LMFDB - Embedded newform 143.4.e.b.133.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [143,4,Mod(100,143)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(143, 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("143.100");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	143.e (of order $3$, degree $2$, 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:	$8.43727313082$
Analytic rank:	$0$
Dimension:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			133.1
Character	$\chi$	$=$	143.133
Dual form			143.4.e.b.100.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.55759 - 4.42988i) q^{2} +(1.79098 + 3.10206i) q^{3} +(-9.08257 + 15.7315i) q^{4} -2.16776 q^{5} +(9.16117 - 15.8676i) q^{6} +(-10.4904 + 18.1698i) q^{7} +51.9966 q^{8} +(7.08482 - 12.2713i) q^{9} +O(q^{10})$	\(q+(-2.55759 - 4.42988i) q^{2} +(1.79098 + 3.10206i) q^{3} +(-9.08257 + 15.7315i) q^{4} -2.16776 q^{5} +(9.16117 - 15.8676i) q^{6} +(-10.4904 + 18.1698i) q^{7} +51.9966 q^{8} +(7.08482 - 12.2713i) q^{9} +(5.54425 + 9.60293i) q^{10} +(-5.50000 - 9.52628i) q^{11} -65.0666 q^{12} +(-3.83951 - 46.7146i) q^{13} +107.320 q^{14} +(-3.88241 - 6.72453i) q^{15} +(-60.3257 - 104.487i) q^{16} +(50.3801 - 87.2610i) q^{17} -72.4803 q^{18} +(81.9901 - 142.011i) q^{19} +(19.6888 - 34.1021i) q^{20} -75.1519 q^{21} +(-28.1335 + 48.7287i) q^{22} +(23.7627 + 41.1582i) q^{23} +(93.1247 + 161.297i) q^{24} -120.301 q^{25} +(-197.120 + 136.486i) q^{26} +147.468 q^{27} +(-190.559 - 330.058i) q^{28} +(122.619 + 212.383i) q^{29} +(-19.8592 + 34.3972i) q^{30} -29.8659 q^{31} +(-100.591 + 174.228i) q^{32} +(19.7007 - 34.1227i) q^{33} -515.408 q^{34} +(22.7406 - 39.3879i) q^{35} +(128.697 + 222.909i) q^{36} +(-97.8621 - 169.502i) q^{37} -838.789 q^{38} +(138.035 - 95.5751i) q^{39} -112.716 q^{40} +(-98.5770 - 170.740i) q^{41} +(192.208 + 332.914i) q^{42} +(4.53680 - 7.85797i) q^{43} +199.817 q^{44} +(-15.3582 + 26.6012i) q^{45} +(121.551 - 210.532i) q^{46} +449.261 q^{47} +(216.084 - 374.268i) q^{48} +(-48.5955 - 84.1699i) q^{49} +(307.681 + 532.918i) q^{50} +360.918 q^{51} +(769.763 + 363.888i) q^{52} -296.513 q^{53} +(-377.162 - 653.264i) q^{54} +(11.9227 + 20.6507i) q^{55} +(-545.464 + 944.771i) q^{56} +587.369 q^{57} +(627.221 - 1086.38i) q^{58} +(353.994 - 613.136i) q^{59} +141.049 q^{60} +(126.657 - 219.376i) q^{61} +(76.3848 + 132.302i) q^{62} +(148.645 + 257.460i) q^{63} +63.8689 q^{64} +(8.32313 + 101.266i) q^{65} -201.546 q^{66} +(-220.164 - 381.335i) q^{67} +(915.162 + 1585.11i) q^{68} +(-85.1168 + 147.427i) q^{69} -232.645 q^{70} +(-169.574 + 293.711i) q^{71} +(368.387 - 638.064i) q^{72} +188.512 q^{73} +(-500.583 + 867.035i) q^{74} +(-215.456 - 373.180i) q^{75} +(1489.36 + 2579.65i) q^{76} +230.788 q^{77} +(-776.425 - 367.037i) q^{78} +252.516 q^{79} +(130.772 + 226.503i) q^{80} +(72.8207 + 126.129i) q^{81} +(-504.240 + 873.369i) q^{82} -710.703 q^{83} +(682.573 - 1182.25i) q^{84} +(-109.212 + 189.161i) q^{85} -46.4132 q^{86} +(-439.217 + 760.746i) q^{87} +(-285.981 - 495.334i) q^{88} +(-691.650 - 1197.97i) q^{89} +157.120 q^{90} +(889.076 + 420.290i) q^{91} -863.306 q^{92} +(-53.4890 - 92.6457i) q^{93} +(-1149.03 - 1990.17i) q^{94} +(-177.735 + 307.846i) q^{95} -720.621 q^{96} +(186.582 - 323.169i) q^{97} +(-248.575 + 430.545i) q^{98} -155.866 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 6 q^{3} - 50 q^{4} - 48 q^{5} - 16 q^{6} + 62 q^{7} - 42 q^{8} - 135 q^{9}+O(q^{10}) $ 34 * q + 6 * q^3 - 50 * q^4 - 48 * q^5 - 16 * q^6 + 62 * q^7 - 42 * q^8 - 135 * q^9	\( 34 q + 6 q^{3} - 50 q^{4} - 48 q^{5} - 16 q^{6} + 62 q^{7} - 42 q^{8} - 135 q^{9} - 2 q^{10} - 187 q^{11} - 254 q^{12} + 76 q^{13} + 148 q^{15} - 126 q^{16} + 74 q^{17} + 180 q^{18} + 159 q^{19} + 222 q^{20} - 368 q^{21} + 215 q^{23} - 214 q^{24} + 190 q^{25} + 123 q^{26} - 384 q^{27} + 358 q^{28} + 157 q^{29} - 829 q^{30} - 788 q^{31} + 553 q^{32} + 66 q^{33} - 1404 q^{34} - 58 q^{35} + 700 q^{36} - 88 q^{37} - 2636 q^{38} + 798 q^{39} + 1466 q^{40} + 512 q^{41} - 337 q^{42} - 927 q^{43} + 1100 q^{44} + 1482 q^{45} + 1361 q^{46} - 286 q^{47} + 178 q^{48} - 1835 q^{49} + 583 q^{50} - 1136 q^{51} + 2306 q^{52} + 212 q^{53} + 67 q^{54} + 264 q^{55} - 2059 q^{56} + 2596 q^{57} + 1690 q^{58} + 266 q^{59} + 74 q^{60} + 624 q^{61} - 643 q^{62} + 2360 q^{63} - 3178 q^{64} + 470 q^{65} + 352 q^{66} + 676 q^{67} + 413 q^{68} - 764 q^{69} - 2122 q^{70} + 763 q^{71} + 1366 q^{72} - 4748 q^{73} + 1649 q^{74} - 2420 q^{75} + 2101 q^{76} - 1364 q^{77} - 5848 q^{78} + 4328 q^{79} + 1013 q^{80} - 537 q^{81} - 3152 q^{82} + 1554 q^{83} + 3381 q^{84} + 1690 q^{85} + 5788 q^{86} + 4200 q^{87} + 231 q^{88} + 1687 q^{89} - 10798 q^{90} - 3380 q^{91} + 11084 q^{92} + 4310 q^{93} - 1777 q^{94} - 1124 q^{95} - 6930 q^{96} + 2047 q^{97} - 1553 q^{98} + 2970 q^{99}+O(q^{100}) \) 34 * q + 6 * q^3 - 50 * q^4 - 48 * q^5 - 16 * q^6 + 62 * q^7 - 42 * q^8 - 135 * q^9 - 2 * q^10 - 187 * q^11 - 254 * q^12 + 76 * q^13 + 148 * q^15 - 126 * q^16 + 74 * q^17 + 180 * q^18 + 159 * q^19 + 222 * q^20 - 368 * q^21 + 215 * q^23 - 214 * q^24 + 190 * q^25 + 123 * q^26 - 384 * q^27 + 358 * q^28 + 157 * q^29 - 829 * q^30 - 788 * q^31 + 553 * q^32 + 66 * q^33 - 1404 * q^34 - 58 * q^35 + 700 * q^36 - 88 * q^37 - 2636 * q^38 + 798 * q^39 + 1466 * q^40 + 512 * q^41 - 337 * q^42 - 927 * q^43 + 1100 * q^44 + 1482 * q^45 + 1361 * q^46 - 286 * q^47 + 178 * q^48 - 1835 * q^49 + 583 * q^50 - 1136 * q^51 + 2306 * q^52 + 212 * q^53 + 67 * q^54 + 264 * q^55 - 2059 * q^56 + 2596 * q^57 + 1690 * q^58 + 266 * q^59 + 74 * q^60 + 624 * q^61 - 643 * q^62 + 2360 * q^63 - 3178 * q^64 + 470 * q^65 + 352 * q^66 + 676 * q^67 + 413 * q^68 - 764 * q^69 - 2122 * q^70 + 763 * q^71 + 1366 * q^72 - 4748 * q^73 + 1649 * q^74 - 2420 * q^75 + 2101 * q^76 - 1364 * q^77 - 5848 * q^78 + 4328 * q^79 + 1013 * q^80 - 537 * q^81 - 3152 * q^82 + 1554 * q^83 + 3381 * q^84 + 1690 * q^85 + 5788 * q^86 + 4200 * q^87 + 231 * q^88 + 1687 * q^89 - 10798 * q^90 - 3380 * q^91 + 11084 * q^92 + 4310 * q^93 - 1777 * q^94 - 1124 * q^95 - 6930 * q^96 + 2047 * q^97 - 1553 * q^98 + 2970 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/143\mathbb{Z}\right)^\times$.

$n$	$67$	$79$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.55759	−	4.42988i	−0.904246	−	1.56620i	−0.821926	−	0.569594i	$-0.807100\pi$
$2$	−2.55759	−	4.42988i	−0.904246	−	1.56620i	−0.0823198	−	0.996606i	$-0.526233\pi$
$3$	1.79098	+	3.10206i	0.344673	+	0.596992i	0.985294	−	0.170865i	$-0.0546564\pi$
$3$	1.79098	+	3.10206i	0.344673	+	0.596992i	−0.640621	+	0.767857i	$0.721323\pi$
$4$	−9.08257	+	15.7315i	−1.13532	+	1.96643i
$5$	−2.16776			−0.193890			−0.0969452	−	0.995290i	$-0.530907\pi$
$5$	−2.16776			−0.193890			−0.0969452	+	0.995290i	$0.530907\pi$
$6$	9.16117	−	15.8676i	0.623339	−	1.07965i
$7$	−10.4904	+	18.1698i	−0.566426	+	0.981079i	0.430489	+	0.902596i	$0.358341\pi$
$7$	−10.4904	+	18.1698i	−0.566426	+	0.981079i	−0.996915	+	0.0784836i	$0.974992\pi$
$8$	51.9966			2.29795
$9$	7.08482	−	12.2713i	0.262401	−	0.454491i
$10$	5.54425	+	9.60293i	0.175325	+	0.303671i
$11$	−5.50000	−	9.52628i	−0.150756	−	0.261116i
$11$	−5.50000	−	9.52628i	−0.150756	−	0.261116i
$12$	−65.0666			−1.56526
$13$	−3.83951	−	46.7146i	−0.0819144	−	0.996639i
$13$	−3.83951	−	46.7146i	−0.0819144	−	0.996639i
$14$	107.320			2.04876
$15$	−3.88241	−	6.72453i	−0.0668289	−	0.115751i
$16$	−60.3257	−	104.487i	−0.942588	−	1.63261i
$17$	50.3801	−	87.2610i	0.718763	−	1.24493i	−0.242727	−	0.970095i	$-0.578042\pi$
$17$	50.3801	−	87.2610i	0.718763	−	1.24493i	0.961490	−	0.274840i	$-0.0886249\pi$
$18$	−72.4803			−0.949099
$19$	81.9901	−	142.011i	0.989990	−	1.71471i	0.372768	−	0.927925i	$-0.378409\pi$
$19$	81.9901	−	142.011i	0.989990	−	1.71471i	0.617223	−	0.786789i	$-0.288258\pi$
$20$	19.6888	−	34.1021i	0.220128	−	0.381273i
$21$	−75.1519			−0.780928
$22$	−28.1335	+	48.7287i	−0.272640	+	0.472227i
$23$	23.7627	+	41.1582i	0.215429	+	0.373134i	0.953405	−	0.301693i	$-0.0975517\pi$
$23$	23.7627	+	41.1582i	0.215429	+	0.373134i	−0.737976	+	0.674827i	$0.764218\pi$
$24$	93.1247	+	161.297i	0.792041	+	1.37186i
$25$	−120.301			−0.962406
$26$	−197.120	+	136.486i	−1.48687	+	1.02950i
$27$	147.468			1.05112
$28$	−190.559	−	330.058i	−1.28615	−	2.22768i
$29$	122.619	+	212.383i	0.785167	+	1.35995i	0.928899	+	0.370333i	$0.120756\pi$
$29$	122.619	+	212.383i	0.785167	+	1.35995i	−0.143732	+	0.989617i	$0.545910\pi$
$30$	−19.8592	+	34.3972i	−0.120859	+	0.209335i
$31$	−29.8659			−0.173034			−0.0865172	−	0.996250i	$-0.527574\pi$
$31$	−29.8659			−0.173034			−0.0865172	+	0.996250i	$0.527574\pi$
$32$	−100.591	+	174.228i	−0.555690	+	0.962483i
$33$	19.7007	−	34.1227i	0.103923	−	0.180000i
$34$	−515.408			−2.59976
$35$	22.7406	−	39.3879i	0.109825	−	0.190222i
$36$	128.697	+	222.909i	0.595818	+	1.03199i
$37$	−97.8621	−	169.502i	−0.434822	−	0.753134i	0.562459	−	0.826825i	$-0.309855\pi$
$37$	−97.8621	−	169.502i	−0.434822	−	0.753134i	−0.997281	+	0.0736909i	$0.976522\pi$
$38$	−838.789			−3.58078
$39$	138.035	−	95.5751i	0.566752	−	0.392417i
$40$	−112.716			−0.445550
$41$	−98.5770	−	170.740i	−0.375491	−	0.650370i	0.614909	−	0.788598i	$-0.289193\pi$
$41$	−98.5770	−	170.740i	−0.375491	−	0.650370i	−0.990400	+	0.138228i	$0.955859\pi$
$42$	192.208	+	332.914i	0.706151	+	1.22309i
$43$	4.53680	−	7.85797i	0.0160897	−	0.0278681i	−0.857868	−	0.513869i	$-0.828212\pi$
$43$	4.53680	−	7.85797i	0.0160897	−	0.0278681i	0.873958	+	0.486001i	$0.161545\pi$
$44$	199.817			0.684625
$45$	−15.3582	+	26.6012i	−0.0508770	+	0.0881215i
$46$	121.551	−	210.532i	0.389602	−	0.674810i
$47$	449.261			1.39429			0.697143	−	0.716932i	$-0.254454\pi$
$47$	449.261			1.39429			0.697143	+	0.716932i	$0.254454\pi$
$48$	216.084	−	374.268i	0.649770	−	1.12543i
$49$	−48.5955	−	84.1699i	−0.141678	−	0.245393i
$50$	307.681	+	532.918i	0.870252	+	1.50732i
$51$	360.918			0.990954
$52$	769.763	+	363.888i	2.05283	+	0.970427i
$53$	−296.513			−0.768474			−0.384237	−	0.923234i	$-0.625535\pi$
$53$	−296.513			−0.768474			−0.384237	+	0.923234i	$0.625535\pi$
$54$	−377.162	−	653.264i	−0.950468	−	1.64626i
$55$	11.9227	+	20.6507i	0.0292301	+	0.0506280i
$56$	−545.464	+	944.771i	−1.30162	+	2.25447i
$57$	587.369			1.36489
$58$	627.221	−	1086.38i	1.41997	−	2.45946i
$59$	353.994	−	613.136i	0.781120	−	1.35294i	−0.150169	−	0.988660i	$-0.547982\pi$
$59$	353.994	−	613.136i	0.781120	−	1.35294i	0.931290	−	0.364280i	$-0.118685\pi$
$60$	141.049			0.303489
$61$	126.657	−	219.376i	0.265848	−	0.460463i	−0.701937	−	0.712239i	$-0.747681\pi$
$61$	126.657	−	219.376i	0.265848	−	0.460463i	0.967786	+	0.251776i	$0.0810147\pi$
$62$	76.3848	+	132.302i	0.156466	+	0.271007i
$63$	148.645	+	257.460i	0.297261	+	0.514872i
$64$	63.8689			0.124744
$65$	8.32313	+	101.266i	0.0158824	+	0.193239i
$66$	−201.546			−0.375888
$67$	−220.164	−	381.335i	−0.401452	−	0.695336i	0.592449	−	0.805608i	$-0.298161\pi$
$67$	−220.164	−	381.335i	−0.401452	−	0.695336i	−0.993901	+	0.110272i	$0.964828\pi$
$68$	915.162	+	1585.11i	1.63206	+	2.82680i
$69$	−85.1168	+	147.427i	−0.148505	+	0.257219i
$70$	−232.645			−0.397234
$71$	−169.574	+	293.711i	−0.283447	+	0.490945i	−0.972232	−	0.234021i	$-0.924812\pi$
$71$	−169.574	+	293.711i	−0.283447	+	0.490945i	0.688784	+	0.724967i	$0.258145\pi$
$72$	368.387	−	638.064i	0.602983	−	1.04440i
$73$	188.512			0.302242			0.151121	−	0.988515i	$-0.451712\pi$
$73$	188.512			0.302242			0.151121	+	0.988515i	$0.451712\pi$
$74$	−500.583	+	867.035i	−0.786373	+	1.36204i
$75$	−215.456	−	373.180i	−0.331716	−	0.574549i
$76$	1489.36	+	2579.65i	2.24791	+	3.89350i
$77$	230.788			0.341568
$78$	−776.425	−	367.037i	−1.12709	−	0.532805i
$79$	252.516			0.359624			0.179812	−	0.983701i	$-0.442451\pi$
$79$	252.516			0.359624			0.179812	+	0.983701i	$0.442451\pi$
$80$	130.772	+	226.503i	0.182759	+	0.316548i
$81$	72.8207	+	126.129i	0.0998912	+	0.173017i
$82$	−504.240	+	873.369i	−0.679073	+	1.17619i
$83$	−710.703			−0.939877			−0.469939	−	0.882699i	$-0.655724\pi$
$83$	−710.703			−0.939877			−0.469939	+	0.882699i	$0.655724\pi$
$84$	682.573	−	1182.25i	0.886605	−	1.53564i
$85$	−109.212	+	189.161i	−0.139361	+	0.241381i
$86$	−46.4132			−0.0581961
$87$	−439.217	+	760.746i	−0.541253	+	0.937477i
$88$	−285.981	−	495.334i	−0.346429	−	0.600032i
$89$	−691.650	−	1197.97i	−0.823762	−	1.42680i	−0.902862	−	0.429930i	$-0.858538\pi$
$89$	−691.650	−	1197.97i	−0.823762	−	1.42680i	0.0791006	−	0.996867i	$-0.474795\pi$
$90$	157.120			0.184021
$91$	889.076	+	420.290i	1.02418	+	0.484158i
$92$	−863.306			−0.978325
$93$	−53.4890	−	92.6457i	−0.0596404	−	0.103300i
$94$	−1149.03	−	1990.17i	−1.26078	−	2.18373i
$95$	−177.735	+	307.846i	−0.191950	+	0.332467i
$96$	−720.621			−0.766126
$97$	186.582	−	323.169i	0.195304	−	0.338277i	−0.751696	−	0.659510i	$-0.770764\pi$
$97$	186.582	−	323.169i	0.195304	−	0.338277i	0.947000	+	0.321233i	$0.104097\pi$
$98$	−248.575	+	430.545i	−0.256223	+	0.443792i
$99$	−155.866			−0.158234
$100$	1092.64	−	1892.51i	1.09264	−	1.89251i
$101$	253.075	+	438.338i	0.249326	+	0.431844i	0.963339	−	0.268288i	$-0.0864578\pi$
$101$	253.075	+	438.338i	0.249326	+	0.431844i	−0.714013	+	0.700132i	$0.753124\pi$
$102$	−923.082	−	1598.83i	−0.896066	−	1.55203i
$103$	−1161.94			−1.11154			−0.555771	−	0.831335i	$-0.687577\pi$
$103$	−1161.94			−1.11154			−0.555771	+	0.831335i	$0.687577\pi$
$104$	−199.641	−	2429.00i	−0.188235	−	2.29023i
$105$	162.911			0.151415
$106$	758.359	+	1313.52i	0.694890	+	1.20358i
$107$	539.361	+	934.201i	0.487309	+	0.844043i	0.999894	−	0.0145934i	$-0.00464538\pi$
$107$	539.361	+	934.201i	0.487309	+	0.844043i	−0.512585	+	0.858637i	$0.671312\pi$
$108$	−1339.38	+	2319.88i	−1.19336	+	2.06695i
$109$	677.905			0.595702			0.297851	−	0.954612i	$-0.403730\pi$
$109$	677.905			0.595702			0.297851	+	0.954612i	$0.403730\pi$
$110$	60.9868	−	105.632i	0.0528624	−	0.0915603i
$111$	350.537	−	607.148i	0.299743	−	0.519171i
$112$	2531.35			2.13563
$113$	−376.372	+	651.896i	−0.313329	+	0.542701i	−0.979081	−	0.203472i	$-0.934777\pi$
$113$	−376.372	+	651.896i	−0.313329	+	0.542701i	0.665752	+	0.746173i	$0.268111\pi$
$114$	−1502.25	−	2601.97i	−1.23420	−	2.13770i
$115$	−51.5119	−	89.2212i	−0.0417696	−	0.0723471i
$116$	−4454.80			−3.56567
$117$	−600.450	−	283.849i	−0.474458	−	0.224289i
$118$	−3621.49			−2.82530
$119$	1057.01	+	1830.80i	0.814253	+	1.41033i
$120$	−201.872	−	349.653i	−0.153569	−	0.265990i
$121$	−60.5000	+	104.789i	−0.0454545	+	0.0787296i
$122$	−1295.75			−0.961569
$123$	353.098	−	611.584i	0.258844	−	0.448330i
$124$	271.259	−	469.834i	0.196450	−	0.340261i
$125$	531.754			0.380492
$126$	760.345	−	1316.96i	0.537595	−	0.931141i
$127$	704.176	+	1219.67i	0.492012	+	0.852189i	0.999958	−	0.00919960i	$-0.00292836\pi$
$127$	704.176	+	1219.67i	0.492012	+	0.852189i	−0.507946	+	0.861389i	$0.669595\pi$
$128$	641.374	+	1110.89i	0.442891	+	0.767109i
$129$	32.5012			0.0221827
$130$	427.310	−	295.868i	0.288289	−	0.199611i
$131$	747.620			0.498625			0.249312	−	0.968423i	$-0.419795\pi$
$131$	747.620			0.498625			0.249312	+	0.968423i	$0.419795\pi$
$132$	357.867	+	619.843i	0.235972	+	0.408715i
$133$	1720.21	+	2979.49i	1.12151	+	1.94252i
$134$	−1126.18	+	1950.60i	−0.726023	+	1.25751i
$135$	−319.674			−0.203801
$136$	2619.60	−	4537.27i	1.65168	−	2.86079i
$137$	−1278.98	+	2215.26i	−0.797595	+	1.38147i	0.123583	+	0.992334i	$0.460561\pi$
$137$	−1278.98	+	2215.26i	−0.797595	+	1.38147i	−0.921178	+	0.389141i	$0.872772\pi$
$138$	870.777			0.537141
$139$	1202.78	−	2083.28i	0.733946	−	1.27123i	−0.221238	−	0.975220i	$-0.571010\pi$
$139$	1202.78	−	2083.28i	0.733946	−	1.27123i	0.955184	−	0.296012i	$-0.0956569\pi$
$140$	413.086	+	715.487i	0.249373	+	0.431926i
$141$	804.615	+	1393.63i	0.480573	+	0.832377i
$142$	1734.81			1.02523
$143$	−423.899	+	293.507i	−0.247890	+	0.171638i
$144$	−1709.58			−0.989343
$145$	−265.810	−	460.396i	−0.152236	−	0.263681i
$146$	−482.137	−	835.085i	−0.273301	−	0.473371i
$147$	174.067	−	301.492i	0.0976652	−	0.169161i
$148$	3555.36			1.97465
$149$	759.029	−	1314.68i	0.417329	−	0.722835i	−0.578341	−	0.815795i	$-0.696300\pi$
$149$	759.029	−	1314.68i	0.417329	−	0.722835i	0.995670	+	0.0929600i	$0.0296329\pi$
$150$	−1102.10	+	1908.89i	−0.599905	+	1.03907i
$151$	−1058.05			−0.570219			−0.285109	−	0.958495i	$-0.592030\pi$
$151$	−1058.05			−0.570219			−0.285109	+	0.958495i	$0.592030\pi$
$152$	4263.21	−	7384.09i	2.27495	−	3.94032i
$153$	−713.868	−	1236.46i	−0.377208	−	0.653343i
$154$	−590.262	−	1022.36i	−0.308861	−	0.534964i
$155$	64.7421			0.0335497
$156$	249.824	+	3039.57i	0.128217	+	1.56000i
$157$	−3240.36			−1.64719			−0.823594	−	0.567179i	$-0.808035\pi$
$157$	−3240.36			−1.64719			−0.823594	+	0.567179i	$0.808035\pi$
$158$	−645.834	−	1118.62i	−0.325188	−	0.563243i
$159$	−531.047	−	919.800i	−0.264873	−	0.458773i
$160$	218.056	−	377.685i	0.107743	−	0.186616i
$161$	−997.118			−0.488099
$162$	372.492	−	645.174i	0.180652	−	0.312899i
$163$	−704.217	+	1219.74i	−0.338396	+	0.586119i	−0.984131	−	0.177443i	$-0.943218\pi$
$163$	−704.217	+	1219.74i	−0.338396	+	0.586119i	0.645735	+	0.763561i	$0.276551\pi$
$164$	3581.33			1.70521
$165$	−42.7065	+	73.9698i	−0.0201497	+	0.0349002i
$166$	1817.69	+	3148.33i	0.849880	+	1.47204i
$167$	−829.054	−	1435.96i	−0.384156	−	0.665378i	0.607495	−	0.794323i	$-0.292174\pi$
$167$	−829.054	−	1435.96i	−0.384156	−	0.665378i	−0.991652	+	0.128945i	$0.958841\pi$
$168$	−3907.65			−1.79453
$169$	−2167.52	+	358.722i	−0.986580	+	0.163278i
$170$	1117.28			0.504068
$171$	−1161.77	−	2012.24i	−0.519548	−	0.899884i
$172$	82.4117	+	142.741i	0.0365339	+	0.0632786i
$173$	1027.95	−	1780.46i	0.451754	−	0.782461i	−0.546741	−	0.837302i	$-0.684132\pi$
$173$	1027.95	−	1780.46i	0.451754	−	0.782461i	0.998495	+	0.0548408i	$0.0174651\pi$
$174$	4493.35			1.95770
$175$	1262.00	−	2185.85i	0.545133	−	0.944197i
$176$	−663.582	+	1149.36i	−0.284201	+	0.492251i
$177$	2535.98			1.07693
$178$	−3537.92	+	6127.86i	−1.48977	+	2.58035i
$179$	2305.07	+	3992.50i	0.962509	+	1.66711i	0.716163	+	0.697933i	$0.245897\pi$
$179$	2305.07	+	3992.50i	0.962509	+	1.66711i	0.246346	+	0.969182i	$0.420770\pi$
$180$	−278.984	−	483.214i	−0.115523	−	0.200092i
$181$	3125.73			1.28361			0.641805	−	0.766868i	$-0.278186\pi$
$181$	3125.73			1.28361			0.641805	+	0.766868i	$0.278186\pi$
$182$	−412.057	−	5013.43i	−0.167823	−	2.04187i
$183$	907.357			0.366523
$184$	1235.58	+	2140.09i	0.495044	+	0.857442i
$185$	212.142	+	367.440i	0.0843079	+	0.146026i
$186$	−273.606	+	473.900i	−0.107859	+	0.186817i
$187$	−1108.36			−0.433431
$188$	−4080.44	+	7067.54i	−1.58296	+	2.74177i
$189$	−1546.99	+	2679.46i	−0.595380	+	1.03123i
$190$	1818.29			0.694279
$191$	1076.82	−	1865.11i	0.407938	−	0.706570i	−0.586720	−	0.809790i	$-0.699581\pi$
$191$	1076.82	−	1865.11i	0.407938	−	0.706570i	0.994659	+	0.103220i	$0.0329145\pi$
$192$	114.388	+	198.125i	0.0429959	+	0.0744711i
$193$	−282.181	−	488.751i	−0.105243	−	0.182285i	0.808595	−	0.588366i	$-0.200229\pi$
$193$	−282.181	−	488.751i	−0.105243	−	0.182285i	−0.913837	+	0.406081i	$0.866895\pi$
$194$	−1908.80			−0.706412
$195$	−299.227	+	207.184i	−0.109888	+	0.0760860i
$196$	1765.49			0.643400
$197$	−620.761	−	1075.19i	−0.224504	−	0.388853i	0.731666	−	0.681663i	$-0.238743\pi$
$197$	−620.761	−	1075.19i	−0.224504	−	0.388853i	−0.956171	+	0.292810i	$0.905410\pi$
$198$	398.642	+	690.468i	0.143082	+	0.247825i
$199$	950.251	−	1645.88i	0.338500	−	0.586299i	−0.645651	−	0.763633i	$-0.723414\pi$
$199$	950.251	−	1645.88i	0.338500	−	0.586299i	0.984151	+	0.177333i	$0.0567471\pi$
$200$	−6255.24			−2.21156
$201$	788.616	−	1365.92i	0.276740	−	0.479327i
$202$	1294.52	−	2242.18i	0.450903	−	0.780987i
$203$	−5145.29			−1.77896
$204$	−3278.07	+	5677.78i	−1.12505	+	1.94865i
$205$	213.691	+	370.124i	0.0728042	+	0.126101i
$206$	2971.76	+	5147.24i	1.00511	+	1.74090i
$207$	673.418			0.226115
$208$	−4649.46	+	3219.27i	−1.54991	+	1.07316i
$209$	−1803.78			−0.596987
$210$	−416.661	−	721.679i	−0.136916	−	0.237145i
$211$	−1772.71	−	3070.42i	−0.578380	−	1.00178i	−0.995665	−	0.0930083i	$-0.970352\pi$
$211$	−1772.71	−	3070.42i	−0.578380	−	1.00178i	0.417285	−	0.908776i	$-0.362982\pi$
$212$	2693.10	−	4664.58i	0.872465	−	1.51115i
$213$	−1214.81			−0.390787
$214$	2758.93	−	4778.61i	0.881294	−	1.52645i
$215$	−9.83470	+	17.0342i	−0.00311963	+	0.00540336i
$216$	7667.82			2.41541
$217$	313.304	−	542.658i	0.0980113	−	0.169761i
$218$	−1733.80	−	3003.04i	−0.538661	−	0.932988i
$219$	337.620	+	584.775i	0.104175	+	0.180436i
$220$	−433.155			−0.132742
$221$	−4269.80	−	2018.45i	−1.29963	−	0.614370i
$222$	−3586.13			−1.08417
$223$	745.636	+	1291.48i	0.223908	+	0.387820i	0.955991	−	0.293395i	$-0.0947852\pi$
$223$	745.636	+	1291.48i	0.223908	+	0.387820i	−0.732083	+	0.681215i	$0.761452\pi$
$224$	−2110.46	−	3655.43i	−0.629515	−	1.09035i
$225$	−852.309	+	1476.24i	−0.252536	+	0.437405i
$226$	3850.43			1.13330
$227$	−944.278	+	1635.54i	−0.276097	+	0.478213i	−0.970411	−	0.241458i	$-0.922374\pi$
$227$	−944.278	+	1635.54i	−0.276097	+	0.478213i	0.694315	+	0.719672i	$0.255708\pi$
$228$	−5334.82	+	9240.18i	−1.54959	+	2.68397i
$229$	−2300.70			−0.663906			−0.331953	−	0.943296i	$-0.607708\pi$
$229$	−2300.70			−0.663906			−0.331953	+	0.943296i	$0.607708\pi$
$230$	−263.493	+	456.383i	−0.0755400	+	0.130839i
$231$	413.336	+	715.918i	0.117729	+	0.203913i
$232$	6375.80	+	11043.2i	1.80427	+	3.12509i
$233$	1680.29			0.472445			0.236223	−	0.971699i	$-0.424091\pi$
$233$	1680.29			0.472445			0.236223	+	0.971699i	$0.424091\pi$
$234$	278.289	+	3385.89i	0.0777449	+	0.945909i
$235$	−973.890			−0.270339
$236$	6430.35	+	11137.7i	1.77365	+	3.07204i
$237$	452.250	+	783.320i	0.123953	+	0.214692i
$238$	5406.81	−	9364.88i	1.47257	−	2.55057i
$239$	5621.13			1.52134			0.760671	−	0.649138i	$-0.224870\pi$
$239$	5621.13			1.52134			0.760671	+	0.649138i	$0.224870\pi$
$240$	−468.417	+	811.323i	−0.125984	+	0.218211i
$241$	−1785.42	+	3092.44i	−0.477217	+	0.826563i	−0.999659	−	0.0261111i	$-0.991688\pi$
$241$	−1785.42	+	3092.44i	−0.477217	+	0.826563i	0.522442	+	0.852675i	$0.325021\pi$
$242$	618.938			0.164408
$243$	1729.97	−	2996.40i	0.456699	−	0.791025i
$244$	2300.74	+	3985.00i	0.603646	+	1.04555i
$245$	105.343	+	182.460i	0.0274700	+	0.0475794i
$246$	−3612.32			−0.936233
$247$	−6948.79	−	3284.89i	−1.79005	−	0.846203i
$248$	−1552.92			−0.397624
$249$	−1272.85	−	2204.64i	−0.323951	−	0.561099i
$250$	−1360.01	−	2355.61i	−0.344058	−	0.595926i
$251$	1079.64	−	1870.00i	0.271500	−	0.470252i	−0.697746	−	0.716345i	$-0.745814\pi$
$251$	1079.64	−	1870.00i	0.271500	−	0.470252i	0.969246	+	0.246093i	$0.0791470\pi$
$252$	−5400.30			−1.34995
$253$	261.390	−	452.740i	0.0649543	−	0.112504i
$254$	3601.99	−	6238.83i	0.889799	−	1.54118i
$255$	−782.385			−0.192137
$256$	3536.22	−	6124.92i	0.863336	−	1.49534i
$257$	4086.72	+	7078.40i	0.991916	+	1.71805i	0.605853	+	0.795577i	$0.292832\pi$
$257$	4086.72	+	7078.40i	0.991916	+	1.71805i	0.386063	+	0.922472i	$0.373835\pi$
$258$	−83.1249	−	143.976i	−0.0200586	−	0.0347426i
$259$	4106.44			0.985180
$260$	−1668.66	−	788.822i	−0.398023	−	0.188157i
$261$	3474.94			0.824114
$262$	−1912.11	−	3311.87i	−0.450880	−	0.780946i
$263$	−2888.05	−	5002.25i	−0.677129	−	1.17282i	−0.975842	−	0.218478i	$-0.929891\pi$
$263$	−2888.05	−	5002.25i	−0.677129	−	1.17282i	0.298713	−	0.954343i	$-0.403443\pi$
$264$	1024.37	−	1774.26i	0.238809	−	0.413630i
$265$	642.768			0.149000
$266$	8799.21	−	15240.7i	2.02825	−	3.51303i
$267$	2477.46	−	4291.08i	0.567857	−	0.983558i
$268$	7998.62			1.82311
$269$	−1123.97	+	1946.77i	−0.254757	+	0.441252i	−0.964829	−	0.262877i	$-0.915329\pi$
$269$	−1123.97	+	1946.77i	−0.254757	+	0.441252i	0.710073	+	0.704129i	$0.248662\pi$
$270$	817.597	+	1416.12i	0.184287	+	0.319194i
$271$	186.138	+	322.401i	0.0417236	+	0.0722675i	0.886133	−	0.463431i	$-0.153382\pi$
$271$	186.138	+	322.401i	0.0417236	+	0.0722675i	−0.844409	+	0.535698i	$0.820048\pi$
$272$	−12156.9			−2.70999
$273$	288.546	+	3510.70i	0.0639693	+	0.778304i
$274$	13084.4			2.88489
$275$	661.654	+	1146.02i	0.145088	+	0.251300i
$276$	−1546.16	−	2678.03i	−0.337202	−	0.584052i
$277$	−3726.39	+	6454.29i	−0.808292	+	1.40000i	0.105754	+	0.994392i	$0.466274\pi$
$277$	−3726.39	+	6454.29i	−0.808292	+	1.40000i	−0.914046	+	0.405611i	$0.867059\pi$
$278$	−12304.9			−2.65467
$279$	−211.594	+	366.492i	−0.0454044	+	0.0786426i
$280$	1182.43	−	2048.04i	0.252371	−	0.437120i
$281$	3561.16			0.756018			0.378009	−	0.925802i	$-0.376609\pi$
$281$	3561.16			0.756018			0.378009	+	0.925802i	$0.376609\pi$
$282$	4115.76	−	7128.70i	0.869113	−	1.50535i
$283$	−2367.21	−	4100.13i	−0.497230	−	0.861228i	0.502765	−	0.864423i	$-0.332316\pi$
$283$	−2367.21	−	4100.13i	−0.497230	−	0.861228i	−0.999995	+	0.00319547i	$0.998983\pi$
$284$	−3080.34	−	5335.31i	−0.643608	−	1.11476i
$285$	−1273.28			−0.264640
$286$	2384.36	+	1127.15i	0.492973	+	0.233042i
$287$	4136.44			0.850753
$288$	1425.33	+	2468.75i	0.291627	+	0.505112i
$289$	−2619.82	−	4537.65i	−0.533242	−	0.923602i
$290$	−1359.67	+	2355.01i	−0.275318	+	0.476865i
$291$	1336.65			0.269265
$292$	−1712.17	+	2965.57i	−0.343142	+	0.594339i
$293$	−256.294	+	443.914i	−0.0511019	+	0.0885111i	−0.890445	−	0.455091i	$-0.849607\pi$
$293$	−256.294	+	443.914i	−0.0511019	+	0.0885111i	0.839343	+	0.543602i	$0.182940\pi$
$294$	−1780.77			−0.353253
$295$	−767.375	+	1329.13i	−0.151452	+	0.262322i
$296$	−5088.50	−	8813.54i	−0.999199	−	1.73066i
$297$	−811.072	−	1404.82i	−0.158462	−	0.274464i
$298$	−7765.15			−1.50947
$299$	1831.45	−	1268.09i	0.354233	−	0.245270i
$300$	7827.57			1.50642
$301$	95.1854	+	164.866i	0.0182272	+	0.0315705i
$302$	2706.07	+	4687.04i	0.515618	+	0.893076i
$303$	−906.501	+	1570.11i	−0.171872	+	0.297691i
$304$	−19784.4			−3.73261
$305$	−274.562	+	475.555i	−0.0515454	+	0.0892793i
$306$	−3651.57	+	6324.70i	−0.682177	+	1.18157i
$307$	−1313.04			−0.244102			−0.122051	−	0.992524i	$-0.538947\pi$
$307$	−1313.04			−0.244102			−0.122051	+	0.992524i	$0.538947\pi$
$308$	−2096.15	+	3630.64i	−0.387790	+	0.671671i
$309$	−2081.00	−	3604.39i	−0.383119	−	0.663582i
$310$	−165.584	−	286.800i	−0.0303372	−	0.0525456i
$311$	9832.07			1.79269			0.896343	−	0.443361i	$-0.146214\pi$
$311$	9832.07			1.79269			0.896343	+	0.443361i	$0.146214\pi$
$312$	7177.36	−	4969.58i	1.30237	−	0.901754i
$313$	−5987.25			−1.08121			−0.540606	−	0.841276i	$-0.681805\pi$
$313$	−5987.25			−1.08121			−0.540606	+	0.841276i	$0.681805\pi$
$314$	8287.52	+	14354.4i	1.48946	+	2.57983i
$315$	−322.226	−	558.112i	−0.0576361	−	0.0998287i
$316$	−2293.50	+	3972.45i	−0.408289	+	0.707177i
$317$	4038.80			0.715589			0.357794	−	0.933800i	$-0.383529\pi$
$317$	4038.80			0.715589			0.357794	+	0.933800i	$0.383529\pi$
$318$	−2716.40	+	4704.95i	−0.479020	+	0.829687i
$319$	1348.81	−	2336.21i	0.236737	−	0.410040i
$320$	−138.452			−0.0241867
$321$	−1931.96	+	3346.26i	−0.335925	+	0.581838i
$322$	2550.22	+	4417.11i	0.441361	+	0.764460i
$323$	−8261.34	−	14309.1i	−1.42314	−	2.46495i
$324$	−2645.60			−0.453635
$325$	461.896	+	5619.81i	0.0788350	+	0.959172i
$326$	7204.40			1.22397
$327$	1214.11	+	2102.90i	0.205322	+	0.355629i
$328$	−5125.67	−	8877.92i	−0.862859	−	1.49452i
$329$	−4712.91	+	8163.00i	−0.789760	+	1.36791i
$330$	436.903			0.0728810
$331$	−5335.86	+	9241.98i	−0.886059	+	1.53470i	−0.0415630	+	0.999136i	$0.513234\pi$
$331$	−5335.86	+	9241.98i	−0.886059	+	1.53470i	−0.844496	+	0.535563i	$0.820100\pi$
$332$	6455.01	−	11180.4i	1.06706	−	1.84821i
$333$	−2773.34			−0.456391
$334$	−4240.77	+	7345.22i	−0.694744	+	1.20333i
$335$	477.263	+	826.643i	0.0778378	+	0.134819i
$336$	4533.59	+	7852.41i	0.736094	+	1.27495i
$337$	888.621			0.143639			0.0718194	−	0.997418i	$-0.477119\pi$
$337$	888.621			0.143639			0.0718194	+	0.997418i	$0.477119\pi$
$338$	7132.72	+	8684.38i	1.14784	+	1.39754i
$339$	−2696.29			−0.431984
$340$	−1983.85	−	3436.14i	−0.316440	−	0.548090i
$341$	164.262	+	284.511i	0.0260859	+	0.0451822i
$342$	−5942.67	+	10293.0i	−0.939598	+	1.62743i
$343$	−5157.25			−0.811853
$344$	235.898	−	408.588i	0.0369732	−	0.0640395i
$345$	184.513	−	319.586i	0.0287937	−	0.0498722i
$346$	−10516.3			−1.63399
$347$	2320.76	−	4019.68i	0.359035	−	0.621867i	−0.628765	−	0.777595i	$-0.716439\pi$
$347$	2320.76	−	4019.68i	0.359035	−	0.621867i	0.987800	+	0.155729i	$0.0497726\pi$
$348$	−7978.43	−	13819.1i	−1.22899	−	2.12868i
$349$	746.285	+	1292.60i	0.114463	+	0.198256i	0.917565	−	0.397586i	$-0.130152\pi$
$349$	746.285	+	1292.60i	0.114463	+	0.198256i	−0.803102	+	0.595842i	$0.796818\pi$
$350$	−12910.7			−1.97174
$351$	−566.203	−	6888.90i	−0.0861016	−	1.04758i
$352$	2212.99			0.335094
$353$	3751.95	+	6498.57i	0.565711	+	0.979841i	0.996983	+	0.0776188i	$0.0247317\pi$
$353$	3751.95	+	6498.57i	0.565711	+	0.979841i	−0.431272	+	0.902222i	$0.641935\pi$
$354$	−6486.00	−	11234.1i	−0.973805	−	1.68668i
$355$	367.597	−	636.696i	0.0549578	−	0.0951896i
$356$	25127.9			3.74094
$357$	−3786.16	+	6557.83i	−0.561303	+	0.972205i
$358$	11790.9	−	20422.4i	1.74069	−	3.01496i
$359$	−2648.70			−0.389396			−0.194698	−	0.980863i	$-0.562373\pi$
$359$	−2648.70			−0.389396			−0.194698	+	0.980863i	$0.562373\pi$
$360$	−798.574	+	1383.17i	−0.116913	+	0.202499i
$361$	−10015.2	−	17346.9i	−1.46016	−	2.52907i
$362$	−7994.34	−	13846.6i	−1.16070	−	2.01039i
$363$	−433.416			−0.0626679
$364$	−14686.9	+	10169.2i	−2.11484	+	1.46431i
$365$	−408.649			−0.0586018
$366$	−2320.65	−	4019.48i	−0.331427	−	0.574049i
$367$	6388.90	+	11065.9i	0.908714	+	1.57394i	0.815853	+	0.578259i	$0.196268\pi$
$367$	6388.90	+	11065.9i	0.908714	+	1.57394i	0.0928606	+	0.995679i	$0.470399\pi$
$368$	2867.00	−	4965.79i	0.406122	−	0.703423i
$369$	−2793.60			−0.394117
$370$	1085.14	−	1879.52i	0.152470	−	0.264086i
$371$	3110.52	−	5387.59i	0.435284	−	0.753934i
$372$	1943.27			0.270844
$373$	−159.980	+	277.093i	−0.0222076	+	0.0384647i	−0.876916	−	0.480644i	$-0.840403\pi$
$373$	−159.980	+	277.093i	−0.0222076	+	0.0384647i	0.854708	+	0.519109i	$0.173736\pi$
$374$	2834.74	+	4909.92i	0.391928	+	0.678839i
$375$	952.357	+	1649.53i	0.131145	+	0.227151i
$376$	23360.0			3.20400
$377$	9450.60	−	6543.57i	1.29106	−	0.893928i
$378$	15826.3			2.15348
$379$	1245.23	+	2156.80i	0.168768	+	0.292315i	0.937987	−	0.346670i	$-0.112688\pi$
$379$	1245.23	+	2156.80i	0.168768	+	0.292315i	−0.769219	+	0.638985i	$0.779354\pi$
$380$	−3228.58	−	5592.07i	−0.435849	−	0.754913i
$381$	−2522.32	+	4368.79i	−0.339167	+	0.587454i
$382$	−11016.3			−1.47551
$383$	2673.59	−	4630.79i	0.356695	−	0.617813i	−0.630712	−	0.776017i	$-0.717237\pi$
$383$	2673.59	−	4630.79i	0.356695	−	0.617813i	0.987406	+	0.158204i	$0.0505703\pi$
$384$	−2297.37	+	3979.16i	−0.305305	+	0.528804i
$385$	−500.293			−0.0662268
$386$	−1443.41	+	2500.05i	−0.190330	+	0.329662i
$387$	−64.2848	−	111.345i	−0.00844388	−	0.0146252i
$388$	3389.29	+	5870.42i	0.443466	+	0.768106i
$389$	−1245.73			−0.162367			−0.0811837	−	0.996699i	$-0.525870\pi$
$389$	−1245.73			−0.162367			−0.0811837	+	0.996699i	$0.525870\pi$
$390$	1683.10	+	795.649i	0.218531	+	0.103306i
$391$	4788.67			0.619370
$392$	−2526.80	−	4376.55i	−0.325568	−	0.563901i
$393$	1338.97	+	2319.16i	0.171863	+	0.297675i
$394$	−3175.31	+	5499.79i	−0.406014	+	0.703237i
$395$	−547.395			−0.0697276
$396$	1415.66	−	2452.00i	0.179646	−	0.311156i
$397$	−214.988	+	372.370i	−0.0271787	+	0.0470749i	−0.879295	−	0.476278i	$-0.841986\pi$
$397$	−214.988	+	372.370i	−0.0271787	+	0.0470749i	0.852116	+	0.523353i	$0.175319\pi$
$398$	−9721.43			−1.22435
$399$	−6161.71	+	10672.4i	−0.773111	+	1.33907i
$400$	7257.23	+	12569.9i	0.907153	+	1.57124i
$401$	2728.14	+	4725.28i	0.339743	+	0.588452i	0.984384	−	0.176033i	$-0.0563267\pi$
$401$	2728.14	+	4725.28i	0.339743	+	0.588452i	−0.644642	+	0.764485i	$0.722993\pi$
$402$	−8067.84			−1.00096
$403$	114.670	+	1395.17i	0.0141740	+	0.172453i
$404$	−9194.28			−1.13226
$405$	−157.858	−	273.418i	−0.0193680	−	0.0335463i
$406$	13159.6	+	22793.0i	1.60862	+	2.78620i
$407$	−1076.48	+	1864.52i	−0.131104	+	0.227079i
$408$	18766.5			2.27716
$409$	5279.90	−	9145.05i	0.638323	−	1.10561i	−0.347478	−	0.937688i	$-0.612962\pi$
$409$	5279.90	−	9145.05i	0.638323	−	1.10561i	0.985801	−	0.167919i	$-0.0537048\pi$
$410$	1093.07	−	1893.26i	0.131666	−	0.228052i
$411$	−9162.47			−1.09964
$412$	10553.4	−	18279.0i	1.26196	−	2.18578i
$413$	7427.05	+	12864.0i	0.884894	+	1.53268i
$414$	−1722.33	−	2983.16i	−0.204463	−	0.354141i
$415$	1540.63			0.182233
$416$	8525.22	+	4030.10i	1.00477	+	0.474981i
$417$	8616.60			1.01189
$418$	4613.34	+	7990.54i	0.539823	+	0.935000i
$419$	2715.03	+	4702.57i	0.316558	+	0.548295i	0.979767	−	0.200139i	$-0.0641394\pi$
$419$	2715.03	+	4702.57i	0.316558	+	0.548295i	−0.663209	+	0.748434i	$0.730806\pi$
$420$	−1479.65	+	2562.84i	−0.171904	+	0.297747i
$421$	7025.98			0.813362			0.406681	−	0.913570i	$-0.366686\pi$
$421$	7025.98			0.813362			0.406681	+	0.913570i	$0.366686\pi$
$422$	−9067.73	+	15705.8i	−1.04600	+	1.81172i
$423$	3182.93	−	5513.00i	0.365861	−	0.633691i
$424$	−15417.7			−1.76591
$425$	−6060.77	+	10497.6i	−0.691743	+	1.19813i
$426$	3107.00	+	5381.48i	0.353368	+	0.612051i
$427$	2657.35	+	4602.67i	0.301167	+	0.521636i
$428$	−19595.1			−2.21301
$429$	−1669.67	−	789.298i	−0.187908	−	0.0888291i
$430$	100.613			0.0112837
$431$	−1473.23	−	2551.71i	−0.164647	−	0.285177i	0.771883	−	0.635765i	$-0.219315\pi$
$431$	−1473.23	−	2551.71i	−0.164647	−	0.285177i	−0.936530	+	0.350588i	$0.885982\pi$
$432$	−8896.08	−	15408.5i	−0.990770	−	1.71606i
$433$	953.107	−	1650.83i	0.105782	−	0.183219i	−0.808276	−	0.588804i	$-0.799599\pi$
$433$	953.107	−	1650.83i	0.105782	−	0.183219i	0.914057	+	0.405585i	$0.132932\pi$
$434$	−3205.22			−0.354505
$435$	952.117	−	1649.11i	0.104944	−	0.181768i
$436$	−6157.12	+	10664.4i	−0.676313	+	1.17141i
$437$	7793.22			0.853090
$438$	1726.99	−	2991.23i	0.188399	−	0.326317i
$439$	−8147.07	−	14111.1i	−0.885737	−	1.53414i	−0.844866	−	0.534977i	$-0.820320\pi$
$439$	−8147.07	−	14111.1i	−0.885737	−	1.53414i	−0.0408709	−	0.999164i	$-0.513013\pi$
$440$	619.939	+	1073.77i	0.0671692	+	0.116340i
$441$	−1377.16			−0.148705
$442$	1978.91	+	24077.1i	0.212957	+	2.59102i
$443$	−757.392			−0.0812298			−0.0406149	−	0.999175i	$-0.512932\pi$
$443$	−757.392			−0.0812298			−0.0406149	+	0.999175i	$0.512932\pi$
$444$	6367.56	+	11028.9i	0.680610	+	1.17885i
$445$	1499.33	+	2596.92i	0.159720	+	0.276642i
$446$	3814.07	−	6606.16i	0.404936	−	0.701369i
$447$	5437.61			0.575369
$448$	−670.008	+	1160.49i	−0.0706582	+	0.122384i
$449$	−2190.65	+	3794.32i	−0.230252	+	0.398809i	−0.957882	−	0.287161i	$-0.907289\pi$
$449$	−2190.65	+	3794.32i	−0.230252	+	0.398809i	0.727630	+	0.685970i	$0.240622\pi$
$450$	8719.44			0.913419
$451$	−1084.35	+	1878.14i	−0.113215	+	0.196094i
$452$	−6836.86	−	11841.8i	−0.711457	−	1.23228i
$453$	−1894.94	−	3282.14i	−0.196539	−	0.340416i
$454$	9660.32			0.998637
$455$	−1927.30	−	911.089i	−0.198579	−	0.0938737i
$456$	30541.2			3.13645
$457$	5489.81	+	9508.62i	0.561931	+	0.973292i	0.997328	+	0.0730540i	$0.0232745\pi$
$457$	5489.81	+	9508.62i	0.561931	+	0.973292i	−0.435397	+	0.900238i	$0.643392\pi$
$458$	5884.26	+	10191.8i	0.600335	+	1.03981i
$459$	7429.44	−	12868.2i	0.755504	−	1.30857i
$460$	1871.44			0.189688
$461$	−3727.19	+	6455.68i	−0.376557	+	0.652215i	−0.990559	−	0.137089i	$-0.956225\pi$
$461$	−3727.19	+	6455.68i	−0.376557	+	0.652215i	0.614002	+	0.789304i	$0.289559\pi$
$462$	2114.29	−	3662.06i	0.212913	−	0.368775i
$463$	−5694.35			−0.571574			−0.285787	−	0.958293i	$-0.592255\pi$
$463$	−5694.35			−0.571574			−0.285787	+	0.958293i	$0.592255\pi$
$464$	14794.2	−	25624.3i	1.48018	−	2.56375i
$465$	115.951	+	200.834i	0.0115637	+	0.0200289i
$466$	−4297.51	−	7443.50i	−0.427207	−	0.739944i
$467$	−4784.89			−0.474129			−0.237064	−	0.971494i	$-0.576185\pi$
$467$	−4784.89			−0.474129			−0.237064	+	0.971494i	$0.576185\pi$
$468$	9918.99	−	6867.88i	0.979713	−	0.678350i
$469$	9238.40			0.909573
$470$	2490.82	+	4314.22i	0.244453	+	0.423404i
$471$	−5803.40	−	10051.8i	−0.567742	−	0.983358i
$472$	18406.5	−	31881.0i	1.79497	−	3.10899i
$473$	−99.8096			−0.00970244
$474$	2313.34	−	4006.83i	0.224168	−	0.388270i
$475$	−9863.47	+	17084.0i	−0.952773	+	1.65025i
$476$	−38401.6			−3.69776
$477$	−2100.74	+	3638.58i	−0.201648	+	0.349265i
$478$	−14376.6	−	24901.0i	−1.37567	−	2.38273i
$479$	−2685.51	−	4651.44i	−0.256167	−	0.443695i	0.709045	−	0.705164i	$-0.249126\pi$
$479$	−2685.51	−	4651.44i	−0.256167	−	0.443695i	−0.965212	+	0.261469i	$0.915793\pi$
$480$	1562.13			0.148544
$481$	−7542.49	+	5222.40i	−0.714985	+	0.495054i
$482$	18265.5			1.72608
$483$	−1785.81	−	3093.12i	−0.168235	−	0.291391i
$484$	−1098.99	−	1903.51i	−0.103211	−	0.178767i
$485$	−404.465	+	700.554i	−0.0378676	+	0.0655887i
$486$	−17698.3			−1.65187
$487$	5555.23	−	9621.94i	0.516902	−	0.895301i	−0.482905	−	0.875673i	$-0.660418\pi$
$487$	5555.23	−	9621.94i	0.516902	−	0.895301i	0.999807	−	0.0196283i	$-0.00624829\pi$
$488$	6585.73	−	11406.8i	0.610905	−	1.05812i
$489$	−5044.94			−0.466544
$490$	538.852	−	933.318i	0.0496793	−	0.0860470i
$491$	4307.79	+	7461.31i	0.395942	+	0.685792i	0.993221	−	0.116242i	$-0.0370847\pi$
$491$	4307.79	+	7461.31i	0.395942	+	0.685792i	−0.597279	+	0.802034i	$0.703751\pi$
$492$	6414.08	+	11109.5i	0.587742	+	1.01800i
$493$	24710.3			2.25740
$494$	3220.54	+	39183.7i	0.293317	+	3.56874i
$495$	337.880			0.0306800
$496$	1801.68	+	3120.60i	0.163100	+	0.282498i
$497$	−3557.79	−	6162.28i	−0.321104	−	0.556169i
$498$	−6510.88	+	11277.2i	−0.585862	+	1.01474i
$499$	6406.12			0.574704			0.287352	−	0.957825i	$-0.407225\pi$
$499$	6406.12			0.574704			0.287352	+	0.957825i	$0.407225\pi$
$500$	−4829.69	+	8365.27i	−0.431981	+	0.748212i
$501$	2969.63	−	5143.55i	0.264817	−	0.458676i
$502$	−11045.2			−0.982011
$503$	2218.71	−	3842.91i	0.196675	−	0.340650i	−0.750774	−	0.660560i	$-0.770319\pi$
$503$	2218.71	−	3842.91i	0.196675	−	0.340650i	0.947448	+	0.319909i	$0.103652\pi$
$504$	7729.02	+	13387.1i	0.683091	+	1.18315i
$505$	−548.606	−	950.213i	−0.0483418	−	0.0837305i
$506$	−2674.12			−0.234939
$507$	−4994.75	−	6081.30i	−0.437524	−	0.532702i
$508$	−25582.9			−2.23437
$509$	8133.08	+	14086.9i	0.708237	+	1.22670i	0.965511	+	0.260364i	$0.0838425\pi$
$509$	8133.08	+	14086.9i	0.708237	+	1.22670i	−0.257274	+	0.966339i	$0.582824\pi$
$510$	2001.02	+	3465.87i	0.173739	+	0.300924i
$511$	−1977.56	+	3425.23i	−0.171198	+	0.296523i
$512$	−25914.9			−2.23689
$513$	12090.9	−	20942.0i	1.04060	−	1.80236i
$514$	20904.3	−	36207.4i	1.79387	−	3.10708i
$515$	2518.80			0.215518
$516$	−295.194	+	511.292i	−0.0251845	+	0.0436209i
$517$	−2470.93	−	4279.78i	−0.210196	−	0.364071i
$518$	−10502.6	−	18191.0i	−0.890845	−	1.54299i
$519$	7364.12			0.622830
$520$	432.775	+	5265.50i	0.0364970	+	0.444053i
$521$	−18667.0			−1.56970			−0.784851	−	0.619684i	$-0.787261\pi$
$521$	−18667.0			−1.56970			−0.784851	+	0.619684i	$0.787261\pi$
$522$	−8887.50	−	15393.6i	−0.745201	−	1.29073i
$523$	4397.72	+	7617.07i	0.367684	+	0.636848i	0.989203	−	0.146551i	$-0.0468174\pi$
$523$	4397.72	+	7617.07i	0.367684	+	0.636848i	−0.621519	+	0.783399i	$0.713484\pi$
$524$	−6790.31	+	11761.2i	−0.566100	+	0.980513i
$525$	9040.84			0.751571
$526$	−14772.9	+	25587.4i	−1.22458	+	2.12104i
$527$	−1504.65	+	2606.12i	−0.124371	+	0.215417i
$528$	−4753.84			−0.391826
$529$	4954.17	−	8580.87i	0.407181	−	0.705258i
$530$	−1643.94	−	2847.39i	−0.134732	−	0.233363i
$531$	−5015.97	−	8687.91i	−0.409933	−	0.710025i
$532$	−62495.8			−5.09311
$533$	−7597.59	+	5260.55i	−0.617426	+	0.427504i
$534$	−25345.3			−2.05393
$535$	−1169.21	−	2025.12i	−0.0944845	−	0.163652i
$536$	−11447.8	−	19828.1i	−0.922516	−	1.59784i
$537$	−8256.65	+	14300.9i	−0.663502	+	1.14922i
$538$	11498.6			0.921452
$539$	−534.551	+	925.869i	−0.0427175	+	0.0739889i
$540$	2903.47	−	5028.95i	0.231380	−	0.400762i
$541$	−20229.3			−1.60763			−0.803813	−	0.594882i	$-0.797199\pi$
$541$	−20229.3			−1.60763			−0.803813	+	0.594882i	$0.797199\pi$
$542$	952.133	−	1649.14i	0.0754569	−	0.130695i
$543$	5598.10	+	9696.19i	0.442426	+	0.766305i
$544$	10135.5	+	17555.3i	0.798819	+	1.38359i
$545$	−1469.54			−0.115501
$546$	14814.0	−	10257.2i	1.16114	−	0.803967i
$547$	−6508.23			−0.508724			−0.254362	−	0.967109i	$-0.581865\pi$
$547$	−6508.23			−0.508724			−0.254362	+	0.967109i	$0.581865\pi$
$548$	−23232.8	−	40240.4i	−1.81105	−	3.13684i
$549$	−1794.68	−	3108.48i	−0.139517	−	0.241651i
$550$	3384.49	−	5862.10i	0.262391	−	0.454474i
$551$	40214.3			3.10923
$552$	−4425.79	+	7665.69i	−0.341257	+	0.591075i
$553$	−2648.99	+	4588.18i	−0.203700	+	0.352820i
$554$	38122.3			2.92358
$555$	−759.881	+	1316.15i	−0.0581174	+	0.100662i
$556$	21848.7	+	37843.0i	1.66653	+	2.88651i
$557$	−3664.53	−	6347.15i	−0.278763	−	0.482832i	0.692315	−	0.721596i	$-0.256591\pi$
$557$	−3664.53	−	6347.15i	−0.278763	−	0.482832i	−0.971078	+	0.238764i	$0.923258\pi$
$558$	2164.69			0.164227
$559$	−384.501	−	181.764i	−0.0290924	−	0.0137528i
$560$	−5487.37			−0.414078
$561$	−1985.05	−	3438.21i	−0.149392	−	0.258754i
$562$	−9108.00	−	15775.5i	−0.683626	−	1.18407i
$563$	−4093.25	+	7089.72i	−0.306412	+	0.530721i	−0.977575	−	0.210589i	$-0.932462\pi$
$563$	−4093.25	+	7089.72i	−0.306412	+	0.530721i	0.671163	+	0.741310i	$0.265795\pi$
$564$	−29231.9			−2.18242
$565$	815.885	−	1413.15i	0.0607514	−	0.105225i
$566$	−12108.7	+	20972.9i	−0.899237	+	1.55752i
$567$	−3055.66			−0.226324
$568$	−8817.29	+	15272.0i	−0.651348	+	1.12817i
$569$	2184.33	+	3783.37i	0.160935	+	0.278747i	0.935204	−	0.354109i	$-0.115216\pi$
$569$	2184.33	+	3783.37i	0.160935	+	0.278747i	−0.774269	+	0.632856i	$0.781882\pi$
$570$	3256.52	+	5640.46i	0.239299	+	0.414479i
$571$	7386.75			0.541376			0.270688	−	0.962667i	$-0.412749\pi$
$571$	7386.75			0.541376			0.270688	+	0.962667i	$0.412749\pi$
$572$	−767.197	−	9334.36i	−0.0560806	−	0.682324i
$573$	7714.26			0.562422
$574$	−10579.3	−	18323.9i	−0.769290	−	1.33245i
$575$	−2858.67	−	4951.37i	−0.207330	−	0.359106i
$576$	452.499	−	783.752i	0.0327329	−	0.0566950i
$577$	−9363.28			−0.675561			−0.337780	−	0.941225i	$-0.609676\pi$
$577$	−9363.28			−0.675561			−0.337780	+	0.941225i	$0.609676\pi$
$578$	−13400.9	+	23211.0i	−0.964363	+	1.67033i
$579$	1010.76	−	1750.68i	0.0725486	−	0.125658i
$580$	9656.94			0.691349
$581$	7455.54	−	12913.4i	0.532371	−	0.922094i
$582$	−3418.62	−	5921.22i	−0.243482	−	0.421722i
$583$	1630.82	+	2824.66i	0.115852	+	0.200661i
$584$	9801.98			0.694536
$585$	1301.63	+	615.317i	0.0919929	+	0.0434876i
$586$	2621.98			0.184835
$587$	3258.11	+	5643.21i	0.229091	+	0.396797i	0.957539	−	0.288304i	$-0.0930913\pi$
$587$	3258.11	+	5643.21i	0.229091	+	0.396797i	−0.728448	+	0.685101i	$0.759758\pi$
$588$	3161.95	+	5476.65i	0.221763	+	0.384104i
$589$	−2448.71	+	4241.28i	−0.171302	+	0.296705i
$590$	7850.53			0.547799
$591$	2223.53	−	3851.27i	0.154761	−	0.268054i
$592$	−11807.2	+	20450.7i	−0.819717	+	1.41979i
$593$	18704.6			1.29529			0.647643	−	0.761944i	$-0.275755\pi$
$593$	18704.6			1.29529			0.647643	+	0.761944i	$0.275755\pi$
$594$	−4148.78	+	7185.90i	−0.286577	+	0.496366i
$595$	−2291.35	−	3968.73i	−0.157876	−	0.273449i
$596$	13787.9	+	23881.3i	0.947606	+	1.64130i
$597$	6807.51			0.466688
$598$	−10301.6	−	4869.86i	−0.704456	−	0.333016i
$599$	6285.10			0.428718			0.214359	−	0.976755i	$-0.431234\pi$
$599$	6285.10			0.428718			0.214359	+	0.976755i	$0.431234\pi$
$600$	−11203.0	−	19404.1i	−0.762266	−	1.32028i
$601$	−11072.4	−	19177.9i	−0.751499	−	1.30163i	−0.947096	−	0.320950i	$-0.895998\pi$
$601$	−11072.4	−	19177.9i	−0.751499	−	1.30163i	0.195597	−	0.980684i	$-0.437335\pi$
$602$	486.891	−	843.320i	0.0329638	−	0.0570950i
$603$	−6239.28			−0.421365
$604$	9609.83	−	16644.7i	0.647382	−	1.12130i
$605$	131.150	−	227.158i	0.00881320	−	0.0152649i
$606$	9273.85			0.621657
$607$	306.880	−	531.532i	0.0205204	−	0.0355424i	−0.855583	−	0.517666i	$-0.826801\pi$
$607$	306.880	−	531.532i	0.0205204	−	0.0355424i	0.876103	+	0.482124i	$0.160134\pi$
$608$	16494.9	+	28569.9i	1.10025	+	1.90570i
$609$	−9215.09	−	15961.0i	−0.613159	−	1.06202i
$610$	2808.87			0.186439
$611$	−1724.94	−	20987.1i	−0.114212	−	1.38960i
$612$	25935.0			1.71301
$613$	−3062.81	−	5304.94i	−0.201804	−	0.349534i	0.747306	−	0.664480i	$-0.231347\pi$
$613$	−3062.81	−	5304.94i	−0.201804	−	0.349534i	−0.949110	+	0.314946i	$0.898014\pi$
$614$	3358.24	+	5816.63i	0.220729	+	0.382313i
$615$	−765.432	+	1325.77i	−0.0501873	+	0.0869270i
$616$	12000.2			0.784905
$617$	−1754.15	+	3038.27i	−0.114456	+	0.198243i	−0.917562	−	0.397592i	$-0.869846\pi$
$617$	−1754.15	+	3038.27i	−0.114456	+	0.198243i	0.803106	+	0.595836i	$0.203179\pi$
$618$	−10644.7	+	18437.2i	−0.692868	+	1.20008i
$619$	30039.5			1.95055			0.975275	−	0.220993i	$-0.0709299\pi$
$619$	30039.5			1.95055			0.975275	+	0.220993i	$0.0709299\pi$
$620$	−588.025	+	1018.49i	−0.0380897	+	0.0659734i
$621$	3504.23	+	6069.50i	0.226441	+	0.392207i
$622$	−25146.4	−	43554.9i	−1.62103	−	2.80771i
$623$	29022.7			1.86640
$624$	−18313.4	−	8657.26i	−1.17488	−	0.555397i
$625$	13884.9			0.888633
$626$	15312.9	+	26522.8i	0.977681	+	1.69339i
$627$	−3230.53	−	5595.44i	−0.205765	−	0.356396i
$628$	29430.8	−	50975.6i	1.87009	−	3.23909i
$629$	−19721.2			−1.25014
$630$	−1648.25	+	2854.85i	−0.104234	+	0.180539i
$631$	8535.39	−	14783.7i	0.538492	−	0.932696i	−0.460493	−	0.887663i	$-0.652327\pi$
$631$	8535.39	−	14783.7i	0.538492	−	0.932696i	0.998986	−	0.0450327i	$-0.0143392\pi$
$632$	13130.0			0.826397
$633$	6349.75	−	10998.1i	0.398704	−	0.690576i
$634$	−10329.6	−	17891.4i	−0.647068	−	1.12076i
$635$	−1526.48	−	2643.95i	−0.0953964	−	0.165231i
$636$	19293.1			1.20286
$637$	−3745.38	+	2593.29i	−0.232963	+	0.161303i
$638$	−13798.9			−0.856273
$639$	2402.81	+	4161.78i	0.148754	+	0.257649i
$640$	−1390.35	−	2408.15i	−0.0858723	−	0.148735i
$641$	−12475.7	+	21608.5i	−0.768734	+	1.33149i	0.169515	+	0.985528i	$0.445780\pi$
$641$	−12475.7	+	21608.5i	−0.768734	+	1.33149i	−0.938250	+	0.345959i	$0.887554\pi$
$642$	19764.7			1.21503
$643$	−8015.55	+	13883.3i	−0.491606	+	0.851486i	−0.999953	−	0.00966588i	$-0.996923\pi$
$643$	−8015.55	+	13883.3i	−0.491606	+	0.851486i	0.508348	+	0.861152i	$0.330257\pi$
$644$	9056.39	−	15686.1i	0.554149	−	0.959814i
$645$	−70.4548			−0.00430102
$646$	−42258.3	+	73193.5i	−2.57373	+	4.45784i
$647$	−3813.28	−	6604.79i	−0.231708	−	0.401331i	0.726603	−	0.687058i	$-0.241098\pi$
$647$	−3813.28	−	6604.79i	−0.231708	−	0.401331i	−0.958311	+	0.285727i	$0.907765\pi$
$648$	3786.43	+	6558.29i	0.229545	+	0.397583i
$649$	−7787.87			−0.471033
$650$	23713.8	−	16419.3i	1.43097	−	0.990799i
$651$	2244.48			0.135128
$652$	−12792.2	−	22156.7i	−0.768376	−	1.33087i
$653$	−11189.1	−	19380.1i	−0.670540	−	1.16141i	−0.977751	−	0.209768i	$-0.932729\pi$
$653$	−11189.1	−	19380.1i	−0.670540	−	1.16141i	0.307211	−	0.951641i	$-0.400604\pi$
$654$	6210.40	−	10756.7i	0.371324	−	0.643152i
$655$	−1620.66			−0.0966786
$656$	−11893.4	+	20600.1i	−0.707868	+	1.22606i
$657$	1335.57	−	2313.28i	0.0793084	−	0.137366i
$658$	48214.8			2.85655
$659$	−102.153	+	176.935i	−0.00603843	+	0.0104589i	−0.869029	−	0.494761i	$-0.835255\pi$
$659$	−102.153	+	176.935i	−0.00603843	+	0.0104589i	0.862990	+	0.505220i	$0.168589\pi$
$660$	−775.769	−	1343.67i	−0.0457527	−	0.0792460i
$661$	11002.7	+	19057.2i	0.647436	+	1.12139i	0.983733	+	0.179636i	$0.0574920\pi$
$661$	11002.7	+	19057.2i	0.647436	+	1.12139i	−0.336297	+	0.941756i	$0.609175\pi$
$662$	54587.8			3.20486
$663$	−1385.75	−	16860.2i	−0.0811734	−	0.987624i
$664$	−36954.2			−2.15979
$665$	−3729.01	−	6458.83i	−0.217451	−	0.376636i
$666$	7093.08	+	12285.6i	0.412689	+	0.714799i
$667$	−5827.54	+	10093.6i	−0.338296	+	0.585945i
$668$	30119.8			1.74456
$669$	−2670.83	+	4626.01i	−0.154350	+	0.267342i
$670$	2441.29	−	4228.44i	0.140769	−	0.243819i
$671$	−2786.45			−0.160313
$672$	7559.58	−	13093.6i	0.433954	−	0.751630i
$673$	−1217.45	−	2108.69i	−0.0697314	−	0.120778i	0.829052	−	0.559172i	$-0.188881\pi$
$673$	−1217.45	−	2108.69i	−0.0697314	−	0.120778i	−0.898783	+	0.438394i	$0.855548\pi$
$674$	−2272.73	−	3936.49i	−0.129885	−	0.224967i
$675$	−17740.5			−1.01160
$676$	14043.4	−	37356.4i	0.799010	−	2.12542i
$677$	4776.11			0.271138			0.135569	−	0.990768i	$-0.456714\pi$
$677$	4776.11			0.271138			0.135569	+	0.990768i	$0.456714\pi$
$678$	6896.02	+	11944.3i	0.390620	+	0.676573i
$679$	3914.62	+	6780.33i	0.221251	+	0.383218i
$680$	−5678.66	+	9835.73i	−0.320245	+	0.554681i
$681$	−6764.72			−0.380653
$682$	840.232	−	1455.33i	0.0471762	−	0.0817116i
$683$	−6994.21	+	12114.3i	−0.391839	+	0.678685i	−0.992692	−	0.120675i	$-0.961494\pi$
$683$	−6994.21	+	12114.3i	−0.391839	+	0.678685i	0.600853	+	0.799359i	$0.294828\pi$
$684$	42207.4			2.35942
$685$	2772.52	−	4802.15i	0.154646	−	0.267855i
$686$	13190.2	+	22846.0i	0.734114	+	1.27152i
$687$	−4120.50	−	7136.91i	−0.228831	−	0.396347i
$688$	−1094.74			−0.0606637
$689$	1138.46	+	13851.5i	0.0629491	+	0.765892i
$690$	−1887.64			−0.104147
$691$	12034.3	+	20844.1i	0.662529	+	1.14753i	0.979949	+	0.199248i	$0.0638500\pi$
$691$	12034.3	+	20844.1i	0.662529	+	1.14753i	−0.317420	+	0.948285i	$0.602817\pi$
$692$	18672.8	+	32342.3i	1.02577	+	1.77669i
$693$	1635.09	−	2832.06i	0.0896277	−	0.155240i
$694$	−23742.3			−1.29862
$695$	−2607.34	+	4516.05i	−0.142305	+	0.246480i
$696$	−22837.8	+	39556.2i	−1.24377	+	2.15427i
$697$	−19865.3			−1.07956
$698$	3817.39	−	6611.91i	0.207006	−	0.358545i
$699$	3009.36	+	5212.37i	0.162839	+	0.282046i
$700$	22924.4	+	39706.2i	1.23780	+	2.14393i
$701$	36641.1			1.97420			0.987102	−	0.160095i	$-0.0511801\pi$
$701$	36641.1			1.97420			0.987102	+	0.160095i	$0.0511801\pi$
$702$	−29068.9	+	20127.2i	−1.56287	+	1.08213i
$703$	−32094.9			−1.72188
$704$	−351.279	−	608.433i	−0.0188059	−	0.0325727i
$705$	−1744.21	−	3021.07i	−0.0931785	−	0.161390i
$706$	19191.9	−	33241.4i	1.02308	−	1.77203i
$707$	−10619.4			−0.564898
$708$	−23033.2	+	39894.7i	−1.22266	+	2.11770i
$709$	5685.68	−	9847.88i	0.301171	−	0.521643i	−0.675231	−	0.737607i	$-0.735956\pi$
$709$	5685.68	−	9847.88i	0.301171	−	0.521643i	0.976401	+	0.215964i	$0.0692893\pi$
$710$	−3760.65			−0.198781
$711$	1789.03	−	3098.69i	0.0943655	−	0.163446i
$712$	−35963.5	−	62290.6i	−1.89296	−	3.27870i
$713$	−709.694	−	1229.23i	−0.0372766	−	0.0645650i
$714$	38733.9			2.03022
$715$	918.913	−	636.253i	0.0480635	−	0.0332790i
$716$	−83743.9			−4.37103
$717$	10067.3	+	17437.1i	0.524366	+	0.908229i
$718$	6774.31	+	11733.4i	0.352110	+	0.609872i
$719$	8458.65	−	14650.8i	0.438741	−	0.759921i	−0.558852	−	0.829267i	$-0.688758\pi$
$719$	8458.65	−	14650.8i	0.438741	−	0.759921i	0.997593	+	0.0693463i	$0.0220914\pi$
$720$	3705.97			0.191824
$721$	12189.1	−	21112.2i	0.629607	−	1.09051i
$722$	−51229.9	+	88732.7i	−2.64069	+	4.57381i
$723$	−12790.6			−0.657935
$724$	−28389.6	+	49172.3i	−1.45731	+	2.52414i
$725$	−14751.2	−	25549.9i	−0.755650	−	1.30882i
$726$	1108.50	+	1919.98i	0.0566672	+	0.0981504i
$727$	3856.69			0.196749			0.0983745	−	0.995149i	$-0.468636\pi$
$727$	3856.69			0.196749			0.0983745	+	0.995149i	$0.468636\pi$
$728$	46228.9	+	21853.7i	2.35351	+	1.11257i
$729$	16325.7			0.829430
$730$	1045.16	+	1810.27i	0.0529904	+	0.0917821i
$731$	−457.129	−	791.771i	−0.0231293	−	0.0400612i
$732$	−8241.13	+	14274.1i	−0.416122	+	0.720744i
$733$	−24883.8			−1.25390			−0.626948	−	0.779061i	$-0.715696\pi$
$733$	−24883.8			−1.25390			−0.626948	+	0.779061i	$0.715696\pi$
$734$	32680.4	−	56604.2i	1.64340	−	2.84645i
$735$	−377.335	+	653.563i	−0.0189363	+	0.0327987i
$736$	−9561.22			−0.478847
$737$	−2421.80	+	4194.69i	−0.121042	+	0.209652i
$738$	7144.89	+	12375.3i	0.356378	+	0.617265i
$739$	9267.46	+	16051.7i	0.461311	+	0.799015i	0.999027	−	0.0441118i	$-0.0140458\pi$
$739$	9267.46	+	16051.7i	0.461311	+	0.799015i	−0.537715	+	0.843127i	$0.680712\pi$
$740$	−7707.17			−0.382866
$741$	−2255.21	−	27438.7i	−0.111804	−	1.36031i
$742$	−31821.8			−1.57442
$743$	15554.0	+	26940.3i	0.767997	+	1.33021i	0.938648	+	0.344877i	$0.112080\pi$
$743$	15554.0	+	26940.3i	0.767997	+	1.33021i	−0.170651	+	0.985332i	$0.554587\pi$
$744$	−2781.25	−	4817.26i	−0.137050	−	0.237378i
$745$	−1645.39	+	2849.90i	−0.0809161	+	0.140151i
$746$	1636.65			0.0803246
$747$	−5035.20	+	8721.22i	−0.246624	+	0.427166i
$748$	10066.8	−	17436.2i	0.492083	−	0.852313i
$749$	−22632.4			−1.10410
$750$	4871.49	−	8437.66i	0.237175	−	0.410800i
$751$	3318.82	+	5748.37i	0.161259	+	0.279309i	0.935320	−	0.353802i	$-0.115111\pi$
$751$	3318.82	+	5748.37i	0.161259	+	0.279309i	−0.774061	+	0.633110i	$0.781778\pi$
$752$	−27102.0	−	46942.0i	−1.31424	−	2.27633i
$753$	7734.45			0.374315
$754$	−53158.0	−	25129.3i	−2.56751	−	1.21373i
$755$	2293.60			0.110560
$756$	−28101.3	−	48672.8i	−1.35190	−	2.34155i
$757$	2066.06	+	3578.53i	0.0991973	+	0.171815i	0.911353	−	0.411626i	$-0.135039\pi$
$757$	2066.06	+	3578.53i	0.0991973	+	0.171815i	−0.812155	+	0.583441i	$0.801706\pi$
$758$	6369.58	−	11032.4i	0.305216	−	0.528649i
$759$	1872.57			0.0895520
$760$	−9241.61	+	16006.9i	−0.441090	+	0.763991i
$761$	−747.296	+	1294.36i	−0.0355972	+	0.0616562i	−0.883275	−	0.468855i	$-0.844667\pi$
$761$	−747.296	+	1294.36i	−0.0355972	+	0.0616562i	0.847678	+	0.530511i	$0.178000\pi$
$762$	25804.3			1.22676
$763$	−7111.47	+	12317.4i	−0.337421	+	0.584431i
$764$	19560.7	+	33880.1i	0.926282	+	1.60437i
$765$	1547.50	+	2680.34i	0.0731370	+	0.126677i
$766$	−27351.8			−1.29016
$767$	−30001.6	−	14182.6i	−1.41238	−	0.667670i
$768$	25333.2			1.19028
$769$	−5613.86	−	9723.49i	−0.263252	−	0.455966i	0.703852	−	0.710347i	$-0.251462\pi$
$769$	−5613.86	−	9723.49i	−0.263252	−	0.455966i	−0.967104	+	0.254380i	$0.918128\pi$
$770$	1279.55	+	2216.24i	0.0598853	+	0.103724i
$771$	−14638.4	+	25354.5i	−0.683774	+	1.18433i
$772$	10251.7			0.477936
$773$	−11063.5	+	19162.5i	−0.514780	+	0.891625i	0.485073	+	0.874474i	$0.338793\pi$
$773$	−11063.5	+	19162.5i	−0.514780	+	0.891625i	−0.999853	+	0.0171515i	$0.994540\pi$
$774$	−328.829	+	569.548i	−0.0152707	+	0.0264496i
$775$	3592.89			0.166530
$776$	9701.63	−	16803.7i	0.448799	−	0.777343i
$777$	7354.52	+	12738.4i	0.339565	+	0.588144i
$778$	3186.07	+	5518.43i	0.146820	+	0.254300i
$779$	−32329.3			−1.48693
$780$	−541.558	−	6589.05i	−0.0248601	−	0.302469i
$781$	3730.64			0.170925
$782$	−12247.5	−	21213.3i	−0.560063	−	0.970057i
$783$	18082.4	+	31319.6i	0.825302	+	1.42947i
$784$	−5863.11	+	10155.2i	−0.267088	+	0.462610i
$785$	7024.32			0.319374
$786$	6849.08	−	11862.9i	0.310812	−	0.538343i
$787$	8520.77	−	14758.4i	0.385938	−	0.668463i	−0.605961	−	0.795494i	$-0.707211\pi$
$787$	8520.77	−	14758.4i	0.385938	−	0.668463i	0.991899	+	0.127031i	$0.0405447\pi$
$788$	22552.4			1.01954
$789$	10344.9	−	17917.8i	0.466776	−	0.808480i
$790$	1400.01	+	2424.89i	0.0630509	+	0.109207i
$791$	−7896.57	−	13677.3i	−0.354955	−	0.614800i
$792$	−8104.50			−0.363612
$793$	−10734.4	−	5074.43i	−0.480692	−	0.227236i
$794$	2199.41			0.0983049
$795$	1151.18	+	1993.91i	0.0513563	+	0.0889516i
$796$	17261.5	+	29897.7i	0.768613	+	1.33128i
$797$	−8752.15	+	15159.2i	−0.388980	+	0.673733i	−0.992313	−	0.123757i	$-0.960506\pi$
$797$	−8752.15	+	15159.2i	−0.388980	+	0.673733i	0.603333	+	0.797490i	$0.293839\pi$
$798$	63036.6			2.79633
$799$	22633.8	−	39202.9i	1.00216	−	1.73579i
$800$	12101.1	−	20959.8i	0.534799	−	0.926300i
$801$	−19600.9			−0.864622
$802$	13954.9	−	24170.7i	0.614422	−	1.06421i
$803$	−1036.82	−	1795.82i	−0.0455647	−	0.0789203i
$804$	14325.3	+	24812.2i	0.628377	+	1.08838i
$805$	2161.51			0.0946377
$806$	5887.18	−	4076.26i	0.257279	−	0.178139i
$807$	−8052.00			−0.351232
$808$	13159.0	+	22792.1i	0.572937	+	0.992356i
$809$	−2745.94	−	4756.11i	−0.119335	−	0.206695i	0.800169	−	0.599774i	$-0.204743\pi$
$809$	−2745.94	−	4756.11i	−0.119335	−	0.206695i	−0.919504	+	0.393080i	$0.871410\pi$
$810$	−807.473	+	1398.58i	−0.0350268	+	0.0606682i
$811$	21887.8			0.947699			0.473849	−	0.880606i	$-0.342864\pi$
$811$	21887.8			0.947699			0.473849	+	0.880606i	$0.342864\pi$
$812$	46732.5	−	80943.0i	2.01969	−	3.49821i
$813$	−666.739	+	1154.83i	−0.0287620	+	0.0498173i
$814$	11012.8			0.474201
$815$	1526.57	−	2644.10i	0.0656117	−	0.113643i
$816$	−21772.6	−	37711.3i	−0.934062	−	1.61784i
$817$	−743.945	−	1288.55i	−0.0318572	−	0.0551783i
$818$	−54015.3			−2.30880
$819$	11456.4	−	7932.40i	0.488791	−	0.338438i
$820$	−7763.47			−0.330625
$821$	−10305.9	−	17850.3i	−0.438096	−	0.758805i	0.559446	−	0.828867i	$-0.311014\pi$
$821$	−10305.9	−	17850.3i	−0.438096	−	0.758805i	−0.997543	+	0.0700613i	$0.977681\pi$
$822$	23433.9	+	40588.7i	0.994344	+	1.72225i
$823$	−15473.3	+	26800.6i	−0.655366	+	1.13513i	0.326435	+	0.945220i	$0.394152\pi$
$823$	−15473.3	+	26800.6i	−0.655366	+	1.13513i	−0.981802	+	0.189908i	$0.939181\pi$
$824$	−60416.7			−2.55427
$825$	−2370.01	+	4104.98i	−0.100016	+	0.173233i
$826$	37990.8	−	65802.0i	1.60032	−	2.77184i
$827$	−435.745			−0.0183221			−0.00916104	−	0.999958i	$-0.502916\pi$
$827$	−435.745			−0.0183221			−0.00916104	+	0.999958i	$0.502916\pi$
$828$	−6116.36	+	10593.9i	−0.256713	+	0.444640i
$829$	17075.2	+	29575.0i	0.715374	+	1.23906i	0.962815	+	0.270161i	$0.0870769\pi$
$829$	17075.2	+	29575.0i	0.715374	+	1.23906i	−0.247441	+	0.968903i	$0.579590\pi$
$830$	−3940.32	−	6824.83i	−0.164784	−	0.285414i
$831$	−26695.5			−1.11439
$832$	−245.225	−	2983.61i	−0.0102183	−	0.124325i
$833$	−9792.99			−0.407331
$834$	−22037.8	−	38170.5i	−0.914995	−	1.58482i
$835$	1797.19	+	3112.83i	0.0744843	+	0.129011i
$836$	16383.0	−	28376.1i	0.677772	−	1.17393i
$837$	−4404.25			−0.181879
$838$	13887.9	−	24054.5i	0.572493	−	0.991587i
$839$	−14715.3	+	25487.7i	−0.605519	+	1.04879i	0.386451	+	0.922310i	$0.373701\pi$
$839$	−14715.3	+	25487.7i	−0.605519	+	1.04879i	−0.991969	+	0.126479i	$0.959632\pi$
$840$	8470.84			0.347943
$841$	−17876.5	+	30963.1i	−0.732976	+	1.26955i
$842$	−17969.6	−	31124.3i	−0.735479	−	1.27389i
$843$	6377.95	+	11046.9i	0.260579	+	0.451336i
$844$	64403.0			2.62659
$845$	4698.66	−	777.624i	0.191288	−	0.0316581i
$846$	−32562.6			−1.32331
$847$	−1269.33	−	2198.55i	−0.0514933	−	0.0891890i
$848$	17887.3	+	30981.7i	0.724355	+	1.25462i
$849$	8479.23	−	14686.5i	0.342764	−	0.593684i
$850$	62004.0			2.50202
$851$	4650.93	−	8055.66i	0.187347	−	0.324494i
$852$	11033.6	−	19110.8i	0.443669	−	0.768457i
$853$	−5380.99			−0.215992			−0.107996	−	0.994151i	$-0.534443\pi$
$853$	−5380.99			−0.215992			−0.107996	+	0.994151i	$0.534443\pi$
$854$	13592.9	−	23543.5i	0.544658	−	0.943375i
$855$	2518.44	+	4362.06i	0.100735	+	0.174479i
$856$	28045.0	+	48575.3i	1.11981	+	1.93957i
$857$	19052.3			0.759409			0.379705	−	0.925108i	$-0.376026\pi$
$857$	19052.3			0.759409			0.379705	+	0.925108i	$0.376026\pi$
$858$	773.836	+	9415.14i	0.0307906	+	0.374624i
$859$	−32175.1			−1.27800			−0.639000	−	0.769207i	$-0.720652\pi$
$859$	−32175.1			−1.27800			−0.639000	+	0.769207i	$0.720652\pi$
$860$	−178.649	−	309.429i	−0.00708357	−	0.0122691i
$861$	7408.25	+	12831.5i	0.293232	+	0.507892i
$862$	−7535.84	+	13052.5i	−0.297763	+	0.515741i
$863$	−8470.66			−0.334119			−0.167059	−	0.985947i	$-0.553427\pi$
$863$	−8470.66			−0.334119			−0.167059	+	0.985947i	$0.553427\pi$
$864$	−14833.8	+	25693.0i	−0.584095	+	1.01168i
$865$	−2228.35	+	3859.61i	−0.0875908	+	0.151712i
$866$	−9750.65			−0.382610
$867$	9384.05	−	16253.7i	0.367588	−	0.636682i
$868$	5691.21	+	9857.47i	0.222549	+	0.385466i
$869$	−1388.84	−	2405.54i	−0.0542153	−	0.0939037i
$870$	−9740.51			−0.379580
$871$	−16968.6	+	11749.0i	−0.660114	+	0.457061i
$872$	35248.8			1.36889
$873$	−2643.80	−	4579.19i	−0.102496	−	0.177528i
$874$	−19931.9	−	34523.1i	−0.771403	−	1.33611i
$875$	−5578.29	+	9661.88i	−0.215521	+	0.373293i
$876$	−12265.8			−0.473087
$877$	−20950.1	+	36286.6i	−0.806652	+	1.39716i	0.108517	+	0.994095i	$0.465390\pi$
$877$	−20950.1	+	36286.6i	−0.806652	+	1.39716i	−0.915170	+	0.403068i	$0.867944\pi$
$878$	−41673.8	+	72181.2i	−1.60185	+	2.77448i
$879$	−1836.06			−0.0704538
$880$	1438.49	−	2491.53i	0.0551039	−	0.0954427i
$881$	−9603.84	−	16634.3i	−0.367266	−	0.636124i	0.621871	−	0.783120i	$-0.286373\pi$
$881$	−9603.84	−	16634.3i	−0.367266	−	0.636124i	−0.989137	+	0.146996i	$0.953040\pi$
$882$	3522.22	+	6100.66i	0.134466	+	0.232902i
$883$	29638.5			1.12957			0.564787	−	0.825237i	$-0.308958\pi$
$883$	29638.5			1.12957			0.564787	+	0.825237i	$0.308958\pi$
$884$	70534.0	−	48837.5i	2.68361	−	1.85813i
$885$	−5497.40			−0.208806
$886$	1937.10	+	3355.16i	0.0734517	+	0.127222i
$887$	21241.2	+	36790.8i	0.804068	+	1.39269i	0.916919	+	0.399074i	$0.130668\pi$
$887$	21241.2	+	36790.8i	0.804068	+	1.39269i	−0.112851	+	0.993612i	$0.535998\pi$
$888$	18226.7	−	31569.6i	0.688794	−	1.19303i
$889$	−29548.2			−1.11475
$890$	7669.37	−	13283.7i	0.288851	−	0.500305i
$891$	801.028	−	1387.42i	0.0301183	−	0.0521665i
$892$	−27089.2			−1.01683
$893$	36834.9	−	63800.0i	1.38033	−	2.39080i
$894$	−13907.2	−	24088.0i	−0.520275	−	0.901143i
$895$	−4996.84	−	8654.79i	−0.186621	−	0.323238i
$896$	−26913.0			−1.00346
$897$	7213.79	+	3410.16i	0.268519	+	0.126936i
$898$	22411.2			0.832820
$899$	−3662.14	−	6343.01i	−0.135861	−	0.235318i
$900$	−15482.3	−	26816.2i	−0.573419	−	0.993191i
$901$	−14938.3	+	25874.0i	−0.552351	+	0.956700i
$902$	11093.3			0.409496
$903$	−340.949	+	590.542i	−0.0125649	+	0.0217630i
$904$	−19570.1	+	33896.4i	−0.720013	+	1.24710i
$905$	−6775.83			−0.248880
$906$	−9692.99	+	16788.8i	−0.355439	+	0.615639i
$907$	25762.7	+	44622.3i	0.943148	+	1.63358i	0.759417	+	0.650604i	$0.225484\pi$
$907$	25762.7	+	44622.3i	0.943148	+	1.63358i	0.183731	+	0.982977i	$0.441182\pi$
$908$	−17153.0	−	29709.8i	−0.626917	−	1.08585i
$909$	7171.95			0.261693
$910$	893.242	+	10867.9i	0.0325392	+	0.395899i
$911$	−9999.32			−0.363658			−0.181829	−	0.983330i	$-0.558202\pi$
$911$	−9999.32			−0.363658			−0.181829	+	0.983330i	$0.558202\pi$
$912$	−35433.4	−	61372.5i	−1.28653	−	2.22834i
$913$	3908.87	+	6770.36i	0.141692	+	0.245417i
$914$	28081.4	−	48638.4i	1.01625	−	1.76019i
$915$	−1966.93			−0.0710653
$916$	20896.3	−	36193.4i	0.753747	−	1.30553i
$917$	−7842.81	+	13584.1i	−0.282434	+	0.489191i
$918$	−76005.9			−2.73265
$919$	−24752.8	+	42873.1i	−0.888487	+	1.53890i	−0.0468225	+	0.998903i	$0.514910\pi$
$919$	−24752.8	+	42873.1i	−0.888487	+	1.53890i	−0.841664	+	0.540001i	$0.818424\pi$
$920$	−2678.44	−	4639.20i	−0.0959844	−	0.166250i
$921$	−2351.63	−	4073.14i	−0.0841356	−	0.145727i
$922$	38130.6			1.36200
$923$	14371.7	+	6793.90i	0.512514	+	0.242279i
$924$	−15016.6			−0.534643
$925$	11772.9	+	20391.2i	0.418476	+	0.724821i
$926$	14563.8	+	25225.3i	0.516843	+	0.895199i
$927$	−8232.10	+	14258.4i	−0.291670	+	0.505186i
$928$	−49337.4			−1.74524
$929$	19665.9	−	34062.4i	0.694530	−	1.20296i	−0.275809	−	0.961212i	$-0.588946\pi$
$929$	19665.9	−	34062.4i	0.694530	−	1.20296i	0.970339	−	0.241748i	$-0.0777209\pi$
$930$	593.113	−	1027.30i	0.0209129	−	0.0362221i
$931$	−15937.4			−0.561039
$932$	−15261.4	+	26433.5i	−0.536377	+	0.929032i
$933$	17609.0	+	30499.7i	0.617891	+	1.07022i
$934$	12237.8	+	21196.5i	0.428729	+	0.742580i
$935$	2402.67			0.0840381
$936$	−31221.4	−	14759.2i	−1.09028	−	0.515405i
$937$	−14333.0			−0.499720			−0.249860	−	0.968282i	$-0.580385\pi$
$937$	−14333.0			−0.499720			−0.249860	+	0.968282i	$0.580385\pi$
$938$	−23628.1	−	40925.0i	−0.822477	−	1.42457i
$939$	−10723.0	−	18572.8i	−0.372665	−	0.645474i
$940$	8845.43	−	15320.7i	0.306921	−	0.531603i
$941$	56634.2			1.96198			0.980990	−	0.194057i	$-0.0621646\pi$
$941$	56634.2			1.96198			0.980990	+	0.194057i	$0.0621646\pi$
$942$	−29685.5	+	51416.7i	−1.02676	+	1.77839i
$943$	4684.91	−	8114.51i	0.161783	−	0.280217i
$944$	−85419.7			−2.94510
$945$	3353.50	−	5808.44i	0.115439	−	0.199945i
$946$	255.273	+	442.145i	0.00877339	+	0.0151960i
$947$	−6315.65	−	10939.0i	−0.216717	−	0.375365i	0.737085	−	0.675800i	$-0.236202\pi$
$947$	−6315.65	−	10939.0i	−0.216717	−	0.375365i	−0.953802	+	0.300435i	$0.902868\pi$
$948$	−16430.4			−0.562905
$949$	−723.792	−	8806.27i	−0.0247580	−	0.301226i
$950$	100907.			3.44616
$951$	7233.39	+	12528.6i	0.246644	+	0.427201i
$952$	54961.1	+	95195.3i	1.87111	+	3.24086i
$953$	16785.6	−	29073.5i	0.570554	−	0.988228i	−0.425955	−	0.904744i	$-0.640062\pi$
$953$	16785.6	−	29073.5i	0.570554	−	0.988228i	0.996509	−	0.0834840i	$-0.0266048\pi$
$954$	21491.3			0.729358
$955$	−2334.30	+	4043.12i	−0.0790953	+	0.136997i
$956$	−51054.3	+	88428.7i	−1.72721	+	2.99162i
$957$	9662.77			0.326388
$958$	−13736.9	+	23793.0i	−0.463276	+	0.802418i
$959$	−26833.9	−	46477.7i	−0.903558	−	1.56501i
$960$	−247.965	−	429.488i	−0.00833649	−	0.0144392i
$961$	−28899.0			−0.970059
$962$	42425.2	+	20055.6i	1.42188	+	0.672159i
$963$	15285.1			0.511480
$964$	−32432.5	−	56174.7i	−1.08359	−	1.87683i
$965$	611.700	+	1059.50i	0.0204055	+	0.0353434i
$966$	−9134.77	+	15821.9i	−0.304251	+	0.526978i
$967$	−12984.6			−0.431806			−0.215903	−	0.976415i	$-0.569269\pi$
$967$	−12984.6			−0.431806			−0.215903	+	0.976415i	$0.569269\pi$
$968$	−3145.80	+	5448.68i	−0.104452	+	0.180916i
$969$	29591.7	−	51254.4i	0.981035	−	1.69920i
$970$	4137.83			0.136967
$971$	20010.4	−	34659.0i	0.661343	−	1.14548i	−0.318920	−	0.947782i	$-0.603320\pi$
$971$	20010.4	−	34659.0i	0.661343	−	1.14548i	0.980263	−	0.197698i	$-0.0633466\pi$
$972$	31425.2	+	54430.0i	1.03700	+	1.79614i
$973$	25235.2	+	43708.7i	0.831453	+	1.44012i
$974$	−56832.1			−1.86963
$975$	−16605.7	+	11497.8i	−0.545446	+	0.377665i
$976$	−30562.6			−1.00234
$977$	−14689.9	−	25443.7i	−0.481037	−	0.833180i	0.518726	−	0.854940i	$-0.326406\pi$
$977$	−14689.9	−	25443.7i	−0.481037	−	0.833180i	−0.999763	+	0.0217602i	$0.993073\pi$
$978$	12902.9	+	22348.5i	0.421870	+	0.730701i
$979$	−7608.15	+	13177.7i	−0.248373	+	0.430195i
$980$	−3827.16			−0.124749
$981$	4802.83	−	8318.75i	0.156312	−	0.270741i
$982$	22035.1	−	38166.0i	0.716059	−	1.24025i
$983$	−35077.8			−1.13816			−0.569078	−	0.822284i	$-0.692700\pi$
$983$	−35077.8			−1.13816			−0.569078	+	0.822284i	$0.692700\pi$
$984$	18359.9	−	31800.3i	0.594809	−	1.03024i
$985$	1345.66	+	2330.75i	0.0435292	+	0.0753949i
$986$	−63199.0	−	109464.i	−2.04124	−	3.53554i
$987$	−33762.8			−1.08884
$988$	114789.	−	79479.6i	3.69628	−	2.55929i
$989$	431.227			0.0138647
$990$	−864.160	−	1496.77i	−0.0277422	−	0.0480510i
$991$	9299.13	+	16106.6i	0.298079	+	0.516289i	0.975697	−	0.219126i	$-0.0703207\pi$
$991$	9299.13	+	16106.6i	0.298079	+	0.516289i	−0.677617	+	0.735415i	$0.736987\pi$
$992$	3004.23	−	5203.47i	0.0961535	−	0.166543i
$993$	−38225.6			−1.22160
$994$	−18198.8	+	31521.2i	−0.580715	+	1.00583i
$995$	−2059.92	+	3567.88i	−0.0656320	+	0.113678i
$996$	46243.1			1.47115
$997$	2733.44	−	4734.45i	0.0868293	−	0.150393i	−0.819340	−	0.573308i	$-0.805660\pi$
$997$	2733.44	−	4734.45i	0.0868293	−	0.150393i	0.906169	+	0.422915i	$0.138993\pi$
$998$	−16384.3	−	28378.4i	−0.519674	−	0.900102i
$999$	−14431.5	−	24996.1i	−0.457049	−	0.791632i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.e.b.133.1	yes	34
13.3	even	3		1859.4.a.g.1.17		17
13.9	even	3	inner	143.4.e.b.100.1	✓	34
13.10	even	6		1859.4.a.h.1.1		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.e.b.100.1	✓	34	13.9	even	3	inner
143.4.e.b.133.1	yes	34	1.1	even	1	trivial
1859.4.a.g.1.17		17	13.3	even	3
1859.4.a.h.1.1		17	13.10	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:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.55759 - 4.42988i) q^{2} +(1.79098 + 3.10206i) q^{3} +(-9.08257 + 15.7315i) q^{4} -2.16776 q^{5} +(9.16117 - 15.8676i) q^{6} +(-10.4904 + 18.1698i) q^{7} +51.9966 q^{8} +(7.08482 - 12.2713i) q^{9} +O(q^{10})\)	\(q+(-2.55759 - 4.42988i) q^{2} +(1.79098 + 3.10206i) q^{3} +(-9.08257 + 15.7315i) q^{4} -2.16776 q^{5} +(9.16117 - 15.8676i) q^{6} +(-10.4904 + 18.1698i) q^{7} +51.9966 q^{8} +(7.08482 - 12.2713i) q^{9} +(5.54425 + 9.60293i) q^{10} +(-5.50000 - 9.52628i) q^{11} -65.0666 q^{12} +(-3.83951 - 46.7146i) q^{13} +107.320 q^{14} +(-3.88241 - 6.72453i) q^{15} +(-60.3257 - 104.487i) q^{16} +(50.3801 - 87.2610i) q^{17} -72.4803 q^{18} +(81.9901 - 142.011i) q^{19} +(19.6888 - 34.1021i) q^{20} -75.1519 q^{21} +(-28.1335 + 48.7287i) q^{22} +(23.7627 + 41.1582i) q^{23} +(93.1247 + 161.297i) q^{24} -120.301 q^{25} +(-197.120 + 136.486i) q^{26} +147.468 q^{27} +(-190.559 - 330.058i) q^{28} +(122.619 + 212.383i) q^{29} +(-19.8592 + 34.3972i) q^{30} -29.8659 q^{31} +(-100.591 + 174.228i) q^{32} +(19.7007 - 34.1227i) q^{33} -515.408 q^{34} +(22.7406 - 39.3879i) q^{35} +(128.697 + 222.909i) q^{36} +(-97.8621 - 169.502i) q^{37} -838.789 q^{38} +(138.035 - 95.5751i) q^{39} -112.716 q^{40} +(-98.5770 - 170.740i) q^{41} +(192.208 + 332.914i) q^{42} +(4.53680 - 7.85797i) q^{43} +199.817 q^{44} +(-15.3582 + 26.6012i) q^{45} +(121.551 - 210.532i) q^{46} +449.261 q^{47} +(216.084 - 374.268i) q^{48} +(-48.5955 - 84.1699i) q^{49} +(307.681 + 532.918i) q^{50} +360.918 q^{51} +(769.763 + 363.888i) q^{52} -296.513 q^{53} +(-377.162 - 653.264i) q^{54} +(11.9227 + 20.6507i) q^{55} +(-545.464 + 944.771i) q^{56} +587.369 q^{57} +(627.221 - 1086.38i) q^{58} +(353.994 - 613.136i) q^{59} +141.049 q^{60} +(126.657 - 219.376i) q^{61} +(76.3848 + 132.302i) q^{62} +(148.645 + 257.460i) q^{63} +63.8689 q^{64} +(8.32313 + 101.266i) q^{65} -201.546 q^{66} +(-220.164 - 381.335i) q^{67} +(915.162 + 1585.11i) q^{68} +(-85.1168 + 147.427i) q^{69} -232.645 q^{70} +(-169.574 + 293.711i) q^{71} +(368.387 - 638.064i) q^{72} +188.512 q^{73} +(-500.583 + 867.035i) q^{74} +(-215.456 - 373.180i) q^{75} +(1489.36 + 2579.65i) q^{76} +230.788 q^{77} +(-776.425 - 367.037i) q^{78} +252.516 q^{79} +(130.772 + 226.503i) q^{80} +(72.8207 + 126.129i) q^{81} +(-504.240 + 873.369i) q^{82} -710.703 q^{83} +(682.573 - 1182.25i) q^{84} +(-109.212 + 189.161i) q^{85} -46.4132 q^{86} +(-439.217 + 760.746i) q^{87} +(-285.981 - 495.334i) q^{88} +(-691.650 - 1197.97i) q^{89} +157.120 q^{90} +(889.076 + 420.290i) q^{91} -863.306 q^{92} +(-53.4890 - 92.6457i) q^{93} +(-1149.03 - 1990.17i) q^{94} +(-177.735 + 307.846i) q^{95} -720.621 q^{96} +(186.582 - 323.169i) q^{97} +(-248.575 + 430.545i) q^{98} -155.866 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 6 q^{3} - 50 q^{4} - 48 q^{5} - 16 q^{6} + 62 q^{7} - 42 q^{8} - 135 q^{9}+O(q^{10}) \) 34 * q + 6 * q^3 - 50 * q^4 - 48 * q^5 - 16 * q^6 + 62 * q^7 - 42 * q^8 - 135 * q^9	\( 34 q + 6 q^{3} - 50 q^{4} - 48 q^{5} - 16 q^{6} + 62 q^{7} - 42 q^{8} - 135 q^{9} - 2 q^{10} - 187 q^{11} - 254 q^{12} + 76 q^{13} + 148 q^{15} - 126 q^{16} + 74 q^{17} + 180 q^{18} + 159 q^{19} + 222 q^{20} - 368 q^{21} + 215 q^{23} - 214 q^{24} + 190 q^{25} + 123 q^{26} - 384 q^{27} + 358 q^{28} + 157 q^{29} - 829 q^{30} - 788 q^{31} + 553 q^{32} + 66 q^{33} - 1404 q^{34} - 58 q^{35} + 700 q^{36} - 88 q^{37} - 2636 q^{38} + 798 q^{39} + 1466 q^{40} + 512 q^{41} - 337 q^{42} - 927 q^{43} + 1100 q^{44} + 1482 q^{45} + 1361 q^{46} - 286 q^{47} + 178 q^{48} - 1835 q^{49} + 583 q^{50} - 1136 q^{51} + 2306 q^{52} + 212 q^{53} + 67 q^{54} + 264 q^{55} - 2059 q^{56} + 2596 q^{57} + 1690 q^{58} + 266 q^{59} + 74 q^{60} + 624 q^{61} - 643 q^{62} + 2360 q^{63} - 3178 q^{64} + 470 q^{65} + 352 q^{66} + 676 q^{67} + 413 q^{68} - 764 q^{69} - 2122 q^{70} + 763 q^{71} + 1366 q^{72} - 4748 q^{73} + 1649 q^{74} - 2420 q^{75} + 2101 q^{76} - 1364 q^{77} - 5848 q^{78} + 4328 q^{79} + 1013 q^{80} - 537 q^{81} - 3152 q^{82} + 1554 q^{83} + 3381 q^{84} + 1690 q^{85} + 5788 q^{86} + 4200 q^{87} + 231 q^{88} + 1687 q^{89} - 10798 q^{90} - 3380 q^{91} + 11084 q^{92} + 4310 q^{93} - 1777 q^{94} - 1124 q^{95} - 6930 q^{96} + 2047 q^{97} - 1553 q^{98} + 2970 q^{99}+O(q^{100}) \) 34 * q + 6 * q^3 - 50 * q^4 - 48 * q^5 - 16 * q^6 + 62 * q^7 - 42 * q^8 - 135 * q^9 - 2 * q^10 - 187 * q^11 - 254 * q^12 + 76 * q^13 + 148 * q^15 - 126 * q^16 + 74 * q^17 + 180 * q^18 + 159 * q^19 + 222 * q^20 - 368 * q^21 + 215 * q^23 - 214 * q^24 + 190 * q^25 + 123 * q^26 - 384 * q^27 + 358 * q^28 + 157 * q^29 - 829 * q^30 - 788 * q^31 + 553 * q^32 + 66 * q^33 - 1404 * q^34 - 58 * q^35 + 700 * q^36 - 88 * q^37 - 2636 * q^38 + 798 * q^39 + 1466 * q^40 + 512 * q^41 - 337 * q^42 - 927 * q^43 + 1100 * q^44 + 1482 * q^45 + 1361 * q^46 - 286 * q^47 + 178 * q^48 - 1835 * q^49 + 583 * q^50 - 1136 * q^51 + 2306 * q^52 + 212 * q^53 + 67 * q^54 + 264 * q^55 - 2059 * q^56 + 2596 * q^57 + 1690 * q^58 + 266 * q^59 + 74 * q^60 + 624 * q^61 - 643 * q^62 + 2360 * q^63 - 3178 * q^64 + 470 * q^65 + 352 * q^66 + 676 * q^67 + 413 * q^68 - 764 * q^69 - 2122 * q^70 + 763 * q^71 + 1366 * q^72 - 4748 * q^73 + 1649 * q^74 - 2420 * q^75 + 2101 * q^76 - 1364 * q^77 - 5848 * q^78 + 4328 * q^79 + 1013 * q^80 - 537 * q^81 - 3152 * q^82 + 1554 * q^83 + 3381 * q^84 + 1690 * q^85 + 5788 * q^86 + 4200 * q^87 + 231 * q^88 + 1687 * q^89 - 10798 * q^90 - 3380 * q^91 + 11084 * q^92 + 4310 * q^93 - 1777 * q^94 - 1124 * q^95 - 6930 * q^96 + 2047 * q^97 - 1553 * q^98 + 2970 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more