58} - 8 q^{59} + 34 q^{61} + 31 q^{62} - 2 q^{63} + 12 q^{64} - 9 q^{66} + 2 q^{67} + 27 q^{68} + q^{69} - 3 q^{71} + 6 q^{72} - 36 q^{73} + 36 q^{74} + 27 q^{76} + 16 q^{77} - 37 q^{78} + 25 q^{79} + 6 q^{81} + 36 q^{82} - 12 q^{83} + 44 q^{84} - 30 q^{86} - 31 q^{87} + 56 q^{88} + 18 q^{89} + 28 q^{91} + 3 q^{92} + 2 q^{93} - 50 q^{94} - 33 q^{96} + 7 q^{97} + 15 q^{98}+O(q^{100}) $ 6 * q + q^2 - 6 * q^3 + 11 * q^4 - q^6 - 2 * q^7 + 6 * q^8 + 6 * q^9 - 11 * q^12 - 4 * q^14 + 17 * q^16 + 2 * q^17 + q^18 - 2 * q^19 + 2 * q^21 + 9 * q^22 - q^23 - 6 * q^24 + 37 * q^26 - 6 * q^27 - 44 * q^28 + 31 * q^29 - 2 * q^31 + 33 * q^32 + 37 * q^34 + 11 * q^36 - 22 * q^37 + 27 * q^38 + 33 * q^41 + 4 * q^42 - 3 * q^43 - 11 * q^44 - 12 * q^46 - 6 * q^47 - 17 * q^48 + 4 * q^49 - 2 * q^51 - 33 * q^52 + 14 * q^53 - q^54 - 30 * q^56 + 2 * q^57 - q^58 - 8 * q^59 + 34 * q^61 + 31 * q^62 - 2 * q^63 + 12 * q^64 - 9 * q^66 + 2 * q^67 + 27 * q^68 + q^69 - 3 * q^71 + 6 * q^72 - 36 * q^73 + 36 * q^74 + 27 * q^76 + 16 * q^77 - 37 * q^78 + 25 * q^79 + 6 * q^81 + 36 * q^82 - 12 * q^83 + 44 * q^84 - 30 * q^86 - 31 * q^87 + 56 * q^88 + 18 * q^89 + 28 * q^91 + 3 * q^92 + 2 * q^93 - 50 * q^94 - 33 * q^96 + 7 * q^97 + 15 * q^98

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 $

$2$	−2.38719	−1.68800	−0.843999	−	0.536345i	$-0.819805\pi$
$2$	−2.38719	−1.68800	−0.843999	+	0.536345i	$0.819805\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.69868	1.84934
$5$	0	0
$5$	0	0
$6$	2.38719	0.974566
$7$	−3.31671	−1.25360	−0.626799	−	0.779181i	$-0.715635\pi$
$7$	−3.31671	−1.25360	−0.626799	+	0.779181i	$0.715635\pi$
$8$	−4.05506	−1.43368
$9$	1.00000	0.333333
$10$	0	0
$11$	−4.36655	−1.31656	−0.658282	−	0.752771i	$-0.728717\pi$
$11$	−4.36655	−1.31656	−0.658282	+	0.752771i	$0.728717\pi$
$12$	−3.69868	−1.06772
$13$	−5.85502	−1.62389	−0.811946	−	0.583733i	$-0.801591\pi$
$13$	−5.85502	−1.62389	−0.811946	+	0.583733i	$0.801591\pi$
$14$	7.91762	2.11607
$15$	0	0
$16$	2.28286	0.570714
$17$	−0.407830	−0.0989132	−0.0494566	−	0.998776i	$-0.515749\pi$
$17$	−0.407830	−0.0989132	−0.0494566	+	0.998776i	$0.515749\pi$
$18$	−2.38719	−0.562666
$19$	−6.64447	−1.52435	−0.762173	−	0.647374i	$-0.775867\pi$
$19$	−6.64447	−1.52435	−0.762173	+	0.647374i	$0.775867\pi$
$20$	0	0
$21$	3.31671	0.723766
$22$	10.4238	2.22236
$23$	−4.61860	−0.963045	−0.481523	−	0.876434i	$-0.659916\pi$
$23$	−4.61860	−0.963045	−0.481523	+	0.876434i	$0.659916\pi$
$24$	4.05506	0.827736
$25$	0	0
$26$	13.9771	2.74113
$27$	−1.00000	−0.192450
$28$	−12.2674	−2.31833
$29$	3.30132	0.613040	0.306520	−	0.951864i	$-0.400835\pi$
$29$	3.30132	0.613040	0.306520	+	0.951864i	$0.400835\pi$
$30$	0	0
$31$	−8.77495	−1.57603	−0.788014	−	0.615658i	$-0.788890\pi$
$31$	−8.77495	−1.57603	−0.788014	+	0.615658i	$0.788890\pi$
$32$	2.66052	0.470318
$33$	4.36655	0.760119
$34$	0.973567	0.166965
$35$	0	0
$36$	3.69868	0.616446
$37$	−3.09911	−0.509491	−0.254745	−	0.967008i	$-0.581992\pi$
$37$	−3.09911	−0.509491	−0.254745	+	0.967008i	$0.581992\pi$
$38$	15.8616	2.57309
$39$	5.85502	0.937554
$40$	0	0
$41$	2.89349	0.451888	0.225944	−	0.974140i	$-0.427453\pi$
$41$	2.89349	0.451888	0.225944	+	0.974140i	$0.427453\pi$
$42$	−7.91762	−1.22172
$43$	−1.33270	−0.203234	−0.101617	−	0.994824i	$-0.532402\pi$
$43$	−1.33270	−0.203234	−0.101617	+	0.994824i	$0.532402\pi$
$44$	−16.1505	−2.43477
$45$	0	0
$46$	11.0255	1.62562
$47$	11.0609	1.61339	0.806696	−	0.590967i	$-0.201254\pi$
$47$	11.0609	1.61339	0.806696	+	0.590967i	$0.201254\pi$
$48$	−2.28286	−0.329502
$49$	4.00057	0.571510
$50$	0	0
$51$	0.407830	0.0571076
$52$	−21.6558	−3.00312
$53$	−2.70021	−0.370903	−0.185451	−	0.982653i	$-0.559375\pi$
$53$	−2.70021	−0.370903	−0.185451	+	0.982653i	$0.559375\pi$
$54$	2.38719	0.324855
$55$	0	0
$56$	13.4495	1.79726
$57$	6.64447	0.880081
$58$	−7.88089	−1.03481
$59$	−5.80518	−0.755770	−0.377885	−	0.925852i	$-0.623349\pi$
$59$	−5.80518	−0.755770	−0.377885	+	0.925852i	$0.623349\pi$
$60$	0	0
$61$	11.2366	1.43870	0.719352	−	0.694646i	$-0.244439\pi$
$61$	11.2366	1.43870	0.719352	+	0.694646i	$0.244439\pi$
$62$	20.9475	2.66033
$63$	−3.31671	−0.417866
$64$	−10.9169	−1.36461
$65$	0	0
$66$	−10.4238	−1.28308
$67$	0.0418484	0.00511260	0.00255630	−	0.999997i	$-0.499186\pi$
$67$	0.0418484	0.00511260	0.00255630	+	0.999997i	$0.499186\pi$
$68$	−1.50843	−0.182924
$69$	4.61860	0.556014
$70$	0	0
$71$	−16.2062	−1.92332	−0.961659	−	0.274250i	$-0.911571\pi$
$71$	−16.2062	−1.92332	−0.961659	+	0.274250i	$0.911571\pi$
$72$	−4.05506	−0.477894
$73$	−5.35799	−0.627105	−0.313553	−	0.949571i	$-0.601519\pi$
$73$	−5.35799	−0.627105	−0.313553	+	0.949571i	$0.601519\pi$
$74$	7.39817	0.860019
$75$	0	0
$76$	−24.5757	−2.81903
$77$	14.4826	1.65044
$78$	−13.9771	−1.58259
$79$	−3.55370	−0.399822	−0.199911	−	0.979814i	$-0.564065\pi$
$79$	−3.55370	−0.399822	−0.199911	+	0.979814i	$0.564065\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−6.90732	−0.762786
$83$	−4.98952	−0.547671	−0.273836	−	0.961776i	$-0.588292\pi$
$83$	−4.98952	−0.547671	−0.273836	+	0.961776i	$0.588292\pi$
$84$	12.2674	1.33849
$85$	0	0
$86$	3.18140	0.343059
$87$	−3.30132	−0.353939
$88$	17.7066	1.88753
$89$	−1.94025	−0.205666	−0.102833	−	0.994699i	$-0.532791\pi$
$89$	−1.94025	−0.205666	−0.102833	+	0.994699i	$0.532791\pi$
$90$	0	0
$91$	19.4194	2.03571
$92$	−17.0827	−1.78100
$93$	8.77495	0.909920
$94$	−26.4044	−2.72340
$95$	0	0
$96$	−2.66052	−0.271538
$97$	−5.99258	−0.608454	−0.304227	−	0.952600i	$-0.598398\pi$
$97$	−5.99258	−0.608454	−0.304227	+	0.952600i	$0.598398\pi$
$98$	−9.55012	−0.964708
$99$	−4.36655	−0.438855
$100$	0	0
$101$	5.06181	0.503669	0.251834	−	0.967770i	$-0.418966\pi$
$101$	5.06181	0.503669	0.251834	+	0.967770i	$0.418966\pi$
$102$	−0.973567	−0.0963975
$103$	−6.90359	−0.680231	−0.340115	−	0.940384i	$-0.610466\pi$
$103$	−6.90359	−0.680231	−0.340115	+	0.940384i	$0.610466\pi$
$104$	23.7425	2.32814
$105$	0	0
$106$	6.44592	0.626083
$107$	17.2723	1.66978	0.834890	−	0.550417i	$-0.185531\pi$
$107$	17.2723	1.66978	0.834890	+	0.550417i	$0.185531\pi$
$108$	−3.69868	−0.355905
$109$	−6.54439	−0.626839	−0.313419	−	0.949615i	$-0.601475\pi$
$109$	−6.54439	−0.626839	−0.313419	+	0.949615i	$0.601475\pi$
$110$	0	0
$111$	3.09911	0.294155
$112$	−7.57157	−0.715446
$113$	−8.66993	−0.815599	−0.407799	−	0.913072i	$-0.633704\pi$
$113$	−8.66993	−0.815599	−0.407799	+	0.913072i	$0.633704\pi$
$114$	−15.8616	−1.48558
$115$	0	0
$116$	12.2105	1.13372
$117$	−5.85502	−0.541297
$118$	13.8581	1.27574
$119$	1.35265	0.123998
$120$	0	0
$121$	8.06676	0.733342
$122$	−26.8240	−2.42853
$123$	−2.89349	−0.260898
$124$	−32.4557	−2.91461
$125$	0	0
$126$	7.91762	0.705358
$127$	3.24595	0.288031	0.144016	−	0.989575i	$-0.453998\pi$
$127$	3.24595	0.288031	0.144016	+	0.989575i	$0.453998\pi$
$128$	20.7396	1.83314
$129$	1.33270	0.117337
$130$	0	0
$131$	−4.40192	−0.384598	−0.192299	−	0.981336i	$-0.561594\pi$
$131$	−4.40192	−0.384598	−0.192299	+	0.981336i	$0.561594\pi$
$132$	16.1505	1.40572
$133$	22.0378	1.91092
$134$	−0.0999001	−0.00863005
$135$	0	0
$136$	1.65378	0.141810
$137$	−1.06523	−0.0910085	−0.0455042	−	0.998964i	$-0.514489\pi$
$137$	−1.06523	−0.0910085	−0.0455042	+	0.998964i	$0.514489\pi$
$138$	−11.0255	−0.938551
$139$	−3.77286	−0.320010	−0.160005	−	0.987116i	$-0.551151\pi$
$139$	−3.77286	−0.320010	−0.160005	+	0.987116i	$0.551151\pi$
$140$	0	0
$141$	−11.0609	−0.931492
$142$	38.6872	3.24656
$143$	25.5663	2.13796
$144$	2.28286	0.190238
$145$	0	0
$146$	12.7905	1.05855
$147$	−4.00057	−0.329961
$148$	−11.4626	−0.942221
$149$	−7.88089	−0.645627	−0.322814	−	0.946463i	$-0.604629\pi$
$149$	−7.88089	−0.645627	−0.322814	+	0.946463i	$0.604629\pi$
$150$	0	0
$151$	7.46432	0.607437	0.303719	−	0.952762i	$-0.401772\pi$
$151$	7.46432	0.607437	0.303719	+	0.952762i	$0.401772\pi$
$152$	26.9437	2.18543
$153$	−0.407830	−0.0329711
$154$	−34.5727	−2.78595
$155$	0	0
$156$	21.6558	1.73385
$157$	−0.268958	−0.0214652	−0.0107326	−	0.999942i	$-0.503416\pi$
$157$	−0.268958	−0.0214652	−0.0107326	+	0.999942i	$0.503416\pi$
$158$	8.48336	0.674900
$159$	2.70021	0.214141
$160$	0	0
$161$	15.3186	1.20727
$162$	−2.38719	−0.187555
$163$	−10.3496	−0.810645	−0.405322	−	0.914174i	$-0.632841\pi$
$163$	−10.3496	−0.810645	−0.405322	+	0.914174i	$0.632841\pi$
$164$	10.7021	0.835693
$165$	0	0
$166$	11.9109	0.924468
$167$	4.26896	0.330342	0.165171	−	0.986265i	$-0.447182\pi$
$167$	4.26896	0.330342	0.165171	+	0.986265i	$0.447182\pi$
$168$	−13.4495	−1.03765
$169$	21.2813	1.63702
$170$	0	0
$171$	−6.64447	−0.508115
$172$	−4.92921	−0.375849
$173$	23.5031	1.78691	0.893454	−	0.449154i	$-0.148275\pi$
$173$	23.5031	1.78691	0.893454	+	0.449154i	$0.148275\pi$
$174$	7.88089	0.597448
$175$	0	0
$176$	−9.96820	−0.751382
$177$	5.80518	0.436344
$178$	4.63175	0.347164
$179$	19.6897	1.47168	0.735840	−	0.677155i	$-0.236788\pi$
$179$	19.6897	1.47168	0.735840	+	0.677155i	$0.236788\pi$
$180$	0	0
$181$	−12.8221	−0.953060	−0.476530	−	0.879158i	$-0.658106\pi$
$181$	−12.8221	−0.953060	−0.476530	+	0.879158i	$0.658106\pi$
$182$	−46.3578	−3.43627
$183$	−11.2366	−0.830636
$184$	18.7287	1.38070
$185$	0	0
$186$	−20.9475	−1.53594
$187$	1.78081	0.130226
$188$	40.9105	2.98371
$189$	3.31671	0.241255
$190$	0	0
$191$	−19.0583	−1.37901	−0.689507	−	0.724279i	$-0.742173\pi$
$191$	−19.0583	−1.37901	−0.689507	+	0.724279i	$0.742173\pi$
$192$	10.9169	0.787857
$193$	−16.9842	−1.22255	−0.611275	−	0.791418i	$-0.709343\pi$
$193$	−16.9842	−1.22255	−0.611275	+	0.791418i	$0.709343\pi$
$194$	14.3054	1.02707
$195$	0	0
$196$	14.7968	1.05692
$197$	0.469462	0.0334478	0.0167239	−	0.999860i	$-0.494676\pi$
$197$	0.469462	0.0334478	0.0167239	+	0.999860i	$0.494676\pi$
$198$	10.4238	0.740786
$199$	7.02491	0.497983	0.248991	−	0.968506i	$-0.419901\pi$
$199$	7.02491	0.497983	0.248991	+	0.968506i	$0.419901\pi$
$200$	0	0
$201$	−0.0418484	−0.00295176
$202$	−12.0835	−0.850192
$203$	−10.9495	−0.768507
$204$	1.50843	0.105611
$205$	0	0
$206$	16.4802	1.14823
$207$	−4.61860	−0.321015
$208$	−13.3662	−0.926777
$209$	29.0134	2.00690
$210$	0	0
$211$	15.7531	1.08449	0.542243	−	0.840222i	$-0.317575\pi$
$211$	15.7531	1.08449	0.542243	+	0.840222i	$0.317575\pi$
$212$	−9.98721	−0.685925
$213$	16.2062	1.11043
$214$	−41.2323	−2.81859
$215$	0	0
$216$	4.05506	0.275912
$217$	29.1040	1.97571
$218$	15.6227	1.05810
$219$	5.35799	0.362059
$220$	0	0
$221$	2.38785	0.160624
$222$	−7.39817	−0.496532
$223$	2.27697	0.152477	0.0762385	−	0.997090i	$-0.475709\pi$
$223$	2.27697	0.152477	0.0762385	+	0.997090i	$0.475709\pi$
$224$	−8.82417	−0.589590
$225$	0	0
$226$	20.6968	1.37673
$227$	20.2674	1.34520	0.672599	−	0.740007i	$-0.265178\pi$
$227$	20.2674	1.34520	0.672599	+	0.740007i	$0.265178\pi$
$228$	24.5757	1.62757
$229$	19.6358	1.29757	0.648786	−	0.760971i	$-0.275277\pi$
$229$	19.6358	1.29757	0.648786	+	0.760971i	$0.275277\pi$
$230$	0	0
$231$	−14.4826	−0.952884
$232$	−13.3871	−0.878905
$233$	17.1468	1.12333	0.561663	−	0.827366i	$-0.310162\pi$
$233$	17.1468	1.12333	0.561663	+	0.827366i	$0.310162\pi$
$234$	13.9771	0.913709
$235$	0	0
$236$	−21.4715	−1.39768
$237$	3.55370	0.230838
$238$	−3.22904	−0.209308
$239$	21.7654	1.40789	0.703945	−	0.710255i	$-0.251420\pi$
$239$	21.7654	1.40789	0.703945	+	0.710255i	$0.251420\pi$
$240$	0	0
$241$	3.90067	0.251264	0.125632	−	0.992077i	$-0.459904\pi$
$241$	3.90067	0.251264	0.125632	+	0.992077i	$0.459904\pi$
$242$	−19.2569	−1.23788
$243$	−1.00000	−0.0641500
$244$	41.5607	2.66065
$245$	0	0
$246$	6.90732	0.440395
$247$	38.9035	2.47537
$248$	35.5830	2.25952
$249$	4.98952	0.316198
$250$	0	0
$251$	−21.8389	−1.37846	−0.689230	−	0.724543i	$-0.742051\pi$
$251$	−21.8389	−1.37846	−0.689230	+	0.724543i	$0.742051\pi$
$252$	−12.2674	−0.772776
$253$	20.1674	1.26791
$254$	−7.74869	−0.486196
$255$	0	0
$256$	−27.6757	−1.72973
$257$	−17.1453	−1.06949	−0.534747	−	0.845012i	$-0.679593\pi$
$257$	−17.1453	−1.06949	−0.534747	+	0.845012i	$0.679593\pi$
$258$	−3.18140	−0.198065
$259$	10.2789	0.638697
$260$	0	0
$261$	3.30132	0.204347
$262$	10.5082	0.649201
$263$	−17.6266	−1.08690	−0.543451	−	0.839441i	$-0.682883\pi$
$263$	−17.6266	−1.08690	−0.543451	+	0.839441i	$0.682883\pi$
$264$	−17.7066	−1.08977
$265$	0	0
$266$	−52.6084	−3.22563
$267$	1.94025	0.118742
$268$	0.154784	0.00945492
$269$	1.94772	0.118755	0.0593773	−	0.998236i	$-0.481088\pi$
$269$	1.94772	0.118755	0.0593773	+	0.998236i	$0.481088\pi$
$270$	0	0
$271$	−13.8707	−0.842583	−0.421292	−	0.906925i	$-0.638423\pi$
$271$	−13.8707	−0.842583	−0.421292	+	0.906925i	$0.638423\pi$
$272$	−0.931016	−0.0564512
$273$	−19.4194	−1.17532
$274$	2.54290	0.153622
$275$	0	0
$276$	17.0827	1.02826
$277$	26.4814	1.59111	0.795556	−	0.605880i	$-0.207179\pi$
$277$	26.4814	1.59111	0.795556	+	0.605880i	$0.207179\pi$
$278$	9.00654	0.540177
$279$	−8.77495	−0.525342
$280$	0	0
$281$	−21.6050	−1.28885	−0.644425	−	0.764668i	$-0.722903\pi$
$281$	−21.6050	−1.28885	−0.644425	+	0.764668i	$0.722903\pi$
$282$	26.4044	1.57236
$283$	2.05287	0.122030	0.0610151	−	0.998137i	$-0.480566\pi$
$283$	2.05287	0.122030	0.0610151	+	0.998137i	$0.480566\pi$
$284$	−59.9413	−3.55686
$285$	0	0
$286$	−61.0315	−3.60887
$287$	−9.59688	−0.566486
$288$	2.66052	0.156773
$289$	−16.8337	−0.990216
$290$	0	0
$291$	5.99258	0.351291
$292$	−19.8175	−1.15973
$293$	−11.9787	−0.699805	−0.349902	−	0.936786i	$-0.613785\pi$
$293$	−11.9787	−0.699805	−0.349902	+	0.936786i	$0.613785\pi$
$294$	9.55012	0.556974
$295$	0	0
$296$	12.5671	0.730447
$297$	4.36655	0.253373
$298$	18.8132	1.08982
$299$	27.0420	1.56388
$300$	0	0
$301$	4.42016	0.254774
$302$	−17.8187	−1.02535
$303$	−5.06181	−0.290793
$304$	−15.1684	−0.869965
$305$	0	0
$306$	0.973567	0.0556551
$307$	−7.07969	−0.404059	−0.202030	−	0.979379i	$-0.564754\pi$
$307$	−7.07969	−0.404059	−0.202030	+	0.979379i	$0.564754\pi$
$308$	53.5664	3.05223
$309$	6.90359	0.392732
$310$	0	0
$311$	−11.4130	−0.647171	−0.323586	−	0.946199i	$-0.604888\pi$
$311$	−11.4130	−0.647171	−0.323586	+	0.946199i	$0.604888\pi$
$312$	−23.7425	−1.34415
$313$	11.9077	0.673064	0.336532	−	0.941672i	$-0.390746\pi$
$313$	11.9077	0.673064	0.336532	+	0.941672i	$0.390746\pi$
$314$	0.642054	0.0362332
$315$	0	0
$316$	−13.1440	−0.739407
$317$	12.7719	0.717340	0.358670	−	0.933465i	$-0.383230\pi$
$317$	12.7719	0.717340	0.358670	+	0.933465i	$0.383230\pi$
$318$	−6.44592	−0.361469
$319$	−14.4154	−0.807107
$320$	0	0
$321$	−17.2723	−0.964048
$322$	−36.5683	−2.03787
$323$	2.70981	0.150778
$324$	3.69868	0.205482
$325$	0	0
$326$	24.7065	1.36837
$327$	6.54439	0.361906
$328$	−11.7333	−0.647863
$329$	−36.6857	−2.02255
$330$	0	0
$331$	8.66041	0.476019	0.238010	−	0.971263i	$-0.423505\pi$
$331$	8.66041	0.476019	0.238010	+	0.971263i	$0.423505\pi$
$332$	−18.4546	−1.01283
$333$	−3.09911	−0.169830
$334$	−10.1908	−0.557617
$335$	0	0
$336$	7.57157	0.413063
$337$	−15.2564	−0.831069	−0.415534	−	0.909577i	$-0.636405\pi$
$337$	−15.2564	−0.831069	−0.415534	+	0.909577i	$0.636405\pi$
$338$	−50.8025	−2.76329
$339$	8.66993	0.470886
$340$	0	0
$341$	38.3163	2.07494
$342$	15.8616	0.857697
$343$	9.94824	0.537155
$344$	5.40416	0.291373
$345$	0	0
$346$	−56.1064	−3.01630
$347$	−21.8540	−1.17319	−0.586593	−	0.809882i	$-0.699531\pi$
$347$	−21.8540	−1.17319	−0.586593	+	0.809882i	$0.699531\pi$
$348$	−12.2105	−0.654553
$349$	7.29614	0.390553	0.195277	−	0.980748i	$-0.437440\pi$
$349$	7.29614	0.390553	0.195277	+	0.980748i	$0.437440\pi$
$350$	0	0
$351$	5.85502	0.312518
$352$	−11.6173	−0.619203
$353$	−30.5320	−1.62506	−0.812528	−	0.582923i	$-0.801909\pi$
$353$	−30.5320	−1.62506	−0.812528	+	0.582923i	$0.801909\pi$
$354$	−13.8581	−0.736548
$355$	0	0
$356$	−7.17637	−0.380347
$357$	−1.35265	−0.0715900
$358$	−47.0031	−2.48419
$359$	3.06747	0.161895	0.0809473	−	0.996718i	$-0.474205\pi$
$359$	3.06747	0.161895	0.0809473	+	0.996718i	$0.474205\pi$
$360$	0	0
$361$	25.1489	1.32363
$362$	30.6088	1.60876
$363$	−8.06676	−0.423395
$364$	71.8261	3.76471
$365$	0	0
$366$	26.8240	1.40211
$367$	−31.6035	−1.64969	−0.824845	−	0.565358i	$-0.808738\pi$
$367$	−31.6035	−1.64969	−0.824845	+	0.565358i	$0.808738\pi$
$368$	−10.5436	−0.549623
$369$	2.89349	0.150629
$370$	0	0
$371$	8.95582	0.464963
$372$	32.4557	1.68275
$373$	−22.4904	−1.16451	−0.582254	−	0.813007i	$-0.697829\pi$
$373$	−22.4904	−1.16451	−0.582254	+	0.813007i	$0.697829\pi$
$374$	−4.25113	−0.219821
$375$	0	0
$376$	−44.8525	−2.31309
$377$	−19.3293	−0.995511
$378$	−7.91762	−0.407238
$379$	30.1612	1.54928	0.774638	−	0.632404i	$-0.217932\pi$
$379$	30.1612	1.54928	0.774638	+	0.632404i	$0.217932\pi$
$380$	0	0
$381$	−3.24595	−0.166295
$382$	45.4959	2.32777
$383$	16.7725	0.857034	0.428517	−	0.903534i	$-0.359036\pi$
$383$	16.7725	0.857034	0.428517	+	0.903534i	$0.359036\pi$
$384$	−20.7396	−1.05836
$385$	0	0
$386$	40.5445	2.06366
$387$	−1.33270	−0.0677447
$388$	−22.1646	−1.12524
$389$	22.4835	1.13996	0.569980	−	0.821659i	$-0.306951\pi$
$389$	22.4835	1.13996	0.569980	+	0.821659i	$0.306951\pi$
$390$	0	0
$391$	1.88360	0.0952579
$392$	−16.2226	−0.819363
$393$	4.40192	0.222048
$394$	−1.12069	−0.0564598
$395$	0	0
$396$	−16.1505	−0.811591
$397$	3.65800	0.183590	0.0917948	−	0.995778i	$-0.470740\pi$
$397$	3.65800	0.183590	0.0917948	+	0.995778i	$0.470740\pi$
$398$	−16.7698	−0.840594
$399$	−22.0378	−1.10327
$400$	0	0
$401$	−25.3774	−1.26729	−0.633643	−	0.773626i	$-0.718441\pi$
$401$	−25.3774	−1.26729	−0.633643	+	0.773626i	$0.718441\pi$
$402$	0.0999001	0.00498256
$403$	51.3775	2.55930
$404$	18.7220	0.931454
$405$	0	0
$406$	26.1386	1.29724
$407$	13.5324	0.670777
$408$	−1.65378	−0.0818741
$409$	−27.8011	−1.37468	−0.687339	−	0.726337i	$-0.741221\pi$
$409$	−27.8011	−1.37468	−0.687339	+	0.726337i	$0.741221\pi$
$410$	0	0
$411$	1.06523	0.0525438
$412$	−25.5341	−1.25798
$413$	19.2541	0.947433
$414$	11.0255	0.541873
$415$	0	0
$416$	−15.5774	−0.763745
$417$	3.77286	0.184758
$418$	−69.2605	−3.38764
$419$	−0.119817	−0.00585344	−0.00292672	−	0.999996i	$-0.500932\pi$
$419$	−0.119817	−0.00585344	−0.00292672	+	0.999996i	$0.500932\pi$
$420$	0	0
$421$	−0.0393633	−0.00191845	−0.000959225	−	1.00000i	$-0.500305\pi$
$421$	−0.0393633	−0.00191845	−0.000959225		1.00000i	$0.500305\pi$
$422$	−37.6056	−1.83061
$423$	11.0609	0.537797
$424$	10.9495	0.531756
$425$	0	0
$426$	−38.6872	−1.87440
$427$	−37.2687	−1.80356
$428$	63.8848	3.08799
$429$	−25.5663	−1.23435
$430$	0	0
$431$	16.3869	0.789328	0.394664	−	0.918825i	$-0.370861\pi$
$431$	16.3869	0.789328	0.394664	+	0.918825i	$0.370861\pi$
$432$	−2.28286	−0.109834
$433$	−17.5610	−0.843930	−0.421965	−	0.906612i	$-0.638660\pi$
$433$	−17.5610	−0.843930	−0.421965	+	0.906612i	$0.638660\pi$
$434$	−69.4767	−3.33499
$435$	0	0
$436$	−24.2056	−1.15924
$437$	30.6882	1.46801
$438$	−12.7905	−0.611156
$439$	−31.1577	−1.48708	−0.743538	−	0.668694i	$-0.766854\pi$
$439$	−31.1577	−1.48708	−0.743538	+	0.668694i	$0.766854\pi$
$440$	0	0
$441$	4.00057	0.190503
$442$	−5.70026	−0.271134
$443$	−13.1787	−0.626141	−0.313071	−	0.949730i	$-0.601358\pi$
$443$	−13.1787	−0.626141	−0.313071	+	0.949730i	$0.601358\pi$
$444$	11.4626	0.543991
$445$	0	0
$446$	−5.43555	−0.257381
$447$	7.88089	0.372753
$448$	36.2081	1.71067
$449$	−29.2119	−1.37859	−0.689297	−	0.724479i	$-0.742080\pi$
$449$	−29.2119	−1.37859	−0.689297	+	0.724479i	$0.742080\pi$
$450$	0	0
$451$	−12.6346	−0.594939
$452$	−32.0673	−1.50832
$453$	−7.46432	−0.350704
$454$	−48.3822	−2.27069
$455$	0	0
$456$	−26.9437	−1.26176
$457$	35.8001	1.67466	0.837330	−	0.546698i	$-0.184115\pi$
$457$	35.8001	1.67466	0.837330	+	0.546698i	$0.184115\pi$
$458$	−46.8745	−2.19030
$459$	0.407830	0.0190359
$460$	0	0
$461$	6.01315	0.280060	0.140030	−	0.990147i	$-0.455280\pi$
$461$	6.01315	0.280060	0.140030	+	0.990147i	$0.455280\pi$
$462$	34.5727	1.60847
$463$	−41.2139	−1.91537	−0.957687	−	0.287813i	$-0.907072\pi$
$463$	−41.2139	−1.91537	−0.957687	+	0.287813i	$0.907072\pi$
$464$	7.53644	0.349871
$465$	0	0
$466$	−40.9328	−1.89617
$467$	−29.9663	−1.38667	−0.693337	−	0.720614i	$-0.743860\pi$
$467$	−29.9663	−1.38667	−0.693337	+	0.720614i	$0.743860\pi$
$468$	−21.6558	−1.00104
$469$	−0.138799	−0.00640914
$470$	0	0
$471$	0.268958	0.0123929
$472$	23.5404	1.08353
$473$	5.81928	0.267571
$474$	−8.48336	−0.389653
$475$	0	0
$476$	5.00303	0.229313
$477$	−2.70021	−0.123634
$478$	−51.9582	−2.37651
$479$	8.33937	0.381036	0.190518	−	0.981684i	$-0.438983\pi$
$479$	8.33937	0.381036	0.190518	+	0.981684i	$0.438983\pi$
$480$	0	0
$481$	18.1454	0.827357
$482$	−9.31165	−0.424134
$483$	−15.3186	−0.697019
$484$	29.8363	1.35620
$485$	0	0
$486$	2.38719	0.108285
$487$	−4.91110	−0.222543	−0.111272	−	0.993790i	$-0.535492\pi$
$487$	−4.91110	−0.222543	−0.111272	+	0.993790i	$0.535492\pi$
$488$	−45.5653	−2.06264
$489$	10.3496	0.468026
$490$	0	0
$491$	4.33484	0.195629	0.0978144	−	0.995205i	$-0.468815\pi$
$491$	4.33484	0.195629	0.0978144	+	0.995205i	$0.468815\pi$
$492$	−10.7021	−0.482488
$493$	−1.34638	−0.0606378
$494$	−92.8701	−4.17842
$495$	0	0
$496$	−20.0319	−0.899461
$497$	53.7511	2.41107
$498$	−11.9109	−0.533742
$499$	36.1803	1.61965	0.809826	−	0.586671i	$-0.199562\pi$
$499$	36.1803	1.61965	0.809826	+	0.586671i	$0.199562\pi$
$500$	0	0
$501$	−4.26896	−0.190723
$502$	52.1336	2.32684
$503$	−37.3990	−1.66754	−0.833769	−	0.552113i	$-0.813822\pi$
$503$	−37.3990	−1.66754	−0.833769	+	0.552113i	$0.813822\pi$
$504$	13.4495	0.599087
$505$	0	0
$506$	−48.1433	−2.14023
$507$	−21.2813	−0.945135
$508$	12.0057	0.532667
$509$	−26.2959	−1.16555	−0.582773	−	0.812635i	$-0.698032\pi$
$509$	−26.2959	−1.16555	−0.582773	+	0.812635i	$0.698032\pi$
$510$	0	0
$511$	17.7709	0.786138
$512$	24.5878	1.08664
$513$	6.64447	0.293360
$514$	40.9291	1.80530
$515$	0	0
$516$	4.92921	0.216996
$517$	−48.2978	−2.12413
$518$	−24.5376	−1.07812
$519$	−23.5031	−1.03167
$520$	0	0
$521$	7.02231	0.307653	0.153826	−	0.988098i	$-0.450840\pi$
$521$	7.02231	0.307653	0.153826	+	0.988098i	$0.450840\pi$
$522$	−7.88089	−0.344937
$523$	13.0796	0.571933	0.285967	−	0.958240i	$-0.407685\pi$
$523$	13.0796	0.571933	0.285967	+	0.958240i	$0.407685\pi$
$524$	−16.2813	−0.711252
$525$	0	0
$526$	42.0780	1.83469
$527$	3.57869	0.155890
$528$	9.96820	0.433810
$529$	−1.66851	−0.0725437
$530$	0	0
$531$	−5.80518	−0.251923
$532$	81.5106	3.53393
$533$	−16.9415	−0.733817
$534$	−4.63175	−0.200436
$535$	0	0
$536$	−0.169698	−0.00732984
$537$	−19.6897	−0.849675
$538$	−4.64958	−0.200458
$539$	−17.4687	−0.752430
$540$	0	0
$541$	−2.08066	−0.0894546	−0.0447273	−	0.998999i	$-0.514242\pi$
$541$	−2.08066	−0.0894546	−0.0447273	+	0.998999i	$0.514242\pi$
$542$	33.1119	1.42228
$543$	12.8221	0.550249
$544$	−1.08504	−0.0465206
$545$	0	0
$546$	46.3578	1.98393
$547$	−36.9553	−1.58009	−0.790046	−	0.613047i	$-0.789944\pi$
$547$	−36.9553	−1.58009	−0.790046	+	0.613047i	$0.789944\pi$
$548$	−3.93993	−0.168305
$549$	11.2366	0.479568
$550$	0	0
$551$	−21.9355	−0.934485
$552$	−18.7287	−0.797148
$553$	11.7866	0.501217
$554$	−63.2161	−2.68579
$555$	0	0
$556$	−13.9546	−0.591807
$557$	−2.67455	−0.113324	−0.0566621	−	0.998393i	$-0.518046\pi$
$557$	−2.67455	−0.113324	−0.0566621	+	0.998393i	$0.518046\pi$
$558$	20.9475	0.886777
$559$	7.80296	0.330030
$560$	0	0
$561$	−1.78081	−0.0751858
$562$	51.5754	2.17557
$563$	13.8746	0.584745	0.292372	−	0.956305i	$-0.405555\pi$
$563$	13.8746	0.584745	0.292372	+	0.956305i	$0.405555\pi$
$564$	−40.9105	−1.72264
$565$	0	0
$566$	−4.90058	−0.205987
$567$	−3.31671	−0.139289
$568$	65.7170	2.75742
$569$	33.3404	1.39770	0.698852	−	0.715266i	$-0.253695\pi$
$569$	33.3404	1.39770	0.698852	+	0.715266i	$0.253695\pi$
$570$	0	0
$571$	35.3794	1.48058	0.740291	−	0.672287i	$-0.234688\pi$
$571$	35.3794	1.48058	0.740291	+	0.672287i	$0.234688\pi$
$572$	94.5613	3.95381
$573$	19.0583	0.796174
$574$	22.9096	0.956227
$575$	0	0
$576$	−10.9169	−0.454870
$577$	16.6041	0.691239	0.345620	−	0.938375i	$-0.387669\pi$
$577$	16.6041	0.691239	0.345620	+	0.938375i	$0.387669\pi$
$578$	40.1852	1.67148
$579$	16.9842	0.705839
$580$	0	0
$581$	16.5488	0.686560
$582$	−14.3054	−0.592979
$583$	11.7906	0.488317
$584$	21.7270	0.899069
$585$	0	0
$586$	28.5955	1.18127
$587$	−26.9696	−1.11315	−0.556576	−	0.830796i	$-0.687885\pi$
$587$	−26.9696	−1.11315	−0.556576	+	0.830796i	$0.687885\pi$
$588$	−14.7968	−0.610210
$589$	58.3049	2.40241
$590$	0	0
$591$	−0.469462	−0.0193111
$592$	−7.07482	−0.290773
$593$	12.7895	0.525201	0.262600	−	0.964905i	$-0.415420\pi$
$593$	12.7895	0.525201	0.262600	+	0.964905i	$0.415420\pi$
$594$	−10.4238	−0.427693
$595$	0	0
$596$	−29.1489	−1.19398
$597$	−7.02491	−0.287511
$598$	−64.5545	−2.63983
$599$	31.1978	1.27471	0.637354	−	0.770571i	$-0.280029\pi$
$599$	31.1978	1.27471	0.637354	+	0.770571i	$0.280029\pi$
$600$	0	0
$601$	19.2310	0.784450	0.392225	−	0.919869i	$-0.371705\pi$
$601$	19.2310	0.784450	0.392225	+	0.919869i	$0.371705\pi$
$602$	−10.5518	−0.430058
$603$	0.0418484	0.00170420
$604$	27.6081	1.12336
$605$	0	0
$606$	12.0835	0.490858
$607$	−8.01104	−0.325158	−0.162579	−	0.986696i	$-0.551981\pi$
$607$	−8.01104	−0.325158	−0.162579	+	0.986696i	$0.551981\pi$
$608$	−17.6777	−0.716926
$609$	10.9495	0.443698
$610$	0	0
$611$	−64.7616	−2.61997
$612$	−1.50843	−0.0609747
$613$	11.3203	0.457224	0.228612	−	0.973518i	$-0.426581\pi$
$613$	11.3203	0.457224	0.228612	+	0.973518i	$0.426581\pi$
$614$	16.9006	0.682052
$615$	0	0
$616$	−58.7278	−2.36621
$617$	−9.71325	−0.391041	−0.195520	−	0.980700i	$-0.562640\pi$
$617$	−9.71325	−0.391041	−0.195520	+	0.980700i	$0.562640\pi$
$618$	−16.4802	−0.662930
$619$	20.4652	0.822567	0.411284	−	0.911507i	$-0.365081\pi$
$619$	20.4652	0.822567	0.411284	+	0.911507i	$0.365081\pi$
$620$	0	0
$621$	4.61860	0.185338
$622$	27.2450	1.09242
$623$	6.43526	0.257823
$624$	13.3662	0.535075
$625$	0	0
$626$	−28.4260	−1.13613
$627$	−29.0134	−1.15868
$628$	−0.994789	−0.0396964
$629$	1.26391	0.0503954
$630$	0	0
$631$	2.46405	0.0980924	0.0490462	−	0.998797i	$-0.484382\pi$
$631$	2.46405	0.0980924	0.0490462	+	0.998797i	$0.484382\pi$
$632$	14.4105	0.573218
$633$	−15.7531	−0.626128
$634$	−30.4889	−1.21087
$635$	0	0
$636$	9.98721	0.396019
$637$	−23.4234	−0.928070
$638$	34.4123	1.36240
$639$	−16.2062	−0.641106
$640$	0	0
$641$	31.7217	1.25293	0.626465	−	0.779449i	$-0.284501\pi$
$641$	31.7217	1.25293	0.626465	+	0.779449i	$0.284501\pi$
$642$	41.2323	1.62731
$643$	−11.5574	−0.455779	−0.227889	−	0.973687i	$-0.573182\pi$
$643$	−11.5574	−0.455779	−0.227889	+	0.973687i	$0.573182\pi$
$644$	56.6584	2.23266
$645$	0	0
$646$	−6.46883	−0.254513
$647$	6.06222	0.238330	0.119165	−	0.992874i	$-0.461978\pi$
$647$	6.06222	0.238330	0.119165	+	0.992874i	$0.461978\pi$
$648$	−4.05506	−0.159298
$649$	25.3486	0.995021
$650$	0	0
$651$	−29.1040	−1.14067
$652$	−38.2799	−1.49916
$653$	26.3569	1.03143	0.515713	−	0.856762i	$-0.327527\pi$
$653$	26.3569	1.03143	0.515713	+	0.856762i	$0.327527\pi$
$654$	−15.6227	−0.610896
$655$	0	0
$656$	6.60543	0.257899
$657$	−5.35799	−0.209035
$658$	87.5756	3.41405
$659$	16.2879	0.634487	0.317243	−	0.948344i	$-0.397243\pi$
$659$	16.2879	0.634487	0.317243	+	0.948344i	$0.397243\pi$
$660$	0	0
$661$	−20.4308	−0.794665	−0.397332	−	0.917675i	$-0.630064\pi$
$661$	−20.4308	−0.794665	−0.397332	+	0.917675i	$0.630064\pi$
$662$	−20.6740	−0.803519
$663$	−2.38785	−0.0927365
$664$	20.2328	0.785186
$665$	0	0
$666$	7.39817	0.286673
$667$	−15.2475	−0.590386
$668$	15.7895	0.610914
$669$	−2.27697	−0.0880326
$670$	0	0
$671$	−49.0653	−1.89415
$672$	8.82417	0.340400
$673$	−20.7479	−0.799772	−0.399886	−	0.916565i	$-0.630950\pi$
$673$	−20.7479	−0.799772	−0.399886	+	0.916565i	$0.630950\pi$
$674$	36.4199	1.40284
$675$	0	0
$676$	78.7126	3.02741
$677$	20.1892	0.775935	0.387967	−	0.921673i	$-0.373177\pi$
$677$	20.1892	0.775935	0.387967	+	0.921673i	$0.373177\pi$
$678$	−20.6968	−0.794855
$679$	19.8756	0.762757
$680$	0	0
$681$	−20.2674	−0.776650
$682$	−91.4682	−3.50250
$683$	−6.69431	−0.256151	−0.128075	−	0.991764i	$-0.540880\pi$
$683$	−6.69431	−0.256151	−0.128075	+	0.991764i	$0.540880\pi$
$684$	−24.5757	−0.939677
$685$	0	0
$686$	−23.7484	−0.906716
$687$	−19.6358	−0.749154
$688$	−3.04235	−0.115989
$689$	15.8098	0.602306
$690$	0	0
$691$	−7.86690	−0.299271	−0.149635	−	0.988741i	$-0.547810\pi$
$691$	−7.86690	−0.299271	−0.149635	+	0.988741i	$0.547810\pi$
$692$	86.9304	3.30460
$693$	14.4826	0.550148
$694$	52.1697	1.98034
$695$	0	0
$696$	13.3871	0.507436
$697$	−1.18005	−0.0446977
$698$	−17.4173	−0.659254
$699$	−17.1468	−0.648553
$700$	0	0
$701$	11.5944	0.437916	0.218958	−	0.975734i	$-0.429734\pi$
$701$	11.5944	0.437916	0.218958	+	0.975734i	$0.429734\pi$
$702$	−13.9771	−0.527530
$703$	20.5919	0.776640
$704$	47.6691	1.79660
$705$	0	0
$706$	72.8857	2.74309
$707$	−16.7885	−0.631398
$708$	21.4715	0.806948
$709$	37.6176	1.41276	0.706379	−	0.707834i	$-0.250327\pi$
$709$	37.6176	1.41276	0.706379	+	0.707834i	$0.250327\pi$
$710$	0	0
$711$	−3.55370	−0.133274
$712$	7.86785	0.294860
$713$	40.5280	1.51779
$714$	3.22904	0.120844
$715$	0	0
$716$	72.8260	2.72163
$717$	−21.7654	−0.812845
$718$	−7.32263	−0.273278
$719$	−21.0855	−0.786355	−0.393177	−	0.919463i	$-0.628624\pi$
$719$	−21.0855	−0.786355	−0.393177	+	0.919463i	$0.628624\pi$
$720$	0	0
$721$	22.8972	0.852737
$722$	−60.0353	−2.23428
$723$	−3.90067	−0.145068
$724$	−47.4248	−1.76253
$725$	0	0
$726$	19.2569	0.714690
$727$	26.1113	0.968416	0.484208	−	0.874953i	$-0.339108\pi$
$727$	26.1113	0.968416	0.484208	+	0.874953i	$0.339108\pi$
$728$	−78.7470	−2.91856
$729$	1.00000	0.0370370
$730$	0	0
$731$	0.543513	0.0201025
$732$	−41.5607	−1.53613
$733$	13.4461	0.496642	0.248321	−	0.968678i	$-0.420121\pi$
$733$	13.4461	0.496642	0.248321	+	0.968678i	$0.420121\pi$
$734$	75.4436	2.78468
$735$	0	0
$736$	−12.2879	−0.452937
$737$	−0.182733	−0.00673106
$738$	−6.90732	−0.254262
$739$	−53.9014	−1.98279	−0.991397	−	0.130887i	$-0.958218\pi$
$739$	−53.9014	−1.98279	−0.991397	+	0.130887i	$0.958218\pi$
$740$	0	0
$741$	−38.9035	−1.42916
$742$	−21.3793	−0.784857
$743$	4.33521	0.159043	0.0795216	−	0.996833i	$-0.474661\pi$
$743$	4.33521	0.159043	0.0795216	+	0.996833i	$0.474661\pi$
$744$	−35.5830	−1.30454
$745$	0	0
$746$	53.6888	1.96569
$747$	−4.98952	−0.182557
$748$	6.58664	0.240831
$749$	−57.2873	−2.09323
$750$	0	0
$751$	−2.87653	−0.104966	−0.0524831	−	0.998622i	$-0.516714\pi$
$751$	−2.87653	−0.104966	−0.0524831	+	0.998622i	$0.516714\pi$
$752$	25.2503	0.920785
$753$	21.8389	0.795854
$754$	46.1428	1.68042
$755$	0	0
$756$	12.2674	0.446162
$757$	−16.0480	−0.583275	−0.291637	−	0.956529i	$-0.594200\pi$
$757$	−16.0480	−0.583275	−0.291637	+	0.956529i	$0.594200\pi$
$758$	−72.0005	−2.61518
$759$	−20.1674	−0.732029
$760$	0	0
$761$	−43.5182	−1.57753	−0.788767	−	0.614692i	$-0.789280\pi$
$761$	−43.5182	−1.57753	−0.788767	+	0.614692i	$0.789280\pi$
$762$	7.74869	0.280706
$763$	21.7058	0.785804
$764$	−70.4907	−2.55026
$765$	0	0
$766$	−40.0391	−1.44667
$767$	33.9895	1.22729
$768$	27.6757	0.998659
$769$	−25.9575	−0.936052	−0.468026	−	0.883715i	$-0.655035\pi$
$769$	−25.9575	−0.936052	−0.468026	+	0.883715i	$0.655035\pi$
$770$	0	0
$771$	17.1453	0.617473
$772$	−62.8191	−2.26091
$773$	−52.9965	−1.90615	−0.953076	−	0.302731i	$-0.902102\pi$
$773$	−52.9965	−1.90615	−0.953076	+	0.302731i	$0.902102\pi$
$774$	3.18140	0.114353
$775$	0	0
$776$	24.3003	0.872329
$777$	−10.2789	−0.368752
$778$	−53.6724	−1.92425
$779$	−19.2257	−0.688833
$780$	0	0
$781$	70.7650	2.53217
$782$	−4.49652	−0.160795
$783$	−3.30132	−0.117980
$784$	9.13272	0.326169
$785$	0	0
$786$	−10.5082	−0.374816
$787$	−13.1832	−0.469929	−0.234964	−	0.972004i	$-0.575497\pi$
$787$	−13.1832	−0.469929	−0.234964	+	0.972004i	$0.575497\pi$
$788$	1.73639	0.0618562
$789$	17.6266	0.627523
$790$	0	0
$791$	28.7557	1.02243
$792$	17.7066	0.629178
$793$	−65.7908	−2.33630
$794$	−8.73233	−0.309899
$795$	0	0
$796$	25.9829	0.920939
$797$	15.6197	0.553280	0.276640	−	0.960974i	$-0.410779\pi$
$797$	15.6197	0.553280	0.276640	+	0.960974i	$0.410779\pi$
$798$	52.6084	1.86232
$799$	−4.51095	−0.159586
$800$	0	0
$801$	−1.94025	−0.0685555
$802$	60.5806	2.13918
$803$	23.3959	0.825625
$804$	−0.154784	−0.00545880
$805$	0	0
$806$	−122.648	−4.32009
$807$	−1.94772	−0.0685630
$808$	−20.5259	−0.722100
$809$	11.7683	0.413750	0.206875	−	0.978367i	$-0.433671\pi$
$809$	11.7683	0.413750	0.206875	+	0.978367i	$0.433671\pi$
$810$	0	0
$811$	−38.3050	−1.34507	−0.672536	−	0.740065i	$-0.734795\pi$
$811$	−38.3050	−1.34507	−0.672536	+	0.740065i	$0.734795\pi$
$812$	−40.4988	−1.42123
$813$	13.8707	0.486466
$814$	−32.3045	−1.13227
$815$	0	0
$816$	0.931016	0.0325921
$817$	8.85505	0.309799
$818$	66.3666	2.32045
$819$	19.4194	0.678569
$820$	0	0
$821$	22.4713	0.784254	0.392127	−	0.919911i	$-0.371739\pi$
$821$	22.4713	0.784254	0.392127	+	0.919911i	$0.371739\pi$
$822$	−2.54290	−0.0886938
$823$	19.8645	0.692434	0.346217	−	0.938155i	$-0.387466\pi$
$823$	19.8645	0.692434	0.346217	+	0.938155i	$0.387466\pi$
$824$	27.9945	0.975235
$825$	0	0
$826$	−45.9632	−1.59927
$827$	21.4039	0.744288	0.372144	−	0.928175i	$-0.378623\pi$
$827$	21.4039	0.744288	0.372144	+	0.928175i	$0.378623\pi$
$828$	−17.0827	−0.593666
$829$	−24.6676	−0.856743	−0.428371	−	0.903603i	$-0.640912\pi$
$829$	−24.6676	−0.856743	−0.428371	+	0.903603i	$0.640912\pi$
$830$	0	0
$831$	−26.4814	−0.918629
$832$	63.9185	2.21598
$833$	−1.63155	−0.0565299
$834$	−9.00654	−0.311871
$835$	0	0
$836$	107.311	3.71143
$837$	8.77495	0.303307
$838$	0.286026	0.00988060
$839$	−4.60054	−0.158828	−0.0794142	−	0.996842i	$-0.525305\pi$
$839$	−4.60054	−0.158828	−0.0794142	+	0.996842i	$0.525305\pi$
$840$	0	0
$841$	−18.1013	−0.624182
$842$	0.0939677	0.00323834
$843$	21.6050	0.744117
$844$	58.2655	2.00558
$845$	0	0
$846$	−26.4044	−0.907801
$847$	−26.7551	−0.919317
$848$	−6.16419	−0.211679
$849$	−2.05287	−0.0704542
$850$	0	0
$851$	14.3136	0.490663
$852$	59.9413	2.05356
$853$	−27.1689	−0.930245	−0.465122	−	0.885246i	$-0.653990\pi$
$853$	−27.1689	−0.930245	−0.465122	+	0.885246i	$0.653990\pi$
$854$	88.9674	3.04440
$855$	0	0
$856$	−70.0404	−2.39393
$857$	7.66692	0.261897	0.130949	−	0.991389i	$-0.458198\pi$
$857$	7.66692	0.261897	0.130949	+	0.991389i	$0.458198\pi$
$858$	61.0315	2.08358
$859$	9.09944	0.310469	0.155234	−	0.987878i	$-0.450387\pi$
$859$	9.09944	0.310469	0.155234	+	0.987878i	$0.450387\pi$
$860$	0	0
$861$	9.59688	0.327061
$862$	−39.1186	−1.33238
$863$	21.7471	0.740279	0.370140	−	0.928976i	$-0.379310\pi$
$863$	21.7471	0.740279	0.370140	+	0.928976i	$0.379310\pi$
$864$	−2.66052	−0.0905127
$865$	0	0
$866$	41.9216	1.42455
$867$	16.8337	0.571702
$868$	107.646	3.65375
$869$	15.5174	0.526392
$870$	0	0
$871$	−0.245023	−0.00830230
$872$	26.5379	0.898687
$873$	−5.99258	−0.202818
$874$	−73.2585	−2.47800
$875$	0	0
$876$	19.8175	0.669570
$877$	−20.9781	−0.708379	−0.354190	−	0.935174i	$-0.615243\pi$
$877$	−20.9781	−0.708379	−0.354190	+	0.935174i	$0.615243\pi$
$878$	74.3794	2.51018
$879$	11.9787	0.404032
$880$	0	0
$881$	40.6001	1.36785	0.683927	−	0.729551i	$-0.260271\pi$
$881$	40.6001	1.36785	0.683927	+	0.729551i	$0.260271\pi$
$882$	−9.55012	−0.321569
$883$	−44.2689	−1.48977	−0.744883	−	0.667195i	$-0.767495\pi$
$883$	−44.2689	−1.48977	−0.744883	+	0.667195i	$0.767495\pi$
$884$	8.83189	0.297049
$885$	0	0
$886$	31.4602	1.05693
$887$	21.2137	0.712285	0.356142	−	0.934432i	$-0.384092\pi$
$887$	21.2137	0.712285	0.356142	+	0.934432i	$0.384092\pi$
$888$	−12.5671	−0.421724
$889$	−10.7659	−0.361076
$890$	0	0
$891$	−4.36655	−0.146285
$892$	8.42177	0.281982
$893$	−73.4935	−2.45937
$894$	−18.8132	−0.629207
$895$	0	0
$896$	−68.7873	−2.29802
$897$	−27.0420	−0.902907
$898$	69.7343	2.32706
$899$	−28.9689	−0.966168
$900$	0	0
$901$	1.10123	0.0366872
$902$	30.1612	1.00426
$903$	−4.42016	−0.147094
$904$	35.1571	1.16931
$905$	0	0
$906$	17.8187	0.591988
$907$	−42.8598	−1.42314	−0.711568	−	0.702617i	$-0.752015\pi$
$907$	−42.8598	−1.42314	−0.711568	+	0.702617i	$0.752015\pi$
$908$	74.9627	2.48772
$909$	5.06181	0.167890
$910$	0	0
$911$	52.6870	1.74560	0.872800	−	0.488078i	$-0.162302\pi$
$911$	52.6870	1.74560	0.872800	+	0.488078i	$0.162302\pi$
$912$	15.1684	0.502274
$913$	21.7870	0.721045
$914$	−85.4617	−2.82682
$915$	0	0
$916$	72.6266	2.39965
$917$	14.5999	0.482131
$918$	−0.973567	−0.0321325
$919$	−17.5655	−0.579434	−0.289717	−	0.957112i	$-0.593561\pi$
$919$	−17.5655	−0.579434	−0.289717	+	0.957112i	$0.593561\pi$
$920$	0	0
$921$	7.07969	0.233284
$922$	−14.3545	−0.472741
$923$	94.8874	3.12326
$924$	−53.5664	−1.76221
$925$	0	0
$926$	98.3855	3.23315
$927$	−6.90359	−0.226744
$928$	8.78323	0.288324
$929$	−58.2546	−1.91127	−0.955636	−	0.294550i	$-0.904830\pi$
$929$	−58.2546	−1.91127	−0.955636	+	0.294550i	$0.904830\pi$
$930$	0	0
$931$	−26.5816	−0.871178
$932$	63.4206	2.07741
$933$	11.4130	0.373644
$934$	71.5352	2.34070
$935$	0	0
$936$	23.7425	0.776048
$937$	21.6766	0.708142	0.354071	−	0.935218i	$-0.384797\pi$
$937$	21.6766	0.708142	0.354071	+	0.935218i	$0.384797\pi$
$938$	0.331340	0.0108186
$939$	−11.9077	−0.388594
$940$	0	0
$941$	−41.9457	−1.36739	−0.683695	−	0.729768i	$-0.739628\pi$
$941$	−41.9457	−1.36739	−0.683695	+	0.729768i	$0.739628\pi$
$942$	−0.642054	−0.0209193
$943$	−13.3639	−0.435188
$944$	−13.2524	−0.431329
$945$	0	0
$946$	−13.8917	−0.451659
$947$	−40.0301	−1.30080	−0.650401	−	0.759591i	$-0.725399\pi$
$947$	−40.0301	−1.30080	−0.650401	+	0.759591i	$0.725399\pi$
$948$	13.1440	0.426897
$949$	31.3712	1.01835
$950$	0	0
$951$	−12.7719	−0.414156
$952$	−5.48510	−0.177773
$953$	−33.1969	−1.07535	−0.537677	−	0.843151i	$-0.680698\pi$
$953$	−33.1969	−1.07535	−0.537677	+	0.843151i	$0.680698\pi$
$954$	6.44592	0.208694
$955$	0	0
$956$	80.5033	2.60366
$957$	14.4154	0.465984
$958$	−19.9077	−0.643187
$959$	3.53305	0.114088
$960$	0	0
$961$	45.9997	1.48386
$962$	−43.3164	−1.39658
$963$	17.2723	0.556593
$964$	14.4273	0.464673
$965$	0	0
$966$	36.5683	1.17657
$967$	20.5477	0.660770	0.330385	−	0.943846i	$-0.392821\pi$
$967$	20.5477	0.660770	0.330385	+	0.943846i	$0.392821\pi$
$968$	−32.7112	−1.05138
$969$	−2.70981	−0.0870517
$970$	0	0
$971$	20.4201	0.655312	0.327656	−	0.944797i	$-0.393741\pi$
$971$	20.4201	0.655312	0.327656	+	0.944797i	$0.393741\pi$
$972$	−3.69868	−0.118635
$973$	12.5135	0.401164
$974$	11.7237	0.375653
$975$	0	0
$976$	25.6516	0.821088
$977$	−27.7767	−0.888655	−0.444327	−	0.895864i	$-0.646557\pi$
$977$	−27.7767	−0.888655	−0.444327	+	0.895864i	$0.646557\pi$
$978$	−24.7065	−0.790027
$979$	8.47221	0.270773
$980$	0	0
$981$	−6.54439	−0.208946
$982$	−10.3481	−0.330221
$983$	−15.7171	−0.501298	−0.250649	−	0.968078i	$-0.580644\pi$
$983$	−15.7171	−0.501298	−0.250649	+	0.968078i	$0.580644\pi$
$984$	11.7333	0.374044
$985$	0	0
$986$	3.21406	0.102357
$987$	36.6857	1.16772
$988$	143.891	4.57780
$989$	6.15519	0.195724
$990$	0	0
$991$	−6.18035	−0.196325	−0.0981627	−	0.995170i	$-0.531297\pi$
$991$	−6.18035	−0.196325	−0.0981627	+	0.995170i	$0.531297\pi$
$992$	−23.3459	−0.741233
$993$	−8.66041	−0.274830
$994$	−128.314	−4.06988
$995$	0	0
$996$	18.4546	0.584757
$997$	−60.9412	−1.93003	−0.965014	−	0.262200i	$-0.915552\pi$
$997$	−60.9412	−1.93003	−0.965014	+	0.262200i	$0.915552\pi$
$998$	−86.3692	−2.73397
$999$	3.09911	0.0980515

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1875.2.a.l.1.1	yes	6
3.2	odd	2		5625.2.a.o.1.6		6
5.2	odd	4		1875.2.b.e.1249.2		12
5.3	odd	4		1875.2.b.e.1249.11		12
5.4	even	2		1875.2.a.i.1.6	✓	6
15.14	odd	2		5625.2.a.r.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1875.2.a.i.1.6	✓	6	5.4	even	2
1875.2.a.l.1.1	yes	6	1.1	even	1	trivial
1875.2.b.e.1249.2		12	5.2	odd	4
1875.2.b.e.1249.11		12	5.3	odd	4
5625.2.a.o.1.6		6	3.2	odd	2
5625.2.a.r.1.1		6	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1875 = 3 \cdot 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1875.a (trivial)

\(f(q)\)	\(=\)	\(q-2.38719 q^{2} -1.00000 q^{3} +3.69868 q^{4} +2.38719 q^{6} -3.31671 q^{7} -4.05506 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.38719 q^{2} -1.00000 q^{3} +3.69868 q^{4} +2.38719 q^{6} -3.31671 q^{7} -4.05506 q^{8} +1.00000 q^{9} -4.36655 q^{11} -3.69868 q^{12} -5.85502 q^{13} +7.91762 q^{14} +2.28286 q^{16} -0.407830 q^{17} -2.38719 q^{18} -6.64447 q^{19} +3.31671 q^{21} +10.4238 q^{22} -4.61860 q^{23} +4.05506 q^{24} +13.9771 q^{26} -1.00000 q^{27} -12.2674 q^{28} +3.30132 q^{29} -8.77495 q^{31} +2.66052 q^{32} +4.36655 q^{33} +0.973567 q^{34} +3.69868 q^{36} -3.09911 q^{37} +15.8616 q^{38} +5.85502 q^{39} +2.89349 q^{41} -7.91762 q^{42} -1.33270 q^{43} -16.1505 q^{44} +11.0255 q^{46} +11.0609 q^{47} -2.28286 q^{48} +4.00057 q^{49} +0.407830 q^{51} -21.6558 q^{52} -2.70021 q^{53} +2.38719 q^{54} +13.4495 q^{56} +6.64447 q^{57} -7.88089 q^{58} -5.80518 q^{59} +11.2366 q^{61} +20.9475 q^{62} -3.31671 q^{63} -10.9169 q^{64} -10.4238 q^{66} +0.0418484 q^{67} -1.50843 q^{68} +4.61860 q^{69} -16.2062 q^{71} -4.05506 q^{72} -5.35799 q^{73} +7.39817 q^{74} -24.5757 q^{76} +14.4826 q^{77} -13.9771 q^{78} -3.55370 q^{79} +1.00000 q^{81} -6.90732 q^{82} -4.98952 q^{83} +12.2674 q^{84} +3.18140 q^{86} -3.30132 q^{87} +17.7066 q^{88} -1.94025 q^{89} +19.4194 q^{91} -17.0827 q^{92} +8.77495 q^{93} -26.4044 q^{94} -2.66052 q^{96} -5.99258 q^{97} -9.55012 q^{98} -4.36655 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} - 6 q^{3} + 11 q^{4} - q^{6} - 2 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q + q^2 - 6 * q^3 + 11 * q^4 - q^6 - 2 * q^7 + 6 * q^8 + 6 * q^9	\( 6 q + q^{2} - 6 q^{3} + 11 q^{4} - q^{6} - 2 q^{7} + 6 q^{8} + 6 q^{9} - 11 q^{12} - 4 q^{14} + 17 q^{16} + 2 q^{17} + q^{18} - 2 q^{19} + 2 q^{21} + 9 q^{22} - q^{23} - 6 q^{24} + 37 q^{26} - 6 q^{27} - 44 q^{28} + 31 q^{29} - 2 q^{31} + 33 q^{32} + 37 q^{34} + 11 q^{36} - 22 q^{37} + 27 q^{38} + 33 q^{41} + 4 q^{42} - 3 q^{43} - 11 q^{44} - 12 q^{46} - 6 q^{47} - 17 q^{48} + 4 q^{49} - 2 q^{51} - 33 q^{52} + 14 q^{53} - q^{54} - 30 q^{56} + 2 q^{57} - q^{58} - 8 q^{59} + 34 q^{61} + 31 q^{62} - 2 q^{63} + 12 q^{64} - 9 q^{66} + 2 q^{67} + 27 q^{68} + q^{69} - 3 q^{71} + 6 q^{72} - 36 q^{73} + 36 q^{74} + 27 q^{76} + 16 q^{77} - 37 q^{78} + 25 q^{79} + 6 q^{81} + 36 q^{82} - 12 q^{83} + 44 q^{84} - 30 q^{86} - 31 q^{87} + 56 q^{88} + 18 q^{89} + 28 q^{91} + 3 q^{92} + 2 q^{93} - 50 q^{94} - 33 q^{96} + 7 q^{97} + 15 q^{98}+O(q^{100}) \) 6 * q + q^2 - 6 * q^3 + 11 * q^4 - q^6 - 2 * q^7 + 6 * q^8 + 6 * q^9 - 11 * q^12 - 4 * q^14 + 17 * q^16 + 2 * q^17 + q^18 - 2 * q^19 + 2 * q^21 + 9 * q^22 - q^23 - 6 * q^24 + 37 * q^26 - 6 * q^27 - 44 * q^28 + 31 * q^29 - 2 * q^31 + 33 * q^32 + 37 * q^34 + 11 * q^36 - 22 * q^37 + 27 * q^38 + 33 * q^41 + 4 * q^42 - 3 * q^43 - 11 * q^44 - 12 * q^46 - 6 * q^47 - 17 * q^48 + 4 * q^49 - 2 * q^51 - 33 * q^52 + 14 * q^53 - q^54 - 30 * q^56 + 2 * q^57 - q^58 - 8 * q^59 + 34 * q^61 + 31 * q^62 - 2 * q^63 + 12 * q^64 - 9 * q^66 + 2 * q^67 + 27 * q^68 + q^69 - 3 * q^71 + 6 * q^72 - 36 * q^73 + 36 * q^74 + 27 * q^76 + 16 * q^77 - 37 * q^78 + 25 * q^79 + 6 * q^81 + 36 * q^82 - 12 * q^83 + 44 * q^84 - 30 * q^86 - 31 * q^87 + 56 * q^88 + 18 * q^89 + 28 * q^91 + 3 * q^92 + 2 * q^93 - 50 * q^94 - 33 * q^96 + 7 * q^97 + 15 * q^98

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