LMFDB - Embedded newform 2667.2.a.j.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:	$1$
Dimension:	$7$
Coefficient field:	7.7.118870813.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 9x^{5} - 3x^{4} + 20x^{3} + 7x^{2} - 13x - 4 $ x^7 - 9x^5 - 3x^4 + 20x^3 + 7x^2 - 13*x - 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.13462$ 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)

$f(q)$	$=$	$q-2.48001 q^{2} +1.00000 q^{3} +4.15043 q^{4} -0.783950 q^{5} -2.48001 q^{6} +1.00000 q^{7} -5.33307 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.48001 q^{2} +1.00000 q^{3} +4.15043 q^{4} -0.783950 q^{5} -2.48001 q^{6} +1.00000 q^{7} -5.33307 q^{8} +1.00000 q^{9} +1.94420 q^{10} +4.88599 q^{11} +4.15043 q^{12} -6.65543 q^{13} -2.48001 q^{14} -0.783950 q^{15} +4.92520 q^{16} +1.25567 q^{17} -2.48001 q^{18} -2.07830 q^{19} -3.25373 q^{20} +1.00000 q^{21} -12.1173 q^{22} +6.86976 q^{23} -5.33307 q^{24} -4.38542 q^{25} +16.5055 q^{26} +1.00000 q^{27} +4.15043 q^{28} -9.79804 q^{29} +1.94420 q^{30} -3.45591 q^{31} -1.54837 q^{32} +4.88599 q^{33} -3.11406 q^{34} -0.783950 q^{35} +4.15043 q^{36} -2.67789 q^{37} +5.15419 q^{38} -6.65543 q^{39} +4.18086 q^{40} -4.19977 q^{41} -2.48001 q^{42} -4.11683 q^{43} +20.2789 q^{44} -0.783950 q^{45} -17.0370 q^{46} -6.51041 q^{47} +4.92520 q^{48} +1.00000 q^{49} +10.8759 q^{50} +1.25567 q^{51} -27.6229 q^{52} +3.48731 q^{53} -2.48001 q^{54} -3.83037 q^{55} -5.33307 q^{56} -2.07830 q^{57} +24.2992 q^{58} +12.2268 q^{59} -3.25373 q^{60} +6.13863 q^{61} +8.57067 q^{62} +1.00000 q^{63} -6.01043 q^{64} +5.21753 q^{65} -12.1173 q^{66} -15.0576 q^{67} +5.21155 q^{68} +6.86976 q^{69} +1.94420 q^{70} -7.18924 q^{71} -5.33307 q^{72} +2.24951 q^{73} +6.64118 q^{74} -4.38542 q^{75} -8.62583 q^{76} +4.88599 q^{77} +16.5055 q^{78} -7.38716 q^{79} -3.86111 q^{80} +1.00000 q^{81} +10.4154 q^{82} -3.82920 q^{83} +4.15043 q^{84} -0.984380 q^{85} +10.2098 q^{86} -9.79804 q^{87} -26.0573 q^{88} -16.4372 q^{89} +1.94420 q^{90} -6.65543 q^{91} +28.5124 q^{92} -3.45591 q^{93} +16.1458 q^{94} +1.62928 q^{95} -1.54837 q^{96} +16.8967 q^{97} -2.48001 q^{98} +4.88599 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 2 q^{2} + 7 q^{3} + 4 q^{4} - 8 q^{5} - 2 q^{6} + 7 q^{7} - 9 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q - 2 * q^2 + 7 * q^3 + 4 * q^4 - 8 * q^5 - 2 * q^6 + 7 * q^7 - 9 * q^8 + 7 * q^9	\( 7 q - 2 q^{2} + 7 q^{3} + 4 q^{4} - 8 q^{5} - 2 q^{6} + 7 q^{7} - 9 q^{8} + 7 q^{9} - 3 q^{11} + 4 q^{12} - 23 q^{13} - 2 q^{14} - 8 q^{15} + 2 q^{16} + 3 q^{17} - 2 q^{18} - 9 q^{19} - 9 q^{20} + 7 q^{21} - 19 q^{22} + 12 q^{23} - 9 q^{24} + 3 q^{25} + 18 q^{26} + 7 q^{27} + 4 q^{28} - 9 q^{29} - 33 q^{31} + 10 q^{32} - 3 q^{33} - 2 q^{34} - 8 q^{35} + 4 q^{36} - 33 q^{37} - 3 q^{38} - 23 q^{39} - 9 q^{40} - 3 q^{41} - 2 q^{42} - 9 q^{43} + 2 q^{44} - 8 q^{45} - 32 q^{46} + 11 q^{47} + 2 q^{48} + 7 q^{49} + 29 q^{50} + 3 q^{51} - 21 q^{52} + q^{53} - 2 q^{54} - 16 q^{55} - 9 q^{56} - 9 q^{57} - 5 q^{58} - 30 q^{59} - 9 q^{60} - 19 q^{61} + 3 q^{62} + 7 q^{63} - 21 q^{64} + 14 q^{65} - 19 q^{66} - 30 q^{67} + 24 q^{68} + 12 q^{69} + 8 q^{71} - 9 q^{72} - 20 q^{73} - 9 q^{74} + 3 q^{75} - 42 q^{76} - 3 q^{77} + 18 q^{78} + 8 q^{79} + 12 q^{80} + 7 q^{81} + 10 q^{82} - 34 q^{83} + 4 q^{84} - 28 q^{85} + 24 q^{86} - 9 q^{87} - q^{88} - 12 q^{89} - 23 q^{91} + 60 q^{92} - 33 q^{93} - 3 q^{94} + 12 q^{95} + 10 q^{96} + 7 q^{97} - 2 q^{98} - 3 q^{99}+O(q^{100}) \) 7 * q - 2 * q^2 + 7 * q^3 + 4 * q^4 - 8 * q^5 - 2 * q^6 + 7 * q^7 - 9 * q^8 + 7 * q^9 - 3 * q^11 + 4 * q^12 - 23 * q^13 - 2 * q^14 - 8 * q^15 + 2 * q^16 + 3 * q^17 - 2 * q^18 - 9 * q^19 - 9 * q^20 + 7 * q^21 - 19 * q^22 + 12 * q^23 - 9 * q^24 + 3 * q^25 + 18 * q^26 + 7 * q^27 + 4 * q^28 - 9 * q^29 - 33 * q^31 + 10 * q^32 - 3 * q^33 - 2 * q^34 - 8 * q^35 + 4 * q^36 - 33 * q^37 - 3 * q^38 - 23 * q^39 - 9 * q^40 - 3 * q^41 - 2 * q^42 - 9 * q^43 + 2 * q^44 - 8 * q^45 - 32 * q^46 + 11 * q^47 + 2 * q^48 + 7 * q^49 + 29 * q^50 + 3 * q^51 - 21 * q^52 + q^53 - 2 * q^54 - 16 * q^55 - 9 * q^56 - 9 * q^57 - 5 * q^58 - 30 * q^59 - 9 * q^60 - 19 * q^61 + 3 * q^62 + 7 * q^63 - 21 * q^64 + 14 * q^65 - 19 * q^66 - 30 * q^67 + 24 * q^68 + 12 * q^69 + 8 * q^71 - 9 * q^72 - 20 * q^73 - 9 * q^74 + 3 * q^75 - 42 * q^76 - 3 * q^77 + 18 * q^78 + 8 * q^79 + 12 * q^80 + 7 * q^81 + 10 * q^82 - 34 * q^83 + 4 * q^84 - 28 * q^85 + 24 * q^86 - 9 * q^87 - q^88 - 12 * q^89 - 23 * q^91 + 60 * q^92 - 33 * q^93 - 3 * q^94 + 12 * q^95 + 10 * q^96 + 7 * q^97 - 2 * q^98 - 3 * 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 $

$2$	−2.48001	−1.75363	−0.876814	−	0.480829i	$-0.840336\pi$
$2$	−2.48001	−1.75363	−0.876814	+	0.480829i	$0.840336\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.15043	2.07521
$5$	−0.783950	−0.350593	−0.175297	−	0.984516i	$-0.556088\pi$
$5$	−0.783950	−0.350593	−0.175297	+	0.984516i	$0.556088\pi$
$6$	−2.48001	−1.01246
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−5.33307	−1.88553
$9$	1.00000	0.333333
$10$	1.94420	0.614810
$11$	4.88599	1.47318	0.736590	−	0.676340i	$-0.236435\pi$
$11$	4.88599	1.47318	0.736590	+	0.676340i	$0.236435\pi$
$12$	4.15043	1.19813
$13$	−6.65543	−1.84589	−0.922943	−	0.384937i	$-0.874223\pi$
$13$	−6.65543	−1.84589	−0.922943	+	0.384937i	$0.874223\pi$
$14$	−2.48001	−0.662809
$15$	−0.783950	−0.202415
$16$	4.92520	1.23130
$17$	1.25567	0.304544	0.152272	−	0.988339i	$-0.451341\pi$
$17$	1.25567	0.304544	0.152272	+	0.988339i	$0.451341\pi$
$18$	−2.48001	−0.584543
$19$	−2.07830	−0.476795	−0.238397	−	0.971168i	$-0.576622\pi$
$19$	−2.07830	−0.476795	−0.238397	+	0.971168i	$0.576622\pi$
$20$	−3.25373	−0.727556
$21$	1.00000	0.218218
$22$	−12.1173	−2.58341
$23$	6.86976	1.43244	0.716222	−	0.697872i	$-0.245870\pi$
$23$	6.86976	1.43244	0.716222	+	0.697872i	$0.245870\pi$
$24$	−5.33307	−1.08861
$25$	−4.38542	−0.877084
$26$	16.5055	3.23700
$27$	1.00000	0.192450
$28$	4.15043	0.784357
$29$	−9.79804	−1.81945	−0.909726	−	0.415210i	$-0.863708\pi$
$29$	−9.79804	−1.81945	−0.909726	+	0.415210i	$0.863708\pi$
$30$	1.94420	0.354961
$31$	−3.45591	−0.620699	−0.310349	−	0.950623i	$-0.600446\pi$
$31$	−3.45591	−0.620699	−0.310349	+	0.950623i	$0.600446\pi$
$32$	−1.54837	−0.273715
$33$	4.88599	0.850541
$34$	−3.11406	−0.534057
$35$	−0.783950	−0.132512
$36$	4.15043	0.691738
$37$	−2.67789	−0.440242	−0.220121	−	0.975473i	$-0.570645\pi$
$37$	−2.67789	−0.440242	−0.220121	+	0.975473i	$0.570645\pi$
$38$	5.15419	0.836121
$39$	−6.65543	−1.06572
$40$	4.18086	0.661052
$41$	−4.19977	−0.655893	−0.327947	−	0.944696i	$-0.606357\pi$
$41$	−4.19977	−0.655893	−0.327947	+	0.944696i	$0.606357\pi$
$42$	−2.48001	−0.382673
$43$	−4.11683	−0.627811	−0.313906	−	0.949454i	$-0.601638\pi$
$43$	−4.11683	−0.627811	−0.313906	+	0.949454i	$0.601638\pi$
$44$	20.2789	3.05716
$45$	−0.783950	−0.116864
$46$	−17.0370	−2.51198
$47$	−6.51041	−0.949640	−0.474820	−	0.880083i	$-0.657487\pi$
$47$	−6.51041	−0.949640	−0.474820	+	0.880083i	$0.657487\pi$
$48$	4.92520	0.710891
$49$	1.00000	0.142857
$50$	10.8759	1.53808
$51$	1.25567	0.175828
$52$	−27.6229	−3.83061
$53$	3.48731	0.479019	0.239510	−	0.970894i	$-0.423013\pi$
$53$	3.48731	0.479019	0.239510	+	0.970894i	$0.423013\pi$
$54$	−2.48001	−0.337486
$55$	−3.83037	−0.516487
$56$	−5.33307	−0.712662
$57$	−2.07830	−0.275277
$58$	24.2992	3.19064
$59$	12.2268	1.59180	0.795899	−	0.605430i	$-0.206999\pi$
$59$	12.2268	1.59180	0.795899	+	0.605430i	$0.206999\pi$
$60$	−3.25373	−0.420054
$61$	6.13863	0.785971	0.392986	−	0.919545i	$-0.371442\pi$
$61$	6.13863	0.785971	0.392986	+	0.919545i	$0.371442\pi$
$62$	8.57067	1.08848
$63$	1.00000	0.125988
$64$	−6.01043	−0.751304
$65$	5.21753	0.647155
$66$	−12.1173	−1.49153
$67$	−15.0576	−1.83958	−0.919790	−	0.392412i	$-0.871641\pi$
$67$	−15.0576	−1.83958	−0.919790	+	0.392412i	$0.871641\pi$
$68$	5.21155	0.631994
$69$	6.86976	0.827022
$70$	1.94420	0.232376
$71$	−7.18924	−0.853206	−0.426603	−	0.904439i	$-0.640290\pi$
$71$	−7.18924	−0.853206	−0.426603	+	0.904439i	$0.640290\pi$
$72$	−5.33307	−0.628509
$73$	2.24951	0.263285	0.131643	−	0.991297i	$-0.457975\pi$
$73$	2.24951	0.263285	0.131643	+	0.991297i	$0.457975\pi$
$74$	6.64118	0.772021
$75$	−4.38542	−0.506385
$76$	−8.62583	−0.989451
$77$	4.88599	0.556810
$78$	16.5055	1.86888
$79$	−7.38716	−0.831120	−0.415560	−	0.909566i	$-0.636414\pi$
$79$	−7.38716	−0.831120	−0.415560	+	0.909566i	$0.636414\pi$
$80$	−3.86111	−0.431685
$81$	1.00000	0.111111
$82$	10.4154	1.15019
$83$	−3.82920	−0.420310	−0.210155	−	0.977668i	$-0.567397\pi$
$83$	−3.82920	−0.420310	−0.210155	+	0.977668i	$0.567397\pi$
$84$	4.15043	0.452849
$85$	−0.984380	−0.106771
$86$	10.2098	1.10095
$87$	−9.79804	−1.05046
$88$	−26.0573	−2.77772
$89$	−16.4372	−1.74234	−0.871171	−	0.490980i	$-0.836639\pi$
$89$	−16.4372	−1.74234	−0.871171	+	0.490980i	$0.836639\pi$
$90$	1.94420	0.204937
$91$	−6.65543	−0.697679
$92$	28.5124	2.97263
$93$	−3.45591	−0.358361
$94$	16.1458	1.66532
$95$	1.62928	0.167161
$96$	−1.54837	−0.158030
$97$	16.8967	1.71560	0.857798	−	0.513987i	$-0.171832\pi$
$97$	16.8967	1.71560	0.857798	+	0.513987i	$0.171832\pi$
$98$	−2.48001	−0.250518
$99$	4.88599	0.491060
$100$	−18.2014	−1.82014
$101$	0.691702	0.0688269	0.0344134	−	0.999408i	$-0.489044\pi$
$101$	0.691702	0.0688269	0.0344134	+	0.999408i	$0.489044\pi$
$102$	−3.11406	−0.308338
$103$	−16.5225	−1.62801	−0.814003	−	0.580861i	$-0.802716\pi$
$103$	−16.5225	−1.62801	−0.814003	+	0.580861i	$0.802716\pi$
$104$	35.4939	3.48047
$105$	−0.783950	−0.0765057
$106$	−8.64855	−0.840022
$107$	−19.1211	−1.84851	−0.924255	−	0.381776i	$-0.875313\pi$
$107$	−19.1211	−1.84851	−0.924255	+	0.381776i	$0.875313\pi$
$108$	4.15043	0.399375
$109$	14.7383	1.41167	0.705837	−	0.708374i	$-0.250571\pi$
$109$	14.7383	1.41167	0.705837	+	0.708374i	$0.250571\pi$
$110$	9.49933	0.905726
$111$	−2.67789	−0.254174
$112$	4.92520	0.465387
$113$	12.5353	1.17922	0.589612	−	0.807686i	$-0.299281\pi$
$113$	12.5353	1.17922	0.589612	+	0.807686i	$0.299281\pi$
$114$	5.15419	0.482735
$115$	−5.38555	−0.502205
$116$	−40.6661	−3.77575
$117$	−6.65543	−0.615295
$118$	−30.3226	−2.79142
$119$	1.25567	0.115107
$120$	4.18086	0.381659
$121$	12.8729	1.17026
$122$	−15.2238	−1.37830
$123$	−4.19977	−0.378680
$124$	−14.3435	−1.28808
$125$	7.35770	0.658093
$126$	−2.48001	−0.220936
$127$	−1.00000	−0.0887357
$127$	−1.00000	−0.0887357
$128$	18.0026	1.59122
$129$	−4.11683	−0.362467
$130$	−12.9395	−1.13487
$131$	−0.687639	−0.0600793	−0.0300397	−	0.999549i	$-0.509563\pi$
$131$	−0.687639	−0.0600793	−0.0300397	+	0.999549i	$0.509563\pi$
$132$	20.2789	1.76505
$133$	−2.07830	−0.180211
$134$	37.3429	3.22594
$135$	−0.783950	−0.0674717
$136$	−6.69656	−0.574225
$137$	−7.96226	−0.680262	−0.340131	−	0.940378i	$-0.610471\pi$
$137$	−7.96226	−0.680262	−0.340131	+	0.940378i	$0.610471\pi$
$138$	−17.0370	−1.45029
$139$	−0.410908	−0.0348528	−0.0174264	−	0.999848i	$-0.505547\pi$
$139$	−0.410908	−0.0348528	−0.0174264	+	0.999848i	$0.505547\pi$
$140$	−3.25373	−0.274990
$141$	−6.51041	−0.548275
$142$	17.8294	1.49621
$143$	−32.5184	−2.71932
$144$	4.92520	0.410433
$145$	7.68118	0.637887
$146$	−5.57880	−0.461705
$147$	1.00000	0.0824786
$148$	−11.1144	−0.913597
$149$	23.6085	1.93408	0.967041	−	0.254620i	$-0.0819502\pi$
$149$	23.6085	1.93408	0.967041	+	0.254620i	$0.0819502\pi$
$150$	10.8759	0.888011
$151$	−6.43593	−0.523748	−0.261874	−	0.965102i	$-0.584341\pi$
$151$	−6.43593	−0.523748	−0.261874	+	0.965102i	$0.584341\pi$
$152$	11.0837	0.899009
$153$	1.25567	0.101515
$154$	−12.1173	−0.976438
$155$	2.70926	0.217613
$156$	−27.6229	−2.21160
$157$	−14.4987	−1.15712	−0.578561	−	0.815639i	$-0.696385\pi$
$157$	−14.4987	−1.15712	−0.578561	+	0.815639i	$0.696385\pi$
$158$	18.3202	1.45748
$159$	3.48731	0.276562
$160$	1.21384	0.0959627
$161$	6.86976	0.541413
$162$	−2.48001	−0.194848
$163$	8.06383	0.631608	0.315804	−	0.948824i	$-0.397726\pi$
$163$	8.06383	0.631608	0.315804	+	0.948824i	$0.397726\pi$
$164$	−17.4308	−1.36112
$165$	−3.83037	−0.298194
$166$	9.49645	0.737067
$167$	4.60533	0.356371	0.178186	−	0.983997i	$-0.442977\pi$
$167$	4.60533	0.356371	0.178186	+	0.983997i	$0.442977\pi$
$168$	−5.33307	−0.411456
$169$	31.2948	2.40729
$170$	2.44127	0.187237
$171$	−2.07830	−0.158932
$172$	−17.0866	−1.30284
$173$	−11.5019	−0.874475	−0.437237	−	0.899346i	$-0.644043\pi$
$173$	−11.5019	−0.874475	−0.437237	+	0.899346i	$0.644043\pi$
$174$	24.2992	1.84212
$175$	−4.38542	−0.331507
$176$	24.0644	1.81393
$177$	12.2268	0.919025
$178$	40.7644	3.05542
$179$	22.8385	1.70703	0.853515	−	0.521068i	$-0.174466\pi$
$179$	22.8385	1.70703	0.853515	+	0.521068i	$0.174466\pi$
$180$	−3.25373	−0.242519
$181$	4.40434	0.327372	0.163686	−	0.986512i	$-0.447662\pi$
$181$	4.40434	0.327372	0.163686	+	0.986512i	$0.447662\pi$
$182$	16.5055	1.22347
$183$	6.13863	0.453781
$184$	−36.6369	−2.70091
$185$	2.09933	0.154346
$186$	8.57067	0.628432
$187$	6.13517	0.448648
$188$	−27.0210	−1.97071
$189$	1.00000	0.0727393
$190$	−4.04063	−0.293138
$191$	20.5561	1.48739	0.743695	−	0.668520i	$-0.233072\pi$
$191$	20.5561	1.48739	0.743695	+	0.668520i	$0.233072\pi$
$192$	−6.01043	−0.433766
$193$	−18.0715	−1.30082	−0.650409	−	0.759584i	$-0.725402\pi$
$193$	−18.0715	−1.30082	−0.650409	+	0.759584i	$0.725402\pi$
$194$	−41.9038	−3.00852
$195$	5.21753	0.373635
$196$	4.15043	0.296459
$197$	−24.7109	−1.76058	−0.880291	−	0.474434i	$-0.842653\pi$
$197$	−24.7109	−1.76058	−0.880291	+	0.474434i	$0.842653\pi$
$198$	−12.1173	−0.861137
$199$	16.6604	1.18102	0.590511	−	0.807030i	$-0.298926\pi$
$199$	16.6604	1.18102	0.590511	+	0.807030i	$0.298926\pi$
$200$	23.3878	1.65377
$201$	−15.0576	−1.06208
$202$	−1.71542	−0.120697
$203$	−9.79804	−0.687688
$204$	5.21155	0.364882
$205$	3.29241	0.229952
$206$	40.9758	2.85492
$207$	6.86976	0.477481
$208$	−32.7793	−2.27284
$209$	−10.1545	−0.702404
$210$	1.94420	0.134163
$211$	14.5672	1.00284	0.501422	−	0.865203i	$-0.332810\pi$
$211$	14.5672	1.00284	0.501422	+	0.865203i	$0.332810\pi$
$212$	14.4738	0.994067
$213$	−7.18924	−0.492599
$214$	47.4205	3.24160
$215$	3.22739	0.220106
$216$	−5.33307	−0.362870
$217$	−3.45591	−0.234602
$218$	−36.5511	−2.47555
$219$	2.24951	0.152008
$220$	−15.8977	−1.07182
$221$	−8.35701	−0.562153
$222$	6.64118	0.445727
$223$	−9.76267	−0.653757	−0.326878	−	0.945066i	$-0.605997\pi$
$223$	−9.76267	−0.653757	−0.326878	+	0.945066i	$0.605997\pi$
$224$	−1.54837	−0.103455
$225$	−4.38542	−0.292361
$226$	−31.0877	−2.06792
$227$	−26.0747	−1.73064	−0.865321	−	0.501219i	$-0.832885\pi$
$227$	−26.0747	−1.73064	−0.865321	+	0.501219i	$0.832885\pi$
$228$	−8.62583	−0.571260
$229$	6.24716	0.412824	0.206412	−	0.978465i	$-0.433821\pi$
$229$	6.24716	0.412824	0.206412	+	0.978465i	$0.433821\pi$
$230$	13.3562	0.880681
$231$	4.88599	0.321474
$232$	52.2537	3.43062
$233$	6.77809	0.444047	0.222024	−	0.975041i	$-0.428734\pi$
$233$	6.77809	0.444047	0.222024	+	0.975041i	$0.428734\pi$
$234$	16.5055	1.07900
$235$	5.10383	0.332937
$236$	50.7466	3.30332
$237$	−7.38716	−0.479847
$238$	−3.11406	−0.201855
$239$	−23.7065	−1.53345	−0.766724	−	0.641977i	$-0.778115\pi$
$239$	−23.7065	−1.53345	−0.766724	+	0.641977i	$0.778115\pi$
$240$	−3.86111	−0.249233
$241$	−9.28434	−0.598057	−0.299028	−	0.954244i	$-0.596663\pi$
$241$	−9.28434	−0.598057	−0.299028	+	0.954244i	$0.596663\pi$
$242$	−31.9247	−2.05220
$243$	1.00000	0.0641500
$244$	25.4779	1.63106
$245$	−0.783950	−0.0500847
$246$	10.4154	0.664064
$247$	13.8320	0.880108
$248$	18.4306	1.17034
$249$	−3.82920	−0.242666
$250$	−18.2471	−1.15405
$251$	0.539366	0.0340445	0.0170222	−	0.999855i	$-0.494581\pi$
$251$	0.539366	0.0340445	0.0170222	+	0.999855i	$0.494581\pi$
$252$	4.15043	0.261452
$253$	33.5656	2.11025
$254$	2.48001	0.155609
$255$	−0.984380	−0.0616442
$256$	−32.6258	−2.03911
$257$	−4.16847	−0.260022	−0.130011	−	0.991513i	$-0.541501\pi$
$257$	−4.16847	−0.260022	−0.130011	+	0.991513i	$0.541501\pi$
$258$	10.2098	0.635633
$259$	−2.67789	−0.166396
$260$	21.6550	1.34298
$261$	−9.79804	−0.606484
$262$	1.70535	0.105357
$263$	−23.9281	−1.47547	−0.737734	−	0.675092i	$-0.764104\pi$
$263$	−23.9281	−1.47547	−0.737734	+	0.675092i	$0.764104\pi$
$264$	−26.0573	−1.60372
$265$	−2.73388	−0.167941
$266$	5.15419	0.316024
$267$	−16.4372	−1.00594
$268$	−62.4955	−3.81752
$269$	−30.9708	−1.88832	−0.944160	−	0.329487i	$-0.893124\pi$
$269$	−30.9708	−1.88832	−0.944160	+	0.329487i	$0.893124\pi$
$270$	1.94420	0.118320
$271$	−23.8214	−1.44705	−0.723523	−	0.690300i	$-0.757478\pi$
$271$	−23.8214	−1.44705	−0.723523	+	0.690300i	$0.757478\pi$
$272$	6.18440	0.374985
$273$	−6.65543	−0.402805
$274$	19.7465	1.19293
$275$	−21.4271	−1.29210
$276$	28.5124	1.71625
$277$	−14.3357	−0.861351	−0.430675	−	0.902507i	$-0.641725\pi$
$277$	−14.3357	−0.861351	−0.430675	+	0.902507i	$0.641725\pi$
$278$	1.01905	0.0611188
$279$	−3.45591	−0.206900
$280$	4.18086	0.249854
$281$	20.6212	1.23016	0.615079	−	0.788466i	$-0.289124\pi$
$281$	20.6212	1.23016	0.615079	+	0.788466i	$0.289124\pi$
$282$	16.1458	0.961471
$283$	3.77609	0.224465	0.112233	−	0.993682i	$-0.464200\pi$
$283$	3.77609	0.224465	0.112233	+	0.993682i	$0.464200\pi$
$284$	−29.8384	−1.77058
$285$	1.62928	0.0965104
$286$	80.6457	4.76868
$287$	−4.19977	−0.247904
$288$	−1.54837	−0.0912384
$289$	−15.4233	−0.907253
$290$	−19.0494	−1.11862
$291$	16.8967	0.990499
$292$	9.33644	0.546374
$293$	−24.2919	−1.41915	−0.709573	−	0.704632i	$-0.751112\pi$
$293$	−24.2919	−1.41915	−0.709573	+	0.704632i	$0.751112\pi$
$294$	−2.48001	−0.144637
$295$	−9.58522	−0.558073
$296$	14.2814	0.830088
$297$	4.88599	0.283514
$298$	−58.5492	−3.39166
$299$	−45.7212	−2.64413
$300$	−18.2014	−1.05086
$301$	−4.11683	−0.237290
$302$	15.9611	0.918460
$303$	0.691702	0.0397372
$304$	−10.2360	−0.587077
$305$	−4.81238	−0.275556
$306$	−3.11406	−0.178019
$307$	−18.6482	−1.06431	−0.532153	−	0.846648i	$-0.678617\pi$
$307$	−18.6482	−1.06431	−0.532153	+	0.846648i	$0.678617\pi$
$308$	20.2789	1.15550
$309$	−16.5225	−0.939929
$310$	−6.71897	−0.381612
$311$	20.8747	1.18370	0.591848	−	0.806050i	$-0.298399\pi$
$311$	20.8747	1.18370	0.591848	+	0.806050i	$0.298399\pi$
$312$	35.4939	2.00945
$313$	−7.93347	−0.448426	−0.224213	−	0.974540i	$-0.571981\pi$
$313$	−7.93347	−0.448426	−0.224213	+	0.974540i	$0.571981\pi$
$314$	35.9568	2.02916
$315$	−0.783950	−0.0441706
$316$	−30.6599	−1.72475
$317$	11.3644	0.638290	0.319145	−	0.947706i	$-0.396604\pi$
$317$	11.3644	0.638290	0.319145	+	0.947706i	$0.396604\pi$
$318$	−8.64855	−0.484987
$319$	−47.8731	−2.68038
$320$	4.71188	0.263402
$321$	−19.1211	−1.06724
$322$	−17.0370	−0.949437
$323$	−2.60965	−0.145205
$324$	4.15043	0.230579
$325$	29.1869	1.61900
$326$	−19.9983	−1.10761
$327$	14.7383	0.815031
$328$	22.3977	1.23670
$329$	−6.51041	−0.358930
$330$	9.49933	0.522921
$331$	−19.1983	−1.05523	−0.527616	−	0.849483i	$-0.676914\pi$
$331$	−19.1983	−1.05523	−0.527616	+	0.849483i	$0.676914\pi$
$332$	−15.8928	−0.872233
$333$	−2.67789	−0.146747
$334$	−11.4213	−0.624943
$335$	11.8044	0.644944
$336$	4.92520	0.268691
$337$	8.90770	0.485234	0.242617	−	0.970122i	$-0.421994\pi$
$337$	8.90770	0.485234	0.242617	+	0.970122i	$0.421994\pi$
$338$	−77.6113	−4.22150
$339$	12.5353	0.680826
$340$	−4.08560	−0.221573
$341$	−16.8855	−0.914401
$342$	5.15419	0.278707
$343$	1.00000	0.0539949
$344$	21.9554	1.18375
$345$	−5.38555	−0.289948
$346$	28.5248	1.53350
$347$	−1.17952	−0.0633201	−0.0316601	−	0.999499i	$-0.510079\pi$
$347$	−1.17952	−0.0633201	−0.0316601	+	0.999499i	$0.510079\pi$
$348$	−40.6661	−2.17993
$349$	−29.5422	−1.58136	−0.790679	−	0.612231i	$-0.790272\pi$
$349$	−29.5422	−1.58136	−0.790679	+	0.612231i	$0.790272\pi$
$350$	10.8759	0.581340
$351$	−6.65543	−0.355241
$352$	−7.56530	−0.403232
$353$	10.1955	0.542653	0.271327	−	0.962487i	$-0.412538\pi$
$353$	10.1955	0.542653	0.271327	+	0.962487i	$0.412538\pi$
$354$	−30.3226	−1.61163
$355$	5.63601	0.299128
$356$	−68.2215	−3.61573
$357$	1.25567	0.0664569
$358$	−56.6396	−2.99350
$359$	30.6151	1.61580	0.807900	−	0.589319i	$-0.200604\pi$
$359$	30.6151	1.61580	0.807900	+	0.589319i	$0.200604\pi$
$360$	4.18086	0.220351
$361$	−14.6807	−0.772667
$362$	−10.9228	−0.574089
$363$	12.8729	0.675649
$364$	−27.6229	−1.44783
$365$	−1.76350	−0.0923061
$366$	−15.2238	−0.795763
$367$	−10.8181	−0.564702	−0.282351	−	0.959311i	$-0.591114\pi$
$367$	−10.8181	−0.564702	−0.282351	+	0.959311i	$0.591114\pi$
$368$	33.8349	1.76377
$369$	−4.19977	−0.218631
$370$	−5.20635	−0.270665
$371$	3.48731	0.181052
$372$	−14.3435	−0.743675
$373$	10.2006	0.528169	0.264085	−	0.964499i	$-0.414930\pi$
$373$	10.2006	0.528169	0.264085	+	0.964499i	$0.414930\pi$
$374$	−15.2153	−0.786762
$375$	7.35770	0.379950
$376$	34.7205	1.79057
$377$	65.2102	3.35850
$378$	−2.48001	−0.127558
$379$	6.58231	0.338110	0.169055	−	0.985607i	$-0.445928\pi$
$379$	6.58231	0.338110	0.169055	+	0.985607i	$0.445928\pi$
$380$	6.76222	0.346895
$381$	−1.00000	−0.0512316
$382$	−50.9793	−2.60833
$383$	−20.2431	−1.03438	−0.517188	−	0.855872i	$-0.673021\pi$
$383$	−20.2431	−1.03438	−0.517188	+	0.855872i	$0.673021\pi$
$384$	18.0026	0.918693
$385$	−3.83037	−0.195214
$386$	44.8175	2.28115
$387$	−4.11683	−0.209270
$388$	70.1283	3.56023
$389$	8.10612	0.410997	0.205498	−	0.978657i	$-0.434118\pi$
$389$	8.10612	0.410997	0.205498	+	0.978657i	$0.434118\pi$
$390$	−12.9395	−0.655217
$391$	8.62613	0.436242
$392$	−5.33307	−0.269361
$393$	−0.687639	−0.0346868
$394$	61.2833	3.08741
$395$	5.79116	0.291385
$396$	20.2789	1.01905
$397$	−15.9348	−0.799745	−0.399872	−	0.916571i	$-0.630946\pi$
$397$	−15.9348	−0.799745	−0.399872	+	0.916571i	$0.630946\pi$
$398$	−41.3178	−2.07107
$399$	−2.07830	−0.104045
$400$	−21.5991	−1.07995
$401$	35.9972	1.79761	0.898807	−	0.438344i	$-0.144435\pi$
$401$	35.9972	1.79761	0.898807	+	0.438344i	$0.144435\pi$
$402$	37.3429	1.86250
$403$	23.0006	1.14574
$404$	2.87086	0.142831
$405$	−0.783950	−0.0389548
$406$	24.2992	1.20595
$407$	−13.0841	−0.648556
$408$	−6.69656	−0.331529
$409$	−21.3091	−1.05367	−0.526833	−	0.849969i	$-0.676621\pi$
$409$	−21.3091	−1.05367	−0.526833	+	0.849969i	$0.676621\pi$
$410$	−8.16519	−0.403250
$411$	−7.96226	−0.392749
$412$	−68.5752	−3.37846
$413$	12.2268	0.601643
$414$	−17.0370	−0.837325
$415$	3.00190	0.147358
$416$	10.3051	0.505247
$417$	−0.410908	−0.0201223
$418$	25.1833	1.23176
$419$	−26.8399	−1.31122	−0.655608	−	0.755101i	$-0.727588\pi$
$419$	−26.8399	−1.31122	−0.655608	+	0.755101i	$0.727588\pi$
$420$	−3.25373	−0.158766
$421$	1.71312	0.0834923	0.0417462	−	0.999128i	$-0.486708\pi$
$421$	1.71312	0.0834923	0.0417462	+	0.999128i	$0.486708\pi$
$422$	−36.1266	−1.75862
$423$	−6.51041	−0.316547
$424$	−18.5981	−0.903203
$425$	−5.50663	−0.267111
$426$	17.8294	0.863835
$427$	6.13863	0.297069
$428$	−79.3609	−3.83605
$429$	−32.5184	−1.57000
$430$	−8.00395	−0.385985
$431$	29.8518	1.43791	0.718954	−	0.695057i	$-0.244621\pi$
$431$	29.8518	1.43791	0.718954	+	0.695057i	$0.244621\pi$
$432$	4.92520	0.236964
$433$	−6.53077	−0.313849	−0.156924	−	0.987611i	$-0.550158\pi$
$433$	−6.53077	−0.313849	−0.156924	+	0.987611i	$0.550158\pi$
$434$	8.57067	0.411405
$435$	7.68118	0.368284
$436$	61.1703	2.92953
$437$	−14.2774	−0.682982
$438$	−5.57880	−0.266566
$439$	−14.9276	−0.712457	−0.356228	−	0.934399i	$-0.615938\pi$
$439$	−14.9276	−0.712457	−0.356228	+	0.934399i	$0.615938\pi$
$440$	20.4276	0.973849
$441$	1.00000	0.0476190
$442$	20.7254	0.985808
$443$	−4.63421	−0.220178	−0.110089	−	0.993922i	$-0.535114\pi$
$443$	−4.63421	−0.220178	−0.110089	+	0.993922i	$0.535114\pi$
$444$	−11.1144	−0.527465
$445$	12.8860	0.610853
$446$	24.2115	1.14645
$447$	23.6085	1.11664
$448$	−6.01043	−0.283966
$449$	−6.63579	−0.313162	−0.156581	−	0.987665i	$-0.550047\pi$
$449$	−6.63579	−0.313162	−0.156581	+	0.987665i	$0.550047\pi$
$450$	10.8759	0.512694
$451$	−20.5200	−0.966249
$452$	52.0270	2.44714
$453$	−6.43593	−0.302386
$454$	64.6655	3.03490
$455$	5.21753	0.244601
$456$	11.0837	0.519043
$457$	−17.6826	−0.827157	−0.413578	−	0.910468i	$-0.635721\pi$
$457$	−17.6826	−0.827157	−0.413578	+	0.910468i	$0.635721\pi$
$458$	−15.4930	−0.723940
$459$	1.25567	0.0586095
$460$	−22.3523	−1.04218
$461$	−40.2668	−1.87541	−0.937706	−	0.347431i	$-0.887054\pi$
$461$	−40.2668	−1.87541	−0.937706	+	0.347431i	$0.887054\pi$
$462$	−12.1173	−0.563746
$463$	−3.88536	−0.180568	−0.0902841	−	0.995916i	$-0.528777\pi$
$463$	−3.88536	−0.180568	−0.0902841	+	0.995916i	$0.528777\pi$
$464$	−48.2573	−2.24029
$465$	2.70926	0.125639
$466$	−16.8097	−0.778694
$467$	−1.32929	−0.0615123	−0.0307561	−	0.999527i	$-0.509792\pi$
$467$	−1.32929	−0.0615123	−0.0307561	+	0.999527i	$0.509792\pi$
$468$	−27.6229	−1.27687
$469$	−15.0576	−0.695296
$470$	−12.6575	−0.583849
$471$	−14.4987	−0.668064
$472$	−65.2066	−3.00138
$473$	−20.1148	−0.924879
$474$	18.3202	0.841474
$475$	9.11422	0.418189
$476$	5.21155	0.238871
$477$	3.48731	0.159673
$478$	58.7923	2.68910
$479$	−10.9654	−0.501022	−0.250511	−	0.968114i	$-0.580599\pi$
$479$	−10.9654	−0.501022	−0.250511	+	0.968114i	$0.580599\pi$
$480$	1.21384	0.0554041
$481$	17.8225	0.812637
$482$	23.0252	1.04877
$483$	6.86976	0.312585
$484$	53.4278	2.42854
$485$	−13.2461	−0.601476
$486$	−2.48001	−0.112495
$487$	7.42363	0.336397	0.168198	−	0.985753i	$-0.446205\pi$
$487$	7.42363	0.336397	0.168198	+	0.985753i	$0.446205\pi$
$488$	−32.7378	−1.48197
$489$	8.06383	0.364659
$490$	1.94420	0.0878300
$491$	10.4742	0.472694	0.236347	−	0.971669i	$-0.424050\pi$
$491$	10.4742	0.472694	0.236347	+	0.971669i	$0.424050\pi$
$492$	−17.4308	−0.785842
$493$	−12.3031	−0.554103
$494$	−34.3034	−1.54338
$495$	−3.83037	−0.172162
$496$	−17.0210	−0.764266
$497$	−7.18924	−0.322482
$498$	9.49645	0.425546
$499$	26.6794	1.19433	0.597167	−	0.802117i	$-0.296293\pi$
$499$	26.6794	1.19433	0.597167	+	0.802117i	$0.296293\pi$
$500$	30.5376	1.36568
$501$	4.60533	0.205751
$502$	−1.33763	−0.0597013
$503$	27.1665	1.21129	0.605646	−	0.795734i	$-0.292915\pi$
$503$	27.1665	1.21129	0.605646	+	0.795734i	$0.292915\pi$
$504$	−5.33307	−0.237554
$505$	−0.542259	−0.0241302
$506$	−83.2428	−3.70059
$507$	31.2948	1.38985
$508$	−4.15043	−0.184145
$509$	−5.67100	−0.251363	−0.125681	−	0.992071i	$-0.540112\pi$
$509$	−5.67100	−0.251363	−0.125681	+	0.992071i	$0.540112\pi$
$510$	2.44127	0.108101
$511$	2.24951	0.0995126
$512$	44.9069	1.98462
$513$	−2.07830	−0.0917592
$514$	10.3378	0.455982
$515$	12.9528	0.570767
$516$	−17.0866	−0.752197
$517$	−31.8098	−1.39899
$518$	6.64118	0.291797
$519$	−11.5019	−0.504878
$520$	−27.8255	−1.22023
$521$	32.7163	1.43333	0.716664	−	0.697419i	$-0.245668\pi$
$521$	32.7163	1.43333	0.716664	+	0.697419i	$0.245668\pi$
$522$	24.2992	1.06355
$523$	20.8450	0.911486	0.455743	−	0.890111i	$-0.349374\pi$
$523$	20.8450	0.911486	0.455743	+	0.890111i	$0.349374\pi$
$524$	−2.85400	−0.124677
$525$	−4.38542	−0.191396
$526$	59.3417	2.58742
$527$	−4.33946	−0.189030
$528$	24.0644	1.04727
$529$	24.1936	1.05190
$530$	6.78003	0.294506
$531$	12.2268	0.530599
$532$	−8.62583	−0.373977
$533$	27.9513	1.21070
$534$	40.7644	1.76405
$535$	14.9900	0.648075
$536$	80.3033	3.46857
$537$	22.8385	0.985554
$538$	76.8077	3.31141
$539$	4.88599	0.210454
$540$	−3.25373	−0.140018
$541$	−21.1270	−0.908319	−0.454159	−	0.890920i	$-0.650060\pi$
$541$	−21.1270	−0.908319	−0.454159	+	0.890920i	$0.650060\pi$
$542$	59.0772	2.53758
$543$	4.40434	0.189008
$544$	−1.94423	−0.0833583
$545$	−11.5541	−0.494923
$546$	16.5055	0.706371
$547$	10.1713	0.434895	0.217448	−	0.976072i	$-0.430227\pi$
$547$	10.1713	0.434895	0.217448	+	0.976072i	$0.430227\pi$
$548$	−33.0468	−1.41169
$549$	6.13863	0.261990
$550$	53.1394	2.26587
$551$	20.3633	0.867504
$552$	−36.6369	−1.55937
$553$	−7.38716	−0.314134
$554$	35.5527	1.51049
$555$	2.09933	0.0891116
$556$	−1.70544	−0.0723270
$557$	−29.5187	−1.25075	−0.625373	−	0.780326i	$-0.715053\pi$
$557$	−29.5187	−1.25075	−0.625373	+	0.780326i	$0.715053\pi$
$558$	8.57067	0.362825
$559$	27.3993	1.15887
$560$	−3.86111	−0.163162
$561$	6.13517	0.259027
$562$	−51.1407	−2.15724
$563$	29.4720	1.24210	0.621049	−	0.783772i	$-0.286707\pi$
$563$	29.4720	1.24210	0.621049	+	0.783772i	$0.286707\pi$
$564$	−27.0210	−1.13779
$565$	−9.82707	−0.413428
$566$	−9.36473	−0.393629
$567$	1.00000	0.0419961
$568$	38.3408	1.60874
$569$	18.1639	0.761471	0.380735	−	0.924684i	$-0.375671\pi$
$569$	18.1639	0.761471	0.380735	+	0.924684i	$0.375671\pi$
$570$	−4.04063	−0.169243
$571$	−5.20524	−0.217832	−0.108916	−	0.994051i	$-0.534738\pi$
$571$	−5.20524	−0.217832	−0.108916	+	0.994051i	$0.534738\pi$
$572$	−134.965	−5.64317
$573$	20.5561	0.858744
$574$	10.4154	0.434732
$575$	−30.1268	−1.25637
$576$	−6.01043	−0.250435
$577$	22.5036	0.936835	0.468418	−	0.883507i	$-0.344824\pi$
$577$	22.5036	0.936835	0.468418	+	0.883507i	$0.344824\pi$
$578$	38.2499	1.59099
$579$	−18.0715	−0.751028
$580$	31.8802	1.32375
$581$	−3.82920	−0.158862
$582$	−41.9038	−1.73697
$583$	17.0390	0.705681
$584$	−11.9968	−0.496432
$585$	5.21753	0.215718
$586$	60.2440	2.48866
$587$	−11.1742	−0.461208	−0.230604	−	0.973048i	$-0.574070\pi$
$587$	−11.1742	−0.461208	−0.230604	+	0.973048i	$0.574070\pi$
$588$	4.15043	0.171161
$589$	7.18241	0.295946
$590$	23.7714	0.978653
$591$	−24.7109	−1.01647
$592$	−13.1891	−0.542070
$593$	10.7553	0.441669	0.220835	−	0.975311i	$-0.429122\pi$
$593$	10.7553	0.441669	0.220835	+	0.975311i	$0.429122\pi$
$594$	−12.1173	−0.497178
$595$	−0.984380	−0.0403556
$596$	97.9853	4.01364
$597$	16.6604	0.681863
$598$	113.389	4.63682
$599$	16.4493	0.672099	0.336049	−	0.941844i	$-0.390909\pi$
$599$	16.4493	0.672099	0.336049	+	0.941844i	$0.390909\pi$
$600$	23.3878	0.954802
$601$	24.6614	1.00596	0.502979	−	0.864298i	$-0.332237\pi$
$601$	24.6614	1.00596	0.502979	+	0.864298i	$0.332237\pi$
$602$	10.2098	0.416119
$603$	−15.0576	−0.613193
$604$	−26.7118	−1.08689
$605$	−10.0917	−0.410285
$606$	−1.71542	−0.0696843
$607$	−6.40510	−0.259975	−0.129988	−	0.991516i	$-0.541494\pi$
$607$	−6.40510	−0.259975	−0.129988	+	0.991516i	$0.541494\pi$
$608$	3.21797	0.130506
$609$	−9.79804	−0.397037
$610$	11.9347	0.483223
$611$	43.3296	1.75293
$612$	5.21155	0.210665
$613$	9.77647	0.394868	0.197434	−	0.980316i	$-0.436739\pi$
$613$	9.77647	0.394868	0.197434	+	0.980316i	$0.436739\pi$
$614$	46.2475	1.86640
$615$	3.29241	0.132763
$616$	−26.0573	−1.04988
$617$	36.0074	1.44960	0.724802	−	0.688958i	$-0.241931\pi$
$617$	36.0074	1.44960	0.724802	+	0.688958i	$0.241931\pi$
$618$	40.9758	1.64829
$619$	−18.4220	−0.740441	−0.370220	−	0.928944i	$-0.620718\pi$
$619$	−18.4220	−0.740441	−0.370220	+	0.928944i	$0.620718\pi$
$620$	11.2446	0.451593
$621$	6.86976	0.275674
$622$	−51.7694	−2.07576
$623$	−16.4372	−0.658543
$624$	−32.7793	−1.31222
$625$	16.1590	0.646362
$626$	19.6750	0.786373
$627$	−10.1545	−0.405533
$628$	−60.1758	−2.40127
$629$	−3.36254	−0.134073
$630$	1.94420	0.0774588
$631$	−21.8713	−0.870682	−0.435341	−	0.900266i	$-0.643372\pi$
$631$	−21.8713	−0.870682	−0.435341	+	0.900266i	$0.643372\pi$
$632$	39.3962	1.56710
$633$	14.5672	0.578992
$634$	−28.1838	−1.11932
$635$	0.783950	0.0311101
$636$	14.4738	0.573925
$637$	−6.65543	−0.263698
$638$	118.726	4.70039
$639$	−7.18924	−0.284402
$640$	−14.1132	−0.557872
$641$	−5.35545	−0.211527	−0.105764	−	0.994391i	$-0.533729\pi$
$641$	−5.35545	−0.211527	−0.105764	+	0.994391i	$0.533729\pi$
$642$	47.4205	1.87154
$643$	12.1586	0.479488	0.239744	−	0.970836i	$-0.422936\pi$
$643$	12.1586	0.479488	0.239744	+	0.970836i	$0.422936\pi$
$644$	28.5124	1.12355
$645$	3.22739	0.127078
$646$	6.47195	0.254635
$647$	−3.92615	−0.154353	−0.0771764	−	0.997017i	$-0.524590\pi$
$647$	−3.92615	−0.154353	−0.0771764	+	0.997017i	$0.524590\pi$
$648$	−5.33307	−0.209503
$649$	59.7401	2.34500
$650$	−72.3837	−2.83912
$651$	−3.45591	−0.135448
$652$	33.4683	1.31072
$653$	3.49414	0.136736	0.0683681	−	0.997660i	$-0.478221\pi$
$653$	3.49414	0.136736	0.0683681	+	0.997660i	$0.478221\pi$
$654$	−36.5511	−1.42926
$655$	0.539075	0.0210634
$656$	−20.6847	−0.807601
$657$	2.24951	0.0877618
$658$	16.1458	0.629431
$659$	26.1167	1.01736	0.508682	−	0.860955i	$-0.330133\pi$
$659$	26.1167	1.01736	0.508682	+	0.860955i	$0.330133\pi$
$660$	−15.8977	−0.618816
$661$	−34.1023	−1.32643	−0.663213	−	0.748431i	$-0.730808\pi$
$661$	−34.1023	−1.32643	−0.663213	+	0.748431i	$0.730808\pi$
$662$	47.6118	1.85049
$663$	−8.35701	−0.324559
$664$	20.4214	0.792505
$665$	1.62928	0.0631809
$666$	6.64118	0.257340
$667$	−67.3102	−2.60626
$668$	19.1141	0.739547
$669$	−9.76267	−0.377447
$670$	−29.2750	−1.13099
$671$	29.9933	1.15788
$672$	−1.54837	−0.0597296
$673$	−11.3642	−0.438058	−0.219029	−	0.975718i	$-0.570289\pi$
$673$	−11.3642	−0.438058	−0.219029	+	0.975718i	$0.570289\pi$
$674$	−22.0912	−0.850920
$675$	−4.38542	−0.168795
$676$	129.887	4.99565
$677$	−8.47890	−0.325870	−0.162935	−	0.986637i	$-0.552096\pi$
$677$	−8.47890	−0.325870	−0.162935	+	0.986637i	$0.552096\pi$
$678$	−31.0877	−1.19392
$679$	16.8967	0.648434
$680$	5.24977	0.201319
$681$	−26.0747	−0.999186
$682$	41.8761	1.60352
$683$	13.5516	0.518537	0.259269	−	0.965805i	$-0.416518\pi$
$683$	13.5516	0.518537	0.259269	+	0.965805i	$0.416518\pi$
$684$	−8.62583	−0.329817
$685$	6.24201	0.238495
$686$	−2.48001	−0.0946871
$687$	6.24716	0.238344
$688$	−20.2762	−0.773023
$689$	−23.2096	−0.884214
$690$	13.3562	0.508462
$691$	−43.4677	−1.65359	−0.826794	−	0.562505i	$-0.809838\pi$
$691$	−43.4677	−1.65359	−0.826794	+	0.562505i	$0.809838\pi$
$692$	−47.7379	−1.81472
$693$	4.88599	0.185603
$694$	2.92522	0.111040
$695$	0.322131	0.0122191
$696$	52.2537	1.98067
$697$	−5.27351	−0.199748
$698$	73.2649	2.77312
$699$	6.77809	0.256371
$700$	−18.2014	−0.687947
$701$	28.8144	1.08831	0.544153	−	0.838986i	$-0.316851\pi$
$701$	28.8144	1.08831	0.544153	+	0.838986i	$0.316851\pi$
$702$	16.5055	0.622960
$703$	5.56545	0.209905
$704$	−29.3669	−1.10681
$705$	5.10383	0.192221
$706$	−25.2850	−0.951612
$707$	0.691702	0.0260141
$708$	50.7466	1.90717
$709$	−20.9862	−0.788154	−0.394077	−	0.919077i	$-0.628936\pi$
$709$	−20.9862	−0.788154	−0.394077	+	0.919077i	$0.628936\pi$
$710$	−13.9773	−0.524560
$711$	−7.38716	−0.277040
$712$	87.6609	3.28523
$713$	−23.7412	−0.889117
$714$	−3.11406	−0.116541
$715$	25.4928	0.953375
$716$	94.7896	3.54245
$717$	−23.7065	−0.885337
$718$	−75.9255	−2.83351
$719$	−4.40085	−0.164124	−0.0820620	−	0.996627i	$-0.526151\pi$
$719$	−4.40085	−0.164124	−0.0820620	+	0.996627i	$0.526151\pi$
$720$	−3.86111	−0.143895
$721$	−16.5225	−0.615328
$722$	36.4081	1.35497
$723$	−9.28434	−0.345288
$724$	18.2799	0.679368
$725$	42.9686	1.59581
$726$	−31.9247	−1.18484
$727$	21.6396	0.802568	0.401284	−	0.915954i	$-0.368564\pi$
$727$	21.6396	0.802568	0.401284	+	0.915954i	$0.368564\pi$
$728$	35.4939	1.31549
$729$	1.00000	0.0370370
$730$	4.37350	0.161871
$731$	−5.16937	−0.191196
$732$	25.4779	0.941692
$733$	30.9010	1.14136	0.570678	−	0.821174i	$-0.306680\pi$
$733$	30.9010	1.14136	0.570678	+	0.821174i	$0.306680\pi$
$734$	26.8291	0.990279
$735$	−0.783950	−0.0289164
$736$	−10.6369	−0.392082
$737$	−73.5712	−2.71003
$738$	10.4154	0.383398
$739$	−32.2746	−1.18724	−0.593620	−	0.804745i	$-0.702302\pi$
$739$	−32.2746	−1.18724	−0.593620	+	0.804745i	$0.702302\pi$
$740$	8.71312	0.320301
$741$	13.8320	0.508131
$742$	−8.64855	−0.317498
$743$	28.5122	1.04601	0.523006	−	0.852329i	$-0.324810\pi$
$743$	28.5122	1.04601	0.523006	+	0.852329i	$0.324810\pi$
$744$	18.4306	0.675699
$745$	−18.5079	−0.678076
$746$	−25.2977	−0.926213
$747$	−3.82920	−0.140103
$748$	25.4636	0.931040
$749$	−19.1211	−0.698671
$750$	−18.2471	−0.666291
$751$	−24.0517	−0.877659	−0.438829	−	0.898570i	$-0.644607\pi$
$751$	−24.0517	−0.877659	−0.438829	+	0.898570i	$0.644607\pi$
$752$	−32.0650	−1.16929
$753$	0.539366	0.0196556
$754$	−161.722	−5.88956
$755$	5.04544	0.183623
$756$	4.15043	0.150950
$757$	−33.1952	−1.20650	−0.603249	−	0.797553i	$-0.706128\pi$
$757$	−33.1952	−1.20650	−0.603249	+	0.797553i	$0.706128\pi$
$758$	−16.3242	−0.592920
$759$	33.5656	1.21835
$760$	−8.68908	−0.315186
$761$	27.5176	0.997511	0.498755	−	0.866743i	$-0.333791\pi$
$761$	27.5176	0.997511	0.498755	+	0.866743i	$0.333791\pi$
$762$	2.48001	0.0898411
$763$	14.7383	0.533563
$764$	85.3167	3.08665
$765$	−0.984380	−0.0355903
$766$	50.2031	1.81391
$767$	−81.3748	−2.93828
$768$	−32.6258	−1.17728
$769$	−14.6074	−0.526757	−0.263378	−	0.964693i	$-0.584837\pi$
$769$	−14.6074	−0.526757	−0.263378	+	0.964693i	$0.584837\pi$
$770$	9.49933	0.342332
$771$	−4.16847	−0.150124
$772$	−75.0046	−2.69948
$773$	4.97622	0.178982	0.0894912	−	0.995988i	$-0.471476\pi$
$773$	4.97622	0.178982	0.0894912	+	0.995988i	$0.471476\pi$
$774$	10.2098	0.366983
$775$	15.1556	0.544405
$776$	−90.1111	−3.23480
$777$	−2.67789	−0.0960687
$778$	−20.1032	−0.720736
$779$	8.72837	0.312726
$780$	21.6550	0.775372
$781$	−35.1265	−1.25693
$782$	−21.3928	−0.765007
$783$	−9.79804	−0.350154
$784$	4.92520	0.175900
$785$	11.3662	0.405679
$786$	1.70535	0.0608278
$787$	20.1321	0.717633	0.358816	−	0.933408i	$-0.383180\pi$
$787$	20.1321	0.717633	0.358816	+	0.933408i	$0.383180\pi$
$788$	−102.561	−3.65358
$789$	−23.9281	−0.851862
$790$	−14.3621	−0.510981
$791$	12.5353	0.445705
$792$	−26.0573	−0.925906
$793$	−40.8553	−1.45081
$794$	39.5184	1.40246
$795$	−2.73388	−0.0969607
$796$	69.1476	2.45087
$797$	−35.3654	−1.25271	−0.626354	−	0.779539i	$-0.715454\pi$
$797$	−35.3654	−1.25271	−0.626354	+	0.779539i	$0.715454\pi$
$798$	5.15419	0.182457
$799$	−8.17490	−0.289207
$800$	6.79025	0.240071
$801$	−16.4372	−0.580781
$802$	−89.2733	−3.15235
$803$	10.9911	0.387867
$804$	−62.4955	−2.20405
$805$	−5.38555	−0.189816
$806$	−57.0415	−2.00920
$807$	−30.9708	−1.09022
$808$	−3.68890	−0.129775
$809$	9.88279	0.347460	0.173730	−	0.984793i	$-0.444418\pi$
$809$	9.88279	0.347460	0.173730	+	0.984793i	$0.444418\pi$
$810$	1.94420	0.0683122
$811$	29.3646	1.03113	0.515566	−	0.856850i	$-0.327582\pi$
$811$	29.3646	1.03113	0.515566	+	0.856850i	$0.327582\pi$
$812$	−40.6661	−1.42710
$813$	−23.8214	−0.835452
$814$	32.4487	1.13733
$815$	−6.32164	−0.221437
$816$	6.18440	0.216497
$817$	8.55601	0.299337
$818$	52.8466	1.84774
$819$	−6.65543	−0.232560
$820$	13.6649	0.477199
$821$	−11.5855	−0.404338	−0.202169	−	0.979351i	$-0.564799\pi$
$821$	−11.5855	−0.404338	−0.202169	+	0.979351i	$0.564799\pi$
$822$	19.7465	0.688737
$823$	32.4979	1.13281	0.566404	−	0.824128i	$-0.308334\pi$
$823$	32.4979	1.13281	0.566404	+	0.824128i	$0.308334\pi$
$824$	88.1154	3.06965
$825$	−21.4271	−0.745996
$826$	−30.3226	−1.05506
$827$	−34.8327	−1.21125	−0.605626	−	0.795749i	$-0.707077\pi$
$827$	−34.8327	−1.21125	−0.605626	+	0.795749i	$0.707077\pi$
$828$	28.5124	0.990876
$829$	25.0563	0.870241	0.435120	−	0.900372i	$-0.356706\pi$
$829$	25.0563	0.870241	0.435120	+	0.900372i	$0.356706\pi$
$830$	−7.44474	−0.258411
$831$	−14.3357	−0.497301
$832$	40.0020	1.38682
$833$	1.25567	0.0435063
$834$	1.01905	0.0352870
$835$	−3.61035	−0.124941
$836$	−42.1457	−1.45764
$837$	−3.45591	−0.119454
$838$	66.5632	2.29939
$839$	−16.0782	−0.555082	−0.277541	−	0.960714i	$-0.589519\pi$
$839$	−16.0782	−0.555082	−0.277541	+	0.960714i	$0.589519\pi$
$840$	4.18086	0.144253
$841$	67.0017	2.31040
$842$	−4.24855	−0.146415
$843$	20.6212	0.710232
$844$	60.4599	2.08112
$845$	−24.5336	−0.843980
$846$	16.1458	0.555106
$847$	12.8729	0.442316
$848$	17.1757	0.589816
$849$	3.77609	0.129595
$850$	13.6565	0.468413
$851$	−18.3965	−0.630622
$852$	−29.8384	−1.02225
$853$	9.71995	0.332805	0.166402	−	0.986058i	$-0.446785\pi$
$853$	9.71995	0.332805	0.166402	+	0.986058i	$0.446785\pi$
$854$	−15.2238	−0.520949
$855$	1.62928	0.0557203
$856$	101.974	3.48541
$857$	41.2846	1.41025	0.705127	−	0.709081i	$-0.250890\pi$
$857$	41.2846	1.41025	0.705127	+	0.709081i	$0.250890\pi$
$858$	80.6457	2.75320
$859$	−1.05236	−0.0359061	−0.0179531	−	0.999839i	$-0.505715\pi$
$859$	−1.05236	−0.0359061	−0.0179531	+	0.999839i	$0.505715\pi$
$860$	13.3951	0.456768
$861$	−4.19977	−0.143128
$862$	−74.0325	−2.52156
$863$	34.4783	1.17365	0.586827	−	0.809712i	$-0.300377\pi$
$863$	34.4783	1.17365	0.586827	+	0.809712i	$0.300377\pi$
$864$	−1.54837	−0.0526765
$865$	9.01693	0.306585
$866$	16.1963	0.550374
$867$	−15.4233	−0.523803
$868$	−14.3435	−0.486850
$869$	−36.0935	−1.22439
$870$	−19.0494	−0.645834
$871$	100.215	3.39565
$872$	−78.6005	−2.66175
$873$	16.8967	0.571865
$874$	35.4081	1.19770
$875$	7.35770	0.248736
$876$	9.33644	0.315449
$877$	41.2483	1.39285	0.696427	−	0.717627i	$-0.254772\pi$
$877$	41.2483	1.39285	0.696427	+	0.717627i	$0.254772\pi$
$878$	37.0206	1.24939
$879$	−24.2919	−0.819345
$880$	−18.8653	−0.635950
$881$	16.3701	0.551523	0.275761	−	0.961226i	$-0.411070\pi$
$881$	16.3701	0.551523	0.275761	+	0.961226i	$0.411070\pi$
$882$	−2.48001	−0.0835061
$883$	39.4843	1.32875	0.664376	−	0.747398i	$-0.268697\pi$
$883$	39.4843	1.32875	0.664376	+	0.747398i	$0.268697\pi$
$884$	−34.6851	−1.16659
$885$	−9.58522	−0.322204
$886$	11.4929	0.386110
$887$	−14.0226	−0.470831	−0.235416	−	0.971895i	$-0.575645\pi$
$887$	−14.0226	−0.470831	−0.235416	+	0.971895i	$0.575645\pi$
$888$	14.2814	0.479252
$889$	−1.00000	−0.0335389
$890$	−31.9572	−1.07121
$891$	4.88599	0.163687
$892$	−40.5193	−1.35669
$893$	13.5306	0.452783
$894$	−58.5492	−1.95818
$895$	−17.9042	−0.598473
$896$	18.0026	0.601426
$897$	−45.7212	−1.52659
$898$	16.4568	0.549171
$899$	33.8611	1.12933
$900$	−18.2014	−0.606713
$901$	4.37890	0.145882
$902$	50.8897	1.69444
$903$	−4.11683	−0.137000
$904$	−66.8518	−2.22346
$905$	−3.45278	−0.114774
$906$	15.9611	0.530273
$907$	−35.6241	−1.18288	−0.591440	−	0.806349i	$-0.701440\pi$
$907$	−35.6241	−1.18288	−0.591440	+	0.806349i	$0.701440\pi$
$908$	−108.221	−3.59145
$909$	0.691702	0.0229423
$910$	−12.9395	−0.428940
$911$	4.45318	0.147541	0.0737703	−	0.997275i	$-0.476497\pi$
$911$	4.45318	0.147541	0.0737703	+	0.997275i	$0.476497\pi$
$912$	−10.2360	−0.338949
$913$	−18.7094	−0.619192
$914$	43.8529	1.45053
$915$	−4.81238	−0.159092
$916$	25.9284	0.856698
$917$	−0.687639	−0.0227078
$918$	−3.11406	−0.102779
$919$	38.4633	1.26879	0.634394	−	0.773010i	$-0.281250\pi$
$919$	38.4633	1.26879	0.634394	+	0.773010i	$0.281250\pi$
$920$	28.7215	0.946921
$921$	−18.6482	−0.614478
$922$	99.8618	3.28877
$923$	47.8475	1.57492
$924$	20.2789	0.667128
$925$	11.7437	0.386130
$926$	9.63572	0.316649
$927$	−16.5225	−0.542668
$928$	15.1710	0.498012
$929$	41.8359	1.37259	0.686295	−	0.727323i	$-0.259236\pi$
$929$	41.8359	1.37259	0.686295	+	0.727323i	$0.259236\pi$
$930$	−6.71897	−0.220324
$931$	−2.07830	−0.0681135
$932$	28.1320	0.921493
$933$	20.8747	0.683407
$934$	3.29665	0.107870
$935$	−4.80966	−0.157293
$936$	35.4939	1.16016
$937$	27.1190	0.885938	0.442969	−	0.896537i	$-0.353925\pi$
$937$	27.1190	0.885938	0.442969	+	0.896537i	$0.353925\pi$
$938$	37.3429	1.21929
$939$	−7.93347	−0.258899
$940$	21.1831	0.690916
$941$	−28.1483	−0.917608	−0.458804	−	0.888538i	$-0.651722\pi$
$941$	−28.1483	−0.917608	−0.458804	+	0.888538i	$0.651722\pi$
$942$	35.9568	1.17154
$943$	−28.8514	−0.939531
$944$	60.2195	1.95998
$945$	−0.783950	−0.0255019
$946$	49.8848	1.62189
$947$	26.7498	0.869251	0.434625	−	0.900611i	$-0.356881\pi$
$947$	26.7498	0.869251	0.434625	+	0.900611i	$0.356881\pi$
$948$	−30.6599	−0.995786
$949$	−14.9715	−0.485995
$950$	−22.6033	−0.733349
$951$	11.3644	0.368517
$952$	−6.69656	−0.217037
$953$	−59.4329	−1.92522	−0.962611	−	0.270888i	$-0.912683\pi$
$953$	−59.4329	−1.92522	−0.962611	+	0.270888i	$0.912683\pi$
$954$	−8.64855	−0.280007
$955$	−16.1150	−0.521468
$956$	−98.3923	−3.18223
$957$	−47.8731	−1.54752
$958$	27.1943	0.878607
$959$	−7.96226	−0.257115
$960$	4.71188	0.152075
$961$	−19.0567	−0.614733
$962$	−44.1999	−1.42506
$963$	−19.1211	−0.616170
$964$	−38.5340	−1.24110
$965$	14.1672	0.456058
$966$	−17.0370	−0.548158
$967$	−4.26909	−0.137285	−0.0686424	−	0.997641i	$-0.521867\pi$
$967$	−4.26909	−0.137285	−0.0686424	+	0.997641i	$0.521867\pi$
$968$	−68.6519	−2.20655
$969$	−2.60965	−0.0838341
$970$	32.8505	1.05477
$971$	53.2969	1.71038	0.855190	−	0.518315i	$-0.173441\pi$
$971$	53.2969	1.71038	0.855190	+	0.518315i	$0.173441\pi$
$972$	4.15043	0.133125
$973$	−0.410908	−0.0131731
$974$	−18.4106	−0.589915
$975$	29.1869	0.934729
$976$	30.2340	0.967766
$977$	19.3371	0.618647	0.309324	−	0.950957i	$-0.399897\pi$
$977$	19.3371	0.618647	0.309324	+	0.950957i	$0.399897\pi$
$978$	−19.9983	−0.639476
$979$	−80.3120	−2.56678
$980$	−3.25373	−0.103937
$981$	14.7383	0.470558
$982$	−25.9761	−0.828930
$983$	−38.4570	−1.22659	−0.613294	−	0.789855i	$-0.710156\pi$
$983$	−38.4570	−1.22659	−0.613294	+	0.789855i	$0.710156\pi$
$984$	22.3977	0.714011
$985$	19.3721	0.617248
$986$	30.5117	0.971690
$987$	−6.51041	−0.207229
$988$	57.4087	1.82641
$989$	−28.2817	−0.899305
$990$	9.49933	0.301909
$991$	25.2038	0.800626	0.400313	−	0.916379i	$-0.368901\pi$
$991$	25.2038	0.800626	0.400313	+	0.916379i	$0.368901\pi$
$992$	5.35101	0.169895
$993$	−19.1983	−0.609238
$994$	17.8294	0.565513
$995$	−13.0609	−0.414058
$996$	−15.8928	−0.503584
$997$	42.0562	1.33193	0.665966	−	0.745982i	$-0.268019\pi$
$997$	42.0562	1.33193	0.665966	+	0.745982i	$0.268019\pi$
$998$	−66.1651	−2.09442
$999$	−2.67789	−0.0847247

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2667.2.a.j.1.1	✓	7
3.2	odd	2		8001.2.a.l.1.7		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2667.2.a.j.1.1	✓	7	1.1	even	1	trivial
8001.2.a.l.1.7		7	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)

\(f(q)\)	\(=\)	\(q-2.48001 q^{2} +1.00000 q^{3} +4.15043 q^{4} -0.783950 q^{5} -2.48001 q^{6} +1.00000 q^{7} -5.33307 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.48001 q^{2} +1.00000 q^{3} +4.15043 q^{4} -0.783950 q^{5} -2.48001 q^{6} +1.00000 q^{7} -5.33307 q^{8} +1.00000 q^{9} +1.94420 q^{10} +4.88599 q^{11} +4.15043 q^{12} -6.65543 q^{13} -2.48001 q^{14} -0.783950 q^{15} +4.92520 q^{16} +1.25567 q^{17} -2.48001 q^{18} -2.07830 q^{19} -3.25373 q^{20} +1.00000 q^{21} -12.1173 q^{22} +6.86976 q^{23} -5.33307 q^{24} -4.38542 q^{25} +16.5055 q^{26} +1.00000 q^{27} +4.15043 q^{28} -9.79804 q^{29} +1.94420 q^{30} -3.45591 q^{31} -1.54837 q^{32} +4.88599 q^{33} -3.11406 q^{34} -0.783950 q^{35} +4.15043 q^{36} -2.67789 q^{37} +5.15419 q^{38} -6.65543 q^{39} +4.18086 q^{40} -4.19977 q^{41} -2.48001 q^{42} -4.11683 q^{43} +20.2789 q^{44} -0.783950 q^{45} -17.0370 q^{46} -6.51041 q^{47} +4.92520 q^{48} +1.00000 q^{49} +10.8759 q^{50} +1.25567 q^{51} -27.6229 q^{52} +3.48731 q^{53} -2.48001 q^{54} -3.83037 q^{55} -5.33307 q^{56} -2.07830 q^{57} +24.2992 q^{58} +12.2268 q^{59} -3.25373 q^{60} +6.13863 q^{61} +8.57067 q^{62} +1.00000 q^{63} -6.01043 q^{64} +5.21753 q^{65} -12.1173 q^{66} -15.0576 q^{67} +5.21155 q^{68} +6.86976 q^{69} +1.94420 q^{70} -7.18924 q^{71} -5.33307 q^{72} +2.24951 q^{73} +6.64118 q^{74} -4.38542 q^{75} -8.62583 q^{76} +4.88599 q^{77} +16.5055 q^{78} -7.38716 q^{79} -3.86111 q^{80} +1.00000 q^{81} +10.4154 q^{82} -3.82920 q^{83} +4.15043 q^{84} -0.984380 q^{85} +10.2098 q^{86} -9.79804 q^{87} -26.0573 q^{88} -16.4372 q^{89} +1.94420 q^{90} -6.65543 q^{91} +28.5124 q^{92} -3.45591 q^{93} +16.1458 q^{94} +1.62928 q^{95} -1.54837 q^{96} +16.8967 q^{97} -2.48001 q^{98} +4.88599 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 2 q^{2} + 7 q^{3} + 4 q^{4} - 8 q^{5} - 2 q^{6} + 7 q^{7} - 9 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q - 2 * q^2 + 7 * q^3 + 4 * q^4 - 8 * q^5 - 2 * q^6 + 7 * q^7 - 9 * q^8 + 7 * q^9	\( 7 q - 2 q^{2} + 7 q^{3} + 4 q^{4} - 8 q^{5} - 2 q^{6} + 7 q^{7} - 9 q^{8} + 7 q^{9} - 3 q^{11} + 4 q^{12} - 23 q^{13} - 2 q^{14} - 8 q^{15} + 2 q^{16} + 3 q^{17} - 2 q^{18} - 9 q^{19} - 9 q^{20} + 7 q^{21} - 19 q^{22} + 12 q^{23} - 9 q^{24} + 3 q^{25} + 18 q^{26} + 7 q^{27} + 4 q^{28} - 9 q^{29} - 33 q^{31} + 10 q^{32} - 3 q^{33} - 2 q^{34} - 8 q^{35} + 4 q^{36} - 33 q^{37} - 3 q^{38} - 23 q^{39} - 9 q^{40} - 3 q^{41} - 2 q^{42} - 9 q^{43} + 2 q^{44} - 8 q^{45} - 32 q^{46} + 11 q^{47} + 2 q^{48} + 7 q^{49} + 29 q^{50} + 3 q^{51} - 21 q^{52} + q^{53} - 2 q^{54} - 16 q^{55} - 9 q^{56} - 9 q^{57} - 5 q^{58} - 30 q^{59} - 9 q^{60} - 19 q^{61} + 3 q^{62} + 7 q^{63} - 21 q^{64} + 14 q^{65} - 19 q^{66} - 30 q^{67} + 24 q^{68} + 12 q^{69} + 8 q^{71} - 9 q^{72} - 20 q^{73} - 9 q^{74} + 3 q^{75} - 42 q^{76} - 3 q^{77} + 18 q^{78} + 8 q^{79} + 12 q^{80} + 7 q^{81} + 10 q^{82} - 34 q^{83} + 4 q^{84} - 28 q^{85} + 24 q^{86} - 9 q^{87} - q^{88} - 12 q^{89} - 23 q^{91} + 60 q^{92} - 33 q^{93} - 3 q^{94} + 12 q^{95} + 10 q^{96} + 7 q^{97} - 2 q^{98} - 3 q^{99}+O(q^{100}) \) 7 * q - 2 * q^2 + 7 * q^3 + 4 * q^4 - 8 * q^5 - 2 * q^6 + 7 * q^7 - 9 * q^8 + 7 * q^9 - 3 * q^11 + 4 * q^12 - 23 * q^13 - 2 * q^14 - 8 * q^15 + 2 * q^16 + 3 * q^17 - 2 * q^18 - 9 * q^19 - 9 * q^20 + 7 * q^21 - 19 * q^22 + 12 * q^23 - 9 * q^24 + 3 * q^25 + 18 * q^26 + 7 * q^27 + 4 * q^28 - 9 * q^29 - 33 * q^31 + 10 * q^32 - 3 * q^33 - 2 * q^34 - 8 * q^35 + 4 * q^36 - 33 * q^37 - 3 * q^38 - 23 * q^39 - 9 * q^40 - 3 * q^41 - 2 * q^42 - 9 * q^43 + 2 * q^44 - 8 * q^45 - 32 * q^46 + 11 * q^47 + 2 * q^48 + 7 * q^49 + 29 * q^50 + 3 * q^51 - 21 * q^52 + q^53 - 2 * q^54 - 16 * q^55 - 9 * q^56 - 9 * q^57 - 5 * q^58 - 30 * q^59 - 9 * q^60 - 19 * q^61 + 3 * q^62 + 7 * q^63 - 21 * q^64 + 14 * q^65 - 19 * q^66 - 30 * q^67 + 24 * q^68 + 12 * q^69 + 8 * q^71 - 9 * q^72 - 20 * q^73 - 9 * q^74 + 3 * q^75 - 42 * q^76 - 3 * q^77 + 18 * q^78 + 8 * q^79 + 12 * q^80 + 7 * q^81 + 10 * q^82 - 34 * q^83 + 4 * q^84 - 28 * q^85 + 24 * q^86 - 9 * q^87 - q^88 - 12 * q^89 - 23 * q^91 + 60 * q^92 - 33 * q^93 - 3 * q^94 + 12 * q^95 + 10 * q^96 + 7 * q^97 - 2 * q^98 - 3 * q^99

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