Properties

Label 2352.2.q.l.1537.1
Level $2352$
Weight $2$
Character 2352.1537
Analytic conductor $18.781$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2352.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.7808145554\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 24)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1537.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 2352.1537
Dual form 2352.2.q.l.961.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{3} +(1.00000 + 1.73205i) q^{5} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{3} +(1.00000 + 1.73205i) q^{5} +(-0.500000 - 0.866025i) q^{9} +(2.00000 - 3.46410i) q^{11} -2.00000 q^{13} -2.00000 q^{15} +(-1.00000 + 1.73205i) q^{17} +(-2.00000 - 3.46410i) q^{19} +(-4.00000 - 6.92820i) q^{23} +(0.500000 - 0.866025i) q^{25} +1.00000 q^{27} +6.00000 q^{29} +(4.00000 - 6.92820i) q^{31} +(2.00000 + 3.46410i) q^{33} +(-3.00000 - 5.19615i) q^{37} +(1.00000 - 1.73205i) q^{39} -6.00000 q^{41} -4.00000 q^{43} +(1.00000 - 1.73205i) q^{45} +(-1.00000 - 1.73205i) q^{51} +(1.00000 - 1.73205i) q^{53} +8.00000 q^{55} +4.00000 q^{57} +(2.00000 - 3.46410i) q^{59} +(1.00000 + 1.73205i) q^{61} +(-2.00000 - 3.46410i) q^{65} +(-2.00000 + 3.46410i) q^{67} +8.00000 q^{69} -8.00000 q^{71} +(-5.00000 + 8.66025i) q^{73} +(0.500000 + 0.866025i) q^{75} +(-4.00000 - 6.92820i) q^{79} +(-0.500000 + 0.866025i) q^{81} +4.00000 q^{83} -4.00000 q^{85} +(-3.00000 + 5.19615i) q^{87} +(3.00000 + 5.19615i) q^{89} +(4.00000 + 6.92820i) q^{93} +(4.00000 - 6.92820i) q^{95} +2.00000 q^{97} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{3} + 2q^{5} - q^{9} + O(q^{10}) \) \( 2q - q^{3} + 2q^{5} - q^{9} + 4q^{11} - 4q^{13} - 4q^{15} - 2q^{17} - 4q^{19} - 8q^{23} + q^{25} + 2q^{27} + 12q^{29} + 8q^{31} + 4q^{33} - 6q^{37} + 2q^{39} - 12q^{41} - 8q^{43} + 2q^{45} - 2q^{51} + 2q^{53} + 16q^{55} + 8q^{57} + 4q^{59} + 2q^{61} - 4q^{65} - 4q^{67} + 16q^{69} - 16q^{71} - 10q^{73} + q^{75} - 8q^{79} - q^{81} + 8q^{83} - 8q^{85} - 6q^{87} + 6q^{89} + 8q^{93} + 8q^{95} + 4q^{97} - 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1471\) \(1765\) \(2257\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) 0 0
\(5\) 1.00000 + 1.73205i 0.447214 + 0.774597i 0.998203 0.0599153i \(-0.0190830\pi\)
−0.550990 + 0.834512i \(0.685750\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0 0
\(11\) 2.00000 3.46410i 0.603023 1.04447i −0.389338 0.921095i \(-0.627296\pi\)
0.992361 0.123371i \(-0.0393705\pi\)
\(12\) 0 0
\(13\) −2.00000 −0.554700 −0.277350 0.960769i \(-0.589456\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) 0 0
\(15\) −2.00000 −0.516398
\(16\) 0 0
\(17\) −1.00000 + 1.73205i −0.242536 + 0.420084i −0.961436 0.275029i \(-0.911312\pi\)
0.718900 + 0.695113i \(0.244646\pi\)
\(18\) 0 0
\(19\) −2.00000 3.46410i −0.458831 0.794719i 0.540068 0.841621i \(-0.318398\pi\)
−0.998899 + 0.0469020i \(0.985065\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −4.00000 6.92820i −0.834058 1.44463i −0.894795 0.446476i \(-0.852679\pi\)
0.0607377 0.998154i \(-0.480655\pi\)
\(24\) 0 0
\(25\) 0.500000 0.866025i 0.100000 0.173205i
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) 4.00000 6.92820i 0.718421 1.24434i −0.243204 0.969975i \(-0.578198\pi\)
0.961625 0.274367i \(-0.0884683\pi\)
\(32\) 0 0
\(33\) 2.00000 + 3.46410i 0.348155 + 0.603023i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −3.00000 5.19615i −0.493197 0.854242i 0.506772 0.862080i \(-0.330838\pi\)
−0.999969 + 0.00783774i \(0.997505\pi\)
\(38\) 0 0
\(39\) 1.00000 1.73205i 0.160128 0.277350i
\(40\) 0 0
\(41\) −6.00000 −0.937043 −0.468521 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) 0 0
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) 0 0
\(45\) 1.00000 1.73205i 0.149071 0.258199i
\(46\) 0 0
\(47\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −1.00000 1.73205i −0.140028 0.242536i
\(52\) 0 0
\(53\) 1.00000 1.73205i 0.137361 0.237915i −0.789136 0.614218i \(-0.789471\pi\)
0.926497 + 0.376303i \(0.122805\pi\)
\(54\) 0 0
\(55\) 8.00000 1.07872
\(56\) 0 0
\(57\) 4.00000 0.529813
\(58\) 0 0
\(59\) 2.00000 3.46410i 0.260378 0.450988i −0.705965 0.708247i \(-0.749486\pi\)
0.966342 + 0.257260i \(0.0828195\pi\)
\(60\) 0 0
\(61\) 1.00000 + 1.73205i 0.128037 + 0.221766i 0.922916 0.385002i \(-0.125799\pi\)
−0.794879 + 0.606768i \(0.792466\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −2.00000 3.46410i −0.248069 0.429669i
\(66\) 0 0
\(67\) −2.00000 + 3.46410i −0.244339 + 0.423207i −0.961946 0.273241i \(-0.911904\pi\)
0.717607 + 0.696449i \(0.245238\pi\)
\(68\) 0 0
\(69\) 8.00000 0.963087
\(70\) 0 0
\(71\) −8.00000 −0.949425 −0.474713 0.880141i \(-0.657448\pi\)
−0.474713 + 0.880141i \(0.657448\pi\)
\(72\) 0 0
\(73\) −5.00000 + 8.66025i −0.585206 + 1.01361i 0.409644 + 0.912245i \(0.365653\pi\)
−0.994850 + 0.101361i \(0.967680\pi\)
\(74\) 0 0
\(75\) 0.500000 + 0.866025i 0.0577350 + 0.100000i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −4.00000 6.92820i −0.450035 0.779484i 0.548352 0.836247i \(-0.315255\pi\)
−0.998388 + 0.0567635i \(0.981922\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 4.00000 0.439057 0.219529 0.975606i \(-0.429548\pi\)
0.219529 + 0.975606i \(0.429548\pi\)
\(84\) 0 0
\(85\) −4.00000 −0.433861
\(86\) 0 0
\(87\) −3.00000 + 5.19615i −0.321634 + 0.557086i
\(88\) 0 0
\(89\) 3.00000 + 5.19615i 0.317999 + 0.550791i 0.980071 0.198650i \(-0.0636557\pi\)
−0.662071 + 0.749441i \(0.730322\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 4.00000 + 6.92820i 0.414781 + 0.718421i
\(94\) 0 0
\(95\) 4.00000 6.92820i 0.410391 0.710819i
\(96\) 0 0
\(97\) 2.00000 0.203069 0.101535 0.994832i \(-0.467625\pi\)
0.101535 + 0.994832i \(0.467625\pi\)
\(98\) 0 0
\(99\) −4.00000 −0.402015
\(100\) 0 0
\(101\) 9.00000 15.5885i 0.895533 1.55111i 0.0623905 0.998052i \(-0.480128\pi\)
0.833143 0.553058i \(-0.186539\pi\)
\(102\) 0 0
\(103\) 8.00000 + 13.8564i 0.788263 + 1.36531i 0.927030 + 0.374987i \(0.122353\pi\)
−0.138767 + 0.990325i \(0.544314\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −6.00000 10.3923i −0.580042 1.00466i −0.995474 0.0950377i \(-0.969703\pi\)
0.415432 0.909624i \(-0.363630\pi\)
\(108\) 0 0
\(109\) 1.00000 1.73205i 0.0957826 0.165900i −0.814152 0.580651i \(-0.802798\pi\)
0.909935 + 0.414751i \(0.136131\pi\)
\(110\) 0 0
\(111\) 6.00000 0.569495
\(112\) 0 0
\(113\) 18.0000 1.69330 0.846649 0.532152i \(-0.178617\pi\)
0.846649 + 0.532152i \(0.178617\pi\)
\(114\) 0 0
\(115\) 8.00000 13.8564i 0.746004 1.29212i
\(116\) 0 0
\(117\) 1.00000 + 1.73205i 0.0924500 + 0.160128i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −2.50000 4.33013i −0.227273 0.393648i
\(122\) 0 0
\(123\) 3.00000 5.19615i 0.270501 0.468521i
\(124\) 0 0
\(125\) 12.0000 1.07331
\(126\) 0 0
\(127\) 8.00000 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) 0 0
\(129\) 2.00000 3.46410i 0.176090 0.304997i
\(130\) 0 0
\(131\) −2.00000 3.46410i −0.174741 0.302660i 0.765331 0.643637i \(-0.222575\pi\)
−0.940072 + 0.340977i \(0.889242\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 1.00000 + 1.73205i 0.0860663 + 0.149071i
\(136\) 0 0
\(137\) 3.00000 5.19615i 0.256307 0.443937i −0.708942 0.705266i \(-0.750827\pi\)
0.965250 + 0.261329i \(0.0841608\pi\)
\(138\) 0 0
\(139\) 12.0000 1.01783 0.508913 0.860818i \(-0.330047\pi\)
0.508913 + 0.860818i \(0.330047\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −4.00000 + 6.92820i −0.334497 + 0.579365i
\(144\) 0 0
\(145\) 6.00000 + 10.3923i 0.498273 + 0.863034i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −7.00000 12.1244i −0.573462 0.993266i −0.996207 0.0870170i \(-0.972267\pi\)
0.422744 0.906249i \(-0.361067\pi\)
\(150\) 0 0
\(151\) −8.00000 + 13.8564i −0.651031 + 1.12762i 0.331842 + 0.943335i \(0.392330\pi\)
−0.982873 + 0.184284i \(0.941004\pi\)
\(152\) 0 0
\(153\) 2.00000 0.161690
\(154\) 0 0
\(155\) 16.0000 1.28515
\(156\) 0 0
\(157\) 1.00000 1.73205i 0.0798087 0.138233i −0.823359 0.567521i \(-0.807902\pi\)
0.903167 + 0.429289i \(0.141236\pi\)
\(158\) 0 0
\(159\) 1.00000 + 1.73205i 0.0793052 + 0.137361i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 6.00000 + 10.3923i 0.469956 + 0.813988i 0.999410 0.0343508i \(-0.0109363\pi\)
−0.529454 + 0.848339i \(0.677603\pi\)
\(164\) 0 0
\(165\) −4.00000 + 6.92820i −0.311400 + 0.539360i
\(166\) 0 0
\(167\) −24.0000 −1.85718 −0.928588 0.371113i \(-0.878976\pi\)
−0.928588 + 0.371113i \(0.878976\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) −2.00000 + 3.46410i −0.152944 + 0.264906i
\(172\) 0 0
\(173\) −3.00000 5.19615i −0.228086 0.395056i 0.729155 0.684349i \(-0.239913\pi\)
−0.957241 + 0.289292i \(0.906580\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 2.00000 + 3.46410i 0.150329 + 0.260378i
\(178\) 0 0
\(179\) 6.00000 10.3923i 0.448461 0.776757i −0.549825 0.835280i \(-0.685306\pi\)
0.998286 + 0.0585225i \(0.0186389\pi\)
\(180\) 0 0
\(181\) 6.00000 0.445976 0.222988 0.974821i \(-0.428419\pi\)
0.222988 + 0.974821i \(0.428419\pi\)
\(182\) 0 0
\(183\) −2.00000 −0.147844
\(184\) 0 0
\(185\) 6.00000 10.3923i 0.441129 0.764057i
\(186\) 0 0
\(187\) 4.00000 + 6.92820i 0.292509 + 0.506640i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(192\) 0 0
\(193\) −1.00000 + 1.73205i −0.0719816 + 0.124676i −0.899770 0.436365i \(-0.856266\pi\)
0.827788 + 0.561041i \(0.189599\pi\)
\(194\) 0 0
\(195\) 4.00000 0.286446
\(196\) 0 0
\(197\) −18.0000 −1.28245 −0.641223 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) 0 0
\(199\) 8.00000 13.8564i 0.567105 0.982255i −0.429745 0.902950i \(-0.641397\pi\)
0.996850 0.0793045i \(-0.0252700\pi\)
\(200\) 0 0
\(201\) −2.00000 3.46410i −0.141069 0.244339i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −6.00000 10.3923i −0.419058 0.725830i
\(206\) 0 0
\(207\) −4.00000 + 6.92820i −0.278019 + 0.481543i
\(208\) 0 0
\(209\) −16.0000 −1.10674
\(210\) 0 0
\(211\) 20.0000 1.37686 0.688428 0.725304i \(-0.258301\pi\)
0.688428 + 0.725304i \(0.258301\pi\)
\(212\) 0 0
\(213\) 4.00000 6.92820i 0.274075 0.474713i
\(214\) 0 0
\(215\) −4.00000 6.92820i −0.272798 0.472500i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −5.00000 8.66025i −0.337869 0.585206i
\(220\) 0 0
\(221\) 2.00000 3.46410i 0.134535 0.233021i
\(222\) 0 0
\(223\) 8.00000 0.535720 0.267860 0.963458i \(-0.413684\pi\)
0.267860 + 0.963458i \(0.413684\pi\)
\(224\) 0 0
\(225\) −1.00000 −0.0666667
\(226\) 0 0
\(227\) 6.00000 10.3923i 0.398234 0.689761i −0.595274 0.803523i \(-0.702957\pi\)
0.993508 + 0.113761i \(0.0362899\pi\)
\(228\) 0 0
\(229\) −11.0000 19.0526i −0.726900 1.25903i −0.958187 0.286143i \(-0.907627\pi\)
0.231287 0.972886i \(-0.425707\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −5.00000 8.66025i −0.327561 0.567352i 0.654466 0.756091i \(-0.272893\pi\)
−0.982027 + 0.188739i \(0.939560\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 8.00000 0.519656
\(238\) 0 0
\(239\) 16.0000 1.03495 0.517477 0.855697i \(-0.326871\pi\)
0.517477 + 0.855697i \(0.326871\pi\)
\(240\) 0 0
\(241\) −9.00000 + 15.5885i −0.579741 + 1.00414i 0.415768 + 0.909471i \(0.363513\pi\)
−0.995509 + 0.0946700i \(0.969820\pi\)
\(242\) 0 0
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 4.00000 + 6.92820i 0.254514 + 0.440831i
\(248\) 0 0
\(249\) −2.00000 + 3.46410i −0.126745 + 0.219529i
\(250\) 0 0
\(251\) −20.0000 −1.26239 −0.631194 0.775625i \(-0.717435\pi\)
−0.631194 + 0.775625i \(0.717435\pi\)
\(252\) 0 0
\(253\) −32.0000 −2.01182
\(254\) 0 0
\(255\) 2.00000 3.46410i 0.125245 0.216930i
\(256\) 0 0
\(257\) −1.00000 1.73205i −0.0623783 0.108042i 0.833150 0.553047i \(-0.186535\pi\)
−0.895528 + 0.445005i \(0.853202\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −3.00000 5.19615i −0.185695 0.321634i
\(262\) 0 0
\(263\) −4.00000 + 6.92820i −0.246651 + 0.427211i −0.962594 0.270947i \(-0.912663\pi\)
0.715944 + 0.698158i \(0.245997\pi\)
\(264\) 0 0
\(265\) 4.00000 0.245718
\(266\) 0 0
\(267\) −6.00000 −0.367194
\(268\) 0 0
\(269\) 5.00000 8.66025i 0.304855 0.528025i −0.672374 0.740212i \(-0.734725\pi\)
0.977229 + 0.212187i \(0.0680585\pi\)
\(270\) 0 0
\(271\) 4.00000 + 6.92820i 0.242983 + 0.420858i 0.961563 0.274586i \(-0.0885408\pi\)
−0.718580 + 0.695444i \(0.755208\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −2.00000 3.46410i −0.120605 0.208893i
\(276\) 0 0
\(277\) 13.0000 22.5167i 0.781094 1.35290i −0.150210 0.988654i \(-0.547995\pi\)
0.931305 0.364241i \(-0.118672\pi\)
\(278\) 0 0
\(279\) −8.00000 −0.478947
\(280\) 0 0
\(281\) 26.0000 1.55103 0.775515 0.631329i \(-0.217490\pi\)
0.775515 + 0.631329i \(0.217490\pi\)
\(282\) 0 0
\(283\) −14.0000 + 24.2487i −0.832214 + 1.44144i 0.0640654 + 0.997946i \(0.479593\pi\)
−0.896279 + 0.443491i \(0.853740\pi\)
\(284\) 0 0
\(285\) 4.00000 + 6.92820i 0.236940 + 0.410391i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 6.50000 + 11.2583i 0.382353 + 0.662255i
\(290\) 0 0
\(291\) −1.00000 + 1.73205i −0.0586210 + 0.101535i
\(292\) 0 0
\(293\) −18.0000 −1.05157 −0.525786 0.850617i \(-0.676229\pi\)
−0.525786 + 0.850617i \(0.676229\pi\)
\(294\) 0 0
\(295\) 8.00000 0.465778
\(296\) 0 0
\(297\) 2.00000 3.46410i 0.116052 0.201008i
\(298\) 0 0
\(299\) 8.00000 + 13.8564i 0.462652 + 0.801337i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 9.00000 + 15.5885i 0.517036 + 0.895533i
\(304\) 0 0
\(305\) −2.00000 + 3.46410i −0.114520 + 0.198354i
\(306\) 0 0
\(307\) −12.0000 −0.684876 −0.342438 0.939540i \(-0.611253\pi\)
−0.342438 + 0.939540i \(0.611253\pi\)
\(308\) 0 0
\(309\) −16.0000 −0.910208
\(310\) 0 0
\(311\) −12.0000 + 20.7846i −0.680458 + 1.17859i 0.294384 + 0.955687i \(0.404886\pi\)
−0.974841 + 0.222900i \(0.928448\pi\)
\(312\) 0 0
\(313\) 3.00000 + 5.19615i 0.169570 + 0.293704i 0.938269 0.345907i \(-0.112429\pi\)
−0.768699 + 0.639611i \(0.779095\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −3.00000 5.19615i −0.168497 0.291845i 0.769395 0.638774i \(-0.220558\pi\)
−0.937892 + 0.346929i \(0.887225\pi\)
\(318\) 0 0
\(319\) 12.0000 20.7846i 0.671871 1.16371i
\(320\) 0 0
\(321\) 12.0000 0.669775
\(322\) 0 0
\(323\) 8.00000 0.445132
\(324\) 0 0
\(325\) −1.00000 + 1.73205i −0.0554700 + 0.0960769i
\(326\) 0 0
\(327\) 1.00000 + 1.73205i 0.0553001 + 0.0957826i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 10.0000 + 17.3205i 0.549650 + 0.952021i 0.998298 + 0.0583130i \(0.0185721\pi\)
−0.448649 + 0.893708i \(0.648095\pi\)
\(332\) 0 0
\(333\) −3.00000 + 5.19615i −0.164399 + 0.284747i
\(334\) 0 0
\(335\) −8.00000 −0.437087
\(336\) 0 0
\(337\) 18.0000 0.980522 0.490261 0.871576i \(-0.336901\pi\)
0.490261 + 0.871576i \(0.336901\pi\)
\(338\) 0 0
\(339\) −9.00000 + 15.5885i −0.488813 + 0.846649i
\(340\) 0 0
\(341\) −16.0000 27.7128i −0.866449 1.50073i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 8.00000 + 13.8564i 0.430706 + 0.746004i
\(346\) 0 0
\(347\) −6.00000 + 10.3923i −0.322097 + 0.557888i −0.980921 0.194409i \(-0.937721\pi\)
0.658824 + 0.752297i \(0.271054\pi\)
\(348\) 0 0
\(349\) 30.0000 1.60586 0.802932 0.596071i \(-0.203272\pi\)
0.802932 + 0.596071i \(0.203272\pi\)
\(350\) 0 0
\(351\) −2.00000 −0.106752
\(352\) 0 0
\(353\) −1.00000 + 1.73205i −0.0532246 + 0.0921878i −0.891410 0.453197i \(-0.850283\pi\)
0.838186 + 0.545385i \(0.183617\pi\)
\(354\) 0 0
\(355\) −8.00000 13.8564i −0.424596 0.735422i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −12.0000 20.7846i −0.633336 1.09697i −0.986865 0.161546i \(-0.948352\pi\)
0.353529 0.935423i \(-0.384981\pi\)
\(360\) 0 0
\(361\) 1.50000 2.59808i 0.0789474 0.136741i
\(362\) 0 0
\(363\) 5.00000 0.262432
\(364\) 0 0
\(365\) −20.0000 −1.04685
\(366\) 0 0
\(367\) −4.00000 + 6.92820i −0.208798 + 0.361649i −0.951336 0.308155i \(-0.900289\pi\)
0.742538 + 0.669804i \(0.233622\pi\)
\(368\) 0 0
\(369\) 3.00000 + 5.19615i 0.156174 + 0.270501i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 5.00000 + 8.66025i 0.258890 + 0.448411i 0.965945 0.258748i \(-0.0833099\pi\)
−0.707055 + 0.707159i \(0.749977\pi\)
\(374\) 0 0
\(375\) −6.00000 + 10.3923i −0.309839 + 0.536656i
\(376\) 0 0
\(377\) −12.0000 −0.618031
\(378\) 0 0
\(379\) −20.0000 −1.02733 −0.513665 0.857991i \(-0.671713\pi\)
−0.513665 + 0.857991i \(0.671713\pi\)
\(380\) 0 0
\(381\) −4.00000 + 6.92820i −0.204926 + 0.354943i
\(382\) 0 0
\(383\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 2.00000 + 3.46410i 0.101666 + 0.176090i
\(388\) 0 0
\(389\) 1.00000 1.73205i 0.0507020 0.0878185i −0.839561 0.543266i \(-0.817187\pi\)
0.890263 + 0.455448i \(0.150521\pi\)
\(390\) 0 0
\(391\) 16.0000 0.809155
\(392\) 0 0
\(393\) 4.00000 0.201773
\(394\) 0 0
\(395\) 8.00000 13.8564i 0.402524 0.697191i
\(396\) 0 0
\(397\) −7.00000 12.1244i −0.351320 0.608504i 0.635161 0.772380i \(-0.280934\pi\)
−0.986481 + 0.163876i \(0.947600\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 15.0000 + 25.9808i 0.749064 + 1.29742i 0.948272 + 0.317460i \(0.102830\pi\)
−0.199207 + 0.979957i \(0.563837\pi\)
\(402\) 0 0
\(403\) −8.00000 + 13.8564i −0.398508 + 0.690237i
\(404\) 0 0
\(405\) −2.00000 −0.0993808
\(406\) 0 0
\(407\) −24.0000 −1.18964
\(408\) 0 0
\(409\) 3.00000 5.19615i 0.148340 0.256933i −0.782274 0.622935i \(-0.785940\pi\)
0.930614 + 0.366002i \(0.119274\pi\)
\(410\) 0 0
\(411\) 3.00000 + 5.19615i 0.147979 + 0.256307i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 4.00000 + 6.92820i 0.196352 + 0.340092i
\(416\) 0 0
\(417\) −6.00000 + 10.3923i −0.293821 + 0.508913i
\(418\) 0 0
\(419\) −12.0000 −0.586238 −0.293119 0.956076i \(-0.594693\pi\)
−0.293119 + 0.956076i \(0.594693\pi\)
\(420\) 0 0
\(421\) −10.0000 −0.487370 −0.243685 0.969854i \(-0.578356\pi\)
−0.243685 + 0.969854i \(0.578356\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 1.00000 + 1.73205i 0.0485071 + 0.0840168i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −4.00000 6.92820i −0.193122 0.334497i
\(430\) 0 0
\(431\) 16.0000 27.7128i 0.770693 1.33488i −0.166491 0.986043i \(-0.553244\pi\)
0.937184 0.348836i \(-0.113423\pi\)
\(432\) 0 0
\(433\) −14.0000 −0.672797 −0.336399 0.941720i \(-0.609209\pi\)
−0.336399 + 0.941720i \(0.609209\pi\)
\(434\) 0 0
\(435\) −12.0000 −0.575356
\(436\) 0 0
\(437\) −16.0000 + 27.7128i −0.765384 + 1.32568i
\(438\) 0 0
\(439\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 10.0000 + 17.3205i 0.475114 + 0.822922i 0.999594 0.0285009i \(-0.00907336\pi\)
−0.524479 + 0.851423i \(0.675740\pi\)
\(444\) 0 0
\(445\) −6.00000 + 10.3923i −0.284427 + 0.492642i
\(446\) 0 0
\(447\) 14.0000 0.662177
\(448\) 0 0
\(449\) −14.0000 −0.660701 −0.330350 0.943858i \(-0.607167\pi\)
−0.330350 + 0.943858i \(0.607167\pi\)
\(450\) 0 0
\(451\) −12.0000 + 20.7846i −0.565058 + 0.978709i
\(452\) 0 0
\(453\) −8.00000 13.8564i −0.375873 0.651031i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 11.0000 + 19.0526i 0.514558 + 0.891241i 0.999857 + 0.0168929i \(0.00537742\pi\)
−0.485299 + 0.874348i \(0.661289\pi\)
\(458\) 0 0
\(459\) −1.00000 + 1.73205i −0.0466760 + 0.0808452i
\(460\) 0 0
\(461\) −26.0000 −1.21094 −0.605470 0.795868i \(-0.707015\pi\)
−0.605470 + 0.795868i \(0.707015\pi\)
\(462\) 0 0
\(463\) −8.00000 −0.371792 −0.185896 0.982569i \(-0.559519\pi\)
−0.185896 + 0.982569i \(0.559519\pi\)
\(464\) 0 0
\(465\) −8.00000 + 13.8564i −0.370991 + 0.642575i
\(466\) 0 0
\(467\) −18.0000 31.1769i −0.832941 1.44270i −0.895696 0.444667i \(-0.853322\pi\)
0.0627555 0.998029i \(-0.480011\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 1.00000 + 1.73205i 0.0460776 + 0.0798087i
\(472\) 0 0
\(473\) −8.00000 + 13.8564i −0.367840 + 0.637118i
\(474\) 0 0
\(475\) −4.00000 −0.183533
\(476\) 0 0
\(477\) −2.00000 −0.0915737
\(478\) 0 0
\(479\) −8.00000 + 13.8564i −0.365529 + 0.633115i −0.988861 0.148842i \(-0.952445\pi\)
0.623332 + 0.781958i \(0.285779\pi\)
\(480\) 0 0
\(481\) 6.00000 + 10.3923i 0.273576 + 0.473848i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 2.00000 + 3.46410i 0.0908153 + 0.157297i
\(486\) 0 0
\(487\) −16.0000 + 27.7128i −0.725029 + 1.25579i 0.233933 + 0.972253i \(0.424840\pi\)
−0.958962 + 0.283535i \(0.908493\pi\)
\(488\) 0 0
\(489\) −12.0000 −0.542659
\(490\) 0 0
\(491\) 12.0000 0.541552 0.270776 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) 0 0
\(493\) −6.00000 + 10.3923i −0.270226 + 0.468046i
\(494\) 0 0
\(495\) −4.00000 6.92820i −0.179787 0.311400i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 6.00000 + 10.3923i 0.268597 + 0.465223i 0.968500 0.249015i \(-0.0801067\pi\)
−0.699903 + 0.714238i \(0.746773\pi\)
\(500\) 0 0
\(501\) 12.0000 20.7846i 0.536120 0.928588i
\(502\) 0 0
\(503\) −24.0000 −1.07011 −0.535054 0.844818i \(-0.679709\pi\)
−0.535054 + 0.844818i \(0.679709\pi\)
\(504\) 0 0
\(505\) 36.0000 1.60198
\(506\) 0 0
\(507\) 4.50000 7.79423i 0.199852 0.346154i
\(508\) 0 0
\(509\) −3.00000 5.19615i −0.132973 0.230315i 0.791849 0.610718i \(-0.209119\pi\)
−0.924821 + 0.380402i \(0.875786\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −2.00000 3.46410i −0.0883022 0.152944i
\(514\) 0 0
\(515\) −16.0000 + 27.7128i −0.705044 + 1.22117i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 6.00000 0.263371
\(520\) 0 0
\(521\) −13.0000 + 22.5167i −0.569540 + 0.986473i 0.427071 + 0.904218i \(0.359545\pi\)
−0.996611 + 0.0822547i \(0.973788\pi\)
\(522\) 0 0
\(523\) 2.00000 + 3.46410i 0.0874539 + 0.151475i 0.906434 0.422347i \(-0.138794\pi\)
−0.818980 + 0.573822i \(0.805460\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 8.00000 + 13.8564i 0.348485 + 0.603595i
\(528\) 0 0
\(529\) −20.5000 + 35.5070i −0.891304 + 1.54378i
\(530\) 0 0
\(531\) −4.00000 −0.173585
\(532\) 0 0
\(533\) 12.0000 0.519778
\(534\) 0 0
\(535\) 12.0000 20.7846i 0.518805 0.898597i
\(536\) 0 0
\(537\) 6.00000 + 10.3923i 0.258919 + 0.448461i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 9.00000 + 15.5885i 0.386940 + 0.670200i 0.992036 0.125952i \(-0.0401986\pi\)
−0.605096 + 0.796152i \(0.706865\pi\)
\(542\) 0 0
\(543\) −3.00000 + 5.19615i −0.128742 + 0.222988i
\(544\) 0 0
\(545\) 4.00000 0.171341
\(546\) 0 0
\(547\) −44.0000 −1.88130 −0.940652 0.339372i \(-0.889785\pi\)
−0.940652 + 0.339372i \(0.889785\pi\)
\(548\) 0 0
\(549\) 1.00000 1.73205i 0.0426790 0.0739221i
\(550\) 0 0
\(551\) −12.0000 20.7846i −0.511217 0.885454i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 6.00000 + 10.3923i 0.254686 + 0.441129i
\(556\) 0 0
\(557\) 13.0000 22.5167i 0.550828 0.954062i −0.447387 0.894340i \(-0.647645\pi\)
0.998215 0.0597213i \(-0.0190212\pi\)
\(558\) 0 0
\(559\) 8.00000 0.338364
\(560\) 0 0
\(561\) −8.00000 −0.337760
\(562\) 0 0
\(563\) 14.0000 24.2487i 0.590030 1.02196i −0.404198 0.914671i \(-0.632449\pi\)
0.994228 0.107290i \(-0.0342173\pi\)
\(564\) 0 0
\(565\) 18.0000 + 31.1769i 0.757266 + 1.31162i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −5.00000 8.66025i −0.209611 0.363057i 0.741981 0.670421i \(-0.233886\pi\)
−0.951592 + 0.307364i \(0.900553\pi\)
\(570\) 0 0
\(571\) 18.0000 31.1769i 0.753277 1.30471i −0.192950 0.981209i \(-0.561806\pi\)
0.946227 0.323505i \(-0.104861\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −8.00000 −0.333623
\(576\) 0 0
\(577\) −1.00000 + 1.73205i −0.0416305 + 0.0721062i −0.886090 0.463513i \(-0.846589\pi\)
0.844459 + 0.535620i \(0.179922\pi\)
\(578\) 0 0
\(579\) −1.00000 1.73205i −0.0415586 0.0719816i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −4.00000 6.92820i −0.165663 0.286937i
\(584\) 0 0
\(585\) −2.00000 + 3.46410i −0.0826898 + 0.143223i
\(586\) 0 0
\(587\) 44.0000 1.81607 0.908037 0.418890i \(-0.137581\pi\)
0.908037 + 0.418890i \(0.137581\pi\)
\(588\) 0 0
\(589\) −32.0000 −1.31854
\(590\) 0 0
\(591\) 9.00000 15.5885i 0.370211 0.641223i
\(592\) 0 0
\(593\) 7.00000 + 12.1244i 0.287456 + 0.497888i 0.973202 0.229953i \(-0.0738573\pi\)
−0.685746 + 0.727841i \(0.740524\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 8.00000 + 13.8564i 0.327418 + 0.567105i
\(598\) 0 0
\(599\) 12.0000 20.7846i 0.490307 0.849236i −0.509631 0.860393i \(-0.670218\pi\)
0.999938 + 0.0111569i \(0.00355143\pi\)
\(600\) 0 0
\(601\) −38.0000 −1.55005 −0.775026 0.631929i \(-0.782263\pi\)
−0.775026 + 0.631929i \(0.782263\pi\)
\(602\) 0 0
\(603\) 4.00000 0.162893
\(604\) 0 0
\(605\) 5.00000 8.66025i 0.203279 0.352089i
\(606\) 0 0
\(607\) −20.0000 34.6410i −0.811775 1.40604i −0.911621 0.411033i \(-0.865168\pi\)
0.0998457 0.995003i \(-0.468165\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −19.0000 + 32.9090i −0.767403 + 1.32918i 0.171564 + 0.985173i \(0.445118\pi\)
−0.938967 + 0.344008i \(0.888215\pi\)
\(614\) 0 0
\(615\) 12.0000 0.483887
\(616\) 0 0
\(617\) 42.0000 1.69086 0.845428 0.534089i \(-0.179345\pi\)
0.845428 + 0.534089i \(0.179345\pi\)
\(618\) 0 0
\(619\) −22.0000 + 38.1051i −0.884255 + 1.53157i −0.0376891 + 0.999290i \(0.512000\pi\)
−0.846566 + 0.532284i \(0.821334\pi\)
\(620\) 0 0
\(621\) −4.00000 6.92820i −0.160514 0.278019i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 9.50000 + 16.4545i 0.380000 + 0.658179i
\(626\) 0 0
\(627\) 8.00000 13.8564i 0.319489 0.553372i
\(628\) 0 0
\(629\) 12.0000 0.478471
\(630\) 0 0
\(631\) −16.0000 −0.636950 −0.318475 0.947931i \(-0.603171\pi\)
−0.318475 + 0.947931i \(0.603171\pi\)
\(632\) 0 0
\(633\) −10.0000 + 17.3205i −0.397464 + 0.688428i
\(634\) 0 0
\(635\) 8.00000 + 13.8564i 0.317470 + 0.549875i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 4.00000 + 6.92820i 0.158238 + 0.274075i
\(640\) 0 0
\(641\) 7.00000 12.1244i 0.276483 0.478883i −0.694025 0.719951i \(-0.744164\pi\)
0.970508 + 0.241068i \(0.0774976\pi\)
\(642\) 0 0
\(643\) −12.0000 −0.473234 −0.236617 0.971603i \(-0.576039\pi\)
−0.236617 + 0.971603i \(0.576039\pi\)
\(644\) 0 0
\(645\) 8.00000 0.315000
\(646\) 0 0
\(647\) 4.00000 6.92820i 0.157256 0.272376i −0.776622 0.629967i \(-0.783068\pi\)
0.933878 + 0.357591i \(0.116402\pi\)
\(648\) 0 0
\(649\) −8.00000 13.8564i −0.314027 0.543912i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −3.00000 5.19615i −0.117399 0.203341i 0.801337 0.598213i \(-0.204122\pi\)
−0.918736 + 0.394872i \(0.870789\pi\)
\(654\) 0 0
\(655\) 4.00000 6.92820i 0.156293 0.270707i
\(656\) 0 0
\(657\) 10.0000 0.390137
\(658\) 0 0
\(659\) −12.0000 −0.467454 −0.233727 0.972302i \(-0.575092\pi\)
−0.233727 + 0.972302i \(0.575092\pi\)
\(660\) 0 0
\(661\) 5.00000 8.66025i 0.194477 0.336845i −0.752252 0.658876i \(-0.771032\pi\)
0.946729 + 0.322031i \(0.104366\pi\)
\(662\) 0 0
\(663\) 2.00000 + 3.46410i 0.0776736 + 0.134535i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −24.0000 41.5692i −0.929284 1.60957i
\(668\) 0 0
\(669\) −4.00000 + 6.92820i −0.154649 + 0.267860i
\(670\) 0 0
\(671\) 8.00000 0.308837
\(672\) 0 0
\(673\) 34.0000 1.31060 0.655302 0.755367i \(-0.272541\pi\)
0.655302 + 0.755367i \(0.272541\pi\)
\(674\) 0 0
\(675\) 0.500000 0.866025i 0.0192450 0.0333333i
\(676\) 0 0
\(677\) 1.00000 + 1.73205i 0.0384331 + 0.0665681i 0.884602 0.466347i \(-0.154430\pi\)
−0.846169 + 0.532915i \(0.821097\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 6.00000 + 10.3923i 0.229920 + 0.398234i
\(682\) 0 0
\(683\) 2.00000 3.46410i 0.0765279 0.132550i −0.825222 0.564809i \(-0.808950\pi\)
0.901750 + 0.432259i \(0.142283\pi\)
\(684\) 0 0
\(685\) 12.0000 0.458496
\(686\) 0 0
\(687\) 22.0000 0.839352
\(688\) 0 0
\(689\) −2.00000 + 3.46410i −0.0761939 + 0.131972i
\(690\) 0 0
\(691\) −2.00000 3.46410i −0.0760836 0.131781i 0.825473 0.564441i \(-0.190908\pi\)
−0.901557 + 0.432660i \(0.857575\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 12.0000 + 20.7846i 0.455186 + 0.788405i
\(696\) 0 0
\(697\) 6.00000 10.3923i 0.227266 0.393637i
\(698\) 0 0
\(699\) 10.0000 0.378235
\(700\) 0 0
\(701\) 6.00000 0.226617 0.113308 0.993560i \(-0.463855\pi\)
0.113308 + 0.993560i \(0.463855\pi\)
\(702\) 0 0
\(703\) −12.0000 + 20.7846i −0.452589 + 0.783906i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 5.00000 + 8.66025i 0.187779 + 0.325243i 0.944509 0.328484i \(-0.106538\pi\)
−0.756730 + 0.653727i \(0.773204\pi\)
\(710\) 0 0
\(711\) −4.00000 + 6.92820i −0.150012 + 0.259828i
\(712\) 0 0
\(713\) −64.0000 −2.39682
\(714\) 0 0
\(715\) −16.0000 −0.598366
\(716\) 0 0
\(717\) −8.00000 + 13.8564i −0.298765 + 0.517477i
\(718\) 0 0
\(719\) −16.0000 27.7128i −0.596699 1.03351i −0.993305 0.115524i \(-0.963145\pi\)
0.396605 0.917989i \(-0.370188\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −9.00000 15.5885i −0.334714 0.579741i
\(724\) 0 0
\(725\) 3.00000 5.19615i 0.111417 0.192980i
\(726\) 0 0
\(727\) −48.0000 −1.78022 −0.890111 0.455744i \(-0.849373\pi\)
−0.890111 + 0.455744i \(0.849373\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 4.00000 6.92820i 0.147945 0.256249i
\(732\) 0 0
\(733\) −7.00000 12.1244i −0.258551 0.447823i 0.707303 0.706910i \(-0.249912\pi\)
−0.965854 + 0.259087i \(0.916578\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 8.00000 + 13.8564i 0.294684 + 0.510407i
\(738\) 0 0
\(739\) −2.00000 + 3.46410i −0.0735712 + 0.127429i −0.900464 0.434930i \(-0.856773\pi\)
0.826893 + 0.562360i \(0.190106\pi\)
\(740\) 0 0
\(741\) −8.00000 −0.293887
\(742\) 0 0
\(743\) 8.00000 0.293492 0.146746 0.989174i \(-0.453120\pi\)
0.146746 + 0.989174i \(0.453120\pi\)
\(744\) 0 0
\(745\) 14.0000 24.2487i 0.512920 0.888404i
\(746\) 0 0
\(747\) −2.00000 3.46410i −0.0731762 0.126745i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 12.0000 + 20.7846i 0.437886 + 0.758441i 0.997526 0.0702946i \(-0.0223939\pi\)
−0.559640 + 0.828736i \(0.689061\pi\)
\(752\) 0 0
\(753\) 10.0000 17.3205i 0.364420 0.631194i
\(754\) 0 0
\(755\) −32.0000 −1.16460
\(756\) 0 0
\(757\) 38.0000 1.38113 0.690567 0.723269i \(-0.257361\pi\)
0.690567 + 0.723269i \(0.257361\pi\)
\(758\) 0 0
\(759\) 16.0000 27.7128i 0.580763 1.00591i
\(760\) 0 0
\(761\) 11.0000 + 19.0526i 0.398750 + 0.690655i 0.993572 0.113203i \(-0.0361109\pi\)
−0.594822 + 0.803857i \(0.702778\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 2.00000 + 3.46410i 0.0723102 + 0.125245i
\(766\) 0 0
\(767\) −4.00000 + 6.92820i −0.144432 + 0.250163i
\(768\) 0 0
\(769\) 2.00000 0.0721218 0.0360609 0.999350i \(-0.488519\pi\)
0.0360609 + 0.999350i \(0.488519\pi\)
\(770\) 0 0
\(771\) 2.00000 0.0720282
\(772\) 0 0
\(773\) 9.00000 15.5885i 0.323708 0.560678i −0.657542 0.753418i \(-0.728404\pi\)
0.981250 + 0.192740i \(0.0617373\pi\)
\(774\) 0 0
\(775\) −4.00000 6.92820i −0.143684 0.248868i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 12.0000 + 20.7846i 0.429945 + 0.744686i
\(780\) 0 0
\(781\) −16.0000 + 27.7128i −0.572525 + 0.991642i
\(782\) 0 0
\(783\) 6.00000 0.214423
\(784\) 0 0
\(785\) 4.00000 0.142766
\(786\) 0 0
\(787\) 14.0000 24.2487i 0.499046 0.864373i −0.500953 0.865474i \(-0.667017\pi\)
0.999999 + 0.00110111i \(0.000350496\pi\)
\(788\) 0 0
\(789\) −4.00000 6.92820i −0.142404 0.246651i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −2.00000 3.46410i −0.0710221 0.123014i
\(794\) 0 0
\(795\) −2.00000 + 3.46410i −0.0709327 + 0.122859i
\(796\) 0 0
\(797\) 22.0000 0.779280 0.389640 0.920967i \(-0.372599\pi\)
0.389640 + 0.920967i \(0.372599\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0