Properties

Label 2352.2.bl.t.31.1
Level $2352$
Weight $2$
Character 2352.31
Analytic conductor $18.781$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2352.bl (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.7808145554\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.339738624.1
Defining polynomial: \(x^{8} - 4 x^{6} + 14 x^{4} - 8 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 31.1
Root \(-1.60021 + 0.923880i\) of defining polynomial
Character \(\chi\) \(=\) 2352.31
Dual form 2352.2.bl.t.607.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{3} +(-2.78415 + 1.60743i) q^{5} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{3} +(-2.78415 + 1.60743i) q^{5} +(-0.500000 - 0.866025i) q^{9} +(-1.18394 - 0.683549i) q^{11} +2.93015i q^{13} +3.21486i q^{15} +(5.98456 + 3.45519i) q^{17} +(-3.67725 - 6.36918i) q^{19} +(3.14171 - 1.81387i) q^{23} +(2.66765 - 4.62051i) q^{25} -1.00000 q^{27} -1.11185 q^{29} +(-4.35159 + 7.53718i) q^{31} +(-1.18394 + 0.683549i) q^{33} +(-3.81896 - 6.61463i) q^{37} +(2.53759 + 1.46508i) q^{39} +0.833147i q^{41} -4.82362i q^{43} +(2.78415 + 1.60743i) q^{45} +(-1.47683 - 2.55795i) q^{47} +(5.98456 - 3.45519i) q^{51} +(2.28897 - 3.96462i) q^{53} +4.39502 q^{55} -7.35449 q^{57} +(7.04923 - 12.2096i) q^{59} +(-9.57981 + 5.53091i) q^{61} +(-4.71001 - 8.15797i) q^{65} +(-10.5261 - 6.07723i) q^{67} -3.62774i q^{69} -12.6249i q^{71} +(-5.62060 - 3.24505i) q^{73} +(-2.66765 - 4.62051i) q^{75} +(-6.74952 + 3.89684i) q^{79} +(-0.500000 + 0.866025i) q^{81} +8.87502 q^{83} -22.2159 q^{85} +(-0.555927 + 0.962893i) q^{87} +(-10.9246 + 6.30731i) q^{89} +(4.35159 + 7.53718i) q^{93} +(20.4760 + 11.8218i) q^{95} -13.8811i q^{97} +1.36710i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{3} - 4q^{9} + O(q^{10}) \) \( 8q + 4q^{3} - 4q^{9} + 24q^{23} + 12q^{25} - 8q^{27} + 16q^{29} - 16q^{31} - 8q^{47} - 8q^{53} + 64q^{55} + 24q^{59} - 48q^{61} + 8q^{65} - 48q^{67} - 48q^{73} - 12q^{75} - 24q^{79} - 4q^{81} - 64q^{85} + 8q^{87} - 48q^{89} + 16q^{93} + 72q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1471\) \(1765\) \(2257\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\)

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
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) 0 0
\(5\) −2.78415 + 1.60743i −1.24511 + 0.718864i −0.970130 0.242586i \(-0.922004\pi\)
−0.274979 + 0.961450i \(0.588671\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0 0
\(11\) −1.18394 0.683549i −0.356972 0.206098i 0.310780 0.950482i \(-0.399410\pi\)
−0.667752 + 0.744384i \(0.732743\pi\)
\(12\) 0 0
\(13\) 2.93015i 0.812678i 0.913722 + 0.406339i \(0.133195\pi\)
−0.913722 + 0.406339i \(0.866805\pi\)
\(14\) 0 0
\(15\) 3.21486i 0.830072i
\(16\) 0 0
\(17\) 5.98456 + 3.45519i 1.45147 + 0.838006i 0.998565 0.0535532i \(-0.0170547\pi\)
0.452904 + 0.891559i \(0.350388\pi\)
\(18\) 0 0
\(19\) −3.67725 6.36918i −0.843618 1.46119i −0.886816 0.462123i \(-0.847088\pi\)
0.0431974 0.999067i \(-0.486246\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3.14171 1.81387i 0.655092 0.378218i −0.135312 0.990803i \(-0.543204\pi\)
0.790405 + 0.612585i \(0.209870\pi\)
\(24\) 0 0
\(25\) 2.66765 4.62051i 0.533530 0.924102i
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −1.11185 −0.206466 −0.103233 0.994657i \(-0.532919\pi\)
−0.103233 + 0.994657i \(0.532919\pi\)
\(30\) 0 0
\(31\) −4.35159 + 7.53718i −0.781569 + 1.35372i 0.149458 + 0.988768i \(0.452247\pi\)
−0.931027 + 0.364949i \(0.881086\pi\)
\(32\) 0 0
\(33\) −1.18394 + 0.683549i −0.206098 + 0.118991i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −3.81896 6.61463i −0.627833 1.08744i −0.987986 0.154546i \(-0.950609\pi\)
0.360152 0.932893i \(-0.382725\pi\)
\(38\) 0 0
\(39\) 2.53759 + 1.46508i 0.406339 + 0.234600i
\(40\) 0 0
\(41\) 0.833147i 0.130116i 0.997881 + 0.0650579i \(0.0207232\pi\)
−0.997881 + 0.0650579i \(0.979277\pi\)
\(42\) 0 0
\(43\) 4.82362i 0.735595i −0.929906 0.367797i \(-0.880112\pi\)
0.929906 0.367797i \(-0.119888\pi\)
\(44\) 0 0
\(45\) 2.78415 + 1.60743i 0.415036 + 0.239621i
\(46\) 0 0
\(47\) −1.47683 2.55795i −0.215418 0.373116i 0.737983 0.674819i \(-0.235778\pi\)
−0.953402 + 0.301703i \(0.902445\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 5.98456 3.45519i 0.838006 0.483823i
\(52\) 0 0
\(53\) 2.28897 3.96462i 0.314414 0.544582i −0.664898 0.746934i \(-0.731525\pi\)
0.979313 + 0.202352i \(0.0648585\pi\)
\(54\) 0 0
\(55\) 4.39502 0.592625
\(56\) 0 0
\(57\) −7.35449 −0.974127
\(58\) 0 0
\(59\) 7.04923 12.2096i 0.917732 1.58956i 0.114880 0.993379i \(-0.463352\pi\)
0.802852 0.596179i \(-0.203315\pi\)
\(60\) 0 0
\(61\) −9.57981 + 5.53091i −1.22657 + 0.708160i −0.966311 0.257379i \(-0.917141\pi\)
−0.260259 + 0.965539i \(0.583808\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −4.71001 8.15797i −0.584205 1.01187i
\(66\) 0 0
\(67\) −10.5261 6.07723i −1.28596 0.742452i −0.308032 0.951376i \(-0.599670\pi\)
−0.977932 + 0.208924i \(0.933004\pi\)
\(68\) 0 0
\(69\) 3.62774i 0.436728i
\(70\) 0 0
\(71\) 12.6249i 1.49830i −0.662402 0.749148i \(-0.730463\pi\)
0.662402 0.749148i \(-0.269537\pi\)
\(72\) 0 0
\(73\) −5.62060 3.24505i −0.657841 0.379805i 0.133613 0.991034i \(-0.457342\pi\)
−0.791454 + 0.611229i \(0.790676\pi\)
\(74\) 0 0
\(75\) −2.66765 4.62051i −0.308034 0.533530i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −6.74952 + 3.89684i −0.759380 + 0.438428i −0.829073 0.559140i \(-0.811131\pi\)
0.0696931 + 0.997568i \(0.477798\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 8.87502 0.974159 0.487080 0.873358i \(-0.338062\pi\)
0.487080 + 0.873358i \(0.338062\pi\)
\(84\) 0 0
\(85\) −22.2159 −2.40965
\(86\) 0 0
\(87\) −0.555927 + 0.962893i −0.0596016 + 0.103233i
\(88\) 0 0
\(89\) −10.9246 + 6.30731i −1.15800 + 0.668574i −0.950825 0.309729i \(-0.899762\pi\)
−0.207179 + 0.978303i \(0.566428\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 4.35159 + 7.53718i 0.451239 + 0.781569i
\(94\) 0 0
\(95\) 20.4760 + 11.8218i 2.10079 + 1.21289i
\(96\) 0 0
\(97\) 13.8811i 1.40942i −0.709497 0.704708i \(-0.751078\pi\)
0.709497 0.704708i \(-0.248922\pi\)
\(98\) 0 0
\(99\) 1.36710i 0.137398i
\(100\) 0 0
\(101\) −1.43666 0.829455i −0.142953 0.0825338i 0.426818 0.904338i \(-0.359635\pi\)
−0.569771 + 0.821804i \(0.692968\pi\)
\(102\) 0 0
\(103\) −0.653953 1.13268i −0.0644359 0.111606i 0.832008 0.554764i \(-0.187191\pi\)
−0.896444 + 0.443158i \(0.853858\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 6.19385 3.57602i 0.598782 0.345707i −0.169780 0.985482i \(-0.554306\pi\)
0.768562 + 0.639775i \(0.220973\pi\)
\(108\) 0 0
\(109\) 7.52215 13.0287i 0.720491 1.24793i −0.240312 0.970696i \(-0.577250\pi\)
0.960803 0.277231i \(-0.0894168\pi\)
\(110\) 0 0
\(111\) −7.63792 −0.724959
\(112\) 0 0
\(113\) −15.4530 −1.45369 −0.726846 0.686800i \(-0.759015\pi\)
−0.726846 + 0.686800i \(0.759015\pi\)
\(114\) 0 0
\(115\) −5.83133 + 10.1002i −0.543774 + 0.941845i
\(116\) 0 0
\(117\) 2.53759 1.46508i 0.234600 0.135446i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −4.56552 7.90772i −0.415047 0.718883i
\(122\) 0 0
\(123\) 0.721527 + 0.416574i 0.0650579 + 0.0375612i
\(124\) 0 0
\(125\) 1.07795i 0.0964149i
\(126\) 0 0
\(127\) 2.16478i 0.192094i −0.995377 0.0960468i \(-0.969380\pi\)
0.995377 0.0960468i \(-0.0306198\pi\)
\(128\) 0 0
\(129\) −4.17738 2.41181i −0.367797 0.212348i
\(130\) 0 0
\(131\) 2.48938 + 4.31174i 0.217499 + 0.376718i 0.954043 0.299671i \(-0.0968769\pi\)
−0.736544 + 0.676390i \(0.763544\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 2.78415 1.60743i 0.239621 0.138345i
\(136\) 0 0
\(137\) 1.84490 3.19546i 0.157620 0.273006i −0.776390 0.630253i \(-0.782951\pi\)
0.934010 + 0.357247i \(0.116284\pi\)
\(138\) 0 0
\(139\) −12.0577 −1.02272 −0.511360 0.859367i \(-0.670858\pi\)
−0.511360 + 0.859367i \(0.670858\pi\)
\(140\) 0 0
\(141\) −2.95367 −0.248744
\(142\) 0 0
\(143\) 2.00290 3.46913i 0.167491 0.290103i
\(144\) 0 0
\(145\) 3.09556 1.78722i 0.257073 0.148421i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1.65131 2.86015i −0.135280 0.234313i 0.790424 0.612560i \(-0.209860\pi\)
−0.925705 + 0.378247i \(0.876527\pi\)
\(150\) 0 0
\(151\) 16.4122 + 9.47557i 1.33560 + 0.771111i 0.986152 0.165843i \(-0.0530346\pi\)
0.349452 + 0.936954i \(0.386368\pi\)
\(152\) 0 0
\(153\) 6.91037i 0.558671i
\(154\) 0 0
\(155\) 27.9795i 2.24737i
\(156\) 0 0
\(157\) 0.767676 + 0.443218i 0.0612672 + 0.0353726i 0.530321 0.847797i \(-0.322072\pi\)
−0.469053 + 0.883170i \(0.655405\pi\)
\(158\) 0 0
\(159\) −2.28897 3.96462i −0.181527 0.314414i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 16.7609 9.67689i 1.31281 0.757953i 0.330251 0.943893i \(-0.392867\pi\)
0.982561 + 0.185941i \(0.0595332\pi\)
\(164\) 0 0
\(165\) 2.19751 3.80620i 0.171076 0.296312i
\(166\) 0 0
\(167\) 25.4855 1.97213 0.986065 0.166360i \(-0.0532014\pi\)
0.986065 + 0.166360i \(0.0532014\pi\)
\(168\) 0 0
\(169\) 4.41421 0.339555
\(170\) 0 0
\(171\) −3.67725 + 6.36918i −0.281206 + 0.487063i
\(172\) 0 0
\(173\) −18.7862 + 10.8462i −1.42829 + 0.824623i −0.996986 0.0775839i \(-0.975279\pi\)
−0.431303 + 0.902207i \(0.641946\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −7.04923 12.2096i −0.529853 0.917732i
\(178\) 0 0
\(179\) −10.6369 6.14122i −0.795039 0.459016i 0.0466943 0.998909i \(-0.485131\pi\)
−0.841734 + 0.539893i \(0.818465\pi\)
\(180\) 0 0
\(181\) 2.74444i 0.203993i −0.994785 0.101996i \(-0.967477\pi\)
0.994785 0.101996i \(-0.0325230\pi\)
\(182\) 0 0
\(183\) 11.0618i 0.817713i
\(184\) 0 0
\(185\) 21.2651 + 12.2774i 1.56344 + 0.902653i
\(186\) 0 0
\(187\) −4.72358 8.18148i −0.345422 0.598289i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −19.8196 + 11.4428i −1.43409 + 0.827974i −0.997430 0.0716507i \(-0.977173\pi\)
−0.436664 + 0.899625i \(0.643840\pi\)
\(192\) 0 0
\(193\) −7.30816 + 12.6581i −0.526053 + 0.911151i 0.473486 + 0.880801i \(0.342995\pi\)
−0.999539 + 0.0303495i \(0.990338\pi\)
\(194\) 0 0
\(195\) −9.42002 −0.674581
\(196\) 0 0
\(197\) 24.5430 1.74861 0.874307 0.485374i \(-0.161316\pi\)
0.874307 + 0.485374i \(0.161316\pi\)
\(198\) 0 0
\(199\) −3.02329 + 5.23650i −0.214316 + 0.371206i −0.953061 0.302779i \(-0.902085\pi\)
0.738745 + 0.673985i \(0.235419\pi\)
\(200\) 0 0
\(201\) −10.5261 + 6.07723i −0.742452 + 0.428655i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −1.33922 2.31960i −0.0935355 0.162008i
\(206\) 0 0
\(207\) −3.14171 1.81387i −0.218364 0.126073i
\(208\) 0 0
\(209\) 10.0543i 0.695471i
\(210\) 0 0
\(211\) 9.33513i 0.642657i 0.946968 + 0.321328i \(0.104129\pi\)
−0.946968 + 0.321328i \(0.895871\pi\)
\(212\) 0 0
\(213\) −10.9335 6.31243i −0.749148 0.432521i
\(214\) 0 0
\(215\) 7.75362 + 13.4297i 0.528792 + 0.915895i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −5.62060 + 3.24505i −0.379805 + 0.219280i
\(220\) 0 0
\(221\) −10.1242 + 17.5357i −0.681029 + 1.17958i
\(222\) 0 0
\(223\) −5.48794 −0.367500 −0.183750 0.982973i \(-0.558824\pi\)
−0.183750 + 0.982973i \(0.558824\pi\)
\(224\) 0 0
\(225\) −5.33530 −0.355687
\(226\) 0 0
\(227\) −0.519063 + 0.899043i −0.0344514 + 0.0596716i −0.882737 0.469867i \(-0.844302\pi\)
0.848286 + 0.529539i \(0.177635\pi\)
\(228\) 0 0
\(229\) −13.5133 + 7.80193i −0.892987 + 0.515566i −0.874918 0.484270i \(-0.839085\pi\)
−0.0180687 + 0.999837i \(0.505752\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −4.60780 7.98095i −0.301867 0.522849i 0.674692 0.738100i \(-0.264277\pi\)
−0.976559 + 0.215250i \(0.930943\pi\)
\(234\) 0 0
\(235\) 8.22345 + 4.74781i 0.536439 + 0.309713i
\(236\) 0 0
\(237\) 7.79367i 0.506253i
\(238\) 0 0
\(239\) 1.54809i 0.100137i 0.998746 + 0.0500687i \(0.0159440\pi\)
−0.998746 + 0.0500687i \(0.984056\pi\)
\(240\) 0 0
\(241\) 3.19154 + 1.84264i 0.205585 + 0.118695i 0.599258 0.800556i \(-0.295462\pi\)
−0.393673 + 0.919251i \(0.628796\pi\)
\(242\) 0 0
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 18.6627 10.7749i 1.18748 0.685590i
\(248\) 0 0
\(249\) 4.43751 7.68599i 0.281216 0.487080i
\(250\) 0 0
\(251\) −26.1940 −1.65335 −0.826676 0.562679i \(-0.809771\pi\)
−0.826676 + 0.562679i \(0.809771\pi\)
\(252\) 0 0
\(253\) −4.95947 −0.311799
\(254\) 0 0
\(255\) −11.1079 + 19.2395i −0.695606 + 1.20482i
\(256\) 0 0
\(257\) −0.721527 + 0.416574i −0.0450076 + 0.0259851i −0.522335 0.852740i \(-0.674939\pi\)
0.477327 + 0.878726i \(0.341606\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0.555927 + 0.962893i 0.0344110 + 0.0596016i
\(262\) 0 0
\(263\) −4.36661 2.52106i −0.269256 0.155455i 0.359293 0.933225i \(-0.383018\pi\)
−0.628550 + 0.777769i \(0.716351\pi\)
\(264\) 0 0
\(265\) 14.7174i 0.904085i
\(266\) 0 0
\(267\) 12.6146i 0.772002i
\(268\) 0 0
\(269\) 4.20537 + 2.42797i 0.256406 + 0.148036i 0.622694 0.782466i \(-0.286038\pi\)
−0.366288 + 0.930501i \(0.619372\pi\)
\(270\) 0 0
\(271\) −11.1244 19.2680i −0.675759 1.17045i −0.976246 0.216664i \(-0.930483\pi\)
0.300487 0.953786i \(-0.402851\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −6.31669 + 3.64694i −0.380910 + 0.219919i
\(276\) 0 0
\(277\) −0.335303 + 0.580762i −0.0201464 + 0.0348946i −0.875923 0.482451i \(-0.839747\pi\)
0.855776 + 0.517346i \(0.173080\pi\)
\(278\) 0 0
\(279\) 8.70319 0.521046
\(280\) 0 0
\(281\) 25.5971 1.52700 0.763499 0.645810i \(-0.223480\pi\)
0.763499 + 0.645810i \(0.223480\pi\)
\(282\) 0 0
\(283\) 5.55574 9.62283i 0.330255 0.572018i −0.652307 0.757955i \(-0.726199\pi\)
0.982562 + 0.185937i \(0.0595320\pi\)
\(284\) 0 0
\(285\) 20.4760 11.8218i 1.21289 0.700264i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 15.3766 + 26.6331i 0.904508 + 1.56665i
\(290\) 0 0
\(291\) −12.0214 6.94057i −0.704708 0.406864i
\(292\) 0 0
\(293\) 19.2818i 1.12645i 0.826303 + 0.563226i \(0.190440\pi\)
−0.826303 + 0.563226i \(0.809560\pi\)
\(294\) 0 0
\(295\) 45.3245i 2.63890i
\(296\) 0 0
\(297\) 1.18394 + 0.683549i 0.0686992 + 0.0396635i
\(298\) 0 0
\(299\) 5.31491 + 9.20569i 0.307369 + 0.532379i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −1.43666 + 0.829455i −0.0825338 + 0.0476509i
\(304\) 0 0
\(305\) 17.7811 30.7977i 1.01814 1.76347i
\(306\) 0 0
\(307\) −26.0058 −1.48423 −0.742115 0.670273i \(-0.766177\pi\)
−0.742115 + 0.670273i \(0.766177\pi\)
\(308\) 0 0
\(309\) −1.30791 −0.0744042
\(310\) 0 0
\(311\) 9.53862 16.5214i 0.540885 0.936841i −0.457968 0.888969i \(-0.651423\pi\)
0.998853 0.0478723i \(-0.0152440\pi\)
\(312\) 0 0
\(313\) 18.4968 10.6791i 1.04550 0.603620i 0.124114 0.992268i \(-0.460391\pi\)
0.921386 + 0.388648i \(0.127058\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −3.87066 6.70417i −0.217398 0.376544i 0.736614 0.676313i \(-0.236424\pi\)
−0.954012 + 0.299770i \(0.903090\pi\)
\(318\) 0 0
\(319\) 1.31637 + 0.760006i 0.0737025 + 0.0425522i
\(320\) 0 0
\(321\) 7.15204i 0.399188i
\(322\) 0 0
\(323\) 50.8223i 2.82783i
\(324\) 0 0
\(325\) 13.5388 + 7.81662i 0.750997 + 0.433588i
\(326\) 0 0
\(327\) −7.52215 13.0287i −0.415976 0.720491i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −0.585423 + 0.337994i −0.0321778 + 0.0185778i −0.516003 0.856587i \(-0.672581\pi\)
0.483825 + 0.875165i \(0.339247\pi\)
\(332\) 0 0
\(333\) −3.81896 + 6.61463i −0.209278 + 0.362480i
\(334\) 0 0
\(335\) 39.0748 2.13489
\(336\) 0 0
\(337\) −0.176755 −0.00962847 −0.00481423 0.999988i \(-0.501532\pi\)
−0.00481423 + 0.999988i \(0.501532\pi\)
\(338\) 0 0
\(339\) −7.72648 + 13.3827i −0.419645 + 0.726846i
\(340\) 0 0
\(341\) 10.3041 5.94905i 0.557996 0.322159i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 5.83133 + 10.1002i 0.313948 + 0.543774i
\(346\) 0 0
\(347\) 5.39220 + 3.11319i 0.289468 + 0.167125i 0.637702 0.770283i \(-0.279885\pi\)
−0.348234 + 0.937408i \(0.613218\pi\)
\(348\) 0 0
\(349\) 17.4414i 0.933616i −0.884359 0.466808i \(-0.845404\pi\)
0.884359 0.466808i \(-0.154596\pi\)
\(350\) 0 0
\(351\) 2.93015i 0.156400i
\(352\) 0 0
\(353\) −7.53631 4.35109i −0.401117 0.231585i 0.285849 0.958275i \(-0.407725\pi\)
−0.686966 + 0.726690i \(0.741058\pi\)
\(354\) 0 0
\(355\) 20.2936 + 35.1495i 1.07707 + 1.86554i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0.661871 0.382131i 0.0349322 0.0201681i −0.482432 0.875933i \(-0.660247\pi\)
0.517364 + 0.855765i \(0.326913\pi\)
\(360\) 0 0
\(361\) −17.5443 + 30.3876i −0.923384 + 1.59935i
\(362\) 0 0
\(363\) −9.13104 −0.479256
\(364\) 0 0
\(365\) 20.8648 1.09211
\(366\) 0 0
\(367\) 13.2581 22.9637i 0.692067 1.19869i −0.279093 0.960264i \(-0.590034\pi\)
0.971160 0.238431i \(-0.0766330\pi\)
\(368\) 0 0
\(369\) 0.721527 0.416574i 0.0375612 0.0216860i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 10.0655 + 17.4340i 0.521173 + 0.902698i 0.999697 + 0.0246235i \(0.00783870\pi\)
−0.478524 + 0.878075i \(0.658828\pi\)
\(374\) 0 0
\(375\) 0.933533 + 0.538976i 0.0482074 + 0.0278326i
\(376\) 0 0
\(377\) 3.25790i 0.167790i
\(378\) 0 0
\(379\) 10.2608i 0.527061i 0.964651 + 0.263531i \(0.0848870\pi\)
−0.964651 + 0.263531i \(0.915113\pi\)
\(380\) 0 0
\(381\) −1.87476 1.08239i −0.0960468 0.0554526i
\(382\) 0 0
\(383\) −1.17157 2.02922i −0.0598646 0.103688i 0.834540 0.550947i \(-0.185734\pi\)
−0.894404 + 0.447259i \(0.852400\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −4.17738 + 2.41181i −0.212348 + 0.122599i
\(388\) 0 0
\(389\) −12.0220 + 20.8227i −0.609540 + 1.05576i 0.381776 + 0.924255i \(0.375313\pi\)
−0.991316 + 0.131500i \(0.958021\pi\)
\(390\) 0 0
\(391\) 25.0690 1.26780
\(392\) 0 0
\(393\) 4.97877 0.251146
\(394\) 0 0
\(395\) 12.5278 21.6987i 0.630340 1.09178i
\(396\) 0 0
\(397\) 15.8938 9.17628i 0.797686 0.460544i −0.0449754 0.998988i \(-0.514321\pi\)
0.842661 + 0.538444i \(0.180988\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 1.48486 + 2.57185i 0.0741503 + 0.128432i 0.900716 0.434407i \(-0.143042\pi\)
−0.826566 + 0.562840i \(0.809709\pi\)
\(402\) 0 0
\(403\) −22.0851 12.7508i −1.10014 0.635164i
\(404\) 0 0
\(405\) 3.21486i 0.159748i
\(406\) 0 0
\(407\) 10.4418i 0.517580i
\(408\) 0 0
\(409\) −20.7415 11.9751i −1.02560 0.592131i −0.109880 0.993945i \(-0.535047\pi\)
−0.915721 + 0.401814i \(0.868380\pi\)
\(410\) 0 0
\(411\) −1.84490 3.19546i −0.0910021 0.157620i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −24.7094 + 14.2660i −1.21293 + 0.700288i
\(416\) 0 0
\(417\) −6.02884 + 10.4423i −0.295234 + 0.511360i
\(418\) 0 0
\(419\) 36.3065 1.77369 0.886844 0.462069i \(-0.152893\pi\)
0.886844 + 0.462069i \(0.152893\pi\)
\(420\) 0 0
\(421\) −22.6274 −1.10279 −0.551396 0.834243i \(-0.685905\pi\)
−0.551396 + 0.834243i \(0.685905\pi\)
\(422\) 0 0
\(423\) −1.47683 + 2.55795i −0.0718061 + 0.124372i
\(424\) 0 0
\(425\) 31.9294 18.4345i 1.54881 0.894203i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −2.00290 3.46913i −0.0967010 0.167491i
\(430\) 0 0
\(431\) −26.5038 15.3020i −1.27664 0.737071i −0.300414 0.953809i \(-0.597125\pi\)
−0.976230 + 0.216738i \(0.930458\pi\)
\(432\) 0 0
\(433\) 14.4650i 0.695146i −0.937653 0.347573i \(-0.887006\pi\)
0.937653 0.347573i \(-0.112994\pi\)
\(434\) 0 0
\(435\) 3.57445i 0.171382i
\(436\) 0 0
\(437\) −23.1057 13.3401i −1.10530 0.638143i
\(438\) 0 0
\(439\) −4.55491 7.88933i −0.217394 0.376537i 0.736617 0.676311i \(-0.236422\pi\)
−0.954010 + 0.299773i \(0.903089\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −2.45362 + 1.41660i −0.116575 + 0.0673045i −0.557154 0.830409i \(-0.688107\pi\)
0.440579 + 0.897714i \(0.354773\pi\)
\(444\) 0 0
\(445\) 20.2771 35.1210i 0.961227 1.66489i
\(446\) 0 0
\(447\) −3.30262 −0.156208
\(448\) 0 0
\(449\) 10.3630 0.489058 0.244529 0.969642i \(-0.421367\pi\)
0.244529 + 0.969642i \(0.421367\pi\)
\(450\) 0 0
\(451\) 0.569497 0.986397i 0.0268166 0.0464476i
\(452\) 0 0
\(453\) 16.4122 9.47557i 0.771111 0.445201i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 3.32976 + 5.76731i 0.155759 + 0.269783i 0.933335 0.359006i \(-0.116884\pi\)
−0.777576 + 0.628789i \(0.783551\pi\)
\(458\) 0 0
\(459\) −5.98456 3.45519i −0.279335 0.161274i
\(460\) 0 0
\(461\) 1.71311i 0.0797873i −0.999204 0.0398936i \(-0.987298\pi\)
0.999204 0.0398936i \(-0.0127019\pi\)
\(462\) 0 0
\(463\) 24.1733i 1.12343i 0.827331 + 0.561715i \(0.189858\pi\)
−0.827331 + 0.561715i \(0.810142\pi\)
\(464\) 0 0
\(465\) −24.2310 13.9897i −1.12368 0.648759i
\(466\) 0 0
\(467\) 18.6327 + 32.2728i 0.862220 + 1.49341i 0.869782 + 0.493437i \(0.164260\pi\)
−0.00756221 + 0.999971i \(0.502407\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0.767676 0.443218i 0.0353726 0.0204224i
\(472\) 0 0
\(473\) −3.29718 + 5.71088i −0.151604 + 0.262587i
\(474\) 0 0
\(475\) −39.2385 −1.80038
\(476\) 0 0
\(477\) −4.57794 −0.209610
\(478\) 0 0
\(479\) 10.9298 18.9310i 0.499395 0.864978i −0.500605 0.865676i \(-0.666889\pi\)
1.00000 0.000698448i \(0.000222323\pi\)
\(480\) 0 0
\(481\) 19.3819 11.1901i 0.883737 0.510226i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 22.3129 + 38.6472i 1.01318 + 1.75488i
\(486\) 0 0
\(487\) −2.92083 1.68634i −0.132356 0.0764155i 0.432360 0.901701i \(-0.357681\pi\)
−0.564716 + 0.825285i \(0.691014\pi\)
\(488\) 0 0
\(489\) 19.3538i 0.875208i
\(490\) 0 0
\(491\) 9.68824i 0.437224i 0.975812 + 0.218612i \(0.0701529\pi\)
−0.975812 + 0.218612i \(0.929847\pi\)
\(492\) 0 0
\(493\) −6.65395 3.84166i −0.299679 0.173020i
\(494\) 0 0
\(495\) −2.19751 3.80620i −0.0987708 0.171076i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 11.8992 6.87003i 0.532683 0.307545i −0.209425 0.977825i \(-0.567159\pi\)
0.742108 + 0.670280i \(0.233826\pi\)
\(500\) 0 0
\(501\) 12.7428 22.0711i 0.569305 0.986065i
\(502\) 0 0
\(503\) 1.92715 0.0859273 0.0429637 0.999077i \(-0.486320\pi\)
0.0429637 + 0.999077i \(0.486320\pi\)
\(504\) 0 0
\(505\) 5.33316 0.237322
\(506\) 0 0
\(507\) 2.20711 3.82282i 0.0980211 0.169777i
\(508\) 0 0
\(509\) 12.2647 7.08104i 0.543624 0.313862i −0.202922 0.979195i \(-0.565044\pi\)
0.746546 + 0.665333i \(0.231711\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 3.67725 + 6.36918i 0.162354 + 0.281206i
\(514\) 0 0
\(515\) 3.64140 + 2.10236i 0.160459 + 0.0926413i
\(516\) 0 0
\(517\) 4.03795i 0.177589i
\(518\) 0 0
\(519\) 21.6924i 0.952193i
\(520\) 0 0
\(521\) 18.7084 + 10.8013i 0.819630 + 0.473213i 0.850289 0.526316i \(-0.176427\pi\)
−0.0306591 + 0.999530i \(0.509761\pi\)
\(522\) 0 0
\(523\) 6.98251 + 12.0941i 0.305324 + 0.528836i 0.977333 0.211706i \(-0.0679020\pi\)
−0.672010 + 0.740542i \(0.734569\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −52.0847 + 30.0711i −2.26885 + 1.30992i
\(528\) 0 0
\(529\) −4.91976 + 8.52127i −0.213903 + 0.370490i
\(530\) 0 0
\(531\) −14.0985 −0.611821
\(532\) 0 0
\(533\) −2.44125 −0.105742
\(534\) 0 0
\(535\) −11.4964 + 19.9123i −0.497032 + 0.860885i
\(536\) 0 0
\(537\) −10.6369 + 6.14122i −0.459016 + 0.265013i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −1.94002 3.36022i −0.0834081 0.144467i 0.821304 0.570491i \(-0.193247\pi\)
−0.904712 + 0.426024i \(0.859914\pi\)
\(542\) 0 0
\(543\) −2.37676 1.37222i −0.101996 0.0588876i
\(544\) 0 0
\(545\) 48.3652i 2.07174i
\(546\) 0 0
\(547\) 35.1640i 1.50351i −0.659445 0.751753i \(-0.729209\pi\)
0.659445 0.751753i \(-0.270791\pi\)
\(548\) 0 0
\(549\) 9.57981 + 5.53091i 0.408856 + 0.236053i
\(550\) 0 0
\(551\) 4.08856 + 7.08159i 0.174178 + 0.301686i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 21.2651 12.2774i 0.902653 0.521147i
\(556\) 0 0
\(557\) −21.2173 + 36.7495i −0.899006 + 1.55712i −0.0702393 + 0.997530i \(0.522376\pi\)
−0.828767 + 0.559594i \(0.810957\pi\)
\(558\) 0 0
\(559\) 14.1339 0.597802
\(560\) 0 0
\(561\) −9.44716 −0.398859
\(562\) 0 0
\(563\) −8.27438 + 14.3316i −0.348724 + 0.604007i −0.986023 0.166609i \(-0.946718\pi\)
0.637299 + 0.770616i \(0.280051\pi\)
\(564\) 0 0
\(565\) 43.0233 24.8395i 1.81000 1.04501i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 12.1283 + 21.0069i 0.508446 + 0.880654i 0.999952 + 0.00978001i \(0.00311312\pi\)
−0.491506 + 0.870874i \(0.663554\pi\)
\(570\) 0 0
\(571\) −4.00591 2.31281i −0.167642 0.0967882i 0.413831 0.910354i \(-0.364190\pi\)
−0.581474 + 0.813565i \(0.697524\pi\)
\(572\) 0 0
\(573\) 22.8857i 0.956062i
\(574\) 0 0
\(575\) 19.3551i 0.807163i
\(576\) 0 0
\(577\) −23.2014 13.3954i −0.965889 0.557656i −0.0679083 0.997692i \(-0.521633\pi\)
−0.897980 + 0.440035i \(0.854966\pi\)
\(578\) 0 0
\(579\) 7.30816 + 12.6581i 0.303717 + 0.526053i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −5.42002 + 3.12925i −0.224474 + 0.129600i
\(584\) 0 0
\(585\) −4.71001 + 8.15797i −0.194735 + 0.337291i
\(586\) 0 0
\(587\) −27.8591 −1.14987 −0.574933 0.818200i \(-0.694972\pi\)
−0.574933 + 0.818200i \(0.694972\pi\)
\(588\) 0 0
\(589\) 64.0075 2.63738
\(590\) 0 0
\(591\) 12.2715 21.2548i 0.504781 0.874307i
\(592\) 0 0
\(593\) −1.35884 + 0.784528i −0.0558010 + 0.0322167i −0.527641 0.849468i \(-0.676923\pi\)
0.471840 + 0.881684i \(0.343590\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 3.02329 + 5.23650i 0.123735 + 0.214316i
\(598\) 0 0
\(599\) 34.7412 + 20.0578i 1.41949 + 0.819540i 0.996254 0.0864809i \(-0.0275621\pi\)
0.423232 + 0.906021i \(0.360895\pi\)
\(600\) 0 0
\(601\) 24.7827i 1.01091i 0.862854 + 0.505453i \(0.168675\pi\)
−0.862854 + 0.505453i \(0.831325\pi\)
\(602\) 0 0
\(603\) 12.1545i 0.494968i
\(604\) 0 0
\(605\) 25.4222 + 14.6775i 1.03356 + 0.596725i
\(606\) 0 0
\(607\) −2.33120 4.03776i −0.0946205 0.163887i 0.814830 0.579700i \(-0.196830\pi\)
−0.909450 + 0.415813i \(0.863497\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 7.49519 4.32735i 0.303223 0.175066i
\(612\) 0 0
\(613\) −14.2909 + 24.7525i −0.577202 + 0.999743i 0.418596 + 0.908172i \(0.362522\pi\)
−0.995799 + 0.0915710i \(0.970811\pi\)
\(614\) 0 0
\(615\) −2.67845 −0.108005
\(616\) 0 0
\(617\) 10.1524 0.408720 0.204360 0.978896i \(-0.434489\pi\)
0.204360 + 0.978896i \(0.434489\pi\)
\(618\) 0 0
\(619\) −4.32011 + 7.48265i −0.173640 + 0.300753i −0.939690 0.342028i \(-0.888886\pi\)
0.766050 + 0.642781i \(0.222220\pi\)
\(620\) 0 0
\(621\) −3.14171 + 1.81387i −0.126073 + 0.0727881i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 11.6055 + 20.1014i 0.464221 + 0.804055i
\(626\) 0 0
\(627\) 8.70729 + 5.02716i 0.347736 + 0.200765i
\(628\) 0 0
\(629\) 52.7809i 2.10451i
\(630\) 0 0
\(631\) 5.46211i 0.217443i 0.994072 + 0.108722i \(0.0346757\pi\)
−0.994072 + 0.108722i \(0.965324\pi\)
\(632\) 0 0
\(633\) 8.08446 + 4.66756i 0.321328 + 0.185519i
\(634\) 0 0
\(635\) 3.47974 + 6.02708i 0.138089 + 0.239177i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −10.9335 + 6.31243i −0.432521 + 0.249716i
\(640\) 0 0
\(641\) −0.714111 + 1.23688i −0.0282057 + 0.0488537i −0.879784 0.475374i \(-0.842313\pi\)
0.851578 + 0.524228i \(0.175646\pi\)
\(642\) 0 0
\(643\) 24.6036 0.970270 0.485135 0.874439i \(-0.338771\pi\)
0.485135 + 0.874439i \(0.338771\pi\)
\(644\) 0 0
\(645\) 15.5072 0.610597
\(646\) 0 0
\(647\) 10.1392 17.5617i 0.398614 0.690420i −0.594941 0.803770i \(-0.702825\pi\)
0.993555 + 0.113349i \(0.0361578\pi\)
\(648\) 0 0
\(649\) −16.6918 + 9.63699i −0.655209 + 0.378285i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −21.4420 37.1387i −0.839092 1.45335i −0.890655 0.454680i \(-0.849754\pi\)
0.0515635 0.998670i \(-0.483580\pi\)
\(654\) 0 0
\(655\) −13.8616 8.00301i −0.541619 0.312704i
\(656\) 0 0
\(657\) 6.49011i 0.253203i
\(658\) 0 0
\(659\) 31.4717i 1.22596i 0.790098 + 0.612981i \(0.210030\pi\)
−0.790098 + 0.612981i \(0.789970\pi\)
\(660\) 0 0
\(661\) −10.6655 6.15771i −0.414839 0.239507i 0.278028 0.960573i \(-0.410319\pi\)
−0.692867 + 0.721066i \(0.743653\pi\)
\(662\) 0 0
\(663\) 10.1242 + 17.5357i 0.393192 + 0.681029i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −3.49312 + 2.01676i −0.135254 + 0.0780891i
\(668\) 0 0
\(669\) −2.74397 + 4.75270i −0.106088 + 0.183750i
\(670\) 0 0
\(671\) 15.1226 0.583801
\(672\) 0 0
\(673\) 37.1864 1.43343 0.716716 0.697365i \(-0.245645\pi\)
0.716716 + 0.697365i \(0.245645\pi\)
\(674\) 0 0
\(675\) −2.66765 + 4.62051i −0.102678 + 0.177843i
\(676\) 0 0
\(677\) −30.8345 + 17.8023i −1.18507 + 0.684198i −0.957181 0.289490i \(-0.906514\pi\)
−0.227885 + 0.973688i \(0.573181\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0.519063 + 0.899043i 0.0198905 + 0.0344514i
\(682\) 0 0
\(683\) −27.8909 16.1028i −1.06722 0.616157i −0.139796 0.990180i \(-0.544645\pi\)
−0.927419 + 0.374023i \(0.877978\pi\)
\(684\) 0 0
\(685\) 11.8622i 0.453230i
\(686\) 0 0
\(687\) 15.6039i 0.595325i
\(688\) 0 0
\(689\) 11.6169 + 6.70703i 0.442570 + 0.255518i
\(690\) 0 0
\(691\) −19.3084 33.4432i −0.734527 1.27224i −0.954931 0.296829i \(-0.904071\pi\)
0.220404 0.975409i \(-0.429263\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 33.5704 19.3819i 1.27340 0.735196i
\(696\) 0 0
\(697\) −2.87868 + 4.98602i −0.109038 + 0.188859i
\(698\) 0 0
\(699\) −9.21561 −0.348566
\(700\) 0 0
\(701\) 30.8725 1.16604 0.583018 0.812459i \(-0.301872\pi\)
0.583018 + 0.812459i \(0.301872\pi\)
\(702\) 0 0
\(703\) −28.0865 + 48.6473i −1.05930 + 1.83477i
\(704\) 0 0
\(705\) 8.22345 4.74781i 0.309713 0.178813i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −19.9226 34.5070i −0.748209 1.29594i −0.948680 0.316237i \(-0.897581\pi\)
0.200471 0.979700i \(-0.435753\pi\)
\(710\) 0 0
\(711\) 6.74952 + 3.89684i 0.253127 + 0.146143i
\(712\) 0 0
\(713\) 31.5729i 1.18241i
\(714\) 0 0
\(715\) 12.8781i 0.481613i
\(716\) 0 0
\(717\) 1.34068 + 0.774044i 0.0500687 + 0.0289072i
\(718\) 0 0
\(719\) 1.04633 + 1.81230i 0.0390216 + 0.0675873i 0.884877 0.465826i \(-0.154243\pi\)
−0.845855 + 0.533413i \(0.820909\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 3.19154 1.84264i 0.118695 0.0685284i
\(724\) 0 0
\(725\) −2.96604 + 5.13733i −0.110156 + 0.190796i
\(726\) 0 0
\(727\) −21.5164 −0.798001 −0.399000 0.916951i \(-0.630643\pi\)
−0.399000 + 0.916951i \(0.630643\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 16.6665 28.8672i 0.616433 1.06769i
\(732\) 0 0
\(733\) −6.69313 + 3.86428i −0.247216 + 0.142730i −0.618489 0.785794i \(-0.712255\pi\)
0.371273 + 0.928524i \(0.378922\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 8.30816 + 14.3902i 0.306035 + 0.530068i
\(738\) 0 0
\(739\) −13.9485 8.05316i −0.513103 0.296240i 0.221005 0.975273i \(-0.429066\pi\)
−0.734108 + 0.679032i \(0.762400\pi\)
\(740\) 0 0
\(741\) 21.5498i 0.791651i
\(742\) 0 0
\(743\) 29.3296i 1.07600i 0.842945 + 0.537999i \(0.180820\pi\)
−0.842945 + 0.537999i \(0.819180\pi\)
\(744\) 0 0
\(745\) 9.19497 + 5.30872i 0.336878 + 0.194496i
\(746\) 0 0
\(747\) −4.43751 7.68599i −0.162360 0.281216i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −11.7772 + 6.79955i −0.429755 + 0.248119i −0.699242 0.714885i \(-0.746479\pi\)
0.269487 + 0.963004i \(0.413146\pi\)
\(752\) 0 0
\(753\) −13.0970 + 22.6847i −0.477281 + 0.826676i
\(754\) 0 0
\(755\) −60.9252 −2.21730
\(756\) 0 0
\(757\) −2.59688 −0.0943851 −0.0471926 0.998886i \(-0.515027\pi\)
−0.0471926 + 0.998886i \(0.515027\pi\)
\(758\) 0 0
\(759\) −2.47974 + 4.29503i −0.0900087 + 0.155900i
\(760\) 0 0
\(761\) 14.9753 8.64598i 0.542853 0.313416i −0.203381 0.979100i \(-0.565193\pi\)
0.746235 + 0.665683i \(0.231860\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 11.1079 + 19.2395i 0.401608 + 0.695606i
\(766\) 0 0
\(767\) 35.7761 + 20.6553i 1.29180 + 0.745820i
\(768\) 0 0
\(769\) 41.4025i 1.49301i −0.665378 0.746507i \(-0.731730\pi\)
0.665378 0.746507i \(-0.268270\pi\)
\(770\) 0 0
\(771\) 0.833147i 0.0300051i
\(772\) 0 0
\(773\) −25.5191 14.7335i −0.917858 0.529925i −0.0349068 0.999391i \(-0.511113\pi\)
−0.882951 + 0.469465i \(0.844447\pi\)
\(774\) 0 0
\(775\) 23.2171 + 40.2131i 0.833982 + 1.44450i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 5.30646 3.06369i 0.190124 0.109768i
\(780\) 0 0
\(781\) −8.62971 + 14.9471i −0.308795 + 0.534849i
\(782\) 0 0
\(783\) 1.11185 0.0397344
\(784\) 0 0
\(785\) −2.84976 −0.101712
\(786\) 0 0
\(787\) −27.0921 + 46.9248i −0.965728 + 1.67269i −0.258081 + 0.966123i \(0.583090\pi\)
−0.707647 + 0.706566i \(0.750243\pi\)
\(788\) 0 0
\(789\) −4.36661 + 2.52106i −0.155455 + 0.0897521i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −16.2064 28.0703i −0.575506 0.996806i
\(794\) 0 0
\(795\) 12.7457 + 7.35872i 0.452042 + 0.260987i
\(796\) 0 0
\(797\) 0.512549i 0.0181554i 0.999959 + 0.00907771i \(0.00288956\pi\)
−0.999959 + 0.00907771i \(0.997110\pi\)
\(798\) 0 0
\(799\) 20.4110i 0.722088i
\(800\) 0 0