Properties

Label 882.4.g.h.667.1
Level $882$
Weight $4$
Character 882.667
Analytic conductor $52.040$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(52.0396846251\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

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

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

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

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
\(5\) 3.00000 5.19615i 0.268328 0.464758i −0.700102 0.714043i \(-0.746862\pi\)
0.968430 + 0.249285i \(0.0801955\pi\)
\(6\) 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 0.583864 0.811851i \(-0.301540\pi\)
−0.995016 + 0.0997155i \(0.968207\pi\)
\(12\) 0 0
\(13\) −2.00000 −0.0426692 −0.0213346 0.999772i \(-0.506792\pi\)
−0.0213346 + 0.999772i \(0.506792\pi\)
\(14\) 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 \(-0.0106304\pi\)
−0.528638 + 0.848847i \(0.677297\pi\)
\(18\) 0 0
\(19\) −26.0000 + 45.0333i −0.313937 + 0.543755i −0.979211 0.202844i \(-0.934982\pi\)
0.665274 + 0.746600i \(0.268315\pi\)
\(20\) −24.0000 −0.268328
\(21\) 0 0
\(22\) 60.0000 0.581456
\(23\) −57.0000 + 98.7269i −0.516753 + 0.895043i 0.483058 + 0.875589i \(0.339526\pi\)
−0.999811 + 0.0194541i \(0.993807\pi\)
\(24\) 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 −0.996785 0.0801272i \(-0.974467\pi\)
0.429000 0.903304i \(-0.358866\pi\)
\(32\) −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 −0.351055 0.936355i \(-0.614177\pi\)
0.986435 0.164155i \(-0.0524898\pi\)
\(38\) −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 \(-0.244177\pi\)
0.719923 + 0.694054i \(0.244177\pi\)
\(42\) 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 \(-0.948444\pi\)
0.633112 + 0.774060i \(0.281777\pi\)
\(48\) 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 0.998446 0.0557323i \(-0.0177493\pi\)
−0.547488 + 0.836813i \(0.684416\pi\)
\(54\) 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 \(-0.292102\pi\)
−0.991622 + 0.129170i \(0.958769\pi\)
\(60\) 0 0
\(61\) −53.0000 + 91.7987i −0.111245 + 0.192682i −0.916273 0.400555i \(-0.868817\pi\)
0.805027 + 0.593238i \(0.202151\pi\)
\(62\) 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 −0.998707 0.0508381i \(-0.983811\pi\)
0.455326 0.890325i \(-0.349523\pi\)
\(68\) 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 −0.893769 0.448528i \(-0.851948\pi\)
0.0584477 0.998290i \(-0.481385\pi\)
\(74\) 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 −0.832992 0.553285i \(-0.813374\pi\)
0.895655 + 0.444750i \(0.146707\pi\)
\(80\) 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 \(-0.0988446\pi\)
0.952172 + 0.305563i \(0.0988446\pi\)
\(84\) 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 −0.0887672 0.996052i \(-0.528293\pi\)
0.906990 0.421152i \(-0.138374\pi\)
\(90\) 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 \(-0.494335\pi\)
0.0177947 + 0.999842i \(0.494335\pi\)
\(98\) 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 \(-0.235888\pi\)
−0.953506 + 0.301374i \(0.902555\pi\)
\(102\) 0 0
\(103\) 838.000 1451.46i 0.801656 1.38851i −0.116869 0.993147i \(-0.537286\pi\)
0.918525 0.395362i \(-0.129381\pi\)
\(104\) −16.0000 −0.0150859
\(105\) 0 0
\(106\) −696.000 −0.637750
\(107\) −1011.00 + 1751.10i −0.913430 + 1.58211i −0.104247 + 0.994551i \(0.533243\pi\)
−0.809183 + 0.587557i \(0.800090\pi\)
\(108\) 0 0
\(109\) 251.000 + 434.745i 0.220564 + 0.382027i 0.954979 0.296673i \(-0.0958770\pi\)
−0.734416 + 0.678700i \(0.762544\pi\)
\(110\) 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 −0.462875 0.886423i \(-0.653182\pi\)
0.999103 0.0423499i \(-0.0134844\pi\)
\(132\) 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 0.916650 + 0.399692i \(0.130883\pi\)
−0.112181 + 0.993688i \(0.535784\pi\)
\(138\) 0 0
\(139\) −2144.00 −1.30829 −0.654143 0.756371i \(-0.726970\pi\)
−0.654143 + 0.756371i \(0.726970\pi\)
\(140\) 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 −0.995148 0.0983907i \(-0.968631\pi\)
0.582783 + 0.812628i \(0.301964\pi\)
\(150\) 0 0
\(151\) 620.000 + 1073.87i 0.334138 + 0.578745i 0.983319 0.181890i \(-0.0582214\pi\)
−0.649181 + 0.760634i \(0.724888\pi\)
\(152\) −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 \(-0.116788\pi\)
−0.777385 + 0.629025i \(0.783454\pi\)
\(158\) 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 −0.876866 0.480735i \(-0.840370\pi\)
0.854762 + 0.519021i \(0.173703\pi\)
\(164\) −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 \(-0.136750\pi\)
0.909126 + 0.416520i \(0.136750\pi\)
\(168\) 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 \(-0.970580\pi\)
0.577794 + 0.816182i \(0.303914\pi\)
\(174\) 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 0.866651 0.498915i \(-0.166268\pi\)
−0.865398 + 0.501084i \(0.832935\pi\)
\(180\) 0 0
\(181\) 2878.00 1.18188 0.590939 0.806716i \(-0.298757\pi\)
0.590939 + 0.806716i \(0.298757\pi\)
\(182\) 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 −0.830549 0.556945i \(-0.811973\pi\)
0.897603 + 0.440804i \(0.145307\pi\)
\(192\) 0 0
\(193\) 2429.00 + 4207.15i 0.905924 + 1.56911i 0.819673 + 0.572832i \(0.194155\pi\)
0.0862509 + 0.996273i \(0.472511\pi\)
\(194\) −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 \(-0.0680350\pi\)
−0.672319 + 0.740262i \(0.734702\pi\)
\(200\) 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 \(-0.537172\pi\)
−0.116513 + 0.993189i \(0.537172\pi\)
\(224\) 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 \(-0.250849\pi\)
−0.966613 + 0.256240i \(0.917516\pi\)
\(228\) 0 0
\(229\) 2701.00 4678.27i 0.779420 1.34999i −0.152857 0.988248i \(-0.548847\pi\)
0.932277 0.361746i \(-0.117819\pi\)
\(230\) −1368.00 −0.392188
\(231\) 0 0
\(232\) 576.000 0.163001
\(233\) −1506.00 + 2608.47i −0.423439 + 0.733418i −0.996273 0.0862531i \(-0.972511\pi\)
0.572834 + 0.819671i \(0.305844\pi\)
\(234\) 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 \(-0.324593\pi\)
−0.999623 + 0.0274554i \(0.991260\pi\)
\(242\) 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 \(-0.638308\pi\)
−0.420964 + 0.907077i \(0.638308\pi\)
\(252\) 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 \(-0.819190\pi\)
0.887379 + 0.461040i \(0.152524\pi\)
\(258\) 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 0.511071 0.859538i \(-0.329249\pi\)
−0.999918 + 0.0128315i \(0.995915\pi\)
\(264\) 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 0.972222 + 0.234062i \(0.0752019\pi\)
−0.283407 + 0.959000i \(0.591465\pi\)
\(270\) 0 0
\(271\) 1234.00 2137.35i 0.276606 0.479095i −0.693933 0.720039i \(-0.744124\pi\)
0.970539 + 0.240944i \(0.0774571\pi\)
\(272\) −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 0.886600 0.462537i \(-0.153061\pi\)
−0.843869 + 0.536550i \(0.819727\pi\)
\(278\) 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 \(-0.211883\pi\)
−0.928089 + 0.372358i \(0.878549\pi\)
\(284\) −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 \(-0.769131\pi\)
−0.748302 + 0.663358i \(0.769131\pi\)
\(294\) 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 \(-0.551950\pi\)
−0.162481 + 0.986712i \(0.551950\pi\)
\(308\) 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 \(-0.199808\pi\)
−0.913300 + 0.407288i \(0.866475\pi\)
\(312\) 0 0
\(313\) 73.0000 126.440i 0.0131828 0.0228332i −0.859359 0.511373i \(-0.829137\pi\)
0.872542 + 0.488540i \(0.162470\pi\)
\(314\) −1228.00 −0.220701
\(315\) 0 0
\(316\) −352.000 −0.0626631
\(317\) 4074.00 7056.37i 0.721825 1.25024i −0.238442 0.971157i \(-0.576637\pi\)
0.960267 0.279081i \(-0.0900300\pi\)
\(318\) 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 −0.110658 0.993859i \(-0.535296\pi\)
0.916036 0.401097i \(-0.131371\pi\)
\(332\) −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 0.978871 0.204480i \(-0.0655504\pi\)
−0.666520 + 0.745487i \(0.732217\pi\)
\(348\) 0 0
\(349\) −10766.0 −1.65126 −0.825631 0.564210i \(-0.809181\pi\)
−0.825631 + 0.564210i \(0.809181\pi\)
\(350\) 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 \(-0.0775331\pi\)
−0.694105 + 0.719873i \(0.744200\pi\)
\(354\) 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 −0.615049 0.788489i \(-0.710864\pi\)
0.990376 + 0.138404i \(0.0441973\pi\)
\(360\) 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 \(-0.301407\pi\)
−0.994974 + 0.100133i \(0.968073\pi\)
\(368\) −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 0.407254 + 0.913315i \(0.366486\pi\)
−0.994581 + 0.103965i \(0.966847\pi\)
\(374\) 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 \(-0.848117\pi\)
0.841877 + 0.539669i \(0.181451\pi\)
\(384\) 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 −0.958673 0.284510i \(-0.908169\pi\)
0.232943 0.972490i \(-0.425164\pi\)
\(390\) 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 −0.288348 0.957526i \(-0.593106\pi\)
0.973416 0.229046i \(-0.0735607\pi\)
\(398\) −3424.00 −0.431230
\(399\) 0 0
\(400\) −1424.00 −0.178000
\(401\) 4182.00 7243.44i 0.520796 0.902045i −0.478912 0.877863i \(-0.658969\pi\)
0.999708 0.0241817i \(-0.00769804\pi\)
\(402\) 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 \(-0.200634\pi\)
−0.914354 + 0.404915i \(0.867301\pi\)
\(410\) 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 \(-0.823383\pi\)
−0.849976 + 0.526822i \(0.823383\pi\)
\(420\) 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 0.651234 0.758877i \(-0.274252\pi\)
−0.982824 + 0.184546i \(0.940918\pi\)
\(432\) 0 0
\(433\) 14758.0 1.63793 0.818966 0.573843i \(-0.194548\pi\)
0.818966 + 0.573843i \(0.194548\pi\)
\(434\) 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 0.370361 + 0.928888i \(0.379234\pi\)
−0.989621 + 0.143702i \(0.954099\pi\)
\(440\) −1440.00 −0.156021
\(441\) 0 0
\(442\) 264.000 0.0284100
\(443\) −3513.00 + 6084.69i −0.376767 + 0.652579i −0.990590 0.136865i \(-0.956298\pi\)
0.613823 + 0.789444i \(0.289631\pi\)
\(444\) 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 −0.735398 0.677635i \(-0.763005\pi\)
0.954548 + 0.298056i \(0.0963381\pi\)
\(458\) 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 \(-0.818075\pi\)
−0.841071 + 0.540924i \(0.818075\pi\)
\(462\) 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 0.380557 + 0.924758i \(0.375732\pi\)
−0.991142 + 0.132807i \(0.957601\pi\)
\(468\) 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 0.839902 + 0.542738i \(0.182613\pi\)
0.0500744 + 0.998745i \(0.484054\pi\)
\(480\) 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 0.934213 0.356716i \(-0.116104\pi\)
−0.776031 + 0.630694i \(0.782770\pi\)
\(488\) −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 −0.843016 0.537889i \(-0.819222\pi\)
0.887333 + 0.461129i \(0.152555\pi\)
\(500\) −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 \(-0.573796\pi\)
−0.229765 + 0.973246i \(0.573796\pi\)
\(504\) 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 −0.221403 0.975182i \(-0.571064\pi\)
0.955234 0.295851i \(-0.0956032\pi\)
\(510\) 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 \(-0.225867\pi\)
−0.943547 + 0.331238i \(0.892534\pi\)
\(522\) 0 0
\(523\) −5336.00 + 9242.22i −0.446132 + 0.772723i −0.998130 0.0611220i \(-0.980532\pi\)
0.551998 + 0.833845i \(0.313865\pi\)
\(524\) −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 0.0811474 + 0.996702i \(0.474142\pi\)
−0.903743 + 0.428075i \(0.859192\pi\)
\(542\) 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 0.999930 0.0118036i \(-0.00375730\pi\)
−0.510187 + 0.860063i \(0.670424\pi\)
\(558\) 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 \(-0.249816\pi\)
−0.965776 + 0.259378i \(0.916482\pi\)
\(564\) 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 0.458226 + 0.888836i \(0.348485\pi\)
−0.998867 + 0.0475826i \(0.984848\pi\)
\(570\) 0 0
\(571\) −190.000 329.090i −0.0139251 0.0241190i 0.858979 0.512011i \(-0.171099\pi\)
−0.872904 + 0.487892i \(0.837766\pi\)
\(572\) 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 \(-0.306710\pi\)
−0.996504 + 0.0835434i \(0.973376\pi\)
\(578\) 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 \(-0.264319\pi\)
0.674594 + 0.738189i \(0.264319\pi\)
\(588\) 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 \(-0.825728\pi\)
0.877724 + 0.479167i \(0.159061\pi\)
\(594\) 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 0.968872 + 0.247561i \(0.0796291\pi\)
−0.270042 + 0.962849i \(0.587038\pi\)
\(600\) 0 0
\(601\) 11590.0 0.786632 0.393316 0.919403i \(-0.371328\pi\)
0.393316 + 0.919403i \(0.371328\pi\)
\(602\) 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 \(-0.902237\pi\)
0.738425 + 0.674336i \(0.235570\pi\)
\(608\) 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 0.980273 0.197650i \(-0.0633311\pi\)
−0.661307 + 0.750116i \(0.729998\pi\)
\(614\) 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 0.954363 + 0.298648i \(0.0965356\pi\)
−0.218545 + 0.975827i \(0.570131\pi\)
\(620\) 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 0.860238 0.509893i \(-0.170315\pi\)
−0.871699 + 0.490042i \(0.836982\pi\)
\(642\) 0 0
\(643\) −3188.00 −0.195525 −0.0977624 0.995210i \(-0.531169\pi\)
−0.0977624 + 0.995210i \(0.531169\pi\)
\(644\) 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 \(-0.293094\pi\)
−0.992020 + 0.126080i \(0.959760\pi\)
\(648\) 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 −0.807464 0.589917i \(-0.799160\pi\)
0.914615 + 0.404326i \(0.132494\pi\)
\(654\) 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 0.978936 + 0.204170i \(0.0654494\pi\)
−0.312652 + 0.949868i \(0.601217\pi\)
\(662\) 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 \(-0.859003\pi\)
0.822933 + 0.568139i \(0.192336\pi\)
\(678\) 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 0.943138 0.332402i \(-0.107859\pi\)
−0.759437 + 0.650580i \(0.774526\pi\)
\(684\) 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 0.391715 + 0.920087i \(0.371882\pi\)
−0.992676 + 0.120809i \(0.961451\pi\)
\(692\) 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 −0.284895 + 0.958559i \(0.591959\pi\)
−0.687689 + 0.726006i \(0.741375\pi\)
\(710\) 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 \(-0.717040\pi\)
0.987504 + 0.157593i \(0.0503734\pi\)
\(720\) 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 \(-0.837742\pi\)
−0.872868 + 0.487957i \(0.837742\pi\)
\(728\) 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 \(-0.945940\pi\)
0.639182 + 0.769056i \(0.279273\pi\)
\(734\) 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 −0.608616 0.793465i \(-0.708275\pi\)
−0.382853 0.923809i \(-0.625059\pi\)
\(740\) −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 −0.922631 0.385684i \(-0.873966\pi\)
0.795327 + 0.606180i \(0.207299\pi\)
\(752\) −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 −0.230808 0.972999i \(-0.574137\pi\)
0.958046 0.286614i \(-0.0925298\pi\)
\(762\) 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 \(-0.113699\pi\)
0.936881 + 0.349650i \(0.113699\pi\)
\(770\) 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 \(-0.196078\pi\)
−0.908465 + 0.417960i \(0.862745\pi\)
\(774\) 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 \(-0.193804\pi\)
−0.905456 + 0.424440i \(0.860471\pi\)
\(788\) 792.000 + 1371.78i 0.0358044 + 0.0620150i
\(789\) 0 0
\(790\) 1056.00 0.0475580
\(791\) 0 0