Properties

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

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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: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 98)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 667.2
Root \(0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 882.667
Dual form 882.4.g.ba.361.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(9.89949 - 17.1464i) q^{5} +8.00000 q^{8} +O(q^{10})\) \(q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(9.89949 - 17.1464i) q^{5} +8.00000 q^{8} +(19.7990 + 34.2929i) q^{10} +(-7.00000 - 12.1244i) q^{11} -50.9117 q^{13} +(-8.00000 + 13.8564i) q^{16} +(-0.707107 - 1.22474i) q^{17} +(-0.707107 + 1.22474i) q^{19} -79.1960 q^{20} +28.0000 q^{22} +(70.0000 - 121.244i) q^{23} +(-133.500 - 231.229i) q^{25} +(50.9117 - 88.1816i) q^{26} +286.000 q^{29} +(-46.6690 - 80.8332i) q^{31} +(-16.0000 - 27.7128i) q^{32} +2.82843 q^{34} +(19.0000 - 32.9090i) q^{37} +(-1.41421 - 2.44949i) q^{38} +(79.1960 - 137.171i) q^{40} -125.865 q^{41} -34.0000 q^{43} +(-28.0000 + 48.4974i) q^{44} +(140.000 + 242.487i) q^{46} +(-261.630 + 453.156i) q^{47} +534.000 q^{50} +(101.823 + 176.363i) q^{52} +(-37.0000 - 64.0859i) q^{53} -277.186 q^{55} +(-286.000 + 495.367i) q^{58} +(-217.082 - 375.997i) q^{59} +(7.07107 - 12.2474i) q^{61} +186.676 q^{62} +64.0000 q^{64} +(-504.000 + 872.954i) q^{65} +(-342.000 - 592.361i) q^{67} +(-2.82843 + 4.89898i) q^{68} -588.000 q^{71} +(-135.057 - 233.926i) q^{73} +(38.0000 + 65.8179i) q^{74} +5.65685 q^{76} +(-610.000 + 1056.55i) q^{79} +(158.392 + 274.343i) q^{80} +(125.865 - 218.005i) q^{82} +422.850 q^{83} -28.0000 q^{85} +(34.0000 - 58.8897i) q^{86} +(-56.0000 - 96.9948i) q^{88} +(-309.006 + 535.214i) q^{89} -560.000 q^{92} +(-523.259 - 906.311i) q^{94} +(14.0000 + 24.2487i) q^{95} -1483.51 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{2} - 8q^{4} + 32q^{8} + O(q^{10}) \) \( 4q - 4q^{2} - 8q^{4} + 32q^{8} - 28q^{11} - 32q^{16} + 112q^{22} + 280q^{23} - 534q^{25} + 1144q^{29} - 64q^{32} + 76q^{37} - 136q^{43} - 112q^{44} + 560q^{46} + 2136q^{50} - 148q^{53} - 1144q^{58} + 256q^{64} - 2016q^{65} - 1368q^{67} - 2352q^{71} + 152q^{74} - 2440q^{79} - 112q^{85} + 136q^{86} - 224q^{88} - 2240q^{92} + 56q^{95} + O(q^{100}) \)

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
\(5\) 9.89949 17.1464i 0.885438 1.53362i 0.0402266 0.999191i \(-0.487192\pi\)
0.845211 0.534433i \(-0.179475\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 8.00000 0.353553
\(9\) 0 0
\(10\) 19.7990 + 34.2929i 0.626099 + 1.08444i
\(11\) −7.00000 12.1244i −0.191871 0.332330i 0.753999 0.656875i \(-0.228122\pi\)
−0.945870 + 0.324545i \(0.894789\pi\)
\(12\) 0 0
\(13\) −50.9117 −1.08618 −0.543091 0.839674i \(-0.682746\pi\)
−0.543091 + 0.839674i \(0.682746\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −8.00000 + 13.8564i −0.125000 + 0.216506i
\(17\) −0.707107 1.22474i −0.0100882 0.0174732i 0.860937 0.508711i \(-0.169878\pi\)
−0.871025 + 0.491238i \(0.836545\pi\)
\(18\) 0 0
\(19\) −0.707107 + 1.22474i −0.00853797 + 0.0147882i −0.870263 0.492588i \(-0.836051\pi\)
0.861725 + 0.507376i \(0.169384\pi\)
\(20\) −79.1960 −0.885438
\(21\) 0 0
\(22\) 28.0000 0.271346
\(23\) 70.0000 121.244i 0.634609 1.09918i −0.351989 0.936004i \(-0.614494\pi\)
0.986598 0.163171i \(-0.0521722\pi\)
\(24\) 0 0
\(25\) −133.500 231.229i −1.06800 1.84983i
\(26\) 50.9117 88.1816i 0.384023 0.665148i
\(27\) 0 0
\(28\) 0 0
\(29\) 286.000 1.83134 0.915670 0.401931i \(-0.131661\pi\)
0.915670 + 0.401931i \(0.131661\pi\)
\(30\) 0 0
\(31\) −46.6690 80.8332i −0.270387 0.468325i 0.698574 0.715538i \(-0.253818\pi\)
−0.968961 + 0.247213i \(0.920485\pi\)
\(32\) −16.0000 27.7128i −0.0883883 0.153093i
\(33\) 0 0
\(34\) 2.82843 0.0142668
\(35\) 0 0
\(36\) 0 0
\(37\) 19.0000 32.9090i 0.0844211 0.146222i −0.820723 0.571326i \(-0.806429\pi\)
0.905144 + 0.425104i \(0.139763\pi\)
\(38\) −1.41421 2.44949i −0.00603726 0.0104568i
\(39\) 0 0
\(40\) 79.1960 137.171i 0.313050 0.542218i
\(41\) −125.865 −0.479434 −0.239717 0.970843i \(-0.577055\pi\)
−0.239717 + 0.970843i \(0.577055\pi\)
\(42\) 0 0
\(43\) −34.0000 −0.120580 −0.0602901 0.998181i \(-0.519203\pi\)
−0.0602901 + 0.998181i \(0.519203\pi\)
\(44\) −28.0000 + 48.4974i −0.0959354 + 0.166165i
\(45\) 0 0
\(46\) 140.000 + 242.487i 0.448736 + 0.777234i
\(47\) −261.630 + 453.156i −0.811970 + 1.40637i 0.0995134 + 0.995036i \(0.468271\pi\)
−0.911483 + 0.411337i \(0.865062\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 534.000 1.51038
\(51\) 0 0
\(52\) 101.823 + 176.363i 0.271545 + 0.470330i
\(53\) −37.0000 64.0859i −0.0958932 0.166092i 0.814088 0.580742i \(-0.197237\pi\)
−0.909981 + 0.414650i \(0.863904\pi\)
\(54\) 0 0
\(55\) −277.186 −0.679559
\(56\) 0 0
\(57\) 0 0
\(58\) −286.000 + 495.367i −0.647477 + 1.12146i
\(59\) −217.082 375.997i −0.479011 0.829671i 0.520699 0.853740i \(-0.325671\pi\)
−0.999710 + 0.0240689i \(0.992338\pi\)
\(60\) 0 0
\(61\) 7.07107 12.2474i 0.0148419 0.0257070i −0.858509 0.512798i \(-0.828609\pi\)
0.873351 + 0.487091i \(0.161942\pi\)
\(62\) 186.676 0.382385
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −504.000 + 872.954i −0.961746 + 1.66579i
\(66\) 0 0
\(67\) −342.000 592.361i −0.623611 1.08013i −0.988808 0.149196i \(-0.952332\pi\)
0.365196 0.930930i \(-0.381002\pi\)
\(68\) −2.82843 + 4.89898i −0.00504408 + 0.00873660i
\(69\) 0 0
\(70\) 0 0
\(71\) −588.000 −0.982856 −0.491428 0.870918i \(-0.663525\pi\)
−0.491428 + 0.870918i \(0.663525\pi\)
\(72\) 0 0
\(73\) −135.057 233.926i −0.216538 0.375055i 0.737209 0.675664i \(-0.236143\pi\)
−0.953747 + 0.300610i \(0.902810\pi\)
\(74\) 38.0000 + 65.8179i 0.0596947 + 0.103394i
\(75\) 0 0
\(76\) 5.65685 0.00853797
\(77\) 0 0
\(78\) 0 0
\(79\) −610.000 + 1056.55i −0.868739 + 1.50470i −0.00545246 + 0.999985i \(0.501736\pi\)
−0.863286 + 0.504715i \(0.831598\pi\)
\(80\) 158.392 + 274.343i 0.221359 + 0.383406i
\(81\) 0 0
\(82\) 125.865 218.005i 0.169506 0.293592i
\(83\) 422.850 0.559202 0.279601 0.960116i \(-0.409798\pi\)
0.279601 + 0.960116i \(0.409798\pi\)
\(84\) 0 0
\(85\) −28.0000 −0.0357297
\(86\) 34.0000 58.8897i 0.0426316 0.0738400i
\(87\) 0 0
\(88\) −56.0000 96.9948i −0.0678366 0.117496i
\(89\) −309.006 + 535.214i −0.368028 + 0.637444i −0.989257 0.146185i \(-0.953300\pi\)
0.621229 + 0.783629i \(0.286634\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −560.000 −0.634609
\(93\) 0 0
\(94\) −523.259 906.311i −0.574149 0.994456i
\(95\) 14.0000 + 24.2487i 0.0151197 + 0.0261881i
\(96\) 0 0
\(97\) −1483.51 −1.55286 −0.776431 0.630202i \(-0.782972\pi\)
−0.776431 + 0.630202i \(0.782972\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −534.000 + 924.915i −0.534000 + 0.924915i
\(101\) −564.271 977.346i −0.555912 0.962867i −0.997832 0.0658130i \(-0.979036\pi\)
0.441920 0.897054i \(-0.354297\pi\)
\(102\) 0 0
\(103\) −434.164 + 751.993i −0.415334 + 0.719380i −0.995463 0.0951446i \(-0.969669\pi\)
0.580129 + 0.814524i \(0.303002\pi\)
\(104\) −407.294 −0.384023
\(105\) 0 0
\(106\) 148.000 0.135613
\(107\) −842.000 + 1458.39i −0.760740 + 1.31764i 0.181729 + 0.983349i \(0.441831\pi\)
−0.942469 + 0.334292i \(0.891503\pi\)
\(108\) 0 0
\(109\) 409.000 + 708.409i 0.359405 + 0.622507i 0.987861 0.155337i \(-0.0496465\pi\)
−0.628457 + 0.777844i \(0.716313\pi\)
\(110\) 277.186 480.100i 0.240260 0.416143i
\(111\) 0 0
\(112\) 0 0
\(113\) 540.000 0.449548 0.224774 0.974411i \(-0.427836\pi\)
0.224774 + 0.974411i \(0.427836\pi\)
\(114\) 0 0
\(115\) −1385.93 2400.50i −1.12381 1.94650i
\(116\) −572.000 990.733i −0.457835 0.792994i
\(117\) 0 0
\(118\) 868.327 0.677424
\(119\) 0 0
\(120\) 0 0
\(121\) 567.500 982.939i 0.426371 0.738496i
\(122\) 14.1421 + 24.4949i 0.0104948 + 0.0181776i
\(123\) 0 0
\(124\) −186.676 + 323.333i −0.135194 + 0.234162i
\(125\) −2811.46 −2.01171
\(126\) 0 0
\(127\) 1720.00 1.20177 0.600887 0.799334i \(-0.294814\pi\)
0.600887 + 0.799334i \(0.294814\pi\)
\(128\) −64.0000 + 110.851i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −1008.00 1745.91i −0.680057 1.17789i
\(131\) 867.620 1502.76i 0.578659 1.00227i −0.416975 0.908918i \(-0.636910\pi\)
0.995634 0.0933484i \(-0.0297571\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 1368.00 0.881919
\(135\) 0 0
\(136\) −5.65685 9.79796i −0.00356670 0.00617771i
\(137\) 414.000 + 717.069i 0.258178 + 0.447178i 0.965754 0.259460i \(-0.0835445\pi\)
−0.707576 + 0.706638i \(0.750211\pi\)
\(138\) 0 0
\(139\) 425.678 0.259752 0.129876 0.991530i \(-0.458542\pi\)
0.129876 + 0.991530i \(0.458542\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 588.000 1018.45i 0.347492 0.601874i
\(143\) 356.382 + 617.271i 0.208407 + 0.360971i
\(144\) 0 0
\(145\) 2831.26 4903.88i 1.62154 2.80859i
\(146\) 540.230 0.306231
\(147\) 0 0
\(148\) −152.000 −0.0844211
\(149\) 1025.00 1775.35i 0.563566 0.976124i −0.433616 0.901098i \(-0.642763\pi\)
0.997182 0.0750264i \(-0.0239041\pi\)
\(150\) 0 0
\(151\) 236.000 + 408.764i 0.127188 + 0.220296i 0.922586 0.385791i \(-0.126071\pi\)
−0.795398 + 0.606087i \(0.792738\pi\)
\(152\) −5.65685 + 9.79796i −0.00301863 + 0.00522842i
\(153\) 0 0
\(154\) 0 0
\(155\) −1848.00 −0.957645
\(156\) 0 0
\(157\) −1105.92 1915.50i −0.562176 0.973717i −0.997306 0.0733498i \(-0.976631\pi\)
0.435130 0.900367i \(-0.356702\pi\)
\(158\) −1220.00 2113.10i −0.614291 1.06398i
\(159\) 0 0
\(160\) −633.568 −0.313050
\(161\) 0 0
\(162\) 0 0
\(163\) −1643.00 + 2845.76i −0.789507 + 1.36747i 0.136762 + 0.990604i \(0.456331\pi\)
−0.926269 + 0.376863i \(0.877003\pi\)
\(164\) 251.730 + 436.009i 0.119859 + 0.207601i
\(165\) 0 0
\(166\) −422.850 + 732.397i −0.197708 + 0.342440i
\(167\) −1490.58 −0.690686 −0.345343 0.938476i \(-0.612237\pi\)
−0.345343 + 0.938476i \(0.612237\pi\)
\(168\) 0 0
\(169\) 395.000 0.179791
\(170\) 28.0000 48.4974i 0.0126324 0.0218799i
\(171\) 0 0
\(172\) 68.0000 + 117.779i 0.0301451 + 0.0522128i
\(173\) 1035.20 1793.03i 0.454943 0.787984i −0.543742 0.839252i \(-0.682993\pi\)
0.998685 + 0.0512682i \(0.0163263\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 224.000 0.0959354
\(177\) 0 0
\(178\) −618.011 1070.43i −0.260235 0.450741i
\(179\) 270.000 + 467.654i 0.112742 + 0.195274i 0.916875 0.399175i \(-0.130703\pi\)
−0.804133 + 0.594449i \(0.797370\pi\)
\(180\) 0 0
\(181\) −3784.44 −1.55412 −0.777058 0.629429i \(-0.783289\pi\)
−0.777058 + 0.629429i \(0.783289\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 560.000 969.948i 0.224368 0.388617i
\(185\) −376.181 651.564i −0.149499 0.258940i
\(186\) 0 0
\(187\) −9.89949 + 17.1464i −0.00387124 + 0.00670519i
\(188\) 2093.04 0.811970
\(189\) 0 0
\(190\) −56.0000 −0.0213825
\(191\) 514.000 890.274i 0.194721 0.337267i −0.752088 0.659063i \(-0.770953\pi\)
0.946809 + 0.321796i \(0.104286\pi\)
\(192\) 0 0
\(193\) −2296.00 3976.79i −0.856320 1.48319i −0.875415 0.483372i \(-0.839412\pi\)
0.0190956 0.999818i \(-0.493921\pi\)
\(194\) 1483.51 2569.51i 0.549020 0.950930i
\(195\) 0 0
\(196\) 0 0
\(197\) −794.000 −0.287158 −0.143579 0.989639i \(-0.545861\pi\)
−0.143579 + 0.989639i \(0.545861\pi\)
\(198\) 0 0
\(199\) 1243.09 + 2153.10i 0.442817 + 0.766981i 0.997897 0.0648153i \(-0.0206458\pi\)
−0.555080 + 0.831797i \(0.687312\pi\)
\(200\) −1068.00 1849.83i −0.377595 0.654014i
\(201\) 0 0
\(202\) 2257.08 0.786178
\(203\) 0 0
\(204\) 0 0
\(205\) −1246.00 + 2158.14i −0.424509 + 0.735272i
\(206\) −868.327 1503.99i −0.293686 0.508678i
\(207\) 0 0
\(208\) 407.294 705.453i 0.135773 0.235165i
\(209\) 19.7990 0.00655275
\(210\) 0 0
\(211\) −2748.00 −0.896588 −0.448294 0.893886i \(-0.647968\pi\)
−0.448294 + 0.893886i \(0.647968\pi\)
\(212\) −148.000 + 256.344i −0.0479466 + 0.0830460i
\(213\) 0 0
\(214\) −1684.00 2916.77i −0.537925 0.931713i
\(215\) −336.583 + 582.979i −0.106766 + 0.184925i
\(216\) 0 0
\(217\) 0 0
\(218\) −1636.00 −0.508275
\(219\) 0 0
\(220\) 554.372 + 960.200i 0.169890 + 0.294258i
\(221\) 36.0000 + 62.3538i 0.0109576 + 0.0189791i
\(222\) 0 0
\(223\) 3428.05 1.02941 0.514707 0.857366i \(-0.327901\pi\)
0.514707 + 0.857366i \(0.327901\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −540.000 + 935.307i −0.158939 + 0.275291i
\(227\) −2645.29 4581.77i −0.773453 1.33966i −0.935660 0.352903i \(-0.885195\pi\)
0.162207 0.986757i \(-0.448139\pi\)
\(228\) 0 0
\(229\) −1374.62 + 2380.90i −0.396669 + 0.687051i −0.993313 0.115456i \(-0.963167\pi\)
0.596644 + 0.802506i \(0.296501\pi\)
\(230\) 5543.72 1.58931
\(231\) 0 0
\(232\) 2288.00 0.647477
\(233\) 36.0000 62.3538i 0.0101221 0.0175319i −0.860920 0.508740i \(-0.830111\pi\)
0.871042 + 0.491208i \(0.163445\pi\)
\(234\) 0 0
\(235\) 5180.00 + 8972.02i 1.43790 + 2.49051i
\(236\) −868.327 + 1503.99i −0.239505 + 0.414836i
\(237\) 0 0
\(238\) 0 0
\(239\) −4308.00 −1.16595 −0.582974 0.812491i \(-0.698111\pi\)
−0.582974 + 0.812491i \(0.698111\pi\)
\(240\) 0 0
\(241\) −770.039 1333.75i −0.205820 0.356490i 0.744574 0.667540i \(-0.232653\pi\)
−0.950394 + 0.311050i \(0.899319\pi\)
\(242\) 1135.00 + 1965.88i 0.301490 + 0.522196i
\(243\) 0 0
\(244\) −56.5685 −0.0148419
\(245\) 0 0
\(246\) 0 0
\(247\) 36.0000 62.3538i 0.00927379 0.0160627i
\(248\) −373.352 646.665i −0.0955964 0.165578i
\(249\) 0 0
\(250\) 2811.46 4869.59i 0.711249 1.23192i
\(251\) 931.967 0.234363 0.117182 0.993110i \(-0.462614\pi\)
0.117182 + 0.993110i \(0.462614\pi\)
\(252\) 0 0
\(253\) −1960.00 −0.487052
\(254\) −1720.00 + 2979.13i −0.424891 + 0.735933i
\(255\) 0 0
\(256\) −128.000 221.703i −0.0312500 0.0541266i
\(257\) −468.812 + 812.006i −0.113789 + 0.197088i −0.917295 0.398209i \(-0.869632\pi\)
0.803506 + 0.595296i \(0.202965\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 4032.00 0.961746
\(261\) 0 0
\(262\) 1735.24 + 3005.52i 0.409174 + 0.708709i
\(263\) 3570.00 + 6183.42i 0.837018 + 1.44976i 0.892377 + 0.451291i \(0.149036\pi\)
−0.0553595 + 0.998466i \(0.517630\pi\)
\(264\) 0 0
\(265\) −1465.13 −0.339630
\(266\) 0 0
\(267\) 0 0
\(268\) −1368.00 + 2369.45i −0.311806 + 0.540063i
\(269\) −2305.17 3992.67i −0.522485 0.904971i −0.999658 0.0261615i \(-0.991672\pi\)
0.477172 0.878810i \(-0.341662\pi\)
\(270\) 0 0
\(271\) −1182.28 + 2047.77i −0.265013 + 0.459016i −0.967567 0.252614i \(-0.918710\pi\)
0.702554 + 0.711630i \(0.252043\pi\)
\(272\) 22.6274 0.00504408
\(273\) 0 0
\(274\) −1656.00 −0.365119
\(275\) −1869.00 + 3237.20i −0.409836 + 0.709857i
\(276\) 0 0
\(277\) −2003.00 3469.30i −0.434472 0.752527i 0.562781 0.826606i \(-0.309731\pi\)
−0.997252 + 0.0740794i \(0.976398\pi\)
\(278\) −425.678 + 737.296i −0.0918363 + 0.159065i
\(279\) 0 0
\(280\) 0 0
\(281\) 5984.00 1.27038 0.635188 0.772358i \(-0.280923\pi\)
0.635188 + 0.772358i \(0.280923\pi\)
\(282\) 0 0
\(283\) −2464.27 4268.24i −0.517617 0.896538i −0.999791 0.0204627i \(-0.993486\pi\)
0.482174 0.876075i \(-0.339847\pi\)
\(284\) 1176.00 + 2036.89i 0.245714 + 0.425589i
\(285\) 0 0
\(286\) −1425.53 −0.294731
\(287\) 0 0
\(288\) 0 0
\(289\) 2455.50 4253.05i 0.499796 0.865673i
\(290\) 5662.51 + 9807.76i 1.14660 + 1.98597i
\(291\) 0 0
\(292\) −540.230 + 935.705i −0.108269 + 0.187527i
\(293\) 1971.41 0.393076 0.196538 0.980496i \(-0.437030\pi\)
0.196538 + 0.980496i \(0.437030\pi\)
\(294\) 0 0
\(295\) −8596.00 −1.69654
\(296\) 152.000 263.272i 0.0298474 0.0516972i
\(297\) 0 0
\(298\) 2050.00 + 3550.70i 0.398501 + 0.690224i
\(299\) −3563.82 + 6172.71i −0.689301 + 1.19390i
\(300\) 0 0
\(301\) 0 0
\(302\) −944.000 −0.179871
\(303\) 0 0
\(304\) −11.3137 19.5959i −0.00213449 0.00369705i
\(305\) −140.000 242.487i −0.0262832 0.0455238i
\(306\) 0 0
\(307\) 4767.31 0.886270 0.443135 0.896455i \(-0.353866\pi\)
0.443135 + 0.896455i \(0.353866\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 1848.00 3200.83i 0.338579 0.586435i
\(311\) 3388.46 + 5868.98i 0.617819 + 1.07009i 0.989883 + 0.141887i \(0.0453169\pi\)
−0.372064 + 0.928207i \(0.621350\pi\)
\(312\) 0 0
\(313\) −3095.01 + 5360.71i −0.558914 + 0.968068i 0.438673 + 0.898647i \(0.355449\pi\)
−0.997587 + 0.0694210i \(0.977885\pi\)
\(314\) 4423.66 0.795037
\(315\) 0 0
\(316\) 4880.00 0.868739
\(317\) 4913.00 8509.57i 0.870478 1.50771i 0.00897524 0.999960i \(-0.497143\pi\)
0.861503 0.507753i \(-0.169524\pi\)
\(318\) 0 0
\(319\) −2002.00 3467.57i −0.351381 0.608609i
\(320\) 633.568 1097.37i 0.110680 0.191703i
\(321\) 0 0
\(322\) 0 0
\(323\) 2.00000 0.000344529
\(324\) 0 0
\(325\) 6796.71 + 11772.2i 1.16004 + 2.00925i
\(326\) −3286.00 5691.52i −0.558266 0.966945i
\(327\) 0 0
\(328\) −1006.92 −0.169506
\(329\) 0 0
\(330\) 0 0
\(331\) 2869.00 4969.25i 0.476418 0.825181i −0.523216 0.852200i \(-0.675268\pi\)
0.999635 + 0.0270189i \(0.00860142\pi\)
\(332\) −845.700 1464.79i −0.139801 0.242142i
\(333\) 0 0
\(334\) 1490.58 2581.76i 0.244195 0.422957i
\(335\) −13542.5 −2.20868
\(336\) 0 0
\(337\) −2254.00 −0.364342 −0.182171 0.983267i \(-0.558312\pi\)
−0.182171 + 0.983267i \(0.558312\pi\)
\(338\) −395.000 + 684.160i −0.0635656 + 0.110099i
\(339\) 0 0
\(340\) 56.0000 + 96.9948i 0.00893243 + 0.0154714i
\(341\) −653.367 + 1131.66i −0.103759 + 0.179716i
\(342\) 0 0
\(343\) 0 0
\(344\) −272.000 −0.0426316
\(345\) 0 0
\(346\) 2070.41 + 3586.05i 0.321693 + 0.557189i
\(347\) −993.000 1719.93i −0.153623 0.266082i 0.778934 0.627106i \(-0.215761\pi\)
−0.932557 + 0.361024i \(0.882427\pi\)
\(348\) 0 0
\(349\) −6771.25 −1.03856 −0.519279 0.854605i \(-0.673800\pi\)
−0.519279 + 0.854605i \(0.673800\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −224.000 + 387.979i −0.0339183 + 0.0587482i
\(353\) −3496.64 6056.36i −0.527217 0.913166i −0.999497 0.0317177i \(-0.989902\pi\)
0.472280 0.881449i \(-0.343431\pi\)
\(354\) 0 0
\(355\) −5820.90 + 10082.1i −0.870258 + 1.50733i
\(356\) 2472.05 0.368028
\(357\) 0 0
\(358\) −1080.00 −0.159441
\(359\) 2972.00 5147.66i 0.436925 0.756777i −0.560525 0.828137i \(-0.689401\pi\)
0.997451 + 0.0713606i \(0.0227341\pi\)
\(360\) 0 0
\(361\) 3428.50 + 5938.34i 0.499854 + 0.865773i
\(362\) 3784.44 6554.83i 0.549463 0.951697i
\(363\) 0 0
\(364\) 0 0
\(365\) −5348.00 −0.766924
\(366\) 0 0
\(367\) −421.436 729.948i −0.0599421 0.103823i 0.834497 0.551012i \(-0.185758\pi\)
−0.894439 + 0.447190i \(0.852425\pi\)
\(368\) 1120.00 + 1939.90i 0.158652 + 0.274794i
\(369\) 0 0
\(370\) 1504.72 0.211424
\(371\) 0 0
\(372\) 0 0
\(373\) 2863.00 4958.86i 0.397428 0.688365i −0.595980 0.802999i \(-0.703236\pi\)
0.993408 + 0.114634i \(0.0365696\pi\)
\(374\) −19.7990 34.2929i −0.00273738 0.00474129i
\(375\) 0 0
\(376\) −2093.04 + 3625.24i −0.287075 + 0.497228i
\(377\) −14560.7 −1.98917
\(378\) 0 0
\(379\) 10330.0 1.40004 0.700022 0.714122i \(-0.253174\pi\)
0.700022 + 0.714122i \(0.253174\pi\)
\(380\) 56.0000 96.9948i 0.00755984 0.0130940i
\(381\) 0 0
\(382\) 1028.00 + 1780.55i 0.137689 + 0.238484i
\(383\) −502.046 + 869.569i −0.0669800 + 0.116013i −0.897571 0.440871i \(-0.854670\pi\)
0.830591 + 0.556884i \(0.188003\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 9184.00 1.21102
\(387\) 0 0
\(388\) 2967.02 + 5139.03i 0.388216 + 0.672409i
\(389\) 2605.00 + 4511.99i 0.339534 + 0.588090i 0.984345 0.176252i \(-0.0563973\pi\)
−0.644811 + 0.764342i \(0.723064\pi\)
\(390\) 0 0
\(391\) −197.990 −0.0256081
\(392\) 0 0
\(393\) 0 0
\(394\) 794.000 1375.25i 0.101526 0.175848i
\(395\) 12077.4 + 20918.6i 1.53843 + 2.66464i
\(396\) 0 0
\(397\) −36.7696 + 63.6867i −0.00464839 + 0.00805125i −0.868340 0.495969i \(-0.834813\pi\)
0.863692 + 0.504020i \(0.168146\pi\)
\(398\) −4972.37 −0.626238
\(399\) 0 0
\(400\) 4272.00 0.534000
\(401\) −249.000 + 431.281i −0.0310086 + 0.0537085i −0.881113 0.472905i \(-0.843205\pi\)
0.850105 + 0.526614i \(0.176539\pi\)
\(402\) 0 0
\(403\) 2376.00 + 4115.35i 0.293690 + 0.508686i
\(404\) −2257.08 + 3909.39i −0.277956 + 0.481434i
\(405\) 0 0
\(406\) 0 0
\(407\) −532.000 −0.0647918
\(408\) 0 0
\(409\) 1677.96 + 2906.32i 0.202861 + 0.351365i 0.949449 0.313921i \(-0.101643\pi\)
−0.746588 + 0.665286i \(0.768309\pi\)
\(410\) −2492.00 4316.27i −0.300173 0.519916i
\(411\) 0 0
\(412\) 3473.31 0.415334
\(413\) 0 0
\(414\) 0 0
\(415\) 4186.00 7250.36i 0.495139 0.857606i
\(416\) 814.587 + 1410.91i 0.0960058 + 0.166287i
\(417\) 0 0
\(418\) −19.7990 + 34.2929i −0.00231675 + 0.00401272i
\(419\) 14545.2 1.69589 0.847946 0.530082i \(-0.177839\pi\)
0.847946 + 0.530082i \(0.177839\pi\)
\(420\) 0 0
\(421\) 10854.0 1.25651 0.628256 0.778007i \(-0.283769\pi\)
0.628256 + 0.778007i \(0.283769\pi\)
\(422\) 2748.00 4759.68i 0.316992 0.549046i
\(423\) 0 0
\(424\) −296.000 512.687i −0.0339034 0.0587224i
\(425\) −188.798 + 327.007i −0.0215483 + 0.0373227i
\(426\) 0 0
\(427\) 0 0
\(428\) 6736.00 0.760740
\(429\) 0 0
\(430\) −673.166 1165.96i −0.0754952 0.130762i
\(431\) −2682.00 4645.36i −0.299739 0.519163i 0.676337 0.736592i \(-0.263566\pi\)
−0.976076 + 0.217429i \(0.930233\pi\)
\(432\) 0 0
\(433\) 6487.00 0.719966 0.359983 0.932959i \(-0.382783\pi\)
0.359983 + 0.932959i \(0.382783\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 1636.00 2833.64i 0.179702 0.311253i
\(437\) 98.9949 + 171.464i 0.0108365 + 0.0187694i
\(438\) 0 0
\(439\) 6966.42 12066.2i 0.757378 1.31182i −0.186806 0.982397i \(-0.559813\pi\)
0.944183 0.329420i \(-0.106853\pi\)
\(440\) −2217.49 −0.240260
\(441\) 0 0
\(442\) −144.000 −0.0154963
\(443\) 2998.00 5192.69i 0.321533 0.556912i −0.659271 0.751905i \(-0.729135\pi\)
0.980805 + 0.194993i \(0.0624684\pi\)
\(444\) 0 0
\(445\) 6118.00 + 10596.7i 0.651733 + 1.12883i
\(446\) −3428.05 + 5937.56i −0.363953 + 0.630385i
\(447\) 0 0
\(448\) 0 0
\(449\) −2622.00 −0.275590 −0.137795 0.990461i \(-0.544001\pi\)
−0.137795 + 0.990461i \(0.544001\pi\)
\(450\) 0 0
\(451\) 881.055 + 1526.03i 0.0919895 + 0.159330i
\(452\) −1080.00 1870.61i −0.112387 0.194660i
\(453\) 0 0
\(454\) 10581.1 1.09383
\(455\) 0 0
\(456\) 0 0
\(457\) −5604.00 + 9706.41i −0.573619 + 0.993538i 0.422571 + 0.906330i \(0.361128\pi\)
−0.996190 + 0.0872080i \(0.972206\pi\)
\(458\) −2749.23 4761.81i −0.280487 0.485818i
\(459\) 0 0
\(460\) −5543.72 + 9602.00i −0.561907 + 0.973251i
\(461\) 9786.36 0.988712 0.494356 0.869260i \(-0.335404\pi\)
0.494356 + 0.869260i \(0.335404\pi\)
\(462\) 0 0
\(463\) 3952.00 0.396685 0.198342 0.980133i \(-0.436444\pi\)
0.198342 + 0.980133i \(0.436444\pi\)
\(464\) −2288.00 + 3962.93i −0.228918 + 0.396497i
\(465\) 0 0
\(466\) 72.0000 + 124.708i 0.00715737 + 0.0123969i
\(467\) −8753.27 + 15161.1i −0.867352 + 1.50230i −0.00265876 + 0.999996i \(0.500846\pi\)
−0.864693 + 0.502301i \(0.832487\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −20720.0 −2.03349
\(471\) 0 0
\(472\) −1736.65 3007.97i −0.169356 0.293333i
\(473\) 238.000 + 412.228i 0.0231358 + 0.0400724i
\(474\) 0 0
\(475\) 377.595 0.0364742
\(476\) 0 0
\(477\) 0 0
\(478\) 4308.00 7461.67i 0.412225 0.713994i
\(479\) −1144.10 1981.64i −0.109134 0.189026i 0.806286 0.591526i \(-0.201474\pi\)
−0.915420 + 0.402501i \(0.868141\pi\)
\(480\) 0 0
\(481\) −967.322 + 1675.45i −0.0916967 + 0.158823i
\(482\) 3080.16 0.291073
\(483\) 0 0
\(484\) −4540.00 −0.426371
\(485\) −14686.0 + 25436.9i −1.37496 + 2.38151i
\(486\) 0 0
\(487\) −486.000 841.777i −0.0452213 0.0783256i 0.842529 0.538651i \(-0.181066\pi\)
−0.887750 + 0.460326i \(0.847733\pi\)
\(488\) 56.5685 97.9796i 0.00524741 0.00908879i
\(489\) 0 0
\(490\) 0 0
\(491\) 7404.00 0.680525 0.340263 0.940330i \(-0.389484\pi\)
0.340263 + 0.940330i \(0.389484\pi\)
\(492\) 0 0
\(493\) −202.233 350.277i −0.0184748 0.0319994i
\(494\) 72.0000 + 124.708i 0.00655756 + 0.0113580i
\(495\) 0 0
\(496\) 1493.41 0.135194
\(497\) 0 0
\(498\) 0 0
\(499\) 6122.00 10603.6i 0.549215 0.951269i −0.449113 0.893475i \(-0.648260\pi\)
0.998329 0.0577938i \(-0.0184066\pi\)
\(500\) 5622.91 + 9739.17i 0.502929 + 0.871098i
\(501\) 0 0
\(502\) −931.967 + 1614.21i −0.0828600 + 0.143518i
\(503\) −2415.48 −0.214117 −0.107058 0.994253i \(-0.534143\pi\)
−0.107058 + 0.994253i \(0.534143\pi\)
\(504\) 0 0
\(505\) −22344.0 −1.96890
\(506\) 1960.00 3394.82i 0.172199 0.298257i
\(507\) 0 0
\(508\) −3440.00 5958.25i −0.300444 0.520383i
\(509\) 2853.88 4943.07i 0.248519 0.430447i −0.714596 0.699537i \(-0.753390\pi\)
0.963115 + 0.269090i \(0.0867228\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 512.000 0.0441942
\(513\) 0 0
\(514\) −937.624 1624.01i −0.0804607 0.139362i
\(515\) 8596.00 + 14888.7i 0.735505 + 1.27393i
\(516\) 0 0
\(517\) 7325.63 0.623173
\(518\) 0 0
\(519\) 0 0
\(520\) −4032.00 + 6983.63i −0.340029 + 0.588947i
\(521\) −0.707107 1.22474i −5.94605e−5 0.000102989i 0.865996 0.500051i \(-0.166686\pi\)
−0.866055 + 0.499949i \(0.833352\pi\)
\(522\) 0 0
\(523\) −6128.49 + 10614.9i −0.512391 + 0.887487i 0.487506 + 0.873120i \(0.337907\pi\)
−0.999897 + 0.0143672i \(0.995427\pi\)
\(524\) −6940.96 −0.578659
\(525\) 0 0
\(526\) −14280.0 −1.18372
\(527\) −66.0000 + 114.315i −0.00545542 + 0.00944906i
\(528\) 0 0
\(529\) −3716.50 6437.17i −0.305457 0.529068i
\(530\) 1465.13 2537.67i 0.120077 0.207980i
\(531\) 0 0
\(532\) 0 0
\(533\) 6408.00 0.520753
\(534\) 0 0
\(535\) 16670.7 + 28874.6i 1.34718 + 2.33338i
\(536\) −2736.00 4738.89i −0.220480 0.381882i
\(537\) 0 0
\(538\) 9220.67 0.738906
\(539\) 0 0
\(540\) 0 0
\(541\) −1025.00 + 1775.35i −0.0814569 + 0.141088i −0.903876 0.427795i \(-0.859291\pi\)
0.822419 + 0.568882i \(0.192624\pi\)
\(542\) −2364.57 4095.55i −0.187393 0.324573i
\(543\) 0 0
\(544\) −22.6274 + 39.1918i −0.00178335 + 0.00308885i
\(545\) 16195.6 1.27292
\(546\) 0 0
\(547\) 14554.0 1.13763 0.568815 0.822465i \(-0.307402\pi\)
0.568815 + 0.822465i \(0.307402\pi\)
\(548\) 1656.00 2868.28i 0.129089 0.223589i
\(549\) 0 0
\(550\) −3738.00 6474.41i −0.289798 0.501945i
\(551\) −202.233 + 350.277i −0.0156359 + 0.0270822i
\(552\) 0 0
\(553\) 0 0
\(554\) 8012.00 0.614435
\(555\) 0 0
\(556\) −851.357 1474.59i −0.0649381 0.112476i
\(557\) 3477.00 + 6022.34i 0.264498 + 0.458123i 0.967432 0.253131i \(-0.0814605\pi\)
−0.702934 + 0.711255i \(0.748127\pi\)
\(558\) 0 0
\(559\) 1731.00 0.130972
\(560\) 0 0
\(561\) 0 0
\(562\) −5984.00 + 10364.6i −0.449146 + 0.777943i
\(563\) 818.123 + 1417.03i 0.0612429 + 0.106076i 0.895021 0.446024i \(-0.147160\pi\)
−0.833778 + 0.552099i \(0.813827\pi\)
\(564\) 0 0
\(565\) 5345.73 9259.07i 0.398047 0.689437i
\(566\) 9857.07 0.732020
\(567\) 0 0
\(568\) −4704.00 −0.347492
\(569\) −3571.00 + 6185.15i −0.263100 + 0.455703i −0.967064 0.254533i \(-0.918078\pi\)
0.703964 + 0.710236i \(0.251412\pi\)
\(570\) 0 0
\(571\) 10303.0 + 17845.3i 0.755109 + 1.30789i 0.945320 + 0.326144i \(0.105749\pi\)
−0.190211 + 0.981743i \(0.560917\pi\)
\(572\) 1425.53 2469.09i 0.104203 0.180485i
\(573\) 0 0
\(574\) 0 0
\(575\) −37380.0 −2.71105
\(576\) 0 0
\(577\) −4401.74 7624.04i −0.317585 0.550074i 0.662398 0.749152i \(-0.269539\pi\)
−0.979984 + 0.199078i \(0.936205\pi\)
\(578\) 4911.00 + 8506.10i 0.353409 + 0.612123i
\(579\) 0 0
\(580\) −22650.0 −1.62154
\(581\) 0 0
\(582\) 0 0
\(583\) −518.000 + 897.202i −0.0367982 + 0.0637364i
\(584\) −1080.46 1871.41i −0.0765577 0.132602i
\(585\) 0 0
\(586\) −1971.41 + 3414.59i −0.138973 + 0.240709i
\(587\) 6503.97 0.457321 0.228661 0.973506i \(-0.426565\pi\)
0.228661 + 0.973506i \(0.426565\pi\)
\(588\) 0 0
\(589\) 132.000 0.00923424
\(590\) 8596.00 14888.7i 0.599816 1.03891i
\(591\) 0 0
\(592\) 304.000 + 526.543i 0.0211053 + 0.0365554i
\(593\) 11570.4 20040.5i 0.801246 1.38780i −0.117550 0.993067i \(-0.537504\pi\)
0.918796 0.394732i \(-0.129163\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −8200.00 −0.563566
\(597\) 0 0
\(598\) −7127.64 12345.4i −0.487409 0.844218i
\(599\) −5648.00 9782.62i −0.385260 0.667291i 0.606545 0.795049i \(-0.292555\pi\)
−0.991805 + 0.127759i \(0.959222\pi\)
\(600\) 0 0
\(601\) −8727.11 −0.592323 −0.296162 0.955138i \(-0.595707\pi\)
−0.296162 + 0.955138i \(0.595707\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 944.000 1635.06i 0.0635941 0.110148i
\(605\) −11235.9 19461.2i −0.755050 1.30779i
\(606\) 0 0
\(607\) 9868.38 17092.5i 0.659877 1.14294i −0.320770 0.947157i \(-0.603942\pi\)
0.980647 0.195783i \(-0.0627249\pi\)
\(608\) 45.2548 0.00301863
\(609\) 0 0
\(610\) 560.000 0.0371701
\(611\) 13320.0 23070.9i 0.881947 1.52758i
\(612\) 0 0
\(613\) −8481.00 14689.5i −0.558800 0.967870i −0.997597 0.0692837i \(-0.977929\pi\)
0.438797 0.898586i \(-0.355405\pi\)
\(614\) −4767.31 + 8257.23i −0.313344 + 0.542727i
\(615\) 0 0
\(616\) 0 0
\(617\) 19034.0 1.24194 0.620972 0.783832i \(-0.286738\pi\)
0.620972 + 0.783832i \(0.286738\pi\)
\(618\) 0 0
\(619\) −9338.76 16175.2i −0.606392 1.05030i −0.991830 0.127568i \(-0.959283\pi\)
0.385438 0.922734i \(-0.374050\pi\)
\(620\) 3696.00 + 6401.66i 0.239411 + 0.414672i
\(621\) 0 0
\(622\) −13553.8 −0.873728
\(623\) 0 0
\(624\) 0 0
\(625\) −11144.5 + 19302.8i −0.713248 + 1.23538i
\(626\) −6190.01 10721.4i −0.395212 0.684527i
\(627\) 0 0
\(628\) −4423.66 + 7662.00i −0.281088 + 0.486859i
\(629\) −53.7401 −0.00340661
\(630\) 0 0
\(631\) −14716.0 −0.928423 −0.464211 0.885724i \(-0.653662\pi\)
−0.464211 + 0.885724i \(0.653662\pi\)
\(632\) −4880.00 + 8452.41i −0.307146 + 0.531992i
\(633\) 0 0
\(634\) 9826.00 + 17019.1i 0.615521 + 1.06611i
\(635\) 17027.1 29491.9i 1.06410 1.84307i
\(636\) 0 0
\(637\) 0 0
\(638\) 8008.00 0.496928
\(639\) 0 0
\(640\) 1267.14 + 2194.74i 0.0782624 + 0.135554i
\(641\) 2365.00 + 4096.30i 0.145728 + 0.252409i 0.929644 0.368458i \(-0.120114\pi\)
−0.783916 + 0.620867i \(0.786781\pi\)
\(642\) 0 0
\(643\) −19056.5 −1.16877 −0.584383 0.811478i \(-0.698663\pi\)
−0.584383 + 0.811478i \(0.698663\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −2.00000 + 3.46410i −0.000121810 + 0.000210980i
\(647\) −4671.15 8090.66i −0.283836 0.491618i 0.688490 0.725245i \(-0.258274\pi\)
−0.972326 + 0.233627i \(0.924940\pi\)
\(648\) 0 0
\(649\) −3039.14 + 5263.95i −0.183816 + 0.318379i
\(650\) −27186.8 −1.64055
\(651\) 0 0
\(652\) 13144.0 0.789507
\(653\) 1887.00 3268.38i 0.113084 0.195868i −0.803928 0.594727i \(-0.797260\pi\)
0.917012 + 0.398859i \(0.130594\pi\)
\(654\) 0 0
\(655\) −17178.0 29753.2i −1.02473 1.77489i
\(656\) 1006.92 1744.04i 0.0599293 0.103801i
\(657\) 0 0
\(658\) 0 0
\(659\) 21150.0 1.25021 0.625104 0.780541i \(-0.285057\pi\)
0.625104 + 0.780541i \(0.285057\pi\)
\(660\) 0 0
\(661\) −5188.75 8987.18i −0.305324 0.528836i 0.672010 0.740542i \(-0.265431\pi\)
−0.977333 + 0.211706i \(0.932098\pi\)
\(662\) 5738.00 + 9938.51i 0.336879 + 0.583491i
\(663\) 0 0
\(664\) 3382.80 0.197708
\(665\) 0 0
\(666\) 0 0
\(667\) 20020.0 34675.7i 1.16219 2.01296i
\(668\) 2981.16 + 5163.52i 0.172672 + 0.299076i
\(669\) 0 0
\(670\) 13542.5 23456.3i 0.780885 1.35253i
\(671\) −197.990 −0.0113909
\(672\) 0 0
\(673\) −1164.00 −0.0666700 −0.0333350 0.999444i \(-0.510613\pi\)
−0.0333350 + 0.999444i \(0.510613\pi\)
\(674\) 2254.00 3904.04i 0.128814 0.223113i
\(675\) 0 0
\(676\) −790.000 1368.32i −0.0449477 0.0778516i
\(677\) −13576.5 + 23515.1i −0.770732 + 1.33495i 0.166431 + 0.986053i \(0.446776\pi\)
−0.937162 + 0.348893i \(0.886558\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −224.000 −0.0126324
\(681\) 0 0
\(682\) −1306.73 2263.33i −0.0733686 0.127078i
\(683\) −8298.00 14372.6i −0.464882 0.805199i 0.534315 0.845286i \(-0.320570\pi\)
−0.999196 + 0.0400871i \(0.987236\pi\)
\(684\) 0 0
\(685\) 16393.6 0.914403
\(686\) 0 0
\(687\) 0 0
\(688\) 272.000 471.118i 0.0150725 0.0261064i
\(689\) 1883.73 + 3262.72i 0.104157 + 0.180406i
\(690\) 0 0
\(691\) 5649.08 9784.49i 0.311000 0.538668i −0.667579 0.744539i \(-0.732669\pi\)
0.978579 + 0.205871i \(0.0660028\pi\)
\(692\) −8281.63 −0.454943
\(693\) 0 0
\(694\) 3972.00 0.217255
\(695\) 4214.00 7298.86i 0.229994 0.398362i
\(696\) 0 0
\(697\) 89.0000 + 154.153i 0.00483661 + 0.00837725i
\(698\) 6771.25 11728.2i 0.367186 0.635985i
\(699\) 0 0
\(700\) 0 0
\(701\) 2754.00 0.148384 0.0741920 0.997244i \(-0.476362\pi\)
0.0741920 + 0.997244i \(0.476362\pi\)
\(702\) 0 0
\(703\) 26.8701 + 46.5403i 0.00144157 + 0.00249687i
\(704\) −448.000 775.959i −0.0239839 0.0415413i
\(705\) 0 0
\(706\) 13986.6 0.745597
\(707\) 0 0
\(708\) 0 0
\(709\) −14717.0 + 25490.6i −0.779561 + 1.35024i 0.152634 + 0.988283i \(0.451224\pi\)
−0.932195 + 0.361956i \(0.882109\pi\)
\(710\) −11641.8 20164.2i −0.615365 1.06584i
\(711\) 0 0
\(712\) −2472.05 + 4281.71i −0.130118 + 0.225370i
\(713\) −13067.3 −0.686361
\(714\) 0 0
\(715\) 14112.0 0.738124
\(716\) 1080.00 1870.61i 0.0563708 0.0976371i
\(717\) 0 0
\(718\) 5944.00 + 10295.3i 0.308953 + 0.535122i
\(719\) 8834.59 15302.0i 0.458240 0.793695i −0.540628 0.841262i \(-0.681813\pi\)
0.998868 + 0.0475666i \(0.0151466\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −13714.0 −0.706901
\(723\) 0 0
\(724\) 7568.87 + 13109.7i 0.388529 + 0.672952i
\(725\) −38181.0 66131.4i −1.95587 3.38767i
\(726\) 0 0
\(727\) −28445.5 −1.45115 −0.725574 0.688144i \(-0.758426\pi\)
−0.725574 + 0.688144i \(0.758426\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 5348.00 9263.01i 0.271148 0.469643i
\(731\) 24.0416 + 41.6413i 0.00121643 + 0.00210692i
\(732\) 0 0
\(733\) 11170.9 19348.5i 0.562900 0.974971i −0.434342 0.900748i \(-0.643019\pi\)
0.997242 0.0742230i \(-0.0236477\pi\)
\(734\) 1685.74 0.0847710
\(735\) 0 0
\(736\) −4480.00 −0.224368
\(737\) −4788.00 + 8293.06i −0.239306 + 0.414490i
\(738\) 0 0
\(739\) −10335.0 17900.7i −0.514451 0.891055i −0.999859 0.0167675i \(-0.994662\pi\)
0.485409 0.874287i \(-0.338671\pi\)
\(740\) −1504.72 + 2606.26i −0.0747496 + 0.129470i
\(741\) 0 0
\(742\) 0 0
\(743\) 25400.0 1.25415 0.627076 0.778958i \(-0.284251\pi\)
0.627076 + 0.778958i \(0.284251\pi\)
\(744\) 0 0
\(745\) −20294.0 35150.2i −0.998004 1.72859i
\(746\) 5726.00 + 9917.72i 0.281024 + 0.486748i
\(747\) 0 0
\(748\) 79.1960 0.00387124
\(749\) 0 0
\(750\) 0 0
\(751\) −14590.0 + 25270.6i −0.708917 + 1.22788i 0.256342 + 0.966586i \(0.417483\pi\)
−0.965259 + 0.261294i \(0.915851\pi\)
\(752\) −4186.07 7250.49i −0.202992 0.351593i
\(753\) 0 0
\(754\) 14560.7 25219.9i 0.703277 1.21811i
\(755\) 9345.12 0.450469
\(756\) 0 0
\(757\) −26206.0 −1.25822 −0.629110 0.777316i \(-0.716581\pi\)
−0.629110 + 0.777316i \(0.716581\pi\)
\(758\) −10330.0 + 17892.1i −0.494990 + 0.857348i
\(759\) 0 0
\(760\) 112.000 + 193.990i 0.00534561 + 0.00925888i
\(761\) −3431.59 + 5943.69i −0.163463 + 0.283125i −0.936108 0.351712i \(-0.885600\pi\)
0.772646 + 0.634838i \(0.218933\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −4112.00 −0.194721
\(765\) 0 0
\(766\) −1004.09 1739.14i −0.0473620 0.0820334i
\(767\) 11052.0 + 19142.6i 0.520293 + 0.901174i
\(768\) 0 0
\(769\) 9058.04 0.424761 0.212380 0.977187i \(-0.431878\pi\)
0.212380 + 0.977187i \(0.431878\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −9184.00 + 15907.2i −0.428160 + 0.741595i
\(773\) 66.4680 + 115.126i 0.00309274 + 0.00535679i 0.867568 0.497319i \(-0.165682\pi\)
−0.864475 + 0.502676i \(0.832349\pi\)
\(774\) 0 0
\(775\) −12460.6 + 21582.5i −0.577547 + 1.00034i
\(776\) −11868.1 −0.549020
\(777\) 0 0
\(778\) −10420.0 −0.480174
\(779\) 89.0000 154.153i 0.00409340 0.00708997i
\(780\) 0 0
\(781\) 4116.00 + 7129.12i 0.188581 + 0.326633i
\(782\) 197.990 342.929i 0.00905384 0.0156817i
\(783\) 0 0
\(784\) 0 0
\(785\) −43792.0 −1.99109
\(786\) 0 0
\(787\) −4364.97 7560.35i −0.197706 0.342436i 0.750078 0.661349i \(-0.230016\pi\)
−0.947784 + 0.318913i \(0.896682\pi\)
\(788\) 1588.00 + 2750.50i 0.0717895 + 0.124343i
\(789\) 0 0
\(790\) −48309.5 −2.17567
\(791\) 0 0