Properties

Label 169.4.e.c.23.1
Level $169$
Weight $4$
Character 169.23
Analytic conductor $9.971$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 169 = 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 169.e (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.97132279097\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 13)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 23.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 169.23
Dual form 169.4.e.c.147.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-3.46410 + 2.00000i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(4.00000 - 6.92820i) q^{4} -17.0000i q^{5} +(6.92820 + 4.00000i) q^{6} +(-17.3205 - 10.0000i) q^{7} +(11.5000 - 19.9186i) q^{9} +O(q^{10})\) \(q+(-3.46410 + 2.00000i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(4.00000 - 6.92820i) q^{4} -17.0000i q^{5} +(6.92820 + 4.00000i) q^{6} +(-17.3205 - 10.0000i) q^{7} +(11.5000 - 19.9186i) q^{9} +(34.0000 + 58.8897i) q^{10} +(-27.7128 + 16.0000i) q^{11} -16.0000 q^{12} +80.0000 q^{14} +(-29.4449 + 17.0000i) q^{15} +(32.0000 + 55.4256i) q^{16} +(-6.50000 + 11.2583i) q^{17} +92.0000i q^{18} +(25.9808 + 15.0000i) q^{19} +(-117.779 - 68.0000i) q^{20} +40.0000i q^{21} +(64.0000 - 110.851i) q^{22} +(39.0000 + 67.5500i) q^{23} -164.000 q^{25} -100.000 q^{27} +(-138.564 + 80.0000i) q^{28} +(-98.5000 - 170.607i) q^{29} +(68.0000 - 117.779i) q^{30} +74.0000i q^{31} +(-221.703 - 128.000i) q^{32} +(55.4256 + 32.0000i) q^{33} -52.0000i q^{34} +(-170.000 + 294.449i) q^{35} +(-92.0000 - 159.349i) q^{36} +(-196.588 + 113.500i) q^{37} -120.000 q^{38} +(142.894 - 82.5000i) q^{41} +(-80.0000 - 138.564i) q^{42} +(-78.0000 + 135.100i) q^{43} +256.000i q^{44} +(-338.616 - 195.500i) q^{45} +(-270.200 - 156.000i) q^{46} -162.000i q^{47} +(64.0000 - 110.851i) q^{48} +(28.5000 + 49.3634i) q^{49} +(568.113 - 328.000i) q^{50} +26.0000 q^{51} +93.0000 q^{53} +(346.410 - 200.000i) q^{54} +(272.000 + 471.118i) q^{55} -60.0000i q^{57} +(682.428 + 394.000i) q^{58} +(748.246 + 432.000i) q^{59} +272.000i q^{60} +(-72.5000 + 125.574i) q^{61} +(-148.000 - 256.344i) q^{62} +(-398.372 + 230.000i) q^{63} +512.000 q^{64} -256.000 q^{66} +(-746.514 + 431.000i) q^{67} +(52.0000 + 90.0666i) q^{68} +(78.0000 - 135.100i) q^{69} -1360.00i q^{70} +(566.381 + 327.000i) q^{71} +215.000i q^{73} +(454.000 - 786.351i) q^{74} +(164.000 + 284.056i) q^{75} +(207.846 - 120.000i) q^{76} +640.000 q^{77} -76.0000 q^{79} +(942.236 - 544.000i) q^{80} +(-210.500 - 364.597i) q^{81} +(-330.000 + 571.577i) q^{82} -628.000i q^{83} +(277.128 + 160.000i) q^{84} +(191.392 + 110.500i) q^{85} -624.000i q^{86} +(-197.000 + 341.214i) q^{87} +(-230.363 + 133.000i) q^{89} +1564.00 q^{90} +624.000 q^{92} +(128.172 - 74.0000i) q^{93} +(324.000 + 561.184i) q^{94} +(255.000 - 441.673i) q^{95} +512.000i q^{96} +(206.114 + 119.000i) q^{97} +(-197.454 - 114.000i) q^{98} +736.000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{3} + 16 q^{4} + 46 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{3} + 16 q^{4} + 46 q^{9} + 136 q^{10} - 64 q^{12} + 320 q^{14} + 128 q^{16} - 26 q^{17} + 256 q^{22} + 156 q^{23} - 656 q^{25} - 400 q^{27} - 394 q^{29} + 272 q^{30} - 680 q^{35} - 368 q^{36} - 480 q^{38} - 320 q^{42} - 312 q^{43} + 256 q^{48} + 114 q^{49} + 104 q^{51} + 372 q^{53} + 1088 q^{55} - 290 q^{61} - 592 q^{62} + 2048 q^{64} - 1024 q^{66} + 208 q^{68} + 312 q^{69} + 1816 q^{74} + 656 q^{75} + 2560 q^{77} - 304 q^{79} - 842 q^{81} - 1320 q^{82} - 788 q^{87} + 6256 q^{90} + 2496 q^{92} + 1296 q^{94} + 1020 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/169\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.46410 + 2.00000i −1.22474 + 0.707107i −0.965926 0.258819i \(-0.916667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(3\) −1.00000 1.73205i −0.192450 0.333333i 0.753612 0.657320i \(-0.228310\pi\)
−0.946062 + 0.323987i \(0.894977\pi\)
\(4\) 4.00000 6.92820i 0.500000 0.866025i
\(5\) 17.0000i 1.52053i −0.649615 0.760263i \(-0.725070\pi\)
0.649615 0.760263i \(-0.274930\pi\)
\(6\) 6.92820 + 4.00000i 0.471405 + 0.272166i
\(7\) −17.3205 10.0000i −0.935220 0.539949i −0.0467610 0.998906i \(-0.514890\pi\)
−0.888459 + 0.458957i \(0.848223\pi\)
\(8\) 0 0
\(9\) 11.5000 19.9186i 0.425926 0.737725i
\(10\) 34.0000 + 58.8897i 1.07517 + 1.86226i
\(11\) −27.7128 + 16.0000i −0.759612 + 0.438562i −0.829156 0.559017i \(-0.811179\pi\)
0.0695447 + 0.997579i \(0.477845\pi\)
\(12\) −16.0000 −0.384900
\(13\) 0 0
\(14\) 80.0000 1.52721
\(15\) −29.4449 + 17.0000i −0.506842 + 0.292625i
\(16\) 32.0000 + 55.4256i 0.500000 + 0.866025i
\(17\) −6.50000 + 11.2583i −0.0927342 + 0.160620i −0.908661 0.417535i \(-0.862894\pi\)
0.815927 + 0.578156i \(0.196227\pi\)
\(18\) 92.0000i 1.20470i
\(19\) 25.9808 + 15.0000i 0.313705 + 0.181118i 0.648583 0.761144i \(-0.275362\pi\)
−0.334878 + 0.942261i \(0.608695\pi\)
\(20\) −117.779 68.0000i −1.31681 0.760263i
\(21\) 40.0000i 0.415653i
\(22\) 64.0000 110.851i 0.620220 1.07425i
\(23\) 39.0000 + 67.5500i 0.353568 + 0.612398i 0.986872 0.161506i \(-0.0516350\pi\)
−0.633304 + 0.773903i \(0.718302\pi\)
\(24\) 0 0
\(25\) −164.000 −1.31200
\(26\) 0 0
\(27\) −100.000 −0.712778
\(28\) −138.564 + 80.0000i −0.935220 + 0.539949i
\(29\) −98.5000 170.607i −0.630724 1.09245i −0.987404 0.158219i \(-0.949425\pi\)
0.356680 0.934227i \(-0.383909\pi\)
\(30\) 68.0000 117.779i 0.413835 0.716783i
\(31\) 74.0000i 0.428735i 0.976753 + 0.214368i \(0.0687691\pi\)
−0.976753 + 0.214368i \(0.931231\pi\)
\(32\) −221.703 128.000i −1.22474 0.707107i
\(33\) 55.4256 + 32.0000i 0.292375 + 0.168803i
\(34\) 52.0000i 0.262292i
\(35\) −170.000 + 294.449i −0.821007 + 1.42203i
\(36\) −92.0000 159.349i −0.425926 0.737725i
\(37\) −196.588 + 113.500i −0.873482 + 0.504305i −0.868504 0.495683i \(-0.834918\pi\)
−0.00497814 + 0.999988i \(0.501585\pi\)
\(38\) −120.000 −0.512278
\(39\) 0 0
\(40\) 0 0
\(41\) 142.894 82.5000i 0.544301 0.314252i −0.202520 0.979278i \(-0.564913\pi\)
0.746820 + 0.665026i \(0.231580\pi\)
\(42\) −80.0000 138.564i −0.293911 0.509069i
\(43\) −78.0000 + 135.100i −0.276625 + 0.479129i −0.970544 0.240924i \(-0.922549\pi\)
0.693919 + 0.720053i \(0.255883\pi\)
\(44\) 256.000i 0.877124i
\(45\) −338.616 195.500i −1.12173 0.647632i
\(46\) −270.200 156.000i −0.866061 0.500021i
\(47\) 162.000i 0.502769i −0.967887 0.251384i \(-0.919114\pi\)
0.967887 0.251384i \(-0.0808858\pi\)
\(48\) 64.0000 110.851i 0.192450 0.333333i
\(49\) 28.5000 + 49.3634i 0.0830904 + 0.143917i
\(50\) 568.113 328.000i 1.60687 0.927724i
\(51\) 26.0000 0.0713868
\(52\) 0 0
\(53\) 93.0000 0.241029 0.120514 0.992712i \(-0.461546\pi\)
0.120514 + 0.992712i \(0.461546\pi\)
\(54\) 346.410 200.000i 0.872971 0.504010i
\(55\) 272.000 + 471.118i 0.666845 + 1.15501i
\(56\) 0 0
\(57\) 60.0000i 0.139424i
\(58\) 682.428 + 394.000i 1.54495 + 0.891978i
\(59\) 748.246 + 432.000i 1.65107 + 0.953248i 0.976632 + 0.214919i \(0.0689489\pi\)
0.674442 + 0.738328i \(0.264384\pi\)
\(60\) 272.000i 0.585251i
\(61\) −72.5000 + 125.574i −0.152175 + 0.263575i −0.932027 0.362389i \(-0.881961\pi\)
0.779852 + 0.625964i \(0.215294\pi\)
\(62\) −148.000 256.344i −0.303162 0.525091i
\(63\) −398.372 + 230.000i −0.796668 + 0.459957i
\(64\) 512.000 1.00000
\(65\) 0 0
\(66\) −256.000 −0.477446
\(67\) −746.514 + 431.000i −1.36121 + 0.785896i −0.989785 0.142566i \(-0.954465\pi\)
−0.371427 + 0.928462i \(0.621131\pi\)
\(68\) 52.0000 + 90.0666i 0.0927342 + 0.160620i
\(69\) 78.0000 135.100i 0.136088 0.235712i
\(70\) 1360.00i 2.32216i
\(71\) 566.381 + 327.000i 0.946718 + 0.546588i 0.892060 0.451917i \(-0.149260\pi\)
0.0546585 + 0.998505i \(0.482593\pi\)
\(72\) 0 0
\(73\) 215.000i 0.344710i 0.985035 + 0.172355i \(0.0551377\pi\)
−0.985035 + 0.172355i \(0.944862\pi\)
\(74\) 454.000 786.351i 0.713195 1.23529i
\(75\) 164.000 + 284.056i 0.252495 + 0.437333i
\(76\) 207.846 120.000i 0.313705 0.181118i
\(77\) 640.000 0.947205
\(78\) 0 0
\(79\) −76.0000 −0.108236 −0.0541182 0.998535i \(-0.517235\pi\)
−0.0541182 + 0.998535i \(0.517235\pi\)
\(80\) 942.236 544.000i 1.31681 0.760263i
\(81\) −210.500 364.597i −0.288752 0.500133i
\(82\) −330.000 + 571.577i −0.444420 + 0.769757i
\(83\) 628.000i 0.830505i −0.909706 0.415253i \(-0.863693\pi\)
0.909706 0.415253i \(-0.136307\pi\)
\(84\) 277.128 + 160.000i 0.359966 + 0.207827i
\(85\) 191.392 + 110.500i 0.244227 + 0.141005i
\(86\) 624.000i 0.782415i
\(87\) −197.000 + 341.214i −0.242766 + 0.420483i
\(88\) 0 0
\(89\) −230.363 + 133.000i −0.274364 + 0.158404i −0.630869 0.775889i \(-0.717302\pi\)
0.356505 + 0.934293i \(0.383968\pi\)
\(90\) 1564.00 1.83178
\(91\) 0 0
\(92\) 624.000 0.707136
\(93\) 128.172 74.0000i 0.142912 0.0825101i
\(94\) 324.000 + 561.184i 0.355511 + 0.615763i
\(95\) 255.000 441.673i 0.275394 0.476997i
\(96\) 512.000i 0.544331i
\(97\) 206.114 + 119.000i 0.215750 + 0.124563i 0.603981 0.796999i \(-0.293580\pi\)
−0.388231 + 0.921562i \(0.626914\pi\)
\(98\) −197.454 114.000i −0.203529 0.117508i
\(99\) 736.000i 0.747180i
\(100\) −656.000 + 1136.23i −0.656000 + 1.13623i
\(101\) −409.500 709.275i −0.403433 0.698767i 0.590704 0.806888i \(-0.298850\pi\)
−0.994138 + 0.108121i \(0.965517\pi\)
\(102\) −90.0666 + 52.0000i −0.0874307 + 0.0504781i
\(103\) −1638.00 −1.56696 −0.783480 0.621417i \(-0.786557\pi\)
−0.783480 + 0.621417i \(0.786557\pi\)
\(104\) 0 0
\(105\) 680.000 0.632011
\(106\) −322.161 + 186.000i −0.295199 + 0.170433i
\(107\) −261.000 452.065i −0.235811 0.408437i 0.723697 0.690118i \(-0.242441\pi\)
−0.959508 + 0.281681i \(0.909108\pi\)
\(108\) −400.000 + 692.820i −0.356389 + 0.617284i
\(109\) 1634.00i 1.43586i 0.696115 + 0.717930i \(0.254910\pi\)
−0.696115 + 0.717930i \(0.745090\pi\)
\(110\) −1884.47 1088.00i −1.63343 0.943061i
\(111\) 393.176 + 227.000i 0.336203 + 0.194107i
\(112\) 1280.00i 1.07990i
\(113\) −163.500 + 283.190i −0.136113 + 0.235755i −0.926022 0.377469i \(-0.876794\pi\)
0.789909 + 0.613224i \(0.210128\pi\)
\(114\) 120.000 + 207.846i 0.0985880 + 0.170759i
\(115\) 1148.35 663.000i 0.931167 0.537609i
\(116\) −1576.00 −1.26145
\(117\) 0 0
\(118\) −3456.00 −2.69619
\(119\) 225.167 130.000i 0.173454 0.100144i
\(120\) 0 0
\(121\) −153.500 + 265.870i −0.115327 + 0.199752i
\(122\) 580.000i 0.430416i
\(123\) −285.788 165.000i −0.209501 0.120956i
\(124\) 512.687 + 296.000i 0.371296 + 0.214368i
\(125\) 663.000i 0.474404i
\(126\) 920.000 1593.49i 0.650477 1.12666i
\(127\) −1079.00 1868.88i −0.753904 1.30580i −0.945918 0.324407i \(-0.894835\pi\)
0.192014 0.981392i \(-0.438498\pi\)
\(128\) 0 0
\(129\) 312.000 0.212946
\(130\) 0 0
\(131\) 730.000 0.486873 0.243437 0.969917i \(-0.421725\pi\)
0.243437 + 0.969917i \(0.421725\pi\)
\(132\) 443.405 256.000i 0.292375 0.168803i
\(133\) −300.000 519.615i −0.195589 0.338770i
\(134\) 1724.00 2986.06i 1.11142 1.92504i
\(135\) 1700.00i 1.08380i
\(136\) 0 0
\(137\) −1447.13 835.500i −0.902456 0.521033i −0.0244601 0.999701i \(-0.507787\pi\)
−0.877996 + 0.478667i \(0.841120\pi\)
\(138\) 624.000i 0.384916i
\(139\) −456.000 + 789.815i −0.278255 + 0.481951i −0.970951 0.239278i \(-0.923089\pi\)
0.692696 + 0.721229i \(0.256423\pi\)
\(140\) 1360.00 + 2355.59i 0.821007 + 1.42203i
\(141\) −280.592 + 162.000i −0.167590 + 0.0967579i
\(142\) −2616.00 −1.54598
\(143\) 0 0
\(144\) 1472.00 0.851852
\(145\) −2900.32 + 1674.50i −1.66109 + 0.959032i
\(146\) −430.000 744.782i −0.243747 0.422182i
\(147\) 57.0000 98.7269i 0.0319815 0.0553936i
\(148\) 1816.00i 1.00861i
\(149\) −1831.64 1057.50i −1.00707 0.581435i −0.0967407 0.995310i \(-0.530842\pi\)
−0.910334 + 0.413875i \(0.864175\pi\)
\(150\) −1136.23 656.000i −0.618483 0.357081i
\(151\) 514.000i 0.277011i 0.990362 + 0.138506i \(0.0442299\pi\)
−0.990362 + 0.138506i \(0.955770\pi\)
\(152\) 0 0
\(153\) 149.500 + 258.942i 0.0789958 + 0.136825i
\(154\) −2217.03 + 1280.00i −1.16008 + 0.669775i
\(155\) 1258.00 0.651903
\(156\) 0 0
\(157\) 2901.00 1.47468 0.737341 0.675521i \(-0.236081\pi\)
0.737341 + 0.675521i \(0.236081\pi\)
\(158\) 263.272 152.000i 0.132562 0.0765346i
\(159\) −93.0000 161.081i −0.0463860 0.0803430i
\(160\) −2176.00 + 3768.94i −1.07517 + 1.86226i
\(161\) 1560.00i 0.763635i
\(162\) 1458.39 + 842.000i 0.707294 + 0.408357i
\(163\) −2043.82 1180.00i −0.982112 0.567023i −0.0792052 0.996858i \(-0.525238\pi\)
−0.902907 + 0.429835i \(0.858572\pi\)
\(164\) 1320.00i 0.628504i
\(165\) 544.000 942.236i 0.256669 0.444563i
\(166\) 1256.00 + 2175.46i 0.587256 + 1.01716i
\(167\) 242.487 140.000i 0.112361 0.0648714i −0.442767 0.896637i \(-0.646003\pi\)
0.555127 + 0.831766i \(0.312670\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) −884.000 −0.398822
\(171\) 597.558 345.000i 0.267230 0.154285i
\(172\) 624.000 + 1080.80i 0.276625 + 0.479129i
\(173\) 663.000 1148.35i 0.291370 0.504667i −0.682764 0.730639i \(-0.739222\pi\)
0.974134 + 0.225972i \(0.0725557\pi\)
\(174\) 1576.00i 0.686645i
\(175\) 2840.56 + 1640.00i 1.22701 + 0.708413i
\(176\) −1773.62 1024.00i −0.759612 0.438562i
\(177\) 1728.00i 0.733810i
\(178\) 532.000 921.451i 0.224017 0.388009i
\(179\) 2132.00 + 3692.73i 0.890241 + 1.54194i 0.839586 + 0.543227i \(0.182798\pi\)
0.0506550 + 0.998716i \(0.483869\pi\)
\(180\) −2708.93 + 1564.00i −1.12173 + 0.647632i
\(181\) 403.000 0.165496 0.0827479 0.996571i \(-0.473630\pi\)
0.0827479 + 0.996571i \(0.473630\pi\)
\(182\) 0 0
\(183\) 290.000 0.117144
\(184\) 0 0
\(185\) 1929.50 + 3341.99i 0.766809 + 1.32815i
\(186\) −296.000 + 512.687i −0.116687 + 0.202108i
\(187\) 416.000i 0.162679i
\(188\) −1122.37 648.000i −0.435410 0.251384i
\(189\) 1732.05 + 1000.00i 0.666604 + 0.384864i
\(190\) 2040.00i 0.778932i
\(191\) 623.000 1079.07i 0.236014 0.408788i −0.723553 0.690269i \(-0.757492\pi\)
0.959567 + 0.281481i \(0.0908255\pi\)
\(192\) −512.000 886.810i −0.192450 0.333333i
\(193\) 231.229 133.500i 0.0862394 0.0497904i −0.456260 0.889846i \(-0.650811\pi\)
0.542500 + 0.840056i \(0.317478\pi\)
\(194\) −952.000 −0.352318
\(195\) 0 0
\(196\) 456.000 0.166181
\(197\) −1106.78 + 639.000i −0.400278 + 0.231101i −0.686604 0.727032i \(-0.740899\pi\)
0.286326 + 0.958132i \(0.407566\pi\)
\(198\) −1472.00 2549.58i −0.528336 0.915104i
\(199\) 2119.00 3670.22i 0.754834 1.30741i −0.190623 0.981663i \(-0.561051\pi\)
0.945457 0.325747i \(-0.105616\pi\)
\(200\) 0 0
\(201\) 1493.03 + 862.000i 0.523931 + 0.302492i
\(202\) 2837.10 + 1638.00i 0.988206 + 0.570541i
\(203\) 3940.00i 1.36224i
\(204\) 104.000 180.133i 0.0356934 0.0618228i
\(205\) −1402.50 2429.20i −0.477829 0.827623i
\(206\) 5674.20 3276.00i 1.91913 1.10801i
\(207\) 1794.00 0.602375
\(208\) 0 0
\(209\) −960.000 −0.317725
\(210\) −2355.59 + 1360.00i −0.774053 + 0.446900i
\(211\) −1535.00 2658.70i −0.500823 0.867452i −1.00000 0.000951154i \(-0.999697\pi\)
0.499176 0.866501i \(-0.333636\pi\)
\(212\) 372.000 644.323i 0.120514 0.208737i
\(213\) 1308.00i 0.420764i
\(214\) 1808.26 + 1044.00i 0.577618 + 0.333488i
\(215\) 2296.70 + 1326.00i 0.728528 + 0.420616i
\(216\) 0 0
\(217\) 740.000 1281.72i 0.231495 0.400962i
\(218\) −3268.00 5660.34i −1.01531 1.75856i
\(219\) 372.391 215.000i 0.114903 0.0663395i
\(220\) 4352.00 1.33369
\(221\) 0 0
\(222\) −1816.00 −0.549018
\(223\) 4657.48 2689.00i 1.39860 0.807483i 0.404356 0.914602i \(-0.367496\pi\)
0.994246 + 0.107119i \(0.0341624\pi\)
\(224\) 2560.00 + 4434.05i 0.763604 + 1.32260i
\(225\) −1886.00 + 3266.65i −0.558815 + 0.967896i
\(226\) 1308.00i 0.384986i
\(227\) −3441.58 1987.00i −1.00628 0.580977i −0.0961811 0.995364i \(-0.530663\pi\)
−0.910101 + 0.414387i \(0.863996\pi\)
\(228\) −415.692 240.000i −0.120745 0.0697122i
\(229\) 6298.00i 1.81740i −0.417455 0.908698i \(-0.637078\pi\)
0.417455 0.908698i \(-0.362922\pi\)
\(230\) −2652.00 + 4593.40i −0.760294 + 1.31687i
\(231\) −640.000 1108.51i −0.182290 0.315735i
\(232\) 0 0
\(233\) −4030.00 −1.13311 −0.566554 0.824025i \(-0.691724\pi\)
−0.566554 + 0.824025i \(0.691724\pi\)
\(234\) 0 0
\(235\) −2754.00 −0.764473
\(236\) 5985.97 3456.00i 1.65107 0.953248i
\(237\) 76.0000 + 131.636i 0.0208301 + 0.0360788i
\(238\) −520.000 + 900.666i −0.141624 + 0.245301i
\(239\) 984.000i 0.266317i 0.991095 + 0.133158i \(0.0425119\pi\)
−0.991095 + 0.133158i \(0.957488\pi\)
\(240\) −1884.47 1088.00i −0.506842 0.292625i
\(241\) −816.662 471.500i −0.218281 0.126025i 0.386873 0.922133i \(-0.373555\pi\)
−0.605154 + 0.796108i \(0.706889\pi\)
\(242\) 1228.00i 0.326194i
\(243\) −1771.00 + 3067.46i −0.467530 + 0.809785i
\(244\) 580.000 + 1004.59i 0.152175 + 0.263575i
\(245\) 839.179 484.500i 0.218829 0.126341i
\(246\) 1320.00 0.342114
\(247\) 0 0
\(248\) 0 0
\(249\) −1087.73 + 628.000i −0.276835 + 0.159831i
\(250\) −1326.00 2296.70i −0.335454 0.581024i
\(251\) −1365.00 + 2364.25i −0.343259 + 0.594542i −0.985036 0.172349i \(-0.944864\pi\)
0.641777 + 0.766891i \(0.278198\pi\)
\(252\) 3680.00i 0.919914i
\(253\) −2161.60 1248.00i −0.537149 0.310123i
\(254\) 7475.53 + 4316.00i 1.84668 + 1.06618i
\(255\) 442.000i 0.108546i
\(256\) −2048.00 + 3547.24i −0.500000 + 0.866025i
\(257\) −942.500 1632.46i −0.228761 0.396225i 0.728680 0.684854i \(-0.240134\pi\)
−0.957441 + 0.288629i \(0.906801\pi\)
\(258\) −1080.80 + 624.000i −0.260805 + 0.150576i
\(259\) 4540.00 1.08920
\(260\) 0 0
\(261\) −4531.00 −1.07457
\(262\) −2528.79 + 1460.00i −0.596296 + 0.344271i
\(263\) −2016.00 3491.81i −0.472669 0.818686i 0.526842 0.849963i \(-0.323376\pi\)
−0.999511 + 0.0312769i \(0.990043\pi\)
\(264\) 0 0
\(265\) 1581.00i 0.366491i
\(266\) 2078.46 + 1200.00i 0.479093 + 0.276604i
\(267\) 460.726 + 266.000i 0.105603 + 0.0609698i
\(268\) 6896.00i 1.57179i
\(269\) −2003.00 + 3469.30i −0.453997 + 0.786345i −0.998630 0.0523292i \(-0.983335\pi\)
0.544633 + 0.838674i \(0.316669\pi\)
\(270\) −3400.00 5888.97i −0.766361 1.32738i
\(271\) −3720.45 + 2148.00i −0.833952 + 0.481482i −0.855204 0.518292i \(-0.826568\pi\)
0.0212520 + 0.999774i \(0.493235\pi\)
\(272\) −832.000 −0.185468
\(273\) 0 0
\(274\) 6684.00 1.47371
\(275\) 4544.90 2624.00i 0.996610 0.575393i
\(276\) −624.000 1080.80i −0.136088 0.235712i
\(277\) −2775.50 + 4807.31i −0.602035 + 1.04275i 0.390478 + 0.920612i \(0.372310\pi\)
−0.992513 + 0.122142i \(0.961024\pi\)
\(278\) 3648.00i 0.787023i
\(279\) 1473.98 + 851.000i 0.316289 + 0.182609i
\(280\) 0 0
\(281\) 5557.00i 1.17973i −0.807504 0.589863i \(-0.799182\pi\)
0.807504 0.589863i \(-0.200818\pi\)
\(282\) 648.000 1122.37i 0.136836 0.237007i
\(283\) 1560.00 + 2702.00i 0.327676 + 0.567552i 0.982050 0.188619i \(-0.0604012\pi\)
−0.654374 + 0.756171i \(0.727068\pi\)
\(284\) 4531.04 2616.00i 0.946718 0.546588i
\(285\) −1020.00 −0.211999
\(286\) 0 0
\(287\) −3300.00 −0.678721
\(288\) −5099.16 + 2944.00i −1.04330 + 0.602350i
\(289\) 2372.00 + 4108.42i 0.482801 + 0.836235i
\(290\) 6698.00 11601.3i 1.35628 2.34914i
\(291\) 476.000i 0.0958887i
\(292\) 1489.56 + 860.000i 0.298528 + 0.172355i
\(293\) −7188.88 4150.50i −1.43337 0.827559i −0.435998 0.899948i \(-0.643604\pi\)
−0.997376 + 0.0723887i \(0.976938\pi\)
\(294\) 456.000i 0.0904573i
\(295\) 7344.00 12720.2i 1.44944 2.51050i
\(296\) 0 0
\(297\) 2771.28 1600.00i 0.541435 0.312597i
\(298\) 8460.00 1.64455
\(299\) 0 0
\(300\) 2624.00 0.504989
\(301\) 2702.00 1560.00i 0.517411 0.298727i
\(302\) −1028.00 1780.55i −0.195877 0.339268i
\(303\) −819.000 + 1418.55i −0.155282 + 0.268956i
\(304\) 1920.00i 0.362235i
\(305\) 2134.75 + 1232.50i 0.400772 + 0.231386i
\(306\) −1035.77 598.000i −0.193499 0.111717i
\(307\) 8678.00i 1.61329i 0.591037 + 0.806644i \(0.298719\pi\)
−0.591037 + 0.806644i \(0.701281\pi\)
\(308\) 2560.00 4434.05i 0.473602 0.820303i
\(309\) 1638.00 + 2837.10i 0.301562 + 0.522320i
\(310\) −4357.84 + 2516.00i −0.798415 + 0.460965i
\(311\) −8658.00 −1.57862 −0.789309 0.613996i \(-0.789561\pi\)
−0.789309 + 0.613996i \(0.789561\pi\)
\(312\) 0 0
\(313\) −5250.00 −0.948075 −0.474038 0.880505i \(-0.657204\pi\)
−0.474038 + 0.880505i \(0.657204\pi\)
\(314\) −10049.4 + 5802.00i −1.80611 + 1.04276i
\(315\) 3910.00 + 6772.32i 0.699376 + 1.21136i
\(316\) −304.000 + 526.543i −0.0541182 + 0.0937354i
\(317\) 6413.00i 1.13625i −0.822944 0.568123i \(-0.807670\pi\)
0.822944 0.568123i \(-0.192330\pi\)
\(318\) 644.323 + 372.000i 0.113622 + 0.0655998i
\(319\) 5459.42 + 3152.00i 0.958210 + 0.553223i
\(320\) 8704.00i 1.52053i
\(321\) −522.000 + 904.131i −0.0907639 + 0.157208i
\(322\) 3120.00 + 5404.00i 0.539971 + 0.935258i
\(323\) −337.750 + 195.000i −0.0581824 + 0.0335916i
\(324\) −3368.00 −0.577503
\(325\) 0 0
\(326\) 9440.00 1.60378
\(327\) 2830.17 1634.00i 0.478620 0.276332i
\(328\) 0 0
\(329\) −1620.00 + 2805.92i −0.271470 + 0.470199i
\(330\) 4352.00i 0.725969i
\(331\) 3020.70 + 1744.00i 0.501609 + 0.289604i 0.729378 0.684111i \(-0.239810\pi\)
−0.227769 + 0.973715i \(0.573143\pi\)
\(332\) −4350.91 2512.00i −0.719239 0.415253i
\(333\) 5221.00i 0.859186i
\(334\) −560.000 + 969.948i −0.0917420 + 0.158902i
\(335\) 7327.00 + 12690.7i 1.19498 + 2.06976i
\(336\) −2217.03 + 1280.00i −0.359966 + 0.207827i
\(337\) 1833.00 0.296290 0.148145 0.988966i \(-0.452670\pi\)
0.148145 + 0.988966i \(0.452670\pi\)
\(338\) 0 0
\(339\) 654.000 0.104780
\(340\) 1531.13 884.000i 0.244227 0.141005i
\(341\) −1184.00 2050.75i −0.188027 0.325672i
\(342\) −1380.00 + 2390.23i −0.218193 + 0.377921i
\(343\) 5720.00i 0.900440i
\(344\) 0 0
\(345\) −2296.70 1326.00i −0.358406 0.206926i
\(346\) 5304.00i 0.824118i
\(347\) −3615.00 + 6261.36i −0.559260 + 0.968667i 0.438298 + 0.898830i \(0.355581\pi\)
−0.997558 + 0.0698377i \(0.977752\pi\)
\(348\) 1576.00 + 2729.71i 0.242766 + 0.420483i
\(349\) −4553.56 + 2629.00i −0.698414 + 0.403230i −0.806757 0.590884i \(-0.798779\pi\)
0.108342 + 0.994114i \(0.465446\pi\)
\(350\) −13120.0 −2.00370
\(351\) 0 0
\(352\) 8192.00 1.24044
\(353\) −2739.24 + 1581.50i −0.413017 + 0.238455i −0.692085 0.721816i \(-0.743308\pi\)
0.279068 + 0.960271i \(0.409974\pi\)
\(354\) 3456.00 + 5985.97i 0.518882 + 0.898730i
\(355\) 5559.00 9628.47i 0.831102 1.43951i
\(356\) 2128.00i 0.316808i
\(357\) −450.333 260.000i −0.0667624 0.0385453i
\(358\) −14770.9 8528.00i −2.18064 1.25899i
\(359\) 10068.0i 1.48014i −0.672532 0.740068i \(-0.734793\pi\)
0.672532 0.740068i \(-0.265207\pi\)
\(360\) 0 0
\(361\) −2979.50 5160.65i −0.434393 0.752390i
\(362\) −1396.03 + 806.000i −0.202690 + 0.117023i
\(363\) 614.000 0.0887786
\(364\) 0 0
\(365\) 3655.00 0.524141
\(366\) −1004.59 + 580.000i −0.143472 + 0.0828336i
\(367\) −3719.00 6441.50i −0.528965 0.916195i −0.999429 0.0337755i \(-0.989247\pi\)
0.470464 0.882419i \(-0.344086\pi\)
\(368\) −2496.00 + 4323.20i −0.353568 + 0.612398i
\(369\) 3795.00i 0.535392i
\(370\) −13368.0 7718.00i −1.87829 1.08443i
\(371\) −1610.81 930.000i −0.225415 0.130143i
\(372\) 1184.00i 0.165020i
\(373\) 4841.50 8385.72i 0.672073 1.16407i −0.305242 0.952275i \(-0.598737\pi\)
0.977315 0.211790i \(-0.0679294\pi\)
\(374\) 832.000 + 1441.07i 0.115031 + 0.199240i
\(375\) 1148.35 663.000i 0.158135 0.0912991i
\(376\) 0 0
\(377\) 0 0
\(378\) −8000.00 −1.08856
\(379\) 919.719 531.000i 0.124651 0.0719674i −0.436378 0.899763i \(-0.643739\pi\)
0.561029 + 0.827796i \(0.310406\pi\)
\(380\) −2040.00 3533.38i −0.275394 0.476997i
\(381\) −2158.00 + 3737.77i −0.290178 + 0.502602i
\(382\) 4984.00i 0.667549i
\(383\) −3058.80 1766.00i −0.408087 0.235609i 0.281880 0.959450i \(-0.409042\pi\)
−0.689968 + 0.723840i \(0.742375\pi\)
\(384\) 0 0
\(385\) 10880.0i 1.44025i
\(386\) −534.000 + 924.915i −0.0704142 + 0.121961i
\(387\) 1794.00 + 3107.30i 0.235644 + 0.408147i
\(388\) 1648.91 952.000i 0.215750 0.124563i
\(389\) 11063.0 1.44194 0.720972 0.692964i \(-0.243696\pi\)
0.720972 + 0.692964i \(0.243696\pi\)
\(390\) 0 0
\(391\) −1014.00 −0.131151
\(392\) 0 0
\(393\) −730.000 1264.40i −0.0936988 0.162291i
\(394\) 2556.00 4427.12i 0.326826 0.566079i
\(395\) 1292.00i 0.164576i
\(396\) 5099.16 + 2944.00i 0.647077 + 0.373590i
\(397\) 5184.03 + 2993.00i 0.655362 + 0.378374i 0.790508 0.612452i \(-0.209817\pi\)
−0.135145 + 0.990826i \(0.543150\pi\)
\(398\) 16952.0i 2.13499i
\(399\) −600.000 + 1039.23i −0.0752821 + 0.130392i
\(400\) −5248.00 9089.80i −0.656000 1.13623i
\(401\) 5139.86 2967.50i 0.640081 0.369551i −0.144565 0.989495i \(-0.546178\pi\)
0.784646 + 0.619945i \(0.212845\pi\)
\(402\) −6896.00 −0.855575
\(403\) 0 0
\(404\) −6552.00 −0.806867
\(405\) −6198.14 + 3578.50i −0.760465 + 0.439055i
\(406\) −7880.00 13648.6i −0.963246 1.66839i
\(407\) 3632.00 6290.81i 0.442338 0.766152i
\(408\) 0 0
\(409\) −13067.5 7544.50i −1.57981 0.912106i −0.994884 0.101023i \(-0.967788\pi\)
−0.584931 0.811083i \(-0.698878\pi\)
\(410\) 9716.81 + 5610.00i 1.17044 + 0.675752i
\(411\) 3342.00i 0.401092i
\(412\) −6552.00 + 11348.4i −0.783480 + 1.35703i
\(413\) −8640.00 14964.9i −1.02941 1.78299i
\(414\) −6214.60 + 3588.00i −0.737756 + 0.425943i
\(415\) −10676.0 −1.26281
\(416\) 0 0
\(417\) 1824.00 0.214201
\(418\) 3325.54 1920.00i 0.389132 0.224666i
\(419\) 5407.00 + 9365.20i 0.630428 + 1.09193i 0.987464 + 0.157843i \(0.0504538\pi\)
−0.357037 + 0.934090i \(0.616213\pi\)
\(420\) 2720.00 4711.18i 0.316006 0.547338i
\(421\) 6535.00i 0.756524i 0.925699 + 0.378262i \(0.123478\pi\)
−0.925699 + 0.378262i \(0.876522\pi\)
\(422\) 10634.8 + 6140.00i 1.22676 + 0.708271i
\(423\) −3226.81 1863.00i −0.370905 0.214142i
\(424\) 0 0
\(425\) 1066.00 1846.37i 0.121667 0.210734i
\(426\) 2616.00 + 4531.04i 0.297525 + 0.515328i
\(427\) 2511.47 1450.00i 0.284634 0.164334i
\(428\) −4176.00 −0.471623
\(429\) 0 0
\(430\) −10608.0 −1.18968
\(431\) −1714.73 + 990.000i −0.191637 + 0.110642i −0.592749 0.805387i \(-0.701957\pi\)
0.401112 + 0.916029i \(0.368624\pi\)
\(432\) −3200.00 5542.56i −0.356389 0.617284i
\(433\) −3464.50 + 6000.69i −0.384511 + 0.665993i −0.991701 0.128564i \(-0.958963\pi\)
0.607190 + 0.794556i \(0.292297\pi\)
\(434\) 5920.00i 0.654767i
\(435\) 5800.64 + 3349.00i 0.639355 + 0.369132i
\(436\) 11320.7 + 6536.00i 1.24349 + 0.717930i
\(437\) 2340.00i 0.256150i
\(438\) −860.000 + 1489.56i −0.0938182 + 0.162498i
\(439\) −2288.00 3962.93i −0.248748 0.430844i 0.714431 0.699706i \(-0.246686\pi\)
−0.963179 + 0.268862i \(0.913352\pi\)
\(440\) 0 0
\(441\) 1311.00 0.141561
\(442\) 0 0
\(443\) −8812.00 −0.945081 −0.472540 0.881309i \(-0.656663\pi\)
−0.472540 + 0.881309i \(0.656663\pi\)
\(444\) 3145.40 1816.00i 0.336203 0.194107i
\(445\) 2261.00 + 3916.17i 0.240858 + 0.417178i
\(446\) −10756.0 + 18629.9i −1.14195 + 1.97792i
\(447\) 4230.00i 0.447589i
\(448\) −8868.10 5120.00i −0.935220 0.539949i
\(449\) −1661.04 959.000i −0.174586 0.100797i 0.410160 0.912013i \(-0.365473\pi\)
−0.584747 + 0.811216i \(0.698806\pi\)
\(450\) 15088.0i 1.58057i
\(451\) −2640.00 + 4572.61i −0.275638 + 0.477419i
\(452\) 1308.00 + 2265.52i 0.136113 + 0.235755i
\(453\) 890.274 514.000i 0.0923371 0.0533109i
\(454\) 15896.0 1.64325
\(455\) 0 0
\(456\) 0 0
\(457\) 10185.3 5880.50i 1.04256 0.601922i 0.122002 0.992530i \(-0.461069\pi\)
0.920557 + 0.390608i \(0.127735\pi\)
\(458\) 12596.0 + 21816.9i 1.28509 + 2.22585i
\(459\) 650.000 1125.83i 0.0660989 0.114487i
\(460\) 10608.0i 1.07522i
\(461\) 780.289 + 450.500i 0.0788323 + 0.0455138i 0.538898 0.842371i \(-0.318841\pi\)
−0.460066 + 0.887885i \(0.652174\pi\)
\(462\) 4434.05 + 2560.00i 0.446517 + 0.257796i
\(463\) 1372.00i 0.137715i 0.997626 + 0.0688577i \(0.0219354\pi\)
−0.997626 + 0.0688577i \(0.978065\pi\)
\(464\) 6304.00 10918.8i 0.630724 1.09245i
\(465\) −1258.00 2178.92i −0.125459 0.217301i
\(466\) 13960.3 8060.00i 1.38777 0.801228i
\(467\) 6396.00 0.633772 0.316886 0.948464i \(-0.397363\pi\)
0.316886 + 0.948464i \(0.397363\pi\)
\(468\) 0 0
\(469\) 17240.0 1.69738
\(470\) 9540.14 5508.00i 0.936284 0.540564i
\(471\) −2901.00 5024.68i −0.283803 0.491561i
\(472\) 0 0
\(473\) 4992.00i 0.485269i
\(474\) −526.543 304.000i −0.0510231 0.0294582i
\(475\) −4260.84 2460.00i −0.411581 0.237626i
\(476\) 2080.00i 0.200287i
\(477\) 1069.50 1852.43i 0.102660 0.177813i
\(478\) −1968.00 3408.68i −0.188314 0.326170i
\(479\) 2831.90 1635.00i 0.270131 0.155960i −0.358816 0.933408i \(-0.616819\pi\)
0.628947 + 0.777448i \(0.283486\pi\)
\(480\) 8704.00 0.827670
\(481\) 0 0
\(482\) 3772.00 0.356452
\(483\) −2702.00 + 1560.00i −0.254545 + 0.146962i
\(484\) 1228.00 + 2126.96i 0.115327 + 0.199752i
\(485\) 2023.00 3503.94i 0.189401 0.328053i
\(486\) 14168.0i 1.32237i
\(487\) 17251.2 + 9960.00i 1.60519 + 0.926757i 0.990426 + 0.138046i \(0.0440823\pi\)
0.614765 + 0.788711i \(0.289251\pi\)
\(488\) 0 0
\(489\) 4720.00i 0.436494i
\(490\) −1938.00 + 3356.71i −0.178673 + 0.309471i
\(491\) 3276.00 + 5674.20i 0.301108 + 0.521534i 0.976387 0.216028i \(-0.0693103\pi\)
−0.675280 + 0.737562i \(0.735977\pi\)
\(492\) −2286.31 + 1320.00i −0.209501 + 0.120956i
\(493\) 2561.00 0.233959
\(494\) 0 0
\(495\) 12512.0 1.13611
\(496\) −4101.50 + 2368.00i −0.371296 + 0.214368i
\(497\) −6540.00 11327.6i −0.590260 1.02236i
\(498\) 2512.00 4350.91i 0.226035 0.391504i
\(499\) 1746.00i 0.156637i −0.996928 0.0783183i \(-0.975045\pi\)
0.996928 0.0783183i \(-0.0249551\pi\)
\(500\) 4593.40 + 2652.00i 0.410846 + 0.237202i
\(501\) −484.974 280.000i −0.0432476 0.0249690i
\(502\) 10920.0i 0.970883i
\(503\) −7346.00 + 12723.6i −0.651177 + 1.12787i 0.331661 + 0.943399i \(0.392391\pi\)
−0.982838 + 0.184473i \(0.940942\pi\)
\(504\) 0 0
\(505\) −12057.7 + 6961.50i −1.06249 + 0.613431i
\(506\) 9984.00 0.877160
\(507\) 0 0
\(508\) −17264.0 −1.50781
\(509\) −6994.89 + 4038.50i −0.609122 + 0.351677i −0.772622 0.634867i \(-0.781055\pi\)
0.163500 + 0.986543i \(0.447722\pi\)
\(510\) 884.000 + 1531.13i 0.0767533 + 0.132941i
\(511\) 2150.00 3723.91i 0.186126 0.322380i
\(512\) 16384.0i 1.41421i
\(513\) −2598.08 1500.00i −0.223602 0.129097i
\(514\) 6529.83 + 3770.00i 0.560347 + 0.323517i
\(515\) 27846.0i 2.38260i
\(516\) 1248.00 2161.60i 0.106473 0.184417i
\(517\) 2592.00 + 4489.48i 0.220495 + 0.381909i
\(518\) −15727.0 + 9080.00i −1.33399 + 0.770178i
\(519\) −2652.00 −0.224296
\(520\) 0 0
\(521\) 11247.0 0.945758 0.472879 0.881127i \(-0.343215\pi\)
0.472879 + 0.881127i \(0.343215\pi\)
\(522\) 15695.8 9062.00i 1.31607 0.759833i
\(523\) −1366.00 2365.98i −0.114208 0.197815i 0.803255 0.595636i \(-0.203100\pi\)
−0.917463 + 0.397821i \(0.869767\pi\)
\(524\) 2920.00 5057.59i 0.243437 0.421645i
\(525\) 6560.00i 0.545337i
\(526\) 13967.3 + 8064.00i 1.15780 + 0.668455i
\(527\) −833.116 481.000i −0.0688636 0.0397584i
\(528\) 4096.00i 0.337605i
\(529\) 3041.50 5268.03i 0.249979 0.432977i
\(530\) 3162.00 + 5476.74i 0.259148 + 0.448858i
\(531\) 17209.7 9936.00i 1.40647 0.812026i
\(532\) −4800.00 −0.391177
\(533\) 0 0
\(534\) −2128.00 −0.172449
\(535\) −7685.11 + 4437.00i −0.621040 + 0.358557i
\(536\) 0 0
\(537\) 4264.00 7385.46i 0.342654 0.593494i
\(538\) 16024.0i 1.28410i
\(539\) −1579.63 912.000i −0.126233 0.0728806i
\(540\) 11777.9 + 6800.00i 0.938596 + 0.541899i
\(541\) 18375.0i 1.46026i −0.683306 0.730132i \(-0.739458\pi\)
0.683306 0.730132i \(-0.260542\pi\)
\(542\) 8592.00 14881.8i 0.680919 1.17939i
\(543\) −403.000 698.016i −0.0318497 0.0551653i
\(544\) 2882.13 1664.00i 0.227151 0.131146i
\(545\) 27778.0 2.18326
\(546\) 0 0
\(547\) −10346.0 −0.808708 −0.404354 0.914603i \(-0.632504\pi\)
−0.404354 + 0.914603i \(0.632504\pi\)
\(548\) −11577.0 + 6684.00i −0.902456 + 0.521033i
\(549\) 1667.50 + 2888.19i 0.129631 + 0.224527i
\(550\) −10496.0 + 18179.6i −0.813729 + 1.40942i
\(551\) 5910.00i 0.456941i
\(552\) 0 0
\(553\) 1316.36 + 760.000i 0.101225 + 0.0584421i
\(554\) 22204.0i 1.70281i
\(555\) 3859.00 6683.98i 0.295145 0.511206i
\(556\) 3648.00 + 6318.52i 0.278255 + 0.481951i
\(557\) 298.779 172.500i 0.0227283 0.0131222i −0.488593 0.872512i \(-0.662490\pi\)
0.511321 + 0.859390i \(0.329156\pi\)
\(558\) −6808.00 −0.516498
\(559\) 0 0
\(560\) −21760.0 −1.64201
\(561\) −720.533 + 416.000i −0.0542263 + 0.0313075i
\(562\) 11114.0 + 19250.0i 0.834192 + 1.44486i
\(563\) −4290.00 + 7430.50i −0.321140 + 0.556231i −0.980724 0.195400i \(-0.937399\pi\)
0.659583 + 0.751631i \(0.270733\pi\)
\(564\) 2592.00i 0.193516i
\(565\) 4814.24 + 2779.50i 0.358472 + 0.206964i
\(566\) −10808.0 6240.00i −0.802640 0.463404i
\(567\) 8420.00i 0.623645i
\(568\) 0 0
\(569\) −9841.00 17045.1i −0.725055 1.25583i −0.958951 0.283570i \(-0.908481\pi\)
0.233897 0.972261i \(-0.424852\pi\)
\(570\) 3533.38 2040.00i 0.259644 0.149906i
\(571\) −26624.0 −1.95128 −0.975639 0.219382i \(-0.929596\pi\)
−0.975639 + 0.219382i \(0.929596\pi\)
\(572\) 0 0
\(573\) −2492.00 −0.181684
\(574\) 11431.5 6600.00i 0.831260 0.479928i
\(575\) −6396.00 11078.2i −0.463881 0.803466i
\(576\) 5888.00 10198.3i 0.425926 0.737725i
\(577\) 14101.0i 1.01739i 0.860948 + 0.508694i \(0.169871\pi\)
−0.860948 + 0.508694i \(0.830129\pi\)
\(578\) −16433.7 9488.00i −1.18262 0.682783i
\(579\) −462.458 267.000i −0.0331936 0.0191643i
\(580\) 26792.0i 1.91806i
\(581\) −6280.00 + 10877.3i −0.448431 + 0.776705i
\(582\) 952.000 + 1648.91i 0.0678036 + 0.117439i
\(583\) −2577.29 + 1488.00i −0.183088 + 0.105706i
\(584\) 0 0
\(585\) 0 0
\(586\) 33204.0 2.34069
\(587\) −1219.36 + 704.000i −0.0857386 + 0.0495012i −0.542256 0.840213i \(-0.682430\pi\)
0.456518 + 0.889714i \(0.349096\pi\)
\(588\) −456.000 789.815i −0.0319815 0.0553936i
\(589\) −1110.00 + 1922.58i −0.0776515 + 0.134496i
\(590\) 58752.0i 4.09963i
\(591\) 2213.56 + 1278.00i 0.154067 + 0.0889508i
\(592\) −12581.6 7264.00i −0.873482 0.504305i
\(593\) 1241.00i 0.0859389i −0.999076 0.0429694i \(-0.986318\pi\)
0.999076 0.0429694i \(-0.0136818\pi\)
\(594\) −6400.00 + 11085.1i −0.442079 + 0.765704i
\(595\) −2210.00 3827.83i −0.152271 0.263741i
\(596\) −14653.1 + 8460.00i −1.00707 + 0.581435i
\(597\) −8476.00 −0.581071
\(598\) 0 0
\(599\) 11078.0 0.755651 0.377825 0.925877i \(-0.376672\pi\)
0.377825 + 0.925877i \(0.376672\pi\)
\(600\) 0 0
\(601\) 6908.50 + 11965.9i 0.468891 + 0.812143i 0.999368 0.0355563i \(-0.0113203\pi\)
−0.530477 + 0.847700i \(0.677987\pi\)
\(602\) −6240.00 + 10808.0i −0.422464 + 0.731729i
\(603\) 19826.0i 1.33893i
\(604\) 3561.10 + 2056.00i 0.239899 + 0.138506i
\(605\) 4519.79 + 2609.50i 0.303728 + 0.175357i
\(606\) 6552.00i 0.439203i
\(607\) −4135.00 + 7162.03i −0.276498 + 0.478909i −0.970512 0.241053i \(-0.922507\pi\)
0.694014 + 0.719962i \(0.255841\pi\)
\(608\) −3840.00 6651.08i −0.256139 0.443646i
\(609\) 6824.28 3940.00i 0.454078 0.262162i
\(610\) −9860.00 −0.654459
\(611\) 0 0
\(612\) 2392.00 0.157992
\(613\) −19289.0 + 11136.5i −1.27092 + 0.733767i −0.975161 0.221496i \(-0.928906\pi\)
−0.295760 + 0.955262i \(0.595573\pi\)
\(614\) −17356.0 30061.5i −1.14077 1.97587i
\(615\) −2805.00 + 4858.40i −0.183916 + 0.318552i
\(616\) 0 0
\(617\) −16445.0 9494.50i −1.07301 0.619504i −0.144010 0.989576i \(-0.546000\pi\)
−0.929003 + 0.370072i \(0.879333\pi\)
\(618\) −11348.4 6552.00i −0.738672 0.426473i
\(619\) 72.0000i 0.00467516i 0.999997 + 0.00233758i \(0.000744076\pi\)
−0.999997 + 0.00233758i \(0.999256\pi\)
\(620\) 5032.00 8715.68i 0.325952 0.564565i
\(621\) −3900.00 6755.00i −0.252015 0.436504i
\(622\) 29992.2 17316.0i 1.93340 1.11625i
\(623\) 5320.00 0.342121
\(624\) 0 0
\(625\) −9229.00 −0.590656
\(626\) 18186.5 10500.0i 1.16115 0.670390i
\(627\) 960.000 + 1662.77i 0.0611463 + 0.105908i
\(628\) 11604.0 20098.7i 0.737341 1.27711i
\(629\) 2951.00i 0.187065i
\(630\) −27089.3 15640.0i −1.71312 0.989067i
\(631\) 20247.7 + 11690.0i 1.27741 + 0.737514i 0.976372 0.216097i \(-0.0693328\pi\)
0.301040 + 0.953611i \(0.402666\pi\)
\(632\) 0 0
\(633\) −3070.00 + 5317.40i −0.192767 + 0.333882i
\(634\) 12826.0 + 22215.3i 0.803447 + 1.39161i
\(635\) −31771.0 + 18343.0i −1.98550 + 1.14633i
\(636\) −1488.00 −0.0927721
\(637\) 0 0
\(638\) −25216.0 −1.56475
\(639\) 13026.8 7521.00i 0.806464 0.465612i
\(640\) 0 0
\(641\) 3191.50 5527.84i 0.196656 0.340619i −0.750786 0.660546i \(-0.770325\pi\)
0.947442 + 0.319927i \(0.103658\pi\)
\(642\) 4176.00i 0.256719i
\(643\) −14812.5 8552.00i −0.908473 0.524507i −0.0285332 0.999593i \(-0.509084\pi\)
−0.879939 + 0.475086i \(0.842417\pi\)
\(644\) −10808.0 6240.00i −0.661327 0.381817i
\(645\) 5304.00i 0.323790i
\(646\) 780.000 1351.00i 0.0475057 0.0822823i
\(647\) 3497.00 + 6056.98i 0.212490 + 0.368044i 0.952493 0.304560i \(-0.0985093\pi\)
−0.740003 + 0.672604i \(0.765176\pi\)
\(648\) 0 0
\(649\) −27648.0 −1.67223
\(650\) 0 0
\(651\) −2960.00 −0.178205
\(652\) −16350.6 + 9440.00i −0.982112 + 0.567023i
\(653\) 2625.00 + 4546.63i 0.157311 + 0.272471i 0.933898 0.357539i \(-0.116384\pi\)
−0.776587 + 0.630010i \(0.783051\pi\)
\(654\) −6536.00 + 11320.7i −0.390792 + 0.676871i
\(655\) 12410.0i 0.740304i
\(656\) 9145.23 + 5280.00i 0.544301 + 0.314252i
\(657\) 4282.50 + 2472.50i 0.254301 + 0.146821i
\(658\) 12960.0i 0.767832i
\(659\) 2170.00 3758.55i 0.128272 0.222173i −0.794735 0.606956i \(-0.792390\pi\)
0.923007 + 0.384783i \(0.125724\pi\)
\(660\) −4352.00 7537.89i −0.256669 0.444563i
\(661\) −3619.12 + 2089.50i −0.212961 + 0.122953i −0.602687 0.797978i \(-0.705903\pi\)
0.389726 + 0.920931i \(0.372570\pi\)
\(662\) −13952.0 −0.819124
\(663\) 0 0
\(664\) 0 0
\(665\) −8833.46 + 5100.00i −0.515108 + 0.297398i
\(666\) −10442.0 18086.1i −0.607536 1.05228i
\(667\) 7683.00 13307.3i 0.446007 0.772508i
\(668\) 2240.00i 0.129743i
\(669\) −9314.97 5378.00i −0.538322 0.310800i
\(670\) −50762.9 29308.0i −2.92708 1.68995i
\(671\) 4640.00i 0.266953i
\(672\) 5120.00 8868.10i 0.293911 0.509069i
\(673\) 11433.5 + 19803.4i 0.654872 + 1.13427i 0.981926 + 0.189266i \(0.0606109\pi\)
−0.327054 + 0.945006i \(0.606056\pi\)
\(674\) −6349.70 + 3666.00i −0.362880 + 0.209509i
\(675\) 16400.0 0.935165
\(676\) 0 0
\(677\) 5410.00 0.307124 0.153562 0.988139i \(-0.450925\pi\)
0.153562 + 0.988139i \(0.450925\pi\)
\(678\) −2265.52 + 1308.00i −0.128329 + 0.0740906i
\(679\) −2380.00 4122.28i −0.134515 0.232988i
\(680\) 0 0
\(681\) 7948.00i 0.447236i
\(682\) 8202.99 + 4736.00i 0.460570 + 0.265910i
\(683\) 11758.9 + 6789.00i 0.658772 + 0.380342i 0.791809 0.610769i \(-0.209139\pi\)
−0.133037 + 0.991111i \(0.542473\pi\)
\(684\) 5520.00i 0.308571i
\(685\) −14203.5 + 24601.2i −0.792245 + 1.37221i
\(686\) −11440.0 19814.7i −0.636707 1.10281i
\(687\) −10908.5 + 6298.00i −0.605798 + 0.349758i
\(688\) −9984.00 −0.553251
\(689\) 0 0
\(690\) 10608.0 0.585275
\(691\) −11036.6 + 6372.00i −0.607602 + 0.350799i −0.772026 0.635590i \(-0.780757\pi\)
0.164424 + 0.986390i \(0.447423\pi\)
\(692\) −5304.00 9186.80i −0.291370 0.504667i
\(693\) 7360.00 12747.9i 0.403439 0.698777i
\(694\) 28920.0i 1.58183i
\(695\) 13426.9 + 7752.00i 0.732820 + 0.423094i
\(696\) 0 0
\(697\) 2145.00i 0.116568i
\(698\) 10516.0 18214.2i 0.570253 0.987707i
\(699\) 4030.00 + 6980.16i 0.218067 + 0.377703i
\(700\) 22724.5 13120.0i 1.22701 0.708413i
\(701\) −16406.0 −0.883946 −0.441973 0.897028i \(-0.645721\pi\)
−0.441973 + 0.897028i \(0.645721\pi\)
\(702\) 0 0
\(703\) −6810.00 −0.365354
\(704\) −14189.0 + 8192.00i −0.759612 + 0.438562i
\(705\) 2754.00 + 4770.07i 0.147123 + 0.254824i
\(706\) 6326.00 10957.0i 0.337227 0.584094i
\(707\) 16380.0i 0.871334i
\(708\) −11971.9 6912.00i −0.635498 0.366905i
\(709\) −614.012 354.500i −0.0325243 0.0187779i 0.483650 0.875262i \(-0.339311\pi\)
−0.516174 + 0.856484i \(0.672644\pi\)
\(710\) 44472.0i 2.35071i
\(711\) −874.000 + 1513.81i −0.0461006 + 0.0798487i
\(712\) 0 0
\(713\) −4998.70 + 2886.00i −0.262556 + 0.151587i
\(714\) 2080.00 0.109022
\(715\) 0 0
\(716\) 34112.0 1.78048
\(717\) 1704.34 984.000i 0.0887722 0.0512527i
\(718\) 20136.0 + 34876.6i 1.04661 + 1.81279i
\(719\) −3822.00 + 6619.90i −0.198243 + 0.343367i −0.947959 0.318393i \(-0.896857\pi\)
0.749716 + 0.661760i \(0.230190\pi\)
\(720\) 25024.0i 1.29526i
\(721\) 28371.0 + 16380.0i 1.46545 + 0.846079i
\(722\) 20642.6 + 11918.0i 1.06404 + 0.614324i
\(723\) 1886.00i 0.0970140i
\(724\) 1612.00 2792.07i 0.0827479 0.143324i
\(725\) 16154.0 + 27979.5i 0.827510 + 1.43329i
\(726\) −2126.96 + 1228.00i −0.108731 + 0.0627760i
\(727\) 15808.0 0.806446 0.403223 0.915102i \(-0.367890\pi\)
0.403223 + 0.915102i \(0.367890\pi\)
\(728\) 0 0
\(729\) −4283.00 −0.217599
\(730\) −12661.3 + 7310.00i −0.641939 + 0.370624i
\(731\) −1014.00 1756.30i −0.0513053 0.0888633i
\(732\) 1160.00 2009.18i 0.0585722 0.101450i
\(733\) 2583.00i 0.130157i 0.997880 + 0.0650786i \(0.0207298\pi\)
−0.997880 + 0.0650786i \(0.979270\pi\)
\(734\) 25766.0 + 14876.0i 1.29569 + 0.748070i
\(735\) −1678.36 969.000i −0.0842274 0.0486287i
\(736\) 19968.0i 1.00004i
\(737\) 13792.0 23888.4i 0.689328 1.19395i
\(738\) 7590.00 + 13146.3i 0.378580 + 0.655719i
\(739\) 3529.92 2038.00i 0.175711 0.101447i −0.409565 0.912281i \(-0.634320\pi\)
0.585276 + 0.810834i \(0.300986\pi\)
\(740\) 30872.0 1.53362
\(741\) 0 0
\(742\) 7440.00 0.368101
\(743\) 29493.4 17028.0i 1.45627 0.840776i 0.457442 0.889239i \(-0.348766\pi\)
0.998825 + 0.0484632i \(0.0154323\pi\)
\(744\) 0 0
\(745\) −17977.5 + 31137.9i −0.884087 + 1.53128i
\(746\) 38732.0i 1.90091i
\(747\) −12508.9 7222.00i −0.612685 0.353734i
\(748\) −2882.13 1664.00i −0.140884 0.0813394i
\(749\) 10440.0i 0.509305i
\(750\) −2652.00 + 4593.40i −0.129116 + 0.223636i
\(751\) −182.000 315.233i −0.00884324 0.0153169i 0.861570 0.507639i \(-0.169482\pi\)
−0.870413 + 0.492322i \(0.836148\pi\)
\(752\) 8978.95 5184.00i 0.435410 0.251384i
\(753\) 5460.00 0.264241
\(754\) 0 0
\(755\) 8738.00 0.421203
\(756\) 13856.4 8000.00i 0.666604 0.384864i
\(757\) 3457.00 + 5987.70i 0.165980 + 0.287486i 0.937003 0.349322i \(-0.113588\pi\)
−0.771023 + 0.636807i \(0.780255\pi\)
\(758\) −2124.00 + 3678.88i −0.101777 + 0.176283i
\(759\) 4992.00i 0.238733i
\(760\) 0 0
\(761\) −12108.8 6991.00i −0.576797 0.333014i 0.183062 0.983101i \(-0.441399\pi\)
−0.759859 + 0.650087i \(0.774732\pi\)
\(762\) 17264.0i 0.820746i
\(763\) 16340.0 28301.7i 0.775292 1.34284i
\(764\) −4984.00 8632.54i −0.236014 0.408788i
\(765\) 4402.01 2541.50i 0.208046 0.120115i
\(766\) 14128.0 0.666404
\(767\) 0 0
\(768\) 8192.00 0.384900
\(769\) 15645.6 9033.00i 0.733674 0.423587i −0.0860907 0.996287i \(-0.527437\pi\)
0.819765 + 0.572700i \(0.194104\pi\)
\(770\) 21760.0 + 37689.4i 1.01841 + 1.76394i
\(771\) −1885.00 + 3264.92i −0.0880501 + 0.152507i
\(772\) 2136.00i 0.0995807i
\(773\) 12500.2 + 7217.00i 0.581632 + 0.335805i 0.761782 0.647834i \(-0.224325\pi\)
−0.180150 + 0.983639i \(0.557658\pi\)
\(774\) −12429.2 7176.00i −0.577207 0.333251i
\(775\) 12136.0i 0.562501i