Properties

Label 169.4.c.e.146.1
Level $169$
Weight $4$
Character 169.146
Analytic conductor $9.971$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 169 = 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 169.c (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.97132279097\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 13)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 146.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 169.146
Dual form 169.4.c.e.22.1

$q$-expansion

\(f(q)\) \(=\) \(q+(2.50000 + 4.33013i) q^{2} +(3.50000 + 6.06218i) q^{3} +(-8.50000 + 14.7224i) q^{4} -7.00000 q^{5} +(-17.5000 + 30.3109i) q^{6} +(6.50000 - 11.2583i) q^{7} -45.0000 q^{8} +(-11.0000 + 19.0526i) q^{9} +O(q^{10})\) \(q+(2.50000 + 4.33013i) q^{2} +(3.50000 + 6.06218i) q^{3} +(-8.50000 + 14.7224i) q^{4} -7.00000 q^{5} +(-17.5000 + 30.3109i) q^{6} +(6.50000 - 11.2583i) q^{7} -45.0000 q^{8} +(-11.0000 + 19.0526i) q^{9} +(-17.5000 - 30.3109i) q^{10} +(13.0000 + 22.5167i) q^{11} -119.000 q^{12} +65.0000 q^{14} +(-24.5000 - 42.4352i) q^{15} +(-44.5000 - 77.0763i) q^{16} +(-38.5000 + 66.6840i) q^{17} -110.000 q^{18} +(63.0000 - 109.119i) q^{19} +(59.5000 - 103.057i) q^{20} +91.0000 q^{21} +(-65.0000 + 112.583i) q^{22} +(48.0000 + 83.1384i) q^{23} +(-157.500 - 272.798i) q^{24} -76.0000 q^{25} +35.0000 q^{27} +(110.500 + 191.392i) q^{28} +(41.0000 + 71.0141i) q^{29} +(122.500 - 212.176i) q^{30} +196.000 q^{31} +(42.5000 - 73.6122i) q^{32} +(-91.0000 + 157.617i) q^{33} -385.000 q^{34} +(-45.5000 + 78.8083i) q^{35} +(-187.000 - 323.894i) q^{36} +(65.5000 + 113.449i) q^{37} +630.000 q^{38} +315.000 q^{40} +(-168.000 - 290.985i) q^{41} +(227.500 + 394.042i) q^{42} +(100.500 - 174.071i) q^{43} -442.000 q^{44} +(77.0000 - 133.368i) q^{45} +(-240.000 + 415.692i) q^{46} -105.000 q^{47} +(311.500 - 539.534i) q^{48} +(87.0000 + 150.688i) q^{49} +(-190.000 - 329.090i) q^{50} -539.000 q^{51} -432.000 q^{53} +(87.5000 + 151.554i) q^{54} +(-91.0000 - 157.617i) q^{55} +(-292.500 + 506.625i) q^{56} +882.000 q^{57} +(-205.000 + 355.070i) q^{58} +(147.000 - 254.611i) q^{59} +833.000 q^{60} +(28.0000 - 48.4974i) q^{61} +(490.000 + 848.705i) q^{62} +(143.000 + 247.683i) q^{63} -287.000 q^{64} -910.000 q^{66} +(-239.000 - 413.960i) q^{67} +(-654.500 - 1133.63i) q^{68} +(-336.000 + 581.969i) q^{69} -455.000 q^{70} +(-4.50000 + 7.79423i) q^{71} +(495.000 - 857.365i) q^{72} +98.0000 q^{73} +(-327.500 + 567.247i) q^{74} +(-266.000 - 460.726i) q^{75} +(1071.00 + 1855.03i) q^{76} +338.000 q^{77} +1304.00 q^{79} +(311.500 + 539.534i) q^{80} +(419.500 + 726.595i) q^{81} +(840.000 - 1454.92i) q^{82} -308.000 q^{83} +(-773.500 + 1339.74i) q^{84} +(269.500 - 466.788i) q^{85} +1005.00 q^{86} +(-287.000 + 497.099i) q^{87} +(-585.000 - 1013.25i) q^{88} +(595.000 + 1030.57i) q^{89} +770.000 q^{90} -1632.00 q^{92} +(686.000 + 1188.19i) q^{93} +(-262.500 - 454.663i) q^{94} +(-441.000 + 763.834i) q^{95} +595.000 q^{96} +(-35.0000 + 60.6218i) q^{97} +(-435.000 + 753.442i) q^{98} -572.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 5q^{2} + 7q^{3} - 17q^{4} - 14q^{5} - 35q^{6} + 13q^{7} - 90q^{8} - 22q^{9} + O(q^{10}) \) \( 2q + 5q^{2} + 7q^{3} - 17q^{4} - 14q^{5} - 35q^{6} + 13q^{7} - 90q^{8} - 22q^{9} - 35q^{10} + 26q^{11} - 238q^{12} + 130q^{14} - 49q^{15} - 89q^{16} - 77q^{17} - 220q^{18} + 126q^{19} + 119q^{20} + 182q^{21} - 130q^{22} + 96q^{23} - 315q^{24} - 152q^{25} + 70q^{27} + 221q^{28} + 82q^{29} + 245q^{30} + 392q^{31} + 85q^{32} - 182q^{33} - 770q^{34} - 91q^{35} - 374q^{36} + 131q^{37} + 1260q^{38} + 630q^{40} - 336q^{41} + 455q^{42} + 201q^{43} - 884q^{44} + 154q^{45} - 480q^{46} - 210q^{47} + 623q^{48} + 174q^{49} - 380q^{50} - 1078q^{51} - 864q^{53} + 175q^{54} - 182q^{55} - 585q^{56} + 1764q^{57} - 410q^{58} + 294q^{59} + 1666q^{60} + 56q^{61} + 980q^{62} + 286q^{63} - 574q^{64} - 1820q^{66} - 478q^{67} - 1309q^{68} - 672q^{69} - 910q^{70} - 9q^{71} + 990q^{72} + 196q^{73} - 655q^{74} - 532q^{75} + 2142q^{76} + 676q^{77} + 2608q^{79} + 623q^{80} + 839q^{81} + 1680q^{82} - 616q^{83} - 1547q^{84} + 539q^{85} + 2010q^{86} - 574q^{87} - 1170q^{88} + 1190q^{89} + 1540q^{90} - 3264q^{92} + 1372q^{93} - 525q^{94} - 882q^{95} + 1190q^{96} - 70q^{97} - 870q^{98} - 1144q^{99} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.50000 + 4.33013i 0.883883 + 1.53093i 0.846988 + 0.531612i \(0.178414\pi\)
0.0368954 + 0.999319i \(0.488253\pi\)
\(3\) 3.50000 + 6.06218i 0.673575 + 1.16667i 0.976883 + 0.213774i \(0.0685756\pi\)
−0.303308 + 0.952893i \(0.598091\pi\)
\(4\) −8.50000 + 14.7224i −1.06250 + 1.84030i
\(5\) −7.00000 −0.626099 −0.313050 0.949737i \(-0.601351\pi\)
−0.313050 + 0.949737i \(0.601351\pi\)
\(6\) −17.5000 + 30.3109i −1.19072 + 2.06239i
\(7\) 6.50000 11.2583i 0.350967 0.607893i −0.635452 0.772140i \(-0.719186\pi\)
0.986419 + 0.164248i \(0.0525196\pi\)
\(8\) −45.0000 −1.98874
\(9\) −11.0000 + 19.0526i −0.407407 + 0.705650i
\(10\) −17.5000 30.3109i −0.553399 0.958514i
\(11\) 13.0000 + 22.5167i 0.356332 + 0.617184i 0.987345 0.158588i \(-0.0506940\pi\)
−0.631013 + 0.775772i \(0.717361\pi\)
\(12\) −119.000 −2.86270
\(13\) 0 0
\(14\) 65.0000 1.24086
\(15\) −24.5000 42.4352i −0.421725 0.730449i
\(16\) −44.5000 77.0763i −0.695312 1.20432i
\(17\) −38.5000 + 66.6840i −0.549272 + 0.951367i 0.449053 + 0.893505i \(0.351762\pi\)
−0.998325 + 0.0578615i \(0.981572\pi\)
\(18\) −110.000 −1.44040
\(19\) 63.0000 109.119i 0.760694 1.31756i −0.181799 0.983336i \(-0.558192\pi\)
0.942493 0.334225i \(-0.108475\pi\)
\(20\) 59.5000 103.057i 0.665230 1.15221i
\(21\) 91.0000 0.945611
\(22\) −65.0000 + 112.583i −0.629911 + 1.09104i
\(23\) 48.0000 + 83.1384i 0.435161 + 0.753720i 0.997309 0.0733164i \(-0.0233583\pi\)
−0.562148 + 0.827037i \(0.690025\pi\)
\(24\) −157.500 272.798i −1.33956 2.32019i
\(25\) −76.0000 −0.608000
\(26\) 0 0
\(27\) 35.0000 0.249472
\(28\) 110.500 + 191.392i 0.745805 + 1.29177i
\(29\) 41.0000 + 71.0141i 0.262535 + 0.454724i 0.966915 0.255099i \(-0.0821082\pi\)
−0.704380 + 0.709823i \(0.748775\pi\)
\(30\) 122.500 212.176i 0.745511 1.29126i
\(31\) 196.000 1.13557 0.567785 0.823177i \(-0.307801\pi\)
0.567785 + 0.823177i \(0.307801\pi\)
\(32\) 42.5000 73.6122i 0.234782 0.406654i
\(33\) −91.0000 + 157.617i −0.480032 + 0.831440i
\(34\) −385.000 −1.94197
\(35\) −45.5000 + 78.8083i −0.219740 + 0.380601i
\(36\) −187.000 323.894i −0.865741 1.49951i
\(37\) 65.5000 + 113.449i 0.291031 + 0.504080i 0.974054 0.226317i \(-0.0726685\pi\)
−0.683023 + 0.730397i \(0.739335\pi\)
\(38\) 630.000 2.68946
\(39\) 0 0
\(40\) 315.000 1.24515
\(41\) −168.000 290.985i −0.639932 1.10839i −0.985447 0.169981i \(-0.945629\pi\)
0.345516 0.938413i \(-0.387704\pi\)
\(42\) 227.500 + 394.042i 0.835810 + 1.44767i
\(43\) 100.500 174.071i 0.356421 0.617339i −0.630939 0.775832i \(-0.717330\pi\)
0.987360 + 0.158493i \(0.0506635\pi\)
\(44\) −442.000 −1.51441
\(45\) 77.0000 133.368i 0.255077 0.441807i
\(46\) −240.000 + 415.692i −0.769262 + 1.33240i
\(47\) −105.000 −0.325869 −0.162934 0.986637i \(-0.552096\pi\)
−0.162934 + 0.986637i \(0.552096\pi\)
\(48\) 311.500 539.534i 0.936691 1.62240i
\(49\) 87.0000 + 150.688i 0.253644 + 0.439325i
\(50\) −190.000 329.090i −0.537401 0.930806i
\(51\) −539.000 −1.47990
\(52\) 0 0
\(53\) −432.000 −1.11962 −0.559809 0.828622i \(-0.689126\pi\)
−0.559809 + 0.828622i \(0.689126\pi\)
\(54\) 87.5000 + 151.554i 0.220504 + 0.381925i
\(55\) −91.0000 157.617i −0.223099 0.386419i
\(56\) −292.500 + 506.625i −0.697981 + 1.20894i
\(57\) 882.000 2.04954
\(58\) −205.000 + 355.070i −0.464100 + 0.803845i
\(59\) 147.000 254.611i 0.324369 0.561824i −0.657015 0.753877i \(-0.728181\pi\)
0.981384 + 0.192054i \(0.0615147\pi\)
\(60\) 833.000 1.79233
\(61\) 28.0000 48.4974i 0.0587710 0.101794i −0.835143 0.550033i \(-0.814615\pi\)
0.893914 + 0.448239i \(0.147948\pi\)
\(62\) 490.000 + 848.705i 1.00371 + 1.73848i
\(63\) 143.000 + 247.683i 0.285973 + 0.495320i
\(64\) −287.000 −0.560547
\(65\) 0 0
\(66\) −910.000 −1.69717
\(67\) −239.000 413.960i −0.435798 0.754825i 0.561562 0.827435i \(-0.310201\pi\)
−0.997360 + 0.0726096i \(0.976867\pi\)
\(68\) −654.500 1133.63i −1.16720 2.02165i
\(69\) −336.000 + 581.969i −0.586227 + 1.01537i
\(70\) −455.000 −0.776899
\(71\) −4.50000 + 7.79423i −0.00752186 + 0.0130282i −0.869762 0.493472i \(-0.835728\pi\)
0.862240 + 0.506500i \(0.169061\pi\)
\(72\) 495.000 857.365i 0.810227 1.40335i
\(73\) 98.0000 0.157124 0.0785619 0.996909i \(-0.474967\pi\)
0.0785619 + 0.996909i \(0.474967\pi\)
\(74\) −327.500 + 567.247i −0.514474 + 0.891096i
\(75\) −266.000 460.726i −0.409534 0.709333i
\(76\) 1071.00 + 1855.03i 1.61648 + 2.79982i
\(77\) 338.000 0.500243
\(78\) 0 0
\(79\) 1304.00 1.85711 0.928554 0.371198i \(-0.121053\pi\)
0.928554 + 0.371198i \(0.121053\pi\)
\(80\) 311.500 + 539.534i 0.435334 + 0.754021i
\(81\) 419.500 + 726.595i 0.575446 + 0.996701i
\(82\) 840.000 1454.92i 1.13125 1.95938i
\(83\) −308.000 −0.407318 −0.203659 0.979042i \(-0.565283\pi\)
−0.203659 + 0.979042i \(0.565283\pi\)
\(84\) −773.500 + 1339.74i −1.00471 + 1.74021i
\(85\) 269.500 466.788i 0.343899 0.595650i
\(86\) 1005.00 1.26014
\(87\) −287.000 + 497.099i −0.353674 + 0.612581i
\(88\) −585.000 1013.25i −0.708650 1.22742i
\(89\) 595.000 + 1030.57i 0.708650 + 1.22742i 0.965358 + 0.260929i \(0.0840289\pi\)
−0.256708 + 0.966489i \(0.582638\pi\)
\(90\) 770.000 0.901835
\(91\) 0 0
\(92\) −1632.00 −1.84943
\(93\) 686.000 + 1188.19i 0.764891 + 1.32483i
\(94\) −262.500 454.663i −0.288030 0.498882i
\(95\) −441.000 + 763.834i −0.476270 + 0.824924i
\(96\) 595.000 0.632572
\(97\) −35.0000 + 60.6218i −0.0366362 + 0.0634558i −0.883762 0.467936i \(-0.844998\pi\)
0.847126 + 0.531392i \(0.178331\pi\)
\(98\) −435.000 + 753.442i −0.448384 + 0.776624i
\(99\) −572.000 −0.580689
\(100\) 646.000 1118.90i 0.646000 1.11890i
\(101\) −210.000 363.731i −0.206889 0.358342i 0.743844 0.668353i \(-0.233001\pi\)
−0.950733 + 0.310011i \(0.899667\pi\)
\(102\) −1347.50 2333.94i −1.30806 2.26563i
\(103\) 588.000 0.562499 0.281249 0.959635i \(-0.409251\pi\)
0.281249 + 0.959635i \(0.409251\pi\)
\(104\) 0 0
\(105\) −637.000 −0.592046
\(106\) −1080.00 1870.61i −0.989612 1.71406i
\(107\) 342.000 + 592.361i 0.308994 + 0.535194i 0.978143 0.207935i \(-0.0666743\pi\)
−0.669148 + 0.743129i \(0.733341\pi\)
\(108\) −297.500 + 515.285i −0.265064 + 0.459105i
\(109\) 373.000 0.327770 0.163885 0.986479i \(-0.447597\pi\)
0.163885 + 0.986479i \(0.447597\pi\)
\(110\) 455.000 788.083i 0.394387 0.683098i
\(111\) −458.500 + 794.145i −0.392062 + 0.679071i
\(112\) −1157.00 −0.976127
\(113\) 867.000 1501.69i 0.721774 1.25015i −0.238514 0.971139i \(-0.576660\pi\)
0.960288 0.279011i \(-0.0900065\pi\)
\(114\) 2205.00 + 3819.17i 1.81155 + 3.13770i
\(115\) −336.000 581.969i −0.272454 0.471903i
\(116\) −1394.00 −1.11577
\(117\) 0 0
\(118\) 1470.00 1.14682
\(119\) 500.500 + 866.891i 0.385553 + 0.667797i
\(120\) 1102.50 + 1909.59i 0.838700 + 1.45267i
\(121\) 327.500 567.247i 0.246056 0.426181i
\(122\) 280.000 0.207787
\(123\) 1176.00 2036.89i 0.862084 1.49317i
\(124\) −1666.00 + 2885.60i −1.20654 + 2.08979i
\(125\) 1407.00 1.00677
\(126\) −715.000 + 1238.42i −0.505534 + 0.875610i
\(127\) −946.000 1638.52i −0.660976 1.14484i −0.980360 0.197218i \(-0.936809\pi\)
0.319384 0.947625i \(-0.396524\pi\)
\(128\) −1057.50 1831.64i −0.730240 1.26481i
\(129\) 1407.00 0.960306
\(130\) 0 0
\(131\) 1435.00 0.957073 0.478536 0.878068i \(-0.341167\pi\)
0.478536 + 0.878068i \(0.341167\pi\)
\(132\) −1547.00 2679.48i −1.02007 1.76681i
\(133\) −819.000 1418.55i −0.533957 0.924841i
\(134\) 1195.00 2069.80i 0.770390 1.33435i
\(135\) −245.000 −0.156194
\(136\) 1732.50 3000.78i 1.09236 1.89202i
\(137\) 888.000 1538.06i 0.553773 0.959164i −0.444224 0.895916i \(-0.646521\pi\)
0.997998 0.0632482i \(-0.0201460\pi\)
\(138\) −3360.00 −2.07262
\(139\) 934.500 1618.60i 0.570239 0.987683i −0.426302 0.904581i \(-0.640184\pi\)
0.996541 0.0831023i \(-0.0264828\pi\)
\(140\) −773.500 1339.74i −0.466948 0.808777i
\(141\) −367.500 636.529i −0.219497 0.380180i
\(142\) −45.0000 −0.0265938
\(143\) 0 0
\(144\) 1958.00 1.13310
\(145\) −287.000 497.099i −0.164373 0.284702i
\(146\) 245.000 + 424.352i 0.138879 + 0.240546i
\(147\) −609.000 + 1054.82i −0.341697 + 0.591837i
\(148\) −2227.00 −1.23688
\(149\) −1233.00 + 2135.62i −0.677928 + 1.17421i 0.297676 + 0.954667i \(0.403789\pi\)
−0.975604 + 0.219539i \(0.929545\pi\)
\(150\) 1330.00 2303.63i 0.723960 1.25394i
\(151\) −3323.00 −1.79087 −0.895437 0.445189i \(-0.853137\pi\)
−0.895437 + 0.445189i \(0.853137\pi\)
\(152\) −2835.00 + 4910.36i −1.51282 + 2.62028i
\(153\) −847.000 1467.05i −0.447555 0.775188i
\(154\) 845.000 + 1463.58i 0.442156 + 0.765837i
\(155\) −1372.00 −0.710979
\(156\) 0 0
\(157\) −2730.00 −1.38776 −0.693878 0.720092i \(-0.744099\pi\)
−0.693878 + 0.720092i \(0.744099\pi\)
\(158\) 3260.00 + 5646.49i 1.64147 + 2.84310i
\(159\) −1512.00 2618.86i −0.754147 1.30622i
\(160\) −297.500 + 515.285i −0.146997 + 0.254605i
\(161\) 1248.00 0.610908
\(162\) −2097.50 + 3632.98i −1.01725 + 1.76194i
\(163\) 272.000 471.118i 0.130704 0.226385i −0.793244 0.608903i \(-0.791610\pi\)
0.923948 + 0.382518i \(0.124943\pi\)
\(164\) 5712.00 2.71971
\(165\) 637.000 1103.32i 0.300548 0.520564i
\(166\) −770.000 1333.68i −0.360022 0.623576i
\(167\) −812.000 1406.43i −0.376254 0.651691i 0.614260 0.789104i \(-0.289455\pi\)
−0.990514 + 0.137413i \(0.956121\pi\)
\(168\) −4095.00 −1.88057
\(169\) 0 0
\(170\) 2695.00 1.21587
\(171\) 1386.00 + 2400.62i 0.619825 + 1.07357i
\(172\) 1708.50 + 2959.21i 0.757395 + 1.31185i
\(173\) 168.000 290.985i 0.0738312 0.127879i −0.826746 0.562575i \(-0.809811\pi\)
0.900577 + 0.434696i \(0.143144\pi\)
\(174\) −2870.00 −1.25043
\(175\) −494.000 + 855.633i −0.213388 + 0.369599i
\(176\) 1157.00 2003.98i 0.495524 0.858272i
\(177\) 2058.00 0.873948
\(178\) −2975.00 + 5152.85i −1.25273 + 2.16979i
\(179\) 1514.50 + 2623.19i 0.632397 + 1.09534i 0.987060 + 0.160350i \(0.0512621\pi\)
−0.354663 + 0.934994i \(0.615405\pi\)
\(180\) 1309.00 + 2267.25i 0.542039 + 0.938840i
\(181\) −28.0000 −0.0114985 −0.00574924 0.999983i \(-0.501830\pi\)
−0.00574924 + 0.999983i \(0.501830\pi\)
\(182\) 0 0
\(183\) 392.000 0.158347
\(184\) −2160.00 3741.23i −0.865420 1.49895i
\(185\) −458.500 794.145i −0.182214 0.315604i
\(186\) −3430.00 + 5940.93i −1.35215 + 2.34199i
\(187\) −2002.00 −0.782892
\(188\) 892.500 1545.86i 0.346235 0.599697i
\(189\) 227.500 394.042i 0.0875566 0.151652i
\(190\) −4410.00 −1.68387
\(191\) −211.000 + 365.463i −0.0799342 + 0.138450i −0.903221 0.429175i \(-0.858804\pi\)
0.823287 + 0.567625i \(0.192138\pi\)
\(192\) −1004.50 1739.85i −0.377571 0.653971i
\(193\) −246.000 426.084i −0.0917485 0.158913i 0.816498 0.577348i \(-0.195912\pi\)
−0.908247 + 0.418435i \(0.862579\pi\)
\(194\) −350.000 −0.129529
\(195\) 0 0
\(196\) −2958.00 −1.07799
\(197\) −1495.50 2590.28i −0.540863 0.936802i −0.998855 0.0478455i \(-0.984765\pi\)
0.457992 0.888956i \(-0.348569\pi\)
\(198\) −1430.00 2476.83i −0.513261 0.888994i
\(199\) 35.0000 60.6218i 0.0124678 0.0215948i −0.859724 0.510759i \(-0.829365\pi\)
0.872192 + 0.489164i \(0.162698\pi\)
\(200\) 3420.00 1.20915
\(201\) 1673.00 2897.72i 0.587086 1.01686i
\(202\) 1050.00 1818.65i 0.365731 0.633465i
\(203\) 1066.00 0.368564
\(204\) 4581.50 7935.39i 1.57240 2.72347i
\(205\) 1176.00 + 2036.89i 0.400661 + 0.693964i
\(206\) 1470.00 + 2546.11i 0.497183 + 0.861147i
\(207\) −2112.00 −0.709150
\(208\) 0 0
\(209\) 3276.00 1.08424
\(210\) −1592.50 2758.29i −0.523300 0.906382i
\(211\) −1425.50 2469.04i −0.465097 0.805572i 0.534109 0.845416i \(-0.320647\pi\)
−0.999206 + 0.0398440i \(0.987314\pi\)
\(212\) 3672.00 6360.09i 1.18959 2.06044i
\(213\) −63.0000 −0.0202661
\(214\) −1710.00 + 2961.81i −0.546230 + 0.946098i
\(215\) −703.500 + 1218.50i −0.223155 + 0.386516i
\(216\) −1575.00 −0.496135
\(217\) 1274.00 2206.63i 0.398547 0.690304i
\(218\) 932.500 + 1615.14i 0.289710 + 0.501793i
\(219\) 343.000 + 594.093i 0.105835 + 0.183311i
\(220\) 3094.00 0.948170
\(221\) 0 0
\(222\) −4585.00 −1.38615
\(223\) −108.500 187.928i −0.0325816 0.0564330i 0.849275 0.527951i \(-0.177040\pi\)
−0.881856 + 0.471518i \(0.843706\pi\)
\(224\) −552.500 956.958i −0.164801 0.285444i
\(225\) 836.000 1447.99i 0.247704 0.429035i
\(226\) 8670.00 2.55186
\(227\) 1288.00 2230.88i 0.376597 0.652285i −0.613968 0.789331i \(-0.710427\pi\)
0.990565 + 0.137046i \(0.0437608\pi\)
\(228\) −7497.00 + 12985.2i −2.17764 + 3.77178i
\(229\) 455.000 0.131298 0.0656490 0.997843i \(-0.479088\pi\)
0.0656490 + 0.997843i \(0.479088\pi\)
\(230\) 1680.00 2909.85i 0.481634 0.834215i
\(231\) 1183.00 + 2049.02i 0.336951 + 0.583616i
\(232\) −1845.00 3195.63i −0.522113 0.904326i
\(233\) 3061.00 0.860656 0.430328 0.902673i \(-0.358398\pi\)
0.430328 + 0.902673i \(0.358398\pi\)
\(234\) 0 0
\(235\) 735.000 0.204026
\(236\) 2499.00 + 4328.39i 0.689284 + 1.19388i
\(237\) 4564.00 + 7905.08i 1.25090 + 2.16662i
\(238\) −2502.50 + 4334.46i −0.681567 + 1.18051i
\(239\) −3477.00 −0.941039 −0.470520 0.882389i \(-0.655934\pi\)
−0.470520 + 0.882389i \(0.655934\pi\)
\(240\) −2180.50 + 3776.74i −0.586461 + 1.01578i
\(241\) 805.000 1394.30i 0.215164 0.372676i −0.738159 0.674627i \(-0.764305\pi\)
0.953323 + 0.301951i \(0.0976379\pi\)
\(242\) 3275.00 0.869938
\(243\) −2464.00 + 4267.77i −0.650476 + 1.12666i
\(244\) 476.000 + 824.456i 0.124888 + 0.216313i
\(245\) −609.000 1054.82i −0.158806 0.275061i
\(246\) 11760.0 3.04793
\(247\) 0 0
\(248\) −8820.00 −2.25835
\(249\) −1078.00 1867.15i −0.274359 0.475204i
\(250\) 3517.50 + 6092.49i 0.889865 + 1.54129i
\(251\) −504.000 + 872.954i −0.126742 + 0.219523i −0.922412 0.386206i \(-0.873785\pi\)
0.795671 + 0.605730i \(0.207119\pi\)
\(252\) −4862.00 −1.21539
\(253\) −1248.00 + 2161.60i −0.310123 + 0.537149i
\(254\) 4730.00 8192.60i 1.16845 2.02382i
\(255\) 3773.00 0.926566
\(256\) 4139.50 7169.82i 1.01062 1.75045i
\(257\) −3020.50 5231.66i −0.733127 1.26981i −0.955540 0.294861i \(-0.904727\pi\)
0.222413 0.974952i \(-0.428607\pi\)
\(258\) 3517.50 + 6092.49i 0.848798 + 1.47016i
\(259\) 1703.00 0.408569
\(260\) 0 0
\(261\) −1804.00 −0.427834
\(262\) 3587.50 + 6213.73i 0.845941 + 1.46521i
\(263\) 1854.00 + 3211.22i 0.434686 + 0.752899i 0.997270 0.0738414i \(-0.0235259\pi\)
−0.562584 + 0.826740i \(0.690193\pi\)
\(264\) 4095.00 7092.75i 0.954658 1.65352i
\(265\) 3024.00 0.700992
\(266\) 4095.00 7092.75i 0.943912 1.63490i
\(267\) −4165.00 + 7213.99i −0.954659 + 1.65352i
\(268\) 8126.00 1.85214
\(269\) −4172.00 + 7226.12i −0.945618 + 1.63786i −0.191110 + 0.981569i \(0.561209\pi\)
−0.754508 + 0.656290i \(0.772125\pi\)
\(270\) −612.500 1060.88i −0.138058 0.239123i
\(271\) 808.500 + 1400.36i 0.181228 + 0.313897i 0.942299 0.334772i \(-0.108659\pi\)
−0.761071 + 0.648669i \(0.775326\pi\)
\(272\) 6853.00 1.52766
\(273\) 0 0
\(274\) 8880.00 1.95788
\(275\) −988.000 1711.27i −0.216650 0.375248i
\(276\) −5712.00 9893.47i −1.24573 2.15767i
\(277\) 1910.00 3308.22i 0.414299 0.717587i −0.581056 0.813864i \(-0.697360\pi\)
0.995355 + 0.0962771i \(0.0306935\pi\)
\(278\) 9345.00 2.01610
\(279\) −2156.00 + 3734.30i −0.462639 + 0.801315i
\(280\) 2047.50 3546.37i 0.437005 0.756916i
\(281\) −6214.00 −1.31920 −0.659602 0.751615i \(-0.729275\pi\)
−0.659602 + 0.751615i \(0.729275\pi\)
\(282\) 1837.50 3182.64i 0.388020 0.672070i
\(283\) 2646.00 + 4583.01i 0.555789 + 0.962655i 0.997842 + 0.0656661i \(0.0209172\pi\)
−0.442052 + 0.896989i \(0.645749\pi\)
\(284\) −76.5000 132.502i −0.0159839 0.0276850i
\(285\) −6174.00 −1.28321
\(286\) 0 0
\(287\) −4368.00 −0.898379
\(288\) 935.000 + 1619.47i 0.191303 + 0.331347i
\(289\) −508.000 879.882i −0.103399 0.179093i
\(290\) 1435.00 2485.49i 0.290573 0.503287i
\(291\) −490.000 −0.0987090
\(292\) −833.000 + 1442.80i −0.166944 + 0.289155i
\(293\) 451.500 782.021i 0.0900236 0.155925i −0.817497 0.575933i \(-0.804639\pi\)
0.907521 + 0.420007i \(0.137972\pi\)
\(294\) −6090.00 −1.20808
\(295\) −1029.00 + 1782.28i −0.203087 + 0.351757i
\(296\) −2947.50 5105.22i −0.578784 1.00248i
\(297\) 455.000 + 788.083i 0.0888949 + 0.153970i
\(298\) −12330.0 −2.39684
\(299\) 0 0
\(300\) 9044.00 1.74052
\(301\) −1306.50 2262.92i −0.250184 0.433332i
\(302\) −8307.50 14389.0i −1.58292 2.74170i
\(303\) 1470.00 2546.11i 0.278711 0.482741i
\(304\) −11214.0 −2.11568
\(305\) −196.000 + 339.482i −0.0367965 + 0.0637334i
\(306\) 4235.00 7335.24i 0.791173 1.37035i
\(307\) 2114.00 0.393004 0.196502 0.980503i \(-0.437042\pi\)
0.196502 + 0.980503i \(0.437042\pi\)
\(308\) −2873.00 + 4976.18i −0.531508 + 0.920598i
\(309\) 2058.00 + 3564.56i 0.378885 + 0.656248i
\(310\) −3430.00 5940.93i −0.628422 1.08846i
\(311\) 3402.00 0.620288 0.310144 0.950690i \(-0.399623\pi\)
0.310144 + 0.950690i \(0.399623\pi\)
\(312\) 0 0
\(313\) −10689.0 −1.93028 −0.965141 0.261732i \(-0.915706\pi\)
−0.965141 + 0.261732i \(0.915706\pi\)
\(314\) −6825.00 11821.2i −1.22661 2.12456i
\(315\) −1001.00 1733.78i −0.179047 0.310119i
\(316\) −11084.0 + 19198.1i −1.97318 + 3.41764i
\(317\) −7054.00 −1.24982 −0.624909 0.780698i \(-0.714864\pi\)
−0.624909 + 0.780698i \(0.714864\pi\)
\(318\) 7560.00 13094.3i 1.33316 2.30909i
\(319\) −1066.00 + 1846.37i −0.187099 + 0.324065i
\(320\) 2009.00 0.350958
\(321\) −2394.00 + 4146.53i −0.416262 + 0.720987i
\(322\) 3120.00 + 5404.00i 0.539971 + 0.935258i
\(323\) 4851.00 + 8402.18i 0.835656 + 1.44740i
\(324\) −14263.0 −2.44564
\(325\) 0 0
\(326\) 2720.00 0.462107
\(327\) 1305.50 + 2261.19i 0.220778 + 0.382398i
\(328\) 7560.00 + 13094.3i 1.27266 + 2.20430i
\(329\) −682.500 + 1182.12i −0.114369 + 0.198093i
\(330\) 6370.00 1.06260
\(331\) −4852.00 + 8403.91i −0.805710 + 1.39553i 0.110101 + 0.993920i \(0.464883\pi\)
−0.915811 + 0.401610i \(0.868451\pi\)
\(332\) 2618.00 4534.51i 0.432775 0.749589i
\(333\) −2882.00 −0.474272
\(334\) 4060.00 7032.13i 0.665130 1.15204i
\(335\) 1673.00 + 2897.72i 0.272853 + 0.472595i
\(336\) −4049.50 7013.94i −0.657495 1.13881i
\(337\) −10449.0 −1.68900 −0.844500 0.535555i \(-0.820103\pi\)
−0.844500 + 0.535555i \(0.820103\pi\)
\(338\) 0 0
\(339\) 12138.0 1.94468
\(340\) 4581.50 + 7935.39i 0.730784 + 1.26576i
\(341\) 2548.00 + 4413.27i 0.404639 + 0.700855i
\(342\) −6930.00 + 12003.1i −1.09571 + 1.89782i
\(343\) 6721.00 1.05802
\(344\) −4522.50 + 7833.20i −0.708828 + 1.22773i
\(345\) 2352.00 4073.78i 0.367036 0.635725i
\(346\) 1680.00 0.261033
\(347\) 310.500 537.802i 0.0480361 0.0832009i −0.841008 0.541023i \(-0.818037\pi\)
0.889044 + 0.457822i \(0.151370\pi\)
\(348\) −4879.00 8450.68i −0.751557 1.30173i
\(349\) −6240.50 10808.9i −0.957153 1.65784i −0.729363 0.684127i \(-0.760183\pi\)
−0.227790 0.973710i \(-0.573150\pi\)
\(350\) −4940.00 −0.754440
\(351\) 0 0
\(352\) 2210.00 0.334640
\(353\) 700.000 + 1212.44i 0.105545 + 0.182809i 0.913961 0.405803i \(-0.133008\pi\)
−0.808416 + 0.588612i \(0.799675\pi\)
\(354\) 5145.00 + 8911.40i 0.772468 + 1.33795i
\(355\) 31.5000 54.5596i 0.00470943 0.00815697i
\(356\) −20230.0 −3.01176
\(357\) −3503.50 + 6068.24i −0.519397 + 0.899623i
\(358\) −7572.50 + 13116.0i −1.11793 + 1.93631i
\(359\) −4968.00 −0.730365 −0.365182 0.930936i \(-0.618993\pi\)
−0.365182 + 0.930936i \(0.618993\pi\)
\(360\) −3465.00 + 6001.56i −0.507282 + 0.878638i
\(361\) −4508.50 7808.95i −0.657312 1.13850i
\(362\) −70.0000 121.244i −0.0101633 0.0176034i
\(363\) 4585.00 0.662948
\(364\) 0 0
\(365\) −686.000 −0.0983750
\(366\) 980.000 + 1697.41i 0.139960 + 0.242418i
\(367\) −4361.00 7553.47i −0.620279 1.07435i −0.989434 0.144987i \(-0.953686\pi\)
0.369155 0.929368i \(-0.379647\pi\)
\(368\) 4272.00 7399.32i 0.605145 1.04814i
\(369\) 7392.00 1.04285
\(370\) 2292.50 3970.73i 0.322112 0.557914i
\(371\) −2808.00 + 4863.60i −0.392949 + 0.680608i
\(372\) −23324.0 −3.25079
\(373\) −5006.00 + 8670.65i −0.694908 + 1.20362i 0.275303 + 0.961357i \(0.411222\pi\)
−0.970212 + 0.242259i \(0.922112\pi\)
\(374\) −5005.00 8668.91i −0.691985 1.19855i
\(375\) 4924.50 + 8529.48i 0.678134 + 1.17456i
\(376\) 4725.00 0.648067
\(377\) 0 0
\(378\) 2275.00 0.309559
\(379\) 1686.00 + 2920.24i 0.228507 + 0.395785i 0.957366 0.288879i \(-0.0932824\pi\)
−0.728859 + 0.684664i \(0.759949\pi\)
\(380\) −7497.00 12985.2i −1.01207 1.75296i
\(381\) 6622.00 11469.6i 0.890434 1.54228i
\(382\) −2110.00 −0.282610
\(383\) 423.500 733.524i 0.0565009 0.0978624i −0.836392 0.548132i \(-0.815339\pi\)
0.892892 + 0.450270i \(0.148672\pi\)
\(384\) 7402.50 12821.5i 0.983743 1.70389i
\(385\) −2366.00 −0.313201
\(386\) 1230.00 2130.42i 0.162190 0.280921i
\(387\) 2211.00 + 3829.56i 0.290417 + 0.503017i
\(388\) −595.000 1030.57i −0.0778519 0.134843i
\(389\) 11314.0 1.47466 0.737330 0.675533i \(-0.236086\pi\)
0.737330 + 0.675533i \(0.236086\pi\)
\(390\) 0 0
\(391\) −7392.00 −0.956086
\(392\) −3915.00 6780.98i −0.504432 0.873702i
\(393\) 5022.50 + 8699.23i 0.644661 + 1.11658i
\(394\) 7477.50 12951.4i 0.956119 1.65605i
\(395\) −9128.00 −1.16273
\(396\) 4862.00 8421.23i 0.616982 1.06864i
\(397\) −931.000 + 1612.54i −0.117697 + 0.203856i −0.918854 0.394597i \(-0.870884\pi\)
0.801158 + 0.598453i \(0.204218\pi\)
\(398\) 350.000 0.0440802
\(399\) 5733.00 9929.85i 0.719321 1.24590i
\(400\) 3382.00 + 5857.80i 0.422750 + 0.732224i
\(401\) −3410.00 5906.29i −0.424657 0.735527i 0.571732 0.820441i \(-0.306272\pi\)
−0.996388 + 0.0849139i \(0.972938\pi\)
\(402\) 16730.0 2.07566
\(403\) 0 0
\(404\) 7140.00 0.879278
\(405\) −2936.50 5086.17i −0.360286 0.624034i
\(406\) 2665.00 + 4615.92i 0.325768 + 0.564246i
\(407\) −1703.00 + 2949.68i −0.207407 + 0.359239i
\(408\) 24255.0 2.94314
\(409\) 6496.00 11251.4i 0.785346 1.36026i −0.143446 0.989658i \(-0.545818\pi\)
0.928792 0.370601i \(-0.120848\pi\)
\(410\) −5880.00 + 10184.5i −0.708274 + 1.22677i
\(411\) 12432.0 1.49203
\(412\) −4998.00 + 8656.79i −0.597655 + 1.03517i
\(413\) −1911.00 3309.95i −0.227686 0.394363i
\(414\) −5280.00 9145.23i −0.626806 1.08566i
\(415\) 2156.00 0.255021
\(416\) 0 0
\(417\) 13083.0 1.53640
\(418\) 8190.00 + 14185.5i 0.958340 + 1.65989i
\(419\) 3671.50 + 6359.22i 0.428078 + 0.741452i 0.996702 0.0811449i \(-0.0258577\pi\)
−0.568625 + 0.822597i \(0.692524\pi\)
\(420\) 5414.50 9378.19i 0.629049 1.08954i
\(421\) −5059.00 −0.585655 −0.292827 0.956165i \(-0.594596\pi\)
−0.292827 + 0.956165i \(0.594596\pi\)
\(422\) 7127.50 12345.2i 0.822183 1.42406i
\(423\) 1155.00 2000.52i 0.132761 0.229949i
\(424\) 19440.0 2.22663
\(425\) 2926.00 5067.98i 0.333957 0.578431i
\(426\) −157.500 272.798i −0.0179129 0.0310261i
\(427\) −364.000 630.466i −0.0412534 0.0714530i
\(428\) −11628.0 −1.31323
\(429\) 0 0
\(430\) −7035.00 −0.788972
\(431\) −1621.50 2808.52i −0.181218 0.313879i 0.761078 0.648661i \(-0.224671\pi\)
−0.942296 + 0.334782i \(0.891337\pi\)
\(432\) −1557.50 2697.67i −0.173461 0.300444i
\(433\) −5799.50 + 10045.0i −0.643663 + 1.11486i 0.340945 + 0.940083i \(0.389253\pi\)
−0.984609 + 0.174774i \(0.944080\pi\)
\(434\) 12740.0 1.40908
\(435\) 2009.00 3479.69i 0.221435 0.383536i
\(436\) −3170.50 + 5491.47i −0.348256 + 0.603196i
\(437\) 12096.0 1.32410
\(438\) −1715.00 + 2970.47i −0.187091 + 0.324051i
\(439\) 8687.00 + 15046.3i 0.944437 + 1.63581i 0.756874 + 0.653560i \(0.226725\pi\)
0.187563 + 0.982253i \(0.439941\pi\)
\(440\) 4095.00 + 7092.75i 0.443685 + 0.768485i
\(441\) −3828.00 −0.413346
\(442\) 0 0
\(443\) 989.000 0.106070 0.0530348 0.998593i \(-0.483111\pi\)
0.0530348 + 0.998593i \(0.483111\pi\)
\(444\) −7794.50 13500.5i −0.833132 1.44303i
\(445\) −4165.00 7213.99i −0.443685 0.768485i
\(446\) 542.500 939.638i 0.0575967 0.0997604i
\(447\) −17262.0 −1.82654
\(448\) −1865.50 + 3231.14i −0.196733 + 0.340752i
\(449\) 7237.00 12534.9i 0.760657 1.31750i −0.181855 0.983325i \(-0.558210\pi\)
0.942512 0.334172i \(-0.108457\pi\)
\(450\) 8360.00 0.875765
\(451\) 4368.00 7565.60i 0.456056 0.789912i
\(452\) 14739.0 + 25528.7i 1.53377 + 2.65657i
\(453\) −11630.5 20144.6i −1.20629 2.08935i
\(454\) 12880.0 1.33147
\(455\) 0 0
\(456\) −39690.0 −4.07600
\(457\) 797.000 + 1380.44i 0.0815801 + 0.141301i 0.903929 0.427683i \(-0.140670\pi\)
−0.822349 + 0.568984i \(0.807337\pi\)
\(458\) 1137.50 + 1970.21i 0.116052 + 0.201008i
\(459\) −1347.50 + 2333.94i −0.137028 + 0.237340i
\(460\) 11424.0 1.15793
\(461\) 2957.50 5122.54i 0.298795 0.517528i −0.677066 0.735923i \(-0.736749\pi\)
0.975861 + 0.218395i \(0.0700820\pi\)
\(462\) −5915.00 + 10245.1i −0.595651 + 1.03170i
\(463\) −11072.0 −1.11136 −0.555680 0.831396i \(-0.687542\pi\)
−0.555680 + 0.831396i \(0.687542\pi\)
\(464\) 3649.00 6320.25i 0.365087 0.632350i
\(465\) −4802.00 8317.31i −0.478898 0.829475i
\(466\) 7652.50 + 13254.5i 0.760719 + 1.31760i
\(467\) 1260.00 0.124852 0.0624260 0.998050i \(-0.480116\pi\)
0.0624260 + 0.998050i \(0.480116\pi\)
\(468\) 0 0
\(469\) −6214.00 −0.611804
\(470\) 1837.50 + 3182.64i 0.180335 + 0.312350i
\(471\) −9555.00 16549.7i −0.934758 1.61905i
\(472\) −6615.00 + 11457.5i −0.645085 + 1.11732i
\(473\) 5226.00 0.508016
\(474\) −22820.0 + 39525.4i −2.21130 + 3.83009i
\(475\) −4788.00 + 8293.06i −0.462502 + 0.801077i
\(476\) −17017.0 −1.63860
\(477\) 4752.00 8230.71i 0.456141 0.790059i
\(478\) −8692.50 15055.9i −0.831769 1.44067i
\(479\) 6016.50 + 10420.9i 0.573906 + 0.994034i 0.996160 + 0.0875564i \(0.0279058\pi\)
−0.422254 + 0.906478i \(0.638761\pi\)
\(480\) −4165.00 −0.396053
\(481\) 0 0
\(482\) 8050.00 0.760721
\(483\) 4368.00 + 7565.60i 0.411493 + 0.712726i
\(484\) 5567.50 + 9643.19i 0.522868 + 0.905634i
\(485\) 245.000 424.352i 0.0229379 0.0397296i
\(486\) −24640.0 −2.29978
\(487\) 1140.00 1974.54i 0.106075 0.183727i −0.808102 0.589042i \(-0.799505\pi\)
0.914177 + 0.405316i \(0.132838\pi\)
\(488\) −1260.00 + 2182.38i −0.116880 + 0.202442i
\(489\) 3808.00 0.352155
\(490\) 3045.00 5274.09i 0.280733 0.486243i
\(491\) −8383.50 14520.6i −0.770554 1.33464i −0.937260 0.348632i \(-0.886646\pi\)
0.166706 0.986007i \(-0.446687\pi\)
\(492\) 19992.0 + 34627.2i 1.83193 + 3.17299i
\(493\) −6314.00 −0.576812
\(494\) 0 0
\(495\) 4004.00 0.363569
\(496\) −8722.00 15106.9i −0.789575 1.36758i
\(497\) 58.5000 + 101.325i 0.00527985 + 0.00914496i
\(498\) 5390.00 9335.75i 0.485003 0.840050i
\(499\) 12840.0 1.15190 0.575949 0.817485i \(-0.304633\pi\)
0.575949 + 0.817485i \(0.304633\pi\)
\(500\) −11959.5 + 20714.5i −1.06969 + 1.85276i
\(501\) 5684.00 9844.98i 0.506871 0.877926i
\(502\) −5040.00 −0.448100
\(503\) 1099.00 1903.52i 0.0974195 0.168735i −0.813196 0.581989i \(-0.802274\pi\)
0.910616 + 0.413254i \(0.135608\pi\)
\(504\) −6435.00 11145.7i −0.568726 0.985062i
\(505\) 1470.00 + 2546.11i 0.129533 + 0.224358i
\(506\) −12480.0 −1.09645
\(507\) 0 0
\(508\) 32164.0 2.80915
\(509\) 8533.00 + 14779.6i 0.743062 + 1.28702i 0.951095 + 0.308899i \(0.0999606\pi\)
−0.208033 + 0.978122i \(0.566706\pi\)
\(510\) 9432.50 + 16337.6i 0.818977 + 1.41851i
\(511\) 637.000 1103.32i 0.0551452 0.0955144i
\(512\) 24475.0 2.11260
\(513\) 2205.00 3819.17i 0.189772 0.328695i
\(514\) 15102.5 26158.3i 1.29600 2.24473i
\(515\) −4116.00 −0.352180
\(516\) −11959.5 + 20714.5i −1.02032 + 1.76725i
\(517\) −1365.00 2364.25i −0.116117 0.201121i
\(518\) 4257.50 + 7374.21i 0.361127 + 0.625490i
\(519\) 2352.00 0.198924
\(520\) 0 0
\(521\) 2583.00 0.217204 0.108602 0.994085i \(-0.465363\pi\)
0.108602 + 0.994085i \(0.465363\pi\)
\(522\) −4510.00 7811.55i −0.378156 0.654985i
\(523\) −9310.00 16125.4i −0.778390 1.34821i −0.932869 0.360215i \(-0.882703\pi\)
0.154480 0.987996i \(-0.450630\pi\)
\(524\) −12197.5 + 21126.7i −1.01689 + 1.76130i
\(525\) −6916.00 −0.574931
\(526\) −9270.00 + 16056.1i −0.768424 + 1.33095i
\(527\) −7546.00 + 13070.1i −0.623736 + 1.08034i
\(528\) 16198.0 1.33509
\(529\) 1475.50 2555.64i 0.121271 0.210047i
\(530\) 7560.00 + 13094.3i 0.619595 + 1.07317i
\(531\) 3234.00 + 5601.45i 0.264301 + 0.457782i
\(532\) 27846.0 2.26932
\(533\) 0 0
\(534\) −41650.0 −3.37523
\(535\) −2394.00 4146.53i −0.193461 0.335084i
\(536\) 10755.0 + 18628.2i 0.866689 + 1.50115i
\(537\) −10601.5 + 18362.3i −0.851934 + 1.47559i
\(538\) −41720.0 −3.34327
\(539\) −2262.00 + 3917.90i −0.180763 + 0.313091i
\(540\) 2082.50 3607.00i 0.165957 0.287445i
\(541\) −16833.0 −1.33772 −0.668861 0.743388i \(-0.733218\pi\)
−0.668861 + 0.743388i \(0.733218\pi\)
\(542\) −4042.50 + 7001.82i −0.320369 + 0.554896i
\(543\) −98.0000 169.741i −0.00774509 0.0134149i
\(544\) 3272.50 + 5668.14i 0.257918 + 0.446727i
\(545\) −2611.00 −0.205216
\(546\) 0 0
\(547\) −8615.00 −0.673402 −0.336701 0.941612i \(-0.609311\pi\)
−0.336701 + 0.941612i \(0.609311\pi\)
\(548\) 15096.0 + 26147.0i 1.17677 + 2.03822i
\(549\) 616.000 + 1066.94i 0.0478875 + 0.0829436i
\(550\) 4940.00 8556.33i 0.382986 0.663351i
\(551\) 10332.0 0.798835
\(552\) 15120.0 26188.6i 1.16585 2.01931i
\(553\) 8476.00 14680.9i 0.651783 1.12892i
\(554\) 19100.0 1.46477
\(555\) 3209.50 5559.02i 0.245470 0.425166i
\(556\) 15886.5 + 27516.2i 1.21176 + 2.09883i
\(557\) −4267.50 7391.53i −0.324632 0.562278i 0.656806 0.754059i \(-0.271907\pi\)
−0.981438 + 0.191781i \(0.938574\pi\)
\(558\) −21560.0 −1.63568
\(559\) 0 0
\(560\) 8099.00 0.611152
\(561\) −7007.00 12136.5i −0.527336 0.913374i
\(562\) −15535.0 26907.4i −1.16602 2.01961i
\(563\) 2320.50 4019.22i 0.173708 0.300871i −0.766006 0.642834i \(-0.777759\pi\)
0.939713 + 0.341963i \(0.111092\pi\)
\(564\) 12495.0 0.932862
\(565\) −6069.00 + 10511.8i −0.451902 + 0.782718i
\(566\) −13230.0 + 22915.0i −0.982506 + 1.70175i
\(567\) 10907.0 0.807850
\(568\) 202.500 350.740i 0.0149590 0.0259097i
\(569\) 2396.50 + 4150.86i 0.176567 + 0.305823i 0.940702 0.339233i \(-0.110168\pi\)
−0.764136 + 0.645056i \(0.776834\pi\)
\(570\) −15435.0 26734.2i −1.13421 1.96451i
\(571\) −5563.00 −0.407713 −0.203857 0.979001i \(-0.565348\pi\)
−0.203857 + 0.979001i \(0.565348\pi\)
\(572\) 0 0
\(573\) −2954.00 −0.215367
\(574\) −10920.0 18914.0i −0.794063 1.37536i
\(575\) −3648.00 6318.52i −0.264578 0.458262i
\(576\) 3157.00 5468.08i 0.228371 0.395550i
\(577\) 24038.0 1.73434 0.867171 0.498011i \(-0.165936\pi\)
0.867171 + 0.498011i \(0.165936\pi\)
\(578\) 2540.00 4399.41i 0.182786 0.316594i
\(579\) 1722.00 2982.59i 0.123599 0.214080i
\(580\) 9758.00 0.698584
\(581\) −2002.00 + 3467.57i −0.142955 + 0.247606i
\(582\) −1225.00 2121.76i −0.0872472 0.151117i
\(583\) −5616.00 9727.20i −0.398955 0.691011i
\(584\) −4410.00 −0.312478
\(585\) 0 0
\(586\) 4515.00 0.318281
\(587\) 10612.0 + 18380.5i 0.746174 + 1.29241i 0.949644 + 0.313330i \(0.101445\pi\)
−0.203470 + 0.979081i \(0.565222\pi\)
\(588\) −10353.0 17931.9i −0.726106 1.25765i
\(589\) 12348.0 21387.4i 0.863821 1.49618i
\(590\) −10290.0 −0.718021
\(591\) 10468.5 18132.0i 0.728624 1.26201i
\(592\) 5829.50 10097.0i 0.404714 0.700986i
\(593\) 4354.00 0.301513 0.150757 0.988571i \(-0.451829\pi\)
0.150757 + 0.988571i \(0.451829\pi\)
\(594\) −2275.00 + 3940.42i −0.157145 + 0.272184i
\(595\) −3503.50 6068.24i −0.241394 0.418107i
\(596\) −20961.0 36305.5i −1.44060 2.49519i
\(597\) 490.000 0.0335919
\(598\) 0 0
\(599\) 7310.00 0.498629 0.249314 0.968423i \(-0.419795\pi\)
0.249314 + 0.968423i \(0.419795\pi\)
\(600\) 11970.0 + 20732.6i 0.814455 + 1.41068i
\(601\) 3797.50 + 6577.46i 0.257743 + 0.446423i 0.965637 0.259895i \(-0.0836880\pi\)
−0.707894 + 0.706318i \(0.750355\pi\)
\(602\) 6532.50 11314.6i 0.442267 0.766029i
\(603\) 10516.0 0.710190
\(604\) 28245.5 48922.6i 1.90280 3.29575i
\(605\) −2292.50 + 3970.73i −0.154055 + 0.266831i
\(606\) 14700.0 0.985391
\(607\) 413.000 715.337i 0.0276164 0.0478330i −0.851887 0.523726i \(-0.824542\pi\)
0.879503 + 0.475893i \(0.157875\pi\)
\(608\) −5355.00 9275.13i −0.357194 0.618678i
\(609\) 3731.00 + 6462.28i 0.248256 + 0.429992i
\(610\) −1960.00 −0.130095
\(611\) 0 0
\(612\) 28798.0 1.90211
\(613\) −7295.00 12635.3i −0.480656 0.832521i 0.519097 0.854715i \(-0.326268\pi\)
−0.999754 + 0.0221940i \(0.992935\pi\)
\(614\) 5285.00 + 9153.89i 0.347370 + 0.601663i
\(615\) −8232.00 + 14258.2i −0.539750 + 0.934875i
\(616\) −15210.0 −0.994851
\(617\) −2444.00 + 4233.13i −0.159468 + 0.276207i −0.934677 0.355498i \(-0.884311\pi\)
0.775209 + 0.631705i \(0.217645\pi\)
\(618\) −10290.0 + 17822.8i −0.669781 + 1.16009i
\(619\) −11004.0 −0.714520 −0.357260 0.934005i \(-0.616289\pi\)
−0.357260 + 0.934005i \(0.616289\pi\)
\(620\) 11662.0 20199.2i 0.755415 1.30842i
\(621\) 1680.00 + 2909.85i 0.108561 + 0.188032i
\(622\) 8505.00 + 14731.1i 0.548263 + 0.949619i
\(623\) 15470.0 0.994851
\(624\) 0 0
\(625\) −349.000 −0.0223360
\(626\) −26722.5 46284.7i −1.70614 2.95513i
\(627\) 11466.0 + 19859.7i 0.730316 + 1.26494i
\(628\) 23205.0 40192.2i 1.47449 2.55389i
\(629\) −10087.0 −0.639420
\(630\) 5005.00 8668.91i 0.316514 0.548219i
\(631\) 2487.50 4308.48i 0.156935 0.271819i −0.776827 0.629714i \(-0.783172\pi\)
0.933762 + 0.357895i \(0.116505\pi\)
\(632\) −58680.0 −3.69330
\(633\) 9978.50 17283.3i 0.626556 1.08523i
\(634\) −17635.0 30544.7i −1.10469 1.91338i
\(635\) 6622.00 + 11469.6i 0.413836 + 0.716786i
\(636\) 51408.0 3.20513
\(637\) 0 0
\(638\) −10660.0 −0.661494
\(639\) −99.0000 171.473i −0.00612892 0.0106156i
\(640\) 7402.50 + 12821.5i 0.457202 + 0.791898i
\(641\) −1975.00 + 3420.80i −0.121697 + 0.210785i −0.920437 0.390891i \(-0.872167\pi\)
0.798740 + 0.601676i \(0.205500\pi\)
\(642\) −23940.0 −1.47171
\(643\) 1841.00 3188.71i 0.112911 0.195568i −0.804032 0.594587i \(-0.797316\pi\)
0.916943 + 0.399019i \(0.130649\pi\)
\(644\) −10608.0 + 18373.6i −0.649090 + 1.12426i
\(645\) −9849.00 −0.601247
\(646\) −24255.0 + 42010.9i −1.47724 + 2.55866i
\(647\) −5201.00 9008.40i −0.316032 0.547383i 0.663625 0.748066i \(-0.269017\pi\)
−0.979656 + 0.200683i \(0.935684\pi\)
\(648\) −18877.5 32696.8i −1.14441 1.98218i
\(649\) 7644.00 0.462332
\(650\) 0 0
\(651\) 17836.0 1.07381
\(652\) 4624.00 + 8009.00i 0.277745 + 0.481069i
\(653\) 15840.0 + 27435.7i 0.949260 + 1.64417i 0.746987 + 0.664838i \(0.231500\pi\)
0.202273 + 0.979329i \(0.435167\pi\)
\(654\) −6527.50 + 11306.0i −0.390284 + 0.675991i
\(655\) −10045.0 −0.599222
\(656\) −14952.0 + 25897.6i −0.889905 + 1.54136i
\(657\) −1078.00 + 1867.15i −0.0640134 + 0.110874i
\(658\) −6825.00 −0.404356
\(659\) −10970.0 + 19000.6i −0.648453 + 1.12315i 0.335039 + 0.942204i \(0.391250\pi\)
−0.983492 + 0.180949i \(0.942083\pi\)
\(660\) 10829.0 + 18756.4i 0.638664 + 1.10620i
\(661\) 15687.0 + 27170.7i 0.923077 + 1.59882i 0.794626 + 0.607100i \(0.207667\pi\)
0.128451 + 0.991716i \(0.459000\pi\)
\(662\) −48520.0 −2.84862
\(663\) 0 0
\(664\) 13860.0 0.810049
\(665\) 5733.00 + 9929.85i 0.334310 + 0.579042i
\(666\) −7205.00 12479.4i −0.419201 0.726078i
\(667\) −3936.00 + 6817.35i −0.228490 + 0.395756i
\(668\) 27608.0 1.59908
\(669\) 759.500 1315.49i 0.0438923 0.0760237i
\(670\) −8365.00 + 14488.6i −0.482341 + 0.835438i
\(671\) 1456.00 0.0837679
\(672\) 3867.50 6698.71i 0.222012 0.384536i
\(673\) −9006.50 15599.7i −0.515862 0.893499i −0.999830 0.0184136i \(-0.994138\pi\)
0.483969 0.875085i \(-0.339195\pi\)
\(674\) −26122.5 45245.5i −1.49288 2.58574i
\(675\) −2660.00 −0.151679
\(676\) 0 0
\(677\) −10640.0 −0.604030 −0.302015 0.953303i \(-0.597659\pi\)
−0.302015 + 0.953303i \(0.597659\pi\)
\(678\) 30345.0 + 52559.1i 1.71887 + 2.97717i
\(679\) 455.000 + 788.083i 0.0257162 + 0.0445418i
\(680\) −12127.5 + 21005.4i −0.683924 + 1.18459i
\(681\) 18032.0 1.01467
\(682\) −12740.0 + 22066.3i −0.715308 + 1.23895i
\(683\) 4668.00 8085.21i 0.261517 0.452961i −0.705128 0.709080i \(-0.749111\pi\)
0.966645 + 0.256119i \(0.0824439\pi\)
\(684\) −47124.0 −2.63426
\(685\) −6216.00 + 10766.4i −0.346717 + 0.600531i
\(686\) 16802.5 + 29102.8i 0.935164 + 1.61975i
\(687\) 1592.50 + 2758.29i 0.0884391 + 0.153181i
\(688\) −17889.0 −0.991296
\(689\) 0 0
\(690\) 23520.0 1.29767
\(691\) −2100.00 3637.31i −0.115612 0.200246i 0.802412 0.596770i \(-0.203550\pi\)
−0.918024 + 0.396524i \(0.870216\pi\)
\(692\) 2856.00 + 4946.74i 0.156891 + 0.271744i
\(693\) −3718.00 + 6439.76i −0.203803 + 0.352996i
\(694\) 3105.00 0.169833
\(695\) −6541.50 + 11330.2i −0.357026 + 0.618388i
\(696\) 12915.0 22369.4i 0.703365 1.21826i
\(697\) 25872.0 1.40599
\(698\) 31202.5 54044.3i 1.69202 2.93067i
\(699\) 10713.5 + 18556.3i 0.579716 + 1.00410i
\(700\) −8398.00 14545.8i −0.453449 0.785397i
\(701\) 9872.00 0.531898 0.265949 0.963987i \(-0.414315\pi\)
0.265949 + 0.963987i \(0.414315\pi\)
\(702\) 0 0
\(703\) 16506.0 0.885541
\(704\) −3731.00 6462.28i −0.199741 0.345961i
\(705\) 2572.50 + 4455.70i 0.137427 + 0.238030i
\(706\) −3500.00 + 6062.18i −0.186578 + 0.323163i
\(707\) −5460.00 −0.290445
\(708\) −17493.0 + 30298.8i −0.928569 + 1.60833i
\(709\) −14225.0 + 24638.4i −0.753499 + 1.30510i 0.192617 + 0.981274i \(0.438302\pi\)
−0.946117 + 0.323825i \(0.895031\pi\)
\(710\) 315.000 0.0166503
\(711\) −14344.0 + 24844.5i −0.756599 + 1.31047i
\(712\) −26775.0 46375.7i −1.40932 2.44101i
\(713\) 9408.00 + 16295.1i 0.494155 + 0.855901i
\(714\) −35035.0 −1.83635
\(715\) 0 0
\(716\) −51493.0 −2.68769
\(717\) −12169.5 21078.2i −0.633861 1.09788i
\(718\) −12420.0 21512.1i −0.645557 1.11814i
\(719\) −16359.0 + 28334.6i −0.848523 + 1.46968i 0.0340039 + 0.999422i \(0.489174\pi\)
−0.882527 + 0.470263i \(0.844159\pi\)
\(720\) −13706.0 −0.709434
\(721\) 3822.00 6619.90i 0.197418 0.341939i
\(722\) 22542.5 39044.8i 1.16197 2.01260i
\(723\) 11270.0 0.579718
\(724\) 238.000 412.228i 0.0122171 0.0211607i
\(725\) −3116.00 5397.07i −0.159621 0.276472i
\(726\) 11462.5 + 19853.6i 0.585969 + 1.01493i
\(727\) −22834.0 −1.16488 −0.582439 0.812874i \(-0.697901\pi\)
−0.582439 + 0.812874i \(0.697901\pi\)
\(728\) 0 0
\(729\) −11843.0 −0.601687
\(730\) −1715.00 2970.47i −0.0869521 0.150605i
\(731\) 7738.50 + 13403.5i 0.391544 + 0.678174i
\(732\) −3332.00 + 5771.19i −0.168244 + 0.291406i
\(733\) 7875.00 0.396821 0.198410 0.980119i \(-0.436422\pi\)
0.198410 + 0.980119i \(0.436422\pi\)
\(734\) 21805.0 37767.4i 1.09651 1.89921i
\(735\) 4263.00 7383.73i 0.213936 0.370548i
\(736\) 8160.00 0.408671
\(737\) 6214.00 10763.0i 0.310578 0.537936i
\(738\) 18480.0 + 32008.3i 0.921759 + 1.59653i
\(739\) 1070.00 + 1853.29i 0.0532620 + 0.0922524i 0.891427 0.453164i \(-0.149705\pi\)
−0.838165 + 0.545416i \(0.816371\pi\)
\(740\) 15589.0 0.774410
\(741\) 0 0
\(742\) −28080.0 −1.38928
\(743\) −15985.5 27687.7i −0.789302 1.36711i −0.926395 0.376552i \(-0.877109\pi\)
0.137094 0.990558i \(-0.456224\pi\)
\(744\) −30870.0 53468.4i −1.52117 2.63474i
\(745\) 8631.00 14949.3i 0.424450 0.735169i
\(746\) −50060.0 −2.45687
\(747\) 3388.00 5868.19i 0.165944 0.287424i
\(748\) 17017.0 29474.3i 0.831822 1.44076i
\(749\) 8892.00 0.433787
\(750\) −24622.5 + 42647.4i −1.19878 + 2.07635i
\(751\) 3716.00 + 6436.30i 0.180558 + 0.312735i 0.942071 0.335415i \(-0.108876\pi\)
−0.761513 + 0.648150i \(0.775543\pi\)
\(752\) 4672.50 + 8093.01i 0.226581 + 0.392449i
\(753\) −7056.00 −0.341481
\(754\) 0 0
\(755\) 23261.0 1.12126
\(756\) 3867.50 + 6698.71i 0.186058 + 0.322261i
\(757\) −10088.0 17472.9i −0.484352 0.838923i 0.515486 0.856898i \(-0.327611\pi\)
−0.999838 + 0.0179753i \(0.994278\pi\)
\(758\) −8430.00 + 14601.2i −0.403946 + 0.699656i
\(759\) −17472.0 −0.835564
\(760\) 19845.0 34372.5i 0.947176 1.64056i
\(761\) 4739.00 8208.19i 0.225741 0.390994i −0.730801 0.682591i \(-0.760853\pi\)
0.956541 + 0.291597i \(0.0941865\pi\)
\(762\) 66220.0 3.14816
\(763\) 2424.50 4199.36i 0.115036 0.199249i
\(764\) −3587.00 6212.87i −0.169860 0.294206i
\(765\) 5929.00 + 10269.3i 0.280214 + 0.485344i
\(766\) 4235.00 0.199761
\(767\) 0 0
\(768\) 57953.0 2.72292
\(769\) 6048.00 + 10475.4i 0.283610 + 0.491228i 0.972271 0.233856i \(-0.0751344\pi\)
−0.688661 + 0.725084i \(0.741801\pi\)
\(770\) −5915.00 10245.1i −0.276834 0.479490i
\(771\) 21143.5 36621.6i 0.987632 1.71063i
\(772\) 8364.00 0.389931
\(773\) −8970.50 + 15537.4i −0.417395 + 0.722950i −0.995677 0.0928877i \(-0.970390\pi\)
0.578281 + 0.815837i \(0.303724\pi\)
\(774\) −11055.0 + 19147.8i −0.513390 + 0.889217i
\(775\) −14896.0 −0.690426
\(776\) 1575.00 2727.98i 0.0728598 0.126197i