LMFDB - Embedded newform 6019.2.a.b.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:	$1$
Dimension:	$101$
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)

$f(q)$	$=$	$q-2.04146 q^{2} +1.76541 q^{3} +2.16756 q^{4} -1.03624 q^{5} -3.60401 q^{6} -3.97509 q^{7} -0.342069 q^{8} +0.116656 q^{9} +O(q^{10})$	\(q-2.04146 q^{2} +1.76541 q^{3} +2.16756 q^{4} -1.03624 q^{5} -3.60401 q^{6} -3.97509 q^{7} -0.342069 q^{8} +0.116656 q^{9} +2.11544 q^{10} -0.912754 q^{11} +3.82662 q^{12} +1.00000 q^{13} +8.11498 q^{14} -1.82938 q^{15} -3.63680 q^{16} -5.97456 q^{17} -0.238149 q^{18} +3.29567 q^{19} -2.24610 q^{20} -7.01764 q^{21} +1.86335 q^{22} +6.24482 q^{23} -0.603890 q^{24} -3.92621 q^{25} -2.04146 q^{26} -5.09027 q^{27} -8.61624 q^{28} +10.1035 q^{29} +3.73460 q^{30} +0.671669 q^{31} +8.10852 q^{32} -1.61138 q^{33} +12.1968 q^{34} +4.11913 q^{35} +0.252859 q^{36} +3.95311 q^{37} -6.72797 q^{38} +1.76541 q^{39} +0.354464 q^{40} +12.2818 q^{41} +14.3262 q^{42} -1.94758 q^{43} -1.97845 q^{44} -0.120883 q^{45} -12.7486 q^{46} +6.19716 q^{47} -6.42043 q^{48} +8.80131 q^{49} +8.01521 q^{50} -10.5475 q^{51} +2.16756 q^{52} -3.69495 q^{53} +10.3916 q^{54} +0.945829 q^{55} +1.35975 q^{56} +5.81819 q^{57} -20.6258 q^{58} +10.3678 q^{59} -3.96529 q^{60} -10.5611 q^{61} -1.37119 q^{62} -0.463718 q^{63} -9.27963 q^{64} -1.03624 q^{65} +3.28957 q^{66} +2.86882 q^{67} -12.9502 q^{68} +11.0246 q^{69} -8.40904 q^{70} -14.6843 q^{71} -0.0399044 q^{72} +12.6841 q^{73} -8.07011 q^{74} -6.93136 q^{75} +7.14356 q^{76} +3.62828 q^{77} -3.60401 q^{78} +4.16749 q^{79} +3.76859 q^{80} -9.33636 q^{81} -25.0727 q^{82} -13.1858 q^{83} -15.2112 q^{84} +6.19106 q^{85} +3.97590 q^{86} +17.8367 q^{87} +0.312224 q^{88} -4.31331 q^{89} +0.246778 q^{90} -3.97509 q^{91} +13.5360 q^{92} +1.18577 q^{93} -12.6513 q^{94} -3.41509 q^{95} +14.3148 q^{96} +4.95458 q^{97} -17.9675 q^{98} -0.106478 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9}+O(q^{10}) $ 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9	\( 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9} - 19 q^{10} - 42 q^{11} - 28 q^{12} + 101 q^{13} - 45 q^{14} - 15 q^{15} + 48 q^{16} - 83 q^{17} - 4 q^{18} - 18 q^{19} - 51 q^{20} - 50 q^{21} - 20 q^{22} - 64 q^{23} - 23 q^{24} + 46 q^{25} - 8 q^{26} - 37 q^{27} - 11 q^{28} - 117 q^{29} - 28 q^{30} - 10 q^{31} - 36 q^{32} - 20 q^{33} - 10 q^{34} - 53 q^{35} - 16 q^{36} - 27 q^{37} - 68 q^{38} - 13 q^{39} - 42 q^{40} - 60 q^{41} - 31 q^{42} - 16 q^{43} - 89 q^{44} - 56 q^{45} + 5 q^{46} - 23 q^{47} - 37 q^{48} + 48 q^{49} - 30 q^{50} - 68 q^{51} + 86 q^{52} - 189 q^{53} - 23 q^{54} + 3 q^{55} - 106 q^{56} - 25 q^{57} - 82 q^{59} + 6 q^{60} - 68 q^{61} - 57 q^{62} + 3 q^{63} - 2 q^{64} - 43 q^{65} - 40 q^{66} - 13 q^{67} - 138 q^{68} - 92 q^{69} + 18 q^{70} - 39 q^{71} - 20 q^{72} + 19 q^{73} - 88 q^{74} - 21 q^{75} - 53 q^{76} - 147 q^{77} - 10 q^{78} - 19 q^{79} - 104 q^{80} - 55 q^{81} + 27 q^{82} - 49 q^{83} - 59 q^{84} - 27 q^{85} - 99 q^{86} - 33 q^{87} - 41 q^{88} - 70 q^{89} - 49 q^{90} - q^{91} - 111 q^{92} - 84 q^{93} + 4 q^{94} - 82 q^{95} - 7 q^{96} + 25 q^{97} - 37 q^{98} - 41 q^{99}+O(q^{100}) \) 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9 - 19 * q^10 - 42 * q^11 - 28 * q^12 + 101 * q^13 - 45 * q^14 - 15 * q^15 + 48 * q^16 - 83 * q^17 - 4 * q^18 - 18 * q^19 - 51 * q^20 - 50 * q^21 - 20 * q^22 - 64 * q^23 - 23 * q^24 + 46 * q^25 - 8 * q^26 - 37 * q^27 - 11 * q^28 - 117 * q^29 - 28 * q^30 - 10 * q^31 - 36 * q^32 - 20 * q^33 - 10 * q^34 - 53 * q^35 - 16 * q^36 - 27 * q^37 - 68 * q^38 - 13 * q^39 - 42 * q^40 - 60 * q^41 - 31 * q^42 - 16 * q^43 - 89 * q^44 - 56 * q^45 + 5 * q^46 - 23 * q^47 - 37 * q^48 + 48 * q^49 - 30 * q^50 - 68 * q^51 + 86 * q^52 - 189 * q^53 - 23 * q^54 + 3 * q^55 - 106 * q^56 - 25 * q^57 - 82 * q^59 + 6 * q^60 - 68 * q^61 - 57 * q^62 + 3 * q^63 - 2 * q^64 - 43 * q^65 - 40 * q^66 - 13 * q^67 - 138 * q^68 - 92 * q^69 + 18 * q^70 - 39 * q^71 - 20 * q^72 + 19 * q^73 - 88 * q^74 - 21 * q^75 - 53 * q^76 - 147 * q^77 - 10 * q^78 - 19 * q^79 - 104 * q^80 - 55 * q^81 + 27 * q^82 - 49 * q^83 - 59 * q^84 - 27 * q^85 - 99 * q^86 - 33 * q^87 - 41 * q^88 - 70 * q^89 - 49 * q^90 - q^91 - 111 * q^92 - 84 * q^93 + 4 * q^94 - 82 * q^95 - 7 * q^96 + 25 * q^97 - 37 * q^98 - 41 * 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 $

$2$	−2.04146	−1.44353	−0.721765	−	0.692138i	$-0.756669\pi$
$2$	−2.04146	−1.44353	−0.721765	+	0.692138i	$0.756669\pi$
$3$	1.76541	1.01926	0.509629	−	0.860394i	$-0.329783\pi$
$3$	1.76541	1.01926	0.509629	+	0.860394i	$0.329783\pi$
$4$	2.16756	1.08378
$5$	−1.03624	−0.463419	−0.231709	−	0.972785i	$-0.574432\pi$
$5$	−1.03624	−0.463419	−0.231709	+	0.972785i	$0.574432\pi$
$6$	−3.60401	−1.47133
$7$	−3.97509	−1.50244	−0.751221	−	0.660051i	$-0.770535\pi$
$7$	−3.97509	−1.50244	−0.751221	+	0.660051i	$0.770535\pi$
$8$	−0.342069	−0.120939
$9$	0.116656	0.0388854
$10$	2.11544	0.668959
$11$	−0.912754	−0.275206	−0.137603	−	0.990487i	$-0.543940\pi$
$11$	−0.912754	−0.275206	−0.137603	+	0.990487i	$0.543940\pi$
$12$	3.82662	1.10465
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	8.11498	2.16882
$15$	−1.82938	−0.472343
$16$	−3.63680	−0.909201
$17$	−5.97456	−1.44904	−0.724522	−	0.689251i	$-0.757940\pi$
$17$	−5.97456	−1.44904	−0.724522	+	0.689251i	$0.757940\pi$
$18$	−0.238149	−0.0561322
$19$	3.29567	0.756078	0.378039	−	0.925790i	$-0.376599\pi$
$19$	3.29567	0.756078	0.378039	+	0.925790i	$0.376599\pi$
$20$	−2.24610	−0.502244
$21$	−7.01764	−1.53137
$22$	1.86335	0.397268
$23$	6.24482	1.30214	0.651068	−	0.759020i	$-0.274321\pi$
$23$	6.24482	1.30214	0.651068	+	0.759020i	$0.274321\pi$
$24$	−0.603890	−0.123268
$25$	−3.92621	−0.785243
$26$	−2.04146	−0.400363
$27$	−5.09027	−0.979623
$28$	−8.61624	−1.62832
$29$	10.1035	1.87616	0.938082	−	0.346413i	$-0.112600\pi$
$29$	10.1035	1.87616	0.938082	+	0.346413i	$0.112600\pi$
$30$	3.73460	0.681842
$31$	0.671669	0.120635	0.0603177	−	0.998179i	$-0.480789\pi$
$31$	0.671669	0.120635	0.0603177	+	0.998179i	$0.480789\pi$
$32$	8.10852	1.43340
$33$	−1.61138	−0.280505
$34$	12.1968	2.09174
$35$	4.11913	0.696260
$36$	0.252859	0.0421432
$37$	3.95311	0.649887	0.324943	−	0.945733i	$-0.394655\pi$
$37$	3.95311	0.649887	0.324943	+	0.945733i	$0.394655\pi$
$38$	−6.72797	−1.09142
$39$	1.76541	0.282691
$40$	0.354464	0.0560456
$41$	12.2818	1.91809	0.959045	−	0.283254i	$-0.0914141\pi$
$41$	12.2818	1.91809	0.959045	+	0.283254i	$0.0914141\pi$
$42$	14.3262	2.21059
$43$	−1.94758	−0.297003	−0.148501	−	0.988912i	$-0.547445\pi$
$43$	−1.94758	−0.297003	−0.148501	+	0.988912i	$0.547445\pi$
$44$	−1.97845	−0.298263
$45$	−0.120883	−0.0180202
$46$	−12.7486	−1.87967
$47$	6.19716	0.903949	0.451975	−	0.892031i	$-0.350720\pi$
$47$	6.19716	0.903949	0.451975	+	0.892031i	$0.350720\pi$
$48$	−6.42043	−0.926709
$49$	8.80131	1.25733
$50$	8.01521	1.13352
$51$	−10.5475	−1.47695
$52$	2.16756	0.300587
$53$	−3.69495	−0.507540	−0.253770	−	0.967265i	$-0.581671\pi$
$53$	−3.69495	−0.507540	−0.253770	+	0.967265i	$0.581671\pi$
$54$	10.3916	1.41412
$55$	0.945829	0.127536
$56$	1.35975	0.181704
$57$	5.81819	0.770638
$58$	−20.6258	−2.70830
$59$	10.3678	1.34977	0.674887	−	0.737921i	$-0.264192\pi$
$59$	10.3678	1.34977	0.674887	+	0.737921i	$0.264192\pi$
$60$	−3.96529	−0.511916
$61$	−10.5611	−1.35221	−0.676106	−	0.736804i	$-0.736334\pi$
$61$	−10.5611	−1.35221	−0.676106	+	0.736804i	$0.736334\pi$
$62$	−1.37119	−0.174141
$63$	−0.463718	−0.0584230
$64$	−9.27963	−1.15995
$65$	−1.03624	−0.128529
$66$	3.28957	0.404918
$67$	2.86882	0.350482	0.175241	−	0.984526i	$-0.443930\pi$
$67$	2.86882	0.350482	0.175241	+	0.984526i	$0.443930\pi$
$68$	−12.9502	−1.57045
$69$	11.0246	1.32721
$70$	−8.40904	−1.00507
$71$	−14.6843	−1.74271	−0.871353	−	0.490657i	$-0.836757\pi$
$71$	−14.6843	−1.74271	−0.871353	+	0.490657i	$0.836757\pi$
$72$	−0.0399044	−0.00470278
$73$	12.6841	1.48456	0.742279	−	0.670091i	$-0.233745\pi$
$73$	12.6841	1.48456	0.742279	+	0.670091i	$0.233745\pi$
$74$	−8.07011	−0.938132
$75$	−6.93136	−0.800365
$76$	7.14356	0.819422
$77$	3.62828	0.413481
$78$	−3.60401	−0.408073
$79$	4.16749	0.468879	0.234440	−	0.972131i	$-0.424674\pi$
$79$	4.16749	0.468879	0.234440	+	0.972131i	$0.424674\pi$
$80$	3.76859	0.421341
$81$	−9.33636	−1.03737
$82$	−25.0727	−2.76882
$83$	−13.1858	−1.44733	−0.723664	−	0.690153i	$-0.757543\pi$
$83$	−13.1858	−1.44733	−0.723664	+	0.690153i	$0.757543\pi$
$84$	−15.2112	−1.65967
$85$	6.19106	0.671515
$86$	3.97590	0.428732
$87$	17.8367	1.91229
$88$	0.312224	0.0332832
$89$	−4.31331	−0.457210	−0.228605	−	0.973519i	$-0.573416\pi$
$89$	−4.31331	−0.457210	−0.228605	+	0.973519i	$0.573416\pi$
$90$	0.246778	0.0260127
$91$	−3.97509	−0.416702
$92$	13.5360	1.41123
$93$	1.18577	0.122958
$94$	−12.6513	−1.30488
$95$	−3.41509	−0.350381
$96$	14.3148	1.46100
$97$	4.95458	0.503062	0.251531	−	0.967849i	$-0.419066\pi$
$97$	4.95458	0.503062	0.251531	+	0.967849i	$0.419066\pi$
$98$	−17.9675	−1.81499
$99$	−0.106478	−0.0107015
$100$	−8.51031	−0.851031
$101$	−14.0950	−1.40251	−0.701255	−	0.712911i	$-0.747376\pi$
$101$	−14.0950	−1.40251	−0.701255	+	0.712911i	$0.747376\pi$
$102$	21.5324	2.13202
$103$	15.5947	1.53659	0.768293	−	0.640098i	$-0.221106\pi$
$103$	15.5947	1.53659	0.768293	+	0.640098i	$0.221106\pi$
$104$	−0.342069	−0.0335426
$105$	7.27193	0.709668
$106$	7.54310	0.732650
$107$	−16.0983	−1.55629	−0.778143	−	0.628088i	$-0.783838\pi$
$107$	−16.0983	−1.55629	−0.778143	+	0.628088i	$0.783838\pi$
$108$	−11.0335	−1.06170
$109$	−5.22470	−0.500435	−0.250218	−	0.968190i	$-0.580502\pi$
$109$	−5.22470	−0.500435	−0.250218	+	0.968190i	$0.580502\pi$
$110$	−1.93087	−0.184101
$111$	6.97884	0.662402
$112$	14.4566	1.36602
$113$	−5.19041	−0.488273	−0.244136	−	0.969741i	$-0.578504\pi$
$113$	−5.19041	−0.488273	−0.244136	+	0.969741i	$0.578504\pi$
$114$	−11.8776	−1.11244
$115$	−6.47111	−0.603434
$116$	21.8999	2.03335
$117$	0.116656	0.0107849
$118$	−21.1655	−1.94844
$119$	23.7494	2.17710
$120$	0.625772	0.0571249
$121$	−10.1669	−0.924262
$122$	21.5601	1.95196
$123$	21.6823	1.95503
$124$	1.45588	0.130742
$125$	9.24967	0.827315
$126$	0.946662	0.0843354
$127$	19.1451	1.69885	0.849427	−	0.527706i	$-0.176948\pi$
$127$	19.1451	1.69885	0.849427	+	0.527706i	$0.176948\pi$
$128$	2.72694	0.241030
$129$	−3.43826	−0.302722
$130$	2.11544	0.185536
$131$	5.48321	0.479071	0.239535	−	0.970888i	$-0.423005\pi$
$131$	5.48321	0.479071	0.239535	+	0.970888i	$0.423005\pi$
$132$	−3.49277	−0.304006
$133$	−13.1006	−1.13596
$134$	−5.85657	−0.505931
$135$	5.27472	0.453976
$136$	2.04371	0.175247
$137$	2.63878	0.225446	0.112723	−	0.993626i	$-0.464043\pi$
$137$	2.63878	0.225446	0.112723	+	0.993626i	$0.464043\pi$
$138$	−22.5064	−1.91587
$139$	−14.8344	−1.25824	−0.629120	−	0.777308i	$-0.716585\pi$
$139$	−14.8344	−1.25824	−0.629120	+	0.777308i	$0.716585\pi$
$140$	8.92846	0.754593
$141$	10.9405	0.921357
$142$	29.9774	2.51565
$143$	−0.912754	−0.0763283
$144$	−0.424255	−0.0353546
$145$	−10.4696	−0.869450
$146$	−25.8940	−2.14300
$147$	15.5379	1.28154
$148$	8.56860	0.704335
$149$	−20.1221	−1.64847	−0.824235	−	0.566248i	$-0.808394\pi$
$149$	−20.1221	−1.64847	−0.824235	+	0.566248i	$0.808394\pi$
$150$	14.1501	1.15535
$151$	−10.8139	−0.880023	−0.440012	−	0.897992i	$-0.645026\pi$
$151$	−10.8139	−0.880023	−0.440012	+	0.897992i	$0.645026\pi$
$152$	−1.12734	−0.0914397
$153$	−0.696969	−0.0563466
$154$	−7.40698	−0.596872
$155$	−0.696008	−0.0559047
$156$	3.82662	0.306375
$157$	−3.63920	−0.290440	−0.145220	−	0.989399i	$-0.546389\pi$
$157$	−3.63920	−0.290440	−0.145220	+	0.989399i	$0.546389\pi$
$158$	−8.50776	−0.676841
$159$	−6.52309	−0.517314
$160$	−8.40235	−0.664264
$161$	−24.8237	−1.95638
$162$	19.0598	1.49748
$163$	−21.1354	−1.65545	−0.827725	−	0.561134i	$-0.810365\pi$
$163$	−21.1354	−1.65545	−0.827725	+	0.561134i	$0.810365\pi$
$164$	26.6215	2.07879
$165$	1.66977	0.129992
$166$	26.9182	2.08926
$167$	10.8984	0.843343	0.421672	−	0.906749i	$-0.361444\pi$
$167$	10.8984	0.843343	0.421672	+	0.906749i	$0.361444\pi$
$168$	2.40051	0.185204
$169$	1.00000	0.0769231
$170$	−12.6388	−0.969352
$171$	0.384460	0.0294004
$172$	−4.22149	−0.321886
$173$	2.93708	0.223302	0.111651	−	0.993747i	$-0.464386\pi$
$173$	2.93708	0.223302	0.111651	+	0.993747i	$0.464386\pi$
$174$	−36.4129	−2.76046
$175$	15.6070	1.17978
$176$	3.31951	0.250217
$177$	18.3034	1.37577
$178$	8.80545	0.659997
$179$	−19.7389	−1.47536	−0.737678	−	0.675152i	$-0.764078\pi$
$179$	−19.7389	−1.47536	−0.737678	+	0.675152i	$0.764078\pi$
$180$	−0.262022	−0.0195300
$181$	−11.8198	−0.878560	−0.439280	−	0.898350i	$-0.644766\pi$
$181$	−11.8198	−0.878560	−0.439280	+	0.898350i	$0.644766\pi$
$182$	8.11498	0.601522
$183$	−18.6447	−1.37825
$184$	−2.13616	−0.157480
$185$	−4.09635	−0.301170
$186$	−2.42070	−0.177494
$187$	5.45331	0.398785
$188$	13.4327	0.979682
$189$	20.2343	1.47183
$190$	6.97177	0.505785
$191$	−10.1576	−0.734978	−0.367489	−	0.930028i	$-0.619782\pi$
$191$	−10.1576	−0.734978	−0.367489	+	0.930028i	$0.619782\pi$
$192$	−16.3823	−1.18229
$193$	23.4025	1.68455	0.842273	−	0.539051i	$-0.181217\pi$
$193$	23.4025	1.68455	0.842273	+	0.539051i	$0.181217\pi$
$194$	−10.1146	−0.726185
$195$	−1.82938	−0.131004
$196$	19.0774	1.36267
$197$	−8.30669	−0.591827	−0.295914	−	0.955215i	$-0.595624\pi$
$197$	−8.30669	−0.591827	−0.295914	+	0.955215i	$0.595624\pi$
$198$	0.217371	0.0154479
$199$	−7.51419	−0.532667	−0.266333	−	0.963881i	$-0.585812\pi$
$199$	−7.51419	−0.532667	−0.266333	+	0.963881i	$0.585812\pi$
$200$	1.34303	0.0949669
$201$	5.06462	0.357231
$202$	28.7745	2.02457
$203$	−40.1621	−2.81883
$204$	−22.8624	−1.60069
$205$	−12.7268	−0.888879
$206$	−31.8359	−2.21811
$207$	0.728496	0.0506340
$208$	−3.63680	−0.252167
$209$	−3.00813	−0.208077
$210$	−14.8454	−1.02443
$211$	−10.5270	−0.724709	−0.362355	−	0.932040i	$-0.618027\pi$
$211$	−10.5270	−0.724709	−0.362355	+	0.932040i	$0.618027\pi$
$212$	−8.00903	−0.550062
$213$	−25.9237	−1.77627
$214$	32.8641	2.24655
$215$	2.01815	0.137637
$216$	1.74122	0.118475
$217$	−2.66994	−0.181248
$218$	10.6660	0.722394
$219$	22.3925	1.51315
$220$	2.05014	0.138221
$221$	−5.97456	−0.401893
$222$	−14.2470	−0.956197
$223$	15.0459	1.00755	0.503774	−	0.863836i	$-0.331944\pi$
$223$	15.0459	1.00755	0.503774	+	0.863836i	$0.331944\pi$
$224$	−32.2321	−2.15360
$225$	−0.458017	−0.0305345
$226$	10.5960	0.704837
$227$	−15.2850	−1.01450	−0.507249	−	0.861800i	$-0.669338\pi$
$227$	−15.2850	−1.01450	−0.507249	+	0.861800i	$0.669338\pi$
$228$	12.6113	0.835202
$229$	−19.1829	−1.26764	−0.633822	−	0.773479i	$-0.718515\pi$
$229$	−19.1829	−1.26764	−0.633822	+	0.773479i	$0.718515\pi$
$230$	13.2105	0.871075
$231$	6.40538	0.421443
$232$	−3.45607	−0.226902
$233$	−6.40461	−0.419580	−0.209790	−	0.977746i	$-0.567278\pi$
$233$	−6.40461	−0.419580	−0.209790	+	0.977746i	$0.567278\pi$
$234$	−0.238149	−0.0155683
$235$	−6.42172	−0.418907
$236$	22.4729	1.46286
$237$	7.35731	0.477908
$238$	−48.4835	−3.14272
$239$	−3.64917	−0.236045	−0.118023	−	0.993011i	$-0.537656\pi$
$239$	−3.64917	−0.236045	−0.118023	+	0.993011i	$0.537656\pi$
$240$	6.65308	0.429455
$241$	12.1299	0.781354	0.390677	−	0.920528i	$-0.372241\pi$
$241$	12.1299	0.781354	0.390677	+	0.920528i	$0.372241\pi$
$242$	20.7553	1.33420
$243$	−1.21165	−0.0777272
$244$	−22.8919	−1.46550
$245$	−9.12024	−0.582671
$246$	−44.2635	−2.82214
$247$	3.29567	0.209698
$248$	−0.229757	−0.0145896
$249$	−23.2782	−1.47520
$250$	−18.8828	−1.19425
$251$	−19.4893	−1.23015	−0.615076	−	0.788468i	$-0.710874\pi$
$251$	−19.4893	−1.23015	−0.615076	+	0.788468i	$0.710874\pi$
$252$	−1.00514	−0.0633177
$253$	−5.69999	−0.358355
$254$	−39.0840	−2.45235
$255$	10.9297	0.684446
$256$	12.9923	0.812019
$257$	−23.3959	−1.45939	−0.729697	−	0.683771i	$-0.760339\pi$
$257$	−23.3959	−1.45939	−0.729697	+	0.683771i	$0.760339\pi$
$258$	7.01907	0.436989
$259$	−15.7139	−0.976417
$260$	−2.24610	−0.139298
$261$	1.17863	0.0729553
$262$	−11.1938	−0.691553
$263$	25.8741	1.59547	0.797734	−	0.603009i	$-0.206032\pi$
$263$	25.8741	1.59547	0.797734	+	0.603009i	$0.206032\pi$
$264$	0.551203	0.0339242
$265$	3.82884	0.235204
$266$	26.7443	1.63980
$267$	−7.61474	−0.466015
$268$	6.21833	0.379845
$269$	31.7522	1.93596	0.967982	−	0.251020i	$-0.0807659\pi$
$269$	31.7522	1.93596	0.967982	+	0.251020i	$0.0807659\pi$
$270$	−10.7681	−0.655328
$271$	−12.2523	−0.744272	−0.372136	−	0.928178i	$-0.621375\pi$
$271$	−12.2523	−0.744272	−0.372136	+	0.928178i	$0.621375\pi$
$272$	21.7283	1.31747
$273$	−7.01764	−0.424727
$274$	−5.38696	−0.325438
$275$	3.58367	0.216103
$276$	23.8966	1.43840
$277$	−13.1609	−0.790763	−0.395382	−	0.918517i	$-0.629388\pi$
$277$	−13.1609	−0.790763	−0.395382	+	0.918517i	$0.629388\pi$
$278$	30.2839	1.81631
$279$	0.0783543	0.00469095
$280$	−1.40902	−0.0842053
$281$	15.9187	0.949628	0.474814	−	0.880086i	$-0.342515\pi$
$281$	15.9187	0.949628	0.474814	+	0.880086i	$0.342515\pi$
$282$	−22.3346	−1.33001
$283$	−31.6263	−1.87999	−0.939993	−	0.341194i	$-0.889169\pi$
$283$	−31.6263	−1.87999	−0.939993	+	0.341194i	$0.889169\pi$
$284$	−31.8291	−1.88871
$285$	−6.02902	−0.357128
$286$	1.86335	0.110182
$287$	−48.8211	−2.88182
$288$	0.945909	0.0557382
$289$	18.6954	1.09973
$290$	21.3732	1.25508
$291$	8.74685	0.512749
$292$	27.4935	1.60893
$293$	−22.9409	−1.34022	−0.670110	−	0.742261i	$-0.733753\pi$
$293$	−22.9409	−1.34022	−0.670110	+	0.742261i	$0.733753\pi$
$294$	−31.7200	−1.84995
$295$	−10.7435	−0.625511
$296$	−1.35223	−0.0785970
$297$	4.64617	0.269598
$298$	41.0785	2.37962
$299$	6.24482	0.361147
$300$	−15.0241	−0.867419
$301$	7.74178	0.446229
$302$	22.0762	1.27034
$303$	−24.8835	−1.42952
$304$	−11.9857	−0.687426
$305$	10.9438	0.626641
$306$	1.42284	0.0813381
$307$	−10.0294	−0.572410	−0.286205	−	0.958168i	$-0.592394\pi$
$307$	−10.0294	−0.572410	−0.286205	+	0.958168i	$0.592394\pi$
$308$	7.86451	0.448122
$309$	27.5309	1.56618
$310$	1.42087	0.0807001
$311$	−3.51855	−0.199518	−0.0997592	−	0.995012i	$-0.531807\pi$
$311$	−3.51855	−0.199518	−0.0997592	+	0.995012i	$0.531807\pi$
$312$	−0.603890	−0.0341885
$313$	2.03487	0.115017	0.0575087	−	0.998345i	$-0.481684\pi$
$313$	2.03487	0.115017	0.0575087	+	0.998345i	$0.481684\pi$
$314$	7.42928	0.419258
$315$	0.480521	0.0270743
$316$	9.03329	0.508162
$317$	4.90757	0.275636	0.137818	−	0.990458i	$-0.455991\pi$
$317$	4.90757	0.275636	0.137818	+	0.990458i	$0.455991\pi$
$318$	13.3166	0.746759
$319$	−9.22197	−0.516331
$320$	9.61589	0.537544
$321$	−28.4201	−1.58626
$322$	50.6766	2.82410
$323$	−19.6902	−1.09559
$324$	−20.2371	−1.12428
$325$	−3.92621	−0.217787
$326$	43.1470	2.38969
$327$	−9.22371	−0.510072
$328$	−4.20121	−0.231973
$329$	−24.6343	−1.35813
$330$	−3.40877	−0.187647
$331$	23.0520	1.26705	0.633526	−	0.773721i	$-0.281607\pi$
$331$	23.0520	1.26705	0.633526	+	0.773721i	$0.281607\pi$
$332$	−28.5810	−1.56858
$333$	0.461154	0.0252711
$334$	−22.2486	−1.21739
$335$	−2.97277	−0.162420
$336$	25.5218	1.39233
$337$	−4.38900	−0.239084	−0.119542	−	0.992829i	$-0.538143\pi$
$337$	−4.38900	−0.239084	−0.119542	+	0.992829i	$0.538143\pi$
$338$	−2.04146	−0.111041
$339$	−9.16318	−0.497676
$340$	13.4195	0.727774
$341$	−0.613069	−0.0331995
$342$	−0.784859	−0.0424403
$343$	−7.16037	−0.386624
$344$	0.666204	0.0359193
$345$	−11.4241	−0.615054
$346$	−5.99594	−0.322344
$347$	28.9611	1.55472	0.777358	−	0.629059i	$-0.216560\pi$
$347$	28.9611	1.55472	0.777358	+	0.629059i	$0.216560\pi$
$348$	38.6621	2.07251
$349$	6.67137	0.357110	0.178555	−	0.983930i	$-0.442858\pi$
$349$	6.67137	0.357110	0.178555	+	0.983930i	$0.442858\pi$
$350$	−31.8612	−1.70305
$351$	−5.09027	−0.271699
$352$	−7.40109	−0.394479
$353$	1.39674	0.0743412	0.0371706	−	0.999309i	$-0.488165\pi$
$353$	1.39674	0.0743412	0.0371706	+	0.999309i	$0.488165\pi$
$354$	−37.3657	−1.98596
$355$	15.2164	0.807603
$356$	−9.34936	−0.495515
$357$	41.9273	2.21903
$358$	40.2962	2.12972
$359$	−4.32069	−0.228037	−0.114019	−	0.993479i	$-0.536372\pi$
$359$	−4.32069	−0.228037	−0.114019	+	0.993479i	$0.536372\pi$
$360$	0.0413504	0.00217935
$361$	−8.13858	−0.428346
$362$	24.1297	1.26823
$363$	−17.9487	−0.942061
$364$	−8.61624	−0.451614
$365$	−13.1437	−0.687972
$366$	38.0623	1.98955
$367$	3.94692	0.206028	0.103014	−	0.994680i	$-0.467151\pi$
$367$	3.94692	0.206028	0.103014	+	0.994680i	$0.467151\pi$
$368$	−22.7112	−1.18390
$369$	1.43274	0.0745856
$370$	8.36254	0.434748
$371$	14.6877	0.762550
$372$	2.57023	0.133260
$373$	31.4430	1.62805	0.814027	−	0.580827i	$-0.197271\pi$
$373$	31.4430	1.62805	0.814027	+	0.580827i	$0.197271\pi$
$374$	−11.1327	−0.575659
$375$	16.3294	0.843247
$376$	−2.11985	−0.109323
$377$	10.1035	0.520354
$378$	−41.3075	−2.12463
$379$	18.2227	0.936037	0.468018	−	0.883719i	$-0.344968\pi$
$379$	18.2227	0.936037	0.468018	+	0.883719i	$0.344968\pi$
$380$	−7.40241	−0.379736
$381$	33.7989	1.73157
$382$	20.7363	1.06096
$383$	−24.6593	−1.26003	−0.630015	−	0.776583i	$-0.716951\pi$
$383$	−24.6593	−1.26003	−0.630015	+	0.776583i	$0.716951\pi$
$384$	4.81416	0.245672
$385$	−3.75975	−0.191615
$386$	−47.7752	−2.43169
$387$	−0.227197	−0.0115491
$388$	10.7394	0.545208
$389$	−17.1209	−0.868066	−0.434033	−	0.900897i	$-0.642910\pi$
$389$	−17.1209	−0.868066	−0.434033	+	0.900897i	$0.642910\pi$
$390$	3.73460	0.189109
$391$	−37.3101	−1.88685
$392$	−3.01065	−0.152061
$393$	9.68009	0.488296
$394$	16.9578	0.854320
$395$	−4.31850	−0.217287
$396$	−0.230798	−0.0115980
$397$	12.2140	0.613003	0.306502	−	0.951870i	$-0.400842\pi$
$397$	12.2140	0.613003	0.306502	+	0.951870i	$0.400842\pi$
$398$	15.3399	0.768921
$399$	−23.1278	−1.15784
$400$	14.2789	0.713943
$401$	17.1762	0.857740	0.428870	−	0.903366i	$-0.358912\pi$
$401$	17.1762	0.857740	0.428870	+	0.903366i	$0.358912\pi$
$402$	−10.3392	−0.515674
$403$	0.671669	0.0334582
$404$	−30.5519	−1.52001
$405$	9.67467	0.480738
$406$	81.9893	4.06906
$407$	−3.60822	−0.178853
$408$	3.60798	0.178621
$409$	6.06351	0.299821	0.149911	−	0.988700i	$-0.452101\pi$
$409$	6.06351	0.299821	0.149911	+	0.988700i	$0.452101\pi$
$410$	25.9813	1.28312
$411$	4.65852	0.229788
$412$	33.8024	1.66532
$413$	−41.2130	−2.02796
$414$	−1.48720	−0.0730917
$415$	13.6636	0.670719
$416$	8.10852	0.397553
$417$	−26.1888	−1.28247
$418$	6.14099	0.300365
$419$	1.60735	0.0785240	0.0392620	−	0.999229i	$-0.487499\pi$
$419$	1.60735	0.0785240	0.0392620	+	0.999229i	$0.487499\pi$
$420$	15.7624	0.769124
$421$	16.6916	0.813497	0.406748	−	0.913540i	$-0.366663\pi$
$421$	16.6916	0.813497	0.406748	+	0.913540i	$0.366663\pi$
$422$	21.4905	1.04614
$423$	0.722937	0.0351504
$424$	1.26393	0.0613817
$425$	23.4574	1.13785
$426$	52.9223	2.56409
$427$	41.9814	2.03162
$428$	−34.8941	−1.68667
$429$	−1.61138	−0.0777982
$430$	−4.11997	−0.198683
$431$	18.1110	0.872378	0.436189	−	0.899855i	$-0.356328\pi$
$431$	18.1110	0.872378	0.436189	+	0.899855i	$0.356328\pi$
$432$	18.5123	0.890674
$433$	34.8023	1.67249	0.836246	−	0.548355i	$-0.184746\pi$
$433$	34.8023	1.67249	0.836246	+	0.548355i	$0.184746\pi$
$434$	5.45058	0.261636
$435$	−18.4830	−0.886193
$436$	−11.3249	−0.542362
$437$	20.5808	0.984516
$438$	−45.7134	−2.18427
$439$	8.16782	0.389829	0.194914	−	0.980820i	$-0.437557\pi$
$439$	8.16782	0.389829	0.194914	+	0.980820i	$0.437557\pi$
$440$	−0.323538	−0.0154241
$441$	1.02673	0.0488917
$442$	12.1968	0.580144
$443$	5.17453	0.245849	0.122925	−	0.992416i	$-0.460773\pi$
$443$	5.17453	0.245849	0.122925	+	0.992416i	$0.460773\pi$
$444$	15.1271	0.717898
$445$	4.46961	0.211880
$446$	−30.7156	−1.45443
$447$	−35.5237	−1.68021
$448$	36.8873	1.74276
$449$	12.3350	0.582125	0.291062	−	0.956704i	$-0.405991\pi$
$449$	12.3350	0.582125	0.291062	+	0.956704i	$0.405991\pi$
$450$	0.935023	0.0440774
$451$	−11.2102	−0.527869
$452$	−11.2505	−0.529181
$453$	−19.0909	−0.896970
$454$	31.2036	1.46446
$455$	4.11913	0.193108
$456$	−1.99022	−0.0932005
$457$	−9.74687	−0.455939	−0.227970	−	0.973668i	$-0.573209\pi$
$457$	−9.74687	−0.455939	−0.227970	+	0.973668i	$0.573209\pi$
$458$	39.1612	1.82988
$459$	30.4121	1.41952
$460$	−14.0265	−0.653990
$461$	−39.7796	−1.85272	−0.926361	−	0.376637i	$-0.877081\pi$
$461$	−39.7796	−1.85272	−0.926361	+	0.376637i	$0.877081\pi$
$462$	−13.0763	−0.608366
$463$	1.00000	0.0464739
$463$	1.00000	0.0464739
$464$	−36.7443	−1.70581
$465$	−1.22874	−0.0569813
$466$	13.0748	0.605677
$467$	−22.1047	−1.02288	−0.511441	−	0.859318i	$-0.670888\pi$
$467$	−22.1047	−1.02288	−0.511441	+	0.859318i	$0.670888\pi$
$468$	0.252859	0.0116884
$469$	−11.4038	−0.526578
$470$	13.1097	0.604705
$471$	−6.42466	−0.296033
$472$	−3.54650	−0.163241
$473$	1.77766	0.0817368
$474$	−15.0197	−0.689876
$475$	−12.9395	−0.593705
$476$	51.4783	2.35950
$477$	−0.431038	−0.0197359
$478$	7.44964	0.340739
$479$	−22.9472	−1.04849	−0.524243	−	0.851569i	$-0.675652\pi$
$479$	−22.9472	−1.04849	−0.524243	+	0.851569i	$0.675652\pi$
$480$	−14.8335	−0.677056
$481$	3.95311	0.180246
$482$	−24.7627	−1.12791
$483$	−43.8239	−1.99406
$484$	−22.0373	−1.00170
$485$	−5.13412	−0.233128
$486$	2.47353	0.112202
$487$	−34.0335	−1.54220	−0.771102	−	0.636712i	$-0.780294\pi$
$487$	−34.0335	−1.54220	−0.771102	+	0.636712i	$0.780294\pi$
$488$	3.61263	0.163536
$489$	−37.3125	−1.68733
$490$	18.6186	0.841103
$491$	20.4742	0.923989	0.461994	−	0.886883i	$-0.347134\pi$
$491$	20.4742	0.923989	0.461994	+	0.886883i	$0.347134\pi$
$492$	46.9977	2.11882
$493$	−60.3637	−2.71865
$494$	−6.72797	−0.302706
$495$	0.110337	0.00495927
$496$	−2.44273	−0.109682
$497$	58.3714	2.61831
$498$	47.5216	2.12949
$499$	19.4687	0.871539	0.435769	−	0.900058i	$-0.356476\pi$
$499$	19.4687	0.871539	0.435769	+	0.900058i	$0.356476\pi$
$500$	20.0492	0.896628
$501$	19.2401	0.859584
$502$	39.7865	1.77576
$503$	24.6046	1.09707	0.548533	−	0.836129i	$-0.315186\pi$
$503$	24.6046	1.09707	0.548533	+	0.836129i	$0.315186\pi$
$504$	0.158623	0.00706564
$505$	14.6058	0.649949
$506$	11.6363	0.517296
$507$	1.76541	0.0784044
$508$	41.4982	1.84119
$509$	−24.6700	−1.09348	−0.546739	−	0.837303i	$-0.684131\pi$
$509$	−24.6700	−1.09348	−0.546739	+	0.837303i	$0.684131\pi$
$510$	−22.3126	−0.988019
$511$	−50.4203	−2.23046
$512$	−31.9772	−1.41320
$513$	−16.7758	−0.740671
$514$	47.7617	2.10668
$515$	−16.1597	−0.712083
$516$	−7.45264	−0.328084
$517$	−5.65649	−0.248772
$518$	32.0794	1.40949
$519$	5.18514	0.227603
$520$	0.354464	0.0155443
$521$	−10.0796	−0.441597	−0.220799	−	0.975319i	$-0.570866\pi$
$521$	−10.0796	−0.441597	−0.220799	+	0.975319i	$0.570866\pi$
$522$	−2.40613	−0.105313
$523$	14.3951	0.629453	0.314727	−	0.949182i	$-0.398087\pi$
$523$	14.3951	0.629453	0.314727	+	0.949182i	$0.398087\pi$
$524$	11.8852	0.519207
$525$	27.5528	1.20250
$526$	−52.8210	−2.30311
$527$	−4.01293	−0.174806
$528$	5.86027	0.255036
$529$	15.9978	0.695556
$530$	−7.81643	−0.339524
$531$	1.20947	0.0524865
$532$	−28.3963	−1.23113
$533$	12.2818	0.531982
$534$	15.5452	0.672706
$535$	16.6817	0.721212
$536$	−0.981331	−0.0423871
$537$	−34.8472	−1.50377
$538$	−64.8208	−2.79462
$539$	−8.03344	−0.346025
$540$	11.4333	0.492010
$541$	3.96061	0.170280	0.0851399	−	0.996369i	$-0.472866\pi$
$541$	3.96061	0.170280	0.0851399	+	0.996369i	$0.472866\pi$
$542$	25.0125	1.07438
$543$	−20.8668	−0.895479
$544$	−48.4449	−2.07706
$545$	5.41402	0.231911
$546$	14.3262	0.613106
$547$	18.4417	0.788508	0.394254	−	0.919001i	$-0.371003\pi$
$547$	18.4417	0.788508	0.394254	+	0.919001i	$0.371003\pi$
$548$	5.71972	0.244334
$549$	−1.23202	−0.0525813
$550$	−7.31592	−0.311952
$551$	33.2976	1.41853
$552$	−3.77118	−0.160512
$553$	−16.5661	−0.704464
$554$	26.8675	1.14149
$555$	−7.23172	−0.306970
$556$	−32.1546	−1.36366
$557$	−31.0520	−1.31572	−0.657858	−	0.753142i	$-0.728538\pi$
$557$	−31.0520	−1.31572	−0.657858	+	0.753142i	$0.728538\pi$
$558$	−0.159957	−0.00677153
$559$	−1.94758	−0.0823737
$560$	−14.9805	−0.633040
$561$	9.62730	0.406465
$562$	−32.4973	−1.37082
$563$	−11.1416	−0.469565	−0.234782	−	0.972048i	$-0.575438\pi$
$563$	−11.1416	−0.469565	−0.234782	+	0.972048i	$0.575438\pi$
$564$	23.7142	0.998548
$565$	5.37849	0.226275
$566$	64.5638	2.71382
$567$	37.1128	1.55859
$568$	5.02304	0.210762
$569$	29.8801	1.25264	0.626320	−	0.779566i	$-0.284560\pi$
$569$	29.8801	1.25264	0.626320	+	0.779566i	$0.284560\pi$
$570$	12.3080	0.515525
$571$	−32.6816	−1.36768	−0.683841	−	0.729631i	$-0.739692\pi$
$571$	−32.6816	−1.36768	−0.683841	+	0.729631i	$0.739692\pi$
$572$	−1.97845	−0.0827232
$573$	−17.9323	−0.749132
$574$	99.6663	4.15999
$575$	−24.5185	−1.02249
$576$	−1.08253	−0.0451052
$577$	−23.7846	−0.990166	−0.495083	−	0.868846i	$-0.664862\pi$
$577$	−23.7846	−0.990166	−0.495083	+	0.868846i	$0.664862\pi$
$578$	−38.1659	−1.58749
$579$	41.3148	1.71699
$580$	−22.6934	−0.942293
$581$	52.4146	2.17452
$582$	−17.8563	−0.740169
$583$	3.37258	0.139678
$584$	−4.33882	−0.179542
$585$	−0.120883	−0.00499791
$586$	46.8329	1.93465
$587$	−20.4201	−0.842828	−0.421414	−	0.906868i	$-0.638466\pi$
$587$	−20.4201	−0.842828	−0.421414	+	0.906868i	$0.638466\pi$
$588$	33.6793	1.38891
$589$	2.21360	0.0912097
$590$	21.9324	0.902944
$591$	−14.6647	−0.603224
$592$	−14.3767	−0.590877
$593$	6.69718	0.275020	0.137510	−	0.990500i	$-0.456090\pi$
$593$	6.69718	0.275020	0.137510	+	0.990500i	$0.456090\pi$
$594$	−9.48496	−0.389173
$595$	−24.6100	−1.00891
$596$	−43.6159	−1.78658
$597$	−13.2656	−0.542925
$598$	−12.7486	−0.521327
$599$	3.78283	0.154562	0.0772810	−	0.997009i	$-0.475376\pi$
$599$	3.78283	0.154562	0.0772810	+	0.997009i	$0.475376\pi$
$600$	2.37100	0.0967957
$601$	−15.5342	−0.633652	−0.316826	−	0.948484i	$-0.602617\pi$
$601$	−15.5342	−0.633652	−0.316826	+	0.948484i	$0.602617\pi$
$602$	−15.8045	−0.644145
$603$	0.334665	0.0136286
$604$	−23.4398	−0.953752
$605$	10.5353	0.428320
$606$	50.7986	2.06355
$607$	−4.75057	−0.192820	−0.0964099	−	0.995342i	$-0.530736\pi$
$607$	−4.75057	−0.192820	−0.0964099	+	0.995342i	$0.530736\pi$
$608$	26.7230	1.08376
$609$	−70.9024	−2.87311
$610$	−22.3414	−0.904575
$611$	6.19716	0.250710
$612$	−1.51072	−0.0610674
$613$	15.0849	0.609272	0.304636	−	0.952469i	$-0.401465\pi$
$613$	15.0849	0.609272	0.304636	+	0.952469i	$0.401465\pi$
$614$	20.4747	0.826291
$615$	−22.4680	−0.905996
$616$	−1.24112	−0.0500061
$617$	−7.35567	−0.296128	−0.148064	−	0.988978i	$-0.547304\pi$
$617$	−7.35567	−0.296128	−0.148064	+	0.988978i	$0.547304\pi$
$618$	−56.2032	−2.26082
$619$	−9.87843	−0.397047	−0.198524	−	0.980096i	$-0.563615\pi$
$619$	−9.87843	−0.397047	−0.198524	+	0.980096i	$0.563615\pi$
$620$	−1.50864	−0.0605884
$621$	−31.7878	−1.27560
$622$	7.18297	0.288011
$623$	17.1458	0.686931
$624$	−6.42043	−0.257023
$625$	10.0462	0.401849
$626$	−4.15410	−0.166031
$627$	−5.31058	−0.212084
$628$	−7.88818	−0.314773
$629$	−23.6181	−0.941715
$630$	−0.980965	−0.0390826
$631$	33.4189	1.33039	0.665194	−	0.746671i	$-0.268349\pi$
$631$	33.4189	1.33039	0.665194	+	0.746671i	$0.268349\pi$
$632$	−1.42557	−0.0567060
$633$	−18.5844	−0.738665
$634$	−10.0186	−0.397890
$635$	−19.8389	−0.787281
$636$	−14.1392	−0.560655
$637$	8.80131	0.348721
$638$	18.8263	0.745340
$639$	−1.71301	−0.0677657
$640$	−2.82576	−0.111698
$641$	−26.2057	−1.03506	−0.517532	−	0.855664i	$-0.673149\pi$
$641$	−26.2057	−1.03506	−0.517532	+	0.855664i	$0.673149\pi$
$642$	58.0185	2.28981
$643$	4.20649	0.165888	0.0829439	−	0.996554i	$-0.473568\pi$
$643$	4.20649	0.165888	0.0829439	+	0.996554i	$0.473568\pi$
$644$	−53.8069	−2.12029
$645$	3.56285	0.140287
$646$	40.1967	1.58152
$647$	−32.5257	−1.27872	−0.639359	−	0.768908i	$-0.720800\pi$
$647$	−32.5257	−1.27872	−0.639359	+	0.768908i	$0.720800\pi$
$648$	3.19367	0.125459
$649$	−9.46327	−0.371466
$650$	8.01521	0.314382
$651$	−4.71353	−0.184738
$652$	−45.8122	−1.79414
$653$	−26.0104	−1.01787	−0.508934	−	0.860806i	$-0.669960\pi$
$653$	−26.0104	−1.01787	−0.508934	+	0.860806i	$0.669960\pi$
$654$	18.8298	0.736305
$655$	−5.68190	−0.222010
$656$	−44.6664	−1.74393
$657$	1.47967	0.0577276
$658$	50.2899	1.96050
$659$	24.6766	0.961265	0.480632	−	0.876922i	$-0.340407\pi$
$659$	24.6766	0.961265	0.480632	+	0.876922i	$0.340407\pi$
$660$	3.61933	0.140882
$661$	21.7698	0.846749	0.423374	−	0.905955i	$-0.360845\pi$
$661$	21.7698	0.846749	0.423374	+	0.905955i	$0.360845\pi$
$662$	−47.0598	−1.82903
$663$	−10.5475	−0.409632
$664$	4.51044	0.175039
$665$	13.5753	0.526427
$666$	−0.941428	−0.0364796
$667$	63.0943	2.44302
$668$	23.6229	0.913999
$669$	26.5621	1.02695
$670$	6.06879	0.234458
$671$	9.63970	0.372137
$672$	−56.9027	−2.19507
$673$	−0.707647	−0.0272778	−0.0136389	−	0.999907i	$-0.504342\pi$
$673$	−0.707647	−0.0272778	−0.0136389	+	0.999907i	$0.504342\pi$
$674$	8.95998	0.345125
$675$	19.9855	0.769242
$676$	2.16756	0.0833677
$677$	9.95300	0.382525	0.191262	−	0.981539i	$-0.438742\pi$
$677$	9.95300	0.382525	0.191262	+	0.981539i	$0.438742\pi$
$678$	18.7063	0.718410
$679$	−19.6949	−0.755821
$680$	−2.11777	−0.0812126
$681$	−26.9841	−1.03403
$682$	1.25156	0.0479246
$683$	29.0225	1.11051	0.555257	−	0.831679i	$-0.312620\pi$
$683$	29.0225	1.11051	0.555257	+	0.831679i	$0.312620\pi$
$684$	0.833340	0.0318635
$685$	−2.73440	−0.104476
$686$	14.6176	0.558103
$687$	−33.8657	−1.29206
$688$	7.08295	0.270035
$689$	−3.69495	−0.140766
$690$	23.3219	0.887850
$691$	−12.8159	−0.487540	−0.243770	−	0.969833i	$-0.578384\pi$
$691$	−12.8159	−0.487540	−0.243770	+	0.969833i	$0.578384\pi$
$692$	6.36631	0.242011
$693$	0.423261	0.0160783
$694$	−59.1230	−2.24428
$695$	15.3720	0.583093
$696$	−6.10137	−0.231272
$697$	−73.3782	−2.77940
$698$	−13.6193	−0.515499
$699$	−11.3067	−0.427660
$700$	33.8292	1.27862
$701$	−30.3626	−1.14678	−0.573390	−	0.819283i	$-0.694372\pi$
$701$	−30.3626	−1.14678	−0.573390	+	0.819283i	$0.694372\pi$
$702$	10.3916	0.392205
$703$	13.0281	0.491365
$704$	8.47002	0.319226
$705$	−11.3369	−0.426974
$706$	−2.85140	−0.107314
$707$	56.0290	2.10719
$708$	39.6737	1.49103
$709$	−30.1489	−1.13227	−0.566133	−	0.824314i	$-0.691561\pi$
$709$	−30.1489	−1.13227	−0.566133	+	0.824314i	$0.691561\pi$
$710$	−31.0637	−1.16580
$711$	0.486163	0.0182325
$712$	1.47545	0.0552947
$713$	4.19445	0.157084
$714$	−85.5930	−3.20324
$715$	0.945829	0.0353720
$716$	−42.7853	−1.59896
$717$	−6.44227	−0.240591
$718$	8.82052	0.329179
$719$	−51.1737	−1.90846	−0.954228	−	0.299081i	$-0.903320\pi$
$719$	−51.1737	−1.90846	−0.954228	+	0.299081i	$0.903320\pi$
$720$	0.439628	0.0163840
$721$	−61.9901	−2.30863
$722$	16.6146	0.618331
$723$	21.4142	0.796401
$724$	−25.6202	−0.952166
$725$	−39.6683	−1.47324
$726$	36.6415	1.35989
$727$	9.46022	0.350860	0.175430	−	0.984492i	$-0.443868\pi$
$727$	9.46022	0.350860	0.175430	+	0.984492i	$0.443868\pi$
$728$	1.35975	0.0503958
$729$	25.8700	0.958149
$730$	26.8323	0.993109
$731$	11.6359	0.430370
$732$	−40.4134	−1.49372
$733$	5.15177	0.190285	0.0951425	−	0.995464i	$-0.469669\pi$
$733$	5.15177	0.190285	0.0951425	+	0.995464i	$0.469669\pi$
$734$	−8.05749	−0.297407
$735$	−16.1009	−0.593891
$736$	50.6363	1.86648
$737$	−2.61852	−0.0964546
$738$	−2.92489	−0.107667
$739$	−30.8922	−1.13639	−0.568194	−	0.822894i	$-0.692358\pi$
$739$	−30.8922	−1.13639	−0.568194	+	0.822894i	$0.692358\pi$
$740$	−8.87909	−0.326402
$741$	5.81819	0.213736
$742$	−29.9845	−1.10076
$743$	−6.08000	−0.223053	−0.111527	−	0.993761i	$-0.535574\pi$
$743$	−6.08000	−0.223053	−0.111527	+	0.993761i	$0.535574\pi$
$744$	−0.405614	−0.0148705
$745$	20.8513	0.763932
$746$	−64.1896	−2.35015
$747$	−1.53820	−0.0562798
$748$	11.8204	0.432196
$749$	63.9923	2.33823
$750$	−33.3358	−1.21725
$751$	1.61313	0.0588638	0.0294319	−	0.999567i	$-0.490630\pi$
$751$	1.61313	0.0588638	0.0294319	+	0.999567i	$0.490630\pi$
$752$	−22.5379	−0.821871
$753$	−34.4064	−1.25384
$754$	−20.6258	−0.751147
$755$	11.2058	0.407819
$756$	43.8590	1.59514
$757$	−36.7599	−1.33606	−0.668030	−	0.744134i	$-0.732862\pi$
$757$	−36.7599	−1.33606	−0.668030	+	0.744134i	$0.732862\pi$
$758$	−37.2009	−1.35120
$759$	−10.0628	−0.365256
$760$	1.16819	0.0423749
$761$	36.5720	1.32573	0.662867	−	0.748737i	$-0.269339\pi$
$761$	36.5720	1.32573	0.662867	+	0.748737i	$0.269339\pi$
$762$	−68.9991	−2.49957
$763$	20.7686	0.751875
$764$	−22.0172	−0.796555
$765$	0.722225	0.0261121
$766$	50.3409	1.81889
$767$	10.3678	0.374360
$768$	22.9367	0.827656
$769$	24.0081	0.865756	0.432878	−	0.901453i	$-0.357498\pi$
$769$	24.0081	0.865756	0.432878	+	0.901453i	$0.357498\pi$
$770$	7.67538	0.276602
$771$	−41.3032	−1.48750
$772$	50.7263	1.82568
$773$	−23.3377	−0.839397	−0.419698	−	0.907664i	$-0.637864\pi$
$773$	−23.3377	−0.839397	−0.419698	+	0.907664i	$0.637864\pi$
$774$	0.463813	0.0166714
$775$	−2.63712	−0.0947281
$776$	−1.69481	−0.0608400
$777$	−27.7415	−0.995220
$778$	34.9517	1.25308
$779$	40.4766	1.45023
$780$	−3.96529	−0.141980
$781$	13.4032	0.479603
$782$	76.1670	2.72373
$783$	−51.4293	−1.83793
$784$	−32.0086	−1.14317
$785$	3.77107	0.134595
$786$	−19.7615	−0.704870
$787$	−12.8337	−0.457471	−0.228736	−	0.973489i	$-0.573459\pi$
$787$	−12.8337	−0.457471	−0.228736	+	0.973489i	$0.573459\pi$
$788$	−18.0053	−0.641411
$789$	45.6784	1.62619
$790$	8.81605	0.313661
$791$	20.6323	0.733601
$792$	0.0364229	0.00129423
$793$	−10.5611	−0.375036
$794$	−24.9344	−0.884889
$795$	6.75946	0.239733
$796$	−16.2875	−0.577294
$797$	−34.0936	−1.20766	−0.603828	−	0.797115i	$-0.706359\pi$
$797$	−34.0936	−1.20766	−0.603828	+	0.797115i	$0.706359\pi$
$798$	47.2145	1.67137
$799$	−37.0253	−1.30986
$800$	−31.8358	−1.12557
$801$	−0.503174	−0.0177788
$802$	−35.0646	−1.23817
$803$	−11.5774	−0.408559
$804$	10.9779	0.387160
$805$	25.7232	0.906624
$806$	−1.37119	−0.0482980
$807$	56.0555	1.97325
$808$	4.82147	0.169619
$809$	−25.6833	−0.902978	−0.451489	−	0.892277i	$-0.649107\pi$
$809$	−25.6833	−0.902978	−0.451489	+	0.892277i	$0.649107\pi$
$810$	−19.7505	−0.693961
$811$	44.6105	1.56649	0.783244	−	0.621715i	$-0.213564\pi$
$811$	44.6105	1.56649	0.783244	+	0.621715i	$0.213564\pi$
$812$	−87.0538	−3.05499
$813$	−21.6302	−0.758605
$814$	7.36603	0.258179
$815$	21.9012	0.767166
$816$	38.3593	1.34284
$817$	−6.41856	−0.224557
$818$	−12.3784	−0.432801
$819$	−0.463718	−0.0162036
$820$	−27.5861	−0.963350
$821$	−36.1911	−1.26308	−0.631539	−	0.775344i	$-0.717576\pi$
$821$	−36.1911	−1.26308	−0.631539	+	0.775344i	$0.717576\pi$
$822$	−9.51018	−0.331705
$823$	−1.96993	−0.0686674	−0.0343337	−	0.999410i	$-0.510931\pi$
$823$	−1.96993	−0.0686674	−0.0343337	+	0.999410i	$0.510931\pi$
$824$	−5.33444	−0.185834
$825$	6.32663	0.220265
$826$	84.1346	2.92742
$827$	−7.50197	−0.260869	−0.130435	−	0.991457i	$-0.541637\pi$
$827$	−7.50197	−0.260869	−0.130435	+	0.991457i	$0.541637\pi$
$828$	1.57906	0.0548761
$829$	−28.2631	−0.981618	−0.490809	−	0.871267i	$-0.663299\pi$
$829$	−28.2631	−0.981618	−0.490809	+	0.871267i	$0.663299\pi$
$830$	−27.8937	−0.968203
$831$	−23.2344	−0.805991
$832$	−9.27963	−0.321713
$833$	−52.5840	−1.82193
$834$	53.4634	1.85129
$835$	−11.2933	−0.390821
$836$	−6.52031	−0.225510
$837$	−3.41898	−0.118177
$838$	−3.28133	−0.113352
$839$	−23.1752	−0.800096	−0.400048	−	0.916494i	$-0.631007\pi$
$839$	−23.1752	−0.800096	−0.400048	+	0.916494i	$0.631007\pi$
$840$	−2.48750	−0.0858269
$841$	73.0798	2.51999
$842$	−34.0752	−1.17431
$843$	28.1029	0.967915
$844$	−22.8179	−0.785425
$845$	−1.03624	−0.0356476
$846$	−1.47585	−0.0507407
$847$	40.4142	1.38865
$848$	13.4378	0.461456
$849$	−55.8332	−1.91619
$850$	−47.8874	−1.64252
$851$	24.6864	0.846240
$852$	−56.1913	−1.92508
$853$	−21.5718	−0.738604	−0.369302	−	0.929309i	$-0.620403\pi$
$853$	−21.5718	−0.738604	−0.369302	+	0.929309i	$0.620403\pi$
$854$	−85.7033	−2.93271
$855$	−0.398391	−0.0136247
$856$	5.50674	0.188216
$857$	29.5798	1.01043	0.505213	−	0.862994i	$-0.331414\pi$
$857$	29.5798	1.01043	0.505213	+	0.862994i	$0.331414\pi$
$858$	3.28957	0.112304
$859$	−48.0139	−1.63821	−0.819106	−	0.573642i	$-0.805530\pi$
$859$	−48.0139	−1.63821	−0.819106	+	0.573642i	$0.805530\pi$
$860$	4.37446	0.149168
$861$	−86.1890	−2.93731
$862$	−36.9729	−1.25930
$863$	−20.6286	−0.702205	−0.351102	−	0.936337i	$-0.614193\pi$
$863$	−20.6286	−0.702205	−0.351102	+	0.936337i	$0.614193\pi$
$864$	−41.2746	−1.40419
$865$	−3.04351	−0.103483
$866$	−71.0475	−2.41429
$867$	33.0050	1.12091
$868$	−5.78726	−0.196433
$869$	−3.80389	−0.129038
$870$	37.7324	1.27925
$871$	2.86882	0.0972061
$872$	1.78720	0.0605224
$873$	0.577982	0.0195617
$874$	−42.0150	−1.42118
$875$	−36.7682	−1.24299
$876$	48.5371	1.63992
$877$	−7.46978	−0.252236	−0.126118	−	0.992015i	$-0.540252\pi$
$877$	−7.46978	−0.252236	−0.126118	+	0.992015i	$0.540252\pi$
$878$	−16.6743	−0.562730
$879$	−40.5000	−1.36603
$880$	−3.43979	−0.115955
$881$	−44.7929	−1.50911	−0.754555	−	0.656236i	$-0.772147\pi$
$881$	−44.7929	−1.50911	−0.754555	+	0.656236i	$0.772147\pi$
$882$	−2.09602	−0.0705767
$883$	31.6078	1.06369	0.531844	−	0.846842i	$-0.321499\pi$
$883$	31.6078	1.06369	0.531844	+	0.846842i	$0.321499\pi$
$884$	−12.9502	−0.435563
$885$	−18.9666	−0.637557
$886$	−10.5636	−0.354891
$887$	−19.9316	−0.669236	−0.334618	−	0.942354i	$-0.608607\pi$
$887$	−19.9316	−0.669236	−0.334618	+	0.942354i	$0.608607\pi$
$888$	−2.38724	−0.0801105
$889$	−76.1035	−2.55243
$890$	−9.12453	−0.305855
$891$	8.52180	0.285491
$892$	32.6129	1.09196
$893$	20.4238	0.683456
$894$	72.5203	2.42544
$895$	20.4542	0.683708
$896$	−10.8398	−0.362134
$897$	11.0246	0.368102
$898$	−25.1814	−0.840315
$899$	6.78618	0.226332
$900$	−0.992779	−0.0330926
$901$	22.0757	0.735449
$902$	22.8852	0.761995
$903$	13.6674	0.454822
$904$	1.77548	0.0590515
$905$	12.2481	0.407141
$906$	38.9734	1.29480
$907$	−32.8498	−1.09076	−0.545380	−	0.838189i	$-0.683614\pi$
$907$	−32.8498	−1.09076	−0.545380	+	0.838189i	$0.683614\pi$
$908$	−33.1311	−1.09949
$909$	−1.64427	−0.0545371
$910$	−8.40904	−0.278757
$911$	−23.1140	−0.765800	−0.382900	−	0.923790i	$-0.625075\pi$
$911$	−23.1140	−0.765800	−0.382900	+	0.923790i	$0.625075\pi$
$912$	−21.1596	−0.700664
$913$	12.0354	0.398313
$914$	19.8979	0.658162
$915$	19.3203	0.638708
$916$	−41.5802	−1.37385
$917$	−21.7962	−0.719775
$918$	−62.0852	−2.04912
$919$	0.584674	0.0192866	0.00964330	−	0.999954i	$-0.496930\pi$
$919$	0.584674	0.0192866	0.00964330	+	0.999954i	$0.496930\pi$
$920$	2.21356	0.0729790
$921$	−17.7060	−0.583433
$922$	81.2085	2.67446
$923$	−14.6843	−0.483340
$924$	13.8840	0.456752
$925$	−15.5207	−0.510319
$926$	−2.04146	−0.0670866
$927$	1.81921	0.0597507
$928$	81.9241	2.68929
$929$	15.8336	0.519484	0.259742	−	0.965678i	$-0.416362\pi$
$929$	15.8336	0.519484	0.259742	+	0.965678i	$0.416362\pi$
$930$	2.50842	0.0822542
$931$	29.0062	0.950640
$932$	−13.8824	−0.454733
$933$	−6.21166	−0.203361
$934$	45.1258	1.47656
$935$	−5.65092	−0.184805
$936$	−0.0399044	−0.00130432
$937$	13.0069	0.424917	0.212458	−	0.977170i	$-0.431853\pi$
$937$	13.0069	0.424917	0.212458	+	0.977170i	$0.431853\pi$
$938$	23.2804	0.760132
$939$	3.59236	0.117232
$940$	−13.9195	−0.454003
$941$	−31.4674	−1.02581	−0.512904	−	0.858446i	$-0.671430\pi$
$941$	−31.4674	−1.02581	−0.512904	+	0.858446i	$0.671430\pi$
$942$	13.1157	0.427332
$943$	76.6974	2.49761
$944$	−37.7057	−1.22722
$945$	−20.9675	−0.682072
$946$	−3.62902	−0.117990
$947$	−12.7472	−0.414230	−0.207115	−	0.978317i	$-0.566407\pi$
$947$	−12.7472	−0.414230	−0.207115	+	0.978317i	$0.566407\pi$
$948$	15.9474	0.517948
$949$	12.6841	0.411742
$950$	26.4155	0.857031
$951$	8.66385	0.280944
$952$	−8.12392	−0.263298
$953$	32.7192	1.05988	0.529939	−	0.848036i	$-0.322215\pi$
$953$	32.7192	1.05988	0.529939	+	0.848036i	$0.322215\pi$
$954$	0.879948	0.0284894
$955$	10.5257	0.340603
$956$	−7.90980	−0.255821
$957$	−16.2805	−0.526274
$958$	46.8459	1.51352
$959$	−10.4894	−0.338720
$960$	16.9759	0.547896
$961$	−30.5489	−0.985447
$962$	−8.07011	−0.260191
$963$	−1.87797	−0.0605167
$964$	26.2923	0.846816
$965$	−24.2505	−0.780651
$966$	89.4647	2.87848
$967$	30.1734	0.970311	0.485156	−	0.874428i	$-0.338763\pi$
$967$	30.1734	0.970311	0.485156	+	0.874428i	$0.338763\pi$
$968$	3.47777	0.111780
$969$	−34.7611	−1.11669
$970$	10.4811	0.336528
$971$	10.8201	0.347235	0.173617	−	0.984813i	$-0.444454\pi$
$971$	10.8201	0.347235	0.173617	+	0.984813i	$0.444454\pi$
$972$	−2.62632	−0.0842392
$973$	58.9682	1.89043
$974$	69.4780	2.22622
$975$	−6.93136	−0.221981
$976$	38.4087	1.22943
$977$	−5.66289	−0.181172	−0.0905859	−	0.995889i	$-0.528874\pi$
$977$	−5.66289	−0.181172	−0.0905859	+	0.995889i	$0.528874\pi$
$978$	76.1720	2.43571
$979$	3.93699	0.125827
$980$	−19.7687	−0.631487
$981$	−0.609493	−0.0194596
$982$	−41.7973	−1.33381
$983$	5.58749	0.178213	0.0891066	−	0.996022i	$-0.471599\pi$
$983$	5.58749	0.178213	0.0891066	+	0.996022i	$0.471599\pi$
$984$	−7.41683	−0.236440
$985$	8.60769	0.274264
$986$	123.230	3.92445
$987$	−43.4895	−1.38428
$988$	7.14356	0.227267
$989$	−12.1623	−0.386737
$990$	−0.225248	−0.00715885
$991$	−59.3748	−1.88610	−0.943051	−	0.332648i	$-0.892058\pi$
$991$	−59.3748	−1.88610	−0.943051	+	0.332648i	$0.892058\pi$
$992$	5.44625	0.172919
$993$	40.6961	1.29145
$994$	−119.163	−3.77961
$995$	7.78648	0.246848
$996$	−50.4570	−1.59879
$997$	14.0978	0.446483	0.223241	−	0.974763i	$-0.428336\pi$
$997$	14.0978	0.446483	0.223241	+	0.974763i	$0.428336\pi$
$998$	−39.7446	−1.25809
$999$	−20.1224	−0.636644

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.b.1.18	✓	101

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.b.1.18	✓	101	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)

\(f(q)\)	\(=\)	\(q-2.04146 q^{2} +1.76541 q^{3} +2.16756 q^{4} -1.03624 q^{5} -3.60401 q^{6} -3.97509 q^{7} -0.342069 q^{8} +0.116656 q^{9} +O(q^{10})\)	\(q-2.04146 q^{2} +1.76541 q^{3} +2.16756 q^{4} -1.03624 q^{5} -3.60401 q^{6} -3.97509 q^{7} -0.342069 q^{8} +0.116656 q^{9} +2.11544 q^{10} -0.912754 q^{11} +3.82662 q^{12} +1.00000 q^{13} +8.11498 q^{14} -1.82938 q^{15} -3.63680 q^{16} -5.97456 q^{17} -0.238149 q^{18} +3.29567 q^{19} -2.24610 q^{20} -7.01764 q^{21} +1.86335 q^{22} +6.24482 q^{23} -0.603890 q^{24} -3.92621 q^{25} -2.04146 q^{26} -5.09027 q^{27} -8.61624 q^{28} +10.1035 q^{29} +3.73460 q^{30} +0.671669 q^{31} +8.10852 q^{32} -1.61138 q^{33} +12.1968 q^{34} +4.11913 q^{35} +0.252859 q^{36} +3.95311 q^{37} -6.72797 q^{38} +1.76541 q^{39} +0.354464 q^{40} +12.2818 q^{41} +14.3262 q^{42} -1.94758 q^{43} -1.97845 q^{44} -0.120883 q^{45} -12.7486 q^{46} +6.19716 q^{47} -6.42043 q^{48} +8.80131 q^{49} +8.01521 q^{50} -10.5475 q^{51} +2.16756 q^{52} -3.69495 q^{53} +10.3916 q^{54} +0.945829 q^{55} +1.35975 q^{56} +5.81819 q^{57} -20.6258 q^{58} +10.3678 q^{59} -3.96529 q^{60} -10.5611 q^{61} -1.37119 q^{62} -0.463718 q^{63} -9.27963 q^{64} -1.03624 q^{65} +3.28957 q^{66} +2.86882 q^{67} -12.9502 q^{68} +11.0246 q^{69} -8.40904 q^{70} -14.6843 q^{71} -0.0399044 q^{72} +12.6841 q^{73} -8.07011 q^{74} -6.93136 q^{75} +7.14356 q^{76} +3.62828 q^{77} -3.60401 q^{78} +4.16749 q^{79} +3.76859 q^{80} -9.33636 q^{81} -25.0727 q^{82} -13.1858 q^{83} -15.2112 q^{84} +6.19106 q^{85} +3.97590 q^{86} +17.8367 q^{87} +0.312224 q^{88} -4.31331 q^{89} +0.246778 q^{90} -3.97509 q^{91} +13.5360 q^{92} +1.18577 q^{93} -12.6513 q^{94} -3.41509 q^{95} +14.3148 q^{96} +4.95458 q^{97} -17.9675 q^{98} -0.106478 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9}+O(q^{10}) \) 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9	\( 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9} - 19 q^{10} - 42 q^{11} - 28 q^{12} + 101 q^{13} - 45 q^{14} - 15 q^{15} + 48 q^{16} - 83 q^{17} - 4 q^{18} - 18 q^{19} - 51 q^{20} - 50 q^{21} - 20 q^{22} - 64 q^{23} - 23 q^{24} + 46 q^{25} - 8 q^{26} - 37 q^{27} - 11 q^{28} - 117 q^{29} - 28 q^{30} - 10 q^{31} - 36 q^{32} - 20 q^{33} - 10 q^{34} - 53 q^{35} - 16 q^{36} - 27 q^{37} - 68 q^{38} - 13 q^{39} - 42 q^{40} - 60 q^{41} - 31 q^{42} - 16 q^{43} - 89 q^{44} - 56 q^{45} + 5 q^{46} - 23 q^{47} - 37 q^{48} + 48 q^{49} - 30 q^{50} - 68 q^{51} + 86 q^{52} - 189 q^{53} - 23 q^{54} + 3 q^{55} - 106 q^{56} - 25 q^{57} - 82 q^{59} + 6 q^{60} - 68 q^{61} - 57 q^{62} + 3 q^{63} - 2 q^{64} - 43 q^{65} - 40 q^{66} - 13 q^{67} - 138 q^{68} - 92 q^{69} + 18 q^{70} - 39 q^{71} - 20 q^{72} + 19 q^{73} - 88 q^{74} - 21 q^{75} - 53 q^{76} - 147 q^{77} - 10 q^{78} - 19 q^{79} - 104 q^{80} - 55 q^{81} + 27 q^{82} - 49 q^{83} - 59 q^{84} - 27 q^{85} - 99 q^{86} - 33 q^{87} - 41 q^{88} - 70 q^{89} - 49 q^{90} - q^{91} - 111 q^{92} - 84 q^{93} + 4 q^{94} - 82 q^{95} - 7 q^{96} + 25 q^{97} - 37 q^{98} - 41 q^{99}+O(q^{100}) \) 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9 - 19 * q^10 - 42 * q^11 - 28 * q^12 + 101 * q^13 - 45 * q^14 - 15 * q^15 + 48 * q^16 - 83 * q^17 - 4 * q^18 - 18 * q^19 - 51 * q^20 - 50 * q^21 - 20 * q^22 - 64 * q^23 - 23 * q^24 + 46 * q^25 - 8 * q^26 - 37 * q^27 - 11 * q^28 - 117 * q^29 - 28 * q^30 - 10 * q^31 - 36 * q^32 - 20 * q^33 - 10 * q^34 - 53 * q^35 - 16 * q^36 - 27 * q^37 - 68 * q^38 - 13 * q^39 - 42 * q^40 - 60 * q^41 - 31 * q^42 - 16 * q^43 - 89 * q^44 - 56 * q^45 + 5 * q^46 - 23 * q^47 - 37 * q^48 + 48 * q^49 - 30 * q^50 - 68 * q^51 + 86 * q^52 - 189 * q^53 - 23 * q^54 + 3 * q^55 - 106 * q^56 - 25 * q^57 - 82 * q^59 + 6 * q^60 - 68 * q^61 - 57 * q^62 + 3 * q^63 - 2 * q^64 - 43 * q^65 - 40 * q^66 - 13 * q^67 - 138 * q^68 - 92 * q^69 + 18 * q^70 - 39 * q^71 - 20 * q^72 + 19 * q^73 - 88 * q^74 - 21 * q^75 - 53 * q^76 - 147 * q^77 - 10 * q^78 - 19 * q^79 - 104 * q^80 - 55 * q^81 + 27 * q^82 - 49 * q^83 - 59 * q^84 - 27 * q^85 - 99 * q^86 - 33 * q^87 - 41 * q^88 - 70 * q^89 - 49 * q^90 - q^91 - 111 * q^92 - 84 * q^93 + 4 * q^94 - 82 * q^95 - 7 * q^96 + 25 * q^97 - 37 * q^98 - 41 * q^99

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