LMFDB - Embedded newform 153.3.j.a.86.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [153,3,Mod(86,153)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(153, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 0])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("153.86"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	153.j (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.16894804471$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			86.14
Character	$\chi$	$=$	153.86
Dual form			153.3.j.a.137.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.510714 + 0.294861i) q^{2} +(-1.38625 + 2.66051i) q^{3} +(-1.82611 + 3.16292i) q^{4} +(4.01198 + 2.31632i) q^{5} +(-0.0765013 - 1.76751i) q^{6} +(2.98103 + 5.16330i) q^{7} -4.51269i q^{8} +(-5.15661 - 7.37627i) q^{9} -2.73197 q^{10} +(-5.45790 + 3.15112i) q^{11} +(-5.88352 - 9.24300i) q^{12} +(-0.650693 + 1.12703i) q^{13} +(-3.04491 - 1.75798i) q^{14} +(-11.7242 + 7.46290i) q^{15} +(-5.97384 - 10.3470i) q^{16} +4.12311i q^{17} +(4.80853 + 2.24669i) q^{18} -25.8689 q^{19} +(-14.6527 + 8.45972i) q^{20} +(-17.8695 + 0.773424i) q^{21} +(1.85829 - 3.21865i) q^{22} +(24.7706 + 14.3013i) q^{23} +(12.0060 + 6.25573i) q^{24} +(-1.76936 - 3.06461i) q^{25} -0.767456i q^{26} +(26.7730 - 3.49382i) q^{27} -21.7748 q^{28} +(21.3205 - 12.3094i) q^{29} +(3.78720 - 7.26842i) q^{30} +(-7.27488 + 12.6005i) q^{31} +(21.7343 + 12.5483i) q^{32} +(-0.817554 - 18.8890i) q^{33} +(-1.21574 - 2.10573i) q^{34} +27.6201i q^{35} +(32.7471 - 2.84004i) q^{36} -36.3386 q^{37} +(13.2116 - 7.62773i) q^{38} +(-2.09646 - 3.29353i) q^{39} +(10.4528 - 18.1048i) q^{40} +(42.5451 + 24.5634i) q^{41} +(8.89814 - 5.66401i) q^{42} +(19.2635 + 33.3654i) q^{43} -23.0172i q^{44} +(-3.60242 - 41.5378i) q^{45} -16.8676 q^{46} +(-13.8385 + 7.98969i) q^{47} +(35.8095 - 1.54990i) q^{48} +(6.72689 - 11.6513i) q^{49} +(1.80727 + 1.04343i) q^{50} +(-10.9696 - 5.71567i) q^{51} +(-2.37648 - 4.11618i) q^{52} +23.1681i q^{53} +(-12.6432 + 9.67866i) q^{54} -29.1960 q^{55} +(23.3004 - 13.4525i) q^{56} +(35.8608 - 68.8244i) q^{57} +(-7.25913 + 12.5732i) q^{58} +(7.88857 + 4.55447i) q^{59} +(-2.19486 - 50.7108i) q^{60} +(33.8608 + 58.6486i) q^{61} -8.58032i q^{62} +(22.7139 - 48.6140i) q^{63} +32.9907 q^{64} +(-5.22113 + 3.01442i) q^{65} +(5.98718 + 9.40585i) q^{66} +(17.7786 - 30.7934i) q^{67} +(-13.0411 - 7.52926i) q^{68} +(-72.3871 + 46.0772i) q^{69} +(-8.14408 - 14.1060i) q^{70} +120.461i q^{71} +(-33.2868 + 23.2702i) q^{72} -23.5416 q^{73} +(18.5587 - 10.7148i) q^{74} +(10.6062 - 0.459056i) q^{75} +(47.2395 - 81.8212i) q^{76} +(-32.5404 - 18.7872i) q^{77} +(2.04182 + 1.06389i) q^{78} +(67.7420 + 117.333i) q^{79} -55.3492i q^{80} +(-27.8188 + 76.0731i) q^{81} -28.9712 q^{82} +(51.8259 - 29.9217i) q^{83} +(30.1854 - 57.9321i) q^{84} +(-9.55042 + 16.5418i) q^{85} +(-19.6763 - 11.3601i) q^{86} +(3.19366 + 73.7874i) q^{87} +(14.2200 + 24.6298i) q^{88} -71.9875i q^{89} +(14.0877 + 20.1517i) q^{90} -7.75894 q^{91} +(-90.4679 + 52.2317i) q^{92} +(-23.4388 - 36.8223i) q^{93} +(4.71170 - 8.16090i) q^{94} +(-103.785 - 59.9205i) q^{95} +(-63.5140 + 40.4291i) q^{96} +(-77.2067 - 133.726i) q^{97} +7.93399i q^{98} +(51.3878 + 24.0099i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 2 q^{3} + 64 q^{4} - 18 q^{5} - 22 q^{6} + 2 q^{7} - 6 q^{9} - 44 q^{12} - 10 q^{13} + 72 q^{14} - 36 q^{15} - 128 q^{16} - 38 q^{18} - 28 q^{19} - 18 q^{20} + 88 q^{21} + 144 q^{23} - 42 q^{24}+ \cdots + 58 q^{99}+O(q^{100}) $ 64 * q - 2 * q^3 + 64 * q^4 - 18 * q^5 - 22 * q^6 + 2 * q^7 - 6 * q^9 - 44 * q^12 - 10 * q^13 + 72 * q^14 - 36 * q^15 - 128 * q^16 - 38 * q^18 - 28 * q^19 - 18 * q^20 + 88 * q^21 + 144 * q^23 - 42 * q^24 + 154 * q^25 - 164 * q^27 + 32 * q^28 - 162 * q^29 - 220 * q^30 + 62 * q^31 + 126 * q^32 - 40 * q^33 + 12 * q^36 + 128 * q^37 - 36 * q^38 - 126 * q^39 - 144 * q^41 + 114 * q^42 - 64 * q^43 - 72 * q^45 - 48 * q^46 + 288 * q^47 - 10 * q^48 - 246 * q^49 + 62 * q^52 + 374 * q^54 - 84 * q^55 + 684 * q^56 + 232 * q^57 + 138 * q^58 - 432 * q^59 - 86 * q^60 + 110 * q^61 + 304 * q^63 - 260 * q^64 + 328 * q^66 - 148 * q^67 + 36 * q^69 - 216 * q^70 - 96 * q^72 - 196 * q^73 - 918 * q^74 + 314 * q^75 - 112 * q^76 - 504 * q^77 + 276 * q^78 + 86 * q^79 + 234 * q^81 - 396 * q^82 - 594 * q^83 + 592 * q^84 + 126 * q^86 + 462 * q^87 + 24 * q^88 - 338 * q^90 + 52 * q^91 - 36 * q^92 - 1006 * q^93 - 186 * q^94 - 144 * q^95 + 18 * q^96 + 140 * q^97 + 58 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.510714	+	0.294861i	−0.255357	+	0.147431i	−0.622215	−	0.782847i	$-0.713767\pi$
$2$	−0.510714	+	0.294861i	−0.255357	+	0.147431i	0.366858	+	0.930277i	$0.380434\pi$
$3$	−1.38625	+	2.66051i	−0.462084	+	0.886836i
$3$	−1.38625	+	2.66051i	−0.462084	+	0.886836i
$4$	−1.82611	+	3.16292i	−0.456528	+	0.790730i
$5$	4.01198	+	2.31632i	0.802396	+	0.463263i	0.844308	−	0.535858i	$-0.180012\pi$
$5$	4.01198	+	2.31632i	0.802396	+	0.463263i	−0.0419125	+	0.999121i	$0.513345\pi$
$6$	−0.0765013	−	1.76751i	−0.0127502	−	0.294585i
$7$	2.98103	+	5.16330i	0.425862	+	0.737614i	0.996500	−	0.0835870i	$-0.0266376\pi$
$7$	2.98103	+	5.16330i	0.425862	+	0.737614i	−0.570639	+	0.821201i	$0.693304\pi$
$8$		−	4.51269i		−	0.564086i
$9$	−5.15661	−	7.37627i	−0.572956	−	0.819586i
$10$	−2.73197			−0.273197
$11$	−5.45790	+	3.15112i	−0.496173	+	0.286466i	−0.727132	−	0.686498i	$-0.759147\pi$
$11$	−5.45790	+	3.15112i	−0.496173	+	0.286466i	0.230959	+	0.972964i	$0.425814\pi$
$12$	−5.88352	−	9.24300i	−0.490294	−	0.770250i
$13$	−0.650693	+	1.12703i	−0.0500533	+	0.0866948i	−0.889967	−	0.456026i	$-0.849272\pi$
$13$	−0.650693	+	1.12703i	−0.0500533	+	0.0866948i	0.839913	+	0.542721i	$0.182606\pi$
$14$	−3.04491	−	1.75798i	−0.217494	−	0.125570i
$15$	−11.7242	+	7.46290i	−0.781613	+	0.497527i
$16$	−5.97384	−	10.3470i	−0.373365	−	0.646687i
$17$			4.12311i			0.242536i
$17$			4.12311i			0.242536i
$18$	4.80853	+	2.24669i	0.267141	+	0.124816i
$19$	−25.8689			−1.36152			−0.680760	−	0.732507i	$-0.738350\pi$
$19$	−25.8689			−1.36152			−0.680760	+	0.732507i	$0.738350\pi$
$20$	−14.6527	+	8.45972i	−0.732633	+	0.422986i
$21$	−17.8695	+	0.773424i	−0.850927	+	0.0368297i
$22$	1.85829	−	3.21865i	0.0844676	−	0.146302i
$23$	24.7706	+	14.3013i	1.07698	+	0.621796i	0.930081	−	0.367355i	$-0.119737\pi$
$23$	24.7706	+	14.3013i	1.07698	+	0.621796i	0.146902	+	0.989151i	$0.453070\pi$
$24$	12.0060	+	6.25573i	0.500252	+	0.260655i
$25$	−1.76936	−	3.06461i	−0.0707742	−	0.122585i
$26$		−	0.767456i		−	0.0295175i
$27$	26.7730	−	3.49382i	0.991592	−	0.129401i
$28$	−21.7748			−0.777672
$29$	21.3205	−	12.3094i	0.735191	−	0.424462i	−0.0851275	−	0.996370i	$-0.527130\pi$
$29$	21.3205	−	12.3094i	0.735191	−	0.424462i	0.820318	+	0.571908i	$0.193796\pi$
$30$	3.78720	−	7.26842i	0.126240	−	0.242281i
$31$	−7.27488	+	12.6005i	−0.234673	+	0.406466i	−0.959178	−	0.282804i	$-0.908735\pi$
$31$	−7.27488	+	12.6005i	−0.234673	+	0.406466i	0.724504	+	0.689270i	$0.242069\pi$
$32$	21.7343	+	12.5483i	0.679196	+	0.392134i
$33$	−0.817554	−	18.8890i	−0.0247744	−	0.572395i
$34$	−1.21574	−	2.10573i	−0.0357572	−	0.0619332i
$35$			27.6201i			0.789145i
$36$	32.7471	−	2.84004i	0.909642	−	0.0788899i
$37$	−36.3386			−0.982125			−0.491062	−	0.871124i	$-0.663391\pi$
$37$	−36.3386			−0.982125			−0.491062	+	0.871124i	$0.663391\pi$
$38$	13.2116	−	7.62773i	0.347674	−	0.200730i
$39$	−2.09646	−	3.29353i	−0.0537553	−	0.0844494i
$40$	10.4528	−	18.1048i	0.261320	−	0.452620i
$41$	42.5451	+	24.5634i	1.03768	+	0.599107i	0.919177	−	0.393846i	$-0.128856\pi$
$41$	42.5451	+	24.5634i	1.03768	+	0.599107i	0.118508	+	0.992953i	$0.462189\pi$
$42$	8.89814	−	5.66401i	0.211861	−	0.134857i
$43$	19.2635	+	33.3654i	0.447988	+	0.775939i	0.998255	−	0.0590502i	$-0.0188072\pi$
$43$	19.2635	+	33.3654i	0.447988	+	0.775939i	−0.550267	+	0.834989i	$0.685474\pi$
$44$		−	23.0172i		−	0.523119i
$45$	−3.60242	−	41.5378i	−0.0800537	−	0.923062i
$46$	−16.8676			−0.366687
$47$	−13.8385	+	7.98969i	−0.294437	+	0.169993i	−0.639941	−	0.768424i	$-0.721041\pi$
$47$	−13.8385	+	7.98969i	−0.294437	+	0.169993i	0.345504	+	0.938417i	$0.387708\pi$
$48$	35.8095	−	1.54990i	0.746031	−	0.0322896i
$49$	6.72689	−	11.6513i	0.137283	−	0.237782i
$50$	1.80727	+	1.04343i	0.0361454	+	0.0208686i
$51$	−10.9696	−	5.71567i	−0.215089	−	0.112072i
$52$	−2.37648	−	4.11618i	−0.0457015	−	0.0791573i
$53$			23.1681i			0.437135i	0.975822	+	0.218567i	$0.0701383\pi$
$53$			23.1681i			0.437135i	−0.975822	+	0.218567i	$0.929862\pi$
$54$	−12.6432	+	9.67866i	−0.234133	+	0.179234i
$55$	−29.1960			−0.530836
$56$	23.3004	−	13.4525i	0.416078	−	0.240223i
$57$	35.8608	−	68.8244i	0.629137	−	1.20744i
$58$	−7.25913	+	12.5732i	−0.125157	+	0.216779i
$59$	7.88857	+	4.55447i	0.133705	+	0.0771944i	0.565360	−	0.824844i	$-0.308737\pi$
$59$	7.88857	+	4.55447i	0.133705	+	0.0771944i	−0.431656	+	0.902038i	$0.642070\pi$
$60$	−2.19486	−	50.7108i	−0.0365810	−	0.845180i
$61$	33.8608	+	58.6486i	0.555094	+	0.961452i	0.997896	+	0.0648323i	$0.0206512\pi$
$61$	33.8608	+	58.6486i	0.555094	+	0.961452i	−0.442802	+	0.896620i	$0.646015\pi$
$62$		−	8.58032i		−	0.138392i
$63$	22.7139	−	48.6140i	0.360538	−	0.771651i
$64$	32.9907			0.515480
$65$	−5.22113	+	3.01442i	−0.0803251	+	0.0463757i
$66$	5.98718	+	9.40585i	0.0907149	+	0.142513i
$67$	17.7786	−	30.7934i	0.265352	−	0.459603i	−0.702304	−	0.711877i	$-0.747845\pi$
$67$	17.7786	−	30.7934i	0.265352	−	0.459603i	0.967656	+	0.252274i	$0.0811785\pi$
$68$	−13.0411	−	7.52926i	−0.191780	−	0.110724i
$69$	−72.3871	+	46.0772i	−1.04909	+	0.667785i
$70$	−8.14408	−	14.1060i	−0.116344	−	0.201514i
$71$			120.461i			1.69664i	0.529487	+	0.848318i	$0.322385\pi$
$71$			120.461i			1.69664i	−0.529487	+	0.848318i	$0.677615\pi$
$72$	−33.2868	+	23.2702i	−0.462317	+	0.323197i
$73$	−23.5416			−0.322488			−0.161244	−	0.986915i	$-0.551551\pi$
$73$	−23.5416			−0.322488			−0.161244	+	0.986915i	$0.551551\pi$
$74$	18.5587	−	10.7148i	0.250793	−	0.144795i
$75$	10.6062	−	0.459056i	0.141416	−	0.00612075i
$76$	47.2395	−	81.8212i	0.621573	−	1.07660i
$77$	−32.5404	−	18.7872i	−0.422602	−	0.243990i
$78$	2.04182	+	1.06389i	0.0261772	+	0.0136396i
$79$	67.7420	+	117.333i	0.857494	+	1.48522i	0.874312	+	0.485365i	$0.161313\pi$
$79$	67.7420	+	117.333i	0.857494	+	1.48522i	−0.0168179	+	0.999859i	$0.505354\pi$
$80$		−	55.3492i		−	0.691865i
$81$	−27.8188	+	76.0731i	−0.343442	+	0.939174i
$82$	−28.9712			−0.353307
$83$	51.8259	−	29.9217i	0.624409	−	0.360503i	−0.154175	−	0.988044i	$-0.549272\pi$
$83$	51.8259	−	29.9217i	0.624409	−	0.360503i	0.778583	+	0.627541i	$0.215939\pi$
$84$	30.1854	−	57.9321i	0.359350	−	0.689668i
$85$	−9.55042	+	16.5418i	−0.112358	+	0.194610i
$86$	−19.6763	−	11.3601i	−0.228794	−	0.132094i
$87$	3.19366	+	73.7874i	0.0367087	+	0.848131i
$88$	14.2200	+	24.6298i	0.161591	+	0.279884i
$89$		−	71.9875i		−	0.808848i	−0.914572	−	0.404424i	$-0.867472\pi$
$89$		−	71.9875i		−	0.808848i	0.914572	−	0.404424i	$-0.132528\pi$
$90$	14.0877	+	20.1517i	0.156530	+	0.223908i
$91$	−7.75894			−0.0852631
$92$	−90.4679	+	52.2317i	−0.983347	+	0.567735i
$93$	−23.4388	−	36.8223i	−0.252030	−	0.395939i
$94$	4.71170	−	8.16090i	0.0501244	−	0.0868181i
$95$	−103.785	−	59.9205i	−1.09248	−	0.630742i
$96$	−63.5140	+	40.4291i	−0.661604	+	0.421136i
$97$	−77.2067	−	133.726i	−0.795945	−	1.37862i	−0.922237	−	0.386625i	$-0.873641\pi$
$97$	−77.2067	−	133.726i	−0.795945	−	1.37862i	0.126292	−	0.991993i	$-0.459693\pi$
$98$			7.93399i			0.0809591i
$99$	51.3878	+	24.0099i	0.519069	+	0.242524i
$100$	12.9242			0.129242
$101$	−53.0880	+	30.6504i	−0.525623	+	0.303469i	−0.739232	−	0.673450i	$-0.764811\pi$
$101$	−53.0880	+	30.6504i	−0.525623	+	0.303469i	0.213609	+	0.976919i	$0.431478\pi$
$102$	7.28764	−	0.315423i	0.0714474	−	0.00309238i
$103$	−88.8238	+	153.847i	−0.862367	+	1.49366i	0.00727092	+	0.999974i	$0.497686\pi$
$103$	−88.8238	+	153.847i	−0.862367	+	1.49366i	−0.869638	+	0.493690i	$0.835648\pi$
$104$	5.08595	+	2.93637i	0.0489034	+	0.0282344i
$105$	−73.4834	−	38.2884i	−0.699842	−	0.364651i
$106$	−6.83138	−	11.8323i	−0.0644470	−	0.111625i
$107$		−	112.532i		−	1.05170i	−0.850577	−	0.525850i	$-0.823747\pi$
$107$		−	112.532i		−	1.05170i	0.850577	−	0.525850i	$-0.176253\pi$
$108$	−37.8398	+	91.0610i	−0.350369	+	0.843157i
$109$	−118.008			−1.08264			−0.541320	−	0.840817i	$-0.682075\pi$
$109$	−118.008			−1.08264			−0.541320	+	0.840817i	$0.682075\pi$
$110$	14.9108	−	8.60876i	0.135553	−	0.0782615i
$111$	50.3745	−	96.6792i	0.453824	−	0.870984i
$112$	35.6164	−	61.6894i	0.318004	−	0.550799i
$113$	102.209	+	59.0106i	0.904508	+	0.522218i	0.878660	−	0.477448i	$-0.158438\pi$
$113$	102.209	+	59.0106i	0.904508	+	0.522218i	0.0258479	+	0.999666i	$0.491771\pi$
$114$	1.97900	+	45.7236i	0.0173597	+	0.401084i
$115$	66.2527	+	114.753i	0.576111	+	0.997853i
$116$			89.9135i			0.775117i
$117$	11.6687	−	1.01198i	0.0997322	−	0.00864940i
$118$	−5.37174			−0.0455232
$119$	−21.2888	+	12.2911i	−0.178898	+	0.103287i
$120$	33.6778	+	52.9076i	0.280648	+	0.440897i
$121$	−40.6409	+	70.3920i	−0.335875	+	0.581752i
$122$	−34.5864	−	19.9684i	−0.283495	−	0.163676i
$123$	−124.329	+	79.1404i	−1.01081	+	0.643418i
$124$	−26.5695	−	46.0197i	−0.214270	−	0.371127i
$125$		−	132.209i		−	1.05768i
$126$	2.73407	+	31.5253i	0.0216990	+	0.250201i
$127$	124.142			0.977493			0.488747	−	0.872426i	$-0.337454\pi$
$127$	124.142			0.977493			0.488747	+	0.872426i	$0.337454\pi$
$128$	−103.786	+	59.9208i	−0.810827	+	0.468131i
$129$	−115.473	+	4.99789i	−0.895139	+	0.0387433i
$130$	1.77767	−	3.07902i	0.0136744	−	0.0236847i
$131$	−25.8211	−	14.9078i	−0.197108	−	0.113800i	0.398198	−	0.917299i	$-0.369636\pi$
$131$	−25.8211	−	14.9078i	−0.197108	−	0.113800i	−0.595306	+	0.803499i	$0.702969\pi$
$132$	61.2375	+	31.9077i	0.463921	+	0.241725i
$133$	−77.1160	−	133.569i	−0.579819	−	1.00428i
$134$			20.9689i			0.156484i
$135$	115.505	+	47.9976i	0.855596	+	0.355538i
$136$	18.6063			0.136811
$137$	180.644	−	104.295i	1.31857	−	0.761277i	0.335072	−	0.942192i	$-0.391239\pi$
$137$	180.644	−	104.295i	1.31857	−	0.761277i	0.983499	+	0.180915i	$0.0579059\pi$
$138$	23.3828	−	44.8764i	0.169440	−	0.325191i
$139$	135.794	−	235.202i	0.976934	−	1.69210i	0.303536	−	0.952820i	$-0.401833\pi$
$139$	135.794	−	235.202i	0.976934	−	1.69210i	0.673398	−	0.739280i	$-0.264834\pi$
$140$	−87.3601	−	50.4374i	−0.624001	−	0.360267i
$141$	−2.07291	−	47.8933i	−0.0147015	−	0.339669i
$142$	−35.5193	−	61.5213i	−0.250136	−	0.433248i
$143$		−	8.20165i		−	0.0573542i
$144$	−45.5175	+	97.4200i	−0.316094	+	0.676528i
$145$	114.050			0.786552
$146$	12.0230	−	6.94150i	0.0823496	−	0.0475445i
$147$	21.6732	+	34.0486i	0.147437	+	0.231623i
$148$	66.3585	−	114.936i	0.448368	−	0.776596i
$149$	−13.8702	−	8.00794i	−0.0930884	−	0.0537446i	0.452733	−	0.891646i	$-0.350449\pi$
$149$	−13.8702	−	8.00794i	−0.0930884	−	0.0537446i	−0.545822	+	0.837901i	$0.683782\pi$
$150$	−5.28138	+	3.36180i	−0.0352092	+	0.0224120i
$151$	67.8591	+	117.535i	0.449398	+	0.778380i	0.998347	−	0.0574758i	$-0.0183052\pi$
$151$	67.8591	+	117.535i	0.449398	+	0.778380i	−0.548949	+	0.835856i	$0.684972\pi$
$152$			116.738i			0.768015i
$153$	30.4132	−	21.2612i	0.198779	−	0.138962i
$154$	22.1585			0.143886
$155$	−58.3733	+	33.7018i	−0.376602	+	0.217431i
$156$	14.2455	−	0.616573i	0.0913175	−	0.00395239i
$157$	100.803	−	174.595i	0.642055	−	1.11207i	−0.342918	−	0.939365i	$-0.611415\pi$
$157$	100.803	−	174.595i	0.642055	−	1.11207i	0.984973	−	0.172707i	$-0.0552514\pi$
$158$	−69.1937	−	39.9490i	−0.437935	−	0.252842i
$159$	−61.6390	−	32.1169i	−0.387667	−	0.201993i
$160$	58.1316	+	100.687i	0.363322	+	0.629293i
$161$			170.531i			1.05920i
$162$	−8.22354	−	47.0543i	−0.0507626	−	0.290459i
$163$	−12.9702			−0.0795718			−0.0397859	−	0.999208i	$-0.512668\pi$
$163$	−12.9702			−0.0795718			−0.0397859	+	0.999208i	$0.512668\pi$
$164$	−155.384	+	89.7111i	−0.947465	+	0.547019i
$165$	40.4730	−	77.6762i	0.245291	−	0.470765i
$166$	−17.6455	+	30.5629i	−0.106298	+	0.184114i
$167$	0.989655	+	0.571377i	0.00592608	+	0.00342142i	0.502960	−	0.864310i	$-0.332244\pi$
$167$	0.989655	+	0.571377i	0.00592608	+	0.00342142i	−0.497034	+	0.867731i	$0.665578\pi$
$168$	3.49022	+	80.6394i	0.0207751	+	0.479996i
$169$	83.6532	+	144.892i	0.494989	+	0.857347i
$170$		−	11.2642i		−	0.0662599i
$171$	133.396	+	190.816i	0.780092	+	1.11588i
$172$	−140.709			−0.818078
$173$	7.62505	−	4.40232i	0.0440754	−	0.0254470i	−0.477800	−	0.878468i	$-0.658566\pi$
$173$	7.62505	−	4.40232i	0.0440754	−	0.0254470i	0.521876	+	0.853021i	$0.325232\pi$
$174$	−23.3881	−	36.7426i	−0.134414	−	0.211164i
$175$	10.5490	−	18.2714i	0.0602801	−	0.104408i
$176$	65.2093	+	37.6486i	0.370507	+	0.213912i
$177$	−23.0527	+	14.6740i	−0.130241	+	0.0829037i
$178$	21.2263	+	36.7650i	0.119249	+	0.206545i
$179$		−	254.573i		−	1.42219i	−0.703094	−	0.711097i	$-0.748199\pi$
$179$		−	254.573i		−	1.42219i	0.703094	−	0.711097i	$-0.251801\pi$
$180$	137.959	+	64.4586i	0.766440	+	0.358103i
$181$	330.723			1.82720			0.913599	−	0.406617i	$-0.133292\pi$
$181$	330.723			1.82720			0.913599	+	0.406617i	$0.133292\pi$
$182$	3.96261	−	2.28781i	0.0217726	−	0.0125704i
$183$	−202.975	+	8.78512i	−1.10915	+	0.0480061i
$184$	64.5374	−	111.782i	0.350747	−	0.607511i
$185$	−145.790	−	84.1717i	−0.788053	−	0.454982i
$186$	22.8280	+	11.8945i	0.122731	+	0.0639488i
$187$	−12.9924	−	22.5035i	−0.0694781	−	0.120340i
$188$		−	58.3603i		−	0.310427i
$189$	97.8508	+	127.822i	0.517729	+	0.676306i
$190$	70.6729			0.371963
$191$	223.842	−	129.235i	1.17195	−	0.676624i	0.217809	−	0.975991i	$-0.430109\pi$
$191$	223.842	−	129.235i	1.17195	−	0.676624i	0.954138	+	0.299368i	$0.0967757\pi$
$192$	−45.7334	+	87.7720i	−0.238195	+	0.457146i
$193$	4.26317	−	7.38403i	0.0220890	−	0.0382592i	−0.854770	−	0.519008i	$-0.826302\pi$
$193$	4.26317	−	7.38403i	0.0220890	−	0.0382592i	0.876859	+	0.480748i	$0.159635\pi$
$194$	78.8612	+	45.5305i	0.406501	+	0.234693i
$195$	−0.782087	−	18.0696i	−0.00401070	−	0.0926646i
$196$	24.5681	+	42.5532i	0.125348	+	0.217108i
$197$		−	241.180i		−	1.22426i	−0.790756	−	0.612131i	$-0.790312\pi$
$197$		−	241.180i		−	1.22426i	0.790756	−	0.612131i	$-0.209688\pi$
$198$	−33.3241	+	2.89007i	−0.168303	+	0.0145963i
$199$	−234.885			−1.18033			−0.590163	−	0.807284i	$-0.700936\pi$
$199$	−234.885			−1.18033			−0.590163	+	0.807284i	$0.700936\pi$
$200$	−13.8296	+	7.98455i	−0.0691482	+	0.0399228i
$201$	57.2805	+	89.9876i	0.284978	+	0.447699i
$202$	18.0752	−	31.3072i	0.0894812	−	0.154986i
$203$	127.114	+	73.3895i	0.626179	+	0.361525i
$204$	38.1099	−	24.2584i	0.186813	−	0.118914i
$205$	113.793	+	197.096i	0.555089	+	0.961442i
$206$		−	104.763i		−	0.508557i
$207$	−22.2419	−	256.461i	−0.107449	−	1.23894i
$208$	15.5485			0.0747526
$209$	141.190	−	81.5160i	0.675550	−	0.390029i
$210$	48.8188	−	2.11297i	0.232470	−	0.0100618i
$211$	44.2130	−	76.5792i	0.209540	−	0.362935i	−0.742029	−	0.670367i	$-0.766137\pi$
$211$	44.2130	−	76.5792i	0.209540	−	0.362935i	0.951570	+	0.307433i	$0.0994699\pi$
$212$	−73.2790	−	42.3076i	−0.345656	−	0.199564i
$213$	−320.488	−	166.990i	−1.50464	−	0.783989i
$214$	33.1813	+	57.4716i	0.155053	+	0.268559i
$215$			178.482i			0.830147i
$216$	−15.7665	−	120.818i	−0.0729932	−	0.559344i
$217$	−86.7466			−0.399754
$218$	60.2683	−	34.7959i	0.276460	−	0.159614i
$219$	32.6346	−	62.6326i	0.149016	−	0.285994i
$220$	53.3152	−	92.3446i	0.242342	−	0.419748i
$221$	−4.64688	−	2.68287i	−0.0210266	−	0.0121397i
$222$	2.77995	+	64.2289i	0.0125223	+	0.289320i
$223$	17.7739	+	30.7853i	0.0797037	+	0.138051i	0.903122	−	0.429384i	$-0.141269\pi$
$223$	17.7739	+	30.7853i	0.0797037	+	0.138051i	−0.823418	+	0.567435i	$0.807936\pi$
$224$			149.627i			0.667979i
$225$	−13.4816	+	28.8543i	−0.0599180	+	0.128241i
$226$	−69.5998			−0.307964
$227$	−198.204	+	114.433i	−0.873145	+	0.504110i	−0.868392	−	0.495878i	$-0.834846\pi$
$227$	−198.204	+	114.433i	−0.873145	+	0.504110i	−0.00475276	+	0.999989i	$0.501513\pi$
$228$	152.200	+	239.106i	0.667545	+	1.04871i
$229$	−163.964	+	283.995i	−0.716002	+	1.24015i	0.246570	+	0.969125i	$0.420697\pi$
$229$	−163.964	+	283.995i	−0.716002	+	1.24015i	−0.962572	+	0.271027i	$0.912637\pi$
$230$	−67.6725	−	39.0707i	−0.294228	−	0.169873i
$231$	95.0927	−	60.5302i	0.411657	−	0.262035i
$232$	−55.5485	−	96.2129i	−0.239433	−	0.414711i
$233$		−	401.760i		−	1.72429i	−0.506659	−	0.862147i	$-0.669120\pi$
$233$		−	401.760i		−	1.72429i	0.506659	−	0.862147i	$-0.330880\pi$
$234$	−5.66096	+	3.95747i	−0.0241922	+	0.0169123i
$235$	−74.0266			−0.315007
$236$	−28.8108	+	16.6340i	−0.122080	+	0.0704828i
$237$	−406.072	+	17.5756i	−1.71338	+	0.0741585i
$238$	7.24834	−	12.5545i	0.0304552	−	0.0527500i
$239$	216.725	+	125.126i	0.906800	+	0.523541i	0.879400	−	0.476083i	$-0.157944\pi$
$239$	216.725	+	125.126i	0.906800	+	0.523541i	0.0274001	+	0.999625i	$0.491277\pi$
$240$	147.257	+	76.7280i	0.613571	+	0.319700i
$241$	−52.4860	−	90.9085i	−0.217784	−	0.377214i	0.736346	−	0.676605i	$-0.236550\pi$
$241$	−52.4860	−	90.9085i	−0.217784	−	0.377214i	−0.954130	+	0.299392i	$0.903216\pi$
$242$		−	47.9336i		−	0.198073i
$243$	−163.829	−	179.469i	−0.674194	−	0.738554i
$244$	−247.334			−1.01367
$245$	53.9762	−	31.1632i	0.220311	−	0.127197i
$246$	40.1614	−	77.0780i	0.163258	−	0.313325i
$247$	16.8327	−	29.1551i	0.0681485	−	0.118037i
$248$	56.8620	+	32.8293i	0.229282	+	0.132376i
$249$	7.76314	+	179.362i	0.0311773	+	0.720331i
$250$	38.9834	+	67.5212i	0.155934	+	0.270085i
$251$			405.400i			1.61514i	0.589772	+	0.807570i	$0.299218\pi$
$251$			405.400i			1.61514i	−0.589772	+	0.807570i	$0.700782\pi$
$252$	112.284	+	160.617i	0.445572	+	0.637369i
$253$	−180.261			−0.712493
$254$	−63.4009	+	36.6045i	−0.249610	+	0.144112i
$255$	−30.7703	−	48.3401i	−0.120668	−	0.189569i
$256$	−30.6448	+	53.0783i	−0.119706	+	0.207337i
$257$	−101.311	−	58.4917i	−0.394205	−	0.227594i	0.289776	−	0.957095i	$-0.406419\pi$
$257$	−101.311	−	58.4917i	−0.394205	−	0.227594i	−0.683980	+	0.729500i	$0.739753\pi$
$258$	57.5000	−	36.6010i	0.222868	−	0.141864i
$259$	−108.327	−	187.627i	−0.418249	−	0.724429i
$260$		−	22.0187i		−	0.0846873i
$261$	−200.739	−	93.7912i	−0.769116	−	0.359353i
$262$	17.5829			0.0671105
$263$	−108.686	+	62.7498i	−0.413254	+	0.238592i	−0.692187	−	0.721718i	$-0.743353\pi$
$263$	−108.686	+	62.7498i	−0.413254	+	0.238592i	0.278933	+	0.960311i	$0.410019\pi$
$264$	−85.2404	+	3.68937i	−0.322880	+	0.0139749i
$265$	−53.6647	+	92.9500i	−0.202508	+	0.350755i
$266$	78.7685	+	45.4770i	0.296122	+	0.170966i
$267$	191.523	+	99.7928i	0.717316	+	0.373756i
$268$	64.9315	+	112.465i	0.242282	+	0.419644i
$269$			139.837i			0.519841i	0.965630	+	0.259920i	$0.0836963\pi$
$269$			139.837i			0.519841i	−0.965630	+	0.259920i	$0.916304\pi$
$270$	−73.1429	+	9.54501i	−0.270900	+	0.0353519i
$271$	−121.908			−0.449844			−0.224922	−	0.974377i	$-0.572213\pi$
$271$	−121.908			−0.449844			−0.224922	+	0.974377i	$0.572213\pi$
$272$	42.6617	−	24.6308i	0.156845	−	0.0905543i
$273$	10.7559	−	20.6427i	0.0393987	−	0.0756144i
$274$	−61.5051	+	106.530i	−0.224471	+	0.388795i
$275$	19.3139	+	11.1509i	0.0702325	+	0.0405488i
$276$	−13.5514	−	313.097i	−0.0490994	−	1.13441i
$277$	−100.411	−	173.916i	−0.362493	−	0.627856i	0.625877	−	0.779921i	$-0.284741\pi$
$277$	−100.411	−	173.916i	−0.362493	−	0.627856i	−0.988370	+	0.152065i	$0.951408\pi$
$278$			160.161i			0.576120i
$279$	130.458	−	11.3141i	0.467592	−	0.0405525i
$280$	124.641			0.445146
$281$	57.9445	−	33.4543i	0.206208	−	0.119054i	−0.393340	−	0.919393i	$-0.628680\pi$
$281$	57.9445	−	33.4543i	0.206208	−	0.119054i	0.599548	+	0.800339i	$0.295347\pi$
$282$	15.1805	+	23.8486i	0.0538317	+	0.0845694i
$283$	−38.4213	+	66.5477i	−0.135764	+	0.235151i	−0.925889	−	0.377795i	$-0.876682\pi$
$283$	−38.4213	+	66.5477i	−0.135764	+	0.235151i	0.790125	+	0.612946i	$0.210016\pi$
$284$	−381.009	−	219.976i	−1.34158	−	0.774563i
$285$	303.292	−	193.057i	1.06418	−	0.677393i
$286$	2.41835	+	4.18870i	0.00845576	+	0.0146458i
$287$			292.897i			1.02055i
$288$	−19.5155	−	225.024i	−0.0677622	−	0.781335i
$289$	−17.0000			−0.0588235
$290$	−58.2470	+	33.6289i	−0.200852	+	0.115962i
$291$	462.807	−	20.0312i	1.59040	−	0.0688356i
$292$	42.9896	−	74.4602i	0.147225	−	0.255001i
$293$	−74.6572	−	43.1034i	−0.254803	−	0.147111i	0.367159	−	0.930158i	$-0.380331\pi$
$293$	−74.6572	−	43.1034i	−0.254803	−	0.147111i	−0.621961	+	0.783048i	$0.713664\pi$
$294$	−21.1084	−	10.9985i	−0.0717974	−	0.0374099i
$295$	21.0992	+	36.5448i	0.0715226	+	0.123881i
$296$			163.985i			0.554003i
$297$	−135.115	+	103.434i	−0.454933	+	0.348262i
$298$	9.44493			0.0316944
$299$	−32.2361	+	18.6115i	−0.107813	+	0.0622459i
$300$	−17.9162	+	34.3849i	−0.0597206	+	0.114616i
$301$	−114.850	+	198.927i	−0.381562	+	0.660885i
$302$	−69.3132	−	40.0180i	−0.229514	−	0.132510i
$303$	−7.95219	−	183.730i	−0.0262448	−	0.606370i
$304$	154.537	+	267.665i	0.508344	+	0.880477i
$305$			313.729i			1.02862i
$306$	−9.26332	+	19.8261i	−0.0302723	+	0.0647911i
$307$	−49.1563			−0.160118			−0.0800591	−	0.996790i	$-0.525511\pi$
$307$	−49.1563			−0.160118			−0.0800591	+	0.996790i	$0.525511\pi$
$308$	118.845	−	68.6151i	0.385860	−	0.222776i
$309$	−286.180	−	449.588i	−0.926149	−	1.45498i
$310$	19.8747	−	34.4240i	0.0641120	−	0.111045i
$311$	516.584	+	298.250i	1.66104	+	0.959002i	0.972219	+	0.234072i	$0.0752050\pi$
$311$	516.584	+	298.250i	1.66104	+	0.959002i	0.688822	+	0.724931i	$0.258128\pi$
$312$	−14.8627	+	9.46065i	−0.0476367	+	0.0303226i
$313$	−48.4462	−	83.9113i	−0.154780	−	0.268087i	0.778199	−	0.628018i	$-0.216134\pi$
$313$	−48.4462	−	83.9113i	−0.154780	−	0.268087i	−0.932979	+	0.359931i	$0.882800\pi$
$314$			118.891i			0.378634i
$315$	203.733	−	142.426i	0.646772	−	0.452145i
$316$	−494.819			−1.56588
$317$	−357.768	+	206.558i	−1.12861	+	0.651601i	−0.943584	−	0.331133i	$-0.892569\pi$
$317$	−357.768	+	206.558i	−1.12861	+	0.651601i	−0.185022	+	0.982734i	$0.559236\pi$
$318$	40.9500	−	1.77239i	0.128773	−	0.00557356i
$319$	−77.5769	+	134.367i	−0.243188	+	0.421214i
$320$	132.358	+	76.4169i	0.413619	+	0.238803i
$321$	299.392	+	155.998i	0.932685	+	0.485974i
$322$	−50.2829	−	87.0925i	−0.156158	−	0.270474i
$323$		−	106.660i		−	0.330217i
$324$	−189.813	−	226.907i	−0.585842	−	0.700330i
$325$	4.60523			0.0141699
$326$	6.62407	−	3.82441i	0.0203192	−	0.0117313i
$327$	163.588	−	313.961i	0.500271	−	0.960124i
$328$	110.847	−	191.993i	0.337948	−	0.585343i
$329$	−82.5063	−	47.6350i	−0.250779	−	0.144787i
$330$	2.23353	+	51.6043i	0.00676827	+	0.156377i
$331$	−203.844	−	353.069i	−0.615844	−	1.06667i	−0.990236	−	0.139402i	$-0.955482\pi$
$331$	−203.844	−	353.069i	−0.615844	−	1.06667i	0.374392	−	0.927271i	$-0.377851\pi$
$332$			218.562i			0.658319i
$333$	187.384	+	268.044i	0.562715	+	0.804936i
$334$	−0.673908			−0.00201769
$335$	142.655	−	82.3617i	0.425835	−	0.245856i
$336$	114.752	+	180.275i	0.341524	+	0.536532i
$337$	−249.846	+	432.746i	−0.741383	+	1.28411i	0.210483	+	0.977598i	$0.432496\pi$
$337$	−249.846	+	432.746i	−0.741383	+	1.28411i	−0.951866	+	0.306515i	$0.900837\pi$
$338$	−85.4458	−	49.3322i	−0.252798	−	0.145953i
$339$	−298.686	+	190.125i	−0.881080	+	0.560842i
$340$	−34.8803	−	60.4145i	−0.102589	−	0.177690i
$341$		−	91.6961i		−	0.268904i
$342$	−124.391	−	58.1192i	−0.363717	−	0.169939i
$343$	372.353			1.08558
$344$	150.568	−	86.9302i	0.437696	−	0.252704i
$345$	−397.145	+	17.1892i	−1.15114	+	0.0498237i
$346$	−2.59615	+	4.49666i	−0.00750332	+	0.0129961i
$347$	109.261	+	63.0821i	0.314875	+	0.181793i	0.649106	−	0.760698i	$-0.275143\pi$
$347$	109.261	+	63.0821i	0.314875	+	0.181793i	−0.334231	+	0.942491i	$0.608477\pi$
$348$	−239.216	−	124.643i	−0.687401	−	0.358169i
$349$	−99.6434	−	172.587i	−0.285511	−	0.494520i	0.687222	−	0.726448i	$-0.258830\pi$
$349$	−99.6434	−	172.587i	−0.285511	−	0.494520i	−0.972733	+	0.231928i	$0.925497\pi$
$350$			12.4420i			0.0355485i
$351$	−13.4833	+	32.4474i	−0.0384141	+	0.0924429i
$352$	−158.165			−0.449332
$353$	393.252	−	227.044i	1.11403	−	0.643184i	0.174158	−	0.984718i	$-0.444280\pi$
$353$	393.252	−	227.044i	1.11403	−	0.643184i	0.939869	+	0.341534i	$0.110946\pi$
$354$	7.44659	−	14.2916i	0.0210356	−	0.0403716i
$355$	−279.026	+	483.288i	−0.785989	+	1.36137i
$356$	227.691	+	131.457i	0.639581	+	0.369262i
$357$	−3.18891	−	73.6777i	−0.00893252	−	0.206380i
$358$	75.0636	+	130.014i	0.209675	+	0.363167i
$359$		−	642.000i		−	1.78830i	−0.447768	−	0.894150i	$-0.647781\pi$
$359$		−	642.000i		−	1.78830i	0.447768	−	0.894150i	$-0.352219\pi$
$360$	−187.447	+	16.2566i	−0.520686	+	0.0451572i
$361$	308.199			0.853737
$362$	−168.905	+	97.5173i	−0.466588	+	0.269385i
$363$	−130.940	−	205.706i	−0.360716	−	0.566684i
$364$	14.1687	−	24.5409i	0.0389250	−	0.0674202i
$365$	−94.4484	−	54.5298i	−0.258763	−	0.149397i
$366$	101.072	−	64.3360i	0.276152	−	0.175781i
$367$	−210.331	−	364.304i	−0.573109	−	0.992654i	−0.996244	−	0.0865873i	$-0.972404\pi$
$367$	−210.331	−	364.304i	−0.573109	−	0.992654i	0.423135	−	0.906067i	$-0.360929\pi$
$368$		−	341.735i		−	0.928628i
$369$	−38.2019	−	440.488i	−0.103528	−	1.19373i
$370$	99.2759			0.268313
$371$	−119.624	+	69.0650i	−0.322437	+	0.186159i
$372$	159.268	−	6.89342i	0.428140	−	0.0185307i
$373$	155.037	−	268.532i	0.415649	−	0.719925i	−0.579848	−	0.814725i	$-0.696888\pi$
$373$	155.037	−	268.532i	0.415649	−	0.719925i	0.995496	+	0.0948003i	$0.0302212\pi$
$374$	13.2708	+	7.66191i	0.0354835	+	0.0204864i
$375$	351.744	+	183.276i	0.937984	+	0.488735i
$376$	36.0550	+	62.4490i	0.0958909	+	0.166088i
$377$			32.0386i			0.0849830i
$378$	−87.6635	−	36.4280i	−0.231914	−	0.0963705i
$379$	128.343			0.338636			0.169318	−	0.985561i	$-0.445843\pi$
$379$	128.343			0.338636			0.169318	+	0.985561i	$0.445843\pi$
$380$	379.048	−	218.843i	0.997494	−	0.575904i
$381$	−172.092	+	330.280i	−0.451684	+	0.866876i
$382$	−76.2128	+	132.005i	−0.199510	+	0.345562i
$383$	249.226	+	143.891i	0.650721	+	0.375694i	0.788732	−	0.614737i	$-0.210738\pi$
$383$	249.226	+	143.891i	0.650721	+	0.375694i	−0.138012	+	0.990431i	$0.544071\pi$
$384$	−15.5464	−	359.189i	−0.0404853	−	0.935387i
$385$	−87.0342	−	150.748i	−0.226063	−	0.391552i
$386$			5.02817i			0.0130264i
$387$	146.778	−	314.145i	0.379271	−	0.811744i
$388$	563.953			1.45349
$389$	324.022	−	187.074i	0.832961	−	0.480910i	−0.0219046	−	0.999760i	$-0.506973\pi$
$389$	324.022	−	187.074i	0.832961	−	0.480910i	0.854865	+	0.518850i	$0.173640\pi$
$390$	5.72745	+	8.99780i	0.0146858	+	0.0230713i
$391$	−58.9658	+	102.132i	−0.150808	+	0.261207i
$392$	−52.5787	−	30.3564i	−0.134129	−	0.0774397i
$393$	75.4569	−	48.0312i	0.192002	−	0.122217i
$394$	71.1145	+	123.174i	0.180494	+	0.312624i
$395$			627.648i			1.58898i
$396$	−169.781	+	118.691i	−0.428741	+	0.299724i
$397$	459.061			1.15632			0.578162	−	0.815922i	$-0.303770\pi$
$397$	459.061			1.15632			0.578162	+	0.815922i	$0.303770\pi$
$398$	119.959	−	69.2584i	0.301405	−	0.174016i
$399$	462.263	−	20.0076i	1.15855	−	0.0501444i
$400$	−21.1397	+	36.6150i	−0.0528492	+	0.0915375i
$401$	112.197	+	64.7768i	0.279792	+	0.161538i	0.633329	−	0.773882i	$-0.281688\pi$
$401$	112.197	+	64.7768i	0.279792	+	0.161538i	−0.353537	+	0.935421i	$0.615021\pi$
$402$	−55.7878	−	29.0681i	−0.138776	−	0.0723088i
$403$	−9.46742	−	16.3981i	−0.0234924	−	0.0406900i
$404$		−	223.884i		−	0.554169i
$405$	−287.818	+	240.766i	−0.710661	+	0.594485i
$406$	−86.5589			−0.213199
$407$	198.333	−	114.507i	0.487304	−	0.281345i
$408$	−25.7930	+	49.5022i	−0.0632182	+	0.121329i
$409$	−301.422	+	522.078i	−0.736972	+	1.27647i	0.216881	+	0.976198i	$0.430412\pi$
$409$	−301.422	+	522.078i	−0.736972	+	1.27647i	−0.953853	+	0.300275i	$0.902922\pi$
$410$	−116.232	−	67.1064i	−0.283492	−	0.163674i
$411$	27.0592	+	625.185i	0.0658374	+	1.52113i
$412$	−324.405	−	561.886i	−0.787390	−	1.36380i
$413$			54.3081i			0.131497i
$414$	86.9796	+	124.420i	0.210096	+	0.300532i
$415$	277.233			0.668030
$416$	−28.2847	+	16.3302i	−0.0679920	+	0.0392552i
$417$	437.512	+	687.330i	1.04919	+	1.64827i
$418$	−48.0718	+	83.2628i	−0.115004	+	0.199193i
$419$	547.793	+	316.268i	1.30738	+	0.754817i	0.981658	−	0.190649i	$-0.0610592\pi$
$419$	547.793	+	316.268i	1.30738	+	0.754817i	0.325722	+	0.945465i	$0.394393\pi$
$420$	255.292	−	162.503i	0.607839	−	0.386913i
$421$	83.3334	+	144.338i	0.197941	+	0.342845i	0.947861	−	0.318685i	$-0.103241\pi$
$421$	83.3334	+	144.338i	0.197941	+	0.342845i	−0.749919	+	0.661529i	$0.769908\pi$
$422$			52.1468i			0.123571i
$423$	130.294	+	60.8772i	0.308024	+	0.143918i
$424$	104.551			0.246582
$425$	12.6357	−	7.29524i	0.0297311	−	0.0171653i
$426$	212.917	−	9.21543i	0.499804	−	0.0216325i
$427$	−201.880	+	349.667i	−0.472787	+	0.818891i
$428$	355.929	+	205.496i	0.831611	+	0.480131i
$429$	21.8206	+	11.3696i	0.0508638	+	0.0265025i
$430$	−52.6273	−	91.1531i	−0.122389	−	0.211984i
$431$		−	387.881i		−	0.899955i	−0.893040	−	0.449978i	$-0.851432\pi$
$431$		−	387.881i		−	0.899955i	0.893040	−	0.449978i	$-0.148568\pi$
$432$	−196.088	−	256.148i	−0.453908	−	0.592936i
$433$	556.386			1.28496			0.642478	−	0.766304i	$-0.277906\pi$
$433$	556.386			1.28496			0.642478	+	0.766304i	$0.277906\pi$
$434$	44.3027	−	25.5782i	0.102080	−	0.0589360i
$435$	−158.102	+	303.431i	−0.363453	+	0.697542i
$436$	215.496	−	373.249i	0.494256	−	0.856076i
$437$	−640.788	−	369.959i	−1.46633	−	0.846588i
$438$	1.80096	+	41.6101i	0.00411179	+	0.0950001i
$439$	−184.332	−	319.273i	−0.419892	−	0.727274i	0.576037	−	0.817424i	$-0.304599\pi$
$439$	−184.332	−	319.273i	−0.419892	−	0.727274i	−0.995928	+	0.0901504i	$0.971265\pi$
$440$			131.752i			0.299437i
$441$	−120.631	+	10.4619i	−0.273540	+	0.0237231i
$442$	3.16430			0.00715905
$443$	−228.655	+	132.014i	−0.516152	+	0.298000i	−0.735359	−	0.677678i	$-0.762986\pi$
$443$	−228.655	+	132.014i	−0.516152	+	0.298000i	0.219207	+	0.975678i	$0.429653\pi$
$444$	213.799	+	335.878i	0.481530	+	0.756482i
$445$	166.746	−	288.812i	0.374710	−	0.649016i
$446$	−18.1548	−	10.4817i	−0.0407058	−	0.0235015i
$447$	40.5328	−	25.8007i	0.0906773	−	0.0577196i
$448$	98.3464	+	170.341i	0.219523	+	0.380225i
$449$		−	140.395i		−	0.312684i	−0.987703	−	0.156342i	$-0.950030\pi$
$449$		−	140.395i		−	0.312684i	0.987703	−	0.156342i	$-0.0499702\pi$
$450$	−1.62278	−	18.7115i	−0.00360617	−	0.0415810i
$451$	−309.609			−0.686495
$452$	−373.292	+	215.520i	−0.825867	+	0.476815i
$453$	−406.774	+	17.6059i	−0.897955	+	0.0388652i
$454$	67.4837	−	116.885i	0.148643	−	0.257456i
$455$	−31.1287	−	17.9722i	−0.0684148	−	0.0394993i
$456$	−310.583	−	161.829i	−0.681103	−	0.354887i
$457$	−45.2544	−	78.3830i	−0.0990250	−	0.171516i	0.812256	−	0.583301i	$-0.198239\pi$
$457$	−45.2544	−	78.3830i	−0.0990250	−	0.171516i	−0.911281	+	0.411784i	$0.864906\pi$
$458$		−	193.387i		−	0.422242i
$459$	14.4054	+	110.388i	0.0313843	+	0.240496i
$460$	−483.940			−1.05204
$461$	−284.835	+	164.450i	−0.617864	+	0.356724i	−0.776037	−	0.630687i	$-0.782773\pi$
$461$	−284.835	+	164.450i	−0.617864	+	0.356724i	0.158173	+	0.987411i	$0.449440\pi$
$462$	−30.7172	+	58.9528i	−0.0664875	+	0.127603i
$463$	130.500	−	226.033i	0.281858	−	0.488192i	−0.689984	−	0.723824i	$-0.742383\pi$
$463$	130.500	−	226.033i	0.281858	−	0.488192i	0.971842	+	0.235632i	$0.0757160\pi$
$464$	−254.731	−	147.069i	−0.548989	−	0.316959i
$465$	−8.74389	−	202.022i	−0.0188041	−	0.434456i
$466$	118.464	+	205.185i	0.254214	+	0.440311i
$467$			422.063i			0.903775i	0.892075	+	0.451887i	$0.149249\pi$
$467$			422.063i			0.903775i	−0.892075	+	0.451887i	$0.850751\pi$
$468$	−18.1075	+	38.7551i	−0.0386912	+	0.0828100i
$469$	211.994			0.452013
$470$	37.8064	−	21.8276i	0.0804392	−	0.0464416i
$471$	324.774	+	510.220i	0.689542	+	1.08327i
$472$	20.5529	−	35.5987i	0.0435443	−	0.0754209i
$473$	−210.277	−	121.403i	−0.444560	−	0.256667i
$474$	202.204	−	128.711i	0.426592	−	0.271542i
$475$	45.7712	+	79.2781i	0.0963605	+	0.166901i
$476$		−	89.7799i		−	0.188613i
$477$	170.894	−	119.469i	0.358269	−	0.250459i
$478$	−147.580			−0.308744
$479$	−590.179	+	340.740i	−1.23211	+	0.711357i	−0.967469	−	0.252990i	$-0.918586\pi$
$479$	−590.179	+	340.740i	−1.23211	+	0.711357i	−0.264638	+	0.964348i	$0.585253\pi$
$480$	−348.463	+	15.0822i	−0.725965	+	0.0314211i
$481$	23.6453	−	40.9548i	0.0491586	−	0.0851451i
$482$	53.6108	+	30.9522i	0.111226	+	0.0642162i
$483$	−453.698	−	236.399i	−0.939334	−	0.489438i
$484$	−148.430	−	257.088i	−0.306673	−	0.531173i
$485$		−	715.341i		−	1.47493i
$486$	136.588	+	43.3504i	0.281046	+	0.0891983i
$487$	81.6117			0.167580			0.0837902	−	0.996483i	$-0.473297\pi$
$487$	81.6117			0.167580			0.0837902	+	0.996483i	$0.473297\pi$
$488$	264.663	−	152.803i	0.542342	−	0.313121i
$489$	17.9800	−	34.5074i	0.0367689	−	0.0705672i
$490$	−18.3776	+	31.8310i	−0.0375054	+	0.0649612i
$491$	−572.031	−	330.262i	−1.16503	−	0.672632i	−0.212528	−	0.977155i	$-0.568170\pi$
$491$	−572.031	−	330.262i	−1.16503	−	0.672632i	−0.952505	+	0.304523i	$0.901503\pi$
$492$	−23.2754	−	537.763i	−0.0473078	−	1.09301i
$493$	50.7530	+	87.9068i	0.102947	+	0.178310i
$494$			19.8532i			0.0401887i
$495$	150.552	+	215.358i	0.304146	+	0.435066i
$496$	173.836			0.350475
$497$	−621.977	+	359.099i	−1.25146	+	0.722533i
$498$	−56.8517	−	89.3139i	−0.114160	−	0.179345i
$499$	63.6779	−	110.293i	0.127611	−	0.221029i	−0.795140	−	0.606427i	$-0.792602\pi$
$499$	63.6779	−	110.293i	0.127611	−	0.221029i	0.922751	+	0.385398i	$0.125936\pi$
$500$	418.168	+	241.429i	0.836336	+	0.482859i
$501$	−2.89207	+	1.84091i	−0.00577259	+	0.00367447i
$502$	−119.537	−	207.044i	−0.238121	−	0.412438i
$503$		−	394.016i		−	0.783332i	−0.920107	−	0.391666i	$-0.871899\pi$
$503$		−	394.016i		−	0.783332i	0.920107	−	0.391666i	$-0.128101\pi$
$504$	−219.380	−	102.501i	−0.435278	−	0.203374i
$505$	−283.984			−0.562344
$506$	92.0618	−	53.1519i	0.181940	−	0.105043i
$507$	−501.450	+	21.7037i	−0.989053	+	0.0428081i
$508$	−226.697	+	392.650i	−0.446253	+	0.772934i
$509$	−12.9844	−	7.49656i	−0.0255097	−	0.0147280i	0.487191	−	0.873295i	$-0.338022\pi$
$509$	−12.9844	−	7.49656i	−0.0255097	−	0.0147280i	−0.512701	+	0.858567i	$0.671355\pi$
$510$	29.9685	+	15.6150i	0.0587617	+	0.0306177i
$511$	−70.1783	−	121.552i	−0.137335	−	0.237872i
$512$		−	515.510i		−	1.00686i
$513$	−692.587	+	90.3812i	−1.35007	+	0.176182i
$514$	68.9877			0.134217
$515$	−712.718	+	411.488i	−1.38392	+	0.799006i
$516$	195.059	−	374.359i	0.378021	−	0.725501i
$517$	50.3530	−	87.2139i	0.0973945	−	0.168692i
$518$	110.648	+	63.8826i	0.213606	+	0.123326i
$519$	1.14218	+	26.3892i	0.00220072	+	0.0508463i
$520$	13.6031	+	23.5613i	0.0261599	+	0.0453103i
$521$			736.434i			1.41350i	0.707463	+	0.706751i	$0.249840\pi$
$521$			736.434i			1.41350i	−0.707463	+	0.706751i	$0.750160\pi$
$522$	130.176	−	11.2897i	0.249379	−	0.0216277i
$523$	−644.391			−1.23211			−0.616053	−	0.787705i	$-0.711269\pi$
$523$	−644.391			−1.23211			−0.616053	+	0.787705i	$0.711269\pi$
$524$	94.3045	−	54.4467i	0.179970	−	0.103906i
$525$	33.9877	+	53.3945i	0.0647384	+	0.101704i
$526$	37.0049	−	64.0944i	0.0703516	−	0.121853i
$527$	−51.9530	−	29.9951i	−0.0985826	−	0.0569167i
$528$	−190.561	+	121.299i	−0.360911	+	0.229734i
$529$	144.555	+	250.377i	0.273261	+	0.473302i
$530$		−	63.2946i		−	0.119424i
$531$	−7.08326	−	81.6738i	−0.0133395	−	0.153811i
$532$	563.290			1.05882
$533$	−55.3675	+	31.9665i	−0.103879	+	0.0599746i
$534$	−127.239	+	5.50713i	−0.238275	+	0.0103130i
$535$	260.659	−	451.475i	0.487214	−	0.843879i
$536$	−138.961	−	80.2293i	−0.259256	−	0.149681i
$537$	677.293	+	352.902i	1.26125	+	0.657173i
$538$	−41.2326	−	71.4169i	−0.0766404	−	0.132745i
$539$			84.7890i			0.157308i
$540$	−362.739	+	277.686i	−0.671738	+	0.514233i
$541$	793.511			1.46675			0.733374	−	0.679825i	$-0.237944\pi$
$541$	793.511			1.46675			0.733374	+	0.679825i	$0.237944\pi$
$542$	62.2600	−	35.9458i	0.114871	−	0.0663207i
$543$	−458.465	+	879.890i	−0.844319	+	1.62042i
$544$	−51.7379	+	89.6127i	−0.0951064	+	0.164729i
$545$	−473.444	−	273.343i	−0.868705	−	0.501547i
$546$	0.593569	+	13.7140i	0.00108712	+	0.0251173i
$547$	−311.893	−	540.214i	−0.570188	−	0.987595i	−0.996546	−	0.0830405i	$-0.973537\pi$
$547$	−311.893	−	540.214i	−0.570188	−	0.987595i	0.426358	−	0.904555i	$-0.359796\pi$
$548$			761.818i			1.39018i
$549$	258.001	−	552.194i	0.469947	−	1.00582i
$550$	−13.1519			−0.0239125
$551$	−551.538	+	318.431i	−1.00098	+	0.577914i
$552$	207.932	+	326.660i	0.376688	+	0.591776i
$553$	−403.882	+	699.545i	−0.730348	+	1.26500i
$554$	102.562	+	59.2144i	0.185130	+	0.106885i
$555$	426.041	−	271.191i	0.767641	−	0.488633i
$556$	495.950	+	859.011i	0.891997	+	1.54498i
$557$		−	309.291i		−	0.555281i	−0.960685	−	0.277640i	$-0.910448\pi$
$557$		−	309.291i		−	0.555281i	0.960685	−	0.277640i	$-0.0895524\pi$
$558$	−63.2907	+	44.2453i	−0.113424	+	0.0792927i
$559$	−50.1385			−0.0896932
$560$	285.785	−	164.998i	0.510330	−	0.294639i
$561$	77.8815	−	3.37086i	0.138826	−	0.00600866i
$562$	−19.7287	+	34.1712i	−0.0351045	+	0.0608028i
$563$	−878.564	−	507.239i	−1.56050	−	0.900958i	−0.997206	−	0.0747045i	$-0.976199\pi$
$563$	−878.564	−	507.239i	−1.56050	−	0.900958i	−0.563299	−	0.826253i	$-0.690468\pi$
$564$	155.268	+	80.9021i	0.275298	+	0.143443i
$565$	273.375	+	473.499i	0.483849	+	0.838051i
$566$		−	45.3158i		−	0.0800633i
$567$	−475.717	+	83.1396i	−0.839007	+	0.146631i
$568$	543.604			0.957049
$569$	559.185	−	322.845i	0.982750	−	0.567391i	0.0796507	−	0.996823i	$-0.474620\pi$
$569$	559.185	−	322.845i	0.982750	−	0.567391i	0.903099	+	0.429432i	$0.141286\pi$
$570$	−97.9705	+	188.026i	−0.171878	+	0.329870i
$571$	344.959	−	597.487i	0.604132	−	1.04639i	−0.388056	−	0.921636i	$-0.626853\pi$
$571$	344.959	−	597.487i	0.604132	−	1.04639i	0.992188	−	0.124751i	$-0.0398132\pi$
$572$	25.9412	+	14.9771i	0.0453517	+	0.0261838i
$573$	33.5299	+	774.686i	0.0585163	+	1.35198i
$574$	−86.3640	−	149.587i	−0.150460	−	0.260604i
$575$		−	101.216i		−	0.176029i
$576$	−170.120	−	243.348i	−0.295347	−	0.422480i
$577$	646.917			1.12117			0.560587	−	0.828096i	$-0.310576\pi$
$577$	646.917			1.12117			0.560587	+	0.828096i	$0.310576\pi$
$578$	8.68215	−	5.01264i	0.0150210	−	0.00867239i
$579$	13.7354	+	21.5783i	0.0237227	+	0.0372683i
$580$	−208.268	+	360.731i	−0.359083	+	0.621950i
$581$	308.990	+	178.395i	0.531824	+	0.307049i
$582$	−230.456	+	146.694i	−0.395972	+	0.252052i
$583$	−73.0056	−	126.449i	−0.125224	−	0.216894i
$584$			106.236i			0.181911i
$585$	49.1585	+	22.9683i	0.0840316	+	0.0392620i
$586$	50.8381			0.0867544
$587$	−89.8988	+	51.9031i	−0.153150	+	0.0884210i	−0.574616	−	0.818423i	$-0.694849\pi$
$587$	−89.8988	+	51.9031i	−0.153150	+	0.0884210i	0.421467	+	0.906844i	$0.361515\pi$
$588$	−147.271	+	6.37416i	−0.250461	+	0.0108404i
$589$	188.193	−	325.960i	0.319513	−	0.553412i
$590$	−21.5513	−	12.4427i	−0.0365276	−	0.0210892i
$591$	641.660	+	334.336i	1.08572	+	0.565712i
$592$	217.081	+	375.995i	0.366691	+	0.635127i
$593$		−	845.095i		−	1.42512i	−0.701612	−	0.712559i	$-0.747536\pi$
$593$		−	845.095i		−	1.42512i	0.701612	−	0.712559i	$-0.252464\pi$
$594$	38.5065	−	92.6654i	0.0648258	−	0.156002i
$595$	−113.880			−0.191396
$596$	50.6570	−	29.2468i	0.0849950	−	0.0490719i
$597$	325.610	−	624.913i	0.545410	−	1.04676i
$598$	10.9756	−	19.0103i	0.0183539	−	0.0317899i
$599$	191.695	+	110.675i	0.320024	+	0.184766i	0.651403	−	0.758732i	$-0.274181\pi$
$599$	191.695	+	110.675i	0.320024	+	0.184766i	−0.331379	+	0.943498i	$0.607514\pi$
$600$	−2.07158	−	47.8625i	−0.00345263	−	0.0797708i
$601$	−301.006	−	521.358i	−0.500842	−	0.867483i	−1.00000		0.000972310i	$-0.999691\pi$
$601$	−301.006	−	521.358i	−0.500842	−	0.867483i	0.499158	−	0.866511i	$-0.333643\pi$
$602$		−	135.460i		−	0.225016i
$603$	−318.818	+	27.6499i	−0.528720	+	0.0458539i
$604$	−495.674			−0.820652
$605$	−326.100	+	188.274i	−0.539009	+	0.311197i
$606$	58.2362	+	91.4888i	0.0960993	+	0.150972i
$607$	−319.749	+	553.821i	−0.526769	+	0.912390i	0.472745	+	0.881199i	$0.343263\pi$
$607$	−319.749	+	553.821i	−0.526769	+	0.912390i	−0.999513	+	0.0311909i	$0.990070\pi$
$608$	−562.241	−	324.610i	−0.924739	−	0.533898i
$609$	−371.466	+	236.452i	−0.609961	+	0.388263i
$610$	−92.5065	−	160.226i	−0.151650	−	0.262665i
$611$		−	20.7953i		−	0.0340349i
$612$	11.7098	+	135.020i	0.0191336	+	0.220621i
$613$	771.938			1.25928			0.629640	−	0.776887i	$-0.283202\pi$
$613$	771.938			1.25928			0.629640	+	0.776887i	$0.283202\pi$
$614$	25.1048	−	14.4943i	0.0408873	−	0.0236063i
$615$	−682.121	+	29.5235i	−1.10914	+	0.0480057i
$616$	−84.7808	+	146.845i	−0.137631	+	0.238384i
$617$	971.077	+	560.651i	1.57387	+	0.908673i	0.995688	+	0.0927638i	$0.0295701\pi$
$617$	971.077	+	560.651i	1.57387	+	0.908673i	0.578180	+	0.815909i	$0.303763\pi$
$618$	278.722	+	145.228i	0.451007	+	0.234996i
$619$	−138.162	−	239.303i	−0.223201	−	0.386596i	0.732577	−	0.680684i	$-0.238317\pi$
$619$	−138.162	−	239.303i	−0.223201	−	0.386596i	−0.955778	+	0.294088i	$0.904984\pi$
$620$		−	246.174i		−	0.397054i
$621$	713.149	+	296.345i	1.14839	+	0.477206i
$622$	−351.769			−0.565545
$623$	371.693	−	214.597i	0.596618	−	0.344458i
$624$	−21.5542	+	41.3670i	−0.0345420	+	0.0662933i
$625$	262.005	−	453.806i	0.419208	−	0.726089i
$626$	49.4843	+	28.5698i	0.0790485	+	0.0456387i
$627$	21.1492	+	488.639i	0.0337308	+	0.779328i
$628$	368.154	+	637.662i	0.586233	+	1.01539i
$629$		−	149.828i		−	0.238200i
$630$	−62.0536	+	132.812i	−0.0984978	+	0.210813i
$631$	−443.016			−0.702085			−0.351043	−	0.936360i	$-0.614173\pi$
$631$	−443.016			−0.702085			−0.351043	+	0.936360i	$0.614173\pi$
$632$	529.486	−	305.699i	0.837794	−	0.483700i
$633$	142.449	+	223.787i	0.225038	+	0.353534i
$634$	121.812	−	210.984i	0.192132	−	0.332782i
$635$	498.053	+	287.551i	0.784336	+	0.452837i
$636$	214.143	−	136.310i	0.336703	−	0.214324i
$637$	8.75427	+	15.1628i	0.0137430	+	0.0238035i
$638$		−	91.4977i		−	0.143413i
$639$	888.554	−	621.171i	1.39054	−	0.972099i
$640$	−555.182			−0.867472
$641$	454.358	−	262.324i	0.708826	−	0.409241i	−0.101800	−	0.994805i	$-0.532460\pi$
$641$	454.358	−	262.324i	0.708826	−	0.409241i	0.810626	+	0.585564i	$0.199127\pi$
$642$	−198.901	+	8.60883i	−0.309815	+	0.0134094i
$643$	152.628	−	264.359i	0.237368	−	0.411134i	−0.722590	−	0.691277i	$-0.757049\pi$
$643$	152.628	−	264.359i	0.237368	−	0.411134i	0.959958	+	0.280143i	$0.0903819\pi$
$644$	−539.375	−	311.409i	−0.837540	−	0.483554i
$645$	−474.852	−	247.420i	−0.736204	−	0.383598i
$646$	31.4499	+	54.4729i	0.0486841	+	0.0843233i
$647$			23.8292i			0.0368303i	0.999830	+	0.0184152i	$0.00586206\pi$
$647$			23.8292i			0.0368303i	−0.999830	+	0.0184152i	$0.994138\pi$
$648$	343.294	+	125.538i	0.529775	+	0.193731i
$649$	−57.4067			−0.0884541
$650$	−2.35196	+	1.35790i	−0.00361839	+	0.00208908i
$651$	120.253	−	230.790i	0.184720	−	0.354516i
$652$	23.6851	−	41.0238i	0.0363268	−	0.0629199i
$653$	−876.400	−	505.990i	−1.34211	−	0.774869i	−0.354996	−	0.934868i	$-0.615518\pi$
$653$	−876.400	−	505.990i	−1.34211	−	0.774869i	−0.987117	+	0.159998i	$0.948851\pi$
$654$	9.02774	+	208.580i	0.0138039	+	0.318930i
$655$	−69.0625	−	119.620i	−0.105439	−	0.182625i
$656$		−	586.951i		−	0.894743i
$657$	121.395	+	173.649i	0.184771	+	0.264306i
$658$	56.1829			0.0853843
$659$	−530.036	+	306.016i	−0.804304	+	0.464365i	−0.844974	−	0.534808i	$-0.820384\pi$
$659$	−530.036	+	306.016i	−0.804304	+	0.464365i	0.0406702	+	0.999173i	$0.487051\pi$
$660$	171.775	+	269.858i	0.260266	+	0.408876i
$661$	253.353	−	438.820i	0.383287	−	0.663873i	−0.608243	−	0.793751i	$-0.708125\pi$
$661$	253.353	−	438.820i	0.383287	−	0.663873i	0.991530	+	0.129878i	$0.0414585\pi$
$662$	208.212	+	120.212i	0.314520	+	0.181588i
$663$	13.5796	−	8.64391i	0.0204820	−	0.0130376i
$664$	−135.027	−	233.874i	−0.203354	−	0.352220i
$665$		−	714.500i		−	1.07444i
$666$	−174.735	−	81.6415i	−0.262365	−	0.122585i
$667$	704.163			1.05572
$668$	−3.61444	+	2.08680i	−0.00541085	+	0.00312395i
$669$	−106.544	+	4.61142i	−0.159258	+	0.00689300i
$670$	−48.5705	+	84.1266i	−0.0724933	+	0.125562i
$671$	−369.618	−	213.399i	−0.550846	−	0.318031i
$672$	−398.085	−	207.421i	−0.592388	−	0.308663i
$673$	447.234	+	774.632i	0.664538	+	1.15101i	0.979410	+	0.201879i	$0.0647049\pi$
$673$	447.234	+	774.632i	0.664538	+	1.15101i	−0.314873	+	0.949134i	$0.601962\pi$
$674$		−	294.680i		−	0.437210i
$675$	−58.0782	−	75.8671i	−0.0860417	−	0.112396i
$676$	−611.041			−0.903907
$677$	424.595	−	245.140i	0.627171	−	0.362097i	−0.152485	−	0.988306i	$-0.548727\pi$
$677$	424.595	−	245.140i	0.627171	−	0.362097i	0.779656	+	0.626208i	$0.215394\pi$
$678$	96.4828	−	185.171i	0.142305	−	0.273113i
$679$	460.311	−	797.283i	0.677926	−	1.17420i
$680$	74.6480	+	43.0981i	0.109777	+	0.0633795i
$681$	−29.6895	−	685.956i	−0.0435969	−	1.00728i
$682$	27.0376	+	46.8305i	0.0396446	+	0.0686665i
$683$			916.941i			1.34252i	0.741222	+	0.671260i	$0.234247\pi$
$683$			916.941i			1.34252i	−0.741222	+	0.671260i	$0.765753\pi$
$684$	−847.131	+	73.4685i	−1.23850	+	0.107410i
$685$	966.321			1.41069
$686$	−190.166	+	109.793i	−0.277210	+	0.160047i
$687$	−528.274	−	829.917i	−0.768958	−	1.20803i
$688$	230.154	−	398.639i	0.334526	−	0.579417i
$689$	−26.1112	−	15.0753i	−0.0378973	−	0.0218800i
$690$	197.759	−	125.881i	0.286607	−	0.182437i
$691$	−305.481	−	529.109i	−0.442086	−	0.765715i	0.555758	−	0.831344i	$-0.312428\pi$
$691$	−305.481	−	529.109i	−0.442086	−	0.765715i	−0.997844	+	0.0656288i	$0.979095\pi$
$692$			32.1566i			0.0464691i
$693$	29.2185	+	336.905i	0.0421623	+	0.486154i
$694$	−74.4019			−0.107207
$695$	1089.60	−	629.083i	1.56778	−	0.905156i
$696$	332.980	−	14.4120i	0.478419	−	0.0207069i
$697$	−101.278	+	175.418i	−0.145305	+	0.251675i
$698$	101.779	+	58.7619i	0.145815	+	0.0841861i
$699$	1068.89	+	556.941i	1.52917	+	0.796769i
$700$	38.5274	+	66.7314i	0.0550391	+	0.0953306i
$701$			1271.46i			1.81378i	0.421364	+	0.906891i	$0.361551\pi$
$701$			1271.46i			1.81378i	−0.421364	+	0.906891i	$0.638449\pi$
$702$	−2.68135	−	20.5471i	−0.00381959	−	0.0292694i
$703$	940.039			1.33718
$704$	−180.060	+	103.958i	−0.255767	+	0.147667i
$705$	102.620	−	196.948i	0.145560	−	0.279359i
$706$	−133.893	+	231.909i	−0.189650	+	0.328483i
$707$	−316.514	−	182.739i	−0.447686	−	0.258472i
$708$	−4.31565	−	99.7104i	−0.00609555	−	0.140834i
$709$	150.111	+	259.999i	0.211722	+	0.366713i	0.952253	−	0.305309i	$-0.0987596\pi$
$709$	150.111	+	259.999i	0.211722	+	0.366713i	−0.740532	+	0.672021i	$0.765426\pi$
$710$		−	329.096i		−	0.463515i
$711$	516.158	−	1104.72i	0.725961	−	1.55376i
$712$	−324.857			−0.456260
$713$	−360.406	+	208.081i	−0.505479	+	0.291838i
$714$	23.3533	+	36.6880i	0.0327077	+	0.0513837i
$715$	18.9976	−	32.9048i	0.0265701	−	0.0460207i
$716$	805.193	+	464.879i	1.12457	+	0.649272i
$717$	−633.336	+	403.143i	−0.883314	+	0.562263i
$718$	189.301	+	327.879i	0.263650	+	0.456655i
$719$			1307.21i			1.81809i	0.416694	+	0.909047i	$0.363189\pi$
$719$			1307.21i			1.81809i	−0.416694	+	0.909047i	$0.636811\pi$
$720$	−408.271	+	285.414i	−0.567043	+	0.396409i
$721$	−1059.15			−1.46900
$722$	−157.402	+	90.8759i	−0.218008	+	0.125867i
$723$	314.622	−	13.6174i	0.435161	−	0.0188346i
$724$	−603.937	+	1046.05i	−0.834168	+	1.44482i
$725$	−75.4472	−	43.5594i	−0.104065	−	0.0600820i
$726$	127.528	+	66.4481i	0.175658	+	0.0915263i
$727$	−48.8430	−	84.5985i	−0.0671843	−	0.116367i	0.830477	−	0.557054i	$-0.188068\pi$
$727$	−48.8430	−	84.5985i	−0.0671843	−	0.116367i	−0.897661	+	0.440687i	$0.854735\pi$
$728$			35.0137i			0.0480957i
$729$	704.586	−	187.080i	0.966511	−	0.256626i
$730$	64.3149			0.0881026
$731$	−137.569	+	79.4255i	−0.188193	+	0.108653i
$732$	342.868	−	658.035i	0.468399	−	0.898955i
$733$	−705.781	+	1222.45i	−0.962866	+	1.66773i	−0.247625	+	0.968856i	$0.579650\pi$
$733$	−705.781	+	1222.45i	−0.962866	+	1.66773i	−0.715241	+	0.698878i	$0.753683\pi$
$734$	214.838	+	124.037i	0.292695	+	0.168988i
$735$	8.08524	+	186.804i	0.0110003	+	0.254156i
$736$	358.914	+	621.657i	0.487655	+	0.844643i
$737$			224.090i			0.304057i
$738$	149.393	+	213.699i	0.202430	+	0.289565i
$739$	−1202.00			−1.62652			−0.813258	−	0.581903i	$-0.802308\pi$
$739$	−1202.00			−1.62652			−0.813258	+	0.581903i	$0.802308\pi$
$740$	532.457	−	307.414i	0.719537	−	0.415425i
$741$	54.2330	+	85.1998i	0.0731889	+	0.114979i
$742$	40.7291	−	70.5450i	0.0548910	−	0.0950741i
$743$	440.339	+	254.230i	0.592650	+	0.342167i	0.766145	−	0.642668i	$-0.222173\pi$
$743$	440.339	+	254.230i	0.592650	+	0.342167i	−0.173495	+	0.984835i	$0.555506\pi$
$744$	−166.168	+	105.772i	−0.223343	+	0.142167i
$745$	−37.0979	−	64.2554i	−0.0497958	−	0.0862488i
$746$			182.858i			0.245117i
$747$	−487.957	−	227.988i	−0.653222	−	0.305204i
$748$	94.9025			0.126875
$749$	581.036	−	335.461i	0.775749	−	0.447879i
$750$	−233.682	+	10.1142i	−0.311576	+	0.0134856i
$751$	372.391	−	645.000i	0.495860	−	0.858855i	−0.504129	−	0.863629i	$-0.668186\pi$
$751$	372.391	−	645.000i	0.495860	−	0.858855i	0.999989	+	0.00477387i	$0.00151957\pi$
$752$	165.338	+	95.4582i	0.219865	+	0.126939i
$753$	−1078.57	−	561.987i	−1.43236	−	0.746331i
$754$	−9.44693	−	16.3626i	−0.0125291	−	0.0217010i
$755$			628.733i			0.832758i
$756$	−582.977	+	76.0773i	−0.771134	+	0.100631i
$757$	29.6534			0.0391723			0.0195862	−	0.999808i	$-0.493765\pi$
$757$	29.6534			0.0391723			0.0195862	+	0.999808i	$0.493765\pi$
$758$	−65.5467	+	37.8434i	−0.0864732	+	0.0499253i
$759$	249.887	−	479.585i	0.329232	−	0.631865i
$760$	−270.403	+	468.351i	−0.355793	+	0.616251i
$761$	876.214	+	505.883i	1.15140	+	0.664760i	0.949228	−	0.314590i	$-0.101867\pi$
$761$	876.214	+	505.883i	1.15140	+	0.664760i	0.202171	+	0.979350i	$0.435200\pi$
$762$	−9.49699	−	219.422i	−0.0124632	−	0.287955i
$763$	−351.785	−	609.309i	−0.461055	−	0.798570i
$764$			943.992i			1.23559i
$765$	171.265	−	14.8531i	0.223875	−	0.0194159i
$766$	−169.711			−0.221555
$767$	−10.2661	+	5.92712i	−0.0133847	+	0.00772766i
$768$	−98.7338	−	155.111i	−0.128560	−	0.201967i
$769$	409.591	−	709.432i	0.532628	−	0.922539i	−0.466646	−	0.884444i	$-0.654538\pi$
$769$	409.591	−	709.432i	0.532628	−	0.922539i	0.999274	−	0.0380947i	$-0.0121288\pi$
$770$	88.8992	+	51.3260i	0.115454	+	0.0666571i
$771$	296.060	−	188.453i	0.383994	−	0.244427i
$772$	15.5701	+	26.9681i	0.0201685	+	0.0349328i
$773$			327.256i			0.423359i	0.977339	+	0.211679i	$0.0678932\pi$
$773$			327.256i			0.423359i	−0.977339	+	0.211679i	$0.932107\pi$
$774$	17.6676	+	203.717i	0.0228264	+	0.263201i
$775$	51.4874			0.0664353
$776$	−603.464	+	348.410i	−0.777659	+	0.448982i
$777$	649.352	−	28.1052i	0.835716	−	0.0361714i
$778$	−110.322	+	191.083i	−0.141802	+	0.245608i
$779$	−1100.59	−	635.428i	−1.41283	−	0.815697i
$780$	58.5809	+	30.5235i	0.0751038	+	0.0391327i
$781$	−379.588	−	657.466i	−0.486028	−	0.841825i
$782$		−	69.5469i		−	0.0889347i
$783$	527.807	−	404.050i	0.674084	−	0.516028i
$784$	−160.741			−0.205027
$785$	808.836	−	466.982i	1.03036	−	0.594881i
$786$	−24.3744	+	46.7796i	−0.0310107	+	0.0595160i
$787$	130.205	−	225.522i	0.165445	−	0.286559i	−0.771368	−	0.636389i	$-0.780427\pi$
$787$	130.205	−	225.522i	0.165445	−	0.286559i	0.936813	+	0.349830i	$0.113761\pi$
$788$	762.832	+	440.421i	0.968061	+	0.558911i
$789$	−16.2803	−	376.147i	−0.0206341	−	0.476738i
$790$	−185.069	−	320.549i	−0.234265	−	0.405758i
$791$			703.650i			0.889571i
$792$	108.349	−	231.897i	0.136804	−	0.292800i
$793$	−88.1318			−0.111137
$794$	−234.449	+	135.359i	−0.295276	+	0.170477i
$795$	−172.901	−	271.628i	−0.217486	−	0.341670i
$796$	428.926	−	742.922i	0.538852	−	0.933319i
$797$	−100.761	−	58.1742i	−0.126425	−	0.0729915i	0.435454	−	0.900211i	$-0.356588\pi$
$797$	−100.761	−	58.1742i	−0.126425	−	0.0729915i	−0.561879	+	0.827220i	$0.689921\pi$
$798$	−230.185	+	146.522i	−0.288452	+	0.183611i
$799$	−32.9423	−	57.0578i	−0.0412294	−	0.0714115i
$800$		−	88.8095i		−	0.111012i
$801$	−530.999	+	371.211i	−0.662920	+	0.463435i
$802$	−76.4007			−0.0952627
$803$	128.488	−	74.1825i	0.160010	−	0.0923816i
$804$	−389.224	+	16.8464i	−0.484110	+	0.0209532i
$805$	−395.003	+	684.166i	−0.490687	+	0.849895i
$806$	9.67030	+	5.58315i	0.0119979	+	0.00692698i
$807$	−372.038	−	193.850i	−0.461014	−	0.240210i
$808$	138.316	+	239.569i	0.171183	+	0.296497i
$809$		−	805.359i		−	0.995500i	−0.867321	−	0.497750i	$-0.834160\pi$
$809$		−	805.359i		−	0.995500i	0.867321	−	0.497750i	$-0.165840\pi$
$810$	76.0000	−	207.829i	0.0938272	−	0.256579i
$811$	−1320.90			−1.62873			−0.814363	−	0.580356i	$-0.802913\pi$
$811$	−1320.90			−1.62873			−0.814363	+	0.580356i	$0.802913\pi$
$812$	−464.251	+	268.035i	−0.571737	+	0.330093i
$813$	168.995	−	324.336i	0.207866	−	0.398938i
$814$	−67.5276	+	116.961i	−0.0829577	+	0.143687i
$815$	−52.0362	−	30.0431i	−0.0638481	−	0.0368627i
$816$	6.39041	+	147.646i	0.00783139	+	0.180939i
$817$	−498.325	−	863.125i	−0.609945	−	1.05646i
$818$		−	355.510i		−	0.434609i
$819$	40.0098	+	57.2321i	0.0488521	+	0.0698804i
$820$	−831.198			−1.01366
$821$	−120.460	+	69.5474i	−0.146723	+	0.0847106i	−0.571564	−	0.820557i	$-0.693663\pi$
$821$	−120.460	+	69.5474i	−0.146723	+	0.0847106i	0.424841	+	0.905268i	$0.360330\pi$
$822$	−198.162	−	311.312i	−0.241073	−	0.378725i
$823$	197.219	−	341.593i	0.239634	−	0.415059i	−0.720975	−	0.692961i	$-0.756306\pi$
$823$	197.219	−	341.593i	0.239634	−	0.415059i	0.960609	+	0.277902i	$0.0896392\pi$
$824$	694.265	+	400.834i	0.842555	+	0.486449i
$825$	−56.4411	+	35.9269i	−0.0684134	+	0.0435478i
$826$	−16.0133	−	27.7359i	−0.0193866	−	0.0335786i
$827$		−	560.889i		−	0.678221i	−0.940746	−	0.339111i	$-0.889874\pi$
$827$		−	560.889i		−	0.678221i	0.940746	−	0.339111i	$-0.110126\pi$
$828$	851.782	+	397.978i	1.02872	+	0.480649i
$829$	164.585			0.198534			0.0992672	−	0.995061i	$-0.468350\pi$
$829$	164.585			0.198534			0.0992672	+	0.995061i	$0.468350\pi$
$830$	−141.587	+	81.7451i	−0.170586	+	0.0984881i
$831$	601.900	−	26.0514i	0.724308	−	0.0313494i
$832$	−21.4668	+	37.1816i	−0.0258015	+	0.0446894i
$833$	48.0396	+	27.7357i	0.0576706	+	0.0332961i
$834$	−426.111	−	222.024i	−0.510924	−	0.266216i
$835$	2.64698	+	4.58471i	0.00317004	+	0.00549067i
$836$			595.430i			0.712237i
$837$	−150.747	+	362.769i	−0.180103	+	0.433416i
$838$	−373.021			−0.445132
$839$	−1050.16	+	606.312i	−1.25168	+	0.722660i	−0.971444	−	0.237269i	$-0.923748\pi$
$839$	−1050.16	+	606.312i	−1.25168	+	0.722660i	−0.280241	+	0.959930i	$0.590414\pi$
$840$	−172.784	+	331.608i	−0.205695	+	0.394771i
$841$	−117.457	+	203.441i	−0.139663	+	0.241904i
$842$	−85.1191	−	49.1435i	−0.101092	−	0.0583652i
$843$	8.67966	+	200.538i	0.0102962	+	0.237886i
$844$	161.476	+	279.685i	0.191322	+	0.331380i
$845$			775.069i			0.917242i
$846$	−84.4934	+	7.32779i	−0.0998740	+	0.00866169i
$847$	−484.607			−0.572145
$848$	239.720	−	138.403i	0.282689	−	0.163211i
$849$	−123.789	−	194.472i	−0.145806	−	0.229060i
$850$	−4.30217	+	7.45157i	−0.00506137	+	0.00876655i
$851$	−900.129	−	519.690i	−1.05773	−	0.610682i
$852$	1113.42	−	708.736i	1.30683	−	0.831850i
$853$	−116.955	−	202.571i	−0.137110	−	0.237481i	0.789292	−	0.614018i	$-0.210448\pi$
$853$	−116.955	−	202.571i	−0.137110	−	0.237481i	−0.926401	+	0.376537i	$0.877115\pi$
$854$		−	238.106i		−	0.278813i
$855$	93.1904	+	1074.54i	0.108995	+	1.25677i
$856$	−507.821			−0.593249
$857$	182.672	−	105.466i	0.213153	−	0.123064i	−0.389623	−	0.920975i	$-0.627395\pi$
$857$	182.672	−	105.466i	0.213153	−	0.123064i	0.602776	+	0.797911i	$0.294061\pi$
$858$	−14.4965	+	0.627436i	−0.0168957	+	0.000731278i
$859$	−561.542	+	972.620i	−0.653716	+	1.13227i	0.328497	+	0.944505i	$0.393458\pi$
$859$	−561.542	+	972.620i	−0.653716	+	1.13227i	−0.982214	+	0.187765i	$0.939876\pi$
$860$	−564.523	−	325.928i	−0.656422	−	0.378986i
$861$	−779.255	−	406.030i	−0.905059	−	0.471579i
$862$	114.371	+	198.096i	0.132681	+	0.229810i
$863$		−	1634.86i		−	1.89440i	−0.320650	−	0.947198i	$-0.603901\pi$
$863$		−	1634.86i		−	1.89440i	0.320650	−	0.947198i	$-0.396099\pi$
$864$	625.733	+	260.019i	0.724228	+	0.300948i
$865$	40.7887			0.0471546
$866$	−284.154	+	164.057i	−0.328123	+	0.189442i
$867$	23.5663	−	45.2286i	0.0271814	−	0.0521668i
$868$	158.409	−	274.373i	0.182499	−	0.316098i
$869$	−739.459	−	426.927i	−0.850931	−	0.491285i
$870$	−8.72497	−	201.585i	−0.0100287	−	0.231707i
$871$	23.1368	+	40.0741i	0.0265635	+	0.0460093i
$872$			532.532i			0.610702i
$873$	−588.274	+	1259.07i	−0.673854	+	1.44223i
$874$	436.346			0.499252
$875$	682.637	−	394.120i	0.780156	−	0.450423i
$876$	138.508	+	217.595i	0.158114	+	0.248396i
$877$	−774.726	+	1341.86i	−0.883382	+	1.53006i	−0.0358252	+	0.999358i	$0.511406\pi$
$877$	−774.726	+	1341.86i	−0.883382	+	1.53006i	−0.847557	+	0.530705i	$0.821927\pi$
$878$	188.282	+	108.705i	0.214445	+	0.123810i
$879$	218.171	−	138.874i	0.248203	−	0.157991i
$880$	174.412	+	302.091i	0.198196	+	0.343285i
$881$			1054.82i			1.19729i	0.801013	+	0.598647i	$0.204295\pi$
$881$			1054.82i			1.19729i	−0.801013	+	0.598647i	$0.795705\pi$
$882$	58.5233	−	40.9125i	0.0663529	−	0.0463860i
$883$	−1522.09			−1.72377			−0.861884	−	0.507105i	$-0.830716\pi$
$883$	−1522.09			−1.72377			−0.861884	+	0.507105i	$0.830716\pi$
$884$	16.9714	−	9.79847i	0.0191985	−	0.0110842i
$885$	−126.477	+	5.47415i	−0.142911	+	0.00618548i
$886$	77.8517	−	134.843i	0.0878687	−	0.152193i
$887$	746.281	+	430.866i	0.841354	+	0.485756i	0.857724	−	0.514110i	$-0.171878\pi$
$887$	746.281	+	430.866i	0.841354	+	0.485756i	−0.0163701	+	0.999866i	$0.505211\pi$
$888$	−436.283	−	227.324i	−0.491310	−	0.255996i
$889$	370.070	+	640.980i	0.416277	+	0.721013i
$890$			196.667i			0.220975i
$891$	−87.8833	−	502.860i	−0.0986345	−	0.564377i
$892$	−129.829			−0.145548
$893$	357.988	−	206.684i	0.400882	−	0.231449i
$894$	−13.0931	+	25.1283i	−0.0146455	+	0.0281077i
$895$	589.671	−	1021.34i	0.658850	−	1.14116i
$896$	−618.778	−	357.252i	−0.690601	−	0.398719i
$897$	−4.82873	−	111.565i	−0.00538320	−	0.124375i
$898$	41.3971	+	71.7018i	0.0460992	+	0.0798461i
$899$			358.198i			0.398440i
$900$	−66.6449	−	95.3322i	−0.0740499	−	0.105925i
$901$	−95.5247			−0.106021
$902$	158.122	−	91.2917i	0.175301	−	0.101210i
$903$	−370.034	−	581.323i	−0.409783	−	0.643768i
$904$	266.297	−	461.239i	0.294576	−	0.510220i
$905$	1326.85	+	766.058i	1.46613	+	0.846473i
$906$	202.554	−	128.933i	0.223569	−	0.142311i
$907$	599.812	+	1038.90i	0.661314	+	1.14543i	0.980271	+	0.197660i	$0.0633342\pi$
$907$	599.812	+	1038.90i	0.661314	+	1.14543i	−0.318957	+	0.947769i	$0.603332\pi$
$908$		−	835.871i		−	0.920563i
$909$	499.839	+	233.539i	0.549878	+	0.256919i
$910$	21.1972			0.0232936
$911$	30.9758	−	17.8839i	0.0340019	−	0.0196310i	−0.482903	−	0.875674i	$-0.660418\pi$
$911$	30.9758	−	17.8839i	0.0340019	−	0.0196310i	0.516905	+	0.856043i	$0.327084\pi$
$912$	−926.352	+	40.0943i	−1.01574	+	0.0439630i
$913$	−188.574	+	326.620i	−0.206543	+	0.357743i
$914$	46.2242	+	26.6875i	0.0505735	+	0.0291986i
$915$	−834.679	−	434.908i	−0.912217	−	0.475309i
$916$	−598.836	−	1037.21i	−0.653751	−	1.13233i
$917$		−	177.763i		−	0.193853i
$918$	−39.9061	−	52.1291i	−0.0434707	−	0.0567855i
$919$	−379.603			−0.413061			−0.206530	−	0.978440i	$-0.566217\pi$
$919$	−379.603			−0.413061			−0.206530	+	0.978440i	$0.566217\pi$
$920$	517.845	−	298.978i	0.562875	−	0.324976i
$921$	68.1430	−	130.781i	0.0739881	−	0.141999i
$922$	96.9797	−	167.974i	0.105184	−	0.182184i
$923$	−135.764	−	78.3832i	−0.147090	−	0.0849222i
$924$	17.8021	+	411.306i	0.0192663	+	0.445136i
$925$	64.2959	+	111.364i	0.0695091	+	0.120393i
$926$			153.918i			0.166218i
$927$	1592.85	−	138.142i	1.71828	−	0.149020i
$928$	617.848			0.665784
$929$	193.270	−	111.585i	0.208041	−	0.120113i	−0.392360	−	0.919812i	$-0.628341\pi$
$929$	193.270	−	111.585i	0.208041	−	0.120113i	0.600401	+	0.799699i	$0.295008\pi$
$930$	64.0340	+	100.597i	0.0688538	+	0.108169i
$931$	−174.017	+	301.406i	−0.186914	+	0.323745i
$932$	1270.74	+	733.660i	1.36345	+	0.787189i
$933$	−1509.61	+	960.926i	−1.61802	+	1.02993i
$934$	−124.450	−	215.554i	−0.133244	−	0.230785i
$935$		−	120.378i		−	0.128747i
$936$	−4.56675	−	52.6571i	−0.00487901	−	0.0562576i
$937$	−1195.68			−1.27608			−0.638038	−	0.770005i	$-0.720254\pi$
$937$	−1195.68			−1.27608			−0.638038	+	0.770005i	$0.720254\pi$
$938$	−108.269	+	62.5089i	−0.115425	+	0.0666406i
$939$	290.405	−	12.5693i	0.309271	−	0.0133858i
$940$	135.181	−	234.140i	0.143810	−	0.249085i
$941$	−36.2350	−	20.9203i	−0.0385069	−	0.0222320i	0.480623	−	0.876927i	$-0.340411\pi$
$941$	−36.2350	−	20.9203i	−0.0385069	−	0.0222320i	−0.519130	+	0.854695i	$0.673744\pi$
$942$	−316.311	−	164.813i	−0.335787	−	0.174961i
$943$	702.578	+	1216.90i	0.745046	+	1.29046i
$944$		−	108.831i		−	0.115287i
$945$	96.4996	+	739.472i	0.102116	+	0.782510i
$946$	143.188			0.151362
$947$	460.512	−	265.877i	0.486285	−	0.280757i	−0.236747	−	0.971571i	$-0.576081\pi$
$947$	460.512	−	265.877i	0.486285	−	0.280757i	0.723032	+	0.690815i	$0.242748\pi$
$948$	685.944	−	1316.47i	0.723569	−	1.38868i
$949$	15.3183	−	26.5322i	0.0161416	−	0.0279580i
$950$	−46.7521	−	26.9923i	−0.0492127	−	0.0284130i
$951$	−53.5910	−	1238.19i	−0.0563523	−	1.30198i
$952$	55.4660	+	96.0699i	0.0582626	+	0.100914i
$953$		−	1606.20i		−	1.68542i	−0.538370	−	0.842709i	$-0.680960\pi$
$953$		−	1606.20i		−	1.68542i	0.538370	−	0.842709i	$-0.319040\pi$
$954$	−52.0515	+	111.405i	−0.0545613	+	0.116776i
$955$	1197.40			1.25382
$956$	−791.530	+	456.990i	−0.827960	+	0.478023i
$957$	−249.944	−	392.661i	−0.261174	−	0.410304i
$958$	200.942	−	348.042i	0.209752	−	0.363300i
$959$	1077.01	+	621.814i	1.12306	+	0.648398i
$960$	−386.789	+	246.206i	−0.402906	+	0.256465i
$961$	374.652	+	648.917i	0.389857	+	0.675252i
$962$			27.8883i			0.0289899i
$963$	−830.066	+	580.283i	−0.861958	+	0.602578i
$964$	383.382			0.397699
$965$	34.2075	−	19.7497i	0.0354482	−	0.0204660i
$966$	301.415	−	13.0458i	0.312024	−	0.0135050i
$967$	−151.504	+	262.413i	−0.156674	+	0.271368i	−0.933667	−	0.358141i	$-0.883411\pi$
$967$	−151.504	+	262.413i	−0.156674	+	0.271368i	0.776993	+	0.629509i	$0.216744\pi$
$968$	317.657	+	183.400i	0.328158	+	0.189462i
$969$	283.770	+	147.858i	0.292848	+	0.152588i
$970$	210.926	+	365.335i	0.217450	+	0.376634i
$971$		−	970.362i		−	0.999343i	−0.866215	−	0.499671i	$-0.833454\pi$
$971$		−	970.362i		−	0.999343i	0.866215	−	0.499671i	$-0.166546\pi$
$972$	866.816	−	190.449i	0.891786	−	0.195935i
$973$	1619.22			1.66416
$974$	−41.6803	+	24.0641i	−0.0427929	+	0.0247065i
$975$	−6.38401	+	12.2522i	−0.00654770	+	0.0125664i
$976$	404.557	−	700.714i	0.414506	−	0.717945i
$977$	−333.170	−	192.356i	−0.341013	−	0.196884i	0.319707	−	0.947517i	$-0.396416\pi$
$977$	−333.170	−	192.356i	−0.341013	−	0.196884i	−0.660720	+	0.750632i	$0.729749\pi$
$978$	0.992237	+	22.9250i	0.00101456	+	0.0234407i
$979$	226.841	+	392.901i	0.231707	+	0.401329i
$980$			227.630i			0.232276i
$981$	608.520	+	870.457i	0.620305	+	0.887316i
$982$	389.526			0.396666
$983$	−1046.54	+	604.222i	−1.06464	+	0.614671i	−0.926713	−	0.375771i	$-0.877378\pi$
$983$	−1046.54	+	604.222i	−1.06464	+	0.614671i	−0.137929	+	0.990442i	$0.544045\pi$
$984$	357.136	+	561.060i	0.362943	+	0.570183i
$985$	558.648	−	967.607i	0.567156	−	0.982343i
$986$	−51.8406	−	29.9302i	−0.0525767	−	0.0303551i
$987$	241.108	−	153.475i	0.244284	−	0.155496i
$988$	61.4768	+	106.481i	0.0622235	+	0.107774i
$989$			1101.97i			1.11423i
$990$	−140.390	−	65.5942i	−0.141808	−	0.0662568i
$991$	−942.890			−0.951453			−0.475726	−	0.879593i	$-0.657815\pi$
$991$	−942.890			−0.951453			−0.475726	+	0.879593i	$0.657815\pi$
$992$	−316.228	+	182.574i	−0.318779	+	0.184047i
$993$	1221.92	−	52.8871i	1.23054	−	0.0532599i
$994$	211.769	−	366.794i	0.213047	−	0.369008i
$995$	−942.353	−	544.068i	−0.947088	−	0.546802i
$996$	−581.485	−	302.982i	−0.583821	−	0.304199i
$997$	73.5466	+	127.386i	0.0737679	+	0.127770i	0.900550	−	0.434753i	$-0.143164\pi$
$997$	73.5466	+	127.386i	0.0737679	+	0.127770i	−0.826782	+	0.562523i	$0.809831\pi$
$998$			75.1046i			0.0752551i
$999$	−972.894	+	126.961i	−0.973867	+	0.127088i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.3.j.a.86.14	✓	64
3.2	odd	2		459.3.j.a.341.19		64
9.2	odd	6	inner	153.3.j.a.137.14	yes	64
9.7	even	3		459.3.j.a.35.19		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.3.j.a.86.14	✓	64	1.1	even	1	trivial
153.3.j.a.137.14	yes	64	9.2	odd	6	inner
459.3.j.a.35.19		64	9.7	even	3
459.3.j.a.341.19		64	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	153.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.510714 + 0.294861i) q^{2} +(-1.38625 + 2.66051i) q^{3} +(-1.82611 + 3.16292i) q^{4} +(4.01198 + 2.31632i) q^{5} +(-0.0765013 - 1.76751i) q^{6} +(2.98103 + 5.16330i) q^{7} -4.51269i q^{8} +(-5.15661 - 7.37627i) q^{9} -2.73197 q^{10} +(-5.45790 + 3.15112i) q^{11} +(-5.88352 - 9.24300i) q^{12} +(-0.650693 + 1.12703i) q^{13} +(-3.04491 - 1.75798i) q^{14} +(-11.7242 + 7.46290i) q^{15} +(-5.97384 - 10.3470i) q^{16} +4.12311i q^{17} +(4.80853 + 2.24669i) q^{18} -25.8689 q^{19} +(-14.6527 + 8.45972i) q^{20} +(-17.8695 + 0.773424i) q^{21} +(1.85829 - 3.21865i) q^{22} +(24.7706 + 14.3013i) q^{23} +(12.0060 + 6.25573i) q^{24} +(-1.76936 - 3.06461i) q^{25} -0.767456i q^{26} +(26.7730 - 3.49382i) q^{27} -21.7748 q^{28} +(21.3205 - 12.3094i) q^{29} +(3.78720 - 7.26842i) q^{30} +(-7.27488 + 12.6005i) q^{31} +(21.7343 + 12.5483i) q^{32} +(-0.817554 - 18.8890i) q^{33} +(-1.21574 - 2.10573i) q^{34} +27.6201i q^{35} +(32.7471 - 2.84004i) q^{36} -36.3386 q^{37} +(13.2116 - 7.62773i) q^{38} +(-2.09646 - 3.29353i) q^{39} +(10.4528 - 18.1048i) q^{40} +(42.5451 + 24.5634i) q^{41} +(8.89814 - 5.66401i) q^{42} +(19.2635 + 33.3654i) q^{43} -23.0172i q^{44} +(-3.60242 - 41.5378i) q^{45} -16.8676 q^{46} +(-13.8385 + 7.98969i) q^{47} +(35.8095 - 1.54990i) q^{48} +(6.72689 - 11.6513i) q^{49} +(1.80727 + 1.04343i) q^{50} +(-10.9696 - 5.71567i) q^{51} +(-2.37648 - 4.11618i) q^{52} +23.1681i q^{53} +(-12.6432 + 9.67866i) q^{54} -29.1960 q^{55} +(23.3004 - 13.4525i) q^{56} +(35.8608 - 68.8244i) q^{57} +(-7.25913 + 12.5732i) q^{58} +(7.88857 + 4.55447i) q^{59} +(-2.19486 - 50.7108i) q^{60} +(33.8608 + 58.6486i) q^{61} -8.58032i q^{62} +(22.7139 - 48.6140i) q^{63} +32.9907 q^{64} +(-5.22113 + 3.01442i) q^{65} +(5.98718 + 9.40585i) q^{66} +(17.7786 - 30.7934i) q^{67} +(-13.0411 - 7.52926i) q^{68} +(-72.3871 + 46.0772i) q^{69} +(-8.14408 - 14.1060i) q^{70} +120.461i q^{71} +(-33.2868 + 23.2702i) q^{72} -23.5416 q^{73} +(18.5587 - 10.7148i) q^{74} +(10.6062 - 0.459056i) q^{75} +(47.2395 - 81.8212i) q^{76} +(-32.5404 - 18.7872i) q^{77} +(2.04182 + 1.06389i) q^{78} +(67.7420 + 117.333i) q^{79} -55.3492i q^{80} +(-27.8188 + 76.0731i) q^{81} -28.9712 q^{82} +(51.8259 - 29.9217i) q^{83} +(30.1854 - 57.9321i) q^{84} +(-9.55042 + 16.5418i) q^{85} +(-19.6763 - 11.3601i) q^{86} +(3.19366 + 73.7874i) q^{87} +(14.2200 + 24.6298i) q^{88} -71.9875i q^{89} +(14.0877 + 20.1517i) q^{90} -7.75894 q^{91} +(-90.4679 + 52.2317i) q^{92} +(-23.4388 - 36.8223i) q^{93} +(4.71170 - 8.16090i) q^{94} +(-103.785 - 59.9205i) q^{95} +(-63.5140 + 40.4291i) q^{96} +(-77.2067 - 133.726i) q^{97} +7.93399i q^{98} +(51.3878 + 24.0099i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 2 q^{3} + 64 q^{4} - 18 q^{5} - 22 q^{6} + 2 q^{7} - 6 q^{9} - 44 q^{12} - 10 q^{13} + 72 q^{14} - 36 q^{15} - 128 q^{16} - 38 q^{18} - 28 q^{19} - 18 q^{20} + 88 q^{21} + 144 q^{23} - 42 q^{24}+ \cdots + 58 q^{99}+O(q^{100}) \) 64 * q - 2 * q^3 + 64 * q^4 - 18 * q^5 - 22 * q^6 + 2 * q^7 - 6 * q^9 - 44 * q^12 - 10 * q^13 + 72 * q^14 - 36 * q^15 - 128 * q^16 - 38 * q^18 - 28 * q^19 - 18 * q^20 + 88 * q^21 + 144 * q^23 - 42 * q^24 + 154 * q^25 - 164 * q^27 + 32 * q^28 - 162 * q^29 - 220 * q^30 + 62 * q^31 + 126 * q^32 - 40 * q^33 + 12 * q^36 + 128 * q^37 - 36 * q^38 - 126 * q^39 - 144 * q^41 + 114 * q^42 - 64 * q^43 - 72 * q^45 - 48 * q^46 + 288 * q^47 - 10 * q^48 - 246 * q^49 + 62 * q^52 + 374 * q^54 - 84 * q^55 + 684 * q^56 + 232 * q^57 + 138 * q^58 - 432 * q^59 - 86 * q^60 + 110 * q^61 + 304 * q^63 - 260 * q^64 + 328 * q^66 - 148 * q^67 + 36 * q^69 - 216 * q^70 - 96 * q^72 - 196 * q^73 - 918 * q^74 + 314 * q^75 - 112 * q^76 - 504 * q^77 + 276 * q^78 + 86 * q^79 + 234 * q^81 - 396 * q^82 - 594 * q^83 + 592 * q^84 + 126 * q^86 + 462 * q^87 + 24 * q^88 - 338 * q^90 + 52 * q^91 - 36 * q^92 - 1006 * q^93 - 186 * q^94 - 144 * q^95 + 18 * q^96 + 140 * q^97 + 58 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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