Properties

Label 3024.2.q.g.2305.3
Level $3024$
Weight $2$
Character 3024.2305
Analytic conductor $24.147$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3024.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(24.1467615712\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
Defining polynomial: \(x^{6} - 3 x^{5} + 10 x^{4} - 15 x^{3} + 19 x^{2} - 12 x + 3\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 2305.3
Root \(0.500000 + 0.224437i\) of defining polynomial
Character \(\chi\) \(=\) 3024.2305
Dual form 3024.2.q.g.2881.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.794182 + 1.37556i) q^{5} +(-1.23855 + 2.33795i) q^{7} +O(q^{10})\) \(q+(0.794182 + 1.37556i) q^{5} +(-1.23855 + 2.33795i) q^{7} +(0.794182 - 1.37556i) q^{11} +(2.40545 - 4.16635i) q^{13} +(2.69963 + 4.67589i) q^{17} +(3.54944 - 6.14781i) q^{19} +(-0.150186 - 0.260130i) q^{23} +(1.23855 - 2.14523i) q^{25} +(-4.13781 - 7.16689i) q^{29} +2.71201 q^{31} +(-4.19963 + 0.153051i) q^{35} +(0.500000 - 0.866025i) q^{37} +(-2.93818 + 5.08907i) q^{41} +(0.833104 + 1.44298i) q^{43} +2.66621 q^{47} +(-3.93199 - 5.79133i) q^{49} +(-2.44437 - 4.23377i) q^{53} +2.52290 q^{55} +6.47710 q^{59} -4.47710 q^{61} +7.64145 q^{65} +10.0531 q^{67} +12.7207 q^{71} +(8.02654 + 13.9024i) q^{73} +(2.23236 + 3.56046i) q^{77} -8.38688 q^{79} +(1.18292 + 2.04887i) q^{83} +(-4.28799 + 7.42702i) q^{85} +(-1.60507 + 2.78007i) q^{89} +(6.76145 + 10.7840i) q^{91} +11.2756 q^{95} +(0.712008 + 1.23323i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - q^{5} - 2q^{7} + O(q^{10}) \) \( 6q - q^{5} - 2q^{7} - q^{11} + 8q^{13} + 4q^{17} + 3q^{19} - 7q^{23} + 2q^{25} + 5q^{29} + 40q^{31} - 13q^{35} + 3q^{37} + 6q^{43} + 18q^{47} + 12q^{49} - 15q^{53} + 26q^{55} + 28q^{59} - 16q^{61} - 24q^{65} + 2q^{67} + 14q^{71} + 19q^{73} - 10q^{77} + 10q^{79} + 2q^{83} - 2q^{85} + 9q^{89} + 46q^{91} + 8q^{95} + 28q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1135\) \(2593\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 0.794182 + 1.37556i 0.355169 + 0.615171i 0.987147 0.159816i \(-0.0510900\pi\)
−0.631978 + 0.774986i \(0.717757\pi\)
\(6\) 0 0
\(7\) −1.23855 + 2.33795i −0.468128 + 0.883661i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 0.794182 1.37556i 0.239455 0.414748i −0.721103 0.692828i \(-0.756365\pi\)
0.960558 + 0.278080i \(0.0896979\pi\)
\(12\) 0 0
\(13\) 2.40545 4.16635i 0.667151 1.15554i −0.311547 0.950231i \(-0.600847\pi\)
0.978697 0.205308i \(-0.0658196\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.69963 + 4.67589i 0.654756 + 1.13407i 0.981955 + 0.189115i \(0.0605620\pi\)
−0.327199 + 0.944955i \(0.606105\pi\)
\(18\) 0 0
\(19\) 3.54944 6.14781i 0.814298 1.41041i −0.0955331 0.995426i \(-0.530456\pi\)
0.909831 0.414979i \(-0.136211\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −0.150186 0.260130i −0.0313159 0.0542408i 0.849943 0.526875i \(-0.176636\pi\)
−0.881259 + 0.472634i \(0.843303\pi\)
\(24\) 0 0
\(25\) 1.23855 2.14523i 0.247710 0.429046i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −4.13781 7.16689i −0.768371 1.33086i −0.938446 0.345427i \(-0.887734\pi\)
0.170074 0.985431i \(-0.445599\pi\)
\(30\) 0 0
\(31\) 2.71201 0.487091 0.243545 0.969889i \(-0.421689\pi\)
0.243545 + 0.969889i \(0.421689\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −4.19963 + 0.153051i −0.709867 + 0.0258703i
\(36\) 0 0
\(37\) 0.500000 0.866025i 0.0821995 0.142374i −0.821995 0.569495i \(-0.807139\pi\)
0.904194 + 0.427121i \(0.140472\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −2.93818 + 5.08907i −0.458866 + 0.794780i −0.998901 0.0468628i \(-0.985078\pi\)
0.540035 + 0.841643i \(0.318411\pi\)
\(42\) 0 0
\(43\) 0.833104 + 1.44298i 0.127047 + 0.220052i 0.922531 0.385922i \(-0.126117\pi\)
−0.795484 + 0.605974i \(0.792783\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 2.66621 0.388906 0.194453 0.980912i \(-0.437707\pi\)
0.194453 + 0.980912i \(0.437707\pi\)
\(48\) 0 0
\(49\) −3.93199 5.79133i −0.561713 0.827332i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −2.44437 4.23377i −0.335760 0.581553i 0.647871 0.761750i \(-0.275660\pi\)
−0.983630 + 0.180197i \(0.942326\pi\)
\(54\) 0 0
\(55\) 2.52290 0.340188
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 6.47710 0.843247 0.421623 0.906771i \(-0.361460\pi\)
0.421623 + 0.906771i \(0.361460\pi\)
\(60\) 0 0
\(61\) −4.47710 −0.573234 −0.286617 0.958045i \(-0.592531\pi\)
−0.286617 + 0.958045i \(0.592531\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 7.64145 0.947805
\(66\) 0 0
\(67\) 10.0531 1.22818 0.614090 0.789236i \(-0.289523\pi\)
0.614090 + 0.789236i \(0.289523\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 12.7207 1.50967 0.754833 0.655917i \(-0.227718\pi\)
0.754833 + 0.655917i \(0.227718\pi\)
\(72\) 0 0
\(73\) 8.02654 + 13.9024i 0.939436 + 1.62715i 0.766527 + 0.642213i \(0.221983\pi\)
0.172909 + 0.984938i \(0.444683\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 2.23236 + 3.56046i 0.254401 + 0.405752i
\(78\) 0 0
\(79\) −8.38688 −0.943597 −0.471799 0.881706i \(-0.656395\pi\)
−0.471799 + 0.881706i \(0.656395\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 1.18292 + 2.04887i 0.129842 + 0.224893i 0.923615 0.383321i \(-0.125220\pi\)
−0.793773 + 0.608214i \(0.791886\pi\)
\(84\) 0 0
\(85\) −4.28799 + 7.42702i −0.465098 + 0.805573i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −1.60507 + 2.78007i −0.170138 + 0.294687i −0.938468 0.345367i \(-0.887755\pi\)
0.768330 + 0.640054i \(0.221088\pi\)
\(90\) 0 0
\(91\) 6.76145 + 10.7840i 0.708793 + 1.13047i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 11.2756 1.15685
\(96\) 0 0
\(97\) 0.712008 + 1.23323i 0.0722934 + 0.125216i 0.899906 0.436084i \(-0.143635\pi\)
−0.827613 + 0.561300i \(0.810302\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 6.01671 10.4212i 0.598685 1.03695i −0.394330 0.918969i \(-0.629023\pi\)
0.993015 0.117984i \(-0.0376432\pi\)
\(102\) 0 0
\(103\) −3.04944 5.28179i −0.300470 0.520430i 0.675772 0.737111i \(-0.263810\pi\)
−0.976243 + 0.216680i \(0.930477\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1.54325 + 2.67299i −0.149192 + 0.258408i −0.930929 0.365200i \(-0.881001\pi\)
0.781737 + 0.623608i \(0.214334\pi\)
\(108\) 0 0
\(109\) 1.14400 + 1.98146i 0.109575 + 0.189789i 0.915598 0.402095i \(-0.131718\pi\)
−0.806023 + 0.591884i \(0.798384\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 9.73236 16.8569i 0.915543 1.58577i 0.109440 0.993993i \(-0.465094\pi\)
0.806104 0.591774i \(-0.201572\pi\)
\(114\) 0 0
\(115\) 0.238550 0.413181i 0.0222449 0.0385293i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −14.2756 + 0.520259i −1.30864 + 0.0476921i
\(120\) 0 0
\(121\) 4.23855 + 7.34138i 0.385323 + 0.667399i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 11.8764 1.06225
\(126\) 0 0
\(127\) 13.4400 1.19260 0.596302 0.802760i \(-0.296636\pi\)
0.596302 + 0.802760i \(0.296636\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 1.58836 + 2.75113i 0.138776 + 0.240367i 0.927034 0.374978i \(-0.122350\pi\)
−0.788258 + 0.615345i \(0.789017\pi\)
\(132\) 0 0
\(133\) 9.97710 + 15.9128i 0.865124 + 1.37981i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −10.6316 + 18.4145i −0.908320 + 1.57326i −0.0919231 + 0.995766i \(0.529301\pi\)
−0.816397 + 0.577491i \(0.804032\pi\)
\(138\) 0 0
\(139\) −6.52654 + 11.3043i −0.553574 + 0.958818i 0.444439 + 0.895809i \(0.353403\pi\)
−0.998013 + 0.0630092i \(0.979930\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −3.82072 6.61769i −0.319505 0.553399i
\(144\) 0 0
\(145\) 6.57234 11.3836i 0.545803 0.945359i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 2.60439 + 4.51093i 0.213360 + 0.369550i 0.952764 0.303712i \(-0.0982261\pi\)
−0.739404 + 0.673262i \(0.764893\pi\)
\(150\) 0 0
\(151\) −0.261450 + 0.452845i −0.0212765 + 0.0368520i −0.876468 0.481461i \(-0.840106\pi\)
0.855191 + 0.518313i \(0.173440\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 2.15383 + 3.73054i 0.173000 + 0.299644i
\(156\) 0 0
\(157\) 8.86398 0.707422 0.353711 0.935355i \(-0.384920\pi\)
0.353711 + 0.935355i \(0.384920\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0.794182 0.0289431i 0.0625903 0.00228104i
\(162\) 0 0
\(163\) −10.9814 + 19.0204i −0.860132 + 1.48979i 0.0116689 + 0.999932i \(0.496286\pi\)
−0.871801 + 0.489860i \(0.837048\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1.65019 2.85821i 0.127695 0.221175i −0.795088 0.606494i \(-0.792575\pi\)
0.922783 + 0.385319i \(0.125909\pi\)
\(168\) 0 0
\(169\) −5.07234 8.78555i −0.390180 0.675812i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −19.1075 −1.45272 −0.726360 0.687315i \(-0.758789\pi\)
−0.726360 + 0.687315i \(0.758789\pi\)
\(174\) 0 0
\(175\) 3.48143 + 5.55264i 0.263171 + 0.419740i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −8.03706 13.9206i −0.600718 1.04047i −0.992712 0.120507i \(-0.961548\pi\)
0.391994 0.919968i \(-0.371785\pi\)
\(180\) 0 0
\(181\) 8.05308 0.598581 0.299291 0.954162i \(-0.403250\pi\)
0.299291 + 0.954162i \(0.403250\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1.58836 0.116779
\(186\) 0 0
\(187\) 8.57598 0.627138
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −23.9629 −1.73389 −0.866946 0.498402i \(-0.833920\pi\)
−0.866946 + 0.498402i \(0.833920\pi\)
\(192\) 0 0
\(193\) 9.76509 0.702907 0.351453 0.936205i \(-0.385688\pi\)
0.351453 + 0.936205i \(0.385688\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 18.2436 1.29980 0.649900 0.760020i \(-0.274811\pi\)
0.649900 + 0.760020i \(0.274811\pi\)
\(198\) 0 0
\(199\) −9.04944 15.6741i −0.641498 1.11111i −0.985098 0.171991i \(-0.944980\pi\)
0.343601 0.939116i \(-0.388353\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 21.8807 0.797418i 1.53572 0.0559678i
\(204\) 0 0
\(205\) −9.33379 −0.651900
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −5.63781 9.76497i −0.389975 0.675457i
\(210\) 0 0
\(211\) −0.166208 + 0.287880i −0.0114422 + 0.0198185i −0.871690 0.490058i \(-0.836976\pi\)
0.860248 + 0.509877i \(0.170309\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −1.32327 + 2.29197i −0.0902464 + 0.156311i
\(216\) 0 0
\(217\) −3.35896 + 6.34053i −0.228021 + 0.430423i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 25.9752 1.74728
\(222\) 0 0
\(223\) −3.16621 5.48403i −0.212025 0.367238i 0.740323 0.672251i \(-0.234672\pi\)
−0.952348 + 0.305013i \(0.901339\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 11.6545 20.1862i 0.773537 1.33981i −0.162075 0.986778i \(-0.551819\pi\)
0.935613 0.353028i \(-0.114848\pi\)
\(228\) 0 0
\(229\) 2.47710 + 4.29046i 0.163691 + 0.283522i 0.936190 0.351495i \(-0.114327\pi\)
−0.772498 + 0.635017i \(0.780993\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 7.13781 12.3630i 0.467613 0.809930i −0.531702 0.846932i \(-0.678447\pi\)
0.999315 + 0.0370017i \(0.0117807\pi\)
\(234\) 0 0
\(235\) 2.11745 + 3.66754i 0.138127 + 0.239244i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 2.48762 4.30868i 0.160911 0.278706i −0.774285 0.632837i \(-0.781890\pi\)
0.935196 + 0.354132i \(0.115224\pi\)
\(240\) 0 0
\(241\) 6.50000 11.2583i 0.418702 0.725213i −0.577107 0.816668i \(-0.695819\pi\)
0.995809 + 0.0914555i \(0.0291519\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 4.84362 10.0081i 0.309448 0.639392i
\(246\) 0 0
\(247\) −17.0760 29.5765i −1.08652 1.88191i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 2.43268 0.153549 0.0767746 0.997048i \(-0.475538\pi\)
0.0767746 + 0.997048i \(0.475538\pi\)
\(252\) 0 0
\(253\) −0.477100 −0.0299950
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −0.493810 0.855304i −0.0308030 0.0533524i 0.850213 0.526439i \(-0.176473\pi\)
−0.881016 + 0.473087i \(0.843140\pi\)
\(258\) 0 0
\(259\) 1.40545 + 2.24159i 0.0873302 + 0.139286i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −8.59269 + 14.8830i −0.529848 + 0.917724i 0.469545 + 0.882908i \(0.344418\pi\)
−0.999394 + 0.0348158i \(0.988916\pi\)
\(264\) 0 0
\(265\) 3.88255 6.72477i 0.238503 0.413099i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −11.4523 19.8360i −0.698262 1.20942i −0.969069 0.246791i \(-0.920624\pi\)
0.270807 0.962634i \(-0.412709\pi\)
\(270\) 0 0
\(271\) −7.00364 + 12.1307i −0.425441 + 0.736885i −0.996462 0.0840504i \(-0.973214\pi\)
0.571021 + 0.820936i \(0.306548\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1.96727 3.40741i −0.118631 0.205474i
\(276\) 0 0
\(277\) −14.1476 + 24.5044i −0.850049 + 1.47233i 0.0311139 + 0.999516i \(0.490095\pi\)
−0.881163 + 0.472813i \(0.843239\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 8.79782 + 15.2383i 0.524834 + 0.909039i 0.999582 + 0.0289175i \(0.00920600\pi\)
−0.474748 + 0.880122i \(0.657461\pi\)
\(282\) 0 0
\(283\) 18.5229 1.10107 0.550536 0.834811i \(-0.314423\pi\)
0.550536 + 0.834811i \(0.314423\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −8.25890 13.1724i −0.487508 0.777541i
\(288\) 0 0
\(289\) −6.07598 + 10.5239i −0.357411 + 0.619054i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 7.04256 12.1981i 0.411431 0.712619i −0.583616 0.812030i \(-0.698362\pi\)
0.995046 + 0.0994108i \(0.0316958\pi\)
\(294\) 0 0
\(295\) 5.14400 + 8.90966i 0.299495 + 0.518741i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −1.44506 −0.0835698
\(300\) 0 0
\(301\) −4.40545 + 0.160552i −0.253926 + 0.00925405i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −3.55563 6.15854i −0.203595 0.352637i
\(306\) 0 0
\(307\) 5.85532 0.334180 0.167090 0.985942i \(-0.446563\pi\)
0.167090 + 0.985942i \(0.446563\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0.810892 0.0459815 0.0229907 0.999736i \(-0.492681\pi\)
0.0229907 + 0.999736i \(0.492681\pi\)
\(312\) 0 0
\(313\) 10.5760 0.597790 0.298895 0.954286i \(-0.403382\pi\)
0.298895 + 0.954286i \(0.403382\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −12.1964 −0.685018 −0.342509 0.939515i \(-0.611277\pi\)
−0.342509 + 0.939515i \(0.611277\pi\)
\(318\) 0 0
\(319\) −13.1447 −0.735961
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 38.3287 2.13267
\(324\) 0 0
\(325\) −5.95853 10.3205i −0.330520 0.572477i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −3.30223 + 6.23345i −0.182058 + 0.343661i
\(330\) 0 0
\(331\) 15.6662 0.861093 0.430546 0.902568i \(-0.358321\pi\)
0.430546 + 0.902568i \(0.358321\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 7.98398 + 13.8287i 0.436211 + 0.755540i
\(336\) 0 0
\(337\) −4.21201 + 7.29541i −0.229443 + 0.397406i −0.957643 0.287958i \(-0.907024\pi\)
0.728200 + 0.685364i \(0.240357\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 2.15383 3.73054i 0.116636 0.202020i
\(342\) 0 0
\(343\) 18.4098 2.01993i 0.994035 0.109066i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0.567323 0.0304555 0.0152277 0.999884i \(-0.495153\pi\)
0.0152277 + 0.999884i \(0.495153\pi\)
\(348\) 0 0
\(349\) −0.00364189 0.00630794i −0.000194946 0.000337656i 0.865928 0.500169i \(-0.166729\pi\)
−0.866123 + 0.499831i \(0.833395\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 3.32691 5.76238i 0.177074 0.306701i −0.763803 0.645449i \(-0.776670\pi\)
0.940877 + 0.338748i \(0.110004\pi\)
\(354\) 0 0
\(355\) 10.1025 + 17.4981i 0.536186 + 0.928702i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −0.398568 + 0.690339i −0.0210356 + 0.0364347i −0.876352 0.481672i \(-0.840030\pi\)
0.855316 + 0.518107i \(0.173363\pi\)
\(360\) 0 0
\(361\) −15.6971 27.1881i −0.826162 1.43095i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −12.7491 + 22.0820i −0.667317 + 1.15583i
\(366\) 0 0
\(367\) −7.71634 + 13.3651i −0.402790 + 0.697652i −0.994061 0.108820i \(-0.965293\pi\)
0.591272 + 0.806472i \(0.298626\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 12.9258 0.471067i 0.671074 0.0244566i
\(372\) 0 0
\(373\) −5.12110 8.87000i −0.265160 0.459271i 0.702445 0.711738i \(-0.252092\pi\)
−0.967606 + 0.252467i \(0.918758\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −39.8131 −2.05048
\(378\) 0 0
\(379\) −25.0087 −1.28461 −0.642304 0.766450i \(-0.722021\pi\)
−0.642304 + 0.766450i \(0.722021\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 3.13348 + 5.42734i 0.160113 + 0.277324i 0.934909 0.354887i \(-0.115481\pi\)
−0.774796 + 0.632211i \(0.782147\pi\)
\(384\) 0 0
\(385\) −3.12474 + 5.89841i −0.159251 + 0.300611i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −10.8171 + 18.7357i −0.548448 + 0.949940i 0.449933 + 0.893062i \(0.351448\pi\)
−0.998381 + 0.0568774i \(0.981886\pi\)
\(390\) 0 0
\(391\) 0.810892 1.40451i 0.0410086 0.0710290i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −6.66071 11.5367i −0.335137 0.580473i
\(396\) 0 0
\(397\) 2.05308 3.55605i 0.103041 0.178473i −0.809895 0.586575i \(-0.800476\pi\)
0.912936 + 0.408102i \(0.133809\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 8.37085 + 14.4987i 0.418021 + 0.724033i 0.995740 0.0922024i \(-0.0293907\pi\)
−0.577720 + 0.816235i \(0.696057\pi\)
\(402\) 0 0
\(403\) 6.52359 11.2992i 0.324963 0.562853i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −0.794182 1.37556i −0.0393661 0.0681842i
\(408\) 0 0
\(409\) −8.76509 −0.433406 −0.216703 0.976238i \(-0.569530\pi\)
−0.216703 + 0.976238i \(0.569530\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −8.02221 + 15.1431i −0.394747 + 0.745144i
\(414\) 0 0
\(415\) −1.87890 + 3.25436i −0.0922318 + 0.159750i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −0.210149 + 0.363988i −0.0102664 + 0.0177820i −0.871113 0.491083i \(-0.836601\pi\)
0.860847 + 0.508865i \(0.169935\pi\)
\(420\) 0 0
\(421\) 3.28799 + 5.69497i 0.160247 + 0.277556i 0.934957 0.354761i \(-0.115438\pi\)
−0.774710 + 0.632316i \(0.782104\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 13.3745 0.648758
\(426\) 0 0
\(427\) 5.54511 10.4672i 0.268347 0.506544i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 11.0439 + 19.1287i 0.531968 + 0.921395i 0.999304 + 0.0373155i \(0.0118806\pi\)
−0.467336 + 0.884080i \(0.654786\pi\)
\(432\) 0 0
\(433\) −9.43268 −0.453306 −0.226653 0.973976i \(-0.572778\pi\)
−0.226653 + 0.973976i \(0.572778\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −2.13231 −0.102002
\(438\) 0 0
\(439\) 31.2064 1.48940 0.744701 0.667398i \(-0.232592\pi\)
0.744701 + 0.667398i \(0.232592\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 13.0545 0.620236 0.310118 0.950698i \(-0.399631\pi\)
0.310118 + 0.950698i \(0.399631\pi\)
\(444\) 0 0
\(445\) −5.09888 −0.241710
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 9.91706 0.468015 0.234008 0.972235i \(-0.424816\pi\)
0.234008 + 0.972235i \(0.424816\pi\)
\(450\) 0 0
\(451\) 4.66690 + 8.08330i 0.219756 + 0.380628i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −9.46431 + 17.8653i −0.443694 + 0.837538i
\(456\) 0 0
\(457\) −24.5229 −1.14713 −0.573566 0.819159i \(-0.694441\pi\)
−0.573566 + 0.819159i \(0.694441\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −1.75526 3.04020i −0.0817506 0.141596i 0.822251 0.569125i \(-0.192718\pi\)
−0.904002 + 0.427528i \(0.859384\pi\)
\(462\) 0 0
\(463\) −8.69413 + 15.0587i −0.404050 + 0.699836i −0.994210 0.107451i \(-0.965731\pi\)
0.590160 + 0.807286i \(0.299065\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 6.69894 11.6029i 0.309990 0.536918i −0.668370 0.743829i \(-0.733008\pi\)
0.978360 + 0.206911i \(0.0663410\pi\)
\(468\) 0 0
\(469\) −12.4512 + 23.5036i −0.574945 + 1.08529i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 2.64654 0.121688
\(474\) 0 0
\(475\) −8.79232 15.2287i −0.403419 0.698743i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −10.4029 + 18.0183i −0.475321 + 0.823279i −0.999600 0.0282667i \(-0.991001\pi\)
0.524280 + 0.851546i \(0.324335\pi\)
\(480\) 0 0
\(481\) −2.40545 4.16635i −0.109679 0.189969i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −1.13093 + 1.95882i −0.0513528 + 0.0889456i
\(486\) 0 0
\(487\) −16.2472 28.1410i −0.736231 1.27519i −0.954181 0.299230i \(-0.903270\pi\)
0.217950 0.975960i \(-0.430063\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −9.66071 + 16.7328i −0.435982 + 0.755142i −0.997375 0.0724067i \(-0.976932\pi\)
0.561394 + 0.827549i \(0.310265\pi\)
\(492\) 0 0
\(493\) 22.3411 38.6959i 1.00619 1.74277i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −15.7552 + 29.7402i −0.706717 + 1.33403i
\(498\) 0 0
\(499\) −5.57530 9.65670i −0.249585 0.432293i 0.713826 0.700323i \(-0.246961\pi\)
−0.963411 + 0.268030i \(0.913627\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −40.7651 −1.81763 −0.908813 0.417204i \(-0.863010\pi\)
−0.908813 + 0.417204i \(0.863010\pi\)
\(504\) 0 0
\(505\) 19.1135 0.850537
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 0.722528 + 1.25146i 0.0320255 + 0.0554698i 0.881594 0.472009i \(-0.156471\pi\)
−0.849568 + 0.527478i \(0.823138\pi\)
\(510\) 0 0
\(511\) −42.4443 + 1.54684i −1.87762 + 0.0684280i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 4.84362 8.38940i 0.213436 0.369681i
\(516\) 0 0
\(517\) 2.11745 3.66754i 0.0931255 0.161298i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −9.64214 16.7007i −0.422430 0.731670i 0.573747 0.819033i \(-0.305489\pi\)
−0.996177 + 0.0873630i \(0.972156\pi\)
\(522\) 0 0
\(523\) 18.3454 31.7752i 0.802189 1.38943i −0.115984 0.993251i \(-0.537002\pi\)
0.918173 0.396180i \(-0.129665\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 7.32141 + 12.6811i 0.318926 + 0.552396i
\(528\) 0 0
\(529\) 11.4549 19.8404i 0.498039 0.862628i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 14.1353 + 24.4830i 0.612266 + 1.06048i
\(534\) 0 0
\(535\) −4.90249 −0.211953
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −11.0891 + 0.809332i −0.477639 + 0.0348604i
\(540\) 0 0
\(541\) −1.62543 + 2.81532i −0.0698825 + 0.121040i −0.898849 0.438258i \(-0.855596\pi\)
0.828967 + 0.559298i \(0.188929\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −1.81708 + 3.14728i −0.0778352 + 0.134815i
\(546\) 0 0
\(547\) 2.95853 + 5.12432i 0.126498 + 0.219100i 0.922317 0.386433i \(-0.126293\pi\)
−0.795820 + 0.605534i \(0.792960\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −58.7476 −2.50273
\(552\) 0 0
\(553\) 10.3876 19.6081i 0.441724 0.833820i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −12.8040 22.1772i −0.542523 0.939678i −0.998758 0.0498188i \(-0.984136\pi\)
0.456235 0.889859i \(-0.349198\pi\)
\(558\) 0 0
\(559\) 8.01594 0.339038
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −46.6377 −1.96555 −0.982773 0.184817i \(-0.940831\pi\)
−0.982773 + 0.184817i \(0.940831\pi\)
\(564\) 0 0
\(565\) 30.9171 1.30069
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −31.1978 −1.30788 −0.653939 0.756547i \(-0.726885\pi\)
−0.653939 + 0.756547i \(0.726885\pi\)
\(570\) 0 0
\(571\) 15.6762 0.656030 0.328015 0.944672i \(-0.393620\pi\)
0.328015 + 0.944672i \(0.393620\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −0.744051 −0.0310291
\(576\) 0 0
\(577\) 6.99567 + 12.1169i 0.291234 + 0.504431i 0.974102 0.226110i \(-0.0726010\pi\)
−0.682868 + 0.730542i \(0.739268\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −6.25526 + 0.227966i −0.259512 + 0.00945763i
\(582\) 0 0
\(583\) −7.76509 −0.321597
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1.44801 + 2.50803i 0.0597658 + 0.103517i 0.894360 0.447348i \(-0.147631\pi\)
−0.834594 + 0.550865i \(0.814298\pi\)
\(588\) 0 0
\(589\) 9.62612 16.6729i 0.396637 0.686996i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 2.04394 3.54021i 0.0839346 0.145379i −0.821002 0.570925i \(-0.806585\pi\)
0.904937 + 0.425546i \(0.139918\pi\)
\(594\) 0 0
\(595\) −12.0531 19.2238i −0.494128 0.788100i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −19.7651 −0.807580 −0.403790 0.914852i \(-0.632307\pi\)
−0.403790 + 0.914852i \(0.632307\pi\)
\(600\) 0 0
\(601\) −13.4320 23.2649i −0.547902 0.948994i −0.998418 0.0562261i \(-0.982093\pi\)
0.450516 0.892768i \(-0.351240\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −6.73236 + 11.6608i −0.273709 + 0.474079i
\(606\) 0 0
\(607\) −7.62110 13.2001i −0.309331 0.535777i 0.668885 0.743366i \(-0.266772\pi\)
−0.978216 + 0.207589i \(0.933438\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 6.41342 11.1084i 0.259459 0.449396i
\(612\) 0 0
\(613\) −1.36033 2.35617i −0.0549434 0.0951648i 0.837246 0.546827i \(-0.184165\pi\)
−0.892189 + 0.451662i \(0.850831\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 9.21812 15.9663i 0.371108 0.642777i −0.618629 0.785684i \(-0.712311\pi\)
0.989736 + 0.142906i \(0.0456448\pi\)
\(618\) 0 0
\(619\) 0.0537728 0.0931373i 0.00216131 0.00374350i −0.864943 0.501871i \(-0.832645\pi\)
0.867104 + 0.498127i \(0.165979\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −4.51169 7.19583i −0.180757 0.288295i
\(624\) 0 0
\(625\) 3.23924 + 5.61053i 0.129570 + 0.224421i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 5.39926 0.215282
\(630\) 0 0
\(631\) −35.7266 −1.42225 −0.711126 0.703064i \(-0.751815\pi\)
−0.711126 + 0.703064i \(0.751815\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 10.6738 + 18.4875i 0.423576 + 0.733655i
\(636\) 0 0
\(637\) −33.5869 + 2.45133i −1.33076 + 0.0971254i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 8.65638 14.9933i 0.341906 0.592199i −0.642880 0.765967i \(-0.722261\pi\)
0.984787 + 0.173767i \(0.0555941\pi\)
\(642\) 0 0
\(643\) −14.4821 + 25.0838i −0.571119 + 0.989207i 0.425332 + 0.905037i \(0.360157\pi\)
−0.996451 + 0.0841700i \(0.973176\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.27816 + 2.21384i 0.0502497 + 0.0870350i 0.890056 0.455851i \(-0.150665\pi\)
−0.839807 + 0.542886i \(0.817332\pi\)
\(648\) 0 0
\(649\) 5.14400 8.90966i 0.201920 0.349735i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 14.9883 + 25.9605i 0.586538 + 1.01591i 0.994682 + 0.102996i \(0.0328428\pi\)
−0.408144 + 0.912918i \(0.633824\pi\)
\(654\) 0 0
\(655\) −2.52290 + 4.36979i −0.0985779 + 0.170742i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −7.63162 13.2183i −0.297286 0.514914i 0.678228 0.734851i \(-0.262748\pi\)
−0.975514 + 0.219937i \(0.929415\pi\)
\(660\) 0 0
\(661\) −27.2522 −1.05999 −0.529994 0.848001i \(-0.677806\pi\)
−0.529994 + 0.848001i \(0.677806\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −13.9654 + 26.3618i −0.541555 + 1.02227i
\(666\) 0 0
\(667\) −1.24288 + 2.15273i −0.0481245 + 0.0833541i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −3.55563 + 6.15854i −0.137264 + 0.237748i
\(672\) 0 0
\(673\) 23.2280 + 40.2320i 0.895372 + 1.55083i 0.833344 + 0.552755i \(0.186423\pi\)
0.0620280 + 0.998074i \(0.480243\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −5.09888 −0.195966 −0.0979830 0.995188i \(-0.531239\pi\)
−0.0979830 + 0.995188i \(0.531239\pi\)
\(678\) 0 0
\(679\) −3.76509 + 0.137215i −0.144491 + 0.00526582i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −7.77197 13.4614i −0.297386 0.515088i 0.678151 0.734923i \(-0.262782\pi\)
−0.975537 + 0.219835i \(0.929448\pi\)
\(684\) 0 0
\(685\) −33.7738 −1.29043
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −23.5192 −0.896009
\(690\) 0 0
\(691\) −23.2967 −0.886246 −0.443123 0.896461i \(-0.646130\pi\)
−0.443123 + 0.896461i \(0.646130\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −20.7330 −0.786449
\(696\) 0 0
\(697\) −31.7280 −1.20178
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 45.6464 1.72404 0.862020 0.506874i \(-0.169199\pi\)
0.862020 + 0.506874i \(0.169199\pi\)
\(702\) 0 0
\(703\) −3.54944 6.14781i −0.133870 0.231869i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 16.9123 + 26.9740i 0.636053 + 1.01446i
\(708\) 0 0
\(709\) 18.0014 0.676056 0.338028 0.941136i \(-0.390240\pi\)
0.338028 + 0.941136i \(0.390240\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −0.407305 0.705474i −0.0152537 0.0264202i
\(714\) 0 0
\(715\) 6.06870 10.5113i 0.226957 0.393100i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 18.4389 31.9371i 0.687654 1.19105i −0.284941 0.958545i \(-0.591974\pi\)
0.972595 0.232506i \(-0.0746926\pi\)
\(720\) 0 0
\(721\) 16.1254 0.587674i 0.600542 0.0218861i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −20.4995 −0.761333
\(726\) 0 0
\(727\) −15.2429 26.4014i −0.565327 0.979175i −0.997019 0.0771543i \(-0.975417\pi\)
0.431692 0.902021i \(-0.357917\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −4.49814 + 7.79101i −0.166370 + 0.288161i
\(732\) 0 0
\(733\) −3.07530 5.32657i −0.113589 0.196741i 0.803626 0.595135i \(-0.202901\pi\)
−0.917215 + 0.398393i \(0.869568\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 7.98398 13.8287i 0.294094 0.509385i
\(738\) 0 0
\(739\) 20.3912 + 35.3186i 0.750103 + 1.29922i 0.947772 + 0.318947i \(0.103329\pi\)
−0.197670 + 0.980269i \(0.563337\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 7.25271 12.5621i 0.266076 0.460858i −0.701769 0.712405i \(-0.747606\pi\)
0.967845 + 0.251547i \(0.0809394\pi\)
\(744\) 0 0
\(745\) −4.13671 + 7.16500i −0.151557 + 0.262505i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −4.33792 6.91867i −0.158504 0.252803i
\(750\) 0 0
\(751\) 2.09455 + 3.62787i 0.0764314 + 0.132383i 0.901708 0.432346i \(-0.142314\pi\)
−0.825276 + 0.564729i \(0.808981\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −0.830556 −0.0302270
\(756\) 0 0
\(757\) 2.38688 0.0867525 0.0433763 0.999059i \(-0.486189\pi\)
0.0433763 + 0.999059i \(0.486189\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 1.81708 + 3.14728i 0.0658692 + 0.114089i 0.897079 0.441870i \(-0.145685\pi\)
−0.831210 + 0.555959i \(0.812351\pi\)
\(762\) 0 0
\(763\) −6.04944 + 0.220465i −0.219005 + 0.00798138i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 15.5803 26.9859i 0.562573 0.974404i
\(768\) 0 0
\(769\) −19.9672 + 34.5842i −0.720035 + 1.24714i 0.240950 + 0.970538i \(0.422541\pi\)
−0.960985 + 0.276600i \(0.910792\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −18.0698 31.2978i −0.649925 1.12570i −0.983140 0.182853i \(-0.941467\pi\)
0.333215 0.942851i \(-0.391867\pi\)
\(774\) 0 0
\(775\) 3.35896 5.81788i 0.120657 0.208985i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 20.8578 + 36.1267i 0.747308 + 1.29438i
\(780\) 0 0
\(781\) 10.1025 17.4981i 0.361497 0.626131i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 7.03961 + 12.1930i 0.251254 + 0.435186i
\(786\) 0 0
\(787\) 44.6377 1.59116 0.795582 0.605846i \(-0.207165\pi\)
0.795582 + 0.605846i \(0.207165\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 27.3566 + 43.6319i 0.972689 + 1.55137i
\(792\) 0 0
\(793\) −10.7694 + 18.6532i −0.382433 + 0.662394i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −26.2836 + 45.5245i −0.931012 + 1.61256i −0.149418 + 0.988774i \(0.547740\pi\)
−0.781595 + 0.623786i \(0.785593\pi\)
\(798\) 0 0
\(799\) 7.19777 + 12.4669i 0.254639 + 0.441047i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 25.4981 0.899810
\(804\) 0 0
\(805\) 0.670538 + 1.06946i 0.0236334 + 0.0376936i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0