Properties

Label 441.4.e.x.226.1
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 226.1
Root \(2.02770 + 3.51207i\) of defining polynomial
Character \(\chi\) \(=\) 441.226
Dual form 441.4.e.x.361.1

$q$-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 \(0.421106\pi\)
−0.962222 + 0.272264i \(0.912227\pi\)
\(3\) 0 0
\(4\) −4.22311 7.31464i −0.527889 0.914330i
\(5\) 4.96020 8.59131i 0.443654 0.768430i −0.554304 0.832314i \(-0.687015\pi\)
0.997957 + 0.0638840i \(0.0203488\pi\)
\(6\) 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 0.758204 0.652017i \(-0.226077\pi\)
−0.943765 + 0.330616i \(0.892744\pi\)
\(12\) 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 \(0.0663850\pi\)
−0.309858 + 0.950783i \(0.600282\pi\)
\(18\) 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 \(0.522212\pi\)
−0.829056 + 0.559165i \(0.811122\pi\)
\(24\) 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 \(-0.706050\pi\)
−0.603054 + 0.797700i \(0.706050\pi\)
\(30\) 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 \(-0.762739\pi\)
−0.734833 + 0.678249i \(0.762739\pi\)
\(42\) 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 −0.996184 0.0872772i \(-0.972183\pi\)
0.573676 + 0.819082i \(0.305517\pi\)
\(48\) 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 0.841056 0.540948i \(-0.181934\pi\)
−0.889002 + 0.457902i \(0.848601\pi\)
\(54\) 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 0.560799 0.827952i \(-0.310494\pi\)
−0.997427 + 0.0716901i \(0.977161\pi\)
\(60\) 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 \(-0.443534\pi\)
0.176463 + 0.984307i \(0.443534\pi\)
\(72\) 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 \(-0.299816\pi\)
0.588253 + 0.808677i \(0.299816\pi\)
\(84\) 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 \(0.405327\pi\)
−0.974531 + 0.224252i \(0.928006\pi\)
\(90\) 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 \(-0.824367\pi\)
−0.0281660 0.999603i \(-0.508967\pi\)
\(102\) 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 −0.795254 0.606276i \(-0.792663\pi\)
0.922678 + 0.385573i \(0.125996\pi\)
\(108\) 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 \(-0.789338\pi\)
−0.788879 + 0.614548i \(0.789338\pi\)
\(114\) 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 −0.993359 0.115057i \(-0.963295\pi\)
0.596322 + 0.802746i \(0.296628\pi\)
\(132\) 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 0.882219 0.470839i \(-0.156049\pi\)
−0.848868 + 0.528605i \(0.822715\pi\)
\(138\) 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 −0.750542 0.660822i \(-0.770208\pi\)
0.947560 + 0.319578i \(0.103541\pi\)
\(150\) 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 \(-0.672860\pi\)
−0.516754 + 0.856134i \(0.672860\pi\)
\(168\) 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 −0.797495 0.603326i \(-0.793842\pi\)
0.921243 + 0.388987i \(0.127175\pi\)
\(174\) 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 0.991637 0.129057i \(-0.0411951\pi\)
−0.607585 + 0.794254i \(0.707862\pi\)
\(180\) 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 \(0.368470\pi\)
−0.993914 + 0.110163i \(0.964863\pi\)
\(192\) 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 \(-0.549188\pi\)
−0.153913 + 0.988084i \(0.549188\pi\)
\(198\) 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 0.999988 0.00493916i \(-0.00157219\pi\)
−0.504271 + 0.863545i \(0.668239\pi\)
\(228\) 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 −0.925282 0.379279i \(-0.876172\pi\)
0.791106 + 0.611679i \(0.209505\pi\)
\(234\) 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 \(-0.508595\pi\)
−0.0269976 + 0.999635i \(0.508595\pi\)
\(240\) 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 \(-0.212243\pi\)
0.785816 + 0.618460i \(0.212243\pi\)
\(252\) 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 −0.533479 0.845813i \(-0.679116\pi\)
0.999235 + 0.0390999i \(0.0124491\pi\)
\(258\) 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 0.877915 0.478816i \(-0.158934\pi\)
−0.853625 + 0.520889i \(0.825601\pi\)
\(264\) 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 \(-0.983408\pi\)
0.454199 0.890900i \(-0.349925\pi\)
\(270\) 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 \(-0.560114\pi\)
−0.187734 + 0.982220i \(0.560114\pi\)
\(282\) 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 \(-0.617986\pi\)
−0.362235 + 0.932087i \(0.617986\pi\)
\(294\) 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 0.807207 0.590268i \(-0.200978\pi\)
−0.914791 + 0.403928i \(0.867645\pi\)
\(312\) 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 \(-0.557968\pi\)
0.942258 0.334889i \(-0.108699\pi\)
\(318\) 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 0.547469 0.836826i \(-0.315591\pi\)
−0.998447 + 0.0557090i \(0.982258\pi\)
\(348\) 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 0.712891 0.701275i \(-0.247385\pi\)
−0.963767 + 0.266744i \(0.914052\pi\)
\(354\) 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 −0.896256 0.443536i \(-0.853724\pi\)
0.832242 + 0.554413i \(0.187057\pi\)
\(360\) 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 −0.509318 0.860578i \(-0.670102\pi\)
0.999942 + 0.0107937i \(0.00343580\pi\)
\(384\) 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 \(0.0346254\pi\)
−0.403025 + 0.915189i \(0.632041\pi\)
\(390\) 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 −0.941085 0.338171i \(-0.890192\pi\)
0.763407 + 0.645918i \(0.223525\pi\)
\(402\) 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 \(-0.680664\pi\)
−0.537587 + 0.843208i \(0.680664\pi\)
\(420\) 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 \(0.00441955\pi\)
−0.487928 + 0.872884i \(0.662247\pi\)
\(432\) 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 −0.718838 0.695177i \(-0.755326\pi\)
0.961460 + 0.274944i \(0.0886592\pi\)
\(444\) 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 \(-0.465195\pi\)
0.109127 + 0.994028i \(0.465195\pi\)
\(450\) 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 \(-0.485895\pi\)
0.0442987 + 0.999018i \(0.485895\pi\)
\(462\) 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 \(-0.444671\pi\)
0.766502 0.642242i \(-0.221996\pi\)
\(468\) 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 0.993673 0.112312i \(-0.0358256\pi\)
−0.594101 + 0.804390i \(0.702492\pi\)
\(480\) 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 \(-0.758887\pi\)
−0.726570 + 0.687092i \(0.758887\pi\)
\(492\) 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 \(-0.418403\pi\)
0.253545 + 0.967323i \(0.418403\pi\)
\(504\) 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 \(-0.601393\pi\)
0.979048 0.203630i \(-0.0652740\pi\)
\(510\) 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 0.759450 0.650566i \(-0.225468\pi\)
−0.943131 + 0.332420i \(0.892135\pi\)
\(522\) 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 0.662101 0.749415i \(-0.269665\pi\)
−0.980063 + 0.198689i \(0.936332\pi\)
\(558\) 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 \(-0.996138\pi\)
0.489455 0.872028i \(-0.337196\pi\)
\(564\) 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 \(-0.640014\pi\)
0.996497 0.0836335i \(-0.0266525\pi\)
\(570\) 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 \(-0.450469\pi\)
0.154980 + 0.987918i \(0.450469\pi\)
\(588\) 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 −0.910640 0.413201i \(-0.864411\pi\)
0.813162 + 0.582037i \(0.197744\pi\)
\(594\) 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 \(0.0681287\pi\)
−0.304646 + 0.952466i \(0.598538\pi\)
\(600\) 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 \(-0.285767\pi\)
0.623361 + 0.781935i \(0.285767\pi\)
\(618\) 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 \(-0.955957\pi\)
0.375776 0.926711i \(-0.377376\pi\)
\(642\) 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 0.649959 0.759969i \(-0.274786\pi\)
−0.983132 + 0.182897i \(0.941453\pi\)
\(648\) 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 −0.992084 0.125579i \(-0.959921\pi\)
0.604796 + 0.796380i \(0.293255\pi\)
\(654\) 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 \(-0.386815\pi\)
0.348137 + 0.937444i \(0.386815\pi\)
\(660\) 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 −0.985349 0.170551i \(-0.945445\pi\)
0.640376 + 0.768061i \(0.278778\pi\)
\(678\) 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 \(-0.972900\pi\)
0.424549 0.905405i \(-0.360433\pi\)
\(684\) 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 \(-0.689363\pi\)
−0.560426 + 0.828204i \(0.689363\pi\)
\(702\) 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 −0.766572 0.642158i \(-0.778039\pi\)
0.939411 + 0.342792i \(0.111373\pi\)
\(720\) 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 \(-0.866991\pi\)
−0.913959 + 0.405805i \(0.866991\pi\)
\(744\) 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 \(0.450358\pi\)
−0.933177 + 0.359417i \(0.882976\pi\)
\(762\) 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 0.899201 0.437536i \(-0.144149\pi\)
−0.828518 + 0.559963i \(0.810815\pi\)
\(774\) 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