Properties

Label 3024.2.q.l.2305.3
Level $3024$
Weight $2$
Character 3024.2305
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.q (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 2305.3
Character \(\chi\) \(=\) 3024.2305
Dual form 3024.2.q.l.2881.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.33425 - 2.31099i) q^{5} +(-2.54743 - 0.714566i) q^{7} +O(q^{10})\) \(q+(-1.33425 - 2.31099i) q^{5} +(-2.54743 - 0.714566i) q^{7} +(1.99189 - 3.45005i) q^{11} +(1.00103 - 1.73384i) q^{13} +(3.57175 + 6.18646i) q^{17} +(4.01956 - 6.96208i) q^{19} +(0.443909 + 0.768873i) q^{23} +(-1.06046 + 1.83677i) q^{25} +(1.35035 + 2.33887i) q^{29} +1.22989 q^{31} +(1.74756 + 6.84051i) q^{35} +(5.26528 - 9.11973i) q^{37} +(1.43477 - 2.48509i) q^{41} +(-3.40053 - 5.88989i) q^{43} -12.1369 q^{47} +(5.97879 + 3.64061i) q^{49} +(2.38665 + 4.13380i) q^{53} -10.6307 q^{55} +9.58058 q^{59} -9.49962 q^{61} -5.34252 q^{65} -10.9889 q^{67} -4.62888 q^{71} +(2.01004 + 3.48149i) q^{73} +(-7.53949 + 7.36543i) q^{77} +1.02997 q^{79} +(-5.26656 - 9.12195i) q^{83} +(9.53125 - 16.5086i) q^{85} +(-1.72788 + 2.99278i) q^{89} +(-3.78900 + 3.70153i) q^{91} -21.4524 q^{95} +(-1.12061 - 1.94096i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q - q^{5} - 5q^{7} + O(q^{10}) \) \( 22q - q^{5} - 5q^{7} + 3q^{11} + 7q^{13} + q^{17} - 13q^{19} - 22q^{25} + 7q^{29} + 12q^{31} + 2q^{35} + 6q^{37} - 4q^{41} - 2q^{43} - 34q^{47} - 25q^{49} - q^{53} - 2q^{55} + 42q^{59} - 62q^{61} - 6q^{65} - 52q^{67} - 32q^{71} + 17q^{73} + q^{77} - 32q^{79} - 36q^{83} + 28q^{85} + 2q^{89} - 15q^{91} + 48q^{95} + 19q^{97} + O(q^{100}) \)

Character values

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

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

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
\(5\) −1.33425 2.31099i −0.596696 1.03351i −0.993305 0.115520i \(-0.963146\pi\)
0.396609 0.917988i \(-0.370187\pi\)
\(6\) 0 0
\(7\) −2.54743 0.714566i −0.962838 0.270081i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 1.99189 3.45005i 0.600577 1.04023i −0.392157 0.919898i \(-0.628271\pi\)
0.992734 0.120332i \(-0.0383958\pi\)
\(12\) 0 0
\(13\) 1.00103 1.73384i 0.277636 0.480880i −0.693161 0.720783i \(-0.743782\pi\)
0.970797 + 0.239903i \(0.0771156\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3.57175 + 6.18646i 0.866278 + 1.50044i 0.865773 + 0.500437i \(0.166827\pi\)
0.000504947 1.00000i \(0.499839\pi\)
\(18\) 0 0
\(19\) 4.01956 6.96208i 0.922150 1.59721i 0.126068 0.992022i \(-0.459764\pi\)
0.796082 0.605189i \(-0.206903\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0.443909 + 0.768873i 0.0925614 + 0.160321i 0.908588 0.417693i \(-0.137161\pi\)
−0.816027 + 0.578014i \(0.803828\pi\)
\(24\) 0 0
\(25\) −1.06046 + 1.83677i −0.212092 + 0.367355i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 1.35035 + 2.33887i 0.250753 + 0.434317i 0.963733 0.266867i \(-0.0859885\pi\)
−0.712980 + 0.701184i \(0.752655\pi\)
\(30\) 0 0
\(31\) 1.22989 0.220894 0.110447 0.993882i \(-0.464772\pi\)
0.110447 + 0.993882i \(0.464772\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1.74756 + 6.84051i 0.295391 + 1.15626i
\(36\) 0 0
\(37\) 5.26528 9.11973i 0.865607 1.49928i −0.000836477 1.00000i \(-0.500266\pi\)
0.866443 0.499275i \(-0.166400\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 1.43477 2.48509i 0.224073 0.388105i −0.731968 0.681339i \(-0.761398\pi\)
0.956041 + 0.293234i \(0.0947313\pi\)
\(42\) 0 0
\(43\) −3.40053 5.88989i −0.518576 0.898200i −0.999767 0.0215840i \(-0.993129\pi\)
0.481191 0.876616i \(-0.340204\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −12.1369 −1.77035 −0.885175 0.465258i \(-0.845961\pi\)
−0.885175 + 0.465258i \(0.845961\pi\)
\(48\) 0 0
\(49\) 5.97879 + 3.64061i 0.854113 + 0.520088i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 2.38665 + 4.13380i 0.327832 + 0.567821i 0.982081 0.188457i \(-0.0603487\pi\)
−0.654250 + 0.756279i \(0.727015\pi\)
\(54\) 0 0
\(55\) −10.6307 −1.43345
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 9.58058 1.24729 0.623643 0.781710i \(-0.285652\pi\)
0.623643 + 0.781710i \(0.285652\pi\)
\(60\) 0 0
\(61\) −9.49962 −1.21630 −0.608151 0.793821i \(-0.708089\pi\)
−0.608151 + 0.793821i \(0.708089\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −5.34252 −0.662658
\(66\) 0 0
\(67\) −10.9889 −1.34251 −0.671255 0.741227i \(-0.734244\pi\)
−0.671255 + 0.741227i \(0.734244\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −4.62888 −0.549347 −0.274673 0.961538i \(-0.588570\pi\)
−0.274673 + 0.961538i \(0.588570\pi\)
\(72\) 0 0
\(73\) 2.01004 + 3.48149i 0.235257 + 0.407478i 0.959347 0.282228i \(-0.0910733\pi\)
−0.724090 + 0.689705i \(0.757740\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −7.53949 + 7.36543i −0.859204 + 0.839368i
\(78\) 0 0
\(79\) 1.02997 0.115881 0.0579406 0.998320i \(-0.481547\pi\)
0.0579406 + 0.998320i \(0.481547\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −5.26656 9.12195i −0.578080 1.00126i −0.995699 0.0926419i \(-0.970469\pi\)
0.417620 0.908622i \(-0.362865\pi\)
\(84\) 0 0
\(85\) 9.53125 16.5086i 1.03381 1.79061i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −1.72788 + 2.99278i −0.183155 + 0.317234i −0.942953 0.332925i \(-0.891964\pi\)
0.759798 + 0.650159i \(0.225298\pi\)
\(90\) 0 0
\(91\) −3.78900 + 3.70153i −0.397195 + 0.388025i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −21.4524 −2.20097
\(96\) 0 0
\(97\) −1.12061 1.94096i −0.113781 0.197075i 0.803511 0.595290i \(-0.202963\pi\)
−0.917292 + 0.398216i \(0.869630\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −2.28415 + 3.95626i −0.227281 + 0.393663i −0.957001 0.290083i \(-0.906317\pi\)
0.729720 + 0.683746i \(0.239650\pi\)
\(102\) 0 0
\(103\) −6.37509 11.0420i −0.628156 1.08800i −0.987922 0.154955i \(-0.950477\pi\)
0.359766 0.933043i \(-0.382857\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −0.659761 + 1.14274i −0.0637815 + 0.110473i −0.896153 0.443746i \(-0.853649\pi\)
0.832371 + 0.554218i \(0.186983\pi\)
\(108\) 0 0
\(109\) −6.31990 10.9464i −0.605337 1.04847i −0.991998 0.126252i \(-0.959705\pi\)
0.386661 0.922222i \(-0.373628\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0.503200 0.871568i 0.0473371 0.0819903i −0.841386 0.540435i \(-0.818260\pi\)
0.888723 + 0.458444i \(0.151593\pi\)
\(114\) 0 0
\(115\) 1.18457 2.05174i 0.110462 0.191326i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −4.67815 18.3118i −0.428846 1.67864i
\(120\) 0 0
\(121\) −2.43524 4.21796i −0.221386 0.383451i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −7.68283 −0.687173
\(126\) 0 0
\(127\) −1.38400 −0.122810 −0.0614051 0.998113i \(-0.519558\pi\)
−0.0614051 + 0.998113i \(0.519558\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0.164862 + 0.285550i 0.0144041 + 0.0249486i 0.873138 0.487474i \(-0.162082\pi\)
−0.858734 + 0.512422i \(0.828748\pi\)
\(132\) 0 0
\(133\) −15.2144 + 14.8632i −1.31926 + 1.28880i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 4.47095 7.74391i 0.381979 0.661607i −0.609366 0.792889i \(-0.708576\pi\)
0.991345 + 0.131282i \(0.0419094\pi\)
\(138\) 0 0
\(139\) −3.92869 + 6.80470i −0.333227 + 0.577167i −0.983143 0.182840i \(-0.941471\pi\)
0.649915 + 0.760007i \(0.274804\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −3.98789 6.90723i −0.333484 0.577611i
\(144\) 0 0
\(145\) 3.60341 6.24128i 0.299247 0.518310i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 8.16075 + 14.1348i 0.668554 + 1.15797i 0.978308 + 0.207153i \(0.0664199\pi\)
−0.309754 + 0.950817i \(0.600247\pi\)
\(150\) 0 0
\(151\) −2.31677 + 4.01276i −0.188536 + 0.326554i −0.944762 0.327756i \(-0.893708\pi\)
0.756226 + 0.654310i \(0.227041\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −1.64098 2.84226i −0.131807 0.228296i
\(156\) 0 0
\(157\) −8.51852 −0.679852 −0.339926 0.940452i \(-0.610402\pi\)
−0.339926 + 0.940452i \(0.610402\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −0.581416 2.27585i −0.0458220 0.179362i
\(162\) 0 0
\(163\) −1.22354 + 2.11923i −0.0958350 + 0.165991i −0.909957 0.414703i \(-0.863885\pi\)
0.814122 + 0.580694i \(0.197219\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −0.0713948 + 0.123659i −0.00552470 + 0.00956906i −0.868775 0.495208i \(-0.835092\pi\)
0.863250 + 0.504777i \(0.168425\pi\)
\(168\) 0 0
\(169\) 4.49587 + 7.78708i 0.345836 + 0.599006i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −17.9967 −1.36826 −0.684131 0.729359i \(-0.739818\pi\)
−0.684131 + 0.729359i \(0.739818\pi\)
\(174\) 0 0
\(175\) 4.01395 3.92128i 0.303426 0.296421i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −1.02413 1.77384i −0.0765468 0.132583i 0.825211 0.564824i \(-0.191056\pi\)
−0.901758 + 0.432242i \(0.857723\pi\)
\(180\) 0 0
\(181\) 1.81165 0.134659 0.0673294 0.997731i \(-0.478552\pi\)
0.0673294 + 0.997731i \(0.478552\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −28.1009 −2.06602
\(186\) 0 0
\(187\) 28.4582 2.08107
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 18.8091 1.36098 0.680491 0.732757i \(-0.261767\pi\)
0.680491 + 0.732757i \(0.261767\pi\)
\(192\) 0 0
\(193\) 6.48714 0.466954 0.233477 0.972362i \(-0.424990\pi\)
0.233477 + 0.972362i \(0.424990\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 10.8356 0.772007 0.386003 0.922497i \(-0.373855\pi\)
0.386003 + 0.922497i \(0.373855\pi\)
\(198\) 0 0
\(199\) 9.43873 + 16.3484i 0.669094 + 1.15890i 0.978158 + 0.207863i \(0.0666508\pi\)
−0.309064 + 0.951041i \(0.600016\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −1.76863 6.92301i −0.124134 0.485900i
\(204\) 0 0
\(205\) −7.65736 −0.534813
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −16.0130 27.7354i −1.10764 1.91850i
\(210\) 0 0
\(211\) 11.9133 20.6344i 0.820145 1.42053i −0.0854297 0.996344i \(-0.527226\pi\)
0.905574 0.424188i \(-0.139440\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −9.07433 + 15.7172i −0.618864 + 1.07190i
\(216\) 0 0
\(217\) −3.13305 0.878836i −0.212685 0.0596593i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 14.3018 0.962041
\(222\) 0 0
\(223\) −6.53734 11.3230i −0.437773 0.758245i 0.559745 0.828665i \(-0.310899\pi\)
−0.997517 + 0.0704203i \(0.977566\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −11.5845 + 20.0649i −0.768890 + 1.33176i 0.169275 + 0.985569i \(0.445858\pi\)
−0.938165 + 0.346188i \(0.887476\pi\)
\(228\) 0 0
\(229\) 10.7794 + 18.6705i 0.712323 + 1.23378i 0.963983 + 0.265964i \(0.0856904\pi\)
−0.251660 + 0.967816i \(0.580976\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 8.05558 13.9527i 0.527739 0.914070i −0.471738 0.881739i \(-0.656373\pi\)
0.999477 0.0323318i \(-0.0102933\pi\)
\(234\) 0 0
\(235\) 16.1937 + 28.0483i 1.05636 + 1.82967i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0.216059 0.374225i 0.0139757 0.0242066i −0.858953 0.512054i \(-0.828885\pi\)
0.872929 + 0.487848i \(0.162218\pi\)
\(240\) 0 0
\(241\) −1.52837 + 2.64721i −0.0984509 + 0.170522i −0.911044 0.412310i \(-0.864722\pi\)
0.812593 + 0.582832i \(0.198055\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0.436221 18.6744i 0.0278691 1.19307i
\(246\) 0 0
\(247\) −8.04741 13.9385i −0.512045 0.886887i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 11.9066 0.751541 0.375770 0.926713i \(-0.377378\pi\)
0.375770 + 0.926713i \(0.377378\pi\)
\(252\) 0 0
\(253\) 3.53687 0.222361
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −15.9726 27.6654i −0.996346 1.72572i −0.572142 0.820155i \(-0.693887\pi\)
−0.424204 0.905567i \(-0.639446\pi\)
\(258\) 0 0
\(259\) −19.9296 + 19.4695i −1.23836 + 1.20977i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −3.35495 + 5.81094i −0.206875 + 0.358318i −0.950728 0.310025i \(-0.899663\pi\)
0.743854 + 0.668343i \(0.232996\pi\)
\(264\) 0 0
\(265\) 6.36879 11.0311i 0.391232 0.677634i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −5.66510 9.81225i −0.345408 0.598263i 0.640020 0.768358i \(-0.278926\pi\)
−0.985428 + 0.170095i \(0.945593\pi\)
\(270\) 0 0
\(271\) 5.06846 8.77884i 0.307887 0.533276i −0.670013 0.742350i \(-0.733711\pi\)
0.977900 + 0.209073i \(0.0670447\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 4.22465 + 7.31730i 0.254756 + 0.441250i
\(276\) 0 0
\(277\) 10.6433 18.4347i 0.639492 1.10763i −0.346052 0.938215i \(-0.612478\pi\)
0.985544 0.169418i \(-0.0541886\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 6.26945 + 10.8590i 0.374004 + 0.647794i 0.990177 0.139817i \(-0.0446513\pi\)
−0.616174 + 0.787610i \(0.711318\pi\)
\(282\) 0 0
\(283\) −24.9497 −1.48311 −0.741554 0.670893i \(-0.765911\pi\)
−0.741554 + 0.670893i \(0.765911\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −5.43072 + 5.30535i −0.320565 + 0.313165i
\(288\) 0 0
\(289\) −17.0149 + 29.4706i −1.00087 + 1.73357i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −7.42625 + 12.8626i −0.433846 + 0.751443i −0.997201 0.0747718i \(-0.976177\pi\)
0.563355 + 0.826215i \(0.309510\pi\)
\(294\) 0 0
\(295\) −12.7829 22.1407i −0.744250 1.28908i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 1.77747 0.102794
\(300\) 0 0
\(301\) 4.45389 + 17.4340i 0.256718 + 1.00488i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 12.6749 + 21.9536i 0.725763 + 1.25706i
\(306\) 0 0
\(307\) 21.9045 1.25016 0.625079 0.780561i \(-0.285067\pi\)
0.625079 + 0.780561i \(0.285067\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −17.5672 −0.996143 −0.498072 0.867136i \(-0.665958\pi\)
−0.498072 + 0.867136i \(0.665958\pi\)
\(312\) 0 0
\(313\) −11.9764 −0.676946 −0.338473 0.940976i \(-0.609910\pi\)
−0.338473 + 0.940976i \(0.609910\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.73327 0.0973499 0.0486750 0.998815i \(-0.484500\pi\)
0.0486750 + 0.998815i \(0.484500\pi\)
\(318\) 0 0
\(319\) 10.7590 0.602386
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 57.4275 3.19535
\(324\) 0 0
\(325\) 2.12311 + 3.67734i 0.117769 + 0.203982i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 30.9179 + 8.67263i 1.70456 + 0.478137i
\(330\) 0 0
\(331\) 0.726254 0.0399185 0.0199593 0.999801i \(-0.493646\pi\)
0.0199593 + 0.999801i \(0.493646\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 14.6620 + 25.3953i 0.801070 + 1.38749i
\(336\) 0 0
\(337\) −6.84810 + 11.8613i −0.373040 + 0.646124i −0.990032 0.140846i \(-0.955018\pi\)
0.616992 + 0.786970i \(0.288351\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 2.44980 4.24317i 0.132664 0.229781i
\(342\) 0 0
\(343\) −12.6291 13.5465i −0.681906 0.731440i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −4.21417 −0.226229 −0.113114 0.993582i \(-0.536083\pi\)
−0.113114 + 0.993582i \(0.536083\pi\)
\(348\) 0 0
\(349\) −10.8070 18.7183i −0.578486 1.00197i −0.995653 0.0931372i \(-0.970310\pi\)
0.417167 0.908830i \(-0.363023\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 2.42558 4.20122i 0.129100 0.223609i −0.794228 0.607620i \(-0.792124\pi\)
0.923328 + 0.384012i \(0.125458\pi\)
\(354\) 0 0
\(355\) 6.17609 + 10.6973i 0.327793 + 0.567754i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 2.90433 5.03045i 0.153285 0.265497i −0.779148 0.626839i \(-0.784348\pi\)
0.932433 + 0.361343i \(0.117682\pi\)
\(360\) 0 0
\(361\) −22.8137 39.5145i −1.20072 2.07971i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 5.36381 9.29038i 0.280754 0.486281i
\(366\) 0 0
\(367\) 10.8445 18.7832i 0.566078 0.980476i −0.430871 0.902414i \(-0.641793\pi\)
0.996949 0.0780619i \(-0.0248732\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −3.12595 12.2360i −0.162291 0.635261i
\(372\) 0 0
\(373\) −12.3552 21.3999i −0.639729 1.10804i −0.985492 0.169721i \(-0.945713\pi\)
0.345764 0.938322i \(-0.387620\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 5.40696 0.278473
\(378\) 0 0
\(379\) 27.9950 1.43801 0.719005 0.695005i \(-0.244598\pi\)
0.719005 + 0.695005i \(0.244598\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 10.3113 + 17.8598i 0.526884 + 0.912591i 0.999509 + 0.0313269i \(0.00997329\pi\)
−0.472625 + 0.881264i \(0.656693\pi\)
\(384\) 0 0
\(385\) 27.0810 + 7.59637i 1.38018 + 0.387147i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 8.70035 15.0694i 0.441125 0.764051i −0.556648 0.830748i \(-0.687913\pi\)
0.997773 + 0.0666973i \(0.0212462\pi\)
\(390\) 0 0
\(391\) −3.17107 + 5.49245i −0.160368 + 0.277765i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −1.37425 2.38026i −0.0691458 0.119764i
\(396\) 0 0
\(397\) 9.74152 16.8728i 0.488913 0.846822i −0.511006 0.859577i \(-0.670727\pi\)
0.999919 + 0.0127553i \(0.00406024\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 3.85264 + 6.67297i 0.192392 + 0.333232i 0.946042 0.324043i \(-0.105042\pi\)
−0.753651 + 0.657275i \(0.771709\pi\)
\(402\) 0 0
\(403\) 1.23116 2.13242i 0.0613282 0.106224i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −20.9757 36.3310i −1.03973 1.80086i
\(408\) 0 0
\(409\) −15.7351 −0.778050 −0.389025 0.921227i \(-0.627188\pi\)
−0.389025 + 0.921227i \(0.627188\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −24.4058 6.84596i −1.20093 0.336868i
\(414\) 0 0
\(415\) −14.0538 + 24.3420i −0.689876 + 1.19490i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −17.3452 + 30.0428i −0.847369 + 1.46769i 0.0361784 + 0.999345i \(0.488482\pi\)
−0.883548 + 0.468341i \(0.844852\pi\)
\(420\) 0 0
\(421\) −0.607053 1.05145i −0.0295860 0.0512444i 0.850853 0.525403i \(-0.176086\pi\)
−0.880439 + 0.474159i \(0.842752\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −15.1508 −0.734924
\(426\) 0 0
\(427\) 24.1996 + 6.78811i 1.17110 + 0.328500i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 1.68495 + 2.91841i 0.0811610 + 0.140575i 0.903749 0.428063i \(-0.140804\pi\)
−0.822588 + 0.568638i \(0.807471\pi\)
\(432\) 0 0
\(433\) −30.8651 −1.48328 −0.741640 0.670798i \(-0.765952\pi\)
−0.741640 + 0.670798i \(0.765952\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 7.13727 0.341422
\(438\) 0 0
\(439\) 33.0789 1.57877 0.789385 0.613898i \(-0.210400\pi\)
0.789385 + 0.613898i \(0.210400\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 2.73364 0.129879 0.0649397 0.997889i \(-0.479315\pi\)
0.0649397 + 0.997889i \(0.479315\pi\)
\(444\) 0 0
\(445\) 9.22172 0.437152
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −22.7472 −1.07351 −0.536753 0.843740i \(-0.680349\pi\)
−0.536753 + 0.843740i \(0.680349\pi\)
\(450\) 0 0
\(451\) −5.71579 9.90003i −0.269146 0.466174i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 13.6097 + 3.81759i 0.638032 + 0.178971i
\(456\) 0 0
\(457\) 3.36324 0.157326 0.0786628 0.996901i \(-0.474935\pi\)
0.0786628 + 0.996901i \(0.474935\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 10.0040 + 17.3275i 0.465934 + 0.807021i 0.999243 0.0388994i \(-0.0123852\pi\)
−0.533309 + 0.845920i \(0.679052\pi\)
\(462\) 0 0
\(463\) −7.29434 + 12.6342i −0.338997 + 0.587160i −0.984244 0.176814i \(-0.943421\pi\)
0.645247 + 0.763974i \(0.276754\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 7.26334 12.5805i 0.336107 0.582155i −0.647590 0.761989i \(-0.724223\pi\)
0.983697 + 0.179834i \(0.0575562\pi\)
\(468\) 0 0
\(469\) 27.9935 + 7.85231i 1.29262 + 0.362586i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −27.0939 −1.24578
\(474\) 0 0
\(475\) 8.52518 + 14.7660i 0.391162 + 0.677513i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 5.66216 9.80714i 0.258710 0.448100i −0.707186 0.707027i \(-0.750036\pi\)
0.965897 + 0.258928i \(0.0833691\pi\)
\(480\) 0 0
\(481\) −10.5414 18.2583i −0.480648 0.832506i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −2.99036 + 5.17946i −0.135785 + 0.235187i
\(486\) 0 0
\(487\) −5.93684 10.2829i −0.269024 0.465963i 0.699586 0.714548i \(-0.253368\pi\)
−0.968610 + 0.248585i \(0.920034\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 11.9598 20.7150i 0.539738 0.934853i −0.459180 0.888343i \(-0.651857\pi\)
0.998918 0.0465101i \(-0.0148100\pi\)
\(492\) 0 0
\(493\) −9.64621 + 16.7077i −0.434443 + 0.752478i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 11.7917 + 3.30764i 0.528932 + 0.148368i
\(498\) 0 0
\(499\) −0.225984 0.391416i −0.0101164 0.0175222i 0.860923 0.508736i \(-0.169887\pi\)
−0.871039 + 0.491213i \(0.836554\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −14.6077 −0.651326 −0.325663 0.945486i \(-0.605587\pi\)
−0.325663 + 0.945486i \(0.605587\pi\)
\(504\) 0 0
\(505\) 12.1905 0.542471
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −0.246585 0.427099i −0.0109297 0.0189308i 0.860509 0.509436i \(-0.170146\pi\)
−0.871439 + 0.490505i \(0.836812\pi\)
\(510\) 0 0
\(511\) −2.63268 10.3052i −0.116463 0.455874i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −17.0120 + 29.4656i −0.749636 + 1.29841i
\(516\) 0 0
\(517\) −24.1754 + 41.8730i −1.06323 + 1.84157i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 6.06874 + 10.5114i 0.265876 + 0.460511i 0.967793 0.251748i \(-0.0810054\pi\)
−0.701917 + 0.712259i \(0.747672\pi\)
\(522\) 0 0
\(523\) −1.34058 + 2.32195i −0.0586193 + 0.101532i −0.893846 0.448374i \(-0.852003\pi\)
0.835227 + 0.549906i \(0.185336\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 4.39285 + 7.60865i 0.191356 + 0.331438i
\(528\) 0 0
\(529\) 11.1059 19.2360i 0.482865 0.836346i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −2.87249 4.97530i −0.124421 0.215504i
\(534\) 0 0
\(535\) 3.52115 0.152233
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 24.4694 13.3754i 1.05397 0.576121i
\(540\) 0 0
\(541\) −13.5072 + 23.3951i −0.580719 + 1.00583i 0.414676 + 0.909969i \(0.363895\pi\)
−0.995394 + 0.0958650i \(0.969438\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −16.8647 + 29.2105i −0.722404 + 1.25124i
\(546\) 0 0
\(547\) 15.2496 + 26.4132i 0.652028 + 1.12935i 0.982630 + 0.185575i \(0.0594149\pi\)
−0.330602 + 0.943770i \(0.607252\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 21.7112 0.924927
\(552\) 0 0
\(553\) −2.62379 0.735985i −0.111575 0.0312973i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 7.39250 + 12.8042i 0.313230 + 0.542531i 0.979060 0.203573i \(-0.0652555\pi\)
−0.665829 + 0.746104i \(0.731922\pi\)
\(558\) 0 0
\(559\) −13.6162 −0.575902
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 2.62822 0.110766 0.0553831 0.998465i \(-0.482362\pi\)
0.0553831 + 0.998465i \(0.482362\pi\)
\(564\) 0 0
\(565\) −2.68559 −0.112983
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 32.1162 1.34638 0.673191 0.739469i \(-0.264923\pi\)
0.673191 + 0.739469i \(0.264923\pi\)
\(570\) 0 0
\(571\) −41.1815 −1.72339 −0.861696 0.507425i \(-0.830597\pi\)
−0.861696 + 0.507425i \(0.830597\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −1.88300 −0.0785263
\(576\) 0 0
\(577\) 12.0735 + 20.9119i 0.502625 + 0.870573i 0.999995 + 0.00303429i \(0.000965847\pi\)
−0.497370 + 0.867539i \(0.665701\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 6.89795 + 27.0008i 0.286175 + 1.12018i
\(582\) 0 0
\(583\) 19.0158 0.787553
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −3.98618 6.90426i −0.164527 0.284969i 0.771960 0.635671i \(-0.219277\pi\)
−0.936487 + 0.350702i \(0.885943\pi\)
\(588\) 0 0
\(589\) 4.94360 8.56257i 0.203698 0.352815i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 2.10338 3.64316i 0.0863753 0.149606i −0.819601 0.572935i \(-0.805805\pi\)
0.905976 + 0.423328i \(0.139138\pi\)
\(594\) 0 0
\(595\) −36.0767 + 35.2438i −1.47900 + 1.44485i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −37.3771 −1.52719 −0.763594 0.645696i \(-0.776567\pi\)
−0.763594 + 0.645696i \(0.776567\pi\)
\(600\) 0 0
\(601\) 6.81596 + 11.8056i 0.278029 + 0.481560i 0.970895 0.239506i \(-0.0769856\pi\)
−0.692866 + 0.721066i \(0.743652\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −6.49846 + 11.2557i −0.264200 + 0.457607i
\(606\) 0 0
\(607\) 1.37114 + 2.37489i 0.0556529 + 0.0963937i 0.892510 0.451028i \(-0.148943\pi\)
−0.836857 + 0.547422i \(0.815609\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −12.1494 + 21.0434i −0.491513 + 0.851326i
\(612\) 0 0
\(613\) 0.798502 + 1.38305i 0.0322512 + 0.0558607i 0.881700 0.471810i \(-0.156399\pi\)
−0.849449 + 0.527670i \(0.823066\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −12.6551 + 21.9192i −0.509473 + 0.882433i 0.490467 + 0.871460i \(0.336826\pi\)
−0.999940 + 0.0109734i \(0.996507\pi\)
\(618\) 0 0
\(619\) −13.5808 + 23.5226i −0.545859 + 0.945455i 0.452694 + 0.891666i \(0.350463\pi\)
−0.998552 + 0.0537888i \(0.982870\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 6.54019 6.38920i 0.262027 0.255978i
\(624\) 0 0
\(625\) 15.5532 + 26.9388i 0.622126 + 1.07755i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 75.2252 2.99942
\(630\) 0 0
\(631\) 29.6597 1.18073 0.590366 0.807136i \(-0.298983\pi\)
0.590366 + 0.807136i \(0.298983\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 1.84661 + 3.19842i 0.0732804 + 0.126925i
\(636\) 0 0
\(637\) 12.2972 6.72188i 0.487233 0.266331i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 21.0987 36.5441i 0.833350 1.44340i −0.0620175 0.998075i \(-0.519753\pi\)
0.895367 0.445329i \(-0.146913\pi\)
\(642\) 0 0
\(643\) −10.1099 + 17.5109i −0.398696 + 0.690562i −0.993565 0.113260i \(-0.963871\pi\)
0.594869 + 0.803823i \(0.297204\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1.08988 1.88772i −0.0428475 0.0742141i 0.843806 0.536648i \(-0.180310\pi\)
−0.886654 + 0.462434i \(0.846976\pi\)
\(648\) 0 0
\(649\) 19.0834 33.0535i 0.749091 1.29746i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −17.0535 29.5375i −0.667354 1.15589i −0.978641 0.205575i \(-0.934094\pi\)
0.311288 0.950316i \(-0.399240\pi\)
\(654\) 0 0
\(655\) 0.439936 0.761991i 0.0171897 0.0297734i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −0.994211 1.72202i −0.0387290 0.0670805i 0.846011 0.533165i \(-0.178998\pi\)
−0.884740 + 0.466085i \(0.845664\pi\)
\(660\) 0 0
\(661\) −8.48409 −0.329993 −0.164997 0.986294i \(-0.552761\pi\)
−0.164997 + 0.986294i \(0.552761\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 54.6486 + 15.3292i 2.11918 + 0.594440i
\(666\) 0 0
\(667\) −1.19886 + 2.07649i −0.0464201 + 0.0804020i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −18.9222 + 32.7742i −0.730483 + 1.26523i
\(672\) 0 0
\(673\) 22.4056 + 38.8077i 0.863674 + 1.49593i 0.868358 + 0.495938i \(0.165176\pi\)
−0.00468438 + 0.999989i \(0.501491\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −8.05367 −0.309528 −0.154764 0.987951i \(-0.549462\pi\)
−0.154764 + 0.987951i \(0.549462\pi\)
\(678\) 0 0
\(679\) 1.46774 + 5.74521i 0.0563267 + 0.220481i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 20.8446 + 36.1039i 0.797597 + 1.38148i 0.921177 + 0.389144i \(0.127229\pi\)
−0.123580 + 0.992335i \(0.539438\pi\)
\(684\) 0 0
\(685\) −23.8615 −0.911701
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 9.55646 0.364072
\(690\) 0 0
\(691\) −11.3269 −0.430895 −0.215448 0.976515i \(-0.569121\pi\)
−0.215448 + 0.976515i \(0.569121\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 20.9675 0.795342
\(696\) 0 0
\(697\) 20.4985 0.776437
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 22.6560 0.855705 0.427853 0.903849i \(-0.359270\pi\)
0.427853 + 0.903849i \(0.359270\pi\)
\(702\) 0 0
\(703\) −42.3282 73.3146i −1.59644 2.76511i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 8.64572 8.44612i 0.325156 0.317649i
\(708\) 0 0
\(709\) 45.2147 1.69807 0.849037 0.528333i \(-0.177183\pi\)
0.849037 + 0.528333i \(0.177183\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0.545958 + 0.945626i 0.0204463 + 0.0354140i
\(714\) 0 0
\(715\) −10.6417 + 18.4320i −0.397977 + 0.689317i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 11.3171 19.6018i 0.422057 0.731024i −0.574084 0.818797i \(-0.694642\pi\)
0.996141 + 0.0877727i \(0.0279749\pi\)
\(720\) 0 0
\(721\) 8.34986 + 32.6841i 0.310965 + 1.21722i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −5.72797 −0.212731
\(726\) 0 0
\(727\) −1.04956 1.81789i −0.0389259 0.0674217i 0.845906 0.533332i \(-0.179060\pi\)
−0.884832 + 0.465910i \(0.845727\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 24.2917 42.0745i 0.898461 1.55618i
\(732\) 0 0
\(733\) 15.6453 + 27.0985i 0.577872 + 1.00090i 0.995723 + 0.0923886i \(0.0294502\pi\)
−0.417851 + 0.908516i \(0.637216\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −21.8887 + 37.9123i −0.806280 + 1.39652i
\(738\) 0 0
\(739\) −21.1229 36.5859i −0.777017 1.34583i −0.933654 0.358177i \(-0.883399\pi\)
0.156637 0.987656i \(-0.449935\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 6.48482 11.2320i 0.237905 0.412064i −0.722208 0.691676i \(-0.756873\pi\)
0.960113 + 0.279612i \(0.0902060\pi\)
\(744\) 0 0
\(745\) 21.7770 37.7189i 0.797848 1.38191i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 2.49726 2.43960i 0.0912478 0.0891412i
\(750\) 0 0
\(751\) 16.3649 + 28.3448i 0.597164 + 1.03432i 0.993238 + 0.116099i \(0.0370391\pi\)
−0.396074 + 0.918219i \(0.629628\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 12.3646 0.449995
\(756\) 0 0
\(757\) 31.6305 1.14963 0.574815 0.818283i \(-0.305074\pi\)
0.574815 + 0.818283i \(0.305074\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −19.1468 33.1632i −0.694070 1.20217i −0.970493 0.241129i \(-0.922482\pi\)
0.276423 0.961036i \(-0.410851\pi\)
\(762\) 0 0
\(763\) 8.27758 + 32.4011i 0.299668 + 1.17300i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 9.59047 16.6112i 0.346292 0.599795i
\(768\) 0 0
\(769\) 11.0674 19.1693i 0.399100 0.691262i −0.594515 0.804085i \(-0.702656\pi\)
0.993615 + 0.112823i \(0.0359892\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −25.8165 44.7155i −0.928555 1.60830i −0.785742 0.618555i \(-0.787719\pi\)
−0.142813 0.989750i \(-0.545615\pi\)
\(774\) 0 0
\(775\) −1.30425 + 2.25902i −0.0468500 + 0.0811466i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −11.5342 19.9779i −0.413257 0.715783i
\(780\) 0 0
\(781\) −9.22021 + 15.9699i −0.329925 + 0.571447i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 11.3659 + 19.6862i 0.405665 + 0.702632i
\(786\) 0 0
\(787\) 32.3046 1.15153 0.575767 0.817614i \(-0.304704\pi\)
0.575767 + 0.817614i \(0.304704\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −1.90466 + 1.86069i −0.0677219 + 0.0661585i
\(792\) 0 0
\(793\) −9.50943 + 16.4708i −0.337690 + 0.584896i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 11.6877 20.2438i 0.414001 0.717071i −0.581322 0.813674i \(-0.697464\pi\)
0.995323 + 0.0966026i \(0.0307976\pi\)