Properties

Label 147.4.e.e.67.1
Level $147$
Weight $4$
Character 147.67
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 67.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 147.67
Dual form 147.4.e.e.79.1

$q$-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 \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).

\(n\) \(50\) \(52\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 0.940775 0.339032i \(-0.110100\pi\)
−0.763998 + 0.645219i \(0.776766\pi\)
\(3\) −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 0.999081 + 0.0428575i \(0.0136462\pi\)
−0.462425 + 0.886658i \(0.653021\pi\)
\(6\) −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 −0.969908 0.243472i \(-0.921714\pi\)
0.695807 + 0.718229i \(0.255047\pi\)
\(12\) 10.5000 + 18.1865i 0.252591 + 0.437500i
\(13\) 84.0000 1.79211 0.896054 0.443945i \(-0.146421\pi\)
0.896054 + 0.443945i \(0.146421\pi\)
\(14\) 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 0.288691 + 0.957422i \(0.406780\pi\)
−0.973498 + 0.228697i \(0.926553\pi\)
\(18\) 4.50000 7.79423i 0.0589256 0.102062i
\(19\) 6.00000 + 10.3923i 0.0724471 + 0.125482i 0.899973 0.435945i \(-0.143586\pi\)
−0.827526 + 0.561427i \(0.810252\pi\)
\(20\) 84.0000 0.939149
\(21\) 0 0
\(22\) −20.0000 −0.193819
\(23\) 88.0000 + 152.420i 0.797794 + 1.38182i 0.921050 + 0.389445i \(0.127333\pi\)
−0.123255 + 0.992375i \(0.539333\pi\)
\(24\) −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 0.175597 + 0.984462i \(0.443815\pi\)
−0.940368 + 0.340160i \(0.889519\pi\)
\(32\) 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 −0.996237 0.0866674i \(-0.972378\pi\)
0.423062 0.906101i \(-0.360955\pi\)
\(38\) −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 −0.986911 0.161266i \(-0.948442\pi\)
0.353795 0.935323i \(-0.384891\pi\)
\(48\) 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 0.162059 0.986781i \(-0.448187\pi\)
0.773548 0.633737i \(-0.218480\pi\)
\(54\) 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 −0.455919 0.890021i \(-0.650689\pi\)
0.998741 0.0501732i \(-0.0159773\pi\)
\(60\) −126.000 + 218.238i −0.271109 + 0.469574i
\(61\) −246.000 426.084i −0.516345 0.894337i −0.999820 0.0189781i \(-0.993959\pi\)
0.483474 0.875358i \(-0.339375\pi\)
\(62\) −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 −0.990420 0.138085i \(-0.955905\pi\)
0.614795 + 0.788687i \(0.289239\pi\)
\(68\) 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 \(-0.771707\pi\)
0.946044 + 0.324038i \(0.105041\pi\)
\(74\) 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 −0.998088 0.0618122i \(-0.980312\pi\)
0.445513 0.895275i \(-0.353021\pi\)
\(80\) 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 \(-0.709223\pi\)
−0.610977 + 0.791648i \(0.709223\pi\)
\(84\) 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 \(-0.312772\pi\)
−0.997914 + 0.0645500i \(0.979439\pi\)
\(90\) 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 \(-0.471976\pi\)
0.0879269 + 0.996127i \(0.471976\pi\)
\(98\) 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 0.196767 + 0.980450i \(0.436956\pi\)
−0.947478 + 0.319820i \(0.896378\pi\)
\(102\) 144.000 249.415i 0.139786 0.242116i
\(103\) −204.000 353.338i −0.195153 0.338014i 0.751798 0.659394i \(-0.229187\pi\)
−0.946951 + 0.321379i \(0.895854\pi\)
\(104\) 1260.00 1.18801
\(105\) 0 0
\(106\) 722.000 0.661574
\(107\) 410.000 + 710.141i 0.370432 + 0.641607i 0.989632 0.143627i \(-0.0458764\pi\)
−0.619200 + 0.785233i \(0.712543\pi\)
\(108\) 94.5000 163.679i 0.0841969 0.145833i
\(109\) 459.000 795.011i 0.403342 0.698608i −0.590785 0.806829i \(-0.701182\pi\)
0.994127 + 0.108221i \(0.0345153\pi\)
\(110\) −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 0.997120 + 0.0758401i \(0.0241638\pi\)
−0.432881 + 0.901451i \(0.642503\pi\)
\(132\) −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 −0.986442 0.164110i \(-0.947525\pi\)
0.635345 + 0.772229i \(0.280858\pi\)
\(138\) −264.000 457.261i −0.162849 0.282063i
\(139\) −1092.00 −0.666347 −0.333173 0.942866i \(-0.608119\pi\)
−0.333173 + 0.942866i \(0.608119\pi\)
\(140\) 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 0.680634 0.732624i \(-0.261704\pi\)
−0.974788 + 0.223134i \(0.928371\pi\)
\(150\) 28.5000 49.3634i 0.0155134 0.0268701i
\(151\) 60.0000 103.923i 0.0323360 0.0560075i −0.849405 0.527742i \(-0.823039\pi\)
0.881741 + 0.471735i \(0.156372\pi\)
\(152\) 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 \(-0.678793\pi\)
0.999274 + 0.0380879i \(0.0121267\pi\)
\(158\) 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 0.734751 0.678337i \(-0.237299\pi\)
−0.954833 + 0.297144i \(0.903966\pi\)
\(164\) 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 \(-0.537254\pi\)
−0.116769 + 0.993159i \(0.537254\pi\)
\(168\) 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 \(-0.298851\pi\)
−0.994138 + 0.108119i \(0.965517\pi\)
\(174\) −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 −0.999985 0.00550156i \(-0.998249\pi\)
0.504757 + 0.863262i \(0.331582\pi\)
\(180\) −378.000 654.715i −0.156525 0.271109i
\(181\) 1092.00 0.448440 0.224220 0.974539i \(-0.428017\pi\)
0.224220 + 0.974539i \(0.428017\pi\)
\(182\) 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 0.523800 0.851842i \(-0.324514\pi\)
−0.999616 + 0.0277030i \(0.991181\pi\)
\(192\) 250.500 433.879i 0.0941577 0.163086i
\(193\) 1215.00 2104.44i 0.453148 0.784876i −0.545431 0.838155i \(-0.683634\pi\)
0.998580 + 0.0532797i \(0.0169675\pi\)
\(194\) 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 −0.446740 0.894664i \(-0.647415\pi\)
0.998172 0.0604433i \(-0.0192514\pi\)
\(200\) −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 \(-0.773206\pi\)
−0.756734 + 0.653723i \(0.773206\pi\)
\(224\) 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 \(-0.730478\pi\)
0.979973 + 0.199130i \(0.0638117\pi\)
\(228\) −126.000 + 218.238i −0.0365989 + 0.0633912i
\(229\) 1350.00 + 2338.27i 0.389566 + 0.674747i 0.992391 0.123126i \(-0.0392918\pi\)
−0.602826 + 0.797873i \(0.705959\pi\)
\(230\) −2112.00 −0.605483
\(231\) 0 0
\(232\) 870.000 0.246200
\(233\) 1901.00 + 3292.63i 0.534501 + 0.925782i 0.999187 + 0.0403071i \(0.0128336\pi\)
−0.464687 + 0.885475i \(0.653833\pi\)
\(234\) 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 \(-0.697550\pi\)
0.995297 + 0.0968696i \(0.0308830\pi\)
\(242\) −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 \(-0.462935\pi\)
0.116180 + 0.993228i \(0.462935\pi\)
\(252\) 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 \(-0.275386\pi\)
−0.983475 + 0.181043i \(0.942053\pi\)
\(258\) −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 −0.693892 0.720079i \(-0.744105\pi\)
0.970553 + 0.240888i \(0.0774387\pi\)
\(264\) −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 \(-0.682764\pi\)
0.998722 + 0.0505501i \(0.0160974\pi\)
\(270\) −162.000 + 280.592i −0.0365148 + 0.0632456i
\(271\) 2400.00 + 4156.92i 0.537969 + 0.931790i 0.999013 + 0.0444126i \(0.0141416\pi\)
−0.461044 + 0.887377i \(0.652525\pi\)
\(272\) 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 0.269676 + 0.962951i \(0.413083\pi\)
−0.968778 + 0.247929i \(0.920250\pi\)
\(278\) −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 0.234442 + 0.972130i \(0.424674\pi\)
−0.959110 + 0.283033i \(0.908660\pi\)
\(284\) 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 \(-0.353617\pi\)
0.443837 + 0.896107i \(0.353617\pi\)
\(294\) 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 \(-0.427294\pi\)
0.226433 + 0.974027i \(0.427294\pi\)
\(308\) 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 0.291525 + 0.956563i \(0.405837\pi\)
−0.974171 + 0.225814i \(0.927496\pi\)
\(312\) −1890.00 + 3273.58i −0.342949 + 0.594006i
\(313\) −876.000 1517.28i −0.158193 0.273999i 0.776024 0.630703i \(-0.217234\pi\)
−0.934217 + 0.356705i \(0.883900\pi\)
\(314\) 1836.00 0.329973
\(315\) 0 0
\(316\) −5432.00 −0.967006
\(317\) 781.000 + 1352.73i 0.138376 + 0.239675i 0.926882 0.375352i \(-0.122478\pi\)
−0.788506 + 0.615027i \(0.789145\pi\)
\(318\) −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 0.994385 + 0.105825i \(0.0337482\pi\)
−0.405546 + 0.914075i \(0.632918\pi\)
\(332\) −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 −0.507687 0.861541i \(-0.669500\pi\)
0.999960 + 0.00889958i \(0.00283286\pi\)
\(348\) 609.000 + 1054.82i 0.0938098 + 0.162483i
\(349\) 10500.0 1.61046 0.805232 0.592960i \(-0.202041\pi\)
0.805232 + 0.592960i \(0.202041\pi\)
\(350\) 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 \(-0.823541\pi\)
0.880995 + 0.473126i \(0.156874\pi\)
\(354\) −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 0.854207 + 0.519933i \(0.174043\pi\)
0.0231719 + 0.999731i \(0.492624\pi\)
\(360\) 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 \(-0.889033\pi\)
0.765754 + 0.643134i \(0.222366\pi\)
\(368\) 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 −0.926309 0.376764i \(-0.877037\pi\)
0.136868 0.990589i \(-0.456296\pi\)
\(374\) 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 −0.968597 0.248636i \(-0.920018\pi\)
0.268973 0.963148i \(-0.413316\pi\)
\(384\) 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 −0.974793 0.223112i \(-0.928379\pi\)
0.680617 + 0.732639i \(0.261712\pi\)
\(390\) −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 \(-0.291271\pi\)
−0.991282 + 0.131759i \(0.957937\pi\)
\(398\) 3096.00 0.389921
\(399\) 0 0
\(400\) 779.000 0.0973750
\(401\) 3385.00 + 5862.99i 0.421543 + 0.730134i 0.996091 0.0883370i \(-0.0281552\pi\)
−0.574547 + 0.818471i \(0.694822\pi\)
\(402\) 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 −0.189105 0.981957i \(-0.560559\pi\)
0.944952 0.327209i \(-0.106108\pi\)
\(410\) 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 \(-0.686654\pi\)
−0.553359 + 0.832943i \(0.686654\pi\)
\(420\) 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 −0.660779 0.750580i \(-0.729774\pi\)
0.980411 + 0.196962i \(0.0631074\pi\)
\(432\) −553.500 958.690i −0.0616442 0.106771i
\(433\) −13608.0 −1.51030 −0.755149 0.655554i \(-0.772435\pi\)
−0.755149 + 0.655554i \(0.772435\pi\)
\(434\) 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 0.968717 + 0.248166i \(0.0798279\pi\)
−0.269440 + 0.963017i \(0.586839\pi\)
\(440\) −3600.00 −0.390053
\(441\) 0 0
\(442\) −8064.00 −0.867795
\(443\) 6626.00 + 11476.6i 0.710634 + 1.23085i 0.964620 + 0.263646i \(0.0849250\pi\)
−0.253986 + 0.967208i \(0.581742\pi\)
\(444\) 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 0.995471 + 0.0950696i \(0.0303074\pi\)
−0.415403 + 0.909638i \(0.636359\pi\)
\(458\) −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 \(-0.474309\pi\)
0.0806216 + 0.996745i \(0.474309\pi\)
\(462\) 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 \(-0.214345\pi\)
−0.930942 + 0.365166i \(0.881012\pi\)
\(468\) −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 \(-0.899019\pi\)
0.745204 + 0.666836i \(0.232352\pi\)
\(480\) −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 −0.610418 0.792079i \(-0.708998\pi\)
0.991170 + 0.132598i \(0.0423318\pi\)
\(488\) −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 0.843402 0.537283i \(-0.180549\pi\)
−0.887002 + 0.461766i \(0.847216\pi\)
\(500\) 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 \(-0.611280\pi\)
−0.342519 + 0.939511i \(0.611280\pi\)
\(504\) 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 0.999982 + 0.00606572i \(0.00193079\pi\)
−0.494738 + 0.869042i \(0.664736\pi\)
\(510\) 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 \(-0.984089\pi\)
0.542648 + 0.839960i \(0.317422\pi\)
\(522\) 261.000 452.065i 0.0218844 0.0379049i
\(523\) −9066.00 15702.8i −0.757989 1.31288i −0.943874 0.330305i \(-0.892848\pi\)
0.185885 0.982572i \(-0.440485\pi\)
\(524\) 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 0.694268 0.719717i \(-0.255728\pi\)
−0.970427 + 0.241395i \(0.922395\pi\)
\(542\) −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 −0.930979 0.365073i \(-0.881044\pi\)
0.781652 + 0.623715i \(0.214377\pi\)
\(558\) 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 0.262084 + 0.965045i \(0.415590\pi\)
−0.966795 + 0.255552i \(0.917743\pi\)
\(564\) 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 0.556122 0.831101i \(-0.312289\pi\)
−0.997815 + 0.0660655i \(0.978955\pi\)
\(570\) 216.000 374.123i 0.0158724 0.0274917i
\(571\) 7858.00 13610.5i 0.575914 0.997513i −0.420027 0.907511i \(-0.637980\pi\)
0.995942 0.0900014i \(-0.0286871\pi\)
\(572\) 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 0.499568 + 0.866275i \(0.333492\pi\)
−1.00000 0.000499291i \(0.999841\pi\)
\(578\) 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 \(-0.600358\pi\)
−0.310085 + 0.950709i \(0.600358\pi\)
\(588\) 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 −0.994976 0.100116i \(-0.968079\pi\)
0.410785 0.911732i \(-0.365255\pi\)
\(594\) −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 −0.744079 0.668092i \(-0.767111\pi\)
0.950624 + 0.310345i \(0.100445\pi\)
\(600\) −427.500 740.452i −0.0290877 0.0503814i
\(601\) −10752.0 −0.729756 −0.364878 0.931055i \(-0.618889\pi\)
−0.364878 + 0.931055i \(0.618889\pi\)
\(602\) 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 0.975810 + 0.218622i \(0.0701561\pi\)
−0.298573 + 0.954387i \(0.596511\pi\)
\(608\) 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 0.143194 0.989695i \(-0.454263\pi\)
0.785504 0.618857i \(-0.212404\pi\)
\(614\) 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 −0.135171 0.990822i \(-0.543158\pi\)
0.925663 0.378350i \(-0.123508\pi\)
\(620\) −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 −0.417600 + 0.908631i \(0.637129\pi\)
−0.578097 + 0.815968i \(0.696205\pi\)
\(642\) −1230.00 2130.42i −0.0756141 0.130967i
\(643\) 3948.00 0.242137 0.121068 0.992644i \(-0.461368\pi\)
0.121068 + 0.992644i \(0.461368\pi\)
\(644\) 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 \(-0.695108\pi\)
0.996011 + 0.0892331i \(0.0284416\pi\)
\(648\) −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 0.909453 0.415808i \(-0.136501\pi\)
−0.814826 + 0.579705i \(0.803168\pi\)
\(654\) −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 \(-0.983728\pi\)
0.543599 + 0.839345i \(0.317061\pi\)
\(662\) −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 \(-0.254177\pi\)
−0.969239 + 0.246121i \(0.920844\pi\)
\(678\) 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 −0.992183 0.124793i \(-0.960173\pi\)
0.604165 + 0.796859i \(0.293507\pi\)
\(684\) −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 \(-0.169506\pi\)
−0.870450 + 0.492256i \(0.836172\pi\)
\(692\) −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 0.999547 0.0300939i \(-0.00958064\pi\)
−0.525836 + 0.850586i \(0.676247\pi\)
\(710\) −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 \(-0.223030\pi\)
−0.940557 + 0.339635i \(0.889697\pi\)
\(720\) −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 \(-0.512279\pi\)
−0.0385674 + 0.999256i \(0.512279\pi\)
\(728\) 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 \(-0.258093\pi\)
−0.972194 + 0.234178i \(0.924760\pi\)
\(734\) −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 −0.840117 0.542405i \(-0.817514\pi\)
0.889795 + 0.456360i \(0.150847\pi\)
\(740\) −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 0.852913 0.522053i \(-0.174834\pi\)
−0.878568 + 0.477617i \(0.841501\pi\)
\(752\) −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 \(-0.0264393\pi\)
−0.570127 + 0.821557i \(0.693106\pi\)
\(762\) −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 \(-0.443278\pi\)
0.177257 + 0.984165i \(0.443278\pi\)
\(770\) 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 \(-0.941226\pi\)
0.650500 + 0.759506i \(0.274559\pi\)
\(774\) 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