LMFDB - Embedded newform 2325.2.a.ba.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2325,2,Mod(1,2325)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2325, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("2325.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2325 = 3 \cdot 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2325.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:	$18.5652184699$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.136751504.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 9x^{4} + 7x^{3} + 20x^{2} - 8x - 12 $ x^6 - x^5 - 9x^4 + 7x^3 + 20x^2 - 8x - 12
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$2.54563$ of defining polynomial
Character	$\chi$	$=$	2325.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.54563 q^{2} -1.00000 q^{3} +4.48022 q^{4} -2.54563 q^{6} -4.63170 q^{7} +6.31371 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.54563 q^{2} -1.00000 q^{3} +4.48022 q^{4} -2.54563 q^{6} -4.63170 q^{7} +6.31371 q^{8} +1.00000 q^{9} +4.61660 q^{11} -4.48022 q^{12} -0.863614 q^{13} -11.7906 q^{14} +7.11191 q^{16} +6.02584 q^{17} +2.54563 q^{18} +7.67866 q^{19} +4.63170 q^{21} +11.7521 q^{22} -3.18068 q^{23} -6.31371 q^{24} -2.19844 q^{26} -1.00000 q^{27} -20.7510 q^{28} +0.501335 q^{29} +1.00000 q^{31} +5.47686 q^{32} -4.61660 q^{33} +15.3396 q^{34} +4.48022 q^{36} +3.39079 q^{37} +19.5470 q^{38} +0.863614 q^{39} +4.36716 q^{41} +11.7906 q^{42} +0.151479 q^{43} +20.6834 q^{44} -8.09682 q^{46} +6.57483 q^{47} -7.11191 q^{48} +14.4526 q^{49} -6.02584 q^{51} -3.86918 q^{52} -12.0784 q^{53} -2.54563 q^{54} -29.2432 q^{56} -7.67866 q^{57} +1.27621 q^{58} +5.62613 q^{59} -4.69932 q^{61} +2.54563 q^{62} -4.63170 q^{63} -0.281777 q^{64} -11.7521 q^{66} +13.5319 q^{67} +26.9971 q^{68} +3.18068 q^{69} -10.3070 q^{71} +6.31371 q^{72} +6.13524 q^{73} +8.63170 q^{74} +34.4021 q^{76} -21.3827 q^{77} +2.19844 q^{78} +15.0668 q^{79} +1.00000 q^{81} +11.1172 q^{82} +6.90791 q^{83} +20.7510 q^{84} +0.385609 q^{86} -0.501335 q^{87} +29.1479 q^{88} -10.9600 q^{89} +4.00000 q^{91} -14.2501 q^{92} -1.00000 q^{93} +16.7371 q^{94} -5.47686 q^{96} -10.5988 q^{97} +36.7910 q^{98} +4.61660 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} - 6 q^{3} + 7 q^{4} - q^{6} - 6 q^{7} + 3 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q + q^2 - 6 * q^3 + 7 * q^4 - q^6 - 6 * q^7 + 3 * q^8 + 6 * q^9	$ 6 q + q^{2} - 6 q^{3} + 7 q^{4} - q^{6} - 6 q^{7} + 3 q^{8} + 6 q^{9} + 9 q^{11} - 7 q^{12} - 4 q^{13} + q^{16} + 2 q^{17} + q^{18} + 17 q^{19} + 6 q^{21} + 2 q^{22} + q^{23} - 3 q^{24} - 4 q^{26} - 6 q^{27} - 14 q^{28} + 10 q^{29} + 6 q^{31} - 3 q^{32} - 9 q^{33} + 23 q^{34} + 7 q^{36} - 8 q^{37} + 26 q^{38} + 4 q^{39} + 6 q^{41} - q^{43} + 34 q^{44} - 10 q^{46} + 7 q^{47} - q^{48} + 18 q^{49} - 2 q^{51} - 12 q^{52} - q^{53} - q^{54} - 36 q^{56} - 17 q^{57} + 7 q^{58} + 22 q^{59} + 14 q^{61} + q^{62} - 6 q^{63} + 9 q^{64} - 2 q^{66} - 7 q^{67} + 37 q^{68} - q^{69} + 5 q^{71} + 3 q^{72} - 4 q^{73} + 30 q^{74} + 18 q^{76} + 4 q^{77} + 4 q^{78} + 19 q^{79} + 6 q^{81} - 16 q^{82} + 19 q^{83} + 14 q^{84} - 5 q^{86} - 10 q^{87} + 46 q^{88} + 14 q^{89} + 24 q^{91} - 8 q^{92} - 6 q^{93} + 35 q^{94} + 3 q^{96} - 34 q^{97} + 61 q^{98} + 9 q^{99}+O(q^{100}) $ 6 * q + q^2 - 6 * q^3 + 7 * q^4 - q^6 - 6 * q^7 + 3 * q^8 + 6 * q^9 + 9 * q^11 - 7 * q^12 - 4 * q^13 + q^16 + 2 * q^17 + q^18 + 17 * q^19 + 6 * q^21 + 2 * q^22 + q^23 - 3 * q^24 - 4 * q^26 - 6 * q^27 - 14 * q^28 + 10 * q^29 + 6 * q^31 - 3 * q^32 - 9 * q^33 + 23 * q^34 + 7 * q^36 - 8 * q^37 + 26 * q^38 + 4 * q^39 + 6 * q^41 - q^43 + 34 * q^44 - 10 * q^46 + 7 * q^47 - q^48 + 18 * q^49 - 2 * q^51 - 12 * q^52 - q^53 - q^54 - 36 * q^56 - 17 * q^57 + 7 * q^58 + 22 * q^59 + 14 * q^61 + q^62 - 6 * q^63 + 9 * q^64 - 2 * q^66 - 7 * q^67 + 37 * q^68 - q^69 + 5 * q^71 + 3 * q^72 - 4 * q^73 + 30 * q^74 + 18 * q^76 + 4 * q^77 + 4 * q^78 + 19 * q^79 + 6 * q^81 - 16 * q^82 + 19 * q^83 + 14 * q^84 - 5 * q^86 - 10 * q^87 + 46 * q^88 + 14 * q^89 + 24 * q^91 - 8 * q^92 - 6 * q^93 + 35 * q^94 + 3 * q^96 - 34 * q^97 + 61 * q^98 + 9 * 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 $

$2$	2.54563	1.80003	0.900015	−	0.435859i	$-0.143555\pi$
$2$	2.54563	1.80003	0.900015	+	0.435859i	$0.143555\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.48022	2.24011
$5$	0	0
$5$	0	0
$6$	−2.54563	−1.03925
$7$	−4.63170	−1.75062	−0.875308	−	0.483565i	$-0.839342\pi$
$7$	−4.63170	−1.75062	−0.875308	+	0.483565i	$0.839342\pi$
$8$	6.31371	2.23223
$9$	1.00000	0.333333
$10$	0	0
$11$	4.61660	1.39196	0.695979	−	0.718062i	$-0.254971\pi$
$11$	4.61660	1.39196	0.695979	+	0.718062i	$0.254971\pi$
$12$	−4.48022	−1.29333
$13$	−0.863614	−0.239524	−0.119762	−	0.992803i	$-0.538213\pi$
$13$	−0.863614	−0.239524	−0.119762	+	0.992803i	$0.538213\pi$
$14$	−11.7906	−3.15116
$15$	0	0
$16$	7.11191	1.77798
$17$	6.02584	1.46148	0.730741	−	0.682655i	$-0.239175\pi$
$17$	6.02584	1.46148	0.730741	+	0.682655i	$0.239175\pi$
$18$	2.54563	0.600010
$19$	7.67866	1.76160	0.880802	−	0.473484i	$-0.157004\pi$
$19$	7.67866	1.76160	0.880802	+	0.473484i	$0.157004\pi$
$20$	0	0
$21$	4.63170	1.01072
$22$	11.7521	2.50557
$23$	−3.18068	−0.663217	−0.331609	−	0.943417i	$-0.607591\pi$
$23$	−3.18068	−0.663217	−0.331609	+	0.943417i	$0.607591\pi$
$24$	−6.31371	−1.28878
$25$	0	0
$26$	−2.19844	−0.431150
$27$	−1.00000	−0.192450
$28$	−20.7510	−3.92157
$29$	0.501335	0.0930955	0.0465477	−	0.998916i	$-0.485178\pi$
$29$	0.501335	0.0930955	0.0465477	+	0.998916i	$0.485178\pi$
$30$	0	0
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	5.47686	0.968182
$33$	−4.61660	−0.803647
$34$	15.3396	2.63071
$35$	0	0
$36$	4.48022	0.746703
$37$	3.39079	0.557443	0.278722	−	0.960372i	$-0.410089\pi$
$37$	3.39079	0.557443	0.278722	+	0.960372i	$0.410089\pi$
$38$	19.5470	3.17094
$39$	0.863614	0.138289
$40$	0	0
$41$	4.36716	0.682036	0.341018	−	0.940057i	$-0.389228\pi$
$41$	4.36716	0.682036	0.341018	+	0.940057i	$0.389228\pi$
$42$	11.7906	1.81932
$43$	0.151479	0.0231003	0.0115501	−	0.999933i	$-0.496323\pi$
$43$	0.151479	0.0231003	0.0115501	+	0.999933i	$0.496323\pi$
$44$	20.6834	3.11814
$45$	0	0
$46$	−8.09682	−1.19381
$47$	6.57483	0.959037	0.479519	−	0.877532i	$-0.340811\pi$
$47$	6.57483	0.959037	0.479519	+	0.877532i	$0.340811\pi$
$48$	−7.11191	−1.02652
$49$	14.4526	2.06466
$50$	0	0
$51$	−6.02584	−0.843787
$52$	−3.86918	−0.536559
$53$	−12.0784	−1.65910	−0.829550	−	0.558432i	$-0.811403\pi$
$53$	−12.0784	−1.65910	−0.829550	+	0.558432i	$0.811403\pi$
$54$	−2.54563	−0.346416
$55$	0	0
$56$	−29.2432	−3.90778
$57$	−7.67866	−1.01706
$58$	1.27621	0.167575
$59$	5.62613	0.732460	0.366230	−	0.930524i	$-0.380648\pi$
$59$	5.62613	0.732460	0.366230	+	0.930524i	$0.380648\pi$
$60$	0	0
$61$	−4.69932	−0.601686	−0.300843	−	0.953674i	$-0.597268\pi$
$61$	−4.69932	−0.601686	−0.300843	+	0.953674i	$0.597268\pi$
$62$	2.54563	0.323295
$63$	−4.63170	−0.583539
$64$	−0.281777	−0.0352221
$65$	0	0
$66$	−11.7521	−1.44659
$67$	13.5319	1.65319	0.826593	−	0.562801i	$-0.190276\pi$
$67$	13.5319	1.65319	0.826593	+	0.562801i	$0.190276\pi$
$68$	26.9971	3.27388
$69$	3.18068	0.382909
$70$	0	0
$71$	−10.3070	−1.22322	−0.611608	−	0.791161i	$-0.709477\pi$
$71$	−10.3070	−1.22322	−0.611608	+	0.791161i	$0.709477\pi$
$72$	6.31371	0.744078
$73$	6.13524	0.718076	0.359038	−	0.933323i	$-0.383105\pi$
$73$	6.13524	0.718076	0.359038	+	0.933323i	$0.383105\pi$
$74$	8.63170	1.00341
$75$	0	0
$76$	34.4021	3.94619
$77$	−21.3827	−2.43679
$78$	2.19844	0.248924
$79$	15.0668	1.69515	0.847573	−	0.530679i	$-0.178063\pi$
$79$	15.0668	1.69515	0.847573	+	0.530679i	$0.178063\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	11.1172	1.22769
$83$	6.90791	0.758241	0.379121	−	0.925347i	$-0.376227\pi$
$83$	6.90791	0.758241	0.379121	+	0.925347i	$0.376227\pi$
$84$	20.7510	2.26412
$85$	0	0
$86$	0.385609	0.0415812
$87$	−0.501335	−0.0537487
$88$	29.1479	3.10718
$89$	−10.9600	−1.16176	−0.580878	−	0.813991i	$-0.697291\pi$
$89$	−10.9600	−1.16176	−0.580878	+	0.813991i	$0.697291\pi$
$90$	0	0
$91$	4.00000	0.419314
$92$	−14.2501	−1.48568
$93$	−1.00000	−0.103695
$94$	16.7371	1.72630
$95$	0	0
$96$	−5.47686	−0.558980
$97$	−10.5988	−1.07615	−0.538075	−	0.842897i	$-0.680848\pi$
$97$	−10.5988	−1.07615	−0.538075	+	0.842897i	$0.680848\pi$
$98$	36.7910	3.71645
$99$	4.61660	0.463986
$100$	0	0
$101$	1.27010	0.126380	0.0631899	−	0.998002i	$-0.479873\pi$
$101$	1.27010	0.126380	0.0631899	+	0.998002i	$0.479873\pi$
$102$	−15.3396	−1.51884
$103$	−4.97263	−0.489968	−0.244984	−	0.969527i	$-0.578783\pi$
$103$	−4.97263	−0.489968	−0.244984	+	0.969527i	$0.578783\pi$
$104$	−5.45261	−0.534672
$105$	0	0
$106$	−30.7472	−2.98643
$107$	10.4198	1.00732	0.503658	−	0.863903i	$-0.331987\pi$
$107$	10.4198	1.00732	0.503658	+	0.863903i	$0.331987\pi$
$108$	−4.48022	−0.431109
$109$	−17.1076	−1.63861	−0.819307	−	0.573355i	$-0.805642\pi$
$109$	−17.1076	−1.63861	−0.819307	+	0.573355i	$0.805642\pi$
$110$	0	0
$111$	−3.39079	−0.321840
$112$	−32.9402	−3.11256
$113$	−16.4782	−1.55014	−0.775071	−	0.631874i	$-0.782286\pi$
$113$	−16.4782	−1.55014	−0.775071	+	0.631874i	$0.782286\pi$
$114$	−19.5470	−1.83074
$115$	0	0
$116$	2.24609	0.208544
$117$	−0.863614	−0.0798412
$118$	14.3220	1.31845
$119$	−27.9099	−2.55849
$120$	0	0
$121$	10.3130	0.937548
$122$	−11.9627	−1.08305
$123$	−4.36716	−0.393774
$124$	4.48022	0.402335
$125$	0	0
$126$	−11.7906	−1.05039
$127$	10.1682	0.902279	0.451139	−	0.892454i	$-0.351018\pi$
$127$	10.1682	0.902279	0.451139	+	0.892454i	$0.351018\pi$
$128$	−11.6710	−1.03158
$129$	−0.151479	−0.0133370
$130$	0	0
$131$	−20.6976	−1.80835	−0.904177	−	0.427158i	$-0.859515\pi$
$131$	−20.6976	−1.80835	−0.904177	+	0.427158i	$0.859515\pi$
$132$	−20.6834	−1.80026
$133$	−35.5652	−3.08389
$134$	34.4472	2.97578
$135$	0	0
$136$	38.0454	3.26237
$137$	3.80162	0.324795	0.162397	−	0.986725i	$-0.448077\pi$
$137$	3.80162	0.324795	0.162397	+	0.986725i	$0.448077\pi$
$138$	8.09682	0.689247
$139$	0.742322	0.0629630	0.0314815	−	0.999504i	$-0.489977\pi$
$139$	0.742322	0.0629630	0.0314815	+	0.999504i	$0.489977\pi$
$140$	0	0
$141$	−6.57483	−0.553700
$142$	−26.2378	−2.20183
$143$	−3.98697	−0.333407
$144$	7.11191	0.592659
$145$	0	0
$146$	15.6180	1.29256
$147$	−14.4526	−1.19203
$148$	15.1915	1.24873
$149$	−11.4886	−0.941183	−0.470591	−	0.882351i	$-0.655959\pi$
$149$	−11.4886	−0.941183	−0.470591	+	0.882351i	$0.655959\pi$
$150$	0	0
$151$	−17.5667	−1.42956	−0.714778	−	0.699352i	$-0.753472\pi$
$151$	−17.5667	−1.42956	−0.714778	+	0.699352i	$0.753472\pi$
$152$	48.4808	3.93231
$153$	6.02584	0.487161
$154$	−54.4324	−4.38629
$155$	0	0
$156$	3.86918	0.309782
$157$	6.21484	0.495998	0.247999	−	0.968760i	$-0.420227\pi$
$157$	6.21484	0.495998	0.247999	+	0.968760i	$0.420227\pi$
$158$	38.3544	3.05131
$159$	12.0784	0.957882
$160$	0	0
$161$	14.7319	1.16104
$162$	2.54563	0.200003
$163$	3.73834	0.292809	0.146405	−	0.989225i	$-0.453230\pi$
$163$	3.73834	0.292809	0.146405	+	0.989225i	$0.453230\pi$
$164$	19.5658	1.52783
$165$	0	0
$166$	17.5850	1.36486
$167$	9.30511	0.720051	0.360025	−	0.932943i	$-0.382768\pi$
$167$	9.30511	0.720051	0.360025	+	0.932943i	$0.382768\pi$
$168$	29.2432	2.25616
$169$	−12.2542	−0.942628
$170$	0	0
$171$	7.67866	0.587202
$172$	0.678658	0.0517472
$173$	4.22469	0.321197	0.160599	−	0.987020i	$-0.448658\pi$
$173$	4.22469	0.321197	0.160599	+	0.987020i	$0.448658\pi$
$174$	−1.27621	−0.0967493
$175$	0	0
$176$	32.8329	2.47487
$177$	−5.62613	−0.422886
$178$	−27.9000	−2.09119
$179$	3.91402	0.292547	0.146274	−	0.989244i	$-0.453272\pi$
$179$	3.91402	0.292547	0.146274	+	0.989244i	$0.453272\pi$
$180$	0	0
$181$	4.85196	0.360643	0.180322	−	0.983608i	$-0.442286\pi$
$181$	4.85196	0.360643	0.180322	+	0.983608i	$0.442286\pi$
$182$	10.1825	0.754778
$183$	4.69932	0.347384
$184$	−20.0819	−1.48046
$185$	0	0
$186$	−2.54563	−0.186654
$187$	27.8189	2.03432
$188$	29.4567	2.14835
$189$	4.63170	0.336906
$190$	0	0
$191$	−5.89748	−0.426727	−0.213363	−	0.976973i	$-0.568442\pi$
$191$	−5.89748	−0.426727	−0.213363	+	0.976973i	$0.568442\pi$
$192$	0.281777	0.0203355
$193$	−20.1364	−1.44945	−0.724724	−	0.689040i	$-0.758033\pi$
$193$	−20.1364	−1.44945	−0.724724	+	0.689040i	$0.758033\pi$
$194$	−26.9807	−1.93710
$195$	0	0
$196$	64.7508	4.62506
$197$	−12.6265	−0.899602	−0.449801	−	0.893129i	$-0.648505\pi$
$197$	−12.6265	−0.899602	−0.449801	+	0.893129i	$0.648505\pi$
$198$	11.7521	0.835189
$199$	−19.5796	−1.38796	−0.693981	−	0.719993i	$-0.744145\pi$
$199$	−19.5796	−1.38796	−0.693981	+	0.719993i	$0.744145\pi$
$200$	0	0
$201$	−13.5319	−0.954467
$202$	3.23321	0.227488
$203$	−2.32203	−0.162975
$204$	−26.9971	−1.89017
$205$	0	0
$206$	−12.6585	−0.881957
$207$	−3.18068	−0.221072
$208$	−6.14195	−0.425868
$209$	35.4493	2.45208
$210$	0	0
$211$	−16.6440	−1.14582	−0.572911	−	0.819617i	$-0.694186\pi$
$211$	−16.6440	−1.14582	−0.572911	+	0.819617i	$0.694186\pi$
$212$	−54.1140	−3.71657
$213$	10.3070	0.706224
$214$	26.5248	1.81320
$215$	0	0
$216$	−6.31371	−0.429593
$217$	−4.63170	−0.314420
$218$	−43.5497	−2.94956
$219$	−6.13524	−0.414581
$220$	0	0
$221$	−5.20401	−0.350059
$222$	−8.63170	−0.579322
$223$	−7.75826	−0.519531	−0.259766	−	0.965672i	$-0.583645\pi$
$223$	−7.75826	−0.519531	−0.259766	+	0.965672i	$0.583645\pi$
$224$	−25.3672	−1.69492
$225$	0	0
$226$	−41.9474	−2.79030
$227$	−29.7695	−1.97587	−0.987934	−	0.154874i	$-0.950503\pi$
$227$	−29.7695	−1.97587	−0.987934	+	0.154874i	$0.950503\pi$
$228$	−34.4021	−2.27833
$229$	7.24832	0.478983	0.239491	−	0.970899i	$-0.423019\pi$
$229$	7.24832	0.478983	0.239491	+	0.970899i	$0.423019\pi$
$230$	0	0
$231$	21.3827	1.40688
$232$	3.16528	0.207811
$233$	7.06067	0.462560	0.231280	−	0.972887i	$-0.425709\pi$
$233$	7.06067	0.462560	0.231280	+	0.972887i	$0.425709\pi$
$234$	−2.19844	−0.143717
$235$	0	0
$236$	25.2063	1.64079
$237$	−15.0668	−0.978693
$238$	−71.0482	−4.60537
$239$	27.2583	1.76319	0.881596	−	0.472005i	$-0.156470\pi$
$239$	27.2583	1.76319	0.881596	+	0.472005i	$0.156470\pi$
$240$	0	0
$241$	18.8981	1.21734	0.608668	−	0.793425i	$-0.291704\pi$
$241$	18.8981	1.21734	0.608668	+	0.793425i	$0.291704\pi$
$242$	26.2531	1.68761
$243$	−1.00000	−0.0641500
$244$	−21.0540	−1.34784
$245$	0	0
$246$	−11.1172	−0.708804
$247$	−6.63140	−0.421946
$248$	6.31371	0.400921
$249$	−6.90791	−0.437771
$250$	0	0
$251$	21.6447	1.36620	0.683099	−	0.730325i	$-0.260632\pi$
$251$	21.6447	1.36620	0.683099	+	0.730325i	$0.260632\pi$
$252$	−20.7510	−1.30719
$253$	−14.6839	−0.923171
$254$	25.8844	1.62413
$255$	0	0
$256$	−29.1465	−1.82166
$257$	17.0678	1.06466	0.532332	−	0.846536i	$-0.321316\pi$
$257$	17.0678	1.06466	0.532332	+	0.846536i	$0.321316\pi$
$258$	−0.385609	−0.0240069
$259$	−15.7051	−0.975869
$260$	0	0
$261$	0.501335	0.0310318
$262$	−52.6883	−3.25509
$263$	0.0768437	0.00473839	0.00236919	−	0.999997i	$-0.499246\pi$
$263$	0.0768437	0.00473839	0.00236919	+	0.999997i	$0.499246\pi$
$264$	−29.1479	−1.79393
$265$	0	0
$266$	−90.5358	−5.55110
$267$	10.9600	0.670740
$268$	60.6259	3.70332
$269$	24.2279	1.47720	0.738600	−	0.674144i	$-0.235487\pi$
$269$	24.2279	1.47720	0.738600	+	0.674144i	$0.235487\pi$
$270$	0	0
$271$	19.4821	1.18345	0.591726	−	0.806139i	$-0.298447\pi$
$271$	19.4821	1.18345	0.591726	+	0.806139i	$0.298447\pi$
$272$	42.8553	2.59848
$273$	−4.00000	−0.242091
$274$	9.67751	0.584640
$275$	0	0
$276$	14.2501	0.857757
$277$	−18.1938	−1.09316	−0.546579	−	0.837408i	$-0.684070\pi$
$277$	−18.1938	−1.09316	−0.546579	+	0.837408i	$0.684070\pi$
$278$	1.88968	0.113335
$279$	1.00000	0.0598684
$280$	0	0
$281$	−7.02606	−0.419140	−0.209570	−	0.977794i	$-0.567206\pi$
$281$	−7.02606	−0.419140	−0.209570	+	0.977794i	$0.567206\pi$
$282$	−16.7371	−0.996677
$283$	−10.9775	−0.652544	−0.326272	−	0.945276i	$-0.605793\pi$
$283$	−10.9775	−0.652544	−0.326272	+	0.945276i	$0.605793\pi$
$284$	−46.1776	−2.74014
$285$	0	0
$286$	−10.1493	−0.600142
$287$	−20.2274	−1.19398
$288$	5.47686	0.322727
$289$	19.3108	1.13593
$290$	0	0
$291$	10.5988	0.621315
$292$	27.4872	1.60857
$293$	−11.9938	−0.700683	−0.350341	−	0.936622i	$-0.613934\pi$
$293$	−11.9938	−0.700683	−0.350341	+	0.936622i	$0.613934\pi$
$294$	−36.7910	−2.14569
$295$	0	0
$296$	21.4085	1.24434
$297$	−4.61660	−0.267882
$298$	−29.2457	−1.69416
$299$	2.74688	0.158856
$300$	0	0
$301$	−0.701604	−0.0404398
$302$	−44.7182	−2.57324
$303$	−1.27010	−0.0729655
$304$	54.6100	3.13210
$305$	0	0
$306$	15.3396	0.876904
$307$	−6.17862	−0.352633	−0.176316	−	0.984334i	$-0.556418\pi$
$307$	−6.17862	−0.352633	−0.176316	+	0.984334i	$0.556418\pi$
$308$	−95.7992	−5.45866
$309$	4.97263	0.282883
$310$	0	0
$311$	6.71093	0.380542	0.190271	−	0.981732i	$-0.439063\pi$
$311$	6.71093	0.380542	0.190271	+	0.981732i	$0.439063\pi$
$312$	5.45261	0.308693
$313$	16.0245	0.905760	0.452880	−	0.891572i	$-0.350397\pi$
$313$	16.0245	0.905760	0.452880	+	0.891572i	$0.350397\pi$
$314$	15.8207	0.892812
$315$	0	0
$316$	67.5025	3.79731
$317$	13.1340	0.737676	0.368838	−	0.929494i	$-0.379756\pi$
$317$	13.1340	0.737676	0.368838	+	0.929494i	$0.379756\pi$
$318$	30.7472	1.72422
$319$	2.31446	0.129585
$320$	0	0
$321$	−10.4198	−0.581574
$322$	37.5020	2.08991
$323$	46.2704	2.57455
$324$	4.48022	0.248901
$325$	0	0
$326$	9.51642	0.527066
$327$	17.1076	0.946054
$328$	27.5730	1.52246
$329$	−30.4526	−1.67891
$330$	0	0
$331$	−4.17427	−0.229439	−0.114719	−	0.993398i	$-0.536597\pi$
$331$	−4.17427	−0.229439	−0.114719	+	0.993398i	$0.536597\pi$
$332$	30.9489	1.69854
$333$	3.39079	0.185814
$334$	23.6873	1.29611
$335$	0	0
$336$	32.9402	1.79704
$337$	−17.5562	−0.956348	−0.478174	−	0.878265i	$-0.658701\pi$
$337$	−17.5562	−0.956348	−0.478174	+	0.878265i	$0.658701\pi$
$338$	−31.1945	−1.69676
$339$	16.4782	0.894975
$340$	0	0
$341$	4.61660	0.250003
$342$	19.5470	1.05698
$343$	−34.5182	−1.86381
$344$	0.956393	0.0515653
$345$	0	0
$346$	10.7545	0.578164
$347$	−15.1216	−0.811769	−0.405885	−	0.913924i	$-0.633037\pi$
$347$	−15.1216	−0.811769	−0.405885	+	0.913924i	$0.633037\pi$
$348$	−2.24609	−0.120403
$349$	−13.7286	−0.734876	−0.367438	−	0.930048i	$-0.619765\pi$
$349$	−13.7286	−0.734876	−0.367438	+	0.930048i	$0.619765\pi$
$350$	0	0
$351$	0.863614	0.0460963
$352$	25.2845	1.34767
$353$	−13.9475	−0.742350	−0.371175	−	0.928563i	$-0.621045\pi$
$353$	−13.9475	−0.742350	−0.371175	+	0.928563i	$0.621045\pi$
$354$	−14.3220	−0.761207
$355$	0	0
$356$	−49.1031	−2.60246
$357$	27.9099	1.47715
$358$	9.96363	0.526594
$359$	5.03157	0.265556	0.132778	−	0.991146i	$-0.457610\pi$
$359$	5.03157	0.265556	0.132778	+	0.991146i	$0.457610\pi$
$360$	0	0
$361$	39.9618	2.10325
$362$	12.3513	0.649169
$363$	−10.3130	−0.541293
$364$	17.9209	0.939309
$365$	0	0
$366$	11.9627	0.625301
$367$	18.9559	0.989487	0.494744	−	0.869039i	$-0.335262\pi$
$367$	18.9559	0.989487	0.494744	+	0.869039i	$0.335262\pi$
$368$	−22.6207	−1.17919
$369$	4.36716	0.227345
$370$	0	0
$371$	55.9436	2.90445
$372$	−4.48022	−0.232288
$373$	11.3431	0.587325	0.293663	−	0.955909i	$-0.405126\pi$
$373$	11.3431	0.587325	0.293663	+	0.955909i	$0.405126\pi$
$374$	70.8166	3.66184
$375$	0	0
$376$	41.5115	2.14079
$377$	−0.432960	−0.0222986
$378$	11.7906	0.606442
$379$	7.79927	0.400622	0.200311	−	0.979732i	$-0.435805\pi$
$379$	7.79927	0.400622	0.200311	+	0.979732i	$0.435805\pi$
$380$	0	0
$381$	−10.1682	−0.520931
$382$	−15.0128	−0.768121
$383$	−0.215920	−0.0110330	−0.00551649	−	0.999985i	$-0.501756\pi$
$383$	−0.215920	−0.0110330	−0.00551649	+	0.999985i	$0.501756\pi$
$384$	11.6710	0.595584
$385$	0	0
$386$	−51.2597	−2.60905
$387$	0.151479	0.00770010
$388$	−47.4851	−2.41069
$389$	−18.3006	−0.927877	−0.463938	−	0.885867i	$-0.653564\pi$
$389$	−18.3006	−0.927877	−0.463938	+	0.885867i	$0.653564\pi$
$390$	0	0
$391$	−19.1663	−0.969280
$392$	91.2496	4.60880
$393$	20.6976	1.04405
$394$	−32.1424	−1.61931
$395$	0	0
$396$	20.6834	1.03938
$397$	20.2390	1.01577	0.507883	−	0.861426i	$-0.330428\pi$
$397$	20.2390	1.01577	0.507883	+	0.861426i	$0.330428\pi$
$398$	−49.8424	−2.49837
$399$	35.5652	1.78049
$400$	0	0
$401$	−8.93527	−0.446206	−0.223103	−	0.974795i	$-0.571619\pi$
$401$	−8.93527	−0.446206	−0.223103	+	0.974795i	$0.571619\pi$
$402$	−34.4472	−1.71807
$403$	−0.863614	−0.0430197
$404$	5.69033	0.283105
$405$	0	0
$406$	−5.91102	−0.293359
$407$	15.6539	0.775937
$408$	−38.0454	−1.88353
$409$	−16.7934	−0.830379	−0.415189	−	0.909735i	$-0.636285\pi$
$409$	−16.7934	−0.830379	−0.415189	+	0.909735i	$0.636285\pi$
$410$	0	0
$411$	−3.80162	−0.187520
$412$	−22.2785	−1.09758
$413$	−26.0585	−1.28226
$414$	−8.09682	−0.397937
$415$	0	0
$416$	−4.72990	−0.231902
$417$	−0.742322	−0.0363517
$418$	90.2407	4.41382
$419$	−15.8971	−0.776626	−0.388313	−	0.921528i	$-0.626942\pi$
$419$	−15.8971	−0.776626	−0.388313	+	0.921528i	$0.626942\pi$
$420$	0	0
$421$	−37.7166	−1.83819	−0.919096	−	0.394033i	$-0.871080\pi$
$421$	−37.7166	−1.83819	−0.919096	+	0.394033i	$0.871080\pi$
$422$	−42.3695	−2.06252
$423$	6.57483	0.319679
$424$	−76.2597	−3.70350
$425$	0	0
$426$	26.2378	1.27122
$427$	21.7658	1.05332
$428$	46.6828	2.25650
$429$	3.98697	0.192492
$430$	0	0
$431$	39.2347	1.88987	0.944934	−	0.327262i	$-0.106126\pi$
$431$	39.2347	1.88987	0.944934	+	0.327262i	$0.106126\pi$
$432$	−7.11191	−0.342172
$433$	35.6850	1.71491	0.857457	−	0.514556i	$-0.172043\pi$
$433$	35.6850	1.71491	0.857457	+	0.514556i	$0.172043\pi$
$434$	−11.7906	−0.565966
$435$	0	0
$436$	−76.6459	−3.67067
$437$	−24.4233	−1.16833
$438$	−15.6180	−0.746259
$439$	31.4226	1.49972	0.749859	−	0.661598i	$-0.230121\pi$
$439$	31.4226	1.49972	0.749859	+	0.661598i	$0.230121\pi$
$440$	0	0
$441$	14.4526	0.688220
$442$	−13.2475	−0.630117
$443$	−4.84179	−0.230041	−0.115020	−	0.993363i	$-0.536693\pi$
$443$	−4.84179	−0.230041	−0.115020	+	0.993363i	$0.536693\pi$
$444$	−15.1915	−0.720956
$445$	0	0
$446$	−19.7496	−0.935172
$447$	11.4886	0.543392
$448$	1.30511	0.0616604
$449$	11.3556	0.535903	0.267951	−	0.963432i	$-0.413653\pi$
$449$	11.3556	0.535903	0.267951	+	0.963432i	$0.413653\pi$
$450$	0	0
$451$	20.1614	0.949365
$452$	−73.8261	−3.47249
$453$	17.5667	0.825354
$454$	−75.7819	−3.55662
$455$	0	0
$456$	−48.4808	−2.27032
$457$	−38.8349	−1.81662	−0.908311	−	0.418296i	$-0.862627\pi$
$457$	−38.8349	−1.81662	−0.908311	+	0.418296i	$0.862627\pi$
$458$	18.4515	0.862183
$459$	−6.02584	−0.281262
$460$	0	0
$461$	−5.78015	−0.269208	−0.134604	−	0.990899i	$-0.542976\pi$
$461$	−5.78015	−0.269208	−0.134604	+	0.990899i	$0.542976\pi$
$462$	54.4324	2.53242
$463$	30.7981	1.43131	0.715655	−	0.698454i	$-0.246128\pi$
$463$	30.7981	1.43131	0.715655	+	0.698454i	$0.246128\pi$
$464$	3.56545	0.165522
$465$	0	0
$466$	17.9738	0.832622
$467$	−15.3266	−0.709230	−0.354615	−	0.935012i	$-0.615388\pi$
$467$	−15.3266	−0.709230	−0.354615	+	0.935012i	$0.615388\pi$
$468$	−3.86918	−0.178853
$469$	−62.6757	−2.89409
$470$	0	0
$471$	−6.21484	−0.286365
$472$	35.5217	1.63502
$473$	0.699317	0.0321547
$474$	−38.3544	−1.76168
$475$	0	0
$476$	−125.042	−5.73131
$477$	−12.0784	−0.553034
$478$	69.3894	3.17380
$479$	−25.6293	−1.17103	−0.585517	−	0.810660i	$-0.699108\pi$
$479$	−25.6293	−1.17103	−0.585517	+	0.810660i	$0.699108\pi$
$480$	0	0
$481$	−2.92834	−0.133521
$482$	48.1076	2.19124
$483$	−14.7319	−0.670326
$484$	46.2046	2.10021
$485$	0	0
$486$	−2.54563	−0.115472
$487$	−3.92376	−0.177802	−0.0889012	−	0.996040i	$-0.528336\pi$
$487$	−3.92376	−0.177802	−0.0889012	+	0.996040i	$0.528336\pi$
$488$	−29.6701	−1.34310
$489$	−3.73834	−0.169054
$490$	0	0
$491$	−26.2863	−1.18629	−0.593143	−	0.805097i	$-0.702113\pi$
$491$	−26.2863	−1.18629	−0.593143	+	0.805097i	$0.702113\pi$
$492$	−19.5658	−0.882096
$493$	3.02096	0.136057
$494$	−16.8811	−0.759515
$495$	0	0
$496$	7.11191	0.319334
$497$	47.7389	2.14138
$498$	−17.5850	−0.788001
$499$	5.01549	0.224524	0.112262	−	0.993679i	$-0.464190\pi$
$499$	5.01549	0.224524	0.112262	+	0.993679i	$0.464190\pi$
$500$	0	0
$501$	−9.30511	−0.415721
$502$	55.0992	2.45920
$503$	−8.47716	−0.377978	−0.188989	−	0.981979i	$-0.560521\pi$
$503$	−8.47716	−0.377978	−0.188989	+	0.981979i	$0.560521\pi$
$504$	−29.2432	−1.30259
$505$	0	0
$506$	−37.3798	−1.66174
$507$	12.2542	0.544227
$508$	45.5556	2.02120
$509$	28.2076	1.25028	0.625139	−	0.780513i	$-0.285042\pi$
$509$	28.2076	1.25028	0.625139	+	0.780513i	$0.285042\pi$
$510$	0	0
$511$	−28.4166	−1.25708
$512$	−50.8541	−2.24746
$513$	−7.67866	−0.339021
$514$	43.4484	1.91643
$515$	0	0
$516$	−0.678658	−0.0298763
$517$	30.3534	1.33494
$518$	−39.9794	−1.75659
$519$	−4.22469	−0.185443
$520$	0	0
$521$	−3.43157	−0.150340	−0.0751700	−	0.997171i	$-0.523950\pi$
$521$	−3.43157	−0.150340	−0.0751700	+	0.997171i	$0.523950\pi$
$522$	1.27621	0.0558582
$523$	14.9496	0.653701	0.326851	−	0.945076i	$-0.394013\pi$
$523$	14.9496	0.653701	0.326851	+	0.945076i	$0.394013\pi$
$524$	−92.7295	−4.05091
$525$	0	0
$526$	0.195615	0.00852924
$527$	6.02584	0.262490
$528$	−32.8329	−1.42887
$529$	−12.8833	−0.560143
$530$	0	0
$531$	5.62613	0.244153
$532$	−159.340	−6.90826
$533$	−3.77154	−0.163364
$534$	27.9000	1.20735
$535$	0	0
$536$	85.4365	3.69030
$537$	−3.91402	−0.168902
$538$	61.6751	2.65900
$539$	66.7220	2.87392
$540$	0	0
$541$	−38.8435	−1.67001	−0.835006	−	0.550241i	$-0.814536\pi$
$541$	−38.8435	−1.67001	−0.835006	+	0.550241i	$0.814536\pi$
$542$	49.5941	2.13025
$543$	−4.85196	−0.208218
$544$	33.0027	1.41498
$545$	0	0
$546$	−10.1825	−0.435771
$547$	5.91452	0.252886	0.126443	−	0.991974i	$-0.459644\pi$
$547$	5.91452	0.252886	0.126443	+	0.991974i	$0.459644\pi$
$548$	17.0321	0.727575
$549$	−4.69932	−0.200562
$550$	0	0
$551$	3.84958	0.163997
$552$	20.0819	0.854741
$553$	−69.7848	−2.96755
$554$	−46.3145	−1.96772
$555$	0	0
$556$	3.32577	0.141044
$557$	13.7379	0.582094	0.291047	−	0.956709i	$-0.405996\pi$
$557$	13.7379	0.582094	0.291047	+	0.956709i	$0.405996\pi$
$558$	2.54563	0.107765
$559$	−0.130819	−0.00553307
$560$	0	0
$561$	−27.8189	−1.17452
$562$	−17.8857	−0.754464
$563$	2.82696	0.119142	0.0595710	−	0.998224i	$-0.481027\pi$
$563$	2.82696	0.119142	0.0595710	+	0.998224i	$0.481027\pi$
$564$	−29.4567	−1.24035
$565$	0	0
$566$	−27.9446	−1.17460
$567$	−4.63170	−0.194513
$568$	−65.0754	−2.73050
$569$	27.9257	1.17071	0.585354	−	0.810778i	$-0.300956\pi$
$569$	27.9257	1.17071	0.585354	+	0.810778i	$0.300956\pi$
$570$	0	0
$571$	−3.34148	−0.139837	−0.0699183	−	0.997553i	$-0.522274\pi$
$571$	−3.34148	−0.139837	−0.0699183	+	0.997553i	$0.522274\pi$
$572$	−17.8625	−0.746867
$573$	5.89748	0.246371
$574$	−51.4913	−2.14921
$575$	0	0
$576$	−0.281777	−0.0117407
$577$	14.6862	0.611395	0.305697	−	0.952129i	$-0.401110\pi$
$577$	14.6862	0.611395	0.305697	+	0.952129i	$0.401110\pi$
$578$	49.1581	2.04471
$579$	20.1364	0.836839
$580$	0	0
$581$	−31.9953	−1.32739
$582$	26.9807	1.11839
$583$	−55.7613	−2.30940
$584$	38.7361	1.60291
$585$	0	0
$586$	−30.5316	−1.26125
$587$	32.0967	1.32477	0.662387	−	0.749162i	$-0.269543\pi$
$587$	32.0967	1.32477	0.662387	+	0.749162i	$0.269543\pi$
$588$	−64.7508	−2.67028
$589$	7.67866	0.316394
$590$	0	0
$591$	12.6265	0.519385
$592$	24.1150	0.991122
$593$	8.50417	0.349224	0.174612	−	0.984637i	$-0.444133\pi$
$593$	8.50417	0.349224	0.174612	+	0.984637i	$0.444133\pi$
$594$	−11.7521	−0.482197
$595$	0	0
$596$	−51.4714	−2.10835
$597$	19.5796	0.801340
$598$	6.99253	0.285946
$599$	−1.47519	−0.0602747	−0.0301374	−	0.999546i	$-0.509594\pi$
$599$	−1.47519	−0.0602747	−0.0301374	+	0.999546i	$0.509594\pi$
$600$	0	0
$601$	26.2782	1.07191	0.535955	−	0.844247i	$-0.319952\pi$
$601$	26.2782	1.07191	0.535955	+	0.844247i	$0.319952\pi$
$602$	−1.78602	−0.0727928
$603$	13.5319	0.551062
$604$	−78.7025	−3.20236
$605$	0	0
$606$	−3.23321	−0.131340
$607$	−26.1723	−1.06230	−0.531151	−	0.847277i	$-0.678240\pi$
$607$	−26.1723	−1.06230	−0.531151	+	0.847277i	$0.678240\pi$
$608$	42.0550	1.70555
$609$	2.32203	0.0940934
$610$	0	0
$611$	−5.67812	−0.229712
$612$	26.9971	1.09129
$613$	−47.8924	−1.93436	−0.967178	−	0.254098i	$-0.918221\pi$
$613$	−47.8924	−1.93436	−0.967178	+	0.254098i	$0.918221\pi$
$614$	−15.7285	−0.634750
$615$	0	0
$616$	−135.004	−5.43947
$617$	2.82786	0.113845	0.0569226	−	0.998379i	$-0.481871\pi$
$617$	2.82786	0.113845	0.0569226	+	0.998379i	$0.481871\pi$
$618$	12.6585	0.509198
$619$	−17.5242	−0.704357	−0.352178	−	0.935933i	$-0.614559\pi$
$619$	−17.5242	−0.704357	−0.352178	+	0.935933i	$0.614559\pi$
$620$	0	0
$621$	3.18068	0.127636
$622$	17.0835	0.684987
$623$	50.7633	2.03379
$624$	6.14195	0.245875
$625$	0	0
$626$	40.7925	1.63040
$627$	−35.4493	−1.41571
$628$	27.8438	1.11109
$629$	20.4324	0.814693
$630$	0	0
$631$	5.75573	0.229132	0.114566	−	0.993416i	$-0.463452\pi$
$631$	5.75573	0.229132	0.114566	+	0.993416i	$0.463452\pi$
$632$	95.1273	3.78396
$633$	16.6440	0.661541
$634$	33.4342	1.32784
$635$	0	0
$636$	54.1140	2.14576
$637$	−12.4815	−0.494534
$638$	5.89176	0.233257
$639$	−10.3070	−0.407739
$640$	0	0
$641$	10.5018	0.414798	0.207399	−	0.978256i	$-0.433500\pi$
$641$	10.5018	0.414798	0.207399	+	0.978256i	$0.433500\pi$
$642$	−26.5248	−1.04685
$643$	−50.2008	−1.97973	−0.989863	−	0.142028i	$-0.954638\pi$
$643$	−50.2008	−1.97973	−0.989863	+	0.142028i	$0.954638\pi$
$644$	66.0023	2.60085
$645$	0	0
$646$	117.787	4.63427
$647$	−29.6947	−1.16742	−0.583710	−	0.811962i	$-0.698400\pi$
$647$	−29.6947	−1.16742	−0.583710	+	0.811962i	$0.698400\pi$
$648$	6.31371	0.248026
$649$	25.9736	1.01955
$650$	0	0
$651$	4.63170	0.181530
$652$	16.7486	0.655925
$653$	−19.8679	−0.777492	−0.388746	−	0.921345i	$-0.627092\pi$
$653$	−19.8679	−0.777492	−0.388746	+	0.921345i	$0.627092\pi$
$654$	43.5497	1.70293
$655$	0	0
$656$	31.0589	1.21265
$657$	6.13524	0.239359
$658$	−77.5210	−3.02208
$659$	−37.1627	−1.44765	−0.723826	−	0.689982i	$-0.757618\pi$
$659$	−37.1627	−1.44765	−0.723826	+	0.689982i	$0.757618\pi$
$660$	0	0
$661$	−5.26491	−0.204781	−0.102391	−	0.994744i	$-0.532649\pi$
$661$	−5.26491	−0.204781	−0.102391	+	0.994744i	$0.532649\pi$
$662$	−10.6261	−0.412997
$663$	5.20401	0.202107
$664$	43.6145	1.69257
$665$	0	0
$666$	8.63170	0.334471
$667$	−1.59458	−0.0617425
$668$	41.6889	1.61299
$669$	7.75826	0.299952
$670$	0	0
$671$	−21.6949	−0.837522
$672$	25.3672	0.978560
$673$	−32.6658	−1.25917	−0.629586	−	0.776931i	$-0.716776\pi$
$673$	−32.6658	−1.25917	−0.629586	+	0.776931i	$0.716776\pi$
$674$	−44.6916	−1.72146
$675$	0	0
$676$	−54.9013	−2.11159
$677$	21.6870	0.833497	0.416749	−	0.909022i	$-0.363169\pi$
$677$	21.6870	0.833497	0.416749	+	0.909022i	$0.363169\pi$
$678$	41.9474	1.61098
$679$	49.0906	1.88392
$680$	0	0
$681$	29.7695	1.14077
$682$	11.7521	0.450013
$683$	44.1611	1.68978	0.844889	−	0.534941i	$-0.179666\pi$
$683$	44.1611	1.68978	0.844889	+	0.534941i	$0.179666\pi$
$684$	34.4021	1.31540
$685$	0	0
$686$	−87.8705	−3.35491
$687$	−7.24832	−0.276541
$688$	1.07730	0.0410718
$689$	10.4311	0.397394
$690$	0	0
$691$	9.25838	0.352205	0.176103	−	0.984372i	$-0.443651\pi$
$691$	9.25838	0.352205	0.176103	+	0.984372i	$0.443651\pi$
$692$	18.9275	0.719516
$693$	−21.3827	−0.812262
$694$	−38.4939	−1.46121
$695$	0	0
$696$	−3.16528	−0.119980
$697$	26.3158	0.996783
$698$	−34.9479	−1.32280
$699$	−7.06067	−0.267059
$700$	0	0
$701$	14.7292	0.556315	0.278157	−	0.960536i	$-0.410276\pi$
$701$	14.7292	0.556315	0.278157	+	0.960536i	$0.410276\pi$
$702$	2.19844	0.0829748
$703$	26.0367	0.981994
$704$	−1.30085	−0.0490277
$705$	0	0
$706$	−35.5051	−1.33625
$707$	−5.88273	−0.221243
$708$	−25.2063	−0.947310
$709$	−8.31658	−0.312336	−0.156168	−	0.987731i	$-0.549914\pi$
$709$	−8.31658	−0.312336	−0.156168	+	0.987731i	$0.549914\pi$
$710$	0	0
$711$	15.0668	0.565048
$712$	−69.1981	−2.59331
$713$	−3.18068	−0.119117
$714$	71.0482	2.65891
$715$	0	0
$716$	17.5356	0.655338
$717$	−27.2583	−1.01798
$718$	12.8085	0.478009
$719$	−19.3564	−0.721872	−0.360936	−	0.932591i	$-0.617543\pi$
$719$	−19.3564	−0.721872	−0.360936	+	0.932591i	$0.617543\pi$
$720$	0	0
$721$	23.0317	0.857746
$722$	101.728	3.78592
$723$	−18.8981	−0.702829
$724$	21.7378	0.807880
$725$	0	0
$726$	−26.2531	−0.974344
$727$	27.5253	1.02086	0.510428	−	0.859921i	$-0.329487\pi$
$727$	27.5253	1.02086	0.510428	+	0.859921i	$0.329487\pi$
$728$	25.2548	0.936006
$729$	1.00000	0.0370370
$730$	0	0
$731$	0.912788	0.0337607
$732$	21.0540	0.778177
$733$	−10.8292	−0.399987	−0.199993	−	0.979797i	$-0.564092\pi$
$733$	−10.8292	−0.399987	−0.199993	+	0.979797i	$0.564092\pi$
$734$	48.2545	1.78111
$735$	0	0
$736$	−17.4201	−0.642115
$737$	62.4714	2.30117
$738$	11.1172	0.409228
$739$	−36.1262	−1.32892	−0.664462	−	0.747322i	$-0.731339\pi$
$739$	−36.1262	−1.32892	−0.664462	+	0.747322i	$0.731339\pi$
$740$	0	0
$741$	6.63140	0.243611
$742$	142.412	5.22810
$743$	22.9780	0.842980	0.421490	−	0.906833i	$-0.361507\pi$
$743$	22.9780	0.842980	0.421490	+	0.906833i	$0.361507\pi$
$744$	−6.31371	−0.231472
$745$	0	0
$746$	28.8754	1.05720
$747$	6.90791	0.252747
$748$	124.635	4.55710
$749$	−48.2611	−1.76342
$750$	0	0
$751$	−50.2827	−1.83484	−0.917420	−	0.397919i	$-0.869732\pi$
$751$	−50.2827	−1.83484	−0.917420	+	0.397919i	$0.869732\pi$
$752$	46.7596	1.70515
$753$	−21.6447	−0.788775
$754$	−1.10215	−0.0401381
$755$	0	0
$756$	20.7510	0.754707
$757$	4.08070	0.148316	0.0741578	−	0.997247i	$-0.476373\pi$
$757$	4.08070	0.148316	0.0741578	+	0.997247i	$0.476373\pi$
$758$	19.8540	0.721131
$759$	14.6839	0.532993
$760$	0	0
$761$	30.5019	1.10569	0.552846	−	0.833284i	$-0.313542\pi$
$761$	30.5019	1.10569	0.552846	+	0.833284i	$0.313542\pi$
$762$	−25.8844	−0.937691
$763$	79.2374	2.86859
$764$	−26.4220	−0.955914
$765$	0	0
$766$	−0.549651	−0.0198597
$767$	−4.85881	−0.175441
$768$	29.1465	1.05173
$769$	−44.4982	−1.60465	−0.802323	−	0.596891i	$-0.796403\pi$
$769$	−44.4982	−1.60465	−0.802323	+	0.596891i	$0.796403\pi$
$770$	0	0
$771$	−17.0678	−0.614684
$772$	−90.2153	−3.24692
$773$	−43.2238	−1.55465	−0.777326	−	0.629098i	$-0.783424\pi$
$773$	−43.2238	−1.55465	−0.777326	+	0.629098i	$0.783424\pi$
$774$	0.385609	0.0138604
$775$	0	0
$776$	−66.9180	−2.40222
$777$	15.7051	0.563418
$778$	−46.5865	−1.67021
$779$	33.5339	1.20148
$780$	0	0
$781$	−47.5833	−1.70267
$782$	−48.7902	−1.74473
$783$	−0.501335	−0.0179162
$784$	102.786	3.67092
$785$	0	0
$786$	52.6883	1.87933
$787$	13.1141	0.467468	0.233734	−	0.972301i	$-0.424905\pi$
$787$	13.1141	0.467468	0.233734	+	0.972301i	$0.424905\pi$
$788$	−56.5695	−2.01521
$789$	−0.0768437	−0.00273571
$790$	0	0
$791$	76.3222	2.71370
$792$	29.1479	1.03573
$793$	4.05840	0.144118
$794$	51.5209	1.82841
$795$	0	0
$796$	−87.7209	−3.10919
$797$	8.50316	0.301197	0.150599	−	0.988595i	$-0.451880\pi$
$797$	8.50316	0.301197	0.150599	+	0.988595i	$0.451880\pi$
$798$	90.5358	3.20493
$799$	39.6189	1.40162
$800$	0	0
$801$	−10.9600	−0.387252
$802$	−22.7459	−0.803184
$803$	28.3240	0.999531
$804$	−60.6259	−2.13811
$805$	0	0
$806$	−2.19844	−0.0774368
$807$	−24.2279	−0.852861
$808$	8.01905	0.282109
$809$	−21.1388	−0.743202	−0.371601	−	0.928393i	$-0.621191\pi$
$809$	−21.1388	−0.743202	−0.371601	+	0.928393i	$0.621191\pi$
$810$	0	0
$811$	42.7479	1.50108	0.750540	−	0.660825i	$-0.229793\pi$
$811$	42.7479	1.50108	0.750540	+	0.660825i	$0.229793\pi$
$812$	−10.4032	−0.365081
$813$	−19.4821	−0.683266
$814$	39.8491	1.39671
$815$	0	0
$816$	−42.8553	−1.50024
$817$	1.16315	0.0406936
$818$	−42.7497	−1.49471
$819$	4.00000	0.139771
$820$	0	0
$821$	0.340613	0.0118875	0.00594374	−	0.999982i	$-0.498108\pi$
$821$	0.340613	0.0118875	0.00594374	+	0.999982i	$0.498108\pi$
$822$	−9.67751	−0.337542
$823$	36.9580	1.28827	0.644137	−	0.764910i	$-0.277217\pi$
$823$	36.9580	1.28827	0.644137	+	0.764910i	$0.277217\pi$
$824$	−31.3957	−1.09372
$825$	0	0
$826$	−66.3353	−2.30810
$827$	−1.45648	−0.0506469	−0.0253234	−	0.999679i	$-0.508062\pi$
$827$	−1.45648	−0.0506469	−0.0253234	+	0.999679i	$0.508062\pi$
$828$	−14.2501	−0.495226
$829$	−8.48197	−0.294591	−0.147295	−	0.989093i	$-0.547057\pi$
$829$	−8.48197	−0.294591	−0.147295	+	0.989093i	$0.547057\pi$
$830$	0	0
$831$	18.1938	0.631135
$832$	0.243347	0.00843653
$833$	87.0892	3.01746
$834$	−1.88968	−0.0654341
$835$	0	0
$836$	158.821	5.49293
$837$	−1.00000	−0.0345651
$838$	−40.4682	−1.39795
$839$	−28.3981	−0.980412	−0.490206	−	0.871607i	$-0.663078\pi$
$839$	−28.3981	−0.980412	−0.490206	+	0.871607i	$0.663078\pi$
$840$	0	0
$841$	−28.7487	−0.991333
$842$	−96.0123	−3.30880
$843$	7.02606	0.241991
$844$	−74.5689	−2.56677
$845$	0	0
$846$	16.7371	0.575432
$847$	−47.7668	−1.64129
$848$	−85.9008	−2.94985
$849$	10.9775	0.376747
$850$	0	0
$851$	−10.7850	−0.369706
$852$	46.1776	1.58202
$853$	−19.9580	−0.683348	−0.341674	−	0.939818i	$-0.610994\pi$
$853$	−19.9580	−0.683348	−0.341674	+	0.939818i	$0.610994\pi$
$854$	55.4076	1.89601
$855$	0	0
$856$	65.7873	2.24856
$857$	−19.0454	−0.650577	−0.325288	−	0.945615i	$-0.605461\pi$
$857$	−19.0454	−0.650577	−0.325288	+	0.945615i	$0.605461\pi$
$858$	10.1493	0.346492
$859$	−10.7631	−0.367233	−0.183616	−	0.982998i	$-0.558780\pi$
$859$	−10.7631	−0.367233	−0.183616	+	0.982998i	$0.558780\pi$
$860$	0	0
$861$	20.2274	0.689347
$862$	99.8768	3.40182
$863$	−13.2953	−0.452579	−0.226289	−	0.974060i	$-0.572660\pi$
$863$	−13.2953	−0.452579	−0.226289	+	0.974060i	$0.572660\pi$
$864$	−5.47686	−0.186327
$865$	0	0
$866$	90.8408	3.08690
$867$	−19.3108	−0.655829
$868$	−20.7510	−0.704335
$869$	69.5574	2.35957
$870$	0	0
$871$	−11.6864	−0.395977
$872$	−108.013	−3.65777
$873$	−10.5988	−0.358716
$874$	−62.1727	−2.10302
$875$	0	0
$876$	−27.4872	−0.928707
$877$	−7.12602	−0.240629	−0.120314	−	0.992736i	$-0.538390\pi$
$877$	−7.12602	−0.240629	−0.120314	+	0.992736i	$0.538390\pi$
$878$	79.9901	2.69954
$879$	11.9938	0.404539
$880$	0	0
$881$	56.8258	1.91451	0.957256	−	0.289244i	$-0.0934037\pi$
$881$	56.8258	1.91451	0.957256	+	0.289244i	$0.0934037\pi$
$882$	36.7910	1.23882
$883$	−4.24212	−0.142759	−0.0713793	−	0.997449i	$-0.522740\pi$
$883$	−4.24212	−0.142759	−0.0713793	+	0.997449i	$0.522740\pi$
$884$	−23.3151	−0.784171
$885$	0	0
$886$	−12.3254	−0.414080
$887$	−2.19786	−0.0737969	−0.0368985	−	0.999319i	$-0.511748\pi$
$887$	−2.19786	−0.0737969	−0.0368985	+	0.999319i	$0.511748\pi$
$888$	−21.4085	−0.718422
$889$	−47.0958	−1.57954
$890$	0	0
$891$	4.61660	0.154662
$892$	−34.7587	−1.16381
$893$	50.4858	1.68944
$894$	29.2457	0.978122
$895$	0	0
$896$	54.0566	1.80591
$897$	−2.74688	−0.0917156
$898$	28.9071	0.964641
$899$	0.501335	0.0167204
$900$	0	0
$901$	−72.7828	−2.42475
$902$	51.3235	1.70889
$903$	0.701604	0.0233479
$904$	−104.039	−3.46028
$905$	0	0
$906$	44.7182	1.48566
$907$	9.73059	0.323099	0.161549	−	0.986865i	$-0.448351\pi$
$907$	9.73059	0.323099	0.161549	+	0.986865i	$0.448351\pi$
$908$	−133.374	−4.42616
$909$	1.27010	0.0421266
$910$	0	0
$911$	14.0913	0.466867	0.233433	−	0.972373i	$-0.425004\pi$
$911$	14.0913	0.466867	0.233433	+	0.972373i	$0.425004\pi$
$912$	−54.6100	−1.80832
$913$	31.8911	1.05544
$914$	−98.8593	−3.26997
$915$	0	0
$916$	32.4741	1.07297
$917$	95.8648	3.16573
$918$	−15.3396	−0.506281
$919$	29.2582	0.965140	0.482570	−	0.875858i	$-0.339703\pi$
$919$	29.2582	0.965140	0.482570	+	0.875858i	$0.339703\pi$
$920$	0	0
$921$	6.17862	0.203593
$922$	−14.7141	−0.484583
$923$	8.90127	0.292989
$924$	95.7992	3.15156
$925$	0	0
$926$	78.4005	2.57640
$927$	−4.97263	−0.163323
$928$	2.74574	0.0901333
$929$	−40.9177	−1.34246	−0.671232	−	0.741247i	$-0.734235\pi$
$929$	−40.9177	−1.34246	−0.671232	+	0.741247i	$0.734235\pi$
$930$	0	0
$931$	110.977	3.63711
$932$	31.6334	1.03618
$933$	−6.71093	−0.219706
$934$	−39.0158	−1.27664
$935$	0	0
$936$	−5.45261	−0.178224
$937$	44.6534	1.45876	0.729382	−	0.684106i	$-0.239808\pi$
$937$	44.6534	1.45876	0.729382	+	0.684106i	$0.239808\pi$
$938$	−159.549	−5.20946
$939$	−16.0245	−0.522941
$940$	0	0
$941$	8.05215	0.262492	0.131246	−	0.991350i	$-0.458102\pi$
$941$	8.05215	0.262492	0.131246	+	0.991350i	$0.458102\pi$
$942$	−15.8207	−0.515465
$943$	−13.8905	−0.452338
$944$	40.0126	1.30230
$945$	0	0
$946$	1.78020	0.0578793
$947$	1.77124	0.0575577	0.0287788	−	0.999586i	$-0.490838\pi$
$947$	1.77124	0.0575577	0.0287788	+	0.999586i	$0.490838\pi$
$948$	−67.5025	−2.19238
$949$	−5.29848	−0.171996
$950$	0	0
$951$	−13.1340	−0.425898
$952$	−176.215	−5.71116
$953$	14.7767	0.478665	0.239333	−	0.970938i	$-0.423071\pi$
$953$	14.7767	0.478665	0.239333	+	0.970938i	$0.423071\pi$
$954$	−30.7472	−0.995477
$955$	0	0
$956$	122.123	3.94974
$957$	−2.31446	−0.0748159
$958$	−65.2427	−2.10790
$959$	−17.6080	−0.568591
$960$	0	0
$961$	1.00000	0.0322581
$962$	−7.45446	−0.240341
$963$	10.4198	0.335772
$964$	84.6678	2.72697
$965$	0	0
$966$	−37.5020	−1.20661
$967$	50.0011	1.60793	0.803963	−	0.594680i	$-0.202721\pi$
$967$	50.0011	1.60793	0.803963	+	0.594680i	$0.202721\pi$
$968$	65.1134	2.09282
$969$	−46.2704	−1.48642
$970$	0	0
$971$	40.3160	1.29380	0.646902	−	0.762574i	$-0.276064\pi$
$971$	40.3160	1.29380	0.646902	+	0.762574i	$0.276064\pi$
$972$	−4.48022	−0.143703
$973$	−3.43821	−0.110224
$974$	−9.98842	−0.320050
$975$	0	0
$976$	−33.4211	−1.06978
$977$	40.3330	1.29037	0.645184	−	0.764028i	$-0.276781\pi$
$977$	40.3330	1.29037	0.645184	+	0.764028i	$0.276781\pi$
$978$	−9.51642	−0.304302
$979$	−50.5979	−1.61711
$980$	0	0
$981$	−17.1076	−0.546205
$982$	−66.9152	−2.13535
$983$	13.2408	0.422315	0.211158	−	0.977452i	$-0.432277\pi$
$983$	13.2408	0.422315	0.211158	+	0.977452i	$0.432277\pi$
$984$	−27.5730	−0.878995
$985$	0	0
$986$	7.69025	0.244907
$987$	30.4526	0.969317
$988$	−29.7101	−0.945205
$989$	−0.481805	−0.0153205
$990$	0	0
$991$	37.9050	1.20409	0.602046	−	0.798461i	$-0.294352\pi$
$991$	37.9050	1.20409	0.602046	+	0.798461i	$0.294352\pi$
$992$	5.47686	0.173891
$993$	4.17427	0.132467
$994$	121.525	3.85455
$995$	0	0
$996$	−30.9489	−0.980654
$997$	−51.9068	−1.64390	−0.821952	−	0.569557i	$-0.807115\pi$
$997$	−51.9068	−1.64390	−0.821952	+	0.569557i	$0.807115\pi$
$998$	12.7676	0.404150
$999$	−3.39079	−0.107280

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2325.2.a.ba.1.6	yes	6
3.2	odd	2		6975.2.a.bz.1.1		6
5.2	odd	4		2325.2.c.q.1024.12		12
5.3	odd	4		2325.2.c.q.1024.1		12
5.4	even	2		2325.2.a.z.1.1	✓	6
15.14	odd	2		6975.2.a.cd.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2325.2.a.z.1.1	✓	6	5.4	even	2
2325.2.a.ba.1.6	yes	6	1.1	even	1	trivial
2325.2.c.q.1024.1		12	5.3	odd	4
2325.2.c.q.1024.12		12	5.2	odd	4
6975.2.a.bz.1.1		6	3.2	odd	2
6975.2.a.cd.1.6		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:	\( N \)	\(=\)	\( 2325 = 3 \cdot 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2325.a (trivial)

\(f(q)\)	\(=\)	\(q+2.54563 q^{2} -1.00000 q^{3} +4.48022 q^{4} -2.54563 q^{6} -4.63170 q^{7} +6.31371 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.54563 q^{2} -1.00000 q^{3} +4.48022 q^{4} -2.54563 q^{6} -4.63170 q^{7} +6.31371 q^{8} +1.00000 q^{9} +4.61660 q^{11} -4.48022 q^{12} -0.863614 q^{13} -11.7906 q^{14} +7.11191 q^{16} +6.02584 q^{17} +2.54563 q^{18} +7.67866 q^{19} +4.63170 q^{21} +11.7521 q^{22} -3.18068 q^{23} -6.31371 q^{24} -2.19844 q^{26} -1.00000 q^{27} -20.7510 q^{28} +0.501335 q^{29} +1.00000 q^{31} +5.47686 q^{32} -4.61660 q^{33} +15.3396 q^{34} +4.48022 q^{36} +3.39079 q^{37} +19.5470 q^{38} +0.863614 q^{39} +4.36716 q^{41} +11.7906 q^{42} +0.151479 q^{43} +20.6834 q^{44} -8.09682 q^{46} +6.57483 q^{47} -7.11191 q^{48} +14.4526 q^{49} -6.02584 q^{51} -3.86918 q^{52} -12.0784 q^{53} -2.54563 q^{54} -29.2432 q^{56} -7.67866 q^{57} +1.27621 q^{58} +5.62613 q^{59} -4.69932 q^{61} +2.54563 q^{62} -4.63170 q^{63} -0.281777 q^{64} -11.7521 q^{66} +13.5319 q^{67} +26.9971 q^{68} +3.18068 q^{69} -10.3070 q^{71} +6.31371 q^{72} +6.13524 q^{73} +8.63170 q^{74} +34.4021 q^{76} -21.3827 q^{77} +2.19844 q^{78} +15.0668 q^{79} +1.00000 q^{81} +11.1172 q^{82} +6.90791 q^{83} +20.7510 q^{84} +0.385609 q^{86} -0.501335 q^{87} +29.1479 q^{88} -10.9600 q^{89} +4.00000 q^{91} -14.2501 q^{92} -1.00000 q^{93} +16.7371 q^{94} -5.47686 q^{96} -10.5988 q^{97} +36.7910 q^{98} +4.61660 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} - 6 q^{3} + 7 q^{4} - q^{6} - 6 q^{7} + 3 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q + q^2 - 6 * q^3 + 7 * q^4 - q^6 - 6 * q^7 + 3 * q^8 + 6 * q^9	\( 6 q + q^{2} - 6 q^{3} + 7 q^{4} - q^{6} - 6 q^{7} + 3 q^{8} + 6 q^{9} + 9 q^{11} - 7 q^{12} - 4 q^{13} + q^{16} + 2 q^{17} + q^{18} + 17 q^{19} + 6 q^{21} + 2 q^{22} + q^{23} - 3 q^{24} - 4 q^{26} - 6 q^{27} - 14 q^{28} + 10 q^{29} + 6 q^{31} - 3 q^{32} - 9 q^{33} + 23 q^{34} + 7 q^{36} - 8 q^{37} + 26 q^{38} + 4 q^{39} + 6 q^{41} - q^{43} + 34 q^{44} - 10 q^{46} + 7 q^{47} - q^{48} + 18 q^{49} - 2 q^{51} - 12 q^{52} - q^{53} - q^{54} - 36 q^{56} - 17 q^{57} + 7 q^{58} + 22 q^{59} + 14 q^{61} + q^{62} - 6 q^{63} + 9 q^{64} - 2 q^{66} - 7 q^{67} + 37 q^{68} - q^{69} + 5 q^{71} + 3 q^{72} - 4 q^{73} + 30 q^{74} + 18 q^{76} + 4 q^{77} + 4 q^{78} + 19 q^{79} + 6 q^{81} - 16 q^{82} + 19 q^{83} + 14 q^{84} - 5 q^{86} - 10 q^{87} + 46 q^{88} + 14 q^{89} + 24 q^{91} - 8 q^{92} - 6 q^{93} + 35 q^{94} + 3 q^{96} - 34 q^{97} + 61 q^{98} + 9 q^{99}+O(q^{100}) \) 6 * q + q^2 - 6 * q^3 + 7 * q^4 - q^6 - 6 * q^7 + 3 * q^8 + 6 * q^9 + 9 * q^11 - 7 * q^12 - 4 * q^13 + q^16 + 2 * q^17 + q^18 + 17 * q^19 + 6 * q^21 + 2 * q^22 + q^23 - 3 * q^24 - 4 * q^26 - 6 * q^27 - 14 * q^28 + 10 * q^29 + 6 * q^31 - 3 * q^32 - 9 * q^33 + 23 * q^34 + 7 * q^36 - 8 * q^37 + 26 * q^38 + 4 * q^39 + 6 * q^41 - q^43 + 34 * q^44 - 10 * q^46 + 7 * q^47 - q^48 + 18 * q^49 - 2 * q^51 - 12 * q^52 - q^53 - q^54 - 36 * q^56 - 17 * q^57 + 7 * q^58 + 22 * q^59 + 14 * q^61 + q^62 - 6 * q^63 + 9 * q^64 - 2 * q^66 - 7 * q^67 + 37 * q^68 - q^69 + 5 * q^71 + 3 * q^72 - 4 * q^73 + 30 * q^74 + 18 * q^76 + 4 * q^77 + 4 * q^78 + 19 * q^79 + 6 * q^81 - 16 * q^82 + 19 * q^83 + 14 * q^84 - 5 * q^86 - 10 * q^87 + 46 * q^88 + 14 * q^89 + 24 * q^91 - 8 * q^92 - 6 * q^93 + 35 * q^94 + 3 * q^96 - 34 * q^97 + 61 * q^98 + 9 * q^99

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