Properties

Label 920.2.e.c.369.14
Level $920$
Weight $2$
Character 920.369
Analytic conductor $7.346$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 920.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.34623698596\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \( x^{16} - 2 x^{15} + 2 x^{14} + 6 x^{13} + 100 x^{12} - 196 x^{11} + 210 x^{10} + 702 x^{9} + 1572 x^{8} - 1594 x^{7} + 2464 x^{6} + 9568 x^{5} + 15457 x^{4} + 4336 x^{3} + \cdots + 1024 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 369.14
Root \(1.81400 - 1.81400i\) of defining polynomial
Character \(\chi\) \(=\) 920.369
Dual form 920.2.e.c.369.3

$q$-expansion

\(f(q)\) \(=\) \(q+2.54092i q^{3} +(-1.30744 - 1.81400i) q^{5} -0.780573i q^{7} -3.45626 q^{9} +O(q^{10})\) \(q+2.54092i q^{3} +(-1.30744 - 1.81400i) q^{5} -0.780573i q^{7} -3.45626 q^{9} +5.16287 q^{11} +3.34898i q^{13} +(4.60923 - 3.32209i) q^{15} +6.62869i q^{17} -6.40858 q^{19} +1.98337 q^{21} +1.00000i q^{23} +(-1.58121 + 4.74339i) q^{25} -1.15931i q^{27} +0.0877744 q^{29} +3.29521 q^{31} +13.1184i q^{33} +(-1.41596 + 1.02055i) q^{35} +4.68291i q^{37} -8.50947 q^{39} -5.75800 q^{41} +2.62914i q^{43} +(4.51884 + 6.26966i) q^{45} -5.13068i q^{47} +6.39071 q^{49} -16.8429 q^{51} +8.80399i q^{53} +(-6.75013 - 9.36546i) q^{55} -16.2837i q^{57} -2.98687 q^{59} -2.05559 q^{61} +2.69786i q^{63} +(6.07505 - 4.37858i) q^{65} +3.60245i q^{67} -2.54092 q^{69} +11.5286 q^{71} -10.4673i q^{73} +(-12.0526 - 4.01772i) q^{75} -4.03000i q^{77} -3.43878 q^{79} -7.42306 q^{81} +3.62938i q^{83} +(12.0245 - 8.66660i) q^{85} +0.223028i q^{87} -14.3109 q^{89} +2.61412 q^{91} +8.37284i q^{93} +(8.37882 + 11.6252i) q^{95} +0.427584i q^{97} -17.8442 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 2 q^{5} - 22 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 2 q^{5} - 22 q^{9} + 14 q^{11} + 6 q^{15} - 22 q^{19} + 12 q^{25} - 44 q^{29} + 18 q^{31} + 20 q^{35} + 14 q^{41} + 14 q^{45} - 78 q^{49} - 38 q^{51} + 30 q^{55} - 64 q^{59} + 34 q^{61} + 6 q^{65} + 6 q^{69} + 30 q^{71} + 56 q^{75} + 4 q^{79} + 48 q^{81} + 52 q^{85} - 92 q^{89} - 70 q^{91} + 38 q^{95} - 122 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/920\mathbb{Z}\right)^\times\).

\(n\) \(231\) \(281\) \(461\) \(737\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 2.54092i 1.46700i 0.679690 + 0.733499i \(0.262114\pi\)
−0.679690 + 0.733499i \(0.737886\pi\)
\(4\) 0 0
\(5\) −1.30744 1.81400i −0.584704 0.811247i
\(6\) 0 0
\(7\) 0.780573i 0.295029i −0.989060 0.147514i \(-0.952873\pi\)
0.989060 0.147514i \(-0.0471273\pi\)
\(8\) 0 0
\(9\) −3.45626 −1.15209
\(10\) 0 0
\(11\) 5.16287 1.55666 0.778332 0.627853i \(-0.216066\pi\)
0.778332 + 0.627853i \(0.216066\pi\)
\(12\) 0 0
\(13\) 3.34898i 0.928839i 0.885615 + 0.464419i \(0.153737\pi\)
−0.885615 + 0.464419i \(0.846263\pi\)
\(14\) 0 0
\(15\) 4.60923 3.32209i 1.19010 0.857760i
\(16\) 0 0
\(17\) 6.62869i 1.60769i 0.594836 + 0.803847i \(0.297217\pi\)
−0.594836 + 0.803847i \(0.702783\pi\)
\(18\) 0 0
\(19\) −6.40858 −1.47023 −0.735114 0.677943i \(-0.762872\pi\)
−0.735114 + 0.677943i \(0.762872\pi\)
\(20\) 0 0
\(21\) 1.98337 0.432807
\(22\) 0 0
\(23\) 1.00000i 0.208514i
\(24\) 0 0
\(25\) −1.58121 + 4.74339i −0.316242 + 0.948679i
\(26\) 0 0
\(27\) 1.15931i 0.223109i
\(28\) 0 0
\(29\) 0.0877744 0.0162993 0.00814965 0.999967i \(-0.497406\pi\)
0.00814965 + 0.999967i \(0.497406\pi\)
\(30\) 0 0
\(31\) 3.29521 0.591837 0.295918 0.955213i \(-0.404374\pi\)
0.295918 + 0.955213i \(0.404374\pi\)
\(32\) 0 0
\(33\) 13.1184i 2.28362i
\(34\) 0 0
\(35\) −1.41596 + 1.02055i −0.239341 + 0.172505i
\(36\) 0 0
\(37\) 4.68291i 0.769865i 0.922945 + 0.384933i \(0.125775\pi\)
−0.922945 + 0.384933i \(0.874225\pi\)
\(38\) 0 0
\(39\) −8.50947 −1.36261
\(40\) 0 0
\(41\) −5.75800 −0.899249 −0.449624 0.893218i \(-0.648442\pi\)
−0.449624 + 0.893218i \(0.648442\pi\)
\(42\) 0 0
\(43\) 2.62914i 0.400940i 0.979700 + 0.200470i \(0.0642469\pi\)
−0.979700 + 0.200470i \(0.935753\pi\)
\(44\) 0 0
\(45\) 4.51884 + 6.26966i 0.673629 + 0.934625i
\(46\) 0 0
\(47\) 5.13068i 0.748387i −0.927351 0.374193i \(-0.877920\pi\)
0.927351 0.374193i \(-0.122080\pi\)
\(48\) 0 0
\(49\) 6.39071 0.912958
\(50\) 0 0
\(51\) −16.8429 −2.35848
\(52\) 0 0
\(53\) 8.80399i 1.20932i 0.796483 + 0.604660i \(0.206691\pi\)
−0.796483 + 0.604660i \(0.793309\pi\)
\(54\) 0 0
\(55\) −6.75013 9.36546i −0.910188 1.26284i
\(56\) 0 0
\(57\) 16.2837i 2.15682i
\(58\) 0 0
\(59\) −2.98687 −0.388858 −0.194429 0.980917i \(-0.562285\pi\)
−0.194429 + 0.980917i \(0.562285\pi\)
\(60\) 0 0
\(61\) −2.05559 −0.263191 −0.131596 0.991303i \(-0.542010\pi\)
−0.131596 + 0.991303i \(0.542010\pi\)
\(62\) 0 0
\(63\) 2.69786i 0.339898i
\(64\) 0 0
\(65\) 6.07505 4.37858i 0.753517 0.543096i
\(66\) 0 0
\(67\) 3.60245i 0.440109i 0.975488 + 0.220054i \(0.0706235\pi\)
−0.975488 + 0.220054i \(0.929376\pi\)
\(68\) 0 0
\(69\) −2.54092 −0.305890
\(70\) 0 0
\(71\) 11.5286 1.36819 0.684096 0.729392i \(-0.260197\pi\)
0.684096 + 0.729392i \(0.260197\pi\)
\(72\) 0 0
\(73\) 10.4673i 1.22510i −0.790431 0.612551i \(-0.790143\pi\)
0.790431 0.612551i \(-0.209857\pi\)
\(74\) 0 0
\(75\) −12.0526 4.01772i −1.39171 0.463927i
\(76\) 0 0
\(77\) 4.03000i 0.459261i
\(78\) 0 0
\(79\) −3.43878 −0.386893 −0.193447 0.981111i \(-0.561967\pi\)
−0.193447 + 0.981111i \(0.561967\pi\)
\(80\) 0 0
\(81\) −7.42306 −0.824785
\(82\) 0 0
\(83\) 3.62938i 0.398376i 0.979961 + 0.199188i \(0.0638304\pi\)
−0.979961 + 0.199188i \(0.936170\pi\)
\(84\) 0 0
\(85\) 12.0245 8.66660i 1.30424 0.940025i
\(86\) 0 0
\(87\) 0.223028i 0.0239111i
\(88\) 0 0
\(89\) −14.3109 −1.51695 −0.758477 0.651700i \(-0.774056\pi\)
−0.758477 + 0.651700i \(0.774056\pi\)
\(90\) 0 0
\(91\) 2.61412 0.274034
\(92\) 0 0
\(93\) 8.37284i 0.868223i
\(94\) 0 0
\(95\) 8.37882 + 11.6252i 0.859649 + 1.19272i
\(96\) 0 0
\(97\) 0.427584i 0.0434146i 0.999764 + 0.0217073i \(0.00691018\pi\)
−0.999764 + 0.0217073i \(0.993090\pi\)
\(98\) 0 0
\(99\) −17.8442 −1.79341
\(100\) 0 0
\(101\) −7.99434 −0.795467 −0.397733 0.917501i \(-0.630203\pi\)
−0.397733 + 0.917501i \(0.630203\pi\)
\(102\) 0 0
\(103\) 10.7780i 1.06199i −0.847376 0.530993i \(-0.821819\pi\)
0.847376 0.530993i \(-0.178181\pi\)
\(104\) 0 0
\(105\) −2.59313 3.59784i −0.253064 0.351113i
\(106\) 0 0
\(107\) 15.1623i 1.46580i 0.680339 + 0.732898i \(0.261833\pi\)
−0.680339 + 0.732898i \(0.738167\pi\)
\(108\) 0 0
\(109\) 16.5127 1.58163 0.790816 0.612054i \(-0.209656\pi\)
0.790816 + 0.612054i \(0.209656\pi\)
\(110\) 0 0
\(111\) −11.8989 −1.12939
\(112\) 0 0
\(113\) 14.5233i 1.36623i 0.730309 + 0.683117i \(0.239376\pi\)
−0.730309 + 0.683117i \(0.760624\pi\)
\(114\) 0 0
\(115\) 1.81400 1.30744i 0.169157 0.121919i
\(116\) 0 0
\(117\) 11.5749i 1.07010i
\(118\) 0 0
\(119\) 5.17418 0.474316
\(120\) 0 0
\(121\) 15.6552 1.42320
\(122\) 0 0
\(123\) 14.6306i 1.31920i
\(124\) 0 0
\(125\) 10.6719 3.33337i 0.954520 0.298146i
\(126\) 0 0
\(127\) 16.4865i 1.46294i −0.681873 0.731471i \(-0.738834\pi\)
0.681873 0.731471i \(-0.261166\pi\)
\(128\) 0 0
\(129\) −6.68042 −0.588178
\(130\) 0 0
\(131\) 4.94157 0.431747 0.215874 0.976421i \(-0.430740\pi\)
0.215874 + 0.976421i \(0.430740\pi\)
\(132\) 0 0
\(133\) 5.00236i 0.433760i
\(134\) 0 0
\(135\) −2.10299 + 1.51572i −0.180996 + 0.130453i
\(136\) 0 0
\(137\) 17.9516i 1.53371i 0.641821 + 0.766854i \(0.278179\pi\)
−0.641821 + 0.766854i \(0.721821\pi\)
\(138\) 0 0
\(139\) 17.4812 1.48274 0.741368 0.671099i \(-0.234177\pi\)
0.741368 + 0.671099i \(0.234177\pi\)
\(140\) 0 0
\(141\) 13.0366 1.09788
\(142\) 0 0
\(143\) 17.2903i 1.44589i
\(144\) 0 0
\(145\) −0.114760 0.159223i −0.00953027 0.0132228i
\(146\) 0 0
\(147\) 16.2382i 1.33931i
\(148\) 0 0
\(149\) 22.0079 1.80295 0.901477 0.432827i \(-0.142484\pi\)
0.901477 + 0.432827i \(0.142484\pi\)
\(150\) 0 0
\(151\) 7.40875 0.602916 0.301458 0.953480i \(-0.402527\pi\)
0.301458 + 0.953480i \(0.402527\pi\)
\(152\) 0 0
\(153\) 22.9104i 1.85220i
\(154\) 0 0
\(155\) −4.30828 5.97751i −0.346049 0.480125i
\(156\) 0 0
\(157\) 5.19240i 0.414399i 0.978299 + 0.207199i \(0.0664348\pi\)
−0.978299 + 0.207199i \(0.933565\pi\)
\(158\) 0 0
\(159\) −22.3702 −1.77407
\(160\) 0 0
\(161\) 0.780573 0.0615178
\(162\) 0 0
\(163\) 11.5618i 0.905588i −0.891615 0.452794i \(-0.850427\pi\)
0.891615 0.452794i \(-0.149573\pi\)
\(164\) 0 0
\(165\) 23.7968 17.1515i 1.85258 1.33524i
\(166\) 0 0
\(167\) 19.4882i 1.50804i −0.656852 0.754019i \(-0.728112\pi\)
0.656852 0.754019i \(-0.271888\pi\)
\(168\) 0 0
\(169\) 1.78436 0.137258
\(170\) 0 0
\(171\) 22.1497 1.69383
\(172\) 0 0
\(173\) 18.9062i 1.43741i 0.695314 + 0.718706i \(0.255265\pi\)
−0.695314 + 0.718706i \(0.744735\pi\)
\(174\) 0 0
\(175\) 3.70256 + 1.23425i 0.279888 + 0.0933005i
\(176\) 0 0
\(177\) 7.58939i 0.570454i
\(178\) 0 0
\(179\) −16.5404 −1.23628 −0.618142 0.786066i \(-0.712114\pi\)
−0.618142 + 0.786066i \(0.712114\pi\)
\(180\) 0 0
\(181\) 5.51586 0.409990 0.204995 0.978763i \(-0.434282\pi\)
0.204995 + 0.978763i \(0.434282\pi\)
\(182\) 0 0
\(183\) 5.22308i 0.386101i
\(184\) 0 0
\(185\) 8.49481 6.12261i 0.624551 0.450143i
\(186\) 0 0
\(187\) 34.2231i 2.50264i
\(188\) 0 0
\(189\) −0.904924 −0.0658235
\(190\) 0 0
\(191\) 24.0346 1.73909 0.869543 0.493858i \(-0.164414\pi\)
0.869543 + 0.493858i \(0.164414\pi\)
\(192\) 0 0
\(193\) 15.2163i 1.09530i −0.836709 0.547648i \(-0.815523\pi\)
0.836709 0.547648i \(-0.184477\pi\)
\(194\) 0 0
\(195\) 11.1256 + 15.4362i 0.796721 + 1.10541i
\(196\) 0 0
\(197\) 8.82490i 0.628748i −0.949299 0.314374i \(-0.898205\pi\)
0.949299 0.314374i \(-0.101795\pi\)
\(198\) 0 0
\(199\) −15.3228 −1.08620 −0.543101 0.839668i \(-0.682750\pi\)
−0.543101 + 0.839668i \(0.682750\pi\)
\(200\) 0 0
\(201\) −9.15352 −0.645639
\(202\) 0 0
\(203\) 0.0685144i 0.00480877i
\(204\) 0 0
\(205\) 7.52823 + 10.4450i 0.525795 + 0.729513i
\(206\) 0 0
\(207\) 3.45626i 0.240226i
\(208\) 0 0
\(209\) −33.0866 −2.28865
\(210\) 0 0
\(211\) 4.67170 0.321613 0.160806 0.986986i \(-0.448591\pi\)
0.160806 + 0.986986i \(0.448591\pi\)
\(212\) 0 0
\(213\) 29.2932i 2.00714i
\(214\) 0 0
\(215\) 4.76926 3.43744i 0.325261 0.234431i
\(216\) 0 0
\(217\) 2.57215i 0.174609i
\(218\) 0 0
\(219\) 26.5965 1.79722
\(220\) 0 0
\(221\) −22.1993 −1.49329
\(222\) 0 0
\(223\) 20.7813i 1.39162i −0.718226 0.695810i \(-0.755046\pi\)
0.718226 0.695810i \(-0.244954\pi\)
\(224\) 0 0
\(225\) 5.46507 16.3944i 0.364338 1.09296i
\(226\) 0 0
\(227\) 13.7696i 0.913920i −0.889487 0.456960i \(-0.848938\pi\)
0.889487 0.456960i \(-0.151062\pi\)
\(228\) 0 0
\(229\) −18.6065 −1.22955 −0.614777 0.788701i \(-0.710754\pi\)
−0.614777 + 0.788701i \(0.710754\pi\)
\(230\) 0 0
\(231\) 10.2399 0.673735
\(232\) 0 0
\(233\) 0.451458i 0.0295760i −0.999891 0.0147880i \(-0.995293\pi\)
0.999891 0.0147880i \(-0.00470733\pi\)
\(234\) 0 0
\(235\) −9.30707 + 6.70805i −0.607126 + 0.437585i
\(236\) 0 0
\(237\) 8.73766i 0.567572i
\(238\) 0 0
\(239\) −12.5522 −0.811937 −0.405969 0.913887i \(-0.633066\pi\)
−0.405969 + 0.913887i \(0.633066\pi\)
\(240\) 0 0
\(241\) 16.7582 1.07949 0.539745 0.841828i \(-0.318521\pi\)
0.539745 + 0.841828i \(0.318521\pi\)
\(242\) 0 0
\(243\) 22.3393i 1.43307i
\(244\) 0 0
\(245\) −8.35545 11.5928i −0.533810 0.740634i
\(246\) 0 0
\(247\) 21.4622i 1.36561i
\(248\) 0 0
\(249\) −9.22194 −0.584417
\(250\) 0 0
\(251\) −6.77866 −0.427865 −0.213933 0.976848i \(-0.568627\pi\)
−0.213933 + 0.976848i \(0.568627\pi\)
\(252\) 0 0
\(253\) 5.16287i 0.324587i
\(254\) 0 0
\(255\) 22.0211 + 30.5531i 1.37902 + 1.91331i
\(256\) 0 0
\(257\) 7.18182i 0.447990i 0.974590 + 0.223995i \(0.0719099\pi\)
−0.974590 + 0.223995i \(0.928090\pi\)
\(258\) 0 0
\(259\) 3.65535 0.227133
\(260\) 0 0
\(261\) −0.303371 −0.0187782
\(262\) 0 0
\(263\) 18.2061i 1.12264i −0.827600 0.561318i \(-0.810294\pi\)
0.827600 0.561318i \(-0.189706\pi\)
\(264\) 0 0
\(265\) 15.9705 11.5107i 0.981057 0.707095i
\(266\) 0 0
\(267\) 36.3628i 2.22537i
\(268\) 0 0
\(269\) 5.56736 0.339448 0.169724 0.985492i \(-0.445712\pi\)
0.169724 + 0.985492i \(0.445712\pi\)
\(270\) 0 0
\(271\) 3.85908 0.234422 0.117211 0.993107i \(-0.462605\pi\)
0.117211 + 0.993107i \(0.462605\pi\)
\(272\) 0 0
\(273\) 6.64226i 0.402008i
\(274\) 0 0
\(275\) −8.16358 + 24.4895i −0.492282 + 1.47677i
\(276\) 0 0
\(277\) 6.01542i 0.361431i −0.983535 0.180716i \(-0.942159\pi\)
0.983535 0.180716i \(-0.0578414\pi\)
\(278\) 0 0
\(279\) −11.3891 −0.681846
\(280\) 0 0
\(281\) −16.8891 −1.00752 −0.503761 0.863843i \(-0.668051\pi\)
−0.503761 + 0.863843i \(0.668051\pi\)
\(282\) 0 0
\(283\) 1.62178i 0.0964047i −0.998838 0.0482023i \(-0.984651\pi\)
0.998838 0.0482023i \(-0.0153492\pi\)
\(284\) 0 0
\(285\) −29.5386 + 21.2899i −1.74972 + 1.26110i
\(286\) 0 0
\(287\) 4.49454i 0.265304i
\(288\) 0 0
\(289\) −26.9395 −1.58468
\(290\) 0 0
\(291\) −1.08645 −0.0636891
\(292\) 0 0
\(293\) 28.3659i 1.65716i −0.559874 0.828578i \(-0.689151\pi\)
0.559874 0.828578i \(-0.310849\pi\)
\(294\) 0 0
\(295\) 3.90515 + 5.41819i 0.227367 + 0.315459i
\(296\) 0 0
\(297\) 5.98535i 0.347305i
\(298\) 0 0
\(299\) −3.34898 −0.193676
\(300\) 0 0
\(301\) 2.05223 0.118289
\(302\) 0 0
\(303\) 20.3130i 1.16695i
\(304\) 0 0
\(305\) 2.68756 + 3.72884i 0.153889 + 0.213513i
\(306\) 0 0
\(307\) 5.54137i 0.316262i −0.987418 0.158131i \(-0.949453\pi\)
0.987418 0.158131i \(-0.0505469\pi\)
\(308\) 0 0
\(309\) 27.3860 1.55793
\(310\) 0 0
\(311\) 9.09153 0.515533 0.257767 0.966207i \(-0.417013\pi\)
0.257767 + 0.966207i \(0.417013\pi\)
\(312\) 0 0
\(313\) 24.6354i 1.39248i −0.717811 0.696238i \(-0.754856\pi\)
0.717811 0.696238i \(-0.245144\pi\)
\(314\) 0 0
\(315\) 4.89392 3.52729i 0.275741 0.198740i
\(316\) 0 0
\(317\) 23.3406i 1.31094i 0.755222 + 0.655469i \(0.227529\pi\)
−0.755222 + 0.655469i \(0.772471\pi\)
\(318\) 0 0
\(319\) 0.453168 0.0253725
\(320\) 0 0
\(321\) −38.5262 −2.15032
\(322\) 0 0
\(323\) 42.4805i 2.36368i
\(324\) 0 0
\(325\) −15.8855 5.29544i −0.881169 0.293738i
\(326\) 0 0
\(327\) 41.9575i 2.32025i
\(328\) 0 0
\(329\) −4.00487 −0.220796
\(330\) 0 0
\(331\) 24.6239 1.35345 0.676725 0.736236i \(-0.263399\pi\)
0.676725 + 0.736236i \(0.263399\pi\)
\(332\) 0 0
\(333\) 16.1853i 0.886950i
\(334\) 0 0
\(335\) 6.53485 4.70998i 0.357037 0.257334i
\(336\) 0 0
\(337\) 14.9958i 0.816875i −0.912786 0.408438i \(-0.866074\pi\)
0.912786 0.408438i \(-0.133926\pi\)
\(338\) 0 0
\(339\) −36.9024 −2.00426
\(340\) 0 0
\(341\) 17.0127 0.921290
\(342\) 0 0
\(343\) 10.4524i 0.564378i
\(344\) 0 0
\(345\) 3.32209 + 4.60923i 0.178855 + 0.248153i
\(346\) 0 0
\(347\) 8.76366i 0.470458i 0.971940 + 0.235229i \(0.0755840\pi\)
−0.971940 + 0.235229i \(0.924416\pi\)
\(348\) 0 0
\(349\) −33.1731 −1.77572 −0.887859 0.460116i \(-0.847808\pi\)
−0.887859 + 0.460116i \(0.847808\pi\)
\(350\) 0 0
\(351\) 3.88249 0.207232
\(352\) 0 0
\(353\) 23.8513i 1.26948i −0.772727 0.634738i \(-0.781108\pi\)
0.772727 0.634738i \(-0.218892\pi\)
\(354\) 0 0
\(355\) −15.0729 20.9129i −0.799988 1.10994i
\(356\) 0 0
\(357\) 13.1472i 0.695821i
\(358\) 0 0
\(359\) 8.53298 0.450353 0.225177 0.974318i \(-0.427704\pi\)
0.225177 + 0.974318i \(0.427704\pi\)
\(360\) 0 0
\(361\) 22.0699 1.16157
\(362\) 0 0
\(363\) 39.7786i 2.08783i
\(364\) 0 0
\(365\) −18.9877 + 13.6853i −0.993860 + 0.716323i
\(366\) 0 0
\(367\) 23.3388i 1.21828i 0.793064 + 0.609138i \(0.208485\pi\)
−0.793064 + 0.609138i \(0.791515\pi\)
\(368\) 0 0
\(369\) 19.9011 1.03601
\(370\) 0 0
\(371\) 6.87216 0.356785
\(372\) 0 0
\(373\) 26.3073i 1.36214i 0.732218 + 0.681070i \(0.238485\pi\)
−0.732218 + 0.681070i \(0.761515\pi\)
\(374\) 0 0
\(375\) 8.46982 + 27.1163i 0.437380 + 1.40028i
\(376\) 0 0
\(377\) 0.293955i 0.0151394i
\(378\) 0 0
\(379\) 33.0601 1.69818 0.849091 0.528246i \(-0.177150\pi\)
0.849091 + 0.528246i \(0.177150\pi\)
\(380\) 0 0
\(381\) 41.8908 2.14613
\(382\) 0 0
\(383\) 23.7177i 1.21192i 0.795496 + 0.605958i \(0.207210\pi\)
−0.795496 + 0.605958i \(0.792790\pi\)
\(384\) 0 0
\(385\) −7.31042 + 5.26897i −0.372574 + 0.268532i
\(386\) 0 0
\(387\) 9.08697i 0.461917i
\(388\) 0 0
\(389\) −4.39287 −0.222728 −0.111364 0.993780i \(-0.535522\pi\)
−0.111364 + 0.993780i \(0.535522\pi\)
\(390\) 0 0
\(391\) −6.62869 −0.335227
\(392\) 0 0
\(393\) 12.5561i 0.633372i
\(394\) 0 0
\(395\) 4.49600 + 6.23796i 0.226218 + 0.313866i
\(396\) 0 0
\(397\) 0.668437i 0.0335479i −0.999859 0.0167740i \(-0.994660\pi\)
0.999859 0.0167740i \(-0.00533957\pi\)
\(398\) 0 0
\(399\) −12.7106 −0.636325
\(400\) 0 0
\(401\) 11.1310 0.555857 0.277928 0.960602i \(-0.410352\pi\)
0.277928 + 0.960602i \(0.410352\pi\)
\(402\) 0 0
\(403\) 11.0356i 0.549721i
\(404\) 0 0
\(405\) 9.70520 + 13.4655i 0.482255 + 0.669104i
\(406\) 0 0
\(407\) 24.1772i 1.19842i
\(408\) 0 0
\(409\) 17.7667 0.878506 0.439253 0.898364i \(-0.355243\pi\)
0.439253 + 0.898364i \(0.355243\pi\)
\(410\) 0 0
\(411\) −45.6135 −2.24995
\(412\) 0 0
\(413\) 2.33147i 0.114724i
\(414\) 0 0
\(415\) 6.58370 4.74519i 0.323181 0.232932i
\(416\) 0 0
\(417\) 44.4182i 2.17517i
\(418\) 0 0
\(419\) 37.4277 1.82846 0.914231 0.405194i \(-0.132796\pi\)
0.914231 + 0.405194i \(0.132796\pi\)
\(420\) 0 0
\(421\) −27.0798 −1.31979 −0.659895 0.751358i \(-0.729399\pi\)
−0.659895 + 0.751358i \(0.729399\pi\)
\(422\) 0 0
\(423\) 17.7329i 0.862205i
\(424\) 0 0
\(425\) −31.4425 10.4814i −1.52518 0.508420i
\(426\) 0 0
\(427\) 1.60454i 0.0776490i
\(428\) 0 0
\(429\) −43.9333 −2.12112
\(430\) 0 0
\(431\) −33.3003 −1.60402 −0.802009 0.597312i \(-0.796235\pi\)
−0.802009 + 0.597312i \(0.796235\pi\)
\(432\) 0 0
\(433\) 2.71773i 0.130606i 0.997865 + 0.0653028i \(0.0208013\pi\)
−0.997865 + 0.0653028i \(0.979199\pi\)
\(434\) 0 0
\(435\) 0.404572 0.291595i 0.0193978 0.0139809i
\(436\) 0 0
\(437\) 6.40858i 0.306564i
\(438\) 0 0
\(439\) 16.7478 0.799331 0.399665 0.916661i \(-0.369126\pi\)
0.399665 + 0.916661i \(0.369126\pi\)
\(440\) 0 0
\(441\) −22.0879 −1.05181
\(442\) 0 0
\(443\) 11.6392i 0.552993i 0.961015 + 0.276497i \(0.0891735\pi\)
−0.961015 + 0.276497i \(0.910827\pi\)
\(444\) 0 0
\(445\) 18.7106 + 25.9600i 0.886969 + 1.23062i
\(446\) 0 0
\(447\) 55.9201i 2.64493i
\(448\) 0 0
\(449\) −10.4132 −0.491430 −0.245715 0.969342i \(-0.579023\pi\)
−0.245715 + 0.969342i \(0.579023\pi\)
\(450\) 0 0
\(451\) −29.7278 −1.39983
\(452\) 0 0
\(453\) 18.8250i 0.884476i
\(454\) 0 0
\(455\) −3.41780 4.74202i −0.160229 0.222309i
\(456\) 0 0
\(457\) 6.66798i 0.311915i 0.987764 + 0.155957i \(0.0498463\pi\)
−0.987764 + 0.155957i \(0.950154\pi\)
\(458\) 0 0
\(459\) 7.68469 0.358690
\(460\) 0 0
\(461\) −10.1142 −0.471064 −0.235532 0.971867i \(-0.575683\pi\)
−0.235532 + 0.971867i \(0.575683\pi\)
\(462\) 0 0
\(463\) 25.4957i 1.18489i −0.805612 0.592443i \(-0.798164\pi\)
0.805612 0.592443i \(-0.201836\pi\)
\(464\) 0 0
\(465\) 15.1884 10.9470i 0.704343 0.507654i
\(466\) 0 0
\(467\) 9.17713i 0.424667i −0.977197 0.212334i \(-0.931894\pi\)
0.977197 0.212334i \(-0.0681063\pi\)
\(468\) 0 0
\(469\) 2.81197 0.129845
\(470\) 0 0
\(471\) −13.1935 −0.607922
\(472\) 0 0
\(473\) 13.5739i 0.624128i
\(474\) 0 0
\(475\) 10.1333 30.3984i 0.464948 1.39477i
\(476\) 0 0
\(477\) 30.4288i 1.39324i
\(478\) 0 0
\(479\) 22.6115 1.03315 0.516574 0.856243i \(-0.327207\pi\)
0.516574 + 0.856243i \(0.327207\pi\)
\(480\) 0 0
\(481\) −15.6829 −0.715081
\(482\) 0 0
\(483\) 1.98337i 0.0902465i
\(484\) 0 0
\(485\) 0.775638 0.559039i 0.0352199 0.0253847i
\(486\) 0 0
\(487\) 6.32242i 0.286496i −0.989687 0.143248i \(-0.954245\pi\)
0.989687 0.143248i \(-0.0457547\pi\)
\(488\) 0 0
\(489\) 29.3775 1.32850
\(490\) 0 0
\(491\) 20.5410 0.927002 0.463501 0.886096i \(-0.346593\pi\)
0.463501 + 0.886096i \(0.346593\pi\)
\(492\) 0 0
\(493\) 0.581830i 0.0262043i
\(494\) 0 0
\(495\) 23.3302 + 32.3694i 1.04861 + 1.45490i
\(496\) 0 0
\(497\) 8.99891i 0.403656i
\(498\) 0 0
\(499\) 33.1588 1.48439 0.742196 0.670183i \(-0.233784\pi\)
0.742196 + 0.670183i \(0.233784\pi\)
\(500\) 0 0
\(501\) 49.5178 2.21229
\(502\) 0 0
\(503\) 16.9045i 0.753736i −0.926267 0.376868i \(-0.877001\pi\)
0.926267 0.376868i \(-0.122999\pi\)
\(504\) 0 0
\(505\) 10.4521 + 14.5018i 0.465113 + 0.645320i
\(506\) 0 0
\(507\) 4.53391i 0.201358i
\(508\) 0 0
\(509\) −28.6358 −1.26926 −0.634631 0.772816i \(-0.718848\pi\)
−0.634631 + 0.772816i \(0.718848\pi\)
\(510\) 0 0
\(511\) −8.17048 −0.361441
\(512\) 0 0
\(513\) 7.42951i 0.328021i
\(514\) 0 0
\(515\) −19.5513 + 14.0915i −0.861533 + 0.620948i
\(516\) 0 0
\(517\) 26.4890i 1.16499i
\(518\) 0 0
\(519\) −48.0391 −2.10868
\(520\) 0 0
\(521\) 38.4207 1.68324 0.841622 0.540068i \(-0.181601\pi\)
0.841622 + 0.540068i \(0.181601\pi\)
\(522\) 0 0
\(523\) 38.6386i 1.68955i −0.535124 0.844773i \(-0.679735\pi\)
0.535124 0.844773i \(-0.320265\pi\)
\(524\) 0 0
\(525\) −3.13613 + 9.40791i −0.136872 + 0.410595i
\(526\) 0 0
\(527\) 21.8429i 0.951492i
\(528\) 0 0
\(529\) −1.00000 −0.0434783
\(530\) 0 0
\(531\) 10.3234 0.447997
\(532\) 0 0
\(533\) 19.2834i 0.835257i
\(534\) 0 0
\(535\) 27.5045 19.8238i 1.18912 0.857057i
\(536\) 0 0
\(537\) 42.0277i 1.81363i
\(538\) 0 0
\(539\) 32.9944 1.42117
\(540\) 0 0
\(541\) 4.42943 0.190436 0.0952180 0.995456i \(-0.469645\pi\)
0.0952180 + 0.995456i \(0.469645\pi\)
\(542\) 0 0
\(543\) 14.0153i 0.601455i
\(544\) 0 0
\(545\) −21.5894 29.9541i −0.924787 1.28309i
\(546\) 0 0
\(547\) 28.1695i 1.20444i 0.798330 + 0.602220i \(0.205717\pi\)
−0.798330 + 0.602220i \(0.794283\pi\)
\(548\) 0 0
\(549\) 7.10464 0.303219
\(550\) 0 0
\(551\) −0.562509 −0.0239637
\(552\) 0 0
\(553\) 2.68422i 0.114145i
\(554\) 0 0
\(555\) 15.5570 + 21.5846i 0.660360 + 0.916215i
\(556\) 0 0
\(557\) 12.1942i 0.516687i −0.966053 0.258343i \(-0.916823\pi\)
0.966053 0.258343i \(-0.0831766\pi\)
\(558\) 0 0
\(559\) −8.80492 −0.372409
\(560\) 0 0
\(561\) −86.9579 −3.67137
\(562\) 0 0
\(563\) 15.8362i 0.667415i 0.942677 + 0.333708i \(0.108300\pi\)
−0.942677 + 0.333708i \(0.891700\pi\)
\(564\) 0 0
\(565\) 26.3452 18.9883i 1.10835 0.798843i
\(566\) 0 0
\(567\) 5.79424i 0.243335i
\(568\) 0 0
\(569\) −0.674355 −0.0282704 −0.0141352 0.999900i \(-0.504500\pi\)
−0.0141352 + 0.999900i \(0.504500\pi\)
\(570\) 0 0
\(571\) −39.9107 −1.67021 −0.835105 0.550090i \(-0.814593\pi\)
−0.835105 + 0.550090i \(0.814593\pi\)
\(572\) 0 0
\(573\) 61.0700i 2.55124i
\(574\) 0 0
\(575\) −4.74339 1.58121i −0.197813 0.0659410i
\(576\) 0 0
\(577\) 0.727423i 0.0302830i 0.999885 + 0.0151415i \(0.00481987\pi\)
−0.999885 + 0.0151415i \(0.995180\pi\)
\(578\) 0 0
\(579\) 38.6635 1.60680
\(580\) 0 0
\(581\) 2.83299 0.117532
\(582\) 0 0
\(583\) 45.4538i 1.88251i
\(584\) 0 0
\(585\) −20.9969 + 15.1335i −0.868116 + 0.625693i
\(586\) 0 0
\(587\) 38.4075i 1.58525i 0.609712 + 0.792623i \(0.291285\pi\)
−0.609712 + 0.792623i \(0.708715\pi\)
\(588\) 0 0
\(589\) −21.1176 −0.870135
\(590\) 0 0
\(591\) 22.4233 0.922373
\(592\) 0 0
\(593\) 9.65052i 0.396299i −0.980172 0.198150i \(-0.936507\pi\)
0.980172 0.198150i \(-0.0634932\pi\)
\(594\) 0 0
\(595\) −6.76492 9.38597i −0.277335 0.384787i
\(596\) 0 0
\(597\) 38.9338i 1.59346i
\(598\) 0 0
\(599\) −35.5951 −1.45438 −0.727189 0.686437i \(-0.759174\pi\)
−0.727189 + 0.686437i \(0.759174\pi\)
\(600\) 0 0
\(601\) −2.48461 −0.101349 −0.0506747 0.998715i \(-0.516137\pi\)
−0.0506747 + 0.998715i \(0.516137\pi\)
\(602\) 0 0
\(603\) 12.4510i 0.507043i
\(604\) 0 0
\(605\) −20.4682 28.3986i −0.832151 1.15457i
\(606\) 0 0
\(607\) 15.0165i 0.609500i −0.952432 0.304750i \(-0.901427\pi\)
0.952432 0.304750i \(-0.0985730\pi\)
\(608\) 0 0
\(609\) 0.174089 0.00705445
\(610\) 0 0
\(611\) 17.1825 0.695131
\(612\) 0 0
\(613\) 4.41556i 0.178343i −0.996016 0.0891714i \(-0.971578\pi\)
0.996016 0.0891714i \(-0.0284219\pi\)
\(614\) 0 0
\(615\) −26.5399 + 19.1286i −1.07019 + 0.771340i
\(616\) 0 0
\(617\) 11.0132i 0.443373i 0.975118 + 0.221686i \(0.0711561\pi\)
−0.975118 + 0.221686i \(0.928844\pi\)
\(618\) 0 0
\(619\) −28.9235 −1.16253 −0.581267 0.813713i \(-0.697443\pi\)
−0.581267 + 0.813713i \(0.697443\pi\)
\(620\) 0 0
\(621\) 1.15931 0.0465214
\(622\) 0 0
\(623\) 11.1707i 0.447545i
\(624\) 0 0
\(625\) −19.9995 15.0006i −0.799982 0.600024i
\(626\) 0 0
\(627\) 84.0704i 3.35745i
\(628\) 0 0
\(629\) −31.0415 −1.23771
\(630\) 0 0
\(631\) −13.6238 −0.542357 −0.271178 0.962529i \(-0.587413\pi\)
−0.271178 + 0.962529i \(0.587413\pi\)
\(632\) 0 0
\(633\) 11.8704i 0.471806i
\(634\) 0 0
\(635\) −29.9066 + 21.5551i −1.18681 + 0.855388i
\(636\) 0 0
\(637\) 21.4023i 0.847991i
\(638\) 0 0
\(639\) −39.8458 −1.57627
\(640\) 0 0
\(641\) −28.1924 −1.11353 −0.556766 0.830670i \(-0.687958\pi\)
−0.556766 + 0.830670i \(0.687958\pi\)
\(642\) 0 0
\(643\) 18.5514i 0.731596i 0.930694 + 0.365798i \(0.119204\pi\)
−0.930694 + 0.365798i \(0.880796\pi\)
\(644\) 0 0
\(645\) 8.73424 + 12.1183i 0.343910 + 0.477158i
\(646\) 0 0
\(647\) 13.6338i 0.535999i 0.963419 + 0.268000i \(0.0863626\pi\)
−0.963419 + 0.268000i \(0.913637\pi\)
\(648\) 0 0
\(649\) −15.4208 −0.605320
\(650\) 0 0
\(651\) 6.53562 0.256151
\(652\) 0 0
\(653\) 37.6196i 1.47217i −0.676890 0.736084i \(-0.736673\pi\)
0.676890 0.736084i \(-0.263327\pi\)
\(654\) 0 0
\(655\) −6.46080 8.96402i −0.252444 0.350253i
\(656\) 0 0
\(657\) 36.1776i 1.41142i
\(658\) 0 0
\(659\) −11.7947 −0.459455 −0.229727 0.973255i \(-0.573783\pi\)
−0.229727 + 0.973255i \(0.573783\pi\)
\(660\) 0 0
\(661\) −6.49839 −0.252758 −0.126379 0.991982i \(-0.540336\pi\)
−0.126379 + 0.991982i \(0.540336\pi\)
\(662\) 0 0
\(663\) 56.4066i 2.19065i
\(664\) 0 0
\(665\) 9.07430 6.54028i 0.351886 0.253621i
\(666\) 0 0
\(667\) 0.0877744i 0.00339864i
\(668\) 0 0
\(669\) 52.8036 2.04150
\(670\) 0 0
\(671\) −10.6127 −0.409700
\(672\) 0 0
\(673\) 45.7524i 1.76362i 0.471601 + 0.881812i \(0.343676\pi\)
−0.471601 + 0.881812i \(0.656324\pi\)
\(674\) 0 0
\(675\) 5.49905 + 1.83311i 0.211658 + 0.0705564i
\(676\) 0 0
\(677\) 25.3462i 0.974133i 0.873365 + 0.487066i \(0.161933\pi\)
−0.873365 + 0.487066i \(0.838067\pi\)
\(678\) 0 0
\(679\) 0.333760 0.0128085
\(680\) 0 0
\(681\) 34.9874 1.34072
\(682\) 0 0
\(683\) 24.3192i 0.930548i 0.885167 + 0.465274i \(0.154044\pi\)
−0.885167 + 0.465274i \(0.845956\pi\)
\(684\) 0 0
\(685\) 32.5642 23.4706i 1.24422 0.896766i
\(686\) 0 0
\(687\) 47.2776i 1.80375i
\(688\) 0 0
\(689\) −29.4843 −1.12326
\(690\) 0 0
\(691\) 13.4950 0.513374 0.256687 0.966495i \(-0.417369\pi\)
0.256687 + 0.966495i \(0.417369\pi\)
\(692\) 0 0
\(693\) 13.9287i 0.529107i
\(694\) 0 0
\(695\) −22.8556 31.7109i −0.866962 1.20286i
\(696\) 0 0
\(697\) 38.1680i 1.44572i
\(698\) 0 0
\(699\) 1.14712 0.0433879
\(700\) 0 0
\(701\) 25.8467 0.976217 0.488109 0.872783i \(-0.337687\pi\)
0.488109 + 0.872783i \(0.337687\pi\)
\(702\) 0 0
\(703\) 30.0108i 1.13188i
\(704\) 0 0
\(705\) −17.0446 23.6485i −0.641937 0.890654i
\(706\) 0 0
\(707\) 6.24017i 0.234686i
\(708\) 0 0
\(709\) 44.9373 1.68766 0.843828 0.536613i \(-0.180296\pi\)
0.843828 + 0.536613i \(0.180296\pi\)
\(710\) 0 0
\(711\) 11.8853 0.445734
\(712\) 0 0
\(713\) 3.29521i 0.123406i
\(714\) 0 0
\(715\) 31.3647 22.6060i 1.17297 0.845418i
\(716\) 0 0
\(717\) 31.8942i 1.19111i
\(718\) 0 0
\(719\) −25.2188 −0.940502 −0.470251 0.882533i \(-0.655837\pi\)
−0.470251 + 0.882533i \(0.655837\pi\)
\(720\) 0 0
\(721\) −8.41300 −0.313317
\(722\) 0 0
\(723\) 42.5812i 1.58361i
\(724\) 0 0
\(725\) −0.138790 + 0.416349i −0.00515453 + 0.0154628i
\(726\) 0 0
\(727\) 18.6009i 0.689868i 0.938627 + 0.344934i \(0.112099\pi\)
−0.938627 + 0.344934i \(0.887901\pi\)
\(728\) 0 0
\(729\) 34.4931 1.27752
\(730\) 0 0
\(731\) −17.4277 −0.644588
\(732\) 0 0
\(733\) 30.0268i 1.10907i 0.832162 + 0.554533i \(0.187103\pi\)
−0.832162 + 0.554533i \(0.812897\pi\)
\(734\) 0 0
\(735\) 29.4562 21.2305i 1.08651 0.783099i
\(736\) 0 0
\(737\) 18.5990i 0.685101i
\(738\) 0 0
\(739\) 21.5513 0.792779 0.396389 0.918082i \(-0.370263\pi\)
0.396389 + 0.918082i \(0.370263\pi\)
\(740\) 0 0
\(741\) 54.5336 2.00334
\(742\) 0 0
\(743\) 0.818910i 0.0300429i 0.999887 + 0.0150215i \(0.00478166\pi\)
−0.999887 + 0.0150215i \(0.995218\pi\)
\(744\) 0 0
\(745\) −28.7739 39.9223i −1.05419 1.46264i
\(746\) 0 0
\(747\) 12.5441i 0.458963i
\(748\) 0 0
\(749\) 11.8353 0.432452
\(750\) 0 0
\(751\) −40.9390 −1.49388 −0.746942 0.664889i \(-0.768479\pi\)
−0.746942 + 0.664889i \(0.768479\pi\)
\(752\) 0 0
\(753\) 17.2240i 0.627678i
\(754\) 0 0
\(755\) −9.68649 13.4395i −0.352527 0.489113i
\(756\) 0 0
\(757\) 5.99781i 0.217994i −0.994042 0.108997i \(-0.965236\pi\)
0.994042 0.108997i \(-0.0347639\pi\)
\(758\) 0 0
\(759\) −13.1184 −0.476168
\(760\) 0 0
\(761\) 35.9456 1.30303 0.651513 0.758637i \(-0.274135\pi\)
0.651513 + 0.758637i \(0.274135\pi\)
\(762\) 0 0
\(763\) 12.8894i 0.466627i
\(764\) 0 0
\(765\) −41.5596 + 29.9540i −1.50259 + 1.08299i
\(766\) 0 0
\(767\) 10.0030i 0.361186i
\(768\) 0 0
\(769\) 52.5292 1.89425 0.947126 0.320861i \(-0.103972\pi\)
0.947126 + 0.320861i \(0.103972\pi\)
\(770\) 0 0
\(771\) −18.2484 −0.657201
\(772\) 0 0
\(773\) 10.2492i 0.368638i −0.982866 0.184319i \(-0.940992\pi\)
0.982866 0.184319i \(-0.0590079\pi\)
\(774\) 0 0
\(775\) −5.21041 + 15.6305i −0.187164 + 0.561463i
\(776\) 0 0
\(777\) 9.28794i 0.333203i
\(778\) 0 0
\(779\) 36.9006 1.32210
\(780\) 0 0
\(781\) 59.5206 2.12982
\(782\) 0 0
\(783\) 0.101758i 0.00363652i
\(784\) 0 0
\(785\) 9.41902 6.78874i 0.336179 0.242301i
\(786\) 0 0
\(787\) 24.2959i 0.866057i 0.901380 + 0.433028i \(0.142555\pi\)
−0.901380 + 0.433028i \(0.857445\pi\)
\(788\) 0 0
\(789\) 46.2602 1.64691
\(790\) 0 0
\(791\) 11.3365 0.403079
\(792\) 0 0
\(793\) 6.88412i 0.244462i
\(794\) 0 0
\(795\) 29.2477 + 40.5796i 1.03731 + 1.43921i
\(796\) 0 0
\(797\) 12.7075i 0.450122i 0.974345 + 0.225061i \(0.0722582\pi\)
−0.974345 + 0.225061i \(0.927742\pi\)
\(798\) 0 0
\(799\) 34.0097 1.20318
\(800\) 0