Properties

Label 1344.2.q.p.961.1
Level $1344$
Weight $2$
Character 1344.961
Analytic conductor $10.732$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1344.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.7318940317\)
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 672)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 961.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1344.961
Dual form 1344.2.q.p.193.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{3} +(0.500000 + 2.59808i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{3} +(0.500000 + 2.59808i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(1.00000 + 1.73205i) q^{11} -5.00000 q^{13} +(1.00000 + 1.73205i) q^{17} +(1.50000 - 2.59808i) q^{19} +(-2.00000 + 1.73205i) q^{21} +(-1.00000 + 1.73205i) q^{23} +(2.50000 + 4.33013i) q^{25} -1.00000 q^{27} -8.00000 q^{29} +(0.500000 + 0.866025i) q^{31} +(-1.00000 + 1.73205i) q^{33} +(-2.50000 + 4.33013i) q^{37} +(-2.50000 - 4.33013i) q^{39} +2.00000 q^{41} -7.00000 q^{43} +(4.00000 - 6.92820i) q^{47} +(-6.50000 + 2.59808i) q^{49} +(-1.00000 + 1.73205i) q^{51} +(-1.00000 - 1.73205i) q^{53} +3.00000 q^{57} +(5.00000 + 8.66025i) q^{59} +(-1.00000 + 1.73205i) q^{61} +(-2.50000 - 0.866025i) q^{63} +(-5.50000 - 9.52628i) q^{67} -2.00000 q^{69} +12.0000 q^{71} +(1.50000 + 2.59808i) q^{73} +(-2.50000 + 4.33013i) q^{75} +(-4.00000 + 3.46410i) q^{77} +(-8.50000 + 14.7224i) q^{79} +(-0.500000 - 0.866025i) q^{81} +16.0000 q^{83} +(-4.00000 - 6.92820i) q^{87} +(-6.00000 + 10.3923i) q^{89} +(-2.50000 - 12.9904i) q^{91} +(-0.500000 + 0.866025i) q^{93} -14.0000 q^{97} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{3} + q^{7} - q^{9} + O(q^{10}) \) \( 2q + q^{3} + q^{7} - q^{9} + 2q^{11} - 10q^{13} + 2q^{17} + 3q^{19} - 4q^{21} - 2q^{23} + 5q^{25} - 2q^{27} - 16q^{29} + q^{31} - 2q^{33} - 5q^{37} - 5q^{39} + 4q^{41} - 14q^{43} + 8q^{47} - 13q^{49} - 2q^{51} - 2q^{53} + 6q^{57} + 10q^{59} - 2q^{61} - 5q^{63} - 11q^{67} - 4q^{69} + 24q^{71} + 3q^{73} - 5q^{75} - 8q^{77} - 17q^{79} - q^{81} + 32q^{83} - 8q^{87} - 12q^{89} - 5q^{91} - q^{93} - 28q^{97} - 4q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(449\) \(577\) \(1093\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) 0 0
\(5\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(6\) 0 0
\(7\) 0.500000 + 2.59808i 0.188982 + 0.981981i
\(8\) 0 0
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) 1.00000 + 1.73205i 0.301511 + 0.522233i 0.976478 0.215615i \(-0.0691756\pi\)
−0.674967 + 0.737848i \(0.735842\pi\)
\(12\) 0 0
\(13\) −5.00000 −1.38675 −0.693375 0.720577i \(-0.743877\pi\)
−0.693375 + 0.720577i \(0.743877\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.00000 + 1.73205i 0.242536 + 0.420084i 0.961436 0.275029i \(-0.0886875\pi\)
−0.718900 + 0.695113i \(0.755354\pi\)
\(18\) 0 0
\(19\) 1.50000 2.59808i 0.344124 0.596040i −0.641071 0.767482i \(-0.721509\pi\)
0.985194 + 0.171442i \(0.0548427\pi\)
\(20\) 0 0
\(21\) −2.00000 + 1.73205i −0.436436 + 0.377964i
\(22\) 0 0
\(23\) −1.00000 + 1.73205i −0.208514 + 0.361158i −0.951247 0.308431i \(-0.900196\pi\)
0.742732 + 0.669588i \(0.233529\pi\)
\(24\) 0 0
\(25\) 2.50000 + 4.33013i 0.500000 + 0.866025i
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −8.00000 −1.48556 −0.742781 0.669534i \(-0.766494\pi\)
−0.742781 + 0.669534i \(0.766494\pi\)
\(30\) 0 0
\(31\) 0.500000 + 0.866025i 0.0898027 + 0.155543i 0.907428 0.420208i \(-0.138043\pi\)
−0.817625 + 0.575751i \(0.804710\pi\)
\(32\) 0 0
\(33\) −1.00000 + 1.73205i −0.174078 + 0.301511i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −2.50000 + 4.33013i −0.410997 + 0.711868i −0.994999 0.0998840i \(-0.968153\pi\)
0.584002 + 0.811752i \(0.301486\pi\)
\(38\) 0 0
\(39\) −2.50000 4.33013i −0.400320 0.693375i
\(40\) 0 0
\(41\) 2.00000 0.312348 0.156174 0.987730i \(-0.450084\pi\)
0.156174 + 0.987730i \(0.450084\pi\)
\(42\) 0 0
\(43\) −7.00000 −1.06749 −0.533745 0.845645i \(-0.679216\pi\)
−0.533745 + 0.845645i \(0.679216\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 4.00000 6.92820i 0.583460 1.01058i −0.411606 0.911362i \(-0.635032\pi\)
0.995066 0.0992202i \(-0.0316348\pi\)
\(48\) 0 0
\(49\) −6.50000 + 2.59808i −0.928571 + 0.371154i
\(50\) 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 \(-0.210529\pi\)
−0.926497 + 0.376303i \(0.877195\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 3.00000 0.397360
\(58\) 0 0
\(59\) 5.00000 + 8.66025i 0.650945 + 1.12747i 0.982894 + 0.184172i \(0.0589603\pi\)
−0.331949 + 0.943297i \(0.607706\pi\)
\(60\) 0 0
\(61\) −1.00000 + 1.73205i −0.128037 + 0.221766i −0.922916 0.385002i \(-0.874201\pi\)
0.794879 + 0.606768i \(0.207534\pi\)
\(62\) 0 0
\(63\) −2.50000 0.866025i −0.314970 0.109109i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −5.50000 9.52628i −0.671932 1.16382i −0.977356 0.211604i \(-0.932131\pi\)
0.305424 0.952217i \(-0.401202\pi\)
\(68\) 0 0
\(69\) −2.00000 −0.240772
\(70\) 0 0
\(71\) 12.0000 1.42414 0.712069 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) 0 0
\(73\) 1.50000 + 2.59808i 0.175562 + 0.304082i 0.940356 0.340193i \(-0.110493\pi\)
−0.764794 + 0.644275i \(0.777159\pi\)
\(74\) 0 0
\(75\) −2.50000 + 4.33013i −0.288675 + 0.500000i
\(76\) 0 0
\(77\) −4.00000 + 3.46410i −0.455842 + 0.394771i
\(78\) 0 0
\(79\) −8.50000 + 14.7224i −0.956325 + 1.65640i −0.225018 + 0.974355i \(0.572244\pi\)
−0.731307 + 0.682048i \(0.761089\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) 16.0000 1.75623 0.878114 0.478451i \(-0.158802\pi\)
0.878114 + 0.478451i \(0.158802\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −4.00000 6.92820i −0.428845 0.742781i
\(88\) 0 0
\(89\) −6.00000 + 10.3923i −0.635999 + 1.10158i 0.350304 + 0.936636i \(0.386078\pi\)
−0.986303 + 0.164946i \(0.947255\pi\)
\(90\) 0 0
\(91\) −2.50000 12.9904i −0.262071 1.36176i
\(92\) 0 0
\(93\) −0.500000 + 0.866025i −0.0518476 + 0.0898027i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −14.0000 −1.42148 −0.710742 0.703452i \(-0.751641\pi\)
−0.710742 + 0.703452i \(0.751641\pi\)
\(98\) 0 0
\(99\) −2.00000 −0.201008
\(100\) 0 0
\(101\) 9.00000 + 15.5885i 0.895533 + 1.55111i 0.833143 + 0.553058i \(0.186539\pi\)
0.0623905 + 0.998052i \(0.480128\pi\)
\(102\) 0 0
\(103\) 0.500000 0.866025i 0.0492665 0.0853320i −0.840341 0.542059i \(-0.817645\pi\)
0.889607 + 0.456727i \(0.150978\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1.00000 1.73205i 0.0966736 0.167444i −0.813632 0.581380i \(-0.802513\pi\)
0.910306 + 0.413936i \(0.135846\pi\)
\(108\) 0 0
\(109\) 0.500000 + 0.866025i 0.0478913 + 0.0829502i 0.888977 0.457951i \(-0.151417\pi\)
−0.841086 + 0.540901i \(0.818083\pi\)
\(110\) 0 0
\(111\) −5.00000 −0.474579
\(112\) 0 0
\(113\) −12.0000 −1.12887 −0.564433 0.825479i \(-0.690905\pi\)
−0.564433 + 0.825479i \(0.690905\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 2.50000 4.33013i 0.231125 0.400320i
\(118\) 0 0
\(119\) −4.00000 + 3.46410i −0.366679 + 0.317554i
\(120\) 0 0
\(121\) 3.50000 6.06218i 0.318182 0.551107i
\(122\) 0 0
\(123\) 1.00000 + 1.73205i 0.0901670 + 0.156174i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 11.0000 0.976092 0.488046 0.872818i \(-0.337710\pi\)
0.488046 + 0.872818i \(0.337710\pi\)
\(128\) 0 0
\(129\) −3.50000 6.06218i −0.308158 0.533745i
\(130\) 0 0
\(131\) −3.00000 + 5.19615i −0.262111 + 0.453990i −0.966803 0.255524i \(-0.917752\pi\)
0.704692 + 0.709514i \(0.251085\pi\)
\(132\) 0 0
\(133\) 7.50000 + 2.59808i 0.650332 + 0.225282i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −2.00000 3.46410i −0.170872 0.295958i 0.767853 0.640626i \(-0.221325\pi\)
−0.938725 + 0.344668i \(0.887992\pi\)
\(138\) 0 0
\(139\) 1.00000 0.0848189 0.0424094 0.999100i \(-0.486497\pi\)
0.0424094 + 0.999100i \(0.486497\pi\)
\(140\) 0 0
\(141\) 8.00000 0.673722
\(142\) 0 0
\(143\) −5.00000 8.66025i −0.418121 0.724207i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −5.50000 4.33013i −0.453632 0.357143i
\(148\) 0 0
\(149\) 6.00000 10.3923i 0.491539 0.851371i −0.508413 0.861113i \(-0.669768\pi\)
0.999953 + 0.00974235i \(0.00310113\pi\)
\(150\) 0 0
\(151\) −4.00000 6.92820i −0.325515 0.563809i 0.656101 0.754673i \(-0.272204\pi\)
−0.981617 + 0.190864i \(0.938871\pi\)
\(152\) 0 0
\(153\) −2.00000 −0.161690
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −3.00000 5.19615i −0.239426 0.414698i 0.721124 0.692806i \(-0.243626\pi\)
−0.960550 + 0.278108i \(0.910293\pi\)
\(158\) 0 0
\(159\) 1.00000 1.73205i 0.0793052 0.137361i
\(160\) 0 0
\(161\) −5.00000 1.73205i −0.394055 0.136505i
\(162\) 0 0
\(163\) 2.00000 3.46410i 0.156652 0.271329i −0.777007 0.629492i \(-0.783263\pi\)
0.933659 + 0.358162i \(0.116597\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 20.0000 1.54765 0.773823 0.633402i \(-0.218342\pi\)
0.773823 + 0.633402i \(0.218342\pi\)
\(168\) 0 0
\(169\) 12.0000 0.923077
\(170\) 0 0
\(171\) 1.50000 + 2.59808i 0.114708 + 0.198680i
\(172\) 0 0
\(173\) −3.00000 + 5.19615i −0.228086 + 0.395056i −0.957241 0.289292i \(-0.906580\pi\)
0.729155 + 0.684349i \(0.239913\pi\)
\(174\) 0 0
\(175\) −10.0000 + 8.66025i −0.755929 + 0.654654i
\(176\) 0 0
\(177\) −5.00000 + 8.66025i −0.375823 + 0.650945i
\(178\) 0 0
\(179\) 6.00000 + 10.3923i 0.448461 + 0.776757i 0.998286 0.0585225i \(-0.0186389\pi\)
−0.549825 + 0.835280i \(0.685306\pi\)
\(180\) 0 0
\(181\) 15.0000 1.11494 0.557471 0.830197i \(-0.311772\pi\)
0.557471 + 0.830197i \(0.311772\pi\)
\(182\) 0 0
\(183\) −2.00000 −0.147844
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −2.00000 + 3.46410i −0.146254 + 0.253320i
\(188\) 0 0
\(189\) −0.500000 2.59808i −0.0363696 0.188982i
\(190\) 0 0
\(191\) −6.00000 + 10.3923i −0.434145 + 0.751961i −0.997225 0.0744412i \(-0.976283\pi\)
0.563081 + 0.826402i \(0.309616\pi\)
\(192\) 0 0
\(193\) −11.5000 19.9186i −0.827788 1.43377i −0.899770 0.436365i \(-0.856266\pi\)
0.0719816 0.997406i \(-0.477068\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) 0 0
\(199\) −2.00000 3.46410i −0.141776 0.245564i 0.786389 0.617731i \(-0.211948\pi\)
−0.928166 + 0.372168i \(0.878615\pi\)
\(200\) 0 0
\(201\) 5.50000 9.52628i 0.387940 0.671932i
\(202\) 0 0
\(203\) −4.00000 20.7846i −0.280745 1.45879i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −1.00000 1.73205i −0.0695048 0.120386i
\(208\) 0 0
\(209\) 6.00000 0.415029
\(210\) 0 0
\(211\) −20.0000 −1.37686 −0.688428 0.725304i \(-0.741699\pi\)
−0.688428 + 0.725304i \(0.741699\pi\)
\(212\) 0 0
\(213\) 6.00000 + 10.3923i 0.411113 + 0.712069i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −2.00000 + 1.73205i −0.135769 + 0.117579i
\(218\) 0 0
\(219\) −1.50000 + 2.59808i −0.101361 + 0.175562i
\(220\) 0 0
\(221\) −5.00000 8.66025i −0.336336 0.582552i
\(222\) 0 0
\(223\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) 0 0
\(225\) −5.00000 −0.333333
\(226\) 0 0
\(227\) 13.0000 + 22.5167i 0.862840 + 1.49448i 0.869176 + 0.494503i \(0.164650\pi\)
−0.00633544 + 0.999980i \(0.502017\pi\)
\(228\) 0 0
\(229\) 6.50000 11.2583i 0.429532 0.743971i −0.567300 0.823511i \(-0.692012\pi\)
0.996832 + 0.0795401i \(0.0253452\pi\)
\(230\) 0 0
\(231\) −5.00000 1.73205i −0.328976 0.113961i
\(232\) 0 0
\(233\) 6.00000 10.3923i 0.393073 0.680823i −0.599780 0.800165i \(-0.704745\pi\)
0.992853 + 0.119342i \(0.0380786\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −17.0000 −1.10427
\(238\) 0 0
\(239\) 30.0000 1.94054 0.970269 0.242028i \(-0.0778125\pi\)
0.970269 + 0.242028i \(0.0778125\pi\)
\(240\) 0 0
\(241\) 11.0000 + 19.0526i 0.708572 + 1.22728i 0.965387 + 0.260822i \(0.0839937\pi\)
−0.256814 + 0.966461i \(0.582673\pi\)
\(242\) 0 0
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −7.50000 + 12.9904i −0.477214 + 0.826558i
\(248\) 0 0
\(249\) 8.00000 + 13.8564i 0.506979 + 0.878114i
\(250\) 0 0
\(251\) 22.0000 1.38863 0.694314 0.719672i \(-0.255708\pi\)
0.694314 + 0.719672i \(0.255708\pi\)
\(252\) 0 0
\(253\) −4.00000 −0.251478
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 8.00000 13.8564i 0.499026 0.864339i −0.500973 0.865463i \(-0.667024\pi\)
0.999999 + 0.00112398i \(0.000357774\pi\)
\(258\) 0 0
\(259\) −12.5000 4.33013i −0.776712 0.269061i
\(260\) 0 0
\(261\) 4.00000 6.92820i 0.247594 0.428845i
\(262\) 0 0
\(263\) −4.00000 6.92820i −0.246651 0.427211i 0.715944 0.698158i \(-0.245997\pi\)
−0.962594 + 0.270947i \(0.912663\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −12.0000 −0.734388
\(268\) 0 0
\(269\) −9.00000 15.5885i −0.548740 0.950445i −0.998361 0.0572259i \(-0.981774\pi\)
0.449622 0.893219i \(-0.351559\pi\)
\(270\) 0 0
\(271\) 8.00000 13.8564i 0.485965 0.841717i −0.513905 0.857847i \(-0.671801\pi\)
0.999870 + 0.0161307i \(0.00513477\pi\)
\(272\) 0 0
\(273\) 10.0000 8.66025i 0.605228 0.524142i
\(274\) 0 0
\(275\) −5.00000 + 8.66025i −0.301511 + 0.522233i
\(276\) 0 0
\(277\) 8.50000 + 14.7224i 0.510716 + 0.884585i 0.999923 + 0.0124177i \(0.00395278\pi\)
−0.489207 + 0.872167i \(0.662714\pi\)
\(278\) 0 0
\(279\) −1.00000 −0.0598684
\(280\) 0 0
\(281\) 18.0000 1.07379 0.536895 0.843649i \(-0.319597\pi\)
0.536895 + 0.843649i \(0.319597\pi\)
\(282\) 0 0
\(283\) 15.5000 + 26.8468i 0.921379 + 1.59588i 0.797283 + 0.603606i \(0.206270\pi\)
0.124096 + 0.992270i \(0.460397\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 1.00000 + 5.19615i 0.0590281 + 0.306719i
\(288\) 0 0
\(289\) 6.50000 11.2583i 0.382353 0.662255i
\(290\) 0 0
\(291\) −7.00000 12.1244i −0.410347 0.710742i
\(292\) 0 0
\(293\) 4.00000 0.233682 0.116841 0.993151i \(-0.462723\pi\)
0.116841 + 0.993151i \(0.462723\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −1.00000 1.73205i −0.0580259 0.100504i
\(298\) 0 0
\(299\) 5.00000 8.66025i 0.289157 0.500835i
\(300\) 0 0
\(301\) −3.50000 18.1865i −0.201737 1.04825i
\(302\) 0 0
\(303\) −9.00000 + 15.5885i −0.517036 + 0.895533i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 23.0000 1.31268 0.656340 0.754466i \(-0.272104\pi\)
0.656340 + 0.754466i \(0.272104\pi\)
\(308\) 0 0
\(309\) 1.00000 0.0568880
\(310\) 0 0
\(311\) 15.0000 + 25.9808i 0.850572 + 1.47323i 0.880693 + 0.473688i \(0.157077\pi\)
−0.0301210 + 0.999546i \(0.509589\pi\)
\(312\) 0 0
\(313\) 8.50000 14.7224i 0.480448 0.832161i −0.519300 0.854592i \(-0.673807\pi\)
0.999748 + 0.0224310i \(0.00714060\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 10.0000 17.3205i 0.561656 0.972817i −0.435696 0.900094i \(-0.643498\pi\)
0.997352 0.0727229i \(-0.0231689\pi\)
\(318\) 0 0
\(319\) −8.00000 13.8564i −0.447914 0.775810i
\(320\) 0 0
\(321\) 2.00000 0.111629
\(322\) 0 0
\(323\) 6.00000 0.333849
\(324\) 0 0
\(325\) −12.5000 21.6506i −0.693375 1.20096i
\(326\) 0 0
\(327\) −0.500000 + 0.866025i −0.0276501 + 0.0478913i
\(328\) 0 0
\(329\) 20.0000 + 6.92820i 1.10264 + 0.381964i
\(330\) 0 0
\(331\) −7.50000 + 12.9904i −0.412237 + 0.714016i −0.995134 0.0985303i \(-0.968586\pi\)
0.582897 + 0.812546i \(0.301919\pi\)
\(332\) 0 0
\(333\) −2.50000 4.33013i −0.136999 0.237289i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 9.00000 0.490261 0.245131 0.969490i \(-0.421169\pi\)
0.245131 + 0.969490i \(0.421169\pi\)
\(338\) 0 0
\(339\) −6.00000 10.3923i −0.325875 0.564433i
\(340\) 0 0
\(341\) −1.00000 + 1.73205i −0.0541530 + 0.0937958i
\(342\) 0 0
\(343\) −10.0000 15.5885i −0.539949 0.841698i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −15.0000 25.9808i −0.805242 1.39472i −0.916127 0.400887i \(-0.868702\pi\)
0.110885 0.993833i \(-0.464631\pi\)
\(348\) 0 0
\(349\) −2.00000 −0.107058 −0.0535288 0.998566i \(-0.517047\pi\)
−0.0535288 + 0.998566i \(0.517047\pi\)
\(350\) 0 0
\(351\) 5.00000 0.266880
\(352\) 0 0
\(353\) −12.0000 20.7846i −0.638696 1.10625i −0.985719 0.168397i \(-0.946141\pi\)
0.347024 0.937856i \(-0.387192\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −5.00000 1.73205i −0.264628 0.0916698i
\(358\) 0 0
\(359\) −16.0000 + 27.7128i −0.844448 + 1.46263i 0.0416523 + 0.999132i \(0.486738\pi\)
−0.886100 + 0.463494i \(0.846596\pi\)
\(360\) 0 0
\(361\) 5.00000 + 8.66025i 0.263158 + 0.455803i
\(362\) 0 0
\(363\) 7.00000 0.367405
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −8.50000 14.7224i −0.443696 0.768505i 0.554264 0.832341i \(-0.313000\pi\)
−0.997960 + 0.0638362i \(0.979666\pi\)
\(368\) 0 0
\(369\) −1.00000 + 1.73205i −0.0520579 + 0.0901670i
\(370\) 0 0
\(371\) 4.00000 3.46410i 0.207670 0.179847i
\(372\) 0 0
\(373\) −10.5000 + 18.1865i −0.543669 + 0.941663i 0.455020 + 0.890481i \(0.349632\pi\)
−0.998689 + 0.0511818i \(0.983701\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 40.0000 2.06010
\(378\) 0 0
\(379\) −1.00000 −0.0513665 −0.0256833 0.999670i \(-0.508176\pi\)
−0.0256833 + 0.999670i \(0.508176\pi\)
\(380\) 0 0
\(381\) 5.50000 + 9.52628i 0.281774 + 0.488046i
\(382\) 0 0
\(383\) 11.0000 19.0526i 0.562074 0.973540i −0.435242 0.900314i \(-0.643337\pi\)
0.997315 0.0732266i \(-0.0233296\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 3.50000 6.06218i 0.177915 0.308158i
\(388\) 0 0
\(389\) −12.0000 20.7846i −0.608424 1.05382i −0.991500 0.130105i \(-0.958469\pi\)
0.383076 0.923717i \(-0.374865\pi\)
\(390\) 0 0
\(391\) −4.00000 −0.202289
\(392\) 0 0
\(393\) −6.00000 −0.302660
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −6.50000 + 11.2583i −0.326226 + 0.565039i −0.981760 0.190126i \(-0.939110\pi\)
0.655534 + 0.755166i \(0.272444\pi\)
\(398\) 0 0
\(399\) 1.50000 + 7.79423i 0.0750939 + 0.390199i
\(400\) 0 0
\(401\) −5.00000 + 8.66025i −0.249688 + 0.432472i −0.963439 0.267927i \(-0.913661\pi\)
0.713751 + 0.700399i \(0.246995\pi\)
\(402\) 0 0
\(403\) −2.50000 4.33013i −0.124534 0.215699i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −10.0000 −0.495682
\(408\) 0 0
\(409\) 17.5000 + 30.3109i 0.865319 + 1.49878i 0.866730 + 0.498778i \(0.166218\pi\)
−0.00141047 + 0.999999i \(0.500449\pi\)
\(410\) 0 0
\(411\) 2.00000 3.46410i 0.0986527 0.170872i
\(412\) 0 0
\(413\) −20.0000 + 17.3205i −0.984136 + 0.852286i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0.500000 + 0.866025i 0.0244851 + 0.0424094i
\(418\) 0 0
\(419\) −18.0000 −0.879358 −0.439679 0.898155i \(-0.644908\pi\)
−0.439679 + 0.898155i \(0.644908\pi\)
\(420\) 0 0
\(421\) −9.00000 −0.438633 −0.219317 0.975654i \(-0.570383\pi\)
−0.219317 + 0.975654i \(0.570383\pi\)
\(422\) 0 0
\(423\) 4.00000 + 6.92820i 0.194487 + 0.336861i
\(424\) 0 0
\(425\) −5.00000 + 8.66025i −0.242536 + 0.420084i
\(426\) 0 0
\(427\) −5.00000 1.73205i −0.241967 0.0838198i
\(428\) 0 0
\(429\) 5.00000 8.66025i 0.241402 0.418121i
\(430\) 0 0
\(431\) −10.0000 17.3205i −0.481683 0.834300i 0.518096 0.855323i \(-0.326641\pi\)
−0.999779 + 0.0210230i \(0.993308\pi\)
\(432\) 0 0
\(433\) −17.0000 −0.816968 −0.408484 0.912766i \(-0.633942\pi\)
−0.408484 + 0.912766i \(0.633942\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 3.00000 + 5.19615i 0.143509 + 0.248566i
\(438\) 0 0
\(439\) 12.0000 20.7846i 0.572729 0.991995i −0.423556 0.905870i \(-0.639218\pi\)
0.996284 0.0861252i \(-0.0274485\pi\)
\(440\) 0 0
\(441\) 1.00000 6.92820i 0.0476190 0.329914i
\(442\) 0 0
\(443\) 3.00000 5.19615i 0.142534 0.246877i −0.785916 0.618333i \(-0.787808\pi\)
0.928450 + 0.371457i \(0.121142\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 12.0000 0.567581
\(448\) 0 0
\(449\) −24.0000 −1.13263 −0.566315 0.824189i \(-0.691631\pi\)
−0.566315 + 0.824189i \(0.691631\pi\)
\(450\) 0 0
\(451\) 2.00000 + 3.46410i 0.0941763 + 0.163118i
\(452\) 0 0
\(453\) 4.00000 6.92820i 0.187936 0.325515i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 11.5000 19.9186i 0.537947 0.931752i −0.461067 0.887365i \(-0.652533\pi\)
0.999014 0.0443868i \(-0.0141334\pi\)
\(458\) 0 0
\(459\) −1.00000 1.73205i −0.0466760 0.0808452i
\(460\) 0 0
\(461\) 20.0000 0.931493 0.465746 0.884918i \(-0.345786\pi\)
0.465746 + 0.884918i \(0.345786\pi\)
\(462\) 0 0
\(463\) 9.00000 0.418265 0.209133 0.977887i \(-0.432936\pi\)
0.209133 + 0.977887i \(0.432936\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 6.00000 10.3923i 0.277647 0.480899i −0.693153 0.720791i \(-0.743779\pi\)
0.970799 + 0.239892i \(0.0771121\pi\)
\(468\) 0 0
\(469\) 22.0000 19.0526i 1.01587 0.879765i
\(470\) 0 0
\(471\) 3.00000 5.19615i 0.138233 0.239426i
\(472\) 0 0
\(473\) −7.00000 12.1244i −0.321860 0.557478i
\(474\) 0 0
\(475\) 15.0000 0.688247
\(476\) 0 0
\(477\) 2.00000 0.0915737
\(478\) 0 0
\(479\) −9.00000 15.5885i −0.411220 0.712255i 0.583803 0.811895i \(-0.301564\pi\)
−0.995023 + 0.0996406i \(0.968231\pi\)
\(480\) 0 0
\(481\) 12.5000 21.6506i 0.569951 0.987184i
\(482\) 0 0
\(483\) −1.00000 5.19615i −0.0455016 0.236433i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −10.5000 18.1865i −0.475800 0.824110i 0.523815 0.851832i \(-0.324508\pi\)
−0.999616 + 0.0277214i \(0.991175\pi\)
\(488\) 0 0
\(489\) 4.00000 0.180886
\(490\) 0 0
\(491\) −32.0000 −1.44414 −0.722070 0.691820i \(-0.756809\pi\)
−0.722070 + 0.691820i \(0.756809\pi\)
\(492\) 0 0
\(493\) −8.00000 13.8564i −0.360302 0.624061i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 6.00000 + 31.1769i 0.269137 + 1.39848i
\(498\) 0 0
\(499\) −20.5000 + 35.5070i −0.917706 + 1.58951i −0.114816 + 0.993387i \(0.536628\pi\)
−0.802890 + 0.596127i \(0.796706\pi\)
\(500\) 0 0
\(501\) 10.0000 + 17.3205i 0.446767 + 0.773823i
\(502\) 0 0
\(503\) 14.0000 0.624229 0.312115 0.950044i \(-0.398963\pi\)
0.312115 + 0.950044i \(0.398963\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 6.00000 + 10.3923i 0.266469 + 0.461538i
\(508\) 0 0
\(509\) −2.00000 + 3.46410i −0.0886484 + 0.153544i −0.906940 0.421260i \(-0.861588\pi\)
0.818292 + 0.574803i \(0.194921\pi\)
\(510\) 0 0
\(511\) −6.00000 + 5.19615i −0.265424 + 0.229864i
\(512\) 0 0
\(513\) −1.50000 + 2.59808i −0.0662266 + 0.114708i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 16.0000 0.703679
\(518\) 0 0
\(519\) −6.00000 −0.263371
\(520\) 0 0
\(521\) −16.0000 27.7128i −0.700973 1.21412i −0.968125 0.250466i \(-0.919416\pi\)
0.267153 0.963654i \(-0.413917\pi\)
\(522\) 0 0
\(523\) −5.50000 + 9.52628i −0.240498 + 0.416555i −0.960856 0.277047i \(-0.910644\pi\)
0.720358 + 0.693602i \(0.243977\pi\)
\(524\) 0 0
\(525\) −12.5000 4.33013i −0.545545 0.188982i
\(526\) 0 0
\(527\) −1.00000 + 1.73205i −0.0435607 + 0.0754493i
\(528\) 0 0
\(529\) 9.50000 + 16.4545i 0.413043 + 0.715412i
\(530\) 0 0
\(531\) −10.0000 −0.433963
\(532\) 0 0
\(533\) −10.0000 −0.433148
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −6.00000 + 10.3923i −0.258919 + 0.448461i
\(538\) 0 0
\(539\) −11.0000 8.66025i −0.473804 0.373024i
\(540\) 0 0
\(541\) −13.5000 + 23.3827i −0.580410 + 1.00530i 0.415020 + 0.909812i \(0.363774\pi\)
−0.995431 + 0.0954880i \(0.969559\pi\)
\(542\) 0 0
\(543\) 7.50000 + 12.9904i 0.321856 + 0.557471i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 44.0000 1.88130 0.940652 0.339372i \(-0.110215\pi\)
0.940652 + 0.339372i \(0.110215\pi\)
\(548\) 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
\(553\) −42.5000 14.7224i −1.80728 0.626061i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 9.00000 + 15.5885i 0.381342 + 0.660504i 0.991254 0.131965i \(-0.0421286\pi\)
−0.609912 + 0.792469i \(0.708795\pi\)
\(558\) 0 0
\(559\) 35.0000 1.48034
\(560\) 0 0
\(561\) −4.00000 −0.168880
\(562\) 0 0
\(563\) −10.0000 17.3205i −0.421450 0.729972i 0.574632 0.818412i \(-0.305145\pi\)
−0.996082 + 0.0884397i \(0.971812\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 2.00000 1.73205i 0.0839921 0.0727393i
\(568\) 0 0
\(569\) −21.0000 + 36.3731i −0.880366 + 1.52484i −0.0294311 + 0.999567i \(0.509370\pi\)
−0.850935 + 0.525271i \(0.823964\pi\)
\(570\) 0 0
\(571\) 11.5000 + 19.9186i 0.481260 + 0.833567i 0.999769 0.0215055i \(-0.00684595\pi\)
−0.518509 + 0.855072i \(0.673513\pi\)
\(572\) 0 0
\(573\) −12.0000 −0.501307
\(574\) 0 0
\(575\) −10.0000 −0.417029
\(576\) 0 0
\(577\) −3.50000 6.06218i −0.145707 0.252372i 0.783930 0.620850i \(-0.213212\pi\)
−0.929636 + 0.368478i \(0.879879\pi\)
\(578\) 0 0
\(579\) 11.5000 19.9186i 0.477924 0.827788i
\(580\) 0 0
\(581\) 8.00000 + 41.5692i 0.331896 + 1.72458i
\(582\) 0 0
\(583\) 2.00000 3.46410i 0.0828315 0.143468i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 24.0000 0.990586 0.495293 0.868726i \(-0.335061\pi\)
0.495293 + 0.868726i \(0.335061\pi\)
\(588\) 0 0
\(589\) 3.00000 0.123613
\(590\) 0 0
\(591\) 9.00000 + 15.5885i 0.370211 + 0.641223i
\(592\) 0 0
\(593\) −15.0000 + 25.9808i −0.615976 + 1.06690i 0.374236 + 0.927333i \(0.377905\pi\)
−0.990212 + 0.139569i \(0.955428\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 2.00000 3.46410i 0.0818546 0.141776i
\(598\) 0 0
\(599\) 18.0000 + 31.1769i 0.735460 + 1.27385i 0.954521 + 0.298143i \(0.0963673\pi\)
−0.219061 + 0.975711i \(0.570299\pi\)
\(600\) 0 0
\(601\) −37.0000 −1.50926 −0.754631 0.656150i \(-0.772184\pi\)
−0.754631 + 0.656150i \(0.772184\pi\)
\(602\) 0 0
\(603\) 11.0000 0.447955
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −16.5000 + 28.5788i −0.669714 + 1.15998i 0.308270 + 0.951299i \(0.400250\pi\)
−0.977984 + 0.208680i \(0.933083\pi\)
\(608\) 0 0
\(609\) 16.0000 13.8564i 0.648353 0.561490i
\(610\) 0 0
\(611\) −20.0000 + 34.6410i −0.809113 + 1.40143i
\(612\) 0 0
\(613\) 13.0000 + 22.5167i 0.525065 + 0.909439i 0.999574 + 0.0291886i \(0.00929235\pi\)
−0.474509 + 0.880251i \(0.657374\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −14.0000 −0.563619 −0.281809 0.959470i \(-0.590935\pi\)
−0.281809 + 0.959470i \(0.590935\pi\)
\(618\) 0 0
\(619\) 2.50000 + 4.33013i 0.100483 + 0.174042i 0.911884 0.410448i \(-0.134628\pi\)
−0.811400 + 0.584491i \(0.801294\pi\)
\(620\) 0 0
\(621\) 1.00000 1.73205i 0.0401286 0.0695048i
\(622\) 0 0
\(623\) −30.0000 10.3923i −1.20192 0.416359i
\(624\) 0 0
\(625\) −12.5000 + 21.6506i −0.500000 + 0.866025i
\(626\) 0 0
\(627\) 3.00000 + 5.19615i 0.119808 + 0.207514i
\(628\) 0 0
\(629\) −10.0000 −0.398726
\(630\) 0 0
\(631\) −4.00000 −0.159237 −0.0796187 0.996825i \(-0.525370\pi\)
−0.0796187 + 0.996825i \(0.525370\pi\)
\(632\) 0 0
\(633\) −10.0000 17.3205i −0.397464 0.688428i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 32.5000 12.9904i 1.28770 0.514698i
\(638\) 0 0
\(639\) −6.00000 + 10.3923i −0.237356 + 0.411113i
\(640\) 0 0
\(641\) −13.0000 22.5167i −0.513469 0.889355i −0.999878 0.0156233i \(-0.995027\pi\)
0.486409 0.873731i \(-0.338307\pi\)
\(642\) 0 0
\(643\) −11.0000 −0.433798 −0.216899 0.976194i \(-0.569594\pi\)
−0.216899 + 0.976194i \(0.569594\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 9.00000 + 15.5885i 0.353827 + 0.612845i 0.986916 0.161233i \(-0.0515470\pi\)
−0.633090 + 0.774078i \(0.718214\pi\)
\(648\) 0 0
\(649\) −10.0000 + 17.3205i −0.392534 + 0.679889i
\(650\) 0 0
\(651\) −2.50000 0.866025i −0.0979827 0.0339422i
\(652\) 0 0
\(653\) −7.00000 + 12.1244i −0.273931 + 0.474463i −0.969865 0.243643i \(-0.921657\pi\)
0.695934 + 0.718106i \(0.254991\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −3.00000 −0.117041
\(658\) 0 0
\(659\) 42.0000 1.63609 0.818044 0.575156i \(-0.195059\pi\)
0.818044 + 0.575156i \(0.195059\pi\)
\(660\) 0 0
\(661\) 1.50000 + 2.59808i 0.0583432 + 0.101053i 0.893722 0.448622i \(-0.148085\pi\)
−0.835379 + 0.549675i \(0.814752\pi\)
\(662\) 0 0
\(663\) 5.00000 8.66025i 0.194184 0.336336i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 8.00000 13.8564i 0.309761 0.536522i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −4.00000 −0.154418
\(672\) 0 0
\(673\) −21.0000 −0.809491 −0.404745 0.914429i \(-0.632640\pi\)
−0.404745 + 0.914429i \(0.632640\pi\)
\(674\) 0 0
\(675\) −2.50000 4.33013i −0.0962250 0.166667i
\(676\) 0 0
\(677\) −6.00000 + 10.3923i −0.230599 + 0.399409i −0.957984 0.286820i \(-0.907402\pi\)
0.727386 + 0.686229i \(0.240735\pi\)
\(678\) 0 0
\(679\) −7.00000 36.3731i −0.268635 1.39587i
\(680\) 0 0
\(681\) −13.0000 + 22.5167i −0.498161 + 0.862840i
\(682\) 0 0
\(683\) −15.0000 25.9808i −0.573959 0.994126i −0.996154 0.0876211i \(-0.972074\pi\)
0.422195 0.906505i \(-0.361260\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 13.0000 0.495981
\(688\) 0 0
\(689\) 5.00000 + 8.66025i 0.190485 + 0.329929i
\(690\) 0 0
\(691\) 2.50000 4.33013i 0.0951045 0.164726i −0.814548 0.580097i \(-0.803015\pi\)
0.909652 + 0.415371i \(0.136348\pi\)
\(692\) 0 0
\(693\) −1.00000 5.19615i −0.0379869 0.197386i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 2.00000 + 3.46410i 0.0757554 + 0.131212i
\(698\) 0 0
\(699\) 12.0000 0.453882
\(700\) 0 0
\(701\) 6.00000 0.226617 0.113308 0.993560i \(-0.463855\pi\)
0.113308 + 0.993560i \(0.463855\pi\)
\(702\) 0 0
\(703\) 7.50000 + 12.9904i 0.282868 + 0.489942i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −36.0000 + 31.1769i −1.35392 + 1.17253i
\(708\) 0 0
\(709\) −11.0000 + 19.0526i −0.413114 + 0.715534i −0.995228 0.0975728i \(-0.968892\pi\)
0.582115 + 0.813107i \(0.302225\pi\)
\(710\) 0 0
\(711\) −8.50000 14.7224i −0.318775 0.552134i
\(712\) 0 0
\(713\) −2.00000 −0.0749006
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 15.0000 + 25.9808i 0.560185 + 0.970269i
\(718\) 0 0
\(719\) 3.00000 5.19615i 0.111881 0.193784i −0.804648 0.593753i \(-0.797646\pi\)
0.916529 + 0.399969i \(0.130979\pi\)
\(720\) 0 0
\(721\) 2.50000 + 0.866025i 0.0931049 + 0.0322525i
\(722\) 0 0
\(723\) −11.0000 + 19.0526i −0.409094 + 0.708572i
\(724\) 0 0
\(725\) −20.0000 34.6410i −0.742781 1.28654i
\(726\) 0 0
\(727\) 13.0000 0.482143 0.241072 0.970507i \(-0.422501\pi\)
0.241072 + 0.970507i \(0.422501\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −7.00000 12.1244i −0.258904 0.448435i
\(732\) 0 0
\(733\) −9.50000 + 16.4545i −0.350891 + 0.607760i −0.986406 0.164328i \(-0.947454\pi\)
0.635515 + 0.772088i \(0.280788\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 11.0000 19.0526i 0.405190 0.701810i
\(738\) 0 0
\(739\) −8.50000 14.7224i −0.312678 0.541573i 0.666264 0.745716i \(-0.267893\pi\)
−0.978941 + 0.204143i \(0.934559\pi\)
\(740\) 0 0
\(741\) −15.0000 −0.551039
\(742\) 0 0
\(743\) −14.0000 −0.513610 −0.256805 0.966463i \(-0.582670\pi\)
−0.256805 + 0.966463i \(0.582670\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −8.00000 + 13.8564i −0.292705 + 0.506979i
\(748\) 0 0
\(749\) 5.00000 + 1.73205i 0.182696 + 0.0632878i
\(750\) 0 0
\(751\) −13.5000 + 23.3827i −0.492622 + 0.853246i −0.999964 0.00849853i \(-0.997295\pi\)
0.507342 + 0.861745i \(0.330628\pi\)
\(752\) 0 0
\(753\) 11.0000 + 19.0526i 0.400862 + 0.694314i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −22.0000 −0.799604 −0.399802 0.916602i \(-0.630921\pi\)
−0.399802 + 0.916602i \(0.630921\pi\)
\(758\) 0 0
\(759\) −2.00000 3.46410i −0.0725954 0.125739i
\(760\) 0 0
\(761\) −15.0000 + 25.9808i −0.543750 + 0.941802i 0.454935 + 0.890525i \(0.349663\pi\)
−0.998684 + 0.0512772i \(0.983671\pi\)
\(762\) 0 0
\(763\) −2.00000 + 1.73205i −0.0724049 + 0.0627044i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −25.0000 43.3013i −0.902698 1.56352i
\(768\) 0 0
\(769\) −9.00000 −0.324548 −0.162274 0.986746i \(-0.551883\pi\)
−0.162274 + 0.986746i \(0.551883\pi\)
\(770\) 0 0
\(771\) 16.0000 0.576226
\(772\) 0 0
\(773\) 9.00000 + 15.5885i 0.323708 + 0.560678i 0.981250 0.192740i \(-0.0617373\pi\)
−0.657542 + 0.753418i \(0.728404\pi\)
\(774\) 0 0
\(775\) −2.50000 + 4.33013i −0.0898027 + 0.155543i
\(776\) 0 0
\(777\) −2.50000 12.9904i −0.0896870 0.466027i
\(778\) 0 0
\(779\) 3.00000 5.19615i 0.107486 0.186171i
\(780\) 0 0
\(781\) 12.0000 + 20.7846i 0.429394 + 0.743732i
\(782\) 0 0
\(783\) 8.00000 0.285897
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −20.0000 34.6410i −0.712923 1.23482i −0.963755 0.266788i \(-0.914038\pi\)
0.250832 0.968031i \(-0.419296\pi\)
\(788\) 0 0
\(789\) 4.00000 6.92820i 0.142404 0.246651i
\(790\) 0 0
\(791\) −6.00000 31.1769i −0.213335 1.10852i
\(792\) 0 0
\(793\) 5.00000 8.66025i 0.177555 0.307535i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 34.0000 1.20434 0.602171 0.798367i \(-0.294303\pi\)
0.602171 + 0.798367i \(0.294303\pi\)
\(798\) 0 0
\(799\) 16.0000 0.566039
\(800\)