Properties

Label 128.4.e.a.33.3
Level $128$
Weight $4$
Character 128.33
Analytic conductor $7.552$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 128.e (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.55224448073\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Defining polynomial: \(x^{10} - 2 x^{9} - x^{8} + 6 x^{7} + 14 x^{6} - 80 x^{5} + 56 x^{4} + 96 x^{3} - 64 x^{2} - 512 x + 1024\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{20} \)
Twist minimal: no (minimal twist has level 16)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 33.3
Root \(-1.62580 + 1.16481i\) of defining polynomial
Character \(\chi\) \(=\) 128.33
Dual form 128.4.e.a.97.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.756776 + 0.756776i) q^{3} +(-8.22587 + 8.22587i) q^{5} +2.67171i q^{7} -25.8546i q^{9} +O(q^{10})\) \(q+(0.756776 + 0.756776i) q^{3} +(-8.22587 + 8.22587i) q^{5} +2.67171i q^{7} -25.8546i q^{9} +(-45.2213 + 45.2213i) q^{11} +(-35.3968 - 35.3968i) q^{13} -12.4503 q^{15} -72.4991 q^{17} +(19.4427 + 19.4427i) q^{19} +(-2.02188 + 2.02188i) q^{21} +139.462i q^{23} -10.3299i q^{25} +(39.9991 - 39.9991i) q^{27} +(-66.0434 - 66.0434i) q^{29} -188.682 q^{31} -68.4447 q^{33} +(-21.9771 - 21.9771i) q^{35} +(84.0653 - 84.0653i) q^{37} -53.5748i q^{39} +104.629i q^{41} +(-31.4857 + 31.4857i) q^{43} +(212.676 + 212.676i) q^{45} +488.151 q^{47} +335.862 q^{49} +(-54.8656 - 54.8656i) q^{51} +(-149.560 + 149.560i) q^{53} -743.968i q^{55} +29.4275i q^{57} +(284.698 - 284.698i) q^{59} +(228.069 + 228.069i) q^{61} +69.0758 q^{63} +582.338 q^{65} +(139.151 + 139.151i) q^{67} +(-105.541 + 105.541i) q^{69} +453.655i q^{71} -259.747i q^{73} +(7.81740 - 7.81740i) q^{75} +(-120.818 - 120.818i) q^{77} -323.190 q^{79} -637.533 q^{81} +(-563.897 - 563.897i) q^{83} +(596.368 - 596.368i) q^{85} -99.9602i q^{87} +866.853i q^{89} +(94.5697 - 94.5697i) q^{91} +(-142.790 - 142.790i) q^{93} -319.866 q^{95} -936.077 q^{97} +(1169.18 + 1169.18i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 2q^{3} + 2q^{5} + O(q^{10}) \) \( 10q - 2q^{3} + 2q^{5} + 18q^{11} + 2q^{13} + 124q^{15} - 4q^{17} - 26q^{19} - 52q^{21} + 184q^{27} + 202q^{29} - 368q^{31} - 4q^{33} + 476q^{35} + 10q^{37} - 838q^{43} - 194q^{45} + 944q^{47} + 94q^{49} - 1500q^{51} + 378q^{53} + 1706q^{59} - 910q^{61} - 2628q^{63} - 492q^{65} + 1942q^{67} - 580q^{69} - 2954q^{75} + 268q^{77} + 4416q^{79} + 482q^{81} - 2562q^{83} + 12q^{85} + 3332q^{91} + 2192q^{93} - 6900q^{95} - 4q^{97} + 4958q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(127\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.756776 + 0.756776i 0.145642 + 0.145642i 0.776168 0.630526i \(-0.217161\pi\)
−0.630526 + 0.776168i \(0.717161\pi\)
\(4\) 0 0
\(5\) −8.22587 + 8.22587i −0.735744 + 0.735744i −0.971751 0.236007i \(-0.924161\pi\)
0.236007 + 0.971751i \(0.424161\pi\)
\(6\) 0 0
\(7\) 2.67171i 0.144259i 0.997395 + 0.0721293i \(0.0229794\pi\)
−0.997395 + 0.0721293i \(0.977021\pi\)
\(8\) 0 0
\(9\) 25.8546i 0.957577i
\(10\) 0 0
\(11\) −45.2213 + 45.2213i −1.23952 + 1.23952i −0.279323 + 0.960197i \(0.590110\pi\)
−0.960197 + 0.279323i \(0.909890\pi\)
\(12\) 0 0
\(13\) −35.3968 35.3968i −0.755176 0.755176i 0.220264 0.975440i \(-0.429308\pi\)
−0.975440 + 0.220264i \(0.929308\pi\)
\(14\) 0 0
\(15\) −12.4503 −0.214310
\(16\) 0 0
\(17\) −72.4991 −1.03433 −0.517165 0.855886i \(-0.673013\pi\)
−0.517165 + 0.855886i \(0.673013\pi\)
\(18\) 0 0
\(19\) 19.4427 + 19.4427i 0.234761 + 0.234761i 0.814676 0.579916i \(-0.196915\pi\)
−0.579916 + 0.814676i \(0.696915\pi\)
\(20\) 0 0
\(21\) −2.02188 + 2.02188i −0.0210100 + 0.0210100i
\(22\) 0 0
\(23\) 139.462i 1.26434i 0.774830 + 0.632170i \(0.217835\pi\)
−0.774830 + 0.632170i \(0.782165\pi\)
\(24\) 0 0
\(25\) 10.3299i 0.0826390i
\(26\) 0 0
\(27\) 39.9991 39.9991i 0.285105 0.285105i
\(28\) 0 0
\(29\) −66.0434 66.0434i −0.422895 0.422895i 0.463304 0.886199i \(-0.346664\pi\)
−0.886199 + 0.463304i \(0.846664\pi\)
\(30\) 0 0
\(31\) −188.682 −1.09317 −0.546584 0.837404i \(-0.684072\pi\)
−0.546584 + 0.837404i \(0.684072\pi\)
\(32\) 0 0
\(33\) −68.4447 −0.361051
\(34\) 0 0
\(35\) −21.9771 21.9771i −0.106137 0.106137i
\(36\) 0 0
\(37\) 84.0653 84.0653i 0.373520 0.373520i −0.495237 0.868758i \(-0.664919\pi\)
0.868758 + 0.495237i \(0.164919\pi\)
\(38\) 0 0
\(39\) 53.5748i 0.219970i
\(40\) 0 0
\(41\) 104.629i 0.398545i 0.979944 + 0.199272i \(0.0638578\pi\)
−0.979944 + 0.199272i \(0.936142\pi\)
\(42\) 0 0
\(43\) −31.4857 + 31.4857i −0.111663 + 0.111663i −0.760731 0.649067i \(-0.775159\pi\)
0.649067 + 0.760731i \(0.275159\pi\)
\(44\) 0 0
\(45\) 212.676 + 212.676i 0.704532 + 0.704532i
\(46\) 0 0
\(47\) 488.151 1.51498 0.757491 0.652846i \(-0.226425\pi\)
0.757491 + 0.652846i \(0.226425\pi\)
\(48\) 0 0
\(49\) 335.862 0.979189
\(50\) 0 0
\(51\) −54.8656 54.8656i −0.150641 0.150641i
\(52\) 0 0
\(53\) −149.560 + 149.560i −0.387617 + 0.387617i −0.873837 0.486220i \(-0.838376\pi\)
0.486220 + 0.873837i \(0.338376\pi\)
\(54\) 0 0
\(55\) 743.968i 1.82394i
\(56\) 0 0
\(57\) 29.4275i 0.0683819i
\(58\) 0 0
\(59\) 284.698 284.698i 0.628212 0.628212i −0.319406 0.947618i \(-0.603483\pi\)
0.947618 + 0.319406i \(0.103483\pi\)
\(60\) 0 0
\(61\) 228.069 + 228.069i 0.478709 + 0.478709i 0.904719 0.426010i \(-0.140081\pi\)
−0.426010 + 0.904719i \(0.640081\pi\)
\(62\) 0 0
\(63\) 69.0758 0.138139
\(64\) 0 0
\(65\) 582.338 1.11123
\(66\) 0 0
\(67\) 139.151 + 139.151i 0.253730 + 0.253730i 0.822498 0.568768i \(-0.192580\pi\)
−0.568768 + 0.822498i \(0.692580\pi\)
\(68\) 0 0
\(69\) −105.541 + 105.541i −0.184140 + 0.184140i
\(70\) 0 0
\(71\) 453.655i 0.758294i 0.925336 + 0.379147i \(0.123783\pi\)
−0.925336 + 0.379147i \(0.876217\pi\)
\(72\) 0 0
\(73\) 259.747i 0.416454i −0.978081 0.208227i \(-0.933231\pi\)
0.978081 0.208227i \(-0.0667692\pi\)
\(74\) 0 0
\(75\) 7.81740 7.81740i 0.0120357 0.0120357i
\(76\) 0 0
\(77\) −120.818 120.818i −0.178811 0.178811i
\(78\) 0 0
\(79\) −323.190 −0.460275 −0.230138 0.973158i \(-0.573918\pi\)
−0.230138 + 0.973158i \(0.573918\pi\)
\(80\) 0 0
\(81\) −637.533 −0.874531
\(82\) 0 0
\(83\) −563.897 563.897i −0.745732 0.745732i 0.227943 0.973674i \(-0.426800\pi\)
−0.973674 + 0.227943i \(0.926800\pi\)
\(84\) 0 0
\(85\) 596.368 596.368i 0.761002 0.761002i
\(86\) 0 0
\(87\) 99.9602i 0.123182i
\(88\) 0 0
\(89\) 866.853i 1.03243i 0.856459 + 0.516215i \(0.172659\pi\)
−0.856459 + 0.516215i \(0.827341\pi\)
\(90\) 0 0
\(91\) 94.5697 94.5697i 0.108941 0.108941i
\(92\) 0 0
\(93\) −142.790 142.790i −0.159211 0.159211i
\(94\) 0 0
\(95\) −319.866 −0.345448
\(96\) 0 0
\(97\) −936.077 −0.979837 −0.489919 0.871768i \(-0.662974\pi\)
−0.489919 + 0.871768i \(0.662974\pi\)
\(98\) 0 0
\(99\) 1169.18 + 1169.18i 1.18694 + 1.18694i
\(100\) 0 0
\(101\) 1.58844 1.58844i 0.00156491 0.00156491i −0.706324 0.707889i \(-0.749648\pi\)
0.707889 + 0.706324i \(0.249648\pi\)
\(102\) 0 0
\(103\) 1388.28i 1.32807i 0.747700 + 0.664036i \(0.231158\pi\)
−0.747700 + 0.664036i \(0.768842\pi\)
\(104\) 0 0
\(105\) 33.2635i 0.0309160i
\(106\) 0 0
\(107\) −821.526 + 821.526i −0.742243 + 0.742243i −0.973009 0.230767i \(-0.925877\pi\)
0.230767 + 0.973009i \(0.425877\pi\)
\(108\) 0 0
\(109\) −532.797 532.797i −0.468190 0.468190i 0.433138 0.901328i \(-0.357406\pi\)
−0.901328 + 0.433138i \(0.857406\pi\)
\(110\) 0 0
\(111\) 127.237 0.108800
\(112\) 0 0
\(113\) −67.2680 −0.0560003 −0.0280002 0.999608i \(-0.508914\pi\)
−0.0280002 + 0.999608i \(0.508914\pi\)
\(114\) 0 0
\(115\) −1147.19 1147.19i −0.930230 0.930230i
\(116\) 0 0
\(117\) −915.168 + 915.168i −0.723140 + 0.723140i
\(118\) 0 0
\(119\) 193.696i 0.149211i
\(120\) 0 0
\(121\) 2758.92i 2.07282i
\(122\) 0 0
\(123\) −79.1808 + 79.1808i −0.0580447 + 0.0580447i
\(124\) 0 0
\(125\) −943.262 943.262i −0.674943 0.674943i
\(126\) 0 0
\(127\) −1903.59 −1.33005 −0.665026 0.746820i \(-0.731579\pi\)
−0.665026 + 0.746820i \(0.731579\pi\)
\(128\) 0 0
\(129\) −47.6552 −0.0325257
\(130\) 0 0
\(131\) 918.430 + 918.430i 0.612546 + 0.612546i 0.943609 0.331062i \(-0.107407\pi\)
−0.331062 + 0.943609i \(0.607407\pi\)
\(132\) 0 0
\(133\) −51.9451 + 51.9451i −0.0338662 + 0.0338662i
\(134\) 0 0
\(135\) 658.054i 0.419528i
\(136\) 0 0
\(137\) 477.234i 0.297612i 0.988866 + 0.148806i \(0.0475430\pi\)
−0.988866 + 0.148806i \(0.952457\pi\)
\(138\) 0 0
\(139\) −1513.89 + 1513.89i −0.923788 + 0.923788i −0.997295 0.0735064i \(-0.976581\pi\)
0.0735064 + 0.997295i \(0.476581\pi\)
\(140\) 0 0
\(141\) 369.421 + 369.421i 0.220644 + 0.220644i
\(142\) 0 0
\(143\) 3201.37 1.87211
\(144\) 0 0
\(145\) 1086.53 0.622285
\(146\) 0 0
\(147\) 254.172 + 254.172i 0.142611 + 0.142611i
\(148\) 0 0
\(149\) −375.353 + 375.353i −0.206377 + 0.206377i −0.802725 0.596349i \(-0.796618\pi\)
0.596349 + 0.802725i \(0.296618\pi\)
\(150\) 0 0
\(151\) 2997.52i 1.61546i −0.589553 0.807730i \(-0.700696\pi\)
0.589553 0.807730i \(-0.299304\pi\)
\(152\) 0 0
\(153\) 1874.43i 0.990451i
\(154\) 0 0
\(155\) 1552.07 1552.07i 0.804293 0.804293i
\(156\) 0 0
\(157\) 1509.01 + 1509.01i 0.767082 + 0.767082i 0.977592 0.210510i \(-0.0675125\pi\)
−0.210510 + 0.977592i \(0.567512\pi\)
\(158\) 0 0
\(159\) −226.368 −0.112906
\(160\) 0 0
\(161\) −372.601 −0.182392
\(162\) 0 0
\(163\) −1425.19 1425.19i −0.684844 0.684844i 0.276244 0.961088i \(-0.410910\pi\)
−0.961088 + 0.276244i \(0.910910\pi\)
\(164\) 0 0
\(165\) 563.017 563.017i 0.265641 0.265641i
\(166\) 0 0
\(167\) 792.415i 0.367179i 0.983003 + 0.183590i \(0.0587717\pi\)
−0.983003 + 0.183590i \(0.941228\pi\)
\(168\) 0 0
\(169\) 308.861i 0.140583i
\(170\) 0 0
\(171\) 502.682 502.682i 0.224802 0.224802i
\(172\) 0 0
\(173\) 773.594 + 773.594i 0.339972 + 0.339972i 0.856357 0.516384i \(-0.172722\pi\)
−0.516384 + 0.856357i \(0.672722\pi\)
\(174\) 0 0
\(175\) 27.5984 0.0119214
\(176\) 0 0
\(177\) 430.905 0.182988
\(178\) 0 0
\(179\) 426.050 + 426.050i 0.177902 + 0.177902i 0.790441 0.612539i \(-0.209852\pi\)
−0.612539 + 0.790441i \(0.709852\pi\)
\(180\) 0 0
\(181\) 2618.06 2618.06i 1.07513 1.07513i 0.0781951 0.996938i \(-0.475084\pi\)
0.996938 0.0781951i \(-0.0249157\pi\)
\(182\) 0 0
\(183\) 345.194i 0.139440i
\(184\) 0 0
\(185\) 1383.02i 0.549631i
\(186\) 0 0
\(187\) 3278.50 3278.50i 1.28207 1.28207i
\(188\) 0 0
\(189\) 106.866 + 106.866i 0.0411288 + 0.0411288i
\(190\) 0 0
\(191\) −3216.39 −1.21848 −0.609240 0.792986i \(-0.708525\pi\)
−0.609240 + 0.792986i \(0.708525\pi\)
\(192\) 0 0
\(193\) 2852.57 1.06390 0.531950 0.846776i \(-0.321459\pi\)
0.531950 + 0.846776i \(0.321459\pi\)
\(194\) 0 0
\(195\) 440.700 + 440.700i 0.161842 + 0.161842i
\(196\) 0 0
\(197\) −1609.02 + 1609.02i −0.581918 + 0.581918i −0.935430 0.353512i \(-0.884987\pi\)
0.353512 + 0.935430i \(0.384987\pi\)
\(198\) 0 0
\(199\) 747.136i 0.266146i −0.991106 0.133073i \(-0.957516\pi\)
0.991106 0.133073i \(-0.0424845\pi\)
\(200\) 0 0
\(201\) 210.612i 0.0739074i
\(202\) 0 0
\(203\) 176.449 176.449i 0.0610062 0.0610062i
\(204\) 0 0
\(205\) −860.666 860.666i −0.293227 0.293227i
\(206\) 0 0
\(207\) 3605.73 1.21070
\(208\) 0 0
\(209\) −1758.44 −0.581981
\(210\) 0 0
\(211\) −2227.13 2227.13i −0.726645 0.726645i 0.243305 0.969950i \(-0.421769\pi\)
−0.969950 + 0.243305i \(0.921769\pi\)
\(212\) 0 0
\(213\) −343.315 + 343.315i −0.110439 + 0.110439i
\(214\) 0 0
\(215\) 517.995i 0.164311i
\(216\) 0 0
\(217\) 504.102i 0.157699i
\(218\) 0 0
\(219\) 196.570 196.570i 0.0606530 0.0606530i
\(220\) 0 0
\(221\) 2566.23 + 2566.23i 0.781102 + 0.781102i
\(222\) 0 0
\(223\) 358.053 0.107520 0.0537601 0.998554i \(-0.482879\pi\)
0.0537601 + 0.998554i \(0.482879\pi\)
\(224\) 0 0
\(225\) −267.075 −0.0791332
\(226\) 0 0
\(227\) 3455.40 + 3455.40i 1.01032 + 1.01032i 0.999946 + 0.0103741i \(0.00330223\pi\)
0.0103741 + 0.999946i \(0.496698\pi\)
\(228\) 0 0
\(229\) 1430.03 1430.03i 0.412659 0.412659i −0.470005 0.882664i \(-0.655748\pi\)
0.882664 + 0.470005i \(0.155748\pi\)
\(230\) 0 0
\(231\) 182.864i 0.0520847i
\(232\) 0 0
\(233\) 926.479i 0.260496i −0.991481 0.130248i \(-0.958423\pi\)
0.991481 0.130248i \(-0.0415774\pi\)
\(234\) 0 0
\(235\) −4015.47 + 4015.47i −1.11464 + 1.11464i
\(236\) 0 0
\(237\) −244.583 244.583i −0.0670352 0.0670352i
\(238\) 0 0
\(239\) 792.472 0.214480 0.107240 0.994233i \(-0.465799\pi\)
0.107240 + 0.994233i \(0.465799\pi\)
\(240\) 0 0
\(241\) 1449.01 0.387299 0.193650 0.981071i \(-0.437967\pi\)
0.193650 + 0.981071i \(0.437967\pi\)
\(242\) 0 0
\(243\) −1562.44 1562.44i −0.412473 0.412473i
\(244\) 0 0
\(245\) −2762.76 + 2762.76i −0.720433 + 0.720433i
\(246\) 0 0
\(247\) 1376.42i 0.354572i
\(248\) 0 0
\(249\) 853.487i 0.217219i
\(250\) 0 0
\(251\) −3580.04 + 3580.04i −0.900280 + 0.900280i −0.995460 0.0951802i \(-0.969657\pi\)
0.0951802 + 0.995460i \(0.469657\pi\)
\(252\) 0 0
\(253\) −6306.64 6306.64i −1.56717 1.56717i
\(254\) 0 0
\(255\) 902.634 0.221667
\(256\) 0 0
\(257\) −4708.87 −1.14292 −0.571461 0.820629i \(-0.693623\pi\)
−0.571461 + 0.820629i \(0.693623\pi\)
\(258\) 0 0
\(259\) 224.598 + 224.598i 0.0538835 + 0.0538835i
\(260\) 0 0
\(261\) −1707.53 + 1707.53i −0.404955 + 0.404955i
\(262\) 0 0
\(263\) 2967.82i 0.695830i 0.937526 + 0.347915i \(0.113110\pi\)
−0.937526 + 0.347915i \(0.886890\pi\)
\(264\) 0 0
\(265\) 2460.53i 0.570374i
\(266\) 0 0
\(267\) −656.013 + 656.013i −0.150365 + 0.150365i
\(268\) 0 0
\(269\) 663.633 + 663.633i 0.150418 + 0.150418i 0.778305 0.627887i \(-0.216080\pi\)
−0.627887 + 0.778305i \(0.716080\pi\)
\(270\) 0 0
\(271\) −8058.74 −1.80640 −0.903199 0.429223i \(-0.858788\pi\)
−0.903199 + 0.429223i \(0.858788\pi\)
\(272\) 0 0
\(273\) 143.136 0.0317326
\(274\) 0 0
\(275\) 467.130 + 467.130i 0.102433 + 0.102433i
\(276\) 0 0
\(277\) −482.477 + 482.477i −0.104654 + 0.104654i −0.757495 0.652841i \(-0.773577\pi\)
0.652841 + 0.757495i \(0.273577\pi\)
\(278\) 0 0
\(279\) 4878.29i 1.04679i
\(280\) 0 0
\(281\) 5899.10i 1.25235i −0.779682 0.626175i \(-0.784619\pi\)
0.779682 0.626175i \(-0.215381\pi\)
\(282\) 0 0
\(283\) −679.897 + 679.897i −0.142812 + 0.142812i −0.774898 0.632086i \(-0.782199\pi\)
0.632086 + 0.774898i \(0.282199\pi\)
\(284\) 0 0
\(285\) −242.067 242.067i −0.0503116 0.0503116i
\(286\) 0 0
\(287\) −279.538 −0.0574935
\(288\) 0 0
\(289\) 343.118 0.0698388
\(290\) 0 0
\(291\) −708.401 708.401i −0.142705 0.142705i
\(292\) 0 0
\(293\) 3552.87 3552.87i 0.708398 0.708398i −0.257800 0.966198i \(-0.582998\pi\)
0.966198 + 0.257800i \(0.0829976\pi\)
\(294\) 0 0
\(295\) 4683.78i 0.924407i
\(296\) 0 0
\(297\) 3617.62i 0.706786i
\(298\) 0 0
\(299\) 4936.50 4936.50i 0.954799 0.954799i
\(300\) 0 0
\(301\) −84.1205 84.1205i −0.0161084 0.0161084i
\(302\) 0 0
\(303\) 2.40419 0.000455831
\(304\) 0 0
\(305\) −3752.13 −0.704415
\(306\) 0 0
\(307\) 2735.56 + 2735.56i 0.508556 + 0.508556i 0.914083 0.405527i \(-0.132912\pi\)
−0.405527 + 0.914083i \(0.632912\pi\)
\(308\) 0 0
\(309\) −1050.62 + 1050.62i −0.193423 + 0.193423i
\(310\) 0 0
\(311\) 5796.70i 1.05692i −0.848960 0.528458i \(-0.822771\pi\)
0.848960 0.528458i \(-0.177229\pi\)
\(312\) 0 0
\(313\) 8362.62i 1.51017i 0.655627 + 0.755085i \(0.272404\pi\)
−0.655627 + 0.755085i \(0.727596\pi\)
\(314\) 0 0
\(315\) −568.209 + 568.209i −0.101635 + 0.101635i
\(316\) 0 0
\(317\) 344.406 + 344.406i 0.0610214 + 0.0610214i 0.736959 0.675938i \(-0.236261\pi\)
−0.675938 + 0.736959i \(0.736261\pi\)
\(318\) 0 0
\(319\) 5973.13 1.04837
\(320\) 0 0
\(321\) −1243.42 −0.216203
\(322\) 0 0
\(323\) −1409.58 1409.58i −0.242820 0.242820i
\(324\) 0 0
\(325\) −365.644 + 365.644i −0.0624071 + 0.0624071i
\(326\) 0 0
\(327\) 806.416i 0.136376i
\(328\) 0 0
\(329\) 1304.20i 0.218549i
\(330\) 0 0
\(331\) 2687.86 2687.86i 0.446339 0.446339i −0.447797 0.894135i \(-0.647791\pi\)
0.894135 + 0.447797i \(0.147791\pi\)
\(332\) 0 0
\(333\) −2173.47 2173.47i −0.357675 0.357675i
\(334\) 0 0
\(335\) −2289.27 −0.373361
\(336\) 0 0
\(337\) −1795.31 −0.290199 −0.145099 0.989417i \(-0.546350\pi\)
−0.145099 + 0.989417i \(0.546350\pi\)
\(338\) 0 0
\(339\) −50.9068 50.9068i −0.00815598 0.00815598i
\(340\) 0 0
\(341\) 8532.42 8532.42i 1.35500 1.35500i
\(342\) 0 0
\(343\) 1813.72i 0.285515i
\(344\) 0 0
\(345\) 1736.34i 0.270960i
\(346\) 0 0
\(347\) −1967.33 + 1967.33i −0.304357 + 0.304357i −0.842716 0.538359i \(-0.819045\pi\)
0.538359 + 0.842716i \(0.319045\pi\)
\(348\) 0 0
\(349\) 7363.37 + 7363.37i 1.12938 + 1.12938i 0.990279 + 0.139097i \(0.0444200\pi\)
0.139097 + 0.990279i \(0.455580\pi\)
\(350\) 0 0
\(351\) −2831.68 −0.430609
\(352\) 0 0
\(353\) 10644.3 1.60493 0.802466 0.596698i \(-0.203521\pi\)
0.802466 + 0.596698i \(0.203521\pi\)
\(354\) 0 0
\(355\) −3731.70 3731.70i −0.557911 0.557911i
\(356\) 0 0
\(357\) 146.585 146.585i 0.0217313 0.0217313i
\(358\) 0 0
\(359\) 7459.42i 1.09664i −0.836269 0.548319i \(-0.815268\pi\)
0.836269 0.548319i \(-0.184732\pi\)
\(360\) 0 0
\(361\) 6102.96i 0.889775i
\(362\) 0 0
\(363\) 2087.89 2087.89i 0.301889 0.301889i
\(364\) 0 0
\(365\) 2136.65 + 2136.65i 0.306403 + 0.306403i
\(366\) 0 0
\(367\) 6251.35 0.889149 0.444574 0.895742i \(-0.353355\pi\)
0.444574 + 0.895742i \(0.353355\pi\)
\(368\) 0 0
\(369\) 2705.14 0.381637
\(370\) 0 0
\(371\) −399.582 399.582i −0.0559171 0.0559171i
\(372\) 0 0
\(373\) −8911.86 + 8911.86i −1.23710 + 1.23710i −0.275921 + 0.961180i \(0.588983\pi\)
−0.961180 + 0.275921i \(0.911017\pi\)
\(374\) 0 0
\(375\) 1427.68i 0.196600i
\(376\) 0 0
\(377\) 4675.45i 0.638721i
\(378\) 0 0
\(379\) 1184.03 1184.03i 0.160473 0.160473i −0.622303 0.782776i \(-0.713803\pi\)
0.782776 + 0.622303i \(0.213803\pi\)
\(380\) 0 0
\(381\) −1440.59 1440.59i −0.193711 0.193711i
\(382\) 0 0
\(383\) 2880.38 0.384283 0.192142 0.981367i \(-0.438457\pi\)
0.192142 + 0.981367i \(0.438457\pi\)
\(384\) 0 0
\(385\) 1987.66 0.263119
\(386\) 0 0
\(387\) 814.050 + 814.050i 0.106926 + 0.106926i
\(388\) 0 0
\(389\) −9244.24 + 9244.24i −1.20489 + 1.20489i −0.232226 + 0.972662i \(0.574601\pi\)
−0.972662 + 0.232226i \(0.925399\pi\)
\(390\) 0 0
\(391\) 10110.9i 1.30774i
\(392\) 0 0
\(393\) 1390.09i 0.178424i
\(394\) 0 0
\(395\) 2658.52 2658.52i 0.338645 0.338645i
\(396\) 0 0
\(397\) 4257.80 + 4257.80i 0.538270 + 0.538270i 0.923020 0.384751i \(-0.125713\pi\)
−0.384751 + 0.923020i \(0.625713\pi\)
\(398\) 0 0
\(399\) −78.6216 −0.00986467
\(400\) 0 0
\(401\) 12722.6 1.58437 0.792187 0.610278i \(-0.208942\pi\)
0.792187 + 0.610278i \(0.208942\pi\)
\(402\) 0 0
\(403\) 6678.72 + 6678.72i 0.825535 + 0.825535i
\(404\) 0 0
\(405\) 5244.26 5244.26i 0.643431 0.643431i
\(406\) 0 0
\(407\) 7603.08i 0.925972i
\(408\) 0 0
\(409\) 232.991i 0.0281678i 0.999901 + 0.0140839i \(0.00448320\pi\)
−0.999901 + 0.0140839i \(0.995517\pi\)
\(410\) 0 0
\(411\) −361.159 + 361.159i −0.0433447 + 0.0433447i
\(412\) 0 0
\(413\) 760.629 + 760.629i 0.0906250 + 0.0906250i
\(414\) 0 0
\(415\) 9277.08 1.09734
\(416\) 0 0
\(417\) −2291.35 −0.269084
\(418\) 0 0
\(419\) −6125.69 6125.69i −0.714223 0.714223i 0.253193 0.967416i \(-0.418519\pi\)
−0.967416 + 0.253193i \(0.918519\pi\)
\(420\) 0 0
\(421\) 8308.44 8308.44i 0.961825 0.961825i −0.0374725 0.999298i \(-0.511931\pi\)
0.999298 + 0.0374725i \(0.0119307\pi\)
\(422\) 0 0
\(423\) 12620.9i 1.45071i
\(424\) 0 0
\(425\) 748.907i 0.0854760i
\(426\) 0 0
\(427\) −609.333 + 609.333i −0.0690579 + 0.0690579i
\(428\) 0 0
\(429\) 2422.72 + 2422.72i 0.272657 + 0.272657i
\(430\) 0 0
\(431\) −8737.57 −0.976506 −0.488253 0.872702i \(-0.662366\pi\)
−0.488253 + 0.872702i \(0.662366\pi\)
\(432\) 0 0
\(433\) −11627.5 −1.29049 −0.645247 0.763974i \(-0.723245\pi\)
−0.645247 + 0.763974i \(0.723245\pi\)
\(434\) 0 0
\(435\) 822.260 + 822.260i 0.0906306 + 0.0906306i
\(436\) 0 0
\(437\) −2711.51 + 2711.51i −0.296817 + 0.296817i
\(438\) 0 0
\(439\) 17631.8i 1.91690i 0.285261 + 0.958450i \(0.407920\pi\)
−0.285261 + 0.958450i \(0.592080\pi\)
\(440\) 0 0
\(441\) 8683.57i 0.937649i
\(442\) 0 0
\(443\) −4549.81 + 4549.81i −0.487964 + 0.487964i −0.907663 0.419699i \(-0.862136\pi\)
0.419699 + 0.907663i \(0.362136\pi\)
\(444\) 0 0
\(445\) −7130.62 7130.62i −0.759604 0.759604i
\(446\) 0 0
\(447\) −568.116 −0.0601140
\(448\) 0 0
\(449\) −12926.5 −1.35867 −0.679334 0.733830i \(-0.737731\pi\)
−0.679334 + 0.733830i \(0.737731\pi\)
\(450\) 0 0
\(451\) −4731.46 4731.46i −0.494004 0.494004i
\(452\) 0 0
\(453\) 2268.45 2268.45i 0.235278 0.235278i
\(454\) 0 0
\(455\) 1555.84i 0.160305i
\(456\) 0 0
\(457\) 9320.32i 0.954018i 0.878898 + 0.477009i \(0.158279\pi\)
−0.878898 + 0.477009i \(0.841721\pi\)
\(458\) 0 0
\(459\) −2899.90 + 2899.90i −0.294892 + 0.294892i
\(460\) 0 0
\(461\) −12885.0 12885.0i −1.30177 1.30177i −0.927200 0.374566i \(-0.877792\pi\)
−0.374566 0.927200i \(-0.622208\pi\)
\(462\) 0 0
\(463\) −7038.37 −0.706482 −0.353241 0.935532i \(-0.614920\pi\)
−0.353241 + 0.935532i \(0.614920\pi\)
\(464\) 0 0
\(465\) 2349.14 0.234277
\(466\) 0 0
\(467\) 6001.76 + 6001.76i 0.594707 + 0.594707i 0.938899 0.344192i \(-0.111847\pi\)
−0.344192 + 0.938899i \(0.611847\pi\)
\(468\) 0 0
\(469\) −371.769 + 371.769i −0.0366028 + 0.0366028i
\(470\) 0 0
\(471\) 2283.96i 0.223438i
\(472\) 0 0
\(473\) 2847.65i 0.276818i
\(474\) 0 0
\(475\) 200.840 200.840i 0.0194004 0.0194004i
\(476\) 0 0
\(477\) 3866.82 + 3866.82i 0.371173 + 0.371173i
\(478\) 0 0
\(479\) 587.317 0.0560234 0.0280117 0.999608i \(-0.491082\pi\)
0.0280117 + 0.999608i \(0.491082\pi\)
\(480\) 0 0
\(481\) −5951.28 −0.564148
\(482\) 0 0
\(483\) −281.975 281.975i −0.0265638 0.0265638i
\(484\) 0 0
\(485\) 7700.05 7700.05i 0.720910 0.720910i
\(486\) 0 0
\(487\) 8366.45i 0.778481i 0.921136 + 0.389240i \(0.127262\pi\)
−0.921136 + 0.389240i \(0.872738\pi\)
\(488\) 0 0
\(489\) 2157.10i 0.199483i
\(490\) 0 0
\(491\) 1529.30 1529.30i 0.140563 0.140563i −0.633324 0.773887i \(-0.718310\pi\)
0.773887 + 0.633324i \(0.218310\pi\)
\(492\) 0 0
\(493\) 4788.09 + 4788.09i 0.437413 + 0.437413i
\(494\) 0 0
\(495\) −19235.0 −1.74656
\(496\) 0 0
\(497\) −1212.03 −0.109390
\(498\) 0 0
\(499\) 11364.5 + 11364.5i 1.01952 + 1.01952i 0.999806 + 0.0197191i \(0.00627718\pi\)
0.0197191 + 0.999806i \(0.493723\pi\)
\(500\) 0 0
\(501\) −599.681 + 599.681i −0.0534766 + 0.0534766i
\(502\) 0 0
\(503\) 12570.2i 1.11427i 0.830421 + 0.557137i \(0.188100\pi\)
−0.830421 + 0.557137i \(0.811900\pi\)
\(504\) 0 0
\(505\) 26.1326i 0.00230274i
\(506\) 0 0
\(507\) −233.738 + 233.738i −0.0204747 + 0.0204747i
\(508\) 0 0
\(509\) −11880.4 11880.4i −1.03456 1.03456i −0.999381 0.0351750i \(-0.988801\pi\)
−0.0351750 0.999381i \(-0.511199\pi\)
\(510\) 0 0
\(511\) 693.968 0.0600770
\(512\) 0 0
\(513\) 1555.38 0.133863
\(514\) 0 0
\(515\) −11419.8 11419.8i −0.977122 0.977122i
\(516\) 0 0
\(517\) −22074.8 + 22074.8i −1.87785 + 1.87785i
\(518\) 0 0
\(519\) 1170.87i 0.0990283i
\(520\) 0 0
\(521\) 6612.98i 0.556085i −0.960569 0.278042i \(-0.910314\pi\)
0.960569 0.278042i \(-0.0896856\pi\)
\(522\) 0 0
\(523\) 5129.30 5129.30i 0.428850 0.428850i −0.459387 0.888236i \(-0.651931\pi\)
0.888236 + 0.459387i \(0.151931\pi\)
\(524\) 0 0
\(525\) 20.8858 + 20.8858i 0.00173625 + 0.00173625i
\(526\) 0 0
\(527\) 13679.3 1.13070
\(528\) 0 0
\(529\) −7282.60 −0.598553
\(530\) 0 0
\(531\) −7360.75 7360.75i −0.601562 0.601562i
\(532\) 0 0
\(533\) 3703.53 3703.53i 0.300972 0.300972i
\(534\) 0 0
\(535\) 13515.5i 1.09220i
\(536\) 0 0
\(537\) 644.849i 0.0518199i
\(538\) 0 0
\(539\) −15188.1 + 15188.1i −1.21372 + 1.21372i
\(540\) 0 0
\(541\) 10968.5 + 10968.5i 0.871672 + 0.871672i 0.992655 0.120983i \(-0.0386047\pi\)
−0.120983 + 0.992655i \(0.538605\pi\)
\(542\) 0 0
\(543\) 3962.57 0.313168
\(544\) 0 0
\(545\) 8765.44 0.688936
\(546\) 0 0
\(547\) 13088.8 + 13088.8i 1.02311 + 1.02311i 0.999727 + 0.0233784i \(0.00744226\pi\)
0.0233784 + 0.999727i \(0.492558\pi\)
\(548\) 0 0
\(549\) 5896.63 5896.63i 0.458401 0.458401i
\(550\) 0 0
\(551\) 2568.12i 0.198558i
\(552\) 0 0
\(553\) 863.469i 0.0663986i
\(554\) 0 0
\(555\) −1046.64 + 1046.64i −0.0800491 + 0.0800491i
\(556\) 0 0
\(557\) −5049.87 5049.87i −0.384147 0.384147i 0.488447 0.872594i \(-0.337564\pi\)
−0.872594 + 0.488447i \(0.837564\pi\)
\(558\) 0 0
\(559\) 2228.98 0.168651
\(560\) 0 0
\(561\) 4962.18 0.373446
\(562\) 0 0
\(563\) −3249.06 3249.06i −0.243217 0.243217i 0.574962 0.818180i \(-0.305017\pi\)
−0.818180 + 0.574962i \(0.805017\pi\)
\(564\) 0 0
\(565\) 553.338 553.338i 0.0412019 0.0412019i
\(566\) 0 0
\(567\) 1703.30i 0.126159i
\(568\) 0 0
\(569\) 2806.05i 0.206741i 0.994643 + 0.103371i \(0.0329628\pi\)
−0.994643 + 0.103371i \(0.967037\pi\)
\(570\) 0 0
\(571\) −12038.8 + 12038.8i −0.882324 + 0.882324i −0.993770 0.111446i \(-0.964452\pi\)
0.111446 + 0.993770i \(0.464452\pi\)
\(572\) 0 0
\(573\) −2434.08 2434.08i −0.177461 0.177461i
\(574\) 0 0
\(575\) 1440.62 0.104484
\(576\) 0 0
\(577\) 7206.84 0.519973 0.259987 0.965612i \(-0.416282\pi\)
0.259987 + 0.965612i \(0.416282\pi\)
\(578\) 0 0
\(579\) 2158.76 + 2158.76i 0.154948 + 0.154948i
\(580\) 0 0
\(581\) 1506.57 1506.57i 0.107578 0.107578i
\(582\) 0 0
\(583\) 13526.6i 0.960918i
\(584\) 0 0
\(585\) 15056.1i 1.06409i
\(586\) 0 0
\(587\) 10377.0 10377.0i 0.729647 0.729647i −0.240903 0.970549i \(-0.577443\pi\)
0.970549 + 0.240903i \(0.0774435\pi\)
\(588\) 0 0
\(589\) −3668.48 3668.48i −0.256633 0.256633i
\(590\) 0 0
\(591\) −2435.33 −0.169503
\(592\) 0 0
\(593\) −4758.60 −0.329531 −0.164766 0.986333i \(-0.552687\pi\)
−0.164766 + 0.986333i \(0.552687\pi\)
\(594\) 0 0
\(595\) 1593.32 + 1593.32i 0.109781 + 0.109781i
\(596\) 0 0
\(597\) 565.414 565.414i 0.0387619 0.0387619i
\(598\) 0 0
\(599\) 14256.4i 0.972455i −0.873832 0.486227i \(-0.838373\pi\)
0.873832 0.486227i \(-0.161627\pi\)
\(600\) 0 0
\(601\) 10385.2i 0.704862i 0.935838 + 0.352431i \(0.114645\pi\)
−0.935838 + 0.352431i \(0.885355\pi\)
\(602\) 0 0
\(603\) 3597.68 3597.68i 0.242966 0.242966i
\(604\) 0 0
\(605\) 22694.5 + 22694.5i 1.52506 + 1.52506i
\(606\) 0 0
\(607\) 16243.6 1.08618 0.543088 0.839676i \(-0.317255\pi\)
0.543088 + 0.839676i \(0.317255\pi\)
\(608\) 0 0
\(609\) 267.064 0.0177701
\(610\) 0 0
\(611\) −17279.0 17279.0i −1.14408 1.14408i
\(612\) 0 0
\(613\) 500.502 500.502i 0.0329773 0.0329773i −0.690426 0.723403i \(-0.742577\pi\)
0.723403 + 0.690426i \(0.242577\pi\)
\(614\) 0 0
\(615\) 1302.66i 0.0854121i
\(616\) 0 0
\(617\) 11575.9i 0.755316i 0.925945 + 0.377658i \(0.123271\pi\)
−0.925945 + 0.377658i \(0.876729\pi\)
\(618\) 0 0
\(619\) 18356.1 18356.1i 1.19191 1.19191i 0.215380 0.976530i \(-0.430901\pi\)
0.976530 0.215380i \(-0.0690992\pi\)
\(620\) 0 0
\(621\) 5578.34 + 5578.34i 0.360469 + 0.360469i
\(622\) 0 0
\(623\) −2315.98 −0.148937
\(624\) 0 0
\(625\) 16809.5 1.07581
\(626\) 0 0
\(627\) −1330.75 1330.75i −0.0847607 0.0847607i
\(628\) 0 0
\(629\) −6094.66 + 6094.66i −0.386343 + 0.386343i
\(630\) 0 0
\(631\) 10224.8i 0.645079i 0.946556 + 0.322539i \(0.104537\pi\)
−0.946556 + 0.322539i \(0.895463\pi\)
\(632\) 0 0
\(633\) 3370.88i 0.211660i
\(634\) 0 0
\(635\) 15658.7 15658.7i 0.978578 0.978578i
\(636\) 0 0
\(637\) −11888.4 11888.4i −0.739461 0.739461i
\(638\) 0 0
\(639\) 11729.0 0.726125
\(640\) 0 0
\(641\) 19804.4 1.22032 0.610162 0.792277i \(-0.291104\pi\)
0.610162 + 0.792277i \(0.291104\pi\)
\(642\) 0 0
\(643\) 15680.7 + 15680.7i 0.961723 + 0.961723i 0.999294 0.0375712i \(-0.0119621\pi\)
−0.0375712 + 0.999294i \(0.511962\pi\)
\(644\) 0 0
\(645\) 392.006 392.006i 0.0239306 0.0239306i
\(646\) 0 0
\(647\) 9232.26i 0.560985i 0.959856 + 0.280493i \(0.0904978\pi\)
−0.959856 + 0.280493i \(0.909502\pi\)
\(648\) 0 0
\(649\) 25748.8i 1.55736i
\(650\) 0 0
\(651\) 381.492 381.492i 0.0229675 0.0229675i
\(652\) 0 0
\(653\) 19697.9 + 19697.9i 1.18046 + 1.18046i 0.979626 + 0.200833i \(0.0643648\pi\)
0.200833 + 0.979626i \(0.435635\pi\)
\(654\) 0 0
\(655\) −15109.8 −0.901355
\(656\) 0 0
\(657\) −6715.66 −0.398786
\(658\) 0 0
\(659\) 3888.06 + 3888.06i 0.229829 + 0.229829i 0.812621 0.582792i \(-0.198040\pi\)
−0.582792 + 0.812621i \(0.698040\pi\)
\(660\) 0 0
\(661\) 8110.20 8110.20i 0.477232 0.477232i −0.427013 0.904245i \(-0.640434\pi\)
0.904245 + 0.427013i \(0.140434\pi\)
\(662\) 0 0
\(663\) 3884.13i 0.227522i
\(664\) 0 0
\(665\) 854.587i 0.0498338i
\(666\) 0 0
\(667\) 9210.54 9210.54i 0.534683 0.534683i
\(668\) 0 0
\(669\) 270.966 + 270.966i 0.0156594 + 0.0156594i
\(670\) 0 0
\(671\) −20627.1 −1.18674
\(672\) 0 0
\(673\) −28428.2 −1.62827 −0.814135 0.580676i \(-0.802788\pi\)
−0.814135 + 0.580676i \(0.802788\pi\)
\(674\) 0 0
\(675\) −413.186 413.186i −0.0235608 0.0235608i
\(676\) 0 0
\(677\) 16967.4 16967.4i 0.963235 0.963235i −0.0361128 0.999348i \(-0.511498\pi\)
0.999348 + 0.0361128i \(0.0114975\pi\)
\(678\) 0 0
\(679\) 2500.92i 0.141350i
\(680\) 0 0
\(681\) 5229.92i 0.294289i
\(682\) 0 0
\(683\) −9550.16 + 9550.16i −0.535032 + 0.535032i −0.922066 0.387034i \(-0.873500\pi\)
0.387034 + 0.922066i \(0.373500\pi\)
\(684\) 0 0
\(685\) −3925.66 3925.66i −0.218966 0.218966i
\(686\) 0 0
\(687\) 2164.42 0.120201
\(688\) 0 0
\(689\) 10587.9 0.585439
\(690\) 0 0
\(691\) −20859.7 20859.7i −1.14839 1.14839i −0.986868 0.161527i \(-0.948358\pi\)
−0.161527 0.986868i \(-0.551642\pi\)
\(692\) 0 0
\(693\) −3123.70 + 3123.70i −0.171226 + 0.171226i
\(694\) 0 0
\(695\) 24906.1i 1.35934i
\(696\) 0 0
\(697\) 7585.52i 0.412227i
\(698\) 0 0
\(699\) 701.137 701.137i 0.0379391 0.0379391i
\(700\) 0 0
\(701\) −23495.4 23495.4i −1.26592 1.26592i −0.948178 0.317740i \(-0.897076\pi\)
−0.317740 0.948178i \(-0.602924\pi\)
\(702\) 0 0
\(703\) 3268.91 0.175376
\(704\) 0 0
\(705\) −6077.62 −0.324676
\(706\) 0 0
\(707\) 4.24384 + 4.24384i 0.000225751 + 0.000225751i
\(708\) 0 0
\(709\) −4559.45 + 4559.45i −0.241515 + 0.241515i −0.817477 0.575962i \(-0.804628\pi\)
0.575962 + 0.817477i \(0.304628\pi\)
\(710\) 0 0
\(711\) 8355.95i 0.440749i
\(712\) 0 0
\(713\) 26313.9i 1.38214i
\(714\) 0 0
\(715\) −26334.1 + 26334.1i −1.37740 + 1.37740i
\(716\) 0 0
\(717\) 599.724 + 599.724i 0.0312372 + 0.0312372i
\(718\) 0 0
\(719\) 6494.67 0.336871 0.168436 0.985713i \(-0.446128\pi\)
0.168436 + 0.985713i \(0.446128\pi\)
\(720\) 0 0
\(721\) −3709.08 −0.191586
\(722\) 0 0
\(723\) 1096.58 + 1096.58i 0.0564069 + 0.0564069i
\(724\) 0 0
\(725\) −682.221 + 682.221i −0.0349476 + 0.0349476i
\(726\) 0 0
\(727\) 24866.4i 1.26856i 0.773103 + 0.634280i \(0.218704\pi\)
−0.773103 + 0.634280i \(0.781296\pi\)
\(728\) 0 0
\(729\) 14848.5i 0.754384i
\(730\) 0 0
\(731\) 2282.68 2282.68i 0.115497 0.115497i
\(732\) 0 0
\(733\) 14914.3 + 14914.3i 0.751533 + 0.751533i 0.974765 0.223232i \(-0.0716607\pi\)
−0.223232 + 0.974765i \(0.571661\pi\)
\(734\) 0 0
\(735\) −4181.58 −0.209850
\(736\) 0 0
\(737\) −12585.1 −0.629008
\(738\) 0 0
\(739\) 8451.86 + 8451.86i 0.420713 + 0.420713i 0.885449 0.464737i \(-0.153851\pi\)
−0.464737 + 0.885449i \(0.653851\pi\)
\(740\) 0 0
\(741\) 1041.64 1041.64i 0.0516404 0.0516404i
\(742\) 0 0
\(743\) 5622.43i 0.277614i 0.990319 + 0.138807i \(0.0443267\pi\)
−0.990319 + 0.138807i \(0.955673\pi\)
\(744\) 0 0
\(745\) 6175.21i 0.303681i
\(746\) 0 0
\(747\) −14579.3 + 14579.3i −0.714095 + 0.714095i
\(748\) 0 0
\(749\) −2194.88 2194.88i −0.107075 0.107075i
\(750\) 0 0
\(751\) 32314.9 1.57016 0.785079 0.619396i \(-0.212622\pi\)
0.785079 + 0.619396i \(0.212622\pi\)
\(752\) 0 0
\(753\) −5418.58 −0.262236
\(754\) 0 0
\(755\) 24657.2 + 24657.2i 1.18857 + 1.18857i
\(756\) 0 0
\(757\) −12692.8 + 12692.8i −0.609418 + 0.609418i −0.942794 0.333376i \(-0.891812\pi\)
0.333376 + 0.942794i \(0.391812\pi\)
\(758\) 0 0
\(759\) 9545.42i 0.456491i
\(760\) 0 0
\(761\) 13108.2i 0.624404i −0.950016 0.312202i \(-0.898933\pi\)
0.950016 0.312202i \(-0.101067\pi\)
\(762\) 0 0
\(763\) 1423.48 1423.48i 0.0675404 0.0675404i
\(764\) 0 0
\(765\) −15418.8 15418.8i −0.728718 0.728718i
\(766\) 0 0
\(767\) −20154.8 −0.948822
\(768\) 0 0
\(769\) 23661.2 1.10955 0.554776 0.832000i \(-0.312804\pi\)
0.554776 + 0.832000i \(0.312804\pi\)
\(770\) 0 0
\(771\) −3563.56 3563.56i −0.166457 0.166457i
\(772\) 0 0
\(773\) −21370.5 + 21370.5i −0.994362 + 0.994362i −0.999984 0.00562228i \(-0.998210\pi\)
0.00562228 + 0.999984i \(0.498210\pi\)
\(774\) 0 0
\(775\) 1949.06i 0.0903384i
\(776\) 0 0
\(777\) 339.940i 0.0156954i
\(778\) 0 0
\(779\) −2034.27 + 2034.27i −0.0935627 + 0.0935627i
\(780\) 0 0
\(781\) −20514.8 20514.8i −0.939921 0.939921i
\(782\) 0 0
\(783\) −5283.35 −0.241139
\(784\) 0 0
\(785\) −24825.8 −1.12875
\(786\) 0 0
\(787\) −20890.9 20890.9i −0.946226 0.946226i 0.0524002 0.998626i \(-0.483313\pi\)
−0.998626 + 0.0524002i \(0.983313\pi\)
\(788\) 0 0
\(789\) −2245.97 + 2245.97i −0.101342 + 0.101342i
\(790\) 0 0
\(791\) 179.720i 0.00807853i
\(792\) 0 0
\(793\) 16145.8i 0.723020i
\(794\) 0 0
\(795\) 1862.07 1862.07i 0.0830702 0.0830702i
\(796\) 0 0
\(797\) 6834.83 + 6834.83i 0.303767