Properties

Label 147.4.e.f.79.1
Level $147$
Weight $4$
Character 147.79
Analytic conductor $8.673$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(8.67328077084\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 147.79
Dual form 147.4.e.f.67.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(1.50000 + 2.59808i) q^{3} +(3.50000 + 6.06218i) q^{4} +(-6.00000 + 10.3923i) q^{5} +3.00000 q^{6} +15.0000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(1.50000 + 2.59808i) q^{3} +(3.50000 + 6.06218i) q^{4} +(-6.00000 + 10.3923i) q^{5} +3.00000 q^{6} +15.0000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(6.00000 + 10.3923i) q^{10} +(-10.0000 - 17.3205i) q^{11} +(-10.5000 + 18.1865i) q^{12} -84.0000 q^{13} -36.0000 q^{15} +(-20.5000 + 35.5070i) q^{16} +(48.0000 + 83.1384i) q^{17} +(4.50000 + 7.79423i) q^{18} +(-6.00000 + 10.3923i) q^{19} -84.0000 q^{20} -20.0000 q^{22} +(88.0000 - 152.420i) q^{23} +(22.5000 + 38.9711i) q^{24} +(-9.50000 - 16.4545i) q^{25} +(-42.0000 + 72.7461i) q^{26} -27.0000 q^{27} +58.0000 q^{29} +(-18.0000 + 31.1769i) q^{30} +(132.000 + 228.631i) q^{31} +(80.5000 + 139.430i) q^{32} +(30.0000 - 51.9615i) q^{33} +96.0000 q^{34} -63.0000 q^{36} +(-129.000 + 223.435i) q^{37} +(6.00000 + 10.3923i) q^{38} +(-126.000 - 218.238i) q^{39} +(-90.0000 + 155.885i) q^{40} +156.000 q^{43} +(70.0000 - 121.244i) q^{44} +(-54.0000 - 93.5307i) q^{45} +(-88.0000 - 152.420i) q^{46} +(204.000 - 353.338i) q^{47} -123.000 q^{48} -19.0000 q^{50} +(-144.000 + 249.415i) q^{51} +(-294.000 - 509.223i) q^{52} +(361.000 + 625.270i) q^{53} +(-13.5000 + 23.3827i) q^{54} +240.000 q^{55} -36.0000 q^{57} +(29.0000 - 50.2295i) q^{58} +(-246.000 - 426.084i) q^{59} +(-126.000 - 218.238i) q^{60} +(246.000 - 426.084i) q^{61} +264.000 q^{62} -167.000 q^{64} +(504.000 - 872.954i) q^{65} +(-30.0000 - 51.9615i) q^{66} +(-206.000 - 356.802i) q^{67} +(-336.000 + 581.969i) q^{68} +528.000 q^{69} +296.000 q^{71} +(-67.5000 + 116.913i) q^{72} +(-120.000 - 207.846i) q^{73} +(129.000 + 223.435i) q^{74} +(28.5000 - 49.3634i) q^{75} -84.0000 q^{76} -252.000 q^{78} +(-388.000 + 672.036i) q^{79} +(-246.000 - 426.084i) q^{80} +(-40.5000 - 70.1481i) q^{81} +924.000 q^{83} -1152.00 q^{85} +(78.0000 - 135.100i) q^{86} +(87.0000 + 150.688i) q^{87} +(-150.000 - 259.808i) q^{88} +(372.000 - 644.323i) q^{89} -108.000 q^{90} +1232.00 q^{92} +(-396.000 + 685.892i) q^{93} +(-204.000 - 353.338i) q^{94} +(-72.0000 - 124.708i) q^{95} +(-241.500 + 418.290i) q^{96} -168.000 q^{97} +180.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} + 3 q^{3} + 7 q^{4} - 12 q^{5} + 6 q^{6} + 30 q^{8} - 9 q^{9} + O(q^{10}) \) \( 2 q + q^{2} + 3 q^{3} + 7 q^{4} - 12 q^{5} + 6 q^{6} + 30 q^{8} - 9 q^{9} + 12 q^{10} - 20 q^{11} - 21 q^{12} - 168 q^{13} - 72 q^{15} - 41 q^{16} + 96 q^{17} + 9 q^{18} - 12 q^{19} - 168 q^{20} - 40 q^{22} + 176 q^{23} + 45 q^{24} - 19 q^{25} - 84 q^{26} - 54 q^{27} + 116 q^{29} - 36 q^{30} + 264 q^{31} + 161 q^{32} + 60 q^{33} + 192 q^{34} - 126 q^{36} - 258 q^{37} + 12 q^{38} - 252 q^{39} - 180 q^{40} + 312 q^{43} + 140 q^{44} - 108 q^{45} - 176 q^{46} + 408 q^{47} - 246 q^{48} - 38 q^{50} - 288 q^{51} - 588 q^{52} + 722 q^{53} - 27 q^{54} + 480 q^{55} - 72 q^{57} + 58 q^{58} - 492 q^{59} - 252 q^{60} + 492 q^{61} + 528 q^{62} - 334 q^{64} + 1008 q^{65} - 60 q^{66} - 412 q^{67} - 672 q^{68} + 1056 q^{69} + 592 q^{71} - 135 q^{72} - 240 q^{73} + 258 q^{74} + 57 q^{75} - 168 q^{76} - 504 q^{78} - 776 q^{79} - 492 q^{80} - 81 q^{81} + 1848 q^{83} - 2304 q^{85} + 156 q^{86} + 174 q^{87} - 300 q^{88} + 744 q^{89} - 216 q^{90} + 2464 q^{92} - 792 q^{93} - 408 q^{94} - 144 q^{95} - 483 q^{96} - 336 q^{97} + 360 q^{99} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.176777 0.306186i −0.763998 0.645219i \(-0.776766\pi\)
0.940775 + 0.339032i \(0.110100\pi\)
\(3\) 1.50000 + 2.59808i 0.288675 + 0.500000i
\(4\) 3.50000 + 6.06218i 0.437500 + 0.757772i
\(5\) −6.00000 + 10.3923i −0.536656 + 0.929516i 0.462425 + 0.886658i \(0.346979\pi\)
−0.999081 + 0.0428575i \(0.986354\pi\)
\(6\) 3.00000 0.204124
\(7\) 0 0
\(8\) 15.0000 0.662913
\(9\) −4.50000 + 7.79423i −0.166667 + 0.288675i
\(10\) 6.00000 + 10.3923i 0.189737 + 0.328634i
\(11\) −10.0000 17.3205i −0.274101 0.474757i 0.695807 0.718229i \(-0.255047\pi\)
−0.969908 + 0.243472i \(0.921714\pi\)
\(12\) −10.5000 + 18.1865i −0.252591 + 0.437500i
\(13\) −84.0000 −1.79211 −0.896054 0.443945i \(-0.853579\pi\)
−0.896054 + 0.443945i \(0.853579\pi\)
\(14\) 0 0
\(15\) −36.0000 −0.619677
\(16\) −20.5000 + 35.5070i −0.320312 + 0.554798i
\(17\) 48.0000 + 83.1384i 0.684806 + 1.18612i 0.973498 + 0.228697i \(0.0734466\pi\)
−0.288691 + 0.957422i \(0.593220\pi\)
\(18\) 4.50000 + 7.79423i 0.0589256 + 0.102062i
\(19\) −6.00000 + 10.3923i −0.0724471 + 0.125482i −0.899973 0.435945i \(-0.856414\pi\)
0.827526 + 0.561427i \(0.189748\pi\)
\(20\) −84.0000 −0.939149
\(21\) 0 0
\(22\) −20.0000 −0.193819
\(23\) 88.0000 152.420i 0.797794 1.38182i −0.123255 0.992375i \(-0.539333\pi\)
0.921050 0.389445i \(-0.127333\pi\)
\(24\) 22.5000 + 38.9711i 0.191366 + 0.331456i
\(25\) −9.50000 16.4545i −0.0760000 0.131636i
\(26\) −42.0000 + 72.7461i −0.316803 + 0.548719i
\(27\) −27.0000 −0.192450
\(28\) 0 0
\(29\) 58.0000 0.371391 0.185695 0.982607i \(-0.440546\pi\)
0.185695 + 0.982607i \(0.440546\pi\)
\(30\) −18.0000 + 31.1769i −0.109545 + 0.189737i
\(31\) 132.000 + 228.631i 0.764771 + 1.32462i 0.940368 + 0.340160i \(0.110481\pi\)
−0.175597 + 0.984462i \(0.556185\pi\)
\(32\) 80.5000 + 139.430i 0.444704 + 0.770250i
\(33\) 30.0000 51.9615i 0.158252 0.274101i
\(34\) 96.0000 0.484231
\(35\) 0 0
\(36\) −63.0000 −0.291667
\(37\) −129.000 + 223.435i −0.573175 + 0.992768i 0.423062 + 0.906101i \(0.360955\pi\)
−0.996237 + 0.0866674i \(0.972378\pi\)
\(38\) 6.00000 + 10.3923i 0.0256139 + 0.0443646i
\(39\) −126.000 218.238i −0.517337 0.896054i
\(40\) −90.0000 + 155.885i −0.355756 + 0.616188i
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) 156.000 0.553251 0.276625 0.960978i \(-0.410784\pi\)
0.276625 + 0.960978i \(0.410784\pi\)
\(44\) 70.0000 121.244i 0.239839 0.415413i
\(45\) −54.0000 93.5307i −0.178885 0.309839i
\(46\) −88.0000 152.420i −0.282063 0.488547i
\(47\) 204.000 353.338i 0.633116 1.09659i −0.353795 0.935323i \(-0.615109\pi\)
0.986911 0.161266i \(-0.0515578\pi\)
\(48\) −123.000 −0.369865
\(49\) 0 0
\(50\) −19.0000 −0.0537401
\(51\) −144.000 + 249.415i −0.395373 + 0.684806i
\(52\) −294.000 509.223i −0.784047 1.35801i
\(53\) 361.000 + 625.270i 0.935607 + 1.62052i 0.773548 + 0.633737i \(0.218480\pi\)
0.162059 + 0.986781i \(0.448187\pi\)
\(54\) −13.5000 + 23.3827i −0.0340207 + 0.0589256i
\(55\) 240.000 0.588393
\(56\) 0 0
\(57\) −36.0000 −0.0836547
\(58\) 29.0000 50.2295i 0.0656532 0.113715i
\(59\) −246.000 426.084i −0.542822 0.940195i −0.998741 0.0501732i \(-0.984023\pi\)
0.455919 0.890021i \(-0.349311\pi\)
\(60\) −126.000 218.238i −0.271109 0.469574i
\(61\) 246.000 426.084i 0.516345 0.894337i −0.483474 0.875358i \(-0.660625\pi\)
0.999820 0.0189781i \(-0.00604127\pi\)
\(62\) 264.000 0.540775
\(63\) 0 0
\(64\) −167.000 −0.326172
\(65\) 504.000 872.954i 0.961746 1.66579i
\(66\) −30.0000 51.9615i −0.0559507 0.0969094i
\(67\) −206.000 356.802i −0.375625 0.650602i 0.614795 0.788687i \(-0.289239\pi\)
−0.990420 + 0.138085i \(0.955905\pi\)
\(68\) −336.000 + 581.969i −0.599206 + 1.03785i
\(69\) 528.000 0.921213
\(70\) 0 0
\(71\) 296.000 0.494771 0.247385 0.968917i \(-0.420429\pi\)
0.247385 + 0.968917i \(0.420429\pi\)
\(72\) −67.5000 + 116.913i −0.110485 + 0.191366i
\(73\) −120.000 207.846i −0.192396 0.333240i 0.753647 0.657279i \(-0.228293\pi\)
−0.946044 + 0.324038i \(0.894959\pi\)
\(74\) 129.000 + 223.435i 0.202648 + 0.350996i
\(75\) 28.5000 49.3634i 0.0438786 0.0760000i
\(76\) −84.0000 −0.126782
\(77\) 0 0
\(78\) −252.000 −0.365813
\(79\) −388.000 + 672.036i −0.552575 + 0.957088i 0.445513 + 0.895275i \(0.353021\pi\)
−0.998088 + 0.0618122i \(0.980312\pi\)
\(80\) −246.000 426.084i −0.343795 0.595471i
\(81\) −40.5000 70.1481i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) 924.000 1.22195 0.610977 0.791648i \(-0.290777\pi\)
0.610977 + 0.791648i \(0.290777\pi\)
\(84\) 0 0
\(85\) −1152.00 −1.47002
\(86\) 78.0000 135.100i 0.0978018 0.169398i
\(87\) 87.0000 + 150.688i 0.107211 + 0.185695i
\(88\) −150.000 259.808i −0.181705 0.314723i
\(89\) 372.000 644.323i 0.443055 0.767394i −0.554859 0.831944i \(-0.687228\pi\)
0.997914 + 0.0645500i \(0.0205612\pi\)
\(90\) −108.000 −0.126491
\(91\) 0 0
\(92\) 1232.00 1.39614
\(93\) −396.000 + 685.892i −0.441541 + 0.764771i
\(94\) −204.000 353.338i −0.223840 0.387703i
\(95\) −72.0000 124.708i −0.0777584 0.134681i
\(96\) −241.500 + 418.290i −0.256750 + 0.444704i
\(97\) −168.000 −0.175854 −0.0879269 0.996127i \(-0.528024\pi\)
−0.0879269 + 0.996127i \(0.528024\pi\)
\(98\) 0 0
\(99\) 180.000 0.182734
\(100\) 66.5000 115.181i 0.0665000 0.115181i
\(101\) 762.000 + 1319.82i 0.750711 + 1.30027i 0.947478 + 0.319820i \(0.103622\pi\)
−0.196767 + 0.980450i \(0.563044\pi\)
\(102\) 144.000 + 249.415i 0.139786 + 0.242116i
\(103\) 204.000 353.338i 0.195153 0.338014i −0.751798 0.659394i \(-0.770813\pi\)
0.946951 + 0.321379i \(0.104146\pi\)
\(104\) −1260.00 −1.18801
\(105\) 0 0
\(106\) 722.000 0.661574
\(107\) 410.000 710.141i 0.370432 0.641607i −0.619200 0.785233i \(-0.712543\pi\)
0.989632 + 0.143627i \(0.0458764\pi\)
\(108\) −94.5000 163.679i −0.0841969 0.145833i
\(109\) 459.000 + 795.011i 0.403342 + 0.698608i 0.994127 0.108221i \(-0.0345153\pi\)
−0.590785 + 0.806829i \(0.701182\pi\)
\(110\) 120.000 207.846i 0.104014 0.180158i
\(111\) −774.000 −0.661845
\(112\) 0 0
\(113\) −110.000 −0.0915746 −0.0457873 0.998951i \(-0.514580\pi\)
−0.0457873 + 0.998951i \(0.514580\pi\)
\(114\) −18.0000 + 31.1769i −0.0147882 + 0.0256139i
\(115\) 1056.00 + 1829.05i 0.856283 + 1.48313i
\(116\) 203.000 + 351.606i 0.162483 + 0.281430i
\(117\) 378.000 654.715i 0.298685 0.517337i
\(118\) −492.000 −0.383833
\(119\) 0 0
\(120\) −540.000 −0.410792
\(121\) 465.500 806.270i 0.349737 0.605762i
\(122\) −246.000 426.084i −0.182556 0.316196i
\(123\) 0 0
\(124\) −924.000 + 1600.41i −0.669175 + 1.15904i
\(125\) −1272.00 −0.910169
\(126\) 0 0
\(127\) 16.0000 0.0111793 0.00558965 0.999984i \(-0.498221\pi\)
0.00558965 + 0.999984i \(0.498221\pi\)
\(128\) −727.500 + 1260.07i −0.502363 + 0.870119i
\(129\) 234.000 + 405.300i 0.159710 + 0.276625i
\(130\) −504.000 872.954i −0.340029 0.588947i
\(131\) −846.000 + 1465.31i −0.564239 + 0.977291i 0.432881 + 0.901451i \(0.357497\pi\)
−0.997120 + 0.0758401i \(0.975836\pi\)
\(132\) 420.000 0.276942
\(133\) 0 0
\(134\) −412.000 −0.265607
\(135\) 162.000 280.592i 0.103280 0.178885i
\(136\) 720.000 + 1247.08i 0.453967 + 0.786294i
\(137\) −563.000 975.145i −0.351097 0.608118i 0.635345 0.772229i \(-0.280858\pi\)
−0.986442 + 0.164110i \(0.947525\pi\)
\(138\) 264.000 457.261i 0.162849 0.282063i
\(139\) 1092.00 0.666347 0.333173 0.942866i \(-0.391881\pi\)
0.333173 + 0.942866i \(0.391881\pi\)
\(140\) 0 0
\(141\) 1224.00 0.731060
\(142\) 148.000 256.344i 0.0874640 0.151492i
\(143\) 840.000 + 1454.92i 0.491219 + 0.850816i
\(144\) −184.500 319.563i −0.106771 0.184933i
\(145\) −348.000 + 602.754i −0.199309 + 0.345214i
\(146\) −240.000 −0.136045
\(147\) 0 0
\(148\) −1806.00 −1.00306
\(149\) −535.000 + 926.647i −0.294154 + 0.509489i −0.974788 0.223134i \(-0.928371\pi\)
0.680634 + 0.732624i \(0.261704\pi\)
\(150\) −28.5000 49.3634i −0.0155134 0.0268701i
\(151\) 60.0000 + 103.923i 0.0323360 + 0.0560075i 0.881741 0.471735i \(-0.156372\pi\)
−0.849405 + 0.527742i \(0.823039\pi\)
\(152\) −90.0000 + 155.885i −0.0480261 + 0.0831836i
\(153\) −864.000 −0.456538
\(154\) 0 0
\(155\) −3168.00 −1.64168
\(156\) 882.000 1527.67i 0.452670 0.784047i
\(157\) −918.000 1590.02i −0.466652 0.808265i 0.532622 0.846353i \(-0.321207\pi\)
−0.999274 + 0.0380879i \(0.987873\pi\)
\(158\) 388.000 + 672.036i 0.195365 + 0.338382i
\(159\) −1083.00 + 1875.81i −0.540173 + 0.935607i
\(160\) −1932.00 −0.954613
\(161\) 0 0
\(162\) −81.0000 −0.0392837
\(163\) −458.000 + 793.279i −0.220082 + 0.381193i −0.954833 0.297144i \(-0.903966\pi\)
0.734751 + 0.678337i \(0.237299\pi\)
\(164\) 0 0
\(165\) 360.000 + 623.538i 0.169854 + 0.294196i
\(166\) 462.000 800.207i 0.216013 0.374145i
\(167\) 504.000 0.233537 0.116769 0.993159i \(-0.462746\pi\)
0.116769 + 0.993159i \(0.462746\pi\)
\(168\) 0 0
\(169\) 4859.00 2.21165
\(170\) −576.000 + 997.661i −0.259866 + 0.450101i
\(171\) −54.0000 93.5307i −0.0241490 0.0418273i
\(172\) 546.000 + 945.700i 0.242047 + 0.419238i
\(173\) 918.000 1590.02i 0.403435 0.698770i −0.590703 0.806889i \(-0.701149\pi\)
0.994138 + 0.108119i \(0.0344828\pi\)
\(174\) 174.000 0.0758098
\(175\) 0 0
\(176\) 820.000 0.351192
\(177\) 738.000 1278.25i 0.313398 0.542822i
\(178\) −372.000 644.323i −0.156644 0.271315i
\(179\) −1186.00 2054.21i −0.495228 0.857760i 0.504757 0.863262i \(-0.331582\pi\)
−0.999985 + 0.00550156i \(0.998249\pi\)
\(180\) 378.000 654.715i 0.156525 0.271109i
\(181\) −1092.00 −0.448440 −0.224220 0.974539i \(-0.571983\pi\)
−0.224220 + 0.974539i \(0.571983\pi\)
\(182\) 0 0
\(183\) 1476.00 0.596224
\(184\) 1320.00 2286.31i 0.528868 0.916026i
\(185\) −1548.00 2681.21i −0.615196 1.06555i
\(186\) 396.000 + 685.892i 0.156108 + 0.270387i
\(187\) 960.000 1662.77i 0.375413 0.650234i
\(188\) 2856.00 1.10795
\(189\) 0 0
\(190\) −144.000 −0.0549835
\(191\) −1256.00 + 2175.46i −0.475817 + 0.824139i −0.999616 0.0277030i \(-0.991181\pi\)
0.523800 + 0.851842i \(0.324514\pi\)
\(192\) −250.500 433.879i −0.0941577 0.163086i
\(193\) 1215.00 + 2104.44i 0.453148 + 0.784876i 0.998580 0.0532797i \(-0.0169675\pi\)
−0.545431 + 0.838155i \(0.683634\pi\)
\(194\) −84.0000 + 145.492i −0.0310868 + 0.0538440i
\(195\) 3024.00 1.11053
\(196\) 0 0
\(197\) −1762.00 −0.637245 −0.318623 0.947882i \(-0.603220\pi\)
−0.318623 + 0.947882i \(0.603220\pi\)
\(198\) 90.0000 155.885i 0.0323031 0.0559507i
\(199\) −1548.00 2681.21i −0.551431 0.955107i −0.998172 0.0604433i \(-0.980749\pi\)
0.446740 0.894664i \(-0.352585\pi\)
\(200\) −142.500 246.817i −0.0503814 0.0872631i
\(201\) 618.000 1070.41i 0.216867 0.375625i
\(202\) 1524.00 0.530833
\(203\) 0 0
\(204\) −2016.00 −0.691903
\(205\) 0 0
\(206\) −204.000 353.338i −0.0689969 0.119506i
\(207\) 792.000 + 1371.78i 0.265931 + 0.460607i
\(208\) 1722.00 2982.59i 0.574035 0.994257i
\(209\) 240.000 0.0794313
\(210\) 0 0
\(211\) 156.000 0.0508980 0.0254490 0.999676i \(-0.491898\pi\)
0.0254490 + 0.999676i \(0.491898\pi\)
\(212\) −2527.00 + 4376.89i −0.818656 + 1.41795i
\(213\) 444.000 + 769.031i 0.142828 + 0.247385i
\(214\) −410.000 710.141i −0.130967 0.226842i
\(215\) −936.000 + 1621.20i −0.296905 + 0.514255i
\(216\) −405.000 −0.127578
\(217\) 0 0
\(218\) 918.000 0.285206
\(219\) 360.000 623.538i 0.111080 0.192396i
\(220\) 840.000 + 1454.92i 0.257422 + 0.445868i
\(221\) −4032.00 6983.63i −1.22725 2.12565i
\(222\) −387.000 + 670.304i −0.116999 + 0.202648i
\(223\) 5040.00 1.51347 0.756734 0.653723i \(-0.226794\pi\)
0.756734 + 0.653723i \(0.226794\pi\)
\(224\) 0 0
\(225\) 171.000 0.0506667
\(226\) −55.0000 + 95.2628i −0.0161883 + 0.0280389i
\(227\) −1086.00 1881.01i −0.317535 0.549986i 0.662438 0.749116i \(-0.269522\pi\)
−0.979973 + 0.199130i \(0.936188\pi\)
\(228\) −126.000 218.238i −0.0365989 0.0633912i
\(229\) −1350.00 + 2338.27i −0.389566 + 0.674747i −0.992391 0.123126i \(-0.960708\pi\)
0.602826 + 0.797873i \(0.294041\pi\)
\(230\) 2112.00 0.605483
\(231\) 0 0
\(232\) 870.000 0.246200
\(233\) 1901.00 3292.63i 0.534501 0.925782i −0.464687 0.885475i \(-0.653833\pi\)
0.999187 0.0403071i \(-0.0128336\pi\)
\(234\) −378.000 654.715i −0.105601 0.182906i
\(235\) 2448.00 + 4240.06i 0.679532 + 1.17698i
\(236\) 1722.00 2982.59i 0.474969 0.822670i
\(237\) −2328.00 −0.638058
\(238\) 0 0
\(239\) −4408.00 −1.19301 −0.596506 0.802609i \(-0.703445\pi\)
−0.596506 + 0.802609i \(0.703445\pi\)
\(240\) 738.000 1278.25i 0.198490 0.343795i
\(241\) −1548.00 2681.21i −0.413757 0.716648i 0.581540 0.813518i \(-0.302450\pi\)
−0.995297 + 0.0968696i \(0.969117\pi\)
\(242\) −465.500 806.270i −0.123651 0.214169i
\(243\) 121.500 210.444i 0.0320750 0.0555556i
\(244\) 3444.00 0.903605
\(245\) 0 0
\(246\) 0 0
\(247\) 504.000 872.954i 0.129833 0.224877i
\(248\) 1980.00 + 3429.46i 0.506976 + 0.878109i
\(249\) 1386.00 + 2400.62i 0.352748 + 0.610977i
\(250\) −636.000 + 1101.58i −0.160897 + 0.278681i
\(251\) −924.000 −0.232360 −0.116180 0.993228i \(-0.537065\pi\)
−0.116180 + 0.993228i \(0.537065\pi\)
\(252\) 0 0
\(253\) −3520.00 −0.874706
\(254\) 8.00000 13.8564i 0.00197624 0.00342295i
\(255\) −1728.00 2992.98i −0.424359 0.735011i
\(256\) 59.5000 + 103.057i 0.0145264 + 0.0251604i
\(257\) 1380.00 2390.23i 0.334950 0.580150i −0.648526 0.761193i \(-0.724614\pi\)
0.983475 + 0.181043i \(0.0579474\pi\)
\(258\) 468.000 0.112932
\(259\) 0 0
\(260\) 7056.00 1.68306
\(261\) −261.000 + 452.065i −0.0618984 + 0.107211i
\(262\) 846.000 + 1465.31i 0.199489 + 0.345525i
\(263\) 1180.00 + 2043.82i 0.276661 + 0.479191i 0.970553 0.240888i \(-0.0774387\pi\)
−0.693892 + 0.720079i \(0.744105\pi\)
\(264\) 450.000 779.423i 0.104908 0.181705i
\(265\) −8664.00 −2.00840
\(266\) 0 0
\(267\) 2232.00 0.511596
\(268\) 1442.00 2497.62i 0.328672 0.569277i
\(269\) −2010.00 3481.42i −0.455583 0.789093i 0.543138 0.839643i \(-0.317236\pi\)
−0.998722 + 0.0505501i \(0.983903\pi\)
\(270\) −162.000 280.592i −0.0365148 0.0632456i
\(271\) −2400.00 + 4156.92i −0.537969 + 0.931790i 0.461044 + 0.887377i \(0.347475\pi\)
−0.999013 + 0.0444126i \(0.985858\pi\)
\(272\) −3936.00 −0.877408
\(273\) 0 0
\(274\) −1126.00 −0.248263
\(275\) −190.000 + 329.090i −0.0416634 + 0.0721631i
\(276\) 1848.00 + 3200.83i 0.403031 + 0.698070i
\(277\) −3223.00 5582.40i −0.699102 1.21088i −0.968778 0.247929i \(-0.920250\pi\)
0.269676 0.962951i \(-0.413083\pi\)
\(278\) 546.000 945.700i 0.117795 0.204026i
\(279\) −2376.00 −0.509847
\(280\) 0 0
\(281\) −2602.00 −0.552393 −0.276196 0.961101i \(-0.589074\pi\)
−0.276196 + 0.961101i \(0.589074\pi\)
\(282\) 612.000 1060.02i 0.129234 0.223840i
\(283\) 3450.00 + 5975.58i 0.724669 + 1.25516i 0.959110 + 0.283033i \(0.0913405\pi\)
−0.234442 + 0.972130i \(0.575326\pi\)
\(284\) 1036.00 + 1794.40i 0.216462 + 0.374924i
\(285\) 216.000 374.123i 0.0448938 0.0777584i
\(286\) 1680.00 0.347344
\(287\) 0 0
\(288\) −1449.00 −0.296469
\(289\) −2151.50 + 3726.51i −0.437920 + 0.758499i
\(290\) 348.000 + 602.754i 0.0704664 + 0.122051i
\(291\) −252.000 436.477i −0.0507646 0.0879269i
\(292\) 840.000 1454.92i 0.168347 0.291585i
\(293\) −4452.00 −0.887674 −0.443837 0.896107i \(-0.646383\pi\)
−0.443837 + 0.896107i \(0.646383\pi\)
\(294\) 0 0
\(295\) 5904.00 1.16523
\(296\) −1935.00 + 3351.52i −0.379965 + 0.658118i
\(297\) 270.000 + 467.654i 0.0527508 + 0.0913671i
\(298\) 535.000 + 926.647i 0.103999 + 0.180132i
\(299\) −7392.00 + 12803.3i −1.42973 + 2.47637i
\(300\) 399.000 0.0767876
\(301\) 0 0
\(302\) 120.000 0.0228650
\(303\) −2286.00 + 3959.47i −0.433423 + 0.750711i
\(304\) −246.000 426.084i −0.0464114 0.0803869i
\(305\) 2952.00 + 5113.01i 0.554200 + 0.959903i
\(306\) −432.000 + 748.246i −0.0807052 + 0.139786i
\(307\) −2436.00 −0.452866 −0.226433 0.974027i \(-0.572706\pi\)
−0.226433 + 0.974027i \(0.572706\pi\)
\(308\) 0 0
\(309\) 1224.00 0.225343
\(310\) −1584.00 + 2743.57i −0.290210 + 0.502659i
\(311\) 3744.00 + 6484.80i 0.682646 + 1.18238i 0.974171 + 0.225814i \(0.0725040\pi\)
−0.291525 + 0.956563i \(0.594163\pi\)
\(312\) −1890.00 3273.58i −0.342949 0.594006i
\(313\) 876.000 1517.28i 0.158193 0.273999i −0.776024 0.630703i \(-0.782766\pi\)
0.934217 + 0.356705i \(0.116100\pi\)
\(314\) −1836.00 −0.329973
\(315\) 0 0
\(316\) −5432.00 −0.967006
\(317\) 781.000 1352.73i 0.138376 0.239675i −0.788506 0.615027i \(-0.789145\pi\)
0.926882 + 0.375352i \(0.122478\pi\)
\(318\) 1083.00 + 1875.81i 0.190980 + 0.330787i
\(319\) −580.000 1004.59i −0.101799 0.176320i
\(320\) 1002.00 1735.51i 0.175042 0.303182i
\(321\) 2460.00 0.427738
\(322\) 0 0
\(323\) −1152.00 −0.198449
\(324\) 283.500 491.036i 0.0486111 0.0841969i
\(325\) 798.000 + 1382.18i 0.136200 + 0.235906i
\(326\) 458.000 + 793.279i 0.0778107 + 0.134772i
\(327\) −1377.00 + 2385.03i −0.232869 + 0.403342i
\(328\) 0 0
\(329\) 0 0
\(330\) 720.000 0.120105
\(331\) 3546.00 6141.85i 0.588839 1.01990i −0.405546 0.914075i \(-0.632918\pi\)
0.994385 0.105825i \(-0.0337482\pi\)
\(332\) 3234.00 + 5601.45i 0.534605 + 0.925963i
\(333\) −1161.00 2010.91i −0.191058 0.330923i
\(334\) 252.000 436.477i 0.0412839 0.0715058i
\(335\) 4944.00 0.806327
\(336\) 0 0
\(337\) 366.000 0.0591611 0.0295805 0.999562i \(-0.490583\pi\)
0.0295805 + 0.999562i \(0.490583\pi\)
\(338\) 2429.50 4208.02i 0.390969 0.677177i
\(339\) −165.000 285.788i −0.0264353 0.0457873i
\(340\) −4032.00 6983.63i −0.643135 1.11394i
\(341\) 2640.00 4572.61i 0.419249 0.726161i
\(342\) −108.000 −0.0170759
\(343\) 0 0
\(344\) 2340.00 0.366757
\(345\) −3168.00 + 5487.14i −0.494375 + 0.856283i
\(346\) −918.000 1590.02i −0.142636 0.247052i
\(347\) 3182.00 + 5511.39i 0.492273 + 0.852642i 0.999960 0.00889958i \(-0.00283286\pi\)
−0.507687 + 0.861541i \(0.669500\pi\)
\(348\) −609.000 + 1054.82i −0.0938098 + 0.162483i
\(349\) −10500.0 −1.61046 −0.805232 0.592960i \(-0.797959\pi\)
−0.805232 + 0.592960i \(0.797959\pi\)
\(350\) 0 0
\(351\) 2268.00 0.344891
\(352\) 1610.00 2788.60i 0.243788 0.422253i
\(353\) −204.000 353.338i −0.0307587 0.0532756i 0.850236 0.526401i \(-0.176459\pi\)
−0.880995 + 0.473126i \(0.843126\pi\)
\(354\) −738.000 1278.25i −0.110803 0.191916i
\(355\) −1776.00 + 3076.12i −0.265522 + 0.459898i
\(356\) 5208.00 0.775347
\(357\) 0 0
\(358\) −2372.00 −0.350179
\(359\) 5968.00 10336.9i 0.877379 1.51966i 0.0231719 0.999731i \(-0.492624\pi\)
0.854207 0.519933i \(-0.174043\pi\)
\(360\) −810.000 1402.96i −0.118585 0.205396i
\(361\) 3357.50 + 5815.36i 0.489503 + 0.847844i
\(362\) −546.000 + 945.700i −0.0792738 + 0.137306i
\(363\) 2793.00 0.403842
\(364\) 0 0
\(365\) 2880.00 0.413003
\(366\) 738.000 1278.25i 0.105399 0.182556i
\(367\) 1224.00 + 2120.03i 0.174093 + 0.301539i 0.939847 0.341595i \(-0.110967\pi\)
−0.765754 + 0.643134i \(0.777634\pi\)
\(368\) 3608.00 + 6249.24i 0.511087 + 0.885229i
\(369\) 0 0
\(370\) −3096.00 −0.435009
\(371\) 0 0
\(372\) −5544.00 −0.772696
\(373\) −5687.00 + 9850.17i −0.789442 + 1.36735i 0.136868 + 0.990589i \(0.456296\pi\)
−0.926309 + 0.376764i \(0.877037\pi\)
\(374\) −960.000 1662.77i −0.132728 0.229892i
\(375\) −1908.00 3304.75i −0.262743 0.455085i
\(376\) 3060.00 5300.08i 0.419701 0.726943i
\(377\) −4872.00 −0.665572
\(378\) 0 0
\(379\) −5892.00 −0.798553 −0.399277 0.916830i \(-0.630739\pi\)
−0.399277 + 0.916830i \(0.630739\pi\)
\(380\) 504.000 872.954i 0.0680386 0.117846i
\(381\) 24.0000 + 41.5692i 0.00322718 + 0.00558965i
\(382\) 1256.00 + 2175.46i 0.168227 + 0.291377i
\(383\) 5244.00 9082.87i 0.699624 1.21178i −0.268973 0.963148i \(-0.586684\pi\)
0.968597 0.248636i \(-0.0799823\pi\)
\(384\) −4365.00 −0.580079
\(385\) 0 0
\(386\) 2430.00 0.320424
\(387\) −702.000 + 1215.90i −0.0922084 + 0.159710i
\(388\) −588.000 1018.45i −0.0769360 0.133257i
\(389\) −2257.00 3909.24i −0.294176 0.509528i 0.680617 0.732639i \(-0.261712\pi\)
−0.974793 + 0.223112i \(0.928379\pi\)
\(390\) 1512.00 2618.86i 0.196316 0.340029i
\(391\) 16896.0 2.18534
\(392\) 0 0
\(393\) −5076.00 −0.651528
\(394\) −881.000 + 1525.94i −0.112650 + 0.195116i
\(395\) −4656.00 8064.43i −0.593086 1.02725i
\(396\) 630.000 + 1091.19i 0.0799462 + 0.138471i
\(397\) 3018.00 5227.33i 0.381534 0.660837i −0.609748 0.792596i \(-0.708729\pi\)
0.991282 + 0.131759i \(0.0420625\pi\)
\(398\) −3096.00 −0.389921
\(399\) 0 0
\(400\) 779.000 0.0973750
\(401\) 3385.00 5862.99i 0.421543 0.730134i −0.574547 0.818471i \(-0.694822\pi\)
0.996091 + 0.0883370i \(0.0281552\pi\)
\(402\) −618.000 1070.41i −0.0766742 0.132804i
\(403\) −11088.0 19205.0i −1.37055 2.37387i
\(404\) −5334.00 + 9238.76i −0.656872 + 1.13774i
\(405\) 972.000 0.119257
\(406\) 0 0
\(407\) 5160.00 0.628432
\(408\) −2160.00 + 3741.23i −0.262098 + 0.453967i
\(409\) −6252.00 10828.8i −0.755847 1.30917i −0.944952 0.327209i \(-0.893892\pi\)
0.189105 0.981957i \(-0.439441\pi\)
\(410\) 0 0
\(411\) 1689.00 2925.43i 0.202706 0.351097i
\(412\) 2856.00 0.341517
\(413\) 0 0
\(414\) 1584.00 0.188042
\(415\) −5544.00 + 9602.49i −0.655769 + 1.13583i
\(416\) −6762.00 11712.1i −0.796958 1.38037i
\(417\) 1638.00 + 2837.10i 0.192358 + 0.333173i
\(418\) 120.000 207.846i 0.0140416 0.0243208i
\(419\) 9492.00 1.10672 0.553359 0.832943i \(-0.313346\pi\)
0.553359 + 0.832943i \(0.313346\pi\)
\(420\) 0 0
\(421\) 5182.00 0.599894 0.299947 0.953956i \(-0.403031\pi\)
0.299947 + 0.953956i \(0.403031\pi\)
\(422\) 78.0000 135.100i 0.00899758 0.0155843i
\(423\) 1836.00 + 3180.05i 0.211039 + 0.365530i
\(424\) 5415.00 + 9379.06i 0.620226 + 1.07426i
\(425\) 912.000 1579.63i 0.104091 0.180290i
\(426\) 888.000 0.100995
\(427\) 0 0
\(428\) 5740.00 0.648256
\(429\) −2520.00 + 4364.77i −0.283605 + 0.491219i
\(430\) 936.000 + 1621.20i 0.104972 + 0.181817i
\(431\) 2860.00 + 4953.67i 0.319632 + 0.553619i 0.980411 0.196962i \(-0.0631074\pi\)
−0.660779 + 0.750580i \(0.729774\pi\)
\(432\) 553.500 958.690i 0.0616442 0.106771i
\(433\) 13608.0 1.51030 0.755149 0.655554i \(-0.227565\pi\)
0.755149 + 0.655554i \(0.227565\pi\)
\(434\) 0 0
\(435\) −2088.00 −0.230142
\(436\) −3213.00 + 5565.08i −0.352924 + 0.611282i
\(437\) 1056.00 + 1829.05i 0.115596 + 0.200218i
\(438\) −360.000 623.538i −0.0392728 0.0680224i
\(439\) −6432.00 + 11140.6i −0.699277 + 1.21118i 0.269440 + 0.963017i \(0.413161\pi\)
−0.968717 + 0.248166i \(0.920172\pi\)
\(440\) 3600.00 0.390053
\(441\) 0 0
\(442\) −8064.00 −0.867795
\(443\) 6626.00 11476.6i 0.710634 1.23085i −0.253986 0.967208i \(-0.581742\pi\)
0.964620 0.263646i \(-0.0849250\pi\)
\(444\) −2709.00 4692.13i −0.289557 0.501528i
\(445\) 4464.00 + 7731.87i 0.475537 + 0.823654i
\(446\) 2520.00 4364.77i 0.267546 0.463403i
\(447\) −3210.00 −0.339659
\(448\) 0 0
\(449\) 226.000 0.0237541 0.0118771 0.999929i \(-0.496219\pi\)
0.0118771 + 0.999929i \(0.496219\pi\)
\(450\) 85.5000 148.090i 0.00895669 0.0155134i
\(451\) 0 0
\(452\) −385.000 666.840i −0.0400639 0.0693927i
\(453\) −180.000 + 311.769i −0.0186692 + 0.0323360i
\(454\) −2172.00 −0.224531
\(455\) 0 0
\(456\) −540.000 −0.0554557
\(457\) 5667.00 9815.53i 0.580068 1.00471i −0.415403 0.909638i \(-0.636359\pi\)
0.995471 0.0950696i \(-0.0303074\pi\)
\(458\) 1350.00 + 2338.27i 0.137732 + 0.238559i
\(459\) −1296.00 2244.74i −0.131791 0.228269i
\(460\) −7392.00 + 12803.3i −0.749247 + 1.29773i
\(461\) −1596.00 −0.161243 −0.0806216 0.996745i \(-0.525691\pi\)
−0.0806216 + 0.996745i \(0.525691\pi\)
\(462\) 0 0
\(463\) 12728.0 1.27758 0.638791 0.769380i \(-0.279435\pi\)
0.638791 + 0.769380i \(0.279435\pi\)
\(464\) −1189.00 + 2059.41i −0.118961 + 0.206047i
\(465\) −4752.00 8230.71i −0.473911 0.820838i
\(466\) −1901.00 3292.63i −0.188975 0.327313i
\(467\) 1506.00 2608.47i 0.149228 0.258470i −0.781715 0.623636i \(-0.785655\pi\)
0.930942 + 0.365166i \(0.118988\pi\)
\(468\) 5292.00 0.522698
\(469\) 0 0
\(470\) 4896.00 0.480501
\(471\) 2754.00 4770.07i 0.269422 0.466652i
\(472\) −3690.00 6391.27i −0.359843 0.623267i
\(473\) −1560.00 2702.00i −0.151647 0.262660i
\(474\) −1164.00 + 2016.11i −0.112794 + 0.195365i
\(475\) 228.000 0.0220239
\(476\) 0 0
\(477\) −6498.00 −0.623738
\(478\) −2204.00 + 3817.44i −0.210897 + 0.365284i
\(479\) 2148.00 + 3720.45i 0.204895 + 0.354888i 0.950099 0.311948i \(-0.100981\pi\)
−0.745204 + 0.666836i \(0.767648\pi\)
\(480\) −2898.00 5019.48i −0.275573 0.477306i
\(481\) 10836.0 18768.5i 1.02719 1.77915i
\(482\) −3096.00 −0.292570
\(483\) 0 0
\(484\) 6517.00 0.612040
\(485\) 1008.00 1745.91i 0.0943730 0.163459i
\(486\) −121.500 210.444i −0.0113402 0.0196419i
\(487\) 4092.00 + 7087.55i 0.380752 + 0.659482i 0.991170 0.132598i \(-0.0423318\pi\)
−0.610418 + 0.792079i \(0.708998\pi\)
\(488\) 3690.00 6391.27i 0.342292 0.592867i
\(489\) −2748.00 −0.254129
\(490\) 0 0
\(491\) −12164.0 −1.11803 −0.559016 0.829157i \(-0.688821\pi\)
−0.559016 + 0.829157i \(0.688821\pi\)
\(492\) 0 0
\(493\) 2784.00 + 4822.03i 0.254331 + 0.440514i
\(494\) −504.000 872.954i −0.0459029 0.0795062i
\(495\) −1080.00 + 1870.61i −0.0980654 + 0.169854i
\(496\) −10824.0 −0.979863
\(497\) 0 0
\(498\) 2772.00 0.249430
\(499\) −486.000 + 841.777i −0.0435999 + 0.0755172i −0.887002 0.461766i \(-0.847216\pi\)
0.843402 + 0.537283i \(0.180549\pi\)
\(500\) −4452.00 7711.09i −0.398199 0.689701i
\(501\) 756.000 + 1309.43i 0.0674163 + 0.116769i
\(502\) −462.000 + 800.207i −0.0410758 + 0.0711454i
\(503\) 7728.00 0.685039 0.342519 0.939511i \(-0.388720\pi\)
0.342519 + 0.939511i \(0.388720\pi\)
\(504\) 0 0
\(505\) −18288.0 −1.61150
\(506\) −1760.00 + 3048.41i −0.154628 + 0.267823i
\(507\) 7288.50 + 12624.1i 0.638449 + 1.10583i
\(508\) 56.0000 + 96.9948i 0.00489094 + 0.00847136i
\(509\) −5802.00 + 10049.4i −0.505244 + 0.875108i 0.494738 + 0.869042i \(0.335264\pi\)
−0.999982 + 0.00606572i \(0.998069\pi\)
\(510\) −3456.00 −0.300067
\(511\) 0 0
\(512\) −11521.0 −0.994455
\(513\) 162.000 280.592i 0.0139424 0.0241490i
\(514\) −1380.00 2390.23i −0.118423 0.205114i
\(515\) 2448.00 + 4240.06i 0.209460 + 0.362795i
\(516\) −1638.00 + 2837.10i −0.139746 + 0.242047i
\(517\) −8160.00 −0.694152
\(518\) 0 0
\(519\) 5508.00 0.465847
\(520\) 7560.00 13094.3i 0.637554 1.10428i
\(521\) 5424.00 + 9394.64i 0.456103 + 0.789994i 0.998751 0.0499665i \(-0.0159115\pi\)
−0.542648 + 0.839960i \(0.682578\pi\)
\(522\) 261.000 + 452.065i 0.0218844 + 0.0379049i
\(523\) 9066.00 15702.8i 0.757989 1.31288i −0.185885 0.982572i \(-0.559515\pi\)
0.943874 0.330305i \(-0.107152\pi\)
\(524\) −11844.0 −0.987419
\(525\) 0 0
\(526\) 2360.00 0.195629
\(527\) −12672.0 + 21948.5i −1.04744 + 1.81422i
\(528\) 1230.00 + 2130.42i 0.101380 + 0.175596i
\(529\) −9404.50 16289.1i −0.772951 1.33879i
\(530\) −4332.00 + 7503.24i −0.355038 + 0.614944i
\(531\) 4428.00 0.361881
\(532\) 0 0
\(533\) 0 0
\(534\) 1116.00 1932.97i 0.0904383 0.156644i
\(535\) 4920.00 + 8521.69i 0.397589 + 0.688644i
\(536\) −3090.00 5352.04i −0.249007 0.431293i
\(537\) 3558.00 6162.64i 0.285920 0.495228i
\(538\) −4020.00 −0.322146
\(539\) 0 0
\(540\) 2268.00 0.180739
\(541\) −3475.00 + 6018.88i −0.276159 + 0.478321i −0.970427 0.241395i \(-0.922395\pi\)
0.694268 + 0.719717i \(0.255728\pi\)
\(542\) 2400.00 + 4156.92i 0.190201 + 0.329437i
\(543\) −1638.00 2837.10i −0.129454 0.224220i
\(544\) −7728.00 + 13385.3i −0.609072 + 1.05494i
\(545\) −11016.0 −0.865823
\(546\) 0 0
\(547\) 17012.0 1.32976 0.664882 0.746949i \(-0.268482\pi\)
0.664882 + 0.746949i \(0.268482\pi\)
\(548\) 3941.00 6826.01i 0.307210 0.532104i
\(549\) 2214.00 + 3834.76i 0.172115 + 0.298112i
\(550\) 190.000 + 329.090i 0.0147302 + 0.0255135i
\(551\) −348.000 + 602.754i −0.0269062 + 0.0466028i
\(552\) 7920.00 0.610684
\(553\) 0 0
\(554\) −6446.00 −0.494340
\(555\) 4644.00 8043.64i 0.355183 0.615196i
\(556\) 3822.00 + 6619.90i 0.291527 + 0.504939i
\(557\) −1963.00 3400.02i −0.149327 0.258641i 0.781652 0.623715i \(-0.214377\pi\)
−0.930979 + 0.365073i \(0.881044\pi\)
\(558\) −1188.00 + 2057.68i −0.0901291 + 0.156108i
\(559\) −13104.0 −0.991485
\(560\) 0 0
\(561\) 5760.00 0.433489
\(562\) −1301.00 + 2253.40i −0.0976501 + 0.169135i
\(563\) 9414.00 + 16305.5i 0.704712 + 1.22060i 0.966795 + 0.255552i \(0.0822571\pi\)
−0.262084 + 0.965045i \(0.584410\pi\)
\(564\) 4284.00 + 7420.11i 0.319839 + 0.553977i
\(565\) 660.000 1143.15i 0.0491441 0.0851201i
\(566\) 6900.00 0.512418
\(567\) 0 0
\(568\) 4440.00 0.327990
\(569\) −5995.00 + 10383.6i −0.441693 + 0.765035i −0.997815 0.0660655i \(-0.978955\pi\)
0.556122 + 0.831101i \(0.312289\pi\)
\(570\) −216.000 374.123i −0.0158724 0.0274917i
\(571\) 7858.00 + 13610.5i 0.575914 + 0.997513i 0.995942 + 0.0900014i \(0.0286871\pi\)
−0.420027 + 0.907511i \(0.637980\pi\)
\(572\) −5880.00 + 10184.5i −0.429817 + 0.744464i
\(573\) −7536.00 −0.549426
\(574\) 0 0
\(575\) −3344.00 −0.242529
\(576\) 751.500 1301.64i 0.0543620 0.0941577i
\(577\) 6936.00 + 12013.5i 0.500432 + 0.866774i 1.00000 0.000499291i \(0.000158929\pi\)
−0.499568 + 0.866275i \(0.666508\pi\)
\(578\) 2151.50 + 3726.51i 0.154828 + 0.268170i
\(579\) −3645.00 + 6313.33i −0.261625 + 0.453148i
\(580\) −4872.00 −0.348791
\(581\) 0 0
\(582\) −504.000 −0.0358960
\(583\) 7220.00 12505.4i 0.512902 0.888372i
\(584\) −1800.00 3117.69i −0.127542 0.220909i
\(585\) 4536.00 + 7856.58i 0.320582 + 0.555264i
\(586\) −2226.00 + 3855.55i −0.156920 + 0.271794i
\(587\) 8820.00 0.620171 0.310085 0.950709i \(-0.399642\pi\)
0.310085 + 0.950709i \(0.399642\pi\)
\(588\) 0 0
\(589\) −3168.00 −0.221622
\(590\) 2952.00 5113.01i 0.205986 0.356779i
\(591\) −2643.00 4577.81i −0.183957 0.318623i
\(592\) −5289.00 9160.82i −0.367190 0.635992i
\(593\) 8436.00 14611.6i 0.584191 1.01185i −0.410785 0.911732i \(-0.634745\pi\)
0.994976 0.100116i \(-0.0319213\pi\)
\(594\) 540.000 0.0373005
\(595\) 0 0
\(596\) −7490.00 −0.514769
\(597\) 4644.00 8043.64i 0.318369 0.551431i
\(598\) 7392.00 + 12803.3i 0.505487 + 0.875530i
\(599\) 3028.00 + 5244.65i 0.206545 + 0.357747i 0.950624 0.310345i \(-0.100445\pi\)
−0.744079 + 0.668092i \(0.767111\pi\)
\(600\) 427.500 740.452i 0.0290877 0.0503814i
\(601\) 10752.0 0.729756 0.364878 0.931055i \(-0.381111\pi\)
0.364878 + 0.931055i \(0.381111\pi\)
\(602\) 0 0
\(603\) 3708.00 0.250417
\(604\) −420.000 + 727.461i −0.0282940 + 0.0490066i
\(605\) 5586.00 + 9675.24i 0.375377 + 0.650172i
\(606\) 2286.00 + 3959.47i 0.153238 + 0.265416i
\(607\) −10128.0 + 17542.2i −0.677237 + 1.17301i 0.298573 + 0.954387i \(0.403489\pi\)
−0.975810 + 0.218622i \(0.929844\pi\)
\(608\) −1932.00 −0.128870
\(609\) 0 0
\(610\) 5904.00 0.391879
\(611\) −17136.0 + 29680.4i −1.13461 + 1.96521i
\(612\) −3024.00 5237.72i −0.199735 0.345952i
\(613\) 14095.0 + 24413.3i 0.928698 + 1.60855i 0.785504 + 0.618857i \(0.212404\pi\)
0.143194 + 0.989695i \(0.454263\pi\)
\(614\) −1218.00 + 2109.64i −0.0800562 + 0.138661i
\(615\) 0 0
\(616\) 0 0
\(617\) 29318.0 1.91296 0.956482 0.291793i \(-0.0942518\pi\)
0.956482 + 0.291793i \(0.0942518\pi\)
\(618\) 612.000 1060.02i 0.0398354 0.0689969i
\(619\) −12174.0 21086.0i −0.790492 1.36917i −0.925663 0.378350i \(-0.876492\pi\)
0.135171 0.990822i \(-0.456842\pi\)
\(620\) −11088.0 19205.0i −0.718234 1.24402i
\(621\) −2376.00 + 4115.35i −0.153536 + 0.265931i
\(622\) 7488.00 0.482703
\(623\) 0 0
\(624\) 10332.0 0.662838
\(625\) 8819.50 15275.8i 0.564448 0.977653i
\(626\) −876.000 1517.28i −0.0559297 0.0968731i
\(627\) 360.000 + 623.538i 0.0229298 + 0.0397157i
\(628\) 6426.00 11130.2i 0.408321 0.707232i
\(629\) −24768.0 −1.57006
\(630\) 0 0
\(631\) −25184.0 −1.58884 −0.794421 0.607368i \(-0.792226\pi\)
−0.794421 + 0.607368i \(0.792226\pi\)
\(632\) −5820.00 + 10080.5i −0.366309 + 0.634465i
\(633\) 234.000 + 405.300i 0.0146930 + 0.0254490i
\(634\) −781.000 1352.73i −0.0489235 0.0847379i
\(635\) −96.0000 + 166.277i −0.00599944 + 0.0103913i
\(636\) −15162.0 −0.945303
\(637\) 0 0
\(638\) −1160.00 −0.0719825
\(639\) −1332.00 + 2307.09i −0.0824618 + 0.142828i
\(640\) −8730.00 15120.8i −0.539193 0.933910i
\(641\) −16159.0 27988.2i −0.995698 1.72460i −0.578097 0.815968i \(-0.696205\pi\)
−0.417600 0.908631i \(-0.637129\pi\)
\(642\) 1230.00 2130.42i 0.0756141 0.130967i
\(643\) −3948.00 −0.242137 −0.121068 0.992644i \(-0.538632\pi\)
−0.121068 + 0.992644i \(0.538632\pi\)
\(644\) 0 0
\(645\) −5616.00 −0.342837
\(646\) −576.000 + 997.661i −0.0350811 + 0.0607623i
\(647\) −6924.00 11992.7i −0.420727 0.728721i 0.575284 0.817954i \(-0.304892\pi\)
−0.996011 + 0.0892331i \(0.971558\pi\)
\(648\) −607.500 1052.22i −0.0368285 0.0637888i
\(649\) −4920.00 + 8521.69i −0.297576 + 0.515417i
\(650\) 1596.00 0.0963081
\(651\) 0 0
\(652\) −6412.00 −0.385143
\(653\) 1579.00 2734.91i 0.0946264 0.163898i −0.814826 0.579705i \(-0.803168\pi\)
0.909453 + 0.415808i \(0.136501\pi\)
\(654\) 1377.00 + 2385.03i 0.0823317 + 0.142603i
\(655\) −10152.0 17583.8i −0.605605 1.04894i
\(656\) 0 0
\(657\) 2160.00 0.128264
\(658\) 0 0
\(659\) −24596.0 −1.45391 −0.726953 0.686687i \(-0.759064\pi\)
−0.726953 + 0.686687i \(0.759064\pi\)
\(660\) −2520.00 + 4364.77i −0.148623 + 0.257422i
\(661\) 7734.00 + 13395.7i 0.455095 + 0.788248i 0.998694 0.0510977i \(-0.0162720\pi\)
−0.543599 + 0.839345i \(0.682939\pi\)
\(662\) −3546.00 6141.85i −0.208186 0.360589i
\(663\) 12096.0 20950.9i 0.708552 1.22725i
\(664\) 13860.0 0.810049
\(665\) 0 0
\(666\) −2322.00 −0.135099
\(667\) 5104.00 8840.39i 0.296293 0.513195i
\(668\) 1764.00 + 3055.34i 0.102172 + 0.176968i
\(669\) 7560.00 + 13094.3i 0.436901 + 0.756734i
\(670\) 2472.00 4281.63i 0.142540 0.246886i
\(671\) −9840.00 −0.566124
\(672\) 0 0
\(673\) 13470.0 0.771516 0.385758 0.922600i \(-0.373940\pi\)
0.385758 + 0.922600i \(0.373940\pi\)
\(674\) 183.000 316.965i 0.0104583 0.0181143i
\(675\) 256.500 + 444.271i 0.0146262 + 0.0253333i
\(676\) 17006.5 + 29456.1i 0.967598 + 1.67593i
\(677\) 4782.00 8282.67i 0.271473 0.470205i −0.697766 0.716326i \(-0.745823\pi\)
0.969239 + 0.246121i \(0.0791559\pi\)
\(678\) −330.000 −0.0186926
\(679\) 0 0
\(680\) −17280.0 −0.974497
\(681\) 3258.00 5643.02i 0.183329 0.317535i
\(682\) −2640.00 4572.61i −0.148227 0.256737i
\(683\) −6926.00 11996.2i −0.388018 0.672066i 0.604165 0.796859i \(-0.293507\pi\)
−0.992183 + 0.124793i \(0.960173\pi\)
\(684\) 378.000 654.715i 0.0211304 0.0365989i
\(685\) 13512.0 0.753674
\(686\) 0 0
\(687\) −8100.00 −0.449832
\(688\) −3198.00 + 5539.10i −0.177213 + 0.306942i
\(689\) −30324.0 52522.7i −1.67671 2.90414i
\(690\) 3168.00 + 5487.14i 0.174788 + 0.302742i
\(691\) 162.000 280.592i 0.00891863 0.0154475i −0.861532 0.507704i \(-0.830494\pi\)
0.870450 + 0.492256i \(0.163828\pi\)
\(692\) 12852.0 0.706011
\(693\) 0 0
\(694\) 6364.00 0.348090
\(695\) −6552.00 + 11348.4i −0.357599 + 0.619380i
\(696\) 1305.00 + 2260.33i 0.0710717 + 0.123100i
\(697\) 0 0
\(698\) −5250.00 + 9093.27i −0.284693 + 0.493102i
\(699\) 11406.0 0.617188
\(700\) 0 0
\(701\) 24922.0 1.34278 0.671392 0.741103i \(-0.265697\pi\)
0.671392 + 0.741103i \(0.265697\pi\)
\(702\) 1134.00 1964.15i 0.0609688 0.105601i
\(703\) −1548.00 2681.21i −0.0830497 0.143846i
\(704\) 1670.00 + 2892.52i 0.0894041 + 0.154852i
\(705\) −7344.00 + 12720.2i −0.392328 + 0.679532i
\(706\) −408.000 −0.0217497
\(707\) 0 0
\(708\) 10332.0 0.548447
\(709\) 8943.00 15489.7i 0.473711 0.820492i −0.525836 0.850586i \(-0.676247\pi\)
0.999547 + 0.0300939i \(0.00958064\pi\)
\(710\) 1776.00 + 3076.12i 0.0938762 + 0.162598i
\(711\) −3492.00 6048.32i −0.184192 0.319029i
\(712\) 5580.00 9664.84i 0.293707 0.508715i
\(713\) 46464.0 2.44052
\(714\) 0 0
\(715\) −20160.0 −1.05446
\(716\) 8302.00 14379.5i 0.433324 0.750540i
\(717\) −6612.00 11452.3i −0.344393 0.596506i
\(718\) −5968.00 10336.9i −0.310200 0.537283i
\(719\) 3396.00 5882.04i 0.176147 0.305095i −0.764411 0.644729i \(-0.776970\pi\)
0.940557 + 0.339635i \(0.110303\pi\)
\(720\) 4428.00 0.229197
\(721\) 0 0
\(722\) 6715.00 0.346131
\(723\) 4644.00 8043.64i 0.238883 0.413757i
\(724\) −3822.00 6619.90i −0.196193 0.339816i
\(725\) −551.000 954.360i −0.0282257 0.0488883i
\(726\) 1396.50 2418.81i 0.0713898 0.123651i
\(727\) 1512.00 0.0771348 0.0385674 0.999256i \(-0.487721\pi\)
0.0385674 + 0.999256i \(0.487721\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 1440.00 2494.15i 0.0730093 0.126456i
\(731\) 7488.00 + 12969.6i 0.378870 + 0.656221i
\(732\) 5166.00 + 8947.77i 0.260848 + 0.451802i
\(733\) 5622.00 9737.59i 0.283292 0.490677i −0.688901 0.724855i \(-0.741907\pi\)
0.972194 + 0.234178i \(0.0752400\pi\)
\(734\) 2448.00 0.123103
\(735\) 0 0
\(736\) 28336.0 1.41913
\(737\) −4120.00 + 7136.05i −0.205919 + 0.356662i
\(738\) 0 0
\(739\) 998.000 + 1728.59i 0.0496780 + 0.0860448i 0.889795 0.456360i \(-0.150847\pi\)
−0.840117 + 0.542405i \(0.817514\pi\)
\(740\) 10836.0 18768.5i 0.538296 0.932357i
\(741\) 3024.00 0.149918
\(742\) 0 0
\(743\) −656.000 −0.0323907 −0.0161954 0.999869i \(-0.505155\pi\)
−0.0161954 + 0.999869i \(0.505155\pi\)
\(744\) −5940.00 + 10288.4i −0.292703 + 0.506976i
\(745\) −6420.00 11119.8i −0.315719 0.546841i
\(746\) 5687.00 + 9850.17i 0.279110 + 0.483432i
\(747\) −4158.00 + 7201.87i −0.203659 + 0.352748i
\(748\) 13440.0 0.656972
\(749\) 0 0
\(750\) −3816.00 −0.185787
\(751\) −528.000 + 914.523i −0.0256551 + 0.0444360i −0.878568 0.477617i \(-0.841501\pi\)
0.852913 + 0.522053i \(0.174834\pi\)
\(752\) 8364.00 + 14486.9i 0.405590 + 0.702503i
\(753\) −1386.00 2400.62i −0.0670766 0.116180i
\(754\) −2436.00 + 4219.28i −0.117658 + 0.203789i
\(755\) −1440.00 −0.0694132
\(756\) 0 0
\(757\) −18702.0 −0.897934 −0.448967 0.893548i \(-0.648208\pi\)
−0.448967 + 0.893548i \(0.648208\pi\)
\(758\) −2946.00 + 5102.62i −0.141166 + 0.244506i
\(759\) −5280.00 9145.23i −0.252506 0.437353i
\(760\) −1080.00 1870.61i −0.0515470 0.0892820i
\(761\) −8952.00 + 15505.3i −0.426425 + 0.738590i −0.996552 0.0829661i \(-0.973561\pi\)
0.570127 + 0.821557i \(0.306894\pi\)
\(762\) 48.0000 0.00228196
\(763\) 0 0
\(764\) −17584.0 −0.832679
\(765\) 5184.00 8978.95i 0.245004 0.424359i
\(766\) −5244.00 9082.87i −0.247354 0.428430i
\(767\) 20664.0 + 35791.1i 0.972795 + 1.68493i
\(768\) −178.500 + 309.171i −0.00838680 + 0.0145264i
\(769\) −7560.00 −0.354513 −0.177257 0.984165i \(-0.556722\pi\)
−0.177257 + 0.984165i \(0.556722\pi\)
\(770\) 0 0
\(771\) 8280.00 0.386766
\(772\) −8505.00 + 14731.1i −0.396505 + 0.686766i
\(773\) 7146.00 + 12377.2i 0.332502 + 0.575910i 0.983002 0.183596i \(-0.0587740\pi\)
−0.650500 + 0.759506i \(0.725441\pi\)
\(774\) 702.000 + 1215.90i 0.0326006 + 0.0564659i
\(775\) 2508.00 4343.98i 0.116245 0.201343i
\(776\) −2520.00 −0.116576
\(777\) 0 0
\(778\) −4514.00 −0.208014
\(779\) 0 0