LMFDB - Embedded newform 6019.2.a.d.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6019,2,Mod(1,6019)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6019, 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("6019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6019 = 13 \cdot 463 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6019.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:	$48.0619569766$
Analytic rank:	$0$
Dimension:	$123$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	6019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.52093 q^{2} +1.18363 q^{3} +4.35509 q^{4} -0.839879 q^{5} -2.98385 q^{6} +2.35424 q^{7} -5.93701 q^{8} -1.59902 q^{9} +O(q^{10})$	\(q-2.52093 q^{2} +1.18363 q^{3} +4.35509 q^{4} -0.839879 q^{5} -2.98385 q^{6} +2.35424 q^{7} -5.93701 q^{8} -1.59902 q^{9} +2.11728 q^{10} -1.38369 q^{11} +5.15481 q^{12} -1.00000 q^{13} -5.93487 q^{14} -0.994107 q^{15} +6.25660 q^{16} +2.81468 q^{17} +4.03101 q^{18} -4.23858 q^{19} -3.65775 q^{20} +2.78655 q^{21} +3.48817 q^{22} +6.54201 q^{23} -7.02722 q^{24} -4.29460 q^{25} +2.52093 q^{26} -5.44354 q^{27} +10.2529 q^{28} -6.12736 q^{29} +2.50607 q^{30} -0.332213 q^{31} -3.89844 q^{32} -1.63777 q^{33} -7.09562 q^{34} -1.97728 q^{35} -6.96386 q^{36} +3.82517 q^{37} +10.6852 q^{38} -1.18363 q^{39} +4.98637 q^{40} +2.01789 q^{41} -7.02469 q^{42} +2.12630 q^{43} -6.02607 q^{44} +1.34298 q^{45} -16.4919 q^{46} +9.55025 q^{47} +7.40551 q^{48} -1.45756 q^{49} +10.8264 q^{50} +3.33155 q^{51} -4.35509 q^{52} +2.47933 q^{53} +13.7228 q^{54} +1.16213 q^{55} -13.9771 q^{56} -5.01692 q^{57} +15.4466 q^{58} +6.77593 q^{59} -4.32942 q^{60} -14.8426 q^{61} +0.837484 q^{62} -3.76447 q^{63} -2.68551 q^{64} +0.839879 q^{65} +4.12871 q^{66} +0.432768 q^{67} +12.2582 q^{68} +7.74332 q^{69} +4.98457 q^{70} +6.38275 q^{71} +9.49338 q^{72} -5.70169 q^{73} -9.64298 q^{74} -5.08322 q^{75} -18.4594 q^{76} -3.25753 q^{77} +2.98385 q^{78} -10.9391 q^{79} -5.25479 q^{80} -1.64608 q^{81} -5.08696 q^{82} +15.1993 q^{83} +12.1357 q^{84} -2.36400 q^{85} -5.36026 q^{86} -7.25253 q^{87} +8.21495 q^{88} -1.34719 q^{89} -3.38557 q^{90} -2.35424 q^{91} +28.4910 q^{92} -0.393217 q^{93} -24.0755 q^{94} +3.55990 q^{95} -4.61432 q^{96} +1.76098 q^{97} +3.67442 q^{98} +2.21254 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9}+O(q^{10}) $ 123 * q + 10 * q^2 + q^3 + 136 * q^4 + 46 * q^5 + 16 * q^6 + 12 * q^7 + 30 * q^8 + 154 * q^9	\( 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9} + 5 q^{10} + 53 q^{11} - 6 q^{12} - 123 q^{13} + 21 q^{14} + 29 q^{15} + 166 q^{16} - 35 q^{17} + 28 q^{18} + 23 q^{19} + 93 q^{20} + 72 q^{21} + 8 q^{22} + 42 q^{23} + 55 q^{24} + 153 q^{25} - 10 q^{26} + 7 q^{27} + 39 q^{28} + 86 q^{29} + 44 q^{30} + 16 q^{31} + 70 q^{32} + 40 q^{33} + 10 q^{34} + 6 q^{35} + 222 q^{36} + 52 q^{37} + 12 q^{38} - q^{39} + 14 q^{40} + 80 q^{41} + 29 q^{42} + 2 q^{43} + 143 q^{44} + 137 q^{45} + 39 q^{46} + 45 q^{47} - 27 q^{48} + 163 q^{49} + 102 q^{50} + 48 q^{51} - 136 q^{52} + 117 q^{53} + 75 q^{54} + 20 q^{55} + 88 q^{56} + 67 q^{57} + 56 q^{58} + 88 q^{59} + 96 q^{60} + 57 q^{61} - 13 q^{62} + 48 q^{63} + 228 q^{64} - 46 q^{65} + 28 q^{66} + 43 q^{67} - 56 q^{68} + 92 q^{69} + 14 q^{70} + 90 q^{71} + 98 q^{72} + 25 q^{73} + 80 q^{74} + 21 q^{75} + 75 q^{76} + 112 q^{77} - 16 q^{78} + 36 q^{79} + 208 q^{80} + 231 q^{81} - 27 q^{82} + 93 q^{83} + 175 q^{84} + 77 q^{85} + 199 q^{86} + 15 q^{87} + 43 q^{88} + 140 q^{89} + 11 q^{90} - 12 q^{91} + 93 q^{92} + 140 q^{93} + 4 q^{94} + 23 q^{95} + 105 q^{96} + 43 q^{97} + 67 q^{98} + 140 q^{99}+O(q^{100}) \) 123 * q + 10 * q^2 + q^3 + 136 * q^4 + 46 * q^5 + 16 * q^6 + 12 * q^7 + 30 * q^8 + 154 * q^9 + 5 * q^10 + 53 * q^11 - 6 * q^12 - 123 * q^13 + 21 * q^14 + 29 * q^15 + 166 * q^16 - 35 * q^17 + 28 * q^18 + 23 * q^19 + 93 * q^20 + 72 * q^21 + 8 * q^22 + 42 * q^23 + 55 * q^24 + 153 * q^25 - 10 * q^26 + 7 * q^27 + 39 * q^28 + 86 * q^29 + 44 * q^30 + 16 * q^31 + 70 * q^32 + 40 * q^33 + 10 * q^34 + 6 * q^35 + 222 * q^36 + 52 * q^37 + 12 * q^38 - q^39 + 14 * q^40 + 80 * q^41 + 29 * q^42 + 2 * q^43 + 143 * q^44 + 137 * q^45 + 39 * q^46 + 45 * q^47 - 27 * q^48 + 163 * q^49 + 102 * q^50 + 48 * q^51 - 136 * q^52 + 117 * q^53 + 75 * q^54 + 20 * q^55 + 88 * q^56 + 67 * q^57 + 56 * q^58 + 88 * q^59 + 96 * q^60 + 57 * q^61 - 13 * q^62 + 48 * q^63 + 228 * q^64 - 46 * q^65 + 28 * q^66 + 43 * q^67 - 56 * q^68 + 92 * q^69 + 14 * q^70 + 90 * q^71 + 98 * q^72 + 25 * q^73 + 80 * q^74 + 21 * q^75 + 75 * q^76 + 112 * q^77 - 16 * q^78 + 36 * q^79 + 208 * q^80 + 231 * q^81 - 27 * q^82 + 93 * q^83 + 175 * q^84 + 77 * q^85 + 199 * q^86 + 15 * q^87 + 43 * q^88 + 140 * q^89 + 11 * q^90 - 12 * q^91 + 93 * q^92 + 140 * q^93 + 4 * q^94 + 23 * q^95 + 105 * q^96 + 43 * q^97 + 67 * q^98 + 140 * 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 $

$2$	−2.52093	−1.78257	−0.891283	−	0.453447i	$-0.850194\pi$
$2$	−2.52093	−1.78257	−0.891283	+	0.453447i	$0.850194\pi$
$3$	1.18363	0.683369	0.341685	−	0.939815i	$-0.389003\pi$
$3$	1.18363	0.683369	0.341685	+	0.939815i	$0.389003\pi$
$4$	4.35509	2.17754
$5$	−0.839879	−0.375605	−0.187803	−	0.982207i	$-0.560137\pi$
$5$	−0.839879	−0.375605	−0.187803	+	0.982207i	$0.560137\pi$
$6$	−2.98385	−1.21815
$7$	2.35424	0.889818	0.444909	−	0.895576i	$-0.353236\pi$
$7$	2.35424	0.889818	0.444909	+	0.895576i	$0.353236\pi$
$8$	−5.93701	−2.09905
$9$	−1.59902	−0.533006
$10$	2.11728	0.669542
$11$	−1.38369	−0.417197	−0.208598	−	0.978001i	$-0.566890\pi$
$11$	−1.38369	−0.417197	−0.208598	+	0.978001i	$0.566890\pi$
$12$	5.15481	1.48807
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−5.93487	−1.58616
$15$	−0.994107	−0.256677
$16$	6.25660	1.56415
$17$	2.81468	0.682661	0.341331	−	0.939943i	$-0.389122\pi$
$17$	2.81468	0.682661	0.341331	+	0.939943i	$0.389122\pi$
$18$	4.03101	0.950119
$19$	−4.23858	−0.972398	−0.486199	−	0.873848i	$-0.661617\pi$
$19$	−4.23858	−0.972398	−0.486199	+	0.873848i	$0.661617\pi$
$20$	−3.65775	−0.817897
$21$	2.78655	0.608075
$22$	3.48817	0.743681
$23$	6.54201	1.36410	0.682051	−	0.731304i	$-0.261088\pi$
$23$	6.54201	1.36410	0.682051	+	0.731304i	$0.261088\pi$
$24$	−7.02722	−1.43443
$25$	−4.29460	−0.858921
$26$	2.52093	0.494395
$27$	−5.44354	−1.04761
$28$	10.2529	1.93762
$29$	−6.12736	−1.13782	−0.568911	−	0.822399i	$-0.692635\pi$
$29$	−6.12736	−1.13782	−0.568911	+	0.822399i	$0.692635\pi$
$30$	2.50607	0.457544
$31$	−0.332213	−0.0596671	−0.0298336	−	0.999555i	$-0.509498\pi$
$31$	−0.332213	−0.0596671	−0.0298336	+	0.999555i	$0.509498\pi$
$32$	−3.89844	−0.689154
$33$	−1.63777	−0.285100
$34$	−7.09562	−1.21689
$35$	−1.97728	−0.334221
$36$	−6.96386	−1.16064
$37$	3.82517	0.628854	0.314427	−	0.949282i	$-0.398188\pi$
$37$	3.82517	0.628854	0.314427	+	0.949282i	$0.398188\pi$
$38$	10.6852	1.73336
$39$	−1.18363	−0.189533
$40$	4.98637	0.788414
$41$	2.01789	0.315142	0.157571	−	0.987508i	$-0.449634\pi$
$41$	2.01789	0.315142	0.157571	+	0.987508i	$0.449634\pi$
$42$	−7.02469	−1.08393
$43$	2.12630	0.324258	0.162129	−	0.986770i	$-0.448164\pi$
$43$	2.12630	0.324258	0.162129	+	0.986770i	$0.448164\pi$
$44$	−6.02607	−0.908464
$45$	1.34298	0.200200
$46$	−16.4919	−2.43160
$47$	9.55025	1.39305	0.696524	−	0.717534i	$-0.254729\pi$
$47$	9.55025	1.39305	0.696524	+	0.717534i	$0.254729\pi$
$48$	7.40551	1.06889
$49$	−1.45756	−0.208223
$50$	10.8264	1.53108
$51$	3.33155	0.466510
$52$	−4.35509	−0.603942
$53$	2.47933	0.340562	0.170281	−	0.985396i	$-0.445532\pi$
$53$	2.47933	0.340562	0.170281	+	0.985396i	$0.445532\pi$
$54$	13.7228	1.86743
$55$	1.16213	0.156701
$56$	−13.9771	−1.86777
$57$	−5.01692	−0.664507
$58$	15.4466	2.02824
$59$	6.77593	0.882151	0.441076	−	0.897470i	$-0.354597\pi$
$59$	6.77593	0.882151	0.441076	+	0.897470i	$0.354597\pi$
$60$	−4.32942	−0.558926
$61$	−14.8426	−1.90040	−0.950202	−	0.311635i	$-0.899123\pi$
$61$	−14.8426	−1.90040	−0.950202	+	0.311635i	$0.899123\pi$
$62$	0.837484	0.106361
$63$	−3.76447	−0.474279
$64$	−2.68551	−0.335688
$65$	0.839879	0.104174
$66$	4.12871	0.508209
$67$	0.432768	0.0528710	0.0264355	−	0.999651i	$-0.491584\pi$
$67$	0.432768	0.0528710	0.0264355	+	0.999651i	$0.491584\pi$
$68$	12.2582	1.48652
$69$	7.74332	0.932186
$70$	4.98457	0.595770
$71$	6.38275	0.757494	0.378747	−	0.925500i	$-0.376355\pi$
$71$	6.38275	0.757494	0.378747	+	0.925500i	$0.376355\pi$
$72$	9.49338	1.11881
$73$	−5.70169	−0.667333	−0.333666	−	0.942691i	$-0.608286\pi$
$73$	−5.70169	−0.667333	−0.333666	+	0.942691i	$0.608286\pi$
$74$	−9.64298	−1.12097
$75$	−5.08322	−0.586960
$76$	−18.4594	−2.11744
$77$	−3.25753	−0.371229
$78$	2.98385	0.337854
$79$	−10.9391	−1.23075	−0.615375	−	0.788235i	$-0.710995\pi$
$79$	−10.9391	−1.23075	−0.615375	+	0.788235i	$0.710995\pi$
$80$	−5.25479	−0.587504
$81$	−1.64608	−0.182898
$82$	−5.08696	−0.561761
$83$	15.1993	1.66833	0.834167	−	0.551512i	$-0.185949\pi$
$83$	15.1993	1.66833	0.834167	+	0.551512i	$0.185949\pi$
$84$	12.1357	1.32411
$85$	−2.36400	−0.256411
$86$	−5.36026	−0.578012
$87$	−7.25253	−0.777553
$88$	8.21495	0.875717
$89$	−1.34719	−0.142802	−0.0714008	−	0.997448i	$-0.522747\pi$
$89$	−1.34719	−0.142802	−0.0714008	+	0.997448i	$0.522747\pi$
$90$	−3.38557	−0.356870
$91$	−2.35424	−0.246791
$92$	28.4910	2.97039
$93$	−0.393217	−0.0407747
$94$	−24.0755	−2.48320
$95$	3.55990	0.365238
$96$	−4.61432	−0.470947
$97$	1.76098	0.178800	0.0894000	−	0.995996i	$-0.471505\pi$
$97$	1.76098	0.178800	0.0894000	+	0.995996i	$0.471505\pi$
$98$	3.67442	0.371172
$99$	2.21254	0.222369
$100$	−18.7034	−1.87034
$101$	−6.45787	−0.642582	−0.321291	−	0.946980i	$-0.604117\pi$
$101$	−6.45787	−0.642582	−0.321291	+	0.946980i	$0.604117\pi$
$102$	−8.39860	−0.831585
$103$	7.82207	0.770732	0.385366	−	0.922764i	$-0.374075\pi$
$103$	7.82207	0.770732	0.385366	+	0.922764i	$0.374075\pi$
$104$	5.93701	0.582171
$105$	−2.34036	−0.228396
$106$	−6.25021	−0.607074
$107$	13.2796	1.28379	0.641895	−	0.766793i	$-0.278149\pi$
$107$	13.2796	1.28379	0.641895	+	0.766793i	$0.278149\pi$
$108$	−23.7071	−2.28121
$109$	17.3193	1.65888	0.829442	−	0.558593i	$-0.188659\pi$
$109$	17.3193	1.65888	0.829442	+	0.558593i	$0.188659\pi$
$110$	−2.92965	−0.279331
$111$	4.52759	0.429740
$112$	14.7295	1.39181
$113$	4.60497	0.433199	0.216600	−	0.976261i	$-0.430503\pi$
$113$	4.60497	0.433199	0.216600	+	0.976261i	$0.430503\pi$
$114$	12.6473	1.18453
$115$	−5.49450	−0.512364
$116$	−26.6852	−2.47766
$117$	1.59902	0.147829
$118$	−17.0817	−1.57249
$119$	6.62644	0.607445
$120$	5.90202	0.538778
$121$	−9.08541	−0.825947
$122$	37.4172	3.38760
$123$	2.38844	0.215358
$124$	−1.44681	−0.129928
$125$	7.80635	0.698221
$126$	9.48996	0.845433
$127$	0.0731679	0.00649260	0.00324630	−	0.999995i	$-0.498967\pi$
$127$	0.0731679	0.00649260	0.00324630	+	0.999995i	$0.498967\pi$
$128$	14.5669	1.28754
$129$	2.51676	0.221588
$130$	−2.11728	−0.185697
$131$	−5.37329	−0.469467	−0.234733	−	0.972060i	$-0.575422\pi$
$131$	−5.37329	−0.469467	−0.234733	+	0.972060i	$0.575422\pi$
$132$	−7.13264	−0.620817
$133$	−9.97863	−0.865257
$134$	−1.09098	−0.0942461
$135$	4.57192	0.393488
$136$	−16.7108	−1.43294
$137$	4.34166	0.370933	0.185466	−	0.982651i	$-0.440620\pi$
$137$	4.34166	0.370933	0.185466	+	0.982651i	$0.440620\pi$
$138$	−19.5204	−1.66168
$139$	16.5110	1.40044	0.700222	−	0.713926i	$-0.253084\pi$
$139$	16.5110	1.40044	0.700222	+	0.713926i	$0.253084\pi$
$140$	−8.61121	−0.727780
$141$	11.3040	0.951966
$142$	−16.0905	−1.35028
$143$	1.38369	0.115710
$144$	−10.0044	−0.833702
$145$	5.14624	0.427372
$146$	14.3736	1.18956
$147$	−1.72522	−0.142294
$148$	16.6589	1.36936
$149$	−17.5077	−1.43429	−0.717144	−	0.696925i	$-0.754551\pi$
$149$	−17.5077	−1.43429	−0.717144	+	0.696925i	$0.754551\pi$
$150$	12.8144	1.04630
$151$	0.0333686	0.00271550	0.00135775	−	0.999999i	$-0.499568\pi$
$151$	0.0333686	0.00271550	0.00135775	+	0.999999i	$0.499568\pi$
$152$	25.1645	2.04111
$153$	−4.50073	−0.363863
$154$	8.21199	0.661741
$155$	0.279018	0.0224113
$156$	−5.15481	−0.412715
$157$	8.36795	0.667835	0.333918	−	0.942602i	$-0.391629\pi$
$157$	8.36795	0.667835	0.333918	+	0.942602i	$0.391629\pi$
$158$	27.5768	2.19389
$159$	2.93461	0.232730
$160$	3.27422	0.258850
$161$	15.4014	1.21380
$162$	4.14966	0.326028
$163$	0.836146	0.0654920	0.0327460	−	0.999464i	$-0.489575\pi$
$163$	0.836146	0.0654920	0.0327460	+	0.999464i	$0.489575\pi$
$164$	8.78809	0.686234
$165$	1.37553	0.107085
$166$	−38.3162	−2.97392
$167$	2.53482	0.196150	0.0980751	−	0.995179i	$-0.468731\pi$
$167$	2.53482	0.196150	0.0980751	+	0.995179i	$0.468731\pi$
$168$	−16.5438	−1.27638
$169$	1.00000	0.0769231
$170$	5.95947	0.457070
$171$	6.77757	0.518294
$172$	9.26023	0.706086
$173$	4.33352	0.329471	0.164736	−	0.986338i	$-0.447323\pi$
$173$	4.33352	0.329471	0.164736	+	0.986338i	$0.447323\pi$
$174$	18.2831	1.38604
$175$	−10.1105	−0.764283
$176$	−8.65717	−0.652559
$177$	8.02020	0.602835
$178$	3.39617	0.254553
$179$	22.6794	1.69514	0.847571	−	0.530682i	$-0.178064\pi$
$179$	22.6794	1.69514	0.847571	+	0.530682i	$0.178064\pi$
$180$	5.84881	0.435944
$181$	14.6016	1.08533	0.542663	−	0.839951i	$-0.317416\pi$
$181$	14.6016	1.08533	0.542663	+	0.839951i	$0.317416\pi$
$182$	5.93487	0.439922
$183$	−17.5682	−1.29868
$184$	−38.8399	−2.86332
$185$	−3.21268	−0.236201
$186$	0.991272	0.0726836
$187$	−3.89464	−0.284804
$188$	41.5922	3.03342
$189$	−12.8154	−0.932182
$190$	−8.97425	−0.651061
$191$	−18.3748	−1.32956	−0.664778	−	0.747041i	$-0.731474\pi$
$191$	−18.3748	−1.32956	−0.664778	+	0.747041i	$0.731474\pi$
$192$	−3.17865	−0.229399
$193$	−7.49191	−0.539280	−0.269640	−	0.962961i	$-0.586905\pi$
$193$	−7.49191	−0.539280	−0.269640	+	0.962961i	$0.586905\pi$
$194$	−4.43929	−0.318723
$195$	0.994107	0.0711895
$196$	−6.34782	−0.453415
$197$	18.3640	1.30838	0.654189	−	0.756331i	$-0.273010\pi$
$197$	18.3640	1.30838	0.654189	+	0.756331i	$0.273010\pi$
$198$	−5.57766	−0.396387
$199$	25.8862	1.83502	0.917511	−	0.397711i	$-0.130195\pi$
$199$	25.8862	1.83502	0.917511	+	0.397711i	$0.130195\pi$
$200$	25.4971	1.80292
$201$	0.512237	0.0361304
$202$	16.2798	1.14545
$203$	−14.4253	−1.01245
$204$	14.5092	1.01585
$205$	−1.69478	−0.118369
$206$	−19.7189	−1.37388
$207$	−10.4608	−0.727075
$208$	−6.25660	−0.433817
$209$	5.86487	0.405681
$210$	5.89989	0.407131
$211$	0.777011	0.0534916	0.0267458	−	0.999642i	$-0.491486\pi$
$211$	0.777011	0.0534916	0.0267458	+	0.999642i	$0.491486\pi$
$212$	10.7977	0.741588
$213$	7.55482	0.517648
$214$	−33.4770	−2.28844
$215$	−1.78584	−0.121793
$216$	32.3183	2.19898
$217$	−0.782107	−0.0530929
$218$	−43.6606	−2.95707
$219$	−6.74870	−0.456035
$220$	5.06117	0.341224
$221$	−2.81468	−0.189336
$222$	−11.4137	−0.766039
$223$	16.9630	1.13593	0.567964	−	0.823054i	$-0.307731\pi$
$223$	16.9630	1.13593	0.567964	+	0.823054i	$0.307731\pi$
$224$	−9.17786	−0.613222
$225$	6.86715	0.457810
$226$	−11.6088	−0.772207
$227$	−3.31394	−0.219954	−0.109977	−	0.993934i	$-0.535078\pi$
$227$	−3.31394	−0.219954	−0.109977	+	0.993934i	$0.535078\pi$
$228$	−21.8491	−1.44699
$229$	−13.6836	−0.904236	−0.452118	−	0.891958i	$-0.649331\pi$
$229$	−13.6836	−0.904236	−0.452118	+	0.891958i	$0.649331\pi$
$230$	13.8512	0.913324
$231$	−3.85571	−0.253687
$232$	36.3782	2.38834
$233$	21.2980	1.39528	0.697640	−	0.716449i	$-0.254234\pi$
$233$	21.2980	1.39528	0.697640	+	0.716449i	$0.254234\pi$
$234$	−4.03101	−0.263516
$235$	−8.02106	−0.523236
$236$	29.5098	1.92092
$237$	−12.9479	−0.841056
$238$	−16.7048	−1.08281
$239$	11.5178	0.745022	0.372511	−	0.928028i	$-0.378497\pi$
$239$	11.5178	0.745022	0.372511	+	0.928028i	$0.378497\pi$
$240$	−6.21973	−0.401482
$241$	23.7126	1.52746	0.763732	−	0.645533i	$-0.223365\pi$
$241$	23.7126	1.52746	0.763732	+	0.645533i	$0.223365\pi$
$242$	22.9037	1.47230
$243$	14.3823	0.922623
$244$	−64.6409	−4.13821
$245$	1.22418	0.0782099
$246$	−6.02108	−0.383890
$247$	4.23858	0.269695
$248$	1.97235	0.125244
$249$	17.9903	1.14009
$250$	−19.6792	−1.24462
$251$	−17.3737	−1.09662	−0.548308	−	0.836276i	$-0.684728\pi$
$251$	−17.3737	−1.09662	−0.548308	+	0.836276i	$0.684728\pi$
$252$	−16.3946	−1.03276
$253$	−9.05208	−0.569099
$254$	−0.184451	−0.0115735
$255$	−2.79810	−0.175224
$256$	−31.3510	−1.95944
$257$	−31.0994	−1.93993	−0.969964	−	0.243248i	$-0.921787\pi$
$257$	−31.0994	−1.93993	−0.969964	+	0.243248i	$0.921787\pi$
$258$	−6.34457	−0.394995
$259$	9.00536	0.559566
$260$	3.65775	0.226844
$261$	9.79776	0.606466
$262$	13.5457	0.836856
$263$	−1.00928	−0.0622348	−0.0311174	−	0.999516i	$-0.509907\pi$
$263$	−1.00928	−0.0622348	−0.0311174	+	0.999516i	$0.509907\pi$
$264$	9.72347	0.598438
$265$	−2.08234	−0.127917
$266$	25.1554	1.54238
$267$	−1.59457	−0.0975863
$268$	1.88474	0.115129
$269$	15.5427	0.947658	0.473829	−	0.880617i	$-0.342871\pi$
$269$	15.5427	0.947658	0.473829	+	0.880617i	$0.342871\pi$
$270$	−11.5255	−0.701418
$271$	−20.9764	−1.27423	−0.637114	−	0.770770i	$-0.719872\pi$
$271$	−20.9764	−1.27423	−0.637114	+	0.770770i	$0.719872\pi$
$272$	17.6104	1.06779
$273$	−2.78655	−0.168650
$274$	−10.9450	−0.661212
$275$	5.94238	0.358339
$276$	33.7228	2.02988
$277$	15.8017	0.949434	0.474717	−	0.880138i	$-0.342550\pi$
$277$	15.8017	0.949434	0.474717	+	0.880138i	$0.342550\pi$
$278$	−41.6230	−2.49638
$279$	0.531214	0.0318030
$280$	11.7391	0.701545
$281$	12.3404	0.736165	0.368083	−	0.929793i	$-0.380014\pi$
$281$	12.3404	0.736165	0.368083	+	0.929793i	$0.380014\pi$
$282$	−28.4965	−1.69694
$283$	4.14996	0.246690	0.123345	−	0.992364i	$-0.460638\pi$
$283$	4.14996	0.246690	0.123345	+	0.992364i	$0.460638\pi$
$284$	27.7974	1.64947
$285$	4.21360	0.249592
$286$	−3.48817	−0.206260
$287$	4.75059	0.280419
$288$	6.23368	0.367323
$289$	−9.07755	−0.533973
$290$	−12.9733	−0.761819
$291$	2.08434	0.122186
$292$	−24.8314	−1.45315
$293$	−23.9933	−1.40170	−0.700852	−	0.713307i	$-0.747196\pi$
$293$	−23.9933	−1.40170	−0.700852	+	0.713307i	$0.747196\pi$
$294$	4.34915	0.253648
$295$	−5.69097	−0.331341
$296$	−22.7101	−1.32000
$297$	7.53215	0.437059
$298$	44.1357	2.55671
$299$	−6.54201	−0.378334
$300$	−22.1379	−1.27813
$301$	5.00582	0.288531
$302$	−0.0841200	−0.00484056
$303$	−7.64374	−0.439121
$304$	−26.5191	−1.52098
$305$	12.4660	0.713802
$306$	11.3460	0.648610
$307$	22.8909	1.30645	0.653226	−	0.757163i	$-0.273415\pi$
$307$	22.8909	1.30645	0.653226	+	0.757163i	$0.273415\pi$
$308$	−14.1868	−0.808368
$309$	9.25844	0.526694
$310$	−0.703386	−0.0399496
$311$	−0.367943	−0.0208641	−0.0104321	−	0.999946i	$-0.503321\pi$
$311$	−0.367943	−0.0208641	−0.0104321	+	0.999946i	$0.503321\pi$
$312$	7.02722	0.397838
$313$	−22.7490	−1.28585	−0.642925	−	0.765929i	$-0.722279\pi$
$313$	−22.7490	−1.28585	−0.642925	+	0.765929i	$0.722279\pi$
$314$	−21.0950	−1.19046
$315$	3.16170	0.178142
$316$	−47.6409	−2.68001
$317$	0.274404	0.0154121	0.00770604	−	0.999970i	$-0.497547\pi$
$317$	0.274404	0.0154121	0.00770604	+	0.999970i	$0.497547\pi$
$318$	−7.39794	−0.414856
$319$	8.47834	0.474696
$320$	2.25550	0.126086
$321$	15.7182	0.877303
$322$	−38.8259	−2.16369
$323$	−11.9303	−0.663818
$324$	−7.16883	−0.398269
$325$	4.29460	0.238222
$326$	−2.10787	−0.116744
$327$	20.4996	1.13363
$328$	−11.9802	−0.661497
$329$	22.4836	1.23956
$330$	−3.46762	−0.190886
$331$	10.6186	0.583651	0.291825	−	0.956472i	$-0.405737\pi$
$331$	10.6186	0.583651	0.291825	+	0.956472i	$0.405737\pi$
$332$	66.1940	3.63287
$333$	−6.11652	−0.335183
$334$	−6.39010	−0.349651
$335$	−0.363473	−0.0198586
$336$	17.4343	0.951120
$337$	11.5305	0.628106	0.314053	−	0.949405i	$-0.398313\pi$
$337$	11.5305	0.628106	0.314053	+	0.949405i	$0.398313\pi$
$338$	−2.52093	−0.137120
$339$	5.45059	0.296035
$340$	−10.2954	−0.558347
$341$	0.459678	0.0248929
$342$	−17.0858	−0.923893
$343$	−19.9111	−1.07510
$344$	−12.6239	−0.680634
$345$	−6.50345	−0.350134
$346$	−10.9245	−0.587304
$347$	−7.81568	−0.419568	−0.209784	−	0.977748i	$-0.567276\pi$
$347$	−7.81568	−0.419568	−0.209784	+	0.977748i	$0.567276\pi$
$348$	−31.5854	−1.69315
$349$	−20.6335	−1.10449	−0.552243	−	0.833683i	$-0.686228\pi$
$349$	−20.6335	−1.10449	−0.552243	+	0.833683i	$0.686228\pi$
$350$	25.4879	1.36239
$351$	5.44354	0.290555
$352$	5.39422	0.287513
$353$	4.99094	0.265641	0.132820	−	0.991140i	$-0.457597\pi$
$353$	4.99094	0.265641	0.132820	+	0.991140i	$0.457597\pi$
$354$	−20.2184	−1.07459
$355$	−5.36074	−0.284519
$356$	−5.86712	−0.310957
$357$	7.84325	0.415109
$358$	−57.1733	−3.02170
$359$	15.0395	0.793754	0.396877	−	0.917872i	$-0.370094\pi$
$359$	15.0395	0.793754	0.396877	+	0.917872i	$0.370094\pi$
$360$	−7.97330	−0.420230
$361$	−1.03442	−0.0544430
$362$	−36.8095	−1.93466
$363$	−10.7538	−0.564427
$364$	−10.2529	−0.537398
$365$	4.78873	0.250654
$366$	44.2882	2.31498
$367$	10.0391	0.524035	0.262018	−	0.965063i	$-0.415612\pi$
$367$	10.0391	0.524035	0.262018	+	0.965063i	$0.415612\pi$
$368$	40.9307	2.13366
$369$	−3.22664	−0.167972
$370$	8.09894	0.421044
$371$	5.83693	0.303038
$372$	−1.71249	−0.0887887
$373$	−4.13109	−0.213900	−0.106950	−	0.994264i	$-0.534108\pi$
$373$	−4.13109	−0.213900	−0.106950	+	0.994264i	$0.534108\pi$
$374$	9.81811	0.507682
$375$	9.23983	0.477143
$376$	−56.6999	−2.92407
$377$	6.12736	0.315575
$378$	32.3067	1.66168
$379$	32.6668	1.67798	0.838990	−	0.544146i	$-0.183146\pi$
$379$	32.6668	1.67798	0.838990	+	0.544146i	$0.183146\pi$
$380$	15.5037	0.795321
$381$	0.0866038	0.00443684
$382$	46.3217	2.37002
$383$	1.86694	0.0953959	0.0476980	−	0.998862i	$-0.484812\pi$
$383$	1.86694	0.0953959	0.0476980	+	0.998862i	$0.484812\pi$
$384$	17.2418	0.879866
$385$	2.73593	0.139436
$386$	18.8866	0.961302
$387$	−3.40000	−0.172832
$388$	7.66920	0.389345
$389$	−28.3962	−1.43974	−0.719872	−	0.694107i	$-0.755799\pi$
$389$	−28.3962	−1.43974	−0.719872	+	0.694107i	$0.755799\pi$
$390$	−2.50607	−0.126900
$391$	18.4137	0.931220
$392$	8.65357	0.437071
$393$	−6.35999	−0.320819
$394$	−46.2942	−2.33227
$395$	9.18756	0.462276
$396$	9.63580	0.484217
$397$	9.78753	0.491222	0.245611	−	0.969368i	$-0.421011\pi$
$397$	9.78753	0.491222	0.245611	+	0.969368i	$0.421011\pi$
$398$	−65.2572	−3.27105
$399$	−11.8110	−0.591290
$400$	−26.8696	−1.34348
$401$	2.57595	0.128637	0.0643183	−	0.997929i	$-0.479513\pi$
$401$	2.57595	0.128637	0.0643183	+	0.997929i	$0.479513\pi$
$402$	−1.29131	−0.0644049
$403$	0.332213	0.0165487
$404$	−28.1246	−1.39925
$405$	1.38251	0.0686975
$406$	36.3651	1.80477
$407$	−5.29283	−0.262356
$408$	−19.7794	−0.979227
$409$	−12.9499	−0.640331	−0.320166	−	0.947362i	$-0.603739\pi$
$409$	−12.9499	−0.640331	−0.320166	+	0.947362i	$0.603739\pi$
$410$	4.27243	0.211000
$411$	5.13892	0.253484
$412$	34.0658	1.67830
$413$	15.9522	0.784954
$414$	26.3709	1.29606
$415$	−12.7655	−0.626636
$416$	3.89844	0.191137
$417$	19.5429	0.957020
$418$	−14.7849	−0.723154
$419$	−6.19421	−0.302607	−0.151303	−	0.988487i	$-0.548347\pi$
$419$	−6.19421	−0.302607	−0.151303	+	0.988487i	$0.548347\pi$
$420$	−10.1925	−0.497342
$421$	−13.2280	−0.644692	−0.322346	−	0.946622i	$-0.604472\pi$
$421$	−13.2280	−0.644692	−0.322346	+	0.946622i	$0.604472\pi$
$422$	−1.95879	−0.0953524
$423$	−15.2710	−0.742503
$424$	−14.7198	−0.714856
$425$	−12.0880	−0.586352
$426$	−19.0452	−0.922742
$427$	−34.9431	−1.69101
$428$	57.8339	2.79551
$429$	1.63777	0.0790724
$430$	4.50197	0.217104
$431$	−9.33736	−0.449765	−0.224882	−	0.974386i	$-0.572200\pi$
$431$	−9.33736	−0.449765	−0.224882	+	0.974386i	$0.572200\pi$
$432$	−34.0581	−1.63862
$433$	27.6526	1.32890	0.664449	−	0.747334i	$-0.268666\pi$
$433$	27.6526	1.32890	0.664449	+	0.747334i	$0.268666\pi$
$434$	1.97164	0.0946416
$435$	6.09125	0.292053
$436$	75.4269	3.61229
$437$	−27.7288	−1.32645
$438$	17.0130	0.812912
$439$	−4.98693	−0.238013	−0.119007	−	0.992893i	$-0.537971\pi$
$439$	−4.98693	−0.238013	−0.119007	+	0.992893i	$0.537971\pi$
$440$	−6.89957	−0.328924
$441$	2.33067	0.110984
$442$	7.09562	0.337504
$443$	−1.13279	−0.0538203	−0.0269101	−	0.999638i	$-0.508567\pi$
$443$	−1.13279	−0.0538203	−0.0269101	+	0.999638i	$0.508567\pi$
$444$	19.7180	0.935777
$445$	1.13148	0.0536371
$446$	−42.7626	−2.02487
$447$	−20.7227	−0.980148
$448$	−6.32232	−0.298701
$449$	−17.0337	−0.803869	−0.401935	−	0.915668i	$-0.631662\pi$
$449$	−17.0337	−0.803869	−0.401935	+	0.915668i	$0.631662\pi$
$450$	−17.3116	−0.816077
$451$	−2.79213	−0.131476
$452$	20.0551	0.943310
$453$	0.0394961	0.00185569
$454$	8.35422	0.392083
$455$	1.97728	0.0926961
$456$	29.7855	1.39483
$457$	−27.4398	−1.28358	−0.641789	−	0.766881i	$-0.721808\pi$
$457$	−27.4398	−1.28358	−0.641789	+	0.766881i	$0.721808\pi$
$458$	34.4953	1.61186
$459$	−15.3218	−0.715163
$460$	−23.9290	−1.11570
$461$	29.9503	1.39492	0.697462	−	0.716622i	$-0.254313\pi$
$461$	29.9503	1.39492	0.697462	+	0.716622i	$0.254313\pi$
$462$	9.71996	0.452214
$463$	1.00000	0.0464739
$463$	1.00000	0.0464739
$464$	−38.3364	−1.77972
$465$	0.330255	0.0153152
$466$	−53.6908	−2.48718
$467$	10.3365	0.478317	0.239159	−	0.970980i	$-0.423128\pi$
$467$	10.3365	0.478317	0.239159	+	0.970980i	$0.423128\pi$
$468$	6.96386	0.321905
$469$	1.01884	0.0470456
$470$	20.2205	0.932703
$471$	9.90456	0.456378
$472$	−40.2288	−1.85168
$473$	−2.94213	−0.135279
$474$	32.6407	1.49924
$475$	18.2030	0.835212
$476$	28.8587	1.32274
$477$	−3.96449	−0.181522
$478$	−29.0355	−1.32805
$479$	13.1940	0.602851	0.301426	−	0.953490i	$-0.402538\pi$
$479$	13.1940	0.602851	0.301426	+	0.953490i	$0.402538\pi$
$480$	3.87547	0.176890
$481$	−3.82517	−0.174413
$482$	−59.7779	−2.72281
$483$	18.2296	0.829476
$484$	−39.5678	−1.79853
$485$	−1.47901	−0.0671582
$486$	−36.2567	−1.64464
$487$	−9.62062	−0.435952	−0.217976	−	0.975954i	$-0.569945\pi$
$487$	−9.62062	−0.435952	−0.217976	+	0.975954i	$0.569945\pi$
$488$	88.1208	3.98904
$489$	0.989688	0.0447552
$490$	−3.08607	−0.139414
$491$	−1.30582	−0.0589309	−0.0294654	−	0.999566i	$-0.509380\pi$
$491$	−1.30582	−0.0589309	−0.0294654	+	0.999566i	$0.509380\pi$
$492$	10.4018	0.468951
$493$	−17.2466	−0.776747
$494$	−10.6852	−0.480748
$495$	−1.85827	−0.0835229
$496$	−2.07852	−0.0933284
$497$	15.0265	0.674032
$498$	−45.3523	−2.03228
$499$	5.97165	0.267328	0.133664	−	0.991027i	$-0.457326\pi$
$499$	5.97165	0.267328	0.133664	+	0.991027i	$0.457326\pi$
$500$	33.9973	1.52041
$501$	3.00029	0.134043
$502$	43.7978	1.95479
$503$	−2.35577	−0.105039	−0.0525193	−	0.998620i	$-0.516725\pi$
$503$	−2.35577	−0.105039	−0.0525193	+	0.998620i	$0.516725\pi$
$504$	22.3497	0.995534
$505$	5.42383	0.241357
$506$	22.8197	1.01446
$507$	1.18363	0.0525669
$508$	0.318652	0.0141379
$509$	2.38980	0.105926	0.0529629	−	0.998596i	$-0.483133\pi$
$509$	2.38980	0.105926	0.0529629	+	0.998596i	$0.483133\pi$
$510$	7.05381	0.312348
$511$	−13.4231	−0.593805
$512$	49.9000	2.20529
$513$	23.0729	1.01869
$514$	78.3994	3.45805
$515$	−6.56960	−0.289491
$516$	10.9607	0.482518
$517$	−13.2145	−0.581175
$518$	−22.7019	−0.997463
$519$	5.12928	0.225151
$520$	−4.98637	−0.218667
$521$	−29.0632	−1.27328	−0.636641	−	0.771160i	$-0.719677\pi$
$521$	−29.0632	−1.27328	−0.636641	+	0.771160i	$0.719677\pi$
$522$	−24.6995	−1.08107
$523$	35.9950	1.57395	0.786976	−	0.616983i	$-0.211645\pi$
$523$	35.9950	1.57395	0.786976	+	0.616983i	$0.211645\pi$
$524$	−23.4011	−1.02228
$525$	−11.9671	−0.522288
$526$	2.54432	0.110938
$527$	−0.935074	−0.0407324
$528$	−10.2469	−0.445939
$529$	19.7979	0.860776
$530$	5.24943	0.228020
$531$	−10.8348	−0.470192
$532$	−43.4578	−1.88413
$533$	−2.01789	−0.0874045
$534$	4.01981	0.173954
$535$	−11.1533	−0.482198
$536$	−2.56935	−0.110979
$537$	26.8441	1.15841
$538$	−39.1822	−1.68926
$539$	2.01681	0.0868702
$540$	19.9111	0.856837
$541$	1.33413	0.0573586	0.0286793	−	0.999589i	$-0.490870\pi$
$541$	1.33413	0.0573586	0.0286793	+	0.999589i	$0.490870\pi$
$542$	52.8801	2.27140
$543$	17.2828	0.741678
$544$	−10.9729	−0.470459
$545$	−14.5461	−0.623086
$546$	7.02469	0.300629
$547$	41.0706	1.75605	0.878025	−	0.478614i	$-0.158861\pi$
$547$	41.0706	1.75605	0.878025	+	0.478614i	$0.158861\pi$
$548$	18.9083	0.807722
$549$	23.7336	1.01293
$550$	−14.9803	−0.638763
$551$	25.9713	1.10642
$552$	−45.9721	−1.95670
$553$	−25.7533	−1.09514
$554$	−39.8351	−1.69243
$555$	−3.80263	−0.161413
$556$	71.9068	3.04953
$557$	1.23294	0.0522413	0.0261207	−	0.999659i	$-0.491685\pi$
$557$	1.23294	0.0522413	0.0261207	+	0.999659i	$0.491685\pi$
$558$	−1.33915	−0.0566909
$559$	−2.12630	−0.0899330
$560$	−12.3710	−0.522771
$561$	−4.60981	−0.194626
$562$	−31.1092	−1.31226
$563$	14.7726	0.622593	0.311296	−	0.950313i	$-0.399237\pi$
$563$	14.7726	0.622593	0.311296	+	0.950313i	$0.399237\pi$
$564$	49.2298	2.07295
$565$	−3.86762	−0.162712
$566$	−10.4618	−0.439741
$567$	−3.87527	−0.162746
$568$	−37.8945	−1.59002
$569$	−31.4199	−1.31719	−0.658595	−	0.752497i	$-0.728849\pi$
$569$	−31.4199	−1.31719	−0.658595	+	0.752497i	$0.728849\pi$
$570$	−10.6222	−0.444915
$571$	4.29866	0.179893	0.0899467	−	0.995947i	$-0.471330\pi$
$571$	4.29866	0.179893	0.0899467	+	0.995947i	$0.471330\pi$
$572$	6.02607	0.251963
$573$	−21.7490	−0.908578
$574$	−11.9759	−0.499865
$575$	−28.0953	−1.17166
$576$	4.29417	0.178924
$577$	−32.5903	−1.35675	−0.678377	−	0.734714i	$-0.737316\pi$
$577$	−32.5903	−1.35675	−0.678377	+	0.734714i	$0.737316\pi$
$578$	22.8839	0.951843
$579$	−8.86766	−0.368527
$580$	22.4123	0.930621
$581$	35.7827	1.48451
$582$	−5.25448	−0.217805
$583$	−3.43061	−0.142081
$584$	33.8510	1.40076
$585$	−1.34298	−0.0555255
$586$	60.4854	2.49863
$587$	30.6564	1.26532	0.632662	−	0.774428i	$-0.281962\pi$
$587$	30.6564	1.26532	0.632662	+	0.774428i	$0.281962\pi$
$588$	−7.51347	−0.309850
$589$	1.40811	0.0580202
$590$	14.3465	0.590637
$591$	21.7361	0.894105
$592$	23.9326	0.983623
$593$	9.58183	0.393478	0.196739	−	0.980456i	$-0.436965\pi$
$593$	9.58183	0.393478	0.196739	+	0.980456i	$0.436965\pi$
$594$	−18.9880	−0.779088
$595$	−5.56541	−0.228160
$596$	−76.2476	−3.12322
$597$	30.6397	1.25400
$598$	16.4919	0.674406
$599$	−25.1899	−1.02923	−0.514616	−	0.857421i	$-0.672066\pi$
$599$	−25.1899	−1.02923	−0.514616	+	0.857421i	$0.672066\pi$
$600$	30.1791	1.23206
$601$	−38.6629	−1.57709	−0.788546	−	0.614976i	$-0.789166\pi$
$601$	−38.6629	−1.57709	−0.788546	+	0.614976i	$0.789166\pi$
$602$	−12.6193	−0.514325
$603$	−0.692004	−0.0281806
$604$	0.145323	0.00591312
$605$	7.63065	0.310230
$606$	19.2693	0.782763
$607$	−14.5807	−0.591811	−0.295905	−	0.955217i	$-0.595621\pi$
$607$	−14.5807	−0.591811	−0.295905	+	0.955217i	$0.595621\pi$
$608$	16.5239	0.670132
$609$	−17.0742	−0.691881
$610$	−31.4260	−1.27240
$611$	−9.55025	−0.386362
$612$	−19.6011	−0.792327
$613$	21.5622	0.870888	0.435444	−	0.900216i	$-0.356591\pi$
$613$	21.5622	0.870888	0.435444	+	0.900216i	$0.356591\pi$
$614$	−57.7063	−2.32884
$615$	−2.00600	−0.0808897
$616$	19.3399	0.779229
$617$	12.3402	0.496798	0.248399	−	0.968658i	$-0.420096\pi$
$617$	12.3402	0.496798	0.248399	+	0.968658i	$0.420096\pi$
$618$	−23.3399	−0.938868
$619$	23.7245	0.953567	0.476783	−	0.879021i	$-0.341803\pi$
$619$	23.7245	0.953567	0.476783	+	0.879021i	$0.341803\pi$
$620$	1.21515	0.0488016
$621$	−35.6117	−1.42905
$622$	0.927558	0.0371917
$623$	−3.17160	−0.127067
$624$	−7.40551	−0.296458
$625$	14.9166	0.596665
$626$	57.3487	2.29211
$627$	6.94183	0.277230
$628$	36.4432	1.45424
$629$	10.7666	0.429294
$630$	−7.97043	−0.317549
$631$	−21.0227	−0.836900	−0.418450	−	0.908240i	$-0.637427\pi$
$631$	−21.0227	−0.836900	−0.418450	+	0.908240i	$0.637427\pi$
$632$	64.9457	2.58340
$633$	0.919694	0.0365545
$634$	−0.691754	−0.0274731
$635$	−0.0614522	−0.00243866
$636$	12.7805	0.506779
$637$	1.45756	0.0577508
$638$	−21.3733	−0.846177
$639$	−10.2061	−0.403749
$640$	−12.2344	−0.483607
$641$	43.4551	1.71637	0.858186	−	0.513338i	$-0.171591\pi$
$641$	43.4551	1.71637	0.858186	+	0.513338i	$0.171591\pi$
$642$	−39.6244	−1.56385
$643$	41.5864	1.64001	0.820005	−	0.572357i	$-0.193971\pi$
$643$	41.5864	1.64001	0.820005	+	0.572357i	$0.193971\pi$
$644$	67.0746	2.64311
$645$	−2.11377	−0.0832297
$646$	30.0754	1.18330
$647$	3.49620	0.137450	0.0687249	−	0.997636i	$-0.478107\pi$
$647$	3.49620	0.137450	0.0687249	+	0.997636i	$0.478107\pi$
$648$	9.77281	0.383912
$649$	−9.37576	−0.368031
$650$	−10.8264	−0.424646
$651$	−0.925726	−0.0362821
$652$	3.64149	0.142612
$653$	19.0512	0.745532	0.372766	−	0.927925i	$-0.378409\pi$
$653$	19.0512	0.745532	0.372766	+	0.927925i	$0.378409\pi$
$654$	−51.6781	−2.02077
$655$	4.51292	0.176334
$656$	12.6251	0.492929
$657$	9.11711	0.355692
$658$	−56.6795	−2.20960
$659$	17.0883	0.665665	0.332833	−	0.942986i	$-0.391996\pi$
$659$	17.0883	0.665665	0.332833	+	0.942986i	$0.391996\pi$
$660$	5.99056	0.233182
$661$	39.9388	1.55344	0.776720	−	0.629847i	$-0.216882\pi$
$661$	39.9388	1.55344	0.776720	+	0.629847i	$0.216882\pi$
$662$	−26.7687	−1.04040
$663$	−3.33155	−0.129387
$664$	−90.2380	−3.50192
$665$	8.38085	0.324995
$666$	15.4193	0.597486
$667$	−40.0852	−1.55211
$668$	11.0394	0.427125
$669$	20.0779	0.776258
$670$	0.916289	0.0353994
$671$	20.5375	0.792843
$672$	−10.8632	−0.419057
$673$	−18.5043	−0.713287	−0.356643	−	0.934241i	$-0.616079\pi$
$673$	−18.5043	−0.713287	−0.356643	+	0.934241i	$0.616079\pi$
$674$	−29.0676	−1.11964
$675$	23.3778	0.899813
$676$	4.35509	0.167503
$677$	−5.22661	−0.200875	−0.100437	−	0.994943i	$-0.532024\pi$
$677$	−5.22661	−0.200875	−0.100437	+	0.994943i	$0.532024\pi$
$678$	−13.7405	−0.527702
$679$	4.14575	0.159099
$680$	14.0351	0.538220
$681$	−3.92249	−0.150310
$682$	−1.15882	−0.0443733
$683$	41.1515	1.57462	0.787309	−	0.616559i	$-0.211474\pi$
$683$	41.1515	1.57462	0.787309	+	0.616559i	$0.211474\pi$
$684$	29.5169	1.12861
$685$	−3.64647	−0.139324
$686$	50.1945	1.91644
$687$	−16.1963	−0.617928
$688$	13.3034	0.507189
$689$	−2.47933	−0.0944549
$690$	16.3948	0.624138
$691$	37.3554	1.42107	0.710533	−	0.703664i	$-0.248454\pi$
$691$	37.3554	1.42107	0.710533	+	0.703664i	$0.248454\pi$
$692$	18.8728	0.717438
$693$	5.20884	0.197868
$694$	19.7028	0.747908
$695$	−13.8672	−0.526014
$696$	43.0583	1.63212
$697$	5.67973	0.215135
$698$	52.0157	1.96882
$699$	25.2090	0.953491
$700$	−44.0322	−1.66426
$701$	30.1327	1.13810	0.569048	−	0.822304i	$-0.307312\pi$
$701$	30.1327	1.13810	0.569048	+	0.822304i	$0.307312\pi$
$702$	−13.7228	−0.517933
$703$	−16.2133	−0.611496
$704$	3.71590	0.140048
$705$	−9.49397	−0.357564
$706$	−12.5818	−0.473522
$707$	−15.2034	−0.571782
$708$	34.9287	1.31270
$709$	36.6296	1.37565	0.687827	−	0.725875i	$-0.258565\pi$
$709$	36.6296	1.37565	0.687827	+	0.725875i	$0.258565\pi$
$710$	13.5141	0.507174
$711$	17.4919	0.655997
$712$	7.99826	0.299748
$713$	−2.17334	−0.0813921
$714$	−19.7723	−0.739959
$715$	−1.16213	−0.0434612
$716$	98.7709	3.69124
$717$	13.6328	0.509125
$718$	−37.9135	−1.41492
$719$	−0.181822	−0.00678081	−0.00339040	−	0.999994i	$-0.501079\pi$
$719$	−0.181822	−0.00678081	−0.00339040	+	0.999994i	$0.501079\pi$
$720$	8.40251	0.313143
$721$	18.4150	0.685811
$722$	2.60769	0.0970483
$723$	28.0670	1.04382
$724$	63.5910	2.36334
$725$	26.3146	0.977298
$726$	27.1095	1.00613
$727$	42.2938	1.56859	0.784296	−	0.620387i	$-0.213024\pi$
$727$	42.2938	1.56859	0.784296	+	0.620387i	$0.213024\pi$
$728$	13.9771	0.518027
$729$	21.9615	0.813390
$730$	−12.0721	−0.446807
$731$	5.98487	0.221358
$732$	−76.5110	−2.82793
$733$	19.0193	0.702494	0.351247	−	0.936283i	$-0.385758\pi$
$733$	19.0193	0.702494	0.351247	+	0.936283i	$0.385758\pi$
$734$	−25.3078	−0.934127
$735$	1.44897	0.0534462
$736$	−25.5036	−0.940077
$737$	−0.598815	−0.0220576
$738$	8.13414	0.299422
$739$	18.0996	0.665803	0.332902	−	0.942962i	$-0.391972\pi$
$739$	18.0996	0.665803	0.332902	+	0.942962i	$0.391972\pi$
$740$	−13.9915	−0.514338
$741$	5.01692	0.184301
$742$	−14.7145	−0.540186
$743$	−24.3013	−0.891528	−0.445764	−	0.895150i	$-0.647068\pi$
$743$	−24.3013	−0.891528	−0.445764	+	0.895150i	$0.647068\pi$
$744$	2.33453	0.0855881
$745$	14.7044	0.538726
$746$	10.4142	0.381291
$747$	−24.3039	−0.889233
$748$	−16.9615	−0.620173
$749$	31.2634	1.14234
$750$	−23.2930	−0.850539
$751$	−31.0450	−1.13285	−0.566424	−	0.824114i	$-0.691674\pi$
$751$	−31.0450	−1.13285	−0.566424	+	0.824114i	$0.691674\pi$
$752$	59.7521	2.17894
$753$	−20.5640	−0.749394
$754$	−15.4466	−0.562533
$755$	−0.0280256	−0.00101996
$756$	−55.8121	−2.02987
$757$	−15.7257	−0.571562	−0.285781	−	0.958295i	$-0.592253\pi$
$757$	−15.7257	−0.571562	−0.285781	+	0.958295i	$0.592253\pi$
$758$	−82.3507	−2.99111
$759$	−10.7143	−0.388905
$760$	−21.1351	−0.766652
$761$	16.3292	0.591935	0.295967	−	0.955198i	$-0.404358\pi$
$761$	16.3292	0.591935	0.295967	+	0.955198i	$0.404358\pi$
$762$	−0.218322	−0.00790897
$763$	40.7737	1.47611
$764$	−80.0240	−2.89517
$765$	3.78007	0.136669
$766$	−4.70641	−0.170050
$767$	−6.77593	−0.244665
$768$	−37.1080	−1.33902
$769$	−36.3585	−1.31112	−0.655561	−	0.755142i	$-0.727568\pi$
$769$	−36.3585	−1.31112	−0.655561	+	0.755142i	$0.727568\pi$
$770$	−6.89708	−0.248554
$771$	−36.8102	−1.32569
$772$	−32.6279	−1.17430
$773$	−38.8140	−1.39604	−0.698022	−	0.716077i	$-0.745936\pi$
$773$	−38.8140	−1.39604	−0.698022	+	0.716077i	$0.745936\pi$
$774$	8.57115	0.308084
$775$	1.42672	0.0512493
$776$	−10.4549	−0.375310
$777$	10.6590	0.382390
$778$	71.5848	2.56644
$779$	−8.55299	−0.306443
$780$	4.32942	0.155018
$781$	−8.83173	−0.316024
$782$	−46.4196	−1.65996
$783$	33.3545	1.19199
$784$	−9.11940	−0.325693
$785$	−7.02807	−0.250843
$786$	16.0331	0.571881
$787$	10.6455	0.379470	0.189735	−	0.981835i	$-0.439237\pi$
$787$	10.6455	0.379470	0.189735	+	0.981835i	$0.439237\pi$
$788$	79.9766	2.84905
$789$	−1.19461	−0.0425293
$790$	−23.1612	−0.824038
$791$	10.8412	0.385469
$792$	−13.1359	−0.466762
$793$	14.8426	0.527077
$794$	−24.6737	−0.875636
$795$	−2.46472	−0.0874145
$796$	112.736	3.99584
$797$	−13.7634	−0.487523	−0.243762	−	0.969835i	$-0.578381\pi$
$797$	−13.7634	−0.487523	−0.243762	+	0.969835i	$0.578381\pi$
$798$	29.7747	1.05401
$799$	26.8810	0.950980
$800$	16.7423	0.591928
$801$	2.15418	0.0761141
$802$	−6.49378	−0.229303
$803$	7.88935	0.278409
$804$	2.23084	0.0786756
$805$	−12.9354	−0.455911
$806$	−0.837484	−0.0294991
$807$	18.3969	0.647601
$808$	38.3404	1.34881
$809$	34.8919	1.22673	0.613366	−	0.789799i	$-0.289815\pi$
$809$	34.8919	1.22673	0.613366	+	0.789799i	$0.289815\pi$
$810$	−3.48521	−0.122458
$811$	27.2520	0.956946	0.478473	−	0.878102i	$-0.341191\pi$
$811$	27.2520	0.956946	0.478473	+	0.878102i	$0.341191\pi$
$812$	−62.8232	−2.20466
$813$	−24.8283	−0.870768
$814$	13.3429	0.467667
$815$	−0.702262	−0.0245992
$816$	20.8442	0.729692
$817$	−9.01251	−0.315308
$818$	32.6458	1.14143
$819$	3.76447	0.131541
$820$	−7.38093	−0.257753
$821$	−24.8560	−0.867479	−0.433740	−	0.901038i	$-0.642806\pi$
$821$	−24.8560	−0.867479	−0.433740	+	0.901038i	$0.642806\pi$
$822$	−12.9549	−0.451852
$823$	48.8760	1.70371	0.851855	−	0.523778i	$-0.175478\pi$
$823$	48.8760	1.70371	0.851855	+	0.523778i	$0.175478\pi$
$824$	−46.4397	−1.61780
$825$	7.03358	0.244878
$826$	−40.2143	−1.39923
$827$	16.6382	0.578566	0.289283	−	0.957244i	$-0.406583\pi$
$827$	16.6382	0.578566	0.289283	+	0.957244i	$0.406583\pi$
$828$	−45.5576	−1.58324
$829$	−39.0692	−1.35693	−0.678464	−	0.734634i	$-0.737354\pi$
$829$	−39.0692	−1.35693	−0.678464	+	0.734634i	$0.737354\pi$
$830$	32.1810	1.11702
$831$	18.7034	0.648814
$832$	2.68551	0.0931032
$833$	−4.10258	−0.142146
$834$	−49.2663	−1.70595
$835$	−2.12894	−0.0736751
$836$	25.5420	0.883388
$837$	1.80841	0.0625079
$838$	15.6152	0.539417
$839$	31.0353	1.07146	0.535729	−	0.844390i	$-0.320037\pi$
$839$	31.0353	1.07146	0.535729	+	0.844390i	$0.320037\pi$
$840$	13.8948	0.479415
$841$	8.54451	0.294638
$842$	33.3468	1.14921
$843$	14.6065	0.503073
$844$	3.38395	0.116480
$845$	−0.839879	−0.0288927
$846$	38.4972	1.32356
$847$	−21.3892	−0.734942
$848$	15.5122	0.532690
$849$	4.91202	0.168580
$850$	30.4729	1.04521
$851$	25.0243	0.857822
$852$	32.9019	1.12720
$853$	55.5264	1.90119	0.950594	−	0.310438i	$-0.100476\pi$
$853$	55.5264	1.90119	0.950594	+	0.310438i	$0.100476\pi$
$854$	88.0890	3.01434
$855$	−5.69234	−0.194674
$856$	−78.8412	−2.69474
$857$	3.88351	0.132658	0.0663291	−	0.997798i	$-0.478871\pi$
$857$	3.88351	0.132658	0.0663291	+	0.997798i	$0.478871\pi$
$858$	−4.12871	−0.140952
$859$	53.9224	1.83981	0.919904	−	0.392143i	$-0.128266\pi$
$859$	53.9224	1.83981	0.919904	+	0.392143i	$0.128266\pi$
$860$	−7.77748	−0.265210
$861$	5.62295	0.191630
$862$	23.5388	0.801736
$863$	56.5283	1.92424	0.962122	−	0.272618i	$-0.0878895\pi$
$863$	56.5283	1.92424	0.962122	+	0.272618i	$0.0878895\pi$
$864$	21.2213	0.721964
$865$	−3.63963	−0.123751
$866$	−69.7102	−2.36885
$867$	−10.7445	−0.364901
$868$	−3.40614	−0.115612
$869$	15.1363	0.513465
$870$	−15.3556	−0.520604
$871$	−0.432768	−0.0146638
$872$	−102.825	−3.48208
$873$	−2.81583	−0.0953015
$874$	69.9024	2.36449
$875$	18.3780	0.621290
$876$	−29.3912	−0.993035
$877$	−1.74131	−0.0587999	−0.0293999	−	0.999568i	$-0.509360\pi$
$877$	−1.74131	−0.0587999	−0.0293999	+	0.999568i	$0.509360\pi$
$878$	12.5717	0.424274
$879$	−28.3992	−0.957881
$880$	7.27098	0.245105
$881$	23.0405	0.776254	0.388127	−	0.921606i	$-0.373122\pi$
$881$	23.0405	0.776254	0.388127	+	0.921606i	$0.373122\pi$
$882$	−5.87546	−0.197837
$883$	−51.3837	−1.72920	−0.864599	−	0.502463i	$-0.832427\pi$
$883$	−51.3837	−1.72920	−0.864599	+	0.502463i	$0.832427\pi$
$884$	−12.2582	−0.412288
$885$	−6.73600	−0.226428
$886$	2.85567	0.0959383
$887$	−25.2767	−0.848708	−0.424354	−	0.905496i	$-0.639499\pi$
$887$	−25.2767	−0.848708	−0.424354	+	0.905496i	$0.639499\pi$
$888$	−26.8803	−0.902044
$889$	0.172255	0.00577723
$890$	−2.85237	−0.0956116
$891$	2.27766	0.0763045
$892$	73.8754	2.47353
$893$	−40.4795	−1.35460
$894$	52.2404	1.74718
$895$	−19.0480	−0.636704
$896$	34.2938	1.14568
$897$	−7.74332	−0.258542
$898$	42.9407	1.43295
$899$	2.03559	0.0678906
$900$	29.9070	0.996901
$901$	6.97853	0.232488
$902$	7.03875	0.234365
$903$	5.92504	0.197173
$904$	−27.3398	−0.909307
$905$	−12.2635	−0.407654
$906$	−0.0995670	−0.00330789
$907$	−23.3014	−0.773710	−0.386855	−	0.922141i	$-0.626439\pi$
$907$	−23.3014	−0.773710	−0.386855	+	0.922141i	$0.626439\pi$
$908$	−14.4325	−0.478960
$909$	10.3263	0.342500
$910$	−4.98457	−0.165237
$911$	7.64980	0.253449	0.126725	−	0.991938i	$-0.459554\pi$
$911$	7.64980	0.253449	0.126725	+	0.991938i	$0.459554\pi$
$912$	−31.3889	−1.03939
$913$	−21.0310	−0.696024
$914$	69.1737	2.28806
$915$	14.7552	0.487791
$916$	−59.5932	−1.96901
$917$	−12.6500	−0.417740
$918$	38.6253	1.27482
$919$	35.0737	1.15697	0.578487	−	0.815692i	$-0.303643\pi$
$919$	35.0737	1.15697	0.578487	+	0.815692i	$0.303643\pi$
$920$	32.6209	1.07548
$921$	27.0944	0.892789
$922$	−75.5025	−2.48654
$923$	−6.38275	−0.210091
$924$	−16.7919	−0.552414
$925$	−16.4276	−0.540136
$926$	−2.52093	−0.0828429
$927$	−12.5076	−0.410805
$928$	23.8872	0.784134
$929$	28.5585	0.936974	0.468487	−	0.883470i	$-0.344799\pi$
$929$	28.5585	0.936974	0.468487	+	0.883470i	$0.344799\pi$
$930$	−0.832549	−0.0273004
$931$	6.17801	0.202476
$932$	92.7547	3.03828
$933$	−0.435508	−0.0142579
$934$	−26.0577	−0.852632
$935$	3.27103	0.106974
$936$	−9.49338	−0.310301
$937$	32.1188	1.04928	0.524638	−	0.851325i	$-0.324201\pi$
$937$	32.1188	1.04928	0.524638	+	0.851325i	$0.324201\pi$
$938$	−2.56842	−0.0838619
$939$	−26.9264	−0.878711
$940$	−34.9324	−1.13937
$941$	−41.7926	−1.36240	−0.681200	−	0.732097i	$-0.738542\pi$
$941$	−41.7926	−1.36240	−0.681200	+	0.732097i	$0.738542\pi$
$942$	−24.9687	−0.813524
$943$	13.2011	0.429885
$944$	42.3943	1.37982
$945$	10.7634	0.350133
$946$	7.41691	0.241145
$947$	12.8566	0.417785	0.208892	−	0.977939i	$-0.433014\pi$
$947$	12.8566	0.417785	0.208892	+	0.977939i	$0.433014\pi$
$948$	−56.3892	−1.83144
$949$	5.70169	0.185085
$950$	−45.8886	−1.48882
$951$	0.324793	0.0105321
$952$	−39.3412	−1.27506
$953$	13.2206	0.428258	0.214129	−	0.976805i	$-0.431309\pi$
$953$	13.2206	0.428258	0.214129	+	0.976805i	$0.431309\pi$
$954$	9.99421	0.323574
$955$	15.4326	0.499389
$956$	50.1608	1.62232
$957$	10.0352	0.324393
$958$	−33.2613	−1.07462
$959$	10.2213	0.330063
$960$	2.66968	0.0861635
$961$	−30.8896	−0.996440
$962$	9.64298	0.310902
$963$	−21.2344	−0.684268
$964$	103.271	3.32612
$965$	6.29230	0.202556
$966$	−45.9556	−1.47860
$967$	−13.6395	−0.438616	−0.219308	−	0.975656i	$-0.570380\pi$
$967$	−13.6395	−0.438616	−0.219308	+	0.975656i	$0.570380\pi$
$968$	53.9402	1.73370
$969$	−14.1210	−0.453633
$970$	3.72847	0.119714
$971$	22.0147	0.706486	0.353243	−	0.935532i	$-0.385079\pi$
$971$	22.0147	0.706486	0.353243	+	0.935532i	$0.385079\pi$
$972$	62.6360	2.00905
$973$	38.8708	1.24614
$974$	24.2529	0.777113
$975$	5.08322	0.162793
$976$	−92.8644	−2.97252
$977$	15.6192	0.499704	0.249852	−	0.968284i	$-0.419618\pi$
$977$	15.6192	0.499704	0.249852	+	0.968284i	$0.419618\pi$
$978$	−2.49493	−0.0797792
$979$	1.86408	0.0595764
$980$	5.33140	0.170305
$981$	−27.6938	−0.884196
$982$	3.29188	0.105048
$983$	−5.06879	−0.161669	−0.0808346	−	0.996728i	$-0.525759\pi$
$983$	−5.06879	−0.161669	−0.0808346	+	0.996728i	$0.525759\pi$
$984$	−14.1802	−0.452047
$985$	−15.4235	−0.491434
$986$	43.4774	1.38460
$987$	26.6122	0.847077
$988$	18.4594	0.587271
$989$	13.9103	0.442321
$990$	4.68456	0.148885
$991$	−5.86211	−0.186216	−0.0931081	−	0.995656i	$-0.529680\pi$
$991$	−5.86211	−0.186216	−0.0931081	+	0.995656i	$0.529680\pi$
$992$	1.29511	0.0411198
$993$	12.5685	0.398849
$994$	−37.8808	−1.20151
$995$	−21.7413	−0.689244
$996$	78.3493	2.48259
$997$	−8.37854	−0.265351	−0.132675	−	0.991160i	$-0.542357\pi$
$997$	−8.37854	−0.265351	−0.132675	+	0.991160i	$0.542357\pi$
$998$	−15.0541	−0.476529
$999$	−20.8225	−0.658794

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.d.1.9	✓	123

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.d.1.9	✓	123	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:	\( N \)	\(=\)	\( 6019 = 13 \cdot 463 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6019.a (trivial)

\(f(q)\)	\(=\)	\(q-2.52093 q^{2} +1.18363 q^{3} +4.35509 q^{4} -0.839879 q^{5} -2.98385 q^{6} +2.35424 q^{7} -5.93701 q^{8} -1.59902 q^{9} +O(q^{10})\)	\(q-2.52093 q^{2} +1.18363 q^{3} +4.35509 q^{4} -0.839879 q^{5} -2.98385 q^{6} +2.35424 q^{7} -5.93701 q^{8} -1.59902 q^{9} +2.11728 q^{10} -1.38369 q^{11} +5.15481 q^{12} -1.00000 q^{13} -5.93487 q^{14} -0.994107 q^{15} +6.25660 q^{16} +2.81468 q^{17} +4.03101 q^{18} -4.23858 q^{19} -3.65775 q^{20} +2.78655 q^{21} +3.48817 q^{22} +6.54201 q^{23} -7.02722 q^{24} -4.29460 q^{25} +2.52093 q^{26} -5.44354 q^{27} +10.2529 q^{28} -6.12736 q^{29} +2.50607 q^{30} -0.332213 q^{31} -3.89844 q^{32} -1.63777 q^{33} -7.09562 q^{34} -1.97728 q^{35} -6.96386 q^{36} +3.82517 q^{37} +10.6852 q^{38} -1.18363 q^{39} +4.98637 q^{40} +2.01789 q^{41} -7.02469 q^{42} +2.12630 q^{43} -6.02607 q^{44} +1.34298 q^{45} -16.4919 q^{46} +9.55025 q^{47} +7.40551 q^{48} -1.45756 q^{49} +10.8264 q^{50} +3.33155 q^{51} -4.35509 q^{52} +2.47933 q^{53} +13.7228 q^{54} +1.16213 q^{55} -13.9771 q^{56} -5.01692 q^{57} +15.4466 q^{58} +6.77593 q^{59} -4.32942 q^{60} -14.8426 q^{61} +0.837484 q^{62} -3.76447 q^{63} -2.68551 q^{64} +0.839879 q^{65} +4.12871 q^{66} +0.432768 q^{67} +12.2582 q^{68} +7.74332 q^{69} +4.98457 q^{70} +6.38275 q^{71} +9.49338 q^{72} -5.70169 q^{73} -9.64298 q^{74} -5.08322 q^{75} -18.4594 q^{76} -3.25753 q^{77} +2.98385 q^{78} -10.9391 q^{79} -5.25479 q^{80} -1.64608 q^{81} -5.08696 q^{82} +15.1993 q^{83} +12.1357 q^{84} -2.36400 q^{85} -5.36026 q^{86} -7.25253 q^{87} +8.21495 q^{88} -1.34719 q^{89} -3.38557 q^{90} -2.35424 q^{91} +28.4910 q^{92} -0.393217 q^{93} -24.0755 q^{94} +3.55990 q^{95} -4.61432 q^{96} +1.76098 q^{97} +3.67442 q^{98} +2.21254 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9}+O(q^{10}) \) 123 * q + 10 * q^2 + q^3 + 136 * q^4 + 46 * q^5 + 16 * q^6 + 12 * q^7 + 30 * q^8 + 154 * q^9	\( 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9} + 5 q^{10} + 53 q^{11} - 6 q^{12} - 123 q^{13} + 21 q^{14} + 29 q^{15} + 166 q^{16} - 35 q^{17} + 28 q^{18} + 23 q^{19} + 93 q^{20} + 72 q^{21} + 8 q^{22} + 42 q^{23} + 55 q^{24} + 153 q^{25} - 10 q^{26} + 7 q^{27} + 39 q^{28} + 86 q^{29} + 44 q^{30} + 16 q^{31} + 70 q^{32} + 40 q^{33} + 10 q^{34} + 6 q^{35} + 222 q^{36} + 52 q^{37} + 12 q^{38} - q^{39} + 14 q^{40} + 80 q^{41} + 29 q^{42} + 2 q^{43} + 143 q^{44} + 137 q^{45} + 39 q^{46} + 45 q^{47} - 27 q^{48} + 163 q^{49} + 102 q^{50} + 48 q^{51} - 136 q^{52} + 117 q^{53} + 75 q^{54} + 20 q^{55} + 88 q^{56} + 67 q^{57} + 56 q^{58} + 88 q^{59} + 96 q^{60} + 57 q^{61} - 13 q^{62} + 48 q^{63} + 228 q^{64} - 46 q^{65} + 28 q^{66} + 43 q^{67} - 56 q^{68} + 92 q^{69} + 14 q^{70} + 90 q^{71} + 98 q^{72} + 25 q^{73} + 80 q^{74} + 21 q^{75} + 75 q^{76} + 112 q^{77} - 16 q^{78} + 36 q^{79} + 208 q^{80} + 231 q^{81} - 27 q^{82} + 93 q^{83} + 175 q^{84} + 77 q^{85} + 199 q^{86} + 15 q^{87} + 43 q^{88} + 140 q^{89} + 11 q^{90} - 12 q^{91} + 93 q^{92} + 140 q^{93} + 4 q^{94} + 23 q^{95} + 105 q^{96} + 43 q^{97} + 67 q^{98} + 140 q^{99}+O(q^{100}) \) 123 * q + 10 * q^2 + q^3 + 136 * q^4 + 46 * q^5 + 16 * q^6 + 12 * q^7 + 30 * q^8 + 154 * q^9 + 5 * q^10 + 53 * q^11 - 6 * q^12 - 123 * q^13 + 21 * q^14 + 29 * q^15 + 166 * q^16 - 35 * q^17 + 28 * q^18 + 23 * q^19 + 93 * q^20 + 72 * q^21 + 8 * q^22 + 42 * q^23 + 55 * q^24 + 153 * q^25 - 10 * q^26 + 7 * q^27 + 39 * q^28 + 86 * q^29 + 44 * q^30 + 16 * q^31 + 70 * q^32 + 40 * q^33 + 10 * q^34 + 6 * q^35 + 222 * q^36 + 52 * q^37 + 12 * q^38 - q^39 + 14 * q^40 + 80 * q^41 + 29 * q^42 + 2 * q^43 + 143 * q^44 + 137 * q^45 + 39 * q^46 + 45 * q^47 - 27 * q^48 + 163 * q^49 + 102 * q^50 + 48 * q^51 - 136 * q^52 + 117 * q^53 + 75 * q^54 + 20 * q^55 + 88 * q^56 + 67 * q^57 + 56 * q^58 + 88 * q^59 + 96 * q^60 + 57 * q^61 - 13 * q^62 + 48 * q^63 + 228 * q^64 - 46 * q^65 + 28 * q^66 + 43 * q^67 - 56 * q^68 + 92 * q^69 + 14 * q^70 + 90 * q^71 + 98 * q^72 + 25 * q^73 + 80 * q^74 + 21 * q^75 + 75 * q^76 + 112 * q^77 - 16 * q^78 + 36 * q^79 + 208 * q^80 + 231 * q^81 - 27 * q^82 + 93 * q^83 + 175 * q^84 + 77 * q^85 + 199 * q^86 + 15 * q^87 + 43 * q^88 + 140 * q^89 + 11 * q^90 - 12 * q^91 + 93 * q^92 + 140 * q^93 + 4 * q^94 + 23 * q^95 + 105 * q^96 + 43 * q^97 + 67 * q^98 + 140 * q^99

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