LMFDB - Embedded newform 6037.2.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6037,2,Mod(1,6037)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6037, 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("6037.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6037 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6037.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:	$48.2056877002$
Analytic rank:	$0$
Dimension:	$259$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	6037.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.75717 q^{2} -1.09794 q^{3} +5.60201 q^{4} +2.84974 q^{5} +3.02722 q^{6} +3.79647 q^{7} -9.93137 q^{8} -1.79452 q^{9} +O(q^{10})$	\(q-2.75717 q^{2} -1.09794 q^{3} +5.60201 q^{4} +2.84974 q^{5} +3.02722 q^{6} +3.79647 q^{7} -9.93137 q^{8} -1.79452 q^{9} -7.85722 q^{10} -0.397993 q^{11} -6.15069 q^{12} -2.48387 q^{13} -10.4675 q^{14} -3.12885 q^{15} +16.1785 q^{16} +2.84790 q^{17} +4.94781 q^{18} -2.45811 q^{19} +15.9642 q^{20} -4.16831 q^{21} +1.09734 q^{22} +3.57879 q^{23} +10.9041 q^{24} +3.12099 q^{25} +6.84846 q^{26} +5.26411 q^{27} +21.2679 q^{28} +1.79285 q^{29} +8.62677 q^{30} -0.342150 q^{31} -24.7442 q^{32} +0.436973 q^{33} -7.85216 q^{34} +10.8189 q^{35} -10.0529 q^{36} -6.20613 q^{37} +6.77745 q^{38} +2.72714 q^{39} -28.3018 q^{40} +1.27240 q^{41} +11.4928 q^{42} -3.33696 q^{43} -2.22956 q^{44} -5.11391 q^{45} -9.86734 q^{46} -0.761099 q^{47} -17.7631 q^{48} +7.41320 q^{49} -8.60512 q^{50} -3.12683 q^{51} -13.9147 q^{52} +3.51736 q^{53} -14.5141 q^{54} -1.13417 q^{55} -37.7042 q^{56} +2.69887 q^{57} -4.94320 q^{58} -0.993904 q^{59} -17.5278 q^{60} +6.36307 q^{61} +0.943366 q^{62} -6.81285 q^{63} +35.8671 q^{64} -7.07837 q^{65} -1.20481 q^{66} -4.46689 q^{67} +15.9540 q^{68} -3.92930 q^{69} -29.8297 q^{70} +4.45247 q^{71} +17.8221 q^{72} +0.508279 q^{73} +17.1114 q^{74} -3.42667 q^{75} -13.7704 q^{76} -1.51097 q^{77} -7.51921 q^{78} -12.9156 q^{79} +46.1045 q^{80} -0.396122 q^{81} -3.50822 q^{82} -2.24676 q^{83} -23.3509 q^{84} +8.11576 q^{85} +9.20057 q^{86} -1.96845 q^{87} +3.95262 q^{88} +5.76691 q^{89} +14.1000 q^{90} -9.42994 q^{91} +20.0484 q^{92} +0.375661 q^{93} +2.09848 q^{94} -7.00497 q^{95} +27.1677 q^{96} +0.292271 q^{97} -20.4395 q^{98} +0.714207 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 259 q + 47 q^{2} + 29 q^{3} + 273 q^{4} + 38 q^{5} + 24 q^{6} + 42 q^{7} + 141 q^{8} + 286 q^{9}+O(q^{10}) $ 259 * q + 47 * q^2 + 29 * q^3 + 273 * q^4 + 38 * q^5 + 24 * q^6 + 42 * q^7 + 141 * q^8 + 286 * q^9	\( 259 q + 47 q^{2} + 29 q^{3} + 273 q^{4} + 38 q^{5} + 24 q^{6} + 42 q^{7} + 141 q^{8} + 286 q^{9} + 18 q^{10} + 108 q^{11} + 46 q^{12} + 33 q^{13} + 35 q^{14} + 40 q^{15} + 301 q^{16} + 67 q^{17} + 117 q^{18} + 69 q^{19} + 103 q^{20} + 24 q^{21} + 42 q^{22} + 162 q^{23} + 45 q^{24} + 291 q^{25} + 41 q^{26} + 101 q^{27} + 87 q^{28} + 78 q^{29} + 48 q^{30} + 25 q^{31} + 314 q^{32} + 67 q^{33} + 9 q^{34} + 252 q^{35} + 337 q^{36} + 49 q^{37} + 59 q^{38} + 93 q^{39} + 44 q^{40} + 60 q^{41} + 38 q^{42} + 178 q^{43} + 171 q^{44} + 67 q^{45} + 43 q^{46} + 185 q^{47} + 67 q^{48} + 273 q^{49} + 204 q^{50} + 145 q^{51} + 83 q^{52} + 112 q^{53} + 60 q^{54} + 57 q^{55} + 93 q^{56} + 109 q^{57} + 63 q^{58} + 228 q^{59} + 53 q^{60} + 20 q^{61} + 126 q^{62} + 153 q^{63} + 345 q^{64} + 113 q^{65} + 5 q^{66} + 208 q^{67} + 166 q^{68} + 10 q^{69} + 69 q^{70} + 150 q^{71} + 331 q^{72} + 75 q^{73} + 84 q^{74} + 72 q^{75} + 102 q^{76} + 166 q^{77} + 69 q^{78} + 52 q^{79} + 180 q^{80} + 327 q^{81} + 43 q^{82} + 434 q^{83} + 75 q^{85} + 133 q^{86} + 144 q^{87} + 111 q^{88} + 78 q^{89} - 8 q^{90} + 35 q^{91} + 372 q^{92} + 160 q^{93} + 36 q^{94} + 154 q^{95} + 60 q^{96} + 35 q^{97} + 254 q^{98} + 234 q^{99}+O(q^{100}) \) 259 * q + 47 * q^2 + 29 * q^3 + 273 * q^4 + 38 * q^5 + 24 * q^6 + 42 * q^7 + 141 * q^8 + 286 * q^9 + 18 * q^10 + 108 * q^11 + 46 * q^12 + 33 * q^13 + 35 * q^14 + 40 * q^15 + 301 * q^16 + 67 * q^17 + 117 * q^18 + 69 * q^19 + 103 * q^20 + 24 * q^21 + 42 * q^22 + 162 * q^23 + 45 * q^24 + 291 * q^25 + 41 * q^26 + 101 * q^27 + 87 * q^28 + 78 * q^29 + 48 * q^30 + 25 * q^31 + 314 * q^32 + 67 * q^33 + 9 * q^34 + 252 * q^35 + 337 * q^36 + 49 * q^37 + 59 * q^38 + 93 * q^39 + 44 * q^40 + 60 * q^41 + 38 * q^42 + 178 * q^43 + 171 * q^44 + 67 * q^45 + 43 * q^46 + 185 * q^47 + 67 * q^48 + 273 * q^49 + 204 * q^50 + 145 * q^51 + 83 * q^52 + 112 * q^53 + 60 * q^54 + 57 * q^55 + 93 * q^56 + 109 * q^57 + 63 * q^58 + 228 * q^59 + 53 * q^60 + 20 * q^61 + 126 * q^62 + 153 * q^63 + 345 * q^64 + 113 * q^65 + 5 * q^66 + 208 * q^67 + 166 * q^68 + 10 * q^69 + 69 * q^70 + 150 * q^71 + 331 * q^72 + 75 * q^73 + 84 * q^74 + 72 * q^75 + 102 * q^76 + 166 * q^77 + 69 * q^78 + 52 * q^79 + 180 * q^80 + 327 * q^81 + 43 * q^82 + 434 * q^83 + 75 * q^85 + 133 * q^86 + 144 * q^87 + 111 * q^88 + 78 * q^89 - 8 * q^90 + 35 * q^91 + 372 * q^92 + 160 * q^93 + 36 * q^94 + 154 * q^95 + 60 * q^96 + 35 * q^97 + 254 * q^98 + 234 * 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 $

$2$	−2.75717	−1.94962	−0.974808	−	0.223044i	$-0.928401\pi$
$2$	−2.75717	−1.94962	−0.974808	+	0.223044i	$0.928401\pi$
$3$	−1.09794	−0.633897	−0.316949	−	0.948443i	$-0.602658\pi$
$3$	−1.09794	−0.633897	−0.316949	+	0.948443i	$0.602658\pi$
$4$	5.60201	2.80101
$5$	2.84974	1.27444	0.637220	−	0.770682i	$-0.280084\pi$
$5$	2.84974	1.27444	0.637220	+	0.770682i	$0.280084\pi$
$6$	3.02722	1.23586
$7$	3.79647	1.43493	0.717466	−	0.696594i	$-0.245302\pi$
$7$	3.79647	1.43493	0.717466	+	0.696594i	$0.245302\pi$
$8$	−9.93137	−3.51127
$9$	−1.79452	−0.598174
$10$	−7.85722	−2.48467
$11$	−0.397993	−0.119999	−0.0599997	−	0.998198i	$-0.519110\pi$
$11$	−0.397993	−0.119999	−0.0599997	+	0.998198i	$0.519110\pi$
$12$	−6.15069	−1.77555
$13$	−2.48387	−0.688901	−0.344451	−	0.938804i	$-0.611935\pi$
$13$	−2.48387	−0.688901	−0.344451	+	0.938804i	$0.611935\pi$
$14$	−10.4675	−2.79757
$15$	−3.12885	−0.807864
$16$	16.1785	4.04463
$17$	2.84790	0.690717	0.345359	−	0.938471i	$-0.387757\pi$
$17$	2.84790	0.690717	0.345359	+	0.938471i	$0.387757\pi$
$18$	4.94781	1.16621
$19$	−2.45811	−0.563930	−0.281965	−	0.959425i	$-0.590986\pi$
$19$	−2.45811	−0.563930	−0.281965	+	0.959425i	$0.590986\pi$
$20$	15.9642	3.56971
$21$	−4.16831	−0.909599
$22$	1.09734	0.233953
$23$	3.57879	0.746228	0.373114	−	0.927785i	$-0.378290\pi$
$23$	3.57879	0.746228	0.373114	+	0.927785i	$0.378290\pi$
$24$	10.9041	2.22579
$25$	3.12099	0.624198
$26$	6.84846	1.34309
$27$	5.26411	1.01308
$28$	21.2679	4.01925
$29$	1.79285	0.332924	0.166462	−	0.986048i	$-0.446766\pi$
$29$	1.79285	0.332924	0.166462	+	0.986048i	$0.446766\pi$
$30$	8.62677	1.57503
$31$	−0.342150	−0.0614519	−0.0307259	−	0.999528i	$-0.509782\pi$
$31$	−0.342150	−0.0614519	−0.0307259	+	0.999528i	$0.509782\pi$
$32$	−24.7442	−4.37420
$33$	0.436973	0.0760673
$34$	−7.85216	−1.34663
$35$	10.8189	1.82873
$36$	−10.0529	−1.67549
$37$	−6.20613	−1.02028	−0.510141	−	0.860091i	$-0.670407\pi$
$37$	−6.20613	−1.02028	−0.510141	+	0.860091i	$0.670407\pi$
$38$	6.77745	1.09945
$39$	2.72714	0.436693
$40$	−28.3018	−4.47491
$41$	1.27240	0.198715	0.0993576	−	0.995052i	$-0.468321\pi$
$41$	1.27240	0.198715	0.0993576	+	0.995052i	$0.468321\pi$
$42$	11.4928	1.77337
$43$	−3.33696	−0.508881	−0.254441	−	0.967088i	$-0.581891\pi$
$43$	−3.33696	−0.508881	−0.254441	+	0.967088i	$0.581891\pi$
$44$	−2.22956	−0.336119
$45$	−5.11391	−0.762337
$46$	−9.86734	−1.45486
$47$	−0.761099	−0.111018	−0.0555088	−	0.998458i	$-0.517678\pi$
$47$	−0.761099	−0.111018	−0.0555088	+	0.998458i	$0.517678\pi$
$48$	−17.7631	−2.56388
$49$	7.41320	1.05903
$50$	−8.60512	−1.21695
$51$	−3.12683	−0.437844
$52$	−13.9147	−1.92962
$53$	3.51736	0.483147	0.241573	−	0.970383i	$-0.422337\pi$
$53$	3.51736	0.483147	0.241573	+	0.970383i	$0.422337\pi$
$54$	−14.5141	−1.97511
$55$	−1.13417	−0.152932
$56$	−37.7042	−5.03843
$57$	2.69887	0.357474
$58$	−4.94320	−0.649075
$59$	−0.993904	−0.129395	−0.0646976	−	0.997905i	$-0.520608\pi$
$59$	−0.993904	−0.129395	−0.0646976	+	0.997905i	$0.520608\pi$
$60$	−17.5278	−2.26283
$61$	6.36307	0.814708	0.407354	−	0.913270i	$-0.366452\pi$
$61$	6.36307	0.814708	0.407354	+	0.913270i	$0.366452\pi$
$62$	0.943366	0.119808
$63$	−6.81285	−0.858339
$64$	35.8671	4.48339
$65$	−7.07837	−0.877964
$66$	−1.20481	−0.148302
$67$	−4.46689	−0.545717	−0.272859	−	0.962054i	$-0.587969\pi$
$67$	−4.46689	−0.545717	−0.272859	+	0.962054i	$0.587969\pi$
$68$	15.9540	1.93470
$69$	−3.92930	−0.473032
$70$	−29.8297	−3.56533
$71$	4.45247	0.528411	0.264206	−	0.964466i	$-0.414890\pi$
$71$	4.45247	0.528411	0.264206	+	0.964466i	$0.414890\pi$
$72$	17.8221	2.10035
$73$	0.508279	0.0594896	0.0297448	−	0.999558i	$-0.490531\pi$
$73$	0.508279	0.0594896	0.0297448	+	0.999558i	$0.490531\pi$
$74$	17.1114	1.98916
$75$	−3.42667	−0.395678
$76$	−13.7704	−1.57957
$77$	−1.51097	−0.172191
$78$	−7.51921	−0.851383
$79$	−12.9156	−1.45311	−0.726557	−	0.687106i	$-0.758881\pi$
$79$	−12.9156	−1.45311	−0.726557	+	0.687106i	$0.758881\pi$
$80$	46.1045	5.15464
$81$	−0.396122	−0.0440136
$82$	−3.50822	−0.387418
$83$	−2.24676	−0.246614	−0.123307	−	0.992369i	$-0.539350\pi$
$83$	−2.24676	−0.246614	−0.123307	+	0.992369i	$0.539350\pi$
$84$	−23.3509	−2.54779
$85$	8.11576	0.880278
$86$	9.20057	0.992123
$87$	−1.96845	−0.211040
$88$	3.95262	0.421350
$89$	5.76691	0.611291	0.305645	−	0.952145i	$-0.401128\pi$
$89$	5.76691	0.611291	0.305645	+	0.952145i	$0.401128\pi$
$90$	14.1000	1.48627
$91$	−9.42994	−0.988526
$92$	20.0484	2.09019
$93$	0.375661	0.0389542
$94$	2.09848	0.216442
$95$	−7.00497	−0.718695
$96$	27.1677	2.77279
$97$	0.292271	0.0296756	0.0148378	−	0.999890i	$-0.495277\pi$
$97$	0.292271	0.0296756	0.0148378	+	0.999890i	$0.495277\pi$
$98$	−20.4395	−2.06470
$99$	0.714207	0.0717805
$100$	17.4838	1.74838
$101$	13.2075	1.31420	0.657100	−	0.753804i	$-0.271783\pi$
$101$	13.2075	1.31420	0.657100	+	0.753804i	$0.271783\pi$
$102$	8.62121	0.853627
$103$	15.9673	1.57330	0.786650	−	0.617399i	$-0.211814\pi$
$103$	15.9673	1.57330	0.786650	+	0.617399i	$0.211814\pi$
$104$	24.6682	2.41892
$105$	−11.8786	−1.15923
$106$	−9.69798	−0.941951
$107$	3.08392	0.298134	0.149067	−	0.988827i	$-0.452373\pi$
$107$	3.08392	0.298134	0.149067	+	0.988827i	$0.452373\pi$
$108$	29.4896	2.83764
$109$	−0.323117	−0.0309490	−0.0154745	−	0.999880i	$-0.504926\pi$
$109$	−0.323117	−0.0309490	−0.0154745	+	0.999880i	$0.504926\pi$
$110$	3.12712	0.298159
$111$	6.81398	0.646754
$112$	61.4212	5.80376
$113$	10.6173	0.998791	0.499396	−	0.866374i	$-0.333555\pi$
$113$	10.6173	0.998791	0.499396	+	0.866374i	$0.333555\pi$
$114$	−7.44125	−0.696937
$115$	10.1986	0.951023
$116$	10.0436	0.932523
$117$	4.45736	0.412083
$118$	2.74037	0.252271
$119$	10.8120	0.991132
$120$	31.0737	2.83663
$121$	−10.8416	−0.985600
$122$	−17.5441	−1.58837
$123$	−1.39702	−0.125965
$124$	−1.91673	−0.172127
$125$	−5.35468	−0.478937
$126$	18.7842	1.67343
$127$	5.19412	0.460904	0.230452	−	0.973084i	$-0.425980\pi$
$127$	5.19412	0.460904	0.230452	+	0.973084i	$0.425980\pi$
$128$	−49.4035	−4.36669
$129$	3.66379	0.322578
$130$	19.5163	1.71169
$131$	9.78458	0.854883	0.427442	−	0.904043i	$-0.359415\pi$
$131$	9.78458	0.854883	0.427442	+	0.904043i	$0.359415\pi$
$132$	2.44793	0.213065
$133$	−9.33216	−0.809201
$134$	12.3160	1.06394
$135$	15.0013	1.29111
$136$	−28.2836	−2.42529
$137$	2.57721	0.220186	0.110093	−	0.993921i	$-0.464885\pi$
$137$	2.57721	0.220186	0.110093	+	0.993921i	$0.464885\pi$
$138$	10.8338	0.922231
$139$	14.6138	1.23952	0.619762	−	0.784789i	$-0.287229\pi$
$139$	14.6138	1.23952	0.619762	+	0.784789i	$0.287229\pi$
$140$	60.6078	5.12230
$141$	0.835642	0.0703738
$142$	−12.2762	−1.03020
$143$	0.988562	0.0826677
$144$	−29.0327	−2.41939
$145$	5.10915	0.424292
$146$	−1.40141	−0.115982
$147$	−8.13927	−0.671315
$148$	−34.7668	−2.85782
$149$	17.1846	1.40782	0.703909	−	0.710290i	$-0.251436\pi$
$149$	17.1846	1.40782	0.703909	+	0.710290i	$0.251436\pi$
$150$	9.44792	0.771420
$151$	6.87461	0.559448	0.279724	−	0.960080i	$-0.409757\pi$
$151$	6.87461	0.559448	0.279724	+	0.960080i	$0.409757\pi$
$152$	24.4125	1.98011
$153$	−5.11062	−0.413169
$154$	4.16600	0.335706
$155$	−0.975036	−0.0783167
$156$	15.2775	1.22318
$157$	1.63569	0.130542	0.0652712	−	0.997868i	$-0.479209\pi$
$157$	1.63569	0.130542	0.0652712	+	0.997868i	$0.479209\pi$
$158$	35.6104	2.83301
$159$	−3.86186	−0.306266
$160$	−70.5145	−5.57466
$161$	13.5868	1.07079
$162$	1.09218	0.0858096
$163$	12.7857	1.00145	0.500725	−	0.865607i	$-0.333067\pi$
$163$	12.7857	1.00145	0.500725	+	0.865607i	$0.333067\pi$
$164$	7.12799	0.556602
$165$	1.24526	0.0969432
$166$	6.19471	0.480803
$167$	15.5911	1.20647	0.603237	−	0.797562i	$-0.293877\pi$
$167$	15.5911	1.20647	0.603237	+	0.797562i	$0.293877\pi$
$168$	41.3970	3.19385
$169$	−6.83040	−0.525415
$170$	−22.3766	−1.71620
$171$	4.41114	0.337328
$172$	−18.6937	−1.42538
$173$	−1.16595	−0.0886456	−0.0443228	−	0.999017i	$-0.514113\pi$
$173$	−1.16595	−0.0886456	−0.0443228	+	0.999017i	$0.514113\pi$
$174$	5.42735	0.411447
$175$	11.8488	0.895682
$176$	−6.43893	−0.485353
$177$	1.09125	0.0820233
$178$	−15.9004	−1.19178
$179$	3.99398	0.298524	0.149262	−	0.988798i	$-0.452310\pi$
$179$	3.99398	0.298524	0.149262	+	0.988798i	$0.452310\pi$
$180$	−28.6482	−2.13531
$181$	−15.5804	−1.15809	−0.579043	−	0.815297i	$-0.696574\pi$
$181$	−15.5804	−1.15809	−0.579043	+	0.815297i	$0.696574\pi$
$182$	26.0000	1.92725
$183$	−6.98629	−0.516441
$184$	−35.5423	−2.62021
$185$	−17.6858	−1.30029
$186$	−1.03576	−0.0759457
$187$	−1.13344	−0.0828856
$188$	−4.26368	−0.310961
$189$	19.9850	1.45370
$190$	19.3139	1.40118
$191$	−20.8941	−1.51184	−0.755922	−	0.654662i	$-0.772811\pi$
$191$	−20.8941	−1.51184	−0.755922	+	0.654662i	$0.772811\pi$
$192$	−39.3800	−2.84201
$193$	−15.0447	−1.08294	−0.541469	−	0.840721i	$-0.682132\pi$
$193$	−15.0447	−1.08294	−0.541469	+	0.840721i	$0.682132\pi$
$194$	−0.805841	−0.0578560
$195$	7.77164	0.556539
$196$	41.5288	2.96634
$197$	27.4853	1.95824	0.979122	−	0.203271i	$-0.0651574\pi$
$197$	27.4853	1.95824	0.979122	+	0.203271i	$0.0651574\pi$
$198$	−1.96919	−0.139945
$199$	−13.3027	−0.943000	−0.471500	−	0.881866i	$-0.656287\pi$
$199$	−13.3027	−0.943000	−0.471500	+	0.881866i	$0.656287\pi$
$200$	−30.9957	−2.19173
$201$	4.90439	0.345929
$202$	−36.4155	−2.56219
$203$	6.80651	0.477723
$204$	−17.5165	−1.22640
$205$	3.62600	0.253251
$206$	−44.0245	−3.06733
$207$	−6.42221	−0.446374
$208$	−40.1853	−2.78635
$209$	0.978312	0.0676713
$210$	32.7513	2.26005
$211$	3.75289	0.258359	0.129180	−	0.991621i	$-0.458766\pi$
$211$	3.75289	0.258359	0.129180	+	0.991621i	$0.458766\pi$
$212$	19.7043	1.35330
$213$	−4.88856	−0.334958
$214$	−8.50290	−0.581247
$215$	−9.50944	−0.648539
$216$	−52.2798	−3.55719
$217$	−1.29896	−0.0881792
$218$	0.890890	0.0603387
$219$	−0.558061	−0.0377103
$220$	−6.35366	−0.428364
$221$	−7.07381	−0.475836
$222$	−18.7873	−1.26092
$223$	7.52079	0.503630	0.251815	−	0.967775i	$-0.418973\pi$
$223$	7.52079	0.503630	0.251815	+	0.967775i	$0.418973\pi$
$224$	−93.9407	−6.27668
$225$	−5.60069	−0.373379
$226$	−29.2737	−1.94726
$227$	16.2101	1.07590	0.537952	−	0.842975i	$-0.319198\pi$
$227$	16.2101	1.07590	0.537952	+	0.842975i	$0.319198\pi$
$228$	15.1191	1.00129
$229$	10.8728	0.718493	0.359247	−	0.933243i	$-0.383034\pi$
$229$	10.8728	0.718493	0.359247	+	0.933243i	$0.383034\pi$
$230$	−28.1193	−1.85413
$231$	1.65896	0.109151
$232$	−17.8055	−1.16899
$233$	4.63581	0.303702	0.151851	−	0.988403i	$-0.451477\pi$
$233$	4.63581	0.303702	0.151851	+	0.988403i	$0.451477\pi$
$234$	−12.2897	−0.803404
$235$	−2.16893	−0.141485
$236$	−5.56786	−0.362437
$237$	14.1805	0.921125
$238$	−29.8105	−1.93233
$239$	−13.2645	−0.858006	−0.429003	−	0.903303i	$-0.641135\pi$
$239$	−13.2645	−0.858006	−0.429003	+	0.903303i	$0.641135\pi$
$240$	−50.6200	−3.26751
$241$	19.1691	1.23479	0.617395	−	0.786653i	$-0.288188\pi$
$241$	19.1691	1.23479	0.617395	+	0.786653i	$0.288188\pi$
$242$	29.8922	1.92154
$243$	−15.3574	−0.985178
$244$	35.6460	2.28200
$245$	21.1257	1.34967
$246$	3.85183	0.245584
$247$	6.10563	0.388492
$248$	3.39802	0.215774
$249$	2.46681	0.156328
$250$	14.7638	0.933744
$251$	2.62057	0.165409	0.0827046	−	0.996574i	$-0.473644\pi$
$251$	2.62057	0.165409	0.0827046	+	0.996574i	$0.473644\pi$
$252$	−38.1657	−2.40421
$253$	−1.42433	−0.0895469
$254$	−14.3211	−0.898585
$255$	−8.91064	−0.558006
$256$	64.4797	4.02998
$257$	−6.26214	−0.390622	−0.195311	−	0.980741i	$-0.562572\pi$
$257$	−6.26214	−0.390622	−0.195311	+	0.980741i	$0.562572\pi$
$258$	−10.1017	−0.628904
$259$	−23.5614	−1.46403
$260$	−39.6531	−2.45918
$261$	−3.21731	−0.199147
$262$	−26.9778	−1.66669
$263$	5.31092	0.327485	0.163743	−	0.986503i	$-0.447643\pi$
$263$	5.31092	0.327485	0.163743	+	0.986503i	$0.447643\pi$
$264$	−4.33975	−0.267093
$265$	10.0236	0.615742
$266$	25.7304	1.57763
$267$	−6.33173	−0.387496
$268$	−25.0236	−1.52856
$269$	−22.9417	−1.39878	−0.699390	−	0.714741i	$-0.746545\pi$
$269$	−22.9417	−1.39878	−0.699390	+	0.714741i	$0.746545\pi$
$270$	−41.3613	−2.51717
$271$	14.2725	0.866995	0.433498	−	0.901155i	$-0.357279\pi$
$271$	14.2725	0.866995	0.433498	+	0.901155i	$0.357279\pi$
$272$	46.0748	2.79369
$273$	10.3535	0.626624
$274$	−7.10582	−0.429278
$275$	−1.24213	−0.0749034
$276$	−22.0120	−1.32497
$277$	9.13943	0.549135	0.274568	−	0.961568i	$-0.411465\pi$
$277$	9.13943	0.549135	0.274568	+	0.961568i	$0.411465\pi$
$278$	−40.2927	−2.41660
$279$	0.613995	0.0367589
$280$	−107.447	−6.42118
$281$	9.55233	0.569844	0.284922	−	0.958551i	$-0.408032\pi$
$281$	9.55233	0.569844	0.284922	+	0.958551i	$0.408032\pi$
$282$	−2.30401	−0.137202
$283$	11.6925	0.695046	0.347523	−	0.937671i	$-0.387023\pi$
$283$	11.6925	0.695046	0.347523	+	0.937671i	$0.387023\pi$
$284$	24.9428	1.48008
$285$	7.69106	0.455579
$286$	−2.72564	−0.161170
$287$	4.83062	0.285143
$288$	44.4041	2.61653
$289$	−8.88947	−0.522910
$290$	−14.0868	−0.827207
$291$	−0.320896	−0.0188113
$292$	2.84739	0.166631
$293$	0.562309	0.0328504	0.0164252	−	0.999865i	$-0.494771\pi$
$293$	0.562309	0.0328504	0.0164252	+	0.999865i	$0.494771\pi$
$294$	22.4414	1.30881
$295$	−2.83236	−0.164907
$296$	61.6354	3.58249
$297$	−2.09508	−0.121569
$298$	−47.3810	−2.74471
$299$	−8.88923	−0.514078
$300$	−19.1962	−1.10830
$301$	−12.6687	−0.730209
$302$	−18.9545	−1.09071
$303$	−14.5011	−0.833067
$304$	−39.7686	−2.28089
$305$	18.1331	1.03830
$306$	14.0909	0.805521
$307$	28.4774	1.62529	0.812645	−	0.582759i	$-0.198027\pi$
$307$	28.4774	1.62529	0.812645	+	0.582759i	$0.198027\pi$
$308$	−8.46446	−0.482308
$309$	−17.5311	−0.997311
$310$	2.68834	0.152688
$311$	4.99213	0.283078	0.141539	−	0.989933i	$-0.454795\pi$
$311$	4.99213	0.283078	0.141539	+	0.989933i	$0.454795\pi$
$312$	−27.0843	−1.53335
$313$	29.7665	1.68250	0.841252	−	0.540643i	$-0.181819\pi$
$313$	29.7665	1.68250	0.841252	+	0.540643i	$0.181819\pi$
$314$	−4.50988	−0.254508
$315$	−19.4148	−1.09390
$316$	−72.3531	−4.07018
$317$	7.55931	0.424573	0.212287	−	0.977207i	$-0.431909\pi$
$317$	7.55931	0.424573	0.212287	+	0.977207i	$0.431909\pi$
$318$	10.6478	0.597101
$319$	−0.713542	−0.0399507
$320$	102.212	5.71381
$321$	−3.38597	−0.188986
$322$	−37.4611	−2.08762
$323$	−7.00046	−0.389516
$324$	−2.21908	−0.123282
$325$	−7.75213	−0.430011
$326$	−35.2523	−1.95244
$327$	0.354764	0.0196185
$328$	−12.6367	−0.697743
$329$	−2.88949	−0.159303
$330$	−3.43339	−0.189002
$331$	−17.3871	−0.955680	−0.477840	−	0.878447i	$-0.658580\pi$
$331$	−17.3871	−0.955680	−0.477840	+	0.878447i	$0.658580\pi$
$332$	−12.5864	−0.690768
$333$	11.1370	0.610306
$334$	−42.9874	−2.35216
$335$	−12.7295	−0.695484
$336$	−67.4370	−3.67899
$337$	−4.32376	−0.235530	−0.117765	−	0.993041i	$-0.537573\pi$
$337$	−4.32376	−0.235530	−0.117765	+	0.993041i	$0.537573\pi$
$338$	18.8326	1.02436
$339$	−11.6572	−0.633131
$340$	45.4646	2.46566
$341$	0.136173	0.00737419
$342$	−12.1623	−0.657661
$343$	1.56870	0.0847016
$344$	33.1406	1.78682
$345$	−11.1975	−0.602851
$346$	3.21473	0.172825
$347$	−6.10499	−0.327733	−0.163867	−	0.986483i	$-0.552397\pi$
$347$	−6.10499	−0.327733	−0.163867	+	0.986483i	$0.552397\pi$
$348$	−11.0273	−0.591124
$349$	−30.8775	−1.65283	−0.826417	−	0.563058i	$-0.809625\pi$
$349$	−30.8775	−1.65283	−0.826417	+	0.563058i	$0.809625\pi$
$350$	−32.6691	−1.74624
$351$	−13.0754	−0.697911
$352$	9.84803	0.524901
$353$	30.2230	1.60861	0.804304	−	0.594218i	$-0.202538\pi$
$353$	30.2230	1.60861	0.804304	+	0.594218i	$0.202538\pi$
$354$	−3.00876	−0.159914
$355$	12.6884	0.673429
$356$	32.3063	1.71223
$357$	−11.8709	−0.628276
$358$	−11.0121	−0.582007
$359$	−2.32282	−0.122594	−0.0612968	−	0.998120i	$-0.519524\pi$
$359$	−2.32282	−0.122594	−0.0612968	+	0.998120i	$0.519524\pi$
$360$	50.7882	2.67677
$361$	−12.9577	−0.681983
$362$	42.9580	2.25782
$363$	11.9035	0.624769
$364$	−52.8266	−2.76887
$365$	1.44846	0.0758159
$366$	19.2624	1.00686
$367$	−15.0709	−0.786693	−0.393347	−	0.919390i	$-0.628683\pi$
$367$	−15.0709	−0.786693	−0.393347	+	0.919390i	$0.628683\pi$
$368$	57.8994	3.01822
$369$	−2.28335	−0.118866
$370$	48.7629	2.53506
$371$	13.3536	0.693283
$372$	2.10445	0.109111
$373$	−20.9214	−1.08327	−0.541634	−	0.840614i	$-0.682194\pi$
$373$	−20.9214	−1.08327	−0.541634	+	0.840614i	$0.682194\pi$
$374$	3.12510	0.161595
$375$	5.87913	0.303597
$376$	7.55875	0.389813
$377$	−4.45321	−0.229352
$378$	−55.1023	−2.83415
$379$	−25.8409	−1.32736	−0.663680	−	0.748016i	$-0.731006\pi$
$379$	−25.8409	−1.32736	−0.663680	+	0.748016i	$0.731006\pi$
$380$	−39.2419	−2.01307
$381$	−5.70284	−0.292166
$382$	57.6087	2.94752
$383$	6.88938	0.352031	0.176015	−	0.984387i	$-0.443679\pi$
$383$	6.88938	0.352031	0.176015	+	0.984387i	$0.443679\pi$
$384$	54.2422	2.76803
$385$	−4.30586	−0.219447
$386$	41.4807	2.11131
$387$	5.98824	0.304399
$388$	1.63730	0.0831215
$389$	12.9194	0.655038	0.327519	−	0.944845i	$-0.393787\pi$
$389$	12.9194	0.655038	0.327519	+	0.944845i	$0.393787\pi$
$390$	−21.4278	−1.08504
$391$	10.1920	0.515433
$392$	−73.6232	−3.71854
$393$	−10.7429	−0.541908
$394$	−75.7817	−3.81783
$395$	−36.8059	−1.85191
$396$	4.00100	0.201058
$397$	34.6691	1.73999	0.869997	−	0.493058i	$-0.164121\pi$
$397$	34.6691	1.73999	0.869997	+	0.493058i	$0.164121\pi$
$398$	36.6777	1.83849
$399$	10.2462	0.512950
$400$	50.4930	2.52465
$401$	32.8690	1.64140	0.820699	−	0.571361i	$-0.193585\pi$
$401$	32.8690	1.64140	0.820699	+	0.571361i	$0.193585\pi$
$402$	−13.5223	−0.674429
$403$	0.849855	0.0423343
$404$	73.9888	3.68108
$405$	−1.12884	−0.0560927
$406$	−18.7667	−0.931378
$407$	2.47000	0.122433
$408$	31.0537	1.53739
$409$	3.74382	0.185120	0.0925601	−	0.995707i	$-0.470495\pi$
$409$	3.74382	0.185120	0.0925601	+	0.995707i	$0.470495\pi$
$410$	−9.99751	−0.493742
$411$	−2.82963	−0.139575
$412$	89.4487	4.40682
$413$	−3.77333	−0.185673
$414$	17.7072	0.870259
$415$	−6.40268	−0.314295
$416$	61.4614	3.01339
$417$	−16.0451	−0.785732
$418$	−2.69738	−0.131933
$419$	−1.40691	−0.0687320	−0.0343660	−	0.999409i	$-0.510941\pi$
$419$	−1.40691	−0.0687320	−0.0343660	+	0.999409i	$0.510941\pi$
$420$	−66.5439	−3.24701
$421$	10.9790	0.535081	0.267541	−	0.963547i	$-0.413789\pi$
$421$	10.9790	0.535081	0.267541	+	0.963547i	$0.413789\pi$
$422$	−10.3474	−0.503702
$423$	1.36581	0.0664079
$424$	−34.9322	−1.69646
$425$	8.88827	0.431144
$426$	13.4786	0.653041
$427$	24.1572	1.16905
$428$	17.2762	0.835074
$429$	−1.08538	−0.0524029
$430$	26.2192	1.26440
$431$	2.49114	0.119994	0.0599969	−	0.998199i	$-0.480891\pi$
$431$	2.49114	0.119994	0.0599969	+	0.998199i	$0.480891\pi$
$432$	85.1654	4.09752
$433$	−1.54120	−0.0740655	−0.0370327	−	0.999314i	$-0.511791\pi$
$433$	−1.54120	−0.0740655	−0.0370327	+	0.999314i	$0.511791\pi$
$434$	3.58146	0.171916
$435$	−5.60956	−0.268958
$436$	−1.81011	−0.0866884
$437$	−8.79706	−0.420821
$438$	1.53867	0.0735206
$439$	−4.05491	−0.193530	−0.0967652	−	0.995307i	$-0.530850\pi$
$439$	−4.05491	−0.193530	−0.0967652	+	0.995307i	$0.530850\pi$
$440$	11.2639	0.536986
$441$	−13.3032	−0.633483
$442$	19.5037	0.927698
$443$	33.2327	1.57893	0.789466	−	0.613794i	$-0.210357\pi$
$443$	33.2327	1.57893	0.789466	+	0.613794i	$0.210357\pi$
$444$	38.1720	1.81156
$445$	16.4342	0.779054
$446$	−20.7361	−0.981885
$447$	−18.8677	−0.892412
$448$	136.169	6.43336
$449$	−37.1219	−1.75189	−0.875946	−	0.482409i	$-0.839762\pi$
$449$	−37.1219	−1.75189	−0.875946	+	0.482409i	$0.839762\pi$
$450$	15.4421	0.727946
$451$	−0.506405	−0.0238457
$452$	59.4782	2.79762
$453$	−7.54793	−0.354633
$454$	−44.6942	−2.09760
$455$	−26.8728	−1.25982
$456$	−26.8035	−1.25519
$457$	22.7120	1.06242	0.531211	−	0.847239i	$-0.321737\pi$
$457$	22.7120	1.06242	0.531211	+	0.847239i	$0.321737\pi$
$458$	−29.9781	−1.40079
$459$	14.9917	0.699750
$460$	57.1326	2.66382
$461$	−2.52455	−0.117580	−0.0587899	−	0.998270i	$-0.518724\pi$
$461$	−2.52455	−0.117580	−0.0587899	+	0.998270i	$0.518724\pi$
$462$	−4.57403	−0.212803
$463$	−10.6338	−0.494196	−0.247098	−	0.968991i	$-0.579477\pi$
$463$	−10.6338	−0.494196	−0.247098	+	0.968991i	$0.579477\pi$
$464$	29.0057	1.34655
$465$	1.07053	0.0496448
$466$	−12.7817	−0.592103
$467$	17.7635	0.821995	0.410998	−	0.911636i	$-0.365180\pi$
$467$	17.7635	0.821995	0.410998	+	0.911636i	$0.365180\pi$
$468$	24.9702	1.15425
$469$	−16.9584	−0.783067
$470$	5.98012	0.275842
$471$	−1.79589	−0.0827504
$472$	9.87083	0.454342
$473$	1.32808	0.0610654
$474$	−39.0982	−1.79584
$475$	−7.67175	−0.352004
$476$	60.5688	2.77617
$477$	−6.31199	−0.289006
$478$	36.5724	1.67278
$479$	−22.4781	−1.02705	−0.513525	−	0.858075i	$-0.671660\pi$
$479$	−22.4781	−1.02705	−0.513525	+	0.858075i	$0.671660\pi$
$480$	77.4208	3.53376
$481$	15.4152	0.702873
$482$	−52.8526	−2.40737
$483$	−14.9175	−0.678769
$484$	−60.7348	−2.76067
$485$	0.832894	0.0378198
$486$	42.3431	1.92072
$487$	−12.2676	−0.555898	−0.277949	−	0.960596i	$-0.589655\pi$
$487$	−12.2676	−0.555898	−0.277949	+	0.960596i	$0.589655\pi$
$488$	−63.1940	−2.86066
$489$	−14.0379	−0.634816
$490$	−58.2471	−2.63134
$491$	−32.6946	−1.47549	−0.737743	−	0.675082i	$-0.764108\pi$
$491$	−32.6946	−1.47549	−0.737743	+	0.675082i	$0.764108\pi$
$492$	−7.82612	−0.352829
$493$	5.10586	0.229956
$494$	−16.8343	−0.757411
$495$	2.03530	0.0914800
$496$	−5.53547	−0.248550
$497$	16.9037	0.758234
$498$	−6.80144	−0.304780
$499$	−17.9868	−0.805199	−0.402599	−	0.915376i	$-0.631893\pi$
$499$	−17.9868	−0.805199	−0.402599	+	0.915376i	$0.631893\pi$
$500$	−29.9970	−1.34151
$501$	−17.1181	−0.764781
$502$	−7.22538	−0.322484
$503$	−14.6166	−0.651722	−0.325861	−	0.945418i	$-0.605654\pi$
$503$	−14.6166	−0.651722	−0.325861	+	0.945418i	$0.605654\pi$
$504$	67.6610	3.01386
$505$	37.6380	1.67487
$506$	3.92713	0.174582
$507$	7.49938	0.333059
$508$	29.0975	1.29099
$509$	−15.1314	−0.670688	−0.335344	−	0.942096i	$-0.608853\pi$
$509$	−15.1314	−0.670688	−0.335344	+	0.942096i	$0.608853\pi$
$510$	24.5682	1.08790
$511$	1.92967	0.0853635
$512$	−78.9750	−3.49023
$513$	−12.9398	−0.571305
$514$	17.2658	0.761562
$515$	45.5024	2.00508
$516$	20.5246	0.903544
$517$	0.302912	0.0133220
$518$	64.9629	2.85431
$519$	1.28015	0.0561922
$520$	70.2979	3.08277
$521$	−15.5065	−0.679352	−0.339676	−	0.940543i	$-0.610317\pi$
$521$	−15.5065	−0.679352	−0.339676	+	0.940543i	$0.610317\pi$
$522$	8.87069	0.388260
$523$	14.3989	0.629618	0.314809	−	0.949155i	$-0.398060\pi$
$523$	14.3989	0.629618	0.314809	+	0.949155i	$0.398060\pi$
$524$	54.8134	2.39453
$525$	−13.0092	−0.567770
$526$	−14.6431	−0.638471
$527$	−0.974407	−0.0424459
$528$	7.06958	0.307664
$529$	−10.1923	−0.443143
$530$	−27.6367	−1.20046
$531$	1.78358	0.0774009
$532$	−52.2789	−2.26658
$533$	−3.16047	−0.136895
$534$	17.4577	0.755468
$535$	8.78835	0.379954
$536$	44.3623	1.91616
$537$	−4.38516	−0.189233
$538$	63.2542	2.72708
$539$	−2.95040	−0.127083
$540$	84.0376	3.61640
$541$	23.3071	1.00205	0.501026	−	0.865432i	$-0.332956\pi$
$541$	23.3071	1.00205	0.501026	+	0.865432i	$0.332956\pi$
$542$	−39.3519	−1.69031
$543$	17.1064	0.734107
$544$	−70.4691	−3.02134
$545$	−0.920798	−0.0394427
$546$	−28.5465	−1.22168
$547$	6.49767	0.277820	0.138910	−	0.990305i	$-0.455640\pi$
$547$	6.49767	0.277820	0.138910	+	0.990305i	$0.455640\pi$
$548$	14.4376	0.616742
$549$	−11.4187	−0.487337
$550$	3.42478	0.146033
$551$	−4.40703	−0.187746
$552$	39.0233	1.66094
$553$	−49.0335	−2.08512
$554$	−25.1990	−1.07060
$555$	19.4180	0.824249
$556$	81.8666	3.47192
$557$	1.60081	0.0678284	0.0339142	−	0.999425i	$-0.489203\pi$
$557$	1.60081	0.0678284	0.0339142	+	0.999425i	$0.489203\pi$
$558$	−1.69289	−0.0716658
$559$	8.28856	0.350569
$560$	175.034	7.39655
$561$	1.24446	0.0525410
$562$	−26.3374	−1.11098
$563$	12.7006	0.535267	0.267634	−	0.963521i	$-0.413758\pi$
$563$	12.7006	0.535267	0.267634	+	0.963521i	$0.413758\pi$
$564$	4.68128	0.197117
$565$	30.2565	1.27290
$566$	−32.2382	−1.35507
$567$	−1.50387	−0.0631564
$568$	−44.2192	−1.85539
$569$	−25.0756	−1.05123	−0.525613	−	0.850724i	$-0.676164\pi$
$569$	−25.0756	−1.05123	−0.525613	+	0.850724i	$0.676164\pi$
$570$	−21.2056	−0.888204
$571$	41.6074	1.74121	0.870607	−	0.491979i	$-0.163726\pi$
$571$	41.6074	1.74121	0.870607	+	0.491979i	$0.163726\pi$
$572$	5.53794	0.231553
$573$	22.9405	0.958354
$574$	−13.3189	−0.555919
$575$	11.1694	0.465794
$576$	−64.3644	−2.68185
$577$	−35.3494	−1.47162	−0.735808	−	0.677190i	$-0.763197\pi$
$577$	−35.3494	−1.47162	−0.735808	+	0.677190i	$0.763197\pi$
$578$	24.5098	1.01947
$579$	16.5182	0.686471
$580$	28.6215	1.18844
$581$	−8.52977	−0.353874
$582$	0.884767	0.0366748
$583$	−1.39989	−0.0579773
$584$	−5.04791	−0.208884
$585$	12.7023	0.525175
$586$	−1.55038	−0.0640458
$587$	39.4334	1.62759	0.813795	−	0.581152i	$-0.197398\pi$
$587$	39.4334	1.62759	0.813795	+	0.581152i	$0.197398\pi$
$588$	−45.5963	−1.88036
$589$	0.841043	0.0346546
$590$	7.80932	0.321505
$591$	−30.1773	−1.24133
$592$	−100.406	−4.12666
$593$	−7.35315	−0.301958	−0.150979	−	0.988537i	$-0.548243\pi$
$593$	−7.35315	−0.301958	−0.150979	+	0.988537i	$0.548243\pi$
$594$	5.77650	0.237013
$595$	30.8113	1.26314
$596$	96.2684	3.94331
$597$	14.6055	0.597765
$598$	24.5092	1.00225
$599$	29.6448	1.21125	0.605627	−	0.795749i	$-0.292922\pi$
$599$	29.6448	1.21125	0.605627	+	0.795749i	$0.292922\pi$
$600$	34.0315	1.38933
$601$	15.6617	0.638854	0.319427	−	0.947611i	$-0.396510\pi$
$601$	15.6617	0.638854	0.319427	+	0.947611i	$0.396510\pi$
$602$	34.9297	1.42363
$603$	8.01593	0.326434
$604$	38.5116	1.56702
$605$	−30.8957	−1.25609
$606$	39.9821	1.62416
$607$	−25.5109	−1.03546	−0.517728	−	0.855545i	$-0.673222\pi$
$607$	−25.5109	−1.03546	−0.517728	+	0.855545i	$0.673222\pi$
$608$	60.8241	2.46674
$609$	−7.47316	−0.302828
$610$	−49.9960	−2.02428
$611$	1.89047	0.0764802
$612$	−28.6297	−1.15729
$613$	48.4431	1.95660	0.978300	−	0.207195i	$-0.0664333\pi$
$613$	48.4431	1.95660	0.978300	+	0.207195i	$0.0664333\pi$
$614$	−78.5171	−3.16869
$615$	−3.98114	−0.160535
$616$	15.0060	0.604609
$617$	−43.0885	−1.73468	−0.867339	−	0.497718i	$-0.834171\pi$
$617$	−43.0885	−1.73468	−0.867339	+	0.497718i	$0.834171\pi$
$618$	48.3364	1.94437
$619$	15.1169	0.607600	0.303800	−	0.952736i	$-0.401745\pi$
$619$	15.1169	0.607600	0.303800	+	0.952736i	$0.401745\pi$
$620$	−5.46216	−0.219366
$621$	18.8391	0.755988
$622$	−13.7642	−0.551893
$623$	21.8939	0.877160
$624$	44.1211	1.76626
$625$	−30.8644	−1.23457
$626$	−82.0715	−3.28024
$627$	−1.07413	−0.0428966
$628$	9.16316	0.365650
$629$	−17.6744	−0.704726
$630$	53.5301	2.13269
$631$	−21.2247	−0.844941	−0.422470	−	0.906377i	$-0.638837\pi$
$631$	−21.2247	−0.844941	−0.422470	+	0.906377i	$0.638837\pi$
$632$	128.269	5.10228
$633$	−4.12045	−0.163773
$634$	−20.8423	−0.827755
$635$	14.8019	0.587394
$636$	−21.6342	−0.857852
$637$	−18.4134	−0.729566
$638$	1.96736	0.0778885
$639$	−7.99006	−0.316082
$640$	−140.787	−5.56509
$641$	4.84075	0.191198	0.0955990	−	0.995420i	$-0.469523\pi$
$641$	4.84075	0.191198	0.0955990	+	0.995420i	$0.469523\pi$
$642$	9.33570	0.368451
$643$	42.6346	1.68134	0.840671	−	0.541546i	$-0.182161\pi$
$643$	42.6346	1.68134	0.840671	+	0.541546i	$0.182161\pi$
$644$	76.1132	2.99928
$645$	10.4408	0.411107
$646$	19.3015	0.759407
$647$	41.8377	1.64481	0.822405	−	0.568902i	$-0.192632\pi$
$647$	41.8377	1.64481	0.822405	+	0.568902i	$0.192632\pi$
$648$	3.93404	0.154544
$649$	0.395567	0.0155274
$650$	21.3740	0.838356
$651$	1.42618	0.0558966
$652$	71.6254	2.80507
$653$	10.4646	0.409513	0.204757	−	0.978813i	$-0.434360\pi$
$653$	10.4646	0.409513	0.204757	+	0.978813i	$0.434360\pi$
$654$	−0.978146	−0.0382486
$655$	27.8835	1.08950
$656$	20.5855	0.803729
$657$	−0.912118	−0.0355851
$658$	7.96683	0.310579
$659$	41.0338	1.59845	0.799226	−	0.601031i	$-0.205243\pi$
$659$	41.0338	1.59845	0.799226	+	0.601031i	$0.205243\pi$
$660$	6.97595	0.271539
$661$	−22.4413	−0.872865	−0.436433	−	0.899737i	$-0.643758\pi$
$661$	−22.4413	−0.872865	−0.436433	+	0.899737i	$0.643758\pi$
$662$	47.9392	1.86321
$663$	7.76663	0.301631
$664$	22.3134	0.865929
$665$	−26.5942	−1.03128
$666$	−30.7068	−1.18986
$667$	6.41623	0.248437
$668$	87.3415	3.37934
$669$	−8.25740	−0.319249
$670$	35.0973	1.35593
$671$	−2.53246	−0.0977644
$672$	103.142	3.97877
$673$	−25.0608	−0.966022	−0.483011	−	0.875614i	$-0.660457\pi$
$673$	−25.0608	−0.966022	−0.483011	+	0.875614i	$0.660457\pi$
$674$	11.9214	0.459193
$675$	16.4292	0.632362
$676$	−38.2640	−1.47169
$677$	−7.81351	−0.300297	−0.150149	−	0.988663i	$-0.547975\pi$
$677$	−7.81351	−0.300297	−0.150149	+	0.988663i	$0.547975\pi$
$678$	32.1409	1.23436
$679$	1.10960	0.0425824
$680$	−80.6006	−3.09089
$681$	−17.7978	−0.682013
$682$	−0.375453	−0.0143768
$683$	16.6413	0.636763	0.318381	−	0.947963i	$-0.396861\pi$
$683$	16.6413	0.636763	0.318381	+	0.947963i	$0.396861\pi$
$684$	24.7113	0.944859
$685$	7.34436	0.280614
$686$	−4.32517	−0.165136
$687$	−11.9377	−0.455451
$688$	−53.9870	−2.05823
$689$	−8.73667	−0.332841
$690$	30.8734	1.17533
$691$	−2.33468	−0.0888154	−0.0444077	−	0.999013i	$-0.514140\pi$
$691$	−2.33468	−0.0888154	−0.0444077	+	0.999013i	$0.514140\pi$
$692$	−6.53167	−0.248297
$693$	2.71147	0.103000
$694$	16.8325	0.638954
$695$	41.6454	1.57970
$696$	19.5494	0.741018
$697$	3.62366	0.137256
$698$	85.1347	3.22239
$699$	−5.08986	−0.192516
$700$	66.3768	2.50881
$701$	−20.1316	−0.760359	−0.380180	−	0.924913i	$-0.624138\pi$
$701$	−20.1316	−0.760359	−0.380180	+	0.924913i	$0.624138\pi$
$702$	36.0510	1.36066
$703$	15.2554	0.575368
$704$	−14.2749	−0.538004
$705$	2.38136	0.0896872
$706$	−83.3301	−3.13617
$707$	50.1421	1.88579
$708$	6.11319	0.229748
$709$	−12.0459	−0.452394	−0.226197	−	0.974082i	$-0.572629\pi$
$709$	−12.0459	−0.452394	−0.226197	+	0.974082i	$0.572629\pi$
$710$	−34.9840	−1.31293
$711$	23.1773	0.869215
$712$	−57.2733	−2.14641
$713$	−1.22448	−0.0458571
$714$	32.7302	1.22490
$715$	2.81714	0.105355
$716$	22.3743	0.836167
$717$	14.5636	0.543888
$718$	6.40442	0.239011
$719$	−44.5043	−1.65973	−0.829865	−	0.557965i	$-0.811582\pi$
$719$	−44.5043	−1.65973	−0.829865	+	0.557965i	$0.811582\pi$
$720$	−82.7355	−3.08337
$721$	60.6192	2.25758
$722$	35.7266	1.32961
$723$	−21.0466	−0.782730
$724$	−87.2818	−3.24380
$725$	5.59547	0.207811
$726$	−32.8199	−1.21806
$727$	−25.3119	−0.938768	−0.469384	−	0.882994i	$-0.655524\pi$
$727$	−25.3119	−0.938768	−0.469384	+	0.882994i	$0.655524\pi$
$728$	93.6522	3.47098
$729$	18.0499	0.668515
$730$	−3.99366	−0.147812
$731$	−9.50332	−0.351493
$732$	−39.1373	−1.44655
$733$	36.5932	1.35160	0.675800	−	0.737085i	$-0.263798\pi$
$733$	36.5932	1.35160	0.675800	+	0.737085i	$0.263798\pi$
$734$	41.5530	1.53375
$735$	−23.1947	−0.855551
$736$	−88.5543	−3.26415
$737$	1.77779	0.0654858
$738$	6.29559	0.231744
$739$	0.195944	0.00720792	0.00360396	−	0.999994i	$-0.498853\pi$
$739$	0.195944	0.00720792	0.00360396	+	0.999994i	$0.498853\pi$
$740$	−99.0762	−3.64212
$741$	−6.70363	−0.246264
$742$	−36.8181	−1.35164
$743$	−26.9426	−0.988429	−0.494215	−	0.869340i	$-0.664544\pi$
$743$	−26.9426	−0.988429	−0.494215	+	0.869340i	$0.664544\pi$
$744$	−3.73082	−0.136779
$745$	48.9716	1.79418
$746$	57.6839	2.11196
$747$	4.03186	0.147518
$748$	−6.34956	−0.232163
$749$	11.7080	0.427802
$750$	−16.2098	−0.591898
$751$	−6.28468	−0.229331	−0.114666	−	0.993404i	$-0.536580\pi$
$751$	−6.28468	−0.229331	−0.114666	+	0.993404i	$0.536580\pi$
$752$	−12.3134	−0.449025
$753$	−2.87724	−0.104852
$754$	12.2783	0.447148
$755$	19.5908	0.712983
$756$	111.956	4.07182
$757$	−41.4628	−1.50699	−0.753496	−	0.657452i	$-0.771634\pi$
$757$	−41.4628	−1.50699	−0.753496	+	0.657452i	$0.771634\pi$
$758$	71.2480	2.58784
$759$	1.56383	0.0567636
$760$	69.5690	2.52353
$761$	−1.08106	−0.0391883	−0.0195942	−	0.999808i	$-0.506237\pi$
$761$	−1.08106	−0.0391883	−0.0195942	+	0.999808i	$0.506237\pi$
$762$	15.7237	0.569611
$763$	−1.22671	−0.0444097
$764$	−117.049	−4.23468
$765$	−14.5639	−0.526559
$766$	−18.9952	−0.686325
$767$	2.46873	0.0891406
$768$	−70.7951	−2.55460
$769$	27.5592	0.993811	0.496905	−	0.867805i	$-0.334470\pi$
$769$	27.5592	0.993811	0.496905	+	0.867805i	$0.334470\pi$
$770$	11.8720	0.427838
$771$	6.87547	0.247614
$772$	−84.2803	−3.03332
$773$	17.9752	0.646523	0.323262	−	0.946310i	$-0.395221\pi$
$773$	17.9752	0.646523	0.323262	+	0.946310i	$0.395221\pi$
$774$	−16.5106	−0.593462
$775$	−1.06785	−0.0383581
$776$	−2.90265	−0.104199
$777$	25.8691	0.928048
$778$	−35.6209	−1.27707
$779$	−3.12770	−0.112061
$780$	43.5368	1.55887
$781$	−1.77205	−0.0634090
$782$	−28.1012	−1.00490
$783$	9.43777	0.337278
$784$	119.934	4.28337
$785$	4.66129	0.166368
$786$	29.6201	1.05651
$787$	2.59217	0.0924007	0.0462004	−	0.998932i	$-0.485289\pi$
$787$	2.59217	0.0924007	0.0462004	+	0.998932i	$0.485289\pi$
$788$	153.973	5.48505
$789$	−5.83108	−0.207592
$790$	101.480	3.61051
$791$	40.3083	1.43320
$792$	−7.09306	−0.252041
$793$	−15.8050	−0.561253
$794$	−95.5888	−3.39232
$795$	−11.0053	−0.390317
$796$	−74.5216	−2.64135
$797$	−27.2886	−0.966611	−0.483305	−	0.875452i	$-0.660564\pi$
$797$	−27.2886	−0.966611	−0.483305	+	0.875452i	$0.660564\pi$
$798$	−28.2505	−1.00006
$799$	−2.16753	−0.0766818
$800$	−77.2265	−2.73037
$801$	−10.3488	−0.365658
$802$	−90.6254	−3.20010
$803$	−0.202292	−0.00713871
$804$	27.4744	0.968949
$805$	38.7187	1.36465
$806$	−2.34320	−0.0825356
$807$	25.1886	0.886682
$808$	−131.169	−4.61451
$809$	−49.9218	−1.75516	−0.877578	−	0.479434i	$-0.840842\pi$
$809$	−49.9218	−1.75516	−0.877578	+	0.479434i	$0.840842\pi$
$810$	3.11242	0.109359
$811$	−26.9446	−0.946152	−0.473076	−	0.881022i	$-0.656856\pi$
$811$	−26.9446	−0.946152	−0.473076	+	0.881022i	$0.656856\pi$
$812$	38.1301	1.33811
$813$	−15.6704	−0.549586
$814$	−6.81021	−0.238698
$815$	36.4357	1.27629
$816$	−50.5874	−1.77091
$817$	8.20262	0.286973
$818$	−10.3224	−0.360913
$819$	16.9222	0.591311
$820$	20.3129	0.709356
$821$	24.2129	0.845035	0.422517	−	0.906355i	$-0.361147\pi$
$821$	24.2129	0.845035	0.422517	+	0.906355i	$0.361147\pi$
$822$	7.80178	0.272118
$823$	19.1779	0.668498	0.334249	−	0.942485i	$-0.391517\pi$
$823$	19.1779	0.668498	0.334249	+	0.942485i	$0.391517\pi$
$824$	−158.577	−5.52428
$825$	1.36379	0.0474811
$826$	10.4037	0.361992
$827$	−42.1158	−1.46451	−0.732256	−	0.681030i	$-0.761532\pi$
$827$	−42.1158	−1.46451	−0.732256	+	0.681030i	$0.761532\pi$
$828$	−35.9773	−1.25030
$829$	−28.6024	−0.993404	−0.496702	−	0.867921i	$-0.665456\pi$
$829$	−28.6024	−0.993404	−0.496702	+	0.867921i	$0.665456\pi$
$830$	17.6533	0.612755
$831$	−10.0346	−0.348095
$832$	−89.0892	−3.08861
$833$	21.1120	0.731489
$834$	44.2391	1.53188
$835$	44.4305	1.53758
$836$	5.48051	0.189548
$837$	−1.80111	−0.0622556
$838$	3.87909	0.134001
$839$	3.92016	0.135339	0.0676694	−	0.997708i	$-0.478444\pi$
$839$	3.92016	0.135339	0.0676694	+	0.997708i	$0.478444\pi$
$840$	117.971	4.07037
$841$	−25.7857	−0.889161
$842$	−30.2709	−1.04320
$843$	−10.4879	−0.361223
$844$	21.0237	0.723666
$845$	−19.4648	−0.669610
$846$	−3.76577	−0.129470
$847$	−41.1598	−1.41427
$848$	56.9057	1.95415
$849$	−12.8377	−0.440588
$850$	−24.5065	−0.840566
$851$	−22.2104	−0.761363
$852$	−27.3858	−0.938221
$853$	18.2311	0.624221	0.312110	−	0.950046i	$-0.398964\pi$
$853$	18.2311	0.624221	0.312110	+	0.950046i	$0.398964\pi$
$854$	−66.6057	−2.27920
$855$	12.5706	0.429905
$856$	−30.6276	−1.04683
$857$	−40.5325	−1.38456	−0.692282	−	0.721627i	$-0.743395\pi$
$857$	−40.5325	−1.38456	−0.692282	+	0.721627i	$0.743395\pi$
$858$	2.99259	0.102165
$859$	−4.23798	−0.144598	−0.0722989	−	0.997383i	$-0.523034\pi$
$859$	−4.23798	−0.144598	−0.0722989	+	0.997383i	$0.523034\pi$
$860$	−53.2720	−1.81656
$861$	−5.30375	−0.180751
$862$	−6.86850	−0.233942
$863$	−16.6849	−0.567960	−0.283980	−	0.958830i	$-0.591655\pi$
$863$	−16.6849	−0.567960	−0.283980	+	0.958830i	$0.591655\pi$
$864$	−130.256	−4.43141
$865$	−3.32265	−0.112974
$866$	4.24936	0.144399
$867$	9.76013	0.331471
$868$	−7.27679	−0.246991
$869$	5.14030	0.174373
$870$	15.4665	0.524364
$871$	11.0952	0.375945
$872$	3.20900	0.108670
$873$	−0.524486	−0.0177512
$874$	24.2550	0.820439
$875$	−20.3289	−0.687242
$876$	−3.12627	−0.105627
$877$	−55.7717	−1.88328	−0.941638	−	0.336626i	$-0.890714\pi$
$877$	−55.7717	−1.88328	−0.941638	+	0.336626i	$0.890714\pi$
$878$	11.1801	0.377310
$879$	−0.617383	−0.0208238
$880$	−18.3492	−0.618553
$881$	51.5797	1.73777	0.868883	−	0.495018i	$-0.164838\pi$
$881$	51.5797	1.73777	0.868883	+	0.495018i	$0.164838\pi$
$882$	36.6791	1.23505
$883$	34.4573	1.15958	0.579790	−	0.814766i	$-0.303135\pi$
$883$	34.4573	1.15958	0.579790	+	0.814766i	$0.303135\pi$
$884$	−39.6276	−1.33282
$885$	3.10977	0.104534
$886$	−91.6283	−3.07831
$887$	−28.2620	−0.948946	−0.474473	−	0.880270i	$-0.657361\pi$
$887$	−28.2620	−0.948946	−0.474473	+	0.880270i	$0.657361\pi$
$888$	−67.6721	−2.27093
$889$	19.7193	0.661365
$890$	−45.3118	−1.51886
$891$	0.157654	0.00528160
$892$	42.1316	1.41067
$893$	1.87087	0.0626062
$894$	52.0216	1.73986
$895$	11.3818	0.380451
$896$	−187.559	−6.26590
$897$	9.75987	0.325872
$898$	102.352	3.41552
$899$	−0.613423	−0.0204588
$900$	−31.3751	−1.04584
$901$	10.0171	0.333718
$902$	1.39625	0.0464900
$903$	13.9095	0.462878
$904$	−105.444	−3.50703
$905$	−44.4001	−1.47591
$906$	20.8110	0.691398
$907$	56.6617	1.88142	0.940710	−	0.339211i	$-0.110160\pi$
$907$	56.6617	1.88142	0.940710	+	0.339211i	$0.110160\pi$
$908$	90.8093	3.01361
$909$	−23.7012	−0.786120
$910$	74.0931	2.45616
$911$	55.3263	1.83304	0.916520	−	0.399988i	$-0.130986\pi$
$911$	55.3263	1.83304	0.916520	+	0.399988i	$0.130986\pi$
$912$	43.6637	1.44585
$913$	0.894195	0.0295935
$914$	−62.6209	−2.07132
$915$	−19.9091	−0.658173
$916$	60.9094	2.01250
$917$	37.1469	1.22670
$918$	−41.3346	−1.36425
$919$	47.7811	1.57615	0.788077	−	0.615577i	$-0.211077\pi$
$919$	47.7811	1.57615	0.788077	+	0.615577i	$0.211077\pi$
$920$	−101.286	−3.33930
$921$	−31.2665	−1.03027
$922$	6.96062	0.229236
$923$	−11.0594	−0.364023
$924$	9.29349	0.305734
$925$	−19.3693	−0.636858
$926$	29.3193	0.963492
$927$	−28.6536	−0.941107
$928$	−44.3627	−1.45628
$929$	7.69006	0.252303	0.126151	−	0.992011i	$-0.459737\pi$
$929$	7.69006	0.252303	0.126151	+	0.992011i	$0.459737\pi$
$930$	−2.95165	−0.0967883
$931$	−18.2225	−0.597218
$932$	25.9699	0.850672
$933$	−5.48107	−0.179442
$934$	−48.9770	−1.60258
$935$	−3.23001	−0.105633
$936$	−44.2677	−1.44693
$937$	56.5139	1.84623	0.923115	−	0.384524i	$-0.125635\pi$
$937$	56.5139	1.84623	0.923115	+	0.384524i	$0.125635\pi$
$938$	46.7573	1.52668
$939$	−32.6819	−1.06653
$940$	−12.1504	−0.396301
$941$	11.3043	0.368509	0.184254	−	0.982879i	$-0.441013\pi$
$941$	11.3043	0.368509	0.184254	+	0.982879i	$0.441013\pi$
$942$	4.95159	0.161332
$943$	4.55364	0.148287
$944$	−16.0799	−0.523356
$945$	56.9521	1.85265
$946$	−3.66176	−0.119054
$947$	1.51932	0.0493712	0.0246856	−	0.999695i	$-0.492142\pi$
$947$	1.51932	0.0493712	0.0246856	+	0.999695i	$0.492142\pi$
$948$	79.4395	2.58008
$949$	−1.26250	−0.0409824
$950$	21.1524	0.686273
$951$	−8.29969	−0.269136
$952$	−107.378	−3.48013
$953$	−28.5691	−0.925444	−0.462722	−	0.886504i	$-0.653127\pi$
$953$	−28.5691	−0.925444	−0.462722	+	0.886504i	$0.653127\pi$
$954$	17.4032	0.563451
$955$	−59.5426	−1.92675
$956$	−74.3076	−2.40328
$957$	0.783428	0.0253246
$958$	61.9760	2.00235
$959$	9.78430	0.315952
$960$	−112.223	−3.62197
$961$	−30.8829	−0.996224
$962$	−42.5024	−1.37033
$963$	−5.53416	−0.178336
$964$	107.386	3.45865
$965$	−42.8733	−1.38014
$966$	41.1301	1.32334
$967$	11.7892	0.379115	0.189558	−	0.981870i	$-0.439295\pi$
$967$	11.7892	0.379115	0.189558	+	0.981870i	$0.439295\pi$
$968$	107.672	3.46071
$969$	7.68610	0.246913
$970$	−2.29643	−0.0737340
$971$	32.0269	1.02779	0.513896	−	0.857853i	$-0.328202\pi$
$971$	32.0269	1.02779	0.513896	+	0.857853i	$0.328202\pi$
$972$	−86.0324	−2.75949
$973$	55.4808	1.77863
$974$	33.8239	1.08379
$975$	8.51139	0.272583
$976$	102.945	3.29519
$977$	11.7665	0.376445	0.188222	−	0.982126i	$-0.439727\pi$
$977$	11.7665	0.376445	0.188222	+	0.982126i	$0.439727\pi$
$978$	38.7050	1.23765
$979$	−2.29519	−0.0733545
$980$	118.346	3.78043
$981$	0.579841	0.0185129
$982$	90.1447	2.87663
$983$	−9.19434	−0.293254	−0.146627	−	0.989192i	$-0.546842\pi$
$983$	−9.19434	−0.293254	−0.146627	+	0.989192i	$0.546842\pi$
$984$	13.8743	0.442297
$985$	78.3258	2.49567
$986$	−14.0777	−0.448327
$987$	3.17249	0.100982
$988$	34.2038	1.08817
$989$	−11.9423	−0.379741
$990$	−5.61168	−0.178351
$991$	−15.3089	−0.486303	−0.243151	−	0.969988i	$-0.578181\pi$
$991$	−15.3089	−0.486303	−0.243151	+	0.969988i	$0.578181\pi$
$992$	8.46622	0.268803
$993$	19.0900	0.605803
$994$	−46.6064	−1.47827
$995$	−37.9090	−1.20180
$996$	13.8191	0.437876
$997$	−43.8493	−1.38872	−0.694361	−	0.719627i	$-0.744313\pi$
$997$	−43.8493	−1.38872	−0.694361	+	0.719627i	$0.744313\pi$
$998$	49.5927	1.56983
$999$	−32.6698	−1.03363

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6037.2.a.b.1.1	✓	259

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6037.2.a.b.1.1	✓	259	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:	\( N \)	\(=\)	\( 6037 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6037.a (trivial)

\(f(q)\)	\(=\)	\(q-2.75717 q^{2} -1.09794 q^{3} +5.60201 q^{4} +2.84974 q^{5} +3.02722 q^{6} +3.79647 q^{7} -9.93137 q^{8} -1.79452 q^{9} +O(q^{10})\)	\(q-2.75717 q^{2} -1.09794 q^{3} +5.60201 q^{4} +2.84974 q^{5} +3.02722 q^{6} +3.79647 q^{7} -9.93137 q^{8} -1.79452 q^{9} -7.85722 q^{10} -0.397993 q^{11} -6.15069 q^{12} -2.48387 q^{13} -10.4675 q^{14} -3.12885 q^{15} +16.1785 q^{16} +2.84790 q^{17} +4.94781 q^{18} -2.45811 q^{19} +15.9642 q^{20} -4.16831 q^{21} +1.09734 q^{22} +3.57879 q^{23} +10.9041 q^{24} +3.12099 q^{25} +6.84846 q^{26} +5.26411 q^{27} +21.2679 q^{28} +1.79285 q^{29} +8.62677 q^{30} -0.342150 q^{31} -24.7442 q^{32} +0.436973 q^{33} -7.85216 q^{34} +10.8189 q^{35} -10.0529 q^{36} -6.20613 q^{37} +6.77745 q^{38} +2.72714 q^{39} -28.3018 q^{40} +1.27240 q^{41} +11.4928 q^{42} -3.33696 q^{43} -2.22956 q^{44} -5.11391 q^{45} -9.86734 q^{46} -0.761099 q^{47} -17.7631 q^{48} +7.41320 q^{49} -8.60512 q^{50} -3.12683 q^{51} -13.9147 q^{52} +3.51736 q^{53} -14.5141 q^{54} -1.13417 q^{55} -37.7042 q^{56} +2.69887 q^{57} -4.94320 q^{58} -0.993904 q^{59} -17.5278 q^{60} +6.36307 q^{61} +0.943366 q^{62} -6.81285 q^{63} +35.8671 q^{64} -7.07837 q^{65} -1.20481 q^{66} -4.46689 q^{67} +15.9540 q^{68} -3.92930 q^{69} -29.8297 q^{70} +4.45247 q^{71} +17.8221 q^{72} +0.508279 q^{73} +17.1114 q^{74} -3.42667 q^{75} -13.7704 q^{76} -1.51097 q^{77} -7.51921 q^{78} -12.9156 q^{79} +46.1045 q^{80} -0.396122 q^{81} -3.50822 q^{82} -2.24676 q^{83} -23.3509 q^{84} +8.11576 q^{85} +9.20057 q^{86} -1.96845 q^{87} +3.95262 q^{88} +5.76691 q^{89} +14.1000 q^{90} -9.42994 q^{91} +20.0484 q^{92} +0.375661 q^{93} +2.09848 q^{94} -7.00497 q^{95} +27.1677 q^{96} +0.292271 q^{97} -20.4395 q^{98} +0.714207 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 259 q + 47 q^{2} + 29 q^{3} + 273 q^{4} + 38 q^{5} + 24 q^{6} + 42 q^{7} + 141 q^{8} + 286 q^{9}+O(q^{10}) \) 259 * q + 47 * q^2 + 29 * q^3 + 273 * q^4 + 38 * q^5 + 24 * q^6 + 42 * q^7 + 141 * q^8 + 286 * q^9	\( 259 q + 47 q^{2} + 29 q^{3} + 273 q^{4} + 38 q^{5} + 24 q^{6} + 42 q^{7} + 141 q^{8} + 286 q^{9} + 18 q^{10} + 108 q^{11} + 46 q^{12} + 33 q^{13} + 35 q^{14} + 40 q^{15} + 301 q^{16} + 67 q^{17} + 117 q^{18} + 69 q^{19} + 103 q^{20} + 24 q^{21} + 42 q^{22} + 162 q^{23} + 45 q^{24} + 291 q^{25} + 41 q^{26} + 101 q^{27} + 87 q^{28} + 78 q^{29} + 48 q^{30} + 25 q^{31} + 314 q^{32} + 67 q^{33} + 9 q^{34} + 252 q^{35} + 337 q^{36} + 49 q^{37} + 59 q^{38} + 93 q^{39} + 44 q^{40} + 60 q^{41} + 38 q^{42} + 178 q^{43} + 171 q^{44} + 67 q^{45} + 43 q^{46} + 185 q^{47} + 67 q^{48} + 273 q^{49} + 204 q^{50} + 145 q^{51} + 83 q^{52} + 112 q^{53} + 60 q^{54} + 57 q^{55} + 93 q^{56} + 109 q^{57} + 63 q^{58} + 228 q^{59} + 53 q^{60} + 20 q^{61} + 126 q^{62} + 153 q^{63} + 345 q^{64} + 113 q^{65} + 5 q^{66} + 208 q^{67} + 166 q^{68} + 10 q^{69} + 69 q^{70} + 150 q^{71} + 331 q^{72} + 75 q^{73} + 84 q^{74} + 72 q^{75} + 102 q^{76} + 166 q^{77} + 69 q^{78} + 52 q^{79} + 180 q^{80} + 327 q^{81} + 43 q^{82} + 434 q^{83} + 75 q^{85} + 133 q^{86} + 144 q^{87} + 111 q^{88} + 78 q^{89} - 8 q^{90} + 35 q^{91} + 372 q^{92} + 160 q^{93} + 36 q^{94} + 154 q^{95} + 60 q^{96} + 35 q^{97} + 254 q^{98} + 234 q^{99}+O(q^{100}) \) 259 * q + 47 * q^2 + 29 * q^3 + 273 * q^4 + 38 * q^5 + 24 * q^6 + 42 * q^7 + 141 * q^8 + 286 * q^9 + 18 * q^10 + 108 * q^11 + 46 * q^12 + 33 * q^13 + 35 * q^14 + 40 * q^15 + 301 * q^16 + 67 * q^17 + 117 * q^18 + 69 * q^19 + 103 * q^20 + 24 * q^21 + 42 * q^22 + 162 * q^23 + 45 * q^24 + 291 * q^25 + 41 * q^26 + 101 * q^27 + 87 * q^28 + 78 * q^29 + 48 * q^30 + 25 * q^31 + 314 * q^32 + 67 * q^33 + 9 * q^34 + 252 * q^35 + 337 * q^36 + 49 * q^37 + 59 * q^38 + 93 * q^39 + 44 * q^40 + 60 * q^41 + 38 * q^42 + 178 * q^43 + 171 * q^44 + 67 * q^45 + 43 * q^46 + 185 * q^47 + 67 * q^48 + 273 * q^49 + 204 * q^50 + 145 * q^51 + 83 * q^52 + 112 * q^53 + 60 * q^54 + 57 * q^55 + 93 * q^56 + 109 * q^57 + 63 * q^58 + 228 * q^59 + 53 * q^60 + 20 * q^61 + 126 * q^62 + 153 * q^63 + 345 * q^64 + 113 * q^65 + 5 * q^66 + 208 * q^67 + 166 * q^68 + 10 * q^69 + 69 * q^70 + 150 * q^71 + 331 * q^72 + 75 * q^73 + 84 * q^74 + 72 * q^75 + 102 * q^76 + 166 * q^77 + 69 * q^78 + 52 * q^79 + 180 * q^80 + 327 * q^81 + 43 * q^82 + 434 * q^83 + 75 * q^85 + 133 * q^86 + 144 * q^87 + 111 * q^88 + 78 * q^89 - 8 * q^90 + 35 * q^91 + 372 * q^92 + 160 * q^93 + 36 * q^94 + 154 * q^95 + 60 * q^96 + 35 * q^97 + 254 * q^98 + 234 * q^99

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