Properties

Label 245.4.e.j.116.2
Level $245$
Weight $4$
Character 245.116
Analytic conductor $14.455$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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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 116.2
Root \(1.65831 + 2.87228i\) of defining polynomial
Character \(\chi\) \(=\) 245.116
Dual form 245.4.e.j.226.2

$q$-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 \(\left(\mathbb{Z}/245\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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 0.994837 0.101490i \(-0.0323610\pi\)
−0.585311 + 0.810809i \(0.699028\pi\)
\(3\) −2.50000 + 4.33013i −0.481125 + 0.833333i −0.999765 0.0216593i \(-0.993105\pi\)
0.518640 + 0.854993i \(0.326438\pi\)
\(4\) 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 0.352623 + 0.935765i \(0.385290\pi\)
−0.986708 + 0.162502i \(0.948044\pi\)
\(12\) 6.58312 + 11.4023i 0.158365 + 0.274297i
\(13\) −61.3325 −1.30851 −0.654253 0.756276i \(-0.727017\pi\)
−0.654253 + 0.756276i \(0.727017\pi\)
\(14\) 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 0.237009 + 0.971507i \(0.423833\pi\)
−0.959855 + 0.280497i \(0.909501\pi\)
\(18\) −2.31662 + 4.01251i −0.0303352 + 0.0525421i
\(19\) −1.83375 3.17615i −0.0221417 0.0383505i 0.854742 0.519053i \(-0.173715\pi\)
−0.876884 + 0.480702i \(0.840382\pi\)
\(20\) −13.1662 −0.147203
\(21\) 0 0
\(22\) −107.182 −1.03870
\(23\) −42.4327 73.4957i −0.384689 0.666300i 0.607037 0.794673i \(-0.292358\pi\)
−0.991726 + 0.128373i \(0.959025\pi\)
\(24\) −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 0.450946 + 0.892551i \(0.351087\pi\)
−0.998445 + 0.0557451i \(0.982247\pi\)
\(32\) 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 0.845257 0.534360i \(-0.179447\pi\)
−0.885398 + 0.464834i \(0.846114\pi\)
\(38\) 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 \(-0.130321\pi\)
0.917354 + 0.398072i \(0.130321\pi\)
\(42\) 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 \(-0.225114\pi\)
−0.942761 + 0.333470i \(0.891781\pi\)
\(48\) −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 0.000801827 1.00000i \(0.499745\pi\)
−0.866426 + 0.499305i \(0.833589\pi\)
\(54\) −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 \(-0.853482\pi\)
0.832662 + 0.553781i \(0.186816\pi\)
\(60\) 32.9156 57.0115i 0.0708231 0.122669i
\(61\) −369.499 639.991i −0.775565 1.34332i −0.934476 0.356025i \(-0.884132\pi\)
0.158911 0.987293i \(-0.449202\pi\)
\(62\) −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 0.496365 + 0.868114i \(0.334668\pi\)
−0.999991 + 0.00419224i \(0.998666\pi\)
\(68\) 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 \(-0.893224\pi\)
0.757218 + 0.653162i \(0.226558\pi\)
\(74\) 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 0.939919 + 0.341398i \(0.110901\pi\)
−0.174300 + 0.984693i \(0.555766\pi\)
\(80\) 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 \(-0.350769\pi\)
0.451835 + 0.892101i \(0.350769\pi\)
\(84\) 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 0.904202 + 0.427106i \(0.140467\pi\)
−0.0822166 + 0.996614i \(0.526200\pi\)
\(90\) 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 \(-0.463602\pi\)
0.114100 + 0.993469i \(0.463602\pi\)
\(98\) 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 −0.232217 0.972664i \(-0.574598\pi\)
0.958460 0.285226i \(-0.0920686\pi\)
\(102\) 586.873 1016.49i 0.569697 0.986745i
\(103\) 405.495 + 702.338i 0.387909 + 0.671878i 0.992168 0.124910i \(-0.0398642\pi\)
−0.604259 + 0.796788i \(0.706531\pi\)
\(104\) −1510.82 −1.42450
\(105\) 0 0
\(106\) −1547.49 −1.41798
\(107\) −220.330 381.623i −0.199066 0.344793i 0.749160 0.662390i \(-0.230458\pi\)
−0.948226 + 0.317596i \(0.897124\pi\)
\(108\) −190.911 + 330.667i −0.170096 + 0.294615i
\(109\) 953.094 1650.81i 0.837522 1.45063i −0.0544393 0.998517i \(-0.517337\pi\)
0.891961 0.452113i \(-0.149330\pi\)
\(110\) 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 \(-0.0144081\pi\)
−0.538675 + 0.842514i \(0.681075\pi\)
\(132\) −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 −0.383661 0.923474i \(-0.625337\pi\)
0.991582 0.129477i \(-0.0413298\pi\)
\(138\) 491.504 + 851.309i 0.303185 + 0.525132i
\(139\) 2800.00 1.70858 0.854291 0.519795i \(-0.173992\pi\)
0.854291 + 0.519795i \(0.173992\pi\)
\(140\) 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 0.993006 0.118068i \(-0.0376700\pi\)
−0.598752 + 0.800934i \(0.704337\pi\)
\(150\) 144.789 250.782i 0.0788132 0.136508i
\(151\) 992.791 1719.56i 0.535047 0.926729i −0.464114 0.885776i \(-0.653627\pi\)
0.999161 0.0409537i \(-0.0130396\pi\)
\(152\) −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 \(-0.836623\pi\)
0.860812 + 0.508923i \(0.169956\pi\)
\(158\) −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 0.745416 + 0.666599i \(0.232251\pi\)
0.204584 + 0.978849i \(0.434416\pi\)
\(164\) 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 \(-0.213606\pi\)
0.783161 + 0.621819i \(0.213606\pi\)
\(168\) 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 −0.966829 0.255424i \(-0.917785\pi\)
0.262210 0.965011i \(-0.415549\pi\)
\(174\) −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 −0.976407 0.215936i \(-0.930720\pi\)
0.675210 + 0.737626i \(0.264053\pi\)
\(180\) −13.1662 22.8046i −0.00545197 0.00944308i
\(181\) −908.680 −0.373158 −0.186579 0.982440i \(-0.559740\pi\)
−0.186579 + 0.982440i \(0.559740\pi\)
\(182\) 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 0.530622 0.847609i \(-0.321958\pi\)
−0.999362 + 0.0357280i \(0.988625\pi\)
\(192\) −1378.31 + 2387.31i −0.518079 + 0.897339i
\(193\) −1766.76 + 3060.12i −0.658934 + 1.14131i 0.321958 + 0.946754i \(0.395659\pi\)
−0.980892 + 0.194553i \(0.937674\pi\)
\(194\) 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 0.235438 + 0.971889i \(0.424348\pi\)
−0.959400 + 0.282049i \(0.908986\pi\)
\(200\) −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 \(-0.547151\pi\)
−0.147589 + 0.989049i \(0.547151\pi\)
\(224\) 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 \(-0.755260\pi\)
0.961518 + 0.274743i \(0.0885929\pi\)
\(228\) 24.1436 41.8180i 0.00701294 0.0121468i
\(229\) 287.164 + 497.382i 0.0828660 + 0.143528i 0.904480 0.426516i \(-0.140259\pi\)
−0.821614 + 0.570044i \(0.806926\pi\)
\(230\) −983.008 −0.281816
\(231\) 0 0
\(232\) 743.875 0.210508
\(233\) 1158.24 + 2006.13i 0.325660 + 0.564059i 0.981646 0.190714i \(-0.0610802\pi\)
−0.655986 + 0.754773i \(0.727747\pi\)
\(234\) 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 \(-0.939349\pi\)
0.654968 + 0.755657i \(0.272682\pi\)
\(242\) 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 \(-0.619205\pi\)
−0.365802 + 0.930693i \(0.619205\pi\)
\(252\) 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 \(-0.173183\pi\)
−0.876079 + 0.482167i \(0.839850\pi\)
\(258\) 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 −0.610764 0.791812i \(-0.709138\pi\)
0.991112 + 0.133031i \(0.0424711\pi\)
\(264\) −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 \(-0.728697\pi\)
0.981072 + 0.193644i \(0.0620306\pi\)
\(270\) −839.776 + 1454.54i −0.189286 + 0.327853i
\(271\) 1425.49 + 2469.02i 0.319529 + 0.553440i 0.980390 0.197068i \(-0.0631421\pi\)
−0.660861 + 0.750508i \(0.729809\pi\)
\(272\) −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 −0.963331 0.268315i \(-0.913533\pi\)
0.714033 + 0.700112i \(0.246867\pi\)
\(278\) 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 0.375487 + 0.926828i \(0.377475\pi\)
−0.990400 + 0.138233i \(0.955858\pi\)
\(284\) −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 \(-0.671081\pi\)
−0.511962 + 0.859008i \(0.671081\pi\)
\(294\) 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 \(-0.437375\pi\)
0.195477 + 0.980708i \(0.437375\pi\)
\(308\) 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 −0.474055 0.880495i \(-0.657210\pi\)
0.999559 0.0297045i \(-0.00945661\pi\)
\(312\) 3777.05 6542.04i 0.685363 1.18708i
\(313\) 680.006 + 1177.81i 0.122799 + 0.212695i 0.920871 0.389868i \(-0.127479\pi\)
−0.798071 + 0.602563i \(0.794146\pi\)
\(314\) −94.1939 −0.0169289
\(315\) 0 0
\(316\) 2831.23 0.504017
\(317\) −2569.47 4450.46i −0.455256 0.788526i 0.543447 0.839443i \(-0.317119\pi\)
−0.998703 + 0.0509173i \(0.983785\pi\)
\(318\) 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 0.780225 0.625499i \(-0.215105\pi\)
−0.931810 + 0.362945i \(0.881771\pi\)
\(332\) 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 −0.983907 0.178682i \(-0.942817\pi\)
0.646696 + 0.762748i \(0.276150\pi\)
\(348\) 198.797 + 344.327i 0.0306225 + 0.0530398i
\(349\) 1689.00 0.259054 0.129527 0.991576i \(-0.458654\pi\)
0.129527 + 0.991576i \(0.458654\pi\)
\(350\) 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 \(-0.737805\pi\)
0.975131 + 0.221631i \(0.0711380\pi\)
\(354\) 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 0.951968 0.306199i \(-0.0990572\pi\)
−0.741160 + 0.671329i \(0.765724\pi\)
\(360\) 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 0.0890605 + 0.996026i \(0.471614\pi\)
−0.907114 + 0.420884i \(0.861720\pi\)
\(368\) 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 0.633743 0.773543i \(-0.281518\pi\)
−0.986780 + 0.162066i \(0.948184\pi\)
\(374\) 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 \(-0.232620\pi\)
−0.950361 + 0.311148i \(0.899286\pi\)
\(384\) −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 −0.582574 0.812777i \(-0.697954\pi\)
0.995173 + 0.0981353i \(0.0312878\pi\)
\(390\) −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 0.939215 + 0.343329i \(0.111555\pi\)
−0.172276 + 0.985049i \(0.555112\pi\)
\(398\) −9416.32 −1.18592
\(399\) 0 0
\(400\) −900.000 −0.112500
\(401\) 135.335 + 234.407i 0.0168536 + 0.0291913i 0.874329 0.485333i \(-0.161302\pi\)
−0.857476 + 0.514525i \(0.827968\pi\)
\(402\) 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 \(-0.911464\pi\)
0.718569 + 0.695456i \(0.244798\pi\)
\(410\) 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 \(-0.454619\pi\)
0.142087 + 0.989854i \(0.454619\pi\)
\(420\) 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 −0.997900 0.0647706i \(-0.979368\pi\)
0.555043 + 0.831822i \(0.312702\pi\)
\(432\) −2610.00 4520.65i −0.290680 0.503472i
\(433\) −11487.3 −1.27492 −0.637462 0.770481i \(-0.720016\pi\)
−0.637462 + 0.770481i \(0.720016\pi\)
\(434\) 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 \(-0.00100112\pi\)
−0.502721 + 0.864449i \(0.667668\pi\)
\(440\) 5698.47 0.617418
\(441\) 0 0
\(442\) 14397.8 1.54939
\(443\) −932.176 1614.58i −0.0999752 0.173162i 0.811699 0.584076i \(-0.198543\pi\)
−0.911674 + 0.410914i \(0.865210\pi\)
\(444\) 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 0.955113 + 0.296241i \(0.0957330\pi\)
−0.221005 + 0.975273i \(0.570934\pi\)
\(458\) −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 \(-0.763019\pi\)
−0.735429 + 0.677602i \(0.763019\pi\)
\(462\) 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 \(-0.262439\pi\)
−0.975300 + 0.220886i \(0.929105\pi\)
\(468\) −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 0.448492 + 0.893787i \(0.351961\pi\)
−0.998288 + 0.0584884i \(0.981372\pi\)
\(480\) 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 0.220180 + 0.975459i \(0.429335\pi\)
−0.954863 + 0.297048i \(0.903998\pi\)
\(488\) −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 0.823303 + 0.567602i \(0.192129\pi\)
0.0799059 + 0.996802i \(0.474538\pi\)
\(500\) 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 \(-0.489393\pi\)
0.0333156 + 0.999445i \(0.489393\pi\)
\(504\) 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 −0.999061 0.0433224i \(-0.986206\pi\)
0.462012 0.886874i \(-0.347128\pi\)
\(510\) −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 \(-0.856593\pi\)
0.827210 + 0.561893i \(0.189927\pi\)
\(522\) −69.9574 + 121.170i −0.00586581 + 0.0101599i
\(523\) −710.710 1230.99i −0.0594210 0.102920i 0.834785 0.550577i \(-0.185592\pi\)
−0.894206 + 0.447656i \(0.852259\pi\)
\(524\) 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 0.728230 0.685333i \(-0.240343\pi\)
−0.957631 + 0.287999i \(0.907010\pi\)
\(542\) −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 −0.702998 0.711192i \(-0.748156\pi\)
0.967409 + 0.253218i \(0.0814889\pi\)
\(558\) −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 −0.0934159 + 0.995627i \(0.529779\pi\)
−0.815530 + 0.578714i \(0.803555\pi\)
\(564\) 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 0.923243 + 0.384217i \(0.125528\pi\)
−0.128880 + 0.991660i \(0.541138\pi\)
\(570\) 106.203 183.949i 0.00780412 0.0135171i
\(571\) 1844.78 3195.25i 0.135204 0.234181i −0.790471 0.612499i \(-0.790164\pi\)
0.925675 + 0.378319i \(0.123498\pi\)
\(572\) −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 −0.119144 0.992877i \(-0.538015\pi\)
0.919429 0.393257i \(-0.128652\pi\)
\(578\) 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 \(-0.378380\pi\)
0.372852 + 0.927891i \(0.378380\pi\)
\(588\) 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 \(-0.236408\pi\)
−0.953997 + 0.299817i \(0.903074\pi\)
\(594\) 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 −0.644383 0.764703i \(-0.722886\pi\)
0.984444 + 0.175700i \(0.0562190\pi\)
\(600\) −1539.58 2666.63i −0.104755 0.181441i
\(601\) −24619.2 −1.67094 −0.835472 0.549533i \(-0.814806\pi\)
−0.835472 + 0.549533i \(0.814806\pi\)
\(602\) 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 \(-0.289446\pi\)
−0.990510 + 0.137439i \(0.956113\pi\)
\(608\) −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 −0.496167 0.868227i \(-0.665260\pi\)
0.999990 0.00442069i \(-0.00140715\pi\)
\(614\) 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 −0.179970 0.983672i \(-0.557600\pi\)
0.941870 0.335978i \(-0.109067\pi\)
\(620\) 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 0.161865 + 0.986813i \(0.448249\pi\)
−0.935538 + 0.353227i \(0.885084\pi\)
\(642\) 2552.11 + 4420.38i 0.156891 + 0.271742i
\(643\) 3095.03 0.189823 0.0949113 0.995486i \(-0.469743\pi\)
0.0949113 + 0.995486i \(0.469743\pi\)
\(644\) 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 \(-0.923291\pi\)
0.692239 + 0.721668i \(0.256624\pi\)
\(648\) 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 0.997099 0.0761147i \(-0.0242515\pi\)
−0.564467 + 0.825456i \(0.690918\pi\)
\(654\) −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 \(-0.928162\pi\)
0.681115 + 0.732177i \(0.261496\pi\)
\(662\) 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 \(-0.195702\pi\)
−0.907970 + 0.419034i \(0.862369\pi\)
\(678\) −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 −0.920316 0.391175i \(-0.872069\pi\)
0.798926 + 0.601430i \(0.205402\pi\)
\(684\) −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 \(-0.0364930\pi\)
−0.595787 + 0.803143i \(0.703160\pi\)
\(692\) −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 0.952130 0.305693i \(-0.0988880\pi\)
−0.740803 + 0.671723i \(0.765555\pi\)
\(710\) −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 0.857744 + 0.514077i \(0.171865\pi\)
0.0163313 + 0.999867i \(0.494801\pi\)
\(720\) 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 \(-0.780889\pi\)
−0.772290 + 0.635270i \(0.780889\pi\)
\(728\) 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 \(-0.328894\pi\)
−0.999903 + 0.0139454i \(0.995561\pi\)
\(734\) −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 0.368259 + 0.929723i \(0.379954\pi\)
−0.989293 + 0.145940i \(0.953379\pi\)
\(740\) 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 0.913632 0.406542i \(-0.133265\pi\)
−0.808892 + 0.587958i \(0.799932\pi\)
\(752\) 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 \(-0.329697\pi\)
−0.999935 + 0.0114227i \(0.996364\pi\)
\(762\) 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 \(-0.522903\pi\)
−0.0718907 + 0.997413i \(0.522903\pi\)
\(770\) 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 \(-0.684387\pi\)
0.998451 + 0.0556429i \(0.0177208\pi\)
\(774\) 226.565 392.422i 0.0105216 0.0182239i
\(775\) −2362.47 4091.92i −0.109500 0.189659i
\(776\) 5370.23 0.248428