Properties

Label 882.4.g.b.361.1
Level $882$
Weight $4$
Character 882.361
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 361.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 882.361
Dual form 882.4.g.b.667.1

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

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

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
\(5\) −7.00000 12.1244i −0.626099 1.08444i −0.988327 0.152346i \(-0.951317\pi\)
0.362228 0.932089i \(-0.382016\pi\)
\(6\) 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 −0.991594 0.129390i \(-0.958698\pi\)
0.607852 + 0.794050i \(0.292031\pi\)
\(12\) 0 0
\(13\) 18.0000 0.384023 0.192012 0.981393i \(-0.438499\pi\)
0.192012 + 0.981393i \(0.438499\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) 37.0000 64.0859i 0.527872 0.914301i −0.471600 0.881812i \(-0.656324\pi\)
0.999472 0.0324882i \(-0.0103431\pi\)
\(18\) 0 0
\(19\) −40.0000 69.2820i −0.482980 0.836547i 0.516829 0.856089i \(-0.327112\pi\)
−0.999809 + 0.0195422i \(0.993779\pi\)
\(20\) 56.0000 0.626099
\(21\) 0 0
\(22\) 56.0000 0.542693
\(23\) −56.0000 96.9948i −0.507687 0.879340i −0.999960 0.00889936i \(-0.997167\pi\)
0.492273 0.870441i \(-0.336166\pi\)
\(24\) 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 \(-0.900216\pi\)
0.742692 + 0.669634i \(0.233549\pi\)
\(32\) −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 0.938281 + 0.345874i \(0.112418\pi\)
−0.169605 + 0.985512i \(0.554249\pi\)
\(38\) −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 \(-0.599840\pi\)
−0.308538 + 0.951212i \(0.599840\pi\)
\(42\) 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 \(-0.154809\pi\)
−0.846804 + 0.531906i \(0.821476\pi\)
\(48\) 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 −0.583036 0.812447i \(-0.698135\pi\)
0.995117 + 0.0987002i \(0.0314685\pi\)
\(54\) 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 \(-0.904154\pi\)
0.734349 + 0.678772i \(0.237488\pi\)
\(60\) 0 0
\(61\) 99.0000 + 171.473i 0.207798 + 0.359916i 0.951020 0.309128i \(-0.100037\pi\)
−0.743223 + 0.669044i \(0.766704\pi\)
\(62\) 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 −0.329658 0.944100i \(-0.606933\pi\)
0.982444 0.186558i \(-0.0597332\pi\)
\(68\) 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 \(-0.975274\pi\)
0.565696 + 0.824614i \(0.308608\pi\)
\(74\) 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 0.767835 0.640647i \(-0.221334\pi\)
−0.938735 + 0.344641i \(0.888001\pi\)
\(80\) −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 \(-0.249219\pi\)
0.708839 + 0.705370i \(0.249219\pi\)
\(84\) 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 \(-0.00644690\pi\)
−0.517436 + 0.855722i \(0.673114\pi\)
\(90\) 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 \(-0.249305\pi\)
0.708649 + 0.705561i \(0.249305\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −142.000 245.951i −0.142000 0.245951i
\(101\) −679.000 + 1176.06i −0.668941 + 1.15864i 0.309260 + 0.950978i \(0.399919\pi\)
−0.978201 + 0.207662i \(0.933415\pi\)
\(102\) 0 0
\(103\) 416.000 + 720.533i 0.397958 + 0.689284i 0.993474 0.114060i \(-0.0363856\pi\)
−0.595516 + 0.803344i \(0.703052\pi\)
\(104\) 144.000 0.135773
\(105\) 0 0
\(106\) −636.000 −0.582772
\(107\) 222.000 + 384.515i 0.200575 + 0.347406i 0.948714 0.316136i \(-0.102386\pi\)
−0.748139 + 0.663542i \(0.769052\pi\)
\(108\) 0 0
\(109\) −935.000 + 1619.47i −0.821622 + 1.42309i 0.0828525 + 0.996562i \(0.473597\pi\)
−0.904474 + 0.426529i \(0.859736\pi\)
\(110\) −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 \(-0.257926\pi\)
−0.972070 + 0.234691i \(0.924592\pi\)
\(132\) 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 −0.132987 + 0.991118i \(0.542457\pi\)
−0.791840 + 0.610729i \(0.790877\pi\)
\(138\) 0 0
\(139\) 2800.00 1.70858 0.854291 0.519795i \(-0.173992\pi\)
0.854291 + 0.519795i \(0.173992\pi\)
\(140\) 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 0.927573 0.373641i \(-0.121891\pi\)
−0.787369 + 0.616482i \(0.788557\pi\)
\(150\) 0 0
\(151\) −296.000 + 512.687i −0.159524 + 0.276304i −0.934697 0.355445i \(-0.884329\pi\)
0.775173 + 0.631749i \(0.217663\pi\)
\(152\) −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 −0.291461 0.956583i \(-0.594141\pi\)
0.974155 0.225879i \(-0.0725254\pi\)
\(158\) −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 0.961609 0.274423i \(-0.0884869\pi\)
−0.718462 + 0.695566i \(0.755154\pi\)
\(164\) 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 \(-0.540225\pi\)
−0.126036 + 0.992026i \(0.540225\pi\)
\(168\) 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 \(-0.0327992\pi\)
−0.586427 + 0.810002i \(0.699466\pi\)
\(174\) 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 −0.895642 0.444775i \(-0.853283\pi\)
0.833008 + 0.553261i \(0.186617\pi\)
\(180\) 0 0
\(181\) −2358.00 −0.968336 −0.484168 0.874975i \(-0.660878\pi\)
−0.484168 + 0.874975i \(0.660878\pi\)
\(182\) 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 0.967214 0.253962i \(-0.0817340\pi\)
−0.703545 + 0.710651i \(0.748401\pi\)
\(192\) 0 0
\(193\) −889.000 + 1539.79i −0.331563 + 0.574284i −0.982818 0.184575i \(-0.940909\pi\)
0.651256 + 0.758858i \(0.274243\pi\)
\(194\) −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 \(-0.892638\pi\)
0.758420 + 0.651766i \(0.225971\pi\)
\(200\) −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 \(-0.296844\pi\)
0.595778 + 0.803149i \(0.296844\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 1378.00 + 2386.77i 0.405589 + 0.702501i
\(227\) −1968.00 + 3408.68i −0.575422 + 0.996660i 0.420574 + 0.907258i \(0.361829\pi\)
−0.995996 + 0.0894015i \(0.971505\pi\)
\(228\) 0 0
\(229\) −2405.00 4165.58i −0.694004 1.20205i −0.970515 0.241039i \(-0.922512\pi\)
0.276512 0.961011i \(-0.410822\pi\)
\(230\) 3136.00 0.899051
\(231\) 0 0
\(232\) −1520.00 −0.430142
\(233\) −1091.00 1889.67i −0.306754 0.531314i 0.670896 0.741551i \(-0.265910\pi\)
−0.977650 + 0.210237i \(0.932576\pi\)
\(234\) 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 \(-0.921315\pi\)
0.696705 + 0.717358i \(0.254649\pi\)
\(242\) 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 \(-0.478852\pi\)
0.0663886 + 0.997794i \(0.478852\pi\)
\(252\) 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 0.973833 + 0.227265i \(0.0729785\pi\)
−0.290099 + 0.956997i \(0.593688\pi\)
\(258\) 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 −0.856010 0.516959i \(-0.827064\pi\)
0.875705 + 0.482847i \(0.160397\pi\)
\(264\) 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 \(-0.880765\pi\)
0.782198 + 0.623030i \(0.214099\pi\)
\(270\) 0 0
\(271\) 1104.00 + 1912.18i 0.247466 + 0.428623i 0.962822 0.270137i \(-0.0870689\pi\)
−0.715356 + 0.698760i \(0.753736\pi\)
\(272\) −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 0.421970 + 0.906610i \(0.361339\pi\)
−0.996132 + 0.0878678i \(0.971995\pi\)
\(278\) −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 \(-0.779861\pi\)
0.937434 + 0.348163i \(0.113194\pi\)
\(284\) 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 \(-0.333090\pi\)
0.500663 + 0.865642i \(0.333090\pi\)
\(294\) 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 \(-0.846800\pi\)
−0.886398 + 0.462924i \(0.846800\pi\)
\(308\) 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 \(-0.861460\pi\)
0.818523 + 0.574474i \(0.194793\pi\)
\(312\) 0 0
\(313\) −1529.00 2648.31i −0.276116 0.478246i 0.694300 0.719685i \(-0.255714\pi\)
−0.970416 + 0.241439i \(0.922381\pi\)
\(314\) −5372.00 −0.965476
\(315\) 0 0
\(316\) 960.000 0.170899
\(317\) −2493.00 4318.00i −0.441706 0.765057i 0.556110 0.831109i \(-0.312293\pi\)
−0.997816 + 0.0660512i \(0.978960\pi\)
\(318\) 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 −0.962943 0.269705i \(-0.913074\pi\)
0.247900 0.968786i \(-0.420259\pi\)
\(332\) −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 −0.778050 0.628203i \(-0.783791\pi\)
0.933064 + 0.359709i \(0.117124\pi\)
\(348\) 0 0
\(349\) 1330.00 0.203992 0.101996 0.994785i \(-0.467477\pi\)
0.101996 + 0.994785i \(0.467477\pi\)
\(350\) 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 \(-0.809843\pi\)
0.900533 + 0.434787i \(0.143176\pi\)
\(354\) 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 −0.964276 0.264899i \(-0.914661\pi\)
0.252729 0.967537i \(-0.418672\pi\)
\(360\) 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 −0.374696 0.927148i \(-0.622253\pi\)
0.990282 0.139077i \(-0.0444136\pi\)
\(368\) −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 0.622656 0.782496i \(-0.286054\pi\)
−0.988989 + 0.147988i \(0.952720\pi\)
\(374\) 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 \(-0.303136\pi\)
−0.995504 + 0.0947240i \(0.969803\pi\)
\(384\) 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 −0.255986 + 0.966680i \(0.582400\pi\)
−0.709177 + 0.705031i \(0.750933\pi\)
\(390\) 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 \(-0.272295\pi\)
−0.981671 + 0.190586i \(0.938961\pi\)
\(398\) 2080.00 0.261962
\(399\) 0 0
\(400\) 1136.00 0.142000
\(401\) 1641.00 + 2842.30i 0.204358 + 0.353959i 0.949928 0.312469i \(-0.101156\pi\)
−0.745570 + 0.666427i \(0.767823\pi\)
\(402\) 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 \(-0.947561\pi\)
0.635256 + 0.772302i \(0.280895\pi\)
\(410\) 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 \(-0.790186\pi\)
−0.790512 + 0.612446i \(0.790186\pi\)
\(420\) 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 −0.828295 0.560292i \(-0.810689\pi\)
0.899374 + 0.437179i \(0.144022\pi\)
\(432\) 0 0
\(433\) −5062.00 −0.561811 −0.280906 0.959735i \(-0.590635\pi\)
−0.280906 + 0.959735i \(0.590635\pi\)
\(434\) 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 \(-0.265853\pi\)
−0.977613 + 0.210410i \(0.932520\pi\)
\(440\) 3136.00 0.339779
\(441\) 0 0
\(442\) −2664.00 −0.286682
\(443\) 6694.00 + 11594.3i 0.717927 + 1.24349i 0.961820 + 0.273683i \(0.0882421\pi\)
−0.243893 + 0.969802i \(0.578425\pi\)
\(444\) 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 0.998616 + 0.0525950i \(0.0167492\pi\)
−0.453759 + 0.891124i \(0.649917\pi\)
\(458\) −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 \(-0.619906\pi\)
−0.367849 + 0.929886i \(0.619906\pi\)
\(462\) 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 \(-0.211222\pi\)
−0.927314 + 0.374285i \(0.877888\pi\)
\(468\) 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 \(-0.881491\pi\)
0.780776 + 0.624811i \(0.214824\pi\)
\(480\) 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 −0.321216 0.947006i \(-0.604091\pi\)
0.980739 0.195322i \(-0.0625752\pi\)
\(488\) 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 0.948547 0.316638i \(-0.102554\pi\)
−0.748489 + 0.663147i \(0.769221\pi\)
\(500\) 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 \(-0.478653\pi\)
0.0670147 + 0.997752i \(0.478653\pi\)
\(504\) 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 −0.999880 0.0154756i \(-0.995074\pi\)
0.486538 0.873660i \(-0.338260\pi\)
\(510\) 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 \(-0.815095\pi\)
0.893237 + 0.449586i \(0.148429\pi\)
\(522\) 0 0
\(523\) −3484.00 6034.47i −0.291290 0.504529i 0.682825 0.730582i \(-0.260751\pi\)
−0.974115 + 0.226053i \(0.927418\pi\)
\(524\) 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 0.690926 0.722926i \(-0.257203\pi\)
−0.971535 + 0.236896i \(0.923870\pi\)
\(542\) 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 −0.972359 0.233490i \(-0.924986\pi\)
0.688388 + 0.725343i \(0.258319\pi\)
\(558\) 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 0.159048 0.987271i \(-0.449158\pi\)
0.775478 0.631375i \(-0.217509\pi\)
\(564\) 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 0.999578 + 0.0290514i \(0.00924865\pi\)
−0.474630 + 0.880186i \(0.657418\pi\)
\(570\) 0 0
\(571\) −3186.00 + 5518.31i −0.233503 + 0.404438i −0.958836 0.283959i \(-0.908352\pi\)
0.725334 + 0.688397i \(0.241685\pi\)
\(572\) −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 \(-0.735745\pi\)
0.976545 + 0.215316i \(0.0690780\pi\)
\(578\) −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 \(-0.754322\pi\)
−0.716642 + 0.697441i \(0.754322\pi\)
\(588\) 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 \(-0.0613993\pi\)
−0.656742 + 0.754115i \(0.728066\pi\)
\(594\) 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 −0.977694 0.210033i \(-0.932643\pi\)
0.670741 + 0.741692i \(0.265976\pi\)
\(600\) 0 0
\(601\) 7562.00 0.513245 0.256623 0.966512i \(-0.417390\pi\)
0.256623 + 0.966512i \(0.417390\pi\)
\(602\) 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 \(-0.134943\pi\)
−0.811978 + 0.583688i \(0.801609\pi\)
\(608\) 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 −0.927849 0.372956i \(-0.878344\pi\)
0.786914 + 0.617063i \(0.211678\pi\)
\(614\) 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 0.409095 + 0.912492i \(0.365845\pi\)
−0.994789 + 0.101959i \(0.967489\pi\)
\(620\) −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 −0.981570 0.191102i \(-0.938794\pi\)
0.656285 + 0.754513i \(0.272127\pi\)
\(642\) 0 0
\(643\) −26152.0 −1.60394 −0.801971 0.597363i \(-0.796215\pi\)
−0.801971 + 0.597363i \(0.796215\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 5920.00 + 10253.7i 0.360556 + 0.624502i
\(647\) 12792.0 22156.4i 0.777288 1.34630i −0.156211 0.987724i \(-0.549928\pi\)
0.933499 0.358579i \(-0.116739\pi\)
\(648\) 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 0.998711 0.0507630i \(-0.0161653\pi\)
−0.543317 + 0.839527i \(0.682832\pi\)
\(654\) 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 \(-0.811608\pi\)
0.898109 + 0.439773i \(0.144941\pi\)
\(662\) −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 0.960221 + 0.279242i \(0.0900831\pi\)
−0.238280 + 0.971197i \(0.576584\pi\)
\(678\) 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 −0.960426 0.278534i \(-0.910151\pi\)
0.721431 + 0.692487i \(0.243485\pi\)
\(684\) 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 −0.996662 0.0816365i \(-0.973985\pi\)
0.427632 0.903953i \(-0.359348\pi\)
\(692\) −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 0.966475 0.256759i \(-0.0826547\pi\)
−0.705598 + 0.708613i \(0.749321\pi\)
\(710\) 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 \(-0.329161\pi\)
−0.999914 + 0.0131086i \(0.995827\pi\)
\(720\) 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 \(-0.0940849\pi\)
0.956634 + 0.291291i \(0.0940849\pi\)
\(728\) 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 \(-0.275758\pi\)
−0.983686 + 0.179894i \(0.942425\pi\)
\(734\) −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 −0.996476 0.0838776i \(-0.973270\pi\)
0.570878 + 0.821035i \(0.306603\pi\)
\(740\) 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 −0.902773 0.430117i \(-0.858472\pi\)
0.0788938 0.996883i \(-0.474861\pi\)
\(752\) 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 −0.903378 0.428844i \(-0.858921\pi\)
0.0802993 0.996771i \(-0.474412\pi\)
\(762\) 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 \(-0.130231\pi\)
0.917467 + 0.397812i \(0.130231\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −3556.00 6159.17i −0.165781 0.287142i
\(773\) −12991.0 + 22501.1i −0.604468 + 1.04697i 0.387667 + 0.921799i \(0.373281\pi\)
−0.992135 + 0.125170i \(0.960052\pi\)
\(774\) 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 0.115895 + 0.993261i \(0.463026\pi\)
−0.918137 + 0.396263i \(0.870307\pi\)
\(788\) 2428.00 4205.42i 0.109764 0.190117i
\(789\) 0 0
\(790\) 6720.00 0.302642