Properties

Label 882.4.g.k.667.1
Level $882$
Weight $4$
Character 882.667
Analytic conductor $52.040$
Analytic rank $0$
Dimension $2$
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: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 14)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 667.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 882.667
Dual form 882.4.g.k.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(7.00000 - 12.1244i) q^{5} +8.00000 q^{8} +O(q^{10})\) \(q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(7.00000 - 12.1244i) q^{5} +8.00000 q^{8} +(14.0000 + 24.2487i) q^{10} +(-14.0000 - 24.2487i) q^{11} -18.0000 q^{13} +(-8.00000 + 13.8564i) q^{16} +(-37.0000 - 64.0859i) q^{17} +(40.0000 - 69.2820i) q^{19} -56.0000 q^{20} +56.0000 q^{22} +(-56.0000 + 96.9948i) q^{23} +(-35.5000 - 61.4878i) q^{25} +(18.0000 - 31.1769i) q^{26} -190.000 q^{29} +(36.0000 + 62.3538i) q^{31} +(-16.0000 - 27.7128i) q^{32} +148.000 q^{34} +(173.000 - 299.645i) q^{37} +(80.0000 + 138.564i) q^{38} +(56.0000 - 96.9948i) q^{40} +162.000 q^{41} -412.000 q^{43} +(-56.0000 + 96.9948i) q^{44} +(-112.000 - 193.990i) q^{46} +(-12.0000 + 20.7846i) q^{47} +142.000 q^{50} +(36.0000 + 62.3538i) q^{52} +(159.000 + 275.396i) q^{53} -392.000 q^{55} +(190.000 - 329.090i) q^{58} +(100.000 + 173.205i) q^{59} +(-99.0000 + 171.473i) q^{61} -144.000 q^{62} +64.0000 q^{64} +(-126.000 + 218.238i) q^{65} +(358.000 + 620.074i) q^{67} +(-148.000 + 256.344i) q^{68} -392.000 q^{71} +(269.000 + 465.922i) q^{73} +(346.000 + 599.290i) q^{74} -320.000 q^{76} +(-120.000 + 207.846i) q^{79} +(112.000 + 193.990i) q^{80} +(-162.000 + 280.592i) q^{82} -1072.00 q^{83} -1036.00 q^{85} +(412.000 - 713.605i) q^{86} +(-112.000 - 193.990i) q^{88} +(-405.000 + 701.481i) q^{89} +448.000 q^{92} +(-24.0000 - 41.5692i) q^{94} +(-560.000 - 969.948i) q^{95} -1354.00 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{2} - 4q^{4} + 14q^{5} + 16q^{8} + O(q^{10}) \) \( 2q - 2q^{2} - 4q^{4} + 14q^{5} + 16q^{8} + 28q^{10} - 28q^{11} - 36q^{13} - 16q^{16} - 74q^{17} + 80q^{19} - 112q^{20} + 112q^{22} - 112q^{23} - 71q^{25} + 36q^{26} - 380q^{29} + 72q^{31} - 32q^{32} + 296q^{34} + 346q^{37} + 160q^{38} + 112q^{40} + 324q^{41} - 824q^{43} - 112q^{44} - 224q^{46} - 24q^{47} + 284q^{50} + 72q^{52} + 318q^{53} - 784q^{55} + 380q^{58} + 200q^{59} - 198q^{61} - 288q^{62} + 128q^{64} - 252q^{65} + 716q^{67} - 296q^{68} - 784q^{71} + 538q^{73} + 692q^{74} - 640q^{76} - 240q^{79} + 224q^{80} - 324q^{82} - 2144q^{83} - 2072q^{85} + 824q^{86} - 224q^{88} - 810q^{89} + 896q^{92} - 48q^{94} - 1120q^{95} - 2708q^{97} + O(q^{100}) \)

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
\(5\) 7.00000 12.1244i 0.626099 1.08444i −0.362228 0.932089i \(-0.617984\pi\)
0.988327 0.152346i \(-0.0486828\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 8.00000 0.353553
\(9\) 0 0
\(10\) 14.0000 + 24.2487i 0.442719 + 0.766812i
\(11\) −14.0000 24.2487i −0.383742 0.664660i 0.607852 0.794050i \(-0.292031\pi\)
−0.991594 + 0.129390i \(0.958698\pi\)
\(12\) 0 0
\(13\) −18.0000 −0.384023 −0.192012 0.981393i \(-0.561501\pi\)
−0.192012 + 0.981393i \(0.561501\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −8.00000 + 13.8564i −0.125000 + 0.216506i
\(17\) −37.0000 64.0859i −0.527872 0.914301i −0.999472 0.0324882i \(-0.989657\pi\)
0.471600 0.881812i \(-0.343676\pi\)
\(18\) 0 0
\(19\) 40.0000 69.2820i 0.482980 0.836547i −0.516829 0.856089i \(-0.672888\pi\)
0.999809 + 0.0195422i \(0.00622087\pi\)
\(20\) −56.0000 −0.626099
\(21\) 0 0
\(22\) 56.0000 0.542693
\(23\) −56.0000 + 96.9948i −0.507687 + 0.879340i 0.492273 + 0.870441i \(0.336166\pi\)
−0.999960 + 0.00889936i \(0.997167\pi\)
\(24\) 0 0
\(25\) −35.5000 61.4878i −0.284000 0.491902i
\(26\) 18.0000 31.1769i 0.135773 0.235165i
\(27\) 0 0
\(28\) 0 0
\(29\) −190.000 −1.21662 −0.608312 0.793698i \(-0.708153\pi\)
−0.608312 + 0.793698i \(0.708153\pi\)
\(30\) 0 0
\(31\) 36.0000 + 62.3538i 0.208574 + 0.361261i 0.951266 0.308373i \(-0.0997845\pi\)
−0.742692 + 0.669634i \(0.766451\pi\)
\(32\) −16.0000 27.7128i −0.0883883 0.153093i
\(33\) 0 0
\(34\) 148.000 0.746523
\(35\) 0 0
\(36\) 0 0
\(37\) 173.000 299.645i 0.768676 1.33139i −0.169605 0.985512i \(-0.554249\pi\)
0.938281 0.345874i \(-0.112418\pi\)
\(38\) 80.0000 + 138.564i 0.341519 + 0.591528i
\(39\) 0 0
\(40\) 56.0000 96.9948i 0.221359 0.383406i
\(41\) 162.000 0.617077 0.308538 0.951212i \(-0.400160\pi\)
0.308538 + 0.951212i \(0.400160\pi\)
\(42\) 0 0
\(43\) −412.000 −1.46115 −0.730575 0.682833i \(-0.760748\pi\)
−0.730575 + 0.682833i \(0.760748\pi\)
\(44\) −56.0000 + 96.9948i −0.191871 + 0.332330i
\(45\) 0 0
\(46\) −112.000 193.990i −0.358989 0.621787i
\(47\) −12.0000 + 20.7846i −0.0372421 + 0.0645053i −0.884046 0.467401i \(-0.845191\pi\)
0.846804 + 0.531906i \(0.178524\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 142.000 0.401637
\(51\) 0 0
\(52\) 36.0000 + 62.3538i 0.0960058 + 0.166287i
\(53\) 159.000 + 275.396i 0.412082 + 0.713746i 0.995117 0.0987002i \(-0.0314685\pi\)
−0.583036 + 0.812447i \(0.698135\pi\)
\(54\) 0 0
\(55\) −392.000 −0.961041
\(56\) 0 0
\(57\) 0 0
\(58\) 190.000 329.090i 0.430142 0.745027i
\(59\) 100.000 + 173.205i 0.220659 + 0.382193i 0.955008 0.296579i \(-0.0958458\pi\)
−0.734349 + 0.678772i \(0.762512\pi\)
\(60\) 0 0
\(61\) −99.0000 + 171.473i −0.207798 + 0.359916i −0.951020 0.309128i \(-0.899963\pi\)
0.743223 + 0.669044i \(0.233296\pi\)
\(62\) −144.000 −0.294968
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −126.000 + 218.238i −0.240437 + 0.416448i
\(66\) 0 0
\(67\) 358.000 + 620.074i 0.652786 + 1.13066i 0.982444 + 0.186558i \(0.0597332\pi\)
−0.329658 + 0.944100i \(0.606933\pi\)
\(68\) −148.000 + 256.344i −0.263936 + 0.457150i
\(69\) 0 0
\(70\) 0 0
\(71\) −392.000 −0.655237 −0.327619 0.944810i \(-0.606246\pi\)
−0.327619 + 0.944810i \(0.606246\pi\)
\(72\) 0 0
\(73\) 269.000 + 465.922i 0.431289 + 0.747014i 0.996985 0.0776001i \(-0.0247257\pi\)
−0.565696 + 0.824614i \(0.691392\pi\)
\(74\) 346.000 + 599.290i 0.543536 + 0.941432i
\(75\) 0 0
\(76\) −320.000 −0.482980
\(77\) 0 0
\(78\) 0 0
\(79\) −120.000 + 207.846i −0.170899 + 0.296006i −0.938735 0.344641i \(-0.888001\pi\)
0.767835 + 0.640647i \(0.221334\pi\)
\(80\) 112.000 + 193.990i 0.156525 + 0.271109i
\(81\) 0 0
\(82\) −162.000 + 280.592i −0.218170 + 0.377881i
\(83\) −1072.00 −1.41768 −0.708839 0.705370i \(-0.750781\pi\)
−0.708839 + 0.705370i \(0.750781\pi\)
\(84\) 0 0
\(85\) −1036.00 −1.32200
\(86\) 412.000 713.605i 0.516594 0.894767i
\(87\) 0 0
\(88\) −112.000 193.990i −0.135673 0.234993i
\(89\) −405.000 + 701.481i −0.482359 + 0.835470i −0.999795 0.0202521i \(-0.993553\pi\)
0.517436 + 0.855722i \(0.326886\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 448.000 0.507687
\(93\) 0 0
\(94\) −24.0000 41.5692i −0.0263342 0.0456121i
\(95\) −560.000 969.948i −0.604787 1.04752i
\(96\) 0 0
\(97\) −1354.00 −1.41730 −0.708649 0.705561i \(-0.750695\pi\)
−0.708649 + 0.705561i \(0.750695\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −142.000 + 245.951i −0.142000 + 0.245951i
\(101\) 679.000 + 1176.06i 0.668941 + 1.15864i 0.978201 + 0.207662i \(0.0665854\pi\)
−0.309260 + 0.950978i \(0.600081\pi\)
\(102\) 0 0
\(103\) −416.000 + 720.533i −0.397958 + 0.689284i −0.993474 0.114060i \(-0.963614\pi\)
0.595516 + 0.803344i \(0.296948\pi\)
\(104\) −144.000 −0.135773
\(105\) 0 0
\(106\) −636.000 −0.582772
\(107\) 222.000 384.515i 0.200575 0.347406i −0.748139 0.663542i \(-0.769052\pi\)
0.948714 + 0.316136i \(0.102386\pi\)
\(108\) 0 0
\(109\) −935.000 1619.47i −0.821622 1.42309i −0.904474 0.426529i \(-0.859736\pi\)
0.0828525 0.996562i \(-0.473597\pi\)
\(110\) 392.000 678.964i 0.339779 0.588515i
\(111\) 0 0
\(112\) 0 0
\(113\) −1378.00 −1.14718 −0.573590 0.819143i \(-0.694450\pi\)
−0.573590 + 0.819143i \(0.694450\pi\)
\(114\) 0 0
\(115\) 784.000 + 1357.93i 0.635725 + 1.10111i
\(116\) 380.000 + 658.179i 0.304156 + 0.526814i
\(117\) 0 0
\(118\) −400.000 −0.312059
\(119\) 0 0
\(120\) 0 0
\(121\) 273.500 473.716i 0.205485 0.355910i
\(122\) −198.000 342.946i −0.146935 0.254499i
\(123\) 0 0
\(124\) 144.000 249.415i 0.104287 0.180630i
\(125\) 756.000 0.540950
\(126\) 0 0
\(127\) 1944.00 1.35828 0.679142 0.734007i \(-0.262352\pi\)
0.679142 + 0.734007i \(0.262352\pi\)
\(128\) −64.0000 + 110.851i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −252.000 436.477i −0.170014 0.294473i
\(131\) 424.000 734.390i 0.282787 0.489801i −0.689283 0.724492i \(-0.742074\pi\)
0.972070 + 0.234691i \(0.0754078\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −1432.00 −0.923179
\(135\) 0 0
\(136\) −296.000 512.687i −0.186631 0.323254i
\(137\) −1483.00 2568.63i −0.924827 1.60185i −0.791840 0.610729i \(-0.790877\pi\)
−0.132987 0.991118i \(-0.542457\pi\)
\(138\) 0 0
\(139\) −2800.00 −1.70858 −0.854291 0.519795i \(-0.826008\pi\)
−0.854291 + 0.519795i \(0.826008\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 392.000 678.964i 0.231661 0.401249i
\(143\) 252.000 + 436.477i 0.147366 + 0.255245i
\(144\) 0 0
\(145\) −1330.00 + 2303.63i −0.761728 + 1.31935i
\(146\) −1076.00 −0.609934
\(147\) 0 0
\(148\) −1384.00 −0.768676
\(149\) 255.000 441.673i 0.140204 0.242841i −0.787369 0.616482i \(-0.788557\pi\)
0.927573 + 0.373641i \(0.121891\pi\)
\(150\) 0 0
\(151\) −296.000 512.687i −0.159524 0.276304i 0.775173 0.631749i \(-0.217663\pi\)
−0.934697 + 0.355445i \(0.884329\pi\)
\(152\) 320.000 554.256i 0.170759 0.295764i
\(153\) 0 0
\(154\) 0 0
\(155\) 1008.00 0.522352
\(156\) 0 0
\(157\) −1343.00 2326.14i −0.682695 1.18246i −0.974155 0.225879i \(-0.927475\pi\)
0.291461 0.956583i \(-0.405859\pi\)
\(158\) −240.000 415.692i −0.120844 0.209308i
\(159\) 0 0
\(160\) −448.000 −0.221359
\(161\) 0 0
\(162\) 0 0
\(163\) 506.000 876.418i 0.243147 0.421143i −0.718462 0.695566i \(-0.755154\pi\)
0.961609 + 0.274423i \(0.0884869\pi\)
\(164\) −324.000 561.184i −0.154269 0.267202i
\(165\) 0 0
\(166\) 1072.00 1856.76i 0.501225 0.868147i
\(167\) 544.000 0.252072 0.126036 0.992026i \(-0.459775\pi\)
0.126036 + 0.992026i \(0.459775\pi\)
\(168\) 0 0
\(169\) −1873.00 −0.852526
\(170\) 1036.00 1794.40i 0.467397 0.809556i
\(171\) 0 0
\(172\) 824.000 + 1427.21i 0.365287 + 0.632696i
\(173\) −929.000 + 1609.08i −0.408269 + 0.707143i −0.994696 0.102859i \(-0.967201\pi\)
0.586427 + 0.810002i \(0.300534\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 448.000 0.191871
\(177\) 0 0
\(178\) −810.000 1402.96i −0.341079 0.590766i
\(179\) −150.000 259.808i −0.0626342 0.108486i 0.833008 0.553261i \(-0.186617\pi\)
−0.895642 + 0.444775i \(0.853283\pi\)
\(180\) 0 0
\(181\) 2358.00 0.968336 0.484168 0.874975i \(-0.339122\pi\)
0.484168 + 0.874975i \(0.339122\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −448.000 + 775.959i −0.179495 + 0.310894i
\(185\) −2422.00 4195.03i −0.962535 1.66716i
\(186\) 0 0
\(187\) −1036.00 + 1794.40i −0.405133 + 0.701710i
\(188\) 96.0000 0.0372421
\(189\) 0 0
\(190\) 2240.00 0.855298
\(191\) 696.000 1205.51i 0.263669 0.456688i −0.703545 0.710651i \(-0.748401\pi\)
0.967214 + 0.253962i \(0.0817340\pi\)
\(192\) 0 0
\(193\) −889.000 1539.79i −0.331563 0.574284i 0.651256 0.758858i \(-0.274243\pi\)
−0.982818 + 0.184575i \(0.940909\pi\)
\(194\) 1354.00 2345.20i 0.501090 0.867914i
\(195\) 0 0
\(196\) 0 0
\(197\) −1214.00 −0.439055 −0.219528 0.975606i \(-0.570452\pi\)
−0.219528 + 0.975606i \(0.570452\pi\)
\(198\) 0 0
\(199\) 520.000 + 900.666i 0.185235 + 0.320837i 0.943656 0.330929i \(-0.107362\pi\)
−0.758420 + 0.651766i \(0.774029\pi\)
\(200\) −284.000 491.902i −0.100409 0.173914i
\(201\) 0 0
\(202\) −2716.00 −0.946025
\(203\) 0 0
\(204\) 0 0
\(205\) 1134.00 1964.15i 0.386351 0.669180i
\(206\) −832.000 1441.07i −0.281399 0.487397i
\(207\) 0 0
\(208\) 144.000 249.415i 0.0480029 0.0831435i
\(209\) −2240.00 −0.741359
\(210\) 0 0
\(211\) −3868.00 −1.26201 −0.631005 0.775779i \(-0.717357\pi\)
−0.631005 + 0.775779i \(0.717357\pi\)
\(212\) 636.000 1101.58i 0.206041 0.356873i
\(213\) 0 0
\(214\) 444.000 + 769.031i 0.141828 + 0.245653i
\(215\) −2884.00 + 4995.23i −0.914824 + 1.58452i
\(216\) 0 0
\(217\) 0 0
\(218\) 3740.00 1.16195
\(219\) 0 0
\(220\) 784.000 + 1357.93i 0.240260 + 0.416143i
\(221\) 666.000 + 1153.55i 0.202715 + 0.351113i
\(222\) 0 0
\(223\) −3968.00 −1.19156 −0.595778 0.803149i \(-0.703156\pi\)
−0.595778 + 0.803149i \(0.703156\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 1378.00 2386.77i 0.405589 0.702501i
\(227\) 1968.00 + 3408.68i 0.575422 + 0.996660i 0.995996 + 0.0894015i \(0.0284954\pi\)
−0.420574 + 0.907258i \(0.638171\pi\)
\(228\) 0 0
\(229\) 2405.00 4165.58i 0.694004 1.20205i −0.276512 0.961011i \(-0.589178\pi\)
0.970515 0.241039i \(-0.0774883\pi\)
\(230\) −3136.00 −0.899051
\(231\) 0 0
\(232\) −1520.00 −0.430142
\(233\) −1091.00 + 1889.67i −0.306754 + 0.531314i −0.977650 0.210237i \(-0.932576\pi\)
0.670896 + 0.741551i \(0.265910\pi\)
\(234\) 0 0
\(235\) 168.000 + 290.985i 0.0466345 + 0.0807734i
\(236\) 400.000 692.820i 0.110330 0.191096i
\(237\) 0 0
\(238\) 0 0
\(239\) 3000.00 0.811941 0.405970 0.913886i \(-0.366934\pi\)
0.405970 + 0.913886i \(0.366934\pi\)
\(240\) 0 0
\(241\) 1021.00 + 1768.42i 0.272898 + 0.472673i 0.969603 0.244685i \(-0.0786845\pi\)
−0.696705 + 0.717358i \(0.745351\pi\)
\(242\) 547.000 + 947.432i 0.145300 + 0.251666i
\(243\) 0 0
\(244\) 792.000 0.207798
\(245\) 0 0
\(246\) 0 0
\(247\) −720.000 + 1247.08i −0.185476 + 0.321253i
\(248\) 288.000 + 498.831i 0.0737420 + 0.127725i
\(249\) 0 0
\(250\) −756.000 + 1309.43i −0.191255 + 0.331263i
\(251\) −528.000 −0.132777 −0.0663886 0.997794i \(-0.521148\pi\)
−0.0663886 + 0.997794i \(0.521148\pi\)
\(252\) 0 0
\(253\) 3136.00 0.779283
\(254\) −1944.00 + 3367.11i −0.480226 + 0.831776i
\(255\) 0 0
\(256\) −128.000 221.703i −0.0312500 0.0541266i
\(257\) −2817.00 + 4879.19i −0.683734 + 1.18426i 0.290099 + 0.956997i \(0.406312\pi\)
−0.973833 + 0.227265i \(0.927022\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 1008.00 0.240437
\(261\) 0 0
\(262\) 848.000 + 1468.78i 0.199960 + 0.346342i
\(263\) 84.0000 + 145.492i 0.0196945 + 0.0341119i 0.875705 0.482847i \(-0.160397\pi\)
−0.856010 + 0.516959i \(0.827064\pi\)
\(264\) 0 0
\(265\) 4452.00 1.03202
\(266\) 0 0
\(267\) 0 0
\(268\) 1432.00 2480.30i 0.326393 0.565329i
\(269\) 655.000 + 1134.49i 0.148461 + 0.257142i 0.930659 0.365888i \(-0.119235\pi\)
−0.782198 + 0.623030i \(0.785901\pi\)
\(270\) 0 0
\(271\) −1104.00 + 1912.18i −0.247466 + 0.428623i −0.962822 0.270137i \(-0.912931\pi\)
0.715356 + 0.698760i \(0.246264\pi\)
\(272\) 1184.00 0.263936
\(273\) 0 0
\(274\) 5932.00 1.30790
\(275\) −994.000 + 1721.66i −0.217965 + 0.377527i
\(276\) 0 0
\(277\) −2647.00 4584.74i −0.574162 0.994477i −0.996132 0.0878678i \(-0.971995\pi\)
0.421970 0.906610i \(-0.361339\pi\)
\(278\) 2800.00 4849.74i 0.604075 1.04629i
\(279\) 0 0
\(280\) 0 0
\(281\) −3242.00 −0.688262 −0.344131 0.938922i \(-0.611826\pi\)
−0.344131 + 0.938922i \(0.611826\pi\)
\(282\) 0 0
\(283\) −796.000 1378.71i −0.167199 0.289597i 0.770235 0.637760i \(-0.220139\pi\)
−0.937434 + 0.348163i \(0.886806\pi\)
\(284\) 784.000 + 1357.93i 0.163809 + 0.283726i
\(285\) 0 0
\(286\) −1008.00 −0.208407
\(287\) 0 0
\(288\) 0 0
\(289\) −281.500 + 487.572i −0.0572970 + 0.0992413i
\(290\) −2660.00 4607.26i −0.538623 0.932922i
\(291\) 0 0
\(292\) 1076.00 1863.69i 0.215644 0.373507i
\(293\) −5022.00 −1.00133 −0.500663 0.865642i \(-0.666910\pi\)
−0.500663 + 0.865642i \(0.666910\pi\)
\(294\) 0 0
\(295\) 2800.00 0.552618
\(296\) 1384.00 2397.16i 0.271768 0.470716i
\(297\) 0 0
\(298\) 510.000 + 883.346i 0.0991393 + 0.171714i
\(299\) 1008.00 1745.91i 0.194964 0.337687i
\(300\) 0 0
\(301\) 0 0
\(302\) 1184.00 0.225601
\(303\) 0 0
\(304\) 640.000 + 1108.51i 0.120745 + 0.209137i
\(305\) 1386.00 + 2400.62i 0.260204 + 0.450686i
\(306\) 0 0
\(307\) 9536.00 1.77280 0.886398 0.462924i \(-0.153200\pi\)
0.886398 + 0.462924i \(0.153200\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −1008.00 + 1745.91i −0.184679 + 0.319874i
\(311\) 484.000 + 838.313i 0.0882480 + 0.152850i 0.906771 0.421624i \(-0.138540\pi\)
−0.818523 + 0.574474i \(0.805207\pi\)
\(312\) 0 0
\(313\) 1529.00 2648.31i 0.276116 0.478246i −0.694300 0.719685i \(-0.744286\pi\)
0.970416 + 0.241439i \(0.0776194\pi\)
\(314\) 5372.00 0.965476
\(315\) 0 0
\(316\) 960.000 0.170899
\(317\) −2493.00 + 4318.00i −0.441706 + 0.765057i −0.997816 0.0660512i \(-0.978960\pi\)
0.556110 + 0.831109i \(0.312293\pi\)
\(318\) 0 0
\(319\) 2660.00 + 4607.26i 0.466870 + 0.808642i
\(320\) 448.000 775.959i 0.0782624 0.135554i
\(321\) 0 0
\(322\) 0 0
\(323\) −5920.00 −1.01981
\(324\) 0 0
\(325\) 639.000 + 1106.78i 0.109063 + 0.188902i
\(326\) 1012.00 + 1752.84i 0.171931 + 0.297793i
\(327\) 0 0
\(328\) 1296.00 0.218170
\(329\) 0 0
\(330\) 0 0
\(331\) −4306.00 + 7458.21i −0.715043 + 1.23849i 0.247900 + 0.968786i \(0.420259\pi\)
−0.962943 + 0.269705i \(0.913074\pi\)
\(332\) 2144.00 + 3713.52i 0.354420 + 0.613873i
\(333\) 0 0
\(334\) −544.000 + 942.236i −0.0891208 + 0.154362i
\(335\) 10024.0 1.63483
\(336\) 0 0
\(337\) −10206.0 −1.64972 −0.824861 0.565336i \(-0.808747\pi\)
−0.824861 + 0.565336i \(0.808747\pi\)
\(338\) 1873.00 3244.13i 0.301414 0.522064i
\(339\) 0 0
\(340\) 2072.00 + 3588.81i 0.330500 + 0.572443i
\(341\) 1008.00 1745.91i 0.160077 0.277262i
\(342\) 0 0
\(343\) 0 0
\(344\) −3296.00 −0.516594
\(345\) 0 0
\(346\) −1858.00 3218.15i −0.288690 0.500026i
\(347\) 1002.00 + 1735.51i 0.155015 + 0.268494i 0.933064 0.359709i \(-0.117124\pi\)
−0.778050 + 0.628203i \(0.783791\pi\)
\(348\) 0 0
\(349\) −1330.00 −0.203992 −0.101996 0.994785i \(-0.532523\pi\)
−0.101996 + 0.994785i \(0.532523\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −448.000 + 775.959i −0.0678366 + 0.117496i
\(353\) −489.000 846.973i −0.0737304 0.127705i 0.826803 0.562492i \(-0.190157\pi\)
−0.900533 + 0.434787i \(0.856824\pi\)
\(354\) 0 0
\(355\) −2744.00 + 4752.75i −0.410243 + 0.710562i
\(356\) 3240.00 0.482359
\(357\) 0 0
\(358\) 600.000 0.0885782
\(359\) −4840.00 + 8383.13i −0.711547 + 1.23244i 0.252729 + 0.967537i \(0.418672\pi\)
−0.964276 + 0.264899i \(0.914661\pi\)
\(360\) 0 0
\(361\) 229.500 + 397.506i 0.0334597 + 0.0579539i
\(362\) −2358.00 + 4084.18i −0.342358 + 0.592982i
\(363\) 0 0
\(364\) 0 0
\(365\) 7532.00 1.08012
\(366\) 0 0
\(367\) −4328.00 7496.32i −0.615585 1.06622i −0.990282 0.139077i \(-0.955586\pi\)
0.374696 0.927148i \(-0.377747\pi\)
\(368\) −896.000 1551.92i −0.126922 0.219835i
\(369\) 0 0
\(370\) 9688.00 1.36123
\(371\) 0 0
\(372\) 0 0
\(373\) −2639.00 + 4570.88i −0.366333 + 0.634508i −0.988989 0.147988i \(-0.952720\pi\)
0.622656 + 0.782496i \(0.286054\pi\)
\(374\) −2072.00 3588.81i −0.286472 0.496184i
\(375\) 0 0
\(376\) −96.0000 + 166.277i −0.0131671 + 0.0228061i
\(377\) 3420.00 0.467212
\(378\) 0 0
\(379\) 6340.00 0.859272 0.429636 0.903002i \(-0.358642\pi\)
0.429636 + 0.903002i \(0.358642\pi\)
\(380\) −2240.00 + 3879.79i −0.302394 + 0.523761i
\(381\) 0 0
\(382\) 1392.00 + 2411.01i 0.186442 + 0.322927i
\(383\) 3116.00 5397.07i 0.415718 0.720045i −0.579785 0.814769i \(-0.696864\pi\)
0.995504 + 0.0947240i \(0.0301968\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 3556.00 0.468901
\(387\) 0 0
\(388\) 2708.00 + 4690.39i 0.354324 + 0.613708i
\(389\) −7405.00 12825.8i −0.965163 1.67171i −0.709177 0.705031i \(-0.750933\pi\)
−0.255986 0.966680i \(-0.582400\pi\)
\(390\) 0 0
\(391\) 8288.00 1.07197
\(392\) 0 0
\(393\) 0 0
\(394\) 1214.00 2102.71i 0.155230 0.268865i
\(395\) 1680.00 + 2909.85i 0.214000 + 0.370659i
\(396\) 0 0
\(397\) 2577.00 4463.49i 0.325783 0.564273i −0.655887 0.754859i \(-0.727705\pi\)
0.981671 + 0.190586i \(0.0610387\pi\)
\(398\) −2080.00 −0.261962
\(399\) 0 0
\(400\) 1136.00 0.142000
\(401\) 1641.00 2842.30i 0.204358 0.353959i −0.745570 0.666427i \(-0.767823\pi\)
0.949928 + 0.312469i \(0.101156\pi\)
\(402\) 0 0
\(403\) −648.000 1122.37i −0.0800972 0.138732i
\(404\) 2716.00 4704.25i 0.334470 0.579320i
\(405\) 0 0
\(406\) 0 0
\(407\) −9688.00 −1.17989
\(408\) 0 0
\(409\) 2905.00 + 5031.61i 0.351205 + 0.608306i 0.986461 0.163996i \(-0.0524386\pi\)
−0.635256 + 0.772302i \(0.719105\pi\)
\(410\) 2268.00 + 3928.29i 0.273192 + 0.473182i
\(411\) 0 0
\(412\) 3328.00 0.397958
\(413\) 0 0
\(414\) 0 0
\(415\) −7504.00 + 12997.3i −0.887607 + 1.53738i
\(416\) 288.000 + 498.831i 0.0339432 + 0.0587913i
\(417\) 0 0
\(418\) 2240.00 3879.79i 0.262110 0.453988i
\(419\) 13560.0 1.58102 0.790512 0.612446i \(-0.209814\pi\)
0.790512 + 0.612446i \(0.209814\pi\)
\(420\) 0 0
\(421\) −738.000 −0.0854345 −0.0427172 0.999087i \(-0.513601\pi\)
−0.0427172 + 0.999087i \(0.513601\pi\)
\(422\) 3868.00 6699.57i 0.446188 0.772820i
\(423\) 0 0
\(424\) 1272.00 + 2203.17i 0.145693 + 0.252347i
\(425\) −2627.00 + 4550.10i −0.299831 + 0.519323i
\(426\) 0 0
\(427\) 0 0
\(428\) −1776.00 −0.200575
\(429\) 0 0
\(430\) −5768.00 9990.47i −0.646878 1.12043i
\(431\) 636.000 + 1101.58i 0.0710790 + 0.123112i 0.899374 0.437179i \(-0.144022\pi\)
−0.828295 + 0.560292i \(0.810689\pi\)
\(432\) 0 0
\(433\) 5062.00 0.561811 0.280906 0.959735i \(-0.409365\pi\)
0.280906 + 0.959735i \(0.409365\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −3740.00 + 6477.87i −0.410811 + 0.711545i
\(437\) 4480.00 + 7759.59i 0.490406 + 0.849408i
\(438\) 0 0
\(439\) 2820.00 4884.38i 0.306586 0.531023i −0.671027 0.741433i \(-0.734147\pi\)
0.977613 + 0.210410i \(0.0674800\pi\)
\(440\) −3136.00 −0.339779
\(441\) 0 0
\(442\) −2664.00 −0.286682
\(443\) 6694.00 11594.3i 0.717927 1.24349i −0.243893 0.969802i \(-0.578425\pi\)
0.961820 0.273683i \(-0.0882421\pi\)
\(444\) 0 0
\(445\) 5670.00 + 9820.73i 0.604008 + 1.04617i
\(446\) 3968.00 6872.78i 0.421279 0.729676i
\(447\) 0 0
\(448\) 0 0
\(449\) 3230.00 0.339495 0.169747 0.985488i \(-0.445705\pi\)
0.169747 + 0.985488i \(0.445705\pi\)
\(450\) 0 0
\(451\) −2268.00 3928.29i −0.236798 0.410146i
\(452\) 2756.00 + 4773.53i 0.286795 + 0.496743i
\(453\) 0 0
\(454\) −7872.00 −0.813769
\(455\) 0 0
\(456\) 0 0
\(457\) 5323.00 9219.71i 0.544857 0.943719i −0.453759 0.891124i \(-0.649917\pi\)
0.998616 0.0525950i \(-0.0167492\pi\)
\(458\) 4810.00 + 8331.16i 0.490735 + 0.849978i
\(459\) 0 0
\(460\) 3136.00 5431.71i 0.317863 0.550554i
\(461\) 7282.00 0.735698 0.367849 0.929886i \(-0.380094\pi\)
0.367849 + 0.929886i \(0.380094\pi\)
\(462\) 0 0
\(463\) 12688.0 1.27357 0.636783 0.771043i \(-0.280265\pi\)
0.636783 + 0.771043i \(0.280265\pi\)
\(464\) 1520.00 2632.72i 0.152078 0.263407i
\(465\) 0 0
\(466\) −2182.00 3779.33i −0.216908 0.375696i
\(467\) 1408.00 2438.73i 0.139517 0.241651i −0.787797 0.615935i \(-0.788778\pi\)
0.927314 + 0.374285i \(0.122112\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −672.000 −0.0659512
\(471\) 0 0
\(472\) 800.000 + 1385.64i 0.0780148 + 0.135126i
\(473\) 5768.00 + 9990.47i 0.560704 + 0.971168i
\(474\) 0 0
\(475\) −5680.00 −0.548666
\(476\) 0 0
\(477\) 0 0
\(478\) −3000.00 + 5196.15i −0.287064 + 0.497210i
\(479\) 1580.00 + 2736.64i 0.150714 + 0.261044i 0.931490 0.363766i \(-0.118509\pi\)
−0.780776 + 0.624811i \(0.785176\pi\)
\(480\) 0 0
\(481\) −3114.00 + 5393.61i −0.295190 + 0.511283i
\(482\) −4084.00 −0.385936
\(483\) 0 0
\(484\) −2188.00 −0.205485
\(485\) −9478.00 + 16416.4i −0.887369 + 1.53697i
\(486\) 0 0
\(487\) 7088.00 + 12276.8i 0.659523 + 1.14233i 0.980739 + 0.195322i \(0.0625752\pi\)
−0.321216 + 0.947006i \(0.604091\pi\)
\(488\) −792.000 + 1371.78i −0.0734675 + 0.127249i
\(489\) 0 0
\(490\) 0 0
\(491\) 11268.0 1.03568 0.517839 0.855478i \(-0.326737\pi\)
0.517839 + 0.855478i \(0.326737\pi\)
\(492\) 0 0
\(493\) 7030.00 + 12176.3i 0.642222 + 1.11236i
\(494\) −1440.00 2494.15i −0.131151 0.227160i
\(495\) 0 0
\(496\) −1152.00 −0.104287
\(497\) 0 0
\(498\) 0 0
\(499\) 2230.00 3862.47i 0.200057 0.346509i −0.748489 0.663147i \(-0.769221\pi\)
0.948547 + 0.316638i \(0.102554\pi\)
\(500\) −1512.00 2618.86i −0.135237 0.234238i
\(501\) 0 0
\(502\) 528.000 914.523i 0.0469438 0.0813091i
\(503\) −1512.00 −0.134029 −0.0670147 0.997752i \(-0.521347\pi\)
−0.0670147 + 0.997752i \(0.521347\pi\)
\(504\) 0 0
\(505\) 19012.0 1.67529
\(506\) −3136.00 + 5431.71i −0.275518 + 0.477212i
\(507\) 0 0
\(508\) −3888.00 6734.21i −0.339571 0.588154i
\(509\) 5895.00 10210.4i 0.513342 0.889135i −0.486538 0.873660i \(-0.661740\pi\)
0.999880 0.0154756i \(-0.00492624\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 512.000 0.0441942
\(513\) 0 0
\(514\) −5634.00 9758.37i −0.483473 0.837400i
\(515\) 5824.00 + 10087.5i 0.498323 + 0.863120i
\(516\) 0 0
\(517\) 672.000 0.0571654
\(518\) 0 0
\(519\) 0 0
\(520\) −1008.00 + 1745.91i −0.0850072 + 0.147237i
\(521\) −681.000 1179.53i −0.0572652 0.0991862i 0.835972 0.548773i \(-0.184905\pi\)
−0.893237 + 0.449586i \(0.851571\pi\)
\(522\) 0 0
\(523\) 3484.00 6034.47i 0.291290 0.504529i −0.682825 0.730582i \(-0.739249\pi\)
0.974115 + 0.226053i \(0.0725822\pi\)
\(524\) −3392.00 −0.282787
\(525\) 0 0
\(526\) −336.000 −0.0278523
\(527\) 2664.00 4614.18i 0.220200 0.381398i
\(528\) 0 0
\(529\) −188.500 326.492i −0.0154927 0.0268342i
\(530\) −4452.00 + 7711.09i −0.364873 + 0.631978i
\(531\) 0 0
\(532\) 0 0
\(533\) −2916.00 −0.236972
\(534\) 0 0
\(535\) −3108.00 5383.21i −0.251160 0.435022i
\(536\) 2864.00 + 4960.59i 0.230795 + 0.399748i
\(537\) 0 0
\(538\) −2620.00 −0.209956
\(539\) 0 0
\(540\) 0 0
\(541\) −3531.00 + 6115.87i −0.280609 + 0.486029i −0.971535 0.236896i \(-0.923870\pi\)
0.690926 + 0.722926i \(0.257203\pi\)
\(542\) −2208.00 3824.37i −0.174985 0.303082i
\(543\) 0 0
\(544\) −1184.00 + 2050.75i −0.0933154 + 0.161627i
\(545\) −26180.0 −2.05767
\(546\) 0 0
\(547\) −8196.00 −0.640650 −0.320325 0.947308i \(-0.603792\pi\)
−0.320325 + 0.947308i \(0.603792\pi\)
\(548\) −5932.00 + 10274.5i −0.462413 + 0.800923i
\(549\) 0 0
\(550\) −1988.00 3443.32i −0.154125 0.266952i
\(551\) −7600.00 + 13163.6i −0.587606 + 1.01776i
\(552\) 0 0
\(553\) 0 0
\(554\) 10588.0 0.811987
\(555\) 0 0
\(556\) 5600.00 + 9699.48i 0.427146 + 0.739838i
\(557\) −3733.00 6465.75i −0.283972 0.491854i 0.688388 0.725343i \(-0.258319\pi\)
−0.972359 + 0.233490i \(0.924986\pi\)
\(558\) 0 0
\(559\) 7416.00 0.561115
\(560\) 0 0
\(561\) 0 0
\(562\) 3242.00 5615.31i 0.243337 0.421472i
\(563\) −12484.0 21622.9i −0.934526 1.61865i −0.775478 0.631375i \(-0.782491\pi\)
−0.159048 0.987271i \(-0.550842\pi\)
\(564\) 0 0
\(565\) −9646.00 + 16707.4i −0.718248 + 1.24404i
\(566\) 3184.00 0.236455
\(567\) 0 0
\(568\) −3136.00 −0.231661
\(569\) 7125.00 12340.9i 0.524948 0.909237i −0.474630 0.880186i \(-0.657418\pi\)
0.999578 0.0290514i \(-0.00924865\pi\)
\(570\) 0 0
\(571\) −3186.00 5518.31i −0.233503 0.404438i 0.725334 0.688397i \(-0.241685\pi\)
−0.958836 + 0.283959i \(0.908352\pi\)
\(572\) 1008.00 1745.91i 0.0736829 0.127622i
\(573\) 0 0
\(574\) 0 0
\(575\) 7952.00 0.576733
\(576\) 0 0
\(577\) −4183.00 7245.17i −0.301803 0.522739i 0.674741 0.738055i \(-0.264255\pi\)
−0.976545 + 0.215316i \(0.930922\pi\)
\(578\) −563.000 975.145i −0.0405151 0.0701742i
\(579\) 0 0
\(580\) 10640.0 0.761728
\(581\) 0 0
\(582\) 0 0
\(583\) 4452.00 7711.09i 0.316266 0.547789i
\(584\) 2152.00 + 3727.37i 0.152484 + 0.264109i
\(585\) 0 0
\(586\) 5022.00 8698.36i 0.354022 0.613184i
\(587\) 20384.0 1.43328 0.716642 0.697441i \(-0.245678\pi\)
0.716642 + 0.697441i \(0.245678\pi\)
\(588\) 0 0
\(589\) 5760.00 0.402948
\(590\) −2800.00 + 4849.74i −0.195380 + 0.338408i
\(591\) 0 0
\(592\) 2768.00 + 4794.32i 0.192169 + 0.332847i
\(593\) −4689.00 + 8121.59i −0.324712 + 0.562417i −0.981454 0.191698i \(-0.938601\pi\)
0.656742 + 0.754115i \(0.271934\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −2040.00 −0.140204
\(597\) 0 0
\(598\) 2016.00 + 3491.81i 0.137860 + 0.238781i
\(599\) −4500.00 7794.23i −0.306953 0.531659i 0.670741 0.741692i \(-0.265976\pi\)
−0.977694 + 0.210033i \(0.932643\pi\)
\(600\) 0 0
\(601\) −7562.00 −0.513245 −0.256623 0.966512i \(-0.582610\pi\)
−0.256623 + 0.966512i \(0.582610\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −1184.00 + 2050.75i −0.0797620 + 0.138152i
\(605\) −3829.00 6632.02i −0.257307 0.445670i
\(606\) 0 0
\(607\) −1488.00 + 2577.29i −0.0994993 + 0.172338i −0.911478 0.411350i \(-0.865057\pi\)
0.811978 + 0.583688i \(0.198391\pi\)
\(608\) −2560.00 −0.170759
\(609\) 0 0
\(610\) −5544.00 −0.367984
\(611\) 216.000 374.123i 0.0143018 0.0247715i
\(612\) 0 0
\(613\) −2139.00 3704.86i −0.140935 0.244107i 0.786914 0.617063i \(-0.211678\pi\)
−0.927849 + 0.372956i \(0.878344\pi\)
\(614\) −9536.00 + 16516.8i −0.626778 + 1.08561i
\(615\) 0 0
\(616\) 0 0
\(617\) −18794.0 −1.22629 −0.613143 0.789972i \(-0.710095\pi\)
−0.613143 + 0.789972i \(0.710095\pi\)
\(618\) 0 0
\(619\) 9020.00 + 15623.1i 0.585694 + 1.01445i 0.994789 + 0.101959i \(0.0325112\pi\)
−0.409095 + 0.912492i \(0.634155\pi\)
\(620\) −2016.00 3491.81i −0.130588 0.226185i
\(621\) 0 0
\(622\) −1936.00 −0.124801
\(623\) 0 0
\(624\) 0 0
\(625\) 9729.50 16852.0i 0.622688 1.07853i
\(626\) 3058.00 + 5296.61i 0.195243 + 0.338171i
\(627\) 0 0
\(628\) −5372.00 + 9304.58i −0.341347 + 0.591231i
\(629\) −25604.0 −1.62305
\(630\) 0 0
\(631\) −21688.0 −1.36828 −0.684141 0.729350i \(-0.739823\pi\)
−0.684141 + 0.729350i \(0.739823\pi\)
\(632\) −960.000 + 1662.77i −0.0604221 + 0.104654i
\(633\) 0 0
\(634\) −4986.00 8636.01i −0.312333 0.540977i
\(635\) 13608.0 23569.7i 0.850420 1.47297i
\(636\) 0 0
\(637\) 0 0
\(638\) −10640.0 −0.660253
\(639\) 0 0
\(640\) 896.000 + 1551.92i 0.0553399 + 0.0958514i
\(641\) −5279.00 9143.50i −0.325285 0.563411i 0.656285 0.754513i \(-0.272127\pi\)
−0.981570 + 0.191102i \(0.938794\pi\)
\(642\) 0 0
\(643\) 26152.0 1.60394 0.801971 0.597363i \(-0.203785\pi\)
0.801971 + 0.597363i \(0.203785\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 5920.00 10253.7i 0.360556 0.624502i
\(647\) −12792.0 22156.4i −0.777288 1.34630i −0.933499 0.358579i \(-0.883261\pi\)
0.156211 0.987724i \(-0.450072\pi\)
\(648\) 0 0
\(649\) 2800.00 4849.74i 0.169352 0.293327i
\(650\) −2556.00 −0.154238
\(651\) 0 0
\(652\) −4048.00 −0.243147
\(653\) 7599.00 13161.9i 0.455393 0.788764i −0.543317 0.839527i \(-0.682832\pi\)
0.998711 + 0.0507630i \(0.0161653\pi\)
\(654\) 0 0
\(655\) −5936.00 10281.5i −0.354105 0.613328i
\(656\) −1296.00 + 2244.74i −0.0771346 + 0.133601i
\(657\) 0 0
\(658\) 0 0
\(659\) 6100.00 0.360580 0.180290 0.983613i \(-0.442296\pi\)
0.180290 + 0.983613i \(0.442296\pi\)
\(660\) 0 0
\(661\) −1159.00 2007.45i −0.0681995 0.118125i 0.829909 0.557898i \(-0.188392\pi\)
−0.898109 + 0.439773i \(0.855059\pi\)
\(662\) −8612.00 14916.4i −0.505612 0.875745i
\(663\) 0 0
\(664\) −8576.00 −0.501225
\(665\) 0 0
\(666\) 0 0
\(667\) 10640.0 18429.0i 0.617665 1.06983i
\(668\) −1088.00 1884.47i −0.0630179 0.109150i
\(669\) 0 0
\(670\) −10024.0 + 17362.1i −0.578001 + 1.00113i
\(671\) 5544.00 0.318962
\(672\) 0 0
\(673\) −10222.0 −0.585482 −0.292741 0.956192i \(-0.594567\pi\)
−0.292741 + 0.956192i \(0.594567\pi\)
\(674\) 10206.0 17677.3i 0.583265 1.01024i
\(675\) 0 0
\(676\) 3746.00 + 6488.26i 0.213132 + 0.369155i
\(677\) −12717.0 + 22026.5i −0.721941 + 1.25044i 0.238280 + 0.971197i \(0.423416\pi\)
−0.960221 + 0.279242i \(0.909917\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −8288.00 −0.467397
\(681\) 0 0
\(682\) 2016.00 + 3491.81i 0.113192 + 0.196053i
\(683\) −4266.00 7388.93i −0.238996 0.413952i 0.721431 0.692487i \(-0.243485\pi\)
−0.960426 + 0.278534i \(0.910151\pi\)
\(684\) 0 0
\(685\) −41524.0 −2.31613
\(686\) 0 0
\(687\) 0 0
\(688\) 3296.00 5708.84i 0.182644 0.316348i
\(689\) −2862.00 4957.13i −0.158249 0.274095i
\(690\) 0 0
\(691\) 10336.0 17902.5i 0.569030 0.985589i −0.427632 0.903953i \(-0.640652\pi\)
0.996662 0.0816365i \(-0.0260146\pi\)
\(692\) 7432.00 0.408269
\(693\) 0 0
\(694\) −4008.00 −0.219224
\(695\) −19600.0 + 33948.2i −1.06974 + 1.85285i
\(696\) 0 0
\(697\) −5994.00 10381.9i −0.325737 0.564194i
\(698\) 1330.00 2303.63i 0.0721221 0.124919i
\(699\) 0 0
\(700\) 0 0
\(701\) 21458.0 1.15614 0.578072 0.815985i \(-0.303805\pi\)
0.578072 + 0.815985i \(0.303805\pi\)
\(702\) 0 0
\(703\) −13840.0 23971.6i −0.742511 1.28607i
\(704\) −896.000 1551.92i −0.0479677 0.0830825i
\(705\) 0 0
\(706\) 1956.00 0.104271
\(707\) 0 0
\(708\) 0 0
\(709\) 4925.00 8530.35i 0.260878 0.451853i −0.705598 0.708613i \(-0.749321\pi\)
0.966475 + 0.256759i \(0.0826547\pi\)
\(710\) −5488.00 9505.49i −0.290086 0.502443i
\(711\) 0 0
\(712\) −3240.00 + 5611.84i −0.170540 + 0.295383i
\(713\) −8064.00 −0.423561
\(714\) 0 0
\(715\) 7056.00 0.369062
\(716\) −600.000 + 1039.23i −0.0313171 + 0.0542428i
\(717\) 0 0
\(718\) −9680.00 16766.3i −0.503140 0.871464i
\(719\) 9420.00 16315.9i 0.488605 0.846288i −0.511309 0.859397i \(-0.670839\pi\)
0.999914 + 0.0131086i \(0.00417273\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −918.000 −0.0473191
\(723\) 0 0
\(724\) −4716.00 8168.35i −0.242084 0.419302i
\(725\) 6745.00 + 11682.7i 0.345521 + 0.598461i
\(726\) 0 0
\(727\) −37504.0 −1.91327 −0.956634 0.291291i \(-0.905915\pi\)
−0.956634 + 0.291291i \(0.905915\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −7532.00 + 13045.8i −0.381879 + 0.661434i
\(731\) 15244.0 + 26403.4i 0.771299 + 1.33593i
\(732\) 0 0
\(733\) 6669.00 11551.0i 0.336051 0.582057i −0.647635 0.761950i \(-0.724242\pi\)
0.983686 + 0.179894i \(0.0575753\pi\)
\(734\) 17312.0 0.870569
\(735\) 0 0
\(736\) 3584.00 0.179495
\(737\) 10024.0 17362.1i 0.501002 0.867762i
\(738\) 0 0
\(739\) −8550.00 14809.0i −0.425598 0.737157i 0.570878 0.821035i \(-0.306603\pi\)
−0.996476 + 0.0838776i \(0.973270\pi\)
\(740\) −9688.00 + 16780.1i −0.481268 + 0.833580i
\(741\) 0 0
\(742\) 0 0
\(743\) 19632.0 0.969352 0.484676 0.874694i \(-0.338938\pi\)
0.484676 + 0.874694i \(0.338938\pi\)
\(744\) 0 0
\(745\) −3570.00 6183.42i −0.175563 0.304085i
\(746\) −5278.00 9141.76i −0.259037 0.448665i
\(747\) 0 0
\(748\) 8288.00 0.405133
\(749\) 0 0
\(750\) 0 0
\(751\) −16956.0 + 29368.7i −0.823879 + 1.42700i 0.0788938 + 0.996883i \(0.474861\pi\)
−0.902773 + 0.430117i \(0.858472\pi\)
\(752\) −192.000 332.554i −0.00931053 0.0161263i
\(753\) 0 0
\(754\) −3420.00 + 5923.61i −0.165184 + 0.286108i
\(755\) −8288.00 −0.399512
\(756\) 0 0
\(757\) −31386.0 −1.50693 −0.753463 0.657490i \(-0.771618\pi\)
−0.753463 + 0.657490i \(0.771618\pi\)
\(758\) −6340.00 + 10981.2i −0.303798 + 0.526194i
\(759\) 0 0
\(760\) −4480.00 7759.59i −0.213825 0.370355i
\(761\) 17279.0 29928.1i 0.823079 1.42561i −0.0802993 0.996771i \(-0.525588\pi\)
0.903378 0.428844i \(-0.141079\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −5568.00 −0.263669
\(765\) 0 0
\(766\) 6232.00 + 10794.1i 0.293957 + 0.509149i
\(767\) −1800.00 3117.69i −0.0847382 0.146771i
\(768\) 0 0
\(769\) −39130.0 −1.83493 −0.917467 0.397812i \(-0.869769\pi\)
−0.917467 + 0.397812i \(0.869769\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −3556.00 + 6159.17i −0.165781 + 0.287142i
\(773\) 12991.0 + 22501.1i 0.604468 + 1.04697i 0.992135 + 0.125170i \(0.0399476\pi\)
−0.387667 + 0.921799i \(0.626719\pi\)
\(774\) 0 0
\(775\) 2556.00 4427.12i 0.118470 0.205196i
\(776\) −10832.0 −0.501090
\(777\) 0 0
\(778\) 29620.0 1.36495
\(779\) 6480.00 11223.7i 0.298036 0.516214i
\(780\) 0 0
\(781\) 5488.00 + 9505.49i 0.251442 + 0.435510i
\(782\) −8288.00 + 14355.2i −0.379000 + 0.656448i
\(783\) 0 0
\(784\) 0 0
\(785\) −37604.0 −1.70974
\(786\) 0 0
\(787\) 17712.0 + 30678.1i 0.802242 + 1.38952i 0.918137 + 0.396263i \(0.129693\pi\)
−0.115895 + 0.993261i \(0.536974\pi\)
\(788\) 2428.00 + 4205.42i 0.109764 + 0.190117i
\(789\) 0 0
\(790\) −6720.00 −0.302642