Properties

Label 403.2.c.a.311.1
Level 403
Weight 2
Character 403.311
Analytic conductor 3.218
Analytic rank 0
Dimension 2
CM no
Inner twists 2

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 403 = 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 403.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.21797120146\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 311.1
Root \(-1.00000i\) of \(x^{2} + 1\)
Character \(\chi\) \(=\) 403.311
Dual form 403.2.c.a.311.2

$q$-expansion

\(f(q)\) \(=\) \(q+2.00000 q^{3} +2.00000 q^{4} -4.00000i q^{5} +2.00000i q^{7} +1.00000 q^{9} +O(q^{10})\) \(q+2.00000 q^{3} +2.00000 q^{4} -4.00000i q^{5} +2.00000i q^{7} +1.00000 q^{9} -1.00000i q^{11} +4.00000 q^{12} +(-2.00000 + 3.00000i) q^{13} -8.00000i q^{15} +4.00000 q^{16} -2.00000 q^{17} +2.00000i q^{19} -8.00000i q^{20} +4.00000i q^{21} -4.00000 q^{23} -11.0000 q^{25} -4.00000 q^{27} +4.00000i q^{28} +8.00000 q^{29} +1.00000i q^{31} -2.00000i q^{33} +8.00000 q^{35} +2.00000 q^{36} +3.00000i q^{37} +(-4.00000 + 6.00000i) q^{39} +4.00000i q^{41} +4.00000 q^{43} -2.00000i q^{44} -4.00000i q^{45} +2.00000i q^{47} +8.00000 q^{48} +3.00000 q^{49} -4.00000 q^{51} +(-4.00000 + 6.00000i) q^{52} -4.00000 q^{53} -4.00000 q^{55} +4.00000i q^{57} -6.00000i q^{59} -16.0000i q^{60} +10.0000 q^{61} +2.00000i q^{63} +8.00000 q^{64} +(12.0000 + 8.00000i) q^{65} -16.0000i q^{67} -4.00000 q^{68} -8.00000 q^{69} +6.00000i q^{71} +7.00000i q^{73} -22.0000 q^{75} +4.00000i q^{76} +2.00000 q^{77} -16.0000 q^{79} -16.0000i q^{80} -11.0000 q^{81} -12.0000i q^{83} +8.00000i q^{84} +8.00000i q^{85} +16.0000 q^{87} +15.0000i q^{89} +(-6.00000 - 4.00000i) q^{91} -8.00000 q^{92} +2.00000i q^{93} +8.00000 q^{95} -2.00000i q^{97} -1.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 4q^{3} + 4q^{4} + 2q^{9} + O(q^{10}) \) \( 2q + 4q^{3} + 4q^{4} + 2q^{9} + 8q^{12} - 4q^{13} + 8q^{16} - 4q^{17} - 8q^{23} - 22q^{25} - 8q^{27} + 16q^{29} + 16q^{35} + 4q^{36} - 8q^{39} + 8q^{43} + 16q^{48} + 6q^{49} - 8q^{51} - 8q^{52} - 8q^{53} - 8q^{55} + 20q^{61} + 16q^{64} + 24q^{65} - 8q^{68} - 16q^{69} - 44q^{75} + 4q^{77} - 32q^{79} - 22q^{81} + 32q^{87} - 12q^{91} - 16q^{92} + 16q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).

\(n\) \(249\) \(313\)
\(\chi(n)\) \(-1\) \(1\)

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 1.00000 \(0\)
−1.00000 \(\pi\)
\(3\) 2.00000 1.15470 0.577350 0.816497i \(-0.304087\pi\)
0.577350 + 0.816497i \(0.304087\pi\)
\(4\) 2.00000 1.00000
\(5\) 4.00000i 1.78885i −0.447214 0.894427i \(-0.647584\pi\)
0.447214 0.894427i \(-0.352416\pi\)
\(6\) 0 0
\(7\) 2.00000i 0.755929i 0.925820 + 0.377964i \(0.123376\pi\)
−0.925820 + 0.377964i \(0.876624\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 1.00000i 0.301511i −0.988571 0.150756i \(-0.951829\pi\)
0.988571 0.150756i \(-0.0481707\pi\)
\(12\) 4.00000 1.15470
\(13\) −2.00000 + 3.00000i −0.554700 + 0.832050i
\(14\) 0 0
\(15\) 8.00000i 2.06559i
\(16\) 4.00000 1.00000
\(17\) −2.00000 −0.485071 −0.242536 0.970143i \(-0.577979\pi\)
−0.242536 + 0.970143i \(0.577979\pi\)
\(18\) 0 0
\(19\) 2.00000i 0.458831i 0.973329 + 0.229416i \(0.0736815\pi\)
−0.973329 + 0.229416i \(0.926318\pi\)
\(20\) 8.00000i 1.78885i
\(21\) 4.00000i 0.872872i
\(22\) 0 0
\(23\) −4.00000 −0.834058 −0.417029 0.908893i \(-0.636929\pi\)
−0.417029 + 0.908893i \(0.636929\pi\)
\(24\) 0 0
\(25\) −11.0000 −2.20000
\(26\) 0 0
\(27\) −4.00000 −0.769800
\(28\) 4.00000i 0.755929i
\(29\) 8.00000 1.48556 0.742781 0.669534i \(-0.233506\pi\)
0.742781 + 0.669534i \(0.233506\pi\)
\(30\) 0 0
\(31\) 1.00000i 0.179605i
\(32\) 0 0
\(33\) 2.00000i 0.348155i
\(34\) 0 0
\(35\) 8.00000 1.35225
\(36\) 2.00000 0.333333
\(37\) 3.00000i 0.493197i 0.969118 + 0.246598i \(0.0793129\pi\)
−0.969118 + 0.246598i \(0.920687\pi\)
\(38\) 0 0
\(39\) −4.00000 + 6.00000i −0.640513 + 0.960769i
\(40\) 0 0
\(41\) 4.00000i 0.624695i 0.949968 + 0.312348i \(0.101115\pi\)
−0.949968 + 0.312348i \(0.898885\pi\)
\(42\) 0 0
\(43\) 4.00000 0.609994 0.304997 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) 2.00000i 0.301511i
\(45\) 4.00000i 0.596285i
\(46\) 0 0
\(47\) 2.00000i 0.291730i 0.989305 + 0.145865i \(0.0465965\pi\)
−0.989305 + 0.145865i \(0.953403\pi\)
\(48\) 8.00000 1.15470
\(49\) 3.00000 0.428571
\(50\) 0 0
\(51\) −4.00000 −0.560112
\(52\) −4.00000 + 6.00000i −0.554700 + 0.832050i
\(53\) −4.00000 −0.549442 −0.274721 0.961524i \(-0.588586\pi\)
−0.274721 + 0.961524i \(0.588586\pi\)
\(54\) 0 0
\(55\) −4.00000 −0.539360
\(56\) 0 0
\(57\) 4.00000i 0.529813i
\(58\) 0 0
\(59\) 6.00000i 0.781133i −0.920575 0.390567i \(-0.872279\pi\)
0.920575 0.390567i \(-0.127721\pi\)
\(60\) 16.0000i 2.06559i
\(61\) 10.0000 1.28037 0.640184 0.768221i \(-0.278858\pi\)
0.640184 + 0.768221i \(0.278858\pi\)
\(62\) 0 0
\(63\) 2.00000i 0.251976i
\(64\) 8.00000 1.00000
\(65\) 12.0000 + 8.00000i 1.48842 + 0.992278i
\(66\) 0 0
\(67\) 16.0000i 1.95471i −0.211604 0.977356i \(-0.567869\pi\)
0.211604 0.977356i \(-0.432131\pi\)
\(68\) −4.00000 −0.485071
\(69\) −8.00000 −0.963087
\(70\) 0 0
\(71\) 6.00000i 0.712069i 0.934473 + 0.356034i \(0.115871\pi\)
−0.934473 + 0.356034i \(0.884129\pi\)
\(72\) 0 0
\(73\) 7.00000i 0.819288i 0.912245 + 0.409644i \(0.134347\pi\)
−0.912245 + 0.409644i \(0.865653\pi\)
\(74\) 0 0
\(75\) −22.0000 −2.54034
\(76\) 4.00000i 0.458831i
\(77\) 2.00000 0.227921
\(78\) 0 0
\(79\) −16.0000 −1.80014 −0.900070 0.435745i \(-0.856485\pi\)
−0.900070 + 0.435745i \(0.856485\pi\)
\(80\) 16.0000i 1.78885i
\(81\) −11.0000 −1.22222
\(82\) 0 0
\(83\) 12.0000i 1.31717i −0.752506 0.658586i \(-0.771155\pi\)
0.752506 0.658586i \(-0.228845\pi\)
\(84\) 8.00000i 0.872872i
\(85\) 8.00000i 0.867722i
\(86\) 0 0
\(87\) 16.0000 1.71538
\(88\) 0 0
\(89\) 15.0000i 1.59000i 0.606612 + 0.794998i \(0.292528\pi\)
−0.606612 + 0.794998i \(0.707472\pi\)
\(90\) 0 0
\(91\) −6.00000 4.00000i −0.628971 0.419314i
\(92\) −8.00000 −0.834058
\(93\) 2.00000i 0.207390i
\(94\) 0 0
\(95\) 8.00000 0.820783
\(96\) 0 0
\(97\) 2.00000i 0.203069i −0.994832 0.101535i \(-0.967625\pi\)
0.994832 0.101535i \(-0.0323753\pi\)
\(98\) 0 0
\(99\) 1.00000i 0.100504i
\(100\) −22.0000 −2.20000
\(101\) −3.00000 −0.298511 −0.149256 0.988799i \(-0.547688\pi\)
−0.149256 + 0.988799i \(0.547688\pi\)
\(102\) 0 0
\(103\) −15.0000 −1.47799 −0.738997 0.673709i \(-0.764700\pi\)
−0.738997 + 0.673709i \(0.764700\pi\)
\(104\) 0 0
\(105\) 16.0000 1.56144
\(106\) 0 0
\(107\) 9.00000 0.870063 0.435031 0.900415i \(-0.356737\pi\)
0.435031 + 0.900415i \(0.356737\pi\)
\(108\) −8.00000 −0.769800
\(109\) 2.00000i 0.191565i 0.995402 + 0.0957826i \(0.0305354\pi\)
−0.995402 + 0.0957826i \(0.969465\pi\)
\(110\) 0 0
\(111\) 6.00000i 0.569495i
\(112\) 8.00000i 0.755929i
\(113\) −17.0000 −1.59923 −0.799613 0.600516i \(-0.794962\pi\)
−0.799613 + 0.600516i \(0.794962\pi\)
\(114\) 0 0
\(115\) 16.0000i 1.49201i
\(116\) 16.0000 1.48556
\(117\) −2.00000 + 3.00000i −0.184900 + 0.277350i
\(118\) 0 0
\(119\) 4.00000i 0.366679i
\(120\) 0 0
\(121\) 10.0000 0.909091
\(122\) 0 0
\(123\) 8.00000i 0.721336i
\(124\) 2.00000i 0.179605i
\(125\) 24.0000i 2.14663i
\(126\) 0 0
\(127\) −4.00000 −0.354943 −0.177471 0.984126i \(-0.556792\pi\)
−0.177471 + 0.984126i \(0.556792\pi\)
\(128\) 0 0
\(129\) 8.00000 0.704361
\(130\) 0 0
\(131\) 1.00000 0.0873704 0.0436852 0.999045i \(-0.486090\pi\)
0.0436852 + 0.999045i \(0.486090\pi\)
\(132\) 4.00000i 0.348155i
\(133\) −4.00000 −0.346844
\(134\) 0 0
\(135\) 16.0000i 1.37706i
\(136\) 0 0
\(137\) 6.00000i 0.512615i −0.966595 0.256307i \(-0.917494\pi\)
0.966595 0.256307i \(-0.0825059\pi\)
\(138\) 0 0
\(139\) −14.0000 −1.18746 −0.593732 0.804663i \(-0.702346\pi\)
−0.593732 + 0.804663i \(0.702346\pi\)
\(140\) 16.0000 1.35225
\(141\) 4.00000i 0.336861i
\(142\) 0 0
\(143\) 3.00000 + 2.00000i 0.250873 + 0.167248i
\(144\) 4.00000 0.333333
\(145\) 32.0000i 2.65746i
\(146\) 0 0
\(147\) 6.00000 0.494872
\(148\) 6.00000i 0.493197i
\(149\) 22.0000i 1.80231i −0.433497 0.901155i \(-0.642720\pi\)
0.433497 0.901155i \(-0.357280\pi\)
\(150\) 0 0
\(151\) 17.0000i 1.38344i −0.722166 0.691720i \(-0.756853\pi\)
0.722166 0.691720i \(-0.243147\pi\)
\(152\) 0 0
\(153\) −2.00000 −0.161690
\(154\) 0 0
\(155\) 4.00000 0.321288
\(156\) −8.00000 + 12.0000i −0.640513 + 0.960769i
\(157\) 13.0000 1.03751 0.518756 0.854922i \(-0.326395\pi\)
0.518756 + 0.854922i \(0.326395\pi\)
\(158\) 0 0
\(159\) −8.00000 −0.634441
\(160\) 0 0
\(161\) 8.00000i 0.630488i
\(162\) 0 0
\(163\) 12.0000i 0.939913i −0.882690 0.469956i \(-0.844270\pi\)
0.882690 0.469956i \(-0.155730\pi\)
\(164\) 8.00000i 0.624695i
\(165\) −8.00000 −0.622799
\(166\) 0 0
\(167\) 3.00000i 0.232147i −0.993241 0.116073i \(-0.962969\pi\)
0.993241 0.116073i \(-0.0370308\pi\)
\(168\) 0 0
\(169\) −5.00000 12.0000i −0.384615 0.923077i
\(170\) 0 0
\(171\) 2.00000i 0.152944i
\(172\) 8.00000 0.609994
\(173\) −9.00000 −0.684257 −0.342129 0.939653i \(-0.611148\pi\)
−0.342129 + 0.939653i \(0.611148\pi\)
\(174\) 0 0
\(175\) 22.0000i 1.66304i
\(176\) 4.00000i 0.301511i
\(177\) 12.0000i 0.901975i
\(178\) 0 0
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) 8.00000i 0.596285i
\(181\) −6.00000 −0.445976 −0.222988 0.974821i \(-0.571581\pi\)
−0.222988 + 0.974821i \(0.571581\pi\)
\(182\) 0 0
\(183\) 20.0000 1.47844
\(184\) 0 0
\(185\) 12.0000 0.882258
\(186\) 0 0
\(187\) 2.00000i 0.146254i
\(188\) 4.00000i 0.291730i
\(189\) 8.00000i 0.581914i
\(190\) 0 0
\(191\) −5.00000 −0.361787 −0.180894 0.983503i \(-0.557899\pi\)
−0.180894 + 0.983503i \(0.557899\pi\)
\(192\) 16.0000 1.15470
\(193\) 14.0000i 1.00774i −0.863779 0.503871i \(-0.831909\pi\)
0.863779 0.503871i \(-0.168091\pi\)
\(194\) 0 0
\(195\) 24.0000 + 16.0000i 1.71868 + 1.14578i
\(196\) 6.00000 0.428571
\(197\) 15.0000i 1.06871i 0.845262 + 0.534353i \(0.179445\pi\)
−0.845262 + 0.534353i \(0.820555\pi\)
\(198\) 0 0
\(199\) 10.0000 0.708881 0.354441 0.935079i \(-0.384671\pi\)
0.354441 + 0.935079i \(0.384671\pi\)
\(200\) 0 0
\(201\) 32.0000i 2.25711i
\(202\) 0 0
\(203\) 16.0000i 1.12298i
\(204\) −8.00000 −0.560112
\(205\) 16.0000 1.11749
\(206\) 0 0
\(207\) −4.00000 −0.278019
\(208\) −8.00000 + 12.0000i −0.554700 + 0.832050i
\(209\) 2.00000 0.138343
\(210\) 0 0
\(211\) 19.0000 1.30801 0.654007 0.756489i \(-0.273087\pi\)
0.654007 + 0.756489i \(0.273087\pi\)
\(212\) −8.00000 −0.549442
\(213\) 12.0000i 0.822226i
\(214\) 0 0
\(215\) 16.0000i 1.09119i
\(216\) 0 0
\(217\) −2.00000 −0.135769
\(218\) 0 0
\(219\) 14.0000i 0.946032i
\(220\) −8.00000 −0.539360
\(221\) 4.00000 6.00000i 0.269069 0.403604i
\(222\) 0 0
\(223\) 19.0000i 1.27233i 0.771551 + 0.636167i \(0.219481\pi\)
−0.771551 + 0.636167i \(0.780519\pi\)
\(224\) 0 0
\(225\) −11.0000 −0.733333
\(226\) 0 0
\(227\) 8.00000i 0.530979i −0.964114 0.265489i \(-0.914466\pi\)
0.964114 0.265489i \(-0.0855335\pi\)
\(228\) 8.00000i 0.529813i
\(229\) 29.0000i 1.91637i 0.286143 + 0.958187i \(0.407627\pi\)
−0.286143 + 0.958187i \(0.592373\pi\)
\(230\) 0 0
\(231\) 4.00000 0.263181
\(232\) 0 0
\(233\) 13.0000 0.851658 0.425829 0.904804i \(-0.359982\pi\)
0.425829 + 0.904804i \(0.359982\pi\)
\(234\) 0 0
\(235\) 8.00000 0.521862
\(236\) 12.0000i 0.781133i
\(237\) −32.0000 −2.07862
\(238\) 0 0
\(239\) 16.0000i 1.03495i 0.855697 + 0.517477i \(0.173129\pi\)
−0.855697 + 0.517477i \(0.826871\pi\)
\(240\) 32.0000i 2.06559i
\(241\) 14.0000i 0.901819i −0.892570 0.450910i \(-0.851100\pi\)
0.892570 0.450910i \(-0.148900\pi\)
\(242\) 0 0
\(243\) −10.0000 −0.641500
\(244\) 20.0000 1.28037
\(245\) 12.0000i 0.766652i
\(246\) 0 0
\(247\) −6.00000 4.00000i −0.381771 0.254514i
\(248\) 0 0
\(249\) 24.0000i 1.52094i
\(250\) 0 0
\(251\) 22.0000 1.38863 0.694314 0.719672i \(-0.255708\pi\)
0.694314 + 0.719672i \(0.255708\pi\)
\(252\) 4.00000i 0.251976i
\(253\) 4.00000i 0.251478i
\(254\) 0 0
\(255\) 16.0000i 1.00196i
\(256\) 16.0000 1.00000
\(257\) 21.0000 1.30994 0.654972 0.755653i \(-0.272680\pi\)
0.654972 + 0.755653i \(0.272680\pi\)
\(258\) 0 0
\(259\) −6.00000 −0.372822
\(260\) 24.0000 + 16.0000i 1.48842 + 0.992278i
\(261\) 8.00000 0.495188
\(262\) 0 0
\(263\) −24.0000 −1.47990 −0.739952 0.672660i \(-0.765152\pi\)
−0.739952 + 0.672660i \(0.765152\pi\)
\(264\) 0 0
\(265\) 16.0000i 0.982872i
\(266\) 0 0
\(267\) 30.0000i 1.83597i
\(268\) 32.0000i 1.95471i
\(269\) 10.0000 0.609711 0.304855 0.952399i \(-0.401392\pi\)
0.304855 + 0.952399i \(0.401392\pi\)
\(270\) 0 0
\(271\) 15.0000i 0.911185i 0.890188 + 0.455593i \(0.150573\pi\)
−0.890188 + 0.455593i \(0.849427\pi\)
\(272\) −8.00000 −0.485071
\(273\) −12.0000 8.00000i −0.726273 0.484182i
\(274\) 0 0
\(275\) 11.0000i 0.663325i
\(276\) −16.0000 −0.963087
\(277\) −16.0000 −0.961347 −0.480673 0.876900i \(-0.659608\pi\)
−0.480673 + 0.876900i \(0.659608\pi\)
\(278\) 0 0
\(279\) 1.00000i 0.0598684i
\(280\) 0 0
\(281\) 24.0000i 1.43172i −0.698244 0.715860i \(-0.746035\pi\)
0.698244 0.715860i \(-0.253965\pi\)
\(282\) 0 0
\(283\) 13.0000 0.772770 0.386385 0.922338i \(-0.373724\pi\)
0.386385 + 0.922338i \(0.373724\pi\)
\(284\) 12.0000i 0.712069i
\(285\) 16.0000 0.947758
\(286\) 0 0
\(287\) −8.00000 −0.472225
\(288\) 0 0
\(289\) −13.0000 −0.764706
\(290\) 0 0
\(291\) 4.00000i 0.234484i
\(292\) 14.0000i 0.819288i
\(293\) 18.0000i 1.05157i 0.850617 + 0.525786i \(0.176229\pi\)
−0.850617 + 0.525786i \(0.823771\pi\)
\(294\) 0 0
\(295\) −24.0000 −1.39733
\(296\) 0 0
\(297\) 4.00000i 0.232104i
\(298\) 0 0
\(299\) 8.00000 12.0000i 0.462652 0.693978i
\(300\) −44.0000 −2.54034
\(301\) 8.00000i 0.461112i
\(302\) 0 0
\(303\) −6.00000 −0.344691
\(304\) 8.00000i 0.458831i
\(305\) 40.0000i 2.29039i
\(306\) 0 0
\(307\) 14.0000i 0.799022i 0.916728 + 0.399511i \(0.130820\pi\)
−0.916728 + 0.399511i \(0.869180\pi\)
\(308\) 4.00000 0.227921
\(309\) −30.0000 −1.70664
\(310\) 0 0
\(311\) 15.0000 0.850572 0.425286 0.905059i \(-0.360174\pi\)
0.425286 + 0.905059i \(0.360174\pi\)
\(312\) 0 0
\(313\) 16.0000 0.904373 0.452187 0.891923i \(-0.350644\pi\)
0.452187 + 0.891923i \(0.350644\pi\)
\(314\) 0 0
\(315\) 8.00000 0.450749
\(316\) −32.0000 −1.80014
\(317\) 24.0000i 1.34797i −0.738743 0.673987i \(-0.764580\pi\)
0.738743 0.673987i \(-0.235420\pi\)
\(318\) 0 0
\(319\) 8.00000i 0.447914i
\(320\) 32.0000i 1.78885i
\(321\) 18.0000 1.00466
\(322\) 0 0
\(323\) 4.00000i 0.222566i
\(324\) −22.0000 −1.22222
\(325\) 22.0000 33.0000i 1.22034 1.83051i
\(326\) 0 0
\(327\) 4.00000i 0.221201i
\(328\) 0 0
\(329\) −4.00000 −0.220527
\(330\) 0 0
\(331\) 4.00000i 0.219860i −0.993939 0.109930i \(-0.964937\pi\)
0.993939 0.109930i \(-0.0350627\pi\)
\(332\) 24.0000i 1.31717i
\(333\) 3.00000i 0.164399i
\(334\) 0 0
\(335\) −64.0000 −3.49669
\(336\) 16.0000i 0.872872i
\(337\) 8.00000 0.435788 0.217894 0.975972i \(-0.430081\pi\)
0.217894 + 0.975972i \(0.430081\pi\)
\(338\) 0 0
\(339\) −34.0000 −1.84663
\(340\) 16.0000i 0.867722i
\(341\) 1.00000 0.0541530
\(342\) 0 0
\(343\) 20.0000i 1.07990i
\(344\) 0 0
\(345\) 32.0000i 1.72282i
\(346\) 0 0
\(347\) −2.00000 −0.107366 −0.0536828 0.998558i \(-0.517096\pi\)
−0.0536828 + 0.998558i \(0.517096\pi\)
\(348\) 32.0000 1.71538
\(349\) 36.0000i 1.92704i 0.267644 + 0.963518i \(0.413755\pi\)
−0.267644 + 0.963518i \(0.586245\pi\)
\(350\) 0 0
\(351\) 8.00000 12.0000i 0.427008 0.640513i
\(352\) 0 0
\(353\) 15.0000i 0.798369i −0.916871 0.399185i \(-0.869293\pi\)
0.916871 0.399185i \(-0.130707\pi\)
\(354\) 0 0
\(355\) 24.0000 1.27379
\(356\) 30.0000i 1.59000i
\(357\) 8.00000i 0.423405i
\(358\) 0 0
\(359\) 20.0000i 1.05556i 0.849381 + 0.527780i \(0.176975\pi\)
−0.849381 + 0.527780i \(0.823025\pi\)
\(360\) 0 0
\(361\) 15.0000 0.789474
\(362\) 0 0
\(363\) 20.0000 1.04973
\(364\) −12.0000 8.00000i −0.628971 0.419314i
\(365\) 28.0000 1.46559
\(366\) 0 0
\(367\) 4.00000 0.208798 0.104399 0.994535i \(-0.466708\pi\)
0.104399 + 0.994535i \(0.466708\pi\)
\(368\) −16.0000 −0.834058
\(369\) 4.00000i 0.208232i
\(370\) 0 0
\(371\) 8.00000i 0.415339i
\(372\) 4.00000i 0.207390i
\(373\) 9.00000 0.466002 0.233001 0.972476i \(-0.425145\pi\)
0.233001 + 0.972476i \(0.425145\pi\)
\(374\) 0 0
\(375\) 48.0000i 2.47871i
\(376\) 0 0
\(377\) −16.0000 + 24.0000i −0.824042 + 1.23606i
\(378\) 0 0
\(379\) 20.0000i 1.02733i −0.857991 0.513665i \(-0.828287\pi\)
0.857991 0.513665i \(-0.171713\pi\)
\(380\) 16.0000 0.820783
\(381\) −8.00000 −0.409852
\(382\) 0 0
\(383\) 13.0000i 0.664269i −0.943232 0.332134i \(-0.892231\pi\)
0.943232 0.332134i \(-0.107769\pi\)
\(384\) 0 0
\(385\) 8.00000i 0.407718i
\(386\) 0 0
\(387\) 4.00000 0.203331
\(388\) 4.00000i 0.203069i
\(389\) 6.00000 0.304212 0.152106 0.988364i \(-0.451394\pi\)
0.152106 + 0.988364i \(0.451394\pi\)
\(390\) 0 0
\(391\) 8.00000 0.404577
\(392\) 0 0
\(393\) 2.00000 0.100887
\(394\) 0 0
\(395\) 64.0000i 3.22019i
\(396\) 2.00000i 0.100504i
\(397\) 6.00000i 0.301131i 0.988600 + 0.150566i \(0.0481095\pi\)
−0.988600 + 0.150566i \(0.951890\pi\)
\(398\) 0 0
\(399\) −8.00000 −0.400501
\(400\) −44.0000 −2.20000
\(401\) 29.0000i 1.44819i −0.689700 0.724095i \(-0.742257\pi\)
0.689700 0.724095i \(-0.257743\pi\)
\(402\) 0 0
\(403\) −3.00000 2.00000i −0.149441 0.0996271i
\(404\) −6.00000 −0.298511
\(405\) 44.0000i 2.18638i
\(406\) 0 0
\(407\) 3.00000 0.148704
\(408\) 0 0
\(409\) 3.00000i 0.148340i 0.997246 + 0.0741702i \(0.0236308\pi\)
−0.997246 + 0.0741702i \(0.976369\pi\)
\(410\) 0 0
\(411\) 12.0000i 0.591916i
\(412\) −30.0000 −1.47799
\(413\) 12.0000 0.590481
\(414\) 0 0
\(415\) −48.0000 −2.35623
\(416\) 0 0
\(417\) −28.0000 −1.37117
\(418\) 0 0
\(419\) −40.0000 −1.95413 −0.977064 0.212946i \(-0.931694\pi\)
−0.977064 + 0.212946i \(0.931694\pi\)
\(420\) 32.0000 1.56144
\(421\) 26.0000i 1.26716i −0.773676 0.633581i \(-0.781584\pi\)
0.773676 0.633581i \(-0.218416\pi\)
\(422\) 0 0
\(423\) 2.00000i 0.0972433i
\(424\) 0 0
\(425\) 22.0000 1.06716
\(426\) 0 0
\(427\) 20.0000i 0.967868i
\(428\) 18.0000 0.870063
\(429\) 6.00000 + 4.00000i 0.289683 + 0.193122i
\(430\) 0 0
\(431\) 18.0000i 0.867029i −0.901146 0.433515i \(-0.857273\pi\)
0.901146 0.433515i \(-0.142727\pi\)
\(432\) −16.0000 −0.769800
\(433\) 16.0000 0.768911 0.384455 0.923144i \(-0.374389\pi\)
0.384455 + 0.923144i \(0.374389\pi\)
\(434\) 0 0
\(435\) 64.0000i 3.06857i
\(436\) 4.00000i 0.191565i
\(437\) 8.00000i 0.382692i
\(438\) 0 0
\(439\) −4.00000 −0.190910 −0.0954548 0.995434i \(-0.530431\pi\)
−0.0954548 + 0.995434i \(0.530431\pi\)
\(440\) 0 0
\(441\) 3.00000 0.142857
\(442\) 0 0
\(443\) −5.00000 −0.237557 −0.118779 0.992921i \(-0.537898\pi\)
−0.118779 + 0.992921i \(0.537898\pi\)
\(444\) 12.0000i 0.569495i
\(445\) 60.0000 2.84427
\(446\) 0 0
\(447\) 44.0000i 2.08113i
\(448\) 16.0000i 0.755929i
\(449\) 6.00000i 0.283158i 0.989927 + 0.141579i \(0.0452178\pi\)
−0.989927 + 0.141579i \(0.954782\pi\)
\(450\) 0 0
\(451\) 4.00000 0.188353
\(452\) −34.0000 −1.59923
\(453\) 34.0000i 1.59746i
\(454\) 0 0
\(455\) −16.0000 + 24.0000i −0.750092 + 1.12514i
\(456\) 0 0
\(457\) 31.0000i 1.45012i 0.688686 + 0.725059i \(0.258188\pi\)
−0.688686 + 0.725059i \(0.741812\pi\)
\(458\) 0 0
\(459\) 8.00000 0.373408
\(460\) 32.0000i 1.49201i
\(461\) 11.0000i 0.512321i 0.966634 + 0.256161i \(0.0824576\pi\)
−0.966634 + 0.256161i \(0.917542\pi\)
\(462\) 0 0
\(463\) 5.00000i 0.232370i −0.993228 0.116185i \(-0.962933\pi\)
0.993228 0.116185i \(-0.0370665\pi\)
\(464\) 32.0000 1.48556
\(465\) 8.00000 0.370991
\(466\) 0 0
\(467\) −36.0000 −1.66588 −0.832941 0.553362i \(-0.813345\pi\)
−0.832941 + 0.553362i \(0.813345\pi\)
\(468\) −4.00000 + 6.00000i −0.184900 + 0.277350i
\(469\) 32.0000 1.47762
\(470\) 0 0
\(471\) 26.0000 1.19802
\(472\) 0 0
\(473\) 4.00000i 0.183920i
\(474\) 0 0
\(475\) 22.0000i 1.00943i
\(476\) 8.00000i 0.366679i
\(477\) −4.00000 −0.183147
\(478\) 0 0
\(479\) 30.0000i 1.37073i −0.728197 0.685367i \(-0.759642\pi\)
0.728197 0.685367i \(-0.240358\pi\)
\(480\) 0 0
\(481\) −9.00000 6.00000i −0.410365 0.273576i
\(482\) 0 0
\(483\) 16.0000i 0.728025i
\(484\) 20.0000 0.909091
\(485\) −8.00000 −0.363261
\(486\) 0 0
\(487\) 16.0000i 0.725029i −0.931978 0.362515i \(-0.881918\pi\)
0.931978 0.362515i \(-0.118082\pi\)
\(488\) 0 0
\(489\) 24.0000i 1.08532i
\(490\) 0 0
\(491\) 20.0000 0.902587 0.451294 0.892375i \(-0.350963\pi\)
0.451294 + 0.892375i \(0.350963\pi\)
\(492\) 16.0000i 0.721336i
\(493\) −16.0000 −0.720604
\(494\) 0 0
\(495\) −4.00000 −0.179787
\(496\) 4.00000i 0.179605i
\(497\) −12.0000 −0.538274
\(498\) 0 0
\(499\) 24.0000i 1.07439i 0.843459 + 0.537194i \(0.180516\pi\)
−0.843459 + 0.537194i \(0.819484\pi\)
\(500\) 48.0000i 2.14663i
\(501\) 6.00000i 0.268060i
\(502\) 0 0
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 12.0000i 0.533993i
\(506\) 0 0
\(507\) −10.0000 24.0000i −0.444116 1.06588i
\(508\) −8.00000 −0.354943
\(509\) 30.0000i 1.32973i −0.746965 0.664863i \(-0.768490\pi\)
0.746965 0.664863i \(-0.231510\pi\)
\(510\) 0 0
\(511\) −14.0000 −0.619324
\(512\) 0 0
\(513\) 8.00000i 0.353209i
\(514\) 0 0
\(515\) 60.0000i 2.64392i
\(516\) 16.0000 0.704361
\(517\) 2.00000 0.0879599
\(518\) 0 0
\(519\) −18.0000 −0.790112
\(520\) 0 0
\(521\) −15.0000 −0.657162 −0.328581 0.944476i \(-0.606570\pi\)
−0.328581 + 0.944476i \(0.606570\pi\)
\(522\) 0 0
\(523\) 22.0000 0.961993 0.480996 0.876723i \(-0.340275\pi\)
0.480996 + 0.876723i \(0.340275\pi\)
\(524\) 2.00000 0.0873704
\(525\) 44.0000i 1.92032i
\(526\) 0 0
\(527\) 2.00000i 0.0871214i
\(528\) 8.00000i 0.348155i
\(529\) −7.00000 −0.304348
\(530\) 0 0
\(531\) 6.00000i 0.260378i
\(532\) −8.00000 −0.346844
\(533\) −12.0000 8.00000i −0.519778 0.346518i
\(534\) 0 0
\(535\) 36.0000i 1.55642i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 3.00000i 0.129219i
\(540\) 32.0000i 1.37706i
\(541\) 20.0000i 0.859867i 0.902861 + 0.429934i \(0.141463\pi\)
−0.902861 + 0.429934i \(0.858537\pi\)
\(542\) 0 0
\(543\) −12.0000 −0.514969
\(544\) 0 0
\(545\) 8.00000 0.342682
\(546\) 0 0
\(547\) −12.0000 −0.513083 −0.256541 0.966533i \(-0.582583\pi\)
−0.256541 + 0.966533i \(0.582583\pi\)
\(548\) 12.0000i 0.512615i
\(549\) 10.0000 0.426790
\(550\) 0 0
\(551\) 16.0000i 0.681623i
\(552\) 0 0
\(553\) 32.0000i 1.36078i
\(554\) 0 0
\(555\) 24.0000 1.01874
\(556\) −28.0000 −1.18746
\(557\) 9.00000i 0.381342i 0.981654 + 0.190671i \(0.0610664\pi\)
−0.981654 + 0.190671i \(0.938934\pi\)
\(558\) 0 0
\(559\) −8.00000 + 12.0000i −0.338364 + 0.507546i
\(560\) 32.0000 1.35225
\(561\) 4.00000i 0.168880i
\(562\) 0 0
\(563\) −31.0000 −1.30649 −0.653247 0.757145i \(-0.726594\pi\)
−0.653247 + 0.757145i \(0.726594\pi\)
\(564\) 8.00000i 0.336861i
\(565\) 68.0000i 2.86078i
\(566\) 0 0
\(567\) 22.0000i 0.923913i
\(568\) 0 0
\(569\) 30.0000 1.25767 0.628833 0.777541i \(-0.283533\pi\)
0.628833 + 0.777541i \(0.283533\pi\)
\(570\) 0 0
\(571\) 18.0000 0.753277 0.376638 0.926360i \(-0.377080\pi\)
0.376638 + 0.926360i \(0.377080\pi\)
\(572\) 6.00000 + 4.00000i 0.250873 + 0.167248i
\(573\) −10.0000 −0.417756
\(574\) 0 0
\(575\) 44.0000 1.83493
\(576\) 8.00000 0.333333
\(577\) 16.0000i 0.666089i −0.942911 0.333044i \(-0.891924\pi\)
0.942911 0.333044i \(-0.108076\pi\)
\(578\) 0 0
\(579\) 28.0000i 1.16364i
\(580\) 64.0000i 2.65746i
\(581\) 24.0000 0.995688
\(582\) 0 0
\(583\) 4.00000i 0.165663i
\(584\) 0 0
\(585\) 12.0000 + 8.00000i 0.496139 + 0.330759i
\(586\) 0 0
\(587\) 31.0000i 1.27951i 0.768580 + 0.639753i \(0.220964\pi\)
−0.768580 + 0.639753i \(0.779036\pi\)
\(588\) 12.0000 0.494872
\(589\) −2.00000 −0.0824086
\(590\) 0 0
\(591\) 30.0000i 1.23404i
\(592\) 12.0000i 0.493197i
\(593\) 42.0000i 1.72473i 0.506284 + 0.862367i \(0.331019\pi\)
−0.506284 + 0.862367i \(0.668981\pi\)
\(594\) 0 0
\(595\) −16.0000 −0.655936
\(596\) 44.0000i 1.80231i
\(597\) 20.0000 0.818546
\(598\) 0 0
\(599\) −24.0000 −0.980613 −0.490307 0.871550i \(-0.663115\pi\)
−0.490307 + 0.871550i \(0.663115\pi\)
\(600\) 0 0
\(601\) −24.0000 −0.978980 −0.489490 0.872009i \(-0.662817\pi\)
−0.489490 + 0.872009i \(0.662817\pi\)
\(602\) 0 0
\(603\) 16.0000i 0.651570i
\(604\) 34.0000i 1.38344i
\(605\) 40.0000i 1.62623i
\(606\) 0 0
\(607\) 37.0000 1.50178 0.750892 0.660425i \(-0.229624\pi\)
0.750892 + 0.660425i \(0.229624\pi\)
\(608\) 0 0
\(609\) 32.0000i 1.29671i
\(610\) 0 0
\(611\) −6.00000 4.00000i −0.242734 0.161823i
\(612\) −4.00000 −0.161690
\(613\) 30.0000i 1.21169i 0.795583 + 0.605844i \(0.207165\pi\)
−0.795583 + 0.605844i \(0.792835\pi\)
\(614\) 0 0
\(615\) 32.0000 1.29036
\(616\) 0 0
\(617\) 22.0000i 0.885687i 0.896599 + 0.442843i \(0.146030\pi\)
−0.896599 + 0.442843i \(0.853970\pi\)
\(618\) 0 0
\(619\) 15.0000i 0.602901i −0.953482 0.301450i \(-0.902529\pi\)
0.953482 0.301450i \(-0.0974708\pi\)
\(620\) 8.00000 0.321288
\(621\) 16.0000 0.642058
\(622\) 0 0
\(623\) −30.0000 −1.20192
\(624\) −16.0000 + 24.0000i −0.640513 + 0.960769i
\(625\) 41.0000 1.64000
\(626\) 0 0
\(627\) 4.00000 0.159745
\(628\) 26.0000 1.03751
\(629\) 6.00000i 0.239236i
\(630\) 0 0
\(631\) 35.0000i 1.39333i 0.717398 + 0.696664i \(0.245333\pi\)
−0.717398 + 0.696664i \(0.754667\pi\)
\(632\) 0 0
\(633\) 38.0000 1.51036
\(634\) 0 0
\(635\) 16.0000i 0.634941i
\(636\) −16.0000 −0.634441
\(637\) −6.00000 + 9.00000i −0.237729 + 0.356593i
\(638\) 0 0
\(639\) 6.00000i 0.237356i
\(640\) 0 0
\(641\) 42.0000 1.65890 0.829450 0.558581i \(-0.188654\pi\)
0.829450 + 0.558581i \(0.188654\pi\)
\(642\) 0 0
\(643\) 49.0000i 1.93237i −0.257847 0.966186i \(-0.583013\pi\)
0.257847 0.966186i \(-0.416987\pi\)
\(644\) 16.0000i 0.630488i
\(645\) 32.0000i 1.26000i
\(646\) 0 0
\(647\) −6.00000 −0.235884 −0.117942 0.993020i \(-0.537630\pi\)
−0.117942 + 0.993020i \(0.537630\pi\)
\(648\) 0 0
\(649\) −6.00000 −0.235521
\(650\) 0 0
\(651\) −4.00000 −0.156772
\(652\) 24.0000i 0.939913i
\(653\) −21.0000 −0.821794 −0.410897 0.911682i \(-0.634784\pi\)
−0.410897 + 0.911682i \(0.634784\pi\)
\(654\) 0 0
\(655\) 4.00000i 0.156293i
\(656\) 16.0000i 0.624695i
\(657\) 7.00000i 0.273096i
\(658\) 0 0
\(659\) −20.0000 −0.779089 −0.389545 0.921008i \(-0.627368\pi\)
−0.389545 + 0.921008i \(0.627368\pi\)
\(660\) −16.0000 −0.622799
\(661\) 42.0000i 1.63361i −0.576913 0.816805i \(-0.695743\pi\)
0.576913 0.816805i \(-0.304257\pi\)
\(662\) 0 0
\(663\) 8.00000 12.0000i 0.310694 0.466041i
\(664\) 0 0
\(665\) 16.0000i 0.620453i
\(666\) 0 0
\(667\) −32.0000 −1.23904
\(668\) 6.00000i 0.232147i
\(669\) 38.0000i 1.46916i
\(670\) 0 0
\(671\) 10.0000i 0.386046i
\(672\) 0 0
\(673\) 10.0000 0.385472 0.192736 0.981251i \(-0.438264\pi\)
0.192736 + 0.981251i \(0.438264\pi\)
\(674\) 0 0
\(675\) 44.0000 1.69356
\(676\) −10.0000 24.0000i −0.384615 0.923077i
\(677\) −16.0000 −0.614930 −0.307465 0.951559i \(-0.599481\pi\)
−0.307465 + 0.951559i \(0.599481\pi\)
\(678\) 0 0
\(679\) 4.00000 0.153506
\(680\) 0 0
\(681\) 16.0000i 0.613121i
\(682\) 0 0
\(683\) 32.0000i 1.22445i −0.790685 0.612223i \(-0.790275\pi\)
0.790685 0.612223i \(-0.209725\pi\)
\(684\) 4.00000i 0.152944i
\(685\) −24.0000 −0.916993
\(686\) 0 0
\(687\) 58.0000i 2.21284i
\(688\) 16.0000 0.609994
\(689\) 8.00000 12.0000i 0.304776 0.457164i
\(690\) 0 0
\(691\) 12.0000i 0.456502i −0.973602 0.228251i \(-0.926699\pi\)
0.973602 0.228251i \(-0.0733006\pi\)
\(692\) −18.0000 −0.684257
\(693\) 2.00000 0.0759737
\(694\) 0 0
\(695\) 56.0000i 2.12420i
\(696\) 0 0
\(697\) 8.00000i 0.303022i
\(698\) 0 0
\(699\) 26.0000 0.983410
\(700\) 44.0000i 1.66304i
\(701\) 41.0000 1.54855 0.774274 0.632850i \(-0.218115\pi\)
0.774274 + 0.632850i \(0.218115\pi\)
\(702\) 0 0
\(703\) −6.00000 −0.226294
\(704\) 8.00000i 0.301511i
\(705\) 16.0000 0.602595
\(706\) 0 0
\(707\) 6.00000i 0.225653i
\(708\) 24.0000i 0.901975i
\(709\) 25.0000i 0.938895i −0.882960 0.469447i \(-0.844453\pi\)
0.882960 0.469447i \(-0.155547\pi\)
\(710\) 0 0
\(711\) −16.0000 −0.600047
\(712\) 0 0
\(713\) 4.00000i 0.149801i
\(714\) 0 0
\(715\) 8.00000 12.0000i 0.299183 0.448775i
\(716\) 0 0
\(717\) 32.0000i 1.19506i
\(718\) 0 0
\(719\) 24.0000 0.895049 0.447524 0.894272i \(-0.352306\pi\)
0.447524 + 0.894272i \(0.352306\pi\)
\(720\) 16.0000i 0.596285i
\(721\) 30.0000i 1.11726i
\(722\) 0 0
\(723\) 28.0000i 1.04133i
\(724\) −12.0000 −0.445976
\(725\) −88.0000 −3.26824
\(726\) 0 0
\(727\) 20.0000 0.741759 0.370879 0.928681i \(-0.379056\pi\)
0.370879 + 0.928681i \(0.379056\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) −8.00000 −0.295891
\(732\) 40.0000 1.47844
\(733\) 8.00000i 0.295487i 0.989026 + 0.147743i \(0.0472010\pi\)
−0.989026 + 0.147743i \(0.952799\pi\)
\(734\) 0 0
\(735\) 24.0000i 0.885253i
\(736\) 0 0
\(737\) −16.0000 −0.589368
\(738\) 0 0
\(739\) 23.0000i 0.846069i 0.906114 + 0.423034i \(0.139035\pi\)
−0.906114 + 0.423034i \(0.860965\pi\)
\(740\) 24.0000 0.882258
\(741\) −12.0000 8.00000i −0.440831 0.293887i
\(742\) 0 0
\(743\) 33.0000i 1.21065i 0.795977 + 0.605326i \(0.206957\pi\)
−0.795977 + 0.605326i \(0.793043\pi\)
\(744\) 0 0
\(745\) −88.0000 −3.22407
\(746\) 0 0
\(747\) 12.0000i 0.439057i
\(748\) 4.00000i 0.146254i
\(749\) 18.0000i 0.657706i
\(750\) 0 0
\(751\) 35.0000 1.27717 0.638584 0.769552i \(-0.279520\pi\)
0.638584 + 0.769552i \(0.279520\pi\)
\(752\) 8.00000i 0.291730i
\(753\) 44.0000 1.60345
\(754\) 0 0
\(755\) −68.0000 −2.47477
\(756\) 16.0000i 0.581914i
\(757\) 10.0000 0.363456 0.181728 0.983349i \(-0.441831\pi\)
0.181728 + 0.983349i \(0.441831\pi\)
\(758\) 0 0
\(759\) 8.00000i 0.290382i
\(760\) 0 0
\(761\) 22.0000i 0.797499i 0.917060 + 0.398750i \(0.130556\pi\)
−0.917060 + 0.398750i \(0.869444\pi\)
\(762\) 0 0
\(763\) −4.00000 −0.144810
\(764\) −10.0000 −0.361787
\(765\) 8.00000i 0.289241i
\(766\) 0 0
\(767\) 18.0000 + 12.0000i 0.649942 + 0.433295i
\(768\) 32.0000 1.15470
\(769\) 2.00000i 0.0721218i 0.999350 + 0.0360609i \(0.0114810\pi\)
−0.999350 + 0.0360609i \(0.988519\pi\)
\(770\) 0 0
\(771\) 42.0000 1.51259
\(772\) 28.0000i 1.00774i
\(773\) 47.0000i 1.69047i 0.534393 + 0.845236i \(0.320540\pi\)
−0.534393 + 0.845236i \(0.679460\pi\)
\(774\) 0 0
\(775\) 11.0000i 0.395132i
\(776\) 0 0
\(777\) −12.0000 −0.430498
\(778\) 0 0
\(779\) −8.00000 −0.286630
\(780\) 48.0000 + 32.0000i 1.71868 + 1.14578i
\(781\) 6.00000 0.214697
\(782\) 0 0
\(783\) −32.0000 −1.14359
\(784\) 12.0000 0.428571
\(785\) 52.0000i 1.85596i
\(786\) 0 0
\(787\) 3.00000i 0.106938i −0.998569 0.0534692i \(-0.982972\pi\)
0.998569 0.0534692i \(-0.0170279\pi\)
\(788\) 30.0000i 1.06871i
\(789\) −48.0000 −1.70885
\(790\) 0 0
\(791\) 34.0000i 1.20890i
\(792\) 0 0
\(793\) −20.0000 + 30.0000i −0.710221 + 1.06533i
\(794\) 0 0
\(795\) 32.0000i 1.13492i
\(796\) 20.0000 0.708881
\(797\) −42.0000 −1.48772 −0.743858 0.668338i \(-0.767006\pi\)
−0.743858 + 0.668338i \(0.767006\pi\)
\(798\) 0 0
\(799\) 4.00000i 0.141510i
\(800\) 0 0
\(801\) 15.0000i 0.529999i
\(802\) 0 0
\(803\) 7.00000 0.247025
\(804\) 64.0000i 2.25711i
\(805\) −32.0000 −1.12785
\(806\) 0 0
\(807\) 20.0000 0.704033
\(808\) 0 0
\(809\) −30.0000 −1.05474 −0.527372 0.849635i \(-0.676823\pi\)
−0.527372 + 0.849635i \(0.676823\pi\)
\(810\) 0 0