Properties

Label 1386.2.g.a.881.3
Level $1386$
Weight $2$
Character 1386.881
Analytic conductor $11.067$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.0672657201\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 4 x^{14} + 8 x^{12} + 80 x^{10} + 1189 x^{8} - 2028 x^{6} + 1800 x^{4} + 1080 x^{2} + 324\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{9}\cdot 3^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 881.3
Root \(-0.221383 - 0.534465i\) of defining polynomial
Character \(\chi\) \(=\) 1386.881
Dual form 1386.2.g.a.881.11

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} -1.00000 q^{4} -1.06893 q^{5} +(0.884677 - 2.49346i) q^{7} +1.00000i q^{8} +O(q^{10})\) \(q-1.00000i q^{2} -1.00000 q^{4} -1.06893 q^{5} +(0.884677 - 2.49346i) q^{7} +1.00000i q^{8} +1.06893i q^{10} +1.00000i q^{11} +(-2.49346 - 0.884677i) q^{14} +1.00000 q^{16} +3.91799 q^{17} -7.49534i q^{19} +1.06893 q^{20} +1.00000 q^{22} +5.33067i q^{23} -3.85739 q^{25} +(-0.884677 + 2.49346i) q^{28} -8.01200i q^{29} -3.65862i q^{31} -1.00000i q^{32} -3.91799i q^{34} +(-0.945659 + 2.66534i) q^{35} -7.33067 q^{37} -7.49534 q^{38} -1.06893i q^{40} -2.50842 q^{41} +0.230645 q^{43} -1.00000i q^{44} +5.33067 q^{46} -0.370555 q^{47} +(-5.43469 - 4.41182i) q^{49} +3.85739i q^{50} +7.56132i q^{53} -1.06893i q^{55} +(2.49346 + 0.884677i) q^{56} -8.01200 q^{58} -2.13786 q^{59} -14.2496i q^{61} -3.65862 q^{62} -1.00000 q^{64} +2.47329 q^{67} -3.91799 q^{68} +(2.66534 + 0.945659i) q^{70} -3.15461i q^{71} -0.370555i q^{73} +7.33067i q^{74} +7.49534i q^{76} +(2.49346 + 0.884677i) q^{77} -4.45068 q^{79} -1.06893 q^{80} +2.50842i q^{82} -12.2229 q^{83} -4.18806 q^{85} -0.230645i q^{86} -1.00000 q^{88} -10.0038 q^{89} -5.33067i q^{92} +0.370555i q^{94} +8.01200i q^{95} -12.8528i q^{97} +(-4.41182 + 5.43469i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 16q^{4} - 8q^{7} + O(q^{10}) \) \( 16q - 16q^{4} - 8q^{7} + 16q^{16} + 16q^{22} + 16q^{25} + 8q^{28} - 16q^{37} + 48q^{43} - 16q^{46} + 8q^{49} - 16q^{58} - 16q^{64} + 16q^{67} - 8q^{70} - 16q^{79} + 112q^{85} - 16q^{88} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(1135\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0 0
\(4\) −1.00000 −0.500000
\(5\) −1.06893 −0.478040 −0.239020 0.971015i \(-0.576826\pi\)
−0.239020 + 0.971015i \(0.576826\pi\)
\(6\) 0 0
\(7\) 0.884677 2.49346i 0.334377 0.942440i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 1.06893i 0.338026i
\(11\) 1.00000i 0.301511i
\(12\) 0 0
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) −2.49346 0.884677i −0.666405 0.236440i
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 3.91799 0.950252 0.475126 0.879918i \(-0.342402\pi\)
0.475126 + 0.879918i \(0.342402\pi\)
\(18\) 0 0
\(19\) 7.49534i 1.71955i −0.510674 0.859774i \(-0.670604\pi\)
0.510674 0.859774i \(-0.329396\pi\)
\(20\) 1.06893 0.239020
\(21\) 0 0
\(22\) 1.00000 0.213201
\(23\) 5.33067i 1.11152i 0.831342 + 0.555761i \(0.187573\pi\)
−0.831342 + 0.555761i \(0.812427\pi\)
\(24\) 0 0
\(25\) −3.85739 −0.771477
\(26\) 0 0
\(27\) 0 0
\(28\) −0.884677 + 2.49346i −0.167188 + 0.471220i
\(29\) 8.01200i 1.48779i −0.668296 0.743895i \(-0.732976\pi\)
0.668296 0.743895i \(-0.267024\pi\)
\(30\) 0 0
\(31\) 3.65862i 0.657108i −0.944485 0.328554i \(-0.893439\pi\)
0.944485 0.328554i \(-0.106561\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) 3.91799i 0.671930i
\(35\) −0.945659 + 2.66534i −0.159846 + 0.450524i
\(36\) 0 0
\(37\) −7.33067 −1.20516 −0.602578 0.798060i \(-0.705860\pi\)
−0.602578 + 0.798060i \(0.705860\pi\)
\(38\) −7.49534 −1.21590
\(39\) 0 0
\(40\) 1.06893i 0.169013i
\(41\) −2.50842 −0.391749 −0.195874 0.980629i \(-0.562754\pi\)
−0.195874 + 0.980629i \(0.562754\pi\)
\(42\) 0 0
\(43\) 0.230645 0.0351730 0.0175865 0.999845i \(-0.494402\pi\)
0.0175865 + 0.999845i \(0.494402\pi\)
\(44\) 1.00000i 0.150756i
\(45\) 0 0
\(46\) 5.33067 0.785965
\(47\) −0.370555 −0.0540510 −0.0270255 0.999635i \(-0.508604\pi\)
−0.0270255 + 0.999635i \(0.508604\pi\)
\(48\) 0 0
\(49\) −5.43469 4.41182i −0.776384 0.630260i
\(50\) 3.85739i 0.545517i
\(51\) 0 0
\(52\) 0 0
\(53\) 7.56132i 1.03863i 0.854584 + 0.519313i \(0.173812\pi\)
−0.854584 + 0.519313i \(0.826188\pi\)
\(54\) 0 0
\(55\) 1.06893i 0.144135i
\(56\) 2.49346 + 0.884677i 0.333203 + 0.118220i
\(57\) 0 0
\(58\) −8.01200 −1.05203
\(59\) −2.13786 −0.278326 −0.139163 0.990269i \(-0.544441\pi\)
−0.139163 + 0.990269i \(0.544441\pi\)
\(60\) 0 0
\(61\) 14.2496i 1.82447i −0.409667 0.912235i \(-0.634355\pi\)
0.409667 0.912235i \(-0.365645\pi\)
\(62\) −3.65862 −0.464646
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 2.47329 0.302160 0.151080 0.988522i \(-0.451725\pi\)
0.151080 + 0.988522i \(0.451725\pi\)
\(68\) −3.91799 −0.475126
\(69\) 0 0
\(70\) 2.66534 + 0.945659i 0.318569 + 0.113028i
\(71\) 3.15461i 0.374383i −0.982323 0.187192i \(-0.940061\pi\)
0.982323 0.187192i \(-0.0599385\pi\)
\(72\) 0 0
\(73\) 0.370555i 0.0433701i −0.999765 0.0216851i \(-0.993097\pi\)
0.999765 0.0216851i \(-0.00690311\pi\)
\(74\) 7.33067i 0.852173i
\(75\) 0 0
\(76\) 7.49534i 0.859774i
\(77\) 2.49346 + 0.884677i 0.284156 + 0.100818i
\(78\) 0 0
\(79\) −4.45068 −0.500740 −0.250370 0.968150i \(-0.580552\pi\)
−0.250370 + 0.968150i \(0.580552\pi\)
\(80\) −1.06893 −0.119510
\(81\) 0 0
\(82\) 2.50842i 0.277008i
\(83\) −12.2229 −1.34164 −0.670818 0.741622i \(-0.734057\pi\)
−0.670818 + 0.741622i \(0.734057\pi\)
\(84\) 0 0
\(85\) −4.18806 −0.454259
\(86\) 0.230645i 0.0248711i
\(87\) 0 0
\(88\) −1.00000 −0.106600
\(89\) −10.0038 −1.06040 −0.530198 0.847874i \(-0.677882\pi\)
−0.530198 + 0.847874i \(0.677882\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 5.33067i 0.555761i
\(93\) 0 0
\(94\) 0.370555i 0.0382198i
\(95\) 8.01200i 0.822013i
\(96\) 0 0
\(97\) 12.8528i 1.30501i −0.757786 0.652503i \(-0.773719\pi\)
0.757786 0.652503i \(-0.226281\pi\)
\(98\) −4.41182 + 5.43469i −0.445661 + 0.548987i
\(99\) 0 0
\(100\) 3.85739 0.385739
\(101\) −14.0030 −1.39335 −0.696676 0.717386i \(-0.745339\pi\)
−0.696676 + 0.717386i \(0.745339\pi\)
\(102\) 0 0
\(103\) 12.2229i 1.20436i 0.798361 + 0.602179i \(0.205701\pi\)
−0.798361 + 0.602179i \(0.794299\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 7.56132 0.734420
\(107\) 20.4081i 1.97292i −0.163988 0.986462i \(-0.552436\pi\)
0.163988 0.986462i \(-0.447564\pi\)
\(108\) 0 0
\(109\) 12.8814 1.23381 0.616906 0.787037i \(-0.288386\pi\)
0.616906 + 0.787037i \(0.288386\pi\)
\(110\) −1.06893 −0.101919
\(111\) 0 0
\(112\) 0.884677 2.49346i 0.0835942 0.235610i
\(113\) 6.92396i 0.651352i −0.945481 0.325676i \(-0.894408\pi\)
0.945481 0.325676i \(-0.105592\pi\)
\(114\) 0 0
\(115\) 5.69812i 0.531352i
\(116\) 8.01200i 0.743895i
\(117\) 0 0
\(118\) 2.13786i 0.196806i
\(119\) 3.46616 9.76935i 0.317742 0.895555i
\(120\) 0 0
\(121\) −1.00000 −0.0909091
\(122\) −14.2496 −1.29009
\(123\) 0 0
\(124\) 3.65862i 0.328554i
\(125\) 9.46793 0.846838
\(126\) 0 0
\(127\) 10.6267 0.942971 0.471485 0.881874i \(-0.343718\pi\)
0.471485 + 0.881874i \(0.343718\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0 0
\(130\) 0 0
\(131\) 3.23670 0.282792 0.141396 0.989953i \(-0.454841\pi\)
0.141396 + 0.989953i \(0.454841\pi\)
\(132\) 0 0
\(133\) −18.6893 6.63096i −1.62057 0.574977i
\(134\) 2.47329i 0.213659i
\(135\) 0 0
\(136\) 3.91799i 0.335965i
\(137\) 10.7159i 0.915523i 0.889075 + 0.457762i \(0.151349\pi\)
−0.889075 + 0.457762i \(0.848651\pi\)
\(138\) 0 0
\(139\) 6.24832i 0.529975i −0.964252 0.264988i \(-0.914632\pi\)
0.964252 0.264988i \(-0.0853679\pi\)
\(140\) 0.945659 2.66534i 0.0799228 0.225262i
\(141\) 0 0
\(142\) −3.15461 −0.264729
\(143\) 0 0
\(144\) 0 0
\(145\) 8.56427i 0.711224i
\(146\) −0.370555 −0.0306673
\(147\) 0 0
\(148\) 7.33067 0.602578
\(149\) 12.8694i 1.05430i 0.849772 + 0.527150i \(0.176740\pi\)
−0.849772 + 0.527150i \(0.823260\pi\)
\(150\) 0 0
\(151\) −8.61475 −0.701058 −0.350529 0.936552i \(-0.613998\pi\)
−0.350529 + 0.936552i \(0.613998\pi\)
\(152\) 7.49534 0.607952
\(153\) 0 0
\(154\) 0.884677 2.49346i 0.0712893 0.200929i
\(155\) 3.91082i 0.314124i
\(156\) 0 0
\(157\) 4.39973i 0.351137i −0.984467 0.175568i \(-0.943824\pi\)
0.984467 0.175568i \(-0.0561763\pi\)
\(158\) 4.45068i 0.354077i
\(159\) 0 0
\(160\) 1.06893i 0.0845064i
\(161\) 13.2918 + 4.71593i 1.04754 + 0.371667i
\(162\) 0 0
\(163\) 12.6933 0.994217 0.497109 0.867688i \(-0.334395\pi\)
0.497109 + 0.867688i \(0.334395\pi\)
\(164\) 2.50842 0.195874
\(165\) 0 0
\(166\) 12.2229i 0.948680i
\(167\) −3.80680 −0.294579 −0.147290 0.989093i \(-0.547055\pi\)
−0.147290 + 0.989093i \(0.547055\pi\)
\(168\) 0 0
\(169\) 13.0000 1.00000
\(170\) 4.18806i 0.321210i
\(171\) 0 0
\(172\) −0.230645 −0.0175865
\(173\) 20.9353 1.59168 0.795842 0.605504i \(-0.207029\pi\)
0.795842 + 0.605504i \(0.207029\pi\)
\(174\) 0 0
\(175\) −3.41254 + 9.61824i −0.257964 + 0.727071i
\(176\) 1.00000i 0.0753778i
\(177\) 0 0
\(178\) 10.0038i 0.749813i
\(179\) 6.47329i 0.483836i 0.970297 + 0.241918i \(0.0777765\pi\)
−0.970297 + 0.241918i \(0.922223\pi\)
\(180\) 0 0
\(181\) 18.1804i 1.35134i 0.737206 + 0.675668i \(0.236145\pi\)
−0.737206 + 0.675668i \(0.763855\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −5.33067 −0.392982
\(185\) 7.83598 0.576113
\(186\) 0 0
\(187\) 3.91799i 0.286512i
\(188\) 0.370555 0.0270255
\(189\) 0 0
\(190\) 8.01200 0.581251
\(191\) 18.2320i 1.31922i 0.751607 + 0.659612i \(0.229279\pi\)
−0.751607 + 0.659612i \(0.770721\pi\)
\(192\) 0 0
\(193\) −1.05343 −0.0758275 −0.0379137 0.999281i \(-0.512071\pi\)
−0.0379137 + 0.999281i \(0.512071\pi\)
\(194\) −12.8528 −0.922778
\(195\) 0 0
\(196\) 5.43469 + 4.41182i 0.388192 + 0.315130i
\(197\) 20.8494i 1.48546i −0.669592 0.742729i \(-0.733531\pi\)
0.669592 0.742729i \(-0.266469\pi\)
\(198\) 0 0
\(199\) 14.3736i 1.01892i 0.860496 + 0.509458i \(0.170154\pi\)
−0.860496 + 0.509458i \(0.829846\pi\)
\(200\) 3.85739i 0.272758i
\(201\) 0 0
\(202\) 14.0030i 0.985249i
\(203\) −19.9776 7.08803i −1.40215 0.497482i
\(204\) 0 0
\(205\) 2.68132 0.187272
\(206\) 12.2229 0.851609
\(207\) 0 0
\(208\) 0 0
\(209\) 7.49534 0.518463
\(210\) 0 0
\(211\) 9.94542 0.684671 0.342335 0.939578i \(-0.388782\pi\)
0.342335 + 0.939578i \(0.388782\pi\)
\(212\) 7.56132i 0.519313i
\(213\) 0 0
\(214\) −20.4081 −1.39507
\(215\) −0.246544 −0.0168141
\(216\) 0 0
\(217\) −9.12264 3.23670i −0.619285 0.219722i
\(218\) 12.8814i 0.872437i
\(219\) 0 0
\(220\) 1.06893i 0.0720673i
\(221\) 0 0
\(222\) 0 0
\(223\) 20.5648i 1.37712i −0.725180 0.688560i \(-0.758243\pi\)
0.725180 0.688560i \(-0.241757\pi\)
\(224\) −2.49346 0.884677i −0.166601 0.0591100i
\(225\) 0 0
\(226\) −6.92396 −0.460575
\(227\) 22.9250 1.52159 0.760794 0.648994i \(-0.224810\pi\)
0.760794 + 0.648994i \(0.224810\pi\)
\(228\) 0 0
\(229\) 27.2136i 1.79832i −0.437617 0.899162i \(-0.644177\pi\)
0.437617 0.899162i \(-0.355823\pi\)
\(230\) −5.69812 −0.375723
\(231\) 0 0
\(232\) 8.01200 0.526013
\(233\) 14.4853i 0.948962i −0.880266 0.474481i \(-0.842636\pi\)
0.880266 0.474481i \(-0.157364\pi\)
\(234\) 0 0
\(235\) 0.396097 0.0258385
\(236\) 2.13786 0.139163
\(237\) 0 0
\(238\) −9.76935 3.46616i −0.633253 0.224678i
\(239\) 7.81595i 0.505572i −0.967522 0.252786i \(-0.918653\pi\)
0.967522 0.252786i \(-0.0813469\pi\)
\(240\) 0 0
\(241\) 23.1844i 1.49344i 0.665140 + 0.746719i \(0.268372\pi\)
−0.665140 + 0.746719i \(0.731628\pi\)
\(242\) 1.00000i 0.0642824i
\(243\) 0 0
\(244\) 14.2496i 0.912235i
\(245\) 5.80931 + 4.71593i 0.371143 + 0.301289i
\(246\) 0 0
\(247\) 0 0
\(248\) 3.65862 0.232323
\(249\) 0 0
\(250\) 9.46793i 0.598805i
\(251\) 12.1117 0.764484 0.382242 0.924062i \(-0.375152\pi\)
0.382242 + 0.924062i \(0.375152\pi\)
\(252\) 0 0
\(253\) −5.33067 −0.335137
\(254\) 10.6267i 0.666781i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 10.0038 0.624017 0.312008 0.950079i \(-0.398998\pi\)
0.312008 + 0.950079i \(0.398998\pi\)
\(258\) 0 0
\(259\) −6.48528 + 18.2787i −0.402976 + 1.13579i
\(260\) 0 0
\(261\) 0 0
\(262\) 3.23670i 0.199964i
\(263\) 7.37464i 0.454740i 0.973808 + 0.227370i \(0.0730127\pi\)
−0.973808 + 0.227370i \(0.926987\pi\)
\(264\) 0 0
\(265\) 8.08252i 0.496506i
\(266\) −6.63096 + 18.6893i −0.406570 + 1.14592i
\(267\) 0 0
\(268\) −2.47329 −0.151080
\(269\) 9.41082 0.573788 0.286894 0.957962i \(-0.407377\pi\)
0.286894 + 0.957962i \(0.407377\pi\)
\(270\) 0 0
\(271\) 27.0725i 1.64454i 0.569101 + 0.822268i \(0.307291\pi\)
−0.569101 + 0.822268i \(0.692709\pi\)
\(272\) 3.91799 0.237563
\(273\) 0 0
\(274\) 10.7159 0.647373
\(275\) 3.85739i 0.232609i
\(276\) 0 0
\(277\) 17.8279 1.07118 0.535589 0.844479i \(-0.320090\pi\)
0.535589 + 0.844479i \(0.320090\pi\)
\(278\) −6.24832 −0.374749
\(279\) 0 0
\(280\) −2.66534 0.945659i −0.159284 0.0565139i
\(281\) 22.9706i 1.37031i −0.728398 0.685154i \(-0.759735\pi\)
0.728398 0.685154i \(-0.240265\pi\)
\(282\) 0 0
\(283\) 10.3615i 0.615926i −0.951398 0.307963i \(-0.900353\pi\)
0.951398 0.307963i \(-0.0996474\pi\)
\(284\) 3.15461i 0.187192i
\(285\) 0 0
\(286\) 0 0
\(287\) −2.21914 + 6.25464i −0.130992 + 0.369200i
\(288\) 0 0
\(289\) −1.64935 −0.0970206
\(290\) 8.56427 0.502911
\(291\) 0 0
\(292\) 0.370555i 0.0216851i
\(293\) 10.9615 0.640377 0.320189 0.947354i \(-0.396254\pi\)
0.320189 + 0.947354i \(0.396254\pi\)
\(294\) 0 0
\(295\) 2.28523 0.133051
\(296\) 7.33067i 0.426087i
\(297\) 0 0
\(298\) 12.8694 0.745503
\(299\) 0 0
\(300\) 0 0
\(301\) 0.204046 0.575104i 0.0117610 0.0331485i
\(302\) 8.61475i 0.495723i
\(303\) 0 0
\(304\) 7.49534i 0.429887i
\(305\) 15.2318i 0.872170i
\(306\) 0 0
\(307\) 30.4845i 1.73985i 0.493188 + 0.869923i \(0.335831\pi\)
−0.493188 + 0.869923i \(0.664169\pi\)
\(308\) −2.49346 0.884677i −0.142078 0.0504092i
\(309\) 0 0
\(310\) 3.91082 0.222119
\(311\) −8.19371 −0.464623 −0.232311 0.972641i \(-0.574629\pi\)
−0.232311 + 0.972641i \(0.574629\pi\)
\(312\) 0 0
\(313\) 33.2694i 1.88050i −0.340487 0.940249i \(-0.610592\pi\)
0.340487 0.940249i \(-0.389408\pi\)
\(314\) −4.39973 −0.248291
\(315\) 0 0
\(316\) 4.45068 0.250370
\(317\) 14.6627i 0.823541i −0.911288 0.411770i \(-0.864911\pi\)
0.911288 0.411770i \(-0.135089\pi\)
\(318\) 0 0
\(319\) 8.01200 0.448586
\(320\) 1.06893 0.0597550
\(321\) 0 0
\(322\) 4.71593 13.2918i 0.262808 0.740724i
\(323\) 29.3667i 1.63400i
\(324\) 0 0
\(325\) 0 0
\(326\) 12.6933i 0.703018i
\(327\) 0 0
\(328\) 2.50842i 0.138504i
\(329\) −0.327821 + 0.923963i −0.0180734 + 0.0509398i
\(330\) 0 0
\(331\) −6.88936 −0.378673 −0.189337 0.981912i \(-0.560634\pi\)
−0.189337 + 0.981912i \(0.560634\pi\)
\(332\) 12.2229 0.670818
\(333\) 0 0
\(334\) 3.80680i 0.208299i
\(335\) −2.64377 −0.144445
\(336\) 0 0
\(337\) −5.12264 −0.279048 −0.139524 0.990219i \(-0.544557\pi\)
−0.139524 + 0.990219i \(0.544557\pi\)
\(338\) 13.0000i 0.707107i
\(339\) 0 0
\(340\) 4.18806 0.227129
\(341\) 3.65862 0.198126
\(342\) 0 0
\(343\) −15.8086 + 9.64815i −0.853586 + 0.520951i
\(344\) 0.230645i 0.0124355i
\(345\) 0 0
\(346\) 20.9353i 1.12549i
\(347\) 11.6399i 0.624862i 0.949940 + 0.312431i \(0.101143\pi\)
−0.949940 + 0.312431i \(0.898857\pi\)
\(348\) 0 0
\(349\) 27.3248i 1.46266i −0.682023 0.731330i \(-0.738900\pi\)
0.682023 0.731330i \(-0.261100\pi\)
\(350\) 9.61824 + 3.41254i 0.514117 + 0.182408i
\(351\) 0 0
\(352\) 1.00000 0.0533002
\(353\) −1.45231 −0.0772985 −0.0386493 0.999253i \(-0.512306\pi\)
−0.0386493 + 0.999253i \(0.512306\pi\)
\(354\) 0 0
\(355\) 3.37206i 0.178970i
\(356\) 10.0038 0.530198
\(357\) 0 0
\(358\) 6.47329 0.342124
\(359\) 0.196041i 0.0103467i 0.999987 + 0.00517333i \(0.00164673\pi\)
−0.999987 + 0.00517333i \(0.998353\pi\)
\(360\) 0 0
\(361\) −37.1801 −1.95685
\(362\) 18.1804 0.955539
\(363\) 0 0
\(364\) 0 0
\(365\) 0.396097i 0.0207327i
\(366\) 0 0
\(367\) 2.02667i 0.105791i −0.998600 0.0528957i \(-0.983155\pi\)
0.998600 0.0528957i \(-0.0168451\pi\)
\(368\) 5.33067i 0.277881i
\(369\) 0 0
\(370\) 7.83598i 0.407373i
\(371\) 18.8538 + 6.68933i 0.978843 + 0.347293i
\(372\) 0 0
\(373\) 26.2001 1.35659 0.678294 0.734791i \(-0.262720\pi\)
0.678294 + 0.734791i \(0.262720\pi\)
\(374\) 3.91799 0.202594
\(375\) 0 0
\(376\) 0.370555i 0.0191099i
\(377\) 0 0
\(378\) 0 0
\(379\) 8.69332 0.446546 0.223273 0.974756i \(-0.428326\pi\)
0.223273 + 0.974756i \(0.428326\pi\)
\(380\) 8.01200i 0.411007i
\(381\) 0 0
\(382\) 18.2320 0.932832
\(383\) −5.89330 −0.301133 −0.150567 0.988600i \(-0.548110\pi\)
−0.150567 + 0.988600i \(0.548110\pi\)
\(384\) 0 0
\(385\) −2.66534 0.945659i −0.135838 0.0481952i
\(386\) 1.05343i 0.0536181i
\(387\) 0 0
\(388\) 12.8528i 0.652503i
\(389\) 11.5853i 0.587398i 0.955898 + 0.293699i \(0.0948864\pi\)
−0.955898 + 0.293699i \(0.905114\pi\)
\(390\) 0 0
\(391\) 20.8855i 1.05623i
\(392\) 4.41182 5.43469i 0.222830 0.274493i
\(393\) 0 0
\(394\) −20.8494 −1.05038
\(395\) 4.75747 0.239374
\(396\) 0 0
\(397\) 28.1414i 1.41238i 0.708024 + 0.706188i \(0.249587\pi\)
−0.708024 + 0.706188i \(0.750413\pi\)
\(398\) 14.3736 0.720482
\(399\) 0 0
\(400\) −3.85739 −0.192869
\(401\) 24.4547i 1.22121i −0.791936 0.610605i \(-0.790927\pi\)
0.791936 0.610605i \(-0.209073\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 14.0030 0.696676
\(405\) 0 0
\(406\) −7.08803 + 19.9776i −0.351773 + 0.991471i
\(407\) 7.33067i 0.363368i
\(408\) 0 0
\(409\) 10.8503i 0.536513i −0.963348 0.268257i \(-0.913553\pi\)
0.963348 0.268257i \(-0.0864475\pi\)
\(410\) 2.68132i 0.132421i
\(411\) 0 0
\(412\) 12.2229i 0.602179i
\(413\) −1.89132 + 5.33067i −0.0930657 + 0.262305i
\(414\) 0 0
\(415\) 13.0654 0.641356
\(416\) 0 0
\(417\) 0 0
\(418\) 7.49534i 0.366609i
\(419\) −8.57709 −0.419018 −0.209509 0.977807i \(-0.567187\pi\)
−0.209509 + 0.977807i \(0.567187\pi\)
\(420\) 0 0
\(421\) 2.36011 0.115025 0.0575124 0.998345i \(-0.481683\pi\)
0.0575124 + 0.998345i \(0.481683\pi\)
\(422\) 9.94542i 0.484135i
\(423\) 0 0
\(424\) −7.56132 −0.367210
\(425\) −15.1132 −0.733098
\(426\) 0 0
\(427\) −35.5307 12.6063i −1.71945 0.610060i
\(428\) 20.4081i 0.986462i
\(429\) 0 0
\(430\) 0.246544i 0.0118894i
\(431\) 39.7508i 1.91473i 0.288886 + 0.957363i \(0.406715\pi\)
−0.288886 + 0.957363i \(0.593285\pi\)
\(432\) 0 0
\(433\) 0.765276i 0.0367768i 0.999831 + 0.0183884i \(0.00585354\pi\)
−0.999831 + 0.0183884i \(0.994146\pi\)
\(434\) −3.23670 + 9.12264i −0.155367 + 0.437901i
\(435\) 0 0
\(436\) −12.8814 −0.616906
\(437\) 39.9552 1.91132
\(438\) 0 0
\(439\) 30.9149i 1.47549i 0.675080 + 0.737744i \(0.264109\pi\)
−0.675080 + 0.737744i \(0.735891\pi\)
\(440\) 1.06893 0.0509593
\(441\) 0 0
\(442\) 0 0
\(443\) 18.3641i 0.872506i 0.899824 + 0.436253i \(0.143695\pi\)
−0.899824 + 0.436253i \(0.856305\pi\)
\(444\) 0 0
\(445\) 10.6933 0.506912
\(446\) −20.5648 −0.973771
\(447\) 0 0
\(448\) −0.884677 + 2.49346i −0.0417971 + 0.117805i
\(449\) 3.80133i 0.179396i −0.995969 0.0896979i \(-0.971410\pi\)
0.995969 0.0896979i \(-0.0285901\pi\)
\(450\) 0 0
\(451\) 2.50842i 0.118117i
\(452\) 6.92396i 0.325676i
\(453\) 0 0
\(454\) 22.9250i 1.07592i
\(455\) 0 0
\(456\) 0 0
\(457\) 6.48528 0.303369 0.151684 0.988429i \(-0.451530\pi\)
0.151684 + 0.988429i \(0.451530\pi\)
\(458\) −27.2136 −1.27161
\(459\) 0 0
\(460\) 5.69812i 0.265676i
\(461\) 11.1839 0.520885 0.260442 0.965489i \(-0.416132\pi\)
0.260442 + 0.965489i \(0.416132\pi\)
\(462\) 0 0
\(463\) 33.7840 1.57007 0.785037 0.619448i \(-0.212644\pi\)
0.785037 + 0.619448i \(0.212644\pi\)
\(464\) 8.01200i 0.371948i
\(465\) 0 0
\(466\) −14.4853 −0.671018
\(467\) 31.8968 1.47601 0.738005 0.674796i \(-0.235768\pi\)
0.738005 + 0.674796i \(0.235768\pi\)
\(468\) 0 0
\(469\) 2.18806 6.16704i 0.101035 0.284767i
\(470\) 0.396097i 0.0182706i
\(471\) 0 0
\(472\) 2.13786i 0.0984030i
\(473\) 0.230645i 0.0106051i
\(474\) 0 0
\(475\) 28.9124i 1.32659i
\(476\) −3.46616 + 9.76935i −0.158871 + 0.447778i
\(477\) 0 0
\(478\) −7.81595 −0.357493
\(479\) −40.1419 −1.83413 −0.917065 0.398737i \(-0.869449\pi\)
−0.917065 + 0.398737i \(0.869449\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 23.1844 1.05602
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) 13.7388i 0.623845i
\(486\) 0 0
\(487\) −5.82394 −0.263908 −0.131954 0.991256i \(-0.542125\pi\)
−0.131954 + 0.991256i \(0.542125\pi\)
\(488\) 14.2496 0.645047
\(489\) 0 0
\(490\) 4.71593 5.80931i 0.213044 0.262438i
\(491\) 15.9920i 0.721710i −0.932622 0.360855i \(-0.882485\pi\)
0.932622 0.360855i \(-0.117515\pi\)
\(492\) 0 0
\(493\) 31.3909i 1.41378i
\(494\) 0 0
\(495\) 0 0
\(496\) 3.65862i 0.164277i
\(497\) −7.86589 2.79081i −0.352833 0.125185i
\(498\) 0 0
\(499\) 17.6199 0.788776 0.394388 0.918944i \(-0.370957\pi\)
0.394388 + 0.918944i \(0.370957\pi\)
\(500\) −9.46793 −0.423419
\(501\) 0 0
\(502\) 12.1117i 0.540572i
\(503\) −0.468921 −0.0209081 −0.0104541 0.999945i \(-0.503328\pi\)
−0.0104541 + 0.999945i \(0.503328\pi\)
\(504\) 0 0
\(505\) 14.9683 0.666079
\(506\) 5.33067i 0.236977i
\(507\) 0 0
\(508\) −10.6267 −0.471485
\(509\) 13.6865 0.606645 0.303323 0.952888i \(-0.401904\pi\)
0.303323 + 0.952888i \(0.401904\pi\)
\(510\) 0 0
\(511\) −0.923963 0.327821i −0.0408737 0.0145020i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 10.0038i 0.441247i
\(515\) 13.0654i 0.575731i
\(516\) 0 0
\(517\) 0.370555i 0.0162970i
\(518\) 18.2787 + 6.48528i 0.803122 + 0.284947i
\(519\) 0 0
\(520\) 0 0
\(521\) 5.70239 0.249826 0.124913 0.992168i \(-0.460135\pi\)
0.124913 + 0.992168i \(0.460135\pi\)
\(522\) 0 0
\(523\) 3.94790i 0.172630i 0.996268 + 0.0863148i \(0.0275091\pi\)
−0.996268 + 0.0863148i \(0.972491\pi\)
\(524\) −3.23670 −0.141396
\(525\) 0 0
\(526\) 7.37464 0.321550
\(527\) 14.3345i 0.624419i
\(528\) 0 0
\(529\) −5.41607 −0.235481
\(530\) −8.08252 −0.351082
\(531\) 0 0
\(532\) 18.6893 + 6.63096i 0.810285 + 0.287488i
\(533\) 0 0
\(534\) 0 0
\(535\) 21.8148i 0.943138i
\(536\) 2.47329i 0.106830i
\(537\) 0 0
\(538\) 9.41082i 0.405729i
\(539\) 4.41182 5.43469i 0.190030 0.234089i
\(540\) 0 0
\(541\) 30.6613 1.31823 0.659117 0.752040i \(-0.270930\pi\)
0.659117 + 0.752040i \(0.270930\pi\)
\(542\) 27.0725 1.16286
\(543\) 0 0
\(544\) 3.91799i 0.167982i
\(545\) −13.7693 −0.589812
\(546\) 0 0
\(547\) 2.05458 0.0878475 0.0439238 0.999035i \(-0.486014\pi\)
0.0439238 + 0.999035i \(0.486014\pi\)
\(548\) 10.7159i 0.457762i
\(549\) 0 0
\(550\) −3.85739 −0.164480
\(551\) −60.0526 −2.55833
\(552\) 0 0
\(553\) −3.93741 + 11.0976i −0.167436 + 0.471918i
\(554\) 17.8279i 0.757437i
\(555\) 0 0
\(556\) 6.24832i 0.264988i
\(557\) 20.8494i 0.883418i −0.897158 0.441709i \(-0.854372\pi\)
0.897158 0.441709i \(-0.145628\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) −0.945659 + 2.66534i −0.0399614 + 0.112631i
\(561\) 0 0
\(562\) −22.9706 −0.968955
\(563\) −41.7225 −1.75839 −0.879197 0.476459i \(-0.841920\pi\)
−0.879197 + 0.476459i \(0.841920\pi\)
\(564\) 0 0
\(565\) 7.40124i 0.311372i
\(566\) −10.3615 −0.435526
\(567\) 0 0
\(568\) 3.15461 0.132364
\(569\) 2.48528i 0.104188i −0.998642 0.0520942i \(-0.983410\pi\)
0.998642 0.0520942i \(-0.0165896\pi\)
\(570\) 0 0
\(571\) −19.4412 −0.813590 −0.406795 0.913520i \(-0.633354\pi\)
−0.406795 + 0.913520i \(0.633354\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 6.25464 + 2.21914i 0.261063 + 0.0926251i
\(575\) 20.5625i 0.857514i
\(576\) 0 0
\(577\) 4.49810i 0.187258i −0.995607 0.0936292i \(-0.970153\pi\)
0.995607 0.0936292i \(-0.0298468\pi\)
\(578\) 1.64935i 0.0686039i
\(579\) 0 0
\(580\) 8.56427i 0.355612i
\(581\) −10.8133 + 30.4773i −0.448612 + 1.26441i
\(582\) 0 0
\(583\) −7.56132 −0.313158
\(584\) 0.370555 0.0153337
\(585\) 0 0
\(586\) 10.9615i 0.452815i
\(587\) −37.2388 −1.53701 −0.768504 0.639845i \(-0.778999\pi\)
−0.768504 + 0.639845i \(0.778999\pi\)
\(588\) 0 0
\(589\) −27.4226 −1.12993
\(590\) 2.28523i 0.0940812i
\(591\) 0 0
\(592\) −7.33067 −0.301289
\(593\) −25.1127 −1.03125 −0.515627 0.856813i \(-0.672441\pi\)
−0.515627 + 0.856813i \(0.672441\pi\)
\(594\) 0 0
\(595\) −3.70508 + 10.4428i −0.151894 + 0.428112i
\(596\) 12.8694i 0.527150i
\(597\) 0 0
\(598\) 0 0
\(599\) 3.99202i 0.163109i 0.996669 + 0.0815547i \(0.0259885\pi\)
−0.996669 + 0.0815547i \(0.974011\pi\)
\(600\) 0 0
\(601\) 24.0624i 0.981526i 0.871293 + 0.490763i \(0.163282\pi\)
−0.871293 + 0.490763i \(0.836718\pi\)
\(602\) −0.575104 0.204046i −0.0234395 0.00831631i
\(603\) 0 0
\(604\) 8.61475 0.350529
\(605\) 1.06893 0.0434582
\(606\) 0 0
\(607\) 15.9243i 0.646345i 0.946340 + 0.323173i \(0.104749\pi\)
−0.946340 + 0.323173i \(0.895251\pi\)
\(608\) −7.49534 −0.303976
\(609\) 0 0
\(610\) 15.2318 0.616717
\(611\) 0 0
\(612\) 0 0
\(613\) 18.6105 0.751669 0.375835 0.926687i \(-0.377356\pi\)
0.375835 + 0.926687i \(0.377356\pi\)
\(614\) 30.4845 1.23026
\(615\) 0 0
\(616\) −0.884677 + 2.49346i −0.0356447 + 0.100464i
\(617\) 15.8053i 0.636299i −0.948041 0.318150i \(-0.896939\pi\)
0.948041 0.318150i \(-0.103061\pi\)
\(618\) 0 0
\(619\) 7.09487i 0.285167i −0.989783 0.142583i \(-0.954459\pi\)
0.989783 0.142583i \(-0.0455409\pi\)
\(620\) 3.91082i 0.157062i
\(621\) 0 0
\(622\) 8.19371i 0.328538i
\(623\) −8.85010 + 24.9440i −0.354572 + 0.999359i
\(624\) 0 0
\(625\) 9.16637 0.366655
\(626\) −33.2694 −1.32971
\(627\) 0 0
\(628\) 4.39973i 0.175568i
\(629\) −28.7215 −1.14520
\(630\) 0 0
\(631\) 12.3521 0.491730 0.245865 0.969304i \(-0.420928\pi\)
0.245865 + 0.969304i \(0.420928\pi\)
\(632\) 4.45068i 0.177038i
\(633\) 0 0
\(634\) −14.6627 −0.582331
\(635\) −11.3593 −0.450778
\(636\) 0 0
\(637\) 0 0
\(638\) 8.01200i 0.317198i
\(639\) 0 0
\(640\) 1.06893i 0.0422532i
\(641\) 7.32006i 0.289125i 0.989496 + 0.144563i \(0.0461775\pi\)
−0.989496 + 0.144563i \(0.953823\pi\)
\(642\) 0 0
\(643\) 37.8173i 1.49137i −0.666299 0.745685i \(-0.732122\pi\)
0.666299 0.745685i \(-0.267878\pi\)
\(644\) −13.2918 4.71593i −0.523771 0.185834i
\(645\) 0 0
\(646\) −29.3667 −1.15542
\(647\) 1.94268 0.0763748 0.0381874 0.999271i \(-0.487842\pi\)
0.0381874 + 0.999271i \(0.487842\pi\)
\(648\) 0 0
\(649\) 2.13786i 0.0839184i
\(650\) 0 0
\(651\) 0 0
\(652\) −12.6933 −0.497109
\(653\) 23.6305i 0.924734i 0.886689 + 0.462367i \(0.153000\pi\)
−0.886689 + 0.462367i \(0.847000\pi\)
\(654\) 0 0
\(655\) −3.45981 −0.135186
\(656\) −2.50842 −0.0979372
\(657\) 0 0
\(658\) 0.923963 + 0.327821i 0.0360198 + 0.0127798i
\(659\) 35.4535i 1.38107i 0.723297 + 0.690537i \(0.242626\pi\)
−0.723297 + 0.690537i \(0.757374\pi\)
\(660\) 0 0
\(661\) 4.84582i 0.188481i −0.995549 0.0942403i \(-0.969958\pi\)
0.995549 0.0942403i \(-0.0300422\pi\)
\(662\) 6.88936i 0.267763i
\(663\) 0 0
\(664\) 12.2229i 0.474340i
\(665\) 19.9776 + 7.08803i 0.774698 + 0.274862i
\(666\) 0 0
\(667\) 42.7093 1.65371
\(668\) 3.80680 0.147290
\(669\) 0 0
\(670\) 2.64377i 0.102138i
\(671\) 14.2496 0.550098
\(672\) 0 0
\(673\) −51.0185 −1.96662 −0.983310 0.181937i \(-0.941763\pi\)
−0.983310 + 0.181937i \(0.941763\pi\)
\(674\) 5.12264i 0.197317i
\(675\) 0 0
\(676\) −13.0000 −0.500000
\(677\) −24.3330 −0.935195 −0.467597 0.883942i \(-0.654880\pi\)
−0.467597 + 0.883942i \(0.654880\pi\)
\(678\) 0 0
\(679\) −32.0480 11.3706i −1.22989 0.436363i
\(680\) 4.18806i 0.160605i
\(681\) 0 0
\(682\) 3.65862i 0.140096i
\(683\) 25.9028i 0.991144i 0.868567 + 0.495572i \(0.165042\pi\)
−0.868567 + 0.495572i \(0.834958\pi\)
\(684\) 0 0
\(685\) 11.4546i 0.437657i
\(686\) 9.64815 + 15.8086i 0.368368 + 0.603577i
\(687\) 0 0
\(688\) 0.230645 0.00879326
\(689\) 0 0
\(690\) 0 0
\(691\) 37.7917i 1.43766i −0.695184 0.718832i \(-0.744677\pi\)
0.695184 0.718832i \(-0.255323\pi\)
\(692\) −20.9353 −0.795842
\(693\) 0 0
\(694\) 11.6399 0.441844
\(695\) 6.67902i 0.253350i
\(696\) 0 0
\(697\) −9.82795 −0.372260
\(698\) −27.3248 −1.03426
\(699\) 0 0
\(700\) 3.41254 9.61824i 0.128982 0.363535i
\(701\) 31.8479i 1.20288i −0.798918 0.601440i \(-0.794594\pi\)
0.798918 0.601440i \(-0.205406\pi\)
\(702\) 0 0
\(703\) 54.9459i 2.07232i
\(704\) 1.00000i 0.0376889i
\(705\) 0 0
\(706\) 1.45231i 0.0546583i
\(707\) −12.3882 + 34.9160i −0.465905 + 1.31315i
\(708\) 0 0
\(709\) −10.7682 −0.404408 −0.202204 0.979343i \(-0.564810\pi\)
−0.202204 + 0.979343i \(0.564810\pi\)
\(710\) 3.37206 0.126551
\(711\) 0 0
\(712\) 10.0038i 0.374906i
\(713\) 19.5029 0.730390
\(714\) 0 0
\(715\) 0 0
\(716\) 6.47329i 0.241918i
\(717\) 0 0
\(718\) 0.196041 0.00731620
\(719\) −22.1726 −0.826897 −0.413449 0.910527i \(-0.635676\pi\)
−0.413449 + 0.910527i \(0.635676\pi\)
\(720\) 0 0
\(721\) 30.4773 + 10.8133i 1.13503 + 0.402709i
\(722\) 37.1801i 1.38370i
\(723\) 0 0
\(724\) 18.1804i 0.675668i
\(725\) 30.9054i 1.14780i
\(726\) 0 0
\(727\) 28.6830i 1.06379i 0.846810 + 0.531896i \(0.178520\pi\)
−0.846810 + 0.531896i \(0.821480\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0.396097 0.0146602
\(731\) 0.903665 0.0334233
\(732\) 0 0
\(733\) 24.2234i 0.894712i −0.894356 0.447356i \(-0.852366\pi\)
0.894356 0.447356i \(-0.147634\pi\)
\(734\) −2.02667 −0.0748059
\(735\) 0 0
\(736\) 5.33067 0.196491
\(737\) 2.47329i 0.0911046i
\(738\) 0 0
\(739\) 5.17722 0.190447 0.0952235 0.995456i \(-0.469643\pi\)
0.0952235 + 0.995456i \(0.469643\pi\)
\(740\) −7.83598 −0.288056
\(741\) 0 0
\(742\) 6.68933 18.8538i 0.245573 0.692147i
\(743\) 26.7625i 0.981822i −0.871210 0.490911i \(-0.836664\pi\)
0.871210 0.490911i \(-0.163336\pi\)
\(744\) 0 0
\(745\) 13.7565i 0.503998i
\(746\) 26.2001i 0.959252i
\(747\) 0 0
\(748\) 3.91799i 0.143256i
\(749\) −50.8868 18.0546i −1.85936 0.659700i
\(750\) 0 0
\(751\) 54.2933 1.98119 0.990594 0.136830i \(-0.0436915\pi\)
0.990594 + 0.136830i \(0.0436915\pi\)
\(752\) −0.370555 −0.0135127
\(753\) 0 0
\(754\) 0 0
\(755\) 9.20857 0.335134
\(756\) 0 0
\(757\) −12.6294 −0.459022 −0.229511 0.973306i \(-0.573713\pi\)
−0.229511 + 0.973306i \(0.573713\pi\)
\(758\) 8.69332i 0.315756i
\(759\) 0 0
\(760\) −8.01200 −0.290626
\(761\) −11.0599 −0.400920 −0.200460 0.979702i \(-0.564244\pi\)
−0.200460 + 0.979702i \(0.564244\pi\)
\(762\) 0 0
\(763\) 11.3959 32.1192i 0.412558 1.16279i
\(764\) 18.2320i 0.659612i
\(765\) 0 0
\(766\) 5.89330i 0.212933i
\(767\) 0 0
\(768\) 0 0
\(769\) 3.96499i 0.142981i 0.997441 + 0.0714906i \(0.0227756\pi\)
−0.997441 + 0.0714906i \(0.977224\pi\)
\(770\) −0.945659 + 2.66534i −0.0340792 + 0.0960521i
\(771\) 0 0
\(772\) 1.05343 0.0379137
\(773\) −10.5369 −0.378985 −0.189492 0.981882i \(-0.560684\pi\)
−0.189492 + 0.981882i \(0.560684\pi\)
\(774\) 0 0
\(775\) 14.1127i 0.506944i
\(776\) 12.8528 0.461389
\(777\) 0 0
\(778\) 11.5853 0.415353
\(779\) 18.8014i 0.673631i
\(780\) 0 0
\(781\) 3.15461 0.112881
\(782\) 20.8855 0.746865
\(783\) 0 0
\(784\) −5.43469 4.41182i −0.194096 0.157565i
\(785\) 4.70301i 0.167858i
\(786\) 0 0
\(787\) 14.4277i 0.514290i 0.966373 + 0.257145i \(0.0827818\pi\)
−0.966373 + 0.257145i \(0.917218\pi\)
\(788\) 20.8494i 0.742729i
\(789\) 0 0
\(790\) 4.75747i 0.169263i
\(791\) −17.2646 6.12547i −0.613860 0.217797i
\(792\) 0 0
\(793\) 0 0
\(794\) 28.1414 0.998701
\(795\) 0 0
\(796\) 14.3736i 0.509458i
\(797\) 23.3640 0.827596 0.413798 0.910369i \(-0.364202\pi\)
0.413798 + 0.910369i \(0.364202\pi\)
\(798\) 0 0
\(799\) −1.45183 −0.0513620
\(800\) 3.85739i 0.136379i