Properties

Label 39.4.e.a.16.1
Level $39$
Weight $4$
Character 39.16
Analytic conductor $2.301$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 39 = 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 39.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.30107449022\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 16.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 39.16
Dual form 39.4.e.a.22.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.50000 - 2.59808i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-0.500000 + 0.866025i) q^{4} -9.00000 q^{5} +(-4.50000 + 7.79423i) q^{6} +(-1.00000 + 1.73205i) q^{7} -21.0000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\) \(q+(-1.50000 - 2.59808i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-0.500000 + 0.866025i) q^{4} -9.00000 q^{5} +(-4.50000 + 7.79423i) q^{6} +(-1.00000 + 1.73205i) q^{7} -21.0000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(13.5000 + 23.3827i) q^{10} +(-15.0000 - 25.9808i) q^{11} +3.00000 q^{12} +(32.5000 - 33.7750i) q^{13} +6.00000 q^{14} +(13.5000 + 23.3827i) q^{15} +(35.5000 + 61.4878i) q^{16} +(55.5000 - 96.1288i) q^{17} +27.0000 q^{18} +(23.0000 - 39.8372i) q^{19} +(4.50000 - 7.79423i) q^{20} +6.00000 q^{21} +(-45.0000 + 77.9423i) q^{22} +(3.00000 + 5.19615i) q^{23} +(31.5000 + 54.5596i) q^{24} -44.0000 q^{25} +(-136.500 - 33.7750i) q^{26} +27.0000 q^{27} +(-1.00000 - 1.73205i) q^{28} +(52.5000 + 90.9327i) q^{29} +(40.5000 - 70.1481i) q^{30} -100.000 q^{31} +(22.5000 - 38.9711i) q^{32} +(-45.0000 + 77.9423i) q^{33} -333.000 q^{34} +(9.00000 - 15.5885i) q^{35} +(-4.50000 - 7.79423i) q^{36} +(-8.50000 - 14.7224i) q^{37} -138.000 q^{38} +(-136.500 - 33.7750i) q^{39} +189.000 q^{40} +(115.500 + 200.052i) q^{41} +(-9.00000 - 15.5885i) q^{42} +(257.000 - 445.137i) q^{43} +30.0000 q^{44} +(40.5000 - 70.1481i) q^{45} +(9.00000 - 15.5885i) q^{46} -162.000 q^{47} +(106.500 - 184.463i) q^{48} +(169.500 + 293.583i) q^{49} +(66.0000 + 114.315i) q^{50} -333.000 q^{51} +(13.0000 + 45.0333i) q^{52} +639.000 q^{53} +(-40.5000 - 70.1481i) q^{54} +(135.000 + 233.827i) q^{55} +(21.0000 - 36.3731i) q^{56} -138.000 q^{57} +(157.500 - 272.798i) q^{58} +(-300.000 + 519.615i) q^{59} -27.0000 q^{60} +(-116.500 + 201.784i) q^{61} +(150.000 + 259.808i) q^{62} +(-9.00000 - 15.5885i) q^{63} +433.000 q^{64} +(-292.500 + 303.975i) q^{65} +270.000 q^{66} +(-463.000 - 801.940i) q^{67} +(55.5000 + 96.1288i) q^{68} +(9.00000 - 15.5885i) q^{69} -54.0000 q^{70} +(465.000 - 805.404i) q^{71} +(94.5000 - 163.679i) q^{72} -253.000 q^{73} +(-25.5000 + 44.1673i) q^{74} +(66.0000 + 114.315i) q^{75} +(23.0000 + 39.8372i) q^{76} +60.0000 q^{77} +(117.000 + 405.300i) q^{78} -1324.00 q^{79} +(-319.500 - 553.390i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(346.500 - 600.156i) q^{82} +810.000 q^{83} +(-3.00000 + 5.19615i) q^{84} +(-499.500 + 865.159i) q^{85} -1542.00 q^{86} +(157.500 - 272.798i) q^{87} +(315.000 + 545.596i) q^{88} +(-249.000 - 431.281i) q^{89} -243.000 q^{90} +(26.0000 + 90.0666i) q^{91} -6.00000 q^{92} +(150.000 + 259.808i) q^{93} +(243.000 + 420.888i) q^{94} +(-207.000 + 358.535i) q^{95} -135.000 q^{96} +(-679.000 + 1176.06i) q^{97} +(508.500 - 880.748i) q^{98} +270.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 3 q^{2} - 3 q^{3} - q^{4} - 18 q^{5} - 9 q^{6} - 2 q^{7} - 42 q^{8} - 9 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 3 q^{2} - 3 q^{3} - q^{4} - 18 q^{5} - 9 q^{6} - 2 q^{7} - 42 q^{8} - 9 q^{9} + 27 q^{10} - 30 q^{11} + 6 q^{12} + 65 q^{13} + 12 q^{14} + 27 q^{15} + 71 q^{16} + 111 q^{17} + 54 q^{18} + 46 q^{19} + 9 q^{20} + 12 q^{21} - 90 q^{22} + 6 q^{23} + 63 q^{24} - 88 q^{25} - 273 q^{26} + 54 q^{27} - 2 q^{28} + 105 q^{29} + 81 q^{30} - 200 q^{31} + 45 q^{32} - 90 q^{33} - 666 q^{34} + 18 q^{35} - 9 q^{36} - 17 q^{37} - 276 q^{38} - 273 q^{39} + 378 q^{40} + 231 q^{41} - 18 q^{42} + 514 q^{43} + 60 q^{44} + 81 q^{45} + 18 q^{46} - 324 q^{47} + 213 q^{48} + 339 q^{49} + 132 q^{50} - 666 q^{51} + 26 q^{52} + 1278 q^{53} - 81 q^{54} + 270 q^{55} + 42 q^{56} - 276 q^{57} + 315 q^{58} - 600 q^{59} - 54 q^{60} - 233 q^{61} + 300 q^{62} - 18 q^{63} + 866 q^{64} - 585 q^{65} + 540 q^{66} - 926 q^{67} + 111 q^{68} + 18 q^{69} - 108 q^{70} + 930 q^{71} + 189 q^{72} - 506 q^{73} - 51 q^{74} + 132 q^{75} + 46 q^{76} + 120 q^{77} + 234 q^{78} - 2648 q^{79} - 639 q^{80} - 81 q^{81} + 693 q^{82} + 1620 q^{83} - 6 q^{84} - 999 q^{85} - 3084 q^{86} + 315 q^{87} + 630 q^{88} - 498 q^{89} - 486 q^{90} + 52 q^{91} - 12 q^{92} + 300 q^{93} + 486 q^{94} - 414 q^{95} - 270 q^{96} - 1358 q^{97} + 1017 q^{98} + 540 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/39\mathbb{Z}\right)^\times\).

\(n\) \(14\) \(28\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.50000 2.59808i −0.530330 0.918559i −0.999374 0.0353837i \(-0.988735\pi\)
0.469044 0.883175i \(-0.344599\pi\)
\(3\) −1.50000 2.59808i −0.288675 0.500000i
\(4\) −0.500000 + 0.866025i −0.0625000 + 0.108253i
\(5\) −9.00000 −0.804984 −0.402492 0.915423i \(-0.631856\pi\)
−0.402492 + 0.915423i \(0.631856\pi\)
\(6\) −4.50000 + 7.79423i −0.306186 + 0.530330i
\(7\) −1.00000 + 1.73205i −0.0539949 + 0.0935220i −0.891760 0.452510i \(-0.850529\pi\)
0.837765 + 0.546032i \(0.183862\pi\)
\(8\) −21.0000 −0.928078
\(9\) −4.50000 + 7.79423i −0.166667 + 0.288675i
\(10\) 13.5000 + 23.3827i 0.426907 + 0.739425i
\(11\) −15.0000 25.9808i −0.411152 0.712136i 0.583864 0.811851i \(-0.301540\pi\)
−0.995016 + 0.0997155i \(0.968207\pi\)
\(12\) 3.00000 0.0721688
\(13\) 32.5000 33.7750i 0.693375 0.720577i
\(14\) 6.00000 0.114541
\(15\) 13.5000 + 23.3827i 0.232379 + 0.402492i
\(16\) 35.5000 + 61.4878i 0.554688 + 0.960747i
\(17\) 55.5000 96.1288i 0.791807 1.37145i −0.133039 0.991111i \(-0.542474\pi\)
0.924847 0.380340i \(-0.124193\pi\)
\(18\) 27.0000 0.353553
\(19\) 23.0000 39.8372i 0.277714 0.481014i −0.693102 0.720839i \(-0.743757\pi\)
0.970816 + 0.239825i \(0.0770900\pi\)
\(20\) 4.50000 7.79423i 0.0503115 0.0871421i
\(21\) 6.00000 0.0623480
\(22\) −45.0000 + 77.9423i −0.436092 + 0.755334i
\(23\) 3.00000 + 5.19615i 0.0271975 + 0.0471075i 0.879304 0.476261i \(-0.158008\pi\)
−0.852106 + 0.523369i \(0.824675\pi\)
\(24\) 31.5000 + 54.5596i 0.267913 + 0.464039i
\(25\) −44.0000 −0.352000
\(26\) −136.500 33.7750i −1.02961 0.254762i
\(27\) 27.0000 0.192450
\(28\) −1.00000 1.73205i −0.00674937 0.0116902i
\(29\) 52.5000 + 90.9327i 0.336173 + 0.582268i 0.983709 0.179766i \(-0.0575341\pi\)
−0.647537 + 0.762034i \(0.724201\pi\)
\(30\) 40.5000 70.1481i 0.246475 0.426907i
\(31\) −100.000 −0.579372 −0.289686 0.957122i \(-0.593551\pi\)
−0.289686 + 0.957122i \(0.593551\pi\)
\(32\) 22.5000 38.9711i 0.124296 0.215287i
\(33\) −45.0000 + 77.9423i −0.237379 + 0.411152i
\(34\) −333.000 −1.67968
\(35\) 9.00000 15.5885i 0.0434651 0.0752837i
\(36\) −4.50000 7.79423i −0.0208333 0.0360844i
\(37\) −8.50000 14.7224i −0.0377673 0.0654149i 0.846524 0.532351i \(-0.178691\pi\)
−0.884291 + 0.466936i \(0.845358\pi\)
\(38\) −138.000 −0.589120
\(39\) −136.500 33.7750i −0.560449 0.138675i
\(40\) 189.000 0.747088
\(41\) 115.500 + 200.052i 0.439953 + 0.762021i 0.997685 0.0680000i \(-0.0216618\pi\)
−0.557732 + 0.830021i \(0.688328\pi\)
\(42\) −9.00000 15.5885i −0.0330650 0.0572703i
\(43\) 257.000 445.137i 0.911445 1.57867i 0.0994205 0.995046i \(-0.468301\pi\)
0.812024 0.583623i \(-0.198366\pi\)
\(44\) 30.0000 0.102788
\(45\) 40.5000 70.1481i 0.134164 0.232379i
\(46\) 9.00000 15.5885i 0.0288473 0.0499651i
\(47\) −162.000 −0.502769 −0.251384 0.967887i \(-0.580886\pi\)
−0.251384 + 0.967887i \(0.580886\pi\)
\(48\) 106.500 184.463i 0.320249 0.554688i
\(49\) 169.500 + 293.583i 0.494169 + 0.855926i
\(50\) 66.0000 + 114.315i 0.186676 + 0.323333i
\(51\) −333.000 −0.914301
\(52\) 13.0000 + 45.0333i 0.0346688 + 0.120096i
\(53\) 639.000 1.65610 0.828051 0.560653i \(-0.189450\pi\)
0.828051 + 0.560653i \(0.189450\pi\)
\(54\) −40.5000 70.1481i −0.102062 0.176777i
\(55\) 135.000 + 233.827i 0.330971 + 0.573258i
\(56\) 21.0000 36.3731i 0.0501115 0.0867956i
\(57\) −138.000 −0.320676
\(58\) 157.500 272.798i 0.356565 0.617588i
\(59\) −300.000 + 519.615i −0.661978 + 1.14658i 0.318118 + 0.948051i \(0.396949\pi\)
−0.980095 + 0.198527i \(0.936384\pi\)
\(60\) −27.0000 −0.0580948
\(61\) −116.500 + 201.784i −0.244529 + 0.423537i −0.961999 0.273052i \(-0.911967\pi\)
0.717470 + 0.696590i \(0.245300\pi\)
\(62\) 150.000 + 259.808i 0.307258 + 0.532187i
\(63\) −9.00000 15.5885i −0.0179983 0.0311740i
\(64\) 433.000 0.845703
\(65\) −292.500 + 303.975i −0.558156 + 0.580053i
\(66\) 270.000 0.503556
\(67\) −463.000 801.940i −0.844246 1.46228i −0.886275 0.463160i \(-0.846716\pi\)
0.0420292 0.999116i \(-0.486618\pi\)
\(68\) 55.5000 + 96.1288i 0.0989759 + 0.171431i
\(69\) 9.00000 15.5885i 0.0157025 0.0271975i
\(70\) −54.0000 −0.0922033
\(71\) 465.000 805.404i 0.777258 1.34625i −0.156258 0.987716i \(-0.549943\pi\)
0.933516 0.358535i \(-0.116724\pi\)
\(72\) 94.5000 163.679i 0.154680 0.267913i
\(73\) −253.000 −0.405636 −0.202818 0.979216i \(-0.565010\pi\)
−0.202818 + 0.979216i \(0.565010\pi\)
\(74\) −25.5000 + 44.1673i −0.0400583 + 0.0693830i
\(75\) 66.0000 + 114.315i 0.101614 + 0.176000i
\(76\) 23.0000 + 39.8372i 0.0347142 + 0.0601268i
\(77\) 60.0000 0.0888004
\(78\) 117.000 + 405.300i 0.169842 + 0.588348i
\(79\) −1324.00 −1.88559 −0.942795 0.333373i \(-0.891813\pi\)
−0.942795 + 0.333373i \(0.891813\pi\)
\(80\) −319.500 553.390i −0.446515 0.773386i
\(81\) −40.5000 70.1481i −0.0555556 0.0962250i
\(82\) 346.500 600.156i 0.466641 0.808245i
\(83\) 810.000 1.07119 0.535597 0.844474i \(-0.320087\pi\)
0.535597 + 0.844474i \(0.320087\pi\)
\(84\) −3.00000 + 5.19615i −0.00389675 + 0.00674937i
\(85\) −499.500 + 865.159i −0.637393 + 1.10400i
\(86\) −1542.00 −1.93347
\(87\) 157.500 272.798i 0.194089 0.336173i
\(88\) 315.000 + 545.596i 0.381581 + 0.660917i
\(89\) −249.000 431.281i −0.296561 0.513659i 0.678786 0.734336i \(-0.262507\pi\)
−0.975347 + 0.220677i \(0.929173\pi\)
\(90\) −243.000 −0.284605
\(91\) 26.0000 + 90.0666i 0.0299510 + 0.103753i
\(92\) −6.00000 −0.00679938
\(93\) 150.000 + 259.808i 0.167250 + 0.289686i
\(94\) 243.000 + 420.888i 0.266633 + 0.461823i
\(95\) −207.000 + 358.535i −0.223555 + 0.387209i
\(96\) −135.000 −0.143525
\(97\) −679.000 + 1176.06i −0.710742 + 1.23104i 0.253837 + 0.967247i \(0.418307\pi\)
−0.964579 + 0.263795i \(0.915026\pi\)
\(98\) 508.500 880.748i 0.524145 0.907847i
\(99\) 270.000 0.274101
\(100\) 22.0000 38.1051i 0.0220000 0.0381051i
\(101\) 178.500 + 309.171i 0.175856 + 0.304591i 0.940457 0.339913i \(-0.110397\pi\)
−0.764601 + 0.644503i \(0.777064\pi\)
\(102\) 499.500 + 865.159i 0.484881 + 0.839839i
\(103\) 1118.00 1.06951 0.534756 0.845006i \(-0.320403\pi\)
0.534756 + 0.845006i \(0.320403\pi\)
\(104\) −682.500 + 709.275i −0.643506 + 0.668751i
\(105\) −54.0000 −0.0501891
\(106\) −958.500 1660.17i −0.878281 1.52123i
\(107\) −357.000 618.342i −0.322547 0.558667i 0.658466 0.752610i \(-0.271206\pi\)
−0.981013 + 0.193943i \(0.937872\pi\)
\(108\) −13.5000 + 23.3827i −0.0120281 + 0.0208333i
\(109\) 2006.00 1.76275 0.881376 0.472416i \(-0.156618\pi\)
0.881376 + 0.472416i \(0.156618\pi\)
\(110\) 405.000 701.481i 0.351048 0.608032i
\(111\) −25.5000 + 44.1673i −0.0218050 + 0.0377673i
\(112\) −142.000 −0.119801
\(113\) 559.500 969.082i 0.465782 0.806758i −0.533455 0.845829i \(-0.679107\pi\)
0.999236 + 0.0390710i \(0.0124399\pi\)
\(114\) 207.000 + 358.535i 0.170064 + 0.294560i
\(115\) −27.0000 46.7654i −0.0218936 0.0379208i
\(116\) −105.000 −0.0840431
\(117\) 117.000 + 405.300i 0.0924500 + 0.320256i
\(118\) 1800.00 1.40427
\(119\) 111.000 + 192.258i 0.0855072 + 0.148103i
\(120\) −283.500 491.036i −0.215666 0.373544i
\(121\) 215.500 373.257i 0.161908 0.280433i
\(122\) 699.000 0.518725
\(123\) 346.500 600.156i 0.254007 0.439953i
\(124\) 50.0000 86.6025i 0.0362107 0.0627189i
\(125\) 1521.00 1.08834
\(126\) −27.0000 + 46.7654i −0.0190901 + 0.0330650i
\(127\) 302.000 + 523.079i 0.211009 + 0.365479i 0.952031 0.306003i \(-0.0989917\pi\)
−0.741021 + 0.671481i \(0.765658\pi\)
\(128\) −829.500 1436.74i −0.572798 0.992115i
\(129\) −1542.00 −1.05245
\(130\) 1228.50 + 303.975i 0.828820 + 0.205080i
\(131\) −1584.00 −1.05645 −0.528224 0.849105i \(-0.677142\pi\)
−0.528224 + 0.849105i \(0.677142\pi\)
\(132\) −45.0000 77.9423i −0.0296723 0.0513940i
\(133\) 46.0000 + 79.6743i 0.0299903 + 0.0519447i
\(134\) −1389.00 + 2405.82i −0.895458 + 1.55098i
\(135\) −243.000 −0.154919
\(136\) −1165.50 + 2018.71i −0.734859 + 1.27281i
\(137\) −358.500 + 620.940i −0.223567 + 0.387230i −0.955889 0.293729i \(-0.905104\pi\)
0.732321 + 0.680959i \(0.238437\pi\)
\(138\) −54.0000 −0.0333100
\(139\) 410.000 710.141i 0.250185 0.433334i −0.713391 0.700766i \(-0.752842\pi\)
0.963577 + 0.267432i \(0.0861751\pi\)
\(140\) 9.00000 + 15.5885i 0.00543313 + 0.00941046i
\(141\) 243.000 + 420.888i 0.145137 + 0.251384i
\(142\) −2790.00 −1.64881
\(143\) −1365.00 337.750i −0.798231 0.197511i
\(144\) −639.000 −0.369792
\(145\) −472.500 818.394i −0.270614 0.468717i
\(146\) 379.500 + 657.313i 0.215121 + 0.372600i
\(147\) 508.500 880.748i 0.285309 0.494169i
\(148\) 17.0000 0.00944183
\(149\) 874.500 1514.68i 0.480818 0.832801i −0.518940 0.854811i \(-0.673673\pi\)
0.999758 + 0.0220100i \(0.00700656\pi\)
\(150\) 198.000 342.946i 0.107778 0.186676i
\(151\) −370.000 −0.199405 −0.0997026 0.995017i \(-0.531789\pi\)
−0.0997026 + 0.995017i \(0.531789\pi\)
\(152\) −483.000 + 836.581i −0.257740 + 0.446419i
\(153\) 499.500 + 865.159i 0.263936 + 0.457150i
\(154\) −90.0000 155.885i −0.0470935 0.0815684i
\(155\) 900.000 0.466385
\(156\) 97.5000 101.325i 0.0500400 0.0520031i
\(157\) −2611.00 −1.32726 −0.663632 0.748059i \(-0.730986\pi\)
−0.663632 + 0.748059i \(0.730986\pi\)
\(158\) 1986.00 + 3439.85i 0.999985 + 1.73203i
\(159\) −958.500 1660.17i −0.478075 0.828051i
\(160\) −202.500 + 350.740i −0.100056 + 0.173303i
\(161\) −12.0000 −0.00587411
\(162\) −121.500 + 210.444i −0.0589256 + 0.102062i
\(163\) 818.000 1416.82i 0.393072 0.680820i −0.599781 0.800164i \(-0.704746\pi\)
0.992853 + 0.119344i \(0.0380790\pi\)
\(164\) −231.000 −0.109988
\(165\) 405.000 701.481i 0.191086 0.330971i
\(166\) −1215.00 2104.44i −0.568086 0.983954i
\(167\) −132.000 228.631i −0.0611645 0.105940i 0.833822 0.552034i \(-0.186148\pi\)
−0.894986 + 0.446094i \(0.852815\pi\)
\(168\) −126.000 −0.0578638
\(169\) −84.5000 2195.37i −0.0384615 0.999260i
\(170\) 2997.00 1.35211
\(171\) 207.000 + 358.535i 0.0925713 + 0.160338i
\(172\) 257.000 + 445.137i 0.113931 + 0.197334i
\(173\) −705.000 + 1221.10i −0.309827 + 0.536637i −0.978324 0.207078i \(-0.933605\pi\)
0.668497 + 0.743715i \(0.266938\pi\)
\(174\) −945.000 −0.411726
\(175\) 44.0000 76.2102i 0.0190062 0.0329197i
\(176\) 1065.00 1844.63i 0.456122 0.790026i
\(177\) 1800.00 0.764386
\(178\) −747.000 + 1293.84i −0.314551 + 0.544818i
\(179\) 237.000 + 410.496i 0.0989621 + 0.171407i 0.911255 0.411842i \(-0.135114\pi\)
−0.812293 + 0.583249i \(0.801781\pi\)
\(180\) 40.5000 + 70.1481i 0.0167705 + 0.0290474i
\(181\) 2249.00 0.923574 0.461787 0.886991i \(-0.347208\pi\)
0.461787 + 0.886991i \(0.347208\pi\)
\(182\) 195.000 202.650i 0.0794196 0.0825352i
\(183\) 699.000 0.282358
\(184\) −63.0000 109.119i −0.0252414 0.0437194i
\(185\) 76.5000 + 132.502i 0.0304021 + 0.0526580i
\(186\) 450.000 779.423i 0.177396 0.307258i
\(187\) −3330.00 −1.30221
\(188\) 81.0000 140.296i 0.0314230 0.0544263i
\(189\) −27.0000 + 46.7654i −0.0103913 + 0.0179983i
\(190\) 1242.00 0.474232
\(191\) −1722.00 + 2982.59i −0.652354 + 1.12991i 0.330197 + 0.943912i \(0.392885\pi\)
−0.982550 + 0.185997i \(0.940448\pi\)
\(192\) −649.500 1124.97i −0.244133 0.422852i
\(193\) 2136.50 + 3700.53i 0.796832 + 1.38015i 0.921669 + 0.387977i \(0.126826\pi\)
−0.124837 + 0.992177i \(0.539841\pi\)
\(194\) 4074.00 1.50771
\(195\) 1228.50 + 303.975i 0.451152 + 0.111631i
\(196\) −339.000 −0.123542
\(197\) 993.000 + 1719.93i 0.359129 + 0.622029i 0.987815 0.155630i \(-0.0497406\pi\)
−0.628687 + 0.777658i \(0.716407\pi\)
\(198\) −405.000 701.481i −0.145364 0.251778i
\(199\) 1193.00 2066.34i 0.424973 0.736074i −0.571445 0.820640i \(-0.693617\pi\)
0.996418 + 0.0845661i \(0.0269504\pi\)
\(200\) 924.000 0.326683
\(201\) −1389.00 + 2405.82i −0.487425 + 0.844246i
\(202\) 535.500 927.513i 0.186523 0.323067i
\(203\) −210.000 −0.0726065
\(204\) 166.500 288.386i 0.0571438 0.0989759i
\(205\) −1039.50 1800.47i −0.354155 0.613415i
\(206\) −1677.00 2904.65i −0.567195 0.982410i
\(207\) −54.0000 −0.0181317
\(208\) 3230.50 + 799.341i 1.07690 + 0.266463i
\(209\) −1380.00 −0.456730
\(210\) 81.0000 + 140.296i 0.0266168 + 0.0461017i
\(211\) 800.000 + 1385.64i 0.261016 + 0.452092i 0.966512 0.256621i \(-0.0826093\pi\)
−0.705497 + 0.708713i \(0.749276\pi\)
\(212\) −319.500 + 553.390i −0.103506 + 0.179278i
\(213\) −2790.00 −0.897501
\(214\) −1071.00 + 1855.03i −0.342112 + 0.592556i
\(215\) −2313.00 + 4006.23i −0.733699 + 1.27080i
\(216\) −567.000 −0.178609
\(217\) 100.000 173.205i 0.0312831 0.0541840i
\(218\) −3009.00 5211.74i −0.934840 1.61919i
\(219\) 379.500 + 657.313i 0.117097 + 0.202818i
\(220\) −270.000 −0.0827427
\(221\) −1443.00 4998.70i −0.439216 1.52149i
\(222\) 153.000 0.0462553
\(223\) 1916.00 + 3318.61i 0.575358 + 0.996549i 0.996003 + 0.0893239i \(0.0284706\pi\)
−0.420645 + 0.907226i \(0.638196\pi\)
\(224\) 45.0000 + 77.9423i 0.0134227 + 0.0232488i
\(225\) 198.000 342.946i 0.0586667 0.101614i
\(226\) −3357.00 −0.988072
\(227\) 699.000 1210.70i 0.204380 0.353997i −0.745555 0.666444i \(-0.767816\pi\)
0.949935 + 0.312448i \(0.101149\pi\)
\(228\) 69.0000 119.512i 0.0200423 0.0347142i
\(229\) 4466.00 1.28874 0.644370 0.764714i \(-0.277120\pi\)
0.644370 + 0.764714i \(0.277120\pi\)
\(230\) −81.0000 + 140.296i −0.0232217 + 0.0402211i
\(231\) −90.0000 155.885i −0.0256345 0.0444002i
\(232\) −1102.50 1909.59i −0.311994 0.540390i
\(233\) −1638.00 −0.460553 −0.230277 0.973125i \(-0.573963\pi\)
−0.230277 + 0.973125i \(0.573963\pi\)
\(234\) 877.500 911.925i 0.245145 0.254762i
\(235\) 1458.00 0.404721
\(236\) −300.000 519.615i −0.0827472 0.143322i
\(237\) 1986.00 + 3439.85i 0.544323 + 0.942795i
\(238\) 333.000 576.773i 0.0906941 0.157087i
\(239\) −594.000 −0.160764 −0.0803821 0.996764i \(-0.525614\pi\)
−0.0803821 + 0.996764i \(0.525614\pi\)
\(240\) −958.500 + 1660.17i −0.257795 + 0.446515i
\(241\) −1151.50 + 1994.46i −0.307779 + 0.533088i −0.977876 0.209185i \(-0.932919\pi\)
0.670098 + 0.742273i \(0.266252\pi\)
\(242\) −1293.00 −0.343459
\(243\) −121.500 + 210.444i −0.0320750 + 0.0555556i
\(244\) −116.500 201.784i −0.0305662 0.0529422i
\(245\) −1525.50 2642.24i −0.397798 0.689007i
\(246\) −2079.00 −0.538830
\(247\) −598.000 2071.53i −0.154048 0.533638i
\(248\) 2100.00 0.537702
\(249\) −1215.00 2104.44i −0.309227 0.535597i
\(250\) −2281.50 3951.67i −0.577179 0.999703i
\(251\) −3162.00 + 5476.74i −0.795154 + 1.37725i 0.127587 + 0.991827i \(0.459277\pi\)
−0.922741 + 0.385420i \(0.874057\pi\)
\(252\) 18.0000 0.00449958
\(253\) 90.0000 155.885i 0.0223646 0.0387367i
\(254\) 906.000 1569.24i 0.223809 0.387649i
\(255\) 2997.00 0.735998
\(256\) −756.500 + 1310.30i −0.184692 + 0.319897i
\(257\) −3916.50 6783.58i −0.950601 1.64649i −0.744127 0.668038i \(-0.767134\pi\)
−0.206474 0.978452i \(-0.566199\pi\)
\(258\) 2313.00 + 4006.23i 0.558144 + 0.966733i
\(259\) 34.0000 0.00815698
\(260\) −117.000 405.300i −0.0279078 0.0966755i
\(261\) −945.000 −0.224115
\(262\) 2376.00 + 4115.35i 0.560266 + 0.970410i
\(263\) 1515.00 + 2624.06i 0.355205 + 0.615233i 0.987153 0.159778i \(-0.0510777\pi\)
−0.631948 + 0.775011i \(0.717744\pi\)
\(264\) 945.000 1636.79i 0.220306 0.381581i
\(265\) −5751.00 −1.33314
\(266\) 138.000 239.023i 0.0318095 0.0550956i
\(267\) −747.000 + 1293.84i −0.171220 + 0.296561i
\(268\) 926.000 0.211061
\(269\) 267.000 462.458i 0.0605178 0.104820i −0.834179 0.551493i \(-0.814058\pi\)
0.894697 + 0.446674i \(0.147391\pi\)
\(270\) 364.500 + 631.333i 0.0821584 + 0.142302i
\(271\) 1844.00 + 3193.90i 0.413340 + 0.715925i 0.995253 0.0973259i \(-0.0310289\pi\)
−0.581913 + 0.813251i \(0.697696\pi\)
\(272\) 7881.00 1.75682
\(273\) 195.000 202.650i 0.0432305 0.0449265i
\(274\) 2151.00 0.474258
\(275\) 660.000 + 1143.15i 0.144725 + 0.250672i
\(276\) 9.00000 + 15.5885i 0.00196281 + 0.00339969i
\(277\) −932.500 + 1615.14i −0.202269 + 0.350340i −0.949259 0.314495i \(-0.898165\pi\)
0.746990 + 0.664835i \(0.231498\pi\)
\(278\) −2460.00 −0.530723
\(279\) 450.000 779.423i 0.0965620 0.167250i
\(280\) −189.000 + 327.358i −0.0403390 + 0.0698691i
\(281\) 2997.00 0.636249 0.318125 0.948049i \(-0.396947\pi\)
0.318125 + 0.948049i \(0.396947\pi\)
\(282\) 729.000 1262.67i 0.153941 0.266633i
\(283\) 2057.00 + 3562.83i 0.432071 + 0.748368i 0.997051 0.0767359i \(-0.0244498\pi\)
−0.564981 + 0.825104i \(0.691116\pi\)
\(284\) 465.000 + 805.404i 0.0971573 + 0.168281i
\(285\) 1242.00 0.258139
\(286\) 1170.00 + 4053.00i 0.241901 + 0.837968i
\(287\) −462.000 −0.0950209
\(288\) 202.500 + 350.740i 0.0414320 + 0.0717624i
\(289\) −3704.00 6415.52i −0.753918 1.30582i
\(290\) −1417.50 + 2455.18i −0.287029 + 0.497149i
\(291\) 4074.00 0.820695
\(292\) 126.500 219.104i 0.0253522 0.0439114i
\(293\) 2332.50 4040.01i 0.465072 0.805528i −0.534133 0.845401i \(-0.679362\pi\)
0.999205 + 0.0398722i \(0.0126951\pi\)
\(294\) −3051.00 −0.605231
\(295\) 2700.00 4676.54i 0.532882 0.922978i
\(296\) 178.500 + 309.171i 0.0350510 + 0.0607101i
\(297\) −405.000 701.481i −0.0791262 0.137051i
\(298\) −5247.00 −1.01997
\(299\) 273.000 + 67.5500i 0.0528027 + 0.0130653i
\(300\) −132.000 −0.0254034
\(301\) 514.000 + 890.274i 0.0984268 + 0.170480i
\(302\) 555.000 + 961.288i 0.105751 + 0.183165i
\(303\) 535.500 927.513i 0.101530 0.175856i
\(304\) 3266.00 0.616177
\(305\) 1048.50 1816.06i 0.196842 0.340941i
\(306\) 1498.50 2595.48i 0.279946 0.484881i
\(307\) 1502.00 0.279230 0.139615 0.990206i \(-0.455413\pi\)
0.139615 + 0.990206i \(0.455413\pi\)
\(308\) −30.0000 + 51.9615i −0.00555003 + 0.00961293i
\(309\) −1677.00 2904.65i −0.308742 0.534756i
\(310\) −1350.00 2338.27i −0.247338 0.428402i
\(311\) 2106.00 0.383988 0.191994 0.981396i \(-0.438505\pi\)
0.191994 + 0.981396i \(0.438505\pi\)
\(312\) 2866.50 + 709.275i 0.520140 + 0.128701i
\(313\) −3898.00 −0.703923 −0.351962 0.936014i \(-0.614485\pi\)
−0.351962 + 0.936014i \(0.614485\pi\)
\(314\) 3916.50 + 6783.58i 0.703888 + 1.21917i
\(315\) 81.0000 + 140.296i 0.0144884 + 0.0250946i
\(316\) 662.000 1146.62i 0.117849 0.204121i
\(317\) 9351.00 1.65680 0.828398 0.560140i \(-0.189253\pi\)
0.828398 + 0.560140i \(0.189253\pi\)
\(318\) −2875.50 + 4980.51i −0.507076 + 0.878281i
\(319\) 1575.00 2727.98i 0.276436 0.478801i
\(320\) −3897.00 −0.680778
\(321\) −1071.00 + 1855.03i −0.186222 + 0.322547i
\(322\) 18.0000 + 31.1769i 0.00311522 + 0.00539572i
\(323\) −2553.00 4421.93i −0.439792 0.761742i
\(324\) 81.0000 0.0138889
\(325\) −1430.00 + 1486.10i −0.244068 + 0.253643i
\(326\) −4908.00 −0.833831
\(327\) −3009.00 5211.74i −0.508863 0.881376i
\(328\) −2425.50 4201.09i −0.408310 0.707214i
\(329\) 162.000 280.592i 0.0271470 0.0470199i
\(330\) −2430.00 −0.405355
\(331\) 4586.00 7943.19i 0.761539 1.31902i −0.180518 0.983572i \(-0.557778\pi\)
0.942057 0.335452i \(-0.108889\pi\)
\(332\) −405.000 + 701.481i −0.0669496 + 0.115960i
\(333\) 153.000 0.0251782
\(334\) −396.000 + 685.892i −0.0648747 + 0.112366i
\(335\) 4167.00 + 7217.46i 0.679605 + 1.17711i
\(336\) 213.000 + 368.927i 0.0345836 + 0.0599006i
\(337\) −11089.0 −1.79245 −0.896226 0.443598i \(-0.853702\pi\)
−0.896226 + 0.443598i \(0.853702\pi\)
\(338\) −5577.00 + 3512.60i −0.897482 + 0.565267i
\(339\) −3357.00 −0.537838
\(340\) −499.500 865.159i −0.0796741 0.138000i
\(341\) 1500.00 + 2598.08i 0.238210 + 0.412592i
\(342\) 621.000 1075.60i 0.0981866 0.170064i
\(343\) −1364.00 −0.214720
\(344\) −5397.00 + 9347.88i −0.845892 + 1.46513i
\(345\) −81.0000 + 140.296i −0.0126403 + 0.0218936i
\(346\) 4230.00 0.657243
\(347\) −4881.00 + 8454.14i −0.755118 + 1.30790i 0.190198 + 0.981746i \(0.439087\pi\)
−0.945316 + 0.326156i \(0.894246\pi\)
\(348\) 157.500 + 272.798i 0.0242612 + 0.0420216i
\(349\) 4145.00 + 7179.35i 0.635750 + 1.10115i 0.986356 + 0.164628i \(0.0526424\pi\)
−0.350606 + 0.936523i \(0.614024\pi\)
\(350\) −264.000 −0.0403183
\(351\) 877.500 911.925i 0.133440 0.138675i
\(352\) −1350.00 −0.204418
\(353\) −6202.50 10743.0i −0.935200 1.61981i −0.774276 0.632848i \(-0.781886\pi\)
−0.160924 0.986967i \(-0.551448\pi\)
\(354\) −2700.00 4676.54i −0.405377 0.702133i
\(355\) −4185.00 + 7248.63i −0.625681 + 1.08371i
\(356\) 498.000 0.0741403
\(357\) 333.000 576.773i 0.0493676 0.0855072i
\(358\) 711.000 1231.49i 0.104965 0.181805i
\(359\) −1098.00 −0.161421 −0.0807106 0.996738i \(-0.525719\pi\)
−0.0807106 + 0.996738i \(0.525719\pi\)
\(360\) −850.500 + 1473.11i −0.124515 + 0.215666i
\(361\) 2371.50 + 4107.56i 0.345750 + 0.598857i
\(362\) −3373.50 5843.07i −0.489799 0.848357i
\(363\) −1293.00 −0.186956
\(364\) −91.0000 22.5167i −0.0131036 0.00324229i
\(365\) 2277.00 0.326530
\(366\) −1048.50 1816.06i −0.149743 0.259363i
\(367\) 2867.00 + 4965.79i 0.407783 + 0.706300i 0.994641 0.103390i \(-0.0329688\pi\)
−0.586858 + 0.809690i \(0.699635\pi\)
\(368\) −213.000 + 368.927i −0.0301723 + 0.0522599i
\(369\) −2079.00 −0.293302
\(370\) 229.500 397.506i 0.0322463 0.0558523i
\(371\) −639.000 + 1106.78i −0.0894211 + 0.154882i
\(372\) −300.000 −0.0418126
\(373\) 4485.50 7769.11i 0.622655 1.07847i −0.366334 0.930483i \(-0.619387\pi\)
0.988989 0.147987i \(-0.0472794\pi\)
\(374\) 4995.00 + 8651.59i 0.690602 + 1.19616i
\(375\) −2281.50 3951.67i −0.314176 0.544170i
\(376\) 3402.00 0.466608
\(377\) 4777.50 + 1182.12i 0.652663 + 0.161492i
\(378\) 162.000 0.0220433
\(379\) −3622.00 6273.49i −0.490896 0.850257i 0.509049 0.860738i \(-0.329997\pi\)
−0.999945 + 0.0104805i \(0.996664\pi\)
\(380\) −207.000 358.535i −0.0279444 0.0484011i
\(381\) 906.000 1569.24i 0.121826 0.211009i
\(382\) 10332.0 1.38385
\(383\) 3156.00 5466.35i 0.421055 0.729289i −0.574988 0.818162i \(-0.694993\pi\)
0.996043 + 0.0888732i \(0.0283266\pi\)
\(384\) −2488.50 + 4310.21i −0.330705 + 0.572798i
\(385\) −540.000 −0.0714830
\(386\) 6409.50 11101.6i 0.845168 1.46387i
\(387\) 2313.00 + 4006.23i 0.303815 + 0.526223i
\(388\) −679.000 1176.06i −0.0888428 0.153880i
\(389\) 3627.00 0.472741 0.236370 0.971663i \(-0.424042\pi\)
0.236370 + 0.971663i \(0.424042\pi\)
\(390\) −1053.00 3647.70i −0.136720 0.473611i
\(391\) 666.000 0.0861408
\(392\) −3559.50 6165.23i −0.458627 0.794366i
\(393\) 2376.00 + 4115.35i 0.304970 + 0.528224i
\(394\) 2979.00 5159.78i 0.380913 0.659761i
\(395\) 11916.0 1.51787
\(396\) −135.000 + 233.827i −0.0171313 + 0.0296723i
\(397\) 1949.00 3375.77i 0.246392 0.426763i −0.716130 0.697967i \(-0.754088\pi\)
0.962522 + 0.271204i \(0.0874217\pi\)
\(398\) −7158.00 −0.901503
\(399\) 138.000 239.023i 0.0173149 0.0299903i
\(400\) −1562.00 2705.46i −0.195250 0.338183i
\(401\) 2851.50 + 4938.94i 0.355105 + 0.615060i 0.987136 0.159883i \(-0.0511118\pi\)
−0.632031 + 0.774943i \(0.717778\pi\)
\(402\) 8334.00 1.03399
\(403\) −3250.00 + 3377.50i −0.401722 + 0.417482i
\(404\) −357.000 −0.0439639
\(405\) 364.500 + 631.333i 0.0447214 + 0.0774597i
\(406\) 315.000 + 545.596i 0.0385054 + 0.0666933i
\(407\) −255.000 + 441.673i −0.0310562 + 0.0537909i
\(408\) 6993.00 0.848542
\(409\) −3155.50 + 5465.49i −0.381490 + 0.660760i −0.991275 0.131806i \(-0.957922\pi\)
0.609785 + 0.792567i \(0.291256\pi\)
\(410\) −3118.50 + 5401.40i −0.375638 + 0.650625i
\(411\) 2151.00 0.258153
\(412\) −559.000 + 968.216i −0.0668445 + 0.115778i
\(413\) −600.000 1039.23i −0.0714869 0.123819i
\(414\) 81.0000 + 140.296i 0.00961578 + 0.0166550i
\(415\) −7290.00 −0.862294
\(416\) −585.000 2026.50i −0.0689471 0.238840i
\(417\) −2460.00 −0.288889
\(418\) 2070.00 + 3585.35i 0.242218 + 0.419533i
\(419\) 1164.00 + 2016.11i 0.135716 + 0.235067i 0.925871 0.377840i \(-0.123333\pi\)
−0.790155 + 0.612908i \(0.790000\pi\)
\(420\) 27.0000 46.7654i 0.00313682 0.00543313i
\(421\) 2045.00 0.236739 0.118370 0.992970i \(-0.462233\pi\)
0.118370 + 0.992970i \(0.462233\pi\)
\(422\) 2400.00 4156.92i 0.276849 0.479516i
\(423\) 729.000 1262.67i 0.0837948 0.145137i
\(424\) −13419.0 −1.53699
\(425\) −2442.00 + 4229.67i −0.278716 + 0.482751i
\(426\) 4185.00 + 7248.63i 0.475972 + 0.824407i
\(427\) −233.000 403.568i −0.0264067 0.0457377i
\(428\) 714.000 0.0806367
\(429\) 1170.00 + 4053.00i 0.131674 + 0.456132i
\(430\) 13878.0 1.55641
\(431\) −2517.00 4359.57i −0.281298 0.487223i 0.690406 0.723422i \(-0.257432\pi\)
−0.971705 + 0.236199i \(0.924098\pi\)
\(432\) 958.500 + 1660.17i 0.106750 + 0.184896i
\(433\) −2141.50 + 3709.19i −0.237676 + 0.411668i −0.960047 0.279838i \(-0.909719\pi\)
0.722371 + 0.691506i \(0.243052\pi\)
\(434\) −600.000 −0.0663616
\(435\) −1417.50 + 2455.18i −0.156239 + 0.270614i
\(436\) −1003.00 + 1737.25i −0.110172 + 0.190823i
\(437\) 276.000 0.0302125
\(438\) 1138.50 1971.94i 0.124200 0.215121i
\(439\) 653.000 + 1131.03i 0.0709931 + 0.122964i 0.899337 0.437257i \(-0.144050\pi\)
−0.828344 + 0.560220i \(0.810716\pi\)
\(440\) −2835.00 4910.36i −0.307167 0.532028i
\(441\) −3051.00 −0.329446
\(442\) −10822.5 + 11247.1i −1.16465 + 1.21034i
\(443\) −5796.00 −0.621617 −0.310808 0.950473i \(-0.600600\pi\)
−0.310808 + 0.950473i \(0.600600\pi\)
\(444\) −25.5000 44.1673i −0.00272562 0.00472092i
\(445\) 2241.00 + 3881.53i 0.238727 + 0.413488i
\(446\) 5748.00 9955.83i 0.610259 1.05700i
\(447\) −5247.00 −0.555200
\(448\) −433.000 + 749.978i −0.0456637 + 0.0790918i
\(449\) −1353.00 + 2343.46i −0.142209 + 0.246314i −0.928328 0.371761i \(-0.878754\pi\)
0.786119 + 0.618075i \(0.212087\pi\)
\(450\) −1188.00 −0.124451
\(451\) 3465.00 6001.56i 0.361775 0.626612i
\(452\) 559.500 + 969.082i 0.0582227 + 0.100845i
\(453\) 555.000 + 961.288i 0.0575633 + 0.0997026i
\(454\) −4194.00 −0.433555
\(455\) −234.000 810.600i −0.0241101 0.0835198i
\(456\) 2898.00 0.297612
\(457\) 414.500 + 717.935i 0.0424278 + 0.0734871i 0.886459 0.462806i \(-0.153157\pi\)
−0.844032 + 0.536293i \(0.819824\pi\)
\(458\) −6699.00 11603.0i −0.683458 1.18378i
\(459\) 1498.50 2595.48i 0.152383 0.263936i
\(460\) 54.0000 0.00547340
\(461\) 2746.50 4757.08i 0.277478 0.480606i −0.693279 0.720669i \(-0.743835\pi\)
0.970757 + 0.240063i \(0.0771682\pi\)
\(462\) −270.000 + 467.654i −0.0271895 + 0.0470935i
\(463\) −15346.0 −1.54037 −0.770183 0.637823i \(-0.779835\pi\)
−0.770183 + 0.637823i \(0.779835\pi\)
\(464\) −3727.50 + 6456.22i −0.372941 + 0.645954i
\(465\) −1350.00 2338.27i −0.134634 0.233193i
\(466\) 2457.00 + 4255.65i 0.244245 + 0.423045i
\(467\) −9594.00 −0.950658 −0.475329 0.879808i \(-0.657671\pi\)
−0.475329 + 0.879808i \(0.657671\pi\)
\(468\) −409.500 101.325i −0.0404469 0.0100080i
\(469\) 1852.00 0.182340
\(470\) −2187.00 3788.00i −0.214636 0.371760i
\(471\) 3916.50 + 6783.58i 0.383148 + 0.663632i
\(472\) 6300.00 10911.9i 0.614367 1.06411i
\(473\) −15420.0 −1.49897
\(474\) 5958.00 10319.6i 0.577342 0.999985i
\(475\) −1012.00 + 1752.84i −0.0977553 + 0.169317i
\(476\) −222.000 −0.0213768
\(477\) −2875.50 + 4980.51i −0.276017 + 0.478075i
\(478\) 891.000 + 1543.26i 0.0852581 + 0.147671i
\(479\) 6420.00 + 11119.8i 0.612395 + 1.06070i 0.990836 + 0.135074i \(0.0431272\pi\)
−0.378440 + 0.925626i \(0.623539\pi\)
\(480\) 1215.00 0.115535
\(481\) −773.500 191.392i −0.0733234 0.0181428i
\(482\) 6909.00 0.652897
\(483\) 18.0000 + 31.1769i 0.00169571 + 0.00293706i
\(484\) 215.500 + 373.257i 0.0202385 + 0.0350542i
\(485\) 6111.00 10584.6i 0.572137 0.990970i
\(486\) 729.000 0.0680414
\(487\) 7043.00 12198.8i 0.655336 1.13508i −0.326473 0.945207i \(-0.605860\pi\)
0.981809 0.189869i \(-0.0608064\pi\)
\(488\) 2446.50 4237.46i 0.226942 0.393076i
\(489\) −4908.00 −0.453880
\(490\) −4576.50 + 7926.73i −0.421929 + 0.730802i
\(491\) −5847.00 10127.3i −0.537416 0.930832i −0.999042 0.0437577i \(-0.986067\pi\)
0.461626 0.887075i \(-0.347266\pi\)
\(492\) 346.500 + 600.156i 0.0317509 + 0.0549941i
\(493\) 11655.0 1.06474
\(494\) −4485.00 + 4660.95i −0.408481 + 0.424506i
\(495\) −2430.00 −0.220647
\(496\) −3550.00 6148.78i −0.321370 0.556630i
\(497\) 930.000 + 1610.81i 0.0839360 + 0.145381i
\(498\) −3645.00 + 6313.33i −0.327985 + 0.568086i
\(499\) −3688.00 −0.330857 −0.165428 0.986222i \(-0.552901\pi\)
−0.165428 + 0.986222i \(0.552901\pi\)
\(500\) −760.500 + 1317.22i −0.0680212 + 0.117816i
\(501\) −396.000 + 685.892i −0.0353133 + 0.0611645i
\(502\) 18972.0 1.68678
\(503\) 2373.00 4110.16i 0.210352 0.364340i −0.741473 0.670983i \(-0.765872\pi\)
0.951825 + 0.306643i \(0.0992058\pi\)
\(504\) 189.000 + 327.358i 0.0167038 + 0.0289319i
\(505\) −1606.50 2782.54i −0.141561 0.245191i
\(506\) −540.000 −0.0474425
\(507\) −5577.00 + 3512.60i −0.488527 + 0.307692i
\(508\) −604.000 −0.0527523
\(509\) 7252.50 + 12561.7i 0.631555 + 1.09389i 0.987234 + 0.159277i \(0.0509163\pi\)
−0.355679 + 0.934608i \(0.615750\pi\)
\(510\) −4495.50 7786.43i −0.390322 0.676057i
\(511\) 253.000 438.209i 0.0219023 0.0379358i
\(512\) −8733.00 −0.753804
\(513\) 621.000 1075.60i 0.0534460 0.0925713i
\(514\) −11749.5 + 20350.7i −1.00827 + 1.74637i
\(515\) −10062.0 −0.860941
\(516\) 771.000 1335.41i 0.0657779 0.113931i
\(517\) 2430.00 + 4208.88i 0.206714 + 0.358040i
\(518\) −51.0000 88.3346i −0.00432589 0.00749266i
\(519\) 4230.00 0.357758
\(520\) 6142.50 6383.47i 0.518012 0.538334i
\(521\) 5085.00 0.427597 0.213798 0.976878i \(-0.431416\pi\)
0.213798 + 0.976878i \(0.431416\pi\)
\(522\) 1417.50 + 2455.18i 0.118855 + 0.205863i
\(523\) 5441.00 + 9424.09i 0.454911 + 0.787929i 0.998683 0.0513043i \(-0.0163378\pi\)
−0.543772 + 0.839233i \(0.683004\pi\)
\(524\) 792.000 1371.78i 0.0660280 0.114364i
\(525\) −264.000 −0.0219465
\(526\) 4545.00 7872.17i 0.376752 0.652553i
\(527\) −5550.00 + 9612.88i −0.458751 + 0.794580i
\(528\) −6390.00 −0.526684
\(529\) 6065.50 10505.8i 0.498521 0.863463i
\(530\) 8626.50 + 14941.5i 0.707002 + 1.22456i
\(531\) −2700.00 4676.54i −0.220659 0.382193i
\(532\) −92.0000 −0.00749757
\(533\) 10510.5 + 2600.67i 0.854147 + 0.211347i
\(534\) 4482.00 0.363212
\(535\) 3213.00 + 5565.08i 0.259645 + 0.449718i
\(536\) 9723.00 + 16840.7i 0.783525 + 1.35711i
\(537\) 711.000 1231.49i 0.0571358 0.0989621i
\(538\) −1602.00 −0.128378
\(539\) 5085.00 8807.48i 0.406357 0.703831i
\(540\) 121.500 210.444i 0.00968246 0.0167705i
\(541\) −4699.00 −0.373430 −0.186715 0.982414i \(-0.559784\pi\)
−0.186715 + 0.982414i \(0.559784\pi\)
\(542\) 5532.00 9581.71i 0.438413 0.759353i
\(543\) −3373.50 5843.07i −0.266613 0.461787i
\(544\) −2497.50 4325.80i −0.196837 0.340932i
\(545\) −18054.0 −1.41899
\(546\) −819.000 202.650i −0.0641941 0.0158839i
\(547\) 8270.00 0.646434 0.323217 0.946325i \(-0.395236\pi\)
0.323217 + 0.946325i \(0.395236\pi\)
\(548\) −358.500 620.940i −0.0279459 0.0484037i
\(549\) −1048.50 1816.06i −0.0815098 0.141179i
\(550\) 1980.00 3429.46i 0.153505 0.265878i
\(551\) 4830.00 0.373439
\(552\) −189.000 + 327.358i −0.0145731 + 0.0252414i
\(553\) 1324.00 2293.24i 0.101812 0.176344i
\(554\) 5595.00 0.429077
\(555\) 229.500 397.506i 0.0175527 0.0304021i
\(556\) 410.000 + 710.141i 0.0312732 + 0.0541667i
\(557\) 11392.5 + 19732.4i 0.866635 + 1.50106i 0.865414 + 0.501057i \(0.167055\pi\)
0.00122056 + 0.999999i \(0.499611\pi\)
\(558\) −2700.00 −0.204839
\(559\) −6682.00 23147.1i −0.505579 1.75138i
\(560\) 1278.00 0.0964381
\(561\) 4995.00 + 8651.59i 0.375916 + 0.651106i
\(562\) −4495.50 7786.43i −0.337422 0.584432i
\(563\) 5964.00 10330.0i 0.446452 0.773278i −0.551700 0.834043i \(-0.686021\pi\)
0.998152 + 0.0607647i \(0.0193539\pi\)
\(564\) −486.000 −0.0362842
\(565\) −5035.50 + 8721.74i −0.374947 + 0.649427i
\(566\) 6171.00 10688.5i 0.458280 0.793764i
\(567\) 162.000 0.0119989
\(568\) −9765.00 + 16913.5i −0.721356 + 1.24943i
\(569\) 3981.00 + 6895.29i 0.293308 + 0.508024i 0.974590 0.223997i \(-0.0719106\pi\)
−0.681282 + 0.732021i \(0.738577\pi\)
\(570\) −1863.00 3226.81i −0.136899 0.237116i
\(571\) 20618.0 1.51110 0.755549 0.655093i \(-0.227370\pi\)
0.755549 + 0.655093i \(0.227370\pi\)
\(572\) 975.000 1013.25i 0.0712706 0.0740666i
\(573\) 10332.0 0.753273
\(574\) 693.000 + 1200.31i 0.0503924 + 0.0872823i
\(575\) −132.000 228.631i −0.00957353 0.0165818i
\(576\) −1948.50 + 3374.90i −0.140951 + 0.244133i
\(577\) −3493.00 −0.252020 −0.126010 0.992029i \(-0.540217\pi\)
−0.126010 + 0.992029i \(0.540217\pi\)
\(578\) −11112.0 + 19246.5i −0.799651 + 1.38504i
\(579\) 6409.50 11101.6i 0.460051 0.796832i
\(580\) 945.000 0.0676534
\(581\) −810.000 + 1402.96i −0.0578390 + 0.100180i
\(582\) −6111.00 10584.6i −0.435239 0.753856i
\(583\) −9585.00 16601.7i −0.680909 1.17937i
\(584\) 5313.00 0.376461
\(585\) −1053.00 3647.70i −0.0744208 0.257801i
\(586\) −13995.0 −0.986567
\(587\) −5208.00 9020.52i −0.366196 0.634270i 0.622771 0.782404i \(-0.286007\pi\)
−0.988967 + 0.148134i \(0.952673\pi\)
\(588\) 508.500 + 880.748i 0.0356636 + 0.0617711i
\(589\) −2300.00 + 3983.72i −0.160900 + 0.278686i
\(590\) −16200.0 −1.13041
\(591\) 2979.00 5159.78i 0.207343 0.359129i
\(592\) 603.500 1045.29i 0.0418981 0.0725697i
\(593\) 2061.00 0.142724 0.0713618 0.997450i \(-0.477266\pi\)
0.0713618 + 0.997450i \(0.477266\pi\)
\(594\) −1215.00 + 2104.44i −0.0839260 + 0.145364i
\(595\) −999.000 1730.32i −0.0688319 0.119220i
\(596\) 874.500 + 1514.68i 0.0601022 + 0.104100i
\(597\) −7158.00 −0.490716
\(598\) −234.000 810.600i −0.0160016 0.0554313i
\(599\) 12456.0 0.849647 0.424823 0.905276i \(-0.360336\pi\)
0.424823 + 0.905276i \(0.360336\pi\)
\(600\) −1386.00 2400.62i −0.0943054 0.163342i
\(601\) 390.500 + 676.366i 0.0265039 + 0.0459061i 0.878973 0.476871i \(-0.158229\pi\)
−0.852469 + 0.522777i \(0.824896\pi\)
\(602\) 1542.00 2670.82i 0.104397 0.180822i
\(603\) 8334.00 0.562830
\(604\) 185.000 320.429i 0.0124628 0.0215862i
\(605\) −1939.50 + 3359.31i −0.130334 + 0.225745i
\(606\) −3213.00 −0.215378
\(607\) −9652.00 + 16717.8i −0.645408 + 1.11788i 0.338799 + 0.940859i \(0.389979\pi\)
−0.984207 + 0.177021i \(0.943354\pi\)
\(608\) −1035.00 1792.67i −0.0690375 0.119576i
\(609\) 315.000 + 545.596i 0.0209597 + 0.0363032i
\(610\) −6291.00 −0.417566
\(611\) −5265.00 + 5471.55i −0.348607 + 0.362283i
\(612\) −999.000 −0.0659840
\(613\) −6020.50 10427.8i −0.396681 0.687072i 0.596633 0.802514i \(-0.296505\pi\)
−0.993314 + 0.115442i \(0.963172\pi\)
\(614\) −2253.00 3902.31i −0.148084 0.256489i
\(615\) −3118.50 + 5401.40i −0.204472 + 0.354155i
\(616\) −1260.00 −0.0824137
\(617\) −4858.50 + 8415.17i −0.317011 + 0.549079i −0.979863 0.199671i \(-0.936013\pi\)
0.662852 + 0.748751i \(0.269346\pi\)
\(618\) −5031.00 + 8713.95i −0.327470 + 0.567195i
\(619\) −21040.0 −1.36619 −0.683093 0.730332i \(-0.739366\pi\)
−0.683093 + 0.730332i \(0.739366\pi\)
\(620\) −450.000 + 779.423i −0.0291491 + 0.0504877i
\(621\) 81.0000 + 140.296i 0.00523417 + 0.00906584i
\(622\) −3159.00 5471.55i −0.203640 0.352716i
\(623\) 996.000 0.0640512
\(624\) −2769.00 9592.10i −0.177642 0.615371i
\(625\) −8189.00 −0.524096
\(626\) 5847.00 + 10127.3i 0.373312 + 0.646595i
\(627\) 2070.00 + 3585.35i 0.131847 + 0.228365i
\(628\) 1305.50 2261.19i 0.0829540 0.143681i
\(629\) −1887.00 −0.119618
\(630\) 243.000 420.888i 0.0153672 0.0266168i
\(631\) 2534.00 4389.02i 0.159868 0.276900i −0.774953 0.632019i \(-0.782226\pi\)
0.934821 + 0.355119i \(0.115560\pi\)
\(632\) 27804.0 1.74997
\(633\) 2400.00 4156.92i 0.150697 0.261016i
\(634\) −14026.5 24294.6i −0.878649 1.52186i
\(635\) −2718.00 4707.71i −0.169859 0.294205i
\(636\) 1917.00 0.119519
\(637\) 15424.5 + 3816.57i 0.959405 + 0.237391i
\(638\) −9450.00 −0.586409
\(639\) 4185.00 + 7248.63i 0.259086 + 0.448750i
\(640\) 7465.50 + 12930.6i 0.461093 + 0.798637i
\(641\) −5092.50 + 8820.47i −0.313794 + 0.543506i −0.979180 0.202992i \(-0.934933\pi\)
0.665387 + 0.746499i \(0.268267\pi\)
\(642\) 6426.00 0.395037
\(643\) −12964.0 + 22454.3i −0.795101 + 1.37716i 0.127673 + 0.991816i \(0.459249\pi\)
−0.922775 + 0.385340i \(0.874084\pi\)
\(644\) 6.00000 10.3923i 0.000367132 0.000635892i
\(645\) 13878.0 0.847203
\(646\) −7659.00 + 13265.8i −0.466470 + 0.807949i
\(647\) −11580.0 20057.1i −0.703643 1.21874i −0.967179 0.254095i \(-0.918222\pi\)
0.263537 0.964649i \(-0.415111\pi\)
\(648\) 850.500 + 1473.11i 0.0515599 + 0.0893043i
\(649\) 18000.0 1.08869
\(650\) 6006.00 + 1486.10i 0.362423 + 0.0896763i
\(651\) −600.000 −0.0361227
\(652\) 818.000 + 1416.82i 0.0491340 + 0.0851025i
\(653\) −8313.00 14398.5i −0.498182 0.862876i 0.501816 0.864974i \(-0.332666\pi\)
−0.999998 + 0.00209801i \(0.999332\pi\)
\(654\) −9027.00 + 15635.2i −0.539730 + 0.934840i
\(655\) 14256.0 0.850424
\(656\) −8200.50 + 14203.7i −0.488073 + 0.845367i
\(657\) 1138.50 1971.94i 0.0676060 0.117097i
\(658\) −972.000 −0.0575874
\(659\) 7404.00 12824.1i 0.437661 0.758052i −0.559847 0.828596i \(-0.689140\pi\)
0.997509 + 0.0705440i \(0.0224735\pi\)
\(660\) 405.000 + 701.481i 0.0238858 + 0.0413714i
\(661\) −2426.50 4202.82i −0.142784 0.247308i 0.785760 0.618531i \(-0.212272\pi\)
−0.928544 + 0.371223i \(0.878939\pi\)
\(662\) −27516.0 −1.61547
\(663\) −10822.5 + 11247.1i −0.633953 + 0.658824i
\(664\) −17010.0 −0.994151
\(665\) −414.000 717.069i −0.0241417 0.0418147i
\(666\) −229.500 397.506i −0.0133528 0.0231277i
\(667\) −315.000 + 545.596i −0.0182861 + 0.0316725i
\(668\) 264.000 0.0152911
\(669\) 5748.00 9955.83i 0.332183 0.575358i
\(670\) 12501.0 21652.4i 0.720829 1.24851i
\(671\) 6990.00 0.402155
\(672\) 135.000 233.827i 0.00774961 0.0134227i
\(673\) 8082.50 + 13999.3i 0.462938 + 0.801833i 0.999106 0.0422789i \(-0.0134618\pi\)
−0.536168 + 0.844112i \(0.680128\pi\)
\(674\) 16633.5 + 28810.1i 0.950591 + 1.64647i
\(675\) −1188.00 −0.0677424
\(676\) 1943.50 + 1024.51i 0.110577 + 0.0582902i
\(677\) −25686.0 −1.45819 −0.729094 0.684414i \(-0.760058\pi\)
−0.729094 + 0.684414i \(0.760058\pi\)
\(678\) 5035.50 + 8721.74i 0.285232 + 0.494036i
\(679\) −1358.00 2352.12i −0.0767530 0.132940i
\(680\) 10489.5 18168.3i 0.591550 1.02459i
\(681\) −4194.00 −0.235998
\(682\) 4500.00 7794.23i 0.252660 0.437619i
\(683\) 9528.00 16503.0i 0.533790 0.924552i −0.465431 0.885084i \(-0.654100\pi\)
0.999221 0.0394675i \(-0.0125662\pi\)
\(684\) −414.000 −0.0231428
\(685\) 3226.50 5588.46i 0.179968 0.311714i
\(686\) 2046.00 + 3543.78i 0.113873 + 0.197233i
\(687\) −6699.00 11603.0i −0.372027 0.644370i
\(688\) 36494.0 2.02227
\(689\) 20767.5 21582.2i 1.14830 1.19335i
\(690\) 486.000 0.0268141
\(691\) 8195.00 + 14194.2i 0.451161 + 0.781434i 0.998458 0.0555040i \(-0.0176766\pi\)
−0.547297 + 0.836938i \(0.684343\pi\)
\(692\) −705.000 1221.10i −0.0387284 0.0670796i
\(693\) −270.000 + 467.654i −0.0148001 + 0.0256345i
\(694\) 29286.0 1.60185
\(695\) −3690.00 + 6391.27i −0.201395 + 0.348827i
\(696\) −3307.50 + 5728.76i −0.180130 + 0.311994i
\(697\) 25641.0 1.39343
\(698\) 12435.0 21538.1i 0.674315 1.16795i
\(699\) 2457.00 + 4255.65i 0.132950 + 0.230277i
\(700\) 44.0000 + 76.2102i 0.00237578 + 0.00411497i
\(701\) −27846.0 −1.50033 −0.750163 0.661253i \(-0.770025\pi\)
−0.750163 + 0.661253i \(0.770025\pi\)
\(702\) −3685.50 911.925i −0.198148 0.0490290i
\(703\) −782.000 −0.0419540
\(704\) −6495.00 11249.7i −0.347712 0.602256i
\(705\) −2187.00 3788.00i −0.116833 0.202360i
\(706\) −18607.5 + 32229.1i −0.991930 + 1.71807i
\(707\) −714.000 −0.0379812
\(708\) −900.000 + 1558.85i −0.0477741 + 0.0827472i
\(709\) 6141.50 10637.4i 0.325316 0.563463i −0.656260 0.754534i \(-0.727863\pi\)
0.981576 + 0.191071i \(0.0611961\pi\)
\(710\) 25110.0 1.32727
\(711\) 5958.00 10319.6i 0.314265 0.544323i
\(712\) 5229.00 + 9056.89i 0.275232 + 0.476716i
\(713\) −300.000 519.615i −0.0157575 0.0272928i
\(714\) −1998.00 −0.104724
\(715\) 12285.0 + 3039.75i 0.642564 + 0.158993i
\(716\) −474.000 −0.0247405
\(717\) 891.000 + 1543.26i 0.0464087 + 0.0803821i
\(718\) 1647.00 + 2852.69i 0.0856065 + 0.148275i
\(719\) −12756.0 + 22094.0i −0.661639 + 1.14599i 0.318546 + 0.947908i \(0.396806\pi\)
−0.980185 + 0.198085i \(0.936528\pi\)
\(720\) 5751.00 0.297677
\(721\) −1118.00 + 1936.43i −0.0577483 + 0.100023i
\(722\) 7114.50 12322.7i 0.366723 0.635184i
\(723\) 6909.00 0.355392
\(724\) −1124.50 + 1947.69i −0.0577234 + 0.0999798i
\(725\) −2310.00 4001.04i −0.118333 0.204958i
\(726\) 1939.50 + 3359.31i 0.0991482 + 0.171730i
\(727\) 6110.00 0.311702 0.155851 0.987781i \(-0.450188\pi\)
0.155851 + 0.987781i \(0.450188\pi\)
\(728\) −546.000 1891.40i −0.0277968 0.0962911i
\(729\) 729.000 0.0370370
\(730\) −3415.50 5915.82i −0.173169 0.299937i
\(731\) −28527.0 49410.2i −1.44338 2.50000i
\(732\) −349.500 + 605.352i −0.0176474 + 0.0305662i
\(733\) −27127.0 −1.36693 −0.683464 0.729984i \(-0.739527\pi\)
−0.683464 + 0.729984i \(0.739527\pi\)
\(734\) 8601.00 14897.4i 0.432519 0.749144i
\(735\) −4576.50 + 7926.73i −0.229669 + 0.397798i
\(736\) 270.000 0.0135222
\(737\) −13890.0 + 24058.2i −0.694226 + 1.20244i
\(738\) 3118.50 + 5401.40i 0.155547 + 0.269415i
\(739\) 440.000 + 762.102i 0.0219021 + 0.0379356i 0.876769 0.480912i \(-0.159694\pi\)
−0.854867 + 0.518848i \(0.826361\pi\)
\(740\) −153.000 −0.00760053
\(741\) −4485.00 + 4660.95i −0.222349 + 0.231072i
\(742\) 3834.00 0.189691
\(743\) 10938.0 + 18945.2i 0.540076 + 0.935439i 0.998899 + 0.0469111i \(0.0149378\pi\)
−0.458823 + 0.888528i \(0.651729\pi\)
\(744\) −3150.00 5455.96i −0.155221 0.268851i
\(745\) −7870.50 + 13632.1i −0.387051 + 0.670392i
\(746\) −26913.0 −1.32085
\(747\) −3645.00 + 6313.33i −0.178532 + 0.309227i
\(748\) 1665.00 2883.86i 0.0813883 0.140969i
\(749\) 1428.00 0.0696635
\(750\) −6844.50 + 11855.0i −0.333234 + 0.577179i
\(751\) −5899.00 10217.4i −0.286628 0.496454i 0.686375 0.727248i \(-0.259201\pi\)
−0.973003 + 0.230794i \(0.925868\pi\)
\(752\) −5751.00 9961.02i −0.278880 0.483033i
\(753\) 18972.0 0.918165
\(754\) −4095.00 14185.5i −0.197787 0.685153i
\(755\) 3330.00 0.160518
\(756\) −27.0000 46.7654i −0.00129892 0.00224979i
\(757\) 4037.00 + 6992.29i 0.193827 + 0.335719i 0.946515 0.322658i \(-0.104577\pi\)
−0.752688 + 0.658377i \(0.771243\pi\)
\(758\) −10866.0 + 18820.5i −0.520674 + 0.901834i
\(759\) −540.000 −0.0258245
\(760\) 4347.00 7529.22i 0.207477 0.359360i
\(761\) −9777.00 + 16934.3i −0.465724 + 0.806658i −0.999234 0.0391362i \(-0.987539\pi\)
0.533510 + 0.845794i \(0.320873\pi\)
\(762\) −5436.00 −0.258432
\(763\) −2006.00 + 3474.49i −0.0951797 + 0.164856i
\(764\) −1722.00 2982.59i −0.0815442 0.141239i
\(765\) −4495.50 7786.43i −0.212464 0.367999i
\(766\) −18936.0 −0.893193
\(767\) 7800.00 + 27020.0i 0.367199 + 1.27201i
\(768\) 4539.00 0.213264
\(769\) −7015.00 12150.3i −0.328956 0.569769i 0.653349 0.757057i \(-0.273364\pi\)
−0.982305 + 0.187288i \(0.940030\pi\)
\(770\) 810.000 + 1402.96i 0.0379096 + 0.0656613i
\(771\) −11749.5 + 20350.7i −0.548830 +