Properties

Label 169.4.e.c.147.1
Level $169$
Weight $4$
Character 169.147
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 147.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 169.147
Dual form 169.4.e.c.23.1

$q$-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 \(\left(\mathbb{Z}/169\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.46410 2.00000i −1.22474 0.707107i −0.258819 0.965926i \(-0.583333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(3\) −1.00000 + 1.73205i −0.192450 + 0.333333i −0.946062 0.323987i \(-0.894977\pi\)
0.753612 + 0.657320i \(0.228310\pi\)
\(4\) 4.00000 + 6.92820i 0.500000 + 0.866025i
\(5\) 17.0000i 1.52053i 0.649615 + 0.760263i \(0.274930\pi\)
−0.649615 + 0.760263i \(0.725070\pi\)
\(6\) 6.92820 4.00000i 0.471405 0.272166i
\(7\) −17.3205 + 10.0000i −0.935220 + 0.539949i −0.888459 0.458957i \(-0.848223\pi\)
−0.0467610 + 0.998906i \(0.514890\pi\)
\(8\) 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 0.0695447 0.997579i \(-0.477845\pi\)
−0.829156 + 0.559017i \(0.811179\pi\)
\(12\) −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 0.815927 0.578156i \(-0.196227\pi\)
−0.908661 + 0.417535i \(0.862894\pi\)
\(18\) 92.0000i 1.20470i
\(19\) 25.9808 15.0000i 0.313705 0.181118i −0.334878 0.942261i \(-0.608695\pi\)
0.648583 + 0.761144i \(0.275362\pi\)
\(20\) −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 −0.633304 0.773903i \(-0.718302\pi\)
0.986872 + 0.161506i \(0.0516350\pi\)
\(24\) 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 0.356680 + 0.934227i \(0.383909\pi\)
−0.987404 + 0.158219i \(0.949425\pi\)
\(30\) 68.0000 + 117.779i 0.413835 + 0.716783i
\(31\) 74.0000i 0.428735i −0.976753 0.214368i \(-0.931231\pi\)
0.976753 0.214368i \(-0.0687691\pi\)
\(32\) −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 −0.00497814 0.999988i \(-0.501585\pi\)
−0.868504 + 0.495683i \(0.834918\pi\)
\(38\) −120.000 −0.512278
\(39\) 0 0
\(40\) 0 0
\(41\) 142.894 + 82.5000i 0.544301 + 0.314252i 0.746820 0.665026i \(-0.231580\pi\)
−0.202520 + 0.979278i \(0.564913\pi\)
\(42\) −80.0000 + 138.564i −0.293911 + 0.509069i
\(43\) −78.0000 135.100i −0.276625 0.479129i 0.693919 0.720053i \(-0.255883\pi\)
−0.970544 + 0.240924i \(0.922549\pi\)
\(44\) 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 \(0.0808858\pi\)
−0.967887 + 0.251384i \(0.919114\pi\)
\(48\) 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 0.674442 0.738328i \(-0.264384\pi\)
0.976632 0.214919i \(-0.0689489\pi\)
\(60\) 272.000i 0.585251i
\(61\) −72.5000 125.574i −0.152175 0.263575i 0.779852 0.625964i \(-0.215294\pi\)
−0.932027 + 0.362389i \(0.881961\pi\)
\(62\) −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 −0.371427 0.928462i \(-0.621131\pi\)
−0.989785 + 0.142566i \(0.954465\pi\)
\(68\) 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 0.0546585 0.998505i \(-0.482593\pi\)
0.892060 + 0.451917i \(0.149260\pi\)
\(72\) 0 0
\(73\) 215.000i 0.344710i −0.985035 0.172355i \(-0.944862\pi\)
0.985035 0.172355i \(-0.0551377\pi\)
\(74\) 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 \(0.136307\pi\)
−0.909706 + 0.415253i \(0.863693\pi\)
\(84\) 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 0.356505 0.934293i \(-0.383968\pi\)
−0.630869 + 0.775889i \(0.717302\pi\)
\(90\) 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 −0.388231 0.921562i \(-0.626914\pi\)
0.603981 + 0.796999i \(0.293580\pi\)
\(98\) −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 −0.994138 0.108121i \(-0.965517\pi\)
0.590704 + 0.806888i \(0.298850\pi\)
\(102\) −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 −0.959508 0.281681i \(-0.909108\pi\)
0.723697 + 0.690118i \(0.242441\pi\)
\(108\) −400.000 692.820i −0.356389 0.617284i
\(109\) 1634.00i 1.43586i −0.696115 0.717930i \(-0.745090\pi\)
0.696115 0.717930i \(-0.254910\pi\)
\(110\) −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 0.789909 0.613224i \(-0.210128\pi\)
−0.926022 + 0.377469i \(0.876794\pi\)
\(114\) 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 0.192014 + 0.981392i \(0.438498\pi\)
−0.945918 + 0.324407i \(0.894835\pi\)
\(128\) 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 −0.877996 0.478667i \(-0.841120\pi\)
−0.0244601 + 0.999701i \(0.507787\pi\)
\(138\) 624.000i 0.384916i
\(139\) −456.000 789.815i −0.278255 0.481951i 0.692696 0.721229i \(-0.256423\pi\)
−0.970951 + 0.239278i \(0.923089\pi\)
\(140\) 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 −0.910334 0.413875i \(-0.864175\pi\)
−0.0967407 + 0.995310i \(0.530842\pi\)
\(150\) −1136.23 + 656.000i −0.618483 + 0.357081i
\(151\) 514.000i 0.277011i −0.990362 0.138506i \(-0.955770\pi\)
0.990362 0.138506i \(-0.0442299\pi\)
\(152\) 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 −0.902907 0.429835i \(-0.858572\pi\)
−0.0792052 + 0.996858i \(0.525238\pi\)
\(164\) 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 0.555127 0.831766i \(-0.312670\pi\)
−0.442767 + 0.896637i \(0.646003\pi\)
\(168\) 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 0.974134 0.225972i \(-0.0725557\pi\)
−0.682764 + 0.730639i \(0.739222\pi\)
\(174\) 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 0.0506550 0.998716i \(-0.483869\pi\)
0.839586 0.543227i \(-0.182798\pi\)
\(180\) −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 0.959567 0.281481i \(-0.0908255\pi\)
−0.723553 + 0.690269i \(0.757492\pi\)
\(192\) −512.000 + 886.810i −0.192450 + 0.333333i
\(193\) 231.229 + 133.500i 0.0862394 + 0.0497904i 0.542500 0.840056i \(-0.317478\pi\)
−0.456260 + 0.889846i \(0.650811\pi\)
\(194\) −952.000 −0.352318
\(195\) 0 0
\(196\) 456.000 0.166181
\(197\) −1106.78 639.000i −0.400278 0.231101i 0.286326 0.958132i \(-0.407566\pi\)
−0.686604 + 0.727032i \(0.740899\pi\)
\(198\) −1472.00 + 2549.58i −0.528336 + 0.915104i
\(199\) 2119.00 + 3670.22i 0.754834 + 1.30741i 0.945457 + 0.325747i \(0.105616\pi\)
−0.190623 + 0.981663i \(0.561051\pi\)
\(200\) 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 0.499176 + 0.866501i \(0.333636\pi\)
−1.00000 0.000951154i \(0.999697\pi\)
\(212\) 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 0.994246 0.107119i \(-0.0341624\pi\)
0.404356 + 0.914602i \(0.367496\pi\)
\(224\) 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 −0.910101 0.414387i \(-0.863996\pi\)
−0.0961811 + 0.995364i \(0.530663\pi\)
\(228\) −415.692 + 240.000i −0.120745 + 0.0697122i
\(229\) 6298.00i 1.81740i 0.417455 + 0.908698i \(0.362922\pi\)
−0.417455 + 0.908698i \(0.637078\pi\)
\(230\) −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 \(-0.957488\pi\)
0.991095 0.133158i \(-0.0425119\pi\)
\(240\) −1884.47 + 1088.00i −0.506842 + 0.292625i
\(241\) −816.662 + 471.500i −0.218281 + 0.126025i −0.605154 0.796108i \(-0.706889\pi\)
0.386873 + 0.922133i \(0.373555\pi\)
\(242\) 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 0.641777 0.766891i \(-0.278198\pi\)
−0.985036 + 0.172349i \(0.944864\pi\)
\(252\) 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 −0.957441 0.288629i \(-0.906801\pi\)
0.728680 + 0.684854i \(0.240134\pi\)
\(258\) −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 −0.999511 0.0312769i \(-0.990043\pi\)
0.526842 + 0.849963i \(0.323376\pi\)
\(264\) 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 0.544633 0.838674i \(-0.316669\pi\)
−0.998630 + 0.0523292i \(0.983335\pi\)
\(270\) −3400.00 + 5888.97i −0.766361 + 1.32738i
\(271\) −3720.45 2148.00i −0.833952 0.481482i 0.0212520 0.999774i \(-0.493235\pi\)
−0.855204 + 0.518292i \(0.826568\pi\)
\(272\) −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 −0.992513 0.122142i \(-0.961024\pi\)
0.390478 0.920612i \(-0.372310\pi\)
\(278\) 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 \(0.200818\pi\)
−0.807504 + 0.589863i \(0.799182\pi\)
\(282\) 648.000 + 1122.37i 0.136836 + 0.237007i
\(283\) 1560.00 2702.00i 0.327676 0.567552i −0.654374 0.756171i \(-0.727068\pi\)
0.982050 + 0.188619i \(0.0604012\pi\)
\(284\) 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 −0.997376 0.0723887i \(-0.976938\pi\)
−0.435998 + 0.899948i \(0.643604\pi\)
\(294\) 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 \(-0.701281\pi\)
0.591037 0.806644i \(-0.298719\pi\)
\(308\) 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 \(0.192330\pi\)
−0.822944 + 0.568123i \(0.807670\pi\)
\(318\) 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 −0.227769 0.973715i \(-0.573143\pi\)
0.729378 + 0.684111i \(0.239810\pi\)
\(332\) −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 −0.997558 0.0698377i \(-0.977752\pi\)
0.438298 0.898830i \(-0.355581\pi\)
\(348\) 1576.00 2729.71i 0.242766 0.420483i
\(349\) −4553.56 2629.00i −0.698414 0.403230i 0.108342 0.994114i \(-0.465446\pi\)
−0.806757 + 0.590884i \(0.798779\pi\)
\(350\) −13120.0 −2.00370
\(351\) 0 0
\(352\) 8192.00 1.24044
\(353\) −2739.24 1581.50i −0.413017 0.238455i 0.279068 0.960271i \(-0.409974\pi\)
−0.692085 + 0.721816i \(0.743308\pi\)
\(354\) 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 \(0.265207\pi\)
−0.672532 + 0.740068i \(0.734793\pi\)
\(360\) 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 0.470464 + 0.882419i \(0.344086\pi\)
−0.999429 + 0.0337755i \(0.989247\pi\)
\(368\) −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 0.977315 + 0.211790i \(0.0679294\pi\)
−0.305242 + 0.952275i \(0.598737\pi\)
\(374\) 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 0.561029 0.827796i \(-0.310406\pi\)
−0.436378 + 0.899763i \(0.643739\pi\)
\(380\) −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 −0.689968 0.723840i \(-0.742375\pi\)
0.281880 + 0.959450i \(0.409042\pi\)
\(384\) 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 −0.135145 0.990826i \(-0.543150\pi\)
0.790508 + 0.612452i \(0.209817\pi\)
\(398\) 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 0.784646 0.619945i \(-0.212845\pi\)
−0.144565 + 0.989495i \(0.546178\pi\)
\(402\) −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 −0.584931 + 0.811083i \(0.698878\pi\)
−0.994884 + 0.101023i \(0.967788\pi\)
\(410\) 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 −0.357037 0.934090i \(-0.616213\pi\)
0.987464 0.157843i \(-0.0504538\pi\)
\(420\) 2720.00 + 4711.18i 0.316006 + 0.547338i
\(421\) 6535.00i 0.756524i −0.925699 0.378262i \(-0.876522\pi\)
0.925699 0.378262i \(-0.123478\pi\)
\(422\) 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 0.401112 0.916029i \(-0.368624\pi\)
−0.592749 + 0.805387i \(0.701957\pi\)
\(432\) −3200.00 + 5542.56i −0.356389 + 0.617284i
\(433\) −3464.50 6000.69i −0.384511 0.665993i 0.607190 0.794556i \(-0.292297\pi\)
−0.991701 + 0.128564i \(0.958963\pi\)
\(434\) 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 −0.963179 0.268862i \(-0.913352\pi\)
0.714431 + 0.699706i \(0.246686\pi\)
\(440\) 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 −0.584747 0.811216i \(-0.698806\pi\)
0.410160 + 0.912013i \(0.365473\pi\)
\(450\) 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 0.920557 0.390608i \(-0.127735\pi\)
0.122002 + 0.992530i \(0.461069\pi\)
\(458\) 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 −0.460066 0.887885i \(-0.652174\pi\)
0.538898 + 0.842371i \(0.318841\pi\)
\(462\) 4434.05 2560.00i 0.446517 0.257796i
\(463\) 1372.00i 0.137715i −0.997626 0.0688577i \(-0.978065\pi\)
0.997626 0.0688577i \(-0.0219354\pi\)
\(464\) 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 0.628947 0.777448i \(-0.283486\pi\)
−0.358816 + 0.933408i \(0.616819\pi\)
\(480\) 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 0.614765 0.788711i \(-0.289251\pi\)
0.990426 0.138046i \(-0.0440823\pi\)
\(488\) 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 −0.675280 0.737562i \(-0.735977\pi\)
0.976387 + 0.216028i \(0.0693103\pi\)
\(492\) −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 \(0.0249551\pi\)
−0.996928 + 0.0783183i \(0.975045\pi\)
\(500\) 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 −0.982838 0.184473i \(-0.940942\pi\)
0.331661 0.943399i \(-0.392391\pi\)
\(504\) 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 0.163500 0.986543i \(-0.447722\pi\)
−0.772622 + 0.634867i \(0.781055\pi\)
\(510\) 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 −0.917463 0.397821i \(-0.869767\pi\)
0.803255 + 0.595636i \(0.203100\pi\)
\(524\) 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 \(0.260542\pi\)
−0.683306 + 0.730132i \(0.739458\pi\)
\(542\) 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 0.511321 0.859390i \(-0.329156\pi\)
−0.488593 + 0.872512i \(0.662490\pi\)
\(558\) −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 0.659583 0.751631i \(-0.270733\pi\)
−0.980724 + 0.195400i \(0.937399\pi\)
\(564\) 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 0.233897 + 0.972261i \(0.424852\pi\)
−0.958951 + 0.283570i \(0.908481\pi\)
\(570\) 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 \(-0.830129\pi\)
0.860948 0.508694i \(-0.169871\pi\)
\(578\) −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 0.456518 0.889714i \(-0.349096\pi\)
−0.542256 + 0.840213i \(0.682430\pi\)
\(588\) −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 \(0.0136818\pi\)
−0.999076 + 0.0429694i \(0.986318\pi\)
\(594\) −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 −0.530477 0.847700i \(-0.677987\pi\)
0.999368 + 0.0355563i \(0.0113203\pi\)
\(602\) −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 0.694014 0.719962i \(-0.255841\pi\)
−0.970512 + 0.241053i \(0.922507\pi\)
\(608\) −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 −0.295760 0.955262i \(-0.595573\pi\)
−0.975161 + 0.221496i \(0.928906\pi\)
\(614\) −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 −0.929003 0.370072i \(-0.879333\pi\)
−0.144010 + 0.989576i \(0.546000\pi\)
\(618\) −11348.4 + 6552.00i −0.738672 + 0.426473i
\(619\) 72.0000i 0.00467516i −0.999997 0.00233758i \(-0.999256\pi\)
0.999997 0.00233758i \(-0.000744076\pi\)
\(620\) 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 0.301040 0.953611i \(-0.402666\pi\)
0.976372 + 0.216097i \(0.0693328\pi\)
\(632\) 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 0.947442 0.319927i \(-0.103658\pi\)
−0.750786 + 0.660546i \(0.770325\pi\)
\(642\) 4176.00i 0.256719i
\(643\) −14812.5 + 8552.00i −0.908473 + 0.524507i −0.879939 0.475086i \(-0.842417\pi\)
−0.0285332 + 0.999593i \(0.509084\pi\)
\(644\) −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 −0.740003 0.672604i \(-0.765176\pi\)
0.952493 + 0.304560i \(0.0985093\pi\)
\(648\) 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 −0.776587 0.630010i \(-0.783051\pi\)
0.933898 + 0.357539i \(0.116384\pi\)
\(654\) −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 0.923007 0.384783i \(-0.125724\pi\)
−0.794735 + 0.606956i \(0.792390\pi\)
\(660\) −4352.00 + 7537.89i −0.256669 + 0.444563i
\(661\) −3619.12 2089.50i −0.212961 0.122953i 0.389726 0.920931i \(-0.372570\pi\)
−0.602687 + 0.797978i \(0.705903\pi\)
\(662\) −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 −0.327054 0.945006i \(-0.606056\pi\)
0.981926 0.189266i \(-0.0606109\pi\)
\(674\) −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 −0.133037 0.991111i \(-0.542473\pi\)
0.791809 + 0.610769i \(0.209139\pi\)
\(684\) 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 0.164424 0.986390i \(-0.447423\pi\)
−0.772026 + 0.635590i \(0.780757\pi\)
\(692\) −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 −0.516174 0.856484i \(-0.672644\pi\)
0.483650 + 0.875262i \(0.339311\pi\)
\(710\) 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 0.749716 0.661760i \(-0.230190\pi\)
−0.947959 + 0.318393i \(0.896857\pi\)
\(720\) 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 \(-0.979270\pi\)
0.997880 0.0650786i \(-0.0207298\pi\)
\(734\) 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 0.585276 0.810834i \(-0.300986\pi\)
−0.409565 + 0.912281i \(0.634320\pi\)
\(740\) 30872.0 1.53362
\(741\) 0 0
\(742\) 7440.00 0.368101
\(743\) 29493.4 + 17028.0i 1.45627 + 0.840776i 0.998825 0.0484632i \(-0.0154323\pi\)
0.457442 + 0.889239i \(0.348766\pi\)
\(744\) 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 −0.870413 0.492322i \(-0.836148\pi\)
0.861570 + 0.507639i \(0.169482\pi\)
\(752\) 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 −0.771023 0.636807i \(-0.780255\pi\)
0.937003 + 0.349322i \(0.113588\pi\)
\(758\) −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 −0.759859 0.650087i \(-0.774732\pi\)
0.183062 + 0.983101i \(0.441399\pi\)
\(762\) 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 0.819765 0.572700i \(-0.194104\pi\)
−0.0860907 + 0.996287i \(0.527437\pi\)
\(770\) 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 −0.180150 0.983639i \(-0.557658\pi\)
0.761782 + 0.647834i \(0.224325\pi\)
\(774\) −12429.2 + 7176.00i −0.577207 + 0.333251i
\(775\) 12136.0i 0.562501i