Properties

Label 39.4.e.c.16.1
Level $39$
Weight $4$
Character 39.16
Analytic conductor $2.301$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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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: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Defining polynomial: \( x^{8} - 2x^{7} + 29x^{6} + 2x^{5} + 595x^{4} - 288x^{3} + 2526x^{2} + 1872x + 6084 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 2^{4}\cdot 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 16.1
Root \(2.66520 + 4.61626i\) of defining polynomial
Character \(\chi\) \(=\) 39.16
Dual form 39.4.e.c.22.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.66520 - 4.61626i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-10.2065 + 17.6783i) q^{4} -16.4131 q^{5} +(7.99559 - 13.8488i) q^{6} +(-4.83984 + 8.38285i) q^{7} +66.1667 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\) \(q+(-2.66520 - 4.61626i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-10.2065 + 17.6783i) q^{4} -16.4131 q^{5} +(7.99559 - 13.8488i) q^{6} +(-4.83984 + 8.38285i) q^{7} +66.1667 q^{8} +(-4.50000 + 7.79423i) q^{9} +(43.7441 + 75.7670i) q^{10} +(-13.7941 - 23.8921i) q^{11} -61.2393 q^{12} +(-37.3033 - 28.3807i) q^{13} +51.5965 q^{14} +(-24.6196 - 42.6425i) q^{15} +(-94.6948 - 164.016i) q^{16} +(-53.9641 + 93.4685i) q^{17} +47.9735 q^{18} +(1.12362 - 1.94616i) q^{19} +(167.521 - 290.155i) q^{20} -29.0391 q^{21} +(-73.5279 + 127.354i) q^{22} +(-20.9045 - 36.2077i) q^{23} +(99.2500 + 171.906i) q^{24} +144.390 q^{25} +(-31.5919 + 247.842i) q^{26} -27.0000 q^{27} +(-98.7961 - 171.120i) q^{28} +(-30.8106 - 53.3656i) q^{29} +(-131.232 + 227.301i) q^{30} +191.932 q^{31} +(-240.094 + 415.855i) q^{32} +(41.3822 - 71.6762i) q^{33} +575.300 q^{34} +(79.4368 - 137.589i) q^{35} +(-91.8589 - 159.104i) q^{36} +(-49.2118 - 85.2373i) q^{37} -11.9786 q^{38} +(17.7803 - 139.488i) q^{39} -1086.00 q^{40} +(15.3726 + 26.6261i) q^{41} +(77.3948 + 134.052i) q^{42} +(-119.163 + 206.396i) q^{43} +563.160 q^{44} +(73.8589 - 127.927i) q^{45} +(-111.429 + 193.001i) q^{46} -511.482 q^{47} +(284.084 - 492.048i) q^{48} +(124.652 + 215.903i) q^{49} +(-384.826 - 666.539i) q^{50} -323.785 q^{51} +(882.459 - 369.788i) q^{52} +492.825 q^{53} +(71.9603 + 124.639i) q^{54} +(226.404 + 392.142i) q^{55} +(-320.236 + 554.665i) q^{56} +6.74170 q^{57} +(-164.233 + 284.460i) q^{58} +(-242.089 + 419.311i) q^{59} +1005.13 q^{60} +(222.011 - 384.534i) q^{61} +(-511.536 - 886.007i) q^{62} +(-43.5586 - 75.4457i) q^{63} +1044.47 q^{64} +(612.262 + 465.815i) q^{65} -441.167 q^{66} +(-95.0568 - 164.643i) q^{67} +(-1101.57 - 1907.98i) q^{68} +(62.7135 - 108.623i) q^{69} -846.858 q^{70} +(-242.392 + 419.836i) q^{71} +(-297.750 + 515.718i) q^{72} -957.780 q^{73} +(-262.318 + 454.348i) q^{74} +(216.584 + 375.135i) q^{75} +(22.9365 + 39.7271i) q^{76} +267.045 q^{77} +(-691.300 + 289.684i) q^{78} -375.216 q^{79} +(1554.23 + 2692.01i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(81.9421 - 141.928i) q^{82} -715.765 q^{83} +(296.388 - 513.360i) q^{84} +(885.717 - 1534.11i) q^{85} +1270.37 q^{86} +(92.4319 - 160.097i) q^{87} +(-912.708 - 1580.86i) q^{88} +(519.076 + 899.066i) q^{89} -787.394 q^{90} +(418.453 - 175.350i) q^{91} +853.451 q^{92} +(287.898 + 498.654i) q^{93} +(1363.20 + 2361.13i) q^{94} +(-18.4420 + 31.9425i) q^{95} -1440.56 q^{96} +(-32.7818 + 56.7797i) q^{97} +(664.443 - 1150.85i) q^{98} +248.293 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 2 q^{2} + 12 q^{3} - 22 q^{4} - 12 q^{5} + 6 q^{6} + 14 q^{7} + 108 q^{8} - 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 2 q^{2} + 12 q^{3} - 22 q^{4} - 12 q^{5} + 6 q^{6} + 14 q^{7} + 108 q^{8} - 36 q^{9} + 62 q^{10} - 40 q^{11} - 132 q^{12} - 60 q^{13} + 80 q^{14} - 18 q^{15} - 122 q^{16} - 98 q^{17} + 36 q^{18} - 124 q^{19} + 466 q^{20} + 84 q^{21} - 220 q^{22} - 104 q^{23} + 162 q^{24} - 116 q^{25} + 14 q^{26} - 216 q^{27} + 144 q^{28} - 194 q^{29} - 186 q^{30} + 52 q^{31} - 654 q^{32} + 120 q^{33} + 2124 q^{34} - 88 q^{35} - 198 q^{36} - 102 q^{37} + 664 q^{38} + 342 q^{39} - 1996 q^{40} + 1054 q^{41} + 120 q^{42} - 450 q^{43} - 88 q^{44} + 54 q^{45} + 172 q^{46} - 192 q^{47} + 366 q^{48} - 1070 q^{49} - 996 q^{50} - 588 q^{51} + 2280 q^{52} + 524 q^{53} + 54 q^{54} - 204 q^{55} - 2164 q^{56} - 744 q^{57} - 722 q^{58} - 308 q^{59} + 2796 q^{60} + 928 q^{61} - 2780 q^{62} + 126 q^{63} + 2052 q^{64} + 2346 q^{65} - 1320 q^{66} + 1134 q^{67} - 1786 q^{68} + 312 q^{69} - 4648 q^{70} - 1064 q^{71} - 486 q^{72} + 1904 q^{73} - 1158 q^{74} - 174 q^{75} + 1708 q^{76} + 5016 q^{77} + 480 q^{78} - 1492 q^{79} + 2922 q^{80} - 324 q^{81} - 1734 q^{82} - 808 q^{83} - 432 q^{84} + 1394 q^{85} + 6336 q^{86} + 582 q^{87} - 3060 q^{88} - 1620 q^{89} - 1116 q^{90} + 3278 q^{91} + 664 q^{92} + 78 q^{93} + 772 q^{94} - 2204 q^{95} - 3924 q^{96} - 2166 q^{97} + 1906 q^{98} + 720 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.66520 4.61626i −0.942289 1.63209i −0.761090 0.648647i \(-0.775335\pi\)
−0.181199 0.983446i \(-0.557998\pi\)
\(3\) 1.50000 + 2.59808i 0.288675 + 0.500000i
\(4\) −10.2065 + 17.6783i −1.27582 + 2.20978i
\(5\) −16.4131 −1.46803 −0.734016 0.679132i \(-0.762356\pi\)
−0.734016 + 0.679132i \(0.762356\pi\)
\(6\) 7.99559 13.8488i 0.544031 0.942289i
\(7\) −4.83984 + 8.38285i −0.261327 + 0.452631i −0.966595 0.256309i \(-0.917493\pi\)
0.705268 + 0.708941i \(0.250827\pi\)
\(8\) 66.1667 2.92418
\(9\) −4.50000 + 7.79423i −0.166667 + 0.288675i
\(10\) 43.7441 + 75.7670i 1.38331 + 2.39596i
\(11\) −13.7941 23.8921i −0.378098 0.654884i 0.612688 0.790325i \(-0.290088\pi\)
−0.990785 + 0.135441i \(0.956755\pi\)
\(12\) −61.2393 −1.47319
\(13\) −37.3033 28.3807i −0.795852 0.605491i
\(14\) 51.5965 0.984982
\(15\) −24.6196 42.6425i −0.423784 0.734016i
\(16\) −94.6948 164.016i −1.47961 2.56275i
\(17\) −53.9641 + 93.4685i −0.769895 + 1.33350i 0.167725 + 0.985834i \(0.446358\pi\)
−0.937619 + 0.347663i \(0.886975\pi\)
\(18\) 47.9735 0.628193
\(19\) 1.12362 1.94616i 0.0135671 0.0234989i −0.859162 0.511703i \(-0.829015\pi\)
0.872729 + 0.488205i \(0.162348\pi\)
\(20\) 167.521 290.155i 1.87294 3.24403i
\(21\) −29.0391 −0.301754
\(22\) −73.5279 + 127.354i −0.712554 + 1.23418i
\(23\) −20.9045 36.2077i −0.189517 0.328253i 0.755572 0.655065i \(-0.227359\pi\)
−0.945089 + 0.326812i \(0.894026\pi\)
\(24\) 99.2500 + 171.906i 0.844138 + 1.46209i
\(25\) 144.390 1.15512
\(26\) −31.5919 + 247.842i −0.238296 + 1.86945i
\(27\) −27.0000 −0.192450
\(28\) −98.7961 171.120i −0.666811 1.15495i
\(29\) −30.8106 53.3656i −0.197289 0.341715i 0.750359 0.661030i \(-0.229881\pi\)
−0.947649 + 0.319315i \(0.896547\pi\)
\(30\) −131.232 + 227.301i −0.798655 + 1.38331i
\(31\) 191.932 1.11200 0.556000 0.831182i \(-0.312335\pi\)
0.556000 + 0.831182i \(0.312335\pi\)
\(32\) −240.094 + 415.855i −1.32634 + 2.29729i
\(33\) 41.3822 71.6762i 0.218295 0.378098i
\(34\) 575.300 2.90185
\(35\) 79.4368 137.589i 0.383636 0.664477i
\(36\) −91.8589 159.104i −0.425273 0.736594i
\(37\) −49.2118 85.2373i −0.218659 0.378728i 0.735740 0.677265i \(-0.236835\pi\)
−0.954398 + 0.298537i \(0.903501\pi\)
\(38\) −11.9786 −0.0511366
\(39\) 17.7803 139.488i 0.0730031 0.572716i
\(40\) −1086.00 −4.29279
\(41\) 15.3726 + 26.6261i 0.0585561 + 0.101422i 0.893817 0.448431i \(-0.148017\pi\)
−0.835261 + 0.549853i \(0.814684\pi\)
\(42\) 77.3948 + 134.052i 0.284340 + 0.492491i
\(43\) −119.163 + 206.396i −0.422608 + 0.731978i −0.996194 0.0871672i \(-0.972219\pi\)
0.573586 + 0.819145i \(0.305552\pi\)
\(44\) 563.160 1.92953
\(45\) 73.8589 127.927i 0.244672 0.423784i
\(46\) −111.429 + 193.001i −0.357160 + 0.618618i
\(47\) −511.482 −1.58739 −0.793695 0.608316i \(-0.791845\pi\)
−0.793695 + 0.608316i \(0.791845\pi\)
\(48\) 284.084 492.048i 0.854251 1.47961i
\(49\) 124.652 + 215.903i 0.363416 + 0.629456i
\(50\) −384.826 666.539i −1.08845 1.88526i
\(51\) −323.785 −0.888998
\(52\) 882.459 369.788i 2.35337 0.986162i
\(53\) 492.825 1.27726 0.638630 0.769514i \(-0.279502\pi\)
0.638630 + 0.769514i \(0.279502\pi\)
\(54\) 71.9603 + 124.639i 0.181344 + 0.314096i
\(55\) 226.404 + 392.142i 0.555059 + 0.961390i
\(56\) −320.236 + 554.665i −0.764167 + 1.32358i
\(57\) 6.74170 0.0156660
\(58\) −164.233 + 284.460i −0.371807 + 0.643989i
\(59\) −242.089 + 419.311i −0.534192 + 0.925248i 0.465010 + 0.885306i \(0.346051\pi\)
−0.999202 + 0.0399427i \(0.987282\pi\)
\(60\) 1005.13 2.16269
\(61\) 222.011 384.534i 0.465993 0.807123i −0.533253 0.845956i \(-0.679031\pi\)
0.999246 + 0.0388329i \(0.0123640\pi\)
\(62\) −511.536 886.007i −1.04783 1.81489i
\(63\) −43.5586 75.4457i −0.0871090 0.150877i
\(64\) 1044.47 2.03998
\(65\) 612.262 + 465.815i 1.16834 + 0.888880i
\(66\) −441.167 −0.822787
\(67\) −95.0568 164.643i −0.173329 0.300215i 0.766253 0.642539i \(-0.222119\pi\)
−0.939582 + 0.342325i \(0.888786\pi\)
\(68\) −1101.57 1907.98i −1.96449 3.40260i
\(69\) 62.7135 108.623i 0.109418 0.189517i
\(70\) −846.858 −1.44598
\(71\) −242.392 + 419.836i −0.405164 + 0.701765i −0.994341 0.106239i \(-0.966119\pi\)
0.589176 + 0.808005i \(0.299452\pi\)
\(72\) −297.750 + 515.718i −0.487363 + 0.844138i
\(73\) −957.780 −1.53561 −0.767806 0.640683i \(-0.778651\pi\)
−0.767806 + 0.640683i \(0.778651\pi\)
\(74\) −262.318 + 454.348i −0.412079 + 0.713742i
\(75\) 216.584 + 375.135i 0.333453 + 0.577558i
\(76\) 22.9365 + 39.7271i 0.0346183 + 0.0599607i
\(77\) 267.045 0.395228
\(78\) −691.300 + 289.684i −1.00352 + 0.420517i
\(79\) −375.216 −0.534368 −0.267184 0.963646i \(-0.586093\pi\)
−0.267184 + 0.963646i \(0.586093\pi\)
\(80\) 1554.23 + 2692.01i 2.17211 + 3.76220i
\(81\) −40.5000 70.1481i −0.0555556 0.0962250i
\(82\) 81.9421 141.928i 0.110354 0.191138i
\(83\) −715.765 −0.946571 −0.473286 0.880909i \(-0.656932\pi\)
−0.473286 + 0.880909i \(0.656932\pi\)
\(84\) 296.388 513.360i 0.384984 0.666811i
\(85\) 885.717 1534.11i 1.13023 1.95762i
\(86\) 1270.37 1.59288
\(87\) 92.4319 160.097i 0.113905 0.197289i
\(88\) −912.708 1580.86i −1.10563 1.91500i
\(89\) 519.076 + 899.066i 0.618224 + 1.07080i 0.989810 + 0.142397i \(0.0454810\pi\)
−0.371585 + 0.928399i \(0.621186\pi\)
\(90\) −787.394 −0.922207
\(91\) 418.453 175.350i 0.482042 0.201996i
\(92\) 853.451 0.967157
\(93\) 287.898 + 498.654i 0.321007 + 0.556000i
\(94\) 1363.20 + 2361.13i 1.49578 + 2.59077i
\(95\) −18.4420 + 31.9425i −0.0199169 + 0.0344972i
\(96\) −1440.56 −1.53153
\(97\) −32.7818 + 56.7797i −0.0343143 + 0.0594341i −0.882673 0.469989i \(-0.844258\pi\)
0.848358 + 0.529423i \(0.177591\pi\)
\(98\) 664.443 1150.85i 0.684887 1.18626i
\(99\) 248.293 0.252065
\(100\) −1473.72 + 2552.56i −1.47372 + 2.55256i
\(101\) −265.899 460.551i −0.261960 0.453728i 0.704803 0.709403i \(-0.251035\pi\)
−0.966763 + 0.255676i \(0.917702\pi\)
\(102\) 862.949 + 1494.67i 0.837693 + 1.45093i
\(103\) −735.984 −0.704064 −0.352032 0.935988i \(-0.614509\pi\)
−0.352032 + 0.935988i \(0.614509\pi\)
\(104\) −2468.23 1877.86i −2.32721 1.77057i
\(105\) 476.621 0.442985
\(106\) −1313.48 2275.01i −1.20355 2.08461i
\(107\) 391.632 + 678.327i 0.353837 + 0.612863i 0.986918 0.161222i \(-0.0515435\pi\)
−0.633081 + 0.774085i \(0.718210\pi\)
\(108\) 275.577 477.313i 0.245531 0.425273i
\(109\) −532.339 −0.467788 −0.233894 0.972262i \(-0.575147\pi\)
−0.233894 + 0.972262i \(0.575147\pi\)
\(110\) 1206.82 2090.27i 1.04605 1.81182i
\(111\) 147.635 255.712i 0.126243 0.218659i
\(112\) 1833.23 1.54664
\(113\) 90.2946 156.395i 0.0751699 0.130198i −0.825990 0.563684i \(-0.809383\pi\)
0.901160 + 0.433486i \(0.142717\pi\)
\(114\) −17.9679 31.1214i −0.0147619 0.0255683i
\(115\) 343.107 + 594.280i 0.278217 + 0.481886i
\(116\) 1257.88 1.00682
\(117\) 389.070 163.037i 0.307432 0.128827i
\(118\) 2580.86 2.01346
\(119\) −522.355 904.746i −0.402389 0.696957i
\(120\) −1629.00 2821.51i −1.23922 2.14639i
\(121\) 284.947 493.542i 0.214085 0.370805i
\(122\) −2366.81 −1.75640
\(123\) −46.1178 + 79.8784i −0.0338074 + 0.0585561i
\(124\) −1958.96 + 3393.02i −1.41871 + 2.45728i
\(125\) −318.242 −0.227716
\(126\) −232.184 + 402.155i −0.164164 + 0.284340i
\(127\) −715.817 1239.83i −0.500146 0.866278i −1.00000 0.000168331i \(-0.999946\pi\)
0.499854 0.866110i \(-0.333387\pi\)
\(128\) −862.972 1494.71i −0.595912 1.03215i
\(129\) −714.976 −0.487986
\(130\) 518.521 4067.85i 0.349825 2.74441i
\(131\) 2067.32 1.37880 0.689400 0.724381i \(-0.257874\pi\)
0.689400 + 0.724381i \(0.257874\pi\)
\(132\) 844.740 + 1463.13i 0.557009 + 0.964767i
\(133\) 10.8762 + 18.8382i 0.00709090 + 0.0122818i
\(134\) −506.690 + 877.613i −0.326652 + 0.565778i
\(135\) 443.153 0.282523
\(136\) −3570.62 + 6184.50i −2.25131 + 3.89939i
\(137\) 193.756 335.595i 0.120830 0.209283i −0.799265 0.600978i \(-0.794778\pi\)
0.920095 + 0.391695i \(0.128111\pi\)
\(138\) −668.575 −0.412412
\(139\) −376.284 + 651.743i −0.229611 + 0.397699i −0.957693 0.287792i \(-0.907079\pi\)
0.728082 + 0.685491i \(0.240412\pi\)
\(140\) 1621.55 + 2808.61i 0.978900 + 1.69550i
\(141\) −767.223 1328.87i −0.458240 0.793695i
\(142\) 2584.09 1.52713
\(143\) −163.508 + 1282.74i −0.0956171 + 0.750126i
\(144\) 1704.51 0.986404
\(145\) 505.698 + 875.894i 0.289627 + 0.501649i
\(146\) 2552.67 + 4421.36i 1.44699 + 2.50626i
\(147\) −373.956 + 647.710i −0.209819 + 0.363416i
\(148\) 2009.13 1.11587
\(149\) 1318.36 2283.47i 0.724862 1.25550i −0.234169 0.972196i \(-0.575237\pi\)
0.959031 0.283301i \(-0.0914296\pi\)
\(150\) 1154.48 1999.62i 0.628419 1.08845i
\(151\) −3332.42 −1.79595 −0.897975 0.440046i \(-0.854962\pi\)
−0.897975 + 0.440046i \(0.854962\pi\)
\(152\) 74.3459 128.771i 0.0396727 0.0687151i
\(153\) −485.677 841.217i −0.256632 0.444499i
\(154\) −711.727 1232.75i −0.372419 0.645049i
\(155\) −3150.20 −1.63245
\(156\) 2284.43 + 1738.01i 1.17244 + 0.892003i
\(157\) −1625.26 −0.826179 −0.413089 0.910690i \(-0.635550\pi\)
−0.413089 + 0.910690i \(0.635550\pi\)
\(158\) 1000.02 + 1732.09i 0.503529 + 0.872138i
\(159\) 739.238 + 1280.40i 0.368713 + 0.638630i
\(160\) 3940.68 6825.46i 1.94711 3.37250i
\(161\) 404.698 0.198104
\(162\) −215.881 + 373.917i −0.104699 + 0.181344i
\(163\) 917.683 1589.47i 0.440972 0.763786i −0.556790 0.830653i \(-0.687967\pi\)
0.997762 + 0.0668673i \(0.0213004\pi\)
\(164\) −627.605 −0.298828
\(165\) −679.211 + 1176.43i −0.320463 + 0.555059i
\(166\) 1907.65 + 3304.15i 0.891944 + 1.54489i
\(167\) −972.498 1684.42i −0.450624 0.780503i 0.547801 0.836609i \(-0.315465\pi\)
−0.998425 + 0.0561052i \(0.982132\pi\)
\(168\) −1921.42 −0.882384
\(169\) 586.072 + 2117.39i 0.266760 + 0.963763i
\(170\) −9442.44 −4.26001
\(171\) 10.1125 + 17.5154i 0.00452237 + 0.00783298i
\(172\) −2432.48 4213.18i −1.07834 1.86774i
\(173\) −1265.81 + 2192.45i −0.556289 + 0.963522i 0.441512 + 0.897255i \(0.354442\pi\)
−0.997802 + 0.0662666i \(0.978891\pi\)
\(174\) −985.397 −0.429326
\(175\) −698.823 + 1210.40i −0.301863 + 0.522842i
\(176\) −2612.46 + 4524.90i −1.11887 + 1.93794i
\(177\) −1452.54 −0.616832
\(178\) 2766.88 4792.38i 1.16509 2.01800i
\(179\) −2131.51 3691.88i −0.890035 1.54159i −0.839831 0.542847i \(-0.817346\pi\)
−0.0502037 0.998739i \(-0.515987\pi\)
\(180\) 1507.69 + 2611.39i 0.624314 + 1.08134i
\(181\) 3944.61 1.61989 0.809946 0.586504i \(-0.199496\pi\)
0.809946 + 0.586504i \(0.199496\pi\)
\(182\) −1924.72 1464.35i −0.783900 0.596398i
\(183\) 1332.06 0.538082
\(184\) −1383.18 2395.74i −0.554182 0.959871i
\(185\) 807.717 + 1399.01i 0.320998 + 0.555984i
\(186\) 1534.61 2658.02i 0.604962 1.04783i
\(187\) 2977.54 1.16438
\(188\) 5220.46 9042.11i 2.02522 3.50779i
\(189\) 130.676 226.337i 0.0502924 0.0871090i
\(190\) 196.606 0.0750701
\(191\) 107.054 185.424i 0.0405559 0.0702449i −0.845035 0.534711i \(-0.820420\pi\)
0.885591 + 0.464466i \(0.153754\pi\)
\(192\) 1566.71 + 2713.62i 0.588893 + 1.01999i
\(193\) 603.593 + 1045.45i 0.225117 + 0.389914i 0.956355 0.292209i \(-0.0943902\pi\)
−0.731238 + 0.682123i \(0.761057\pi\)
\(194\) 349.480 0.129336
\(195\) −291.829 + 2289.43i −0.107171 + 0.840765i
\(196\) −5089.06 −1.85461
\(197\) 463.816 + 803.352i 0.167744 + 0.290541i 0.937626 0.347645i \(-0.113019\pi\)
−0.769883 + 0.638186i \(0.779685\pi\)
\(198\) −661.751 1146.19i −0.237518 0.411394i
\(199\) −239.476 + 414.784i −0.0853064 + 0.147755i −0.905522 0.424300i \(-0.860520\pi\)
0.820215 + 0.572055i \(0.193854\pi\)
\(200\) 9553.77 3.37777
\(201\) 285.170 493.930i 0.100072 0.173329i
\(202\) −1417.35 + 2454.92i −0.493684 + 0.855086i
\(203\) 596.474 0.206228
\(204\) 3304.72 5723.95i 1.13420 1.96449i
\(205\) −252.312 437.017i −0.0859621 0.148891i
\(206\) 1961.54 + 3397.49i 0.663432 + 1.14910i
\(207\) 376.281 0.126345
\(208\) −1122.46 + 8805.85i −0.374178 + 2.93546i
\(209\) −61.9970 −0.0205188
\(210\) −1270.29 2200.20i −0.417420 0.722992i
\(211\) 725.477 + 1256.56i 0.236701 + 0.409978i 0.959766 0.280802i \(-0.0906005\pi\)
−0.723065 + 0.690780i \(0.757267\pi\)
\(212\) −5030.04 + 8712.29i −1.62955 + 2.82246i
\(213\) −1454.35 −0.467843
\(214\) 2087.55 3615.75i 0.666833 1.15499i
\(215\) 1955.83 3387.59i 0.620402 1.07457i
\(216\) −1786.50 −0.562759
\(217\) −928.920 + 1608.94i −0.290595 + 0.503326i
\(218\) 1418.79 + 2457.41i 0.440791 + 0.763473i
\(219\) −1436.67 2488.38i −0.443293 0.767806i
\(220\) −9243.19 −2.83262
\(221\) 4665.74 1955.15i 1.42014 0.595101i
\(222\) −1573.91 −0.475828
\(223\) 1029.89 + 1783.83i 0.309268 + 0.535668i 0.978202 0.207654i \(-0.0665827\pi\)
−0.668935 + 0.743321i \(0.733249\pi\)
\(224\) −2324.03 4025.34i −0.693218 1.20069i
\(225\) −649.753 + 1125.41i −0.192519 + 0.333453i
\(226\) −962.612 −0.283327
\(227\) −2241.23 + 3881.93i −0.655311 + 1.13503i 0.326504 + 0.945196i \(0.394129\pi\)
−0.981816 + 0.189837i \(0.939204\pi\)
\(228\) −68.8094 + 119.181i −0.0199869 + 0.0346183i
\(229\) −1630.39 −0.470477 −0.235239 0.971938i \(-0.575587\pi\)
−0.235239 + 0.971938i \(0.575587\pi\)
\(230\) 1828.90 3167.74i 0.524321 0.908151i
\(231\) 400.567 + 693.803i 0.114093 + 0.197614i
\(232\) −2038.64 3531.02i −0.576910 0.999237i
\(233\) −1903.69 −0.535258 −0.267629 0.963522i \(-0.586240\pi\)
−0.267629 + 0.963522i \(0.586240\pi\)
\(234\) −1789.57 1361.52i −0.499948 0.380365i
\(235\) 8395.00 2.33034
\(236\) −4941.79 8559.44i −1.36306 2.36090i
\(237\) −562.824 974.839i −0.154259 0.267184i
\(238\) −2784.36 + 4822.65i −0.758333 + 1.31347i
\(239\) 3763.79 1.01866 0.509328 0.860572i \(-0.329894\pi\)
0.509328 + 0.860572i \(0.329894\pi\)
\(240\) −4662.70 + 8076.04i −1.25407 + 2.17211i
\(241\) 1807.37 3130.46i 0.483083 0.836724i −0.516728 0.856149i \(-0.672850\pi\)
0.999811 + 0.0194250i \(0.00618357\pi\)
\(242\) −3037.75 −0.806918
\(243\) 121.500 210.444i 0.0320750 0.0555556i
\(244\) 4531.92 + 7849.52i 1.18904 + 2.05948i
\(245\) −2045.92 3543.64i −0.533507 0.924061i
\(246\) 491.652 0.127425
\(247\) −97.1479 + 40.7092i −0.0250258 + 0.0104869i
\(248\) 12699.5 3.25169
\(249\) −1073.65 1859.61i −0.273252 0.473286i
\(250\) 848.178 + 1469.09i 0.214574 + 0.371653i
\(251\) 2864.88 4962.12i 0.720438 1.24783i −0.240387 0.970677i \(-0.577274\pi\)
0.960824 0.277158i \(-0.0893924\pi\)
\(252\) 1778.33 0.444541
\(253\) −576.717 + 998.903i −0.143312 + 0.248223i
\(254\) −3815.59 + 6608.79i −0.942564 + 1.63257i
\(255\) 5314.30 1.30508
\(256\) −422.095 + 731.091i −0.103051 + 0.178489i
\(257\) 2762.89 + 4785.47i 0.670602 + 1.16152i 0.977734 + 0.209849i \(0.0672974\pi\)
−0.307132 + 0.951667i \(0.599369\pi\)
\(258\) 1905.55 + 3300.51i 0.459824 + 0.796438i
\(259\) 952.709 0.228565
\(260\) −14483.9 + 6069.37i −3.45482 + 1.44772i
\(261\) 554.591 0.131526
\(262\) −5509.82 9543.28i −1.29923 2.25033i
\(263\) −2611.60 4523.43i −0.612313 1.06056i −0.990850 0.134971i \(-0.956906\pi\)
0.378536 0.925586i \(-0.376427\pi\)
\(264\) 2738.12 4742.57i 0.638333 1.10563i
\(265\) −8088.78 −1.87506
\(266\) 57.9747 100.415i 0.0133634 0.0231460i
\(267\) −1557.23 + 2697.20i −0.356932 + 0.618224i
\(268\) 3880.81 0.884545
\(269\) −3601.94 + 6238.75i −0.816410 + 1.41406i 0.0919010 + 0.995768i \(0.470706\pi\)
−0.908311 + 0.418295i \(0.862628\pi\)
\(270\) −1181.09 2045.71i −0.266218 0.461103i
\(271\) 4288.84 + 7428.49i 0.961360 + 1.66512i 0.719091 + 0.694916i \(0.244558\pi\)
0.242269 + 0.970209i \(0.422108\pi\)
\(272\) 20440.5 4.55656
\(273\) 1083.25 + 824.148i 0.240152 + 0.182710i
\(274\) −2065.59 −0.455427
\(275\) −1991.72 3449.76i −0.436747 0.756467i
\(276\) 1280.18 + 2217.33i 0.279194 + 0.483578i
\(277\) −3584.60 + 6208.70i −0.777536 + 1.34673i 0.155822 + 0.987785i \(0.450197\pi\)
−0.933358 + 0.358947i \(0.883136\pi\)
\(278\) 4011.48 0.865442
\(279\) −863.694 + 1495.96i −0.185333 + 0.321007i
\(280\) 5256.06 9103.77i 1.12182 1.94305i
\(281\) 849.157 0.180272 0.0901360 0.995929i \(-0.471270\pi\)
0.0901360 + 0.995929i \(0.471270\pi\)
\(282\) −4089.60 + 7083.40i −0.863589 + 1.49578i
\(283\) −557.686 965.941i −0.117141 0.202895i 0.801492 0.598005i \(-0.204040\pi\)
−0.918634 + 0.395110i \(0.870706\pi\)
\(284\) −4947.97 8570.14i −1.03383 1.79065i
\(285\) −110.652 −0.0229981
\(286\) 6357.23 2663.95i 1.31437 0.550779i
\(287\) −297.604 −0.0612091
\(288\) −2160.84 3742.69i −0.442114 0.765765i
\(289\) −3367.75 5833.11i −0.685476 1.18728i
\(290\) 2695.57 4668.86i 0.545825 0.945396i
\(291\) −196.691 −0.0396227
\(292\) 9775.62 16931.9i 1.95916 3.39337i
\(293\) 931.764 1613.86i 0.185782 0.321784i −0.758058 0.652188i \(-0.773851\pi\)
0.943840 + 0.330403i \(0.107185\pi\)
\(294\) 3986.66 0.790839
\(295\) 3973.43 6882.19i 0.784211 1.35829i
\(296\) −3256.18 5639.87i −0.639397 1.10747i
\(297\) 372.440 + 645.085i 0.0727649 + 0.126033i
\(298\) −14054.8 −2.73212
\(299\) −247.792 + 1943.95i −0.0479269 + 0.375992i
\(300\) −8842.31 −1.70170
\(301\) −1153.46 1997.85i −0.220878 0.382571i
\(302\) 8881.55 + 15383.3i 1.69230 + 2.93116i
\(303\) 797.697 1381.65i 0.151243 0.261960i
\(304\) −425.602 −0.0802959
\(305\) −3643.88 + 6311.39i −0.684092 + 1.18488i
\(306\) −2588.85 + 4484.02i −0.483642 + 0.837693i
\(307\) −6387.50 −1.18747 −0.593736 0.804660i \(-0.702348\pi\)
−0.593736 + 0.804660i \(0.702348\pi\)
\(308\) −2725.60 + 4720.89i −0.504239 + 0.873368i
\(309\) −1103.98 1912.14i −0.203246 0.352032i
\(310\) 8395.89 + 14542.1i 1.53824 + 2.66431i
\(311\) −3492.59 −0.636806 −0.318403 0.947955i \(-0.603147\pi\)
−0.318403 + 0.947955i \(0.603147\pi\)
\(312\) 1176.46 9229.44i 0.213474 1.67473i
\(313\) −5912.01 −1.06762 −0.533812 0.845603i \(-0.679241\pi\)
−0.533812 + 0.845603i \(0.679241\pi\)
\(314\) 4331.64 + 7502.63i 0.778499 + 1.34840i
\(315\) 714.931 + 1238.30i 0.127879 + 0.221492i
\(316\) 3829.66 6633.16i 0.681756 1.18084i
\(317\) −1677.54 −0.297224 −0.148612 0.988896i \(-0.547481\pi\)
−0.148612 + 0.988896i \(0.547481\pi\)
\(318\) 3940.43 6825.02i 0.694869 1.20355i
\(319\) −850.009 + 1472.26i −0.149189 + 0.258403i
\(320\) −17143.0 −2.99476
\(321\) −1174.90 + 2034.98i −0.204288 + 0.353837i
\(322\) −1078.60 1868.19i −0.186671 0.323323i
\(323\) 121.270 + 210.045i 0.0208905 + 0.0361834i
\(324\) 1653.46 0.283515
\(325\) −5386.21 4097.88i −0.919301 0.699413i
\(326\) −9783.22 −1.66209
\(327\) −798.509 1383.06i −0.135039 0.233894i
\(328\) 1017.15 + 1761.76i 0.171228 + 0.296576i
\(329\) 2475.49 4287.68i 0.414828 0.718503i
\(330\) 7240.92 1.20788
\(331\) −1005.15 + 1740.98i −0.166913 + 0.289102i −0.937333 0.348435i \(-0.886713\pi\)
0.770420 + 0.637537i \(0.220047\pi\)
\(332\) 7305.49 12653.5i 1.20765 2.09172i
\(333\) 885.812 0.145772
\(334\) −5183.80 + 8978.60i −0.849236 + 1.47092i
\(335\) 1560.18 + 2702.30i 0.254452 + 0.440724i
\(336\) 2749.85 + 4762.87i 0.446477 + 0.773322i
\(337\) 7139.24 1.15400 0.577002 0.816743i \(-0.304222\pi\)
0.577002 + 0.816743i \(0.304222\pi\)
\(338\) 8212.40 8348.71i 1.32159 1.34352i
\(339\) 541.768 0.0867988
\(340\) 18080.2 + 31315.9i 2.88394 + 4.99512i
\(341\) −2647.53 4585.65i −0.420444 0.728231i
\(342\) 53.9038 93.3642i 0.00852276 0.0147619i
\(343\) −5733.31 −0.902536
\(344\) −7884.60 + 13656.5i −1.23578 + 2.14044i
\(345\) −1029.32 + 1782.84i −0.160629 + 0.278217i
\(346\) 13494.6 2.09674
\(347\) −0.569949 + 0.987181i −8.81743e−5 + 0.000152722i −0.866069 0.499924i \(-0.833361\pi\)
0.865981 + 0.500076i \(0.166695\pi\)
\(348\) 1886.82 + 3268.07i 0.290644 + 0.503411i
\(349\) −6099.55 10564.7i −0.935535 1.62039i −0.773678 0.633579i \(-0.781585\pi\)
−0.161857 0.986814i \(-0.551748\pi\)
\(350\) 7450.00 1.13777
\(351\) 1007.19 + 766.279i 0.153162 + 0.116527i
\(352\) 13247.5 2.00595
\(353\) 5446.15 + 9433.01i 0.821160 + 1.42229i 0.904819 + 0.425796i \(0.140006\pi\)
−0.0836595 + 0.996494i \(0.526661\pi\)
\(354\) 3871.29 + 6705.28i 0.581234 + 1.00673i
\(355\) 3978.41 6890.80i 0.594794 1.03021i
\(356\) −21191.9 −3.15497
\(357\) 1567.07 2714.24i 0.232319 0.402389i
\(358\) −11361.8 + 19679.2i −1.67734 + 2.90524i
\(359\) −3525.78 −0.518339 −0.259169 0.965832i \(-0.583449\pi\)
−0.259169 + 0.965832i \(0.583449\pi\)
\(360\) 4887.00 8464.53i 0.715465 1.23922i
\(361\) 3426.97 + 5935.69i 0.499632 + 0.865388i
\(362\) −10513.2 18209.3i −1.52641 2.64382i
\(363\) 1709.68 0.247204
\(364\) −1171.08 + 9187.24i −0.168630 + 1.32292i
\(365\) 15720.1 2.25433
\(366\) −3550.21 6149.15i −0.507029 0.878200i
\(367\) −1191.88 2064.39i −0.169525 0.293625i 0.768728 0.639576i \(-0.220890\pi\)
−0.938253 + 0.345950i \(0.887557\pi\)
\(368\) −3959.09 + 6857.35i −0.560821 + 0.971370i
\(369\) −276.707 −0.0390374
\(370\) 4305.45 7457.26i 0.604945 1.04780i
\(371\) −2385.20 + 4131.28i −0.333782 + 0.578128i
\(372\) −11753.8 −1.63818
\(373\) 6641.10 11502.7i 0.921885 1.59675i 0.125390 0.992108i \(-0.459982\pi\)
0.796495 0.604645i \(-0.206685\pi\)
\(374\) −7935.73 13745.1i −1.09718 1.90038i
\(375\) −477.363 826.818i −0.0657358 0.113858i
\(376\) −33843.1 −4.64181
\(377\) −365.214 + 2865.14i −0.0498925 + 0.391412i
\(378\) −1393.11 −0.189560
\(379\) 2218.36 + 3842.32i 0.300659 + 0.520756i 0.976285 0.216488i \(-0.0694601\pi\)
−0.675627 + 0.737244i \(0.736127\pi\)
\(380\) −376.458 652.045i −0.0508208 0.0880242i
\(381\) 2147.45 3719.50i 0.288759 0.500146i
\(382\) −1141.28 −0.152862
\(383\) 405.206 701.838i 0.0540602 0.0936351i −0.837729 0.546086i \(-0.816117\pi\)
0.891789 + 0.452451i \(0.149450\pi\)
\(384\) 2588.92 4484.14i 0.344050 0.595912i
\(385\) −4383.03 −0.580207
\(386\) 3217.39 5572.68i 0.424251 0.734824i
\(387\) −1072.46 1857.56i −0.140869 0.243993i
\(388\) −669.177 1159.05i −0.0875576 0.151654i
\(389\) 3463.79 0.451469 0.225734 0.974189i \(-0.427522\pi\)
0.225734 + 0.974189i \(0.427522\pi\)
\(390\) 11346.4 4754.62i 1.47319 0.617332i
\(391\) 4512.37 0.583633
\(392\) 8247.80 + 14285.6i 1.06270 + 1.84064i
\(393\) 3100.98 + 5371.06i 0.398025 + 0.689400i
\(394\) 2472.32 4282.18i 0.316126 0.547546i
\(395\) 6158.45 0.784469
\(396\) −2534.22 + 4389.40i −0.321589 + 0.557009i
\(397\) −212.703 + 368.412i −0.0268898 + 0.0465745i −0.879157 0.476532i \(-0.841894\pi\)
0.852267 + 0.523106i \(0.175227\pi\)
\(398\) 2553.00 0.321533
\(399\) −32.6287 + 56.5146i −0.00409394 + 0.00709090i
\(400\) −13672.9 23682.2i −1.70912 2.96028i
\(401\) 593.424 + 1027.84i 0.0739007 + 0.128000i 0.900608 0.434633i \(-0.143122\pi\)
−0.826707 + 0.562633i \(0.809789\pi\)
\(402\) −3040.14 −0.377185
\(403\) −7159.70 5447.16i −0.884987 0.673306i
\(404\) 10855.6 1.33685
\(405\) 664.730 + 1151.35i 0.0815573 + 0.141261i
\(406\) −1589.72 2753.48i −0.194327 0.336583i
\(407\) −1357.66 + 2351.54i −0.165349 + 0.286392i
\(408\) −21423.7 −2.59959
\(409\) −4003.71 + 6934.63i −0.484036 + 0.838375i −0.999832 0.0183369i \(-0.994163\pi\)
0.515796 + 0.856711i \(0.327496\pi\)
\(410\) −1344.92 + 2329.47i −0.162002 + 0.280596i
\(411\) 1162.54 0.139522
\(412\) 7511.85 13010.9i 0.898258 1.55583i
\(413\) −2343.35 4058.80i −0.279198 0.483585i
\(414\) −1002.86 1737.01i −0.119053 0.206206i
\(415\) 11747.9 1.38960
\(416\) 20758.5 8698.72i 2.44656 1.02522i
\(417\) −2257.70 −0.265132
\(418\) 165.234 + 286.194i 0.0193346 + 0.0334885i
\(419\) −3416.23 5917.08i −0.398314 0.689901i 0.595204 0.803575i \(-0.297071\pi\)
−0.993518 + 0.113674i \(0.963738\pi\)
\(420\) −4864.65 + 8425.82i −0.565168 + 0.978900i
\(421\) 10739.6 1.24326 0.621632 0.783309i \(-0.286470\pi\)
0.621632 + 0.783309i \(0.286470\pi\)
\(422\) 3867.08 6697.98i 0.446082 0.772636i
\(423\) 2301.67 3986.61i 0.264565 0.458240i
\(424\) 32608.6 3.73494
\(425\) −7791.85 + 13495.9i −0.889318 + 1.54034i
\(426\) 3876.14 + 6713.67i 0.440844 + 0.763564i
\(427\) 2148.99 + 3722.16i 0.243553 + 0.421846i
\(428\) −15988.9 −1.80573
\(429\) −3577.91 + 1499.30i −0.402665 + 0.168734i
\(430\) −20850.7 −2.33839
\(431\) −2607.22 4515.84i −0.291382 0.504688i 0.682755 0.730647i \(-0.260782\pi\)
−0.974137 + 0.225959i \(0.927448\pi\)
\(432\) 2556.76 + 4428.44i 0.284750 + 0.493202i
\(433\) −4321.12 + 7484.40i −0.479584 + 0.830664i −0.999726 0.0234161i \(-0.992546\pi\)
0.520142 + 0.854080i \(0.325879\pi\)
\(434\) 9903.02 1.09530
\(435\) −1517.09 + 2627.68i −0.167216 + 0.289627i
\(436\) 5433.34 9410.83i 0.596812 1.03371i
\(437\) −93.9545 −0.0102848
\(438\) −7658.01 + 13264.1i −0.835420 + 1.44699i
\(439\) 6513.12 + 11281.1i 0.708097 + 1.22646i 0.965562 + 0.260172i \(0.0837793\pi\)
−0.257466 + 0.966287i \(0.582887\pi\)
\(440\) 14980.4 + 25946.8i 1.62309 + 2.81128i
\(441\) −2243.73 −0.242278
\(442\) −21460.6 16327.4i −2.30945 1.75705i
\(443\) −11533.0 −1.23690 −0.618450 0.785824i \(-0.712239\pi\)
−0.618450 + 0.785824i \(0.712239\pi\)
\(444\) 3013.69 + 5219.87i 0.322125 + 0.557937i
\(445\) −8519.64 14756.5i −0.907573 1.57196i
\(446\) 5489.74 9508.50i 0.582840 1.00951i
\(447\) 7910.17 0.836998
\(448\) −5055.08 + 8755.65i −0.533103 + 0.923361i
\(449\) −4941.37 + 8558.71i −0.519372 + 0.899578i 0.480375 + 0.877063i \(0.340501\pi\)
−0.999747 + 0.0225149i \(0.992833\pi\)
\(450\) 6926.88 0.725636
\(451\) 424.102 734.566i 0.0442798 0.0766949i
\(452\) 1843.19 + 3192.50i 0.191806 + 0.332218i
\(453\) −4998.63 8657.88i −0.518446 0.897975i
\(454\) 23893.3 2.46997
\(455\) −6868.11 + 2878.04i −0.707653 + 0.296537i
\(456\) 446.075 0.0458101
\(457\) 7814.04 + 13534.3i 0.799836 + 1.38536i 0.919722 + 0.392569i \(0.128414\pi\)
−0.119886 + 0.992788i \(0.538253\pi\)
\(458\) 4345.31 + 7526.31i 0.443326 + 0.767863i
\(459\) 1457.03 2523.65i 0.148166 0.256632i
\(460\) −14007.8 −1.41982
\(461\) 3873.73 6709.50i 0.391361 0.677858i −0.601268 0.799047i \(-0.705338\pi\)
0.992629 + 0.121190i \(0.0386709\pi\)
\(462\) 2135.18 3698.24i 0.215016 0.372419i
\(463\) −333.422 −0.0334675 −0.0167337 0.999860i \(-0.505327\pi\)
−0.0167337 + 0.999860i \(0.505327\pi\)
\(464\) −5835.21 + 10106.9i −0.583821 + 1.01121i
\(465\) −4725.29 8184.45i −0.471248 0.816225i
\(466\) 5073.71 + 8787.93i 0.504368 + 0.873590i
\(467\) 8198.33 0.812363 0.406182 0.913792i \(-0.366860\pi\)
0.406182 + 0.913792i \(0.366860\pi\)
\(468\) −1088.85 + 8542.13i −0.107547 + 0.843719i
\(469\) 1840.24 0.181182
\(470\) −22374.3 38753.5i −2.19585 3.80333i
\(471\) −2437.89 4222.56i −0.238497 0.413089i
\(472\) −16018.2 + 27744.4i −1.56208 + 2.70559i
\(473\) 6574.96 0.639148
\(474\) −3000.07 + 5196.28i −0.290713 + 0.503529i
\(475\) 162.238 281.005i 0.0156716 0.0271440i
\(476\) 21325.8 2.05350
\(477\) −2217.71 + 3841.19i −0.212877 + 0.368713i
\(478\) −10031.2 17374.6i −0.959870 1.66254i
\(479\) 3217.94 + 5573.64i 0.306955 + 0.531662i 0.977695 0.210031i \(-0.0673565\pi\)
−0.670740 + 0.741693i \(0.734023\pi\)
\(480\) 23644.1 2.24833
\(481\) −583.332 + 4576.30i −0.0552966 + 0.433807i
\(482\) −19268.0 −1.82082
\(483\) 607.047 + 1051.44i 0.0571876 + 0.0990518i
\(484\) 5816.64 + 10074.7i 0.546266 + 0.946160i
\(485\) 538.050 931.931i 0.0503745 0.0872511i
\(486\) −1295.29 −0.120896
\(487\) −4047.69 + 7010.80i −0.376629 + 0.652340i −0.990569 0.137012i \(-0.956250\pi\)
0.613941 + 0.789352i \(0.289583\pi\)
\(488\) 14689.7 25443.3i 1.36265 2.36017i
\(489\) 5506.10 0.509191
\(490\) −10905.6 + 18889.0i −1.00544 + 1.74147i
\(491\) −2558.23 4430.99i −0.235135 0.407266i 0.724177 0.689614i \(-0.242220\pi\)
−0.959312 + 0.282348i \(0.908887\pi\)
\(492\) −941.408 1630.57i −0.0862641 0.149414i
\(493\) 6650.67 0.607568
\(494\) 446.842 + 339.962i 0.0406971 + 0.0309628i
\(495\) −4075.26 −0.370039
\(496\) −18175.0 31479.9i −1.64532 2.84978i
\(497\) −2346.28 4063.88i −0.211761 0.366780i
\(498\) −5722.96 + 9912.46i −0.514964 + 0.891944i
\(499\) −18050.7 −1.61936 −0.809682 0.586870i \(-0.800360\pi\)
−0.809682 + 0.586870i \(0.800360\pi\)
\(500\) 3248.15 5625.97i 0.290524 0.503202i
\(501\) 2917.50 5053.25i 0.260168 0.450624i
\(502\) −30541.9 −2.71544
\(503\) −5265.53 + 9120.16i −0.466756 + 0.808445i −0.999279 0.0379705i \(-0.987911\pi\)
0.532523 + 0.846416i \(0.321244\pi\)
\(504\) −2882.13 4991.99i −0.254722 0.441192i
\(505\) 4364.22 + 7559.06i 0.384565 + 0.666087i
\(506\) 6148.25 0.540165
\(507\) −4622.02 + 4698.74i −0.404874 + 0.411595i
\(508\) 29224.1 2.55238
\(509\) 981.654 + 1700.27i 0.0854834 + 0.148062i 0.905597 0.424139i \(-0.139423\pi\)
−0.820114 + 0.572201i \(0.806090\pi\)
\(510\) −14163.7 24532.2i −1.22976 2.13001i
\(511\) 4635.50 8028.93i 0.401297 0.695066i
\(512\) −9307.69 −0.803409
\(513\) −30.3376 + 52.5463i −0.00261099 + 0.00452237i
\(514\) 14727.3 25508.5i 1.26380 2.18897i
\(515\) 12079.8 1.03359
\(516\) 7297.44 12639.5i 0.622581 1.07834i
\(517\) 7055.43 + 12220.4i 0.600188 + 1.03956i
\(518\) −2539.16 4397.95i −0.215375 0.373040i
\(519\) −7594.89 −0.642348
\(520\) 40511.4 + 30821.4i 3.41642 + 2.59925i
\(521\) −7044.93 −0.592407 −0.296203 0.955125i \(-0.595721\pi\)
−0.296203 + 0.955125i \(0.595721\pi\)
\(522\) −1478.10 2560.14i −0.123936 0.214663i
\(523\) 1606.65 + 2782.79i 0.134328 + 0.232664i 0.925341 0.379137i \(-0.123779\pi\)
−0.791012 + 0.611800i \(0.790446\pi\)
\(524\) −21100.2 + 36546.6i −1.75910 + 3.04685i
\(525\) −4192.94 −0.348561
\(526\) −13920.9 + 24111.7i −1.15395 + 1.99870i
\(527\) −10357.4 + 17939.6i −0.856123 + 1.48285i
\(528\) −15674.7 −1.29196
\(529\) 5209.50 9023.13i 0.428167 0.741606i
\(530\) 21558.2 + 37339.9i 1.76685 + 3.06027i
\(531\) −2178.80 3773.80i −0.178064 0.308416i
\(532\) −444.036 −0.0361868
\(533\) 182.219 1429.53i 0.0148082 0.116172i
\(534\) 16601.3 1.34533
\(535\) −6427.90 11133.4i −0.519443 0.899702i
\(536\) −6289.59 10893.9i −0.506845 0.877882i
\(537\) 6394.52 11075.6i 0.513862 0.890035i
\(538\) 38399.5 3.07718
\(539\) 3438.92 5956.38i 0.274814 0.475991i
\(540\) −4523.07 + 7834.18i −0.360448 + 0.624314i
\(541\) 11251.4 0.894150 0.447075 0.894497i \(-0.352466\pi\)
0.447075 + 0.894497i \(0.352466\pi\)
\(542\) 22861.2 39596.8i 1.81176 3.13806i
\(543\) 5916.91 + 10248.4i 0.467623 + 0.809946i
\(544\) −25912.9 44882.4i −2.04229 3.53735i
\(545\) 8737.33 0.686727
\(546\) 917.399 7197.09i 0.0719067 0.564115i
\(547\) 1533.54 0.119871 0.0599353 0.998202i \(-0.480911\pi\)
0.0599353 + 0.998202i \(0.480911\pi\)
\(548\) 3955.16 + 6850.53i 0.308314 + 0.534015i
\(549\) 1998.10 + 3460.80i 0.155331 + 0.269041i
\(550\) −10616.7 + 18388.6i −0.823083 + 1.42562i
\(551\) −138.477 −0.0107066
\(552\) 4149.54 7187.22i 0.319957 0.554182i
\(553\) 1815.98 3145.38i 0.139645 0.241872i
\(554\) 38214.6 2.93066
\(555\) −2423.15 + 4197.02i −0.185328 + 0.320998i
\(556\) −7681.12 13304.1i −0.585885 1.01478i
\(557\) −8422.84 14588.8i −0.640731 1.10978i −0.985270 0.171006i \(-0.945298\pi\)
0.344539 0.938772i \(-0.388035\pi\)
\(558\) 9207.65 0.698550
\(559\) 10302.8 4317.33i 0.779540 0.326661i
\(560\) −30089.0 −2.27052
\(561\) 4466.31 + 7735.88i 0.336128 + 0.582191i
\(562\) −2263.17 3919.92i −0.169868 0.294221i
\(563\) 10410.0 18030.7i 0.779273 1.34974i −0.153089 0.988212i \(-0.548922\pi\)
0.932361 0.361528i \(-0.117745\pi\)
\(564\) 31322.8 2.33852
\(565\) −1482.01 + 2566.92i −0.110352 + 0.191135i
\(566\) −2972.69 + 5148.84i −0.220762 + 0.382371i
\(567\) 784.054 0.0580726
\(568\) −16038.3 + 27779.1i −1.18477 + 2.05209i
\(569\) −11818.3 20469.9i −0.870735 1.50816i −0.861237 0.508203i \(-0.830310\pi\)
−0.00949803 0.999955i \(-0.503023\pi\)
\(570\) 294.909 + 510.798i 0.0216709 + 0.0375351i
\(571\) −26955.1 −1.97554 −0.987771 0.155913i \(-0.950168\pi\)
−0.987771 + 0.155913i \(0.950168\pi\)
\(572\) −21007.7 15982.9i −1.53562 1.16832i
\(573\) 642.326 0.0468300
\(574\) 793.173 + 1373.82i 0.0576767 + 0.0998989i
\(575\) −3018.39 5228.01i −0.218914 0.379170i
\(576\) −4700.12 + 8140.85i −0.339997 + 0.588893i
\(577\) 23499.8 1.69551 0.847755 0.530388i \(-0.177954\pi\)
0.847755 + 0.530388i \(0.177954\pi\)
\(578\) −17951.4 + 31092.8i −1.29183 + 2.23752i
\(579\) −1810.78 + 3136.36i −0.129971 + 0.225117i
\(580\) −20645.7 −1.47805
\(581\) 3464.19 6000.15i 0.247365 0.428448i
\(582\) 524.219 + 907.975i 0.0373361 + 0.0646680i
\(583\) −6798.07 11774.6i −0.482929 0.836457i
\(584\) −63373.1 −4.49040
\(585\) −6385.85 + 2675.95i −0.451320 + 0.189123i
\(586\) −9933.33 −0.700243
\(587\) −2318.75 4016.19i −0.163041 0.282395i 0.772917 0.634507i \(-0.218797\pi\)
−0.935958 + 0.352112i \(0.885464\pi\)
\(588\) −7633.59 13221.8i −0.535381 0.927307i
\(589\) 215.658 373.530i 0.0150866 0.0261308i
\(590\) −42359.9 −2.95582
\(591\) −1391.45 + 2410.06i −0.0968468 + 0.167744i
\(592\) −9320.20 + 16143.1i −0.647057 + 1.12074i
\(593\) 12633.5 0.874869 0.437434 0.899250i \(-0.355887\pi\)
0.437434 + 0.899250i \(0.355887\pi\)
\(594\) 1985.25 3438.56i 0.137131 0.237518i
\(595\) 8573.47 + 14849.7i 0.590719 + 1.02316i
\(596\) 26911.8 + 46612.7i 1.84958 + 3.20357i
\(597\) −1436.85 −0.0985033
\(598\) 9634.18 4037.14i 0.658814 0.276072i
\(599\) −18757.1 −1.27946 −0.639730 0.768600i \(-0.720954\pi\)
−0.639730 + 0.768600i \(0.720954\pi\)
\(600\) 14330.7 + 24821.4i 0.975078 + 1.68888i
\(601\) 1816.49 + 3146.25i 0.123288 + 0.213541i 0.921062 0.389415i \(-0.127323\pi\)
−0.797774 + 0.602956i \(0.793989\pi\)
\(602\) −6148.38 + 10649.3i −0.416261 + 0.720986i
\(603\) 1711.02 0.115553
\(604\) 34012.5 58911.4i 2.29131 3.96866i
\(605\) −4676.85 + 8100.55i −0.314283 + 0.544354i
\(606\) −8504.08 −0.570057
\(607\) 6349.99 10998.5i 0.424610 0.735445i −0.571774 0.820411i \(-0.693745\pi\)
0.996384 + 0.0849656i \(0.0270781\pi\)
\(608\) 539.546 + 934.522i 0.0359893 + 0.0623353i
\(609\) 894.712 + 1549.69i 0.0595329 + 0.103114i
\(610\) 38846.6 2.57845
\(611\) 19080.0 + 14516.2i 1.26333 + 0.961151i
\(612\) 19828.3 1.30966
\(613\) −10820.1 18740.9i −0.712918 1.23481i −0.963757 0.266781i \(-0.914040\pi\)
0.250839 0.968029i \(-0.419293\pi\)
\(614\) 17023.9 + 29486.3i 1.11894 + 1.93806i
\(615\) 756.936 1311.05i 0.0496303 0.0859621i
\(616\) 17669.5 1.15572
\(617\) 8270.85 14325.5i 0.539663 0.934723i −0.459259 0.888302i \(-0.651885\pi\)
0.998922 0.0464208i \(-0.0147815\pi\)
\(618\) −5884.62 + 10192.5i −0.383033 + 0.663432i
\(619\) −21138.9 −1.37261 −0.686303 0.727316i \(-0.740767\pi\)
−0.686303 + 0.727316i \(0.740767\pi\)
\(620\) 32152.6 55690.0i 2.08271 3.60736i
\(621\) 564.421 + 977.607i 0.0364726 + 0.0631723i
\(622\) 9308.44 + 16122.7i 0.600055 + 1.03933i
\(623\) −10049.0 −0.646235
\(624\) −24562.0 + 10292.5i −1.57575 + 0.660305i
\(625\) −12825.4 −0.820823
\(626\) 15756.7 + 27291.3i 1.00601 + 1.74246i
\(627\) −92.9955 161.073i −0.00592326 0.0102594i
\(628\) 16588.3 28731.8i 1.05405 1.82568i
\(629\) 10622.7 0.673377
\(630\) 3810.86 6600.61i 0.240997 0.417420i
\(631\) −2744.90 + 4754.31i −0.173174 + 0.299946i −0.939528 0.342473i \(-0.888736\pi\)
0.766354 + 0.642419i \(0.222069\pi\)
\(632\) −24826.8 −1.56259
\(633\) −2176.43 + 3769.69i −0.136659 + 0.236701i
\(634\) 4470.97 + 7743.94i 0.280071 + 0.485097i
\(635\) 11748.8 + 20349.5i 0.734230 + 1.27172i
\(636\) −30180.3 −1.88164
\(637\) 1477.56 11591.6i 0.0919044 0.720999i
\(638\) 9061.76 0.562318
\(639\) −2181.53 3778.52i −0.135055 0.233922i
\(640\) 14164.0 + 24532.8i 0.874817 + 1.51523i
\(641\) −2148.52 + 3721.35i −0.132389 + 0.229305i −0.924597 0.380946i \(-0.875598\pi\)
0.792208 + 0.610251i \(0.208932\pi\)
\(642\) 12525.3 0.769993
\(643\) −12848.5 + 22254.2i −0.788016 + 1.36488i 0.139164 + 0.990269i \(0.455558\pi\)
−0.927181 + 0.374615i \(0.877775\pi\)
\(644\) −4130.57 + 7154.35i −0.252744 + 0.437766i
\(645\) 11735.0 0.716378
\(646\) 646.416 1119.62i 0.0393698 0.0681905i
\(647\) −1087.49 1883.59i −0.0660798 0.114454i 0.831093 0.556134i \(-0.187716\pi\)
−0.897172 + 0.441680i \(0.854383\pi\)
\(648\) −2679.75 4641.46i −0.162454 0.281379i
\(649\) 13357.6 0.807907
\(650\) −4561.54 + 35785.7i −0.275259 + 2.15943i
\(651\) −5573.52 −0.335551
\(652\) 18732.7 + 32446.1i 1.12520 + 1.94890i
\(653\) 7727.27 + 13384.0i 0.463080 + 0.802078i 0.999113 0.0421191i \(-0.0134109\pi\)
−0.536032 + 0.844197i \(0.680078\pi\)
\(654\) −4256.37 + 7372.24i −0.254491 + 0.440791i
\(655\) −33931.1 −2.02412
\(656\) 2911.41 5042.71i 0.173280 0.300129i
\(657\) 4310.01 7465.15i 0.255935 0.443293i
\(658\) −26390.7 −1.56355
\(659\) 1574.39 2726.92i 0.0930643 0.161192i −0.815735 0.578426i \(-0.803667\pi\)
0.908799 + 0.417234i \(0.137000\pi\)
\(660\) −13864.8 24014.5i −0.817706 1.41631i
\(661\) 1049.85 + 1818.39i 0.0617767 + 0.107000i 0.895260 0.445545i \(-0.146990\pi\)
−0.833483 + 0.552545i \(0.813657\pi\)
\(662\) 10715.7 0.629122
\(663\) 12078.2 + 9189.23i 0.707511 + 0.538281i
\(664\) −47359.8 −2.76795
\(665\) −178.513 309.193i −0.0104097 0.0180301i
\(666\) −2360.86 4089.14i −0.137360 0.237914i
\(667\) −1288.16 + 2231.16i −0.0747794 + 0.129522i
\(668\) 39703.4 2.29966
\(669\) −3089.68 + 5351.48i −0.178556 + 0.309268i
\(670\) 8316.35 14404.3i 0.479535 0.830580i
\(671\) −12249.7 −0.704763
\(672\) 6972.09 12076.0i 0.400230 0.693218i
\(673\) −15485.4 26821.5i −0.886950 1.53624i −0.843462 0.537189i \(-0.819486\pi\)
−0.0434884 0.999054i \(-0.513847\pi\)
\(674\) −19027.5 32956.6i −1.08741 1.88344i
\(675\) −3898.52 −0.222302
\(676\) −43413.5 11250.5i −2.47004 0.640104i
\(677\) 14640.6 0.831141 0.415570 0.909561i \(-0.363582\pi\)
0.415570 + 0.909561i \(0.363582\pi\)
\(678\) −1443.92 2500.94i −0.0817895 0.141664i
\(679\) −317.317 549.610i −0.0179345 0.0310635i
\(680\) 58605.0 101507.i 3.30500 5.72442i
\(681\) −13447.4 −0.756688
\(682\) −14112.4 + 24443.3i −0.792360 + 1.37241i
\(683\) 3342.92 5790.10i 0.187281 0.324381i −0.757062 0.653343i \(-0.773366\pi\)
0.944343 + 0.328963i \(0.106699\pi\)
\(684\) −412.856 −0.0230789
\(685\) −3180.13 + 5508.15i −0.177382 + 0.307235i
\(686\) 15280.4 + 26466.4i 0.850450 + 1.47302i
\(687\) −2445.59 4235.88i −0.135815 0.235239i
\(688\) 45136.3 2.50117
\(689\) −18384.0 13986.7i −1.01651 0.773370i
\(690\) 10973.4 0.605434
\(691\) 15097.0 + 26148.8i 0.831141 + 1.43958i 0.897134 + 0.441758i \(0.145645\pi\)
−0.0659934 + 0.997820i \(0.521022\pi\)
\(692\) −25839.2 44754.8i −1.41945 2.45856i
\(693\) −1201.70 + 2081.41i −0.0658714 + 0.114093i
\(694\) 6.07611 0.000332343
\(695\) 6175.98 10697.1i 0.337077 0.583834i
\(696\) 6115.91 10593.1i 0.333079 0.576910i
\(697\) −3318.28 −0.180328
\(698\) −32513.0 + 56314.2i −1.76309 + 3.05376i
\(699\) −2855.54 4945.94i −0.154516 0.267629i
\(700\) −14265.1 24707.9i −0.770245 1.33410i
\(701\) −30300.9 −1.63260 −0.816298 0.577631i \(-0.803977\pi\)
−0.816298 + 0.577631i \(0.803977\pi\)
\(702\) 852.982 6691.73i 0.0458600 0.359776i
\(703\) −221.181 −0.0118663
\(704\) −14407.5 24954.6i −0.771313 1.33595i
\(705\) 12592.5 + 21810.9i 0.672711 + 1.16517i
\(706\) 29030.1 50281.7i 1.54754 2.68042i
\(707\) 5147.64 0.273829
\(708\) 14825.4 25678.3i 0.786966 1.36306i
\(709\) −13061.6 + 22623.4i −0.691875 + 1.19836i 0.279348 + 0.960190i \(0.409882\pi\)
−0.971223 + 0.238173i \(0.923452\pi\)
\(710\) −42412.9 −2.24187
\(711\) 1688.47 2924.52i 0.0890613 0.154259i
\(712\) 34345.5 + 59488.2i 1.80780 + 3.13120i
\(713\) −4012.24 6949.41i −0.210743 0.365017i
\(714\) −16706.2 −0.875647
\(715\) 2683.68 21053.7i 0.140369 1.10121i
\(716\) 87021.3 4.54209
\(717\) 5645.68 + 9778.60i 0.294061 + 0.509328i
\(718\) 9396.90 + 16275.9i 0.488425 + 0.845977i
\(719\) −9662.83 + 16736.5i −0.501200 + 0.868104i 0.498799 + 0.866718i \(0.333775\pi\)
−0.999999 + 0.00138631i \(0.999559\pi\)
\(720\) −27976.2 −1.44807
\(721\) 3562.05 6169.64i 0.183991 0.318682i
\(722\) 18267.1 31639.6i 0.941595 1.63089i
\(723\) 10844.2 0.557816
\(724\) −40260.8 + 69733.8i −2.06669 + 3.57961i
\(725\) −4448.73 7705.43i −0.227892 0.394721i
\(726\) −4556.63 7892.32i −0.232937 0.403459i
\(727\) 26065.8 1.32975 0.664875 0.746954i \(-0.268485\pi\)
0.664875 + 0.746954i \(0.268485\pi\)
\(728\) 27687.7 11602.3i 1.40958 0.590674i
\(729\) 729.000 0.0370370
\(730\) −41897.2 72568.1i −2.12423 3.67927i
\(731\) −12861.0 22275.9i −0.650727 1.12709i
\(732\) −13595.8 + 23548.6i −0.686495 + 1.18904i
\(733\) 1055.45 0.0531843 0.0265921 0.999646i \(-0.491534\pi\)
0.0265921 + 0.999646i \(0.491534\pi\)
\(734\) −6353.18 + 11004.0i −0.319482 + 0.553359i
\(735\) 6137.77 10630.9i 0.308020 0.533507i
\(736\) 20076.2 1.00546
\(737\) −2622.44 + 4542.21i −0.131070 + 0.227021i
\(738\) 737.479 + 1277.35i 0.0367845 + 0.0637126i
\(739\) −4705.20 8149.64i −0.234213 0.405669i 0.724831 0.688927i \(-0.241918\pi\)
−0.959044 + 0.283258i \(0.908585\pi\)
\(740\) −32976.0 −1.63814
\(741\) −251.487 191.334i −0.0124678 0.00948560i
\(742\) 25428.1 1.25808
\(743\) 3761.85 + 6515.72i 0.185746 + 0.321721i 0.943827 0.330439i \(-0.107197\pi\)
−0.758082 + 0.652159i \(0.773863\pi\)
\(744\) 19049.2 + 32994.3i 0.938682 + 1.62584i
\(745\) −21638.4 + 37478.8i −1.06412 + 1.84311i
\(746\) −70799.4 −3.47473
\(747\) 3220.94 5578.84i 0.157762 0.273252i
\(748\) −30390.4 + 52637.7i −1.48554 + 2.57303i
\(749\) −7581.76 −0.369868
\(750\) −2544.53 + 4407.26i −0.123884 + 0.214574i
\(751\) 6492.03 + 11244.5i 0.315443 + 0.546363i 0.979532 0.201291i \(-0.0645136\pi\)
−0.664089 + 0.747654i \(0.731180\pi\)
\(752\) 48434.7 + 83891.3i 2.34871 + 4.06809i
\(753\) 17189.3 0.831890
\(754\) 14199.6 5950.24i 0.685833 0.287394i
\(755\) 54695.3 2.63651
\(756\) 2667.50 + 4620.24i 0.128328 + 0.222270i
\(757\) 13967.3 + 24192.1i 0.670609 + 1.16153i 0.977732 + 0.209859i \(0.0673004\pi\)
−0.307123 + 0.951670i \(0.599366\pi\)
\(758\) 11824.7 20481.1i 0.566615 0.981406i
\(759\) −3460.30 −0.165482
\(760\) −1220.25 + 2113.53i −0.0582408 + 0.100876i
\(761\) 7759.63 13440.1i 0.369627 0.640214i −0.619880 0.784697i \(-0.712819\pi\)
0.989507 + 0.144483i \(0.0461520\pi\)
\(762\) −22893.5 −1.08838
\(763\) 2576.44 4462.52i 0.122246 0.211735i
\(764\) 2185.31 + 3785.07i 0.103484 + 0.179240i
\(765\) 7971.46 + 13807.0i 0.376743 + 0.652539i
\(766\) −4319.82 −0.203761
\(767\) 20931.1 8771.02i 0.985368 0.412912i
\(768\) −2532.57 −0.118993
\(769\) −6442.59 11158.9i −0.302114 0.523277i 0.674501 0.738274i \(-0.264359\pi\)
−0.976615 + 0.214997i \(0.931026\pi\)
\(770\) 11681.6 + 20233.2i 0.546723 + 0.946952i
\(771\) −8288.68 + 14356.4i