Properties

Label 672.2.h.d.575.3
Level 672
Weight 2
Character 672.575
Analytic conductor 5.366
Analytic rank 0
Dimension 4
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 672.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.36594701583\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{8})\)
Defining polynomial: \(x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 575.3
Root \(0.707107 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 672.575
Dual form 672.2.h.d.575.4

$q$-expansion

\(f(q)\) \(=\) \(q+(1.70711 - 0.292893i) q^{3} -0.585786i q^{5} -1.00000i q^{7} +(2.82843 - 1.00000i) q^{9} +O(q^{10})\) \(q+(1.70711 - 0.292893i) q^{3} -0.585786i q^{5} -1.00000i q^{7} +(2.82843 - 1.00000i) q^{9} +2.00000 q^{11} +0.585786 q^{13} +(-0.171573 - 1.00000i) q^{15} +0.828427i q^{17} -2.24264i q^{19} +(-0.292893 - 1.70711i) q^{21} -4.00000 q^{23} +4.65685 q^{25} +(4.53553 - 2.53553i) q^{27} +0.828427i q^{29} -6.82843i q^{31} +(3.41421 - 0.585786i) q^{33} -0.585786 q^{35} +4.82843 q^{37} +(1.00000 - 0.171573i) q^{39} +10.0000i q^{41} -6.48528i q^{43} +(-0.585786 - 1.65685i) q^{45} -9.65685 q^{47} -1.00000 q^{49} +(0.242641 + 1.41421i) q^{51} +9.31371i q^{53} -1.17157i q^{55} +(-0.656854 - 3.82843i) q^{57} +2.24264 q^{59} +5.75736 q^{61} +(-1.00000 - 2.82843i) q^{63} -0.343146i q^{65} +13.3137i q^{67} +(-6.82843 + 1.17157i) q^{69} -11.6569 q^{71} -8.82843 q^{73} +(7.94975 - 1.36396i) q^{75} -2.00000i q^{77} -4.00000i q^{79} +(7.00000 - 5.65685i) q^{81} +8.58579 q^{83} +0.485281 q^{85} +(0.242641 + 1.41421i) q^{87} +3.65685i q^{89} -0.585786i q^{91} +(-2.00000 - 11.6569i) q^{93} -1.31371 q^{95} -17.3137 q^{97} +(5.65685 - 2.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{3} + O(q^{10}) \) \( 4q + 4q^{3} + 8q^{11} + 8q^{13} - 12q^{15} - 4q^{21} - 16q^{23} - 4q^{25} + 4q^{27} + 8q^{33} - 8q^{35} + 8q^{37} + 4q^{39} - 8q^{45} - 16q^{47} - 4q^{49} - 16q^{51} + 20q^{57} - 8q^{59} + 40q^{61} - 4q^{63} - 16q^{69} - 24q^{71} - 24q^{73} + 12q^{75} + 28q^{81} + 40q^{83} - 32q^{85} - 16q^{87} - 8q^{93} + 40q^{95} - 24q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/672\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(421\) \(449\) \(577\)
\(\chi(n)\) \(-1\) \(1\) \(-1\) \(1\)

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
\(3\) 1.70711 0.292893i 0.985599 0.169102i
\(4\) 0 0
\(5\) 0.585786i 0.261972i −0.991384 0.130986i \(-0.958186\pi\)
0.991384 0.130986i \(-0.0418142\pi\)
\(6\) 0 0
\(7\) 1.00000i 0.377964i
\(8\) 0 0
\(9\) 2.82843 1.00000i 0.942809 0.333333i
\(10\) 0 0
\(11\) 2.00000 0.603023 0.301511 0.953463i \(-0.402509\pi\)
0.301511 + 0.953463i \(0.402509\pi\)
\(12\) 0 0
\(13\) 0.585786 0.162468 0.0812340 0.996695i \(-0.474114\pi\)
0.0812340 + 0.996695i \(0.474114\pi\)
\(14\) 0 0
\(15\) −0.171573 1.00000i −0.0442999 0.258199i
\(16\) 0 0
\(17\) 0.828427i 0.200923i 0.994941 + 0.100462i \(0.0320319\pi\)
−0.994941 + 0.100462i \(0.967968\pi\)
\(18\) 0 0
\(19\) 2.24264i 0.514497i −0.966345 0.257249i \(-0.917184\pi\)
0.966345 0.257249i \(-0.0828159\pi\)
\(20\) 0 0
\(21\) −0.292893 1.70711i −0.0639145 0.372521i
\(22\) 0 0
\(23\) −4.00000 −0.834058 −0.417029 0.908893i \(-0.636929\pi\)
−0.417029 + 0.908893i \(0.636929\pi\)
\(24\) 0 0
\(25\) 4.65685 0.931371
\(26\) 0 0
\(27\) 4.53553 2.53553i 0.872864 0.487964i
\(28\) 0 0
\(29\) 0.828427i 0.153835i 0.997037 + 0.0769175i \(0.0245078\pi\)
−0.997037 + 0.0769175i \(0.975492\pi\)
\(30\) 0 0
\(31\) 6.82843i 1.22642i −0.789919 0.613211i \(-0.789878\pi\)
0.789919 0.613211i \(-0.210122\pi\)
\(32\) 0 0
\(33\) 3.41421 0.585786i 0.594338 0.101972i
\(34\) 0 0
\(35\) −0.585786 −0.0990160
\(36\) 0 0
\(37\) 4.82843 0.793789 0.396894 0.917864i \(-0.370088\pi\)
0.396894 + 0.917864i \(0.370088\pi\)
\(38\) 0 0
\(39\) 1.00000 0.171573i 0.160128 0.0274736i
\(40\) 0 0
\(41\) 10.0000i 1.56174i 0.624695 + 0.780869i \(0.285223\pi\)
−0.624695 + 0.780869i \(0.714777\pi\)
\(42\) 0 0
\(43\) 6.48528i 0.988996i −0.869179 0.494498i \(-0.835352\pi\)
0.869179 0.494498i \(-0.164648\pi\)
\(44\) 0 0
\(45\) −0.585786 1.65685i −0.0873239 0.246989i
\(46\) 0 0
\(47\) −9.65685 −1.40860 −0.704298 0.709904i \(-0.748738\pi\)
−0.704298 + 0.709904i \(0.748738\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) 0 0
\(51\) 0.242641 + 1.41421i 0.0339765 + 0.198030i
\(52\) 0 0
\(53\) 9.31371i 1.27934i 0.768651 + 0.639668i \(0.220928\pi\)
−0.768651 + 0.639668i \(0.779072\pi\)
\(54\) 0 0
\(55\) 1.17157i 0.157975i
\(56\) 0 0
\(57\) −0.656854 3.82843i −0.0870025 0.507088i
\(58\) 0 0
\(59\) 2.24264 0.291967 0.145983 0.989287i \(-0.453365\pi\)
0.145983 + 0.989287i \(0.453365\pi\)
\(60\) 0 0
\(61\) 5.75736 0.737154 0.368577 0.929597i \(-0.379845\pi\)
0.368577 + 0.929597i \(0.379845\pi\)
\(62\) 0 0
\(63\) −1.00000 2.82843i −0.125988 0.356348i
\(64\) 0 0
\(65\) 0.343146i 0.0425620i
\(66\) 0 0
\(67\) 13.3137i 1.62653i 0.581895 + 0.813264i \(0.302312\pi\)
−0.581895 + 0.813264i \(0.697688\pi\)
\(68\) 0 0
\(69\) −6.82843 + 1.17157i −0.822046 + 0.141041i
\(70\) 0 0
\(71\) −11.6569 −1.38341 −0.691707 0.722178i \(-0.743141\pi\)
−0.691707 + 0.722178i \(0.743141\pi\)
\(72\) 0 0
\(73\) −8.82843 −1.03329 −0.516645 0.856200i \(-0.672819\pi\)
−0.516645 + 0.856200i \(0.672819\pi\)
\(74\) 0 0
\(75\) 7.94975 1.36396i 0.917958 0.157497i
\(76\) 0 0
\(77\) 2.00000i 0.227921i
\(78\) 0 0
\(79\) 4.00000i 0.450035i −0.974355 0.225018i \(-0.927756\pi\)
0.974355 0.225018i \(-0.0722440\pi\)
\(80\) 0 0
\(81\) 7.00000 5.65685i 0.777778 0.628539i
\(82\) 0 0
\(83\) 8.58579 0.942412 0.471206 0.882023i \(-0.343819\pi\)
0.471206 + 0.882023i \(0.343819\pi\)
\(84\) 0 0
\(85\) 0.485281 0.0526362
\(86\) 0 0
\(87\) 0.242641 + 1.41421i 0.0260138 + 0.151620i
\(88\) 0 0
\(89\) 3.65685i 0.387626i 0.981039 + 0.193813i \(0.0620855\pi\)
−0.981039 + 0.193813i \(0.937915\pi\)
\(90\) 0 0
\(91\) 0.585786i 0.0614071i
\(92\) 0 0
\(93\) −2.00000 11.6569i −0.207390 1.20876i
\(94\) 0 0
\(95\) −1.31371 −0.134784
\(96\) 0 0
\(97\) −17.3137 −1.75794 −0.878970 0.476876i \(-0.841769\pi\)
−0.878970 + 0.476876i \(0.841769\pi\)
\(98\) 0 0
\(99\) 5.65685 2.00000i 0.568535 0.201008i
\(100\) 0 0
\(101\) 9.75736i 0.970894i 0.874266 + 0.485447i \(0.161343\pi\)
−0.874266 + 0.485447i \(0.838657\pi\)
\(102\) 0 0
\(103\) 16.9706i 1.67216i 0.548608 + 0.836080i \(0.315158\pi\)
−0.548608 + 0.836080i \(0.684842\pi\)
\(104\) 0 0
\(105\) −1.00000 + 0.171573i −0.0975900 + 0.0167438i
\(106\) 0 0
\(107\) −2.48528 −0.240261 −0.120131 0.992758i \(-0.538331\pi\)
−0.120131 + 0.992758i \(0.538331\pi\)
\(108\) 0 0
\(109\) 14.4853 1.38744 0.693719 0.720246i \(-0.255971\pi\)
0.693719 + 0.720246i \(0.255971\pi\)
\(110\) 0 0
\(111\) 8.24264 1.41421i 0.782357 0.134231i
\(112\) 0 0
\(113\) 17.3137i 1.62874i −0.580348 0.814368i \(-0.697084\pi\)
0.580348 0.814368i \(-0.302916\pi\)
\(114\) 0 0
\(115\) 2.34315i 0.218499i
\(116\) 0 0
\(117\) 1.65685 0.585786i 0.153176 0.0541560i
\(118\) 0 0
\(119\) 0.828427 0.0759418
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) 0 0
\(123\) 2.92893 + 17.0711i 0.264093 + 1.53925i
\(124\) 0 0
\(125\) 5.65685i 0.505964i
\(126\) 0 0
\(127\) 2.00000i 0.177471i 0.996055 + 0.0887357i \(0.0282826\pi\)
−0.996055 + 0.0887357i \(0.971717\pi\)
\(128\) 0 0
\(129\) −1.89949 11.0711i −0.167241 0.974753i
\(130\) 0 0
\(131\) −9.55635 −0.834942 −0.417471 0.908690i \(-0.637083\pi\)
−0.417471 + 0.908690i \(0.637083\pi\)
\(132\) 0 0
\(133\) −2.24264 −0.194462
\(134\) 0 0
\(135\) −1.48528 2.65685i −0.127833 0.228666i
\(136\) 0 0
\(137\) 11.3137i 0.966595i 0.875456 + 0.483298i \(0.160561\pi\)
−0.875456 + 0.483298i \(0.839439\pi\)
\(138\) 0 0
\(139\) 10.2426i 0.868769i −0.900727 0.434385i \(-0.856966\pi\)
0.900727 0.434385i \(-0.143034\pi\)
\(140\) 0 0
\(141\) −16.4853 + 2.82843i −1.38831 + 0.238197i
\(142\) 0 0
\(143\) 1.17157 0.0979718
\(144\) 0 0
\(145\) 0.485281 0.0403004
\(146\) 0 0
\(147\) −1.70711 + 0.292893i −0.140800 + 0.0241574i
\(148\) 0 0
\(149\) 3.65685i 0.299581i 0.988718 + 0.149791i \(0.0478599\pi\)
−0.988718 + 0.149791i \(0.952140\pi\)
\(150\) 0 0
\(151\) 18.0000i 1.46482i 0.680864 + 0.732410i \(0.261604\pi\)
−0.680864 + 0.732410i \(0.738396\pi\)
\(152\) 0 0
\(153\) 0.828427 + 2.34315i 0.0669744 + 0.189432i
\(154\) 0 0
\(155\) −4.00000 −0.321288
\(156\) 0 0
\(157\) −6.24264 −0.498217 −0.249108 0.968476i \(-0.580138\pi\)
−0.249108 + 0.968476i \(0.580138\pi\)
\(158\) 0 0
\(159\) 2.72792 + 15.8995i 0.216338 + 1.26091i
\(160\) 0 0
\(161\) 4.00000i 0.315244i
\(162\) 0 0
\(163\) 20.1421i 1.57765i 0.614615 + 0.788827i \(0.289311\pi\)
−0.614615 + 0.788827i \(0.710689\pi\)
\(164\) 0 0
\(165\) −0.343146 2.00000i −0.0267139 0.155700i
\(166\) 0 0
\(167\) −5.17157 −0.400188 −0.200094 0.979777i \(-0.564125\pi\)
−0.200094 + 0.979777i \(0.564125\pi\)
\(168\) 0 0
\(169\) −12.6569 −0.973604
\(170\) 0 0
\(171\) −2.24264 6.34315i −0.171499 0.485072i
\(172\) 0 0
\(173\) 21.5563i 1.63890i −0.573151 0.819449i \(-0.694279\pi\)
0.573151 0.819449i \(-0.305721\pi\)
\(174\) 0 0
\(175\) 4.65685i 0.352025i
\(176\) 0 0
\(177\) 3.82843 0.656854i 0.287762 0.0493722i
\(178\) 0 0
\(179\) −10.4853 −0.783707 −0.391853 0.920028i \(-0.628166\pi\)
−0.391853 + 0.920028i \(0.628166\pi\)
\(180\) 0 0
\(181\) −16.3848 −1.21787 −0.608935 0.793220i \(-0.708403\pi\)
−0.608935 + 0.793220i \(0.708403\pi\)
\(182\) 0 0
\(183\) 9.82843 1.68629i 0.726538 0.124654i
\(184\) 0 0
\(185\) 2.82843i 0.207950i
\(186\) 0 0
\(187\) 1.65685i 0.121161i
\(188\) 0 0
\(189\) −2.53553 4.53553i −0.184433 0.329912i
\(190\) 0 0
\(191\) 7.65685 0.554031 0.277015 0.960866i \(-0.410655\pi\)
0.277015 + 0.960866i \(0.410655\pi\)
\(192\) 0 0
\(193\) 6.34315 0.456590 0.228295 0.973592i \(-0.426685\pi\)
0.228295 + 0.973592i \(0.426685\pi\)
\(194\) 0 0
\(195\) −0.100505 0.585786i −0.00719732 0.0419490i
\(196\) 0 0
\(197\) 26.0000i 1.85242i 0.377004 + 0.926212i \(0.376954\pi\)
−0.377004 + 0.926212i \(0.623046\pi\)
\(198\) 0 0
\(199\) 15.3137i 1.08556i −0.839875 0.542780i \(-0.817372\pi\)
0.839875 0.542780i \(-0.182628\pi\)
\(200\) 0 0
\(201\) 3.89949 + 22.7279i 0.275049 + 1.60310i
\(202\) 0 0
\(203\) 0.828427 0.0581442
\(204\) 0 0
\(205\) 5.85786 0.409131
\(206\) 0 0
\(207\) −11.3137 + 4.00000i −0.786357 + 0.278019i
\(208\) 0 0
\(209\) 4.48528i 0.310253i
\(210\) 0 0
\(211\) 11.6569i 0.802491i −0.915971 0.401245i \(-0.868577\pi\)
0.915971 0.401245i \(-0.131423\pi\)
\(212\) 0 0
\(213\) −19.8995 + 3.41421i −1.36349 + 0.233938i
\(214\) 0 0
\(215\) −3.79899 −0.259089
\(216\) 0 0
\(217\) −6.82843 −0.463544
\(218\) 0 0
\(219\) −15.0711 + 2.58579i −1.01841 + 0.174731i
\(220\) 0 0
\(221\) 0.485281i 0.0326436i
\(222\) 0 0
\(223\) 2.82843i 0.189405i −0.995506 0.0947027i \(-0.969810\pi\)
0.995506 0.0947027i \(-0.0301901\pi\)
\(224\) 0 0
\(225\) 13.1716 4.65685i 0.878105 0.310457i
\(226\) 0 0
\(227\) −4.10051 −0.272160 −0.136080 0.990698i \(-0.543450\pi\)
−0.136080 + 0.990698i \(0.543450\pi\)
\(228\) 0 0
\(229\) 13.0711 0.863760 0.431880 0.901931i \(-0.357850\pi\)
0.431880 + 0.901931i \(0.357850\pi\)
\(230\) 0 0
\(231\) −0.585786 3.41421i −0.0385419 0.224639i
\(232\) 0 0
\(233\) 24.9706i 1.63588i 0.575306 + 0.817938i \(0.304883\pi\)
−0.575306 + 0.817938i \(0.695117\pi\)
\(234\) 0 0
\(235\) 5.65685i 0.369012i
\(236\) 0 0
\(237\) −1.17157 6.82843i −0.0761018 0.443554i
\(238\) 0 0
\(239\) 11.3137 0.731823 0.365911 0.930650i \(-0.380757\pi\)
0.365911 + 0.930650i \(0.380757\pi\)
\(240\) 0 0
\(241\) −7.65685 −0.493221 −0.246611 0.969115i \(-0.579317\pi\)
−0.246611 + 0.969115i \(0.579317\pi\)
\(242\) 0 0
\(243\) 10.2929 11.7071i 0.660289 0.751011i
\(244\) 0 0
\(245\) 0.585786i 0.0374245i
\(246\) 0 0
\(247\) 1.31371i 0.0835893i
\(248\) 0 0
\(249\) 14.6569 2.51472i 0.928840 0.159364i
\(250\) 0 0
\(251\) −23.4142 −1.47789 −0.738946 0.673765i \(-0.764676\pi\)
−0.738946 + 0.673765i \(0.764676\pi\)
\(252\) 0 0
\(253\) −8.00000 −0.502956
\(254\) 0 0
\(255\) 0.828427 0.142136i 0.0518781 0.00890088i
\(256\) 0 0
\(257\) 2.48528i 0.155028i −0.996991 0.0775138i \(-0.975302\pi\)
0.996991 0.0775138i \(-0.0246982\pi\)
\(258\) 0 0
\(259\) 4.82843i 0.300024i
\(260\) 0 0
\(261\) 0.828427 + 2.34315i 0.0512784 + 0.145037i
\(262\) 0 0
\(263\) 21.3137 1.31426 0.657130 0.753777i \(-0.271770\pi\)
0.657130 + 0.753777i \(0.271770\pi\)
\(264\) 0 0
\(265\) 5.45584 0.335150
\(266\) 0 0
\(267\) 1.07107 + 6.24264i 0.0655483 + 0.382043i
\(268\) 0 0
\(269\) 6.72792i 0.410209i 0.978740 + 0.205104i \(0.0657534\pi\)
−0.978740 + 0.205104i \(0.934247\pi\)
\(270\) 0 0
\(271\) 4.48528i 0.272461i 0.990677 + 0.136231i \(0.0434988\pi\)
−0.990677 + 0.136231i \(0.956501\pi\)
\(272\) 0 0
\(273\) −0.171573 1.00000i −0.0103841 0.0605228i
\(274\) 0 0
\(275\) 9.31371 0.561638
\(276\) 0 0
\(277\) 21.3137 1.28062 0.640308 0.768118i \(-0.278807\pi\)
0.640308 + 0.768118i \(0.278807\pi\)
\(278\) 0 0
\(279\) −6.82843 19.3137i −0.408807 1.15628i
\(280\) 0 0
\(281\) 24.9706i 1.48962i −0.667277 0.744809i \(-0.732540\pi\)
0.667277 0.744809i \(-0.267460\pi\)
\(282\) 0 0
\(283\) 1.75736i 0.104464i −0.998635 0.0522321i \(-0.983366\pi\)
0.998635 0.0522321i \(-0.0166336\pi\)
\(284\) 0 0
\(285\) −2.24264 + 0.384776i −0.132843 + 0.0227922i
\(286\) 0 0
\(287\) 10.0000 0.590281
\(288\) 0 0
\(289\) 16.3137 0.959630
\(290\) 0 0
\(291\) −29.5563 + 5.07107i −1.73262 + 0.297271i
\(292\) 0 0
\(293\) 26.7279i 1.56146i −0.624867 0.780731i \(-0.714847\pi\)
0.624867 0.780731i \(-0.285153\pi\)
\(294\) 0 0
\(295\) 1.31371i 0.0764871i
\(296\) 0 0
\(297\) 9.07107 5.07107i 0.526357 0.294253i
\(298\) 0 0
\(299\) −2.34315 −0.135508
\(300\) 0 0
\(301\) −6.48528 −0.373805
\(302\) 0 0
\(303\) 2.85786 + 16.6569i 0.164180 + 0.956911i
\(304\) 0 0
\(305\) 3.37258i 0.193114i
\(306\) 0 0
\(307\) 21.5563i 1.23029i −0.788416 0.615143i \(-0.789098\pi\)
0.788416 0.615143i \(-0.210902\pi\)
\(308\) 0 0
\(309\) 4.97056 + 28.9706i 0.282765 + 1.64808i
\(310\) 0 0
\(311\) 19.7990 1.12270 0.561349 0.827579i \(-0.310283\pi\)
0.561349 + 0.827579i \(0.310283\pi\)
\(312\) 0 0
\(313\) −3.17157 −0.179268 −0.0896339 0.995975i \(-0.528570\pi\)
−0.0896339 + 0.995975i \(0.528570\pi\)
\(314\) 0 0
\(315\) −1.65685 + 0.585786i −0.0933532 + 0.0330053i
\(316\) 0 0
\(317\) 10.0000i 0.561656i −0.959758 0.280828i \(-0.909391\pi\)
0.959758 0.280828i \(-0.0906090\pi\)
\(318\) 0 0
\(319\) 1.65685i 0.0927660i
\(320\) 0 0
\(321\) −4.24264 + 0.727922i −0.236801 + 0.0406286i
\(322\) 0 0
\(323\) 1.85786 0.103374
\(324\) 0 0
\(325\) 2.72792 0.151318
\(326\) 0 0
\(327\) 24.7279 4.24264i 1.36746 0.234619i
\(328\) 0 0
\(329\) 9.65685i 0.532400i
\(330\) 0 0
\(331\) 0.828427i 0.0455345i 0.999741 + 0.0227672i \(0.00724766\pi\)
−0.999741 + 0.0227672i \(0.992752\pi\)
\(332\) 0 0
\(333\) 13.6569 4.82843i 0.748391 0.264596i
\(334\) 0 0
\(335\) 7.79899 0.426104
\(336\) 0 0
\(337\) 4.68629 0.255279 0.127639 0.991821i \(-0.459260\pi\)
0.127639 + 0.991821i \(0.459260\pi\)
\(338\) 0 0
\(339\) −5.07107 29.5563i −0.275423 1.60528i
\(340\) 0 0
\(341\) 13.6569i 0.739560i
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) 0 0
\(345\) 0.686292 + 4.00000i 0.0369487 + 0.215353i
\(346\) 0 0
\(347\) 11.6569 0.625773 0.312886 0.949791i \(-0.398704\pi\)
0.312886 + 0.949791i \(0.398704\pi\)
\(348\) 0 0
\(349\) 29.0711 1.55614 0.778069 0.628178i \(-0.216199\pi\)
0.778069 + 0.628178i \(0.216199\pi\)
\(350\) 0 0
\(351\) 2.65685 1.48528i 0.141812 0.0792785i
\(352\) 0 0
\(353\) 31.4558i 1.67423i −0.547030 0.837113i \(-0.684242\pi\)
0.547030 0.837113i \(-0.315758\pi\)
\(354\) 0 0
\(355\) 6.82843i 0.362415i
\(356\) 0 0
\(357\) 1.41421 0.242641i 0.0748481 0.0128419i
\(358\) 0 0
\(359\) 18.6274 0.983117 0.491559 0.870844i \(-0.336427\pi\)
0.491559 + 0.870844i \(0.336427\pi\)
\(360\) 0 0
\(361\) 13.9706 0.735293
\(362\) 0 0
\(363\) −11.9497 + 2.05025i −0.627199 + 0.107610i
\(364\) 0 0
\(365\) 5.17157i 0.270692i
\(366\) 0 0
\(367\) 18.8284i 0.982836i −0.870924 0.491418i \(-0.836479\pi\)
0.870924 0.491418i \(-0.163521\pi\)
\(368\) 0 0
\(369\) 10.0000 + 28.2843i 0.520579 + 1.47242i
\(370\) 0 0
\(371\) 9.31371 0.483544
\(372\) 0 0
\(373\) 10.9706 0.568034 0.284017 0.958819i \(-0.408333\pi\)
0.284017 + 0.958819i \(0.408333\pi\)
\(374\) 0 0
\(375\) −1.65685 9.65685i −0.0855596 0.498678i
\(376\) 0 0
\(377\) 0.485281i 0.0249933i
\(378\) 0 0
\(379\) 17.5147i 0.899671i −0.893112 0.449835i \(-0.851483\pi\)
0.893112 0.449835i \(-0.148517\pi\)
\(380\) 0 0
\(381\) 0.585786 + 3.41421i 0.0300107 + 0.174915i
\(382\) 0 0
\(383\) −5.65685 −0.289052 −0.144526 0.989501i \(-0.546166\pi\)
−0.144526 + 0.989501i \(0.546166\pi\)
\(384\) 0 0
\(385\) −1.17157 −0.0597089
\(386\) 0 0
\(387\) −6.48528 18.3431i −0.329665 0.932435i
\(388\) 0 0
\(389\) 10.4853i 0.531625i 0.964025 + 0.265812i \(0.0856402\pi\)
−0.964025 + 0.265812i \(0.914360\pi\)
\(390\) 0 0
\(391\) 3.31371i 0.167581i
\(392\) 0 0
\(393\) −16.3137 + 2.79899i −0.822918 + 0.141190i
\(394\) 0 0
\(395\) −2.34315 −0.117896
\(396\) 0 0
\(397\) 9.75736 0.489708 0.244854 0.969560i \(-0.421260\pi\)
0.244854 + 0.969560i \(0.421260\pi\)
\(398\) 0 0
\(399\) −3.82843 + 0.656854i −0.191661 + 0.0328838i
\(400\) 0 0
\(401\) 20.3431i 1.01589i 0.861390 + 0.507944i \(0.169594\pi\)
−0.861390 + 0.507944i \(0.830406\pi\)
\(402\) 0 0
\(403\) 4.00000i 0.199254i
\(404\) 0 0
\(405\) −3.31371 4.10051i −0.164659 0.203756i
\(406\) 0 0
\(407\) 9.65685 0.478672
\(408\) 0 0
\(409\) 9.51472 0.470473 0.235236 0.971938i \(-0.424414\pi\)
0.235236 + 0.971938i \(0.424414\pi\)
\(410\) 0 0
\(411\) 3.31371 + 19.3137i 0.163453 + 0.952675i
\(412\) 0 0
\(413\) 2.24264i 0.110353i
\(414\) 0 0
\(415\) 5.02944i 0.246885i
\(416\) 0 0
\(417\) −3.00000 17.4853i −0.146911 0.856258i
\(418\) 0 0
\(419\) 6.72792 0.328681 0.164340 0.986404i \(-0.447450\pi\)
0.164340 + 0.986404i \(0.447450\pi\)
\(420\) 0 0
\(421\) −4.34315 −0.211672 −0.105836 0.994384i \(-0.533752\pi\)
−0.105836 + 0.994384i \(0.533752\pi\)
\(422\) 0 0
\(423\) −27.3137 + 9.65685i −1.32804 + 0.469532i
\(424\) 0 0
\(425\) 3.85786i 0.187134i
\(426\) 0 0
\(427\) 5.75736i 0.278618i
\(428\) 0 0
\(429\) 2.00000 0.343146i 0.0965609 0.0165672i
\(430\) 0 0
\(431\) −16.0000 −0.770693 −0.385346 0.922772i \(-0.625918\pi\)
−0.385346 + 0.922772i \(0.625918\pi\)
\(432\) 0 0
\(433\) −18.9706 −0.911667 −0.455834 0.890065i \(-0.650659\pi\)
−0.455834 + 0.890065i \(0.650659\pi\)
\(434\) 0 0
\(435\) 0.828427 0.142136i 0.0397200 0.00681488i
\(436\) 0 0
\(437\) 8.97056i 0.429120i
\(438\) 0 0
\(439\) 16.2843i 0.777206i −0.921405 0.388603i \(-0.872958\pi\)
0.921405 0.388603i \(-0.127042\pi\)
\(440\) 0 0
\(441\) −2.82843 + 1.00000i −0.134687 + 0.0476190i
\(442\) 0 0
\(443\) 28.8284 1.36968 0.684840 0.728694i \(-0.259872\pi\)
0.684840 + 0.728694i \(0.259872\pi\)
\(444\) 0 0
\(445\) 2.14214 0.101547
\(446\) 0 0
\(447\) 1.07107 + 6.24264i 0.0506598 + 0.295267i
\(448\) 0 0
\(449\) 29.6569i 1.39959i −0.714342 0.699797i \(-0.753274\pi\)
0.714342 0.699797i \(-0.246726\pi\)
\(450\) 0 0
\(451\) 20.0000i 0.941763i
\(452\) 0 0
\(453\) 5.27208 + 30.7279i 0.247704 + 1.44372i
\(454\) 0 0
\(455\) −0.343146 −0.0160869
\(456\) 0 0
\(457\) −24.0000 −1.12267 −0.561336 0.827588i \(-0.689713\pi\)
−0.561336 + 0.827588i \(0.689713\pi\)
\(458\) 0 0
\(459\) 2.10051 + 3.75736i 0.0980432 + 0.175379i
\(460\) 0 0
\(461\) 26.0416i 1.21288i −0.795129 0.606440i \(-0.792597\pi\)
0.795129 0.606440i \(-0.207403\pi\)
\(462\) 0 0
\(463\) 9.65685i 0.448792i 0.974498 + 0.224396i \(0.0720409\pi\)
−0.974498 + 0.224396i \(0.927959\pi\)
\(464\) 0 0
\(465\) −6.82843 + 1.17157i −0.316661 + 0.0543304i
\(466\) 0 0
\(467\) −30.0416 −1.39016 −0.695080 0.718932i \(-0.744631\pi\)
−0.695080 + 0.718932i \(0.744631\pi\)
\(468\) 0 0
\(469\) 13.3137 0.614770
\(470\) 0 0
\(471\) −10.6569 + 1.82843i −0.491042 + 0.0842495i
\(472\) 0 0
\(473\) 12.9706i 0.596387i
\(474\) 0 0
\(475\) 10.4437i 0.479188i
\(476\) 0 0
\(477\) 9.31371 + 26.3431i 0.426445 + 1.20617i
\(478\) 0 0
\(479\) 11.3137 0.516937 0.258468 0.966020i \(-0.416782\pi\)
0.258468 + 0.966020i \(0.416782\pi\)
\(480\) 0 0
\(481\) 2.82843 0.128965
\(482\) 0 0
\(483\) 1.17157 + 6.82843i 0.0533084 + 0.310704i
\(484\) 0 0
\(485\) 10.1421i 0.460531i
\(486\) 0 0
\(487\) 22.0000i 0.996915i 0.866914 + 0.498458i \(0.166100\pi\)
−0.866914 + 0.498458i \(0.833900\pi\)
\(488\) 0 0
\(489\) 5.89949 + 34.3848i 0.266784 + 1.55493i
\(490\) 0 0
\(491\) −12.8284 −0.578939 −0.289469 0.957187i \(-0.593479\pi\)
−0.289469 + 0.957187i \(0.593479\pi\)
\(492\) 0 0
\(493\) −0.686292 −0.0309090
\(494\) 0 0
\(495\) −1.17157 3.31371i −0.0526583 0.148940i
\(496\) 0 0
\(497\) 11.6569i 0.522881i
\(498\) 0 0
\(499\) 8.62742i 0.386216i −0.981177 0.193108i \(-0.938143\pi\)
0.981177 0.193108i \(-0.0618568\pi\)
\(500\) 0 0
\(501\) −8.82843 + 1.51472i −0.394425 + 0.0676726i
\(502\) 0 0
\(503\) −25.4558 −1.13502 −0.567510 0.823367i \(-0.692093\pi\)
−0.567510 + 0.823367i \(0.692093\pi\)
\(504\) 0 0
\(505\) 5.71573 0.254347
\(506\) 0 0
\(507\) −21.6066 + 3.70711i −0.959583 + 0.164638i
\(508\) 0 0
\(509\) 32.8701i 1.45694i −0.685078 0.728470i \(-0.740232\pi\)
0.685078 0.728470i \(-0.259768\pi\)
\(510\) 0 0
\(511\) 8.82843i 0.390547i
\(512\) 0 0
\(513\) −5.68629 10.1716i −0.251056 0.449086i
\(514\) 0 0
\(515\) 9.94113 0.438058
\(516\) 0 0
\(517\) −19.3137 −0.849416
\(518\) 0 0
\(519\) −6.31371 36.7990i −0.277141 1.61530i
\(520\) 0 0
\(521\) 23.6569i 1.03643i 0.855252 + 0.518213i \(0.173402\pi\)
−0.855252 + 0.518213i \(0.826598\pi\)
\(522\) 0 0
\(523\) 20.1005i 0.878934i 0.898259 + 0.439467i \(0.144833\pi\)
−0.898259 + 0.439467i \(0.855167\pi\)
\(524\) 0 0
\(525\) −1.36396 7.94975i −0.0595281 0.346955i
\(526\) 0 0
\(527\) 5.65685 0.246416
\(528\) 0 0
\(529\) −7.00000 −0.304348
\(530\) 0 0
\(531\) 6.34315 2.24264i 0.275269 0.0973223i
\(532\) 0 0
\(533\) 5.85786i 0.253732i
\(534\) 0 0
\(535\) 1.45584i 0.0629416i
\(536\) 0 0
\(537\) −17.8995 + 3.07107i −0.772420 + 0.132526i
\(538\) 0 0
\(539\) −2.00000 −0.0861461
\(540\) 0 0
\(541\) −32.6274 −1.40276 −0.701381 0.712786i \(-0.747433\pi\)
−0.701381 + 0.712786i \(0.747433\pi\)
\(542\) 0 0
\(543\) −27.9706 + 4.79899i −1.20033 + 0.205944i
\(544\) 0 0
\(545\) 8.48528i 0.363470i
\(546\) 0 0
\(547\) 20.1421i 0.861216i 0.902539 + 0.430608i \(0.141701\pi\)
−0.902539 + 0.430608i \(0.858299\pi\)
\(548\) 0 0
\(549\) 16.2843 5.75736i 0.694996 0.245718i
\(550\) 0 0
\(551\) 1.85786 0.0791477
\(552\) 0 0
\(553\) −4.00000 −0.170097
\(554\) 0 0
\(555\) −0.828427 4.82843i −0.0351648 0.204955i
\(556\) 0 0
\(557\) 29.3137i 1.24206i 0.783786 + 0.621031i \(0.213286\pi\)
−0.783786 + 0.621031i \(0.786714\pi\)
\(558\) 0 0
\(559\) 3.79899i 0.160680i
\(560\) 0 0
\(561\) 0.485281 + 2.82843i 0.0204886 + 0.119416i
\(562\) 0 0
\(563\) 35.2132 1.48406 0.742030 0.670367i \(-0.233863\pi\)
0.742030 + 0.670367i \(0.233863\pi\)
\(564\) 0 0
\(565\) −10.1421 −0.426683
\(566\) 0 0
\(567\) −5.65685 7.00000i −0.237566 0.293972i
\(568\) 0 0
\(569\) 21.3137i 0.893517i −0.894655 0.446759i \(-0.852578\pi\)
0.894655 0.446759i \(-0.147422\pi\)
\(570\) 0 0
\(571\) 20.1421i 0.842922i −0.906846 0.421461i \(-0.861517\pi\)
0.906846 0.421461i \(-0.138483\pi\)
\(572\) 0 0
\(573\) 13.0711 2.24264i 0.546052 0.0936877i
\(574\) 0 0
\(575\) −18.6274 −0.776817
\(576\) 0 0
\(577\) 6.68629 0.278354 0.139177 0.990268i \(-0.455554\pi\)
0.139177 + 0.990268i \(0.455554\pi\)
\(578\) 0 0
\(579\) 10.8284 1.85786i 0.450014 0.0772102i
\(580\) 0 0
\(581\) 8.58579i 0.356198i
\(582\) 0 0
\(583\) 18.6274i 0.771469i
\(584\) 0 0
\(585\) −0.343146 0.970563i −0.0141873 0.0401278i
\(586\) 0 0
\(587\) 5.27208 0.217602 0.108801 0.994064i \(-0.465299\pi\)
0.108801 + 0.994064i \(0.465299\pi\)
\(588\) 0 0
\(589\) −15.3137 −0.630990
\(590\) 0 0
\(591\) 7.61522 + 44.3848i 0.313248 + 1.82575i
\(592\) 0 0
\(593\) 5.51472i 0.226462i 0.993569 + 0.113231i \(0.0361201\pi\)
−0.993569 + 0.113231i \(0.963880\pi\)
\(594\) 0 0
\(595\) 0.485281i 0.0198946i
\(596\) 0 0
\(597\) −4.48528 26.1421i −0.183570 1.06993i
\(598\) 0 0
\(599\) 28.6274 1.16968 0.584842 0.811147i \(-0.301156\pi\)
0.584842 + 0.811147i \(0.301156\pi\)
\(600\) 0 0
\(601\) 12.1421 0.495288 0.247644 0.968851i \(-0.420344\pi\)
0.247644 + 0.968851i \(0.420344\pi\)
\(602\) 0 0
\(603\) 13.3137 + 37.6569i 0.542176 + 1.53351i
\(604\) 0 0
\(605\) 4.10051i 0.166709i
\(606\) 0 0
\(607\) 26.1421i 1.06108i −0.847661 0.530538i \(-0.821990\pi\)
0.847661 0.530538i \(-0.178010\pi\)
\(608\) 0 0
\(609\) 1.41421 0.242641i 0.0573068 0.00983230i
\(610\) 0 0
\(611\) −5.65685 −0.228852
\(612\) 0 0
\(613\) −46.7696 −1.88900 −0.944502 0.328505i \(-0.893455\pi\)
−0.944502 + 0.328505i \(0.893455\pi\)
\(614\) 0 0
\(615\) 10.0000 1.71573i 0.403239 0.0691849i
\(616\) 0 0
\(617\) 16.6274i 0.669395i −0.942326 0.334697i \(-0.891366\pi\)
0.942326 0.334697i \(-0.108634\pi\)
\(618\) 0 0
\(619\) 9.75736i 0.392181i 0.980586 + 0.196091i \(0.0628247\pi\)
−0.980586 + 0.196091i \(0.937175\pi\)
\(620\) 0 0
\(621\) −18.1421 + 10.1421i −0.728019 + 0.406990i
\(622\) 0 0
\(623\) 3.65685 0.146509
\(624\) 0 0
\(625\) 19.9706 0.798823
\(626\) 0 0
\(627\) −1.31371 7.65685i −0.0524645 0.305785i
\(628\) 0 0
\(629\) 4.00000i 0.159490i
\(630\) 0 0
\(631\) 24.9706i 0.994062i 0.867733 + 0.497031i \(0.165577\pi\)
−0.867733 + 0.497031i \(0.834423\pi\)
\(632\) 0 0
\(633\) −3.41421 19.8995i −0.135703 0.790934i
\(634\) 0 0
\(635\) 1.17157 0.0464925
\(636\) 0 0
\(637\) −0.585786 −0.0232097
\(638\) 0 0
\(639\) −32.9706 + 11.6569i −1.30430 + 0.461138i
\(640\) 0 0
\(641\) 15.6569i 0.618409i −0.950996 0.309204i \(-0.899937\pi\)
0.950996 0.309204i \(-0.100063\pi\)
\(642\) 0 0
\(643\) 46.2426i 1.82363i 0.410599 + 0.911816i \(0.365319\pi\)
−0.410599 + 0.911816i \(0.634681\pi\)
\(644\) 0 0
\(645\) −6.48528 + 1.11270i −0.255358 + 0.0438125i
\(646\) 0 0
\(647\) −29.4558 −1.15803 −0.579014 0.815317i \(-0.696562\pi\)
−0.579014 + 0.815317i \(0.696562\pi\)
\(648\) 0 0
\(649\) 4.48528 0.176063
\(650\) 0 0
\(651\) −11.6569 + 2.00000i −0.456868 + 0.0783862i
\(652\) 0 0
\(653\) 14.4853i 0.566853i −0.958994 0.283426i \(-0.908529\pi\)
0.958994 0.283426i \(-0.0914712\pi\)
\(654\) 0 0
\(655\) 5.59798i 0.218731i
\(656\) 0 0
\(657\) −24.9706 + 8.82843i −0.974194 + 0.344430i
\(658\) 0 0
\(659\) 18.9706 0.738988 0.369494 0.929233i \(-0.379531\pi\)
0.369494 + 0.929233i \(0.379531\pi\)
\(660\) 0 0
\(661\) −36.1838 −1.40739 −0.703693 0.710504i \(-0.748467\pi\)
−0.703693 + 0.710504i \(0.748467\pi\)
\(662\) 0 0
\(663\) 0.142136 + 0.828427i 0.00552009 + 0.0321734i
\(664\) 0 0
\(665\) 1.31371i 0.0509434i
\(666\) 0 0
\(667\) 3.31371i 0.128307i
\(668\) 0 0
\(669\) −0.828427 4.82843i −0.0320288 0.186678i
\(670\) 0 0
\(671\) 11.5147 0.444521
\(672\) 0 0
\(673\) 2.00000 0.0770943 0.0385472 0.999257i \(-0.487727\pi\)
0.0385472 + 0.999257i \(0.487727\pi\)
\(674\) 0 0
\(675\) 21.1213 11.8076i 0.812960 0.454475i
\(676\) 0 0
\(677\) 48.8701i 1.87823i −0.343605 0.939114i \(-0.611648\pi\)
0.343605 0.939114i \(-0.388352\pi\)
\(678\) 0 0
\(679\) 17.3137i 0.664439i
\(680\) 0 0
\(681\) −7.00000 + 1.20101i −0.268241 + 0.0460228i
\(682\) 0 0
\(683\) 46.4853 1.77871 0.889355 0.457217i \(-0.151154\pi\)
0.889355 + 0.457217i \(0.151154\pi\)
\(684\) 0 0
\(685\) 6.62742 0.253221
\(686\) 0 0
\(687\) 22.3137 3.82843i 0.851321 0.146064i
\(688\) 0 0
\(689\) 5.45584i 0.207851i
\(690\) 0 0
\(691\) 26.0416i 0.990670i 0.868702 + 0.495335i \(0.164955\pi\)
−0.868702 + 0.495335i \(0.835045\pi\)
\(692\) 0 0
\(693\) −2.00000 5.65685i −0.0759737 0.214886i
\(694\) 0 0
\(695\) −6.00000 −0.227593
\(696\) 0 0
\(697\) −8.28427 −0.313789
\(698\) 0 0
\(699\) 7.31371 + 42.6274i 0.276630 + 1.61232i
\(700\) 0 0
\(701\) 0.142136i 0.00536839i 0.999996 + 0.00268419i \(0.000854407\pi\)
−0.999996 + 0.00268419i \(0.999146\pi\)
\(702\) 0 0
\(703\) 10.8284i 0.408402i
\(704\) 0 0
\(705\) 1.65685 + 9.65685i 0.0624007 + 0.363698i
\(706\) 0 0
\(707\) 9.75736 0.366963
\(708\) 0 0
\(709\) 22.4853 0.844452 0.422226 0.906490i \(-0.361249\pi\)
0.422226 + 0.906490i \(0.361249\pi\)
\(710\) 0 0
\(711\) −4.00000 11.3137i −0.150012 0.424297i
\(712\) 0 0
\(713\) 27.3137i 1.02291i
\(714\) 0 0
\(715\) 0.686292i 0.0256658i
\(716\) 0 0
\(717\) 19.3137 3.31371i 0.721284 0.123753i
\(718\) 0 0
\(719\) −43.3137 −1.61533 −0.807664 0.589642i \(-0.799269\pi\)
−0.807664 + 0.589642i \(0.799269\pi\)
\(720\) 0 0
\(721\) 16.9706 0.632017
\(722\) 0 0
\(723\) −13.0711 + 2.24264i −0.486118 + 0.0834047i
\(724\) 0 0
\(725\) 3.85786i 0.143277i
\(726\) 0 0
\(727\) 34.6274i 1.28426i 0.766596 + 0.642130i \(0.221949\pi\)
−0.766596 + 0.642130i \(0.778051\pi\)
\(728\) 0 0
\(729\) 14.1421 23.0000i 0.523783 0.851852i
\(730\) 0 0
\(731\) 5.37258 0.198712
\(732\) 0 0
\(733\) −36.3848 −1.34390 −0.671951 0.740595i \(-0.734544\pi\)
−0.671951 + 0.740595i \(0.734544\pi\)
\(734\) 0 0
\(735\) 0.171573 + 1.00000i 0.00632856 + 0.0368856i
\(736\) 0 0
\(737\) 26.6274i 0.980834i
\(738\) 0 0
\(739\) 40.1421i 1.47665i −0.674444 0.738326i \(-0.735617\pi\)
0.674444 0.738326i \(-0.264383\pi\)
\(740\) 0 0
\(741\) −0.384776 2.24264i −0.0141351 0.0823855i
\(742\) 0 0
\(743\) −45.9411 −1.68542 −0.842708 0.538371i \(-0.819040\pi\)
−0.842708 + 0.538371i \(0.819040\pi\)
\(744\) 0 0
\(745\) 2.14214 0.0784818
\(746\) 0 0
\(747\) 24.2843 8.58579i 0.888515 0.314137i
\(748\) 0 0
\(749\) 2.48528i 0.0908102i
\(750\) 0 0
\(751\) 26.2843i 0.959127i −0.877507 0.479563i \(-0.840795\pi\)
0.877507 0.479563i \(-0.159205\pi\)
\(752\) 0 0
\(753\) −39.9706 + 6.85786i −1.45661 + 0.249914i
\(754\) 0 0
\(755\) 10.5442 0.383741
\(756\) 0 0
\(757\) 13.1127 0.476589 0.238295 0.971193i \(-0.423412\pi\)
0.238295 + 0.971193i \(0.423412\pi\)
\(758\) 0 0
\(759\) −13.6569 + 2.34315i −0.495712 + 0.0850508i
\(760\) 0 0
\(761\) 34.9706i 1.26768i −0.773463 0.633841i \(-0.781477\pi\)
0.773463 0.633841i \(-0.218523\pi\)
\(762\) 0 0
\(763\) 14.4853i 0.524402i
\(764\) 0 0
\(765\) 1.37258 0.485281i 0.0496258 0.0175454i
\(766\) 0 0
\(767\) 1.31371 0.0474353
\(768\) 0 0
\(769\) 19.6569 0.708844 0.354422 0.935086i \(-0.384678\pi\)
0.354422 + 0.935086i \(0.384678\pi\)
\(770\) 0 0
\(771\) −0.727922 4.24264i −0.0262155 0.152795i
\(772\) 0 0
\(773\) 26.7279i 0.961337i 0.876903 + 0.480668i \(0.159606\pi\)
−0.876903 + 0.480668i \(0.840394\pi\)
\(774\) 0 0
\(775\) 31.7990i 1.14225i
\(776\) 0 0
\(777\) −1.41421 8.24264i −0.0507346 0.295703i
\(778\) 0 0
\(779\) 22.4264 0.803509
\(780\) 0 0
\(781\) −23.3137 −0.834230
\(782\) 0 0
\(783\) 2.10051 + 3.75736i 0.0750659 + 0.134277i
\(784\) 0 0
\(785\) 3.65685i 0.130519i
\(786\) 0 0
\(787\) 42.2426i 1.50579i 0.658142 + 0.752894i \(0.271343\pi\)
−0.658142 + 0.752894i \(0.728657\pi\)
\(788\) 0 0
\(789\) 36.3848 6.24264i 1.29533 0.222244i
\(790\) 0 0
\(791\) −17.3137 −0.615605
\(792\) 0 0
\(793\) 3.37258 0.119764
\(794\) 0 0
\(795\) 9.31371 1.59798i 0.330323 0.0566745i
\(796\) 0 0
\(797\) 31.8995i 1.12994i 0.825112 + 0.564969i \(0.191112\pi\)
−0.825112 + 0.564969i \(0.808888\pi\)
\(798\) 0 0
\(799\) 8.00000i 0.283020i
\(800\) 0 0
\(801\) 3.65685 + 10.3431i 0.129209 + 0.365457i
\(802\) 0 0
\(803\) −17.6569 −0.623097
\(804\) 0 0
\(805\) 2.34315 0.0825850
\(806\) 0 0
\(807\) 1.97056 + 11.4853i 0.0693671 + 0.404301i
\(808\) 0 0
\(809\) 33.3137i