Properties

Label 2268.2.k.g.1297.3
Level $2268$
Weight $2$
Character 2268.1297
Analytic conductor $18.110$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2268.k (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.1100711784\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \( x^{16} - 9x^{14} + 31x^{12} - 282x^{10} + 1695x^{8} - 3318x^{6} + 4606x^{4} - 4116x^{2} + 2401 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 3^{7} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1297.3
Root \(1.04556 - 0.339889i\) of defining polynomial
Character \(\chi\) \(=\) 2268.1297
Dual form 2268.2.k.g.1621.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.515559 + 0.892975i) q^{5} +(1.55575 - 2.14001i) q^{7} +O(q^{10})\) \(q+(-0.515559 + 0.892975i) q^{5} +(1.55575 - 2.14001i) q^{7} +(0.792879 + 1.37331i) q^{11} +5.04830 q^{13} +(-2.58242 - 4.47288i) q^{17} +(-0.392975 + 0.680652i) q^{19} +(2.93289 - 5.07991i) q^{23} +(1.96840 + 3.40936i) q^{25} -8.89021 q^{29} +(0.575423 + 0.996661i) q^{31} +(1.10889 + 2.49255i) q^{35} +(4.07991 - 7.06661i) q^{37} +7.74411 q^{41} -2.53256 q^{43} +(-4.24595 + 7.35420i) q^{47} +(-2.15926 - 6.65865i) q^{49} +(2.41270 + 4.17892i) q^{53} -1.63510 q^{55} +(-1.93622 - 3.35364i) q^{59} +(4.82204 - 8.35201i) q^{61} +(-2.60270 + 4.50801i) q^{65} +(0.837220 + 1.45011i) q^{67} +14.2795 q^{71} +(3.04382 + 5.27205i) q^{73} +(4.17241 + 0.439762i) q^{77} +(4.15533 - 7.19724i) q^{79} -14.2419 q^{83} +5.32556 q^{85} +(6.69272 - 11.5921i) q^{89} +(7.85392 - 10.8034i) q^{91} +(-0.405203 - 0.701833i) q^{95} +5.34999 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 6 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 6 q^{7} - 20 q^{13} + 8 q^{19} - 8 q^{31} - 4 q^{37} + 20 q^{43} + 10 q^{49} - 32 q^{55} + 28 q^{61} + 18 q^{67} - 20 q^{79} + 76 q^{85} - 2 q^{91} - 84 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(1135\) \(1541\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −0.515559 + 0.892975i −0.230565 + 0.399350i −0.957975 0.286853i \(-0.907391\pi\)
0.727409 + 0.686204i \(0.240724\pi\)
\(6\) 0 0
\(7\) 1.55575 2.14001i 0.588020 0.808846i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 0.792879 + 1.37331i 0.239062 + 0.414067i 0.960445 0.278468i \(-0.0898268\pi\)
−0.721383 + 0.692536i \(0.756493\pi\)
\(12\) 0 0
\(13\) 5.04830 1.40015 0.700074 0.714071i \(-0.253150\pi\)
0.700074 + 0.714071i \(0.253150\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −2.58242 4.47288i −0.626329 1.08483i −0.988282 0.152637i \(-0.951223\pi\)
0.361954 0.932196i \(-0.382110\pi\)
\(18\) 0 0
\(19\) −0.392975 + 0.680652i −0.0901546 + 0.156152i −0.907576 0.419888i \(-0.862069\pi\)
0.817421 + 0.576040i \(0.195403\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 2.93289 5.07991i 0.611549 1.05923i −0.379431 0.925220i \(-0.623880\pi\)
0.990980 0.134014i \(-0.0427866\pi\)
\(24\) 0 0
\(25\) 1.96840 + 3.40936i 0.393679 + 0.681873i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −8.89021 −1.65087 −0.825435 0.564496i \(-0.809070\pi\)
−0.825435 + 0.564496i \(0.809070\pi\)
\(30\) 0 0
\(31\) 0.575423 + 0.996661i 0.103349 + 0.179006i 0.913062 0.407820i \(-0.133711\pi\)
−0.809713 + 0.586825i \(0.800377\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1.10889 + 2.49255i 0.187436 + 0.421318i
\(36\) 0 0
\(37\) 4.07991 7.06661i 0.670732 1.16174i −0.306964 0.951721i \(-0.599313\pi\)
0.977697 0.210022i \(-0.0673535\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 7.74411 1.20943 0.604714 0.796443i \(-0.293288\pi\)
0.604714 + 0.796443i \(0.293288\pi\)
\(42\) 0 0
\(43\) −2.53256 −0.386212 −0.193106 0.981178i \(-0.561856\pi\)
−0.193106 + 0.981178i \(0.561856\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −4.24595 + 7.35420i −0.619335 + 1.07272i 0.370272 + 0.928923i \(0.379264\pi\)
−0.989607 + 0.143796i \(0.954069\pi\)
\(48\) 0 0
\(49\) −2.15926 6.65865i −0.308465 0.951236i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 2.41270 + 4.17892i 0.331410 + 0.574019i 0.982789 0.184734i \(-0.0591423\pi\)
−0.651378 + 0.758753i \(0.725809\pi\)
\(54\) 0 0
\(55\) −1.63510 −0.220477
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −1.93622 3.35364i −0.252075 0.436607i 0.712022 0.702157i \(-0.247780\pi\)
−0.964097 + 0.265551i \(0.914446\pi\)
\(60\) 0 0
\(61\) 4.82204 8.35201i 0.617398 1.06937i −0.372560 0.928008i \(-0.621520\pi\)
0.989959 0.141357i \(-0.0451467\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −2.60270 + 4.50801i −0.322825 + 0.559150i
\(66\) 0 0
\(67\) 0.837220 + 1.45011i 0.102283 + 0.177159i 0.912625 0.408798i \(-0.134052\pi\)
−0.810342 + 0.585957i \(0.800719\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 14.2795 1.69467 0.847333 0.531062i \(-0.178207\pi\)
0.847333 + 0.531062i \(0.178207\pi\)
\(72\) 0 0
\(73\) 3.04382 + 5.27205i 0.356252 + 0.617047i 0.987331 0.158671i \(-0.0507211\pi\)
−0.631079 + 0.775718i \(0.717388\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 4.17241 + 0.439762i 0.475490 + 0.0501155i
\(78\) 0 0
\(79\) 4.15533 7.19724i 0.467511 0.809753i −0.531800 0.846870i \(-0.678484\pi\)
0.999311 + 0.0371172i \(0.0118175\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −14.2419 −1.56325 −0.781626 0.623747i \(-0.785609\pi\)
−0.781626 + 0.623747i \(0.785609\pi\)
\(84\) 0 0
\(85\) 5.32556 0.577638
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 6.69272 11.5921i 0.709426 1.22876i −0.255644 0.966771i \(-0.582287\pi\)
0.965070 0.261992i \(-0.0843793\pi\)
\(90\) 0 0
\(91\) 7.85392 10.8034i 0.823315 1.13250i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −0.405203 0.701833i −0.0415730 0.0720065i
\(96\) 0 0
\(97\) 5.34999 0.543210 0.271605 0.962409i \(-0.412446\pi\)
0.271605 + 0.962409i \(0.412446\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1.59038 + 2.75462i 0.158249 + 0.274095i 0.934237 0.356652i \(-0.116082\pi\)
−0.775988 + 0.630747i \(0.782749\pi\)
\(102\) 0 0
\(103\) 5.70660 9.88412i 0.562288 0.973911i −0.435008 0.900426i \(-0.643255\pi\)
0.997296 0.0734850i \(-0.0234121\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −0.311386 + 0.539337i −0.0301028 + 0.0521396i −0.880684 0.473704i \(-0.842917\pi\)
0.850582 + 0.525843i \(0.176250\pi\)
\(108\) 0 0
\(109\) 0.971921 + 1.68342i 0.0930932 + 0.161242i 0.908811 0.417208i \(-0.136991\pi\)
−0.815718 + 0.578450i \(0.803658\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 3.58833 0.337561 0.168781 0.985654i \(-0.446017\pi\)
0.168781 + 0.985654i \(0.446017\pi\)
\(114\) 0 0
\(115\) 3.02415 + 5.23798i 0.282004 + 0.488445i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −13.5896 1.43231i −1.24576 0.131300i
\(120\) 0 0
\(121\) 4.24269 7.34855i 0.385699 0.668050i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −9.21489 −0.824205
\(126\) 0 0
\(127\) 11.6202 1.03113 0.515563 0.856852i \(-0.327583\pi\)
0.515563 + 0.856852i \(0.327583\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 4.07898 7.06501i 0.356382 0.617272i −0.630971 0.775806i \(-0.717343\pi\)
0.987354 + 0.158534i \(0.0506767\pi\)
\(132\) 0 0
\(133\) 0.845228 + 1.89990i 0.0732906 + 0.164742i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 7.28181 + 12.6125i 0.622127 + 1.07756i 0.989089 + 0.147320i \(0.0470647\pi\)
−0.366962 + 0.930236i \(0.619602\pi\)
\(138\) 0 0
\(139\) −11.8343 −1.00377 −0.501884 0.864935i \(-0.667360\pi\)
−0.501884 + 0.864935i \(0.667360\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 4.00269 + 6.93287i 0.334722 + 0.579756i
\(144\) 0 0
\(145\) 4.58343 7.93873i 0.380633 0.659276i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 7.02477 12.1673i 0.575492 0.996781i −0.420496 0.907294i \(-0.638144\pi\)
0.995988 0.0894868i \(-0.0285227\pi\)
\(150\) 0 0
\(151\) −1.24269 2.15240i −0.101128 0.175159i 0.811021 0.585016i \(-0.198912\pi\)
−0.912150 + 0.409857i \(0.865579\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −1.18666 −0.0953147
\(156\) 0 0
\(157\) 1.51967 + 2.63214i 0.121283 + 0.210068i 0.920274 0.391275i \(-0.127966\pi\)
−0.798991 + 0.601343i \(0.794633\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −6.30818 14.1795i −0.497154 1.11750i
\(162\) 0 0
\(163\) −8.75883 + 15.1707i −0.686045 + 1.18826i 0.287063 + 0.957912i \(0.407321\pi\)
−0.973107 + 0.230352i \(0.926012\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 24.5476 1.89955 0.949775 0.312935i \(-0.101312\pi\)
0.949775 + 0.312935i \(0.101312\pi\)
\(168\) 0 0
\(169\) 12.4854 0.960413
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0.0344569 0.0596811i 0.00261971 0.00453747i −0.864713 0.502267i \(-0.832499\pi\)
0.867332 + 0.497730i \(0.165833\pi\)
\(174\) 0 0
\(175\) 10.3584 + 1.09175i 0.783022 + 0.0825286i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 3.96086 + 6.86041i 0.296049 + 0.512771i 0.975228 0.221201i \(-0.0709976\pi\)
−0.679180 + 0.733972i \(0.737664\pi\)
\(180\) 0 0
\(181\) 3.59688 0.267354 0.133677 0.991025i \(-0.457322\pi\)
0.133677 + 0.991025i \(0.457322\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 4.20687 + 7.28651i 0.309295 + 0.535715i
\(186\) 0 0
\(187\) 4.09509 7.09291i 0.299463 0.518685i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −8.02458 + 13.8990i −0.580638 + 1.00569i 0.414766 + 0.909928i \(0.363864\pi\)
−0.995404 + 0.0957664i \(0.969470\pi\)
\(192\) 0 0
\(193\) 10.7865 + 18.6828i 0.776430 + 1.34482i 0.933987 + 0.357306i \(0.116305\pi\)
−0.157558 + 0.987510i \(0.550362\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −20.4441 −1.45659 −0.728293 0.685266i \(-0.759686\pi\)
−0.728293 + 0.685266i \(0.759686\pi\)
\(198\) 0 0
\(199\) −6.50056 11.2593i −0.460812 0.798150i 0.538189 0.842824i \(-0.319109\pi\)
−0.999002 + 0.0446737i \(0.985775\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −13.8310 + 19.0251i −0.970745 + 1.33530i
\(204\) 0 0
\(205\) −3.99255 + 6.91530i −0.278852 + 0.482985i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −1.24633 −0.0862101
\(210\) 0 0
\(211\) 4.23849 0.291789 0.145895 0.989300i \(-0.453394\pi\)
0.145895 + 0.989300i \(0.453394\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1.30569 2.26151i 0.0890470 0.154234i
\(216\) 0 0
\(217\) 3.02808 + 0.319152i 0.205559 + 0.0216655i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −13.0368 22.5805i −0.876953 1.51893i
\(222\) 0 0
\(223\) −11.6666 −0.781252 −0.390626 0.920549i \(-0.627742\pi\)
−0.390626 + 0.920549i \(0.627742\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −2.08989 3.61980i −0.138711 0.240255i 0.788298 0.615294i \(-0.210963\pi\)
−0.927009 + 0.375039i \(0.877629\pi\)
\(228\) 0 0
\(229\) 4.19086 7.25878i 0.276940 0.479674i −0.693683 0.720280i \(-0.744013\pi\)
0.970623 + 0.240607i \(0.0773464\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0.499512 0.865180i 0.0327241 0.0566798i −0.849200 0.528072i \(-0.822915\pi\)
0.881924 + 0.471392i \(0.156248\pi\)
\(234\) 0 0
\(235\) −4.37807 7.58305i −0.285594 0.494663i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −12.3082 −0.796154 −0.398077 0.917352i \(-0.630322\pi\)
−0.398077 + 0.917352i \(0.630322\pi\)
\(240\) 0 0
\(241\) −3.23916 5.61039i −0.208653 0.361397i 0.742638 0.669694i \(-0.233575\pi\)
−0.951290 + 0.308296i \(0.900241\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 7.05923 + 1.50477i 0.450998 + 0.0961360i
\(246\) 0 0
\(247\) −1.98386 + 3.43614i −0.126230 + 0.218636i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 12.2236 0.771544 0.385772 0.922594i \(-0.373935\pi\)
0.385772 + 0.922594i \(0.373935\pi\)
\(252\) 0 0
\(253\) 9.30169 0.584792
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −7.96355 + 13.7933i −0.496753 + 0.860401i −0.999993 0.00374541i \(-0.998808\pi\)
0.503240 + 0.864147i \(0.332141\pi\)
\(258\) 0 0
\(259\) −8.77525 19.7249i −0.545267 1.22565i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −11.5305 19.9714i −0.711002 1.23149i −0.964481 0.264150i \(-0.914908\pi\)
0.253480 0.967341i \(-0.418425\pi\)
\(264\) 0 0
\(265\) −4.97556 −0.305647
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 5.51107 + 9.54546i 0.336016 + 0.581997i 0.983679 0.179930i \(-0.0575871\pi\)
−0.647663 + 0.761927i \(0.724254\pi\)
\(270\) 0 0
\(271\) 2.74213 4.74951i 0.166572 0.288512i −0.770640 0.637271i \(-0.780063\pi\)
0.937213 + 0.348759i \(0.113397\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −3.12140 + 5.40643i −0.188228 + 0.326020i
\(276\) 0 0
\(277\) 15.0331 + 26.0381i 0.903253 + 1.56448i 0.823246 + 0.567685i \(0.192161\pi\)
0.0800068 + 0.996794i \(0.474506\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 11.8182 0.705013 0.352506 0.935809i \(-0.385329\pi\)
0.352506 + 0.935809i \(0.385329\pi\)
\(282\) 0 0
\(283\) −10.5605 18.2914i −0.627758 1.08731i −0.988001 0.154450i \(-0.950639\pi\)
0.360243 0.932859i \(-0.382694\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 12.0479 16.5725i 0.711167 0.978241i
\(288\) 0 0
\(289\) −4.83778 + 8.37928i −0.284575 + 0.492899i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 12.3020 0.718688 0.359344 0.933205i \(-0.383000\pi\)
0.359344 + 0.933205i \(0.383000\pi\)
\(294\) 0 0
\(295\) 3.99295 0.232479
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 14.8061 25.6449i 0.856259 1.48308i
\(300\) 0 0
\(301\) −3.94005 + 5.41970i −0.227100 + 0.312386i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 4.97209 + 8.61191i 0.284701 + 0.493117i
\(306\) 0 0
\(307\) −33.5033 −1.91213 −0.956067 0.293147i \(-0.905297\pi\)
−0.956067 + 0.293147i \(0.905297\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −14.8057 25.6442i −0.839555 1.45415i −0.890268 0.455438i \(-0.849483\pi\)
0.0507130 0.998713i \(-0.483851\pi\)
\(312\) 0 0
\(313\) 5.85745 10.1454i 0.331082 0.573452i −0.651642 0.758527i \(-0.725920\pi\)
0.982724 + 0.185075i \(0.0592529\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1.08084 + 1.87207i −0.0607061 + 0.105146i −0.894781 0.446505i \(-0.852669\pi\)
0.834075 + 0.551651i \(0.186002\pi\)
\(318\) 0 0
\(319\) −7.04886 12.2090i −0.394660 0.683572i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 4.05930 0.225866
\(324\) 0 0
\(325\) 9.93707 + 17.2115i 0.551209 + 0.954723i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 9.13238 + 20.5277i 0.503484 + 1.13173i
\(330\) 0 0
\(331\) −15.6001 + 27.0202i −0.857461 + 1.48517i 0.0168824 + 0.999857i \(0.494626\pi\)
−0.874343 + 0.485308i \(0.838707\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −1.72655 −0.0943313
\(336\) 0 0
\(337\) 3.88849 0.211820 0.105910 0.994376i \(-0.466225\pi\)
0.105910 + 0.994376i \(0.466225\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −0.912481 + 1.58046i −0.0494136 + 0.0855869i
\(342\) 0 0
\(343\) −17.6088 5.73840i −0.950787 0.309845i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −8.37831 14.5117i −0.449771 0.779027i 0.548600 0.836085i \(-0.315161\pi\)
−0.998371 + 0.0570585i \(0.981828\pi\)
\(348\) 0 0
\(349\) −31.8194 −1.70325 −0.851625 0.524151i \(-0.824383\pi\)
−0.851625 + 0.524151i \(0.824383\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −3.66867 6.35431i −0.195263 0.338206i 0.751723 0.659478i \(-0.229223\pi\)
−0.946987 + 0.321272i \(0.895889\pi\)
\(354\) 0 0
\(355\) −7.36193 + 12.7512i −0.390731 + 0.676765i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −7.16644 + 12.4126i −0.378230 + 0.655114i −0.990805 0.135299i \(-0.956801\pi\)
0.612574 + 0.790413i \(0.290134\pi\)
\(360\) 0 0
\(361\) 9.19114 + 15.9195i 0.483744 + 0.837870i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −6.27708 −0.328557
\(366\) 0 0
\(367\) −12.7865 22.1469i −0.667450 1.15606i −0.978615 0.205702i \(-0.934052\pi\)
0.311165 0.950356i \(-0.399281\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 12.6965 + 1.33818i 0.659169 + 0.0694748i
\(372\) 0 0
\(373\) −15.5734 + 26.9739i −0.806361 + 1.39666i 0.109008 + 0.994041i \(0.465233\pi\)
−0.915368 + 0.402617i \(0.868101\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −44.8805 −2.31146
\(378\) 0 0
\(379\) −6.72979 −0.345686 −0.172843 0.984949i \(-0.555295\pi\)
−0.172843 + 0.984949i \(0.555295\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −18.7673 + 32.5060i −0.958967 + 1.66098i −0.233949 + 0.972249i \(0.575165\pi\)
−0.725018 + 0.688730i \(0.758168\pi\)
\(384\) 0 0
\(385\) −2.54382 + 3.49913i −0.129645 + 0.178332i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 15.3213 + 26.5372i 0.776819 + 1.34549i 0.933766 + 0.357883i \(0.116501\pi\)
−0.156947 + 0.987607i \(0.550165\pi\)
\(390\) 0 0
\(391\) −30.2958 −1.53212
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 4.28464 + 7.42121i 0.215583 + 0.373401i
\(396\) 0 0
\(397\) −2.65885 + 4.60527i −0.133444 + 0.231132i −0.925002 0.379962i \(-0.875937\pi\)
0.791558 + 0.611094i \(0.209270\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −0.328399 + 0.568803i −0.0163994 + 0.0284047i −0.874109 0.485730i \(-0.838554\pi\)
0.857709 + 0.514135i \(0.171887\pi\)
\(402\) 0 0
\(403\) 2.90491 + 5.03145i 0.144704 + 0.250634i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 12.9395 0.641387
\(408\) 0 0
\(409\) 15.7994 + 27.3654i 0.781230 + 1.35313i 0.931226 + 0.364443i \(0.118741\pi\)
−0.149995 + 0.988687i \(0.547926\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −10.1891 1.07391i −0.501373 0.0528435i
\(414\) 0 0
\(415\) 7.34254 12.7177i 0.360431 0.624285i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 20.8848 1.02029 0.510146 0.860088i \(-0.329592\pi\)
0.510146 + 0.860088i \(0.329592\pi\)
\(420\) 0 0
\(421\) 13.5958 0.662617 0.331309 0.943522i \(-0.392510\pi\)
0.331309 + 0.943522i \(0.392510\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 10.1665 17.6088i 0.493145 0.854153i
\(426\) 0 0
\(427\) −10.3715 23.3129i −0.501910 1.12819i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 13.9416 + 24.1475i 0.671541 + 1.16314i 0.977467 + 0.211088i \(0.0677006\pi\)
−0.305926 + 0.952055i \(0.598966\pi\)
\(432\) 0 0
\(433\) −22.7059 −1.09118 −0.545589 0.838053i \(-0.683694\pi\)
−0.545589 + 0.838053i \(0.683694\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2.30510 + 3.99255i 0.110268 + 0.190990i
\(438\) 0 0
\(439\) −15.9508 + 27.6276i −0.761290 + 1.31859i 0.180895 + 0.983502i \(0.442100\pi\)
−0.942186 + 0.335091i \(0.891233\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 17.5629 30.4198i 0.834436 1.44529i −0.0600520 0.998195i \(-0.519127\pi\)
0.894488 0.447091i \(-0.147540\pi\)
\(444\) 0 0
\(445\) 6.90098 + 11.9529i 0.327138 + 0.566620i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −0.0966532 −0.00456135 −0.00228067 0.999997i \(-0.500726\pi\)
−0.00228067 + 0.999997i \(0.500726\pi\)
\(450\) 0 0
\(451\) 6.14014 + 10.6350i 0.289128 + 0.500785i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 5.59800 + 12.5831i 0.262438 + 0.589907i
\(456\) 0 0
\(457\) 8.50925 14.7385i 0.398046 0.689436i −0.595439 0.803401i \(-0.703022\pi\)
0.993485 + 0.113965i \(0.0363551\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 16.1763 0.753407 0.376704 0.926334i \(-0.377058\pi\)
0.376704 + 0.926334i \(0.377058\pi\)
\(462\) 0 0
\(463\) −12.4859 −0.580271 −0.290135 0.956986i \(-0.593700\pi\)
−0.290135 + 0.956986i \(0.593700\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 6.72717 11.6518i 0.311296 0.539181i −0.667347 0.744747i \(-0.732570\pi\)
0.978643 + 0.205566i \(0.0659035\pi\)
\(468\) 0 0
\(469\) 4.40575 + 0.464355i 0.203439 + 0.0214419i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −2.00802 3.47798i −0.0923286 0.159918i
\(474\) 0 0
\(475\) −3.09412 −0.141968
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 6.98107 + 12.0916i 0.318973 + 0.552478i 0.980274 0.197643i \(-0.0633287\pi\)
−0.661301 + 0.750121i \(0.729995\pi\)
\(480\) 0 0
\(481\) 20.5966 35.6744i 0.939124 1.62661i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −2.75824 + 4.77741i −0.125245 + 0.216931i
\(486\) 0 0
\(487\) 14.4858 + 25.0901i 0.656413 + 1.13694i 0.981538 + 0.191270i \(0.0612605\pi\)
−0.325124 + 0.945671i \(0.605406\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −41.7550 −1.88438 −0.942189 0.335081i \(-0.891236\pi\)
−0.942189 + 0.335081i \(0.891236\pi\)
\(492\) 0 0
\(493\) 22.9583 + 39.7649i 1.03399 + 1.79092i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 22.2154 30.5582i 0.996497 1.37072i
\(498\) 0 0
\(499\) −10.7230 + 18.5728i −0.480028 + 0.831433i −0.999738 0.0229099i \(-0.992707\pi\)
0.519709 + 0.854343i \(0.326040\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −28.3098 −1.26227 −0.631135 0.775673i \(-0.717411\pi\)
−0.631135 + 0.775673i \(0.717411\pi\)
\(504\) 0 0
\(505\) −3.27974 −0.145947
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −15.8142 + 27.3910i −0.700951 + 1.21408i 0.267182 + 0.963646i \(0.413908\pi\)
−0.968133 + 0.250437i \(0.919426\pi\)
\(510\) 0 0
\(511\) 16.0177 + 1.68822i 0.708580 + 0.0746826i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 5.88418 + 10.1917i 0.259288 + 0.449100i
\(516\) 0 0
\(517\) −13.4661 −0.592238
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −15.0364 26.0439i −0.658759 1.14100i −0.980937 0.194325i \(-0.937749\pi\)
0.322179 0.946679i \(-0.395585\pi\)
\(522\) 0 0
\(523\) 7.73793 13.4025i 0.338356 0.586050i −0.645768 0.763534i \(-0.723463\pi\)
0.984124 + 0.177484i \(0.0567959\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 2.97197 5.14760i 0.129461 0.224233i
\(528\) 0 0
\(529\) −5.70363 9.87898i −0.247984 0.429521i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 39.0946 1.69338
\(534\) 0 0
\(535\) −0.321076 0.556120i −0.0138813 0.0240432i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 7.43234 8.24482i 0.320133 0.355130i
\(540\) 0 0
\(541\) −8.11884 + 14.0622i −0.349056 + 0.604583i −0.986082 0.166259i \(-0.946831\pi\)
0.637026 + 0.770842i \(0.280164\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −2.00433 −0.0858562
\(546\) 0 0
\(547\) −38.9081 −1.66359 −0.831795 0.555083i \(-0.812687\pi\)
−0.831795 + 0.555083i \(0.812687\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 3.49363 6.05114i 0.148834 0.257787i
\(552\) 0 0
\(553\) −8.93747 20.0896i −0.380060 0.854296i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −2.86210 4.95730i −0.121271 0.210048i 0.798998 0.601334i \(-0.205364\pi\)
−0.920269 + 0.391286i \(0.872030\pi\)
\(558\) 0 0
\(559\) −12.7851 −0.540754
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 2.47334 + 4.28394i 0.104239 + 0.180547i 0.913427 0.407003i \(-0.133426\pi\)
−0.809188 + 0.587549i \(0.800093\pi\)
\(564\) 0 0
\(565\) −1.84999 + 3.20429i −0.0778299 + 0.134805i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 8.10972 14.0465i 0.339977 0.588858i −0.644451 0.764646i \(-0.722914\pi\)
0.984428 + 0.175788i \(0.0562473\pi\)
\(570\) 0 0
\(571\) 18.3029 + 31.7016i 0.765954 + 1.32667i 0.939741 + 0.341887i \(0.111066\pi\)
−0.173787 + 0.984783i \(0.555601\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 23.0923 0.963017
\(576\) 0 0
\(577\) −18.2684 31.6417i −0.760522 1.31726i −0.942582 0.333975i \(-0.891610\pi\)
0.182060 0.983287i \(-0.441723\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −22.1569 + 30.4778i −0.919223 + 1.26443i
\(582\) 0 0
\(583\) −3.82596 + 6.62676i −0.158455 + 0.274452i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −23.8474 −0.984289 −0.492144 0.870514i \(-0.663787\pi\)
−0.492144 + 0.870514i \(0.663787\pi\)
\(588\) 0 0
\(589\) −0.904506 −0.0372695
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 6.54751 11.3406i 0.268874 0.465704i −0.699697 0.714439i \(-0.746682\pi\)
0.968571 + 0.248736i \(0.0800151\pi\)
\(594\) 0 0
\(595\) 8.28526 11.3967i 0.339663 0.467220i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −18.5770 32.1762i −0.759034 1.31469i −0.943344 0.331817i \(-0.892338\pi\)
0.184310 0.982868i \(-0.440995\pi\)
\(600\) 0 0
\(601\) −17.0627 −0.696000 −0.348000 0.937494i \(-0.613139\pi\)
−0.348000 + 0.937494i \(0.613139\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 4.37471 + 7.57722i 0.177857 + 0.308058i
\(606\) 0 0
\(607\) −11.5973 + 20.0871i −0.470719 + 0.815310i −0.999439 0.0334867i \(-0.989339\pi\)
0.528720 + 0.848796i \(0.322672\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −21.4348 + 37.1262i −0.867160 + 1.50197i
\(612\) 0 0
\(613\) 22.2875 + 38.6030i 0.900182 + 1.55916i 0.827257 + 0.561824i \(0.189900\pi\)
0.0729255 + 0.997337i \(0.476766\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −6.25406 −0.251779 −0.125890 0.992044i \(-0.540178\pi\)
−0.125890 + 0.992044i \(0.540178\pi\)
\(618\) 0 0
\(619\) 0.770208 + 1.33404i 0.0309573 + 0.0536196i 0.881089 0.472951i \(-0.156811\pi\)
−0.850132 + 0.526570i \(0.823478\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −14.3950 32.3570i −0.576723 1.29635i
\(624\) 0 0
\(625\) −5.09116 + 8.81816i −0.203647 + 0.352726i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −42.1441 −1.68040
\(630\) 0 0
\(631\) −44.5148 −1.77210 −0.886052 0.463585i \(-0.846563\pi\)
−0.886052 + 0.463585i \(0.846563\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −5.99090 + 10.3765i −0.237742 + 0.411781i
\(636\) 0 0
\(637\) −10.9006 33.6149i −0.431897 1.33187i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 1.87520 + 3.24794i 0.0740660 + 0.128286i 0.900680 0.434484i \(-0.143069\pi\)
−0.826614 + 0.562770i \(0.809736\pi\)
\(642\) 0 0
\(643\) 1.63678 0.0645485 0.0322742 0.999479i \(-0.489725\pi\)
0.0322742 + 0.999479i \(0.489725\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 10.0748 + 17.4501i 0.396082 + 0.686034i 0.993239 0.116091i \(-0.0370363\pi\)
−0.597157 + 0.802125i \(0.703703\pi\)
\(648\) 0 0
\(649\) 3.07038 5.31806i 0.120523 0.208752i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 21.4570 37.1646i 0.839677 1.45436i −0.0504888 0.998725i \(-0.516078\pi\)
0.890165 0.455638i \(-0.150589\pi\)
\(654\) 0 0
\(655\) 4.20591 + 7.28486i 0.164339 + 0.284643i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −21.7052 −0.845515 −0.422758 0.906243i \(-0.638938\pi\)
−0.422758 + 0.906243i \(0.638938\pi\)
\(660\) 0 0
\(661\) 12.6907 + 21.9810i 0.493613 + 0.854962i 0.999973 0.00735996i \(-0.00234277\pi\)
−0.506360 + 0.862322i \(0.669009\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −2.13232 0.224742i −0.0826880 0.00871511i
\(666\) 0 0
\(667\) −26.0740 + 45.1614i −1.00959 + 1.74866i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 15.2932 0.590386
\(672\) 0 0
\(673\) −15.7735 −0.608024 −0.304012 0.952668i \(-0.598326\pi\)
−0.304012 + 0.952668i \(0.598326\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −5.32531 + 9.22370i −0.204668 + 0.354496i −0.950027 0.312168i \(-0.898945\pi\)
0.745359 + 0.666664i \(0.232278\pi\)
\(678\) 0 0
\(679\) 8.32328 11.4490i 0.319418 0.439373i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 14.3656 + 24.8819i 0.549683 + 0.952078i 0.998296 + 0.0583524i \(0.0185847\pi\)
−0.448613 + 0.893726i \(0.648082\pi\)
\(684\) 0 0
\(685\) −15.0168 −0.573763
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 12.1801 + 21.0965i 0.464023 + 0.803712i
\(690\) 0 0
\(691\) 19.6136 33.9717i 0.746136 1.29235i −0.203526 0.979069i \(-0.565240\pi\)
0.949662 0.313276i \(-0.101426\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 6.10126 10.5677i 0.231434 0.400855i
\(696\) 0 0
\(697\) −19.9985 34.6385i −0.757499 1.31203i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 34.1643 1.29037 0.645184 0.764028i \(-0.276781\pi\)
0.645184 + 0.764028i \(0.276781\pi\)
\(702\) 0 0
\(703\) 3.20660 + 5.55399i 0.120939 + 0.209473i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 8.36915 + 0.882088i 0.314754 + 0.0331743i
\(708\) 0 0
\(709\) −9.85352 + 17.0668i −0.370057 + 0.640957i −0.989574 0.144026i \(-0.953995\pi\)
0.619517 + 0.784983i \(0.287328\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 6.75060 0.252812
\(714\) 0 0
\(715\) −8.25450 −0.308701
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 5.87829 10.1815i 0.219223 0.379705i −0.735348 0.677690i \(-0.762981\pi\)
0.954571 + 0.297985i \(0.0963144\pi\)
\(720\) 0 0
\(721\) −12.2740 27.5894i −0.457108 1.02748i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −17.4995 30.3100i −0.649914 1.12568i
\(726\) 0 0
\(727\) −45.6322 −1.69240 −0.846202 0.532862i \(-0.821117\pi\)
−0.846202 + 0.532862i \(0.821117\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 6.54014 + 11.3279i 0.241896 + 0.418976i
\(732\) 0 0
\(733\) −19.4901 + 33.7579i −0.719885 + 1.24688i 0.241160 + 0.970485i \(0.422472\pi\)
−0.961045 + 0.276392i \(0.910861\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −1.32763 + 2.29952i −0.0489038 + 0.0847039i
\(738\) 0 0
\(739\) −11.7719 20.3895i −0.433036 0.750040i 0.564097 0.825708i \(-0.309224\pi\)
−0.997133 + 0.0756686i \(0.975891\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −8.19224 −0.300544 −0.150272 0.988645i \(-0.548015\pi\)
−0.150272 + 0.988645i \(0.548015\pi\)
\(744\) 0 0
\(745\) 7.24337 + 12.5459i 0.265377 + 0.459646i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0.669743 + 1.50544i 0.0244719 + 0.0550077i
\(750\) 0 0
\(751\) 14.0936 24.4109i 0.514284 0.890766i −0.485578 0.874193i \(-0.661391\pi\)
0.999863 0.0165733i \(-0.00527570\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 2.56271 0.0932667
\(756\) 0 0
\(757\) 7.42352 0.269812 0.134906 0.990858i \(-0.456927\pi\)
0.134906 + 0.990858i \(0.456927\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −15.3534 + 26.5928i −0.556559 + 0.963988i 0.441222 + 0.897398i \(0.354545\pi\)
−0.997780 + 0.0665900i \(0.978788\pi\)
\(762\) 0 0
\(763\) 5.11460 + 0.539066i 0.185161 + 0.0195155i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −9.77465 16.9302i −0.352942 0.611314i
\(768\) 0 0
\(769\) −40.1946 −1.44945 −0.724727 0.689037i \(-0.758034\pi\)
−0.724727 + 0.689037i \(0.758034\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −1.69611 2.93775i −0.0610050 0.105664i 0.833910 0.551901i \(-0.186097\pi\)
−0.894915 + 0.446237i \(0.852764\pi\)
\(774\) 0 0
\(775\) −2.26532 + 3.92365i −0.0813727 + 0.140942i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −3.04324 + 5.27105i −0.109035 + 0.188855i
\(780\) 0 0
\(781\) 11.3219 + 19.6101i 0.405130 + 0.701706i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −3.13392 −0.111854
\(786\) 0 0
\(787\) −5.41657 9.38177i −0.193080 0.334424i 0.753190 0.657804i \(-0.228514\pi\)
−0.946269 + 0.323379i \(0.895181\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 5.58256 7.67904i 0.198493 0.273035i
\(792\) 0 0
\(793\) 24.3431 42.1635i 0.864449 1.49727i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 46.9965 1.66470 0.832350 0.554250i \(-0.186995\pi\)
0.832350 + 0.554250i \(0.186995\pi\)
\(798\) 0 0
\(799\) 43.8593 1.55163
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0