Properties

Label 731.2.e.a.307.18
Level 731
Weight 2
Character 731.307
Analytic conductor 5.837
Analytic rank 0
Dimension 58
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 731 = 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 731.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.83706438776\)
Analytic rank: \(0\)
Dimension: \(58\)
Relative dimension: \(29\) over \(\Q(\zeta_{3})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 307.18
Character \(\chi\) = 731.307
Dual form 731.2.e.a.681.18

$q$-expansion

\(f(q)\) \(=\) \(q+0.576537 q^{2} +(0.0377307 - 0.0653514i) q^{3} -1.66761 q^{4} +(0.551580 - 0.955365i) q^{5} +(0.0217531 - 0.0376775i) q^{6} +(0.781254 + 1.35317i) q^{7} -2.11451 q^{8} +(1.49715 + 2.59314i) q^{9} +O(q^{10})\) \(q+0.576537 q^{2} +(0.0377307 - 0.0653514i) q^{3} -1.66761 q^{4} +(0.551580 - 0.955365i) q^{5} +(0.0217531 - 0.0376775i) q^{6} +(0.781254 + 1.35317i) q^{7} -2.11451 q^{8} +(1.49715 + 2.59314i) q^{9} +(0.318006 - 0.550803i) q^{10} -3.20387 q^{11} +(-0.0629199 + 0.108980i) q^{12} +(1.63462 + 2.83124i) q^{13} +(0.450421 + 0.780152i) q^{14} +(-0.0416230 - 0.0720931i) q^{15} +2.11612 q^{16} +(0.500000 + 0.866025i) q^{17} +(0.863163 + 1.49504i) q^{18} +(2.42124 - 4.19371i) q^{19} +(-0.919818 + 1.59317i) q^{20} +0.117909 q^{21} -1.84715 q^{22} +(-3.80446 + 6.58951i) q^{23} +(-0.0797818 + 0.138186i) q^{24} +(1.89152 + 3.27621i) q^{25} +(0.942416 + 1.63231i) q^{26} +0.452338 q^{27} +(-1.30282 - 2.25656i) q^{28} +(4.10020 + 7.10176i) q^{29} +(-0.0239972 - 0.0415643i) q^{30} +(-0.597849 + 1.03551i) q^{31} +5.44904 q^{32} +(-0.120884 + 0.209377i) q^{33} +(0.288268 + 0.499295i) q^{34} +1.72370 q^{35} +(-2.49666 - 4.32434i) q^{36} +(-0.803255 + 1.39128i) q^{37} +(1.39593 - 2.41783i) q^{38} +0.246701 q^{39} +(-1.16632 + 2.02013i) q^{40} +5.43670 q^{41} +0.0679788 q^{42} +(4.43002 - 4.83476i) q^{43} +5.34279 q^{44} +3.30320 q^{45} +(-2.19341 + 3.79909i) q^{46} -6.80050 q^{47} +(0.0798426 - 0.138291i) q^{48} +(2.27929 - 3.94784i) q^{49} +(1.09053 + 1.88885i) q^{50} +0.0754613 q^{51} +(-2.72590 - 4.72139i) q^{52} +(-6.18028 + 10.7046i) q^{53} +0.260790 q^{54} +(-1.76719 + 3.06086i) q^{55} +(-1.65197 - 2.86129i) q^{56} +(-0.182710 - 0.316463i) q^{57} +(2.36392 + 4.09442i) q^{58} +2.33740 q^{59} +(0.0694107 + 0.120223i) q^{60} +(0.222026 + 0.384561i) q^{61} +(-0.344682 + 0.597007i) q^{62} +(-2.33931 + 4.05181i) q^{63} -1.09067 q^{64} +3.60649 q^{65} +(-0.0696941 + 0.120714i) q^{66} +(-0.315484 + 0.546434i) q^{67} +(-0.833803 - 1.44419i) q^{68} +(0.287089 + 0.497253i) q^{69} +0.993774 q^{70} +(4.82381 + 8.35508i) q^{71} +(-3.16574 - 5.48323i) q^{72} +(-4.07923 - 7.06544i) q^{73} +(-0.463106 + 0.802123i) q^{74} +0.285473 q^{75} +(-4.03767 + 6.99345i) q^{76} +(-2.50303 - 4.33538i) q^{77} +0.142232 q^{78} +(-3.27184 - 5.66699i) q^{79} +(1.16721 - 2.02167i) q^{80} +(-4.47439 + 7.74987i) q^{81} +3.13446 q^{82} +(4.40743 - 7.63388i) q^{83} -0.196626 q^{84} +1.10316 q^{85} +(2.55407 - 2.78742i) q^{86} +0.618813 q^{87} +6.77460 q^{88} +(-2.55776 + 4.43018i) q^{89} +1.90442 q^{90} +(-2.55410 + 4.42383i) q^{91} +(6.34433 - 10.9887i) q^{92} +(0.0451145 + 0.0781406i) q^{93} -3.92074 q^{94} +(-2.67101 - 4.62633i) q^{95} +(0.205596 - 0.356102i) q^{96} -16.9192 q^{97} +(1.31409 - 2.27607i) q^{98} +(-4.79668 - 8.30809i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 58q - 6q^{2} + 3q^{3} + 54q^{4} - q^{5} + 12q^{6} + 7q^{7} - 12q^{8} - 22q^{9} + O(q^{10}) \) \( 58q - 6q^{2} + 3q^{3} + 54q^{4} - q^{5} + 12q^{6} + 7q^{7} - 12q^{8} - 22q^{9} + 4q^{10} + 16q^{11} + 12q^{12} + 2q^{13} - 11q^{14} + 7q^{15} + 30q^{16} + 29q^{17} + 8q^{18} + 8q^{19} - 33q^{20} - 26q^{21} - 22q^{22} - 5q^{23} + 12q^{24} - 36q^{25} - 12q^{27} + 15q^{28} + 2q^{29} + 11q^{30} + 3q^{31} - 40q^{32} + 17q^{33} - 3q^{34} + 38q^{35} - 7q^{36} + 2q^{37} + q^{38} - 54q^{39} + 5q^{40} + 14q^{41} - 112q^{42} + 31q^{43} - 24q^{44} - 46q^{45} - 13q^{46} - 28q^{47} - 28q^{49} - 13q^{50} + 6q^{51} + 85q^{52} - 10q^{53} + 34q^{54} + 36q^{55} - 54q^{56} - 23q^{57} + 3q^{58} + 12q^{59} + 2q^{60} - q^{61} - q^{62} - 14q^{63} + 28q^{64} + 80q^{65} - 74q^{66} + 11q^{67} + 27q^{68} - 11q^{69} + 2q^{70} + 16q^{71} + 21q^{72} + 14q^{73} + 21q^{74} - 54q^{75} + 44q^{76} + 25q^{77} + 88q^{78} - 4q^{79} - 112q^{80} + 11q^{81} - 176q^{82} - 3q^{83} + 100q^{84} - 2q^{85} + 44q^{86} + 8q^{87} - 106q^{88} + 82q^{89} + 54q^{90} - 15q^{91} + 42q^{92} + 88q^{94} + 29q^{95} + 20q^{96} + 20q^{97} + 44q^{98} - 54q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).

\(n\) \(173\) \(562\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.576537 0.407673 0.203836 0.979005i \(-0.434659\pi\)
0.203836 + 0.979005i \(0.434659\pi\)
\(3\) 0.0377307 0.0653514i 0.0217838 0.0377307i −0.854928 0.518747i \(-0.826399\pi\)
0.876712 + 0.481016i \(0.159732\pi\)
\(4\) −1.66761 −0.833803
\(5\) 0.551580 0.955365i 0.246674 0.427252i −0.715927 0.698175i \(-0.753996\pi\)
0.962601 + 0.270923i \(0.0873289\pi\)
\(6\) 0.0217531 0.0376775i 0.00888067 0.0153818i
\(7\) 0.781254 + 1.35317i 0.295286 + 0.511450i 0.975051 0.221979i \(-0.0712517\pi\)
−0.679765 + 0.733430i \(0.737918\pi\)
\(8\) −2.11451 −0.747592
\(9\) 1.49715 + 2.59314i 0.499051 + 0.864382i
\(10\) 0.318006 0.550803i 0.100562 0.174179i
\(11\) −3.20387 −0.966002 −0.483001 0.875620i \(-0.660453\pi\)
−0.483001 + 0.875620i \(0.660453\pi\)
\(12\) −0.0629199 + 0.108980i −0.0181634 + 0.0314599i
\(13\) 1.63462 + 2.83124i 0.453361 + 0.785244i 0.998592 0.0530413i \(-0.0168915\pi\)
−0.545231 + 0.838286i \(0.683558\pi\)
\(14\) 0.450421 + 0.780152i 0.120380 + 0.208505i
\(15\) −0.0416230 0.0720931i −0.0107470 0.0186144i
\(16\) 2.11612 0.529030
\(17\) 0.500000 + 0.866025i 0.121268 + 0.210042i
\(18\) 0.863163 + 1.49504i 0.203450 + 0.352385i
\(19\) 2.42124 4.19371i 0.555470 0.962103i −0.442397 0.896820i \(-0.645872\pi\)
0.997867 0.0652831i \(-0.0207950\pi\)
\(20\) −0.919818 + 1.59317i −0.205678 + 0.356244i
\(21\) 0.117909 0.0257298
\(22\) −1.84715 −0.393813
\(23\) −3.80446 + 6.58951i −0.793284 + 1.37401i 0.130639 + 0.991430i \(0.458297\pi\)
−0.923923 + 0.382578i \(0.875036\pi\)
\(24\) −0.0797818 + 0.138186i −0.0162854 + 0.0282071i
\(25\) 1.89152 + 3.27621i 0.378304 + 0.655241i
\(26\) 0.942416 + 1.63231i 0.184823 + 0.320123i
\(27\) 0.452338 0.0870526
\(28\) −1.30282 2.25656i −0.246210 0.426449i
\(29\) 4.10020 + 7.10176i 0.761388 + 1.31876i 0.942135 + 0.335234i \(0.108815\pi\)
−0.180747 + 0.983530i \(0.557851\pi\)
\(30\) −0.0239972 0.0415643i −0.00438126 0.00758857i
\(31\) −0.597849 + 1.03551i −0.107377 + 0.185982i −0.914707 0.404118i \(-0.867578\pi\)
0.807330 + 0.590100i \(0.200912\pi\)
\(32\) 5.44904 0.963263
\(33\) −0.120884 + 0.209377i −0.0210432 + 0.0364479i
\(34\) 0.288268 + 0.499295i 0.0494376 + 0.0856284i
\(35\) 1.72370 0.291358
\(36\) −2.49666 4.32434i −0.416110 0.720724i
\(37\) −0.803255 + 1.39128i −0.132054 + 0.228725i −0.924468 0.381259i \(-0.875491\pi\)
0.792414 + 0.609984i \(0.208824\pi\)
\(38\) 1.39593 2.41783i 0.226450 0.392223i
\(39\) 0.246701 0.0395037
\(40\) −1.16632 + 2.02013i −0.184412 + 0.319410i
\(41\) 5.43670 0.849070 0.424535 0.905412i \(-0.360438\pi\)
0.424535 + 0.905412i \(0.360438\pi\)
\(42\) 0.0679788 0.0104894
\(43\) 4.43002 4.83476i 0.675572 0.737294i
\(44\) 5.34279 0.805455
\(45\) 3.30320 0.492412
\(46\) −2.19341 + 3.79909i −0.323400 + 0.560146i
\(47\) −6.80050 −0.991955 −0.495978 0.868335i \(-0.665190\pi\)
−0.495978 + 0.868335i \(0.665190\pi\)
\(48\) 0.0798426 0.138291i 0.0115243 0.0199607i
\(49\) 2.27929 3.94784i 0.325612 0.563977i
\(50\) 1.09053 + 1.88885i 0.154224 + 0.267124i
\(51\) 0.0754613 0.0105667
\(52\) −2.72590 4.72139i −0.378014 0.654739i
\(53\) −6.18028 + 10.7046i −0.848927 + 1.47038i 0.0332404 + 0.999447i \(0.489417\pi\)
−0.882167 + 0.470937i \(0.843916\pi\)
\(54\) 0.260790 0.0354890
\(55\) −1.76719 + 3.06086i −0.238288 + 0.412727i
\(56\) −1.65197 2.86129i −0.220753 0.382356i
\(57\) −0.182710 0.316463i −0.0242005 0.0419165i
\(58\) 2.36392 + 4.09442i 0.310397 + 0.537624i
\(59\) 2.33740 0.304304 0.152152 0.988357i \(-0.451380\pi\)
0.152152 + 0.988357i \(0.451380\pi\)
\(60\) 0.0694107 + 0.120223i 0.00896089 + 0.0155207i
\(61\) 0.222026 + 0.384561i 0.0284276 + 0.0492380i 0.879889 0.475179i \(-0.157617\pi\)
−0.851462 + 0.524417i \(0.824283\pi\)
\(62\) −0.344682 + 0.597007i −0.0437747 + 0.0758199i
\(63\) −2.33931 + 4.05181i −0.294726 + 0.510480i
\(64\) −1.09067 −0.136334
\(65\) 3.60649 0.447330
\(66\) −0.0696941 + 0.120714i −0.00857875 + 0.0148588i
\(67\) −0.315484 + 0.546434i −0.0385425 + 0.0667575i −0.884653 0.466250i \(-0.845605\pi\)
0.846111 + 0.533007i \(0.178938\pi\)
\(68\) −0.833803 1.44419i −0.101113 0.175134i
\(69\) 0.287089 + 0.497253i 0.0345615 + 0.0598623i
\(70\) 0.993774 0.118779
\(71\) 4.82381 + 8.35508i 0.572480 + 0.991565i 0.996310 + 0.0858233i \(0.0273521\pi\)
−0.423830 + 0.905742i \(0.639315\pi\)
\(72\) −3.16574 5.48323i −0.373086 0.646204i
\(73\) −4.07923 7.06544i −0.477438 0.826947i 0.522228 0.852806i \(-0.325101\pi\)
−0.999666 + 0.0258592i \(0.991768\pi\)
\(74\) −0.463106 + 0.802123i −0.0538350 + 0.0932449i
\(75\) 0.285473 0.0329636
\(76\) −4.03767 + 6.99345i −0.463153 + 0.802204i
\(77\) −2.50303 4.33538i −0.285247 0.494062i
\(78\) 0.142232 0.0161046
\(79\) −3.27184 5.66699i −0.368110 0.637586i 0.621160 0.783684i \(-0.286662\pi\)
−0.989270 + 0.146098i \(0.953328\pi\)
\(80\) 1.16721 2.02167i 0.130498 0.226029i
\(81\) −4.47439 + 7.74987i −0.497155 + 0.861097i
\(82\) 3.13446 0.346143
\(83\) 4.40743 7.63388i 0.483778 0.837928i −0.516049 0.856559i \(-0.672598\pi\)
0.999826 + 0.0186316i \(0.00593096\pi\)
\(84\) −0.196626 −0.0214536
\(85\) 1.10316 0.119655
\(86\) 2.55407 2.78742i 0.275412 0.300575i
\(87\) 0.618813 0.0663438
\(88\) 6.77460 0.722175
\(89\) −2.55776 + 4.43018i −0.271122 + 0.469598i −0.969150 0.246474i \(-0.920728\pi\)
0.698027 + 0.716071i \(0.254061\pi\)
\(90\) 1.90442 0.200743
\(91\) −2.55410 + 4.42383i −0.267742 + 0.463743i
\(92\) 6.34433 10.9887i 0.661442 1.14565i
\(93\) 0.0451145 + 0.0781406i 0.00467816 + 0.00810281i
\(94\) −3.92074 −0.404393
\(95\) −2.67101 4.62633i −0.274040 0.474652i
\(96\) 0.205596 0.356102i 0.0209835 0.0363446i
\(97\) −16.9192 −1.71789 −0.858944 0.512070i \(-0.828879\pi\)
−0.858944 + 0.512070i \(0.828879\pi\)
\(98\) 1.31409 2.27607i 0.132743 0.229918i
\(99\) −4.79668 8.30809i −0.482084 0.834994i
\(100\) −3.15431 5.46342i −0.315431 0.546342i
\(101\) −7.36305 12.7532i −0.732651 1.26899i −0.955746 0.294192i \(-0.904949\pi\)
0.223095 0.974797i \(-0.428384\pi\)
\(102\) 0.0435062 0.00430776
\(103\) −8.43683 14.6130i −0.831306 1.43986i −0.897003 0.442024i \(-0.854261\pi\)
0.0656978 0.997840i \(-0.479073\pi\)
\(104\) −3.45641 5.98668i −0.338929 0.587042i
\(105\) 0.0650362 0.112646i 0.00634688 0.0109931i
\(106\) −3.56316 + 6.17157i −0.346084 + 0.599436i
\(107\) 10.2509 0.990990 0.495495 0.868611i \(-0.334987\pi\)
0.495495 + 0.868611i \(0.334987\pi\)
\(108\) −0.754322 −0.0725847
\(109\) −3.67488 + 6.36507i −0.351989 + 0.609663i −0.986598 0.163170i \(-0.947828\pi\)
0.634609 + 0.772834i \(0.281161\pi\)
\(110\) −1.01885 + 1.76470i −0.0971435 + 0.168257i
\(111\) 0.0606147 + 0.104988i 0.00575329 + 0.00996500i
\(112\) 1.65323 + 2.86347i 0.156215 + 0.270573i
\(113\) 14.2462 1.34017 0.670085 0.742284i \(-0.266258\pi\)
0.670085 + 0.742284i \(0.266258\pi\)
\(114\) −0.105339 0.182452i −0.00986590 0.0170882i
\(115\) 4.19693 + 7.26929i 0.391365 + 0.677865i
\(116\) −6.83752 11.8429i −0.634848 1.09959i
\(117\) −4.89454 + 8.47759i −0.452501 + 0.783754i
\(118\) 1.34760 0.124057
\(119\) −0.781254 + 1.35317i −0.0716174 + 0.124045i
\(120\) 0.0880122 + 0.152442i 0.00803437 + 0.0139159i
\(121\) −0.735238 −0.0668398
\(122\) 0.128006 + 0.221714i 0.0115892 + 0.0200730i
\(123\) 0.205130 0.355296i 0.0184960 0.0320360i
\(124\) 0.996977 1.72681i 0.0895312 0.155073i
\(125\) 9.68910 0.866619
\(126\) −1.34870 + 2.33601i −0.120152 + 0.208109i
\(127\) 3.30243 0.293043 0.146522 0.989207i \(-0.453192\pi\)
0.146522 + 0.989207i \(0.453192\pi\)
\(128\) −11.5269 −1.01884
\(129\) −0.148811 0.471927i −0.0131021 0.0415509i
\(130\) 2.07927 0.182364
\(131\) −7.56871 −0.661281 −0.330640 0.943757i \(-0.607265\pi\)
−0.330640 + 0.943757i \(0.607265\pi\)
\(132\) 0.201587 0.349159i 0.0175459 0.0303904i
\(133\) 7.56640 0.656090
\(134\) −0.181888 + 0.315039i −0.0157127 + 0.0272152i
\(135\) 0.249501 0.432148i 0.0214736 0.0371934i
\(136\) −1.05725 1.83122i −0.0906588 0.157026i
\(137\) 0.103039 0.00880318 0.00440159 0.999990i \(-0.498599\pi\)
0.00440159 + 0.999990i \(0.498599\pi\)
\(138\) 0.165518 + 0.286685i 0.0140898 + 0.0244042i
\(139\) 7.71565 13.3639i 0.654433 1.13351i −0.327602 0.944816i \(-0.606241\pi\)
0.982036 0.188696i \(-0.0604261\pi\)
\(140\) −2.87445 −0.242935
\(141\) −0.256587 + 0.444423i −0.0216086 + 0.0374271i
\(142\) 2.78110 + 4.81701i 0.233385 + 0.404234i
\(143\) −5.23709 9.07091i −0.437948 0.758548i
\(144\) 3.16815 + 5.48740i 0.264013 + 0.457284i
\(145\) 9.04636 0.751259
\(146\) −2.35183 4.07348i −0.194639 0.337124i
\(147\) −0.171998 0.297909i −0.0141862 0.0245711i
\(148\) 1.33951 2.32010i 0.110107 0.190711i
\(149\) 7.22399 12.5123i 0.591812 1.02505i −0.402176 0.915562i \(-0.631746\pi\)
0.993988 0.109487i \(-0.0349207\pi\)
\(150\) 0.164586 0.0134384
\(151\) 12.6411 1.02872 0.514360 0.857574i \(-0.328030\pi\)
0.514360 + 0.857574i \(0.328030\pi\)
\(152\) −5.11973 + 8.86763i −0.415265 + 0.719260i
\(153\) −1.49715 + 2.59314i −0.121038 + 0.209643i
\(154\) −1.44309 2.49950i −0.116287 0.201416i
\(155\) 0.659524 + 1.14233i 0.0529742 + 0.0917540i
\(156\) −0.411400 −0.0329383
\(157\) −1.88503 3.26497i −0.150442 0.260573i 0.780948 0.624596i \(-0.214736\pi\)
−0.931390 + 0.364023i \(0.881403\pi\)
\(158\) −1.88633 3.26722i −0.150069 0.259926i
\(159\) 0.466372 + 0.807780i 0.0369857 + 0.0640611i
\(160\) 3.00558 5.20582i 0.237612 0.411556i
\(161\) −11.8890 −0.936983
\(162\) −2.57965 + 4.46809i −0.202676 + 0.351046i
\(163\) −2.05350 3.55677i −0.160842 0.278587i 0.774329 0.632784i \(-0.218088\pi\)
−0.935171 + 0.354196i \(0.884754\pi\)
\(164\) −9.06627 −0.707957
\(165\) 0.133354 + 0.230977i 0.0103816 + 0.0179815i
\(166\) 2.54104 4.40121i 0.197223 0.341600i
\(167\) 4.11199 7.12217i 0.318195 0.551130i −0.661916 0.749578i \(-0.730257\pi\)
0.980112 + 0.198448i \(0.0635900\pi\)
\(168\) −0.249319 −0.0192354
\(169\) 1.15606 2.00235i 0.0889275 0.154027i
\(170\) 0.636012 0.0487799
\(171\) 14.4999 1.10883
\(172\) −7.38753 + 8.06247i −0.563294 + 0.614758i
\(173\) 4.17383 0.317330 0.158665 0.987332i \(-0.449281\pi\)
0.158665 + 0.987332i \(0.449281\pi\)
\(174\) 0.356769 0.0270466
\(175\) −2.95551 + 5.11910i −0.223416 + 0.386967i
\(176\) −6.77977 −0.511044
\(177\) 0.0881918 0.152753i 0.00662890 0.0114816i
\(178\) −1.47464 + 2.55416i −0.110529 + 0.191442i
\(179\) 3.01879 + 5.22870i 0.225635 + 0.390812i 0.956510 0.291700i \(-0.0942209\pi\)
−0.730875 + 0.682512i \(0.760888\pi\)
\(180\) −5.50843 −0.410574
\(181\) 8.91907 + 15.4483i 0.662949 + 1.14826i 0.979837 + 0.199799i \(0.0640289\pi\)
−0.316887 + 0.948463i \(0.602638\pi\)
\(182\) −1.47253 + 2.55050i −0.109151 + 0.189056i
\(183\) 0.0335088 0.00247704
\(184\) 8.04456 13.9336i 0.593053 1.02720i
\(185\) 0.886119 + 1.53480i 0.0651488 + 0.112841i
\(186\) 0.0260102 + 0.0450509i 0.00190716 + 0.00330329i
\(187\) −1.60193 2.77463i −0.117145 0.202901i
\(188\) 11.3406 0.827095
\(189\) 0.353391 + 0.612091i 0.0257054 + 0.0445231i
\(190\) −1.53994 2.66725i −0.111719 0.193503i
\(191\) −8.08708 + 14.0072i −0.585160 + 1.01353i 0.409695 + 0.912223i \(0.365635\pi\)
−0.994855 + 0.101305i \(0.967698\pi\)
\(192\) −0.0411517 + 0.0712769i −0.00296987 + 0.00514396i
\(193\) −8.29926 −0.597394 −0.298697 0.954348i \(-0.596552\pi\)
−0.298697 + 0.954348i \(0.596552\pi\)
\(194\) −9.75455 −0.700336
\(195\) 0.136075 0.235689i 0.00974455 0.0168781i
\(196\) −3.80095 + 6.58344i −0.271496 + 0.470246i
\(197\) 3.36468 + 5.82780i 0.239724 + 0.415214i 0.960635 0.277814i \(-0.0896098\pi\)
−0.720911 + 0.693028i \(0.756276\pi\)
\(198\) −2.76546 4.78992i −0.196533 0.340405i
\(199\) −7.23463 −0.512849 −0.256425 0.966564i \(-0.582545\pi\)
−0.256425 + 0.966564i \(0.582545\pi\)
\(200\) −3.99963 6.92757i −0.282817 0.489853i
\(201\) 0.0238068 + 0.0412346i 0.00167920 + 0.00290847i
\(202\) −4.24507 7.35267i −0.298682 0.517332i
\(203\) −6.40659 + 11.0965i −0.449655 + 0.778825i
\(204\) −0.125840 −0.00881055
\(205\) 2.99878 5.19403i 0.209444 0.362767i
\(206\) −4.86414 8.42494i −0.338901 0.586993i
\(207\) −22.7834 −1.58356
\(208\) 3.45904 + 5.99124i 0.239842 + 0.415418i
\(209\) −7.75733 + 13.4361i −0.536585 + 0.929393i
\(210\) 0.0374957 0.0649445i 0.00258745 0.00448160i
\(211\) 15.6814 1.07955 0.539775 0.841809i \(-0.318509\pi\)
0.539775 + 0.841809i \(0.318509\pi\)
\(212\) 10.3063 17.8510i 0.707837 1.22601i
\(213\) 0.728022 0.0498832
\(214\) 5.91001 0.404000
\(215\) −2.17545 6.89905i −0.148364 0.470511i
\(216\) −0.956473 −0.0650798
\(217\) −1.86829 −0.126828
\(218\) −2.11870 + 3.66970i −0.143496 + 0.248543i
\(219\) −0.615649 −0.0416017
\(220\) 2.94698 5.10431i 0.198685 0.344133i
\(221\) −1.63462 + 2.83124i −0.109956 + 0.190450i
\(222\) 0.0349466 + 0.0605293i 0.00234546 + 0.00406246i
\(223\) 20.7561 1.38993 0.694965 0.719043i \(-0.255420\pi\)
0.694965 + 0.719043i \(0.255420\pi\)
\(224\) 4.25708 + 7.37348i 0.284438 + 0.492661i
\(225\) −5.66378 + 9.80996i −0.377586 + 0.653997i
\(226\) 8.21346 0.546351
\(227\) −8.57834 + 14.8581i −0.569364 + 0.986168i 0.427265 + 0.904127i \(0.359477\pi\)
−0.996629 + 0.0820412i \(0.973856\pi\)
\(228\) 0.304688 + 0.527735i 0.0201785 + 0.0349501i
\(229\) −6.56925 11.3783i −0.434108 0.751898i 0.563114 0.826379i \(-0.309603\pi\)
−0.997222 + 0.0744813i \(0.976270\pi\)
\(230\) 2.41968 + 4.19101i 0.159549 + 0.276347i
\(231\) −0.377764 −0.0248551
\(232\) −8.66991 15.0167i −0.569208 0.985896i
\(233\) 8.43527 + 14.6103i 0.552613 + 0.957154i 0.998085 + 0.0618577i \(0.0197025\pi\)
−0.445472 + 0.895296i \(0.646964\pi\)
\(234\) −2.82188 + 4.88764i −0.184472 + 0.319515i
\(235\) −3.75102 + 6.49696i −0.244690 + 0.423815i
\(236\) −3.89787 −0.253730
\(237\) −0.493794 −0.0320754
\(238\) −0.450421 + 0.780152i −0.0291965 + 0.0505698i
\(239\) 8.87667 15.3748i 0.574184 0.994516i −0.421945 0.906621i \(-0.638653\pi\)
0.996130 0.0878951i \(-0.0280140\pi\)
\(240\) −0.0880792 0.152558i −0.00568549 0.00984756i
\(241\) −10.3456 17.9191i −0.666417 1.15427i −0.978899 0.204344i \(-0.934494\pi\)
0.312482 0.949924i \(-0.398840\pi\)
\(242\) −0.423892 −0.0272488
\(243\) 1.01615 + 1.76003i 0.0651861 + 0.112906i
\(244\) −0.370253 0.641296i −0.0237030 0.0410548i
\(245\) −2.51442 4.35510i −0.160640 0.278237i
\(246\) 0.118265 0.204841i 0.00754031 0.0130602i
\(247\) 15.8312 1.00731
\(248\) 1.26416 2.18959i 0.0802741 0.139039i
\(249\) −0.332590 0.576063i −0.0210770 0.0365065i
\(250\) 5.58612 0.353297
\(251\) 10.6492 + 18.4450i 0.672173 + 1.16424i 0.977287 + 0.211922i \(0.0679722\pi\)
−0.305114 + 0.952316i \(0.598694\pi\)
\(252\) 3.90105 6.75682i 0.245743 0.425639i
\(253\) 12.1890 21.1119i 0.766314 1.32729i
\(254\) 1.90397 0.119466
\(255\) 0.0416230 0.0720931i 0.00260653 0.00451465i
\(256\) −4.46433 −0.279021
\(257\) −15.4160 −0.961624 −0.480812 0.876824i \(-0.659658\pi\)
−0.480812 + 0.876824i \(0.659658\pi\)
\(258\) −0.0857949 0.272083i −0.00534136 0.0169392i
\(259\) −2.51018 −0.155975
\(260\) −6.01420 −0.372985
\(261\) −12.2773 + 21.2648i −0.759943 + 1.31626i
\(262\) −4.36364 −0.269586
\(263\) 11.2503 19.4861i 0.693722 1.20156i −0.276888 0.960902i \(-0.589303\pi\)
0.970610 0.240659i \(-0.0773636\pi\)
\(264\) 0.255610 0.442730i 0.0157317 0.0272482i
\(265\) 6.81784 + 11.8088i 0.418817 + 0.725412i
\(266\) 4.36231 0.267470
\(267\) 0.193012 + 0.334307i 0.0118122 + 0.0204593i
\(268\) 0.526102 0.911236i 0.0321368 0.0556626i
\(269\) 17.4368 1.06314 0.531570 0.847014i \(-0.321602\pi\)
0.531570 + 0.847014i \(0.321602\pi\)
\(270\) 0.143846 0.249149i 0.00875421 0.0151627i
\(271\) −13.2168 22.8922i −0.802866 1.39060i −0.917722 0.397223i \(-0.869974\pi\)
0.114856 0.993382i \(-0.463359\pi\)
\(272\) 1.05806 + 1.83261i 0.0641543 + 0.111119i
\(273\) 0.192736 + 0.333828i 0.0116649 + 0.0202042i
\(274\) 0.0594055 0.00358882
\(275\) −6.06017 10.4965i −0.365442 0.632964i
\(276\) −0.478752 0.829223i −0.0288175 0.0499133i
\(277\) −13.8870 + 24.0530i −0.834390 + 1.44521i 0.0601364 + 0.998190i \(0.480846\pi\)
−0.894526 + 0.447015i \(0.852487\pi\)
\(278\) 4.44836 7.70478i 0.266795 0.462102i
\(279\) −3.58029 −0.214346
\(280\) −3.64477 −0.217817
\(281\) −7.75408 + 13.4305i −0.462570 + 0.801194i −0.999088 0.0426945i \(-0.986406\pi\)
0.536519 + 0.843889i \(0.319739\pi\)
\(282\) −0.147932 + 0.256226i −0.00880923 + 0.0152580i
\(283\) −1.92623 3.33632i −0.114502 0.198324i 0.803078 0.595873i \(-0.203194\pi\)
−0.917581 + 0.397550i \(0.869861\pi\)
\(284\) −8.04421 13.9330i −0.477336 0.826770i
\(285\) −0.403117 −0.0238786
\(286\) −3.01938 5.22971i −0.178539 0.309239i
\(287\) 4.24744 + 7.35678i 0.250718 + 0.434257i
\(288\) 8.15804 + 14.1301i 0.480717 + 0.832627i
\(289\) −0.500000 + 0.866025i −0.0294118 + 0.0509427i
\(290\) 5.21556 0.306268
\(291\) −0.638374 + 1.10570i −0.0374221 + 0.0648170i
\(292\) 6.80255 + 11.7824i 0.398089 + 0.689511i
\(293\) 11.7268 0.685087 0.342544 0.939502i \(-0.388712\pi\)
0.342544 + 0.939502i \(0.388712\pi\)
\(294\) −0.0991631 0.171756i −0.00578331 0.0100170i
\(295\) 1.28927 2.23307i 0.0750640 0.130015i
\(296\) 1.69849 2.94187i 0.0987227 0.170993i
\(297\) −1.44923 −0.0840930
\(298\) 4.16489 7.21381i 0.241266 0.417885i
\(299\) −24.8753 −1.43858
\(300\) −0.476056 −0.0274851
\(301\) 10.0032 + 2.21740i 0.576576 + 0.127809i
\(302\) 7.28807 0.419381
\(303\) −1.11125 −0.0638397
\(304\) 5.12363 8.87439i 0.293860 0.508981i
\(305\) 0.489862 0.0280494
\(306\) −0.863163 + 1.49504i −0.0493438 + 0.0854659i
\(307\) 8.48641 14.6989i 0.484345 0.838910i −0.515493 0.856894i \(-0.672391\pi\)
0.999838 + 0.0179834i \(0.00572459\pi\)
\(308\) 4.17407 + 7.22970i 0.237840 + 0.411951i
\(309\) −1.27331 −0.0724360
\(310\) 0.380240 + 0.658594i 0.0215962 + 0.0374056i
\(311\) −14.5094 + 25.1311i −0.822755 + 1.42505i 0.0808686 + 0.996725i \(0.474231\pi\)
−0.903623 + 0.428328i \(0.859103\pi\)
\(312\) −0.521651 −0.0295327
\(313\) 5.82162 10.0833i 0.329058 0.569945i −0.653267 0.757127i \(-0.726602\pi\)
0.982325 + 0.187183i \(0.0599356\pi\)
\(314\) −1.08679 1.88238i −0.0613311 0.106229i
\(315\) 2.58064 + 4.46979i 0.145402 + 0.251844i
\(316\) 5.45613 + 9.45030i 0.306931 + 0.531621i
\(317\) 25.1023 1.40989 0.704944 0.709263i \(-0.250972\pi\)
0.704944 + 0.709263i \(0.250972\pi\)
\(318\) 0.268881 + 0.465715i 0.0150781 + 0.0261160i
\(319\) −13.1365 22.7531i −0.735503 1.27393i
\(320\) −0.601592 + 1.04199i −0.0336300 + 0.0582489i
\(321\) 0.386773 0.669910i 0.0215875 0.0373907i
\(322\) −6.85443 −0.381983
\(323\) 4.84248 0.269443
\(324\) 7.46152 12.9237i 0.414529 0.717985i
\(325\) −6.18382 + 10.7107i −0.343016 + 0.594122i
\(326\) −1.18392 2.05061i −0.0655711 0.113573i
\(327\) 0.277311 + 0.480317i 0.0153353 + 0.0265616i
\(328\) −11.4959 −0.634758
\(329\) −5.31292 9.20224i −0.292911 0.507336i
\(330\) 0.0768837 + 0.133167i 0.00423231 + 0.00733058i
\(331\) 6.42684 + 11.1316i 0.353251 + 0.611849i 0.986817 0.161840i \(-0.0517427\pi\)
−0.633566 + 0.773689i \(0.718409\pi\)
\(332\) −7.34985 + 12.7303i −0.403375 + 0.698666i
\(333\) −4.81038 −0.263607
\(334\) 2.37071 4.10619i 0.129720 0.224681i
\(335\) 0.348029 + 0.602804i 0.0190149 + 0.0329347i
\(336\) 0.249509 0.0136118
\(337\) 1.30157 + 2.25439i 0.0709011 + 0.122804i 0.899296 0.437339i \(-0.144079\pi\)
−0.828395 + 0.560144i \(0.810746\pi\)
\(338\) 0.666509 1.15443i 0.0362533 0.0627926i
\(339\) 0.537519 0.931010i 0.0291940 0.0505655i
\(340\) −1.83964 −0.0997683
\(341\) 1.91543 3.31762i 0.103726 0.179659i
\(342\) 8.35970 0.452041
\(343\) 18.0603 0.975167
\(344\) −9.36732 + 10.2231i −0.505052 + 0.551195i
\(345\) 0.633411 0.0341017
\(346\) 2.40637 0.129367
\(347\) −7.65209 + 13.2538i −0.410786 + 0.711502i −0.994976 0.100115i \(-0.968079\pi\)
0.584190 + 0.811617i \(0.301412\pi\)
\(348\) −1.03194 −0.0553176
\(349\) 11.4288 19.7952i 0.611767 1.05961i −0.379175 0.925325i \(-0.623792\pi\)
0.990942 0.134287i \(-0.0428744\pi\)
\(350\) −1.70396 + 2.95135i −0.0910805 + 0.157756i
\(351\) 0.739400 + 1.28068i 0.0394662 + 0.0683575i
\(352\) −17.4580 −0.930514
\(353\) −7.78945 13.4917i −0.414591 0.718092i 0.580795 0.814050i \(-0.302742\pi\)
−0.995385 + 0.0959581i \(0.969409\pi\)
\(354\) 0.0508458 0.0880675i 0.00270242 0.00468074i
\(355\) 10.6429 0.564865
\(356\) 4.26534 7.38779i 0.226063 0.391552i
\(357\) 0.0589544 + 0.102112i 0.00312020 + 0.00540434i
\(358\) 1.74044 + 3.01454i 0.0919854 + 0.159323i
\(359\) 11.8151 + 20.4644i 0.623577 + 1.08007i 0.988814 + 0.149153i \(0.0476547\pi\)
−0.365237 + 0.930915i \(0.619012\pi\)
\(360\) −6.98464 −0.368123
\(361\) −2.22479 3.85345i −0.117094 0.202813i
\(362\) 5.14217 + 8.90650i 0.270267 + 0.468115i
\(363\) −0.0277410 + 0.0480489i −0.00145603 + 0.00252191i
\(364\) 4.25923 7.37721i 0.223244 0.386671i
\(365\) −9.00010 −0.471087
\(366\) 0.0193191 0.00100982
\(367\) −0.870077 + 1.50702i −0.0454176 + 0.0786656i −0.887841 0.460151i \(-0.847795\pi\)
0.842423 + 0.538817i \(0.181129\pi\)
\(368\) −8.05069 + 13.9442i −0.419671 + 0.726891i
\(369\) 8.13957 + 14.0981i 0.423729 + 0.733920i
\(370\) 0.510880 + 0.884870i 0.0265594 + 0.0460022i
\(371\) −19.3135 −1.00270
\(372\) −0.0752332 0.130308i −0.00390066 0.00675614i
\(373\) 11.2019 + 19.4023i 0.580015 + 1.00461i 0.995477 + 0.0950043i \(0.0302865\pi\)
−0.415462 + 0.909610i \(0.636380\pi\)
\(374\) −0.923573 1.59968i −0.0477568 0.0827173i
\(375\) 0.365576 0.633197i 0.0188783 0.0326981i
\(376\) 14.3797 0.741577
\(377\) −13.4045 + 23.2173i −0.690368 + 1.19575i
\(378\) 0.203743 + 0.352893i 0.0104794 + 0.0181508i
\(379\) 8.33592 0.428188 0.214094 0.976813i \(-0.431320\pi\)
0.214094 + 0.976813i \(0.431320\pi\)
\(380\) 4.45420 + 7.71490i 0.228496 + 0.395766i
\(381\) 0.124603 0.215819i 0.00638360 0.0110567i
\(382\) −4.66250 + 8.07568i −0.238554 + 0.413188i
\(383\) −34.7108 −1.77364 −0.886819 0.462117i \(-0.847090\pi\)
−0.886819 + 0.462117i \(0.847090\pi\)
\(384\) −0.434917 + 0.753299i −0.0221943 + 0.0384416i
\(385\) −5.52249 −0.281452
\(386\) −4.78483 −0.243541
\(387\) 19.1697 + 4.24931i 0.974448 + 0.216005i
\(388\) 28.2146 1.43238
\(389\) 14.6740 0.743999 0.371999 0.928233i \(-0.378672\pi\)
0.371999 + 0.928233i \(0.378672\pi\)
\(390\) 0.0784524 0.135883i 0.00397259 0.00688073i
\(391\) −7.60891 −0.384799
\(392\) −4.81957 + 8.34774i −0.243425 + 0.421625i
\(393\) −0.285572 + 0.494626i −0.0144052 + 0.0249506i
\(394\) 1.93986 + 3.35994i 0.0977289 + 0.169271i
\(395\) −7.21872 −0.363213
\(396\) 7.99897 + 13.8546i 0.401963 + 0.696221i
\(397\) −0.0734515 + 0.127222i −0.00368642 + 0.00638508i −0.867863 0.496804i \(-0.834507\pi\)
0.864176 + 0.503189i \(0.167840\pi\)
\(398\) −4.17103 −0.209075
\(399\) 0.285486 0.494475i 0.0142922 0.0247547i
\(400\) 4.00268 + 6.93284i 0.200134 + 0.346642i
\(401\) 11.2343 + 19.4584i 0.561014 + 0.971705i 0.997408 + 0.0719495i \(0.0229220\pi\)
−0.436394 + 0.899756i \(0.643745\pi\)
\(402\) 0.0137255 + 0.0237733i 0.000684566 + 0.00118570i
\(403\) −3.90902 −0.194722
\(404\) 12.2787 + 21.2673i 0.610886 + 1.05809i
\(405\) 4.93597 + 8.54935i 0.245270 + 0.424821i
\(406\) −3.69364 + 6.39756i −0.183312 + 0.317506i
\(407\) 2.57352 4.45747i 0.127565 0.220949i
\(408\) −0.159564 −0.00789958
\(409\) 35.8298 1.77167 0.885834 0.464002i \(-0.153587\pi\)
0.885834 + 0.464002i \(0.153587\pi\)
\(410\) 1.72890 2.99455i 0.0853845 0.147890i
\(411\) 0.00388771 0.00673372i 0.000191767 0.000332150i
\(412\) 14.0693 + 24.3688i 0.693145 + 1.20056i
\(413\) 1.82610 + 3.16291i 0.0898567 + 0.155636i
\(414\) −13.1355 −0.645573
\(415\) −4.86210 8.42140i −0.238671 0.413390i
\(416\) 8.90709 + 15.4275i 0.436706 + 0.756397i
\(417\) −0.582234 1.00846i −0.0285121 0.0493844i
\(418\) −4.47238 + 7.74639i −0.218751 + 0.378888i
\(419\) −4.32288 −0.211186 −0.105593 0.994409i \(-0.533674\pi\)
−0.105593 + 0.994409i \(0.533674\pi\)
\(420\) −0.108455 + 0.187849i −0.00529205 + 0.00916610i
\(421\) −11.5406 19.9890i −0.562457 0.974204i −0.997281 0.0736885i \(-0.976523\pi\)
0.434824 0.900515i \(-0.356810\pi\)
\(422\) 9.04089 0.440104
\(423\) −10.1814 17.6347i −0.495036 0.857428i
\(424\) 13.0683 22.6349i 0.634651 1.09925i
\(425\) −1.89152 + 3.27621i −0.0917521 + 0.158919i
\(426\) 0.419731 0.0203360
\(427\) −0.346918 + 0.600879i −0.0167885 + 0.0290786i
\(428\) −17.0944 −0.826290
\(429\) −0.790396 −0.0381607
\(430\) −1.25423 3.97755i −0.0604841 0.191815i
\(431\) −15.8020 −0.761153 −0.380577 0.924749i \(-0.624275\pi\)
−0.380577 + 0.924749i \(0.624275\pi\)
\(432\) 0.957202 0.0460534
\(433\) 11.4695 19.8658i 0.551191 0.954691i −0.446998 0.894535i \(-0.647507\pi\)
0.998189 0.0601563i \(-0.0191599\pi\)
\(434\) −1.07714 −0.0517042
\(435\) 0.341325 0.591193i 0.0163653 0.0283455i
\(436\) 6.12824 10.6144i 0.293490 0.508339i
\(437\) 18.4230 + 31.9096i 0.881291 + 1.52644i
\(438\) −0.354944 −0.0169599
\(439\) 12.1766 + 21.0905i 0.581156 + 1.00659i 0.995343 + 0.0964002i \(0.0307329\pi\)
−0.414186 + 0.910192i \(0.635934\pi\)
\(440\) 3.73674 6.47222i 0.178142 0.308551i
\(441\) 13.6498 0.649988
\(442\) −0.942416 + 1.63231i −0.0448262 + 0.0776412i
\(443\) −13.9170 24.1050i −0.661219 1.14526i −0.980296 0.197536i \(-0.936706\pi\)
0.319077 0.947729i \(-0.396627\pi\)
\(444\) −0.101081 0.175078i −0.00479711 0.00830884i
\(445\) 2.82162 + 4.88720i 0.133758 + 0.231675i
\(446\) 11.9666 0.566637
\(447\) −0.545132 0.944196i −0.0257839 0.0446590i
\(448\) −0.852090 1.47586i −0.0402575 0.0697280i
\(449\) 20.4595 35.4370i 0.965545 1.67237i 0.257403 0.966304i \(-0.417133\pi\)
0.708143 0.706069i \(-0.249533\pi\)
\(450\) −3.26538 + 5.65580i −0.153931 + 0.266617i
\(451\) −17.4185 −0.820203
\(452\) −23.7571 −1.11744
\(453\) 0.476958 0.826115i 0.0224094 0.0388143i
\(454\) −4.94572 + 8.56625i −0.232114 + 0.402034i
\(455\) 2.81758 + 4.88020i 0.132090 + 0.228787i
\(456\) 0.386342 + 0.669163i 0.0180921 + 0.0313364i
\(457\) −5.43823 −0.254390 −0.127195 0.991878i \(-0.540597\pi\)
−0.127195 + 0.991878i \(0.540597\pi\)
\(458\) −3.78741 6.55999i −0.176974 0.306528i
\(459\) 0.226169 + 0.391736i 0.0105567 + 0.0182847i
\(460\) −6.99882 12.1223i −0.326322 0.565205i
\(461\) −6.56899 + 11.3778i −0.305948 + 0.529918i −0.977472 0.211065i \(-0.932307\pi\)
0.671524 + 0.740983i \(0.265640\pi\)
\(462\) −0.217795 −0.0101327
\(463\) −2.68453 + 4.64974i −0.124761 + 0.216092i −0.921639 0.388048i \(-0.873150\pi\)
0.796879 + 0.604139i \(0.206483\pi\)
\(464\) 8.67652 + 15.0282i 0.402797 + 0.697665i
\(465\) 0.0995371 0.00461592
\(466\) 4.86324 + 8.42338i 0.225285 + 0.390206i
\(467\) 5.24976 9.09286i 0.242930 0.420767i −0.718618 0.695406i \(-0.755225\pi\)
0.961548 + 0.274638i \(0.0885581\pi\)
\(468\) 8.16217 14.1373i 0.377296 0.653496i
\(469\) −0.985891 −0.0455242
\(470\) −2.16260 + 3.74574i −0.0997534 + 0.172778i
\(471\) −0.284494 −0.0131088
\(472\) −4.94246 −0.227495
\(473\) −14.1932 + 15.4899i −0.652604 + 0.712228i
\(474\) −0.284690 −0.0130763
\(475\) 18.3193 0.840546
\(476\) 1.30282 2.25656i 0.0597148 0.103429i
\(477\) −37.0113 −1.69463
\(478\) 5.11773 8.86416i 0.234079 0.405437i
\(479\) −0.00930282 + 0.0161130i −0.000425057 + 0.000736220i −0.866238 0.499632i \(-0.833469\pi\)
0.865813 + 0.500368i \(0.166802\pi\)
\(480\) −0.226805 0.392838i −0.0103522 0.0179305i
\(481\) −5.25206 −0.239473
\(482\) −5.96460 10.3310i −0.271680 0.470564i
\(483\) −0.448579 + 0.776962i −0.0204111 + 0.0353530i
\(484\) 1.22609 0.0557312
\(485\) −9.33231 + 16.1640i −0.423758 + 0.733971i
\(486\) 0.585848 + 1.01472i 0.0265746 + 0.0460286i
\(487\) −8.09791 14.0260i −0.366951 0.635578i 0.622136 0.782909i \(-0.286265\pi\)
−0.989087 + 0.147331i \(0.952932\pi\)
\(488\) −0.469477 0.813158i −0.0212522 0.0368099i
\(489\) −0.309920 −0.0140151
\(490\) −1.44965 2.51087i −0.0654887 0.113430i
\(491\) −1.25459 2.17301i −0.0566186 0.0980664i 0.836327 0.548231i \(-0.184699\pi\)
−0.892946 + 0.450165i \(0.851365\pi\)
\(492\) −0.342076 + 0.592494i −0.0154220 + 0.0267117i
\(493\) −4.10020 + 7.10176i −0.184664 + 0.319847i
\(494\) 9.12726 0.410655
\(495\) −10.5830 −0.475671
\(496\) −1.26512 + 2.19125i −0.0568056 + 0.0983902i
\(497\) −7.53723 + 13.0549i −0.338091 + 0.585591i
\(498\) −0.191750 0.332121i −0.00859254 0.0148827i
\(499\) 11.2034 + 19.4048i 0.501531 + 0.868677i 0.999998 + 0.00176877i \(0.000563017\pi\)
−0.498467 + 0.866908i \(0.666104\pi\)
\(500\) −16.1576 −0.722590
\(501\) −0.310296 0.537449i −0.0138630 0.0240114i
\(502\) 6.13967 + 10.6342i 0.274027 + 0.474628i
\(503\) −13.8446 23.9796i −0.617302 1.06920i −0.989976 0.141236i \(-0.954892\pi\)
0.372674 0.927962i \(-0.378441\pi\)
\(504\) 4.94649 8.56758i 0.220334 0.381630i
\(505\) −16.2453 −0.722904
\(506\) 7.02739 12.1718i 0.312405 0.541102i
\(507\) −0.0872376 0.151100i −0.00387436 0.00671058i
\(508\) −5.50715 −0.244340
\(509\) 10.4527 + 18.1045i 0.463306 + 0.802470i 0.999123 0.0418642i \(-0.0133297\pi\)
−0.535817 + 0.844334i \(0.679996\pi\)
\(510\) 0.0239972 0.0415643i 0.00106261 0.00184050i
\(511\) 6.37383 11.0398i 0.281962 0.488372i
\(512\) 20.4799 0.905093
\(513\) 1.09522 1.89697i 0.0483551 0.0837535i
\(514\) −8.88789 −0.392028
\(515\) −18.6144 −0.820246
\(516\) 0.248158 + 0.786988i 0.0109245 + 0.0346452i
\(517\) 21.7879 0.958231
\(518\) −1.44721 −0.0635869
\(519\) 0.157481 0.272766i 0.00691267 0.0119731i
\(520\) −7.62595 −0.334420
\(521\) 16.5945 28.7424i 0.727016 1.25923i −0.231123 0.972925i \(-0.574240\pi\)
0.958139 0.286304i \(-0.0924268\pi\)
\(522\) −7.07829 + 12.2600i −0.309808 + 0.536604i
\(523\) −12.8697 22.2910i −0.562754 0.974719i −0.997255 0.0740473i \(-0.976408\pi\)
0.434501 0.900672i \(-0.356925\pi\)
\(524\) 12.6216 0.551378
\(525\) 0.223027 + 0.386294i 0.00973369 + 0.0168592i
\(526\) 6.48620 11.2344i 0.282812 0.489844i
\(527\) −1.19570 −0.0520855
\(528\) −0.255805 + 0.443067i −0.0111325 + 0.0192820i
\(529\) −17.4478 30.2204i −0.758599 1.31393i
\(530\) 3.93073 + 6.80823i 0.170740 + 0.295731i
\(531\) 3.49945 + 6.06123i 0.151863 + 0.263035i
\(532\) −12.6178 −0.547050
\(533\) 8.88692 + 15.3926i 0.384935 + 0.666727i
\(534\) 0.111279 + 0.192740i 0.00481550 + 0.00834069i
\(535\) 5.65418 9.79333i 0.244452 0.423403i
\(536\) 0.667093 1.15544i 0.0288140 0.0499074i
\(537\) 0.455604 0.0196608
\(538\) 10.0529 0.433413
\(539\) −7.30253 + 12.6483i −0.314542 + 0.544803i
\(540\) −0.416069 + 0.720653i −0.0179048 + 0.0310120i
\(541\) −0.769661 1.33309i −0.0330903 0.0573141i 0.849006 0.528383i \(-0.177202\pi\)
−0.882096 + 0.471069i \(0.843868\pi\)
\(542\) −7.61999 13.1982i −0.327307 0.566912i
\(543\) 1.34609 0.0577663
\(544\) 2.72452 + 4.71901i 0.116813 + 0.202326i
\(545\) 4.05398 + 7.02169i 0.173653 + 0.300776i
\(546\) 0.111119 + 0.192464i 0.00475546 + 0.00823671i
\(547\) −17.4221 + 30.1760i −0.744915 + 1.29023i 0.205319 + 0.978695i \(0.434177\pi\)
−0.950234 + 0.311536i \(0.899157\pi\)
\(548\) −0.171828 −0.00734012
\(549\) −0.664815 + 1.15149i −0.0283736 + 0.0491445i
\(550\) −3.49391 6.05163i −0.148981 0.258042i
\(551\) 39.7103 1.69171
\(552\) −0.607053 1.05145i −0.0258379 0.0447525i
\(553\) 5.11227 8.85470i 0.217396 0.376540i
\(554\) −8.00637 + 13.8674i −0.340158 + 0.589171i
\(555\) 0.133735 0.00567676
\(556\) −12.8667 + 22.2857i −0.545668 + 0.945125i
\(557\) 25.3487 1.07406 0.537029 0.843564i \(-0.319547\pi\)
0.537029 + 0.843564i \(0.319547\pi\)
\(558\) −2.06417 −0.0873831
\(559\) 20.9297 + 4.63947i 0.885234 + 0.196229i
\(560\) 3.64755 0.154137
\(561\) −0.241768 −0.0102075
\(562\) −4.47051 + 7.74315i −0.188577 + 0.326625i
\(563\) −5.50735 −0.232107 −0.116054 0.993243i \(-0.537024\pi\)
−0.116054 + 0.993243i \(0.537024\pi\)
\(564\) 0.427887 0.741122i 0.0180173 0.0312068i
\(565\) 7.85793 13.6103i 0.330585 0.572591i
\(566\) −1.11054 1.92351i −0.0466795 0.0808512i
\(567\) −13.9825 −0.587211
\(568\) −10.2000 17.6669i −0.427982 0.741286i
\(569\) 12.4688 21.5966i 0.522720 0.905377i −0.476931 0.878941i \(-0.658251\pi\)
0.999650 0.0264363i \(-0.00841592\pi\)
\(570\) −0.232412 −0.00973465
\(571\) 22.1813 38.4191i 0.928257 1.60779i 0.142021 0.989864i \(-0.454640\pi\)
0.786237 0.617925i \(-0.212027\pi\)
\(572\) 8.73341 + 15.1267i 0.365162 + 0.632479i
\(573\) 0.610262 + 1.05700i 0.0254941 + 0.0441570i
\(574\) 2.44880 + 4.24145i 0.102211 + 0.177035i
\(575\) −28.7848 −1.20041
\(576\) −1.63290 2.82827i −0.0680375 0.117844i
\(577\) 7.80634 + 13.5210i 0.324982 + 0.562885i 0.981509 0.191417i \(-0.0613084\pi\)
−0.656527 + 0.754303i \(0.727975\pi\)
\(578\) −0.288268 + 0.499295i −0.0119904 + 0.0207679i
\(579\) −0.313137 + 0.542369i −0.0130135 + 0.0225401i
\(580\) −15.0858 −0.626402
\(581\) 13.7733 0.571411
\(582\) −0.368046 + 0.637474i −0.0152560 + 0.0264242i
\(583\) 19.8008 34.2960i 0.820065 1.42039i
\(584\) 8.62557 + 14.9399i 0.356929 + 0.618219i
\(585\) 5.39946 + 9.35215i 0.223240 + 0.386664i
\(586\) 6.76093 0.279291
\(587\) −8.32286 14.4156i −0.343521 0.594996i 0.641563 0.767070i \(-0.278286\pi\)
−0.985084 + 0.172075i \(0.944953\pi\)
\(588\) 0.286825 + 0.496795i 0.0118285 + 0.0204875i
\(589\) 2.89507 + 5.01441i 0.119289 + 0.206615i
\(590\) 0.743309 1.28745i 0.0306015 0.0530034i
\(591\) 0.507807 0.0208884
\(592\) −1.69978 + 2.94411i −0.0698607 + 0.121002i
\(593\) −4.41409 7.64544i −0.181265 0.313960i 0.761046 0.648697i \(-0.224686\pi\)
−0.942312 + 0.334737i \(0.891353\pi\)
\(594\) −0.835535 −0.0342824
\(595\) 0.861848 + 1.49276i 0.0353323 + 0.0611974i
\(596\) −12.0468 + 20.8656i −0.493455 + 0.854689i
\(597\) −0.272968 + 0.472794i −0.0111718 + 0.0193502i
\(598\) −14.3415 −0.586469
\(599\) 11.3047 19.5803i 0.461897 0.800030i −0.537158 0.843482i \(-0.680502\pi\)
0.999056 + 0.0434517i \(0.0138355\pi\)
\(600\) −0.603635 −0.0246433
\(601\) 5.98956 0.244319 0.122160 0.992510i \(-0.461018\pi\)
0.122160 + 0.992510i \(0.461018\pi\)
\(602\) 5.76723 + 1.27841i 0.235055 + 0.0521043i
\(603\) −1.88931 −0.0769386
\(604\) −21.0804 −0.857749
\(605\) −0.405543 + 0.702421i −0.0164877 + 0.0285575i
\(606\) −0.640677 −0.0260257
\(607\) −1.89509 + 3.28239i −0.0769192 + 0.133228i −0.901919 0.431905i \(-0.857842\pi\)
0.825000 + 0.565133i \(0.191175\pi\)
\(608\) 13.1934 22.8517i 0.535064 0.926758i
\(609\) 0.483450 + 0.837360i 0.0195904 + 0.0339315i
\(610\) 0.282423 0.0114350
\(611\) −11.1162 19.2538i −0.449714 0.778927i
\(612\) 2.49666 4.32434i 0.100922 0.174801i
\(613\) 37.8274 1.52783 0.763917 0.645315i \(-0.223274\pi\)
0.763917 + 0.645315i \(0.223274\pi\)
\(614\) 4.89273 8.47445i 0.197454 0.342001i
\(615\) −0.226292 0.391949i −0.00912496 0.0158049i
\(616\) 5.29268 + 9.16720i 0.213248 + 0.369357i
\(617\) −8.38633 14.5256i −0.337621 0.584777i 0.646364 0.763030i \(-0.276289\pi\)
−0.983985 + 0.178253i \(0.942956\pi\)
\(618\) −0.734109 −0.0295302
\(619\) −10.3903 17.9965i −0.417620 0.723339i 0.578080 0.815980i \(-0.303802\pi\)
−0.995700 + 0.0926413i \(0.970469\pi\)
\(620\) −1.09983 1.90495i −0.0441701 0.0765048i
\(621\) −1.72090 + 2.98069i −0.0690574 + 0.119611i
\(622\) −8.36522 + 14.4890i −0.335415 + 0.580955i
\(623\) −7.99305 −0.320235
\(624\) 0.522048 0.0208987
\(625\) −4.11328 + 7.12440i −0.164531 + 0.284976i
\(626\) 3.35638 5.81342i 0.134148 0.232351i
\(627\) 0.585378 + 1.01390i 0.0233778 + 0.0404915i
\(628\) 3.14349 + 5.44468i 0.125439 + 0.217267i
\(629\) −1.60651 −0.0640558
\(630\) 1.48783 + 2.57700i 0.0592766 + 0.102670i
\(631\) −10.8198 18.7404i −0.430728 0.746043i 0.566208 0.824262i \(-0.308410\pi\)
−0.996936 + 0.0782193i \(0.975077\pi\)
\(632\) 6.91832 + 11.9829i 0.275196 + 0.476654i
\(633\) 0.591669 1.02480i 0.0235167 0.0407322i
\(634\) 14.4724 0.574773
\(635\) 1.82156 3.15503i 0.0722863 0.125203i
\(636\) −0.777725 1.34706i −0.0308388 0.0534144i
\(637\) 14.9030 0.590480
\(638\) −7.57367 13.1180i −0.299845 0.519346i
\(639\) −14.4439 + 25.0177i −0.571394 + 0.989683i
\(640\) −6.35800 + 11.0124i −0.251322 + 0.435303i
\(641\) −20.9472 −0.827364 −0.413682 0.910421i \(-0.635758\pi\)
−0.413682 + 0.910421i \(0.635758\pi\)
\(642\) 0.222988 0.386227i 0.00880065 0.0152432i
\(643\) −40.0814 −1.58066 −0.790328 0.612684i \(-0.790090\pi\)
−0.790328 + 0.612684i \(0.790090\pi\)
\(644\) 19.8261 0.781259
\(645\) −0.532944 0.118137i −0.0209846 0.00465164i
\(646\) 2.79186 0.109844
\(647\) 26.6008 1.04579 0.522893 0.852398i \(-0.324853\pi\)
0.522893 + 0.852398i \(0.324853\pi\)
\(648\) 9.46114 16.3872i 0.371669 0.643749i
\(649\) −7.48873 −0.293958
\(650\) −3.56520 + 6.17510i −0.139838 + 0.242207i
\(651\) −0.0704917 + 0.122095i −0.00276279 + 0.00478529i
\(652\) 3.42443 + 5.93128i 0.134111 + 0.232287i
\(653\) −23.3963 −0.915569 −0.457785 0.889063i \(-0.651357\pi\)
−0.457785 + 0.889063i \(0.651357\pi\)
\(654\) 0.159880 + 0.276920i 0.00625180 + 0.0108284i
\(655\) −4.17475 + 7.23088i −0.163121 + 0.282534i
\(656\) 11.5047 0.449183
\(657\) 12.2145 21.1561i 0.476532 0.825377i
\(658\) −3.06309 5.30543i −0.119412 0.206827i
\(659\) −15.7508 27.2812i −0.613565 1.06273i −0.990635 0.136540i \(-0.956402\pi\)
0.377070 0.926185i \(-0.376932\pi\)
\(660\) −0.222383 0.385178i −0.00865623 0.0149930i
\(661\) −19.5370 −0.759900 −0.379950 0.925007i \(-0.624059\pi\)
−0.379950 + 0.925007i \(0.624059\pi\)
\(662\) 3.70531 + 6.41779i 0.144011 + 0.249434i
\(663\) 0.123350 + 0.213649i 0.00479053 + 0.00829744i
\(664\) −9.31954 + 16.1419i −0.361668 + 0.626428i
\(665\) 4.17348 7.22868i 0.161841 0.280316i
\(666\) −2.77336 −0.107466
\(667\) −62.3962 −2.41599
\(668\) −6.85717 + 11.8770i −0.265312 + 0.459534i
\(669\) 0.783141 1.35644i 0.0302780 0.0524430i
\(670\) 0.200652 + 0.347539i 0.00775185 + 0.0134266i
\(671\) −0.711343 1.23208i −0.0274611 0.0475640i
\(672\) 0.642490 0.0247846
\(673\) 24.3356 + 42.1506i 0.938070 + 1.62479i 0.769065 + 0.639170i \(0.220722\pi\)
0.169005 + 0.985615i \(0.445945\pi\)
\(674\) 0.750404 + 1.29974i 0.0289045 + 0.0500640i
\(675\) 0.855606 + 1.48195i 0.0329323 + 0.0570404i
\(676\) −1.92785 + 3.33913i −0.0741480 + 0.128428i
\(677\) −17.1876 −0.660572 −0.330286 0.943881i \(-0.607145\pi\)
−0.330286 + 0.943881i \(0.607145\pi\)
\(678\) 0.309899 0.536761i 0.0119016 0.0206142i
\(679\) −13.2182 22.8946i −0.507268 0.878614i
\(680\) −2.33264 −0.0894528
\(681\) 0.647333 + 1.12121i 0.0248058 + 0.0429650i
\(682\) 1.10432 1.91273i 0.0422864 0.0732422i
\(683\) −2.96851 + 5.14162i −0.113587 + 0.196738i −0.917214 0.398395i \(-0.869567\pi\)
0.803627 + 0.595133i \(0.202901\pi\)
\(684\) −24.1800 −0.924547
\(685\) 0.0568340 0.0984395i 0.00217152 0.00376118i
\(686\) 10.4125 0.397549
\(687\) −0.991449 −0.0378262
\(688\) 9.37446 10.2309i 0.357398 0.390051i
\(689\) −40.4095 −1.53948
\(690\) 0.365185 0.0139023
\(691\) 21.3689 37.0120i 0.812911 1.40800i −0.0979079 0.995195i \(-0.531215\pi\)
0.910819 0.412807i \(-0.135452\pi\)
\(692\) −6.96030 −0.264591
\(693\) 7.49484 12.9814i 0.284706 0.493124i
\(694\) −4.41171 + 7.64130i −0.167466 + 0.290060i
\(695\) −8.51161 14.7425i −0.322864 0.559216i
\(696\) −1.30849 −0.0495980
\(697\) 2.71835 + 4.70832i 0.102965 + 0.178340i
\(698\) 6.58909 11.4126i 0.249401 0.431975i
\(699\) 1.27307 0.0481521
\(700\) 4.92863 8.53663i 0.186285 0.322654i
\(701\) −13.1199 22.7243i −0.495530 0.858283i 0.504457 0.863437i \(-0.331693\pi\)
−0.999987 + 0.00515370i \(0.998360\pi\)
\(702\) 0.426291 + 0.738358i 0.0160893 + 0.0278675i
\(703\) 3.88974 + 6.73723i 0.146704 + 0.254100i
\(704\) 3.49436 0.131699
\(705\) 0.283057 + 0.490269i 0.0106605 + 0.0184646i
\(706\) −4.49090 7.77847i −0.169017 0.292747i
\(707\) 11.5048 19.9269i 0.432683 0.749429i
\(708\) −0.147069 + 0.254731i −0.00552720 + 0.00957339i
\(709\) −7.84763 −0.294724 −0.147362 0.989083i \(-0.547078\pi\)
−0.147362 + 0.989083i \(0.547078\pi\)
\(710\) 6.13600 0.230280
\(711\) 9.79688 16.9687i 0.367412 0.636375i
\(712\) 5.40841 9.36765i 0.202689 0.351067i
\(713\) −4.54898 7.87907i −0.170361 0.295074i
\(714\) 0.0339894 + 0.0588713i 0.00127202 + 0.00220320i
\(715\) −11.5547 −0.432122
\(716\) −5.03416 8.71942i −0.188135 0.325860i
\(717\) −0.669846 1.16021i −0.0250158 0.0433287i
\(718\) 6.81184 + 11.7985i 0.254216 + 0.440314i
\(719\) 10.8532 18.7984i 0.404758 0.701061i −0.589536 0.807742i \(-0.700689\pi\)
0.994293 + 0.106682i \(0.0340226\pi\)
\(720\) 6.98997 0.260501
\(721\) 13.1826 22.8329i 0.490946 0.850343i
\(722\) −1.28267 2.22166i −0.0477362 0.0826815i
\(723\) −1.56138 −0.0580684
\(724\) −14.8735 25.7616i −0.552769 0.957424i
\(725\) −15.5112 + 26.8662i −0.576072 + 0.997786i
\(726\) −0.0159937 + 0.0277019i −0.000593582 + 0.00102812i
\(727\) −2.10971 −0.0782449 −0.0391224 0.999234i \(-0.512456\pi\)
−0.0391224 + 0.999234i \(0.512456\pi\)
\(728\) 5.40067 9.35423i 0.200162 0.346691i
\(729\) −26.6930 −0.988629
\(730\) −5.18888 −0.192049
\(731\) 6.40204 + 1.41913i 0.236788 + 0.0524885i
\(732\) −0.0558795 −0.00206537
\(733\) 31.6318 1.16835 0.584174 0.811628i \(-0.301418\pi\)
0.584174 + 0.811628i \(0.301418\pi\)
\(734\) −0.501631 + 0.868850i −0.0185155 + 0.0320699i
\(735\) −0.379483 −0.0139974
\(736\) −20.7306 + 35.9065i −0.764141 + 1.32353i
\(737\) 1.01077 1.75070i 0.0372321 0.0644879i
\(738\) 4.69276 + 8.12810i 0.172743 + 0.299199i
\(739\) −14.1562 −0.520743 −0.260372 0.965508i \(-0.583845\pi\)
−0.260372 + 0.965508i \(0.583845\pi\)
\(740\) −1.47770 2.55945i −0.0543212 0.0940871i
\(741\) 0.597321 1.03459i 0.0219431 0.0380066i
\(742\) −11.1349 −0.408776
\(743\) −9.94804 + 17.2305i −0.364958 + 0.632126i −0.988769 0.149449i \(-0.952250\pi\)
0.623811 + 0.781575i \(0.285583\pi\)
\(744\) −0.0953950 0.165229i −0.00349735 0.00605759i
\(745\) −7.96922 13.8031i −0.291970 0.505706i
\(746\) 6.45833 + 11.1862i 0.236456 + 0.409554i
\(747\) 26.3944 0.965719
\(748\) 2.67139 + 4.62699i 0.0976758 + 0.169179i
\(749\) 8.00853 + 13.8712i 0.292625 + 0.506842i
\(750\) 0.210768 0.365061i 0.00769616 0.0133301i
\(751\) −24.5751 + 42.5652i −0.896756 + 1.55323i −0.0651408 + 0.997876i \(0.520750\pi\)
−0.831616 + 0.555352i \(0.812584\pi\)
\(752\) −14.3907 −0.524774
\(753\) 1.60721 0.0585700
\(754\) −7.72819 + 13.3856i −0.281444 + 0.487476i
\(755\) 6.97259 12.0769i 0.253759 0.439523i
\(756\) −0.589317 1.02073i −0.0214332 0.0371235i
\(757\) 3.35258 + 5.80685i 0.121852 + 0.211053i 0.920498 0.390747i \(-0.127783\pi\)
−0.798646 + 0.601801i \(0.794450\pi\)
\(758\) 4.80596 0.174560
\(759\) −0.919796 1.59313i −0.0333865 0.0578271i
\(760\) 5.64788 + 9.78242i 0.204870 + 0.354846i
\(761\) 16.0707 + 27.8353i 0.582562 + 1.00903i 0.995175 + 0.0981207i \(0.0312831\pi\)
−0.412612 + 0.910907i \(0.635384\pi\)
\(762\) 0.0718382 0.124427i 0.00260242 0.00450753i
\(763\) −11.4840 −0.415750
\(764\) 13.4861 23.3585i 0.487908 0.845082i
\(765\) 1.65160 + 2.86065i 0.0597137 + 0.103427i
\(766\) −20.0120 −0.723064
\(767\) 3.82076 + 6.61775i 0.137960