LMFDB - Embedded newform 2667.2.a.o.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2667,2,Mod(1,2667)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2667, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("2667.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2667 = 3 \cdot 7 \cdot 127 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2667.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:	$21.2961022191$
Analytic rank:	$0$
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} - 5 x^{15} - 13 x^{14} + 98 x^{13} + 9 x^{12} - 712 x^{11} + 565 x^{10} + 2282 x^{9} - 3082 x^{8} + \cdots + 4 $ x^16 - 5x^15 - 13x^14 + 98x^13 + 9x^12 - 712x^11 + 565x^10 + 2282x^9 - 3082x^8 - 2747x^7 + 5821x^6 - 158x^5 - 3341x^4 + 1002x^3 + 416x^2 - 148*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.48981$ of defining polynomial
Character	$\chi$	$=$	2667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.48981 q^{2} -1.00000 q^{3} +4.19916 q^{4} +1.44828 q^{5} +2.48981 q^{6} -1.00000 q^{7} -5.47548 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.48981 q^{2} -1.00000 q^{3} +4.19916 q^{4} +1.44828 q^{5} +2.48981 q^{6} -1.00000 q^{7} -5.47548 q^{8} +1.00000 q^{9} -3.60594 q^{10} -3.27519 q^{11} -4.19916 q^{12} -3.24893 q^{13} +2.48981 q^{14} -1.44828 q^{15} +5.23459 q^{16} +2.00096 q^{17} -2.48981 q^{18} -7.49049 q^{19} +6.08155 q^{20} +1.00000 q^{21} +8.15461 q^{22} -5.11491 q^{23} +5.47548 q^{24} -2.90249 q^{25} +8.08921 q^{26} -1.00000 q^{27} -4.19916 q^{28} -2.27043 q^{29} +3.60594 q^{30} -9.36316 q^{31} -2.08219 q^{32} +3.27519 q^{33} -4.98200 q^{34} -1.44828 q^{35} +4.19916 q^{36} +6.96565 q^{37} +18.6499 q^{38} +3.24893 q^{39} -7.93002 q^{40} +11.0274 q^{41} -2.48981 q^{42} -7.34145 q^{43} -13.7531 q^{44} +1.44828 q^{45} +12.7352 q^{46} +3.00580 q^{47} -5.23459 q^{48} +1.00000 q^{49} +7.22664 q^{50} -2.00096 q^{51} -13.6427 q^{52} +10.8847 q^{53} +2.48981 q^{54} -4.74340 q^{55} +5.47548 q^{56} +7.49049 q^{57} +5.65295 q^{58} -8.25654 q^{59} -6.08155 q^{60} +9.29811 q^{61} +23.3125 q^{62} -1.00000 q^{63} -5.28494 q^{64} -4.70535 q^{65} -8.15461 q^{66} +2.47721 q^{67} +8.40233 q^{68} +5.11491 q^{69} +3.60594 q^{70} +6.76717 q^{71} -5.47548 q^{72} +10.4082 q^{73} -17.3432 q^{74} +2.90249 q^{75} -31.4537 q^{76} +3.27519 q^{77} -8.08921 q^{78} +6.43106 q^{79} +7.58115 q^{80} +1.00000 q^{81} -27.4562 q^{82} +15.7272 q^{83} +4.19916 q^{84} +2.89794 q^{85} +18.2788 q^{86} +2.27043 q^{87} +17.9333 q^{88} -9.26856 q^{89} -3.60594 q^{90} +3.24893 q^{91} -21.4783 q^{92} +9.36316 q^{93} -7.48388 q^{94} -10.8483 q^{95} +2.08219 q^{96} +3.36147 q^{97} -2.48981 q^{98} -3.27519 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 5 q^{2} - 16 q^{3} + 19 q^{4} - q^{5} - 5 q^{6} - 16 q^{7} + 6 q^{8} + 16 q^{9}+O(q^{10}) $ 16 * q + 5 * q^2 - 16 * q^3 + 19 * q^4 - q^5 - 5 * q^6 - 16 * q^7 + 6 * q^8 + 16 * q^9	\( 16 q + 5 q^{2} - 16 q^{3} + 19 q^{4} - q^{5} - 5 q^{6} - 16 q^{7} + 6 q^{8} + 16 q^{9} - 12 q^{10} + 11 q^{11} - 19 q^{12} + 18 q^{13} - 5 q^{14} + q^{15} + 25 q^{16} - 5 q^{17} + 5 q^{18} - 11 q^{19} - q^{20} + 16 q^{21} + q^{22} + 13 q^{23} - 6 q^{24} + 33 q^{25} + 8 q^{26} - 16 q^{27} - 19 q^{28} + 24 q^{29} + 12 q^{30} - 42 q^{31} + 42 q^{32} - 11 q^{33} + 9 q^{34} + q^{35} + 19 q^{36} + 40 q^{37} + 38 q^{38} - 18 q^{39} - 61 q^{40} + 9 q^{41} + 5 q^{42} + 7 q^{43} + 3 q^{44} - q^{45} + 24 q^{46} + 31 q^{47} - 25 q^{48} + 16 q^{49} + 6 q^{50} + 5 q^{51} + 52 q^{52} + 66 q^{53} - 5 q^{54} - 36 q^{55} - 6 q^{56} + 11 q^{57} + 19 q^{58} - 7 q^{59} + q^{60} + 6 q^{61} + 52 q^{62} - 16 q^{63} + 10 q^{64} + 51 q^{65} - q^{66} + 16 q^{67} + 14 q^{68} - 13 q^{69} + 12 q^{70} + 46 q^{71} + 6 q^{72} + 39 q^{73} + 72 q^{74} - 33 q^{75} + 24 q^{76} - 11 q^{77} - 8 q^{78} + 4 q^{79} - 2 q^{80} + 16 q^{81} - 18 q^{82} + 15 q^{83} + 19 q^{84} - 4 q^{85} + 14 q^{86} - 24 q^{87} + 58 q^{88} - q^{89} - 12 q^{90} - 18 q^{91} + 26 q^{92} + 42 q^{93} + 5 q^{94} + 44 q^{95} - 42 q^{96} + 41 q^{97} + 5 q^{98} + 11 q^{99}+O(q^{100}) \) 16 * q + 5 * q^2 - 16 * q^3 + 19 * q^4 - q^5 - 5 * q^6 - 16 * q^7 + 6 * q^8 + 16 * q^9 - 12 * q^10 + 11 * q^11 - 19 * q^12 + 18 * q^13 - 5 * q^14 + q^15 + 25 * q^16 - 5 * q^17 + 5 * q^18 - 11 * q^19 - q^20 + 16 * q^21 + q^22 + 13 * q^23 - 6 * q^24 + 33 * q^25 + 8 * q^26 - 16 * q^27 - 19 * q^28 + 24 * q^29 + 12 * q^30 - 42 * q^31 + 42 * q^32 - 11 * q^33 + 9 * q^34 + q^35 + 19 * q^36 + 40 * q^37 + 38 * q^38 - 18 * q^39 - 61 * q^40 + 9 * q^41 + 5 * q^42 + 7 * q^43 + 3 * q^44 - q^45 + 24 * q^46 + 31 * q^47 - 25 * q^48 + 16 * q^49 + 6 * q^50 + 5 * q^51 + 52 * q^52 + 66 * q^53 - 5 * q^54 - 36 * q^55 - 6 * q^56 + 11 * q^57 + 19 * q^58 - 7 * q^59 + q^60 + 6 * q^61 + 52 * q^62 - 16 * q^63 + 10 * q^64 + 51 * q^65 - q^66 + 16 * q^67 + 14 * q^68 - 13 * q^69 + 12 * q^70 + 46 * q^71 + 6 * q^72 + 39 * q^73 + 72 * q^74 - 33 * q^75 + 24 * q^76 - 11 * q^77 - 8 * q^78 + 4 * q^79 - 2 * q^80 + 16 * q^81 - 18 * q^82 + 15 * q^83 + 19 * q^84 - 4 * q^85 + 14 * q^86 - 24 * q^87 + 58 * q^88 - q^89 - 12 * q^90 - 18 * q^91 + 26 * q^92 + 42 * q^93 + 5 * q^94 + 44 * q^95 - 42 * q^96 + 41 * q^97 + 5 * q^98 + 11 * 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 $

$2$	−2.48981	−1.76056	−0.880281	−	0.474453i	$-0.842646\pi$
$2$	−2.48981	−1.76056	−0.880281	+	0.474453i	$0.842646\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.19916	2.09958
$5$	1.44828	0.647690	0.323845	−	0.946110i	$-0.395024\pi$
$5$	1.44828	0.647690	0.323845	+	0.946110i	$0.395024\pi$
$6$	2.48981	1.01646
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−5.47548	−1.93587
$9$	1.00000	0.333333
$10$	−3.60594	−1.14030
$11$	−3.27519	−0.987508	−0.493754	−	0.869602i	$-0.664376\pi$
$11$	−3.27519	−0.987508	−0.493754	+	0.869602i	$0.664376\pi$
$12$	−4.19916	−1.21219
$13$	−3.24893	−0.901090	−0.450545	−	0.892754i	$-0.648770\pi$
$13$	−3.24893	−0.901090	−0.450545	+	0.892754i	$0.648770\pi$
$14$	2.48981	0.665430
$15$	−1.44828	−0.373944
$16$	5.23459	1.30865
$17$	2.00096	0.485303	0.242652	−	0.970113i	$-0.421983\pi$
$17$	2.00096	0.485303	0.242652	+	0.970113i	$0.421983\pi$
$18$	−2.48981	−0.586854
$19$	−7.49049	−1.71844	−0.859218	−	0.511609i	$-0.829050\pi$
$19$	−7.49049	−1.71844	−0.859218	+	0.511609i	$0.829050\pi$
$20$	6.08155	1.35988
$21$	1.00000	0.218218
$22$	8.15461	1.73857
$23$	−5.11491	−1.06653	−0.533266	−	0.845947i	$-0.679036\pi$
$23$	−5.11491	−1.06653	−0.533266	+	0.845947i	$0.679036\pi$
$24$	5.47548	1.11768
$25$	−2.90249	−0.580498
$26$	8.08921	1.58642
$27$	−1.00000	−0.192450
$28$	−4.19916	−0.793566
$29$	−2.27043	−0.421609	−0.210804	−	0.977528i	$-0.567608\pi$
$29$	−2.27043	−0.421609	−0.210804	+	0.977528i	$0.567608\pi$
$30$	3.60594	0.658352
$31$	−9.36316	−1.68167	−0.840837	−	0.541288i	$-0.817937\pi$
$31$	−9.36316	−1.68167	−0.840837	+	0.541288i	$0.817937\pi$
$32$	−2.08219	−0.368082
$33$	3.27519	0.570138
$34$	−4.98200	−0.854407
$35$	−1.44828	−0.244804
$36$	4.19916	0.699859
$37$	6.96565	1.14515	0.572573	−	0.819854i	$-0.305945\pi$
$37$	6.96565	1.14515	0.572573	+	0.819854i	$0.305945\pi$
$38$	18.6499	3.02541
$39$	3.24893	0.520245
$40$	−7.93002	−1.25385
$41$	11.0274	1.72219	0.861097	−	0.508441i	$-0.169778\pi$
$41$	11.0274	1.72219	0.861097	+	0.508441i	$0.169778\pi$
$42$	−2.48981	−0.384186
$43$	−7.34145	−1.11956	−0.559781	−	0.828641i	$-0.689115\pi$
$43$	−7.34145	−1.11956	−0.559781	+	0.828641i	$0.689115\pi$
$44$	−13.7531	−2.07335
$45$	1.44828	0.215897
$46$	12.7352	1.87770
$47$	3.00580	0.438442	0.219221	−	0.975675i	$-0.429648\pi$
$47$	3.00580	0.438442	0.219221	+	0.975675i	$0.429648\pi$
$48$	−5.23459	−0.755548
$49$	1.00000	0.142857
$50$	7.22664	1.02200
$51$	−2.00096	−0.280190
$52$	−13.6427	−1.89191
$53$	10.8847	1.49513	0.747565	−	0.664189i	$-0.231223\pi$
$53$	10.8847	1.49513	0.747565	+	0.664189i	$0.231223\pi$
$54$	2.48981	0.338820
$55$	−4.74340	−0.639599
$56$	5.47548	0.731692
$57$	7.49049	0.992140
$58$	5.65295	0.742268
$59$	−8.25654	−1.07491	−0.537455	−	0.843293i	$-0.680614\pi$
$59$	−8.25654	−1.07491	−0.537455	+	0.843293i	$0.680614\pi$
$60$	−6.08155	−0.785124
$61$	9.29811	1.19050	0.595250	−	0.803540i	$-0.297053\pi$
$61$	9.29811	1.19050	0.595250	+	0.803540i	$0.297053\pi$
$62$	23.3125	2.96069
$63$	−1.00000	−0.125988
$64$	−5.28494	−0.660617
$65$	−4.70535	−0.583627
$66$	−8.15461	−1.00376
$67$	2.47721	0.302639	0.151320	−	0.988485i	$-0.451648\pi$
$67$	2.47721	0.302639	0.151320	+	0.988485i	$0.451648\pi$
$68$	8.40233	1.01893
$69$	5.11491	0.615763
$70$	3.60594	0.430992
$71$	6.76717	0.803115	0.401558	−	0.915834i	$-0.368469\pi$
$71$	6.76717	0.803115	0.401558	+	0.915834i	$0.368469\pi$
$72$	−5.47548	−0.645291
$73$	10.4082	1.21818	0.609092	−	0.793100i	$-0.291534\pi$
$73$	10.4082	1.21818	0.609092	+	0.793100i	$0.291534\pi$
$74$	−17.3432	−2.01610
$75$	2.90249	0.335150
$76$	−31.4537	−3.60799
$77$	3.27519	0.373243
$78$	−8.08921	−0.915923
$79$	6.43106	0.723551	0.361776	−	0.932265i	$-0.382171\pi$
$79$	6.43106	0.723551	0.361776	+	0.932265i	$0.382171\pi$
$80$	7.58115	0.847598
$81$	1.00000	0.111111
$82$	−27.4562	−3.03203
$83$	15.7272	1.72629	0.863144	−	0.504958i	$-0.168492\pi$
$83$	15.7272	1.72629	0.863144	+	0.504958i	$0.168492\pi$
$84$	4.19916	0.458165
$85$	2.89794	0.314326
$86$	18.2788	1.97106
$87$	2.27043	0.243416
$88$	17.9333	1.91169
$89$	−9.26856	−0.982466	−0.491233	−	0.871028i	$-0.663454\pi$
$89$	−9.26856	−0.982466	−0.491233	+	0.871028i	$0.663454\pi$
$90$	−3.60594	−0.380099
$91$	3.24893	0.340580
$92$	−21.4783	−2.23927
$93$	9.36316	0.970915
$94$	−7.48388	−0.771903
$95$	−10.8483	−1.11301
$96$	2.08219	0.212512
$97$	3.36147	0.341305	0.170653	−	0.985331i	$-0.445412\pi$
$97$	3.36147	0.341305	0.170653	+	0.985331i	$0.445412\pi$
$98$	−2.48981	−0.251509
$99$	−3.27519	−0.329169
$100$	−12.1880	−1.21880
$101$	−3.15143	−0.313579	−0.156789	−	0.987632i	$-0.550114\pi$
$101$	−3.15143	−0.313579	−0.156789	+	0.987632i	$0.550114\pi$
$102$	4.98200	0.493292
$103$	−7.60402	−0.749246	−0.374623	−	0.927177i	$-0.622228\pi$
$103$	−7.60402	−0.749246	−0.374623	+	0.927177i	$0.622228\pi$
$104$	17.7894	1.74440
$105$	1.44828	0.141338
$106$	−27.1008	−2.63227
$107$	5.11898	0.494871	0.247435	−	0.968904i	$-0.420412\pi$
$107$	5.11898	0.494871	0.247435	+	0.968904i	$0.420412\pi$
$108$	−4.19916	−0.404064
$109$	−1.82377	−0.174686	−0.0873429	−	0.996178i	$-0.527838\pi$
$109$	−1.82377	−0.174686	−0.0873429	+	0.996178i	$0.527838\pi$
$110$	11.8102	1.12605
$111$	−6.96565	−0.661151
$112$	−5.23459	−0.494623
$113$	−2.11000	−0.198492	−0.0992462	−	0.995063i	$-0.531643\pi$
$113$	−2.11000	−0.198492	−0.0992462	+	0.995063i	$0.531643\pi$
$114$	−18.6499	−1.74672
$115$	−7.40782	−0.690782
$116$	−9.53390	−0.885200
$117$	−3.24893	−0.300363
$118$	20.5572	1.89244
$119$	−2.00096	−0.183427
$120$	7.93002	0.723909
$121$	−0.273100	−0.0248272
$122$	−23.1505	−2.09595
$123$	−11.0274	−0.994309
$124$	−39.3174	−3.53081
$125$	−11.4450	−1.02367
$126$	2.48981	0.221810
$127$	1.00000	0.0887357
$127$	1.00000	0.0887357
$128$	17.3229	1.53114
$129$	7.34145	0.646379
$130$	11.7154	1.02751
$131$	5.42636	0.474103	0.237051	−	0.971497i	$-0.423819\pi$
$131$	5.42636	0.474103	0.237051	+	0.971497i	$0.423819\pi$
$132$	13.7531	1.19705
$133$	7.49049	0.649508
$134$	−6.16778	−0.532815
$135$	−1.44828	−0.124648
$136$	−10.9562	−0.939486
$137$	3.18573	0.272175	0.136088	−	0.990697i	$-0.456547\pi$
$137$	3.18573	0.272175	0.136088	+	0.990697i	$0.456547\pi$
$138$	−12.7352	−1.08409
$139$	−1.32574	−0.112448	−0.0562239	−	0.998418i	$-0.517906\pi$
$139$	−1.32574	−0.112448	−0.0562239	+	0.998418i	$0.517906\pi$
$140$	−6.08155	−0.513985
$141$	−3.00580	−0.253134
$142$	−16.8490	−1.41393
$143$	10.6409	0.889834
$144$	5.23459	0.436216
$145$	−3.28822	−0.273072
$146$	−25.9144	−2.14469
$147$	−1.00000	−0.0824786
$148$	29.2499	2.40432
$149$	−0.108116	−0.00885717	−0.00442859	−	0.999990i	$-0.501410\pi$
$149$	−0.108116	−0.00885717	−0.00442859	+	0.999990i	$0.501410\pi$
$150$	−7.22664	−0.590053
$151$	−14.0462	−1.14306	−0.571531	−	0.820581i	$-0.693650\pi$
$151$	−14.0462	−1.14306	−0.571531	+	0.820581i	$0.693650\pi$
$152$	41.0140	3.32668
$153$	2.00096	0.161768
$154$	−8.15461	−0.657117
$155$	−13.5605	−1.08920
$156$	13.6427	1.09229
$157$	−16.9071	−1.34933	−0.674667	−	0.738122i	$-0.735713\pi$
$157$	−16.9071	−1.34933	−0.674667	+	0.738122i	$0.735713\pi$
$158$	−16.0121	−1.27386
$159$	−10.8847	−0.863213
$160$	−3.01559	−0.238403
$161$	5.11491	0.403111
$162$	−2.48981	−0.195618
$163$	18.6355	1.45965	0.729824	−	0.683635i	$-0.239602\pi$
$163$	18.6355	1.45965	0.729824	+	0.683635i	$0.239602\pi$
$164$	46.3058	3.61588
$165$	4.74340	0.369273
$166$	−39.1578	−3.03924
$167$	−3.24655	−0.251226	−0.125613	−	0.992079i	$-0.540090\pi$
$167$	−3.24655	−0.251226	−0.125613	+	0.992079i	$0.540090\pi$
$168$	−5.47548	−0.422442
$169$	−2.44448	−0.188037
$170$	−7.21533	−0.553391
$171$	−7.49049	−0.572812
$172$	−30.8279	−2.35061
$173$	−2.23879	−0.170212	−0.0851060	−	0.996372i	$-0.527123\pi$
$173$	−2.23879	−0.170212	−0.0851060	+	0.996372i	$0.527123\pi$
$174$	−5.65295	−0.428549
$175$	2.90249	0.219407
$176$	−17.1443	−1.29230
$177$	8.25654	0.620599
$178$	23.0770	1.72969
$179$	7.77245	0.580940	0.290470	−	0.956884i	$-0.406188\pi$
$179$	7.77245	0.580940	0.290470	+	0.956884i	$0.406188\pi$
$180$	6.08155	0.453292
$181$	20.1554	1.49814	0.749069	−	0.662492i	$-0.230501\pi$
$181$	20.1554	1.49814	0.749069	+	0.662492i	$0.230501\pi$
$182$	−8.08921	−0.599612
$183$	−9.29811	−0.687336
$184$	28.0066	2.06467
$185$	10.0882	0.741700
$186$	−23.3125	−1.70936
$187$	−6.55352	−0.479241
$188$	12.6218	0.920542
$189$	1.00000	0.0727393
$190$	27.0103	1.95953
$191$	7.90565	0.572033	0.286016	−	0.958225i	$-0.407669\pi$
$191$	7.90565	0.572033	0.286016	+	0.958225i	$0.407669\pi$
$192$	5.28494	0.381408
$193$	−15.6092	−1.12357	−0.561786	−	0.827282i	$-0.689886\pi$
$193$	−15.6092	−1.12357	−0.561786	+	0.827282i	$0.689886\pi$
$194$	−8.36941	−0.600889
$195$	4.70535	0.336957
$196$	4.19916	0.299940
$197$	23.4362	1.66976	0.834881	−	0.550431i	$-0.185536\pi$
$197$	23.4362	1.66976	0.834881	+	0.550431i	$0.185536\pi$
$198$	8.15461	0.579523
$199$	17.5614	1.24489	0.622447	−	0.782662i	$-0.286139\pi$
$199$	17.5614	1.24489	0.622447	+	0.782662i	$0.286139\pi$
$200$	15.8925	1.12377
$201$	−2.47721	−0.174729
$202$	7.84646	0.552075
$203$	2.27043	0.159353
$204$	−8.40233	−0.588281
$205$	15.9708	1.11545
$206$	18.9326	1.31909
$207$	−5.11491	−0.355511
$208$	−17.0068	−1.17921
$209$	24.5328	1.69697
$210$	−3.60594	−0.248833
$211$	15.1757	1.04474	0.522371	−	0.852719i	$-0.325048\pi$
$211$	15.1757	1.04474	0.522371	+	0.852719i	$0.325048\pi$
$212$	45.7066	3.13914
$213$	−6.76717	−0.463679
$214$	−12.7453	−0.871250
$215$	−10.6325	−0.725129
$216$	5.47548	0.372559
$217$	9.36316	0.635613
$218$	4.54085	0.307545
$219$	−10.4082	−0.703319
$220$	−19.9183	−1.34289
$221$	−6.50096	−0.437302
$222$	17.3432	1.16400
$223$	15.5556	1.04168	0.520841	−	0.853654i	$-0.325619\pi$
$223$	15.5556	1.04168	0.520841	+	0.853654i	$0.325619\pi$
$224$	2.08219	0.139122
$225$	−2.90249	−0.193499
$226$	5.25351	0.349458
$227$	24.0255	1.59463	0.797314	−	0.603564i	$-0.206253\pi$
$227$	24.0255	1.59463	0.797314	+	0.603564i	$0.206253\pi$
$228$	31.4537	2.08307
$229$	−25.7078	−1.69882	−0.849409	−	0.527735i	$-0.823041\pi$
$229$	−25.7078	−1.69882	−0.849409	+	0.527735i	$0.823041\pi$
$230$	18.4441	1.21617
$231$	−3.27519	−0.215492
$232$	12.4317	0.816181
$233$	4.47472	0.293149	0.146574	−	0.989200i	$-0.453175\pi$
$233$	4.47472	0.293149	0.146574	+	0.989200i	$0.453175\pi$
$234$	8.08921	0.528808
$235$	4.35324	0.283974
$236$	−34.6705	−2.25686
$237$	−6.43106	−0.417743
$238$	4.98200	0.322935
$239$	3.71050	0.240012	0.120006	−	0.992773i	$-0.461709\pi$
$239$	3.71050	0.240012	0.120006	+	0.992773i	$0.461709\pi$
$240$	−7.58115	−0.489361
$241$	−23.5929	−1.51975	−0.759875	−	0.650069i	$-0.774740\pi$
$241$	−23.5929	−1.51975	−0.759875	+	0.650069i	$0.774740\pi$
$242$	0.679966	0.0437099
$243$	−1.00000	−0.0641500
$244$	39.0442	2.49955
$245$	1.44828	0.0925271
$246$	27.4562	1.75054
$247$	24.3361	1.54847
$248$	51.2678	3.25551
$249$	−15.7272	−0.996673
$250$	28.4959	1.80224
$251$	16.0972	1.01604	0.508022	−	0.861344i	$-0.330377\pi$
$251$	16.0972	1.01604	0.508022	+	0.861344i	$0.330377\pi$
$252$	−4.19916	−0.264522
$253$	16.7523	1.05321
$254$	−2.48981	−0.156225
$255$	−2.89794	−0.181476
$256$	−32.5608	−2.03505
$257$	−15.7376	−0.981682	−0.490841	−	0.871249i	$-0.663310\pi$
$257$	−15.7376	−0.981682	−0.490841	+	0.871249i	$0.663310\pi$
$258$	−18.2788	−1.13799
$259$	−6.96565	−0.432825
$260$	−19.7585	−1.22537
$261$	−2.27043	−0.140536
$262$	−13.5106	−0.834687
$263$	4.31962	0.266359	0.133180	−	0.991092i	$-0.457481\pi$
$263$	4.31962	0.266359	0.133180	+	0.991092i	$0.457481\pi$
$264$	−17.9333	−1.10372
$265$	15.7641	0.968380
$266$	−18.6499	−1.14350
$267$	9.26856	0.567227
$268$	10.4022	0.635415
$269$	−30.7930	−1.87748	−0.938741	−	0.344623i	$-0.888007\pi$
$269$	−30.7930	−1.87748	−0.938741	+	0.344623i	$0.888007\pi$
$270$	3.60594	0.219451
$271$	2.75638	0.167438	0.0837190	−	0.996489i	$-0.473320\pi$
$271$	2.75638	0.167438	0.0837190	+	0.996489i	$0.473320\pi$
$272$	10.4742	0.635091
$273$	−3.24893	−0.196634
$274$	−7.93186	−0.479181
$275$	9.50621	0.573246
$276$	21.4783	1.29284
$277$	−15.0763	−0.905845	−0.452922	−	0.891550i	$-0.649619\pi$
$277$	−15.0763	−0.905845	−0.452922	+	0.891550i	$0.649619\pi$
$278$	3.30084	0.197971
$279$	−9.36316	−0.560558
$280$	7.93002	0.473909
$281$	−4.56741	−0.272469	−0.136234	−	0.990677i	$-0.543500\pi$
$281$	−4.56741	−0.272469	−0.136234	+	0.990677i	$0.543500\pi$
$282$	7.48388	0.445659
$283$	22.2507	1.32267	0.661334	−	0.750091i	$-0.269991\pi$
$283$	22.2507	1.32267	0.661334	+	0.750091i	$0.269991\pi$
$284$	28.4164	1.68620
$285$	10.8483	0.642599
$286$	−26.4937	−1.56661
$287$	−11.0274	−0.650928
$288$	−2.08219	−0.122694
$289$	−12.9962	−0.764481
$290$	8.18704	0.480760
$291$	−3.36147	−0.197053
$292$	43.7055	2.55767
$293$	22.4715	1.31280	0.656399	−	0.754414i	$-0.272079\pi$
$293$	22.4715	1.31280	0.656399	+	0.754414i	$0.272079\pi$
$294$	2.48981	0.145209
$295$	−11.9578	−0.696208
$296$	−38.1403	−2.21686
$297$	3.27519	0.190046
$298$	0.269187	0.0155936
$299$	16.6180	0.961042
$300$	12.1880	0.703674
$301$	7.34145	0.423154
$302$	34.9723	2.01243
$303$	3.15143	0.181045
$304$	−39.2097	−2.24883
$305$	13.4663	0.771075
$306$	−4.98200	−0.284802
$307$	15.5752	0.888922	0.444461	−	0.895798i	$-0.353395\pi$
$307$	15.5752	0.888922	0.444461	+	0.895798i	$0.353395\pi$
$308$	13.7531	0.783653
$309$	7.60402	0.432578
$310$	33.7630	1.91761
$311$	−20.5657	−1.16617	−0.583086	−	0.812410i	$-0.698155\pi$
$311$	−20.5657	−1.16617	−0.583086	+	0.812410i	$0.698155\pi$
$312$	−17.7894	−1.00713
$313$	21.9001	1.23787	0.618935	−	0.785442i	$-0.287565\pi$
$313$	21.9001	1.23787	0.618935	+	0.785442i	$0.287565\pi$
$314$	42.0955	2.37559
$315$	−1.44828	−0.0816013
$316$	27.0050	1.51915
$317$	12.3293	0.692482	0.346241	−	0.938146i	$-0.387458\pi$
$317$	12.3293	0.692482	0.346241	+	0.938146i	$0.387458\pi$
$318$	27.1008	1.51974
$319$	7.43611	0.416342
$320$	−7.65407	−0.427875
$321$	−5.11898	−0.285714
$322$	−12.7352	−0.709703
$323$	−14.9882	−0.833963
$324$	4.19916	0.233286
$325$	9.42997	0.523081
$326$	−46.3990	−2.56980
$327$	1.82377	0.100855
$328$	−60.3804	−3.33395
$329$	−3.00580	−0.165715
$330$	−11.8102	−0.650128
$331$	−25.5146	−1.40241	−0.701206	−	0.712959i	$-0.747355\pi$
$331$	−25.5146	−1.40241	−0.701206	+	0.712959i	$0.747355\pi$
$332$	66.0411	3.62447
$333$	6.96565	0.381716
$334$	8.08331	0.442299
$335$	3.58769	0.196016
$336$	5.23459	0.285570
$337$	16.8065	0.915507	0.457753	−	0.889079i	$-0.348654\pi$
$337$	16.8065	0.915507	0.457753	+	0.889079i	$0.348654\pi$
$338$	6.08629	0.331051
$339$	2.11000	0.114600
$340$	12.1689	0.659952
$341$	30.6662	1.66067
$342$	18.6499	1.00847
$343$	−1.00000	−0.0539949
$344$	40.1980	2.16733
$345$	7.40782	0.398823
$346$	5.57416	0.299669
$347$	−27.1445	−1.45719	−0.728596	−	0.684944i	$-0.759827\pi$
$347$	−27.1445	−1.45719	−0.728596	+	0.684944i	$0.759827\pi$
$348$	9.53390	0.511071
$349$	21.2339	1.13662	0.568311	−	0.822814i	$-0.307597\pi$
$349$	21.2339	1.13662	0.568311	+	0.822814i	$0.307597\pi$
$350$	−7.22664	−0.386280
$351$	3.24893	0.173415
$352$	6.81956	0.363484
$353$	−27.5779	−1.46782	−0.733911	−	0.679246i	$-0.762307\pi$
$353$	−27.5779	−1.46782	−0.733911	+	0.679246i	$0.762307\pi$
$354$	−20.5572	−1.09260
$355$	9.80075	0.520170
$356$	−38.9201	−2.06276
$357$	2.00096	0.105902
$358$	−19.3519	−1.02278
$359$	11.4069	0.602035	0.301017	−	0.953619i	$-0.402674\pi$
$359$	11.4069	0.602035	0.301017	+	0.953619i	$0.402674\pi$
$360$	−7.93002	−0.417949
$361$	37.1075	1.95302
$362$	−50.1831	−2.63757
$363$	0.273100	0.0143340
$364$	13.6427	0.715074
$365$	15.0739	0.789005
$366$	23.1505	1.21010
$367$	24.6520	1.28682	0.643412	−	0.765520i	$-0.277518\pi$
$367$	24.6520	1.28682	0.643412	+	0.765520i	$0.277518\pi$
$368$	−26.7745	−1.39572
$369$	11.0274	0.574064
$370$	−25.1177	−1.30581
$371$	−10.8847	−0.565106
$372$	39.3174	2.03851
$373$	−31.0058	−1.60542	−0.802711	−	0.596368i	$-0.796610\pi$
$373$	−31.0058	−1.60542	−0.802711	+	0.596368i	$0.796610\pi$
$374$	16.3170	0.843734
$375$	11.4450	0.591018
$376$	−16.4582	−0.848768
$377$	7.37647	0.379907
$378$	−2.48981	−0.128062
$379$	22.9048	1.17654	0.588270	−	0.808665i	$-0.299809\pi$
$379$	22.9048	1.17654	0.588270	+	0.808665i	$0.299809\pi$
$380$	−45.5538	−2.33686
$381$	−1.00000	−0.0512316
$382$	−19.6836	−1.00710
$383$	−29.0013	−1.48190	−0.740948	−	0.671562i	$-0.765624\pi$
$383$	−29.0013	−1.48190	−0.740948	+	0.671562i	$0.765624\pi$
$384$	−17.3229	−0.884004
$385$	4.74340	0.241746
$386$	38.8639	1.97812
$387$	−7.34145	−0.373187
$388$	14.1153	0.716597
$389$	16.5467	0.838948	0.419474	−	0.907767i	$-0.362214\pi$
$389$	16.5467	0.838948	0.419474	+	0.907767i	$0.362214\pi$
$390$	−11.7154	−0.593234
$391$	−10.2347	−0.517592
$392$	−5.47548	−0.276553
$393$	−5.42636	−0.273723
$394$	−58.3517	−2.93972
$395$	9.31398	0.468637
$396$	−13.7531	−0.691117
$397$	8.20972	0.412034	0.206017	−	0.978548i	$-0.433950\pi$
$397$	8.20972	0.412034	0.206017	+	0.978548i	$0.433950\pi$
$398$	−43.7245	−2.19171
$399$	−7.49049	−0.374994
$400$	−15.1933	−0.759667
$401$	30.2608	1.51115	0.755577	−	0.655060i	$-0.227357\pi$
$401$	30.2608	1.51115	0.755577	+	0.655060i	$0.227357\pi$
$402$	6.16778	0.307621
$403$	30.4202	1.51534
$404$	−13.2333	−0.658383
$405$	1.44828	0.0719656
$406$	−5.65295	−0.280551
$407$	−22.8139	−1.13084
$408$	10.9562	0.542413
$409$	−8.23789	−0.407338	−0.203669	−	0.979040i	$-0.565287\pi$
$409$	−8.23789	−0.407338	−0.203669	+	0.979040i	$0.565287\pi$
$410$	−39.7642	−1.96381
$411$	−3.18573	−0.157140
$412$	−31.9305	−1.57310
$413$	8.25654	0.406278
$414$	12.7352	0.625899
$415$	22.7774	1.11810
$416$	6.76487	0.331675
$417$	1.32574	0.0649217
$418$	−61.0821	−2.98762
$419$	26.3050	1.28508	0.642540	−	0.766252i	$-0.277880\pi$
$419$	26.3050	1.28508	0.642540	+	0.766252i	$0.277880\pi$
$420$	6.08155	0.296749
$421$	17.1178	0.834269	0.417135	−	0.908845i	$-0.363034\pi$
$421$	17.1178	0.834269	0.417135	+	0.908845i	$0.363034\pi$
$422$	−37.7847	−1.83933
$423$	3.00580	0.146147
$424$	−59.5990	−2.89438
$425$	−5.80775	−0.281717
$426$	16.8490	0.816335
$427$	−9.29811	−0.449967
$428$	21.4954	1.03902
$429$	−10.6409	−0.513746
$430$	26.4728	1.27663
$431$	25.7041	1.23812	0.619061	−	0.785343i	$-0.287514\pi$
$431$	25.7041	1.23812	0.619061	+	0.785343i	$0.287514\pi$
$432$	−5.23459	−0.251849
$433$	19.9912	0.960715	0.480358	−	0.877073i	$-0.340507\pi$
$433$	19.9912	0.960715	0.480358	+	0.877073i	$0.340507\pi$
$434$	−23.3125	−1.11904
$435$	3.28822	0.157658
$436$	−7.65831	−0.366766
$437$	38.3132	1.83277
$438$	25.9144	1.23824
$439$	−23.7707	−1.13451	−0.567257	−	0.823541i	$-0.691996\pi$
$439$	−23.7707	−1.13451	−0.567257	+	0.823541i	$0.691996\pi$
$440$	25.9724	1.23818
$441$	1.00000	0.0476190
$442$	16.1862	0.769897
$443$	−40.7424	−1.93573	−0.967865	−	0.251469i	$-0.919086\pi$
$443$	−40.7424	−1.93573	−0.967865	+	0.251469i	$0.919086\pi$
$444$	−29.2499	−1.38814
$445$	−13.4235	−0.636333
$446$	−38.7305	−1.83394
$447$	0.108116	0.00511369
$448$	5.28494	0.249690
$449$	−24.5392	−1.15808	−0.579038	−	0.815301i	$-0.696572\pi$
$449$	−24.5392	−1.15808	−0.579038	+	0.815301i	$0.696572\pi$
$450$	7.22664	0.340667
$451$	−36.1169	−1.70068
$452$	−8.86023	−0.416750
$453$	14.0462	0.659947
$454$	−59.8189	−2.80744
$455$	4.70535	0.220590
$456$	−41.0140	−1.92066
$457$	13.4338	0.628407	0.314203	−	0.949356i	$-0.398263\pi$
$457$	13.4338	0.628407	0.314203	+	0.949356i	$0.398263\pi$
$458$	64.0075	2.99087
$459$	−2.00096	−0.0933967
$460$	−31.1066	−1.45035
$461$	−26.8553	−1.25078	−0.625389	−	0.780313i	$-0.715060\pi$
$461$	−26.8553	−1.25078	−0.625389	+	0.780313i	$0.715060\pi$
$462$	8.15461	0.379387
$463$	−9.24734	−0.429760	−0.214880	−	0.976640i	$-0.568936\pi$
$463$	−9.24734	−0.429760	−0.214880	+	0.976640i	$0.568936\pi$
$464$	−11.8848	−0.551738
$465$	13.5605	0.628852
$466$	−11.1412	−0.516106
$467$	−21.5833	−0.998754	−0.499377	−	0.866385i	$-0.666438\pi$
$467$	−21.5833	−0.998754	−0.499377	+	0.866385i	$0.666438\pi$
$468$	−13.6427	−0.630636
$469$	−2.47721	−0.114387
$470$	−10.8387	−0.499954
$471$	16.9071	0.779038
$472$	45.2085	2.08089
$473$	24.0447	1.10558
$474$	16.0121	0.735462
$475$	21.7411	0.997548
$476$	−8.40233	−0.385120
$477$	10.8847	0.498376
$478$	−9.23844	−0.422556
$479$	−9.92648	−0.453553	−0.226776	−	0.973947i	$-0.572819\pi$
$479$	−9.92648	−0.453553	−0.226776	+	0.973947i	$0.572819\pi$
$480$	3.01559	0.137642
$481$	−22.6309	−1.03188
$482$	58.7418	2.67561
$483$	−5.11491	−0.232736
$484$	−1.14679	−0.0521267
$485$	4.86834	0.221060
$486$	2.48981	0.112940
$487$	17.5491	0.795227	0.397613	−	0.917553i	$-0.369839\pi$
$487$	17.5491	0.795227	0.397613	+	0.917553i	$0.369839\pi$
$488$	−50.9116	−2.30466
$489$	−18.6355	−0.842728
$490$	−3.60594	−0.162900
$491$	11.9827	0.540770	0.270385	−	0.962752i	$-0.412849\pi$
$491$	11.9827	0.540770	0.270385	+	0.962752i	$0.412849\pi$
$492$	−46.3058	−2.08763
$493$	−4.54304	−0.204608
$494$	−60.5922	−2.72617
$495$	−4.74340	−0.213200
$496$	−49.0124	−2.20072
$497$	−6.76717	−0.303549
$498$	39.1578	1.75470
$499$	−17.7117	−0.792885	−0.396442	−	0.918060i	$-0.629755\pi$
$499$	−17.7117	−0.792885	−0.396442	+	0.918060i	$0.629755\pi$
$500$	−48.0594	−2.14928
$501$	3.24655	0.145045
$502$	−40.0789	−1.78881
$503$	8.29004	0.369635	0.184817	−	0.982773i	$-0.440831\pi$
$503$	8.29004	0.369635	0.184817	+	0.982773i	$0.440831\pi$
$504$	5.47548	0.243897
$505$	−4.56415	−0.203102
$506$	−41.7101	−1.85424
$507$	2.44448	0.108563
$508$	4.19916	0.186307
$509$	18.1248	0.803365	0.401683	−	0.915779i	$-0.368425\pi$
$509$	18.1248	0.803365	0.401683	+	0.915779i	$0.368425\pi$
$510$	7.21533	0.319500
$511$	−10.4082	−0.460430
$512$	46.4244	2.05169
$513$	7.49049	0.330713
$514$	39.1835	1.72831
$515$	−11.0127	−0.485279
$516$	30.8279	1.35712
$517$	−9.84459	−0.432965
$518$	17.3432	0.762015
$519$	2.23879	0.0982719
$520$	25.7640	1.12983
$521$	−26.6839	−1.16904	−0.584522	−	0.811378i	$-0.698718\pi$
$521$	−26.6839	−1.16904	−0.584522	+	0.811378i	$0.698718\pi$
$522$	5.65295	0.247423
$523$	−3.04549	−0.133170	−0.0665849	−	0.997781i	$-0.521210\pi$
$523$	−3.04549	−0.133170	−0.0665849	+	0.997781i	$0.521210\pi$
$524$	22.7861	0.995416
$525$	−2.90249	−0.126675
$526$	−10.7550	−0.468942
$527$	−18.7353	−0.816122
$528$	17.1443	0.746110
$529$	3.16231	0.137492
$530$	−39.2496	−1.70489
$531$	−8.25654	−0.358303
$532$	31.4537	1.36369
$533$	−35.8273	−1.55185
$534$	−23.0770	−0.998638
$535$	7.41371	0.320523
$536$	−13.5639	−0.585872
$537$	−7.77245	−0.335406
$538$	76.6687	3.30542
$539$	−3.27519	−0.141073
$540$	−6.08155	−0.261708
$541$	26.4448	1.13695	0.568474	−	0.822701i	$-0.307534\pi$
$541$	26.4448	1.13695	0.568474	+	0.822701i	$0.307534\pi$
$542$	−6.86286	−0.294785
$543$	−20.1554	−0.864951
$544$	−4.16636	−0.178631
$545$	−2.64133	−0.113142
$546$	8.08921	0.346186
$547$	25.9693	1.11037	0.555183	−	0.831728i	$-0.312648\pi$
$547$	25.9693	1.11037	0.555183	+	0.831728i	$0.312648\pi$
$548$	13.3774	0.571453
$549$	9.29811	0.396833
$550$	−23.6687	−1.00924
$551$	17.0067	0.724508
$552$	−28.0066	−1.19204
$553$	−6.43106	−0.273477
$554$	37.5370	1.59480
$555$	−10.0882	−0.428221
$556$	−5.56698	−0.236093
$557$	31.5443	1.33657	0.668287	−	0.743904i	$-0.267028\pi$
$557$	31.5443	1.33657	0.668287	+	0.743904i	$0.267028\pi$
$558$	23.3125	0.986897
$559$	23.8518	1.00883
$560$	−7.58115	−0.320362
$561$	6.55352	0.276690
$562$	11.3720	0.479698
$563$	33.1892	1.39876	0.699378	−	0.714752i	$-0.253460\pi$
$563$	33.1892	1.39876	0.699378	+	0.714752i	$0.253460\pi$
$564$	−12.6218	−0.531475
$565$	−3.05587	−0.128562
$566$	−55.4001	−2.32864
$567$	−1.00000	−0.0419961
$568$	−37.0535	−1.55473
$569$	10.6871	0.448026	0.224013	−	0.974586i	$-0.428084\pi$
$569$	10.6871	0.448026	0.224013	+	0.974586i	$0.428084\pi$
$570$	−27.0103	−1.13134
$571$	5.13536	0.214908	0.107454	−	0.994210i	$-0.465730\pi$
$571$	5.13536	0.214908	0.107454	+	0.994210i	$0.465730\pi$
$572$	44.6826	1.86828
$573$	−7.90565	−0.330263
$574$	27.4562	1.14600
$575$	14.8460	0.619120
$576$	−5.28494	−0.220206
$577$	−34.0207	−1.41630	−0.708150	−	0.706062i	$-0.750470\pi$
$577$	−34.0207	−1.41630	−0.708150	+	0.706062i	$0.750470\pi$
$578$	32.3580	1.34592
$579$	15.6092	0.648695
$580$	−13.8077	−0.573335
$581$	−15.7272	−0.652475
$582$	8.36941	0.346923
$583$	−35.6495	−1.47645
$584$	−56.9897	−2.35825
$585$	−4.70535	−0.194542
$586$	−55.9498	−2.31126
$587$	24.3928	1.00680	0.503400	−	0.864053i	$-0.332082\pi$
$587$	24.3928	1.00680	0.503400	+	0.864053i	$0.332082\pi$
$588$	−4.19916	−0.173170
$589$	70.1347	2.88985
$590$	29.7726	1.22572
$591$	−23.4362	−0.964037
$592$	36.4624	1.49859
$593$	9.66401	0.396853	0.198427	−	0.980116i	$-0.436417\pi$
$593$	9.66401	0.396853	0.198427	+	0.980116i	$0.436417\pi$
$594$	−8.15461	−0.334588
$595$	−2.89794	−0.118804
$596$	−0.453994	−0.0185963
$597$	−17.5614	−0.718739
$598$	−41.3756	−1.69197
$599$	−40.5869	−1.65834	−0.829168	−	0.558999i	$-0.811185\pi$
$599$	−40.5869	−1.65834	−0.829168	+	0.558999i	$0.811185\pi$
$600$	−15.8925	−0.648809
$601$	−39.6171	−1.61602	−0.808008	−	0.589172i	$-0.799454\pi$
$601$	−39.6171	−1.61602	−0.808008	+	0.589172i	$0.799454\pi$
$602$	−18.2788	−0.744989
$603$	2.47721	0.100880
$604$	−58.9821	−2.39995
$605$	−0.395524	−0.0160804
$606$	−7.84646	−0.318741
$607$	−34.1486	−1.38605	−0.693023	−	0.720915i	$-0.743722\pi$
$607$	−34.1486	−1.38605	−0.693023	+	0.720915i	$0.743722\pi$
$608$	15.5966	0.632525
$609$	−2.27043	−0.0920026
$610$	−33.5284	−1.35753
$611$	−9.76563	−0.395075
$612$	8.40233	0.339644
$613$	−10.6189	−0.428894	−0.214447	−	0.976736i	$-0.568795\pi$
$613$	−10.6189	−0.428894	−0.214447	+	0.976736i	$0.568795\pi$
$614$	−38.7792	−1.56500
$615$	−15.9708	−0.644004
$616$	−17.9333	−0.722552
$617$	−12.6928	−0.510994	−0.255497	−	0.966810i	$-0.582239\pi$
$617$	−12.6928	−0.510994	−0.255497	+	0.966810i	$0.582239\pi$
$618$	−18.9326	−0.761580
$619$	−16.8524	−0.677357	−0.338678	−	0.940902i	$-0.609980\pi$
$619$	−16.8524	−0.677357	−0.338678	+	0.940902i	$0.609980\pi$
$620$	−56.9425	−2.28687
$621$	5.11491	0.205254
$622$	51.2046	2.05312
$623$	9.26856	0.371337
$624$	17.0068	0.680817
$625$	−2.06312	−0.0825249
$626$	−54.5272	−2.17935
$627$	−24.5328	−0.979746
$628$	−70.9955	−2.83303
$629$	13.9380	0.555744
$630$	3.60594	0.143664
$631$	−25.6820	−1.02238	−0.511191	−	0.859467i	$-0.670796\pi$
$631$	−25.6820	−1.02238	−0.511191	+	0.859467i	$0.670796\pi$
$632$	−35.2132	−1.40070
$633$	−15.1757	−0.603182
$634$	−30.6976	−1.21916
$635$	1.44828	0.0574732
$636$	−45.7066	−1.81238
$637$	−3.24893	−0.128727
$638$	−18.5145	−0.732996
$639$	6.76717	0.267705
$640$	25.0883	0.991704
$641$	3.88658	0.153511	0.0767554	−	0.997050i	$-0.475544\pi$
$641$	3.88658	0.153511	0.0767554	+	0.997050i	$0.475544\pi$
$642$	12.7453	0.503016
$643$	−21.5878	−0.851339	−0.425669	−	0.904879i	$-0.639961\pi$
$643$	−21.5878	−0.851339	−0.425669	+	0.904879i	$0.639961\pi$
$644$	21.4783	0.846364
$645$	10.6325	0.418653
$646$	37.3177	1.46824
$647$	−43.9149	−1.72647	−0.863236	−	0.504801i	$-0.831566\pi$
$647$	−43.9149	−1.72647	−0.863236	+	0.504801i	$0.831566\pi$
$648$	−5.47548	−0.215097
$649$	27.0418	1.06148
$650$	−23.4788	−0.920916
$651$	−9.36316	−0.366971
$652$	78.2535	3.06464
$653$	−6.36272	−0.248992	−0.124496	−	0.992220i	$-0.539731\pi$
$653$	−6.36272	−0.248992	−0.124496	+	0.992220i	$0.539731\pi$
$654$	−4.54085	−0.177561
$655$	7.85888	0.307072
$656$	57.7240	2.25375
$657$	10.4082	0.406061
$658$	7.48388	0.291752
$659$	13.5416	0.527505	0.263752	−	0.964590i	$-0.415040\pi$
$659$	13.5416	0.527505	0.263752	+	0.964590i	$0.415040\pi$
$660$	19.9183	0.775317
$661$	45.4713	1.76863	0.884315	−	0.466892i	$-0.154626\pi$
$661$	45.4713	1.76863	0.884315	+	0.466892i	$0.154626\pi$
$662$	63.5266	2.46903
$663$	6.50096	0.252476
$664$	−86.1141	−3.34188
$665$	10.8483	0.420680
$666$	−17.3432	−0.672034
$667$	11.6131	0.449659
$668$	−13.6328	−0.527468
$669$	−15.5556	−0.601415
$670$	−8.93267	−0.345099
$671$	−30.4531	−1.17563
$672$	−2.08219	−0.0803221
$673$	33.3052	1.28382	0.641911	−	0.766779i	$-0.278142\pi$
$673$	33.3052	1.28382	0.641911	+	0.766779i	$0.278142\pi$
$674$	−41.8449	−1.61181
$675$	2.90249	0.111717
$676$	−10.2648	−0.394798
$677$	−13.7600	−0.528841	−0.264421	−	0.964407i	$-0.585181\pi$
$677$	−13.7600	−0.528841	−0.264421	+	0.964407i	$0.585181\pi$
$678$	−5.25351	−0.201760
$679$	−3.36147	−0.129001
$680$	−15.8676	−0.608496
$681$	−24.0255	−0.920659
$682$	−76.3530	−2.92371
$683$	−3.68291	−0.140922	−0.0704612	−	0.997515i	$-0.522447\pi$
$683$	−3.68291	−0.140922	−0.0704612	+	0.997515i	$0.522447\pi$
$684$	−31.4537	−1.20266
$685$	4.61382	0.176285
$686$	2.48981	0.0950614
$687$	25.7078	0.980813
$688$	−38.4295	−1.46511
$689$	−35.3636	−1.34725
$690$	−18.4441	−0.702153
$691$	17.0240	0.647622	0.323811	−	0.946122i	$-0.395036\pi$
$691$	17.0240	0.647622	0.323811	+	0.946122i	$0.395036\pi$
$692$	−9.40102	−0.357373
$693$	3.27519	0.124414
$694$	67.5846	2.56548
$695$	−1.92004	−0.0728313
$696$	−12.4317	−0.471223
$697$	22.0654	0.835786
$698$	−52.8683	−2.00109
$699$	−4.47472	−0.169249
$700$	12.1880	0.460663
$701$	21.8960	0.827001	0.413501	−	0.910504i	$-0.364306\pi$
$701$	21.8960	0.827001	0.413501	+	0.910504i	$0.364306\pi$
$702$	−8.08921	−0.305308
$703$	−52.1762	−1.96786
$704$	17.3092	0.652365
$705$	−4.35324	−0.163953
$706$	68.6637	2.58419
$707$	3.15143	0.118522
$708$	34.6705	1.30300
$709$	4.17525	0.156805	0.0784024	−	0.996922i	$-0.475018\pi$
$709$	4.17525	0.156805	0.0784024	+	0.996922i	$0.475018\pi$
$710$	−24.4020	−0.915791
$711$	6.43106	0.241184
$712$	50.7498	1.90193
$713$	47.8917	1.79356
$714$	−4.98200	−0.186447
$715$	15.4109	0.576336
$716$	32.6377	1.21973
$717$	−3.71050	−0.138571
$718$	−28.4011	−1.05992
$719$	18.8713	0.703781	0.351890	−	0.936041i	$-0.385539\pi$
$719$	18.8713	0.703781	0.351890	+	0.936041i	$0.385539\pi$
$720$	7.58115	0.282533
$721$	7.60402	0.283188
$722$	−92.3906	−3.43842
$723$	23.5929	0.877428
$724$	84.6356	3.14546
$725$	6.58990	0.244743
$726$	−0.679966	−0.0252359
$727$	−28.0662	−1.04092	−0.520458	−	0.853887i	$-0.674239\pi$
$727$	−28.0662	−1.04092	−0.520458	+	0.853887i	$0.674239\pi$
$728$	−17.7894	−0.659320
$729$	1.00000	0.0370370
$730$	−37.5312	−1.38909
$731$	−14.6899	−0.543327
$732$	−39.0442	−1.44311
$733$	25.7440	0.950875	0.475437	−	0.879750i	$-0.342290\pi$
$733$	25.7440	0.950875	0.475437	+	0.879750i	$0.342290\pi$
$734$	−61.3788	−2.26553
$735$	−1.44828	−0.0534206
$736$	10.6502	0.392571
$737$	−8.11334	−0.298859
$738$	−27.4562	−1.01068
$739$	−13.7151	−0.504517	−0.252259	−	0.967660i	$-0.581173\pi$
$739$	−13.7151	−0.504517	−0.252259	+	0.967660i	$0.581173\pi$
$740$	42.3620	1.55726
$741$	−24.3361	−0.894007
$742$	27.1008	0.994903
$743$	44.3812	1.62819	0.814094	−	0.580733i	$-0.197234\pi$
$743$	44.3812	1.62819	0.814094	+	0.580733i	$0.197234\pi$
$744$	−51.2678	−1.87957
$745$	−0.156582	−0.00573670
$746$	77.1987	2.82644
$747$	15.7272	0.575429
$748$	−27.5193	−1.00620
$749$	−5.11898	−0.187043
$750$	−28.4959	−1.04052
$751$	38.9092	1.41982	0.709909	−	0.704294i	$-0.248736\pi$
$751$	38.9092	1.41982	0.709909	+	0.704294i	$0.248736\pi$
$752$	15.7342	0.573766
$753$	−16.0972	−0.586614
$754$	−18.3660	−0.668850
$755$	−20.3428	−0.740350
$756$	4.19916	0.152722
$757$	−7.16594	−0.260451	−0.130225	−	0.991484i	$-0.541570\pi$
$757$	−7.16594	−0.260451	−0.130225	+	0.991484i	$0.541570\pi$
$758$	−57.0286	−2.07137
$759$	−16.7523	−0.608071
$760$	59.3998	2.15466
$761$	−3.29004	−0.119264	−0.0596318	−	0.998220i	$-0.518993\pi$
$761$	−3.29004	−0.119264	−0.0596318	+	0.998220i	$0.518993\pi$
$762$	2.48981	0.0901963
$763$	1.82377	0.0660250
$764$	33.1970	1.20103
$765$	2.89794	0.104775
$766$	72.2077	2.60897
$767$	26.8249	0.968590
$768$	32.5608	1.17494
$769$	−8.91144	−0.321355	−0.160677	−	0.987007i	$-0.551368\pi$
$769$	−8.91144	−0.321355	−0.160677	+	0.987007i	$0.551368\pi$
$770$	−11.8102	−0.425608
$771$	15.7376	0.566774
$772$	−65.5453	−2.35903
$773$	−33.6491	−1.21027	−0.605137	−	0.796121i	$-0.706882\pi$
$773$	−33.6491	−1.21027	−0.605137	+	0.796121i	$0.706882\pi$
$774$	18.2788	0.657019
$775$	27.1765	0.976208
$776$	−18.4056	−0.660724
$777$	6.96565	0.249891
$778$	−41.1980	−1.47702
$779$	−82.6008	−2.95948
$780$	19.7585	0.707468
$781$	−22.1638	−0.793083
$782$	25.4825	0.911252
$783$	2.27043	0.0811386
$784$	5.23459	0.186950
$785$	−24.4862	−0.873950
$786$	13.5106	0.481907
$787$	24.5016	0.873387	0.436694	−	0.899610i	$-0.356149\pi$
$787$	24.5016	0.873387	0.436694	+	0.899610i	$0.356149\pi$
$788$	98.4123	3.50579
$789$	−4.31962	−0.153783
$790$	−23.1900	−0.825064
$791$	2.11000	0.0750231
$792$	17.9333	0.637231
$793$	−30.2089	−1.07275
$794$	−20.4406	−0.725411
$795$	−15.7641	−0.559095
$796$	73.7429	2.61375
$797$	11.5574	0.409384	0.204692	−	0.978826i	$-0.434381\pi$
$797$	11.5574	0.409384	0.204692	+	0.978826i	$0.434381\pi$
$798$	18.6499	0.660199
$799$	6.01449	0.212777
$800$	6.04352	0.213671
$801$	−9.26856	−0.327489
$802$	−75.3438	−2.66048
$803$	−34.0888	−1.20297
$804$	−10.4022	−0.366857
$805$	7.40782	0.261091
$806$	−75.7406	−2.66785
$807$	30.7930	1.08396
$808$	17.2556	0.607049
$809$	−28.4257	−0.999395	−0.499697	−	0.866200i	$-0.666555\pi$
$809$	−28.4257	−0.999395	−0.499697	+	0.866200i	$0.666555\pi$
$810$	−3.60594	−0.126700
$811$	43.5857	1.53050	0.765251	−	0.643732i	$-0.222615\pi$
$811$	43.5857	1.53050	0.765251	+	0.643732i	$0.222615\pi$
$812$	9.53390	0.334574
$813$	−2.75638	−0.0966704
$814$	56.8022	1.99092
$815$	26.9895	0.945400
$816$	−10.4742	−0.366670
$817$	54.9911	1.92389
$818$	20.5108	0.717143
$819$	3.24893	0.113527
$820$	67.0638	2.34197
$821$	16.6400	0.580738	0.290369	−	0.956915i	$-0.406222\pi$
$821$	16.6400	0.580738	0.290369	+	0.956915i	$0.406222\pi$
$822$	7.93186	0.276655
$823$	41.4873	1.44616	0.723078	−	0.690767i	$-0.242727\pi$
$823$	41.4873	1.44616	0.723078	+	0.690767i	$0.242727\pi$
$824$	41.6356	1.45045
$825$	−9.50621	−0.330964
$826$	−20.5572	−0.715277
$827$	−10.8714	−0.378035	−0.189018	−	0.981974i	$-0.560530\pi$
$827$	−10.8714	−0.378035	−0.189018	+	0.981974i	$0.560530\pi$
$828$	−21.4783	−0.746423
$829$	−29.5467	−1.02620	−0.513099	−	0.858330i	$-0.671503\pi$
$829$	−29.5467	−1.02620	−0.513099	+	0.858330i	$0.671503\pi$
$830$	−56.7114	−1.96848
$831$	15.0763	0.522990
$832$	17.1704	0.595276
$833$	2.00096	0.0693291
$834$	−3.30084	−0.114299
$835$	−4.70192	−0.162717
$836$	103.017	3.56292
$837$	9.36316	0.323638
$838$	−65.4943	−2.26246
$839$	32.2794	1.11441	0.557204	−	0.830376i	$-0.311874\pi$
$839$	32.2794	1.11441	0.557204	+	0.830376i	$0.311874\pi$
$840$	−7.93002	−0.273612
$841$	−23.8451	−0.822246
$842$	−42.6200	−1.46878
$843$	4.56741	0.157310
$844$	63.7253	2.19352
$845$	−3.54029	−0.121790
$846$	−7.48388	−0.257301
$847$	0.273100	0.00938382
$848$	56.9770	1.95660
$849$	−22.2507	−0.763643
$850$	14.4602	0.495981
$851$	−35.6287	−1.22134
$852$	−28.4164	−0.973530
$853$	−33.2528	−1.13855	−0.569277	−	0.822145i	$-0.692777\pi$
$853$	−33.2528	−1.13855	−0.569277	+	0.822145i	$0.692777\pi$
$854$	23.1505	0.792194
$855$	−10.8483	−0.371005
$856$	−28.0289	−0.958007
$857$	37.1866	1.27027	0.635135	−	0.772401i	$-0.280945\pi$
$857$	37.1866	1.27027	0.635135	+	0.772401i	$0.280945\pi$
$858$	26.4937	0.904481
$859$	−57.8946	−1.97534	−0.987668	−	0.156561i	$-0.949959\pi$
$859$	−57.8946	−1.97534	−0.987668	+	0.156561i	$0.949959\pi$
$860$	−44.6474	−1.52246
$861$	11.0274	0.375813
$862$	−63.9982	−2.17979
$863$	46.7651	1.59190	0.795951	−	0.605362i	$-0.206972\pi$
$863$	46.7651	1.59190	0.795951	+	0.605362i	$0.206972\pi$
$864$	2.08219	0.0708374
$865$	−3.24239	−0.110245
$866$	−49.7743	−1.69140
$867$	12.9962	0.441373
$868$	39.3174	1.33452
$869$	−21.0630	−0.714513
$870$	−8.18704	−0.277567
$871$	−8.04827	−0.272705
$872$	9.98603	0.338170
$873$	3.36147	0.113768
$874$	−95.3926	−3.22670
$875$	11.4450	0.386912
$876$	−43.7055	−1.47667
$877$	43.8243	1.47984	0.739921	−	0.672694i	$-0.234863\pi$
$877$	43.8243	1.47984	0.739921	+	0.672694i	$0.234863\pi$
$878$	59.1846	1.99738
$879$	−22.4715	−0.757945
$880$	−24.8297	−0.837011
$881$	−17.1037	−0.576239	−0.288119	−	0.957594i	$-0.593030\pi$
$881$	−17.1037	−0.576239	−0.288119	+	0.957594i	$0.593030\pi$
$882$	−2.48981	−0.0838363
$883$	−1.94657	−0.0655073	−0.0327537	−	0.999463i	$-0.510428\pi$
$883$	−1.94657	−0.0655073	−0.0327537	+	0.999463i	$0.510428\pi$
$884$	−27.2985	−0.918149
$885$	11.9578	0.401956
$886$	101.441	3.40797
$887$	3.52396	0.118323	0.0591615	−	0.998248i	$-0.481157\pi$
$887$	3.52396	0.118323	0.0591615	+	0.998248i	$0.481157\pi$
$888$	38.1403	1.27990
$889$	−1.00000	−0.0335389
$890$	33.4219	1.12030
$891$	−3.27519	−0.109723
$892$	65.3205	2.18709
$893$	−22.5150	−0.753434
$894$	−0.269187	−0.00900297
$895$	11.2567	0.376269
$896$	−17.3229	−0.578716
$897$	−16.6180	−0.554858
$898$	61.0979	2.03886
$899$	21.2584	0.709008
$900$	−12.1880	−0.406267
$901$	21.7798	0.725591
$902$	89.9243	2.99415
$903$	−7.34145	−0.244308
$904$	11.5533	0.384256
$905$	29.1906	0.970330
$906$	−34.9723	−1.16188
$907$	44.0478	1.46258	0.731292	−	0.682065i	$-0.238918\pi$
$907$	44.0478	1.46258	0.731292	+	0.682065i	$0.238918\pi$
$908$	100.887	3.34805
$909$	−3.15143	−0.104526
$910$	−11.7154	−0.388363
$911$	−35.9406	−1.19077	−0.595383	−	0.803442i	$-0.703000\pi$
$911$	−35.9406	−1.19077	−0.595383	+	0.803442i	$0.703000\pi$
$912$	39.2097	1.29836
$913$	−51.5097	−1.70472
$914$	−33.4476	−1.10635
$915$	−13.4663	−0.445181
$916$	−107.951	−3.56680
$917$	−5.42636	−0.179194
$918$	4.98200	0.164431
$919$	26.8856	0.886874	0.443437	−	0.896305i	$-0.353759\pi$
$919$	26.8856	0.886874	0.443437	+	0.896305i	$0.353759\pi$
$920$	40.5613	1.33727
$921$	−15.5752	−0.513220
$922$	66.8647	2.20207
$923$	−21.9860	−0.723679
$924$	−13.7531	−0.452442
$925$	−20.2177	−0.664755
$926$	23.0241	0.756619
$927$	−7.60402	−0.249749
$928$	4.72746	0.155187
$929$	25.1460	0.825013	0.412506	−	0.910955i	$-0.364653\pi$
$929$	25.1460	0.825013	0.412506	+	0.910955i	$0.364653\pi$
$930$	−33.7630	−1.10713
$931$	−7.49049	−0.245491
$932$	18.7900	0.615488
$933$	20.5657	0.673290
$934$	53.7382	1.75837
$935$	−9.49133	−0.310400
$936$	17.7894	0.581466
$937$	−3.58973	−0.117271	−0.0586357	−	0.998279i	$-0.518675\pi$
$937$	−3.58973	−0.117271	−0.0586357	+	0.998279i	$0.518675\pi$
$938$	6.16778	0.201385
$939$	−21.9001	−0.714684
$940$	18.2799	0.596226
$941$	19.4890	0.635323	0.317662	−	0.948204i	$-0.397102\pi$
$941$	19.4890	0.635323	0.317662	+	0.948204i	$0.397102\pi$
$942$	−42.0955	−1.37154
$943$	−56.4042	−1.83678
$944$	−43.2196	−1.40668
$945$	1.44828	0.0471125
$946$	−59.8667	−1.94643
$947$	−11.2713	−0.366268	−0.183134	−	0.983088i	$-0.558624\pi$
$947$	−11.2713	−0.366268	−0.183134	+	0.983088i	$0.558624\pi$
$948$	−27.0050	−0.877083
$949$	−33.8154	−1.09769
$950$	−54.1311	−1.75625
$951$	−12.3293	−0.399804
$952$	10.9562	0.355092
$953$	−34.6856	−1.12358	−0.561788	−	0.827281i	$-0.689886\pi$
$953$	−34.6856	−1.12358	−0.561788	+	0.827281i	$0.689886\pi$
$954$	−27.1008	−0.877422
$955$	11.4496	0.370500
$956$	15.5810	0.503924
$957$	−7.43611	−0.240375
$958$	24.7151	0.798507
$959$	−3.18573	−0.102873
$960$	7.65407	0.247034
$961$	56.6689	1.82803
$962$	56.3466	1.81669
$963$	5.11898	0.164957
$964$	−99.0701	−3.19083
$965$	−22.6064	−0.727727
$966$	12.7352	0.409747
$967$	−34.2544	−1.10155	−0.550774	−	0.834655i	$-0.685667\pi$
$967$	−34.2544	−1.10155	−0.550774	+	0.834655i	$0.685667\pi$
$968$	1.49535	0.0480624
$969$	14.9882	0.481489
$970$	−12.1212	−0.389190
$971$	25.1782	0.808007	0.404004	−	0.914757i	$-0.367618\pi$
$971$	25.1782	0.808007	0.404004	+	0.914757i	$0.367618\pi$
$972$	−4.19916	−0.134688
$973$	1.32574	0.0425012
$974$	−43.6940	−1.40005
$975$	−9.42997	−0.302001
$976$	48.6718	1.55795
$977$	52.0600	1.66555	0.832773	−	0.553614i	$-0.186752\pi$
$977$	52.0600	1.66555	0.832773	+	0.553614i	$0.186752\pi$
$978$	46.3990	1.48368
$979$	30.3563	0.970193
$980$	6.08155	0.194268
$981$	−1.82377	−0.0582286
$982$	−29.8346	−0.952059
$983$	−2.90281	−0.0925852	−0.0462926	−	0.998928i	$-0.514741\pi$
$983$	−2.90281	−0.0925852	−0.0462926	+	0.998928i	$0.514741\pi$
$984$	60.3804	1.92486
$985$	33.9422	1.08149
$986$	11.3113	0.360225
$987$	3.00580	0.0956758
$988$	102.191	3.25112
$989$	37.5509	1.19405
$990$	11.8102	0.375351
$991$	49.2426	1.56424	0.782121	−	0.623127i	$-0.214138\pi$
$991$	49.2426	1.56424	0.782121	+	0.623127i	$0.214138\pi$
$992$	19.4958	0.618994
$993$	25.5146	0.809683
$994$	16.8490	0.534417
$995$	25.4338	0.806305
$996$	−66.0411	−2.09259
$997$	−24.3407	−0.770878	−0.385439	−	0.922733i	$-0.625950\pi$
$997$	−24.3407	−0.770878	−0.385439	+	0.922733i	$0.625950\pi$
$998$	44.0988	1.39592
$999$	−6.96565	−0.220384

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2667.2.a.o.1.1	✓	16
3.2	odd	2		8001.2.a.r.1.16		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2667.2.a.o.1.1	✓	16	1.1	even	1	trivial
8001.2.a.r.1.16		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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 2667 = 3 \cdot 7 \cdot 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2667.a (trivial)

\(f(q)\)	\(=\)	\(q-2.48981 q^{2} -1.00000 q^{3} +4.19916 q^{4} +1.44828 q^{5} +2.48981 q^{6} -1.00000 q^{7} -5.47548 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.48981 q^{2} -1.00000 q^{3} +4.19916 q^{4} +1.44828 q^{5} +2.48981 q^{6} -1.00000 q^{7} -5.47548 q^{8} +1.00000 q^{9} -3.60594 q^{10} -3.27519 q^{11} -4.19916 q^{12} -3.24893 q^{13} +2.48981 q^{14} -1.44828 q^{15} +5.23459 q^{16} +2.00096 q^{17} -2.48981 q^{18} -7.49049 q^{19} +6.08155 q^{20} +1.00000 q^{21} +8.15461 q^{22} -5.11491 q^{23} +5.47548 q^{24} -2.90249 q^{25} +8.08921 q^{26} -1.00000 q^{27} -4.19916 q^{28} -2.27043 q^{29} +3.60594 q^{30} -9.36316 q^{31} -2.08219 q^{32} +3.27519 q^{33} -4.98200 q^{34} -1.44828 q^{35} +4.19916 q^{36} +6.96565 q^{37} +18.6499 q^{38} +3.24893 q^{39} -7.93002 q^{40} +11.0274 q^{41} -2.48981 q^{42} -7.34145 q^{43} -13.7531 q^{44} +1.44828 q^{45} +12.7352 q^{46} +3.00580 q^{47} -5.23459 q^{48} +1.00000 q^{49} +7.22664 q^{50} -2.00096 q^{51} -13.6427 q^{52} +10.8847 q^{53} +2.48981 q^{54} -4.74340 q^{55} +5.47548 q^{56} +7.49049 q^{57} +5.65295 q^{58} -8.25654 q^{59} -6.08155 q^{60} +9.29811 q^{61} +23.3125 q^{62} -1.00000 q^{63} -5.28494 q^{64} -4.70535 q^{65} -8.15461 q^{66} +2.47721 q^{67} +8.40233 q^{68} +5.11491 q^{69} +3.60594 q^{70} +6.76717 q^{71} -5.47548 q^{72} +10.4082 q^{73} -17.3432 q^{74} +2.90249 q^{75} -31.4537 q^{76} +3.27519 q^{77} -8.08921 q^{78} +6.43106 q^{79} +7.58115 q^{80} +1.00000 q^{81} -27.4562 q^{82} +15.7272 q^{83} +4.19916 q^{84} +2.89794 q^{85} +18.2788 q^{86} +2.27043 q^{87} +17.9333 q^{88} -9.26856 q^{89} -3.60594 q^{90} +3.24893 q^{91} -21.4783 q^{92} +9.36316 q^{93} -7.48388 q^{94} -10.8483 q^{95} +2.08219 q^{96} +3.36147 q^{97} -2.48981 q^{98} -3.27519 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 5 q^{2} - 16 q^{3} + 19 q^{4} - q^{5} - 5 q^{6} - 16 q^{7} + 6 q^{8} + 16 q^{9}+O(q^{10}) \) 16 * q + 5 * q^2 - 16 * q^3 + 19 * q^4 - q^5 - 5 * q^6 - 16 * q^7 + 6 * q^8 + 16 * q^9	\( 16 q + 5 q^{2} - 16 q^{3} + 19 q^{4} - q^{5} - 5 q^{6} - 16 q^{7} + 6 q^{8} + 16 q^{9} - 12 q^{10} + 11 q^{11} - 19 q^{12} + 18 q^{13} - 5 q^{14} + q^{15} + 25 q^{16} - 5 q^{17} + 5 q^{18} - 11 q^{19} - q^{20} + 16 q^{21} + q^{22} + 13 q^{23} - 6 q^{24} + 33 q^{25} + 8 q^{26} - 16 q^{27} - 19 q^{28} + 24 q^{29} + 12 q^{30} - 42 q^{31} + 42 q^{32} - 11 q^{33} + 9 q^{34} + q^{35} + 19 q^{36} + 40 q^{37} + 38 q^{38} - 18 q^{39} - 61 q^{40} + 9 q^{41} + 5 q^{42} + 7 q^{43} + 3 q^{44} - q^{45} + 24 q^{46} + 31 q^{47} - 25 q^{48} + 16 q^{49} + 6 q^{50} + 5 q^{51} + 52 q^{52} + 66 q^{53} - 5 q^{54} - 36 q^{55} - 6 q^{56} + 11 q^{57} + 19 q^{58} - 7 q^{59} + q^{60} + 6 q^{61} + 52 q^{62} - 16 q^{63} + 10 q^{64} + 51 q^{65} - q^{66} + 16 q^{67} + 14 q^{68} - 13 q^{69} + 12 q^{70} + 46 q^{71} + 6 q^{72} + 39 q^{73} + 72 q^{74} - 33 q^{75} + 24 q^{76} - 11 q^{77} - 8 q^{78} + 4 q^{79} - 2 q^{80} + 16 q^{81} - 18 q^{82} + 15 q^{83} + 19 q^{84} - 4 q^{85} + 14 q^{86} - 24 q^{87} + 58 q^{88} - q^{89} - 12 q^{90} - 18 q^{91} + 26 q^{92} + 42 q^{93} + 5 q^{94} + 44 q^{95} - 42 q^{96} + 41 q^{97} + 5 q^{98} + 11 q^{99}+O(q^{100}) \) 16 * q + 5 * q^2 - 16 * q^3 + 19 * q^4 - q^5 - 5 * q^6 - 16 * q^7 + 6 * q^8 + 16 * q^9 - 12 * q^10 + 11 * q^11 - 19 * q^12 + 18 * q^13 - 5 * q^14 + q^15 + 25 * q^16 - 5 * q^17 + 5 * q^18 - 11 * q^19 - q^20 + 16 * q^21 + q^22 + 13 * q^23 - 6 * q^24 + 33 * q^25 + 8 * q^26 - 16 * q^27 - 19 * q^28 + 24 * q^29 + 12 * q^30 - 42 * q^31 + 42 * q^32 - 11 * q^33 + 9 * q^34 + q^35 + 19 * q^36 + 40 * q^37 + 38 * q^38 - 18 * q^39 - 61 * q^40 + 9 * q^41 + 5 * q^42 + 7 * q^43 + 3 * q^44 - q^45 + 24 * q^46 + 31 * q^47 - 25 * q^48 + 16 * q^49 + 6 * q^50 + 5 * q^51 + 52 * q^52 + 66 * q^53 - 5 * q^54 - 36 * q^55 - 6 * q^56 + 11 * q^57 + 19 * q^58 - 7 * q^59 + q^60 + 6 * q^61 + 52 * q^62 - 16 * q^63 + 10 * q^64 + 51 * q^65 - q^66 + 16 * q^67 + 14 * q^68 - 13 * q^69 + 12 * q^70 + 46 * q^71 + 6 * q^72 + 39 * q^73 + 72 * q^74 - 33 * q^75 + 24 * q^76 - 11 * q^77 - 8 * q^78 + 4 * q^79 - 2 * q^80 + 16 * q^81 - 18 * q^82 + 15 * q^83 + 19 * q^84 - 4 * q^85 + 14 * q^86 - 24 * q^87 + 58 * q^88 - q^89 - 12 * q^90 - 18 * q^91 + 26 * q^92 + 42 * q^93 + 5 * q^94 + 44 * q^95 - 42 * q^96 + 41 * q^97 + 5 * q^98 + 11 * q^99

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