LMFDB - Embedded newform 147.4.e.l.67.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,4,Mod(67,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("147.67");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	147.e (of order $3$, degree $2$, not minimal)

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:	no
Analytic conductor:	$8.67328077084$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-19})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} - 5x + 25 $ x^4 - x^3 - 4x^2 - 5x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.1
Root			$-1.63746 - 1.52274i$ of defining polynomial
Character	$\chi$	$=$	147.67
Dual form			147.4.e.l.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.13746 - 1.97014i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(1.41238 - 2.44631i) q^{4} +(2.27492 + 3.94027i) q^{5} +6.82475 q^{6} -24.6254 q^{8} +(-4.50000 - 7.79423i) q^{9} +(5.17525 - 8.96379i) q^{10} +(20.3746 - 35.2898i) q^{11} +(4.23713 + 7.33892i) q^{12} +53.2990 q^{13} -13.6495 q^{15} +(16.7114 + 28.9450i) q^{16} +(-2.27492 + 3.94027i) q^{17} +(-10.2371 + 17.7312i) q^{18} +(-61.2990 - 106.173i) q^{19} +12.8522 q^{20} -92.7010 q^{22} +(-65.6736 - 113.750i) q^{23} +(36.9381 - 63.9787i) q^{24} +(52.1495 - 90.3256i) q^{25} +(-60.6254 - 105.006i) q^{26} +27.0000 q^{27} -216.598 q^{29} +(15.5257 + 26.8914i) q^{30} +(125.897 - 218.060i) q^{31} +(-60.4846 + 104.762i) q^{32} +(61.1238 + 105.869i) q^{33} +10.3505 q^{34} -25.4228 q^{36} +(-5.94851 - 10.3031i) q^{37} +(-139.450 + 241.535i) q^{38} +(-79.9485 + 138.475i) q^{39} +(-56.0208 - 97.0308i) q^{40} -111.752 q^{41} +369.196 q^{43} +(-57.5531 - 99.6850i) q^{44} +(20.4743 - 35.4624i) q^{45} +(-149.402 + 258.772i) q^{46} +(131.347 + 227.500i) q^{47} -100.268 q^{48} -237.272 q^{50} +(-6.82475 - 11.8208i) q^{51} +(75.2782 - 130.386i) q^{52} +(283.550 - 491.123i) q^{53} +(-30.7114 - 53.1937i) q^{54} +185.402 q^{55} +367.794 q^{57} +(246.371 + 426.728i) q^{58} +(-419.945 + 727.366i) q^{59} +(-19.2782 + 33.3909i) q^{60} +(242.897 + 420.710i) q^{61} -572.811 q^{62} +542.577 q^{64} +(121.251 + 210.013i) q^{65} +(139.051 - 240.844i) q^{66} +(166.846 - 288.985i) q^{67} +(6.42608 + 11.1303i) q^{68} +394.042 q^{69} +590.248 q^{71} +(110.814 + 191.936i) q^{72} +(-245.350 + 424.960i) q^{73} +(-13.5324 + 23.4387i) q^{74} +(156.449 + 270.977i) q^{75} -346.309 q^{76} +363.752 q^{78} +(-60.8455 - 105.388i) q^{79} +(-76.0340 + 131.695i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(127.114 + 220.168i) q^{82} +609.608 q^{83} -20.7010 q^{85} +(-419.945 - 727.366i) q^{86} +(324.897 - 562.738i) q^{87} +(-501.733 + 869.026i) q^{88} +(-359.519 - 622.705i) q^{89} -93.1545 q^{90} -371.023 q^{92} +(377.691 + 654.180i) q^{93} +(298.804 - 517.544i) q^{94} +(278.900 - 483.070i) q^{95} +(-181.454 - 314.287i) q^{96} -637.877 q^{97} -366.743 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} - 6 q^{3} - 17 q^{4} - 6 q^{5} - 18 q^{6} - 174 q^{8} - 18 q^{9} + 66 q^{10} + 6 q^{11} - 51 q^{12} + 32 q^{13} + 36 q^{15} - 137 q^{16} + 6 q^{17} + 27 q^{18} - 64 q^{19} + 444 q^{20} - 552 q^{22}+ \cdots - 108 q^{99}+O(q^{100}) $ 4 * q + 3 * q^2 - 6 * q^3 - 17 * q^4 - 6 * q^5 - 18 * q^6 - 174 * q^8 - 18 * q^9 + 66 * q^10 + 6 * q^11 - 51 * q^12 + 32 * q^13 + 36 * q^15 - 137 * q^16 + 6 * q^17 + 27 * q^18 - 64 * q^19 + 444 * q^20 - 552 * q^22 - 6 * q^23 + 261 * q^24 + 118 * q^25 - 318 * q^26 + 108 * q^27 - 504 * q^29 + 198 * q^30 - 40 * q^31 + 279 * q^32 + 18 * q^33 + 132 * q^34 + 306 * q^36 + 248 * q^37 - 588 * q^38 - 48 * q^39 + 546 * q^40 - 900 * q^41 + 752 * q^43 - 804 * q^44 - 54 * q^45 - 960 * q^46 + 12 * q^47 + 822 * q^48 - 330 * q^50 + 18 * q^51 + 890 * q^52 + 1104 * q^53 + 81 * q^54 + 1104 * q^55 + 384 * q^57 + 306 * q^58 - 804 * q^59 - 666 * q^60 + 428 * q^61 - 4224 * q^62 + 2578 * q^64 + 636 * q^65 + 828 * q^66 - 148 * q^67 + 222 * q^68 + 36 * q^69 + 1908 * q^71 + 783 * q^72 - 1072 * q^73 - 1398 * q^74 + 354 * q^75 - 3016 * q^76 + 1908 * q^78 + 572 * q^79 - 1950 * q^80 - 162 * q^81 - 1530 * q^82 + 3888 * q^83 - 264 * q^85 - 804 * q^86 + 756 * q^87 + 1164 * q^88 - 366 * q^89 - 1188 * q^90 - 5712 * q^92 - 120 * q^93 + 1920 * q^94 + 1176 * q^95 + 837 * q^96 + 1616 * q^97 - 108 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.13746	−	1.97014i	−0.402152	−	0.696548i	0.591833	−	0.806061i	$-0.298404\pi$
$2$	−1.13746	−	1.97014i	−0.402152	−	0.696548i	−0.993985	+	0.109512i	$0.965071\pi$
$3$	−1.50000	+	2.59808i	−0.288675	+	0.500000i
$3$	−1.50000	+	2.59808i	−0.288675	+	0.500000i
$4$	1.41238	−	2.44631i	0.176547	−	0.305788i
$5$	2.27492	+	3.94027i	0.203475	+	0.352429i	0.949646	−	0.313326i	$-0.101443\pi$
$5$	2.27492	+	3.94027i	0.203475	+	0.352429i	−0.746171	+	0.665754i	$0.768110\pi$
$6$	6.82475			0.464366
$7$		0			0
$7$		0			0
$8$	−24.6254			−1.08830
$9$	−4.50000	−	7.79423i	−0.166667	−	0.288675i
$10$	5.17525	−	8.96379i	0.163656	−	0.283460i
$11$	20.3746	−	35.2898i	0.558470	−	0.967298i	−0.439155	−	0.898412i	$-0.644722\pi$
$11$	20.3746	−	35.2898i	0.558470	−	0.967298i	0.997624	−	0.0688867i	$-0.0219447\pi$
$12$	4.23713	+	7.33892i	0.101929	+	0.176547i
$13$	53.2990			1.13711			0.568557	−	0.822644i	$-0.307502\pi$
$13$	53.2990			1.13711			0.568557	+	0.822644i	$0.307502\pi$
$14$		0			0
$15$	−13.6495			−0.234952
$16$	16.7114	+	28.9450i	0.261115	+	0.452265i
$17$	−2.27492	+	3.94027i	−0.0324558	+	0.0562151i	−0.881797	−	0.471629i	$-0.843666\pi$
$17$	−2.27492	+	3.94027i	−0.0324558	+	0.0562151i	0.849341	+	0.527844i	$0.176999\pi$
$18$	−10.2371	+	17.7312i	−0.134051	+	0.232183i
$19$	−61.2990	−	106.173i	−0.740156	−	1.28199i	−0.952424	−	0.304776i	$-0.901418\pi$
$19$	−61.2990	−	106.173i	−0.740156	−	1.28199i	0.212269	−	0.977211i	$-0.431915\pi$
$20$	12.8522			0.143691
$21$		0			0
$22$	−92.7010			−0.898360
$23$	−65.6736	−	113.750i	−0.595387	−	1.03124i	−0.993492	−	0.113900i	$-0.963666\pi$
$23$	−65.6736	−	113.750i	−0.595387	−	1.03124i	0.398106	−	0.917340i	$-0.369668\pi$
$24$	36.9381	−	63.9787i	0.314165	−	0.544150i
$25$	52.1495	−	90.3256i	0.417196	−	0.722605i
$26$	−60.6254	−	105.006i	−0.457293	−	0.792055i
$27$	27.0000			0.192450
$28$		0			0
$29$	−216.598			−1.38694			−0.693470	−	0.720486i	$-0.743919\pi$
$29$	−216.598			−1.38694			−0.693470	+	0.720486i	$0.743919\pi$
$30$	15.5257	+	26.8914i	0.0944867	+	0.163656i
$31$	125.897	−	218.060i	0.729412	−	1.26338i	−0.227720	−	0.973727i	$-0.573127\pi$
$31$	125.897	−	218.060i	0.729412	−	1.26338i	0.957132	−	0.289652i	$-0.0935396\pi$
$32$	−60.4846	+	104.762i	−0.334134	+	0.578736i
$33$	61.1238	+	105.869i	0.322433	+	0.558470i
$34$	10.3505			0.0522087
$35$		0			0
$36$	−25.4228			−0.117698
$37$	−5.94851	−	10.3031i	−0.0264305	−	0.0457790i	0.852508	−	0.522715i	$-0.175081\pi$
$37$	−5.94851	−	10.3031i	−0.0264305	−	0.0457790i	−0.878938	+	0.476936i	$0.841747\pi$
$38$	−139.450	+	241.535i	−0.595311	+	1.03111i
$39$	−79.9485	+	138.475i	−0.328257	+	0.568557i
$40$	−56.0208	−	97.0308i	−0.221442	−	0.383548i
$41$	−111.752			−0.425678			−0.212839	−	0.977087i	$-0.568271\pi$
$41$	−111.752			−0.425678			−0.212839	+	0.977087i	$0.568271\pi$
$42$		0			0
$43$	369.196			1.30935			0.654673	−	0.755912i	$-0.272806\pi$
$43$	369.196			1.30935			0.654673	+	0.755912i	$0.272806\pi$
$44$	−57.5531	−	99.6850i	−0.197192	−	0.341547i
$45$	20.4743	−	35.4624i	0.0678249	−	0.117476i
$46$	−149.402	+	258.772i	−0.478872	+	0.829431i
$47$	131.347	+	227.500i	0.407637	+	0.706049i	0.994624	−	0.103548i	$-0.0330194\pi$
$47$	131.347	+	227.500i	0.407637	+	0.706049i	−0.586987	+	0.809596i	$0.699686\pi$
$48$	−100.268			−0.301510
$49$		0			0
$50$	−237.272			−0.671105
$51$	−6.82475	−	11.8208i	−0.0187384	−	0.0324558i
$52$	75.2782	−	130.386i	0.200754	−	0.347716i
$53$	283.550	−	491.123i	0.734879	−	1.27285i	−0.219898	−	0.975523i	$-0.570572\pi$
$53$	283.550	−	491.123i	0.734879	−	1.27285i	0.954777	−	0.297324i	$-0.0960942\pi$
$54$	−30.7114	−	53.1937i	−0.0773943	−	0.134051i
$55$	185.402			0.454538
$56$		0			0
$57$	367.794			0.854658
$58$	246.371	+	426.728i	0.557761	+	0.966070i
$59$	−419.945	+	727.366i	−0.926648	+	1.60500i	−0.137758	+	0.990466i	$0.543990\pi$
$59$	−419.945	+	727.366i	−0.926648	+	1.60500i	−0.788890	+	0.614535i	$0.789344\pi$
$60$	−19.2782	+	33.3909i	−0.0414801	+	0.0718457i
$61$	242.897	+	420.710i	0.509832	+	0.883056i	0.999935	+	0.0113909i	$0.00362593\pi$
$61$	242.897	+	420.710i	0.509832	+	0.883056i	−0.490103	+	0.871665i	$0.663041\pi$
$62$	−572.811			−1.17334
$63$		0			0
$64$	542.577			1.05972
$65$	121.251	+	210.013i	0.231374	+	0.400752i
$66$	139.051	−	240.844i	0.259334	−	0.449180i
$67$	166.846	−	288.985i	0.304230	−	0.526942i	−0.672859	−	0.739770i	$-0.734934\pi$
$67$	166.846	−	288.985i	0.304230	−	0.526942i	0.977090	+	0.212828i	$0.0682675\pi$
$68$	6.42608	+	11.1303i	0.0114599	+	0.0198492i
$69$	394.042			0.687493
$70$		0			0
$71$	590.248			0.986613			0.493306	−	0.869856i	$-0.335788\pi$
$71$	590.248			0.986613			0.493306	+	0.869856i	$0.335788\pi$
$72$	110.814	+	191.936i	0.181383	+	0.314165i
$73$	−245.350	+	424.960i	−0.393371	+	0.681339i	−0.992892	−	0.119020i	$-0.962025\pi$
$73$	−245.350	+	424.960i	−0.393371	+	0.681339i	0.599521	+	0.800359i	$0.295358\pi$
$74$	−13.5324	+	23.4387i	−0.0212582	+	0.0368203i
$75$	156.449	+	270.977i	0.240868	+	0.417196i
$76$	−346.309			−0.522689
$77$		0			0
$78$	363.752			0.528037
$79$	−60.8455	−	105.388i	−0.0866539	−	0.150089i	0.819441	−	0.573164i	$-0.194284\pi$
$79$	−60.8455	−	105.388i	−0.0866539	−	0.150089i	−0.906095	+	0.423075i	$0.860951\pi$
$80$	−76.0340	+	131.695i	−0.106261	+	0.184049i
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$	127.114	+	220.168i	0.171187	+	0.296505i
$83$	609.608			0.806183			0.403091	−	0.915160i	$-0.367936\pi$
$83$	609.608			0.806183			0.403091	+	0.915160i	$0.367936\pi$
$84$		0			0
$85$	−20.7010			−0.0264157
$86$	−419.945	−	727.366i	−0.526556	−	0.912023i
$87$	324.897	−	562.738i	0.400375	−	0.693470i
$88$	−501.733	+	869.026i	−0.607783	+	1.05271i
$89$	−359.519	−	622.705i	−0.428190	−	0.741648i	0.568522	−	0.822668i	$-0.307515\pi$
$89$	−359.519	−	622.705i	−0.428190	−	0.741648i	−0.996712	+	0.0810204i	$0.974182\pi$
$90$	−93.1545			−0.109104
$91$		0			0
$92$	−371.023			−0.420455
$93$	377.691	+	654.180i	0.421126	+	0.729412i
$94$	298.804	−	517.544i	0.327865	−	0.567878i
$95$	278.900	−	483.070i	0.301206	−	0.521704i
$96$	−181.454	−	314.287i	−0.192912	−	0.334134i
$97$	−637.877			−0.667697			−0.333849	−	0.942627i	$-0.608347\pi$
$97$	−637.877			−0.667697			−0.333849	+	0.942627i	$0.608347\pi$
$98$		0			0
$99$	−366.743			−0.372313
$100$	−147.309	−	255.147i	−0.147309	−	0.255147i
$101$	−335.574	+	581.231i	−0.330603	+	0.572620i	−0.982630	−	0.185575i	$-0.940585\pi$
$101$	−335.574	+	581.231i	−0.330603	+	0.572620i	0.652028	+	0.758195i	$0.273919\pi$
$102$	−15.5257	+	26.8914i	−0.0150714	+	0.0261043i
$103$	456.206	+	790.172i	0.436420	+	0.755902i	0.997410	−	0.0719202i	$-0.0229127\pi$
$103$	456.206	+	790.172i	0.436420	+	0.755902i	−0.560990	+	0.827823i	$0.689579\pi$
$104$	−1312.51			−1.23752
$105$		0			0
$106$	−1290.10			−1.18213
$107$	58.3680	+	101.096i	0.0527350	+	0.0913397i	0.891188	−	0.453634i	$-0.149873\pi$
$107$	58.3680	+	101.096i	0.0527350	+	0.0913397i	−0.838453	+	0.544974i	$0.816539\pi$
$108$	38.1341	−	66.0503i	0.0339765	−	0.0588490i
$109$	−418.588	+	725.016i	−0.367830	+	0.637100i	−0.989226	−	0.146396i	$-0.953232\pi$
$109$	−418.588	+	725.016i	−0.367830	+	0.637100i	0.621396	+	0.783497i	$0.286566\pi$
$110$	−210.887	−	365.267i	−0.182794	−	0.316608i
$111$	35.6911			0.0305193
$112$		0			0
$113$	−1086.58			−0.904572			−0.452286	−	0.891873i	$-0.649391\pi$
$113$	−1086.58			−0.904572			−0.452286	+	0.891873i	$0.649391\pi$
$114$	−418.350	−	724.604i	−0.343703	−	0.595311i
$115$	298.804	−	517.544i	0.242292	−	0.419663i
$116$	−305.918	+	529.865i	−0.244860	+	0.424110i
$117$	−239.846	−	415.425i	−0.189519	−	0.328257i
$118$	1910.68			1.49061
$119$		0			0
$120$	336.125			0.255699
$121$	−164.748	−	285.351i	−0.123777	−	0.214388i
$122$	552.571	−	957.080i	0.410061	−	0.710246i
$123$	167.629	−	290.341i	0.122883	−	0.212839i
$124$	−355.628	−	615.965i	−0.257551	−	0.446091i
$125$	1043.27			0.746505
$126$		0			0
$127$	−537.113			−0.375284			−0.187642	−	0.982237i	$-0.560084\pi$
$127$	−537.113			−0.375284			−0.187642	+	0.982237i	$0.560084\pi$
$128$	−133.282	−	230.851i	−0.0920357	−	0.159411i
$129$	−553.794	+	959.199i	−0.377976	+	0.654673i
$130$	275.836	−	477.761i	0.186095	−	0.322326i
$131$	−748.694	−	1296.78i	−0.499341	−	0.864885i	0.500658	−	0.865645i	$-0.333091\pi$
$131$	−748.694	−	1296.78i	−0.499341	−	0.864885i	−1.00000		0.000760253i	$0.999758\pi$
$132$	345.319			0.227698
$133$		0			0
$134$	−759.120			−0.489388
$135$	61.4228	+	106.387i	0.0391587	+	0.0678249i
$136$	56.0208	−	97.0308i	0.0353216	−	0.0611789i
$137$	690.045	−	1195.19i	0.430325	−	0.745345i	−0.566576	−	0.824009i	$-0.691732\pi$
$137$	690.045	−	1195.19i	0.430325	−	0.745345i	0.996901	+	0.0786647i	$0.0250657\pi$
$138$	−448.206	−	776.315i	−0.276477	−	0.478872i
$139$	−141.980			−0.0866374			−0.0433187	−	0.999061i	$-0.513793\pi$
$139$	−141.980			−0.0866374			−0.0433187	+	0.999061i	$0.513793\pi$
$140$		0			0
$141$	−788.083			−0.470699
$142$	−671.382	−	1162.87i	−0.396769	−	0.687223i
$143$	1085.95	−	1880.91i	0.635044	−	1.09993i
$144$	150.402	−	260.505i	0.0870385	−	0.150755i
$145$	−492.743	−	853.455i	−0.282207	−	0.488797i
$146$	1116.30			0.632781
$147$		0			0
$148$	−33.6061			−0.0186649
$149$	971.935	+	1683.44i	0.534390	+	0.925590i	0.999193	+	0.0401757i	$0.0127918\pi$
$149$	971.935	+	1683.44i	0.534390	+	0.925590i	−0.464803	+	0.885414i	$0.653875\pi$
$150$	355.907	−	616.450i	0.193731	−	0.335553i
$151$	1327.38	−	2299.09i	0.715370	−	1.23906i	−0.247447	−	0.968901i	$-0.579592\pi$
$151$	1327.38	−	2299.09i	0.715370	−	1.23906i	0.962817	−	0.270155i	$-0.0870750\pi$
$152$	1509.51	+	2614.55i	0.805511	+	1.39519i
$153$	40.9485			0.0216372
$154$		0			0
$155$	1145.62			0.593668
$156$	225.835	+	391.157i	0.115905	+	0.200754i
$157$	−832.608	+	1442.12i	−0.423244	+	0.733081i	−0.996255	−	0.0864675i	$-0.972442\pi$
$157$	−832.608	+	1442.12i	−0.423244	+	0.733081i	0.573010	+	0.819548i	$0.305775\pi$
$158$	−138.419	+	239.748i	−0.0696961	+	0.120717i
$159$	850.650	+	1473.37i	0.424282	+	0.734879i
$160$	−550.390			−0.271951
$161$		0			0
$162$	184.268			0.0893672
$163$	16.5366	+	28.6422i	0.00794629	+	0.0137634i	0.869971	−	0.493103i	$-0.164137\pi$
$163$	16.5366	+	28.6422i	0.00794629	+	0.0137634i	−0.862025	+	0.506866i	$0.830804\pi$
$164$	−157.837	+	273.381i	−0.0751522	+	0.130167i
$165$	−278.103	+	481.688i	−0.131214	+	0.227269i
$166$	−693.404	−	1201.01i	−0.324208	−	0.561545i
$167$	1654.48			0.766630			0.383315	−	0.923618i	$-0.374782\pi$
$167$	1654.48			0.766630			0.383315	+	0.923618i	$0.374782\pi$
$168$		0			0
$169$	643.784			0.293029
$170$	23.5465	+	40.7838i	0.0106232	+	0.0183998i
$171$	−551.691	+	955.557i	−0.246719	+	0.427329i
$172$	521.444	−	903.167i	0.231161	−	0.400383i
$173$	−32.0954	−	55.5909i	−0.0141050	−	0.0244306i	0.858887	−	0.512166i	$-0.171157\pi$
$173$	−32.0954	−	55.5909i	−0.0141050	−	0.0244306i	−0.872992	+	0.487735i	$0.837823\pi$
$174$	−1478.23			−0.644047
$175$		0			0
$176$	1361.95			0.583300
$177$	−1259.84	−	2182.10i	−0.535000	−	0.926648i
$178$	−817.876	+	1416.60i	−0.344396	+	0.596511i
$179$	−1957.34	+	3390.21i	−0.817309	+	1.41562i	0.0903489	+	0.995910i	$0.471202\pi$
$179$	−1957.34	+	3390.21i	−0.817309	+	1.41562i	−0.907658	+	0.419711i	$0.862132\pi$
$180$	−57.8347	−	100.173i	−0.0239486	−	0.0414801i
$181$	−2058.04			−0.845156			−0.422578	−	0.906327i	$-0.638875\pi$
$181$	−2058.04			−0.845156			−0.422578	+	0.906327i	$0.638875\pi$
$182$		0			0
$183$	−1457.38			−0.588704
$184$	1617.24	+	2801.14i	0.647959	+	1.12230i
$185$	27.0647	−	46.8775i	0.0107559	−	0.0186297i
$186$	859.216	−	1488.21i	0.338714	−	0.586670i
$187$	92.7010	+	160.563i	0.0362512	+	0.0627889i
$188$	742.046			0.287869
$189$		0			0
$190$	−1268.95			−0.484523
$191$	−214.024	−	370.701i	−0.0810798	−	0.140434i	0.822634	−	0.568571i	$-0.192504\pi$
$191$	−214.024	−	370.701i	−0.0810798	−	0.140434i	−0.903714	+	0.428137i	$0.859170\pi$
$192$	−813.866	+	1409.66i	−0.305915	+	0.529861i
$193$	−802.463	+	1389.91i	−0.299288	+	0.518382i	−0.975973	−	0.217890i	$-0.930082\pi$
$193$	−802.463	+	1389.91i	−0.299288	+	0.518382i	0.676685	+	0.736272i	$0.263416\pi$
$194$	725.559	+	1256.70i	0.268516	+	0.465083i
$195$	−727.505			−0.267168
$196$		0			0
$197$	3738.83			1.35218			0.676092	−	0.736817i	$-0.263672\pi$
$197$	3738.83			1.35218			0.676092	+	0.736817i	$0.263672\pi$
$198$	417.154	+	722.533i	0.149727	+	0.259334i
$199$	174.515	−	302.269i	0.0621660	−	0.107675i	−0.833267	−	0.552870i	$-0.813533\pi$
$199$	174.515	−	302.269i	0.0621660	−	0.107675i	0.895433	+	0.445196i	$0.146866\pi$
$200$	−1284.20	+	2224.31i	−0.454034	+	0.786411i
$201$	500.537	+	866.955i	0.175647	+	0.304230i
$202$	1526.81			0.531810
$203$		0			0
$204$	−38.5565			−0.0132328
$205$	−254.228	−	440.335i	−0.0866148	−	0.150021i
$206$	1037.83	−	1797.58i	0.351015	−	0.607976i
$207$	−591.062	+	1023.75i	−0.198462	+	0.343747i
$208$	890.700	+	1542.74i	0.296918	+	0.514277i
$209$	−4995.77			−1.65342
$210$		0			0
$211$	2588.58			0.844574			0.422287	−	0.906462i	$-0.361227\pi$
$211$	2588.58			0.844574			0.422287	+	0.906462i	$0.361227\pi$
$212$	−800.958	−	1387.30i	−0.259481	−	0.449435i
$213$	−885.371	+	1533.51i	−0.284811	+	0.493306i
$214$	132.782	−	229.986i	0.0424150	−	0.0734649i
$215$	839.890	+	1454.73i	0.266419	+	0.461451i
$216$	−664.886			−0.209443
$217$		0			0
$218$	1904.51			0.591695
$219$	−736.051	−	1274.88i	−0.227113	−	0.393371i
$220$	261.857	−	453.550i	0.0802473	−	0.138992i
$221$	−121.251	+	210.013i	−0.0369059	+	0.0639230i
$222$	−40.5971	−	70.3162i	−0.0122734	−	0.0212582i
$223$	−3236.21			−0.971804			−0.485902	−	0.874013i	$-0.661509\pi$
$223$	−3236.21			−0.971804			−0.485902	+	0.874013i	$0.661509\pi$
$224$		0			0
$225$	−938.691			−0.278131
$226$	1235.94	+	2140.71i	0.363776	+	0.630078i
$227$	2815.81	−	4877.12i	0.823312	−	1.42602i	−0.0798906	−	0.996804i	$-0.525457\pi$
$227$	2815.81	−	4877.12i	0.823312	−	1.42602i	0.903203	−	0.429215i	$-0.141210\pi$
$228$	519.463	−	899.737i	0.150887	−	0.261344i
$229$	−1885.12	−	3265.13i	−0.543985	−	0.942210i	−0.998670	−	0.0515573i	$-0.983582\pi$
$229$	−1885.12	−	3265.13i	−0.543985	−	0.942210i	0.454685	−	0.890652i	$-0.349752\pi$
$230$	−1359.51			−0.389754
$231$		0			0
$232$	5333.82			1.50941
$233$	3280.45	+	5681.91i	0.922358	+	1.59757i	0.795756	+	0.605618i	$0.207074\pi$
$233$	3280.45	+	5681.91i	0.922358	+	1.59757i	0.126602	+	0.991954i	$0.459593\pi$
$234$	−545.629	+	945.057i	−0.152431	+	0.264018i
$235$	−597.608	+	1035.09i	−0.165888	+	0.287326i
$236$	1186.24	+	2054.63i	0.327194	+	0.566716i
$237$	365.073			0.100059
$238$		0			0
$239$	−771.444			−0.208789			−0.104394	−	0.994536i	$-0.533290\pi$
$239$	−771.444			−0.208789			−0.104394	+	0.994536i	$0.533290\pi$
$240$	−228.102	−	395.084i	−0.0613497	−	0.106261i
$241$	−626.051	+	1084.35i	−0.167334	+	0.289831i	−0.937482	−	0.348035i	$-0.886849\pi$
$241$	−626.051	+	1084.35i	−0.167334	+	0.289831i	0.770148	+	0.637866i	$0.220183\pi$
$242$	−374.787	+	649.150i	−0.0995546	+	0.172434i
$243$	−121.500	−	210.444i	−0.0320750	−	0.0555556i
$244$	1372.25			0.360037
$245$		0			0
$246$	−762.683			−0.197670
$247$	−3267.18	−	5658.92i	−0.841641	−	1.45777i
$248$	−3100.27	+	5369.82i	−0.793819	+	1.37493i
$249$	−914.412	+	1583.81i	−0.232725	+	0.403091i
$250$	−1186.68	−	2055.39i	−0.300209	−	0.519977i
$251$	5166.27			1.29917			0.649586	−	0.760288i	$-0.274942\pi$
$251$	5166.27			1.29917			0.649586	+	0.760288i	$0.274942\pi$
$252$		0			0
$253$	−5352.29			−1.33002
$254$	610.944	+	1058.19i	0.150921	+	0.261403i
$255$	31.0515	−	53.7828i	0.00762557	−	0.0132079i
$256$	1867.10	−	3233.92i	0.455836	−	0.789531i
$257$	−1383.73	−	2396.68i	−0.335854	−	0.581716i	0.647795	−	0.761815i	$-0.275691\pi$
$257$	−1383.73	−	2396.68i	−0.335854	−	0.581716i	−0.983648	+	0.180099i	$0.942358\pi$
$258$	2519.67			0.608015
$259$		0			0
$260$	685.007			0.163394
$261$	974.691	+	1688.21i	0.231157	+	0.400375i
$262$	−1703.22	+	2950.06i	−0.401623	+	0.695631i
$263$	2050.89	−	3552.25i	0.480849	−	0.832855i	−0.518909	−	0.854829i	$-0.673662\pi$
$263$	2050.89	−	3552.25i	0.480849	−	0.832855i	0.999759	+	0.0219739i	$0.00699507\pi$
$264$	−1505.20	−	2607.08i	−0.350903	−	0.607783i
$265$	2580.21			0.598117
$266$		0			0
$267$	2157.11			0.494432
$268$	−471.297	−	816.311i	−0.107422	−	0.186060i
$269$	3475.42	−	6019.60i	0.787732	−	1.36439i	−0.139621	−	0.990205i	$-0.544588\pi$
$269$	3475.42	−	6019.60i	0.787732	−	1.36439i	0.927353	−	0.374187i	$-0.122078\pi$
$270$	139.732	−	242.022i	0.0314956	−	0.0545519i
$271$	3570.15	+	6183.67i	0.800262	+	1.38609i	0.919444	+	0.393222i	$0.128639\pi$
$271$	3570.15	+	6183.67i	0.800262	+	1.38609i	−0.119182	+	0.992872i	$0.538027\pi$
$272$	−152.068			−0.0338988
$273$		0			0
$274$	−3139.59			−0.692225
$275$	−2125.05	−	3680.69i	−0.465983	−	0.807106i
$276$	556.535	−	963.946i	0.121375	−	0.210227i
$277$	−660.257	+	1143.60i	−0.143217	+	0.248059i	−0.928706	−	0.370816i	$-0.879078\pi$
$277$	−660.257	+	1143.60i	−0.143217	+	0.248059i	0.785490	+	0.618875i	$0.212411\pi$
$278$	161.497	+	279.720i	0.0348414	+	0.0603471i
$279$	−2266.15			−0.486275
$280$		0			0
$281$	−204.309			−0.0433738			−0.0216869	−	0.999765i	$-0.506904\pi$
$281$	−204.309			−0.0433738			−0.0216869	+	0.999765i	$0.506904\pi$
$282$	896.412	+	1552.63i	0.189293	+	0.327865i
$283$	−487.897	+	845.062i	−0.102482	+	0.177504i	−0.912707	−	0.408615i	$-0.866012\pi$
$283$	−487.897	+	845.062i	−0.102482	+	0.177504i	0.810225	+	0.586120i	$0.199345\pi$
$284$	833.651	−	1443.93i	0.174183	−	0.301695i
$285$	836.701	+	1449.21i	0.173901	+	0.301206i
$286$	−4940.87			−1.02154
$287$		0			0
$288$	1088.72			0.222756
$289$	2446.15	+	4236.86i	0.497893	+	0.862376i
$290$	−1120.95	+	1941.54i	−0.226981	+	0.393142i
$291$	956.816	−	1657.25i	0.192748	−	0.333849i
$292$	693.054	+	1200.41i	0.138897	+	0.240577i
$293$	607.919			0.121212			0.0606058	−	0.998162i	$-0.480697\pi$
$293$	607.919			0.121212			0.0606058	+	0.998162i	$0.480697\pi$
$294$		0			0
$295$	−3821.36			−0.754198
$296$	146.485	+	253.719i	0.0287643	+	0.0498213i
$297$	550.114	−	952.825i	0.107478	−	0.186157i
$298$	2211.07	−	3829.69i	0.429812	−	0.744456i
$299$	−3500.34	−	6062.76i	−0.677023	−	1.17264i
$300$	883.856			0.170098
$301$		0			0
$302$	−6039.37			−1.15075
$303$	−1006.72	−	1743.69i	−0.190873	−	0.330603i
$304$	2048.78	−	3548.60i	0.386532	−	0.669493i
$305$	−1105.14	+	1914.16i	−0.207476	+	0.359359i
$306$	−46.5772	−	80.6741i	−0.00870145	−	0.0150714i
$307$	8037.08			1.49414			0.747069	−	0.664747i	$-0.231461\pi$
$307$	8037.08			1.49414			0.747069	+	0.664747i	$0.231461\pi$
$308$		0			0
$309$	−2737.24			−0.503935
$310$	−1303.10	−	2257.03i	−0.238745	−	0.413518i
$311$	−2655.80	+	4599.98i	−0.484234	+	0.838718i	−0.999836	−	0.0181104i	$-0.994235\pi$
$311$	−2655.80	+	4599.98i	−0.484234	+	0.838718i	0.515602	+	0.856828i	$0.327568\pi$
$312$	1968.77	−	3410.00i	0.357242	−	0.618761i
$313$	765.804	+	1326.41i	0.138293	+	0.239531i	0.926851	−	0.375430i	$-0.122505\pi$
$313$	765.804	+	1326.41i	0.138293	+	0.239531i	−0.788557	+	0.614961i	$0.789172\pi$
$314$	3788.23			0.680835
$315$		0			0
$316$	−343.747			−0.0611939
$317$	−2109.59	−	3653.92i	−0.373775	−	0.647397i	0.616368	−	0.787458i	$-0.288603\pi$
$317$	−2109.59	−	3653.92i	−0.373775	−	0.647397i	−0.990143	+	0.140061i	$0.955270\pi$
$318$	1935.16	−	3351.79i	0.341252	−	0.591066i
$319$	−4413.09	+	7643.70i	−0.774564	+	1.34158i
$320$	1234.32	+	2137.90i	0.215627	+	0.373476i
$321$	−350.208			−0.0608931
$322$		0			0
$323$	557.801			0.0960893
$324$	114.402	+	198.151i	0.0196163	+	0.0339765i
$325$	2779.52	−	4814.26i	0.474400	−	0.821684i
$326$	37.6194	−	65.1587i	0.00639124	−	0.0110700i
$327$	−1255.76	−	2175.05i	−0.212367	−	0.367830i
$328$	2751.95			0.463265
$329$		0			0
$330$	1265.32			0.211072
$331$	−4149.09	−	7186.44i	−0.688987	−	1.19336i	−0.972166	−	0.234294i	$-0.924722\pi$
$331$	−4149.09	−	7186.44i	−0.688987	−	1.19336i	0.283179	−	0.959067i	$-0.408611\pi$
$332$	860.996	−	1491.29i	0.142329	−	0.246521i
$333$	−53.5366	+	92.7281i	−0.00881017	+	0.0152597i
$334$	−1881.90	−	3259.54i	−0.308302	−	0.533994i
$335$	1518.24			0.247613
$336$		0			0
$337$	−4348.44			−0.702892			−0.351446	−	0.936208i	$-0.614310\pi$
$337$	−4348.44			−0.702892			−0.351446	+	0.936208i	$0.614310\pi$
$338$	−732.278	−	1268.34i	−0.117842	−	0.204109i
$339$	1629.87	−	2823.01i	0.261128	−	0.452286i
$340$	−29.2376	+	50.6410i	−0.00466362	+	0.00807763i
$341$	−5130.20	−	8885.77i	−0.814709	−	1.41112i
$342$	2510.10			0.396874
$343$		0			0
$344$	−9091.60			−1.42496
$345$	896.412	+	1552.63i	0.139888	+	0.242292i
$346$	−73.0145	+	126.465i	−0.0113447	+	0.0196497i
$347$	4172.77	−	7227.45i	0.645550	−	1.11813i	−0.338624	−	0.940922i	$-0.609961\pi$
$347$	4172.77	−	7227.45i	0.645550	−	1.11813i	0.984174	−	0.177204i	$-0.0567053\pi$
$348$	−917.753	−	1589.60i	−0.141370	−	0.244860i
$349$	−9982.54			−1.53110			−0.765549	−	0.643378i	$-0.777532\pi$
$349$	−9982.54			−1.53110			−0.765549	+	0.643378i	$0.777532\pi$
$350$		0			0
$351$	1439.07			0.218838
$352$	2464.70	+	4268.98i	0.373207	+	0.646414i
$353$	−4400.79	+	7622.40i	−0.663543	+	1.14929i	0.316135	+	0.948714i	$0.397615\pi$
$353$	−4400.79	+	7622.40i	−0.663543	+	1.14929i	−0.979678	+	0.200576i	$0.935719\pi$
$354$	−2866.02	+	4964.10i	−0.430303	+	0.745307i
$355$	1342.76	+	2325.74i	0.200751	+	0.347711i
$356$	−2031.10			−0.302383
$357$		0			0
$358$	8905.56			1.31473
$359$	262.019	+	453.831i	0.0385205	+	0.0667194i	0.884643	−	0.466269i	$-0.154402\pi$
$359$	262.019	+	453.831i	0.0385205	+	0.0667194i	−0.846122	+	0.532989i	$0.821069\pi$
$360$	−504.187	+	873.278i	−0.0738139	+	0.127849i
$361$	−4085.64	+	7076.53i	−0.595661	+	1.03171i
$362$	2340.94	+	4054.63i	0.339881	+	0.588692i
$363$	988.485			0.142926
$364$		0			0
$365$	−2232.61			−0.320165
$366$	1657.71	+	2871.24i	0.236749	+	0.410061i
$367$	3181.36	−	5510.28i	0.452495	−	0.783745i	−0.546045	−	0.837756i	$-0.683867\pi$
$367$	3181.36	−	5510.28i	0.452495	−	0.783745i	0.998540	+	0.0540110i	$0.0172006\pi$
$368$	2194.99	−	3801.84i	0.310929	−	0.538545i
$369$	502.886	+	871.024i	0.0709464	+	0.122883i
$370$	−123.140			−0.0173020
$371$		0			0
$372$	2133.77			0.297394
$373$	5632.92	+	9756.50i	0.781935	+	1.35435i	0.930813	+	0.365495i	$0.119100\pi$
$373$	5632.92	+	9756.50i	0.781935	+	1.35435i	−0.148879	+	0.988855i	$0.547566\pi$
$374$	210.887	−	365.267i	0.0291570	−	0.0505014i
$375$	−1564.91	+	2710.50i	−0.215497	+	0.373253i
$376$	−3234.48	−	5602.28i	−0.443632	−	0.768393i
$377$	−11544.5			−1.57711
$378$		0			0
$379$	−1151.71			−0.156094			−0.0780470	−	0.996950i	$-0.524868\pi$
$379$	−1151.71			−0.156094			−0.0780470	+	0.996950i	$0.524868\pi$
$380$	−787.824	−	1364.55i	−0.106354	−	0.184211i
$381$	805.669	−	1395.46i	0.108335	−	0.187642i
$382$	−486.887	+	843.313i	−0.0652129	+	0.112952i
$383$	75.7772	+	131.250i	0.0101097	+	0.0175106i	0.871036	−	0.491219i	$-0.163449\pi$
$383$	75.7772	+	131.250i	0.0101097	+	0.0175106i	−0.860926	+	0.508730i	$0.830115\pi$
$384$	799.692			0.106274
$385$		0			0
$386$	3651.08			0.481437
$387$	−1661.38	−	2877.60i	−0.218224	−	0.377976i
$388$	−900.922	+	1560.44i	−0.117880	+	0.204174i
$389$	−2397.09	+	4151.88i	−0.312435	+	0.541154i	−0.978889	−	0.204393i	$-0.934478\pi$
$389$	−2397.09	+	4151.88i	−0.312435	+	0.541154i	0.666454	+	0.745546i	$0.267811\pi$
$390$	827.507	+	1433.28i	0.107442	+	0.186095i
$391$	597.608			0.0772950
$392$		0			0
$393$	4492.17			0.576590
$394$	−4252.76	−	7366.00i	−0.543784	−	0.941862i
$395$	276.837	−	479.496i	0.0352638	−	0.0610786i
$396$	−517.978	+	897.165i	−0.0657308	+	0.113849i
$397$	2311.97	+	4004.45i	0.292278	+	0.506241i	0.974348	−	0.225046i	$-0.0722533\pi$
$397$	2311.97	+	4004.45i	0.292278	+	0.506241i	−0.682070	+	0.731287i	$0.738920\pi$
$398$	−794.014			−0.100001
$399$		0			0
$400$	3485.96			0.435745
$401$	1805.32	+	3126.90i	0.224821	+	0.389402i	0.956266	−	0.292499i	$-0.0944869\pi$
$401$	1805.32	+	3126.90i	0.224821	+	0.389402i	−0.731445	+	0.681901i	$0.761154\pi$
$402$	1138.68	−	1972.25i	0.141274	−	0.244694i
$403$	6710.19	−	11622.4i	0.829425	−	1.43661i
$404$	947.913	+	1641.83i	0.116734	+	0.202189i
$405$	−368.537			−0.0452166
$406$		0			0
$407$	−484.794			−0.0590426
$408$	168.062	+	291.093i	0.0203930	+	0.0353216i
$409$	−4479.79	+	7759.22i	−0.541592	+	0.938065i	0.457221	+	0.889353i	$0.348845\pi$
$409$	−4479.79	+	7759.22i	−0.541592	+	0.938065i	−0.998813	+	0.0487118i	$0.984488\pi$
$410$	−578.347	+	1001.73i	−0.0696647	+	0.120663i
$411$	2070.13	+	3585.58i	0.248448	+	0.430325i
$412$	2577.34			0.308195
$413$		0			0
$414$	2689.24			0.319248
$415$	1386.81	+	2402.02i	0.164038	+	0.284122i
$416$	−3223.77	+	5583.74i	−0.379948	+	0.658089i
$417$	212.970	−	368.875i	0.0250101	−	0.0433187i
$418$	5682.48	+	9842.34i	0.664926	+	1.15169i
$419$	−7078.28			−0.825290			−0.412645	−	0.910892i	$-0.635395\pi$
$419$	−7078.28			−0.825290			−0.412645	+	0.910892i	$0.635395\pi$
$420$		0			0
$421$	11551.5			1.33725			0.668626	−	0.743599i	$-0.266883\pi$
$421$	11551.5			1.33725			0.668626	+	0.743599i	$0.266883\pi$
$422$	−2944.40	−	5099.85i	−0.339647	−	0.588286i
$423$	1182.12	−	2047.50i	0.135879	−	0.235350i
$424$	−6982.53	+	12094.1i	−0.799768	+	1.38524i
$425$	237.272	+	410.966i	0.0270809	+	0.0469054i
$426$	4028.29			0.458149
$427$		0			0
$428$	329.750			0.0372408
$429$	3257.84	+	5642.74i	0.366643	+	0.635044i
$430$	1910.68	−	3309.40i	0.214282	−	0.371147i
$431$	2032.19	−	3519.85i	0.227116	−	0.393377i	−0.729836	−	0.683622i	$-0.760404\pi$
$431$	2032.19	−	3519.85i	0.227116	−	0.393377i	0.956952	+	0.290245i	$0.0937370\pi$
$432$	451.207	+	781.514i	0.0502517	+	0.0870385i
$433$	17456.3			1.93740			0.968701	−	0.248229i	$-0.0798487\pi$
$433$	17456.3			1.93740			0.968701	+	0.248229i	$0.0798487\pi$
$434$		0			0
$435$	2956.46			0.325865
$436$	1182.41	+	2047.99i	0.129879	+	0.224956i
$437$	−8051.45	+	13945.5i	−0.881357	+	1.52656i
$438$	−1674.46	+	2900.24i	−0.182668	+	0.316390i
$439$	−2297.69	−	3979.72i	−0.249802	−	0.432669i	0.713669	−	0.700483i	$-0.247032\pi$
$439$	−2297.69	−	3979.72i	−0.249802	−	0.432669i	−0.963471	+	0.267814i	$0.913699\pi$
$440$	−4565.60			−0.494674
$441$		0			0
$442$	551.671			0.0593672
$443$	153.107	+	265.189i	0.0164206	+	0.0284413i	0.874119	−	0.485712i	$-0.161440\pi$
$443$	153.107	+	265.189i	0.0164206	+	0.0284413i	−0.857698	+	0.514153i	$0.828106\pi$
$444$	50.4092	−	87.3113i	0.00538810	−	0.00933245i
$445$	1635.75	−	2833.21i	0.174252	−	0.301813i
$446$	3681.05	+	6375.77i	0.390813	+	0.676909i
$447$	−5831.61			−0.617060
$448$		0			0
$449$	9229.22			0.970053			0.485026	−	0.874500i	$-0.338810\pi$
$449$	9229.22			0.970053			0.485026	+	0.874500i	$0.338810\pi$
$450$	1067.72	+	1849.35i	0.111851	+	0.193731i
$451$	−2276.91	+	3943.72i	−0.237728	+	0.411758i
$452$	−1534.66	+	2658.10i	−0.159700	+	0.276608i
$453$	3982.15	+	6897.28i	0.413019	+	0.715370i
$454$	−12811.5			−1.32439
$455$		0			0
$456$	−9057.08			−0.930124
$457$	5496.12	+	9519.55i	0.562577	+	0.974411i	0.997271	+	0.0738330i	$0.0235232\pi$
$457$	5496.12	+	9519.55i	0.562577	+	0.974411i	−0.434694	+	0.900578i	$0.643143\pi$
$458$	−4288.50	+	7427.90i	−0.437530	+	0.757824i
$459$	−61.4228	+	106.387i	−0.00624612	+	0.0108186i
$460$	−844.047	−	1461.93i	−0.0855519	−	0.148180i
$461$	7387.88			0.746394			0.373197	−	0.927752i	$-0.378261\pi$
$461$	7387.88			0.746394			0.373197	+	0.927752i	$0.378261\pi$
$462$		0			0
$463$	10163.8			1.02020			0.510101	−	0.860114i	$-0.329608\pi$
$463$	10163.8			1.02020			0.510101	+	0.860114i	$0.329608\pi$
$464$	−3619.65	−	6269.42i	−0.362151	−	0.627264i
$465$	−1718.43	+	2976.41i	−0.171377	+	0.296834i
$466$	7462.75	−	12925.9i	0.741857	−	1.28493i
$467$	7907.29	+	13695.8i	0.783524	+	1.35710i	0.929877	+	0.367871i	$0.119913\pi$
$467$	7907.29	+	13695.8i	0.783524	+	1.35710i	−0.146353	+	0.989232i	$0.546754\pi$
$468$	−1355.01			−0.133836
$469$		0			0
$470$	2719.02			0.266849
$471$	−2497.82	−	4326.36i	−0.244360	−	0.423244i
$472$	10341.3	−	17911.7i	1.00847	−	1.74672i
$473$	7522.22	−	13028.9i	0.731230	−	1.26653i
$474$	−415.256	−	719.244i	−0.0402391	−	0.0696961i
$475$	−12786.9			−1.23516
$476$		0			0
$477$	−5103.90			−0.489919
$478$	877.485	+	1519.85i	0.0839649	+	0.145432i
$479$	722.427	−	1251.28i	0.0689113	−	0.119358i	−0.829511	−	0.558490i	$-0.811381\pi$
$479$	722.427	−	1251.28i	0.0689113	−	0.119358i	0.898422	+	0.439132i	$0.144714\pi$
$480$	825.585	−	1429.96i	0.0785055	−	0.135976i
$481$	−317.050	−	549.146i	−0.0300545	−	0.0520559i
$482$	2848.43			0.269175
$483$		0			0
$484$	−930.742			−0.0874100
$485$	−1451.12	−	2513.41i	−0.135860	−	0.235316i
$486$	−276.402	+	478.743i	−0.0257981	+	0.0446836i
$487$	244.701	−	423.835i	0.0227689	−	0.0394369i	−0.854416	−	0.519589i	$-0.826085\pi$
$487$	244.701	−	423.835i	0.0227689	−	0.0394369i	0.877185	+	0.480152i	$0.159418\pi$
$488$	−5981.44	−	10360.2i	−0.554851	−	0.961029i
$489$	−99.2195			−0.00917559
$490$		0			0
$491$	−3941.30			−0.362257			−0.181129	−	0.983459i	$-0.557975\pi$
$491$	−3941.30			−0.362257			−0.181129	+	0.983459i	$0.557975\pi$
$492$	−473.510	−	820.143i	−0.0433891	−	0.0751522i
$493$	492.743	−	853.455i	0.0450142	−	0.0779669i
$494$	−7432.56	+	12873.6i	−0.676936	+	1.17249i
$495$	−834.309	−	1445.07i	−0.0757564	−	0.131214i
$496$	8415.65			0.761843
$497$		0			0
$498$	4160.42			0.374363
$499$	−5.54470	−	9.60371i	−0.000497425	−	0.000861565i	0.865777	−	0.500431i	$-0.166825\pi$
$499$	−5.54470	−	9.60371i	−0.000497425	−	0.000861565i	−0.866274	+	0.499569i	$0.833492\pi$
$500$	1473.49	−	2552.16i	0.131793	−	0.228273i
$501$	−2481.71	+	4298.45i	−0.221307	+	0.383315i
$502$	−5876.42	−	10178.3i	−0.522465	−	0.904936i
$503$	7088.41			0.628343			0.314172	−	0.949366i	$-0.398273\pi$
$503$	7088.41			0.628343			0.314172	+	0.949366i	$0.398273\pi$
$504$		0			0
$505$	−3053.61			−0.269077
$506$	6088.01	+	10544.7i	0.534871	+	0.926424i
$507$	−965.676	+	1672.60i	−0.0845901	+	0.146514i
$508$	−758.605	+	1313.94i	−0.0662553	+	0.114757i
$509$	−8794.22	−	15232.0i	−0.765810	−	1.32642i	−0.939817	−	0.341677i	$-0.889005\pi$
$509$	−8794.22	−	15232.0i	−0.765810	−	1.32642i	0.174008	−	0.984744i	$-0.444328\pi$
$510$	−141.279			−0.0122666
$511$		0			0
$512$	−10627.5			−0.917333
$513$	−1655.07	−	2866.67i	−0.142443	−	0.246719i
$514$	−3147.86	+	5452.25i	−0.270129	+	0.467877i
$515$	−2075.66	+	3595.15i	−0.177601	+	0.307614i
$516$	1564.33	+	2709.50i	0.133461	+	0.231161i
$517$	10704.6			0.910613
$518$		0			0
$519$	192.573			0.0162871
$520$	−2985.85	−	5171.65i	−0.251804	−	0.436138i
$521$	5823.30	−	10086.2i	0.489680	−	0.848151i	−0.510249	−	0.860026i	$-0.670447\pi$
$521$	5823.30	−	10086.2i	0.489680	−	0.848151i	0.999929	+	0.0118758i	$0.00378028\pi$
$522$	2217.34	−	3840.55i	0.185920	−	0.322023i
$523$	−4482.91	−	7764.63i	−0.374807	−	0.649185i	0.615491	−	0.788144i	$-0.288958\pi$
$523$	−4482.91	−	7764.63i	−0.374807	−	0.649185i	−0.990298	+	0.138959i	$0.955624\pi$
$524$	−4229.75			−0.352629
$525$		0			0
$526$	−9331.22			−0.773499
$527$	572.811	+	992.137i	0.0473473	+	0.0820079i
$528$	−2042.93	+	3538.45i	−0.168384	+	0.291650i
$529$	−2542.54	+	4403.81i	−0.208970	+	0.361947i
$530$	−2934.88	−	5083.36i	−0.240534	−	0.416617i
$531$	7559.01			0.617765
$532$		0			0
$533$	−5956.30			−0.484045
$534$	−2453.63	−	4249.81i	−0.198837	−	0.344396i
$535$	−265.565	+	459.971i	−0.0214605	+	0.0371706i
$536$	−4108.64	+	7116.37i	−0.331094	+	0.573471i
$537$	−5872.01	−	10170.6i	−0.471874	−	0.817309i
$538$	−15812.6			−1.26715
$539$		0			0
$540$	347.008			0.0276534
$541$	97.6359	+	169.110i	0.00775914	+	0.0134392i	0.869879	−	0.493265i	$-0.164197\pi$
$541$	97.6359	+	169.110i	0.00775914	+	0.0134392i	−0.862120	+	0.506705i	$0.830863\pi$
$542$	8121.79	−	14067.3i	0.643654	−	1.11484i
$543$	3087.07	−	5346.95i	0.243975	−	0.422578i
$544$	−275.195	−	476.652i	−0.0216891	−	0.0375667i
$545$	−3809.01			−0.299376
$546$		0			0
$547$	−1399.26			−0.109375			−0.0546874	−	0.998504i	$-0.517416\pi$
$547$	−1399.26			−0.109375			−0.0546874	+	0.998504i	$0.517416\pi$
$548$	−1949.21	−	3376.12i	−0.151945	−	0.263177i
$549$	2186.07	−	3786.39i	0.169944	−	0.294352i
$550$	−4834.31	+	8373.27i	−0.374792	+	0.649159i
$551$	13277.2	+	22996.9i	1.02655	+	1.77804i
$552$	−9703.44			−0.748199
$553$		0			0
$554$	3004.06			0.230380
$555$	81.1942	+	140.632i	0.00620991	+	0.0107559i
$556$	−200.529	+	347.327i	−0.0152956	+	0.0264927i
$557$	−21.5233	+	37.2795i	−0.00163730	+	0.00283588i	−0.866843	−	0.498581i	$-0.833855\pi$
$557$	−21.5233	+	37.2795i	−0.00163730	+	0.00283588i	0.865206	+	0.501417i	$0.167188\pi$
$558$	2577.65	+	4464.62i	0.195557	+	0.338714i
$559$	19677.8			1.48888
$560$		0			0
$561$	−556.206			−0.0418592
$562$	232.393	+	402.516i	0.0174429	+	0.0302120i
$563$	9616.43	−	16656.1i	0.719865	−	1.24684i	−0.241187	−	0.970479i	$-0.577537\pi$
$563$	9616.43	−	16656.1i	0.719865	−	1.24684i	0.961053	−	0.276365i	$-0.0891298\pi$
$564$	−1113.07	+	1927.89i	−0.0831005	+	0.143934i
$565$	−2471.88	−	4281.41i	−0.184058	−	0.318797i
$566$	2219.85			0.164854
$567$		0			0
$568$	−14535.1			−1.07373
$569$	−2581.99	−	4472.14i	−0.190233	−	0.329493i	0.755094	−	0.655616i	$-0.227591\pi$
$569$	−2581.99	−	4472.14i	−0.190233	−	0.329493i	−0.945327	+	0.326123i	$0.894258\pi$
$570$	1903.43	−	3296.83i	0.139870	−	0.242261i
$571$	5115.96	−	8861.10i	0.374950	−	0.649432i	−0.615370	−	0.788238i	$-0.710993\pi$
$571$	5115.96	−	8861.10i	0.374950	−	0.649432i	0.990319	+	0.138807i	$0.0443267\pi$
$572$	−3067.53	−	5313.11i	−0.224230	−	0.388378i
$573$	1284.14			0.0936229
$574$		0			0
$575$	−13699.4			−0.993572
$576$	−2441.60	−	4228.97i	−0.176620	−	0.305915i
$577$	−8281.87	+	14344.6i	−0.597537	+	1.03496i	0.395647	+	0.918403i	$0.370520\pi$
$577$	−8281.87	+	14344.6i	−0.597537	+	1.03496i	−0.993184	+	0.116561i	$0.962813\pi$
$578$	5564.79	−	9638.49i	0.400458	−	0.693613i
$579$	−2407.39	−	4169.72i	−0.172794	−	0.299288i
$580$	−2783.75			−0.199291
$581$		0			0
$582$	−4353.35			−0.310055
$583$	−11554.4	−	20012.8i	−0.820815	−	1.42169i
$584$	6041.86	−	10464.8i	0.428106	−	0.741501i
$585$	1091.26	−	1890.11i	0.0771247	−	0.133584i
$586$	−691.482	−	1197.68i	−0.0487455	−	0.0844297i
$587$	16020.6			1.12648			0.563239	−	0.826294i	$-0.309555\pi$
$587$	16020.6			1.12648			0.563239	+	0.826294i	$0.309555\pi$
$588$		0			0
$589$	−30869.4			−2.15951
$590$	4346.64	+	7528.60i	0.303302	+	0.525335i
$591$	−5608.24	+	9713.76i	−0.390342	+	0.676092i
$592$	198.816	−	344.359i	0.0138028	−	0.0239072i
$593$	3385.57	+	5863.98i	0.234450	+	0.406079i	0.959113	−	0.283025i	$-0.0913378\pi$
$593$	3385.57	+	5863.98i	0.234450	+	0.406079i	−0.724663	+	0.689104i	$0.758004\pi$
$594$	−2502.93			−0.172889
$595$		0			0
$596$	5490.95			0.377379
$597$	523.545	+	906.806i	0.0358916	+	0.0621660i
$598$	−7962.98	+	13792.3i	−0.544532	+	0.943158i
$599$	−5535.11	+	9587.09i	−0.377560	+	0.653953i	−0.990707	−	0.136016i	$-0.956570\pi$
$599$	−5535.11	+	9587.09i	−0.377560	+	0.653953i	0.613147	+	0.789969i	$0.289903\pi$
$600$	−3852.61	−	6672.92i	−0.262137	−	0.454034i
$601$	−24187.7			−1.64166			−0.820830	−	0.571173i	$-0.806489\pi$
$601$	−24187.7			−1.64166			−0.820830	+	0.571173i	$0.806489\pi$
$602$		0			0
$603$	−3003.22			−0.202820
$604$	−3749.52	−	6494.37i	−0.252593	−	0.437503i
$605$	749.574	−	1298.30i	0.0503711	−	0.0872453i
$606$	−2290.21	+	3966.76i	−0.153520	+	0.265905i
$607$	5037.04	+	8724.40i	0.336816	+	0.583382i	0.983832	−	0.179095i	$-0.0573168\pi$
$607$	5037.04	+	8724.40i	0.336816	+	0.583382i	−0.647016	+	0.762476i	$0.723983\pi$
$608$	14830.6			0.989243
$609$		0			0
$610$	5028.21			0.333748
$611$	7000.67	+	12125.5i	0.463530	+	0.802858i
$612$	57.8347	−	100.173i	0.00381998	−	0.00661640i
$613$	5557.29	−	9625.51i	0.366161	−	0.634210i	−0.622800	−	0.782381i	$-0.714005\pi$
$613$	5557.29	−	9625.51i	0.366161	−	0.634210i	0.988962	+	0.148171i	$0.0473385\pi$
$614$	−9141.84	−	15834.1i	−0.600871	−	1.04074i
$615$	1525.37			0.100014
$616$		0			0
$617$	20496.4			1.33737			0.668683	−	0.743548i	$-0.266858\pi$
$617$	20496.4			1.33737			0.668683	+	0.743548i	$0.266858\pi$
$618$	3113.49	+	5392.73i	0.202659	+	0.351015i
$619$	8357.22	−	14475.1i	0.542658	−	0.939910i	−0.456093	−	0.889932i	$-0.650751\pi$
$619$	8357.22	−	14475.1i	0.542658	−	0.939910i	0.998750	−	0.0499782i	$-0.0159152\pi$
$620$	1618.05	−	2802.54i	0.104810	−	0.181537i
$621$	−1773.19	−	3071.25i	−0.114582	−	0.198462i
$622$	12083.5			0.778943
$623$		0			0
$624$	−5344.20			−0.342851
$625$	−4145.33	−	7179.92i	−0.265301	−	0.459515i
$626$	1742.14	−	3017.48i	0.111230	−	0.192656i
$627$	7493.65	−	12979.4i	0.477301	−	0.826709i
$628$	2351.91	+	4073.63i	0.149445	+	0.258846i
$629$	54.1295			0.00343129
$630$		0			0
$631$	9168.53			0.578437			0.289218	−	0.957263i	$-0.406605\pi$
$631$	9168.53			0.578437			0.289218	+	0.957263i	$0.406605\pi$
$632$	1498.35	+	2595.21i	0.0943054	+	0.163342i
$633$	−3882.87	+	6725.32i	−0.243807	+	0.422287i
$634$	−4799.15	+	8312.37i	−0.300629	+	0.520704i
$635$	−1221.89	−	2116.37i	−0.0763608	−	0.132261i
$636$	4805.75			0.299623
$637$		0			0
$638$	20078.9			1.24597
$639$	−2656.11	−	4600.52i	−0.164435	−	0.284811i
$640$	606.411	−	1050.33i	0.0374539	−	0.0648721i
$641$	2136.68	−	3700.84i	0.131660	−	0.228041i	−0.792657	−	0.609668i	$-0.791303\pi$
$641$	2136.68	−	3700.84i	0.131660	−	0.228041i	0.924316	+	0.381627i	$0.124636\pi$
$642$	398.347	+	689.957i	0.0244883	+	0.0424150i
$643$	2955.75			0.181281			0.0906404	−	0.995884i	$-0.471109\pi$
$643$	2955.75			0.181281			0.0906404	+	0.995884i	$0.471109\pi$
$644$		0			0
$645$	−5039.34			−0.307634
$646$	−634.475	−	1098.94i	−0.0386426	−	0.0669309i
$647$	−11350.6	+	19659.8i	−0.689704	+	1.19460i	0.282229	+	0.959347i	$0.408926\pi$
$647$	−11350.6	+	19659.8i	−0.689704	+	1.19460i	−0.971934	+	0.235256i	$0.924407\pi$
$648$	997.329	−	1727.42i	0.0604611	−	0.104722i
$649$	17112.4	+	29639.6i	1.03501	+	1.79269i
$650$	−12646.3			−0.763124
$651$		0			0
$652$	93.4235			0.00561158
$653$	−768.907	−	1331.79i	−0.0460791	−	0.0798113i	0.842066	−	0.539375i	$-0.181339\pi$
$653$	−768.907	−	1331.79i	−0.0460791	−	0.0798113i	−0.888145	+	0.459563i	$0.848006\pi$
$654$	−2856.76	+	4948.05i	−0.170808	+	0.295847i
$655$	3406.44	−	5900.12i	0.203207	−	0.351964i
$656$	−1867.54	−	3234.67i	−0.111151	−	0.192519i
$657$	4416.31			0.262248
$658$		0			0
$659$	12338.1			0.729323			0.364661	−	0.931140i	$-0.381185\pi$
$659$	12338.1			0.729323			0.364661	+	0.931140i	$0.381185\pi$
$660$	785.572	+	1360.65i	0.0463308	+	0.0802473i
$661$	−922.548	+	1597.90i	−0.0542859	+	0.0940259i	−0.891891	−	0.452250i	$-0.850622\pi$
$661$	−922.548	+	1597.90i	−0.0542859	+	0.0940259i	0.837605	+	0.546276i	$0.183955\pi$
$662$	−9438.84	+	16348.6i	−0.554156	+	0.959826i
$663$	−363.752	−	630.038i	−0.0213077	−	0.0369059i
$664$	−15011.8			−0.877369
$665$		0			0
$666$	243.583			0.0141721
$667$	14224.8	+	24638.0i	0.825765	+	1.43027i
$668$	2336.74	−	4047.35i	0.135346	−	0.234426i
$669$	4854.31	−	8407.91i	0.280536	−	0.485902i
$670$	−1726.93	−	2991.14i	−0.0995780	−	0.172474i
$671$	19795.7			1.13890
$672$		0			0
$673$	23955.4			1.37208			0.686041	−	0.727563i	$-0.259347\pi$
$673$	23955.4			1.37208			0.686041	+	0.727563i	$0.259347\pi$
$674$	4946.17	+	8567.02i	0.282670	+	0.489598i
$675$	1408.04	−	2438.79i	0.0802894	−	0.139065i
$676$	909.265	−	1574.89i	0.0517333	−	0.0896048i
$677$	1839.13	+	3185.46i	0.104407	+	0.180838i	0.913496	−	0.406848i	$-0.133372\pi$
$677$	1839.13	+	3185.46i	0.104407	+	0.180838i	−0.809089	+	0.587686i	$0.800039\pi$
$678$	−7415.63			−0.420052
$679$		0			0
$680$	509.771			0.0287482
$681$	8447.43	+	14631.4i	0.475339	+	0.823312i
$682$	−11670.8	+	20214.4i	−0.655275	+	1.13497i
$683$	−2195.43	+	3802.60i	−0.122996	+	0.213034i	−0.920948	−	0.389686i	$-0.872583\pi$
$683$	−2195.43	+	3802.60i	−0.122996	+	0.213034i	0.797952	+	0.602721i	$0.205917\pi$
$684$	1558.39	+	2699.21i	0.0871148	+	0.150887i
$685$	6279.18			0.350241
$686$		0			0
$687$	11310.7			0.628140
$688$	6169.78	+	10686.4i	0.341890	+	0.592171i
$689$	15112.9	−	26176.4i	0.835641	−	1.44737i
$690$	2039.26	−	3532.11i	0.112512	−	0.194877i
$691$	−5185.84	−	8982.13i	−0.285497	−	0.494496i	0.687232	−	0.726438i	$-0.258825\pi$
$691$	−5185.84	−	8982.13i	−0.285497	−	0.494496i	−0.972730	+	0.231942i	$0.925492\pi$
$692$	−181.323			−0.00996081
$693$		0			0
$694$	−18985.4			−1.03844
$695$	−322.993	−	559.440i	−0.0176285	−	0.0305335i
$696$	−8000.72	+	13857.7i	−0.435728	+	0.754703i
$697$	254.228	−	440.335i	0.0138157	−	0.0239295i
$698$	11354.7	+	19667.0i	0.615734	+	1.06648i
$699$	−19682.7			−1.06505
$700$		0			0
$701$	109.675			0.00590922			0.00295461	−	0.999996i	$-0.499060\pi$
$701$	109.675			0.00590922			0.00295461	+	0.999996i	$0.499060\pi$
$702$	−1636.89	−	2835.17i	−0.0880061	−	0.152431i
$703$	−729.275	+	1263.14i	−0.0391254	+	0.0677672i
$704$	11054.8	−	19147.5i	0.591822	−	1.02507i
$705$	−1792.82	−	3105.26i	−0.0957754	−	0.165888i
$706$	20022.9			1.06738
$707$		0			0
$708$	−7117.45			−0.377811
$709$	−13459.4	−	23312.3i	−0.712944	−	1.23486i	−0.963747	−	0.266818i	$-0.914028\pi$
$709$	−13459.4	−	23312.3i	−0.712944	−	1.23486i	0.250803	−	0.968038i	$-0.419306\pi$
$710$	3054.68	−	5290.86i	0.161465	−	0.279665i
$711$	−547.610	+	948.488i	−0.0288846	+	0.0500296i
$712$	8853.31	+	15334.4i	0.466000	+	0.807135i
$713$	−33072.4			−1.73713
$714$		0			0
$715$	9881.74			0.516862
$716$	5528.99	+	9576.50i	0.288587	+	0.499847i
$717$	1157.17	−	2004.27i	0.0602721	−	0.104394i
$718$	596.072	−	1032.43i	0.0309822	−	0.0536627i
$719$	−7585.38	−	13138.3i	−0.393445	−	0.681466i	0.599457	−	0.800407i	$-0.295383\pi$
$719$	−7585.38	−	13138.3i	−0.393445	−	0.681466i	−0.992901	+	0.118941i	$0.962050\pi$
$720$	1368.61			0.0708405
$721$		0			0
$722$	18589.0			0.958185
$723$	−1878.15	−	3253.06i	−0.0966104	−	0.167334i
$724$	−2906.73	+	5034.61i	−0.149210	+	0.258439i
$725$	−11295.5	+	19564.3i	−0.578626	+	1.00221i
$726$	−1124.36	−	1947.45i	−0.0574779	−	0.0995546i
$727$	−33286.9			−1.69813			−0.849066	−	0.528288i	$-0.822834\pi$
$727$	−33286.9			−1.69813			−0.849066	+	0.528288i	$0.822834\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$	2539.50	+	4398.54i	0.128755	+	0.223010i
$731$	−839.890	+	1454.73i	−0.0424959	+	0.0736050i
$732$	−2058.37	+	3565.20i	−0.103934	+	0.180019i
$733$	−10272.0	−	17791.7i	−0.517607	−	0.896521i	−0.999791	−	0.0204512i	$-0.993490\pi$
$733$	−10272.0	−	17791.7i	−0.517607	−	0.896521i	0.482184	−	0.876070i	$-0.339844\pi$
$734$	−14474.7			−0.727888
$735$		0			0
$736$	15889.0			0.795755
$737$	−6798.82	−	11775.9i	−0.339807	−	0.588563i
$738$	1144.02	−	1981.51i	0.0570625	−	0.0988351i
$739$	−17178.6	+	29754.2i	−0.855109	+	1.48109i	0.0214356	+	0.999770i	$0.493176\pi$
$739$	−17178.6	+	29754.2i	−0.855109	+	1.48109i	−0.876544	+	0.481321i	$0.840157\pi$
$740$	−76.4512	−	132.417i	−0.00379784	−	0.00657805i
$741$	19603.1			0.971844
$742$		0			0
$743$	8166.99			0.403254			0.201627	−	0.979462i	$-0.435377\pi$
$743$	8166.99			0.403254			0.201627	+	0.979462i	$0.435377\pi$
$744$	−9300.80	−	16109.5i	−0.458312	−	0.793819i
$745$	−4422.14	+	7659.38i	−0.217470	+	0.376668i
$746$	12814.4	−	22195.2i	0.628914	−	1.08931i
$747$	−2743.24	−	4751.42i	−0.134364	−	0.232725i
$748$	523.715			0.0256001
$749$		0			0
$750$	7120.08			0.346651
$751$	−8540.05	−	14791.8i	−0.414954	−	0.718722i	0.580469	−	0.814282i	$-0.302869\pi$
$751$	−8540.05	−	14791.8i	−0.414954	−	0.718722i	−0.995424	+	0.0955601i	$0.969536\pi$
$752$	−4389.99	+	7603.68i	−0.212881	+	0.368720i
$753$	−7749.40	+	13422.4i	−0.375038	+	0.649586i
$754$	13131.3	+	22744.2i	0.634238	+	1.09853i
$755$	12078.7			0.582239
$756$		0			0
$757$	−16324.0			−0.783758			−0.391879	−	0.920017i	$-0.628175\pi$
$757$	−16324.0			−0.783758			−0.391879	+	0.920017i	$0.628175\pi$
$758$	1310.03	+	2269.03i	0.0627735	+	0.108727i
$759$	8028.43	−	13905.7i	0.383944	−	0.665011i
$760$	−6868.04	+	11895.8i	−0.327802	+	0.567770i
$761$	16183.1	+	28029.9i	0.770875	+	1.33520i	0.937084	+	0.349105i	$0.113514\pi$
$761$	16183.1	+	28029.9i	0.770875	+	1.33520i	−0.166208	+	0.986091i	$0.553152\pi$
$762$	−3665.66			−0.174269
$763$		0			0
$764$	−1209.13			−0.0572576
$765$	93.1545	+	161.348i	0.00440262	+	0.00762557i
$766$	172.387	−	298.583i	0.00813131	−	0.0140838i
$767$	−22382.7	+	38767.9i	−1.05370	+	1.82507i
$768$	5601.31	+	9701.75i	0.263177	+	0.455836i
$769$	−7948.44			−0.372728			−0.186364	−	0.982481i	$-0.559670\pi$
$769$	−7948.44			−0.372728			−0.186364	+	0.982481i	$0.559670\pi$
$770$		0			0
$771$	8302.35			0.387810
$772$	2266.76	+	3926.14i	0.105677	+	0.183038i
$773$	−8909.64	+	15432.0i	−0.414564	+	0.718045i	−0.995383	−	0.0959876i	$-0.969399\pi$
$773$	−8909.64	+	15432.0i	−0.414564	+	0.718045i	0.580819	+	0.814033i	$0.302732\pi$
$774$	−3779.51	+	6546.30i	−0.175519	+	0.304008i
$775$	−13130.9	−	22743.4i	−0.608616	−	1.05415i
$776$	15708.0			0.726655
$777$		0			0
$778$	10906.4			0.502586
$779$	6850.32	+	11865.1i	0.315068	+	0.545714i
$780$	−1027.51	+	1779.70i	−0.0471677	+	0.0816968i
$781$	12026.0	−	20829.7i	0.550993	−	0.954349i
$782$	−679.754	−	1177.37i	−0.0310844	−	0.0538397i
$783$	−5848.15			−0.266917
$784$		0			0
$785$	−7576.46			−0.344478
$786$	−5109.65	−	8850.18i	−0.231877	−	0.401623i
$787$	−1456.19	+	2522.19i	−0.0659562	+	0.114240i	−0.897118	−	0.441791i	$-0.854343\pi$
$787$	−1456.19	+	2522.19i	−0.0659562	+	0.114240i	0.831162	+	0.556031i	$0.187676\pi$
$788$	5280.63	−	9146.32i	0.238724	−	0.413482i
$789$	6152.67	+	10656.7i	0.277618	+	0.480849i
$790$	−1259.56			−0.0567256
$791$		0			0
$792$	9031.19			0.405188
$793$	12946.2	+	22423.4i	0.579738	+	1.00414i
$794$	5259.54	−	9109.79i	0.235081	−	0.407172i
$795$	−3870.31	+	6703.58i	−0.172662	+	0.299059i
$796$	−492.961	−	853.834i	−0.0219504	−	0.0380193i
$797$	−33789.1			−1.50172			−0.750861	−	0.660460i	$-0.770361\pi$
$797$	−33789.1			−1.50172			−0.750861	+	0.660460i	$0.770361\pi$
$798$		0			0
$799$	−1195.22			−0.0529208
$800$	6308.49	+	10926.6i	0.278798	+	0.482893i
$801$	−3235.67	+	5604.35i	−0.142730	+	0.247216i
$802$	4106.95	−	7113.44i	0.180825	−	0.313197i
$803$	9997.83	+	17316.7i	0.439372	+	0.761015i
$804$	2827.78			0.124040
$805$		0			0
$806$	−30530.2			−1.33422
$807$	10426.3	+	18058.8i	0.454797	+	0.787732i
$808$	8263.65	−	14313.1i	0.359795	−	0.623183i
$809$	−626.064	+	1084.37i	−0.0272079	+	0.0471255i	−0.879309	−	0.476252i	$-0.841995\pi$
$809$	−626.064	+	1084.37i	−0.0272079	+	0.0471255i	0.852101	+	0.523378i	$0.175328\pi$
$810$	419.195	+	726.067i	0.0181840	+	0.0314956i
$811$	−31913.1			−1.38178			−0.690889	−	0.722961i	$-0.742781\pi$
$811$	−31913.1			−1.38178			−0.690889	+	0.722961i	$0.742781\pi$
$812$		0			0
$813$	−21420.9			−0.924063
$814$	551.433	+	955.110i	0.0237441	+	0.0411260i
$815$	−75.2387	+	130.317i	−0.00323374	+	0.00560100i
$816$	228.102	−	395.084i	0.00978575	−	0.0169494i
$817$	−22631.3	−	39198.6i	−0.969120	−	1.67856i
$818$	20382.3			0.871210
$819$		0			0
$820$	−1436.26			−0.0611663
$821$	−15371.2	−	26623.7i	−0.653421	−	1.13176i	−0.982287	−	0.187382i	$-0.940000\pi$
$821$	−15371.2	−	26623.7i	−0.653421	−	1.13176i	0.328866	−	0.944376i	$-0.393333\pi$
$822$	4709.38	−	8156.89i	0.199828	−	0.346112i
$823$	6911.28	−	11970.7i	0.292724	−	0.507014i	−0.681729	−	0.731605i	$-0.738771\pi$
$823$	6911.28	−	11970.7i	0.292724	−	0.507014i	0.974453	+	0.224592i	$0.0721048\pi$
$824$	−11234.3	−	19458.3i	−0.474956	−	0.822648i
$825$	12750.3			0.538071
$826$		0			0
$827$	−42107.1			−1.77051			−0.885253	−	0.465110i	$-0.846015\pi$
$827$	−42107.1			−1.77051			−0.885253	+	0.465110i	$0.846015\pi$
$828$	1669.60	+	2891.84i	0.0700758	+	0.121375i
$829$	19381.9	−	33570.4i	0.812015	−	1.40645i	−0.0994360	−	0.995044i	$-0.531704\pi$
$829$	19381.9	−	33570.4i	0.812015	−	1.40645i	0.911451	−	0.411408i	$-0.134963\pi$
$830$	3154.87	−	5464.40i	0.131936	−	0.228521i
$831$	−1980.77	−	3430.80i	−0.0826862	−	0.143217i
$832$	28918.8			1.20502
$833$		0			0
$834$	−968.979			−0.0402314
$835$	3763.79	+	6519.08i	0.155990	+	0.270182i
$836$	−7055.90	+	12221.2i	−0.291906	+	0.505596i
$837$	3399.22	−	5887.62i	0.140375	−	0.243137i
$838$	8051.25	+	13945.2i	0.331892	+	0.574854i
$839$	16896.3			0.695262			0.347631	−	0.937631i	$-0.386986\pi$
$839$	16896.3			0.695262			0.347631	+	0.937631i	$0.386986\pi$
$840$		0			0
$841$	22525.7			0.923601
$842$	−13139.3	−	22757.9i	−0.537779	−	0.931461i
$843$	306.463	−	530.810i	0.0125209	−	0.0216869i
$844$	3656.05	−	6332.46i	0.149107	−	0.258261i
$845$	1464.56	+	2536.68i	0.0596240	+	0.103272i
$846$	−5378.47			−0.218576
$847$		0			0
$848$	18954.0			0.767552
$849$	−1463.69	−	2535.19i	−0.0591681	−	0.102482i
$850$	539.773	−	934.915i	0.0217813	−	0.0377262i
$851$	−781.320	+	1353.29i	−0.0314727	+	0.0545124i
$852$	2500.95	+	4331.78i	0.100565	+	0.174183i
$853$	46429.3			1.86367			0.931833	−	0.362887i	$-0.118209\pi$
$853$	46429.3			1.86367			0.931833	+	0.362887i	$0.118209\pi$
$854$		0			0
$855$	−5020.21			−0.200804
$856$	−1437.34	−	2489.54i	−0.0573915	−	0.0994050i
$857$	−10603.2	+	18365.3i	−0.422636	+	0.732027i	−0.996196	−	0.0871364i	$-0.972228\pi$
$857$	−10603.2	+	18365.3i	−0.422636	+	0.732027i	0.573561	+	0.819163i	$0.305562\pi$
$858$	7411.31	−	12836.8i	0.294893	−	0.510769i
$859$	−6938.09	−	12017.1i	−0.275581	−	0.477321i	0.694700	−	0.719299i	$-0.255537\pi$
$859$	−6938.09	−	12017.1i	−0.275581	−	0.477321i	−0.970282	+	0.241978i	$0.922204\pi$
$860$	4744.96			0.188142
$861$		0			0
$862$	−9246.12			−0.365341
$863$	−7168.53	−	12416.3i	−0.282757	−	0.489750i	0.689306	−	0.724471i	$-0.257916\pi$
$863$	−7168.53	−	12416.3i	−0.282757	−	0.489750i	−0.972063	+	0.234721i	$0.924582\pi$
$864$	−1633.09	+	2828.59i	−0.0643040	+	0.111378i
$865$	146.029	−	252.930i	0.00574004	−	0.00994204i
$866$	−19855.8	−	34391.2i	−0.779131	−	1.34949i
$867$	−14676.9			−0.574918
$868$		0			0
$869$	−4958.81			−0.193574
$870$	−3362.85	−	5824.62i	−0.131047	−	0.226981i
$871$	8892.70	−	15402.6i	0.345945	−	0.599193i
$872$	10307.9	−	17853.8i	0.400309	−	0.693356i
$873$	2870.45	+	4971.76i	0.111283	+	0.192748i
$874$	36632.8			1.41776
$875$		0			0
$876$	−4158.33			−0.160384
$877$	12184.6	+	21104.4i	0.469152	+	0.812595i	0.999378	−	0.0352614i	$-0.0112264\pi$
$877$	12184.6	+	21104.4i	0.469152	+	0.812595i	−0.530226	+	0.847856i	$0.677893\pi$
$878$	−5227.07	+	9053.54i	−0.200917	+	0.347998i
$879$	−911.878	+	1579.42i	−0.0349908	+	0.0606058i
$880$	3098.32	+	5366.45i	0.118687	+	0.205572i
$881$	−26127.0			−0.999140			−0.499570	−	0.866273i	$-0.666509\pi$
$881$	−26127.0			−0.999140			−0.499570	+	0.866273i	$0.666509\pi$
$882$		0			0
$883$	−15713.1			−0.598855			−0.299428	−	0.954119i	$-0.596796\pi$
$883$	−15713.1			−0.598855			−0.299428	+	0.954119i	$0.596796\pi$
$884$	342.503	+	593.233i	0.0130313	+	0.0225708i
$885$	5732.04	−	9928.19i	0.217718	−	0.377099i
$886$	348.305	−	603.283i	0.0132072	−	0.0228755i
$887$	−6569.74	−	11379.1i	−0.248692	−	0.430748i	0.714471	−	0.699665i	$-0.246667\pi$
$887$	−6569.74	−	11379.1i	−0.248692	−	0.430748i	−0.963163	+	0.268917i	$0.913334\pi$
$888$	−878.907			−0.0332142
$889$		0			0
$890$	−7442.40			−0.280303
$891$	1650.34	+	2858.48i	0.0620522	+	0.107478i
$892$	−4570.74	+	7916.75i	−0.171569	+	0.297166i
$893$	16102.9	−	27891.0i	0.603430	−	1.04517i
$894$	6633.22	+	11489.1i	0.248152	+	0.429812i
$895$	−17811.1			−0.665207
$896$		0			0
$897$	21002.0			0.781758
$898$	−10497.9	−	18182.8i	−0.390109	−	0.675689i
$899$	−27269.0	+	47231.4i	−1.01165	+	1.75223i
$900$	−1325.78	+	2296.33i	−0.0491031	+	0.0850491i
$901$	1290.10	+	2234.53i	0.0477021	+	0.0826225i
$902$	10359.6			0.382412
$903$		0			0
$904$	26757.4			0.984446
$905$	−4681.88	−	8109.25i	−0.171968	−	0.297857i
$906$	9059.05	−	15690.7i	0.332193	−	0.575375i
$907$	1899.85	−	3290.64i	0.0695519	−	0.120467i	−0.829152	−	0.559023i	$-0.811176\pi$
$907$	1899.85	−	3290.64i	0.0695519	−	0.120467i	0.898704	+	0.438555i	$0.144510\pi$
$908$	−7953.96	−	13776.7i	−0.290706	−	0.503518i
$909$	6040.33			0.220402
$910$		0			0
$911$	−51528.4			−1.87400			−0.936998	−	0.349334i	$-0.886408\pi$
$911$	−51528.4			−1.87400			−0.936998	+	0.349334i	$0.886408\pi$
$912$	6146.35	+	10645.8i	0.223164	+	0.386532i
$913$	12420.5	−	21513.0i	0.450229	−	0.779819i
$914$	12503.2	−	21656.2i	0.452483	−	0.783723i
$915$	−3315.42	−	5742.48i	−0.119786	−	0.207476i
$916$	−10650.0			−0.384156
$917$		0			0
$918$	279.463			0.0100476
$919$	8492.37	+	14709.2i	0.304828	+	0.527978i	0.977223	−	0.212214i	$-0.0680675\pi$
$919$	8492.37	+	14709.2i	0.304828	+	0.527978i	−0.672395	+	0.740193i	$0.734734\pi$
$920$	−7358.17	+	12744.7i	−0.263687	+	0.456719i
$921$	−12055.6	+	20880.9i	−0.431320	+	0.747069i
$922$	−8403.41	−	14555.1i	−0.300164	−	0.519900i
$923$	31459.6			1.12189
$924$		0			0
$925$	−1240.85			−0.0441068
$926$	−11560.9	−	20024.1i	−0.410277	−	0.710620i
$927$	4105.85	−	7111.55i	0.145473	−	0.251967i
$928$	13100.9	−	22691.3i	0.463423	−	0.802672i
$929$	2725.93	+	4721.44i	0.0962699	+	0.166744i	0.910138	−	0.414305i	$-0.135975\pi$
$929$	2725.93	+	4721.44i	0.0962699	+	0.166744i	−0.813868	+	0.581050i	$0.802642\pi$
$930$	7818.58			0.275679
$931$		0			0
$932$	18532.9			0.651358
$933$	−7967.41	−	13800.0i	−0.279573	−	0.484234i
$934$	17988.4	−	31156.9i	0.630192	−	1.09152i
$935$	−421.774	+	730.534i	−0.0147524	+	0.0255519i
$936$	5906.30	+	10230.0i	0.206254	+	0.357242i
$937$	42429.4			1.47930			0.739652	−	0.672989i	$-0.234990\pi$
$937$	42429.4			1.47930			0.739652	+	0.672989i	$0.234990\pi$
$938$		0			0
$939$	−4594.82			−0.159687
$940$	1688.09	+	2923.86i	0.0585740	+	0.101453i
$941$	16488.9	−	28559.7i	0.571226	−	0.989393i	−0.425214	−	0.905093i	$-0.639801\pi$
$941$	16488.9	−	28559.7i	0.571226	−	0.989393i	0.996440	−	0.0843003i	$-0.0268655\pi$
$942$	−5682.34	+	9842.11i	−0.196540	+	0.340417i
$943$	7339.19	+	12711.8i	0.253443	+	0.438976i
$944$	−28071.5			−0.967848
$945$		0			0
$946$	−34224.8			−1.17626
$947$	11876.7	+	20571.1i	0.407541	+	0.705882i	0.994614	−	0.103653i	$-0.0330530\pi$
$947$	11876.7	+	20571.1i	0.407541	+	0.705882i	−0.587073	+	0.809534i	$0.699720\pi$
$948$	515.621	−	893.081i	0.0176652	−	0.0305970i
$949$	−13076.9	+	22649.9i	−0.447308	+	0.774760i
$950$	14544.5	+	25191.8i	0.496722	+	0.860349i
$951$	12657.6			0.431598
$952$		0			0
$953$	−28074.3			−0.954267			−0.477134	−	0.878831i	$-0.658324\pi$
$953$	−28074.3			−0.954267			−0.477134	+	0.878831i	$0.658324\pi$
$954$	5805.47	+	10055.4i	0.197022	+	0.341252i
$955$	973.774	−	1686.63i	0.0329954	−	0.0571497i
$956$	−1089.57	+	1887.19i	−0.0368610	+	0.0638452i
$957$	−13239.3	−	22931.1i	−0.447195	−	0.774564i
$958$	−3286.92			−0.110851
$959$		0			0
$960$	−7405.91			−0.248984
$961$	−16804.6	−	29106.5i	−0.564084	−	0.977022i
$962$	−721.262	+	1249.26i	−0.0241730	+	0.0418688i
$963$	525.312	−	909.867i	0.0175783	−	0.0304466i
$964$	1768.44	+	3063.03i	0.0590847	+	0.102338i
$965$	−7302.15			−0.243590
$966$		0			0
$967$	−11150.3			−0.370806			−0.185403	−	0.982663i	$-0.559359\pi$
$967$	−11150.3			−0.370806			−0.185403	+	0.982663i	$0.559359\pi$
$968$	4056.98	+	7026.89i	0.134707	+	0.233319i
$969$	−836.701	+	1449.21i	−0.0277386	+	0.0480447i
$970$	−3301.17	+	5717.80i	−0.109272	+	0.189265i
$971$	−3029.52	−	5247.29i	−0.100126	−	0.173423i	0.811611	−	0.584199i	$-0.198591\pi$
$971$	−3029.52	−	5247.29i	−0.100126	−	0.173423i	−0.911736	+	0.410776i	$0.865258\pi$
$972$	−686.415			−0.0226510
$973$		0			0
$974$	−1113.35			−0.0366263
$975$	8338.55	+	14442.8i	0.273895	+	0.474400i
$976$	−8118.29	+	14061.3i	−0.266250	+	0.461159i
$977$	−2850.24	+	4936.77i	−0.0933341	+	0.161659i	−0.908912	−	0.416988i	$-0.863086\pi$
$977$	−2850.24	+	4936.77i	−0.0933341	+	0.161659i	0.815578	+	0.578647i	$0.196419\pi$
$978$	112.858	+	195.476i	0.00368998	+	0.00639124i
$979$	−29300.2			−0.956526
$980$		0			0
$981$	7534.59			0.245220
$982$	4483.06	+	7764.89i	0.145683	+	0.252330i
$983$	−98.7401	+	171.023i	−0.00320378	+	0.00554912i	−0.867623	−	0.497223i	$-0.834353\pi$
$983$	−98.7401	+	171.023i	−0.00320378	+	0.00554912i	0.864419	+	0.502772i	$0.167686\pi$
$984$	−4127.93	+	7149.78i	−0.133733	+	0.231633i
$985$	8505.52	+	14732.0i	0.275136	+	0.476549i
$986$	−2241.90			−0.0724103
$987$		0			0
$988$	−18457.9			−0.594357
$989$	−24246.4	−	41996.0i	−0.779567	−	1.35025i
$990$	−1897.98	+	3287.40i	−0.0609312	+	0.105536i
$991$	−10310.4	+	17858.1i	−0.330495	+	0.572434i	−0.982609	−	0.185687i	$-0.940549\pi$
$991$	−10310.4	+	17858.1i	−0.330495	+	0.572434i	0.652114	+	0.758121i	$0.273882\pi$
$992$	15229.7	+	26378.6i	0.487442	+	0.844275i
$993$	24894.6			0.795574
$994$		0			0
$995$	1588.03			0.0505969
$996$	2582.99	+	4473.86i	0.0821738	+	0.142329i
$997$	−9663.41	+	16737.5i	−0.306964	+	0.531678i	−0.977697	−	0.210022i	$-0.932647\pi$
$997$	−9663.41	+	16737.5i	−0.306964	+	0.531678i	0.670733	+	0.741699i	$0.265980\pi$
$998$	−12.6137	+	21.8476i	−0.000400081	+	0.000692961i
$999$	−160.610	−	278.184i	−0.00508655	−	0.00881017i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.4.e.l.67.1		4
3.2	odd	2		441.4.e.q.361.2		4
7.2	even	3	inner	147.4.e.l.79.1		4
7.3	odd	6		147.4.a.i.1.2		2
7.4	even	3		21.4.a.c.1.2	✓	2
7.5	odd	6		147.4.e.m.79.1		4
7.6	odd	2		147.4.e.m.67.1		4
21.2	odd	6		441.4.e.q.226.2		4
21.5	even	6		441.4.e.p.226.2		4
21.11	odd	6		63.4.a.e.1.1		2
21.17	even	6		441.4.a.r.1.1		2
21.20	even	2		441.4.e.p.361.2		4
28.3	even	6		2352.4.a.bz.1.2		2
28.11	odd	6		336.4.a.m.1.1		2
35.4	even	6		525.4.a.n.1.1		2
35.18	odd	12		525.4.d.g.274.2		4
35.32	odd	12		525.4.d.g.274.3		4
56.11	odd	6		1344.4.a.bo.1.2		2
56.53	even	6		1344.4.a.bg.1.2		2
84.11	even	6		1008.4.a.ba.1.2		2
105.74	odd	6		1575.4.a.p.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.a.c.1.2	✓	2	7.4	even	3
63.4.a.e.1.1		2	21.11	odd	6
147.4.a.i.1.2		2	7.3	odd	6
147.4.e.l.67.1		4	1.1	even	1	trivial
147.4.e.l.79.1		4	7.2	even	3	inner
147.4.e.m.67.1		4	7.6	odd	2
147.4.e.m.79.1		4	7.5	odd	6
336.4.a.m.1.1		2	28.11	odd	6
441.4.a.r.1.1		2	21.17	even	6
441.4.e.p.226.2		4	21.5	even	6
441.4.e.p.361.2		4	21.20	even	2
441.4.e.q.226.2		4	21.2	odd	6
441.4.e.q.361.2		4	3.2	odd	2
525.4.a.n.1.1		2	35.4	even	6
525.4.d.g.274.2		4	35.18	odd	12
525.4.d.g.274.3		4	35.32	odd	12
1008.4.a.ba.1.2		2	84.11	even	6
1344.4.a.bg.1.2		2	56.53	even	6
1344.4.a.bo.1.2		2	56.11	odd	6
1575.4.a.p.1.2		2	105.74	odd	6
2352.4.a.bz.1.2		2	28.3	even	6

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:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	147.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.13746 - 1.97014i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(1.41238 - 2.44631i) q^{4} +(2.27492 + 3.94027i) q^{5} +6.82475 q^{6} -24.6254 q^{8} +(-4.50000 - 7.79423i) q^{9} +(5.17525 - 8.96379i) q^{10} +(20.3746 - 35.2898i) q^{11} +(4.23713 + 7.33892i) q^{12} +53.2990 q^{13} -13.6495 q^{15} +(16.7114 + 28.9450i) q^{16} +(-2.27492 + 3.94027i) q^{17} +(-10.2371 + 17.7312i) q^{18} +(-61.2990 - 106.173i) q^{19} +12.8522 q^{20} -92.7010 q^{22} +(-65.6736 - 113.750i) q^{23} +(36.9381 - 63.9787i) q^{24} +(52.1495 - 90.3256i) q^{25} +(-60.6254 - 105.006i) q^{26} +27.0000 q^{27} -216.598 q^{29} +(15.5257 + 26.8914i) q^{30} +(125.897 - 218.060i) q^{31} +(-60.4846 + 104.762i) q^{32} +(61.1238 + 105.869i) q^{33} +10.3505 q^{34} -25.4228 q^{36} +(-5.94851 - 10.3031i) q^{37} +(-139.450 + 241.535i) q^{38} +(-79.9485 + 138.475i) q^{39} +(-56.0208 - 97.0308i) q^{40} -111.752 q^{41} +369.196 q^{43} +(-57.5531 - 99.6850i) q^{44} +(20.4743 - 35.4624i) q^{45} +(-149.402 + 258.772i) q^{46} +(131.347 + 227.500i) q^{47} -100.268 q^{48} -237.272 q^{50} +(-6.82475 - 11.8208i) q^{51} +(75.2782 - 130.386i) q^{52} +(283.550 - 491.123i) q^{53} +(-30.7114 - 53.1937i) q^{54} +185.402 q^{55} +367.794 q^{57} +(246.371 + 426.728i) q^{58} +(-419.945 + 727.366i) q^{59} +(-19.2782 + 33.3909i) q^{60} +(242.897 + 420.710i) q^{61} -572.811 q^{62} +542.577 q^{64} +(121.251 + 210.013i) q^{65} +(139.051 - 240.844i) q^{66} +(166.846 - 288.985i) q^{67} +(6.42608 + 11.1303i) q^{68} +394.042 q^{69} +590.248 q^{71} +(110.814 + 191.936i) q^{72} +(-245.350 + 424.960i) q^{73} +(-13.5324 + 23.4387i) q^{74} +(156.449 + 270.977i) q^{75} -346.309 q^{76} +363.752 q^{78} +(-60.8455 - 105.388i) q^{79} +(-76.0340 + 131.695i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(127.114 + 220.168i) q^{82} +609.608 q^{83} -20.7010 q^{85} +(-419.945 - 727.366i) q^{86} +(324.897 - 562.738i) q^{87} +(-501.733 + 869.026i) q^{88} +(-359.519 - 622.705i) q^{89} -93.1545 q^{90} -371.023 q^{92} +(377.691 + 654.180i) q^{93} +(298.804 - 517.544i) q^{94} +(278.900 - 483.070i) q^{95} +(-181.454 - 314.287i) q^{96} -637.877 q^{97} -366.743 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} - 6 q^{3} - 17 q^{4} - 6 q^{5} - 18 q^{6} - 174 q^{8} - 18 q^{9} + 66 q^{10} + 6 q^{11} - 51 q^{12} + 32 q^{13} + 36 q^{15} - 137 q^{16} + 6 q^{17} + 27 q^{18} - 64 q^{19} + 444 q^{20} - 552 q^{22}+ \cdots - 108 q^{99}+O(q^{100}) \) 4 * q + 3 * q^2 - 6 * q^3 - 17 * q^4 - 6 * q^5 - 18 * q^6 - 174 * q^8 - 18 * q^9 + 66 * q^10 + 6 * q^11 - 51 * q^12 + 32 * q^13 + 36 * q^15 - 137 * q^16 + 6 * q^17 + 27 * q^18 - 64 * q^19 + 444 * q^20 - 552 * q^22 - 6 * q^23 + 261 * q^24 + 118 * q^25 - 318 * q^26 + 108 * q^27 - 504 * q^29 + 198 * q^30 - 40 * q^31 + 279 * q^32 + 18 * q^33 + 132 * q^34 + 306 * q^36 + 248 * q^37 - 588 * q^38 - 48 * q^39 + 546 * q^40 - 900 * q^41 + 752 * q^43 - 804 * q^44 - 54 * q^45 - 960 * q^46 + 12 * q^47 + 822 * q^48 - 330 * q^50 + 18 * q^51 + 890 * q^52 + 1104 * q^53 + 81 * q^54 + 1104 * q^55 + 384 * q^57 + 306 * q^58 - 804 * q^59 - 666 * q^60 + 428 * q^61 - 4224 * q^62 + 2578 * q^64 + 636 * q^65 + 828 * q^66 - 148 * q^67 + 222 * q^68 + 36 * q^69 + 1908 * q^71 + 783 * q^72 - 1072 * q^73 - 1398 * q^74 + 354 * q^75 - 3016 * q^76 + 1908 * q^78 + 572 * q^79 - 1950 * q^80 - 162 * q^81 - 1530 * q^82 + 3888 * q^83 - 264 * q^85 - 804 * q^86 + 756 * q^87 + 1164 * q^88 - 366 * q^89 - 1188 * q^90 - 5712 * q^92 - 120 * q^93 + 1920 * q^94 + 1176 * q^95 + 837 * q^96 + 1616 * q^97 - 108 * q^99

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