Properties

Label 169.4.e.e.147.2
Level $169$
Weight $4$
Character 169.147
Analytic conductor $9.971$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 169 = 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 169.e (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.97132279097\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 13)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 147.2
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 169.147
Dual form 169.4.e.e.23.2

$q$-expansion

\(f(q)\) \(=\) \(q+(4.33013 + 2.50000i) q^{2} +(3.50000 - 6.06218i) q^{3} +(8.50000 + 14.7224i) q^{4} -7.00000i q^{5} +(30.3109 - 17.5000i) q^{6} +(11.2583 - 6.50000i) q^{7} +45.0000i q^{8} +(-11.0000 - 19.0526i) q^{9} +O(q^{10})\) \(q+(4.33013 + 2.50000i) q^{2} +(3.50000 - 6.06218i) q^{3} +(8.50000 + 14.7224i) q^{4} -7.00000i q^{5} +(30.3109 - 17.5000i) q^{6} +(11.2583 - 6.50000i) q^{7} +45.0000i q^{8} +(-11.0000 - 19.0526i) q^{9} +(17.5000 - 30.3109i) q^{10} +(-22.5167 - 13.0000i) q^{11} +119.000 q^{12} +65.0000 q^{14} +(-42.4352 - 24.5000i) q^{15} +(-44.5000 + 77.0763i) q^{16} +(38.5000 + 66.6840i) q^{17} -110.000i q^{18} +(-109.119 + 63.0000i) q^{19} +(103.057 - 59.5000i) q^{20} -91.0000i q^{21} +(-65.0000 - 112.583i) q^{22} +(-48.0000 + 83.1384i) q^{23} +(272.798 + 157.500i) q^{24} +76.0000 q^{25} +35.0000 q^{27} +(191.392 + 110.500i) q^{28} +(41.0000 - 71.0141i) q^{29} +(-122.500 - 212.176i) q^{30} +196.000i q^{31} +(-73.6122 + 42.5000i) q^{32} +(-157.617 + 91.0000i) q^{33} +385.000i q^{34} +(-45.5000 - 78.8083i) q^{35} +(187.000 - 323.894i) q^{36} +(-113.449 - 65.5000i) q^{37} -630.000 q^{38} +315.000 q^{40} +(-290.985 - 168.000i) q^{41} +(227.500 - 394.042i) q^{42} +(-100.500 - 174.071i) q^{43} -442.000i q^{44} +(-133.368 + 77.0000i) q^{45} +(-415.692 + 240.000i) q^{46} +105.000i q^{47} +(311.500 + 539.534i) q^{48} +(-87.0000 + 150.688i) q^{49} +(329.090 + 190.000i) q^{50} +539.000 q^{51} -432.000 q^{53} +(151.554 + 87.5000i) q^{54} +(-91.0000 + 157.617i) q^{55} +(292.500 + 506.625i) q^{56} +882.000i q^{57} +(355.070 - 205.000i) q^{58} +(254.611 - 147.000i) q^{59} -833.000i q^{60} +(28.0000 + 48.4974i) q^{61} +(-490.000 + 848.705i) q^{62} +(-247.683 - 143.000i) q^{63} +287.000 q^{64} -910.000 q^{66} +(-413.960 - 239.000i) q^{67} +(-654.500 + 1133.63i) q^{68} +(336.000 + 581.969i) q^{69} -455.000i q^{70} +(7.79423 - 4.50000i) q^{71} +(857.365 - 495.000i) q^{72} -98.0000i q^{73} +(-327.500 - 567.247i) q^{74} +(266.000 - 460.726i) q^{75} +(-1855.03 - 1071.00i) q^{76} -338.000 q^{77} +1304.00 q^{79} +(539.534 + 311.500i) q^{80} +(419.500 - 726.595i) q^{81} +(-840.000 - 1454.92i) q^{82} -308.000i q^{83} +(1339.74 - 773.500i) q^{84} +(466.788 - 269.500i) q^{85} -1005.00i q^{86} +(-287.000 - 497.099i) q^{87} +(585.000 - 1013.25i) q^{88} +(-1030.57 - 595.000i) q^{89} -770.000 q^{90} -1632.00 q^{92} +(1188.19 + 686.000i) q^{93} +(-262.500 + 454.663i) q^{94} +(441.000 + 763.834i) q^{95} +595.000i q^{96} +(60.6218 - 35.0000i) q^{97} +(-753.442 + 435.000i) q^{98} +572.000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 14 q^{3} + 34 q^{4} - 44 q^{9} + O(q^{10}) \) \( 4 q + 14 q^{3} + 34 q^{4} - 44 q^{9} + 70 q^{10} + 476 q^{12} + 260 q^{14} - 178 q^{16} + 154 q^{17} - 260 q^{22} - 192 q^{23} + 304 q^{25} + 140 q^{27} + 164 q^{29} - 490 q^{30} - 182 q^{35} + 748 q^{36} - 2520 q^{38} + 1260 q^{40} + 910 q^{42} - 402 q^{43} + 1246 q^{48} - 348 q^{49} + 2156 q^{51} - 1728 q^{53} - 364 q^{55} + 1170 q^{56} + 112 q^{61} - 1960 q^{62} + 1148 q^{64} - 3640 q^{66} - 2618 q^{68} + 1344 q^{69} - 1310 q^{74} + 1064 q^{75} - 1352 q^{77} + 5216 q^{79} + 1678 q^{81} - 3360 q^{82} - 1148 q^{87} + 2340 q^{88} - 3080 q^{90} - 6528 q^{92} - 1050 q^{94} + 1764 q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/169\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.33013 + 2.50000i 1.53093 + 0.883883i 0.999319 + 0.0368954i \(0.0117469\pi\)
0.531612 + 0.846988i \(0.321586\pi\)
\(3\) 3.50000 6.06218i 0.673575 1.16667i −0.303308 0.952893i \(-0.598091\pi\)
0.976883 0.213774i \(-0.0685756\pi\)
\(4\) 8.50000 + 14.7224i 1.06250 + 1.84030i
\(5\) 7.00000i 0.626099i −0.949737 0.313050i \(-0.898649\pi\)
0.949737 0.313050i \(-0.101351\pi\)
\(6\) 30.3109 17.5000i 2.06239 1.19072i
\(7\) 11.2583 6.50000i 0.607893 0.350967i −0.164248 0.986419i \(-0.552520\pi\)
0.772140 + 0.635452i \(0.219186\pi\)
\(8\) 45.0000i 1.98874i
\(9\) −11.0000 19.0526i −0.407407 0.705650i
\(10\) 17.5000 30.3109i 0.553399 0.958514i
\(11\) −22.5167 13.0000i −0.617184 0.356332i 0.158588 0.987345i \(-0.449306\pi\)
−0.775772 + 0.631013i \(0.782639\pi\)
\(12\) 119.000 2.86270
\(13\) 0 0
\(14\) 65.0000 1.24086
\(15\) −42.4352 24.5000i −0.730449 0.421725i
\(16\) −44.5000 + 77.0763i −0.695312 + 1.20432i
\(17\) 38.5000 + 66.6840i 0.549272 + 0.951367i 0.998325 + 0.0578615i \(0.0184282\pi\)
−0.449053 + 0.893505i \(0.648238\pi\)
\(18\) 110.000i 1.44040i
\(19\) −109.119 + 63.0000i −1.31756 + 0.760694i −0.983336 0.181799i \(-0.941808\pi\)
−0.334225 + 0.942493i \(0.608475\pi\)
\(20\) 103.057 59.5000i 1.15221 0.665230i
\(21\) 91.0000i 0.945611i
\(22\) −65.0000 112.583i −0.629911 1.09104i
\(23\) −48.0000 + 83.1384i −0.435161 + 0.753720i −0.997309 0.0733164i \(-0.976642\pi\)
0.562148 + 0.827037i \(0.309975\pi\)
\(24\) 272.798 + 157.500i 2.32019 + 1.33956i
\(25\) 76.0000 0.608000
\(26\) 0 0
\(27\) 35.0000 0.249472
\(28\) 191.392 + 110.500i 1.29177 + 0.745805i
\(29\) 41.0000 71.0141i 0.262535 0.454724i −0.704380 0.709823i \(-0.748775\pi\)
0.966915 + 0.255099i \(0.0821082\pi\)
\(30\) −122.500 212.176i −0.745511 1.29126i
\(31\) 196.000i 1.13557i 0.823177 + 0.567785i \(0.192199\pi\)
−0.823177 + 0.567785i \(0.807801\pi\)
\(32\) −73.6122 + 42.5000i −0.406654 + 0.234782i
\(33\) −157.617 + 91.0000i −0.831440 + 0.480032i
\(34\) 385.000i 1.94197i
\(35\) −45.5000 78.8083i −0.219740 0.380601i
\(36\) 187.000 323.894i 0.865741 1.49951i
\(37\) −113.449 65.5000i −0.504080 0.291031i 0.226317 0.974054i \(-0.427331\pi\)
−0.730397 + 0.683023i \(0.760665\pi\)
\(38\) −630.000 −2.68946
\(39\) 0 0
\(40\) 315.000 1.24515
\(41\) −290.985 168.000i −1.10839 0.639932i −0.169981 0.985447i \(-0.554371\pi\)
−0.938413 + 0.345516i \(0.887704\pi\)
\(42\) 227.500 394.042i 0.835810 1.44767i
\(43\) −100.500 174.071i −0.356421 0.617339i 0.630939 0.775832i \(-0.282670\pi\)
−0.987360 + 0.158493i \(0.949336\pi\)
\(44\) 442.000i 1.51441i
\(45\) −133.368 + 77.0000i −0.441807 + 0.255077i
\(46\) −415.692 + 240.000i −1.33240 + 0.769262i
\(47\) 105.000i 0.325869i 0.986637 + 0.162934i \(0.0520959\pi\)
−0.986637 + 0.162934i \(0.947904\pi\)
\(48\) 311.500 + 539.534i 0.936691 + 1.62240i
\(49\) −87.0000 + 150.688i −0.253644 + 0.439325i
\(50\) 329.090 + 190.000i 0.930806 + 0.537401i
\(51\) 539.000 1.47990
\(52\) 0 0
\(53\) −432.000 −1.11962 −0.559809 0.828622i \(-0.689126\pi\)
−0.559809 + 0.828622i \(0.689126\pi\)
\(54\) 151.554 + 87.5000i 0.381925 + 0.220504i
\(55\) −91.0000 + 157.617i −0.223099 + 0.386419i
\(56\) 292.500 + 506.625i 0.697981 + 1.20894i
\(57\) 882.000i 2.04954i
\(58\) 355.070 205.000i 0.803845 0.464100i
\(59\) 254.611 147.000i 0.561824 0.324369i −0.192054 0.981384i \(-0.561515\pi\)
0.753877 + 0.657015i \(0.228181\pi\)
\(60\) 833.000i 1.79233i
\(61\) 28.0000 + 48.4974i 0.0587710 + 0.101794i 0.893914 0.448239i \(-0.147948\pi\)
−0.835143 + 0.550033i \(0.814615\pi\)
\(62\) −490.000 + 848.705i −1.00371 + 1.73848i
\(63\) −247.683 143.000i −0.495320 0.285973i
\(64\) 287.000 0.560547
\(65\) 0 0
\(66\) −910.000 −1.69717
\(67\) −413.960 239.000i −0.754825 0.435798i 0.0726096 0.997360i \(-0.476867\pi\)
−0.827435 + 0.561562i \(0.810201\pi\)
\(68\) −654.500 + 1133.63i −1.16720 + 2.02165i
\(69\) 336.000 + 581.969i 0.586227 + 1.01537i
\(70\) 455.000i 0.776899i
\(71\) 7.79423 4.50000i 0.0130282 0.00752186i −0.493472 0.869762i \(-0.664272\pi\)
0.506500 + 0.862240i \(0.330939\pi\)
\(72\) 857.365 495.000i 1.40335 0.810227i
\(73\) 98.0000i 0.157124i −0.996909 0.0785619i \(-0.974967\pi\)
0.996909 0.0785619i \(-0.0250328\pi\)
\(74\) −327.500 567.247i −0.514474 0.891096i
\(75\) 266.000 460.726i 0.409534 0.709333i
\(76\) −1855.03 1071.00i −2.79982 1.61648i
\(77\) −338.000 −0.500243
\(78\) 0 0
\(79\) 1304.00 1.85711 0.928554 0.371198i \(-0.121053\pi\)
0.928554 + 0.371198i \(0.121053\pi\)
\(80\) 539.534 + 311.500i 0.754021 + 0.435334i
\(81\) 419.500 726.595i 0.575446 0.996701i
\(82\) −840.000 1454.92i −1.13125 1.95938i
\(83\) 308.000i 0.407318i −0.979042 0.203659i \(-0.934717\pi\)
0.979042 0.203659i \(-0.0652834\pi\)
\(84\) 1339.74 773.500i 1.74021 1.00471i
\(85\) 466.788 269.500i 0.595650 0.343899i
\(86\) 1005.00i 1.26014i
\(87\) −287.000 497.099i −0.353674 0.612581i
\(88\) 585.000 1013.25i 0.708650 1.22742i
\(89\) −1030.57 595.000i −1.22742 0.708650i −0.260929 0.965358i \(-0.584029\pi\)
−0.966489 + 0.256708i \(0.917362\pi\)
\(90\) −770.000 −0.901835
\(91\) 0 0
\(92\) −1632.00 −1.84943
\(93\) 1188.19 + 686.000i 1.32483 + 0.764891i
\(94\) −262.500 + 454.663i −0.288030 + 0.498882i
\(95\) 441.000 + 763.834i 0.476270 + 0.824924i
\(96\) 595.000i 0.632572i
\(97\) 60.6218 35.0000i 0.0634558 0.0366362i −0.467936 0.883762i \(-0.655002\pi\)
0.531392 + 0.847126i \(0.321669\pi\)
\(98\) −753.442 + 435.000i −0.776624 + 0.448384i
\(99\) 572.000i 0.580689i
\(100\) 646.000 + 1118.90i 0.646000 + 1.11890i
\(101\) 210.000 363.731i 0.206889 0.358342i −0.743844 0.668353i \(-0.766999\pi\)
0.950733 + 0.310011i \(0.100333\pi\)
\(102\) 2333.94 + 1347.50i 2.26563 + 1.30806i
\(103\) −588.000 −0.562499 −0.281249 0.959635i \(-0.590749\pi\)
−0.281249 + 0.959635i \(0.590749\pi\)
\(104\) 0 0
\(105\) −637.000 −0.592046
\(106\) −1870.61 1080.00i −1.71406 0.989612i
\(107\) 342.000 592.361i 0.308994 0.535194i −0.669148 0.743129i \(-0.733341\pi\)
0.978143 + 0.207935i \(0.0666743\pi\)
\(108\) 297.500 + 515.285i 0.265064 + 0.459105i
\(109\) 373.000i 0.327770i 0.986479 + 0.163885i \(0.0524026\pi\)
−0.986479 + 0.163885i \(0.947597\pi\)
\(110\) −788.083 + 455.000i −0.683098 + 0.394387i
\(111\) −794.145 + 458.500i −0.679071 + 0.392062i
\(112\) 1157.00i 0.976127i
\(113\) 867.000 + 1501.69i 0.721774 + 1.25015i 0.960288 + 0.279011i \(0.0900065\pi\)
−0.238514 + 0.971139i \(0.576660\pi\)
\(114\) −2205.00 + 3819.17i −1.81155 + 3.13770i
\(115\) 581.969 + 336.000i 0.471903 + 0.272454i
\(116\) 1394.00 1.11577
\(117\) 0 0
\(118\) 1470.00 1.14682
\(119\) 866.891 + 500.500i 0.667797 + 0.385553i
\(120\) 1102.50 1909.59i 0.838700 1.45267i
\(121\) −327.500 567.247i −0.246056 0.426181i
\(122\) 280.000i 0.207787i
\(123\) −2036.89 + 1176.00i −1.49317 + 0.862084i
\(124\) −2885.60 + 1666.00i −2.08979 + 1.20654i
\(125\) 1407.00i 1.00677i
\(126\) −715.000 1238.42i −0.505534 0.875610i
\(127\) 946.000 1638.52i 0.660976 1.14484i −0.319384 0.947625i \(-0.603476\pi\)
0.980360 0.197218i \(-0.0631907\pi\)
\(128\) 1831.64 + 1057.50i 1.26481 + 0.730240i
\(129\) −1407.00 −0.960306
\(130\) 0 0
\(131\) 1435.00 0.957073 0.478536 0.878068i \(-0.341167\pi\)
0.478536 + 0.878068i \(0.341167\pi\)
\(132\) −2679.48 1547.00i −1.76681 1.02007i
\(133\) −819.000 + 1418.55i −0.533957 + 0.924841i
\(134\) −1195.00 2069.80i −0.770390 1.33435i
\(135\) 245.000i 0.156194i
\(136\) −3000.78 + 1732.50i −1.89202 + 1.09236i
\(137\) 1538.06 888.000i 0.959164 0.553773i 0.0632482 0.997998i \(-0.479854\pi\)
0.895916 + 0.444224i \(0.146521\pi\)
\(138\) 3360.00i 2.07262i
\(139\) 934.500 + 1618.60i 0.570239 + 0.987683i 0.996541 + 0.0831023i \(0.0264828\pi\)
−0.426302 + 0.904581i \(0.640184\pi\)
\(140\) 773.500 1339.74i 0.466948 0.808777i
\(141\) 636.529 + 367.500i 0.380180 + 0.219497i
\(142\) 45.0000 0.0265938
\(143\) 0 0
\(144\) 1958.00 1.13310
\(145\) −497.099 287.000i −0.284702 0.164373i
\(146\) 245.000 424.352i 0.138879 0.240546i
\(147\) 609.000 + 1054.82i 0.341697 + 0.591837i
\(148\) 2227.00i 1.23688i
\(149\) 2135.62 1233.00i 1.17421 0.677928i 0.219539 0.975604i \(-0.429545\pi\)
0.954667 + 0.297676i \(0.0962114\pi\)
\(150\) 2303.63 1330.00i 1.25394 0.723960i
\(151\) 3323.00i 1.79087i 0.445189 + 0.895437i \(0.353137\pi\)
−0.445189 + 0.895437i \(0.646863\pi\)
\(152\) −2835.00 4910.36i −1.51282 2.62028i
\(153\) 847.000 1467.05i 0.447555 0.775188i
\(154\) −1463.58 845.000i −0.765837 0.442156i
\(155\) 1372.00 0.710979
\(156\) 0 0
\(157\) −2730.00 −1.38776 −0.693878 0.720092i \(-0.744099\pi\)
−0.693878 + 0.720092i \(0.744099\pi\)
\(158\) 5646.49 + 3260.00i 2.84310 + 1.64147i
\(159\) −1512.00 + 2618.86i −0.754147 + 1.30622i
\(160\) 297.500 + 515.285i 0.146997 + 0.254605i
\(161\) 1248.00i 0.610908i
\(162\) 3632.98 2097.50i 1.76194 1.01725i
\(163\) 471.118 272.000i 0.226385 0.130704i −0.382518 0.923948i \(-0.624943\pi\)
0.608903 + 0.793244i \(0.291610\pi\)
\(164\) 5712.00i 2.71971i
\(165\) 637.000 + 1103.32i 0.300548 + 0.520564i
\(166\) 770.000 1333.68i 0.360022 0.623576i
\(167\) 1406.43 + 812.000i 0.651691 + 0.376254i 0.789104 0.614260i \(-0.210545\pi\)
−0.137413 + 0.990514i \(0.543879\pi\)
\(168\) 4095.00 1.88057
\(169\) 0 0
\(170\) 2695.00 1.21587
\(171\) 2400.62 + 1386.00i 1.07357 + 0.619825i
\(172\) 1708.50 2959.21i 0.757395 1.31185i
\(173\) −168.000 290.985i −0.0738312 0.127879i 0.826746 0.562575i \(-0.190189\pi\)
−0.900577 + 0.434696i \(0.856856\pi\)
\(174\) 2870.00i 1.25043i
\(175\) 855.633 494.000i 0.369599 0.213388i
\(176\) 2003.98 1157.00i 0.858272 0.495524i
\(177\) 2058.00i 0.873948i
\(178\) −2975.00 5152.85i −1.25273 2.16979i
\(179\) −1514.50 + 2623.19i −0.632397 + 1.09534i 0.354663 + 0.934994i \(0.384595\pi\)
−0.987060 + 0.160350i \(0.948738\pi\)
\(180\) −2267.25 1309.00i −0.938840 0.542039i
\(181\) 28.0000 0.0114985 0.00574924 0.999983i \(-0.498170\pi\)
0.00574924 + 0.999983i \(0.498170\pi\)
\(182\) 0 0
\(183\) 392.000 0.158347
\(184\) −3741.23 2160.00i −1.49895 0.865420i
\(185\) −458.500 + 794.145i −0.182214 + 0.315604i
\(186\) 3430.00 + 5940.93i 1.35215 + 2.34199i
\(187\) 2002.00i 0.782892i
\(188\) −1545.86 + 892.500i −0.599697 + 0.346235i
\(189\) 394.042 227.500i 0.151652 0.0875566i
\(190\) 4410.00i 1.68387i
\(191\) −211.000 365.463i −0.0799342 0.138450i 0.823287 0.567625i \(-0.192138\pi\)
−0.903221 + 0.429175i \(0.858804\pi\)
\(192\) 1004.50 1739.85i 0.377571 0.653971i
\(193\) 426.084 + 246.000i 0.158913 + 0.0917485i 0.577348 0.816498i \(-0.304088\pi\)
−0.418435 + 0.908247i \(0.637421\pi\)
\(194\) 350.000 0.129529
\(195\) 0 0
\(196\) −2958.00 −1.07799
\(197\) −2590.28 1495.50i −0.936802 0.540863i −0.0478455 0.998855i \(-0.515235\pi\)
−0.888956 + 0.457992i \(0.848569\pi\)
\(198\) −1430.00 + 2476.83i −0.513261 + 0.888994i
\(199\) −35.0000 60.6218i −0.0124678 0.0215948i 0.859724 0.510759i \(-0.170635\pi\)
−0.872192 + 0.489164i \(0.837302\pi\)
\(200\) 3420.00i 1.20915i
\(201\) −2897.72 + 1673.00i −1.01686 + 0.587086i
\(202\) 1818.65 1050.00i 0.633465 0.365731i
\(203\) 1066.00i 0.368564i
\(204\) 4581.50 + 7935.39i 1.57240 + 2.72347i
\(205\) −1176.00 + 2036.89i −0.400661 + 0.693964i
\(206\) −2546.11 1470.00i −0.861147 0.497183i
\(207\) 2112.00 0.709150
\(208\) 0 0
\(209\) 3276.00 1.08424
\(210\) −2758.29 1592.50i −0.906382 0.523300i
\(211\) −1425.50 + 2469.04i −0.465097 + 0.805572i −0.999206 0.0398440i \(-0.987314\pi\)
0.534109 + 0.845416i \(0.320647\pi\)
\(212\) −3672.00 6360.09i −1.18959 2.06044i
\(213\) 63.0000i 0.0202661i
\(214\) 2961.81 1710.00i 0.946098 0.546230i
\(215\) −1218.50 + 703.500i −0.386516 + 0.223155i
\(216\) 1575.00i 0.496135i
\(217\) 1274.00 + 2206.63i 0.398547 + 0.690304i
\(218\) −932.500 + 1615.14i −0.289710 + 0.501793i
\(219\) −594.093 343.000i −0.183311 0.105835i
\(220\) −3094.00 −0.948170
\(221\) 0 0
\(222\) −4585.00 −1.38615
\(223\) −187.928 108.500i −0.0564330 0.0325816i 0.471518 0.881856i \(-0.343706\pi\)
−0.527951 + 0.849275i \(0.677040\pi\)
\(224\) −552.500 + 956.958i −0.164801 + 0.285444i
\(225\) −836.000 1447.99i −0.247704 0.429035i
\(226\) 8670.00i 2.55186i
\(227\) −2230.88 + 1288.00i −0.652285 + 0.376597i −0.789331 0.613968i \(-0.789573\pi\)
0.137046 + 0.990565i \(0.456239\pi\)
\(228\) −12985.2 + 7497.00i −3.77178 + 2.17764i
\(229\) 455.000i 0.131298i −0.997843 0.0656490i \(-0.979088\pi\)
0.997843 0.0656490i \(-0.0209118\pi\)
\(230\) 1680.00 + 2909.85i 0.481634 + 0.834215i
\(231\) −1183.00 + 2049.02i −0.336951 + 0.583616i
\(232\) 3195.63 + 1845.00i 0.904326 + 0.522113i
\(233\) −3061.00 −0.860656 −0.430328 0.902673i \(-0.641602\pi\)
−0.430328 + 0.902673i \(0.641602\pi\)
\(234\) 0 0
\(235\) 735.000 0.204026
\(236\) 4328.39 + 2499.00i 1.19388 + 0.689284i
\(237\) 4564.00 7905.08i 1.25090 2.16662i
\(238\) 2502.50 + 4334.46i 0.681567 + 1.18051i
\(239\) 3477.00i 0.941039i −0.882389 0.470520i \(-0.844066\pi\)
0.882389 0.470520i \(-0.155934\pi\)
\(240\) 3776.74 2180.50i 1.01578 0.586461i
\(241\) 1394.30 805.000i 0.372676 0.215164i −0.301951 0.953323i \(-0.597638\pi\)
0.674627 + 0.738159i \(0.264305\pi\)
\(242\) 3275.00i 0.869938i
\(243\) −2464.00 4267.77i −0.650476 1.12666i
\(244\) −476.000 + 824.456i −0.124888 + 0.216313i
\(245\) 1054.82 + 609.000i 0.275061 + 0.158806i
\(246\) −11760.0 −3.04793
\(247\) 0 0
\(248\) −8820.00 −2.25835
\(249\) −1867.15 1078.00i −0.475204 0.274359i
\(250\) 3517.50 6092.49i 0.889865 1.54129i
\(251\) 504.000 + 872.954i 0.126742 + 0.219523i 0.922412 0.386206i \(-0.126215\pi\)
−0.795671 + 0.605730i \(0.792881\pi\)
\(252\) 4862.00i 1.21539i
\(253\) 2161.60 1248.00i 0.537149 0.310123i
\(254\) 8192.60 4730.00i 2.02382 1.16845i
\(255\) 3773.00i 0.926566i
\(256\) 4139.50 + 7169.82i 1.01062 + 1.75045i
\(257\) 3020.50 5231.66i 0.733127 1.26981i −0.222413 0.974952i \(-0.571393\pi\)
0.955540 0.294861i \(-0.0952732\pi\)
\(258\) −6092.49 3517.50i −1.47016 0.848798i
\(259\) −1703.00 −0.408569
\(260\) 0 0
\(261\) −1804.00 −0.427834
\(262\) 6213.73 + 3587.50i 1.46521 + 0.845941i
\(263\) 1854.00 3211.22i 0.434686 0.752899i −0.562584 0.826740i \(-0.690193\pi\)
0.997270 + 0.0738414i \(0.0235259\pi\)
\(264\) −4095.00 7092.75i −0.954658 1.65352i
\(265\) 3024.00i 0.700992i
\(266\) −7092.75 + 4095.00i −1.63490 + 0.943912i
\(267\) −7213.99 + 4165.00i −1.65352 + 0.954659i
\(268\) 8126.00i 1.85214i
\(269\) −4172.00 7226.12i −0.945618 1.63786i −0.754508 0.656290i \(-0.772125\pi\)
−0.191110 0.981569i \(-0.561209\pi\)
\(270\) 612.500 1060.88i 0.138058 0.239123i
\(271\) −1400.36 808.500i −0.313897 0.181228i 0.334772 0.942299i \(-0.391341\pi\)
−0.648669 + 0.761071i \(0.724674\pi\)
\(272\) −6853.00 −1.52766
\(273\) 0 0
\(274\) 8880.00 1.95788
\(275\) −1711.27 988.000i −0.375248 0.216650i
\(276\) −5712.00 + 9893.47i −1.24573 + 2.15767i
\(277\) −1910.00 3308.22i −0.414299 0.717587i 0.581056 0.813864i \(-0.302640\pi\)
−0.995355 + 0.0962771i \(0.969306\pi\)
\(278\) 9345.00i 2.01610i
\(279\) 3734.30 2156.00i 0.801315 0.462639i
\(280\) 3546.37 2047.50i 0.756916 0.437005i
\(281\) 6214.00i 1.31920i 0.751615 + 0.659602i \(0.229275\pi\)
−0.751615 + 0.659602i \(0.770725\pi\)
\(282\) 1837.50 + 3182.64i 0.388020 + 0.672070i
\(283\) −2646.00 + 4583.01i −0.555789 + 0.962655i 0.442052 + 0.896989i \(0.354251\pi\)
−0.997842 + 0.0656661i \(0.979083\pi\)
\(284\) 132.502 + 76.5000i 0.0276850 + 0.0159839i
\(285\) 6174.00 1.28321
\(286\) 0 0
\(287\) −4368.00 −0.898379
\(288\) 1619.47 + 935.000i 0.331347 + 0.191303i
\(289\) −508.000 + 879.882i −0.103399 + 0.179093i
\(290\) −1435.00 2485.49i −0.290573 0.503287i
\(291\) 490.000i 0.0987090i
\(292\) 1442.80 833.000i 0.289155 0.166944i
\(293\) 782.021 451.500i 0.155925 0.0900236i −0.420007 0.907521i \(-0.637972\pi\)
0.575933 + 0.817497i \(0.304639\pi\)
\(294\) 6090.00i 1.20808i
\(295\) −1029.00 1782.28i −0.203087 0.351757i
\(296\) 2947.50 5105.22i 0.578784 1.00248i
\(297\) −788.083 455.000i −0.153970 0.0888949i
\(298\) 12330.0 2.39684
\(299\) 0 0
\(300\) 9044.00 1.74052
\(301\) −2262.92 1306.50i −0.433332 0.250184i
\(302\) −8307.50 + 14389.0i −1.58292 + 2.74170i
\(303\) −1470.00 2546.11i −0.278711 0.482741i
\(304\) 11214.0i 2.11568i
\(305\) 339.482 196.000i 0.0637334 0.0367965i
\(306\) 7335.24 4235.00i 1.37035 0.791173i
\(307\) 2114.00i 0.393004i −0.980503 0.196502i \(-0.937042\pi\)
0.980503 0.196502i \(-0.0629583\pi\)
\(308\) −2873.00 4976.18i −0.531508 0.920598i
\(309\) −2058.00 + 3564.56i −0.378885 + 0.656248i
\(310\) 5940.93 + 3430.00i 1.08846 + 0.628422i
\(311\) −3402.00 −0.620288 −0.310144 0.950690i \(-0.600377\pi\)
−0.310144 + 0.950690i \(0.600377\pi\)
\(312\) 0 0
\(313\) −10689.0 −1.93028 −0.965141 0.261732i \(-0.915706\pi\)
−0.965141 + 0.261732i \(0.915706\pi\)
\(314\) −11821.2 6825.00i −2.12456 1.22661i
\(315\) −1001.00 + 1733.78i −0.179047 + 0.310119i
\(316\) 11084.0 + 19198.1i 1.97318 + 3.41764i
\(317\) 7054.00i 1.24982i −0.780698 0.624909i \(-0.785136\pi\)
0.780698 0.624909i \(-0.214864\pi\)
\(318\) −13094.3 + 7560.00i −2.30909 + 1.33316i
\(319\) −1846.37 + 1066.00i −0.324065 + 0.187099i
\(320\) 2009.00i 0.350958i
\(321\) −2394.00 4146.53i −0.416262 0.720987i
\(322\) −3120.00 + 5404.00i −0.539971 + 0.935258i
\(323\) −8402.18 4851.00i −1.44740 0.835656i
\(324\) 14263.0 2.44564
\(325\) 0 0
\(326\) 2720.00 0.462107
\(327\) 2261.19 + 1305.50i 0.382398 + 0.220778i
\(328\) 7560.00 13094.3i 1.27266 2.20430i
\(329\) 682.500 + 1182.12i 0.114369 + 0.198093i
\(330\) 6370.00i 1.06260i
\(331\) 8403.91 4852.00i 1.39553 0.805710i 0.401610 0.915811i \(-0.368451\pi\)
0.993920 + 0.110101i \(0.0351173\pi\)
\(332\) 4534.51 2618.00i 0.749589 0.432775i
\(333\) 2882.00i 0.474272i
\(334\) 4060.00 + 7032.13i 0.665130 + 1.15204i
\(335\) −1673.00 + 2897.72i −0.272853 + 0.472595i
\(336\) 7013.94 + 4049.50i 1.13881 + 0.657495i
\(337\) 10449.0 1.68900 0.844500 0.535555i \(-0.179897\pi\)
0.844500 + 0.535555i \(0.179897\pi\)
\(338\) 0 0
\(339\) 12138.0 1.94468
\(340\) 7935.39 + 4581.50i 1.26576 + 0.730784i
\(341\) 2548.00 4413.27i 0.404639 0.700855i
\(342\) 6930.00 + 12003.1i 1.09571 + 1.89782i
\(343\) 6721.00i 1.05802i
\(344\) 7833.20 4522.50i 1.22773 0.708828i
\(345\) 4073.78 2352.00i 0.635725 0.367036i
\(346\) 1680.00i 0.261033i
\(347\) 310.500 + 537.802i 0.0480361 + 0.0832009i 0.889044 0.457822i \(-0.151370\pi\)
−0.841008 + 0.541023i \(0.818037\pi\)
\(348\) 4879.00 8450.68i 0.751557 1.30173i
\(349\) 10808.9 + 6240.50i 1.65784 + 0.957153i 0.973710 + 0.227790i \(0.0731499\pi\)
0.684127 + 0.729363i \(0.260183\pi\)
\(350\) 4940.00 0.754440
\(351\) 0 0
\(352\) 2210.00 0.334640
\(353\) 1212.44 + 700.000i 0.182809 + 0.105545i 0.588612 0.808416i \(-0.299675\pi\)
−0.405803 + 0.913961i \(0.633008\pi\)
\(354\) 5145.00 8911.40i 0.772468 1.33795i
\(355\) −31.5000 54.5596i −0.00470943 0.00815697i
\(356\) 20230.0i 3.01176i
\(357\) 6068.24 3503.50i 0.899623 0.519397i
\(358\) −13116.0 + 7572.50i −1.93631 + 1.11793i
\(359\) 4968.00i 0.730365i 0.930936 + 0.365182i \(0.118993\pi\)
−0.930936 + 0.365182i \(0.881007\pi\)
\(360\) −3465.00 6001.56i −0.507282 0.878638i
\(361\) 4508.50 7808.95i 0.657312 1.13850i
\(362\) 121.244 + 70.0000i 0.0176034 + 0.0101633i
\(363\) −4585.00 −0.662948
\(364\) 0 0
\(365\) −686.000 −0.0983750
\(366\) 1697.41 + 980.000i 0.242418 + 0.139960i
\(367\) −4361.00 + 7553.47i −0.620279 + 1.07435i 0.369155 + 0.929368i \(0.379647\pi\)
−0.989434 + 0.144987i \(0.953686\pi\)
\(368\) −4272.00 7399.32i −0.605145 1.04814i
\(369\) 7392.00i 1.04285i
\(370\) −3970.73 + 2292.50i −0.557914 + 0.322112i
\(371\) −4863.60 + 2808.00i −0.680608 + 0.392949i
\(372\) 23324.0i 3.25079i
\(373\) −5006.00 8670.65i −0.694908 1.20362i −0.970212 0.242259i \(-0.922112\pi\)
0.275303 0.961357i \(-0.411222\pi\)
\(374\) 5005.00 8668.91i 0.691985 1.19855i
\(375\) −8529.48 4924.50i −1.17456 0.678134i
\(376\) −4725.00 −0.648067
\(377\) 0 0
\(378\) 2275.00 0.309559
\(379\) 2920.24 + 1686.00i 0.395785 + 0.228507i 0.684664 0.728859i \(-0.259949\pi\)
−0.288879 + 0.957366i \(0.593282\pi\)
\(380\) −7497.00 + 12985.2i −1.01207 + 1.75296i
\(381\) −6622.00 11469.6i −0.890434 1.54228i
\(382\) 2110.00i 0.282610i
\(383\) −733.524 + 423.500i −0.0978624 + 0.0565009i −0.548132 0.836392i \(-0.684661\pi\)
0.450270 + 0.892892i \(0.351328\pi\)
\(384\) 12821.5 7402.50i 1.70389 0.983743i
\(385\) 2366.00i 0.313201i
\(386\) 1230.00 + 2130.42i 0.162190 + 0.280921i
\(387\) −2211.00 + 3829.56i −0.290417 + 0.503017i
\(388\) 1030.57 + 595.000i 0.134843 + 0.0778519i
\(389\) −11314.0 −1.47466 −0.737330 0.675533i \(-0.763914\pi\)
−0.737330 + 0.675533i \(0.763914\pi\)
\(390\) 0 0
\(391\) −7392.00 −0.956086
\(392\) −6780.98 3915.00i −0.873702 0.504432i
\(393\) 5022.50 8699.23i 0.644661 1.11658i
\(394\) −7477.50 12951.4i −0.956119 1.65605i
\(395\) 9128.00i 1.16273i
\(396\) −8421.23 + 4862.00i −1.06864 + 0.616982i
\(397\) −1612.54 + 931.000i −0.203856 + 0.117697i −0.598453 0.801158i \(-0.704218\pi\)
0.394597 + 0.918854i \(0.370884\pi\)
\(398\) 350.000i 0.0440802i
\(399\) 5733.00 + 9929.85i 0.719321 + 1.24590i
\(400\) −3382.00 + 5857.80i −0.422750 + 0.732224i
\(401\) 5906.29 + 3410.00i 0.735527 + 0.424657i 0.820441 0.571732i \(-0.193728\pi\)
−0.0849139 + 0.996388i \(0.527062\pi\)
\(402\) −16730.0 −2.07566
\(403\) 0 0
\(404\) 7140.00 0.879278
\(405\) −5086.17 2936.50i −0.624034 0.360286i
\(406\) 2665.00 4615.92i 0.325768 0.564246i
\(407\) 1703.00 + 2949.68i 0.207407 + 0.359239i
\(408\) 24255.0i 2.94314i
\(409\) −11251.4 + 6496.00i −1.36026 + 0.785346i −0.989658 0.143446i \(-0.954182\pi\)
−0.370601 + 0.928792i \(0.620848\pi\)
\(410\) −10184.5 + 5880.00i −1.22677 + 0.708274i
\(411\) 12432.0i 1.49203i
\(412\) −4998.00 8656.79i −0.597655 1.03517i
\(413\) 1911.00 3309.95i 0.227686 0.394363i
\(414\) 9145.23 + 5280.00i 1.08566 + 0.626806i
\(415\) −2156.00 −0.255021
\(416\) 0 0
\(417\) 13083.0 1.53640
\(418\) 14185.5 + 8190.00i 1.65989 + 0.958340i
\(419\) 3671.50 6359.22i 0.428078 0.741452i −0.568625 0.822597i \(-0.692524\pi\)
0.996702 + 0.0811449i \(0.0258577\pi\)
\(420\) −5414.50 9378.19i −0.629049 1.08954i
\(421\) 5059.00i 0.585655i −0.956165 0.292827i \(-0.905404\pi\)
0.956165 0.292827i \(-0.0945961\pi\)
\(422\) −12345.2 + 7127.50i −1.42406 + 0.822183i
\(423\) 2000.52 1155.00i 0.229949 0.132761i
\(424\) 19440.0i 2.22663i
\(425\) 2926.00 + 5067.98i 0.333957 + 0.578431i
\(426\) 157.500 272.798i 0.0179129 0.0310261i
\(427\) 630.466 + 364.000i 0.0714530 + 0.0412534i
\(428\) 11628.0 1.31323
\(429\) 0 0
\(430\) −7035.00 −0.788972
\(431\) −2808.52 1621.50i −0.313879 0.181218i 0.334782 0.942296i \(-0.391337\pi\)
−0.648661 + 0.761078i \(0.724671\pi\)
\(432\) −1557.50 + 2697.67i −0.173461 + 0.300444i
\(433\) 5799.50 + 10045.0i 0.643663 + 1.11486i 0.984609 + 0.174774i \(0.0559196\pi\)
−0.340945 + 0.940083i \(0.610747\pi\)
\(434\) 12740.0i 1.40908i
\(435\) −3479.69 + 2009.00i −0.383536 + 0.221435i
\(436\) −5491.47 + 3170.50i −0.603196 + 0.348256i
\(437\) 12096.0i 1.32410i
\(438\) −1715.00 2970.47i −0.187091 0.324051i
\(439\) −8687.00 + 15046.3i −0.944437 + 1.63581i −0.187563 + 0.982253i \(0.560059\pi\)
−0.756874 + 0.653560i \(0.773275\pi\)
\(440\) −7092.75 4095.00i −0.768485 0.443685i
\(441\) 3828.00 0.413346
\(442\) 0 0
\(443\) 989.000 0.106070 0.0530348 0.998593i \(-0.483111\pi\)
0.0530348 + 0.998593i \(0.483111\pi\)
\(444\) −13500.5 7794.50i −1.44303 0.833132i
\(445\) −4165.00 + 7213.99i −0.443685 + 0.768485i
\(446\) −542.500 939.638i −0.0575967 0.0997604i
\(447\) 17262.0i 1.82654i
\(448\) 3231.14 1865.50i 0.340752 0.196733i
\(449\) 12534.9 7237.00i 1.31750 0.760657i 0.334172 0.942512i \(-0.391543\pi\)
0.983325 + 0.181855i \(0.0582101\pi\)
\(450\) 8360.00i 0.875765i
\(451\) 4368.00 + 7565.60i 0.456056 + 0.789912i
\(452\) −14739.0 + 25528.7i −1.53377 + 2.65657i
\(453\) 20144.6 + 11630.5i 2.08935 + 1.20629i
\(454\) −12880.0 −1.33147
\(455\) 0 0
\(456\) −39690.0 −4.07600
\(457\) 1380.44 + 797.000i 0.141301 + 0.0815801i 0.568984 0.822349i \(-0.307337\pi\)
−0.427683 + 0.903929i \(0.640670\pi\)
\(458\) 1137.50 1970.21i 0.116052 0.201008i
\(459\) 1347.50 + 2333.94i 0.137028 + 0.237340i
\(460\) 11424.0i 1.15793i
\(461\) −5122.54 + 2957.50i −0.517528 + 0.298795i −0.735923 0.677066i \(-0.763251\pi\)
0.218395 + 0.975861i \(0.429918\pi\)
\(462\) −10245.1 + 5915.00i −1.03170 + 0.595651i
\(463\) 11072.0i 1.11136i 0.831396 + 0.555680i \(0.187542\pi\)
−0.831396 + 0.555680i \(0.812458\pi\)
\(464\) 3649.00 + 6320.25i 0.365087 + 0.632350i
\(465\) 4802.00 8317.31i 0.478898 0.829475i
\(466\) −13254.5 7652.50i −1.31760 0.760719i
\(467\) −1260.00 −0.124852 −0.0624260 0.998050i \(-0.519884\pi\)
−0.0624260 + 0.998050i \(0.519884\pi\)
\(468\) 0 0
\(469\) −6214.00 −0.611804
\(470\) 3182.64 + 1837.50i 0.312350 + 0.180335i
\(471\) −9555.00 + 16549.7i −0.934758 + 1.61905i
\(472\) 6615.00 + 11457.5i 0.645085 + 1.11732i
\(473\) 5226.00i 0.508016i
\(474\) 39525.4 22820.0i 3.83009 2.21130i
\(475\) −8293.06 + 4788.00i −0.801077 + 0.462502i
\(476\) 17017.0i 1.63860i
\(477\) 4752.00 + 8230.71i 0.456141 + 0.790059i
\(478\) 8692.50 15055.9i 0.831769 1.44067i
\(479\) −10420.9 6016.50i −0.994034 0.573906i −0.0875564 0.996160i \(-0.527906\pi\)
−0.906478 + 0.422254i \(0.861239\pi\)
\(480\) 4165.00 0.396053
\(481\) 0 0
\(482\) 8050.00 0.760721
\(483\) 7565.60 + 4368.00i 0.712726 + 0.411493i
\(484\) 5567.50 9643.19i 0.522868 0.905634i
\(485\) −245.000 424.352i −0.0229379 0.0397296i
\(486\) 24640.0i 2.29978i
\(487\) −1974.54 + 1140.00i −0.183727 + 0.106075i −0.589042 0.808102i \(-0.700495\pi\)
0.405316 + 0.914177i \(0.367162\pi\)
\(488\) −2182.38 + 1260.00i −0.202442 + 0.116880i
\(489\) 3808.00i 0.352155i
\(490\) 3045.00 + 5274.09i 0.280733 + 0.486243i
\(491\) 8383.50 14520.6i 0.770554 1.33464i −0.166706 0.986007i \(-0.553313\pi\)
0.937260 0.348632i \(-0.113354\pi\)
\(492\) −34627.2 19992.0i −3.17299 1.83193i
\(493\) 6314.00 0.576812
\(494\) 0 0
\(495\) 4004.00 0.363569
\(496\) −15106.9 8722.00i −1.36758 0.789575i
\(497\) 58.5000 101.325i 0.00527985 0.00914496i
\(498\) −5390.00 9335.75i −0.485003 0.840050i
\(499\) 12840.0i 1.15190i 0.817485 + 0.575949i \(0.195367\pi\)
−0.817485 + 0.575949i \(0.804633\pi\)
\(500\) 20714.5 11959.5i 1.85276 1.06969i
\(501\) 9844.98 5684.00i 0.877926 0.506871i
\(502\) 5040.00i 0.448100i
\(503\) 1099.00 + 1903.52i 0.0974195 + 0.168735i 0.910616 0.413254i \(-0.135608\pi\)
−0.813196 + 0.581989i \(0.802274\pi\)
\(504\) 6435.00 11145.7i 0.568726 0.985062i
\(505\) −2546.11 1470.00i −0.224358 0.129533i
\(506\) 12480.0 1.09645
\(507\) 0 0
\(508\) 32164.0 2.80915
\(509\) 14779.6 + 8533.00i 1.28702 + 0.743062i 0.978122 0.208033i \(-0.0667060\pi\)
0.308899 + 0.951095i \(0.400039\pi\)
\(510\) 9432.50 16337.6i 0.818977 1.41851i
\(511\) −637.000 1103.32i −0.0551452 0.0955144i
\(512\) 24475.0i 2.11260i
\(513\) −3819.17 + 2205.00i −0.328695 + 0.189772i
\(514\) 26158.3 15102.5i 2.24473 1.29600i
\(515\) 4116.00i 0.352180i
\(516\) −11959.5 20714.5i −1.02032 1.76725i
\(517\) 1365.00 2364.25i 0.116117 0.201121i
\(518\) −7374.21 4257.50i −0.625490 0.361127i
\(519\) −2352.00 −0.198924
\(520\) 0 0
\(521\) 2583.00 0.217204 0.108602 0.994085i \(-0.465363\pi\)
0.108602 + 0.994085i \(0.465363\pi\)
\(522\) −7811.55 4510.00i −0.654985 0.378156i
\(523\) −9310.00 + 16125.4i −0.778390 + 1.34821i 0.154480 + 0.987996i \(0.450630\pi\)
−0.932869 + 0.360215i \(0.882703\pi\)
\(524\) 12197.5 + 21126.7i 1.01689 + 1.76130i
\(525\) 6916.00i 0.574931i
\(526\) 16056.1 9270.00i 1.33095 0.768424i
\(527\) −13070.1 + 7546.00i −1.08034 + 0.623736i
\(528\) 16198.0i 1.33509i
\(529\) 1475.50 + 2555.64i 0.121271 + 0.210047i
\(530\) −7560.00 + 13094.3i −0.619595 + 1.07317i
\(531\) −5601.45 3234.00i −0.457782 0.264301i
\(532\) −27846.0 −2.26932
\(533\) 0 0
\(534\) −41650.0 −3.37523
\(535\) −4146.53 2394.00i −0.335084 0.193461i
\(536\) 10755.0 18628.2i 0.866689 1.50115i
\(537\) 10601.5 + 18362.3i 0.851934 + 1.47559i
\(538\) 41720.0i 3.34327i
\(539\) 3917.90 2262.00i 0.313091 0.180763i
\(540\) 3607.00 2082.50i 0.287445 0.165957i
\(541\) 16833.0i 1.33772i 0.743388 + 0.668861i \(0.233218\pi\)
−0.743388 + 0.668861i \(0.766782\pi\)
\(542\) −4042.50 7001.82i −0.320369 0.554896i
\(543\) 98.0000 169.741i 0.00774509 0.0134149i
\(544\) −5668.14 3272.50i −0.446727 0.257918i
\(545\) 2611.00 0.205216
\(546\) 0 0
\(547\) −8615.00 −0.673402 −0.336701 0.941612i \(-0.609311\pi\)
−0.336701 + 0.941612i \(0.609311\pi\)
\(548\) 26147.0 + 15096.0i 2.03822 + 1.17677i
\(549\) 616.000 1066.94i 0.0478875 0.0829436i
\(550\) −4940.00 8556.33i −0.382986 0.663351i
\(551\) 10332.0i 0.798835i
\(552\) −26188.6 + 15120.0i −2.01931 + 1.16585i
\(553\) 14680.9 8476.00i 1.12892 0.651783i
\(554\) 19100.0i 1.46477i
\(555\) 3209.50 + 5559.02i 0.245470 + 0.425166i
\(556\) −15886.5 + 27516.2i −1.21176 + 2.09883i
\(557\) 7391.53 + 4267.50i 0.562278 + 0.324632i 0.754059 0.656806i \(-0.228093\pi\)
−0.191781 + 0.981438i \(0.561426\pi\)
\(558\) 21560.0 1.63568
\(559\) 0 0
\(560\) 8099.00 0.611152
\(561\) −12136.5 7007.00i −0.913374 0.527336i
\(562\) −15535.0 + 26907.4i −1.16602 + 2.01961i
\(563\) −2320.50 4019.22i −0.173708 0.300871i 0.766006 0.642834i \(-0.222241\pi\)
−0.939713 + 0.341963i \(0.888908\pi\)
\(564\) 12495.0i 0.932862i
\(565\) 10511.8 6069.00i 0.782718 0.451902i
\(566\) −22915.0 + 13230.0i −1.70175 + 0.982506i
\(567\) 10907.0i 0.807850i
\(568\) 202.500 + 350.740i 0.0149590 + 0.0259097i
\(569\) −2396.50 + 4150.86i −0.176567 + 0.305823i −0.940702 0.339233i \(-0.889832\pi\)
0.764136 + 0.645056i \(0.223166\pi\)
\(570\) 26734.2 + 15435.0i 1.96451 + 1.13421i
\(571\) 5563.00 0.407713 0.203857 0.979001i \(-0.434652\pi\)
0.203857 + 0.979001i \(0.434652\pi\)
\(572\) 0 0
\(573\) −2954.00 −0.215367
\(574\) −18914.0 10920.0i −1.37536 0.794063i
\(575\) −3648.00 + 6318.52i −0.264578 + 0.458262i
\(576\) −3157.00 5468.08i −0.228371 0.395550i
\(577\) 24038.0i 1.73434i 0.498011 + 0.867171i \(0.334064\pi\)
−0.498011 + 0.867171i \(0.665936\pi\)
\(578\) −4399.41 + 2540.00i −0.316594 + 0.182786i
\(579\) 2982.59 1722.00i 0.214080 0.123599i
\(580\) 9758.00i 0.698584i
\(581\) −2002.00 3467.57i −0.142955 0.247606i
\(582\) 1225.00 2121.76i 0.0872472 0.151117i
\(583\) 9727.20 + 5616.00i 0.691011 + 0.398955i
\(584\) 4410.00 0.312478
\(585\) 0 0
\(586\) 4515.00 0.318281
\(587\) 18380.5 + 10612.0i 1.29241 + 0.746174i 0.979081 0.203470i \(-0.0652220\pi\)
0.313330 + 0.949644i \(0.398555\pi\)
\(588\) −10353.0 + 17931.9i −0.726106 + 1.25765i
\(589\) −12348.0 21387.4i −0.863821 1.49618i
\(590\) 10290.0i 0.718021i
\(591\) −18132.0 + 10468.5i −1.26201 + 0.728624i
\(592\) 10097.0 5829.50i 0.700986 0.404714i
\(593\) 4354.00i 0.301513i −0.988571 0.150757i \(-0.951829\pi\)
0.988571 0.150757i \(-0.0481710\pi\)
\(594\) −2275.00 3940.42i −0.157145 0.272184i
\(595\) 3503.50 6068.24i 0.241394 0.418107i
\(596\) 36305.5 + 20961.0i 2.49519 + 1.44060i
\(597\) −490.000 −0.0335919
\(598\) 0 0
\(599\) 7310.00 0.498629 0.249314 0.968423i \(-0.419795\pi\)
0.249314 + 0.968423i \(0.419795\pi\)
\(600\) 20732.6 + 11970.0i 1.41068 + 0.814455i
\(601\) 3797.50 6577.46i 0.257743 0.446423i −0.707894 0.706318i \(-0.750355\pi\)
0.965637 + 0.259895i \(0.0836880\pi\)
\(602\) −6532.50 11314.6i −0.442267 0.766029i
\(603\) 10516.0i 0.710190i
\(604\) −48922.6 + 28245.5i −3.29575 + 1.90280i
\(605\) −3970.73 + 2292.50i −0.266831 + 0.154055i
\(606\) 14700.0i 0.985391i
\(607\) 413.000 + 715.337i 0.0276164 + 0.0478330i 0.879503 0.475893i \(-0.157875\pi\)
−0.851887 + 0.523726i \(0.824542\pi\)
\(608\) 5355.00 9275.13i 0.357194 0.618678i
\(609\) −6462.28 3731.00i −0.429992 0.248256i
\(610\) 1960.00 0.130095
\(611\) 0 0
\(612\) 28798.0 1.90211
\(613\) −12635.3 7295.00i −0.832521 0.480656i 0.0221940 0.999754i \(-0.492935\pi\)
−0.854715 + 0.519097i \(0.826268\pi\)
\(614\) 5285.00 9153.89i 0.347370 0.601663i
\(615\) 8232.00 + 14258.2i 0.539750 + 0.934875i
\(616\) 15210.0i 0.994851i
\(617\) 4233.13 2444.00i 0.276207 0.159468i −0.355498 0.934677i \(-0.615689\pi\)
0.631705 + 0.775209i \(0.282355\pi\)
\(618\) −17822.8 + 10290.0i −1.16009 + 0.669781i
\(619\) 11004.0i 0.714520i 0.934005 + 0.357260i \(0.116289\pi\)
−0.934005 + 0.357260i \(0.883711\pi\)
\(620\) 11662.0 + 20199.2i 0.755415 + 1.30842i
\(621\) −1680.00 + 2909.85i −0.108561 + 0.188032i
\(622\) −14731.1 8505.00i −0.949619 0.548263i
\(623\) −15470.0 −0.994851
\(624\) 0 0
\(625\) −349.000 −0.0223360
\(626\) −46284.7 26722.5i −2.95513 1.70614i
\(627\) 11466.0 19859.7i 0.730316 1.26494i
\(628\) −23205.0 40192.2i −1.47449 2.55389i
\(629\) 10087.0i 0.639420i
\(630\) −8668.91 + 5005.00i −0.548219 + 0.316514i
\(631\) 4308.48 2487.50i 0.271819 0.156935i −0.357895 0.933762i \(-0.616505\pi\)
0.629714 + 0.776827i \(0.283172\pi\)
\(632\) 58680.0i 3.69330i
\(633\) 9978.50 + 17283.3i 0.626556 + 1.08523i
\(634\) 17635.0 30544.7i 1.10469 1.91338i
\(635\) −11469.6 6622.00i −0.716786 0.413836i
\(636\) −51408.0 −3.20513
\(637\) 0 0
\(638\) −10660.0 −0.661494
\(639\) −171.473 99.0000i −0.0106156 0.00612892i
\(640\) 7402.50 12821.5i 0.457202 0.791898i
\(641\) 1975.00 + 3420.80i 0.121697 + 0.210785i 0.920437 0.390891i \(-0.127833\pi\)
−0.798740 + 0.601676i \(0.794500\pi\)
\(642\) 23940.0i 1.47171i
\(643\) −3188.71 + 1841.00i −0.195568 + 0.112911i −0.594587 0.804032i \(-0.702684\pi\)
0.399019 + 0.916943i \(0.369351\pi\)
\(644\) −18373.6 + 10608.0i −1.12426 + 0.649090i
\(645\) 9849.00i 0.601247i
\(646\) −24255.0 42010.9i −1.47724 2.55866i
\(647\) 5201.00 9008.40i 0.316032 0.547383i −0.663625 0.748066i \(-0.730983\pi\)
0.979656 + 0.200683i \(0.0643161\pi\)
\(648\) 32696.8 + 18877.5i 1.98218 + 1.14441i
\(649\) −7644.00 −0.462332
\(650\) 0 0
\(651\) 17836.0 1.07381
\(652\) 8009.00 + 4624.00i 0.481069 + 0.277745i
\(653\) 15840.0 27435.7i 0.949260 1.64417i 0.202273 0.979329i \(-0.435167\pi\)
0.746987 0.664838i \(-0.231500\pi\)
\(654\) 6527.50 + 11306.0i 0.390284 + 0.675991i
\(655\) 10045.0i 0.599222i
\(656\) 25897.6 14952.0i 1.54136 0.889905i
\(657\) −1867.15 + 1078.00i −0.110874 + 0.0640134i
\(658\) 6825.00i 0.404356i
\(659\) −10970.0 19000.6i −0.648453 1.12315i −0.983492 0.180949i \(-0.942083\pi\)
0.335039 0.942204i \(-0.391250\pi\)
\(660\) −10829.0 + 18756.4i −0.638664 + 1.10620i
\(661\) −27170.7 15687.0i −1.59882 0.923077i −0.991716 0.128451i \(-0.959000\pi\)
−0.607100 0.794626i \(-0.707667\pi\)
\(662\) 48520.0 2.84862
\(663\) 0 0
\(664\) 13860.0 0.810049
\(665\) 9929.85 + 5733.00i 0.579042 + 0.334310i
\(666\) −7205.00 + 12479.4i −0.419201 + 0.726078i
\(667\) 3936.00 + 6817.35i 0.228490 + 0.395756i
\(668\) 27608.0i 1.59908i
\(669\) −1315.49 + 759.500i −0.0760237 + 0.0438923i
\(670\) −14488.6 + 8365.00i −0.835438 + 0.482341i
\(671\) 1456.00i 0.0837679i
\(672\) 3867.50 + 6698.71i 0.222012 + 0.384536i
\(673\) 9006.50 15599.7i 0.515862 0.893499i −0.483969 0.875085i \(-0.660805\pi\)
0.999830 0.0184136i \(-0.00586157\pi\)
\(674\) 45245.5 + 26122.5i 2.58574 + 1.49288i
\(675\) 2660.00 0.151679
\(676\) 0 0
\(677\) −10640.0 −0.604030 −0.302015 0.953303i \(-0.597659\pi\)
−0.302015 + 0.953303i \(0.597659\pi\)
\(678\) 52559.1 + 30345.0i 2.97717 + 1.71887i
\(679\) 455.000 788.083i 0.0257162 0.0445418i
\(680\) 12127.5 + 21005.4i 0.683924 + 1.18459i
\(681\) 18032.0i 1.01467i
\(682\) 22066.3 12740.0i 1.23895 0.715308i
\(683\) 8085.21 4668.00i 0.452961 0.261517i −0.256119 0.966645i \(-0.582444\pi\)
0.709080 + 0.705128i \(0.249111\pi\)
\(684\) 47124.0i 2.63426i
\(685\) −6216.00 10766.4i −0.346717 0.600531i
\(686\) −16802.5 + 29102.8i −0.935164 + 1.61975i
\(687\) −2758.29 1592.50i −0.153181 0.0884391i
\(688\) 17889.0 0.991296
\(689\) 0 0
\(690\) 23520.0 1.29767
\(691\) −3637.31 2100.00i −0.200246 0.115612i 0.396524 0.918024i \(-0.370216\pi\)
−0.596770 + 0.802412i \(0.703550\pi\)
\(692\) 2856.00 4946.74i 0.156891 0.271744i
\(693\) 3718.00 + 6439.76i 0.203803 + 0.352996i
\(694\) 3105.00i 0.169833i
\(695\) 11330.2 6541.50i 0.618388 0.357026i
\(696\) 22369.4 12915.0i 1.21826 0.703365i
\(697\) 25872.0i 1.40599i
\(698\) 31202.5 + 54044.3i 1.69202 + 2.93067i
\(699\) −10713.5 + 18556.3i −0.579716 + 1.00410i
\(700\) 14545.8 + 8398.00i 0.785397 + 0.453449i
\(701\) −9872.00 −0.531898 −0.265949 0.963987i \(-0.585685\pi\)
−0.265949 + 0.963987i \(0.585685\pi\)
\(702\) 0 0
\(703\) 16506.0 0.885541
\(704\) −6462.28 3731.00i −0.345961 0.199741i
\(705\) 2572.50 4455.70i 0.137427 0.238030i
\(706\) 3500.00 + 6062.18i 0.186578 + 0.323163i
\(707\) 5460.00i 0.290445i
\(708\) 30298.8 17493.0i 1.60833 0.928569i
\(709\) −24638.4 + 14225.0i −1.30510 + 0.753499i −0.981274 0.192617i \(-0.938302\pi\)
−0.323825 + 0.946117i \(0.604969\pi\)
\(710\) 315.000i 0.0166503i
\(711\) −14344.0 24844.5i −0.756599 1.31047i
\(712\) 26775.0 46375.7i 1.40932 2.44101i
\(713\) −16295.1 9408.00i −0.855901 0.494155i
\(714\) 35035.0 1.83635
\(715\) 0 0
\(716\) −51493.0 −2.68769
\(717\) −21078.2 12169.5i −1.09788 0.633861i
\(718\) −12420.0 + 21512.1i −0.645557 + 1.11814i
\(719\) 16359.0 + 28334.6i 0.848523 + 1.46968i 0.882527 + 0.470263i \(0.155841\pi\)
−0.0340039 + 0.999422i \(0.510826\pi\)
\(720\) 13706.0i 0.709434i
\(721\) −6619.90 + 3822.00i −0.341939 + 0.197418i
\(722\) 39044.8 22542.5i 2.01260 1.16197i
\(723\) 11270.0i 0.579718i
\(724\) 238.000 + 412.228i 0.0122171 + 0.0211607i
\(725\) 3116.00 5397.07i 0.159621 0.276472i
\(726\) −19853.6 11462.5i −1.01493 0.585969i
\(727\) 22834.0 1.16488 0.582439 0.812874i \(-0.302099\pi\)
0.582439 + 0.812874i \(0.302099\pi\)
\(728\) 0 0
\(729\) −11843.0 −0.601687
\(730\) −2970.47 1715.00i −0.150605 0.0869521i
\(731\) 7738.50 13403.5i 0.391544 0.678174i
\(732\) 3332.00 + 5771.19i 0.168244 + 0.291406i
\(733\) 7875.00i 0.396821i 0.980119 + 0.198410i \(0.0635779\pi\)
−0.980119 + 0.198410i \(0.936422\pi\)
\(734\) −37767.4 + 21805.0i −1.89921 + 1.09651i
\(735\) 7383.73 4263.00i 0.370548 0.213936i
\(736\) 8160.00i 0.408671i
\(737\) 6214.00 + 10763.0i 0.310578 + 0.537936i
\(738\) −18480.0 + 32008.3i −0.921759 + 1.59653i
\(739\) −1853.29 1070.00i −0.0922524 0.0532620i 0.453164 0.891427i \(-0.350295\pi\)
−0.545416 + 0.838165i \(0.683629\pi\)
\(740\) −15589.0 −0.774410
\(741\) 0 0
\(742\) −28080.0 −1.38928
\(743\) −27687.7 15985.5i −1.36711 0.789302i −0.376552 0.926395i \(-0.622891\pi\)
−0.990558 + 0.137094i \(0.956224\pi\)
\(744\) −30870.0 + 53468.4i −1.52117 + 2.63474i
\(745\) −8631.00 14949.3i −0.424450 0.735169i
\(746\) 50060.0i 2.45687i
\(747\) −5868.19 + 3388.00i −0.287424 + 0.165944i
\(748\) 29474.3 17017.0i 1.44076 0.831822i
\(749\) 8892.00i 0.433787i
\(750\) −24622.5 42647.4i −1.19878 2.07635i
\(751\) −3716.00 + 6436.30i −0.180558 + 0.312735i −0.942071 0.335415i \(-0.891124\pi\)
0.761513 + 0.648150i \(0.224457\pi\)
\(752\) −8093.01 4672.50i −0.392449 0.226581i
\(753\) 7056.00 0.341481
\(754\) 0 0
\(755\) 23261.0 1.12126
\(756\) 6698.71 + 3867.50i 0.322261 + 0.186058i
\(757\) −10088.0 + 17472.9i −0.484352 + 0.838923i −0.999838 0.0179753i \(-0.994278\pi\)
0.515486 + 0.856898i \(0.327611\pi\)
\(758\) 8430.00 + 14601.2i 0.403946 + 0.699656i
\(759\) 17472.0i 0.835564i
\(760\) −34372.5 + 19845.0i −1.64056 + 0.947176i
\(761\) 8208.19 4739.00i 0.390994 0.225741i −0.291597 0.956541i \(-0.594186\pi\)
0.682591 + 0.730801i \(0.260853\pi\)
\(762\) 66220.0i 3.14816i
\(763\) 2424.50 + 4199.36i 0.115036 + 0.199249i
\(764\) 3587.00 6212.87i 0.169860 0.294206i
\(765\) −10269.3 5929.00i −0.485344 0.280214i
\(766\) −4235.00 −0.199761
\(767\) 0 0
\(768\) 57953.0 2.72292
\(769\) 10475.4 + 6048.00i 0.491228 + 0.283610i 0.725084 0.688661i \(-0.241801\pi\)
−0.233856 + 0.972271i \(0.575134\pi\)
\(770\) −5915.00 + 10245.1i −0.276834 + 0.479490i
\(771\) −21143.5 36621.6i −0.987632 1.71063i
\(772\) 8364.00i 0.389931i
\(773\) 15537.4 8970.50i 0.722950 0.417395i −0.0928877 0.995677i \(-0.529610\pi\)
0.815837 + 0.578281i \(0.196276\pi\)
\(774\)