Properties

Label 2394.2.b.i.1709.6
Level $2394$
Weight $2$
Character 2394.1709
Analytic conductor $19.116$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2394.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(19.1161862439\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} + \cdots)\)
Defining polynomial: \( x^{8} + 10x^{6} + 30x^{4} + 24x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{5}\cdot 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1709.6
Root \(0.209899i\) of defining polynomial
Character \(\chi\) \(=\) 2394.1709
Dual form 2394.2.b.i.1709.3

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{4} +2.76612i q^{5} -1.00000 q^{7} -1.00000 q^{8} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{4} +2.76612i q^{5} -1.00000 q^{7} -1.00000 q^{8} -2.76612i q^{10} +4.92827i q^{11} +2.93944i q^{13} +1.00000 q^{14} +1.00000 q^{16} +4.92827i q^{17} +(1.87745 + 3.93385i) q^{19} +2.76612i q^{20} -4.92827i q^{22} -0.685627i q^{23} -2.65142 q^{25} -2.93944i q^{26} -1.00000 q^{28} +1.65142 q^{29} -2.16215i q^{31} -1.00000 q^{32} -4.92827i q^{34} -2.76612i q^{35} -9.77488i q^{37} +(-1.87745 - 3.93385i) q^{38} -2.76612i q^{40} +2.37594 q^{41} -8.15699 q^{43} +4.92827i q^{44} +0.685627i q^{46} +5.87887i q^{47} +1.00000 q^{49} +2.65142 q^{50} +2.93944i q^{52} +3.47519 q^{53} -13.6322 q^{55} +1.00000 q^{56} -1.65142 q^{58} -4.26046 q^{61} +2.16215i q^{62} +1.00000 q^{64} -8.13083 q^{65} +6.56450i q^{67} +4.92827i q^{68} +2.76612i q^{70} +11.1266 q^{71} +2.85415 q^{73} +9.77488i q^{74} +(1.87745 + 3.93385i) q^{76} -4.92827i q^{77} -11.0781i q^{79} +2.76612i q^{80} -2.37594 q^{82} +7.07681i q^{83} -13.6322 q^{85} +8.15699 q^{86} -4.92827i q^{88} -13.5026 q^{89} -2.93944i q^{91} -0.685627i q^{92} -5.87887i q^{94} +(-10.8815 + 5.19325i) q^{95} +3.11275i q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 8 q^{2} + 8 q^{4} - 8 q^{7} - 8 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 8 q^{2} + 8 q^{4} - 8 q^{7} - 8 q^{8} + 8 q^{14} + 8 q^{16} + 12 q^{19} - 24 q^{25} - 8 q^{28} + 16 q^{29} - 8 q^{32} - 12 q^{38} - 24 q^{41} - 32 q^{43} + 8 q^{49} + 24 q^{50} - 48 q^{53} + 8 q^{56} - 16 q^{58} + 8 q^{61} + 8 q^{64} - 16 q^{65} + 16 q^{71} - 16 q^{73} + 12 q^{76} + 24 q^{82} + 32 q^{86} + 8 q^{89} - 8 q^{95} - 8 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2394\mathbb{Z}\right)^\times\).

\(n\) \(533\) \(1009\) \(1711\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) 2.76612i 1.23705i 0.785766 + 0.618523i \(0.212269\pi\)
−0.785766 + 0.618523i \(0.787731\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 2.76612i 0.874724i
\(11\) 4.92827i 1.48593i 0.669331 + 0.742964i \(0.266581\pi\)
−0.669331 + 0.742964i \(0.733419\pi\)
\(12\) 0 0
\(13\) 2.93944i 0.815253i 0.913149 + 0.407626i \(0.133643\pi\)
−0.913149 + 0.407626i \(0.866357\pi\)
\(14\) 1.00000 0.267261
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 4.92827i 1.19528i 0.801764 + 0.597640i \(0.203895\pi\)
−0.801764 + 0.597640i \(0.796105\pi\)
\(18\) 0 0
\(19\) 1.87745 + 3.93385i 0.430716 + 0.902488i
\(20\) 2.76612i 0.618523i
\(21\) 0 0
\(22\) 4.92827i 1.05071i
\(23\) 0.685627i 0.142963i −0.997442 0.0714816i \(-0.977227\pi\)
0.997442 0.0714816i \(-0.0227727\pi\)
\(24\) 0 0
\(25\) −2.65142 −0.530284
\(26\) 2.93944i 0.576471i
\(27\) 0 0
\(28\) −1.00000 −0.188982
\(29\) 1.65142 0.306661 0.153331 0.988175i \(-0.451000\pi\)
0.153331 + 0.988175i \(0.451000\pi\)
\(30\) 0 0
\(31\) 2.16215i 0.388333i −0.980969 0.194167i \(-0.937800\pi\)
0.980969 0.194167i \(-0.0622002\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) 4.92827i 0.845191i
\(35\) 2.76612i 0.467560i
\(36\) 0 0
\(37\) 9.77488i 1.60698i −0.595318 0.803490i \(-0.702974\pi\)
0.595318 0.803490i \(-0.297026\pi\)
\(38\) −1.87745 3.93385i −0.304562 0.638155i
\(39\) 0 0
\(40\) 2.76612i 0.437362i
\(41\) 2.37594 0.371059 0.185530 0.982639i \(-0.440600\pi\)
0.185530 + 0.982639i \(0.440600\pi\)
\(42\) 0 0
\(43\) −8.15699 −1.24393 −0.621965 0.783045i \(-0.713665\pi\)
−0.621965 + 0.783045i \(0.713665\pi\)
\(44\) 4.92827i 0.742964i
\(45\) 0 0
\(46\) 0.685627i 0.101090i
\(47\) 5.87887i 0.857522i 0.903418 + 0.428761i \(0.141050\pi\)
−0.903418 + 0.428761i \(0.858950\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 2.65142 0.374968
\(51\) 0 0
\(52\) 2.93944i 0.407626i
\(53\) 3.47519 0.477354 0.238677 0.971099i \(-0.423286\pi\)
0.238677 + 0.971099i \(0.423286\pi\)
\(54\) 0 0
\(55\) −13.6322 −1.83816
\(56\) 1.00000 0.133631
\(57\) 0 0
\(58\) −1.65142 −0.216842
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) −4.26046 −0.545496 −0.272748 0.962085i \(-0.587933\pi\)
−0.272748 + 0.962085i \(0.587933\pi\)
\(62\) 2.16215i 0.274593i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −8.13083 −1.00851
\(66\) 0 0
\(67\) 6.56450i 0.801981i 0.916082 + 0.400991i \(0.131334\pi\)
−0.916082 + 0.400991i \(0.868666\pi\)
\(68\) 4.92827i 0.597640i
\(69\) 0 0
\(70\) 2.76612i 0.330615i
\(71\) 11.1266 1.32049 0.660243 0.751052i \(-0.270453\pi\)
0.660243 + 0.751052i \(0.270453\pi\)
\(72\) 0 0
\(73\) 2.85415 0.334053 0.167026 0.985952i \(-0.446584\pi\)
0.167026 + 0.985952i \(0.446584\pi\)
\(74\) 9.77488i 1.13631i
\(75\) 0 0
\(76\) 1.87745 + 3.93385i 0.215358 + 0.451244i
\(77\) 4.92827i 0.561628i
\(78\) 0 0
\(79\) 11.0781i 1.24638i −0.782070 0.623191i \(-0.785836\pi\)
0.782070 0.623191i \(-0.214164\pi\)
\(80\) 2.76612i 0.309262i
\(81\) 0 0
\(82\) −2.37594 −0.262379
\(83\) 7.07681i 0.776781i 0.921495 + 0.388390i \(0.126969\pi\)
−0.921495 + 0.388390i \(0.873031\pi\)
\(84\) 0 0
\(85\) −13.6322 −1.47862
\(86\) 8.15699 0.879591
\(87\) 0 0
\(88\) 4.92827i 0.525355i
\(89\) −13.5026 −1.43127 −0.715634 0.698476i \(-0.753862\pi\)
−0.715634 + 0.698476i \(0.753862\pi\)
\(90\) 0 0
\(91\) 2.93944i 0.308137i
\(92\) 0.685627i 0.0714816i
\(93\) 0 0
\(94\) 5.87887i 0.606359i
\(95\) −10.8815 + 5.19325i −1.11642 + 0.532816i
\(96\) 0 0
\(97\) 3.11275i 0.316052i 0.987435 + 0.158026i \(0.0505130\pi\)
−0.987435 + 0.158026i \(0.949487\pi\)
\(98\) −1.00000 −0.101015
\(99\) 0 0
\(100\) −2.65142 −0.265142
\(101\) 8.64499i 0.860209i −0.902779 0.430104i \(-0.858477\pi\)
0.902779 0.430104i \(-0.141523\pi\)
\(102\) 0 0
\(103\) 4.49761i 0.443163i 0.975142 + 0.221581i \(0.0711218\pi\)
−0.975142 + 0.221581i \(0.928878\pi\)
\(104\) 2.93944i 0.288235i
\(105\) 0 0
\(106\) −3.47519 −0.337540
\(107\) −9.66678 −0.934523 −0.467261 0.884119i \(-0.654759\pi\)
−0.467261 + 0.884119i \(0.654759\pi\)
\(108\) 0 0
\(109\) 14.6895i 1.40700i −0.710694 0.703502i \(-0.751619\pi\)
0.710694 0.703502i \(-0.248381\pi\)
\(110\) 13.6322 1.29978
\(111\) 0 0
\(112\) −1.00000 −0.0944911
\(113\) 11.0111 1.03584 0.517920 0.855429i \(-0.326706\pi\)
0.517920 + 0.855429i \(0.326706\pi\)
\(114\) 0 0
\(115\) 1.89653 0.176852
\(116\) 1.65142 0.153331
\(117\) 0 0
\(118\) 0 0
\(119\) 4.92827i 0.451774i
\(120\) 0 0
\(121\) −13.2878 −1.20798
\(122\) 4.26046 0.385724
\(123\) 0 0
\(124\) 2.16215i 0.194167i
\(125\) 6.49645i 0.581060i
\(126\) 0 0
\(127\) 1.56818i 0.139154i −0.997577 0.0695768i \(-0.977835\pi\)
0.997577 0.0695768i \(-0.0221649\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0 0
\(130\) 8.13083 0.713121
\(131\) 15.8330i 1.38334i −0.722214 0.691669i \(-0.756876\pi\)
0.722214 0.691669i \(-0.243124\pi\)
\(132\) 0 0
\(133\) −1.87745 3.93385i −0.162795 0.341108i
\(134\) 6.56450i 0.567086i
\(135\) 0 0
\(136\) 4.92827i 0.422595i
\(137\) 5.61390i 0.479627i 0.970819 + 0.239814i \(0.0770864\pi\)
−0.970819 + 0.239814i \(0.922914\pi\)
\(138\) 0 0
\(139\) 22.0770 1.87255 0.936273 0.351273i \(-0.114251\pi\)
0.936273 + 0.351273i \(0.114251\pi\)
\(140\) 2.76612i 0.233780i
\(141\) 0 0
\(142\) −11.1266 −0.933725
\(143\) −14.4863 −1.21141
\(144\) 0 0
\(145\) 4.56803i 0.379354i
\(146\) −2.85415 −0.236211
\(147\) 0 0
\(148\) 9.77488i 0.803490i
\(149\) 1.37125i 0.112338i 0.998421 + 0.0561688i \(0.0178885\pi\)
−0.998421 + 0.0561688i \(0.982112\pi\)
\(150\) 0 0
\(151\) 22.8358i 1.85835i 0.369636 + 0.929177i \(0.379482\pi\)
−0.369636 + 0.929177i \(0.620518\pi\)
\(152\) −1.87745 3.93385i −0.152281 0.319078i
\(153\) 0 0
\(154\) 4.92827i 0.397131i
\(155\) 5.98076 0.480386
\(156\) 0 0
\(157\) 5.53595 0.441817 0.220908 0.975295i \(-0.429098\pi\)
0.220908 + 0.975295i \(0.429098\pi\)
\(158\) 11.0781i 0.881325i
\(159\) 0 0
\(160\) 2.76612i 0.218681i
\(161\) 0.685627i 0.0540350i
\(162\) 0 0
\(163\) −21.9200 −1.71691 −0.858454 0.512891i \(-0.828574\pi\)
−0.858454 + 0.512891i \(0.828574\pi\)
\(164\) 2.37594 0.185530
\(165\) 0 0
\(166\) 7.07681i 0.549267i
\(167\) −17.7892 −1.37657 −0.688284 0.725442i \(-0.741636\pi\)
−0.688284 + 0.725442i \(0.741636\pi\)
\(168\) 0 0
\(169\) 4.35972 0.335363
\(170\) 13.6322 1.04554
\(171\) 0 0
\(172\) −8.15699 −0.621965
\(173\) −9.66678 −0.734952 −0.367476 0.930033i \(-0.619778\pi\)
−0.367476 + 0.930033i \(0.619778\pi\)
\(174\) 0 0
\(175\) 2.65142 0.200429
\(176\) 4.92827i 0.371482i
\(177\) 0 0
\(178\) 13.5026 1.01206
\(179\) −14.4295 −1.07851 −0.539254 0.842143i \(-0.681294\pi\)
−0.539254 + 0.842143i \(0.681294\pi\)
\(180\) 0 0
\(181\) 11.5880i 0.861331i −0.902512 0.430666i \(-0.858279\pi\)
0.902512 0.430666i \(-0.141721\pi\)
\(182\) 2.93944i 0.217886i
\(183\) 0 0
\(184\) 0.685627i 0.0505451i
\(185\) 27.0385 1.98791
\(186\) 0 0
\(187\) −24.2878 −1.77610
\(188\) 5.87887i 0.428761i
\(189\) 0 0
\(190\) 10.8815 5.19325i 0.789428 0.376758i
\(191\) 3.36772i 0.243680i 0.992550 + 0.121840i \(0.0388794\pi\)
−0.992550 + 0.121840i \(0.961121\pi\)
\(192\) 0 0
\(193\) 16.0064i 1.15216i −0.817392 0.576081i \(-0.804581\pi\)
0.817392 0.576081i \(-0.195419\pi\)
\(194\) 3.11275i 0.223483i
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) 5.87887i 0.418852i −0.977824 0.209426i \(-0.932840\pi\)
0.977824 0.209426i \(-0.0671596\pi\)
\(198\) 0 0
\(199\) 7.43368 0.526959 0.263480 0.964665i \(-0.415130\pi\)
0.263480 + 0.964665i \(0.415130\pi\)
\(200\) 2.65142 0.187484
\(201\) 0 0
\(202\) 8.64499i 0.608260i
\(203\) −1.65142 −0.115907
\(204\) 0 0
\(205\) 6.57214i 0.459018i
\(206\) 4.49761i 0.313363i
\(207\) 0 0
\(208\) 2.93944i 0.203813i
\(209\) −19.3871 + 9.25256i −1.34103 + 0.640013i
\(210\) 0 0
\(211\) 7.18208i 0.494435i 0.968960 + 0.247217i \(0.0795161\pi\)
−0.968960 + 0.247217i \(0.920484\pi\)
\(212\) 3.47519 0.238677
\(213\) 0 0
\(214\) 9.66678 0.660807
\(215\) 22.5632i 1.53880i
\(216\) 0 0
\(217\) 2.16215i 0.146776i
\(218\) 14.6895i 0.994902i
\(219\) 0 0
\(220\) −13.6322 −0.919082
\(221\) −14.4863 −0.974456
\(222\) 0 0
\(223\) 25.7653i 1.72537i 0.505742 + 0.862685i \(0.331219\pi\)
−0.505742 + 0.862685i \(0.668781\pi\)
\(224\) 1.00000 0.0668153
\(225\) 0 0
\(226\) −11.0111 −0.732450
\(227\) −16.9350 −1.12402 −0.562009 0.827131i \(-0.689971\pi\)
−0.562009 + 0.827131i \(0.689971\pi\)
\(228\) 0 0
\(229\) 10.2878 0.679839 0.339919 0.940455i \(-0.389600\pi\)
0.339919 + 0.940455i \(0.389600\pi\)
\(230\) −1.89653 −0.125053
\(231\) 0 0
\(232\) −1.65142 −0.108421
\(233\) 3.97169i 0.260194i 0.991501 + 0.130097i \(0.0415289\pi\)
−0.991501 + 0.130097i \(0.958471\pi\)
\(234\) 0 0
\(235\) −16.2617 −1.06079
\(236\) 0 0
\(237\) 0 0
\(238\) 4.92827i 0.319452i
\(239\) 16.8753i 1.09157i 0.837924 + 0.545786i \(0.183769\pi\)
−0.837924 + 0.545786i \(0.816231\pi\)
\(240\) 0 0
\(241\) 9.88015i 0.636436i 0.948018 + 0.318218i \(0.103084\pi\)
−0.948018 + 0.318218i \(0.896916\pi\)
\(242\) 13.2878 0.854174
\(243\) 0 0
\(244\) −4.26046 −0.272748
\(245\) 2.76612i 0.176721i
\(246\) 0 0
\(247\) −11.5633 + 5.51864i −0.735756 + 0.351142i
\(248\) 2.16215i 0.137297i
\(249\) 0 0
\(250\) 6.49645i 0.410872i
\(251\) 10.6202i 0.670342i 0.942157 + 0.335171i \(0.108794\pi\)
−0.942157 + 0.335171i \(0.891206\pi\)
\(252\) 0 0
\(253\) 3.37895 0.212433
\(254\) 1.56818i 0.0983965i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 5.18857 0.323654 0.161827 0.986819i \(-0.448261\pi\)
0.161827 + 0.986819i \(0.448261\pi\)
\(258\) 0 0
\(259\) 9.77488i 0.607382i
\(260\) −8.13083 −0.504253
\(261\) 0 0
\(262\) 15.8330i 0.978168i
\(263\) 1.13990i 0.0702890i −0.999382 0.0351445i \(-0.988811\pi\)
0.999382 0.0351445i \(-0.0111891\pi\)
\(264\) 0 0
\(265\) 9.61280i 0.590510i
\(266\) 1.87745 + 3.93385i 0.115114 + 0.241200i
\(267\) 0 0
\(268\) 6.56450i 0.400991i
\(269\) 8.79339 0.536143 0.268071 0.963399i \(-0.413614\pi\)
0.268071 + 0.963399i \(0.413614\pi\)
\(270\) 0 0
\(271\) −9.88452 −0.600442 −0.300221 0.953870i \(-0.597060\pi\)
−0.300221 + 0.953870i \(0.597060\pi\)
\(272\) 4.92827i 0.298820i
\(273\) 0 0
\(274\) 5.61390i 0.339148i
\(275\) 13.0669i 0.787965i
\(276\) 0 0
\(277\) 26.3687 1.58434 0.792171 0.610299i \(-0.208951\pi\)
0.792171 + 0.610299i \(0.208951\pi\)
\(278\) −22.0770 −1.32409
\(279\) 0 0
\(280\) 2.76612i 0.165307i
\(281\) −12.9504 −0.772555 −0.386278 0.922383i \(-0.626239\pi\)
−0.386278 + 0.922383i \(0.626239\pi\)
\(282\) 0 0
\(283\) 6.88151 0.409063 0.204532 0.978860i \(-0.434433\pi\)
0.204532 + 0.978860i \(0.434433\pi\)
\(284\) 11.1266 0.660243
\(285\) 0 0
\(286\) 14.4863 0.856595
\(287\) −2.37594 −0.140247
\(288\) 0 0
\(289\) −7.28782 −0.428696
\(290\) 4.56803i 0.268244i
\(291\) 0 0
\(292\) 2.85415 0.167026
\(293\) 2.67792 0.156446 0.0782228 0.996936i \(-0.475075\pi\)
0.0782228 + 0.996936i \(0.475075\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 9.77488i 0.568153i
\(297\) 0 0
\(298\) 1.37125i 0.0794346i
\(299\) 2.01536 0.116551
\(300\) 0 0
\(301\) 8.15699 0.470161
\(302\) 22.8358i 1.31405i
\(303\) 0 0
\(304\) 1.87745 + 3.93385i 0.107679 + 0.225622i
\(305\) 11.7850i 0.674804i
\(306\) 0 0
\(307\) 29.0597i 1.65852i −0.558861 0.829261i \(-0.688761\pi\)
0.558861 0.829261i \(-0.311239\pi\)
\(308\) 4.92827i 0.280814i
\(309\) 0 0
\(310\) −5.98076 −0.339684
\(311\) 13.1562i 0.746020i −0.927827 0.373010i \(-0.878326\pi\)
0.927827 0.373010i \(-0.121674\pi\)
\(312\) 0 0
\(313\) −1.50979 −0.0853383 −0.0426692 0.999089i \(-0.513586\pi\)
−0.0426692 + 0.999089i \(0.513586\pi\)
\(314\) −5.53595 −0.312411
\(315\) 0 0
\(316\) 11.0781i 0.623191i
\(317\) −27.1573 −1.52531 −0.762654 0.646807i \(-0.776104\pi\)
−0.762654 + 0.646807i \(0.776104\pi\)
\(318\) 0 0
\(319\) 8.13865i 0.455677i
\(320\) 2.76612i 0.154631i
\(321\) 0 0
\(322\) 0.685627i 0.0382085i
\(323\) −19.3871 + 9.25256i −1.07873 + 0.514826i
\(324\) 0 0
\(325\) 7.79369i 0.432316i
\(326\) 21.9200 1.21404
\(327\) 0 0
\(328\) −2.37594 −0.131189
\(329\) 5.87887i 0.324113i
\(330\) 0 0
\(331\) 5.35655i 0.294423i 0.989105 + 0.147211i \(0.0470298\pi\)
−0.989105 + 0.147211i \(0.952970\pi\)
\(332\) 7.07681i 0.388390i
\(333\) 0 0
\(334\) 17.7892 0.973380
\(335\) −18.1582 −0.992088
\(336\) 0 0
\(337\) 17.8875i 0.974397i −0.873291 0.487198i \(-0.838019\pi\)
0.873291 0.487198i \(-0.161981\pi\)
\(338\) −4.35972 −0.237137
\(339\) 0 0
\(340\) −13.6322 −0.739309
\(341\) 10.6556 0.577035
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 8.15699 0.439795
\(345\) 0 0
\(346\) 9.66678 0.519689
\(347\) 18.5992i 0.998455i −0.866471 0.499228i \(-0.833617\pi\)
0.866471 0.499228i \(-0.166383\pi\)
\(348\) 0 0
\(349\) −12.7507 −0.682528 −0.341264 0.939968i \(-0.610855\pi\)
−0.341264 + 0.939968i \(0.610855\pi\)
\(350\) −2.65142 −0.141724
\(351\) 0 0
\(352\) 4.92827i 0.262678i
\(353\) 17.5745i 0.935398i 0.883888 + 0.467699i \(0.154917\pi\)
−0.883888 + 0.467699i \(0.845083\pi\)
\(354\) 0 0
\(355\) 30.7776i 1.63350i
\(356\) −13.5026 −0.715634
\(357\) 0 0
\(358\) 14.4295 0.762621
\(359\) 17.6290i 0.930422i 0.885200 + 0.465211i \(0.154022\pi\)
−0.885200 + 0.465211i \(0.845978\pi\)
\(360\) 0 0
\(361\) −11.9504 + 14.7712i −0.628968 + 0.777432i
\(362\) 11.5880i 0.609053i
\(363\) 0 0
\(364\) 2.93944i 0.154068i
\(365\) 7.89491i 0.413239i
\(366\) 0 0
\(367\) 32.1925 1.68043 0.840217 0.542251i \(-0.182428\pi\)
0.840217 + 0.542251i \(0.182428\pi\)
\(368\) 0.685627i 0.0357408i
\(369\) 0 0
\(370\) −27.0385 −1.40566
\(371\) −3.47519 −0.180423
\(372\) 0 0
\(373\) 23.4458i 1.21398i −0.794711 0.606988i \(-0.792378\pi\)
0.794711 0.606988i \(-0.207622\pi\)
\(374\) 24.2878 1.25589
\(375\) 0 0
\(376\) 5.87887i 0.303180i
\(377\) 4.85425i 0.250007i
\(378\) 0 0
\(379\) 1.27600i 0.0655435i −0.999463 0.0327717i \(-0.989567\pi\)
0.999463 0.0327717i \(-0.0104334\pi\)
\(380\) −10.8815 + 5.19325i −0.558210 + 0.266408i
\(381\) 0 0
\(382\) 3.36772i 0.172308i
\(383\) −9.66343 −0.493778 −0.246889 0.969044i \(-0.579408\pi\)
−0.246889 + 0.969044i \(0.579408\pi\)
\(384\) 0 0
\(385\) 13.6322 0.694760
\(386\) 16.0064i 0.814702i
\(387\) 0 0
\(388\) 3.11275i 0.158026i
\(389\) 27.3098i 1.38466i −0.721579 0.692332i \(-0.756584\pi\)
0.721579 0.692332i \(-0.243416\pi\)
\(390\) 0 0
\(391\) 3.37895 0.170881
\(392\) −1.00000 −0.0505076
\(393\) 0 0
\(394\) 5.87887i 0.296173i
\(395\) 30.6433 1.54183
\(396\) 0 0
\(397\) 22.6018 1.13435 0.567176 0.823597i \(-0.308036\pi\)
0.567176 + 0.823597i \(0.308036\pi\)
\(398\) −7.43368 −0.372617
\(399\) 0 0
\(400\) −2.65142 −0.132571
\(401\) −28.1771 −1.40710 −0.703549 0.710647i \(-0.748402\pi\)
−0.703549 + 0.710647i \(0.748402\pi\)
\(402\) 0 0
\(403\) 6.35549 0.316590
\(404\) 8.64499i 0.430104i
\(405\) 0 0
\(406\) 1.65142 0.0819587
\(407\) 48.1732 2.38786
\(408\) 0 0
\(409\) 23.9581i 1.18465i 0.805699 + 0.592325i \(0.201790\pi\)
−0.805699 + 0.592325i \(0.798210\pi\)
\(410\) 6.57214i 0.324575i
\(411\) 0 0
\(412\) 4.49761i 0.221581i
\(413\) 0 0
\(414\) 0 0
\(415\) −19.5753 −0.960914
\(416\) 2.93944i 0.144118i
\(417\) 0 0
\(418\) 19.3871 9.25256i 0.948253 0.452558i
\(419\) 29.5796i 1.44506i −0.691340 0.722529i \(-0.742979\pi\)
0.691340 0.722529i \(-0.257021\pi\)
\(420\) 0 0
\(421\) 15.2467i 0.743079i −0.928417 0.371540i \(-0.878830\pi\)
0.928417 0.371540i \(-0.121170\pi\)
\(422\) 7.18208i 0.349618i
\(423\) 0 0
\(424\) −3.47519 −0.168770
\(425\) 13.0669i 0.633839i
\(426\) 0 0
\(427\) 4.26046 0.206178
\(428\) −9.66678 −0.467261
\(429\) 0 0
\(430\) 22.5632i 1.08809i
\(431\) 23.7215 1.14262 0.571312 0.820733i \(-0.306435\pi\)
0.571312 + 0.820733i \(0.306435\pi\)
\(432\) 0 0
\(433\) 13.8306i 0.664656i 0.943164 + 0.332328i \(0.107834\pi\)
−0.943164 + 0.332328i \(0.892166\pi\)
\(434\) 2.16215i 0.103786i
\(435\) 0 0
\(436\) 14.6895i 0.703502i
\(437\) 2.69716 1.28723i 0.129022 0.0615765i
\(438\) 0 0
\(439\) 29.5039i 1.40815i 0.710128 + 0.704073i \(0.248637\pi\)
−0.710128 + 0.704073i \(0.751363\pi\)
\(440\) 13.6322 0.649889
\(441\) 0 0
\(442\) 14.4863 0.689044
\(443\) 0.257341i 0.0122267i −0.999981 0.00611333i \(-0.998054\pi\)
0.999981 0.00611333i \(-0.00194594\pi\)
\(444\) 0 0
\(445\) 37.3497i 1.77055i
\(446\) 25.7653i 1.22002i
\(447\) 0 0
\(448\) −1.00000 −0.0472456
\(449\) 22.3687 1.05564 0.527822 0.849355i \(-0.323009\pi\)
0.527822 + 0.849355i \(0.323009\pi\)
\(450\) 0 0
\(451\) 11.7093i 0.551368i
\(452\) 11.0111 0.517920
\(453\) 0 0
\(454\) 16.9350 0.794800
\(455\) 8.13083 0.381179
\(456\) 0 0
\(457\) −33.2990 −1.55766 −0.778830 0.627235i \(-0.784186\pi\)
−0.778830 + 0.627235i \(0.784186\pi\)
\(458\) −10.2878 −0.480718
\(459\) 0 0
\(460\) 1.89653 0.0884260
\(461\) 1.90481i 0.0887157i −0.999016 0.0443578i \(-0.985876\pi\)
0.999016 0.0443578i \(-0.0141242\pi\)
\(462\) 0 0
\(463\) −5.22888 −0.243007 −0.121503 0.992591i \(-0.538772\pi\)
−0.121503 + 0.992591i \(0.538772\pi\)
\(464\) 1.65142 0.0766653
\(465\) 0 0
\(466\) 3.97169i 0.183985i
\(467\) 31.1342i 1.44072i −0.693601 0.720359i \(-0.743977\pi\)
0.693601 0.720359i \(-0.256023\pi\)
\(468\) 0 0
\(469\) 6.56450i 0.303120i
\(470\) 16.2617 0.750095
\(471\) 0 0
\(472\) 0 0
\(473\) 40.1998i 1.84839i
\(474\) 0 0
\(475\) −4.97790 10.4303i −0.228402 0.478575i
\(476\) 4.92827i 0.225887i
\(477\) 0 0
\(478\) 16.8753i 0.771858i
\(479\) 7.25013i 0.331267i −0.986187 0.165633i \(-0.947033\pi\)
0.986187 0.165633i \(-0.0529668\pi\)
\(480\) 0 0
\(481\) 28.7326 1.31010
\(482\) 9.88015i 0.450028i
\(483\) 0 0
\(484\) −13.2878 −0.603992
\(485\) −8.61025 −0.390971
\(486\) 0 0
\(487\) 16.2637i 0.736978i 0.929632 + 0.368489i \(0.120125\pi\)
−0.929632 + 0.368489i \(0.879875\pi\)
\(488\) 4.26046 0.192862
\(489\) 0 0
\(490\) 2.76612i 0.124961i
\(491\) 31.7282i 1.43187i −0.698166 0.715936i \(-0.746000\pi\)
0.698166 0.715936i \(-0.254000\pi\)
\(492\) 0 0
\(493\) 8.13865i 0.366546i
\(494\) 11.5633 5.51864i 0.520258 0.248295i
\(495\) 0 0
\(496\) 2.16215i 0.0970833i
\(497\) −11.1266 −0.499097
\(498\) 0 0
\(499\) 2.29171 0.102591 0.0512954 0.998684i \(-0.483665\pi\)
0.0512954 + 0.998684i \(0.483665\pi\)
\(500\) 6.49645i 0.290530i
\(501\) 0 0
\(502\) 10.6202i 0.474004i
\(503\) 21.0239i 0.937410i 0.883355 + 0.468705i \(0.155279\pi\)
−0.883355 + 0.468705i \(0.844721\pi\)
\(504\) 0 0
\(505\) 23.9131 1.06412
\(506\) −3.37895 −0.150213
\(507\) 0 0
\(508\) 1.56818i 0.0695768i
\(509\) 40.6364 1.80118 0.900588 0.434673i \(-0.143136\pi\)
0.900588 + 0.434673i \(0.143136\pi\)
\(510\) 0 0
\(511\) −2.85415 −0.126260
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −5.18857 −0.228858
\(515\) −12.4409 −0.548213
\(516\) 0 0
\(517\) −28.9727 −1.27422
\(518\) 9.77488i 0.429484i
\(519\) 0 0
\(520\) 8.13083 0.356561
\(521\) 40.8857 1.79124 0.895619 0.444823i \(-0.146733\pi\)
0.895619 + 0.444823i \(0.146733\pi\)
\(522\) 0 0
\(523\) 19.1427i 0.837053i 0.908205 + 0.418526i \(0.137453\pi\)
−0.908205 + 0.418526i \(0.862547\pi\)
\(524\) 15.8330i 0.691669i
\(525\) 0 0
\(526\) 1.13990i 0.0497018i
\(527\) 10.6556 0.464167
\(528\) 0 0
\(529\) 22.5299 0.979562
\(530\) 9.61280i 0.417553i
\(531\) 0 0
\(532\) −1.87745 3.93385i −0.0813977 0.170554i
\(533\) 6.98392i 0.302507i
\(534\) 0 0
\(535\) 26.7395i 1.15605i
\(536\) 6.56450i 0.283543i
\(537\) 0 0
\(538\) −8.79339 −0.379110
\(539\) 4.92827i 0.212276i
\(540\) 0 0
\(541\) 45.2190 1.94412 0.972058 0.234742i \(-0.0754246\pi\)
0.972058 + 0.234742i \(0.0754246\pi\)
\(542\) 9.88452 0.424577
\(543\) 0 0
\(544\) 4.92827i 0.211298i
\(545\) 40.6330 1.74053
\(546\) 0 0
\(547\) 19.0274i 0.813555i 0.913527 + 0.406777i \(0.133348\pi\)
−0.913527 + 0.406777i \(0.866652\pi\)
\(548\) 5.61390i 0.239814i
\(549\) 0 0
\(550\) 13.0669i 0.557175i
\(551\) 3.10046 + 6.49645i 0.132084 + 0.276758i
\(552\) 0 0
\(553\) 11.0781i 0.471088i
\(554\) −26.3687 −1.12030
\(555\) 0 0
\(556\) 22.0770 0.936273
\(557\) 26.1219i 1.10682i 0.832909 + 0.553410i \(0.186674\pi\)
−0.832909 + 0.553410i \(0.813326\pi\)
\(558\) 0 0
\(559\) 23.9770i 1.01412i
\(560\) 2.76612i 0.116890i
\(561\) 0 0
\(562\) 12.9504 0.546279
\(563\) −23.9615 −1.00986 −0.504929 0.863161i \(-0.668481\pi\)
−0.504929 + 0.863161i \(0.668481\pi\)
\(564\) 0 0
\(565\) 30.4581i 1.28138i
\(566\) −6.88151 −0.289251
\(567\) 0 0
\(568\) −11.1266 −0.466862
\(569\) 28.0316 1.17515 0.587573 0.809171i \(-0.300084\pi\)
0.587573 + 0.809171i \(0.300084\pi\)
\(570\) 0 0
\(571\) −8.54017 −0.357395 −0.178697 0.983904i \(-0.557188\pi\)
−0.178697 + 0.983904i \(0.557188\pi\)
\(572\) −14.4863 −0.605704
\(573\) 0 0
\(574\) 2.37594 0.0991698
\(575\) 1.81789i 0.0758111i
\(576\) 0 0
\(577\) 38.2424 1.59205 0.796027 0.605262i \(-0.206932\pi\)
0.796027 + 0.605262i \(0.206932\pi\)
\(578\) 7.28782 0.303134
\(579\) 0 0
\(580\) 4.56803i 0.189677i
\(581\) 7.07681i 0.293596i
\(582\) 0 0
\(583\) 17.1267i 0.709314i
\(584\) −2.85415 −0.118105
\(585\) 0 0
\(586\) −2.67792 −0.110624
\(587\) 20.0697i 0.828366i −0.910194 0.414183i \(-0.864067\pi\)
0.910194 0.414183i \(-0.135933\pi\)
\(588\) 0 0
\(589\) 8.50557 4.05932i 0.350466 0.167261i
\(590\) 0 0
\(591\) 0 0
\(592\) 9.77488i 0.401745i
\(593\) 32.8000i 1.34693i 0.739217 + 0.673467i \(0.235196\pi\)
−0.739217 + 0.673467i \(0.764804\pi\)
\(594\) 0 0
\(595\) 13.6322 0.558865
\(596\) 1.37125i 0.0561688i
\(597\) 0 0
\(598\) −2.01536 −0.0824141
\(599\) −5.73230 −0.234215 −0.117108 0.993119i \(-0.537362\pi\)
−0.117108 + 0.993119i \(0.537362\pi\)
\(600\) 0 0
\(601\) 19.3428i 0.789010i 0.918894 + 0.394505i \(0.129084\pi\)
−0.918894 + 0.394505i \(0.870916\pi\)
\(602\) −8.15699 −0.332454
\(603\) 0 0
\(604\) 22.8358i 0.929177i
\(605\) 36.7557i 1.49433i
\(606\) 0 0
\(607\) 19.9940i 0.811532i 0.913977 + 0.405766i \(0.132995\pi\)
−0.913977 + 0.405766i \(0.867005\pi\)
\(608\) −1.87745 3.93385i −0.0761405 0.159539i
\(609\) 0 0
\(610\) 11.7850i 0.477159i
\(611\) −17.2806 −0.699097
\(612\) 0 0
\(613\) 6.43790 0.260024 0.130012 0.991512i \(-0.458498\pi\)
0.130012 + 0.991512i \(0.458498\pi\)
\(614\) 29.0597i 1.17275i
\(615\) 0 0
\(616\) 4.92827i 0.198566i
\(617\) 32.9557i 1.32675i 0.748289 + 0.663373i \(0.230876\pi\)
−0.748289 + 0.663373i \(0.769124\pi\)
\(618\) 0 0
\(619\) 12.8995 0.518476 0.259238 0.965813i \(-0.416529\pi\)
0.259238 + 0.965813i \(0.416529\pi\)
\(620\) 5.98076 0.240193
\(621\) 0 0
\(622\) 13.1562i 0.527516i
\(623\) 13.5026 0.540968
\(624\) 0 0
\(625\) −31.2271 −1.24908
\(626\) 1.50979 0.0603433
\(627\) 0 0
\(628\) 5.53595 0.220908
\(629\) 48.1732 1.92079
\(630\) 0 0
\(631\) 20.0307 0.797410 0.398705 0.917079i \(-0.369460\pi\)
0.398705 + 0.917079i \(0.369460\pi\)
\(632\) 11.0781i 0.440663i
\(633\) 0 0
\(634\) 27.1573 1.07856
\(635\) 4.33778 0.172140
\(636\) 0 0
\(637\) 2.93944i 0.116465i
\(638\) 8.13865i 0.322212i
\(639\) 0 0
\(640\) 2.76612i 0.109341i
\(641\) 2.95641 0.116771 0.0583857 0.998294i \(-0.481405\pi\)
0.0583857 + 0.998294i \(0.481405\pi\)
\(642\) 0 0
\(643\) −3.45292 −0.136170 −0.0680849 0.997680i \(-0.521689\pi\)
−0.0680849 + 0.997680i \(0.521689\pi\)
\(644\) 0.685627i 0.0270175i
\(645\) 0 0
\(646\) 19.3871 9.25256i 0.762774 0.364037i
\(647\) 19.8964i 0.782208i 0.920346 + 0.391104i \(0.127907\pi\)
−0.920346 + 0.391104i \(0.872093\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 7.79369i 0.305693i
\(651\) 0 0
\(652\) −21.9200 −0.858454
\(653\) 6.90350i 0.270155i 0.990835 + 0.135077i \(0.0431283\pi\)
−0.990835 + 0.135077i \(0.956872\pi\)
\(654\) 0 0
\(655\) 43.7961 1.71125
\(656\) 2.37594 0.0927649
\(657\) 0 0
\(658\) 5.87887i 0.229182i
\(659\) −25.4214 −0.990275 −0.495138 0.868815i \(-0.664882\pi\)
−0.495138 + 0.868815i \(0.664882\pi\)
\(660\) 0 0
\(661\) 14.4866i 0.563465i −0.959493 0.281733i \(-0.909091\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(662\) 5.35655i 0.208188i
\(663\) 0 0
\(664\) 7.07681i 0.274634i
\(665\) 10.8815 5.19325i 0.421967 0.201385i
\(666\) 0 0
\(667\) 1.13226i 0.0438413i
\(668\) −17.7892 −0.688284
\(669\) 0 0
\(670\) 18.1582 0.701512
\(671\) 20.9967i 0.810569i
\(672\) 0 0
\(673\) 36.1465i 1.39334i −0.717390 0.696672i \(-0.754663\pi\)
0.717390 0.696672i \(-0.245337\pi\)
\(674\) 17.8875i 0.689003i
\(675\) 0 0
\(676\) 4.35972 0.167681
\(677\) −42.5564 −1.63558 −0.817788 0.575520i \(-0.804800\pi\)
−0.817788 + 0.575520i \(0.804800\pi\)
\(678\) 0 0
\(679\) 3.11275i 0.119456i
\(680\) 13.6322 0.522770
\(681\) 0 0
\(682\) −10.6556 −0.408026
\(683\) −14.0355 −0.537053 −0.268526 0.963272i \(-0.586537\pi\)
−0.268526 + 0.963272i \(0.586537\pi\)
\(684\) 0 0
\(685\) −15.5287 −0.593322
\(686\) 1.00000 0.0381802
\(687\) 0 0
\(688\) −8.15699 −0.310982
\(689\) 10.2151i 0.389164i
\(690\) 0 0
\(691\) −8.90410 −0.338728 −0.169364 0.985554i \(-0.554171\pi\)
−0.169364 + 0.985554i \(0.554171\pi\)
\(692\) −9.66678 −0.367476
\(693\) 0 0
\(694\) 18.5992i 0.706014i
\(695\) 61.0676i 2.31643i
\(696\) 0 0
\(697\) 11.7093i 0.443520i
\(698\) 12.7507 0.482620
\(699\) 0 0
\(700\) 2.65142 0.100214
\(701\) 47.9871i 1.81245i 0.422798 + 0.906224i \(0.361048\pi\)
−0.422798 + 0.906224i \(0.638952\pi\)
\(702\) 0 0
\(703\) 38.4529 18.3518i 1.45028 0.692152i
\(704\) 4.92827i 0.185741i
\(705\) 0 0
\(706\) 17.5745i 0.661426i
\(707\) 8.64499i 0.325128i
\(708\) 0 0
\(709\) −24.3533 −0.914609 −0.457305 0.889310i \(-0.651185\pi\)
−0.457305 + 0.889310i \(0.651185\pi\)
\(710\) 30.7776i 1.15506i
\(711\) 0 0
\(712\) 13.5026 0.506030
\(713\) −1.48243 −0.0555173
\(714\) 0 0
\(715\) 40.0709i 1.49857i
\(716\) −14.4295 −0.539254
\(717\) 0 0
\(718\) 17.6290i 0.657908i
\(719\) 8.86512i 0.330613i 0.986242 + 0.165307i \(0.0528614\pi\)
−0.986242 + 0.165307i \(0.947139\pi\)
\(720\) 0 0
\(721\) 4.49761i 0.167500i
\(722\) 11.9504 14.7712i 0.444747 0.549727i
\(723\) 0 0
\(724\) 11.5880i 0.430666i
\(725\) −4.37862 −0.162618
\(726\) 0 0
\(727\) −19.1573 −0.710506 −0.355253 0.934770i \(-0.615605\pi\)
−0.355253 + 0.934770i \(0.615605\pi\)
\(728\) 2.93944i 0.108943i
\(729\) 0 0
\(730\) 7.89491i 0.292204i
\(731\) 40.1998i 1.48684i
\(732\) 0 0
\(733\) 40.2220 1.48563 0.742816 0.669495i \(-0.233490\pi\)
0.742816 + 0.669495i \(0.233490\pi\)
\(734\) −32.1925 −1.18825
\(735\) 0 0
\(736\) 0.685627i 0.0252726i
\(737\) −32.3516 −1.19169
\(738\) 0 0
\(739\) 47.6138 1.75150 0.875752 0.482762i \(-0.160366\pi\)
0.875752 + 0.482762i \(0.160366\pi\)
\(740\) 27.0385 0.993955
\(741\) 0 0
\(742\) 3.47519 0.127578
\(743\) 39.8593 1.46229 0.731147 0.682220i \(-0.238985\pi\)
0.731147 + 0.682220i \(0.238985\pi\)
\(744\) 0 0
\(745\) −3.79305 −0.138967
\(746\) 23.4458i 0.858411i
\(747\) 0 0
\(748\) −24.2878 −0.888051
\(749\) 9.66678 0.353216
\(750\) 0 0
\(751\) 47.3831i 1.72904i 0.502603 + 0.864518i \(0.332376\pi\)
−0.502603 + 0.864518i \(0.667624\pi\)
\(752\) 5.87887i 0.214380i
\(753\) 0 0
\(754\) 4.85425i 0.176781i
\(755\) −63.1667 −2.29887
\(756\) 0 0
\(757\) 39.0966 1.42099 0.710495 0.703703i \(-0.248471\pi\)
0.710495 + 0.703703i \(0.248471\pi\)
\(758\) 1.27600i 0.0463462i
\(759\) 0 0
\(760\) 10.8815 5.19325i 0.394714 0.188379i
\(761\) 53.0230i 1.92208i −0.276404 0.961041i \(-0.589143\pi\)
0.276404 0.961041i \(-0.410857\pi\)
\(762\) 0 0
\(763\) 14.6895i 0.531797i
\(764\) 3.36772i 0.121840i
\(765\) 0 0
\(766\) 9.66343 0.349154
\(767\) 0 0
\(768\) 0 0
\(769\) 2.90410 0.104725 0.0523623 0.998628i \(-0.483325\pi\)
0.0523623 + 0.998628i \(0.483325\pi\)
\(770\) −13.6322 −0.491270
\(771\) 0 0
\(772\) 16.0064i 0.576081i
\(773\) 38.0162 1.36735 0.683675 0.729787i \(-0.260381\pi\)
0.683675 + 0.729787i \(0.260381\pi\)
\(774\) 0 0
\(775\) 5.73277i 0.205927i
\(776\) 3.11275i 0.111741i
\(777\) 0 0
\(778\) 27.3098i 0.979105i
\(779\) 4.46070 + 9.34660i 0.159821 + 0.334877i
\(780\) 0 0
\(781\) 54.8349i 1.96215i
\(782\) −3.37895 −0.120831
\(783\) 0 0
\(784\) 1.00000 0.0357143
\(785\) 15.3131i 0.546548i
\(786\) 0 0
\(787\) 53.0094i 1.88958i −0.327674 0.944791i \(-0.606265\pi\)
0.327674 0.944791i \(-0.393735\pi\)
\(788\) 5.87887i 0.209426i
\(789\) 0 0
\(790\) −30.6433 −1.09024
\(791\) −11.0111 −0.391511
\(792\) 0 0
\(793\) 12.5234i 0.444718i
\(794\) −22.6018 −0.802108
\(795\) 0 0
\(796\) 7.43368 0.263480
\(797\) 46.9727 1.66386 0.831928 0.554883i \(-0.187237\pi\)
0.831928 + 0.554883i \(0.1872