LMFDB - Embedded newform 6019.2.a.d.1.19

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			1.19
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)

$f(q)$	$=$	$q-2.14591 q^{2} -1.26575 q^{3} +2.60492 q^{4} +3.62169 q^{5} +2.71619 q^{6} +0.00950737 q^{7} -1.29811 q^{8} -1.39787 q^{9} +O(q^{10})$	\(q-2.14591 q^{2} -1.26575 q^{3} +2.60492 q^{4} +3.62169 q^{5} +2.71619 q^{6} +0.00950737 q^{7} -1.29811 q^{8} -1.39787 q^{9} -7.77182 q^{10} -4.02197 q^{11} -3.29719 q^{12} -1.00000 q^{13} -0.0204020 q^{14} -4.58417 q^{15} -2.42423 q^{16} +4.68093 q^{17} +2.99970 q^{18} -3.31040 q^{19} +9.43423 q^{20} -0.0120340 q^{21} +8.63078 q^{22} -2.61417 q^{23} +1.64308 q^{24} +8.11667 q^{25} +2.14591 q^{26} +5.56662 q^{27} +0.0247660 q^{28} -1.28402 q^{29} +9.83722 q^{30} -0.373308 q^{31} +7.79838 q^{32} +5.09082 q^{33} -10.0448 q^{34} +0.0344328 q^{35} -3.64134 q^{36} +1.90075 q^{37} +7.10381 q^{38} +1.26575 q^{39} -4.70135 q^{40} -11.2710 q^{41} +0.0258238 q^{42} -9.96676 q^{43} -10.4769 q^{44} -5.06265 q^{45} +5.60976 q^{46} -3.97506 q^{47} +3.06847 q^{48} -6.99991 q^{49} -17.4176 q^{50} -5.92490 q^{51} -2.60492 q^{52} -8.36326 q^{53} -11.9454 q^{54} -14.5663 q^{55} -0.0123416 q^{56} +4.19015 q^{57} +2.75540 q^{58} +4.24112 q^{59} -11.9414 q^{60} +9.96534 q^{61} +0.801085 q^{62} -0.0132900 q^{63} -11.8862 q^{64} -3.62169 q^{65} -10.9244 q^{66} +15.6963 q^{67} +12.1935 q^{68} +3.30889 q^{69} -0.0738896 q^{70} +9.53611 q^{71} +1.81458 q^{72} +2.12882 q^{73} -4.07884 q^{74} -10.2737 q^{75} -8.62333 q^{76} -0.0382384 q^{77} -2.71619 q^{78} -0.401961 q^{79} -8.77980 q^{80} -2.85236 q^{81} +24.1866 q^{82} -7.44366 q^{83} -0.0313476 q^{84} +16.9529 q^{85} +21.3878 q^{86} +1.62526 q^{87} +5.22095 q^{88} -6.62965 q^{89} +10.8640 q^{90} -0.00950737 q^{91} -6.80970 q^{92} +0.472516 q^{93} +8.53011 q^{94} -11.9893 q^{95} -9.87083 q^{96} +17.2034 q^{97} +15.0212 q^{98} +5.62218 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.14591	−1.51739	−0.758693	−	0.651448i	$-0.774162\pi$
$2$	−2.14591	−1.51739	−0.758693	+	0.651448i	$0.774162\pi$
$3$	−1.26575	−0.730783	−0.365392	−	0.930854i	$-0.619065\pi$
$3$	−1.26575	−0.730783	−0.365392	+	0.930854i	$0.619065\pi$
$4$	2.60492	1.30246
$5$	3.62169	1.61967	0.809836	−	0.586657i	$-0.199556\pi$
$5$	3.62169	1.61967	0.809836	+	0.586657i	$0.199556\pi$
$6$	2.71619	1.10888
$7$	0.00950737	0.00359345	0.00179672	−	0.999998i	$-0.499428\pi$
$7$	0.00950737	0.00359345	0.00179672	+	0.999998i	$0.499428\pi$
$8$	−1.29811	−0.458950
$9$	−1.39787	−0.465956
$10$	−7.77182	−2.45767
$11$	−4.02197	−1.21267	−0.606335	−	0.795210i	$-0.707361\pi$
$11$	−4.02197	−1.21267	−0.606335	+	0.795210i	$0.707361\pi$
$12$	−3.29719	−0.951817
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−0.0204020	−0.00545265
$15$	−4.58417	−1.18363
$16$	−2.42423	−0.606056
$17$	4.68093	1.13529	0.567646	−	0.823273i	$-0.307854\pi$
$17$	4.68093	1.13529	0.567646	+	0.823273i	$0.307854\pi$
$18$	2.99970	0.707035
$19$	−3.31040	−0.759457	−0.379729	−	0.925098i	$-0.623983\pi$
$19$	−3.31040	−0.759457	−0.379729	+	0.925098i	$0.623983\pi$
$20$	9.43423	2.10956
$21$	−0.0120340	−0.00262603
$22$	8.63078	1.84009
$23$	−2.61417	−0.545092	−0.272546	−	0.962143i	$-0.587866\pi$
$23$	−2.61417	−0.545092	−0.272546	+	0.962143i	$0.587866\pi$
$24$	1.64308	0.335393
$25$	8.11667	1.62333
$26$	2.14591	0.420847
$27$	5.56662	1.07130
$28$	0.0247660	0.00468033
$29$	−1.28402	−0.238437	−0.119219	−	0.992868i	$-0.538039\pi$
$29$	−1.28402	−0.238437	−0.119219	+	0.992868i	$0.538039\pi$
$30$	9.83722	1.79602
$31$	−0.373308	−0.0670481	−0.0335241	−	0.999438i	$-0.510673\pi$
$31$	−0.373308	−0.0670481	−0.0335241	+	0.999438i	$0.510673\pi$
$32$	7.79838	1.37857
$33$	5.09082	0.886198
$34$	−10.0448	−1.72268
$35$	0.0344328	0.00582021
$36$	−3.64134	−0.606889
$37$	1.90075	0.312482	0.156241	−	0.987719i	$-0.450062\pi$
$37$	1.90075	0.312482	0.156241	+	0.987719i	$0.450062\pi$
$38$	7.10381	1.15239
$39$	1.26575	0.202683
$40$	−4.70135	−0.743348
$41$	−11.2710	−1.76024	−0.880121	−	0.474750i	$-0.842538\pi$
$41$	−11.2710	−1.76024	−0.880121	+	0.474750i	$0.842538\pi$
$42$	0.0258238	0.00398471
$43$	−9.96676	−1.51992	−0.759959	−	0.649972i	$-0.774781\pi$
$43$	−9.96676	−1.51992	−0.759959	+	0.649972i	$0.774781\pi$
$44$	−10.4769	−1.57945
$45$	−5.06265	−0.754695
$46$	5.60976	0.827115
$47$	−3.97506	−0.579822	−0.289911	−	0.957054i	$-0.593626\pi$
$47$	−3.97506	−0.579822	−0.289911	+	0.957054i	$0.593626\pi$
$48$	3.06847	0.442896
$49$	−6.99991	−0.999987
$50$	−17.4176	−2.46323
$51$	−5.92490	−0.829652
$52$	−2.60492	−0.361238
$53$	−8.36326	−1.14878	−0.574391	−	0.818581i	$-0.694761\pi$
$53$	−8.36326	−1.14878	−0.574391	+	0.818581i	$0.694761\pi$
$54$	−11.9454	−1.62557
$55$	−14.5663	−1.96413
$56$	−0.0123416	−0.00164921
$57$	4.19015	0.554999
$58$	2.75540	0.361801
$59$	4.24112	0.552147	0.276074	−	0.961137i	$-0.410967\pi$
$59$	4.24112	0.552147	0.276074	+	0.961137i	$0.410967\pi$
$60$	−11.9414	−1.54163
$61$	9.96534	1.27593	0.637966	−	0.770065i	$-0.279776\pi$
$61$	9.96534	1.27593	0.637966	+	0.770065i	$0.279776\pi$
$62$	0.801085	0.101738
$63$	−0.0132900	−0.00167439
$64$	−11.8862	−1.48577
$65$	−3.62169	−0.449216
$66$	−10.9244	−1.34471
$67$	15.6963	1.91761	0.958804	−	0.284067i	$-0.0916839\pi$
$67$	15.6963	1.91761	0.958804	+	0.284067i	$0.0916839\pi$
$68$	12.1935	1.47867
$69$	3.30889	0.398344
$70$	−0.0738896	−0.00883150
$71$	9.53611	1.13173	0.565864	−	0.824499i	$-0.308543\pi$
$71$	9.53611	1.13173	0.565864	+	0.824499i	$0.308543\pi$
$72$	1.81458	0.213851
$73$	2.12882	0.249159	0.124580	−	0.992210i	$-0.460242\pi$
$73$	2.12882	0.249159	0.124580	+	0.992210i	$0.460242\pi$
$74$	−4.07884	−0.474156
$75$	−10.2737	−1.18631
$76$	−8.62333	−0.989164
$77$	−0.0382384	−0.00435767
$78$	−2.71619	−0.307548
$79$	−0.401961	−0.0452242	−0.0226121	−	0.999744i	$-0.507198\pi$
$79$	−0.401961	−0.0452242	−0.0226121	+	0.999744i	$0.507198\pi$
$80$	−8.77980	−0.981612
$81$	−2.85236	−0.316929
$82$	24.1866	2.67097
$83$	−7.44366	−0.817048	−0.408524	−	0.912748i	$-0.633956\pi$
$83$	−7.44366	−0.817048	−0.408524	+	0.912748i	$0.633956\pi$
$84$	−0.0313476	−0.00342031
$85$	16.9529	1.83880
$86$	21.3878	2.30630
$87$	1.62526	0.174246
$88$	5.22095	0.556555
$89$	−6.62965	−0.702742	−0.351371	−	0.936236i	$-0.614284\pi$
$89$	−6.62965	−0.702742	−0.351371	+	0.936236i	$0.614284\pi$
$90$	10.8640	1.14516
$91$	−0.00950737	−0.000996644 0
$92$	−6.80970	−0.709961
$93$	0.472516	0.0489977
$94$	8.53011	0.879813
$95$	−11.9893	−1.23007
$96$	−9.87083	−1.00744
$97$	17.2034	1.74674	0.873370	−	0.487057i	$-0.161930\pi$
$97$	17.2034	1.74674	0.873370	+	0.487057i	$0.161930\pi$
$98$	15.0212	1.51737
$99$	5.62218	0.565050
$100$	21.1433	2.11433
$101$	12.4270	1.23653	0.618265	−	0.785970i	$-0.287836\pi$
$101$	12.4270	1.23653	0.618265	+	0.785970i	$0.287836\pi$
$102$	12.7143	1.25890
$103$	7.69463	0.758174	0.379087	−	0.925361i	$-0.376238\pi$
$103$	7.69463	0.758174	0.379087	+	0.925361i	$0.376238\pi$
$104$	1.29811	0.127290
$105$	−0.0435835	−0.00425331
$106$	17.9468	1.74315
$107$	17.4232	1.68437	0.842184	−	0.539191i	$-0.181270\pi$
$107$	17.4232	1.68437	0.842184	+	0.539191i	$0.181270\pi$
$108$	14.5006	1.39532
$109$	7.46842	0.715344	0.357672	−	0.933847i	$-0.383571\pi$
$109$	7.46842	0.715344	0.357672	+	0.933847i	$0.383571\pi$
$110$	31.2580	2.98034
$111$	−2.40588	−0.228356
$112$	−0.0230480	−0.00217783
$113$	14.0529	1.32198	0.660991	−	0.750394i	$-0.270136\pi$
$113$	14.0529	1.32198	0.660991	+	0.750394i	$0.270136\pi$
$114$	−8.99168	−0.842148
$115$	−9.46772	−0.882869
$116$	−3.34478	−0.310555
$117$	1.39787	0.129233
$118$	−9.10106	−0.837820
$119$	0.0445033	0.00407961
$120$	5.95075	0.543227
$121$	5.17623	0.470567
$122$	−21.3847	−1.93608
$123$	14.2664	1.28635
$124$	−0.972439	−0.0873276
$125$	11.2876	1.00960
$126$	0.0285192	0.00254069
$127$	−7.14376	−0.633906	−0.316953	−	0.948441i	$-0.602660\pi$
$127$	−7.14376	−0.633906	−0.316953	+	0.948441i	$0.602660\pi$
$128$	9.90984	0.875914
$129$	12.6155	1.11073
$130$	7.77182	0.681634
$131$	−9.20824	−0.804528	−0.402264	−	0.915524i	$-0.631777\pi$
$131$	−9.20824	−0.804528	−0.402264	+	0.915524i	$0.631777\pi$
$132$	13.2612	1.15424
$133$	−0.0314732	−0.00272907
$134$	−33.6828	−2.90975
$135$	20.1606	1.73515
$136$	−6.07635	−0.521042
$137$	14.4172	1.23174	0.615871	−	0.787847i	$-0.288804\pi$
$137$	14.4172	1.23174	0.615871	+	0.787847i	$0.288804\pi$
$138$	−7.10058	−0.604442
$139$	−17.9039	−1.51859	−0.759293	−	0.650748i	$-0.774455\pi$
$139$	−17.9039	−1.51859	−0.759293	+	0.650748i	$0.774455\pi$
$140$	0.0896948	0.00758059
$141$	5.03144	0.423724
$142$	−20.4636	−1.71727
$143$	4.02197	0.336334
$144$	3.38875	0.282395
$145$	−4.65034	−0.386190
$146$	−4.56824	−0.378071
$147$	8.86016	0.730774
$148$	4.95131	0.406995
$149$	−22.8914	−1.87534	−0.937670	−	0.347528i	$-0.887021\pi$
$149$	−22.8914	−1.87534	−0.937670	+	0.347528i	$0.887021\pi$
$150$	22.0464	1.80008
$151$	−0.168012	−0.0136726	−0.00683630	−	0.999977i	$-0.502176\pi$
$151$	−0.168012	−0.0136726	−0.00683630	+	0.999977i	$0.502176\pi$
$152$	4.29725	0.348553
$153$	−6.54332	−0.528996
$154$	0.0820560	0.00661226
$155$	−1.35201	−0.108596
$156$	3.29719	0.263986
$157$	−5.54632	−0.442645	−0.221322	−	0.975201i	$-0.571037\pi$
$157$	−5.54632	−0.442645	−0.221322	+	0.975201i	$0.571037\pi$
$158$	0.862572	0.0686225
$159$	10.5858	0.839511
$160$	28.2433	2.23283
$161$	−0.0248539	−0.00195876
$162$	6.12091	0.480904
$163$	−0.720500	−0.0564339	−0.0282169	−	0.999602i	$-0.508983\pi$
$163$	−0.720500	−0.0564339	−0.0282169	+	0.999602i	$0.508983\pi$
$164$	−29.3602	−2.29265
$165$	18.4374	1.43535
$166$	15.9734	1.23978
$167$	−9.82383	−0.760191	−0.380096	−	0.924947i	$-0.624109\pi$
$167$	−9.82383	−0.760191	−0.380096	+	0.924947i	$0.624109\pi$
$168$	0.0156214	0.00120522
$169$	1.00000	0.0769231
$170$	−36.3793	−2.79017
$171$	4.62750	0.353874
$172$	−25.9626	−1.97963
$173$	2.56703	0.195168	0.0975838	−	0.995227i	$-0.468889\pi$
$173$	2.56703	0.195168	0.0975838	+	0.995227i	$0.468889\pi$
$174$	−3.48765	−0.264398
$175$	0.0771682	0.00583337
$176$	9.75016	0.734946
$177$	−5.36822	−0.403500
$178$	14.2266	1.06633
$179$	2.96010	0.221248	0.110624	−	0.993862i	$-0.464715\pi$
$179$	2.96010	0.221248	0.110624	+	0.993862i	$0.464715\pi$
$180$	−13.1878	−0.982961
$181$	14.1821	1.05415	0.527075	−	0.849819i	$-0.323289\pi$
$181$	14.1821	1.05415	0.527075	+	0.849819i	$0.323289\pi$
$182$	0.0204020	0.00151229
$183$	−12.6137	−0.932429
$184$	3.39347	0.250170
$185$	6.88395	0.506118
$186$	−1.01398	−0.0743484
$187$	−18.8265	−1.37673
$188$	−10.3547	−0.755195
$189$	0.0529239	0.00384965
$190$	25.7278	1.86649
$191$	4.41544	0.319490	0.159745	−	0.987158i	$-0.448933\pi$
$191$	4.41544	0.319490	0.159745	+	0.987158i	$0.448933\pi$
$192$	15.0449	1.08578
$193$	−2.49308	−0.179456	−0.0897279	−	0.995966i	$-0.528600\pi$
$193$	−2.49308	−0.179456	−0.0897279	+	0.995966i	$0.528600\pi$
$194$	−36.9169	−2.65048
$195$	4.58417	0.328279
$196$	−18.2342	−1.30244
$197$	23.4897	1.67357	0.836787	−	0.547529i	$-0.184432\pi$
$197$	23.4897	1.67357	0.836787	+	0.547529i	$0.184432\pi$
$198$	−12.0647	−0.857400
$199$	15.0495	1.06683	0.533416	−	0.845853i	$-0.320908\pi$
$199$	15.0495	1.06683	0.533416	+	0.845853i	$0.320908\pi$
$200$	−10.5363	−0.745030
$201$	−19.8677	−1.40136
$202$	−26.6671	−1.87629
$203$	−0.0122077	−0.000856812 0
$204$	−15.4339	−1.08059
$205$	−40.8203	−2.85101
$206$	−16.5120	−1.15044
$207$	3.65426	0.253989
$208$	2.42423	0.168090
$209$	13.3143	0.920971
$210$	0.0935261	0.00645391
$211$	5.21328	0.358897	0.179449	−	0.983767i	$-0.442569\pi$
$211$	5.21328	0.358897	0.179449	+	0.983767i	$0.442569\pi$
$212$	−21.7856	−1.49624
$213$	−12.0704	−0.827048
$214$	−37.3887	−2.55584
$215$	−36.0966	−2.46177
$216$	−7.22607	−0.491671
$217$	−0.00354918	−0.000240934 0
$218$	−16.0265	−1.08545
$219$	−2.69456	−0.182081
$220$	−37.9442	−2.55820
$221$	−4.68093	−0.314873
$222$	5.16281	0.346505
$223$	−19.6635	−1.31676	−0.658382	−	0.752684i	$-0.728759\pi$
$223$	−19.6635	−1.31676	−0.658382	+	0.752684i	$0.728759\pi$
$224$	0.0741421	0.00495383
$225$	−11.3460	−0.756402
$226$	−30.1562	−2.00596
$227$	−7.61773	−0.505606	−0.252803	−	0.967518i	$-0.581352\pi$
$227$	−7.61773	−0.505606	−0.252803	+	0.967518i	$0.581352\pi$
$228$	10.9150	0.722864
$229$	19.3077	1.27589	0.637943	−	0.770083i	$-0.279785\pi$
$229$	19.3077	1.27589	0.637943	+	0.770083i	$0.279785\pi$
$230$	20.3169	1.33965
$231$	0.0484004	0.00318451
$232$	1.66680	0.109431
$233$	25.3615	1.66149	0.830744	−	0.556654i	$-0.187915\pi$
$233$	25.3615	1.66149	0.830744	+	0.556654i	$0.187915\pi$
$234$	−2.99970	−0.196096
$235$	−14.3964	−0.939120
$236$	11.0478	0.719150
$237$	0.508784	0.0330491
$238$	−0.0955001	−0.00619035
$239$	4.51117	0.291804	0.145902	−	0.989299i	$-0.453392\pi$
$239$	4.51117	0.291804	0.145902	+	0.989299i	$0.453392\pi$
$240$	11.1131	0.717346
$241$	1.67126	0.107655	0.0538276	−	0.998550i	$-0.482858\pi$
$241$	1.67126	0.107655	0.0538276	+	0.998550i	$0.482858\pi$
$242$	−11.1077	−0.714031
$243$	−13.0895	−0.839689
$244$	25.9589	1.66185
$245$	−25.3515	−1.61965
$246$	−30.6143	−1.95190
$247$	3.31040	0.210636
$248$	0.484594	0.0307718
$249$	9.42184	0.597085
$250$	−24.2222	−1.53195
$251$	26.3780	1.66497	0.832484	−	0.554049i	$-0.186918\pi$
$251$	26.3780	1.66497	0.832484	+	0.554049i	$0.186918\pi$
$252$	−0.0346195	−0.00218083
$253$	10.5141	0.661016
$254$	15.3298	0.961880
$255$	−21.4582	−1.34376
$256$	2.50670	0.156669
$257$	18.6556	1.16371	0.581854	−	0.813293i	$-0.302328\pi$
$257$	18.6556	1.16371	0.581854	+	0.813293i	$0.302328\pi$
$258$	−27.0716	−1.68541
$259$	0.0180712	0.00112289
$260$	−9.43423	−0.585086
$261$	1.79489	0.111101
$262$	19.7600	1.22078
$263$	12.9661	0.799525	0.399763	−	0.916619i	$-0.369093\pi$
$263$	12.9661	0.799525	0.399763	+	0.916619i	$0.369093\pi$
$264$	−6.60843	−0.406721
$265$	−30.2892	−1.86065
$266$	0.0675386	0.00414106
$267$	8.39151	0.513552
$268$	40.8876	2.49761
$269$	15.5943	0.950800	0.475400	−	0.879770i	$-0.342303\pi$
$269$	15.5943	0.950800	0.475400	+	0.879770i	$0.342303\pi$
$270$	−43.2628	−2.63289
$271$	21.9511	1.33344	0.666718	−	0.745310i	$-0.267698\pi$
$271$	21.9511	1.33344	0.666718	+	0.745310i	$0.267698\pi$
$272$	−11.3476	−0.688051
$273$	0.0120340	0.000728330 0
$274$	−30.9379	−1.86903
$275$	−32.6450	−1.96857
$276$	8.61941	0.518827
$277$	−5.14559	−0.309169	−0.154584	−	0.987980i	$-0.549404\pi$
$277$	−5.14559	−0.309169	−0.154584	+	0.987980i	$0.549404\pi$
$278$	38.4201	2.30428
$279$	0.521835	0.0312415
$280$	−0.0446975	−0.00267119
$281$	16.0030	0.954658	0.477329	−	0.878725i	$-0.341605\pi$
$281$	16.0030	0.954658	0.477329	+	0.878725i	$0.341605\pi$
$282$	−10.7970	−0.642953
$283$	−16.1783	−0.961700	−0.480850	−	0.876803i	$-0.659672\pi$
$283$	−16.1783	−0.961700	−0.480850	+	0.876803i	$0.659672\pi$
$284$	24.8408	1.47403
$285$	15.1754	0.898916
$286$	−8.63078	−0.510348
$287$	−0.107158	−0.00632534
$288$	−10.9011	−0.642354
$289$	4.91109	0.288887
$290$	9.97921	0.585999
$291$	−21.7753	−1.27649
$292$	5.54540	0.324520
$293$	−21.0720	−1.23104	−0.615521	−	0.788121i	$-0.711054\pi$
$293$	−21.0720	−1.23104	−0.615521	+	0.788121i	$0.711054\pi$
$294$	−19.0131	−1.10887
$295$	15.3601	0.894297
$296$	−2.46738	−0.143414
$297$	−22.3888	−1.29913
$298$	49.1229	2.84561
$299$	2.61417	0.151181
$300$	−26.7622	−1.54512
$301$	−0.0947577	−0.00546175
$302$	0.360538	0.0207466
$303$	−15.7295	−0.903635
$304$	8.02515	0.460274
$305$	36.0914	2.06659
$306$	14.0414	0.802691
$307$	−5.67950	−0.324146	−0.162073	−	0.986779i	$-0.551818\pi$
$307$	−5.67950	−0.324146	−0.162073	+	0.986779i	$0.551818\pi$
$308$	−0.0996080	−0.00567569
$309$	−9.73950	−0.554061
$310$	2.90129	0.164782
$311$	−4.13901	−0.234702	−0.117351	−	0.993091i	$-0.537440\pi$
$311$	−4.13901	−0.234702	−0.117351	+	0.993091i	$0.537440\pi$
$312$	−1.64308	−0.0930213
$313$	7.79273	0.440471	0.220236	−	0.975447i	$-0.429317\pi$
$313$	7.79273	0.440471	0.220236	+	0.975447i	$0.429317\pi$
$314$	11.9019	0.671663
$315$	−0.0481325	−0.00271196
$316$	−1.04708	−0.0589027
$317$	13.7559	0.772608	0.386304	−	0.922371i	$-0.373752\pi$
$317$	13.7559	0.772608	0.386304	+	0.922371i	$0.373752\pi$
$318$	−22.7162	−1.27386
$319$	5.16430	0.289145
$320$	−43.0480	−2.40646
$321$	−22.0535	−1.23091
$322$	0.0533341	0.00297220
$323$	−15.4957	−0.862206
$324$	−7.43019	−0.412788
$325$	−8.11667	−0.450232
$326$	1.54613	0.0856320
$327$	−9.45317	−0.522762
$328$	14.6310	0.807863
$329$	−0.0377924	−0.00208356
$330$	−39.5650	−2.17798
$331$	3.39243	0.186465	0.0932325	−	0.995644i	$-0.470280\pi$
$331$	3.39243	0.186465	0.0932325	+	0.995644i	$0.470280\pi$
$332$	−19.3902	−1.06417
$333$	−2.65700	−0.145603
$334$	21.0810	1.15350
$335$	56.8472	3.10590
$336$	0.0291731	0.00159152
$337$	−0.975426	−0.0531348	−0.0265674	−	0.999647i	$-0.508458\pi$
$337$	−0.975426	−0.0531348	−0.0265674	+	0.999647i	$0.508458\pi$
$338$	−2.14591	−0.116722
$339$	−17.7875	−0.966082
$340$	44.1610	2.39496
$341$	1.50143	0.0813072
$342$	−9.93019	−0.536963
$343$	−0.133102	−0.00718685
$344$	12.9379	0.697566
$345$	11.9838	0.645186
$346$	−5.50861	−0.296145
$347$	−19.4574	−1.04453	−0.522265	−	0.852784i	$-0.674913\pi$
$347$	−19.4574	−1.04453	−0.522265	+	0.852784i	$0.674913\pi$
$348$	4.23367	0.226948
$349$	−4.60409	−0.246451	−0.123226	−	0.992379i	$-0.539324\pi$
$349$	−4.60409	−0.246451	−0.123226	+	0.992379i	$0.539324\pi$
$350$	−0.165596	−0.00885148
$351$	−5.56662	−0.297124
$352$	−31.3648	−1.67175
$353$	−9.62800	−0.512447	−0.256223	−	0.966618i	$-0.582478\pi$
$353$	−9.62800	−0.512447	−0.256223	+	0.966618i	$0.582478\pi$
$354$	11.5197	0.612265
$355$	34.5369	1.83303
$356$	−17.2697	−0.915294
$357$	−0.0563303	−0.00298131
$358$	−6.35210	−0.335719
$359$	−13.9793	−0.737801	−0.368900	−	0.929469i	$-0.620266\pi$
$359$	−13.9793	−0.737801	−0.368900	+	0.929469i	$0.620266\pi$
$360$	6.57186	0.346368
$361$	−8.04126	−0.423224
$362$	−30.4336	−1.59955
$363$	−6.55184	−0.343882
$364$	−0.0247660	−0.00129809
$365$	7.70992	0.403556
$366$	27.0678	1.41486
$367$	−35.1668	−1.83569	−0.917846	−	0.396938i	$-0.870073\pi$
$367$	−35.1668	−1.83569	−0.917846	+	0.396938i	$0.870073\pi$
$368$	6.33733	0.330356
$369$	15.7554	0.820195
$370$	−14.7723	−0.767976
$371$	−0.0795127	−0.00412809
$372$	1.23087	0.0638175
$373$	35.1446	1.81972	0.909860	−	0.414915i	$-0.136189\pi$
$373$	35.1446	1.81972	0.909860	+	0.414915i	$0.136189\pi$
$374$	40.4000	2.08904
$375$	−14.2874	−0.737797
$376$	5.16005	0.266109
$377$	1.28402	0.0661306
$378$	−0.113570	−0.00584140
$379$	−17.3002	−0.888650	−0.444325	−	0.895866i	$-0.646556\pi$
$379$	−17.3002	−0.888650	−0.444325	+	0.895866i	$0.646556\pi$
$380$	−31.2311	−1.60212
$381$	9.04223	0.463248
$382$	−9.47512	−0.484789
$383$	−19.0311	−0.972442	−0.486221	−	0.873836i	$-0.661625\pi$
$383$	−19.0311	−0.972442	−0.486221	+	0.873836i	$0.661625\pi$
$384$	−12.5434	−0.640104
$385$	−0.138488	−0.00705799
$386$	5.34992	0.272304
$387$	13.9322	0.708214
$388$	44.8135	2.27506
$389$	10.6936	0.542185	0.271092	−	0.962553i	$-0.412615\pi$
$389$	10.6936	0.542185	0.271092	+	0.962553i	$0.412615\pi$
$390$	−9.83722	−0.498127
$391$	−12.2367	−0.618838
$392$	9.08663	0.458944
$393$	11.6554	0.587936
$394$	−50.4068	−2.53946
$395$	−1.45578	−0.0732483
$396$	14.6453	0.735956
$397$	−4.73455	−0.237620	−0.118810	−	0.992917i	$-0.537908\pi$
$397$	−4.73455	−0.237620	−0.118810	+	0.992917i	$0.537908\pi$
$398$	−32.2949	−1.61880
$399$	0.0398373	0.00199436
$400$	−19.6766	−0.983832
$401$	17.8200	0.889888	0.444944	−	0.895558i	$-0.353224\pi$
$401$	17.8200	0.889888	0.444944	+	0.895558i	$0.353224\pi$
$402$	42.6342	2.12640
$403$	0.373308	0.0185958
$404$	32.3713	1.61053
$405$	−10.3304	−0.513321
$406$	0.0261966	0.00130011
$407$	−7.64477	−0.378937
$408$	7.69116	0.380769
$409$	−8.47145	−0.418886	−0.209443	−	0.977821i	$-0.567165\pi$
$409$	−8.47145	−0.418886	−0.209443	+	0.977821i	$0.567165\pi$
$410$	87.5966	4.32609
$411$	−18.2486	−0.900137
$412$	20.0439	0.987492
$413$	0.0403219	0.00198411
$414$	−7.84171	−0.385399
$415$	−26.9587	−1.32335
$416$	−7.79838	−0.382347
$417$	22.6619	1.10976
$418$	−28.5713	−1.39747
$419$	−5.31537	−0.259673	−0.129836	−	0.991535i	$-0.541445\pi$
$419$	−5.31537	−0.259673	−0.129836	+	0.991535i	$0.541445\pi$
$420$	−0.113532	−0.00553977
$421$	−23.1813	−1.12979	−0.564893	−	0.825164i	$-0.691083\pi$
$421$	−23.1813	−1.12979	−0.564893	+	0.825164i	$0.691083\pi$
$422$	−11.1872	−0.544585
$423$	5.55660	0.270171
$424$	10.8564	0.527234
$425$	37.9936	1.84296
$426$	25.9019	1.25495
$427$	0.0947442	0.00458499
$428$	45.3862	2.19382
$429$	−5.09082	−0.245787
$430$	77.4599	3.73545
$431$	1.19515	0.0575683	0.0287841	−	0.999586i	$-0.490836\pi$
$431$	1.19515	0.0575683	0.0287841	+	0.999586i	$0.490836\pi$
$432$	−13.4947	−0.649266
$433$	−20.9168	−1.00520	−0.502600	−	0.864519i	$-0.667623\pi$
$433$	−20.9168	−1.00520	−0.502600	+	0.864519i	$0.667623\pi$
$434$	0.00761622	0.000365590 0
$435$	5.88619	0.282221
$436$	19.4546	0.931708
$437$	8.65394	0.413974
$438$	5.78227	0.276288
$439$	26.7894	1.27859	0.639293	−	0.768963i	$-0.279227\pi$
$439$	26.7894	1.27859	0.639293	+	0.768963i	$0.279227\pi$
$440$	18.9087	0.901436
$441$	9.78495	0.465950
$442$	10.0448	0.477784
$443$	−18.7639	−0.891498	−0.445749	−	0.895158i	$-0.647063\pi$
$443$	−18.7639	−0.891498	−0.445749	+	0.895158i	$0.647063\pi$
$444$	−6.26714	−0.297425
$445$	−24.0106	−1.13821
$446$	42.1960	1.99804
$447$	28.9749	1.37047
$448$	−0.113006	−0.00533904
$449$	1.74946	0.0825622	0.0412811	−	0.999148i	$-0.486856\pi$
$449$	1.74946	0.0825622	0.0412811	+	0.999148i	$0.486856\pi$
$450$	24.3475	1.14775
$451$	45.3318	2.13459
$452$	36.6066	1.72183
$453$	0.212661	0.00999170
$454$	16.3469	0.767200
$455$	−0.0344328	−0.00161423
$456$	−5.43926	−0.254717
$457$	26.1108	1.22141	0.610707	−	0.791857i	$-0.290885\pi$
$457$	26.1108	1.22141	0.610707	+	0.791857i	$0.290885\pi$
$458$	−41.4325	−1.93601
$459$	26.0569	1.21623
$460$	−24.6627	−1.14990
$461$	29.4690	1.37251	0.686254	−	0.727362i	$-0.259254\pi$
$461$	29.4690	1.37251	0.686254	+	0.727362i	$0.259254\pi$
$462$	−0.103863	−0.00483213
$463$	1.00000	0.0464739
$463$	1.00000	0.0464739
$464$	3.11276	0.144506
$465$	1.71131	0.0793601
$466$	−54.4235	−2.52112
$467$	0.437243	0.0202332	0.0101166	−	0.999949i	$-0.496780\pi$
$467$	0.437243	0.0202332	0.0101166	+	0.999949i	$0.496780\pi$
$468$	3.64134	0.168321
$469$	0.149231	0.00689083
$470$	30.8934	1.42501
$471$	7.02028	0.323477
$472$	−5.50543	−0.253408
$473$	40.0860	1.84316
$474$	−1.09180	−0.0501482
$475$	−26.8694	−1.23285
$476$	0.115928	0.00531354
$477$	11.6907	0.535282
$478$	−9.68056	−0.442779
$479$	6.19935	0.283256	0.141628	−	0.989920i	$-0.454766\pi$
$479$	6.19935	0.283256	0.141628	+	0.989920i	$0.454766\pi$
$480$	−35.7491	−1.63172
$481$	−1.90075	−0.0866669
$482$	−3.58636	−0.163354
$483$	0.0314589	0.00143143
$484$	13.4837	0.612895
$485$	62.3054	2.82914
$486$	28.0888	1.27413
$487$	−4.17211	−0.189056	−0.0945281	−	0.995522i	$-0.530134\pi$
$487$	−4.17211	−0.189056	−0.0945281	+	0.995522i	$0.530134\pi$
$488$	−12.9361	−0.585589
$489$	0.911975	0.0412409
$490$	54.4021	2.45763
$491$	−1.65615	−0.0747412	−0.0373706	−	0.999301i	$-0.511898\pi$
$491$	−1.65615	−0.0747412	−0.0373706	+	0.999301i	$0.511898\pi$
$492$	37.1628	1.67543
$493$	−6.01042	−0.270696
$494$	−7.10381	−0.319616
$495$	20.3618	0.915196
$496$	0.904983	0.0406350
$497$	0.0906633	0.00406681
$498$	−20.2184	−0.906008
$499$	−33.2146	−1.48689	−0.743444	−	0.668798i	$-0.766809\pi$
$499$	−33.2146	−1.48689	−0.743444	+	0.668798i	$0.766809\pi$
$500$	29.4034	1.31496
$501$	12.4346	0.555535
$502$	−56.6049	−2.52640
$503$	−16.0295	−0.714719	−0.357359	−	0.933967i	$-0.616323\pi$
$503$	−16.0295	−0.714719	−0.357359	+	0.933967i	$0.616323\pi$
$504$	0.0172519	0.000768461 0
$505$	45.0067	2.00277
$506$	−22.5623	−1.00302
$507$	−1.26575	−0.0562141
$508$	−18.6089	−0.825638
$509$	9.16033	0.406025	0.203012	−	0.979176i	$-0.434927\pi$
$509$	9.16033	0.406025	0.203012	+	0.979176i	$0.434927\pi$
$510$	46.0473	2.03901
$511$	0.0202395	0.000895341 0
$512$	−25.1988	−1.11364
$513$	−18.4277	−0.813604
$514$	−40.0333	−1.76579
$515$	27.8676	1.22799
$516$	32.8623	1.44668
$517$	15.9876	0.703132
$518$	−0.0387791	−0.00170385
$519$	−3.24923	−0.142625
$520$	4.70135	0.206168
$521$	−18.8758	−0.826963	−0.413482	−	0.910512i	$-0.635687\pi$
$521$	−18.8758	−0.826963	−0.413482	+	0.910512i	$0.635687\pi$
$522$	−3.85168	−0.168583
$523$	1.52821	0.0668240	0.0334120	−	0.999442i	$-0.489363\pi$
$523$	1.52821	0.0668240	0.0334120	+	0.999442i	$0.489363\pi$
$524$	−23.9868	−1.04787
$525$	−0.0976760	−0.00426293
$526$	−27.8241	−1.21319
$527$	−1.74743	−0.0761192
$528$	−12.3413	−0.537086
$529$	−16.1661	−0.702875
$530$	64.9978	2.82332
$531$	−5.92853	−0.257276
$532$	−0.0819852	−0.00355451
$533$	11.2710	0.488203
$534$	−18.0074	−0.779256
$535$	63.1016	2.72812
$536$	−20.3755	−0.880087
$537$	−3.74676	−0.161685
$538$	−33.4639	−1.44273
$539$	28.1534	1.21265
$540$	52.5168	2.25996
$541$	17.5293	0.753644	0.376822	−	0.926286i	$-0.377017\pi$
$541$	17.5293	0.753644	0.376822	+	0.926286i	$0.377017\pi$
$542$	−47.1051	−2.02334
$543$	−17.9511	−0.770356
$544$	36.5037	1.56508
$545$	27.0483	1.15862
$546$	−0.0258238	−0.00110516
$547$	7.94293	0.339615	0.169807	−	0.985477i	$-0.445685\pi$
$547$	7.94293	0.339615	0.169807	+	0.985477i	$0.445685\pi$
$548$	37.5556	1.60430
$549$	−13.9302	−0.594527
$550$	70.0532	2.98708
$551$	4.25063	0.181083
$552$	−4.29530	−0.182820
$553$	−0.00382160	−0.000162511 0
$554$	11.0420	0.469128
$555$	−8.71338	−0.369862
$556$	−46.6382	−1.97790
$557$	43.3010	1.83472	0.917362	−	0.398054i	$-0.130314\pi$
$557$	43.3010	1.83472	0.917362	+	0.398054i	$0.130314\pi$
$558$	−1.11981	−0.0474054
$559$	9.96676	0.421549
$560$	−0.0834729	−0.00352737
$561$	23.8298	1.00609
$562$	−34.3409	−1.44858
$563$	15.7769	0.664916	0.332458	−	0.943118i	$-0.392122\pi$
$563$	15.7769	0.664916	0.332458	+	0.943118i	$0.392122\pi$
$564$	13.1065	0.551884
$565$	50.8952	2.14118
$566$	34.7171	1.45927
$567$	−0.0271185	−0.00113887
$568$	−12.3789	−0.519407
$569$	−0.973336	−0.0408044	−0.0204022	−	0.999792i	$-0.506495\pi$
$569$	−0.973336	−0.0408044	−0.0204022	+	0.999792i	$0.506495\pi$
$570$	−32.5651	−1.36400
$571$	34.0675	1.42568	0.712841	−	0.701325i	$-0.247408\pi$
$571$	34.0675	1.42568	0.712841	+	0.701325i	$0.247408\pi$
$572$	10.4769	0.438062
$573$	−5.58886	−0.233478
$574$	0.229951	0.00959798
$575$	−21.2183	−0.884866
$576$	16.6153	0.692303
$577$	4.32402	0.180011	0.0900056	−	0.995941i	$-0.471311\pi$
$577$	4.32402	0.180011	0.0900056	+	0.995941i	$0.471311\pi$
$578$	−10.5387	−0.438354
$579$	3.15563	0.131143
$580$	−12.1138	−0.502997
$581$	−0.0707697	−0.00293602
$582$	46.7277	1.93693
$583$	33.6368	1.39309
$584$	−2.76343	−0.114352
$585$	5.06265	0.209315
$586$	45.2187	1.86797
$587$	−2.00324	−0.0826827	−0.0413414	−	0.999145i	$-0.513163\pi$
$587$	−2.00324	−0.0826827	−0.0413414	+	0.999145i	$0.513163\pi$
$588$	23.0800	0.951804
$589$	1.23580	0.0509202
$590$	−32.9613	−1.35699
$591$	−29.7322	−1.22302
$592$	−4.60785	−0.189382
$593$	17.5170	0.719339	0.359669	−	0.933080i	$-0.382890\pi$
$593$	17.5170	0.719339	0.359669	+	0.933080i	$0.382890\pi$
$594$	48.0442	1.97128
$595$	0.161177	0.00660763
$596$	−59.6304	−2.44256
$597$	−19.0490	−0.779623
$598$	−5.60976	−0.229400
$599$	18.5345	0.757299	0.378649	−	0.925540i	$-0.376389\pi$
$599$	18.5345	0.757299	0.378649	+	0.925540i	$0.376389\pi$
$600$	13.3364	0.544455
$601$	−27.0187	−1.10212	−0.551058	−	0.834467i	$-0.685776\pi$
$601$	−27.0187	−1.10212	−0.551058	+	0.834467i	$0.685776\pi$
$602$	0.203341	0.00828758
$603$	−21.9414	−0.893521
$604$	−0.437657	−0.0178080
$605$	18.7467	0.762163
$606$	33.7540	1.37116
$607$	−37.0620	−1.50430	−0.752150	−	0.658992i	$-0.770983\pi$
$607$	−37.0620	−1.50430	−0.752150	+	0.658992i	$0.770983\pi$
$608$	−25.8157	−1.04697
$609$	0.0154519	0.000626144 0
$610$	−77.4489	−3.13581
$611$	3.97506	0.160814
$612$	−17.0448	−0.688996
$613$	23.5935	0.952932	0.476466	−	0.879193i	$-0.341918\pi$
$613$	23.5935	0.952932	0.476466	+	0.879193i	$0.341918\pi$
$614$	12.1877	0.491855
$615$	51.6684	2.08347
$616$	0.0496375	0.00199995
$617$	16.8143	0.676919	0.338459	−	0.940981i	$-0.390094\pi$
$617$	16.8143	0.676919	0.338459	+	0.940981i	$0.390094\pi$
$618$	20.9001	0.840724
$619$	49.4933	1.98930	0.994652	−	0.103284i	$-0.0329351\pi$
$619$	49.4933	1.98930	0.994652	+	0.103284i	$0.0329351\pi$
$620$	−3.52188	−0.141442
$621$	−14.5521	−0.583955
$622$	8.88193	0.356133
$623$	−0.0630306	−0.00252527
$624$	−3.06847	−0.122837
$625$	0.297013	0.0118805
$626$	−16.7225	−0.668365
$627$	−16.8526	−0.673030
$628$	−14.4477	−0.576527
$629$	8.89729	0.354758
$630$	0.103288	0.00411509
$631$	3.30292	0.131487	0.0657436	−	0.997837i	$-0.479058\pi$
$631$	3.30292	0.131487	0.0657436	+	0.997837i	$0.479058\pi$
$632$	0.521789	0.0207556
$633$	−6.59873	−0.262276
$634$	−29.5189	−1.17234
$635$	−25.8725	−1.02672
$636$	27.5753	1.09343
$637$	6.99991	0.277347
$638$	−11.0821	−0.438745
$639$	−13.3302	−0.527335
$640$	35.8904	1.41869
$641$	−33.4054	−1.31943	−0.659716	−	0.751515i	$-0.729324\pi$
$641$	−33.4054	−1.31943	−0.659716	+	0.751515i	$0.729324\pi$
$642$	47.3248	1.86776
$643$	18.4908	0.729206	0.364603	−	0.931163i	$-0.381205\pi$
$643$	18.4908	0.729206	0.364603	+	0.931163i	$0.381205\pi$
$644$	−0.0647424	−0.00255121
$645$	45.6894	1.79902
$646$	33.2524	1.30830
$647$	−3.76470	−0.148006	−0.0740029	−	0.997258i	$-0.523577\pi$
$647$	−3.76470	−0.148006	−0.0740029	+	0.997258i	$0.523577\pi$
$648$	3.70267	0.145455
$649$	−17.0577	−0.669572
$650$	17.4176	0.683176
$651$	0.00449239	0.000176071 0
$652$	−1.87685	−0.0735029
$653$	−31.8835	−1.24770	−0.623849	−	0.781545i	$-0.714432\pi$
$653$	−31.8835	−1.24770	−0.623849	+	0.781545i	$0.714432\pi$
$654$	20.2856	0.793232
$655$	−33.3494	−1.30307
$656$	27.3236	1.06681
$657$	−2.97580	−0.116097
$658$	0.0810989	0.00316157
$659$	21.5282	0.838618	0.419309	−	0.907844i	$-0.362272\pi$
$659$	21.5282	0.838618	0.419309	+	0.907844i	$0.362272\pi$
$660$	48.0280	1.86949
$661$	−24.4846	−0.952342	−0.476171	−	0.879353i	$-0.657976\pi$
$661$	−24.4846	−0.952342	−0.476171	+	0.879353i	$0.657976\pi$
$662$	−7.27985	−0.282939
$663$	5.92490	0.230104
$664$	9.66267	0.374984
$665$	−0.113986	−0.00442020
$666$	5.70168	0.220936
$667$	3.35665	0.129970
$668$	−25.5903	−0.990119
$669$	24.8891	0.962270
$670$	−121.989	−4.71284
$671$	−40.0803	−1.54728
$672$	−0.0938457	−0.00362017
$673$	11.7086	0.451334	0.225667	−	0.974205i	$-0.427544\pi$
$673$	11.7086	0.451334	0.225667	+	0.974205i	$0.427544\pi$
$674$	2.09317	0.0806261
$675$	45.1824	1.73907
$676$	2.60492	0.100189
$677$	44.3872	1.70594	0.852969	−	0.521961i	$-0.174800\pi$
$677$	44.3872	1.70594	0.852969	+	0.521961i	$0.174800\pi$
$678$	38.1703	1.46592
$679$	0.163559	0.00627682
$680$	−22.0067	−0.843917
$681$	9.64217	0.369489
$682$	−3.22194	−0.123374
$683$	−25.3004	−0.968091	−0.484046	−	0.875043i	$-0.660833\pi$
$683$	−25.3004	−0.968091	−0.484046	+	0.875043i	$0.660833\pi$
$684$	12.0543	0.460907
$685$	52.2146	1.99502
$686$	0.285625	0.0109052
$687$	−24.4388	−0.932397
$688$	24.1617	0.921155
$689$	8.36326	0.318615
$690$	−25.7161	−0.978997
$691$	20.6882	0.787016	0.393508	−	0.919321i	$-0.371261\pi$
$691$	20.6882	0.787016	0.393508	+	0.919321i	$0.371261\pi$
$692$	6.68691	0.254198
$693$	0.0534522	0.00203048
$694$	41.7538	1.58495
$695$	−64.8424	−2.45961
$696$	−2.10976	−0.0799702
$697$	−52.7589	−1.99839
$698$	9.87996	0.373962
$699$	−32.1014	−1.21419
$700$	0.201017	0.00759774
$701$	47.0488	1.77701	0.888504	−	0.458869i	$-0.151745\pi$
$701$	47.0488	1.77701	0.888504	+	0.458869i	$0.151745\pi$
$702$	11.9454	0.450852
$703$	−6.29225	−0.237317
$704$	47.8057	1.80175
$705$	18.2224	0.686293
$706$	20.6608	0.777580
$707$	0.118148	0.00444341
$708$	−13.9838	−0.525543
$709$	30.3058	1.13816	0.569078	−	0.822283i	$-0.307300\pi$
$709$	30.3058	1.13816	0.569078	+	0.822283i	$0.307300\pi$
$710$	−74.1129	−2.78141
$711$	0.561889	0.0210725
$712$	8.60600	0.322523
$713$	0.975891	0.0365474
$714$	0.120880	0.00452380
$715$	14.5663	0.544750
$716$	7.71083	0.288167
$717$	−5.71003	−0.213245
$718$	29.9983	1.11953
$719$	45.8429	1.70965	0.854827	−	0.518914i	$-0.173663\pi$
$719$	45.8429	1.70965	0.854827	+	0.518914i	$0.173663\pi$
$720$	12.2730	0.457388
$721$	0.0731557	0.00272446
$722$	17.2558	0.642195
$723$	−2.11540	−0.0786726
$724$	36.9434	1.37299
$725$	−10.4220	−0.387063
$726$	14.0596	0.521802
$727$	24.5337	0.909905	0.454952	−	0.890516i	$-0.349656\pi$
$727$	24.5337	0.909905	0.454952	+	0.890516i	$0.349656\pi$
$728$	0.0123416	0.000457410 0
$729$	25.1251	0.930560
$730$	−16.5448	−0.612350
$731$	−46.6537	−1.72555
$732$	−32.8576	−1.21445
$733$	42.1546	1.55701	0.778507	−	0.627636i	$-0.215977\pi$
$733$	42.1546	1.55701	0.778507	+	0.627636i	$0.215977\pi$
$734$	75.4647	2.78545
$735$	32.0888	1.18361
$736$	−20.3863	−0.751448
$737$	−63.1300	−2.32542
$738$	−33.8097	−1.24455
$739$	−44.6375	−1.64202	−0.821009	−	0.570915i	$-0.806589\pi$
$739$	−44.6375	−1.64202	−0.821009	+	0.570915i	$0.806589\pi$
$740$	17.9321	0.659199
$741$	−4.19015	−0.153929
$742$	0.170627	0.00626391
$743$	24.8053	0.910019	0.455009	−	0.890487i	$-0.349636\pi$
$743$	24.8053	0.910019	0.455009	+	0.890487i	$0.349636\pi$
$744$	−0.613377	−0.0224875
$745$	−82.9058	−3.03743
$746$	−75.4172	−2.76122
$747$	10.4052	0.380708
$748$	−49.0417	−1.79314
$749$	0.165649	0.00605269
$750$	30.6594	1.11952
$751$	−25.5412	−0.932010	−0.466005	−	0.884782i	$-0.654307\pi$
$751$	−25.5412	−0.932010	−0.466005	+	0.884782i	$0.654307\pi$
$752$	9.63643	0.351405
$753$	−33.3881	−1.21673
$754$	−2.75540	−0.100346
$755$	−0.608487	−0.0221451
$756$	0.137863	0.00501402
$757$	−1.70483	−0.0619632	−0.0309816	−	0.999520i	$-0.509863\pi$
$757$	−1.70483	−0.0619632	−0.0309816	+	0.999520i	$0.509863\pi$
$758$	37.1246	1.34843
$759$	−13.3083	−0.483059
$760$	15.5633	0.564541
$761$	29.8661	1.08265	0.541324	−	0.840814i	$-0.317923\pi$
$761$	29.8661	1.08265	0.541324	+	0.840814i	$0.317923\pi$
$762$	−19.4038	−0.702926
$763$	0.0710050	0.00257055
$764$	11.5019	0.416123
$765$	−23.6979	−0.856799
$766$	40.8389	1.47557
$767$	−4.24112	−0.153138
$768$	−3.17287	−0.114491
$769$	8.20400	0.295844	0.147922	−	0.988999i	$-0.452742\pi$
$769$	8.20400	0.295844	0.147922	+	0.988999i	$0.452742\pi$
$770$	0.297182	0.0107097
$771$	−23.6135	−0.850418
$772$	−6.49428	−0.233734
$773$	−28.2807	−1.01719	−0.508593	−	0.861007i	$-0.669834\pi$
$773$	−28.2807	−1.01719	−0.508593	+	0.861007i	$0.669834\pi$
$774$	−29.8973	−1.07463
$775$	−3.03002	−0.108842
$776$	−22.3318	−0.801667
$777$	−0.0228736	−0.000820588 0
$778$	−22.9474	−0.822704
$779$	37.3116	1.33683
$780$	11.9414	0.427571
$781$	−38.3539	−1.37241
$782$	26.2589	0.939016
$783$	−7.14767	−0.255437
$784$	16.9694	0.606048
$785$	−20.0871	−0.716939
$786$	−25.0114	−0.892125
$787$	−26.1025	−0.930453	−0.465226	−	0.885192i	$-0.654027\pi$
$787$	−26.1025	−0.930453	−0.465226	+	0.885192i	$0.654027\pi$
$788$	61.1889	2.17976
$789$	−16.4119	−0.584280
$790$	3.12397	0.111146
$791$	0.133606	0.00475048
$792$	−7.29819	−0.259330
$793$	−9.96534	−0.353880
$794$	10.1599	0.360562
$795$	38.3386	1.35973
$796$	39.2028	1.38951
$797$	−44.0503	−1.56034	−0.780171	−	0.625567i	$-0.784868\pi$
$797$	−44.0503	−1.56034	−0.780171	+	0.625567i	$0.784868\pi$
$798$	−0.0854872	−0.00302621
$799$	−18.6070	−0.658267
$800$	63.2969	2.23788
$801$	9.26737	0.327447
$802$	−38.2401	−1.35030
$803$	−8.56203	−0.302148
$804$	−51.7537	−1.82521
$805$	−0.0900131	−0.00317255
$806$	−0.801085	−0.0282170
$807$	−19.7385	−0.694829
$808$	−16.1315	−0.567505
$809$	−9.36960	−0.329418	−0.164709	−	0.986342i	$-0.552668\pi$
$809$	−9.36960	−0.329418	−0.164709	+	0.986342i	$0.552668\pi$
$810$	22.1681	0.778907
$811$	39.4609	1.38566	0.692829	−	0.721102i	$-0.256364\pi$
$811$	39.4609	1.38566	0.692829	+	0.721102i	$0.256364\pi$
$812$	−0.0318001	−0.00111596
$813$	−27.7847	−0.974453
$814$	16.4050	0.574994
$815$	−2.60943	−0.0914043
$816$	14.3633	0.502816
$817$	32.9940	1.15431
$818$	18.1789	0.635612
$819$	0.0132900	0.000464392 0
$820$	−106.334	−3.71333
$821$	11.0078	0.384176	0.192088	−	0.981378i	$-0.438474\pi$
$821$	11.0078	0.384176	0.192088	+	0.981378i	$0.438474\pi$
$822$	39.1598	1.36586
$823$	−2.07774	−0.0724253	−0.0362127	−	0.999344i	$-0.511529\pi$
$823$	−2.07774	−0.0724253	−0.0362127	+	0.999344i	$0.511529\pi$
$824$	−9.98845	−0.347964
$825$	41.3205	1.43860
$826$	−0.0865272	−0.00301067
$827$	23.7182	0.824763	0.412381	−	0.911011i	$-0.364697\pi$
$827$	23.7182	0.824763	0.412381	+	0.911011i	$0.364697\pi$
$828$	9.51906	0.330810
$829$	−7.22232	−0.250841	−0.125421	−	0.992104i	$-0.540028\pi$
$829$	−7.22232	−0.250841	−0.125421	+	0.992104i	$0.540028\pi$
$830$	57.8508	2.00803
$831$	6.51305	0.225935
$832$	11.8862	0.412078
$833$	−32.7661	−1.13528
$834$	−48.6304	−1.68393
$835$	−35.5789	−1.23126
$836$	34.6828	1.19953
$837$	−2.07806	−0.0718284
$838$	11.4063	0.394024
$839$	26.1339	0.902243	0.451122	−	0.892463i	$-0.351024\pi$
$839$	26.1339	0.902243	0.451122	+	0.892463i	$0.351024\pi$
$840$	0.0565760	0.00195206
$841$	−27.3513	−0.943148
$842$	49.7449	1.71432
$843$	−20.2558	−0.697648
$844$	13.5802	0.467449
$845$	3.62169	0.124590
$846$	−11.9240	−0.409954
$847$	0.0492124	0.00169096
$848$	20.2744	0.696227
$849$	20.4777	0.702794
$850$	−81.5307	−2.79648
$851$	−4.96889	−0.170331
$852$	−31.4424	−1.07720
$853$	−30.1152	−1.03113	−0.515563	−	0.856852i	$-0.672417\pi$
$853$	−30.1152	−1.03113	−0.515563	+	0.856852i	$0.672417\pi$
$854$	−0.203312	−0.00695721
$855$	16.7594	0.573159
$856$	−22.6172	−0.773041
$857$	17.9197	0.612124	0.306062	−	0.952012i	$-0.400988\pi$
$857$	17.9197	0.612124	0.306062	+	0.952012i	$0.400988\pi$
$858$	10.9244	0.372954
$859$	−53.6531	−1.83062	−0.915309	−	0.402752i	$-0.868054\pi$
$859$	−53.6531	−1.83062	−0.915309	+	0.402752i	$0.868054\pi$
$860$	−94.0288	−3.20635
$861$	0.135636	0.00462245
$862$	−2.56468	−0.0873533
$863$	11.6565	0.396793	0.198397	−	0.980122i	$-0.436427\pi$
$863$	11.6565	0.396793	0.198397	+	0.980122i	$0.436427\pi$
$864$	43.4106	1.47686
$865$	9.29699	0.316107
$866$	44.8856	1.52528
$867$	−6.21623	−0.211114
$868$	−0.00924534	−0.000313807 0
$869$	1.61668	0.0548420
$870$	−12.6312	−0.428238
$871$	−15.6963	−0.531849
$872$	−9.69480	−0.328307
$873$	−24.0481	−0.813904
$874$	−18.5706	−0.628158
$875$	0.107316	0.00362794
$876$	−7.01911	−0.237154
$877$	−14.9223	−0.503891	−0.251945	−	0.967741i	$-0.581070\pi$
$877$	−14.9223	−0.503891	−0.251945	+	0.967741i	$0.581070\pi$
$878$	−57.4875	−1.94011
$879$	26.6720	0.899625
$880$	35.3121	1.19037
$881$	53.3208	1.79642	0.898212	−	0.439562i	$-0.144866\pi$
$881$	53.3208	1.79642	0.898212	+	0.439562i	$0.144866\pi$
$882$	−20.9976	−0.707026
$883$	46.6057	1.56841	0.784204	−	0.620503i	$-0.213071\pi$
$883$	46.6057	1.56841	0.784204	+	0.620503i	$0.213071\pi$
$884$	−12.1935	−0.410110
$885$	−19.4420	−0.653537
$886$	40.2655	1.35275
$887$	−5.48281	−0.184095	−0.0920474	−	0.995755i	$-0.529341\pi$
$887$	−5.48281	−0.184095	−0.0920474	+	0.995755i	$0.529341\pi$
$888$	3.12310	0.104804
$889$	−0.0679184	−0.00227791
$890$	51.5245	1.72710
$891$	11.4721	0.384330
$892$	−51.2219	−1.71503
$893$	13.1590	0.440350
$894$	−62.1775	−2.07953
$895$	10.7206	0.358349
$896$	0.0942166	0.00314755
$897$	−3.30889	−0.110481
$898$	−3.75418	−0.125279
$899$	0.479337	0.0159868
$900$	−29.5555	−0.985184
$901$	−39.1478	−1.30420
$902$	−97.2779	−3.23900
$903$	0.119940	0.00399135
$904$	−18.2421	−0.606724
$905$	51.3634	1.70738
$906$	−0.456352	−0.0151613
$907$	−2.39187	−0.0794207	−0.0397103	−	0.999211i	$-0.512644\pi$
$907$	−2.39187	−0.0794207	−0.0397103	+	0.999211i	$0.512644\pi$
$908$	−19.8436	−0.658532
$909$	−17.3713	−0.576168
$910$	0.0738896	0.00244942
$911$	15.2548	0.505416	0.252708	−	0.967543i	$-0.418679\pi$
$911$	15.2548	0.505416	0.252708	+	0.967543i	$0.418679\pi$
$912$	−10.1579	−0.336361
$913$	29.9382	0.990809
$914$	−56.0315	−1.85336
$915$	−45.6828	−1.51023
$916$	50.2950	1.66179
$917$	−0.0875462	−0.00289103
$918$	−55.9158	−1.84550
$919$	0.216114	0.00712895	0.00356447	−	0.999994i	$-0.498865\pi$
$919$	0.216114	0.00712895	0.00356447	+	0.999994i	$0.498865\pi$
$920$	12.2901	0.405193
$921$	7.18885	0.236881
$922$	−63.2377	−2.08262
$923$	−9.53611	−0.313885
$924$	0.126079	0.00414770
$925$	15.4278	0.507263
$926$	−2.14591	−0.0705189
$927$	−10.7561	−0.353276
$928$	−10.0133	−0.328703
$929$	58.8183	1.92977	0.964883	−	0.262680i	$-0.0846064\pi$
$929$	58.8183	1.92977	0.964883	+	0.262680i	$0.0846064\pi$
$930$	−3.67231	−0.120420
$931$	23.1725	0.759448
$932$	66.0648	2.16402
$933$	5.23896	0.171516
$934$	−0.938283	−0.0307015
$935$	−68.1840	−2.22986
$936$	−1.81458	−0.0593115
$937$	37.3835	1.22127	0.610634	−	0.791913i	$-0.290915\pi$
$937$	37.3835	1.22127	0.610634	+	0.791913i	$0.290915\pi$
$938$	−0.320235	−0.0104561
$939$	−9.86368	−0.321889
$940$	−37.5016	−1.22317
$941$	−30.9860	−1.01011	−0.505057	−	0.863086i	$-0.668529\pi$
$941$	−30.9860	−1.01011	−0.505057	+	0.863086i	$0.668529\pi$
$942$	−15.0649	−0.490840
$943$	29.4644	0.959493
$944$	−10.2814	−0.334632
$945$	0.191674	0.00623516
$946$	−86.0209	−2.79678
$947$	29.4867	0.958189	0.479095	−	0.877763i	$-0.340965\pi$
$947$	29.4867	0.958189	0.479095	+	0.877763i	$0.340965\pi$
$948$	1.32534	0.0430451
$949$	−2.12882	−0.0691043
$950$	57.6593	1.87072
$951$	−17.4116	−0.564609
$952$	−0.0577701	−0.00187234
$953$	−9.20954	−0.298326	−0.149163	−	0.988813i	$-0.547658\pi$
$953$	−9.20954	−0.298326	−0.149163	+	0.988813i	$0.547658\pi$
$954$	−25.0872	−0.812229
$955$	15.9914	0.517468
$956$	11.7513	0.380063
$957$	−6.53674	−0.211303
$958$	−13.3032	−0.429808
$959$	0.137070	0.00442621
$960$	54.4882	1.75860
$961$	−30.8606	−0.995505
$962$	4.07884	0.131507
$963$	−24.3554	−0.784841
$964$	4.35349	0.140217
$965$	−9.02917	−0.290659
$966$	−0.0675079	−0.00217203
$967$	−0.664081	−0.0213554	−0.0106777	−	0.999943i	$-0.503399\pi$
$967$	−0.664081	−0.0213554	−0.0106777	+	0.999943i	$0.503399\pi$
$968$	−6.71931	−0.215967
$969$	19.6138	0.630086
$970$	−133.702	−4.29290
$971$	52.4090	1.68189	0.840943	−	0.541124i	$-0.182001\pi$
$971$	52.4090	1.68189	0.840943	+	0.541124i	$0.182001\pi$
$972$	−34.0970	−1.09366
$973$	−0.170219	−0.00545697
$974$	8.95296	0.286871
$975$	10.2737	0.329022
$976$	−24.1582	−0.773286
$977$	−47.6037	−1.52298	−0.761488	−	0.648179i	$-0.775531\pi$
$977$	−47.6037	−1.52298	−0.761488	+	0.648179i	$0.775531\pi$
$978$	−1.95701	−0.0625784
$979$	26.6642	0.852193
$980$	−66.0388	−2.10953
$981$	−10.4399	−0.333319
$982$	3.55395	0.113411
$983$	27.4523	0.875594	0.437797	−	0.899074i	$-0.355759\pi$
$983$	27.4523	0.875594	0.437797	+	0.899074i	$0.355759\pi$
$984$	−18.5193	−0.590373
$985$	85.0726	2.71064
$986$	12.8978	0.410750
$987$	0.0478358	0.00152263
$988$	8.62333	0.274345
$989$	26.0548	0.828494
$990$	−43.6946	−1.38871
$991$	28.9981	0.921155	0.460577	−	0.887620i	$-0.347642\pi$
$991$	28.9981	0.921155	0.460577	+	0.887620i	$0.347642\pi$
$992$	−2.91120	−0.0924307
$993$	−4.29398	−0.136265
$994$	−0.194555	−0.00617092
$995$	54.5047	1.72792
$996$	24.5432	0.777680
$997$	−22.7190	−0.719519	−0.359760	−	0.933045i	$-0.617141\pi$
$997$	−22.7190	−0.719519	−0.359760	+	0.933045i	$0.617141\pi$
$998$	71.2754	2.25618
$999$	10.5808	0.334761

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.d.1.19	✓	123

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.d.1.19	✓	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)

\(f(q)\)	\(=\)	\(q-2.14591 q^{2} -1.26575 q^{3} +2.60492 q^{4} +3.62169 q^{5} +2.71619 q^{6} +0.00950737 q^{7} -1.29811 q^{8} -1.39787 q^{9} +O(q^{10})\)	\(q-2.14591 q^{2} -1.26575 q^{3} +2.60492 q^{4} +3.62169 q^{5} +2.71619 q^{6} +0.00950737 q^{7} -1.29811 q^{8} -1.39787 q^{9} -7.77182 q^{10} -4.02197 q^{11} -3.29719 q^{12} -1.00000 q^{13} -0.0204020 q^{14} -4.58417 q^{15} -2.42423 q^{16} +4.68093 q^{17} +2.99970 q^{18} -3.31040 q^{19} +9.43423 q^{20} -0.0120340 q^{21} +8.63078 q^{22} -2.61417 q^{23} +1.64308 q^{24} +8.11667 q^{25} +2.14591 q^{26} +5.56662 q^{27} +0.0247660 q^{28} -1.28402 q^{29} +9.83722 q^{30} -0.373308 q^{31} +7.79838 q^{32} +5.09082 q^{33} -10.0448 q^{34} +0.0344328 q^{35} -3.64134 q^{36} +1.90075 q^{37} +7.10381 q^{38} +1.26575 q^{39} -4.70135 q^{40} -11.2710 q^{41} +0.0258238 q^{42} -9.96676 q^{43} -10.4769 q^{44} -5.06265 q^{45} +5.60976 q^{46} -3.97506 q^{47} +3.06847 q^{48} -6.99991 q^{49} -17.4176 q^{50} -5.92490 q^{51} -2.60492 q^{52} -8.36326 q^{53} -11.9454 q^{54} -14.5663 q^{55} -0.0123416 q^{56} +4.19015 q^{57} +2.75540 q^{58} +4.24112 q^{59} -11.9414 q^{60} +9.96534 q^{61} +0.801085 q^{62} -0.0132900 q^{63} -11.8862 q^{64} -3.62169 q^{65} -10.9244 q^{66} +15.6963 q^{67} +12.1935 q^{68} +3.30889 q^{69} -0.0738896 q^{70} +9.53611 q^{71} +1.81458 q^{72} +2.12882 q^{73} -4.07884 q^{74} -10.2737 q^{75} -8.62333 q^{76} -0.0382384 q^{77} -2.71619 q^{78} -0.401961 q^{79} -8.77980 q^{80} -2.85236 q^{81} +24.1866 q^{82} -7.44366 q^{83} -0.0313476 q^{84} +16.9529 q^{85} +21.3878 q^{86} +1.62526 q^{87} +5.22095 q^{88} -6.62965 q^{89} +10.8640 q^{90} -0.00950737 q^{91} -6.80970 q^{92} +0.472516 q^{93} +8.53011 q^{94} -11.9893 q^{95} -9.87083 q^{96} +17.2034 q^{97} +15.0212 q^{98} +5.62218 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9}+O(q^{10}) \) 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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