LMFDB - Embedded newform 6001.2.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6001,2,Mod(1,6001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6001, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6001 = 17 \cdot 353 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6001.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:	$47.9182262530$
Analytic rank:	$0$
Dimension:	$121$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	6001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.75847 q^{2} -2.11283 q^{3} +5.60915 q^{4} +3.70679 q^{5} +5.82818 q^{6} -2.88565 q^{7} -9.95572 q^{8} +1.46406 q^{9} +O(q^{10})$	\(q-2.75847 q^{2} -2.11283 q^{3} +5.60915 q^{4} +3.70679 q^{5} +5.82818 q^{6} -2.88565 q^{7} -9.95572 q^{8} +1.46406 q^{9} -10.2251 q^{10} +1.36743 q^{11} -11.8512 q^{12} -2.58949 q^{13} +7.95998 q^{14} -7.83184 q^{15} +16.2442 q^{16} -1.00000 q^{17} -4.03857 q^{18} -0.139083 q^{19} +20.7920 q^{20} +6.09690 q^{21} -3.77202 q^{22} +3.49986 q^{23} +21.0348 q^{24} +8.74032 q^{25} +7.14302 q^{26} +3.24518 q^{27} -16.1861 q^{28} +2.31083 q^{29} +21.6039 q^{30} +9.69726 q^{31} -24.8978 q^{32} -2.88916 q^{33} +2.75847 q^{34} -10.6965 q^{35} +8.21215 q^{36} -0.0894272 q^{37} +0.383656 q^{38} +5.47116 q^{39} -36.9038 q^{40} +5.03695 q^{41} -16.8181 q^{42} +6.61940 q^{43} +7.67013 q^{44} +5.42698 q^{45} -9.65426 q^{46} -7.84196 q^{47} -34.3214 q^{48} +1.32699 q^{49} -24.1099 q^{50} +2.11283 q^{51} -14.5248 q^{52} -9.20590 q^{53} -8.95172 q^{54} +5.06879 q^{55} +28.7287 q^{56} +0.293859 q^{57} -6.37436 q^{58} +10.9446 q^{59} -43.9299 q^{60} -13.8657 q^{61} -26.7496 q^{62} -4.22478 q^{63} +36.1913 q^{64} -9.59870 q^{65} +7.96964 q^{66} +11.8594 q^{67} -5.60915 q^{68} -7.39463 q^{69} +29.5060 q^{70} -2.63645 q^{71} -14.5758 q^{72} +4.76518 q^{73} +0.246682 q^{74} -18.4668 q^{75} -0.780137 q^{76} -3.94593 q^{77} -15.0920 q^{78} -3.15590 q^{79} +60.2140 q^{80} -11.2487 q^{81} -13.8943 q^{82} -7.09567 q^{83} +34.1984 q^{84} -3.70679 q^{85} -18.2594 q^{86} -4.88241 q^{87} -13.6138 q^{88} -15.9467 q^{89} -14.9702 q^{90} +7.47236 q^{91} +19.6313 q^{92} -20.4887 q^{93} +21.6318 q^{94} -0.515552 q^{95} +52.6049 q^{96} +15.2637 q^{97} -3.66046 q^{98} +2.00201 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 121 q + 9 q^{2} + 13 q^{3} + 127 q^{4} + 21 q^{5} + 19 q^{6} - 13 q^{7} + 24 q^{8} + 134 q^{9}+O(q^{10}) $ 121 * q + 9 * q^2 + 13 * q^3 + 127 * q^4 + 21 * q^5 + 19 * q^6 - 13 * q^7 + 24 * q^8 + 134 * q^9	\( 121 q + 9 q^{2} + 13 q^{3} + 127 q^{4} + 21 q^{5} + 19 q^{6} - 13 q^{7} + 24 q^{8} + 134 q^{9} - q^{10} + 40 q^{11} + 41 q^{12} + 14 q^{13} + 32 q^{14} + 49 q^{15} + 135 q^{16} - 121 q^{17} + 28 q^{18} + 34 q^{19} + 64 q^{20} + 34 q^{21} - 18 q^{22} + 37 q^{23} + 54 q^{24} + 128 q^{25} + 91 q^{26} + 55 q^{27} - 28 q^{28} + 45 q^{29} + 30 q^{30} + 67 q^{31} + 47 q^{32} + 40 q^{33} - 9 q^{34} + 59 q^{35} + 138 q^{36} - 16 q^{37} + 30 q^{38} + 37 q^{39} + 14 q^{40} + 89 q^{41} + 33 q^{42} + 16 q^{43} + 90 q^{44} + 83 q^{45} - 9 q^{46} + 135 q^{47} + 96 q^{48} + 128 q^{49} + 71 q^{50} - 13 q^{51} + 47 q^{52} + 52 q^{53} + 90 q^{54} + 93 q^{55} + 69 q^{56} - 4 q^{57} + 5 q^{58} + 170 q^{59} + 78 q^{60} - 2 q^{61} + 46 q^{62} - 10 q^{63} + 182 q^{64} + 50 q^{65} + 68 q^{66} + 46 q^{67} - 127 q^{68} + 97 q^{69} + 46 q^{70} + 191 q^{71} + 57 q^{72} - 12 q^{73} + 68 q^{74} + 86 q^{75} + 108 q^{76} + 62 q^{77} - 10 q^{78} + 130 q^{80} + 149 q^{81} + 14 q^{82} + 83 q^{83} + 126 q^{84} - 21 q^{85} + 132 q^{86} + 50 q^{87} - 42 q^{88} + 144 q^{89} + 9 q^{90} + 13 q^{91} + 50 q^{92} + 43 q^{93} + 41 q^{94} + 82 q^{95} + 110 q^{96} - 3 q^{97} + 36 q^{98} + 89 q^{99}+O(q^{100}) \) 121 * q + 9 * q^2 + 13 * q^3 + 127 * q^4 + 21 * q^5 + 19 * q^6 - 13 * q^7 + 24 * q^8 + 134 * q^9 - q^10 + 40 * q^11 + 41 * q^12 + 14 * q^13 + 32 * q^14 + 49 * q^15 + 135 * q^16 - 121 * q^17 + 28 * q^18 + 34 * q^19 + 64 * q^20 + 34 * q^21 - 18 * q^22 + 37 * q^23 + 54 * q^24 + 128 * q^25 + 91 * q^26 + 55 * q^27 - 28 * q^28 + 45 * q^29 + 30 * q^30 + 67 * q^31 + 47 * q^32 + 40 * q^33 - 9 * q^34 + 59 * q^35 + 138 * q^36 - 16 * q^37 + 30 * q^38 + 37 * q^39 + 14 * q^40 + 89 * q^41 + 33 * q^42 + 16 * q^43 + 90 * q^44 + 83 * q^45 - 9 * q^46 + 135 * q^47 + 96 * q^48 + 128 * q^49 + 71 * q^50 - 13 * q^51 + 47 * q^52 + 52 * q^53 + 90 * q^54 + 93 * q^55 + 69 * q^56 - 4 * q^57 + 5 * q^58 + 170 * q^59 + 78 * q^60 - 2 * q^61 + 46 * q^62 - 10 * q^63 + 182 * q^64 + 50 * q^65 + 68 * q^66 + 46 * q^67 - 127 * q^68 + 97 * q^69 + 46 * q^70 + 191 * q^71 + 57 * q^72 - 12 * q^73 + 68 * q^74 + 86 * q^75 + 108 * q^76 + 62 * q^77 - 10 * q^78 + 130 * q^80 + 149 * q^81 + 14 * q^82 + 83 * q^83 + 126 * q^84 - 21 * q^85 + 132 * q^86 + 50 * q^87 - 42 * q^88 + 144 * q^89 + 9 * q^90 + 13 * q^91 + 50 * q^92 + 43 * q^93 + 41 * q^94 + 82 * q^95 + 110 * q^96 - 3 * q^97 + 36 * q^98 + 89 * 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 $

$2$	−2.75847	−1.95053	−0.975266	−	0.221035i	$-0.929056\pi$
$2$	−2.75847	−1.95053	−0.975266	+	0.221035i	$0.929056\pi$
$3$	−2.11283	−1.21984	−0.609922	−	0.792461i	$-0.708799\pi$
$3$	−2.11283	−1.21984	−0.609922	+	0.792461i	$0.708799\pi$
$4$	5.60915	2.80457
$5$	3.70679	1.65773	0.828864	−	0.559450i	$-0.188988\pi$
$5$	3.70679	1.65773	0.828864	+	0.559450i	$0.188988\pi$
$6$	5.82818	2.37935
$7$	−2.88565	−1.09067	−0.545337	−	0.838217i	$-0.683598\pi$
$7$	−2.88565	−1.09067	−0.545337	+	0.838217i	$0.683598\pi$
$8$	−9.95572	−3.51988
$9$	1.46406	0.488021
$10$	−10.2251	−3.23345
$11$	1.36743	0.412296	0.206148	−	0.978521i	$-0.433907\pi$
$11$	1.36743	0.412296	0.206148	+	0.978521i	$0.433907\pi$
$12$	−11.8512	−3.42114
$13$	−2.58949	−0.718195	−0.359097	−	0.933300i	$-0.616915\pi$
$13$	−2.58949	−0.718195	−0.359097	+	0.933300i	$0.616915\pi$
$14$	7.95998	2.12739
$15$	−7.83184	−2.02217
$16$	16.2442	4.06106
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−4.03857	−0.951901
$19$	−0.139083	−0.0319078	−0.0159539	−	0.999873i	$-0.505079\pi$
$19$	−0.139083	−0.0319078	−0.0159539	+	0.999873i	$0.505079\pi$
$20$	20.7920	4.64922
$21$	6.09690	1.33045
$22$	−3.77202	−0.804197
$23$	3.49986	0.729772	0.364886	−	0.931052i	$-0.381108\pi$
$23$	3.49986	0.729772	0.364886	+	0.931052i	$0.381108\pi$
$24$	21.0348	4.29370
$25$	8.74032	1.74806
$26$	7.14302	1.40086
$27$	3.24518	0.624535
$28$	−16.1861	−3.05888
$29$	2.31083	0.429111	0.214555	−	0.976712i	$-0.431170\pi$
$29$	2.31083	0.429111	0.214555	+	0.976712i	$0.431170\pi$
$30$	21.6039	3.94431
$31$	9.69726	1.74168	0.870840	−	0.491567i	$-0.163576\pi$
$31$	9.69726	1.74168	0.870840	+	0.491567i	$0.163576\pi$
$32$	−24.8978	−4.40135
$33$	−2.88916	−0.502937
$34$	2.75847	0.473073
$35$	−10.6965	−1.80804
$36$	8.21215	1.36869
$37$	−0.0894272	−0.0147017	−0.00735087	−	0.999973i	$-0.502340\pi$
$37$	−0.0894272	−0.0147017	−0.00735087	+	0.999973i	$0.502340\pi$
$38$	0.383656	0.0622372
$39$	5.47116	0.876086
$40$	−36.9038	−5.83500
$41$	5.03695	0.786639	0.393319	−	0.919402i	$-0.371327\pi$
$41$	5.03695	0.786639	0.393319	+	0.919402i	$0.371327\pi$
$42$	−16.8181	−2.59509
$43$	6.61940	1.00945	0.504724	−	0.863281i	$-0.331594\pi$
$43$	6.61940	1.00945	0.504724	+	0.863281i	$0.331594\pi$
$44$	7.67013	1.15631
$45$	5.42698	0.809007
$46$	−9.65426	−1.42344
$47$	−7.84196	−1.14387	−0.571933	−	0.820300i	$-0.693806\pi$
$47$	−7.84196	−1.14387	−0.571933	+	0.820300i	$0.693806\pi$
$48$	−34.3214	−4.95386
$49$	1.32699	0.189570
$50$	−24.1099	−3.40965
$51$	2.11283	0.295856
$52$	−14.5248	−2.01423
$53$	−9.20590	−1.26453	−0.632264	−	0.774753i	$-0.717874\pi$
$53$	−9.20590	−1.26453	−0.632264	+	0.774753i	$0.717874\pi$
$54$	−8.95172	−1.21817
$55$	5.06879	0.683475
$56$	28.7287	3.83904
$57$	0.293859	0.0389226
$58$	−6.37436	−0.836994
$59$	10.9446	1.42486	0.712431	−	0.701742i	$-0.247594\pi$
$59$	10.9446	1.42486	0.712431	+	0.701742i	$0.247594\pi$
$60$	−43.9299	−5.67133
$61$	−13.8657	−1.77533	−0.887663	−	0.460494i	$-0.847672\pi$
$61$	−13.8657	−1.77533	−0.887663	+	0.460494i	$0.847672\pi$
$62$	−26.7496	−3.39720
$63$	−4.22478	−0.532272
$64$	36.1913	4.52391
$65$	−9.59870	−1.19057
$66$	7.96964	0.980995
$67$	11.8594	1.44886	0.724428	−	0.689351i	$-0.242104\pi$
$67$	11.8594	1.44886	0.724428	+	0.689351i	$0.242104\pi$
$68$	−5.60915	−0.680209
$69$	−7.39463	−0.890209
$70$	29.5060	3.52664
$71$	−2.63645	−0.312890	−0.156445	−	0.987687i	$-0.550003\pi$
$71$	−2.63645	−0.312890	−0.156445	+	0.987687i	$0.550003\pi$
$72$	−14.5758	−1.71778
$73$	4.76518	0.557722	0.278861	−	0.960331i	$-0.410043\pi$
$73$	4.76518	0.557722	0.278861	+	0.960331i	$0.410043\pi$
$74$	0.246682	0.0286762
$75$	−18.4668	−2.13237
$76$	−0.780137	−0.0894878
$77$	−3.94593	−0.449681
$78$	−15.0920	−1.70883
$79$	−3.15590	−0.355067	−0.177533	−	0.984115i	$-0.556812\pi$
$79$	−3.15590	−0.355067	−0.177533	+	0.984115i	$0.556812\pi$
$80$	60.2140	6.73213
$81$	−11.2487	−1.24986
$82$	−13.8943	−1.53436
$83$	−7.09567	−0.778851	−0.389425	−	0.921058i	$-0.627326\pi$
$83$	−7.09567	−0.778851	−0.389425	+	0.921058i	$0.627326\pi$
$84$	34.1984	3.73135
$85$	−3.70679	−0.402058
$86$	−18.2594	−1.96896
$87$	−4.88241	−0.523449
$88$	−13.6138	−1.45123
$89$	−15.9467	−1.69034	−0.845172	−	0.534494i	$-0.820502\pi$
$89$	−15.9467	−1.69034	−0.845172	+	0.534494i	$0.820502\pi$
$90$	−14.9702	−1.57799
$91$	7.47236	0.783316
$92$	19.6313	2.04670
$93$	−20.4887	−2.12458
$94$	21.6318	2.23115
$95$	−0.515552	−0.0528945
$96$	52.6049	5.36896
$97$	15.2637	1.54980	0.774899	−	0.632085i	$-0.217801\pi$
$97$	15.2637	1.54980	0.774899	+	0.632085i	$0.217801\pi$
$98$	−3.66046	−0.369763
$99$	2.00201	0.201209
$100$	49.0257	4.90257
$101$	−1.94491	−0.193526	−0.0967629	−	0.995307i	$-0.530849\pi$
$101$	−1.94491	−0.193526	−0.0967629	+	0.995307i	$0.530849\pi$
$102$	−5.82818	−0.577076
$103$	−7.30244	−0.719531	−0.359765	−	0.933043i	$-0.617143\pi$
$103$	−7.30244	−0.719531	−0.359765	+	0.933043i	$0.617143\pi$
$104$	25.7802	2.52796
$105$	22.6000	2.20553
$106$	25.3942	2.46650
$107$	−0.435900	−0.0421401	−0.0210700	−	0.999778i	$-0.506707\pi$
$107$	−0.435900	−0.0421401	−0.0210700	+	0.999778i	$0.506707\pi$
$108$	18.2027	1.75155
$109$	4.68306	0.448556	0.224278	−	0.974525i	$-0.427998\pi$
$109$	4.68306	0.448556	0.224278	+	0.974525i	$0.427998\pi$
$110$	−13.9821	−1.33314
$111$	0.188945	0.0179338
$112$	−46.8752	−4.42929
$113$	19.5024	1.83463	0.917317	−	0.398157i	$-0.130350\pi$
$113$	19.5024	1.83463	0.917317	+	0.398157i	$0.130350\pi$
$114$	−0.810601	−0.0759197
$115$	12.9733	1.20976
$116$	12.9618	1.20347
$117$	−3.79118	−0.350494
$118$	−30.1902	−2.77924
$119$	2.88565	0.264527
$120$	77.9716	7.11780
$121$	−9.13013	−0.830012
$122$	38.2482	3.46283
$123$	−10.6422	−0.959577
$124$	54.3934	4.88467
$125$	13.8646	1.24009
$126$	11.6539	1.03821
$127$	−4.83502	−0.429039	−0.214520	−	0.976720i	$-0.568819\pi$
$127$	−4.83502	−0.429039	−0.214520	+	0.976720i	$0.568819\pi$
$128$	−50.0369	−4.42268
$129$	−13.9857	−1.23137
$130$	26.4777	2.32225
$131$	12.8749	1.12489	0.562443	−	0.826836i	$-0.309862\pi$
$131$	12.8749	1.12489	0.562443	+	0.826836i	$0.309862\pi$
$132$	−16.2057	−1.41052
$133$	0.401345	0.0348010
$134$	−32.7138	−2.82604
$135$	12.0292	1.03531
$136$	9.95572	0.853696
$137$	0.969276	0.0828108	0.0414054	−	0.999142i	$-0.486816\pi$
$137$	0.969276	0.0828108	0.0414054	+	0.999142i	$0.486816\pi$
$138$	20.3979	1.73638
$139$	−1.75825	−0.149133	−0.0745664	−	0.997216i	$-0.523757\pi$
$139$	−1.75825	−0.149133	−0.0745664	+	0.997216i	$0.523757\pi$
$140$	−59.9983	−5.07079
$141$	16.5687	1.39534
$142$	7.27258	0.610301
$143$	−3.54095	−0.296109
$144$	23.7826	1.98188
$145$	8.56578	0.711349
$146$	−13.1446	−1.08786
$147$	−2.80371	−0.231246
$148$	−0.501610	−0.0412321
$149$	7.23175	0.592448	0.296224	−	0.955119i	$-0.404273\pi$
$149$	7.23175	0.592448	0.296224	+	0.955119i	$0.404273\pi$
$150$	50.9402	4.15925
$151$	0.854517	0.0695396	0.0347698	−	0.999395i	$-0.488930\pi$
$151$	0.854517	0.0695396	0.0347698	+	0.999395i	$0.488930\pi$
$152$	1.38467	0.112312
$153$	−1.46406	−0.118363
$154$	10.8847	0.877117
$155$	35.9457	2.88723
$156$	30.6885	2.45705
$157$	−19.8942	−1.58773	−0.793864	−	0.608095i	$-0.791934\pi$
$157$	−19.8942	−1.58773	−0.793864	+	0.608095i	$0.791934\pi$
$158$	8.70546	0.692569
$159$	19.4505	1.54253
$160$	−92.2909	−7.29624
$161$	−10.0994	−0.795944
$162$	31.0292	2.43788
$163$	−23.2619	−1.82201	−0.911007	−	0.412390i	$-0.864694\pi$
$163$	−23.2619	−1.82201	−0.911007	+	0.412390i	$0.864694\pi$
$164$	28.2530	2.20619
$165$	−10.7095	−0.833734
$166$	19.5732	1.51917
$167$	13.7585	1.06467	0.532333	−	0.846535i	$-0.321316\pi$
$167$	13.7585	1.06467	0.532333	+	0.846535i	$0.321316\pi$
$168$	−60.6990	−4.68303
$169$	−6.29455	−0.484197
$170$	10.2251	0.784227
$171$	−0.203626	−0.0155717
$172$	37.1292	2.83107
$173$	17.4157	1.32409	0.662045	−	0.749464i	$-0.269689\pi$
$173$	17.4157	1.32409	0.662045	+	0.749464i	$0.269689\pi$
$174$	13.4680	1.02100
$175$	−25.2215	−1.90657
$176$	22.2129	1.67436
$177$	−23.1240	−1.73811
$178$	43.9884	3.29707
$179$	0.478913	0.0357956	0.0178978	−	0.999840i	$-0.494303\pi$
$179$	0.478913	0.0357956	0.0178978	+	0.999840i	$0.494303\pi$
$180$	30.4407	2.26892
$181$	10.4053	0.773417	0.386709	−	0.922202i	$-0.373612\pi$
$181$	10.4053	0.773417	0.386709	+	0.922202i	$0.373612\pi$
$182$	−20.6123	−1.52788
$183$	29.2960	2.16562
$184$	−34.8437	−2.56871
$185$	−0.331488	−0.0243715
$186$	56.5174	4.14406
$187$	−1.36743	−0.0999965
$188$	−43.9867	−3.20806
$189$	−9.36445	−0.681164
$190$	1.42213	0.103172
$191$	12.9362	0.936031	0.468015	−	0.883720i	$-0.344969\pi$
$191$	12.9362	0.936031	0.468015	+	0.883720i	$0.344969\pi$
$192$	−76.4661	−5.51846
$193$	−10.8985	−0.784490	−0.392245	−	0.919861i	$-0.628301\pi$
$193$	−10.8985	−0.784490	−0.392245	+	0.919861i	$0.628301\pi$
$194$	−42.1045	−3.02293
$195$	20.2804	1.45231
$196$	7.44329	0.531663
$197$	−24.8696	−1.77188	−0.885941	−	0.463798i	$-0.846486\pi$
$197$	−24.8696	−1.77188	−0.885941	+	0.463798i	$0.846486\pi$
$198$	−5.52247	−0.392465
$199$	0.752985	0.0533777	0.0266889	−	0.999644i	$-0.491504\pi$
$199$	0.752985	0.0533777	0.0266889	+	0.999644i	$0.491504\pi$
$200$	−87.0161	−6.15297
$201$	−25.0569	−1.76738
$202$	5.36497	0.377478
$203$	−6.66826	−0.468020
$204$	11.8512	0.829749
$205$	18.6709	1.30403
$206$	20.1435	1.40347
$207$	5.12403	0.356144
$208$	−42.0643	−2.91663
$209$	−0.190186	−0.0131555
$210$	−62.3413	−4.30196
$211$	12.7672	0.878931	0.439465	−	0.898260i	$-0.355168\pi$
$211$	12.7672	0.878931	0.439465	+	0.898260i	$0.355168\pi$
$212$	−51.6373	−3.54646
$213$	5.57039	0.381677
$214$	1.20242	0.0821955
$215$	24.5367	1.67339
$216$	−32.3081	−2.19829
$217$	−27.9829	−1.89960
$218$	−12.9181	−0.874922
$219$	−10.0680	−0.680335
$220$	28.4316	1.91686
$221$	2.58949	0.174188
$222$	−0.521198	−0.0349805
$223$	−6.51652	−0.436378	−0.218189	−	0.975907i	$-0.570015\pi$
$223$	−6.51652	−0.436378	−0.218189	+	0.975907i	$0.570015\pi$
$224$	71.8463	4.80044
$225$	12.7964	0.853092
$226$	−53.7968	−3.57851
$227$	−9.15685	−0.607762	−0.303881	−	0.952710i	$-0.598282\pi$
$227$	−9.15685	−0.607762	−0.303881	+	0.952710i	$0.598282\pi$
$228$	1.64830	0.109161
$229$	−7.16979	−0.473793	−0.236897	−	0.971535i	$-0.576130\pi$
$229$	−7.16979	−0.473793	−0.236897	+	0.971535i	$0.576130\pi$
$230$	−35.7864	−2.35968
$231$	8.33710	0.548541
$232$	−23.0060	−1.51042
$233$	9.49202	0.621843	0.310921	−	0.950436i	$-0.399362\pi$
$233$	9.49202	0.621843	0.310921	+	0.950436i	$0.399362\pi$
$234$	10.4578	0.683650
$235$	−29.0685	−1.89622
$236$	61.3897	3.99613
$237$	6.66789	0.433126
$238$	−7.95998	−0.515969
$239$	−4.00137	−0.258827	−0.129414	−	0.991591i	$-0.541310\pi$
$239$	−4.00137	−0.258827	−0.129414	+	0.991591i	$0.541310\pi$
$240$	−127.222	−8.21216
$241$	−3.52362	−0.226977	−0.113488	−	0.993539i	$-0.536202\pi$
$241$	−3.52362	−0.226977	−0.113488	+	0.993539i	$0.536202\pi$
$242$	25.1852	1.61896
$243$	14.0311	0.900096
$244$	−77.7750	−4.97903
$245$	4.91888	0.314256
$246$	29.3563	1.87169
$247$	0.360154	0.0229160
$248$	−96.5432	−6.13050
$249$	14.9920	0.950077
$250$	−38.2450	−2.41883
$251$	−9.81023	−0.619216	−0.309608	−	0.950864i	$-0.600198\pi$
$251$	−9.81023	−0.619216	−0.309608	+	0.950864i	$0.600198\pi$
$252$	−23.6974	−1.49280
$253$	4.78583	0.300882
$254$	13.3373	0.836854
$255$	7.83184	0.490449
$256$	65.6426	4.10266
$257$	16.0493	1.00113	0.500564	−	0.865700i	$-0.333126\pi$
$257$	16.0493	1.00113	0.500564	+	0.865700i	$0.333126\pi$
$258$	38.5791	2.40183
$259$	0.258056	0.0160348
$260$	−53.8405	−3.33905
$261$	3.38321	0.209415
$262$	−35.5150	−2.19413
$263$	8.95838	0.552397	0.276199	−	0.961101i	$-0.410925\pi$
$263$	8.95838	0.552397	0.276199	+	0.961101i	$0.410925\pi$
$264$	28.7636	1.77028
$265$	−34.1244	−2.09624
$266$	−1.10710	−0.0678805
$267$	33.6927	2.06196
$268$	66.5211	4.06342
$269$	14.0330	0.855605	0.427802	−	0.903872i	$-0.359288\pi$
$269$	14.0330	0.855605	0.427802	+	0.903872i	$0.359288\pi$
$270$	−33.1822	−2.01940
$271$	5.43854	0.330368	0.165184	−	0.986263i	$-0.447178\pi$
$271$	5.43854	0.330368	0.165184	+	0.986263i	$0.447178\pi$
$272$	−16.2442	−0.984952
$273$	−15.7879	−0.955524
$274$	−2.67372	−0.161525
$275$	11.9518	0.720720
$276$	−41.4776	−2.49666
$277$	3.87991	0.233121	0.116561	−	0.993184i	$-0.462813\pi$
$277$	3.87991	0.233121	0.116561	+	0.993184i	$0.462813\pi$
$278$	4.85008	0.290888
$279$	14.1974	0.849977
$280$	106.492	6.36409
$281$	−6.16013	−0.367483	−0.183741	−	0.982975i	$-0.558821\pi$
$281$	−6.16013	−0.367483	−0.183741	+	0.982975i	$0.558821\pi$
$282$	−45.7044	−2.72165
$283$	−19.4910	−1.15862	−0.579311	−	0.815107i	$-0.696678\pi$
$283$	−19.4910	−1.15862	−0.579311	+	0.815107i	$0.696678\pi$
$284$	−14.7883	−0.877522
$285$	1.08928	0.0645231
$286$	9.76759	0.577570
$287$	−14.5349	−0.857967
$288$	−36.4519	−2.14795
$289$	1.00000	0.0588235
$290$	−23.6284	−1.38751
$291$	−32.2497	−1.89051
$292$	26.7286	1.56417
$293$	34.1295	1.99387	0.996934	−	0.0782533i	$-0.0249343\pi$
$293$	34.1295	1.99387	0.996934	+	0.0782533i	$0.0249343\pi$
$294$	7.73395	0.451053
$295$	40.5693	2.36203
$296$	0.890312	0.0517483
$297$	4.43756	0.257493
$298$	−19.9485	−1.15559
$299$	−9.06285	−0.524118
$300$	−103.583	−5.98038
$301$	−19.1013	−1.10098
$302$	−2.35716	−0.135639
$303$	4.10927	0.236071
$304$	−2.25930	−0.129580
$305$	−51.3974	−2.94301
$306$	4.03857	0.230870
$307$	−14.0979	−0.804608	−0.402304	−	0.915506i	$-0.631790\pi$
$307$	−14.0979	−0.804608	−0.402304	+	0.915506i	$0.631790\pi$
$308$	−22.1333	−1.26116
$309$	15.4288	0.877716
$310$	−99.1552	−5.63164
$311$	30.7174	1.74182	0.870911	−	0.491441i	$-0.163530\pi$
$311$	30.7174	1.74182	0.870911	+	0.491441i	$0.163530\pi$
$312$	−54.4693	−3.08372
$313$	26.1214	1.47647	0.738233	−	0.674545i	$-0.235660\pi$
$313$	26.1214	1.47647	0.738233	+	0.674545i	$0.235660\pi$
$314$	54.8775	3.09691
$315$	−15.6604	−0.882363
$316$	−17.7019	−0.995811
$317$	−13.9760	−0.784970	−0.392485	−	0.919758i	$-0.628384\pi$
$317$	−13.9760	−0.784970	−0.392485	+	0.919758i	$0.628384\pi$
$318$	−53.6537	−3.00875
$319$	3.15991	0.176921
$320$	134.154	7.49941
$321$	0.920984	0.0514043
$322$	27.8589	1.55251
$323$	0.139083	0.00773878
$324$	−63.0957	−3.50531
$325$	−22.6329	−1.25545
$326$	64.1673	3.55390
$327$	−9.89452	−0.547168
$328$	−50.1464	−2.76887
$329$	22.6292	1.24759
$330$	29.5418	1.62622
$331$	23.4789	1.29051	0.645257	−	0.763965i	$-0.276750\pi$
$331$	23.4789	1.29051	0.645257	+	0.763965i	$0.276750\pi$
$332$	−39.8007	−2.18434
$333$	−0.130927	−0.00717476
$334$	−37.9524	−2.07666
$335$	43.9603	2.40181
$336$	99.0395	5.40305
$337$	6.67847	0.363799	0.181900	−	0.983317i	$-0.441775\pi$
$337$	6.67847	0.363799	0.181900	+	0.983317i	$0.441775\pi$
$338$	17.3633	0.944441
$339$	−41.2054	−2.23797
$340$	−20.7920	−1.12760
$341$	13.2603	0.718088
$342$	0.561697	0.0303731
$343$	16.3703	0.883915
$344$	−65.9009	−3.55314
$345$	−27.4104	−1.47572
$346$	−48.0406	−2.58268
$347$	33.8375	1.81649	0.908247	−	0.418434i	$-0.137421\pi$
$347$	33.8375	1.81649	0.908247	+	0.418434i	$0.137421\pi$
$348$	−27.3861	−1.46805
$349$	−34.0290	−1.82153	−0.910764	−	0.412927i	$-0.864506\pi$
$349$	−34.0290	−1.82153	−0.910764	+	0.412927i	$0.864506\pi$
$350$	69.5728	3.71882
$351$	−8.40334	−0.448537
$352$	−34.0460	−1.81466
$353$	1.00000	0.0532246
$353$	1.00000	0.0532246
$354$	63.7869	3.39024
$355$	−9.77279	−0.518686
$356$	−89.4472	−4.74069
$357$	−6.09690	−0.322682
$358$	−1.32107	−0.0698205
$359$	14.8863	0.785669	0.392835	−	0.919609i	$-0.371494\pi$
$359$	14.8863	0.785669	0.392835	+	0.919609i	$0.371494\pi$
$360$	−54.0295	−2.84761
$361$	−18.9807	−0.998982
$362$	−28.7026	−1.50857
$363$	19.2904	1.01249
$364$	41.9136	2.19687
$365$	17.6635	0.924552
$366$	−80.8121	−4.22411
$367$	−15.1053	−0.788489	−0.394245	−	0.919006i	$-0.628994\pi$
$367$	−15.1053	−0.788489	−0.394245	+	0.919006i	$0.628994\pi$
$368$	56.8526	2.96365
$369$	7.37441	0.383897
$370$	0.914399	0.0475374
$371$	26.5650	1.37919
$372$	−114.924	−5.95854
$373$	−15.9246	−0.824545	−0.412272	−	0.911061i	$-0.635265\pi$
$373$	−15.9246	−0.824545	−0.412272	+	0.911061i	$0.635265\pi$
$374$	3.77202	0.195046
$375$	−29.2936	−1.51271
$376$	78.0723	4.02627
$377$	−5.98387	−0.308185
$378$	25.8315	1.32863
$379$	9.29878	0.477646	0.238823	−	0.971063i	$-0.423238\pi$
$379$	9.29878	0.477646	0.238823	+	0.971063i	$0.423238\pi$
$380$	−2.89181	−0.148347
$381$	10.2156	0.523361
$382$	−35.6841	−1.82576
$383$	28.5498	1.45883	0.729413	−	0.684074i	$-0.239793\pi$
$383$	28.5498	1.45883	0.729413	+	0.684074i	$0.239793\pi$
$384$	105.720	5.39498
$385$	−14.6268	−0.745449
$386$	30.0631	1.53017
$387$	9.69122	0.492633
$388$	85.6165	4.34652
$389$	15.1237	0.766803	0.383402	−	0.923582i	$-0.374753\pi$
$389$	15.1237	0.766803	0.383402	+	0.923582i	$0.374753\pi$
$390$	−55.9430	−2.83278
$391$	−3.49986	−0.176996
$392$	−13.2111	−0.667264
$393$	−27.2025	−1.37219
$394$	68.6019	3.45611
$395$	−11.6983	−0.588604
$396$	11.2296	0.564306
$397$	10.9955	0.551851	0.275925	−	0.961179i	$-0.411016\pi$
$397$	10.9955	0.551851	0.275925	+	0.961179i	$0.411016\pi$
$398$	−2.07709	−0.104115
$399$	−0.847975	−0.0424519
$400$	141.980	7.09899
$401$	−32.6848	−1.63220	−0.816102	−	0.577908i	$-0.803869\pi$
$401$	−32.6848	−1.63220	−0.816102	+	0.577908i	$0.803869\pi$
$402$	69.1187	3.44733
$403$	−25.1109	−1.25086
$404$	−10.9093	−0.542757
$405$	−41.6966	−2.07192
$406$	18.3942	0.912888
$407$	−0.122286	−0.00606147
$408$	−21.0348	−1.04138
$409$	−18.4985	−0.914692	−0.457346	−	0.889289i	$-0.651200\pi$
$409$	−18.4985	−0.914692	−0.457346	+	0.889289i	$0.651200\pi$
$410$	−51.5031	−2.54356
$411$	−2.04792	−0.101016
$412$	−40.9605	−2.01798
$413$	−31.5822	−1.55406
$414$	−14.1345	−0.694671
$415$	−26.3022	−1.29112
$416$	64.4725	3.16102
$417$	3.71489	0.181919
$418$	0.524623	0.0256602
$419$	−23.7805	−1.16176	−0.580878	−	0.813991i	$-0.697291\pi$
$419$	−23.7805	−1.16176	−0.580878	+	0.813991i	$0.697291\pi$
$420$	126.766	6.18557
$421$	32.9556	1.60616	0.803078	−	0.595873i	$-0.203194\pi$
$421$	32.9556	1.60616	0.803078	+	0.595873i	$0.203194\pi$
$422$	−35.2179	−1.71438
$423$	−11.4811	−0.558231
$424$	91.6513	4.45098
$425$	−8.74032	−0.423968
$426$	−15.3657	−0.744473
$427$	40.0117	1.93630
$428$	−2.44503	−0.118185
$429$	7.48143	0.361207
$430$	−67.6838	−3.26400
$431$	−19.1477	−0.922314	−0.461157	−	0.887319i	$-0.652565\pi$
$431$	−19.1477	−0.922314	−0.461157	+	0.887319i	$0.652565\pi$
$432$	52.7154	2.53627
$433$	−20.4347	−0.982031	−0.491016	−	0.871151i	$-0.663374\pi$
$433$	−20.4347	−0.982031	−0.491016	+	0.871151i	$0.663374\pi$
$434$	77.1900	3.70524
$435$	−18.0981	−0.867736
$436$	26.2680	1.25801
$437$	−0.486772	−0.0232854
$438$	27.7724	1.32701
$439$	11.1491	0.532115	0.266058	−	0.963957i	$-0.414279\pi$
$439$	11.1491	0.532115	0.266058	+	0.963957i	$0.414279\pi$
$440$	−50.4634	−2.40575
$441$	1.94280	0.0925143
$442$	−7.14302	−0.339759
$443$	25.6768	1.21994	0.609970	−	0.792424i	$-0.291181\pi$
$443$	25.6768	1.21994	0.609970	+	0.792424i	$0.291181\pi$
$444$	1.05982	0.0502968
$445$	−59.1110	−2.80213
$446$	17.9756	0.851169
$447$	−15.2795	−0.722694
$448$	−104.435	−4.93411
$449$	27.1261	1.28016	0.640080	−	0.768308i	$-0.278901\pi$
$449$	27.1261	1.28016	0.640080	+	0.768308i	$0.278901\pi$
$450$	−35.2984	−1.66398
$451$	6.88768	0.324328
$452$	109.392	5.14537
$453$	−1.80545	−0.0848276
$454$	25.2589	1.18546
$455$	27.6985	1.29853
$456$	−2.92558	−0.137003
$457$	0.0274938	0.00128611	0.000643053	−	1.00000i	$-0.499795\pi$
$457$	0.0274938	0.00128611	0.000643053		1.00000i	$0.499795\pi$
$458$	19.7777	0.924149
$459$	−3.24518	−0.151472
$460$	72.7690	3.39287
$461$	−15.8195	−0.736786	−0.368393	−	0.929670i	$-0.620092\pi$
$461$	−15.8195	−0.736786	−0.368393	+	0.929670i	$0.620092\pi$
$462$	−22.9976	−1.06995
$463$	29.0633	1.35069	0.675344	−	0.737503i	$-0.263995\pi$
$463$	29.0633	1.35069	0.675344	+	0.737503i	$0.263995\pi$
$464$	37.5377	1.74265
$465$	−75.9474	−3.52197
$466$	−26.1834	−1.21292
$467$	17.0403	0.788531	0.394266	−	0.918997i	$-0.370999\pi$
$467$	17.0403	0.788531	0.394266	+	0.918997i	$0.370999\pi$
$468$	−21.2653	−0.982987
$469$	−34.2221	−1.58023
$470$	80.1846	3.69864
$471$	42.0331	1.93678
$472$	−108.961	−5.01534
$473$	9.05158	0.416192
$474$	−18.3932	−0.844827
$475$	−1.21563	−0.0557769
$476$	16.1861	0.741886
$477$	−13.4780	−0.617116
$478$	11.0377	0.504851
$479$	10.0147	0.457584	0.228792	−	0.973475i	$-0.426523\pi$
$479$	10.0147	0.457584	0.228792	+	0.973475i	$0.426523\pi$
$480$	194.995	8.90028
$481$	0.231571	0.0105587
$482$	9.71980	0.442725
$483$	21.3383	0.970928
$484$	−51.2122	−2.32783
$485$	56.5795	2.56914
$486$	−38.7044	−1.75567
$487$	24.7972	1.12367	0.561834	−	0.827250i	$-0.310096\pi$
$487$	24.7972	1.12367	0.561834	+	0.827250i	$0.310096\pi$
$488$	138.043	6.24893
$489$	49.1486	2.22258
$490$	−13.5686	−0.612966
$491$	−9.08692	−0.410087	−0.205043	−	0.978753i	$-0.565734\pi$
$491$	−9.08692	−0.410087	−0.205043	+	0.978753i	$0.565734\pi$
$492$	−59.6938	−2.69121
$493$	−2.31083	−0.104075
$494$	−0.993472	−0.0446984
$495$	7.42103	0.333550
$496$	157.525	7.07306
$497$	7.60789	0.341261
$498$	−41.3549	−1.85316
$499$	17.8711	0.800018	0.400009	−	0.916511i	$-0.369007\pi$
$499$	17.8711	0.800018	0.400009	+	0.916511i	$0.369007\pi$
$500$	77.7685	3.47791
$501$	−29.0694	−1.29873
$502$	27.0612	1.20780
$503$	28.8979	1.28849	0.644246	−	0.764818i	$-0.277171\pi$
$503$	28.8979	1.28849	0.644246	+	0.764818i	$0.277171\pi$
$504$	42.0607	1.87353
$505$	−7.20938	−0.320813
$506$	−13.2015	−0.586880
$507$	13.2993	0.590645
$508$	−27.1204	−1.20327
$509$	−11.6792	−0.517671	−0.258836	−	0.965921i	$-0.583339\pi$
$509$	−11.6792	−0.517671	−0.258836	+	0.965921i	$0.583339\pi$
$510$	−21.6039	−0.956636
$511$	−13.7507	−0.608293
$512$	−80.9993	−3.57970
$513$	−0.451349	−0.0199275
$514$	−44.2715	−1.95273
$515$	−27.0686	−1.19279
$516$	−78.4478	−3.45347
$517$	−10.7233	−0.471612
$518$	−0.711839	−0.0312764
$519$	−36.7964	−1.61518
$520$	95.5619	4.19067
$521$	13.6093	0.596236	0.298118	−	0.954529i	$-0.403641\pi$
$521$	13.6093	0.596236	0.298118	+	0.954529i	$0.403641\pi$
$522$	−9.33247	−0.408471
$523$	2.90921	0.127211	0.0636054	−	0.997975i	$-0.479740\pi$
$523$	2.90921	0.127211	0.0636054	+	0.997975i	$0.479740\pi$
$524$	72.2173	3.15483
$525$	53.2889	2.32572
$526$	−24.7114	−1.07747
$527$	−9.69726	−0.422419
$528$	−46.9321	−2.04246
$529$	−10.7509	−0.467433
$530$	94.1310	4.08879
$531$	16.0235	0.695363
$532$	2.25120	0.0976021
$533$	−13.0431	−0.564960
$534$	−92.9401	−4.02191
$535$	−1.61579	−0.0698568
$536$	−118.069	−5.09980
$537$	−1.01186	−0.0436651
$538$	−38.7095	−1.66888
$539$	1.81457	0.0781591
$540$	67.4736	2.90360
$541$	−0.688304	−0.0295925	−0.0147962	−	0.999891i	$-0.504710\pi$
$541$	−0.688304	−0.0295925	−0.0147962	+	0.999891i	$0.504710\pi$
$542$	−15.0020	−0.644393
$543$	−21.9846	−0.943449
$544$	24.8978	1.06748
$545$	17.3591	0.743583
$546$	43.5503	1.86378
$547$	−0.713686	−0.0305150	−0.0152575	−	0.999884i	$-0.504857\pi$
$547$	−0.713686	−0.0305150	−0.0152575	+	0.999884i	$0.504857\pi$
$548$	5.43681	0.232249
$549$	−20.3003	−0.866397
$550$	−32.9686	−1.40579
$551$	−0.321398	−0.0136920
$552$	73.6188	3.13343
$553$	9.10684	0.387262
$554$	−10.7026	−0.454710
$555$	0.700379	0.0297294
$556$	−9.86229	−0.418254
$557$	−30.1350	−1.27686	−0.638431	−	0.769679i	$-0.720416\pi$
$557$	−30.1350	−1.27686	−0.638431	+	0.769679i	$0.720416\pi$
$558$	−39.1631	−1.65791
$559$	−17.1409	−0.724981
$560$	−173.757	−7.34256
$561$	2.88916	0.121980
$562$	16.9925	0.716786
$563$	−29.6742	−1.25062	−0.625308	−	0.780378i	$-0.715027\pi$
$563$	−29.6742	−1.25062	−0.625308	+	0.780378i	$0.715027\pi$
$564$	92.9365	3.91333
$565$	72.2915	3.04133
$566$	53.7654	2.25993
$567$	32.4599	1.36319
$568$	26.2478	1.10133
$569$	17.5226	0.734585	0.367293	−	0.930105i	$-0.380285\pi$
$569$	17.5226	0.734585	0.367293	+	0.930105i	$0.380285\pi$
$570$	−3.00473	−0.125854
$571$	38.3518	1.60497	0.802486	−	0.596671i	$-0.203510\pi$
$571$	38.3518	1.60497	0.802486	+	0.596671i	$0.203510\pi$
$572$	−19.8617	−0.830459
$573$	−27.3320	−1.14181
$574$	40.0940	1.67349
$575$	30.5899	1.27569
$576$	52.9863	2.20776
$577$	6.14656	0.255885	0.127942	−	0.991782i	$-0.459163\pi$
$577$	6.14656	0.255885	0.127942	+	0.991782i	$0.459163\pi$
$578$	−2.75847	−0.114737
$579$	23.0267	0.956956
$580$	48.0467	1.99503
$581$	20.4756	0.849473
$582$	88.9599	3.68750
$583$	−12.5884	−0.521360
$584$	−47.4408	−1.96311
$585$	−14.0531	−0.581024
$586$	−94.1452	−3.88910
$587$	38.0097	1.56883	0.784414	−	0.620238i	$-0.212964\pi$
$587$	38.0097	1.56883	0.784414	+	0.620238i	$0.212964\pi$
$588$	−15.7264	−0.648547
$589$	−1.34872	−0.0555732
$590$	−111.909	−4.60722
$591$	52.5452	2.16142
$592$	−1.45268	−0.0597046
$593$	−35.0097	−1.43767	−0.718837	−	0.695179i	$-0.755325\pi$
$593$	−35.0097	−1.43767	−0.718837	+	0.695179i	$0.755325\pi$
$594$	−12.2409	−0.502249
$595$	10.6965	0.438515
$596$	40.5639	1.66156
$597$	−1.59093	−0.0651125
$598$	24.9996	1.02231
$599$	6.80373	0.277993	0.138996	−	0.990293i	$-0.455612\pi$
$599$	6.80373	0.277993	0.138996	+	0.990293i	$0.455612\pi$
$600$	183.851	7.50567
$601$	12.9863	0.529724	0.264862	−	0.964286i	$-0.414674\pi$
$601$	12.9863	0.529724	0.264862	+	0.964286i	$0.414674\pi$
$602$	52.6903	2.14750
$603$	17.3629	0.707072
$604$	4.79311	0.195029
$605$	−33.8435	−1.37593
$606$	−11.3353	−0.460465
$607$	24.7611	1.00502	0.502510	−	0.864571i	$-0.332410\pi$
$607$	24.7611	1.00502	0.502510	+	0.864571i	$0.332410\pi$
$608$	3.46286	0.140437
$609$	14.0889	0.570912
$610$	141.778	5.74043
$611$	20.3066	0.821519
$612$	−8.21215	−0.331956
$613$	5.36093	0.216526	0.108263	−	0.994122i	$-0.465471\pi$
$613$	5.36093	0.216526	0.108263	+	0.994122i	$0.465471\pi$
$614$	38.8885	1.56941
$615$	−39.4485	−1.59072
$616$	39.2846	1.58282
$617$	−41.4404	−1.66833	−0.834165	−	0.551515i	$-0.814050\pi$
$617$	−41.4404	−1.66833	−0.834165	+	0.551515i	$0.814050\pi$
$618$	−42.5600	−1.71201
$619$	14.1974	0.570640	0.285320	−	0.958432i	$-0.407900\pi$
$619$	14.1974	0.570640	0.285320	+	0.958432i	$0.407900\pi$
$620$	201.625	8.09745
$621$	11.3577	0.455768
$622$	−84.7329	−3.39748
$623$	46.0166	1.84361
$624$	88.8747	3.55784
$625$	7.69157	0.307663
$626$	−72.0550	−2.87990
$627$	0.401832	0.0160476
$628$	−111.589	−4.45290
$629$	0.0894272	0.00356569
$630$	43.1987	1.72108
$631$	−12.3202	−0.490461	−0.245230	−	0.969465i	$-0.578864\pi$
$631$	−12.3202	−0.490461	−0.245230	+	0.969465i	$0.578864\pi$
$632$	31.4193	1.24979
$633$	−26.9750	−1.07216
$634$	38.5523	1.53111
$635$	−17.9224	−0.711230
$636$	109.101	4.32613
$637$	−3.43623	−0.136148
$638$	−8.71650	−0.345090
$639$	−3.85994	−0.152697
$640$	−185.476	−7.33160
$641$	9.85637	0.389303	0.194652	−	0.980872i	$-0.437642\pi$
$641$	9.85637	0.389303	0.194652	+	0.980872i	$0.437642\pi$
$642$	−2.54051	−0.100266
$643$	−22.7611	−0.897610	−0.448805	−	0.893630i	$-0.648150\pi$
$643$	−22.7611	−0.897610	−0.448805	+	0.893630i	$0.648150\pi$
$644$	−56.6490	−2.23228
$645$	−51.8420	−2.04128
$646$	−0.383656	−0.0150947
$647$	14.5428	0.571735	0.285868	−	0.958269i	$-0.407718\pi$
$647$	14.5428	0.571735	0.285868	+	0.958269i	$0.407718\pi$
$648$	111.989	4.39934
$649$	14.9659	0.587465
$650$	62.4323	2.44879
$651$	59.1232	2.31722
$652$	−130.480	−5.10997
$653$	18.3693	0.718848	0.359424	−	0.933174i	$-0.382973\pi$
$653$	18.3693	0.718848	0.359424	+	0.933174i	$0.382973\pi$
$654$	27.2937	1.06727
$655$	47.7246	1.86476
$656$	81.8214	3.19459
$657$	6.97653	0.272180
$658$	−62.4218	−2.43346
$659$	−40.9389	−1.59475	−0.797376	−	0.603482i	$-0.793779\pi$
$659$	−40.9389	−1.59475	−0.797376	+	0.603482i	$0.793779\pi$
$660$	−60.0712	−2.33827
$661$	12.3476	0.480265	0.240132	−	0.970740i	$-0.422809\pi$
$661$	12.3476	0.480265	0.240132	+	0.970740i	$0.422809\pi$
$662$	−64.7657	−2.51719
$663$	−5.47116	−0.212482
$664$	70.6425	2.74146
$665$	1.48770	0.0576907
$666$	0.361158	0.0139946
$667$	8.08760	0.313153
$668$	77.1735	2.98593
$669$	13.7683	0.532314
$670$	−121.263	−4.68481
$671$	−18.9605	−0.731960
$672$	−151.799	−5.85579
$673$	14.7844	0.569896	0.284948	−	0.958543i	$-0.408024\pi$
$673$	14.7844	0.569896	0.284948	+	0.958543i	$0.408024\pi$
$674$	−18.4223	−0.709602
$675$	28.3639	1.09173
$676$	−35.3071	−1.35796
$677$	31.6718	1.21725	0.608623	−	0.793459i	$-0.291722\pi$
$677$	31.6718	1.21725	0.608623	+	0.793459i	$0.291722\pi$
$678$	113.664	4.36523
$679$	−44.0458	−1.69032
$680$	36.9038	1.41520
$681$	19.3469	0.741375
$682$	−36.5782	−1.40065
$683$	−24.4506	−0.935575	−0.467787	−	0.883841i	$-0.654949\pi$
$683$	−24.4506	−0.935575	−0.467787	+	0.883841i	$0.654949\pi$
$684$	−1.14217	−0.0436720
$685$	3.59291	0.137278
$686$	−45.1570	−1.72410
$687$	15.1486	0.577954
$688$	107.527	4.09943
$689$	23.8386	0.908177
$690$	75.6106	2.87845
$691$	28.7370	1.09321	0.546604	−	0.837391i	$-0.315920\pi$
$691$	28.7370	1.09321	0.546604	+	0.837391i	$0.315920\pi$
$692$	97.6871	3.71351
$693$	−5.77710	−0.219454
$694$	−93.3398	−3.54313
$695$	−6.51747	−0.247222
$696$	48.6078	1.84248
$697$	−5.03695	−0.190788
$698$	93.8678	3.55295
$699$	−20.0551	−0.758552
$700$	−141.471	−5.34711
$701$	−6.62392	−0.250182	−0.125091	−	0.992145i	$-0.539922\pi$
$701$	−6.62392	−0.250182	−0.125091	+	0.992145i	$0.539922\pi$
$702$	23.1804	0.874886
$703$	0.0124378	0.000469100 0
$704$	49.4891	1.86519
$705$	61.4169	2.31309
$706$	−2.75847	−0.103816
$707$	5.61233	0.211074
$708$	−129.706	−4.87466
$709$	−35.9475	−1.35004	−0.675019	−	0.737801i	$-0.735864\pi$
$709$	−35.9475	−1.35004	−0.675019	+	0.737801i	$0.735864\pi$
$710$	26.9579	1.01171
$711$	−4.62044	−0.173280
$712$	158.761	5.94981
$713$	33.9391	1.27103
$714$	16.8181	0.629402
$715$	−13.1256	−0.490868
$716$	2.68629	0.100391
$717$	8.45424	0.315729
$718$	−41.0634	−1.53247
$719$	−13.2892	−0.495604	−0.247802	−	0.968811i	$-0.579708\pi$
$719$	−13.2892	−0.495604	−0.247802	+	0.968811i	$0.579708\pi$
$720$	88.1572	3.28542
$721$	21.0723	0.784774
$722$	52.3575	1.94855
$723$	7.44483	0.276876
$724$	58.3647	2.16911
$725$	20.1974	0.750113
$726$	−53.2121	−1.97489
$727$	−37.6736	−1.39724	−0.698618	−	0.715495i	$-0.746201\pi$
$727$	−37.6736	−1.39724	−0.698618	+	0.715495i	$0.746201\pi$
$728$	−74.3927	−2.75718
$729$	4.10072	0.151879
$730$	−48.7243	−1.80337
$731$	−6.61940	−0.244827
$732$	164.326	6.07365
$733$	6.91096	0.255262	0.127631	−	0.991822i	$-0.459263\pi$
$733$	6.91096	0.255262	0.127631	+	0.991822i	$0.459263\pi$
$734$	41.6674	1.53797
$735$	−10.3928	−0.383343
$736$	−87.1388	−3.21198
$737$	16.2169	0.597358
$738$	−20.3421	−0.748802
$739$	−12.2805	−0.451744	−0.225872	−	0.974157i	$-0.572523\pi$
$739$	−12.2805	−0.451744	−0.225872	+	0.974157i	$0.572523\pi$
$740$	−1.85937	−0.0683516
$741$	−0.760945	−0.0279540
$742$	−73.2788	−2.69015
$743$	48.9046	1.79413	0.897067	−	0.441894i	$-0.145693\pi$
$743$	48.9046	1.79413	0.897067	+	0.441894i	$0.145693\pi$
$744$	203.980	7.47826
$745$	26.8066	0.982118
$746$	43.9275	1.60830
$747$	−10.3885	−0.380096
$748$	−7.67013	−0.280448
$749$	1.25786	0.0459611
$750$	80.8054	2.95059
$751$	−15.5899	−0.568882	−0.284441	−	0.958694i	$-0.591808\pi$
$751$	−15.5899	−0.568882	−0.284441	+	0.958694i	$0.591808\pi$
$752$	−127.387	−4.64531
$753$	20.7274	0.755348
$754$	16.5063	0.601125
$755$	3.16752	0.115278
$756$	−52.5266	−1.91037
$757$	51.9451	1.88798	0.943989	−	0.329977i	$-0.107041\pi$
$757$	51.9451	1.88798	0.943989	+	0.329977i	$0.107041\pi$
$758$	−25.6504	−0.931664
$759$	−10.1117	−0.367030
$760$	5.13269	0.186182
$761$	−24.5359	−0.889425	−0.444713	−	0.895673i	$-0.646694\pi$
$761$	−24.5359	−0.889425	−0.444713	+	0.895673i	$0.646694\pi$
$762$	−28.1794	−1.02083
$763$	−13.5137	−0.489228
$764$	72.5611	2.62517
$765$	−5.42698	−0.196213
$766$	−78.7537	−2.84549
$767$	−28.3408	−1.02333
$768$	−138.692	−5.00461
$769$	−3.62266	−0.130636	−0.0653182	−	0.997864i	$-0.520806\pi$
$769$	−3.62266	−0.130636	−0.0653182	+	0.997864i	$0.520806\pi$
$770$	40.3475	1.45402
$771$	−33.9095	−1.22122
$772$	−61.1312	−2.20016
$773$	42.7412	1.53730	0.768648	−	0.639672i	$-0.220930\pi$
$773$	42.7412	1.53730	0.768648	+	0.639672i	$0.220930\pi$
$774$	−26.7329	−0.960895
$775$	84.7571	3.04457
$776$	−151.961	−5.45510
$777$	−0.545229	−0.0195600
$778$	−41.7183	−1.49567
$779$	−0.700554	−0.0250999
$780$	113.756	4.07312
$781$	−3.60517	−0.129003
$782$	9.65426	0.345236
$783$	7.49906	0.267995
$784$	21.5560	0.769856
$785$	−73.7436	−2.63202
$786$	75.0373	2.67649
$787$	25.7756	0.918802	0.459401	−	0.888229i	$-0.348064\pi$
$787$	25.7756	0.918802	0.459401	+	0.888229i	$0.348064\pi$
$788$	−139.497	−4.96937
$789$	−18.9276	−0.673839
$790$	32.2693	1.14809
$791$	−56.2772	−2.00099
$792$	−19.9314	−0.708232
$793$	35.9052	1.27503
$794$	−30.3309	−1.07640
$795$	72.0991	2.55709
$796$	4.22360	0.149702
$797$	35.2718	1.24939	0.624696	−	0.780868i	$-0.285223\pi$
$797$	35.2718	1.24939	0.624696	+	0.780868i	$0.285223\pi$
$798$	2.33911	0.0828037
$799$	7.84196	0.277428
$800$	−217.615	−7.69383
$801$	−23.3470	−0.824924
$802$	90.1601	3.18366
$803$	6.51606	0.229947
$804$	−140.548	−4.95674
$805$	−37.4364	−1.31946
$806$	69.2677	2.43985
$807$	−29.6493	−1.04370
$808$	19.3630	0.681187
$809$	−22.4503	−0.789312	−0.394656	−	0.918829i	$-0.629136\pi$
$809$	−22.4503	−0.789312	−0.394656	+	0.918829i	$0.629136\pi$
$810$	115.019	4.04135
$811$	18.0261	0.632982	0.316491	−	0.948596i	$-0.397495\pi$
$811$	18.0261	0.632982	0.316491	+	0.948596i	$0.397495\pi$
$812$	−37.4033	−1.31260
$813$	−11.4907	−0.402997
$814$	0.337321	0.0118231
$815$	−86.2272	−3.02041
$816$	34.3214	1.20149
$817$	−0.920646	−0.0322093
$818$	51.0275	1.78414
$819$	10.9400	0.382275
$820$	104.728	3.65726
$821$	11.5284	0.402345	0.201172	−	0.979556i	$-0.435525\pi$
$821$	11.5284	0.402345	0.201172	+	0.979556i	$0.435525\pi$
$822$	5.64912	0.197036
$823$	38.8748	1.35509	0.677546	−	0.735481i	$-0.263044\pi$
$823$	38.8748	1.35509	0.677546	+	0.735481i	$0.263044\pi$
$824$	72.7010	2.53266
$825$	−25.2521	−0.879167
$826$	87.1186	3.03124
$827$	16.0812	0.559197	0.279598	−	0.960117i	$-0.409799\pi$
$827$	16.0812	0.559197	0.279598	+	0.960117i	$0.409799\pi$
$828$	28.7414	0.998833
$829$	25.7739	0.895166	0.447583	−	0.894242i	$-0.352285\pi$
$829$	25.7739	0.895166	0.447583	+	0.894242i	$0.352285\pi$
$830$	72.5537	2.51838
$831$	−8.19760	−0.284372
$832$	−93.7168	−3.24905
$833$	−1.32699	−0.0459775
$834$	−10.2474	−0.354839
$835$	51.0000	1.76493
$836$	−1.06678	−0.0368955
$837$	31.4693	1.08774
$838$	65.5979	2.26604
$839$	14.2093	0.490559	0.245280	−	0.969452i	$-0.421120\pi$
$839$	14.2093	0.490559	0.245280	+	0.969452i	$0.421120\pi$
$840$	−224.999	−7.76320
$841$	−23.6600	−0.815864
$842$	−90.9069	−3.13286
$843$	13.0153	0.448272
$844$	71.6131	2.46503
$845$	−23.3326	−0.802666
$846$	31.6703	1.08885
$847$	26.3464	0.905272
$848$	−149.543	−5.13532
$849$	41.1813	1.41334
$850$	24.1099	0.826962
$851$	−0.312983	−0.0107289
$852$	31.2451	1.07044
$853$	15.5110	0.531086	0.265543	−	0.964099i	$-0.414449\pi$
$853$	15.5110	0.531086	0.265543	+	0.964099i	$0.414449\pi$
$854$	−110.371	−3.77682
$855$	−0.754801	−0.0258136
$856$	4.33970	0.148328
$857$	55.1170	1.88276	0.941380	−	0.337348i	$-0.109530\pi$
$857$	55.1170	1.88276	0.941380	+	0.337348i	$0.109530\pi$
$858$	−20.6373	−0.704545
$859$	−20.2061	−0.689424	−0.344712	−	0.938708i	$-0.612023\pi$
$859$	−20.2061	−0.689424	−0.344712	+	0.938708i	$0.612023\pi$
$860$	137.630	4.69315
$861$	30.7098	1.04659
$862$	52.8184	1.79900
$863$	37.4852	1.27601	0.638005	−	0.770032i	$-0.279760\pi$
$863$	37.4852	1.27601	0.638005	+	0.770032i	$0.279760\pi$
$864$	−80.7977	−2.74879
$865$	64.5563	2.19498
$866$	56.3686	1.91548
$867$	−2.11283	−0.0717556
$868$	−156.960	−5.32758
$869$	−4.31548	−0.146393
$870$	49.9229	1.69255
$871$	−30.7098	−1.04056
$872$	−46.6232	−1.57886
$873$	22.3471	0.756334
$874$	1.34274	0.0454190
$875$	−40.0084	−1.35253
$876$	−56.4731	−1.90805
$877$	−51.3933	−1.73543	−0.867715	−	0.497062i	$-0.834412\pi$
$877$	−51.3933	−1.73543	−0.867715	+	0.497062i	$0.834412\pi$
$878$	−30.7543	−1.03791
$879$	−72.1100	−2.43221
$880$	82.3386	2.77563
$881$	27.1065	0.913240	0.456620	−	0.889662i	$-0.349060\pi$
$881$	27.1065	0.913240	0.456620	+	0.889662i	$0.349060\pi$
$882$	−5.35915	−0.180452
$883$	5.20090	0.175024	0.0875121	−	0.996163i	$-0.472108\pi$
$883$	5.20090	0.175024	0.0875121	+	0.996163i	$0.472108\pi$
$884$	14.5248	0.488522
$885$	−85.7161	−2.88131
$886$	−70.8286	−2.37953
$887$	−32.2930	−1.08429	−0.542147	−	0.840284i	$-0.682388\pi$
$887$	−32.2930	−1.08429	−0.542147	+	0.840284i	$0.682388\pi$
$888$	−1.88108	−0.0631249
$889$	13.9522	0.467942
$890$	163.056	5.46565
$891$	−15.3818	−0.515311
$892$	−36.5521	−1.22385
$893$	1.09068	0.0364983
$894$	42.1479	1.40964
$895$	1.77523	0.0593394
$896$	144.389	4.82370
$897$	19.1483	0.639343
$898$	−74.8265	−2.49699
$899$	22.4088	0.747374
$900$	71.7768	2.39256
$901$	9.20590	0.306693
$902$	−18.9995	−0.632613
$903$	40.3578	1.34302
$904$	−194.161	−6.45769
$905$	38.5702	1.28212
$906$	4.98028	0.165459
$907$	−0.374397	−0.0124317	−0.00621583	−	0.999981i	$-0.501979\pi$
$907$	−0.374397	−0.0124317	−0.00621583	+	0.999981i	$0.501979\pi$
$908$	−51.3621	−1.70451
$909$	−2.84747	−0.0944447
$910$	−76.4054	−2.53282
$911$	11.2448	0.372557	0.186278	−	0.982497i	$-0.440357\pi$
$911$	11.2448	0.372557	0.186278	+	0.982497i	$0.440357\pi$
$912$	4.77352	0.158067
$913$	−9.70284	−0.321117
$914$	−0.0758408	−0.00250859
$915$	108.594	3.59001
$916$	−40.2164	−1.32879
$917$	−37.1525	−1.22688
$918$	8.95172	0.295451
$919$	−43.5071	−1.43517	−0.717583	−	0.696473i	$-0.754752\pi$
$919$	−43.5071	−1.43517	−0.717583	+	0.696473i	$0.754752\pi$
$920$	−129.158	−4.25822
$921$	29.7864	0.981497
$922$	43.6375	1.43712
$923$	6.82707	0.224716
$924$	46.7640	1.53842
$925$	−0.781622	−0.0256996
$926$	−80.1703	−2.63456
$927$	−10.6912	−0.351146
$928$	−57.5346	−1.88867
$929$	20.9606	0.687696	0.343848	−	0.939025i	$-0.388270\pi$
$929$	20.9606	0.687696	0.343848	+	0.939025i	$0.388270\pi$
$930$	209.498	6.86972
$931$	−0.184562	−0.00604877
$932$	53.2421	1.74400
$933$	−64.9007	−2.12475
$934$	−47.0051	−1.53805
$935$	−5.06879	−0.165767
$936$	37.7439	1.23370
$937$	−31.1958	−1.01912	−0.509561	−	0.860434i	$-0.670192\pi$
$937$	−31.1958	−1.01912	−0.509561	+	0.860434i	$0.670192\pi$
$938$	94.4006	3.08229
$939$	−55.1901	−1.80106
$940$	−163.050	−5.31809
$941$	40.8800	1.33265	0.666324	−	0.745662i	$-0.267867\pi$
$941$	40.8800	1.33265	0.666324	+	0.745662i	$0.267867\pi$
$942$	−115.947	−3.77776
$943$	17.6286	0.574067
$944$	177.786	5.78645
$945$	−34.7121	−1.12918
$946$	−24.9685	−0.811795
$947$	−43.1825	−1.40324	−0.701621	−	0.712551i	$-0.747540\pi$
$947$	−43.1825	−1.40324	−0.701621	+	0.712551i	$0.747540\pi$
$948$	37.4012	1.21473
$949$	−12.3394	−0.400553
$950$	3.35328	0.108795
$951$	29.5289	0.957541
$952$	−28.7287	−0.931104
$953$	−49.7169	−1.61049	−0.805244	−	0.592943i	$-0.797966\pi$
$953$	−49.7169	−1.61049	−0.805244	+	0.592943i	$0.797966\pi$
$954$	37.1787	1.20371
$955$	47.9518	1.55168
$956$	−22.4443	−0.725900
$957$	−6.67636	−0.215816
$958$	−27.6252	−0.892531
$959$	−2.79699	−0.0903197
$960$	−283.444	−9.14812
$961$	63.0369	2.03345
$962$	−0.638780	−0.0205951
$963$	−0.638186	−0.0205652
$964$	−19.7645	−0.636572
$965$	−40.3984	−1.30047
$966$	−58.8611	−1.89383
$967$	19.2560	0.619232	0.309616	−	0.950862i	$-0.399800\pi$
$967$	19.2560	0.619232	0.309616	+	0.950862i	$0.399800\pi$
$968$	90.8970	2.92154
$969$	−0.293859	−0.00944012
$970$	−156.073	−5.01120
$971$	−33.8964	−1.08779	−0.543893	−	0.839155i	$-0.683050\pi$
$971$	−33.8964	−1.08779	−0.543893	+	0.839155i	$0.683050\pi$
$972$	78.7026	2.52439
$973$	5.07370	0.162655
$974$	−68.4023	−2.19175
$975$	47.8196	1.53145
$976$	−225.238	−7.20970
$977$	−27.9640	−0.894648	−0.447324	−	0.894372i	$-0.647623\pi$
$977$	−27.9640	−0.894648	−0.447324	+	0.894372i	$0.647623\pi$
$978$	−135.575	−4.33520
$979$	−21.8060	−0.696922
$980$	27.5907	0.881354
$981$	6.85630	0.218905
$982$	25.0660	0.799887
$983$	−17.6658	−0.563453	−0.281727	−	0.959495i	$-0.590907\pi$
$983$	−17.6658	−0.563453	−0.281727	+	0.959495i	$0.590907\pi$
$984$	105.951	3.37760
$985$	−92.1863	−2.93730
$986$	6.37436	0.203001
$987$	−47.8116	−1.52186
$988$	2.02015	0.0642697
$989$	23.1670	0.736668
$990$	−20.4707	−0.650601
$991$	−39.9812	−1.27004	−0.635022	−	0.772494i	$-0.719009\pi$
$991$	−39.9812	−1.27004	−0.635022	+	0.772494i	$0.719009\pi$
$992$	−241.440	−7.66573
$993$	−49.6069	−1.57423
$994$	−20.9861	−0.665640
$995$	2.79116	0.0884857
$996$	84.0921	2.66456
$997$	32.2634	1.02179	0.510897	−	0.859642i	$-0.329313\pi$
$997$	32.2634	1.02179	0.510897	+	0.859642i	$0.329313\pi$
$998$	−49.2967	−1.56046
$999$	−0.290207	−0.00918174

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6001.2.a.c.1.2	✓	121

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6001.2.a.c.1.2	✓	121	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:	\( N \)	\(=\)	\( 6001 = 17 \cdot 353 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.75847 q^{2} -2.11283 q^{3} +5.60915 q^{4} +3.70679 q^{5} +5.82818 q^{6} -2.88565 q^{7} -9.95572 q^{8} +1.46406 q^{9} +O(q^{10})\)	\(q-2.75847 q^{2} -2.11283 q^{3} +5.60915 q^{4} +3.70679 q^{5} +5.82818 q^{6} -2.88565 q^{7} -9.95572 q^{8} +1.46406 q^{9} -10.2251 q^{10} +1.36743 q^{11} -11.8512 q^{12} -2.58949 q^{13} +7.95998 q^{14} -7.83184 q^{15} +16.2442 q^{16} -1.00000 q^{17} -4.03857 q^{18} -0.139083 q^{19} +20.7920 q^{20} +6.09690 q^{21} -3.77202 q^{22} +3.49986 q^{23} +21.0348 q^{24} +8.74032 q^{25} +7.14302 q^{26} +3.24518 q^{27} -16.1861 q^{28} +2.31083 q^{29} +21.6039 q^{30} +9.69726 q^{31} -24.8978 q^{32} -2.88916 q^{33} +2.75847 q^{34} -10.6965 q^{35} +8.21215 q^{36} -0.0894272 q^{37} +0.383656 q^{38} +5.47116 q^{39} -36.9038 q^{40} +5.03695 q^{41} -16.8181 q^{42} +6.61940 q^{43} +7.67013 q^{44} +5.42698 q^{45} -9.65426 q^{46} -7.84196 q^{47} -34.3214 q^{48} +1.32699 q^{49} -24.1099 q^{50} +2.11283 q^{51} -14.5248 q^{52} -9.20590 q^{53} -8.95172 q^{54} +5.06879 q^{55} +28.7287 q^{56} +0.293859 q^{57} -6.37436 q^{58} +10.9446 q^{59} -43.9299 q^{60} -13.8657 q^{61} -26.7496 q^{62} -4.22478 q^{63} +36.1913 q^{64} -9.59870 q^{65} +7.96964 q^{66} +11.8594 q^{67} -5.60915 q^{68} -7.39463 q^{69} +29.5060 q^{70} -2.63645 q^{71} -14.5758 q^{72} +4.76518 q^{73} +0.246682 q^{74} -18.4668 q^{75} -0.780137 q^{76} -3.94593 q^{77} -15.0920 q^{78} -3.15590 q^{79} +60.2140 q^{80} -11.2487 q^{81} -13.8943 q^{82} -7.09567 q^{83} +34.1984 q^{84} -3.70679 q^{85} -18.2594 q^{86} -4.88241 q^{87} -13.6138 q^{88} -15.9467 q^{89} -14.9702 q^{90} +7.47236 q^{91} +19.6313 q^{92} -20.4887 q^{93} +21.6318 q^{94} -0.515552 q^{95} +52.6049 q^{96} +15.2637 q^{97} -3.66046 q^{98} +2.00201 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 121 q + 9 q^{2} + 13 q^{3} + 127 q^{4} + 21 q^{5} + 19 q^{6} - 13 q^{7} + 24 q^{8} + 134 q^{9}+O(q^{10}) \) 121 * q + 9 * q^2 + 13 * q^3 + 127 * q^4 + 21 * q^5 + 19 * q^6 - 13 * q^7 + 24 * q^8 + 134 * q^9	\( 121 q + 9 q^{2} + 13 q^{3} + 127 q^{4} + 21 q^{5} + 19 q^{6} - 13 q^{7} + 24 q^{8} + 134 q^{9} - q^{10} + 40 q^{11} + 41 q^{12} + 14 q^{13} + 32 q^{14} + 49 q^{15} + 135 q^{16} - 121 q^{17} + 28 q^{18} + 34 q^{19} + 64 q^{20} + 34 q^{21} - 18 q^{22} + 37 q^{23} + 54 q^{24} + 128 q^{25} + 91 q^{26} + 55 q^{27} - 28 q^{28} + 45 q^{29} + 30 q^{30} + 67 q^{31} + 47 q^{32} + 40 q^{33} - 9 q^{34} + 59 q^{35} + 138 q^{36} - 16 q^{37} + 30 q^{38} + 37 q^{39} + 14 q^{40} + 89 q^{41} + 33 q^{42} + 16 q^{43} + 90 q^{44} + 83 q^{45} - 9 q^{46} + 135 q^{47} + 96 q^{48} + 128 q^{49} + 71 q^{50} - 13 q^{51} + 47 q^{52} + 52 q^{53} + 90 q^{54} + 93 q^{55} + 69 q^{56} - 4 q^{57} + 5 q^{58} + 170 q^{59} + 78 q^{60} - 2 q^{61} + 46 q^{62} - 10 q^{63} + 182 q^{64} + 50 q^{65} + 68 q^{66} + 46 q^{67} - 127 q^{68} + 97 q^{69} + 46 q^{70} + 191 q^{71} + 57 q^{72} - 12 q^{73} + 68 q^{74} + 86 q^{75} + 108 q^{76} + 62 q^{77} - 10 q^{78} + 130 q^{80} + 149 q^{81} + 14 q^{82} + 83 q^{83} + 126 q^{84} - 21 q^{85} + 132 q^{86} + 50 q^{87} - 42 q^{88} + 144 q^{89} + 9 q^{90} + 13 q^{91} + 50 q^{92} + 43 q^{93} + 41 q^{94} + 82 q^{95} + 110 q^{96} - 3 q^{97} + 36 q^{98} + 89 q^{99}+O(q^{100}) \) 121 * q + 9 * q^2 + 13 * q^3 + 127 * q^4 + 21 * q^5 + 19 * q^6 - 13 * q^7 + 24 * q^8 + 134 * q^9 - q^10 + 40 * q^11 + 41 * q^12 + 14 * q^13 + 32 * q^14 + 49 * q^15 + 135 * q^16 - 121 * q^17 + 28 * q^18 + 34 * q^19 + 64 * q^20 + 34 * q^21 - 18 * q^22 + 37 * q^23 + 54 * q^24 + 128 * q^25 + 91 * q^26 + 55 * q^27 - 28 * q^28 + 45 * q^29 + 30 * q^30 + 67 * q^31 + 47 * q^32 + 40 * q^33 - 9 * q^34 + 59 * q^35 + 138 * q^36 - 16 * q^37 + 30 * q^38 + 37 * q^39 + 14 * q^40 + 89 * q^41 + 33 * q^42 + 16 * q^43 + 90 * q^44 + 83 * q^45 - 9 * q^46 + 135 * q^47 + 96 * q^48 + 128 * q^49 + 71 * q^50 - 13 * q^51 + 47 * q^52 + 52 * q^53 + 90 * q^54 + 93 * q^55 + 69 * q^56 - 4 * q^57 + 5 * q^58 + 170 * q^59 + 78 * q^60 - 2 * q^61 + 46 * q^62 - 10 * q^63 + 182 * q^64 + 50 * q^65 + 68 * q^66 + 46 * q^67 - 127 * q^68 + 97 * q^69 + 46 * q^70 + 191 * q^71 + 57 * q^72 - 12 * q^73 + 68 * q^74 + 86 * q^75 + 108 * q^76 + 62 * q^77 - 10 * q^78 + 130 * q^80 + 149 * q^81 + 14 * q^82 + 83 * q^83 + 126 * q^84 - 21 * q^85 + 132 * q^86 + 50 * q^87 - 42 * q^88 + 144 * q^89 + 9 * q^90 + 13 * q^91 + 50 * q^92 + 43 * q^93 + 41 * q^94 + 82 * q^95 + 110 * q^96 - 3 * q^97 + 36 * q^98 + 89 * q^99

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