Properties

Label 882.4.g.bf.361.2
Level $882$
Weight $4$
Character 882.361
Analytic conductor $52.040$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 882.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(52.0396846251\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{1345})\)
Defining polynomial: \(x^{4} - x^{3} + 337 x^{2} + 336 x + 112896\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 42)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.2
Root \(-8.91856 - 15.4474i\) of defining polynomial
Character \(\chi\) \(=\) 882.361
Dual form 882.4.g.bf.667.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(7.91856 + 13.7153i) q^{5} -8.00000 q^{8} +O(q^{10})\) \(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(7.91856 + 13.7153i) q^{5} -8.00000 q^{8} +(-15.8371 + 27.4307i) q^{10} +(25.9186 - 44.8923i) q^{11} -38.8371 q^{13} +(-8.00000 - 13.8564i) q^{16} +(-13.6742 + 23.6845i) q^{17} +(38.2557 + 66.2608i) q^{19} -63.3485 q^{20} +103.674 q^{22} +(73.6742 + 127.608i) q^{23} +(-62.9072 + 108.958i) q^{25} +(-38.8371 - 67.2679i) q^{26} -240.208 q^{29} +(-148.337 + 256.927i) q^{31} +(16.0000 - 27.7128i) q^{32} -54.6970 q^{34} +(80.7670 + 139.893i) q^{37} +(-76.5114 + 132.522i) q^{38} +(-63.3485 - 109.723i) q^{40} -102.977 q^{41} -328.557 q^{43} +(103.674 + 179.569i) q^{44} +(-147.348 + 255.215i) q^{46} +(-33.9773 - 58.8504i) q^{47} -251.629 q^{50} +(77.6742 - 134.536i) q^{52} +(-33.2443 + 57.5808i) q^{53} +820.951 q^{55} +(-240.208 - 416.053i) q^{58} +(230.964 - 400.041i) q^{59} +(92.6742 + 160.516i) q^{61} -593.348 q^{62} +64.0000 q^{64} +(-307.534 - 532.665i) q^{65} +(-272.604 + 472.164i) q^{67} +(-54.6970 - 94.7379i) q^{68} +130.742 q^{71} +(90.6496 - 157.010i) q^{73} +(-161.534 + 279.785i) q^{74} -306.045 q^{76} +(204.848 + 354.808i) q^{79} +(126.697 - 219.446i) q^{80} +(-102.977 - 178.362i) q^{82} +347.928 q^{83} -433.121 q^{85} +(-328.557 - 569.077i) q^{86} +(-207.348 + 359.138i) q^{88} +(-578.580 - 1002.13i) q^{89} -589.394 q^{92} +(67.9546 - 117.701i) q^{94} +(-605.860 + 1049.38i) q^{95} -1618.30 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{2} - 8q^{4} - 5q^{5} - 32q^{8} + O(q^{10}) \) \( 4q + 4q^{2} - 8q^{4} - 5q^{5} - 32q^{8} + 10q^{10} + 67q^{11} - 82q^{13} - 32q^{16} + 92q^{17} + 43q^{19} + 40q^{20} + 268q^{22} + 148q^{23} - 435q^{25} - 82q^{26} - 154q^{29} - 520q^{31} + 64q^{32} + 368q^{34} - 7q^{37} - 86q^{38} + 40q^{40} - 852q^{41} - 214q^{43} + 268q^{44} - 296q^{46} - 576q^{47} - 1740q^{50} + 164q^{52} - 243q^{53} + 1010q^{55} - 154q^{58} + 7q^{59} + 224q^{61} - 2080q^{62} + 256q^{64} - 570q^{65} - 687q^{67} + 368q^{68} - 944q^{71} - 921q^{73} + 14q^{74} - 344q^{76} + 526q^{79} - 80q^{80} - 852q^{82} - 442q^{83} - 5840q^{85} - 214q^{86} - 536q^{88} - 774q^{89} - 1184q^{92} + 1152q^{94} - 1910q^{95} - 3906q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.73205i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −2.00000 + 3.46410i −0.250000 + 0.433013i
\(5\) 7.91856 + 13.7153i 0.708258 + 1.22674i 0.965503 + 0.260392i \(0.0838518\pi\)
−0.257245 + 0.966346i \(0.582815\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −8.00000 −0.353553
\(9\) 0 0
\(10\) −15.8371 + 27.4307i −0.500814 + 0.867435i
\(11\) 25.9186 44.8923i 0.710431 1.23050i −0.254265 0.967135i \(-0.581833\pi\)
0.964696 0.263368i \(-0.0848333\pi\)
\(12\) 0 0
\(13\) −38.8371 −0.828575 −0.414288 0.910146i \(-0.635969\pi\)
−0.414288 + 0.910146i \(0.635969\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) −13.6742 + 23.6845i −0.195088 + 0.337902i −0.946929 0.321442i \(-0.895832\pi\)
0.751842 + 0.659344i \(0.229166\pi\)
\(18\) 0 0
\(19\) 38.2557 + 66.2608i 0.461919 + 0.800067i 0.999057 0.0434278i \(-0.0138279\pi\)
−0.537138 + 0.843494i \(0.680495\pi\)
\(20\) −63.3485 −0.708258
\(21\) 0 0
\(22\) 103.674 1.00470
\(23\) 73.6742 + 127.608i 0.667919 + 1.15687i 0.978485 + 0.206318i \(0.0661482\pi\)
−0.310566 + 0.950552i \(0.600519\pi\)
\(24\) 0 0
\(25\) −62.9072 + 108.958i −0.503258 + 0.871668i
\(26\) −38.8371 67.2679i −0.292946 0.507397i
\(27\) 0 0
\(28\) 0 0
\(29\) −240.208 −1.53812 −0.769061 0.639175i \(-0.779276\pi\)
−0.769061 + 0.639175i \(0.779276\pi\)
\(30\) 0 0
\(31\) −148.337 + 256.927i −0.859424 + 1.48857i 0.0130559 + 0.999915i \(0.495844\pi\)
−0.872480 + 0.488651i \(0.837489\pi\)
\(32\) 16.0000 27.7128i 0.0883883 0.153093i
\(33\) 0 0
\(34\) −54.6970 −0.275896
\(35\) 0 0
\(36\) 0 0
\(37\) 80.7670 + 139.893i 0.358865 + 0.621573i 0.987772 0.155908i \(-0.0498304\pi\)
−0.628906 + 0.777481i \(0.716497\pi\)
\(38\) −76.5114 + 132.522i −0.326626 + 0.565733i
\(39\) 0 0
\(40\) −63.3485 109.723i −0.250407 0.433717i
\(41\) −102.977 −0.392252 −0.196126 0.980579i \(-0.562836\pi\)
−0.196126 + 0.980579i \(0.562836\pi\)
\(42\) 0 0
\(43\) −328.557 −1.16522 −0.582610 0.812752i \(-0.697968\pi\)
−0.582610 + 0.812752i \(0.697968\pi\)
\(44\) 103.674 + 179.569i 0.355215 + 0.615251i
\(45\) 0 0
\(46\) −147.348 + 255.215i −0.472290 + 0.818031i
\(47\) −33.9773 58.8504i −0.105449 0.182643i 0.808473 0.588534i \(-0.200295\pi\)
−0.913921 + 0.405891i \(0.866961\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −251.629 −0.711714
\(51\) 0 0
\(52\) 77.6742 134.536i 0.207144 0.358784i
\(53\) −33.2443 + 57.5808i −0.0861596 + 0.149233i −0.905885 0.423524i \(-0.860793\pi\)
0.819725 + 0.572757i \(0.194126\pi\)
\(54\) 0 0
\(55\) 820.951 2.01267
\(56\) 0 0
\(57\) 0 0
\(58\) −240.208 416.053i −0.543809 0.941904i
\(59\) 230.964 400.041i 0.509643 0.882728i −0.490294 0.871557i \(-0.663111\pi\)
0.999938 0.0111711i \(-0.00355595\pi\)
\(60\) 0 0
\(61\) 92.6742 + 160.516i 0.194520 + 0.336919i 0.946743 0.321990i \(-0.104352\pi\)
−0.752223 + 0.658909i \(0.771018\pi\)
\(62\) −593.348 −1.21541
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −307.534 532.665i −0.586845 1.01644i
\(66\) 0 0
\(67\) −272.604 + 472.164i −0.497073 + 0.860956i −0.999994 0.00337637i \(-0.998925\pi\)
0.502921 + 0.864332i \(0.332259\pi\)
\(68\) −54.6970 94.7379i −0.0975438 0.168951i
\(69\) 0 0
\(70\) 0 0
\(71\) 130.742 0.218539 0.109270 0.994012i \(-0.465149\pi\)
0.109270 + 0.994012i \(0.465149\pi\)
\(72\) 0 0
\(73\) 90.6496 157.010i 0.145339 0.251734i −0.784160 0.620558i \(-0.786906\pi\)
0.929499 + 0.368824i \(0.120239\pi\)
\(74\) −161.534 + 279.785i −0.253756 + 0.439519i
\(75\) 0 0
\(76\) −306.045 −0.461919
\(77\) 0 0
\(78\) 0 0
\(79\) 204.848 + 354.808i 0.291737 + 0.505304i 0.974221 0.225597i \(-0.0724333\pi\)
−0.682483 + 0.730901i \(0.739100\pi\)
\(80\) 126.697 219.446i 0.177064 0.306685i
\(81\) 0 0
\(82\) −102.977 178.362i −0.138682 0.240205i
\(83\) 347.928 0.460121 0.230061 0.973176i \(-0.426108\pi\)
0.230061 + 0.973176i \(0.426108\pi\)
\(84\) 0 0
\(85\) −433.121 −0.552689
\(86\) −328.557 569.077i −0.411967 0.713548i
\(87\) 0 0
\(88\) −207.348 + 359.138i −0.251175 + 0.435048i
\(89\) −578.580 1002.13i −0.689093 1.19354i −0.972132 0.234436i \(-0.924676\pi\)
0.283038 0.959109i \(-0.408658\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −589.394 −0.667919
\(93\) 0 0
\(94\) 67.9546 117.701i 0.0745636 0.129148i
\(95\) −605.860 + 1049.38i −0.654315 + 1.13331i
\(96\) 0 0
\(97\) −1618.30 −1.69395 −0.846976 0.531631i \(-0.821579\pi\)
−0.846976 + 0.531631i \(0.821579\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −251.629 435.834i −0.251629 0.435834i
\(101\) −359.371 + 622.449i −0.354047 + 0.613228i −0.986954 0.161000i \(-0.948528\pi\)
0.632907 + 0.774228i \(0.281861\pi\)
\(102\) 0 0
\(103\) −805.790 1395.67i −0.770843 1.33514i −0.937102 0.349057i \(-0.886502\pi\)
0.166259 0.986082i \(-0.446831\pi\)
\(104\) 310.697 0.292946
\(105\) 0 0
\(106\) −132.977 −0.121848
\(107\) 467.335 + 809.448i 0.422234 + 0.731330i 0.996158 0.0875784i \(-0.0279128\pi\)
−0.573924 + 0.818909i \(0.694580\pi\)
\(108\) 0 0
\(109\) 598.509 1036.65i 0.525934 0.910944i −0.473610 0.880735i \(-0.657049\pi\)
0.999544 0.0302095i \(-0.00961746\pi\)
\(110\) 820.951 + 1421.93i 0.711587 + 1.23251i
\(111\) 0 0
\(112\) 0 0
\(113\) 2384.64 1.98521 0.992604 0.121400i \(-0.0387384\pi\)
0.992604 + 0.121400i \(0.0387384\pi\)
\(114\) 0 0
\(115\) −1166.79 + 2020.94i −0.946118 + 1.63872i
\(116\) 480.417 832.106i 0.384531 0.666027i
\(117\) 0 0
\(118\) 923.856 0.720744
\(119\) 0 0
\(120\) 0 0
\(121\) −678.044 1174.41i −0.509424 0.882349i
\(122\) −185.348 + 321.033i −0.137546 + 0.238237i
\(123\) 0 0
\(124\) −593.348 1027.71i −0.429712 0.744283i
\(125\) −12.8977 −0.00922883
\(126\) 0 0
\(127\) −2673.92 −1.86829 −0.934143 0.356898i \(-0.883834\pi\)
−0.934143 + 0.356898i \(0.883834\pi\)
\(128\) 64.0000 + 110.851i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 615.068 1065.33i 0.414962 0.718735i
\(131\) 19.4299 + 33.6536i 0.0129588 + 0.0224453i 0.872432 0.488735i \(-0.162542\pi\)
−0.859473 + 0.511181i \(0.829208\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −1090.42 −0.702968
\(135\) 0 0
\(136\) 109.394 189.476i 0.0689739 0.119466i
\(137\) −384.072 + 665.232i −0.239514 + 0.414851i −0.960575 0.278021i \(-0.910322\pi\)
0.721061 + 0.692872i \(0.243655\pi\)
\(138\) 0 0
\(139\) −1052.55 −0.642274 −0.321137 0.947033i \(-0.604065\pi\)
−0.321137 + 0.947033i \(0.604065\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 130.742 + 226.453i 0.0772652 + 0.133827i
\(143\) −1006.60 + 1743.49i −0.588646 + 1.01956i
\(144\) 0 0
\(145\) −1902.10 3294.54i −1.08939 1.88687i
\(146\) 362.598 0.205540
\(147\) 0 0
\(148\) −646.136 −0.358865
\(149\) 180.489 + 312.615i 0.0992363 + 0.171882i 0.911369 0.411591i \(-0.135027\pi\)
−0.812132 + 0.583473i \(0.801693\pi\)
\(150\) 0 0
\(151\) −774.195 + 1340.95i −0.417239 + 0.722679i −0.995661 0.0930587i \(-0.970336\pi\)
0.578422 + 0.815738i \(0.303669\pi\)
\(152\) −306.045 530.086i −0.163313 0.282866i
\(153\) 0 0
\(154\) 0 0
\(155\) −4698.47 −2.43477
\(156\) 0 0
\(157\) −483.534 + 837.506i −0.245798 + 0.425734i −0.962356 0.271794i \(-0.912383\pi\)
0.716558 + 0.697528i \(0.245717\pi\)
\(158\) −409.697 + 709.616i −0.206289 + 0.357304i
\(159\) 0 0
\(160\) 506.788 0.250407
\(161\) 0 0
\(162\) 0 0
\(163\) 663.250 + 1148.78i 0.318710 + 0.552022i 0.980219 0.197915i \(-0.0634170\pi\)
−0.661509 + 0.749937i \(0.730084\pi\)
\(164\) 205.955 356.724i 0.0980631 0.169850i
\(165\) 0 0
\(166\) 347.928 + 602.629i 0.162677 + 0.281766i
\(167\) 1416.70 0.656451 0.328225 0.944599i \(-0.393549\pi\)
0.328225 + 0.944599i \(0.393549\pi\)
\(168\) 0 0
\(169\) −688.678 −0.313463
\(170\) −433.121 750.188i −0.195405 0.338452i
\(171\) 0 0
\(172\) 657.114 1138.15i 0.291305 0.504555i
\(173\) 518.299 + 897.721i 0.227778 + 0.394523i 0.957149 0.289595i \(-0.0935207\pi\)
−0.729371 + 0.684118i \(0.760187\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −829.394 −0.355215
\(177\) 0 0
\(178\) 1157.16 2004.26i 0.487263 0.843964i
\(179\) −383.716 + 664.615i −0.160225 + 0.277518i −0.934949 0.354781i \(-0.884555\pi\)
0.774724 + 0.632299i \(0.217889\pi\)
\(180\) 0 0
\(181\) 3957.71 1.62527 0.812636 0.582772i \(-0.198032\pi\)
0.812636 + 0.582772i \(0.198032\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −589.394 1020.86i −0.236145 0.409015i
\(185\) −1279.12 + 2215.50i −0.508338 + 0.880468i
\(186\) 0 0
\(187\) 708.833 + 1227.74i 0.277193 + 0.480112i
\(188\) 271.818 0.105449
\(189\) 0 0
\(190\) −2423.44 −0.925341
\(191\) −902.648 1563.43i −0.341954 0.592282i 0.642841 0.765999i \(-0.277756\pi\)
−0.984796 + 0.173717i \(0.944422\pi\)
\(192\) 0 0
\(193\) −1685.42 + 2919.23i −0.628597 + 1.08876i 0.359237 + 0.933247i \(0.383037\pi\)
−0.987833 + 0.155515i \(0.950296\pi\)
\(194\) −1618.30 2802.98i −0.598903 1.03733i
\(195\) 0 0
\(196\) 0 0
\(197\) 4612.31 1.66809 0.834044 0.551697i \(-0.186020\pi\)
0.834044 + 0.551697i \(0.186020\pi\)
\(198\) 0 0
\(199\) −1114.93 + 1931.12i −0.397163 + 0.687906i −0.993375 0.114921i \(-0.963339\pi\)
0.596212 + 0.802827i \(0.296672\pi\)
\(200\) 503.258 871.668i 0.177928 0.308181i
\(201\) 0 0
\(202\) −1437.48 −0.500698
\(203\) 0 0
\(204\) 0 0
\(205\) −815.432 1412.37i −0.277816 0.481191i
\(206\) 1611.58 2791.34i 0.545068 0.944086i
\(207\) 0 0
\(208\) 310.697 + 538.143i 0.103572 + 0.179392i
\(209\) 3966.13 1.31265
\(210\) 0 0
\(211\) 912.614 0.297758 0.148879 0.988855i \(-0.452434\pi\)
0.148879 + 0.988855i \(0.452434\pi\)
\(212\) −132.977 230.323i −0.0430798 0.0746164i
\(213\) 0 0
\(214\) −934.670 + 1618.90i −0.298564 + 0.517129i
\(215\) −2601.70 4506.27i −0.825276 1.42942i
\(216\) 0 0
\(217\) 0 0
\(218\) 2394.04 0.743783
\(219\) 0 0
\(220\) −1641.90 + 2843.86i −0.503168 + 0.871513i
\(221\) 531.068 919.837i 0.161645 0.279977i
\(222\) 0 0
\(223\) 4319.47 1.29710 0.648549 0.761173i \(-0.275376\pi\)
0.648549 + 0.761173i \(0.275376\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 2384.64 + 4130.32i 0.701877 + 1.21569i
\(227\) −1030.64 + 1785.12i −0.301349 + 0.521951i −0.976442 0.215782i \(-0.930770\pi\)
0.675093 + 0.737733i \(0.264103\pi\)
\(228\) 0 0
\(229\) −1737.32 3009.12i −0.501332 0.868333i −0.999999 0.00153905i \(-0.999510\pi\)
0.498667 0.866794i \(-0.333823\pi\)
\(230\) −4667.15 −1.33801
\(231\) 0 0
\(232\) 1921.67 0.543809
\(233\) 388.049 + 672.121i 0.109107 + 0.188979i 0.915409 0.402525i \(-0.131868\pi\)
−0.806302 + 0.591505i \(0.798534\pi\)
\(234\) 0 0
\(235\) 538.102 932.020i 0.149370 0.258716i
\(236\) 923.856 + 1600.17i 0.254822 + 0.441364i
\(237\) 0 0
\(238\) 0 0
\(239\) −2006.80 −0.543133 −0.271567 0.962420i \(-0.587542\pi\)
−0.271567 + 0.962420i \(0.587542\pi\)
\(240\) 0 0
\(241\) 402.824 697.711i 0.107669 0.186488i −0.807157 0.590337i \(-0.798995\pi\)
0.914825 + 0.403850i \(0.132328\pi\)
\(242\) 1356.09 2348.81i 0.360217 0.623915i
\(243\) 0 0
\(244\) −741.394 −0.194520
\(245\) 0 0
\(246\) 0 0
\(247\) −1485.74 2573.38i −0.382734 0.662915i
\(248\) 1186.70 2055.42i 0.303852 0.526287i
\(249\) 0 0
\(250\) −12.8977 22.3394i −0.00326289 0.00565148i
\(251\) 1421.78 0.357539 0.178769 0.983891i \(-0.442788\pi\)
0.178769 + 0.983891i \(0.442788\pi\)
\(252\) 0 0
\(253\) 7638.12 1.89804
\(254\) −2673.92 4631.37i −0.660539 1.14409i
\(255\) 0 0
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) 732.909 + 1269.44i 0.177890 + 0.308114i 0.941157 0.337968i \(-0.109740\pi\)
−0.763268 + 0.646082i \(0.776406\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 2460.27 0.586845
\(261\) 0 0
\(262\) −38.8598 + 67.3072i −0.00916324 + 0.0158712i
\(263\) 3495.69 6054.72i 0.819596 1.41958i −0.0863847 0.996262i \(-0.527531\pi\)
0.905980 0.423320i \(-0.139135\pi\)
\(264\) 0 0
\(265\) −1052.99 −0.244093
\(266\) 0 0
\(267\) 0 0
\(268\) −1090.42 1888.66i −0.248537 0.430478i
\(269\) −404.479 + 700.578i −0.0916786 + 0.158792i −0.908218 0.418498i \(-0.862557\pi\)
0.816539 + 0.577290i \(0.195890\pi\)
\(270\) 0 0
\(271\) 3330.88 + 5769.26i 0.746630 + 1.29320i 0.949429 + 0.313981i \(0.101663\pi\)
−0.202799 + 0.979220i \(0.565004\pi\)
\(272\) 437.576 0.0975438
\(273\) 0 0
\(274\) −1536.29 −0.338725
\(275\) 3260.93 + 5648.09i 0.715059 + 1.23852i
\(276\) 0 0
\(277\) 3765.73 6522.44i 0.816827 1.41479i −0.0911823 0.995834i \(-0.529065\pi\)
0.908009 0.418951i \(-0.137602\pi\)
\(278\) −1052.55 1823.07i −0.227078 0.393311i
\(279\) 0 0
\(280\) 0 0
\(281\) −1690.19 −0.358819 −0.179410 0.983774i \(-0.557419\pi\)
−0.179410 + 0.983774i \(0.557419\pi\)
\(282\) 0 0
\(283\) 1589.12 2752.43i 0.333792 0.578145i −0.649460 0.760396i \(-0.725005\pi\)
0.983252 + 0.182251i \(0.0583384\pi\)
\(284\) −261.485 + 452.905i −0.0546348 + 0.0946302i
\(285\) 0 0
\(286\) −4026.41 −0.832470
\(287\) 0 0
\(288\) 0 0
\(289\) 2082.53 + 3607.05i 0.423882 + 0.734184i
\(290\) 3804.21 6589.08i 0.770313 1.33422i
\(291\) 0 0
\(292\) 362.598 + 628.039i 0.0726694 + 0.125867i
\(293\) −2176.53 −0.433974 −0.216987 0.976174i \(-0.569623\pi\)
−0.216987 + 0.976174i \(0.569623\pi\)
\(294\) 0 0
\(295\) 7315.61 1.44383
\(296\) −646.136 1119.14i −0.126878 0.219759i
\(297\) 0 0
\(298\) −360.977 + 625.231i −0.0701706 + 0.121539i
\(299\) −2861.30 4955.91i −0.553421 0.958554i
\(300\) 0 0
\(301\) 0 0
\(302\) −3096.78 −0.590065
\(303\) 0 0
\(304\) 612.091 1060.17i 0.115480 0.200017i
\(305\) −1467.69 + 2542.12i −0.275541 + 0.477250i
\(306\) 0 0
\(307\) −623.504 −0.115913 −0.0579564 0.998319i \(-0.518458\pi\)
−0.0579564 + 0.998319i \(0.518458\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −4698.47 8137.98i −0.860822 1.49099i
\(311\) −233.996 + 405.293i −0.0426647 + 0.0738973i −0.886569 0.462596i \(-0.846918\pi\)
0.843905 + 0.536493i \(0.180251\pi\)
\(312\) 0 0
\(313\) 1806.41 + 3128.79i 0.326211 + 0.565014i 0.981757 0.190141i \(-0.0608946\pi\)
−0.655546 + 0.755156i \(0.727561\pi\)
\(314\) −1934.14 −0.347610
\(315\) 0 0
\(316\) −1638.79 −0.291737
\(317\) 2265.87 + 3924.60i 0.401463 + 0.695355i 0.993903 0.110260i \(-0.0351684\pi\)
−0.592439 + 0.805615i \(0.701835\pi\)
\(318\) 0 0
\(319\) −6225.85 + 10783.5i −1.09273 + 1.89266i
\(320\) 506.788 + 877.782i 0.0885322 + 0.153342i
\(321\) 0 0
\(322\) 0 0
\(323\) −2092.47 −0.360459
\(324\) 0 0
\(325\) 2443.13 4231.63i 0.416987 0.722242i
\(326\) −1326.50 + 2297.57i −0.225362 + 0.390339i
\(327\) 0 0
\(328\) 823.818 0.138682
\(329\) 0 0
\(330\) 0 0
\(331\) 618.528 + 1071.32i 0.102711 + 0.177901i 0.912801 0.408405i \(-0.133915\pi\)
−0.810090 + 0.586306i \(0.800582\pi\)
\(332\) −695.856 + 1205.26i −0.115030 + 0.199238i
\(333\) 0 0
\(334\) 1416.70 + 2453.79i 0.232090 + 0.401992i
\(335\) −8634.53 −1.40822
\(336\) 0 0
\(337\) −1867.83 −0.301921 −0.150960 0.988540i \(-0.548237\pi\)
−0.150960 + 0.988540i \(0.548237\pi\)
\(338\) −688.678 1192.83i −0.110826 0.191956i
\(339\) 0 0
\(340\) 866.242 1500.38i 0.138172 0.239322i
\(341\) 7689.37 + 13318.4i 1.22112 + 2.11505i
\(342\) 0 0
\(343\) 0 0
\(344\) 2628.45 0.411967
\(345\) 0 0
\(346\) −1036.60 + 1795.44i −0.161063 + 0.278970i
\(347\) −31.6819 + 54.8746i −0.00490136 + 0.00848940i −0.868466 0.495749i \(-0.834893\pi\)
0.863564 + 0.504239i \(0.168227\pi\)
\(348\) 0 0
\(349\) −1223.79 −0.187702 −0.0938508 0.995586i \(-0.529918\pi\)
−0.0938508 + 0.995586i \(0.529918\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −829.394 1436.55i −0.125588 0.217524i
\(353\) 2257.81 3910.64i 0.340428 0.589638i −0.644085 0.764954i \(-0.722762\pi\)
0.984512 + 0.175316i \(0.0560949\pi\)
\(354\) 0 0
\(355\) 1035.29 + 1793.18i 0.154782 + 0.268090i
\(356\) 4628.64 0.689093
\(357\) 0 0
\(358\) −1534.86 −0.226592
\(359\) 1114.25 + 1929.93i 0.163810 + 0.283727i 0.936232 0.351383i \(-0.114288\pi\)
−0.772422 + 0.635109i \(0.780955\pi\)
\(360\) 0 0
\(361\) 502.506 870.365i 0.0732622 0.126894i
\(362\) 3957.71 + 6854.95i 0.574620 + 0.995271i
\(363\) 0 0
\(364\) 0 0
\(365\) 2871.26 0.411749
\(366\) 0 0
\(367\) −718.670 + 1244.77i −0.102219 + 0.177048i −0.912598 0.408857i \(-0.865928\pi\)
0.810380 + 0.585905i \(0.199261\pi\)
\(368\) 1178.79 2041.72i 0.166980 0.289217i
\(369\) 0 0
\(370\) −5116.47 −0.718899
\(371\) 0 0
\(372\) 0 0
\(373\) 6118.71 + 10597.9i 0.849370 + 1.47115i 0.881771 + 0.471677i \(0.156351\pi\)
−0.0324014 + 0.999475i \(0.510315\pi\)
\(374\) −1417.67 + 2455.47i −0.196005 + 0.339490i
\(375\) 0 0
\(376\) 271.818 + 470.803i 0.0372818 + 0.0645740i
\(377\) 9329.00 1.27445
\(378\) 0 0
\(379\) −10647.0 −1.44301 −0.721503 0.692411i \(-0.756549\pi\)
−0.721503 + 0.692411i \(0.756549\pi\)
\(380\) −2423.44 4197.52i −0.327157 0.566653i
\(381\) 0 0
\(382\) 1805.30 3126.86i 0.241798 0.418807i
\(383\) 3357.41 + 5815.20i 0.447925 + 0.775829i 0.998251 0.0591208i \(-0.0188297\pi\)
−0.550326 + 0.834950i \(0.685496\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −6741.68 −0.888970
\(387\) 0 0
\(388\) 3236.60 5605.95i 0.423488 0.733503i
\(389\) −5326.54 + 9225.83i −0.694258 + 1.20249i 0.276173 + 0.961108i \(0.410934\pi\)
−0.970430 + 0.241381i \(0.922400\pi\)
\(390\) 0 0
\(391\) −4029.76 −0.521211
\(392\) 0 0
\(393\) 0 0
\(394\) 4612.31 + 7988.76i 0.589758 + 1.02149i
\(395\) −3244.21 + 5619.14i −0.413250 + 0.715771i
\(396\) 0 0
\(397\) 1610.52 + 2789.50i 0.203601 + 0.352648i 0.949686 0.313203i \(-0.101402\pi\)
−0.746085 + 0.665851i \(0.768069\pi\)
\(398\) −4459.73 −0.561673
\(399\) 0 0
\(400\) 2013.03 0.251629
\(401\) 6242.50 + 10812.3i 0.777395 + 1.34649i 0.933438 + 0.358738i \(0.116793\pi\)
−0.156043 + 0.987750i \(0.549874\pi\)
\(402\) 0 0
\(403\) 5760.99 9978.32i 0.712097 1.23339i
\(404\) −1437.48 2489.80i −0.177024 0.306614i
\(405\) 0 0
\(406\) 0 0
\(407\) 8373.46 1.01980
\(408\) 0 0
\(409\) 3518.69 6094.56i 0.425399 0.736813i −0.571059 0.820909i \(-0.693467\pi\)
0.996458 + 0.0840967i \(0.0268004\pi\)
\(410\) 1630.86 2824.74i 0.196445 0.340253i
\(411\) 0 0
\(412\) 6446.32 0.770843
\(413\) 0 0
\(414\) 0 0
\(415\) 2755.09 + 4771.95i 0.325884 + 0.564448i
\(416\) −621.394 + 1076.29i −0.0732364 + 0.126849i
\(417\) 0 0
\(418\) 3966.13 + 6869.54i 0.464090 + 0.803828i
\(419\) −1549.66 −0.180682 −0.0903410 0.995911i \(-0.528796\pi\)
−0.0903410 + 0.995911i \(0.528796\pi\)
\(420\) 0 0
\(421\) 5531.63 0.640369 0.320184 0.947355i \(-0.396255\pi\)
0.320184 + 0.947355i \(0.396255\pi\)
\(422\) 912.614 + 1580.69i 0.105273 + 0.182339i
\(423\) 0 0
\(424\) 265.955 460.647i 0.0304620 0.0527618i
\(425\) −1720.42 2979.85i −0.196359 0.340103i
\(426\) 0 0
\(427\) 0 0
\(428\) −3738.68 −0.422234
\(429\) 0 0
\(430\) 5203.39 9012.54i 0.583558 1.01075i
\(431\) −1014.97 + 1757.97i −0.113432 + 0.196470i −0.917152 0.398538i \(-0.869518\pi\)
0.803720 + 0.595008i \(0.202851\pi\)
\(432\) 0 0
\(433\) 327.739 0.0363744 0.0181872 0.999835i \(-0.494211\pi\)
0.0181872 + 0.999835i \(0.494211\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 2394.04 + 4146.60i 0.262967 + 0.455472i
\(437\) −5636.92 + 9763.43i −0.617049 + 1.06876i
\(438\) 0 0
\(439\) 3954.34 + 6849.12i 0.429910 + 0.744625i 0.996865 0.0791234i \(-0.0252121\pi\)
−0.566955 + 0.823749i \(0.691879\pi\)
\(440\) −6567.61 −0.711587
\(441\) 0 0
\(442\) 2124.27 0.228600
\(443\) −1460.41 2529.51i −0.156628 0.271288i 0.777023 0.629473i \(-0.216729\pi\)
−0.933651 + 0.358185i \(0.883396\pi\)
\(444\) 0 0
\(445\) 9163.03 15870.8i 0.976111 1.69067i
\(446\) 4319.47 + 7481.53i 0.458593 + 0.794307i
\(447\) 0 0
\(448\) 0 0
\(449\) 10240.2 1.07631 0.538156 0.842845i \(-0.319121\pi\)
0.538156 + 0.842845i \(0.319121\pi\)
\(450\) 0 0
\(451\) −2669.02 + 4622.88i −0.278668 + 0.482668i
\(452\) −4769.29 + 8260.65i −0.496302 + 0.859620i
\(453\) 0 0
\(454\) −4122.57 −0.426171
\(455\) 0 0
\(456\) 0 0
\(457\) −2946.31 5103.17i −0.301582 0.522355i 0.674913 0.737897i \(-0.264181\pi\)
−0.976494 + 0.215543i \(0.930848\pi\)
\(458\) 3474.63 6018.24i 0.354495 0.614004i
\(459\) 0 0
\(460\) −4667.15 8083.74i −0.473059 0.819362i
\(461\) −12643.4 −1.27735 −0.638677 0.769475i \(-0.720518\pi\)
−0.638677 + 0.769475i \(0.720518\pi\)
\(462\) 0 0
\(463\) 15093.2 1.51499 0.757494 0.652842i \(-0.226423\pi\)
0.757494 + 0.652842i \(0.226423\pi\)
\(464\) 1921.67 + 3328.42i 0.192265 + 0.333013i
\(465\) 0 0
\(466\) −776.099 + 1344.24i −0.0771504 + 0.133628i
\(467\) 1410.12 + 2442.39i 0.139727 + 0.242014i 0.927393 0.374088i \(-0.122044\pi\)
−0.787666 + 0.616102i \(0.788711\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 2152.41 0.211241
\(471\) 0 0
\(472\) −1847.71 + 3200.33i −0.180186 + 0.312091i
\(473\) −8515.72 + 14749.7i −0.827808 + 1.43381i
\(474\) 0 0
\(475\) −9626.23 −0.929856
\(476\) 0 0
\(477\) 0 0
\(478\) −2006.80 3475.87i −0.192027 0.332600i
\(479\) 8224.25 14244.8i 0.784500 1.35879i −0.144798 0.989461i \(-0.546253\pi\)
0.929297 0.369332i \(-0.120414\pi\)
\(480\) 0 0
\(481\) −3136.76 5433.03i −0.297347 0.515020i
\(482\) 1611.30 0.152267
\(483\) 0 0
\(484\) 5424.35 0.509424
\(485\) −12814.6 22195.5i −1.19975 2.07804i
\(486\) 0 0
\(487\) −3165.53 + 5482.87i −0.294546 + 0.510169i −0.974879 0.222734i \(-0.928502\pi\)
0.680333 + 0.732903i \(0.261835\pi\)
\(488\) −741.394 1284.13i −0.0687732 0.119119i
\(489\) 0 0
\(490\) 0 0
\(491\) 9286.90 0.853588 0.426794 0.904349i \(-0.359643\pi\)
0.426794 + 0.904349i \(0.359643\pi\)
\(492\) 0 0
\(493\) 3284.67 5689.21i 0.300069 0.519735i
\(494\) 2971.48 5146.76i 0.270634 0.468752i
\(495\) 0 0
\(496\) 4746.79 0.429712
\(497\) 0 0
\(498\) 0 0
\(499\) 121.725 + 210.835i 0.0109202 + 0.0189143i 0.871434 0.490513i \(-0.163191\pi\)
−0.860514 + 0.509427i \(0.829857\pi\)
\(500\) 25.7954 44.6789i 0.00230721 0.00399620i
\(501\) 0 0
\(502\) 1421.78 + 2462.60i 0.126409 + 0.218947i
\(503\) 8499.30 0.753409 0.376705 0.926333i \(-0.377057\pi\)
0.376705 + 0.926333i \(0.377057\pi\)
\(504\) 0 0
\(505\) −11382.8 −1.00303
\(506\) 7638.12 + 13229.6i 0.671059 + 1.16231i
\(507\) 0 0
\(508\) 5347.85 9262.75i 0.467072 0.808992i
\(509\) 3841.55 + 6653.76i 0.334526 + 0.579416i 0.983394 0.181485i \(-0.0580904\pi\)
−0.648868 + 0.760901i \(0.724757\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −512.000 −0.0441942
\(513\) 0 0
\(514\) −1465.82 + 2538.87i −0.125787 + 0.217869i
\(515\) 12761.4 22103.4i 1.09191 1.89124i
\(516\) 0 0
\(517\) −3522.57 −0.299656
\(518\) 0 0
\(519\) 0 0
\(520\) 2460.27 + 4261.32i 0.207481 + 0.359368i
\(521\) 10765.3 18646.1i 0.905253 1.56794i 0.0846750 0.996409i \(-0.473015\pi\)
0.820578 0.571535i \(-0.193652\pi\)
\(522\) 0 0
\(523\) −8423.53 14590.0i −0.704274 1.21984i −0.966953 0.254955i \(-0.917939\pi\)
0.262679 0.964883i \(-0.415394\pi\)
\(524\) −155.439 −0.0129588
\(525\) 0 0
\(526\) 13982.8 1.15908
\(527\) −4056.80 7026.58i −0.335326 0.580802i
\(528\) 0 0
\(529\) −4772.29 + 8265.84i −0.392232 + 0.679366i
\(530\) −1052.99 1823.83i −0.0862998 0.149476i
\(531\) 0 0
\(532\) 0 0
\(533\) 3999.34 0.325011
\(534\) 0 0
\(535\) −7401.24 + 12819.3i −0.598100 + 1.03594i
\(536\) 2180.83 3777.31i 0.175742 0.304394i
\(537\) 0 0
\(538\) −1617.92 −0.129653
\(539\) 0 0
\(540\) 0 0
\(541\) −8720.02 15103.5i −0.692981 1.20028i −0.970856 0.239662i \(-0.922963\pi\)
0.277875 0.960617i \(-0.410370\pi\)
\(542\) −6661.77 + 11538.5i −0.527947 + 0.914432i
\(543\) 0 0
\(544\) 437.576 + 757.903i 0.0344870 + 0.0597332i
\(545\) 18957.3 1.48999
\(546\) 0 0
\(547\) 11520.7 0.900530 0.450265 0.892895i \(-0.351329\pi\)
0.450265 + 0.892895i \(0.351329\pi\)
\(548\) −1536.29 2660.93i −0.119757 0.207426i
\(549\) 0 0
\(550\) −6521.86 + 11296.2i −0.505623 + 0.875765i
\(551\) −9189.33 15916.4i −0.710488 1.23060i
\(552\) 0 0
\(553\) 0 0
\(554\) 15062.9 1.15517
\(555\) 0 0
\(556\) 2105.10 3646.14i 0.160568 0.278113i
\(557\) 5746.51 9953.25i 0.437141 0.757151i −0.560327 0.828272i \(-0.689324\pi\)
0.997468 + 0.0711212i \(0.0226577\pi\)
\(558\) 0 0
\(559\) 12760.2 0.965472
\(560\) 0 0
\(561\) 0 0
\(562\) −1690.19 2927.49i −0.126862 0.219731i
\(563\) −9055.65 + 15684.8i −0.677886 + 1.17413i 0.297730 + 0.954650i \(0.403770\pi\)
−0.975616 + 0.219483i \(0.929563\pi\)
\(564\) 0 0
\(565\) 18882.9 + 32706.2i 1.40604 + 2.43533i
\(566\) 6356.46 0.472053
\(567\) 0 0
\(568\) −1045.94 −0.0772652
\(569\) 2208.81 + 3825.77i 0.162738 + 0.281871i 0.935850 0.352399i \(-0.114634\pi\)
−0.773112 + 0.634270i \(0.781301\pi\)
\(570\) 0 0
\(571\) −6609.87 + 11448.6i −0.484439 + 0.839073i −0.999840 0.0178762i \(-0.994310\pi\)
0.515401 + 0.856949i \(0.327643\pi\)
\(572\) −4026.41 6973.95i −0.294323 0.509782i
\(573\) 0 0
\(574\) 0 0
\(575\) −18538.6 −1.34454
\(576\) 0 0
\(577\) −8748.20 + 15152.3i −0.631182 + 1.09324i 0.356128 + 0.934437i \(0.384097\pi\)
−0.987310 + 0.158803i \(0.949237\pi\)
\(578\) −4165.06 + 7214.10i −0.299730 + 0.519147i
\(579\) 0 0
\(580\) 15216.8 1.08939
\(581\) 0 0
\(582\) 0 0
\(583\) 1723.29 + 2984.83i 0.122421 + 0.212039i
\(584\) −725.197 + 1256.08i −0.0513850 + 0.0890015i
\(585\) 0 0
\(586\) −2176.53 3769.87i −0.153433 0.265754i
\(587\) −4280.53 −0.300982 −0.150491 0.988611i \(-0.548085\pi\)
−0.150491 + 0.988611i \(0.548085\pi\)
\(588\) 0 0
\(589\) −22699.0 −1.58794
\(590\) 7315.61 + 12671.0i 0.510473 + 0.884165i
\(591\) 0 0
\(592\) 1292.27 2238.28i 0.0897164 0.155393i
\(593\) 795.466 + 1377.79i 0.0550858 + 0.0954114i 0.892253 0.451535i \(-0.149123\pi\)
−0.837168 + 0.546946i \(0.815790\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −1443.91 −0.0992363
\(597\) 0 0
\(598\) 5722.59 9911.82i 0.391328 0.677800i
\(599\) −6961.42 + 12057.5i −0.474851 + 0.822467i −0.999585 0.0287997i \(-0.990831\pi\)
0.524734 + 0.851266i \(0.324165\pi\)
\(600\) 0 0
\(601\) −12559.7 −0.852446 −0.426223 0.904618i \(-0.640156\pi\)
−0.426223 + 0.904618i \(0.640156\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −3096.78 5363.78i −0.208620 0.361340i
\(605\) 10738.3 18599.2i 0.721607 1.24986i
\(606\) 0 0
\(607\) 3839.19 + 6649.66i 0.256718 + 0.444648i 0.965361 0.260919i \(-0.0840256\pi\)
−0.708643 + 0.705567i \(0.750692\pi\)
\(608\) 2448.36 0.163313
\(609\) 0 0
\(610\) −5870.77 −0.389673
\(611\) 1319.58 + 2285.58i 0.0873723 + 0.151333i
\(612\) 0 0
\(613\) −3079.19 + 5333.31i −0.202883 + 0.351403i −0.949456 0.313900i \(-0.898364\pi\)
0.746573 + 0.665303i \(0.231698\pi\)
\(614\) −623.504 1079.94i −0.0409814 0.0709818i
\(615\) 0 0
\(616\) 0 0
\(617\) −8813.12 −0.575045 −0.287523 0.957774i \(-0.592832\pi\)
−0.287523 + 0.957774i \(0.592832\pi\)
\(618\) 0 0
\(619\) 11595.0 20083.1i 0.752894 1.30405i −0.193521 0.981096i \(-0.561991\pi\)
0.946415 0.322954i \(-0.104676\pi\)
\(620\) 9396.93 16276.0i 0.608693 1.05429i
\(621\) 0 0
\(622\) −935.985 −0.0603369
\(623\) 0 0
\(624\) 0 0
\(625\) 7761.27 + 13442.9i 0.496721 + 0.860346i
\(626\) −3612.81 + 6257.57i −0.230666 + 0.399525i
\(627\) 0 0
\(628\) −1934.14 3350.02i −0.122899 0.212867i
\(629\) −4417.71 −0.280041
\(630\) 0 0
\(631\) 7936.94 0.500736 0.250368 0.968151i \(-0.419448\pi\)
0.250368 + 0.968151i \(0.419448\pi\)
\(632\) −1638.79 2838.46i −0.103145 0.178652i
\(633\) 0 0
\(634\) −4531.74 + 7849.20i −0.283877 + 0.491690i
\(635\) −21173.6 36673.8i −1.32323 2.29190i
\(636\) 0 0
\(637\) 0 0
\(638\) −24903.4 −1.54535
\(639\) 0 0
\(640\) −1013.58 + 1755.56i −0.0626017 + 0.108429i
\(641\) 16057.3 27812.1i 0.989432 1.71375i 0.369146 0.929371i \(-0.379650\pi\)
0.620286 0.784376i \(-0.287016\pi\)
\(642\) 0 0
\(643\) 24786.7 1.52021 0.760104 0.649802i \(-0.225148\pi\)
0.760104 + 0.649802i \(0.225148\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −2092.47 3624.26i −0.127441 0.220735i
\(647\) −3772.80 + 6534.67i −0.229249 + 0.397070i −0.957586 0.288149i \(-0.906960\pi\)
0.728337 + 0.685219i \(0.240294\pi\)
\(648\) 0 0
\(649\) −11972.5 20737.0i −0.724133 1.25423i
\(650\) 9772.54 0.589708
\(651\) 0 0
\(652\) −5306.00 −0.318710
\(653\) −2444.49 4233.99i −0.146494 0.253735i 0.783435 0.621473i \(-0.213466\pi\)
−0.929929 + 0.367738i \(0.880132\pi\)
\(654\) 0 0
\(655\) −307.714 + 532.976i −0.0183563 + 0.0317941i
\(656\) 823.818 + 1426.89i 0.0490316 + 0.0849251i
\(657\) 0 0
\(658\) 0 0
\(659\) −25895.9 −1.53075 −0.765374 0.643586i \(-0.777446\pi\)
−0.765374 + 0.643586i \(0.777446\pi\)
\(660\) 0 0
\(661\) 4091.68 7087.00i 0.240769 0.417023i −0.720165 0.693803i \(-0.755934\pi\)
0.960933 + 0.276780i \(0.0892672\pi\)
\(662\) −1237.06 + 2142.65i −0.0726278 + 0.125795i
\(663\) 0 0
\(664\) −2783.42 −0.162677
\(665\) 0 0
\(666\) 0 0
\(667\) −17697.2 30652.4i −1.02734 1.77941i
\(668\) −2833.39 + 4907.58i −0.164113 + 0.284252i
\(669\) 0 0
\(670\) −8634.53 14955.4i −0.497882 0.862357i
\(671\) 9607.93 0.552772
\(672\) 0 0
\(673\) −4635.02 −0.265478 −0.132739 0.991151i \(-0.542377\pi\)
−0.132739 + 0.991151i \(0.542377\pi\)
\(674\) −1867.83 3235.18i −0.106745 0.184888i
\(675\) 0 0
\(676\) 1377.36 2385.65i 0.0783657 0.135733i
\(677\) 12192.9 + 21118.7i 0.692187 + 1.19890i 0.971120 + 0.238593i \(0.0766862\pi\)
−0.278932 + 0.960311i \(0.589980\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 3464.97 0.195405
\(681\) 0 0
\(682\) −15378.7 + 26636.8i −0.863464 + 1.49556i
\(683\) −9196.71 + 15929.2i −0.515230 + 0.892405i 0.484613 + 0.874728i \(0.338960\pi\)
−0.999844 + 0.0176767i \(0.994373\pi\)
\(684\) 0 0
\(685\) −12165.2 −0.678552
\(686\) 0 0
\(687\) 0 0
\(688\) 2628.45 + 4552.62i 0.145652 + 0.252277i
\(689\) 1291.11 2236.27i 0.0713897 0.123651i
\(690\) 0 0
\(691\) −7449.44 12902.8i −0.410116 0.710341i 0.584786 0.811187i \(-0.301178\pi\)
−0.994902 + 0.100846i \(0.967845\pi\)
\(692\) −4146.39 −0.227778
\(693\) 0 0
\(694\) −126.727 −0.00693157
\(695\) −8334.67 14436.1i −0.454895 0.787902i
\(696\) 0 0
\(697\) 1408.14 2438.96i 0.0765236 0.132543i
\(698\) −1223.79 2119.66i −0.0663625 0.114943i
\(699\) 0 0
\(700\) 0 0
\(701\) 5725.70 0.308497 0.154249 0.988032i \(-0.450704\pi\)
0.154249 + 0.988032i \(0.450704\pi\)
\(702\) 0 0
\(703\) −6179.60 + 10703.4i −0.331533 + 0.574232i
\(704\) 1658.79 2873.10i 0.0888039 0.153813i
\(705\) 0 0
\(706\) 9031.23 0.481437
\(707\) 0 0
\(708\) 0 0
\(709\) 11728.4 + 20314.2i 0.621255 + 1.07604i 0.989252 + 0.146218i \(0.0467101\pi\)
−0.367998 + 0.929827i \(0.619957\pi\)
\(710\) −2070.58 + 3586.36i −0.109447 + 0.189568i
\(711\) 0 0
\(712\) 4628.64 + 8017.03i 0.243631 + 0.421982i
\(713\) −43714.5 −2.29610
\(714\) 0 0
\(715\) −31883.4 −1.66765
\(716\) −1534.86 2658.46i −0.0801125 0.138759i
\(717\) 0 0
\(718\) −2228.49 + 3859.86i −0.115831 + 0.200625i
\(719\) 4229.50 + 7325.71i 0.219379 + 0.379976i 0.954618 0.297832i \(-0.0962634\pi\)
−0.735239 + 0.677808i \(0.762930\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 2010.02 0.103608
\(723\) 0 0
\(724\) −7915.42 + 13709.9i −0.406318 + 0.703763i
\(725\) 15110.8 26172.7i 0.774072 1.34073i
\(726\) 0 0
\(727\) 11822.2 0.603111 0.301555 0.953449i \(-0.402494\pi\)
0.301555 + 0.953449i \(0.402494\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 2871.26 + 4973.16i 0.145575 + 0.252144i
\(731\) 4492.77 7781.70i 0.227320 0.393730i
\(732\) 0 0
\(733\) 2514.48 + 4355.20i 0.126704 + 0.219458i 0.922398 0.386241i \(-0.126227\pi\)
−0.795694 + 0.605699i \(0.792893\pi\)
\(734\) −2874.68 −0.144559
\(735\) 0 0
\(736\) 4715.15 0.236145
\(737\) 14131.0 + 24475.6i 0.706272 + 1.22330i
\(738\) 0 0
\(739\) 8871.95 15366.7i 0.441624 0.764914i −0.556187 0.831057i \(-0.687736\pi\)
0.997810 + 0.0661431i \(0.0210694\pi\)
\(740\) −5116.47 8861.99i −0.254169 0.440234i
\(741\) 0 0
\(742\) 0 0
\(743\) 13202.3 0.651877 0.325938 0.945391i \(-0.394320\pi\)
0.325938 + 0.945391i \(0.394320\pi\)
\(744\) 0 0
\(745\) −2858.42 + 4950.93i −0.140570 + 0.243474i
\(746\) −12237.4 + 21195.8i −0.600595 + 1.04026i
\(747\) 0 0
\(748\) −5670.67 −0.277193
\(749\) 0 0
\(750\) 0 0
\(751\) −7800.49 13510.8i −0.379020 0.656482i 0.611900 0.790935i \(-0.290406\pi\)
−0.990920 + 0.134453i \(0.957072\pi\)
\(752\) −543.636 + 941.606i −0.0263622 + 0.0456607i
\(753\) 0 0
\(754\) 9329.00 + 16158.3i 0.450586 + 0.780439i
\(755\) −24522.0 −1.18205
\(756\) 0 0
\(757\) 2948.08 0.141545 0.0707725 0.997492i \(-0.477454\pi\)
0.0707725 + 0.997492i \(0.477454\pi\)
\(758\) −10647.0 18441.1i −0.510180 0.883657i
\(759\) 0 0
\(760\) 4846.88 8395.04i 0.231335 0.400684i
\(761\) −848.515 1469.67i −0.0404187 0.0700073i 0.845108 0.534595i \(-0.179536\pi\)
−0.885527 + 0.464588i \(0.846203\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 7221.18 0.341954
\(765\) 0 0
\(766\) −6714.81 + 11630.4i −0.316731 + 0.548594i
\(767\) −8969.98 + 15536.5i −0.422278 + 0.731407i
\(768\) 0 0
\(769\) 96.7799 0.00453833 0.00226916 0.999997i \(-0.499278\pi\)
0.00226916 + 0.999997i \(0.499278\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −6741.68 11676.9i −0.314298 0.544381i
\(773\) −18163.4 + 31459.9i −0.845138 + 1.46382i 0.0403629 + 0.999185i \(0.487149\pi\)
−0.885501 + 0.464637i \(0.846185\pi\)
\(774\) 0 0
\(775\) −18662.9 32325.2i −0.865023 1.49826i
\(776\) 12946.4 0.598903
\(777\) 0 0
\(778\) −21306.2 −0.981828
\(779\) −3939.47 6823.35i −0.181189 0.313828i
\(780\) 0 0
\(781\) 3388.66 5869.32i 0.155257 0.268913i
\(782\) −4029.76 6979.74i −0.184276 0.319175i
\(783\) 0 0
\(784\) 0 0
\(785\) −15315.6 −0.696352
\(786\) 0 0
\(787\) 3548.23 6145.72i 0.160713 0.278362i −0.774412 0.632682i \(-0.781954\pi\)
0.935124 + 0.354319i \(0.115287\pi\)
\(788\) −9224.62 + 15977.5i −0.417022 + 0.722304i
\(789\) 0 0
\(790\) −12976.8 −0.584424
\(791\)