LMFDB - Embedded newform 2013.2.a.h.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2013,2,Mod(1,2013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2013, 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("2013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2013 = 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2013.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:	$16.0738859269$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} - 21 x^{12} + 20 x^{11} + 167 x^{10} - 148 x^{9} - 627 x^{8} + 497 x^{7} + 1123 x^{6} + \cdots - 1 $ x^14 - x^13 - 21x^12 + 20x^11 + 167x^10 - 148x^9 - 627x^8 + 497x^7 + 1123x^6 - 745x^5 - 802x^4 + 386x^3 + 74x^2 - 15x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-1.18140$ of defining polynomial
Character	$\chi$	$=$	2013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.18140 q^{2} -1.00000 q^{3} -0.604292 q^{4} -2.90081 q^{5} -1.18140 q^{6} -0.528840 q^{7} -3.07671 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.18140 q^{2} -1.00000 q^{3} -0.604292 q^{4} -2.90081 q^{5} -1.18140 q^{6} -0.528840 q^{7} -3.07671 q^{8} +1.00000 q^{9} -3.42702 q^{10} -1.00000 q^{11} +0.604292 q^{12} -0.150802 q^{13} -0.624772 q^{14} +2.90081 q^{15} -2.42625 q^{16} +0.0673519 q^{17} +1.18140 q^{18} -0.482246 q^{19} +1.75293 q^{20} +0.528840 q^{21} -1.18140 q^{22} -4.10835 q^{23} +3.07671 q^{24} +3.41469 q^{25} -0.178158 q^{26} -1.00000 q^{27} +0.319574 q^{28} -5.83447 q^{29} +3.42702 q^{30} -2.84419 q^{31} +3.28705 q^{32} +1.00000 q^{33} +0.0795696 q^{34} +1.53406 q^{35} -0.604292 q^{36} +6.02828 q^{37} -0.569726 q^{38} +0.150802 q^{39} +8.92495 q^{40} +11.4101 q^{41} +0.624772 q^{42} +11.3555 q^{43} +0.604292 q^{44} -2.90081 q^{45} -4.85361 q^{46} -3.90970 q^{47} +2.42625 q^{48} -6.72033 q^{49} +4.03411 q^{50} -0.0673519 q^{51} +0.0911284 q^{52} -0.588357 q^{53} -1.18140 q^{54} +2.90081 q^{55} +1.62709 q^{56} +0.482246 q^{57} -6.89285 q^{58} +11.9392 q^{59} -1.75293 q^{60} +1.00000 q^{61} -3.36013 q^{62} -0.528840 q^{63} +8.73582 q^{64} +0.437448 q^{65} +1.18140 q^{66} +9.38126 q^{67} -0.0407002 q^{68} +4.10835 q^{69} +1.81234 q^{70} +12.6773 q^{71} -3.07671 q^{72} +13.0690 q^{73} +7.12182 q^{74} -3.41469 q^{75} +0.291417 q^{76} +0.528840 q^{77} +0.178158 q^{78} +9.65447 q^{79} +7.03808 q^{80} +1.00000 q^{81} +13.4799 q^{82} -11.6417 q^{83} -0.319574 q^{84} -0.195375 q^{85} +13.4154 q^{86} +5.83447 q^{87} +3.07671 q^{88} -12.7098 q^{89} -3.42702 q^{90} +0.0797502 q^{91} +2.48264 q^{92} +2.84419 q^{93} -4.61892 q^{94} +1.39890 q^{95} -3.28705 q^{96} -1.66875 q^{97} -7.93940 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - q^{2} - 14 q^{3} + 15 q^{4} + q^{5} + q^{6} + 9 q^{7} + 14 q^{9}+O(q^{10}) $ 14 * q - q^2 - 14 * q^3 + 15 * q^4 + q^5 + q^6 + 9 * q^7 + 14 * q^9	\( 14 q - q^{2} - 14 q^{3} + 15 q^{4} + q^{5} + q^{6} + 9 q^{7} + 14 q^{9} + 6 q^{10} - 14 q^{11} - 15 q^{12} + q^{13} - 7 q^{14} - q^{15} + 17 q^{16} - 9 q^{17} - q^{18} + 22 q^{19} + 23 q^{20} - 9 q^{21} + q^{22} + q^{23} + 25 q^{25} + 4 q^{26} - 14 q^{27} + 37 q^{28} - 6 q^{29} - 6 q^{30} + 9 q^{31} + 4 q^{32} + 14 q^{33} + 8 q^{34} + 18 q^{35} + 15 q^{36} + 18 q^{37} + 8 q^{38} - q^{39} + 16 q^{40} - 25 q^{41} + 7 q^{42} + 25 q^{43} - 15 q^{44} + q^{45} + 20 q^{46} + 36 q^{47} - 17 q^{48} + 25 q^{49} + 2 q^{50} + 9 q^{51} - 13 q^{52} + q^{54} - q^{55} - 40 q^{56} - 22 q^{57} + 33 q^{58} + 17 q^{59} - 23 q^{60} + 14 q^{61} - 13 q^{62} + 9 q^{63} - 6 q^{64} - 61 q^{65} - q^{66} + 22 q^{67} + 66 q^{68} - q^{69} + 44 q^{70} - 13 q^{71} + 20 q^{73} - 12 q^{74} - 25 q^{75} + 49 q^{76} - 9 q^{77} - 4 q^{78} + 31 q^{79} + 88 q^{80} + 14 q^{81} + 2 q^{82} + 32 q^{83} - 37 q^{84} + 2 q^{85} - 14 q^{86} + 6 q^{87} - 21 q^{89} + 6 q^{90} + 45 q^{91} - 14 q^{92} - 9 q^{93} - 31 q^{94} + 23 q^{95} - 4 q^{96} + 37 q^{97} - 38 q^{98} - 14 q^{99}+O(q^{100}) \) 14 * q - q^2 - 14 * q^3 + 15 * q^4 + q^5 + q^6 + 9 * q^7 + 14 * q^9 + 6 * q^10 - 14 * q^11 - 15 * q^12 + q^13 - 7 * q^14 - q^15 + 17 * q^16 - 9 * q^17 - q^18 + 22 * q^19 + 23 * q^20 - 9 * q^21 + q^22 + q^23 + 25 * q^25 + 4 * q^26 - 14 * q^27 + 37 * q^28 - 6 * q^29 - 6 * q^30 + 9 * q^31 + 4 * q^32 + 14 * q^33 + 8 * q^34 + 18 * q^35 + 15 * q^36 + 18 * q^37 + 8 * q^38 - q^39 + 16 * q^40 - 25 * q^41 + 7 * q^42 + 25 * q^43 - 15 * q^44 + q^45 + 20 * q^46 + 36 * q^47 - 17 * q^48 + 25 * q^49 + 2 * q^50 + 9 * q^51 - 13 * q^52 + q^54 - q^55 - 40 * q^56 - 22 * q^57 + 33 * q^58 + 17 * q^59 - 23 * q^60 + 14 * q^61 - 13 * q^62 + 9 * q^63 - 6 * q^64 - 61 * q^65 - q^66 + 22 * q^67 + 66 * q^68 - q^69 + 44 * q^70 - 13 * q^71 + 20 * q^73 - 12 * q^74 - 25 * q^75 + 49 * q^76 - 9 * q^77 - 4 * q^78 + 31 * q^79 + 88 * q^80 + 14 * q^81 + 2 * q^82 + 32 * q^83 - 37 * q^84 + 2 * q^85 - 14 * q^86 + 6 * q^87 - 21 * q^89 + 6 * q^90 + 45 * q^91 - 14 * q^92 - 9 * q^93 - 31 * q^94 + 23 * q^95 - 4 * q^96 + 37 * q^97 - 38 * q^98 - 14 * 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 $

$2$	1.18140	0.835377	0.417688	−	0.908590i	$-0.362840\pi$
$2$	1.18140	0.835377	0.417688	+	0.908590i	$0.362840\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.604292	−0.302146
$5$	−2.90081	−1.29728	−0.648640	−	0.761095i	$-0.724662\pi$
$5$	−2.90081	−1.29728	−0.648640	+	0.761095i	$0.724662\pi$
$6$	−1.18140	−0.482305
$7$	−0.528840	−0.199883	−0.0999414	−	0.994993i	$-0.531866\pi$
$7$	−0.528840	−0.199883	−0.0999414	+	0.994993i	$0.531866\pi$
$8$	−3.07671	−1.08778
$9$	1.00000	0.333333
$10$	−3.42702	−1.08372
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.604292	0.174444
$13$	−0.150802	−0.0418250	−0.0209125	−	0.999781i	$-0.506657\pi$
$13$	−0.150802	−0.0418250	−0.0209125	+	0.999781i	$0.506657\pi$
$14$	−0.624772	−0.166977
$15$	2.90081	0.748985
$16$	−2.42625	−0.606562
$17$	0.0673519	0.0163352	0.00816762	−	0.999967i	$-0.497400\pi$
$17$	0.0673519	0.0163352	0.00816762	+	0.999967i	$0.497400\pi$
$18$	1.18140	0.278459
$19$	−0.482246	−0.110635	−0.0553174	−	0.998469i	$-0.517617\pi$
$19$	−0.482246	−0.110635	−0.0553174	+	0.998469i	$0.517617\pi$
$20$	1.75293	0.391968
$21$	0.528840	0.115402
$22$	−1.18140	−0.251876
$23$	−4.10835	−0.856651	−0.428325	−	0.903625i	$-0.640896\pi$
$23$	−4.10835	−0.856651	−0.428325	+	0.903625i	$0.640896\pi$
$24$	3.07671	0.628031
$25$	3.41469	0.682937
$26$	−0.178158	−0.0349396
$27$	−1.00000	−0.192450
$28$	0.319574	0.0603937
$29$	−5.83447	−1.08343	−0.541717	−	0.840561i	$-0.682226\pi$
$29$	−5.83447	−1.08343	−0.541717	+	0.840561i	$0.682226\pi$
$30$	3.42702	0.625685
$31$	−2.84419	−0.510832	−0.255416	−	0.966831i	$-0.582213\pi$
$31$	−2.84419	−0.510832	−0.255416	+	0.966831i	$0.582213\pi$
$32$	3.28705	0.581074
$33$	1.00000	0.174078
$34$	0.0795696	0.0136461
$35$	1.53406	0.259304
$36$	−0.604292	−0.100715
$37$	6.02828	0.991043	0.495522	−	0.868596i	$-0.334977\pi$
$37$	6.02828	0.991043	0.495522	+	0.868596i	$0.334977\pi$
$38$	−0.569726	−0.0924217
$39$	0.150802	0.0241477
$40$	8.92495	1.41116
$41$	11.4101	1.78196	0.890982	−	0.454038i	$-0.150017\pi$
$41$	11.4101	1.78196	0.890982	+	0.454038i	$0.150017\pi$
$42$	0.624772	0.0964044
$43$	11.3555	1.73170	0.865849	−	0.500305i	$-0.166779\pi$
$43$	11.3555	1.73170	0.865849	+	0.500305i	$0.166779\pi$
$44$	0.604292	0.0911004
$45$	−2.90081	−0.432427
$46$	−4.85361	−0.715626
$47$	−3.90970	−0.570288	−0.285144	−	0.958485i	$-0.592041\pi$
$47$	−3.90970	−0.570288	−0.285144	+	0.958485i	$0.592041\pi$
$48$	2.42625	0.350199
$49$	−6.72033	−0.960047
$50$	4.03411	0.570510
$51$	−0.0673519	−0.00943115
$52$	0.0911284	0.0126372
$53$	−0.588357	−0.0808171	−0.0404085	−	0.999183i	$-0.512866\pi$
$53$	−0.588357	−0.0808171	−0.0404085	+	0.999183i	$0.512866\pi$
$54$	−1.18140	−0.160768
$55$	2.90081	0.391145
$56$	1.62709	0.217429
$57$	0.482246	0.0638750
$58$	−6.89285	−0.905076
$59$	11.9392	1.55435	0.777176	−	0.629284i	$-0.216652\pi$
$59$	11.9392	1.55435	0.777176	+	0.629284i	$0.216652\pi$
$60$	−1.75293	−0.226303
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	−3.36013	−0.426738
$63$	−0.528840	−0.0666276
$64$	8.73582	1.09198
$65$	0.437448	0.0542587
$66$	1.18140	0.145420
$67$	9.38126	1.14610	0.573052	−	0.819519i	$-0.305759\pi$
$67$	9.38126	1.14610	0.573052	+	0.819519i	$0.305759\pi$
$68$	−0.0407002	−0.00493562
$69$	4.10835	0.494587
$70$	1.81234	0.216617
$71$	12.6773	1.50452	0.752258	−	0.658869i	$-0.228965\pi$
$71$	12.6773	1.50452	0.752258	+	0.658869i	$0.228965\pi$
$72$	−3.07671	−0.362594
$73$	13.0690	1.52961	0.764806	−	0.644261i	$-0.222835\pi$
$73$	13.0690	1.52961	0.764806	+	0.644261i	$0.222835\pi$
$74$	7.12182	0.827894
$75$	−3.41469	−0.394294
$76$	0.291417	0.0334278
$77$	0.528840	0.0602669
$78$	0.178158	0.0201724
$79$	9.65447	1.08621	0.543107	−	0.839664i	$-0.317248\pi$
$79$	9.65447	1.08621	0.543107	+	0.839664i	$0.317248\pi$
$80$	7.03808	0.786881
$81$	1.00000	0.111111
$82$	13.4799	1.48861
$83$	−11.6417	−1.27784	−0.638919	−	0.769274i	$-0.720618\pi$
$83$	−11.6417	−1.27784	−0.638919	+	0.769274i	$0.720618\pi$
$84$	−0.319574	−0.0348683
$85$	−0.195375	−0.0211914
$86$	13.4154	1.44662
$87$	5.83447	0.625521
$88$	3.07671	0.327979
$89$	−12.7098	−1.34724	−0.673620	−	0.739078i	$-0.735262\pi$
$89$	−12.7098	−1.34724	−0.673620	+	0.739078i	$0.735262\pi$
$90$	−3.42702	−0.361239
$91$	0.0797502	0.00836009
$92$	2.48264	0.258833
$93$	2.84419	0.294929
$94$	−4.61892	−0.476406
$95$	1.39890	0.143524
$96$	−3.28705	−0.335483
$97$	−1.66875	−0.169436	−0.0847178	−	0.996405i	$-0.526999\pi$
$97$	−1.66875	−0.169436	−0.0847178	+	0.996405i	$0.526999\pi$
$98$	−7.93940	−0.802001
$99$	−1.00000	−0.100504
$100$	−2.06347	−0.206347
$101$	7.21215	0.717636	0.358818	−	0.933408i	$-0.383180\pi$
$101$	7.21215	0.717636	0.358818	+	0.933408i	$0.383180\pi$
$102$	−0.0795696	−0.00787856
$103$	10.7724	1.06143	0.530717	−	0.847549i	$-0.321923\pi$
$103$	10.7724	1.06143	0.530717	+	0.847549i	$0.321923\pi$
$104$	0.463975	0.0454965
$105$	−1.53406	−0.149709
$106$	−0.695086	−0.0675127
$107$	−2.91453	−0.281759	−0.140879	−	0.990027i	$-0.544993\pi$
$107$	−2.91453	−0.281759	−0.140879	+	0.990027i	$0.544993\pi$
$108$	0.604292	0.0581480
$109$	−15.6562	−1.49960	−0.749798	−	0.661667i	$-0.769849\pi$
$109$	−15.6562	−1.49960	−0.749798	+	0.661667i	$0.769849\pi$
$110$	3.42702	0.326753
$111$	−6.02828	−0.572179
$112$	1.28310	0.121241
$113$	−17.6863	−1.66379	−0.831895	−	0.554933i	$-0.812744\pi$
$113$	−17.6863	−1.66379	−0.831895	+	0.554933i	$0.812744\pi$
$114$	0.569726	0.0533597
$115$	11.9175	1.11132
$116$	3.52572	0.327355
$117$	−0.150802	−0.0139417
$118$	14.1050	1.29847
$119$	−0.0356184	−0.00326513
$120$	−8.92495	−0.814733
$121$	1.00000	0.0909091
$122$	1.18140	0.106959
$123$	−11.4101	−1.02882
$124$	1.71872	0.154346
$125$	4.59869	0.411319
$126$	−0.624772	−0.0556591
$127$	−20.8464	−1.84981	−0.924907	−	0.380192i	$-0.875858\pi$
$127$	−20.8464	−1.84981	−0.924907	+	0.380192i	$0.875858\pi$
$128$	3.74641	0.331139
$129$	−11.3555	−0.999797
$130$	0.516801	0.0453265
$131$	−8.61884	−0.753031	−0.376516	−	0.926410i	$-0.622878\pi$
$131$	−8.61884	−0.753031	−0.376516	+	0.926410i	$0.622878\pi$
$132$	−0.604292	−0.0525968
$133$	0.255031	0.0221140
$134$	11.0830	0.957428
$135$	2.90081	0.249662
$136$	−0.207222	−0.0177692
$137$	3.31289	0.283039	0.141520	−	0.989935i	$-0.454801\pi$
$137$	3.31289	0.283039	0.141520	+	0.989935i	$0.454801\pi$
$138$	4.85361	0.413167
$139$	16.9686	1.43926	0.719628	−	0.694360i	$-0.244312\pi$
$139$	16.9686	1.43926	0.719628	+	0.694360i	$0.244312\pi$
$140$	−0.927022	−0.0783476
$141$	3.90970	0.329256
$142$	14.9769	1.25684
$143$	0.150802	0.0126107
$144$	−2.42625	−0.202187
$145$	16.9247	1.40552
$146$	15.4397	1.27780
$147$	6.72033	0.554283
$148$	−3.64284	−0.299440
$149$	−10.5728	−0.866156	−0.433078	−	0.901356i	$-0.642573\pi$
$149$	−10.5728	−0.866156	−0.433078	+	0.901356i	$0.642573\pi$
$150$	−4.03411	−0.329384
$151$	−11.7619	−0.957168	−0.478584	−	0.878042i	$-0.658850\pi$
$151$	−11.7619	−0.957168	−0.478584	+	0.878042i	$0.658850\pi$
$152$	1.48373	0.120347
$153$	0.0673519	0.00544508
$154$	0.624772	0.0503456
$155$	8.25046	0.662693
$156$	−0.0911284	−0.00729611
$157$	14.7885	1.18025	0.590126	−	0.807311i	$-0.299078\pi$
$157$	14.7885	1.18025	0.590126	+	0.807311i	$0.299078\pi$
$158$	11.4058	0.907397
$159$	0.588357	0.0466598
$160$	−9.53511	−0.753817
$161$	2.17266	0.171230
$162$	1.18140	0.0928196
$163$	−20.8054	−1.62961	−0.814803	−	0.579739i	$-0.803155\pi$
$163$	−20.8054	−1.62961	−0.814803	+	0.579739i	$0.803155\pi$
$164$	−6.89505	−0.538413
$165$	−2.90081	−0.225828
$166$	−13.7535	−1.06748
$167$	−13.2699	−1.02686	−0.513430	−	0.858132i	$-0.671625\pi$
$167$	−13.2699	−1.02686	−0.513430	+	0.858132i	$0.671625\pi$
$168$	−1.62709	−0.125533
$169$	−12.9773	−0.998251
$170$	−0.230816	−0.0177028
$171$	−0.482246	−0.0368783
$172$	−6.86204	−0.523226
$173$	12.4101	0.943521	0.471760	−	0.881727i	$-0.343619\pi$
$173$	12.4101	0.943521	0.471760	+	0.881727i	$0.343619\pi$
$174$	6.89285	0.522546
$175$	−1.80582	−0.136507
$176$	2.42625	0.182885
$177$	−11.9392	−0.897405
$178$	−15.0154	−1.12545
$179$	8.62506	0.644668	0.322334	−	0.946626i	$-0.395533\pi$
$179$	8.62506	0.644668	0.322334	+	0.946626i	$0.395533\pi$
$180$	1.75293	0.130656
$181$	−1.29192	−0.0960277	−0.0480139	−	0.998847i	$-0.515289\pi$
$181$	−1.29192	−0.0960277	−0.0480139	+	0.998847i	$0.515289\pi$
$182$	0.0942169	0.00698382
$183$	−1.00000	−0.0739221
$184$	12.6402	0.931849
$185$	−17.4869	−1.28566
$186$	3.36013	0.246377
$187$	−0.0673519	−0.00492526
$188$	2.36260	0.172310
$189$	0.528840	0.0384675
$190$	1.65266	0.119897
$191$	9.07558	0.656686	0.328343	−	0.944559i	$-0.393510\pi$
$191$	9.07558	0.656686	0.328343	+	0.944559i	$0.393510\pi$
$192$	−8.73582	−0.630454
$193$	21.0767	1.51713	0.758566	−	0.651596i	$-0.225900\pi$
$193$	21.0767	1.51713	0.758566	+	0.651596i	$0.225900\pi$
$194$	−1.97146	−0.141543
$195$	−0.437448	−0.0313263
$196$	4.06104	0.290074
$197$	6.18993	0.441014	0.220507	−	0.975385i	$-0.429229\pi$
$197$	6.18993	0.441014	0.220507	+	0.975385i	$0.429229\pi$
$198$	−1.18140	−0.0839585
$199$	−20.3389	−1.44179	−0.720894	−	0.693045i	$-0.756269\pi$
$199$	−20.3389	−1.44179	−0.720894	+	0.693045i	$0.756269\pi$
$200$	−10.5060	−0.742887
$201$	−9.38126	−0.661703
$202$	8.52045	0.599496
$203$	3.08550	0.216560
$204$	0.0407002	0.00284958
$205$	−33.0986	−2.31171
$206$	12.7265	0.886697
$207$	−4.10835	−0.285550
$208$	0.365883	0.0253694
$209$	0.482246	0.0333576
$210$	−1.81234	−0.125064
$211$	28.7585	1.97981	0.989907	−	0.141717i	$-0.0452623\pi$
$211$	28.7585	1.97981	0.989907	+	0.141717i	$0.0452623\pi$
$212$	0.355539	0.0244185
$213$	−12.6773	−0.868633
$214$	−3.44323	−0.235374
$215$	−32.9401	−2.24650
$216$	3.07671	0.209344
$217$	1.50412	0.102107
$218$	−18.4963	−1.25273
$219$	−13.0690	−0.883122
$220$	−1.75293	−0.118183
$221$	−0.0101568	−0.000683220 0
$222$	−7.12182	−0.477985
$223$	−21.4498	−1.43639	−0.718194	−	0.695843i	$-0.755031\pi$
$223$	−21.4498	−1.43639	−0.718194	+	0.695843i	$0.755031\pi$
$224$	−1.73833	−0.116147
$225$	3.41469	0.227646
$226$	−20.8946	−1.38989
$227$	20.1374	1.33657	0.668283	−	0.743908i	$-0.267030\pi$
$227$	20.1374	1.33657	0.668283	+	0.743908i	$0.267030\pi$
$228$	−0.291417	−0.0192996
$229$	23.4322	1.54844	0.774221	−	0.632915i	$-0.218142\pi$
$229$	23.4322	1.54844	0.774221	+	0.632915i	$0.218142\pi$
$230$	14.0794	0.928368
$231$	−0.528840	−0.0347951
$232$	17.9510	1.17854
$233$	−1.49700	−0.0980719	−0.0490360	−	0.998797i	$-0.515615\pi$
$233$	−1.49700	−0.0980719	−0.0490360	+	0.998797i	$0.515615\pi$
$234$	−0.178158	−0.0116465
$235$	11.3413	0.739824
$236$	−7.21476	−0.469641
$237$	−9.65447	−0.627125
$238$	−0.0420796	−0.00272761
$239$	11.3579	0.734680	0.367340	−	0.930087i	$-0.380269\pi$
$239$	11.3579	0.734680	0.367340	+	0.930087i	$0.380269\pi$
$240$	−7.03808	−0.454306
$241$	19.2590	1.24058	0.620290	−	0.784373i	$-0.287015\pi$
$241$	19.2590	1.24058	0.620290	+	0.784373i	$0.287015\pi$
$242$	1.18140	0.0759433
$243$	−1.00000	−0.0641500
$244$	−0.604292	−0.0386858
$245$	19.4944	1.24545
$246$	−13.4799	−0.859450
$247$	0.0727237	0.00462730
$248$	8.75077	0.555675
$249$	11.6417	0.737760
$250$	5.43290	0.343607
$251$	−9.41617	−0.594344	−0.297172	−	0.954824i	$-0.596043\pi$
$251$	−9.41617	−0.594344	−0.297172	+	0.954824i	$0.596043\pi$
$252$	0.319574	0.0201312
$253$	4.10835	0.258290
$254$	−24.6279	−1.54529
$255$	0.195375	0.0122348
$256$	−13.0456	−0.815353
$257$	15.6633	0.977049	0.488524	−	0.872550i	$-0.337535\pi$
$257$	15.6633	0.977049	0.488524	+	0.872550i	$0.337535\pi$
$258$	−13.4154	−0.835207
$259$	−3.18800	−0.198092
$260$	−0.264346	−0.0163940
$261$	−5.83447	−0.361145
$262$	−10.1823	−0.629065
$263$	−7.59913	−0.468582	−0.234291	−	0.972166i	$-0.575277\pi$
$263$	−7.59913	−0.468582	−0.234291	+	0.972166i	$0.575277\pi$
$264$	−3.07671	−0.189359
$265$	1.70671	0.104842
$266$	0.301294	0.0184735
$267$	12.7098	0.777830
$268$	−5.66902	−0.346290
$269$	−24.2461	−1.47831	−0.739154	−	0.673536i	$-0.764774\pi$
$269$	−24.2461	−1.47831	−0.739154	+	0.673536i	$0.764774\pi$
$270$	3.42702	0.208562
$271$	3.99382	0.242607	0.121304	−	0.992615i	$-0.461293\pi$
$271$	3.99382	0.242607	0.121304	+	0.992615i	$0.461293\pi$
$272$	−0.163412	−0.00990833
$273$	−0.0797502	−0.00482670
$274$	3.91385	0.236445
$275$	−3.41469	−0.205913
$276$	−2.48264	−0.149438
$277$	7.93878	0.476995	0.238497	−	0.971143i	$-0.423345\pi$
$277$	7.93878	0.476995	0.238497	+	0.971143i	$0.423345\pi$
$278$	20.0467	1.20232
$279$	−2.84419	−0.170277
$280$	−4.71987	−0.282066
$281$	3.12368	0.186343	0.0931717	−	0.995650i	$-0.470299\pi$
$281$	3.12368	0.186343	0.0931717	+	0.995650i	$0.470299\pi$
$282$	4.61892	0.275053
$283$	5.18624	0.308290	0.154145	−	0.988048i	$-0.450738\pi$
$283$	5.18624	0.308290	0.154145	+	0.988048i	$0.450738\pi$
$284$	−7.66077	−0.454583
$285$	−1.39890	−0.0828638
$286$	0.178158	0.0105347
$287$	−6.03414	−0.356184
$288$	3.28705	0.193691
$289$	−16.9955	−0.999733
$290$	19.9948	1.17414
$291$	1.66875	0.0978237
$292$	−7.89749	−0.462166
$293$	−22.5194	−1.31560	−0.657799	−	0.753194i	$-0.728512\pi$
$293$	−22.5194	−1.31560	−0.657799	+	0.753194i	$0.728512\pi$
$294$	7.93940	0.463035
$295$	−34.6333	−2.01643
$296$	−18.5473	−1.07804
$297$	1.00000	0.0580259
$298$	−12.4907	−0.723567
$299$	0.619548	0.0358294
$300$	2.06347	0.119134
$301$	−6.00525	−0.346137
$302$	−13.8955	−0.799596
$303$	−7.21215	−0.414327
$304$	1.17005	0.0671069
$305$	−2.90081	−0.166100
$306$	0.0795696	0.00454869
$307$	−6.51791	−0.371997	−0.185998	−	0.982550i	$-0.559552\pi$
$307$	−6.51791	−0.371997	−0.185998	+	0.982550i	$0.559552\pi$
$308$	−0.319574	−0.0182094
$309$	−10.7724	−0.612819
$310$	9.74711	0.553598
$311$	17.4530	0.989667	0.494834	−	0.868988i	$-0.335229\pi$
$311$	17.4530	0.989667	0.494834	+	0.868988i	$0.335229\pi$
$312$	−0.463975	−0.0262674
$313$	20.6548	1.16748	0.583739	−	0.811941i	$-0.301589\pi$
$313$	20.6548	1.16748	0.583739	+	0.811941i	$0.301589\pi$
$314$	17.4712	0.985955
$315$	1.53406	0.0864347
$316$	−5.83412	−0.328195
$317$	−13.7550	−0.772558	−0.386279	−	0.922382i	$-0.626240\pi$
$317$	−13.7550	−0.772558	−0.386279	+	0.922382i	$0.626240\pi$
$318$	0.695086	0.0389785
$319$	5.83447	0.326668
$320$	−25.3409	−1.41660
$321$	2.91453	0.162673
$322$	2.56678	0.143041
$323$	−0.0324802	−0.00180724
$324$	−0.604292	−0.0335718
$325$	−0.514942	−0.0285638
$326$	−24.5795	−1.36133
$327$	15.6562	0.865792
$328$	−35.1057	−1.93839
$329$	2.06761	0.113991
$330$	−3.42702	−0.188651
$331$	26.0426	1.43143	0.715716	−	0.698392i	$-0.246101\pi$
$331$	26.0426	1.43143	0.715716	+	0.698392i	$0.246101\pi$
$332$	7.03495	0.386093
$333$	6.02828	0.330348
$334$	−15.6771	−0.857814
$335$	−27.2132	−1.48682
$336$	−1.28310	−0.0699987
$337$	32.9988	1.79756	0.898781	−	0.438399i	$-0.144454\pi$
$337$	32.9988	1.79756	0.898781	+	0.438399i	$0.144454\pi$
$338$	−15.3313	−0.833915
$339$	17.6863	0.960590
$340$	0.118063	0.00640289
$341$	2.84419	0.154022
$342$	−0.569726	−0.0308072
$343$	7.25586	0.391780
$344$	−34.9376	−1.88371
$345$	−11.9175	−0.641619
$346$	14.6613	0.788195
$347$	26.3834	1.41633	0.708166	−	0.706045i	$-0.249523\pi$
$347$	26.3834	1.41633	0.708166	+	0.706045i	$0.249523\pi$
$348$	−3.52572	−0.188999
$349$	−14.5133	−0.776881	−0.388441	−	0.921474i	$-0.626986\pi$
$349$	−14.5133	−0.776881	−0.388441	+	0.921474i	$0.626986\pi$
$350$	−2.13340	−0.114035
$351$	0.150802	0.00804922
$352$	−3.28705	−0.175201
$353$	34.6089	1.84205	0.921024	−	0.389507i	$-0.127355\pi$
$353$	34.6089	1.84205	0.921024	+	0.389507i	$0.127355\pi$
$354$	−14.1050	−0.749671
$355$	−36.7743	−1.95178
$356$	7.68045	0.407063
$357$	0.0356184	0.00188512
$358$	10.1897	0.538540
$359$	19.3153	1.01942	0.509712	−	0.860345i	$-0.329752\pi$
$359$	19.3153	1.01942	0.509712	+	0.860345i	$0.329752\pi$
$360$	8.92495	0.470386
$361$	−18.7674	−0.987760
$362$	−1.52628	−0.0802193
$363$	−1.00000	−0.0524864
$364$	−0.0481924	−0.00252597
$365$	−37.9107	−1.98434
$366$	−1.18140	−0.0617528
$367$	14.0802	0.734979	0.367489	−	0.930028i	$-0.380217\pi$
$367$	14.0802	0.734979	0.367489	+	0.930028i	$0.380217\pi$
$368$	9.96788	0.519612
$369$	11.4101	0.593988
$370$	−20.6590	−1.07401
$371$	0.311147	0.0161539
$372$	−1.71872	−0.0891116
$373$	26.0491	1.34877	0.674386	−	0.738379i	$-0.264409\pi$
$373$	26.0491	1.34877	0.674386	+	0.738379i	$0.264409\pi$
$374$	−0.0795696	−0.00411445
$375$	−4.59869	−0.237475
$376$	12.0290	0.620349
$377$	0.879850	0.0453146
$378$	0.624772	0.0321348
$379$	14.8469	0.762635	0.381317	−	0.924444i	$-0.375470\pi$
$379$	14.8469	0.762635	0.381317	+	0.924444i	$0.375470\pi$
$380$	−0.845345	−0.0433653
$381$	20.8464	1.06799
$382$	10.7219	0.548580
$383$	11.6961	0.597643	0.298821	−	0.954309i	$-0.403407\pi$
$383$	11.6961	0.597643	0.298821	+	0.954309i	$0.403407\pi$
$384$	−3.74641	−0.191183
$385$	−1.53406	−0.0781831
$386$	24.9000	1.26738
$387$	11.3555	0.577233
$388$	1.00841	0.0511943
$389$	−14.7146	−0.746059	−0.373029	−	0.927820i	$-0.621681\pi$
$389$	−14.7146	−0.746059	−0.373029	+	0.927820i	$0.621681\pi$
$390$	−0.516801	−0.0261692
$391$	−0.276705	−0.0139936
$392$	20.6765	1.04432
$393$	8.61884	0.434763
$394$	7.31279	0.368413
$395$	−28.0058	−1.40912
$396$	0.604292	0.0303668
$397$	29.4067	1.47588	0.737940	−	0.674867i	$-0.235799\pi$
$397$	29.4067	1.47588	0.737940	+	0.674867i	$0.235799\pi$
$398$	−24.0284	−1.20444
$399$	−0.255031	−0.0127675
$400$	−8.28488	−0.414244
$401$	−17.6578	−0.881786	−0.440893	−	0.897560i	$-0.645338\pi$
$401$	−17.6578	−0.881786	−0.440893	+	0.897560i	$0.645338\pi$
$402$	−11.0830	−0.552771
$403$	0.428910	0.0213656
$404$	−4.35824	−0.216831
$405$	−2.90081	−0.144142
$406$	3.64522	0.180909
$407$	−6.02828	−0.298811
$408$	0.207222	0.0102590
$409$	−11.0602	−0.546893	−0.273447	−	0.961887i	$-0.588164\pi$
$409$	−11.0602	−0.546893	−0.273447	+	0.961887i	$0.588164\pi$
$410$	−39.1027	−1.93115
$411$	−3.31289	−0.163413
$412$	−6.50965	−0.320708
$413$	−6.31393	−0.310688
$414$	−4.85361	−0.238542
$415$	33.7702	1.65771
$416$	−0.495694	−0.0243034
$417$	−16.9686	−0.830955
$418$	0.569726	0.0278662
$419$	9.64189	0.471037	0.235519	−	0.971870i	$-0.424321\pi$
$419$	9.64189	0.471037	0.235519	+	0.971870i	$0.424321\pi$
$420$	0.927022	0.0452340
$421$	31.6981	1.54487	0.772435	−	0.635094i	$-0.219039\pi$
$421$	31.6981	1.54487	0.772435	+	0.635094i	$0.219039\pi$
$422$	33.9753	1.65389
$423$	−3.90970	−0.190096
$424$	1.81021	0.0879114
$425$	0.229986	0.0111559
$426$	−14.9769	−0.725636
$427$	−0.528840	−0.0255924
$428$	1.76123	0.0851322
$429$	−0.150802	−0.00728079
$430$	−38.9155	−1.87667
$431$	−19.2048	−0.925061	−0.462530	−	0.886603i	$-0.653058\pi$
$431$	−19.2048	−0.925061	−0.462530	+	0.886603i	$0.653058\pi$
$432$	2.42625	0.116733
$433$	−13.3020	−0.639254	−0.319627	−	0.947544i	$-0.603558\pi$
$433$	−13.3020	−0.639254	−0.319627	+	0.947544i	$0.603558\pi$
$434$	1.77697	0.0852975
$435$	−16.9247	−0.811476
$436$	9.46094	0.453097
$437$	1.98124	0.0947753
$438$	−15.4397	−0.737739
$439$	37.7505	1.80174	0.900868	−	0.434094i	$-0.142931\pi$
$439$	37.7505	1.80174	0.900868	+	0.434094i	$0.142931\pi$
$440$	−8.92495	−0.425480
$441$	−6.72033	−0.320016
$442$	−0.0119993	−0.000570746 0
$443$	12.5575	0.596623	0.298311	−	0.954469i	$-0.403577\pi$
$443$	12.5575	0.596623	0.298311	+	0.954469i	$0.403577\pi$
$444$	3.64284	0.172881
$445$	36.8688	1.74775
$446$	−25.3409	−1.19992
$447$	10.5728	0.500076
$448$	−4.61985	−0.218268
$449$	−27.8448	−1.31408	−0.657040	−	0.753856i	$-0.728192\pi$
$449$	−27.8448	−1.31408	−0.657040	+	0.753856i	$0.728192\pi$
$450$	4.03411	0.190170
$451$	−11.4101	−0.537282
$452$	10.6877	0.502707
$453$	11.7619	0.552621
$454$	23.7903	1.11654
$455$	−0.231340	−0.0108454
$456$	−1.48373	−0.0694821
$457$	−15.9549	−0.746338	−0.373169	−	0.927763i	$-0.621729\pi$
$457$	−15.9549	−0.746338	−0.373169	+	0.927763i	$0.621729\pi$
$458$	27.6828	1.29353
$459$	−0.0673519	−0.00314372
$460$	−7.20167	−0.335780
$461$	−21.5790	−1.00503	−0.502517	−	0.864568i	$-0.667592\pi$
$461$	−21.5790	−1.00503	−0.502517	+	0.864568i	$0.667592\pi$
$462$	−0.624772	−0.0290670
$463$	−1.41157	−0.0656011	−0.0328006	−	0.999462i	$-0.510443\pi$
$463$	−1.41157	−0.0656011	−0.0328006	+	0.999462i	$0.510443\pi$
$464$	14.1559	0.657170
$465$	−8.25046	−0.382606
$466$	−1.76856	−0.0819270
$467$	−1.05698	−0.0489112	−0.0244556	−	0.999701i	$-0.507785\pi$
$467$	−1.05698	−0.0489112	−0.0244556	+	0.999701i	$0.507785\pi$
$468$	0.0911284	0.00421241
$469$	−4.96119	−0.229086
$470$	13.3986	0.618032
$471$	−14.7885	−0.681418
$472$	−36.7335	−1.69080
$473$	−11.3555	−0.522127
$474$	−11.4058	−0.523886
$475$	−1.64672	−0.0755566
$476$	0.0215239	0.000986546 0
$477$	−0.588357	−0.0269390
$478$	13.4182	0.613734
$479$	−24.6689	−1.12715	−0.563575	−	0.826065i	$-0.690574\pi$
$479$	−24.6689	−1.12715	−0.563575	+	0.826065i	$0.690574\pi$
$480$	9.53511	0.435216
$481$	−0.909077	−0.0414503
$482$	22.7526	1.03635
$483$	−2.17266	−0.0988595
$484$	−0.604292	−0.0274678
$485$	4.84072	0.219806
$486$	−1.18140	−0.0535894
$487$	8.86822	0.401857	0.200929	−	0.979606i	$-0.435604\pi$
$487$	8.86822	0.401857	0.200929	+	0.979606i	$0.435604\pi$
$488$	−3.07671	−0.139276
$489$	20.8054	0.940853
$490$	23.0307	1.04042
$491$	14.8167	0.668670	0.334335	−	0.942454i	$-0.391488\pi$
$491$	14.8167	0.668670	0.334335	+	0.942454i	$0.391488\pi$
$492$	6.89505	0.310853
$493$	−0.392963	−0.0176981
$494$	0.0859158	0.00386553
$495$	2.90081	0.130382
$496$	6.90072	0.309852
$497$	−6.70425	−0.300727
$498$	13.7535	0.616307
$499$	−1.89914	−0.0850174	−0.0425087	−	0.999096i	$-0.513535\pi$
$499$	−1.89914	−0.0850174	−0.0425087	+	0.999096i	$0.513535\pi$
$500$	−2.77895	−0.124278
$501$	13.2699	0.592857
$502$	−11.1243	−0.496501
$503$	22.0264	0.982109	0.491055	−	0.871129i	$-0.336612\pi$
$503$	22.0264	0.982109	0.491055	+	0.871129i	$0.336612\pi$
$504$	1.62709	0.0724763
$505$	−20.9211	−0.930976
$506$	4.85361	0.215769
$507$	12.9773	0.576340
$508$	12.5973	0.558914
$509$	−32.0102	−1.41882	−0.709412	−	0.704794i	$-0.751040\pi$
$509$	−32.0102	−1.41882	−0.709412	+	0.704794i	$0.751040\pi$
$510$	0.230816	0.0102207
$511$	−6.91142	−0.305743
$512$	−22.9049	−1.01227
$513$	0.482246	0.0212917
$514$	18.5046	0.816204
$515$	−31.2486	−1.37698
$516$	6.86204	0.302084
$517$	3.90970	0.171948
$518$	−3.76630	−0.165482
$519$	−12.4101	−0.544742
$520$	−1.34590	−0.0590217
$521$	28.1925	1.23514	0.617569	−	0.786517i	$-0.288118\pi$
$521$	28.1925	1.23514	0.617569	+	0.786517i	$0.288118\pi$
$522$	−6.89285	−0.301692
$523$	−8.41440	−0.367936	−0.183968	−	0.982932i	$-0.558894\pi$
$523$	−8.41440	−0.367936	−0.183968	+	0.982932i	$0.558894\pi$
$524$	5.20829	0.227525
$525$	1.80582	0.0788126
$526$	−8.97762	−0.391443
$527$	−0.191562	−0.00834457
$528$	−2.42625	−0.105589
$529$	−6.12144	−0.266150
$530$	2.01631	0.0875829
$531$	11.9392	0.518117
$532$	−0.154113	−0.00668165
$533$	−1.72067	−0.0745306
$534$	15.0154	0.649781
$535$	8.45450	0.365520
$536$	−28.8634	−1.24671
$537$	−8.62506	−0.372199
$538$	−28.6443	−1.23494
$539$	6.72033	0.289465
$540$	−1.75293	−0.0754343
$541$	27.0427	1.16266	0.581329	−	0.813669i	$-0.302533\pi$
$541$	27.0427	1.16266	0.581329	+	0.813669i	$0.302533\pi$
$542$	4.71830	0.202668
$543$	1.29192	0.0554416
$544$	0.221389	0.00949199
$545$	45.4158	1.94540
$546$	−0.0942169	−0.00403211
$547$	16.9856	0.726253	0.363126	−	0.931740i	$-0.381709\pi$
$547$	16.9856	0.726253	0.363126	+	0.931740i	$0.381709\pi$
$548$	−2.00195	−0.0855192
$549$	1.00000	0.0426790
$550$	−4.03411	−0.172015
$551$	2.81365	0.119865
$552$	−12.6402	−0.538003
$553$	−5.10567	−0.217115
$554$	9.37888	0.398470
$555$	17.4869	0.742277
$556$	−10.2540	−0.434865
$557$	−29.1185	−1.23379	−0.616896	−	0.787045i	$-0.711610\pi$
$557$	−29.1185	−1.23379	−0.616896	+	0.787045i	$0.711610\pi$
$558$	−3.36013	−0.142246
$559$	−1.71243	−0.0724282
$560$	−3.72202	−0.157284
$561$	0.0673519	0.00284360
$562$	3.69032	0.155667
$563$	33.1163	1.39569	0.697843	−	0.716250i	$-0.254143\pi$
$563$	33.1163	1.39569	0.697843	+	0.716250i	$0.254143\pi$
$564$	−2.36260	−0.0994834
$565$	51.3046	2.15840
$566$	6.12703	0.257538
$567$	−0.528840	−0.0222092
$568$	−39.0043	−1.63659
$569$	−9.13425	−0.382928	−0.191464	−	0.981500i	$-0.561323\pi$
$569$	−9.13425	−0.382928	−0.191464	+	0.981500i	$0.561323\pi$
$570$	−1.65266	−0.0692225
$571$	31.6452	1.32431	0.662156	−	0.749366i	$-0.269642\pi$
$571$	31.6452	1.32431	0.662156	+	0.749366i	$0.269642\pi$
$572$	−0.0911284	−0.00381027
$573$	−9.07558	−0.379138
$574$	−7.12874	−0.297548
$575$	−14.0287	−0.585039
$576$	8.73582	0.363993
$577$	−5.78481	−0.240825	−0.120412	−	0.992724i	$-0.538422\pi$
$577$	−5.78481	−0.240825	−0.120412	+	0.992724i	$0.538422\pi$
$578$	−20.0785	−0.835154
$579$	−21.0767	−0.875917
$580$	−10.2274	−0.424671
$581$	6.15657	0.255418
$582$	1.97146	0.0817196
$583$	0.588357	0.0243673
$584$	−40.2096	−1.66388
$585$	0.437448	0.0180862
$586$	−26.6044	−1.09902
$587$	−8.04522	−0.332062	−0.166031	−	0.986121i	$-0.553095\pi$
$587$	−8.04522	−0.332062	−0.166031	+	0.986121i	$0.553095\pi$
$588$	−4.06104	−0.167474
$589$	1.37160	0.0565158
$590$	−40.9158	−1.68448
$591$	−6.18993	−0.254620
$592$	−14.6261	−0.601129
$593$	−7.77065	−0.319103	−0.159551	−	0.987190i	$-0.551005\pi$
$593$	−7.77065	−0.319103	−0.159551	+	0.987190i	$0.551005\pi$
$594$	1.18140	0.0484735
$595$	0.103322	0.00423579
$596$	6.38905	0.261706
$597$	20.3389	0.832417
$598$	0.731935	0.0299310
$599$	5.13824	0.209943	0.104971	−	0.994475i	$-0.466525\pi$
$599$	5.13824	0.209943	0.104971	+	0.994475i	$0.466525\pi$
$600$	10.5060	0.428906
$601$	−18.9195	−0.771744	−0.385872	−	0.922552i	$-0.626099\pi$
$601$	−18.9195	−0.771744	−0.385872	+	0.922552i	$0.626099\pi$
$602$	−7.09461	−0.289155
$603$	9.38126	0.382034
$604$	7.10760	0.289204
$605$	−2.90081	−0.117935
$606$	−8.52045	−0.346119
$607$	31.8620	1.29324	0.646620	−	0.762812i	$-0.276182\pi$
$607$	31.8620	1.29324	0.646620	+	0.762812i	$0.276182\pi$
$608$	−1.58517	−0.0642870
$609$	−3.08550	−0.125031
$610$	−3.42702	−0.138756
$611$	0.589591	0.0238523
$612$	−0.0407002	−0.00164521
$613$	−14.7696	−0.596539	−0.298269	−	0.954482i	$-0.596409\pi$
$613$	−14.7696	−0.596539	−0.298269	+	0.954482i	$0.596409\pi$
$614$	−7.70027	−0.310758
$615$	33.0986	1.33467
$616$	−1.62709	−0.0655573
$617$	−45.2708	−1.82253	−0.911266	−	0.411817i	$-0.864894\pi$
$617$	−45.2708	−1.82253	−0.911266	+	0.411817i	$0.864894\pi$
$618$	−12.7265	−0.511935
$619$	39.0064	1.56780	0.783900	−	0.620887i	$-0.213227\pi$
$619$	39.0064	1.56780	0.783900	+	0.620887i	$0.213227\pi$
$620$	−4.98569	−0.200230
$621$	4.10835	0.164862
$622$	20.6190	0.826745
$623$	6.72147	0.269290
$624$	−0.365883	−0.0146471
$625$	−30.4133	−1.21653
$626$	24.4016	0.975284
$627$	−0.482246	−0.0192590
$628$	−8.93657	−0.356608
$629$	0.406016	0.0161889
$630$	1.81234	0.0722055
$631$	−37.8923	−1.50847	−0.754235	−	0.656605i	$-0.771992\pi$
$631$	−37.8923	−1.50847	−0.754235	+	0.656605i	$0.771992\pi$
$632$	−29.7040	−1.18156
$633$	−28.7585	−1.14305
$634$	−16.2502	−0.645377
$635$	60.4713	2.39973
$636$	−0.355539	−0.0140981
$637$	1.01344	0.0401539
$638$	6.89285	0.272891
$639$	12.6773	0.501505
$640$	−10.8676	−0.429580
$641$	−15.2355	−0.601767	−0.300883	−	0.953661i	$-0.597281\pi$
$641$	−15.2355	−0.601767	−0.300883	+	0.953661i	$0.597281\pi$
$642$	3.44323	0.135894
$643$	0.685252	0.0270237	0.0135118	−	0.999909i	$-0.495699\pi$
$643$	0.685252	0.0270237	0.0135118	+	0.999909i	$0.495699\pi$
$644$	−1.31292	−0.0517363
$645$	32.9401	1.29702
$646$	−0.0383721	−0.00150973
$647$	32.3211	1.27067	0.635337	−	0.772235i	$-0.280861\pi$
$647$	32.3211	1.27067	0.635337	+	0.772235i	$0.280861\pi$
$648$	−3.07671	−0.120865
$649$	−11.9392	−0.468655
$650$	−0.608353	−0.0238616
$651$	−1.50412	−0.0589513
$652$	12.5725	0.492378
$653$	−19.3514	−0.757281	−0.378640	−	0.925544i	$-0.623608\pi$
$653$	−19.3514	−0.757281	−0.378640	+	0.925544i	$0.623608\pi$
$654$	18.4963	0.723263
$655$	25.0016	0.976893
$656$	−27.6838	−1.08087
$657$	13.0690	0.509871
$658$	2.44267	0.0952253
$659$	35.8402	1.39613	0.698067	−	0.716032i	$-0.254044\pi$
$659$	35.8402	1.39613	0.698067	+	0.716032i	$0.254044\pi$
$660$	1.75293	0.0682329
$661$	22.2012	0.863526	0.431763	−	0.901987i	$-0.357892\pi$
$661$	22.2012	0.863526	0.431763	+	0.901987i	$0.357892\pi$
$662$	30.7668	1.19578
$663$	0.0101568	0.000394458 0
$664$	35.8180	1.39001
$665$	−0.739796	−0.0286880
$666$	7.12182	0.275965
$667$	23.9701	0.928125
$668$	8.01892	0.310261
$669$	21.4498	0.829299
$670$	−32.1497	−1.24205
$671$	−1.00000	−0.0386046
$672$	1.73833	0.0670574
$673$	−1.26748	−0.0488576	−0.0244288	−	0.999702i	$-0.507777\pi$
$673$	−1.26748	−0.0488576	−0.0244288	+	0.999702i	$0.507777\pi$
$674$	38.9849	1.50164
$675$	−3.41469	−0.131431
$676$	7.84205	0.301617
$677$	22.7065	0.872681	0.436340	−	0.899782i	$-0.356274\pi$
$677$	22.7065	0.872681	0.436340	+	0.899782i	$0.356274\pi$
$678$	20.8946	0.802454
$679$	0.882501	0.0338673
$680$	0.601112	0.0230516
$681$	−20.1374	−0.771666
$682$	3.36013	0.128666
$683$	−34.5294	−1.32123	−0.660616	−	0.750724i	$-0.729705\pi$
$683$	−34.5294	−1.32123	−0.660616	+	0.750724i	$0.729705\pi$
$684$	0.291417	0.0111426
$685$	−9.61006	−0.367182
$686$	8.57208	0.327284
$687$	−23.4322	−0.893994
$688$	−27.5513	−1.05038
$689$	0.0887255	0.00338017
$690$	−14.0794	−0.535993
$691$	−22.4560	−0.854265	−0.427132	−	0.904189i	$-0.640476\pi$
$691$	−22.4560	−0.854265	−0.427132	+	0.904189i	$0.640476\pi$
$692$	−7.49931	−0.285081
$693$	0.528840	0.0200890
$694$	31.1693	1.18317
$695$	−49.2226	−1.86712
$696$	−17.9510	−0.680431
$697$	0.768494	0.0291088
$698$	−17.1461	−0.648988
$699$	1.49700	0.0566219
$700$	1.09124	0.0412451
$701$	−31.5776	−1.19267	−0.596335	−	0.802736i	$-0.703377\pi$
$701$	−31.5776	−1.19267	−0.596335	+	0.802736i	$0.703377\pi$
$702$	0.178158	0.00672413
$703$	−2.90711	−0.109644
$704$	−8.73582	−0.329244
$705$	−11.3413	−0.427138
$706$	40.8870	1.53880
$707$	−3.81408	−0.143443
$708$	7.21476	0.271147
$709$	−9.16530	−0.344210	−0.172105	−	0.985079i	$-0.555057\pi$
$709$	−9.16530	−0.344210	−0.172105	+	0.985079i	$0.555057\pi$
$710$	−43.4453	−1.63047
$711$	9.65447	0.362071
$712$	39.1045	1.46550
$713$	11.6850	0.437605
$714$	0.0420796	0.00157479
$715$	−0.437448	−0.0163596
$716$	−5.21205	−0.194784
$717$	−11.3579	−0.424167
$718$	22.8191	0.851603
$719$	−3.15397	−0.117623	−0.0588116	−	0.998269i	$-0.518731\pi$
$719$	−3.15397	−0.117623	−0.0588116	+	0.998269i	$0.518731\pi$
$720$	7.03808	0.262294
$721$	−5.69686	−0.212162
$722$	−22.1719	−0.825152
$723$	−19.2590	−0.716249
$724$	0.780697	0.0290144
$725$	−19.9229	−0.739917
$726$	−1.18140	−0.0438459
$727$	39.5017	1.46504	0.732519	−	0.680747i	$-0.238345\pi$
$727$	39.5017	1.46504	0.732519	+	0.680747i	$0.238345\pi$
$728$	−0.245368	−0.00909396
$729$	1.00000	0.0370370
$730$	−44.7877	−1.65767
$731$	0.764815	0.0282877
$732$	0.604292	0.0223353
$733$	23.5163	0.868595	0.434297	−	0.900770i	$-0.356997\pi$
$733$	23.5163	0.868595	0.434297	+	0.900770i	$0.356997\pi$
$734$	16.6343	0.613984
$735$	−19.4944	−0.719061
$736$	−13.5044	−0.497778
$737$	−9.38126	−0.345563
$738$	13.4799	0.496204
$739$	28.9368	1.06446	0.532228	−	0.846601i	$-0.321355\pi$
$739$	28.9368	1.06446	0.532228	+	0.846601i	$0.321355\pi$
$740$	10.5672	0.388457
$741$	−0.0727237	−0.00267157
$742$	0.367589	0.0134946
$743$	−36.1642	−1.32674	−0.663369	−	0.748293i	$-0.730874\pi$
$743$	−36.1642	−1.32674	−0.663369	+	0.748293i	$0.730874\pi$
$744$	−8.75077	−0.320819
$745$	30.6696	1.12365
$746$	30.7744	1.12673
$747$	−11.6417	−0.425946
$748$	0.0407002	0.00148815
$749$	1.54132	0.0563187
$750$	−5.43290	−0.198381
$751$	−37.9916	−1.38633	−0.693167	−	0.720777i	$-0.743785\pi$
$751$	−37.9916	−1.38633	−0.693167	+	0.720777i	$0.743785\pi$
$752$	9.48590	0.345915
$753$	9.41617	0.343144
$754$	1.03946	0.0378548
$755$	34.1189	1.24172
$756$	−0.319574	−0.0116228
$757$	−6.48633	−0.235750	−0.117875	−	0.993028i	$-0.537608\pi$
$757$	−6.48633	−0.235750	−0.117875	+	0.993028i	$0.537608\pi$
$758$	17.5402	0.637087
$759$	−4.10835	−0.149124
$760$	−4.30402	−0.156123
$761$	−0.142118	−0.00515178	−0.00257589	−	0.999997i	$-0.500820\pi$
$761$	−0.142118	−0.00515178	−0.00257589	+	0.999997i	$0.500820\pi$
$762$	24.6279	0.892175
$763$	8.27965	0.299743
$764$	−5.48430	−0.198415
$765$	−0.195375	−0.00706379
$766$	13.8178	0.499257
$767$	−1.80046	−0.0650107
$768$	13.0456	0.470744
$769$	37.9256	1.36763	0.683816	−	0.729655i	$-0.260319\pi$
$769$	37.9256	1.36763	0.683816	+	0.729655i	$0.260319\pi$
$770$	−1.81234	−0.0653124
$771$	−15.6633	−0.564099
$772$	−12.7365	−0.458395
$773$	7.81766	0.281182	0.140591	−	0.990068i	$-0.455100\pi$
$773$	7.81766	0.281182	0.140591	+	0.990068i	$0.455100\pi$
$774$	13.4154	0.482207
$775$	−9.71203	−0.348867
$776$	5.13426	0.184309
$777$	3.18800	0.114369
$778$	−17.3838	−0.623240
$779$	−5.50249	−0.197147
$780$	0.264346	0.00946511
$781$	−12.6773	−0.453629
$782$	−0.326900	−0.0116899
$783$	5.83447	0.208507
$784$	16.3052	0.582328
$785$	−42.8986	−1.53112
$786$	10.1823	0.363191
$787$	20.2740	0.722692	0.361346	−	0.932432i	$-0.382317\pi$
$787$	20.2740	0.722692	0.361346	+	0.932432i	$0.382317\pi$
$788$	−3.74052	−0.133251
$789$	7.59913	0.270536
$790$	−33.0860	−1.17715
$791$	9.35324	0.332563
$792$	3.07671	0.109326
$793$	−0.150802	−0.00535514
$794$	34.7411	1.23292
$795$	−1.70671	−0.0605308
$796$	12.2906	0.435630
$797$	5.99639	0.212403	0.106201	−	0.994345i	$-0.466131\pi$
$797$	5.99639	0.212403	0.106201	+	0.994345i	$0.466131\pi$
$798$	−0.301294	−0.0106657
$799$	−0.263326	−0.00931579
$800$	11.2243	0.396837
$801$	−12.7098	−0.449080
$802$	−20.8609	−0.736624
$803$	−13.0690	−0.461195
$804$	5.66902	0.199931
$805$	−6.30247	−0.222133
$806$	0.506715	0.0178483
$807$	24.2461	0.853502
$808$	−22.1897	−0.780632
$809$	−38.7682	−1.36302	−0.681508	−	0.731811i	$-0.738676\pi$
$809$	−38.7682	−1.36302	−0.681508	+	0.731811i	$0.738676\pi$
$810$	−3.42702	−0.120413
$811$	−20.8789	−0.733159	−0.366579	−	0.930387i	$-0.619471\pi$
$811$	−20.8789	−0.733159	−0.366579	+	0.930387i	$0.619471\pi$
$812$	−1.86454	−0.0654326
$813$	−3.99382	−0.140069
$814$	−7.12182	−0.249620
$815$	60.3525	2.11406
$816$	0.163412	0.00572058
$817$	−5.47615	−0.191586
$818$	−13.0666	−0.456862
$819$	0.0797502	0.00278670
$820$	20.0012	0.698473
$821$	33.6755	1.17528	0.587642	−	0.809121i	$-0.300056\pi$
$821$	33.6755	1.17528	0.587642	+	0.809121i	$0.300056\pi$
$822$	−3.91385	−0.136511
$823$	−48.6794	−1.69686	−0.848428	−	0.529311i	$-0.822450\pi$
$823$	−48.6794	−1.69686	−0.848428	+	0.529311i	$0.822450\pi$
$824$	−33.1435	−1.15461
$825$	3.41469	0.118884
$826$	−7.45928	−0.259542
$827$	2.49408	0.0867276	0.0433638	−	0.999059i	$-0.486193\pi$
$827$	2.49408	0.0867276	0.0433638	+	0.999059i	$0.486193\pi$
$828$	2.48264	0.0862778
$829$	20.9559	0.727829	0.363915	−	0.931432i	$-0.381440\pi$
$829$	20.9559	0.727829	0.363915	+	0.931432i	$0.381440\pi$
$830$	39.8962	1.38482
$831$	−7.93878	−0.275393
$832$	−1.31738	−0.0456719
$833$	−0.452627	−0.0156826
$834$	−20.0467	−0.694160
$835$	38.4936	1.33212
$836$	−0.291417	−0.0100789
$837$	2.84419	0.0983098
$838$	11.3909	0.393493
$839$	46.2064	1.59522	0.797611	−	0.603172i	$-0.206097\pi$
$839$	46.2064	1.59522	0.797611	+	0.603172i	$0.206097\pi$
$840$	4.71987	0.162851
$841$	5.04106	0.173830
$842$	37.4481	1.29055
$843$	−3.12368	−0.107585
$844$	−17.3785	−0.598193
$845$	37.6445	1.29501
$846$	−4.61892	−0.158802
$847$	−0.528840	−0.0181712
$848$	1.42750	0.0490206
$849$	−5.18624	−0.177991
$850$	0.271705	0.00931941
$851$	−24.7663	−0.848978
$852$	7.66077	0.262454
$853$	−12.1396	−0.415653	−0.207826	−	0.978166i	$-0.566639\pi$
$853$	−12.1396	−0.415653	−0.207826	+	0.978166i	$0.566639\pi$
$854$	−0.624772	−0.0213793
$855$	1.39890	0.0478414
$856$	8.96718	0.306492
$857$	−39.4393	−1.34722	−0.673610	−	0.739087i	$-0.735257\pi$
$857$	−39.4393	−1.34722	−0.673610	+	0.739087i	$0.735257\pi$
$858$	−0.178158	−0.00608220
$859$	−25.7414	−0.878285	−0.439143	−	0.898417i	$-0.644718\pi$
$859$	−25.7414	−0.878285	−0.439143	+	0.898417i	$0.644718\pi$
$860$	19.9055	0.678770
$861$	6.03414	0.205643
$862$	−22.6885	−0.772774
$863$	15.9889	0.544269	0.272134	−	0.962259i	$-0.412270\pi$
$863$	15.9889	0.544269	0.272134	+	0.962259i	$0.412270\pi$
$864$	−3.28705	−0.111828
$865$	−35.9992	−1.22401
$866$	−15.7150	−0.534018
$867$	16.9955	0.577196
$868$	−0.908930	−0.0308511
$869$	−9.65447	−0.327506
$870$	−19.9948	−0.677888
$871$	−1.41471	−0.0479357
$872$	48.1698	1.63123
$873$	−1.66875	−0.0564785
$874$	2.34063	0.0791731
$875$	−2.43197	−0.0822157
$876$	7.89749	0.266832
$877$	49.8159	1.68216	0.841082	−	0.540908i	$-0.181919\pi$
$877$	49.8159	1.68216	0.841082	+	0.540908i	$0.181919\pi$
$878$	44.5985	1.50513
$879$	22.5194	0.759560
$880$	−7.03808	−0.237254
$881$	26.3085	0.886355	0.443178	−	0.896434i	$-0.353851\pi$
$881$	26.3085	0.886355	0.443178	+	0.896434i	$0.353851\pi$
$882$	−7.93940	−0.267334
$883$	−27.4250	−0.922925	−0.461462	−	0.887160i	$-0.652675\pi$
$883$	−27.4250	−0.922925	−0.461462	+	0.887160i	$0.652675\pi$
$884$	0.00613767	0.000206432 0
$885$	34.6333	1.16419
$886$	14.8354	0.498405
$887$	−32.1898	−1.08083	−0.540413	−	0.841400i	$-0.681732\pi$
$887$	−32.1898	−1.08083	−0.540413	+	0.841400i	$0.681732\pi$
$888$	18.5473	0.622406
$889$	11.0244	0.369746
$890$	43.5568	1.46003
$891$	−1.00000	−0.0335013
$892$	12.9620	0.433998
$893$	1.88544	0.0630937
$894$	12.4907	0.417751
$895$	−25.0197	−0.836315
$896$	−1.98125	−0.0661889
$897$	−0.619548	−0.0206861
$898$	−32.8959	−1.09775
$899$	16.5944	0.553453
$900$	−2.06347	−0.0687822
$901$	−0.0396270	−0.00132017
$902$	−13.4799	−0.448833
$903$	6.00525	0.199842
$904$	54.4158	1.80984
$905$	3.74762	0.124575
$906$	13.8955	0.461647
$907$	−1.28331	−0.0426114	−0.0213057	−	0.999773i	$-0.506782\pi$
$907$	−1.28331	−0.0426114	−0.0213057	+	0.999773i	$0.506782\pi$
$908$	−12.1689	−0.403838
$909$	7.21215	0.239212
$910$	−0.273305	−0.00905998
$911$	−49.4716	−1.63907	−0.819534	−	0.573030i	$-0.805768\pi$
$911$	−49.4716	−1.63907	−0.819534	+	0.573030i	$0.805768\pi$
$912$	−1.17005	−0.0387442
$913$	11.6417	0.385283
$914$	−18.8491	−0.623473
$915$	2.90081	0.0958977
$916$	−14.1599	−0.467856
$917$	4.55799	0.150518
$918$	−0.0795696	−0.00262619
$919$	−29.7366	−0.980921	−0.490461	−	0.871463i	$-0.663171\pi$
$919$	−29.7366	−0.980921	−0.490461	+	0.871463i	$0.663171\pi$
$920$	−36.6668	−1.20887
$921$	6.51791	0.214772
$922$	−25.4934	−0.839581
$923$	−1.91176	−0.0629263
$924$	0.319574	0.0105132
$925$	20.5847	0.676820
$926$	−1.66763	−0.0548017
$927$	10.7724	0.353811
$928$	−19.1782	−0.629556
$929$	9.03584	0.296456	0.148228	−	0.988953i	$-0.452643\pi$
$929$	9.03584	0.296456	0.148228	+	0.988953i	$0.452643\pi$
$930$	−9.74711	−0.319620
$931$	3.24085	0.106215
$932$	0.904626	0.0296320
$933$	−17.4530	−0.571385
$934$	−1.24872	−0.0408593
$935$	0.195375	0.00638944
$936$	0.463975	0.0151655
$937$	−16.0261	−0.523551	−0.261776	−	0.965129i	$-0.584308\pi$
$937$	−16.0261	−0.523551	−0.261776	+	0.965129i	$0.584308\pi$
$938$	−5.86115	−0.191373
$939$	−20.6548	−0.674044
$940$	−6.85344	−0.223535
$941$	−3.42319	−0.111593	−0.0557963	−	0.998442i	$-0.517770\pi$
$941$	−3.42319	−0.111593	−0.0557963	+	0.998442i	$0.517770\pi$
$942$	−17.4712	−0.569241
$943$	−46.8769	−1.52652
$944$	−28.9675	−0.942811
$945$	−1.53406	−0.0499031
$946$	−13.4154	−0.436173
$947$	26.8391	0.872153	0.436076	−	0.899910i	$-0.356368\pi$
$947$	26.8391	0.872153	0.436076	+	0.899910i	$0.356368\pi$
$948$	5.83412	0.189483
$949$	−1.97083	−0.0639760
$950$	−1.94543	−0.0631182
$951$	13.7550	0.446037
$952$	0.109588	0.00355175
$953$	5.87575	0.190334	0.0951671	−	0.995461i	$-0.469661\pi$
$953$	5.87575	0.190334	0.0951671	+	0.995461i	$0.469661\pi$
$954$	−0.695086	−0.0225042
$955$	−26.3265	−0.851906
$956$	−6.86347	−0.221980
$957$	−5.83447	−0.188602
$958$	−29.1438	−0.941595
$959$	−1.75199	−0.0565747
$960$	25.3409	0.817876
$961$	−22.9106	−0.739050
$962$	−1.07398	−0.0346267
$963$	−2.91453	−0.0939195
$964$	−11.6380	−0.374836
$965$	−61.1394	−1.96815
$966$	−2.56678	−0.0825849
$967$	41.7810	1.34359	0.671793	−	0.740739i	$-0.265525\pi$
$967$	41.7810	1.34359	0.671793	+	0.740739i	$0.265525\pi$
$968$	−3.07671	−0.0988893
$969$	0.0324802	0.00104341
$970$	5.71883	0.183620
$971$	30.2221	0.969873	0.484937	−	0.874549i	$-0.338843\pi$
$971$	30.2221	0.969873	0.484937	+	0.874549i	$0.338843\pi$
$972$	0.604292	0.0193827
$973$	−8.97366	−0.287682
$974$	10.4769	0.335702
$975$	0.514942	0.0164913
$976$	−2.42625	−0.0776623
$977$	12.5432	0.401292	0.200646	−	0.979664i	$-0.435696\pi$
$977$	12.5432	0.401292	0.200646	+	0.979664i	$0.435696\pi$
$978$	24.5795	0.785967
$979$	12.7098	0.406208
$980$	−11.7803	−0.376308
$981$	−15.6562	−0.499865
$982$	17.5045	0.558591
$983$	35.7613	1.14061	0.570304	−	0.821434i	$-0.306825\pi$
$983$	35.7613	1.14061	0.570304	+	0.821434i	$0.306825\pi$
$984$	35.1057	1.11913
$985$	−17.9558	−0.572119
$986$	−0.464246	−0.0147846
$987$	−2.06761	−0.0658126
$988$	−0.0439463	−0.00139812
$989$	−46.6524	−1.48346
$990$	3.42702	0.108918
$991$	26.5390	0.843039	0.421519	−	0.906819i	$-0.361497\pi$
$991$	26.5390	0.843039	0.421519	+	0.906819i	$0.361497\pi$
$992$	−9.34902	−0.296832
$993$	−26.0426	−0.826437
$994$	−7.92041	−0.251220
$995$	58.9993	1.87040
$996$	−7.03495	−0.222911
$997$	−0.481491	−0.0152490	−0.00762448	−	0.999971i	$-0.502427\pi$
$997$	−0.481491	−0.0152490	−0.00762448	+	0.999971i	$0.502427\pi$
$998$	−2.24365	−0.0710216
$999$	−6.02828	−0.190726

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.2.a.h.1.10	✓	14
3.2	odd	2		6039.2.a.j.1.5		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.2.a.h.1.10	✓	14	1.1	even	1	trivial
6039.2.a.j.1.5		14	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:	\( N \)	\(=\)	\( 2013 = 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2013.a (trivial)

\(f(q)\)	\(=\)	\(q+1.18140 q^{2} -1.00000 q^{3} -0.604292 q^{4} -2.90081 q^{5} -1.18140 q^{6} -0.528840 q^{7} -3.07671 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.18140 q^{2} -1.00000 q^{3} -0.604292 q^{4} -2.90081 q^{5} -1.18140 q^{6} -0.528840 q^{7} -3.07671 q^{8} +1.00000 q^{9} -3.42702 q^{10} -1.00000 q^{11} +0.604292 q^{12} -0.150802 q^{13} -0.624772 q^{14} +2.90081 q^{15} -2.42625 q^{16} +0.0673519 q^{17} +1.18140 q^{18} -0.482246 q^{19} +1.75293 q^{20} +0.528840 q^{21} -1.18140 q^{22} -4.10835 q^{23} +3.07671 q^{24} +3.41469 q^{25} -0.178158 q^{26} -1.00000 q^{27} +0.319574 q^{28} -5.83447 q^{29} +3.42702 q^{30} -2.84419 q^{31} +3.28705 q^{32} +1.00000 q^{33} +0.0795696 q^{34} +1.53406 q^{35} -0.604292 q^{36} +6.02828 q^{37} -0.569726 q^{38} +0.150802 q^{39} +8.92495 q^{40} +11.4101 q^{41} +0.624772 q^{42} +11.3555 q^{43} +0.604292 q^{44} -2.90081 q^{45} -4.85361 q^{46} -3.90970 q^{47} +2.42625 q^{48} -6.72033 q^{49} +4.03411 q^{50} -0.0673519 q^{51} +0.0911284 q^{52} -0.588357 q^{53} -1.18140 q^{54} +2.90081 q^{55} +1.62709 q^{56} +0.482246 q^{57} -6.89285 q^{58} +11.9392 q^{59} -1.75293 q^{60} +1.00000 q^{61} -3.36013 q^{62} -0.528840 q^{63} +8.73582 q^{64} +0.437448 q^{65} +1.18140 q^{66} +9.38126 q^{67} -0.0407002 q^{68} +4.10835 q^{69} +1.81234 q^{70} +12.6773 q^{71} -3.07671 q^{72} +13.0690 q^{73} +7.12182 q^{74} -3.41469 q^{75} +0.291417 q^{76} +0.528840 q^{77} +0.178158 q^{78} +9.65447 q^{79} +7.03808 q^{80} +1.00000 q^{81} +13.4799 q^{82} -11.6417 q^{83} -0.319574 q^{84} -0.195375 q^{85} +13.4154 q^{86} +5.83447 q^{87} +3.07671 q^{88} -12.7098 q^{89} -3.42702 q^{90} +0.0797502 q^{91} +2.48264 q^{92} +2.84419 q^{93} -4.61892 q^{94} +1.39890 q^{95} -3.28705 q^{96} -1.66875 q^{97} -7.93940 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - q^{2} - 14 q^{3} + 15 q^{4} + q^{5} + q^{6} + 9 q^{7} + 14 q^{9}+O(q^{10}) \) 14 * q - q^2 - 14 * q^3 + 15 * q^4 + q^5 + q^6 + 9 * q^7 + 14 * q^9	\( 14 q - q^{2} - 14 q^{3} + 15 q^{4} + q^{5} + q^{6} + 9 q^{7} + 14 q^{9} + 6 q^{10} - 14 q^{11} - 15 q^{12} + q^{13} - 7 q^{14} - q^{15} + 17 q^{16} - 9 q^{17} - q^{18} + 22 q^{19} + 23 q^{20} - 9 q^{21} + q^{22} + q^{23} + 25 q^{25} + 4 q^{26} - 14 q^{27} + 37 q^{28} - 6 q^{29} - 6 q^{30} + 9 q^{31} + 4 q^{32} + 14 q^{33} + 8 q^{34} + 18 q^{35} + 15 q^{36} + 18 q^{37} + 8 q^{38} - q^{39} + 16 q^{40} - 25 q^{41} + 7 q^{42} + 25 q^{43} - 15 q^{44} + q^{45} + 20 q^{46} + 36 q^{47} - 17 q^{48} + 25 q^{49} + 2 q^{50} + 9 q^{51} - 13 q^{52} + q^{54} - q^{55} - 40 q^{56} - 22 q^{57} + 33 q^{58} + 17 q^{59} - 23 q^{60} + 14 q^{61} - 13 q^{62} + 9 q^{63} - 6 q^{64} - 61 q^{65} - q^{66} + 22 q^{67} + 66 q^{68} - q^{69} + 44 q^{70} - 13 q^{71} + 20 q^{73} - 12 q^{74} - 25 q^{75} + 49 q^{76} - 9 q^{77} - 4 q^{78} + 31 q^{79} + 88 q^{80} + 14 q^{81} + 2 q^{82} + 32 q^{83} - 37 q^{84} + 2 q^{85} - 14 q^{86} + 6 q^{87} - 21 q^{89} + 6 q^{90} + 45 q^{91} - 14 q^{92} - 9 q^{93} - 31 q^{94} + 23 q^{95} - 4 q^{96} + 37 q^{97} - 38 q^{98} - 14 q^{99}+O(q^{100}) \) 14 * q - q^2 - 14 * q^3 + 15 * q^4 + q^5 + q^6 + 9 * q^7 + 14 * q^9 + 6 * q^10 - 14 * q^11 - 15 * q^12 + q^13 - 7 * q^14 - q^15 + 17 * q^16 - 9 * q^17 - q^18 + 22 * q^19 + 23 * q^20 - 9 * q^21 + q^22 + q^23 + 25 * q^25 + 4 * q^26 - 14 * q^27 + 37 * q^28 - 6 * q^29 - 6 * q^30 + 9 * q^31 + 4 * q^32 + 14 * q^33 + 8 * q^34 + 18 * q^35 + 15 * q^36 + 18 * q^37 + 8 * q^38 - q^39 + 16 * q^40 - 25 * q^41 + 7 * q^42 + 25 * q^43 - 15 * q^44 + q^45 + 20 * q^46 + 36 * q^47 - 17 * q^48 + 25 * q^49 + 2 * q^50 + 9 * q^51 - 13 * q^52 + q^54 - q^55 - 40 * q^56 - 22 * q^57 + 33 * q^58 + 17 * q^59 - 23 * q^60 + 14 * q^61 - 13 * q^62 + 9 * q^63 - 6 * q^64 - 61 * q^65 - q^66 + 22 * q^67 + 66 * q^68 - q^69 + 44 * q^70 - 13 * q^71 + 20 * q^73 - 12 * q^74 - 25 * q^75 + 49 * q^76 - 9 * q^77 - 4 * q^78 + 31 * q^79 + 88 * q^80 + 14 * q^81 + 2 * q^82 + 32 * q^83 - 37 * q^84 + 2 * q^85 - 14 * q^86 + 6 * q^87 - 21 * q^89 + 6 * q^90 + 45 * q^91 - 14 * q^92 - 9 * q^93 - 31 * q^94 + 23 * q^95 - 4 * q^96 + 37 * q^97 - 38 * q^98 - 14 * q^99

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