Properties

Label 336.4.h.a.239.4
Level $336$
Weight $4$
Character 336.239
Analytic conductor $19.825$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 336.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(19.8246417619\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
Defining polynomial: \(x^{12} + 152 x^{10} + 8222 x^{8} + 194132 x^{6} + 1882697 x^{4} + 5152508 x^{2} + 4008004\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{7}\cdot 3^{2}\cdot 7^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 239.4
Root \(8.01905i\) of defining polynomial
Character \(\chi\) \(=\) 336.239
Dual form 336.4.h.a.239.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-4.59729 + 2.42176i) q^{3} +2.41112i q^{5} +7.00000i q^{7} +(15.2701 - 22.2671i) q^{9} +O(q^{10})\) \(q+(-4.59729 + 2.42176i) q^{3} +2.41112i q^{5} +7.00000i q^{7} +(15.2701 - 22.2671i) q^{9} -37.7507 q^{11} -24.8242 q^{13} +(-5.83916 - 11.0846i) q^{15} -22.2390i q^{17} +68.4449i q^{19} +(-16.9523 - 32.1810i) q^{21} -44.4616 q^{23} +119.187 q^{25} +(-16.2756 + 139.349i) q^{27} -178.080i q^{29} -109.914i q^{31} +(173.551 - 91.4233i) q^{33} -16.8778 q^{35} +168.159 q^{37} +(114.124 - 60.1182i) q^{39} -383.222i q^{41} -371.398i q^{43} +(53.6886 + 36.8181i) q^{45} +323.418 q^{47} -49.0000 q^{49} +(53.8576 + 102.239i) q^{51} -401.885i q^{53} -91.0214i q^{55} +(-165.757 - 314.661i) q^{57} +34.0932 q^{59} +25.4725 q^{61} +(155.870 + 106.891i) q^{63} -59.8540i q^{65} +118.410i q^{67} +(204.403 - 107.675i) q^{69} +106.743 q^{71} +1016.99 q^{73} +(-547.935 + 288.641i) q^{75} -264.255i q^{77} -649.676i q^{79} +(-262.646 - 680.043i) q^{81} -250.812 q^{83} +53.6208 q^{85} +(431.269 + 818.687i) q^{87} -4.02791i q^{89} -173.769i q^{91} +(266.187 + 505.308i) q^{93} -165.029 q^{95} -454.703 q^{97} +(-576.458 + 840.598i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 76 q^{9} + O(q^{10}) \) \( 12 q + 76 q^{9} - 96 q^{13} + 112 q^{21} - 1068 q^{25} - 832 q^{33} - 720 q^{37} + 392 q^{45} - 588 q^{49} - 2336 q^{57} + 432 q^{61} - 424 q^{69} + 1656 q^{73} - 868 q^{81} - 1464 q^{85} + 696 q^{93} - 6264 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(1\) \(-1\) \(-1\) \(1\)

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
\(3\) −4.59729 + 2.42176i −0.884749 + 0.466068i
\(4\) 0 0
\(5\) 2.41112i 0.215657i 0.994170 + 0.107828i \(0.0343897\pi\)
−0.994170 + 0.107828i \(0.965610\pi\)
\(6\) 0 0
\(7\) 7.00000i 0.377964i
\(8\) 0 0
\(9\) 15.2701 22.2671i 0.565560 0.824707i
\(10\) 0 0
\(11\) −37.7507 −1.03475 −0.517376 0.855758i \(-0.673091\pi\)
−0.517376 + 0.855758i \(0.673091\pi\)
\(12\) 0 0
\(13\) −24.8242 −0.529614 −0.264807 0.964301i \(-0.585308\pi\)
−0.264807 + 0.964301i \(0.585308\pi\)
\(14\) 0 0
\(15\) −5.83916 11.0846i −0.100511 0.190802i
\(16\) 0 0
\(17\) 22.2390i 0.317279i −0.987337 0.158640i \(-0.949289\pi\)
0.987337 0.158640i \(-0.0507108\pi\)
\(18\) 0 0
\(19\) 68.4449i 0.826439i 0.910631 + 0.413220i \(0.135596\pi\)
−0.910631 + 0.413220i \(0.864404\pi\)
\(20\) 0 0
\(21\) −16.9523 32.1810i −0.176157 0.334404i
\(22\) 0 0
\(23\) −44.4616 −0.403082 −0.201541 0.979480i \(-0.564595\pi\)
−0.201541 + 0.979480i \(0.564595\pi\)
\(24\) 0 0
\(25\) 119.187 0.953492
\(26\) 0 0
\(27\) −16.2756 + 139.349i −0.116009 + 0.993248i
\(28\) 0 0
\(29\) 178.080i 1.14030i −0.821540 0.570150i \(-0.806885\pi\)
0.821540 0.570150i \(-0.193115\pi\)
\(30\) 0 0
\(31\) 109.914i 0.636813i −0.947954 0.318406i \(-0.896852\pi\)
0.947954 0.318406i \(-0.103148\pi\)
\(32\) 0 0
\(33\) 173.551 91.4233i 0.915495 0.482265i
\(34\) 0 0
\(35\) −16.8778 −0.0815107
\(36\) 0 0
\(37\) 168.159 0.747167 0.373583 0.927597i \(-0.378129\pi\)
0.373583 + 0.927597i \(0.378129\pi\)
\(38\) 0 0
\(39\) 114.124 60.1182i 0.468575 0.246836i
\(40\) 0 0
\(41\) 383.222i 1.45974i −0.683587 0.729869i \(-0.739581\pi\)
0.683587 0.729869i \(-0.260419\pi\)
\(42\) 0 0
\(43\) 371.398i 1.31715i −0.752514 0.658577i \(-0.771159\pi\)
0.752514 0.658577i \(-0.228841\pi\)
\(44\) 0 0
\(45\) 53.6886 + 36.8181i 0.177854 + 0.121967i
\(46\) 0 0
\(47\) 323.418 1.00373 0.501865 0.864946i \(-0.332647\pi\)
0.501865 + 0.864946i \(0.332647\pi\)
\(48\) 0 0
\(49\) −49.0000 −0.142857
\(50\) 0 0
\(51\) 53.8576 + 102.239i 0.147874 + 0.280712i
\(52\) 0 0
\(53\) 401.885i 1.04157i −0.853688 0.520785i \(-0.825639\pi\)
0.853688 0.520785i \(-0.174361\pi\)
\(54\) 0 0
\(55\) 91.0214i 0.223151i
\(56\) 0 0
\(57\) −165.757 314.661i −0.385177 0.731191i
\(58\) 0 0
\(59\) 34.0932 0.0752297 0.0376148 0.999292i \(-0.488024\pi\)
0.0376148 + 0.999292i \(0.488024\pi\)
\(60\) 0 0
\(61\) 25.4725 0.0534658 0.0267329 0.999643i \(-0.491490\pi\)
0.0267329 + 0.999643i \(0.491490\pi\)
\(62\) 0 0
\(63\) 155.870 + 106.891i 0.311710 + 0.213762i
\(64\) 0 0
\(65\) 59.8540i 0.114215i
\(66\) 0 0
\(67\) 118.410i 0.215911i 0.994156 + 0.107956i \(0.0344304\pi\)
−0.994156 + 0.107956i \(0.965570\pi\)
\(68\) 0 0
\(69\) 204.403 107.675i 0.356626 0.187864i
\(70\) 0 0
\(71\) 106.743 0.178423 0.0892115 0.996013i \(-0.471565\pi\)
0.0892115 + 0.996013i \(0.471565\pi\)
\(72\) 0 0
\(73\) 1016.99 1.63054 0.815270 0.579081i \(-0.196589\pi\)
0.815270 + 0.579081i \(0.196589\pi\)
\(74\) 0 0
\(75\) −547.935 + 288.641i −0.843601 + 0.444393i
\(76\) 0 0
\(77\) 264.255i 0.391099i
\(78\) 0 0
\(79\) 649.676i 0.925243i −0.886556 0.462622i \(-0.846909\pi\)
0.886556 0.462622i \(-0.153091\pi\)
\(80\) 0 0
\(81\) −262.646 680.043i −0.360283 0.932843i
\(82\) 0 0
\(83\) −250.812 −0.331689 −0.165845 0.986152i \(-0.553035\pi\)
−0.165845 + 0.986152i \(0.553035\pi\)
\(84\) 0 0
\(85\) 53.6208 0.0684235
\(86\) 0 0
\(87\) 431.269 + 818.687i 0.531458 + 1.00888i
\(88\) 0 0
\(89\) 4.02791i 0.00479727i −0.999997 0.00239864i \(-0.999236\pi\)
0.999997 0.00239864i \(-0.000763511\pi\)
\(90\) 0 0
\(91\) 173.769i 0.200175i
\(92\) 0 0
\(93\) 266.187 + 505.308i 0.296798 + 0.563419i
\(94\) 0 0
\(95\) −165.029 −0.178227
\(96\) 0 0
\(97\) −454.703 −0.475960 −0.237980 0.971270i \(-0.576485\pi\)
−0.237980 + 0.971270i \(0.576485\pi\)
\(98\) 0 0
\(99\) −576.458 + 840.598i −0.585215 + 0.853367i
\(100\) 0 0
\(101\) 1954.31i 1.92536i 0.270640 + 0.962681i \(0.412765\pi\)
−0.270640 + 0.962681i \(0.587235\pi\)
\(102\) 0 0
\(103\) 981.037i 0.938489i −0.883068 0.469245i \(-0.844526\pi\)
0.883068 0.469245i \(-0.155474\pi\)
\(104\) 0 0
\(105\) 77.5922 40.8741i 0.0721164 0.0379895i
\(106\) 0 0
\(107\) −1587.20 −1.43402 −0.717010 0.697063i \(-0.754490\pi\)
−0.717010 + 0.697063i \(0.754490\pi\)
\(108\) 0 0
\(109\) −1665.68 −1.46370 −0.731849 0.681467i \(-0.761342\pi\)
−0.731849 + 0.681467i \(0.761342\pi\)
\(110\) 0 0
\(111\) −773.075 + 407.241i −0.661055 + 0.348231i
\(112\) 0 0
\(113\) 1200.27i 0.999218i −0.866251 0.499609i \(-0.833477\pi\)
0.866251 0.499609i \(-0.166523\pi\)
\(114\) 0 0
\(115\) 107.202i 0.0869273i
\(116\) 0 0
\(117\) −379.068 + 552.762i −0.299529 + 0.436776i
\(118\) 0 0
\(119\) 155.673 0.119920
\(120\) 0 0
\(121\) 94.1163 0.0707110
\(122\) 0 0
\(123\) 928.073 + 1761.78i 0.680338 + 1.29150i
\(124\) 0 0
\(125\) 588.762i 0.421284i
\(126\) 0 0
\(127\) 280.128i 0.195727i 0.995200 + 0.0978637i \(0.0312009\pi\)
−0.995200 + 0.0978637i \(0.968799\pi\)
\(128\) 0 0
\(129\) 899.437 + 1707.42i 0.613884 + 1.16535i
\(130\) 0 0
\(131\) 1897.21 1.26535 0.632673 0.774419i \(-0.281958\pi\)
0.632673 + 0.774419i \(0.281958\pi\)
\(132\) 0 0
\(133\) −479.115 −0.312365
\(134\) 0 0
\(135\) −335.987 39.2424i −0.214201 0.0250181i
\(136\) 0 0
\(137\) 273.452i 0.170530i 0.996358 + 0.0852650i \(0.0271737\pi\)
−0.996358 + 0.0852650i \(0.972826\pi\)
\(138\) 0 0
\(139\) 2371.66i 1.44721i −0.690216 0.723603i \(-0.742485\pi\)
0.690216 0.723603i \(-0.257515\pi\)
\(140\) 0 0
\(141\) −1486.84 + 783.241i −0.888048 + 0.467807i
\(142\) 0 0
\(143\) 937.130 0.548019
\(144\) 0 0
\(145\) 429.373 0.245914
\(146\) 0 0
\(147\) 225.267 118.666i 0.126393 0.0665812i
\(148\) 0 0
\(149\) 2675.69i 1.47115i 0.677444 + 0.735575i \(0.263088\pi\)
−0.677444 + 0.735575i \(0.736912\pi\)
\(150\) 0 0
\(151\) 1868.48i 1.00698i −0.864000 0.503492i \(-0.832048\pi\)
0.864000 0.503492i \(-0.167952\pi\)
\(152\) 0 0
\(153\) −495.198 339.592i −0.261662 0.179441i
\(154\) 0 0
\(155\) 265.016 0.137333
\(156\) 0 0
\(157\) −646.503 −0.328640 −0.164320 0.986407i \(-0.552543\pi\)
−0.164320 + 0.986407i \(0.552543\pi\)
\(158\) 0 0
\(159\) 973.271 + 1847.58i 0.485443 + 0.921528i
\(160\) 0 0
\(161\) 311.231i 0.152351i
\(162\) 0 0
\(163\) 3433.29i 1.64979i −0.565286 0.824895i \(-0.691234\pi\)
0.565286 0.824895i \(-0.308766\pi\)
\(164\) 0 0
\(165\) 220.432 + 418.452i 0.104004 + 0.197433i
\(166\) 0 0
\(167\) −694.557 −0.321835 −0.160917 0.986968i \(-0.551445\pi\)
−0.160917 + 0.986968i \(0.551445\pi\)
\(168\) 0 0
\(169\) −1580.76 −0.719509
\(170\) 0 0
\(171\) 1524.07 + 1045.16i 0.681570 + 0.467401i
\(172\) 0 0
\(173\) 3480.40i 1.52954i 0.644306 + 0.764768i \(0.277146\pi\)
−0.644306 + 0.764768i \(0.722854\pi\)
\(174\) 0 0
\(175\) 834.306i 0.360386i
\(176\) 0 0
\(177\) −156.736 + 82.5655i −0.0665594 + 0.0350622i
\(178\) 0 0
\(179\) 1492.12 0.623054 0.311527 0.950237i \(-0.399160\pi\)
0.311527 + 0.950237i \(0.399160\pi\)
\(180\) 0 0
\(181\) −1970.41 −0.809170 −0.404585 0.914500i \(-0.632584\pi\)
−0.404585 + 0.914500i \(0.632584\pi\)
\(182\) 0 0
\(183\) −117.104 + 61.6882i −0.0473038 + 0.0249187i
\(184\) 0 0
\(185\) 405.451i 0.161132i
\(186\) 0 0
\(187\) 839.538i 0.328305i
\(188\) 0 0
\(189\) −975.442 113.929i −0.375413 0.0438472i
\(190\) 0 0
\(191\) −4547.39 −1.72271 −0.861354 0.508005i \(-0.830383\pi\)
−0.861354 + 0.508005i \(0.830383\pi\)
\(192\) 0 0
\(193\) 1824.96 0.680641 0.340320 0.940310i \(-0.389464\pi\)
0.340320 + 0.940310i \(0.389464\pi\)
\(194\) 0 0
\(195\) 144.952 + 275.166i 0.0532320 + 0.101052i
\(196\) 0 0
\(197\) 1566.13i 0.566406i 0.959060 + 0.283203i \(0.0913971\pi\)
−0.959060 + 0.283203i \(0.908603\pi\)
\(198\) 0 0
\(199\) 686.532i 0.244558i 0.992496 + 0.122279i \(0.0390202\pi\)
−0.992496 + 0.122279i \(0.960980\pi\)
\(200\) 0 0
\(201\) −286.760 544.364i −0.100629 0.191027i
\(202\) 0 0
\(203\) 1246.56 0.430993
\(204\) 0 0
\(205\) 923.994 0.314803
\(206\) 0 0
\(207\) −678.934 + 990.029i −0.227967 + 0.332424i
\(208\) 0 0
\(209\) 2583.85i 0.855159i
\(210\) 0 0
\(211\) 4544.91i 1.48287i −0.671027 0.741433i \(-0.734147\pi\)
0.671027 0.741433i \(-0.265853\pi\)
\(212\) 0 0
\(213\) −490.727 + 258.506i −0.157859 + 0.0831573i
\(214\) 0 0
\(215\) 895.483 0.284053
\(216\) 0 0
\(217\) 769.401 0.240693
\(218\) 0 0
\(219\) −4675.39 + 2462.90i −1.44262 + 0.759943i
\(220\) 0 0
\(221\) 552.064i 0.168036i
\(222\) 0 0
\(223\) 577.067i 0.173288i 0.996239 + 0.0866442i \(0.0276143\pi\)
−0.996239 + 0.0866442i \(0.972386\pi\)
\(224\) 0 0
\(225\) 1819.99 2653.94i 0.539257 0.786352i
\(226\) 0 0
\(227\) 4149.48 1.21326 0.606631 0.794983i \(-0.292521\pi\)
0.606631 + 0.794983i \(0.292521\pi\)
\(228\) 0 0
\(229\) 1006.19 0.290353 0.145176 0.989406i \(-0.453625\pi\)
0.145176 + 0.989406i \(0.453625\pi\)
\(230\) 0 0
\(231\) 639.963 + 1214.86i 0.182279 + 0.346025i
\(232\) 0 0
\(233\) 965.117i 0.271360i −0.990753 0.135680i \(-0.956678\pi\)
0.990753 0.135680i \(-0.0433219\pi\)
\(234\) 0 0
\(235\) 779.798i 0.216461i
\(236\) 0 0
\(237\) 1573.36 + 2986.75i 0.431227 + 0.818608i
\(238\) 0 0
\(239\) −5927.88 −1.60436 −0.802182 0.597080i \(-0.796328\pi\)
−0.802182 + 0.597080i \(0.796328\pi\)
\(240\) 0 0
\(241\) −61.2238 −0.0163642 −0.00818209 0.999967i \(-0.502604\pi\)
−0.00818209 + 0.999967i \(0.502604\pi\)
\(242\) 0 0
\(243\) 2854.36 + 2490.29i 0.753529 + 0.657415i
\(244\) 0 0
\(245\) 118.145i 0.0308081i
\(246\) 0 0
\(247\) 1699.09i 0.437694i
\(248\) 0 0
\(249\) 1153.06 607.408i 0.293462 0.154590i
\(250\) 0 0
\(251\) −5820.29 −1.46364 −0.731820 0.681498i \(-0.761329\pi\)
−0.731820 + 0.681498i \(0.761329\pi\)
\(252\) 0 0
\(253\) 1678.46 0.417089
\(254\) 0 0
\(255\) −246.510 + 129.857i −0.0605376 + 0.0318900i
\(256\) 0 0
\(257\) 7692.91i 1.86720i −0.358316 0.933600i \(-0.616649\pi\)
0.358316 0.933600i \(-0.383351\pi\)
\(258\) 0 0
\(259\) 1177.11i 0.282402i
\(260\) 0 0
\(261\) −3965.33 2719.31i −0.940414 0.644909i
\(262\) 0 0
\(263\) 5540.66 1.29906 0.649528 0.760338i \(-0.274967\pi\)
0.649528 + 0.760338i \(0.274967\pi\)
\(264\) 0 0
\(265\) 968.993 0.224622
\(266\) 0 0
\(267\) 9.75464 + 18.5175i 0.00223586 + 0.00424438i
\(268\) 0 0
\(269\) 5877.35i 1.33215i −0.745885 0.666075i \(-0.767973\pi\)
0.745885 0.666075i \(-0.232027\pi\)
\(270\) 0 0
\(271\) 4057.27i 0.909451i 0.890632 + 0.454726i \(0.150263\pi\)
−0.890632 + 0.454726i \(0.849737\pi\)
\(272\) 0 0
\(273\) 420.828 + 798.867i 0.0932954 + 0.177105i
\(274\) 0 0
\(275\) −4499.38 −0.986628
\(276\) 0 0
\(277\) −2789.26 −0.605019 −0.302509 0.953146i \(-0.597824\pi\)
−0.302509 + 0.953146i \(0.597824\pi\)
\(278\) 0 0
\(279\) −2447.47 1678.41i −0.525184 0.360156i
\(280\) 0 0
\(281\) 1384.14i 0.293847i −0.989148 0.146923i \(-0.953063\pi\)
0.989148 0.146923i \(-0.0469370\pi\)
\(282\) 0 0
\(283\) 876.881i 0.184188i 0.995750 + 0.0920940i \(0.0293560\pi\)
−0.995750 + 0.0920940i \(0.970644\pi\)
\(284\) 0 0
\(285\) 758.685 399.661i 0.157686 0.0830661i
\(286\) 0 0
\(287\) 2682.56 0.551729
\(288\) 0 0
\(289\) 4418.43 0.899334
\(290\) 0 0
\(291\) 2090.40 1101.18i 0.421105 0.221830i
\(292\) 0 0
\(293\) 1594.57i 0.317938i 0.987284 + 0.158969i \(0.0508170\pi\)
−0.987284 + 0.158969i \(0.949183\pi\)
\(294\) 0 0
\(295\) 82.2026i 0.0162238i
\(296\) 0 0
\(297\) 614.415 5260.52i 0.120040 1.02777i
\(298\) 0 0
\(299\) 1103.72 0.213478
\(300\) 0 0
\(301\) 2599.78 0.497837
\(302\) 0 0
\(303\) −4732.88 8984.54i −0.897350 1.70346i
\(304\) 0 0
\(305\) 61.4171i 0.0115303i
\(306\) 0 0
\(307\) 5857.68i 1.08897i −0.838769 0.544487i \(-0.816724\pi\)
0.838769 0.544487i \(-0.183276\pi\)
\(308\) 0 0
\(309\) 2375.84 + 4510.11i 0.437400 + 0.830327i
\(310\) 0 0
\(311\) 9903.55 1.80572 0.902860 0.429936i \(-0.141464\pi\)
0.902860 + 0.429936i \(0.141464\pi\)
\(312\) 0 0
\(313\) −1632.28 −0.294767 −0.147384 0.989079i \(-0.547085\pi\)
−0.147384 + 0.989079i \(0.547085\pi\)
\(314\) 0 0
\(315\) −257.727 + 375.820i −0.0460992 + 0.0672224i
\(316\) 0 0
\(317\) 9820.23i 1.73993i −0.493109 0.869967i \(-0.664140\pi\)
0.493109 0.869967i \(-0.335860\pi\)
\(318\) 0 0
\(319\) 6722.67i 1.17993i
\(320\) 0 0
\(321\) 7296.80 3843.81i 1.26875 0.668351i
\(322\) 0 0
\(323\) 1522.15 0.262212
\(324\) 0 0
\(325\) −2958.70 −0.504983
\(326\) 0 0
\(327\) 7657.61 4033.88i 1.29500 0.682183i
\(328\) 0 0
\(329\) 2263.92i 0.379374i
\(330\) 0 0
\(331\) 5254.69i 0.872580i −0.899806 0.436290i \(-0.856292\pi\)
0.899806 0.436290i \(-0.143708\pi\)
\(332\) 0 0
\(333\) 2567.81 3744.41i 0.422568 0.616193i
\(334\) 0 0
\(335\) −285.500 −0.0465627
\(336\) 0 0
\(337\) 6544.56 1.05788 0.528939 0.848660i \(-0.322590\pi\)
0.528939 + 0.848660i \(0.322590\pi\)
\(338\) 0 0
\(339\) 2906.76 + 5517.97i 0.465704 + 0.884057i
\(340\) 0 0
\(341\) 4149.35i 0.658943i
\(342\) 0 0
\(343\) 343.000i 0.0539949i
\(344\) 0 0
\(345\) 259.618 + 492.839i 0.0405141 + 0.0769088i
\(346\) 0 0
\(347\) 1817.39 0.281161 0.140580 0.990069i \(-0.455103\pi\)
0.140580 + 0.990069i \(0.455103\pi\)
\(348\) 0 0
\(349\) 1436.93 0.220392 0.110196 0.993910i \(-0.464852\pi\)
0.110196 + 0.993910i \(0.464852\pi\)
\(350\) 0 0
\(351\) 404.028 3459.22i 0.0614399 0.526038i
\(352\) 0 0
\(353\) 6308.88i 0.951240i −0.879651 0.475620i \(-0.842224\pi\)
0.879651 0.475620i \(-0.157776\pi\)
\(354\) 0 0
\(355\) 257.369i 0.0384781i
\(356\) 0 0
\(357\) −715.673 + 377.003i −0.106099 + 0.0558911i
\(358\) 0 0
\(359\) −11978.9 −1.76107 −0.880535 0.473981i \(-0.842817\pi\)
−0.880535 + 0.473981i \(0.842817\pi\)
\(360\) 0 0
\(361\) 2174.29 0.316998
\(362\) 0 0
\(363\) −432.680 + 227.927i −0.0625614 + 0.0329561i
\(364\) 0 0
\(365\) 2452.08i 0.351637i
\(366\) 0 0
\(367\) 7399.78i 1.05249i 0.850332 + 0.526247i \(0.176401\pi\)
−0.850332 + 0.526247i \(0.823599\pi\)
\(368\) 0 0
\(369\) −8533.24 5851.85i −1.20386 0.825570i
\(370\) 0 0
\(371\) 2813.20 0.393676
\(372\) 0 0
\(373\) −7730.94 −1.07317 −0.536586 0.843846i \(-0.680286\pi\)
−0.536586 + 0.843846i \(0.680286\pi\)
\(374\) 0 0
\(375\) −1425.84 2706.71i −0.196347 0.372731i
\(376\) 0 0
\(377\) 4420.70i 0.603919i
\(378\) 0 0
\(379\) 10114.3i 1.37081i 0.728161 + 0.685406i \(0.240375\pi\)
−0.728161 + 0.685406i \(0.759625\pi\)
\(380\) 0 0
\(381\) −678.404 1287.83i −0.0912223 0.173169i
\(382\) 0 0
\(383\) 8232.70 1.09836 0.549179 0.835705i \(-0.314940\pi\)
0.549179 + 0.835705i \(0.314940\pi\)
\(384\) 0 0
\(385\) 637.150 0.0843433
\(386\) 0 0
\(387\) −8269.94 5671.29i −1.08627 0.744930i
\(388\) 0 0
\(389\) 4161.68i 0.542430i 0.962519 + 0.271215i \(0.0874255\pi\)
−0.962519 + 0.271215i \(0.912575\pi\)
\(390\) 0 0
\(391\) 988.780i 0.127889i
\(392\) 0 0
\(393\) −8722.04 + 4594.60i −1.11951 + 0.589738i
\(394\) 0 0
\(395\) 1566.44 0.199535
\(396\) 0 0
\(397\) 7101.70 0.897794 0.448897 0.893583i \(-0.351817\pi\)
0.448897 + 0.893583i \(0.351817\pi\)
\(398\) 0 0
\(399\) 2202.63 1160.30i 0.276364 0.145583i
\(400\) 0 0
\(401\) 5017.40i 0.624830i 0.949946 + 0.312415i \(0.101138\pi\)
−0.949946 + 0.312415i \(0.898862\pi\)
\(402\) 0 0
\(403\) 2728.53i 0.337265i
\(404\) 0 0
\(405\) 1639.66 633.271i 0.201174 0.0776975i
\(406\) 0 0
\(407\) −6348.12 −0.773132
\(408\) 0 0
\(409\) −11218.3 −1.35625 −0.678126 0.734946i \(-0.737208\pi\)
−0.678126 + 0.734946i \(0.737208\pi\)
\(410\) 0 0
\(411\) −662.237 1257.14i −0.0794787 0.150876i
\(412\) 0 0
\(413\) 238.652i 0.0284341i
\(414\) 0 0
\(415\) 604.738i 0.0715311i
\(416\) 0 0
\(417\) 5743.60 + 10903.2i 0.674497 + 1.28041i
\(418\) 0 0
\(419\) −14752.8 −1.72010 −0.860051 0.510209i \(-0.829568\pi\)
−0.860051 + 0.510209i \(0.829568\pi\)
\(420\) 0 0
\(421\) 9057.10 1.04849 0.524247 0.851566i \(-0.324347\pi\)
0.524247 + 0.851566i \(0.324347\pi\)
\(422\) 0 0
\(423\) 4938.63 7201.57i 0.567670 0.827783i
\(424\) 0 0
\(425\) 2650.59i 0.302523i
\(426\) 0 0
\(427\) 178.307i 0.0202082i
\(428\) 0 0
\(429\) −4308.26 + 2269.51i −0.484859 + 0.255414i
\(430\) 0 0
\(431\) 4986.14 0.557248 0.278624 0.960400i \(-0.410122\pi\)
0.278624 + 0.960400i \(0.410122\pi\)
\(432\) 0 0
\(433\) −16409.6 −1.82123 −0.910617 0.413251i \(-0.864393\pi\)
−0.910617 + 0.413251i \(0.864393\pi\)
\(434\) 0 0
\(435\) −1973.95 + 1039.84i −0.217572 + 0.114613i
\(436\) 0 0
\(437\) 3043.17i 0.333122i
\(438\) 0 0
\(439\) 13082.8i 1.42235i 0.703017 + 0.711173i \(0.251836\pi\)
−0.703017 + 0.711173i \(0.748164\pi\)
\(440\) 0 0
\(441\) −748.236 + 1091.09i −0.0807943 + 0.117815i
\(442\) 0 0
\(443\) −13847.4 −1.48512 −0.742561 0.669778i \(-0.766389\pi\)
−0.742561 + 0.669778i \(0.766389\pi\)
\(444\) 0 0
\(445\) 9.71176 0.00103457
\(446\) 0 0
\(447\) −6479.89 12300.9i −0.685656 1.30160i
\(448\) 0 0
\(449\) 6503.16i 0.683526i 0.939786 + 0.341763i \(0.111024\pi\)
−0.939786 + 0.341763i \(0.888976\pi\)
\(450\) 0 0
\(451\) 14466.9i 1.51047i
\(452\) 0 0
\(453\) 4525.01 + 8589.93i 0.469323 + 0.890927i
\(454\) 0 0
\(455\) 418.978 0.0431692
\(456\) 0 0
\(457\) 9221.66 0.943920 0.471960 0.881620i \(-0.343547\pi\)
0.471960 + 0.881620i \(0.343547\pi\)
\(458\) 0 0
\(459\) 3098.98 + 361.953i 0.315137 + 0.0368072i
\(460\) 0 0
\(461\) 1969.78i 0.199006i 0.995037 + 0.0995031i \(0.0317253\pi\)
−0.995037 + 0.0995031i \(0.968275\pi\)
\(462\) 0 0
\(463\) 6311.84i 0.633556i −0.948500 0.316778i \(-0.897399\pi\)
0.948500 0.316778i \(-0.102601\pi\)
\(464\) 0 0
\(465\) −1218.36 + 641.807i −0.121505 + 0.0640066i
\(466\) 0 0
\(467\) 5728.26 0.567607 0.283803 0.958883i \(-0.408404\pi\)
0.283803 + 0.958883i \(0.408404\pi\)
\(468\) 0 0
\(469\) −828.868 −0.0816067
\(470\) 0 0
\(471\) 2972.16 1565.68i 0.290764 0.153169i
\(472\) 0 0
\(473\) 14020.5i 1.36293i
\(474\) 0 0
\(475\) 8157.71i 0.788003i
\(476\) 0 0
\(477\) −8948.82 6136.84i −0.858990 0.589071i
\(478\) 0 0
\(479\) −1699.72 −0.162134 −0.0810668 0.996709i \(-0.525833\pi\)
−0.0810668 + 0.996709i \(0.525833\pi\)
\(480\) 0 0
\(481\) −4174.41 −0.395710
\(482\) 0 0
\(483\) 753.727 + 1430.82i 0.0710058 + 0.134792i
\(484\) 0 0
\(485\) 1096.34i 0.102644i
\(486\) 0 0
\(487\) 14278.4i 1.32858i 0.747477 + 0.664288i \(0.231265\pi\)
−0.747477 + 0.664288i \(0.768735\pi\)
\(488\) 0 0
\(489\) 8314.61 + 15783.8i 0.768915 + 1.45965i
\(490\) 0 0
\(491\) 5211.87 0.479039 0.239520 0.970892i \(-0.423010\pi\)
0.239520 + 0.970892i \(0.423010\pi\)
\(492\) 0 0
\(493\) −3960.33 −0.361794
\(494\) 0 0
\(495\) −2026.78 1389.91i −0.184034 0.126206i
\(496\) 0 0
\(497\) 747.199i 0.0674375i
\(498\) 0 0
\(499\) 11136.0i 0.999030i −0.866305 0.499515i \(-0.833512\pi\)
0.866305 0.499515i \(-0.166488\pi\)
\(500\) 0 0
\(501\) 3193.08 1682.05i 0.284743 0.149997i
\(502\) 0 0
\(503\) 7580.62 0.671975 0.335987 0.941867i \(-0.390930\pi\)
0.335987 + 0.941867i \(0.390930\pi\)
\(504\) 0 0
\(505\) −4712.08 −0.415217
\(506\) 0 0
\(507\) 7267.22 3828.23i 0.636585 0.335340i
\(508\) 0 0
\(509\) 7729.01i 0.673050i 0.941675 + 0.336525i \(0.109252\pi\)
−0.941675 + 0.336525i \(0.890748\pi\)
\(510\) 0 0
\(511\) 7118.91i 0.616286i
\(512\) 0 0
\(513\) −9537.72 1113.98i −0.820859 0.0958743i
\(514\) 0 0
\(515\) 2365.39 0.202392
\(516\) 0 0
\(517\) −12209.2 −1.03861
\(518\) 0 0
\(519\) −8428.70 16000.4i −0.712869 1.35326i
\(520\) 0 0
\(521\) 17904.5i 1.50559i 0.658256 + 0.752794i \(0.271294\pi\)
−0.658256 + 0.752794i \(0.728706\pi\)
\(522\) 0 0
\(523\) 3895.89i 0.325728i −0.986649 0.162864i \(-0.947927\pi\)
0.986649 0.162864i \(-0.0520731\pi\)
\(524\) 0 0
\(525\) −2020.49 3835.54i −0.167965 0.318851i
\(526\) 0 0
\(527\) −2444.38 −0.202048
\(528\) 0 0
\(529\) −10190.2 −0.837525
\(530\) 0 0
\(531\) 520.607 759.155i 0.0425469 0.0620424i
\(532\) 0 0
\(533\) 9513.17i 0.773098i
\(534\) 0 0
\(535\) 3826.92i 0.309256i
\(536\) 0 0
\(537\) −6859.73 + 3613.57i −0.551246 + 0.290386i
\(538\) 0 0
\(539\) 1849.78 0.147822
\(540\) 0 0
\(541\) 3979.74 0.316271 0.158135 0.987417i \(-0.449452\pi\)
0.158135 + 0.987417i \(0.449452\pi\)
\(542\) 0 0
\(543\) 9058.56 4771.88i 0.715912 0.377128i
\(544\) 0 0
\(545\) 4016.15i 0.315657i
\(546\) 0 0
\(547\) 7097.89i 0.554815i −0.960752 0.277408i \(-0.910525\pi\)
0.960752 0.277408i \(-0.0894753\pi\)
\(548\) 0 0
\(549\) 388.968 567.197i 0.0302381 0.0440936i
\(550\) 0 0
\(551\) 12188.7 0.942389
\(552\) 0 0
\(553\) 4547.73 0.349709
\(554\) 0 0
\(555\) −981.906 1863.98i −0.0750984 0.142561i
\(556\) 0 0
\(557\) 22347.7i 1.70001i −0.526777 0.850004i \(-0.676600\pi\)
0.526777 0.850004i \(-0.323400\pi\)
\(558\) 0 0
\(559\) 9219.63i 0.697583i
\(560\) 0 0
\(561\) −2033.16 3859.60i −0.153013 0.290468i
\(562\) 0 0
\(563\) 19988.9 1.49632 0.748161 0.663517i \(-0.230937\pi\)
0.748161 + 0.663517i \(0.230937\pi\)
\(564\) 0 0
\(565\) 2893.98 0.215488
\(566\) 0 0
\(567\) 4760.30 1838.52i 0.352582 0.136174i
\(568\) 0 0
\(569\) 20769.4i 1.53023i 0.643896 + 0.765113i \(0.277317\pi\)
−0.643896 + 0.765113i \(0.722683\pi\)
\(570\) 0 0
\(571\) 21679.8i 1.58892i −0.607317 0.794460i \(-0.707754\pi\)
0.607317 0.794460i \(-0.292246\pi\)
\(572\) 0 0
\(573\) 20905.6 11012.7i 1.52416 0.802900i
\(574\) 0 0
\(575\) −5299.22 −0.384335
\(576\) 0 0
\(577\) 18551.7 1.33850 0.669251 0.743036i \(-0.266615\pi\)
0.669251 + 0.743036i \(0.266615\pi\)
\(578\) 0 0
\(579\) −8389.88 + 4419.63i −0.602196 + 0.317225i
\(580\) 0 0
\(581\) 1755.69i 0.125367i
\(582\) 0 0
\(583\) 15171.5i 1.07777i
\(584\) 0 0
\(585\) −1332.77 913.978i −0.0941938 0.0645954i
\(586\) 0 0
\(587\) 661.018 0.0464789 0.0232395 0.999730i \(-0.492602\pi\)
0.0232395 + 0.999730i \(0.492602\pi\)
\(588\) 0 0
\(589\) 7523.08 0.526287
\(590\) 0 0
\(591\) −3792.79 7199.95i −0.263984 0.501127i
\(592\) 0 0
\(593\) 2711.13i 0.187745i −0.995584 0.0938723i \(-0.970075\pi\)
0.995584 0.0938723i \(-0.0299246\pi\)
\(594\) 0 0
\(595\) 375.346i 0.0258616i
\(596\) 0 0
\(597\) −1662.62 3156.18i −0.113981 0.216372i
\(598\) 0 0
\(599\) −15508.6 −1.05787 −0.528934 0.848663i \(-0.677408\pi\)
−0.528934 + 0.848663i \(0.677408\pi\)
\(600\) 0 0
\(601\) −15678.2 −1.06410 −0.532051 0.846712i \(-0.678579\pi\)
−0.532051 + 0.846712i \(0.678579\pi\)
\(602\) 0 0
\(603\) 2636.64 + 1808.13i 0.178063 + 0.122111i
\(604\) 0 0
\(605\) 226.925i 0.0152493i
\(606\) 0 0
\(607\) 13795.5i 0.922474i 0.887277 + 0.461237i \(0.152594\pi\)
−0.887277 + 0.461237i \(0.847406\pi\)
\(608\) 0 0
\(609\) −5730.81 + 3018.88i −0.381321 + 0.200872i
\(610\) 0 0
\(611\) −8028.57 −0.531589
\(612\) 0 0
\(613\) −15763.8 −1.03865 −0.519327 0.854576i \(-0.673817\pi\)
−0.519327 + 0.854576i \(0.673817\pi\)
\(614\) 0 0
\(615\) −4247.87 + 2237.69i −0.278521 + 0.146720i
\(616\) 0 0
\(617\) 18857.2i 1.23041i −0.788369 0.615203i \(-0.789074\pi\)
0.788369 0.615203i \(-0.210926\pi\)
\(618\) 0 0
\(619\) 6139.48i 0.398653i −0.979933 0.199327i \(-0.936125\pi\)
0.979933 0.199327i \(-0.0638755\pi\)
\(620\) 0 0
\(621\) 723.638 6195.67i 0.0467611 0.400360i
\(622\) 0 0
\(623\) 28.1954 0.00181320
\(624\) 0 0
\(625\) 13478.7 0.862639
\(626\) 0 0
\(627\) 6257.46 + 11878.7i 0.398563 + 0.756601i
\(628\) 0 0
\(629\) 3739.69i 0.237060i
\(630\) 0 0
\(631\) 13375.9i 0.843879i 0.906624 + 0.421940i \(0.138651\pi\)
−0.906624 + 0.421940i \(0.861349\pi\)
\(632\) 0 0
\(633\) 11006.7 + 20894.3i 0.691117 + 1.31196i
\(634\) 0 0
\(635\) −675.422 −0.0422100
\(636\) 0 0
\(637\) 1216.38 0.0756592
\(638\) 0 0
\(639\) 1629.98 2376.85i 0.100909 0.147147i
\(640\) 0 0
\(641\) 11907.6i 0.733730i −0.930274 0.366865i \(-0.880431\pi\)
0.930274 0.366865i \(-0.119569\pi\)
\(642\) 0 0
\(643\) 19204.9i 1.17787i −0.808181 0.588934i \(-0.799548\pi\)
0.808181 0.588934i \(-0.200452\pi\)
\(644\) 0 0
\(645\) −4116.79 + 2168.65i −0.251316 + 0.132388i
\(646\) 0 0
\(647\) −21782.7 −1.32359 −0.661797 0.749683i \(-0.730206\pi\)
−0.661797 + 0.749683i \(0.730206\pi\)
\(648\) 0 0
\(649\) −1287.04 −0.0778440
\(650\) 0 0
\(651\) −3537.16 + 1863.31i −0.212953 + 0.112179i
\(652\) 0 0
\(653\) 18414.7i 1.10356i −0.833991 0.551779i \(-0.813949\pi\)
0.833991 0.551779i \(-0.186051\pi\)
\(654\) 0 0
\(655\) 4574.40i 0.272881i
\(656\) 0 0
\(657\) 15529.5 22645.4i 0.922169 1.34472i
\(658\) 0 0
\(659\) 13295.2 0.785900 0.392950 0.919560i \(-0.371455\pi\)
0.392950 + 0.919560i \(0.371455\pi\)
\(660\) 0 0
\(661\) 7708.91 0.453619 0.226809 0.973939i \(-0.427171\pi\)
0.226809 + 0.973939i \(0.427171\pi\)
\(662\) 0 0
\(663\) −1336.97 2538.00i −0.0783161 0.148669i
\(664\) 0 0
\(665\) 1155.20i 0.0673636i
\(666\) 0 0
\(667\) 7917.74i 0.459634i
\(668\) 0 0
\(669\) −1397.52 2652.95i −0.0807642 0.153317i
\(670\) 0 0
\(671\) −961.603 −0.0553238
\(672\) 0 0
\(673\) 5161.68 0.295644 0.147822 0.989014i \(-0.452774\pi\)
0.147822 + 0.989014i \(0.452774\pi\)
\(674\) 0 0
\(675\) −1939.83 + 16608.5i −0.110614 + 0.947054i
\(676\) 0 0
\(677\) 8893.85i 0.504902i −0.967610 0.252451i \(-0.918763\pi\)
0.967610 0.252451i \(-0.0812366\pi\)
\(678\) 0 0
\(679\) 3182.92i 0.179896i
\(680\) 0 0
\(681\) −19076.3 + 10049.1i −1.07343 + 0.565463i
\(682\) 0 0
\(683\) 6631.37 0.371511 0.185756 0.982596i \(-0.440527\pi\)
0.185756 + 0.982596i \(0.440527\pi\)
\(684\) 0 0
\(685\) −659.326 −0.0367760
\(686\) 0 0
\(687\) −4625.74 + 2436.75i −0.256889 + 0.135324i
\(688\) 0 0
\(689\) 9976.47i 0.551630i
\(690\) 0 0
\(691\) 12990.2i 0.715151i −0.933884 0.357575i \(-0.883603\pi\)
0.933884 0.357575i \(-0.116397\pi\)
\(692\) 0 0
\(693\) −5884.19 4035.21i −0.322542 0.221190i
\(694\) 0 0
\(695\) 5718.36 0.312100
\(696\) 0 0
\(697\) −8522.48 −0.463145
\(698\) 0 0
\(699\) 2337.28 + 4436.92i 0.126472 + 0.240085i
\(700\) 0 0
\(701\) 29785.7i 1.60484i −0.596762 0.802418i \(-0.703546\pi\)
0.596762 0.802418i \(-0.296454\pi\)
\(702\) 0 0
\(703\) 11509.6i 0.617488i
\(704\) 0 0
\(705\) −1888.49 3584.96i −0.100886 0.191514i
\(706\) 0 0
\(707\) −13680.2 −0.727718
\(708\) 0 0
\(709\) 36620.8 1.93980 0.969902 0.243494i \(-0.0782938\pi\)
0.969902 + 0.243494i \(0.0782938\pi\)
\(710\) 0 0
\(711\) −14466.4 9920.63i −0.763055 0.523281i
\(712\) 0 0
\(713\) 4886.96i 0.256688i
\(714\) 0 0
\(715\) 2259.53i 0.118184i
\(716\) 0 0
\(717\) 27252.2 14355.9i 1.41946 0.747743i
\(718\) 0 0
\(719\) 2869.67 0.148846 0.0744232 0.997227i \(-0.476288\pi\)
0.0744232 + 0.997227i \(0.476288\pi\)
\(720\) 0 0
\(721\) 6867.26 0.354716
\(722\) 0 0
\(723\) 281.463 148.269i 0.0144782 0.00762683i
\(724\) 0 0
\(725\) 21224.8i 1.08727i
\(726\) 0 0
\(727\) 2342.77i 0.119517i −0.998213 0.0597584i \(-0.980967\pi\)
0.998213 0.0597584i \(-0.0190330\pi\)
\(728\) 0 0
\(729\) −19153.2 4535.97i −0.973084 0.230451i
\(730\) 0 0
\(731\) −8259.51 −0.417905
\(732\) 0 0
\(733\) 35353.2 1.78144 0.890722 0.454548i \(-0.150199\pi\)
0.890722 + 0.454548i \(0.150199\pi\)
\(734\) 0 0
\(735\) 286.119 + 543.146i 0.0143587 + 0.0272575i
\(736\) 0 0
\(737\) 4470.05i 0.223414i
\(738\) 0 0
\(739\) 13978.6i 0.695819i 0.937528 + 0.347909i \(0.113108\pi\)
−0.937528 + 0.347909i \(0.886892\pi\)
\(740\) 0 0
\(741\) 4114.79 + 7811.20i 0.203995 + 0.387249i
\(742\) 0 0
\(743\) −21198.8 −1.04671 −0.523357 0.852114i \(-0.675320\pi\)
−0.523357 + 0.852114i \(0.675320\pi\)
\(744\) 0 0
\(745\) −6451.41 −0.317264
\(746\) 0 0
\(747\) −3829.93 + 5584.86i −0.187590 + 0.273546i
\(748\) 0 0
\(749\) 11110.4i 0.542008i
\(750\) 0 0
\(751\) 17481.5i 0.849415i −0.905331 0.424707i \(-0.860377\pi\)
0.905331 0.424707i \(-0.139623\pi\)
\(752\) 0 0
\(753\) 26757.6 14095.4i 1.29495 0.682157i
\(754\) 0 0
\(755\) 4505.12 0.217163
\(756\) 0 0
\(757\) 10387.5 0.498732 0.249366 0.968409i \(-0.419778\pi\)
0.249366 + 0.968409i \(0.419778\pi\)
\(758\) 0 0
\(759\) −7716.34 + 4064.82i −0.369019 + 0.194392i
\(760\) 0 0
\(761\) 2749.45i 0.130969i 0.997854 + 0.0654846i \(0.0208593\pi\)
−0.997854 + 0.0654846i \(0.979141\pi\)
\(762\) 0 0
\(763\) 11659.7i 0.553226i
\(764\) 0 0
\(765\) 818.797 1193.98i 0.0386976 0.0564293i
\(766\) 0 0
\(767\) −846.334 −0.0398427
\(768\) 0 0
\(769\) −35169.0 −1.64919 −0.824596 0.565722i \(-0.808597\pi\)
−0.824596 + 0.565722i \(0.808597\pi\)
\(770\) 0 0
\(771\) 18630.4 + 35366.5i 0.870243 + 1.65200i
\(772\) 0 0
\(773\) 11491.6i 0.534702i 0.963599 + 0.267351i \(0.0861484\pi\)
−0.963599 + 0.267351i \(0.913852\pi\)
\(774\) 0 0
\(775\) 13100.3i 0.607196i
\(776\) 0 0
\(777\) −2850.69 5411.53i −0.131619 0.249855i
\(778\) 0 0
\(779\) 26229.6 1.20638
\(780\) 0 0
\(781\) −4029.61 −0.184623
\(782\) 0 0
\(783\) 24815.3 + 2898.37i 1.13260 + 0.132285i
\(784\) 0 0
\(785\) 1558.79i 0.0708736i
\(786\) 0 0
\(787\) 38854.5i 1.75987i −0.475098 0.879933i \(-0.657587\pi\)
0.475098 0.879933i \(-0.342413\pi\)
\(788\) 0 0
\(789\) −25472.0 + 13418.2i −1.14934 + 0.605449i
\(790\) 0 0
\(791\) 8401.87 0.377669
\(792\) 0 0
\(793\) −632.332 −0.0283162
\(794\) 0 0
\(795\) −4454.74 + 2346.67i −0.198734 + 0.104689i
\(796\) 0 0
\(797\) 15824.5i 0.703302i −0.936131 0.351651i \(-0.885620\pi\)
0.936131 0.351651i \(-0.114380\pi\)