Properties

Label 882.4.g.e.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 126)
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.e.667.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-3.00000 - 5.19615i) q^{5} +8.00000 q^{8} +O(q^{10})\) \(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-3.00000 - 5.19615i) q^{5} +8.00000 q^{8} +(-6.00000 + 10.3923i) q^{10} +(-15.0000 + 25.9808i) q^{11} +2.00000 q^{13} +(-8.00000 - 13.8564i) q^{16} +(-33.0000 + 57.1577i) q^{17} +(26.0000 + 45.0333i) q^{19} +24.0000 q^{20} +60.0000 q^{22} +(-57.0000 - 98.7269i) q^{23} +(44.5000 - 77.0763i) q^{25} +(-2.00000 - 3.46410i) q^{26} +72.0000 q^{29} +(98.0000 - 169.741i) q^{31} +(-16.0000 + 27.7128i) q^{32} +132.000 q^{34} +(143.000 + 247.683i) q^{37} +(52.0000 - 90.0666i) q^{38} +(-24.0000 - 41.5692i) q^{40} -378.000 q^{41} +164.000 q^{43} +(-60.0000 - 103.923i) q^{44} +(-114.000 + 197.454i) q^{46} +(114.000 + 197.454i) q^{47} -178.000 q^{50} +(-4.00000 + 6.92820i) q^{52} +(174.000 - 301.377i) q^{53} +180.000 q^{55} +(-72.0000 - 124.708i) q^{58} +(174.000 - 301.377i) q^{59} +(53.0000 + 91.7987i) q^{61} -392.000 q^{62} +64.0000 q^{64} +(-6.00000 - 10.3923i) q^{65} +(-298.000 + 516.151i) q^{67} +(-132.000 - 228.631i) q^{68} +630.000 q^{71} +(521.000 - 902.398i) q^{73} +(286.000 - 495.367i) q^{74} -208.000 q^{76} +(44.0000 + 76.2102i) q^{79} +(-48.0000 + 83.1384i) q^{80} +(378.000 + 654.715i) q^{82} -1440.00 q^{83} +396.000 q^{85} +(-164.000 - 284.056i) q^{86} +(-120.000 + 207.846i) q^{88} +(-687.000 - 1189.92i) q^{89} +456.000 q^{92} +(228.000 - 394.908i) q^{94} +(156.000 - 270.200i) q^{95} -34.0000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{2} - 4q^{4} - 6q^{5} + 16q^{8} + O(q^{10}) \) \( 2q - 2q^{2} - 4q^{4} - 6q^{5} + 16q^{8} - 12q^{10} - 30q^{11} + 4q^{13} - 16q^{16} - 66q^{17} + 52q^{19} + 48q^{20} + 120q^{22} - 114q^{23} + 89q^{25} - 4q^{26} + 144q^{29} + 196q^{31} - 32q^{32} + 264q^{34} + 286q^{37} + 104q^{38} - 48q^{40} - 756q^{41} + 328q^{43} - 120q^{44} - 228q^{46} + 228q^{47} - 356q^{50} - 8q^{52} + 348q^{53} + 360q^{55} - 144q^{58} + 348q^{59} + 106q^{61} - 784q^{62} + 128q^{64} - 12q^{65} - 596q^{67} - 264q^{68} + 1260q^{71} + 1042q^{73} + 572q^{74} - 416q^{76} + 88q^{79} - 96q^{80} + 756q^{82} - 2880q^{83} + 792q^{85} - 328q^{86} - 240q^{88} - 1374q^{89} + 912q^{92} + 456q^{94} + 312q^{95} - 68q^{97} + O(q^{100}) \)

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
\(5\) −3.00000 5.19615i −0.268328 0.464758i 0.700102 0.714043i \(-0.253138\pi\)
−0.968430 + 0.249285i \(0.919804\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 8.00000 0.353553
\(9\) 0 0
\(10\) −6.00000 + 10.3923i −0.189737 + 0.328634i
\(11\) −15.0000 + 25.9808i −0.411152 + 0.712136i −0.995016 0.0997155i \(-0.968207\pi\)
0.583864 + 0.811851i \(0.301540\pi\)
\(12\) 0 0
\(13\) 2.00000 0.0426692 0.0213346 0.999772i \(-0.493208\pi\)
0.0213346 + 0.999772i \(0.493208\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) −33.0000 + 57.1577i −0.470804 + 0.815457i −0.999442 0.0333902i \(-0.989370\pi\)
0.528638 + 0.848847i \(0.322703\pi\)
\(18\) 0 0
\(19\) 26.0000 + 45.0333i 0.313937 + 0.543755i 0.979211 0.202844i \(-0.0650185\pi\)
−0.665274 + 0.746600i \(0.731685\pi\)
\(20\) 24.0000 0.268328
\(21\) 0 0
\(22\) 60.0000 0.581456
\(23\) −57.0000 98.7269i −0.516753 0.895043i −0.999811 0.0194541i \(-0.993807\pi\)
0.483058 0.875589i \(-0.339526\pi\)
\(24\) 0 0
\(25\) 44.5000 77.0763i 0.356000 0.616610i
\(26\) −2.00000 3.46410i −0.0150859 0.0261295i
\(27\) 0 0
\(28\) 0 0
\(29\) 72.0000 0.461037 0.230518 0.973068i \(-0.425958\pi\)
0.230518 + 0.973068i \(0.425958\pi\)
\(30\) 0 0
\(31\) 98.0000 169.741i 0.567785 0.983432i −0.429000 0.903304i \(-0.641134\pi\)
0.996785 0.0801272i \(-0.0255326\pi\)
\(32\) −16.0000 + 27.7128i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 132.000 0.665818
\(35\) 0 0
\(36\) 0 0
\(37\) 143.000 + 247.683i 0.635380 + 1.10051i 0.986435 + 0.164155i \(0.0524898\pi\)
−0.351055 + 0.936355i \(0.614177\pi\)
\(38\) 52.0000 90.0666i 0.221987 0.384493i
\(39\) 0 0
\(40\) −24.0000 41.5692i −0.0948683 0.164317i
\(41\) −378.000 −1.43985 −0.719923 0.694054i \(-0.755823\pi\)
−0.719923 + 0.694054i \(0.755823\pi\)
\(42\) 0 0
\(43\) 164.000 0.581622 0.290811 0.956780i \(-0.406075\pi\)
0.290811 + 0.956780i \(0.406075\pi\)
\(44\) −60.0000 103.923i −0.205576 0.356068i
\(45\) 0 0
\(46\) −114.000 + 197.454i −0.365400 + 0.632891i
\(47\) 114.000 + 197.454i 0.353800 + 0.612800i 0.986912 0.161261i \(-0.0515560\pi\)
−0.633112 + 0.774060i \(0.718223\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −178.000 −0.503460
\(51\) 0 0
\(52\) −4.00000 + 6.92820i −0.0106673 + 0.0184763i
\(53\) 174.000 301.377i 0.450957 0.781081i −0.547488 0.836813i \(-0.684416\pi\)
0.998446 + 0.0557323i \(0.0177493\pi\)
\(54\) 0 0
\(55\) 180.000 0.441294
\(56\) 0 0
\(57\) 0 0
\(58\) −72.0000 124.708i −0.163001 0.282326i
\(59\) 174.000 301.377i 0.383947 0.665016i −0.607676 0.794185i \(-0.707898\pi\)
0.991622 + 0.129170i \(0.0412312\pi\)
\(60\) 0 0
\(61\) 53.0000 + 91.7987i 0.111245 + 0.192682i 0.916273 0.400555i \(-0.131183\pi\)
−0.805027 + 0.593238i \(0.797849\pi\)
\(62\) −392.000 −0.802969
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −6.00000 10.3923i −0.0114494 0.0198309i
\(66\) 0 0
\(67\) −298.000 + 516.151i −0.543381 + 0.941163i 0.455326 + 0.890325i \(0.349523\pi\)
−0.998707 + 0.0508381i \(0.983811\pi\)
\(68\) −132.000 228.631i −0.235402 0.407729i
\(69\) 0 0
\(70\) 0 0
\(71\) 630.000 1.05306 0.526530 0.850157i \(-0.323493\pi\)
0.526530 + 0.850157i \(0.323493\pi\)
\(72\) 0 0
\(73\) 521.000 902.398i 0.835321 1.44682i −0.0584477 0.998290i \(-0.518615\pi\)
0.893769 0.448528i \(-0.148052\pi\)
\(74\) 286.000 495.367i 0.449281 0.778178i
\(75\) 0 0
\(76\) −208.000 −0.313937
\(77\) 0 0
\(78\) 0 0
\(79\) 44.0000 + 76.2102i 0.0626631 + 0.108536i 0.895655 0.444750i \(-0.146707\pi\)
−0.832992 + 0.553285i \(0.813374\pi\)
\(80\) −48.0000 + 83.1384i −0.0670820 + 0.116190i
\(81\) 0 0
\(82\) 378.000 + 654.715i 0.509062 + 0.881722i
\(83\) −1440.00 −1.90434 −0.952172 0.305563i \(-0.901155\pi\)
−0.952172 + 0.305563i \(0.901155\pi\)
\(84\) 0 0
\(85\) 396.000 0.505320
\(86\) −164.000 284.056i −0.205635 0.356170i
\(87\) 0 0
\(88\) −120.000 + 207.846i −0.145364 + 0.251778i
\(89\) −687.000 1189.92i −0.818223 1.41720i −0.906990 0.421152i \(-0.861626\pi\)
0.0887672 0.996052i \(-0.471707\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 456.000 0.516753
\(93\) 0 0
\(94\) 228.000 394.908i 0.250175 0.433315i
\(95\) 156.000 270.200i 0.168476 0.291810i
\(96\) 0 0
\(97\) −34.0000 −0.0355895 −0.0177947 0.999842i \(-0.505665\pi\)
−0.0177947 + 0.999842i \(0.505665\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 178.000 + 308.305i 0.178000 + 0.308305i
\(101\) 219.000 379.319i 0.215756 0.373700i −0.737750 0.675074i \(-0.764112\pi\)
0.953506 + 0.301374i \(0.0974452\pi\)
\(102\) 0 0
\(103\) −838.000 1451.46i −0.801656 1.38851i −0.918525 0.395362i \(-0.870619\pi\)
0.116869 0.993147i \(-0.462714\pi\)
\(104\) 16.0000 0.0150859
\(105\) 0 0
\(106\) −696.000 −0.637750
\(107\) −1011.00 1751.10i −0.913430 1.58211i −0.809183 0.587557i \(-0.800090\pi\)
−0.104247 0.994551i \(-0.533243\pi\)
\(108\) 0 0
\(109\) 251.000 434.745i 0.220564 0.382027i −0.734416 0.678700i \(-0.762544\pi\)
0.954979 + 0.296673i \(0.0958770\pi\)
\(110\) −180.000 311.769i −0.156021 0.270237i
\(111\) 0 0
\(112\) 0 0
\(113\) 2016.00 1.67831 0.839156 0.543890i \(-0.183049\pi\)
0.839156 + 0.543890i \(0.183049\pi\)
\(114\) 0 0
\(115\) −342.000 + 592.361i −0.277319 + 0.480330i
\(116\) −144.000 + 249.415i −0.115259 + 0.199635i
\(117\) 0 0
\(118\) −696.000 −0.542983
\(119\) 0 0
\(120\) 0 0
\(121\) 215.500 + 373.257i 0.161908 + 0.280433i
\(122\) 106.000 183.597i 0.0786622 0.136247i
\(123\) 0 0
\(124\) 392.000 + 678.964i 0.283892 + 0.491716i
\(125\) −1284.00 −0.918756
\(126\) 0 0
\(127\) 1784.00 1.24649 0.623246 0.782026i \(-0.285814\pi\)
0.623246 + 0.782026i \(0.285814\pi\)
\(128\) −64.0000 110.851i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) −12.0000 + 20.7846i −0.00809592 + 0.0140225i
\(131\) −804.000 1392.57i −0.536228 0.928773i −0.999103 0.0423499i \(-0.986516\pi\)
0.462875 0.886423i \(-0.346818\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 1192.00 0.768456
\(135\) 0 0
\(136\) −264.000 + 457.261i −0.166455 + 0.288308i
\(137\) 1290.00 2234.35i 0.804468 1.39338i −0.112181 0.993688i \(-0.535784\pi\)
0.916650 0.399692i \(-0.130883\pi\)
\(138\) 0 0
\(139\) 2144.00 1.30829 0.654143 0.756371i \(-0.273030\pi\)
0.654143 + 0.756371i \(0.273030\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −630.000 1091.19i −0.372313 0.644865i
\(143\) −30.0000 + 51.9615i −0.0175435 + 0.0303863i
\(144\) 0 0
\(145\) −216.000 374.123i −0.123709 0.214270i
\(146\) −2084.00 −1.18132
\(147\) 0 0
\(148\) −1144.00 −0.635380
\(149\) −750.000 1299.04i −0.412365 0.714237i 0.582783 0.812628i \(-0.301964\pi\)
−0.995148 + 0.0983907i \(0.968631\pi\)
\(150\) 0 0
\(151\) 620.000 1073.87i 0.334138 0.578745i −0.649181 0.760634i \(-0.724888\pi\)
0.983319 + 0.181890i \(0.0582214\pi\)
\(152\) 208.000 + 360.267i 0.110994 + 0.192247i
\(153\) 0 0
\(154\) 0 0
\(155\) −1176.00 −0.609410
\(156\) 0 0
\(157\) −307.000 + 531.740i −0.156059 + 0.270302i −0.933444 0.358723i \(-0.883212\pi\)
0.777385 + 0.629025i \(0.216546\pi\)
\(158\) 88.0000 152.420i 0.0443095 0.0767463i
\(159\) 0 0
\(160\) 192.000 0.0948683
\(161\) 0 0
\(162\) 0 0
\(163\) −46.0000 79.6743i −0.0221043 0.0382857i 0.854762 0.519021i \(-0.173703\pi\)
−0.876866 + 0.480735i \(0.840370\pi\)
\(164\) 756.000 1309.43i 0.359961 0.623472i
\(165\) 0 0
\(166\) 1440.00 + 2494.15i 0.673287 + 1.16617i
\(167\) −3924.00 −1.81825 −0.909126 0.416520i \(-0.863250\pi\)
−0.909126 + 0.416520i \(0.863250\pi\)
\(168\) 0 0
\(169\) −2193.00 −0.998179
\(170\) −396.000 685.892i −0.178658 0.309444i
\(171\) 0 0
\(172\) −328.000 + 568.113i −0.145406 + 0.251850i
\(173\) 951.000 + 1647.18i 0.417938 + 0.723889i 0.995732 0.0922934i \(-0.0294198\pi\)
−0.577794 + 0.816182i \(0.696086\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 480.000 0.205576
\(177\) 0 0
\(178\) −1374.00 + 2379.84i −0.578571 + 1.00211i
\(179\) 3.00000 5.19615i 0.00125268 0.00216971i −0.865398 0.501084i \(-0.832935\pi\)
0.866651 + 0.498915i \(0.166268\pi\)
\(180\) 0 0
\(181\) −2878.00 −1.18188 −0.590939 0.806716i \(-0.701243\pi\)
−0.590939 + 0.806716i \(0.701243\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −456.000 789.815i −0.182700 0.316445i
\(185\) 858.000 1486.10i 0.340981 0.590596i
\(186\) 0 0
\(187\) −990.000 1714.73i −0.387144 0.670553i
\(188\) −912.000 −0.353800
\(189\) 0 0
\(190\) −624.000 −0.238262
\(191\) 177.000 + 306.573i 0.0670538 + 0.116141i 0.897603 0.440804i \(-0.145307\pi\)
−0.830549 + 0.556945i \(0.811973\pi\)
\(192\) 0 0
\(193\) 2429.00 4207.15i 0.905924 1.56911i 0.0862509 0.996273i \(-0.472511\pi\)
0.819673 0.572832i \(-0.194155\pi\)
\(194\) 34.0000 + 58.8897i 0.0125828 + 0.0217940i
\(195\) 0 0
\(196\) 0 0
\(197\) −396.000 −0.143217 −0.0716087 0.997433i \(-0.522813\pi\)
−0.0716087 + 0.997433i \(0.522813\pi\)
\(198\) 0 0
\(199\) −856.000 + 1482.64i −0.304926 + 0.528147i −0.977245 0.212115i \(-0.931965\pi\)
0.672319 + 0.740262i \(0.265298\pi\)
\(200\) 356.000 616.610i 0.125865 0.218005i
\(201\) 0 0
\(202\) −876.000 −0.305124
\(203\) 0 0
\(204\) 0 0
\(205\) 1134.00 + 1964.15i 0.386351 + 0.669180i
\(206\) −1676.00 + 2902.92i −0.566857 + 0.981824i
\(207\) 0 0
\(208\) −16.0000 27.7128i −0.00533366 0.00923816i
\(209\) −1560.00 −0.516304
\(210\) 0 0
\(211\) −772.000 −0.251880 −0.125940 0.992038i \(-0.540195\pi\)
−0.125940 + 0.992038i \(0.540195\pi\)
\(212\) 696.000 + 1205.51i 0.225479 + 0.390540i
\(213\) 0 0
\(214\) −2022.00 + 3502.21i −0.645893 + 1.11872i
\(215\) −492.000 852.169i −0.156066 0.270314i
\(216\) 0 0
\(217\) 0 0
\(218\) −1004.00 −0.311924
\(219\) 0 0
\(220\) −360.000 + 623.538i −0.110324 + 0.191086i
\(221\) −66.0000 + 114.315i −0.0200889 + 0.0347949i
\(222\) 0 0
\(223\) 776.000 0.233026 0.116513 0.993189i \(-0.462828\pi\)
0.116513 + 0.993189i \(0.462828\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −2016.00 3491.81i −0.593373 1.02775i
\(227\) 894.000 1548.45i 0.261396 0.452751i −0.705217 0.708991i \(-0.749151\pi\)
0.966613 + 0.256240i \(0.0824839\pi\)
\(228\) 0 0
\(229\) −2701.00 4678.27i −0.779420 1.34999i −0.932277 0.361746i \(-0.882181\pi\)
0.152857 0.988248i \(-0.451153\pi\)
\(230\) 1368.00 0.392188
\(231\) 0 0
\(232\) 576.000 0.163001
\(233\) −1506.00 2608.47i −0.423439 0.733418i 0.572834 0.819671i \(-0.305844\pi\)
−0.996273 + 0.0862531i \(0.972511\pi\)
\(234\) 0 0
\(235\) 684.000 1184.72i 0.189869 0.328863i
\(236\) 696.000 + 1205.51i 0.191973 + 0.332508i
\(237\) 0 0
\(238\) 0 0
\(239\) 3546.00 0.959714 0.479857 0.877347i \(-0.340689\pi\)
0.479857 + 0.877347i \(0.340689\pi\)
\(240\) 0 0
\(241\) 1781.00 3084.78i 0.476034 0.824516i −0.523589 0.851971i \(-0.675407\pi\)
0.999623 + 0.0274554i \(0.00874043\pi\)
\(242\) 431.000 746.514i 0.114486 0.198296i
\(243\) 0 0
\(244\) −424.000 −0.111245
\(245\) 0 0
\(246\) 0 0
\(247\) 52.0000 + 90.0666i 0.0133955 + 0.0232016i
\(248\) 784.000 1357.93i 0.200742 0.347696i
\(249\) 0 0
\(250\) 1284.00 + 2223.95i 0.324829 + 0.562621i
\(251\) 3348.00 0.841928 0.420964 0.907077i \(-0.361692\pi\)
0.420964 + 0.907077i \(0.361692\pi\)
\(252\) 0 0
\(253\) 3420.00 0.849856
\(254\) −1784.00 3089.98i −0.440701 0.763317i
\(255\) 0 0
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) −183.000 316.965i −0.0444172 0.0769329i 0.842962 0.537973i \(-0.180810\pi\)
−0.887379 + 0.461040i \(0.847476\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 48.0000 0.0114494
\(261\) 0 0
\(262\) −1608.00 + 2785.14i −0.379170 + 0.656742i
\(263\) −2085.00 + 3611.33i −0.488846 + 0.846707i −0.999918 0.0128315i \(-0.995915\pi\)
0.511071 + 0.859538i \(0.329249\pi\)
\(264\) 0 0
\(265\) −2088.00 −0.484018
\(266\) 0 0
\(267\) 0 0
\(268\) −1192.00 2064.60i −0.271690 0.470581i
\(269\) −3039.00 + 5263.70i −0.688814 + 1.19306i 0.283407 + 0.959000i \(0.408535\pi\)
−0.972222 + 0.234062i \(0.924798\pi\)
\(270\) 0 0
\(271\) −1234.00 2137.35i −0.276606 0.479095i 0.693933 0.720039i \(-0.255876\pi\)
−0.970539 + 0.240944i \(0.922543\pi\)
\(272\) 1056.00 0.235402
\(273\) 0 0
\(274\) −5160.00 −1.13769
\(275\) 1335.00 + 2312.29i 0.292740 + 0.507041i
\(276\) 0 0
\(277\) 197.000 341.214i 0.0427313 0.0740129i −0.843869 0.536550i \(-0.819727\pi\)
0.886600 + 0.462537i \(0.153061\pi\)
\(278\) −2144.00 3713.52i −0.462549 0.801158i
\(279\) 0 0
\(280\) 0 0
\(281\) −396.000 −0.0840690 −0.0420345 0.999116i \(-0.513384\pi\)
−0.0420345 + 0.999116i \(0.513384\pi\)
\(282\) 0 0
\(283\) 674.000 1167.40i 0.141573 0.245212i −0.786516 0.617570i \(-0.788117\pi\)
0.928089 + 0.372358i \(0.121451\pi\)
\(284\) −1260.00 + 2182.38i −0.263265 + 0.455988i
\(285\) 0 0
\(286\) 120.000 0.0248103
\(287\) 0 0
\(288\) 0 0
\(289\) 278.500 + 482.376i 0.0566863 + 0.0981836i
\(290\) −432.000 + 748.246i −0.0874756 + 0.151512i
\(291\) 0 0
\(292\) 2084.00 + 3609.59i 0.417661 + 0.723409i
\(293\) 7506.00 1.49660 0.748302 0.663358i \(-0.230869\pi\)
0.748302 + 0.663358i \(0.230869\pi\)
\(294\) 0 0
\(295\) −2088.00 −0.412095
\(296\) 1144.00 + 1981.47i 0.224641 + 0.389089i
\(297\) 0 0
\(298\) −1500.00 + 2598.08i −0.291586 + 0.505042i
\(299\) −114.000 197.454i −0.0220495 0.0381908i
\(300\) 0 0
\(301\) 0 0
\(302\) −2480.00 −0.472543
\(303\) 0 0
\(304\) 416.000 720.533i 0.0784843 0.135939i
\(305\) 318.000 550.792i 0.0597004 0.103404i
\(306\) 0 0
\(307\) 1748.00 0.324963 0.162481 0.986712i \(-0.448050\pi\)
0.162481 + 0.986712i \(0.448050\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 1176.00 + 2036.89i 0.215459 + 0.373186i
\(311\) 570.000 987.269i 0.103928 0.180009i −0.809371 0.587297i \(-0.800192\pi\)
0.913300 + 0.407288i \(0.133525\pi\)
\(312\) 0 0
\(313\) −73.0000 126.440i −0.0131828 0.0228332i 0.859359 0.511373i \(-0.170863\pi\)
−0.872542 + 0.488540i \(0.837530\pi\)
\(314\) 1228.00 0.220701
\(315\) 0 0
\(316\) −352.000 −0.0626631
\(317\) 4074.00 + 7056.37i 0.721825 + 1.25024i 0.960267 + 0.279081i \(0.0900300\pi\)
−0.238442 + 0.971157i \(0.576637\pi\)
\(318\) 0 0
\(319\) −1080.00 + 1870.61i −0.189556 + 0.328321i
\(320\) −192.000 332.554i −0.0335410 0.0580948i
\(321\) 0 0
\(322\) 0 0
\(323\) −3432.00 −0.591212
\(324\) 0 0
\(325\) 89.0000 154.153i 0.0151903 0.0263103i
\(326\) −92.0000 + 159.349i −0.0156301 + 0.0270721i
\(327\) 0 0
\(328\) −3024.00 −0.509062
\(329\) 0 0
\(330\) 0 0
\(331\) 4850.00 + 8400.45i 0.805378 + 1.39496i 0.916036 + 0.401097i \(0.131371\pi\)
−0.110658 + 0.993859i \(0.535296\pi\)
\(332\) 2880.00 4988.31i 0.476086 0.824605i
\(333\) 0 0
\(334\) 3924.00 + 6796.57i 0.642849 + 1.11345i
\(335\) 3576.00 0.583217
\(336\) 0 0
\(337\) 8174.00 1.32126 0.660632 0.750710i \(-0.270288\pi\)
0.660632 + 0.750710i \(0.270288\pi\)
\(338\) 2193.00 + 3798.39i 0.352910 + 0.611258i
\(339\) 0 0
\(340\) −792.000 + 1371.78i −0.126330 + 0.218810i
\(341\) 2940.00 + 5092.23i 0.466891 + 0.808679i
\(342\) 0 0
\(343\) 0 0
\(344\) 1312.00 0.205635
\(345\) 0 0
\(346\) 1902.00 3294.36i 0.295526 0.511867i
\(347\) 2019.00 3497.01i 0.312350 0.541007i −0.666520 0.745487i \(-0.732217\pi\)
0.978871 + 0.204480i \(0.0655504\pi\)
\(348\) 0 0
\(349\) 10766.0 1.65126 0.825631 0.564210i \(-0.190819\pi\)
0.825631 + 0.564210i \(0.190819\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −480.000 831.384i −0.0726821 0.125889i
\(353\) −1833.00 + 3174.85i −0.276376 + 0.478697i −0.970481 0.241176i \(-0.922467\pi\)
0.694105 + 0.719873i \(0.255800\pi\)
\(354\) 0 0
\(355\) −1890.00 3273.58i −0.282566 0.489418i
\(356\) 5496.00 0.818223
\(357\) 0 0
\(358\) −12.0000 −0.00177156
\(359\) 2553.00 + 4421.93i 0.375326 + 0.650084i 0.990376 0.138404i \(-0.0441973\pi\)
−0.615049 + 0.788489i \(0.710864\pi\)
\(360\) 0 0
\(361\) 2077.50 3598.34i 0.302887 0.524615i
\(362\) 2878.00 + 4984.84i 0.417857 + 0.723750i
\(363\) 0 0
\(364\) 0 0
\(365\) −6252.00 −0.896561
\(366\) 0 0
\(367\) 2888.00 5002.16i 0.410769 0.711473i −0.584205 0.811606i \(-0.698593\pi\)
0.994974 + 0.100133i \(0.0319268\pi\)
\(368\) −912.000 + 1579.63i −0.129188 + 0.223761i
\(369\) 0 0
\(370\) −3432.00 −0.482219
\(371\) 0 0
\(372\) 0 0
\(373\) −4231.00 7328.31i −0.587327 1.01728i −0.994581 0.103965i \(-0.966847\pi\)
0.407254 0.913315i \(-0.366486\pi\)
\(374\) −1980.00 + 3429.46i −0.273752 + 0.474153i
\(375\) 0 0
\(376\) 912.000 + 1579.63i 0.125087 + 0.216657i
\(377\) 144.000 0.0196721
\(378\) 0 0
\(379\) 6860.00 0.929748 0.464874 0.885377i \(-0.346100\pi\)
0.464874 + 0.885377i \(0.346100\pi\)
\(380\) 624.000 + 1080.80i 0.0842382 + 0.145905i
\(381\) 0 0
\(382\) 354.000 613.146i 0.0474142 0.0821238i
\(383\) 348.000 + 602.754i 0.0464281 + 0.0804159i 0.888306 0.459253i \(-0.151883\pi\)
−0.841877 + 0.539669i \(0.818549\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −9716.00 −1.28117
\(387\) 0 0
\(388\) 68.0000 117.779i 0.00889736 0.0154107i
\(389\) −5568.00 + 9644.06i −0.725730 + 1.25700i 0.232943 + 0.972490i \(0.425164\pi\)
−0.958673 + 0.284510i \(0.908169\pi\)
\(390\) 0 0
\(391\) 7524.00 0.973159
\(392\) 0 0
\(393\) 0 0
\(394\) 396.000 + 685.892i 0.0506350 + 0.0877024i
\(395\) 264.000 457.261i 0.0336286 0.0582464i
\(396\) 0 0
\(397\) −5419.00 9385.98i −0.685068 1.18657i −0.973416 0.229046i \(-0.926439\pi\)
0.288348 0.957526i \(-0.406894\pi\)
\(398\) 3424.00 0.431230
\(399\) 0 0
\(400\) −1424.00 −0.178000
\(401\) 4182.00 + 7243.44i 0.520796 + 0.902045i 0.999708 + 0.0241817i \(0.00769804\pi\)
−0.478912 + 0.877863i \(0.658969\pi\)
\(402\) 0 0
\(403\) 196.000 339.482i 0.0242269 0.0419623i
\(404\) 876.000 + 1517.28i 0.107878 + 0.186850i
\(405\) 0 0
\(406\) 0 0
\(407\) −8580.00 −1.04495
\(408\) 0 0
\(409\) 881.000 1525.94i 0.106510 0.184481i −0.807844 0.589396i \(-0.799366\pi\)
0.914354 + 0.404915i \(0.132699\pi\)
\(410\) 2268.00 3928.29i 0.273192 0.473182i
\(411\) 0 0
\(412\) 6704.00 0.801656
\(413\) 0 0
\(414\) 0 0
\(415\) 4320.00 + 7482.46i 0.510989 + 0.885059i
\(416\) −32.0000 + 55.4256i −0.00377146 + 0.00653237i
\(417\) 0 0
\(418\) 1560.00 + 2702.00i 0.182541 + 0.316170i
\(419\) 14580.0 1.69995 0.849976 0.526822i \(-0.176617\pi\)
0.849976 + 0.526822i \(0.176617\pi\)
\(420\) 0 0
\(421\) 8534.00 0.987938 0.493969 0.869480i \(-0.335546\pi\)
0.493969 + 0.869480i \(0.335546\pi\)
\(422\) 772.000 + 1337.14i 0.0890530 + 0.154244i
\(423\) 0 0
\(424\) 1392.00 2411.01i 0.159437 0.276154i
\(425\) 2937.00 + 5087.03i 0.335213 + 0.580606i
\(426\) 0 0
\(427\) 0 0
\(428\) 8088.00 0.913430
\(429\) 0 0
\(430\) −984.000 + 1704.34i −0.110355 + 0.191141i
\(431\) −2967.00 + 5138.99i −0.331590 + 0.574331i −0.982824 0.184546i \(-0.940918\pi\)
0.651234 + 0.758877i \(0.274252\pi\)
\(432\) 0 0
\(433\) −14758.0 −1.63793 −0.818966 0.573843i \(-0.805452\pi\)
−0.818966 + 0.573843i \(0.805452\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 1004.00 + 1738.98i 0.110282 + 0.191014i
\(437\) 2964.00 5133.80i 0.324456 0.561975i
\(438\) 0 0
\(439\) 5696.00 + 9865.76i 0.619260 + 1.07259i 0.989621 + 0.143702i \(0.0459007\pi\)
−0.370361 + 0.928888i \(0.620766\pi\)
\(440\) 1440.00 0.156021
\(441\) 0 0
\(442\) 264.000 0.0284100
\(443\) −3513.00 6084.69i −0.376767 0.652579i 0.613823 0.789444i \(-0.289631\pi\)
−0.990590 + 0.136865i \(0.956298\pi\)
\(444\) 0 0
\(445\) −4122.00 + 7139.51i −0.439105 + 0.760551i
\(446\) −776.000 1344.07i −0.0823871 0.142699i
\(447\) 0 0
\(448\) 0 0
\(449\) −3384.00 −0.355681 −0.177841 0.984059i \(-0.556911\pi\)
−0.177841 + 0.984059i \(0.556911\pi\)
\(450\) 0 0
\(451\) 5670.00 9820.73i 0.591995 1.02537i
\(452\) −4032.00 + 6983.63i −0.419578 + 0.726731i
\(453\) 0 0
\(454\) −3576.00 −0.369670
\(455\) 0 0
\(456\) 0 0
\(457\) 2141.00 + 3708.32i 0.219150 + 0.379580i 0.954548 0.298056i \(-0.0963381\pi\)
−0.735398 + 0.677635i \(0.763005\pi\)
\(458\) −5402.00 + 9356.54i −0.551133 + 0.954590i
\(459\) 0 0
\(460\) −1368.00 2369.45i −0.138659 0.240165i
\(461\) 16650.0 1.68214 0.841071 0.540924i \(-0.181925\pi\)
0.841071 + 0.540924i \(0.181925\pi\)
\(462\) 0 0
\(463\) −9664.00 −0.970031 −0.485015 0.874506i \(-0.661186\pi\)
−0.485015 + 0.874506i \(0.661186\pi\)
\(464\) −576.000 997.661i −0.0576296 0.0998174i
\(465\) 0 0
\(466\) −3012.00 + 5216.94i −0.299417 + 0.518605i
\(467\) 6162.00 + 10672.9i 0.610585 + 1.05756i 0.991142 + 0.132807i \(0.0423991\pi\)
−0.380557 + 0.924758i \(0.624268\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −2736.00 −0.268515
\(471\) 0 0
\(472\) 1392.00 2411.01i 0.135746 0.235119i
\(473\) −2460.00 + 4260.84i −0.239135 + 0.414194i
\(474\) 0 0
\(475\) 4628.00 0.447047
\(476\) 0 0
\(477\) 0 0
\(478\) −3546.00 6141.85i −0.339310 0.587702i
\(479\) −9330.00 + 16160.0i −0.889976 + 1.54148i −0.0500744 + 0.998745i \(0.515946\pi\)
−0.839902 + 0.542738i \(0.817387\pi\)
\(480\) 0 0
\(481\) 286.000 + 495.367i 0.0271112 + 0.0469579i
\(482\) −7124.00 −0.673214
\(483\) 0 0
\(484\) −1724.00 −0.161908
\(485\) 102.000 + 176.669i 0.00954965 + 0.0165405i
\(486\) 0 0
\(487\) 1700.00 2944.49i 0.158181 0.273978i −0.776031 0.630694i \(-0.782770\pi\)
0.934213 + 0.356716i \(0.116104\pi\)
\(488\) 424.000 + 734.390i 0.0393311 + 0.0681235i
\(489\) 0 0
\(490\) 0 0
\(491\) 2970.00 0.272982 0.136491 0.990641i \(-0.456418\pi\)
0.136491 + 0.990641i \(0.456418\pi\)
\(492\) 0 0
\(493\) −2376.00 + 4115.35i −0.217058 + 0.375956i
\(494\) 104.000 180.133i 0.00947203 0.0164060i
\(495\) 0 0
\(496\) −3136.00 −0.283892
\(497\) 0 0
\(498\) 0 0
\(499\) 494.000 + 855.633i 0.0443176 + 0.0767603i 0.887333 0.461129i \(-0.152555\pi\)
−0.843016 + 0.537889i \(0.819222\pi\)
\(500\) 2568.00 4447.91i 0.229689 0.397833i
\(501\) 0 0
\(502\) −3348.00 5798.91i −0.297666 0.515573i
\(503\) 5184.00 0.459529 0.229765 0.973246i \(-0.426204\pi\)
0.229765 + 0.973246i \(0.426204\pi\)
\(504\) 0 0
\(505\) −2628.00 −0.231573
\(506\) −3420.00 5923.61i −0.300469 0.520428i
\(507\) 0 0
\(508\) −3568.00 + 6179.96i −0.311623 + 0.539747i
\(509\) −8427.00 14596.0i −0.733831 1.27103i −0.955234 0.295851i \(-0.904397\pi\)
0.221403 0.975182i \(-0.428936\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 512.000 0.0441942
\(513\) 0 0
\(514\) −366.000 + 633.931i −0.0314077 + 0.0543998i
\(515\) −5028.00 + 8708.75i −0.430214 + 0.745152i
\(516\) 0 0
\(517\) −6840.00 −0.581862
\(518\) 0 0
\(519\) 0 0
\(520\) −48.0000 83.1384i −0.00404796 0.00701127i
\(521\) 2199.00 3808.78i 0.184914 0.320280i −0.758634 0.651517i \(-0.774133\pi\)
0.943547 + 0.331238i \(0.107466\pi\)
\(522\) 0 0
\(523\) 5336.00 + 9242.22i 0.446132 + 0.772723i 0.998130 0.0611220i \(-0.0194679\pi\)
−0.551998 + 0.833845i \(0.686135\pi\)
\(524\) 6432.00 0.536228
\(525\) 0 0
\(526\) 8340.00 0.691333
\(527\) 6468.00 + 11202.9i 0.534631 + 0.926008i
\(528\) 0 0
\(529\) −414.500 + 717.935i −0.0340676 + 0.0590067i
\(530\) 2088.00 + 3616.52i 0.171126 + 0.296399i
\(531\) 0 0
\(532\) 0 0
\(533\) −756.000 −0.0614371
\(534\) 0 0
\(535\) −6066.00 + 10506.6i −0.490198 + 0.849048i
\(536\) −2384.00 + 4129.21i −0.192114 + 0.332751i
\(537\) 0 0
\(538\) 12156.0 0.974131
\(539\) 0 0
\(540\) 0 0
\(541\) −10351.0 17928.5i −0.822596 1.42478i −0.903743 0.428075i \(-0.859192\pi\)
0.0811474 0.996702i \(-0.474142\pi\)
\(542\) −2468.00 + 4274.70i −0.195590 + 0.338771i
\(543\) 0 0
\(544\) −1056.00 1829.05i −0.0832273 0.144154i
\(545\) −3012.00 −0.236734
\(546\) 0 0
\(547\) −22876.0 −1.78813 −0.894065 0.447937i \(-0.852159\pi\)
−0.894065 + 0.447937i \(0.852159\pi\)
\(548\) 5160.00 + 8937.38i 0.402234 + 0.696690i
\(549\) 0 0
\(550\) 2670.00 4624.58i 0.206999 0.358532i
\(551\) 1872.00 + 3242.40i 0.144737 + 0.250691i
\(552\) 0 0
\(553\) 0 0
\(554\) −788.000 −0.0604312
\(555\) 0 0
\(556\) −4288.00 + 7427.03i −0.327071 + 0.566504i
\(557\) 6438.00 11150.9i 0.489743 0.848260i −0.510187 0.860063i \(-0.670424\pi\)
0.999930 + 0.0118036i \(0.00375730\pi\)
\(558\) 0 0
\(559\) 328.000 0.0248174
\(560\) 0 0
\(561\) 0 0
\(562\) 396.000 + 685.892i 0.0297229 + 0.0514815i
\(563\) 3450.00 5975.58i 0.258260 0.447319i −0.707516 0.706697i \(-0.750184\pi\)
0.965776 + 0.259378i \(0.0835177\pi\)
\(564\) 0 0
\(565\) −6048.00 10475.4i −0.450339 0.780009i
\(566\) −2696.00 −0.200214
\(567\) 0 0
\(568\) 5040.00 0.372313
\(569\) −7338.00 12709.8i −0.540641 0.936418i −0.998867 0.0475826i \(-0.984848\pi\)
0.458226 0.888836i \(-0.348485\pi\)
\(570\) 0 0
\(571\) −190.000 + 329.090i −0.0139251 + 0.0241190i −0.872904 0.487892i \(-0.837766\pi\)
0.858979 + 0.512011i \(0.171099\pi\)
\(572\) −120.000 207.846i −0.00877177 0.0151932i
\(573\) 0 0
\(574\) 0 0
\(575\) −10146.0 −0.735856
\(576\) 0 0
\(577\) 5903.00 10224.3i 0.425901 0.737683i −0.570603 0.821226i \(-0.693290\pi\)
0.996504 + 0.0835434i \(0.0266237\pi\)
\(578\) 557.000 964.752i 0.0400833 0.0694263i
\(579\) 0 0
\(580\) 1728.00 0.123709
\(581\) 0 0
\(582\) 0 0
\(583\) 5220.00 + 9041.31i 0.370824 + 0.642286i
\(584\) 4168.00 7219.19i 0.295331 0.511528i
\(585\) 0 0
\(586\) −7506.00 13000.8i −0.529130 0.916480i
\(587\) −19188.0 −1.34919 −0.674594 0.738189i \(-0.735681\pi\)
−0.674594 + 0.738189i \(0.735681\pi\)
\(588\) 0 0
\(589\) 10192.0 0.712995
\(590\) 2088.00 + 3616.52i 0.145698 + 0.252356i
\(591\) 0 0
\(592\) 2288.00 3962.93i 0.158845 0.275128i
\(593\) −345.000 597.558i −0.0238912 0.0413807i 0.853833 0.520548i \(-0.174272\pi\)
−0.877724 + 0.479167i \(0.840939\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 6000.00 0.412365
\(597\) 0 0
\(598\) −228.000 + 394.908i −0.0155913 + 0.0270050i
\(599\) 10245.0 17744.9i 0.698830 1.21041i −0.270042 0.962849i \(-0.587038\pi\)
0.968872 0.247561i \(-0.0796291\pi\)
\(600\) 0 0
\(601\) −11590.0 −0.786632 −0.393316 0.919403i \(-0.628672\pi\)
−0.393316 + 0.919403i \(0.628672\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 2480.00 + 4295.49i 0.167069 + 0.289372i
\(605\) 1293.00 2239.54i 0.0868891 0.150496i
\(606\) 0 0
\(607\) 3212.00 + 5563.35i 0.214779 + 0.372009i 0.953204 0.302327i \(-0.0977634\pi\)
−0.738425 + 0.674336i \(0.764430\pi\)
\(608\) −1664.00 −0.110994
\(609\) 0 0
\(610\) −1272.00 −0.0844291
\(611\) 228.000 + 394.908i 0.0150964 + 0.0261477i
\(612\) 0 0
\(613\) 4841.00 8384.86i 0.318966 0.552465i −0.661307 0.750116i \(-0.729998\pi\)
0.980273 + 0.197650i \(0.0633311\pi\)
\(614\) −1748.00 3027.62i −0.114892 0.198998i
\(615\) 0 0
\(616\) 0 0
\(617\) 5076.00 0.331203 0.165601 0.986193i \(-0.447044\pi\)
0.165601 + 0.986193i \(0.447044\pi\)
\(618\) 0 0
\(619\) −11332.0 + 19627.6i −0.735818 + 1.27447i 0.218545 + 0.975827i \(0.429869\pi\)
−0.954363 + 0.298648i \(0.903464\pi\)
\(620\) 2352.00 4073.78i 0.152353 0.263882i
\(621\) 0 0
\(622\) −2280.00 −0.146977
\(623\) 0 0
\(624\) 0 0
\(625\) −1710.50 2962.67i −0.109472 0.189611i
\(626\) −146.000 + 252.879i −0.00932162 + 0.0161455i
\(627\) 0 0
\(628\) −1228.00 2126.96i −0.0780295 0.135151i
\(629\) −18876.0 −1.19656
\(630\) 0 0
\(631\) −8584.00 −0.541559 −0.270779 0.962641i \(-0.587281\pi\)
−0.270779 + 0.962641i \(0.587281\pi\)
\(632\) 352.000 + 609.682i 0.0221548 + 0.0383732i
\(633\) 0 0
\(634\) 8148.00 14112.7i 0.510408 0.884052i
\(635\) −5352.00 9269.94i −0.334469 0.579317i
\(636\) 0 0
\(637\) 0 0
\(638\) 4320.00 0.268073
\(639\) 0 0
\(640\) −384.000 + 665.108i −0.0237171 + 0.0410792i
\(641\) −186.000 + 322.161i −0.0114611 + 0.0198512i −0.871699 0.490042i \(-0.836982\pi\)
0.860238 + 0.509893i \(0.170315\pi\)
\(642\) 0 0
\(643\) 3188.00 0.195525 0.0977624 0.995210i \(-0.468831\pi\)
0.0977624 + 0.995210i \(0.468831\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 3432.00 + 5944.40i 0.209025 + 0.362042i
\(647\) 6366.00 11026.2i 0.386821 0.669994i −0.605199 0.796074i \(-0.706906\pi\)
0.992020 + 0.126080i \(0.0402397\pi\)
\(648\) 0 0
\(649\) 5220.00 + 9041.31i 0.315721 + 0.546845i
\(650\) −356.000 −0.0214823
\(651\) 0 0
\(652\) 368.000 0.0221043
\(653\) 1788.00 + 3096.91i 0.107151 + 0.185592i 0.914615 0.404326i \(-0.132494\pi\)
−0.807464 + 0.589917i \(0.799160\pi\)
\(654\) 0 0
\(655\) −4824.00 + 8355.41i −0.287770 + 0.498432i
\(656\) 3024.00 + 5237.72i 0.179981 + 0.311736i
\(657\) 0 0
\(658\) 0 0
\(659\) 11430.0 0.675644 0.337822 0.941210i \(-0.390310\pi\)
0.337822 + 0.941210i \(0.390310\pi\)
\(660\) 0 0
\(661\) −11323.0 + 19612.0i −0.666284 + 1.15404i 0.312652 + 0.949868i \(0.398783\pi\)
−0.978936 + 0.204170i \(0.934551\pi\)
\(662\) 9700.00 16800.9i 0.569488 0.986383i
\(663\) 0 0
\(664\) −11520.0 −0.673287
\(665\) 0 0
\(666\) 0 0
\(667\) −4104.00 7108.34i −0.238242 0.412648i
\(668\) 7848.00 13593.1i 0.454563 0.787327i
\(669\) 0 0
\(670\) −3576.00 6193.81i −0.206198 0.357146i
\(671\) −3180.00 −0.182955
\(672\) 0 0
\(673\) −13570.0 −0.777244 −0.388622 0.921397i \(-0.627049\pi\)
−0.388622 + 0.921397i \(0.627049\pi\)
\(674\) −8174.00 14157.8i −0.467138 0.809106i
\(675\) 0 0
\(676\) 4386.00 7596.77i 0.249545 0.432224i
\(677\) 1419.00 + 2457.78i 0.0805563 + 0.139528i 0.903489 0.428611i \(-0.140997\pi\)
−0.822933 + 0.568139i \(0.807664\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 3168.00 0.178658
\(681\) 0 0
\(682\) 5880.00 10184.5i 0.330142 0.571823i
\(683\) 3279.00 5679.39i 0.183701 0.318179i −0.759437 0.650580i \(-0.774526\pi\)
0.943138 + 0.332402i \(0.107859\pi\)
\(684\) 0 0
\(685\) −15480.0 −0.863446
\(686\) 0 0
\(687\) 0 0
\(688\) −1312.00 2272.45i −0.0727028 0.125925i
\(689\) 348.000 602.754i 0.0192420 0.0333281i
\(690\) 0 0
\(691\) 10916.0 + 18907.1i 0.600961 + 1.04090i 0.992676 + 0.120809i \(0.0385487\pi\)
−0.391715 + 0.920087i \(0.628118\pi\)
\(692\) −7608.00 −0.417938
\(693\) 0 0
\(694\) −8076.00 −0.441730
\(695\) −6432.00 11140.6i −0.351050 0.608036i
\(696\) 0 0
\(697\) 12474.0 21605.6i 0.677886 1.17413i
\(698\) −10766.0 18647.3i −0.583810 1.01119i
\(699\) 0 0
\(700\) 0 0
\(701\) 16200.0 0.872847 0.436423 0.899741i \(-0.356245\pi\)
0.436423 + 0.899741i \(0.356245\pi\)
\(702\) 0 0
\(703\) −7436.00 + 12879.5i −0.398939 + 0.690982i
\(704\) −960.000 + 1662.77i −0.0513940 + 0.0890170i
\(705\) 0 0
\(706\) 7332.00 0.390855
\(707\) 0 0
\(708\) 0 0
\(709\) −18361.0 31802.2i −0.972584 1.68456i −0.687689 0.726006i \(-0.741375\pi\)
−0.284895 0.958559i \(-0.591959\pi\)
\(710\) −3780.00 + 6547.15i −0.199804 + 0.346071i
\(711\) 0 0
\(712\) −5496.00 9519.35i −0.289286 0.501057i
\(713\) −22344.0 −1.17362
\(714\) 0 0
\(715\) 360.000 0.0188297
\(716\) 12.0000 + 20.7846i 0.000626342 + 0.00108486i
\(717\) 0 0
\(718\) 5106.00 8843.85i 0.265396 0.459679i
\(719\) −6888.00 11930.4i −0.357273 0.618814i 0.630231 0.776407i \(-0.282960\pi\)
−0.987504 + 0.157593i \(0.949627\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −8310.00 −0.428347
\(723\) 0 0
\(724\) 5756.00 9969.68i 0.295470 0.511769i
\(725\) 3204.00 5549.49i 0.164129 0.284280i
\(726\) 0 0
\(727\) 34220.0 1.74574 0.872868 0.487957i \(-0.162258\pi\)
0.872868 + 0.487957i \(0.162258\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 6252.00 + 10828.8i 0.316982 + 0.549029i
\(731\) −5412.00 + 9373.86i −0.273830 + 0.474288i
\(732\) 0 0
\(733\) 6875.00 + 11907.8i 0.346431 + 0.600036i 0.985613 0.169020i \(-0.0540601\pi\)
−0.639182 + 0.769056i \(0.720727\pi\)
\(734\) −11552.0 −0.580916
\(735\) 0 0
\(736\) 3648.00 0.182700
\(737\) −8940.00 15484.5i −0.446824 0.773922i
\(738\) 0 0
\(739\) −19918.0 + 34499.0i −0.991469 + 1.71727i −0.382853 + 0.923809i \(0.625059\pi\)
−0.608616 + 0.793465i \(0.708275\pi\)
\(740\) 3432.00 + 5944.40i 0.170490 + 0.295298i
\(741\) 0 0
\(742\) 0 0
\(743\) 34470.0 1.70199 0.850997 0.525170i \(-0.175998\pi\)
0.850997 + 0.525170i \(0.175998\pi\)
\(744\) 0 0
\(745\) −4500.00 + 7794.23i −0.221298 + 0.383300i
\(746\) −8462.00 + 14656.6i −0.415303 + 0.719325i
\(747\) 0 0
\(748\) 7920.00 0.387144
\(749\) 0 0
\(750\) 0 0
\(751\) −2620.00 4537.97i −0.127304 0.220497i 0.795327 0.606180i \(-0.207299\pi\)
−0.922631 + 0.385684i \(0.873966\pi\)
\(752\) 1824.00 3159.26i 0.0884500 0.153200i
\(753\) 0 0
\(754\) −144.000 249.415i −0.00695513 0.0120466i
\(755\) −7440.00 −0.358635
\(756\) 0 0
\(757\) 18578.0 0.891980 0.445990 0.895038i \(-0.352852\pi\)
0.445990 + 0.895038i \(0.352852\pi\)
\(758\) −6860.00 11881.9i −0.328716 0.569352i
\(759\) 0 0
\(760\) 1248.00 2161.60i 0.0595654 0.103170i
\(761\) −15267.0 26443.2i −0.727238 1.25961i −0.958046 0.286614i \(-0.907470\pi\)
0.230808 0.972999i \(-0.425863\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −1416.00 −0.0670538
\(765\) 0 0
\(766\) 696.000 1205.51i 0.0328296 0.0568626i
\(767\) 348.000 602.754i 0.0163827 0.0283757i
\(768\) 0 0
\(769\) −39958.0 −1.87376 −0.936881 0.349650i \(-0.886301\pi\)
−0.936881 + 0.349650i \(0.886301\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 9716.00 + 16828.6i 0.452962 + 0.784553i
\(773\) 1983.00 3434.66i 0.0922685 0.159814i −0.816197 0.577774i \(-0.803922\pi\)
0.908465 + 0.417960i \(0.137255\pi\)
\(774\) 0 0
\(775\) −8722.00 15106.9i −0.404263 0.700203i
\(776\) −272.000 −0.0125828
\(777\) 0 0
\(778\) 22272.0 1.02634
\(779\) −9828.00 17022.6i −0.452021 0.782924i
\(780\) 0 0
\(781\) −9450.00 + 16367.9i −0.432967 + 0.749922i
\(782\) −7524.00 13032.0i −0.344064 0.595936i
\(783\) 0 0
\(784\) 0 0
\(785\) 3684.00 0.167500
\(786\) 0 0
\(787\) 1880.00 3256.26i 0.0851522 0.147488i −0.820304 0.571928i \(-0.806196\pi\)
0.905456 + 0.424440i \(0.139529\pi\)
\(788\) 792.000 1371.78i 0.0358044 0.0620150i
\(789\) 0 0
\(790\) −1056.00 −0.0475580
\(791\) 0