Properties

Label 882.4.g.ba.361.1
Level $882$
Weight $4$
Character 882.361
Analytic conductor $52.040$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(52.0396846251\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
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 361.1
Root \(-0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 882.361
Dual form 882.4.g.ba.667.1

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

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

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
\(5\) −9.89949 17.1464i −0.885438 1.53362i −0.845211 0.534433i \(-0.820525\pi\)
−0.0402266 0.999191i \(-0.512808\pi\)
\(6\) 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 −0.945870 0.324545i \(-0.894789\pi\)
0.753999 + 0.656875i \(0.228122\pi\)
\(12\) 0 0
\(13\) 50.9117 1.08618 0.543091 0.839674i \(-0.317254\pi\)
0.543091 + 0.839674i \(0.317254\pi\)
\(14\) 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 \(-0.830122\pi\)
0.871025 + 0.491238i \(0.163455\pi\)
\(18\) 0 0
\(19\) 0.707107 + 1.22474i 0.00853797 + 0.0147882i 0.870263 0.492588i \(-0.163949\pi\)
−0.861725 + 0.507376i \(0.830616\pi\)
\(20\) 79.1960 0.885438
\(21\) 0 0
\(22\) 28.0000 0.271346
\(23\) 70.0000 + 121.244i 0.634609 + 1.09918i 0.986598 + 0.163171i \(0.0521722\pi\)
−0.351989 + 0.936004i \(0.614494\pi\)
\(24\) 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 \(-0.746182\pi\)
0.968961 + 0.247213i \(0.0795149\pi\)
\(32\) −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 0.905144 0.425104i \(-0.139763\pi\)
−0.820723 + 0.571326i \(0.806429\pi\)
\(38\) 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 \(-0.422945\pi\)
0.239717 + 0.970843i \(0.422945\pi\)
\(42\) 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 0.911483 + 0.411337i \(0.134938\pi\)
−0.0995134 + 0.995036i \(0.531729\pi\)
\(48\) 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 −0.909981 0.414650i \(-0.863904\pi\)
0.814088 + 0.580742i \(0.197237\pi\)
\(54\) 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 \(-0.674329\pi\)
0.999710 + 0.0240689i \(0.00766211\pi\)
\(60\) 0 0
\(61\) −7.07107 12.2474i −0.0148419 0.0257070i 0.858509 0.512798i \(-0.171391\pi\)
−0.873351 + 0.487091i \(0.838058\pi\)
\(62\) −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 0.365196 + 0.930930i \(0.381002\pi\)
−0.988808 + 0.149196i \(0.952332\pi\)
\(68\) 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 \(-0.763857\pi\)
0.953747 + 0.300610i \(0.0971902\pi\)
\(74\) 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 −0.863286 0.504715i \(-0.831598\pi\)
−0.00545246 0.999985i \(-0.501736\pi\)
\(80\) −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 \(-0.590202\pi\)
−0.279601 + 0.960116i \(0.590202\pi\)
\(84\) 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 \(-0.0466996\pi\)
−0.621229 + 0.783629i \(0.713366\pi\)
\(90\) 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 \(-0.217028\pi\)
0.776431 + 0.630202i \(0.217028\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −534.000 924.915i −0.534000 0.924915i
\(101\) 564.271 977.346i 0.555912 0.962867i −0.441920 0.897054i \(-0.645703\pi\)
0.997832 0.0658130i \(-0.0209641\pi\)
\(102\) 0 0
\(103\) 434.164 + 751.993i 0.415334 + 0.719380i 0.995463 0.0951446i \(-0.0303314\pi\)
−0.580129 + 0.814524i \(0.696998\pi\)
\(104\) 407.294 0.384023
\(105\) 0 0
\(106\) 148.000 0.135613
\(107\) −842.000 1458.39i −0.760740 1.31764i −0.942469 0.334292i \(-0.891503\pi\)
0.181729 0.983349i \(-0.441831\pi\)
\(108\) 0 0
\(109\) 409.000 708.409i 0.359405 0.622507i −0.628457 0.777844i \(-0.716313\pi\)
0.987861 + 0.155337i \(0.0496465\pi\)
\(110\) −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 −0.995634 0.0933484i \(-0.970243\pi\)
0.416975 0.908918i \(-0.363090\pi\)
\(132\) 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 −0.707576 0.706638i \(-0.750211\pi\)
0.965754 + 0.259460i \(0.0835445\pi\)
\(138\) 0 0
\(139\) −425.678 −0.259752 −0.129876 0.991530i \(-0.541458\pi\)
−0.129876 + 0.991530i \(0.541458\pi\)
\(140\) 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 0.997182 + 0.0750264i \(0.0239041\pi\)
−0.433616 + 0.901098i \(0.642763\pi\)
\(150\) 0 0
\(151\) 236.000 408.764i 0.127188 0.220296i −0.795398 0.606087i \(-0.792738\pi\)
0.922586 + 0.385791i \(0.126071\pi\)
\(152\) 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 −0.435130 0.900367i \(-0.643298\pi\)
0.997306 0.0733498i \(-0.0233690\pi\)
\(158\) −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 −0.926269 0.376863i \(-0.877003\pi\)
0.136762 0.990604i \(-0.456331\pi\)
\(164\) −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 \(-0.387763\pi\)
0.345343 + 0.938476i \(0.387763\pi\)
\(168\) 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 \(-0.317007\pi\)
−0.998685 + 0.0512682i \(0.983674\pi\)
\(174\) 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 −0.804133 0.594449i \(-0.797370\pi\)
0.916875 + 0.399175i \(0.130703\pi\)
\(180\) 0 0
\(181\) 3784.44 1.55412 0.777058 0.629429i \(-0.216711\pi\)
0.777058 + 0.629429i \(0.216711\pi\)
\(182\) 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 0.946809 0.321796i \(-0.104286\pi\)
−0.752088 + 0.659063i \(0.770953\pi\)
\(192\) 0 0
\(193\) −2296.00 + 3976.79i −0.856320 + 1.48319i 0.0190956 + 0.999818i \(0.493921\pi\)
−0.875415 + 0.483372i \(0.839412\pi\)
\(194\) −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 \(-0.979354\pi\)
0.555080 + 0.831797i \(0.312688\pi\)
\(200\) −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 \(-0.672099\pi\)
−0.514707 + 0.857366i \(0.672099\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −540.000 935.307i −0.158939 0.275291i
\(227\) 2645.29 4581.77i 0.773453 1.33966i −0.162207 0.986757i \(-0.551861\pi\)
0.935660 0.352903i \(-0.114805\pi\)
\(228\) 0 0
\(229\) 1374.62 + 2380.90i 0.396669 + 0.687051i 0.993313 0.115456i \(-0.0368328\pi\)
−0.596644 + 0.802506i \(0.703499\pi\)
\(230\) −5543.72 −1.58931
\(231\) 0 0
\(232\) 2288.00 0.647477
\(233\) 36.0000 + 62.3538i 0.0101221 + 0.0175319i 0.871042 0.491208i \(-0.163445\pi\)
−0.860920 + 0.508740i \(0.830111\pi\)
\(234\) 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 \(-0.767347\pi\)
0.950394 + 0.311050i \(0.100681\pi\)
\(242\) 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 \(-0.537386\pi\)
−0.117182 + 0.993110i \(0.537386\pi\)
\(252\) 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 \(-0.130368\pi\)
−0.803506 + 0.595296i \(0.797035\pi\)
\(258\) 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 −0.0553595 0.998466i \(-0.517630\pi\)
0.892377 0.451291i \(-0.149036\pi\)
\(264\) 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 −0.477172 0.878810i \(-0.658338\pi\)
0.999658 0.0261615i \(-0.00832843\pi\)
\(270\) 0 0
\(271\) 1182.28 + 2047.77i 0.265013 + 0.459016i 0.967567 0.252614i \(-0.0812904\pi\)
−0.702554 + 0.711630i \(0.747957\pi\)
\(272\) −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 −0.997252 0.0740794i \(-0.976398\pi\)
0.562781 + 0.826606i \(0.309731\pi\)
\(278\) 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 −0.482174 0.876075i \(-0.660153\pi\)
0.999791 0.0204627i \(-0.00651393\pi\)
\(284\) 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 \(-0.562970\pi\)
−0.196538 + 0.980496i \(0.562970\pi\)
\(294\) 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 \(-0.646134\pi\)
−0.443135 + 0.896455i \(0.646134\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 1848.00 + 3200.83i 0.338579 + 0.586435i
\(311\) −3388.46 + 5868.98i −0.617819 + 1.07009i 0.372064 + 0.928207i \(0.378650\pi\)
−0.989883 + 0.141887i \(0.954683\pi\)
\(312\) 0 0
\(313\) 3095.01 + 5360.71i 0.558914 + 0.968068i 0.997587 + 0.0694210i \(0.0221152\pi\)
−0.438673 + 0.898647i \(0.644551\pi\)
\(314\) −4423.66 −0.795037
\(315\) 0 0
\(316\) 4880.00 0.868739
\(317\) 4913.00 + 8509.57i 0.870478 + 1.50771i 0.861503 + 0.507753i \(0.169524\pi\)
0.00897524 + 0.999960i \(0.497143\pi\)
\(318\) 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 0.999635 0.0270189i \(-0.00860142\pi\)
−0.523216 + 0.852200i \(0.675268\pi\)
\(332\) 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 −0.932557 0.361024i \(-0.882427\pi\)
0.778934 + 0.627106i \(0.215761\pi\)
\(348\) 0 0
\(349\) 6771.25 1.03856 0.519279 0.854605i \(-0.326200\pi\)
0.519279 + 0.854605i \(0.326200\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −224.000 387.979i −0.0339183 0.0587482i
\(353\) 3496.64 6056.36i 0.527217 0.913166i −0.472280 0.881449i \(-0.656569\pi\)
0.999497 0.0317177i \(-0.0100978\pi\)
\(354\) 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 0.997451 0.0713606i \(-0.0227341\pi\)
−0.560525 + 0.828137i \(0.689401\pi\)
\(360\) 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 \(-0.814242\pi\)
0.894439 + 0.447190i \(0.147575\pi\)
\(368\) 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 0.993408 0.114634i \(-0.0365696\pi\)
−0.595980 + 0.802999i \(0.703236\pi\)
\(374\) 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 \(-0.145330\pi\)
−0.830591 + 0.556884i \(0.811997\pi\)
\(384\) 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 −0.644811 0.764342i \(-0.723064\pi\)
0.984345 + 0.176252i \(0.0563973\pi\)
\(390\) 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 \(-0.165187\pi\)
−0.863692 + 0.504020i \(0.831854\pi\)
\(398\) 4972.37 0.626238
\(399\) 0 0
\(400\) 4272.00 0.534000
\(401\) −249.000 431.281i −0.0310086 0.0537085i 0.850105 0.526614i \(-0.176539\pi\)
−0.881113 + 0.472905i \(0.843205\pi\)
\(402\) 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 \(-0.898357\pi\)
0.746588 + 0.665286i \(0.231691\pi\)
\(410\) −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 \(-0.822161\pi\)
−0.847946 + 0.530082i \(0.822161\pi\)
\(420\) 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 −0.976076 0.217429i \(-0.930233\pi\)
0.676337 + 0.736592i \(0.263566\pi\)
\(432\) 0 0
\(433\) −6487.00 −0.719966 −0.359983 0.932959i \(-0.617217\pi\)
−0.359983 + 0.932959i \(0.617217\pi\)
\(434\) 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 −0.944183 0.329420i \(-0.893147\pi\)
0.186806 0.982397i \(-0.440187\pi\)
\(440\) 2217.49 0.240260
\(441\) 0 0
\(442\) −144.000 −0.0154963
\(443\) 2998.00 + 5192.69i 0.321533 + 0.556912i 0.980805 0.194993i \(-0.0624684\pi\)
−0.659271 + 0.751905i \(0.729135\pi\)
\(444\) 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 −0.996190 0.0872080i \(-0.972206\pi\)
0.422571 0.906330i \(-0.361128\pi\)
\(458\) 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 \(-0.664596\pi\)
−0.494356 + 0.869260i \(0.664596\pi\)
\(462\) 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 0.864693 + 0.502301i \(0.167513\pi\)
0.00265876 + 0.999996i \(0.499154\pi\)
\(468\) 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 \(-0.798526\pi\)
0.915420 + 0.402501i \(0.131859\pi\)
\(480\) 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 −0.887750 0.460326i \(-0.847733\pi\)
0.842529 + 0.538651i \(0.181066\pi\)
\(488\) −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 0.998329 + 0.0577938i \(0.0184066\pi\)
−0.449113 + 0.893475i \(0.648260\pi\)
\(500\) −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 \(-0.465857\pi\)
0.107058 + 0.994253i \(0.465857\pi\)
\(504\) 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 \(-0.246610\pi\)
−0.963115 + 0.269090i \(0.913277\pi\)
\(510\) 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 \(-0.833314\pi\)
0.866055 + 0.499949i \(0.166648\pi\)
\(522\) 0 0
\(523\) 6128.49 + 10614.9i 0.512391 + 0.887487i 0.999897 + 0.0143672i \(0.00457337\pi\)
−0.487506 + 0.873120i \(0.662093\pi\)
\(524\) 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 0.822419 0.568882i \(-0.192624\pi\)
−0.903876 + 0.427795i \(0.859291\pi\)
\(542\) 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 −0.702934 0.711255i \(-0.748127\pi\)
0.967432 + 0.253131i \(0.0814605\pi\)
\(558\) 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 \(-0.852840\pi\)
0.833778 + 0.552099i \(0.186173\pi\)
\(564\) 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 0.703964 0.710236i \(-0.251412\pi\)
−0.967064 + 0.254533i \(0.918078\pi\)
\(570\) 0 0
\(571\) 10303.0 17845.3i 0.755109 1.30789i −0.190211 0.981743i \(-0.560917\pi\)
0.945320 0.326144i \(-0.105749\pi\)
\(572\) −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 \(-0.730461\pi\)
0.979984 + 0.199078i \(0.0637946\pi\)
\(578\) 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 \(-0.573435\pi\)
−0.228661 + 0.973506i \(0.573435\pi\)
\(588\) 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 −0.918796 0.394732i \(-0.870837\pi\)
0.117550 0.993067i \(-0.462496\pi\)
\(594\) 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 −0.991805 0.127759i \(-0.959222\pi\)
0.606545 + 0.795049i \(0.292555\pi\)
\(600\) 0 0
\(601\) 8727.11 0.592323 0.296162 0.955138i \(-0.404293\pi\)
0.296162 + 0.955138i \(0.404293\pi\)
\(602\) 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 −0.980647 0.195783i \(-0.937275\pi\)
0.320770 0.947157i \(-0.396058\pi\)
\(608\) −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 0.438797 + 0.898586i \(0.355405\pi\)
−0.997597 + 0.0692837i \(0.977929\pi\)
\(614\) 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 −0.385438 0.922734i \(-0.625950\pi\)
0.991830 0.127568i \(-0.0407169\pi\)
\(620\) 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 −0.783916 0.620867i \(-0.786781\pi\)
0.929644 + 0.368458i \(0.120114\pi\)
\(642\) 0 0
\(643\) 19056.5 1.16877 0.584383 0.811478i \(-0.301337\pi\)
0.584383 + 0.811478i \(0.301337\pi\)
\(644\) 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 \(-0.741726\pi\)
0.972326 + 0.233627i \(0.0750596\pi\)
\(648\) 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 0.917012 0.398859i \(-0.130594\pi\)
−0.803928 + 0.594727i \(0.797260\pi\)
\(654\) 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 \(-0.734569\pi\)
0.977333 + 0.211706i \(0.0679020\pi\)
\(662\) 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 0.937162 + 0.348893i \(0.113442\pi\)
−0.166431 + 0.986053i \(0.553224\pi\)
\(678\) 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 −0.999196 0.0400871i \(-0.987236\pi\)
0.534315 + 0.845286i \(0.320570\pi\)
\(684\) 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 \(-0.267331\pi\)
−0.978579 + 0.205871i \(0.933997\pi\)
\(692\) 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 −0.932195 0.361956i \(-0.882109\pi\)
0.152634 0.988283i \(-0.451224\pi\)
\(710\) 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 \(-0.318187\pi\)
−0.998868 + 0.0475666i \(0.984853\pi\)
\(720\) 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 \(-0.241574\pi\)
0.725574 + 0.688144i \(0.241574\pi\)
\(728\) 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 −0.997242 0.0742230i \(-0.976352\pi\)
0.434342 0.900748i \(-0.356981\pi\)
\(734\) −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 0.485409 + 0.874287i \(0.338671\pi\)
−0.999859 + 0.0167675i \(0.994662\pi\)
\(740\) 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 −0.965259 0.261294i \(-0.915851\pi\)
0.256342 0.966586i \(-0.417483\pi\)
\(752\) 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 \(-0.114400\pi\)
−0.772646 + 0.634838i \(0.781067\pi\)
\(762\) 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 \(-0.568122\pi\)
−0.212380 + 0.977187i \(0.568122\pi\)
\(770\) 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 \(-0.834318\pi\)
0.864475 + 0.502676i \(0.167651\pi\)
\(774\) 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 \(-0.769984\pi\)
0.947784 + 0.318913i \(0.103318\pi\)
\(788\) 1588.00 2750.50i 0.0717895 0.124343i
\(789\) 0 0
\(790\) 48309.5 2.17567
\(791\) 0 0