Properties

Label 39.4.j.b.4.1
Level $39$
Weight $4$
Character 39.4
Analytic conductor $2.301$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 39 = 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 39.j (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.30107449022\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-17})\)
Defining polynomial: \( x^{4} - 17x^{2} + 289 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 4.1
Root \(-3.57071 - 2.06155i\) of defining polynomial
Character \(\chi\) \(=\) 39.4
Dual form 39.4.j.b.10.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-3.57071 - 2.06155i) q^{2} +(1.50000 - 2.59808i) q^{3} +(4.50000 + 7.79423i) q^{4} -13.4424i q^{5} +(-10.7121 + 6.18466i) q^{6} +(-27.2121 + 15.7109i) q^{7} -4.12311i q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\) \(q+(-3.57071 - 2.06155i) q^{2} +(1.50000 - 2.59808i) q^{3} +(4.50000 + 7.79423i) q^{4} -13.4424i q^{5} +(-10.7121 + 6.18466i) q^{6} +(-27.2121 + 15.7109i) q^{7} -4.12311i q^{8} +(-4.50000 - 7.79423i) q^{9} +(-27.7121 + 47.9988i) q^{10} +(-35.0707 - 20.2481i) q^{11} +27.0000 q^{12} +(42.1364 - 20.5310i) q^{13} +129.556 q^{14} +(-34.9243 - 20.1635i) q^{15} +(27.5000 - 47.6314i) q^{16} +(-21.5707 - 37.3616i) q^{17} +37.1080i q^{18} +(23.3636 - 13.4890i) q^{19} +(104.773 - 60.4906i) q^{20} +94.2656i q^{21} +(83.4850 + 144.600i) q^{22} +(-9.50500 + 16.4631i) q^{23} +(-10.7121 - 6.18466i) q^{24} -55.6971 q^{25} +(-192.783 - 13.5562i) q^{26} -27.0000 q^{27} +(-244.909 - 141.398i) q^{28} +(77.0557 - 133.464i) q^{29} +(83.1364 + 143.997i) q^{30} -308.270i q^{31} +(-224.955 + 129.878i) q^{32} +(-105.212 + 60.7443i) q^{33} +177.877i q^{34} +(211.192 + 365.796i) q^{35} +(40.5000 - 70.1481i) q^{36} +(-37.6821 - 21.7558i) q^{37} -111.233 q^{38} +(9.86357 - 140.270i) q^{39} -55.4243 q^{40} +(41.4293 + 23.9192i) q^{41} +(194.334 - 336.596i) q^{42} +(171.061 + 296.286i) q^{43} -364.466i q^{44} +(-104.773 + 60.4906i) q^{45} +(67.8793 - 39.1901i) q^{46} +133.468i q^{47} +(-82.5000 - 142.894i) q^{48} +(322.167 - 558.010i) q^{49} +(198.879 + 114.823i) q^{50} -129.424 q^{51} +(349.637 + 236.032i) q^{52} -438.454 q^{53} +(96.4093 + 55.6619i) q^{54} +(-272.182 + 471.433i) q^{55} +(64.7779 + 112.199i) q^{56} -80.9338i q^{57} +(-550.288 + 317.709i) q^{58} +(511.434 - 295.277i) q^{59} -362.944i q^{60} +(270.652 + 468.783i) q^{61} +(-635.516 + 1100.75i) q^{62} +(244.909 + 141.398i) q^{63} +631.000 q^{64} +(-275.985 - 566.413i) q^{65} +500.910 q^{66} +(-199.485 - 115.173i) q^{67} +(194.136 - 336.254i) q^{68} +(28.5150 + 49.3894i) q^{69} -1741.54i q^{70} +(-389.202 + 224.706i) q^{71} +(-32.1364 + 18.5540i) q^{72} -389.711i q^{73} +(89.7014 + 155.367i) q^{74} +(-83.5457 + 144.705i) q^{75} +(210.272 + 121.401i) q^{76} +1272.47 q^{77} +(-324.394 + 480.530i) q^{78} -897.820 q^{79} +(-640.279 - 369.665i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-98.6214 - 170.817i) q^{82} +1300.24i q^{83} +(-734.728 + 424.195i) q^{84} +(-502.228 + 289.961i) q^{85} -1410.60i q^{86} +(-231.167 - 400.393i) q^{87} +(-83.4850 + 144.600i) q^{88} +(801.113 + 462.523i) q^{89} +498.819 q^{90} +(-824.061 + 1220.69i) q^{91} -171.090 q^{92} +(-800.910 - 462.406i) q^{93} +(275.151 - 476.575i) q^{94} +(-181.324 - 314.062i) q^{95} +779.267i q^{96} +(1351.43 - 780.247i) q^{97} +(-2300.73 + 1328.33i) q^{98} +364.466i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 6 q^{3} + 18 q^{4} - 66 q^{7} - 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 6 q^{3} + 18 q^{4} - 66 q^{7} - 18 q^{9} - 68 q^{10} - 126 q^{11} + 108 q^{12} + 40 q^{13} + 204 q^{14} - 54 q^{15} + 110 q^{16} - 72 q^{17} + 222 q^{19} + 162 q^{20} + 34 q^{22} - 138 q^{23} + 120 q^{25} - 714 q^{26} - 108 q^{27} - 594 q^{28} - 6 q^{29} + 204 q^{30} - 378 q^{33} + 402 q^{35} + 162 q^{36} + 492 q^{37} + 612 q^{38} + 168 q^{39} - 136 q^{40} + 180 q^{41} + 306 q^{42} + 470 q^{43} - 162 q^{45} - 714 q^{46} - 330 q^{48} + 346 q^{49} + 1224 q^{50} - 432 q^{51} - 144 q^{52} - 2268 q^{53} - 446 q^{55} + 102 q^{56} - 2244 q^{58} + 2160 q^{59} - 160 q^{61} - 1428 q^{62} + 594 q^{63} + 2524 q^{64} - 804 q^{65} + 204 q^{66} - 498 q^{67} + 648 q^{68} + 414 q^{69} - 1314 q^{71} + 1530 q^{74} + 180 q^{75} + 1998 q^{76} + 2976 q^{77} - 612 q^{78} + 8 q^{79} - 990 q^{80} - 162 q^{81} + 34 q^{82} - 1782 q^{84} - 852 q^{85} + 18 q^{87} - 34 q^{88} - 252 q^{89} + 1224 q^{90} - 1668 q^{91} - 2484 q^{92} - 1404 q^{93} + 2686 q^{94} - 54 q^{95} - 336 q^{97} - 6732 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/39\mathbb{Z}\right)^\times\).

\(n\) \(14\) \(28\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.57071 2.06155i −1.26244 0.728869i −0.288892 0.957362i \(-0.593287\pi\)
−0.973546 + 0.228493i \(0.926620\pi\)
\(3\) 1.50000 2.59808i 0.288675 0.500000i
\(4\) 4.50000 + 7.79423i 0.562500 + 0.974279i
\(5\) 13.4424i 1.20232i −0.799128 0.601161i \(-0.794705\pi\)
0.799128 0.601161i \(-0.205295\pi\)
\(6\) −10.7121 + 6.18466i −0.728869 + 0.420813i
\(7\) −27.2121 + 15.7109i −1.46932 + 0.848311i −0.999408 0.0344037i \(-0.989047\pi\)
−0.469910 + 0.882715i \(0.655713\pi\)
\(8\) 4.12311i 0.182217i
\(9\) −4.50000 7.79423i −0.166667 0.288675i
\(10\) −27.7121 + 47.9988i −0.876335 + 1.51786i
\(11\) −35.0707 20.2481i −0.961293 0.555003i −0.0647219 0.997903i \(-0.520616\pi\)
−0.896571 + 0.442901i \(0.853949\pi\)
\(12\) 27.0000 0.649519
\(13\) 42.1364 20.5310i 0.898965 0.438021i
\(14\) 129.556 2.47323
\(15\) −34.9243 20.1635i −0.601161 0.347080i
\(16\) 27.5000 47.6314i 0.429688 0.744241i
\(17\) −21.5707 37.3616i −0.307745 0.533030i 0.670124 0.742249i \(-0.266241\pi\)
−0.977869 + 0.209219i \(0.932908\pi\)
\(18\) 37.1080i 0.485913i
\(19\) 23.3636 13.4890i 0.282104 0.162873i −0.352272 0.935898i \(-0.614591\pi\)
0.634375 + 0.773025i \(0.281257\pi\)
\(20\) 104.773 60.4906i 1.17140 0.676306i
\(21\) 94.2656i 0.979545i
\(22\) 83.4850 + 144.600i 0.809048 + 1.40131i
\(23\) −9.50500 + 16.4631i −0.0861709 + 0.149252i −0.905890 0.423514i \(-0.860796\pi\)
0.819719 + 0.572766i \(0.194130\pi\)
\(24\) −10.7121 6.18466i −0.0911086 0.0526016i
\(25\) −55.6971 −0.445577
\(26\) −192.783 13.5562i −1.45415 0.102253i
\(27\) −27.0000 −0.192450
\(28\) −244.909 141.398i −1.65298 0.954350i
\(29\) 77.0557 133.464i 0.493410 0.854611i −0.506561 0.862204i \(-0.669084\pi\)
0.999971 + 0.00759297i \(0.00241694\pi\)
\(30\) 83.1364 + 143.997i 0.505952 + 0.876335i
\(31\) 308.270i 1.78603i −0.450025 0.893016i \(-0.648585\pi\)
0.450025 0.893016i \(-0.351415\pi\)
\(32\) −224.955 + 129.878i −1.24271 + 0.717480i
\(33\) −105.212 + 60.7443i −0.555003 + 0.320431i
\(34\) 177.877i 0.897223i
\(35\) 211.192 + 365.796i 1.01994 + 1.76659i
\(36\) 40.5000 70.1481i 0.187500 0.324760i
\(37\) −37.6821 21.7558i −0.167430 0.0966657i 0.413944 0.910303i \(-0.364151\pi\)
−0.581373 + 0.813637i \(0.697484\pi\)
\(38\) −111.233 −0.474851
\(39\) 9.86357 140.270i 0.0404983 0.575928i
\(40\) −55.4243 −0.219084
\(41\) 41.4293 + 23.9192i 0.157809 + 0.0911110i 0.576825 0.816868i \(-0.304292\pi\)
−0.419016 + 0.907979i \(0.637625\pi\)
\(42\) 194.334 336.596i 0.713960 1.23662i
\(43\) 171.061 + 296.286i 0.606663 + 1.05077i 0.991786 + 0.127906i \(0.0408256\pi\)
−0.385123 + 0.922865i \(0.625841\pi\)
\(44\) 364.466i 1.24876i
\(45\) −104.773 + 60.4906i −0.347080 + 0.200387i
\(46\) 67.8793 39.1901i 0.217571 0.125615i
\(47\) 133.468i 0.414218i 0.978318 + 0.207109i \(0.0664055\pi\)
−0.978318 + 0.207109i \(0.933594\pi\)
\(48\) −82.5000 142.894i −0.248080 0.429688i
\(49\) 322.167 558.010i 0.939263 1.62685i
\(50\) 198.879 + 114.823i 0.562514 + 0.324767i
\(51\) −129.424 −0.355353
\(52\) 349.637 + 236.032i 0.932422 + 0.629455i
\(53\) −438.454 −1.13635 −0.568173 0.822909i \(-0.692350\pi\)
−0.568173 + 0.822909i \(0.692350\pi\)
\(54\) 96.4093 + 55.6619i 0.242956 + 0.140271i
\(55\) −272.182 + 471.433i −0.667291 + 1.15578i
\(56\) 64.7779 + 112.199i 0.154577 + 0.267735i
\(57\) 80.9338i 0.188069i
\(58\) −550.288 + 317.709i −1.24580 + 0.719262i
\(59\) 511.434 295.277i 1.12853 0.651555i 0.184963 0.982746i \(-0.440784\pi\)
0.943564 + 0.331190i \(0.107450\pi\)
\(60\) 362.944i 0.780931i
\(61\) 270.652 + 468.783i 0.568089 + 0.983960i 0.996755 + 0.0804965i \(0.0256506\pi\)
−0.428665 + 0.903463i \(0.641016\pi\)
\(62\) −635.516 + 1100.75i −1.30178 + 2.25476i
\(63\) 244.909 + 141.398i 0.489773 + 0.282770i
\(64\) 631.000 1.23242
\(65\) −275.985 566.413i −0.526642 1.08084i
\(66\) 500.910 0.934208
\(67\) −199.485 115.173i −0.363746 0.210009i 0.306977 0.951717i \(-0.400683\pi\)
−0.670723 + 0.741708i \(0.734016\pi\)
\(68\) 194.136 336.254i 0.346213 0.599659i
\(69\) 28.5150 + 49.3894i 0.0497508 + 0.0861709i
\(70\) 1741.54i 2.97362i
\(71\) −389.202 + 224.706i −0.650561 + 0.375601i −0.788671 0.614816i \(-0.789230\pi\)
0.138110 + 0.990417i \(0.455897\pi\)
\(72\) −32.1364 + 18.5540i −0.0526016 + 0.0303695i
\(73\) 389.711i 0.624826i −0.949946 0.312413i \(-0.898863\pi\)
0.949946 0.312413i \(-0.101137\pi\)
\(74\) 89.7014 + 155.367i 0.140913 + 0.244069i
\(75\) −83.5457 + 144.705i −0.128627 + 0.222789i
\(76\) 210.272 + 121.401i 0.317367 + 0.183232i
\(77\) 1272.47 1.88326
\(78\) −324.394 + 480.530i −0.470903 + 0.697556i
\(79\) −897.820 −1.27864 −0.639321 0.768940i \(-0.720784\pi\)
−0.639321 + 0.768940i \(0.720784\pi\)
\(80\) −640.279 369.665i −0.894816 0.516623i
\(81\) −40.5000 + 70.1481i −0.0555556 + 0.0962250i
\(82\) −98.6214 170.817i −0.132816 0.230044i
\(83\) 1300.24i 1.71952i 0.510700 + 0.859759i \(0.329386\pi\)
−0.510700 + 0.859759i \(0.670614\pi\)
\(84\) −734.728 + 424.195i −0.954350 + 0.550994i
\(85\) −502.228 + 289.961i −0.640874 + 0.370009i
\(86\) 1410.60i 1.76871i
\(87\) −231.167 400.393i −0.284870 0.493410i
\(88\) −83.4850 + 144.600i −0.101131 + 0.175164i
\(89\) 801.113 + 462.523i 0.954132 + 0.550869i 0.894362 0.447344i \(-0.147630\pi\)
0.0597703 + 0.998212i \(0.480963\pi\)
\(90\) 498.819 0.584223
\(91\) −824.061 + 1220.69i −0.949287 + 1.40619i
\(92\) −171.090 −0.193884
\(93\) −800.910 462.406i −0.893016 0.515583i
\(94\) 275.151 476.575i 0.301911 0.522925i
\(95\) −181.324 314.062i −0.195825 0.339179i
\(96\) 779.267i 0.828475i
\(97\) 1351.43 780.247i 1.41460 0.816722i 0.418787 0.908085i \(-0.362455\pi\)
0.995818 + 0.0913623i \(0.0291221\pi\)
\(98\) −2300.73 + 1328.33i −2.37152 + 1.36920i
\(99\) 364.466i 0.370002i
\(100\) −250.637 434.116i −0.250637 0.434116i
\(101\) 479.420 830.380i 0.472318 0.818078i −0.527181 0.849753i \(-0.676751\pi\)
0.999498 + 0.0316752i \(0.0100842\pi\)
\(102\) 462.137 + 266.815i 0.448612 + 0.259006i
\(103\) −635.153 −0.607606 −0.303803 0.952735i \(-0.598257\pi\)
−0.303803 + 0.952735i \(0.598257\pi\)
\(104\) −84.6514 173.733i −0.0798150 0.163807i
\(105\) 1267.15 1.17773
\(106\) 1565.59 + 903.897i 1.43457 + 0.828247i
\(107\) 724.162 1254.29i 0.654275 1.13324i −0.327800 0.944747i \(-0.606307\pi\)
0.982075 0.188490i \(-0.0603593\pi\)
\(108\) −121.500 210.444i −0.108253 0.187500i
\(109\) 331.084i 0.290937i 0.989363 + 0.145468i \(0.0464689\pi\)
−0.989363 + 0.145468i \(0.953531\pi\)
\(110\) 1943.77 1122.24i 1.68483 0.972736i
\(111\) −113.046 + 65.2674i −0.0966657 + 0.0558100i
\(112\) 1728.20i 1.45803i
\(113\) −347.602 602.065i −0.289378 0.501217i 0.684284 0.729216i \(-0.260115\pi\)
−0.973661 + 0.227999i \(0.926782\pi\)
\(114\) −166.849 + 288.991i −0.137078 + 0.237426i
\(115\) 221.304 + 127.770i 0.179449 + 0.103605i
\(116\) 1387.00 1.11017
\(117\) −349.637 236.032i −0.276273 0.186505i
\(118\) −2434.91 −1.89959
\(119\) 1173.97 + 677.792i 0.904351 + 0.522127i
\(120\) −83.1364 + 143.997i −0.0632440 + 0.109542i
\(121\) 154.470 + 267.550i 0.116056 + 0.201014i
\(122\) 2231.85i 1.65625i
\(123\) 124.288 71.7576i 0.0911110 0.0526030i
\(124\) 2402.73 1387.22i 1.74009 1.00464i
\(125\) 931.594i 0.666595i
\(126\) −583.001 1009.79i −0.412205 0.713960i
\(127\) 123.577 214.042i 0.0863441 0.149552i −0.819619 0.572909i \(-0.805815\pi\)
0.905963 + 0.423357i \(0.139148\pi\)
\(128\) −453.481 261.817i −0.313144 0.180794i
\(129\) 1026.36 0.700514
\(130\) −182.227 + 2591.46i −0.122941 + 1.74835i
\(131\) 472.243 0.314962 0.157481 0.987522i \(-0.449663\pi\)
0.157481 + 0.987522i \(0.449663\pi\)
\(132\) −946.909 546.698i −0.624378 0.360485i
\(133\) −423.849 + 734.127i −0.276333 + 0.478623i
\(134\) 474.869 + 822.498i 0.306138 + 0.530246i
\(135\) 362.944i 0.231387i
\(136\) −154.046 + 88.9383i −0.0971273 + 0.0560765i
\(137\) −1585.43 + 915.349i −0.988704 + 0.570829i −0.904887 0.425652i \(-0.860045\pi\)
−0.0838175 + 0.996481i \(0.526711\pi\)
\(138\) 235.141i 0.145047i
\(139\) 50.0000 + 86.6025i 0.0305104 + 0.0528456i 0.880877 0.473344i \(-0.156953\pi\)
−0.850367 + 0.526190i \(0.823620\pi\)
\(140\) −1900.73 + 3292.16i −1.14744 + 1.98742i
\(141\) 346.759 + 200.202i 0.207109 + 0.119575i
\(142\) 1852.97 1.09506
\(143\) −1893.47 133.146i −1.10727 0.0778615i
\(144\) −495.000 −0.286458
\(145\) −1794.08 1035.81i −1.02752 0.593237i
\(146\) −803.411 + 1391.55i −0.455416 + 0.788804i
\(147\) −966.501 1674.03i −0.542284 0.939263i
\(148\) 391.604i 0.217498i
\(149\) −129.520 + 74.7784i −0.0712127 + 0.0411147i −0.535184 0.844736i \(-0.679758\pi\)
0.463971 + 0.885850i \(0.346424\pi\)
\(150\) 596.636 344.468i 0.324767 0.187505i
\(151\) 800.032i 0.431163i −0.976486 0.215582i \(-0.930835\pi\)
0.976486 0.215582i \(-0.0691647\pi\)
\(152\) −55.6164 96.3305i −0.0296782 0.0514042i
\(153\) −194.136 + 336.254i −0.102582 + 0.177677i
\(154\) −4543.61 2623.26i −2.37750 1.37265i
\(155\) −4143.88 −2.14739
\(156\) 1137.68 554.337i 0.583895 0.284503i
\(157\) −2706.16 −1.37564 −0.687818 0.725884i \(-0.741431\pi\)
−0.687818 + 0.725884i \(0.741431\pi\)
\(158\) 3205.86 + 1850.90i 1.61421 + 0.931962i
\(159\) −657.681 + 1139.14i −0.328035 + 0.568173i
\(160\) 1745.86 + 3023.93i 0.862642 + 1.49414i
\(161\) 597.330i 0.292399i
\(162\) 289.228 166.986i 0.140271 0.0809854i
\(163\) 3185.46 1839.12i 1.53070 0.883750i 0.531371 0.847139i \(-0.321677\pi\)
0.999330 0.0366108i \(-0.0116562\pi\)
\(164\) 430.546i 0.205000i
\(165\) 816.546 + 1414.30i 0.385261 + 0.667291i
\(166\) 2680.52 4642.79i 1.25330 2.17079i
\(167\) 2791.30 + 1611.56i 1.29339 + 0.746742i 0.979254 0.202635i \(-0.0649504\pi\)
0.314140 + 0.949377i \(0.398284\pi\)
\(168\) 388.667 0.178490
\(169\) 1353.96 1730.20i 0.616275 0.787531i
\(170\) 2391.08 1.07875
\(171\) −210.272 121.401i −0.0940346 0.0542909i
\(172\) −1539.55 + 2666.57i −0.682496 + 1.18212i
\(173\) −1344.77 2329.21i −0.590988 1.02362i −0.994100 0.108471i \(-0.965405\pi\)
0.403111 0.915151i \(-0.367929\pi\)
\(174\) 1906.25i 0.830533i
\(175\) 1515.64 875.054i 0.654694 0.377988i
\(176\) −1928.89 + 1113.64i −0.826111 + 0.476955i
\(177\) 1771.66i 0.752351i
\(178\) −1907.03 3303.07i −0.803022 1.39088i
\(179\) −762.021 + 1319.86i −0.318191 + 0.551122i −0.980111 0.198452i \(-0.936409\pi\)
0.661920 + 0.749574i \(0.269742\pi\)
\(180\) −942.956 544.416i −0.390465 0.225435i
\(181\) −476.881 −0.195836 −0.0979180 0.995194i \(-0.531218\pi\)
−0.0979180 + 0.995194i \(0.531218\pi\)
\(182\) 5459.01 2659.91i 2.22335 1.08333i
\(183\) 1623.91 0.655973
\(184\) 67.8793 + 39.1901i 0.0271963 + 0.0157018i
\(185\) −292.449 + 506.537i −0.116223 + 0.201305i
\(186\) 1906.55 + 3302.24i 0.751585 + 1.30178i
\(187\) 1747.06i 0.683197i
\(188\) −1040.28 + 600.605i −0.403564 + 0.232998i
\(189\) 734.728 424.195i 0.282770 0.163258i
\(190\) 1495.23i 0.570924i
\(191\) 684.871 + 1186.23i 0.259453 + 0.449386i 0.966096 0.258185i \(-0.0831243\pi\)
−0.706642 + 0.707571i \(0.749791\pi\)
\(192\) 946.500 1639.39i 0.355770 0.616211i
\(193\) 1857.38 + 1072.36i 0.692732 + 0.399949i 0.804635 0.593770i \(-0.202361\pi\)
−0.111903 + 0.993719i \(0.535695\pi\)
\(194\) −6434.08 −2.38113
\(195\) −1885.56 132.590i −0.692451 0.0486920i
\(196\) 5799.01 2.11334
\(197\) −207.620 119.869i −0.0750879 0.0433520i 0.461986 0.886887i \(-0.347137\pi\)
−0.537074 + 0.843535i \(0.680470\pi\)
\(198\) 751.365 1301.40i 0.269683 0.467104i
\(199\) −794.969 1376.93i −0.283185 0.490491i 0.688982 0.724778i \(-0.258058\pi\)
−0.972167 + 0.234287i \(0.924724\pi\)
\(200\) 229.645i 0.0811918i
\(201\) −598.455 + 345.518i −0.210009 + 0.121249i
\(202\) −3423.74 + 1976.70i −1.19254 + 0.688515i
\(203\) 4842.47i 1.67426i
\(204\) −582.409 1008.76i −0.199886 0.346213i
\(205\) 321.531 556.908i 0.109545 0.189737i
\(206\) 2267.95 + 1309.40i 0.767066 + 0.442866i
\(207\) 171.090 0.0574472
\(208\) 180.832 2571.62i 0.0602810 0.857258i
\(209\) −1092.50 −0.361579
\(210\) −4524.64 2612.30i −1.48681 0.858410i
\(211\) 936.427 1621.94i 0.305527 0.529189i −0.671851 0.740686i \(-0.734501\pi\)
0.977379 + 0.211497i \(0.0678339\pi\)
\(212\) −1973.04 3417.41i −0.639195 1.10712i
\(213\) 1348.24i 0.433707i
\(214\) −5171.55 + 2985.80i −1.65196 + 0.953761i
\(215\) 3982.78 2299.46i 1.26337 0.729404i
\(216\) 111.324i 0.0350677i
\(217\) 4843.22 + 8388.70i 1.51511 + 2.62425i
\(218\) 682.547 1182.21i 0.212055 0.367290i
\(219\) −1012.50 584.567i −0.312413 0.180372i
\(220\) −4899.28 −1.50141
\(221\) −1675.98 1131.42i −0.510130 0.344377i
\(222\) 538.209 0.162713
\(223\) −48.6085 28.0642i −0.0145967 0.00842742i 0.492684 0.870208i \(-0.336016\pi\)
−0.507281 + 0.861781i \(0.669349\pi\)
\(224\) 4081.00 7068.51i 1.21729 2.10841i
\(225\) 250.637 + 434.116i 0.0742629 + 0.128627i
\(226\) 2866.40i 0.843673i
\(227\) 577.976 333.695i 0.168994 0.0975687i −0.413117 0.910678i \(-0.635560\pi\)
0.582111 + 0.813109i \(0.302227\pi\)
\(228\) 630.816 364.202i 0.183232 0.105789i
\(229\) 723.299i 0.208720i 0.994540 + 0.104360i \(0.0332795\pi\)
−0.994540 + 0.104360i \(0.966721\pi\)
\(230\) −526.808 912.458i −0.151029 0.261590i
\(231\) 1908.70 3305.96i 0.543650 0.941629i
\(232\) −550.288 317.709i −0.155725 0.0899078i
\(233\) 275.451 0.0774482 0.0387241 0.999250i \(-0.487671\pi\)
0.0387241 + 0.999250i \(0.487671\pi\)
\(234\) 761.863 + 1563.60i 0.212840 + 0.436818i
\(235\) 1794.12 0.498024
\(236\) 4602.91 + 2657.49i 1.26959 + 0.733000i
\(237\) −1346.73 + 2332.60i −0.369112 + 0.639321i
\(238\) −2794.61 4840.41i −0.761124 1.31831i
\(239\) 1529.39i 0.413925i 0.978349 + 0.206963i \(0.0663579\pi\)
−0.978349 + 0.206963i \(0.933642\pi\)
\(240\) −1920.84 + 1109.00i −0.516623 + 0.298272i
\(241\) 844.830 487.763i 0.225810 0.130372i −0.382827 0.923820i \(-0.625050\pi\)
0.608638 + 0.793448i \(0.291716\pi\)
\(242\) 1273.79i 0.338357i
\(243\) 121.500 + 210.444i 0.0320750 + 0.0555556i
\(244\) −2435.87 + 4219.05i −0.639101 + 1.10695i
\(245\) −7500.97 4330.69i −1.95600 1.12930i
\(246\) −591.729 −0.153363
\(247\) 707.516 1048.05i 0.182260 0.269984i
\(248\) −1271.03 −0.325446
\(249\) 3378.13 + 1950.36i 0.859759 + 0.496382i
\(250\) −1920.53 + 3326.46i −0.485860 + 0.841534i
\(251\) −937.070 1623.05i −0.235647 0.408152i 0.723814 0.689995i \(-0.242387\pi\)
−0.959460 + 0.281843i \(0.909054\pi\)
\(252\) 2545.17i 0.636233i
\(253\) 666.694 384.916i 0.165671 0.0956501i
\(254\) −882.517 + 509.522i −0.218008 + 0.125867i
\(255\) 1739.77i 0.427249i
\(256\) −1444.50 2501.95i −0.352661 0.610827i
\(257\) −909.094 + 1574.60i −0.220653 + 0.382181i −0.955006 0.296586i \(-0.904152\pi\)
0.734354 + 0.678767i \(0.237485\pi\)
\(258\) −3664.85 2115.90i −0.884356 0.510583i
\(259\) 1367.22 0.328010
\(260\) 3172.82 4699.95i 0.756808 1.12107i
\(261\) −1387.00 −0.328940
\(262\) −1686.24 973.554i −0.397620 0.229566i
\(263\) −336.899 + 583.527i −0.0789890 + 0.136813i −0.902814 0.430031i \(-0.858503\pi\)
0.823825 + 0.566844i \(0.191836\pi\)
\(264\) 250.455 + 433.801i 0.0583880 + 0.101131i
\(265\) 5893.86i 1.36625i
\(266\) 3026.88 1747.57i 0.697707 0.402822i
\(267\) 2403.34 1387.57i 0.550869 0.318044i
\(268\) 2073.11i 0.472520i
\(269\) 1678.20 + 2906.73i 0.380378 + 0.658834i 0.991116 0.132998i \(-0.0424605\pi\)
−0.610738 + 0.791833i \(0.709127\pi\)
\(270\) 748.228 1295.97i 0.168651 0.292112i
\(271\) −7721.09 4457.77i −1.73071 0.999227i −0.885013 0.465567i \(-0.845850\pi\)
−0.845699 0.533660i \(-0.820816\pi\)
\(272\) −2372.78 −0.528937
\(273\) 1935.37 + 3972.02i 0.429061 + 0.880577i
\(274\) 7548.16 1.66424
\(275\) 1953.34 + 1127.76i 0.428330 + 0.247296i
\(276\) −256.635 + 444.505i −0.0559696 + 0.0969422i
\(277\) 2008.65 + 3479.09i 0.435698 + 0.754651i 0.997352 0.0727208i \(-0.0231682\pi\)
−0.561654 + 0.827372i \(0.689835\pi\)
\(278\) 412.311i 0.0889523i
\(279\) −2402.73 + 1387.22i −0.515583 + 0.297672i
\(280\) 1508.21 870.768i 0.321904 0.185851i
\(281\) 1841.12i 0.390860i 0.980718 + 0.195430i \(0.0626103\pi\)
−0.980718 + 0.195430i \(0.937390\pi\)
\(282\) −825.452 1429.73i −0.174308 0.301911i
\(283\) 2424.70 4199.70i 0.509305 0.882143i −0.490637 0.871364i \(-0.663236\pi\)
0.999942 0.0107784i \(-0.00343094\pi\)
\(284\) −3502.82 2022.35i −0.731881 0.422551i
\(285\) −1087.94 −0.226120
\(286\) 6486.55 + 4378.91i 1.34111 + 0.905351i
\(287\) −1503.17 −0.309162
\(288\) 2024.59 + 1168.90i 0.414238 + 0.239160i
\(289\) 1525.91 2642.95i 0.310586 0.537951i
\(290\) 4270.76 + 7397.17i 0.864785 + 1.49785i
\(291\) 4681.48i 0.943070i
\(292\) 3037.50 1753.70i 0.608754 0.351464i
\(293\) −1224.43 + 706.927i −0.244137 + 0.140953i −0.617077 0.786903i \(-0.711683\pi\)
0.372940 + 0.927856i \(0.378350\pi\)
\(294\) 7969.97i 1.58101i
\(295\) −3969.22 6874.89i −0.783379 1.35685i
\(296\) −89.7014 + 155.367i −0.0176142 + 0.0305086i
\(297\) 946.909 + 546.698i 0.185001 + 0.106810i
\(298\) 616.639 0.119869
\(299\) −62.5022 + 888.845i −0.0120889 + 0.171917i
\(300\) −1503.82 −0.289411
\(301\) −9309.86 5375.05i −1.78276 1.02928i
\(302\) −1649.31 + 2856.68i −0.314262 + 0.544317i
\(303\) −1438.26 2491.14i −0.272693 0.472318i
\(304\) 1483.79i 0.279937i
\(305\) 6301.55 3638.20i 1.18304 0.683026i
\(306\) 1386.41 800.445i 0.259006 0.149537i
\(307\) 4625.64i 0.859932i −0.902845 0.429966i \(-0.858526\pi\)
0.902845 0.429966i \(-0.141474\pi\)
\(308\) 5726.10 + 9917.89i 1.05933 + 1.83482i
\(309\) −952.729 + 1650.18i −0.175401 + 0.303803i
\(310\) 14796.6 + 8542.83i 2.71094 + 1.56516i
\(311\) 6060.79 1.10507 0.552534 0.833490i \(-0.313661\pi\)
0.552534 + 0.833490i \(0.313661\pi\)
\(312\) −578.349 40.6685i −0.104944 0.00737950i
\(313\) 969.946 0.175158 0.0875792 0.996158i \(-0.472087\pi\)
0.0875792 + 0.996158i \(0.472087\pi\)
\(314\) 9662.91 + 5578.88i 1.73665 + 1.00266i
\(315\) 1900.73 3292.16i 0.339981 0.588864i
\(316\) −4040.19 6997.81i −0.719236 1.24575i
\(317\) 8741.63i 1.54883i −0.632679 0.774414i \(-0.718045\pi\)
0.632679 0.774414i \(-0.281955\pi\)
\(318\) 4696.78 2711.69i 0.828247 0.478189i
\(319\) −5404.80 + 3120.46i −0.948623 + 0.547687i
\(320\) 8482.13i 1.48177i
\(321\) −2172.49 3762.86i −0.377746 0.654275i
\(322\) −1231.43 + 2132.89i −0.213120 + 0.369135i
\(323\) −1007.94 581.933i −0.173632 0.100247i
\(324\) −729.000 −0.125000
\(325\) −2346.88 + 1143.52i −0.400558 + 0.195172i
\(326\) −15165.8 −2.57655
\(327\) 860.181 + 496.626i 0.145468 + 0.0839862i
\(328\) 98.6214 170.817i 0.0166020 0.0287555i
\(329\) −2096.90 3631.94i −0.351386 0.608618i
\(330\) 6733.41i 1.12322i
\(331\) −6051.57 + 3493.88i −1.00491 + 0.580184i −0.909697 0.415273i \(-0.863686\pi\)
−0.0952114 + 0.995457i \(0.530353\pi\)
\(332\) −10134.4 + 5851.09i −1.67529 + 0.967229i
\(333\) 391.604i 0.0644438i
\(334\) −6644.61 11508.8i −1.08855 1.88543i
\(335\) −1548.19 + 2681.55i −0.252498 + 0.437339i
\(336\) 4490.00 + 2592.30i 0.729017 + 0.420898i
\(337\) 4156.59 0.671881 0.335940 0.941883i \(-0.390946\pi\)
0.335940 + 0.941883i \(0.390946\pi\)
\(338\) −8401.50 + 3386.81i −1.35202 + 0.545025i
\(339\) −2085.61 −0.334144
\(340\) −4520.05 2609.65i −0.720983 0.416260i
\(341\) −6241.89 + 10811.3i −0.991252 + 1.71690i
\(342\) 500.548 + 866.974i 0.0791419 + 0.137078i
\(343\) 9468.49i 1.49053i
\(344\) 1221.62 705.301i 0.191469 0.110544i
\(345\) 663.911 383.309i 0.103605 0.0598164i
\(346\) 11089.3i 1.72301i
\(347\) 156.256 + 270.644i 0.0241737 + 0.0418701i 0.877859 0.478919i \(-0.158971\pi\)
−0.853685 + 0.520789i \(0.825638\pi\)
\(348\) 2080.50 3603.54i 0.320479 0.555086i
\(349\) 3861.39 + 2229.37i 0.592251 + 0.341936i 0.765987 0.642856i \(-0.222251\pi\)
−0.173736 + 0.984792i \(0.555584\pi\)
\(350\) −7215.88 −1.10201
\(351\) −1137.68 + 554.337i −0.173006 + 0.0842972i
\(352\) 10519.1 1.59281
\(353\) −1947.84 1124.59i −0.293692 0.169563i 0.345914 0.938266i \(-0.387569\pi\)
−0.639605 + 0.768703i \(0.720902\pi\)
\(354\) −3652.37 + 6326.09i −0.548365 + 0.949797i
\(355\) 3020.58 + 5231.80i 0.451594 + 0.782183i
\(356\) 8325.41i 1.23945i
\(357\) 3521.91 2033.38i 0.522127 0.301450i
\(358\) 5441.92 3141.89i 0.803392 0.463838i
\(359\) 7842.79i 1.15300i −0.817098 0.576499i \(-0.804418\pi\)
0.817098 0.576499i \(-0.195582\pi\)
\(360\) 249.409 + 431.990i 0.0365140 + 0.0632440i
\(361\) −3065.60 + 5309.77i −0.446945 + 0.774131i
\(362\) 1702.81 + 983.116i 0.247231 + 0.142739i
\(363\) 926.820 0.134009
\(364\) −13222.7 929.796i −1.90400 0.133886i
\(365\) −5238.64 −0.751241
\(366\) −5798.53 3347.78i −0.828126 0.478118i
\(367\) −3330.12 + 5767.94i −0.473653 + 0.820392i −0.999545 0.0301597i \(-0.990398\pi\)
0.525892 + 0.850552i \(0.323732\pi\)
\(368\) 522.775 + 905.473i 0.0740531 + 0.128264i
\(369\) 430.546i 0.0607407i
\(370\) 2088.51 1205.80i 0.293449 0.169423i
\(371\) 11931.3 6888.53i 1.66965 0.963975i
\(372\) 8323.30i 1.16006i
\(373\) 18.4936 + 32.0319i 0.00256720 + 0.00444651i 0.867306 0.497775i \(-0.165850\pi\)
−0.864739 + 0.502222i \(0.832516\pi\)
\(374\) 3601.66 6238.26i 0.497961 0.862494i
\(375\) −2420.35 1397.39i −0.333297 0.192429i
\(376\) 550.301 0.0754777
\(377\) 506.696 7205.74i 0.0692207 0.984389i
\(378\) −3498.00 −0.475973
\(379\) 10461.5 + 6039.93i 1.41786 + 0.818603i 0.996111 0.0881092i \(-0.0280825\pi\)
0.421751 + 0.906712i \(0.361416\pi\)
\(380\) 1631.91 2826.55i 0.220303 0.381577i
\(381\) −370.731 642.126i −0.0498508 0.0863441i
\(382\) 5647.59i 0.756429i
\(383\) 9151.63 5283.69i 1.22096 0.704919i 0.255835 0.966721i \(-0.417650\pi\)
0.965122 + 0.261801i \(0.0843164\pi\)
\(384\) −1360.44 + 785.452i −0.180794 + 0.104381i
\(385\) 17104.9i 2.26428i
\(386\) −4421.45 7658.18i −0.583021 1.00982i
\(387\) 1539.55 2666.57i 0.202221 0.350257i
\(388\) 12162.8 + 7022.22i 1.59143 + 0.918813i
\(389\) 9757.49 1.27179 0.635893 0.771778i \(-0.280632\pi\)
0.635893 + 0.771778i \(0.280632\pi\)
\(390\) 6459.46 + 4360.63i 0.838686 + 0.566177i
\(391\) 820.119 0.106075
\(392\) −2300.73 1328.33i −0.296440 0.171150i
\(393\) 708.364 1226.92i 0.0909218 0.157481i
\(394\) 494.234 + 856.039i 0.0631959 + 0.109458i
\(395\) 12068.8i 1.53734i
\(396\) −2840.73 + 1640.09i −0.360485 + 0.208126i
\(397\) −12298.0 + 7100.26i −1.55471 + 0.897612i −0.556962 + 0.830538i \(0.688033\pi\)
−0.997748 + 0.0670737i \(0.978634\pi\)
\(398\) 6555.48i 0.825620i
\(399\) 1271.55 + 2202.38i 0.159541 + 0.276333i
\(400\) −1531.67 + 2652.93i −0.191459 + 0.331617i
\(401\) 10978.1 + 6338.19i 1.36713 + 0.789313i 0.990561 0.137076i \(-0.0437705\pi\)
0.376569 + 0.926389i \(0.377104\pi\)
\(402\) 2849.22 0.353497
\(403\) −6329.10 12989.4i −0.782319 1.60558i
\(404\) 8629.56 1.06271
\(405\) 942.956 + 544.416i 0.115693 + 0.0667956i
\(406\) 9983.01 17291.1i 1.22032 2.11365i
\(407\) 881.026 + 1525.98i 0.107299 + 0.185848i
\(408\) 533.630i 0.0647515i
\(409\) −1328.20 + 766.838i −0.160576 + 0.0927083i −0.578134 0.815942i \(-0.696219\pi\)
0.417559 + 0.908650i \(0.362886\pi\)
\(410\) −2296.19 + 1325.71i −0.276587 + 0.159688i
\(411\) 5492.09i 0.659136i
\(412\) −2858.19 4950.53i −0.341779 0.591978i
\(413\) −9278.15 + 16070.2i −1.10544 + 1.91468i
\(414\) −610.914 352.711i −0.0725236 0.0418715i
\(415\) 17478.3 2.06741
\(416\) −6812.28 + 10091.1i −0.802883 + 1.18932i
\(417\) 300.000 0.0352304
\(418\) 3901.02 + 2252.25i 0.456471 + 0.263544i
\(419\) 1082.95 1875.72i 0.126266 0.218699i −0.795961 0.605348i \(-0.793034\pi\)
0.922227 + 0.386649i \(0.126367\pi\)
\(420\) 5702.19 + 9876.48i 0.662472 + 1.14744i
\(421\) 734.575i 0.0850380i −0.999096 0.0425190i \(-0.986462\pi\)
0.999096 0.0425190i \(-0.0135383\pi\)
\(422\) −6687.43 + 3860.99i −0.771419 + 0.445379i
\(423\) 1040.28 600.605i 0.119575 0.0690364i
\(424\) 1807.79i 0.207062i
\(425\) 1201.43 + 2080.93i 0.137124 + 0.237506i
\(426\) 2779.46 4814.16i 0.316116 0.547528i
\(427\) −14730.0 8504.40i −1.66941 0.963833i
\(428\) 13034.9 1.47212
\(429\) −3186.12 + 4719.66i −0.358572 + 0.531159i
\(430\) −18961.8 −2.12656
\(431\) −11872.6 6854.66i −1.32688 0.766073i −0.342061 0.939678i \(-0.611125\pi\)
−0.984815 + 0.173605i \(0.944458\pi\)
\(432\) −742.500 + 1286.05i −0.0826934 + 0.143229i
\(433\) 5024.97 + 8703.50i 0.557701 + 0.965967i 0.997688 + 0.0679624i \(0.0216498\pi\)
−0.439987 + 0.898004i \(0.645017\pi\)
\(434\) 39938.2i 4.41727i
\(435\) −5382.23 + 3107.43i −0.593237 + 0.342506i
\(436\) −2580.54 + 1489.88i −0.283453 + 0.163652i
\(437\) 512.850i 0.0561395i
\(438\) 2410.23 + 4174.64i 0.262935 + 0.455416i
\(439\) −4066.73 + 7043.79i −0.442129 + 0.765790i −0.997847 0.0655807i \(-0.979110\pi\)
0.555718 + 0.831371i \(0.312443\pi\)
\(440\) 1943.77 + 1122.24i 0.210604 + 0.121592i
\(441\) −5799.01 −0.626175
\(442\) 3651.98 + 7495.09i 0.393003 + 0.806572i
\(443\) −2370.78 −0.254264 −0.127132 0.991886i \(-0.540577\pi\)
−0.127132 + 0.991886i \(0.540577\pi\)
\(444\) −1017.42 587.406i −0.108749 0.0627862i
\(445\) 6217.40 10768.9i 0.662321 1.14717i
\(446\) 115.711 + 200.418i 0.0122850 + 0.0212782i
\(447\) 448.670i 0.0474751i
\(448\) −17170.9 + 9913.60i −1.81082 + 1.04548i
\(449\) 11191.8 6461.60i 1.17634 0.679158i 0.221172 0.975235i \(-0.429012\pi\)
0.955164 + 0.296077i \(0.0956785\pi\)
\(450\) 2066.81i 0.216512i
\(451\) −968.636 1677.73i −0.101134 0.175169i
\(452\) 3128.42 5418.58i 0.325550 0.563869i
\(453\) −2078.54 1200.05i −0.215582 0.124466i
\(454\) −2751.72 −0.284459
\(455\) 16409.0 + 11077.3i 1.69070 + 1.14135i
\(456\) −333.699 −0.0342694
\(457\) 7275.71 + 4200.63i 0.744734 + 0.429972i 0.823788 0.566898i \(-0.191857\pi\)
−0.0790543 + 0.996870i \(0.525190\pi\)
\(458\) 1491.12 2582.70i 0.152130 0.263497i
\(459\) 582.409 + 1008.76i 0.0592256 + 0.102582i
\(460\) 2299.85i 0.233111i
\(461\) −15265.7 + 8813.67i −1.54229 + 0.890441i −0.543596 + 0.839347i \(0.682937\pi\)
−0.998694 + 0.0510940i \(0.983729\pi\)
\(462\) −13630.8 + 7869.77i −1.37265 + 0.792499i
\(463\) 5461.81i 0.548233i −0.961697 0.274116i \(-0.911615\pi\)
0.961697 0.274116i \(-0.0883853\pi\)
\(464\) −4238.06 7340.54i −0.424024 0.734431i
\(465\) −6215.82 + 10766.1i −0.619897 + 1.07369i
\(466\) −983.558 567.858i −0.0977735 0.0564496i
\(467\) −8262.19 −0.818691 −0.409345 0.912379i \(-0.634243\pi\)
−0.409345 + 0.912379i \(0.634243\pi\)
\(468\) 266.316 3787.29i 0.0263044 0.374076i
\(469\) 7237.89 0.712611
\(470\) −6406.29 3698.68i −0.628724 0.362994i
\(471\) −4059.23 + 7030.80i −0.397112 + 0.687818i
\(472\) −1217.46 2108.70i −0.118725 0.205637i
\(473\) 13854.6i 1.34680i
\(474\) 9617.58 5552.71i 0.931962 0.538068i
\(475\) −1301.28 + 751.297i −0.125699 + 0.0725723i
\(476\) 12200.3i 1.17479i
\(477\) 1973.04 + 3417.41i 0.189391 + 0.328035i
\(478\) 3152.92 5461.02i 0.301697 0.522555i
\(479\) 1364.74 + 787.935i 0.130181 + 0.0751601i 0.563676 0.825996i \(-0.309387\pi\)
−0.433495 + 0.901156i \(0.642720\pi\)
\(480\) 10475.2 0.996093
\(481\) −2034.46 143.060i −0.192855 0.0135613i
\(482\) −4022.20 −0.380095
\(483\) −1551.91 895.995i −0.146199 0.0844082i
\(484\) −1390.23 + 2407.95i −0.130563 + 0.226141i
\(485\) −10488.4 18166.4i −0.981963 1.70081i
\(486\) 1001.91i 0.0935139i
\(487\) 10908.2 6297.84i 1.01498 0.586001i 0.102337 0.994750i \(-0.467368\pi\)
0.912647 + 0.408749i \(0.134035\pi\)
\(488\) 1932.84 1115.93i 0.179294 0.103516i
\(489\) 11034.7i 1.02047i
\(490\) 17855.9 + 30927.3i 1.64622 + 2.85133i
\(491\) −535.606 + 927.697i −0.0492293 + 0.0852676i −0.889590 0.456760i \(-0.849010\pi\)
0.840361 + 0.542028i \(0.182343\pi\)
\(492\) 1118.59 + 645.819i 0.102500 + 0.0591784i
\(493\) −6648.59 −0.607378
\(494\) −4686.96 + 2283.72i −0.426875 + 0.207995i
\(495\) 4899.28 0.444861
\(496\) −14683.3 8477.44i −1.32924 0.767436i
\(497\) 7060.68 12229.5i 0.637253 1.10376i
\(498\) −8041.55 13928.4i −0.723595 1.25330i
\(499\) 1422.30i 0.127597i 0.997963 + 0.0637985i \(0.0203215\pi\)
−0.997963 + 0.0637985i \(0.979678\pi\)
\(500\) 7261.06 4192.17i 0.649449 0.374959i
\(501\) 8373.89 4834.67i 0.746742 0.431132i
\(502\) 7727.28i 0.687022i
\(503\) 4674.67 + 8096.76i 0.414380 + 0.717727i 0.995363 0.0961884i \(-0.0306651\pi\)
−0.580983 + 0.813916i \(0.697332\pi\)
\(504\) 583.001 1009.79i 0.0515256 0.0892450i
\(505\) −11162.3 6444.54i −0.983593 0.567878i
\(506\) −3174.10 −0.278866
\(507\) −2464.27 6112.99i −0.215862 0.535478i
\(508\) 2224.39 0.194274
\(509\) 11896.0 + 6868.15i 1.03591 + 0.598086i 0.918673 0.395018i \(-0.129262\pi\)
0.117241 + 0.993103i \(0.462595\pi\)
\(510\) 3586.62 6212.22i 0.311409 0.539376i
\(511\) 6122.73 + 10604.9i 0.530046 + 0.918067i
\(512\) 16100.7i 1.38976i
\(513\) −630.816 + 364.202i −0.0542909 + 0.0313449i
\(514\) 6492.23 3748.29i 0.557120 0.321654i
\(515\) 8537.96i 0.730538i
\(516\) 4618.64 + 7999.72i 0.394039 + 0.682496i
\(517\) 2702.47 4680.81i 0.229892 0.398185i
\(518\) −4881.94 2818.59i −0.414093 0.239076i
\(519\) −8068.62 −0.682414
\(520\) −2335.38 + 1137.92i −0.196949 + 0.0959632i
\(521\) 11052.3 0.929386 0.464693 0.885472i \(-0.346165\pi\)
0.464693 + 0.885472i \(0.346165\pi\)
\(522\) 4952.59 + 2859.38i 0.415266 + 0.239754i
\(523\) −3238.52 + 5609.28i −0.270766 + 0.468980i −0.969058 0.246832i \(-0.920610\pi\)
0.698292 + 0.715813i \(0.253944\pi\)
\(524\) 2125.09 + 3680.77i 0.177166 + 0.306861i
\(525\) 5250.33i 0.436463i
\(526\) 2405.94 1389.07i 0.199437 0.115145i
\(527\) −11517.5 + 6649.61i −0.952009 + 0.549643i
\(528\) 6681.87i 0.550741i
\(529\) 5902.81 + 10224.0i 0.485149 + 0.840303i
\(530\) 12150.5 21045.3i 0.995819 1.72481i
\(531\) −4602.91 2657.49i −0.376176 0.217185i
\(532\) −7629.27 −0.621750
\(533\) 2236.77 + 157.286i 0.181773 + 0.0127820i
\(534\) −11442.2 −0.927250
\(535\) −16860.6 9734.45i −1.36252 0.786649i
\(536\) −474.869 + 822.498i −0.0382672 + 0.0662808i
\(537\) 2286.06 + 3959.58i 0.183707 + 0.318191i
\(538\) 13838.8i 1.10898i
\(539\) −22597.3 + 13046.5i −1.80581 + 1.04259i
\(540\) −2828.87 + 1633.25i −0.225435 + 0.130155i
\(541\) 18341.5i 1.45761i 0.684723 + 0.728803i \(0.259923\pi\)
−0.684723 + 0.728803i \(0.740077\pi\)
\(542\) 18379.9 + 31834.9i 1.45661 + 2.52292i
\(543\) −715.322 + 1238.97i −0.0565330 + 0.0979180i
\(544\) 9704.88 + 5603.11i 0.764877 + 0.441602i
\(545\) 4450.55 0.349799
\(546\) 1277.88 18172.8i 0.100162 1.42440i
\(547\) −18943.1 −1.48071 −0.740356 0.672215i \(-0.765343\pi\)
−0.740356 + 0.672215i \(0.765343\pi\)
\(548\) −14268.9 8238.14i −1.11229 0.642182i
\(549\) 2435.87 4219.05i 0.189363 0.327987i
\(550\) −4649.88 8053.82i −0.360493 0.624393i
\(551\) 4157.61i 0.321452i
\(552\) 203.638 117.570i 0.0157018 0.00906545i
\(553\) 24431.6 14105.6i 1.87873 1.08469i
\(554\) 16563.8i 1.27027i
\(555\) 877.348 + 1519.61i 0.0671015 + 0.116223i
\(556\) −450.000 + 779.423i −0.0343242 + 0.0594512i
\(557\) −359.861 207.766i −0.0273749 0.0158049i 0.486250 0.873820i \(-0.338364\pi\)
−0.513625 + 0.858015i \(0.671698\pi\)
\(558\) 11439.3 0.867856
\(559\) 13290.9 + 8972.38i 1.00563 + 0.678875i
\(560\) 23231.1 1.75303
\(561\) 4539.00 + 2620.59i 0.341599 + 0.197222i
\(562\) 3795.56 6574.10i 0.284886 0.493437i
\(563\) 9145.90 + 15841.2i 0.684643 + 1.18584i 0.973549 + 0.228478i \(0.0733750\pi\)
−0.288907 + 0.957357i \(0.593292\pi\)
\(564\) 3603.63i 0.269043i
\(565\) −8093.17 + 4672.59i −0.602623 + 0.347925i
\(566\) −17315.8 + 9997.29i −1.28593 + 0.742434i
\(567\) 2545.17i 0.188514i
\(568\) 926.486 + 1604.72i 0.0684410 + 0.118543i
\(569\) 2173.73 3765.02i 0.160154 0.277395i −0.774770 0.632244i \(-0.782134\pi\)
0.934924 + 0.354848i \(0.115468\pi\)
\(570\) 3884.73 + 2242.85i 0.285462 + 0.164812i
\(571\) 16756.0 1.22805 0.614024 0.789288i \(-0.289550\pi\)
0.614024 + 0.789288i \(0.289550\pi\)
\(572\) −7482.84 15357.3i −0.546981 1.12259i
\(573\) 4109.23 0.299591
\(574\) 5367.40 + 3098.87i 0.390298 + 0.225339i
\(575\) 529.401 916.950i 0.0383958 0.0665034i
\(576\) −2839.50 4918.16i −0.205404 0.355770i
\(577\) 19974.7i 1.44117i −0.693364 0.720587i \(-0.743872\pi\)
0.693364 0.720587i \(-0.256128\pi\)
\(578\) −10897.2 + 6291.48i −0.784191 + 0.452753i
\(579\) 5572.14 3217.08i 0.399949 0.230911i
\(580\) 18644.6i 1.33478i
\(581\) −20428.0 35382.4i −1.45869 2.52652i
\(582\) −9651.12 + 16716.2i −0.687374 + 1.19057i
\(583\) 15376.9 + 8877.86i 1.09236 + 0.630675i
\(584\) −1606.82 −0.113854
\(585\) −3172.82 + 4699.95i −0.224239 + 0.332169i
\(586\) 5829.47 0.410944
\(587\) −13638.7 7874.33i −0.958996 0.553677i −0.0631321 0.998005i \(-0.520109\pi\)
−0.895864 + 0.444329i \(0.853442\pi\)
\(588\) 8698.51 15066.3i 0.610069 1.05667i
\(589\) −4158.25 7202.30i −0.290896 0.503846i
\(590\) 32731.0i 2.28392i
\(591\) −622.860 + 359.608i −0.0433520 + 0.0250293i
\(592\) −2072.52 + 1196.57i −0.143885 + 0.0830721i
\(593\) 13318.4i 0.922297i 0.887323 + 0.461148i \(0.152562\pi\)
−0.887323 + 0.461148i \(0.847438\pi\)
\(594\) −2254.09 3904.21i −0.155701 0.269683i
\(595\) 9111.13 15780.9i 0.627765 1.08732i
\(596\) −1165.68 673.006i −0.0801143 0.0462540i
\(597\) −4769.82 −0.326994
\(598\) 2055.58 3044.96i 0.140567 0.208224i
\(599\) 2970.80 0.202644 0.101322 0.994854i \(-0.467693\pi\)
0.101322 + 0.994854i \(0.467693\pi\)
\(600\) 596.636 + 344.468i 0.0405959 + 0.0234381i
\(601\) −5316.31 + 9208.13i −0.360827 + 0.624971i −0.988097 0.153831i \(-0.950839\pi\)
0.627270 + 0.778802i \(0.284172\pi\)
\(602\) 22161.9 + 38385.5i 1.50042 + 2.59880i
\(603\) 2073.11i 0.140006i
\(604\) 6235.63 3600.14i 0.420073 0.242529i
\(605\) 3596.50 2076.44i 0.241684 0.139536i
\(606\) 11860.2i 0.795029i
\(607\) −5793.94 10035.4i −0.387428 0.671045i 0.604675 0.796472i \(-0.293303\pi\)
−0.992103 + 0.125428i \(0.959970\pi\)
\(608\) −3503.83 + 6068.82i −0.233716 + 0.404808i
\(609\) 12581.1 + 7263.71i 0.837130 + 0.483317i
\(610\) −30001.4 −1.99135
\(611\) 2740.22 + 5623.85i 0.181436 + 0.372368i
\(612\) −3494.46 −0.230809
\(613\) 18006.7 + 10396.2i 1.18643 + 0.684988i 0.957494 0.288453i \(-0.0931409\pi\)
0.228939 + 0.973441i \(0.426474\pi\)
\(614\) −9536.00 + 16516.8i −0.626778 + 1.08561i
\(615\) −964.592 1670.72i −0.0632457 0.109545i
\(616\) 5246.51i 0.343162i
\(617\) 1353.40 781.388i 0.0883079 0.0509846i −0.455196 0.890391i \(-0.650431\pi\)
0.543504 + 0.839407i \(0.317097\pi\)
\(618\) 6803.85 3928.20i 0.442866 0.255689i
\(619\) 758.406i 0.0492454i 0.999697 + 0.0246227i \(0.00783844\pi\)
−0.999697 + 0.0246227i \(0.992162\pi\)
\(620\) −18647.5 32298.4i −1.20790 2.09215i
\(621\) 256.635 444.505i 0.0165836 0.0287236i
\(622\) −21641.4 12494.6i −1.39508 0.805450i
\(623\) −29066.7 −1.86923
\(624\) −6410.01 4327.24i −0.411227 0.277610i
\(625\) −19485.0 −1.24704
\(626\) −3463.40 1999.59i −0.221127 0.127668i
\(627\) −1638.75 + 2838.41i −0.104379 + 0.180789i
\(628\) −12177.7 21092.4i −0.773795 1.34025i
\(629\) 1877.15i 0.118994i
\(630\) −13573.9 + 7836.91i −0.858410 + 0.495603i
\(631\) −12354.0 + 7132.59i −0.779406 + 0.449990i −0.836220 0.548394i \(-0.815239\pi\)
0.0568136 + 0.998385i \(0.481906\pi\)
\(632\) 3701.81i 0.232990i
\(633\) −2809.28 4865.82i −0.176396 0.305527i
\(634\) −18021.3 + 31213.9i −1.12889 + 1.95530i
\(635\) −2877.23 1661.17i −0.179810 0.103813i
\(636\) −11838.3 −0.738078
\(637\) 2118.48 30127.0i 0.131770 1.87390i
\(638\) 25732.0 1.59677
\(639\) 3502.82 + 2022.35i 0.216854 + 0.125200i
\(640\) −3519.44 + 6095.85i −0.217372 + 0.376500i
\(641\) 1992.82 + 3451.67i 0.122795 + 0.212688i 0.920869 0.389872i \(-0.127481\pi\)
−0.798074 + 0.602560i \(0.794147\pi\)
\(642\) 17914.8i 1.10131i
\(643\) 7063.78 4078.28i 0.433232 0.250127i −0.267490 0.963561i \(-0.586194\pi\)
0.700723 + 0.713434i \(0.252861\pi\)
\(644\) 4655.73 2687.98i 0.284878 0.164474i
\(645\) 13796.8i 0.842243i
\(646\) 2399.37 + 4155.83i 0.146133 + 0.253110i
\(647\) 5639.62 9768.11i 0.342684 0.593546i −0.642246 0.766498i \(-0.721997\pi\)
0.984930 + 0.172953i \(0.0553307\pi\)
\(648\) 289.228 + 166.986i 0.0175339 + 0.0101232i
\(649\) −23915.2 −1.44646
\(650\) 10737.5 + 755.041i 0.647935 + 0.0455617i
\(651\) 29059.3 1.74950
\(652\) 28669.1 + 16552.1i 1.72204 + 0.994219i
\(653\) −3282.88 + 5686.11i −0.196736 + 0.340757i −0.947468 0.319850i \(-0.896368\pi\)
0.750732 + 0.660607i \(0.229701\pi\)
\(654\) −2047.64 3546.62i −0.122430 0.212055i
\(655\) 6348.06i 0.378686i
\(656\) 2278.61 1315.56i 0.135617 0.0782986i
\(657\) −3037.50 + 1753.70i −0.180372 + 0.104138i
\(658\) 17291.5i 1.02446i
\(659\) −2399.67 4156.36i −0.141848 0.245688i 0.786344 0.617788i \(-0.211971\pi\)
−0.928193 + 0.372100i \(0.878638\pi\)
\(660\) −7348.92 + 12728.7i −0.433419 + 0.750703i
\(661\) −13504.5 7796.80i −0.794648 0.458790i 0.0469482 0.998897i \(-0.485050\pi\)
−0.841596 + 0.540107i \(0.818384\pi\)
\(662\) 28811.3 1.69151
\(663\) −5453.48 + 2657.21i −0.319450 + 0.155652i
\(664\) 5361.03 0.313326
\(665\) 9868.41 + 5697.53i 0.575459 + 0.332242i
\(666\) 807.313 1398.31i 0.0469711 0.0813563i
\(667\) 1464.83 + 2537.16i 0.0850351 + 0.147285i
\(668\) 29008.0i 1.68017i
\(669\) −145.826 + 84.1925i −0.00842742 + 0.00486557i
\(670\) 11056.3 6383.37i 0.637526 0.368076i
\(671\) 21920.8i 1.26116i
\(672\) −12243.0 21205.5i −0.702804 1.21729i
\(673\) −1102.77 + 1910.06i −0.0631630 + 0.109402i −0.895878 0.444301i \(-0.853452\pi\)
0.832715 + 0.553702i \(0.186785\pi\)
\(674\) −14842.0 8569.03i −0.848208 0.489713i
\(675\) 1503.82 0.0857514
\(676\) 19578.4 + 2767.13i 1.11393 + 0.157438i
\(677\) −15046.4 −0.854182 −0.427091 0.904209i \(-0.640462\pi\)
−0.427091 + 0.904209i \(0.640462\pi\)
\(678\) 7447.13 + 4299.60i 0.421837 + 0.243547i
\(679\) −24516.8 + 42464.4i −1.38567 + 2.40005i
\(680\) 1195.54 + 2070.74i 0.0674219 + 0.116778i
\(681\) 2002.17i 0.112663i
\(682\) 44576.0 25736.0i 2.50279 1.44499i
\(683\) 26528.5 15316.3i 1.48622 0.858068i 0.486340 0.873770i \(-0.338332\pi\)
0.999877 + 0.0157020i \(0.00499830\pi\)
\(684\) 2185.21i 0.122155i
\(685\) 12304.5 + 21311.9i 0.686320 + 1.18874i
\(686\) 19519.8 33809.3i 1.08640 1.88170i
\(687\) 1879.19 + 1084.95i 0.104360 + 0.0602524i
\(688\) 18816.7 1.04270
\(689\) −18474.9 + 9001.90i −1.02153 + 0.497743i
\(690\) −3160.85 −0.174393
\(691\) 1884.22 + 1087.86i 0.103733 + 0.0598901i 0.550969 0.834526i \(-0.314258\pi\)
−0.447236 + 0.894416i \(0.647592\pi\)
\(692\) 12102.9 20962.9i 0.664862 1.15157i
\(693\) −5726.10 9917.89i −0.313876 0.543650i
\(694\) 1288.52i 0.0704780i
\(695\) 1164.14 672.118i 0.0635373 0.0366833i
\(696\) −1650.86 + 953.127i −0.0899078 + 0.0519083i
\(697\) 2063.82i 0.112156i
\(698\) −9191.95 15920.9i −0.498453 0.863346i
\(699\) 413.177 715.644i 0.0223574 0.0387241i
\(700\) 13640.7 + 7875.49i 0.736531 + 0.425236i
\(701\) 32718.2 1.76284 0.881419 0.472335i \(-0.156589\pi\)
0.881419 + 0.472335i \(0.156589\pi\)
\(702\) 5205.14 + 366.017i 0.279851 + 0.0196787i
\(703\) −1173.85 −0.0629768
\(704\) −22129.6 12776.5i −1.18472 0.683997i
\(705\) 2691.18 4661.26i 0.143767 0.249012i
\(706\) 4636.79 + 8031.15i 0.247178 + 0.428125i
\(707\) 30128.6i 1.60269i
\(708\) 13808.7 7972.47i 0.733000 0.423197i
\(709\) −21840.9 + 12609.8i −1.15691 + 0.667945i −0.950563 0.310533i \(-0.899492\pi\)
−0.206352 + 0.978478i \(0.566159\pi\)
\(710\) 24908.3i 1.31661i
\(711\) 4040.19 + 6997.81i 0.213107 + 0.369112i
\(712\) 1907.03 3303.07i 0.100378 0.173859i
\(713\) 5075.10 + 2930.11i 0.266569 + 0.153904i
\(714\) −16767.7 −0.878871
\(715\) −1789.79 + 25452.7i −0.0936146 + 1.33130i
\(716\) −13716.4 −0.715929
\(717\) 3973.48 + 2294.09i 0.206963 + 0.119490i
\(718\) −16168.3 + 28004.4i −0.840385 + 1.45559i
\(719\) −17733.1 30714.6i −0.919796 1.59313i −0.799724 0.600368i \(-0.795021\pi\)
−0.120071 0.992765i \(-0.538312\pi\)
\(720\) 6653.97i 0.344415i
\(721\) 17283.9 9978.85i 0.892767 0.515439i
\(722\) 21892.7 12639.8i 1.12848 0.651529i
\(723\) 2926.58i 0.150540i
\(724\) −2145.97 3716.92i −0.110158 0.190799i
\(725\) −4291.78 + 7433.59i −0.219852 + 0.380795i
\(726\) −3309.41 1910.69i −0.169179 0.0976753i
\(727\) 14262.2 0.727588 0.363794 0.931479i \(-0.381481\pi\)
0.363794 + 0.931479i \(0.381481\pi\)
\(728\) 5033.05 + 3397.69i 0.256233 + 0.172976i
\(729\) 729.000 0.0370370
\(730\) 18705.7 + 10799.7i 0.948396 + 0.547557i
\(731\) 7379.80 12782.2i 0.373395 0.646739i
\(732\) 7307.61 + 12657.1i 0.368985 + 0.639101i
\(733\) 16022.5i 0.807371i −0.914898 0.403685i \(-0.867729\pi\)
0.914898 0.403685i \(-0.132271\pi\)
\(734\) 23781.8 13730.4i 1.19592 0.690463i
\(735\) −22502.9 + 12992.1i −1.12930 + 0.651999i
\(736\) 4937.96i 0.247304i
\(737\) 4664.05 + 8078.38i 0.233111 + 0.403760i
\(738\) −887.593 + 1537.36i −0.0442720 + 0.0766814i
\(739\) −3287.61 1898.11i −0.163649 0.0944830i 0.415939 0.909393i \(-0.363453\pi\)
−0.579588 + 0.814910i \(0.696786\pi\)
\(740\) −5264.09 −0.261502
\(741\) −1661.65 3410.26i −0.0823782 0.169068i
\(742\) −56804.3 −2.81044
\(743\) −26266.0 15164.7i −1.29691 0.748772i −0.317042 0.948412i \(-0.602690\pi\)
−0.979869 + 0.199639i \(0.936023\pi\)
\(744\) −1906.55 + 3302.24i −0.0939481 + 0.162723i
\(745\) 1005.20 + 1741.05i 0.0494331 + 0.0856206i
\(746\) 152.502i 0.00748460i
\(747\) 10134.4 5851.09i 0.496382 0.286586i
\(748\) −13617.0 + 7861.78i −0.665624 + 0.384298i
\(749\) 45509.1i 2.22011i
\(750\) 5761.59 + 9979.37i 0.280511 + 0.485860i
\(751\) 10775.9 18664.5i 0.523595 0.906893i −0.476028 0.879430i \(-0.657924\pi\)
0.999623 0.0274629i \(-0.00874280\pi\)
\(752\) 6357.25 + 3670.36i 0.308278 + 0.177984i
\(753\) −5622.42 −0.272101
\(754\) −16664.3 + 24685.1i −0.804877 + 1.19228i
\(755\) −10754.3 −0.518397
\(756\) 6612.55 + 3817.76i 0.318117 + 0.183665i
\(757\) 10208.8 17682.2i 0.490153 0.848970i −0.509783 0.860303i \(-0.670274\pi\)
0.999936 + 0.0113335i \(0.00360764\pi\)
\(758\) −24903.3 43133.7i −1.19331 2.06687i
\(759\) 2309.50i 0.110447i
\(760\) −1294.91 + 747.616i −0.0618043 + 0.0356828i
\(761\) −27171.9 + 15687.7i −1.29432 + 0.747278i −0.979417 0.201845i \(-0.935306\pi\)
−0.314906 + 0.949123i \(0.601973\pi\)
\(762\) 3057.13i 0.145339i
\(763\) −5201.64 9009.50i −0.246805 0.427478i
\(764\) −6163.84 + 10676.1i −0.291885 + 0.505559i
\(765\) 4520.05 + 2609.65i 0.213625 + 0.123336i
\(766\) −43570.5 −2.05518
\(767\) 15487.7 22942.2i 0.729111 1.08004i
\(768\) −8667.00 −0.407218
\(769\) 10784.3 + 6226.33i 0.505712 + 0.291973i 0.731069 0.682303i \(-0.239022\pi\)
−0.225357 <