LMFDB - Embedded newform 6019.2.a.e.1.18

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:	$130$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
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)

$f(q)$	$=$	$q-2.28421 q^{2} +0.124993 q^{3} +3.21761 q^{4} -2.44620 q^{5} -0.285511 q^{6} -2.39008 q^{7} -2.78127 q^{8} -2.98438 q^{9} +O(q^{10})$	\(q-2.28421 q^{2} +0.124993 q^{3} +3.21761 q^{4} -2.44620 q^{5} -0.285511 q^{6} -2.39008 q^{7} -2.78127 q^{8} -2.98438 q^{9} +5.58762 q^{10} -3.70380 q^{11} +0.402180 q^{12} +1.00000 q^{13} +5.45943 q^{14} -0.305759 q^{15} -0.0822180 q^{16} +8.08820 q^{17} +6.81694 q^{18} -2.96906 q^{19} -7.87090 q^{20} -0.298744 q^{21} +8.46025 q^{22} -1.81227 q^{23} -0.347640 q^{24} +0.983882 q^{25} -2.28421 q^{26} -0.748008 q^{27} -7.69033 q^{28} +0.322802 q^{29} +0.698416 q^{30} -6.34155 q^{31} +5.75034 q^{32} -0.462951 q^{33} -18.4751 q^{34} +5.84660 q^{35} -9.60255 q^{36} +5.18632 q^{37} +6.78196 q^{38} +0.124993 q^{39} +6.80353 q^{40} -4.46936 q^{41} +0.682393 q^{42} +0.947078 q^{43} -11.9174 q^{44} +7.30037 q^{45} +4.13960 q^{46} -6.28086 q^{47} -0.0102767 q^{48} -1.28754 q^{49} -2.24739 q^{50} +1.01097 q^{51} +3.21761 q^{52} +1.56655 q^{53} +1.70861 q^{54} +9.06022 q^{55} +6.64744 q^{56} -0.371113 q^{57} -0.737347 q^{58} -13.0860 q^{59} -0.983811 q^{60} -2.94956 q^{61} +14.4854 q^{62} +7.13289 q^{63} -12.9705 q^{64} -2.44620 q^{65} +1.05748 q^{66} -0.395320 q^{67} +26.0247 q^{68} -0.226522 q^{69} -13.3548 q^{70} -9.53870 q^{71} +8.30035 q^{72} -7.78093 q^{73} -11.8466 q^{74} +0.122979 q^{75} -9.55328 q^{76} +8.85236 q^{77} -0.285511 q^{78} -11.3270 q^{79} +0.201121 q^{80} +8.85963 q^{81} +10.2090 q^{82} -13.4529 q^{83} -0.961240 q^{84} -19.7853 q^{85} -2.16332 q^{86} +0.0403481 q^{87} +10.3013 q^{88} -6.95232 q^{89} -16.6756 q^{90} -2.39008 q^{91} -5.83116 q^{92} -0.792653 q^{93} +14.3468 q^{94} +7.26291 q^{95} +0.718755 q^{96} -16.5075 q^{97} +2.94100 q^{98} +11.0535 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 130 q + 10 q^{2} + 11 q^{3} + 146 q^{4} + 40 q^{5} + 4 q^{6} + 8 q^{7} + 24 q^{8} + 181 q^{9}+O(q^{10}) $ 130 * q + 10 * q^2 + 11 * q^3 + 146 * q^4 + 40 * q^5 + 4 * q^6 + 8 * q^7 + 24 * q^8 + 181 * q^9	\( 130 q + 10 q^{2} + 11 q^{3} + 146 q^{4} + 40 q^{5} + 4 q^{6} + 8 q^{7} + 24 q^{8} + 181 q^{9} + 5 q^{10} + 43 q^{11} + 28 q^{12} + 130 q^{13} + 47 q^{14} + 29 q^{15} + 170 q^{16} + 85 q^{17} + 20 q^{18} + 3 q^{19} + 73 q^{20} + 62 q^{21} + 12 q^{22} + 62 q^{23} - 5 q^{24} + 178 q^{25} + 10 q^{26} + 35 q^{27} - q^{28} + 134 q^{29} + 24 q^{30} + 14 q^{31} + 48 q^{32} + 4 q^{33} + 4 q^{34} + 50 q^{35} + 244 q^{36} + 32 q^{37} + 76 q^{38} + 11 q^{39} - 6 q^{40} + 48 q^{41} + 9 q^{42} + 34 q^{43} + 123 q^{44} + 115 q^{45} + 5 q^{46} + 25 q^{47} + 35 q^{48} + 210 q^{49} + 24 q^{50} + 20 q^{51} + 146 q^{52} + 193 q^{53} - 39 q^{54} + 32 q^{55} + 122 q^{56} + 7 q^{57} - 4 q^{58} + 50 q^{59} + 42 q^{60} + 57 q^{61} + 51 q^{62} + 8 q^{63} + 172 q^{64} + 40 q^{65} - 4 q^{66} + 21 q^{67} + 132 q^{68} + 92 q^{69} - 46 q^{70} + 58 q^{71} - 26 q^{72} + 15 q^{73} + 120 q^{74} + 23 q^{75} - 65 q^{76} + 192 q^{77} + 4 q^{78} + 32 q^{79} + 66 q^{80} + 326 q^{81} + 11 q^{82} + 33 q^{83} + 5 q^{84} + 43 q^{85} + 105 q^{86} + 31 q^{87} - 17 q^{88} + 84 q^{89} - 73 q^{90} + 8 q^{91} + 161 q^{92} + 52 q^{93} + 4 q^{94} + 59 q^{95} - 77 q^{96} + 9 q^{97} - 61 q^{98} + 100 q^{99}+O(q^{100}) \) 130 * q + 10 * q^2 + 11 * q^3 + 146 * q^4 + 40 * q^5 + 4 * q^6 + 8 * q^7 + 24 * q^8 + 181 * q^9 + 5 * q^10 + 43 * q^11 + 28 * q^12 + 130 * q^13 + 47 * q^14 + 29 * q^15 + 170 * q^16 + 85 * q^17 + 20 * q^18 + 3 * q^19 + 73 * q^20 + 62 * q^21 + 12 * q^22 + 62 * q^23 - 5 * q^24 + 178 * q^25 + 10 * q^26 + 35 * q^27 - q^28 + 134 * q^29 + 24 * q^30 + 14 * q^31 + 48 * q^32 + 4 * q^33 + 4 * q^34 + 50 * q^35 + 244 * q^36 + 32 * q^37 + 76 * q^38 + 11 * q^39 - 6 * q^40 + 48 * q^41 + 9 * q^42 + 34 * q^43 + 123 * q^44 + 115 * q^45 + 5 * q^46 + 25 * q^47 + 35 * q^48 + 210 * q^49 + 24 * q^50 + 20 * q^51 + 146 * q^52 + 193 * q^53 - 39 * q^54 + 32 * q^55 + 122 * q^56 + 7 * q^57 - 4 * q^58 + 50 * q^59 + 42 * q^60 + 57 * q^61 + 51 * q^62 + 8 * q^63 + 172 * q^64 + 40 * q^65 - 4 * q^66 + 21 * q^67 + 132 * q^68 + 92 * q^69 - 46 * q^70 + 58 * q^71 - 26 * q^72 + 15 * q^73 + 120 * q^74 + 23 * q^75 - 65 * q^76 + 192 * q^77 + 4 * q^78 + 32 * q^79 + 66 * q^80 + 326 * q^81 + 11 * q^82 + 33 * q^83 + 5 * q^84 + 43 * q^85 + 105 * q^86 + 31 * q^87 - 17 * q^88 + 84 * q^89 - 73 * q^90 + 8 * q^91 + 161 * q^92 + 52 * q^93 + 4 * q^94 + 59 * q^95 - 77 * q^96 + 9 * q^97 - 61 * q^98 + 100 * 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 $

$2$	−2.28421	−1.61518	−0.807590	−	0.589745i	$-0.799228\pi$
$2$	−2.28421	−1.61518	−0.807590	+	0.589745i	$0.799228\pi$
$3$	0.124993	0.0721650	0.0360825	−	0.999349i	$-0.488512\pi$
$3$	0.124993	0.0721650	0.0360825	+	0.999349i	$0.488512\pi$
$4$	3.21761	1.60880
$5$	−2.44620	−1.09397	−0.546986	−	0.837142i	$-0.684225\pi$
$5$	−2.44620	−1.09397	−0.546986	+	0.837142i	$0.684225\pi$
$6$	−0.285511	−0.116559
$7$	−2.39008	−0.903364	−0.451682	−	0.892179i	$-0.649176\pi$
$7$	−2.39008	−0.903364	−0.451682	+	0.892179i	$0.649176\pi$
$8$	−2.78127	−0.983327
$9$	−2.98438	−0.994792
$10$	5.58762	1.76696
$11$	−3.70380	−1.11674	−0.558369	−	0.829593i	$-0.688573\pi$
$11$	−3.70380	−1.11674	−0.558369	+	0.829593i	$0.688573\pi$
$12$	0.402180	0.116099
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	5.45943	1.45909
$15$	−0.305759	−0.0789465
$16$	−0.0822180	−0.0205545
$17$	8.08820	1.96168	0.980838	−	0.194823i	$-0.0624132\pi$
$17$	8.08820	1.96168	0.980838	+	0.194823i	$0.0624132\pi$
$18$	6.81694	1.60677
$19$	−2.96906	−0.681150	−0.340575	−	0.940217i	$-0.610622\pi$
$19$	−2.96906	−0.681150	−0.340575	+	0.940217i	$0.610622\pi$
$20$	−7.87090	−1.75999
$21$	−0.298744	−0.0651912
$22$	8.46025	1.80373
$23$	−1.81227	−0.377884	−0.188942	−	0.981988i	$-0.560506\pi$
$23$	−1.81227	−0.377884	−0.188942	+	0.981988i	$0.560506\pi$
$24$	−0.347640	−0.0709618
$25$	0.983882	0.196776
$26$	−2.28421	−0.447970
$27$	−0.748008	−0.143954
$28$	−7.69033	−1.45334
$29$	0.322802	0.0599428	0.0299714	−	0.999551i	$-0.490458\pi$
$29$	0.322802	0.0599428	0.0299714	+	0.999551i	$0.490458\pi$
$30$	0.698416	0.127513
$31$	−6.34155	−1.13898	−0.569488	−	0.821999i	$-0.692859\pi$
$31$	−6.34155	−1.13898	−0.569488	+	0.821999i	$0.692859\pi$
$32$	5.75034	1.01653
$33$	−0.462951	−0.0805893
$34$	−18.4751	−3.16846
$35$	5.84660	0.988255
$36$	−9.60255	−1.60043
$37$	5.18632	0.852625	0.426312	−	0.904576i	$-0.359812\pi$
$37$	5.18632	0.852625	0.426312	+	0.904576i	$0.359812\pi$
$38$	6.78196	1.10018
$39$	0.124993	0.0200150
$40$	6.80353	1.07573
$41$	−4.46936	−0.697997	−0.348998	−	0.937123i	$-0.613478\pi$
$41$	−4.46936	−0.697997	−0.348998	+	0.937123i	$0.613478\pi$
$42$	0.682393	0.105296
$43$	0.947078	0.144428	0.0722140	−	0.997389i	$-0.476994\pi$
$43$	0.947078	0.144428	0.0722140	+	0.997389i	$0.476994\pi$
$44$	−11.9174	−1.79661
$45$	7.30037	1.08828
$46$	4.13960	0.610350
$47$	−6.28086	−0.916158	−0.458079	−	0.888912i	$-0.651462\pi$
$47$	−6.28086	−0.916158	−0.458079	+	0.888912i	$0.651462\pi$
$48$	−0.0102767	−0.00148332
$49$	−1.28754	−0.183934
$50$	−2.24739	−0.317829
$51$	1.01097	0.141564
$52$	3.21761	0.446202
$53$	1.56655	0.215182	0.107591	−	0.994195i	$-0.465686\pi$
$53$	1.56655	0.215182	0.107591	+	0.994195i	$0.465686\pi$
$54$	1.70861	0.232512
$55$	9.06022	1.22168
$56$	6.64744	0.888302
$57$	−0.371113	−0.0491552
$58$	−0.737347	−0.0968184
$59$	−13.0860	−1.70365	−0.851824	−	0.523827i	$-0.824504\pi$
$59$	−13.0860	−1.70365	−0.851824	+	0.523827i	$0.824504\pi$
$60$	−0.983811	−0.127009
$61$	−2.94956	−0.377652	−0.188826	−	0.982011i	$-0.560468\pi$
$61$	−2.94956	−0.377652	−0.188826	+	0.982011i	$0.560468\pi$
$62$	14.4854	1.83965
$63$	7.13289	0.898659
$64$	−12.9705	−1.62132
$65$	−2.44620	−0.303413
$66$	1.05748	0.130166
$67$	−0.395320	−0.0482961	−0.0241480	−	0.999708i	$-0.507687\pi$
$67$	−0.395320	−0.0482961	−0.0241480	+	0.999708i	$0.507687\pi$
$68$	26.0247	3.15595
$69$	−0.226522	−0.0272700
$70$	−13.3548	−1.59621
$71$	−9.53870	−1.13204	−0.566018	−	0.824393i	$-0.691517\pi$
$71$	−9.53870	−1.13204	−0.566018	+	0.824393i	$0.691517\pi$
$72$	8.30035	0.978206
$73$	−7.78093	−0.910689	−0.455345	−	0.890315i	$-0.650484\pi$
$73$	−7.78093	−0.910689	−0.455345	+	0.890315i	$0.650484\pi$
$74$	−11.8466	−1.37714
$75$	0.122979	0.0142004
$76$	−9.55328	−1.09584
$77$	8.85236	1.00882
$78$	−0.285511	−0.0323278
$79$	−11.3270	−1.27439	−0.637195	−	0.770703i	$-0.719905\pi$
$79$	−11.3270	−1.27439	−0.637195	+	0.770703i	$0.719905\pi$
$80$	0.201121	0.0224861
$81$	8.85963	0.984404
$82$	10.2090	1.12739
$83$	−13.4529	−1.47665	−0.738324	−	0.674447i	$-0.764382\pi$
$83$	−13.4529	−1.47665	−0.738324	+	0.674447i	$0.764382\pi$
$84$	−0.961240	−0.104880
$85$	−19.7853	−2.14602
$86$	−2.16332	−0.233277
$87$	0.0403481	0.00432577
$88$	10.3013	1.09812
$89$	−6.95232	−0.736944	−0.368472	−	0.929639i	$-0.620119\pi$
$89$	−6.95232	−0.736944	−0.368472	+	0.929639i	$0.620119\pi$
$90$	−16.6756	−1.75776
$91$	−2.39008	−0.250548
$92$	−5.83116	−0.607941
$93$	−0.792653	−0.0821943
$94$	14.3468	1.47976
$95$	7.26291	0.745159
$96$	0.718755	0.0733576
$97$	−16.5075	−1.67609	−0.838044	−	0.545603i	$-0.816301\pi$
$97$	−16.5075	−1.67609	−0.838044	+	0.545603i	$0.816301\pi$
$98$	2.94100	0.297086
$99$	11.0535	1.11092
$100$	3.16574	0.316574
$101$	−18.1885	−1.80982	−0.904912	−	0.425600i	$-0.860063\pi$
$101$	−18.1885	−1.80982	−0.904912	+	0.425600i	$0.860063\pi$
$102$	−2.30927	−0.228652
$103$	−19.0427	−1.87633	−0.938165	−	0.346189i	$-0.887476\pi$
$103$	−19.0427	−1.87633	−0.938165	+	0.346189i	$0.887476\pi$
$104$	−2.78127	−0.272726
$105$	0.730786	0.0713174
$106$	−3.57832	−0.347557
$107$	0.0540256	0.00522285	0.00261143	−	0.999997i	$-0.499169\pi$
$107$	0.0540256	0.00522285	0.00261143	+	0.999997i	$0.499169\pi$
$108$	−2.40680	−0.231594
$109$	5.94138	0.569081	0.284541	−	0.958664i	$-0.408159\pi$
$109$	5.94138	0.569081	0.284541	+	0.958664i	$0.408159\pi$
$110$	−20.6954	−1.97323
$111$	0.648255	0.0615297
$112$	0.196507	0.0185682
$113$	8.55577	0.804859	0.402430	−	0.915451i	$-0.368166\pi$
$113$	8.55577	0.804859	0.402430	+	0.915451i	$0.368166\pi$
$114$	0.847700	0.0793944
$115$	4.43316	0.413395
$116$	1.03865	0.0964362
$117$	−2.98438	−0.275906
$118$	29.8911	2.75170
$119$	−19.3314	−1.77211
$120$	0.850397	0.0776303
$121$	2.71813	0.247103
$122$	6.73741	0.609976
$123$	−0.558641	−0.0503709
$124$	−20.4046	−1.83239
$125$	9.82422	0.878705
$126$	−16.2930	−1.45150
$127$	5.58460	0.495553	0.247777	−	0.968817i	$-0.420300\pi$
$127$	5.58460	0.495553	0.247777	+	0.968817i	$0.420300\pi$
$128$	18.1267	1.60219
$129$	0.118379	0.0104227
$130$	5.58762	0.490067
$131$	19.2668	1.68334	0.841672	−	0.539988i	$-0.181571\pi$
$131$	19.2668	1.68334	0.841672	+	0.539988i	$0.181571\pi$
$132$	−1.48959	−0.129652
$133$	7.09629	0.615326
$134$	0.902994	0.0780068
$135$	1.82977	0.157482
$136$	−22.4955	−1.92897
$137$	15.2650	1.30418	0.652090	−	0.758142i	$-0.273893\pi$
$137$	15.2650	1.30418	0.652090	+	0.758142i	$0.273893\pi$
$138$	0.517422	0.0440459
$139$	−19.0841	−1.61869	−0.809347	−	0.587331i	$-0.800179\pi$
$139$	−19.0841	−1.61869	−0.809347	+	0.587331i	$0.800179\pi$
$140$	18.8121	1.58991
$141$	−0.785066	−0.0661145
$142$	21.7884	1.82844
$143$	−3.70380	−0.309727
$144$	0.245369	0.0204475
$145$	−0.789637	−0.0655758
$146$	17.7733	1.47093
$147$	−0.160934	−0.0132736
$148$	16.6875	1.37171
$149$	19.3558	1.58569	0.792844	−	0.609424i	$-0.208599\pi$
$149$	19.3558	1.58569	0.792844	+	0.609424i	$0.208599\pi$
$150$	−0.280909	−0.0229361
$151$	0.763405	0.0621250	0.0310625	−	0.999517i	$-0.490111\pi$
$151$	0.763405	0.0621250	0.0310625	+	0.999517i	$0.490111\pi$
$152$	8.25776	0.669793
$153$	−24.1382	−1.95146
$154$	−20.2206	−1.62943
$155$	15.5127	1.24601
$156$	0.402180	0.0322002
$157$	1.64073	0.130945	0.0654723	−	0.997854i	$-0.479145\pi$
$157$	1.64073	0.130945	0.0654723	+	0.997854i	$0.479145\pi$
$158$	25.8733	2.05837
$159$	0.195808	0.0155286
$160$	−14.0665	−1.11205
$161$	4.33146	0.341367
$162$	−20.2372	−1.58999
$163$	−6.43405	−0.503953	−0.251977	−	0.967733i	$-0.581081\pi$
$163$	−6.43405	−0.503953	−0.251977	+	0.967733i	$0.581081\pi$
$164$	−14.3806	−1.12294
$165$	1.13247	0.0881625
$166$	30.7292	2.38505
$167$	1.03572	0.0801468	0.0400734	−	0.999197i	$-0.487241\pi$
$167$	1.03572	0.0801468	0.0400734	+	0.999197i	$0.487241\pi$
$168$	0.830887	0.0641043
$169$	1.00000	0.0769231
$170$	45.1938	3.46621
$171$	8.86080	0.677603
$172$	3.04733	0.232356
$173$	−16.6543	−1.26620	−0.633101	−	0.774070i	$-0.718218\pi$
$173$	−16.6543	−1.26620	−0.633101	+	0.774070i	$0.718218\pi$
$174$	−0.0921635	−0.00698690
$175$	−2.35155	−0.177761
$176$	0.304519	0.0229540
$177$	−1.63566	−0.122944
$178$	15.8805	1.19030
$179$	2.55730	0.191141	0.0955707	−	0.995423i	$-0.469532\pi$
$179$	2.55730	0.191141	0.0955707	+	0.995423i	$0.469532\pi$
$180$	23.4897	1.75082
$181$	−0.277281	−0.0206102	−0.0103051	−	0.999947i	$-0.503280\pi$
$181$	−0.277281	−0.0206102	−0.0103051	+	0.999947i	$0.503280\pi$
$182$	5.45943	0.404680
$183$	−0.368676	−0.0272533
$184$	5.04040	0.371583
$185$	−12.6868	−0.932748
$186$	1.81058	0.132758
$187$	−29.9571	−2.19068
$188$	−20.2093	−1.47392
$189$	1.78780	0.130043
$190$	−16.5900	−1.20357
$191$	−20.3676	−1.47375	−0.736875	−	0.676029i	$-0.763699\pi$
$191$	−20.3676	−1.47375	−0.736875	+	0.676029i	$0.763699\pi$
$192$	−1.62123	−0.117002
$193$	24.0879	1.73388	0.866942	−	0.498408i	$-0.166082\pi$
$193$	24.0879	1.73388	0.866942	+	0.498408i	$0.166082\pi$
$194$	37.7067	2.70718
$195$	−0.305759	−0.0218958
$196$	−4.14279	−0.295913
$197$	10.8311	0.771686	0.385843	−	0.922564i	$-0.373911\pi$
$197$	10.8311	0.771686	0.385843	+	0.922564i	$0.373911\pi$
$198$	−25.2486	−1.79434
$199$	0.328443	0.0232827	0.0116414	−	0.999932i	$-0.496294\pi$
$199$	0.328443	0.0232827	0.0116414	+	0.999932i	$0.496294\pi$
$200$	−2.73644	−0.193495
$201$	−0.0494124	−0.00348528
$202$	41.5463	2.92319
$203$	−0.771521	−0.0541502
$204$	3.25291	0.227749
$205$	10.9329	0.763590
$206$	43.4974	3.03061
$207$	5.40849	0.375916
$208$	−0.0822180	−0.00570079
$209$	10.9968	0.760665
$210$	−1.66927	−0.115190
$211$	−24.8158	−1.70839	−0.854196	−	0.519952i	$-0.825950\pi$
$211$	−24.8158	−1.70839	−0.854196	+	0.519952i	$0.825950\pi$
$212$	5.04053	0.346185
$213$	−1.19228	−0.0816934
$214$	−0.123406	−0.00843584
$215$	−2.31674	−0.158000
$216$	2.08041	0.141554
$217$	15.1568	1.02891
$218$	−13.5714	−0.919168
$219$	−0.972565	−0.0657199
$220$	29.1522	1.96544
$221$	8.08820	0.544071
$222$	−1.48075	−0.0993814
$223$	1.79696	0.120333	0.0601665	−	0.998188i	$-0.480837\pi$
$223$	1.79696	0.120333	0.0601665	+	0.998188i	$0.480837\pi$
$224$	−13.7438	−0.918293
$225$	−2.93627	−0.195752
$226$	−19.5432	−1.29999
$227$	−10.2787	−0.682219	−0.341109	−	0.940024i	$-0.610803\pi$
$227$	−10.2787	−0.682219	−0.341109	+	0.940024i	$0.610803\pi$
$228$	−1.19410	−0.0790810
$229$	−28.3504	−1.87345	−0.936724	−	0.350068i	$-0.886158\pi$
$229$	−28.3504	−1.87345	−0.936724	+	0.350068i	$0.886158\pi$
$230$	−10.1263	−0.667706
$231$	1.10649	0.0728015
$232$	−0.897799	−0.0589434
$233$	18.9877	1.24393	0.621963	−	0.783047i	$-0.286335\pi$
$233$	18.9877	1.24393	0.621963	+	0.783047i	$0.286335\pi$
$234$	6.81694	0.445637
$235$	15.3642	1.00225
$236$	−42.1055	−2.74084
$237$	−1.41580	−0.0919663
$238$	44.1570	2.86227
$239$	18.9278	1.22434	0.612170	−	0.790726i	$-0.290297\pi$
$239$	18.9278	1.22434	0.612170	+	0.790726i	$0.290297\pi$
$240$	0.0251389	0.00162271
$241$	22.7088	1.46280	0.731401	−	0.681947i	$-0.238867\pi$
$241$	22.7088	1.46280	0.731401	+	0.681947i	$0.238867\pi$
$242$	−6.20877	−0.399115
$243$	3.35142	0.214994
$244$	−9.49053	−0.607569
$245$	3.14957	0.201219
$246$	1.27605	0.0813581
$247$	−2.96906	−0.188917
$248$	17.6376	1.11999
$249$	−1.68152	−0.106562
$250$	−22.4406	−1.41927
$251$	−9.69161	−0.611729	−0.305865	−	0.952075i	$-0.598945\pi$
$251$	−9.69161	−0.611729	−0.305865	+	0.952075i	$0.598945\pi$
$252$	22.9508	1.44577
$253$	6.71227	0.421997
$254$	−12.7564	−0.800407
$255$	−2.47304	−0.154868
$256$	−15.4641	−0.966509
$257$	−4.64878	−0.289983	−0.144992	−	0.989433i	$-0.546315\pi$
$257$	−4.64878	−0.289983	−0.144992	+	0.989433i	$0.546315\pi$
$258$	−0.270401	−0.0168344
$259$	−12.3957	−0.770231
$260$	−7.87090	−0.488133
$261$	−0.963363	−0.0596306
$262$	−44.0093	−2.71890
$263$	28.2578	1.74245	0.871225	−	0.490884i	$-0.163326\pi$
$263$	28.2578	1.74245	0.871225	+	0.490884i	$0.163326\pi$
$264$	1.28759	0.0792457
$265$	−3.83208	−0.235403
$266$	−16.2094	−0.993862
$267$	−0.868994	−0.0531816
$268$	−1.27199	−0.0776989
$269$	1.12171	0.0683921	0.0341961	−	0.999415i	$-0.489113\pi$
$269$	1.12171	0.0683921	0.0341961	+	0.999415i	$0.489113\pi$
$270$	−4.17959	−0.254362
$271$	−5.44713	−0.330890	−0.165445	−	0.986219i	$-0.552906\pi$
$271$	−5.44713	−0.330890	−0.165445	+	0.986219i	$0.552906\pi$
$272$	−0.664996	−0.0403213
$273$	−0.298744	−0.0180808
$274$	−34.8685	−2.10648
$275$	−3.64410	−0.219747
$276$	−0.728857	−0.0438721
$277$	20.0122	1.20242	0.601209	−	0.799091i	$-0.294686\pi$
$277$	20.0122	1.20242	0.601209	+	0.799091i	$0.294686\pi$
$278$	43.5921	2.61448
$279$	18.9256	1.13305
$280$	−16.2610	−0.971778
$281$	28.2860	1.68740	0.843700	−	0.536816i	$-0.180373\pi$
$281$	28.2860	1.68740	0.843700	+	0.536816i	$0.180373\pi$
$282$	1.79326	0.106787
$283$	−25.2786	−1.50266	−0.751328	−	0.659929i	$-0.770586\pi$
$283$	−25.2786	−1.50266	−0.751328	+	0.659929i	$0.770586\pi$
$284$	−30.6918	−1.82122
$285$	0.907817	0.0537744
$286$	8.46025	0.500265
$287$	10.6821	0.630545
$288$	−17.1612	−1.01123
$289$	48.4190	2.84818
$290$	1.80370	0.105917
$291$	−2.06333	−0.120955
$292$	−25.0360	−1.46512
$293$	0.903849	0.0528034	0.0264017	−	0.999651i	$-0.491595\pi$
$293$	0.903849	0.0528034	0.0264017	+	0.999651i	$0.491595\pi$
$294$	0.367606	0.0214392
$295$	32.0109	1.86375
$296$	−14.4245	−0.838409
$297$	2.77047	0.160759
$298$	−44.2127	−2.56117
$299$	−1.81227	−0.104806
$300$	0.395697	0.0228456
$301$	−2.26359	−0.130471
$302$	−1.74378	−0.100343
$303$	−2.27344	−0.130606
$304$	0.244110	0.0140007
$305$	7.21521	0.413141
$306$	55.1368	3.15196
$307$	−9.98716	−0.569997	−0.284999	−	0.958528i	$-0.591993\pi$
$307$	−9.98716	−0.569997	−0.284999	+	0.958528i	$0.591993\pi$
$308$	28.4834	1.62299
$309$	−2.38021	−0.135405
$310$	−35.4342	−2.01253
$311$	21.4368	1.21557	0.607785	−	0.794102i	$-0.292058\pi$
$311$	21.4368	1.21557	0.607785	+	0.794102i	$0.292058\pi$
$312$	−0.347640	−0.0196813
$313$	−18.8889	−1.06767	−0.533833	−	0.845590i	$-0.679249\pi$
$313$	−18.8889	−1.06767	−0.533833	+	0.845590i	$0.679249\pi$
$314$	−3.74777	−0.211499
$315$	−17.4484	−0.983109
$316$	−36.4459	−2.05024
$317$	−19.0563	−1.07031	−0.535155	−	0.844754i	$-0.679747\pi$
$317$	−19.0563	−1.07031	−0.535155	+	0.844754i	$0.679747\pi$
$318$	−0.447266	−0.0250814
$319$	−1.19559	−0.0669404
$320$	31.7285	1.77368
$321$	0.00675285	0.000376907 0
$322$	−9.89395	−0.551368
$323$	−24.0144	−1.33620
$324$	28.5068	1.58371
$325$	0.983882	0.0545759
$326$	14.6967	0.813975
$327$	0.742634	0.0410677
$328$	12.4305	0.686359
$329$	15.0117	0.827624
$330$	−2.58679	−0.142398
$331$	−26.9549	−1.48158	−0.740788	−	0.671739i	$-0.765548\pi$
$331$	−26.9549	−1.48158	−0.740788	+	0.671739i	$0.765548\pi$
$332$	−43.2861	−2.37564
$333$	−15.4779	−0.848185
$334$	−2.36581	−0.129451
$335$	0.967031	0.0528346
$336$	0.0245621	0.00133997
$337$	−21.7736	−1.18608	−0.593041	−	0.805172i	$-0.702073\pi$
$337$	−21.7736	−1.18608	−0.593041	+	0.805172i	$0.702073\pi$
$338$	−2.28421	−0.124245
$339$	1.06942	0.0580827
$340$	−63.6614	−3.45253
$341$	23.4878	1.27194
$342$	−20.2399	−1.09445
$343$	19.8078	1.06952
$344$	−2.63408	−0.142020
$345$	0.554116	0.0298326
$346$	38.0418	2.04514
$347$	22.6009	1.21328	0.606640	−	0.794977i	$-0.292517\pi$
$347$	22.6009	1.21328	0.606640	+	0.794977i	$0.292517\pi$
$348$	0.129824	0.00695932
$349$	0.667903	0.0357520	0.0178760	−	0.999840i	$-0.494310\pi$
$349$	0.667903	0.0357520	0.0178760	+	0.999840i	$0.494310\pi$
$350$	5.37143	0.287115
$351$	−0.748008	−0.0399257
$352$	−21.2981	−1.13519
$353$	−23.5592	−1.25393	−0.626966	−	0.779047i	$-0.715704\pi$
$353$	−23.5592	−1.25393	−0.626966	+	0.779047i	$0.715704\pi$
$354$	3.73619	0.198576
$355$	23.3336	1.23842
$356$	−22.3698	−1.18560
$357$	−2.41630	−0.127884
$358$	−5.84140	−0.308728
$359$	−2.36755	−0.124954	−0.0624772	−	0.998046i	$-0.519900\pi$
$359$	−2.36755	−0.124954	−0.0624772	+	0.998046i	$0.519900\pi$
$360$	−20.3043	−1.07013
$361$	−10.1847	−0.536035
$362$	0.633368	0.0332891
$363$	0.339748	0.0178322
$364$	−7.69033	−0.403083
$365$	19.0337	0.996269
$366$	0.842132	0.0440189
$367$	−11.1390	−0.581453	−0.290727	−	0.956806i	$-0.593897\pi$
$367$	−11.1390	−0.581453	−0.290727	+	0.956806i	$0.593897\pi$
$368$	0.149001	0.00776721
$369$	13.3383	0.694362
$370$	28.9792	1.50656
$371$	−3.74416	−0.194387
$372$	−2.55045	−0.132234
$373$	5.53012	0.286339	0.143169	−	0.989698i	$-0.454271\pi$
$373$	5.53012	0.286339	0.143169	+	0.989698i	$0.454271\pi$
$374$	68.4282	3.53834
$375$	1.22796	0.0634117
$376$	17.4688	0.900883
$377$	0.322802	0.0166251
$378$	−4.08370	−0.210043
$379$	−24.8750	−1.27774	−0.638872	−	0.769313i	$-0.720598\pi$
$379$	−24.8750	−1.27774	−0.638872	+	0.769313i	$0.720598\pi$
$380$	23.3692	1.19881
$381$	0.698038	0.0357616
$382$	46.5239	2.38037
$383$	4.41668	0.225682	0.112841	−	0.993613i	$-0.464005\pi$
$383$	4.41668	0.225682	0.112841	+	0.993613i	$0.464005\pi$
$384$	2.26572	0.115622
$385$	−21.6546	−1.10362
$386$	−55.0218	−2.80053
$387$	−2.82644	−0.143676
$388$	−53.1148	−2.69650
$389$	−4.10564	−0.208164	−0.104082	−	0.994569i	$-0.533190\pi$
$389$	−4.10564	−0.208164	−0.104082	+	0.994569i	$0.533190\pi$
$390$	0.698416	0.0353657
$391$	−14.6580	−0.741286
$392$	3.58098	0.180867
$393$	2.40822	0.121479
$394$	−24.7406	−1.24641
$395$	27.7081	1.39415
$396$	35.5659	1.78725
$397$	−31.0818	−1.55995	−0.779976	−	0.625809i	$-0.784769\pi$
$397$	−31.0818	−1.55995	−0.779976	+	0.625809i	$0.784769\pi$
$398$	−0.750233	−0.0376058
$399$	0.886989	0.0444050
$400$	−0.0808928	−0.00404464
$401$	35.5799	1.77678	0.888388	−	0.459094i	$-0.151826\pi$
$401$	35.5799	1.77678	0.888388	+	0.459094i	$0.151826\pi$
$402$	0.112868	0.00562936
$403$	−6.34155	−0.315895
$404$	−58.5234	−2.91165
$405$	−21.6724	−1.07691
$406$	1.76232	0.0874622
$407$	−19.2091	−0.952158
$408$	−2.81178	−0.139204
$409$	−17.4530	−0.862993	−0.431497	−	0.902115i	$-0.642014\pi$
$409$	−17.4530	−0.862993	−0.431497	+	0.902115i	$0.642014\pi$
$410$	−24.9731	−1.23333
$411$	1.90803	0.0941161
$412$	−61.2718	−3.01865
$413$	31.2765	1.53901
$414$	−12.3541	−0.607172
$415$	32.9084	1.61541
$416$	5.75034	0.281934
$417$	−2.38539	−0.116813
$418$	−25.1190	−1.22861
$419$	24.6083	1.20219	0.601097	−	0.799176i	$-0.294731\pi$
$419$	24.6083	1.20219	0.601097	+	0.799176i	$0.294731\pi$
$420$	2.35138	0.114736
$421$	−16.3792	−0.798273	−0.399137	−	0.916891i	$-0.630690\pi$
$421$	−16.3792	−0.798273	−0.399137	+	0.916891i	$0.630690\pi$
$422$	56.6845	2.75936
$423$	18.7445	0.911387
$424$	−4.35699	−0.211594
$425$	7.95783	0.386012
$426$	2.72341	0.131949
$427$	7.04967	0.341158
$428$	0.173833	0.00840255
$429$	−0.462951	−0.0223515
$430$	5.29192	0.255199
$431$	−22.8438	−1.10035	−0.550174	−	0.835050i	$-0.685438\pi$
$431$	−22.8438	−1.10035	−0.550174	+	0.835050i	$0.685438\pi$
$432$	0.0614997	0.00295891
$433$	−2.26848	−0.109016	−0.0545081	−	0.998513i	$-0.517359\pi$
$433$	−2.26848	−0.109016	−0.0545081	+	0.998513i	$0.517359\pi$
$434$	−34.6213	−1.66187
$435$	−0.0986995	−0.00473228
$436$	19.1170	0.915540
$437$	5.38074	0.257396
$438$	2.22154	0.106149
$439$	29.1619	1.39182	0.695912	−	0.718128i	$-0.255001\pi$
$439$	29.1619	1.39182	0.695912	+	0.718128i	$0.255001\pi$
$440$	−25.1989	−1.20131
$441$	3.84249	0.182976
$442$	−18.4751	−0.878773
$443$	29.9764	1.42422	0.712111	−	0.702067i	$-0.247739\pi$
$443$	29.9764	1.42422	0.712111	+	0.702067i	$0.247739\pi$
$444$	2.08583	0.0989892
$445$	17.0067	0.806197
$446$	−4.10462	−0.194359
$447$	2.41935	0.114431
$448$	31.0006	1.46464
$449$	−29.7302	−1.40305	−0.701527	−	0.712643i	$-0.747498\pi$
$449$	−29.7302	−1.40305	−0.701527	+	0.712643i	$0.747498\pi$
$450$	6.70706	0.316174
$451$	16.5536	0.779479
$452$	27.5291	1.29486
$453$	0.0954206	0.00448325
$454$	23.4786	1.10191
$455$	5.84660	0.274093
$456$	1.03217	0.0483356
$457$	7.94896	0.371837	0.185918	−	0.982565i	$-0.440474\pi$
$457$	7.94896	0.371837	0.185918	+	0.982565i	$0.440474\pi$
$458$	64.7583	3.02596
$459$	−6.05004	−0.282392
$460$	14.2642	0.665071
$461$	10.4000	0.484378	0.242189	−	0.970229i	$-0.422135\pi$
$461$	10.4000	0.484378	0.242189	+	0.970229i	$0.422135\pi$
$462$	−2.52745	−0.117587
$463$	−1.00000	−0.0464739
$463$	−1.00000	−0.0464739
$464$	−0.0265401	−0.00123209
$465$	1.93898	0.0899183
$466$	−43.3719	−2.00916
$467$	−6.42811	−0.297457	−0.148729	−	0.988878i	$-0.547518\pi$
$467$	−6.42811	−0.297457	−0.148729	+	0.988878i	$0.547518\pi$
$468$	−9.60255	−0.443878
$469$	0.944845	0.0436289
$470$	−35.0951	−1.61882
$471$	0.205081	0.00944961
$472$	36.3956	1.67524
$473$	−3.50779	−0.161288
$474$	3.23399	0.148542
$475$	−2.92121	−0.134034
$476$	−62.2009	−2.85097
$477$	−4.67516	−0.214061
$478$	−43.2351	−1.97753
$479$	43.0727	1.96804	0.984021	−	0.178050i	$-0.0569790\pi$
$479$	43.0727	1.96804	0.984021	+	0.178050i	$0.0569790\pi$
$480$	−1.75822	−0.0802512
$481$	5.18632	0.236476
$482$	−51.8716	−2.36269
$483$	0.541404	0.0246347
$484$	8.74587	0.397539
$485$	40.3807	1.83359
$486$	−7.65534	−0.347253
$487$	−17.7002	−0.802073	−0.401037	−	0.916062i	$-0.631350\pi$
$487$	−17.7002	−0.802073	−0.401037	+	0.916062i	$0.631350\pi$
$488$	8.20352	0.371356
$489$	−0.804213	−0.0363678
$490$	−7.19427	−0.325004
$491$	1.22415	0.0552452	0.0276226	−	0.999618i	$-0.491206\pi$
$491$	1.22415	0.0552452	0.0276226	+	0.999618i	$0.491206\pi$
$492$	−1.79749	−0.0810370
$493$	2.61089	0.117588
$494$	6.78196	0.305135
$495$	−27.0391	−1.21532
$496$	0.521390	0.0234111
$497$	22.7982	1.02264
$498$	3.84095	0.172117
$499$	−5.93284	−0.265590	−0.132795	−	0.991143i	$-0.542395\pi$
$499$	−5.93284	−0.265590	−0.132795	+	0.991143i	$0.542395\pi$
$500$	31.6105	1.41366
$501$	0.129459	0.00578379
$502$	22.1377	0.988052
$503$	−18.1515	−0.809334	−0.404667	−	0.914464i	$-0.632613\pi$
$503$	−18.1515	−0.809334	−0.404667	+	0.914464i	$0.632613\pi$
$504$	−19.8385	−0.883676
$505$	44.4927	1.97990
$506$	−15.3322	−0.681601
$507$	0.124993	0.00555115
$508$	17.9690	0.797248
$509$	−30.1710	−1.33730	−0.668652	−	0.743575i	$-0.733128\pi$
$509$	−30.1710	−1.33730	−0.668652	+	0.743575i	$0.733128\pi$
$510$	5.64893	0.250139
$511$	18.5970	0.822684
$512$	−0.930122	−0.0411060
$513$	2.22088	0.0980543
$514$	10.6188	0.468375
$515$	46.5821	2.05265
$516$	0.380896	0.0167680
$517$	23.2630	1.02311
$518$	28.3143	1.24406
$519$	−2.08167	−0.0913754
$520$	6.80353	0.298355
$521$	−6.53430	−0.286273	−0.143136	−	0.989703i	$-0.545719\pi$
$521$	−6.53430	−0.286273	−0.143136	+	0.989703i	$0.545719\pi$
$522$	2.20052	0.0963142
$523$	−21.5620	−0.942839	−0.471420	−	0.881909i	$-0.656258\pi$
$523$	−21.5620	−0.942839	−0.471420	+	0.881909i	$0.656258\pi$
$524$	61.9929	2.70817
$525$	−0.293929	−0.0128281
$526$	−64.5467	−2.81437
$527$	−51.2918	−2.23430
$528$	0.0380629	0.00165647
$529$	−19.7157	−0.857204
$530$	8.75327	0.380218
$531$	39.0535	1.69478
$532$	22.8331	0.989939
$533$	−4.46936	−0.193590
$534$	1.98496	0.0858978
$535$	−0.132157	−0.00571366
$536$	1.09949	0.0474908
$537$	0.319646	0.0137937
$538$	−2.56223	−0.110466
$539$	4.76878	0.205406
$540$	5.88750	0.253357
$541$	36.1771	1.55538	0.777688	−	0.628650i	$-0.216392\pi$
$541$	36.1771	1.55538	0.777688	+	0.628650i	$0.216392\pi$
$542$	12.4424	0.534446
$543$	−0.0346583	−0.00148733
$544$	46.5099	1.99410
$545$	−14.5338	−0.622559
$546$	0.682393	0.0292037
$547$	−4.67524	−0.199899	−0.0999494	−	0.994993i	$-0.531868\pi$
$547$	−4.67524	−0.199899	−0.0999494	+	0.994993i	$0.531868\pi$
$548$	49.1169	2.09817
$549$	8.80260	0.375686
$550$	8.32388	0.354932
$551$	−0.958419	−0.0408300
$552$	0.630017	0.0268153
$553$	27.0724	1.15124
$554$	−45.7121	−1.94212
$555$	−1.58576	−0.0673118
$556$	−61.4052	−2.60416
$557$	−6.16897	−0.261388	−0.130694	−	0.991423i	$-0.541721\pi$
$557$	−6.16897	−0.261388	−0.130694	+	0.991423i	$0.541721\pi$
$558$	−43.2300	−1.83007
$559$	0.947078	0.0400571
$560$	−0.480696	−0.0203131
$561$	−3.74444	−0.158090
$562$	−64.6110	−2.72545
$563$	33.0673	1.39362	0.696810	−	0.717256i	$-0.254602\pi$
$563$	33.0673	1.39362	0.696810	+	0.717256i	$0.254602\pi$
$564$	−2.52604	−0.106365
$565$	−20.9291	−0.880494
$566$	57.7416	2.42706
$567$	−21.1752	−0.889275
$568$	26.5297	1.11316
$569$	4.63643	0.194369	0.0971847	−	0.995266i	$-0.469016\pi$
$569$	4.63643	0.194369	0.0971847	+	0.995266i	$0.469016\pi$
$570$	−2.07364	−0.0868553
$571$	16.7760	0.702053	0.351027	−	0.936365i	$-0.385833\pi$
$571$	16.7760	0.702053	0.351027	+	0.936365i	$0.385833\pi$
$572$	−11.9174	−0.498290
$573$	−2.54582	−0.106353
$574$	−24.4002	−1.01844
$575$	−1.78306	−0.0743586
$576$	38.7090	1.61287
$577$	−5.50839	−0.229317	−0.114659	−	0.993405i	$-0.536577\pi$
$577$	−5.50839	−0.229317	−0.114659	+	0.993405i	$0.536577\pi$
$578$	−110.599	−4.60031
$579$	3.01083	0.125126
$580$	−2.54074	−0.105499
$581$	32.1534	1.33395
$582$	4.71309	0.195364
$583$	−5.80217	−0.240301
$584$	21.6409	0.895505
$585$	7.30037	0.301833
$586$	−2.06458	−0.0852870
$587$	−2.50416	−0.103358	−0.0516788	−	0.998664i	$-0.516457\pi$
$587$	−2.50416	−0.103358	−0.0516788	+	0.998664i	$0.516457\pi$
$588$	−0.517821	−0.0213546
$589$	18.8285	0.775814
$590$	−73.1195	−3.01028
$591$	1.35382	0.0556887
$592$	−0.426408	−0.0175253
$593$	22.1990	0.911604	0.455802	−	0.890081i	$-0.349353\pi$
$593$	22.1990	0.911604	0.455802	+	0.890081i	$0.349353\pi$
$594$	−6.32833	−0.259655
$595$	47.2885	1.93864
$596$	62.2793	2.55106
$597$	0.0410533	0.00168020
$598$	4.13960	0.169281
$599$	−24.6319	−1.00643	−0.503217	−	0.864160i	$-0.667850\pi$
$599$	−24.6319	−1.00643	−0.503217	+	0.864160i	$0.667850\pi$
$600$	−0.342037	−0.0139636
$601$	25.6784	1.04744	0.523722	−	0.851889i	$-0.324543\pi$
$601$	25.6784	1.04744	0.523722	+	0.851889i	$0.324543\pi$
$602$	5.17051	0.210734
$603$	1.17978	0.0480445
$604$	2.45634	0.0999469
$605$	−6.64908	−0.270323
$606$	5.19302	0.210952
$607$	31.3819	1.27375	0.636877	−	0.770966i	$-0.280226\pi$
$607$	31.3819	1.27375	0.636877	+	0.770966i	$0.280226\pi$
$608$	−17.0731	−0.692407
$609$	−0.0964351	−0.00390775
$610$	−16.4810	−0.667297
$611$	−6.28086	−0.254096
$612$	−77.6674	−3.13952
$613$	17.4111	0.703226	0.351613	−	0.936145i	$-0.385633\pi$
$613$	17.4111	0.703226	0.351613	+	0.936145i	$0.385633\pi$
$614$	22.8127	0.920648
$615$	1.36655	0.0551044
$616$	−24.6208	−0.992000
$617$	14.0581	0.565958	0.282979	−	0.959126i	$-0.408677\pi$
$617$	14.0581	0.565958	0.282979	+	0.959126i	$0.408677\pi$
$618$	5.43689	0.218704
$619$	−14.6026	−0.586928	−0.293464	−	0.955970i	$-0.594808\pi$
$619$	−14.6026	−0.586928	−0.293464	+	0.955970i	$0.594808\pi$
$620$	49.9138	2.00458
$621$	1.35559	0.0543980
$622$	−48.9661	−1.96336
$623$	16.6166	0.665729
$624$	−0.0102767	−0.000411398 0
$625$	−28.9514	−1.15806
$626$	43.1463	1.72447
$627$	1.37453	0.0548934
$628$	5.27923	0.210664
$629$	41.9480	1.67257
$630$	39.8559	1.58790
$631$	−37.7828	−1.50411	−0.752054	−	0.659101i	$-0.770937\pi$
$631$	−37.7828	−1.50411	−0.752054	+	0.659101i	$0.770937\pi$
$632$	31.5035	1.25314
$633$	−3.10181	−0.123286
$634$	43.5286	1.72874
$635$	−13.6610	−0.542121
$636$	0.630033	0.0249824
$637$	−1.28754	−0.0510141
$638$	2.73098	0.108121
$639$	28.4671	1.12614
$640$	−44.3416	−1.75275
$641$	−38.6376	−1.52609	−0.763047	−	0.646343i	$-0.776298\pi$
$641$	−38.6376	−1.52609	−0.763047	+	0.646343i	$0.776298\pi$
$642$	−0.0154249	−0.000608773 0
$643$	9.19284	0.362530	0.181265	−	0.983434i	$-0.441981\pi$
$643$	9.19284	0.362530	0.181265	+	0.983434i	$0.441981\pi$
$644$	13.9369	0.549192
$645$	−0.289577	−0.0114021
$646$	54.8538	2.15820
$647$	18.3600	0.721805	0.360902	−	0.932604i	$-0.382469\pi$
$647$	18.3600	0.721805	0.360902	+	0.932604i	$0.382469\pi$
$648$	−24.6410	−0.967991
$649$	48.4678	1.90253
$650$	−2.24739	−0.0881499
$651$	1.89450	0.0742513
$652$	−20.7022	−0.810762
$653$	−11.0926	−0.434087	−0.217044	−	0.976162i	$-0.569641\pi$
$653$	−11.0926	−0.434087	−0.217044	+	0.976162i	$0.569641\pi$
$654$	−1.69633	−0.0663318
$655$	−47.1303	−1.84153
$656$	0.367462	0.0143470
$657$	23.2212	0.905947
$658$	−34.2899	−1.33676
$659$	17.5301	0.682875	0.341438	−	0.939904i	$-0.389086\pi$
$659$	17.5301	0.682875	0.341438	+	0.939904i	$0.389086\pi$
$660$	3.64384	0.141836
$661$	−29.6638	−1.15379	−0.576893	−	0.816820i	$-0.695735\pi$
$661$	−29.6638	−1.15379	−0.576893	+	0.816820i	$0.695735\pi$
$662$	61.5707	2.39301
$663$	1.01097	0.0392629
$664$	37.4161	1.45203
$665$	−17.3589	−0.673150
$666$	35.3548	1.36997
$667$	−0.585003	−0.0226514
$668$	3.33255	0.128940
$669$	0.224608	0.00868384
$670$	−2.20890	−0.0853373
$671$	10.9246	0.421739
$672$	−1.71788	−0.0662686
$673$	18.2872	0.704919	0.352459	−	0.935827i	$-0.385345\pi$
$673$	18.2872	0.704919	0.352459	+	0.935827i	$0.385345\pi$
$674$	49.7354	1.91574
$675$	−0.735951	−0.0283268
$676$	3.21761	0.123754
$677$	−27.7211	−1.06541	−0.532704	−	0.846301i	$-0.678824\pi$
$677$	−27.7211	−1.06541	−0.532704	+	0.846301i	$0.678824\pi$
$678$	−2.44277	−0.0938139
$679$	39.4543	1.51412
$680$	55.0283	2.11024
$681$	−1.28476	−0.0492323
$682$	−53.6511	−2.05441
$683$	2.12535	0.0813241	0.0406621	−	0.999173i	$-0.487053\pi$
$683$	2.12535	0.0813241	0.0406621	+	0.999173i	$0.487053\pi$
$684$	28.5106	1.09013
$685$	−37.3413	−1.42674
$686$	−45.2452	−1.72747
$687$	−3.54362	−0.135197
$688$	−0.0778669	−0.00296865
$689$	1.56655	0.0596807
$690$	−1.26572	−0.0481850
$691$	21.0054	0.799084	0.399542	−	0.916715i	$-0.369169\pi$
$691$	21.0054	0.799084	0.399542	+	0.916715i	$0.369169\pi$
$692$	−53.5869	−2.03707
$693$	−26.4188	−1.00357
$694$	−51.6251	−1.95966
$695$	46.6835	1.77081
$696$	−0.112219	−0.00425365
$697$	−36.1491	−1.36924
$698$	−1.52563	−0.0577459
$699$	2.37334	0.0897679
$700$	−7.56637	−0.285982
$701$	15.1464	0.572071	0.286036	−	0.958219i	$-0.407662\pi$
$701$	15.1464	0.572071	0.286036	+	0.958219i	$0.407662\pi$
$702$	1.70861	0.0644872
$703$	−15.3985	−0.580765
$704$	48.0403	1.81059
$705$	1.92043	0.0723275
$706$	53.8142	2.02533
$707$	43.4719	1.63493
$708$	−5.26291	−0.197792
$709$	10.2297	0.384186	0.192093	−	0.981377i	$-0.438473\pi$
$709$	10.2297	0.384186	0.192093	+	0.981377i	$0.438473\pi$
$710$	−53.2987	−2.00026
$711$	33.8041	1.26775
$712$	19.3363	0.724657
$713$	11.4926	0.430401
$714$	5.51933	0.206556
$715$	9.06022	0.338833
$716$	8.22838	0.307509
$717$	2.36586	0.0883545
$718$	5.40797	0.201824
$719$	40.2814	1.50224	0.751122	−	0.660164i	$-0.229513\pi$
$719$	40.2814	1.50224	0.751122	+	0.660164i	$0.229513\pi$
$720$	−0.600222	−0.0223690
$721$	45.5134	1.69501
$722$	23.2639	0.865792
$723$	2.83845	0.105563
$724$	−0.892182	−0.0331577
$725$	0.317599	0.0117953
$726$	−0.776055	−0.0288021
$727$	10.5443	0.391065	0.195533	−	0.980697i	$-0.437356\pi$
$727$	10.5443	0.391065	0.195533	+	0.980697i	$0.437356\pi$
$728$	6.64744	0.246371
$729$	−26.1600	−0.968889
$730$	−43.4769	−1.60915
$731$	7.66016	0.283321
$732$	−1.18625	−0.0438452
$733$	33.1285	1.22363	0.611815	−	0.791001i	$-0.290440\pi$
$733$	33.1285	1.22363	0.611815	+	0.791001i	$0.290440\pi$
$734$	25.4439	0.939151
$735$	0.393675	0.0145209
$736$	−10.4212	−0.384129
$737$	1.46419	0.0539340
$738$	−30.4674	−1.12152
$739$	46.7174	1.71853	0.859263	−	0.511534i	$-0.170922\pi$
$739$	46.7174	1.71853	0.859263	+	0.511534i	$0.170922\pi$
$740$	−40.8210	−1.50061
$741$	−0.371113	−0.0136332
$742$	8.55245	0.313970
$743$	−40.9192	−1.50118	−0.750591	−	0.660768i	$-0.770231\pi$
$743$	−40.9192	−1.50118	−0.750591	+	0.660768i	$0.770231\pi$
$744$	2.20458	0.0808238
$745$	−47.3481	−1.73470
$746$	−12.6319	−0.462488
$747$	40.1485	1.46896
$748$	−96.3901	−3.52437
$749$	−0.129125	−0.00471814
$750$	−2.80492	−0.102421
$751$	2.03450	0.0742401	0.0371200	−	0.999311i	$-0.488182\pi$
$751$	2.03450	0.0742401	0.0371200	+	0.999311i	$0.488182\pi$
$752$	0.516400	0.0188312
$753$	−1.21139	−0.0441454
$754$	−0.737347	−0.0268526
$755$	−1.86744	−0.0679631
$756$	5.75242	0.209214
$757$	−12.3427	−0.448602	−0.224301	−	0.974520i	$-0.572010\pi$
$757$	−12.3427	−0.448602	−0.224301	+	0.974520i	$0.572010\pi$
$758$	56.8197	2.06378
$759$	0.838990	0.0304534
$760$	−20.2001	−0.732735
$761$	−40.9101	−1.48299	−0.741495	−	0.670958i	$-0.765883\pi$
$761$	−40.9101	−1.48299	−0.741495	+	0.670958i	$0.765883\pi$
$762$	−1.59446	−0.0577614
$763$	−14.2004	−0.514087
$764$	−65.5350	−2.37097
$765$	59.0469	2.13484
$766$	−10.0886	−0.364517
$767$	−13.0860	−0.472507
$768$	−1.93292	−0.0697481
$769$	3.51667	0.126814	0.0634072	−	0.997988i	$-0.479803\pi$
$769$	3.51667	0.126814	0.0634072	+	0.997988i	$0.479803\pi$
$770$	49.4637	1.78255
$771$	−0.581067	−0.0209266
$772$	77.5054	2.78948
$773$	36.9426	1.32873	0.664367	−	0.747406i	$-0.268701\pi$
$773$	36.9426	1.32873	0.664367	+	0.747406i	$0.268701\pi$
$774$	6.45617	0.232062
$775$	−6.23934	−0.224124
$776$	45.9119	1.64814
$777$	−1.54938	−0.0555837
$778$	9.37813	0.336222
$779$	13.2698	0.475440
$780$	−0.983811	−0.0352261
$781$	35.3294	1.26419
$782$	33.4819	1.19731
$783$	−0.241458	−0.00862902
$784$	0.105859	0.00378067
$785$	−4.01355	−0.143250
$786$	−5.50087	−0.196210
$787$	8.41629	0.300008	0.150004	−	0.988685i	$-0.452071\pi$
$787$	8.41629	0.300008	0.150004	+	0.988685i	$0.452071\pi$
$788$	34.8503	1.24149
$789$	3.53204	0.125744
$790$	−63.2911	−2.25180
$791$	−20.4489	−0.727081
$792$	−30.7428	−1.09240
$793$	−2.94956	−0.104742
$794$	70.9974	2.51960
$795$	−0.478985	−0.0169878
$796$	1.05680	0.0374573
$797$	−9.28111	−0.328754	−0.164377	−	0.986398i	$-0.552561\pi$
$797$	−9.28111	−0.328754	−0.164377	+	0.986398i	$0.552561\pi$
$798$	−2.02607	−0.0717220
$799$	−50.8009	−1.79721
$800$	5.65765	0.200028
$801$	20.7483	0.733106
$802$	−81.2719	−2.86981
$803$	28.8190	1.01700
$804$	−0.158990	−0.00560714
$805$	−10.5956	−0.373446
$806$	14.4854	0.510228
$807$	0.140207	0.00493552
$808$	50.5871	1.77965
$809$	51.7090	1.81799	0.908996	−	0.416805i	$-0.136850\pi$
$809$	51.7090	1.81799	0.908996	+	0.416805i	$0.136850\pi$
$810$	49.5043	1.73940
$811$	−16.6107	−0.583282	−0.291641	−	0.956528i	$-0.594201\pi$
$811$	−16.6107	−0.583282	−0.291641	+	0.956528i	$0.594201\pi$
$812$	−2.48245	−0.0871170
$813$	−0.680856	−0.0238786
$814$	43.8775	1.53791
$815$	15.7389	0.551311
$816$	−0.0831201	−0.00290979
$817$	−2.81194	−0.0983772
$818$	39.8662	1.39389
$819$	7.13289	0.249243
$820$	35.1779	1.22847
$821$	4.65721	0.162538	0.0812689	−	0.996692i	$-0.474103\pi$
$821$	4.65721	0.162538	0.0812689	+	0.996692i	$0.474103\pi$
$822$	−4.35833	−0.152014
$823$	−39.1474	−1.36459	−0.682297	−	0.731075i	$-0.739019\pi$
$823$	−39.1474	−1.36459	−0.682297	+	0.731075i	$0.739019\pi$
$824$	52.9628	1.84505
$825$	−0.455489	−0.0158581
$826$	−71.4420	−2.48578
$827$	−7.02734	−0.244364	−0.122182	−	0.992508i	$-0.538989\pi$
$827$	−7.02734	−0.244364	−0.122182	+	0.992508i	$0.538989\pi$
$828$	17.4024	0.604775
$829$	23.5874	0.819224	0.409612	−	0.912260i	$-0.365664\pi$
$829$	23.5874	0.819224	0.409612	+	0.912260i	$0.365664\pi$
$830$	−75.1697	−2.60918
$831$	2.50140	0.0867726
$832$	−12.9705	−0.449673
$833$	−10.4139	−0.360819
$834$	5.44873	0.188674
$835$	−2.53359	−0.0876784
$836$	35.3834	1.22376
$837$	4.74353	0.163960
$838$	−56.2105	−1.94176
$839$	−1.85195	−0.0639364	−0.0319682	−	0.999489i	$-0.510178\pi$
$839$	−1.85195	−0.0639364	−0.0319682	+	0.999489i	$0.510178\pi$
$840$	−2.03251	−0.0701284
$841$	−28.8958	−0.996407
$842$	37.4135	1.28935
$843$	3.53556	0.121771
$844$	−79.8475	−2.74847
$845$	−2.44620	−0.0841517
$846$	−42.8162	−1.47205
$847$	−6.49653	−0.223223
$848$	−0.128798	−0.00442295
$849$	−3.15966	−0.108439
$850$	−18.1773	−0.623478
$851$	−9.39899	−0.322193
$852$	−3.83627	−0.131429
$853$	−7.11912	−0.243754	−0.121877	−	0.992545i	$-0.538891\pi$
$853$	−7.11912	−0.243754	−0.121877	+	0.992545i	$0.538891\pi$
$854$	−16.1029	−0.551031
$855$	−21.6753	−0.741279
$856$	−0.150260	−0.00513577
$857$	−54.4918	−1.86141	−0.930703	−	0.365777i	$-0.880803\pi$
$857$	−54.4918	−1.86141	−0.930703	+	0.365777i	$0.880803\pi$
$858$	1.05748	0.0361016
$859$	36.9881	1.26202	0.631009	−	0.775776i	$-0.282641\pi$
$859$	36.9881	1.26202	0.631009	+	0.775776i	$0.282641\pi$
$860$	−7.45436	−0.254192
$861$	1.33519	0.0455033
$862$	52.1800	1.77726
$863$	36.5439	1.24397	0.621985	−	0.783029i	$-0.286327\pi$
$863$	36.5439	1.24397	0.621985	+	0.783029i	$0.286327\pi$
$864$	−4.30130	−0.146333
$865$	40.7396	1.38519
$866$	5.18168	0.176081
$867$	6.05206	0.205539
$868$	48.7686	1.65531
$869$	41.9530	1.42316
$870$	0.225450	0.00764348
$871$	−0.395320	−0.0133949
$872$	−16.5246	−0.559593
$873$	49.2647	1.66736
$874$	−12.2907	−0.415740
$875$	−23.4806	−0.793790
$876$	−3.12933	−0.105730
$877$	18.4683	0.623629	0.311814	−	0.950143i	$-0.399063\pi$
$877$	18.4683	0.623629	0.311814	+	0.950143i	$0.399063\pi$
$878$	−66.6119	−2.24804
$879$	0.112975	0.00381056
$880$	−0.744913	−0.0251110
$881$	−19.8048	−0.667242	−0.333621	−	0.942707i	$-0.608271\pi$
$881$	−19.8048	−0.667242	−0.333621	+	0.942707i	$0.608271\pi$
$882$	−8.77706	−0.295539
$883$	57.2378	1.92621	0.963103	−	0.269134i	$-0.0867374\pi$
$883$	57.2378	1.92621	0.963103	+	0.269134i	$0.0867374\pi$
$884$	26.0247	0.875304
$885$	4.00115	0.134497
$886$	−68.4723	−2.30037
$887$	−38.3976	−1.28927	−0.644633	−	0.764492i	$-0.722990\pi$
$887$	−38.3976	−1.28927	−0.644633	+	0.764492i	$0.722990\pi$
$888$	−1.80297	−0.0605038
$889$	−13.3476	−0.447665
$890$	−38.8469	−1.30215
$891$	−32.8143	−1.09932
$892$	5.78190	0.193592
$893$	18.6483	0.624041
$894$	−5.52629	−0.184827
$895$	−6.25566	−0.209104
$896$	−43.3243	−1.44736
$897$	−0.226522	−0.00756333
$898$	67.9099	2.26618
$899$	−2.04707	−0.0682735
$900$	−9.44777	−0.314926
$901$	12.6705	0.422117
$902$	−37.8119	−1.25900
$903$	−0.282934	−0.00941545
$904$	−23.7959	−0.791440
$905$	0.678285	0.0225469
$906$	−0.217961	−0.00724125
$907$	−16.6063	−0.551403	−0.275702	−	0.961243i	$-0.588910\pi$
$907$	−16.6063	−0.551403	−0.275702	+	0.961243i	$0.588910\pi$
$908$	−33.0727	−1.09756
$909$	54.2813	1.80040
$910$	−13.3548	−0.442709
$911$	−38.4781	−1.27484	−0.637418	−	0.770518i	$-0.719998\pi$
$911$	−38.4781	−1.27484	−0.637418	+	0.770518i	$0.719998\pi$
$912$	0.0305122	0.00101036
$913$	49.8268	1.64903
$914$	−18.1571	−0.600583
$915$	0.901853	0.0298144
$916$	−91.2205	−3.01401
$917$	−46.0490	−1.52067
$918$	13.8195	0.456113
$919$	32.2937	1.06527	0.532636	−	0.846345i	$-0.321202\pi$
$919$	32.2937	1.06527	0.532636	+	0.846345i	$0.321202\pi$
$920$	−12.3298	−0.406502
$921$	−1.24833	−0.0411338
$922$	−23.7559	−0.782358
$923$	−9.53870	−0.313970
$924$	3.56024	0.117123
$925$	5.10272	0.167776
$926$	2.28421	0.0750637
$927$	56.8305	1.86656
$928$	1.85622	0.0609334
$929$	−29.2249	−0.958838	−0.479419	−	0.877586i	$-0.659153\pi$
$929$	−29.2249	−0.958838	−0.479419	+	0.877586i	$0.659153\pi$
$930$	−4.42905	−0.145234
$931$	3.82278	0.125286
$932$	61.0950	2.00123
$933$	2.67946	0.0877216
$934$	14.6831	0.480447
$935$	73.2809	2.39654
$936$	8.30035	0.271306
$937$	2.20764	0.0721205	0.0360603	−	0.999350i	$-0.488519\pi$
$937$	2.20764	0.0721205	0.0360603	+	0.999350i	$0.488519\pi$
$938$	−2.15822	−0.0704685
$939$	−2.36099	−0.0770481
$940$	49.4360	1.61243
$941$	28.2102	0.919626	0.459813	−	0.888016i	$-0.347916\pi$
$941$	28.2102	0.919626	0.459813	+	0.888016i	$0.347916\pi$
$942$	−0.468447	−0.0152628
$943$	8.09968	0.263762
$944$	1.07590	0.0350177
$945$	−4.37330	−0.142263
$946$	8.01252	0.260509
$947$	36.6309	1.19034	0.595172	−	0.803599i	$-0.297084\pi$
$947$	36.6309	1.19034	0.595172	+	0.803599i	$0.297084\pi$
$948$	−4.55550	−0.147956
$949$	−7.78093	−0.252580
$950$	6.67264	0.216489
$951$	−2.38192	−0.0772389
$952$	53.7659	1.74256
$953$	−18.3311	−0.593803	−0.296902	−	0.954908i	$-0.595953\pi$
$953$	−18.3311	−0.593803	−0.296902	+	0.954908i	$0.595953\pi$
$954$	10.6790	0.345747
$955$	49.8232	1.61224
$956$	60.9024	1.96972
$957$	−0.149441	−0.00483075
$958$	−98.3871	−3.17874
$959$	−36.4846	−1.17815
$960$	3.96585	0.127997
$961$	9.21532	0.297268
$962$	−11.8466	−0.381950
$963$	−0.161233	−0.00519565
$964$	73.0680	2.35336
$965$	−58.9238	−1.89682
$966$	−1.23668	−0.0397895
$967$	29.8523	0.959987	0.479993	−	0.877272i	$-0.340639\pi$
$967$	29.8523	0.959987	0.479993	+	0.877272i	$0.340639\pi$
$968$	−7.55984	−0.242983
$969$	−3.00164	−0.0964266
$970$	−92.2380	−2.96158
$971$	−42.6522	−1.36878	−0.684388	−	0.729118i	$-0.739930\pi$
$971$	−42.6522	−1.36878	−0.684388	+	0.729118i	$0.739930\pi$
$972$	10.7836	0.345883
$973$	45.6125	1.46227
$974$	40.4310	1.29549
$975$	0.122979	0.00393847
$976$	0.242507	0.00776246
$977$	−15.7677	−0.504453	−0.252227	−	0.967668i	$-0.581163\pi$
$977$	−15.7677	−0.504453	−0.252227	+	0.967668i	$0.581163\pi$
$978$	1.83699	0.0587405
$979$	25.7500	0.822973
$980$	10.1341	0.323721
$981$	−17.7313	−0.566118
$982$	−2.79622	−0.0892310
$983$	30.1040	0.960168	0.480084	−	0.877223i	$-0.340606\pi$
$983$	30.1040	0.960168	0.480084	+	0.877223i	$0.340606\pi$
$984$	1.55373	0.0495311
$985$	−26.4951	−0.844204
$986$	−5.96381	−0.189926
$987$	1.87637	0.0597255
$988$	−9.55328	−0.303930
$989$	−1.71636	−0.0545770
$990$	61.7630	1.96296
$991$	56.4717	1.79388	0.896941	−	0.442150i	$-0.145784\pi$
$991$	56.4717	1.79388	0.896941	+	0.442150i	$0.145784\pi$
$992$	−36.4661	−1.15780
$993$	−3.36919	−0.106918
$994$	−52.0759	−1.65175
$995$	−0.803437	−0.0254707
$996$	−5.41048	−0.171438
$997$	16.1307	0.510865	0.255433	−	0.966827i	$-0.417782\pi$
$997$	16.1307	0.510865	0.255433	+	0.966827i	$0.417782\pi$
$998$	13.5518	0.428976
$999$	−3.87940	−0.122739

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.e.1.18	✓	130

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.e.1.18	✓	130	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)

\(f(q)\)	\(=\)	\(q-2.28421 q^{2} +0.124993 q^{3} +3.21761 q^{4} -2.44620 q^{5} -0.285511 q^{6} -2.39008 q^{7} -2.78127 q^{8} -2.98438 q^{9} +O(q^{10})\)	\(q-2.28421 q^{2} +0.124993 q^{3} +3.21761 q^{4} -2.44620 q^{5} -0.285511 q^{6} -2.39008 q^{7} -2.78127 q^{8} -2.98438 q^{9} +5.58762 q^{10} -3.70380 q^{11} +0.402180 q^{12} +1.00000 q^{13} +5.45943 q^{14} -0.305759 q^{15} -0.0822180 q^{16} +8.08820 q^{17} +6.81694 q^{18} -2.96906 q^{19} -7.87090 q^{20} -0.298744 q^{21} +8.46025 q^{22} -1.81227 q^{23} -0.347640 q^{24} +0.983882 q^{25} -2.28421 q^{26} -0.748008 q^{27} -7.69033 q^{28} +0.322802 q^{29} +0.698416 q^{30} -6.34155 q^{31} +5.75034 q^{32} -0.462951 q^{33} -18.4751 q^{34} +5.84660 q^{35} -9.60255 q^{36} +5.18632 q^{37} +6.78196 q^{38} +0.124993 q^{39} +6.80353 q^{40} -4.46936 q^{41} +0.682393 q^{42} +0.947078 q^{43} -11.9174 q^{44} +7.30037 q^{45} +4.13960 q^{46} -6.28086 q^{47} -0.0102767 q^{48} -1.28754 q^{49} -2.24739 q^{50} +1.01097 q^{51} +3.21761 q^{52} +1.56655 q^{53} +1.70861 q^{54} +9.06022 q^{55} +6.64744 q^{56} -0.371113 q^{57} -0.737347 q^{58} -13.0860 q^{59} -0.983811 q^{60} -2.94956 q^{61} +14.4854 q^{62} +7.13289 q^{63} -12.9705 q^{64} -2.44620 q^{65} +1.05748 q^{66} -0.395320 q^{67} +26.0247 q^{68} -0.226522 q^{69} -13.3548 q^{70} -9.53870 q^{71} +8.30035 q^{72} -7.78093 q^{73} -11.8466 q^{74} +0.122979 q^{75} -9.55328 q^{76} +8.85236 q^{77} -0.285511 q^{78} -11.3270 q^{79} +0.201121 q^{80} +8.85963 q^{81} +10.2090 q^{82} -13.4529 q^{83} -0.961240 q^{84} -19.7853 q^{85} -2.16332 q^{86} +0.0403481 q^{87} +10.3013 q^{88} -6.95232 q^{89} -16.6756 q^{90} -2.39008 q^{91} -5.83116 q^{92} -0.792653 q^{93} +14.3468 q^{94} +7.26291 q^{95} +0.718755 q^{96} -16.5075 q^{97} +2.94100 q^{98} +11.0535 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 130 q + 10 q^{2} + 11 q^{3} + 146 q^{4} + 40 q^{5} + 4 q^{6} + 8 q^{7} + 24 q^{8} + 181 q^{9}+O(q^{10}) \) 130 * q + 10 * q^2 + 11 * q^3 + 146 * q^4 + 40 * q^5 + 4 * q^6 + 8 * q^7 + 24 * q^8 + 181 * q^9	\( 130 q + 10 q^{2} + 11 q^{3} + 146 q^{4} + 40 q^{5} + 4 q^{6} + 8 q^{7} + 24 q^{8} + 181 q^{9} + 5 q^{10} + 43 q^{11} + 28 q^{12} + 130 q^{13} + 47 q^{14} + 29 q^{15} + 170 q^{16} + 85 q^{17} + 20 q^{18} + 3 q^{19} + 73 q^{20} + 62 q^{21} + 12 q^{22} + 62 q^{23} - 5 q^{24} + 178 q^{25} + 10 q^{26} + 35 q^{27} - q^{28} + 134 q^{29} + 24 q^{30} + 14 q^{31} + 48 q^{32} + 4 q^{33} + 4 q^{34} + 50 q^{35} + 244 q^{36} + 32 q^{37} + 76 q^{38} + 11 q^{39} - 6 q^{40} + 48 q^{41} + 9 q^{42} + 34 q^{43} + 123 q^{44} + 115 q^{45} + 5 q^{46} + 25 q^{47} + 35 q^{48} + 210 q^{49} + 24 q^{50} + 20 q^{51} + 146 q^{52} + 193 q^{53} - 39 q^{54} + 32 q^{55} + 122 q^{56} + 7 q^{57} - 4 q^{58} + 50 q^{59} + 42 q^{60} + 57 q^{61} + 51 q^{62} + 8 q^{63} + 172 q^{64} + 40 q^{65} - 4 q^{66} + 21 q^{67} + 132 q^{68} + 92 q^{69} - 46 q^{70} + 58 q^{71} - 26 q^{72} + 15 q^{73} + 120 q^{74} + 23 q^{75} - 65 q^{76} + 192 q^{77} + 4 q^{78} + 32 q^{79} + 66 q^{80} + 326 q^{81} + 11 q^{82} + 33 q^{83} + 5 q^{84} + 43 q^{85} + 105 q^{86} + 31 q^{87} - 17 q^{88} + 84 q^{89} - 73 q^{90} + 8 q^{91} + 161 q^{92} + 52 q^{93} + 4 q^{94} + 59 q^{95} - 77 q^{96} + 9 q^{97} - 61 q^{98} + 100 q^{99}+O(q^{100}) \) 130 * q + 10 * q^2 + 11 * q^3 + 146 * q^4 + 40 * q^5 + 4 * q^6 + 8 * q^7 + 24 * q^8 + 181 * q^9 + 5 * q^10 + 43 * q^11 + 28 * q^12 + 130 * q^13 + 47 * q^14 + 29 * q^15 + 170 * q^16 + 85 * q^17 + 20 * q^18 + 3 * q^19 + 73 * q^20 + 62 * q^21 + 12 * q^22 + 62 * q^23 - 5 * q^24 + 178 * q^25 + 10 * q^26 + 35 * q^27 - q^28 + 134 * q^29 + 24 * q^30 + 14 * q^31 + 48 * q^32 + 4 * q^33 + 4 * q^34 + 50 * q^35 + 244 * q^36 + 32 * q^37 + 76 * q^38 + 11 * q^39 - 6 * q^40 + 48 * q^41 + 9 * q^42 + 34 * q^43 + 123 * q^44 + 115 * q^45 + 5 * q^46 + 25 * q^47 + 35 * q^48 + 210 * q^49 + 24 * q^50 + 20 * q^51 + 146 * q^52 + 193 * q^53 - 39 * q^54 + 32 * q^55 + 122 * q^56 + 7 * q^57 - 4 * q^58 + 50 * q^59 + 42 * q^60 + 57 * q^61 + 51 * q^62 + 8 * q^63 + 172 * q^64 + 40 * q^65 - 4 * q^66 + 21 * q^67 + 132 * q^68 + 92 * q^69 - 46 * q^70 + 58 * q^71 - 26 * q^72 + 15 * q^73 + 120 * q^74 + 23 * q^75 - 65 * q^76 + 192 * q^77 + 4 * q^78 + 32 * q^79 + 66 * q^80 + 326 * q^81 + 11 * q^82 + 33 * q^83 + 5 * q^84 + 43 * q^85 + 105 * q^86 + 31 * q^87 - 17 * q^88 + 84 * q^89 - 73 * q^90 + 8 * q^91 + 161 * q^92 + 52 * q^93 + 4 * q^94 + 59 * q^95 - 77 * q^96 + 9 * q^97 - 61 * q^98 + 100 * q^99

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