Properties

Label 16.5.f.a.3.6
Level $16$
Weight $5$
Character 16.3
Analytic conductor $1.654$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 16 = 2^{4} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 16.f (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.65391940934\)
Analytic rank: \(0\)
Dimension: \(14\)
Relative dimension: \(7\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Defining polynomial: \(x^{14} - 4 x^{13} + 15 x^{12} - 34 x^{11} + 62 x^{10} - 312 x^{9} + 1432 x^{8} - 4960 x^{7} + 11456 x^{6} - 19968 x^{5} + 31744 x^{4} - 139264 x^{3} + 491520 x^{2} - 1048576 x + 2097152\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{21} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 3.6
Root \(0.336831 + 2.80830i\) of defining polynomial
Character \(\chi\) \(=\) 16.3
Dual form 16.5.f.a.11.6

$q$-expansion

\(f(q)\) \(=\) \(q+(2.47147 + 3.14513i) q^{2} +(-7.86839 + 7.86839i) q^{3} +(-3.78368 + 15.5462i) q^{4} +(27.2309 - 27.2309i) q^{5} +(-44.1936 - 5.30063i) q^{6} +50.3097 q^{7} +(-58.2460 + 26.5217i) q^{8} -42.8233i q^{9} +O(q^{10})\) \(q+(2.47147 + 3.14513i) q^{2} +(-7.86839 + 7.86839i) q^{3} +(-3.78368 + 15.5462i) q^{4} +(27.2309 - 27.2309i) q^{5} +(-44.1936 - 5.30063i) q^{6} +50.3097 q^{7} +(-58.2460 + 26.5217i) q^{8} -42.8233i q^{9} +(152.945 + 18.3444i) q^{10} +(-53.1047 - 53.1047i) q^{11} +(-92.5520 - 152.095i) q^{12} +(-125.128 - 125.128i) q^{13} +(124.339 + 158.231i) q^{14} +428.528i q^{15} +(-227.367 - 117.644i) q^{16} +286.271 q^{17} +(134.685 - 105.836i) q^{18} +(-99.5010 + 99.5010i) q^{19} +(320.304 + 526.370i) q^{20} +(-395.857 + 395.857i) q^{21} +(35.7745 - 298.268i) q^{22} -100.505 q^{23} +(249.619 - 666.986i) q^{24} -858.049i q^{25} +(84.2940 - 702.795i) q^{26} +(-300.390 - 300.390i) q^{27} +(-190.356 + 782.124i) q^{28} +(343.872 + 343.872i) q^{29} +(-1347.78 + 1059.09i) q^{30} -208.400i q^{31} +(-191.927 - 1005.85i) q^{32} +835.697 q^{33} +(707.510 + 900.360i) q^{34} +(1369.98 - 1369.98i) q^{35} +(665.738 + 162.030i) q^{36} +(-1159.47 + 1159.47i) q^{37} +(-558.857 - 67.0299i) q^{38} +1969.12 q^{39} +(-863.882 + 2308.31i) q^{40} +2335.63i q^{41} +(-2223.37 - 266.673i) q^{42} +(-2079.41 - 2079.41i) q^{43} +(1026.51 - 624.643i) q^{44} +(-1166.12 - 1166.12i) q^{45} +(-248.396 - 316.103i) q^{46} +1054.04i q^{47} +(2714.68 - 863.350i) q^{48} +130.069 q^{49} +(2698.67 - 2120.64i) q^{50} +(-2252.49 + 2252.49i) q^{51} +(2418.71 - 1471.82i) q^{52} +(2136.46 - 2136.46i) q^{53} +(202.361 - 1687.17i) q^{54} -2892.18 q^{55} +(-2930.34 + 1334.30i) q^{56} -1565.83i q^{57} +(-231.653 + 1931.39i) q^{58} +(3721.44 + 3721.44i) q^{59} +(-6661.97 - 1621.41i) q^{60} +(2496.46 + 2496.46i) q^{61} +(655.446 - 515.055i) q^{62} -2154.43i q^{63} +(2689.20 - 3089.57i) q^{64} -6814.72 q^{65} +(2065.40 + 2628.37i) q^{66} +(-329.116 + 329.116i) q^{67} +(-1083.16 + 4450.42i) q^{68} +(790.817 - 790.817i) q^{69} +(7694.64 + 922.903i) q^{70} -1040.71 q^{71} +(1135.75 + 2494.28i) q^{72} -2673.24i q^{73} +(-6512.27 - 781.089i) q^{74} +(6751.46 + 6751.46i) q^{75} +(-1170.38 - 1923.34i) q^{76} +(-2671.68 - 2671.68i) q^{77} +(4866.61 + 6193.13i) q^{78} -4475.80i q^{79} +(-9394.98 + 2987.88i) q^{80} +8195.85 q^{81} +(-7345.86 + 5772.43i) q^{82} +(1457.69 - 1457.69i) q^{83} +(-4656.26 - 7651.86i) q^{84} +(7795.43 - 7795.43i) q^{85} +(1400.82 - 11679.2i) q^{86} -5411.44 q^{87} +(4501.56 + 1684.71i) q^{88} +1146.97i q^{89} +(785.568 - 6549.62i) q^{90} +(-6295.17 - 6295.17i) q^{91} +(380.281 - 1562.48i) q^{92} +(1639.78 + 1639.78i) q^{93} +(-3315.11 + 2605.04i) q^{94} +5419.01i q^{95} +(9424.60 + 6404.29i) q^{96} -13101.5 q^{97} +(321.461 + 409.084i) q^{98} +(-2274.11 + 2274.11i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 2q^{2} - 2q^{3} - 8q^{4} - 2q^{5} + 64q^{6} - 4q^{7} - 92q^{8} + O(q^{10}) \) \( 14q - 2q^{2} - 2q^{3} - 8q^{4} - 2q^{5} + 64q^{6} - 4q^{7} - 92q^{8} - 100q^{10} + 94q^{11} - 332q^{12} - 2q^{13} + 44q^{14} - 168q^{16} - 4q^{17} + 1390q^{18} - 706q^{19} + 1900q^{20} - 164q^{21} + 900q^{22} + 1148q^{23} - 1872q^{24} - 3416q^{26} - 1664q^{27} - 3784q^{28} + 862q^{29} - 3740q^{30} + 3208q^{32} - 4q^{33} + 7508q^{34} + 1340q^{35} + 11468q^{36} - 1826q^{37} + 3568q^{38} + 2684q^{39} - 5144q^{40} - 17064q^{42} + 1694q^{43} - 14636q^{44} + 1410q^{45} - 5316q^{46} + 6888q^{48} + 682q^{49} + 20070q^{50} - 3012q^{51} + 20452q^{52} - 482q^{53} + 10784q^{54} - 11780q^{55} - 6952q^{56} - 20456q^{58} - 2786q^{59} - 29920q^{60} - 3778q^{61} - 11472q^{62} + 15808q^{64} - 2020q^{65} + 30148q^{66} + 7998q^{67} + 18032q^{68} + 9628q^{69} + 15296q^{70} + 19964q^{71} - 17708q^{72} - 23780q^{74} + 17570q^{75} - 23996q^{76} - 9508q^{77} - 8052q^{78} + 1384q^{80} + 1454q^{81} + 16016q^{82} - 17282q^{83} + 19624q^{84} + 9948q^{85} - 4796q^{86} - 49284q^{87} + 7288q^{88} - 5416q^{90} - 28036q^{91} - 14632q^{92} + 8896q^{93} + 432q^{94} + 6064q^{96} - 4q^{97} - 12246q^{98} + 49214q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.47147 + 3.14513i 0.617867 + 0.786282i
\(3\) −7.86839 + 7.86839i −0.874266 + 0.874266i −0.992934 0.118668i \(-0.962138\pi\)
0.118668 + 0.992934i \(0.462138\pi\)
\(4\) −3.78368 + 15.5462i −0.236480 + 0.971636i
\(5\) 27.2309 27.2309i 1.08924 1.08924i 0.0936308 0.995607i \(-0.470153\pi\)
0.995607 0.0936308i \(-0.0298473\pi\)
\(6\) −44.1936 5.30063i −1.22760 0.147240i
\(7\) 50.3097 1.02673 0.513365 0.858171i \(-0.328399\pi\)
0.513365 + 0.858171i \(0.328399\pi\)
\(8\) −58.2460 + 26.5217i −0.910094 + 0.414402i
\(9\) 42.8233i 0.528682i
\(10\) 152.945 + 18.3444i 1.52945 + 0.183444i
\(11\) −53.1047 53.1047i −0.438881 0.438881i 0.452754 0.891635i \(-0.350442\pi\)
−0.891635 + 0.452754i \(0.850442\pi\)
\(12\) −92.5520 152.095i −0.642722 1.05622i
\(13\) −125.128 125.128i −0.740404 0.740404i 0.232252 0.972656i \(-0.425391\pi\)
−0.972656 + 0.232252i \(0.925391\pi\)
\(14\) 124.339 + 158.231i 0.634382 + 0.807299i
\(15\) 428.528i 1.90457i
\(16\) −227.367 117.644i −0.888154 0.459546i
\(17\) 286.271 0.990557 0.495279 0.868734i \(-0.335066\pi\)
0.495279 + 0.868734i \(0.335066\pi\)
\(18\) 134.685 105.836i 0.415694 0.326655i
\(19\) −99.5010 + 99.5010i −0.275626 + 0.275626i −0.831360 0.555734i \(-0.812437\pi\)
0.555734 + 0.831360i \(0.312437\pi\)
\(20\) 320.304 + 526.370i 0.800760 + 1.31593i
\(21\) −395.857 + 395.857i −0.897635 + 0.897635i
\(22\) 35.7745 298.268i 0.0739143 0.616255i
\(23\) −100.505 −0.189991 −0.0949957 0.995478i \(-0.530284\pi\)
−0.0949957 + 0.995478i \(0.530284\pi\)
\(24\) 249.619 666.986i 0.433367 1.15796i
\(25\) 858.049i 1.37288i
\(26\) 84.2940 702.795i 0.124695 1.03964i
\(27\) −300.390 300.390i −0.412057 0.412057i
\(28\) −190.356 + 782.124i −0.242801 + 0.997607i
\(29\) 343.872 + 343.872i 0.408885 + 0.408885i 0.881350 0.472465i \(-0.156636\pi\)
−0.472465 + 0.881350i \(0.656636\pi\)
\(30\) −1347.78 + 1059.09i −1.49753 + 1.17677i
\(31\) 208.400i 0.216858i −0.994104 0.108429i \(-0.965418\pi\)
0.994104 0.108429i \(-0.0345820\pi\)
\(32\) −191.927 1005.85i −0.187429 0.982278i
\(33\) 835.697 0.767398
\(34\) 707.510 + 900.360i 0.612033 + 0.778858i
\(35\) 1369.98 1369.98i 1.11835 1.11835i
\(36\) 665.738 + 162.030i 0.513687 + 0.125023i
\(37\) −1159.47 + 1159.47i −0.846946 + 0.846946i −0.989751 0.142805i \(-0.954388\pi\)
0.142805 + 0.989751i \(0.454388\pi\)
\(38\) −558.857 67.0299i −0.387020 0.0464196i
\(39\) 1969.12 1.29462
\(40\) −863.882 + 2308.31i −0.539927 + 1.44269i
\(41\) 2335.63i 1.38943i 0.719286 + 0.694714i \(0.244469\pi\)
−0.719286 + 0.694714i \(0.755531\pi\)
\(42\) −2223.37 266.673i −1.26041 0.151175i
\(43\) −2079.41 2079.41i −1.12461 1.12461i −0.991039 0.133575i \(-0.957354\pi\)
−0.133575 0.991039i \(-0.542646\pi\)
\(44\) 1026.51 624.643i 0.530220 0.322646i
\(45\) −1166.12 1166.12i −0.575861 0.575861i
\(46\) −248.396 316.103i −0.117389 0.149387i
\(47\) 1054.04i 0.477159i 0.971123 + 0.238580i \(0.0766818\pi\)
−0.971123 + 0.238580i \(0.923318\pi\)
\(48\) 2714.68 863.350i 1.17825 0.374718i
\(49\) 130.069 0.0541728
\(50\) 2698.67 2120.64i 1.07947 0.848256i
\(51\) −2252.49 + 2252.49i −0.866011 + 0.866011i
\(52\) 2418.71 1471.82i 0.894494 0.544312i
\(53\) 2136.46 2136.46i 0.760576 0.760576i −0.215850 0.976426i \(-0.569252\pi\)
0.976426 + 0.215850i \(0.0692523\pi\)
\(54\) 202.361 1687.17i 0.0693967 0.578590i
\(55\) −2892.18 −0.956092
\(56\) −2930.34 + 1334.30i −0.934420 + 0.425479i
\(57\) 1565.83i 0.481941i
\(58\) −231.653 + 1931.39i −0.0688625 + 0.574136i
\(59\) 3721.44 + 3721.44i 1.06907 + 1.06907i 0.997431 + 0.0716407i \(0.0228235\pi\)
0.0716407 + 0.997431i \(0.477177\pi\)
\(60\) −6661.97 1621.41i −1.85055 0.450393i
\(61\) 2496.46 + 2496.46i 0.670912 + 0.670912i 0.957926 0.287014i \(-0.0926628\pi\)
−0.287014 + 0.957926i \(0.592663\pi\)
\(62\) 655.446 515.055i 0.170512 0.133989i
\(63\) 2154.43i 0.542814i
\(64\) 2689.20 3089.57i 0.656542 0.754289i
\(65\) −6814.72 −1.61295
\(66\) 2065.40 + 2628.37i 0.474150 + 0.603392i
\(67\) −329.116 + 329.116i −0.0733162 + 0.0733162i −0.742814 0.669498i \(-0.766509\pi\)
0.669498 + 0.742814i \(0.266509\pi\)
\(68\) −1083.16 + 4450.42i −0.234247 + 0.962461i
\(69\) 790.817 790.817i 0.166103 0.166103i
\(70\) 7694.64 + 922.903i 1.57033 + 0.188348i
\(71\) −1040.71 −0.206449 −0.103225 0.994658i \(-0.532916\pi\)
−0.103225 + 0.994658i \(0.532916\pi\)
\(72\) 1135.75 + 2494.28i 0.219087 + 0.481151i
\(73\) 2673.24i 0.501639i −0.968034 0.250820i \(-0.919300\pi\)
0.968034 0.250820i \(-0.0807001\pi\)
\(74\) −6512.27 781.089i −1.18924 0.142639i
\(75\) 6751.46 + 6751.46i 1.20026 + 1.20026i
\(76\) −1170.38 1923.34i −0.202628 0.332988i
\(77\) −2671.68 2671.68i −0.450612 0.450612i
\(78\) 4866.61 + 6193.13i 0.799903 + 1.01794i
\(79\) 4475.80i 0.717161i −0.933499 0.358580i \(-0.883261\pi\)
0.933499 0.358580i \(-0.116739\pi\)
\(80\) −9394.98 + 2987.88i −1.46797 + 0.466857i
\(81\) 8195.85 1.24918
\(82\) −7345.86 + 5772.43i −1.09248 + 0.858482i
\(83\) 1457.69 1457.69i 0.211597 0.211597i −0.593349 0.804945i \(-0.702195\pi\)
0.804945 + 0.593349i \(0.202195\pi\)
\(84\) −4656.26 7651.86i −0.659901 1.08445i
\(85\) 7795.43 7795.43i 1.07895 1.07895i
\(86\) 1400.82 11679.2i 0.189402 1.57913i
\(87\) −5411.44 −0.714948
\(88\) 4501.56 + 1684.71i 0.581297 + 0.217550i
\(89\) 1146.97i 0.144801i 0.997376 + 0.0724003i \(0.0230659\pi\)
−0.997376 + 0.0724003i \(0.976934\pi\)
\(90\) 785.568 6549.62i 0.0969838 0.808595i
\(91\) −6295.17 6295.17i −0.760194 0.760194i
\(92\) 380.281 1562.48i 0.0449292 0.184603i
\(93\) 1639.78 + 1639.78i 0.189592 + 0.189592i
\(94\) −3315.11 + 2605.04i −0.375182 + 0.294821i
\(95\) 5419.01i 0.600444i
\(96\) 9424.60 + 6404.29i 1.02264 + 0.694910i
\(97\) −13101.5 −1.39244 −0.696222 0.717826i \(-0.745137\pi\)
−0.696222 + 0.717826i \(0.745137\pi\)
\(98\) 321.461 + 409.084i 0.0334716 + 0.0425952i
\(99\) −2274.11 + 2274.11i −0.232029 + 0.232029i
\(100\) 13339.4 + 3246.59i 1.33394 + 0.324659i
\(101\) −7488.18 + 7488.18i −0.734063 + 0.734063i −0.971422 0.237359i \(-0.923718\pi\)
0.237359 + 0.971422i \(0.423718\pi\)
\(102\) −12651.4 1517.42i −1.21601 0.145849i
\(103\) 7141.23 0.673129 0.336565 0.941660i \(-0.390735\pi\)
0.336565 + 0.941660i \(0.390735\pi\)
\(104\) 10606.8 + 3969.60i 0.980662 + 0.367012i
\(105\) 21559.1i 1.95547i
\(106\) 11999.6 + 1439.25i 1.06796 + 0.128093i
\(107\) 1794.26 + 1794.26i 0.156718 + 0.156718i 0.781111 0.624393i \(-0.214654\pi\)
−0.624393 + 0.781111i \(0.714654\pi\)
\(108\) 5806.49 3533.33i 0.497813 0.302926i
\(109\) 5362.57 + 5362.57i 0.451357 + 0.451357i 0.895805 0.444448i \(-0.146600\pi\)
−0.444448 + 0.895805i \(0.646600\pi\)
\(110\) −7147.93 9096.28i −0.590738 0.751759i
\(111\) 18246.3i 1.48091i
\(112\) −11438.8 5918.62i −0.911894 0.471829i
\(113\) −5165.40 −0.404527 −0.202263 0.979331i \(-0.564830\pi\)
−0.202263 + 0.979331i \(0.564830\pi\)
\(114\) 4924.73 3869.89i 0.378942 0.297775i
\(115\) −2736.86 + 2736.86i −0.206946 + 0.206946i
\(116\) −6647.00 + 4044.80i −0.493981 + 0.300594i
\(117\) −5358.40 + 5358.40i −0.391438 + 0.391438i
\(118\) −2506.99 + 20901.8i −0.180048 + 1.50114i
\(119\) 14402.2 1.01703
\(120\) −11365.3 24960.0i −0.789256 1.73334i
\(121\) 9000.79i 0.614766i
\(122\) −1681.77 + 14021.6i −0.112992 + 0.942061i
\(123\) −18377.6 18377.6i −1.21473 1.21473i
\(124\) 3239.83 + 788.521i 0.210707 + 0.0512826i
\(125\) −6346.13 6346.13i −0.406152 0.406152i
\(126\) 6775.95 5324.60i 0.426805 0.335387i
\(127\) 22886.9i 1.41899i 0.704711 + 0.709495i \(0.251077\pi\)
−0.704711 + 0.709495i \(0.748923\pi\)
\(128\) 16363.4 + 822.099i 0.998740 + 0.0501770i
\(129\) 32723.3 1.96642
\(130\) −16842.4 21433.2i −0.996590 1.26824i
\(131\) 19202.2 19202.2i 1.11894 1.11894i 0.127048 0.991897i \(-0.459450\pi\)
0.991897 0.127048i \(-0.0405502\pi\)
\(132\) −3162.01 + 12991.9i −0.181475 + 0.745632i
\(133\) −5005.87 + 5005.87i −0.282993 + 0.282993i
\(134\) −1848.51 221.713i −0.102947 0.0123476i
\(135\) −16359.8 −0.897656
\(136\) −16674.1 + 7592.40i −0.901500 + 0.410489i
\(137\) 33680.5i 1.79448i −0.441547 0.897238i \(-0.645570\pi\)
0.441547 0.897238i \(-0.354430\pi\)
\(138\) 4441.70 + 532.742i 0.233234 + 0.0279743i
\(139\) 11747.9 + 11747.9i 0.608036 + 0.608036i 0.942432 0.334397i \(-0.108532\pi\)
−0.334397 + 0.942432i \(0.608532\pi\)
\(140\) 16114.4 + 26481.6i 0.822163 + 1.35110i
\(141\) −8293.64 8293.64i −0.417164 0.417164i
\(142\) −2572.09 3273.17i −0.127558 0.162328i
\(143\) 13289.8i 0.649899i
\(144\) −5037.89 + 9736.62i −0.242954 + 0.469551i
\(145\) 18727.9 0.890746
\(146\) 8407.68 6606.82i 0.394430 0.309947i
\(147\) −1023.43 + 1023.43i −0.0473615 + 0.0473615i
\(148\) −13638.2 22412.4i −0.622637 1.02321i
\(149\) −14877.7 + 14877.7i −0.670136 + 0.670136i −0.957747 0.287611i \(-0.907139\pi\)
0.287611 + 0.957747i \(0.407139\pi\)
\(150\) −4548.20 + 37920.3i −0.202142 + 1.68535i
\(151\) −8005.74 −0.351114 −0.175557 0.984469i \(-0.556173\pi\)
−0.175557 + 0.984469i \(0.556173\pi\)
\(152\) 3156.60 8434.47i 0.136626 0.365065i
\(153\) 12259.1i 0.523690i
\(154\) 1799.81 15005.8i 0.0758900 0.632727i
\(155\) −5674.94 5674.94i −0.236210 0.236210i
\(156\) −7450.51 + 30612.2i −0.306152 + 1.25790i
\(157\) 12150.9 + 12150.9i 0.492958 + 0.492958i 0.909237 0.416279i \(-0.136666\pi\)
−0.416279 + 0.909237i \(0.636666\pi\)
\(158\) 14077.0 11061.8i 0.563891 0.443110i
\(159\) 33621.0i 1.32989i
\(160\) −32616.7 22164.0i −1.27409 0.865780i
\(161\) −5056.40 −0.195070
\(162\) 20255.8 + 25777.0i 0.771826 + 0.982206i
\(163\) −23646.5 + 23646.5i −0.890002 + 0.890002i −0.994523 0.104520i \(-0.966669\pi\)
0.104520 + 0.994523i \(0.466669\pi\)
\(164\) −36310.1 8837.28i −1.35002 0.328572i
\(165\) 22756.8 22756.8i 0.835879 0.835879i
\(166\) 8187.26 + 981.989i 0.297113 + 0.0356361i
\(167\) 42493.7 1.52367 0.761836 0.647770i \(-0.224298\pi\)
0.761836 + 0.647770i \(0.224298\pi\)
\(168\) 12558.3 33555.9i 0.444950 1.18891i
\(169\) 2753.14i 0.0963950i
\(170\) 43783.8 + 5251.48i 1.51501 + 0.181712i
\(171\) 4260.96 + 4260.96i 0.145719 + 0.145719i
\(172\) 40194.7 24459.1i 1.35866 0.826767i
\(173\) −16142.1 16142.1i −0.539347 0.539347i 0.383990 0.923337i \(-0.374550\pi\)
−0.923337 + 0.383990i \(0.874550\pi\)
\(174\) −13374.2 17019.7i −0.441743 0.562151i
\(175\) 43168.2i 1.40957i
\(176\) 5826.84 + 18321.7i 0.188108 + 0.591480i
\(177\) −58563.5 −1.86931
\(178\) −3607.36 + 2834.69i −0.113854 + 0.0894676i
\(179\) −22442.0 + 22442.0i −0.700415 + 0.700415i −0.964500 0.264084i \(-0.914930\pi\)
0.264084 + 0.964500i \(0.414930\pi\)
\(180\) 22540.9 13716.5i 0.695707 0.423347i
\(181\) −9891.06 + 9891.06i −0.301916 + 0.301916i −0.841763 0.539847i \(-0.818482\pi\)
0.539847 + 0.841763i \(0.318482\pi\)
\(182\) 4240.81 35357.4i 0.128028 1.06743i
\(183\) −39286.3 −1.17311
\(184\) 5854.04 2665.58i 0.172910 0.0787328i
\(185\) 63146.9i 1.84505i
\(186\) −1104.65 + 9209.97i −0.0319301 + 0.266215i
\(187\) −15202.3 15202.3i −0.434737 0.434737i
\(188\) −16386.4 3988.17i −0.463625 0.112839i
\(189\) −15112.5 15112.5i −0.423071 0.423071i
\(190\) −17043.5 + 13392.9i −0.472119 + 0.370995i
\(191\) 2033.60i 0.0557442i −0.999611 0.0278721i \(-0.991127\pi\)
0.999611 0.0278721i \(-0.00887311\pi\)
\(192\) 3150.29 + 45469.6i 0.0854570 + 1.23344i
\(193\) 29257.4 0.785453 0.392727 0.919655i \(-0.371532\pi\)
0.392727 + 0.919655i \(0.371532\pi\)
\(194\) −32380.0 41206.0i −0.860346 1.09486i
\(195\) 53620.9 53620.9i 1.41015 1.41015i
\(196\) −492.140 + 2022.08i −0.0128108 + 0.0526363i
\(197\) 28194.9 28194.9i 0.726504 0.726504i −0.243417 0.969922i \(-0.578268\pi\)
0.969922 + 0.243417i \(0.0782684\pi\)
\(198\) −12772.8 1531.98i −0.325803 0.0390772i
\(199\) 54100.9 1.36615 0.683075 0.730348i \(-0.260642\pi\)
0.683075 + 0.730348i \(0.260642\pi\)
\(200\) 22756.9 + 49977.9i 0.568923 + 1.24945i
\(201\) 5179.24i 0.128196i
\(202\) −42058.1 5044.49i −1.03073 0.123627i
\(203\) 17300.1 + 17300.1i 0.419814 + 0.419814i
\(204\) −26494.9 43540.4i −0.636653 1.04624i
\(205\) 63601.4 + 63601.4i 1.51342 + 1.51342i
\(206\) 17649.3 + 22460.1i 0.415905 + 0.529270i
\(207\) 4303.97i 0.100445i
\(208\) 13729.5 + 43170.6i 0.317343 + 0.997842i
\(209\) 10567.9 0.241934
\(210\) −67806.2 + 53282.7i −1.53756 + 1.20822i
\(211\) −31994.1 + 31994.1i −0.718630 + 0.718630i −0.968325 0.249694i \(-0.919670\pi\)
0.249694 + 0.968325i \(0.419670\pi\)
\(212\) 25130.1 + 41297.5i 0.559142 + 0.918865i
\(213\) 8188.73 8188.73i 0.180492 0.180492i
\(214\) −1208.72 + 10077.6i −0.0263937 + 0.220055i
\(215\) −113249. −2.44994
\(216\) 25463.3 + 9529.65i 0.545768 + 0.204253i
\(217\) 10484.6i 0.222654i
\(218\) −3612.56 + 30119.4i −0.0760155 + 0.633773i
\(219\) 21034.1 + 21034.1i 0.438566 + 0.438566i
\(220\) 10943.1 44962.3i 0.226097 0.928974i
\(221\) −35820.6 35820.6i −0.733412 0.733412i
\(222\) 57387.0 45095.2i 1.16442 0.915007i
\(223\) 94185.8i 1.89398i −0.321261 0.946991i \(-0.604107\pi\)
0.321261 0.946991i \(-0.395893\pi\)
\(224\) −9655.79 50604.2i −0.192438 1.00853i
\(225\) −36744.4 −0.725816
\(226\) −12766.1 16245.9i −0.249944 0.318072i
\(227\) 62683.9 62683.9i 1.21648 1.21648i 0.247622 0.968857i \(-0.420351\pi\)
0.968857 0.247622i \(-0.0796490\pi\)
\(228\) 24342.6 + 5924.59i 0.468271 + 0.113969i
\(229\) −19781.9 + 19781.9i −0.377221 + 0.377221i −0.870099 0.492877i \(-0.835945\pi\)
0.492877 + 0.870099i \(0.335945\pi\)
\(230\) −15371.8 1843.72i −0.290583 0.0348528i
\(231\) 42043.7 0.787910
\(232\) −29149.3 10909.1i −0.541566 0.202681i
\(233\) 25062.1i 0.461642i 0.972996 + 0.230821i \(0.0741412\pi\)
−0.972996 + 0.230821i \(0.925859\pi\)
\(234\) −30096.0 3609.75i −0.549638 0.0659242i
\(235\) 28702.6 + 28702.6i 0.519740 + 0.519740i
\(236\) −71934.9 + 43773.4i −1.29156 + 0.785934i
\(237\) 35217.4 + 35217.4i 0.626989 + 0.626989i
\(238\) 35594.6 + 45296.9i 0.628392 + 0.799676i
\(239\) 93041.8i 1.62885i −0.580265 0.814427i \(-0.697051\pi\)
0.580265 0.814427i \(-0.302949\pi\)
\(240\) 50413.6 97433.2i 0.875236 1.69155i
\(241\) −80981.9 −1.39429 −0.697146 0.716929i \(-0.745547\pi\)
−0.697146 + 0.716929i \(0.745547\pi\)
\(242\) 28308.7 22245.2i 0.483380 0.379844i
\(243\) −40156.6 + 40156.6i −0.680056 + 0.680056i
\(244\) −48256.3 + 29364.6i −0.810540 + 0.493225i
\(245\) 3541.90 3541.90i 0.0590071 0.0590071i
\(246\) 12380.3 103220.i 0.204579 1.70566i
\(247\) 24900.8 0.408149
\(248\) 5527.14 + 12138.5i 0.0898663 + 0.197361i
\(249\) 22939.3i 0.369984i
\(250\) 4275.14 35643.7i 0.0684023 0.570299i
\(251\) 25910.0 + 25910.0i 0.411264 + 0.411264i 0.882179 0.470915i \(-0.156076\pi\)
−0.470915 + 0.882179i \(0.656076\pi\)
\(252\) 33493.1 + 8151.67i 0.527417 + 0.128365i
\(253\) 5337.31 + 5337.31i 0.0833837 + 0.0833837i
\(254\) −71982.2 + 56564.2i −1.11573 + 0.876747i
\(255\) 122675.i 1.88658i
\(256\) 37855.9 + 53496.7i 0.577636 + 0.816295i
\(257\) 15800.6 0.239225 0.119613 0.992821i \(-0.461835\pi\)
0.119613 + 0.992821i \(0.461835\pi\)
\(258\) 80874.5 + 102919.i 1.21499 + 1.54616i
\(259\) −58332.6 + 58332.6i −0.869584 + 0.869584i
\(260\) 25784.7 105943.i 0.381431 1.56720i
\(261\) 14725.7 14725.7i 0.216170 0.216170i
\(262\) 107851. + 12935.8i 1.57117 + 0.188447i
\(263\) −82043.7 −1.18613 −0.593067 0.805153i \(-0.702083\pi\)
−0.593067 + 0.805153i \(0.702083\pi\)
\(264\) −48676.0 + 22164.1i −0.698405 + 0.318011i
\(265\) 116356.i 1.65690i
\(266\) −28115.9 3372.26i −0.397365 0.0476604i
\(267\) −9024.78 9024.78i −0.126594 0.126594i
\(268\) −3871.23 6361.78i −0.0538988 0.0885745i
\(269\) −30820.2 30820.2i −0.425923 0.425923i 0.461314 0.887237i \(-0.347378\pi\)
−0.887237 + 0.461314i \(0.847378\pi\)
\(270\) −40432.7 51453.6i −0.554632 0.705811i
\(271\) 110808.i 1.50880i 0.656412 + 0.754402i \(0.272073\pi\)
−0.656412 + 0.754402i \(0.727927\pi\)
\(272\) −65088.7 33678.0i −0.879768 0.455206i
\(273\) 99065.7 1.32922
\(274\) 105930. 83240.4i 1.41097 1.10875i
\(275\) −45566.4 + 45566.4i −0.602531 + 0.602531i
\(276\) 9301.98 + 15286.4i 0.122112 + 0.200672i
\(277\) 25634.0 25634.0i 0.334084 0.334084i −0.520051 0.854135i \(-0.674087\pi\)
0.854135 + 0.520051i \(0.174087\pi\)
\(278\) −7914.08 + 65983.0i −0.102403 + 0.853773i
\(279\) −8924.39 −0.114649
\(280\) −43461.7 + 116130.i −0.554358 + 1.48125i
\(281\) 48800.5i 0.618033i 0.951057 + 0.309017i \(0.0999999\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(282\) 5587.10 46582.0i 0.0702568 0.585761i
\(283\) −111466. 111466.i −1.39178 1.39178i −0.821340 0.570439i \(-0.806773\pi\)
−0.570439 0.821340i \(-0.693227\pi\)
\(284\) 3937.72 16179.1i 0.0488212 0.200594i
\(285\) −42638.9 42638.9i −0.524948 0.524948i
\(286\) −41798.1 + 32845.3i −0.511004 + 0.401551i
\(287\) 117505.i 1.42657i
\(288\) −43073.9 + 8218.94i −0.519313 + 0.0990902i
\(289\) −1569.88 −0.0187963
\(290\) 46285.5 + 58901.8i 0.550363 + 0.700378i
\(291\) 103088. 103088.i 1.21737 1.21737i
\(292\) 41558.6 + 10114.7i 0.487411 + 0.118628i
\(293\) 13093.1 13093.1i 0.152514 0.152514i −0.626726 0.779240i \(-0.715605\pi\)
0.779240 + 0.626726i \(0.215605\pi\)
\(294\) −5748.22 689.448i −0.0665026 0.00797640i
\(295\) 202676. 2.32895
\(296\) 36783.3 98285.6i 0.419824 1.12178i
\(297\) 31904.2i 0.361688i
\(298\) −83562.0 10022.5i −0.940971 0.112861i
\(299\) 12576.1 + 12576.1i 0.140670 + 0.140670i
\(300\) −130505. + 79414.1i −1.45005 + 0.882379i
\(301\) −104615. 104615.i −1.15467 1.15467i
\(302\) −19785.9 25179.1i −0.216942 0.276075i
\(303\) 117840.i 1.28353i
\(304\) 34328.9 10917.6i 0.371461 0.118136i
\(305\) 135962. 1.46156
\(306\) 38556.3 30297.9i 0.411768 0.323571i
\(307\) 25274.9 25274.9i 0.268171 0.268171i −0.560192 0.828363i \(-0.689273\pi\)
0.828363 + 0.560192i \(0.189273\pi\)
\(308\) 51643.2 31425.6i 0.544392 0.331270i
\(309\) −56190.0 + 56190.0i −0.588494 + 0.588494i
\(310\) 3822.99 31873.9i 0.0397813 0.331674i
\(311\) 53808.0 0.556322 0.278161 0.960534i \(-0.410275\pi\)
0.278161 + 0.960534i \(0.410275\pi\)
\(312\) −114693. + 52224.4i −1.17823 + 0.536493i
\(313\) 137345.i 1.40192i −0.713199 0.700961i \(-0.752755\pi\)
0.713199 0.700961i \(-0.247245\pi\)
\(314\) −8185.60 + 68246.8i −0.0830217 + 0.692187i
\(315\) −58667.1 58667.1i −0.591253 0.591253i
\(316\) 69581.6 + 16935.0i 0.696819 + 0.169594i
\(317\) 115546. + 115546.i 1.14984 + 1.14984i 0.986584 + 0.163252i \(0.0521982\pi\)
0.163252 + 0.986584i \(0.447802\pi\)
\(318\) −105742. + 83093.3i −1.04567 + 0.821697i
\(319\) 36522.4i 0.358904i
\(320\) −10902.5 157361.i −0.106470 1.53673i
\(321\) −28235.9 −0.274026
\(322\) −12496.7 15903.0i −0.120527 0.153380i
\(323\) −28484.2 + 28484.2i −0.273023 + 0.273023i
\(324\) −31010.5 + 127414.i −0.295406 + 1.21375i
\(325\) −107366. + 107366.i −1.01648 + 1.01648i
\(326\) −132813. 15929.7i −1.24970 0.149890i
\(327\) −84389.7 −0.789213
\(328\) −61944.9 136041.i −0.575782 1.26451i
\(329\) 53028.7i 0.489913i
\(330\) 127816. + 15330.4i 1.17370 + 0.140775i
\(331\) 68009.3 + 68009.3i 0.620744 + 0.620744i 0.945722 0.324978i \(-0.105357\pi\)
−0.324978 + 0.945722i \(0.605357\pi\)
\(332\) 17146.1 + 28176.9i 0.155557 + 0.255633i
\(333\) 49652.2 + 49652.2i 0.447765 + 0.447765i
\(334\) 105022. + 133648.i 0.941427 + 1.19804i
\(335\) 17924.3i 0.159718i
\(336\) 136575. 43434.9i 1.20974 0.384734i
\(337\) −146703. −1.29176 −0.645878 0.763440i \(-0.723509\pi\)
−0.645878 + 0.763440i \(0.723509\pi\)
\(338\) −8658.97 + 6804.29i −0.0757937 + 0.0595593i
\(339\) 40643.4 40643.4i 0.353664 0.353664i
\(340\) 91693.7 + 150685.i 0.793198 + 1.30350i
\(341\) −11067.0 + 11067.0i −0.0951749 + 0.0951749i
\(342\) −2870.44 + 23932.1i −0.0245412 + 0.204611i
\(343\) −114250. −0.971108
\(344\) 176267. + 65967.9i 1.48955 + 0.557462i
\(345\) 43069.4i 0.361851i
\(346\) 10874.3 90663.8i 0.0908343 0.757324i
\(347\) −80120.9 80120.9i −0.665406 0.665406i 0.291243 0.956649i \(-0.405931\pi\)
−0.956649 + 0.291243i \(0.905931\pi\)
\(348\) 20475.2 84127.3i 0.169071 0.694670i
\(349\) 100990. + 100990.i 0.829143 + 0.829143i 0.987398 0.158255i \(-0.0505869\pi\)
−0.158255 + 0.987398i \(0.550587\pi\)
\(350\) 135770. 106689.i 1.10832 0.870929i
\(351\) 75174.4i 0.610177i
\(352\) −43223.3 + 63607.7i −0.348845 + 0.513363i
\(353\) 129855. 1.04210 0.521052 0.853525i \(-0.325540\pi\)
0.521052 + 0.853525i \(0.325540\pi\)
\(354\) −144738. 184190.i −1.15498 1.46980i
\(355\) −28339.6 + 28339.6i −0.224873 + 0.224873i
\(356\) −17830.9 4339.76i −0.140694 0.0342425i
\(357\) −113322. + 113322.i −0.889158 + 0.889158i
\(358\) −126048. 15118.3i −0.983488 0.117961i
\(359\) −55943.2 −0.434068 −0.217034 0.976164i \(-0.569638\pi\)
−0.217034 + 0.976164i \(0.569638\pi\)
\(360\) 98849.2 + 36994.3i 0.762725 + 0.285450i
\(361\) 110520.i 0.848061i
\(362\) −55554.1 6663.23i −0.423935 0.0508472i
\(363\) 70821.8 + 70821.8i 0.537469 + 0.537469i
\(364\) 121685. 74046.9i 0.918403 0.558861i
\(365\) −72794.8 72794.8i −0.546405 0.546405i
\(366\) −97094.9 123561.i −0.724827 0.922397i
\(367\) 144947.i 1.07616i −0.842892 0.538082i \(-0.819149\pi\)
0.842892 0.538082i \(-0.180851\pi\)
\(368\) 22851.7 + 11823.8i 0.168742 + 0.0873097i
\(369\) 100019. 0.734566
\(370\) −198605. + 156066.i −1.45073 + 1.14000i
\(371\) 107485. 107485.i 0.780906 0.780906i
\(372\) −31696.7 + 19287.9i −0.229049 + 0.139379i
\(373\) 24034.7 24034.7i 0.172751 0.172751i −0.615436 0.788187i \(-0.711020\pi\)
0.788187 + 0.615436i \(0.211020\pi\)
\(374\) 10241.2 85385.4i 0.0732164 0.610436i
\(375\) 99867.8 0.710171
\(376\) −27955.1 61393.9i −0.197736 0.434260i
\(377\) 86056.2i 0.605480i
\(378\) 10180.7 84881.0i 0.0712516 0.594055i
\(379\) −27907.2 27907.2i −0.194284 0.194284i 0.603260 0.797544i \(-0.293868\pi\)
−0.797544 + 0.603260i \(0.793868\pi\)
\(380\) −84244.9 20503.8i −0.583414 0.141993i
\(381\) −180083. 180083.i −1.24057 1.24057i
\(382\) 6395.95 5025.99i 0.0438307 0.0344425i
\(383\) 96652.7i 0.658895i 0.944174 + 0.329448i \(0.106863\pi\)
−0.944174 + 0.329448i \(0.893137\pi\)
\(384\) −135222. + 122285.i −0.917033 + 0.829297i
\(385\) −145505. −0.981648
\(386\) 72308.6 + 92018.2i 0.485306 + 0.617588i
\(387\) −89047.2 + 89047.2i −0.594564 + 0.594564i
\(388\) 49572.0 203678.i 0.329286 1.35295i
\(389\) 133129. 133129.i 0.879777 0.879777i −0.113734 0.993511i \(-0.536281\pi\)
0.993511 + 0.113734i \(0.0362813\pi\)
\(390\) 301167. + 36122.3i 1.98006 + 0.237491i
\(391\) −28771.8 −0.188197
\(392\) −7576.00 + 3449.65i −0.0493024 + 0.0224493i
\(393\) 302181.i 1.95651i
\(394\) 158359. + 18993.8i 1.02012 + 0.122354i
\(395\) −121880. 121880.i −0.781159 0.781159i
\(396\) −26749.3 43958.3i −0.170577 0.280318i
\(397\) 33406.1 + 33406.1i 0.211956 + 0.211956i 0.805098 0.593142i \(-0.202113\pi\)
−0.593142 + 0.805098i \(0.702113\pi\)
\(398\) 133709. + 170154.i 0.844100 + 1.07418i
\(399\) 78776.3i 0.494823i
\(400\) −100944. + 195092.i −0.630900 + 1.21933i
\(401\) −87329.7 −0.543092 −0.271546 0.962425i \(-0.587535\pi\)
−0.271546 + 0.962425i \(0.587535\pi\)
\(402\) 16289.4 12800.3i 0.100798 0.0792079i
\(403\) −26076.8 + 26076.8i −0.160562 + 0.160562i
\(404\) −88079.6 144745.i −0.539651 0.886834i
\(405\) 223181. 223181.i 1.36065 1.36065i
\(406\) −11654.4 + 97167.8i −0.0707031 + 0.589482i
\(407\) 123146. 0.743418
\(408\) 71458.8 190939.i 0.429275 1.14703i
\(409\) 47133.9i 0.281765i −0.990026 0.140883i \(-0.955006\pi\)
0.990026 0.140883i \(-0.0449940\pi\)
\(410\) −42845.8 + 357223.i −0.254883 + 2.12506i
\(411\) 265012. + 265012.i 1.56885 + 1.56885i
\(412\) −27020.2 + 111019.i −0.159182 + 0.654037i
\(413\) 187224. + 187224.i 1.09765 + 1.09765i
\(414\) −13536.6 + 10637.1i −0.0789782 + 0.0620617i
\(415\) 79388.5i 0.460958i
\(416\) −101845. + 149876.i −0.588509 + 0.866055i
\(417\) −184874. −1.06317
\(418\) 26118.3 + 33237.5i 0.149483 + 0.190229i
\(419\) −70487.1 + 70487.1i −0.401497 + 0.401497i −0.878760 0.477264i \(-0.841629\pi\)
0.477264 + 0.878760i \(0.341629\pi\)
\(420\) −335162. 81572.9i −1.90001 0.462431i
\(421\) 109929. 109929.i 0.620225 0.620225i −0.325364 0.945589i \(-0.605487\pi\)
0.945589 + 0.325364i \(0.105487\pi\)
\(422\) −179698. 21553.2i −1.00906 0.121028i
\(423\) 45137.6 0.252266
\(424\) −67777.6 + 181103.i −0.377012 + 1.00738i
\(425\) 245634.i 1.35991i
\(426\) 45992.8 + 5516.43i 0.253437 + 0.0303976i
\(427\) 125596. + 125596.i 0.688845 + 0.688845i
\(428\) −34682.8 + 21105.0i −0.189333 + 0.115212i
\(429\) −104569. 104569.i −0.568184 0.568184i
\(430\) −279891. 356182.i −1.51374 1.92635i
\(431\) 8391.44i 0.0451733i 0.999745 + 0.0225867i \(0.00719017\pi\)
−0.999745 + 0.0225867i \(0.992810\pi\)
\(432\) 32959.9 + 103638.i 0.176611 + 0.555329i
\(433\) 112221. 0.598545 0.299272 0.954168i \(-0.403256\pi\)
0.299272 + 0.954168i \(0.403256\pi\)
\(434\) 32975.3 25912.3i 0.175069 0.137571i
\(435\) −147359. + 147359.i −0.778749 + 0.778749i
\(436\) −103658. + 63077.3i −0.545292 + 0.331818i
\(437\) 10000.4 10000.4i 0.0523666 0.0523666i
\(438\) −14169.8 + 118140.i −0.0738613 + 0.615813i
\(439\) −95834.1 −0.497269 −0.248634 0.968597i \(-0.579982\pi\)
−0.248634 + 0.968597i \(0.579982\pi\)
\(440\) 168458. 76705.6i 0.870134 0.396206i
\(441\) 5569.98i 0.0286402i
\(442\) 24130.9 201190.i 0.123518 1.02982i
\(443\) 48800.8 + 48800.8i 0.248668 + 0.248668i 0.820424 0.571756i \(-0.193738\pi\)
−0.571756 + 0.820424i \(0.693738\pi\)
\(444\) 283661. + 69038.3i 1.43891 + 0.350206i
\(445\) 31233.0 + 31233.0i 0.157722 + 0.157722i
\(446\) 296227. 232777.i 1.48920 1.17023i
\(447\) 234127.i 1.17175i
\(448\) 135293. 155435.i 0.674091 0.774451i
\(449\) −246669. −1.22355 −0.611776 0.791031i \(-0.709545\pi\)
−0.611776 + 0.791031i \(0.709545\pi\)
\(450\) −90812.7 115566.i −0.448458 0.570697i
\(451\) 124033. 124033.i 0.609794 0.609794i
\(452\) 19544.3 80302.3i 0.0956626 0.393053i
\(453\) 62992.3 62992.3i 0.306967 0.306967i
\(454\) 352070. + 42227.7i 1.70812 + 0.204874i
\(455\) −342847. −1.65606
\(456\) 41528.4 + 91203.1i 0.199717 + 0.438611i
\(457\) 6030.04i 0.0288727i 0.999896 + 0.0144364i \(0.00459540\pi\)
−0.999896 + 0.0144364i \(0.995405\pi\)
\(458\) −111107. 13326.3i −0.529675 0.0635298i
\(459\) −85992.8 85992.8i −0.408166 0.408166i
\(460\) −32192.3 52903.1i −0.152137 0.250015i
\(461\) 13122.6 + 13122.6i 0.0617473 + 0.0617473i 0.737306 0.675559i \(-0.236098\pi\)
−0.675559 + 0.737306i \(0.736098\pi\)
\(462\) 103910. + 132233.i 0.486824 + 0.619520i
\(463\) 408077.i 1.90362i 0.306689 + 0.951810i \(0.400779\pi\)
−0.306689 + 0.951810i \(0.599221\pi\)
\(464\) −37731.0 118640.i −0.175252 0.551054i
\(465\) 89305.3 0.413020
\(466\) −78823.5 + 61940.1i −0.362981 + 0.285233i
\(467\) −108240. + 108240.i −0.496311 + 0.496311i −0.910288 0.413977i \(-0.864140\pi\)
0.413977 + 0.910288i \(0.364140\pi\)
\(468\) −63028.1 103577.i −0.287768 0.472903i
\(469\) −16557.8 + 16557.8i −0.0752759 + 0.0752759i
\(470\) −19335.8 + 161211.i −0.0875321 + 0.729792i
\(471\) −191216. −0.861953
\(472\) −315458. 118060.i −1.41598 0.529930i
\(473\) 220853.i 0.987144i
\(474\) −23724.6 + 197802.i −0.105595 + 0.880387i
\(475\) 85376.7 + 85376.7i 0.378401 + 0.378401i
\(476\) −54493.5 + 223900.i −0.240508 + 0.988187i
\(477\) −91490.1 91490.1i −0.402103 0.402103i
\(478\) 292629. 229950.i 1.28074 1.00642i
\(479\) 223150.i 0.972583i −0.873797 0.486291i \(-0.838349\pi\)
0.873797 0.486291i \(-0.161651\pi\)
\(480\) 431036. 82246.0i 1.87081 0.356970i
\(481\) 290165. 1.25416
\(482\) −200144. 254699.i −0.861488 1.09631i
\(483\) 39785.8 39785.8i 0.170543 0.170543i
\(484\) 139928. + 34056.2i 0.597329 + 0.145380i
\(485\) −356767. + 356767.i −1.51670 + 1.51670i
\(486\) −225544. 27052.0i −0.954901 0.114532i
\(487\) 225880. 0.952399 0.476200 0.879337i \(-0.342014\pi\)
0.476200 + 0.879337i \(0.342014\pi\)
\(488\) −211620. 79198.5i −0.888620 0.332566i
\(489\) 372120.i 1.55620i
\(490\) 19893.4 + 2386.04i 0.0828548 + 0.00993770i
\(491\) −101698. 101698.i −0.421842 0.421842i 0.463996 0.885837i \(-0.346415\pi\)
−0.885837 + 0.463996i \(0.846415\pi\)
\(492\) 355237. 216167.i 1.46754 0.893016i
\(493\) 98440.7 + 98440.7i 0.405024 + 0.405024i
\(494\) 61541.4 + 78316.1i 0.252182 + 0.320920i
\(495\) 123853.i 0.505469i
\(496\) −24517.0 + 47383.5i −0.0996561 + 0.192603i
\(497\) −52357.9 −0.211968
\(498\) −72147.2 + 56693.9i −0.290912 + 0.228601i
\(499\) 226481. 226481.i 0.909559 0.909559i −0.0866770 0.996236i \(-0.527625\pi\)
0.996236 + 0.0866770i \(0.0276248\pi\)
\(500\) 122670. 74646.4i 0.490680 0.298585i
\(501\) −334357. + 334357.i −1.33209 + 1.33209i
\(502\) −17454.6 + 145526.i −0.0692631 + 0.577476i
\(503\) 125734. 0.496956 0.248478 0.968637i \(-0.420070\pi\)
0.248478 + 0.968637i \(0.420070\pi\)
\(504\) 57139.1 + 125487.i 0.224943 + 0.494011i
\(505\) 407820.i 1.59914i
\(506\) −3595.54 + 29977.5i −0.0140431 + 0.117083i
\(507\) −21662.8 21662.8i −0.0842749 0.0842749i
\(508\) −355804. 86596.7i −1.37874 0.335563i
\(509\) −82499.2 82499.2i −0.318430 0.318430i 0.529734 0.848164i \(-0.322292\pi\)
−0.848164 + 0.529734i \(0.822292\pi\)
\(510\) −385829. + 303188.i −1.48339 + 1.16566i
\(511\) 134490.i 0.515048i
\(512\) −74694.3 + 251277.i −0.284936 + 0.958546i
\(513\) 59778.1 0.227147
\(514\) 39050.7 + 49694.9i 0.147809 + 0.188099i
\(515\) 194462. 194462.i 0.733198 0.733198i
\(516\) −123814. + 508722.i −0.465020 + 1.91065i
\(517\) 55974.7 55974.7i 0.209416 0.209416i
\(518\) −327631. 39296.4i −1.22103 0.146451i
\(519\) 254025. 0.943066
\(520\) 396930. 180738.i 1.46794 0.668410i
\(521\) 225057.i 0.829120i 0.910022 + 0.414560i \(0.136064\pi\)
−0.910022 + 0.414560i \(0.863936\pi\)
\(522\) 82708.5 + 9920.15i 0.303535 + 0.0364064i
\(523\) −230384. 230384.i −0.842264 0.842264i 0.146889 0.989153i \(-0.453074\pi\)
−0.989153 + 0.146889i \(0.953074\pi\)
\(524\) 225866. + 371176.i 0.822599 + 1.35182i
\(525\) 339664. + 339664.i 1.23234 + 1.23234i
\(526\) −202768. 258038.i −0.732873 0.932636i
\(527\) 59659.0i 0.214810i
\(528\) −190010. 98314.4i −0.681568 0.352655i
\(529\) −269740. −0.963903
\(530\) 365953. 287569.i 1.30279 1.02374i
\(531\) 159364. 159364.i 0.565199 0.565199i
\(532\) −58881.5 96762.7i −0.208044 0.341889i
\(533\) 292253. 292253.i 1.02874 1.02874i
\(534\) 6079.64 50688.6i 0.0213204 0.177757i
\(535\) 97718.9 0.341406
\(536\) 10441.0 27898.5i 0.0363423 0.0971070i
\(537\) 353165.i 1.22470i
\(538\) 20762.4 173105.i 0.0717319 0.598060i
\(539\) −6907.27 6907.27i −0.0237755 0.0237755i
\(540\) 61900.3 254332.i 0.212278 0.872195i
\(541\) −183995. 183995.i −0.628655 0.628655i 0.319074 0.947730i \(-0.396628\pi\)
−0.947730 + 0.319074i \(0.896628\pi\)
\(542\) −348506. + 273859.i −1.18635 + 0.932241i
\(543\) 155654.i 0.527909i
\(544\) −54943.1 287947.i −0.185659 0.973003i
\(545\) 292056. 0.983271
\(546\) 244838. + 311575.i 0.821284 + 1.04515i
\(547\) −416851. + 416851.i −1.39318 + 1.39318i −0.575075 + 0.818100i \(0.695027\pi\)
−0.818100 + 0.575075i \(0.804973\pi\)
\(548\) 523604. + 127436.i 1.74358 + 0.424358i
\(549\) 106907. 106907.i 0.354699 0.354699i
\(550\) −255928. 30696.3i −0.846043 0.101475i
\(551\) −68431.2 −0.225399
\(552\) −25088.1 + 67035.7i −0.0823360 + 0.220003i
\(553\) 225176.i 0.736330i
\(554\) 143976. + 17268.6i 0.469104 + 0.0562649i
\(555\) −496864. 496864.i −1.61307 1.61307i
\(556\) −227085. + 138184.i −0.734578 + 0.447001i
\(557\) −233211. 233211.i −0.751691 0.751691i 0.223104 0.974795i \(-0.428381\pi\)
−0.974795 + 0.223104i \(0.928381\pi\)
\(558\) −22056.3 28068.4i −0.0708378 0.0901465i
\(559\) 520386.i 1.66534i
\(560\) −472659. + 150320.i −1.50720 + 0.479335i
\(561\) 239236. 0.760152
\(562\) −153484. + 120609.i −0.485949 + 0.381862i
\(563\) −82256.5 + 82256.5i −0.259510 + 0.259510i −0.824855 0.565345i \(-0.808743\pi\)
0.565345 + 0.824855i \(0.308743\pi\)
\(564\) 160315. 97553.9i 0.503983 0.306681i
\(565\) −140659. + 140659.i −0.440626 + 0.440626i
\(566\) 75090.4 626061.i 0.234397 1.95427i
\(567\) 412331. 1.28257
\(568\) 60617.3 27601.5i 0.187888 0.0855530i
\(569\) 130218.i 0.402203i −0.979570 0.201102i \(-0.935548\pi\)
0.979570 0.201102i \(-0.0644522\pi\)
\(570\) 28724.2 239486.i 0.0884093 0.737106i
\(571\) 62508.2 + 62508.2i 0.191719 + 0.191719i 0.796438 0.604720i \(-0.206715\pi\)
−0.604720 + 0.796438i \(0.706715\pi\)
\(572\) −206605. 50284.3i −0.631465 0.153688i
\(573\) 16001.2 + 16001.2i 0.0487353 + 0.0487353i
\(574\) −369568. + 290410.i −1.12168 + 0.881429i
\(575\) 86238.6i 0.260835i
\(576\) −132305. 115160.i −0.398779 0.347102i
\(577\) 522256. 1.56867 0.784336 0.620336i \(-0.213004\pi\)
0.784336 + 0.620336i \(0.213004\pi\)
\(578\) −3879.92 4937.49i −0.0116136 0.0147792i
\(579\) −230208. + 230208.i −0.686695 + 0.686695i
\(580\) −70860.6 + 291148.i −0.210644 + 0.865481i
\(581\) 73336.0 73336.0i 0.217252 0.217252i
\(582\) 579003. + 69446.3i 1.70937 + 0.205023i
\(583\) −226912. −0.667606
\(584\) 70898.8 + 155705.i 0.207880 + 0.456539i
\(585\) 291829.i 0.852739i
\(586\) 73538.9 + 8820.34i 0.214152 + 0.0256856i
\(587\) 309702. + 309702.i 0.898811 + 0.898811i 0.995331 0.0965202i \(-0.0307712\pi\)
−0.0965202 + 0.995331i \(0.530771\pi\)
\(588\) −12038.1 19782.8i −0.0348181 0.0572182i
\(589\) 20736.0 + 20736.0i 0.0597717 + 0.0597717i
\(590\) 500909. + 637444.i 1.43898 + 1.83121i
\(591\) 443697.i 1.27032i
\(592\) 400030. 127221.i 1.14143 0.363008i
\(593\) −447350. −1.27215 −0.636075 0.771628i \(-0.719443\pi\)
−0.636075 + 0.771628i \(0.719443\pi\)
\(594\) −100343. + 78850.2i −0.284389 + 0.223475i
\(595\) 392186. 392186.i 1.10779 1.10779i
\(596\) −174999. 287584.i −0.492655 0.809603i
\(597\) −425687. + 425687.i −1.19438 + 1.19438i
\(598\) −8472.01 + 70634.7i −0.0236910 + 0.197522i
\(599\) 462149. 1.28804 0.644019 0.765009i \(-0.277266\pi\)
0.644019 + 0.765009i \(0.277266\pi\)
\(600\) −572306. 214185.i −1.58974 0.594960i
\(601\) 374481.i 1.03677i 0.855149 + 0.518383i \(0.173466\pi\)
−0.855149 + 0.518383i \(0.826534\pi\)
\(602\) 70474.8 587578.i 0.194465 1.62134i
\(603\) 14093.8 + 14093.8i 0.0387610 + 0.0387610i
\(604\) 30291.2 124459.i 0.0830315 0.341155i
\(605\) −245100. 245100.i −0.669627 0.669627i
\(606\) 370622. 291238.i 1.00922 0.793053i
\(607\) 86755.6i 0.235462i 0.993046 + 0.117731i \(0.0375620\pi\)
−0.993046 + 0.117731i \(0.962438\pi\)
\(608\) 119180. + 80986.4i 0.322402 + 0.219081i
\(609\) −272248. −0.734058
\(610\) 336026. + 427618.i 0.903053 + 1.14920i
\(611\) 131891. 131891.i 0.353290 0.353290i
\(612\) 190582. + 46384.4i 0.508836 + 0.123842i
\(613\) −112325. + 112325.i −0.298920 + 0.298920i −0.840591 0.541671i \(-0.817792\pi\)
0.541671 + 0.840591i \(0.317792\pi\)
\(614\) 141959. + 17026.7i 0.376553 + 0.0451642i
\(615\) −1.00088e6 −2.64626
\(616\) 226472. + 84757.2i 0.596834 + 0.223365i
\(617\) 602706.i 1.58320i −0.611041 0.791599i \(-0.709249\pi\)
0.611041 0.791599i \(-0.290751\pi\)
\(618\) −315597. 37853.0i −0.826334 0.0991114i
\(619\) −150969. 150969.i −0.394010 0.394010i 0.482104 0.876114i \(-0.339873\pi\)
−0.876114 + 0.482104i \(0.839873\pi\)
\(620\) 109696. 66751.5i 0.285369 0.173651i
\(621\) 30190.8 + 30190.8i 0.0782873 + 0.0782873i
\(622\) 132985. + 169233.i 0.343733 + 0.437426i
\(623\) 57703.6i 0.148671i
\(624\) −447713. 231654.i −1.14982 0.594937i
\(625\) 190658. 0.488084
\(626\) 431968. 339444.i 1.10231 0.866202i
\(627\) −83152.6 + 83152.6i −0.211515 + 0.211515i
\(628\) −234876. + 142925.i −0.595551 + 0.362401i
\(629\) −331922. + 331922.i −0.838948 + 0.838948i
\(630\) 39521.7 329509.i 0.0995761 0.830208i
\(631\) −693714. −1.74230 −0.871148 0.491020i \(-0.836624\pi\)
−0.871148 + 0.491020i \(0.836624\pi\)
\(632\) 118706. + 260698.i 0.297193 + 0.652684i
\(633\) 503485.i 1.25655i
\(634\) −77838.8 + 648975.i −0.193650 + 1.61454i
\(635\) 623231. + 623231.i 1.54562 + 1.54562i
\(636\) −522678. 127211.i −1.29217 0.314493i
\(637\) −16275.3 16275.3i −0.0401098 0.0401098i
\(638\) 114868. 90264.0i 0.282200 0.221755i
\(639\) 44566.7i 0.109146i
\(640\) 467976. 423203.i 1.14252 1.03321i
\(641\) −17843.0 −0.0434261 −0.0217131 0.999764i \(-0.506912\pi\)
−0.0217131 + 0.999764i \(0.506912\pi\)
\(642\) −69784.2 88805.6i −0.169312 0.215462i
\(643\) −230136. + 230136.i −0.556626 + 0.556626i −0.928345 0.371719i \(-0.878768\pi\)
0.371719 + 0.928345i \(0.378768\pi\)
\(644\) 19131.8 78607.8i 0.0461301 0.189537i
\(645\) 891085. 891085.i 2.14190 2.14190i
\(646\) −159985. 19188.7i −0.383366 0.0459813i
\(647\) 568528. 1.35814 0.679068 0.734075i \(-0.262384\pi\)
0.679068 + 0.734075i \(0.262384\pi\)
\(648\) −477376. + 217368.i −1.13687 + 0.517661i
\(649\) 395251.i 0.938391i
\(650\) −603032. 72328.4i −1.42730 0.171191i
\(651\) 82496.7 + 82496.7i 0.194659 + 0.194659i
\(652\) −278142. 457083.i −0.654291 1.07523i
\(653\) 371799. + 371799.i 0.871932 + 0.871932i 0.992683 0.120751i \(-0.0385303\pi\)
−0.120751 + 0.992683i \(0.538530\pi\)
\(654\) −208567. 265417.i −0.487629 0.620544i
\(655\) 1.04579e6i 2.43759i
\(656\) 274772. 531046.i 0.638506 1.23403i
\(657\) −114477. −0.265208
\(658\) −166782. + 131059.i −0.385210 + 0.302701i
\(659\) −71107.3 + 71107.3i −0.163736 + 0.163736i −0.784219 0.620484i \(-0.786936\pi\)
0.620484 + 0.784219i \(0.286936\pi\)
\(660\) 267677. + 439886.i 0.614502 + 1.00984i
\(661\) 570193. 570193.i 1.30502 1.30502i 0.380065 0.924960i \(-0.375902\pi\)
0.924960 0.380065i \(-0.124098\pi\)
\(662\) −45815.2 + 381981.i −0.104543 + 0.871617i
\(663\) 563701. 1.28239
\(664\) −46244.2 + 123565.i −0.104887 + 0.280259i
\(665\) 272629.i 0.616494i
\(666\) −33448.8 + 278877.i −0.0754105 + 0.628730i
\(667\) −34561.0 34561.0i −0.0776846 0.0776846i
\(668\) −160783. + 660615.i −0.360318 + 1.48046i
\(669\) 741091. + 741091.i 1.65584 + 1.65584i
\(670\) −56374.3 + 44299.4i −0.125583 + 0.0986842i
\(671\) 265148.i 0.588901i
\(672\) 474149. + 322198.i 1.04997 + 0.713484i
\(673\) −57084.2 −0.126033 −0.0630167 0.998012i \(-0.520072\pi\)
−0.0630167 + 0.998012i \(0.520072\pi\)
\(674\) −362573. 461402.i −0.798134 1.01569i
\(675\) −257749. + 257749.i −0.565704 + 0.565704i
\(676\) −42800.8 10417.0i −0.0936609 0.0227955i
\(677\) −107264. + 107264.i −0.234032 + 0.234032i −0.814373 0.580341i \(-0.802919\pi\)
0.580341 + 0.814373i \(0.302919\pi\)
\(678\) 228278. + 27379.9i 0.496597 + 0.0595624i
\(679\) −659134. −1.42966
\(680\) −247305. + 660801.i −0.534828 + 1.42907i
\(681\) 986444.i 2.12705i
\(682\) −62159.1 7455.43i −0.133640 0.0160289i
\(683\) 41763.8 + 41763.8i 0.0895280 + 0.0895280i 0.750452 0.660924i \(-0.229836\pi\)
−0.660924 + 0.750452i \(0.729836\pi\)
\(684\) −82363.7 + 50119.5i −0.176045 + 0.107126i
\(685\) −917153. 917153.i −1.95461 1.95461i
\(686\) −282365. 359331.i −0.600016 0.763565i
\(687\) 311303.i 0.659583i
\(688\) 228161. + 717420.i 0.482019 + 1.51564i
\(689\) −534662. −1.12627
\(690\) 135459. 106445.i 0.284517 0.223576i
\(691\) 473605. 473605.i 0.991882 0.991882i −0.00808568 0.999967i \(-0.502574\pi\)
0.999967 + 0.00808568i \(0.00257378\pi\)
\(692\) 312025. 189872.i 0.651594 0.396504i
\(693\) −114410. + 114410.i −0.238231 + 0.238231i
\(694\) 53974.3 450007.i 0.112065 0.934330i
\(695\) 639811. 1.32459
\(696\) 315195. 143521.i 0.650670 0.296276i
\(697\) 668623.i 1.37631i
\(698\) −68033.3 + 567223.i −0.139640 + 1.16424i
\(699\) −197198. 197198.i −0.403598 0.403598i
\(700\) 671101. + 163335.i 1.36959 + 0.333336i
\(701\) −139642. 139642.i −0.284170 0.284170i 0.550599 0.834770i \(-0.314399\pi\)
−0.834770 + 0.550599i \(0.814399\pi\)
\(702\) −236433. + 185791.i −0.479772 + 0.377008i
\(703\) 230737.i 0.466880i
\(704\) −306879. + 21261.6i −0.619188 + 0.0428994i
\(705\) −451687. −0.908782
\(706\) 320934. + 408412.i 0.643882 + 0.819388i
\(707\) −376728. + 376728.i −0.753684 + 0.753684i
\(708\) 221586. 910438.i 0.442054 1.81628i
\(709\) −161047. + 161047.i −0.320377 + 0.320377i −0.848912 0.528535i \(-0.822742\pi\)
0.528535 + 0.848912i \(0.322742\pi\)
\(710\) −159172. 19091.3i −0.315755 0.0378720i
\(711\) −191668. −0.379150
\(712\) −30419.5 66806.2i −0.0600057 0.131782i
\(713\) 20945.4i 0.0412011i
\(714\) −636486. 76340.9i −1.24851 0.149748i
\(715\) 361893. + 361893.i 0.707894 + 0.707894i
\(716\) −263974. 433801.i −0.514914 0.846183i
\(717\) 732090. + 732090.i 1.42405 + 1.42405i
\(718\) −138262. 175949.i −0.268197 0.341300i
\(719\) 132212.i 0.255749i 0.991790 + 0.127874i \(0.0408154\pi\)
−0.991790 + 0.127874i \(0.959185\pi\)
\(720\) 127951. + 402324.i 0.246819 + 0.776087i
\(721\) 359273. 0.691122
\(722\) −347600. + 273147.i −0.666815 + 0.523989i
\(723\) 637198. 637198.i 1.21898 1.21898i
\(724\) −116344. 191193.i −0.221955 0.364749i
\(725\) 295059. 295059.i 0.561349 0.561349i
\(726\) −47709.9 + 397778.i −0.0905180 + 0.754687i
\(727\) 98417.4 0.186210 0.0931050 0.995656i \(-0.470321\pi\)
0.0931050 + 0.995656i \(0.470321\pi\)
\(728\) 533627. + 199710.i 1.00687 + 0.376822i
\(729\) 31927.4i 0.0600770i
\(730\) 49039.0 408859.i 0.0920229 0.767234i
\(731\) −595275. 595275.i −1.11399 1.11399i
\(732\) 148647. 610752.i 0.277418 1.13984i
\(733\) −369797. 369797.i −0.688265 0.688265i 0.273584 0.961848i \(-0.411791\pi\)
−0.961848 + 0.273584i \(0.911791\pi\)
\(734\) 455879. 358233.i 0.846169 0.664927i
\(735\) 55738.2i 0.103176i
\(736\) 19289.7 + 101094.i 0.0356098 + 0.186624i
\(737\) 34955.2 0.0643542
\(738\) 247194. + 314574.i 0.453864 + 0.577576i
\(739\) 117481. 117481.i 0.215120 0.215120i −0.591318 0.806438i \(-0.701392\pi\)
0.806438 + 0.591318i \(0.201392\pi\)
\(740\) −981693. 238928.i −1.79272 0.436318i
\(741\) −195929. + 195929.i −0.356831 + 0.356831i
\(742\) 603698. + 72408.2i 1.09651 + 0.131516i
\(743\) −273733. −0.495849 −0.247925 0.968779i \(-0.579749\pi\)
−0.247925 + 0.968779i \(0.579749\pi\)
\(744\) −139000. 52020.8i −0.251113 0.0939790i
\(745\) 810267.i 1.45988i
\(746\) 134993. + 16191.2i 0.242568 + 0.0290939i
\(747\) −62423.0 62423.0i −0.111867 0.111867i
\(748\) 293859. 178817.i 0.525213 0.319600i
\(749\) 90268.8 + 90268.8i 0.160907 + 0.160907i
\(750\) 246820. + 314097.i 0.438791 + 0.558395i
\(751\) 875863.i 1.55295i 0.630150 + 0.776473i \(0.282993\pi\)
−0.630150 + 0.776473i \(0.717007\pi\)
\(752\) 124002. 239655.i 0.219276 0.423791i
\(753\) −407741. −0.719108
\(754\) 270658. 212685.i 0.476078 0.374106i
\(755\) −218004. + 218004.i −0.382446 + 0.382446i
\(756\) 292123. 177761.i 0.511119 0.311023i
\(757\) 66071.4 66071.4i 0.115298 0.115298i −0.647104 0.762402i \(-0.724020\pi\)
0.762402 + 0.647104i \(0.224020\pi\)
\(758\) 18800.0 156743.i 0.0327204 0.272804i
\(759\) −83992.1 −0.145799
\(760\) −143721. 315636.i −0.248825 0.546461i
\(761\) 333176.i 0.575314i −0.957734 0.287657i \(-0.907124\pi\)
0.957734 0.287657i \(-0.0928763\pi\)
\(762\) 121315. 1.01145e6i 0.208932 1.74195i
\(763\) 269790. + 269790.i 0.463422 + 0.463422i
\(764\) 31614.8 + 7694.51i 0.0541631 + 0.0131824i
\(765\) −333826. 333826.i −0.570423 0.570423i
\(766\) −303985. + 238874.i −0.518078 + 0.407110i
\(767\) 931313.i 1.58309i
\(768\) −718798. 123068.i −1.21867 0.208652i
\(769\) −110911. −0.187552 −0.0937762 0.995593i \(-0.529894\pi\)
−0.0937762 + 0.995593i \(0.529894\pi\)
\(770\) −359610. 457631.i −0.606528 0.771853i
\(771\) −124325. + 124325.i