Properties

Label 245.4.e.k.226.2
Level $245$
Weight $4$
Character 245.226
Analytic conductor $14.455$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 245 = 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 245.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.4554679514\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{11})\)
Defining polynomial: \( x^{4} + 11x^{2} + 121 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 226.2
Root \(1.65831 - 2.87228i\) of defining polynomial
Character \(\chi\) \(=\) 245.226
Dual form 245.4.e.k.116.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.15831 - 2.00626i) q^{2} +(2.50000 + 4.33013i) q^{3} +(1.31662 + 2.28046i) q^{4} +(2.50000 - 4.33013i) q^{5} +11.5831 q^{6} +24.6332 q^{8} +(1.00000 - 1.73205i) q^{9} +O(q^{10})\) \(q+(1.15831 - 2.00626i) q^{2} +(2.50000 + 4.33013i) q^{3} +(1.31662 + 2.28046i) q^{4} +(2.50000 - 4.33013i) q^{5} +11.5831 q^{6} +24.6332 q^{8} +(1.00000 - 1.73205i) q^{9} +(-5.79156 - 10.0313i) q^{10} +(-23.1332 - 40.0680i) q^{11} +(-6.58312 + 11.4023i) q^{12} +61.3325 q^{13} +25.0000 q^{15} +(18.0000 - 31.1769i) q^{16} +(50.6662 + 87.7565i) q^{17} +(-2.31662 - 4.01251i) q^{18} +(1.83375 - 3.17615i) q^{19} +13.1662 q^{20} -107.182 q^{22} +(-42.4327 + 73.4957i) q^{23} +(61.5831 + 106.665i) q^{24} +(-12.5000 - 21.6506i) q^{25} +(71.0422 - 123.049i) q^{26} +145.000 q^{27} +30.1980 q^{29} +(28.9578 - 50.1564i) q^{30} +(94.4987 + 163.677i) q^{31} +(56.8338 + 98.4389i) q^{32} +(115.666 - 200.340i) q^{33} +234.749 q^{34} +5.26650 q^{36} +(-9.03425 + 15.6478i) q^{37} +(-4.24812 - 7.35795i) q^{38} +(153.331 + 265.577i) q^{39} +(61.5831 - 106.665i) q^{40} -481.662 q^{41} -97.7995 q^{43} +(60.9156 - 105.509i) q^{44} +(-5.00000 - 8.66025i) q^{45} +(98.3008 + 170.262i) q^{46} +(58.8325 - 101.901i) q^{47} +180.000 q^{48} -57.9156 q^{50} +(-253.331 + 438.783i) q^{51} +(80.7519 + 139.866i) q^{52} +(-333.997 - 578.501i) q^{53} +(167.955 - 290.907i) q^{54} -231.332 q^{55} +18.3375 q^{57} +(34.9787 - 60.5849i) q^{58} +(28.6675 + 49.6536i) q^{59} +(32.9156 + 57.0115i) q^{60} +(369.499 - 639.991i) q^{61} +437.836 q^{62} +551.325 q^{64} +(153.331 - 265.577i) q^{65} +(-267.955 - 464.112i) q^{66} +(-276.198 - 478.389i) q^{67} +(-133.417 + 231.085i) q^{68} -424.327 q^{69} -740.264 q^{71} +(24.6332 - 42.6660i) q^{72} +(116.662 + 202.065i) q^{73} +(20.9290 + 36.2501i) q^{74} +(62.5000 - 108.253i) q^{75} +9.65745 q^{76} +710.422 q^{78} +(537.593 - 931.138i) q^{79} +(-90.0000 - 155.885i) q^{80} +(335.500 + 581.103i) q^{81} +(-557.916 + 966.338i) q^{82} -683.325 q^{83} +506.662 q^{85} +(-113.282 + 196.211i) q^{86} +(75.4950 + 130.761i) q^{87} +(-569.847 - 987.004i) q^{88} +(-690.159 + 1195.39i) q^{89} -23.1662 q^{90} -223.472 q^{92} +(-472.494 + 818.383i) q^{93} +(-136.293 - 236.066i) q^{94} +(-9.16876 - 15.8808i) q^{95} +(-284.169 + 492.195i) q^{96} -218.008 q^{97} -92.5330 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} + 10 q^{3} - 8 q^{4} + 10 q^{5} - 20 q^{6} + 72 q^{8} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} + 10 q^{3} - 8 q^{4} + 10 q^{5} - 20 q^{6} + 72 q^{8} + 4 q^{9} + 10 q^{10} - 66 q^{11} + 40 q^{12} - 20 q^{13} + 100 q^{15} + 72 q^{16} + 70 q^{17} + 4 q^{18} + 140 q^{19} - 80 q^{20} - 44 q^{22} + 16 q^{23} + 180 q^{24} - 50 q^{25} + 450 q^{26} + 580 q^{27} - 516 q^{29} - 50 q^{30} - 20 q^{31} + 360 q^{32} + 330 q^{33} + 740 q^{34} - 32 q^{36} - 328 q^{37} + 580 q^{38} - 50 q^{39} + 180 q^{40} - 600 q^{41} - 232 q^{43} - 88 q^{44} - 20 q^{45} + 632 q^{46} - 30 q^{47} + 720 q^{48} + 100 q^{50} - 350 q^{51} + 920 q^{52} - 540 q^{53} - 290 q^{54} - 660 q^{55} + 1400 q^{57} + 1314 q^{58} + 380 q^{59} - 200 q^{60} + 1080 q^{61} + 2680 q^{62} - 448 q^{64} - 50 q^{65} - 110 q^{66} - 468 q^{67} - 600 q^{68} + 160 q^{69} - 2112 q^{71} + 72 q^{72} - 860 q^{73} - 1296 q^{74} + 250 q^{75} - 2880 q^{76} + 4500 q^{78} - 158 q^{79} - 360 q^{80} + 1342 q^{81} - 1900 q^{82} - 80 q^{83} + 700 q^{85} - 148 q^{86} - 1290 q^{87} - 1364 q^{88} - 240 q^{89} + 40 q^{90} - 2592 q^{92} + 100 q^{93} - 910 q^{94} - 700 q^{95} - 1800 q^{96} - 3260 q^{97} - 264 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/245\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.15831 2.00626i 0.409525 0.709319i −0.585311 0.810809i \(-0.699028\pi\)
0.994837 + 0.101490i \(0.0323610\pi\)
\(3\) 2.50000 + 4.33013i 0.481125 + 0.833333i 0.999765 0.0216593i \(-0.00689490\pi\)
−0.518640 + 0.854993i \(0.673562\pi\)
\(4\) 1.31662 + 2.28046i 0.164578 + 0.285058i
\(5\) 2.50000 4.33013i 0.223607 0.387298i
\(6\) 11.5831 0.788132
\(7\) 0 0
\(8\) 24.6332 1.08865
\(9\) 1.00000 1.73205i 0.0370370 0.0641500i
\(10\) −5.79156 10.0313i −0.183145 0.317217i
\(11\) −23.1332 40.0680i −0.634085 1.09827i −0.986708 0.162502i \(-0.948044\pi\)
0.352623 0.935765i \(-0.385290\pi\)
\(12\) −6.58312 + 11.4023i −0.158365 + 0.274297i
\(13\) 61.3325 1.30851 0.654253 0.756276i \(-0.272983\pi\)
0.654253 + 0.756276i \(0.272983\pi\)
\(14\) 0 0
\(15\) 25.0000 0.430331
\(16\) 18.0000 31.1769i 0.281250 0.487139i
\(17\) 50.6662 + 87.7565i 0.722845 + 1.25200i 0.959855 + 0.280497i \(0.0904994\pi\)
−0.237009 + 0.971507i \(0.576167\pi\)
\(18\) −2.31662 4.01251i −0.0303352 0.0525421i
\(19\) 1.83375 3.17615i 0.0221417 0.0383505i −0.854742 0.519053i \(-0.826285\pi\)
0.876884 + 0.480702i \(0.159618\pi\)
\(20\) 13.1662 0.147203
\(21\) 0 0
\(22\) −107.182 −1.03870
\(23\) −42.4327 + 73.4957i −0.384689 + 0.666300i −0.991726 0.128373i \(-0.959025\pi\)
0.607037 + 0.794673i \(0.292358\pi\)
\(24\) 61.5831 + 106.665i 0.523775 + 0.907205i
\(25\) −12.5000 21.6506i −0.100000 0.173205i
\(26\) 71.0422 123.049i 0.535866 0.928147i
\(27\) 145.000 1.03353
\(28\) 0 0
\(29\) 30.1980 0.193366 0.0966832 0.995315i \(-0.469177\pi\)
0.0966832 + 0.995315i \(0.469177\pi\)
\(30\) 28.9578 50.1564i 0.176232 0.305242i
\(31\) 94.4987 + 163.677i 0.547499 + 0.948296i 0.998445 + 0.0557451i \(0.0177534\pi\)
−0.450946 + 0.892551i \(0.648913\pi\)
\(32\) 56.8338 + 98.4389i 0.313965 + 0.543803i
\(33\) 115.666 200.340i 0.610149 1.05681i
\(34\) 234.749 1.18409
\(35\) 0 0
\(36\) 5.26650 0.0243819
\(37\) −9.03425 + 15.6478i −0.0401411 + 0.0695265i −0.885398 0.464834i \(-0.846114\pi\)
0.845257 + 0.534360i \(0.179447\pi\)
\(38\) −4.24812 7.35795i −0.0181351 0.0314110i
\(39\) 153.331 + 265.577i 0.629555 + 1.09042i
\(40\) 61.5831 106.665i 0.243429 0.421631i
\(41\) −481.662 −1.83471 −0.917354 0.398072i \(-0.869679\pi\)
−0.917354 + 0.398072i \(0.869679\pi\)
\(42\) 0 0
\(43\) −97.7995 −0.346844 −0.173422 0.984848i \(-0.555482\pi\)
−0.173422 + 0.984848i \(0.555482\pi\)
\(44\) 60.9156 105.509i 0.208713 0.361502i
\(45\) −5.00000 8.66025i −0.0165635 0.0286888i
\(46\) 98.3008 + 170.262i 0.315079 + 0.545734i
\(47\) 58.8325 101.901i 0.182587 0.316250i −0.760174 0.649720i \(-0.774886\pi\)
0.942761 + 0.333470i \(0.108219\pi\)
\(48\) 180.000 0.541266
\(49\) 0 0
\(50\) −57.9156 −0.163810
\(51\) −253.331 + 438.783i −0.695558 + 1.20474i
\(52\) 80.7519 + 139.866i 0.215351 + 0.373000i
\(53\) −333.997 578.501i −0.865624 1.49931i −0.866426 0.499305i \(-0.833589\pi\)
0.000801827 1.00000i \(-0.499745\pi\)
\(54\) 167.955 290.907i 0.423256 0.733101i
\(55\) −231.332 −0.567143
\(56\) 0 0
\(57\) 18.3375 0.0426116
\(58\) 34.9787 60.5849i 0.0791884 0.137158i
\(59\) 28.6675 + 49.6536i 0.0632575 + 0.109565i 0.895920 0.444216i \(-0.146518\pi\)
−0.832662 + 0.553781i \(0.813184\pi\)
\(60\) 32.9156 + 57.0115i 0.0708231 + 0.122669i
\(61\) 369.499 639.991i 0.775565 1.34332i −0.158911 0.987293i \(-0.550798\pi\)
0.934476 0.356025i \(-0.115868\pi\)
\(62\) 437.836 0.896859
\(63\) 0 0
\(64\) 551.325 1.07681
\(65\) 153.331 265.577i 0.292591 0.506782i
\(66\) −267.955 464.112i −0.499743 0.865580i
\(67\) −276.198 478.389i −0.503626 0.872306i −0.999991 0.00419224i \(-0.998666\pi\)
0.496365 0.868114i \(-0.334668\pi\)
\(68\) −133.417 + 231.085i −0.237929 + 0.412105i
\(69\) −424.327 −0.740334
\(70\) 0 0
\(71\) −740.264 −1.23737 −0.618684 0.785640i \(-0.712334\pi\)
−0.618684 + 0.785640i \(0.712334\pi\)
\(72\) 24.6332 42.6660i 0.0403202 0.0698367i
\(73\) 116.662 + 202.065i 0.187045 + 0.323972i 0.944264 0.329190i \(-0.106776\pi\)
−0.757218 + 0.653162i \(0.773442\pi\)
\(74\) 20.9290 + 36.2501i 0.0328776 + 0.0569457i
\(75\) 62.5000 108.253i 0.0962250 0.166667i
\(76\) 9.65745 0.0145761
\(77\) 0 0
\(78\) 710.422 1.03127
\(79\) 537.593 931.138i 0.765619 1.32609i −0.174300 0.984693i \(-0.555766\pi\)
0.939919 0.341398i \(-0.110901\pi\)
\(80\) −90.0000 155.885i −0.125779 0.217855i
\(81\) 335.500 + 581.103i 0.460219 + 0.797124i
\(82\) −557.916 + 966.338i −0.751359 + 1.30139i
\(83\) −683.325 −0.903671 −0.451835 0.892101i \(-0.649231\pi\)
−0.451835 + 0.892101i \(0.649231\pi\)
\(84\) 0 0
\(85\) 506.662 0.646532
\(86\) −113.282 + 196.211i −0.142041 + 0.246023i
\(87\) 75.4950 + 130.761i 0.0930335 + 0.161139i
\(88\) −569.847 987.004i −0.690294 1.19562i
\(89\) −690.159 + 1195.39i −0.821985 + 1.42372i 0.0822166 + 0.996614i \(0.473800\pi\)
−0.904202 + 0.427106i \(0.859533\pi\)
\(90\) −23.1662 −0.0271326
\(91\) 0 0
\(92\) −223.472 −0.253245
\(93\) −472.494 + 818.383i −0.526831 + 0.912499i
\(94\) −136.293 236.066i −0.149548 0.259025i
\(95\) −9.16876 15.8808i −0.00990205 0.0171509i
\(96\) −284.169 + 492.195i −0.302113 + 0.523275i
\(97\) −218.008 −0.228199 −0.114100 0.993469i \(-0.536398\pi\)
−0.114100 + 0.993469i \(0.536398\pi\)
\(98\) 0 0
\(99\) −92.5330 −0.0939385
\(100\) 32.9156 57.0115i 0.0329156 0.0570115i
\(101\) −737.164 1276.81i −0.726243 1.25789i −0.958460 0.285226i \(-0.907931\pi\)
0.232217 0.972664i \(-0.425402\pi\)
\(102\) 586.873 + 1016.49i 0.569697 + 0.986745i
\(103\) −405.495 + 702.338i −0.387909 + 0.671878i −0.992168 0.124910i \(-0.960136\pi\)
0.604259 + 0.796788i \(0.293469\pi\)
\(104\) 1510.82 1.42450
\(105\) 0 0
\(106\) −1547.49 −1.41798
\(107\) −220.330 + 381.623i −0.199066 + 0.344793i −0.948226 0.317596i \(-0.897124\pi\)
0.749160 + 0.662390i \(0.230458\pi\)
\(108\) 190.911 + 330.667i 0.170096 + 0.294615i
\(109\) 953.094 + 1650.81i 0.837522 + 1.45063i 0.891961 + 0.452113i \(0.149330\pi\)
−0.0544393 + 0.998517i \(0.517337\pi\)
\(110\) −267.955 + 464.112i −0.232259 + 0.402285i
\(111\) −90.3425 −0.0772517
\(112\) 0 0
\(113\) 962.470 0.801252 0.400626 0.916242i \(-0.368793\pi\)
0.400626 + 0.916242i \(0.368793\pi\)
\(114\) 21.2406 36.7898i 0.0174505 0.0302252i
\(115\) 212.164 + 367.478i 0.172038 + 0.297979i
\(116\) 39.7594 + 68.8653i 0.0318239 + 0.0551206i
\(117\) 61.3325 106.231i 0.0484632 0.0839407i
\(118\) 132.824 0.103622
\(119\) 0 0
\(120\) 615.831 0.468479
\(121\) −404.794 + 701.125i −0.304128 + 0.526765i
\(122\) −855.990 1482.62i −0.635227 1.10025i
\(123\) −1204.16 2085.66i −0.882724 1.52892i
\(124\) −248.839 + 431.001i −0.180213 + 0.312138i
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) −1621.74 −1.13312 −0.566558 0.824022i \(-0.691725\pi\)
−0.566558 + 0.824022i \(0.691725\pi\)
\(128\) 183.937 318.587i 0.127014 0.219995i
\(129\) −244.499 423.484i −0.166875 0.289037i
\(130\) −355.211 615.243i −0.239647 0.415080i
\(131\) −690.159 + 1195.39i −0.460301 + 0.797265i −0.998976 0.0452490i \(-0.985592\pi\)
0.538675 + 0.842514i \(0.318925\pi\)
\(132\) 609.156 0.401668
\(133\) 0 0
\(134\) −1279.69 −0.824991
\(135\) 362.500 627.868i 0.231104 0.400284i
\(136\) 1248.07 + 2161.73i 0.786923 + 1.36299i
\(137\) 974.829 + 1688.45i 0.607921 + 1.05295i 0.991582 + 0.129477i \(0.0413298\pi\)
−0.383661 + 0.923474i \(0.625337\pi\)
\(138\) −491.504 + 851.309i −0.303185 + 0.525132i
\(139\) −2800.00 −1.70858 −0.854291 0.519795i \(-0.826008\pi\)
−0.854291 + 0.519795i \(0.826008\pi\)
\(140\) 0 0
\(141\) 588.325 0.351389
\(142\) −857.457 + 1485.16i −0.506734 + 0.877689i
\(143\) −1418.82 2457.47i −0.829704 1.43709i
\(144\) −36.0000 62.3538i −0.0208333 0.0360844i
\(145\) 75.4950 130.761i 0.0432380 0.0748905i
\(146\) 540.526 0.306399
\(147\) 0 0
\(148\) −47.5789 −0.0264254
\(149\) 717.058 1241.98i 0.394253 0.682866i −0.598752 0.800934i \(-0.704337\pi\)
0.993006 + 0.118068i \(0.0376700\pi\)
\(150\) −144.789 250.782i −0.0788132 0.136508i
\(151\) 992.791 + 1719.56i 0.535047 + 0.926729i 0.999161 + 0.0409537i \(0.0130396\pi\)
−0.464114 + 0.885776i \(0.653627\pi\)
\(152\) 45.1713 78.2389i 0.0241044 0.0417501i
\(153\) 202.665 0.107088
\(154\) 0 0
\(155\) 944.987 0.489698
\(156\) −403.759 + 699.332i −0.207222 + 0.358919i
\(157\) 20.3300 + 35.2126i 0.0103345 + 0.0178998i 0.871146 0.491023i \(-0.163377\pi\)
−0.860812 + 0.508923i \(0.830044\pi\)
\(158\) −1245.40 2157.10i −0.627081 1.08614i
\(159\) 1669.99 2892.50i 0.832947 1.44271i
\(160\) 568.338 0.280819
\(161\) 0 0
\(162\) 1554.46 0.753886
\(163\) 1976.99 3424.25i 0.950000 1.64545i 0.204584 0.978849i \(-0.434416\pi\)
0.745416 0.666599i \(-0.232251\pi\)
\(164\) −634.169 1098.41i −0.301953 0.522998i
\(165\) −578.331 1001.70i −0.272867 0.472619i
\(166\) −791.504 + 1370.92i −0.370076 + 0.640990i
\(167\) −3380.30 −1.56632 −0.783161 0.621819i \(-0.786394\pi\)
−0.783161 + 0.621819i \(0.786394\pi\)
\(168\) 0 0
\(169\) 1564.68 0.712187
\(170\) 586.873 1016.49i 0.264771 0.458598i
\(171\) −3.66750 6.35230i −0.00164012 0.00284078i
\(172\) −128.765 223.028i −0.0570829 0.0988705i
\(173\) 1603.33 2777.05i 0.704619 1.22044i −0.262210 0.965011i \(-0.584451\pi\)
0.966829 0.255424i \(-0.0822152\pi\)
\(174\) 349.787 0.152398
\(175\) 0 0
\(176\) −1665.59 −0.713346
\(177\) −143.338 + 248.268i −0.0608695 + 0.105429i
\(178\) 1598.84 + 2769.27i 0.673247 + 1.16610i
\(179\) −721.325 1249.37i −0.301198 0.521689i 0.675210 0.737626i \(-0.264053\pi\)
−0.976407 + 0.215936i \(0.930720\pi\)
\(180\) 13.1662 22.8046i 0.00545197 0.00944308i
\(181\) 908.680 0.373158 0.186579 0.982440i \(-0.440260\pi\)
0.186579 + 0.982440i \(0.440260\pi\)
\(182\) 0 0
\(183\) 3694.99 1.49258
\(184\) −1045.26 + 1810.44i −0.418790 + 0.725365i
\(185\) 45.1713 + 78.2389i 0.0179517 + 0.0310932i
\(186\) 1094.59 + 1895.89i 0.431502 + 0.747383i
\(187\) 2344.15 4060.19i 0.916691 1.58776i
\(188\) 309.841 0.120199
\(189\) 0 0
\(190\) −42.4812 −0.0162206
\(191\) −1237.32 + 2143.10i −0.468739 + 0.811881i −0.999362 0.0357280i \(-0.988625\pi\)
0.530622 + 0.847609i \(0.321958\pi\)
\(192\) 1378.31 + 2387.31i 0.518079 + 0.897339i
\(193\) −1766.76 3060.12i −0.658934 1.14131i −0.980892 0.194553i \(-0.937674\pi\)
0.321958 0.946754i \(-0.395659\pi\)
\(194\) −252.521 + 437.379i −0.0934533 + 0.161866i
\(195\) 1533.31 0.563091
\(196\) 0 0
\(197\) −1952.57 −0.706165 −0.353083 0.935592i \(-0.614867\pi\)
−0.353083 + 0.935592i \(0.614867\pi\)
\(198\) −107.182 + 185.645i −0.0384702 + 0.0666324i
\(199\) 2032.34 + 3520.11i 0.723962 + 1.25394i 0.959400 + 0.282049i \(0.0910142\pi\)
−0.235438 + 0.971889i \(0.575652\pi\)
\(200\) −307.916 533.325i −0.108865 0.188559i
\(201\) 1380.99 2391.94i 0.484615 0.839377i
\(202\) −3415.46 −1.18966
\(203\) 0 0
\(204\) −1334.17 −0.457895
\(205\) −1204.16 + 2085.66i −0.410253 + 0.710579i
\(206\) 939.380 + 1627.05i 0.317717 + 0.550302i
\(207\) 84.8655 + 146.991i 0.0284955 + 0.0493556i
\(208\) 1103.98 1912.16i 0.368017 0.637425i
\(209\) −169.683 −0.0561588
\(210\) 0 0
\(211\) −4325.34 −1.41123 −0.705613 0.708598i \(-0.749328\pi\)
−0.705613 + 0.708598i \(0.749328\pi\)
\(212\) 879.499 1523.34i 0.284926 0.493506i
\(213\) −1850.66 3205.44i −0.595329 1.03114i
\(214\) 510.422 + 884.077i 0.163045 + 0.282403i
\(215\) −244.499 + 423.484i −0.0775566 + 0.134332i
\(216\) 3571.82 1.12515
\(217\) 0 0
\(218\) 4415.92 1.37194
\(219\) −583.312 + 1010.33i −0.179984 + 0.311742i
\(220\) −304.578 527.545i −0.0933393 0.161668i
\(221\) 3107.49 + 5382.33i 0.945847 + 1.63826i
\(222\) −104.645 + 181.250i −0.0316365 + 0.0547960i
\(223\) 982.970 0.295177 0.147589 0.989049i \(-0.452849\pi\)
0.147589 + 0.989049i \(0.452849\pi\)
\(224\) 0 0
\(225\) −50.0000 −0.0148148
\(226\) 1114.84 1930.96i 0.328133 0.568343i
\(227\) −830.482 1438.44i −0.242824 0.420584i 0.718694 0.695327i \(-0.244740\pi\)
−0.961518 + 0.274743i \(0.911407\pi\)
\(228\) 24.1436 + 41.8180i 0.00701294 + 0.0121468i
\(229\) −287.164 + 497.382i −0.0828660 + 0.143528i −0.904480 0.426516i \(-0.859741\pi\)
0.821614 + 0.570044i \(0.193074\pi\)
\(230\) 983.008 0.281816
\(231\) 0 0
\(232\) 743.875 0.210508
\(233\) 1158.24 2006.13i 0.325660 0.564059i −0.655986 0.754773i \(-0.727747\pi\)
0.981646 + 0.190714i \(0.0610802\pi\)
\(234\) −142.084 246.097i −0.0396938 0.0687517i
\(235\) −294.162 509.504i −0.0816555 0.141431i
\(236\) −75.4887 + 130.750i −0.0208216 + 0.0360641i
\(237\) 5375.93 1.47343
\(238\) 0 0
\(239\) −3659.31 −0.990382 −0.495191 0.868784i \(-0.664902\pi\)
−0.495191 + 0.868784i \(0.664902\pi\)
\(240\) 450.000 779.423i 0.121031 0.209631i
\(241\) 1223.17 + 2118.59i 0.326934 + 0.566266i 0.981902 0.189391i \(-0.0606512\pi\)
−0.654968 + 0.755657i \(0.727318\pi\)
\(242\) 937.757 + 1624.24i 0.249096 + 0.431447i
\(243\) 280.000 484.974i 0.0739177 0.128029i
\(244\) 1945.96 0.510564
\(245\) 0 0
\(246\) −5579.16 −1.44599
\(247\) 112.469 194.801i 0.0289725 0.0501818i
\(248\) 2327.81 + 4031.89i 0.596033 + 1.03236i
\(249\) −1708.31 2958.88i −0.434779 0.753059i
\(250\) −144.789 + 250.782i −0.0366291 + 0.0634434i
\(251\) 2909.29 0.731605 0.365802 0.930693i \(-0.380795\pi\)
0.365802 + 0.930693i \(0.380795\pi\)
\(252\) 0 0
\(253\) 3926.43 0.975702
\(254\) −1878.48 + 3253.62i −0.464040 + 0.803741i
\(255\) 1266.66 + 2193.91i 0.311063 + 0.538777i
\(256\) 1779.19 + 3081.64i 0.434372 + 0.752354i
\(257\) 84.3400 146.081i 0.0204708 0.0354564i −0.855609 0.517623i \(-0.826817\pi\)
0.876079 + 0.482167i \(0.160150\pi\)
\(258\) −1132.82 −0.273359
\(259\) 0 0
\(260\) 807.519 0.192616
\(261\) 30.1980 52.3045i 0.00716172 0.0124045i
\(262\) 1598.84 + 2769.27i 0.377010 + 0.653000i
\(263\) 1622.24 + 2809.80i 0.380347 + 0.658781i 0.991112 0.133031i \(-0.0424711\pi\)
−0.610764 + 0.791812i \(0.709138\pi\)
\(264\) 2849.24 4935.02i 0.664236 1.15049i
\(265\) −3339.97 −0.774238
\(266\) 0 0
\(267\) −6901.59 −1.58191
\(268\) 727.298 1259.72i 0.165772 0.287125i
\(269\) −1424.33 2467.01i −0.322836 0.559168i 0.658236 0.752811i \(-0.271303\pi\)
−0.981072 + 0.193644i \(0.937969\pi\)
\(270\) −839.776 1454.54i −0.189286 0.327853i
\(271\) −1425.49 + 2469.02i −0.319529 + 0.553440i −0.980390 0.197068i \(-0.936858\pi\)
0.660861 + 0.750508i \(0.270191\pi\)
\(272\) 3647.97 0.813201
\(273\) 0 0
\(274\) 4516.62 0.995837
\(275\) −578.331 + 1001.70i −0.126817 + 0.219654i
\(276\) −558.680 967.662i −0.121843 0.211038i
\(277\) −1149.31 1990.67i −0.249298 0.431797i 0.714033 0.700112i \(-0.246867\pi\)
−0.963331 + 0.268315i \(0.913533\pi\)
\(278\) −3243.27 + 5617.52i −0.699708 + 1.21193i
\(279\) 377.995 0.0811110
\(280\) 0 0
\(281\) 6109.20 1.29695 0.648477 0.761234i \(-0.275406\pi\)
0.648477 + 0.761234i \(0.275406\pi\)
\(282\) 681.464 1180.33i 0.143903 0.249247i
\(283\) 2927.47 + 5070.54i 0.614913 + 1.06506i 0.990400 + 0.138233i \(0.0441421\pi\)
−0.375487 + 0.926828i \(0.622525\pi\)
\(284\) −974.650 1688.14i −0.203644 0.352721i
\(285\) 45.8438 79.4038i 0.00952825 0.0165034i
\(286\) −6573.75 −1.35914
\(287\) 0 0
\(288\) 227.335 0.0465133
\(289\) −2677.64 + 4637.80i −0.545011 + 0.943986i
\(290\) −174.894 302.924i −0.0354141 0.0613391i
\(291\) −545.019 944.000i −0.109792 0.190166i
\(292\) −307.201 + 532.088i −0.0615671 + 0.106637i
\(293\) 5135.34 1.02392 0.511962 0.859008i \(-0.328919\pi\)
0.511962 + 0.859008i \(0.328919\pi\)
\(294\) 0 0
\(295\) 286.675 0.0565792
\(296\) −222.543 + 385.456i −0.0436995 + 0.0756898i
\(297\) −3354.32 5809.85i −0.655345 1.13509i
\(298\) −1661.16 2877.21i −0.322913 0.559302i
\(299\) −2602.51 + 4507.67i −0.503367 + 0.871858i
\(300\) 329.156 0.0633461
\(301\) 0 0
\(302\) 4599.85 0.876462
\(303\) 3685.82 6384.03i 0.698828 1.21040i
\(304\) −66.0151 114.341i −0.0124547 0.0215721i
\(305\) −1847.49 3199.95i −0.346843 0.600750i
\(306\) 234.749 406.598i 0.0438553 0.0759596i
\(307\) −2102.97 −0.390954 −0.195477 0.980708i \(-0.562625\pi\)
−0.195477 + 0.980708i \(0.562625\pi\)
\(308\) 0 0
\(309\) −4054.95 −0.746531
\(310\) 1094.59 1895.89i 0.200544 0.347352i
\(311\) −2882.15 4992.03i −0.525504 0.910200i −0.999559 0.0297045i \(-0.990543\pi\)
0.474055 0.880495i \(-0.342790\pi\)
\(312\) 3777.05 + 6542.04i 0.685363 + 1.18708i
\(313\) −680.006 + 1177.81i −0.122799 + 0.212695i −0.920871 0.389868i \(-0.872521\pi\)
0.798071 + 0.602563i \(0.205854\pi\)
\(314\) 94.1939 0.0169289
\(315\) 0 0
\(316\) 2831.23 0.504017
\(317\) −2569.47 + 4450.46i −0.455256 + 0.788526i −0.998703 0.0509173i \(-0.983785\pi\)
0.543447 + 0.839443i \(0.317119\pi\)
\(318\) −3868.73 6700.84i −0.682226 1.18165i
\(319\) −698.578 1209.97i −0.122611 0.212368i
\(320\) 1378.31 2387.31i 0.240781 0.417045i
\(321\) −2203.30 −0.383103
\(322\) 0 0
\(323\) 371.637 0.0640200
\(324\) −883.455 + 1530.19i −0.151484 + 0.262378i
\(325\) −766.656 1327.89i −0.130851 0.226640i
\(326\) −4579.95 7932.71i −0.778098 1.34771i
\(327\) −4765.47 + 8254.04i −0.805905 + 1.39587i
\(328\) −11864.9 −1.99735
\(329\) 0 0
\(330\) −2679.55 −0.446983
\(331\) −912.850 + 1581.10i −0.151585 + 0.262554i −0.931810 0.362945i \(-0.881771\pi\)
0.780225 + 0.625499i \(0.215105\pi\)
\(332\) −899.683 1558.30i −0.148724 0.257598i
\(333\) 18.0685 + 31.2956i 0.00297342 + 0.00515011i
\(334\) −3915.45 + 6781.76i −0.641449 + 1.11102i
\(335\) −2761.98 −0.450457
\(336\) 0 0
\(337\) 153.985 0.0248905 0.0124452 0.999923i \(-0.496038\pi\)
0.0124452 + 0.999923i \(0.496038\pi\)
\(338\) 1812.38 3139.14i 0.291659 0.505168i
\(339\) 2406.17 + 4167.62i 0.385503 + 0.667710i
\(340\) 667.084 + 1155.42i 0.106405 + 0.184299i
\(341\) 4372.13 7572.74i 0.694322 1.20260i
\(342\) −16.9925 −0.00268669
\(343\) 0 0
\(344\) −2409.12 −0.377590
\(345\) −1060.82 + 1837.39i −0.165544 + 0.286730i
\(346\) −3714.32 6433.39i −0.577118 0.999598i
\(347\) −2179.69 3775.34i −0.337211 0.584066i 0.646696 0.762748i \(-0.276150\pi\)
−0.983907 + 0.178682i \(0.942817\pi\)
\(348\) −198.797 + 344.327i −0.0306225 + 0.0530398i
\(349\) −1689.00 −0.259054 −0.129527 0.991576i \(-0.541346\pi\)
−0.129527 + 0.991576i \(0.541346\pi\)
\(350\) 0 0
\(351\) 8893.21 1.35238
\(352\) 2629.50 4554.43i 0.398161 0.689635i
\(353\) −1960.68 3396.00i −0.295627 0.512041i 0.679503 0.733672i \(-0.262195\pi\)
−0.975131 + 0.221631i \(0.928862\pi\)
\(354\) 332.059 + 575.143i 0.0498552 + 0.0863518i
\(355\) −1850.66 + 3205.44i −0.276684 + 0.479231i
\(356\) −3634.72 −0.541123
\(357\) 0 0
\(358\) −3342.08 −0.493392
\(359\) 1433.93 2483.64i 0.210808 0.365130i −0.741160 0.671329i \(-0.765724\pi\)
0.951968 + 0.306199i \(0.0990572\pi\)
\(360\) −123.166 213.330i −0.0180318 0.0312319i
\(361\) 3422.77 + 5928.42i 0.499019 + 0.864327i
\(362\) 1052.54 1823.04i 0.152818 0.264688i
\(363\) −4047.94 −0.585295
\(364\) 0 0
\(365\) 1166.62 0.167298
\(366\) 4279.95 7413.09i 0.611247 1.05871i
\(367\) 5751.50 + 9961.89i 0.818054 + 1.41691i 0.907114 + 0.420884i \(0.138280\pi\)
−0.0890605 + 0.996026i \(0.528386\pi\)
\(368\) 1527.58 + 2645.84i 0.216387 + 0.374794i
\(369\) −481.662 + 834.264i −0.0679522 + 0.117697i
\(370\) 209.290 0.0294066
\(371\) 0 0
\(372\) −2488.39 −0.346820
\(373\) −2543.21 + 4404.98i −0.353037 + 0.611477i −0.986780 0.162066i \(-0.948184\pi\)
0.633743 + 0.773543i \(0.281518\pi\)
\(374\) −5430.52 9405.93i −0.750816 1.30045i
\(375\) −312.500 541.266i −0.0430331 0.0745356i
\(376\) 1449.24 2510.15i 0.198773 0.344285i
\(377\) 1852.12 0.253021
\(378\) 0 0
\(379\) 954.827 0.129409 0.0647047 0.997904i \(-0.479389\pi\)
0.0647047 + 0.997904i \(0.479389\pi\)
\(380\) 24.1436 41.8180i 0.00325932 0.00564531i
\(381\) −4054.34 7022.32i −0.545171 0.944264i
\(382\) 2866.40 + 4964.76i 0.383921 + 0.664971i
\(383\) 1541.95 2670.74i 0.205719 0.356315i −0.744643 0.667463i \(-0.767380\pi\)
0.950361 + 0.311148i \(0.100714\pi\)
\(384\) 1839.37 0.244439
\(385\) 0 0
\(386\) −8185.84 −1.07940
\(387\) −97.7995 + 169.394i −0.0128461 + 0.0222500i
\(388\) −287.034 497.158i −0.0375566 0.0650499i
\(389\) 3165.57 + 5482.93i 0.412599 + 0.714642i 0.995173 0.0981353i \(-0.0312878\pi\)
−0.582574 + 0.812777i \(0.697954\pi\)
\(390\) 1776.05 3076.22i 0.230600 0.399411i
\(391\) −8599.63 −1.11228
\(392\) 0 0
\(393\) −6901.59 −0.885850
\(394\) −2261.68 + 3917.35i −0.289193 + 0.500896i
\(395\) −2687.96 4655.69i −0.342395 0.593046i
\(396\) −121.831 211.018i −0.0154602 0.0267779i
\(397\) −6066.62 + 10507.7i −0.766939 + 1.32838i 0.172276 + 0.985049i \(0.444888\pi\)
−0.939215 + 0.343329i \(0.888445\pi\)
\(398\) 9416.32 1.18592
\(399\) 0 0
\(400\) −900.000 −0.112500
\(401\) 135.335 234.407i 0.0168536 0.0291913i −0.857476 0.514525i \(-0.827968\pi\)
0.874329 + 0.485333i \(0.161302\pi\)
\(402\) −3199.24 5541.24i −0.396924 0.687492i
\(403\) 5795.84 + 10038.7i 0.716406 + 1.24085i
\(404\) 1941.14 3362.15i 0.239047 0.414042i
\(405\) 3355.00 0.411633
\(406\) 0 0
\(407\) 835.967 0.101812
\(408\) −6240.37 + 10808.6i −0.757217 + 1.31154i
\(409\) 2009.96 + 3481.36i 0.242998 + 0.420885i 0.961567 0.274571i \(-0.0885358\pi\)
−0.718569 + 0.695456i \(0.755202\pi\)
\(410\) 2789.58 + 4831.69i 0.336018 + 0.582001i
\(411\) −4874.14 + 8442.26i −0.584973 + 1.01320i
\(412\) −2135.54 −0.255365
\(413\) 0 0
\(414\) 393.203 0.0466784
\(415\) −1708.31 + 2958.88i −0.202067 + 0.349990i
\(416\) 3485.76 + 6037.51i 0.410825 + 0.711570i
\(417\) −7000.00 12124.4i −0.822042 1.42382i
\(418\) −196.545 + 340.427i −0.0229984 + 0.0398345i
\(419\) −2437.28 −0.284175 −0.142087 0.989854i \(-0.545381\pi\)
−0.142087 + 0.989854i \(0.545381\pi\)
\(420\) 0 0
\(421\) −4751.36 −0.550041 −0.275020 0.961438i \(-0.588685\pi\)
−0.275020 + 0.961438i \(0.588685\pi\)
\(422\) −5010.09 + 8677.73i −0.577932 + 1.00101i
\(423\) −117.665 203.802i −0.0135250 0.0234260i
\(424\) −8227.44 14250.4i −0.942358 1.63221i
\(425\) 1266.66 2193.91i 0.144569 0.250401i
\(426\) −8574.57 −0.975210
\(427\) 0 0
\(428\) −1160.37 −0.131048
\(429\) 7094.10 12287.3i 0.798383 1.38284i
\(430\) 566.412 + 981.054i 0.0635228 + 0.110025i
\(431\) −3962.59 6863.41i −0.442857 0.767051i 0.555043 0.831822i \(-0.312702\pi\)
−0.997900 + 0.0647706i \(0.979368\pi\)
\(432\) 2610.00 4520.65i 0.290680 0.503472i
\(433\) 11487.3 1.27492 0.637462 0.770481i \(-0.279984\pi\)
0.637462 + 0.770481i \(0.279984\pi\)
\(434\) 0 0
\(435\) 754.950 0.0832117
\(436\) −2509.73 + 4346.99i −0.275675 + 0.477484i
\(437\) 155.622 + 269.546i 0.0170353 + 0.0295060i
\(438\) 1351.32 + 2340.55i 0.147416 + 0.255333i
\(439\) −4573.96 + 7922.33i −0.497274 + 0.861303i −0.999995 0.00314511i \(-0.998999\pi\)
0.502721 + 0.864449i \(0.332332\pi\)
\(440\) −5698.47 −0.617418
\(441\) 0 0
\(442\) 14397.8 1.54939
\(443\) −932.176 + 1614.58i −0.0999752 + 0.173162i −0.911674 0.410914i \(-0.865210\pi\)
0.811699 + 0.584076i \(0.198543\pi\)
\(444\) −118.947 206.023i −0.0127139 0.0220212i
\(445\) 3450.79 + 5976.95i 0.367603 + 0.636707i
\(446\) 1138.59 1972.09i 0.120883 0.209375i
\(447\) 7170.58 0.758741
\(448\) 0 0
\(449\) 4490.88 0.472022 0.236011 0.971750i \(-0.424160\pi\)
0.236011 + 0.971750i \(0.424160\pi\)
\(450\) −57.9156 + 100.313i −0.00606704 + 0.0105084i
\(451\) 11142.4 + 19299.2i 1.16336 + 2.01500i
\(452\) 1267.21 + 2194.87i 0.131869 + 0.228403i
\(453\) −4963.95 + 8597.82i −0.514850 + 0.891746i
\(454\) −3847.83 −0.397770
\(455\) 0 0
\(456\) 451.713 0.0463890
\(457\) 7171.91 12422.1i 0.734109 1.27151i −0.221005 0.975273i \(-0.570934\pi\)
0.955113 0.296241i \(-0.0957330\pi\)
\(458\) 665.251 + 1152.25i 0.0678714 + 0.117557i
\(459\) 7346.61 + 12724.7i 0.747081 + 1.29398i
\(460\) −558.680 + 967.662i −0.0566274 + 0.0980815i
\(461\) 14558.7 1.47086 0.735429 0.677602i \(-0.236981\pi\)
0.735429 + 0.677602i \(0.236981\pi\)
\(462\) 0 0
\(463\) −1809.56 −0.181636 −0.0908178 0.995868i \(-0.528948\pi\)
−0.0908178 + 0.995868i \(0.528948\pi\)
\(464\) 543.564 941.480i 0.0543843 0.0941964i
\(465\) 2362.47 + 4091.92i 0.235606 + 0.408082i
\(466\) −2683.20 4647.45i −0.266732 0.461993i
\(467\) 2990.82 5180.26i 0.296357 0.513306i −0.678942 0.734192i \(-0.737561\pi\)
0.975300 + 0.220886i \(0.0708947\pi\)
\(468\) 323.008 0.0319039
\(469\) 0 0
\(470\) −1362.93 −0.133760
\(471\) −101.650 + 176.063i −0.00994433 + 0.0172241i
\(472\) 706.174 + 1223.13i 0.0688650 + 0.119278i
\(473\) 2262.42 + 3918.63i 0.219929 + 0.380927i
\(474\) 6227.00 10785.5i 0.603409 1.04513i
\(475\) −91.6876 −0.00885666
\(476\) 0 0
\(477\) −1335.99 −0.128241
\(478\) −4238.63 + 7341.52i −0.405586 + 0.702496i
\(479\) 5763.75 + 9983.11i 0.549796 + 0.952275i 0.998288 + 0.0584884i \(0.0186281\pi\)
−0.448492 + 0.893787i \(0.648039\pi\)
\(480\) 1420.84 + 2460.97i 0.135109 + 0.234016i
\(481\) −554.093 + 959.718i −0.0525249 + 0.0909758i
\(482\) 5667.23 0.535551
\(483\) 0 0
\(484\) −2131.85 −0.200211
\(485\) −545.019 + 944.000i −0.0510269 + 0.0883811i
\(486\) −648.655 1123.50i −0.0605424 0.104862i
\(487\) −7895.74 13675.8i −0.734682 1.27251i −0.954863 0.297048i \(-0.903998\pi\)
0.220180 0.975459i \(-0.429335\pi\)
\(488\) 9101.95 15765.0i 0.844316 1.46240i
\(489\) 19769.9 1.82828
\(490\) 0 0
\(491\) 13064.9 1.20083 0.600417 0.799687i \(-0.295001\pi\)
0.600417 + 0.799687i \(0.295001\pi\)
\(492\) 3170.84 5492.06i 0.290554 0.503255i
\(493\) 1530.02 + 2650.07i 0.139774 + 0.242096i
\(494\) −260.548 451.282i −0.0237299 0.0411015i
\(495\) −231.332 + 400.680i −0.0210053 + 0.0363822i
\(496\) 6803.91 0.615937
\(497\) 0 0
\(498\) −7915.04 −0.712211
\(499\) 10067.9 17438.1i 0.903209 1.56440i 0.0799059 0.996802i \(-0.474538\pi\)
0.823303 0.567602i \(-0.192129\pi\)
\(500\) −164.578 285.058i −0.0147203 0.0254963i
\(501\) −8450.76 14637.1i −0.753597 1.30527i
\(502\) 3369.87 5836.78i 0.299611 0.518941i
\(503\) −751.675 −0.0666313 −0.0333156 0.999445i \(-0.510607\pi\)
−0.0333156 + 0.999445i \(0.510607\pi\)
\(504\) 0 0
\(505\) −7371.64 −0.649571
\(506\) 4548.03 7877.42i 0.399574 0.692083i
\(507\) 3911.69 + 6775.24i 0.342651 + 0.593489i
\(508\) −2135.22 3698.31i −0.186486 0.323004i
\(509\) 6167.23 10682.0i 0.537049 0.930196i −0.462012 0.886874i \(-0.652872\pi\)
0.999061 0.0433224i \(-0.0137943\pi\)
\(510\) 5868.73 0.509553
\(511\) 0 0
\(512\) 11186.4 0.965574
\(513\) 265.894 460.542i 0.0228840 0.0396363i
\(514\) −195.384 338.415i −0.0167666 0.0290406i
\(515\) 2027.47 + 3511.69i 0.173478 + 0.300473i
\(516\) 643.826 1115.14i 0.0549280 0.0951382i
\(517\) −5443.95 −0.463104
\(518\) 0 0
\(519\) 16033.3 1.35604
\(520\) 3777.05 6542.04i 0.318528 0.551706i
\(521\) 868.216 + 1503.80i 0.0730082 + 0.126454i 0.900218 0.435439i \(-0.143407\pi\)
−0.827210 + 0.561893i \(0.810073\pi\)
\(522\) −69.9574 121.170i −0.00586581 0.0101599i
\(523\) 710.710 1230.99i 0.0594210 0.102920i −0.834785 0.550577i \(-0.814408\pi\)
0.894206 + 0.447656i \(0.147741\pi\)
\(524\) −3634.72 −0.303022
\(525\) 0 0
\(526\) 7516.23 0.623048
\(527\) −9575.79 + 16585.8i −0.791514 + 1.37094i
\(528\) −4163.98 7212.23i −0.343209 0.594455i
\(529\) 2482.42 + 4299.68i 0.204029 + 0.353389i
\(530\) −3868.73 + 6700.84i −0.317070 + 0.549181i
\(531\) 114.670 0.00937148
\(532\) 0 0
\(533\) −29541.6 −2.40073
\(534\) −7994.19 + 13846.3i −0.647833 + 1.12208i
\(535\) 1101.65 + 1908.11i 0.0890252 + 0.154196i
\(536\) −6803.65 11784.3i −0.548271 0.949633i
\(537\) 3606.62 6246.86i 0.289827 0.501996i
\(538\) −6599.26 −0.528837
\(539\) 0 0
\(540\) 1909.11 0.152139
\(541\) −2886.63 + 4999.79i −0.229401 + 0.397334i −0.957631 0.287999i \(-0.907010\pi\)
0.728230 + 0.685333i \(0.240343\pi\)
\(542\) 3302.32 + 5719.79i 0.261710 + 0.453295i
\(543\) 2271.70 + 3934.70i 0.179536 + 0.310965i
\(544\) −5759.11 + 9975.06i −0.453896 + 0.786172i
\(545\) 9530.94 0.749102
\(546\) 0 0
\(547\) −3941.30 −0.308076 −0.154038 0.988065i \(-0.549228\pi\)
−0.154038 + 0.988065i \(0.549228\pi\)
\(548\) −2566.97 + 4446.12i −0.200101 + 0.346585i
\(549\) −738.997 1279.98i −0.0574493 0.0995050i
\(550\) 1339.78 + 2320.56i 0.103870 + 0.179907i
\(551\) 55.3756 95.9134i 0.00428145 0.00741570i
\(552\) −10452.6 −0.805961
\(553\) 0 0
\(554\) −5325.06 −0.408376
\(555\) −225.856 + 391.195i −0.0172740 + 0.0299194i
\(556\) −3686.55 6385.29i −0.281195 0.487044i
\(557\) 3475.87 + 6020.38i 0.264412 + 0.457974i 0.967409 0.253218i \(-0.0814889\pi\)
−0.702998 + 0.711192i \(0.748156\pi\)
\(558\) 437.836 758.355i 0.0332170 0.0575335i
\(559\) −5998.29 −0.453847
\(560\) 0 0
\(561\) 23441.5 1.76417
\(562\) 7076.36 12256.6i 0.531136 0.919954i
\(563\) 12142.3 + 21031.1i 0.908946 + 1.57434i 0.815530 + 0.578714i \(0.196445\pi\)
0.0934159 + 0.995627i \(0.470221\pi\)
\(564\) 774.603 + 1341.65i 0.0578310 + 0.100166i
\(565\) 2406.17 4167.62i 0.179165 0.310324i
\(566\) 13563.7 1.00729
\(567\) 0 0
\(568\) −18235.1 −1.34706
\(569\) 10781.7 18674.5i 0.794363 1.37588i −0.128880 0.991660i \(-0.541138\pi\)
0.923243 0.384217i \(-0.125528\pi\)
\(570\) −106.203 183.949i −0.00780412 0.0135171i
\(571\) 1844.78 + 3195.25i 0.135204 + 0.234181i 0.925675 0.378319i \(-0.123498\pi\)
−0.790471 + 0.612499i \(0.790164\pi\)
\(572\) 3736.11 6471.13i 0.273102 0.473027i
\(573\) −12373.2 −0.902090
\(574\) 0 0
\(575\) 2121.64 0.153875
\(576\) 551.325 954.923i 0.0398817 0.0690772i
\(577\) −11092.0 19211.8i −0.800285 1.38613i −0.919429 0.393257i \(-0.871348\pi\)
0.119144 0.992877i \(-0.461985\pi\)
\(578\) 6203.08 + 10744.1i 0.446391 + 0.773172i
\(579\) 8833.80 15300.6i 0.634059 1.09822i
\(580\) 397.594 0.0284641
\(581\) 0 0
\(582\) −2525.21 −0.179851
\(583\) −15452.9 + 26765.2i −1.09776 + 1.90137i
\(584\) 2873.78 + 4977.53i 0.203626 + 0.352691i
\(585\) −306.662 531.155i −0.0216734 0.0375394i
\(586\) 5948.33 10302.8i 0.419323 0.726289i
\(587\) −10605.3 −0.745705 −0.372852 0.927891i \(-0.621620\pi\)
−0.372852 + 0.927891i \(0.621620\pi\)
\(588\) 0 0
\(589\) 693.149 0.0484902
\(590\) 332.059 575.143i 0.0231706 0.0401327i
\(591\) −4881.42 8454.86i −0.339754 0.588471i
\(592\) 325.233 + 563.320i 0.0225794 + 0.0391087i
\(593\) 3138.62 5436.26i 0.217349 0.376459i −0.736648 0.676277i \(-0.763592\pi\)
0.953997 + 0.299817i \(0.0969258\pi\)
\(594\) −15541.4 −1.07352
\(595\) 0 0
\(596\) 3776.39 0.259542
\(597\) −10161.7 + 17600.5i −0.696633 + 1.20660i
\(598\) 6029.03 + 10442.6i 0.412283 + 0.714096i
\(599\) 4985.36 + 8634.90i 0.340061 + 0.589003i 0.984444 0.175700i \(-0.0562190\pi\)
−0.644383 + 0.764703i \(0.722886\pi\)
\(600\) 1539.58 2666.63i 0.104755 0.181441i
\(601\) 24619.2 1.67094 0.835472 0.549533i \(-0.185194\pi\)
0.835472 + 0.549533i \(0.185194\pi\)
\(602\) 0 0
\(603\) −1104.79 −0.0746113
\(604\) −2614.27 + 4528.04i −0.176114 + 0.305039i
\(605\) 2023.97 + 3505.62i 0.136010 + 0.235577i
\(606\) −8538.66 14789.4i −0.572375 0.991383i
\(607\) 5626.47 9745.34i 0.376230 0.651649i −0.614281 0.789088i \(-0.710554\pi\)
0.990510 + 0.137439i \(0.0438870\pi\)
\(608\) 416.876 0.0278068
\(609\) 0 0
\(610\) −8559.90 −0.568164
\(611\) 3608.34 6249.83i 0.238916 0.413815i
\(612\) 266.834 + 462.170i 0.0176244 + 0.0305263i
\(613\) 7646.61 + 13244.3i 0.503824 + 0.872648i 0.999990 + 0.00442069i \(0.00140715\pi\)
−0.496167 + 0.868227i \(0.665260\pi\)
\(614\) −2435.90 + 4219.10i −0.160105 + 0.277311i
\(615\) −12041.6 −0.789533
\(616\) 0 0
\(617\) −17589.4 −1.14769 −0.573843 0.818966i \(-0.694548\pi\)
−0.573843 + 0.818966i \(0.694548\pi\)
\(618\) −4696.90 + 8135.27i −0.305723 + 0.529528i
\(619\) −11733.7 20323.3i −0.761900 1.31965i −0.941870 0.335978i \(-0.890933\pi\)
0.179970 0.983672i \(-0.442400\pi\)
\(620\) 1244.19 + 2155.01i 0.0805936 + 0.139592i
\(621\) −6152.75 + 10656.9i −0.397587 + 0.688640i
\(622\) −13353.7 −0.860829
\(623\) 0 0
\(624\) 11039.8 0.708249
\(625\) −312.500 + 541.266i −0.0200000 + 0.0346410i
\(626\) 1575.32 + 2728.53i 0.100579 + 0.174208i
\(627\) −424.206 734.747i −0.0270194 0.0467990i
\(628\) −53.5339 + 92.7235i −0.00340165 + 0.00589183i
\(629\) −1830.93 −0.116063
\(630\) 0 0
\(631\) −6040.86 −0.381114 −0.190557 0.981676i \(-0.561029\pi\)
−0.190557 + 0.981676i \(0.561029\pi\)
\(632\) 13242.7 22937.0i 0.833488 1.44364i
\(633\) −10813.3 18729.3i −0.678976 1.17602i
\(634\) 5952.51 + 10310.0i 0.372877 + 0.645843i
\(635\) −4054.34 + 7022.32i −0.253373 + 0.438854i
\(636\) 8794.99 0.548340
\(637\) 0 0
\(638\) −3236.68 −0.200849
\(639\) −740.264 + 1282.17i −0.0458285 + 0.0793772i
\(640\) −919.683 1592.94i −0.0568026 0.0983849i
\(641\) −12555.8 21747.3i −0.773673 1.34004i −0.935538 0.353227i \(-0.885084\pi\)
0.161865 0.986813i \(-0.448249\pi\)
\(642\) −2552.11 + 4420.38i −0.156891 + 0.271742i
\(643\) −3095.03 −0.189823 −0.0949113 0.995486i \(-0.530257\pi\)
−0.0949113 + 0.995486i \(0.530257\pi\)
\(644\) 0 0
\(645\) −2444.99 −0.149258
\(646\) 430.472 745.600i 0.0262178 0.0454106i
\(647\) 4589.31 + 7948.93i 0.278863 + 0.483005i 0.971103 0.238663i \(-0.0767090\pi\)
−0.692239 + 0.721668i \(0.743376\pi\)
\(648\) 8264.46 + 14314.5i 0.501016 + 0.867785i
\(649\) 1326.35 2297.30i 0.0802213 0.138947i
\(650\) −3552.11 −0.214346
\(651\) 0 0
\(652\) 10411.8 0.625397
\(653\) 7219.19 12504.0i 0.432632 0.749341i −0.564467 0.825456i \(-0.690918\pi\)
0.997099 + 0.0761147i \(0.0242515\pi\)
\(654\) 11039.8 + 19121.5i 0.660077 + 1.14329i
\(655\) 3450.79 + 5976.95i 0.205853 + 0.356548i
\(656\) −8669.92 + 15016.7i −0.516012 + 0.893759i
\(657\) 466.650 0.0277104
\(658\) 0 0
\(659\) −2900.64 −0.171461 −0.0857305 0.996318i \(-0.527322\pi\)
−0.0857305 + 0.996318i \(0.527322\pi\)
\(660\) 1522.89 2637.72i 0.0898158 0.155566i
\(661\) 4988.26 + 8639.92i 0.293526 + 0.508403i 0.974641 0.223774i \(-0.0718378\pi\)
−0.681115 + 0.732177i \(0.738504\pi\)
\(662\) 2114.73 + 3662.82i 0.124156 + 0.215045i
\(663\) −15537.4 + 26911.6i −0.910142 + 1.57641i
\(664\) −16832.5 −0.983777
\(665\) 0 0
\(666\) 83.7159 0.00487076
\(667\) −1281.38 + 2219.42i −0.0743859 + 0.128840i
\(668\) −4450.59 7708.65i −0.257782 0.446492i
\(669\) 2457.42 + 4256.38i 0.142017 + 0.245981i
\(670\) −3199.24 + 5541.24i −0.184474 + 0.319517i
\(671\) −34190.8 −1.96710
\(672\) 0 0
\(673\) 20760.8 1.18911 0.594554 0.804055i \(-0.297329\pi\)
0.594554 + 0.804055i \(0.297329\pi\)
\(674\) 178.363 308.933i 0.0101933 0.0176553i
\(675\) −1812.50 3139.34i −0.103353 0.179012i
\(676\) 2060.09 + 3568.18i 0.117210 + 0.203014i
\(677\) 1604.56 2779.19i 0.0910907 0.157774i −0.816880 0.576808i \(-0.804298\pi\)
0.907970 + 0.419034i \(0.137631\pi\)
\(678\) 11148.4 0.631492
\(679\) 0 0
\(680\) 12480.7 0.703845
\(681\) 4152.41 7192.19i 0.233658 0.404707i
\(682\) −10128.6 17543.2i −0.568685 0.984991i
\(683\) −2166.79 3752.98i −0.121391 0.210255i 0.798926 0.601430i \(-0.205402\pi\)
−0.920316 + 0.391175i \(0.872069\pi\)
\(684\) 9.65745 16.7272i 0.000539857 0.000935059i
\(685\) 9748.29 0.543741
\(686\) 0 0
\(687\) −2871.64 −0.159476
\(688\) −1760.39 + 3049.09i −0.0975498 + 0.168961i
\(689\) −20484.9 35480.9i −1.13267 1.96185i
\(690\) 2457.52 + 4256.55i 0.135589 + 0.234846i
\(691\) −7222.98 + 12510.6i −0.397649 + 0.688748i −0.993435 0.114395i \(-0.963507\pi\)
0.595787 + 0.803143i \(0.296840\pi\)
\(692\) 8443.94 0.463859
\(693\) 0 0
\(694\) −10099.1 −0.552385
\(695\) −7000.00 + 12124.4i −0.382051 + 0.661731i
\(696\) 1859.69 + 3221.07i 0.101281 + 0.175423i
\(697\) −24404.0 42269.0i −1.32621 2.29706i
\(698\) −1956.39 + 3388.56i −0.106089 + 0.183752i
\(699\) 11582.4 0.626733
\(700\) 0 0
\(701\) −859.801 −0.0463256 −0.0231628 0.999732i \(-0.507374\pi\)
−0.0231628 + 0.999732i \(0.507374\pi\)
\(702\) 10301.1 17842.1i 0.553833 0.959267i
\(703\) 33.1332 + 57.3883i 0.00177758 + 0.00307886i
\(704\) −12753.9 22090.5i −0.682787 1.18262i
\(705\) 1470.81 2547.52i 0.0785730 0.136093i
\(706\) −9084.31 −0.484267
\(707\) 0 0
\(708\) −754.887 −0.0400712
\(709\) 3989.56 6910.13i 0.211327 0.366030i −0.740803 0.671723i \(-0.765555\pi\)
0.952130 + 0.305693i \(0.0988880\pi\)
\(710\) 4287.28 + 7425.80i 0.226618 + 0.392514i
\(711\) −1075.19 1862.28i −0.0567125 0.0982290i
\(712\) −17000.9 + 29446.3i −0.894851 + 1.54993i
\(713\) −16039.4 −0.842467
\(714\) 0 0
\(715\) −14188.2 −0.742110
\(716\) 1899.43 3289.91i 0.0991410 0.171717i
\(717\) −9148.28 15845.3i −0.476498 0.825318i
\(718\) −3321.88 5753.67i −0.172662 0.299060i
\(719\) −16851.6 + 29187.9i −0.874076 + 1.51394i −0.0163313 + 0.999867i \(0.505199\pi\)
−0.857744 + 0.514077i \(0.828135\pi\)
\(720\) −360.000 −0.0186339
\(721\) 0 0
\(722\) 15858.6 0.817444
\(723\) −6115.83 + 10592.9i −0.314592 + 0.544890i
\(724\) 1196.39 + 2072.21i 0.0614137 + 0.106372i
\(725\) −377.475 653.806i −0.0193366 0.0334920i
\(726\) −4688.78 + 8121.21i −0.239693 + 0.415160i
\(727\) 30277.0 1.54458 0.772290 0.635270i \(-0.219111\pi\)
0.772290 + 0.635270i \(0.219111\pi\)
\(728\) 0 0
\(729\) 20917.0 1.06269
\(730\) 1351.32 2340.55i 0.0685129 0.118668i
\(731\) −4955.13 8582.54i −0.250714 0.434250i
\(732\) 4864.91 + 8426.27i 0.245645 + 0.425470i
\(733\) 9681.97 16769.7i 0.487874 0.845023i −0.512028 0.858968i \(-0.671106\pi\)
0.999903 + 0.0139454i \(0.00443911\pi\)
\(734\) 26648.1 1.34005
\(735\) 0 0
\(736\) −9646.45 −0.483115
\(737\) −12778.7 + 22133.4i −0.638684 + 1.10623i
\(738\) 1115.83 + 1932.68i 0.0556563 + 0.0963995i
\(739\) −12476.2 21609.4i −0.621035 1.07566i −0.989293 0.145940i \(-0.953379\pi\)
0.368259 0.929723i \(-0.379954\pi\)
\(740\) −118.947 + 206.023i −0.00590890 + 0.0102345i
\(741\) 1124.69 0.0557576
\(742\) 0 0
\(743\) −8154.54 −0.402640 −0.201320 0.979526i \(-0.564523\pi\)
−0.201320 + 0.979526i \(0.564523\pi\)
\(744\) −11639.1 + 20159.4i −0.573533 + 0.993388i
\(745\) −3585.29 6209.91i −0.176315 0.305387i
\(746\) 5891.67 + 10204.7i 0.289155 + 0.500831i
\(747\) −683.325 + 1183.55i −0.0334693 + 0.0579705i
\(748\) 12345.5 0.603469
\(749\) 0 0
\(750\) −1447.89 −0.0704926
\(751\) 2155.63 3733.66i 0.104740 0.181416i −0.808892 0.587958i \(-0.799932\pi\)
0.913632 + 0.406542i \(0.133265\pi\)
\(752\) −2117.97 3668.43i −0.102705 0.177891i
\(753\) 7273.22 + 12597.6i 0.351993 + 0.609670i
\(754\) 2145.33 3715.82i 0.103619 0.179473i
\(755\) 9927.91 0.478561
\(756\) 0 0
\(757\) 3624.79 0.174036 0.0870179 0.996207i \(-0.472266\pi\)
0.0870179 + 0.996207i \(0.472266\pi\)
\(758\) 1105.99 1915.63i 0.0529964 0.0917925i
\(759\) 9816.07 + 17001.9i 0.469435 + 0.813085i
\(760\) −225.856 391.195i −0.0107798 0.0186712i
\(761\) 10288.2 17819.7i 0.490075 0.848835i −0.509860 0.860258i \(-0.670303\pi\)
0.999935 + 0.0114227i \(0.00363604\pi\)
\(762\) −18784.8 −0.893045
\(763\) 0 0
\(764\) −6516.34 −0.308577
\(765\) 506.662 877.565i 0.0239456 0.0414751i
\(766\) −3572.13 6187.11i −0.168494 0.291840i
\(767\) 1758.25 + 3045.38i 0.0827728 + 0.143367i
\(768\) −8895.94 + 15408.2i −0.417975 + 0.723953i
\(769\) 3066.14 0.143781 0.0718907 0.997413i \(-0.477097\pi\)
0.0718907 + 0.997413i \(0.477097\pi\)
\(770\) 0 0
\(771\) 843.400 0.0393960
\(772\) 4652.32 8058.06i 0.216892 0.375668i
\(773\) −9693.52 16789.7i −0.451037 0.781219i 0.547413 0.836862i \(-0.315613\pi\)
−0.998451 + 0.0556429i \(0.982279\pi\)
\(774\) 226.565 + 392.422i 0.0105216 + 0.0182239i
\(775\) 2362.47 4091.92i 0.109500 0.189659i
\(776\) −5370.23 −0.248428
\(777\) 0 0