Properties

Label 441.4.e.x.226.4
Level $441$
Weight $4$
Character 441.226
Analytic conductor $26.020$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 441.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(26.0198423125\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} + \cdots)\)
Defining polynomial: \(x^{8} + 19 x^{6} + 319 x^{4} + 798 x^{2} + 1764\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{2}\cdot 3 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 226.4
Root \(-2.02770 - 3.51207i\) of defining polynomial
Character \(\chi\) \(=\) 441.226
Dual form 441.4.e.x.361.4

$q$-expansion

\(f(q)\) \(=\) \(q+(2.02770 - 3.51207i) q^{2} +(-4.22311 - 7.31464i) q^{4} +(-4.96020 + 8.59131i) q^{5} -1.80961 q^{8} +O(q^{10})\) \(q+(2.02770 - 3.51207i) q^{2} +(-4.22311 - 7.31464i) q^{4} +(-4.96020 + 8.59131i) q^{5} -1.80961 q^{8} +(20.1156 + 34.8412i) q^{10} +(6.76980 + 11.7256i) q^{11} -18.5538 q^{13} +(30.1156 - 52.1617i) q^{16} +(-46.8551 - 81.1555i) q^{17} +(65.9542 - 114.236i) q^{19} +83.7899 q^{20} +54.9084 q^{22} +(99.1391 - 171.714i) q^{23} +(13.2929 + 23.0240i) q^{25} +(-37.6214 + 65.1622i) q^{26} +188.358 q^{29} +(-41.9622 - 72.6807i) q^{31} +(-129.369 - 224.073i) q^{32} -380.032 q^{34} +(-40.0778 + 69.4167i) q^{37} +(-267.470 - 463.272i) q^{38} +(8.97600 - 15.5469i) q^{40} +385.828 q^{41} -397.048 q^{43} +(57.1793 - 99.0374i) q^{44} +(-402.048 - 696.368i) q^{46} +(136.139 - 235.799i) q^{47} +107.816 q^{50} +(78.3547 + 135.714i) q^{52} +(18.4998 + 32.0426i) q^{53} -134.318 q^{55} +(381.932 - 661.526i) q^{58} +(197.874 + 342.728i) q^{59} +(6.73689 - 11.6686i) q^{61} -340.347 q^{62} -567.435 q^{64} +(92.0304 - 159.401i) q^{65} +(-170.261 - 294.901i) q^{67} +(-395.749 + 685.457i) q^{68} -211.140 q^{71} +(243.062 + 420.995i) q^{73} +(162.531 + 281.512i) q^{74} -1114.13 q^{76} +(-146.871 + 254.387i) q^{79} +(298.758 + 517.464i) q^{80} +(782.343 - 1355.06i) q^{82} -889.635 q^{83} +929.643 q^{85} +(-805.093 + 1394.46i) q^{86} +(-12.2507 - 21.2188i) q^{88} +(572.182 - 991.048i) q^{89} -1674.70 q^{92} +(-552.096 - 956.258i) q^{94} +(654.292 + 1133.27i) q^{95} -1384.61 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 6q^{4} + O(q^{10}) \) \( 8q - 6q^{4} + 22q^{10} - 204q^{13} + 102q^{16} + 222q^{19} - 172q^{22} - 366q^{25} + 220q^{31} - 2040q^{34} + 374q^{37} + 822q^{40} - 1676q^{43} - 1716q^{46} - 40q^{52} - 5020q^{55} + 1694q^{58} + 1332q^{61} - 1372q^{64} - 1890q^{67} + 1750q^{73} - 4912q^{76} - 8q^{79} + 2480q^{82} - 2232q^{85} - 2682q^{88} - 1416q^{94} - 6020q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.02770 3.51207i 0.716899 1.24171i −0.245323 0.969441i \(-0.578894\pi\)
0.962222 0.272264i \(-0.0877726\pi\)
\(3\) 0 0
\(4\) −4.22311 7.31464i −0.527889 0.914330i
\(5\) −4.96020 + 8.59131i −0.443654 + 0.768430i −0.997957 0.0638840i \(-0.979651\pi\)
0.554304 + 0.832314i \(0.312985\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −1.80961 −0.0799740
\(9\) 0 0
\(10\) 20.1156 + 34.8412i 0.636110 + 1.10177i
\(11\) 6.76980 + 11.7256i 0.185561 + 0.321401i 0.943765 0.330616i \(-0.107256\pi\)
−0.758204 + 0.652017i \(0.773923\pi\)
\(12\) 0 0
\(13\) −18.5538 −0.395838 −0.197919 0.980218i \(-0.563418\pi\)
−0.197919 + 0.980218i \(0.563418\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 30.1156 52.1617i 0.470556 0.815026i
\(17\) −46.8551 81.1555i −0.668473 1.15783i −0.978331 0.207046i \(-0.933615\pi\)
0.309858 0.950783i \(-0.399718\pi\)
\(18\) 0 0
\(19\) 65.9542 114.236i 0.796365 1.37934i −0.125604 0.992080i \(-0.540087\pi\)
0.921969 0.387264i \(-0.126580\pi\)
\(20\) 83.7899 0.936799
\(21\) 0 0
\(22\) 54.9084 0.532115
\(23\) 99.1391 171.714i 0.898779 1.55673i 0.0697230 0.997566i \(-0.477788\pi\)
0.829056 0.559165i \(-0.188878\pi\)
\(24\) 0 0
\(25\) 13.2929 + 23.0240i 0.106343 + 0.184192i
\(26\) −37.6214 + 65.1622i −0.283776 + 0.491514i
\(27\) 0 0
\(28\) 0 0
\(29\) 188.358 1.20611 0.603054 0.797700i \(-0.293950\pi\)
0.603054 + 0.797700i \(0.293950\pi\)
\(30\) 0 0
\(31\) −41.9622 72.6807i −0.243117 0.421092i 0.718483 0.695544i \(-0.244837\pi\)
−0.961601 + 0.274453i \(0.911503\pi\)
\(32\) −129.369 224.073i −0.714669 1.23784i
\(33\) 0 0
\(34\) −380.032 −1.91691
\(35\) 0 0
\(36\) 0 0
\(37\) −40.0778 + 69.4167i −0.178074 + 0.308434i −0.941221 0.337792i \(-0.890320\pi\)
0.763147 + 0.646225i \(0.223653\pi\)
\(38\) −267.470 463.272i −1.14183 1.97770i
\(39\) 0 0
\(40\) 8.97600 15.5469i 0.0354808 0.0614545i
\(41\) 385.828 1.46967 0.734833 0.678249i \(-0.237261\pi\)
0.734833 + 0.678249i \(0.237261\pi\)
\(42\) 0 0
\(43\) −397.048 −1.40812 −0.704061 0.710139i \(-0.748632\pi\)
−0.704061 + 0.710139i \(0.748632\pi\)
\(44\) 57.1793 99.0374i 0.195911 0.339328i
\(45\) 0 0
\(46\) −402.048 696.368i −1.28867 2.23204i
\(47\) 136.139 235.799i 0.422508 0.731805i −0.573676 0.819082i \(-0.694483\pi\)
0.996184 + 0.0872772i \(0.0278166\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 107.816 0.304949
\(51\) 0 0
\(52\) 78.3547 + 135.714i 0.208958 + 0.361927i
\(53\) 18.4998 + 32.0426i 0.0479461 + 0.0830451i 0.889002 0.457902i \(-0.151399\pi\)
−0.841056 + 0.540948i \(0.818066\pi\)
\(54\) 0 0
\(55\) −134.318 −0.329299
\(56\) 0 0
\(57\) 0 0
\(58\) 381.932 661.526i 0.864658 1.49763i
\(59\) 197.874 + 342.728i 0.436628 + 0.756262i 0.997427 0.0716901i \(-0.0228393\pi\)
−0.560799 + 0.827952i \(0.689506\pi\)
\(60\) 0 0
\(61\) 6.73689 11.6686i 0.0141405 0.0244921i −0.858869 0.512196i \(-0.828832\pi\)
0.873009 + 0.487704i \(0.162165\pi\)
\(62\) −340.347 −0.697162
\(63\) 0 0
\(64\) −567.435 −1.10827
\(65\) 92.0304 159.401i 0.175615 0.304174i
\(66\) 0 0
\(67\) −170.261 294.901i −0.310458 0.537729i 0.668004 0.744158i \(-0.267149\pi\)
−0.978462 + 0.206429i \(0.933816\pi\)
\(68\) −395.749 + 685.457i −0.705759 + 1.22241i
\(69\) 0 0
\(70\) 0 0
\(71\) −211.140 −0.352925 −0.176463 0.984307i \(-0.556466\pi\)
−0.176463 + 0.984307i \(0.556466\pi\)
\(72\) 0 0
\(73\) 243.062 + 420.995i 0.389702 + 0.674983i 0.992409 0.122979i \(-0.0392448\pi\)
−0.602708 + 0.797962i \(0.705911\pi\)
\(74\) 162.531 + 281.512i 0.255323 + 0.442232i
\(75\) 0 0
\(76\) −1114.13 −1.68157
\(77\) 0 0
\(78\) 0 0
\(79\) −146.871 + 254.387i −0.209168 + 0.362289i −0.951453 0.307795i \(-0.900409\pi\)
0.742285 + 0.670084i \(0.233742\pi\)
\(80\) 298.758 + 517.464i 0.417527 + 0.723178i
\(81\) 0 0
\(82\) 782.343 1355.06i 1.05360 1.82489i
\(83\) −889.635 −1.17651 −0.588253 0.808677i \(-0.700184\pi\)
−0.588253 + 0.808677i \(0.700184\pi\)
\(84\) 0 0
\(85\) 929.643 1.18628
\(86\) −805.093 + 1394.46i −1.00948 + 1.74847i
\(87\) 0 0
\(88\) −12.2507 21.2188i −0.0148401 0.0257038i
\(89\) 572.182 991.048i 0.681474 1.18035i −0.293057 0.956095i \(-0.594673\pi\)
0.974531 0.224252i \(-0.0719939\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −1674.70 −1.89782
\(93\) 0 0
\(94\) −552.096 956.258i −0.605791 1.04926i
\(95\) 654.292 + 1133.27i 0.706620 + 1.22390i
\(96\) 0 0
\(97\) −1384.61 −1.44933 −0.724667 0.689099i \(-0.758007\pi\)
−0.724667 + 0.689099i \(0.758007\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 112.275 194.465i 0.112275 0.194465i
\(101\) 892.994 + 1546.71i 0.879765 + 1.52380i 0.851599 + 0.524194i \(0.175633\pi\)
0.0281660 + 0.999603i \(0.491033\pi\)
\(102\) 0 0
\(103\) 244.831 424.059i 0.234212 0.405668i −0.724831 0.688927i \(-0.758082\pi\)
0.959044 + 0.283259i \(0.0914155\pi\)
\(104\) 33.5750 0.0316568
\(105\) 0 0
\(106\) 150.048 0.137490
\(107\) −141.034 + 244.278i −0.127423 + 0.220703i −0.922678 0.385573i \(-0.874004\pi\)
0.795254 + 0.606276i \(0.207337\pi\)
\(108\) 0 0
\(109\) 143.616 + 248.749i 0.126201 + 0.218586i 0.922202 0.386709i \(-0.126388\pi\)
−0.796001 + 0.605295i \(0.793055\pi\)
\(110\) −272.357 + 471.736i −0.236074 + 0.408893i
\(111\) 0 0
\(112\) 0 0
\(113\) 1895.21 1.57776 0.788879 0.614548i \(-0.210662\pi\)
0.788879 + 0.614548i \(0.210662\pi\)
\(114\) 0 0
\(115\) 983.499 + 1703.47i 0.797493 + 1.38130i
\(116\) −795.456 1377.77i −0.636691 1.10278i
\(117\) 0 0
\(118\) 1604.92 1.25207
\(119\) 0 0
\(120\) 0 0
\(121\) 573.840 993.919i 0.431134 0.746746i
\(122\) −27.3208 47.3209i −0.0202746 0.0351167i
\(123\) 0 0
\(124\) −354.422 + 613.877i −0.256678 + 0.444579i
\(125\) −1503.79 −1.07603
\(126\) 0 0
\(127\) −1222.92 −0.854463 −0.427231 0.904142i \(-0.640511\pi\)
−0.427231 + 0.904142i \(0.640511\pi\)
\(128\) −115.635 + 200.285i −0.0798496 + 0.138304i
\(129\) 0 0
\(130\) −373.220 646.435i −0.251796 0.436124i
\(131\) 595.303 1031.10i 0.397037 0.687689i −0.596322 0.802746i \(-0.703372\pi\)
0.993359 + 0.115057i \(0.0367051\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −1380.95 −0.890268
\(135\) 0 0
\(136\) 84.7893 + 146.859i 0.0534605 + 0.0925963i
\(137\) −53.4807 92.6313i −0.0333516 0.0577666i 0.848868 0.528605i \(-0.177285\pi\)
−0.882219 + 0.470839i \(0.843951\pi\)
\(138\) 0 0
\(139\) 1096.78 0.669262 0.334631 0.942349i \(-0.391388\pi\)
0.334631 + 0.942349i \(0.391388\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −428.128 + 741.539i −0.253012 + 0.438230i
\(143\) −125.605 217.555i −0.0734521 0.127223i
\(144\) 0 0
\(145\) −934.292 + 1618.24i −0.535094 + 0.926811i
\(146\) 1971.42 1.11751
\(147\) 0 0
\(148\) 677.012 0.376014
\(149\) −358.331 + 620.647i −0.197018 + 0.341244i −0.947560 0.319578i \(-0.896459\pi\)
0.750542 + 0.660822i \(0.229792\pi\)
\(150\) 0 0
\(151\) −77.1840 133.687i −0.0415970 0.0720481i 0.844477 0.535591i \(-0.179911\pi\)
−0.886074 + 0.463543i \(0.846578\pi\)
\(152\) −119.351 + 206.722i −0.0636885 + 0.110312i
\(153\) 0 0
\(154\) 0 0
\(155\) 832.564 0.431439
\(156\) 0 0
\(157\) −1046.87 1813.24i −0.532163 0.921734i −0.999295 0.0375459i \(-0.988046\pi\)
0.467132 0.884188i \(-0.345287\pi\)
\(158\) 595.618 + 1031.64i 0.299904 + 0.519449i
\(159\) 0 0
\(160\) 2566.78 1.26826
\(161\) 0 0
\(162\) 0 0
\(163\) −1503.93 + 2604.88i −0.722680 + 1.25172i 0.237242 + 0.971451i \(0.423757\pi\)
−0.959922 + 0.280268i \(0.909577\pi\)
\(164\) −1629.40 2822.20i −0.775820 1.34376i
\(165\) 0 0
\(166\) −1803.91 + 3124.46i −0.843437 + 1.46088i
\(167\) 2230.43 1.03351 0.516754 0.856134i \(-0.327140\pi\)
0.516754 + 0.856134i \(0.327140\pi\)
\(168\) 0 0
\(169\) −1852.76 −0.843312
\(170\) 1885.03 3264.97i 0.850444 1.47301i
\(171\) 0 0
\(172\) 1676.78 + 2904.26i 0.743332 + 1.28749i
\(173\) −281.585 + 487.719i −0.123749 + 0.214339i −0.921243 0.388987i \(-0.872825\pi\)
0.797495 + 0.603326i \(0.206158\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 815.506 0.349267
\(177\) 0 0
\(178\) −2320.42 4019.09i −0.977096 1.69238i
\(179\) −919.749 1593.05i −0.384052 0.665197i 0.607585 0.794254i \(-0.292138\pi\)
−0.991637 + 0.129057i \(0.958805\pi\)
\(180\) 0 0
\(181\) −2324.71 −0.954664 −0.477332 0.878723i \(-0.658396\pi\)
−0.477332 + 0.878723i \(0.658396\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −179.403 + 310.735i −0.0718790 + 0.124498i
\(185\) −397.587 688.641i −0.158006 0.273675i
\(186\) 0 0
\(187\) 634.400 1098.81i 0.248085 0.429696i
\(188\) −2299.71 −0.892149
\(189\) 0 0
\(190\) 5306.82 2.02630
\(191\) 1563.64 2708.30i 0.592360 1.02600i −0.401553 0.915836i \(-0.631530\pi\)
0.993914 0.110163i \(-0.0351372\pi\)
\(192\) 0 0
\(193\) 1854.64 + 3212.34i 0.691711 + 1.19808i 0.971277 + 0.237952i \(0.0764761\pi\)
−0.279566 + 0.960126i \(0.590191\pi\)
\(194\) −2807.56 + 4862.84i −1.03903 + 1.79965i
\(195\) 0 0
\(196\) 0 0
\(197\) 851.150 0.307827 0.153913 0.988084i \(-0.450812\pi\)
0.153913 + 0.988084i \(0.450812\pi\)
\(198\) 0 0
\(199\) 1698.89 + 2942.57i 0.605182 + 1.04821i 0.992023 + 0.126060i \(0.0402331\pi\)
−0.386840 + 0.922147i \(0.626434\pi\)
\(200\) −24.0549 41.6643i −0.00850469 0.0147306i
\(201\) 0 0
\(202\) 7242.89 2.52281
\(203\) 0 0
\(204\) 0 0
\(205\) −1913.78 + 3314.77i −0.652022 + 1.12934i
\(206\) −992.885 1719.73i −0.335813 0.581646i
\(207\) 0 0
\(208\) −558.757 + 967.796i −0.186264 + 0.322618i
\(209\) 1785.99 0.591098
\(210\) 0 0
\(211\) 216.732 0.0707132 0.0353566 0.999375i \(-0.488743\pi\)
0.0353566 + 0.999375i \(0.488743\pi\)
\(212\) 156.253 270.639i 0.0506204 0.0876772i
\(213\) 0 0
\(214\) 571.948 + 990.644i 0.182699 + 0.316444i
\(215\) 1969.44 3411.16i 0.624718 1.08204i
\(216\) 0 0
\(217\) 0 0
\(218\) 1164.84 0.361893
\(219\) 0 0
\(220\) 567.241 + 982.490i 0.173833 + 0.301088i
\(221\) 869.340 + 1505.74i 0.264607 + 0.458312i
\(222\) 0 0
\(223\) 2254.86 0.677115 0.338558 0.940946i \(-0.390061\pi\)
0.338558 + 0.940946i \(0.390061\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 3842.92 6656.13i 1.13109 1.95911i
\(227\) −1695.40 2936.52i −0.495716 0.858606i 0.504271 0.863545i \(-0.331761\pi\)
−0.999988 + 0.00493916i \(0.998428\pi\)
\(228\) 0 0
\(229\) 1293.92 2241.14i 0.373384 0.646720i −0.616700 0.787198i \(-0.711531\pi\)
0.990084 + 0.140479i \(0.0448641\pi\)
\(230\) 7976.95 2.28689
\(231\) 0 0
\(232\) −340.853 −0.0964574
\(233\) 477.210 826.552i 0.134176 0.232400i −0.791106 0.611679i \(-0.790495\pi\)
0.925282 + 0.379279i \(0.123828\pi\)
\(234\) 0 0
\(235\) 1350.55 + 2339.22i 0.374894 + 0.649336i
\(236\) 1671.29 2894.76i 0.460982 0.798444i
\(237\) 0 0
\(238\) 0 0
\(239\) 199.504 0.0539951 0.0269976 0.999635i \(-0.491405\pi\)
0.0269976 + 0.999635i \(0.491405\pi\)
\(240\) 0 0
\(241\) 2397.21 + 4152.10i 0.640739 + 1.10979i 0.985268 + 0.171017i \(0.0547052\pi\)
−0.344529 + 0.938776i \(0.611961\pi\)
\(242\) −2327.15 4030.73i −0.618159 1.07068i
\(243\) 0 0
\(244\) −113.803 −0.0298585
\(245\) 0 0
\(246\) 0 0
\(247\) −1223.70 + 2119.51i −0.315231 + 0.545997i
\(248\) 75.9351 + 131.523i 0.0194431 + 0.0336764i
\(249\) 0 0
\(250\) −3049.23 + 5281.42i −0.771401 + 1.33611i
\(251\) −6249.73 −1.57163 −0.785816 0.618460i \(-0.787757\pi\)
−0.785816 + 0.618460i \(0.787757\pi\)
\(252\) 0 0
\(253\) 2684.61 0.667114
\(254\) −2479.71 + 4294.99i −0.612564 + 1.06099i
\(255\) 0 0
\(256\) −1800.79 3119.07i −0.439647 0.761491i
\(257\) −1918.93 + 3323.68i −0.465756 + 0.806713i −0.999235 0.0390999i \(-0.987551\pi\)
0.533479 + 0.845813i \(0.320884\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −1554.62 −0.370821
\(261\) 0 0
\(262\) −2414.19 4181.50i −0.569271 0.986007i
\(263\) −103.602 179.443i −0.0242903 0.0420721i 0.853625 0.520889i \(-0.174399\pi\)
−0.877915 + 0.478816i \(0.841066\pi\)
\(264\) 0 0
\(265\) −367.051 −0.0850858
\(266\) 0 0
\(267\) 0 0
\(268\) −1438.06 + 2490.80i −0.327775 + 0.567722i
\(269\) 2402.04 + 4160.46i 0.544442 + 0.943002i 0.998642 + 0.0521018i \(0.0165920\pi\)
−0.454199 + 0.890900i \(0.650075\pi\)
\(270\) 0 0
\(271\) 1607.88 2784.92i 0.360411 0.624251i −0.627617 0.778522i \(-0.715970\pi\)
0.988029 + 0.154271i \(0.0493030\pi\)
\(272\) −5644.27 −1.25821
\(273\) 0 0
\(274\) −433.771 −0.0956388
\(275\) −179.980 + 311.735i −0.0394663 + 0.0683576i
\(276\) 0 0
\(277\) −1027.20 1779.16i −0.222810 0.385918i 0.732850 0.680390i \(-0.238190\pi\)
−0.955660 + 0.294472i \(0.904856\pi\)
\(278\) 2223.93 3851.97i 0.479794 0.831027i
\(279\) 0 0
\(280\) 0 0
\(281\) 1768.61 0.375468 0.187734 0.982220i \(-0.439886\pi\)
0.187734 + 0.982220i \(0.439886\pi\)
\(282\) 0 0
\(283\) 1170.26 + 2026.96i 0.245813 + 0.425760i 0.962360 0.271779i \(-0.0876119\pi\)
−0.716547 + 0.697539i \(0.754279\pi\)
\(284\) 891.668 + 1544.41i 0.186305 + 0.322690i
\(285\) 0 0
\(286\) −1018.76 −0.210631
\(287\) 0 0
\(288\) 0 0
\(289\) −1934.31 + 3350.32i −0.393712 + 0.681929i
\(290\) 3788.92 + 6562.60i 0.767217 + 1.32886i
\(291\) 0 0
\(292\) 2052.95 3555.82i 0.411438 0.712632i
\(293\) 3633.47 0.724470 0.362235 0.932087i \(-0.382014\pi\)
0.362235 + 0.932087i \(0.382014\pi\)
\(294\) 0 0
\(295\) −3925.98 −0.774846
\(296\) 72.5250 125.617i 0.0142413 0.0246667i
\(297\) 0 0
\(298\) 1453.17 + 2516.97i 0.282483 + 0.489276i
\(299\) −1839.40 + 3185.94i −0.355771 + 0.616213i
\(300\) 0 0
\(301\) 0 0
\(302\) −626.023 −0.119283
\(303\) 0 0
\(304\) −3972.50 6880.56i −0.749468 1.29812i
\(305\) 66.8326 + 115.758i 0.0125470 + 0.0217320i
\(306\) 0 0
\(307\) −5954.32 −1.10694 −0.553471 0.832868i \(-0.686697\pi\)
−0.553471 + 0.832868i \(0.686697\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 1688.19 2924.03i 0.309299 0.535721i
\(311\) 590.047 + 1021.99i 0.107584 + 0.186340i 0.914791 0.403928i \(-0.132355\pi\)
−0.807207 + 0.590268i \(0.799022\pi\)
\(312\) 0 0
\(313\) −4873.12 + 8440.50i −0.880017 + 1.52423i −0.0286960 + 0.999588i \(0.509135\pi\)
−0.851321 + 0.524646i \(0.824198\pi\)
\(314\) −8490.97 −1.52603
\(315\) 0 0
\(316\) 2481.00 0.441669
\(317\) −4295.96 + 7440.81i −0.761151 + 1.31835i 0.181106 + 0.983464i \(0.442032\pi\)
−0.942258 + 0.334889i \(0.891301\pi\)
\(318\) 0 0
\(319\) 1275.14 + 2208.62i 0.223807 + 0.387645i
\(320\) 2814.59 4875.01i 0.491688 0.851629i
\(321\) 0 0
\(322\) 0 0
\(323\) −12361.2 −2.12939
\(324\) 0 0
\(325\) −246.633 427.181i −0.0420946 0.0729100i
\(326\) 6099.02 + 10563.8i 1.03618 + 1.79471i
\(327\) 0 0
\(328\) −698.197 −0.117535
\(329\) 0 0
\(330\) 0 0
\(331\) 2625.60 4547.67i 0.436000 0.755174i −0.561377 0.827560i \(-0.689728\pi\)
0.997377 + 0.0723864i \(0.0230615\pi\)
\(332\) 3757.03 + 6507.36i 0.621065 + 1.07572i
\(333\) 0 0
\(334\) 4522.64 7833.44i 0.740921 1.28331i
\(335\) 3378.11 0.550943
\(336\) 0 0
\(337\) −8496.45 −1.37339 −0.686693 0.726947i \(-0.740938\pi\)
−0.686693 + 0.726947i \(0.740938\pi\)
\(338\) −3756.83 + 6507.02i −0.604570 + 1.04715i
\(339\) 0 0
\(340\) −3925.98 6800.00i −0.626225 1.08465i
\(341\) 568.152 984.068i 0.0902263 0.156276i
\(342\) 0 0
\(343\) 0 0
\(344\) 718.500 0.112613
\(345\) 0 0
\(346\) 1141.94 + 1977.89i 0.177430 + 0.307319i
\(347\) 2915.07 + 5049.06i 0.450978 + 0.781117i 0.998447 0.0557090i \(-0.0177419\pi\)
−0.547469 + 0.836826i \(0.684409\pi\)
\(348\) 0 0
\(349\) −1811.13 −0.277786 −0.138893 0.990307i \(-0.544354\pi\)
−0.138893 + 0.990307i \(0.544354\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 1751.60 3033.87i 0.265230 0.459391i
\(353\) 1663.88 + 2881.92i 0.250876 + 0.434531i 0.963767 0.266744i \(-0.0859479\pi\)
−0.712891 + 0.701275i \(0.752615\pi\)
\(354\) 0 0
\(355\) 1047.30 1813.97i 0.156577 0.271199i
\(356\) −9665.55 −1.43897
\(357\) 0 0
\(358\) −7459.89 −1.10131
\(359\) 435.430 754.188i 0.0640143 0.110876i −0.832242 0.554413i \(-0.812943\pi\)
0.896256 + 0.443536i \(0.146276\pi\)
\(360\) 0 0
\(361\) −5270.42 9128.63i −0.768395 1.33090i
\(362\) −4713.80 + 8164.55i −0.684398 + 1.18541i
\(363\) 0 0
\(364\) 0 0
\(365\) −4822.54 −0.691570
\(366\) 0 0
\(367\) 587.358 + 1017.33i 0.0835418 + 0.144699i 0.904769 0.425903i \(-0.140043\pi\)
−0.821227 + 0.570601i \(0.806710\pi\)
\(368\) −5971.26 10342.5i −0.845851 1.46506i
\(369\) 0 0
\(370\) −3224.75 −0.453099
\(371\) 0 0
\(372\) 0 0
\(373\) −1814.17 + 3142.23i −0.251834 + 0.436189i −0.964031 0.265791i \(-0.914367\pi\)
0.712197 + 0.701980i \(0.247700\pi\)
\(374\) −2572.74 4456.12i −0.355704 0.616097i
\(375\) 0 0
\(376\) −246.357 + 426.703i −0.0337897 + 0.0585254i
\(377\) −3494.75 −0.477424
\(378\) 0 0
\(379\) 7321.99 0.992362 0.496181 0.868219i \(-0.334735\pi\)
0.496181 + 0.868219i \(0.334735\pi\)
\(380\) 5526.29 9571.82i 0.746034 1.29217i
\(381\) 0 0
\(382\) −6341.17 10983.2i −0.849325 1.47107i
\(383\) −3677.45 + 6369.52i −0.490623 + 0.849784i −0.999942 0.0107937i \(-0.996564\pi\)
0.509318 + 0.860578i \(0.329898\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 15042.6 1.98355
\(387\) 0 0
\(388\) 5847.35 + 10127.9i 0.765088 + 1.32517i
\(389\) −4534.81 7854.52i −0.591064 1.02375i −0.994089 0.108564i \(-0.965375\pi\)
0.403025 0.915189i \(-0.367959\pi\)
\(390\) 0 0
\(391\) −18580.7 −2.40324
\(392\) 0 0
\(393\) 0 0
\(394\) 1725.87 2989.30i 0.220681 0.382230i
\(395\) −1457.01 2523.62i −0.185596 0.321462i
\(396\) 0 0
\(397\) 3688.41 6388.52i 0.466288 0.807634i −0.532971 0.846134i \(-0.678925\pi\)
0.999259 + 0.0384997i \(0.0122579\pi\)
\(398\) 13779.4 1.73542
\(399\) 0 0
\(400\) 1601.29 0.200161
\(401\) 1426.76 2471.21i 0.177678 0.307747i −0.763407 0.645918i \(-0.776475\pi\)
0.941085 + 0.338171i \(0.109808\pi\)
\(402\) 0 0
\(403\) 778.558 + 1348.50i 0.0962350 + 0.166684i
\(404\) 7542.43 13063.9i 0.928836 1.60879i
\(405\) 0 0
\(406\) 0 0
\(407\) −1085.27 −0.132175
\(408\) 0 0
\(409\) 5630.03 + 9751.49i 0.680652 + 1.17892i 0.974782 + 0.223159i \(0.0716369\pi\)
−0.294130 + 0.955766i \(0.595030\pi\)
\(410\) 7761.15 + 13442.7i 0.934868 + 1.61924i
\(411\) 0 0
\(412\) −4135.79 −0.494553
\(413\) 0 0
\(414\) 0 0
\(415\) 4412.76 7643.13i 0.521961 0.904064i
\(416\) 2400.28 + 4157.41i 0.282893 + 0.489985i
\(417\) 0 0
\(418\) 3621.44 6272.52i 0.423757 0.733969i
\(419\) 9221.47 1.07517 0.537587 0.843208i \(-0.319336\pi\)
0.537587 + 0.843208i \(0.319336\pi\)
\(420\) 0 0
\(421\) −8520.28 −0.986349 −0.493175 0.869930i \(-0.664164\pi\)
−0.493175 + 0.869930i \(0.664164\pi\)
\(422\) 439.468 761.181i 0.0506942 0.0878049i
\(423\) 0 0
\(424\) −33.4774 57.9845i −0.00383444 0.00664145i
\(425\) 1245.68 2157.58i 0.142175 0.246254i
\(426\) 0 0
\(427\) 0 0
\(428\) 2382.41 0.269061
\(429\) 0 0
\(430\) −7986.84 13833.6i −0.895720 1.55143i
\(431\) −4581.05 7934.62i −0.511976 0.886768i −0.999904 0.0138840i \(-0.995580\pi\)
0.487928 0.872884i \(-0.337753\pi\)
\(432\) 0 0
\(433\) 10976.2 1.21820 0.609100 0.793093i \(-0.291531\pi\)
0.609100 + 0.793093i \(0.291531\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 1213.01 2100.99i 0.133240 0.230778i
\(437\) −13077.3 22650.5i −1.43151 2.47945i
\(438\) 0 0
\(439\) 1991.59 3449.54i 0.216523 0.375028i −0.737220 0.675653i \(-0.763862\pi\)
0.953743 + 0.300625i \(0.0971951\pi\)
\(440\) 243.063 0.0263354
\(441\) 0 0
\(442\) 7051.03 0.758786
\(443\) −2262.22 + 3918.29i −0.242622 + 0.420234i −0.961460 0.274944i \(-0.911341\pi\)
0.718838 + 0.695177i \(0.244674\pi\)
\(444\) 0 0
\(445\) 5676.27 + 9831.59i 0.604676 + 1.04733i
\(446\) 4572.18 7919.24i 0.485423 0.840778i
\(447\) 0 0
\(448\) 0 0
\(449\) −2076.49 −0.218253 −0.109127 0.994028i \(-0.534805\pi\)
−0.109127 + 0.994028i \(0.534805\pi\)
\(450\) 0 0
\(451\) 2611.98 + 4524.09i 0.272713 + 0.472352i
\(452\) −8003.70 13862.8i −0.832881 1.44259i
\(453\) 0 0
\(454\) −13751.0 −1.42151
\(455\) 0 0
\(456\) 0 0
\(457\) 923.795 1600.06i 0.0945587 0.163780i −0.814866 0.579650i \(-0.803189\pi\)
0.909424 + 0.415869i \(0.136523\pi\)
\(458\) −5247.37 9088.71i −0.535357 0.927266i
\(459\) 0 0
\(460\) 8306.85 14387.9i 0.841976 1.45834i
\(461\) −876.945 −0.0885974 −0.0442987 0.999018i \(-0.514105\pi\)
−0.0442987 + 0.999018i \(0.514105\pi\)
\(462\) 0 0
\(463\) 16245.2 1.63062 0.815310 0.579025i \(-0.196566\pi\)
0.815310 + 0.579025i \(0.196566\pi\)
\(464\) 5672.50 9825.05i 0.567541 0.983010i
\(465\) 0 0
\(466\) −1935.27 3351.99i −0.192382 0.333215i
\(467\) −9480.88 + 16421.4i −0.939449 + 1.62717i −0.172947 + 0.984931i \(0.555329\pi\)
−0.766502 + 0.642242i \(0.778004\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 10954.0 1.07505
\(471\) 0 0
\(472\) −358.075 620.204i −0.0349189 0.0604813i
\(473\) −2687.94 4655.64i −0.261293 0.452572i
\(474\) 0 0
\(475\) 3506.89 0.338752
\(476\) 0 0
\(477\) 0 0
\(478\) 404.533 700.672i 0.0387090 0.0670460i
\(479\) −4188.88 7255.35i −0.399572 0.692078i 0.594101 0.804390i \(-0.297508\pi\)
−0.993673 + 0.112312i \(0.964174\pi\)
\(480\) 0 0
\(481\) 743.594 1287.94i 0.0704885 0.122090i
\(482\) 19443.3 1.83738
\(483\) 0 0
\(484\) −9693.55 −0.910364
\(485\) 6867.92 11895.6i 0.643002 1.11371i
\(486\) 0 0
\(487\) 2279.42 + 3948.08i 0.212096 + 0.367360i 0.952370 0.304944i \(-0.0986378\pi\)
−0.740275 + 0.672305i \(0.765304\pi\)
\(488\) −12.1911 + 21.1156i −0.00113087 + 0.00195873i
\(489\) 0 0
\(490\) 0 0
\(491\) 15809.9 1.45314 0.726570 0.687092i \(-0.241113\pi\)
0.726570 + 0.687092i \(0.241113\pi\)
\(492\) 0 0
\(493\) −8825.53 15286.3i −0.806251 1.39647i
\(494\) 4962.59 + 8595.45i 0.451978 + 0.782849i
\(495\) 0 0
\(496\) −5054.86 −0.457601
\(497\) 0 0
\(498\) 0 0
\(499\) −6693.04 + 11592.7i −0.600444 + 1.04000i 0.392309 + 0.919833i \(0.371676\pi\)
−0.992754 + 0.120167i \(0.961657\pi\)
\(500\) 6350.67 + 10999.7i 0.568022 + 0.983842i
\(501\) 0 0
\(502\) −12672.6 + 21949.5i −1.12670 + 1.95150i
\(503\) −5720.55 −0.507091 −0.253545 0.967323i \(-0.581597\pi\)
−0.253545 + 0.967323i \(0.581597\pi\)
\(504\) 0 0
\(505\) −17717.7 −1.56124
\(506\) 5443.57 9428.54i 0.478254 0.828359i
\(507\) 0 0
\(508\) 5164.53 + 8945.24i 0.451061 + 0.781261i
\(509\) −7646.59 + 13244.3i −0.665873 + 1.15333i 0.313175 + 0.949695i \(0.398607\pi\)
−0.979048 + 0.203630i \(0.934726\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −16456.0 −1.42043
\(513\) 0 0
\(514\) 7782.00 + 13478.8i 0.667800 + 1.15666i
\(515\) 2428.82 + 4206.83i 0.207818 + 0.359952i
\(516\) 0 0
\(517\) 3686.53 0.313604
\(518\) 0 0
\(519\) 0 0
\(520\) −166.539 + 288.454i −0.0140446 + 0.0243260i
\(521\) 2184.35 + 3783.40i 0.183681 + 0.318145i 0.943131 0.332420i \(-0.107865\pi\)
−0.759450 + 0.650566i \(0.774532\pi\)
\(522\) 0 0
\(523\) −1211.08 + 2097.66i −0.101256 + 0.175381i −0.912202 0.409740i \(-0.865619\pi\)
0.810946 + 0.585121i \(0.198953\pi\)
\(524\) −10056.1 −0.838366
\(525\) 0 0
\(526\) −840.291 −0.0696548
\(527\) −3932.29 + 6810.93i −0.325035 + 0.562976i
\(528\) 0 0
\(529\) −13573.6 23510.2i −1.11561 1.93229i
\(530\) −744.268 + 1289.11i −0.0609980 + 0.105652i
\(531\) 0 0
\(532\) 0 0
\(533\) −7158.57 −0.581749
\(534\) 0 0
\(535\) −1399.11 2423.33i −0.113063 0.195832i
\(536\) 308.105 + 533.654i 0.0248286 + 0.0430044i
\(537\) 0 0
\(538\) 19482.4 1.56124
\(539\) 0 0
\(540\) 0 0
\(541\) −6581.27 + 11399.1i −0.523014 + 0.905888i 0.476627 + 0.879106i \(0.341859\pi\)
−0.999641 + 0.0267819i \(0.991474\pi\)
\(542\) −6520.57 11294.0i −0.516757 0.895050i
\(543\) 0 0
\(544\) −12123.2 + 20998.0i −0.955473 + 1.65493i
\(545\) −2849.45 −0.223958
\(546\) 0 0
\(547\) 12112.4 0.946778 0.473389 0.880853i \(-0.343031\pi\)
0.473389 + 0.880853i \(0.343031\pi\)
\(548\) −451.710 + 782.384i −0.0352118 + 0.0609887i
\(549\) 0 0
\(550\) 729.892 + 1264.21i 0.0565867 + 0.0980110i
\(551\) 12423.0 21517.2i 0.960503 1.66364i
\(552\) 0 0
\(553\) 0 0
\(554\) −8331.38 −0.638928
\(555\) 0 0
\(556\) −4631.81 8022.54i −0.353296 0.611927i
\(557\) 4179.82 + 7239.67i 0.317962 + 0.550726i 0.980063 0.198689i \(-0.0636682\pi\)
−0.662101 + 0.749415i \(0.730335\pi\)
\(558\) 0 0
\(559\) 7366.74 0.557388
\(560\) 0 0
\(561\) 0 0
\(562\) 3586.21 6211.50i 0.269173 0.466221i
\(563\) 6819.20 + 11811.2i 0.510471 + 0.884162i 0.999926 + 0.0121334i \(0.00386228\pi\)
−0.489455 + 0.872028i \(0.662804\pi\)
\(564\) 0 0
\(565\) −9400.63 + 16282.4i −0.699978 + 1.21240i
\(566\) 9491.76 0.704891
\(567\) 0 0
\(568\) 382.080 0.0282249
\(569\) −7745.67 + 13415.9i −0.570677 + 0.988442i 0.425820 + 0.904808i \(0.359986\pi\)
−0.996497 + 0.0836335i \(0.973348\pi\)
\(570\) 0 0
\(571\) 2324.08 + 4025.42i 0.170332 + 0.295024i 0.938536 0.345182i \(-0.112183\pi\)
−0.768204 + 0.640205i \(0.778849\pi\)
\(572\) −1060.89 + 1837.52i −0.0775491 + 0.134319i
\(573\) 0 0
\(574\) 0 0
\(575\) 5271.38 0.382316
\(576\) 0 0
\(577\) −2739.53 4745.01i −0.197657 0.342352i 0.750111 0.661312i \(-0.230000\pi\)
−0.947768 + 0.318959i \(0.896667\pi\)
\(578\) 7844.37 + 13586.8i 0.564503 + 0.977748i
\(579\) 0 0
\(580\) 15782.5 1.12988
\(581\) 0 0
\(582\) 0 0
\(583\) −250.480 + 433.844i −0.0177939 + 0.0308199i
\(584\) −439.846 761.836i −0.0311660 0.0539811i
\(585\) 0 0
\(586\) 7367.59 12761.0i 0.519372 0.899579i
\(587\) −4408.22 −0.309960 −0.154980 0.987918i \(-0.549531\pi\)
−0.154980 + 0.987918i \(0.549531\pi\)
\(588\) 0 0
\(589\) −11070.3 −0.774441
\(590\) −7960.71 + 13788.3i −0.555487 + 0.962131i
\(591\) 0 0
\(592\) 2413.93 + 4181.05i 0.167588 + 0.290270i
\(593\) 1407.63 2438.08i 0.0974779 0.168837i −0.813162 0.582037i \(-0.802256\pi\)
0.910640 + 0.413201i \(0.135589\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 6053.09 0.416014
\(597\) 0 0
\(598\) 7459.51 + 12920.2i 0.510104 + 0.883526i
\(599\) −9859.53 17077.2i −0.672537 1.16487i −0.977182 0.212402i \(-0.931871\pi\)
0.304646 0.952466i \(-0.401462\pi\)
\(600\) 0 0
\(601\) 13982.8 0.949033 0.474517 0.880247i \(-0.342623\pi\)
0.474517 + 0.880247i \(0.342623\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −651.913 + 1129.15i −0.0439172 + 0.0760667i
\(605\) 5692.71 + 9860.07i 0.382548 + 0.662593i
\(606\) 0 0
\(607\) 6694.14 11594.6i 0.447622 0.775305i −0.550608 0.834764i \(-0.685604\pi\)
0.998231 + 0.0594590i \(0.0189376\pi\)
\(608\) −34129.7 −2.27655
\(609\) 0 0
\(610\) 542.065 0.0359797
\(611\) −2525.89 + 4374.96i −0.167245 + 0.289676i
\(612\) 0 0
\(613\) 13895.9 + 24068.5i 0.915582 + 1.58583i 0.806047 + 0.591852i \(0.201603\pi\)
0.109535 + 0.993983i \(0.465064\pi\)
\(614\) −12073.6 + 20912.0i −0.793566 + 1.37450i
\(615\) 0 0
\(616\) 0 0
\(617\) −19107.2 −1.24672 −0.623361 0.781935i \(-0.714233\pi\)
−0.623361 + 0.781935i \(0.714233\pi\)
\(618\) 0 0
\(619\) 546.469 + 946.512i 0.0354837 + 0.0614596i 0.883222 0.468955i \(-0.155369\pi\)
−0.847738 + 0.530415i \(0.822036\pi\)
\(620\) −3516.01 6089.90i −0.227752 0.394478i
\(621\) 0 0
\(622\) 4785.75 0.308507
\(623\) 0 0
\(624\) 0 0
\(625\) 5797.49 10041.5i 0.371039 0.642659i
\(626\) 19762.4 + 34229.5i 1.26177 + 2.18544i
\(627\) 0 0
\(628\) −8842.13 + 15315.0i −0.561846 + 0.973146i
\(629\) 7511.40 0.476151
\(630\) 0 0
\(631\) 19235.2 1.21353 0.606767 0.794879i \(-0.292466\pi\)
0.606767 + 0.794879i \(0.292466\pi\)
\(632\) 265.778 460.341i 0.0167280 0.0289737i
\(633\) 0 0
\(634\) 17421.8 + 30175.4i 1.09134 + 1.89025i
\(635\) 6065.93 10506.5i 0.379085 0.656595i
\(636\) 0 0
\(637\) 0 0
\(638\) 10342.4 0.641788
\(639\) 0 0
\(640\) −1147.14 1986.91i −0.0708511 0.122718i
\(641\) 9975.33 + 17277.8i 0.614667 + 1.06463i 0.990443 + 0.137924i \(0.0440430\pi\)
−0.375776 + 0.926711i \(0.622624\pi\)
\(642\) 0 0
\(643\) −688.125 −0.0422037 −0.0211019 0.999777i \(-0.506717\pi\)
−0.0211019 + 0.999777i \(0.506717\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −25064.7 + 43413.4i −1.52656 + 2.64408i
\(647\) 5483.09 + 9497.00i 0.333173 + 0.577072i 0.983132 0.182897i \(-0.0585475\pi\)
−0.649959 + 0.759969i \(0.725214\pi\)
\(648\) 0 0
\(649\) −2679.14 + 4640.41i −0.162042 + 0.280666i
\(650\) −2000.39 −0.120710
\(651\) 0 0
\(652\) 25405.0 1.52598
\(653\) 6462.54 11193.4i 0.387287 0.670802i −0.604796 0.796380i \(-0.706745\pi\)
0.992084 + 0.125579i \(0.0400788\pi\)
\(654\) 0 0
\(655\) 5905.64 + 10228.9i 0.352294 + 0.610191i
\(656\) 11619.4 20125.5i 0.691559 1.19782i
\(657\) 0 0
\(658\) 0 0
\(659\) −11779.0 −0.696273 −0.348137 0.937444i \(-0.613185\pi\)
−0.348137 + 0.937444i \(0.613185\pi\)
\(660\) 0 0
\(661\) −12520.0 21685.3i −0.736721 1.27604i −0.953964 0.299921i \(-0.903040\pi\)
0.217243 0.976118i \(-0.430294\pi\)
\(662\) −10647.8 18442.6i −0.625136 1.08277i
\(663\) 0 0
\(664\) 1609.89 0.0940900
\(665\) 0 0
\(666\) 0 0
\(667\) 18673.6 32343.6i 1.08403 1.87759i
\(668\) −9419.36 16314.8i −0.545578 0.944968i
\(669\) 0 0
\(670\) 6849.78 11864.2i 0.394971 0.684109i
\(671\) 182.430 0.0104957
\(672\) 0 0
\(673\) 4104.64 0.235100 0.117550 0.993067i \(-0.462496\pi\)
0.117550 + 0.993067i \(0.462496\pi\)
\(674\) −17228.2 + 29840.2i −0.984580 + 1.70534i
\(675\) 0 0
\(676\) 7824.40 + 13552.3i 0.445175 + 0.771066i
\(677\) 6076.70 10525.1i 0.344973 0.597510i −0.640376 0.768061i \(-0.721222\pi\)
0.985349 + 0.170551i \(0.0545549\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −1682.29 −0.0948717
\(681\) 0 0
\(682\) −2304.08 3990.78i −0.129366 0.224069i
\(683\) 10207.0 + 17679.0i 0.571830 + 0.990438i 0.996378 + 0.0850328i \(0.0270995\pi\)
−0.424549 + 0.905405i \(0.639567\pi\)
\(684\) 0 0
\(685\) 1061.10 0.0591862
\(686\) 0 0
\(687\) 0 0
\(688\) −11957.3 + 20710.7i −0.662600 + 1.14766i
\(689\) −343.241 594.511i −0.0189789 0.0328724i
\(690\) 0 0
\(691\) 8046.76 13937.4i 0.443000 0.767299i −0.554910 0.831910i \(-0.687247\pi\)
0.997911 + 0.0646110i \(0.0205807\pi\)
\(692\) 4756.66 0.261302
\(693\) 0 0
\(694\) 23643.6 1.29322
\(695\) −5440.23 + 9422.76i −0.296921 + 0.514282i
\(696\) 0 0
\(697\) −18078.0 31312.1i −0.982431 1.70162i
\(698\) −3672.42 + 6360.81i −0.199145 + 0.344929i
\(699\) 0 0
\(700\) 0 0
\(701\) 20803.0 1.12085 0.560426 0.828204i \(-0.310637\pi\)
0.560426 + 0.828204i \(0.310637\pi\)
\(702\) 0 0
\(703\) 5286.60 + 9156.65i 0.283624 + 0.491251i
\(704\) −3841.42 6653.54i −0.205652 0.356200i
\(705\) 0 0
\(706\) 13495.4 0.719412
\(707\) 0 0
\(708\) 0 0
\(709\) −70.7460 + 122.536i −0.00374742 + 0.00649073i −0.867893 0.496751i \(-0.834526\pi\)
0.864146 + 0.503242i \(0.167860\pi\)
\(710\) −4247.20 7356.36i −0.224499 0.388844i
\(711\) 0 0
\(712\) −1035.42 + 1793.41i −0.0545002 + 0.0943971i
\(713\) −16640.4 −0.874035
\(714\) 0 0
\(715\) 2492.11 0.130349
\(716\) −7768.40 + 13455.3i −0.405473 + 0.702300i
\(717\) 0 0
\(718\) −1765.84 3058.53i −0.0917836 0.158974i
\(719\) −3332.23 + 5771.59i −0.172839 + 0.299366i −0.939411 0.342792i \(-0.888627\pi\)
0.766572 + 0.642158i \(0.221961\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −42747.2 −2.20345
\(723\) 0 0
\(724\) 9817.50 + 17004.4i 0.503957 + 0.872878i
\(725\) 2503.82 + 4336.74i 0.128261 + 0.222155i
\(726\) 0 0
\(727\) 4837.23 0.246772 0.123386 0.992359i \(-0.460625\pi\)
0.123386 + 0.992359i \(0.460625\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −9778.65 + 16937.1i −0.495786 + 0.858727i
\(731\) 18603.7 + 32222.6i 0.941291 + 1.63036i
\(732\) 0 0
\(733\) −15801.3 + 27368.6i −0.796225 + 1.37910i 0.125834 + 0.992051i \(0.459839\pi\)
−0.922059 + 0.387050i \(0.873494\pi\)
\(734\) 4763.93 0.239564
\(735\) 0 0
\(736\) −51302.0 −2.56932
\(737\) 2305.27 3992.84i 0.115218 0.199563i
\(738\) 0 0
\(739\) 4113.79 + 7125.30i 0.204774 + 0.354680i 0.950061 0.312065i \(-0.101021\pi\)
−0.745286 + 0.666744i \(0.767687\pi\)
\(740\) −3358.11 + 5816.42i −0.166820 + 0.288940i
\(741\) 0 0
\(742\) 0 0
\(743\) 37020.3 1.82792 0.913959 0.405805i \(-0.133009\pi\)
0.913959 + 0.405805i \(0.133009\pi\)
\(744\) 0 0
\(745\) −3554.78 6157.07i −0.174815 0.302789i
\(746\) 7357.16 + 12743.0i 0.361079 + 0.625407i
\(747\) 0 0
\(748\) −10716.6 −0.523846
\(749\) 0 0
\(750\) 0 0
\(751\) 12575.0 21780.5i 0.611008 1.05830i −0.380063 0.924960i \(-0.624098\pi\)
0.991071 0.133336i \(-0.0425689\pi\)
\(752\) −8199.78 14202.4i −0.397627 0.688710i
\(753\) 0 0
\(754\) −7086.29 + 12273.8i −0.342265 + 0.592820i
\(755\) 1531.39 0.0738186
\(756\) 0 0
\(757\) 20460.8 0.982377 0.491189 0.871053i \(-0.336563\pi\)
0.491189 + 0.871053i \(0.336563\pi\)
\(758\) 14846.8 25715.4i 0.711424 1.23222i
\(759\) 0 0
\(760\) −1184.01 2050.77i −0.0565113 0.0978804i
\(761\) 16329.6 28283.6i 0.777853 1.34728i −0.155324 0.987864i \(-0.549642\pi\)
0.933177 0.359417i \(-0.117024\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −26413.7 −1.25080
\(765\) 0 0
\(766\) 14913.5 + 25830.9i 0.703455 + 1.21842i
\(767\) −3671.32 6358.91i −0.172834 0.299357i
\(768\) 0 0
\(769\) 11005.3 0.516075 0.258037 0.966135i \(-0.416924\pi\)
0.258037 + 0.966135i \(0.416924\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 15664.7 27132.1i 0.730293 1.26490i
\(773\) −1519.09 2631.14i −0.0706829 0.122426i 0.828518 0.559963i \(-0.189185\pi\)
−0.899201 + 0.437536i \(0.855851\pi\)
\(774\) 0 0
\(775\) 1115.60 1932.27i 0.0517077 0.0895604i
\(776\) 2505.59 0.115909
\(777\) 0 0
\(778\) −36780.9 −1.69493
\(779\) 25447.0 44075.5i 1.17039 2.02717i
\(780\) 0 0
\(781\) −1429.38 2475.75i −0.0654893 0.113431i
\(782\) −37676.0 + 65256.8i −1.72288 + 2.98411i
\(783\) 0 0
\(784\) 0 0
\(785\) 20770.8 0.944384
\(786\) 0 0
\(787\) −6153.38 10658.0i −0.278710 0.482739i 0.692355 0.721557i \(-0.256573\pi\)
−0.971064 + 0.238818i \(0.923240\pi\)
\(788\) −3594.50 6225.86i −0.162498 0.281455i
\(789\) 0 0
\(790\) −11817.5 −0.532214
\(791\) 0 0
\(792\) 0 0