LMFDB - Embedded newform 8027.2.a.c.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8027,2,Mod(1,8027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8027, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("8027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8027 = 23 \cdot 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8027.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:	$64.0959177025$
Analytic rank:	$1$
Dimension:	$143$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	8027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.66984 q^{2} -0.755713 q^{3} +5.12803 q^{4} +0.937284 q^{5} +2.01763 q^{6} +2.29767 q^{7} -8.35133 q^{8} -2.42890 q^{9} +O(q^{10})$	\(q-2.66984 q^{2} -0.755713 q^{3} +5.12803 q^{4} +0.937284 q^{5} +2.01763 q^{6} +2.29767 q^{7} -8.35133 q^{8} -2.42890 q^{9} -2.50240 q^{10} -0.731692 q^{11} -3.87532 q^{12} -3.54288 q^{13} -6.13441 q^{14} -0.708317 q^{15} +12.0406 q^{16} +5.00612 q^{17} +6.48476 q^{18} +3.42077 q^{19} +4.80642 q^{20} -1.73638 q^{21} +1.95350 q^{22} +1.00000 q^{23} +6.31120 q^{24} -4.12150 q^{25} +9.45891 q^{26} +4.10269 q^{27} +11.7825 q^{28} +1.40991 q^{29} +1.89109 q^{30} -9.02733 q^{31} -15.4438 q^{32} +0.552949 q^{33} -13.3655 q^{34} +2.15357 q^{35} -12.4555 q^{36} -0.577752 q^{37} -9.13291 q^{38} +2.67740 q^{39} -7.82756 q^{40} -11.5574 q^{41} +4.63585 q^{42} +4.93810 q^{43} -3.75214 q^{44} -2.27657 q^{45} -2.66984 q^{46} +0.106337 q^{47} -9.09925 q^{48} -1.72070 q^{49} +11.0037 q^{50} -3.78319 q^{51} -18.1680 q^{52} +9.95652 q^{53} -10.9535 q^{54} -0.685803 q^{55} -19.1886 q^{56} -2.58512 q^{57} -3.76424 q^{58} -0.553039 q^{59} -3.63227 q^{60} +10.2171 q^{61} +24.1015 q^{62} -5.58081 q^{63} +17.1513 q^{64} -3.32068 q^{65} -1.47628 q^{66} +8.54694 q^{67} +25.6715 q^{68} -0.755713 q^{69} -5.74969 q^{70} +9.49580 q^{71} +20.2845 q^{72} -11.1910 q^{73} +1.54250 q^{74} +3.11467 q^{75} +17.5418 q^{76} -1.68119 q^{77} -7.14822 q^{78} -11.7322 q^{79} +11.2855 q^{80} +4.18624 q^{81} +30.8564 q^{82} -1.97468 q^{83} -8.90421 q^{84} +4.69216 q^{85} -13.1839 q^{86} -1.06549 q^{87} +6.11060 q^{88} +13.6653 q^{89} +6.07806 q^{90} -8.14038 q^{91} +5.12803 q^{92} +6.82207 q^{93} -0.283903 q^{94} +3.20624 q^{95} +11.6711 q^{96} +8.23823 q^{97} +4.59398 q^{98} +1.77721 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9}+O(q^{10}) $ 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9	\( 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9} - 22 q^{10} - 14 q^{11} - 36 q^{12} - 87 q^{13} - 18 q^{14} - 19 q^{15} + 81 q^{16} - 14 q^{17} - 60 q^{18} - 18 q^{19} - 25 q^{20} - 26 q^{21} - 62 q^{22} + 143 q^{23} - 21 q^{24} + 67 q^{25} - 5 q^{26} - 47 q^{27} - 76 q^{28} - 54 q^{29} - 22 q^{30} - 62 q^{31} - 117 q^{32} - 59 q^{33} - 35 q^{34} - 52 q^{35} + 52 q^{36} - 190 q^{37} - 19 q^{38} - 43 q^{39} - 41 q^{40} - 50 q^{41} + 8 q^{42} - 50 q^{43} - 18 q^{44} - 75 q^{45} - 17 q^{46} - 63 q^{47} - 35 q^{48} + 74 q^{49} - 53 q^{50} - 33 q^{51} - 124 q^{52} - 100 q^{53} - 46 q^{54} - 61 q^{55} - 3 q^{56} - 80 q^{57} - 112 q^{58} - 109 q^{59} - 55 q^{60} - 76 q^{61} - 6 q^{62} - 93 q^{63} + 57 q^{64} - 17 q^{65} + 50 q^{66} - 120 q^{67} + 26 q^{68} - 17 q^{69} - 109 q^{71} - 153 q^{72} - 94 q^{73} + 35 q^{74} - 105 q^{75} - 16 q^{76} - 52 q^{77} - 59 q^{78} - 29 q^{79} - 30 q^{80} + 39 q^{81} - 65 q^{82} + 8 q^{83} + 11 q^{84} - 155 q^{85} - 15 q^{86} - 25 q^{87} - 139 q^{88} + 6 q^{89} + 82 q^{90} - 34 q^{91} + 121 q^{92} - 151 q^{93} - 3 q^{94} - 70 q^{95} - 23 q^{96} - 203 q^{97} - 18 q^{98} - 49 q^{99}+O(q^{100}) \) 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9 - 22 * q^10 - 14 * q^11 - 36 * q^12 - 87 * q^13 - 18 * q^14 - 19 * q^15 + 81 * q^16 - 14 * q^17 - 60 * q^18 - 18 * q^19 - 25 * q^20 - 26 * q^21 - 62 * q^22 + 143 * q^23 - 21 * q^24 + 67 * q^25 - 5 * q^26 - 47 * q^27 - 76 * q^28 - 54 * q^29 - 22 * q^30 - 62 * q^31 - 117 * q^32 - 59 * q^33 - 35 * q^34 - 52 * q^35 + 52 * q^36 - 190 * q^37 - 19 * q^38 - 43 * q^39 - 41 * q^40 - 50 * q^41 + 8 * q^42 - 50 * q^43 - 18 * q^44 - 75 * q^45 - 17 * q^46 - 63 * q^47 - 35 * q^48 + 74 * q^49 - 53 * q^50 - 33 * q^51 - 124 * q^52 - 100 * q^53 - 46 * q^54 - 61 * q^55 - 3 * q^56 - 80 * q^57 - 112 * q^58 - 109 * q^59 - 55 * q^60 - 76 * q^61 - 6 * q^62 - 93 * q^63 + 57 * q^64 - 17 * q^65 + 50 * q^66 - 120 * q^67 + 26 * q^68 - 17 * q^69 - 109 * q^71 - 153 * q^72 - 94 * q^73 + 35 * q^74 - 105 * q^75 - 16 * q^76 - 52 * q^77 - 59 * q^78 - 29 * q^79 - 30 * q^80 + 39 * q^81 - 65 * q^82 + 8 * q^83 + 11 * q^84 - 155 * q^85 - 15 * q^86 - 25 * q^87 - 139 * q^88 + 6 * q^89 + 82 * q^90 - 34 * q^91 + 121 * q^92 - 151 * q^93 - 3 * q^94 - 70 * q^95 - 23 * q^96 - 203 * q^97 - 18 * q^98 - 49 * 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 $

$2$	−2.66984	−1.88786	−0.943930	−	0.330146i	$-0.892902\pi$
$2$	−2.66984	−1.88786	−0.943930	+	0.330146i	$0.892902\pi$
$3$	−0.755713	−0.436311	−0.218156	−	0.975914i	$-0.570004\pi$
$3$	−0.755713	−0.436311	−0.218156	+	0.975914i	$0.570004\pi$
$4$	5.12803	2.56401
$5$	0.937284	0.419166	0.209583	−	0.977791i	$-0.432789\pi$
$5$	0.937284	0.419166	0.209583	+	0.977791i	$0.432789\pi$
$6$	2.01763	0.823694
$7$	2.29767	0.868439	0.434219	−	0.900807i	$-0.357024\pi$
$7$	2.29767	0.868439	0.434219	+	0.900807i	$0.357024\pi$
$8$	−8.35133	−2.95264
$9$	−2.42890	−0.809633
$10$	−2.50240	−0.791327
$11$	−0.731692	−0.220614	−0.110307	−	0.993898i	$-0.535183\pi$
$11$	−0.731692	−0.220614	−0.110307	+	0.993898i	$0.535183\pi$
$12$	−3.87532	−1.11871
$13$	−3.54288	−0.982618	−0.491309	−	0.870985i	$-0.663481\pi$
$13$	−3.54288	−0.982618	−0.491309	+	0.870985i	$0.663481\pi$
$14$	−6.13441	−1.63949
$15$	−0.708317	−0.182887
$16$	12.0406	3.01016
$17$	5.00612	1.21416	0.607081	−	0.794640i	$-0.292340\pi$
$17$	5.00612	1.21416	0.607081	+	0.794640i	$0.292340\pi$
$18$	6.48476	1.52847
$19$	3.42077	0.784779	0.392390	−	0.919799i	$-0.371648\pi$
$19$	3.42077	0.784779	0.392390	+	0.919799i	$0.371648\pi$
$20$	4.80642	1.07475
$21$	−1.73638	−0.378909
$22$	1.95350	0.416487
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	6.31120	1.28827
$25$	−4.12150	−0.824300
$26$	9.45891	1.85504
$27$	4.10269	0.789563
$28$	11.7825	2.22669
$29$	1.40991	0.261814	0.130907	−	0.991395i	$-0.458211\pi$
$29$	1.40991	0.261814	0.130907	+	0.991395i	$0.458211\pi$
$30$	1.89109	0.345265
$31$	−9.02733	−1.62136	−0.810678	−	0.585492i	$-0.800901\pi$
$31$	−9.02733	−1.62136	−0.810678	+	0.585492i	$0.800901\pi$
$32$	−15.4438	−2.73011
$33$	0.552949	0.0962561
$34$	−13.3655	−2.29217
$35$	2.15357	0.364020
$36$	−12.4555	−2.07591
$37$	−0.577752	−0.0949818	−0.0474909	−	0.998872i	$-0.515123\pi$
$37$	−0.577752	−0.0949818	−0.0474909	+	0.998872i	$0.515123\pi$
$38$	−9.13291	−1.48155
$39$	2.67740	0.428727
$40$	−7.82756	−1.23765
$41$	−11.5574	−1.80496	−0.902482	−	0.430728i	$-0.858257\pi$
$41$	−11.5574	−1.80496	−0.902482	+	0.430728i	$0.858257\pi$
$42$	4.63585	0.715328
$43$	4.93810	0.753053	0.376527	−	0.926406i	$-0.377118\pi$
$43$	4.93810	0.753053	0.376527	+	0.926406i	$0.377118\pi$
$44$	−3.75214	−0.565656
$45$	−2.27657	−0.339371
$46$	−2.66984	−0.393646
$47$	0.106337	0.0155109	0.00775544	−	0.999970i	$-0.497531\pi$
$47$	0.106337	0.0155109	0.00775544	+	0.999970i	$0.497531\pi$
$48$	−9.09925	−1.31336
$49$	−1.72070	−0.245814
$50$	11.0037	1.55616
$51$	−3.78319	−0.529752
$52$	−18.1680	−2.51945
$53$	9.95652	1.36763	0.683817	−	0.729654i	$-0.260319\pi$
$53$	9.95652	1.36763	0.683817	+	0.729654i	$0.260319\pi$
$54$	−10.9535	−1.49058
$55$	−0.685803	−0.0924737
$56$	−19.1886	−2.56419
$57$	−2.58512	−0.342408
$58$	−3.76424	−0.494269
$59$	−0.553039	−0.0719995	−0.0359998	−	0.999352i	$-0.511462\pi$
$59$	−0.553039	−0.0719995	−0.0359998	+	0.999352i	$0.511462\pi$
$60$	−3.63227	−0.468924
$61$	10.2171	1.30816	0.654081	−	0.756424i	$-0.273055\pi$
$61$	10.2171	1.30816	0.654081	+	0.756424i	$0.273055\pi$
$62$	24.1015	3.06089
$63$	−5.58081	−0.703117
$64$	17.1513	2.14391
$65$	−3.32068	−0.411880
$66$	−1.47628	−0.181718
$67$	8.54694	1.04418	0.522088	−	0.852892i	$-0.325153\pi$
$67$	8.54694	1.04418	0.522088	+	0.852892i	$0.325153\pi$
$68$	25.6715	3.11313
$69$	−0.755713	−0.0909771
$70$	−5.74969	−0.687219
$71$	9.49580	1.12694	0.563472	−	0.826135i	$-0.309465\pi$
$71$	9.49580	1.12694	0.563472	+	0.826135i	$0.309465\pi$
$72$	20.2845	2.39055
$73$	−11.1910	−1.30981	−0.654905	−	0.755712i	$-0.727291\pi$
$73$	−11.1910	−1.30981	−0.654905	+	0.755712i	$0.727291\pi$
$74$	1.54250	0.179312
$75$	3.11467	0.359651
$76$	17.5418	2.01219
$77$	−1.68119	−0.191589
$78$	−7.14822	−0.809376
$79$	−11.7322	−1.31997	−0.659986	−	0.751278i	$-0.729438\pi$
$79$	−11.7322	−1.31997	−0.659986	+	0.751278i	$0.729438\pi$
$80$	11.2855	1.26176
$81$	4.18624	0.465138
$82$	30.8564	3.40752
$83$	−1.97468	−0.216749	−0.108375	−	0.994110i	$-0.534565\pi$
$83$	−1.97468	−0.216749	−0.108375	+	0.994110i	$0.534565\pi$
$84$	−8.90421	−0.971529
$85$	4.69216	0.508936
$86$	−13.1839	−1.42166
$87$	−1.06549	−0.114232
$88$	6.11060	0.651392
$89$	13.6653	1.44852	0.724262	−	0.689525i	$-0.242181\pi$
$89$	13.6653	1.44852	0.724262	+	0.689525i	$0.242181\pi$
$90$	6.07806	0.640684
$91$	−8.14038	−0.853343
$92$	5.12803	0.534634
$93$	6.82207	0.707415
$94$	−0.283903	−0.0292824
$95$	3.20624	0.328953
$96$	11.6711	1.19118
$97$	8.23823	0.836466	0.418233	−	0.908340i	$-0.362650\pi$
$97$	8.23823	0.836466	0.418233	+	0.908340i	$0.362650\pi$
$98$	4.59398	0.464062
$99$	1.77721	0.178616
$100$	−21.1352	−2.11352
$101$	14.8038	1.47303	0.736517	−	0.676419i	$-0.236469\pi$
$101$	14.8038	1.47303	0.736517	+	0.676419i	$0.236469\pi$
$102$	10.1005	1.00010
$103$	−17.2702	−1.70168	−0.850842	−	0.525422i	$-0.823908\pi$
$103$	−17.2702	−1.70168	−0.850842	+	0.525422i	$0.823908\pi$
$104$	29.5877	2.90132
$105$	−1.62748	−0.158826
$106$	−26.5823	−2.58190
$107$	−1.13182	−0.109417	−0.0547084	−	0.998502i	$-0.517423\pi$
$107$	−1.13182	−0.109417	−0.0547084	+	0.998502i	$0.517423\pi$
$108$	21.0387	2.02445
$109$	−1.22752	−0.117575	−0.0587873	−	0.998271i	$-0.518723\pi$
$109$	−1.22752	−0.117575	−0.0587873	+	0.998271i	$0.518723\pi$
$110$	1.83098	0.174577
$111$	0.436615	0.0414416
$112$	27.6654	2.61414
$113$	−5.75820	−0.541686	−0.270843	−	0.962623i	$-0.587302\pi$
$113$	−5.75820	−0.541686	−0.270843	+	0.962623i	$0.587302\pi$
$114$	6.90186	0.646418
$115$	0.937284	0.0874022
$116$	7.23008	0.671296
$117$	8.60529	0.795559
$118$	1.47652	0.135925
$119$	11.5024	1.05443
$120$	5.91539	0.539999
$121$	−10.4646	−0.951330
$122$	−27.2779	−2.46963
$123$	8.73408	0.787525
$124$	−46.2924	−4.15718
$125$	−8.54943	−0.764685
$126$	14.8999	1.32739
$127$	5.19920	0.461355	0.230677	−	0.973030i	$-0.425906\pi$
$127$	5.19920	0.461355	0.230677	+	0.973030i	$0.425906\pi$
$128$	−14.9035	−1.31729
$129$	−3.73179	−0.328565
$130$	8.86568	0.777572
$131$	−17.6877	−1.54538	−0.772692	−	0.634781i	$-0.781090\pi$
$131$	−17.6877	−1.54538	−0.772692	+	0.634781i	$0.781090\pi$
$132$	2.83554	0.246802
$133$	7.85982	0.681533
$134$	−22.8189	−1.97126
$135$	3.84538	0.330958
$136$	−41.8077	−3.58498
$137$	−13.5541	−1.15800	−0.579002	−	0.815326i	$-0.696558\pi$
$137$	−13.5541	−1.15800	−0.579002	+	0.815326i	$0.696558\pi$
$138$	2.01763	0.171752
$139$	−0.356530	−0.0302405	−0.0151202	−	0.999886i	$-0.504813\pi$
$139$	−0.356530	−0.0302405	−0.0151202	+	0.999886i	$0.504813\pi$
$140$	11.0436	0.933353
$141$	−0.0803604	−0.00676757
$142$	−25.3522	−2.12751
$143$	2.59230	0.216779
$144$	−29.2454	−2.43712
$145$	1.32149	0.109744
$146$	29.8782	2.47274
$147$	1.30035	0.107251
$148$	−2.96273	−0.243535
$149$	22.8574	1.87255	0.936277	−	0.351262i	$-0.114247\pi$
$149$	22.8574	1.87255	0.936277	+	0.351262i	$0.114247\pi$
$150$	−8.31566	−0.678971
$151$	−3.16756	−0.257772	−0.128886	−	0.991659i	$-0.541140\pi$
$151$	−3.16756	−0.257772	−0.128886	+	0.991659i	$0.541140\pi$
$152$	−28.5680	−2.31717
$153$	−12.1594	−0.983026
$154$	4.48850	0.361694
$155$	−8.46117	−0.679617
$156$	13.7298	1.09926
$157$	−5.83038	−0.465315	−0.232658	−	0.972559i	$-0.574742\pi$
$157$	−5.83038	−0.465315	−0.232658	+	0.972559i	$0.574742\pi$
$158$	31.3230	2.49192
$159$	−7.52427	−0.596714
$160$	−14.4753	−1.14437
$161$	2.29767	0.181082
$162$	−11.1766	−0.878115
$163$	−20.7334	−1.62396	−0.811981	−	0.583684i	$-0.801611\pi$
$163$	−20.7334	−1.62396	−0.811981	+	0.583684i	$0.801611\pi$
$164$	−59.2667	−4.62795
$165$	0.518270	0.0403473
$166$	5.27208	0.409192
$167$	−5.64087	−0.436504	−0.218252	−	0.975892i	$-0.570035\pi$
$167$	−5.64087	−0.436504	−0.218252	+	0.975892i	$0.570035\pi$
$168$	14.5011	1.11878
$169$	−0.448014	−0.0344626
$170$	−12.5273	−0.960799
$171$	−8.30871	−0.635383
$172$	25.3227	1.93084
$173$	−23.0372	−1.75149	−0.875743	−	0.482778i	$-0.839628\pi$
$173$	−23.0372	−1.75149	−0.875743	+	0.482778i	$0.839628\pi$
$174$	2.84468	0.215655
$175$	−9.46986	−0.715854
$176$	−8.81003	−0.664081
$177$	0.417938	0.0314142
$178$	−36.4843	−2.73461
$179$	−5.08157	−0.379815	−0.189907	−	0.981802i	$-0.560819\pi$
$179$	−5.08157	−0.379815	−0.189907	+	0.981802i	$0.560819\pi$
$180$	−11.6743	−0.870151
$181$	10.8250	0.804619	0.402309	−	0.915504i	$-0.368208\pi$
$181$	10.8250	0.804619	0.402309	+	0.915504i	$0.368208\pi$
$182$	21.7335	1.61099
$183$	−7.72117	−0.570766
$184$	−8.35133	−0.615668
$185$	−0.541518	−0.0398132
$186$	−18.2138	−1.33550
$187$	−3.66294	−0.267861
$188$	0.545301	0.0397701
$189$	9.42664	0.685687
$190$	−8.56013	−0.621017
$191$	9.03844	0.653998	0.326999	−	0.945025i	$-0.393963\pi$
$191$	9.03844	0.653998	0.326999	+	0.945025i	$0.393963\pi$
$192$	−12.9615	−0.935412
$193$	−16.0148	−1.15277	−0.576386	−	0.817178i	$-0.695537\pi$
$193$	−16.0148	−1.15277	−0.576386	+	0.817178i	$0.695537\pi$
$194$	−21.9947	−1.57913
$195$	2.50948	0.179708
$196$	−8.82378	−0.630270
$197$	5.39014	0.384032	0.192016	−	0.981392i	$-0.438497\pi$
$197$	5.39014	0.384032	0.192016	+	0.981392i	$0.438497\pi$
$198$	−4.74485	−0.337202
$199$	27.4274	1.94428	0.972138	−	0.234409i	$-0.0753155\pi$
$199$	27.4274	1.94428	0.972138	+	0.234409i	$0.0753155\pi$
$200$	34.4200	2.43386
$201$	−6.45903	−0.455585
$202$	−39.5238	−2.78088
$203$	3.23952	0.227370
$204$	−19.4003	−1.35829
$205$	−10.8326	−0.756579
$206$	46.1086	3.21254
$207$	−2.42890	−0.168820
$208$	−42.6585	−2.95783
$209$	−2.50295	−0.173133
$210$	4.34511	0.299841
$211$	5.91693	0.407338	0.203669	−	0.979040i	$-0.434713\pi$
$211$	5.91693	0.407338	0.203669	+	0.979040i	$0.434713\pi$
$212$	51.0573	3.50663
$213$	−7.17609	−0.491698
$214$	3.02177	0.206564
$215$	4.62840	0.315654
$216$	−34.2629	−2.33129
$217$	−20.7418	−1.40805
$218$	3.27727	0.221964
$219$	8.45719	0.571484
$220$	−3.51682	−0.237104
$221$	−17.7361	−1.19306
$222$	−1.16569	−0.0782360
$223$	−18.5124	−1.23968	−0.619841	−	0.784727i	$-0.712803\pi$
$223$	−18.5124	−1.23968	−0.619841	+	0.784727i	$0.712803\pi$
$224$	−35.4849	−2.37094
$225$	10.0107	0.667380
$226$	15.3735	1.02263
$227$	−16.6094	−1.10240	−0.551202	−	0.834372i	$-0.685831\pi$
$227$	−16.6094	−1.10240	−0.551202	+	0.834372i	$0.685831\pi$
$228$	−13.2566	−0.877939
$229$	−1.86237	−0.123069	−0.0615345	−	0.998105i	$-0.519599\pi$
$229$	−1.86237	−0.123069	−0.0615345	+	0.998105i	$0.519599\pi$
$230$	−2.50240	−0.165003
$231$	1.27050	0.0835925
$232$	−11.7746	−0.773044
$233$	2.89859	0.189893	0.0949466	−	0.995482i	$-0.469732\pi$
$233$	2.89859	0.189893	0.0949466	+	0.995482i	$0.469732\pi$
$234$	−22.9747	−1.50190
$235$	0.0996682	0.00650164
$236$	−2.83600	−0.184608
$237$	8.86615	0.575918
$238$	−30.7096	−1.99061
$239$	−22.1154	−1.43053	−0.715264	−	0.698854i	$-0.753694\pi$
$239$	−22.1154	−1.43053	−0.715264	+	0.698854i	$0.753694\pi$
$240$	−8.52858	−0.550518
$241$	4.43734	0.285834	0.142917	−	0.989735i	$-0.454352\pi$
$241$	4.43734	0.285834	0.142917	+	0.989735i	$0.454352\pi$
$242$	27.9388	1.79598
$243$	−15.4717	−0.992507
$244$	52.3934	3.35415
$245$	−1.61278	−0.103037
$246$	−23.3186	−1.48674
$247$	−12.1194	−0.771138
$248$	75.3902	4.78728
$249$	1.49229	0.0945702
$250$	22.8256	1.44362
$251$	10.4358	0.658699	0.329350	−	0.944208i	$-0.393170\pi$
$251$	10.4358	0.658699	0.329350	+	0.944208i	$0.393170\pi$
$252$	−28.6186	−1.80280
$253$	−0.731692	−0.0460011
$254$	−13.8810	−0.870973
$255$	−3.54592	−0.222054
$256$	5.48726	0.342954
$257$	28.2446	1.76185	0.880925	−	0.473256i	$-0.156921\pi$
$257$	28.2446	1.76185	0.880925	+	0.473256i	$0.156921\pi$
$258$	9.96326	0.620286
$259$	−1.32749	−0.0824859
$260$	−17.0286	−1.05607
$261$	−3.42454	−0.211973
$262$	47.2234	2.91747
$263$	14.8305	0.914491	0.457245	−	0.889341i	$-0.348836\pi$
$263$	14.8305	0.914491	0.457245	+	0.889341i	$0.348836\pi$
$264$	−4.61786	−0.284210
$265$	9.33209	0.573266
$266$	−20.9844	−1.28664
$267$	−10.3271	−0.632007
$268$	43.8290	2.67728
$269$	30.2252	1.84286	0.921432	−	0.388539i	$-0.127020\pi$
$269$	30.2252	1.84286	0.921432	+	0.388539i	$0.127020\pi$
$270$	−10.2665	−0.624802
$271$	1.63598	0.0993788	0.0496894	−	0.998765i	$-0.484177\pi$
$271$	1.63598	0.0993788	0.0496894	+	0.998765i	$0.484177\pi$
$272$	60.2768	3.65482
$273$	6.15179	0.372323
$274$	36.1872	2.18615
$275$	3.01567	0.181852
$276$	−3.87532	−0.233267
$277$	7.43649	0.446815	0.223408	−	0.974725i	$-0.428282\pi$
$277$	7.43649	0.446815	0.223408	+	0.974725i	$0.428282\pi$
$278$	0.951877	0.0570898
$279$	21.9265	1.31270
$280$	−17.9852	−1.07482
$281$	−19.1649	−1.14328	−0.571642	−	0.820503i	$-0.693694\pi$
$281$	−19.1649	−1.14328	−0.571642	+	0.820503i	$0.693694\pi$
$282$	0.214549	0.0127762
$283$	21.5991	1.28393	0.641966	−	0.766733i	$-0.278119\pi$
$283$	21.5991	1.28393	0.641966	+	0.766733i	$0.278119\pi$
$284$	48.6947	2.88950
$285$	−2.42299	−0.143526
$286$	−6.92101	−0.409248
$287$	−26.5551	−1.56750
$288$	37.5115	2.21039
$289$	8.06124	0.474191
$290$	−3.52816	−0.207181
$291$	−6.22574	−0.364959
$292$	−57.3878	−3.35837
$293$	28.3700	1.65739	0.828697	−	0.559697i	$-0.189083\pi$
$293$	28.3700	1.65739	0.828697	+	0.559697i	$0.189083\pi$
$294$	−3.47173	−0.202475
$295$	−0.518354	−0.0301798
$296$	4.82500	0.280447
$297$	−3.00190	−0.174188
$298$	−61.0256	−3.53512
$299$	−3.54288	−0.204890
$300$	15.9721	0.922151
$301$	11.3461	0.653981
$302$	8.45687	0.486638
$303$	−11.1874	−0.642701
$304$	41.1882	2.36231
$305$	9.57630	0.548337
$306$	32.4635	1.85581
$307$	−23.1957	−1.32385	−0.661925	−	0.749570i	$-0.730260\pi$
$307$	−23.1957	−1.32385	−0.661925	+	0.749570i	$0.730260\pi$
$308$	−8.62119	−0.491238
$309$	13.0513	0.742463
$310$	22.5899	1.28302
$311$	2.40923	0.136615	0.0683075	−	0.997664i	$-0.478240\pi$
$311$	2.40923	0.136615	0.0683075	+	0.997664i	$0.478240\pi$
$312$	−22.3598	−1.26588
$313$	−14.0155	−0.792203	−0.396101	−	0.918207i	$-0.629637\pi$
$313$	−14.0155	−0.792203	−0.396101	+	0.918207i	$0.629637\pi$
$314$	15.5662	0.878449
$315$	−5.23081	−0.294723
$316$	−60.1629	−3.38443
$317$	−25.2964	−1.42079	−0.710394	−	0.703804i	$-0.751483\pi$
$317$	−25.2964	−1.42079	−0.710394	+	0.703804i	$0.751483\pi$
$318$	20.0886	1.12651
$319$	−1.03162	−0.0577598
$320$	16.0756	0.898655
$321$	0.855329	0.0477398
$322$	−6.13441	−0.341857
$323$	17.1248	0.952850
$324$	21.4672	1.19262
$325$	14.6020	0.809971
$326$	55.3547	3.06581
$327$	0.927649	0.0512991
$328$	96.5197	5.32941
$329$	0.244328	0.0134703
$330$	−1.38370	−0.0761700
$331$	−28.3841	−1.56013	−0.780065	−	0.625699i	$-0.784814\pi$
$331$	−28.3841	−1.56013	−0.780065	+	0.625699i	$0.784814\pi$
$332$	−10.1262	−0.555749
$333$	1.40330	0.0769004
$334$	15.0602	0.824058
$335$	8.01091	0.437683
$336$	−20.9071	−1.14058
$337$	−14.1557	−0.771108	−0.385554	−	0.922685i	$-0.625990\pi$
$337$	−14.1557	−0.771108	−0.385554	+	0.922685i	$0.625990\pi$
$338$	1.19612	0.0650605
$339$	4.35155	0.236344
$340$	24.0615	1.30492
$341$	6.60522	0.357693
$342$	22.1829	1.19951
$343$	−20.0373	−1.08191
$344$	−41.2397	−2.22350
$345$	−0.708317	−0.0381345
$346$	61.5056	3.30656
$347$	−6.07873	−0.326323	−0.163162	−	0.986599i	$-0.552169\pi$
$347$	−6.07873	−0.326323	−0.163162	+	0.986599i	$0.552169\pi$
$348$	−5.46386	−0.292894
$349$	1.00000	0.0535288
$349$	1.00000	0.0535288
$350$	25.2830	1.35143
$351$	−14.5353	−0.775838
$352$	11.3001	0.602299
$353$	−26.4791	−1.40934	−0.704670	−	0.709535i	$-0.748905\pi$
$353$	−26.4791	−1.40934	−0.704670	+	0.709535i	$0.748905\pi$
$354$	−1.11583	−0.0593056
$355$	8.90026	0.472377
$356$	70.0763	3.71404
$357$	−8.69253	−0.460058
$358$	13.5670	0.717037
$359$	28.4425	1.50114	0.750569	−	0.660792i	$-0.229779\pi$
$359$	28.4425	1.50114	0.750569	+	0.660792i	$0.229779\pi$
$360$	19.0124	1.00204
$361$	−7.29830	−0.384121
$362$	−28.9011	−1.51901
$363$	7.90825	0.415076
$364$	−41.7441	−2.18798
$365$	−10.4892	−0.549028
$366$	20.6143	1.07753
$367$	−31.2700	−1.63228	−0.816139	−	0.577855i	$-0.803890\pi$
$367$	−31.2700	−1.63228	−0.816139	+	0.577855i	$0.803890\pi$
$368$	12.0406	0.627661
$369$	28.0718	1.46136
$370$	1.44576	0.0751617
$371$	22.8768	1.18771
$372$	34.9838	1.81382
$373$	−25.3913	−1.31471	−0.657356	−	0.753580i	$-0.728325\pi$
$373$	−25.3913	−1.31471	−0.657356	+	0.753580i	$0.728325\pi$
$374$	9.77945	0.505683
$375$	6.46092	0.333640
$376$	−0.888057	−0.0457981
$377$	−4.99515	−0.257263
$378$	−25.1676	−1.29448
$379$	15.6098	0.801820	0.400910	−	0.916117i	$-0.368694\pi$
$379$	15.6098	0.801820	0.400910	+	0.916117i	$0.368694\pi$
$380$	16.4417	0.843440
$381$	−3.92910	−0.201294
$382$	−24.1312	−1.23466
$383$	1.90126	0.0971500	0.0485750	−	0.998820i	$-0.484532\pi$
$383$	1.90126	0.0971500	0.0485750	+	0.998820i	$0.484532\pi$
$384$	11.2627	0.574750
$385$	−1.57575	−0.0803078
$386$	42.7569	2.17627
$387$	−11.9941	−0.609697
$388$	42.2459	2.14471
$389$	21.6960	1.10003	0.550014	−	0.835155i	$-0.314622\pi$
$389$	21.6960	1.10003	0.550014	+	0.835155i	$0.314622\pi$
$390$	−6.69991	−0.339263
$391$	5.00612	0.253170
$392$	14.3701	0.725800
$393$	13.3668	0.674268
$394$	−14.3908	−0.724998
$395$	−10.9964	−0.553287
$396$	9.11356	0.457974
$397$	−3.47694	−0.174503	−0.0872514	−	0.996186i	$-0.527808\pi$
$397$	−3.47694	−0.174503	−0.0872514	+	0.996186i	$0.527808\pi$
$398$	−73.2267	−3.67052
$399$	−5.93977	−0.297360
$400$	−49.6254	−2.48127
$401$	6.27385	0.313301	0.156651	−	0.987654i	$-0.449930\pi$
$401$	6.27385	0.313301	0.156651	+	0.987654i	$0.449930\pi$
$402$	17.2446	0.860081
$403$	31.9827	1.59317
$404$	75.9144	3.77688
$405$	3.92370	0.194970
$406$	−8.64899	−0.429242
$407$	0.422737	0.0209543
$408$	31.5946	1.56417
$409$	9.89857	0.489453	0.244726	−	0.969592i	$-0.421302\pi$
$409$	9.89857	0.489453	0.244726	+	0.969592i	$0.421302\pi$
$410$	28.9212	1.42832
$411$	10.2430	0.505250
$412$	−88.5621	−4.36314
$413$	−1.27070	−0.0625272
$414$	6.48476	0.318709
$415$	−1.85084	−0.0908540
$416$	54.7157	2.68266
$417$	0.269434	0.0131943
$418$	6.68248	0.326851
$419$	−32.6684	−1.59596	−0.797979	−	0.602685i	$-0.794097\pi$
$419$	−32.6684	−1.59596	−0.797979	+	0.602685i	$0.794097\pi$
$420$	−8.34578	−0.407232
$421$	13.0986	0.638385	0.319192	−	0.947690i	$-0.396588\pi$
$421$	13.0986	0.638385	0.319192	+	0.947690i	$0.396588\pi$
$422$	−15.7972	−0.768998
$423$	−0.258282	−0.0125581
$424$	−83.1502	−4.03813
$425$	−20.6327	−1.00083
$426$	19.1590	0.928257
$427$	23.4755	1.13606
$428$	−5.80399	−0.280546
$429$	−1.95903	−0.0945829
$430$	−12.3571	−0.595911
$431$	−17.2038	−0.828679	−0.414339	−	0.910122i	$-0.635987\pi$
$431$	−17.2038	−0.828679	−0.414339	+	0.910122i	$0.635987\pi$
$432$	49.3989	2.37671
$433$	−29.9601	−1.43979	−0.719896	−	0.694082i	$-0.755810\pi$
$433$	−29.9601	−1.43979	−0.719896	+	0.694082i	$0.755810\pi$
$434$	55.3774	2.65820
$435$	−0.998666	−0.0478824
$436$	−6.29473	−0.301463
$437$	3.42077	0.163638
$438$	−22.5793	−1.07888
$439$	4.07339	0.194412	0.0972061	−	0.995264i	$-0.469009\pi$
$439$	4.07339	0.194412	0.0972061	+	0.995264i	$0.469009\pi$
$440$	5.72737	0.273042
$441$	4.17940	0.199019
$442$	47.3524	2.25233
$443$	−7.59557	−0.360876	−0.180438	−	0.983586i	$-0.557752\pi$
$443$	−7.59557	−0.360876	−0.180438	+	0.983586i	$0.557752\pi$
$444$	2.23897	0.106257
$445$	12.8083	0.607172
$446$	49.4251	2.34035
$447$	−17.2737	−0.817016
$448$	39.4081	1.86186
$449$	−17.8205	−0.841000	−0.420500	−	0.907293i	$-0.638145\pi$
$449$	−17.8205	−0.841000	−0.420500	+	0.907293i	$0.638145\pi$
$450$	−26.7269	−1.25992
$451$	8.45646	0.398199
$452$	−29.5282	−1.38889
$453$	2.39377	0.112469
$454$	44.3444	2.08118
$455$	−7.62984	−0.357693
$456$	21.5892	1.01101
$457$	3.32322	0.155453	0.0777267	−	0.996975i	$-0.475234\pi$
$457$	3.32322	0.155453	0.0777267	+	0.996975i	$0.475234\pi$
$458$	4.97223	0.232337
$459$	20.5385	0.958657
$460$	4.80642	0.224100
$461$	−5.36360	−0.249808	−0.124904	−	0.992169i	$-0.539862\pi$
$461$	−5.36360	−0.249808	−0.124904	+	0.992169i	$0.539862\pi$
$462$	−3.39202	−0.157811
$463$	−14.4281	−0.670530	−0.335265	−	0.942124i	$-0.608826\pi$
$463$	−14.4281	−0.670530	−0.335265	+	0.942124i	$0.608826\pi$
$464$	16.9762	0.788102
$465$	6.39421	0.296525
$466$	−7.73878	−0.358492
$467$	21.3657	0.988685	0.494342	−	0.869267i	$-0.335409\pi$
$467$	21.3657	0.988685	0.494342	+	0.869267i	$0.335409\pi$
$468$	44.1282	2.03983
$469$	19.6381	0.906803
$470$	−0.266098	−0.0122742
$471$	4.40609	0.203022
$472$	4.61861	0.212589
$473$	−3.61317	−0.166134
$474$	−23.6712	−1.08725
$475$	−14.0987	−0.646893
$476$	58.9848	2.70356
$477$	−24.1834	−1.10728
$478$	59.0446	2.70064
$479$	−2.26280	−0.103390	−0.0516950	−	0.998663i	$-0.516462\pi$
$479$	−2.26280	−0.103390	−0.0516950	+	0.998663i	$0.516462\pi$
$480$	10.9391	0.499301
$481$	2.04690	0.0933308
$482$	−11.8470	−0.539615
$483$	−1.73638	−0.0790081
$484$	−53.6629	−2.43922
$485$	7.72156	0.350618
$486$	41.3068	1.87371
$487$	3.19271	0.144676	0.0723378	−	0.997380i	$-0.476954\pi$
$487$	3.19271	0.144676	0.0723378	+	0.997380i	$0.476954\pi$
$488$	−85.3261	−3.86253
$489$	15.6685	0.708553
$490$	4.30586	0.194519
$491$	5.20281	0.234800	0.117400	−	0.993085i	$-0.462544\pi$
$491$	5.20281	0.234800	0.117400	+	0.993085i	$0.462544\pi$
$492$	44.7886	2.01923
$493$	7.05820	0.317885
$494$	32.3568	1.45580
$495$	1.66575	0.0748697
$496$	−108.695	−4.88053
$497$	21.8182	0.978682
$498$	−3.98418	−0.178535
$499$	14.2842	0.639449	0.319724	−	0.947511i	$-0.396410\pi$
$499$	14.2842	0.639449	0.319724	+	0.947511i	$0.396410\pi$
$500$	−43.8417	−1.96066
$501$	4.26288	0.190451
$502$	−27.8618	−1.24353
$503$	0.407622	0.0181749	0.00908747	−	0.999959i	$-0.497107\pi$
$503$	0.407622	0.0181749	0.00908747	+	0.999959i	$0.497107\pi$
$504$	46.6072	2.07605
$505$	13.8754	0.617446
$506$	1.95350	0.0868436
$507$	0.338570	0.0150364
$508$	26.6617	1.18292
$509$	−20.1606	−0.893602	−0.446801	−	0.894633i	$-0.647437\pi$
$509$	−20.1606	−0.893602	−0.446801	+	0.894633i	$0.647437\pi$
$510$	9.46703	0.419207
$511$	−25.7133	−1.13749
$512$	15.1569	0.669845
$513$	14.0344	0.619633
$514$	−75.4085	−3.32613
$515$	−16.1871	−0.713288
$516$	−19.1367	−0.842447
$517$	−0.0778061	−0.00342191
$518$	3.54417	0.155722
$519$	17.4095	0.764193
$520$	27.7321	1.21613
$521$	7.91255	0.346655	0.173328	−	0.984864i	$-0.444548\pi$
$521$	7.91255	0.346655	0.173328	+	0.984864i	$0.444548\pi$
$522$	9.14295	0.400176
$523$	−0.584514	−0.0255590	−0.0127795	−	0.999918i	$-0.504068\pi$
$523$	−0.584514	−0.0255590	−0.0127795	+	0.999918i	$0.504068\pi$
$524$	−90.7032	−3.96239
$525$	7.15649	0.312335
$526$	−39.5951	−1.72643
$527$	−45.1919	−1.96859
$528$	6.65785	0.289746
$529$	1.00000	0.0434783
$530$	−24.9152	−1.08224
$531$	1.34327	0.0582932
$532$	40.3054	1.74746
$533$	40.9465	1.77359
$534$	27.5716	1.19314
$535$	−1.06083	−0.0458638
$536$	−71.3783	−3.08307
$537$	3.84021	0.165717
$538$	−80.6964	−3.47907
$539$	1.25902	0.0542298
$540$	19.7192	0.848581
$541$	−12.7231	−0.547009	−0.273504	−	0.961871i	$-0.588183\pi$
$541$	−12.7231	−0.547009	−0.273504	+	0.961871i	$0.588183\pi$
$542$	−4.36781	−0.187613
$543$	−8.18062	−0.351064
$544$	−77.3137	−3.31480
$545$	−1.15053	−0.0492833
$546$	−16.4243	−0.702894
$547$	33.1977	1.41943	0.709715	−	0.704489i	$-0.248824\pi$
$547$	33.1977	1.41943	0.709715	+	0.704489i	$0.248824\pi$
$548$	−69.5057	−2.96914
$549$	−24.8162	−1.05913
$550$	−8.05134	−0.343310
$551$	4.82300	0.205467
$552$	6.31120	0.268623
$553$	−26.9567	−1.14631
$554$	−19.8542	−0.843525
$555$	0.409232	0.0173709
$556$	−1.82830	−0.0775370
$557$	12.9073	0.546901	0.273450	−	0.961886i	$-0.411835\pi$
$557$	12.9073	0.546901	0.273450	+	0.961886i	$0.411835\pi$
$558$	−58.5401	−2.47820
$559$	−17.4951	−0.739964
$560$	25.9303	1.09576
$561$	2.76813	0.116871
$562$	51.1673	2.15836
$563$	−31.3446	−1.32102	−0.660509	−	0.750818i	$-0.729659\pi$
$563$	−31.3446	−1.32102	−0.660509	+	0.750818i	$0.729659\pi$
$564$	−0.412091	−0.0173521
$565$	−5.39707	−0.227057
$566$	−57.6660	−2.42388
$567$	9.61861	0.403944
$568$	−79.3025	−3.32746
$569$	−36.7390	−1.54018	−0.770090	−	0.637935i	$-0.779789\pi$
$569$	−36.7390	−1.54018	−0.770090	+	0.637935i	$0.779789\pi$
$570$	6.46900	0.270957
$571$	−5.23115	−0.218917	−0.109458	−	0.993991i	$-0.534912\pi$
$571$	−5.23115	−0.218917	−0.109458	+	0.993991i	$0.534912\pi$
$572$	13.2934	0.555824
$573$	−6.83046	−0.285347
$574$	70.8979	2.95922
$575$	−4.12150	−0.171878
$576$	−41.6588	−1.73578
$577$	−32.3734	−1.34772	−0.673860	−	0.738859i	$-0.735365\pi$
$577$	−32.3734	−1.34772	−0.673860	+	0.738859i	$0.735365\pi$
$578$	−21.5222	−0.895205
$579$	12.1026	0.502967
$580$	6.77664	0.281384
$581$	−4.53717	−0.188234
$582$	16.6217	0.688992
$583$	−7.28511	−0.301718
$584$	93.4598	3.86740
$585$	8.06560	0.333472
$586$	−75.7433	−3.12893
$587$	−8.90323	−0.367475	−0.183738	−	0.982975i	$-0.558820\pi$
$587$	−8.90323	−0.367475	−0.183738	+	0.982975i	$0.558820\pi$
$588$	6.66825	0.274994
$589$	−30.8804	−1.27241
$590$	1.38392	0.0569751
$591$	−4.07340	−0.167557
$592$	−6.95649	−0.285910
$593$	−21.0754	−0.865461	−0.432731	−	0.901523i	$-0.642450\pi$
$593$	−21.0754	−0.865461	−0.432731	+	0.901523i	$0.642450\pi$
$594$	8.01460	0.328843
$595$	10.7810	0.441980
$596$	117.214	4.80126
$597$	−20.7272	−0.848309
$598$	9.45891	0.386803
$599$	6.51940	0.266375	0.133188	−	0.991091i	$-0.457479\pi$
$599$	6.51940	0.266375	0.133188	+	0.991091i	$0.457479\pi$
$600$	−26.0116	−1.06192
$601$	−0.0510149	−0.00208094	−0.00104047	−	0.999999i	$-0.500331\pi$
$601$	−0.0510149	−0.00208094	−0.00104047	+	0.999999i	$0.500331\pi$
$602$	−30.2924	−1.23462
$603$	−20.7597	−0.845399
$604$	−16.2433	−0.660932
$605$	−9.80833	−0.398765
$606$	29.8686	1.21333
$607$	18.6029	0.755069	0.377534	−	0.925996i	$-0.376772\pi$
$607$	18.6029	0.755069	0.377534	+	0.925996i	$0.376772\pi$
$608$	−52.8299	−2.14254
$609$	−2.44815	−0.0992039
$610$	−25.5672	−1.03518
$611$	−0.376740	−0.0152413
$612$	−62.3535	−2.52049
$613$	25.4103	1.02631	0.513157	−	0.858295i	$-0.328476\pi$
$613$	25.4103	1.02631	0.513157	+	0.858295i	$0.328476\pi$
$614$	61.9288	2.49924
$615$	8.18631	0.330104
$616$	14.0402	0.565694
$617$	42.3163	1.70359	0.851795	−	0.523875i	$-0.175514\pi$
$617$	42.3163	1.70359	0.851795	+	0.523875i	$0.175514\pi$
$618$	−34.8449	−1.40167
$619$	−9.33578	−0.375237	−0.187618	−	0.982242i	$-0.560077\pi$
$619$	−9.33578	−0.375237	−0.187618	+	0.982242i	$0.560077\pi$
$620$	−43.3891	−1.74255
$621$	4.10269	0.164635
$622$	−6.43225	−0.257910
$623$	31.3985	1.25795
$624$	32.2375	1.29053
$625$	12.5942	0.503770
$626$	37.4191	1.49557
$627$	1.89151	0.0755398
$628$	−29.8984	−1.19307
$629$	−2.89230	−0.115323
$630$	13.9654	0.556395
$631$	−19.7081	−0.784567	−0.392283	−	0.919844i	$-0.628315\pi$
$631$	−19.7081	−0.784567	−0.392283	+	0.919844i	$0.628315\pi$
$632$	97.9791	3.89740
$633$	−4.47150	−0.177726
$634$	67.5373	2.68225
$635$	4.87313	0.193384
$636$	−38.5847	−1.52998
$637$	6.09622	0.241541
$638$	2.75426	0.109042
$639$	−23.0643	−0.912410
$640$	−13.9688	−0.552165
$641$	10.5825	0.417982	0.208991	−	0.977918i	$-0.432982\pi$
$641$	10.5825	0.417982	0.208991	+	0.977918i	$0.432982\pi$
$642$	−2.28359	−0.0901260
$643$	43.8868	1.73073	0.865363	−	0.501146i	$-0.167088\pi$
$643$	43.8868	1.73073	0.865363	+	0.501146i	$0.167088\pi$
$644$	11.7825	0.464297
$645$	−3.49774	−0.137724
$646$	−45.7204	−1.79885
$647$	26.5762	1.04482	0.522409	−	0.852695i	$-0.325034\pi$
$647$	26.5762	1.04482	0.522409	+	0.852695i	$0.325034\pi$
$648$	−34.9607	−1.37338
$649$	0.404654	0.0158841
$650$	−38.9849	−1.52911
$651$	15.6749	0.614347
$652$	−106.321	−4.16386
$653$	−2.95487	−0.115633	−0.0578165	−	0.998327i	$-0.518414\pi$
$653$	−2.95487	−0.115633	−0.0578165	+	0.998327i	$0.518414\pi$
$654$	−2.47667	−0.0968455
$655$	−16.5784	−0.647773
$656$	−139.158	−5.43322
$657$	27.1818	1.06046
$658$	−0.652317	−0.0254300
$659$	36.2928	1.41377	0.706883	−	0.707330i	$-0.250101\pi$
$659$	36.2928	1.41377	0.706883	+	0.707330i	$0.250101\pi$
$660$	2.65771	0.103451
$661$	−5.23603	−0.203658	−0.101829	−	0.994802i	$-0.532469\pi$
$661$	−5.23603	−0.203658	−0.101829	+	0.994802i	$0.532469\pi$
$662$	75.7808	2.94531
$663$	13.4034	0.520544
$664$	16.4912	0.639983
$665$	7.36688	0.285676
$666$	−3.74658	−0.145177
$667$	1.40991	0.0545921
$668$	−28.9265	−1.11920
$669$	13.9901	0.540887
$670$	−21.3878	−0.826284
$671$	−7.47575	−0.288598
$672$	26.8164	1.03447
$673$	−30.3696	−1.17066	−0.585330	−	0.810795i	$-0.699035\pi$
$673$	−30.3696	−1.17066	−0.585330	+	0.810795i	$0.699035\pi$
$674$	37.7933	1.45574
$675$	−16.9092	−0.650836
$676$	−2.29743	−0.0883626
$677$	−19.6931	−0.756867	−0.378433	−	0.925629i	$-0.623537\pi$
$677$	−19.6931	−0.756867	−0.378433	+	0.925629i	$0.623537\pi$
$678$	−11.6179	−0.446184
$679$	18.9288	0.726420
$680$	−39.1857	−1.50270
$681$	12.5519	0.480991
$682$	−17.6349	−0.675274
$683$	46.3060	1.77185	0.885925	−	0.463829i	$-0.153525\pi$
$683$	46.3060	1.77185	0.885925	+	0.463829i	$0.153525\pi$
$684$	−42.6073	−1.62913
$685$	−12.7040	−0.485396
$686$	53.4964	2.04250
$687$	1.40742	0.0536963
$688$	59.4578	2.26681
$689$	−35.2747	−1.34386
$690$	1.89109	0.0719926
$691$	−5.32511	−0.202577	−0.101288	−	0.994857i	$-0.532296\pi$
$691$	−5.32511	−0.202577	−0.101288	+	0.994857i	$0.532296\pi$
$692$	−118.135	−4.49083
$693$	4.08344	0.155117
$694$	16.2292	0.616052
$695$	−0.334170	−0.0126758
$696$	8.89825	0.337287
$697$	−57.8578	−2.19152
$698$	−2.66984	−0.101055
$699$	−2.19051	−0.0828525
$700$	−48.5617	−1.83546
$701$	−42.0504	−1.58822	−0.794111	−	0.607773i	$-0.792063\pi$
$701$	−42.0504	−1.58822	−0.794111	+	0.607773i	$0.792063\pi$
$702$	38.8069	1.46467
$703$	−1.97636	−0.0745398
$704$	−12.5495	−0.472976
$705$	−0.0753205	−0.00283674
$706$	70.6949	2.66064
$707$	34.0143	1.27924
$708$	2.14320	0.0805464
$709$	21.0269	0.789682	0.394841	−	0.918750i	$-0.370800\pi$
$709$	21.0269	0.789682	0.394841	+	0.918750i	$0.370800\pi$
$710$	−23.7622	−0.891781
$711$	28.4962	1.06869
$712$	−114.124	−4.27697
$713$	−9.02733	−0.338076
$714$	23.2076	0.868524
$715$	2.42972	0.0908663
$716$	−26.0585	−0.973850
$717$	16.7129	0.624155
$718$	−75.9369	−2.83394
$719$	40.3727	1.50565	0.752823	−	0.658223i	$-0.228691\pi$
$719$	40.3727	1.50565	0.752823	+	0.658223i	$0.228691\pi$
$720$	−27.4113	−1.02156
$721$	−39.6813	−1.47781
$722$	19.4853	0.725167
$723$	−3.35336	−0.124713
$724$	55.5111	2.06305
$725$	−5.81096	−0.215814
$726$	−21.1137	−0.783605
$727$	11.1236	0.412550	0.206275	−	0.978494i	$-0.433866\pi$
$727$	11.1236	0.412550	0.206275	+	0.978494i	$0.433866\pi$
$728$	67.9829	2.51962
$729$	−0.866590	−0.0320959
$730$	28.0043	1.03649
$731$	24.7207	0.914329
$732$	−39.5944	−1.46345
$733$	15.2465	0.563143	0.281572	−	0.959540i	$-0.409144\pi$
$733$	15.2465	0.563143	0.281572	+	0.959540i	$0.409144\pi$
$734$	83.4857	3.08151
$735$	1.21880	0.0449561
$736$	−15.4438	−0.569268
$737$	−6.25373	−0.230359
$738$	−74.9470	−2.75884
$739$	15.8151	0.581767	0.290883	−	0.956759i	$-0.406051\pi$
$739$	15.8151	0.581767	0.290883	+	0.956759i	$0.406051\pi$
$740$	−2.77692	−0.102082
$741$	9.15878	0.336456
$742$	−61.0774	−2.24222
$743$	−23.6552	−0.867824	−0.433912	−	0.900955i	$-0.642867\pi$
$743$	−23.6552	−0.867824	−0.433912	+	0.900955i	$0.642867\pi$
$744$	−56.9733	−2.08874
$745$	21.4239	0.784911
$746$	67.7907	2.48199
$747$	4.79630	0.175487
$748$	−18.7837	−0.686799
$749$	−2.60055	−0.0950219
$750$	−17.2496	−0.629866
$751$	−27.6955	−1.01062	−0.505312	−	0.862937i	$-0.668623\pi$
$751$	−27.6955	−1.01062	−0.505312	+	0.862937i	$0.668623\pi$
$752$	1.28037	0.0466902
$753$	−7.88644	−0.287398
$754$	13.3362	0.485677
$755$	−2.96890	−0.108049
$756$	48.3401	1.75811
$757$	−23.0246	−0.836843	−0.418421	−	0.908253i	$-0.637416\pi$
$757$	−23.0246	−0.836843	−0.418421	+	0.908253i	$0.637416\pi$
$758$	−41.6755	−1.51372
$759$	0.552949	0.0200708
$760$	−26.7763	−0.971279
$761$	39.3546	1.42660	0.713302	−	0.700857i	$-0.247199\pi$
$761$	39.3546	1.42660	0.713302	+	0.700857i	$0.247199\pi$
$762$	10.4901	0.380015
$763$	−2.82043	−0.102106
$764$	46.3494	1.67686
$765$	−11.3968	−0.412051
$766$	−5.07606	−0.183405
$767$	1.95935	0.0707480
$768$	−4.14679	−0.149635
$769$	36.0734	1.30084	0.650421	−	0.759574i	$-0.274593\pi$
$769$	36.0734	1.30084	0.650421	+	0.759574i	$0.274593\pi$
$770$	4.20700	0.151610
$771$	−21.3448	−0.768715
$772$	−82.1244	−2.95572
$773$	10.7956	0.388290	0.194145	−	0.980973i	$-0.437807\pi$
$773$	10.7956	0.388290	0.194145	+	0.980973i	$0.437807\pi$
$774$	32.0224	1.15102
$775$	37.2061	1.33648
$776$	−68.8002	−2.46978
$777$	1.00320	0.0359895
$778$	−57.9246	−2.07670
$779$	−39.5353	−1.41650
$780$	12.8687	0.460773
$781$	−6.94800	−0.248619
$782$	−13.3655	−0.477950
$783$	5.78444	0.206719
$784$	−20.7183	−0.739938
$785$	−5.46472	−0.195044
$786$	−35.6873	−1.27292
$787$	−32.5414	−1.15997	−0.579987	−	0.814626i	$-0.696942\pi$
$787$	−32.5414	−1.15997	−0.579987	+	0.814626i	$0.696942\pi$
$788$	27.6408	0.984663
$789$	−11.2076	−0.399002
$790$	29.3585	1.04453
$791$	−13.2305	−0.470421
$792$	−14.8420	−0.527388
$793$	−36.1978	−1.28542
$794$	9.28287	0.329437
$795$	−7.05238	−0.250122
$796$	140.648	4.98515
$797$	2.40384	0.0851485	0.0425742	−	0.999093i	$-0.486444\pi$
$797$	2.40384	0.0851485	0.0425742	+	0.999093i	$0.486444\pi$
$798$	15.8582	0.561375
$799$	0.532337	0.0188327
$800$	63.6518	2.25043
$801$	−33.1917	−1.17277
$802$	−16.7502	−0.591469
$803$	8.18838	0.288962
$804$	−33.1221	−1.16813
$805$	2.15357	0.0759035
$806$	−85.3886	−3.00769
$807$	−22.8416	−0.804062
$808$	−123.631	−4.34934
$809$	13.7993	0.485159	0.242579	−	0.970132i	$-0.422007\pi$
$809$	13.7993	0.485159	0.242579	+	0.970132i	$0.422007\pi$
$810$	−10.4756	−0.368076
$811$	18.6755	0.655786	0.327893	−	0.944715i	$-0.393661\pi$
$811$	18.6755	0.655786	0.327893	+	0.944715i	$0.393661\pi$
$812$	16.6124	0.582979
$813$	−1.23633	−0.0433601
$814$	−1.12864	−0.0395587
$815$	−19.4330	−0.680710
$816$	−45.5520	−1.59464
$817$	16.8921	0.590981
$818$	−26.4276	−0.924018
$819$	19.7721	0.690895
$820$	−55.5497	−1.93988
$821$	−49.8993	−1.74150	−0.870749	−	0.491728i	$-0.836366\pi$
$821$	−49.8993	−1.74150	−0.870749	+	0.491728i	$0.836366\pi$
$822$	−27.3471	−0.953840
$823$	−1.00764	−0.0351241	−0.0175621	−	0.999846i	$-0.505590\pi$
$823$	−1.00764	−0.0351241	−0.0175621	+	0.999846i	$0.505590\pi$
$824$	144.229	5.02446
$825$	−2.27898	−0.0793439
$826$	3.39257	0.118043
$827$	−42.7115	−1.48523	−0.742613	−	0.669721i	$-0.766414\pi$
$827$	−42.7115	−1.48523	−0.742613	+	0.669721i	$0.766414\pi$
$828$	−12.4555	−0.432857
$829$	−18.8735	−0.655502	−0.327751	−	0.944764i	$-0.606291\pi$
$829$	−18.8735	−0.655502	−0.327751	+	0.944764i	$0.606291\pi$
$830$	4.94143	0.171520
$831$	−5.61985	−0.194950
$832$	−60.7650	−2.10665
$833$	−8.61401	−0.298458
$834$	−0.719345	−0.0249089
$835$	−5.28710	−0.182968
$836$	−12.8352	−0.443915
$837$	−37.0363	−1.28016
$838$	87.2194	3.01294
$839$	−37.7115	−1.30195	−0.650973	−	0.759101i	$-0.725639\pi$
$839$	−37.7115	−1.30195	−0.650973	+	0.759101i	$0.725639\pi$
$840$	13.5916	0.468956
$841$	−27.0121	−0.931453
$842$	−34.9710	−1.20518
$843$	14.4832	0.498828
$844$	30.3422	1.04442
$845$	−0.419916	−0.0144456
$846$	0.689572	0.0237080
$847$	−24.0443	−0.826172
$848$	119.883	4.11679
$849$	−16.3227	−0.560194
$850$	55.0860	1.88943
$851$	−0.577752	−0.0198051
$852$	−36.7992	−1.26072
$853$	−57.4899	−1.96842	−0.984209	−	0.177012i	$-0.943357\pi$
$853$	−57.4899	−1.96842	−0.984209	+	0.177012i	$0.943357\pi$
$854$	−62.6758	−2.14472
$855$	−7.78762	−0.266331
$856$	9.45217	0.323069
$857$	22.0222	0.752264	0.376132	−	0.926566i	$-0.377254\pi$
$857$	22.0222	0.752264	0.376132	+	0.926566i	$0.377254\pi$
$858$	5.23029	0.178559
$859$	45.3909	1.54872	0.774358	−	0.632748i	$-0.218073\pi$
$859$	45.3909	1.54872	0.774358	+	0.632748i	$0.218073\pi$
$860$	23.7346	0.809343
$861$	20.0681	0.683918
$862$	45.9314	1.56443
$863$	−47.6742	−1.62285	−0.811424	−	0.584458i	$-0.801307\pi$
$863$	−47.6742	−1.62285	−0.811424	+	0.584458i	$0.801307\pi$
$864$	−63.3613	−2.15559
$865$	−21.5924	−0.734163
$866$	79.9886	2.71812
$867$	−6.09198	−0.206895
$868$	−106.365	−3.61026
$869$	8.58433	0.291204
$870$	2.66628	0.0903952
$871$	−30.2808	−1.02603
$872$	10.2514	0.347156
$873$	−20.0098	−0.677230
$874$	−9.13291	−0.308925
$875$	−19.6438	−0.664082
$876$	43.3687	1.46529
$877$	−32.2031	−1.08742	−0.543710	−	0.839273i	$-0.682981\pi$
$877$	−32.2031	−1.08742	−0.543710	+	0.839273i	$0.682981\pi$
$878$	−10.8753	−0.367023
$879$	−21.4396	−0.723139
$880$	−8.25750	−0.278360
$881$	−28.2768	−0.952669	−0.476335	−	0.879264i	$-0.658035\pi$
$881$	−28.2768	−0.952669	−0.476335	+	0.879264i	$0.658035\pi$
$882$	−11.1583	−0.375720
$883$	−3.77521	−0.127046	−0.0635229	−	0.997980i	$-0.520234\pi$
$883$	−3.77521	−0.127046	−0.0635229	+	0.997980i	$0.520234\pi$
$884$	−90.9511	−3.05902
$885$	0.391727	0.0131678
$886$	20.2789	0.681284
$887$	51.9232	1.74341	0.871706	−	0.490030i	$-0.163014\pi$
$887$	51.9232	1.74341	0.871706	+	0.490030i	$0.163014\pi$
$888$	−3.64631	−0.122362
$889$	11.9461	0.400658
$890$	−34.1961	−1.14626
$891$	−3.06304	−0.102616
$892$	−94.9321	−3.17856
$893$	0.363756	0.0121726
$894$	46.1179	1.54241
$895$	−4.76288	−0.159205
$896$	−34.2433	−1.14399
$897$	2.67740	0.0893957
$898$	47.5777	1.58769
$899$	−12.7278	−0.424494
$900$	51.3352	1.71117
$901$	49.8435	1.66053
$902$	−22.5774	−0.751744
$903$	−8.57443	−0.285339
$904$	48.0886	1.59940
$905$	10.1461	0.337269
$906$	−6.39097	−0.212326
$907$	−27.0369	−0.897745	−0.448872	−	0.893596i	$-0.648174\pi$
$907$	−27.0369	−0.897745	−0.448872	+	0.893596i	$0.648174\pi$
$908$	−85.1734	−2.82658
$909$	−35.9569	−1.19262
$910$	20.3704	0.675274
$911$	−1.54550	−0.0512046	−0.0256023	−	0.999672i	$-0.508150\pi$
$911$	−1.54550	−0.0512046	−0.0256023	+	0.999672i	$0.508150\pi$
$912$	−31.1265	−1.03070
$913$	1.44486	0.0478178
$914$	−8.87244	−0.293474
$915$	−7.23693	−0.239246
$916$	−9.55029	−0.315550
$917$	−40.6406	−1.34207
$918$	−54.8346	−1.80981
$919$	−27.7808	−0.916404	−0.458202	−	0.888848i	$-0.651506\pi$
$919$	−27.7808	−0.916404	−0.458202	+	0.888848i	$0.651506\pi$
$920$	−7.82756	−0.258067
$921$	17.5293	0.577610
$922$	14.3199	0.471602
$923$	−33.6424	−1.10735
$924$	6.51514	0.214332
$925$	2.38120	0.0782935
$926$	38.5206	1.26587
$927$	41.9476	1.37774
$928$	−21.7745	−0.714782
$929$	−25.3782	−0.832633	−0.416316	−	0.909220i	$-0.636679\pi$
$929$	−25.3782	−0.832633	−0.416316	+	0.909220i	$0.636679\pi$
$930$	−17.0715	−0.559797
$931$	−5.88611	−0.192910
$932$	14.8641	0.486889
$933$	−1.82069	−0.0596066
$934$	−57.0428	−1.86650
$935$	−3.43321	−0.112278
$936$	−71.8656	−2.34900
$937$	2.48126	0.0810592	0.0405296	−	0.999178i	$-0.487095\pi$
$937$	2.48126	0.0810592	0.0405296	+	0.999178i	$0.487095\pi$
$938$	−52.4305	−1.71192
$939$	10.5917	0.345647
$940$	0.511101	0.0166703
$941$	−40.4105	−1.31734	−0.658672	−	0.752430i	$-0.728881\pi$
$941$	−40.4105	−1.31734	−0.658672	+	0.752430i	$0.728881\pi$
$942$	−11.7635	−0.383277
$943$	−11.5574	−0.376361
$944$	−6.65893	−0.216730
$945$	8.83544	0.287417
$946$	9.64658	0.313637
$947$	12.6371	0.410649	0.205325	−	0.978694i	$-0.434175\pi$
$947$	12.6371	0.410649	0.205325	+	0.978694i	$0.434175\pi$
$948$	45.4658	1.47666
$949$	39.6484	1.28704
$950$	37.6413	1.22124
$951$	19.1168	0.619906
$952$	−96.0605	−3.11334
$953$	8.59996	0.278580	0.139290	−	0.990252i	$-0.455518\pi$
$953$	8.59996	0.278580	0.139290	+	0.990252i	$0.455518\pi$
$954$	64.5657	2.09039
$955$	8.47158	0.274134
$956$	−113.409	−3.66790
$957$	0.779611	0.0252012
$958$	6.04131	0.195186
$959$	−31.1429	−1.00566
$960$	−12.1486	−0.392093
$961$	50.4926	1.62879
$962$	−5.46490	−0.176196
$963$	2.74907	0.0885875
$964$	22.7548	0.732883
$965$	−15.0104	−0.483203
$966$	4.63585	0.149156
$967$	−17.3377	−0.557543	−0.278772	−	0.960357i	$-0.589927\pi$
$967$	−17.3377	−0.557543	−0.278772	+	0.960357i	$0.589927\pi$
$968$	87.3935	2.80893
$969$	−12.9414	−0.415739
$970$	−20.6153	−0.661918
$971$	47.2701	1.51697	0.758484	−	0.651691i	$-0.225940\pi$
$971$	47.2701	1.51697	0.758484	+	0.651691i	$0.225940\pi$
$972$	−79.3391	−2.54480
$973$	−0.819189	−0.0262620
$974$	−8.52402	−0.273127
$975$	−11.0349	−0.353399
$976$	123.020	3.93777
$977$	9.30424	0.297669	0.148834	−	0.988862i	$-0.452448\pi$
$977$	9.30424	0.297669	0.148834	+	0.988862i	$0.452448\pi$
$978$	−41.8323	−1.33765
$979$	−9.99883	−0.319564
$980$	−8.27039	−0.264188
$981$	2.98151	0.0951923
$982$	−13.8907	−0.443269
$983$	−31.9330	−1.01850	−0.509251	−	0.860618i	$-0.670078\pi$
$983$	−31.9330	−1.01850	−0.509251	+	0.860618i	$0.670078\pi$
$984$	−72.9411	−2.32528
$985$	5.05209	0.160973
$986$	−18.8442	−0.600123
$987$	−0.184642	−0.00587722
$988$	−62.1486	−1.97721
$989$	4.93810	0.157022
$990$	−4.44727	−0.141344
$991$	−43.2864	−1.37504	−0.687518	−	0.726167i	$-0.741300\pi$
$991$	−43.2864	−1.37504	−0.687518	+	0.726167i	$0.741300\pi$
$992$	139.417	4.42648
$993$	21.4502	0.680702
$994$	−58.2511	−1.84761
$995$	25.7073	0.814975
$996$	7.65252	0.242479
$997$	17.7662	0.562662	0.281331	−	0.959611i	$-0.409224\pi$
$997$	17.7662	0.562662	0.281331	+	0.959611i	$0.409224\pi$
$998$	−38.1365	−1.20719
$999$	−2.37034	−0.0749941

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.c.1.5	✓	143

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.c.1.5	✓	143	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8027 = 23 \cdot 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.66984 q^{2} -0.755713 q^{3} +5.12803 q^{4} +0.937284 q^{5} +2.01763 q^{6} +2.29767 q^{7} -8.35133 q^{8} -2.42890 q^{9} +O(q^{10})\)	\(q-2.66984 q^{2} -0.755713 q^{3} +5.12803 q^{4} +0.937284 q^{5} +2.01763 q^{6} +2.29767 q^{7} -8.35133 q^{8} -2.42890 q^{9} -2.50240 q^{10} -0.731692 q^{11} -3.87532 q^{12} -3.54288 q^{13} -6.13441 q^{14} -0.708317 q^{15} +12.0406 q^{16} +5.00612 q^{17} +6.48476 q^{18} +3.42077 q^{19} +4.80642 q^{20} -1.73638 q^{21} +1.95350 q^{22} +1.00000 q^{23} +6.31120 q^{24} -4.12150 q^{25} +9.45891 q^{26} +4.10269 q^{27} +11.7825 q^{28} +1.40991 q^{29} +1.89109 q^{30} -9.02733 q^{31} -15.4438 q^{32} +0.552949 q^{33} -13.3655 q^{34} +2.15357 q^{35} -12.4555 q^{36} -0.577752 q^{37} -9.13291 q^{38} +2.67740 q^{39} -7.82756 q^{40} -11.5574 q^{41} +4.63585 q^{42} +4.93810 q^{43} -3.75214 q^{44} -2.27657 q^{45} -2.66984 q^{46} +0.106337 q^{47} -9.09925 q^{48} -1.72070 q^{49} +11.0037 q^{50} -3.78319 q^{51} -18.1680 q^{52} +9.95652 q^{53} -10.9535 q^{54} -0.685803 q^{55} -19.1886 q^{56} -2.58512 q^{57} -3.76424 q^{58} -0.553039 q^{59} -3.63227 q^{60} +10.2171 q^{61} +24.1015 q^{62} -5.58081 q^{63} +17.1513 q^{64} -3.32068 q^{65} -1.47628 q^{66} +8.54694 q^{67} +25.6715 q^{68} -0.755713 q^{69} -5.74969 q^{70} +9.49580 q^{71} +20.2845 q^{72} -11.1910 q^{73} +1.54250 q^{74} +3.11467 q^{75} +17.5418 q^{76} -1.68119 q^{77} -7.14822 q^{78} -11.7322 q^{79} +11.2855 q^{80} +4.18624 q^{81} +30.8564 q^{82} -1.97468 q^{83} -8.90421 q^{84} +4.69216 q^{85} -13.1839 q^{86} -1.06549 q^{87} +6.11060 q^{88} +13.6653 q^{89} +6.07806 q^{90} -8.14038 q^{91} +5.12803 q^{92} +6.82207 q^{93} -0.283903 q^{94} +3.20624 q^{95} +11.6711 q^{96} +8.23823 q^{97} +4.59398 q^{98} +1.77721 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9}+O(q^{10}) \) 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9	\( 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9} - 22 q^{10} - 14 q^{11} - 36 q^{12} - 87 q^{13} - 18 q^{14} - 19 q^{15} + 81 q^{16} - 14 q^{17} - 60 q^{18} - 18 q^{19} - 25 q^{20} - 26 q^{21} - 62 q^{22} + 143 q^{23} - 21 q^{24} + 67 q^{25} - 5 q^{26} - 47 q^{27} - 76 q^{28} - 54 q^{29} - 22 q^{30} - 62 q^{31} - 117 q^{32} - 59 q^{33} - 35 q^{34} - 52 q^{35} + 52 q^{36} - 190 q^{37} - 19 q^{38} - 43 q^{39} - 41 q^{40} - 50 q^{41} + 8 q^{42} - 50 q^{43} - 18 q^{44} - 75 q^{45} - 17 q^{46} - 63 q^{47} - 35 q^{48} + 74 q^{49} - 53 q^{50} - 33 q^{51} - 124 q^{52} - 100 q^{53} - 46 q^{54} - 61 q^{55} - 3 q^{56} - 80 q^{57} - 112 q^{58} - 109 q^{59} - 55 q^{60} - 76 q^{61} - 6 q^{62} - 93 q^{63} + 57 q^{64} - 17 q^{65} + 50 q^{66} - 120 q^{67} + 26 q^{68} - 17 q^{69} - 109 q^{71} - 153 q^{72} - 94 q^{73} + 35 q^{74} - 105 q^{75} - 16 q^{76} - 52 q^{77} - 59 q^{78} - 29 q^{79} - 30 q^{80} + 39 q^{81} - 65 q^{82} + 8 q^{83} + 11 q^{84} - 155 q^{85} - 15 q^{86} - 25 q^{87} - 139 q^{88} + 6 q^{89} + 82 q^{90} - 34 q^{91} + 121 q^{92} - 151 q^{93} - 3 q^{94} - 70 q^{95} - 23 q^{96} - 203 q^{97} - 18 q^{98} - 49 q^{99}+O(q^{100}) \) 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9 - 22 * q^10 - 14 * q^11 - 36 * q^12 - 87 * q^13 - 18 * q^14 - 19 * q^15 + 81 * q^16 - 14 * q^17 - 60 * q^18 - 18 * q^19 - 25 * q^20 - 26 * q^21 - 62 * q^22 + 143 * q^23 - 21 * q^24 + 67 * q^25 - 5 * q^26 - 47 * q^27 - 76 * q^28 - 54 * q^29 - 22 * q^30 - 62 * q^31 - 117 * q^32 - 59 * q^33 - 35 * q^34 - 52 * q^35 + 52 * q^36 - 190 * q^37 - 19 * q^38 - 43 * q^39 - 41 * q^40 - 50 * q^41 + 8 * q^42 - 50 * q^43 - 18 * q^44 - 75 * q^45 - 17 * q^46 - 63 * q^47 - 35 * q^48 + 74 * q^49 - 53 * q^50 - 33 * q^51 - 124 * q^52 - 100 * q^53 - 46 * q^54 - 61 * q^55 - 3 * q^56 - 80 * q^57 - 112 * q^58 - 109 * q^59 - 55 * q^60 - 76 * q^61 - 6 * q^62 - 93 * q^63 + 57 * q^64 - 17 * q^65 + 50 * q^66 - 120 * q^67 + 26 * q^68 - 17 * q^69 - 109 * q^71 - 153 * q^72 - 94 * q^73 + 35 * q^74 - 105 * q^75 - 16 * q^76 - 52 * q^77 - 59 * q^78 - 29 * q^79 - 30 * q^80 + 39 * q^81 - 65 * q^82 + 8 * q^83 + 11 * q^84 - 155 * q^85 - 15 * q^86 - 25 * q^87 - 139 * q^88 + 6 * q^89 + 82 * q^90 - 34 * q^91 + 121 * q^92 - 151 * q^93 - 3 * q^94 - 70 * q^95 - 23 * q^96 - 203 * q^97 - 18 * q^98 - 49 * q^99

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