LMFDB - Embedded newform 6047.2.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6047,2,Mod(1,6047)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6047, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6047.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6047 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6047.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:	$48.2855381023$
Analytic rank:	$1$
Dimension:	$217$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	6047.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.78935 q^{2} +0.603668 q^{3} +5.78045 q^{4} +3.11422 q^{5} -1.68384 q^{6} +0.146622 q^{7} -10.5450 q^{8} -2.63558 q^{9} +O(q^{10})$	\(q-2.78935 q^{2} +0.603668 q^{3} +5.78045 q^{4} +3.11422 q^{5} -1.68384 q^{6} +0.146622 q^{7} -10.5450 q^{8} -2.63558 q^{9} -8.68663 q^{10} +5.95238 q^{11} +3.48947 q^{12} -2.13466 q^{13} -0.408979 q^{14} +1.87995 q^{15} +17.8527 q^{16} -3.51865 q^{17} +7.35156 q^{18} +2.37433 q^{19} +18.0016 q^{20} +0.0885108 q^{21} -16.6032 q^{22} -3.35265 q^{23} -6.36567 q^{24} +4.69836 q^{25} +5.95430 q^{26} -3.40202 q^{27} +0.847539 q^{28} +1.70921 q^{29} -5.24384 q^{30} -2.22831 q^{31} -28.7074 q^{32} +3.59326 q^{33} +9.81474 q^{34} +0.456612 q^{35} -15.2349 q^{36} -6.81464 q^{37} -6.62283 q^{38} -1.28863 q^{39} -32.8394 q^{40} -2.99107 q^{41} -0.246887 q^{42} -7.86014 q^{43} +34.4074 q^{44} -8.20779 q^{45} +9.35171 q^{46} -6.38720 q^{47} +10.7771 q^{48} -6.97850 q^{49} -13.1053 q^{50} -2.12410 q^{51} -12.3393 q^{52} -8.02904 q^{53} +9.48942 q^{54} +18.5370 q^{55} -1.54612 q^{56} +1.43331 q^{57} -4.76758 q^{58} -0.780236 q^{59} +10.8670 q^{60} +10.2256 q^{61} +6.21552 q^{62} -0.386434 q^{63} +44.3694 q^{64} -6.64780 q^{65} -10.0229 q^{66} +0.544504 q^{67} -20.3394 q^{68} -2.02389 q^{69} -1.27365 q^{70} +0.166754 q^{71} +27.7922 q^{72} +3.03385 q^{73} +19.0084 q^{74} +2.83625 q^{75} +13.7247 q^{76} +0.872748 q^{77} +3.59442 q^{78} -17.2844 q^{79} +55.5972 q^{80} +5.85306 q^{81} +8.34312 q^{82} +13.5790 q^{83} +0.511632 q^{84} -10.9579 q^{85} +21.9246 q^{86} +1.03179 q^{87} -62.7677 q^{88} -9.95654 q^{89} +22.8944 q^{90} -0.312987 q^{91} -19.3798 q^{92} -1.34516 q^{93} +17.8161 q^{94} +7.39419 q^{95} -17.3297 q^{96} -13.2742 q^{97} +19.4655 q^{98} -15.6880 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 217 q - 20 q^{2} - 27 q^{3} + 184 q^{4} - 19 q^{5} - 17 q^{6} - 48 q^{7} - 57 q^{8} + 152 q^{9}+O(q^{10}) $ 217 * q - 20 * q^2 - 27 * q^3 + 184 * q^4 - 19 * q^5 - 17 * q^6 - 48 * q^7 - 57 * q^8 + 152 * q^9	\( 217 q - 20 q^{2} - 27 q^{3} + 184 q^{4} - 19 q^{5} - 17 q^{6} - 48 q^{7} - 57 q^{8} + 152 q^{9} - 46 q^{10} - 32 q^{11} - 72 q^{12} - 80 q^{13} - 22 q^{14} - 43 q^{15} + 122 q^{16} - 61 q^{17} - 88 q^{18} - 43 q^{19} - 41 q^{20} - 61 q^{21} - 93 q^{22} - 60 q^{23} - 41 q^{24} + 26 q^{25} - 9 q^{26} - 93 q^{27} - 126 q^{28} - 47 q^{29} - 36 q^{30} - 100 q^{31} - 114 q^{32} - 133 q^{33} - 75 q^{34} - 37 q^{35} + 75 q^{36} - 264 q^{37} - 35 q^{38} - 47 q^{39} - 118 q^{40} - 72 q^{41} - 64 q^{42} - 107 q^{43} - 59 q^{44} - 69 q^{45} - 111 q^{46} - 54 q^{47} - 135 q^{48} + 33 q^{49} - 42 q^{50} - 26 q^{51} - 173 q^{52} - 103 q^{53} - 28 q^{54} - 78 q^{55} - 44 q^{56} - 205 q^{57} - 189 q^{58} - 38 q^{59} - 105 q^{60} - 108 q^{61} - 14 q^{62} - 116 q^{63} + 39 q^{64} - 146 q^{65} + 5 q^{66} - 206 q^{67} - 62 q^{68} - 55 q^{69} - 125 q^{70} - 78 q^{71} - 225 q^{72} - 326 q^{73} + 3 q^{74} - 95 q^{75} - 84 q^{76} - 79 q^{77} - 86 q^{78} - 117 q^{79} - 39 q^{80} + q^{81} - 96 q^{82} - 23 q^{83} - 57 q^{84} - 224 q^{85} - 7 q^{86} - 45 q^{87} - 250 q^{88} - 104 q^{89} - 36 q^{90} - 96 q^{91} - 137 q^{92} - 155 q^{93} - 48 q^{94} - 38 q^{95} - 33 q^{96} - 447 q^{97} - 46 q^{98} - 94 q^{99}+O(q^{100}) \) 217 * q - 20 * q^2 - 27 * q^3 + 184 * q^4 - 19 * q^5 - 17 * q^6 - 48 * q^7 - 57 * q^8 + 152 * q^9 - 46 * q^10 - 32 * q^11 - 72 * q^12 - 80 * q^13 - 22 * q^14 - 43 * q^15 + 122 * q^16 - 61 * q^17 - 88 * q^18 - 43 * q^19 - 41 * q^20 - 61 * q^21 - 93 * q^22 - 60 * q^23 - 41 * q^24 + 26 * q^25 - 9 * q^26 - 93 * q^27 - 126 * q^28 - 47 * q^29 - 36 * q^30 - 100 * q^31 - 114 * q^32 - 133 * q^33 - 75 * q^34 - 37 * q^35 + 75 * q^36 - 264 * q^37 - 35 * q^38 - 47 * q^39 - 118 * q^40 - 72 * q^41 - 64 * q^42 - 107 * q^43 - 59 * q^44 - 69 * q^45 - 111 * q^46 - 54 * q^47 - 135 * q^48 + 33 * q^49 - 42 * q^50 - 26 * q^51 - 173 * q^52 - 103 * q^53 - 28 * q^54 - 78 * q^55 - 44 * q^56 - 205 * q^57 - 189 * q^58 - 38 * q^59 - 105 * q^60 - 108 * q^61 - 14 * q^62 - 116 * q^63 + 39 * q^64 - 146 * q^65 + 5 * q^66 - 206 * q^67 - 62 * q^68 - 55 * q^69 - 125 * q^70 - 78 * q^71 - 225 * q^72 - 326 * q^73 + 3 * q^74 - 95 * q^75 - 84 * q^76 - 79 * q^77 - 86 * q^78 - 117 * q^79 - 39 * q^80 + q^81 - 96 * q^82 - 23 * q^83 - 57 * q^84 - 224 * q^85 - 7 * q^86 - 45 * q^87 - 250 * q^88 - 104 * q^89 - 36 * q^90 - 96 * q^91 - 137 * q^92 - 155 * q^93 - 48 * q^94 - 38 * q^95 - 33 * q^96 - 447 * q^97 - 46 * q^98 - 94 * 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 $

$2$	−2.78935	−1.97237	−0.986183	−	0.165662i	$-0.947024\pi$
$2$	−2.78935	−1.97237	−0.986183	+	0.165662i	$0.947024\pi$
$3$	0.603668	0.348528	0.174264	−	0.984699i	$-0.444245\pi$
$3$	0.603668	0.348528	0.174264	+	0.984699i	$0.444245\pi$
$4$	5.78045	2.89022
$5$	3.11422	1.39272	0.696360	−	0.717692i	$-0.254802\pi$
$5$	3.11422	1.39272	0.696360	+	0.717692i	$0.254802\pi$
$6$	−1.68384	−0.687424
$7$	0.146622	0.0554178	0.0277089	−	0.999616i	$-0.491179\pi$
$7$	0.146622	0.0554178	0.0277089	+	0.999616i	$0.491179\pi$
$8$	−10.5450	−3.72821
$9$	−2.63558	−0.878528
$10$	−8.68663	−2.74695
$11$	5.95238	1.79471	0.897355	−	0.441309i	$-0.145486\pi$
$11$	5.95238	1.79471	0.897355	+	0.441309i	$0.145486\pi$
$12$	3.48947	1.00732
$13$	−2.13466	−0.592048	−0.296024	−	0.955180i	$-0.595661\pi$
$13$	−2.13466	−0.592048	−0.296024	+	0.955180i	$0.595661\pi$
$14$	−0.408979	−0.109304
$15$	1.87995	0.485402
$16$	17.8527	4.46317
$17$	−3.51865	−0.853399	−0.426699	−	0.904393i	$-0.640324\pi$
$17$	−3.51865	−0.853399	−0.426699	+	0.904393i	$0.640324\pi$
$18$	7.35156	1.73278
$19$	2.37433	0.544709	0.272355	−	0.962197i	$-0.412198\pi$
$19$	2.37433	0.544709	0.272355	+	0.962197i	$0.412198\pi$
$20$	18.0016	4.02528
$21$	0.0885108	0.0193146
$22$	−16.6032	−3.53982
$23$	−3.35265	−0.699076	−0.349538	−	0.936922i	$-0.613661\pi$
$23$	−3.35265	−0.699076	−0.349538	+	0.936922i	$0.613661\pi$
$24$	−6.36567	−1.29939
$25$	4.69836	0.939672
$26$	5.95430	1.16774
$27$	−3.40202	−0.654720
$28$	0.847539	0.160170
$29$	1.70921	0.317392	0.158696	−	0.987327i	$-0.449271\pi$
$29$	1.70921	0.317392	0.158696	+	0.987327i	$0.449271\pi$
$30$	−5.24384	−0.957390
$31$	−2.22831	−0.400216	−0.200108	−	0.979774i	$-0.564129\pi$
$31$	−2.22831	−0.400216	−0.200108	+	0.979774i	$0.564129\pi$
$32$	−28.7074	−5.07480
$33$	3.59326	0.625507
$34$	9.81474	1.68321
$35$	0.456612	0.0771815
$36$	−15.2349	−2.53914
$37$	−6.81464	−1.12032	−0.560160	−	0.828385i	$-0.689260\pi$
$37$	−6.81464	−1.12032	−0.560160	+	0.828385i	$0.689260\pi$
$38$	−6.62283	−1.07437
$39$	−1.28863	−0.206345
$40$	−32.8394	−5.19236
$41$	−2.99107	−0.467126	−0.233563	−	0.972342i	$-0.575038\pi$
$41$	−2.99107	−0.467126	−0.233563	+	0.972342i	$0.575038\pi$
$42$	−0.246887	−0.0380955
$43$	−7.86014	−1.19866	−0.599330	−	0.800502i	$-0.704566\pi$
$43$	−7.86014	−1.19866	−0.599330	+	0.800502i	$0.704566\pi$
$44$	34.4074	5.18712
$45$	−8.20779	−1.22354
$46$	9.35171	1.37883
$47$	−6.38720	−0.931668	−0.465834	−	0.884872i	$-0.654246\pi$
$47$	−6.38720	−0.931668	−0.465834	+	0.884872i	$0.654246\pi$
$48$	10.7771	1.55554
$49$	−6.97850	−0.996929
$50$	−13.1053	−1.85338
$51$	−2.12410	−0.297433
$52$	−12.3393	−1.71115
$53$	−8.02904	−1.10287	−0.551437	−	0.834217i	$-0.685920\pi$
$53$	−8.02904	−1.10287	−0.551437	+	0.834217i	$0.685920\pi$
$54$	9.48942	1.29135
$55$	18.5370	2.49953
$56$	−1.54612	−0.206609
$57$	1.43331	0.189846
$58$	−4.76758	−0.626013
$59$	−0.780236	−0.101578	−0.0507890	−	0.998709i	$-0.516174\pi$
$59$	−0.780236	−0.101578	−0.0507890	+	0.998709i	$0.516174\pi$
$60$	10.8670	1.40292
$61$	10.2256	1.30925	0.654626	−	0.755953i	$-0.272826\pi$
$61$	10.2256	1.30925	0.654626	+	0.755953i	$0.272826\pi$
$62$	6.21552	0.789372
$63$	−0.386434	−0.0486861
$64$	44.3694	5.54618
$65$	−6.64780	−0.824558
$66$	−10.0229	−1.23373
$67$	0.544504	0.0665218	0.0332609	−	0.999447i	$-0.489411\pi$
$67$	0.544504	0.0665218	0.0332609	+	0.999447i	$0.489411\pi$
$68$	−20.3394	−2.46651
$69$	−2.02389	−0.243648
$70$	−1.27365	−0.152230
$71$	0.166754	0.0197900	0.00989501	−	0.999951i	$-0.496850\pi$
$71$	0.166754	0.0197900	0.00989501	+	0.999951i	$0.496850\pi$
$72$	27.7922	3.27534
$73$	3.03385	0.355085	0.177543	−	0.984113i	$-0.443185\pi$
$73$	3.03385	0.355085	0.177543	+	0.984113i	$0.443185\pi$
$74$	19.0084	2.20968
$75$	2.83625	0.327502
$76$	13.7247	1.57433
$77$	0.872748	0.0994589
$78$	3.59442	0.406988
$79$	−17.2844	−1.94465	−0.972325	−	0.233634i	$-0.924938\pi$
$79$	−17.2844	−1.94465	−0.972325	+	0.233634i	$0.924938\pi$
$80$	55.5972	6.21596
$81$	5.85306	0.650340
$82$	8.34312	0.921343
$83$	13.5790	1.49049	0.745244	−	0.666792i	$-0.232333\pi$
$83$	13.5790	1.49049	0.745244	+	0.666792i	$0.232333\pi$
$84$	0.511632	0.0558237
$85$	−10.9579	−1.18855
$86$	21.9246	2.36419
$87$	1.03179	0.110620
$88$	−62.7677	−6.69106
$89$	−9.95654	−1.05539	−0.527695	−	0.849434i	$-0.676944\pi$
$89$	−9.95654	−1.05539	−0.527695	+	0.849434i	$0.676944\pi$
$90$	22.8944	2.41328
$91$	−0.312987	−0.0328100
$92$	−19.3798	−2.02049
$93$	−1.34516	−0.139486
$94$	17.8161	1.83759
$95$	7.39419	0.758628
$96$	−17.3297	−1.76871
$97$	−13.2742	−1.34779	−0.673893	−	0.738829i	$-0.735379\pi$
$97$	−13.2742	−1.34779	−0.673893	+	0.738829i	$0.735379\pi$
$98$	19.4655	1.96631
$99$	−15.6880	−1.57670
$100$	27.1586	2.71586
$101$	4.34471	0.432315	0.216158	−	0.976358i	$-0.430647\pi$
$101$	4.34471	0.432315	0.216158	+	0.976358i	$0.430647\pi$
$102$	5.92485	0.586647
$103$	−7.59892	−0.748743	−0.374372	−	0.927279i	$-0.622142\pi$
$103$	−7.59892	−0.748743	−0.374372	+	0.927279i	$0.622142\pi$
$104$	22.5099	2.20728
$105$	0.275642	0.0268999
$106$	22.3958	2.17527
$107$	−12.1109	−1.17081	−0.585403	−	0.810742i	$-0.699064\pi$
$107$	−12.1109	−1.17081	−0.585403	+	0.810742i	$0.699064\pi$
$108$	−19.6652	−1.89229
$109$	14.0215	1.34302	0.671508	−	0.740998i	$-0.265647\pi$
$109$	14.0215	1.34302	0.671508	+	0.740998i	$0.265647\pi$
$110$	−51.7061	−4.92999
$111$	−4.11378	−0.390463
$112$	2.61759	0.247339
$113$	−8.15613	−0.767264	−0.383632	−	0.923486i	$-0.625327\pi$
$113$	−8.15613	−0.767264	−0.383632	+	0.923486i	$0.625327\pi$
$114$	−3.99799	−0.374446
$115$	−10.4409	−0.973618
$116$	9.88000	0.917335
$117$	5.62608	0.520131
$118$	2.17635	0.200349
$119$	−0.515911	−0.0472935
$120$	−19.8241	−1.80968
$121$	24.4308	2.22099
$122$	−28.5227	−2.58232
$123$	−1.80561	−0.162806
$124$	−12.8806	−1.15671
$125$	−0.939380	−0.0840207
$126$	1.07790	0.0960268
$127$	−19.0134	−1.68716	−0.843581	−	0.537001i	$-0.819557\pi$
$127$	−19.0134	−1.68716	−0.843581	+	0.537001i	$0.819557\pi$
$128$	−66.3469	−5.86429
$129$	−4.74491	−0.417766
$130$	18.5430	1.62633
$131$	−0.369172	−0.0322547	−0.0161274	−	0.999870i	$-0.505134\pi$
$131$	−0.369172	−0.0322547	−0.0161274	+	0.999870i	$0.505134\pi$
$132$	20.7707	1.80785
$133$	0.348129	0.0301866
$134$	−1.51881	−0.131205
$135$	−10.5946	−0.911842
$136$	37.1041	3.18165
$137$	11.4170	0.975420	0.487710	−	0.873006i	$-0.337832\pi$
$137$	11.4170	0.975420	0.487710	+	0.873006i	$0.337832\pi$
$138$	5.64533	0.480562
$139$	−11.6731	−0.990102	−0.495051	−	0.868864i	$-0.664851\pi$
$139$	−11.6731	−0.990102	−0.495051	+	0.868864i	$0.664851\pi$
$140$	2.63942	0.223072
$141$	−3.85575	−0.324712
$142$	−0.465134	−0.0390331
$143$	−12.7063	−1.06255
$144$	−47.0523	−3.92103
$145$	5.32285	0.442039
$146$	−8.46245	−0.700358
$147$	−4.21270	−0.347458
$148$	−39.3917	−3.23798
$149$	5.31409	0.435348	0.217674	−	0.976022i	$-0.430153\pi$
$149$	5.31409	0.435348	0.217674	+	0.976022i	$0.430153\pi$
$150$	−7.91128	−0.645953
$151$	−3.89096	−0.316641	−0.158321	−	0.987388i	$-0.550608\pi$
$151$	−3.89096	−0.316641	−0.158321	+	0.987388i	$0.550608\pi$
$152$	−25.0373	−2.03079
$153$	9.27371	0.749735
$154$	−2.43440	−0.196169
$155$	−6.93944	−0.557389
$156$	−7.44884	−0.596384
$157$	−7.19304	−0.574067	−0.287033	−	0.957921i	$-0.592669\pi$
$157$	−7.19304	−0.574067	−0.287033	+	0.957921i	$0.592669\pi$
$158$	48.2122	3.83556
$159$	−4.84688	−0.384382
$160$	−89.4011	−7.06778
$161$	−0.491572	−0.0387413
$162$	−16.3262	−1.28271
$163$	1.98301	0.155322	0.0776608	−	0.996980i	$-0.475255\pi$
$163$	1.98301	0.155322	0.0776608	+	0.996980i	$0.475255\pi$
$164$	−17.2897	−1.35010
$165$	11.1902	0.871156
$166$	−37.8765	−2.93979
$167$	21.3922	1.65538	0.827690	−	0.561185i	$-0.189654\pi$
$167$	21.3922	1.65538	0.827690	+	0.561185i	$0.189654\pi$
$168$	−0.933345	−0.0720091
$169$	−8.44323	−0.649479
$170$	30.5653	2.34425
$171$	−6.25775	−0.478542
$172$	−45.4351	−3.46440
$173$	22.0184	1.67403	0.837014	−	0.547182i	$-0.184300\pi$
$173$	22.0184	1.67403	0.837014	+	0.547182i	$0.184300\pi$
$174$	−2.87803	−0.218183
$175$	0.688881	0.0520745
$176$	106.266	8.01011
$177$	−0.471003	−0.0354028
$178$	27.7722	2.08162
$179$	−13.7766	−1.02971	−0.514857	−	0.857276i	$-0.672155\pi$
$179$	−13.7766	−1.02971	−0.514857	+	0.857276i	$0.672155\pi$
$180$	−47.4447	−3.53632
$181$	0.892525	0.0663409	0.0331704	−	0.999450i	$-0.489440\pi$
$181$	0.892525	0.0663409	0.0331704	+	0.999450i	$0.489440\pi$
$182$	0.873030	0.0647133
$183$	6.17286	0.456311
$184$	35.3537	2.60631
$185$	−21.2223	−1.56029
$186$	3.75211	0.275118
$187$	−20.9444	−1.53160
$188$	−36.9209	−2.69273
$189$	−0.498810	−0.0362831
$190$	−20.6249	−1.49629
$191$	−24.4872	−1.77184	−0.885918	−	0.463843i	$-0.846470\pi$
$191$	−24.4872	−1.77184	−0.885918	+	0.463843i	$0.846470\pi$
$192$	26.7844	1.93300
$193$	9.34731	0.672834	0.336417	−	0.941713i	$-0.390785\pi$
$193$	9.34731	0.672834	0.336417	+	0.941713i	$0.390785\pi$
$194$	37.0262	2.65833
$195$	−4.01306	−0.287381
$196$	−40.3389	−2.88135
$197$	−15.2725	−1.08812	−0.544060	−	0.839047i	$-0.683113\pi$
$197$	−15.2725	−1.08812	−0.544060	+	0.839047i	$0.683113\pi$
$198$	43.7593	3.10984
$199$	−4.06137	−0.287903	−0.143951	−	0.989585i	$-0.545981\pi$
$199$	−4.06137	−0.287903	−0.143951	+	0.989585i	$0.545981\pi$
$200$	−49.5441	−3.50330
$201$	0.328700	0.0231847
$202$	−12.1189	−0.852684
$203$	0.250607	0.0175892
$204$	−12.2782	−0.859649
$205$	−9.31483	−0.650576
$206$	21.1960	1.47680
$207$	8.83620	0.614158
$208$	−38.1094	−2.64241
$209$	14.1329	0.977595
$210$	−0.768861	−0.0530565
$211$	−2.51231	−0.172955	−0.0864773	−	0.996254i	$-0.527561\pi$
$211$	−2.51231	−0.172955	−0.0864773	+	0.996254i	$0.527561\pi$
$212$	−46.4115	−3.18755
$213$	0.100664	0.00689737
$214$	33.7815	2.30926
$215$	−24.4782	−1.66940
$216$	35.8743	2.44093
$217$	−0.326718	−0.0221791
$218$	−39.1108	−2.64892
$219$	1.83144	0.123757
$220$	107.152	7.22421
$221$	7.51113	0.505253
$222$	11.4748	0.770135
$223$	−8.79909	−0.589230	−0.294615	−	0.955616i	$-0.595191\pi$
$223$	−8.79909	−0.589230	−0.294615	+	0.955616i	$0.595191\pi$
$224$	−4.20913	−0.281234
$225$	−12.3829	−0.825528
$226$	22.7503	1.51333
$227$	5.32608	0.353504	0.176752	−	0.984255i	$-0.443441\pi$
$227$	5.32608	0.353504	0.176752	+	0.984255i	$0.443441\pi$
$228$	8.28516	0.548698
$229$	−5.46179	−0.360925	−0.180463	−	0.983582i	$-0.557760\pi$
$229$	−5.46179	−0.360925	−0.180463	+	0.983582i	$0.557760\pi$
$230$	29.1233	1.92033
$231$	0.526850	0.0346642
$232$	−18.0236	−1.18331
$233$	12.6603	0.829401	0.414701	−	0.909958i	$-0.363886\pi$
$233$	12.6603	0.829401	0.414701	+	0.909958i	$0.363886\pi$
$234$	−15.6931	−1.02589
$235$	−19.8911	−1.29755
$236$	−4.51011	−0.293583
$237$	−10.4341	−0.677764
$238$	1.43905	0.0932800
$239$	23.0755	1.49263	0.746314	−	0.665595i	$-0.231822\pi$
$239$	23.0755	1.49263	0.746314	+	0.665595i	$0.231822\pi$
$240$	33.5623	2.16643
$241$	−24.0218	−1.54738	−0.773690	−	0.633565i	$-0.781591\pi$
$241$	−24.0218	−1.54738	−0.773690	+	0.633565i	$0.781591\pi$
$242$	−68.1461	−4.38059
$243$	13.7394	0.881381
$244$	59.1085	3.78403
$245$	−21.7326	−1.38844
$246$	5.03647	0.321114
$247$	−5.06839	−0.322494
$248$	23.4975	1.49209
$249$	8.19720	0.519477
$250$	2.62026	0.165720
$251$	−10.5674	−0.667005	−0.333503	−	0.942749i	$-0.608231\pi$
$251$	−10.5674	−0.667005	−0.333503	+	0.942749i	$0.608231\pi$
$252$	−2.23376	−0.140714
$253$	−19.9563	−1.25464
$254$	53.0348	3.32770
$255$	−6.61491	−0.414242
$256$	96.3256	6.02035
$257$	24.6727	1.53904	0.769522	−	0.638620i	$-0.220495\pi$
$257$	24.6727	1.53904	0.769522	+	0.638620i	$0.220495\pi$
$258$	13.2352	0.823988
$259$	−0.999174	−0.0620856
$260$	−38.4273	−2.38316
$261$	−4.50477	−0.278838
$262$	1.02975	0.0636181
$263$	12.0946	0.745783	0.372892	−	0.927875i	$-0.378366\pi$
$263$	12.0946	0.745783	0.372892	+	0.927875i	$0.378366\pi$
$264$	−37.8909	−2.33202
$265$	−25.0042	−1.53600
$266$	−0.971051	−0.0595389
$267$	−6.01044	−0.367833
$268$	3.14748	0.192263
$269$	−8.57163	−0.522622	−0.261311	−	0.965255i	$-0.584155\pi$
$269$	−8.57163	−0.522622	−0.261311	+	0.965255i	$0.584155\pi$
$270$	29.5521	1.79848
$271$	−5.50129	−0.334179	−0.167090	−	0.985942i	$-0.553437\pi$
$271$	−5.50129	−0.334179	−0.167090	+	0.985942i	$0.553437\pi$
$272$	−62.8175	−3.80887
$273$	−0.188940	−0.0114352
$274$	−31.8460	−1.92388
$275$	27.9664	1.68644
$276$	−11.6990	−0.704196
$277$	−11.3337	−0.680977	−0.340489	−	0.940249i	$-0.610592\pi$
$277$	−11.3337	−0.680977	−0.340489	+	0.940249i	$0.610592\pi$
$278$	32.5604	1.95284
$279$	5.87289	0.351601
$280$	−4.81496	−0.287749
$281$	−12.8954	−0.769275	−0.384637	−	0.923068i	$-0.625673\pi$
$281$	−12.8954	−0.769275	−0.384637	+	0.923068i	$0.625673\pi$
$282$	10.7550	0.640452
$283$	31.5986	1.87834	0.939170	−	0.343453i	$-0.111597\pi$
$283$	31.5986	1.87834	0.939170	+	0.343453i	$0.111597\pi$
$284$	0.963911	0.0571976
$285$	4.46363	0.264403
$286$	35.4423	2.09575
$287$	−0.438555	−0.0258871
$288$	75.6608	4.45835
$289$	−4.61907	−0.271710
$290$	−14.8473	−0.871862
$291$	−8.01318	−0.469741
$292$	17.5370	1.02628
$293$	19.0481	1.11280	0.556400	−	0.830914i	$-0.312182\pi$
$293$	19.0481	1.11280	0.556400	+	0.830914i	$0.312182\pi$
$294$	11.7507	0.685313
$295$	−2.42982	−0.141470
$296$	71.8602	4.17679
$297$	−20.2501	−1.17503
$298$	−14.8228	−0.858664
$299$	7.15677	0.413887
$300$	16.3948	0.946554
$301$	−1.15247	−0.0664271
$302$	10.8532	0.624533
$303$	2.62277	0.150674
$304$	42.3882	2.43113
$305$	31.8447	1.82342
$306$	−25.8676	−1.47875
$307$	23.5582	1.34454	0.672268	−	0.740308i	$-0.265320\pi$
$307$	23.5582	1.34454	0.672268	+	0.740308i	$0.265320\pi$
$308$	5.04488	0.287459
$309$	−4.58722	−0.260958
$310$	19.3565	1.09937
$311$	0.623393	0.0353494	0.0176747	−	0.999844i	$-0.494374\pi$
$311$	0.623393	0.0353494	0.0176747	+	0.999844i	$0.494374\pi$
$312$	13.5885	0.769299
$313$	4.49134	0.253866	0.126933	−	0.991911i	$-0.459487\pi$
$313$	4.49134	0.253866	0.126933	+	0.991911i	$0.459487\pi$
$314$	20.0639	1.13227
$315$	−1.20344	−0.0678061
$316$	−99.9117	−5.62047
$317$	22.4566	1.26129	0.630644	−	0.776072i	$-0.282791\pi$
$317$	22.4566	1.26129	0.630644	+	0.776072i	$0.282791\pi$
$318$	13.5196	0.758142
$319$	10.1739	0.569627
$320$	138.176	7.72428
$321$	−7.31097	−0.408059
$322$	1.37116	0.0764119
$323$	−8.35445	−0.464854
$324$	33.8333	1.87963
$325$	−10.0294	−0.556331
$326$	−5.53131	−0.306351
$327$	8.46433	0.468078
$328$	31.5407	1.74155
$329$	−0.936502	−0.0516310
$330$	−31.2133	−1.71824
$331$	11.9739	0.658145	0.329072	−	0.944305i	$-0.393264\pi$
$331$	11.9739	0.658145	0.329072	+	0.944305i	$0.393264\pi$
$332$	78.4927	4.30784
$333$	17.9606	0.984232
$334$	−59.6703	−3.26502
$335$	1.69570	0.0926462
$336$	1.58016	0.0862046
$337$	−11.5360	−0.628408	−0.314204	−	0.949355i	$-0.601738\pi$
$337$	−11.5360	−0.628408	−0.314204	+	0.949355i	$0.601738\pi$
$338$	23.5511	1.28101
$339$	−4.92360	−0.267413
$340$	−63.3413	−3.43517
$341$	−13.2637	−0.718272
$342$	17.4550	0.943860
$343$	−2.04955	−0.110665
$344$	82.8850	4.46886
$345$	−6.30283	−0.339333
$346$	−61.4169	−3.30179
$347$	34.7824	1.86722	0.933609	−	0.358292i	$-0.116641\pi$
$347$	34.7824	1.86722	0.933609	+	0.358292i	$0.116641\pi$
$348$	5.96424	0.319717
$349$	−14.7234	−0.788125	−0.394063	−	0.919084i	$-0.628931\pi$
$349$	−14.7234	−0.788125	−0.394063	+	0.919084i	$0.628931\pi$
$350$	−1.92153	−0.102710
$351$	7.26216	0.387625
$352$	−170.877	−9.10779
$353$	−2.56771	−0.136665	−0.0683327	−	0.997663i	$-0.521768\pi$
$353$	−2.56771	−0.136665	−0.0683327	+	0.997663i	$0.521768\pi$
$354$	1.31379	0.0698272
$355$	0.519307	0.0275620
$356$	−57.5533	−3.05032
$357$	−0.311439	−0.0164831
$358$	38.4278	2.03097
$359$	5.99448	0.316376	0.158188	−	0.987409i	$-0.449435\pi$
$359$	5.99448	0.316376	0.158188	+	0.987409i	$0.449435\pi$
$360$	86.5510	4.56164
$361$	−13.3625	−0.703292
$362$	−2.48956	−0.130848
$363$	14.7481	0.774075
$364$	−1.80921	−0.0948283
$365$	9.44807	0.494534
$366$	−17.2182	−0.900012
$367$	−14.8711	−0.776265	−0.388132	−	0.921604i	$-0.626880\pi$
$367$	−14.8711	−0.776265	−0.388132	+	0.921604i	$0.626880\pi$
$368$	−59.8539	−3.12010
$369$	7.88321	0.410383
$370$	59.1963	3.07747
$371$	−1.17723	−0.0611188
$372$	−7.77562	−0.403147
$373$	33.6745	1.74360	0.871801	−	0.489860i	$-0.162952\pi$
$373$	33.6745	1.74360	0.871801	+	0.489860i	$0.162952\pi$
$374$	58.4211	3.02088
$375$	−0.567074	−0.0292836
$376$	67.3529	3.47346
$377$	−3.64858	−0.187911
$378$	1.39135	0.0715635
$379$	−12.2864	−0.631110	−0.315555	−	0.948907i	$-0.602191\pi$
$379$	−12.2864	−0.631110	−0.315555	+	0.948907i	$0.602191\pi$
$380$	42.7417	2.19260
$381$	−11.4778	−0.588023
$382$	68.3034	3.49471
$383$	−3.59376	−0.183633	−0.0918164	−	0.995776i	$-0.529267\pi$
$383$	−3.59376	−0.183633	−0.0918164	+	0.995776i	$0.529267\pi$
$384$	−40.0515	−2.04387
$385$	2.71793	0.138518
$386$	−26.0729	−1.32708
$387$	20.7161	1.05306
$388$	−76.7306	−3.89540
$389$	−10.1484	−0.514545	−0.257273	−	0.966339i	$-0.582824\pi$
$389$	−10.1484	−0.514545	−0.257273	+	0.966339i	$0.582824\pi$
$390$	11.1938	0.566821
$391$	11.7968	0.596591
$392$	73.5882	3.71676
$393$	−0.222858	−0.0112417
$394$	42.6002	2.14617
$395$	−53.8275	−2.70835
$396$	−90.6837	−4.55703
$397$	−13.1624	−0.660600	−0.330300	−	0.943876i	$-0.607150\pi$
$397$	−13.1624	−0.660600	−0.330300	+	0.943876i	$0.607150\pi$
$398$	11.3286	0.567849
$399$	0.210154	0.0105209
$400$	83.8784	4.19392
$401$	32.6107	1.62850	0.814251	−	0.580513i	$-0.197148\pi$
$401$	32.6107	1.62850	0.814251	+	0.580513i	$0.197148\pi$
$402$	−0.916857	−0.0457287
$403$	4.75668	0.236947
$404$	25.1144	1.24949
$405$	18.2277	0.905743
$406$	−0.699030	−0.0346923
$407$	−40.5633	−2.01065
$408$	22.3986	1.10890
$409$	2.07085	0.102397	0.0511985	−	0.998688i	$-0.483696\pi$
$409$	2.07085	0.102397	0.0511985	+	0.998688i	$0.483696\pi$
$410$	25.9823	1.28317
$411$	6.89208	0.339961
$412$	−43.9251	−2.16404
$413$	−0.114399	−0.00562923
$414$	−24.6472	−1.21134
$415$	42.2879	2.07583
$416$	61.2805	3.00452
$417$	−7.04669	−0.345078
$418$	−39.4216	−1.92817
$419$	−34.9792	−1.70885	−0.854424	−	0.519577i	$-0.826090\pi$
$419$	−34.9792	−1.70885	−0.854424	+	0.519577i	$0.826090\pi$
$420$	1.59334	0.0777468
$421$	8.22263	0.400746	0.200373	−	0.979720i	$-0.435785\pi$
$421$	8.22263	0.400746	0.200373	+	0.979720i	$0.435785\pi$
$422$	7.00770	0.341129
$423$	16.8340	0.818497
$424$	84.6661	4.11175
$425$	−16.5319	−0.801915
$426$	−0.280786	−0.0136041
$427$	1.49929	0.0725559
$428$	−70.0065	−3.38389
$429$	−7.67039	−0.370330
$430$	68.2781	3.29266
$431$	16.3871	0.789337	0.394669	−	0.918824i	$-0.370859\pi$
$431$	16.3871	0.789337	0.394669	+	0.918824i	$0.370859\pi$
$432$	−60.7353	−2.92213
$433$	−21.8970	−1.05230	−0.526152	−	0.850390i	$-0.676366\pi$
$433$	−21.8970	−1.05230	−0.526152	+	0.850390i	$0.676366\pi$
$434$	0.911330	0.0437452
$435$	3.21324	0.154063
$436$	81.0505	3.88162
$437$	−7.96031	−0.380793
$438$	−5.10851	−0.244094
$439$	13.7995	0.658616	0.329308	−	0.944222i	$-0.393184\pi$
$439$	13.7995	0.658616	0.329308	+	0.944222i	$0.393184\pi$
$440$	−195.472	−9.31878
$441$	18.3924	0.875830
$442$	−20.9511	−0.996544
$443$	−10.4209	−0.495110	−0.247555	−	0.968874i	$-0.579627\pi$
$443$	−10.4209	−0.495110	−0.247555	+	0.968874i	$0.579627\pi$
$444$	−23.7795	−1.12852
$445$	−31.0068	−1.46986
$446$	24.5437	1.16218
$447$	3.20795	0.151731
$448$	6.50552	0.307357
$449$	34.1754	1.61284	0.806418	−	0.591346i	$-0.201403\pi$
$449$	34.1754	1.61284	0.806418	+	0.591346i	$0.201403\pi$
$450$	34.5402	1.62824
$451$	−17.8040	−0.838356
$452$	−47.1461	−2.21757
$453$	−2.34885	−0.110358
$454$	−14.8563	−0.697240
$455$	−0.974711	−0.0456952
$456$	−15.1142	−0.707788
$457$	−17.1955	−0.804369	−0.402185	−	0.915559i	$-0.631749\pi$
$457$	−17.1955	−0.804369	−0.402185	+	0.915559i	$0.631749\pi$
$458$	15.2348	0.711877
$459$	11.9705	0.558737
$460$	−60.3530	−2.81398
$461$	5.44389	0.253547	0.126774	−	0.991932i	$-0.459538\pi$
$461$	5.44389	0.253547	0.126774	+	0.991932i	$0.459538\pi$
$462$	−1.46957	−0.0683705
$463$	25.9390	1.20549	0.602744	−	0.797935i	$-0.294074\pi$
$463$	25.9390	1.20549	0.602744	+	0.797935i	$0.294074\pi$
$464$	30.5140	1.41658
$465$	−4.18912	−0.194266
$466$	−35.3139	−1.63588
$467$	−4.87311	−0.225501	−0.112750	−	0.993623i	$-0.535966\pi$
$467$	−4.87311	−0.225501	−0.112750	+	0.993623i	$0.535966\pi$
$468$	32.5213	1.50330
$469$	0.0798361	0.00368649
$470$	55.4832	2.55925
$471$	−4.34221	−0.200078
$472$	8.22757	0.378705
$473$	−46.7865	−2.15125
$474$	29.1042	1.33680
$475$	11.1555	0.511848
$476$	−2.98220	−0.136689
$477$	21.1612	0.968906
$478$	−64.3654	−2.94401
$479$	21.5693	0.985528	0.492764	−	0.870163i	$-0.335987\pi$
$479$	21.5693	0.985528	0.492764	+	0.870163i	$0.335987\pi$
$480$	−53.9686	−2.46332
$481$	14.5469	0.663283
$482$	67.0051	3.05200
$483$	−0.296746	−0.0135024
$484$	141.221	6.41915
$485$	−41.3386	−1.87709
$486$	−38.3239	−1.73841
$487$	−8.92980	−0.404648	−0.202324	−	0.979319i	$-0.564849\pi$
$487$	−8.92980	−0.404648	−0.202324	+	0.979319i	$0.564849\pi$
$488$	−107.829	−4.88117
$489$	1.19708	0.0541339
$490$	60.6197	2.73852
$491$	30.2194	1.36378	0.681891	−	0.731454i	$-0.261158\pi$
$491$	30.2194	1.36378	0.681891	+	0.731454i	$0.261158\pi$
$492$	−10.4372	−0.470547
$493$	−6.01412	−0.270862
$494$	14.1375	0.636076
$495$	−48.8559	−2.19591
$496$	−39.7813	−1.78623
$497$	0.0244497	0.00109672
$498$	−22.8648	−1.02460
$499$	12.7182	0.569347	0.284673	−	0.958625i	$-0.408115\pi$
$499$	12.7182	0.569347	0.284673	+	0.958625i	$0.408115\pi$
$500$	−5.43004	−0.242839
$501$	12.9138	0.576946
$502$	29.4760	1.31558
$503$	−35.4007	−1.57844	−0.789220	−	0.614110i	$-0.789515\pi$
$503$	−35.4007	−1.57844	−0.789220	+	0.614110i	$0.789515\pi$
$504$	4.07494	0.181512
$505$	13.5304	0.602094
$506$	55.6649	2.47461
$507$	−5.09691	−0.226362
$508$	−109.906	−4.87628
$509$	22.0016	0.975205	0.487602	−	0.873066i	$-0.337872\pi$
$509$	22.0016	0.975205	0.487602	+	0.873066i	$0.337872\pi$
$510$	18.4513	0.817036
$511$	0.444828	0.0196780
$512$	−135.992	−6.01004
$513$	−8.07753	−0.356632
$514$	−68.8208	−3.03556
$515$	−23.6647	−1.04279
$516$	−27.4277	−1.20744
$517$	−38.0190	−1.67208
$518$	2.78704	0.122456
$519$	13.2918	0.583445
$520$	70.1009	3.07413
$521$	23.3575	1.02331	0.511656	−	0.859190i	$-0.329032\pi$
$521$	23.3575	1.02331	0.511656	+	0.859190i	$0.329032\pi$
$522$	12.5654	0.549970
$523$	30.2439	1.32247	0.661237	−	0.750177i	$-0.270032\pi$
$523$	30.2439	1.32247	0.661237	+	0.750177i	$0.270032\pi$
$524$	−2.13398	−0.0932234
$525$	0.415856	0.0181494
$526$	−33.7359	−1.47096
$527$	7.84064	0.341544
$528$	64.1494	2.79175
$529$	−11.7597	−0.511292
$530$	69.7453	3.02954
$531$	2.05638	0.0892392
$532$	2.01234	0.0872460
$533$	6.38491	0.276561
$534$	16.7652	0.725501
$535$	−37.7160	−1.63061
$536$	−5.74179	−0.248007
$537$	−8.31651	−0.358884
$538$	23.9092	1.03080
$539$	−41.5387	−1.78920
$540$	−61.2418	−2.63543
$541$	25.6488	1.10273	0.551364	−	0.834265i	$-0.314108\pi$
$541$	25.6488	1.10273	0.551364	+	0.834265i	$0.314108\pi$
$542$	15.3450	0.659124
$543$	0.538789	0.0231216
$544$	101.011	4.33083
$545$	43.6660	1.87045
$546$	0.527020	0.0225544
$547$	−27.4179	−1.17230	−0.586152	−	0.810201i	$-0.699358\pi$
$547$	−27.4179	−1.17230	−0.586152	+	0.810201i	$0.699358\pi$
$548$	65.9954	2.81918
$549$	−26.9504	−1.15022
$550$	−78.0080	−3.32627
$551$	4.05823	0.172886
$552$	21.3419	0.908370
$553$	−2.53427	−0.107768
$554$	31.6137	1.34314
$555$	−12.8112	−0.543805
$556$	−67.4759	−2.86162
$557$	16.6884	0.707111	0.353556	−	0.935414i	$-0.384973\pi$
$557$	16.6884	0.707111	0.353556	+	0.935414i	$0.384973\pi$
$558$	−16.3815	−0.693486
$559$	16.7787	0.709664
$560$	8.15176	0.344475
$561$	−12.6434	−0.533807
$562$	35.9697	1.51729
$563$	−33.8088	−1.42487	−0.712435	−	0.701738i	$-0.752408\pi$
$563$	−33.8088	−1.42487	−0.712435	+	0.701738i	$0.752408\pi$
$564$	−22.2879	−0.938492
$565$	−25.4000	−1.06858
$566$	−88.1393	−3.70477
$567$	0.858186	0.0360404
$568$	−1.75841	−0.0737814
$569$	9.34218	0.391645	0.195822	−	0.980639i	$-0.437262\pi$
$569$	9.34218	0.391645	0.195822	+	0.980639i	$0.437262\pi$
$570$	−12.4506	−0.521499
$571$	−47.2998	−1.97944	−0.989718	−	0.143034i	$-0.954314\pi$
$571$	−47.2998	−1.97944	−0.989718	+	0.143034i	$0.954314\pi$
$572$	−73.4482	−3.07102
$573$	−14.7822	−0.617534
$574$	1.22328	0.0510588
$575$	−15.7520	−0.656902
$576$	−116.939	−4.87247
$577$	5.37219	0.223647	0.111824	−	0.993728i	$-0.464331\pi$
$577$	5.37219	0.223647	0.111824	+	0.993728i	$0.464331\pi$
$578$	12.8842	0.535912
$579$	5.64267	0.234502
$580$	30.7685	1.27759
$581$	1.99097	0.0825995
$582$	22.3515	0.926501
$583$	−47.7919	−1.97934
$584$	−31.9919	−1.32383
$585$	17.5208	0.724397
$586$	−53.1317	−2.19485
$587$	12.4830	0.515229	0.257615	−	0.966248i	$-0.417064\pi$
$587$	12.4830	0.515229	0.257615	+	0.966248i	$0.417064\pi$
$588$	−24.3513	−1.00423
$589$	−5.29074	−0.218001
$590$	6.77762	0.279030
$591$	−9.21951	−0.379240
$592$	−121.660	−5.00018
$593$	−34.2950	−1.40833	−0.704164	−	0.710038i	$-0.748678\pi$
$593$	−34.2950	−1.40833	−0.704164	+	0.710038i	$0.748678\pi$
$594$	56.4846	2.31759
$595$	−1.60666	−0.0658666
$596$	30.7178	1.25825
$597$	−2.45172	−0.100342
$598$	−19.9627	−0.816336
$599$	−46.8779	−1.91538	−0.957690	−	0.287800i	$-0.907076\pi$
$599$	−46.8779	−1.91538	−0.957690	+	0.287800i	$0.907076\pi$
$600$	−29.9082	−1.22100
$601$	−37.4903	−1.52926	−0.764630	−	0.644469i	$-0.777078\pi$
$601$	−37.4903	−1.52926	−0.764630	+	0.644469i	$0.777078\pi$
$602$	3.21463	0.131018
$603$	−1.43509	−0.0584413
$604$	−22.4915	−0.915165
$605$	76.0830	3.09321
$606$	−7.31580	−0.297184
$607$	−17.2696	−0.700952	−0.350476	−	0.936572i	$-0.613980\pi$
$607$	−17.2696	−0.700952	−0.350476	+	0.936572i	$0.613980\pi$
$608$	−68.1609	−2.76429
$609$	0.151284	0.00613032
$610$	−88.8259	−3.59646
$611$	13.6345	0.551592
$612$	53.6062	2.16690
$613$	−21.1978	−0.856171	−0.428086	−	0.903738i	$-0.640812\pi$
$613$	−21.1978	−0.856171	−0.428086	+	0.903738i	$0.640812\pi$
$614$	−65.7118	−2.65191
$615$	−5.62307	−0.226744
$616$	−9.20311	−0.370804
$617$	29.5842	1.19102	0.595508	−	0.803350i	$-0.296951\pi$
$617$	29.5842	1.19102	0.595508	+	0.803350i	$0.296951\pi$
$618$	12.7953	0.514704
$619$	−34.3827	−1.38196	−0.690978	−	0.722875i	$-0.742820\pi$
$619$	−34.3827	−1.38196	−0.690978	+	0.722875i	$0.742820\pi$
$620$	−40.1131	−1.61098
$621$	11.4058	0.457699
$622$	−1.73886	−0.0697219
$623$	−1.45984	−0.0584874
$624$	−23.0054	−0.920955
$625$	−26.4172	−1.05669
$626$	−12.5279	−0.500716
$627$	8.53160	0.340719
$628$	−41.5790	−1.65918
$629$	23.9784	0.956079
$630$	3.35681	0.133738
$631$	30.5125	1.21468	0.607341	−	0.794441i	$-0.292236\pi$
$631$	30.5125	1.21468	0.607341	+	0.794441i	$0.292236\pi$
$632$	182.264	7.25007
$633$	−1.51660	−0.0602795
$634$	−62.6392	−2.48772
$635$	−59.2118	−2.34975
$636$	−28.0171	−1.11095
$637$	14.8967	0.590230
$638$	−28.3784	−1.12351
$639$	−0.439493	−0.0173861
$640$	−206.619	−8.16732
$641$	−3.08571	−0.121878	−0.0609391	−	0.998141i	$-0.519410\pi$
$641$	−3.08571	−0.121878	−0.0609391	+	0.998141i	$0.519410\pi$
$642$	20.3928	0.804841
$643$	−3.20195	−0.126273	−0.0631363	−	0.998005i	$-0.520110\pi$
$643$	−3.20195	−0.126273	−0.0631363	+	0.998005i	$0.520110\pi$
$644$	−2.84150	−0.111971
$645$	−14.7767	−0.581832
$646$	23.3035	0.916862
$647$	37.8012	1.48612	0.743060	−	0.669225i	$-0.233374\pi$
$647$	37.8012	1.48612	0.743060	+	0.669225i	$0.233374\pi$
$648$	−61.7204	−2.42461
$649$	−4.64426	−0.182303
$650$	27.9754	1.09729
$651$	−0.197229	−0.00773003
$652$	11.4627	0.448914
$653$	18.3117	0.716593	0.358297	−	0.933608i	$-0.383358\pi$
$653$	18.3117	0.716593	0.358297	+	0.933608i	$0.383358\pi$
$654$	−23.6099	−0.923221
$655$	−1.14968	−0.0449218
$656$	−53.3986	−2.08486
$657$	−7.99597	−0.311952
$658$	2.61223	0.101835
$659$	−44.5433	−1.73516	−0.867580	−	0.497297i	$-0.834326\pi$
$659$	−44.5433	−1.73516	−0.867580	+	0.497297i	$0.834326\pi$
$660$	64.6844	2.51784
$661$	2.66514	0.103662	0.0518310	−	0.998656i	$-0.483494\pi$
$661$	2.66514	0.103662	0.0518310	+	0.998656i	$0.483494\pi$
$662$	−33.3993	−1.29810
$663$	4.53423	0.176095
$664$	−143.190	−5.55686
$665$	1.08415	0.0420415
$666$	−50.0982	−1.94127
$667$	−5.73038	−0.221881
$668$	123.657	4.78442
$669$	−5.31173	−0.205363
$670$	−4.72991	−0.182732
$671$	60.8666	2.34973
$672$	−2.54091	−0.0980179
$673$	−21.1637	−0.815799	−0.407900	−	0.913027i	$-0.633739\pi$
$673$	−21.1637	−0.815799	−0.407900	+	0.913027i	$0.633739\pi$
$674$	32.1780	1.23945
$675$	−15.9839	−0.615221
$676$	−48.8057	−1.87714
$677$	−32.4025	−1.24533	−0.622664	−	0.782489i	$-0.713950\pi$
$677$	−32.4025	−1.24533	−0.622664	+	0.782489i	$0.713950\pi$
$678$	13.7336	0.527436
$679$	−1.94628	−0.0746913
$680$	115.550	4.43116
$681$	3.21519	0.123206
$682$	36.9971	1.41669
$683$	30.8331	1.17980	0.589899	−	0.807477i	$-0.299168\pi$
$683$	30.8331	1.17980	0.589899	+	0.807477i	$0.299168\pi$
$684$	−36.1726	−1.38309
$685$	35.5550	1.35849
$686$	5.71691	0.218273
$687$	−3.29711	−0.125793
$688$	−140.325	−5.34983
$689$	17.1393	0.652954
$690$	17.5808	0.669289
$691$	27.7925	1.05728	0.528639	−	0.848847i	$-0.322703\pi$
$691$	27.7925	1.05728	0.528639	+	0.848847i	$0.322703\pi$
$692$	127.276	4.83831
$693$	−2.30020	−0.0873774
$694$	−97.0202	−3.68284
$695$	−36.3527	−1.37894
$696$	−10.8803	−0.412415
$697$	10.5245	0.398645
$698$	41.0686	1.55447
$699$	7.64260	0.289070
$700$	3.98204	0.150507
$701$	−9.87871	−0.373114	−0.186557	−	0.982444i	$-0.559733\pi$
$701$	−9.87871	−0.373114	−0.186557	+	0.982444i	$0.559733\pi$
$702$	−20.2567	−0.764539
$703$	−16.1802	−0.610248
$704$	264.104	9.95378
$705$	−12.0076	−0.452234
$706$	7.16223	0.269554
$707$	0.637029	0.0239580
$708$	−2.72261	−0.102322
$709$	11.5740	0.434672	0.217336	−	0.976097i	$-0.430263\pi$
$709$	11.5740	0.434672	0.217336	+	0.976097i	$0.430263\pi$
$710$	−1.44853	−0.0543623
$711$	45.5546	1.70843
$712$	104.991	3.93472
$713$	7.47074	0.279781
$714$	0.868711	0.0325107
$715$	−39.5702	−1.47984
$716$	−79.6351	−2.97610
$717$	13.9299	0.520222
$718$	−16.7207	−0.624010
$719$	−2.99122	−0.111554	−0.0557769	−	0.998443i	$-0.517764\pi$
$719$	−2.99122	−0.111554	−0.0557769	+	0.998443i	$0.517764\pi$
$720$	−146.531	−5.46089
$721$	−1.11417	−0.0414937
$722$	37.2728	1.38715
$723$	−14.5012	−0.539305
$724$	5.15920	0.191740
$725$	8.03048	0.298244
$726$	−41.1376	−1.52676
$727$	14.4920	0.537477	0.268738	−	0.963213i	$-0.413393\pi$
$727$	14.4920	0.537477	0.268738	+	0.963213i	$0.413393\pi$
$728$	3.30045	0.122323
$729$	−9.26517	−0.343154
$730$	−26.3539	−0.975403
$731$	27.6571	1.02293
$732$	35.6819	1.31884
$733$	−0.529893	−0.0195720	−0.00978602	−	0.999952i	$-0.503115\pi$
$733$	−0.529893	−0.0195720	−0.00978602	+	0.999952i	$0.503115\pi$
$734$	41.4806	1.53108
$735$	−13.1193	−0.483911
$736$	96.2459	3.54767
$737$	3.24110	0.119387
$738$	−21.9890	−0.809426
$739$	7.16136	0.263435	0.131718	−	0.991287i	$-0.457951\pi$
$739$	7.16136	0.263435	0.131718	+	0.991287i	$0.457951\pi$
$740$	−122.674	−4.50960
$741$	−3.05962	−0.112398
$742$	3.28371	0.120549
$743$	7.98146	0.292811	0.146406	−	0.989225i	$-0.453230\pi$
$743$	7.98146	0.292811	0.146406	+	0.989225i	$0.453230\pi$
$744$	14.1847	0.520035
$745$	16.5492	0.606318
$746$	−93.9300	−3.43902
$747$	−35.7886	−1.30944
$748$	−121.068	−4.42668
$749$	−1.77572	−0.0648835
$750$	1.58176	0.0577579
$751$	9.51391	0.347168	0.173584	−	0.984819i	$-0.444465\pi$
$751$	9.51391	0.347168	0.173584	+	0.984819i	$0.444465\pi$
$752$	−114.029	−4.15820
$753$	−6.37917	−0.232470
$754$	10.1772	0.370630
$755$	−12.1173	−0.440993
$756$	−2.88335	−0.104866
$757$	2.81053	0.102150	0.0510752	−	0.998695i	$-0.483735\pi$
$757$	2.81053	0.102150	0.0510752	+	0.998695i	$0.483735\pi$
$758$	34.2710	1.24478
$759$	−12.0470	−0.437277
$760$	−77.9716	−2.82833
$761$	−41.2442	−1.49510	−0.747550	−	0.664206i	$-0.768770\pi$
$761$	−41.2442	−1.49510	−0.747550	+	0.664206i	$0.768770\pi$
$762$	32.0154	1.15980
$763$	2.05585	0.0744269
$764$	−141.547	−5.12100
$765$	28.8804	1.04417
$766$	10.0243	0.362191
$767$	1.66554	0.0601391
$768$	58.1487	2.09826
$769$	5.90954	0.213103	0.106552	−	0.994307i	$-0.466019\pi$
$769$	5.90954	0.213103	0.106552	+	0.994307i	$0.466019\pi$
$770$	−7.58124	−0.273209
$771$	14.8942	0.536400
$772$	54.0317	1.94464
$773$	−34.7797	−1.25094	−0.625469	−	0.780249i	$-0.715093\pi$
$773$	−34.7797	−1.25094	−0.625469	+	0.780249i	$0.715093\pi$
$774$	−57.7842	−2.07701
$775$	−10.4694	−0.376071
$776$	139.976	5.02483
$777$	−0.603169	−0.0216386
$778$	28.3074	1.01487
$779$	−7.10178	−0.254448
$780$	−23.1973	−0.830597
$781$	0.992581	0.0355173
$782$	−32.9054	−1.17670
$783$	−5.81477	−0.207803
$784$	−124.585	−4.44947
$785$	−22.4007	−0.799515
$786$	0.621627	0.0221727
$787$	−2.26503	−0.0807396	−0.0403698	−	0.999185i	$-0.512854\pi$
$787$	−2.26503	−0.0807396	−0.0403698	+	0.999185i	$0.512854\pi$
$788$	−88.2818	−3.14491
$789$	7.30111	0.259926
$790$	150.143	5.34186
$791$	−1.19587	−0.0425201
$792$	165.430	5.87829
$793$	−21.8281	−0.775140
$794$	36.7144	1.30294
$795$	−15.0942	−0.535337
$796$	−23.4765	−0.832104
$797$	32.9420	1.16687	0.583433	−	0.812161i	$-0.301709\pi$
$797$	32.9420	1.16687	0.583433	+	0.812161i	$0.301709\pi$
$798$	−0.586192	−0.0207510
$799$	22.4743	0.795085
$800$	−134.878	−4.76864
$801$	26.2413	0.927191
$802$	−90.9626	−3.21200
$803$	18.0586	0.637275
$804$	1.90003	0.0670090
$805$	−1.53086	−0.0539558
$806$	−13.2680	−0.467346
$807$	−5.17442	−0.182148
$808$	−45.8149	−1.61176
$809$	44.0717	1.54948	0.774740	−	0.632280i	$-0.217881\pi$
$809$	44.0717	1.54948	0.774740	+	0.632280i	$0.217881\pi$
$810$	−50.8434	−1.78646
$811$	−47.7442	−1.67653	−0.838263	−	0.545265i	$-0.816429\pi$
$811$	−47.7442	−1.67653	−0.838263	+	0.545265i	$0.816429\pi$
$812$	1.44862	0.0508367
$813$	−3.32095	−0.116471
$814$	113.145	3.96573
$815$	6.17554	0.216320
$816$	−37.9209	−1.32750
$817$	−18.6626	−0.652921
$818$	−5.77632	−0.201964
$819$	0.824905	0.0288245
$820$	−53.8439	−1.88031
$821$	1.76381	0.0615575	0.0307788	−	0.999526i	$-0.490201\pi$
$821$	1.76381	0.0615575	0.0307788	+	0.999526i	$0.490201\pi$
$822$	−19.2244	−0.670528
$823$	46.3728	1.61645	0.808226	−	0.588872i	$-0.200428\pi$
$823$	46.3728	1.61645	0.808226	+	0.588872i	$0.200428\pi$
$824$	80.1304	2.79148
$825$	16.8824	0.587771
$826$	0.319100	0.0111029
$827$	46.9845	1.63381	0.816905	−	0.576772i	$-0.195688\pi$
$827$	46.9845	1.63381	0.816905	+	0.576772i	$0.195688\pi$
$828$	51.0772	1.77506
$829$	46.9269	1.62984	0.814919	−	0.579575i	$-0.196781\pi$
$829$	46.9269	1.62984	0.814919	+	0.579575i	$0.196781\pi$
$830$	−117.956	−4.09430
$831$	−6.84180	−0.237340
$832$	−94.7136	−3.28360
$833$	24.5549	0.850778
$834$	19.6557	0.680620
$835$	66.6201	2.30548
$836$	81.6947	2.82547
$837$	7.58075	0.262029
$838$	97.5692	3.37047
$839$	−9.60690	−0.331667	−0.165834	−	0.986154i	$-0.553031\pi$
$839$	−9.60690	−0.331667	−0.165834	+	0.986154i	$0.553031\pi$
$840$	−2.90664	−0.100289
$841$	−26.0786	−0.899262
$842$	−22.9358	−0.790418
$843$	−7.78454	−0.268114
$844$	−14.5223	−0.499877
$845$	−26.2941	−0.904543
$846$	−46.9558	−1.61438
$847$	3.58209	0.123082
$848$	−143.340	−4.92232
$849$	19.0750	0.654654
$850$	46.1132	1.58167
$851$	22.8471	0.783189
$852$	0.581882	0.0199350
$853$	13.4838	0.461675	0.230837	−	0.972992i	$-0.425853\pi$
$853$	13.4838	0.461675	0.230837	+	0.972992i	$0.425853\pi$
$854$	−4.18205	−0.143107
$855$	−19.4880	−0.666476
$856$	127.709	4.36502
$857$	6.64582	0.227017	0.113508	−	0.993537i	$-0.463791\pi$
$857$	6.64582	0.227017	0.113508	+	0.993537i	$0.463791\pi$
$858$	21.3954	0.730426
$859$	20.9278	0.714046	0.357023	−	0.934096i	$-0.383792\pi$
$859$	20.9278	0.714046	0.357023	+	0.934096i	$0.383792\pi$
$860$	−141.495	−4.82494
$861$	−0.264742	−0.00902237
$862$	−45.7092	−1.55686
$863$	13.7324	0.467456	0.233728	−	0.972302i	$-0.424907\pi$
$863$	13.7324	0.467456	0.233728	+	0.972302i	$0.424907\pi$
$864$	97.6632	3.32257
$865$	68.5701	2.33145
$866$	61.0784	2.07553
$867$	−2.78839	−0.0946986
$868$	−1.88858	−0.0641025
$869$	−102.883	−3.49008
$870$	−8.96282	−0.303868
$871$	−1.16233	−0.0393841
$872$	−147.856	−5.00705
$873$	34.9852	1.18407
$874$	22.2040	0.751063
$875$	−0.137734	−0.00465624
$876$	10.5865	0.357686
$877$	13.2694	0.448075	0.224038	−	0.974580i	$-0.428076\pi$
$877$	13.2694	0.448075	0.224038	+	0.974580i	$0.428076\pi$
$878$	−38.4917	−1.29903
$879$	11.4987	0.387842
$880$	330.936	11.1558
$881$	−36.0131	−1.21331	−0.606656	−	0.794965i	$-0.707489\pi$
$881$	−36.0131	−1.21331	−0.606656	+	0.794965i	$0.707489\pi$
$882$	−51.3029	−1.72746
$883$	10.4730	0.352444	0.176222	−	0.984350i	$-0.443612\pi$
$883$	10.4730	0.352444	0.176222	+	0.984350i	$0.443612\pi$
$884$	43.4177	1.46030
$885$	−1.46681	−0.0493062
$886$	29.0674	0.976537
$887$	19.5314	0.655801	0.327901	−	0.944712i	$-0.393659\pi$
$887$	19.5314	0.655801	0.327901	+	0.944712i	$0.393659\pi$
$888$	43.3797	1.45573
$889$	−2.78777	−0.0934988
$890$	86.4888	2.89911
$891$	34.8397	1.16717
$892$	−50.8627	−1.70301
$893$	−15.1653	−0.507488
$894$	−8.94808	−0.299268
$895$	−42.9034	−1.43410
$896$	−9.72790	−0.324986
$897$	4.32031	0.144251
$898$	−95.3270	−3.18110
$899$	−3.80864	−0.127025
$900$	−71.5788	−2.38596
$901$	28.2514	0.941191
$902$	49.6614	1.65354
$903$	−0.695707	−0.0231517
$904$	86.0062	2.86053
$905$	2.77952	0.0923943
$906$	6.55174	0.217667
$907$	−12.6400	−0.419704	−0.209852	−	0.977733i	$-0.567298\pi$
$907$	−12.6400	−0.419704	−0.209852	+	0.977733i	$0.567298\pi$
$908$	30.7871	1.02171
$909$	−11.4509	−0.379801
$910$	2.71881	0.0901276
$911$	52.4979	1.73933	0.869667	−	0.493638i	$-0.164333\pi$
$911$	52.4979	1.73933	0.869667	+	0.493638i	$0.164333\pi$
$912$	25.5884	0.847317
$913$	80.8273	2.67499
$914$	47.9641	1.58651
$915$	19.2236	0.635514
$916$	−31.5716	−1.04316
$917$	−0.0541287	−0.00178749
$918$	−33.3900	−1.10203
$919$	10.0680	0.332112	0.166056	−	0.986116i	$-0.446897\pi$
$919$	10.0680	0.332112	0.166056	+	0.986116i	$0.446897\pi$
$920$	110.099	3.62986
$921$	14.2213	0.468608
$922$	−15.1849	−0.500088
$923$	−0.355962	−0.0117166
$924$	3.04543	0.100187
$925$	−32.0176	−1.05273
$926$	−72.3528	−2.37766
$927$	20.0276	0.657792
$928$	−49.0669	−1.61070
$929$	−34.3278	−1.12626	−0.563130	−	0.826368i	$-0.690403\pi$
$929$	−34.3278	−1.12626	−0.563130	+	0.826368i	$0.690403\pi$
$930$	11.6849	0.383163
$931$	−16.5693	−0.543036
$932$	73.1820	2.39716
$933$	0.376323	0.0123202
$934$	13.5928	0.444770
$935$	−65.2253	−2.13310
$936$	−59.3269	−1.93916
$937$	4.49397	0.146811	0.0734057	−	0.997302i	$-0.476613\pi$
$937$	4.49397	0.146811	0.0734057	+	0.997302i	$0.476613\pi$
$938$	−0.222691	−0.00727110
$939$	2.71128	0.0884792
$940$	−114.980	−3.75022
$941$	−27.2886	−0.889584	−0.444792	−	0.895634i	$-0.646722\pi$
$941$	−27.2886	−0.889584	−0.444792	+	0.895634i	$0.646722\pi$
$942$	12.1119	0.394627
$943$	10.0280	0.326557
$944$	−13.9293	−0.453360
$945$	−1.55340	−0.0505322
$946$	130.504	4.24304
$947$	41.9448	1.36302	0.681512	−	0.731807i	$-0.261323\pi$
$947$	41.9448	1.36302	0.681512	+	0.731807i	$0.261323\pi$
$948$	−60.3135	−1.95889
$949$	−6.47623	−0.210227
$950$	−31.1164	−1.00955
$951$	13.5563	0.439594
$952$	5.44027	0.176320
$953$	−36.9496	−1.19692	−0.598458	−	0.801154i	$-0.704220\pi$
$953$	−36.9496	−1.19692	−0.598458	+	0.801154i	$0.704220\pi$
$954$	−59.0260	−1.91104
$955$	−76.2586	−2.46767
$956$	133.387	4.31403
$957$	6.14164	0.198531
$958$	−60.1643	−1.94382
$959$	1.67398	0.0540556
$960$	83.4125	2.69213
$961$	−26.0346	−0.839827
$962$	−40.5764	−1.30824
$963$	31.9193	1.02859
$964$	−138.857	−4.47227
$965$	29.1096	0.937070
$966$	0.827727	0.0266317
$967$	25.0645	0.806021	0.403011	−	0.915195i	$-0.367964\pi$
$967$	25.0645	0.806021	0.403011	+	0.915195i	$0.367964\pi$
$968$	−257.623	−8.28031
$969$	−5.04331	−0.162015
$970$	115.308	3.70231
$971$	−3.03491	−0.0973948	−0.0486974	−	0.998814i	$-0.515507\pi$
$971$	−3.03491	−0.0973948	−0.0486974	+	0.998814i	$0.515507\pi$
$972$	79.4198	2.54739
$973$	−1.71153	−0.0548692
$974$	24.9083	0.798113
$975$	−6.05442	−0.193897
$976$	182.554	5.84342
$977$	7.18446	0.229851	0.114926	−	0.993374i	$-0.463337\pi$
$977$	7.18446	0.229851	0.114926	+	0.993374i	$0.463337\pi$
$978$	−3.33908	−0.106772
$979$	−59.2651	−1.89412
$980$	−125.624	−4.01291
$981$	−36.9548	−1.17988
$982$	−84.2923	−2.68988
$983$	2.54157	0.0810635	0.0405318	−	0.999178i	$-0.487095\pi$
$983$	2.54157	0.0810635	0.0405318	+	0.999178i	$0.487095\pi$
$984$	19.0401	0.606977
$985$	−47.5618	−1.51545
$986$	16.7754	0.534239
$987$	−0.565336	−0.0179948
$988$	−29.2976	−0.932080
$989$	26.3523	0.837955
$990$	136.276	4.33113
$991$	−31.7026	−1.00707	−0.503533	−	0.863976i	$-0.667967\pi$
$991$	−31.7026	−1.00707	−0.503533	+	0.863976i	$0.667967\pi$
$992$	63.9689	2.03101
$993$	7.22826	0.229382
$994$	−0.0681987	−0.00216313
$995$	−12.6480	−0.400968
$996$	47.3835	1.50140
$997$	−24.9331	−0.789638	−0.394819	−	0.918759i	$-0.629193\pi$
$997$	−24.9331	−0.789638	−0.394819	+	0.918759i	$0.629193\pi$
$998$	−35.4756	−1.12296
$999$	23.1836	0.733495

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6047.2.a.a.1.2	✓	217

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6047.2.a.a.1.2	✓	217	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:	\( N \)	\(=\)	\( 6047 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6047.a (trivial)

\(f(q)\)	\(=\)	\(q-2.78935 q^{2} +0.603668 q^{3} +5.78045 q^{4} +3.11422 q^{5} -1.68384 q^{6} +0.146622 q^{7} -10.5450 q^{8} -2.63558 q^{9} +O(q^{10})\)	\(q-2.78935 q^{2} +0.603668 q^{3} +5.78045 q^{4} +3.11422 q^{5} -1.68384 q^{6} +0.146622 q^{7} -10.5450 q^{8} -2.63558 q^{9} -8.68663 q^{10} +5.95238 q^{11} +3.48947 q^{12} -2.13466 q^{13} -0.408979 q^{14} +1.87995 q^{15} +17.8527 q^{16} -3.51865 q^{17} +7.35156 q^{18} +2.37433 q^{19} +18.0016 q^{20} +0.0885108 q^{21} -16.6032 q^{22} -3.35265 q^{23} -6.36567 q^{24} +4.69836 q^{25} +5.95430 q^{26} -3.40202 q^{27} +0.847539 q^{28} +1.70921 q^{29} -5.24384 q^{30} -2.22831 q^{31} -28.7074 q^{32} +3.59326 q^{33} +9.81474 q^{34} +0.456612 q^{35} -15.2349 q^{36} -6.81464 q^{37} -6.62283 q^{38} -1.28863 q^{39} -32.8394 q^{40} -2.99107 q^{41} -0.246887 q^{42} -7.86014 q^{43} +34.4074 q^{44} -8.20779 q^{45} +9.35171 q^{46} -6.38720 q^{47} +10.7771 q^{48} -6.97850 q^{49} -13.1053 q^{50} -2.12410 q^{51} -12.3393 q^{52} -8.02904 q^{53} +9.48942 q^{54} +18.5370 q^{55} -1.54612 q^{56} +1.43331 q^{57} -4.76758 q^{58} -0.780236 q^{59} +10.8670 q^{60} +10.2256 q^{61} +6.21552 q^{62} -0.386434 q^{63} +44.3694 q^{64} -6.64780 q^{65} -10.0229 q^{66} +0.544504 q^{67} -20.3394 q^{68} -2.02389 q^{69} -1.27365 q^{70} +0.166754 q^{71} +27.7922 q^{72} +3.03385 q^{73} +19.0084 q^{74} +2.83625 q^{75} +13.7247 q^{76} +0.872748 q^{77} +3.59442 q^{78} -17.2844 q^{79} +55.5972 q^{80} +5.85306 q^{81} +8.34312 q^{82} +13.5790 q^{83} +0.511632 q^{84} -10.9579 q^{85} +21.9246 q^{86} +1.03179 q^{87} -62.7677 q^{88} -9.95654 q^{89} +22.8944 q^{90} -0.312987 q^{91} -19.3798 q^{92} -1.34516 q^{93} +17.8161 q^{94} +7.39419 q^{95} -17.3297 q^{96} -13.2742 q^{97} +19.4655 q^{98} -15.6880 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 217 q - 20 q^{2} - 27 q^{3} + 184 q^{4} - 19 q^{5} - 17 q^{6} - 48 q^{7} - 57 q^{8} + 152 q^{9}+O(q^{10}) \) 217 * q - 20 * q^2 - 27 * q^3 + 184 * q^4 - 19 * q^5 - 17 * q^6 - 48 * q^7 - 57 * q^8 + 152 * q^9	\( 217 q - 20 q^{2} - 27 q^{3} + 184 q^{4} - 19 q^{5} - 17 q^{6} - 48 q^{7} - 57 q^{8} + 152 q^{9} - 46 q^{10} - 32 q^{11} - 72 q^{12} - 80 q^{13} - 22 q^{14} - 43 q^{15} + 122 q^{16} - 61 q^{17} - 88 q^{18} - 43 q^{19} - 41 q^{20} - 61 q^{21} - 93 q^{22} - 60 q^{23} - 41 q^{24} + 26 q^{25} - 9 q^{26} - 93 q^{27} - 126 q^{28} - 47 q^{29} - 36 q^{30} - 100 q^{31} - 114 q^{32} - 133 q^{33} - 75 q^{34} - 37 q^{35} + 75 q^{36} - 264 q^{37} - 35 q^{38} - 47 q^{39} - 118 q^{40} - 72 q^{41} - 64 q^{42} - 107 q^{43} - 59 q^{44} - 69 q^{45} - 111 q^{46} - 54 q^{47} - 135 q^{48} + 33 q^{49} - 42 q^{50} - 26 q^{51} - 173 q^{52} - 103 q^{53} - 28 q^{54} - 78 q^{55} - 44 q^{56} - 205 q^{57} - 189 q^{58} - 38 q^{59} - 105 q^{60} - 108 q^{61} - 14 q^{62} - 116 q^{63} + 39 q^{64} - 146 q^{65} + 5 q^{66} - 206 q^{67} - 62 q^{68} - 55 q^{69} - 125 q^{70} - 78 q^{71} - 225 q^{72} - 326 q^{73} + 3 q^{74} - 95 q^{75} - 84 q^{76} - 79 q^{77} - 86 q^{78} - 117 q^{79} - 39 q^{80} + q^{81} - 96 q^{82} - 23 q^{83} - 57 q^{84} - 224 q^{85} - 7 q^{86} - 45 q^{87} - 250 q^{88} - 104 q^{89} - 36 q^{90} - 96 q^{91} - 137 q^{92} - 155 q^{93} - 48 q^{94} - 38 q^{95} - 33 q^{96} - 447 q^{97} - 46 q^{98} - 94 q^{99}+O(q^{100}) \) 217 * q - 20 * q^2 - 27 * q^3 + 184 * q^4 - 19 * q^5 - 17 * q^6 - 48 * q^7 - 57 * q^8 + 152 * q^9 - 46 * q^10 - 32 * q^11 - 72 * q^12 - 80 * q^13 - 22 * q^14 - 43 * q^15 + 122 * q^16 - 61 * q^17 - 88 * q^18 - 43 * q^19 - 41 * q^20 - 61 * q^21 - 93 * q^22 - 60 * q^23 - 41 * q^24 + 26 * q^25 - 9 * q^26 - 93 * q^27 - 126 * q^28 - 47 * q^29 - 36 * q^30 - 100 * q^31 - 114 * q^32 - 133 * q^33 - 75 * q^34 - 37 * q^35 + 75 * q^36 - 264 * q^37 - 35 * q^38 - 47 * q^39 - 118 * q^40 - 72 * q^41 - 64 * q^42 - 107 * q^43 - 59 * q^44 - 69 * q^45 - 111 * q^46 - 54 * q^47 - 135 * q^48 + 33 * q^49 - 42 * q^50 - 26 * q^51 - 173 * q^52 - 103 * q^53 - 28 * q^54 - 78 * q^55 - 44 * q^56 - 205 * q^57 - 189 * q^58 - 38 * q^59 - 105 * q^60 - 108 * q^61 - 14 * q^62 - 116 * q^63 + 39 * q^64 - 146 * q^65 + 5 * q^66 - 206 * q^67 - 62 * q^68 - 55 * q^69 - 125 * q^70 - 78 * q^71 - 225 * q^72 - 326 * q^73 + 3 * q^74 - 95 * q^75 - 84 * q^76 - 79 * q^77 - 86 * q^78 - 117 * q^79 - 39 * q^80 + q^81 - 96 * q^82 - 23 * q^83 - 57 * q^84 - 224 * q^85 - 7 * q^86 - 45 * q^87 - 250 * q^88 - 104 * q^89 - 36 * q^90 - 96 * q^91 - 137 * q^92 - 155 * q^93 - 48 * q^94 - 38 * q^95 - 33 * q^96 - 447 * q^97 - 46 * q^98 - 94 * q^99

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