LMFDB - Embedded newform 2001.4.a.h.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2001,4,Mod(1,2001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2001, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("2001.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2001 = 3 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2001.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:	$118.062821921$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	2001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.18892 q^{2} +3.00000 q^{3} -3.20863 q^{4} +10.5230 q^{5} -6.56676 q^{6} +30.7082 q^{7} +24.5348 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.18892 q^{2} +3.00000 q^{3} -3.20863 q^{4} +10.5230 q^{5} -6.56676 q^{6} +30.7082 q^{7} +24.5348 q^{8} +9.00000 q^{9} -23.0341 q^{10} -12.4931 q^{11} -9.62589 q^{12} +71.5574 q^{13} -67.2177 q^{14} +31.5691 q^{15} -28.0357 q^{16} -7.40252 q^{17} -19.7003 q^{18} -74.5110 q^{19} -33.7646 q^{20} +92.1245 q^{21} +27.3464 q^{22} +23.0000 q^{23} +73.6044 q^{24} -14.2655 q^{25} -156.634 q^{26} +27.0000 q^{27} -98.5312 q^{28} -29.0000 q^{29} -69.1023 q^{30} +297.563 q^{31} -134.911 q^{32} -37.4793 q^{33} +16.2035 q^{34} +323.144 q^{35} -28.8777 q^{36} +128.865 q^{37} +163.099 q^{38} +214.672 q^{39} +258.181 q^{40} +416.593 q^{41} -201.653 q^{42} +197.851 q^{43} +40.0857 q^{44} +94.7074 q^{45} -50.3452 q^{46} -48.3569 q^{47} -84.1070 q^{48} +599.992 q^{49} +31.2260 q^{50} -22.2076 q^{51} -229.601 q^{52} -251.839 q^{53} -59.1008 q^{54} -131.465 q^{55} +753.419 q^{56} -223.533 q^{57} +63.4787 q^{58} -578.780 q^{59} -101.294 q^{60} +590.197 q^{61} -651.342 q^{62} +276.374 q^{63} +519.594 q^{64} +753.002 q^{65} +82.0392 q^{66} -442.009 q^{67} +23.7519 q^{68} +69.0000 q^{69} -707.335 q^{70} +264.326 q^{71} +220.813 q^{72} +95.8959 q^{73} -282.075 q^{74} -42.7965 q^{75} +239.078 q^{76} -383.640 q^{77} -469.901 q^{78} +84.0406 q^{79} -295.021 q^{80} +81.0000 q^{81} -911.888 q^{82} +1033.13 q^{83} -295.593 q^{84} -77.8971 q^{85} -433.080 q^{86} -87.0000 q^{87} -306.516 q^{88} -615.481 q^{89} -207.307 q^{90} +2197.40 q^{91} -73.7985 q^{92} +892.689 q^{93} +105.849 q^{94} -784.083 q^{95} -404.732 q^{96} -1465.26 q^{97} -1313.33 q^{98} -112.438 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 6 q^{2} + 132 q^{3} + 210 q^{4} + 15 q^{5} + 18 q^{6} + 78 q^{7} + 12 q^{8} + 396 q^{9}+O(q^{10}) $ 44 * q + 6 * q^2 + 132 * q^3 + 210 * q^4 + 15 * q^5 + 18 * q^6 + 78 * q^7 + 12 * q^8 + 396 * q^9	\( 44 q + 6 q^{2} + 132 q^{3} + 210 q^{4} + 15 q^{5} + 18 q^{6} + 78 q^{7} + 12 q^{8} + 396 q^{9} + 214 q^{10} + 111 q^{11} + 630 q^{12} + 275 q^{13} + 104 q^{14} + 45 q^{15} + 1062 q^{16} - 58 q^{17} + 54 q^{18} + 331 q^{19} + 287 q^{20} + 234 q^{21} + 285 q^{22} + 1012 q^{23} + 36 q^{24} + 1903 q^{25} + 1084 q^{26} + 1188 q^{27} + 222 q^{28} - 1276 q^{29} + 642 q^{30} + 1394 q^{31} + 42 q^{32} + 333 q^{33} + 373 q^{34} + 567 q^{35} + 1890 q^{36} + 1229 q^{37} + 733 q^{38} + 825 q^{39} + 2483 q^{40} - 107 q^{41} + 312 q^{42} + 1165 q^{43} + 1639 q^{44} + 135 q^{45} + 138 q^{46} + 964 q^{47} + 3186 q^{48} + 4264 q^{49} + 495 q^{50} - 174 q^{51} + 2679 q^{52} - 380 q^{53} + 162 q^{54} + 1260 q^{55} + 2229 q^{56} + 993 q^{57} - 174 q^{58} + 897 q^{59} + 861 q^{60} + 2584 q^{61} + 3034 q^{62} + 702 q^{63} + 6866 q^{64} - 286 q^{65} + 855 q^{66} + 2277 q^{67} - 1554 q^{68} + 3036 q^{69} + 689 q^{70} + 4304 q^{71} + 108 q^{72} + 4712 q^{73} - 1005 q^{74} + 5709 q^{75} + 2877 q^{76} + 919 q^{77} + 3252 q^{78} + 3864 q^{79} + 2593 q^{80} + 3564 q^{81} + 3297 q^{82} - 540 q^{83} + 666 q^{84} + 6537 q^{85} + 3789 q^{86} - 3828 q^{87} + 1707 q^{88} - 331 q^{89} + 1926 q^{90} + 4311 q^{91} + 4830 q^{92} + 4182 q^{93} + 6189 q^{94} + 3267 q^{95} + 126 q^{96} + 5572 q^{97} + 2588 q^{98} + 999 q^{99}+O(q^{100}) \) 44 * q + 6 * q^2 + 132 * q^3 + 210 * q^4 + 15 * q^5 + 18 * q^6 + 78 * q^7 + 12 * q^8 + 396 * q^9 + 214 * q^10 + 111 * q^11 + 630 * q^12 + 275 * q^13 + 104 * q^14 + 45 * q^15 + 1062 * q^16 - 58 * q^17 + 54 * q^18 + 331 * q^19 + 287 * q^20 + 234 * q^21 + 285 * q^22 + 1012 * q^23 + 36 * q^24 + 1903 * q^25 + 1084 * q^26 + 1188 * q^27 + 222 * q^28 - 1276 * q^29 + 642 * q^30 + 1394 * q^31 + 42 * q^32 + 333 * q^33 + 373 * q^34 + 567 * q^35 + 1890 * q^36 + 1229 * q^37 + 733 * q^38 + 825 * q^39 + 2483 * q^40 - 107 * q^41 + 312 * q^42 + 1165 * q^43 + 1639 * q^44 + 135 * q^45 + 138 * q^46 + 964 * q^47 + 3186 * q^48 + 4264 * q^49 + 495 * q^50 - 174 * q^51 + 2679 * q^52 - 380 * q^53 + 162 * q^54 + 1260 * q^55 + 2229 * q^56 + 993 * q^57 - 174 * q^58 + 897 * q^59 + 861 * q^60 + 2584 * q^61 + 3034 * q^62 + 702 * q^63 + 6866 * q^64 - 286 * q^65 + 855 * q^66 + 2277 * q^67 - 1554 * q^68 + 3036 * q^69 + 689 * q^70 + 4304 * q^71 + 108 * q^72 + 4712 * q^73 - 1005 * q^74 + 5709 * q^75 + 2877 * q^76 + 919 * q^77 + 3252 * q^78 + 3864 * q^79 + 2593 * q^80 + 3564 * q^81 + 3297 * q^82 - 540 * q^83 + 666 * q^84 + 6537 * q^85 + 3789 * q^86 - 3828 * q^87 + 1707 * q^88 - 331 * q^89 + 1926 * q^90 + 4311 * q^91 + 4830 * q^92 + 4182 * q^93 + 6189 * q^94 + 3267 * q^95 + 126 * q^96 + 5572 * q^97 + 2588 * q^98 + 999 * 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 $

$2$	−2.18892	−0.773900	−0.386950	−	0.922101i	$-0.626471\pi$
$2$	−2.18892	−0.773900	−0.386950	+	0.922101i	$0.626471\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−3.20863	−0.401079
$5$	10.5230	0.941210	0.470605	−	0.882344i	$-0.344036\pi$
$5$	10.5230	0.941210	0.470605	+	0.882344i	$0.344036\pi$
$6$	−6.56676	−0.446811
$7$	30.7082	1.65809	0.829043	−	0.559185i	$-0.188886\pi$
$7$	30.7082	1.65809	0.829043	+	0.559185i	$0.188886\pi$
$8$	24.5348	1.08429
$9$	9.00000	0.333333
$10$	−23.0341	−0.728402
$11$	−12.4931	−0.342437	−0.171219	−	0.985233i	$-0.554770\pi$
$11$	−12.4931	−0.342437	−0.171219	+	0.985233i	$0.554770\pi$
$12$	−9.62589	−0.231563
$13$	71.5574	1.52665	0.763326	−	0.646014i	$-0.223565\pi$
$13$	71.5574	1.52665	0.763326	+	0.646014i	$0.223565\pi$
$14$	−67.2177	−1.28319
$15$	31.5691	0.543408
$16$	−28.0357	−0.438057
$17$	−7.40252	−0.105610	−0.0528051	−	0.998605i	$-0.516816\pi$
$17$	−7.40252	−0.105610	−0.0528051	+	0.998605i	$0.516816\pi$
$18$	−19.7003	−0.257967
$19$	−74.5110	−0.899684	−0.449842	−	0.893108i	$-0.648520\pi$
$19$	−74.5110	−0.899684	−0.449842	+	0.893108i	$0.648520\pi$
$20$	−33.7646	−0.377499
$21$	92.1245	0.957296
$22$	27.3464	0.265012
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	73.6044	0.626018
$25$	−14.2655	−0.114124
$26$	−156.634	−1.18148
$27$	27.0000	0.192450
$28$	−98.5312	−0.665023
$29$	−29.0000	−0.185695
$29$	−29.0000	−0.185695
$30$	−69.1023	−0.420543
$31$	297.563	1.72400	0.861999	−	0.506910i	$-0.169213\pi$
$31$	297.563	1.72400	0.861999	+	0.506910i	$0.169213\pi$
$32$	−134.911	−0.745282
$33$	−37.4793	−0.197706
$34$	16.2035	0.0817318
$35$	323.144	1.56061
$36$	−28.8777	−0.133693
$37$	128.865	0.572575	0.286287	−	0.958144i	$-0.407579\pi$
$37$	128.865	0.572575	0.286287	+	0.958144i	$0.407579\pi$
$38$	163.099	0.696266
$39$	214.672	0.881412
$40$	258.181	1.02055
$41$	416.593	1.58685	0.793425	−	0.608668i	$-0.208296\pi$
$41$	416.593	1.58685	0.793425	+	0.608668i	$0.208296\pi$
$42$	−201.653	−0.740851
$43$	197.851	0.701675	0.350837	−	0.936436i	$-0.385897\pi$
$43$	197.851	0.701675	0.350837	+	0.936436i	$0.385897\pi$
$44$	40.0857	0.137344
$45$	94.7074	0.313737
$46$	−50.3452	−0.161369
$47$	−48.3569	−0.150076	−0.0750381	−	0.997181i	$-0.523908\pi$
$47$	−48.3569	−0.150076	−0.0750381	+	0.997181i	$0.523908\pi$
$48$	−84.1070	−0.252912
$49$	599.992	1.74925
$50$	31.2260	0.0883206
$51$	−22.2076	−0.0609741
$52$	−229.601	−0.612307
$53$	−251.839	−0.652694	−0.326347	−	0.945250i	$-0.605818\pi$
$53$	−251.839	−0.652694	−0.326347	+	0.945250i	$0.605818\pi$
$54$	−59.1008	−0.148937
$55$	−131.465	−0.322305
$56$	753.419	1.79785
$57$	−223.533	−0.519433
$58$	63.4787	0.143710
$59$	−578.780	−1.27713	−0.638565	−	0.769568i	$-0.720472\pi$
$59$	−578.780	−1.27713	−0.638565	+	0.769568i	$0.720472\pi$
$60$	−101.294	−0.217949
$61$	590.197	1.23880	0.619401	−	0.785075i	$-0.287375\pi$
$61$	590.197	1.23880	0.619401	+	0.785075i	$0.287375\pi$
$62$	−651.342	−1.33420
$63$	276.374	0.552695
$64$	519.594	1.01483
$65$	753.002	1.43690
$66$	82.0392	0.153005
$67$	−442.009	−0.805970	−0.402985	−	0.915207i	$-0.632027\pi$
$67$	−442.009	−0.805970	−0.402985	+	0.915207i	$0.632027\pi$
$68$	23.7519	0.0423580
$69$	69.0000	0.120386
$70$	−707.335	−1.20775
$71$	264.326	0.441828	0.220914	−	0.975293i	$-0.429096\pi$
$71$	264.326	0.441828	0.220914	+	0.975293i	$0.429096\pi$
$72$	220.813	0.361432
$73$	95.8959	0.153750	0.0768751	−	0.997041i	$-0.475506\pi$
$73$	95.8959	0.153750	0.0768751	+	0.997041i	$0.475506\pi$
$74$	−282.075	−0.443115
$75$	−42.7965	−0.0658895
$76$	239.078	0.360844
$77$	−383.640	−0.567790
$78$	−469.901	−0.682125
$79$	84.0406	0.119687	0.0598437	−	0.998208i	$-0.480940\pi$
$79$	84.0406	0.119687	0.0598437	+	0.998208i	$0.480940\pi$
$80$	−295.021	−0.412304
$81$	81.0000	0.111111
$82$	−911.888	−1.22806
$83$	1033.13	1.36627	0.683134	−	0.730293i	$-0.260616\pi$
$83$	1033.13	1.36627	0.683134	+	0.730293i	$0.260616\pi$
$84$	−295.593	−0.383951
$85$	−77.8971	−0.0994014
$86$	−433.080	−0.543026
$87$	−87.0000	−0.107211
$88$	−306.516	−0.371303
$89$	−615.481	−0.733043	−0.366521	−	0.930410i	$-0.619451\pi$
$89$	−615.481	−0.733043	−0.366521	+	0.930410i	$0.619451\pi$
$90$	−207.307	−0.242801
$91$	2197.40	2.53132
$92$	−73.7985	−0.0836307
$93$	892.689	0.995350
$94$	105.849	0.116144
$95$	−784.083	−0.846792
$96$	−404.732	−0.430289
$97$	−1465.26	−1.53375	−0.766877	−	0.641794i	$-0.778190\pi$
$97$	−1465.26	−1.53375	−0.766877	+	0.641794i	$0.778190\pi$
$98$	−1313.33	−1.35374
$99$	−112.438	−0.114146
$100$	45.7727	0.0457727
$101$	570.942	0.562484	0.281242	−	0.959637i	$-0.409254\pi$
$101$	570.942	0.562484	0.281242	+	0.959637i	$0.409254\pi$
$102$	48.6106	0.0471879
$103$	−516.102	−0.493719	−0.246860	−	0.969051i	$-0.579399\pi$
$103$	−516.102	−0.493719	−0.246860	+	0.969051i	$0.579399\pi$
$104$	1755.65	1.65534
$105$	969.431	0.901016
$106$	551.256	0.505120
$107$	223.313	0.201761	0.100881	−	0.994899i	$-0.467834\pi$
$107$	223.313	0.201761	0.100881	+	0.994899i	$0.467834\pi$
$108$	−86.6330	−0.0771876
$109$	−487.957	−0.428787	−0.214394	−	0.976747i	$-0.568778\pi$
$109$	−487.957	−0.428787	−0.214394	+	0.976747i	$0.568778\pi$
$110$	287.767	0.249432
$111$	386.595	0.330576
$112$	−860.924	−0.726336
$113$	21.5983	0.0179805	0.00899026	−	0.999960i	$-0.497138\pi$
$113$	21.5983	0.0179805	0.00899026	+	0.999960i	$0.497138\pi$
$114$	489.296	0.401989
$115$	242.030	0.196256
$116$	93.0503	0.0744784
$117$	644.017	0.508884
$118$	1266.90	0.988372
$119$	−227.318	−0.175111
$120$	774.542	0.589214
$121$	−1174.92	−0.882737
$122$	−1291.89	−0.958709
$123$	1249.78	0.916168
$124$	−954.770	−0.691459
$125$	−1465.50	−1.04862
$126$	−604.960	−0.427731
$127$	1298.40	0.907199	0.453599	−	0.891206i	$-0.350140\pi$
$127$	1298.40	0.907199	0.453599	+	0.891206i	$0.350140\pi$
$128$	−58.0645	−0.0400955
$129$	593.553	0.405112
$130$	−1648.26	−1.11202
$131$	−793.336	−0.529115	−0.264558	−	0.964370i	$-0.585226\pi$
$131$	−793.336	−0.529115	−0.264558	+	0.964370i	$0.585226\pi$
$132$	120.257	0.0792958
$133$	−2288.10	−1.49175
$134$	967.522	0.623740
$135$	284.122	0.181136
$136$	−181.619	−0.114513
$137$	−2707.70	−1.68857	−0.844287	−	0.535891i	$-0.819976\pi$
$137$	−2707.70	−1.68857	−0.844287	+	0.535891i	$0.819976\pi$
$138$	−151.035	−0.0931666
$139$	−1781.69	−1.08720	−0.543600	−	0.839344i	$-0.682939\pi$
$139$	−1781.69	−1.08720	−0.543600	+	0.839344i	$0.682939\pi$
$140$	−1036.85	−0.625926
$141$	−145.071	−0.0866466
$142$	−578.589	−0.341930
$143$	−893.974	−0.522782
$144$	−252.321	−0.146019
$145$	−305.168	−0.174778
$146$	−209.908	−0.118987
$147$	1799.98	1.00993
$148$	−413.480	−0.229647
$149$	1647.75	0.905967	0.452983	−	0.891519i	$-0.350360\pi$
$149$	1647.75	0.905967	0.452983	+	0.891519i	$0.350360\pi$
$150$	93.6781	0.0509919
$151$	1039.06	0.559985	0.279992	−	0.960002i	$-0.409668\pi$
$151$	1039.06	0.559985	0.279992	+	0.960002i	$0.409668\pi$
$152$	−1828.11	−0.975523
$153$	−66.6227	−0.0352034
$154$	839.758	0.439413
$155$	3131.27	1.62264
$156$	−688.804	−0.353516
$157$	215.144	0.109365	0.0546827	−	0.998504i	$-0.482585\pi$
$157$	215.144	0.109365	0.0546827	+	0.998504i	$0.482585\pi$
$158$	−183.958	−0.0926261
$159$	−755.518	−0.376833
$160$	−1419.67	−0.701467
$161$	706.288	0.345735
$162$	−177.303	−0.0859889
$163$	−846.810	−0.406916	−0.203458	−	0.979084i	$-0.565218\pi$
$163$	−846.810	−0.406916	−0.203458	+	0.979084i	$0.565218\pi$
$164$	−1336.69	−0.636452
$165$	−394.396	−0.186083
$166$	−2261.43	−1.05735
$167$	−2504.62	−1.16056	−0.580280	−	0.814417i	$-0.697057\pi$
$167$	−2504.62	−1.16056	−0.580280	+	0.814417i	$0.697057\pi$
$168$	2260.26	1.03799
$169$	2923.47	1.33066
$170$	170.510	0.0769268
$171$	−670.599	−0.299895
$172$	−634.831	−0.281427
$173$	3164.02	1.39050	0.695248	−	0.718770i	$-0.255295\pi$
$173$	3164.02	1.39050	0.695248	+	0.718770i	$0.255295\pi$
$174$	190.436	0.0829708
$175$	−438.068	−0.189227
$176$	350.252	0.150007
$177$	−1736.34	−0.737352
$178$	1347.24	0.567302
$179$	960.895	0.401233	0.200616	−	0.979670i	$-0.435706\pi$
$179$	960.895	0.401233	0.200616	+	0.979670i	$0.435706\pi$
$180$	−303.881	−0.125833
$181$	3078.72	1.26430	0.632152	−	0.774844i	$-0.282172\pi$
$181$	3078.72	1.26430	0.632152	+	0.774844i	$0.282172\pi$
$182$	−4809.93	−1.95899
$183$	1770.59	0.715223
$184$	564.300	0.226091
$185$	1356.05	0.538913
$186$	−1954.03	−0.770302
$187$	92.4804	0.0361649
$188$	155.160	0.0601924
$189$	829.121	0.319099
$190$	1716.29	0.655332
$191$	4296.84	1.62779	0.813897	−	0.581009i	$-0.197342\pi$
$191$	4296.84	1.62779	0.813897	+	0.581009i	$0.197342\pi$
$192$	1558.78	0.585913
$193$	−1851.36	−0.690486	−0.345243	−	0.938513i	$-0.612204\pi$
$193$	−1851.36	−0.690486	−0.345243	+	0.938513i	$0.612204\pi$
$194$	3207.33	1.18697
$195$	2259.01	0.829594
$196$	−1925.15	−0.701586
$197$	2856.88	1.03322	0.516611	−	0.856220i	$-0.327193\pi$
$197$	2856.88	1.03322	0.516611	+	0.856220i	$0.327193\pi$
$198$	246.118	0.0883374
$199$	−1868.01	−0.665425	−0.332712	−	0.943028i	$-0.607964\pi$
$199$	−1868.01	−0.665425	−0.332712	+	0.943028i	$0.607964\pi$
$200$	−350.001	−0.123744
$201$	−1326.03	−0.465327
$202$	−1249.75	−0.435306
$203$	−890.537	−0.307899
$204$	71.2558	0.0244554
$205$	4383.82	1.49356
$206$	1129.71	0.382089
$207$	207.000	0.0695048
$208$	−2006.16	−0.668760
$209$	930.873	0.308085
$210$	−2122.01	−0.697297
$211$	2135.23	0.696660	0.348330	−	0.937372i	$-0.386749\pi$
$211$	2135.23	0.696660	0.348330	+	0.937372i	$0.386749\pi$
$212$	808.059	0.261782
$213$	792.979	0.255089
$214$	−488.814	−0.156143
$215$	2082.00	0.660423
$216$	662.439	0.208673
$217$	9137.62	2.85854
$218$	1068.10	0.331838
$219$	287.688	0.0887677
$220$	421.824	0.129270
$221$	−529.705	−0.161230
$222$	−846.225	−0.255833
$223$	4558.79	1.36896	0.684482	−	0.729030i	$-0.260028\pi$
$223$	4558.79	1.36896	0.684482	+	0.729030i	$0.260028\pi$
$224$	−4142.86	−1.23574
$225$	−128.390	−0.0380413
$226$	−47.2770	−0.0139151
$227$	−1504.71	−0.439961	−0.219980	−	0.975504i	$-0.570599\pi$
$227$	−1504.71	−0.439961	−0.219980	+	0.975504i	$0.570599\pi$
$228$	717.235	0.208333
$229$	−6240.41	−1.80078	−0.900388	−	0.435088i	$-0.856717\pi$
$229$	−6240.41	−1.80078	−0.900388	+	0.435088i	$0.856717\pi$
$230$	−529.784	−0.151882
$231$	−1150.92	−0.327814
$232$	−711.509	−0.201349
$233$	−3598.03	−1.01165	−0.505826	−	0.862636i	$-0.668812\pi$
$233$	−3598.03	−1.01165	−0.505826	+	0.862636i	$0.668812\pi$
$234$	−1409.70	−0.393825
$235$	−508.862	−0.141253
$236$	1857.09	0.512230
$237$	252.122	0.0691015
$238$	497.581	0.135518
$239$	−3538.06	−0.957565	−0.478783	−	0.877933i	$-0.658922\pi$
$239$	−3538.06	−0.957565	−0.478783	+	0.877933i	$0.658922\pi$
$240$	−885.062	−0.238044
$241$	2541.62	0.679336	0.339668	−	0.940545i	$-0.389685\pi$
$241$	2541.62	0.679336	0.339668	+	0.940545i	$0.389685\pi$
$242$	2571.81	0.683150
$243$	243.000	0.0641500
$244$	−1893.72	−0.496857
$245$	6313.74	1.64641
$246$	−2735.66	−0.709023
$247$	−5331.82	−1.37350
$248$	7300.65	1.86932
$249$	3099.38	0.788815
$250$	3207.86	0.811531
$251$	−5718.01	−1.43792	−0.718959	−	0.695053i	$-0.755381\pi$
$251$	−5718.01	−1.43792	−0.718959	+	0.695053i	$0.755381\pi$
$252$	−886.780	−0.221674
$253$	−287.341	−0.0714031
$254$	−2842.09	−0.702081
$255$	−233.691	−0.0573894
$256$	−4029.65	−0.983801
$257$	4730.26	1.14812	0.574058	−	0.818815i	$-0.305368\pi$
$257$	4730.26	1.14812	0.574058	+	0.818815i	$0.305368\pi$
$258$	−1299.24	−0.313516
$259$	3957.21	0.949378
$260$	−2416.11	−0.576310
$261$	−261.000	−0.0618984
$262$	1736.55	0.409482
$263$	−3744.86	−0.878016	−0.439008	−	0.898483i	$-0.644670\pi$
$263$	−3744.86	−0.878016	−0.439008	+	0.898483i	$0.644670\pi$
$264$	−919.547	−0.214372
$265$	−2650.12	−0.614322
$266$	5008.46	1.15447
$267$	−1846.44	−0.423222
$268$	1418.24	0.323257
$269$	1446.95	0.327964	0.163982	−	0.986463i	$-0.447566\pi$
$269$	1446.95	0.327964	0.163982	+	0.986463i	$0.447566\pi$
$270$	−621.921	−0.140181
$271$	7519.68	1.68556	0.842782	−	0.538255i	$-0.180916\pi$
$271$	7519.68	1.68556	0.842782	+	0.538255i	$0.180916\pi$
$272$	207.535	0.0462633
$273$	6592.20	1.46146
$274$	5926.95	1.30679
$275$	178.220	0.0390803
$276$	−221.395	−0.0482842
$277$	3824.86	0.829652	0.414826	−	0.909901i	$-0.363842\pi$
$277$	3824.86	0.829652	0.414826	+	0.909901i	$0.363842\pi$
$278$	3899.97	0.841384
$279$	2678.07	0.574666
$280$	7928.26	1.69216
$281$	−8291.97	−1.76035	−0.880174	−	0.474651i	$-0.842574\pi$
$281$	−8291.97	−1.76035	−0.880174	+	0.474651i	$0.842574\pi$
$282$	317.548	0.0670558
$283$	−7203.46	−1.51308	−0.756539	−	0.653948i	$-0.773111\pi$
$283$	−7203.46	−1.51308	−0.756539	+	0.653948i	$0.773111\pi$
$284$	−848.125	−0.177208
$285$	−2352.25	−0.488895
$286$	1956.84	0.404581
$287$	12792.8	2.63113
$288$	−1214.19	−0.248427
$289$	−4858.20	−0.988846
$290$	667.989	0.135261
$291$	−4395.77	−0.885513
$292$	−307.694	−0.0616659
$293$	−8154.38	−1.62588	−0.812942	−	0.582345i	$-0.802135\pi$
$293$	−8154.38	−1.62588	−0.812942	+	0.582345i	$0.802135\pi$
$294$	−3940.00	−0.781584
$295$	−6090.53	−1.20205
$296$	3161.67	0.620840
$297$	−337.314	−0.0659021
$298$	−3606.79	−0.701128
$299$	1645.82	0.318329
$300$	137.318	0.0264269
$301$	6075.65	1.16344
$302$	−2274.42	−0.433372
$303$	1712.83	0.324750
$304$	2088.97	0.394113
$305$	6210.67	1.16597
$306$	145.832	0.0272439
$307$	5363.86	0.997172	0.498586	−	0.866840i	$-0.333853\pi$
$307$	5363.86	0.997172	0.498586	+	0.866840i	$0.333853\pi$
$308$	1230.96	0.227729
$309$	−1548.31	−0.285049
$310$	−6854.10	−1.25576
$311$	8078.83	1.47302	0.736509	−	0.676428i	$-0.236473\pi$
$311$	8078.83	1.47302	0.736509	+	0.676428i	$0.236473\pi$
$312$	5266.94	0.955711
$313$	309.452	0.0558826	0.0279413	−	0.999610i	$-0.491105\pi$
$313$	309.452	0.0558826	0.0279413	+	0.999610i	$0.491105\pi$
$314$	−470.933	−0.0846379
$315$	2908.29	0.520202
$316$	−269.655	−0.0480041
$317$	−5031.64	−0.891499	−0.445750	−	0.895158i	$-0.647063\pi$
$317$	−5031.64	−0.891499	−0.445750	+	0.895158i	$0.647063\pi$
$318$	1653.77	0.291631
$319$	362.300	0.0635890
$320$	5467.71	0.955169
$321$	669.939	0.116487
$322$	−1546.01	−0.267564
$323$	551.569	0.0950159
$324$	−259.899	−0.0445643
$325$	−1020.80	−0.174228
$326$	1853.60	0.314912
$327$	−1463.87	−0.247560
$328$	10221.0	1.72061
$329$	−1484.95	−0.248839
$330$	863.302	0.144010
$331$	−2107.50	−0.349966	−0.174983	−	0.984571i	$-0.555987\pi$
$331$	−2107.50	−0.349966	−0.174983	+	0.984571i	$0.555987\pi$
$332$	−3314.92	−0.547981
$333$	1159.78	0.190858
$334$	5482.42	0.898158
$335$	−4651.28	−0.758587
$336$	−2582.77	−0.419350
$337$	2259.16	0.365175	0.182588	−	0.983190i	$-0.441553\pi$
$337$	2259.16	0.365175	0.182588	+	0.983190i	$0.441553\pi$
$338$	−6399.24	−1.02980
$339$	64.7950	0.0103811
$340$	249.943	0.0398678
$341$	−3717.49	−0.590361
$342$	1467.89	0.232089
$343$	7891.75	1.24232
$344$	4854.24	0.760822
$345$	726.090	0.113308
$346$	−6925.78	−1.07610
$347$	8518.39	1.31784	0.658921	−	0.752212i	$-0.271013\pi$
$347$	8518.39	1.31784	0.658921	+	0.752212i	$0.271013\pi$
$348$	279.151	0.0430002
$349$	3130.15	0.480096	0.240048	−	0.970761i	$-0.422837\pi$
$349$	3130.15	0.480096	0.240048	+	0.970761i	$0.422837\pi$
$350$	958.895	0.146443
$351$	1932.05	0.293804
$352$	1685.45	0.255213
$353$	−1188.22	−0.179157	−0.0895784	−	0.995980i	$-0.528552\pi$
$353$	−1188.22	−0.179157	−0.0895784	+	0.995980i	$0.528552\pi$
$354$	3800.71	0.570637
$355$	2781.52	0.415852
$356$	1974.85	0.294008
$357$	−681.954	−0.101100
$358$	−2103.32	−0.310514
$359$	5389.50	0.792332	0.396166	−	0.918179i	$-0.370341\pi$
$359$	5389.50	0.792332	0.396166	+	0.918179i	$0.370341\pi$
$360$	2323.63	0.340183
$361$	−1307.11	−0.190568
$362$	−6739.06	−0.978445
$363$	−3524.77	−0.509648
$364$	−7050.64	−1.01526
$365$	1009.12	0.144711
$366$	−3875.68	−0.553511
$367$	9317.62	1.32527	0.662637	−	0.748940i	$-0.269437\pi$
$367$	9317.62	1.32527	0.662637	+	0.748940i	$0.269437\pi$
$368$	−644.820	−0.0913412
$369$	3749.33	0.528950
$370$	−2968.29	−0.417065
$371$	−7733.53	−1.08222
$372$	−2864.31	−0.399214
$373$	13058.5	1.81271	0.906356	−	0.422516i	$-0.138853\pi$
$373$	13058.5	1.81271	0.906356	+	0.422516i	$0.138853\pi$
$374$	−202.432	−0.0279880
$375$	−4396.49	−0.605424
$376$	−1186.43	−0.162727
$377$	−2075.17	−0.283492
$378$	−1814.88	−0.246950
$379$	3342.94	0.453075	0.226537	−	0.974002i	$-0.427259\pi$
$379$	3342.94	0.453075	0.226537	+	0.974002i	$0.427259\pi$
$380$	2515.83	0.339630
$381$	3895.20	0.523771
$382$	−9405.44	−1.25975
$383$	−10807.7	−1.44191	−0.720953	−	0.692984i	$-0.756296\pi$
$383$	−10807.7	−1.44191	−0.720953	+	0.692984i	$0.756296\pi$
$384$	−174.194	−0.0231492
$385$	−4037.06	−0.534410
$386$	4052.48	0.534367
$387$	1780.66	0.233892
$388$	4701.46	0.615156
$389$	−11343.3	−1.47848	−0.739241	−	0.673441i	$-0.764815\pi$
$389$	−11343.3	−1.47848	−0.739241	+	0.673441i	$0.764815\pi$
$390$	−4944.79	−0.642023
$391$	−170.258	−0.0220213
$392$	14720.7	1.89670
$393$	−2380.01	−0.305485
$394$	−6253.49	−0.799610
$395$	884.363	0.112651
$396$	360.772	0.0457814
$397$	8915.62	1.12711	0.563554	−	0.826079i	$-0.309434\pi$
$397$	8915.62	1.12711	0.563554	+	0.826079i	$0.309434\pi$
$398$	4088.92	0.514972
$399$	−6864.29	−0.861264
$400$	399.943	0.0499929
$401$	475.335	0.0591947	0.0295974	−	0.999562i	$-0.490577\pi$
$401$	475.335	0.0591947	0.0295974	+	0.999562i	$0.490577\pi$
$402$	2902.57	0.360117
$403$	21292.9	2.63194
$404$	−1831.94	−0.225600
$405$	852.367	0.104579
$406$	1949.31	0.238283
$407$	−1609.92	−0.196071
$408$	−544.858	−0.0661139
$409$	1326.13	0.160325	0.0801626	−	0.996782i	$-0.474456\pi$
$409$	1326.13	0.160325	0.0801626	+	0.996782i	$0.474456\pi$
$410$	−9595.84	−1.15587
$411$	−8123.11	−0.974899
$412$	1655.98	0.198020
$413$	−17773.3	−2.11759
$414$	−453.106	−0.0537898
$415$	10871.6	1.28594
$416$	−9653.85	−1.13779
$417$	−5345.06	−0.627695
$418$	−2037.61	−0.238427
$419$	−861.676	−0.100467	−0.0502334	−	0.998738i	$-0.515997\pi$
$419$	−861.676	−0.100467	−0.0502334	+	0.998738i	$0.515997\pi$
$420$	−3110.54	−0.361379
$421$	−7210.49	−0.834722	−0.417361	−	0.908741i	$-0.637045\pi$
$421$	−7210.49	−0.834722	−0.417361	+	0.908741i	$0.637045\pi$
$422$	−4673.84	−0.539145
$423$	−435.213	−0.0500254
$424$	−6178.83	−0.707713
$425$	105.601	0.0120527
$426$	−1735.77	−0.197414
$427$	18123.9	2.05404
$428$	−716.529	−0.0809222
$429$	−2681.92	−0.301829
$430$	−4557.32	−0.511102
$431$	−11044.4	−1.23432	−0.617158	−	0.786840i	$-0.711716\pi$
$431$	−11044.4	−1.23432	−0.617158	+	0.786840i	$0.711716\pi$
$432$	−756.963	−0.0843041
$433$	11298.1	1.25393	0.626964	−	0.779048i	$-0.284297\pi$
$433$	11298.1	1.25393	0.626964	+	0.779048i	$0.284297\pi$
$434$	−20001.5	−2.21222
$435$	−915.505	−0.100908
$436$	1565.67	0.171977
$437$	−1713.75	−0.187597
$438$	−629.725	−0.0686973
$439$	−4357.47	−0.473737	−0.236869	−	0.971542i	$-0.576121\pi$
$439$	−4357.47	−0.473737	−0.236869	+	0.971542i	$0.576121\pi$
$440$	−3225.48	−0.349474
$441$	5399.93	0.583082
$442$	1159.48	0.124776
$443$	1466.60	0.157292	0.0786459	−	0.996903i	$-0.474940\pi$
$443$	1466.60	0.157292	0.0786459	+	0.996903i	$0.474940\pi$
$444$	−1240.44	−0.132587
$445$	−6476.73	−0.689947
$446$	−9978.82	−1.05944
$447$	4943.25	0.523060
$448$	15955.8	1.68268
$449$	7717.99	0.811213	0.405606	−	0.914048i	$-0.367060\pi$
$449$	7717.99	0.811213	0.405606	+	0.914048i	$0.367060\pi$
$450$	281.034	0.0294402
$451$	−5204.53	−0.543397
$452$	−69.3010	−0.00721160
$453$	3117.19	0.323307
$454$	3293.69	0.340486
$455$	23123.3	2.38250
$456$	−5484.34	−0.563218
$457$	14853.2	1.52036	0.760181	−	0.649712i	$-0.225110\pi$
$457$	14853.2	1.52036	0.760181	+	0.649712i	$0.225110\pi$
$458$	13659.8	1.39362
$459$	−199.868	−0.0203247
$460$	−776.585	−0.0787140
$461$	−13192.1	−1.33279	−0.666396	−	0.745598i	$-0.732164\pi$
$461$	−13192.1	−1.33279	−0.666396	+	0.745598i	$0.732164\pi$
$462$	2519.27	0.253695
$463$	10105.9	1.01439	0.507195	−	0.861831i	$-0.330682\pi$
$463$	10105.9	1.01439	0.507195	+	0.861831i	$0.330682\pi$
$464$	813.034	0.0813452
$465$	9393.81	0.936834
$466$	7875.80	0.782917
$467$	6069.53	0.601422	0.300711	−	0.953715i	$-0.402776\pi$
$467$	6069.53	0.601422	0.300711	+	0.953715i	$0.402776\pi$
$468$	−2066.41	−0.204102
$469$	−13573.3	−1.33637
$470$	1113.86	0.109316
$471$	645.432	0.0631422
$472$	−14200.2	−1.38479
$473$	−2471.77	−0.240280
$474$	−551.874	−0.0534777
$475$	1062.94	0.102676
$476$	729.379	0.0702332
$477$	−2266.55	−0.217565
$478$	7744.53	0.741060
$479$	13193.4	1.25850	0.629249	−	0.777204i	$-0.283363\pi$
$479$	13193.4	1.25850	0.629249	+	0.777204i	$0.283363\pi$
$480$	−4259.01	−0.404992
$481$	9221.24	0.874122
$482$	−5563.39	−0.525738
$483$	2118.86	0.199610
$484$	3769.89	0.354047
$485$	−15419.0	−1.44358
$486$	−531.908	−0.0496457
$487$	−18550.0	−1.72604	−0.863021	−	0.505168i	$-0.831431\pi$
$487$	−18550.0	−1.72604	−0.863021	+	0.505168i	$0.831431\pi$
$488$	14480.4	1.34323
$489$	−2540.43	−0.234933
$490$	−13820.3	−1.27416
$491$	1772.52	0.162918	0.0814588	−	0.996677i	$-0.474042\pi$
$491$	1772.52	0.162918	0.0814588	+	0.996677i	$0.474042\pi$
$492$	−4010.07	−0.367456
$493$	214.673	0.0196113
$494$	11670.9	1.06295
$495$	−1183.19	−0.107435
$496$	−8342.38	−0.755209
$497$	8116.98	0.732588
$498$	−6784.29	−0.610464
$499$	13843.9	1.24196	0.620981	−	0.783826i	$-0.286734\pi$
$499$	13843.9	1.24196	0.620981	+	0.783826i	$0.286734\pi$
$500$	4702.24	0.420581
$501$	−7513.87	−0.670050
$502$	12516.3	1.11280
$503$	8874.78	0.786694	0.393347	−	0.919390i	$-0.371317\pi$
$503$	8874.78	0.786694	0.393347	+	0.919390i	$0.371317\pi$
$504$	6780.77	0.599285
$505$	6008.05	0.529415
$506$	628.967	0.0552589
$507$	8770.41	0.768259
$508$	−4166.08	−0.363858
$509$	−16581.7	−1.44395	−0.721977	−	0.691917i	$-0.756766\pi$
$509$	−16581.7	−1.44395	−0.721977	+	0.691917i	$0.756766\pi$
$510$	511.531	0.0444137
$511$	2944.79	0.254931
$512$	9285.10	0.801459
$513$	−2011.80	−0.173144
$514$	−10354.2	−0.888527
$515$	−5430.97	−0.464693
$516$	−1904.49	−0.162482
$517$	604.128	0.0513917
$518$	−8662.01	−0.734723
$519$	9492.05	0.802803
$520$	18474.8	1.55802
$521$	1596.00	0.134207	0.0671035	−	0.997746i	$-0.478624\pi$
$521$	1596.00	0.134207	0.0671035	+	0.997746i	$0.478624\pi$
$522$	571.308	0.0479032
$523$	12314.9	1.02962	0.514812	−	0.857303i	$-0.327862\pi$
$523$	12314.9	1.02962	0.514812	+	0.857303i	$0.327862\pi$
$524$	2545.52	0.212217
$525$	−1314.20	−0.109250
$526$	8197.21	0.679497
$527$	−2202.72	−0.182072
$528$	1050.76	0.0866067
$529$	529.000	0.0434783
$530$	5800.89	0.475424
$531$	−5209.02	−0.425710
$532$	7341.66	0.598310
$533$	29810.3	2.42257
$534$	4041.71	0.327532
$535$	2349.93	0.189900
$536$	−10844.6	−0.873909
$537$	2882.68	0.231652
$538$	−3167.27	−0.253811
$539$	−7495.76	−0.599008
$540$	−911.643	−0.0726498
$541$	18530.5	1.47262	0.736311	−	0.676643i	$-0.236566\pi$
$541$	18530.5	1.47262	0.736311	+	0.676643i	$0.236566\pi$
$542$	−16460.0	−1.30446
$543$	9236.15	0.729947
$544$	998.678	0.0787095
$545$	−5134.79	−0.403579
$546$	−14429.8	−1.13102
$547$	−5728.20	−0.447752	−0.223876	−	0.974618i	$-0.571871\pi$
$547$	−5728.20	−0.447752	−0.223876	+	0.974618i	$0.571871\pi$
$548$	8688.02	0.677251
$549$	5311.77	0.412934
$550$	−390.110	−0.0302443
$551$	2160.82	0.167067
$552$	1692.90	0.130534
$553$	2580.73	0.198452
$554$	−8372.32	−0.642068
$555$	4068.15	0.311141
$556$	5716.78	0.436053
$557$	−23181.1	−1.76340	−0.881700	−	0.471811i	$-0.843600\pi$
$557$	−23181.1	−1.76340	−0.881700	+	0.471811i	$0.843600\pi$
$558$	−5862.08	−0.444734
$559$	14157.7	1.07121
$560$	−9059.54	−0.683635
$561$	277.441	0.0208798
$562$	18150.5	1.36233
$563$	−4038.33	−0.302301	−0.151150	−	0.988511i	$-0.548298\pi$
$563$	−4038.33	−0.302301	−0.151150	+	0.988511i	$0.548298\pi$
$564$	465.479	0.0347521
$565$	227.280	0.0169234
$566$	15767.8	1.17097
$567$	2487.36	0.184232
$568$	6485.19	0.479071
$569$	13023.4	0.959524	0.479762	−	0.877399i	$-0.340723\pi$
$569$	13023.4	0.959524	0.479762	+	0.877399i	$0.340723\pi$
$570$	5148.88	0.378356
$571$	15070.5	1.10452	0.552261	−	0.833671i	$-0.313765\pi$
$571$	15070.5	1.10452	0.552261	+	0.833671i	$0.313765\pi$
$572$	2868.43	0.209677
$573$	12890.5	0.939807
$574$	−28002.4	−2.03623
$575$	−328.107	−0.0237965
$576$	4676.34	0.338277
$577$	959.290	0.0692128	0.0346064	−	0.999401i	$-0.488982\pi$
$577$	959.290	0.0692128	0.0346064	+	0.999401i	$0.488982\pi$
$578$	10634.2	0.765268
$579$	−5554.08	−0.398652
$580$	979.172	0.0700998
$581$	31725.4	2.26539
$582$	9621.98	0.685299
$583$	3146.25	0.223507
$584$	2352.78	0.166711
$585$	6777.02	0.478966
$586$	17849.3	1.25827
$587$	−3824.64	−0.268926	−0.134463	−	0.990919i	$-0.542931\pi$
$587$	−3824.64	−0.268926	−0.134463	+	0.990919i	$0.542931\pi$
$588$	−5775.46	−0.405061
$589$	−22171.7	−1.55105
$590$	13331.7	0.930265
$591$	8570.65	0.596531
$592$	−3612.81	−0.250820
$593$	−9227.11	−0.638974	−0.319487	−	0.947591i	$-0.603511\pi$
$593$	−9227.11	−0.638974	−0.319487	+	0.947591i	$0.603511\pi$
$594$	738.353	0.0510016
$595$	−2392.08	−0.164816
$596$	−5287.02	−0.363364
$597$	−5604.02	−0.384183
$598$	−3602.57	−0.246355
$599$	12304.1	0.839284	0.419642	−	0.907690i	$-0.362156\pi$
$599$	12304.1	0.839284	0.419642	+	0.907690i	$0.362156\pi$
$600$	−1050.00	−0.0714437
$601$	−3491.17	−0.236951	−0.118476	−	0.992957i	$-0.537801\pi$
$601$	−3491.17	−0.236951	−0.118476	+	0.992957i	$0.537801\pi$
$602$	−13299.1	−0.900384
$603$	−3978.08	−0.268657
$604$	−3333.97	−0.224598
$605$	−12363.8	−0.830840
$606$	−3749.24	−0.251324
$607$	15320.7	1.02446	0.512230	−	0.858848i	$-0.328820\pi$
$607$	15320.7	1.02446	0.512230	+	0.858848i	$0.328820\pi$
$608$	10052.3	0.670519
$609$	−2671.61	−0.177765
$610$	−13594.7	−0.902347
$611$	−3460.30	−0.229114
$612$	213.767	0.0141193
$613$	9166.58	0.603972	0.301986	−	0.953312i	$-0.402350\pi$
$613$	9166.58	0.603972	0.301986	+	0.953312i	$0.402350\pi$
$614$	−11741.1	−0.771711
$615$	13151.5	0.862306
$616$	−9412.53	−0.615652
$617$	2272.72	0.148292	0.0741459	−	0.997247i	$-0.476377\pi$
$617$	2272.72	0.148292	0.0741459	+	0.997247i	$0.476377\pi$
$618$	3389.12	0.220599
$619$	−21295.8	−1.38279	−0.691397	−	0.722475i	$-0.743004\pi$
$619$	−21295.8	−1.38279	−0.691397	+	0.722475i	$0.743004\pi$
$620$	−10047.1	−0.650808
$621$	621.000	0.0401286
$622$	−17683.9	−1.13997
$623$	−18900.3	−1.21545
$624$	−6018.48	−0.386109
$625$	−13638.3	−0.872852
$626$	−677.365	−0.0432475
$627$	2792.62	0.177873
$628$	−690.318	−0.0438641
$629$	−953.925	−0.0604698
$630$	−6366.02	−0.402584
$631$	−1670.56	−0.105394	−0.0526972	−	0.998611i	$-0.516782\pi$
$631$	−1670.56	−0.105394	−0.0526972	+	0.998611i	$0.516782\pi$
$632$	2061.92	0.129776
$633$	6405.68	0.402217
$634$	11013.9	0.689931
$635$	13663.1	0.853864
$636$	2424.18	0.151140
$637$	42933.9	2.67049
$638$	−793.045	−0.0492115
$639$	2378.94	0.147276
$640$	−611.016	−0.0377383
$641$	4654.22	0.286787	0.143394	−	0.989666i	$-0.454199\pi$
$641$	4654.22	0.286787	0.143394	+	0.989666i	$0.454199\pi$
$642$	−1466.44	−0.0901493
$643$	−28277.3	−1.73429	−0.867144	−	0.498057i	$-0.834047\pi$
$643$	−28277.3	−1.73429	−0.867144	+	0.498057i	$0.834047\pi$
$644$	−2266.22	−0.138667
$645$	6245.99	0.381296
$646$	−1207.34	−0.0735328
$647$	−9136.26	−0.555152	−0.277576	−	0.960704i	$-0.589531\pi$
$647$	−9136.26	−0.555152	−0.277576	+	0.960704i	$0.589531\pi$
$648$	1987.32	0.120477
$649$	7230.75	0.437337
$650$	2234.46	0.134835
$651$	27412.9	1.65038
$652$	2717.10	0.163205
$653$	15263.5	0.914714	0.457357	−	0.889283i	$-0.348796\pi$
$653$	15263.5	0.914714	0.457357	+	0.889283i	$0.348796\pi$
$654$	3204.30	0.191587
$655$	−8348.31	−0.498008
$656$	−11679.4	−0.695131
$657$	863.063	0.0512500
$658$	3250.44	0.192577
$659$	−4207.74	−0.248726	−0.124363	−	0.992237i	$-0.539689\pi$
$659$	−4207.74	−0.248726	−0.124363	+	0.992237i	$0.539689\pi$
$660$	1265.47	0.0746340
$661$	−25481.5	−1.49942	−0.749708	−	0.661768i	$-0.769806\pi$
$661$	−25481.5	−1.49942	−0.749708	+	0.661768i	$0.769806\pi$
$662$	4613.15	0.270839
$663$	−1589.12	−0.0930862
$664$	25347.5	1.48144
$665$	−24077.7	−1.40405
$666$	−2538.67	−0.147705
$667$	−667.000	−0.0387202
$668$	8036.41	0.465476
$669$	13676.4	0.790372
$670$	10181.3	0.587070
$671$	−7373.39	−0.424212
$672$	−12428.6	−0.713456
$673$	33402.1	1.91316	0.956579	−	0.291475i	$-0.0941459\pi$
$673$	33402.1	1.91316	0.956579	+	0.291475i	$0.0941459\pi$
$674$	−4945.11	−0.282609
$675$	−385.169	−0.0219632
$676$	−9380.33	−0.533701
$677$	20519.7	1.16490	0.582448	−	0.812868i	$-0.302095\pi$
$677$	20519.7	1.16490	0.582448	+	0.812868i	$0.302095\pi$
$678$	−141.831	−0.00803390
$679$	−44995.3	−2.54310
$680$	−1911.19	−0.107780
$681$	−4514.13	−0.254012
$682$	8137.28	0.456881
$683$	−22506.5	−1.26089	−0.630444	−	0.776234i	$-0.717127\pi$
$683$	−22506.5	−1.26089	−0.630444	+	0.776234i	$0.717127\pi$
$684$	2151.70	0.120281
$685$	−28493.3	−1.58930
$686$	−17274.4	−0.961429
$687$	−18721.2	−1.03968
$688$	−5546.89	−0.307374
$689$	−18021.0	−0.996436
$690$	−1589.35	−0.0876893
$691$	21134.1	1.16350	0.581749	−	0.813368i	$-0.302369\pi$
$691$	21134.1	1.16350	0.581749	+	0.813368i	$0.302369\pi$
$692$	−10152.2	−0.557698
$693$	−3452.76	−0.189263
$694$	−18646.1	−1.01988
$695$	−18748.8	−1.02328
$696$	−2134.53	−0.116249
$697$	−3083.84	−0.167588
$698$	−6851.66	−0.371546
$699$	−10794.1	−0.584077
$700$	1405.60	0.0758951
$701$	−21241.7	−1.14449	−0.572247	−	0.820082i	$-0.693928\pi$
$701$	−21241.7	−1.14449	−0.572247	+	0.820082i	$0.693928\pi$
$702$	−4229.11	−0.227375
$703$	−9601.85	−0.515136
$704$	−6491.33	−0.347516
$705$	−1526.59	−0.0815526
$706$	2600.91	0.138649
$707$	17532.6	0.932646
$708$	5571.27	0.295736
$709$	−17885.1	−0.947378	−0.473689	−	0.880692i	$-0.657078\pi$
$709$	−17885.1	−0.947378	−0.473689	+	0.880692i	$0.657078\pi$
$710$	−6088.52	−0.321828
$711$	756.365	0.0398958
$712$	−15100.7	−0.794835
$713$	6843.95	0.359478
$714$	1492.74	0.0782415
$715$	−9407.33	−0.492048
$716$	−3083.16	−0.160926
$717$	−10614.2	−0.552851
$718$	−11797.2	−0.613186
$719$	−9140.10	−0.474087	−0.237043	−	0.971499i	$-0.576178\pi$
$719$	−9140.10	−0.474087	−0.237043	+	0.971499i	$0.576178\pi$
$720$	−2655.18	−0.137435
$721$	−15848.6	−0.818628
$722$	2861.16	0.147481
$723$	7624.85	0.392215
$724$	−9878.46	−0.507086
$725$	413.700	0.0211923
$726$	7715.43	0.394417
$727$	4161.13	0.212280	0.106140	−	0.994351i	$-0.466151\pi$
$727$	4161.13	0.212280	0.106140	+	0.994351i	$0.466151\pi$
$728$	53912.7	2.74470
$729$	729.000	0.0370370
$730$	−2208.88	−0.111992
$731$	−1464.60	−0.0741041
$732$	−5681.17	−0.286861
$733$	3163.22	0.159395	0.0796974	−	0.996819i	$-0.474605\pi$
$733$	3163.22	0.159395	0.0796974	+	0.996819i	$0.474605\pi$
$734$	−20395.5	−1.02563
$735$	18941.2	0.950555
$736$	−3102.94	−0.155402
$737$	5522.06	0.275994
$738$	−8206.99	−0.409354
$739$	24433.7	1.21625	0.608125	−	0.793841i	$-0.291922\pi$
$739$	24433.7	1.21625	0.608125	+	0.793841i	$0.291922\pi$
$740$	−4351.07	−0.216146
$741$	−15995.5	−0.792993
$742$	16928.1	0.837532
$743$	−21373.5	−1.05534	−0.527671	−	0.849449i	$-0.676935\pi$
$743$	−21373.5	−1.05534	−0.527671	+	0.849449i	$0.676935\pi$
$744$	21902.0	1.07925
$745$	17339.4	0.852705
$746$	−28583.9	−1.40286
$747$	9298.13	0.455423
$748$	−296.735	−0.0145050
$749$	6857.53	0.334538
$750$	9623.57	0.468537
$751$	−10428.2	−0.506700	−0.253350	−	0.967375i	$-0.581532\pi$
$751$	−10428.2	−0.506700	−0.253350	+	0.967375i	$0.581532\pi$
$752$	1355.72	0.0657420
$753$	−17154.0	−0.830182
$754$	4542.37	0.219394
$755$	10934.1	0.527063
$756$	−2660.34	−0.127984
$757$	−35552.7	−1.70698	−0.853492	−	0.521106i	$-0.825520\pi$
$757$	−35552.7	−1.70698	−0.853492	+	0.521106i	$0.825520\pi$
$758$	−7317.43	−0.350635
$759$	−862.024	−0.0412246
$760$	−19237.3	−0.918172
$761$	−6324.86	−0.301283	−0.150641	−	0.988588i	$-0.548134\pi$
$761$	−6324.86	−0.301283	−0.150641	+	0.988588i	$0.548134\pi$
$762$	−8526.27	−0.405347
$763$	−14984.3	−0.710966
$764$	−13787.0	−0.652873
$765$	−701.073	−0.0331338
$766$	23657.3	1.11589
$767$	−41416.0	−1.94973
$768$	−12089.0	−0.567998
$769$	36415.4	1.70764	0.853819	−	0.520569i	$-0.174280\pi$
$769$	36415.4	1.70764	0.853819	+	0.520569i	$0.174280\pi$
$770$	8836.81	0.413580
$771$	14190.8	0.662865
$772$	5940.33	0.276939
$773$	28796.1	1.33988	0.669938	−	0.742417i	$-0.266321\pi$
$773$	28796.1	1.33988	0.669938	+	0.742417i	$0.266321\pi$
$774$	−3897.72	−0.181009
$775$	−4244.89	−0.196750
$776$	−35949.7	−1.66304
$777$	11871.6	0.548123
$778$	24829.6	1.14420
$779$	−31040.7	−1.42766
$780$	−7248.32	−0.332733
$781$	−3302.25	−0.151298
$782$	372.681	0.0170423
$783$	−783.000	−0.0357371
$784$	−16821.2	−0.766270
$785$	2263.97	0.102936
$786$	5209.65	0.236415
$787$	36673.5	1.66108	0.830540	−	0.556960i	$-0.188032\pi$
$787$	36673.5	1.66108	0.830540	+	0.556960i	$0.188032\pi$
$788$	−9166.68	−0.414403
$789$	−11234.6	−0.506923
$790$	−1935.80	−0.0871806
$791$	663.245	0.0298132
$792$	−2758.64	−0.123768
$793$	42233.0	1.89122
$794$	−19515.6	−0.872269
$795$	−7950.35	−0.354679
$796$	5993.75	0.266888
$797$	−3567.58	−0.158557	−0.0792786	−	0.996852i	$-0.525262\pi$
$797$	−3567.58	−0.158557	−0.0792786	+	0.996852i	$0.525262\pi$
$798$	15025.4	0.666532
$799$	357.963	0.0158496
$800$	1924.57	0.0850546
$801$	−5539.32	−0.244348
$802$	−1040.47	−0.0458108
$803$	−1198.04	−0.0526498
$804$	4254.73	0.186633
$805$	7432.30	0.325409
$806$	−46608.4	−2.03686
$807$	4340.86	0.189350
$808$	14007.9	0.609898
$809$	−21679.8	−0.942178	−0.471089	−	0.882086i	$-0.656139\pi$
$809$	−21679.8	−0.942178	−0.471089	+	0.882086i	$0.656139\pi$
$810$	−1865.76	−0.0809336
$811$	17087.3	0.739849	0.369924	−	0.929062i	$-0.379384\pi$
$811$	17087.3	0.739849	0.369924	+	0.929062i	$0.379384\pi$
$812$	2857.40	0.123492
$813$	22559.0	0.973161
$814$	3523.99	0.151739
$815$	−8911.02	−0.382993
$816$	622.604	0.0267102
$817$	−14742.1	−0.631286
$818$	−2902.80	−0.124076
$819$	19776.6	0.843773
$820$	−14066.1	−0.599035
$821$	−5341.63	−0.227069	−0.113535	−	0.993534i	$-0.536217\pi$
$821$	−5341.63	−0.227069	−0.113535	+	0.993534i	$0.536217\pi$
$822$	17780.8	0.754475
$823$	−22750.4	−0.963584	−0.481792	−	0.876286i	$-0.660014\pi$
$823$	−22750.4	−0.963584	−0.481792	+	0.876286i	$0.660014\pi$
$824$	−12662.5	−0.535337
$825$	534.661	0.0225630
$826$	38904.3	1.63880
$827$	−16636.1	−0.699511	−0.349755	−	0.936841i	$-0.613735\pi$
$827$	−16636.1	−0.699511	−0.349755	+	0.936841i	$0.613735\pi$
$828$	−664.186	−0.0278769
$829$	−6489.59	−0.271885	−0.135942	−	0.990717i	$-0.543406\pi$
$829$	−6489.59	−0.271885	−0.135942	+	0.990717i	$0.543406\pi$
$830$	−23797.1	−0.995193
$831$	11474.6	0.479000
$832$	37180.8	1.54929
$833$	−4441.45	−0.184739
$834$	11699.9	0.485773
$835$	−26356.3	−1.09233
$836$	−2986.83	−0.123567
$837$	8034.21	0.331783
$838$	1886.14	0.0777513
$839$	−17764.2	−0.730974	−0.365487	−	0.930816i	$-0.619098\pi$
$839$	−17764.2	−0.730974	−0.365487	+	0.930816i	$0.619098\pi$
$840$	23784.8	0.976968
$841$	841.000	0.0344828
$842$	15783.2	0.645991
$843$	−24875.9	−1.01634
$844$	−6851.16	−0.279415
$845$	30763.8	1.25243
$846$	952.645	0.0387147
$847$	−36079.7	−1.46365
$848$	7060.48	0.285917
$849$	−21610.4	−0.873576
$850$	−231.151	−0.00932756
$851$	2963.89	0.119390
$852$	−2544.38	−0.102311
$853$	−33967.9	−1.36347	−0.681734	−	0.731600i	$-0.738774\pi$
$853$	−33967.9	−1.36347	−0.681734	+	0.731600i	$0.738774\pi$
$854$	−39671.7	−1.58962
$855$	−7056.75	−0.282264
$856$	5478.94	0.218769
$857$	26004.3	1.03651	0.518255	−	0.855226i	$-0.326582\pi$
$857$	26004.3	1.03651	0.518255	+	0.855226i	$0.326582\pi$
$858$	5870.51	0.233585
$859$	−21992.2	−0.873532	−0.436766	−	0.899575i	$-0.643876\pi$
$859$	−21992.2	−0.873532	−0.436766	+	0.899575i	$0.643876\pi$
$860$	−6680.36	−0.264882
$861$	38378.4	1.51908
$862$	24175.3	0.955237
$863$	−43793.0	−1.72738	−0.863691	−	0.504022i	$-0.831853\pi$
$863$	−43793.0	−1.72738	−0.863691	+	0.504022i	$0.831853\pi$
$864$	−3642.58	−0.143430
$865$	33295.1	1.30875
$866$	−24730.6	−0.970415
$867$	−14574.6	−0.570911
$868$	−29319.2	−1.14650
$869$	−1049.93	−0.0409854
$870$	2003.97	0.0780929
$871$	−31629.0	−1.23044
$872$	−11971.9	−0.464932
$873$	−13187.3	−0.511251
$874$	3751.27	0.145181
$875$	−45002.7	−1.73871
$876$	−923.083	−0.0356028
$877$	−16591.0	−0.638811	−0.319406	−	0.947618i	$-0.603483\pi$
$877$	−16591.0	−0.638811	−0.319406	+	0.947618i	$0.603483\pi$
$878$	9538.15	0.366625
$879$	−24463.1	−0.938704
$880$	3685.72	0.141188
$881$	−23457.4	−0.897048	−0.448524	−	0.893771i	$-0.648050\pi$
$881$	−23457.4	−0.897048	−0.448524	+	0.893771i	$0.648050\pi$
$882$	−11820.0	−0.451248
$883$	−36641.1	−1.39646	−0.698229	−	0.715875i	$-0.746028\pi$
$883$	−36641.1	−1.39646	−0.698229	+	0.715875i	$0.746028\pi$
$884$	1699.63	0.0646659
$885$	−18271.6	−0.694003
$886$	−3210.27	−0.121728
$887$	10226.4	0.387114	0.193557	−	0.981089i	$-0.437997\pi$
$887$	10226.4	0.387114	0.193557	+	0.981089i	$0.437997\pi$
$888$	9485.02	0.358442
$889$	39871.4	1.50421
$890$	14177.0	0.533950
$891$	−1011.94	−0.0380486
$892$	−14627.5	−0.549063
$893$	3603.13	0.135021
$894$	−10820.4	−0.404796
$895$	10111.5	0.377644
$896$	−1783.06	−0.0664818
$897$	4937.46	0.183787
$898$	−16894.1	−0.627798
$899$	−8629.33	−0.320138
$900$	411.955	0.0152576
$901$	1864.25	0.0689312
$902$	11392.3	0.420535
$903$	18226.9	0.671711
$904$	529.910	0.0194962
$905$	32397.5	1.18998
$906$	−6823.27	−0.250207
$907$	35875.7	1.31338	0.656689	−	0.754162i	$-0.271957\pi$
$907$	35875.7	1.31338	0.656689	+	0.754162i	$0.271957\pi$
$908$	4828.06	0.176459
$909$	5138.48	0.187495
$910$	−50615.1	−1.84382
$911$	−23455.8	−0.853046	−0.426523	−	0.904477i	$-0.640262\pi$
$911$	−23455.8	−0.853046	−0.426523	+	0.904477i	$0.640262\pi$
$912$	6266.90	0.227541
$913$	−12906.9	−0.467861
$914$	−32512.6	−1.17661
$915$	18632.0	0.673175
$916$	20023.2	0.722253
$917$	−24361.9	−0.877318
$918$	437.495	0.0157293
$919$	9682.06	0.347532	0.173766	−	0.984787i	$-0.444406\pi$
$919$	9682.06	0.347532	0.173766	+	0.984787i	$0.444406\pi$
$920$	5938.16	0.212799
$921$	16091.6	0.575717
$922$	28876.4	1.03145
$923$	18914.5	0.674517
$924$	3692.88	0.131479
$925$	−1838.32	−0.0653445
$926$	−22121.1	−0.785037
$927$	−4644.92	−0.164573
$928$	3912.41	0.138395
$929$	43737.5	1.54465	0.772326	−	0.635227i	$-0.219093\pi$
$929$	43737.5	1.54465	0.772326	+	0.635227i	$0.219093\pi$
$930$	−20562.3	−0.725016
$931$	−44706.0	−1.57377
$932$	11544.8	0.405752
$933$	24236.5	0.850447
$934$	−13285.7	−0.465441
$935$	973.176	0.0340388
$936$	15800.8	0.551780
$937$	−36235.7	−1.26336	−0.631680	−	0.775229i	$-0.717634\pi$
$937$	−36235.7	−1.26336	−0.631680	+	0.775229i	$0.717634\pi$
$938$	29710.8	1.03421
$939$	928.355	0.0322638
$940$	1632.75	0.0566537
$941$	−27121.2	−0.939559	−0.469779	−	0.882784i	$-0.655667\pi$
$941$	−27121.2	−0.939559	−0.469779	+	0.882784i	$0.655667\pi$
$942$	−1412.80	−0.0488657
$943$	9581.63	0.330881
$944$	16226.5	0.559456
$945$	8724.87	0.300339
$946$	5410.51	0.185952
$947$	−8679.31	−0.297824	−0.148912	−	0.988850i	$-0.547577\pi$
$947$	−8679.31	−0.297824	−0.148912	+	0.988850i	$0.547577\pi$
$948$	−808.965	−0.0277152
$949$	6862.06	0.234723
$950$	−2326.68	−0.0794606
$951$	−15094.9	−0.514707
$952$	−5577.20	−0.189872
$953$	42812.5	1.45523	0.727615	−	0.685986i	$-0.240629\pi$
$953$	42812.5	1.45523	0.727615	+	0.685986i	$0.240629\pi$
$954$	4961.30	0.168373
$955$	45215.9	1.53210
$956$	11352.3	0.384059
$957$	1086.90	0.0367131
$958$	−28879.2	−0.973951
$959$	−83148.6	−2.79980
$960$	16403.1	0.551467
$961$	58752.8	1.97217
$962$	−20184.6	−0.676483
$963$	2009.82	0.0672538
$964$	−8155.11	−0.272467
$965$	−19482.0	−0.649892
$966$	−4638.02	−0.154478
$967$	34395.2	1.14382	0.571910	−	0.820316i	$-0.306203\pi$
$967$	34395.2	1.14382	0.571910	+	0.820316i	$0.306203\pi$
$968$	−28826.5	−0.957147
$969$	1654.71	0.0548574
$970$	33750.8	1.11719
$971$	3316.66	0.109616	0.0548078	−	0.998497i	$-0.482545\pi$
$971$	3316.66	0.109616	0.0548078	+	0.998497i	$0.482545\pi$
$972$	−779.697	−0.0257292
$973$	−54712.4	−1.80267
$974$	40604.6	1.33578
$975$	−3062.41	−0.100590
$976$	−16546.6	−0.542666
$977$	−8302.06	−0.271859	−0.135930	−	0.990719i	$-0.543402\pi$
$977$	−8302.06	−0.271859	−0.135930	+	0.990719i	$0.543402\pi$
$978$	5560.80	0.181815
$979$	7689.26	0.251021
$980$	−20258.5	−0.660340
$981$	−4391.61	−0.142929
$982$	−3879.90	−0.126082
$983$	−13626.5	−0.442133	−0.221067	−	0.975259i	$-0.570954\pi$
$983$	−13626.5	−0.442133	−0.221067	+	0.975259i	$0.570954\pi$
$984$	30663.0	0.993396
$985$	30063.1	0.972478
$986$	−469.902	−0.0151772
$987$	−4454.86	−0.143667
$988$	17107.8	0.550883
$989$	4550.58	0.146309
$990$	2589.91	0.0831441
$991$	−32157.2	−1.03079	−0.515393	−	0.856954i	$-0.672354\pi$
$991$	−32157.2	−1.03079	−0.515393	+	0.856954i	$0.672354\pi$
$992$	−40144.4	−1.28487
$993$	−6322.50	−0.202053
$994$	−17767.4	−0.566950
$995$	−19657.1	−0.626305
$996$	−9944.75	−0.316377
$997$	−30973.1	−0.983878	−0.491939	−	0.870630i	$-0.663712\pi$
$997$	−30973.1	−0.983878	−0.491939	+	0.870630i	$0.663712\pi$
$998$	−30303.2	−0.961154
$999$	3479.35	0.110192

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.4.a.h.1.15	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.4.a.h.1.15	✓	44	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:	\( N \)	\(=\)	\( 2001 = 3 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.18892 q^{2} +3.00000 q^{3} -3.20863 q^{4} +10.5230 q^{5} -6.56676 q^{6} +30.7082 q^{7} +24.5348 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.18892 q^{2} +3.00000 q^{3} -3.20863 q^{4} +10.5230 q^{5} -6.56676 q^{6} +30.7082 q^{7} +24.5348 q^{8} +9.00000 q^{9} -23.0341 q^{10} -12.4931 q^{11} -9.62589 q^{12} +71.5574 q^{13} -67.2177 q^{14} +31.5691 q^{15} -28.0357 q^{16} -7.40252 q^{17} -19.7003 q^{18} -74.5110 q^{19} -33.7646 q^{20} +92.1245 q^{21} +27.3464 q^{22} +23.0000 q^{23} +73.6044 q^{24} -14.2655 q^{25} -156.634 q^{26} +27.0000 q^{27} -98.5312 q^{28} -29.0000 q^{29} -69.1023 q^{30} +297.563 q^{31} -134.911 q^{32} -37.4793 q^{33} +16.2035 q^{34} +323.144 q^{35} -28.8777 q^{36} +128.865 q^{37} +163.099 q^{38} +214.672 q^{39} +258.181 q^{40} +416.593 q^{41} -201.653 q^{42} +197.851 q^{43} +40.0857 q^{44} +94.7074 q^{45} -50.3452 q^{46} -48.3569 q^{47} -84.1070 q^{48} +599.992 q^{49} +31.2260 q^{50} -22.2076 q^{51} -229.601 q^{52} -251.839 q^{53} -59.1008 q^{54} -131.465 q^{55} +753.419 q^{56} -223.533 q^{57} +63.4787 q^{58} -578.780 q^{59} -101.294 q^{60} +590.197 q^{61} -651.342 q^{62} +276.374 q^{63} +519.594 q^{64} +753.002 q^{65} +82.0392 q^{66} -442.009 q^{67} +23.7519 q^{68} +69.0000 q^{69} -707.335 q^{70} +264.326 q^{71} +220.813 q^{72} +95.8959 q^{73} -282.075 q^{74} -42.7965 q^{75} +239.078 q^{76} -383.640 q^{77} -469.901 q^{78} +84.0406 q^{79} -295.021 q^{80} +81.0000 q^{81} -911.888 q^{82} +1033.13 q^{83} -295.593 q^{84} -77.8971 q^{85} -433.080 q^{86} -87.0000 q^{87} -306.516 q^{88} -615.481 q^{89} -207.307 q^{90} +2197.40 q^{91} -73.7985 q^{92} +892.689 q^{93} +105.849 q^{94} -784.083 q^{95} -404.732 q^{96} -1465.26 q^{97} -1313.33 q^{98} -112.438 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 6 q^{2} + 132 q^{3} + 210 q^{4} + 15 q^{5} + 18 q^{6} + 78 q^{7} + 12 q^{8} + 396 q^{9}+O(q^{10}) \) 44 * q + 6 * q^2 + 132 * q^3 + 210 * q^4 + 15 * q^5 + 18 * q^6 + 78 * q^7 + 12 * q^8 + 396 * q^9	\( 44 q + 6 q^{2} + 132 q^{3} + 210 q^{4} + 15 q^{5} + 18 q^{6} + 78 q^{7} + 12 q^{8} + 396 q^{9} + 214 q^{10} + 111 q^{11} + 630 q^{12} + 275 q^{13} + 104 q^{14} + 45 q^{15} + 1062 q^{16} - 58 q^{17} + 54 q^{18} + 331 q^{19} + 287 q^{20} + 234 q^{21} + 285 q^{22} + 1012 q^{23} + 36 q^{24} + 1903 q^{25} + 1084 q^{26} + 1188 q^{27} + 222 q^{28} - 1276 q^{29} + 642 q^{30} + 1394 q^{31} + 42 q^{32} + 333 q^{33} + 373 q^{34} + 567 q^{35} + 1890 q^{36} + 1229 q^{37} + 733 q^{38} + 825 q^{39} + 2483 q^{40} - 107 q^{41} + 312 q^{42} + 1165 q^{43} + 1639 q^{44} + 135 q^{45} + 138 q^{46} + 964 q^{47} + 3186 q^{48} + 4264 q^{49} + 495 q^{50} - 174 q^{51} + 2679 q^{52} - 380 q^{53} + 162 q^{54} + 1260 q^{55} + 2229 q^{56} + 993 q^{57} - 174 q^{58} + 897 q^{59} + 861 q^{60} + 2584 q^{61} + 3034 q^{62} + 702 q^{63} + 6866 q^{64} - 286 q^{65} + 855 q^{66} + 2277 q^{67} - 1554 q^{68} + 3036 q^{69} + 689 q^{70} + 4304 q^{71} + 108 q^{72} + 4712 q^{73} - 1005 q^{74} + 5709 q^{75} + 2877 q^{76} + 919 q^{77} + 3252 q^{78} + 3864 q^{79} + 2593 q^{80} + 3564 q^{81} + 3297 q^{82} - 540 q^{83} + 666 q^{84} + 6537 q^{85} + 3789 q^{86} - 3828 q^{87} + 1707 q^{88} - 331 q^{89} + 1926 q^{90} + 4311 q^{91} + 4830 q^{92} + 4182 q^{93} + 6189 q^{94} + 3267 q^{95} + 126 q^{96} + 5572 q^{97} + 2588 q^{98} + 999 q^{99}+O(q^{100}) \) 44 * q + 6 * q^2 + 132 * q^3 + 210 * q^4 + 15 * q^5 + 18 * q^6 + 78 * q^7 + 12 * q^8 + 396 * q^9 + 214 * q^10 + 111 * q^11 + 630 * q^12 + 275 * q^13 + 104 * q^14 + 45 * q^15 + 1062 * q^16 - 58 * q^17 + 54 * q^18 + 331 * q^19 + 287 * q^20 + 234 * q^21 + 285 * q^22 + 1012 * q^23 + 36 * q^24 + 1903 * q^25 + 1084 * q^26 + 1188 * q^27 + 222 * q^28 - 1276 * q^29 + 642 * q^30 + 1394 * q^31 + 42 * q^32 + 333 * q^33 + 373 * q^34 + 567 * q^35 + 1890 * q^36 + 1229 * q^37 + 733 * q^38 + 825 * q^39 + 2483 * q^40 - 107 * q^41 + 312 * q^42 + 1165 * q^43 + 1639 * q^44 + 135 * q^45 + 138 * q^46 + 964 * q^47 + 3186 * q^48 + 4264 * q^49 + 495 * q^50 - 174 * q^51 + 2679 * q^52 - 380 * q^53 + 162 * q^54 + 1260 * q^55 + 2229 * q^56 + 993 * q^57 - 174 * q^58 + 897 * q^59 + 861 * q^60 + 2584 * q^61 + 3034 * q^62 + 702 * q^63 + 6866 * q^64 - 286 * q^65 + 855 * q^66 + 2277 * q^67 - 1554 * q^68 + 3036 * q^69 + 689 * q^70 + 4304 * q^71 + 108 * q^72 + 4712 * q^73 - 1005 * q^74 + 5709 * q^75 + 2877 * q^76 + 919 * q^77 + 3252 * q^78 + 3864 * q^79 + 2593 * q^80 + 3564 * q^81 + 3297 * q^82 - 540 * q^83 + 666 * q^84 + 6537 * q^85 + 3789 * q^86 - 3828 * q^87 + 1707 * q^88 - 331 * q^89 + 1926 * q^90 + 4311 * q^91 + 4830 * q^92 + 4182 * q^93 + 6189 * q^94 + 3267 * q^95 + 126 * q^96 + 5572 * q^97 + 2588 * q^98 + 999 * q^99

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