LMFDB - Embedded newform 966.4.a.p.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,4,Mod(1,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("966.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	966.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:	$56.9958450655$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 456x^{3} - 1295x^{2} + 36752x + 117404 $ x^5 - 456x^3 - 1295x^2 + 36752*x + 117404
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$20.4354$ of defining polynomial
Character	$\chi$	$=$	966.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +18.4354 q^{5} -6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +18.4354 q^{5} -6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +36.8709 q^{10} +34.5380 q^{11} -12.0000 q^{12} -64.3019 q^{13} -14.0000 q^{14} -55.3063 q^{15} +16.0000 q^{16} +55.4917 q^{17} +18.0000 q^{18} +52.9741 q^{19} +73.7417 q^{20} +21.0000 q^{21} +69.0760 q^{22} +23.0000 q^{23} -24.0000 q^{24} +214.865 q^{25} -128.604 q^{26} -27.0000 q^{27} -28.0000 q^{28} +9.74033 q^{29} -110.613 q^{30} +134.733 q^{31} +32.0000 q^{32} -103.614 q^{33} +110.983 q^{34} -129.048 q^{35} +36.0000 q^{36} +17.8032 q^{37} +105.948 q^{38} +192.906 q^{39} +147.483 q^{40} +108.436 q^{41} +42.0000 q^{42} +359.669 q^{43} +138.152 q^{44} +165.919 q^{45} +46.0000 q^{46} -420.523 q^{47} -48.0000 q^{48} +49.0000 q^{49} +429.730 q^{50} -166.475 q^{51} -257.208 q^{52} -413.245 q^{53} -54.0000 q^{54} +636.723 q^{55} -56.0000 q^{56} -158.922 q^{57} +19.4807 q^{58} -13.4889 q^{59} -221.225 q^{60} -72.2361 q^{61} +269.466 q^{62} -63.0000 q^{63} +64.0000 q^{64} -1185.43 q^{65} -207.228 q^{66} +337.587 q^{67} +221.967 q^{68} -69.0000 q^{69} -258.096 q^{70} +686.403 q^{71} +72.0000 q^{72} -513.396 q^{73} +35.6063 q^{74} -644.595 q^{75} +211.896 q^{76} -241.766 q^{77} +385.811 q^{78} +27.3435 q^{79} +294.967 q^{80} +81.0000 q^{81} +216.871 q^{82} -477.519 q^{83} +84.0000 q^{84} +1023.01 q^{85} +719.338 q^{86} -29.2210 q^{87} +276.304 q^{88} +1379.60 q^{89} +331.838 q^{90} +450.113 q^{91} +92.0000 q^{92} -404.200 q^{93} -841.045 q^{94} +976.600 q^{95} -96.0000 q^{96} +1448.81 q^{97} +98.0000 q^{98} +310.842 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 10 q^{2} - 15 q^{3} + 20 q^{4} - 10 q^{5} - 30 q^{6} - 35 q^{7} + 40 q^{8} + 45 q^{9}+O(q^{10}) $ 5 * q + 10 * q^2 - 15 * q^3 + 20 * q^4 - 10 * q^5 - 30 * q^6 - 35 * q^7 + 40 * q^8 + 45 * q^9	\( 5 q + 10 q^{2} - 15 q^{3} + 20 q^{4} - 10 q^{5} - 30 q^{6} - 35 q^{7} + 40 q^{8} + 45 q^{9} - 20 q^{10} + 9 q^{11} - 60 q^{12} - 102 q^{13} - 70 q^{14} + 30 q^{15} + 80 q^{16} - 30 q^{17} + 90 q^{18} - 27 q^{19} - 40 q^{20} + 105 q^{21} + 18 q^{22} + 115 q^{23} - 120 q^{24} + 307 q^{25} - 204 q^{26} - 135 q^{27} - 140 q^{28} + 135 q^{29} + 60 q^{30} + 160 q^{31} + 160 q^{32} - 27 q^{33} - 60 q^{34} + 70 q^{35} + 180 q^{36} + 153 q^{37} - 54 q^{38} + 306 q^{39} - 80 q^{40} + 76 q^{41} + 210 q^{42} + 980 q^{43} + 36 q^{44} - 90 q^{45} + 230 q^{46} - 8 q^{47} - 240 q^{48} + 245 q^{49} + 614 q^{50} + 90 q^{51} - 408 q^{52} + 676 q^{53} - 270 q^{54} + 1403 q^{55} - 280 q^{56} + 81 q^{57} + 270 q^{58} - 208 q^{59} + 120 q^{60} + 204 q^{61} + 320 q^{62} - 315 q^{63} + 320 q^{64} + 971 q^{65} - 54 q^{66} + 767 q^{67} - 120 q^{68} - 345 q^{69} + 140 q^{70} + 1353 q^{71} + 360 q^{72} + 92 q^{73} + 306 q^{74} - 921 q^{75} - 108 q^{76} - 63 q^{77} + 612 q^{78} + 2958 q^{79} - 160 q^{80} + 405 q^{81} + 152 q^{82} + 1370 q^{83} + 420 q^{84} + 1725 q^{85} + 1960 q^{86} - 405 q^{87} + 72 q^{88} + 1207 q^{89} - 180 q^{90} + 714 q^{91} + 460 q^{92} - 480 q^{93} - 16 q^{94} + 2995 q^{95} - 480 q^{96} + 1633 q^{97} + 490 q^{98} + 81 q^{99}+O(q^{100}) \) 5 * q + 10 * q^2 - 15 * q^3 + 20 * q^4 - 10 * q^5 - 30 * q^6 - 35 * q^7 + 40 * q^8 + 45 * q^9 - 20 * q^10 + 9 * q^11 - 60 * q^12 - 102 * q^13 - 70 * q^14 + 30 * q^15 + 80 * q^16 - 30 * q^17 + 90 * q^18 - 27 * q^19 - 40 * q^20 + 105 * q^21 + 18 * q^22 + 115 * q^23 - 120 * q^24 + 307 * q^25 - 204 * q^26 - 135 * q^27 - 140 * q^28 + 135 * q^29 + 60 * q^30 + 160 * q^31 + 160 * q^32 - 27 * q^33 - 60 * q^34 + 70 * q^35 + 180 * q^36 + 153 * q^37 - 54 * q^38 + 306 * q^39 - 80 * q^40 + 76 * q^41 + 210 * q^42 + 980 * q^43 + 36 * q^44 - 90 * q^45 + 230 * q^46 - 8 * q^47 - 240 * q^48 + 245 * q^49 + 614 * q^50 + 90 * q^51 - 408 * q^52 + 676 * q^53 - 270 * q^54 + 1403 * q^55 - 280 * q^56 + 81 * q^57 + 270 * q^58 - 208 * q^59 + 120 * q^60 + 204 * q^61 + 320 * q^62 - 315 * q^63 + 320 * q^64 + 971 * q^65 - 54 * q^66 + 767 * q^67 - 120 * q^68 - 345 * q^69 + 140 * q^70 + 1353 * q^71 + 360 * q^72 + 92 * q^73 + 306 * q^74 - 921 * q^75 - 108 * q^76 - 63 * q^77 + 612 * q^78 + 2958 * q^79 - 160 * q^80 + 405 * q^81 + 152 * q^82 + 1370 * q^83 + 420 * q^84 + 1725 * q^85 + 1960 * q^86 - 405 * q^87 + 72 * q^88 + 1207 * q^89 - 180 * q^90 + 714 * q^91 + 460 * q^92 - 480 * q^93 - 16 * q^94 + 2995 * q^95 - 480 * q^96 + 1633 * q^97 + 490 * q^98 + 81 * 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 $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	4.00000	0.500000
$5$	18.4354	1.64892	0.824458	−	0.565924i	$-0.191480\pi$
$5$	18.4354	1.64892	0.824458	+	0.565924i	$0.191480\pi$
$6$	−6.00000	−0.408248
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	36.8709	1.16596
$11$	34.5380	0.946691	0.473345	−	0.880877i	$-0.343046\pi$
$11$	34.5380	0.946691	0.473345	+	0.880877i	$0.343046\pi$
$12$	−12.0000	−0.288675
$13$	−64.3019	−1.37186	−0.685928	−	0.727669i	$-0.740604\pi$
$13$	−64.3019	−1.37186	−0.685928	+	0.727669i	$0.740604\pi$
$14$	−14.0000	−0.267261
$15$	−55.3063	−0.952002
$16$	16.0000	0.250000
$17$	55.4917	0.791688	0.395844	−	0.918318i	$-0.370452\pi$
$17$	55.4917	0.791688	0.395844	+	0.918318i	$0.370452\pi$
$18$	18.0000	0.235702
$19$	52.9741	0.639636	0.319818	−	0.947479i	$-0.396378\pi$
$19$	52.9741	0.639636	0.319818	+	0.947479i	$0.396378\pi$
$20$	73.7417	0.824458
$21$	21.0000	0.218218
$22$	69.0760	0.669411
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	−24.0000	−0.204124
$25$	214.865	1.71892
$26$	−128.604	−0.970049
$27$	−27.0000	−0.192450
$28$	−28.0000	−0.188982
$29$	9.74033	0.0623701	0.0311851	−	0.999514i	$-0.490072\pi$
$29$	9.74033	0.0623701	0.0311851	+	0.999514i	$0.490072\pi$
$30$	−110.613	−0.673167
$31$	134.733	0.780607	0.390303	−	0.920686i	$-0.372370\pi$
$31$	134.733	0.780607	0.390303	+	0.920686i	$0.372370\pi$
$32$	32.0000	0.176777
$33$	−103.614	−0.546572
$34$	110.983	0.559808
$35$	−129.048	−0.623231
$36$	36.0000	0.166667
$37$	17.8032	0.0791033	0.0395516	−	0.999218i	$-0.487407\pi$
$37$	17.8032	0.0791033	0.0395516	+	0.999218i	$0.487407\pi$
$38$	105.948	0.452291
$39$	192.906	0.792042
$40$	147.483	0.582980
$41$	108.436	0.413044	0.206522	−	0.978442i	$-0.433785\pi$
$41$	108.436	0.413044	0.206522	+	0.978442i	$0.433785\pi$
$42$	42.0000	0.154303
$43$	359.669	1.27556	0.637779	−	0.770220i	$-0.279853\pi$
$43$	359.669	1.27556	0.637779	+	0.770220i	$0.279853\pi$
$44$	138.152	0.473345
$45$	165.919	0.549638
$46$	46.0000	0.147442
$47$	−420.523	−1.30510	−0.652548	−	0.757747i	$-0.726300\pi$
$47$	−420.523	−1.30510	−0.652548	+	0.757747i	$0.726300\pi$
$48$	−48.0000	−0.144338
$49$	49.0000	0.142857
$50$	429.730	1.21546
$51$	−166.475	−0.457082
$52$	−257.208	−0.685928
$53$	−413.245	−1.07101	−0.535505	−	0.844532i	$-0.679879\pi$
$53$	−413.245	−1.07101	−0.535505	+	0.844532i	$0.679879\pi$
$54$	−54.0000	−0.136083
$55$	636.723	1.56101
$56$	−56.0000	−0.133631
$57$	−158.922	−0.369294
$58$	19.4807	0.0441023
$59$	−13.4889	−0.0297645	−0.0148823	−	0.999889i	$-0.504737\pi$
$59$	−13.4889	−0.0297645	−0.0148823	+	0.999889i	$0.504737\pi$
$60$	−221.225	−0.476001
$61$	−72.2361	−0.151621	−0.0758105	−	0.997122i	$-0.524154\pi$
$61$	−72.2361	−0.151621	−0.0758105	+	0.997122i	$0.524154\pi$
$62$	269.466	0.551972
$63$	−63.0000	−0.125988
$64$	64.0000	0.125000
$65$	−1185.43	−2.26208
$66$	−207.228	−0.386485
$67$	337.587	0.615565	0.307782	−	0.951457i	$-0.400413\pi$
$67$	337.587	0.615565	0.307782	+	0.951457i	$0.400413\pi$
$68$	221.967	0.395844
$69$	−69.0000	−0.120386
$70$	−258.096	−0.440691
$71$	686.403	1.14734	0.573670	−	0.819087i	$-0.305519\pi$
$71$	686.403	1.14734	0.573670	+	0.819087i	$0.305519\pi$
$72$	72.0000	0.117851
$73$	−513.396	−0.823129	−0.411564	−	0.911381i	$-0.635017\pi$
$73$	−513.396	−0.823129	−0.411564	+	0.911381i	$0.635017\pi$
$74$	35.6063	0.0559345
$75$	−644.595	−0.992420
$76$	211.896	0.319818
$77$	−241.766	−0.357815
$78$	385.811	0.560058
$79$	27.3435	0.0389415	0.0194708	−	0.999810i	$-0.493802\pi$
$79$	27.3435	0.0389415	0.0194708	+	0.999810i	$0.493802\pi$
$80$	294.967	0.412229
$81$	81.0000	0.111111
$82$	216.871	0.292066
$83$	−477.519	−0.631500	−0.315750	−	0.948842i	$-0.602256\pi$
$83$	−477.519	−0.631500	−0.315750	+	0.948842i	$0.602256\pi$
$84$	84.0000	0.109109
$85$	1023.01	1.30543
$86$	719.338	0.901955
$87$	−29.2210	−0.0360094
$88$	276.304	0.334706
$89$	1379.60	1.64312	0.821560	−	0.570123i	$-0.193104\pi$
$89$	1379.60	1.64312	0.821560	+	0.570123i	$0.193104\pi$
$90$	331.838	0.388653
$91$	450.113	0.518513
$92$	92.0000	0.104257
$93$	−404.200	−0.450683
$94$	−841.045	−0.922842
$95$	976.600	1.05471
$96$	−96.0000	−0.102062
$97$	1448.81	1.51654	0.758268	−	0.651943i	$-0.226046\pi$
$97$	1448.81	1.51654	0.758268	+	0.651943i	$0.226046\pi$
$98$	98.0000	0.101015
$99$	310.842	0.315564
$100$	859.461	0.859461
$101$	771.449	0.760020	0.380010	−	0.924982i	$-0.375921\pi$
$101$	771.449	0.760020	0.380010	+	0.924982i	$0.375921\pi$
$102$	−332.950	−0.323205
$103$	474.602	0.454019	0.227010	−	0.973893i	$-0.427105\pi$
$103$	474.602	0.454019	0.227010	+	0.973893i	$0.427105\pi$
$104$	−514.415	−0.485025
$105$	387.144	0.359823
$106$	−826.490	−0.757319
$107$	−136.377	−0.123215	−0.0616077	−	0.998100i	$-0.519623\pi$
$107$	−136.377	−0.123215	−0.0616077	+	0.998100i	$0.519623\pi$
$108$	−108.000	−0.0962250
$109$	−117.956	−0.103653	−0.0518264	−	0.998656i	$-0.516504\pi$
$109$	−117.956	−0.103653	−0.0518264	+	0.998656i	$0.516504\pi$
$110$	1273.45	1.10380
$111$	−53.4095	−0.0456703
$112$	−112.000	−0.0944911
$113$	−390.082	−0.324742	−0.162371	−	0.986730i	$-0.551914\pi$
$113$	−390.082	−0.324742	−0.162371	+	0.986730i	$0.551914\pi$
$114$	−317.844	−0.261130
$115$	424.015	0.343823
$116$	38.9613	0.0311851
$117$	−578.717	−0.457286
$118$	−26.9778	−0.0210467
$119$	−388.442	−0.299230
$120$	−442.450	−0.336583
$121$	−138.127	−0.103777
$122$	−144.472	−0.107212
$123$	−325.307	−0.238471
$124$	538.933	0.390303
$125$	1656.70	1.18544
$126$	−126.000	−0.0890871
$127$	207.481	0.144968	0.0724840	−	0.997370i	$-0.476907\pi$
$127$	207.481	0.144968	0.0724840	+	0.997370i	$0.476907\pi$
$128$	128.000	0.0883883
$129$	−1079.01	−0.736444
$130$	−2370.87	−1.59953
$131$	−880.035	−0.586939	−0.293470	−	0.955968i	$-0.594810\pi$
$131$	−880.035	−0.586939	−0.293470	+	0.955968i	$0.594810\pi$
$132$	−414.456	−0.273286
$133$	−370.818	−0.241760
$134$	675.175	0.435270
$135$	−497.757	−0.317334
$136$	443.933	0.279904
$137$	1352.23	0.843278	0.421639	−	0.906764i	$-0.361455\pi$
$137$	1352.23	0.843278	0.421639	+	0.906764i	$0.361455\pi$
$138$	−138.000	−0.0851257
$139$	2747.07	1.67628	0.838141	−	0.545454i	$-0.183643\pi$
$139$	2747.07	1.67628	0.838141	+	0.545454i	$0.183643\pi$
$140$	−516.192	−0.311616
$141$	1261.57	0.753498
$142$	1372.81	0.811291
$143$	−2220.86	−1.29872
$144$	144.000	0.0833333
$145$	179.567	0.102843
$146$	−1026.79	−0.582040
$147$	−147.000	−0.0824786
$148$	71.2126	0.0395516
$149$	−3299.19	−1.81396	−0.906982	−	0.421170i	$-0.861620\pi$
$149$	−3299.19	−1.81396	−0.906982	+	0.421170i	$0.861620\pi$
$150$	−1289.19	−0.701747
$151$	2301.20	1.24019	0.620096	−	0.784526i	$-0.287094\pi$
$151$	2301.20	1.24019	0.620096	+	0.784526i	$0.287094\pi$
$152$	423.792	0.226145
$153$	499.425	0.263896
$154$	−483.532	−0.253014
$155$	2483.87	1.28715
$156$	771.623	0.396021
$157$	−2137.42	−1.08653	−0.543264	−	0.839562i	$-0.682812\pi$
$157$	−2137.42	−1.08653	−0.543264	+	0.839562i	$0.682812\pi$
$158$	54.6869	0.0275358
$159$	1239.73	0.618348
$160$	589.934	0.291490
$161$	−161.000	−0.0788110
$162$	162.000	0.0785674
$163$	859.516	0.413022	0.206511	−	0.978444i	$-0.433789\pi$
$163$	859.516	0.413022	0.206511	+	0.978444i	$0.433789\pi$
$164$	433.743	0.206522
$165$	−1910.17	−0.901251
$166$	−955.038	−0.446538
$167$	−1414.22	−0.655301	−0.327651	−	0.944799i	$-0.606257\pi$
$167$	−1414.22	−0.655301	−0.327651	+	0.944799i	$0.606257\pi$
$168$	168.000	0.0771517
$169$	1937.73	0.881990
$170$	2046.03	0.923076
$171$	476.767	0.213212
$172$	1438.68	0.637779
$173$	2442.56	1.07343	0.536717	−	0.843762i	$-0.319664\pi$
$173$	2442.56	1.07343	0.536717	+	0.843762i	$0.319664\pi$
$174$	−58.4420	−0.0254625
$175$	−1504.06	−0.649691
$176$	552.608	0.236673
$177$	40.4668	0.0171846
$178$	2759.21	1.16186
$179$	2753.31	1.14968	0.574838	−	0.818267i	$-0.305065\pi$
$179$	2753.31	1.14968	0.574838	+	0.818267i	$0.305065\pi$
$180$	663.676	0.274819
$181$	−4530.10	−1.86033	−0.930164	−	0.367145i	$-0.880335\pi$
$181$	−4530.10	−1.86033	−0.930164	+	0.367145i	$0.880335\pi$
$182$	900.226	0.366644
$183$	216.708	0.0875384
$184$	184.000	0.0737210
$185$	328.209	0.130435
$186$	−808.399	−0.318681
$187$	1916.57	0.749484
$188$	−1682.09	−0.652548
$189$	189.000	0.0727393
$190$	1953.20	0.745789
$191$	727.613	0.275645	0.137823	−	0.990457i	$-0.455990\pi$
$191$	727.613	0.275645	0.137823	+	0.990457i	$0.455990\pi$
$192$	−192.000	−0.0721688
$193$	2742.57	1.02287	0.511437	−	0.859321i	$-0.329113\pi$
$193$	2742.57	1.02287	0.511437	+	0.859321i	$0.329113\pi$
$194$	2897.61	1.07235
$195$	3556.30	1.30601
$196$	196.000	0.0714286
$197$	−255.351	−0.0923503	−0.0461752	−	0.998933i	$-0.514703\pi$
$197$	−255.351	−0.0923503	−0.0461752	+	0.998933i	$0.514703\pi$
$198$	621.684	0.223137
$199$	1038.75	0.370026	0.185013	−	0.982736i	$-0.440767\pi$
$199$	1038.75	0.370026	0.185013	+	0.982736i	$0.440767\pi$
$200$	1718.92	0.607730
$201$	−1012.76	−0.355397
$202$	1542.90	0.537415
$203$	−68.1823	−0.0235737
$204$	−665.900	−0.228541
$205$	1999.06	0.681075
$206$	949.205	0.321040
$207$	207.000	0.0695048
$208$	−1028.83	−0.342964
$209$	1829.62	0.605537
$210$	774.288	0.254433
$211$	3270.25	1.06698	0.533491	−	0.845806i	$-0.320880\pi$
$211$	3270.25	1.06698	0.533491	+	0.845806i	$0.320880\pi$
$212$	−1652.98	−0.535505
$213$	−2059.21	−0.662417
$214$	−272.754	−0.0871265
$215$	6630.65	2.10329
$216$	−216.000	−0.0680414
$217$	−943.133	−0.295042
$218$	−235.912	−0.0732935
$219$	1540.19	0.475234
$220$	2546.89	0.780506
$221$	−3568.22	−1.08608
$222$	−106.819	−0.0322938
$223$	−5514.61	−1.65599	−0.827994	−	0.560737i	$-0.810518\pi$
$223$	−5514.61	−1.65599	−0.827994	+	0.560737i	$0.810518\pi$
$224$	−224.000	−0.0668153
$225$	1933.79	0.572974
$226$	−780.165	−0.229627
$227$	3838.86	1.12244	0.561221	−	0.827666i	$-0.310332\pi$
$227$	3838.86	1.12244	0.561221	+	0.827666i	$0.310332\pi$
$228$	−635.689	−0.184647
$229$	−1852.49	−0.534569	−0.267285	−	0.963618i	$-0.586126\pi$
$229$	−1852.49	−0.534569	−0.267285	+	0.963618i	$0.586126\pi$
$230$	848.030	0.243119
$231$	725.298	0.206585
$232$	77.9226	0.0220512
$233$	−942.090	−0.264886	−0.132443	−	0.991191i	$-0.542282\pi$
$233$	−942.090	−0.264886	−0.132443	+	0.991191i	$0.542282\pi$
$234$	−1157.43	−0.323350
$235$	−7752.51	−2.15199
$236$	−53.9557	−0.0148823
$237$	−82.0304	−0.0224829
$238$	−776.883	−0.211588
$239$	772.803	0.209157	0.104578	−	0.994517i	$-0.466651\pi$
$239$	772.803	0.209157	0.104578	+	0.994517i	$0.466651\pi$
$240$	−884.901	−0.238000
$241$	−4102.40	−1.09651	−0.548254	−	0.836312i	$-0.684707\pi$
$241$	−4102.40	−1.09651	−0.548254	+	0.836312i	$0.684707\pi$
$242$	−276.253	−0.0733811
$243$	−243.000	−0.0641500
$244$	−288.944	−0.0758105
$245$	903.336	0.235559
$246$	−650.614	−0.168625
$247$	−3406.33	−0.877489
$248$	1077.87	0.275986
$249$	1432.56	0.364597
$250$	3313.41	0.838233
$251$	−4195.43	−1.05503	−0.527516	−	0.849545i	$-0.676877\pi$
$251$	−4195.43	−1.05503	−0.527516	+	0.849545i	$0.676877\pi$
$252$	−252.000	−0.0629941
$253$	794.374	0.197399
$254$	414.961	0.102508
$255$	−3069.04	−0.753689
$256$	256.000	0.0625000
$257$	−1703.22	−0.413400	−0.206700	−	0.978404i	$-0.566272\pi$
$257$	−1703.22	−0.413400	−0.206700	+	0.978404i	$0.566272\pi$
$258$	−2158.01	−0.520744
$259$	−124.622	−0.0298982
$260$	−4741.73	−1.13104
$261$	87.6629	0.0207900
$262$	−1760.07	−0.415029
$263$	−1347.09	−0.315837	−0.157918	−	0.987452i	$-0.550478\pi$
$263$	−1347.09	−0.315837	−0.157918	+	0.987452i	$0.550478\pi$
$264$	−828.912	−0.193242
$265$	−7618.35	−1.76600
$266$	−741.637	−0.170950
$267$	−4138.81	−0.948655
$268$	1350.35	0.307782
$269$	−4838.85	−1.09677	−0.548383	−	0.836227i	$-0.684756\pi$
$269$	−4838.85	−1.09677	−0.548383	+	0.836227i	$0.684756\pi$
$270$	−995.513	−0.224389
$271$	4314.12	0.967025	0.483513	−	0.875337i	$-0.339361\pi$
$271$	4314.12	0.967025	0.483513	+	0.875337i	$0.339361\pi$
$272$	887.867	0.197922
$273$	−1350.34	−0.299364
$274$	2704.47	0.596288
$275$	7421.01	1.62729
$276$	−276.000	−0.0601929
$277$	−8047.33	−1.74555	−0.872775	−	0.488123i	$-0.837682\pi$
$277$	−8047.33	−1.74555	−0.872775	+	0.488123i	$0.837682\pi$
$278$	5494.13	1.18531
$279$	1212.60	0.260202
$280$	−1032.38	−0.220346
$281$	−3296.85	−0.699906	−0.349953	−	0.936767i	$-0.613802\pi$
$281$	−3296.85	−0.699906	−0.349953	+	0.936767i	$0.613802\pi$
$282$	2523.14	0.532803
$283$	−1400.79	−0.294235	−0.147118	−	0.989119i	$-0.547000\pi$
$283$	−1400.79	−0.294235	−0.147118	+	0.989119i	$0.547000\pi$
$284$	2745.61	0.573670
$285$	−2929.80	−0.608934
$286$	−4441.72	−0.918337
$287$	−759.050	−0.156116
$288$	288.000	0.0589256
$289$	−1833.68	−0.373229
$290$	359.134	0.0727210
$291$	−4346.42	−0.875572
$292$	−2053.58	−0.411564
$293$	−5287.90	−1.05434	−0.527171	−	0.849759i	$-0.676747\pi$
$293$	−5287.90	−1.05434	−0.527171	+	0.849759i	$0.676747\pi$
$294$	−294.000	−0.0583212
$295$	−248.674	−0.0490792
$296$	142.425	0.0279672
$297$	−932.526	−0.182191
$298$	−6598.39	−1.28267
$299$	−1478.94	−0.286052
$300$	−2578.38	−0.496210
$301$	−2517.68	−0.482115
$302$	4602.40	0.876948
$303$	−2314.35	−0.438798
$304$	847.585	0.159909
$305$	−1331.70	−0.250010
$306$	998.850	0.186603
$307$	−183.549	−0.0341228	−0.0170614	−	0.999854i	$-0.505431\pi$
$307$	−183.549	−0.0341228	−0.0170614	+	0.999854i	$0.505431\pi$
$308$	−967.064	−0.178908
$309$	−1423.81	−0.262128
$310$	4967.73	0.910155
$311$	−7241.01	−1.32026	−0.660128	−	0.751153i	$-0.729498\pi$
$311$	−7241.01	−1.32026	−0.660128	+	0.751153i	$0.729498\pi$
$312$	1543.25	0.280029
$313$	−3091.04	−0.558198	−0.279099	−	0.960262i	$-0.590036\pi$
$313$	−3091.04	−0.558198	−0.279099	+	0.960262i	$0.590036\pi$
$314$	−4274.84	−0.768291
$315$	−1161.43	−0.207744
$316$	109.374	0.0194708
$317$	−3273.40	−0.579977	−0.289988	−	0.957030i	$-0.593651\pi$
$317$	−3273.40	−0.579977	−0.289988	+	0.957030i	$0.593651\pi$
$318$	2479.47	0.437238
$319$	336.411	0.0590452
$320$	1179.87	0.206114
$321$	409.131	0.0711385
$322$	−322.000	−0.0557278
$323$	2939.62	0.506392
$324$	324.000	0.0555556
$325$	−13816.2	−2.35811
$326$	1719.03	0.292050
$327$	353.868	0.0598439
$328$	867.486	0.146033
$329$	2943.66	0.493280
$330$	−3820.34	−0.637281
$331$	5541.20	0.920158	0.460079	−	0.887878i	$-0.347821\pi$
$331$	5541.20	0.920158	0.460079	+	0.887878i	$0.347821\pi$
$332$	−1910.08	−0.315750
$333$	160.228	0.0263678
$334$	−2828.43	−0.463368
$335$	6223.57	1.01501
$336$	336.000	0.0545545
$337$	517.008	0.0835704	0.0417852	−	0.999127i	$-0.486695\pi$
$337$	517.008	0.0835704	0.0417852	+	0.999127i	$0.486695\pi$
$338$	3875.47	0.623661
$339$	1170.25	0.187490
$340$	4092.05	0.652714
$341$	4653.42	0.738993
$342$	953.533	0.150764
$343$	−343.000	−0.0539949
$344$	2877.35	0.450978
$345$	−1272.04	−0.198506
$346$	4885.12	0.759033
$347$	5393.68	0.834432	0.417216	−	0.908807i	$-0.363006\pi$
$347$	5393.68	0.834432	0.417216	+	0.908807i	$0.363006\pi$
$348$	−116.884	−0.0180047
$349$	2872.79	0.440621	0.220310	−	0.975430i	$-0.429293\pi$
$349$	2872.79	0.440621	0.220310	+	0.975430i	$0.429293\pi$
$350$	−3008.11	−0.459401
$351$	1736.15	0.264014
$352$	1105.22	0.167353
$353$	−8957.15	−1.35054	−0.675270	−	0.737570i	$-0.735973\pi$
$353$	−8957.15	−1.35054	−0.675270	+	0.737570i	$0.735973\pi$
$354$	80.9335	0.0121513
$355$	12654.1	1.89187
$356$	5518.41	0.821560
$357$	1165.32	0.172761
$358$	5506.62	0.812944
$359$	−2952.45	−0.434052	−0.217026	−	0.976166i	$-0.569636\pi$
$359$	−2952.45	−0.434052	−0.217026	+	0.976166i	$0.569636\pi$
$360$	1327.35	0.194327
$361$	−4052.75	−0.590866
$362$	−9060.19	−1.31545
$363$	414.380	0.0599154
$364$	1800.45	0.259257
$365$	−9464.67	−1.35727
$366$	433.416	0.0618990
$367$	1053.35	0.149821	0.0749105	−	0.997190i	$-0.476133\pi$
$367$	1053.35	0.149821	0.0749105	+	0.997190i	$0.476133\pi$
$368$	368.000	0.0521286
$369$	975.921	0.137681
$370$	656.418	0.0922312
$371$	2892.71	0.404804
$372$	−1616.80	−0.225342
$373$	−6765.88	−0.939207	−0.469603	−	0.882877i	$-0.655603\pi$
$373$	−6765.88	−0.939207	−0.469603	+	0.882877i	$0.655603\pi$
$374$	3833.14	0.529965
$375$	−4970.11	−0.684414
$376$	−3364.18	−0.461421
$377$	−626.321	−0.0855628
$378$	378.000	0.0514344
$379$	6674.73	0.904639	0.452319	−	0.891856i	$-0.350597\pi$
$379$	6674.73	0.904639	0.452319	+	0.891856i	$0.350597\pi$
$380$	3906.40	0.527353
$381$	−622.442	−0.0836973
$382$	1455.23	0.194911
$383$	6205.80	0.827941	0.413971	−	0.910290i	$-0.364142\pi$
$383$	6205.80	0.827941	0.413971	+	0.910290i	$0.364142\pi$
$384$	−384.000	−0.0510310
$385$	−4457.06	−0.590007
$386$	5485.15	0.723282
$387$	3237.02	0.425186
$388$	5795.22	0.758268
$389$	307.509	0.0400806	0.0200403	−	0.999799i	$-0.493621\pi$
$389$	307.509	0.0400806	0.0200403	+	0.999799i	$0.493621\pi$
$390$	7112.60	0.923488
$391$	1276.31	0.165078
$392$	392.000	0.0505076
$393$	2640.11	0.338870
$394$	−510.702	−0.0653016
$395$	504.088	0.0642112
$396$	1243.37	0.157782
$397$	−14252.8	−1.80184	−0.900919	−	0.433987i	$-0.857107\pi$
$397$	−14252.8	−1.80184	−0.900919	+	0.433987i	$0.857107\pi$
$398$	2077.50	0.261648
$399$	1112.46	0.139580
$400$	3437.84	0.429730
$401$	2983.31	0.371520	0.185760	−	0.982595i	$-0.440525\pi$
$401$	2983.31	0.371520	0.185760	+	0.982595i	$0.440525\pi$
$402$	−2025.52	−0.251303
$403$	−8663.60	−1.07088
$404$	3085.80	0.380010
$405$	1493.27	0.183213
$406$	−136.365	−0.0166691
$407$	614.885	0.0748863
$408$	−1331.80	−0.161603
$409$	5071.88	0.613175	0.306587	−	0.951842i	$-0.400813\pi$
$409$	5071.88	0.613175	0.306587	+	0.951842i	$0.400813\pi$
$410$	3998.12	0.481593
$411$	−4056.70	−0.486867
$412$	1898.41	0.227010
$413$	94.4225	0.0112499
$414$	414.000	0.0491473
$415$	−8803.27	−1.04129
$416$	−2057.66	−0.242512
$417$	−8241.20	−0.967802
$418$	3659.24	0.428180
$419$	−13489.0	−1.57275	−0.786373	−	0.617752i	$-0.788044\pi$
$419$	−13489.0	−1.57275	−0.786373	+	0.617752i	$0.788044\pi$
$420$	1548.58	0.179911
$421$	5034.90	0.582865	0.291432	−	0.956591i	$-0.405868\pi$
$421$	5034.90	0.582865	0.291432	+	0.956591i	$0.405868\pi$
$422$	6540.50	0.754470
$423$	−3784.70	−0.435032
$424$	−3305.96	−0.378659
$425$	11923.2	1.36085
$426$	−4118.42	−0.468399
$427$	505.652	0.0573073
$428$	−545.508	−0.0616077
$429$	6662.58	0.749819
$430$	13261.3	1.48725
$431$	−12264.4	−1.37067	−0.685334	−	0.728229i	$-0.740344\pi$
$431$	−12264.4	−1.37067	−0.685334	+	0.728229i	$0.740344\pi$
$432$	−432.000	−0.0481125
$433$	−13144.9	−1.45890	−0.729448	−	0.684037i	$-0.760223\pi$
$433$	−13144.9	−1.45890	−0.729448	+	0.684037i	$0.760223\pi$
$434$	−1886.27	−0.208626
$435$	−538.701	−0.0593764
$436$	−471.824	−0.0518264
$437$	1218.40	0.133373
$438$	3080.37	0.336041
$439$	−15067.1	−1.63807	−0.819035	−	0.573744i	$-0.805490\pi$
$439$	−15067.1	−1.63807	−0.819035	+	0.573744i	$0.805490\pi$
$440$	5093.78	0.551901
$441$	441.000	0.0476190
$442$	−7136.44	−0.767977
$443$	−5902.02	−0.632987	−0.316493	−	0.948595i	$-0.602506\pi$
$443$	−5902.02	−0.632987	−0.316493	+	0.948595i	$0.602506\pi$
$444$	−213.638	−0.0228351
$445$	25433.6	2.70936
$446$	−11029.2	−1.17096
$447$	9897.58	1.04729
$448$	−448.000	−0.0472456
$449$	5993.75	0.629983	0.314992	−	0.949094i	$-0.397998\pi$
$449$	5993.75	0.629983	0.314992	+	0.949094i	$0.397998\pi$
$450$	3867.57	0.405154
$451$	3745.15	0.391025
$452$	−1560.33	−0.162371
$453$	−6903.60	−0.716025
$454$	7677.73	0.793686
$455$	8298.03	0.854984
$456$	−1271.38	−0.130565
$457$	−8901.84	−0.911182	−0.455591	−	0.890189i	$-0.650572\pi$
$457$	−8901.84	−0.911182	−0.455591	+	0.890189i	$0.650572\pi$
$458$	−3704.99	−0.377997
$459$	−1498.27	−0.152361
$460$	1696.06	0.171911
$461$	12402.1	1.25298	0.626490	−	0.779430i	$-0.284491\pi$
$461$	12402.1	1.25298	0.626490	+	0.779430i	$0.284491\pi$
$462$	1450.60	0.146078
$463$	−13832.0	−1.38840	−0.694200	−	0.719782i	$-0.744242\pi$
$463$	−13832.0	−1.38840	−0.694200	+	0.719782i	$0.744242\pi$
$464$	155.845	0.0155925
$465$	−7451.60	−0.743139
$466$	−1884.18	−0.187302
$467$	3318.71	0.328848	0.164424	−	0.986390i	$-0.447424\pi$
$467$	3318.71	0.328848	0.164424	+	0.986390i	$0.447424\pi$
$468$	−2314.87	−0.228643
$469$	−2363.11	−0.232662
$470$	−15505.0	−1.52169
$471$	6412.27	0.627307
$472$	−107.911	−0.0105234
$473$	12422.2	1.20756
$474$	−164.061	−0.0158978
$475$	11382.3	1.09948
$476$	−1553.77	−0.149615
$477$	−3719.20	−0.357003
$478$	1545.61	0.147896
$479$	−18915.9	−1.80436	−0.902179	−	0.431361i	$-0.858033\pi$
$479$	−18915.9	−1.80436	−0.902179	+	0.431361i	$0.858033\pi$
$480$	−1769.80	−0.168292
$481$	−1144.78	−0.108518
$482$	−8204.79	−0.775349
$483$	483.000	0.0455016
$484$	−552.506	−0.0518883
$485$	26709.4	2.50064
$486$	−486.000	−0.0453609
$487$	10350.8	0.963121	0.481560	−	0.876413i	$-0.340070\pi$
$487$	10350.8	0.963121	0.481560	+	0.876413i	$0.340070\pi$
$488$	−577.888	−0.0536061
$489$	−2578.55	−0.238458
$490$	1806.67	0.166566
$491$	10735.4	0.986728	0.493364	−	0.869823i	$-0.335767\pi$
$491$	10735.4	0.986728	0.493364	+	0.869823i	$0.335767\pi$
$492$	−1301.23	−0.119236
$493$	540.507	0.0493777
$494$	−6812.66	−0.620478
$495$	5730.51	0.520338
$496$	2155.73	0.195152
$497$	−4804.82	−0.433653
$498$	2865.11	0.257809
$499$	12637.1	1.13370	0.566848	−	0.823823i	$-0.308163\pi$
$499$	12637.1	1.13370	0.566848	+	0.823823i	$0.308163\pi$
$500$	6626.81	0.592720
$501$	4242.65	0.378338
$502$	−8390.86	−0.746021
$503$	1946.40	0.172537	0.0862683	−	0.996272i	$-0.472506\pi$
$503$	1946.40	0.172537	0.0862683	+	0.996272i	$0.472506\pi$
$504$	−504.000	−0.0445435
$505$	14222.0	1.25321
$506$	1588.75	0.139582
$507$	−5813.20	−0.509217
$508$	829.923	0.0724840
$509$	−9888.62	−0.861111	−0.430555	−	0.902564i	$-0.641682\pi$
$509$	−9888.62	−0.861111	−0.430555	+	0.902564i	$0.641682\pi$
$510$	−6138.08	−0.532938
$511$	3593.77	0.311113
$512$	512.000	0.0441942
$513$	−1430.30	−0.123098
$514$	−3406.44	−0.292318
$515$	8749.50	0.748639
$516$	−4316.03	−0.368222
$517$	−14524.0	−1.23552
$518$	−249.244	−0.0211412
$519$	−7327.67	−0.619748
$520$	−9483.46	−0.799764
$521$	−4292.75	−0.360977	−0.180488	−	0.983577i	$-0.557768\pi$
$521$	−4292.75	−0.360977	−0.180488	+	0.983577i	$0.557768\pi$
$522$	175.326	0.0147008
$523$	−20360.4	−1.70229	−0.851145	−	0.524931i	$-0.824091\pi$
$523$	−20360.4	−1.70229	−0.851145	+	0.524931i	$0.824091\pi$
$524$	−3520.14	−0.293470
$525$	4512.17	0.375099
$526$	−2694.18	−0.223330
$527$	7476.57	0.617997
$528$	−1657.82	−0.136643
$529$	529.000	0.0434783
$530$	−15236.7	−1.24875
$531$	−121.400	−0.00992152
$532$	−1483.27	−0.120880
$533$	−6972.62	−0.566637
$534$	−8277.62	−0.670801
$535$	−2514.17	−0.203172
$536$	2700.70	0.217635
$537$	−8259.93	−0.663766
$538$	−9677.71	−0.775531
$539$	1692.36	0.135242
$540$	−1991.03	−0.158667
$541$	9384.08	0.745754	0.372877	−	0.927881i	$-0.378371\pi$
$541$	9384.08	0.745754	0.372877	+	0.927881i	$0.378371\pi$
$542$	8628.23	0.683790
$543$	13590.3	1.07406
$544$	1775.73	0.139952
$545$	−2174.57	−0.170915
$546$	−2700.68	−0.211682
$547$	14738.4	1.15204	0.576022	−	0.817434i	$-0.304604\pi$
$547$	14738.4	1.15204	0.576022	+	0.817434i	$0.304604\pi$
$548$	5408.94	0.421639
$549$	−650.124	−0.0505403
$550$	14842.0	1.15067
$551$	515.985	0.0398942
$552$	−552.000	−0.0425628
$553$	−191.404	−0.0147185
$554$	−16094.7	−1.23429
$555$	−984.627	−0.0753064
$556$	10988.3	0.838141
$557$	25077.8	1.90769	0.953843	−	0.300306i	$-0.0970888\pi$
$557$	25077.8	1.90769	0.953843	+	0.300306i	$0.0970888\pi$
$558$	2425.20	0.183991
$559$	−23127.4	−1.74988
$560$	−2064.77	−0.155808
$561$	−5749.71	−0.432715
$562$	−6593.70	−0.494908
$563$	−11183.5	−0.837174	−0.418587	−	0.908177i	$-0.637475\pi$
$563$	−11183.5	−0.837174	−0.418587	+	0.908177i	$0.637475\pi$
$564$	5046.27	0.376749
$565$	−7191.34	−0.535472
$566$	−2801.59	−0.208056
$567$	−567.000	−0.0419961
$568$	5491.23	0.405646
$569$	15086.2	1.11151	0.555754	−	0.831347i	$-0.312430\pi$
$569$	15086.2	1.11151	0.555754	+	0.831347i	$0.312430\pi$
$570$	−5859.60	−0.430582
$571$	10312.0	0.755772	0.377886	−	0.925852i	$-0.376651\pi$
$571$	10312.0	0.755772	0.377886	+	0.925852i	$0.376651\pi$
$572$	−8883.43	−0.649362
$573$	−2182.84	−0.159144
$574$	−1518.10	−0.110391
$575$	4941.90	0.358420
$576$	576.000	0.0416667
$577$	−26467.9	−1.90966	−0.954828	−	0.297157i	$-0.903961\pi$
$577$	−26467.9	−1.90966	−0.954828	+	0.297157i	$0.903961\pi$
$578$	−3667.35	−0.263913
$579$	−8227.72	−0.590557
$580$	718.268	0.0514215
$581$	3342.63	0.238685
$582$	−8692.83	−0.619123
$583$	−14272.6	−1.01392
$584$	−4107.16	−0.291020
$585$	−10668.9	−0.754025
$586$	−10575.8	−0.745532
$587$	−2904.42	−0.204222	−0.102111	−	0.994773i	$-0.532560\pi$
$587$	−2904.42	−0.204222	−0.102111	+	0.994773i	$0.532560\pi$
$588$	−588.000	−0.0412393
$589$	7137.37	0.499304
$590$	−497.348	−0.0347042
$591$	766.054	0.0533185
$592$	284.851	0.0197758
$593$	23842.3	1.65107	0.825535	−	0.564350i	$-0.190873\pi$
$593$	23842.3	1.65107	0.825535	+	0.564350i	$0.190873\pi$
$594$	−1865.05	−0.128828
$595$	−7161.09	−0.493405
$596$	−13196.8	−0.906982
$597$	−3116.25	−0.213634
$598$	−2957.89	−0.202269
$599$	16598.0	1.13218	0.566090	−	0.824344i	$-0.308456\pi$
$599$	16598.0	1.13218	0.566090	+	0.824344i	$0.308456\pi$
$600$	−5156.76	−0.350873
$601$	5656.47	0.383914	0.191957	−	0.981403i	$-0.438517\pi$
$601$	5656.47	0.383914	0.191957	+	0.981403i	$0.438517\pi$
$602$	−5035.36	−0.340907
$603$	3038.29	0.205188
$604$	9204.79	0.620096
$605$	−2546.42	−0.171119
$606$	−4628.69	−0.310277
$607$	−19688.3	−1.31651	−0.658256	−	0.752794i	$-0.728706\pi$
$607$	−19688.3	−1.31651	−0.658256	+	0.752794i	$0.728706\pi$
$608$	1695.17	0.113073
$609$	204.547	0.0136103
$610$	−2663.41	−0.176784
$611$	27040.4	1.79040
$612$	1997.70	0.131948
$613$	10991.0	0.724181	0.362090	−	0.932143i	$-0.382063\pi$
$613$	10991.0	0.724181	0.362090	+	0.932143i	$0.382063\pi$
$614$	−367.099	−0.0241285
$615$	−5997.18	−0.393219
$616$	−1934.13	−0.126507
$617$	−2640.92	−0.172317	−0.0861583	−	0.996281i	$-0.527459\pi$
$617$	−2640.92	−0.172317	−0.0861583	+	0.996281i	$0.527459\pi$
$618$	−2847.61	−0.185353
$619$	25733.5	1.67095	0.835473	−	0.549532i	$-0.185194\pi$
$619$	25733.5	1.67095	0.835473	+	0.549532i	$0.185194\pi$
$620$	9935.46	0.643577
$621$	−621.000	−0.0401286
$622$	−14482.0	−0.933562
$623$	−9657.22	−0.621041
$624$	3086.49	0.198010
$625$	3683.89	0.235769
$626$	−6182.08	−0.394705
$627$	−5488.85	−0.349607
$628$	−8549.69	−0.543264
$629$	987.927	0.0626251
$630$	−2322.86	−0.146897
$631$	−9798.75	−0.618197	−0.309098	−	0.951030i	$-0.600027\pi$
$631$	−9798.75	−0.618197	−0.309098	+	0.951030i	$0.600027\pi$
$632$	218.748	0.0137679
$633$	−9810.74	−0.616022
$634$	−6546.80	−0.410105
$635$	3825.00	0.239040
$636$	4958.94	0.309174
$637$	−3150.79	−0.195980
$638$	672.823	0.0417513
$639$	6177.63	0.382446
$640$	2359.74	0.145745
$641$	434.132	0.0267507	0.0133753	−	0.999911i	$-0.495742\pi$
$641$	434.132	0.0267507	0.0133753	+	0.999911i	$0.495742\pi$
$642$	818.262	0.0503025
$643$	−9611.94	−0.589515	−0.294757	−	0.955572i	$-0.595239\pi$
$643$	−9611.94	−0.589515	−0.294757	+	0.955572i	$0.595239\pi$
$644$	−644.000	−0.0394055
$645$	−19891.9	−1.21433
$646$	5879.24	0.358073
$647$	12654.9	0.768955	0.384478	−	0.923134i	$-0.374382\pi$
$647$	12654.9	0.768955	0.384478	+	0.923134i	$0.374382\pi$
$648$	648.000	0.0392837
$649$	−465.880	−0.0281778
$650$	−27632.5	−1.66744
$651$	2829.40	0.170342
$652$	3438.07	0.206511
$653$	−7314.00	−0.438314	−0.219157	−	0.975690i	$-0.570331\pi$
$653$	−7314.00	−0.438314	−0.219157	+	0.975690i	$0.570331\pi$
$654$	707.737	0.0423160
$655$	−16223.8	−0.967813
$656$	1734.97	0.103261
$657$	−4620.56	−0.274376
$658$	5887.32	0.348802
$659$	−10721.1	−0.633740	−0.316870	−	0.948469i	$-0.602632\pi$
$659$	−10721.1	−0.633740	−0.316870	+	0.948469i	$0.602632\pi$
$660$	−7640.68	−0.450626
$661$	−31514.2	−1.85440	−0.927202	−	0.374562i	$-0.877793\pi$
$661$	−31514.2	−1.85440	−0.927202	+	0.374562i	$0.877793\pi$
$662$	11082.4	0.650650
$663$	10704.7	0.627050
$664$	−3820.15	−0.223269
$665$	−6836.20	−0.398641
$666$	320.457	0.0186448
$667$	224.027	0.0130051
$668$	−5656.86	−0.327651
$669$	16543.8	0.956085
$670$	12447.1	0.717723
$671$	−2494.89	−0.143538
$672$	672.000	0.0385758
$673$	−15337.5	−0.878479	−0.439239	−	0.898370i	$-0.644752\pi$
$673$	−15337.5	−0.878479	−0.439239	+	0.898370i	$0.644752\pi$
$674$	1034.02	0.0590932
$675$	−5801.36	−0.330807
$676$	7750.93	0.440995
$677$	22203.9	1.26051	0.630254	−	0.776389i	$-0.282951\pi$
$677$	22203.9	1.26051	0.630254	+	0.776389i	$0.282951\pi$
$678$	2340.49	0.132575
$679$	−10141.6	−0.573196
$680$	8184.10	0.461538
$681$	−11516.6	−0.648042
$682$	9306.83	0.522547
$683$	−31328.5	−1.75513	−0.877565	−	0.479458i	$-0.840833\pi$
$683$	−31328.5	−1.75513	−0.877565	+	0.479458i	$0.840833\pi$
$684$	1907.07	0.106606
$685$	24929.0	1.39049
$686$	−686.000	−0.0381802
$687$	5557.48	0.308634
$688$	5754.70	0.318889
$689$	26572.4	1.46927
$690$	−2544.09	−0.140365
$691$	−33017.3	−1.81771	−0.908855	−	0.417112i	$-0.863042\pi$
$691$	−33017.3	−1.81771	−0.908855	+	0.417112i	$0.863042\pi$
$692$	9770.23	0.536717
$693$	−2175.89	−0.119272
$694$	10787.4	0.590033
$695$	50643.4	2.76405
$696$	−233.768	−0.0127312
$697$	6017.28	0.327002
$698$	5745.57	0.311566
$699$	2826.27	0.152932
$700$	−6016.22	−0.324846
$701$	−16509.2	−0.889504	−0.444752	−	0.895654i	$-0.646708\pi$
$701$	−16509.2	−0.889504	−0.444752	+	0.895654i	$0.646708\pi$
$702$	3472.30	0.186686
$703$	943.105	0.0505973
$704$	2210.43	0.118336
$705$	23257.5	1.24245
$706$	−17914.3	−0.954976
$707$	−5400.14	−0.287261
$708$	161.867	0.00859228
$709$	−29509.6	−1.56313	−0.781564	−	0.623825i	$-0.785578\pi$
$709$	−29509.6	−1.56313	−0.781564	+	0.623825i	$0.785578\pi$
$710$	25308.3	1.33775
$711$	246.091	0.0129805
$712$	11036.8	0.580930
$713$	3098.86	0.162768
$714$	2330.65	0.122160
$715$	−40942.5	−2.14149
$716$	11013.2	0.574838
$717$	−2318.41	−0.120757
$718$	−5904.91	−0.306921
$719$	5239.54	0.271769	0.135885	−	0.990725i	$-0.456612\pi$
$719$	5239.54	0.271769	0.135885	+	0.990725i	$0.456612\pi$
$720$	2654.70	0.137410
$721$	−3322.22	−0.171603
$722$	−8105.50	−0.417805
$723$	12307.2	0.633070
$724$	−18120.4	−0.930164
$725$	2092.86	0.107209
$726$	828.759	0.0423666
$727$	−15182.6	−0.774539	−0.387269	−	0.921967i	$-0.626582\pi$
$727$	−15182.6	−0.774539	−0.387269	+	0.921967i	$0.626582\pi$
$728$	3600.91	0.183322
$729$	729.000	0.0370370
$730$	−18929.3	−0.959735
$731$	19958.6	1.00984
$732$	866.833	0.0437692
$733$	2252.82	0.113520	0.0567598	−	0.998388i	$-0.481923\pi$
$733$	2252.82	0.113520	0.0567598	+	0.998388i	$0.481923\pi$
$734$	2106.70	0.105939
$735$	−2710.01	−0.136000
$736$	736.000	0.0368605
$737$	11659.6	0.582750
$738$	1951.84	0.0973555
$739$	18929.8	0.942279	0.471139	−	0.882059i	$-0.343843\pi$
$739$	18929.8	0.942279	0.471139	+	0.882059i	$0.343843\pi$
$740$	1312.84	0.0652173
$741$	10219.0	0.506618
$742$	5785.43	0.286240
$743$	−15651.2	−0.772793	−0.386397	−	0.922333i	$-0.626280\pi$
$743$	−15651.2	−0.772793	−0.386397	+	0.922333i	$0.626280\pi$
$744$	−3233.60	−0.159341
$745$	−60822.1	−2.99107
$746$	−13531.8	−0.664120
$747$	−4297.67	−0.210500
$748$	7666.28	0.374742
$749$	954.639	0.0465711
$750$	−9940.22	−0.483954
$751$	17516.0	0.851088	0.425544	−	0.904938i	$-0.360083\pi$
$751$	17516.0	0.851088	0.425544	+	0.904938i	$0.360083\pi$
$752$	−6728.36	−0.326274
$753$	12586.3	0.609124
$754$	−1252.64	−0.0605021
$755$	42423.6	2.04497
$756$	756.000	0.0363696
$757$	27907.9	1.33993	0.669966	−	0.742391i	$-0.266308\pi$
$757$	27907.9	1.33993	0.669966	+	0.742391i	$0.266308\pi$
$758$	13349.5	0.639676
$759$	−2383.12	−0.113968
$760$	7812.80	0.372895
$761$	12068.4	0.574875	0.287437	−	0.957799i	$-0.407197\pi$
$761$	12068.4	0.574875	0.287437	+	0.957799i	$0.407197\pi$
$762$	−1244.88	−0.0591829
$763$	825.693	0.0391770
$764$	2910.45	0.137823
$765$	9207.11	0.435142
$766$	12411.6	0.585443
$767$	867.363	0.0408327
$768$	−768.000	−0.0360844
$769$	30637.0	1.43667	0.718336	−	0.695697i	$-0.244904\pi$
$769$	30637.0	1.43667	0.718336	+	0.695697i	$0.244904\pi$
$770$	−8914.12	−0.417198
$771$	5109.65	0.238677
$772$	10970.3	0.511437
$773$	1303.20	0.0606374	0.0303187	−	0.999540i	$-0.490348\pi$
$773$	1303.20	0.0606374	0.0303187	+	0.999540i	$0.490348\pi$
$774$	6474.04	0.300652
$775$	28949.5	1.34180
$776$	11590.4	0.536176
$777$	373.866	0.0172617
$778$	615.019	0.0283412
$779$	5744.28	0.264198
$780$	14225.2	0.653005
$781$	23707.0	1.08618
$782$	2552.62	0.116728
$783$	−262.989	−0.0120031
$784$	784.000	0.0357143
$785$	−39404.3	−1.79159
$786$	5280.21	0.239617
$787$	18239.1	0.826119	0.413059	−	0.910704i	$-0.364460\pi$
$787$	18239.1	0.826119	0.413059	+	0.910704i	$0.364460\pi$
$788$	−1021.40	−0.0461752
$789$	4041.27	0.182349
$790$	1008.18	0.0454042
$791$	2730.58	0.122741
$792$	2486.74	0.111569
$793$	4644.91	0.208002
$794$	−28505.7	−1.27409
$795$	22855.0	1.01960
$796$	4155.01	0.185013
$797$	28260.8	1.25602	0.628010	−	0.778206i	$-0.283870\pi$
$797$	28260.8	1.25602	0.628010	+	0.778206i	$0.283870\pi$
$798$	2224.91	0.0986980
$799$	−23335.5	−1.03323
$800$	6875.68	0.303865
$801$	12416.4	0.547706
$802$	5966.63	0.262704
$803$	−17731.7	−0.779248
$804$	−4051.05	−0.177698
$805$	−2968.10	−0.129953
$806$	−17327.2	−0.757227
$807$	14516.6	0.633218
$808$	6171.59	0.268708
$809$	−26382.5	−1.14655	−0.573275	−	0.819363i	$-0.694328\pi$
$809$	−26382.5	−1.14655	−0.573275	+	0.819363i	$0.694328\pi$
$810$	2986.54	0.129551
$811$	−38186.8	−1.65341	−0.826707	−	0.562633i	$-0.809789\pi$
$811$	−38186.8	−1.65341	−0.826707	+	0.562633i	$0.809789\pi$
$812$	−272.729	−0.0117868
$813$	−12942.3	−0.558312
$814$	1229.77	0.0529526
$815$	15845.6	0.681037
$816$	−2663.60	−0.114270
$817$	19053.1	0.815892
$818$	10143.8	0.433580
$819$	4051.02	0.172838
$820$	7996.24	0.340537
$821$	40532.5	1.72301	0.861506	−	0.507747i	$-0.169522\pi$
$821$	40532.5	1.72301	0.861506	+	0.507747i	$0.169522\pi$
$822$	−8113.40	−0.344267
$823$	25607.7	1.08460	0.542302	−	0.840184i	$-0.317553\pi$
$823$	25607.7	1.08460	0.542302	+	0.840184i	$0.317553\pi$
$824$	3796.82	0.160520
$825$	−22263.0	−0.939514
$826$	188.845	0.00795491
$827$	−2436.36	−0.102443	−0.0512215	−	0.998687i	$-0.516311\pi$
$827$	−2436.36	−0.102443	−0.0512215	+	0.998687i	$0.516311\pi$
$828$	828.000	0.0347524
$829$	−8037.00	−0.336715	−0.168357	−	0.985726i	$-0.553846\pi$
$829$	−8037.00	−0.336715	−0.168357	+	0.985726i	$0.553846\pi$
$830$	−17606.5	−0.736303
$831$	24142.0	1.00779
$832$	−4115.32	−0.171482
$833$	2719.09	0.113098
$834$	−16482.4	−0.684339
$835$	−26071.7	−1.08054
$836$	7318.47	0.302769
$837$	−3637.80	−0.150228
$838$	−26978.0	−1.11210
$839$	−32137.2	−1.32241	−0.661204	−	0.750206i	$-0.729954\pi$
$839$	−32137.2	−1.32241	−0.661204	+	0.750206i	$0.729954\pi$
$840$	3097.15	0.127217
$841$	−24294.1	−0.996110
$842$	10069.8	0.412147
$843$	9890.55	0.404091
$844$	13081.0	0.533491
$845$	35722.9	1.45433
$846$	−7569.41	−0.307614
$847$	966.886	0.0392238
$848$	−6611.92	−0.267753
$849$	4202.38	0.169877
$850$	23846.4	0.962266
$851$	409.473	0.0164942
$852$	−8236.84	−0.331208
$853$	23868.0	0.958060	0.479030	−	0.877799i	$-0.340989\pi$
$853$	23868.0	0.958060	0.479030	+	0.877799i	$0.340989\pi$
$854$	1011.30	0.0405224
$855$	8789.40	0.351568
$856$	−1091.02	−0.0435633
$857$	733.599	0.0292407	0.0146203	−	0.999893i	$-0.495346\pi$
$857$	733.599	0.0292407	0.0146203	+	0.999893i	$0.495346\pi$
$858$	13325.2	0.530202
$859$	−14120.1	−0.560850	−0.280425	−	0.959876i	$-0.590475\pi$
$859$	−14120.1	−0.560850	−0.280425	+	0.959876i	$0.590475\pi$
$860$	26522.6	1.05164
$861$	2277.15	0.0901336
$862$	−24528.9	−0.969208
$863$	12079.1	0.476451	0.238226	−	0.971210i	$-0.423434\pi$
$863$	12079.1	0.476451	0.238226	+	0.971210i	$0.423434\pi$
$864$	−864.000	−0.0340207
$865$	45029.6	1.77000
$866$	−26289.7	−1.03159
$867$	5501.03	0.215484
$868$	−3772.53	−0.147521
$869$	944.388	0.0368656
$870$	−1077.40	−0.0419855
$871$	−21707.5	−0.844467
$872$	−943.649	−0.0366468
$873$	13039.3	0.505512
$874$	2436.81	0.0943092
$875$	−11596.9	−0.448054
$876$	6160.75	0.237617
$877$	−268.608	−0.0103424	−0.00517118	−	0.999987i	$-0.501646\pi$
$877$	−268.608	−0.0103424	−0.00517118	+	0.999987i	$0.501646\pi$
$878$	−30134.2	−1.15829
$879$	15863.7	0.608725
$880$	10187.6	0.390253
$881$	−50422.8	−1.92825	−0.964125	−	0.265450i	$-0.914479\pi$
$881$	−50422.8	−1.92825	−0.964125	+	0.265450i	$0.914479\pi$
$882$	882.000	0.0336718
$883$	9972.07	0.380053	0.190026	−	0.981779i	$-0.439143\pi$
$883$	9972.07	0.380053	0.190026	+	0.981779i	$0.439143\pi$
$884$	−14272.9	−0.543042
$885$	746.022	0.0283359
$886$	−11804.0	−0.447589
$887$	43414.2	1.64341	0.821706	−	0.569912i	$-0.193023\pi$
$887$	43414.2	1.64341	0.821706	+	0.569912i	$0.193023\pi$
$888$	−427.276	−0.0161469
$889$	−1452.36	−0.0547927
$890$	50867.1	1.91581
$891$	2797.58	0.105188
$892$	−22058.4	−0.827994
$893$	−22276.8	−0.834786
$894$	19795.2	0.740547
$895$	50758.5	1.89572
$896$	−896.000	−0.0334077
$897$	4436.83	0.165152
$898$	11987.5	0.445466
$899$	1312.35	0.0486865
$900$	7735.15	0.286487
$901$	−22931.6	−0.847906
$902$	7490.31	0.276497
$903$	7553.05	0.278350
$904$	−3120.66	−0.114814
$905$	−83514.3	−3.06752
$906$	−13807.2	−0.506306
$907$	20768.0	0.760298	0.380149	−	0.924925i	$-0.375873\pi$
$907$	20768.0	0.760298	0.380149	+	0.924925i	$0.375873\pi$
$908$	15355.5	0.561221
$909$	6943.04	0.253340
$910$	16596.1	0.604565
$911$	24531.1	0.892152	0.446076	−	0.894995i	$-0.352821\pi$
$911$	24531.1	0.892152	0.446076	+	0.894995i	$0.352821\pi$
$912$	−2542.75	−0.0923235
$913$	−16492.5	−0.597835
$914$	−17803.7	−0.644303
$915$	3995.11	0.144343
$916$	−7409.98	−0.267285
$917$	6160.25	0.221842
$918$	−2996.55	−0.107735
$919$	7129.29	0.255902	0.127951	−	0.991781i	$-0.459160\pi$
$919$	7129.29	0.255902	0.127951	+	0.991781i	$0.459160\pi$
$920$	3392.12	0.121560
$921$	550.648	0.0197008
$922$	24804.2	0.885990
$923$	−44137.0	−1.57398
$924$	2901.19	0.103292
$925$	3825.28	0.135972
$926$	−27664.1	−0.981747
$927$	4271.42	0.151340
$928$	311.690	0.0110256
$929$	−27971.7	−0.987858	−0.493929	−	0.869502i	$-0.664440\pi$
$929$	−27971.7	−0.987858	−0.493929	+	0.869502i	$0.664440\pi$
$930$	−14903.2	−0.525478
$931$	2595.73	0.0913766
$932$	−3768.36	−0.132443
$933$	21723.0	0.762250
$934$	6637.43	0.232530
$935$	35332.8	1.23584
$936$	−4629.74	−0.161675
$937$	40944.1	1.42752	0.713760	−	0.700390i	$-0.246991\pi$
$937$	40944.1	1.42752	0.713760	+	0.700390i	$0.246991\pi$
$938$	−4726.22	−0.164517
$939$	9273.12	0.322276
$940$	−31010.1	−1.07600
$941$	−21899.9	−0.758679	−0.379339	−	0.925258i	$-0.623849\pi$
$941$	−21899.9	−0.758679	−0.379339	+	0.925258i	$0.623849\pi$
$942$	12824.5	0.443573
$943$	2494.02	0.0861257
$944$	−215.823	−0.00744114
$945$	3484.30	0.119941
$946$	24844.5	0.853873
$947$	−48519.8	−1.66492	−0.832461	−	0.554084i	$-0.813068\pi$
$947$	−48519.8	−1.66492	−0.832461	+	0.554084i	$0.813068\pi$
$948$	−328.122	−0.0112414
$949$	33012.3	1.12921
$950$	22764.6	0.777452
$951$	9820.21	0.334850
$952$	−3107.53	−0.105794
$953$	24180.2	0.821902	0.410951	−	0.911658i	$-0.365197\pi$
$953$	24180.2	0.821902	0.410951	+	0.911658i	$0.365197\pi$
$954$	−7438.41	−0.252440
$955$	13413.9	0.454515
$956$	3091.21	0.104578
$957$	−1009.23	−0.0340898
$958$	−37831.7	−1.27587
$959$	−9465.64	−0.318729
$960$	−3539.60	−0.119000
$961$	−11638.0	−0.390653
$962$	−2289.55	−0.0767341
$963$	−1227.39	−0.0410718
$964$	−16409.6	−0.548254
$965$	50560.5	1.68663
$966$	966.000	0.0321745
$967$	−11379.5	−0.378428	−0.189214	−	0.981936i	$-0.560594\pi$
$967$	−11379.5	−0.378428	−0.189214	+	0.981936i	$0.560594\pi$
$968$	−1105.01	−0.0366905
$969$	−8818.85	−0.292366
$970$	53418.7	1.76822
$971$	−13704.1	−0.452920	−0.226460	−	0.974020i	$-0.572715\pi$
$971$	−13704.1	−0.452920	−0.226460	+	0.974020i	$0.572715\pi$
$972$	−972.000	−0.0320750
$973$	−19229.5	−0.633575
$974$	20701.6	0.681029
$975$	41448.7	1.36146
$976$	−1155.78	−0.0379052
$977$	−47741.6	−1.56335	−0.781673	−	0.623688i	$-0.785633\pi$
$977$	−47741.6	−1.56335	−0.781673	+	0.623688i	$0.785633\pi$
$978$	−5157.10	−0.168615
$979$	47648.7	1.55553
$980$	3613.34	0.117780
$981$	−1061.60	−0.0345509
$982$	21470.9	0.697722
$983$	−15138.6	−0.491196	−0.245598	−	0.969372i	$-0.578984\pi$
$983$	−15138.6	−0.491196	−0.245598	+	0.969372i	$0.578984\pi$
$984$	−2602.46	−0.0843123
$985$	−4707.51	−0.152278
$986$	1081.01	0.0349153
$987$	−8830.97	−0.284795
$988$	−13625.3	−0.438744
$989$	8272.38	0.265972
$990$	11461.0	0.367934
$991$	14809.0	0.474697	0.237349	−	0.971425i	$-0.423722\pi$
$991$	14809.0	0.474697	0.237349	+	0.971425i	$0.423722\pi$
$992$	4311.46	0.137993
$993$	−16623.6	−0.531253
$994$	−9609.65	−0.306639
$995$	19149.8	0.610141
$996$	5730.23	0.182298
$997$	−42156.0	−1.33911	−0.669555	−	0.742762i	$-0.733515\pi$
$997$	−42156.0	−1.33911	−0.669555	+	0.742762i	$0.733515\pi$
$998$	25274.2	0.801644
$999$	−480.685	−0.0152234

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.4.a.p.1.5	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.4.a.p.1.5	✓	5	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	966.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +18.4354 q^{5} -6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +18.4354 q^{5} -6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +36.8709 q^{10} +34.5380 q^{11} -12.0000 q^{12} -64.3019 q^{13} -14.0000 q^{14} -55.3063 q^{15} +16.0000 q^{16} +55.4917 q^{17} +18.0000 q^{18} +52.9741 q^{19} +73.7417 q^{20} +21.0000 q^{21} +69.0760 q^{22} +23.0000 q^{23} -24.0000 q^{24} +214.865 q^{25} -128.604 q^{26} -27.0000 q^{27} -28.0000 q^{28} +9.74033 q^{29} -110.613 q^{30} +134.733 q^{31} +32.0000 q^{32} -103.614 q^{33} +110.983 q^{34} -129.048 q^{35} +36.0000 q^{36} +17.8032 q^{37} +105.948 q^{38} +192.906 q^{39} +147.483 q^{40} +108.436 q^{41} +42.0000 q^{42} +359.669 q^{43} +138.152 q^{44} +165.919 q^{45} +46.0000 q^{46} -420.523 q^{47} -48.0000 q^{48} +49.0000 q^{49} +429.730 q^{50} -166.475 q^{51} -257.208 q^{52} -413.245 q^{53} -54.0000 q^{54} +636.723 q^{55} -56.0000 q^{56} -158.922 q^{57} +19.4807 q^{58} -13.4889 q^{59} -221.225 q^{60} -72.2361 q^{61} +269.466 q^{62} -63.0000 q^{63} +64.0000 q^{64} -1185.43 q^{65} -207.228 q^{66} +337.587 q^{67} +221.967 q^{68} -69.0000 q^{69} -258.096 q^{70} +686.403 q^{71} +72.0000 q^{72} -513.396 q^{73} +35.6063 q^{74} -644.595 q^{75} +211.896 q^{76} -241.766 q^{77} +385.811 q^{78} +27.3435 q^{79} +294.967 q^{80} +81.0000 q^{81} +216.871 q^{82} -477.519 q^{83} +84.0000 q^{84} +1023.01 q^{85} +719.338 q^{86} -29.2210 q^{87} +276.304 q^{88} +1379.60 q^{89} +331.838 q^{90} +450.113 q^{91} +92.0000 q^{92} -404.200 q^{93} -841.045 q^{94} +976.600 q^{95} -96.0000 q^{96} +1448.81 q^{97} +98.0000 q^{98} +310.842 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 10 q^{2} - 15 q^{3} + 20 q^{4} - 10 q^{5} - 30 q^{6} - 35 q^{7} + 40 q^{8} + 45 q^{9}+O(q^{10}) \) 5 * q + 10 * q^2 - 15 * q^3 + 20 * q^4 - 10 * q^5 - 30 * q^6 - 35 * q^7 + 40 * q^8 + 45 * q^9	\( 5 q + 10 q^{2} - 15 q^{3} + 20 q^{4} - 10 q^{5} - 30 q^{6} - 35 q^{7} + 40 q^{8} + 45 q^{9} - 20 q^{10} + 9 q^{11} - 60 q^{12} - 102 q^{13} - 70 q^{14} + 30 q^{15} + 80 q^{16} - 30 q^{17} + 90 q^{18} - 27 q^{19} - 40 q^{20} + 105 q^{21} + 18 q^{22} + 115 q^{23} - 120 q^{24} + 307 q^{25} - 204 q^{26} - 135 q^{27} - 140 q^{28} + 135 q^{29} + 60 q^{30} + 160 q^{31} + 160 q^{32} - 27 q^{33} - 60 q^{34} + 70 q^{35} + 180 q^{36} + 153 q^{37} - 54 q^{38} + 306 q^{39} - 80 q^{40} + 76 q^{41} + 210 q^{42} + 980 q^{43} + 36 q^{44} - 90 q^{45} + 230 q^{46} - 8 q^{47} - 240 q^{48} + 245 q^{49} + 614 q^{50} + 90 q^{51} - 408 q^{52} + 676 q^{53} - 270 q^{54} + 1403 q^{55} - 280 q^{56} + 81 q^{57} + 270 q^{58} - 208 q^{59} + 120 q^{60} + 204 q^{61} + 320 q^{62} - 315 q^{63} + 320 q^{64} + 971 q^{65} - 54 q^{66} + 767 q^{67} - 120 q^{68} - 345 q^{69} + 140 q^{70} + 1353 q^{71} + 360 q^{72} + 92 q^{73} + 306 q^{74} - 921 q^{75} - 108 q^{76} - 63 q^{77} + 612 q^{78} + 2958 q^{79} - 160 q^{80} + 405 q^{81} + 152 q^{82} + 1370 q^{83} + 420 q^{84} + 1725 q^{85} + 1960 q^{86} - 405 q^{87} + 72 q^{88} + 1207 q^{89} - 180 q^{90} + 714 q^{91} + 460 q^{92} - 480 q^{93} - 16 q^{94} + 2995 q^{95} - 480 q^{96} + 1633 q^{97} + 490 q^{98} + 81 q^{99}+O(q^{100}) \) 5 * q + 10 * q^2 - 15 * q^3 + 20 * q^4 - 10 * q^5 - 30 * q^6 - 35 * q^7 + 40 * q^8 + 45 * q^9 - 20 * q^10 + 9 * q^11 - 60 * q^12 - 102 * q^13 - 70 * q^14 + 30 * q^15 + 80 * q^16 - 30 * q^17 + 90 * q^18 - 27 * q^19 - 40 * q^20 + 105 * q^21 + 18 * q^22 + 115 * q^23 - 120 * q^24 + 307 * q^25 - 204 * q^26 - 135 * q^27 - 140 * q^28 + 135 * q^29 + 60 * q^30 + 160 * q^31 + 160 * q^32 - 27 * q^33 - 60 * q^34 + 70 * q^35 + 180 * q^36 + 153 * q^37 - 54 * q^38 + 306 * q^39 - 80 * q^40 + 76 * q^41 + 210 * q^42 + 980 * q^43 + 36 * q^44 - 90 * q^45 + 230 * q^46 - 8 * q^47 - 240 * q^48 + 245 * q^49 + 614 * q^50 + 90 * q^51 - 408 * q^52 + 676 * q^53 - 270 * q^54 + 1403 * q^55 - 280 * q^56 + 81 * q^57 + 270 * q^58 - 208 * q^59 + 120 * q^60 + 204 * q^61 + 320 * q^62 - 315 * q^63 + 320 * q^64 + 971 * q^65 - 54 * q^66 + 767 * q^67 - 120 * q^68 - 345 * q^69 + 140 * q^70 + 1353 * q^71 + 360 * q^72 + 92 * q^73 + 306 * q^74 - 921 * q^75 - 108 * q^76 - 63 * q^77 + 612 * q^78 + 2958 * q^79 - 160 * q^80 + 405 * q^81 + 152 * q^82 + 1370 * q^83 + 420 * q^84 + 1725 * q^85 + 1960 * q^86 - 405 * q^87 + 72 * q^88 + 1207 * q^89 - 180 * q^90 + 714 * q^91 + 460 * q^92 - 480 * q^93 - 16 * q^94 + 2995 * q^95 - 480 * q^96 + 1633 * q^97 + 490 * q^98 + 81 * q^99

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