Properties

Label 3024.2.t.l.289.11
Level $3024$
Weight $2$
Character 3024.289
Analytic conductor $24.147$
Analytic rank $0$
Dimension $22$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(24.1467615712\)
Analytic rank: \(0\)
Dimension: \(22\)
Relative dimension: \(11\) over \(\Q(\zeta_{3})\)
Twist minimal: no (minimal twist has level 504)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 289.11
Character \(\chi\) \(=\) 3024.289
Dual form 3024.2.t.l.1873.11

$q$-expansion

\(f(q)\) \(=\) \(q+3.52959 q^{5} +(-1.16715 - 2.37440i) q^{7} +O(q^{10})\) \(q+3.52959 q^{5} +(-1.16715 - 2.37440i) q^{7} -2.32073 q^{11} +(-2.35884 - 4.08563i) q^{13} +(0.636946 + 1.10322i) q^{17} +(-2.78386 + 4.82178i) q^{19} -3.29710 q^{23} +7.45798 q^{25} +(4.32116 - 7.48447i) q^{29} +(4.25821 - 7.37543i) q^{31} +(-4.11956 - 8.38064i) q^{35} +(-2.84024 + 4.91943i) q^{37} +(-1.66553 - 2.88478i) q^{41} +(-0.0444165 + 0.0769317i) q^{43} +(-3.52607 - 6.10733i) q^{47} +(-4.27552 + 5.54256i) q^{49} +(-3.41816 - 5.92042i) q^{53} -8.19121 q^{55} +(3.99745 - 6.92378i) q^{59} +(-6.67764 - 11.5660i) q^{61} +(-8.32572 - 14.4206i) q^{65} +(3.06402 - 5.30704i) q^{67} +1.30202 q^{71} +(6.64529 + 11.5100i) q^{73} +(2.70864 + 5.51033i) q^{77} +(-5.01403 - 8.68455i) q^{79} +(-5.90243 + 10.2233i) q^{83} +(2.24815 + 3.89392i) q^{85} +(-0.561496 + 0.972540i) q^{89} +(-6.94778 + 10.3694i) q^{91} +(-9.82586 + 17.0189i) q^{95} +(-3.50818 + 6.07635i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q + 6q^{5} - 7q^{7} + O(q^{10}) \) \( 22q + 6q^{5} - 7q^{7} + 6q^{11} - 3q^{13} - 7q^{17} + q^{19} - 4q^{23} + 20q^{25} - 9q^{29} + 4q^{31} + 14q^{35} + 2q^{37} - 16q^{41} + 5q^{47} - 15q^{49} - 11q^{53} - 22q^{55} - 19q^{59} - 13q^{61} - 13q^{65} - 26q^{67} - 48q^{71} - 35q^{73} + 4q^{77} - 10q^{79} - 28q^{83} - 20q^{85} - 6q^{89} + 37q^{91} + 12q^{95} - 29q^{97} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 3.52959 1.57848 0.789239 0.614086i \(-0.210475\pi\)
0.789239 + 0.614086i \(0.210475\pi\)
\(6\) 0 0
\(7\) −1.16715 2.37440i −0.441141 0.897438i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −2.32073 −0.699726 −0.349863 0.936801i \(-0.613772\pi\)
−0.349863 + 0.936801i \(0.613772\pi\)
\(12\) 0 0
\(13\) −2.35884 4.08563i −0.654224 1.13315i −0.982088 0.188424i \(-0.939662\pi\)
0.327864 0.944725i \(-0.393671\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0.636946 + 1.10322i 0.154482 + 0.267571i 0.932870 0.360212i \(-0.117296\pi\)
−0.778388 + 0.627783i \(0.783962\pi\)
\(18\) 0 0
\(19\) −2.78386 + 4.82178i −0.638661 + 1.10619i 0.347066 + 0.937841i \(0.387178\pi\)
−0.985727 + 0.168352i \(0.946155\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −3.29710 −0.687492 −0.343746 0.939063i \(-0.611696\pi\)
−0.343746 + 0.939063i \(0.611696\pi\)
\(24\) 0 0
\(25\) 7.45798 1.49160
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 4.32116 7.48447i 0.802419 1.38983i −0.115601 0.993296i \(-0.536879\pi\)
0.918020 0.396535i \(-0.129787\pi\)
\(30\) 0 0
\(31\) 4.25821 7.37543i 0.764797 1.32467i −0.175557 0.984469i \(-0.556173\pi\)
0.940354 0.340197i \(-0.110494\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −4.11956 8.38064i −0.696332 1.41659i
\(36\) 0 0
\(37\) −2.84024 + 4.91943i −0.466932 + 0.808750i −0.999286 0.0377716i \(-0.987974\pi\)
0.532354 + 0.846522i \(0.321307\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −1.66553 2.88478i −0.260112 0.450528i 0.706159 0.708053i \(-0.250426\pi\)
−0.966272 + 0.257525i \(0.917093\pi\)
\(42\) 0 0
\(43\) −0.0444165 + 0.0769317i −0.00677346 + 0.0117320i −0.869392 0.494123i \(-0.835489\pi\)
0.862619 + 0.505855i \(0.168823\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −3.52607 6.10733i −0.514330 0.890845i −0.999862 0.0166264i \(-0.994707\pi\)
0.485532 0.874219i \(-0.338626\pi\)
\(48\) 0 0
\(49\) −4.27552 + 5.54256i −0.610789 + 0.791794i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −3.41816 5.92042i −0.469520 0.813233i 0.529873 0.848077i \(-0.322240\pi\)
−0.999393 + 0.0348444i \(0.988906\pi\)
\(54\) 0 0
\(55\) −8.19121 −1.10450
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 3.99745 6.92378i 0.520423 0.901400i −0.479295 0.877654i \(-0.659107\pi\)
0.999718 0.0237457i \(-0.00755920\pi\)
\(60\) 0 0
\(61\) −6.67764 11.5660i −0.854985 1.48088i −0.876659 0.481112i \(-0.840233\pi\)
0.0216747 0.999765i \(-0.493100\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −8.32572 14.4206i −1.03268 1.78865i
\(66\) 0 0
\(67\) 3.06402 5.30704i 0.374330 0.648358i −0.615897 0.787827i \(-0.711206\pi\)
0.990226 + 0.139469i \(0.0445394\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 1.30202 0.154522 0.0772609 0.997011i \(-0.475383\pi\)
0.0772609 + 0.997011i \(0.475383\pi\)
\(72\) 0 0
\(73\) 6.64529 + 11.5100i 0.777772 + 1.34714i 0.933223 + 0.359297i \(0.116984\pi\)
−0.155451 + 0.987844i \(0.549683\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 2.70864 + 5.51033i 0.308678 + 0.627961i
\(78\) 0 0
\(79\) −5.01403 8.68455i −0.564122 0.977088i −0.997131 0.0756985i \(-0.975881\pi\)
0.433009 0.901390i \(-0.357452\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −5.90243 + 10.2233i −0.647876 + 1.12215i 0.335753 + 0.941950i \(0.391009\pi\)
−0.983629 + 0.180204i \(0.942324\pi\)
\(84\) 0 0
\(85\) 2.24815 + 3.89392i 0.243847 + 0.422355i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −0.561496 + 0.972540i −0.0595185 + 0.103089i −0.894249 0.447569i \(-0.852290\pi\)
0.834731 + 0.550658i \(0.185623\pi\)
\(90\) 0 0
\(91\) −6.94778 + 10.3694i −0.728325 + 1.08700i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −9.82586 + 17.0189i −1.00811 + 1.74610i
\(96\) 0 0
\(97\) −3.50818 + 6.07635i −0.356202 + 0.616960i −0.987323 0.158724i \(-0.949262\pi\)
0.631121 + 0.775685i \(0.282595\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 9.74111 0.969277 0.484638 0.874715i \(-0.338951\pi\)
0.484638 + 0.874715i \(0.338951\pi\)
\(102\) 0 0
\(103\) −10.2856 −1.01347 −0.506734 0.862103i \(-0.669147\pi\)
−0.506734 + 0.862103i \(0.669147\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 2.72201 4.71465i 0.263146 0.455783i −0.703930 0.710269i \(-0.748573\pi\)
0.967076 + 0.254487i \(0.0819065\pi\)
\(108\) 0 0
\(109\) 0.417404 + 0.722965i 0.0399800 + 0.0692475i 0.885323 0.464977i \(-0.153937\pi\)
−0.845343 + 0.534224i \(0.820604\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −5.44881 9.43761i −0.512581 0.887815i −0.999894 0.0145882i \(-0.995356\pi\)
0.487313 0.873227i \(-0.337977\pi\)
\(114\) 0 0
\(115\) −11.6374 −1.08519
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 1.87608 2.79999i 0.171980 0.256674i
\(120\) 0 0
\(121\) −5.61421 −0.510383
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 8.67565 0.775974
\(126\) 0 0
\(127\) 9.90354 0.878797 0.439399 0.898292i \(-0.355192\pi\)
0.439399 + 0.898292i \(0.355192\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 17.1844 1.50141 0.750704 0.660639i \(-0.229715\pi\)
0.750704 + 0.660639i \(0.229715\pi\)
\(132\) 0 0
\(133\) 14.6980 + 0.982238i 1.27448 + 0.0851708i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 16.0939 1.37500 0.687498 0.726186i \(-0.258709\pi\)
0.687498 + 0.726186i \(0.258709\pi\)
\(138\) 0 0
\(139\) −1.11151 1.92519i −0.0942768 0.163292i 0.815030 0.579419i \(-0.196721\pi\)
−0.909307 + 0.416127i \(0.863387\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 5.47422 + 9.48163i 0.457778 + 0.792894i
\(144\) 0 0
\(145\) 15.2519 26.4171i 1.26660 2.19382i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −6.93692 −0.568295 −0.284147 0.958781i \(-0.591710\pi\)
−0.284147 + 0.958781i \(0.591710\pi\)
\(150\) 0 0
\(151\) −15.5167 −1.26273 −0.631365 0.775486i \(-0.717505\pi\)
−0.631365 + 0.775486i \(0.717505\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 15.0297 26.0322i 1.20722 2.09096i
\(156\) 0 0
\(157\) −0.401055 + 0.694648i −0.0320077 + 0.0554389i −0.881586 0.472024i \(-0.843523\pi\)
0.849578 + 0.527463i \(0.176857\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 3.84821 + 7.82862i 0.303281 + 0.616982i
\(162\) 0 0
\(163\) −1.77500 + 3.07438i −0.139028 + 0.240804i −0.927129 0.374742i \(-0.877731\pi\)
0.788101 + 0.615546i \(0.211065\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0.865131 + 1.49845i 0.0669459 + 0.115954i 0.897556 0.440901i \(-0.145341\pi\)
−0.830610 + 0.556855i \(0.812008\pi\)
\(168\) 0 0
\(169\) −4.62823 + 8.01633i −0.356018 + 0.616641i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1.11729 + 1.93521i 0.0849462 + 0.147131i 0.905368 0.424627i \(-0.139595\pi\)
−0.820422 + 0.571758i \(0.806262\pi\)
\(174\) 0 0
\(175\) −8.70458 17.7082i −0.658005 1.33861i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −0.350412 0.606931i −0.0261910 0.0453641i 0.852633 0.522511i \(-0.175004\pi\)
−0.878824 + 0.477146i \(0.841671\pi\)
\(180\) 0 0
\(181\) −19.6339 −1.45938 −0.729688 0.683780i \(-0.760335\pi\)
−0.729688 + 0.683780i \(0.760335\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −10.0249 + 17.3636i −0.737042 + 1.27659i
\(186\) 0 0
\(187\) −1.47818 2.56028i −0.108095 0.187226i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −8.04289 13.9307i −0.581963 1.00799i −0.995247 0.0973872i \(-0.968951\pi\)
0.413284 0.910602i \(-0.364382\pi\)
\(192\) 0 0
\(193\) 0.292732 0.507026i 0.0210713 0.0364965i −0.855297 0.518137i \(-0.826626\pi\)
0.876369 + 0.481641i \(0.159959\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 17.2923 1.23203 0.616014 0.787735i \(-0.288746\pi\)
0.616014 + 0.787735i \(0.288746\pi\)
\(198\) 0 0
\(199\) 12.2119 + 21.1517i 0.865681 + 1.49940i 0.866369 + 0.499404i \(0.166448\pi\)
−0.000687656 1.00000i \(0.500219\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −22.8145 1.52465i −1.60127 0.107009i
\(204\) 0 0
\(205\) −5.87864 10.1821i −0.410582 0.711149i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 6.46058 11.1900i 0.446888 0.774032i
\(210\) 0 0
\(211\) 5.58733 + 9.67754i 0.384648 + 0.666230i 0.991720 0.128417i \(-0.0409895\pi\)
−0.607072 + 0.794647i \(0.707656\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −0.156772 + 0.271537i −0.0106918 + 0.0185187i
\(216\) 0 0
\(217\) −22.4822 1.50244i −1.52619 0.101992i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 3.00490 5.20464i 0.202132 0.350102i
\(222\) 0 0
\(223\) 1.32951 2.30277i 0.0890303 0.154205i −0.818071 0.575117i \(-0.804957\pi\)
0.907101 + 0.420912i \(0.138290\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 11.9157 0.790874 0.395437 0.918493i \(-0.370593\pi\)
0.395437 + 0.918493i \(0.370593\pi\)
\(228\) 0 0
\(229\) −29.6128 −1.95687 −0.978434 0.206561i \(-0.933773\pi\)
−0.978434 + 0.206561i \(0.933773\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −1.84417 + 3.19420i −0.120816 + 0.209259i −0.920090 0.391708i \(-0.871884\pi\)
0.799274 + 0.600967i \(0.205218\pi\)
\(234\) 0 0
\(235\) −12.4456 21.5563i −0.811859 1.40618i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 8.03590 + 13.9186i 0.519799 + 0.900319i 0.999735 + 0.0230153i \(0.00732663\pi\)
−0.479936 + 0.877304i \(0.659340\pi\)
\(240\) 0 0
\(241\) 4.49867 0.289785 0.144892 0.989447i \(-0.453716\pi\)
0.144892 + 0.989447i \(0.453716\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −15.0908 + 19.5629i −0.964117 + 1.24983i
\(246\) 0 0
\(247\) 26.2667 1.67131
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −17.2696 −1.09005 −0.545023 0.838421i \(-0.683479\pi\)
−0.545023 + 0.838421i \(0.683479\pi\)
\(252\) 0 0
\(253\) 7.65167 0.481057
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −4.82173 −0.300771 −0.150386 0.988627i \(-0.548052\pi\)
−0.150386 + 0.988627i \(0.548052\pi\)
\(258\) 0 0
\(259\) 14.9957 + 1.00213i 0.931786 + 0.0622693i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 28.0903 1.73212 0.866062 0.499936i \(-0.166643\pi\)
0.866062 + 0.499936i \(0.166643\pi\)
\(264\) 0 0
\(265\) −12.0647 20.8966i −0.741128 1.28367i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −12.4126 21.4993i −0.756810 1.31083i −0.944469 0.328599i \(-0.893423\pi\)
0.187659 0.982234i \(-0.439910\pi\)
\(270\) 0 0
\(271\) 4.79671 8.30815i 0.291379 0.504684i −0.682757 0.730646i \(-0.739219\pi\)
0.974136 + 0.225962i \(0.0725524\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −17.3080 −1.04371
\(276\) 0 0
\(277\) 16.9383 1.01772 0.508862 0.860848i \(-0.330067\pi\)
0.508862 + 0.860848i \(0.330067\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −11.4291 + 19.7958i −0.681805 + 1.18092i 0.292625 + 0.956227i \(0.405471\pi\)
−0.974430 + 0.224693i \(0.927862\pi\)
\(282\) 0 0
\(283\) 4.17811 7.23669i 0.248363 0.430177i −0.714709 0.699422i \(-0.753441\pi\)
0.963072 + 0.269245i \(0.0867742\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −4.90570 + 7.32161i −0.289574 + 0.432181i
\(288\) 0 0
\(289\) 7.68860 13.3170i 0.452271 0.783356i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 2.16141 + 3.74368i 0.126271 + 0.218708i 0.922229 0.386644i \(-0.126366\pi\)
−0.795958 + 0.605352i \(0.793032\pi\)
\(294\) 0 0
\(295\) 14.1093 24.4381i 0.821477 1.42284i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 7.77732 + 13.4707i 0.449774 + 0.779031i
\(300\) 0 0
\(301\) 0.234507 + 0.0156716i 0.0135168 + 0.000903298i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −23.5693 40.8233i −1.34958 2.33753i
\(306\) 0 0
\(307\) 9.22888 0.526720 0.263360 0.964698i \(-0.415169\pi\)
0.263360 + 0.964698i \(0.415169\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 9.55365 16.5474i 0.541738 0.938317i −0.457067 0.889432i \(-0.651100\pi\)
0.998804 0.0488847i \(-0.0155667\pi\)
\(312\) 0 0
\(313\) −2.83951 4.91818i −0.160499 0.277992i 0.774549 0.632514i \(-0.217977\pi\)
−0.935048 + 0.354522i \(0.884644\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −14.1341 24.4809i −0.793848 1.37499i −0.923568 0.383434i \(-0.874741\pi\)
0.129720 0.991551i \(-0.458592\pi\)
\(318\) 0 0
\(319\) −10.0282 + 17.3694i −0.561474 + 0.972501i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −7.09266 −0.394646
\(324\) 0 0
\(325\) −17.5922 30.4705i −0.975838 1.69020i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −10.3858 + 15.5005i −0.572586 + 0.854568i
\(330\) 0 0
\(331\) −3.34045 5.78584i −0.183608 0.318018i 0.759499 0.650509i \(-0.225444\pi\)
−0.943107 + 0.332491i \(0.892111\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 10.8147 18.7317i 0.590872 1.02342i
\(336\) 0 0
\(337\) −3.49421 6.05215i −0.190342 0.329681i 0.755022 0.655700i \(-0.227626\pi\)
−0.945363 + 0.326018i \(0.894293\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −9.88215 + 17.1164i −0.535148 + 0.926904i
\(342\) 0 0
\(343\) 18.1504 + 3.68279i 0.980030 + 0.198852i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −4.14410 + 7.17780i −0.222467 + 0.385324i −0.955557 0.294808i \(-0.904744\pi\)
0.733089 + 0.680132i \(0.238078\pi\)
\(348\) 0 0
\(349\) 3.05373 5.28921i 0.163462 0.283125i −0.772646 0.634837i \(-0.781067\pi\)
0.936108 + 0.351712i \(0.114400\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 26.7208 1.42221 0.711104 0.703087i \(-0.248196\pi\)
0.711104 + 0.703087i \(0.248196\pi\)
\(354\) 0 0
\(355\) 4.59561 0.243909
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 2.45603 4.25397i 0.129624 0.224516i −0.793907 0.608040i \(-0.791956\pi\)
0.923531 + 0.383523i \(0.125289\pi\)
\(360\) 0 0
\(361\) −5.99972 10.3918i −0.315775 0.546938i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 23.4551 + 40.6255i 1.22770 + 2.12643i
\(366\) 0 0
\(367\) 30.7064 1.60286 0.801430 0.598089i \(-0.204073\pi\)
0.801430 + 0.598089i \(0.204073\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −10.0679 + 15.0261i −0.522701 + 0.780116i
\(372\) 0 0
\(373\) 16.5838 0.858676 0.429338 0.903144i \(-0.358747\pi\)
0.429338 + 0.903144i \(0.358747\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −40.7716 −2.09985
\(378\) 0 0
\(379\) −4.08857 −0.210016 −0.105008 0.994471i \(-0.533487\pi\)
−0.105008 + 0.994471i \(0.533487\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 30.3538 1.55101 0.775503 0.631344i \(-0.217496\pi\)
0.775503 + 0.631344i \(0.217496\pi\)
\(384\) 0 0
\(385\) 9.56038 + 19.4492i 0.487242 + 0.991223i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 3.46764 0.175816 0.0879082 0.996129i \(-0.471982\pi\)
0.0879082 + 0.996129i \(0.471982\pi\)
\(390\) 0 0
\(391\) −2.10007 3.63743i −0.106205 0.183953i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −17.6974 30.6529i −0.890455 1.54231i
\(396\) 0 0
\(397\) −7.04243 + 12.1979i −0.353450 + 0.612193i −0.986851 0.161630i \(-0.948325\pi\)
0.633402 + 0.773823i \(0.281658\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 10.9319 0.545911 0.272955 0.962027i \(-0.411999\pi\)
0.272955 + 0.962027i \(0.411999\pi\)
\(402\) 0 0
\(403\) −40.1777 −2.00139
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 6.59142 11.4167i 0.326725 0.565904i
\(408\) 0 0
\(409\) −7.99397 + 13.8460i −0.395276 + 0.684639i −0.993136 0.116962i \(-0.962685\pi\)
0.597860 + 0.801600i \(0.296018\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −21.1054 1.41043i −1.03853 0.0694029i
\(414\) 0 0
\(415\) −20.8331 + 36.0841i −1.02266 + 1.77130i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −3.56197 6.16951i −0.174014 0.301400i 0.765806 0.643072i \(-0.222340\pi\)
−0.939819 + 0.341671i \(0.889007\pi\)
\(420\) 0 0
\(421\) −16.6326 + 28.8086i −0.810625 + 1.40404i 0.101802 + 0.994805i \(0.467539\pi\)
−0.912427 + 0.409239i \(0.865794\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 4.75033 + 8.22781i 0.230425 + 0.399107i
\(426\) 0 0
\(427\) −19.6685 + 29.3547i −0.951826 + 1.42057i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −2.62382 4.54459i −0.126385 0.218905i 0.795889 0.605443i \(-0.207004\pi\)
−0.922273 + 0.386538i \(0.873671\pi\)
\(432\) 0 0
\(433\) 22.1053 1.06231 0.531156 0.847274i \(-0.321758\pi\)
0.531156 + 0.847274i \(0.321758\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 9.17865 15.8979i 0.439074 0.760499i
\(438\) 0 0
\(439\) 17.3083 + 29.9788i 0.826079 + 1.43081i 0.901092 + 0.433628i \(0.142767\pi\)
−0.0750132 + 0.997183i \(0.523900\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 2.20461 + 3.81850i 0.104744 + 0.181423i 0.913634 0.406538i \(-0.133264\pi\)
−0.808889 + 0.587961i \(0.799931\pi\)
\(444\) 0 0
\(445\) −1.98185 + 3.43266i −0.0939486 + 0.162724i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 19.6336 0.926568 0.463284 0.886210i \(-0.346671\pi\)
0.463284 + 0.886210i \(0.346671\pi\)
\(450\) 0 0
\(451\) 3.86525 + 6.69481i 0.182007 + 0.315246i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −24.5228 + 36.5995i −1.14965 + 1.71581i
\(456\) 0 0
\(457\) 15.4196 + 26.7075i 0.721297 + 1.24932i 0.960480 + 0.278349i \(0.0897872\pi\)
−0.239183 + 0.970975i \(0.576879\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 13.6297 23.6074i 0.634800 1.09951i −0.351757 0.936091i \(-0.614416\pi\)
0.986557 0.163415i \(-0.0522510\pi\)
\(462\) 0 0
\(463\) 0.959750 + 1.66234i 0.0446034 + 0.0772553i 0.887465 0.460875i \(-0.152464\pi\)
−0.842862 + 0.538130i \(0.819131\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 4.88655 8.46376i 0.226123 0.391656i −0.730533 0.682877i \(-0.760728\pi\)
0.956656 + 0.291221i \(0.0940616\pi\)
\(468\) 0 0
\(469\) −16.1772 1.08109i −0.746994 0.0499201i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0.103079 0.178538i 0.00473957 0.00820917i
\(474\) 0 0
\(475\) −20.7619 + 35.9607i −0.952623 + 1.64999i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 15.3762 0.702556 0.351278 0.936271i \(-0.385747\pi\)
0.351278 + 0.936271i \(0.385747\pi\)
\(480\) 0 0
\(481\) 26.7986 1.22191
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −12.3824 + 21.4470i −0.562258 + 0.973859i
\(486\) 0 0
\(487\) −5.18342 8.97794i −0.234883 0.406829i 0.724356 0.689427i \(-0.242137\pi\)
−0.959239 + 0.282597i \(0.908804\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −6.94718 12.0329i −0.313522 0.543035i 0.665600 0.746308i \(-0.268175\pi\)
−0.979122 + 0.203273i \(0.934842\pi\)
\(492\) 0 0
\(493\) 11.0094 0.495837
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −1.51966 3.09152i −0.0681660 0.138674i
\(498\) 0 0
\(499\) 3.40977 0.152642 0.0763210 0.997083i \(-0.475683\pi\)
0.0763210 + 0.997083i \(0.475683\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 43.8911 1.95701 0.978504 0.206227i \(-0.0661185\pi\)
0.978504 + 0.206227i \(0.0661185\pi\)
\(504\) 0 0
\(505\) 34.3821 1.52998
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −39.3348 −1.74348 −0.871742 0.489966i \(-0.837009\pi\)
−0.871742 + 0.489966i \(0.837009\pi\)
\(510\) 0 0
\(511\) 19.5732 29.2124i 0.865868 1.29228i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −36.3038 −1.59974
\(516\) 0 0
\(517\) 8.18305 + 14.1735i 0.359890 + 0.623348i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −12.4779 21.6124i −0.546669 0.946858i −0.998500 0.0547547i \(-0.982562\pi\)
0.451831 0.892104i \(-0.350771\pi\)
\(522\) 0 0
\(523\) 15.1575 26.2536i 0.662792 1.14799i −0.317086 0.948397i \(-0.602704\pi\)
0.979879 0.199594i \(-0.0639622\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 10.8490 0.472589
\(528\) 0 0
\(529\) −12.1291 −0.527354
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −7.85744 + 13.6095i −0.340343 + 0.589492i
\(534\) 0 0
\(535\) 9.60755 16.6408i 0.415371 0.719443i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 9.92233 12.8628i 0.427385 0.554039i
\(540\) 0 0
\(541\) −14.2812 + 24.7357i −0.613996 + 1.06347i 0.376563 + 0.926391i \(0.377106\pi\)
−0.990560 + 0.137082i \(0.956228\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 1.47326 + 2.55177i 0.0631077 + 0.109306i
\(546\) 0 0
\(547\) −3.89233 + 6.74171i −0.166424 + 0.288255i −0.937160 0.348900i \(-0.886555\pi\)
0.770736 + 0.637154i \(0.219889\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 24.0590 + 41.6714i 1.02495 + 1.77526i
\(552\) 0 0
\(553\) −14.7684 + 22.0415i −0.628018 + 0.937299i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 23.2470 + 40.2650i 0.985008 + 1.70608i 0.641900 + 0.766788i \(0.278146\pi\)
0.343108 + 0.939296i \(0.388520\pi\)
\(558\) 0 0
\(559\) 0.419086 0.0177254
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −13.9913 + 24.2336i −0.589663 + 1.02133i 0.404614 + 0.914488i \(0.367406\pi\)
−0.994276 + 0.106838i \(0.965927\pi\)
\(564\) 0 0
\(565\) −19.2320 33.3109i −0.809098 1.40140i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 4.44979 + 7.70726i 0.186545 + 0.323105i 0.944096 0.329671i \(-0.106938\pi\)
−0.757551 + 0.652776i \(0.773604\pi\)
\(570\) 0 0
\(571\) −16.1652 + 27.9989i −0.676492 + 1.17172i 0.299539 + 0.954084i \(0.403167\pi\)
−0.976031 + 0.217634i \(0.930166\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −24.5897 −1.02546
\(576\) 0 0
\(577\) −16.8414 29.1701i −0.701115 1.21437i −0.968075 0.250659i \(-0.919353\pi\)
0.266960 0.963707i \(-0.413981\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 31.1632 + 2.08257i 1.29287 + 0.0863997i
\(582\) 0 0
\(583\) 7.93262 + 13.7397i 0.328536 + 0.569040i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −1.24076 + 2.14907i −0.0512118 + 0.0887015i −0.890495 0.454993i \(-0.849642\pi\)
0.839283 + 0.543695i \(0.182975\pi\)
\(588\) 0 0
\(589\) 23.7085 + 41.0643i 0.976891 + 1.69202i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 15.0903 26.1371i 0.619684 1.07332i −0.369859 0.929088i \(-0.620594\pi\)
0.989543 0.144236i \(-0.0460725\pi\)
\(594\) 0 0
\(595\) 6.62177 9.88280i 0.271466 0.405155i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 8.20414 14.2100i 0.335212 0.580604i −0.648314 0.761373i \(-0.724525\pi\)
0.983526 + 0.180769i \(0.0578588\pi\)
\(600\) 0 0
\(601\) −2.96998 + 5.14416i −0.121148 + 0.209835i −0.920221 0.391400i \(-0.871991\pi\)
0.799073 + 0.601235i \(0.205324\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −19.8159 −0.805629
\(606\) 0 0
\(607\) 5.95146 0.241563 0.120781 0.992679i \(-0.461460\pi\)
0.120781 + 0.992679i \(0.461460\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −16.6348 + 28.8124i −0.672974 + 1.16562i
\(612\) 0 0
\(613\) 15.5920 + 27.0062i 0.629756 + 1.09077i 0.987601 + 0.156988i \(0.0501783\pi\)
−0.357845 + 0.933781i \(0.616488\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 11.1437 + 19.3014i 0.448627 + 0.777045i 0.998297 0.0583367i \(-0.0185797\pi\)
−0.549670 + 0.835382i \(0.685246\pi\)
\(618\) 0 0
\(619\) −34.5887 −1.39024 −0.695118 0.718895i \(-0.744648\pi\)
−0.695118 + 0.718895i \(0.744648\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 2.96454 + 0.198115i 0.118772 + 0.00793729i
\(624\) 0 0
\(625\) −6.66844 −0.266738
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −7.23631 −0.288530
\(630\) 0 0
\(631\) 26.2933 1.04672 0.523360 0.852112i \(-0.324678\pi\)
0.523360 + 0.852112i \(0.324678\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 34.9554 1.38716
\(636\) 0 0
\(637\) 32.7301 + 4.39419i 1.29681 + 0.174104i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 32.5346 1.28504 0.642519 0.766269i \(-0.277889\pi\)
0.642519 + 0.766269i \(0.277889\pi\)
\(642\) 0 0
\(643\) −5.21987 9.04107i −0.205851 0.356545i 0.744552 0.667564i \(-0.232663\pi\)
−0.950404 + 0.311019i \(0.899330\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0.685824 + 1.18788i 0.0269625 + 0.0467005i 0.879192 0.476468i \(-0.158083\pi\)
−0.852229 + 0.523168i \(0.824750\pi\)
\(648\) 0 0
\(649\) −9.27699 + 16.0682i −0.364154 + 0.630733i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 7.25134 0.283767 0.141883 0.989883i \(-0.454684\pi\)
0.141883 + 0.989883i \(0.454684\pi\)
\(654\) 0 0
\(655\) 60.6538 2.36994
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −13.3187 + 23.0686i −0.518822 + 0.898626i 0.480939 + 0.876754i \(0.340296\pi\)
−0.999761 + 0.0218722i \(0.993037\pi\)
\(660\) 0 0
\(661\) 17.4099 30.1549i 0.677168 1.17289i −0.298662 0.954359i \(-0.596540\pi\)
0.975830 0.218531i \(-0.0701265\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 51.8779 + 3.46689i 2.01174 + 0.134440i
\(666\) 0 0
\(667\) −14.2473 + 24.6770i −0.551657 + 0.955498i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 15.4970 + 26.8416i 0.598255 + 1.03621i
\(672\) 0 0
\(673\) 8.23841 14.2693i 0.317567 0.550043i −0.662412 0.749139i \(-0.730467\pi\)
0.979980 + 0.199096i \(0.0638007\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −10.5827 18.3297i −0.406725 0.704469i 0.587795 0.809010i \(-0.299996\pi\)
−0.994521 + 0.104541i \(0.966663\pi\)
\(678\) 0 0
\(679\) 18.5223 + 1.23780i 0.710819 + 0.0475026i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 14.0756 + 24.3796i 0.538587 + 0.932859i 0.998980 + 0.0451447i \(0.0143749\pi\)
−0.460394 + 0.887715i \(0.652292\pi\)
\(684\) 0 0
\(685\) 56.8049 2.17040
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −16.1258 + 27.9306i −0.614343 + 1.06407i
\(690\) 0 0
\(691\) 9.53980 + 16.5234i 0.362911 + 0.628580i 0.988439 0.151622i \(-0.0484496\pi\)
−0.625528 + 0.780202i \(0.715116\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −3.92316 6.79511i −0.148814 0.257753i
\(696\) 0 0
\(697\) 2.12171 3.67490i 0.0803653 0.139197i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −23.8508 −0.900834 −0.450417 0.892818i \(-0.648725\pi\)
−0.450417 + 0.892818i \(0.648725\pi\)
\(702\) 0 0
\(703\) −15.8136 27.3900i −0.596422 1.03303i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −11.3693 23.1293i −0.427588 0.869865i
\(708\) 0 0
\(709\) −10.0493 17.4059i −0.377409 0.653691i 0.613276 0.789869i \(-0.289851\pi\)
−0.990684 + 0.136178i \(0.956518\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −14.0397 + 24.3175i −0.525792 + 0.910698i
\(714\) 0 0
\(715\) 19.3217 + 33.4662i 0.722592 + 1.25157i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −3.29246 + 5.70270i −0.122788 + 0.212675i −0.920866 0.389879i \(-0.872517\pi\)
0.798078 + 0.602554i \(0.205850\pi\)
\(720\) 0 0
\(721\) 12.0048 + 24.4220i 0.447082 + 0.909524i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 32.2271 55.8190i 1.19688 2.07307i
\(726\) 0 0
\(727\) −18.2342 + 31.5826i −0.676269 + 1.17133i 0.299827 + 0.953994i \(0.403071\pi\)
−0.976096 + 0.217339i \(0.930262\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −0.113164 −0.00418551
\(732\) 0 0
\(733\) 23.3647 0.862997 0.431498 0.902114i \(-0.357985\pi\)
0.431498 + 0.902114i \(0.357985\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −7.11077 + 12.3162i −0.261928 + 0.453673i
\(738\) 0 0
\(739\) −14.4596 25.0448i −0.531906 0.921288i −0.999306 0.0372422i \(-0.988143\pi\)
0.467400 0.884046i \(-0.345191\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 11.6794 + 20.2292i 0.428474 + 0.742139i 0.996738 0.0807074i \(-0.0257179\pi\)
−0.568264 + 0.822847i \(0.692385\pi\)
\(744\) 0 0
\(745\) −24.4845 −0.897041
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −14.3714 0.960415i −0.525121 0.0350928i
\(750\) 0 0
\(751\) 1.71323 0.0625167 0.0312584 0.999511i \(-0.490049\pi\)
0.0312584 + 0.999511i \(0.490049\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −54.7675 −1.99319
\(756\) 0 0
\(757\) 28.4587 1.03435 0.517175 0.855880i \(-0.326984\pi\)
0.517175 + 0.855880i \(0.326984\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 34.1051 1.23631 0.618154 0.786057i \(-0.287881\pi\)
0.618154 + 0.786057i \(0.287881\pi\)
\(762\) 0 0
\(763\) 1.22943 1.83489i 0.0445084 0.0664275i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −37.7173 −1.36189
\(768\) 0 0
\(769\) 2.48467 + 4.30357i 0.0895995 + 0.155191i 0.907342 0.420394i \(-0.138108\pi\)
−0.817742 + 0.575584i \(0.804775\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 5.74814 + 9.95607i 0.206746 + 0.358095i 0.950688 0.310150i \(-0.100379\pi\)
−0.743941 + 0.668245i \(0.767046\pi\)
\(774\) 0 0
\(775\) 31.7576 55.0058i 1.14077 1.97587i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 18.5464 0.664494
\(780\) 0 0
\(781\) −3.02165 −0.108123
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −1.41556 + 2.45182i −0.0505235 + 0.0875092i
\(786\) 0 0
\(787\) 24.3005 42.0898i 0.866221 1.50034i 0.000391003 1.00000i \(-0.499876\pi\)
0.865830 0.500339i \(-0.166791\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −16.0491 + 23.9527i −0.570639 + 0.851661i
\(792\) 0 0
\(793\) −31.5030 + 54.5647i −1.11870 + 1.93765i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −16.8556 29.1947i −0.597056 1.03413i −0.993253 0.115965i \(-0.963004\pi\)
0.396198 0.918165i \(-0.370330\pi\)
\(798\) 0 0
\(799\) 4.49183 7.78007i 0.158909 0.275239i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −15.4219 26.7115i −0.544228 0.942630i
\(804\) 0 0
\(805\) 13.5826 + 27.6318i 0.478723 + 0.973892i
\(806\) 0 0