LMFDB - Embedded newform 147.4.e.l.79.1

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			79.1
Root			$-1.63746 + 1.52274i$ of defining polynomial
Character	$\chi$	$=$	147.79
Dual form			147.4.e.l.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.13746 + 1.97014i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(1.41238 + 2.44631i) q^{4} +(2.27492 - 3.94027i) q^{5} +6.82475 q^{6} -24.6254 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 4 * q + 3 * q^2 - 6 * q^3 - 17 * q^4 - 6 * q^5 - 18 * q^6 - 174 * q^8 - 18 * q^9	\( 4 q + 3 q^{2} - 6 q^{3} - 17 q^{4} - 6 q^{5} - 18 q^{6} - 174 q^{8} - 18 q^{9} + 66 q^{10} + 6 q^{11} - 51 q^{12} + 32 q^{13} + 36 q^{15} - 137 q^{16} + 6 q^{17} + 27 q^{18} - 64 q^{19} + 444 q^{20} - 552 q^{22} - 6 q^{23} + 261 q^{24} + 118 q^{25} - 318 q^{26} + 108 q^{27} - 504 q^{29} + 198 q^{30} - 40 q^{31} + 279 q^{32} + 18 q^{33} + 132 q^{34} + 306 q^{36} + 248 q^{37} - 588 q^{38} - 48 q^{39} + 546 q^{40} - 900 q^{41} + 752 q^{43} - 804 q^{44} - 54 q^{45} - 960 q^{46} + 12 q^{47} + 822 q^{48} - 330 q^{50} + 18 q^{51} + 890 q^{52} + 1104 q^{53} + 81 q^{54} + 1104 q^{55} + 384 q^{57} + 306 q^{58} - 804 q^{59} - 666 q^{60} + 428 q^{61} - 4224 q^{62} + 2578 q^{64} + 636 q^{65} + 828 q^{66} - 148 q^{67} + 222 q^{68} + 36 q^{69} + 1908 q^{71} + 783 q^{72} - 1072 q^{73} - 1398 q^{74} + 354 q^{75} - 3016 q^{76} + 1908 q^{78} + 572 q^{79} - 1950 q^{80} - 162 q^{81} - 1530 q^{82} + 3888 q^{83} - 264 q^{85} - 804 q^{86} + 756 q^{87} + 1164 q^{88} - 366 q^{89} - 1188 q^{90} - 5712 q^{92} - 120 q^{93} + 1920 q^{94} + 1176 q^{95} + 837 q^{96} + 1616 q^{97} - 108 q^{99}+O(q^{100}) \) 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

Display 100 coefficients 10 coefficients

Character values

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

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

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	−0.993985	−	0.109512i	$-0.965071\pi$
$2$	−1.13746	+	1.97014i	−0.402152	+	0.696548i	0.591833	+	0.806061i	$0.298404\pi$
$3$	−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	−0.746171	−	0.665754i	$-0.768110\pi$
$5$	2.27492	−	3.94027i	0.203475	−	0.352429i	0.949646	+	0.313326i	$0.101443\pi$
$6$	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	0.997624	+	0.0688867i	$0.0219447\pi$
$11$	20.3746	+	35.2898i	0.558470	+	0.967298i	−0.439155	+	0.898412i	$0.644722\pi$
$12$	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	0.849341	−	0.527844i	$-0.176999\pi$
$17$	−2.27492	−	3.94027i	−0.0324558	−	0.0562151i	−0.881797	+	0.471629i	$0.843666\pi$
$18$	−10.2371	−	17.7312i	−0.134051	−	0.232183i
$19$	−61.2990	+	106.173i	−0.740156	+	1.28199i	0.212269	+	0.977211i	$0.431915\pi$
$19$	−61.2990	+	106.173i	−0.740156	+	1.28199i	−0.952424	+	0.304776i	$0.901418\pi$
$20$	12.8522			0.143691
$21$		0			0
$22$	−92.7010			−0.898360
$23$	−65.6736	+	113.750i	−0.595387	+	1.03124i	0.398106	+	0.917340i	$0.369668\pi$
$23$	−65.6736	+	113.750i	−0.595387	+	1.03124i	−0.993492	+	0.113900i	$0.963666\pi$
$24$	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	0.957132	+	0.289652i	$0.0935396\pi$
$31$	125.897	+	218.060i	0.729412	+	1.26338i	−0.227720	+	0.973727i	$0.573127\pi$
$32$	−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	−0.878938	−	0.476936i	$-0.841747\pi$
$37$	−5.94851	+	10.3031i	−0.0264305	+	0.0457790i	0.852508	+	0.522715i	$0.175081\pi$
$38$	−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	−0.586987	−	0.809596i	$-0.699686\pi$
$47$	131.347	−	227.500i	0.407637	−	0.706049i	0.994624	+	0.103548i	$0.0330194\pi$
$48$	−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	0.954777	+	0.297324i	$0.0960942\pi$
$53$	283.550	+	491.123i	0.734879	+	1.27285i	−0.219898	+	0.975523i	$0.570572\pi$
$54$	−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	−0.788890	−	0.614535i	$-0.789344\pi$
$59$	−419.945	−	727.366i	−0.926648	−	1.60500i	−0.137758	−	0.990466i	$-0.543990\pi$
$60$	−19.2782	−	33.3909i	−0.0414801	−	0.0718457i
$61$	242.897	−	420.710i	0.509832	−	0.883056i	−0.490103	−	0.871665i	$-0.663041\pi$
$61$	242.897	−	420.710i	0.509832	−	0.883056i	0.999935	−	0.0113909i	$-0.00362593\pi$
$62$	−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	0.977090	−	0.212828i	$-0.0682675\pi$
$67$	166.846	+	288.985i	0.304230	+	0.526942i	−0.672859	+	0.739770i	$0.734934\pi$
$68$	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	0.599521	−	0.800359i	$-0.295358\pi$
$73$	−245.350	−	424.960i	−0.393371	−	0.681339i	−0.992892	+	0.119020i	$0.962025\pi$
$74$	−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	−0.906095	−	0.423075i	$-0.860951\pi$
$79$	−60.8455	+	105.388i	−0.0866539	+	0.150089i	0.819441	+	0.573164i	$0.194284\pi$
$80$	−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	−0.996712	−	0.0810204i	$-0.974182\pi$
$89$	−359.519	+	622.705i	−0.428190	+	0.741648i	0.568522	+	0.822668i	$0.307515\pi$
$90$	−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	0.652028	−	0.758195i	$-0.273919\pi$
$101$	−335.574	−	581.231i	−0.330603	−	0.572620i	−0.982630	+	0.185575i	$0.940585\pi$
$102$	−15.5257	−	26.8914i	−0.0150714	−	0.0261043i
$103$	456.206	−	790.172i	0.436420	−	0.755902i	−0.560990	−	0.827823i	$-0.689579\pi$
$103$	456.206	−	790.172i	0.436420	−	0.755902i	0.997410	+	0.0719202i	$0.0229127\pi$
$104$	−1312.51			−1.23752
$105$		0			0
$106$	−1290.10			−1.18213
$107$	58.3680	−	101.096i	0.0527350	−	0.0913397i	−0.838453	−	0.544974i	$-0.816539\pi$
$107$	58.3680	−	101.096i	0.0527350	−	0.0913397i	0.891188	+	0.453634i	$0.149873\pi$
$108$	38.1341	+	66.0503i	0.0339765	+	0.0588490i
$109$	−418.588	−	725.016i	−0.367830	−	0.637100i	0.621396	−	0.783497i	$-0.286566\pi$
$109$	−418.588	−	725.016i	−0.367830	−	0.637100i	−0.989226	+	0.146396i	$0.953232\pi$
$110$	−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	−1.00000		0.000760253i	$-0.999758\pi$
$131$	−748.694	+	1296.78i	−0.499341	+	0.864885i	0.500658	+	0.865645i	$0.333091\pi$
$132$	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	0.996901	−	0.0786647i	$-0.0250657\pi$
$137$	690.045	+	1195.19i	0.430325	+	0.745345i	−0.566576	+	0.824009i	$0.691732\pi$
$138$	−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	−0.464803	−	0.885414i	$-0.653875\pi$
$149$	971.935	−	1683.44i	0.534390	−	0.925590i	0.999193	−	0.0401757i	$-0.0127918\pi$
$150$	355.907	+	616.450i	0.193731	+	0.335553i
$151$	1327.38	+	2299.09i	0.715370	+	1.23906i	0.962817	+	0.270155i	$0.0870750\pi$
$151$	1327.38	+	2299.09i	0.715370	+	1.23906i	−0.247447	+	0.968901i	$0.579592\pi$
$152$	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	0.573010	−	0.819548i	$-0.305775\pi$
$157$	−832.608	−	1442.12i	−0.423244	−	0.733081i	−0.996255	+	0.0864675i	$0.972442\pi$
$158$	−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	−0.862025	−	0.506866i	$-0.830804\pi$
$163$	16.5366	−	28.6422i	0.00794629	−	0.0137634i	0.869971	+	0.493103i	$0.164137\pi$
$164$	−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	−0.872992	−	0.487735i	$-0.837823\pi$
$173$	−32.0954	+	55.5909i	−0.0141050	+	0.0244306i	0.858887	+	0.512166i	$0.171157\pi$
$174$	−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	−0.907658	−	0.419711i	$-0.862132\pi$
$179$	−1957.34	−	3390.21i	−0.817309	−	1.41562i	0.0903489	−	0.995910i	$-0.471202\pi$
$180$	−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	−0.903714	−	0.428137i	$-0.859170\pi$
$191$	−214.024	+	370.701i	−0.0810798	+	0.140434i	0.822634	+	0.568571i	$0.192504\pi$
$192$	−813.866	−	1409.66i	−0.305915	−	0.529861i
$193$	−802.463	−	1389.91i	−0.299288	−	0.518382i	0.676685	−	0.736272i	$-0.263416\pi$
$193$	−802.463	−	1389.91i	−0.299288	−	0.518382i	−0.975973	+	0.217890i	$0.930082\pi$
$194$	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	0.895433	−	0.445196i	$-0.146866\pi$
$199$	174.515	+	302.269i	0.0621660	+	0.107675i	−0.833267	+	0.552870i	$0.813533\pi$
$200$	−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	0.903203	+	0.429215i	$0.141210\pi$
$227$	2815.81	+	4877.12i	0.823312	+	1.42602i	−0.0798906	+	0.996804i	$0.525457\pi$
$228$	519.463	+	899.737i	0.150887	+	0.261344i
$229$	−1885.12	+	3265.13i	−0.543985	+	0.942210i	0.454685	+	0.890652i	$0.349752\pi$
$229$	−1885.12	+	3265.13i	−0.543985	+	0.942210i	−0.998670	+	0.0515573i	$0.983582\pi$
$230$	−1359.51			−0.389754
$231$		0			0
$232$	5333.82			1.50941
$233$	3280.45	−	5681.91i	0.922358	−	1.59757i	0.126602	−	0.991954i	$-0.459593\pi$
$233$	3280.45	−	5681.91i	0.922358	−	1.59757i	0.795756	−	0.605618i	$-0.207074\pi$
$234$	−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	0.770148	−	0.637866i	$-0.220183\pi$
$241$	−626.051	−	1084.35i	−0.167334	−	0.289831i	−0.937482	+	0.348035i	$0.886849\pi$
$242$	−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	−0.983648	−	0.180099i	$-0.942358\pi$
$257$	−1383.73	+	2396.68i	−0.335854	+	0.581716i	0.647795	+	0.761815i	$0.275691\pi$
$258$	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	0.999759	−	0.0219739i	$-0.00699507\pi$
$263$	2050.89	+	3552.25i	0.480849	+	0.832855i	−0.518909	+	0.854829i	$0.673662\pi$
$264$	−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	0.927353	+	0.374187i	$0.122078\pi$
$269$	3475.42	+	6019.60i	0.787732	+	1.36439i	−0.139621	+	0.990205i	$0.544588\pi$
$270$	139.732	+	242.022i	0.0314956	+	0.0545519i
$271$	3570.15	−	6183.67i	0.800262	−	1.38609i	−0.119182	−	0.992872i	$-0.538027\pi$
$271$	3570.15	−	6183.67i	0.800262	−	1.38609i	0.919444	−	0.393222i	$-0.128639\pi$
$272$	−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	0.785490	−	0.618875i	$-0.212411\pi$
$277$	−660.257	−	1143.60i	−0.143217	−	0.248059i	−0.928706	+	0.370816i	$0.879078\pi$
$278$	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	0.810225	−	0.586120i	$-0.199345\pi$
$283$	−487.897	−	845.062i	−0.102482	−	0.177504i	−0.912707	+	0.408615i	$0.866012\pi$
$284$	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	0.515602	−	0.856828i	$-0.327568\pi$
$311$	−2655.80	−	4599.98i	−0.484234	−	0.838718i	−0.999836	+	0.0181104i	$0.994235\pi$
$312$	1968.77	+	3410.00i	0.357242	+	0.618761i
$313$	765.804	−	1326.41i	0.138293	−	0.239531i	−0.788557	−	0.614961i	$-0.789172\pi$
$313$	765.804	−	1326.41i	0.138293	−	0.239531i	0.926851	+	0.375430i	$0.122505\pi$
$314$	3788.23			0.680835
$315$		0			0
$316$	−343.747			−0.0611939
$317$	−2109.59	+	3653.92i	−0.373775	+	0.647397i	−0.990143	−	0.140061i	$-0.955270\pi$
$317$	−2109.59	+	3653.92i	−0.373775	+	0.647397i	0.616368	+	0.787458i	$0.288603\pi$
$318$	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	0.283179	+	0.959067i	$0.408611\pi$
$331$	−4149.09	+	7186.44i	−0.688987	+	1.19336i	−0.972166	+	0.234294i	$0.924722\pi$
$332$	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	0.984174	+	0.177204i	$0.0567053\pi$
$347$	4172.77	+	7227.45i	0.645550	+	1.11813i	−0.338624	+	0.940922i	$0.609961\pi$
$348$	−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	−0.979678	−	0.200576i	$-0.935719\pi$
$353$	−4400.79	−	7622.40i	−0.663543	−	1.14929i	0.316135	−	0.948714i	$-0.397615\pi$
$354$	−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	−0.846122	−	0.532989i	$-0.821069\pi$
$359$	262.019	−	453.831i	0.0385205	−	0.0667194i	0.884643	+	0.466269i	$0.154402\pi$
$360$	−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	0.998540	−	0.0540110i	$-0.0172006\pi$
$367$	3181.36	+	5510.28i	0.452495	+	0.783745i	−0.546045	+	0.837756i	$0.683867\pi$
$368$	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	−0.148879	−	0.988855i	$-0.547566\pi$
$373$	5632.92	−	9756.50i	0.781935	−	1.35435i	0.930813	−	0.365495i	$-0.119100\pi$
$374$	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	−0.860926	−	0.508730i	$-0.830115\pi$
$383$	75.7772	−	131.250i	0.0101097	−	0.0175106i	0.871036	+	0.491219i	$0.163449\pi$
$384$	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	0.666454	−	0.745546i	$-0.267811\pi$
$389$	−2397.09	−	4151.88i	−0.312435	−	0.541154i	−0.978889	+	0.204393i	$0.934478\pi$
$390$	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	−0.682070	−	0.731287i	$-0.738920\pi$
$397$	2311.97	−	4004.45i	0.292278	−	0.506241i	0.974348	+	0.225046i	$0.0722533\pi$
$398$	−794.014			−0.100001
$399$		0			0
$400$	3485.96			0.435745
$401$	1805.32	−	3126.90i	0.224821	−	0.389402i	−0.731445	−	0.681901i	$-0.761154\pi$
$401$	1805.32	−	3126.90i	0.224821	−	0.389402i	0.956266	+	0.292499i	$0.0944869\pi$
$402$	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	−0.998813	−	0.0487118i	$-0.984488\pi$
$409$	−4479.79	−	7759.22i	−0.541592	−	0.938065i	0.457221	−	0.889353i	$-0.348845\pi$
$410$	−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	0.956952	−	0.290245i	$-0.0937370\pi$
$431$	2032.19	+	3519.85i	0.227116	+	0.393377i	−0.729836	+	0.683622i	$0.760404\pi$
$432$	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	−0.963471	−	0.267814i	$-0.913699\pi$
$439$	−2297.69	+	3979.72i	−0.249802	+	0.432669i	0.713669	+	0.700483i	$0.247032\pi$
$440$	−4565.60			−0.494674
$441$		0			0
$442$	551.671			0.0593672
$443$	153.107	−	265.189i	0.0164206	−	0.0284413i	−0.857698	−	0.514153i	$-0.828106\pi$
$443$	153.107	−	265.189i	0.0164206	−	0.0284413i	0.874119	+	0.485712i	$0.161440\pi$
$444$	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	−0.434694	−	0.900578i	$-0.643143\pi$
$457$	5496.12	−	9519.55i	0.562577	−	0.974411i	0.997271	−	0.0738330i	$-0.0235232\pi$
$458$	−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	−0.146353	−	0.989232i	$-0.546754\pi$
$467$	7907.29	−	13695.8i	0.783524	−	1.35710i	0.929877	−	0.367871i	$-0.119913\pi$
$468$	−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	0.898422	−	0.439132i	$-0.144714\pi$
$479$	722.427	+	1251.28i	0.0689113	+	0.119358i	−0.829511	+	0.558490i	$0.811381\pi$
$480$	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	0.877185	−	0.480152i	$-0.159418\pi$
$487$	244.701	+	423.835i	0.0227689	+	0.0394369i	−0.854416	+	0.519589i	$0.826085\pi$
$488$	−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	−0.866274	−	0.499569i	$-0.833492\pi$
$499$	−5.54470	+	9.60371i	−0.000497425	+	0.000861565i	0.865777	+	0.500431i	$0.166825\pi$
$500$	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	0.174008	+	0.984744i	$0.444328\pi$
$509$	−8794.22	+	15232.0i	−0.765810	+	1.32642i	−0.939817	+	0.341677i	$0.889005\pi$
$510$	−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	0.999929	−	0.0118758i	$-0.00378028\pi$
$521$	5823.30	+	10086.2i	0.489680	+	0.848151i	−0.510249	+	0.860026i	$0.670447\pi$
$522$	2217.34	+	3840.55i	0.185920	+	0.322023i
$523$	−4482.91	+	7764.63i	−0.374807	+	0.649185i	−0.990298	−	0.138959i	$-0.955624\pi$
$523$	−4482.91	+	7764.63i	−0.374807	+	0.649185i	0.615491	+	0.788144i	$0.288958\pi$
$524$	−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	−0.862120	−	0.506705i	$-0.830863\pi$
$541$	97.6359	−	169.110i	0.00775914	−	0.0134392i	0.869879	+	0.493265i	$0.164197\pi$
$542$	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	0.865206	−	0.501417i	$-0.167188\pi$
$557$	−21.5233	−	37.2795i	−0.00163730	−	0.00283588i	−0.866843	+	0.498581i	$0.833855\pi$
$558$	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	0.961053	+	0.276365i	$0.0891298\pi$
$563$	9616.43	+	16656.1i	0.719865	+	1.24684i	−0.241187	+	0.970479i	$0.577537\pi$
$564$	−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	−0.945327	−	0.326123i	$-0.894258\pi$
$569$	−2581.99	+	4472.14i	−0.190233	+	0.329493i	0.755094	+	0.655616i	$0.227591\pi$
$570$	1903.43	+	3296.83i	0.139870	+	0.242261i
$571$	5115.96	+	8861.10i	0.374950	+	0.649432i	0.990319	−	0.138807i	$-0.0443267\pi$
$571$	5115.96	+	8861.10i	0.374950	+	0.649432i	−0.615370	+	0.788238i	$0.710993\pi$
$572$	−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	−0.993184	−	0.116561i	$-0.962813\pi$
$577$	−8281.87	−	14344.6i	−0.597537	−	1.03496i	0.395647	−	0.918403i	$-0.370520\pi$
$578$	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	−0.724663	−	0.689104i	$-0.758004\pi$
$593$	3385.57	−	5863.98i	0.234450	−	0.406079i	0.959113	+	0.283025i	$0.0913378\pi$
$594$	−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	0.613147	−	0.789969i	$-0.289903\pi$
$599$	−5535.11	−	9587.09i	−0.377560	−	0.653953i	−0.990707	+	0.136016i	$0.956570\pi$
$600$	−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	−0.647016	−	0.762476i	$-0.723983\pi$
$607$	5037.04	−	8724.40i	0.336816	−	0.583382i	0.983832	+	0.179095i	$0.0573168\pi$
$608$	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	0.988962	−	0.148171i	$-0.0473385\pi$
$613$	5557.29	+	9625.51i	0.366161	+	0.634210i	−0.622800	+	0.782381i	$0.714005\pi$
$614$	−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	0.998750	+	0.0499782i	$0.0159152\pi$
$619$	8357.22	+	14475.1i	0.542658	+	0.939910i	−0.456093	+	0.889932i	$0.650751\pi$
$620$	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	0.924316	−	0.381627i	$-0.124636\pi$
$641$	2136.68	+	3700.84i	0.131660	+	0.228041i	−0.792657	+	0.609668i	$0.791303\pi$
$642$	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	−0.971934	−	0.235256i	$-0.924407\pi$
$647$	−11350.6	−	19659.8i	−0.689704	−	1.19460i	0.282229	−	0.959347i	$-0.408926\pi$
$648$	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	−0.888145	−	0.459563i	$-0.848006\pi$
$653$	−768.907	+	1331.79i	−0.0460791	+	0.0798113i	0.842066	+	0.539375i	$0.181339\pi$
$654$	−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	0.837605	−	0.546276i	$-0.183955\pi$
$661$	−922.548	−	1597.90i	−0.0542859	−	0.0940259i	−0.891891	+	0.452250i	$0.850622\pi$
$662$	−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	−0.809089	−	0.587686i	$-0.800039\pi$
$677$	1839.13	−	3185.46i	0.104407	−	0.180838i	0.913496	+	0.406848i	$0.133372\pi$
$678$	−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	0.797952	−	0.602721i	$-0.205917\pi$
$683$	−2195.43	−	3802.60i	−0.122996	−	0.213034i	−0.920948	+	0.389686i	$0.872583\pi$
$684$	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	−0.972730	−	0.231942i	$-0.925492\pi$
$691$	−5185.84	+	8982.13i	−0.285497	+	0.494496i	0.687232	+	0.726438i	$0.258825\pi$
$692$	−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	0.250803	+	0.968038i	$0.419306\pi$
$709$	−13459.4	+	23312.3i	−0.712944	+	1.23486i	−0.963747	+	0.266818i	$0.914028\pi$
$710$	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	−0.992901	−	0.118941i	$-0.962050\pi$
$719$	−7585.38	+	13138.3i	−0.393445	+	0.681466i	0.599457	+	0.800407i	$0.295383\pi$
$720$	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	0.482184	+	0.876070i	$0.339844\pi$
$733$	−10272.0	+	17791.7i	−0.517607	+	0.896521i	−0.999791	+	0.0204512i	$0.993490\pi$
$734$	−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	−0.876544	−	0.481321i	$-0.840157\pi$
$739$	−17178.6	−	29754.2i	−0.855109	−	1.48109i	0.0214356	−	0.999770i	$-0.493176\pi$
$740$	−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	−0.995424	−	0.0955601i	$-0.969536\pi$
$751$	−8540.05	+	14791.8i	−0.414954	+	0.718722i	0.580469	+	0.814282i	$0.302869\pi$
$752$	−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	−0.166208	−	0.986091i	$-0.553152\pi$
$761$	16183.1	−	28029.9i	0.770875	−	1.33520i	0.937084	−	0.349105i	$-0.113514\pi$
$762$	−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

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)

\(f(q)\)	\(=\)	\(q+(-1.13746 + 1.97014i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(1.41238 + 2.44631i) q^{4} +(2.27492 - 3.94027i) q^{5} +6.82475 q^{6} -24.6254 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} - 6 q^{3} - 17 q^{4} - 6 q^{5} - 18 q^{6} - 174 q^{8} - 18 q^{9}+O(q^{10}) \) 4 * q + 3 * q^2 - 6 * q^3 - 17 * q^4 - 6 * q^5 - 18 * q^6 - 174 * q^8 - 18 * q^9	\( 4 q + 3 q^{2} - 6 q^{3} - 17 q^{4} - 6 q^{5} - 18 q^{6} - 174 q^{8} - 18 q^{9} + 66 q^{10} + 6 q^{11} - 51 q^{12} + 32 q^{13} + 36 q^{15} - 137 q^{16} + 6 q^{17} + 27 q^{18} - 64 q^{19} + 444 q^{20} - 552 q^{22} - 6 q^{23} + 261 q^{24} + 118 q^{25} - 318 q^{26} + 108 q^{27} - 504 q^{29} + 198 q^{30} - 40 q^{31} + 279 q^{32} + 18 q^{33} + 132 q^{34} + 306 q^{36} + 248 q^{37} - 588 q^{38} - 48 q^{39} + 546 q^{40} - 900 q^{41} + 752 q^{43} - 804 q^{44} - 54 q^{45} - 960 q^{46} + 12 q^{47} + 822 q^{48} - 330 q^{50} + 18 q^{51} + 890 q^{52} + 1104 q^{53} + 81 q^{54} + 1104 q^{55} + 384 q^{57} + 306 q^{58} - 804 q^{59} - 666 q^{60} + 428 q^{61} - 4224 q^{62} + 2578 q^{64} + 636 q^{65} + 828 q^{66} - 148 q^{67} + 222 q^{68} + 36 q^{69} + 1908 q^{71} + 783 q^{72} - 1072 q^{73} - 1398 q^{74} + 354 q^{75} - 3016 q^{76} + 1908 q^{78} + 572 q^{79} - 1950 q^{80} - 162 q^{81} - 1530 q^{82} + 3888 q^{83} - 264 q^{85} - 804 q^{86} + 756 q^{87} + 1164 q^{88} - 366 q^{89} - 1188 q^{90} - 5712 q^{92} - 120 q^{93} + 1920 q^{94} + 1176 q^{95} + 837 q^{96} + 1616 q^{97} - 108 q^{99}+O(q^{100}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more