LMFDB - Embedded newform 6031.2.a.e.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6031,2,Mod(1,6031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6031, 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("6031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6031 = 37 \cdot 163 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6031.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:	$48.1577774590$
Analytic rank:	$0$
Dimension:	$134$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	6031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.70867 q^{2} -0.769737 q^{3} +5.33687 q^{4} -2.82113 q^{5} +2.08496 q^{6} -1.98436 q^{7} -9.03847 q^{8} -2.40750 q^{9} +O(q^{10})$	\(q-2.70867 q^{2} -0.769737 q^{3} +5.33687 q^{4} -2.82113 q^{5} +2.08496 q^{6} -1.98436 q^{7} -9.03847 q^{8} -2.40750 q^{9} +7.64150 q^{10} +5.86359 q^{11} -4.10799 q^{12} -4.15890 q^{13} +5.37497 q^{14} +2.17153 q^{15} +13.8084 q^{16} +0.131901 q^{17} +6.52113 q^{18} -1.74514 q^{19} -15.0560 q^{20} +1.52744 q^{21} -15.8825 q^{22} -3.96895 q^{23} +6.95724 q^{24} +2.95877 q^{25} +11.2651 q^{26} +4.16236 q^{27} -10.5903 q^{28} -5.29680 q^{29} -5.88194 q^{30} -2.89897 q^{31} -19.3255 q^{32} -4.51342 q^{33} -0.357275 q^{34} +5.59814 q^{35} -12.8485 q^{36} +1.00000 q^{37} +4.72699 q^{38} +3.20126 q^{39} +25.4987 q^{40} +11.8420 q^{41} -4.13731 q^{42} -4.23169 q^{43} +31.2932 q^{44} +6.79188 q^{45} +10.7506 q^{46} -11.5382 q^{47} -10.6289 q^{48} -3.06232 q^{49} -8.01432 q^{50} -0.101529 q^{51} -22.1955 q^{52} +0.945611 q^{53} -11.2744 q^{54} -16.5419 q^{55} +17.9356 q^{56} +1.34330 q^{57} +14.3472 q^{58} +1.13851 q^{59} +11.5892 q^{60} -9.99019 q^{61} +7.85233 q^{62} +4.77736 q^{63} +24.7295 q^{64} +11.7328 q^{65} +12.2253 q^{66} +11.6564 q^{67} +0.703938 q^{68} +3.05505 q^{69} -15.1635 q^{70} -4.11208 q^{71} +21.7601 q^{72} -0.961523 q^{73} -2.70867 q^{74} -2.27748 q^{75} -9.31357 q^{76} -11.6355 q^{77} -8.67114 q^{78} -4.32769 q^{79} -38.9554 q^{80} +4.01859 q^{81} -32.0761 q^{82} +5.06118 q^{83} +8.15172 q^{84} -0.372109 q^{85} +11.4622 q^{86} +4.07714 q^{87} -52.9978 q^{88} -14.4164 q^{89} -18.3969 q^{90} +8.25275 q^{91} -21.1818 q^{92} +2.23144 q^{93} +31.2531 q^{94} +4.92326 q^{95} +14.8756 q^{96} -18.8746 q^{97} +8.29479 q^{98} -14.1166 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 134 q + 9 q^{2} + 7 q^{3} + 149 q^{4} + 22 q^{5} + 20 q^{6} + 11 q^{7} + 27 q^{8} + 181 q^{9}+O(q^{10}) $ 134 * q + 9 * q^2 + 7 * q^3 + 149 * q^4 + 22 * q^5 + 20 * q^6 + 11 * q^7 + 27 * q^8 + 181 * q^9	\( 134 q + 9 q^{2} + 7 q^{3} + 149 q^{4} + 22 q^{5} + 20 q^{6} + 11 q^{7} + 27 q^{8} + 181 q^{9} + 15 q^{10} + 20 q^{11} + 28 q^{12} + 11 q^{13} + 17 q^{14} - 13 q^{15} + 143 q^{16} + 76 q^{17} + 23 q^{18} + 15 q^{19} + 67 q^{20} + 63 q^{21} + 2 q^{22} + 22 q^{23} + 33 q^{24} + 160 q^{25} + 65 q^{26} + 31 q^{27} + 10 q^{28} + 73 q^{29} + 20 q^{30} + 10 q^{31} + 53 q^{32} + 72 q^{33} - 7 q^{34} + 52 q^{35} + 201 q^{36} + 134 q^{37} + 70 q^{38} + 6 q^{39} + 11 q^{40} + 182 q^{41} - 15 q^{42} + 12 q^{43} + 33 q^{44} + 29 q^{45} + 24 q^{46} + 80 q^{47} + 21 q^{48} + 229 q^{49} + 37 q^{50} + 57 q^{51} - 15 q^{52} + 75 q^{53} + 95 q^{54} - 9 q^{55} + 39 q^{56} + 19 q^{57} - 21 q^{58} + 91 q^{59} + 62 q^{60} + 58 q^{61} + 108 q^{62} + 9 q^{63} + 167 q^{64} + 76 q^{65} + 105 q^{66} - 17 q^{67} + 109 q^{68} + 48 q^{69} - 55 q^{70} + 56 q^{71} + 48 q^{72} + 54 q^{73} + 9 q^{74} + 28 q^{75} + 82 q^{76} + 156 q^{77} + 16 q^{78} - 2 q^{79} + 98 q^{80} + 270 q^{81} - 42 q^{82} + 130 q^{83} + 229 q^{84} + 22 q^{85} + 72 q^{86} + 22 q^{87} + 61 q^{88} + 157 q^{89} + 176 q^{90} + 31 q^{91} - 18 q^{92} + 36 q^{93} + 83 q^{94} + 98 q^{95} + 111 q^{96} + 35 q^{97} + 53 q^{98} + 55 q^{99}+O(q^{100}) \) 134 * q + 9 * q^2 + 7 * q^3 + 149 * q^4 + 22 * q^5 + 20 * q^6 + 11 * q^7 + 27 * q^8 + 181 * q^9 + 15 * q^10 + 20 * q^11 + 28 * q^12 + 11 * q^13 + 17 * q^14 - 13 * q^15 + 143 * q^16 + 76 * q^17 + 23 * q^18 + 15 * q^19 + 67 * q^20 + 63 * q^21 + 2 * q^22 + 22 * q^23 + 33 * q^24 + 160 * q^25 + 65 * q^26 + 31 * q^27 + 10 * q^28 + 73 * q^29 + 20 * q^30 + 10 * q^31 + 53 * q^32 + 72 * q^33 - 7 * q^34 + 52 * q^35 + 201 * q^36 + 134 * q^37 + 70 * q^38 + 6 * q^39 + 11 * q^40 + 182 * q^41 - 15 * q^42 + 12 * q^43 + 33 * q^44 + 29 * q^45 + 24 * q^46 + 80 * q^47 + 21 * q^48 + 229 * q^49 + 37 * q^50 + 57 * q^51 - 15 * q^52 + 75 * q^53 + 95 * q^54 - 9 * q^55 + 39 * q^56 + 19 * q^57 - 21 * q^58 + 91 * q^59 + 62 * q^60 + 58 * q^61 + 108 * q^62 + 9 * q^63 + 167 * q^64 + 76 * q^65 + 105 * q^66 - 17 * q^67 + 109 * q^68 + 48 * q^69 - 55 * q^70 + 56 * q^71 + 48 * q^72 + 54 * q^73 + 9 * q^74 + 28 * q^75 + 82 * q^76 + 156 * q^77 + 16 * q^78 - 2 * q^79 + 98 * q^80 + 270 * q^81 - 42 * q^82 + 130 * q^83 + 229 * q^84 + 22 * q^85 + 72 * q^86 + 22 * q^87 + 61 * q^88 + 157 * q^89 + 176 * q^90 + 31 * q^91 - 18 * q^92 + 36 * q^93 + 83 * q^94 + 98 * q^95 + 111 * q^96 + 35 * q^97 + 53 * q^98 + 55 * 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 $

$2$	−2.70867	−1.91532	−0.957658	−	0.287908i	$-0.907040\pi$
$2$	−2.70867	−1.91532	−0.957658	+	0.287908i	$0.907040\pi$
$3$	−0.769737	−0.444408	−0.222204	−	0.975000i	$-0.571325\pi$
$3$	−0.769737	−0.444408	−0.222204	+	0.975000i	$0.571325\pi$
$4$	5.33687	2.66843
$5$	−2.82113	−1.26165	−0.630824	−	0.775926i	$-0.717283\pi$
$5$	−2.82113	−1.26165	−0.630824	+	0.775926i	$0.717283\pi$
$6$	2.08496	0.851182
$7$	−1.98436	−0.750017	−0.375009	−	0.927021i	$-0.622360\pi$
$7$	−1.98436	−0.750017	−0.375009	+	0.927021i	$0.622360\pi$
$8$	−9.03847	−3.19558
$9$	−2.40750	−0.802502
$10$	7.64150	2.41645
$11$	5.86359	1.76794	0.883969	−	0.467546i	$-0.154862\pi$
$11$	5.86359	1.76794	0.883969	+	0.467546i	$0.154862\pi$
$12$	−4.10799	−1.18587
$13$	−4.15890	−1.15347	−0.576736	−	0.816931i	$-0.695674\pi$
$13$	−4.15890	−1.15347	−0.576736	+	0.816931i	$0.695674\pi$
$14$	5.37497	1.43652
$15$	2.17153	0.560686
$16$	13.8084	3.45211
$17$	0.131901	0.0319907	0.0159953	−	0.999872i	$-0.494908\pi$
$17$	0.131901	0.0319907	0.0159953	+	0.999872i	$0.494908\pi$
$18$	6.52113	1.53704
$19$	−1.74514	−0.400362	−0.200181	−	0.979759i	$-0.564153\pi$
$19$	−1.74514	−0.400362	−0.200181	+	0.979759i	$0.564153\pi$
$20$	−15.0560	−3.36662
$21$	1.52744	0.333314
$22$	−15.8825	−3.38616
$23$	−3.96895	−0.827583	−0.413791	−	0.910372i	$-0.635796\pi$
$23$	−3.96895	−0.827583	−0.413791	+	0.910372i	$0.635796\pi$
$24$	6.95724	1.42014
$25$	2.95877	0.591754
$26$	11.2651	2.20926
$27$	4.16236	0.801046
$28$	−10.5903	−2.00137
$29$	−5.29680	−0.983590	−0.491795	−	0.870711i	$-0.663659\pi$
$29$	−5.29680	−0.983590	−0.491795	+	0.870711i	$0.663659\pi$
$30$	−5.88194	−1.07389
$31$	−2.89897	−0.520670	−0.260335	−	0.965518i	$-0.583833\pi$
$31$	−2.89897	−0.520670	−0.260335	+	0.965518i	$0.583833\pi$
$32$	−19.3255	−3.41630
$33$	−4.51342	−0.785686
$34$	−0.357275	−0.0612722
$35$	5.59814	0.946258
$36$	−12.8485	−2.14142
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	4.72699	0.766819
$39$	3.20126	0.512612
$40$	25.4987	4.03170
$41$	11.8420	1.84941	0.924707	−	0.380680i	$-0.124310\pi$
$41$	11.8420	1.84941	0.924707	+	0.380680i	$0.124310\pi$
$42$	−4.13731	−0.638401
$43$	−4.23169	−0.645327	−0.322663	−	0.946514i	$-0.604578\pi$
$43$	−4.23169	−0.645327	−0.322663	+	0.946514i	$0.604578\pi$
$44$	31.2932	4.71763
$45$	6.79188	1.01247
$46$	10.7506	1.58508
$47$	−11.5382	−1.68302	−0.841510	−	0.540241i	$-0.818333\pi$
$47$	−11.5382	−1.68302	−0.841510	+	0.540241i	$0.818333\pi$
$48$	−10.6289	−1.53415
$49$	−3.06232	−0.437474
$50$	−8.01432	−1.13340
$51$	−0.101529	−0.0142169
$52$	−22.1955	−3.07796
$53$	0.945611	0.129890	0.0649448	−	0.997889i	$-0.479313\pi$
$53$	0.945611	0.129890	0.0649448	+	0.997889i	$0.479313\pi$
$54$	−11.2744	−1.53426
$55$	−16.5419	−2.23051
$56$	17.9356	2.39674
$57$	1.34330	0.177924
$58$	14.3472	1.88389
$59$	1.13851	0.148222	0.0741108	−	0.997250i	$-0.476388\pi$
$59$	1.13851	0.148222	0.0741108	+	0.997250i	$0.476388\pi$
$60$	11.5892	1.49615
$61$	−9.99019	−1.27911	−0.639556	−	0.768744i	$-0.720882\pi$
$61$	−9.99019	−1.27911	−0.639556	+	0.768744i	$0.720882\pi$
$62$	7.85233	0.997247
$63$	4.77736	0.601890
$64$	24.7295	3.09119
$65$	11.7328	1.45527
$66$	12.2253	1.50484
$67$	11.6564	1.42406	0.712028	−	0.702151i	$-0.247777\pi$
$67$	11.6564	1.42406	0.712028	+	0.702151i	$0.247777\pi$
$68$	0.703938	0.0853650
$69$	3.05505	0.367784
$70$	−15.1635	−1.81238
$71$	−4.11208	−0.488014	−0.244007	−	0.969773i	$-0.578462\pi$
$71$	−4.11208	−0.488014	−0.244007	+	0.969773i	$0.578462\pi$
$72$	21.7601	2.56446
$73$	−0.961523	−0.112538	−0.0562689	−	0.998416i	$-0.517920\pi$
$73$	−0.961523	−0.112538	−0.0562689	+	0.998416i	$0.517920\pi$
$74$	−2.70867	−0.314876
$75$	−2.27748	−0.262980
$76$	−9.31357	−1.06834
$77$	−11.6355	−1.32598
$78$	−8.67114	−0.981814
$79$	−4.32769	−0.486903	−0.243451	−	0.969913i	$-0.578280\pi$
$79$	−4.32769	−0.486903	−0.243451	+	0.969913i	$0.578280\pi$
$80$	−38.9554	−4.35535
$81$	4.01859	0.446510
$82$	−32.0761	−3.54221
$83$	5.06118	0.555536	0.277768	−	0.960648i	$-0.410405\pi$
$83$	5.06118	0.555536	0.277768	+	0.960648i	$0.410405\pi$
$84$	8.15172	0.889426
$85$	−0.372109	−0.0403609
$86$	11.4622	1.23600
$87$	4.07714	0.437115
$88$	−52.9978	−5.64959
$89$	−14.4164	−1.52813	−0.764066	−	0.645138i	$-0.776800\pi$
$89$	−14.4164	−1.52813	−0.764066	+	0.645138i	$0.776800\pi$
$90$	−18.3969	−1.93921
$91$	8.25275	0.865124
$92$	−21.1818	−2.20835
$93$	2.23144	0.231390
$94$	31.2531	3.22352
$95$	4.92326	0.505115
$96$	14.8756	1.51823
$97$	−18.8746	−1.91642	−0.958211	−	0.286062i	$-0.907654\pi$
$97$	−18.8746	−1.91642	−0.958211	+	0.286062i	$0.907654\pi$
$98$	8.29479	0.837901
$99$	−14.1166	−1.41877
$100$	15.7906	1.57906
$101$	−5.89018	−0.586095	−0.293047	−	0.956098i	$-0.594669\pi$
$101$	−5.89018	−0.586095	−0.293047	+	0.956098i	$0.594669\pi$
$102$	0.275008	0.0272299
$103$	−5.46527	−0.538509	−0.269255	−	0.963069i	$-0.586777\pi$
$103$	−5.46527	−0.538509	−0.269255	+	0.963069i	$0.586777\pi$
$104$	37.5901	3.68601
$105$	−4.30909	−0.420524
$106$	−2.56134	−0.248780
$107$	−2.96699	−0.286830	−0.143415	−	0.989663i	$-0.545808\pi$
$107$	−2.96699	−0.286830	−0.143415	+	0.989663i	$0.545808\pi$
$108$	22.2140	2.13754
$109$	−13.9734	−1.33841	−0.669203	−	0.743079i	$-0.733365\pi$
$109$	−13.9734	−1.33841	−0.669203	+	0.743079i	$0.733365\pi$
$110$	44.8066	4.27214
$111$	−0.769737	−0.0730602
$112$	−27.4009	−2.58914
$113$	−11.7960	−1.10968	−0.554838	−	0.831959i	$-0.687220\pi$
$113$	−11.7960	−1.10968	−0.554838	+	0.831959i	$0.687220\pi$
$114$	−3.63854	−0.340781
$115$	11.1969	1.04412
$116$	−28.2683	−2.62465
$117$	10.0126	0.925662
$118$	−3.08385	−0.283891
$119$	−0.261739	−0.0239936
$120$	−19.6273	−1.79172
$121$	23.3817	2.12560
$122$	27.0601	2.44990
$123$	−9.11525	−0.821894
$124$	−15.4714	−1.38937
$125$	5.75857	0.515062
$126$	−12.9403	−1.15281
$127$	−13.1595	−1.16771	−0.583857	−	0.811856i	$-0.698457\pi$
$127$	−13.1595	−1.16771	−0.583857	+	0.811856i	$0.698457\pi$
$128$	−28.3329	−2.50430
$129$	3.25729	0.286788
$130$	−31.7802	−2.78731
$131$	21.0971	1.84327	0.921633	−	0.388063i	$-0.126856\pi$
$131$	21.0971	1.84327	0.921633	+	0.388063i	$0.126856\pi$
$132$	−24.0875	−2.09655
$133$	3.46298	0.300278
$134$	−31.5733	−2.72752
$135$	−11.7425	−1.01064
$136$	−1.19218	−0.102229
$137$	−7.55670	−0.645612	−0.322806	−	0.946465i	$-0.604626\pi$
$137$	−7.55670	−0.645612	−0.322806	+	0.946465i	$0.604626\pi$
$138$	−8.27510	−0.704423
$139$	−21.3268	−1.80891	−0.904456	−	0.426567i	$-0.859723\pi$
$139$	−21.3268	−1.80891	−0.904456	+	0.426567i	$0.859723\pi$
$140$	29.8765	2.52503
$141$	8.88138	0.747947
$142$	11.1383	0.934702
$143$	−24.3861	−2.03927
$144$	−33.2439	−2.77032
$145$	14.9429	1.24094
$146$	2.60444	0.215545
$147$	2.35718	0.194417
$148$	5.33687	0.438688
$149$	2.12187	0.173830	0.0869151	−	0.996216i	$-0.472299\pi$
$149$	2.12187	0.173830	0.0869151	+	0.996216i	$0.472299\pi$
$150$	6.16892	0.503690
$151$	−6.49382	−0.528459	−0.264230	−	0.964460i	$-0.585118\pi$
$151$	−6.49382	−0.528459	−0.264230	+	0.964460i	$0.585118\pi$
$152$	15.7734	1.27939
$153$	−0.317552	−0.0256726
$154$	31.5166	2.53968
$155$	8.17836	0.656901
$156$	17.0847	1.36787
$157$	−15.2571	−1.21765	−0.608823	−	0.793306i	$-0.708358\pi$
$157$	−15.2571	−1.21765	−0.608823	+	0.793306i	$0.708358\pi$
$158$	11.7223	0.932573
$159$	−0.727872	−0.0577240
$160$	54.5198	4.31017
$161$	7.87582	0.620702
$162$	−10.8850	−0.855208
$163$	−1.00000	−0.0783260
$163$	−1.00000	−0.0783260
$164$	63.1993	4.93504
$165$	12.7329	0.991258
$166$	−13.7090	−1.06403
$167$	12.5931	0.974487	0.487243	−	0.873266i	$-0.338002\pi$
$167$	12.5931	0.974487	0.487243	+	0.873266i	$0.338002\pi$
$168$	−13.8057	−1.06513
$169$	4.29645	0.330496
$170$	1.00792	0.0773039
$171$	4.20142	0.321291
$172$	−22.5840	−1.72201
$173$	3.42308	0.260252	0.130126	−	0.991497i	$-0.458462\pi$
$173$	3.42308	0.260252	0.130126	+	0.991497i	$0.458462\pi$
$174$	−11.0436	−0.837214
$175$	−5.87127	−0.443826
$176$	80.9670	6.10312
$177$	−0.876354	−0.0658708
$178$	39.0491	2.92686
$179$	4.45749	0.333168	0.166584	−	0.986027i	$-0.446726\pi$
$179$	4.45749	0.333168	0.166584	+	0.986027i	$0.446726\pi$
$180$	36.2474	2.70172
$181$	8.79964	0.654072	0.327036	−	0.945012i	$-0.393950\pi$
$181$	8.79964	0.654072	0.327036	+	0.945012i	$0.393950\pi$
$182$	−22.3539	−1.65698
$183$	7.68982	0.568448
$184$	35.8732	2.64461
$185$	−2.82113	−0.207414
$186$	−6.04423	−0.443184
$187$	0.773412	0.0565575
$188$	−61.5779	−4.49103
$189$	−8.25961	−0.600799
$190$	−13.3355	−0.967456
$191$	19.7066	1.42592	0.712960	−	0.701204i	$-0.247354\pi$
$191$	19.7066	1.42592	0.712960	+	0.701204i	$0.247354\pi$
$192$	−19.0352	−1.37375
$193$	−26.6766	−1.92023	−0.960113	−	0.279611i	$-0.909794\pi$
$193$	−26.6766	−1.92023	−0.960113	+	0.279611i	$0.909794\pi$
$194$	51.1249	3.67055
$195$	−9.03117	−0.646735
$196$	−16.3432	−1.16737
$197$	−18.8570	−1.34350	−0.671752	−	0.740776i	$-0.734458\pi$
$197$	−18.8570	−1.34350	−0.671752	+	0.740776i	$0.734458\pi$
$198$	38.2372	2.71740
$199$	19.7510	1.40011	0.700056	−	0.714088i	$-0.253158\pi$
$199$	19.7510	1.40011	0.700056	+	0.714088i	$0.253158\pi$
$200$	−26.7427	−1.89100
$201$	−8.97237	−0.632862
$202$	15.9545	1.12256
$203$	10.5107	0.737710
$204$	−0.541847	−0.0379369
$205$	−33.4079	−2.33331
$206$	14.8036	1.03142
$207$	9.55526	0.664136
$208$	−57.4279	−3.98191
$209$	−10.2328	−0.707815
$210$	11.6719	0.805437
$211$	−12.8397	−0.883921	−0.441960	−	0.897035i	$-0.645717\pi$
$211$	−12.8397	−0.883921	−0.441960	+	0.897035i	$0.645717\pi$
$212$	5.04660	0.346602
$213$	3.16522	0.216877
$214$	8.03659	0.549370
$215$	11.9381	0.814175
$216$	−37.6213	−2.55981
$217$	5.75259	0.390511
$218$	37.8492	2.56347
$219$	0.740120	0.0500127
$220$	−88.2822	−5.95198
$221$	−0.548563	−0.0369003
$222$	2.08496	0.139933
$223$	−11.6783	−0.782040	−0.391020	−	0.920382i	$-0.627878\pi$
$223$	−11.6783	−0.782040	−0.391020	+	0.920382i	$0.627878\pi$
$224$	38.3488	2.56229
$225$	−7.12325	−0.474884
$226$	31.9515	2.12538
$227$	−2.08189	−0.138180	−0.0690901	−	0.997610i	$-0.522010\pi$
$227$	−2.08189	−0.138180	−0.0690901	+	0.997610i	$0.522010\pi$
$228$	7.16900	0.474779
$229$	−3.13025	−0.206853	−0.103427	−	0.994637i	$-0.532981\pi$
$229$	−3.13025	−0.206853	−0.103427	+	0.994637i	$0.532981\pi$
$230$	−30.3287	−1.99982
$231$	8.95625	0.589278
$232$	47.8749	3.14314
$233$	−0.384512	−0.0251902	−0.0125951	−	0.999921i	$-0.504009\pi$
$233$	−0.384512	−0.0251902	−0.0125951	+	0.999921i	$0.504009\pi$
$234$	−27.1207	−1.77294
$235$	32.5508	2.12338
$236$	6.07609	0.395519
$237$	3.33118	0.216383
$238$	0.708963	0.0459552
$239$	−5.52624	−0.357463	−0.178731	−	0.983898i	$-0.557199\pi$
$239$	−5.52624	−0.357463	−0.178731	+	0.983898i	$0.557199\pi$
$240$	29.9854	1.93555
$241$	6.48846	0.417958	0.208979	−	0.977920i	$-0.432986\pi$
$241$	6.48846	0.417958	0.208979	+	0.977920i	$0.432986\pi$
$242$	−63.3331	−4.07120
$243$	−15.5803	−0.999479
$244$	−53.3163	−3.41323
$245$	8.63919	0.551938
$246$	24.6902	1.57419
$247$	7.25785	0.461806
$248$	26.2022	1.66384
$249$	−3.89578	−0.246885
$250$	−15.5980	−0.986507
$251$	7.13937	0.450633	0.225317	−	0.974286i	$-0.427658\pi$
$251$	7.13937	0.450633	0.225317	+	0.974286i	$0.427658\pi$
$252$	25.4961	1.60610
$253$	−23.2723	−1.46311
$254$	35.6446	2.23654
$255$	0.286426	0.0179367
$256$	27.2853	1.70533
$257$	3.38045	0.210867	0.105433	−	0.994426i	$-0.466377\pi$
$257$	3.38045	0.210867	0.105433	+	0.994426i	$0.466377\pi$
$258$	−8.82291	−0.549290
$259$	−1.98436	−0.123302
$260$	62.6164	3.88330
$261$	12.7521	0.789333
$262$	−57.1451	−3.53044
$263$	12.1643	0.750083	0.375042	−	0.927008i	$-0.377628\pi$
$263$	12.1643	0.750083	0.375042	+	0.927008i	$0.377628\pi$
$264$	40.7944	2.51072
$265$	−2.66769	−0.163875
$266$	−9.38005	−0.575128
$267$	11.0968	0.679114
$268$	62.2087	3.80000
$269$	−11.2779	−0.687628	−0.343814	−	0.939038i	$-0.611719\pi$
$269$	−11.2779	−0.687628	−0.343814	+	0.939038i	$0.611719\pi$
$270$	31.8066	1.93569
$271$	−9.53287	−0.579080	−0.289540	−	0.957166i	$-0.593502\pi$
$271$	−9.53287	−0.579080	−0.289540	+	0.957166i	$0.593502\pi$
$272$	1.82135	0.110435
$273$	−6.35245	−0.384468
$274$	20.4686	1.23655
$275$	17.3490	1.04618
$276$	16.3044	0.981409
$277$	−10.4629	−0.628657	−0.314328	−	0.949314i	$-0.601779\pi$
$277$	−10.4629	−0.628657	−0.314328	+	0.949314i	$0.601779\pi$
$278$	57.7670	3.46464
$279$	6.97927	0.417838
$280$	−50.5986	−3.02384
$281$	6.90310	0.411804	0.205902	−	0.978573i	$-0.433987\pi$
$281$	6.90310	0.411804	0.205902	+	0.978573i	$0.433987\pi$
$282$	−24.0567	−1.43256
$283$	22.0043	1.30802	0.654010	−	0.756486i	$-0.273085\pi$
$283$	22.0043	1.30802	0.654010	+	0.756486i	$0.273085\pi$
$284$	−21.9456	−1.30223
$285$	−3.78961	−0.224477
$286$	66.0537	3.90584
$287$	−23.4988	−1.38709
$288$	46.5263	2.74159
$289$	−16.9826	−0.998977
$290$	−40.4754	−2.37680
$291$	14.5285	0.851673
$292$	−5.13152	−0.300300
$293$	7.92971	0.463259	0.231629	−	0.972804i	$-0.425594\pi$
$293$	7.92971	0.463259	0.231629	+	0.972804i	$0.425594\pi$
$294$	−6.38481	−0.372370
$295$	−3.21189	−0.187003
$296$	−9.03847	−0.525350
$297$	24.4063	1.41620
$298$	−5.74743	−0.332940
$299$	16.5065	0.954593
$300$	−12.1546	−0.701746
$301$	8.39720	0.484006
$302$	17.5896	1.01217
$303$	4.53389	0.260465
$304$	−24.0976	−1.38209
$305$	28.1836	1.61379
$306$	0.860142	0.0491711
$307$	−13.2999	−0.759064	−0.379532	−	0.925179i	$-0.623915\pi$
$307$	−13.2999	−0.759064	−0.379532	+	0.925179i	$0.623915\pi$
$308$	−62.0970	−3.53830
$309$	4.20682	0.239318
$310$	−22.1524	−1.25817
$311$	−29.9914	−1.70066	−0.850329	−	0.526251i	$-0.823597\pi$
$311$	−29.9914	−1.70066	−0.850329	+	0.526251i	$0.823597\pi$
$312$	−28.9345	−1.63809
$313$	−3.15124	−0.178119	−0.0890593	−	0.996026i	$-0.528386\pi$
$313$	−3.15124	−0.178119	−0.0890593	+	0.996026i	$0.528386\pi$
$314$	41.3263	2.33218
$315$	−13.4775	−0.759373
$316$	−23.0963	−1.29927
$317$	−29.4894	−1.65629	−0.828145	−	0.560514i	$-0.810604\pi$
$317$	−29.4894	−1.65629	−0.828145	+	0.560514i	$0.810604\pi$
$318$	1.97156	0.110560
$319$	−31.0582	−1.73893
$320$	−69.7651	−3.89999
$321$	2.28380	0.127469
$322$	−21.3330	−1.18884
$323$	−0.230185	−0.0128078
$324$	21.4467	1.19148
$325$	−12.3052	−0.682571
$326$	2.70867	0.150019
$327$	10.7558	0.594799
$328$	−107.034	−5.90995
$329$	22.8959	1.26229
$330$	−34.4893	−1.89857
$331$	7.95636	0.437321	0.218661	−	0.975801i	$-0.429831\pi$
$331$	7.95636	0.437321	0.218661	+	0.975801i	$0.429831\pi$
$332$	27.0108	1.48241
$333$	−2.40750	−0.131930
$334$	−34.1106	−1.86645
$335$	−32.8842	−1.79666
$336$	21.0915	1.15064
$337$	−23.2456	−1.26627	−0.633135	−	0.774041i	$-0.718232\pi$
$337$	−23.2456	−1.26627	−0.633135	+	0.774041i	$0.718232\pi$
$338$	−11.6376	−0.633004
$339$	9.07983	0.493149
$340$	−1.98590	−0.107701
$341$	−16.9983	−0.920511
$342$	−11.3803	−0.615374
$343$	19.9673	1.07813
$344$	38.2480	2.06219
$345$	−8.61868	−0.464014
$346$	−9.27197	−0.498464
$347$	−21.2953	−1.14319	−0.571595	−	0.820536i	$-0.693675\pi$
$347$	−21.2953	−1.14319	−0.571595	+	0.820536i	$0.693675\pi$
$348$	21.7592	1.16641
$349$	−1.67065	−0.0894277	−0.0447139	−	0.999000i	$-0.514238\pi$
$349$	−1.67065	−0.0894277	−0.0447139	+	0.999000i	$0.514238\pi$
$350$	15.9033	0.850067
$351$	−17.3108	−0.923984
$352$	−113.317	−6.03981
$353$	−8.54841	−0.454986	−0.227493	−	0.973780i	$-0.573053\pi$
$353$	−8.54841	−0.454986	−0.227493	+	0.973780i	$0.573053\pi$
$354$	2.37375	0.126163
$355$	11.6007	0.615702
$356$	−76.9383	−4.07772
$357$	0.201470	0.0106629
$358$	−12.0738	−0.638122
$359$	−37.4285	−1.97540	−0.987701	−	0.156357i	$-0.950025\pi$
$359$	−37.4285	−1.97540	−0.987701	+	0.156357i	$0.950025\pi$
$360$	−61.3882	−3.23544
$361$	−15.9545	−0.839710
$362$	−23.8353	−1.25275
$363$	−17.9977	−0.944636
$364$	44.0439	2.30853
$365$	2.71258	0.141983
$366$	−20.8291	−1.08876
$367$	1.07875	0.0563104	0.0281552	−	0.999604i	$-0.491037\pi$
$367$	1.07875	0.0563104	0.0281552	+	0.999604i	$0.491037\pi$
$368$	−54.8050	−2.85691
$369$	−28.5097	−1.48416
$370$	7.64150	0.397262
$371$	−1.87643	−0.0974195
$372$	11.9089	0.617448
$373$	11.2768	0.583891	0.291946	−	0.956435i	$-0.405697\pi$
$373$	11.2768	0.583891	0.291946	+	0.956435i	$0.405697\pi$
$374$	−2.09492	−0.108325
$375$	−4.43259	−0.228898
$376$	104.288	5.37823
$377$	22.0288	1.13454
$378$	22.3725	1.15072
$379$	6.06841	0.311713	0.155857	−	0.987780i	$-0.450186\pi$
$379$	6.06841	0.311713	0.155857	+	0.987780i	$0.450186\pi$
$380$	26.2748	1.34787
$381$	10.1293	0.518942
$382$	−53.3786	−2.73109
$383$	3.89773	0.199165	0.0995824	−	0.995029i	$-0.468249\pi$
$383$	3.89773	0.199165	0.0995824	+	0.995029i	$0.468249\pi$
$384$	21.8089	1.11293
$385$	32.8252	1.67292
$386$	72.2581	3.67784
$387$	10.1878	0.517876
$388$	−100.731	−5.11385
$389$	14.3845	0.729323	0.364661	−	0.931140i	$-0.381185\pi$
$389$	14.3845	0.729323	0.364661	+	0.931140i	$0.381185\pi$
$390$	24.4624	1.23870
$391$	−0.523508	−0.0264749
$392$	27.6786	1.39798
$393$	−16.2393	−0.819162
$394$	51.0773	2.57323
$395$	12.2090	0.614300
$396$	−75.3385	−3.78590
$397$	−19.9747	−1.00250	−0.501252	−	0.865301i	$-0.667127\pi$
$397$	−19.9747	−1.00250	−0.501252	+	0.865301i	$0.667127\pi$
$398$	−53.4989	−2.68166
$399$	−2.66558	−0.133446
$400$	40.8560	2.04280
$401$	22.1586	1.10655	0.553275	−	0.832999i	$-0.313378\pi$
$401$	22.1586	1.10655	0.553275	+	0.832999i	$0.313378\pi$
$402$	24.3031	1.21213
$403$	12.0565	0.600577
$404$	−31.4351	−1.56396
$405$	−11.3370	−0.563339
$406$	−28.4701	−1.41295
$407$	5.86359	0.290647
$408$	0.917666	0.0454313
$409$	−5.53158	−0.273519	−0.136759	−	0.990604i	$-0.543669\pi$
$409$	−5.53158	−0.273519	−0.136759	+	0.990604i	$0.543669\pi$
$410$	90.4908	4.46902
$411$	5.81667	0.286915
$412$	−29.1674	−1.43698
$413$	−2.25922	−0.111169
$414$	−25.8820	−1.27203
$415$	−14.2782	−0.700891
$416$	80.3729	3.94061
$417$	16.4160	0.803895
$418$	27.7171	1.35569
$419$	30.0460	1.46784	0.733921	−	0.679235i	$-0.237688\pi$
$419$	30.0460	1.46784	0.733921	+	0.679235i	$0.237688\pi$
$420$	−22.9971	−1.12214
$421$	−18.4081	−0.897156	−0.448578	−	0.893744i	$-0.648069\pi$
$421$	−18.4081	−0.897156	−0.448578	+	0.893744i	$0.648069\pi$
$422$	34.7784	1.69299
$423$	27.7783	1.35063
$424$	−8.54687	−0.415073
$425$	0.390264	0.0189306
$426$	−8.57353	−0.415389
$427$	19.8241	0.959356
$428$	−15.8344	−0.765387
$429$	18.7709	0.906266
$430$	−32.3365	−1.55940
$431$	5.11667	0.246461	0.123231	−	0.992378i	$-0.460675\pi$
$431$	5.11667	0.246461	0.123231	+	0.992378i	$0.460675\pi$
$432$	57.4757	2.76530
$433$	39.2742	1.88740	0.943699	−	0.330806i	$-0.107320\pi$
$433$	39.2742	1.88740	0.943699	+	0.330806i	$0.107320\pi$
$434$	−15.5818	−0.747952
$435$	−11.5021	−0.551485
$436$	−74.5741	−3.57145
$437$	6.92636	0.331333
$438$	−2.00474	−0.0957900
$439$	28.3059	1.35097	0.675484	−	0.737374i	$-0.263935\pi$
$439$	28.3059	1.35097	0.675484	+	0.737374i	$0.263935\pi$
$440$	149.514	7.12779
$441$	7.37254	0.351073
$442$	1.48587	0.0706757
$443$	−27.5858	−1.31064	−0.655320	−	0.755352i	$-0.727466\pi$
$443$	−27.5858	−1.31064	−0.655320	+	0.755352i	$0.727466\pi$
$444$	−4.10799	−0.194956
$445$	40.6704	1.92796
$446$	31.6327	1.49785
$447$	−1.63328	−0.0772515
$448$	−49.0722	−2.31844
$449$	−20.5388	−0.969288	−0.484644	−	0.874712i	$-0.661051\pi$
$449$	−20.5388	−0.969288	−0.484644	+	0.874712i	$0.661051\pi$
$450$	19.2945	0.909552
$451$	69.4367	3.26965
$452$	−62.9538	−2.96110
$453$	4.99853	0.234851
$454$	5.63916	0.264659
$455$	−23.2821	−1.09148
$456$	−12.1413	−0.568570
$457$	22.0923	1.03344	0.516718	−	0.856156i	$-0.327153\pi$
$457$	22.0923	1.03344	0.516718	+	0.856156i	$0.327153\pi$
$458$	8.47881	0.396189
$459$	0.549019	0.0256260
$460$	59.7565	2.78616
$461$	28.6952	1.33647	0.668234	−	0.743951i	$-0.267051\pi$
$461$	28.6952	1.33647	0.668234	+	0.743951i	$0.267051\pi$
$462$	−24.2595	−1.12865
$463$	7.00693	0.325639	0.162820	−	0.986656i	$-0.447941\pi$
$463$	7.00693	0.325639	0.162820	+	0.986656i	$0.447941\pi$
$464$	−73.1405	−3.39546
$465$	−6.29518	−0.291932
$466$	1.04151	0.0482472
$467$	38.7552	1.79338	0.896689	−	0.442661i	$-0.145965\pi$
$467$	38.7552	1.79338	0.896689	+	0.442661i	$0.145965\pi$
$468$	53.4358	2.47007
$469$	−23.1305	−1.06807
$470$	−88.1691	−4.06694
$471$	11.7439	0.541132
$472$	−10.2904	−0.473654
$473$	−24.8129	−1.14090
$474$	−9.02306	−0.414443
$475$	−5.16346	−0.236916
$476$	−1.39687	−0.0640252
$477$	−2.27656	−0.104237
$478$	14.9687	0.684654
$479$	15.1657	0.692939	0.346470	−	0.938061i	$-0.387380\pi$
$479$	15.1657	0.692939	0.346470	+	0.938061i	$0.387380\pi$
$480$	−41.9659	−1.91547
$481$	−4.15890	−0.189630
$482$	−17.5751	−0.800522
$483$	−6.06231	−0.275845
$484$	124.785	5.67204
$485$	53.2476	2.41785
$486$	42.2019	1.91432
$487$	10.3152	0.467428	0.233714	−	0.972305i	$-0.424912\pi$
$487$	10.3152	0.467428	0.233714	+	0.972305i	$0.424912\pi$
$488$	90.2959	4.08751
$489$	0.769737	0.0348087
$490$	−23.4007	−1.05713
$491$	−43.5299	−1.96448	−0.982238	−	0.187641i	$-0.939916\pi$
$491$	−43.5299	−1.96448	−0.982238	+	0.187641i	$0.939916\pi$
$492$	−48.6469	−2.19317
$493$	−0.698652	−0.0314657
$494$	−19.6591	−0.884504
$495$	39.8248	1.78999
$496$	−40.0302	−1.79741
$497$	8.15985	0.366019
$498$	10.5524	0.472862
$499$	0.826322	0.0369913	0.0184956	−	0.999829i	$-0.494112\pi$
$499$	0.826322	0.0369913	0.0184956	+	0.999829i	$0.494112\pi$
$500$	30.7327	1.37441
$501$	−9.69341	−0.433070
$502$	−19.3382	−0.863105
$503$	33.4824	1.49291	0.746453	−	0.665438i	$-0.231755\pi$
$503$	33.4824	1.49291	0.746453	+	0.665438i	$0.231755\pi$
$504$	−43.1800	−1.92339
$505$	16.6170	0.739445
$506$	63.0368	2.80233
$507$	−3.30713	−0.146875
$508$	−70.2304	−3.11597
$509$	36.8541	1.63353	0.816765	−	0.576970i	$-0.195765\pi$
$509$	36.8541	1.63353	0.816765	+	0.576970i	$0.195765\pi$
$510$	−0.775834	−0.0343545
$511$	1.90801	0.0844053
$512$	−17.2411	−0.761955
$513$	−7.26388	−0.320708
$514$	−9.15651	−0.403876
$515$	15.4182	0.679409
$516$	17.3837	0.765276
$517$	−67.6553	−2.97548
$518$	5.37497	0.236162
$519$	−2.63487	−0.115658
$520$	−106.046	−4.65044
$521$	−15.7322	−0.689242	−0.344621	−	0.938742i	$-0.611992\pi$
$521$	−15.7322	−0.689242	−0.344621	+	0.938742i	$0.611992\pi$
$522$	−34.5411	−1.51182
$523$	8.32995	0.364243	0.182122	−	0.983276i	$-0.441704\pi$
$523$	8.32995	0.364243	0.182122	+	0.983276i	$0.441704\pi$
$524$	112.593	4.91864
$525$	4.51933	0.197240
$526$	−32.9490	−1.43665
$527$	−0.382376	−0.0166566
$528$	−62.3233	−2.71227
$529$	−7.24746	−0.315107
$530$	7.22588	0.313872
$531$	−2.74097	−0.118948
$532$	18.4815	0.801273
$533$	−49.2498	−2.13325
$534$	−30.0576	−1.30072
$535$	8.37026	0.361878
$536$	−105.356	−4.55069
$537$	−3.43109	−0.148063
$538$	30.5481	1.31702
$539$	−17.9562	−0.773427
$540$	−62.6685	−2.69682
$541$	−4.19739	−0.180460	−0.0902299	−	0.995921i	$-0.528760\pi$
$541$	−4.19739	−0.180460	−0.0902299	+	0.995921i	$0.528760\pi$
$542$	25.8213	1.10912
$543$	−6.77341	−0.290675
$544$	−2.54905	−0.109290
$545$	39.4207	1.68860
$546$	17.2067	0.736377
$547$	29.8202	1.27502	0.637509	−	0.770443i	$-0.279965\pi$
$547$	29.8202	1.27502	0.637509	+	0.770443i	$0.279965\pi$
$548$	−40.3291	−1.72277
$549$	24.0514	1.02649
$550$	−46.9927	−2.00377
$551$	9.24363	0.393792
$552$	−27.6129	−1.17528
$553$	8.58769	0.365186
$554$	28.3406	1.20408
$555$	2.17153	0.0921762
$556$	−113.818	−4.82696
$557$	−3.09739	−0.131241	−0.0656203	−	0.997845i	$-0.520903\pi$
$557$	−3.09739	−0.131241	−0.0656203	+	0.997845i	$0.520903\pi$
$558$	−18.9045	−0.800292
$559$	17.5992	0.744366
$560$	77.3015	3.26659
$561$	−0.595324	−0.0251346
$562$	−18.6982	−0.788735
$563$	27.8722	1.17467	0.587336	−	0.809343i	$-0.300177\pi$
$563$	27.8722	1.17467	0.587336	+	0.809343i	$0.300177\pi$
$564$	47.3988	1.99585
$565$	33.2781	1.40002
$566$	−59.6023	−2.50527
$567$	−7.97433	−0.334891
$568$	37.1669	1.55949
$569$	15.4100	0.646021	0.323011	−	0.946395i	$-0.395305\pi$
$569$	15.4100	0.646021	0.323011	+	0.946395i	$0.395305\pi$
$570$	10.2648	0.429945
$571$	32.5757	1.36325	0.681626	−	0.731701i	$-0.261273\pi$
$571$	32.5757	1.36325	0.681626	+	0.731701i	$0.261273\pi$
$572$	−130.145	−5.44165
$573$	−15.1689	−0.633691
$574$	63.6505	2.65672
$575$	−11.7432	−0.489726
$576$	−59.5364	−2.48068
$577$	−29.0565	−1.20964	−0.604820	−	0.796363i	$-0.706755\pi$
$577$	−29.0565	−1.20964	−0.604820	+	0.796363i	$0.706755\pi$
$578$	46.0002	1.91336
$579$	20.5340	0.853364
$580$	79.7486	3.31138
$581$	−10.0432	−0.416662
$582$	−39.3527	−1.63122
$583$	5.54467	0.229637
$584$	8.69069	0.359623
$585$	−28.2468	−1.16786
$586$	−21.4789	−0.887287
$587$	26.9569	1.11263	0.556314	−	0.830972i	$-0.312215\pi$
$587$	26.9569	1.11263	0.556314	+	0.830972i	$0.312215\pi$
$588$	12.5800	0.518789
$589$	5.05909	0.208456
$590$	8.69993	0.358170
$591$	14.5149	0.597064
$592$	13.8084	0.567523
$593$	40.2946	1.65470	0.827350	−	0.561687i	$-0.189848\pi$
$593$	40.2946	1.65470	0.827350	+	0.561687i	$0.189848\pi$
$594$	−66.1086	−2.71247
$595$	0.738399	0.0302714
$596$	11.3241	0.463855
$597$	−15.2031	−0.622221
$598$	−44.7105	−1.82835
$599$	−41.7598	−1.70626	−0.853129	−	0.521700i	$-0.825298\pi$
$599$	−41.7598	−1.70626	−0.853129	+	0.521700i	$0.825298\pi$
$600$	20.5849	0.840374
$601$	38.2124	1.55872	0.779358	−	0.626579i	$-0.215545\pi$
$601$	38.2124	1.55872	0.779358	+	0.626579i	$0.215545\pi$
$602$	−22.7452	−0.927025
$603$	−28.0628	−1.14281
$604$	−34.6567	−1.41016
$605$	−65.9627	−2.68176
$606$	−12.2808	−0.498873
$607$	12.3625	0.501778	0.250889	−	0.968016i	$-0.419277\pi$
$607$	12.3625	0.501778	0.250889	+	0.968016i	$0.419277\pi$
$608$	33.7257	1.36776
$609$	−8.09051	−0.327844
$610$	−76.3400	−3.09091
$611$	47.9862	1.94132
$612$	−1.69473	−0.0685055
$613$	−24.6760	−0.996656	−0.498328	−	0.866989i	$-0.666052\pi$
$613$	−24.6760	−0.996656	−0.498328	+	0.866989i	$0.666052\pi$
$614$	36.0249	1.45385
$615$	25.7153	1.03694
$616$	105.167	4.23729
$617$	−28.6217	−1.15226	−0.576132	−	0.817356i	$-0.695439\pi$
$617$	−28.6217	−1.15226	−0.576132	+	0.817356i	$0.695439\pi$
$618$	−11.3949	−0.458369
$619$	26.6866	1.07263	0.536313	−	0.844019i	$-0.319817\pi$
$619$	26.6866	1.07263	0.536313	+	0.844019i	$0.319817\pi$
$620$	43.6468	1.75290
$621$	−16.5202	−0.662932
$622$	81.2368	3.25730
$623$	28.6073	1.14613
$624$	44.2044	1.76959
$625$	−31.0395	−1.24158
$626$	8.53565	0.341153
$627$	7.87654	0.314559
$628$	−81.4249	−3.24921
$629$	0.131901	0.00525923
$630$	36.5061	1.45444
$631$	15.3312	0.610327	0.305164	−	0.952300i	$-0.401289\pi$
$631$	15.3312	0.610327	0.305164	+	0.952300i	$0.401289\pi$
$632$	39.1156	1.55594
$633$	9.88319	0.392821
$634$	79.8769	3.17232
$635$	37.1246	1.47324
$636$	−3.88456	−0.154033
$637$	12.7359	0.504613
$638$	84.1263	3.33059
$639$	9.89986	0.391632
$640$	79.9307	3.15954
$641$	27.3788	1.08140	0.540698	−	0.841216i	$-0.318160\pi$
$641$	27.3788	1.08140	0.540698	+	0.841216i	$0.318160\pi$
$642$	−6.18606	−0.244144
$643$	−19.5008	−0.769037	−0.384519	−	0.923117i	$-0.625633\pi$
$643$	−19.5008	−0.769037	−0.384519	+	0.923117i	$0.625633\pi$
$644$	42.0322	1.65630
$645$	−9.18924	−0.361826
$646$	0.623494	0.0245311
$647$	−2.25935	−0.0888244	−0.0444122	−	0.999013i	$-0.514141\pi$
$647$	−2.25935	−0.0888244	−0.0444122	+	0.999013i	$0.514141\pi$
$648$	−36.3219	−1.42686
$649$	6.67576	0.262046
$650$	33.3308	1.30734
$651$	−4.42798	−0.173546
$652$	−5.33687	−0.209008
$653$	−1.41193	−0.0552532	−0.0276266	−	0.999618i	$-0.508795\pi$
$653$	−1.41193	−0.0552532	−0.0276266	+	0.999618i	$0.508795\pi$
$654$	−29.1339	−1.13923
$655$	−59.5178	−2.32555
$656$	163.520	6.38438
$657$	2.31487	0.0903117
$658$	−62.0175	−2.41769
$659$	−9.17199	−0.357290	−0.178645	−	0.983914i	$-0.557171\pi$
$659$	−9.17199	−0.357290	−0.178645	+	0.983914i	$0.557171\pi$
$660$	67.9541	2.64511
$661$	−31.0519	−1.20778	−0.603889	−	0.797069i	$-0.706383\pi$
$661$	−31.0519	−1.20778	−0.603889	+	0.797069i	$0.706383\pi$
$662$	−21.5511	−0.837608
$663$	0.422249	0.0163988
$664$	−45.7453	−1.77526
$665$	−9.76951	−0.378845
$666$	6.52113	0.252688
$667$	21.0227	0.814002
$668$	67.2080	2.60035
$669$	8.98926	0.347545
$670$	89.0724	3.44117
$671$	−58.5783	−2.26139
$672$	−29.5185	−1.13870
$673$	11.9995	0.462548	0.231274	−	0.972889i	$-0.425711\pi$
$673$	11.9995	0.462548	0.231274	+	0.972889i	$0.425711\pi$
$674$	62.9646	2.42531
$675$	12.3155	0.474022
$676$	22.9296	0.881907
$677$	−9.39642	−0.361134	−0.180567	−	0.983563i	$-0.557793\pi$
$677$	−9.39642	−0.361134	−0.180567	+	0.983563i	$0.557793\pi$
$678$	−24.5942	−0.944535
$679$	37.4539	1.43735
$680$	3.36330	0.128977
$681$	1.60251	0.0614084
$682$	46.0428	1.76307
$683$	0.865087	0.0331017	0.0165508	−	0.999863i	$-0.494731\pi$
$683$	0.865087	0.0331017	0.0165508	+	0.999863i	$0.494731\pi$
$684$	22.4225	0.857344
$685$	21.3184	0.814535
$686$	−54.0846	−2.06496
$687$	2.40947	0.0919271
$688$	−58.4331	−2.22774
$689$	−3.93270	−0.149824
$690$	23.3451	0.888734
$691$	27.7784	1.05674	0.528369	−	0.849015i	$-0.322804\pi$
$691$	27.7784	1.05674	0.528369	+	0.849015i	$0.322804\pi$
$692$	18.2685	0.694464
$693$	28.0124	1.06410
$694$	57.6818	2.18957
$695$	60.1655	2.28221
$696$	−36.8511	−1.39684
$697$	1.56197	0.0591640
$698$	4.52523	0.171282
$699$	0.295973	0.0111947
$700$	−31.3342	−1.18432
$701$	−35.7896	−1.35175	−0.675877	−	0.737015i	$-0.736235\pi$
$701$	−35.7896	−1.35175	−0.675877	+	0.737015i	$0.736235\pi$
$702$	46.8892	1.76972
$703$	−1.74514	−0.0658191
$704$	145.004	5.46503
$705$	−25.0555	−0.943646
$706$	23.1548	0.871442
$707$	11.6882	0.439581
$708$	−4.67699	−0.175772
$709$	22.0641	0.828636	0.414318	−	0.910132i	$-0.364020\pi$
$709$	22.0641	0.828636	0.414318	+	0.910132i	$0.364020\pi$
$710$	−31.4225	−1.17926
$711$	10.4189	0.390740
$712$	130.302	4.88327
$713$	11.5058	0.430897
$714$	−0.545715	−0.0204229
$715$	68.7963	2.57283
$716$	23.7890	0.889038
$717$	4.25375	0.158859
$718$	101.381	3.78352
$719$	−17.0964	−0.637589	−0.318794	−	0.947824i	$-0.603278\pi$
$719$	−17.0964	−0.637589	−0.318794	+	0.947824i	$0.603278\pi$
$720$	93.7853	3.49517
$721$	10.8451	0.403891
$722$	43.2154	1.60831
$723$	−4.99441	−0.185744
$724$	46.9625	1.74535
$725$	−15.6720	−0.582044
$726$	48.7498	1.80928
$727$	−14.5391	−0.539227	−0.269613	−	0.962969i	$-0.586896\pi$
$727$	−14.5391	−0.539227	−0.269613	+	0.962969i	$0.586896\pi$
$728$	−74.5922	−2.76457
$729$	−0.0630193	−0.00233405
$730$	−7.34747	−0.271942
$731$	−0.558164	−0.0206444
$732$	41.0396	1.51687
$733$	45.2695	1.67207	0.836034	−	0.548677i	$-0.184868\pi$
$733$	45.2695	1.67207	0.836034	+	0.548677i	$0.184868\pi$
$734$	−2.92198	−0.107852
$735$	−6.64991	−0.245285
$736$	76.7020	2.82727
$737$	68.3483	2.51764
$738$	77.2233	2.84263
$739$	−23.0494	−0.847884	−0.423942	−	0.905689i	$-0.639354\pi$
$739$	−23.0494	−0.847884	−0.423942	+	0.905689i	$0.639354\pi$
$740$	−15.0560	−0.553470
$741$	−5.58664	−0.205230
$742$	5.08263	0.186589
$743$	22.5117	0.825875	0.412938	−	0.910759i	$-0.364503\pi$
$743$	22.5117	0.825875	0.412938	+	0.910759i	$0.364503\pi$
$744$	−20.1688	−0.739424
$745$	−5.98606	−0.219312
$746$	−30.5451	−1.11834
$747$	−12.1848	−0.445819
$748$	4.12760	0.150920
$749$	5.88758	0.215127
$750$	12.0064	0.438412
$751$	5.79860	0.211594	0.105797	−	0.994388i	$-0.466261\pi$
$751$	5.79860	0.211594	0.105797	+	0.994388i	$0.466261\pi$
$752$	−159.325	−5.80997
$753$	−5.49544	−0.200265
$754$	−59.6688	−2.17301
$755$	18.3199	0.666729
$756$	−44.0805	−1.60319
$757$	12.8881	0.468425	0.234213	−	0.972185i	$-0.424749\pi$
$757$	12.8881	0.468425	0.234213	+	0.972185i	$0.424749\pi$
$758$	−16.4373	−0.597030
$759$	17.9135	0.650220
$760$	−44.4987	−1.61414
$761$	−28.8267	−1.04497	−0.522484	−	0.852649i	$-0.674994\pi$
$761$	−28.8267	−1.04497	−0.522484	+	0.852649i	$0.674994\pi$
$762$	−27.4370	−0.993937
$763$	27.7282	1.00383
$764$	105.172	3.80498
$765$	0.895855	0.0323897
$766$	−10.5577	−0.381464
$767$	−4.73495	−0.170969
$768$	−21.0025	−0.757864
$769$	−34.6725	−1.25032	−0.625162	−	0.780495i	$-0.714967\pi$
$769$	−34.6725	−1.25032	−0.625162	+	0.780495i	$0.714967\pi$
$770$	−88.9124	−3.20418
$771$	−2.60206	−0.0937109
$772$	−142.370	−5.12400
$773$	11.3473	0.408133	0.204067	−	0.978957i	$-0.434584\pi$
$773$	11.3473	0.408133	0.204067	+	0.978957i	$0.434584\pi$
$774$	−27.5954	−0.991896
$775$	−8.57737	−0.308108
$776$	170.597	6.12408
$777$	1.52744	0.0547964
$778$	−38.9628	−1.39688
$779$	−20.6660	−0.740435
$780$	−48.1982	−1.72577
$781$	−24.1116	−0.862779
$782$	1.41801	0.0507078
$783$	−22.0472	−0.787901
$784$	−42.2858	−1.51021
$785$	43.0421	1.53624
$786$	43.9867	1.56895
$787$	10.2909	0.366832	0.183416	−	0.983035i	$-0.441285\pi$
$787$	10.2909	0.366832	0.183416	+	0.983035i	$0.441285\pi$
$788$	−100.637	−3.58505
$789$	−9.36332	−0.333343
$790$	−33.0700	−1.17658
$791$	23.4075	0.832276
$792$	127.593	4.53380
$793$	41.5482	1.47542
$794$	54.1049	1.92011
$795$	2.05342	0.0728273
$796$	105.409	3.73611
$797$	7.93445	0.281053	0.140526	−	0.990077i	$-0.455121\pi$
$797$	7.93445	0.281053	0.140526	+	0.990077i	$0.455121\pi$
$798$	7.22017	0.255591
$799$	−1.52190	−0.0538409
$800$	−57.1798	−2.02161
$801$	34.7075	1.22633
$802$	−60.0204	−2.11939
$803$	−5.63797	−0.198960
$804$	−47.8844	−1.68875
$805$	−22.2187	−0.783106
$806$	−32.6570	−1.15030
$807$	8.68104	0.305587
$808$	53.2382	1.87291
$809$	−30.4669	−1.07116	−0.535579	−	0.844485i	$-0.679907\pi$
$809$	−30.4669	−1.07116	−0.535579	+	0.844485i	$0.679907\pi$
$810$	30.7081	1.07897
$811$	25.8494	0.907696	0.453848	−	0.891079i	$-0.350051\pi$
$811$	25.8494	0.907696	0.453848	+	0.891079i	$0.350051\pi$
$812$	56.0945	1.96853
$813$	7.33780	0.257348
$814$	−15.8825	−0.556681
$815$	2.82113	0.0988199
$816$	−1.40196	−0.0490783
$817$	7.38488	0.258364
$818$	14.9832	0.523875
$819$	−19.8685	−0.694263
$820$	−178.294	−6.22628
$821$	−18.3344	−0.639875	−0.319937	−	0.947439i	$-0.603662\pi$
$821$	−18.3344	−0.639875	−0.319937	+	0.947439i	$0.603662\pi$
$822$	−15.7554	−0.549533
$823$	22.6455	0.789371	0.394685	−	0.918816i	$-0.370854\pi$
$823$	22.6455	0.789371	0.394685	+	0.918816i	$0.370854\pi$
$824$	49.3977	1.72085
$825$	−13.3542	−0.464933
$826$	6.11946	0.212923
$827$	−29.0469	−1.01006	−0.505029	−	0.863102i	$-0.668518\pi$
$827$	−29.0469	−1.01006	−0.505029	+	0.863102i	$0.668518\pi$
$828$	50.9952	1.77220
$829$	47.3766	1.64546	0.822729	−	0.568434i	$-0.192450\pi$
$829$	47.3766	1.64546	0.822729	+	0.568434i	$0.192450\pi$
$830$	38.6750	1.34243
$831$	8.05371	0.279380
$832$	−102.847	−3.56559
$833$	−0.403922	−0.0139951
$834$	−44.4654	−1.53971
$835$	−35.5269	−1.22946
$836$	−54.6109	−1.88876
$837$	−12.0665	−0.417080
$838$	−81.3845	−2.81138
$839$	−34.3129	−1.18461	−0.592306	−	0.805713i	$-0.701782\pi$
$839$	−34.3129	−1.18461	−0.592306	+	0.805713i	$0.701782\pi$
$840$	38.9476	1.34382
$841$	−0.943952	−0.0325501
$842$	49.8614	1.71834
$843$	−5.31357	−0.183009
$844$	−68.5238	−2.35868
$845$	−12.1208	−0.416969
$846$	−75.2421	−2.58688
$847$	−46.3976	−1.59424
$848$	13.0574	0.448394
$849$	−16.9375	−0.581295
$850$	−1.05710	−0.0362581
$851$	−3.96895	−0.136054
$852$	16.8924	0.578723
$853$	13.5004	0.462246	0.231123	−	0.972925i	$-0.425760\pi$
$853$	13.5004	0.462246	0.231123	+	0.972925i	$0.425760\pi$
$854$	−53.6969	−1.83747
$855$	−11.8528	−0.405356
$856$	26.8170	0.916588
$857$	41.0012	1.40057	0.700286	−	0.713862i	$-0.253056\pi$
$857$	41.0012	1.40057	0.700286	+	0.713862i	$0.253056\pi$
$858$	−50.8440	−1.73579
$859$	−22.5200	−0.768371	−0.384185	−	0.923256i	$-0.625518\pi$
$859$	−22.5200	−0.768371	−0.384185	+	0.923256i	$0.625518\pi$
$860$	63.7124	2.17257
$861$	18.0879	0.616435
$862$	−13.8593	−0.472051
$863$	44.7402	1.52297	0.761487	−	0.648180i	$-0.224470\pi$
$863$	44.7402	1.52297	0.761487	+	0.648180i	$0.224470\pi$
$864$	−80.4397	−2.73661
$865$	−9.65694	−0.328346
$866$	−106.381	−3.61496
$867$	13.0721	0.443953
$868$	30.7008	1.04205
$869$	−25.3758	−0.860814
$870$	31.1555	1.05627
$871$	−48.4778	−1.64261
$872$	126.298	4.27699
$873$	45.4406	1.53793
$874$	−18.7612	−0.634606
$875$	−11.4271	−0.386306
$876$	3.94992	0.133456
$877$	−15.3559	−0.518533	−0.259266	−	0.965806i	$-0.583481\pi$
$877$	−15.3559	−0.518533	−0.259266	+	0.965806i	$0.583481\pi$
$878$	−76.6713	−2.58753
$879$	−6.10380	−0.205876
$880$	−228.418	−7.69998
$881$	38.4373	1.29498	0.647492	−	0.762072i	$-0.275818\pi$
$881$	38.4373	1.29498	0.647492	+	0.762072i	$0.275818\pi$
$882$	−19.9698	−0.672416
$883$	−20.6550	−0.695095	−0.347547	−	0.937662i	$-0.612985\pi$
$883$	−20.6550	−0.695095	−0.347547	+	0.937662i	$0.612985\pi$
$884$	−2.92761	−0.0984661
$885$	2.47231	0.0831057
$886$	74.7206	2.51029
$887$	42.0918	1.41330	0.706652	−	0.707561i	$-0.250205\pi$
$887$	42.0918	1.41330	0.706652	+	0.707561i	$0.250205\pi$
$888$	6.95724	0.233470
$889$	26.1131	0.875806
$890$	−110.163	−3.69266
$891$	23.5634	0.789403
$892$	−62.3258	−2.08682
$893$	20.1357	0.673817
$894$	4.42401	0.147961
$895$	−12.5751	−0.420341
$896$	56.2226	1.87827
$897$	−12.7056	−0.424229
$898$	55.6328	1.85649
$899$	15.3552	0.512126
$900$	−38.0159	−1.26720
$901$	0.124727	0.00415526
$902$	−188.081	−6.26241
$903$	−6.46364	−0.215096
$904$	106.618	3.54606
$905$	−24.8249	−0.825208
$906$	−13.5394	−0.449815
$907$	51.9734	1.72575	0.862874	−	0.505420i	$-0.168662\pi$
$907$	51.9734	1.72575	0.862874	+	0.505420i	$0.168662\pi$
$908$	−11.1108	−0.368725
$909$	14.1806	0.470342
$910$	63.0634	2.09053
$911$	−51.9475	−1.72110	−0.860549	−	0.509368i	$-0.829879\pi$
$911$	−51.9475	−1.72110	−0.860549	+	0.509368i	$0.829879\pi$
$912$	18.5488	0.614213
$913$	29.6767	0.982154
$914$	−59.8408	−1.97936
$915$	−21.6940	−0.717180
$916$	−16.7058	−0.551974
$917$	−41.8643	−1.38248
$918$	−1.48711	−0.0490819
$919$	2.33182	0.0769198	0.0384599	−	0.999260i	$-0.487755\pi$
$919$	2.33182	0.0769198	0.0384599	+	0.999260i	$0.487755\pi$
$920$	−101.203	−3.33656
$921$	10.2374	0.337334
$922$	−77.7257	−2.55976
$923$	17.1017	0.562911
$924$	47.7983	1.57245
$925$	2.95877	0.0972838
$926$	−18.9794	−0.623702
$927$	13.1577	0.432155
$928$	102.363	3.36024
$929$	35.7397	1.17258	0.586291	−	0.810101i	$-0.300588\pi$
$929$	35.7397	1.17258	0.586291	+	0.810101i	$0.300588\pi$
$930$	17.0516	0.559142
$931$	5.34416	0.175148
$932$	−2.05209	−0.0672184
$933$	23.0855	0.755786
$934$	−104.975	−3.43489
$935$	−2.18190	−0.0713556
$936$	−90.4983	−2.95803
$937$	−26.8792	−0.878105	−0.439052	−	0.898462i	$-0.644686\pi$
$937$	−26.8792	−0.878105	−0.439052	+	0.898462i	$0.644686\pi$
$938$	62.6528	2.04569
$939$	2.42563	0.0791573
$940$	173.719	5.66610
$941$	−26.1521	−0.852535	−0.426268	−	0.904597i	$-0.640172\pi$
$941$	−26.1521	−0.852535	−0.426268	+	0.904597i	$0.640172\pi$
$942$	−31.8104	−1.03644
$943$	−47.0004	−1.53054
$944$	15.7211	0.511677
$945$	23.3014	0.757996
$946$	67.2098	2.18518
$947$	11.8296	0.384411	0.192205	−	0.981355i	$-0.438436\pi$
$947$	11.8296	0.384411	0.192205	+	0.981355i	$0.438436\pi$
$948$	17.7781	0.577405
$949$	3.99888	0.129809
$950$	13.9861	0.453769
$951$	22.6991	0.736069
$952$	2.36572	0.0766733
$953$	30.3430	0.982905	0.491452	−	0.870904i	$-0.336466\pi$
$953$	30.3430	0.982905	0.491452	+	0.870904i	$0.336466\pi$
$954$	6.16645	0.199646
$955$	−55.5949	−1.79901
$956$	−29.4928	−0.953866
$957$	23.9067	0.772793
$958$	−41.0788	−1.32720
$959$	14.9952	0.484220
$960$	53.7008	1.73319
$961$	−22.5960	−0.728903
$962$	11.2651	0.363200
$963$	7.14304	0.230181
$964$	34.6280	1.11529
$965$	75.2583	2.42265
$966$	16.4208	0.528330
$967$	29.4849	0.948171	0.474085	−	0.880479i	$-0.342779\pi$
$967$	29.4849	0.948171	0.474085	+	0.880479i	$0.342779\pi$
$968$	−211.334	−6.79254
$969$	0.177182	0.00569191
$970$	−144.230	−4.63094
$971$	−4.98402	−0.159945	−0.0799724	−	0.996797i	$-0.525483\pi$
$971$	−4.98402	−0.159945	−0.0799724	+	0.996797i	$0.525483\pi$
$972$	−83.1502	−2.66704
$973$	42.3199	1.35672
$974$	−27.9406	−0.895273
$975$	9.47179	0.303340
$976$	−137.949	−4.41564
$977$	−8.85143	−0.283182	−0.141591	−	0.989925i	$-0.545222\pi$
$977$	−8.85143	−0.283182	−0.141591	+	0.989925i	$0.545222\pi$
$978$	−2.08496	−0.0666697
$979$	−84.5316	−2.70164
$980$	46.1062	1.47281
$981$	33.6410	1.07407
$982$	117.908	3.76259
$983$	−27.9797	−0.892415	−0.446207	−	0.894930i	$-0.647226\pi$
$983$	−27.9797	−0.892415	−0.446207	+	0.894930i	$0.647226\pi$
$984$	82.3878	2.62643
$985$	53.1980	1.69503
$986$	1.89241	0.0602668
$987$	−17.6239	−0.560974
$988$	38.7342	1.23230
$989$	16.7954	0.534061
$990$	−107.872	−3.42840
$991$	−30.2840	−0.962003	−0.481002	−	0.876720i	$-0.659727\pi$
$991$	−30.2840	−0.962003	−0.481002	+	0.876720i	$0.659727\pi$
$992$	56.0240	1.77876
$993$	−6.12431	−0.194349
$994$	−22.1023	−0.701043
$995$	−55.7202	−1.76645
$996$	−20.7913	−0.658796
$997$	31.4158	0.994947	0.497474	−	0.867479i	$-0.334261\pi$
$997$	31.4158	0.994947	0.497474	+	0.867479i	$0.334261\pi$
$998$	−2.23823	−0.0708500
$999$	4.16236	0.131691

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6031.2.a.e.1.4	✓	134

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6031.2.a.e.1.4	✓	134	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:	\( N \)	\(=\)	\( 6031 = 37 \cdot 163 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.70867 q^{2} -0.769737 q^{3} +5.33687 q^{4} -2.82113 q^{5} +2.08496 q^{6} -1.98436 q^{7} -9.03847 q^{8} -2.40750 q^{9} +O(q^{10})\)	\(q-2.70867 q^{2} -0.769737 q^{3} +5.33687 q^{4} -2.82113 q^{5} +2.08496 q^{6} -1.98436 q^{7} -9.03847 q^{8} -2.40750 q^{9} +7.64150 q^{10} +5.86359 q^{11} -4.10799 q^{12} -4.15890 q^{13} +5.37497 q^{14} +2.17153 q^{15} +13.8084 q^{16} +0.131901 q^{17} +6.52113 q^{18} -1.74514 q^{19} -15.0560 q^{20} +1.52744 q^{21} -15.8825 q^{22} -3.96895 q^{23} +6.95724 q^{24} +2.95877 q^{25} +11.2651 q^{26} +4.16236 q^{27} -10.5903 q^{28} -5.29680 q^{29} -5.88194 q^{30} -2.89897 q^{31} -19.3255 q^{32} -4.51342 q^{33} -0.357275 q^{34} +5.59814 q^{35} -12.8485 q^{36} +1.00000 q^{37} +4.72699 q^{38} +3.20126 q^{39} +25.4987 q^{40} +11.8420 q^{41} -4.13731 q^{42} -4.23169 q^{43} +31.2932 q^{44} +6.79188 q^{45} +10.7506 q^{46} -11.5382 q^{47} -10.6289 q^{48} -3.06232 q^{49} -8.01432 q^{50} -0.101529 q^{51} -22.1955 q^{52} +0.945611 q^{53} -11.2744 q^{54} -16.5419 q^{55} +17.9356 q^{56} +1.34330 q^{57} +14.3472 q^{58} +1.13851 q^{59} +11.5892 q^{60} -9.99019 q^{61} +7.85233 q^{62} +4.77736 q^{63} +24.7295 q^{64} +11.7328 q^{65} +12.2253 q^{66} +11.6564 q^{67} +0.703938 q^{68} +3.05505 q^{69} -15.1635 q^{70} -4.11208 q^{71} +21.7601 q^{72} -0.961523 q^{73} -2.70867 q^{74} -2.27748 q^{75} -9.31357 q^{76} -11.6355 q^{77} -8.67114 q^{78} -4.32769 q^{79} -38.9554 q^{80} +4.01859 q^{81} -32.0761 q^{82} +5.06118 q^{83} +8.15172 q^{84} -0.372109 q^{85} +11.4622 q^{86} +4.07714 q^{87} -52.9978 q^{88} -14.4164 q^{89} -18.3969 q^{90} +8.25275 q^{91} -21.1818 q^{92} +2.23144 q^{93} +31.2531 q^{94} +4.92326 q^{95} +14.8756 q^{96} -18.8746 q^{97} +8.29479 q^{98} -14.1166 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 134 q + 9 q^{2} + 7 q^{3} + 149 q^{4} + 22 q^{5} + 20 q^{6} + 11 q^{7} + 27 q^{8} + 181 q^{9}+O(q^{10}) \) 134 * q + 9 * q^2 + 7 * q^3 + 149 * q^4 + 22 * q^5 + 20 * q^6 + 11 * q^7 + 27 * q^8 + 181 * q^9	\( 134 q + 9 q^{2} + 7 q^{3} + 149 q^{4} + 22 q^{5} + 20 q^{6} + 11 q^{7} + 27 q^{8} + 181 q^{9} + 15 q^{10} + 20 q^{11} + 28 q^{12} + 11 q^{13} + 17 q^{14} - 13 q^{15} + 143 q^{16} + 76 q^{17} + 23 q^{18} + 15 q^{19} + 67 q^{20} + 63 q^{21} + 2 q^{22} + 22 q^{23} + 33 q^{24} + 160 q^{25} + 65 q^{26} + 31 q^{27} + 10 q^{28} + 73 q^{29} + 20 q^{30} + 10 q^{31} + 53 q^{32} + 72 q^{33} - 7 q^{34} + 52 q^{35} + 201 q^{36} + 134 q^{37} + 70 q^{38} + 6 q^{39} + 11 q^{40} + 182 q^{41} - 15 q^{42} + 12 q^{43} + 33 q^{44} + 29 q^{45} + 24 q^{46} + 80 q^{47} + 21 q^{48} + 229 q^{49} + 37 q^{50} + 57 q^{51} - 15 q^{52} + 75 q^{53} + 95 q^{54} - 9 q^{55} + 39 q^{56} + 19 q^{57} - 21 q^{58} + 91 q^{59} + 62 q^{60} + 58 q^{61} + 108 q^{62} + 9 q^{63} + 167 q^{64} + 76 q^{65} + 105 q^{66} - 17 q^{67} + 109 q^{68} + 48 q^{69} - 55 q^{70} + 56 q^{71} + 48 q^{72} + 54 q^{73} + 9 q^{74} + 28 q^{75} + 82 q^{76} + 156 q^{77} + 16 q^{78} - 2 q^{79} + 98 q^{80} + 270 q^{81} - 42 q^{82} + 130 q^{83} + 229 q^{84} + 22 q^{85} + 72 q^{86} + 22 q^{87} + 61 q^{88} + 157 q^{89} + 176 q^{90} + 31 q^{91} - 18 q^{92} + 36 q^{93} + 83 q^{94} + 98 q^{95} + 111 q^{96} + 35 q^{97} + 53 q^{98} + 55 q^{99}+O(q^{100}) \) 134 * q + 9 * q^2 + 7 * q^3 + 149 * q^4 + 22 * q^5 + 20 * q^6 + 11 * q^7 + 27 * q^8 + 181 * q^9 + 15 * q^10 + 20 * q^11 + 28 * q^12 + 11 * q^13 + 17 * q^14 - 13 * q^15 + 143 * q^16 + 76 * q^17 + 23 * q^18 + 15 * q^19 + 67 * q^20 + 63 * q^21 + 2 * q^22 + 22 * q^23 + 33 * q^24 + 160 * q^25 + 65 * q^26 + 31 * q^27 + 10 * q^28 + 73 * q^29 + 20 * q^30 + 10 * q^31 + 53 * q^32 + 72 * q^33 - 7 * q^34 + 52 * q^35 + 201 * q^36 + 134 * q^37 + 70 * q^38 + 6 * q^39 + 11 * q^40 + 182 * q^41 - 15 * q^42 + 12 * q^43 + 33 * q^44 + 29 * q^45 + 24 * q^46 + 80 * q^47 + 21 * q^48 + 229 * q^49 + 37 * q^50 + 57 * q^51 - 15 * q^52 + 75 * q^53 + 95 * q^54 - 9 * q^55 + 39 * q^56 + 19 * q^57 - 21 * q^58 + 91 * q^59 + 62 * q^60 + 58 * q^61 + 108 * q^62 + 9 * q^63 + 167 * q^64 + 76 * q^65 + 105 * q^66 - 17 * q^67 + 109 * q^68 + 48 * q^69 - 55 * q^70 + 56 * q^71 + 48 * q^72 + 54 * q^73 + 9 * q^74 + 28 * q^75 + 82 * q^76 + 156 * q^77 + 16 * q^78 - 2 * q^79 + 98 * q^80 + 270 * q^81 - 42 * q^82 + 130 * q^83 + 229 * q^84 + 22 * q^85 + 72 * q^86 + 22 * q^87 + 61 * q^88 + 157 * q^89 + 176 * q^90 + 31 * q^91 - 18 * q^92 + 36 * q^93 + 83 * q^94 + 98 * q^95 + 111 * q^96 + 35 * q^97 + 53 * q^98 + 55 * q^99

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