LMFDB - Embedded newform 501.4.a.b.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [501,4,Mod(1,501)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(501, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("501.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 501 = 3 \cdot 167 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	501.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:	$29.5599569129$
Analytic rank:	$1$
Dimension:	$19$
Coefficient field:	$\mathbb{Q}[x]/(x^{19} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{19} - x^{18} - 105 x^{17} + 101 x^{16} + 4534 x^{15} - 4163 x^{14} - 103845 x^{13} + 89794 x^{12} + \cdots - 362016 $ x^19 - x^18 - 105x^17 + 101x^16 + 4534x^15 - 4163x^14 - 103845x^13 + 89794x^12 + 1356761x^11 - 1079599x^10 - 10105015x^9 + 7121073x^8 + 40212888x^7 - 23631389x^6 - 71822499x^5 + 31594800x^4 + 33681568x^3 + 488616x^2 - 2731104*x - 362016
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$1.13862$ of defining polynomial
Character	$\chi$	$=$	501.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.13862 q^{2} -3.00000 q^{3} -6.70355 q^{4} -7.78898 q^{5} -3.41585 q^{6} +30.6595 q^{7} -16.7417 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+1.13862 q^{2} -3.00000 q^{3} -6.70355 q^{4} -7.78898 q^{5} -3.41585 q^{6} +30.6595 q^{7} -16.7417 q^{8} +9.00000 q^{9} -8.86867 q^{10} -31.3983 q^{11} +20.1107 q^{12} +53.7510 q^{13} +34.9094 q^{14} +23.3670 q^{15} +34.5660 q^{16} +34.0219 q^{17} +10.2475 q^{18} -136.577 q^{19} +52.2139 q^{20} -91.9785 q^{21} -35.7506 q^{22} +192.660 q^{23} +50.2251 q^{24} -64.3317 q^{25} +61.2018 q^{26} -27.0000 q^{27} -205.528 q^{28} +198.833 q^{29} +26.6060 q^{30} -297.918 q^{31} +173.291 q^{32} +94.1948 q^{33} +38.7380 q^{34} -238.806 q^{35} -60.3320 q^{36} -207.325 q^{37} -155.509 q^{38} -161.253 q^{39} +130.401 q^{40} -162.111 q^{41} -104.728 q^{42} -37.7473 q^{43} +210.480 q^{44} -70.1009 q^{45} +219.365 q^{46} -474.460 q^{47} -103.698 q^{48} +597.006 q^{49} -73.2492 q^{50} -102.066 q^{51} -360.323 q^{52} -58.6290 q^{53} -30.7426 q^{54} +244.561 q^{55} -513.293 q^{56} +409.731 q^{57} +226.395 q^{58} -466.502 q^{59} -156.642 q^{60} -842.621 q^{61} -339.214 q^{62} +275.936 q^{63} -79.2161 q^{64} -418.666 q^{65} +107.252 q^{66} -858.756 q^{67} -228.068 q^{68} -577.979 q^{69} -271.909 q^{70} +753.392 q^{71} -150.675 q^{72} -624.100 q^{73} -236.063 q^{74} +192.995 q^{75} +915.550 q^{76} -962.656 q^{77} -183.605 q^{78} -445.525 q^{79} -269.234 q^{80} +81.0000 q^{81} -184.582 q^{82} -789.023 q^{83} +616.583 q^{84} -264.996 q^{85} -42.9797 q^{86} -596.500 q^{87} +525.661 q^{88} +1164.54 q^{89} -79.8180 q^{90} +1647.98 q^{91} -1291.50 q^{92} +893.753 q^{93} -540.228 q^{94} +1063.80 q^{95} -519.873 q^{96} -24.5196 q^{97} +679.761 q^{98} -282.585 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q + q^{2} - 57 q^{3} + 59 q^{4} + 12 q^{5} - 3 q^{6} - 28 q^{7} - 3 q^{8} + 171 q^{9}+O(q^{10}) $ 19 * q + q^2 - 57 * q^3 + 59 * q^4 + 12 * q^5 - 3 * q^6 - 28 * q^7 - 3 * q^8 + 171 * q^9	\( 19 q + q^{2} - 57 q^{3} + 59 q^{4} + 12 q^{5} - 3 q^{6} - 28 q^{7} - 3 q^{8} + 171 q^{9} - 69 q^{10} - 120 q^{11} - 177 q^{12} - 92 q^{13} - 69 q^{14} - 36 q^{15} + 83 q^{16} + 54 q^{17} + 9 q^{18} - 400 q^{19} - 93 q^{20} + 84 q^{21} - 273 q^{22} + 114 q^{23} + 9 q^{24} + 171 q^{25} + q^{26} - 513 q^{27} - 521 q^{28} + 72 q^{29} + 207 q^{30} - 712 q^{31} + 42 q^{32} + 360 q^{33} - 468 q^{34} - 306 q^{35} + 531 q^{36} - 448 q^{37} + 50 q^{38} + 276 q^{39} - 1030 q^{40} - 310 q^{41} + 207 q^{42} - 852 q^{43} - 757 q^{44} + 108 q^{45} - 2187 q^{46} - 1244 q^{47} - 249 q^{48} + 47 q^{49} - 1670 q^{50} - 162 q^{51} - 2548 q^{52} + 58 q^{53} - 27 q^{54} - 2190 q^{55} - 2541 q^{56} + 1200 q^{57} - 3481 q^{58} - 2736 q^{59} + 279 q^{60} - 2922 q^{61} + 486 q^{62} - 252 q^{63} - 3677 q^{64} - 380 q^{65} + 819 q^{66} - 2658 q^{67} - 1558 q^{68} - 342 q^{69} - 4887 q^{70} - 636 q^{71} - 27 q^{72} - 2304 q^{73} - 3137 q^{74} - 513 q^{75} - 6536 q^{76} + 230 q^{77} - 3 q^{78} - 2666 q^{79} - 1644 q^{80} + 1539 q^{81} - 1949 q^{82} - 2552 q^{83} + 1563 q^{84} - 2816 q^{85} - 4825 q^{86} - 216 q^{87} - 5144 q^{88} - 1136 q^{89} - 621 q^{90} - 6128 q^{91} - 755 q^{92} + 2136 q^{93} - 1776 q^{94} - 468 q^{95} - 126 q^{96} - 3560 q^{97} + 1635 q^{98} - 1080 q^{99}+O(q^{100}) \) 19 * q + q^2 - 57 * q^3 + 59 * q^4 + 12 * q^5 - 3 * q^6 - 28 * q^7 - 3 * q^8 + 171 * q^9 - 69 * q^10 - 120 * q^11 - 177 * q^12 - 92 * q^13 - 69 * q^14 - 36 * q^15 + 83 * q^16 + 54 * q^17 + 9 * q^18 - 400 * q^19 - 93 * q^20 + 84 * q^21 - 273 * q^22 + 114 * q^23 + 9 * q^24 + 171 * q^25 + q^26 - 513 * q^27 - 521 * q^28 + 72 * q^29 + 207 * q^30 - 712 * q^31 + 42 * q^32 + 360 * q^33 - 468 * q^34 - 306 * q^35 + 531 * q^36 - 448 * q^37 + 50 * q^38 + 276 * q^39 - 1030 * q^40 - 310 * q^41 + 207 * q^42 - 852 * q^43 - 757 * q^44 + 108 * q^45 - 2187 * q^46 - 1244 * q^47 - 249 * q^48 + 47 * q^49 - 1670 * q^50 - 162 * q^51 - 2548 * q^52 + 58 * q^53 - 27 * q^54 - 2190 * q^55 - 2541 * q^56 + 1200 * q^57 - 3481 * q^58 - 2736 * q^59 + 279 * q^60 - 2922 * q^61 + 486 * q^62 - 252 * q^63 - 3677 * q^64 - 380 * q^65 + 819 * q^66 - 2658 * q^67 - 1558 * q^68 - 342 * q^69 - 4887 * q^70 - 636 * q^71 - 27 * q^72 - 2304 * q^73 - 3137 * q^74 - 513 * q^75 - 6536 * q^76 + 230 * q^77 - 3 * q^78 - 2666 * q^79 - 1644 * q^80 + 1539 * q^81 - 1949 * q^82 - 2552 * q^83 + 1563 * q^84 - 2816 * q^85 - 4825 * q^86 - 216 * q^87 - 5144 * q^88 - 1136 * q^89 - 621 * q^90 - 6128 * q^91 - 755 * q^92 + 2136 * q^93 - 1776 * q^94 - 468 * q^95 - 126 * q^96 - 3560 * q^97 + 1635 * q^98 - 1080 * 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 $

$2$	1.13862	0.402562	0.201281	−	0.979534i	$-0.435490\pi$
$2$	1.13862	0.402562	0.201281	+	0.979534i	$0.435490\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−6.70355	−0.837944
$5$	−7.78898	−0.696668	−0.348334	−	0.937370i	$-0.613252\pi$
$5$	−7.78898	−0.696668	−0.348334	+	0.937370i	$0.613252\pi$
$6$	−3.41585	−0.232419
$7$	30.6595	1.65546	0.827729	−	0.561128i	$-0.189632\pi$
$7$	30.6595	1.65546	0.827729	+	0.561128i	$0.189632\pi$
$8$	−16.7417	−0.739886
$9$	9.00000	0.333333
$10$	−8.86867	−0.280452
$11$	−31.3983	−0.860631	−0.430315	−	0.902679i	$-0.641598\pi$
$11$	−31.3983	−0.860631	−0.430315	+	0.902679i	$0.641598\pi$
$12$	20.1107	0.483787
$13$	53.7510	1.14676	0.573378	−	0.819291i	$-0.305632\pi$
$13$	53.7510	1.14676	0.573378	+	0.819291i	$0.305632\pi$
$14$	34.9094	0.666424
$15$	23.3670	0.402221
$16$	34.5660	0.540094
$17$	34.0219	0.485384	0.242692	−	0.970103i	$-0.421969\pi$
$17$	34.0219	0.485384	0.242692	+	0.970103i	$0.421969\pi$
$18$	10.2475	0.134187
$19$	−136.577	−1.64910	−0.824549	−	0.565790i	$-0.808571\pi$
$19$	−136.577	−1.64910	−0.824549	+	0.565790i	$0.808571\pi$
$20$	52.2139	0.583769
$21$	−91.9785	−0.955779
$22$	−35.7506	−0.346457
$23$	192.660	1.74662	0.873311	−	0.487163i	$-0.161968\pi$
$23$	192.660	1.74662	0.873311	+	0.487163i	$0.161968\pi$
$24$	50.2251	0.427173
$25$	−64.3317	−0.514654
$26$	61.2018	0.461641
$27$	−27.0000	−0.192450
$28$	−205.528	−1.38718
$29$	198.833	1.27319	0.636594	−	0.771199i	$-0.280343\pi$
$29$	198.833	1.27319	0.636594	+	0.771199i	$0.280343\pi$
$30$	26.6060	0.161919
$31$	−297.918	−1.72605	−0.863026	−	0.505160i	$-0.831434\pi$
$31$	−297.918	−1.72605	−0.863026	+	0.505160i	$0.831434\pi$
$32$	173.291	0.957307
$33$	94.1948	0.496885
$34$	38.7380	0.195397
$35$	−238.806	−1.15330
$36$	−60.3320	−0.279315
$37$	−207.325	−0.921188	−0.460594	−	0.887611i	$-0.652364\pi$
$37$	−207.325	−0.921188	−0.460594	+	0.887611i	$0.652364\pi$
$38$	−155.509	−0.663864
$39$	−161.253	−0.662080
$40$	130.401	0.515455
$41$	−162.111	−0.617500	−0.308750	−	0.951143i	$-0.599911\pi$
$41$	−162.111	−0.617500	−0.308750	+	0.951143i	$0.599911\pi$
$42$	−104.728	−0.384760
$43$	−37.7473	−0.133870	−0.0669351	−	0.997757i	$-0.521322\pi$
$43$	−37.7473	−0.133870	−0.0669351	+	0.997757i	$0.521322\pi$
$44$	210.480	0.721160
$45$	−70.1009	−0.232223
$46$	219.365	0.703123
$47$	−474.460	−1.47249	−0.736246	−	0.676714i	$-0.763403\pi$
$47$	−474.460	−1.47249	−0.736246	+	0.676714i	$0.763403\pi$
$48$	−103.698	−0.311824
$49$	597.006	1.74054
$50$	−73.2492	−0.207180
$51$	−102.066	−0.280237
$52$	−360.323	−0.960918
$53$	−58.6290	−0.151949	−0.0759747	−	0.997110i	$-0.524207\pi$
$53$	−58.6290	−0.151949	−0.0759747	+	0.997110i	$0.524207\pi$
$54$	−30.7426	−0.0774731
$55$	244.561	0.599574
$56$	−513.293	−1.22485
$57$	409.731	0.952108
$58$	226.395	0.512537
$59$	−466.502	−1.02938	−0.514690	−	0.857376i	$-0.672093\pi$
$59$	−466.502	−1.02938	−0.514690	+	0.857376i	$0.672093\pi$
$60$	−156.642	−0.337039
$61$	−842.621	−1.76863	−0.884317	−	0.466888i	$-0.845375\pi$
$61$	−842.621	−1.76863	−0.884317	+	0.466888i	$0.845375\pi$
$62$	−339.214	−0.694842
$63$	275.936	0.551819
$64$	−79.2161	−0.154719
$65$	−418.666	−0.798909
$66$	107.252	0.200027
$67$	−858.756	−1.56588	−0.782938	−	0.622100i	$-0.786280\pi$
$67$	−858.756	−1.56588	−0.782938	+	0.622100i	$0.786280\pi$
$68$	−228.068	−0.406725
$69$	−577.979	−1.00841
$70$	−271.909	−0.464276
$71$	753.392	1.25931	0.629656	−	0.776874i	$-0.283196\pi$
$71$	753.392	1.25931	0.629656	+	0.776874i	$0.283196\pi$
$72$	−150.675	−0.246629
$73$	−624.100	−1.00062	−0.500311	−	0.865846i	$-0.666781\pi$
$73$	−624.100	−1.00062	−0.500311	+	0.865846i	$0.666781\pi$
$74$	−236.063	−0.370835
$75$	192.995	0.297135
$76$	915.550	1.38185
$77$	−962.656	−1.42474
$78$	−183.605	−0.266528
$79$	−445.525	−0.634500	−0.317250	−	0.948342i	$-0.602759\pi$
$79$	−445.525	−0.634500	−0.317250	+	0.948342i	$0.602759\pi$
$80$	−269.234	−0.376266
$81$	81.0000	0.111111
$82$	−184.582	−0.248582
$83$	−789.023	−1.04345	−0.521726	−	0.853113i	$-0.674712\pi$
$83$	−789.023	−1.04345	−0.521726	+	0.853113i	$0.674712\pi$
$84$	616.583	0.800889
$85$	−264.996	−0.338152
$86$	−42.9797	−0.0538910
$87$	−596.500	−0.735075
$88$	525.661	0.636769
$89$	1164.54	1.38698	0.693490	−	0.720466i	$-0.256072\pi$
$89$	1164.54	1.38698	0.693490	+	0.720466i	$0.256072\pi$
$90$	−79.8180	−0.0934840
$91$	1647.98	1.89841
$92$	−1291.50	−1.46357
$93$	893.753	0.996536
$94$	−540.228	−0.592769
$95$	1063.80	1.14887
$96$	−519.873	−0.552702
$97$	−24.5196	−0.0256658	−0.0128329	−	0.999918i	$-0.504085\pi$
$97$	−24.5196	−0.0256658	−0.0128329	+	0.999918i	$0.504085\pi$
$98$	679.761	0.700675
$99$	−282.585	−0.286877
$100$	431.251	0.431251
$101$	841.771	0.829300	0.414650	−	0.909981i	$-0.363904\pi$
$101$	841.771	0.829300	0.414650	+	0.909981i	$0.363904\pi$
$102$	−116.214	−0.112813
$103$	541.124	0.517656	0.258828	−	0.965923i	$-0.416664\pi$
$103$	541.124	0.517656	0.258828	+	0.965923i	$0.416664\pi$
$104$	−899.883	−0.848469
$105$	716.419	0.665861
$106$	−66.7560	−0.0611690
$107$	2012.21	1.81802	0.909008	−	0.416779i	$-0.136841\pi$
$107$	2012.21	1.81802	0.909008	+	0.416779i	$0.136841\pi$
$108$	180.996	0.161262
$109$	243.954	0.214372	0.107186	−	0.994239i	$-0.465816\pi$
$109$	243.954	0.214372	0.107186	+	0.994239i	$0.465816\pi$
$110$	278.461	0.241366
$111$	621.974	0.531848
$112$	1059.78	0.894103
$113$	−642.610	−0.534971	−0.267485	−	0.963562i	$-0.586193\pi$
$113$	−642.610	−0.534971	−0.267485	+	0.963562i	$0.586193\pi$
$114$	466.526	0.383282
$115$	−1500.62	−1.21682
$116$	−1332.89	−1.06686
$117$	483.759	0.382252
$118$	−531.167	−0.414389
$119$	1043.10	0.803533
$120$	−391.203	−0.297598
$121$	−345.148	−0.259315
$122$	−959.423	−0.711984
$123$	486.333	0.356514
$124$	1997.11	1.44633
$125$	1474.70	1.05521
$126$	314.185	0.222141
$127$	−70.7744	−0.0494505	−0.0247252	−	0.999694i	$-0.507871\pi$
$127$	−70.7744	−0.0494505	−0.0247252	+	0.999694i	$0.507871\pi$
$128$	−1476.53	−1.01959
$129$	113.242	0.0772899
$130$	−476.700	−0.321610
$131$	−563.198	−0.375625	−0.187812	−	0.982205i	$-0.560140\pi$
$131$	−563.198	−0.375625	−0.187812	+	0.982205i	$0.560140\pi$
$132$	−631.440	−0.416362
$133$	−4187.38	−2.73001
$134$	−977.794	−0.630362
$135$	210.303	0.134074
$136$	−569.586	−0.359129
$137$	−971.081	−0.605584	−0.302792	−	0.953057i	$-0.597919\pi$
$137$	−971.081	−0.605584	−0.302792	+	0.953057i	$0.597919\pi$
$138$	−658.096	−0.405948
$139$	−385.260	−0.235089	−0.117544	−	0.993068i	$-0.537502\pi$
$139$	−385.260	−0.235089	−0.117544	+	0.993068i	$0.537502\pi$
$140$	1600.85	0.966405
$141$	1423.38	0.850144
$142$	857.824	0.506951
$143$	−1687.69	−0.986934
$144$	311.094	0.180031
$145$	−1548.71	−0.886989
$146$	−710.610	−0.402812
$147$	−1791.02	−1.00490
$148$	1389.81	0.771904
$149$	−673.772	−0.370453	−0.185227	−	0.982696i	$-0.559302\pi$
$149$	−673.772	−0.370453	−0.185227	+	0.982696i	$0.559302\pi$
$150$	219.748	0.119615
$151$	2383.10	1.28433	0.642164	−	0.766567i	$-0.278037\pi$
$151$	2383.10	1.28433	0.642164	+	0.766567i	$0.278037\pi$
$152$	2286.53	1.22015
$153$	306.198	0.161795
$154$	−1096.10	−0.573545
$155$	2320.48	1.20248
$156$	1080.97	0.554786
$157$	−413.494	−0.210194	−0.105097	−	0.994462i	$-0.533515\pi$
$157$	−413.494	−0.210194	−0.105097	+	0.994462i	$0.533515\pi$
$158$	−507.282	−0.255425
$159$	175.887	0.0877280
$160$	−1349.76	−0.666925
$161$	5906.85	2.89146
$162$	92.2279	0.0447291
$163$	−3251.05	−1.56222	−0.781110	−	0.624394i	$-0.785346\pi$
$163$	−3251.05	−1.56222	−0.781110	+	0.624394i	$0.785346\pi$
$164$	1086.72	0.517431
$165$	−733.682	−0.346164
$166$	−898.394	−0.420054
$167$	167.000	0.0773823
$167$	167.000	0.0773823
$168$	1539.88	0.707168
$169$	692.168	0.315051
$170$	−301.729	−0.136127
$171$	−1229.19	−0.549700
$172$	253.041	0.112176
$173$	−2743.22	−1.20557	−0.602783	−	0.797905i	$-0.705941\pi$
$173$	−2743.22	−1.20557	−0.602783	+	0.797905i	$0.705941\pi$
$174$	−679.185	−0.295913
$175$	−1972.38	−0.851988
$176$	−1085.31	−0.464822
$177$	1399.51	0.594313
$178$	1325.97	0.558345
$179$	−1949.31	−0.813959	−0.406979	−	0.913437i	$-0.633418\pi$
$179$	−1949.31	−0.813959	−0.406979	+	0.913437i	$0.633418\pi$
$180$	469.925	0.194590
$181$	3620.01	1.48659	0.743296	−	0.668962i	$-0.233261\pi$
$181$	3620.01	1.48659	0.743296	+	0.668962i	$0.233261\pi$
$182$	1876.42	0.764227
$183$	2527.86	1.02112
$184$	−3225.45	−1.29230
$185$	1614.85	0.641762
$186$	1017.64	0.401167
$187$	−1068.23	−0.417737
$188$	3180.57	1.23387
$189$	−827.807	−0.318593
$190$	1211.25	0.462493
$191$	−3657.79	−1.38570	−0.692849	−	0.721083i	$-0.743645\pi$
$191$	−3657.79	−1.38570	−0.692849	+	0.721083i	$0.743645\pi$
$192$	237.648	0.0893270
$193$	557.230	0.207825	0.103913	−	0.994586i	$-0.466864\pi$
$193$	557.230	0.207825	0.103913	+	0.994586i	$0.466864\pi$
$194$	−27.9184	−0.0103321
$195$	1256.00	0.461250
$196$	−4002.06	−1.45848
$197$	−5440.87	−1.96775	−0.983873	−	0.178870i	$-0.942756\pi$
$197$	−5440.87	−1.96775	−0.983873	+	0.178870i	$0.942756\pi$
$198$	−321.755	−0.115486
$199$	−5031.11	−1.79219	−0.896095	−	0.443862i	$-0.853608\pi$
$199$	−5031.11	−1.79219	−0.896095	+	0.443862i	$0.853608\pi$
$200$	1077.02	0.380785
$201$	2576.27	0.904059
$202$	958.454	0.333844
$203$	6096.13	2.10771
$204$	684.204	0.234823
$205$	1262.68	0.430193
$206$	616.133	0.208388
$207$	1733.94	0.582207
$208$	1857.96	0.619357
$209$	4288.28	1.41927
$210$	815.727	0.268050
$211$	4201.99	1.37098	0.685490	−	0.728082i	$-0.259588\pi$
$211$	4201.99	1.37098	0.685490	+	0.728082i	$0.259588\pi$
$212$	393.023	0.127325
$213$	−2260.17	−0.727064
$214$	2291.14	0.731864
$215$	294.013	0.0932630
$216$	452.026	0.142391
$217$	−9134.01	−2.85741
$218$	277.770	0.0862979
$219$	1872.30	0.577709
$220$	−1639.43	−0.502409
$221$	1828.71	0.556618
$222$	708.190	0.214102
$223$	3496.49	1.04996	0.524982	−	0.851113i	$-0.324072\pi$
$223$	3496.49	1.04996	0.524982	+	0.851113i	$0.324072\pi$
$224$	5313.02	1.58478
$225$	−578.985	−0.171551
$226$	−731.687	−0.215359
$227$	1469.58	0.429690	0.214845	−	0.976648i	$-0.431075\pi$
$227$	1469.58	0.429690	0.214845	+	0.976648i	$0.431075\pi$
$228$	−2746.65	−0.797813
$229$	−3481.75	−1.00472	−0.502358	−	0.864659i	$-0.667534\pi$
$229$	−3481.75	−1.00472	−0.502358	+	0.864659i	$0.667534\pi$
$230$	−1708.63	−0.489844
$231$	2887.97	0.822573
$232$	−3328.81	−0.942013
$233$	−1028.97	−0.289314	−0.144657	−	0.989482i	$-0.546208\pi$
$233$	−1028.97	−0.289314	−0.144657	+	0.989482i	$0.546208\pi$
$234$	550.816	0.153880
$235$	3695.56	1.02584
$236$	3127.22	0.862563
$237$	1336.57	0.366329
$238$	1187.69	0.323472
$239$	−2404.80	−0.650851	−0.325426	−	0.945568i	$-0.605508\pi$
$239$	−2404.80	−0.650851	−0.325426	+	0.945568i	$0.605508\pi$
$240$	807.703	0.217237
$241$	−5013.41	−1.34001	−0.670004	−	0.742357i	$-0.733708\pi$
$241$	−5013.41	−1.34001	−0.670004	+	0.742357i	$0.733708\pi$
$242$	−392.991	−0.104390
$243$	−243.000	−0.0641500
$244$	5648.56	1.48202
$245$	−4650.07	−1.21258
$246$	553.747	0.143519
$247$	−7341.14	−1.89112
$248$	4987.65	1.27708
$249$	2367.07	0.602437
$250$	1679.12	0.424788
$251$	1314.42	0.330539	0.165270	−	0.986248i	$-0.447151\pi$
$251$	1314.42	0.330539	0.165270	+	0.986248i	$0.447151\pi$
$252$	−1849.75	−0.462394
$253$	−6049.18	−1.50320
$254$	−80.5849	−0.0199069
$255$	794.989	0.195232
$256$	−1047.47	−0.255730
$257$	4067.37	0.987220	0.493610	−	0.869683i	$-0.335677\pi$
$257$	4067.37	0.987220	0.493610	+	0.869683i	$0.335677\pi$
$258$	128.939	0.0311140
$259$	−6356.47	−1.52499
$260$	2806.55	0.669441
$261$	1789.50	0.424396
$262$	−641.266	−0.151212
$263$	−86.9630	−0.0203892	−0.0101946	−	0.999948i	$-0.503245\pi$
$263$	−86.9630	−0.0203892	−0.0101946	+	0.999948i	$0.503245\pi$
$264$	−1576.98	−0.367639
$265$	456.661	0.105858
$266$	−4767.82	−1.09900
$267$	−3493.63	−0.800774
$268$	5756.71	1.31212
$269$	−2444.27	−0.554013	−0.277007	−	0.960868i	$-0.589342\pi$
$269$	−2444.27	−0.554013	−0.277007	+	0.960868i	$0.589342\pi$
$270$	239.454	0.0539730
$271$	5227.97	1.17187	0.585935	−	0.810358i	$-0.300727\pi$
$271$	5227.97	1.17187	0.585935	+	0.810358i	$0.300727\pi$
$272$	1176.00	0.262153
$273$	−4943.94	−1.09605
$274$	−1105.69	−0.243785
$275$	2019.91	0.442927
$276$	3874.51	0.844994
$277$	4118.90	0.893432	0.446716	−	0.894676i	$-0.352593\pi$
$277$	4118.90	0.893432	0.446716	+	0.894676i	$0.352593\pi$
$278$	−438.664	−0.0946378
$279$	−2681.26	−0.575351
$280$	3998.03	0.853314
$281$	5961.29	1.26555	0.632777	−	0.774334i	$-0.281915\pi$
$281$	5961.29	1.26555	0.632777	+	0.774334i	$0.281915\pi$
$282$	1620.68	0.342235
$283$	4875.91	1.02418	0.512089	−	0.858932i	$-0.328872\pi$
$283$	4875.91	1.02418	0.512089	+	0.858932i	$0.328872\pi$
$284$	−5050.40	−1.05523
$285$	−3191.39	−0.663303
$286$	−1921.63	−0.397302
$287$	−4970.25	−1.02225
$288$	1559.62	0.319102
$289$	−3755.51	−0.764402
$290$	−1763.39	−0.357068
$291$	73.5587	0.0148182
$292$	4183.69	0.838465
$293$	−6813.92	−1.35861	−0.679306	−	0.733855i	$-0.737719\pi$
$293$	−6813.92	−1.35861	−0.679306	+	0.733855i	$0.737719\pi$
$294$	−2039.28	−0.404535
$295$	3633.58	0.717136
$296$	3470.97	0.681574
$297$	847.754	0.165628
$298$	−767.168	−0.149130
$299$	10355.6	2.00295
$300$	−1293.75	−0.248983
$301$	−1157.31	−0.221616
$302$	2713.43	0.517022
$303$	−2525.31	−0.478797
$304$	−4720.92	−0.890669
$305$	6563.17	1.23215
$306$	348.642	0.0651324
$307$	−655.877	−0.121931	−0.0609656	−	0.998140i	$-0.519418\pi$
$307$	−655.877	−0.121931	−0.0609656	+	0.998140i	$0.519418\pi$
$308$	6453.21	1.19385
$309$	−1623.37	−0.298869
$310$	2642.13	0.484074
$311$	−6460.22	−1.17789	−0.588947	−	0.808171i	$-0.700457\pi$
$311$	−6460.22	−1.17789	−0.588947	+	0.808171i	$0.700457\pi$
$312$	2699.65	0.489864
$313$	6817.56	1.23115	0.615577	−	0.788077i	$-0.288923\pi$
$313$	6817.56	1.23115	0.615577	+	0.788077i	$0.288923\pi$
$314$	−470.812	−0.0846160
$315$	−2149.26	−0.384435
$316$	2986.60	0.531675
$317$	−6519.93	−1.15519	−0.577596	−	0.816323i	$-0.696009\pi$
$317$	−6519.93	−1.15519	−0.577596	+	0.816323i	$0.696009\pi$
$318$	200.268	0.0353159
$319$	−6243.03	−1.09574
$320$	617.013	0.107788
$321$	−6036.63	−1.04963
$322$	6725.64	1.16399
$323$	−4646.61	−0.800447
$324$	−542.988	−0.0931049
$325$	−3457.89	−0.590183
$326$	−3701.70	−0.628890
$327$	−731.861	−0.123768
$328$	2714.02	0.456880
$329$	−14546.7	−2.43765
$330$	−835.383	−0.139352
$331$	3085.09	0.512302	0.256151	−	0.966637i	$-0.417546\pi$
$331$	3085.09	0.512302	0.256151	+	0.966637i	$0.417546\pi$
$332$	5289.25	0.874354
$333$	−1865.92	−0.307063
$334$	190.149	0.0311512
$335$	6688.84	1.09090
$336$	−3179.33	−0.516211
$337$	8163.23	1.31952	0.659762	−	0.751475i	$-0.270657\pi$
$337$	8163.23	1.31952	0.659762	+	0.751475i	$0.270657\pi$
$338$	788.114	0.126828
$339$	1927.83	0.308865
$340$	1776.42	0.283352
$341$	9354.10	1.48549
$342$	−1399.58	−0.221288
$343$	7787.69	1.22594
$344$	631.955	0.0990486
$345$	4501.87	0.702529
$346$	−3123.47	−0.485315
$347$	−4113.08	−0.636316	−0.318158	−	0.948038i	$-0.603064\pi$
$347$	−4113.08	−0.636316	−0.318158	+	0.948038i	$0.603064\pi$
$348$	3998.67	0.615952
$349$	−10714.7	−1.64339	−0.821696	−	0.569926i	$-0.806972\pi$
$349$	−10714.7	−1.64339	−0.821696	+	0.569926i	$0.806972\pi$
$350$	−2245.78	−0.342978
$351$	−1451.28	−0.220693
$352$	−5441.04	−0.823888
$353$	−965.216	−0.145533	−0.0727666	−	0.997349i	$-0.523183\pi$
$353$	−965.216	−0.145533	−0.0727666	+	0.997349i	$0.523183\pi$
$354$	1593.50	0.239248
$355$	−5868.16	−0.877322
$356$	−7806.57	−1.16221
$357$	−3129.29	−0.463920
$358$	−2219.52	−0.327669
$359$	3841.80	0.564798	0.282399	−	0.959297i	$-0.408870\pi$
$359$	3841.80	0.564798	0.282399	+	0.959297i	$0.408870\pi$
$360$	1173.61	0.171818
$361$	11794.2	1.71953
$362$	4121.80	0.598445
$363$	1035.44	0.149715
$364$	−11047.3	−1.59076
$365$	4861.10	0.697101
$366$	2878.27	0.411064
$367$	−6986.06	−0.993649	−0.496825	−	0.867851i	$-0.665501\pi$
$367$	−6986.06	−0.993649	−0.496825	+	0.867851i	$0.665501\pi$
$368$	6659.48	0.943341
$369$	−1459.00	−0.205833
$370$	1838.69	0.258349
$371$	−1797.54	−0.251546
$372$	−5991.32	−0.835042
$373$	869.512	0.120701	0.0603507	−	0.998177i	$-0.480778\pi$
$373$	869.512	0.120701	0.0603507	+	0.998177i	$0.480778\pi$
$374$	−1216.31	−0.168165
$375$	−4424.11	−0.609226
$376$	7943.27	1.08948
$377$	10687.5	1.46004
$378$	−942.555	−0.128253
$379$	−4838.60	−0.655784	−0.327892	−	0.944715i	$-0.606338\pi$
$379$	−4838.60	−0.655784	−0.327892	+	0.944715i	$0.606338\pi$
$380$	−7131.21	−0.962692
$381$	212.323	0.0285502
$382$	−4164.82	−0.557829
$383$	5316.56	0.709304	0.354652	−	0.934998i	$-0.384599\pi$
$383$	5316.56	0.709304	0.354652	+	0.934998i	$0.384599\pi$
$384$	4429.58	0.588661
$385$	7498.11	0.992569
$386$	634.471	0.0836625
$387$	−339.726	−0.0446234
$388$	164.368	0.0215065
$389$	10242.1	1.33495	0.667475	−	0.744632i	$-0.267375\pi$
$389$	10242.1	1.33495	0.667475	+	0.744632i	$0.267375\pi$
$390$	1430.10	0.185682
$391$	6554.66	0.847783
$392$	−9994.90	−1.28780
$393$	1689.59	0.216867
$394$	−6195.06	−0.792139
$395$	3470.19	0.442036
$396$	1894.32	0.240387
$397$	−764.215	−0.0966117	−0.0483059	−	0.998833i	$-0.515382\pi$
$397$	−764.215	−0.0966117	−0.0483059	+	0.998833i	$0.515382\pi$
$398$	−5728.50	−0.721467
$399$	12562.1	1.57617
$400$	−2223.69	−0.277961
$401$	−453.962	−0.0565331	−0.0282666	−	0.999600i	$-0.508999\pi$
$401$	−453.962	−0.0565331	−0.0282666	+	0.999600i	$0.508999\pi$
$402$	2933.38	0.363940
$403$	−16013.4	−1.97936
$404$	−5642.85	−0.694907
$405$	−630.908	−0.0774076
$406$	6941.16	0.848483
$407$	6509.64	0.792803
$408$	1708.76	0.207343
$409$	−1026.41	−0.124089	−0.0620447	−	0.998073i	$-0.519762\pi$
$409$	−1026.41	−0.124089	−0.0620447	+	0.998073i	$0.519762\pi$
$410$	1437.71	0.173179
$411$	2913.24	0.349634
$412$	−3627.45	−0.433766
$413$	−14302.7	−1.70410
$414$	1974.29	0.234374
$415$	6145.68	0.726939
$416$	9314.57	1.09780
$417$	1155.78	0.135729
$418$	4882.71	0.571342
$419$	6338.52	0.739038	0.369519	−	0.929223i	$-0.379522\pi$
$419$	6338.52	0.739038	0.369519	+	0.929223i	$0.379522\pi$
$420$	−4802.55	−0.557954
$421$	−5834.74	−0.675458	−0.337729	−	0.941243i	$-0.609659\pi$
$421$	−5834.74	−0.675458	−0.337729	+	0.941243i	$0.609659\pi$
$422$	4784.45	0.551904
$423$	−4270.14	−0.490831
$424$	981.550	0.112425
$425$	−2188.69	−0.249805
$426$	−2573.47	−0.292688
$427$	−25834.4	−2.92790
$428$	−13489.0	−1.52340
$429$	5063.07	0.569807
$430$	334.769	0.0375441
$431$	−1340.73	−0.149840	−0.0749198	−	0.997190i	$-0.523870\pi$
$431$	−1340.73	−0.149840	−0.0749198	+	0.997190i	$0.523870\pi$
$432$	−933.283	−0.103941
$433$	12263.0	1.36102	0.680509	−	0.732739i	$-0.261759\pi$
$433$	12263.0	1.36102	0.680509	+	0.732739i	$0.261759\pi$
$434$	−10400.1	−1.15028
$435$	4646.13	0.512103
$436$	−1635.36	−0.179632
$437$	−26312.8	−2.88035
$438$	2131.83	0.232564
$439$	−14261.0	−1.55043	−0.775217	−	0.631694i	$-0.782360\pi$
$439$	−14261.0	−1.55043	−0.775217	+	0.631694i	$0.782360\pi$
$440$	−4094.36	−0.443616
$441$	5373.05	0.580180
$442$	2082.20	0.224073
$443$	−12976.1	−1.39168	−0.695839	−	0.718198i	$-0.744967\pi$
$443$	−12976.1	−1.39168	−0.695839	+	0.718198i	$0.744967\pi$
$444$	−4169.44	−0.445659
$445$	−9070.60	−0.966265
$446$	3981.16	0.422675
$447$	2021.32	0.213881
$448$	−2428.73	−0.256131
$449$	6707.70	0.705025	0.352512	−	0.935807i	$-0.385327\pi$
$449$	6707.70	0.705025	0.352512	+	0.935807i	$0.385327\pi$
$450$	−659.243	−0.0690600
$451$	5090.01	0.531440
$452$	4307.77	0.448275
$453$	−7149.29	−0.741507
$454$	1673.29	0.172977
$455$	−12836.1	−1.32256
$456$	−6859.59	−0.704451
$457$	8156.62	0.834903	0.417451	−	0.908699i	$-0.362923\pi$
$457$	8156.62	0.834903	0.417451	+	0.908699i	$0.362923\pi$
$458$	−3964.37	−0.404461
$459$	−918.593	−0.0934123
$460$	10059.5	1.01962
$461$	12494.1	1.26228	0.631139	−	0.775670i	$-0.282588\pi$
$461$	12494.1	1.26228	0.631139	+	0.775670i	$0.282588\pi$
$462$	3288.29	0.331136
$463$	−5454.60	−0.547509	−0.273755	−	0.961800i	$-0.588266\pi$
$463$	−5454.60	−0.547509	−0.273755	+	0.961800i	$0.588266\pi$
$464$	6872.88	0.687641
$465$	−6961.43	−0.694255
$466$	−1171.61	−0.116467
$467$	−18883.8	−1.87117	−0.935585	−	0.353101i	$-0.885127\pi$
$467$	−18883.8	−1.87117	−0.935585	+	0.353101i	$0.885127\pi$
$468$	−3242.90	−0.320306
$469$	−26329.0	−2.59224
$470$	4207.83	0.412963
$471$	1240.48	0.121356
$472$	7810.05	0.761624
$473$	1185.20	0.115213
$474$	1521.85	0.147470
$475$	8786.22	0.848715
$476$	−6992.45	−0.673316
$477$	−527.661	−0.0506498
$478$	−2738.14	−0.262008
$479$	11913.0	1.13636	0.568181	−	0.822904i	$-0.307647\pi$
$479$	11913.0	1.13636	0.568181	+	0.822904i	$0.307647\pi$
$480$	4049.29	0.385050
$481$	−11143.9	−1.05638
$482$	−5708.35	−0.539436
$483$	−17720.6	−1.66939
$484$	2313.72	0.217291
$485$	190.982	0.0178805
$486$	−276.684	−0.0258244
$487$	−8343.64	−0.776358	−0.388179	−	0.921584i	$-0.626896\pi$
$487$	−8343.64	−0.776358	−0.388179	+	0.921584i	$0.626896\pi$
$488$	14106.9	1.30859
$489$	9753.14	0.901948
$490$	−5294.64	−0.488138
$491$	7779.69	0.715056	0.357528	−	0.933902i	$-0.383620\pi$
$491$	7779.69	0.715056	0.357528	+	0.933902i	$0.383620\pi$
$492$	−3260.16	−0.298739
$493$	6764.70	0.617985
$494$	−8358.74	−0.761291
$495$	2201.05	0.199858
$496$	−10297.8	−0.932230
$497$	23098.6	2.08474
$498$	2695.18	0.242518
$499$	−15617.7	−1.40109	−0.700544	−	0.713610i	$-0.747059\pi$
$499$	−15617.7	−1.40109	−0.700544	+	0.713610i	$0.747059\pi$
$500$	−9885.74	−0.884208
$501$	−501.000	−0.0446767
$502$	1496.62	0.133062
$503$	−1055.81	−0.0935907	−0.0467953	−	0.998904i	$-0.514901\pi$
$503$	−1055.81	−0.0935907	−0.0467953	+	0.998904i	$0.514901\pi$
$504$	−4619.63	−0.408283
$505$	−6556.54	−0.577747
$506$	−6887.70	−0.605130
$507$	−2076.50	−0.181895
$508$	474.440	0.0414367
$509$	88.7993	0.00773273	0.00386637	−	0.999993i	$-0.498769\pi$
$509$	88.7993	0.00773273	0.00386637	+	0.999993i	$0.498769\pi$
$510$	905.188	0.0785929
$511$	−19134.6	−1.65649
$512$	10619.5	0.916644
$513$	3687.58	0.317369
$514$	4631.18	0.397417
$515$	−4214.81	−0.360634
$516$	−759.124	−0.0647646
$517$	14897.2	1.26727
$518$	−7237.59	−0.613902
$519$	8229.65	0.696033
$520$	7009.18	0.591101
$521$	13563.0	1.14051	0.570256	−	0.821467i	$-0.306844\pi$
$521$	13563.0	1.14051	0.570256	+	0.821467i	$0.306844\pi$
$522$	2037.56	0.170846
$523$	−2822.42	−0.235977	−0.117988	−	0.993015i	$-0.537645\pi$
$523$	−2822.42	−0.235977	−0.117988	+	0.993015i	$0.537645\pi$
$524$	3775.43	0.314752
$525$	5917.14	0.491895
$526$	−99.0175	−0.00820793
$527$	−10135.7	−0.837798
$528$	3255.94	0.268365
$529$	24950.7	2.05069
$530$	519.961	0.0426145
$531$	−4198.52	−0.343127
$532$	28070.3	2.28760
$533$	−8713.63	−0.708123
$534$	−3977.90	−0.322361
$535$	−15673.1	−1.26655
$536$	14377.0	1.15857
$537$	5847.94	0.469939
$538$	−2783.08	−0.223025
$539$	−18745.0	−1.49796
$540$	−1409.77	−0.112346
$541$	17414.8	1.38395	0.691977	−	0.721919i	$-0.256740\pi$
$541$	17414.8	1.38395	0.691977	+	0.721919i	$0.256740\pi$
$542$	5952.65	0.471750
$543$	−10860.0	−0.858285
$544$	5895.70	0.464662
$545$	−1900.15	−0.149346
$546$	−5629.25	−0.441226
$547$	1912.20	0.149470	0.0747348	−	0.997203i	$-0.476189\pi$
$547$	1912.20	0.149470	0.0747348	+	0.997203i	$0.476189\pi$
$548$	6509.69	0.507446
$549$	−7583.59	−0.589544
$550$	2299.90	0.178305
$551$	−27156.0	−2.09961
$552$	9676.36	0.746111
$553$	−13659.6	−1.05039
$554$	4689.85	0.359662
$555$	−4844.55	−0.370522
$556$	2582.61	0.196991
$557$	10659.5	0.810877	0.405438	−	0.914122i	$-0.367119\pi$
$557$	10659.5	0.810877	0.405438	+	0.914122i	$0.367119\pi$
$558$	−3052.93	−0.231614
$559$	−2028.96	−0.153516
$560$	−8254.59	−0.622893
$561$	3204.69	0.241180
$562$	6787.62	0.509464
$563$	21721.7	1.62604	0.813022	−	0.582234i	$-0.197821\pi$
$563$	21721.7	1.62604	0.813022	+	0.582234i	$0.197821\pi$
$564$	−9541.71	−0.712373
$565$	5005.28	0.372697
$566$	5551.79	0.412295
$567$	2483.42	0.183940
$568$	−12613.1	−0.931747
$569$	2870.58	0.211495	0.105748	−	0.994393i	$-0.466276\pi$
$569$	2870.58	0.211495	0.105748	+	0.994393i	$0.466276\pi$
$570$	−3633.76	−0.267020
$571$	6697.66	0.490873	0.245437	−	0.969413i	$-0.421069\pi$
$571$	6697.66	0.490873	0.245437	+	0.969413i	$0.421069\pi$
$572$	11313.5	0.826996
$573$	10973.4	0.800033
$574$	−5659.21	−0.411517
$575$	−12394.1	−0.898906
$576$	−712.944	−0.0515730
$577$	15882.6	1.14593	0.572966	−	0.819579i	$-0.305793\pi$
$577$	15882.6	1.14593	0.572966	+	0.819579i	$0.305793\pi$
$578$	−4276.08	−0.307719
$579$	−1671.69	−0.119988
$580$	10381.9	0.743247
$581$	−24191.0	−1.72739
$582$	83.7551	0.00596523
$583$	1840.85	0.130772
$584$	10448.5	0.740346
$585$	−3767.99	−0.266303
$586$	−7758.44	−0.546925
$587$	−3449.49	−0.242548	−0.121274	−	0.992619i	$-0.538698\pi$
$587$	−3449.49	−0.242548	−0.121274	+	0.992619i	$0.538698\pi$
$588$	12006.2	0.842052
$589$	40688.7	2.84643
$590$	4137.25	0.288692
$591$	16322.6	1.13608
$592$	−7166.39	−0.497528
$593$	−18682.7	−1.29377	−0.646884	−	0.762588i	$-0.723928\pi$
$593$	−18682.7	−1.29377	−0.646884	+	0.762588i	$0.723928\pi$
$594$	965.266	0.0666757
$595$	−8124.66	−0.559796
$596$	4516.67	0.310419
$597$	15093.3	1.03472
$598$	11791.1	0.806312
$599$	−2826.68	−0.192813	−0.0964067	−	0.995342i	$-0.530735\pi$
$599$	−2826.68	−0.192813	−0.0964067	+	0.995342i	$0.530735\pi$
$600$	−3231.07	−0.219846
$601$	16942.3	1.14990	0.574952	−	0.818187i	$-0.305021\pi$
$601$	16942.3	1.14990	0.574952	+	0.818187i	$0.305021\pi$
$602$	−1317.74	−0.0892143
$603$	−7728.80	−0.521959
$604$	−15975.2	−1.07620
$605$	2688.35	0.180656
$606$	−2875.36	−0.192745
$607$	−13046.0	−0.872360	−0.436180	−	0.899859i	$-0.643669\pi$
$607$	−13046.0	−0.872360	−0.436180	+	0.899859i	$0.643669\pi$
$608$	−23667.6	−1.57869
$609$	−18288.4	−1.21689
$610$	7472.93	0.496016
$611$	−25502.7	−1.68859
$612$	−2052.61	−0.135575
$613$	8024.22	0.528703	0.264352	−	0.964426i	$-0.414842\pi$
$613$	8024.22	0.528703	0.264352	+	0.964426i	$0.414842\pi$
$614$	−746.792	−0.0490848
$615$	−3788.04	−0.248372
$616$	16116.5	1.05414
$617$	7942.38	0.518231	0.259115	−	0.965846i	$-0.416569\pi$
$617$	7942.38	0.518231	0.259115	+	0.965846i	$0.416569\pi$
$618$	−1848.40	−0.120313
$619$	−25525.1	−1.65742	−0.828708	−	0.559681i	$-0.810924\pi$
$619$	−25525.1	−1.65742	−0.828708	+	0.559681i	$0.810924\pi$
$620$	−15555.4	−1.00761
$621$	−5201.81	−0.336138
$622$	−7355.71	−0.474175
$623$	35704.3	2.29609
$624$	−5573.87	−0.357586
$625$	−3444.96	−0.220478
$626$	7762.58	0.495615
$627$	−12864.8	−0.819413
$628$	2771.88	0.176131
$629$	−7053.59	−0.447130
$630$	−2447.18	−0.154759
$631$	−10860.6	−0.685189	−0.342595	−	0.939483i	$-0.611306\pi$
$631$	−10860.6	−0.685189	−0.342595	+	0.939483i	$0.611306\pi$
$632$	7458.85	0.469457
$633$	−12606.0	−0.791535
$634$	−7423.70	−0.465036
$635$	551.261	0.0344506
$636$	−1179.07	−0.0735112
$637$	32089.6	1.99598
$638$	−7108.41	−0.441105
$639$	6780.52	0.419771
$640$	11500.6	0.710317
$641$	−10065.5	−0.620223	−0.310111	−	0.950700i	$-0.600366\pi$
$641$	−10065.5	−0.620223	−0.310111	+	0.950700i	$0.600366\pi$
$642$	−6873.41	−0.422542
$643$	−17762.1	−1.08938	−0.544689	−	0.838638i	$-0.683352\pi$
$643$	−17762.1	−1.08938	−0.544689	+	0.838638i	$0.683352\pi$
$644$	−39596.9	−2.42288
$645$	−882.040	−0.0538454
$646$	−5290.71	−0.322229
$647$	−23008.7	−1.39809	−0.699047	−	0.715076i	$-0.746392\pi$
$647$	−23008.7	−1.39809	−0.699047	+	0.715076i	$0.746392\pi$
$648$	−1356.08	−0.0822096
$649$	14647.4	0.885916
$650$	−3937.21	−0.237585
$651$	27402.0	1.64972
$652$	21793.6	1.30905
$653$	21831.4	1.30832	0.654158	−	0.756358i	$-0.273023\pi$
$653$	21831.4	1.30832	0.654158	+	0.756358i	$0.273023\pi$
$654$	−833.309	−0.0498241
$655$	4386.74	0.261686
$656$	−5603.54	−0.333508
$657$	−5616.90	−0.333540
$658$	−16563.1	−0.981304
$659$	−8326.08	−0.492167	−0.246083	−	0.969249i	$-0.579144\pi$
$659$	−8326.08	−0.492167	−0.246083	+	0.969249i	$0.579144\pi$
$660$	4918.28	0.290066
$661$	−10871.1	−0.639691	−0.319846	−	0.947470i	$-0.603631\pi$
$661$	−10871.1	−0.639691	−0.319846	+	0.947470i	$0.603631\pi$
$662$	3512.74	0.206233
$663$	−5486.14	−0.321363
$664$	13209.6	0.772035
$665$	32615.4	1.90191
$666$	−2124.57	−0.123612
$667$	38307.2	2.22378
$668$	−1119.49	−0.0648421
$669$	−10489.5	−0.606197
$670$	7616.02	0.439153
$671$	26456.9	1.52214
$672$	−15939.1	−0.914974
$673$	14437.3	0.826917	0.413458	−	0.910523i	$-0.364321\pi$
$673$	14437.3	0.826917	0.413458	+	0.910523i	$0.364321\pi$
$674$	9294.79	0.531190
$675$	1736.96	0.0990452
$676$	−4639.99	−0.263996
$677$	12990.9	0.737490	0.368745	−	0.929531i	$-0.379788\pi$
$677$	12990.9	0.737490	0.368745	+	0.929531i	$0.379788\pi$
$678$	2195.06	0.124337
$679$	−751.758	−0.0424887
$680$	4436.49	0.250194
$681$	−4408.75	−0.248082
$682$	10650.7	0.598003
$683$	−604.874	−0.0338871	−0.0169435	−	0.999856i	$-0.505394\pi$
$683$	−604.874	−0.0338871	−0.0169435	+	0.999856i	$0.505394\pi$
$684$	8239.95	0.460618
$685$	7563.73	0.421891
$686$	8867.19	0.493515
$687$	10445.2	0.580074
$688$	−1304.78	−0.0723025
$689$	−3151.37	−0.174249
$690$	5125.90	0.282811
$691$	10878.6	0.598904	0.299452	−	0.954111i	$-0.403196\pi$
$691$	10878.6	0.598904	0.299452	+	0.954111i	$0.403196\pi$
$692$	18389.3	1.01020
$693$	−8663.90	−0.474913
$694$	−4683.22	−0.256157
$695$	3000.79	0.163779
$696$	9986.43	0.543872
$697$	−5515.34	−0.299725
$698$	−12199.9	−0.661567
$699$	3086.92	0.167036
$700$	13221.9	0.713918
$701$	10181.3	0.548561	0.274280	−	0.961650i	$-0.411560\pi$
$701$	10181.3	0.548561	0.274280	+	0.961650i	$0.411560\pi$
$702$	−1652.45	−0.0888428
$703$	28315.8	1.51913
$704$	2487.25	0.133156
$705$	−11086.7	−0.592268
$706$	−1099.01	−0.0585861
$707$	25808.3	1.37287
$708$	−9381.67	−0.498001
$709$	−5968.59	−0.316157	−0.158078	−	0.987427i	$-0.550530\pi$
$709$	−5968.59	−0.316157	−0.158078	+	0.987427i	$0.550530\pi$
$710$	−6681.58	−0.353176
$711$	−4009.72	−0.211500
$712$	−19496.4	−1.02621
$713$	−57396.7	−3.01476
$714$	−3563.06	−0.186757
$715$	13145.4	0.687566
$716$	13067.3	0.682052
$717$	7214.40	0.375769
$718$	4374.34	0.227366
$719$	27408.5	1.42165	0.710824	−	0.703370i	$-0.248322\pi$
$719$	27408.5	1.42165	0.710824	+	0.703370i	$0.248322\pi$
$720$	−2423.11	−0.125422
$721$	16590.6	0.856957
$722$	13429.1	0.692216
$723$	15040.2	0.773654
$724$	−24266.9	−1.24568
$725$	−12791.3	−0.655251
$726$	1178.97	0.0602697
$727$	31067.6	1.58492	0.792458	−	0.609927i	$-0.208801\pi$
$727$	31067.6	1.58492	0.792458	+	0.609927i	$0.208801\pi$
$728$	−27590.0	−1.40461
$729$	729.000	0.0370370
$730$	5534.93	0.280626
$731$	−1284.24	−0.0649785
$732$	−16945.7	−0.855642
$733$	−8221.82	−0.414297	−0.207149	−	0.978309i	$-0.566418\pi$
$733$	−8221.82	−0.414297	−0.207149	+	0.978309i	$0.566418\pi$
$734$	−7954.44	−0.400005
$735$	13950.2	0.700083
$736$	33386.2	1.67205
$737$	26963.5	1.34764
$738$	−1661.24	−0.0828607
$739$	2949.53	0.146821	0.0734103	−	0.997302i	$-0.476612\pi$
$739$	2949.53	0.146821	0.0734103	+	0.997302i	$0.476612\pi$
$740$	−10825.2	−0.537761
$741$	22023.4	1.09184
$742$	−2046.71	−0.101263
$743$	−8386.16	−0.414076	−0.207038	−	0.978333i	$-0.566382\pi$
$743$	−8386.16	−0.414076	−0.207038	+	0.978333i	$0.566382\pi$
$744$	−14963.0	−0.737323
$745$	5248.00	0.258083
$746$	990.040	0.0485898
$747$	−7101.20	−0.347817
$748$	7160.94	0.350040
$749$	61693.4	3.00965
$750$	−5037.36	−0.245251
$751$	−3683.19	−0.178963	−0.0894816	−	0.995988i	$-0.528521\pi$
$751$	−3683.19	−0.178963	−0.0894816	+	0.995988i	$0.528521\pi$
$752$	−16400.2	−0.795284
$753$	−3943.26	−0.190837
$754$	12169.0	0.587755
$755$	−18561.9	−0.894751
$756$	5549.25	0.266963
$757$	15706.1	0.754091	0.377045	−	0.926195i	$-0.376940\pi$
$757$	15706.1	0.754091	0.377045	+	0.926195i	$0.376940\pi$
$758$	−5509.31	−0.263993
$759$	18147.5	0.867871
$760$	−17809.7	−0.850036
$761$	16038.1	0.763969	0.381985	−	0.924169i	$-0.375241\pi$
$761$	16038.1	0.763969	0.381985	+	0.924169i	$0.375241\pi$
$762$	241.755	0.0114932
$763$	7479.50	0.354884
$764$	24520.2	1.16114
$765$	−2384.97	−0.112717
$766$	6053.52	0.285539
$767$	−25075.0	−1.18045
$768$	3142.41	0.147646
$769$	14997.5	0.703282	0.351641	−	0.936135i	$-0.385624\pi$
$769$	14997.5	0.703282	0.351641	+	0.936135i	$0.385624\pi$
$770$	8537.48	0.399570
$771$	−12202.1	−0.569972
$772$	−3735.42	−0.174146
$773$	−8378.86	−0.389866	−0.194933	−	0.980817i	$-0.562449\pi$
$773$	−8378.86	−0.389866	−0.194933	+	0.980817i	$0.562449\pi$
$774$	−386.818	−0.0179637
$775$	19165.6	0.888319
$776$	410.499	0.0189898
$777$	19069.4	0.880453
$778$	11661.8	0.537400
$779$	22140.6	1.01832
$780$	−8419.64	−0.386502
$781$	−23655.2	−1.08380
$782$	7463.24	0.341285
$783$	−5368.50	−0.245025
$784$	20636.1	0.940056
$785$	3220.70	0.146435
$786$	1923.80	0.0873023
$787$	−32322.1	−1.46399	−0.731995	−	0.681310i	$-0.761411\pi$
$787$	−32322.1	−1.46399	−0.731995	+	0.681310i	$0.761411\pi$
$788$	36473.1	1.64886
$789$	260.889	0.0117717
$790$	3951.21	0.177947
$791$	−19702.1	−0.885621
$792$	4730.95	0.212256
$793$	−45291.7	−2.02819
$794$	−870.148	−0.0388922
$795$	−1369.98	−0.0611173
$796$	33726.3	1.50175
$797$	−24625.7	−1.09446	−0.547232	−	0.836981i	$-0.684319\pi$
$797$	−24625.7	−1.09446	−0.547232	+	0.836981i	$0.684319\pi$
$798$	14303.5	0.634508
$799$	−16142.1	−0.714725
$800$	−11148.1	−0.492682
$801$	10480.9	0.462327
$802$	−516.889	−0.0227581
$803$	19595.7	0.861165
$804$	−17270.1	−0.757551
$805$	−46008.4	−2.01439
$806$	−18233.1	−0.796815
$807$	7332.80	0.319860
$808$	−14092.7	−0.613587
$809$	14324.5	0.622523	0.311261	−	0.950324i	$-0.399249\pi$
$809$	14324.5	0.622523	0.311261	+	0.950324i	$0.399249\pi$
$810$	−718.362	−0.0311613
$811$	19442.0	0.841803	0.420901	−	0.907106i	$-0.361714\pi$
$811$	19442.0	0.841803	0.420901	+	0.907106i	$0.361714\pi$
$812$	−40865.8	−1.76614
$813$	−15683.9	−0.676579
$814$	7411.98	0.319152
$815$	25322.4	1.08835
$816$	−3528.01	−0.151354
$817$	5155.41	0.220765
$818$	−1168.68	−0.0499537
$819$	14831.8	0.632803
$820$	−8464.45	−0.360477
$821$	36615.5	1.55650	0.778252	−	0.627952i	$-0.216106\pi$
$821$	36615.5	1.55650	0.778252	+	0.627952i	$0.216106\pi$
$822$	3317.07	0.140749
$823$	45586.4	1.93079	0.965396	−	0.260789i	$-0.0839828\pi$
$823$	45586.4	1.93079	0.965396	+	0.260789i	$0.0839828\pi$
$824$	−9059.34	−0.383006
$825$	−6059.72	−0.255724
$826$	−16285.3	−0.686004
$827$	103.414	0.00434830	0.00217415	−	0.999998i	$-0.499308\pi$
$827$	103.414	0.00434830	0.00217415	+	0.999998i	$0.499308\pi$
$828$	−11623.5	−0.487857
$829$	16905.1	0.708251	0.354125	−	0.935198i	$-0.384779\pi$
$829$	16905.1	0.708251	0.354125	+	0.935198i	$0.384779\pi$
$830$	6997.58	0.292638
$831$	−12356.7	−0.515823
$832$	−4257.94	−0.177425
$833$	20311.3	0.844832
$834$	1315.99	0.0546391
$835$	−1300.76	−0.0539098
$836$	−28746.7	−1.18926
$837$	8043.78	0.332179
$838$	7217.15	0.297509
$839$	−12689.1	−0.522141	−0.261070	−	0.965320i	$-0.584076\pi$
$839$	−12689.1	−0.522141	−0.261070	+	0.965320i	$0.584076\pi$
$840$	−11994.1	−0.492661
$841$	15145.7	0.621006
$842$	−6643.53	−0.271914
$843$	−17883.9	−0.730668
$844$	−28168.2	−1.14880
$845$	−5391.29	−0.219486
$846$	−4862.05	−0.197590
$847$	−10582.1	−0.429285
$848$	−2026.57	−0.0820670
$849$	−14627.7	−0.591310
$850$	−2492.08	−0.100562
$851$	−39943.1	−1.60897
$852$	15151.2	0.609239
$853$	−22808.3	−0.915524	−0.457762	−	0.889075i	$-0.651349\pi$
$853$	−22808.3	−0.915524	−0.457762	+	0.889075i	$0.651349\pi$
$854$	−29415.4	−1.17866
$855$	9574.16	0.382958
$856$	−33687.8	−1.34512
$857$	−11022.1	−0.439331	−0.219666	−	0.975575i	$-0.570497\pi$
$857$	−11022.1	−0.439331	−0.219666	+	0.975575i	$0.570497\pi$
$858$	5764.89	0.229382
$859$	6703.21	0.266252	0.133126	−	0.991099i	$-0.457498\pi$
$859$	6703.21	0.266252	0.133126	+	0.991099i	$0.457498\pi$
$860$	−1970.93	−0.0781492
$861$	14910.7	0.590194
$862$	−1526.58	−0.0603197
$863$	−21097.1	−0.832161	−0.416080	−	0.909328i	$-0.636596\pi$
$863$	−21097.1	−0.832161	−0.416080	+	0.909328i	$0.636596\pi$
$864$	−4678.86	−0.184234
$865$	21366.9	0.839879
$866$	13962.8	0.547894
$867$	11266.5	0.441328
$868$	61230.3	2.39435
$869$	13988.7	0.546070
$870$	5290.16	0.206153
$871$	−46159.0	−1.79568
$872$	−4084.20	−0.158611
$873$	−220.676	−0.00855527
$874$	−29960.2	−1.15952
$875$	45213.6	1.74686
$876$	−12551.1	−0.484088
$877$	−6161.84	−0.237252	−0.118626	−	0.992939i	$-0.537849\pi$
$877$	−6161.84	−0.237252	−0.118626	+	0.992939i	$0.537849\pi$
$878$	−16237.8	−0.624146
$879$	20441.8	0.784395
$880$	8453.49	0.323826
$881$	−24168.0	−0.924223	−0.462111	−	0.886822i	$-0.652908\pi$
$881$	−24168.0	−0.924223	−0.462111	+	0.886822i	$0.652908\pi$
$882$	6117.85	0.233558
$883$	31183.9	1.18847	0.594237	−	0.804290i	$-0.297454\pi$
$883$	31183.9	1.18847	0.594237	+	0.804290i	$0.297454\pi$
$884$	−12258.9	−0.466415
$885$	−10900.7	−0.414039
$886$	−14774.8	−0.560236
$887$	−39183.5	−1.48326	−0.741631	−	0.670808i	$-0.765947\pi$
$887$	−39183.5	−1.48326	−0.741631	+	0.670808i	$0.765947\pi$
$888$	−10412.9	−0.393507
$889$	−2169.91	−0.0818632
$890$	−10327.9	−0.388981
$891$	−2543.26	−0.0956256
$892$	−23438.9	−0.879811
$893$	64800.3	2.42829
$894$	2301.50	0.0861004
$895$	15183.2	0.567059
$896$	−45269.6	−1.68789
$897$	−31066.9	−1.15640
$898$	7637.50	0.283816
$899$	−59236.0	−2.19759
$900$	3881.26	0.143750
$901$	−1994.67	−0.0737539
$902$	5795.57	0.213937
$903$	3471.94	0.127950
$904$	10758.4	0.395817
$905$	−28196.2	−1.03566
$906$	−8140.30	−0.298503
$907$	11847.0	0.433709	0.216855	−	0.976204i	$-0.430420\pi$
$907$	11847.0	0.433709	0.216855	+	0.976204i	$0.430420\pi$
$908$	−9851.43	−0.360056
$909$	7575.93	0.276433
$910$	−14615.4	−0.532412
$911$	15538.5	0.565108	0.282554	−	0.959251i	$-0.408818\pi$
$911$	15538.5	0.565108	0.282554	+	0.959251i	$0.408818\pi$
$912$	14162.8	0.514228
$913$	24774.0	0.898027
$914$	9287.26	0.336100
$915$	−19689.5	−0.711382
$916$	23340.1	0.841897
$917$	−17267.4	−0.621831
$918$	−1045.92	−0.0376042
$919$	−22944.3	−0.823571	−0.411786	−	0.911281i	$-0.635095\pi$
$919$	−22944.3	−0.823571	−0.411786	+	0.911281i	$0.635095\pi$
$920$	25123.0	0.900305
$921$	1967.63	0.0703970
$922$	14226.0	0.508145
$923$	40495.5	1.44412
$924$	−19359.6	−0.689270
$925$	13337.6	0.474093
$926$	−6210.70	−0.220406
$927$	4870.11	0.172552
$928$	34456.1	1.21883
$929$	17702.8	0.625199	0.312599	−	0.949885i	$-0.398800\pi$
$929$	17702.8	0.625199	0.312599	+	0.949885i	$0.398800\pi$
$930$	−7926.40	−0.279481
$931$	−81537.2	−2.87032
$932$	6897.78	0.242429
$933$	19380.6	0.680058
$934$	−21501.4	−0.753262
$935$	8320.43	0.291024
$936$	−8098.95	−0.282823
$937$	−56334.3	−1.96410	−0.982049	−	0.188626i	$-0.939597\pi$
$937$	−56334.3	−1.96410	−0.982049	+	0.188626i	$0.939597\pi$
$938$	−29978.7	−1.04354
$939$	−20452.7	−0.710807
$940$	−24773.4	−0.859595
$941$	31715.4	1.09872	0.549358	−	0.835587i	$-0.314872\pi$
$941$	31715.4	1.09872	0.549358	+	0.835587i	$0.314872\pi$
$942$	1412.43	0.0488531
$943$	−31232.3	−1.07854
$944$	−16125.1	−0.555962
$945$	6447.77	0.221954
$946$	1349.49	0.0463802
$947$	25434.8	0.872776	0.436388	−	0.899758i	$-0.356257\pi$
$947$	25434.8	0.872776	0.436388	+	0.899758i	$0.356257\pi$
$948$	−8959.80	−0.306963
$949$	−33546.0	−1.14747
$950$	10004.1	0.341660
$951$	19559.8	0.666950
$952$	−17463.2	−0.594523
$953$	12373.4	0.420580	0.210290	−	0.977639i	$-0.432559\pi$
$953$	12373.4	0.420580	0.210290	+	0.977639i	$0.432559\pi$
$954$	−600.804	−0.0203897
$955$	28490.5	0.965371
$956$	16120.7	0.545377
$957$	18729.1	0.632628
$958$	13564.3	0.457456
$959$	−29772.9	−1.00252
$960$	−1851.04	−0.0622312
$961$	58964.0	1.97925
$962$	−12688.6	−0.425258
$963$	18109.9	0.606005
$964$	33607.6	1.12285
$965$	−4340.25	−0.144785
$966$	−20176.9	−0.672031
$967$	44702.7	1.48660	0.743299	−	0.668959i	$-0.233260\pi$
$967$	44702.7	1.48660	0.743299	+	0.668959i	$0.233260\pi$
$968$	5778.37	0.191863
$969$	13939.8	0.462138
$970$	217.456	0.00719803
$971$	−49592.6	−1.63903	−0.819517	−	0.573054i	$-0.805758\pi$
$971$	−49592.6	−1.63903	−0.819517	+	0.573054i	$0.805758\pi$
$972$	1628.96	0.0537541
$973$	−11811.9	−0.389180
$974$	−9500.20	−0.312532
$975$	10373.7	0.340742
$976$	−29126.1	−0.955228
$977$	28695.9	0.939676	0.469838	−	0.882753i	$-0.344312\pi$
$977$	28695.9	0.939676	0.469838	+	0.882753i	$0.344312\pi$
$978$	11105.1	0.363090
$979$	−36564.6	−1.19368
$980$	31172.0	1.01607
$981$	2195.58	0.0714573
$982$	8858.09	0.287854
$983$	−13934.6	−0.452130	−0.226065	−	0.974112i	$-0.572586\pi$
$983$	−13934.6	−0.452130	−0.226065	+	0.974112i	$0.572586\pi$
$984$	−8142.05	−0.263780
$985$	42378.8	1.37087
$986$	7702.40	0.248777
$987$	43640.2	1.40738
$988$	49211.7	1.58465
$989$	−7272.39	−0.233821
$990$	2506.15	0.0804552
$991$	43393.1	1.39095	0.695473	−	0.718552i	$-0.255195\pi$
$991$	43393.1	1.39095	0.695473	+	0.718552i	$0.255195\pi$
$992$	−51626.5	−1.65236
$993$	−9255.28	−0.295778
$994$	26300.5	0.839236
$995$	39187.2	1.24856
$996$	−15867.8	−0.504809
$997$	12897.4	0.409694	0.204847	−	0.978794i	$-0.434330\pi$
$997$	12897.4	0.409694	0.204847	+	0.978794i	$0.434330\pi$
$998$	−17782.5	−0.564024
$999$	5597.77	0.177283

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	501.4.a.b.1.12	✓	19
3.2	odd	2		1503.4.a.b.1.8		19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
501.4.a.b.1.12	✓	19	1.1	even	1	trivial
1503.4.a.b.1.8		19	3.2	odd	2

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:	\( N \)	\(=\)	\( 501 = 3 \cdot 167 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	501.a (trivial)

\(f(q)\)	\(=\)	\(q+1.13862 q^{2} -3.00000 q^{3} -6.70355 q^{4} -7.78898 q^{5} -3.41585 q^{6} +30.6595 q^{7} -16.7417 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+1.13862 q^{2} -3.00000 q^{3} -6.70355 q^{4} -7.78898 q^{5} -3.41585 q^{6} +30.6595 q^{7} -16.7417 q^{8} +9.00000 q^{9} -8.86867 q^{10} -31.3983 q^{11} +20.1107 q^{12} +53.7510 q^{13} +34.9094 q^{14} +23.3670 q^{15} +34.5660 q^{16} +34.0219 q^{17} +10.2475 q^{18} -136.577 q^{19} +52.2139 q^{20} -91.9785 q^{21} -35.7506 q^{22} +192.660 q^{23} +50.2251 q^{24} -64.3317 q^{25} +61.2018 q^{26} -27.0000 q^{27} -205.528 q^{28} +198.833 q^{29} +26.6060 q^{30} -297.918 q^{31} +173.291 q^{32} +94.1948 q^{33} +38.7380 q^{34} -238.806 q^{35} -60.3320 q^{36} -207.325 q^{37} -155.509 q^{38} -161.253 q^{39} +130.401 q^{40} -162.111 q^{41} -104.728 q^{42} -37.7473 q^{43} +210.480 q^{44} -70.1009 q^{45} +219.365 q^{46} -474.460 q^{47} -103.698 q^{48} +597.006 q^{49} -73.2492 q^{50} -102.066 q^{51} -360.323 q^{52} -58.6290 q^{53} -30.7426 q^{54} +244.561 q^{55} -513.293 q^{56} +409.731 q^{57} +226.395 q^{58} -466.502 q^{59} -156.642 q^{60} -842.621 q^{61} -339.214 q^{62} +275.936 q^{63} -79.2161 q^{64} -418.666 q^{65} +107.252 q^{66} -858.756 q^{67} -228.068 q^{68} -577.979 q^{69} -271.909 q^{70} +753.392 q^{71} -150.675 q^{72} -624.100 q^{73} -236.063 q^{74} +192.995 q^{75} +915.550 q^{76} -962.656 q^{77} -183.605 q^{78} -445.525 q^{79} -269.234 q^{80} +81.0000 q^{81} -184.582 q^{82} -789.023 q^{83} +616.583 q^{84} -264.996 q^{85} -42.9797 q^{86} -596.500 q^{87} +525.661 q^{88} +1164.54 q^{89} -79.8180 q^{90} +1647.98 q^{91} -1291.50 q^{92} +893.753 q^{93} -540.228 q^{94} +1063.80 q^{95} -519.873 q^{96} -24.5196 q^{97} +679.761 q^{98} -282.585 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q + q^{2} - 57 q^{3} + 59 q^{4} + 12 q^{5} - 3 q^{6} - 28 q^{7} - 3 q^{8} + 171 q^{9}+O(q^{10}) \) 19 * q + q^2 - 57 * q^3 + 59 * q^4 + 12 * q^5 - 3 * q^6 - 28 * q^7 - 3 * q^8 + 171 * q^9	\( 19 q + q^{2} - 57 q^{3} + 59 q^{4} + 12 q^{5} - 3 q^{6} - 28 q^{7} - 3 q^{8} + 171 q^{9} - 69 q^{10} - 120 q^{11} - 177 q^{12} - 92 q^{13} - 69 q^{14} - 36 q^{15} + 83 q^{16} + 54 q^{17} + 9 q^{18} - 400 q^{19} - 93 q^{20} + 84 q^{21} - 273 q^{22} + 114 q^{23} + 9 q^{24} + 171 q^{25} + q^{26} - 513 q^{27} - 521 q^{28} + 72 q^{29} + 207 q^{30} - 712 q^{31} + 42 q^{32} + 360 q^{33} - 468 q^{34} - 306 q^{35} + 531 q^{36} - 448 q^{37} + 50 q^{38} + 276 q^{39} - 1030 q^{40} - 310 q^{41} + 207 q^{42} - 852 q^{43} - 757 q^{44} + 108 q^{45} - 2187 q^{46} - 1244 q^{47} - 249 q^{48} + 47 q^{49} - 1670 q^{50} - 162 q^{51} - 2548 q^{52} + 58 q^{53} - 27 q^{54} - 2190 q^{55} - 2541 q^{56} + 1200 q^{57} - 3481 q^{58} - 2736 q^{59} + 279 q^{60} - 2922 q^{61} + 486 q^{62} - 252 q^{63} - 3677 q^{64} - 380 q^{65} + 819 q^{66} - 2658 q^{67} - 1558 q^{68} - 342 q^{69} - 4887 q^{70} - 636 q^{71} - 27 q^{72} - 2304 q^{73} - 3137 q^{74} - 513 q^{75} - 6536 q^{76} + 230 q^{77} - 3 q^{78} - 2666 q^{79} - 1644 q^{80} + 1539 q^{81} - 1949 q^{82} - 2552 q^{83} + 1563 q^{84} - 2816 q^{85} - 4825 q^{86} - 216 q^{87} - 5144 q^{88} - 1136 q^{89} - 621 q^{90} - 6128 q^{91} - 755 q^{92} + 2136 q^{93} - 1776 q^{94} - 468 q^{95} - 126 q^{96} - 3560 q^{97} + 1635 q^{98} - 1080 q^{99}+O(q^{100}) \) 19 * q + q^2 - 57 * q^3 + 59 * q^4 + 12 * q^5 - 3 * q^6 - 28 * q^7 - 3 * q^8 + 171 * q^9 - 69 * q^10 - 120 * q^11 - 177 * q^12 - 92 * q^13 - 69 * q^14 - 36 * q^15 + 83 * q^16 + 54 * q^17 + 9 * q^18 - 400 * q^19 - 93 * q^20 + 84 * q^21 - 273 * q^22 + 114 * q^23 + 9 * q^24 + 171 * q^25 + q^26 - 513 * q^27 - 521 * q^28 + 72 * q^29 + 207 * q^30 - 712 * q^31 + 42 * q^32 + 360 * q^33 - 468 * q^34 - 306 * q^35 + 531 * q^36 - 448 * q^37 + 50 * q^38 + 276 * q^39 - 1030 * q^40 - 310 * q^41 + 207 * q^42 - 852 * q^43 - 757 * q^44 + 108 * q^45 - 2187 * q^46 - 1244 * q^47 - 249 * q^48 + 47 * q^49 - 1670 * q^50 - 162 * q^51 - 2548 * q^52 + 58 * q^53 - 27 * q^54 - 2190 * q^55 - 2541 * q^56 + 1200 * q^57 - 3481 * q^58 - 2736 * q^59 + 279 * q^60 - 2922 * q^61 + 486 * q^62 - 252 * q^63 - 3677 * q^64 - 380 * q^65 + 819 * q^66 - 2658 * q^67 - 1558 * q^68 - 342 * q^69 - 4887 * q^70 - 636 * q^71 - 27 * q^72 - 2304 * q^73 - 3137 * q^74 - 513 * q^75 - 6536 * q^76 + 230 * q^77 - 3 * q^78 - 2666 * q^79 - 1644 * q^80 + 1539 * q^81 - 1949 * q^82 - 2552 * q^83 + 1563 * q^84 - 2816 * q^85 - 4825 * q^86 - 216 * q^87 - 5144 * q^88 - 1136 * q^89 - 621 * q^90 - 6128 * q^91 - 755 * q^92 + 2136 * q^93 - 1776 * q^94 - 468 * q^95 - 126 * q^96 - 3560 * q^97 + 1635 * q^98 - 1080 * q^99

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