Properties

Label 324.4.i.a.37.4
Level 324
Weight 4
Character 324.37
Analytic conductor 19.117
Analytic rank 0
Dimension 54
CM no
Inner twists 2

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 324.i (of order \(9\), degree \(6\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(19.1166188419\)
Analytic rank: \(0\)
Dimension: \(54\)
Relative dimension: \(9\) over \(\Q(\zeta_{9})\)
Twist minimal: no (minimal twist has level 108)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 37.4
Character \(\chi\) \(=\) 324.37
Dual form 324.4.i.a.289.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-5.21695 + 1.89881i) q^{5} +(1.58868 + 9.00985i) q^{7} +O(q^{10})\) \(q+(-5.21695 + 1.89881i) q^{5} +(1.58868 + 9.00985i) q^{7} +(67.4972 + 24.5670i) q^{11} +(-63.1985 - 53.0298i) q^{13} +(-21.0212 + 36.4097i) q^{17} +(-22.5218 - 39.0089i) q^{19} +(-12.1174 + 68.7214i) q^{23} +(-72.1445 + 60.5364i) q^{25} +(-142.727 + 119.762i) q^{29} +(-46.3221 + 262.706i) q^{31} +(-25.3961 - 43.9873i) q^{35} +(-40.4209 + 70.0111i) q^{37} +(216.792 + 181.910i) q^{41} +(-249.820 - 90.9271i) q^{43} +(10.5496 + 59.8299i) q^{47} +(243.661 - 88.6854i) q^{49} -206.241 q^{53} -398.778 q^{55} +(-558.381 + 203.234i) q^{59} +(124.554 + 706.379i) q^{61} +(430.397 + 156.652i) q^{65} +(23.6459 + 19.8412i) q^{67} +(-155.414 + 269.185i) q^{71} +(-263.889 - 457.070i) q^{73} +(-114.113 + 647.169i) q^{77} +(-500.648 + 420.094i) q^{79} +(883.108 - 741.015i) q^{83} +(40.5310 - 229.863i) q^{85} +(-240.988 - 417.404i) q^{89} +(377.389 - 653.656i) q^{91} +(191.566 + 160.743i) q^{95} +(-858.230 - 312.370i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 54q - 12q^{5} + O(q^{10}) \) \( 54q - 12q^{5} + 87q^{11} - 204q^{17} - 96q^{23} - 216q^{25} - 318q^{29} - 54q^{31} - 6q^{35} - 867q^{41} - 513q^{43} + 1548q^{47} + 594q^{49} + 1068q^{53} + 1218q^{59} - 54q^{61} - 96q^{65} - 2997q^{67} + 120q^{71} - 216q^{73} - 3480q^{77} + 2808q^{79} - 4464q^{83} + 2160q^{85} - 4029q^{89} + 270q^{91} + 1650q^{95} - 3483q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).

\(n\) \(163\) \(245\)
\(\chi(n)\) \(1\) \(e\left(\frac{7}{9}\right)\)

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 0
\(4\) 0 0
\(5\) −5.21695 + 1.89881i −0.466618 + 0.169835i −0.564620 0.825351i \(-0.690977\pi\)
0.0980017 + 0.995186i \(0.468755\pi\)
\(6\) 0 0
\(7\) 1.58868 + 9.00985i 0.0857806 + 0.486486i 0.997185 + 0.0749750i \(0.0238877\pi\)
−0.911405 + 0.411511i \(0.865001\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 67.4972 + 24.5670i 1.85011 + 0.673384i 0.985189 + 0.171472i \(0.0548522\pi\)
0.864918 + 0.501912i \(0.167370\pi\)
\(12\) 0 0
\(13\) −63.1985 53.0298i −1.34832 1.13137i −0.979405 0.201907i \(-0.935286\pi\)
−0.368911 0.929465i \(-0.620269\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −21.0212 + 36.4097i −0.299905 + 0.519450i −0.976114 0.217259i \(-0.930288\pi\)
0.676209 + 0.736710i \(0.263622\pi\)
\(18\) 0 0
\(19\) −22.5218 39.0089i −0.271940 0.471013i 0.697419 0.716664i \(-0.254332\pi\)
−0.969358 + 0.245650i \(0.920998\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −12.1174 + 68.7214i −0.109855 + 0.623018i 0.879315 + 0.476241i \(0.158001\pi\)
−0.989170 + 0.146777i \(0.953110\pi\)
\(24\) 0 0
\(25\) −72.1445 + 60.5364i −0.577156 + 0.484291i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −142.727 + 119.762i −0.913924 + 0.766873i −0.972861 0.231388i \(-0.925673\pi\)
0.0589376 + 0.998262i \(0.481229\pi\)
\(30\) 0 0
\(31\) −46.3221 + 262.706i −0.268377 + 1.52204i 0.490866 + 0.871235i \(0.336680\pi\)
−0.759243 + 0.650807i \(0.774431\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −25.3961 43.9873i −0.122649 0.212435i
\(36\) 0 0
\(37\) −40.4209 + 70.0111i −0.179599 + 0.311074i −0.941743 0.336333i \(-0.890813\pi\)
0.762144 + 0.647407i \(0.224147\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 216.792 + 181.910i 0.825787 + 0.692918i 0.954320 0.298788i \(-0.0965822\pi\)
−0.128533 + 0.991705i \(0.541027\pi\)
\(42\) 0 0
\(43\) −249.820 90.9271i −0.885982 0.322471i −0.141361 0.989958i \(-0.545148\pi\)
−0.744621 + 0.667487i \(0.767370\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 10.5496 + 59.8299i 0.0327409 + 0.185683i 0.996792 0.0800335i \(-0.0255027\pi\)
−0.964051 + 0.265716i \(0.914392\pi\)
\(48\) 0 0
\(49\) 243.661 88.6854i 0.710382 0.258558i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −206.241 −0.534517 −0.267258 0.963625i \(-0.586118\pi\)
−0.267258 + 0.963625i \(0.586118\pi\)
\(54\) 0 0
\(55\) −398.778 −0.977658
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −558.381 + 203.234i −1.23212 + 0.448455i −0.874323 0.485345i \(-0.838694\pi\)
−0.357797 + 0.933800i \(0.616472\pi\)
\(60\) 0 0
\(61\) 124.554 + 706.379i 0.261434 + 1.48266i 0.779002 + 0.627022i \(0.215726\pi\)
−0.517568 + 0.855642i \(0.673163\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 430.397 + 156.652i 0.821295 + 0.298927i
\(66\) 0 0
\(67\) 23.6459 + 19.8412i 0.0431164 + 0.0361790i 0.664091 0.747652i \(-0.268819\pi\)
−0.620975 + 0.783831i \(0.713263\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −155.414 + 269.185i −0.259779 + 0.449950i −0.966182 0.257859i \(-0.916983\pi\)
0.706404 + 0.707809i \(0.250316\pi\)
\(72\) 0 0
\(73\) −263.889 457.070i −0.423094 0.732821i 0.573146 0.819453i \(-0.305723\pi\)
−0.996240 + 0.0866322i \(0.972389\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −114.113 + 647.169i −0.168889 + 0.957815i
\(78\) 0 0
\(79\) −500.648 + 420.094i −0.713004 + 0.598281i −0.925440 0.378893i \(-0.876305\pi\)
0.212436 + 0.977175i \(0.431860\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 883.108 741.015i 1.16788 0.979964i 0.167893 0.985805i \(-0.446304\pi\)
0.999983 + 0.00584137i \(0.00185938\pi\)
\(84\) 0 0
\(85\) 40.5310 229.863i 0.0517201 0.293319i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −240.988 417.404i −0.287019 0.497132i 0.686078 0.727528i \(-0.259331\pi\)
−0.973097 + 0.230397i \(0.925998\pi\)
\(90\) 0 0
\(91\) 377.389 653.656i 0.434737 0.752987i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 191.566 + 160.743i 0.206887 + 0.173598i
\(96\) 0 0
\(97\) −858.230 312.370i −0.898351 0.326973i −0.148759 0.988873i \(-0.547528\pi\)
−0.749592 + 0.661901i \(0.769750\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 92.4446 + 524.279i 0.0910750 + 0.516512i 0.995880 + 0.0906852i \(0.0289057\pi\)
−0.904805 + 0.425827i \(0.859983\pi\)
\(102\) 0 0
\(103\) 303.355 110.412i 0.290199 0.105624i −0.192819 0.981234i \(-0.561763\pi\)
0.483017 + 0.875611i \(0.339541\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 209.423 0.189212 0.0946062 0.995515i \(-0.469841\pi\)
0.0946062 + 0.995515i \(0.469841\pi\)
\(108\) 0 0
\(109\) −196.115 −0.172334 −0.0861672 0.996281i \(-0.527462\pi\)
−0.0861672 + 0.996281i \(0.527462\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −203.446 + 74.0482i −0.169368 + 0.0616448i −0.425312 0.905047i \(-0.639836\pi\)
0.255945 + 0.966691i \(0.417614\pi\)
\(114\) 0 0
\(115\) −67.2731 381.525i −0.0545500 0.309368i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −361.442 131.554i −0.278431 0.101341i
\(120\) 0 0
\(121\) 2932.73 + 2460.86i 2.20341 + 1.84888i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 608.412 1053.80i 0.435344 0.754038i
\(126\) 0 0
\(127\) −611.723 1059.53i −0.427414 0.740303i 0.569228 0.822180i \(-0.307242\pi\)
−0.996642 + 0.0818763i \(0.973909\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −194.741 + 1104.43i −0.129882 + 0.736599i 0.848405 + 0.529347i \(0.177563\pi\)
−0.978288 + 0.207252i \(0.933548\pi\)
\(132\) 0 0
\(133\) 315.684 264.891i 0.205814 0.172699i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1967.06 1650.56i 1.22670 1.02932i 0.228252 0.973602i \(-0.426699\pi\)
0.998446 0.0557200i \(-0.0177454\pi\)
\(138\) 0 0
\(139\) 434.934 2466.63i 0.265400 1.50516i −0.502494 0.864581i \(-0.667584\pi\)
0.767894 0.640577i \(-0.221305\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −2962.94 5131.96i −1.73268 3.00109i
\(144\) 0 0
\(145\) 517.194 895.807i 0.296211 0.513053i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −88.5089 74.2678i −0.0486640 0.0408339i 0.618131 0.786075i \(-0.287890\pi\)
−0.666795 + 0.745241i \(0.732334\pi\)
\(150\) 0 0
\(151\) 1464.39 + 532.995i 0.789209 + 0.287249i 0.705007 0.709200i \(-0.250944\pi\)
0.0842019 + 0.996449i \(0.473166\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −257.169 1458.48i −0.133267 0.755792i
\(156\) 0 0
\(157\) 1712.19 623.186i 0.870367 0.316788i 0.132052 0.991243i \(-0.457844\pi\)
0.738316 + 0.674455i \(0.235621\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −638.420 −0.312513
\(162\) 0 0
\(163\) 1785.32 0.857897 0.428948 0.903329i \(-0.358884\pi\)
0.428948 + 0.903329i \(0.358884\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1097.06 + 399.298i −0.508343 + 0.185022i −0.583442 0.812154i \(-0.698295\pi\)
0.0751000 + 0.997176i \(0.476072\pi\)
\(168\) 0 0
\(169\) 800.382 + 4539.19i 0.364307 + 2.06609i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 3928.51 + 1429.86i 1.72647 + 0.628383i 0.998369 0.0570873i \(-0.0181813\pi\)
0.728100 + 0.685471i \(0.240404\pi\)
\(174\) 0 0
\(175\) −660.038 553.838i −0.285110 0.239235i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −918.530 + 1590.94i −0.383543 + 0.664316i −0.991566 0.129604i \(-0.958629\pi\)
0.608023 + 0.793919i \(0.291963\pi\)
\(180\) 0 0
\(181\) −1157.45 2004.76i −0.475318 0.823275i 0.524282 0.851544i \(-0.324334\pi\)
−0.999600 + 0.0282697i \(0.991000\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 77.9358 441.996i 0.0309727 0.175655i
\(186\) 0 0
\(187\) −2313.35 + 1941.13i −0.904646 + 0.759088i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1309.35 + 1098.67i −0.496027 + 0.416216i −0.856180 0.516677i \(-0.827169\pi\)
0.360153 + 0.932893i \(0.382724\pi\)
\(192\) 0 0
\(193\) −538.413 + 3053.49i −0.200808 + 1.13884i 0.703095 + 0.711096i \(0.251801\pi\)
−0.903902 + 0.427740i \(0.859310\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 269.298 + 466.438i 0.0973943 + 0.168692i 0.910605 0.413277i \(-0.135616\pi\)
−0.813211 + 0.581969i \(0.802283\pi\)
\(198\) 0 0
\(199\) 1847.26 3199.55i 0.658035 1.13975i −0.323089 0.946369i \(-0.604721\pi\)
0.981124 0.193381i \(-0.0619454\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −1305.79 1095.69i −0.451470 0.378828i
\(204\) 0 0
\(205\) −1476.41 537.369i −0.503009 0.183080i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −561.828 3186.28i −0.185945 1.05455i
\(210\) 0 0
\(211\) 3344.47 1217.29i 1.09120 0.397164i 0.267134 0.963660i \(-0.413924\pi\)
0.824065 + 0.566496i \(0.191701\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1475.95 0.468182
\(216\) 0 0
\(217\) −2440.53 −0.763474
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 3259.31 1186.29i 0.992058 0.361080i
\(222\) 0 0
\(223\) −932.642 5289.28i −0.280064 1.58832i −0.722401 0.691474i \(-0.756962\pi\)
0.442337 0.896849i \(-0.354150\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1788.67 + 651.023i 0.522988 + 0.190352i 0.590005 0.807400i \(-0.299126\pi\)
−0.0670166 + 0.997752i \(0.521348\pi\)
\(228\) 0 0
\(229\) −1969.18 1652.34i −0.568240 0.476810i 0.312821 0.949812i \(-0.398726\pi\)
−0.881061 + 0.473002i \(0.843170\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −1769.64 + 3065.11i −0.497567 + 0.861811i −0.999996 0.00280750i \(-0.999106\pi\)
0.502429 + 0.864618i \(0.332440\pi\)
\(234\) 0 0
\(235\) −168.643 292.098i −0.0468129 0.0810823i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −1060.55 + 6014.68i −0.287035 + 1.62786i 0.410890 + 0.911685i \(0.365218\pi\)
−0.697925 + 0.716171i \(0.745893\pi\)
\(240\) 0 0
\(241\) −2459.06 + 2063.40i −0.657270 + 0.551515i −0.909267 0.416213i \(-0.863357\pi\)
0.251997 + 0.967728i \(0.418913\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −1102.77 + 925.334i −0.287565 + 0.241296i
\(246\) 0 0
\(247\) −645.292 + 3659.63i −0.166230 + 0.942740i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −1804.49 3125.47i −0.453778 0.785967i 0.544839 0.838541i \(-0.316591\pi\)
−0.998617 + 0.0525736i \(0.983258\pi\)
\(252\) 0 0
\(253\) −2506.17 + 4340.82i −0.622773 + 1.07868i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 4944.99 + 4149.34i 1.20023 + 1.00712i 0.999623 + 0.0274439i \(0.00873676\pi\)
0.200610 + 0.979671i \(0.435708\pi\)
\(258\) 0 0
\(259\) −695.005 252.961i −0.166739 0.0606882i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 1324.95 + 7514.17i 0.310646 + 1.76176i 0.595657 + 0.803239i \(0.296892\pi\)
−0.285011 + 0.958524i \(0.591997\pi\)
\(264\) 0 0
\(265\) 1075.95 391.613i 0.249415 0.0907797i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 7418.04 1.68136 0.840681 0.541531i \(-0.182155\pi\)
0.840681 + 0.541531i \(0.182155\pi\)
\(270\) 0 0
\(271\) −5946.94 −1.33303 −0.666515 0.745492i \(-0.732215\pi\)
−0.666515 + 0.745492i \(0.732215\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −6356.75 + 2313.67i −1.39391 + 0.507343i
\(276\) 0 0
\(277\) 105.510 + 598.379i 0.0228863 + 0.129795i 0.994110 0.108373i \(-0.0345642\pi\)
−0.971224 + 0.238168i \(0.923453\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −6387.32 2324.79i −1.35600 0.493543i −0.441184 0.897417i \(-0.645441\pi\)
−0.914815 + 0.403874i \(0.867664\pi\)
\(282\) 0 0
\(283\) −56.9781 47.8103i −0.0119682 0.0100425i 0.636784 0.771042i \(-0.280264\pi\)
−0.648752 + 0.761000i \(0.724709\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −1294.57 + 2242.26i −0.266258 + 0.461173i
\(288\) 0 0
\(289\) 1572.72 + 2724.03i 0.320114 + 0.554454i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 17.3041 98.1364i 0.00345023 0.0195672i −0.983034 0.183423i \(-0.941282\pi\)
0.986484 + 0.163856i \(0.0523932\pi\)
\(294\) 0 0
\(295\) 2527.14 2120.52i 0.498766 0.418514i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 4410.09 3700.50i 0.852983 0.715738i
\(300\) 0 0
\(301\) 422.355 2395.30i 0.0808776 0.458680i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −1991.07 3448.64i −0.373798 0.647437i
\(306\) 0 0
\(307\) −2496.99 + 4324.91i −0.464204 + 0.804024i −0.999165 0.0408521i \(-0.986993\pi\)
0.534962 + 0.844876i \(0.320326\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −5733.38 4810.88i −1.04537 0.877170i −0.0527712 0.998607i \(-0.516805\pi\)
−0.992599 + 0.121437i \(0.961250\pi\)
\(312\) 0 0
\(313\) 4171.87 + 1518.44i 0.753380 + 0.274208i 0.690027 0.723783i \(-0.257599\pi\)
0.0633524 + 0.997991i \(0.479821\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 299.891 + 1700.77i 0.0531342 + 0.301339i 0.999781 0.0209343i \(-0.00666407\pi\)
−0.946647 + 0.322273i \(0.895553\pi\)
\(318\) 0 0
\(319\) −12575.9 + 4577.25i −2.20726 + 0.803376i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 1893.74 0.326224
\(324\) 0 0
\(325\) 7769.66 1.32610
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −522.298 + 190.101i −0.0875235 + 0.0318559i
\(330\) 0 0
\(331\) −146.572 831.251i −0.0243393 0.138035i 0.970217 0.242239i \(-0.0778818\pi\)
−0.994556 + 0.104204i \(0.966771\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −161.034 58.6116i −0.0262634 0.00955908i
\(336\) 0 0
\(337\) 25.8927 + 21.7265i 0.00418536 + 0.00351193i 0.644878 0.764286i \(-0.276908\pi\)
−0.640693 + 0.767798i \(0.721353\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −9580.49 + 16593.9i −1.52145 + 2.63522i
\(342\) 0 0
\(343\) 2755.17 + 4772.09i 0.433717 + 0.751220i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1785.27 10124.8i 0.276191 1.56636i −0.458963 0.888455i \(-0.651779\pi\)
0.735154 0.677900i \(-0.237110\pi\)
\(348\) 0 0
\(349\) −5099.40 + 4278.91i −0.782134 + 0.656289i −0.943785 0.330559i \(-0.892763\pi\)
0.161651 + 0.986848i \(0.448318\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −6159.61 + 5168.53i −0.928734 + 0.779300i −0.975590 0.219601i \(-0.929524\pi\)
0.0468557 + 0.998902i \(0.485080\pi\)
\(354\) 0 0
\(355\) 299.655 1699.43i 0.0448001 0.254074i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 1712.40 + 2965.97i 0.251747 + 0.436039i 0.964007 0.265877i \(-0.0856615\pi\)
−0.712260 + 0.701916i \(0.752328\pi\)
\(360\) 0 0
\(361\) 2415.04 4182.97i 0.352098 0.609851i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 2244.59 + 1883.43i 0.321882 + 0.270091i
\(366\) 0 0
\(367\) −3402.99 1238.59i −0.484018 0.176168i 0.0884742 0.996078i \(-0.471801\pi\)
−0.572492 + 0.819910i \(0.694023\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −327.651 1858.20i −0.0458512 0.260035i
\(372\) 0 0
\(373\) −1812.31 + 659.627i −0.251576 + 0.0915662i −0.464730 0.885452i \(-0.653849\pi\)
0.213154 + 0.977019i \(0.431626\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 15371.1 2.09988
\(378\) 0 0
\(379\) 4403.13 0.596763 0.298382 0.954447i \(-0.403553\pi\)
0.298382 + 0.954447i \(0.403553\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 10231.3 3723.88i 1.36500 0.496819i 0.447402 0.894333i \(-0.352349\pi\)
0.917596 + 0.397515i \(0.130127\pi\)
\(384\) 0 0
\(385\) −633.530 3592.93i −0.0838641 0.475617i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −7053.47 2567.25i −0.919345 0.334614i −0.161367 0.986894i \(-0.551590\pi\)
−0.757978 + 0.652280i \(0.773813\pi\)
\(390\) 0 0
\(391\) −2247.41 1885.80i −0.290681 0.243910i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 1814.18 3142.25i 0.231091 0.400262i
\(396\) 0 0
\(397\) −3635.79 6297.37i −0.459635 0.796111i 0.539307 0.842110i \(-0.318686\pi\)
−0.998942 + 0.0459984i \(0.985353\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 2014.16 11422.9i 0.250828 1.42252i −0.555729 0.831363i \(-0.687561\pi\)
0.806558 0.591155i \(-0.201328\pi\)
\(402\) 0 0
\(403\) 16858.7 14146.1i 2.08385 1.74856i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −4448.26 + 3732.53i −0.541750 + 0.454582i
\(408\) 0 0
\(409\) 1420.37 8055.31i 0.171718 0.973862i −0.770146 0.637868i \(-0.779817\pi\)
0.941864 0.335994i \(-0.109072\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −2718.20 4708.06i −0.323859 0.560940i
\(414\) 0 0
\(415\) −3200.08 + 5542.70i −0.378520 + 0.655615i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 6454.20 + 5415.71i 0.752525 + 0.631444i 0.936169 0.351549i \(-0.114345\pi\)
−0.183644 + 0.982993i \(0.558789\pi\)
\(420\) 0 0
\(421\) 4401.68 + 1602.08i 0.509560 + 0.185465i 0.583989 0.811762i \(-0.301491\pi\)
−0.0744290 + 0.997226i \(0.523713\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −687.553 3899.31i −0.0784735 0.445045i
\(426\) 0 0
\(427\) −6166.49 + 2244.42i −0.698869 + 0.254368i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 8784.41 0.981740 0.490870 0.871233i \(-0.336679\pi\)
0.490870 + 0.871233i \(0.336679\pi\)
\(432\) 0 0
\(433\) −6469.85 −0.718063 −0.359031 0.933325i \(-0.616893\pi\)
−0.359031 + 0.933325i \(0.616893\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2953.65 1075.04i 0.323323 0.117680i
\(438\) 0 0
\(439\) −148.990 844.963i −0.0161979 0.0918631i 0.975637 0.219391i \(-0.0704070\pi\)
−0.991835 + 0.127528i \(0.959296\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −412.777 150.239i −0.0442701 0.0161130i 0.319790 0.947488i \(-0.396388\pi\)
−0.364060 + 0.931375i \(0.618610\pi\)
\(444\) 0 0
\(445\) 2049.80 + 1719.98i 0.218359 + 0.183225i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −1510.09 + 2615.54i −0.158720 + 0.274911i −0.934407 0.356206i \(-0.884070\pi\)
0.775687 + 0.631117i \(0.217403\pi\)
\(450\) 0 0
\(451\) 10163.9 + 17604.4i 1.06120 + 1.83804i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −727.645 + 4126.68i −0.0749726 + 0.425191i
\(456\) 0 0
\(457\) 5728.39 4806.69i 0.586352 0.492008i −0.300674 0.953727i \(-0.597212\pi\)
0.887026 + 0.461719i \(0.152767\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −4559.80 + 3826.13i −0.460675 + 0.386552i −0.843379 0.537319i \(-0.819437\pi\)
0.382705 + 0.923871i \(0.374993\pi\)
\(462\) 0 0
\(463\) 299.450 1698.27i 0.0300575 0.170465i −0.966084 0.258229i \(-0.916861\pi\)
0.996141 + 0.0877642i \(0.0279722\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −7069.94 12245.5i −0.700552 1.21339i −0.968273 0.249895i \(-0.919604\pi\)
0.267721 0.963496i \(-0.413729\pi\)
\(468\) 0 0
\(469\) −141.201 + 244.567i −0.0139020 + 0.0240790i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −14628.4 12274.7i −1.42202 1.19321i
\(474\) 0 0
\(475\) 3986.28 + 1450.89i 0.385059 + 0.140150i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −467.551 2651.62i −0.0445991 0.252934i 0.954354 0.298677i \(-0.0965455\pi\)
−0.998953 + 0.0457434i \(0.985434\pi\)
\(480\) 0 0
\(481\) 6267.22 2281.08i 0.594097 0.216234i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 5070.47 0.474718
\(486\) 0 0
\(487\) 12687.7 1.18056 0.590280 0.807199i \(-0.299017\pi\)
0.590280 + 0.807199i \(0.299017\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 5094.55 1854.26i 0.468256 0.170431i −0.0971061 0.995274i \(-0.530959\pi\)
0.565362 + 0.824843i \(0.308736\pi\)
\(492\) 0 0
\(493\) −1360.22 7714.21i −0.124262 0.704727i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −2672.22 972.609i −0.241178 0.0877817i
\(498\) 0 0
\(499\) −10451.5 8769.82i −0.937619 0.786756i 0.0395506 0.999218i \(-0.487407\pi\)
−0.977169 + 0.212462i \(0.931852\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −3966.78 + 6870.66i −0.351630 + 0.609041i −0.986535 0.163549i \(-0.947706\pi\)
0.634905 + 0.772590i \(0.281039\pi\)
\(504\) 0 0
\(505\) −1477.79 2559.60i −0.130219 0.225546i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 3183.90 18056.8i 0.277257 1.57240i −0.454443 0.890776i \(-0.650162\pi\)
0.731700 0.681627i \(-0.238727\pi\)
\(510\) 0 0
\(511\) 3698.89 3103.74i 0.320214 0.268691i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −1372.94 + 1152.03i −0.117473 + 0.0985718i
\(516\) 0 0
\(517\) −757.769 + 4297.52i −0.0644616 + 0.365580i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 3020.36 + 5231.43i 0.253982 + 0.439910i 0.964618 0.263650i \(-0.0849263\pi\)
−0.710637 + 0.703559i \(0.751593\pi\)
\(522\) 0 0
\(523\) 2909.21 5038.90i 0.243233 0.421292i −0.718400 0.695630i \(-0.755125\pi\)
0.961633 + 0.274338i \(0.0884586\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −8591.29 7208.95i −0.710138 0.595876i
\(528\) 0 0
\(529\) 6857.44 + 2495.90i 0.563610 + 0.205137i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −4054.27 22992.9i −0.329475 1.86854i
\(534\) 0 0
\(535\) −1092.55 + 397.656i −0.0882899 + 0.0321349i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 18625.2 1.48839
\(540\) 0 0
\(541\) 6742.32 0.535813 0.267907 0.963445i \(-0.413668\pi\)
0.267907 + 0.963445i \(0.413668\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 1023.12 372.387i 0.0804144 0.0292684i
\(546\) 0 0
\(547\) 996.065 + 5648.96i 0.0778586 + 0.441558i 0.998670 + 0.0515507i \(0.0164164\pi\)
−0.920812 + 0.390007i \(0.872473\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 7886.27 + 2870.37i 0.609740 + 0.221927i
\(552\) 0 0
\(553\) −4580.35 3843.37i −0.352217 0.295546i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −11916.4 + 20639.9i −0.906492 + 1.57009i −0.0875890 + 0.996157i \(0.527916\pi\)
−0.818902 + 0.573933i \(0.805417\pi\)
\(558\) 0 0
\(559\) 10966.4 + 18994.4i 0.829749 + 1.43717i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −143.937 + 816.308i −0.0107748 + 0.0611070i −0.989721 0.143011i \(-0.954322\pi\)
0.978946 + 0.204118i \(0.0654327\pi\)
\(564\) 0 0
\(565\) 920.762 772.611i 0.0685606 0.0575292i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −809.884 + 679.573i −0.0596698 + 0.0500689i −0.672135 0.740429i \(-0.734622\pi\)
0.612465 + 0.790498i \(0.290178\pi\)
\(570\) 0 0
\(571\) −4496.33 + 25499.9i −0.329537 + 1.86890i 0.146124 + 0.989266i \(0.453320\pi\)
−0.475661 + 0.879629i \(0.657791\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −3285.94 5691.42i −0.238319 0.412780i
\(576\) 0 0
\(577\) −1489.92 + 2580.62i −0.107498 + 0.186192i −0.914756 0.404007i \(-0.867617\pi\)
0.807258 + 0.590199i \(0.200951\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 8079.41 + 6779.43i 0.576920 + 0.484093i
\(582\) 0 0
\(583\) −13920.7 5066.72i −0.988913 0.359935i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 3085.89 + 17501.0i 0.216982 + 1.23057i 0.877434 + 0.479698i \(0.159254\pi\)
−0.660452 + 0.750868i \(0.729635\pi\)
\(588\) 0 0
\(589\) 11291.1 4109.63i 0.789884 0.287494i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 3329.70 0.230581 0.115290 0.993332i \(-0.463220\pi\)
0.115290 + 0.993332i \(0.463220\pi\)
\(594\) 0 0
\(595\) 2135.42 0.147132
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −12799.7 + 4658.71i −0.873090 + 0.317779i −0.739418 0.673247i \(-0.764899\pi\)
−0.133672 + 0.991026i \(0.542677\pi\)
\(600\) 0 0
\(601\) 447.186 + 2536.12i 0.0303513 + 0.172131i 0.996215 0.0869185i \(-0.0277020\pi\)
−0.965864 + 0.259049i \(0.916591\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −19972.6 7269.45i −1.34215 0.488504i
\(606\) 0 0
\(607\) −8011.80 6722.70i −0.535731 0.449532i 0.334344 0.942451i \(-0.391485\pi\)
−0.870075 + 0.492919i \(0.835930\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 2506.05 4340.60i 0.165931 0.287401i
\(612\) 0 0
\(613\) −12357.4 21403.7i −0.814211 1.41025i −0.909893 0.414842i \(-0.863837\pi\)
0.0956826 0.995412i \(-0.469497\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −1578.77 + 8953.67i −0.103013 + 0.584216i 0.888982 + 0.457942i \(0.151413\pi\)
−0.991995 + 0.126274i \(0.959698\pi\)
\(618\) 0 0
\(619\) 7255.84 6088.37i 0.471142 0.395335i −0.376069 0.926592i \(-0.622725\pi\)
0.847211 + 0.531257i \(0.178280\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 3377.89 2834.39i 0.217227 0.182275i
\(624\) 0 0
\(625\) 871.146 4940.52i 0.0557534 0.316193i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −1699.39 2943.43i −0.107725 0.186585i
\(630\) 0 0
\(631\) −7345.25 + 12722.3i −0.463407 + 0.802644i −0.999128 0.0417505i \(-0.986707\pi\)
0.535721 + 0.844395i \(0.320040\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 5203.19 + 4365.99i 0.325169 + 0.272849i
\(636\) 0 0
\(637\) −20102.0 7316.53i −1.25035 0.455088i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 4526.38 + 25670.4i 0.278910 + 1.58178i 0.726261 + 0.687419i \(0.241256\pi\)
−0.447351 + 0.894359i \(0.647632\pi\)
\(642\) 0 0
\(643\) 2079.34 756.817i 0.127529 0.0464167i −0.277467 0.960735i \(-0.589495\pi\)
0.404996 + 0.914318i \(0.367273\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 13758.7 0.836027 0.418013 0.908441i \(-0.362727\pi\)
0.418013 + 0.908441i \(0.362727\pi\)
\(648\) 0 0
\(649\) −42682.0 −2.58154
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 15288.2 5564.44i 0.916191 0.333466i 0.159469 0.987203i \(-0.449022\pi\)
0.756722 + 0.653737i \(0.226800\pi\)
\(654\) 0 0
\(655\) −1081.15 6131.53i −0.0644949 0.365769i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 10222.0 + 3720.52i 0.604240 + 0.219925i 0.625981 0.779838i \(-0.284699\pi\)
−0.0217411 + 0.999764i \(0.506921\pi\)
\(660\) 0 0
\(661\) 316.290 + 265.399i 0.0186116 + 0.0156170i 0.652046 0.758179i \(-0.273911\pi\)
−0.633434 + 0.773796i \(0.718355\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −1143.93 + 1981.35i −0.0667063 + 0.115539i
\(666\) 0 0
\(667\) −6500.75 11259.6i −0.377377 0.653635i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −8946.57 + 50738.5i −0.514722 + 2.91913i
\(672\) 0 0
\(673\) −18608.4 + 15614.3i −1.06582 + 0.894333i −0.994668 0.103133i \(-0.967113\pi\)
−0.0711564 + 0.997465i \(0.522669\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 8328.43 6988.38i 0.472803 0.396729i −0.375013 0.927020i \(-0.622362\pi\)
0.847816 + 0.530291i \(0.177917\pi\)
\(678\) 0 0
\(679\) 1450.95 8228.77i 0.0820067 0.465083i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −6279.52 10876.5i −0.351800 0.609335i 0.634765 0.772705i \(-0.281097\pi\)
−0.986565 + 0.163370i \(0.947764\pi\)
\(684\) 0 0
\(685\) −7127.96 + 12346.0i −0.397585 + 0.688637i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 13034.1 + 10936.9i 0.720698 + 0.604737i
\(690\) 0 0
\(691\) 16718.3 + 6084.96i 0.920396 + 0.334997i 0.758396 0.651794i \(-0.225983\pi\)
0.162000 + 0.986791i \(0.448206\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 2414.65 + 13694.2i 0.131788 + 0.747408i
\(696\) 0 0
\(697\) −11180.5 + 4069.38i −0.607594 + 0.221146i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −21646.4 −1.16629 −0.583147 0.812367i \(-0.698179\pi\)
−0.583147 + 0.812367i \(0.698179\pi\)
\(702\) 0 0
\(703\) 3641.41 0.195360
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −4576.81 + 1665.82i −0.243463 + 0.0886135i
\(708\) 0 0
\(709\) 3459.28 + 19618.5i 0.183238 + 1.03920i 0.928198 + 0.372086i \(0.121357\pi\)
−0.744960 + 0.667109i \(0.767532\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −17492.2 6366.64i −0.918777 0.334407i
\(714\) 0 0
\(715\) 25202.2 + 21147.1i 1.31819 + 1.10609i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −10932.0 + 18934.8i −0.567031 + 0.982126i 0.429827 + 0.902911i \(0.358575\pi\)
−0.996858 + 0.0792148i \(0.974759\pi\)
\(720\) 0 0
\(721\) 1476.73 + 2557.77i 0.0762779 + 0.132117i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 3047.00 17280.4i 0.156087 0.885211i
\(726\) 0 0
\(727\) −25330.4 + 21254.7i −1.29223 + 1.08431i −0.300799 + 0.953688i \(0.597253\pi\)
−0.991432 + 0.130623i \(0.958302\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 8562.15 7184.49i 0.433218 0.363513i
\(732\) 0 0
\(733\) 2985.32 16930.6i 0.150430 0.853131i −0.812416 0.583079i \(-0.801848\pi\)
0.962846 0.270052i \(-0.0870410\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1108.59 + 1920.14i 0.0554077 + 0.0959689i
\(738\) 0 0
\(739\) 9649.35 16713.2i 0.480321 0.831940i −0.519424 0.854516i \(-0.673854\pi\)
0.999745 + 0.0225766i \(0.00718696\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −20573.9 17263.5i −1.01586 0.852405i −0.0267555 0.999642i \(-0.508518\pi\)
−0.989101 + 0.147237i \(0.952962\pi\)
\(744\) 0 0
\(745\) 602.767 + 219.389i 0.0296425 + 0.0107890i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 332.707 + 1886.87i 0.0162308 + 0.0920492i
\(750\) 0 0
\(751\) −27645.8 + 10062.2i −1.34329 + 0.488916i −0.910846 0.412746i \(-0.864570\pi\)
−0.432440 + 0.901663i \(0.642347\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −8651.72 −0.417044
\(756\) 0 0
\(757\) 24191.8 1.16151 0.580756 0.814077i \(-0.302757\pi\)
0.580756 + 0.814077i \(0.302757\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −12610.5 + 4589.85i −0.600698 + 0.218636i −0.624428 0.781082i \(-0.714668\pi\)
0.0237304 + 0.999718i \(0.492446\pi\)
\(762\) 0 0
\(763\) −311.565 1766.97i −0.0147830 0.0838383i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 46066.3 + 16766.8i 2.16866 + 0.789326i
\(768\) 0 0
\(769\) 16690.9 + 14005.3i 0.782689 + 0.656754i 0.943924 0.330162i \(-0.107103\pi\)
−0.161235 + 0.986916i \(0.551548\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 670.497 1161.34i 0.0311981 0.0540367i −0.850005 0.526775i \(-0.823401\pi\)
0.881203 + 0.472738i \(0.156734\pi\)
\(774\) 0 0
\(775\) −12561.4 21756.9i −0.582216 1.00843i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 2213.57 12553.8i 0.101809 0.577389i
\(780\) 0 0
\(781\) −17103.1 + 14351.2i −0.783607 + 0.657524i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −7749.10 + 6502.26i −0.352327 + 0.295638i
\(786\) 0 0
\(787\) −508.621 + 2884.53i −0.0230373 + 0.130651i −0.994157 0.107940i \(-0.965575\pi\)
0.971120 + 0.238591i \(0.0766856\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −990.373 1715.38i