Properties

Label 882.4.g.bf.667.2
Level $882$
Weight $4$
Character 882.667
Analytic conductor $52.040$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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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 667.2
Root \(-8.91856 + 15.4474i\) of defining polynomial
Character \(\chi\) \(=\) 882.667
Dual form 882.4.g.bf.361.2

$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

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

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 −0.257245 0.966346i \(-0.582815\pi\)
0.965503 0.260392i \(-0.0838518\pi\)
\(6\) 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 0.964696 + 0.263368i \(0.0848333\pi\)
−0.254265 + 0.967135i \(0.581833\pi\)
\(12\) 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 0.751842 0.659344i \(-0.229166\pi\)
−0.946929 + 0.321442i \(0.895832\pi\)
\(18\) 0 0
\(19\) 38.2557 66.2608i 0.461919 0.800067i −0.537138 0.843494i \(-0.680495\pi\)
0.999057 + 0.0434278i \(0.0138279\pi\)
\(20\) −63.3485 −0.708258
\(21\) 0 0
\(22\) 103.674 1.00470
\(23\) 73.6742 127.608i 0.667919 1.15687i −0.310566 0.950552i \(-0.600519\pi\)
0.978485 0.206318i \(-0.0661482\pi\)
\(24\) 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 −0.872480 0.488651i \(-0.837489\pi\)
0.0130559 0.999915i \(-0.495844\pi\)
\(32\) 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 −0.628906 0.777481i \(-0.716497\pi\)
0.987772 + 0.155908i \(0.0498304\pi\)
\(38\) −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 −0.913921 0.405891i \(-0.866961\pi\)
0.808473 + 0.588534i \(0.200295\pi\)
\(48\) 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 0.819725 0.572757i \(-0.194126\pi\)
−0.905885 + 0.423524i \(0.860793\pi\)
\(54\) 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 0.999938 + 0.0111711i \(0.00355595\pi\)
−0.490294 + 0.871557i \(0.663111\pi\)
\(60\) 0 0
\(61\) 92.6742 160.516i 0.194520 0.336919i −0.752223 0.658909i \(-0.771018\pi\)
0.946743 + 0.321990i \(0.104352\pi\)
\(62\) −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 0.502921 0.864332i \(-0.332259\pi\)
−0.999994 + 0.00337637i \(0.998925\pi\)
\(68\) −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 0.929499 0.368824i \(-0.120239\pi\)
−0.784160 + 0.620558i \(0.786906\pi\)
\(74\) −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 −0.682483 0.730901i \(-0.739100\pi\)
0.974221 + 0.225597i \(0.0724333\pi\)
\(80\) 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 0.283038 + 0.959109i \(0.408658\pi\)
−0.972132 + 0.234436i \(0.924676\pi\)
\(90\) 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 0.632907 0.774228i \(-0.281861\pi\)
−0.986954 + 0.161000i \(0.948528\pi\)
\(102\) 0 0
\(103\) −805.790 + 1395.67i −0.770843 + 1.33514i 0.166259 + 0.986082i \(0.446831\pi\)
−0.937102 + 0.349057i \(0.886502\pi\)
\(104\) 310.697 0.292946
\(105\) 0 0
\(106\) −132.977 −0.121848
\(107\) 467.335 809.448i 0.422234 0.731330i −0.573924 0.818909i \(-0.694580\pi\)
0.996158 + 0.0875784i \(0.0279128\pi\)
\(108\) 0 0
\(109\) 598.509 + 1036.65i 0.525934 + 0.910944i 0.999544 + 0.0302095i \(0.00961746\pi\)
−0.473610 + 0.880735i \(0.657049\pi\)
\(110\) 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 −0.859473 0.511181i \(-0.829208\pi\)
0.872432 + 0.488735i \(0.162542\pi\)
\(132\) 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 0.721061 0.692872i \(-0.243655\pi\)
−0.960575 + 0.278021i \(0.910322\pi\)
\(138\) 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 −0.812132 0.583473i \(-0.801693\pi\)
0.911369 + 0.411591i \(0.135027\pi\)
\(150\) 0 0
\(151\) −774.195 1340.95i −0.417239 0.722679i 0.578422 0.815738i \(-0.303669\pi\)
−0.995661 + 0.0930587i \(0.970336\pi\)
\(152\) −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 0.716558 0.697528i \(-0.245717\pi\)
−0.962356 + 0.271794i \(0.912383\pi\)
\(158\) −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 −0.661509 0.749937i \(-0.730084\pi\)
0.980219 + 0.197915i \(0.0634170\pi\)
\(164\) 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 −0.729371 0.684118i \(-0.760187\pi\)
0.957149 + 0.289595i \(0.0935207\pi\)
\(174\) 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 0.774724 0.632299i \(-0.217889\pi\)
−0.934949 + 0.354781i \(0.884555\pi\)
\(180\) 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 −0.984796 0.173717i \(-0.944422\pi\)
0.642841 + 0.765999i \(0.277756\pi\)
\(192\) 0 0
\(193\) −1685.42 2919.23i −0.628597 1.08876i −0.987833 0.155515i \(-0.950296\pi\)
0.359237 0.933247i \(-0.383037\pi\)
\(194\) −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 0.596212 0.802827i \(-0.296672\pi\)
−0.993375 + 0.114921i \(0.963339\pi\)
\(200\) 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 0.675093 0.737733i \(-0.264103\pi\)
−0.976442 + 0.215782i \(0.930770\pi\)
\(228\) 0 0
\(229\) −1737.32 + 3009.12i −0.501332 + 0.868333i 0.498667 + 0.866794i \(0.333823\pi\)
−0.999999 + 0.00153905i \(0.999510\pi\)
\(230\) −4667.15 −1.33801
\(231\) 0 0
\(232\) 1921.67 0.543809
\(233\) 388.049 672.121i 0.109107 0.188979i −0.806302 0.591505i \(-0.798534\pi\)
0.915409 + 0.402525i \(0.131868\pi\)
\(234\) 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 0.914825 0.403850i \(-0.132328\pi\)
−0.807157 + 0.590337i \(0.798995\pi\)
\(242\) 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 −0.763268 0.646082i \(-0.776406\pi\)
0.941157 + 0.337968i \(0.109740\pi\)
\(258\) 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 0.905980 + 0.423320i \(0.139135\pi\)
−0.0863847 + 0.996262i \(0.527531\pi\)
\(264\) 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 0.816539 0.577290i \(-0.195890\pi\)
−0.908218 + 0.418498i \(0.862557\pi\)
\(270\) 0 0
\(271\) 3330.88 5769.26i 0.746630 1.29320i −0.202799 0.979220i \(-0.565004\pi\)
0.949429 0.313981i \(-0.101663\pi\)
\(272\) 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 0.908009 + 0.418951i \(0.137602\pi\)
−0.0911823 + 0.995834i \(0.529065\pi\)
\(278\) −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 0.983252 0.182251i \(-0.0583384\pi\)
−0.649460 + 0.760396i \(0.725005\pi\)
\(284\) −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 0.843905 0.536493i \(-0.180251\pi\)
−0.886569 + 0.462596i \(0.846918\pi\)
\(312\) 0 0
\(313\) 1806.41 3128.79i 0.326211 0.565014i −0.655546 0.755156i \(-0.727561\pi\)
0.981757 + 0.190141i \(0.0608946\pi\)
\(314\) −1934.14 −0.347610
\(315\) 0 0
\(316\) −1638.79 −0.291737
\(317\) 2265.87 3924.60i 0.401463 0.695355i −0.592439 0.805615i \(-0.701835\pi\)
0.993903 + 0.110260i \(0.0351684\pi\)
\(318\) 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 −0.810090 0.586306i \(-0.800582\pi\)
0.912801 + 0.408405i \(0.133915\pi\)
\(332\) −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 0.863564 0.504239i \(-0.168227\pi\)
−0.868466 + 0.495749i \(0.834893\pi\)
\(348\) 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 0.984512 0.175316i \(-0.0560949\pi\)
−0.644085 + 0.764954i \(0.722762\pi\)
\(354\) 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 −0.772422 0.635109i \(-0.780955\pi\)
0.936232 + 0.351383i \(0.114288\pi\)
\(360\) 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 0.810380 0.585905i \(-0.199261\pi\)
−0.912598 + 0.408857i \(0.865928\pi\)
\(368\) 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 −0.0324014 0.999475i \(-0.510315\pi\)
0.881771 0.471677i \(-0.156351\pi\)
\(374\) −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 −0.550326 0.834950i \(-0.685496\pi\)
0.998251 + 0.0591208i \(0.0188297\pi\)
\(384\) 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 −0.970430 0.241381i \(-0.922400\pi\)
0.276173 0.961108i \(-0.410934\pi\)
\(390\) 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 −0.746085 0.665851i \(-0.768069\pi\)
0.949686 + 0.313203i \(0.101402\pi\)
\(398\) −4459.73 −0.561673
\(399\) 0 0
\(400\) 2013.03 0.251629
\(401\) 6242.50 10812.3i 0.777395 1.34649i −0.156043 0.987750i \(-0.549874\pi\)
0.933438 0.358738i \(-0.116793\pi\)
\(402\) 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 0.996458 0.0840967i \(-0.0268004\pi\)
−0.571059 + 0.820909i \(0.693467\pi\)
\(410\) 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 0.803720 0.595008i \(-0.202851\pi\)
−0.917152 + 0.398538i \(0.869518\pi\)
\(432\) 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 −0.566955 0.823749i \(-0.691879\pi\)
0.996865 + 0.0791234i \(0.0252121\pi\)
\(440\) −6567.61 −0.711587
\(441\) 0 0
\(442\) 2124.27 0.228600
\(443\) −1460.41 + 2529.51i −0.156628 + 0.271288i −0.933651 0.358185i \(-0.883396\pi\)
0.777023 + 0.629473i \(0.216729\pi\)
\(444\) 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 −0.976494 0.215543i \(-0.930848\pi\)
0.674913 + 0.737897i \(0.264181\pi\)
\(458\) 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 −0.787666 0.616102i \(-0.788711\pi\)
0.927393 + 0.374088i \(0.122044\pi\)
\(468\) 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 0.929297 + 0.369332i \(0.120414\pi\)
−0.144798 + 0.989461i \(0.546253\pi\)
\(480\) 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 0.680333 0.732903i \(-0.261835\pi\)
−0.974879 + 0.222734i \(0.928502\pi\)
\(488\) −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 −0.860514 0.509427i \(-0.829857\pi\)
0.871434 + 0.490513i \(0.163191\pi\)
\(500\) 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 −0.648868 0.760901i \(-0.724757\pi\)
0.983394 + 0.181485i \(0.0580904\pi\)
\(510\) 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 0.820578 + 0.571535i \(0.193652\pi\)
0.0846750 + 0.996409i \(0.473015\pi\)
\(522\) 0 0
\(523\) −8423.53 + 14590.0i −0.704274 + 1.21984i 0.262679 + 0.964883i \(0.415394\pi\)
−0.966953 + 0.254955i \(0.917939\pi\)
\(524\) −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 0.277875 + 0.960617i \(0.410370\pi\)
−0.970856 + 0.239662i \(0.922963\pi\)
\(542\) −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 0.997468 0.0711212i \(-0.0226577\pi\)
−0.560327 + 0.828272i \(0.689324\pi\)
\(558\) 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 −0.975616 0.219483i \(-0.929563\pi\)
0.297730 0.954650i \(-0.403770\pi\)
\(564\) 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 −0.773112 0.634270i \(-0.781301\pi\)
0.935850 + 0.352399i \(0.114634\pi\)
\(570\) 0 0
\(571\) −6609.87 11448.6i −0.484439 0.839073i 0.515401 0.856949i \(-0.327643\pi\)
−0.999840 + 0.0178762i \(0.994310\pi\)
\(572\) −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 −0.987310 0.158803i \(-0.949237\pi\)
0.356128 0.934437i \(-0.384097\pi\)
\(578\) −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 −0.837168 0.546946i \(-0.815790\pi\)
0.892253 + 0.451535i \(0.149123\pi\)
\(594\) 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 0.524734 0.851266i \(-0.324165\pi\)
−0.999585 + 0.0287997i \(0.990831\pi\)
\(600\) 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 −0.708643 0.705567i \(-0.750692\pi\)
0.965361 + 0.260919i \(0.0840256\pi\)
\(608\) 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 0.746573 0.665303i \(-0.231698\pi\)
−0.949456 + 0.313900i \(0.898364\pi\)
\(614\) −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 0.946415 + 0.322954i \(0.104676\pi\)
−0.193521 + 0.981096i \(0.561991\pi\)
\(620\) 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 0.620286 + 0.784376i \(0.287016\pi\)
0.369146 + 0.929371i \(0.379650\pi\)
\(642\) 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 0.728337 0.685219i \(-0.240294\pi\)
−0.957586 + 0.288149i \(0.906960\pi\)
\(648\) 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 −0.929929 0.367738i \(-0.880132\pi\)
0.783435 + 0.621473i \(0.213466\pi\)
\(654\) 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 0.960933 0.276780i \(-0.0892672\pi\)
−0.720165 + 0.693803i \(0.755934\pi\)
\(662\) −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 −0.278932 0.960311i \(-0.589980\pi\)
0.971120 0.238593i \(-0.0766862\pi\)
\(678\) 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 −0.999844 0.0176767i \(-0.994373\pi\)
0.484613 0.874728i \(-0.338960\pi\)
\(684\) 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 −0.994902 0.100846i \(-0.967845\pi\)
0.584786 + 0.811187i \(0.301178\pi\)
\(692\) −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 −0.367998 0.929827i \(-0.619957\pi\)
0.989252 0.146218i \(-0.0467101\pi\)
\(710\) −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 −0.735239 0.677808i \(-0.762930\pi\)
0.954618 + 0.297832i \(0.0962634\pi\)
\(720\) 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 −0.795694 0.605699i \(-0.792893\pi\)
0.922398 + 0.386241i \(0.126227\pi\)
\(734\) −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 0.997810 0.0661431i \(-0.0210694\pi\)
−0.556187 + 0.831057i \(0.687736\pi\)
\(740\) −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 −0.990920 0.134453i \(-0.957072\pi\)
0.611900 + 0.790935i \(0.290406\pi\)
\(752\) −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 −0.885527 0.464588i \(-0.846203\pi\)
0.845108 + 0.534595i \(0.179536\pi\)
\(762\) 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 −0.885501 0.464637i \(-0.846185\pi\)
0.0403629 0.999185i \(-0.487149\pi\)
\(774\) 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 0.935124 0.354319i \(-0.115287\pi\)
−0.774412 + 0.632682i \(0.781954\pi\)
\(788\) −9224.62 15977.5i −0.417022 0.722304i
\(789\) 0 0
\(790\) −12976.8 −0.584424