Properties

Label 3024.2.q.i.2881.4
Level $3024$
Weight $2$
Character 3024.2881
Analytic conductor $24.147$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(24.1467615712\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: 10.0.991381711347.1
Defining polynomial: \(x^{10} - 2 x^{9} + 9 x^{8} - 8 x^{7} + 40 x^{6} - 36 x^{5} + 90 x^{4} - 3 x^{3} + 36 x^{2} - 9 x + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 2881.4
Root \(0.920620 - 1.59456i\) of defining polynomial
Character \(\chi\) \(=\) 3024.2881
Dual form 3024.2.q.i.2305.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.667377 - 1.15593i) q^{5} +(-1.90267 - 1.83844i) q^{7} +O(q^{10})\) \(q+(0.667377 - 1.15593i) q^{5} +(-1.90267 - 1.83844i) q^{7} +(-0.756508 - 1.31031i) q^{11} +(-2.58800 - 4.48254i) q^{13} +(-0.774463 + 1.34141i) q^{17} +(1.25211 + 2.16872i) q^{19} +(3.68039 - 6.37463i) q^{23} +(1.60922 + 2.78725i) q^{25} +(0.0309713 - 0.0536439i) q^{29} +3.84777 q^{31} +(-3.39490 + 0.972416i) q^{35} +(-0.281608 - 0.487760i) q^{37} +(-4.51188 - 7.81481i) q^{41} +(-5.09988 + 8.83325i) q^{43} -9.51851 q^{47} +(0.240269 + 6.99588i) q^{49} +(-0.755374 + 1.30835i) q^{53} -2.01950 q^{55} -8.44331 q^{59} +3.23917 q^{61} -6.90868 q^{65} -6.93339 q^{67} -12.3304 q^{71} +(-1.37936 + 2.38912i) q^{73} +(-0.969547 + 3.88388i) q^{77} +5.91938 q^{79} +(2.80111 - 4.85167i) q^{83} +(1.03372 + 1.79045i) q^{85} +(-0.703287 - 1.21813i) q^{89} +(-3.31680 + 13.2867i) q^{91} +3.34251 q^{95} +(-6.09713 + 10.5605i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 4q^{5} + 4q^{7} + O(q^{10}) \) \( 10q - 4q^{5} + 4q^{7} + 4q^{11} - 8q^{13} - 12q^{17} - q^{19} + 3q^{23} - q^{25} - 7q^{29} - 6q^{31} + 5q^{35} - 5q^{41} + 7q^{43} - 54q^{47} - 8q^{49} + 21q^{53} - 4q^{55} - 60q^{59} + 28q^{61} - 22q^{65} - 4q^{67} - 6q^{71} + 15q^{73} - 11q^{77} - 8q^{79} + 9q^{83} - 6q^{85} - 28q^{89} + 4q^{91} + 28q^{95} - 12q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(757\) \(785\) \(1135\) \(2593\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 0.667377 1.15593i 0.298460 0.516948i −0.677324 0.735685i \(-0.736860\pi\)
0.975784 + 0.218737i \(0.0701937\pi\)
\(6\) 0 0
\(7\) −1.90267 1.83844i −0.719140 0.694865i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −0.756508 1.31031i −0.228096 0.395073i 0.729148 0.684356i \(-0.239917\pi\)
−0.957244 + 0.289283i \(0.906583\pi\)
\(12\) 0 0
\(13\) −2.58800 4.48254i −0.717781 1.24323i −0.961877 0.273482i \(-0.911824\pi\)
0.244096 0.969751i \(-0.421509\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −0.774463 + 1.34141i −0.187835 + 0.325340i −0.944528 0.328430i \(-0.893480\pi\)
0.756693 + 0.653770i \(0.226814\pi\)
\(18\) 0 0
\(19\) 1.25211 + 2.16872i 0.287254 + 0.497538i 0.973153 0.230158i \(-0.0739244\pi\)
−0.685900 + 0.727696i \(0.740591\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3.68039 6.37463i 0.767415 1.32920i −0.171545 0.985176i \(-0.554876\pi\)
0.938960 0.344025i \(-0.111791\pi\)
\(24\) 0 0
\(25\) 1.60922 + 2.78725i 0.321843 + 0.557449i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 0.0309713 0.0536439i 0.00575123 0.00996143i −0.863135 0.504972i \(-0.831503\pi\)
0.868887 + 0.495011i \(0.164836\pi\)
\(30\) 0 0
\(31\) 3.84777 0.691080 0.345540 0.938404i \(-0.387696\pi\)
0.345540 + 0.938404i \(0.387696\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −3.39490 + 0.972416i −0.573844 + 0.164368i
\(36\) 0 0
\(37\) −0.281608 0.487760i −0.0462961 0.0801872i 0.841949 0.539557i \(-0.181408\pi\)
−0.888245 + 0.459370i \(0.848075\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −4.51188 7.81481i −0.704638 1.22047i −0.966822 0.255450i \(-0.917776\pi\)
0.262185 0.965018i \(-0.415557\pi\)
\(42\) 0 0
\(43\) −5.09988 + 8.83325i −0.777724 + 1.34706i 0.155526 + 0.987832i \(0.450293\pi\)
−0.933251 + 0.359226i \(0.883041\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −9.51851 −1.38842 −0.694209 0.719774i \(-0.744245\pi\)
−0.694209 + 0.719774i \(0.744245\pi\)
\(48\) 0 0
\(49\) 0.240269 + 6.99588i 0.0343242 + 0.999411i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −0.755374 + 1.30835i −0.103759 + 0.179715i −0.913230 0.407444i \(-0.866420\pi\)
0.809472 + 0.587159i \(0.199754\pi\)
\(54\) 0 0
\(55\) −2.01950 −0.272310
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −8.44331 −1.09923 −0.549613 0.835419i \(-0.685225\pi\)
−0.549613 + 0.835419i \(0.685225\pi\)
\(60\) 0 0
\(61\) 3.23917 0.414733 0.207367 0.978263i \(-0.433511\pi\)
0.207367 + 0.978263i \(0.433511\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −6.90868 −0.856916
\(66\) 0 0
\(67\) −6.93339 −0.847049 −0.423524 0.905885i \(-0.639207\pi\)
−0.423524 + 0.905885i \(0.639207\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −12.3304 −1.46335 −0.731673 0.681656i \(-0.761260\pi\)
−0.731673 + 0.681656i \(0.761260\pi\)
\(72\) 0 0
\(73\) −1.37936 + 2.38912i −0.161442 + 0.279625i −0.935386 0.353629i \(-0.884948\pi\)
0.773944 + 0.633254i \(0.218281\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −0.969547 + 3.88388i −0.110490 + 0.442609i
\(78\) 0 0
\(79\) 5.91938 0.665982 0.332991 0.942930i \(-0.391942\pi\)
0.332991 + 0.942930i \(0.391942\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 2.80111 4.85167i 0.307462 0.532540i −0.670344 0.742050i \(-0.733854\pi\)
0.977806 + 0.209510i \(0.0671870\pi\)
\(84\) 0 0
\(85\) 1.03372 + 1.79045i 0.112122 + 0.194202i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −0.703287 1.21813i −0.0745483 0.129121i 0.826341 0.563169i \(-0.190418\pi\)
−0.900890 + 0.434048i \(0.857085\pi\)
\(90\) 0 0
\(91\) −3.31680 + 13.2867i −0.347695 + 1.39282i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 3.34251 0.342935
\(96\) 0 0
\(97\) −6.09713 + 10.5605i −0.619070 + 1.07226i 0.370586 + 0.928798i \(0.379157\pi\)
−0.989656 + 0.143462i \(0.954176\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 0.559336 + 0.968798i 0.0556560 + 0.0963990i 0.892511 0.451025i \(-0.148942\pi\)
−0.836855 + 0.547425i \(0.815608\pi\)
\(102\) 0 0
\(103\) 0.965224 1.67182i 0.0951063 0.164729i −0.814547 0.580098i \(-0.803014\pi\)
0.909653 + 0.415369i \(0.136348\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 2.88969 + 5.00509i 0.279357 + 0.483860i 0.971225 0.238163i \(-0.0765454\pi\)
−0.691868 + 0.722024i \(0.743212\pi\)
\(108\) 0 0
\(109\) −4.12106 + 7.13788i −0.394726 + 0.683685i −0.993066 0.117557i \(-0.962494\pi\)
0.598340 + 0.801242i \(0.295827\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −7.25105 12.5592i −0.682121 1.18147i −0.974332 0.225115i \(-0.927724\pi\)
0.292211 0.956354i \(-0.405609\pi\)
\(114\) 0 0
\(115\) −4.91242 8.50856i −0.458085 0.793427i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 3.93965 1.12845i 0.361147 0.103445i
\(120\) 0 0
\(121\) 4.35539 7.54376i 0.395945 0.685796i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 10.9696 0.981149
\(126\) 0 0
\(127\) −8.50004 −0.754257 −0.377128 0.926161i \(-0.623088\pi\)
−0.377128 + 0.926161i \(0.623088\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 1.00673 1.74371i 0.0879585 0.152349i −0.818690 0.574236i \(-0.805299\pi\)
0.906648 + 0.421888i \(0.138632\pi\)
\(132\) 0 0
\(133\) 1.60471 6.42827i 0.139146 0.557402i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1.10870 + 1.92032i 0.0947225 + 0.164064i 0.909493 0.415720i \(-0.136470\pi\)
−0.814770 + 0.579784i \(0.803137\pi\)
\(138\) 0 0
\(139\) −0.377669 0.654143i −0.0320335 0.0554836i 0.849564 0.527485i \(-0.176865\pi\)
−0.881598 + 0.472002i \(0.843532\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −3.91568 + 6.78216i −0.327446 + 0.567153i
\(144\) 0 0
\(145\) −0.0413391 0.0716014i −0.00343303 0.00594618i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 3.29249 5.70277i 0.269732 0.467189i −0.699061 0.715062i \(-0.746398\pi\)
0.968792 + 0.247873i \(0.0797317\pi\)
\(150\) 0 0
\(151\) 6.33356 + 10.9700i 0.515417 + 0.892729i 0.999840 + 0.0178950i \(0.00569645\pi\)
−0.484422 + 0.874834i \(0.660970\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 2.56791 4.44775i 0.206260 0.357252i
\(156\) 0 0
\(157\) −17.3074 −1.38128 −0.690642 0.723197i \(-0.742672\pi\)
−0.690642 + 0.723197i \(0.742672\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −18.7219 + 5.36260i −1.47549 + 0.422632i
\(162\) 0 0
\(163\) −6.10963 10.5822i −0.478543 0.828861i 0.521154 0.853463i \(-0.325502\pi\)
−0.999697 + 0.0246014i \(0.992168\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1.76248 + 3.05270i 0.136385 + 0.236225i 0.926126 0.377215i \(-0.123118\pi\)
−0.789741 + 0.613440i \(0.789785\pi\)
\(168\) 0 0
\(169\) −6.89546 + 11.9433i −0.530420 + 0.918714i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −10.1409 −0.770999 −0.385500 0.922708i \(-0.625971\pi\)
−0.385500 + 0.922708i \(0.625971\pi\)
\(174\) 0 0
\(175\) 2.06239 8.26164i 0.155902 0.624522i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0.850579 1.47325i 0.0635752 0.110116i −0.832486 0.554046i \(-0.813083\pi\)
0.896061 + 0.443931i \(0.146416\pi\)
\(180\) 0 0
\(181\) −16.9941 −1.26316 −0.631581 0.775310i \(-0.717594\pi\)
−0.631581 + 0.775310i \(0.717594\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −0.751755 −0.0552701
\(186\) 0 0
\(187\) 2.34355 0.171377
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 22.6939 1.64208 0.821038 0.570873i \(-0.193395\pi\)
0.821038 + 0.570873i \(0.193395\pi\)
\(192\) 0 0
\(193\) 6.18698 0.445348 0.222674 0.974893i \(-0.428521\pi\)
0.222674 + 0.974893i \(0.428521\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −9.77010 −0.696091 −0.348045 0.937478i \(-0.613154\pi\)
−0.348045 + 0.937478i \(0.613154\pi\)
\(198\) 0 0
\(199\) 4.33973 7.51664i 0.307636 0.532840i −0.670209 0.742172i \(-0.733796\pi\)
0.977845 + 0.209332i \(0.0671289\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −0.157549 + 0.0451275i −0.0110578 + 0.00316733i
\(204\) 0 0
\(205\) −12.0445 −0.841224
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1.89446 3.28130i 0.131043 0.226973i
\(210\) 0 0
\(211\) 2.84219 + 4.92283i 0.195665 + 0.338901i 0.947118 0.320885i \(-0.103980\pi\)
−0.751453 + 0.659786i \(0.770647\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 6.80708 + 11.7902i 0.464239 + 0.804086i
\(216\) 0 0
\(217\) −7.32102 7.07390i −0.496983 0.480207i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 8.01723 0.539298
\(222\) 0 0
\(223\) −5.86133 + 10.1521i −0.392503 + 0.679836i −0.992779 0.119957i \(-0.961724\pi\)
0.600276 + 0.799793i \(0.295058\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −5.59154 9.68482i −0.371123 0.642804i 0.618615 0.785694i \(-0.287694\pi\)
−0.989739 + 0.142890i \(0.954361\pi\)
\(228\) 0 0
\(229\) 4.82824 8.36275i 0.319059 0.552626i −0.661233 0.750181i \(-0.729967\pi\)
0.980292 + 0.197554i \(0.0632999\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 9.64492 + 16.7055i 0.631860 + 1.09441i 0.987171 + 0.159666i \(0.0510416\pi\)
−0.355311 + 0.934748i \(0.615625\pi\)
\(234\) 0 0
\(235\) −6.35243 + 11.0027i −0.414387 + 0.717739i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −0.194641 0.337128i −0.0125903 0.0218070i 0.859662 0.510864i \(-0.170674\pi\)
−0.872252 + 0.489057i \(0.837341\pi\)
\(240\) 0 0
\(241\) −5.31807 9.21117i −0.342567 0.593344i 0.642342 0.766419i \(-0.277963\pi\)
−0.984909 + 0.173075i \(0.944630\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 8.24709 + 4.39115i 0.526888 + 0.280540i
\(246\) 0 0
\(247\) 6.48091 11.2253i 0.412370 0.714247i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −3.26628 −0.206166 −0.103083 0.994673i \(-0.532871\pi\)
−0.103083 + 0.994673i \(0.532871\pi\)
\(252\) 0 0
\(253\) −11.1370 −0.700176
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −2.34787 + 4.06663i −0.146456 + 0.253669i −0.929915 0.367774i \(-0.880120\pi\)
0.783459 + 0.621443i \(0.213453\pi\)
\(258\) 0 0
\(259\) −0.360911 + 1.44576i −0.0224259 + 0.0898354i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −9.77491 16.9306i −0.602747 1.04399i −0.992403 0.123028i \(-0.960740\pi\)
0.389656 0.920960i \(-0.372594\pi\)
\(264\) 0 0
\(265\) 1.00824 + 1.74632i 0.0619355 + 0.107276i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −7.88365 + 13.6549i −0.480675 + 0.832553i −0.999754 0.0221730i \(-0.992942\pi\)
0.519079 + 0.854726i \(0.326275\pi\)
\(270\) 0 0
\(271\) −7.39882 12.8151i −0.449446 0.778464i 0.548904 0.835886i \(-0.315045\pi\)
−0.998350 + 0.0574218i \(0.981712\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 2.43477 4.21715i 0.146822 0.254304i
\(276\) 0 0
\(277\) 3.72561 + 6.45295i 0.223850 + 0.387720i 0.955974 0.293452i \(-0.0948040\pi\)
−0.732124 + 0.681172i \(0.761471\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 12.9938 22.5060i 0.775146 1.34259i −0.159566 0.987187i \(-0.551009\pi\)
0.934712 0.355406i \(-0.115657\pi\)
\(282\) 0 0
\(283\) −18.7554 −1.11489 −0.557445 0.830214i \(-0.688218\pi\)
−0.557445 + 0.830214i \(0.688218\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −5.78246 + 23.1638i −0.341328 + 1.36732i
\(288\) 0 0
\(289\) 7.30041 + 12.6447i 0.429436 + 0.743805i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1.23089 + 2.13196i 0.0719093 + 0.124551i 0.899738 0.436430i \(-0.143757\pi\)
−0.827829 + 0.560981i \(0.810424\pi\)
\(294\) 0 0
\(295\) −5.63487 + 9.75988i −0.328075 + 0.568242i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −38.0994 −2.20334
\(300\) 0 0
\(301\) 25.9428 7.43089i 1.49532 0.428309i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 2.16175 3.74425i 0.123781 0.214395i
\(306\) 0 0
\(307\) 4.66277 0.266118 0.133059 0.991108i \(-0.457520\pi\)
0.133059 + 0.991108i \(0.457520\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 27.4821 1.55837 0.779183 0.626797i \(-0.215634\pi\)
0.779183 + 0.626797i \(0.215634\pi\)
\(312\) 0 0
\(313\) 5.49332 0.310501 0.155250 0.987875i \(-0.450382\pi\)
0.155250 + 0.987875i \(0.450382\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −9.87758 −0.554780 −0.277390 0.960757i \(-0.589469\pi\)
−0.277390 + 0.960757i \(0.589469\pi\)
\(318\) 0 0
\(319\) −0.0937203 −0.00524733
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −3.87885 −0.215825
\(324\) 0 0
\(325\) 8.32930 14.4268i 0.462026 0.800253i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 18.1105 + 17.4992i 0.998466 + 0.964763i
\(330\) 0 0
\(331\) 20.6942 1.13746 0.568729 0.822525i \(-0.307435\pi\)
0.568729 + 0.822525i \(0.307435\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −4.62718 + 8.01452i −0.252810 + 0.437880i
\(336\) 0 0
\(337\) 0.748747 + 1.29687i 0.0407869 + 0.0706449i 0.885698 0.464261i \(-0.153680\pi\)
−0.844911 + 0.534906i \(0.820347\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −2.91087 5.04177i −0.157632 0.273027i
\(342\) 0 0
\(343\) 12.4044 13.7525i 0.669772 0.742567i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −29.5388 −1.58572 −0.792862 0.609401i \(-0.791410\pi\)
−0.792862 + 0.609401i \(0.791410\pi\)
\(348\) 0 0
\(349\) 18.0006 31.1780i 0.963551 1.66892i 0.250094 0.968222i \(-0.419539\pi\)
0.713458 0.700698i \(-0.247128\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −14.7465 25.5417i −0.784877 1.35945i −0.929073 0.369897i \(-0.879393\pi\)
0.144196 0.989549i \(-0.453940\pi\)
\(354\) 0 0
\(355\) −8.22900 + 14.2530i −0.436750 + 0.756473i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 2.70535 + 4.68580i 0.142783 + 0.247307i 0.928544 0.371224i \(-0.121062\pi\)
−0.785761 + 0.618531i \(0.787728\pi\)
\(360\) 0 0
\(361\) 6.36444 11.0235i 0.334971 0.580186i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1.84110 + 3.18888i 0.0963676 + 0.166914i
\(366\) 0 0
\(367\) −11.5422 19.9916i −0.602496 1.04355i −0.992442 0.122715i \(-0.960840\pi\)
0.389946 0.920838i \(-0.372494\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 3.84254 1.10063i 0.199495 0.0571421i
\(372\) 0 0
\(373\) −10.7515 + 18.6222i −0.556692 + 0.964219i 0.441078 + 0.897469i \(0.354596\pi\)
−0.997770 + 0.0667498i \(0.978737\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −0.320615 −0.0165125
\(378\) 0 0
\(379\) −5.72168 −0.293903 −0.146952 0.989144i \(-0.546946\pi\)
−0.146952 + 0.989144i \(0.546946\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 17.4604 30.2424i 0.892187 1.54531i 0.0549390 0.998490i \(-0.482504\pi\)
0.837248 0.546823i \(-0.184163\pi\)
\(384\) 0 0
\(385\) 3.84244 + 3.71274i 0.195829 + 0.189219i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −14.4411 25.0127i −0.732192 1.26819i −0.955944 0.293548i \(-0.905164\pi\)
0.223752 0.974646i \(-0.428169\pi\)
\(390\) 0 0
\(391\) 5.70066 + 9.87383i 0.288295 + 0.499341i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 3.95046 6.84239i 0.198769 0.344278i
\(396\) 0 0
\(397\) 5.59226 + 9.68607i 0.280667 + 0.486130i 0.971549 0.236838i \(-0.0761109\pi\)
−0.690882 + 0.722968i \(0.742778\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −0.541061 + 0.937146i −0.0270193 + 0.0467988i −0.879219 0.476418i \(-0.841935\pi\)
0.852200 + 0.523217i \(0.175268\pi\)
\(402\) 0 0
\(403\) −9.95802 17.2478i −0.496044 0.859174i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −0.426078 + 0.737988i −0.0211199 + 0.0365807i
\(408\) 0 0
\(409\) −21.7349 −1.07472 −0.537360 0.843353i \(-0.680578\pi\)
−0.537360 + 0.843353i \(0.680578\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 16.0648 + 15.5225i 0.790497 + 0.763814i
\(414\) 0 0
\(415\) −3.73879 6.47578i −0.183530 0.317884i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 12.5906 + 21.8075i 0.615090 + 1.06537i 0.990369 + 0.138455i \(0.0442135\pi\)
−0.375279 + 0.926912i \(0.622453\pi\)
\(420\) 0 0
\(421\) −14.8304 + 25.6869i −0.722788 + 1.25191i 0.237090 + 0.971488i \(0.423806\pi\)
−0.959878 + 0.280418i \(0.909527\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −4.98512 −0.241814
\(426\) 0 0
\(427\) −6.16305 5.95502i −0.298251 0.288184i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 2.44517 4.23516i 0.117780 0.204000i −0.801108 0.598520i \(-0.795756\pi\)
0.918887 + 0.394520i \(0.129089\pi\)
\(432\) 0 0
\(433\) 9.71430 0.466839 0.233420 0.972376i \(-0.425008\pi\)
0.233420 + 0.972376i \(0.425008\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 18.4330 0.881771
\(438\) 0 0
\(439\) 14.8235 0.707488 0.353744 0.935342i \(-0.384908\pi\)
0.353744 + 0.935342i \(0.384908\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −21.9020 −1.04059 −0.520297 0.853986i \(-0.674179\pi\)
−0.520297 + 0.853986i \(0.674179\pi\)
\(444\) 0 0
\(445\) −1.87743 −0.0889987
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −21.4952 −1.01442 −0.507212 0.861822i \(-0.669324\pi\)
−0.507212 + 0.861822i \(0.669324\pi\)
\(450\) 0 0
\(451\) −6.82655 + 11.8239i −0.321450 + 0.556767i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 13.1449 + 12.7012i 0.616242 + 0.595441i
\(456\) 0 0
\(457\) 40.6255 1.90038 0.950190 0.311670i \(-0.100888\pi\)
0.950190 + 0.311670i \(0.100888\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −1.41541 + 2.45155i −0.0659220 + 0.114180i −0.897103 0.441822i \(-0.854332\pi\)
0.831181 + 0.556003i \(0.187666\pi\)
\(462\) 0 0
\(463\) 13.9324 + 24.1317i 0.647494 + 1.12149i 0.983719 + 0.179711i \(0.0575164\pi\)
−0.336225 + 0.941782i \(0.609150\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −13.3219 23.0742i −0.616464 1.06775i −0.990126 0.140182i \(-0.955231\pi\)
0.373661 0.927565i \(-0.378102\pi\)
\(468\) 0 0
\(469\) 13.1919 + 12.7466i 0.609146 + 0.588585i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 15.4324 0.709582
\(474\) 0 0
\(475\) −4.02983 + 6.97987i −0.184901 + 0.320258i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 15.7895 + 27.3483i 0.721443 + 1.24958i 0.960422 + 0.278551i \(0.0898540\pi\)
−0.238979 + 0.971025i \(0.576813\pi\)
\(480\) 0 0
\(481\) −1.45760 + 2.52464i −0.0664609 + 0.115114i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 8.13817 + 14.0957i 0.369535 + 0.640054i
\(486\) 0 0
\(487\) 0.153087 0.265154i 0.00693703 0.0120153i −0.862536 0.505996i \(-0.831125\pi\)
0.869473 + 0.493980i \(0.164459\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −9.06981 15.7094i −0.409315 0.708954i 0.585498 0.810674i \(-0.300899\pi\)
−0.994813 + 0.101720i \(0.967566\pi\)
\(492\) 0 0
\(493\) 0.0479723 + 0.0830905i 0.00216057 + 0.00374221i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 23.4606 + 22.6687i 1.05235 + 1.01683i
\(498\) 0 0
\(499\) −10.6546 + 18.4543i −0.476964 + 0.826126i −0.999652 0.0263983i \(-0.991596\pi\)
0.522687 + 0.852524i \(0.324930\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −17.0738 −0.761285 −0.380642 0.924722i \(-0.624297\pi\)
−0.380642 + 0.924722i \(0.624297\pi\)
\(504\) 0 0
\(505\) 1.49315 0.0664443
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 18.3868 31.8468i 0.814979 1.41159i −0.0943635 0.995538i \(-0.530082\pi\)
0.909343 0.416048i \(-0.136585\pi\)
\(510\) 0 0
\(511\) 7.01670 2.00982i 0.310401 0.0889093i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −1.28834 2.23146i −0.0567709 0.0983300i
\(516\) 0 0
\(517\) 7.20083 + 12.4722i 0.316692 + 0.548527i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 9.57535 16.5850i 0.419504 0.726602i −0.576386 0.817178i \(-0.695537\pi\)
0.995890 + 0.0905758i \(0.0288707\pi\)
\(522\) 0 0
\(523\) 20.9715 + 36.3236i 0.917018 + 1.58832i 0.803920 + 0.594737i \(0.202744\pi\)
0.113097 + 0.993584i \(0.463923\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −2.97996 + 5.16144i −0.129809 + 0.224836i
\(528\) 0 0
\(529\) −15.5906 27.0037i −0.677851 1.17407i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −23.3535 + 40.4494i −1.01155 + 1.75206i
\(534\) 0 0
\(535\) 7.71405 0.333507
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 8.98500 5.60726i 0.387011 0.241522i
\(540\) 0 0
\(541\) −1.44272 2.49886i −0.0620273 0.107434i 0.833344 0.552754i \(-0.186423\pi\)
−0.895371 + 0.445320i \(0.853090\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 5.50059 + 9.52731i 0.235620 + 0.408105i
\(546\) 0 0
\(547\) −1.38738 + 2.40301i −0.0593201 + 0.102745i −0.894160 0.447747i \(-0.852227\pi\)
0.834840 + 0.550492i \(0.185560\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0.155118 0.00660825
\(552\) 0 0
\(553\) −11.2626 10.8824i −0.478935 0.462768i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −15.5344 + 26.9064i −0.658214 + 1.14006i 0.322864 + 0.946445i \(0.395354\pi\)
−0.981078 + 0.193614i \(0.937979\pi\)
\(558\) 0 0
\(559\) 52.7939 2.23294
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0.288041 0.0121395 0.00606973 0.999982i \(-0.498068\pi\)
0.00606973 + 0.999982i \(0.498068\pi\)
\(564\) 0 0
\(565\) −19.3567 −0.814344
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 16.0801 0.674112 0.337056 0.941485i \(-0.390569\pi\)
0.337056 + 0.941485i \(0.390569\pi\)
\(570\) 0 0
\(571\) 15.2858 0.639690 0.319845 0.947470i \(-0.396369\pi\)
0.319845 + 0.947470i \(0.396369\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 23.6902 0.987950
\(576\) 0 0
\(577\) 12.0812 20.9253i 0.502949 0.871133i −0.497045 0.867725i \(-0.665582\pi\)
0.999994 0.00340833i \(-0.00108491\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −14.2491 + 4.08142i −0.591152 + 0.169326i
\(582\) 0 0
\(583\) 2.28579 0.0946676
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 18.0145 31.2020i 0.743537 1.28784i −0.207339 0.978269i \(-0.566480\pi\)
0.950875 0.309574i \(-0.100186\pi\)
\(588\) 0 0
\(589\) 4.81783 + 8.34472i 0.198515 + 0.343838i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −12.4668 21.5932i −0.511951 0.886726i −0.999904 0.0138558i \(-0.995589\pi\)
0.487953 0.872870i \(-0.337744\pi\)
\(594\) 0 0
\(595\) 1.32482 5.30706i 0.0543124 0.217568i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 39.5283 1.61508 0.807542 0.589810i \(-0.200797\pi\)
0.807542 + 0.589810i \(0.200797\pi\)
\(600\) 0 0
\(601\) 1.86447 3.22936i 0.0760534 0.131728i −0.825490 0.564416i \(-0.809101\pi\)
0.901544 + 0.432688i \(0.142435\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −5.81337 10.0691i −0.236347 0.409365i
\(606\) 0 0
\(607\) 11.8264 20.4839i 0.480018 0.831415i −0.519719 0.854337i \(-0.673964\pi\)
0.999737 + 0.0229218i \(0.00729686\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 24.6339 + 42.6671i 0.996580 + 1.72613i
\(612\) 0 0
\(613\) 1.89952 3.29006i 0.0767208 0.132884i −0.825113 0.564968i \(-0.808888\pi\)
0.901833 + 0.432084i \(0.142222\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 17.5615 + 30.4174i 0.706999 + 1.22456i 0.965965 + 0.258672i \(0.0832849\pi\)
−0.258966 + 0.965886i \(0.583382\pi\)
\(618\) 0 0
\(619\) −10.5816 18.3279i −0.425311 0.736660i 0.571138 0.820854i \(-0.306502\pi\)
−0.996449 + 0.0841934i \(0.973169\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −0.901339 + 3.61064i −0.0361114 + 0.144657i
\(624\) 0 0
\(625\) −0.725240 + 1.25615i −0.0290096 + 0.0502461i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0.872381 0.0347841
\(630\) 0 0
\(631\) −4.74845 −0.189033 −0.0945164 0.995523i \(-0.530130\pi\)
−0.0945164 + 0.995523i \(0.530130\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −5.67273 + 9.82546i −0.225115 + 0.389911i
\(636\) 0 0
\(637\) 30.7375 19.1823i 1.21786 0.760031i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −4.93735 8.55174i −0.195013 0.337773i 0.751891 0.659287i \(-0.229142\pi\)
−0.946905 + 0.321514i \(0.895808\pi\)
\(642\) 0 0
\(643\) −21.9748 38.0615i −0.866602 1.50100i −0.865448 0.501000i \(-0.832966\pi\)
−0.00115462 0.999999i \(-0.500368\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 22.1936 38.4404i 0.872521 1.51125i 0.0131398 0.999914i \(-0.495817\pi\)
0.859381 0.511336i \(-0.170849\pi\)
\(648\) 0 0
\(649\) 6.38743 + 11.0634i 0.250729 + 0.434275i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 20.9956 36.3655i 0.821622 1.42309i −0.0828523 0.996562i \(-0.526403\pi\)
0.904474 0.426529i \(-0.140264\pi\)
\(654\) 0 0
\(655\) −1.34374 2.32742i −0.0525042 0.0909399i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −19.6365 + 34.0114i −0.764928 + 1.32489i 0.175356 + 0.984505i \(0.443892\pi\)
−0.940284 + 0.340390i \(0.889441\pi\)
\(660\) 0 0
\(661\) −0.186739 −0.00726330 −0.00363165 0.999993i \(-0.501156\pi\)
−0.00363165 + 0.999993i \(0.501156\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −6.35969 6.14502i −0.246618 0.238293i
\(666\) 0 0
\(667\) −0.227973 0.394862i −0.00882717 0.0152891i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −2.45046 4.24432i −0.0945989 0.163850i
\(672\) 0 0
\(673\) −5.43382 + 9.41166i −0.209458 + 0.362793i −0.951544 0.307512i \(-0.900503\pi\)
0.742086 + 0.670305i \(0.233837\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −28.3901 −1.09112 −0.545560 0.838072i \(-0.683683\pi\)
−0.545560 + 0.838072i \(0.683683\pi\)
\(678\) 0 0
\(679\) 31.0157 8.88396i 1.19027 0.340935i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 5.92034 10.2543i 0.226536 0.392371i −0.730243 0.683187i \(-0.760593\pi\)
0.956779 + 0.290816i \(0.0939267\pi\)
\(684\) 0 0
\(685\) 2.95968 0.113083
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 7.81962 0.297904
\(690\) 0 0
\(691\) −11.9083 −0.453014 −0.226507 0.974010i \(-0.572731\pi\)
−0.226507 + 0.974010i \(0.572731\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −1.00819 −0.0382429
\(696\) 0 0
\(697\) 13.9771 0.529422
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 31.3902 1.18559 0.592795 0.805353i \(-0.298024\pi\)
0.592795 + 0.805353i \(0.298024\pi\)
\(702\) 0 0
\(703\) 0.705208 1.22146i 0.0265974 0.0460681i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0.716849 2.87160i 0.0269599 0.107998i
\(708\) 0 0
\(709\) 0.625218 0.0234806 0.0117403 0.999931i \(-0.496263\pi\)
0.0117403 + 0.999931i \(0.496263\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 14.1613 24.5281i 0.530345 0.918584i
\(714\) 0 0
\(715\) 5.22647 + 9.05251i 0.195459 + 0.338545i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 12.1969 + 21.1257i 0.454869 + 0.787857i 0.998681 0.0513506i \(-0.0163526\pi\)
−0.543811 + 0.839208i \(0.683019\pi\)
\(720\) 0 0
\(721\) −4.91003 + 1.40640i −0.182859 + 0.0523771i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0.199358 0.00740399
\(726\) 0 0
\(727\) 18.9253 32.7796i 0.701900 1.21573i −0.265899 0.964001i \(-0.585669\pi\)
0.967799 0.251726i \(-0.0809980\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −7.89934 13.6821i −0.292168 0.506049i
\(732\) 0 0
\(733\) −1.20077 + 2.07980i −0.0443516 + 0.0768193i −0.887349 0.461098i \(-0.847456\pi\)
0.842997 + 0.537918i \(0.180789\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 5.24517 + 9.08490i 0.193208 + 0.334646i
\(738\) 0 0
\(739\) 15.1940 26.3167i 0.558920 0.968077i −0.438667 0.898650i \(-0.644549\pi\)
0.997587 0.0694277i \(-0.0221173\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −2.54785 4.41300i −0.0934715 0.161897i 0.815498 0.578760i \(-0.196463\pi\)
−0.908970 + 0.416862i \(0.863130\pi\)
\(744\) 0 0
\(745\) −4.39467 7.61179i −0.161008 0.278874i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 3.70345 14.8355i 0.135321 0.542079i
\(750\) 0 0
\(751\) −0.487506 + 0.844384i −0.0177893 + 0.0308120i −0.874783 0.484515i \(-0.838996\pi\)
0.856994 + 0.515327i \(0.172329\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 16.9075 0.615326
\(756\) 0 0
\(757\) 11.6346 0.422865 0.211433 0.977393i \(-0.432187\pi\)
0.211433 + 0.977393i \(0.432187\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −27.0875 + 46.9169i −0.981920 + 1.70073i −0.327023 + 0.945016i \(0.606045\pi\)
−0.654897 + 0.755718i \(0.727288\pi\)
\(762\) 0 0
\(763\) 20.9636 6.00468i 0.758932 0.217384i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 21.8513 + 37.8475i 0.789004 + 1.36659i
\(768\) 0 0
\(769\) −10.4326 18.0698i −0.376208 0.651612i 0.614299 0.789074i \(-0.289439\pi\)
−0.990507 + 0.137462i \(0.956106\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 27.4972 47.6266i 0.989007 1.71301i 0.366447 0.930439i \(-0.380574\pi\)
0.622561 0.782572i \(-0.286092\pi\)
\(774\) 0 0
\(775\) 6.19189 + 10.7247i 0.222419 + 0.385242i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 11.2987 19.5700i 0.404819 0.701168i
\(780\) 0 0
\(781\) 9.32802 + 16.1566i 0.333783 + 0.578129i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −11.5506 + 20.0062i −0.412258 + 0.714051i
\(786\) 0 0
\(787\) −9.18949 −0.327570 −0.163785 0.986496i \(-0.552370\pi\)
−0.163785 + 0.986496i \(0.552370\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −9.29301 + 37.2266i −0.330421 + 1.32362i
\(792\) 0 0
\(793\) −8.38296 14.5197i −0.297688 0.515610i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −3.53774 6.12754i −0.125313 0.217049i 0.796542 0.604583i \(-0.206660\pi\)
−0.921855 + 0.387534i \(0.873327\pi\)
\(798\) 0 0
\(799\) 7.37174 12.7682i 0.260793 0.451707i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 4.17398 0.147297