Properties

Label 16.5.f.a.11.6
Level $16$
Weight $5$
Character 16.11
Analytic conductor $1.654$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $2$

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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 11.6
Root \(0.336831 - 2.80830i\) of defining polynomial
Character \(\chi\) \(=\) 16.11
Dual form 16.5.f.a.3.6

$q$-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 \(\left(\mathbb{Z}/16\mathbb{Z}\right)^\times\).

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

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 0.118668 0.992934i \(-0.462138\pi\)
−0.992934 + 0.118668i \(0.962138\pi\)
\(4\) −3.78368 15.5462i −0.236480 0.971636i
\(5\) 27.2309 + 27.2309i 1.08924 + 1.08924i 0.995607 + 0.0936308i \(0.0298473\pi\)
0.0936308 + 0.995607i \(0.470153\pi\)
\(6\) −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 −0.891635 0.452754i \(-0.850442\pi\)
0.452754 + 0.891635i \(0.350442\pi\)
\(12\) −92.5520 + 152.095i −0.642722 + 1.05622i
\(13\) −125.128 + 125.128i −0.740404 + 0.740404i −0.972656 0.232252i \(-0.925391\pi\)
0.232252 + 0.972656i \(0.425391\pi\)
\(14\) 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 0.555734 0.831360i \(-0.312437\pi\)
−0.831360 + 0.555734i \(0.812437\pi\)
\(20\) 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 −0.472465 0.881350i \(-0.656636\pi\)
0.881350 + 0.472465i \(0.156636\pi\)
\(30\) −1347.78 1059.09i −1.49753 1.17677i
\(31\) 208.400i 0.216858i 0.994104 + 0.108429i \(0.0345820\pi\)
−0.994104 + 0.108429i \(0.965418\pi\)
\(32\) −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 0.142805 0.989751i \(-0.454388\pi\)
−0.989751 + 0.142805i \(0.954388\pi\)
\(38\) −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 \(-0.755531\pi\)
0.719286 0.694714i \(-0.244469\pi\)
\(42\) −2223.37 + 266.673i −1.26041 + 0.151175i
\(43\) −2079.41 + 2079.41i −1.12461 + 1.12461i −0.133575 + 0.991039i \(0.542646\pi\)
−0.991039 + 0.133575i \(0.957354\pi\)
\(44\) 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 \(-0.923318\pi\)
0.971123 0.238580i \(-0.0766818\pi\)
\(48\) 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 0.976426 0.215850i \(-0.0692523\pi\)
−0.215850 + 0.976426i \(0.569252\pi\)
\(54\) 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 0.0716407 0.997431i \(-0.477177\pi\)
0.997431 0.0716407i \(-0.0228235\pi\)
\(60\) −6661.97 + 1621.41i −1.85055 + 0.450393i
\(61\) 2496.46 2496.46i 0.670912 0.670912i −0.287014 0.957926i \(-0.592663\pi\)
0.957926 + 0.287014i \(0.0926628\pi\)
\(62\) 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 0.669498 0.742814i \(-0.266509\pi\)
−0.742814 + 0.669498i \(0.766509\pi\)
\(68\) −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 \(0.0807001\pi\)
−0.968034 + 0.250820i \(0.919300\pi\)
\(74\) −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 \(0.116739\pi\)
−0.933499 + 0.358580i \(0.883261\pi\)
\(80\) −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 0.804945 0.593349i \(-0.202195\pi\)
−0.593349 + 0.804945i \(0.702195\pi\)
\(84\) −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 \(-0.976934\pi\)
0.997376 0.0724003i \(-0.0230659\pi\)
\(90\) 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 0.237359 0.971422i \(-0.423718\pi\)
−0.971422 + 0.237359i \(0.923718\pi\)
\(102\) −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 −0.624393 0.781111i \(-0.714654\pi\)
0.781111 + 0.624393i \(0.214654\pi\)
\(108\) 5806.49 + 3533.33i 0.497813 + 0.302926i
\(109\) 5362.57 5362.57i 0.451357 0.451357i −0.444448 0.895805i \(-0.646600\pi\)
0.895805 + 0.444448i \(0.146600\pi\)
\(110\) −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 \(-0.748923\pi\)
0.704711 0.709495i \(-0.251077\pi\)
\(128\) 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 0.991897 + 0.127048i \(0.0405502\pi\)
0.127048 + 0.991897i \(0.459450\pi\)
\(132\) −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 \(0.354430\pi\)
−0.441547 + 0.897238i \(0.645570\pi\)
\(138\) 4441.70 532.742i 0.233234 0.0279743i
\(139\) 11747.9 11747.9i 0.608036 0.608036i −0.334397 0.942432i \(-0.608532\pi\)
0.942432 + 0.334397i \(0.108532\pi\)
\(140\) 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 0.287611 0.957747i \(-0.407139\pi\)
−0.957747 + 0.287611i \(0.907139\pi\)
\(150\) −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 −0.416279 0.909237i \(-0.636666\pi\)
0.909237 + 0.416279i \(0.136666\pi\)
\(158\) 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 0.104520 0.994523i \(-0.466669\pi\)
−0.994523 + 0.104520i \(0.966669\pi\)
\(164\) −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 −0.923337 0.383990i \(-0.874550\pi\)
0.383990 + 0.923337i \(0.374550\pi\)
\(174\) −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 0.264084 0.964500i \(-0.414930\pi\)
−0.964500 + 0.264084i \(0.914930\pi\)
\(180\) 22540.9 + 13716.5i 0.695707 + 0.423347i
\(181\) −9891.06 9891.06i −0.301916 0.301916i 0.539847 0.841763i \(-0.318482\pi\)
−0.841763 + 0.539847i \(0.818482\pi\)
\(182\) 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 \(0.00887311\pi\)
−0.999611 + 0.0278721i \(0.991127\pi\)
\(192\) 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 0.969922 0.243417i \(-0.0782684\pi\)
−0.243417 + 0.969922i \(0.578268\pi\)
\(198\) −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 0.249694 0.968325i \(-0.419670\pi\)
−0.968325 + 0.249694i \(0.919670\pi\)
\(212\) 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 \(0.395893\pi\)
−0.321261 + 0.946991i \(0.604107\pi\)
\(224\) −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 0.968857 + 0.247622i \(0.0796490\pi\)
0.247622 + 0.968857i \(0.420351\pi\)
\(228\) 24342.6 5924.59i 0.468271 0.113969i
\(229\) −19781.9 19781.9i −0.377221 0.377221i 0.492877 0.870099i \(-0.335945\pi\)
−0.870099 + 0.492877i \(0.835945\pi\)
\(230\) −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 \(-0.925859\pi\)
0.972996 0.230821i \(-0.0741412\pi\)
\(234\) −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 \(0.302949\pi\)
−0.580265 + 0.814427i \(0.697051\pi\)
\(240\) 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 −0.470915 0.882179i \(-0.656076\pi\)
0.882179 + 0.470915i \(0.156076\pi\)
\(252\) 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 −0.887237 0.461314i \(-0.847378\pi\)
0.461314 + 0.887237i \(0.347378\pi\)
\(270\) −40432.7 + 51453.6i −0.554632 + 0.705811i
\(271\) 110808.i 1.50880i −0.656412 0.754402i \(-0.727927\pi\)
0.656412 0.754402i \(-0.272073\pi\)
\(272\) −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 0.854135 0.520051i \(-0.174087\pi\)
−0.520051 + 0.854135i \(0.674087\pi\)
\(278\) −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 \(-0.900000\pi\)
0.951057 0.309017i \(-0.0999999\pi\)
\(282\) 5587.10 + 46582.0i 0.0702568 + 0.585761i
\(283\) −111466. + 111466.i −1.39178 + 1.39178i −0.570439 + 0.821340i \(0.693227\pi\)
−0.821340 + 0.570439i \(0.806773\pi\)
\(284\) 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 0.779240 0.626726i \(-0.215605\pi\)
−0.626726 + 0.779240i \(0.715605\pi\)
\(294\) −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 0.828363 0.560192i \(-0.189273\pi\)
−0.560192 + 0.828363i \(0.689273\pi\)
\(308\) 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 \(0.247245\pi\)
−0.713199 + 0.700961i \(0.752755\pi\)
\(314\) −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 0.163252 0.986584i \(-0.447802\pi\)
0.986584 0.163252i \(-0.0521982\pi\)
\(318\) −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 −0.324978 0.945722i \(-0.605357\pi\)
0.945722 + 0.324978i \(0.105357\pi\)
\(332\) 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 −0.956649 0.291243i \(-0.905931\pi\)
0.291243 + 0.956649i \(0.405931\pi\)
\(348\) 20475.2 + 84127.3i 0.169071 + 0.694670i
\(349\) 100990. 100990.i 0.829143 0.829143i −0.158255 0.987398i \(-0.550587\pi\)
0.987398 + 0.158255i \(0.0505869\pi\)
\(350\) 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 \(0.180851\pi\)
−0.842892 + 0.538082i \(0.819149\pi\)
\(368\) 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 0.788187 0.615436i \(-0.211020\pi\)
−0.615436 + 0.788187i \(0.711020\pi\)
\(374\) 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 −0.797544 0.603260i \(-0.793868\pi\)
0.603260 + 0.797544i \(0.293868\pi\)
\(380\) −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 \(-0.893137\pi\)
0.944174 0.329448i \(-0.106863\pi\)
\(384\) −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 0.993511 0.113734i \(-0.0362813\pi\)
−0.113734 + 0.993511i \(0.536281\pi\)
\(390\) 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 −0.593142 0.805098i \(-0.702113\pi\)
0.805098 + 0.593142i \(0.202113\pi\)
\(398\) 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 \(0.0449940\pi\)
−0.990026 + 0.140883i \(0.955006\pi\)
\(410\) −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 0.477264 0.878760i \(-0.341629\pi\)
−0.878760 + 0.477264i \(0.841629\pi\)
\(420\) −335162. + 81572.9i −1.90001 + 0.462431i
\(421\) 109929. + 109929.i 0.620225 + 0.620225i 0.945589 0.325364i \(-0.105487\pi\)
−0.325364 + 0.945589i \(0.605487\pi\)
\(422\) −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 \(-0.992810\pi\)
0.999745 0.0225867i \(-0.00719017\pi\)
\(432\) 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 −0.571756 0.820424i \(-0.693738\pi\)
0.820424 + 0.571756i \(0.193738\pi\)
\(444\) 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 \(-0.995405\pi\)
0.999896 0.0144364i \(-0.00459540\pi\)
\(458\) −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 −0.675559 0.737306i \(-0.736098\pi\)
0.737306 + 0.675559i \(0.236098\pi\)
\(462\) 103910. 132233.i 0.486824 0.619520i
\(463\) 408077.i 1.90362i −0.306689 0.951810i \(-0.599221\pi\)
0.306689 0.951810i \(-0.400779\pi\)
\(464\) −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 0.413977 0.910288i \(-0.364140\pi\)
−0.910288 + 0.413977i \(0.864140\pi\)
\(468\) −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 \(0.161651\pi\)
−0.873797 + 0.486291i \(0.838349\pi\)
\(480\) 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 −0.885837 0.463996i \(-0.846415\pi\)
0.463996 + 0.885837i \(0.346415\pi\)
\(492\) 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 0.996236 0.0866770i \(-0.0276248\pi\)
−0.0866770 + 0.996236i \(0.527625\pi\)
\(500\) 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 −0.848164 0.529734i \(-0.822292\pi\)
0.529734 + 0.848164i \(0.322292\pi\)
\(510\) −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 \(-0.863936\pi\)
0.910022 0.414560i \(-0.136064\pi\)
\(522\) 82708.5 9920.15i 0.303535 0.0364064i
\(523\) −230384. + 230384.i −0.842264 + 0.842264i −0.989153 0.146889i \(-0.953074\pi\)
0.146889 + 0.989153i \(0.453074\pi\)
\(524\) 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 −0.947730 0.319074i \(-0.896628\pi\)
0.319074 + 0.947730i \(0.396628\pi\)
\(542\) −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 −0.818100 0.575075i \(-0.804973\pi\)
−0.575075 0.818100i \(-0.695027\pi\)
\(548\) 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 −0.974795 0.223104i \(-0.928381\pi\)
0.223104 + 0.974795i \(0.428381\pi\)
\(558\) −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 0.565345 0.824855i \(-0.308743\pi\)
−0.824855 + 0.565345i \(0.808743\pi\)
\(564\) 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 \(0.0644522\pi\)
−0.979570 + 0.201102i \(0.935548\pi\)
\(570\) 28724.2 + 239486.i 0.0884093 + 0.737106i
\(571\) 62508.2 62508.2i 0.191719 0.191719i −0.604720 0.796438i \(-0.706715\pi\)
0.796438 + 0.604720i \(0.206715\pi\)
\(572\) −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 −0.0965202 0.995331i \(-0.530771\pi\)
0.995331 + 0.0965202i \(0.0307712\pi\)
\(588\) −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 \(-0.826534\pi\)
0.855149 0.518383i \(-0.173466\pi\)
\(602\) 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 \(-0.962438\pi\)
0.993046 0.117731i \(-0.0375620\pi\)
\(608\) 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 0.541671 0.840591i \(-0.317792\pi\)
−0.840591 + 0.541671i \(0.817792\pi\)
\(614\) 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 \(0.290751\pi\)
−0.611041 + 0.791599i \(0.709249\pi\)
\(618\) −315597. + 37853.0i −0.826334 + 0.0991114i
\(619\) −150969. + 150969.i −0.394010 + 0.394010i −0.876114 0.482104i \(-0.839873\pi\)
0.482104 + 0.876114i \(0.339873\pi\)
\(620\) 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 0.371719 0.928345i \(-0.378768\pi\)
−0.928345 + 0.371719i \(0.878768\pi\)
\(644\) 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 −0.120751 0.992683i \(-0.538530\pi\)
0.992683 + 0.120751i \(0.0385303\pi\)
\(654\) −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 0.620484 0.784219i \(-0.286936\pi\)
−0.784219 + 0.620484i \(0.786936\pi\)
\(660\) 267677. 439886.i 0.614502 1.00984i
\(661\) 570193. + 570193.i 1.30502 + 1.30502i 0.924960 + 0.380065i \(0.124098\pi\)
0.380065 + 0.924960i \(0.375902\pi\)
\(662\) −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 0.580341 0.814373i \(-0.302919\pi\)
−0.814373 + 0.580341i \(0.802919\pi\)
\(678\) 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 −0.660924 0.750452i \(-0.729836\pi\)
0.750452 + 0.660924i \(0.229836\pi\)
\(684\) −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 0.999967 0.00808568i \(-0.00257378\pi\)
−0.00808568 + 0.999967i \(0.502574\pi\)
\(692\) 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 −0.834770 0.550599i \(-0.814399\pi\)
0.550599 + 0.834770i \(0.314399\pi\)
\(702\) −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 0.528535 0.848912i \(-0.322742\pi\)
−0.848912 + 0.528535i \(0.822742\pi\)
\(710\) −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 \(-0.959185\pi\)
0.991790 0.127874i \(-0.0408154\pi\)
\(720\) 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 −0.961848 0.273584i \(-0.911791\pi\)
0.273584 + 0.961848i \(0.411791\pi\)
\(734\) 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 0.806438 0.591318i \(-0.201392\pi\)
−0.591318 + 0.806438i \(0.701392\pi\)
\(740\) −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 \(-0.717007\pi\)
0.630150 0.776473i \(-0.282993\pi\)
\(752\) 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 0.762402 0.647104i \(-0.224020\pi\)
−0.647104 + 0.762402i \(0.724020\pi\)
\(758\) 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 \(0.0928763\pi\)
−0.957734 + 0.287657i \(0.907124\pi\)
\(762\) 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. &minu