LMFDB - Embedded newform 961.2.a.l.1.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(1,961)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("961.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(961, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.a (trivial)

Newform invariants

comment:select newform

sage:traces = [16,-8,0,8,-16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$7.67362363425$
Analytic rank:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 24x^{14} + 220x^{12} - 992x^{10} + 2366x^{8} - 2944x^{6} + 1688x^{4} - 288x^{2} + 4 $ x^16 - 24x^14 + 220x^12 - 992x^10 + 2366x^8 - 2944x^6 + 1688x^4 - 288*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-2.46287$ of defining polynomial
Character	$\chi$	$=$	961.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.45116 q^{2} -2.46287 q^{3} +0.105856 q^{4} -3.68139 q^{5} +3.57401 q^{6} -0.804403 q^{7} +2.74870 q^{8} +3.06572 q^{9} +5.34227 q^{10} -2.63285 q^{11} -0.260710 q^{12} +1.95809 q^{13} +1.16731 q^{14} +9.06678 q^{15} -4.20051 q^{16} -0.337845 q^{17} -4.44885 q^{18} +2.70022 q^{19} -0.389698 q^{20} +1.98114 q^{21} +3.82067 q^{22} +2.03034 q^{23} -6.76969 q^{24} +8.55262 q^{25} -2.84150 q^{26} -0.161872 q^{27} -0.0851512 q^{28} +10.0042 q^{29} -13.1573 q^{30} +0.598196 q^{32} +6.48436 q^{33} +0.490266 q^{34} +2.96132 q^{35} +0.324526 q^{36} +3.22174 q^{37} -3.91845 q^{38} -4.82252 q^{39} -10.1190 q^{40} -7.11112 q^{41} -2.87494 q^{42} +3.61543 q^{43} -0.278704 q^{44} -11.2861 q^{45} -2.94634 q^{46} -11.0484 q^{47} +10.3453 q^{48} -6.35294 q^{49} -12.4112 q^{50} +0.832068 q^{51} +0.207276 q^{52} -3.87793 q^{53} +0.234902 q^{54} +9.69253 q^{55} -2.21106 q^{56} -6.65029 q^{57} -14.5177 q^{58} -7.58824 q^{59} +0.959776 q^{60} +9.67616 q^{61} -2.46608 q^{63} +7.53294 q^{64} -7.20849 q^{65} -9.40982 q^{66} +7.35125 q^{67} -0.0357631 q^{68} -5.00045 q^{69} -4.29734 q^{70} +1.63738 q^{71} +8.42676 q^{72} +1.16793 q^{73} -4.67525 q^{74} -21.0640 q^{75} +0.285836 q^{76} +2.11787 q^{77} +6.99823 q^{78} -15.6642 q^{79} +15.4637 q^{80} -8.79851 q^{81} +10.3194 q^{82} +1.22692 q^{83} +0.209716 q^{84} +1.24374 q^{85} -5.24655 q^{86} -24.6391 q^{87} -7.23691 q^{88} +3.85715 q^{89} +16.3779 q^{90} -1.57509 q^{91} +0.214924 q^{92} +16.0330 q^{94} -9.94057 q^{95} -1.47328 q^{96} +6.14722 q^{97} +9.21911 q^{98} -8.07158 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{2} + 8 q^{4} - 16 q^{5} - 16 q^{7} + 8 q^{10} - 8 q^{14} - 8 q^{16} - 24 q^{18} - 32 q^{19} - 24 q^{20} - 8 q^{28} - 8 q^{32} - 32 q^{33} - 16 q^{35} - 40 q^{36} - 24 q^{38} - 32 q^{39} - 32 q^{41}+ \cdots + 16 q^{98}+O(q^{100}) $ 16 * q - 8 * q^2 + 8 * q^4 - 16 * q^5 - 16 * q^7 + 8 * q^10 - 8 * q^14 - 8 * q^16 - 24 * q^18 - 32 * q^19 - 24 * q^20 - 8 * q^28 - 8 * q^32 - 32 * q^33 - 16 * q^35 - 40 * q^36 - 24 * q^38 - 32 * q^39 - 32 * q^41 - 16 * q^45 - 32 * q^47 - 16 * q^49 - 32 * q^50 - 32 * q^51 - 48 * q^56 - 64 * q^59 - 16 * q^63 - 16 * q^64 + 16 * q^67 - 32 * q^69 + 88 * q^70 - 48 * q^71 + 48 * q^72 + 40 * q^76 + 32 * q^78 - 40 * q^80 - 16 * q^81 + 88 * q^82 - 32 * q^87 + 40 * q^90 - 32 * q^94 - 48 * q^95 + 16 * q^98

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 $

$2$	−1.45116	−1.02612	−0.513061	−	0.858352i	$-0.671489\pi$
$2$	−1.45116	−1.02612	−0.513061	+	0.858352i	$0.671489\pi$
$3$	−2.46287	−1.42194	−0.710969	−	0.703223i	$-0.751743\pi$
$3$	−2.46287	−1.42194	−0.710969	+	0.703223i	$0.751743\pi$
$4$	0.105856	0.0529282
$5$	−3.68139	−1.64637	−0.823183	−	0.567775i	$-0.807804\pi$
$5$	−3.68139	−1.64637	−0.823183	+	0.567775i	$0.807804\pi$
$6$	3.57401	1.45908
$7$	−0.804403	−0.304036	−0.152018	−	0.988378i	$-0.548577\pi$
$7$	−0.804403	−0.304036	−0.152018	+	0.988378i	$0.548577\pi$
$8$	2.74870	0.971812
$9$	3.06572	1.02191
$10$	5.34227	1.68937
$11$	−2.63285	−0.793833	−0.396917	−	0.917855i	$-0.629920\pi$
$11$	−2.63285	−0.793833	−0.396917	+	0.917855i	$0.629920\pi$
$12$	−0.260710	−0.0752606
$13$	1.95809	0.543077	0.271538	−	0.962428i	$-0.412468\pi$
$13$	1.95809	0.543077	0.271538	+	0.962428i	$0.412468\pi$
$14$	1.16731	0.311978
$15$	9.06678	2.34103
$16$	−4.20051	−1.05013
$17$	−0.337845	−0.0819395	−0.0409697	−	0.999160i	$-0.513045\pi$
$17$	−0.337845	−0.0819395	−0.0409697	+	0.999160i	$0.513045\pi$
$18$	−4.44885	−1.04860
$19$	2.70022	0.619473	0.309737	−	0.950822i	$-0.399759\pi$
$19$	2.70022	0.619473	0.309737	+	0.950822i	$0.399759\pi$
$20$	−0.389698	−0.0871392
$21$	1.98114	0.432320
$22$	3.82067	0.814570
$23$	2.03034	0.423354	0.211677	−	0.977340i	$-0.432107\pi$
$23$	2.03034	0.423354	0.211677	+	0.977340i	$0.432107\pi$
$24$	−6.76969	−1.38186
$25$	8.55262	1.71052
$26$	−2.84150	−0.557263
$27$	−0.161872	−0.0311523
$28$	−0.0851512	−0.0160921
$29$	10.0042	1.85774	0.928868	−	0.370412i	$-0.120783\pi$
$29$	10.0042	1.85774	0.928868	+	0.370412i	$0.120783\pi$
$30$	−13.1573	−2.40219
$31$	0	0
$31$	0	0
$32$	0.598196	0.105747
$33$	6.48436	1.12878
$34$	0.490266	0.0840800
$35$	2.96132	0.500554
$36$	0.324526	0.0540877
$37$	3.22174	0.529651	0.264825	−	0.964296i	$-0.414686\pi$
$37$	3.22174	0.529651	0.264825	+	0.964296i	$0.414686\pi$
$38$	−3.91845	−0.635656
$39$	−4.82252	−0.772221
$40$	−10.1190	−1.59996
$41$	−7.11112	−1.11057	−0.555285	−	0.831660i	$-0.687391\pi$
$41$	−7.11112	−1.11057	−0.555285	+	0.831660i	$0.687391\pi$
$42$	−2.87494	−0.443613
$43$	3.61543	0.551348	0.275674	−	0.961251i	$-0.411099\pi$
$43$	3.61543	0.551348	0.275674	+	0.961251i	$0.411099\pi$
$44$	−0.278704	−0.0420161
$45$	−11.2861	−1.68244
$46$	−2.94634	−0.434414
$47$	−11.0484	−1.61158	−0.805788	−	0.592205i	$-0.798258\pi$
$47$	−11.0484	−1.61158	−0.805788	+	0.592205i	$0.798258\pi$
$48$	10.3453	1.49322
$49$	−6.35294	−0.907562
$50$	−12.4112	−1.75521
$51$	0.832068	0.116513
$52$	0.207276	0.0287441
$53$	−3.87793	−0.532674	−0.266337	−	0.963880i	$-0.585813\pi$
$53$	−3.87793	−0.532674	−0.266337	+	0.963880i	$0.585813\pi$
$54$	0.234902	0.0319661
$55$	9.69253	1.30694
$56$	−2.21106	−0.295466
$57$	−6.65029	−0.880853
$58$	−14.5177	−1.90626
$59$	−7.58824	−0.987904	−0.493952	−	0.869489i	$-0.664448\pi$
$59$	−7.58824	−0.987904	−0.493952	+	0.869489i	$0.664448\pi$
$60$	0.959776	0.123907
$61$	9.67616	1.23891	0.619453	−	0.785034i	$-0.287355\pi$
$61$	9.67616	1.23891	0.619453	+	0.785034i	$0.287355\pi$
$62$	0	0
$63$	−2.46608	−0.310697
$64$	7.53294	0.941617
$65$	−7.20849	−0.894103
$66$	−9.40982	−1.15827
$67$	7.35125	0.898098	0.449049	−	0.893507i	$-0.351763\pi$
$67$	7.35125	0.898098	0.449049	+	0.893507i	$0.351763\pi$
$68$	−0.0357631	−0.00433691
$69$	−5.00045	−0.601984
$70$	−4.29734	−0.513630
$71$	1.63738	0.194321	0.0971605	−	0.995269i	$-0.469024\pi$
$71$	1.63738	0.194321	0.0971605	+	0.995269i	$0.469024\pi$
$72$	8.42676	0.993103
$73$	1.16793	0.136696	0.0683482	−	0.997662i	$-0.478227\pi$
$73$	1.16793	0.136696	0.0683482	+	0.997662i	$0.478227\pi$
$74$	−4.67525	−0.543487
$75$	−21.0640	−2.43226
$76$	0.285836	0.0327876
$77$	2.11787	0.241354
$78$	6.99823	0.792394
$79$	−15.6642	−1.76236	−0.881182	−	0.472777i	$-0.843252\pi$
$79$	−15.6642	−1.76236	−0.881182	+	0.472777i	$0.843252\pi$
$80$	15.4637	1.72889
$81$	−8.79851	−0.977612
$82$	10.3194	1.13958
$83$	1.22692	0.134672	0.0673362	−	0.997730i	$-0.478550\pi$
$83$	1.22692	0.134672	0.0673362	+	0.997730i	$0.478550\pi$
$84$	0.209716	0.0228819
$85$	1.24374	0.134902
$86$	−5.24655	−0.565750
$87$	−24.6391	−2.64158
$88$	−7.23691	−0.771457
$89$	3.85715	0.408857	0.204428	−	0.978882i	$-0.434466\pi$
$89$	3.85715	0.408857	0.204428	+	0.978882i	$0.434466\pi$
$90$	16.3779	1.72639
$91$	−1.57509	−0.165115
$92$	0.214924	0.0224074
$93$	0	0
$94$	16.0330	1.65367
$95$	−9.94057	−1.01988
$96$	−1.47328	−0.150366
$97$	6.14722	0.624156	0.312078	−	0.950057i	$-0.398975\pi$
$97$	6.14722	0.624156	0.312078	+	0.950057i	$0.398975\pi$
$98$	9.21911	0.931270
$99$	−8.07158	−0.811225
$100$	0.905349	0.0905349
$101$	−6.30373	−0.627245	−0.313622	−	0.949548i	$-0.601543\pi$
$101$	−6.30373	−0.627245	−0.313622	+	0.949548i	$0.601543\pi$
$102$	−1.20746	−0.119557
$103$	10.8617	1.07023	0.535115	−	0.844779i	$-0.320268\pi$
$103$	10.8617	1.07023	0.535115	+	0.844779i	$0.320268\pi$
$104$	5.38220	0.527768
$105$	−7.29334	−0.711757
$106$	5.62748	0.546589
$107$	7.27395	0.703199	0.351600	−	0.936150i	$-0.385638\pi$
$107$	7.27395	0.703199	0.351600	+	0.936150i	$0.385638\pi$
$108$	−0.0171352	−0.00164883
$109$	10.0689	0.964421	0.482211	−	0.876055i	$-0.339834\pi$
$109$	10.0689	0.964421	0.482211	+	0.876055i	$0.339834\pi$
$110$	−14.0654	−1.34108
$111$	−7.93473	−0.753131
$112$	3.37890	0.319276
$113$	−6.74387	−0.634410	−0.317205	−	0.948357i	$-0.602744\pi$
$113$	−6.74387	−0.634410	−0.317205	+	0.948357i	$0.602744\pi$
$114$	9.65062	0.903863
$115$	−7.47446	−0.696997
$116$	1.05901	0.0983266
$117$	6.00297	0.554974
$118$	11.0117	1.01371
$119$	0.271764	0.0249125
$120$	24.9218	2.27504
$121$	−4.06812	−0.369829
$122$	−14.0416	−1.27127
$123$	17.5138	1.57916
$124$	0	0
$125$	−13.0786	−1.16978
$126$	3.57867	0.318813
$127$	10.5932	0.939992	0.469996	−	0.882668i	$-0.344255\pi$
$127$	10.5932	0.939992	0.469996	+	0.882668i	$0.344255\pi$
$128$	−12.1279	−1.07196
$129$	−8.90432	−0.783982
$130$	10.4607	0.917460
$131$	−5.66035	−0.494547	−0.247273	−	0.968946i	$-0.579535\pi$
$131$	−5.66035	−0.494547	−0.247273	+	0.968946i	$0.579535\pi$
$132$	0.686410	0.0597444
$133$	−2.17207	−0.188342
$134$	−10.6678	−0.921559
$135$	0.595914	0.0512881
$136$	−0.928635	−0.0796298
$137$	19.6630	1.67992	0.839961	−	0.542647i	$-0.182578\pi$
$137$	19.6630	1.67992	0.839961	+	0.542647i	$0.182578\pi$
$138$	7.25644	0.617709
$139$	−13.6363	−1.15662	−0.578309	−	0.815818i	$-0.696287\pi$
$139$	−13.6363	−1.15662	−0.578309	+	0.815818i	$0.696287\pi$
$140$	0.313475	0.0264934
$141$	27.2108	2.29156
$142$	−2.37609	−0.199397
$143$	−5.15535	−0.431112
$144$	−12.8776	−1.07313
$145$	−36.8294	−3.05851
$146$	−1.69486	−0.140267
$147$	15.6465	1.29050
$148$	0.341042	0.0280335
$149$	10.2733	0.841625	0.420813	−	0.907148i	$-0.361745\pi$
$149$	10.2733	0.841625	0.420813	+	0.907148i	$0.361745\pi$
$150$	30.5671	2.49580
$151$	−2.69534	−0.219344	−0.109672	−	0.993968i	$-0.534980\pi$
$151$	−2.69534	−0.219344	−0.109672	+	0.993968i	$0.534980\pi$
$152$	7.42210	0.602012
$153$	−1.03574	−0.0837346
$154$	−3.07336	−0.247659
$155$	0	0
$156$	−0.510494	−0.0408723
$157$	−20.2177	−1.61355	−0.806776	−	0.590858i	$-0.798789\pi$
$157$	−20.2177	−1.61355	−0.806776	+	0.590858i	$0.798789\pi$
$158$	22.7313	1.80840
$159$	9.55083	0.757430
$160$	−2.20219	−0.174098
$161$	−1.63321	−0.128715
$162$	12.7680	1.00315
$163$	16.6109	1.30106	0.650531	−	0.759480i	$-0.274546\pi$
$163$	16.6109	1.30106	0.650531	+	0.759480i	$0.274546\pi$
$164$	−0.752757	−0.0587805
$165$	−23.8714	−1.85839
$166$	−1.78046	−0.138190
$167$	8.76987	0.678633	0.339316	−	0.940672i	$-0.389804\pi$
$167$	8.76987	0.678633	0.339316	+	0.940672i	$0.389804\pi$
$168$	5.44556	0.420134
$169$	−9.16588	−0.705068
$170$	−1.80486	−0.138426
$171$	8.27814	0.633045
$172$	0.382716	0.0291818
$173$	−3.01862	−0.229501	−0.114751	−	0.993394i	$-0.536607\pi$
$173$	−3.01862	−0.229501	−0.114751	+	0.993394i	$0.536607\pi$
$174$	35.7551	2.71059
$175$	−6.87975	−0.520060
$176$	11.0593	0.833626
$177$	18.6888	1.40474
$178$	−5.59733	−0.419538
$179$	−23.2975	−1.74134	−0.870669	−	0.491870i	$-0.836313\pi$
$179$	−23.2975	−1.74134	−0.870669	+	0.491870i	$0.836313\pi$
$180$	−1.19471	−0.0890483
$181$	10.0945	0.750320	0.375160	−	0.926960i	$-0.377588\pi$
$181$	10.0945	0.750320	0.375160	+	0.926960i	$0.377588\pi$
$182$	2.28571	0.169428
$183$	−23.8311	−1.76165
$184$	5.58078	0.411421
$185$	−11.8605	−0.872000
$186$	0	0
$187$	0.889494	0.0650463
$188$	−1.16954	−0.0852978
$189$	0.130210	0.00947141
$190$	14.4253	1.04652
$191$	−18.5623	−1.34312	−0.671559	−	0.740951i	$-0.734375\pi$
$191$	−18.5623	−1.34312	−0.671559	+	0.740951i	$0.734375\pi$
$192$	−18.5526	−1.33892
$193$	21.6917	1.56140	0.780701	−	0.624905i	$-0.214862\pi$
$193$	21.6917	1.56140	0.780701	+	0.624905i	$0.214862\pi$
$194$	−8.92058	−0.640460
$195$	17.7536	1.27136
$196$	−0.672499	−0.0480356
$197$	−1.08846	−0.0775495	−0.0387748	−	0.999248i	$-0.512345\pi$
$197$	−1.08846	−0.0775495	−0.0387748	+	0.999248i	$0.512345\pi$
$198$	11.7131	0.832416
$199$	−19.1493	−1.35746	−0.678730	−	0.734388i	$-0.737469\pi$
$199$	−19.1493	−1.35746	−0.678730	+	0.734388i	$0.737469\pi$
$200$	23.5086	1.66231
$201$	−18.1052	−1.27704
$202$	9.14771	0.643630
$203$	−8.04742	−0.564818
$204$	0.0880797	0.00616681
$205$	26.1788	1.82841
$206$	−15.7620	−1.09819
$207$	6.22445	0.432629
$208$	−8.22497	−0.570299
$209$	−7.10927	−0.491759
$210$	10.5838	0.730351
$211$	−1.08773	−0.0748826	−0.0374413	−	0.999299i	$-0.511921\pi$
$211$	−1.08773	−0.0748826	−0.0374413	+	0.999299i	$0.511921\pi$
$212$	−0.410503	−0.0281935
$213$	−4.03265	−0.276313
$214$	−10.5556	−0.721569
$215$	−13.3098	−0.907720
$216$	−0.444937	−0.0302742
$217$	0	0
$218$	−14.6115	−0.989615
$219$	−2.87647	−0.194374
$220$	1.02602	0.0691740
$221$	−0.661531	−0.0444994
$222$	11.5145	0.772805
$223$	−7.61758	−0.510111	−0.255055	−	0.966926i	$-0.582094\pi$
$223$	−7.61758	−0.510111	−0.255055	+	0.966926i	$0.582094\pi$
$224$	−0.481190	−0.0321509
$225$	26.2200	1.74800
$226$	9.78642	0.650983
$227$	9.50717	0.631013	0.315507	−	0.948923i	$-0.397826\pi$
$227$	9.50717	0.631013	0.315507	+	0.948923i	$0.397826\pi$
$228$	−0.703976	−0.0466219
$229$	3.64526	0.240885	0.120443	−	0.992720i	$-0.461569\pi$
$229$	3.64526	0.240885	0.120443	+	0.992720i	$0.461569\pi$
$230$	10.8466	0.715204
$231$	−5.21604	−0.343190
$232$	27.4986	1.80537
$233$	−22.5815	−1.47936	−0.739681	−	0.672958i	$-0.765023\pi$
$233$	−22.5815	−1.47936	−0.739681	+	0.672958i	$0.765023\pi$
$234$	−8.71125	−0.569472
$235$	40.6735	2.65324
$236$	−0.803263	−0.0522880
$237$	38.5790	2.50597
$238$	−0.394372	−0.0255633
$239$	0.370713	0.0239794	0.0119897	−	0.999928i	$-0.496183\pi$
$239$	0.370713	0.0239794	0.0119897	+	0.999928i	$0.496183\pi$
$240$	−38.0851	−2.45838
$241$	21.8633	1.40834	0.704170	−	0.710032i	$-0.251319\pi$
$241$	21.8633	1.40834	0.704170	+	0.710032i	$0.251319\pi$
$242$	5.90348	0.379490
$243$	22.1552	1.42126
$244$	1.02428	0.0655730
$245$	23.3876	1.49418
$246$	−25.4152	−1.62041
$247$	5.28728	0.336422
$248$	0	0
$249$	−3.02175	−0.191496
$250$	18.9791	1.20034
$251$	−16.1640	−1.02026	−0.510131	−	0.860097i	$-0.670403\pi$
$251$	−16.1640	−1.02026	−0.510131	+	0.860097i	$0.670403\pi$
$252$	−0.261050	−0.0164446
$253$	−5.34556	−0.336073
$254$	−15.3724	−0.964548
$255$	−3.06317	−0.191823
$256$	2.53356	0.158348
$257$	15.6247	0.974645	0.487323	−	0.873222i	$-0.337974\pi$
$257$	15.6247	0.974645	0.487323	+	0.873222i	$0.337974\pi$
$258$	12.9216	0.804462
$259$	−2.59158	−0.161033
$260$	−0.763065	−0.0473233
$261$	30.6702	1.89844
$262$	8.21405	0.507466
$263$	−18.0040	−1.11017	−0.555087	−	0.831792i	$-0.687315\pi$
$263$	−18.0040	−1.11017	−0.555087	+	0.831792i	$0.687315\pi$
$264$	17.8236	1.09696
$265$	14.2762	0.876977
$266$	3.15201	0.193262
$267$	−9.49965	−0.581369
$268$	0.778176	0.0475347
$269$	27.9191	1.70226	0.851129	−	0.524956i	$-0.175918\pi$
$269$	27.9191	1.70226	0.851129	+	0.524956i	$0.175918\pi$
$270$	−0.864764	−0.0526279
$271$	−23.1794	−1.40805	−0.704025	−	0.710175i	$-0.748616\pi$
$271$	−23.1794	−1.40805	−0.704025	+	0.710175i	$0.748616\pi$
$272$	1.41912	0.0860468
$273$	3.87925	0.234783
$274$	−28.5341	−1.72381
$275$	−22.5177	−1.35787
$276$	−0.529330	−0.0318619
$277$	12.0314	0.722894	0.361447	−	0.932393i	$-0.382283\pi$
$277$	12.0314	0.722894	0.361447	+	0.932393i	$0.382283\pi$
$278$	19.7884	1.18683
$279$	0	0
$280$	8.13978	0.486445
$281$	−4.13615	−0.246742	−0.123371	−	0.992361i	$-0.539370\pi$
$281$	−4.13615	−0.246742	−0.123371	+	0.992361i	$0.539370\pi$
$282$	−39.4871	−2.35142
$283$	−26.9812	−1.60387	−0.801933	−	0.597414i	$-0.796195\pi$
$283$	−26.9812	−1.60387	−0.801933	+	0.597414i	$0.796195\pi$
$284$	0.173327	0.0102851
$285$	24.4823	1.45021
$286$	7.48123	0.442374
$287$	5.72021	0.337653
$288$	1.83390	0.108064
$289$	−16.8859	−0.993286
$290$	53.4452	3.13841
$291$	−15.1398	−0.887511
$292$	0.123633	0.00723509
$293$	−9.23220	−0.539351	−0.269676	−	0.962951i	$-0.586916\pi$
$293$	−9.23220	−0.539351	−0.269676	+	0.962951i	$0.586916\pi$
$294$	−22.7055	−1.32421
$295$	27.9352	1.62645
$296$	8.85560	0.514721
$297$	0.426184	0.0247297
$298$	−14.9082	−0.863611
$299$	3.97558	0.229914
$300$	−2.22976	−0.128735
$301$	−2.90826	−0.167629
$302$	3.91137	0.225074
$303$	15.5253	0.891903
$304$	−11.3423	−0.650526
$305$	−35.6217	−2.03969
$306$	1.50302	0.0859220
$307$	13.2188	0.754435	0.377217	−	0.926125i	$-0.376881\pi$
$307$	13.2188	0.754435	0.377217	+	0.926125i	$0.376881\pi$
$308$	0.224190	0.0127744
$309$	−26.7508	−1.52180
$310$	0	0
$311$	−11.2939	−0.640417	−0.320208	−	0.947347i	$-0.603753\pi$
$311$	−11.2939	−0.640417	−0.320208	+	0.947347i	$0.603753\pi$
$312$	−13.2557	−0.750454
$313$	0.835438	0.0472217	0.0236109	−	0.999721i	$-0.492484\pi$
$313$	0.835438	0.0472217	0.0236109	+	0.999721i	$0.492484\pi$
$314$	29.3391	1.65570
$315$	9.07859	0.511521
$316$	−1.65816	−0.0932788
$317$	19.1556	1.07589	0.537943	−	0.842981i	$-0.319202\pi$
$317$	19.1556	1.07589	0.537943	+	0.842981i	$0.319202\pi$
$318$	−13.8597	−0.777216
$319$	−26.3396	−1.47473
$320$	−27.7317	−1.55025
$321$	−17.9148	−0.999906
$322$	2.37004	0.132077
$323$	−0.912257	−0.0507593
$324$	−0.931378	−0.0517432
$325$	16.7468	0.928946
$326$	−24.1050	−1.33505
$327$	−24.7983	−1.37135
$328$	−19.5463	−1.07927
$329$	8.88737	0.489977
$330$	34.6412	1.90694
$331$	−11.9078	−0.654512	−0.327256	−	0.944936i	$-0.606124\pi$
$331$	−11.9078	−0.654512	−0.327256	+	0.944936i	$0.606124\pi$
$332$	0.129878	0.00712796
$333$	9.87697	0.541255
$334$	−12.7265	−0.696361
$335$	−27.0628	−1.47860
$336$	−8.32179	−0.453991
$337$	6.28775	0.342516	0.171258	−	0.985226i	$-0.445217\pi$
$337$	6.28775	0.342516	0.171258	+	0.985226i	$0.445217\pi$
$338$	13.3011	0.723486
$339$	16.6093	0.902092
$340$	0.131658	0.00714014
$341$	0	0
$342$	−12.0129	−0.649582
$343$	10.7411	0.579967
$344$	9.93772	0.535806
$345$	18.4086	0.991086
$346$	4.38049	0.235497
$347$	−15.9236	−0.854823	−0.427411	−	0.904057i	$-0.640574\pi$
$347$	−15.9236	−0.854823	−0.427411	+	0.904057i	$0.640574\pi$
$348$	−2.60820	−0.139814
$349$	9.16029	0.490339	0.245169	−	0.969480i	$-0.421156\pi$
$349$	9.16029	0.490339	0.245169	+	0.969480i	$0.421156\pi$
$350$	9.98360	0.533646
$351$	−0.316960	−0.0169181
$352$	−1.57496	−0.0839455
$353$	−24.5217	−1.30516	−0.652580	−	0.757720i	$-0.726313\pi$
$353$	−24.5217	−1.30516	−0.652580	+	0.757720i	$0.726313\pi$
$354$	−27.1204	−1.44143
$355$	−6.02783	−0.319924
$356$	0.408304	0.0216401
$357$	−0.669318	−0.0354241
$358$	33.8083	1.78683
$359$	4.83492	0.255177	0.127589	−	0.991827i	$-0.459276\pi$
$359$	4.83492	0.255177	0.127589	+	0.991827i	$0.459276\pi$
$360$	−31.0222	−1.63501
$361$	−11.7088	−0.616253
$362$	−14.6487	−0.769920
$363$	10.0192	0.525874
$364$	−0.166734	−0.00873922
$365$	−4.29962	−0.225052
$366$	34.5827	1.80767
$367$	6.30941	0.329348	0.164674	−	0.986348i	$-0.447343\pi$
$367$	6.30941	0.329348	0.164674	+	0.986348i	$0.447343\pi$
$368$	−8.52844	−0.444576
$369$	−21.8007	−1.13490
$370$	17.2114	0.894779
$371$	3.11942	0.161952
$372$	0	0
$373$	−22.8028	−1.18069	−0.590343	−	0.807153i	$-0.701007\pi$
$373$	−22.8028	−1.18069	−0.590343	+	0.807153i	$0.701007\pi$
$374$	−1.29080	−0.0667455
$375$	32.2108	1.66336
$376$	−30.3687	−1.56615
$377$	19.5892	1.00889
$378$	−0.188956	−0.00971883
$379$	−4.65946	−0.239340	−0.119670	−	0.992814i	$-0.538184\pi$
$379$	−4.65946	−0.239340	−0.119670	+	0.992814i	$0.538184\pi$
$380$	−1.05227	−0.0539804
$381$	−26.0896	−1.33661
$382$	26.9368	1.37820
$383$	−30.6191	−1.56456	−0.782282	−	0.622925i	$-0.785944\pi$
$383$	−30.6191	−1.56456	−0.782282	+	0.622925i	$0.785944\pi$
$384$	29.8694	1.52426
$385$	−7.79670	−0.397357
$386$	−31.4780	−1.60219
$387$	11.0839	0.563427
$388$	0.650722	0.0330354
$389$	−25.9587	−1.31616	−0.658080	−	0.752948i	$-0.728631\pi$
$389$	−25.9587	−1.31616	−0.658080	+	0.752948i	$0.728631\pi$
$390$	−25.7632	−1.30457
$391$	−0.685939	−0.0346894
$392$	−17.4623	−0.881980
$393$	13.9407	0.703215
$394$	1.57953	0.0795753
$395$	57.6661	2.90150
$396$	−0.854429	−0.0429366
$397$	−1.16988	−0.0587146	−0.0293573	−	0.999569i	$-0.509346\pi$
$397$	−1.16988	−0.0587146	−0.0293573	+	0.999569i	$0.509346\pi$
$398$	27.7887	1.39292
$399$	5.34952	0.267811
$400$	−35.9253	−1.79627
$401$	14.0956	0.703901	0.351951	−	0.936019i	$-0.385519\pi$
$401$	14.0956	0.703901	0.351951	+	0.936019i	$0.385519\pi$
$402$	26.2734	1.31040
$403$	0	0
$404$	−0.667290	−0.0331989
$405$	32.3907	1.60951
$406$	11.6781	0.579573
$407$	−8.48235	−0.420454
$408$	2.28711	0.113229
$409$	−10.2362	−0.506149	−0.253074	−	0.967447i	$-0.581442\pi$
$409$	−10.2362	−0.506149	−0.253074	+	0.967447i	$0.581442\pi$
$410$	−37.9895	−1.87617
$411$	−48.4273	−2.38874
$412$	1.14977	0.0566453
$413$	6.10400	0.300358
$414$	−9.03266	−0.443931
$415$	−4.51678	−0.221720
$416$	1.17132	0.0574288
$417$	33.5845	1.64464
$418$	10.3167	0.504605
$419$	−16.3036	−0.796483	−0.398242	−	0.917281i	$-0.630379\pi$
$419$	−16.3036	−0.796483	−0.398242	+	0.917281i	$0.630379\pi$
$420$	−0.772047	−0.0376720
$421$	−1.13829	−0.0554770	−0.0277385	−	0.999615i	$-0.508831\pi$
$421$	−1.13829	−0.0554770	−0.0277385	+	0.999615i	$0.508831\pi$
$422$	1.57847	0.0768387
$423$	−33.8714	−1.64688
$424$	−10.6593	−0.517659
$425$	−2.88946	−0.140159
$426$	5.85201	0.283531
$427$	−7.78353	−0.376672
$428$	0.769994	0.0372191
$429$	12.6970	0.613015
$430$	19.3146	0.931433
$431$	17.6823	0.851725	0.425862	−	0.904788i	$-0.359971\pi$
$431$	17.6823	0.851725	0.425862	+	0.904788i	$0.359971\pi$
$432$	0.679944	0.0327138
$433$	−25.9217	−1.24572	−0.622859	−	0.782334i	$-0.714029\pi$
$433$	−25.9217	−1.24572	−0.622859	+	0.782334i	$0.714029\pi$
$434$	0	0
$435$	90.7060	4.34902
$436$	1.06585	0.0510451
$437$	5.48236	0.262257
$438$	4.17421	0.199451
$439$	17.7168	0.845576	0.422788	−	0.906229i	$-0.361052\pi$
$439$	17.7168	0.845576	0.422788	+	0.906229i	$0.361052\pi$
$440$	26.6419	1.27010
$441$	−19.4764	−0.927445
$442$	0.959986	0.0456619
$443$	4.20714	0.199887	0.0999437	−	0.994993i	$-0.468134\pi$
$443$	4.20714	0.199887	0.0999437	+	0.994993i	$0.468134\pi$
$444$	−0.839941	−0.0398618
$445$	−14.1997	−0.673129
$446$	11.0543	0.523436
$447$	−25.3019	−1.19674
$448$	−6.05952	−0.286285
$449$	0.940169	0.0443693	0.0221847	−	0.999754i	$-0.492938\pi$
$449$	0.940169	0.0443693	0.0221847	+	0.999754i	$0.492938\pi$
$450$	−38.0493	−1.79366
$451$	18.7225	0.881608
$452$	−0.713882	−0.0335782
$453$	6.63828	0.311894
$454$	−13.7964	−0.647497
$455$	5.79853	0.271839
$456$	−18.2797	−0.856024
$457$	−9.75840	−0.456479	−0.228239	−	0.973605i	$-0.573297\pi$
$457$	−9.75840	−0.456479	−0.228239	+	0.973605i	$0.573297\pi$
$458$	−5.28984	−0.247178
$459$	0.0546877	0.00255260
$460$	−0.791219	−0.0368908
$461$	−8.95245	−0.416957	−0.208478	−	0.978027i	$-0.566851\pi$
$461$	−8.95245	−0.416957	−0.208478	+	0.978027i	$0.566851\pi$
$462$	7.56929	0.352155
$463$	−30.7935	−1.43109	−0.715547	−	0.698564i	$-0.753823\pi$
$463$	−30.7935	−1.43109	−0.715547	+	0.698564i	$0.753823\pi$
$464$	−42.0228	−1.95086
$465$	0	0
$466$	32.7693	1.51801
$467$	−23.9225	−1.10700	−0.553501	−	0.832848i	$-0.686709\pi$
$467$	−23.9225	−1.10700	−0.553501	+	0.832848i	$0.686709\pi$
$468$	0.635452	0.0293738
$469$	−5.91336	−0.273054
$470$	−59.0236	−2.72255
$471$	49.7937	2.29437
$472$	−20.8578	−0.960057
$473$	−9.51887	−0.437678
$474$	−55.9841	−2.57144
$475$	23.0940	1.05962
$476$	0.0287679	0.00131857
$477$	−11.8887	−0.544344
$478$	−0.537963	−0.0246058
$479$	−21.3748	−0.976640	−0.488320	−	0.872665i	$-0.662390\pi$
$479$	−21.3748	−0.976640	−0.488320	+	0.872665i	$0.662390\pi$
$480$	5.42371	0.247557
$481$	6.30846	0.287641
$482$	−31.7271	−1.44513
$483$	4.02238	0.183025
$484$	−0.430636	−0.0195744
$485$	−22.6303	−1.02759
$486$	−32.1506	−1.45838
$487$	−14.5002	−0.657066	−0.328533	−	0.944492i	$-0.606554\pi$
$487$	−14.5002	−0.657066	−0.328533	+	0.944492i	$0.606554\pi$
$488$	26.5969	1.20398
$489$	−40.9104	−1.85003
$490$	−33.9391	−1.53321
$491$	8.09491	0.365318	0.182659	−	0.983176i	$-0.441530\pi$
$491$	8.09491	0.365318	0.182659	+	0.983176i	$0.441530\pi$
$492$	1.85394	0.0835822
$493$	−3.37987	−0.152222
$494$	−7.67267	−0.345210
$495$	29.7146	1.33557
$496$	0	0
$497$	−1.31711	−0.0590806
$498$	4.38504	0.196498
$499$	−13.3542	−0.597815	−0.298908	−	0.954282i	$-0.596622\pi$
$499$	−13.3542	−0.597815	−0.298908	+	0.954282i	$0.596622\pi$
$500$	−1.38445	−0.0619145
$501$	−21.5990	−0.964974
$502$	23.4565	1.04691
$503$	−34.8655	−1.55458	−0.777288	−	0.629146i	$-0.783405\pi$
$503$	−34.8655	−1.55458	−0.777288	+	0.629146i	$0.783405\pi$
$504$	−6.77851	−0.301939
$505$	23.2065	1.03268
$506$	7.75725	0.344852
$507$	22.5744	1.00256
$508$	1.12136	0.0497521
$509$	−12.6151	−0.559156	−0.279578	−	0.960123i	$-0.590195\pi$
$509$	−12.6151	−0.559156	−0.279578	+	0.960123i	$0.590195\pi$
$510$	4.44514	0.196834
$511$	−0.939490	−0.0415606
$512$	20.5791	0.909478
$513$	−0.437090	−0.0192980
$514$	−22.6740	−1.00011
$515$	−39.9860	−1.76199
$516$	−0.942579	−0.0414947
$517$	29.0888	1.27932
$518$	3.76079	0.165239
$519$	7.43446	0.326337
$520$	−19.8140	−0.868900
$521$	29.3709	1.28676	0.643382	−	0.765546i	$-0.277531\pi$
$521$	29.3709	1.28676	0.643382	+	0.765546i	$0.277531\pi$
$522$	−44.5072	−1.94803
$523$	26.5759	1.16208	0.581041	−	0.813874i	$-0.302646\pi$
$523$	26.5759	1.16208	0.581041	+	0.813874i	$0.302646\pi$
$524$	−0.599184	−0.0261755
$525$	16.9439	0.739494
$526$	26.1266	1.13917
$527$	0	0
$528$	−27.2376	−1.18536
$529$	−18.8777	−0.820771
$530$	−20.7169	−0.899886
$531$	−23.2634	−1.00955
$532$	−0.229927	−0.00996860
$533$	−13.9242	−0.603125
$534$	13.7855	0.596556
$535$	−26.7782	−1.15772
$536$	20.2064	0.872782
$537$	57.3787	2.47607
$538$	−40.5150	−1.74673
$539$	16.7263	0.720453
$540$	0.0630812	0.00271458
$541$	5.09485	0.219045	0.109522	−	0.993984i	$-0.465068\pi$
$541$	5.09485	0.219045	0.109522	+	0.993984i	$0.465068\pi$
$542$	33.6370	1.44483
$543$	−24.8615	−1.06691
$544$	−0.202097	−0.00866486
$545$	−37.0674	−1.58779
$546$	−5.62940	−0.240916
$547$	17.9635	0.768064	0.384032	−	0.923320i	$-0.374535\pi$
$547$	17.9635	0.768064	0.384032	+	0.923320i	$0.374535\pi$
$548$	2.08145	0.0889152
$549$	29.6644	1.26605
$550$	32.6768	1.39334
$551$	27.0136	1.15082
$552$	−13.7447	−0.585015
$553$	12.6004	0.535822
$554$	−17.4594	−0.741778
$555$	29.2108	1.23993
$556$	−1.44349	−0.0612176
$557$	7.73709	0.327831	0.163915	−	0.986474i	$-0.447588\pi$
$557$	7.73709	0.327831	0.163915	+	0.986474i	$0.447588\pi$
$558$	0	0
$559$	7.07933	0.299424
$560$	−12.4390	−0.525646
$561$	−2.19071	−0.0924918
$562$	6.00220	0.253187
$563$	32.5640	1.37241	0.686204	−	0.727409i	$-0.259276\pi$
$563$	32.5640	1.37241	0.686204	+	0.727409i	$0.259276\pi$
$564$	2.88043	0.121288
$565$	24.8268	1.04447
$566$	39.1540	1.64576
$567$	7.07754	0.297229
$568$	4.50066	0.188844
$569$	42.2518	1.77129	0.885643	−	0.464367i	$-0.153718\pi$
$569$	42.2518	1.77129	0.885643	+	0.464367i	$0.153718\pi$
$570$	−35.5277	−1.48809
$571$	13.1181	0.548977	0.274489	−	0.961590i	$-0.411491\pi$
$571$	13.1181	0.548977	0.274489	+	0.961590i	$0.411491\pi$
$572$	−0.545727	−0.0228180
$573$	45.7164	1.90983
$574$	−8.30092	−0.346474
$575$	17.3647	0.724158
$576$	23.0939	0.962247
$577$	−26.5738	−1.10628	−0.553141	−	0.833088i	$-0.686571\pi$
$577$	−26.5738	−1.10628	−0.553141	+	0.833088i	$0.686571\pi$
$578$	24.5040	1.01923
$579$	−53.4238	−2.22022
$580$	−3.89862	−0.161882
$581$	−0.986941	−0.0409452
$582$	21.9702	0.910695
$583$	10.2100	0.422855
$584$	3.21030	0.132843
$585$	−22.0993	−0.913692
$586$	13.3974	0.553440
$587$	29.9704	1.23701	0.618505	−	0.785781i	$-0.287739\pi$
$587$	29.9704	1.23701	0.618505	+	0.785781i	$0.287739\pi$
$588$	1.65628	0.0683037
$589$	0	0
$590$	−40.5384	−1.66894
$591$	2.68073	0.110271
$592$	−13.5329	−0.556201
$593$	9.66897	0.397057	0.198528	−	0.980095i	$-0.436384\pi$
$593$	9.66897	0.397057	0.198528	+	0.980095i	$0.436384\pi$
$594$	−0.618460	−0.0253757
$595$	−1.00047	−0.0410152
$596$	1.08750	0.0445457
$597$	47.1623	1.93023
$598$	−5.76919	−0.235920
$599$	−20.5576	−0.839962	−0.419981	−	0.907533i	$-0.637963\pi$
$599$	−20.5576	−0.839962	−0.419981	+	0.907533i	$0.637963\pi$
$600$	−57.8986	−2.36370
$601$	−3.58806	−0.146360	−0.0731801	−	0.997319i	$-0.523315\pi$
$601$	−3.58806	−0.146360	−0.0731801	+	0.997319i	$0.523315\pi$
$602$	4.22034	0.172008
$603$	22.5369	0.917773
$604$	−0.285319	−0.0116095
$605$	14.9763	0.608874
$606$	−22.5296	−0.915203
$607$	−38.9073	−1.57920	−0.789600	−	0.613622i	$-0.789712\pi$
$607$	−38.9073	−1.57920	−0.789600	+	0.613622i	$0.789712\pi$
$608$	1.61526	0.0655075
$609$	19.8197	0.803136
$610$	51.6927	2.09298
$611$	−21.6338	−0.875209
$612$	−0.109640	−0.00443192
$613$	5.90364	0.238446	0.119223	−	0.992868i	$-0.461960\pi$
$613$	5.90364	0.238446	0.119223	+	0.992868i	$0.461960\pi$
$614$	−19.1825	−0.774143
$615$	−64.4750	−2.59988
$616$	5.82139	0.234550
$617$	−8.19887	−0.330074	−0.165037	−	0.986287i	$-0.552774\pi$
$617$	−8.19887	−0.330074	−0.165037	+	0.986287i	$0.552774\pi$
$618$	38.8196	1.56156
$619$	−28.1122	−1.12992	−0.564962	−	0.825117i	$-0.691109\pi$
$619$	−28.1122	−1.12992	−0.564962	+	0.825117i	$0.691109\pi$
$620$	0	0
$621$	−0.328655	−0.0131885
$622$	16.3892	0.657146
$623$	−3.10270	−0.124307
$624$	20.2570	0.810930
$625$	5.38421	0.215368
$626$	−1.21235	−0.0484553
$627$	17.5092	0.699250
$628$	−2.14018	−0.0854023
$629$	−1.08845	−0.0433993
$630$	−13.1745	−0.524883
$631$	29.4301	1.17160	0.585798	−	0.810457i	$-0.300781\pi$
$631$	29.4301	1.17160	0.585798	+	0.810457i	$0.300781\pi$
$632$	−43.0563	−1.71269
$633$	2.67894	0.106478
$634$	−27.7978	−1.10399
$635$	−38.9976	−1.54757
$636$	1.01102	0.0400894
$637$	−12.4396	−0.492876
$638$	38.2228	1.51326
$639$	5.01975	0.198578
$640$	44.6474	1.76484
$641$	21.4049	0.845441	0.422720	−	0.906260i	$-0.361075\pi$
$641$	21.4049	0.845441	0.422720	+	0.906260i	$0.361075\pi$
$642$	25.9972	1.02603
$643$	−28.8174	−1.13645	−0.568223	−	0.822875i	$-0.692369\pi$
$643$	−28.8174	−1.13645	−0.568223	+	0.822875i	$0.692369\pi$
$644$	−0.172886	−0.00681264
$645$	32.7803	1.29072
$646$	1.32383	0.0520853
$647$	23.8618	0.938104	0.469052	−	0.883170i	$-0.344596\pi$
$647$	23.8618	0.938104	0.469052	+	0.883170i	$0.344596\pi$
$648$	−24.1844	−0.950055
$649$	19.9787	0.784231
$650$	−24.3022	−0.953212
$651$	0	0
$652$	1.75836	0.0688629
$653$	30.8291	1.20644	0.603218	−	0.797576i	$-0.293885\pi$
$653$	30.8291	1.20644	0.603218	+	0.797576i	$0.293885\pi$
$654$	35.9862	1.40717
$655$	20.8379	0.814206
$656$	29.8703	1.16624
$657$	3.58056	0.139691
$658$	−12.8970	−0.502776
$659$	−28.1233	−1.09553	−0.547764	−	0.836633i	$-0.684521\pi$
$659$	−28.1233	−1.09553	−0.547764	+	0.836633i	$0.684521\pi$
$660$	−2.52694	−0.0983611
$661$	−37.1871	−1.44641	−0.723205	−	0.690633i	$-0.757332\pi$
$661$	−37.1871	−1.44641	−0.723205	+	0.690633i	$0.757332\pi$
$662$	17.2801	0.671610
$663$	1.62927	0.0632754
$664$	3.37244	0.130876
$665$	7.99622	0.310080
$666$	−14.3330	−0.555394
$667$	20.3119	0.786480
$668$	0.928347	0.0359188
$669$	18.7611	0.725346
$670$	39.2724	1.51722
$671$	−25.4758	−0.983484
$672$	1.18511	0.0457166
$673$	41.2504	1.59009	0.795044	−	0.606552i	$-0.207448\pi$
$673$	41.2504	1.59009	0.795044	+	0.606552i	$0.207448\pi$
$674$	−9.12451	−0.351463
$675$	−1.38443	−0.0532867
$676$	−0.970267	−0.0373180
$677$	−15.3831	−0.591221	−0.295610	−	0.955309i	$-0.595523\pi$
$677$	−15.3831	−0.591221	−0.295610	+	0.955309i	$0.595523\pi$
$678$	−24.1027	−0.925657
$679$	−4.94484	−0.189766
$680$	3.41866	0.131100
$681$	−23.4149	−0.897262
$682$	0	0
$683$	8.40720	0.321693	0.160846	−	0.986979i	$-0.448578\pi$
$683$	8.40720	0.321693	0.160846	+	0.986979i	$0.448578\pi$
$684$	0.876294	0.0335059
$685$	−72.3871	−2.76577
$686$	−15.5871	−0.595118
$687$	−8.97779	−0.342524
$688$	−15.1866	−0.578985
$689$	−7.59333	−0.289283
$690$	−26.7138	−1.01698
$691$	−35.4158	−1.34728	−0.673641	−	0.739059i	$-0.735271\pi$
$691$	−35.4158	−1.34728	−0.673641	+	0.739059i	$0.735271\pi$
$692$	−0.319540	−0.0121471
$693$	6.49281	0.246641
$694$	23.1076	0.877153
$695$	50.2006	1.90422
$696$	−67.7254	−2.56712
$697$	2.40246	0.0909996
$698$	−13.2930	−0.503148
$699$	55.6152	2.10356
$700$	−0.728266	−0.0275259
$701$	9.83851	0.371595	0.185798	−	0.982588i	$-0.440513\pi$
$701$	9.83851	0.371595	0.185798	+	0.982588i	$0.440513\pi$
$702$	0.459959	0.0173600
$703$	8.69942	0.328105
$704$	−19.8331	−0.747487
$705$	−100.173	−3.77275
$706$	35.5849	1.33925
$707$	5.07074	0.190705
$708$	1.97833	0.0743503
$709$	−32.3251	−1.21399	−0.606997	−	0.794704i	$-0.707626\pi$
$709$	−32.3251	−1.21399	−0.606997	+	0.794704i	$0.707626\pi$
$710$	8.74732	0.328281
$711$	−48.0222	−1.80098
$712$	10.6021	0.397332
$713$	0	0
$714$	0.971286	0.0363495
$715$	18.9789	0.709769
$716$	−2.46619	−0.0921658
$717$	−0.913018	−0.0340973
$718$	−7.01622	−0.261843
$719$	−18.0309	−0.672438	−0.336219	−	0.941784i	$-0.609148\pi$
$719$	−18.0309	−0.672438	−0.336219	+	0.941784i	$0.609148\pi$
$720$	47.4074	1.76677
$721$	−8.73714	−0.325388
$722$	16.9913	0.632351
$723$	−53.8465	−2.00257
$724$	1.06857	0.0397131
$725$	85.5622	3.17770
$726$	−14.5395	−0.539611
$727$	18.1609	0.673552	0.336776	−	0.941585i	$-0.390663\pi$
$727$	18.1609	0.673552	0.336776	+	0.941585i	$0.390663\pi$
$728$	−4.32946	−0.160460
$729$	−28.1698	−1.04333
$730$	6.23942	0.230931
$731$	−1.22145	−0.0451771
$732$	−2.52268	−0.0932408
$733$	15.5734	0.575217	0.287609	−	0.957748i	$-0.407140\pi$
$733$	15.5734	0.575217	0.287609	+	0.957748i	$0.407140\pi$
$734$	−9.15594	−0.337952
$735$	−57.6007	−2.12463
$736$	1.21454	0.0447685
$737$	−19.3547	−0.712940
$738$	31.6363	1.16455
$739$	48.4264	1.78139	0.890697	−	0.454598i	$-0.150217\pi$
$739$	48.4264	1.78139	0.890697	+	0.454598i	$0.150217\pi$
$740$	−1.25551	−0.0461534
$741$	−13.0219	−0.478371
$742$	−4.52676	−0.166183
$743$	−2.38112	−0.0873550	−0.0436775	−	0.999046i	$-0.513907\pi$
$743$	−2.38112	−0.0873550	−0.0436775	+	0.999046i	$0.513907\pi$
$744$	0	0
$745$	−37.8202	−1.38562
$746$	33.0905	1.21153
$747$	3.76141	0.137623
$748$	0.0941586	0.00344278
$749$	−5.85119	−0.213798
$750$	−46.7429	−1.70681
$751$	−21.3110	−0.777651	−0.388826	−	0.921311i	$-0.627119\pi$
$751$	−21.3110	−0.777651	−0.388826	+	0.921311i	$0.627119\pi$
$752$	46.4089	1.69236
$753$	39.8098	1.45075
$754$	−28.4269	−1.03525
$755$	9.92260	0.361121
$756$	0.0137836	0.000501304 0
$757$	−37.2388	−1.35347	−0.676734	−	0.736228i	$-0.736605\pi$
$757$	−37.2388	−1.35347	−0.676734	+	0.736228i	$0.736605\pi$
$758$	6.76161	0.245593
$759$	13.1654	0.477875
$760$	−27.3236	−0.991132
$761$	52.2356	1.89354	0.946769	−	0.321914i	$-0.104326\pi$
$761$	52.2356	1.89354	0.946769	+	0.321914i	$0.104326\pi$
$762$	37.8601	1.37153
$763$	−8.09941	−0.293219
$764$	−1.96493	−0.0710888
$765$	3.81296	0.137858
$766$	44.4331	1.60543
$767$	−14.8585	−0.536508
$768$	−6.23983	−0.225160
$769$	−8.38478	−0.302363	−0.151182	−	0.988506i	$-0.548308\pi$
$769$	−8.38478	−0.302363	−0.151182	+	0.988506i	$0.548308\pi$
$770$	11.3142	0.407737
$771$	−38.4817	−1.38589
$772$	2.29620	0.0826421
$773$	−43.9279	−1.57998	−0.789988	−	0.613122i	$-0.789913\pi$
$773$	−43.9279	−1.57998	−0.789988	+	0.613122i	$0.789913\pi$
$774$	−16.0845	−0.578145
$775$	0	0
$776$	16.8969	0.606562
$777$	6.38272	0.228979
$778$	37.6702	1.35054
$779$	−19.2016	−0.687969
$780$	1.87933	0.0672908
$781$	−4.31097	−0.154259
$782$	0.995405	0.0355956
$783$	−1.61940	−0.0578727
$784$	26.6856	0.953055
$785$	74.4294	2.65650
$786$	−20.2301	−0.721585
$787$	−27.3815	−0.976043	−0.488022	−	0.872832i	$-0.662281\pi$
$787$	−27.3815	−0.976043	−0.488022	+	0.872832i	$0.662281\pi$
$788$	−0.115220	−0.00410456
$789$	44.3415	1.57860
$790$	−83.6826	−2.97729
$791$	5.42479	0.192883
$792$	−22.1864	−0.788358
$793$	18.9468	0.672820
$794$	1.69768	0.0602484
$795$	−35.1603	−1.24701
$796$	−2.02708	−0.0718479
$797$	−32.9641	−1.16765	−0.583823	−	0.811881i	$-0.698444\pi$
$797$	−32.9641	−1.16765	−0.583823	+	0.811881i	$0.698444\pi$
$798$	−7.76299	−0.274807
$799$	3.73265	0.132052
$800$	5.11614	0.180883
$801$	11.8250	0.417814
$802$	−20.4549	−0.722289
$803$	−3.07499	−0.108514
$804$	−1.91655	−0.0675914
$805$	6.01248	0.211912
$806$	0	0
$807$	−68.7611	−2.42051
$808$	−17.3271	−0.609564
$809$	23.6402	0.831146	0.415573	−	0.909560i	$-0.363581\pi$
$809$	23.6402	0.831146	0.415573	+	0.909560i	$0.363581\pi$
$810$	−47.0040	−1.65155
$811$	−26.3421	−0.924995	−0.462498	−	0.886620i	$-0.653047\pi$
$811$	−26.3421	−0.924995	−0.462498	+	0.886620i	$0.653047\pi$
$812$	−0.851870	−0.0298948
$813$	57.0879	2.00216
$814$	12.3092	0.431438
$815$	−61.1510	−2.14203
$816$	−3.49511	−0.122353
$817$	9.76246	0.341545
$818$	14.8544	0.519371
$819$	−4.82880	−0.168732
$820$	2.77119	0.0967742
$821$	29.7368	1.03782	0.518911	−	0.854828i	$-0.326337\pi$
$821$	29.7368	1.03782	0.518911	+	0.854828i	$0.326337\pi$
$822$	70.2757	2.45115
$823$	−30.2207	−1.05343	−0.526714	−	0.850043i	$-0.676576\pi$
$823$	−30.2207	−1.05343	−0.526714	+	0.850043i	$0.676576\pi$
$824$	29.8554	1.04006
$825$	55.4582	1.93081
$826$	−8.85786	−0.308204
$827$	33.9383	1.18015	0.590075	−	0.807348i	$-0.299098\pi$
$827$	33.9383	1.18015	0.590075	+	0.807348i	$0.299098\pi$
$828$	0.658898	0.0228983
$829$	21.1978	0.736231	0.368115	−	0.929780i	$-0.380003\pi$
$829$	21.1978	0.736231	0.368115	+	0.929780i	$0.380003\pi$
$830$	6.55456	0.227512
$831$	−29.6316	−1.02791
$832$	14.7502	0.511370
$833$	2.14631	0.0743652
$834$	−48.7363	−1.68760
$835$	−32.2853	−1.11728
$836$	−0.752562	−0.0260279
$837$	0	0
$838$	23.6591	0.817290
$839$	−2.36633	−0.0816947	−0.0408473	−	0.999165i	$-0.513006\pi$
$839$	−2.36633	−0.0816947	−0.0408473	+	0.999165i	$0.513006\pi$
$840$	−20.0472	−0.691694
$841$	71.0842	2.45118
$842$	1.65184	0.0569262
$843$	10.1868	0.350852
$844$	−0.115143	−0.00396340
$845$	33.7432	1.16080
$846$	49.1527	1.68990
$847$	3.27241	0.112441
$848$	16.2893	0.559376
$849$	66.4512	2.28060
$850$	4.19306	0.143821
$851$	6.54122	0.224230
$852$	−0.426882	−0.0146247
$853$	−33.3658	−1.14242	−0.571211	−	0.820803i	$-0.693526\pi$
$853$	−33.3658	−1.14242	−0.571211	+	0.820803i	$0.693526\pi$
$854$	11.2951	0.386511
$855$	−30.4750	−1.04222
$856$	19.9939	0.683378
$857$	18.0395	0.616219	0.308109	−	0.951351i	$-0.400304\pi$
$857$	18.0395	0.616219	0.308109	+	0.951351i	$0.400304\pi$
$858$	−18.4253	−0.629029
$859$	34.6322	1.18164	0.590818	−	0.806805i	$-0.298805\pi$
$859$	34.6322	1.18164	0.590818	+	0.806805i	$0.298805\pi$
$860$	−1.40893	−0.0480440
$861$	−14.0881	−0.480122
$862$	−25.6597	−0.873974
$863$	−9.27126	−0.315597	−0.157799	−	0.987471i	$-0.550440\pi$
$863$	−9.27126	−0.315597	−0.157799	+	0.987471i	$0.550440\pi$
$864$	−0.0968311	−0.00329426
$865$	11.1127	0.377843
$866$	37.6165	1.27826
$867$	41.5877	1.41239
$868$	0	0
$869$	41.2415	1.39902
$870$	−131.629	−4.46263
$871$	14.3944	0.487736
$872$	27.6763	0.937236
$873$	18.8457	0.637830
$874$	−7.95576	−0.269108
$875$	10.5204	0.355656
$876$	−0.304493	−0.0102878
$877$	24.7877	0.837021	0.418511	−	0.908212i	$-0.362552\pi$
$877$	24.7877	0.837021	0.418511	+	0.908212i	$0.362552\pi$
$878$	−25.7098	−0.867665
$879$	22.7377	0.766924
$880$	−40.7135	−1.37245
$881$	31.1875	1.05073	0.525367	−	0.850876i	$-0.323928\pi$
$881$	31.1875	1.05073	0.525367	+	0.850876i	$0.323928\pi$
$882$	28.2632	0.951673
$883$	−13.8748	−0.466925	−0.233463	−	0.972366i	$-0.575006\pi$
$883$	−13.8748	−0.466925	−0.233463	+	0.972366i	$0.575006\pi$
$884$	−0.0700273	−0.00235527
$885$	−68.8008	−2.31272
$886$	−6.10522	−0.205109
$887$	22.0130	0.739124	0.369562	−	0.929206i	$-0.379508\pi$
$887$	22.0130	0.739124	0.369562	+	0.929206i	$0.379508\pi$
$888$	−21.8102	−0.731902
$889$	−8.52118	−0.285791
$890$	20.6059	0.690713
$891$	23.1651	0.776061
$892$	−0.806369	−0.0269992
$893$	−29.8331	−0.998328
$894$	36.7170	1.22800
$895$	85.7671	2.86688
$896$	9.75569	0.325915
$897$	−9.79134	−0.326923
$898$	−1.36433	−0.0455284
$899$	0	0
$900$	2.77555	0.0925184
$901$	1.31014	0.0436470
$902$	−27.1693	−0.904638
$903$	7.16267	0.238359
$904$	−18.5369	−0.616528
$905$	−37.1618	−1.23530
$906$	−9.63318	−0.320041
$907$	11.4865	0.381403	0.190701	−	0.981648i	$-0.438924\pi$
$907$	11.4865	0.381403	0.190701	+	0.981648i	$0.438924\pi$
$908$	1.00639	0.0333984
$909$	−19.3255	−0.640987
$910$	−8.41458	−0.278941
$911$	−42.5542	−1.40988	−0.704942	−	0.709265i	$-0.749027\pi$
$911$	−42.5542	−1.40988	−0.704942	+	0.709265i	$0.749027\pi$
$912$	27.9346	0.925007
$913$	−3.23030	−0.106907
$914$	14.1610	0.468403
$915$	87.7316	2.90032
$916$	0.385873	0.0127496
$917$	4.55320	0.150360
$918$	−0.0793604	−0.00261928
$919$	16.0130	0.528220	0.264110	−	0.964493i	$-0.414922\pi$
$919$	16.0130	0.528220	0.264110	+	0.964493i	$0.414922\pi$
$920$	−20.5450	−0.677350
$921$	−32.5561	−1.07276
$922$	12.9914	0.427849
$923$	3.20614	0.105531
$924$	−0.552151	−0.0181644
$925$	27.5543	0.905981
$926$	44.6862	1.46848
$927$	33.2988	1.09368
$928$	5.98448	0.196450
$929$	17.4278	0.571788	0.285894	−	0.958261i	$-0.407709\pi$
$929$	17.4278	0.571788	0.285894	+	0.958261i	$0.407709\pi$
$930$	0	0
$931$	−17.1543	−0.562211
$932$	−2.39039	−0.0782999
$933$	27.8153	0.910633
$934$	34.7153	1.13592
$935$	−3.27457	−0.107090
$936$	16.5004	0.539331
$937$	−14.7986	−0.483448	−0.241724	−	0.970345i	$-0.577713\pi$
$937$	−14.7986	−0.483448	−0.241724	+	0.970345i	$0.577713\pi$
$938$	8.58122	0.280187
$939$	−2.05757	−0.0671464
$940$	4.30554	0.140431
$941$	−6.09091	−0.198558	−0.0992790	−	0.995060i	$-0.531654\pi$
$941$	−6.09091	−0.198558	−0.0992790	+	0.995060i	$0.531654\pi$
$942$	−72.2584	−2.35431
$943$	−14.4380	−0.470165
$944$	31.8744	1.03742
$945$	−0.479355	−0.0155934
$946$	13.8134	0.449111
$947$	−50.1684	−1.63025	−0.815126	−	0.579283i	$-0.803333\pi$
$947$	−50.1684	−1.63025	−0.815126	+	0.579283i	$0.803333\pi$
$948$	4.08383	0.132637
$949$	2.28692	0.0742366
$950$	−33.5130	−1.08730
$951$	−47.1777	−1.52984
$952$	0.746996	0.0242103
$953$	−0.599640	−0.0194242	−0.00971212	−	0.999953i	$-0.503092\pi$
$953$	−0.599640	−0.0194242	−0.00971212	+	0.999953i	$0.503092\pi$
$954$	17.2523	0.558564
$955$	68.3349	2.21127
$956$	0.0392423	0.00126919
$957$	64.8709	2.09698
$958$	31.0182	1.00215
$959$	−15.8170	−0.510756
$960$	68.2995	2.20436
$961$	0	0
$962$	−9.15456	−0.295155
$963$	22.2999	0.718605
$964$	2.31437	0.0745409
$965$	−79.8555	−2.57064
$966$	−5.83710	−0.187806
$967$	51.1635	1.64531	0.822654	−	0.568543i	$-0.192493\pi$
$967$	51.1635	1.64531	0.822654	+	0.568543i	$0.192493\pi$
$968$	−11.1820	−0.359404
$969$	2.24677	0.0721766
$970$	32.8401	1.05443
$971$	−8.58287	−0.275437	−0.137719	−	0.990471i	$-0.543977\pi$
$971$	−8.58287	−0.275437	−0.137719	+	0.990471i	$0.543977\pi$
$972$	2.34527	0.0752245
$973$	10.9691	0.351653
$974$	21.0421	0.674231
$975$	−41.2452	−1.32090
$976$	−40.6448	−1.30101
$977$	37.3558	1.19512	0.597559	−	0.801825i	$-0.296137\pi$
$977$	37.3558	1.19512	0.597559	+	0.801825i	$0.296137\pi$
$978$	59.3673	1.89836
$979$	−10.1553	−0.324564
$980$	2.47573	0.0790843
$981$	30.8683	0.985550
$982$	−11.7470	−0.374861
$983$	−2.52379	−0.0804965	−0.0402483	−	0.999190i	$-0.512815\pi$
$983$	−2.52379	−0.0804965	−0.0402483	+	0.999190i	$0.512815\pi$
$984$	48.1401	1.53465
$985$	4.00704	0.127675
$986$	4.90473	0.156198
$987$	−21.8884	−0.696716
$988$	0.559692	0.0178062
$989$	7.34053	0.233415
$990$	−43.1206	−1.37046
$991$	30.5038	0.968984	0.484492	−	0.874796i	$-0.339005\pi$
$991$	30.5038	0.968984	0.484492	+	0.874796i	$0.339005\pi$
$992$	0	0
$993$	29.3274	0.930675
$994$	1.91134	0.0606239
$995$	70.4962	2.23488
$996$	−0.319872	−0.0101355
$997$	−37.9043	−1.20044	−0.600221	−	0.799834i	$-0.704921\pi$
$997$	−37.9043	−1.20044	−0.600221	+	0.799834i	$0.704921\pi$
$998$	19.3790	0.613432
$999$	−0.521510	−0.0164998

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.a.l.1.5	✓	16
3.2	odd	2		8649.2.a.bs.1.12		16
31.2	even	5		961.2.d.s.531.5		64
31.3	odd	30		961.2.g.w.846.5		128
31.4	even	5		961.2.d.s.388.12		64
31.5	even	3		961.2.c.l.521.6		32
31.6	odd	6		961.2.c.l.439.5		32
31.7	even	15		961.2.g.w.235.11		128
31.8	even	5		961.2.d.s.374.12		64
31.9	even	15		961.2.g.w.732.11		128
31.10	even	15		961.2.g.w.844.6		128
31.11	odd	30		961.2.g.w.338.11		128
31.12	odd	30		961.2.g.w.547.6		128
31.13	odd	30		961.2.g.w.448.6		128
31.14	even	15		961.2.g.w.816.12		128
31.15	odd	10		961.2.d.s.628.6		64
31.16	even	5		961.2.d.s.628.5		64
31.17	odd	30		961.2.g.w.816.11		128
31.18	even	15		961.2.g.w.448.5		128
31.19	even	15		961.2.g.w.547.5		128
31.20	even	15		961.2.g.w.338.12		128
31.21	odd	30		961.2.g.w.844.5		128
31.22	odd	30		961.2.g.w.732.12		128
31.23	odd	10		961.2.d.s.374.11		64
31.24	odd	30		961.2.g.w.235.12		128
31.25	even	3		961.2.c.l.439.6		32
31.26	odd	6		961.2.c.l.521.5		32
31.27	odd	10		961.2.d.s.388.11		64
31.28	even	15		961.2.g.w.846.6		128
31.29	odd	10		961.2.d.s.531.6		64
31.30	odd	2	inner	961.2.a.l.1.6	yes	16
93.92	even	2		8649.2.a.bs.1.11		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
961.2.a.l.1.5	✓	16	1.1	even	1	trivial
961.2.a.l.1.6	yes	16	31.30	odd	2	inner
961.2.c.l.439.5		32	31.6	odd	6
961.2.c.l.439.6		32	31.25	even	3
961.2.c.l.521.5		32	31.26	odd	6
961.2.c.l.521.6		32	31.5	even	3
961.2.d.s.374.11		64	31.23	odd	10
961.2.d.s.374.12		64	31.8	even	5
961.2.d.s.388.11		64	31.27	odd	10
961.2.d.s.388.12		64	31.4	even	5
961.2.d.s.531.5		64	31.2	even	5
961.2.d.s.531.6		64	31.29	odd	10
961.2.d.s.628.5		64	31.16	even	5
961.2.d.s.628.6		64	31.15	odd	10
961.2.g.w.235.11		128	31.7	even	15
961.2.g.w.235.12		128	31.24	odd	30
961.2.g.w.338.11		128	31.11	odd	30
961.2.g.w.338.12		128	31.20	even	15
961.2.g.w.448.5		128	31.18	even	15
961.2.g.w.448.6		128	31.13	odd	30
961.2.g.w.547.5		128	31.19	even	15
961.2.g.w.547.6		128	31.12	odd	30
961.2.g.w.732.11		128	31.9	even	15
961.2.g.w.732.12		128	31.22	odd	30
961.2.g.w.816.11		128	31.17	odd	30
961.2.g.w.816.12		128	31.14	even	15
961.2.g.w.844.5		128	31.21	odd	30
961.2.g.w.844.6		128	31.10	even	15
961.2.g.w.846.5		128	31.3	odd	30
961.2.g.w.846.6		128	31.28	even	15
8649.2.a.bs.1.11		16	93.92	even	2
8649.2.a.bs.1.12		16	3.2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.a (trivial)

\(f(q)\)	\(=\)	\(q-1.45116 q^{2} -2.46287 q^{3} +0.105856 q^{4} -3.68139 q^{5} +3.57401 q^{6} -0.804403 q^{7} +2.74870 q^{8} +3.06572 q^{9} +5.34227 q^{10} -2.63285 q^{11} -0.260710 q^{12} +1.95809 q^{13} +1.16731 q^{14} +9.06678 q^{15} -4.20051 q^{16} -0.337845 q^{17} -4.44885 q^{18} +2.70022 q^{19} -0.389698 q^{20} +1.98114 q^{21} +3.82067 q^{22} +2.03034 q^{23} -6.76969 q^{24} +8.55262 q^{25} -2.84150 q^{26} -0.161872 q^{27} -0.0851512 q^{28} +10.0042 q^{29} -13.1573 q^{30} +0.598196 q^{32} +6.48436 q^{33} +0.490266 q^{34} +2.96132 q^{35} +0.324526 q^{36} +3.22174 q^{37} -3.91845 q^{38} -4.82252 q^{39} -10.1190 q^{40} -7.11112 q^{41} -2.87494 q^{42} +3.61543 q^{43} -0.278704 q^{44} -11.2861 q^{45} -2.94634 q^{46} -11.0484 q^{47} +10.3453 q^{48} -6.35294 q^{49} -12.4112 q^{50} +0.832068 q^{51} +0.207276 q^{52} -3.87793 q^{53} +0.234902 q^{54} +9.69253 q^{55} -2.21106 q^{56} -6.65029 q^{57} -14.5177 q^{58} -7.58824 q^{59} +0.959776 q^{60} +9.67616 q^{61} -2.46608 q^{63} +7.53294 q^{64} -7.20849 q^{65} -9.40982 q^{66} +7.35125 q^{67} -0.0357631 q^{68} -5.00045 q^{69} -4.29734 q^{70} +1.63738 q^{71} +8.42676 q^{72} +1.16793 q^{73} -4.67525 q^{74} -21.0640 q^{75} +0.285836 q^{76} +2.11787 q^{77} +6.99823 q^{78} -15.6642 q^{79} +15.4637 q^{80} -8.79851 q^{81} +10.3194 q^{82} +1.22692 q^{83} +0.209716 q^{84} +1.24374 q^{85} -5.24655 q^{86} -24.6391 q^{87} -7.23691 q^{88} +3.85715 q^{89} +16.3779 q^{90} -1.57509 q^{91} +0.214924 q^{92} +16.0330 q^{94} -9.94057 q^{95} -1.47328 q^{96} +6.14722 q^{97} +9.21911 q^{98} -8.07158 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{2} + 8 q^{4} - 16 q^{5} - 16 q^{7} + 8 q^{10} - 8 q^{14} - 8 q^{16} - 24 q^{18} - 32 q^{19} - 24 q^{20} - 8 q^{28} - 8 q^{32} - 32 q^{33} - 16 q^{35} - 40 q^{36} - 24 q^{38} - 32 q^{39} - 32 q^{41}+ \cdots + 16 q^{98}+O(q^{100}) \) 16 * q - 8 * q^2 + 8 * q^4 - 16 * q^5 - 16 * q^7 + 8 * q^10 - 8 * q^14 - 8 * q^16 - 24 * q^18 - 32 * q^19 - 24 * q^20 - 8 * q^28 - 8 * q^32 - 32 * q^33 - 16 * q^35 - 40 * q^36 - 24 * q^38 - 32 * q^39 - 32 * q^41 - 16 * q^45 - 32 * q^47 - 16 * q^49 - 32 * q^50 - 32 * q^51 - 48 * q^56 - 64 * q^59 - 16 * q^63 - 16 * q^64 + 16 * q^67 - 32 * q^69 + 88 * q^70 - 48 * q^71 + 48 * q^72 + 40 * q^76 + 32 * q^78 - 40 * q^80 - 16 * q^81 + 88 * q^82 - 32 * q^87 + 40 * q^90 - 32 * q^94 - 48 * q^95 + 16 * q^98

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