Properties

Label 16.4.e.a.13.2
Level 16
Weight 4
Character 16.13
Analytic conductor 0.944
Analytic rank 0
Dimension 10
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 16 = 2^{4} \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 16.e (of order \(4\) and degree \(2\))

Newform invariants

Self dual: No
Analytic conductor: \(0.944030560092\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{10} \)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 13.2
Root \(1.97476 + 0.316760i\)
Character \(\chi\) = 16.13
Dual form 16.4.e.a.5.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.29152 - 1.65800i) q^{2} +(-5.96513 - 5.96513i) q^{3} +(2.50210 + 7.59865i) q^{4} +(8.67959 - 8.67959i) q^{5} +(3.77903 + 23.5594i) q^{6} -1.63924i q^{7} +(6.86495 - 21.5609i) q^{8} +44.1656i q^{9} +O(q^{10})\) \(q+(-2.29152 - 1.65800i) q^{2} +(-5.96513 - 5.96513i) q^{3} +(2.50210 + 7.59865i) q^{4} +(8.67959 - 8.67959i) q^{5} +(3.77903 + 23.5594i) q^{6} -1.63924i q^{7} +(6.86495 - 21.5609i) q^{8} +44.1656i q^{9} +(-34.2802 + 5.49869i) q^{10} +(18.2021 - 18.2021i) q^{11} +(30.4016 - 60.2523i) q^{12} +(-9.34700 - 9.34700i) q^{13} +(-2.71786 + 3.75636i) q^{14} -103.550 q^{15} +(-51.4790 + 38.0251i) q^{16} +53.6113 q^{17} +(73.2264 - 101.206i) q^{18} +(70.9870 + 70.9870i) q^{19} +(87.6704 + 44.2360i) q^{20} +(-9.77831 + 9.77831i) q^{21} +(-71.8893 + 11.5314i) q^{22} +25.1189i q^{23} +(-169.564 + 87.6633i) q^{24} -25.6706i q^{25} +(5.92151 + 36.9161i) q^{26} +(102.395 - 102.395i) q^{27} +(12.4560 - 4.10155i) q^{28} +(-181.094 - 181.094i) q^{29} +(237.286 + 171.685i) q^{30} +132.684 q^{31} +(181.011 - 1.78308i) q^{32} -217.155 q^{33} +(-122.851 - 88.8874i) q^{34} +(-14.2280 - 14.2280i) q^{35} +(-335.599 + 110.507i) q^{36} +(174.872 - 174.872i) q^{37} +(-44.9717 - 280.364i) q^{38} +111.512i q^{39} +(-127.555 - 246.725i) q^{40} +198.660i q^{41} +(38.6196 - 6.19475i) q^{42} +(-285.717 + 285.717i) q^{43} +(183.854 + 92.7678i) q^{44} +(383.339 + 383.339i) q^{45} +(41.6471 - 57.5605i) q^{46} +78.3629 q^{47} +(533.904 + 80.2545i) q^{48} +340.313 q^{49} +(-42.5617 + 58.8245i) q^{50} +(-319.799 - 319.799i) q^{51} +(47.6375 - 94.4117i) q^{52} +(-525.776 + 525.776i) q^{53} +(-404.411 + 64.8694i) q^{54} -315.973i q^{55} +(-35.3436 - 11.2533i) q^{56} -846.894i q^{57} +(114.727 + 715.232i) q^{58} +(46.5301 - 46.5301i) q^{59} +(-259.091 - 786.839i) q^{60} +(193.318 + 193.318i) q^{61} +(-304.047 - 219.990i) q^{62} +72.3982 q^{63} +(-417.745 - 296.029i) q^{64} -162.256 q^{65} +(497.615 + 360.043i) q^{66} +(282.182 + 282.182i) q^{67} +(134.141 + 407.374i) q^{68} +(149.838 - 149.838i) q^{69} +(9.01370 + 56.1935i) q^{70} -727.536i q^{71} +(952.250 + 303.195i) q^{72} +106.065i q^{73} +(-690.659 + 110.785i) q^{74} +(-153.128 + 153.128i) q^{75} +(-361.789 + 717.022i) q^{76} +(-29.8376 - 29.8376i) q^{77} +(184.887 - 255.532i) q^{78} -58.9970 q^{79} +(-116.775 + 776.859i) q^{80} -29.1298 q^{81} +(329.378 - 455.233i) q^{82} +(-410.156 - 410.156i) q^{83} +(-98.7682 - 49.8357i) q^{84} +(465.324 - 465.324i) q^{85} +(1128.44 - 181.007i) q^{86} +2160.50i q^{87} +(-267.497 - 517.409i) q^{88} +768.959i q^{89} +(-242.853 - 1514.00i) q^{90} +(-15.3220 + 15.3220i) q^{91} +(-190.870 + 62.8500i) q^{92} +(-791.477 - 791.477i) q^{93} +(-179.570 - 129.925i) q^{94} +1232.28 q^{95} +(-1090.39 - 1069.12i) q^{96} -809.953 q^{97} +(-779.833 - 564.238i) q^{98} +(803.905 + 803.905i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 2q^{2} - 2q^{3} + 8q^{4} - 2q^{5} - 32q^{6} - 44q^{8} + O(q^{10}) \) \( 10q - 2q^{2} - 2q^{3} + 8q^{4} - 2q^{5} - 32q^{6} - 44q^{8} - 68q^{10} + 18q^{11} + 100q^{12} - 2q^{13} + 188q^{14} - 124q^{15} + 280q^{16} - 4q^{17} + 174q^{18} - 26q^{19} - 196q^{20} + 52q^{21} - 588q^{22} - 848q^{24} - 264q^{26} + 184q^{27} + 280q^{28} - 202q^{29} + 1236q^{30} + 368q^{31} + 968q^{32} - 4q^{33} + 436q^{34} + 476q^{35} - 596q^{36} - 10q^{37} - 1232q^{38} - 1336q^{40} - 680q^{42} - 838q^{43} + 868q^{44} + 194q^{45} + 1132q^{46} - 944q^{47} + 1768q^{48} + 94q^{49} + 726q^{50} - 1500q^{51} - 236q^{52} - 378q^{53} - 1376q^{54} - 488q^{56} + 8q^{58} + 1706q^{59} - 192q^{60} + 910q^{61} - 80q^{62} + 2628q^{63} + 512q^{64} - 492q^{65} - 428q^{66} + 1942q^{67} - 880q^{68} + 580q^{69} + 160q^{70} + 1092q^{72} - 452q^{74} - 2954q^{75} - 1228q^{76} - 268q^{77} - 772q^{78} - 4416q^{79} - 2648q^{80} + 482q^{81} - 704q^{82} - 2562q^{83} + 1960q^{84} - 12q^{85} + 3764q^{86} + 1528q^{88} + 1896q^{90} + 3332q^{91} + 632q^{92} - 2192q^{93} - 3248q^{94} + 6900q^{95} - 4432q^{96} - 4q^{97} + 314q^{98} + 4958q^{99} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/16\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(15\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.29152 1.65800i −0.810173 0.586190i
\(3\) −5.96513 5.96513i −1.14799 1.14799i −0.986947 0.161043i \(-0.948514\pi\)
−0.161043 0.986947i \(-0.551486\pi\)
\(4\) 2.50210 + 7.59865i 0.312762 + 0.949832i
\(5\) 8.67959 8.67959i 0.776326 0.776326i −0.202878 0.979204i \(-0.565029\pi\)
0.979204 + 0.202878i \(0.0650295\pi\)
\(6\) 3.77903 + 23.5594i 0.257130 + 1.60301i
\(7\) 1.63924i 0.0885109i −0.999020 0.0442554i \(-0.985908\pi\)
0.999020 0.0442554i \(-0.0140915\pi\)
\(8\) 6.86495 21.5609i 0.303391 0.952866i
\(9\) 44.1656i 1.63576i
\(10\) −34.2802 + 5.49869i −1.08403 + 0.173884i
\(11\) 18.2021 18.2021i 0.498921 0.498921i −0.412181 0.911102i \(-0.635233\pi\)
0.911102 + 0.412181i \(0.135233\pi\)
\(12\) 30.4016 60.2523i 0.731350 1.44945i
\(13\) −9.34700 9.34700i −0.199415 0.199415i 0.600334 0.799749i \(-0.295034\pi\)
−0.799749 + 0.600334i \(0.795034\pi\)
\(14\) −2.71786 + 3.75636i −0.0518842 + 0.0717092i
\(15\) −103.550 −1.78243
\(16\) −51.4790 + 38.0251i −0.804360 + 0.594142i
\(17\) 53.6113 0.764862 0.382431 0.923984i \(-0.375087\pi\)
0.382431 + 0.923984i \(0.375087\pi\)
\(18\) 73.2264 101.206i 0.958869 1.32525i
\(19\) 70.9870 + 70.9870i 0.857133 + 0.857133i 0.990999 0.133866i \(-0.0427392\pi\)
−0.133866 + 0.990999i \(0.542739\pi\)
\(20\) 87.6704 + 44.2360i 0.980184 + 0.494574i
\(21\) −9.77831 + 9.77831i −0.101610 + 0.101610i
\(22\) −71.8893 + 11.5314i −0.696675 + 0.111750i
\(23\) 25.1189i 0.227724i 0.993497 + 0.113862i \(0.0363222\pi\)
−0.993497 + 0.113862i \(0.963678\pi\)
\(24\) −169.564 + 87.6633i −1.44217 + 0.745592i
\(25\) 25.6706i 0.205365i
\(26\) 5.92151 + 36.9161i 0.0446656 + 0.278456i
\(27\) 102.395 102.395i 0.729850 0.729850i
\(28\) 12.4560 4.10155i 0.0840704 0.0276828i
\(29\) −181.094 181.094i −1.15960 1.15960i −0.984563 0.175033i \(-0.943997\pi\)
−0.175033 0.984563i \(-0.556003\pi\)
\(30\) 237.286 + 171.685i 1.44408 + 1.04484i
\(31\) 132.684 0.768733 0.384367 0.923180i \(-0.374420\pi\)
0.384367 + 0.923180i \(0.374420\pi\)
\(32\) 181.011 1.78308i 0.999951 0.00985023i
\(33\) −217.155 −1.14551
\(34\) −122.851 88.8874i −0.619671 0.448355i
\(35\) −14.2280 14.2280i −0.0687133 0.0687133i
\(36\) −335.599 + 110.507i −1.55370 + 0.511604i
\(37\) 174.872 174.872i 0.776994 0.776994i −0.202324 0.979319i \(-0.564849\pi\)
0.979319 + 0.202324i \(0.0648495\pi\)
\(38\) −44.9717 280.364i −0.191983 1.19687i
\(39\) 111.512i 0.457853i
\(40\) −127.555 246.725i −0.504205 0.975265i
\(41\) 198.660i 0.756720i 0.925658 + 0.378360i \(0.123512\pi\)
−0.925658 + 0.378360i \(0.876488\pi\)
\(42\) 38.6196 6.19475i 0.141884 0.0227588i
\(43\) −285.717 + 285.717i −1.01329 + 1.01329i −0.0133770 + 0.999911i \(0.504258\pi\)
−0.999911 + 0.0133770i \(0.995742\pi\)
\(44\) 183.854 + 92.7678i 0.629934 + 0.317847i
\(45\) 383.339 + 383.339i 1.26989 + 1.26989i
\(46\) 41.6471 57.5605i 0.133490 0.184496i
\(47\) 78.3629 0.243200 0.121600 0.992579i \(-0.461197\pi\)
0.121600 + 0.992579i \(0.461197\pi\)
\(48\) 533.904 + 80.2545i 1.60547 + 0.241328i
\(49\) 340.313 0.992166
\(50\) −42.5617 + 58.8245i −0.120383 + 0.166381i
\(51\) −319.799 319.799i −0.878054 0.878054i
\(52\) 47.6375 94.4117i 0.127041 0.251780i
\(53\) −525.776 + 525.776i −1.36266 + 1.36266i −0.492143 + 0.870515i \(0.663786\pi\)
−0.870515 + 0.492143i \(0.836214\pi\)
\(54\) −404.411 + 64.8694i −1.01914 + 0.163474i
\(55\) 315.973i 0.774650i
\(56\) −35.3436 11.2533i −0.0843390 0.0268534i
\(57\) 846.894i 1.96796i
\(58\) 114.727 + 715.232i 0.259730 + 1.61922i
\(59\) 46.5301 46.5301i 0.102673 0.102673i −0.653904 0.756577i \(-0.726870\pi\)
0.756577 + 0.653904i \(0.226870\pi\)
\(60\) −259.091 786.839i −0.557476 1.69301i
\(61\) 193.318 + 193.318i 0.405767 + 0.405767i 0.880259 0.474493i \(-0.157368\pi\)
−0.474493 + 0.880259i \(0.657368\pi\)
\(62\) −304.047 219.990i −0.622807 0.450624i
\(63\) 72.3982 0.144783
\(64\) −417.745 296.029i −0.815908 0.578181i
\(65\) −162.256 −0.309622
\(66\) 497.615 + 360.043i 0.928063 + 0.671488i
\(67\) 282.182 + 282.182i 0.514538 + 0.514538i 0.915914 0.401375i \(-0.131468\pi\)
−0.401375 + 0.915914i \(0.631468\pi\)
\(68\) 134.141 + 407.374i 0.239220 + 0.726490i
\(69\) 149.838 149.838i 0.261425 0.261425i
\(70\) 9.01370 + 56.1935i 0.0153906 + 0.0959488i
\(71\) 727.536i 1.21609i −0.793901 0.608046i \(-0.791953\pi\)
0.793901 0.608046i \(-0.208047\pi\)
\(72\) 952.250 + 303.195i 1.55866 + 0.496275i
\(73\) 106.065i 0.170054i 0.996379 + 0.0850270i \(0.0270977\pi\)
−0.996379 + 0.0850270i \(0.972902\pi\)
\(74\) −690.659 + 110.785i −1.08497 + 0.174034i
\(75\) −153.128 + 153.128i −0.235757 + 0.235757i
\(76\) −361.789 + 717.022i −0.546054 + 1.08221i
\(77\) −29.8376 29.8376i −0.0441599 0.0441599i
\(78\) 184.887 255.532i 0.268389 0.370940i
\(79\) −58.9970 −0.0840213 −0.0420107 0.999117i \(-0.513376\pi\)
−0.0420107 + 0.999117i \(0.513376\pi\)
\(80\) −116.775 + 776.859i −0.163198 + 1.08569i
\(81\) −29.1298 −0.0399586
\(82\) 329.378 455.233i 0.443582 0.613075i
\(83\) −410.156 410.156i −0.542416 0.542416i 0.381821 0.924236i \(-0.375297\pi\)
−0.924236 + 0.381821i \(0.875297\pi\)
\(84\) −98.7682 49.8357i −0.128292 0.0647324i
\(85\) 465.324 465.324i 0.593783 0.593783i
\(86\) 1128.44 181.007i 1.41492 0.226959i
\(87\) 2160.50i 2.66241i
\(88\) −267.497 517.409i −0.324037 0.626772i
\(89\) 768.959i 0.915837i 0.888994 + 0.457918i \(0.151405\pi\)
−0.888994 + 0.457918i \(0.848595\pi\)
\(90\) −242.853 1514.00i −0.284433 1.77322i
\(91\) −15.3220 + 15.3220i −0.0176504 + 0.0176504i
\(92\) −190.870 + 62.8500i −0.216300 + 0.0712235i
\(93\) −791.477 791.477i −0.882499 0.882499i
\(94\) −179.570 129.925i −0.197034 0.142562i
\(95\) 1232.28 1.33083
\(96\) −1090.39 1069.12i −1.15924 1.13663i
\(97\) −809.953 −0.847817 −0.423908 0.905705i \(-0.639342\pi\)
−0.423908 + 0.905705i \(0.639342\pi\)
\(98\) −779.833 564.238i −0.803826 0.581598i
\(99\) 803.905 + 803.905i 0.816116 + 0.816116i
\(100\) 195.062 64.2302i 0.195062 0.0642302i
\(101\) −303.189 + 303.189i −0.298698 + 0.298698i −0.840504 0.541806i \(-0.817741\pi\)
0.541806 + 0.840504i \(0.317741\pi\)
\(102\) 202.599 + 1263.05i 0.196669 + 1.22608i
\(103\) 962.201i 0.920471i −0.887797 0.460235i \(-0.847765\pi\)
0.887797 0.460235i \(-0.152235\pi\)
\(104\) −265.697 + 137.363i −0.250516 + 0.129515i
\(105\) 169.743i 0.157764i
\(106\) 2076.56 333.089i 1.90277 0.305212i
\(107\) 728.337 728.337i 0.658046 0.658046i −0.296871 0.954918i \(-0.595943\pi\)
0.954918 + 0.296871i \(0.0959432\pi\)
\(108\) 1034.27 + 521.863i 0.921504 + 0.464965i
\(109\) −593.258 593.258i −0.521319 0.521319i 0.396651 0.917970i \(-0.370172\pi\)
−0.917970 + 0.396651i \(0.870172\pi\)
\(110\) −523.882 + 724.057i −0.454092 + 0.627601i
\(111\) −2086.27 −1.78396
\(112\) 62.3324 + 84.3867i 0.0525880 + 0.0711946i
\(113\) 351.938 0.292987 0.146493 0.989212i \(-0.453201\pi\)
0.146493 + 0.989212i \(0.453201\pi\)
\(114\) −1404.15 + 1940.67i −1.15360 + 1.59439i
\(115\) 218.022 + 218.022i 0.176788 + 0.176788i
\(116\) 922.955 1829.18i 0.738743 1.46410i
\(117\) 412.816 412.816i 0.326195 0.326195i
\(118\) −183.771 + 29.4778i −0.143369 + 0.0229970i
\(119\) 87.8821i 0.0676986i
\(120\) −710.864 + 2232.63i −0.540773 + 1.69842i
\(121\) 668.370i 0.502157i
\(122\) −122.471 763.510i −0.0908849 0.566598i
\(123\) 1185.04 1185.04i 0.868707 0.868707i
\(124\) 331.988 + 1008.22i 0.240431 + 0.730167i
\(125\) 862.139 + 862.139i 0.616896 + 0.616896i
\(126\) −165.902 120.036i −0.117299 0.0848703i
\(127\) −2365.81 −1.65301 −0.826504 0.562931i \(-0.809674\pi\)
−0.826504 + 0.562931i \(0.809674\pi\)
\(128\) 466.455 + 1370.97i 0.322103 + 0.946705i
\(129\) 3408.67 2.32649
\(130\) 371.813 + 269.020i 0.250847 + 0.181497i
\(131\) 403.454 + 403.454i 0.269083 + 0.269083i 0.828731 0.559647i \(-0.189063\pi\)
−0.559647 + 0.828731i \(0.689063\pi\)
\(132\) −543.343 1650.09i −0.358272 1.08804i
\(133\) 116.365 116.365i 0.0758656 0.0758656i
\(134\) −178.768 1114.48i −0.115248 0.718483i
\(135\) 1777.50i 1.13320i
\(136\) 368.039 1155.91i 0.232052 0.728811i
\(137\) 856.850i 0.534348i −0.963648 0.267174i \(-0.913910\pi\)
0.963648 0.267174i \(-0.0860898\pi\)
\(138\) −591.786 + 94.9252i −0.365045 + 0.0585549i
\(139\) −1689.33 + 1689.33i −1.03084 + 1.03084i −0.0313345 + 0.999509i \(0.509976\pi\)
−0.999509 + 0.0313345i \(0.990024\pi\)
\(140\) 72.5137 143.713i 0.0437752 0.0867570i
\(141\) −467.445 467.445i −0.279191 0.279191i
\(142\) −1206.25 + 1667.16i −0.712862 + 0.985246i
\(143\) −340.269 −0.198984
\(144\) −1679.40 2273.60i −0.971876 1.31574i
\(145\) −3143.64 −1.80045
\(146\) 175.855 243.049i 0.0996840 0.137773i
\(147\) −2030.01 2030.01i −1.13900 1.13900i
\(148\) 1766.34 + 891.246i 0.981028 + 0.495000i
\(149\) −32.2208 + 32.2208i −0.0177156 + 0.0177156i −0.715909 0.698193i \(-0.753988\pi\)
0.698193 + 0.715909i \(0.253988\pi\)
\(150\) 604.782 97.0099i 0.329202 0.0528055i
\(151\) 1077.06i 0.580460i 0.956957 + 0.290230i \(0.0937319\pi\)
−0.956957 + 0.290230i \(0.906268\pi\)
\(152\) 2017.87 1043.22i 1.07678 0.556687i
\(153\) 2367.78i 1.25113i
\(154\) 18.9027 + 117.844i 0.00989107 + 0.0616633i
\(155\) 1151.64 1151.64i 0.596788 0.596788i
\(156\) −847.343 + 279.014i −0.434883 + 0.143199i
\(157\) 1905.61 + 1905.61i 0.968691 + 0.968691i 0.999525 0.0308332i \(-0.00981607\pi\)
−0.0308332 + 0.999525i \(0.509816\pi\)
\(158\) 135.193 + 97.8169i 0.0680718 + 0.0492525i
\(159\) 6272.64 3.12863
\(160\) 1555.62 1586.57i 0.768641 0.783935i
\(161\) 41.1761 0.0201561
\(162\) 66.7514 + 48.2971i 0.0323734 + 0.0234233i
\(163\) 709.828 + 709.828i 0.341092 + 0.341092i 0.856778 0.515686i \(-0.172463\pi\)
−0.515686 + 0.856778i \(0.672463\pi\)
\(164\) −1509.55 + 497.067i −0.718757 + 0.236673i
\(165\) −1884.82 + 1884.82i −0.889291 + 0.889291i
\(166\) 259.842 + 1619.92i 0.121492 + 0.757410i
\(167\) 3460.66i 1.60356i 0.597623 + 0.801778i \(0.296112\pi\)
−0.597623 + 0.801778i \(0.703888\pi\)
\(168\) 143.702 + 277.957i 0.0659930 + 0.127648i
\(169\) 2022.27i 0.920467i
\(170\) −1837.80 + 294.792i −0.829136 + 0.132997i
\(171\) −3135.18 + 3135.18i −1.40207 + 1.40207i
\(172\) −2885.95 1456.17i −1.27937 0.645535i
\(173\) −1303.54 1303.54i −0.572871 0.572871i 0.360059 0.932930i \(-0.382757\pi\)
−0.932930 + 0.360059i \(0.882757\pi\)
\(174\) 3582.10 4950.81i 1.56068 2.15701i
\(175\) −42.0803 −0.0181770
\(176\) −244.889 + 1629.16i −0.104882 + 0.697742i
\(177\) −555.117 −0.235735
\(178\) 1274.93 1762.08i 0.536855 0.741987i
\(179\) −1082.35 1082.35i −0.451947 0.451947i 0.444054 0.896000i \(-0.353540\pi\)
−0.896000 + 0.444054i \(0.853540\pi\)
\(180\) −1953.71 + 3872.01i −0.809006 + 1.60335i
\(181\) 2943.93 2943.93i 1.20895 1.20895i 0.237588 0.971366i \(-0.423643\pi\)
0.971366 0.237588i \(-0.0763567\pi\)
\(182\) 60.5145 9.70681i 0.0246463 0.00395339i
\(183\) 2306.33i 0.931633i
\(184\) 541.587 + 172.440i 0.216991 + 0.0690895i
\(185\) 3035.64i 1.20640i
\(186\) 501.417 + 3125.95i 0.197665 + 1.23229i
\(187\) 975.837 975.837i 0.381606 0.381606i
\(188\) 196.072 + 595.453i 0.0760637 + 0.230999i
\(189\) −167.851 167.851i −0.0645997 0.0645997i
\(190\) −2823.78 2043.11i −1.07820 0.780120i
\(191\) −430.650 −0.163145 −0.0815726 0.996667i \(-0.525994\pi\)
−0.0815726 + 0.996667i \(0.525994\pi\)
\(192\) 726.053 + 4257.76i 0.272908 + 1.60040i
\(193\) −2266.98 −0.845497 −0.422749 0.906247i \(-0.638935\pi\)
−0.422749 + 0.906247i \(0.638935\pi\)
\(194\) 1856.02 + 1342.90i 0.686879 + 0.496982i
\(195\) 967.881 + 967.881i 0.355443 + 0.355443i
\(196\) 851.495 + 2585.92i 0.310312 + 0.942390i
\(197\) −1039.41 + 1039.41i −0.375913 + 0.375913i −0.869625 0.493712i \(-0.835640\pi\)
0.493712 + 0.869625i \(0.335640\pi\)
\(198\) −509.290 3175.03i −0.182796 1.13959i
\(199\) 4989.44i 1.77735i −0.458540 0.888674i \(-0.651627\pi\)
0.458540 0.888674i \(-0.348373\pi\)
\(200\) −553.481 176.227i −0.195685 0.0623057i
\(201\) 3366.51i 1.18137i
\(202\) 1197.45 192.077i 0.417091 0.0669033i
\(203\) −296.857 + 296.857i −0.102637 + 0.102637i
\(204\) 1629.87 3230.21i 0.559382 1.10863i
\(205\) 1724.29 + 1724.29i 0.587462 + 0.587462i
\(206\) −1595.33 + 2204.90i −0.539571 + 0.745741i
\(207\) −1109.39 −0.372503
\(208\) 836.596 + 125.754i 0.278882 + 0.0419205i
\(209\) 2584.22 0.855283
\(210\) 281.434 388.970i 0.0924800 0.127817i
\(211\) 2651.50 + 2651.50i 0.865103 + 0.865103i 0.991925 0.126823i \(-0.0404779\pi\)
−0.126823 + 0.991925i \(0.540478\pi\)
\(212\) −5310.73 2679.65i −1.72048 0.868108i
\(213\) −4339.85 + 4339.85i −1.39606 + 1.39606i
\(214\) −2876.58 + 461.416i −0.918872 + 0.147391i
\(215\) 4959.80i 1.57328i
\(216\) −1504.79 2910.67i −0.474020 0.916879i
\(217\) 217.501i 0.0680413i
\(218\) 375.841 + 2343.08i 0.116767 + 0.727951i
\(219\) 632.691 632.691i 0.195220 0.195220i
\(220\) 2400.97 790.594i 0.735787 0.242281i
\(221\) −501.105 501.105i −0.152525 0.152525i
\(222\) 4780.72 + 3459.03i 1.44532 + 1.04574i
\(223\) 3690.85 1.10833 0.554165 0.832407i \(-0.313038\pi\)
0.554165 + 0.832407i \(0.313038\pi\)
\(224\) −2.92291 296.721i −0.000871853 0.0885066i
\(225\) 1133.76 0.335928
\(226\) −806.471 583.512i −0.237370 0.171746i
\(227\) −1710.42 1710.42i −0.500108 0.500108i 0.411363 0.911471i \(-0.365053\pi\)
−0.911471 + 0.411363i \(0.865053\pi\)
\(228\) 6435.25 2119.01i 1.86923 0.615503i
\(229\) −91.8012 + 91.8012i −0.0264908 + 0.0264908i −0.720228 0.693737i \(-0.755963\pi\)
0.693737 + 0.720228i \(0.255963\pi\)
\(230\) −138.121 861.081i −0.0395976 0.246861i
\(231\) 355.971i 0.101390i
\(232\) −5147.74 + 2661.35i −1.45675 + 0.753129i
\(233\) 4259.71i 1.19769i 0.800863 + 0.598847i \(0.204374\pi\)
−0.800863 + 0.598847i \(0.795626\pi\)
\(234\) −1630.42 + 261.527i −0.455487 + 0.0730623i
\(235\) 680.158 680.158i 0.188803 0.188803i
\(236\) 469.989 + 237.144i 0.129634 + 0.0654099i
\(237\) 351.925 + 351.925i 0.0964556 + 0.0964556i
\(238\) −145.708 + 201.383i −0.0396843 + 0.0548476i
\(239\) −5053.12 −1.36761 −0.683806 0.729664i \(-0.739676\pi\)
−0.683806 + 0.729664i \(0.739676\pi\)
\(240\) 5330.64 3937.49i 1.43372 1.05902i
\(241\) 48.8379 0.0130536 0.00652681 0.999979i \(-0.497922\pi\)
0.00652681 + 0.999979i \(0.497922\pi\)
\(242\) 1108.16 1531.58i 0.294359 0.406834i
\(243\) −2590.91 2590.91i −0.683978 0.683978i
\(244\) −985.254 + 1952.65i −0.258502 + 0.512319i
\(245\) 2953.78 2953.78i 0.770244 0.770244i
\(246\) −4680.31 + 750.743i −1.21303 + 0.194576i
\(247\) 1327.03i 0.341850i
\(248\) 910.868 2860.79i 0.233227 0.732500i
\(249\) 4893.28i 1.24538i
\(250\) −546.182 3405.03i −0.138174 0.861412i
\(251\) −2604.76 + 2604.76i −0.655025 + 0.655025i −0.954199 0.299174i \(-0.903289\pi\)
0.299174 + 0.954199i \(0.403289\pi\)
\(252\) 181.147 + 550.129i 0.0452826 + 0.137519i
\(253\) 457.216 + 457.216i 0.113616 + 0.113616i
\(254\) 5421.30 + 3922.51i 1.33922 + 0.968977i
\(255\) −5551.44 −1.36331
\(256\) 1204.18 3914.99i 0.293990 0.955808i
\(257\) 739.054 0.179381 0.0896905 0.995970i \(-0.471412\pi\)
0.0896905 + 0.995970i \(0.471412\pi\)
\(258\) −7811.03 5651.57i −1.88486 1.36376i
\(259\) −286.658 286.658i −0.0687724 0.0687724i
\(260\) −405.981 1232.93i −0.0968379 0.294089i
\(261\) 7998.12 7998.12i 1.89682 1.89682i
\(262\) −255.596 1593.45i −0.0602701 0.375738i
\(263\) 2448.30i 0.574025i −0.957927 0.287012i \(-0.907338\pi\)
0.957927 0.287012i \(-0.0926621\pi\)
\(264\) −1490.76 + 4682.07i −0.347538 + 1.09152i
\(265\) 9127.03i 2.11573i
\(266\) −459.585 + 73.7196i −0.105936 + 0.0169926i
\(267\) 4586.94 4586.94i 1.05137 1.05137i
\(268\) −1438.16 + 2850.25i −0.327797 + 0.649653i
\(269\) −829.952 829.952i −0.188116 0.188116i 0.606765 0.794881i \(-0.292467\pi\)
−0.794881 + 0.606765i \(0.792467\pi\)
\(270\) −2947.08 + 4073.16i −0.664273 + 0.918091i
\(271\) 1404.85 0.314902 0.157451 0.987527i \(-0.449672\pi\)
0.157451 + 0.987527i \(0.449672\pi\)
\(272\) −2759.86 + 2038.58i −0.615225 + 0.454437i
\(273\) 182.796 0.0405249
\(274\) −1420.65 + 1963.49i −0.313229 + 0.432914i
\(275\) −467.257 467.257i −0.102461 0.102461i
\(276\) 1513.47 + 763.657i 0.330074 + 0.166546i
\(277\) −2245.69 + 2245.69i −0.487112 + 0.487112i −0.907394 0.420281i \(-0.861931\pi\)
0.420281 + 0.907394i \(0.361931\pi\)
\(278\) 6672.04 1070.23i 1.43943 0.230892i
\(279\) 5860.07i 1.25747i
\(280\) −404.442 + 209.094i −0.0863216 + 0.0446276i
\(281\) 6045.97i 1.28353i −0.766900 0.641766i \(-0.778202\pi\)
0.766900 0.641766i \(-0.221798\pi\)
\(282\) 296.136 + 1846.18i 0.0625342 + 0.389853i
\(283\) 2459.63 2459.63i 0.516643 0.516643i −0.399911 0.916554i \(-0.630959\pi\)
0.916554 + 0.399911i \(0.130959\pi\)
\(284\) 5528.29 1820.36i 1.15508 0.380347i
\(285\) −7350.69 7350.69i −1.52778 1.52778i
\(286\) 779.733 + 564.165i 0.161212 + 0.116643i
\(287\) 325.653 0.0669780
\(288\) 78.7509 + 7994.44i 0.0161126 + 1.63568i
\(289\) −2038.82 −0.414986
\(290\) 7203.70 + 5212.14i 1.45868 + 1.05541i
\(291\) 4831.48 + 4831.48i 0.973286 + 0.973286i
\(292\) −805.950 + 265.384i −0.161523 + 0.0531864i
\(293\) −1852.49 + 1852.49i −0.369364 + 0.369364i −0.867245 0.497881i \(-0.834112\pi\)
0.497881 + 0.867245i \(0.334112\pi\)
\(294\) 1286.05 + 8017.56i 0.255116 + 1.59045i
\(295\) 807.725i 0.159415i
\(296\) −2569.91 4970.89i −0.504639 0.976105i
\(297\) 3727.60i 0.728275i
\(298\) 127.256 20.4125i 0.0247375 0.00396801i
\(299\) 234.787 234.787i 0.0454116 0.0454116i
\(300\) −1546.71 780.427i −0.297665 0.150193i
\(301\) 468.359 + 468.359i 0.0896870 + 0.0896870i
\(302\) 1785.75 2468.09i 0.340260 0.470274i
\(303\) 3617.13 0.685804
\(304\) −6353.63 955.055i −1.19870 0.180185i
\(305\) 3355.83 0.630015
\(306\) 3925.77 5425.80i 0.733402 1.01364i
\(307\) 2107.35 + 2107.35i 0.391768 + 0.391768i 0.875317 0.483549i \(-0.160653\pi\)
−0.483549 + 0.875317i \(0.660653\pi\)
\(308\) 152.069 301.382i 0.0281329 0.0557560i
\(309\) −5739.66 + 5739.66i −1.05669 + 1.05669i
\(310\) −4548.43 + 729.588i −0.833333 + 0.133670i
\(311\) 5294.90i 0.965422i −0.875780 0.482711i \(-0.839652\pi\)
0.875780 0.482711i \(-0.160348\pi\)
\(312\) 2404.30 + 765.526i 0.436272 + 0.138908i
\(313\) 4005.87i 0.723403i −0.932294 0.361702i \(-0.882196\pi\)
0.932294 0.361702i \(-0.117804\pi\)
\(314\) −1207.24 7526.25i −0.216971 1.35265i
\(315\) 628.387 628.387i 0.112399 0.112399i
\(316\) −147.616 448.298i −0.0262787 0.0798061i
\(317\) 809.240 + 809.240i 0.143380 + 0.143380i 0.775153 0.631773i \(-0.217673\pi\)
−0.631773 + 0.775153i \(0.717673\pi\)
\(318\) −14373.9 10400.0i −2.53474 1.83398i
\(319\) −6592.56 −1.15709
\(320\) −6195.27 + 1056.45i −1.08227 + 0.184554i
\(321\) −8689.25 −1.51086
\(322\) −94.3557 68.2698i −0.0163299 0.0118153i
\(323\) 3805.71 + 3805.71i 0.655589 + 0.655589i
\(324\) −72.8856 221.347i −0.0124975 0.0379539i
\(325\) −239.943 + 239.943i −0.0409527 + 0.0409527i
\(326\) −449.690 2803.47i −0.0763989 0.476289i
\(327\) 7077.72i 1.19694i
\(328\) 4283.30 + 1363.79i 0.721053 + 0.229582i
\(329\) 128.456i 0.0215259i
\(330\) 7444.12 1194.07i 1.24177 0.199186i
\(331\) −4229.66 + 4229.66i −0.702366 + 0.702366i −0.964918 0.262552i \(-0.915436\pi\)
0.262552 + 0.964918i \(0.415436\pi\)
\(332\) 2090.39 4142.89i 0.345557 0.684851i
\(333\) 7723.33 + 7723.33i 1.27098 + 1.27098i
\(334\) 5737.76 7930.15i 0.939988 1.29916i
\(335\) 4898.46 0.798899
\(336\) 131.557 875.199i 0.0213601 0.142101i
\(337\) 10002.6 1.61684 0.808419 0.588607i \(-0.200323\pi\)
0.808419 + 0.588607i \(0.200323\pi\)
\(338\) −3352.91 + 4634.06i −0.539569 + 0.745738i
\(339\) −2099.36 2099.36i −0.336346 0.336346i
\(340\) 4700.12 + 2371.55i 0.749706 + 0.378281i
\(341\) 2415.12 2415.12i 0.383537 0.383537i
\(342\) 12382.5 1986.20i 1.95780 0.314039i
\(343\) 1120.12i 0.176328i
\(344\) 4198.88 + 8121.74i 0.658106 + 1.27295i
\(345\) 2601.06i 0.405903i
\(346\) 825.821 + 5148.37i 0.128313 + 0.799936i
\(347\) −6409.49 + 6409.49i −0.991583 + 0.991583i −0.999965 0.00838198i \(-0.997332\pi\)
0.00838198 + 0.999965i \(0.497332\pi\)
\(348\) −16416.9 + 5405.77i −2.52884 + 0.832700i
\(349\) −5503.23 5503.23i −0.844071 0.844071i 0.145314 0.989386i \(-0.453581\pi\)
−0.989386 + 0.145314i \(0.953581\pi\)
\(350\) 96.4278 + 69.7691i 0.0147265 + 0.0106552i
\(351\) −1914.18 −0.291086
\(352\) 3262.31 3327.22i 0.493982 0.503811i
\(353\) −1411.35 −0.212800 −0.106400 0.994323i \(-0.533932\pi\)
−0.106400 + 0.994323i \(0.533932\pi\)
\(354\) 1272.06 + 920.382i 0.190986 + 0.138186i
\(355\) −6314.71 6314.71i −0.944085 0.944085i
\(356\) −5843.05 + 1924.01i −0.869891 + 0.286439i
\(357\) −524.228 + 524.228i −0.0777174 + 0.0777174i
\(358\) 685.689 + 4274.75i 0.101228 + 0.631082i
\(359\) 2160.73i 0.317658i 0.987306 + 0.158829i \(0.0507718\pi\)
−0.987306 + 0.158829i \(0.949228\pi\)
\(360\) 10896.7 5633.54i 1.59530 0.824760i
\(361\) 3219.31i 0.469355i
\(362\) −11627.1 + 1865.04i −1.68814 + 0.270785i
\(363\) 3986.92 3986.92i 0.576471 0.576471i
\(364\) −154.764 78.0896i −0.0222853 0.0112445i
\(365\) 920.599 + 920.599i 0.132017 + 0.132017i
\(366\) −3823.89 + 5284.99i −0.546114 + 0.754784i
\(367\) 10757.7 1.53010 0.765052 0.643969i \(-0.222713\pi\)
0.765052 + 0.643969i \(0.222713\pi\)
\(368\) −955.150 1293.10i −0.135301 0.183172i
\(369\) −8773.95 −1.23782
\(370\) −5033.07 + 6956.21i −0.707181 + 0.977395i
\(371\) 861.875 + 861.875i 0.120610 + 0.120610i
\(372\) 4033.81 7994.51i 0.562213 1.11424i
\(373\) 1406.99 1406.99i 0.195312 0.195312i −0.602675 0.797987i \(-0.705898\pi\)
0.797987 + 0.602675i \(0.205898\pi\)
\(374\) −3854.08 + 618.212i −0.532860 + 0.0854732i
\(375\) 10285.5i 1.41638i
\(376\) 537.957 1689.58i 0.0737847 0.231737i
\(377\) 3385.37i 0.462481i
\(378\) 106.337 + 662.928i 0.0144692 + 0.0902046i
\(379\) −1146.95 + 1146.95i −0.155449 + 0.155449i −0.780547 0.625098i \(-0.785059\pi\)
0.625098 + 0.780547i \(0.285059\pi\)
\(380\) 3083.27 + 9363.64i 0.416233 + 1.26406i
\(381\) 14112.4 + 14112.4i 1.89764 + 1.89764i
\(382\) 986.842 + 714.016i 0.132176 + 0.0956342i
\(383\) 9042.17 1.20635 0.603176 0.797608i \(-0.293902\pi\)
0.603176 + 0.797608i \(0.293902\pi\)
\(384\) 5395.58 10960.5i 0.717037 1.45658i
\(385\) −517.957 −0.0685650
\(386\) 5194.83 + 3758.65i 0.684999 + 0.495622i
\(387\) −12618.8 12618.8i −1.65750 1.65750i
\(388\) −2026.58 6154.55i −0.265165 0.805283i
\(389\) 2575.34 2575.34i 0.335668 0.335668i −0.519066 0.854734i \(-0.673720\pi\)
0.854734 + 0.519066i \(0.173720\pi\)
\(390\) −613.172 3822.66i −0.0796132 0.496328i
\(391\) 1346.66i 0.174178i
\(392\) 2336.23 7337.45i 0.301014 0.945401i
\(393\) 4813.31i 0.617810i
\(394\) 4105.16 658.486i 0.524911 0.0841981i
\(395\) −512.070 + 512.070i −0.0652279 + 0.0652279i
\(396\) −4097.15 + 8120.04i −0.519923 + 1.03042i
\(397\) −7121.46 7121.46i −0.900292 0.900292i 0.0951695 0.995461i \(-0.469661\pi\)
−0.995461 + 0.0951695i \(0.969661\pi\)
\(398\) −8272.48 + 11433.4i −1.04186 + 1.43996i
\(399\) −1388.27 −0.174186
\(400\) 976.126 + 1321.50i 0.122016 + 0.165187i
\(401\) −3025.14 −0.376729 −0.188365 0.982099i \(-0.560319\pi\)
−0.188365 + 0.982099i \(0.560319\pi\)
\(402\) −5581.66 + 7714.42i −0.692508 + 0.957115i
\(403\) −1240.20 1240.20i −0.153297 0.153297i
\(404\) −3062.44 1545.22i −0.377134 0.190291i
\(405\) −252.835 + 252.835i −0.0310209 + 0.0310209i
\(406\) 1172.44 188.065i 0.143318 0.0229889i
\(407\) 6366.06i 0.775317i
\(408\) −9090.55 + 4699.75i −1.10306 + 0.570275i
\(409\) 9440.21i 1.14129i −0.821196 0.570646i \(-0.806693\pi\)
0.821196 0.570646i \(-0.193307\pi\)
\(410\) −1092.37 6810.11i −0.131581 0.820310i
\(411\) −5111.22 + 5111.22i −0.613426 + 0.613426i
\(412\) 7311.43 2407.52i 0.874292 0.287888i
\(413\) −76.2743 76.2743i −0.00908768 0.00908768i
\(414\) 2542.19 + 1839.37i 0.301792 + 0.218358i
\(415\) −7119.98 −0.842183
\(416\) −1708.57 1675.24i −0.201369 0.197441i
\(417\) 20154.2 2.36680
\(418\) −5921.78 4284.63i −0.692928 0.501359i
\(419\) −3255.69 3255.69i −0.379597 0.379597i 0.491360 0.870957i \(-0.336500\pi\)
−0.870957 + 0.491360i \(0.836500\pi\)
\(420\) −1289.82 + 424.714i −0.149850 + 0.0493427i
\(421\) −9438.04 + 9438.04i −1.09259 + 1.09259i −0.0973423 + 0.995251i \(0.531034\pi\)
−0.995251 + 0.0973423i \(0.968966\pi\)
\(422\) −1679.78 10472.1i −0.193768 1.20800i
\(423\) 3460.95i 0.397818i
\(424\) 7726.77 + 14945.6i 0.885013 + 1.71185i
\(425\) 1376.23i 0.157076i
\(426\) 17140.3 2749.38i 1.94941 0.312694i
\(427\) 316.895 316.895i 0.0359148 0.0359148i
\(428\) 7356.75 + 3712.01i 0.830845 + 0.419221i
\(429\) 2029.75 + 2029.75i 0.228432 + 0.228432i
\(430\) 8223.34 11365.5i 0.922243 1.27463i
\(431\) −10617.7 −1.18663 −0.593314 0.804971i \(-0.702181\pi\)
−0.593314 + 0.804971i \(0.702181\pi\)
\(432\) −1377.62 + 9164.79i −0.153427 + 1.02070i
\(433\) 706.479 0.0784093 0.0392046 0.999231i \(-0.487518\pi\)
0.0392046 + 0.999231i \(0.487518\pi\)
\(434\) −360.617 + 498.408i −0.0398851 + 0.0551252i
\(435\) 18752.2 + 18752.2i 2.06690 + 2.06690i
\(436\) 3023.57 5992.35i 0.332117 0.658214i
\(437\) −1783.12 + 1783.12i −0.195190 + 0.195190i
\(438\) −2498.82 + 400.822i −0.272599 + 0.0437261i
\(439\) 13611.8i 1.47985i 0.672688 + 0.739926i \(0.265140\pi\)
−0.672688 + 0.739926i \(0.734860\pi\)
\(440\) −6812.66 2169.14i −0.738138 0.235022i
\(441\) 15030.1i 1.62295i
\(442\) 317.460 + 1979.12i 0.0341630 + 0.212980i
\(443\) 3126.97 3126.97i 0.335366 0.335366i −0.519254 0.854620i \(-0.673790\pi\)
0.854620 + 0.519254i \(0.173790\pi\)
\(444\) −5220.05 15852.8i −0.557956 1.69447i
\(445\) 6674.25 + 6674.25i 0.710988 + 0.710988i
\(446\) −8457.64 6119.42i −0.897939 0.649692i
\(447\) 384.403 0.0406748
\(448\) −485.264 + 684.786i −0.0511753 + 0.0722167i
\(449\) −5231.76 −0.549893 −0.274947 0.961460i \(-0.588660\pi\)
−0.274947 + 0.961460i \(0.588660\pi\)
\(450\) −2598.02 1879.76i −0.272160 0.196918i
\(451\) 3616.03 + 3616.03i 0.377543 + 0.377543i
\(452\) 880.582 + 2674.25i 0.0916352 + 0.278288i
\(453\) 6424.78 6424.78i 0.666363 0.666363i
\(454\) 1083.58 + 6755.32i 0.112016 + 0.698333i
\(455\) 265.978i 0.0274049i
\(456\) −18259.8 5813.88i −1.87520 0.597061i
\(457\) 6833.10i 0.699429i −0.936856 0.349715i \(-0.886279\pi\)
0.936856 0.349715i \(-0.113721\pi\)
\(458\) 362.570 58.1579i 0.0369908 0.00593350i
\(459\) 5489.54 5489.54i 0.558235 0.558235i
\(460\) −1111.16 + 2202.19i −0.112627 + 0.223212i
\(461\) −5975.90 5975.90i −0.603742 0.603742i 0.337561 0.941304i \(-0.390398\pi\)
−0.941304 + 0.337561i \(0.890398\pi\)
\(462\) 590.198 815.713i 0.0594340 0.0821437i
\(463\) −4273.38 −0.428943 −0.214472 0.976730i \(-0.568803\pi\)
−0.214472 + 0.976730i \(0.568803\pi\)
\(464\) 16208.6 + 2436.42i 1.62170 + 0.243768i
\(465\) −13739.4 −1.37021
\(466\) 7062.59 9761.20i 0.702077 0.970341i
\(467\) 12245.6 + 12245.6i 1.21340 + 1.21340i 0.969901 + 0.243500i \(0.0782956\pi\)
0.243500 + 0.969901i \(0.421704\pi\)
\(468\) 4169.75 + 2103.94i 0.411852 + 0.207809i
\(469\) 462.566 462.566i 0.0455422 0.0455422i
\(470\) −2686.29 + 430.894i −0.263637 + 0.0422886i
\(471\) 22734.5i 2.22410i
\(472\) −683.805 1322.66i −0.0666836 0.128984i
\(473\) 10401.3i 1.01110i
\(474\) −222.952 1389.93i −0.0216044 0.134687i
\(475\) 1822.28 1822.28i 0.176025 0.176025i
\(476\) 667.785 219.889i 0.0643023 0.0211736i
\(477\) −23221.2 23221.2i −2.22898 2.22898i
\(478\) 11579.3 + 8378.05i 1.10800 + 0.801681i
\(479\) −4067.97 −0.388038 −0.194019 0.980998i \(-0.562152\pi\)
−0.194019 + 0.980998i \(0.562152\pi\)
\(480\) −18743.6 + 184.638i −1.78234 + 0.0175573i
\(481\) −3269.06 −0.309888
\(482\) −111.913 80.9730i −0.0105757 0.00765191i
\(483\) −245.621 245.621i −0.0231390 0.0231390i
\(484\) −5078.71 + 1672.33i −0.476964 + 0.157055i
\(485\) −7030.06 + 7030.06i −0.658182 + 0.658182i
\(486\) 1641.39 + 10232.8i 0.153200 + 0.955082i
\(487\) 16174.3i 1.50499i 0.658600 + 0.752493i \(0.271149\pi\)
−0.658600 + 0.752493i \(0.728851\pi\)
\(488\) 5495.22 2840.99i 0.509747 0.263536i
\(489\) 8468.44i 0.783141i
\(490\) −11666.0 + 1871.28i −1.07554 + 0.172522i
\(491\) 13596.7 13596.7i 1.24971 1.24971i 0.293866 0.955847i \(-0.405058\pi\)
0.955847 0.293866i \(-0.0949420\pi\)
\(492\) 11969.7 + 6039.60i 1.09682 + 0.553427i
\(493\) −9708.68 9708.68i −0.886931 0.886931i
\(494\) −2200.21 + 3040.91i −0.200389 + 0.276958i
\(495\) 13955.1 1.26714
\(496\) −6830.44 + 5045.32i −0.618338 + 0.456737i
\(497\) −1192.61 −0.107637
\(498\) 8113.03 11213.0i 0.730028 1.00897i
\(499\) −14646.7 14646.7i −1.31398 1.31398i −0.918453 0.395530i \(-0.870561\pi\)
−0.395530 0.918453i \(-0.629439\pi\)
\(500\) −4393.94 + 8708.25i −0.393006 + 0.778889i
\(501\) 20643.3 20643.3i 1.84087 1.84087i
\(502\) 10287.5 1650.17i 0.914652 0.146714i
\(503\) 9828.84i 0.871265i 0.900125 + 0.435632i \(0.143475\pi\)
−0.900125 + 0.435632i \(0.856525\pi\)
\(504\) 497.010 1560.97i 0.0439258 0.137959i
\(505\) 5263.12i 0.463774i
\(506\) −289.656 1805.78i −0.0254482 0.158650i
\(507\) −12063.1 + 12063.1i −1.05669 + 1.05669i
\(508\) −5919.49 17977.0i −0.516998 1.57008i
\(509\) 13456.1 + 13456.1i 1.17177 + 1.17177i 0.981787 + 0.189985i \(0.0608439\pi\)
0.189985 + 0.981787i \(0.439156\pi\)
\(510\) 12721.2 + 9204.27i 1.10452 + 0.799161i
\(511\) 173.866 0.0150516
\(512\) −9250.45 + 6974.74i −0.798469 + 0.602037i
\(513\) 14537.5 1.25116
\(514\) −1693.55 1225.35i −0.145330 0.105151i
\(515\) −8351.51 8351.51i −0.714585 0.714585i
\(516\) 8528.83 + 25901.3i 0.727637 + 2.20977i
\(517\) 1426.37 1426.37i 0.121338 0.121338i
\(518\) 181.604 + 1132.16i 0.0154039 + 0.0960313i
\(519\) 15551.6i 1.31530i
\(520\) −1113.88 + 3498.39i −0.0939364 + 0.295028i
\(521\) 10607.1i 0.891950i 0.895045 + 0.445975i \(0.147143\pi\)
−0.895045 + 0.445975i \(0.852857\pi\)
\(522\) −31588.7 + 5066.97i −2.64866 + 0.424857i
\(523\) 3903.15 3903.15i 0.326334 0.326334i −0.524857 0.851191i \(-0.675881\pi\)
0.851191 + 0.524857i \(0.175881\pi\)
\(524\) −2056.22 + 4075.18i −0.171425 + 0.339743i
\(525\) 251.015 + 251.015i 0.0208670 + 0.0208670i
\(526\) −4059.27 + 5610.32i −0.336488 + 0.465060i
\(527\) 7113.36 0.587975
\(528\) 11178.9 8257.35i 0.921404 0.680597i
\(529\) 11536.0 0.948142
\(530\) 15132.6 20914.7i 1.24022 1.71411i
\(531\) 2055.03 + 2055.03i 0.167949 + 0.167949i
\(532\) 1175.37 + 593.061i 0.0957874 + 0.0483317i
\(533\) 1856.88 1856.88i 0.150901 0.150901i
\(534\) −18116.2 + 2905.92i −1.46810 + 0.235489i
\(535\) 12643.3i 1.02172i
\(536\) 8021.28 4146.94i 0.646392 0.334180i
\(537\) 12912.7i 1.03766i
\(538\) 525.791 + 3277.91i 0.0421347 + 0.262678i
\(539\) 6194.39 6194.39i 0.495012 0.495012i
\(540\) 13506.6 4447.46i 1.07635 0.354423i
\(541\) 9532.77 + 9532.77i 0.757570 + 0.757570i 0.975880 0.218309i \(-0.0700541\pi\)
−0.218309 + 0.975880i \(0.570054\pi\)
\(542\) −3219.23 2329.23i −0.255125 0.184592i
\(543\) −35121.9 −2.77573
\(544\) 9704.22 95.5934i 0.764825 0.00753407i
\(545\) −10298.5 −0.809427
\(546\) −418.880 303.075i −0.0328322 0.0237553i
\(547\) −1232.88 1232.88i −0.0963693 0.0963693i 0.657278 0.753648i \(-0.271708\pi\)
−0.753648 + 0.657278i \(0.771708\pi\)
\(548\) 6510.90 2143.92i 0.507540 0.167124i
\(549\) −8537.99 + 8537.99i −0.663739 + 0.663739i
\(550\) 296.017 + 1845.44i 0.0229494 + 0.143072i
\(551\) 25710.6i 1.98786i
\(552\) −2202.01 4259.27i −0.169789 0.328417i
\(553\) 96.7105i 0.00743680i
\(554\) 8869.36 1422.69i 0.680186 0.109105i
\(555\) −18108.0 + 18108.0i −1.38494 + 1.38494i
\(556\) −17063.5 8609.78i −1.30154 0.656719i
\(557\) −2889.57 2889.57i −0.219812 0.219812i 0.588607 0.808419i \(-0.299676\pi\)
−0.808419 + 0.588607i \(0.799676\pi\)
\(558\) 9715.97 13428.4i 0.737114 1.01877i
\(559\) 5341.19 0.404129
\(560\) 1273.46 + 191.422i 0.0960957 + 0.0144448i
\(561\) −11642.0 −0.876159
\(562\) −10024.2 + 13854.4i −0.752394 + 1.03988i
\(563\) 70.0753 + 70.0753i 0.00524569 + 0.00524569i 0.709725 0.704479i \(-0.248819\pi\)
−0.704479 + 0.709725i \(0.748819\pi\)
\(564\) 2382.36 4721.55i 0.177864 0.352505i
\(565\) 3054.68 3054.68i 0.227453 0.227453i
\(566\) −9714.35 + 1558.23i −0.721422 + 0.115719i
\(567\) 47.7509i 0.00353677i
\(568\) −15686.3 4994.49i −1.15877 0.368951i
\(569\) 8915.23i 0.656847i −0.944531 0.328423i \(-0.893483\pi\)
0.944531 0.328423i \(-0.106517\pi\)
\(570\) 4656.81 + 29031.6i 0.342197 + 2.13334i
\(571\) 4946.30 4946.30i 0.362515 0.362515i −0.502223 0.864738i \(-0.667484\pi\)
0.864738 + 0.502223i \(0.167484\pi\)
\(572\) −851.386 2585.59i −0.0622347 0.189002i
\(573\) 2568.89 + 2568.89i 0.187289 + 0.187289i
\(574\) −746.239 539.931i −0.0542638 0.0392618i
\(575\) 644.818 0.0467665
\(576\) 13074.3 18450.0i 0.945768 1.33463i
\(577\) 17911.5 1.29232 0.646159 0.763203i \(-0.276374\pi\)
0.646159 + 0.763203i \(0.276374\pi\)
\(578\) 4672.00 + 3380.36i 0.336210 + 0.243261i
\(579\) 13522.8 + 13522.8i 0.970622 + 0.970622i
\(580\) −7865.68 23887.4i −0.563112 1.71012i
\(581\) −672.347 + 672.347i −0.0480097 + 0.0480097i
\(582\) −3060.84 19082.0i −0.218000 1.35906i
\(583\) 19140.4i 1.35972i
\(584\) 2286.85 + 728.129i 0.162039 + 0.0515928i
\(585\) 7166.15i 0.506468i
\(586\) 7316.44 1173.59i 0.515767 0.0827314i
\(587\) 7940.26 7940.26i 0.558312 0.558312i −0.370514 0.928827i \(-0.620819\pi\)
0.928827 + 0.370514i \(0.120819\pi\)
\(588\) 10346.1 20504.6i 0.725620 1.43809i
\(589\) 9418.83 + 9418.83i 0.658907 + 0.658907i
\(590\) −1339.21 + 1850.92i −0.0934478 + 0.129154i
\(591\) 12400.4 0.863088
\(592\) −2352.72 + 15651.8i −0.163338 + 1.08663i
\(593\) −7006.26 −0.485181 −0.242591 0.970129i \(-0.577997\pi\)
−0.242591 + 0.970129i \(0.577997\pi\)
\(594\) −6180.36 + 8541.87i −0.426908 + 0.590029i
\(595\) −762.780 762.780i −0.0525562 0.0525562i
\(596\) −325.454 164.215i −0.0223677 0.0112861i
\(597\) −29762.7 + 29762.7i −2.04038 + 2.04038i
\(598\) −927.294 + 148.742i −0.0634111 + 0.0101714i
\(599\) 8502.74i 0.579987i −0.957029 0.289994i \(-0.906347\pi\)
0.957029 0.289994i \(-0.0936532\pi\)
\(600\) 2250.37 + 4352.80i 0.153118 + 0.296171i
\(601\) 11936.2i 0.810127i −0.914289 0.405063i \(-0.867249\pi\)
0.914289 0.405063i \(-0.132751\pi\)
\(602\) −296.715 1849.79i −0.0200884 0.125236i
\(603\) −12462.8 + 12462.8i −0.841663 + 0.841663i
\(604\) −8184.17 + 2694.89i −0.551340 + 0.181546i
\(605\) 5801.18 + 5801.18i 0.389837 + 0.389837i
\(606\) −8288.71 5997.19i −0.555620 0.402012i
\(607\) −3850.00 −0.257441 −0.128721 0.991681i \(-0.541087\pi\)
−0.128721 + 0.991681i \(0.541087\pi\)
\(608\) 12976.0 + 12722.8i 0.865535 + 0.848649i
\(609\) 3541.58 0.235652
\(610\) −7689.95 5563.96i −0.510421 0.369309i
\(611\) −732.459 732.459i −0.0484977 0.0484977i
\(612\) −17991.9 + 5924.40i −1.18837 + 0.391307i
\(613\) −6320.36 + 6320.36i −0.416439 + 0.416439i −0.883974 0.467536i \(-0.845142\pi\)
0.467536 + 0.883974i \(0.345142\pi\)
\(614\) −1335.05 8323.01i −0.0877494 0.547051i
\(615\) 20571.2i 1.34880i
\(616\) −848.160 + 438.492i −0.0554762 + 0.0286808i
\(617\) 2585.09i 0.168674i −0.996437 0.0843370i \(-0.973123\pi\)
0.996437 0.0843370i \(-0.0268772\pi\)
\(618\) 22668.8 3636.19i 1.47553 0.236681i
\(619\) 7325.02 7325.02i 0.475634 0.475634i −0.428098 0.903732i \(-0.640816\pi\)
0.903732 + 0.428098i \(0.140816\pi\)
\(620\) 11632.4 + 5869.41i 0.753501 + 0.380195i
\(621\) 2572.06 + 2572.06i 0.166205 + 0.166205i
\(622\) −8778.92 + 12133.3i −0.565921 + 0.782159i
\(623\) 1260.51 0.0810615
\(624\) −4240.26 5740.54i −0.272030 0.368278i
\(625\) 18174.8 1.16319
\(626\) −6641.72 + 9179.52i −0.424052 + 0.586082i
\(627\) −15415.2 15415.2i −0.981857 0.981857i
\(628\) −9712.07 + 19248.1i −0.617124 + 1.22306i
\(629\) 9375.13 9375.13i 0.594294 0.594294i
\(630\) −2481.82 + 398.096i −0.156949 + 0.0251754i
\(631\) 14411.5i 0.909210i 0.890693 + 0.454605i \(0.150220\pi\)
−0.890693 + 0.454605i \(0.849780\pi\)
\(632\) −405.011 + 1272.03i −0.0254913 + 0.0800611i
\(633\) 31633.1i 1.98626i
\(634\) −512.670 3196.10i −0.0321147 0.200211i
\(635\) −20534.3 + 20534.3i −1.28327 + 1.28327i
\(636\) 15694.7 + 47663.6i 0.978518 + 2.97168i
\(637\) −3180.91 3180.91i −0.197853 0.197853i
\(638\) 15107.0 + 10930.4i 0.937445 + 0.678276i
\(639\) 32132.1 1.98924
\(640\) 15948.1 + 7850.86i 0.985008 + 0.484895i
\(641\) −25724.0 −1.58508 −0.792542 0.609818i \(-0.791243\pi\)
−0.792542 + 0.609818i \(0.791243\pi\)
\(642\) 19911.6 + 14406.7i 1.22406 + 0.885653i
\(643\) −7835.74 7835.74i −0.480578 0.480578i 0.424738 0.905316i \(-0.360366\pi\)
−0.905316 + 0.424738i \(0.860366\pi\)
\(644\) 103.026 + 312.883i 0.00630406 + 0.0191449i
\(645\) 29585.9 29585.9i 1.80611 1.80611i
\(646\) −2410.99 15030.7i −0.146841 0.915441i
\(647\) 1247.43i 0.0757981i −0.999282 0.0378991i \(-0.987933\pi\)
0.999282 0.0378991i \(-0.0120665\pi\)
\(648\) −199.975 + 628.065i −0.0121231 + 0.0380752i
\(649\) 1693.89i 0.102451i
\(650\) 947.658 152.009i 0.0571849 0.00917272i
\(651\) −1297.42 + 1297.42i −0.0781107 + 0.0781107i
\(652\) −3617.68 + 7169.79i −0.217299 + 0.430661i
\(653\) 8302.21 + 8302.21i 0.497535 + 0.497535i 0.910670 0.413135i \(-0.135566\pi\)
−0.413135 + 0.910670i \(0.635566\pi\)
\(654\) 11734.8 16218.7i 0.701634 0.969728i
\(655\) 7003.63 0.417793
\(656\) −7554.08 10226.8i −0.449599 0.608675i
\(657\) −4684.42 −0.278168
\(658\) −212.980 + 294.359i −0.0126182 + 0.0174397i
\(659\) 1696.16 + 1696.16i 0.100262 + 0.100262i 0.755459 0.655196i \(-0.227414\pi\)
−0.655196 + 0.755459i \(0.727414\pi\)
\(660\) −19038.1 9606.09i −1.12281 0.566540i
\(661\) −8788.30 + 8788.30i −0.517134 + 0.517134i −0.916703 0.399569i \(-0.869160\pi\)
0.399569 + 0.916703i \(0.369160\pi\)
\(662\) 16705.1 2679.57i 0.980758 0.157318i
\(663\) 5978.32i 0.350194i
\(664\) −11659.0 + 6027.64i −0.681414 + 0.352286i
\(665\) 2020.00i 0.117793i
\(666\) −4892.88 30503.4i −0.284678 1.77475i
\(667\) 4548.88 4548.88i 0.264068 0.264068i
\(668\) −26296.3 + 8658.89i −1.52311 + 0.501531i
\(669\) −22016.4 22016.4i −1.27235 1.27235i
\(670\) −11224.9 8121.62i −0.647247 0.468307i
\(671\) 7037.56 0.404891
\(672\) −1752.54 + 1787.41i −0.100604 + 0.102606i
\(673\) −23869.3 −1.36716 −0.683578 0.729878i \(-0.739577\pi\)
−0.683578 + 0.729878i \(0.739577\pi\)
\(674\) −22921.1 16584.2i −1.30992 0.947775i
\(675\) −2628.54 2628.54i −0.149885 0.149885i
\(676\) 15366.5 5059.90i 0.874289 0.287887i
\(677\) −5663.30 + 5663.30i −0.321504 + 0.321504i −0.849344 0.527840i \(-0.823002\pi\)
0.527840 + 0.849344i \(0.323002\pi\)
\(678\) 1329.98 + 8291.43i 0.0753359 + 0.469662i
\(679\) 1327.71i 0.0750410i
\(680\) −6838.39 13227.2i −0.385647 0.745943i
\(681\) 20405.8i 1.14824i
\(682\) −9538.55 + 1530.03i −0.535557 + 0.0859058i
\(683\) −9152.80 + 9152.80i −0.512770 + 0.512770i −0.915374 0.402604i \(-0.868105\pi\)
0.402604 + 0.915374i \(0.368105\pi\)
\(684\) −31667.7 15978.6i −1.77024 0.893215i
\(685\) −7437.11 7437.11i −0.414828 0.414828i
\(686\) −1857.15 + 2566.77i −0.103362 + 0.142857i
\(687\) 1095.21 0.0608224
\(688\) 3844.01 25572.8i 0.213011 1.41708i
\(689\) 9828.85 0.543468
\(690\) −4312.55 + 5960.38i −0.237936 + 0.328852i
\(691\) 17057.9 + 17057.9i 0.939091 + 0.939091i 0.998249 0.0591580i \(-0.0188416\pi\)
−0.0591580 + 0.998249i \(0.518842\pi\)
\(692\) 6643.59 13166.8i 0.364959 0.723303i
\(693\) 1317.80 1317.80i 0.0722351 0.0722351i
\(694\) 25314.3 4060.54i 1.38461 0.222098i
\(695\) 29325.4i 1.60054i
\(696\) 46582.3 + 14831.7i 2.53692 + 0.807750i
\(697\) 10650.4i 0.578787i
\(698\) 3486.40 + 21735.1i 0.189058 + 1.17863i
\(699\) 25409.7 25409.7i 1.37494 1.37494i
\(700\) −105.289 319.754i −0.00568507 0.0172651i
\(701\) −7720.44 7720.44i −0.415973 0.415973i 0.467840 0.883813i \(-0.345032\pi\)
−0.883813 + 0.467840i \(0.845032\pi\)
\(702\) 4386.37 + 3173.70i 0.235830 + 0.170632i
\(703\) 24827.3 1.33198
\(704\) −12992.2 + 2215.48i −0.695540 + 0.118607i
\(705\) −8114.47 −0.433487
\(706\) 3234.13 + 2340.01i 0.172405 + 0.124741i
\(707\) 497.001 + 497.001i 0.0264380 + 0.0264380i
\(708\) −1388.96 4218.14i −0.0737290 0.223909i
\(709\) 4577.66 4577.66i 0.242479 0.242479i −0.575396 0.817875i \(-0.695152\pi\)
0.817875 + 0.575396i \(0.195152\pi\)
\(710\) 4000.50 + 24940.0i 0.211459 + 1.31829i
\(711\) 2605.64i 0.137439i
\(712\) 16579.4 + 5278.86i 0.872670 + 0.277856i
\(713\) 3332.88i 0.175059i
\(714\) 2070.45 332.109i 0.108522 0.0174074i
\(715\) −2953.40 + 2953.40i −0.154477 + 0.154477i
\(716\) 5516.25 10932.5i 0.287921 0.570625i
\(717\) 30142.5 + 30142.5i 1.57000 + 1.57000i
\(718\) 3582.49 4951.36i 0.186208 0.257358i
\(719\) −30210.0 −1.56696 −0.783479 0.621418i \(-0.786557\pi\)
−0.783479 + 0.621418i \(0.786557\pi\)
\(720\) −34310.5 5157.42i −1.77594 0.266953i
\(721\) −1577.28 −0.0814717
\(722\) 5337.60 7377.10i 0.275132 0.380259i
\(723\) −291.324 291.324i −0.0149854 0.0149854i
\(724\) 29735.9 + 15003.9i 1.52642 + 0.770188i
\(725\) −4648.78 + 4648.78i −0.238140 + 0.238140i
\(726\) −15746.4 + 2525.79i −0.804963 + 0.129120i
\(727\) 20721.3i 1.05710i −0.848903 0.528549i \(-0.822736\pi\)
0.848903 0.528549i \(-0.177264\pi\)
\(728\) 225.172 + 435.541i 0.0114635 + 0.0221734i
\(729\) 31696.7i 1.61036i
\(730\) −583.218 3635.92i −0.0295697 0.184344i
\(731\) −15317.6 + 15317.6i −0.775025 + 0.775025i
\(732\) 17525.0 5770.66i 0.884894 0.291379i
\(733\) −13879.8 13879.8i −0.699404 0.699404i 0.264878 0.964282i \(-0.414668\pi\)
−0.964282 + 0.264878i \(0.914668\pi\)
\(734\) −24651.5 17836.2i −1.23965 0.896932i
\(735\) −35239.3 −1.76847
\(736\) 44.7891 + 4546.79i 0.00224314 + 0.227713i
\(737\) 10272.6 0.513428
\(738\) 20105.7 + 14547.2i 1.00284 + 0.725595i
\(739\) 8793.93 + 8793.93i 0.437740 + 0.437740i 0.891251 0.453511i \(-0.149829\pi\)
−0.453511 + 0.891251i \(0.649829\pi\)
\(740\) 23066.7 7595.45i 1.14588 0.377317i
\(741\) −7915.92 + 7915.92i −0.392441 + 0.392441i
\(742\) −546.015 3403.98i −0.0270146 0.168415i
\(743\) 7669.27i 0.378678i −0.981912 0.189339i \(-0.939365\pi\)
0.981912 0.189339i \(-0.0606346\pi\)
\(744\) −22498.4 + 11631.5i −1.10864 + 0.573161i
\(745\) 559.327i 0.0275062i
\(746\) −5556.94 + 891.359i −0.272727 + 0.0437466i
\(747\) 18114.8 18114.8i 0.887264 0.887264i
\(748\) 9856.68 + 4973.41i 0.481813 + 0.243109i
\(749\) −1193.92 1193.92i −0.0582443 0.0582443i
\(750\) −17053.4 + 23569.5i −0.830269 + 1.14751i
\(751\) −26531.8 −1.28916 −0.644580 0.764537i \(-0.722968\pi\)
−0.644580 + 0.764537i \(0.722968\pi\)
\(752\) −4034.05 + 2979.76i −0.195620 + 0.144495i
\(753\) 31075.5 1.50392
\(754\) 5612.93 7757.63i 0.271102 0.374690i
\(755\) 9348.40 + 9348.40i 0.450627 + 0.450627i
\(756\) 855.461 1695.42i 0.0411545 0.0815631i
\(757\) −79.4192 + 79.4192i −0.00381313 + 0.00381313i −0.709011 0.705198i \(-0.750858\pi\)
0.705198 + 0.709011i \(0.250858\pi\)
\(758\) 4529.91 726.619i 0.217063 0.0348179i
\(759\) 5454.71i 0.260861i
\(760\) 8459.51 26569.0i 0.403761 1.26810i
\(761\) 36991.3i 1.76207i −0.473055 0.881033i \(-0.656849\pi\)
0.473055 0.881033i \(-0.343151\pi\)
\(762\) −8940.48 55737.1i −0.425039 2.64979i
\(763\) −972.494 + 972.494i −0.0461424 + 0.0461424i
\(764\) −1077.53 3272.36i −0.0510256 0.154961i
\(765\) 20551.3 + 20551.3i 0.971288 + 0.971288i
\(766\) −20720.3 14991.9i −0.977355 0.707152i
\(767\) −869.835 −0.0409490
\(768\) −30536.6 + 16170.3i −1.43476 + 0.759761i
\(769\) 26637.0 1.24910 0.624548 0.780987i \(-0.285283\pi\)
0.624548 + 0.780987i \(0.285283\pi\)
\(770\) 1186.91 + 858.770i 0.0555495 + 0.0401921i
\(771\) −4408.55 4408.55i −0.205928 0.205928i
\(772\) −5672.20 17226.0i −0.264439 0.803080i
\(773\) 19743.6 19743.6i 0.918667 0.918667i −0.0782657 0.996933i