Properties

Label 1232.2.q.e.529.1
Level $1232$
Weight $2$
Character 1232.529
Analytic conductor $9.838$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1232.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.83756952902\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 154)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 529.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1232.529
Dual form 1232.2.q.e.177.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.50000 - 2.59808i) q^{3} +(-1.00000 - 1.73205i) q^{5} +(2.50000 + 0.866025i) q^{7} +(-3.00000 - 5.19615i) q^{9} +O(q^{10})\) \(q+(1.50000 - 2.59808i) q^{3} +(-1.00000 - 1.73205i) q^{5} +(2.50000 + 0.866025i) q^{7} +(-3.00000 - 5.19615i) q^{9} +(-0.500000 + 0.866025i) q^{11} -7.00000 q^{13} -6.00000 q^{15} +(-1.00000 + 1.73205i) q^{17} +(6.00000 - 5.19615i) q^{21} +(-4.00000 - 6.92820i) q^{23} +(0.500000 - 0.866025i) q^{25} -9.00000 q^{27} -5.00000 q^{29} +(2.00000 - 3.46410i) q^{31} +(1.50000 + 2.59808i) q^{33} +(-1.00000 - 5.19615i) q^{35} +(-2.00000 - 3.46410i) q^{37} +(-10.5000 + 18.1865i) q^{39} +4.00000 q^{41} +8.00000 q^{43} +(-6.00000 + 10.3923i) q^{45} +(1.00000 + 1.73205i) q^{47} +(5.50000 + 4.33013i) q^{49} +(3.00000 + 5.19615i) q^{51} +(3.00000 - 5.19615i) q^{53} +2.00000 q^{55} +(1.50000 - 2.59808i) q^{59} +(-0.500000 - 0.866025i) q^{61} +(-3.00000 - 15.5885i) q^{63} +(7.00000 + 12.1244i) q^{65} +(4.50000 - 7.79423i) q^{67} -24.0000 q^{69} +2.00000 q^{71} +(-2.00000 + 3.46410i) q^{73} +(-1.50000 - 2.59808i) q^{75} +(-2.00000 + 1.73205i) q^{77} +(4.50000 + 7.79423i) q^{79} +(-4.50000 + 7.79423i) q^{81} -6.00000 q^{83} +4.00000 q^{85} +(-7.50000 + 12.9904i) q^{87} +(-3.00000 - 5.19615i) q^{89} +(-17.5000 - 6.06218i) q^{91} +(-6.00000 - 10.3923i) q^{93} +7.00000 q^{97} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 3 q^{3} - 2 q^{5} + 5 q^{7} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 3 q^{3} - 2 q^{5} + 5 q^{7} - 6 q^{9} - q^{11} - 14 q^{13} - 12 q^{15} - 2 q^{17} + 12 q^{21} - 8 q^{23} + q^{25} - 18 q^{27} - 10 q^{29} + 4 q^{31} + 3 q^{33} - 2 q^{35} - 4 q^{37} - 21 q^{39} + 8 q^{41} + 16 q^{43} - 12 q^{45} + 2 q^{47} + 11 q^{49} + 6 q^{51} + 6 q^{53} + 4 q^{55} + 3 q^{59} - q^{61} - 6 q^{63} + 14 q^{65} + 9 q^{67} - 48 q^{69} + 4 q^{71} - 4 q^{73} - 3 q^{75} - 4 q^{77} + 9 q^{79} - 9 q^{81} - 12 q^{83} + 8 q^{85} - 15 q^{87} - 6 q^{89} - 35 q^{91} - 12 q^{93} + 14 q^{97} + 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1232\mathbb{Z}\right)^\times\).

\(n\) \(309\) \(353\) \(463\) \(673\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.50000 2.59808i 0.866025 1.50000i 1.00000i \(-0.5\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(4\) 0 0
\(5\) −1.00000 1.73205i −0.447214 0.774597i 0.550990 0.834512i \(-0.314250\pi\)
−0.998203 + 0.0599153i \(0.980917\pi\)
\(6\) 0 0
\(7\) 2.50000 + 0.866025i 0.944911 + 0.327327i
\(8\) 0 0
\(9\) −3.00000 5.19615i −1.00000 1.73205i
\(10\) 0 0
\(11\) −0.500000 + 0.866025i −0.150756 + 0.261116i
\(12\) 0 0
\(13\) −7.00000 −1.94145 −0.970725 0.240192i \(-0.922790\pi\)
−0.970725 + 0.240192i \(0.922790\pi\)
\(14\) 0 0
\(15\) −6.00000 −1.54919
\(16\) 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
\(19\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(20\) 0 0
\(21\) 6.00000 5.19615i 1.30931 1.13389i
\(22\) 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
\(27\) −9.00000 −1.73205
\(28\) 0 0
\(29\) −5.00000 −0.928477 −0.464238 0.885710i \(-0.653672\pi\)
−0.464238 + 0.885710i \(0.653672\pi\)
\(30\) 0 0
\(31\) 2.00000 3.46410i 0.359211 0.622171i −0.628619 0.777714i \(-0.716379\pi\)
0.987829 + 0.155543i \(0.0497126\pi\)
\(32\) 0 0
\(33\) 1.50000 + 2.59808i 0.261116 + 0.452267i
\(34\) 0 0
\(35\) −1.00000 5.19615i −0.169031 0.878310i
\(36\) 0 0
\(37\) −2.00000 3.46410i −0.328798 0.569495i 0.653476 0.756948i \(-0.273310\pi\)
−0.982274 + 0.187453i \(0.939977\pi\)
\(38\) 0 0
\(39\) −10.5000 + 18.1865i −1.68135 + 2.91218i
\(40\) 0 0
\(41\) 4.00000 0.624695 0.312348 0.949968i \(-0.398885\pi\)
0.312348 + 0.949968i \(0.398885\pi\)
\(42\) 0 0
\(43\) 8.00000 1.21999 0.609994 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) 0 0
\(45\) −6.00000 + 10.3923i −0.894427 + 1.54919i
\(46\) 0 0
\(47\) 1.00000 + 1.73205i 0.145865 + 0.252646i 0.929695 0.368329i \(-0.120070\pi\)
−0.783830 + 0.620975i \(0.786737\pi\)
\(48\) 0 0
\(49\) 5.50000 + 4.33013i 0.785714 + 0.618590i
\(50\) 0 0
\(51\) 3.00000 + 5.19615i 0.420084 + 0.727607i
\(52\) 0 0
\(53\) 3.00000 5.19615i 0.412082 0.713746i −0.583036 0.812447i \(-0.698135\pi\)
0.995117 + 0.0987002i \(0.0314685\pi\)
\(54\) 0 0
\(55\) 2.00000 0.269680
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 1.50000 2.59808i 0.195283 0.338241i −0.751710 0.659494i \(-0.770771\pi\)
0.946993 + 0.321253i \(0.104104\pi\)
\(60\) 0 0
\(61\) −0.500000 0.866025i −0.0640184 0.110883i 0.832240 0.554416i \(-0.187058\pi\)
−0.896258 + 0.443533i \(0.853725\pi\)
\(62\) 0 0
\(63\) −3.00000 15.5885i −0.377964 1.96396i
\(64\) 0 0
\(65\) 7.00000 + 12.1244i 0.868243 + 1.50384i
\(66\) 0 0
\(67\) 4.50000 7.79423i 0.549762 0.952217i −0.448528 0.893769i \(-0.648052\pi\)
0.998290 0.0584478i \(-0.0186151\pi\)
\(68\) 0 0
\(69\) −24.0000 −2.88926
\(70\) 0 0
\(71\) 2.00000 0.237356 0.118678 0.992933i \(-0.462134\pi\)
0.118678 + 0.992933i \(0.462134\pi\)
\(72\) 0 0
\(73\) −2.00000 + 3.46410i −0.234082 + 0.405442i −0.959006 0.283387i \(-0.908542\pi\)
0.724923 + 0.688830i \(0.241875\pi\)
\(74\) 0 0
\(75\) −1.50000 2.59808i −0.173205 0.300000i
\(76\) 0 0
\(77\) −2.00000 + 1.73205i −0.227921 + 0.197386i
\(78\) 0 0
\(79\) 4.50000 + 7.79423i 0.506290 + 0.876919i 0.999974 + 0.00727784i \(0.00231663\pi\)
−0.493684 + 0.869641i \(0.664350\pi\)
\(80\) 0 0
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) 0 0
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) 0 0
\(85\) 4.00000 0.433861
\(86\) 0 0
\(87\) −7.50000 + 12.9904i −0.804084 + 1.39272i
\(88\) 0 0
\(89\) −3.00000 5.19615i −0.317999 0.550791i 0.662071 0.749441i \(-0.269678\pi\)
−0.980071 + 0.198650i \(0.936344\pi\)
\(90\) 0 0
\(91\) −17.5000 6.06218i −1.83450 0.635489i
\(92\) 0 0
\(93\) −6.00000 10.3923i −0.622171 1.07763i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 7.00000 0.710742 0.355371 0.934725i \(-0.384354\pi\)
0.355371 + 0.934725i \(0.384354\pi\)
\(98\) 0 0
\(99\) 6.00000 0.603023
\(100\) 0 0
\(101\) 4.50000 7.79423i 0.447767 0.775555i −0.550474 0.834853i \(-0.685553\pi\)
0.998240 + 0.0592978i \(0.0188862\pi\)
\(102\) 0 0
\(103\) 9.00000 + 15.5885i 0.886796 + 1.53598i 0.843641 + 0.536908i \(0.180408\pi\)
0.0431555 + 0.999068i \(0.486259\pi\)
\(104\) 0 0
\(105\) −15.0000 5.19615i −1.46385 0.507093i
\(106\) 0 0
\(107\) 1.00000 + 1.73205i 0.0966736 + 0.167444i 0.910306 0.413936i \(-0.135846\pi\)
−0.813632 + 0.581380i \(0.802513\pi\)
\(108\) 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
\(111\) −12.0000 −1.13899
\(112\) 0 0
\(113\) 5.00000 0.470360 0.235180 0.971952i \(-0.424432\pi\)
0.235180 + 0.971952i \(0.424432\pi\)
\(114\) 0 0
\(115\) −8.00000 + 13.8564i −0.746004 + 1.29212i
\(116\) 0 0
\(117\) 21.0000 + 36.3731i 1.94145 + 3.36269i
\(118\) 0 0
\(119\) −4.00000 + 3.46410i −0.366679 + 0.317554i
\(120\) 0 0
\(121\) −0.500000 0.866025i −0.0454545 0.0787296i
\(122\) 0 0
\(123\) 6.00000 10.3923i 0.541002 0.937043i
\(124\) 0 0
\(125\) −12.0000 −1.07331
\(126\) 0 0
\(127\) 19.0000 1.68598 0.842989 0.537931i \(-0.180794\pi\)
0.842989 + 0.537931i \(0.180794\pi\)
\(128\) 0 0
\(129\) 12.0000 20.7846i 1.05654 1.82998i
\(130\) 0 0
\(131\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 9.00000 + 15.5885i 0.774597 + 1.34164i
\(136\) 0 0
\(137\) −1.50000 + 2.59808i −0.128154 + 0.221969i −0.922961 0.384893i \(-0.874238\pi\)
0.794808 + 0.606861i \(0.207572\pi\)
\(138\) 0 0
\(139\) 4.00000 0.339276 0.169638 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 0 0
\(141\) 6.00000 0.505291
\(142\) 0 0
\(143\) 3.50000 6.06218i 0.292685 0.506945i
\(144\) 0 0
\(145\) 5.00000 + 8.66025i 0.415227 + 0.719195i
\(146\) 0 0
\(147\) 19.5000 7.79423i 1.60833 0.642857i
\(148\) 0 0
\(149\) 5.00000 + 8.66025i 0.409616 + 0.709476i 0.994847 0.101391i \(-0.0323294\pi\)
−0.585231 + 0.810867i \(0.698996\pi\)
\(150\) 0 0
\(151\) −1.50000 + 2.59808i −0.122068 + 0.211428i −0.920583 0.390547i \(-0.872286\pi\)
0.798515 + 0.601975i \(0.205619\pi\)
\(152\) 0 0
\(153\) 12.0000 0.970143
\(154\) 0 0
\(155\) −8.00000 −0.642575
\(156\) 0 0
\(157\) −8.00000 + 13.8564i −0.638470 + 1.10586i 0.347299 + 0.937754i \(0.387099\pi\)
−0.985769 + 0.168107i \(0.946235\pi\)
\(158\) 0 0
\(159\) −9.00000 15.5885i −0.713746 1.23625i
\(160\) 0 0
\(161\) −4.00000 20.7846i −0.315244 1.63806i
\(162\) 0 0
\(163\) −8.50000 14.7224i −0.665771 1.15315i −0.979076 0.203497i \(-0.934769\pi\)
0.313304 0.949653i \(-0.398564\pi\)
\(164\) 0 0
\(165\) 3.00000 5.19615i 0.233550 0.404520i
\(166\) 0 0
\(167\) −19.0000 −1.47026 −0.735132 0.677924i \(-0.762880\pi\)
−0.735132 + 0.677924i \(0.762880\pi\)
\(168\) 0 0
\(169\) 36.0000 2.76923
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −12.5000 21.6506i −0.950357 1.64607i −0.744652 0.667453i \(-0.767384\pi\)
−0.205706 0.978614i \(-0.565949\pi\)
\(174\) 0 0
\(175\) 2.00000 1.73205i 0.151186 0.130931i
\(176\) 0 0
\(177\) −4.50000 7.79423i −0.338241 0.585850i
\(178\) 0 0
\(179\) 9.50000 16.4545i 0.710063 1.22987i −0.254770 0.967002i \(-0.582000\pi\)
0.964833 0.262864i \(-0.0846670\pi\)
\(180\) 0 0
\(181\) −22.0000 −1.63525 −0.817624 0.575753i \(-0.804709\pi\)
−0.817624 + 0.575753i \(0.804709\pi\)
\(182\) 0 0
\(183\) −3.00000 −0.221766
\(184\) 0 0
\(185\) −4.00000 + 6.92820i −0.294086 + 0.509372i
\(186\) 0 0
\(187\) −1.00000 1.73205i −0.0731272 0.126660i
\(188\) 0 0
\(189\) −22.5000 7.79423i −1.63663 0.566947i
\(190\) 0 0
\(191\) 1.00000 + 1.73205i 0.0723575 + 0.125327i 0.899934 0.436026i \(-0.143614\pi\)
−0.827577 + 0.561353i \(0.810281\pi\)
\(192\) 0 0
\(193\) −4.00000 + 6.92820i −0.287926 + 0.498703i −0.973315 0.229475i \(-0.926299\pi\)
0.685388 + 0.728178i \(0.259632\pi\)
\(194\) 0 0
\(195\) 42.0000 3.00768
\(196\) 0 0
\(197\) 15.0000 1.06871 0.534353 0.845262i \(-0.320555\pi\)
0.534353 + 0.845262i \(0.320555\pi\)
\(198\) 0 0
\(199\) 2.00000 3.46410i 0.141776 0.245564i −0.786389 0.617731i \(-0.788052\pi\)
0.928166 + 0.372168i \(0.121385\pi\)
\(200\) 0 0
\(201\) −13.5000 23.3827i −0.952217 1.64929i
\(202\) 0 0
\(203\) −12.5000 4.33013i −0.877328 0.303915i
\(204\) 0 0
\(205\) −4.00000 6.92820i −0.279372 0.483887i
\(206\) 0 0
\(207\) −24.0000 + 41.5692i −1.66812 + 2.88926i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 20.0000 1.37686 0.688428 0.725304i \(-0.258301\pi\)
0.688428 + 0.725304i \(0.258301\pi\)
\(212\) 0 0
\(213\) 3.00000 5.19615i 0.205557 0.356034i
\(214\) 0 0
\(215\) −8.00000 13.8564i −0.545595 0.944999i
\(216\) 0 0
\(217\) 8.00000 6.92820i 0.543075 0.470317i
\(218\) 0 0
\(219\) 6.00000 + 10.3923i 0.405442 + 0.702247i
\(220\) 0 0
\(221\) 7.00000 12.1244i 0.470871 0.815572i
\(222\) 0 0
\(223\) −4.00000 −0.267860 −0.133930 0.990991i \(-0.542760\pi\)
−0.133930 + 0.990991i \(0.542760\pi\)
\(224\) 0 0
\(225\) −6.00000 −0.400000
\(226\) 0 0
\(227\) −1.00000 + 1.73205i −0.0663723 + 0.114960i −0.897302 0.441417i \(-0.854476\pi\)
0.830930 + 0.556378i \(0.187809\pi\)
\(228\) 0 0
\(229\) 14.0000 + 24.2487i 0.925146 + 1.60240i 0.791326 + 0.611394i \(0.209391\pi\)
0.133820 + 0.991006i \(0.457276\pi\)
\(230\) 0 0
\(231\) 1.50000 + 7.79423i 0.0986928 + 0.512823i
\(232\) 0 0
\(233\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(234\) 0 0
\(235\) 2.00000 3.46410i 0.130466 0.225973i
\(236\) 0 0
\(237\) 27.0000 1.75384
\(238\) 0 0
\(239\) 5.00000 0.323423 0.161712 0.986838i \(-0.448299\pi\)
0.161712 + 0.986838i \(0.448299\pi\)
\(240\) 0 0
\(241\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 2.00000 13.8564i 0.127775 0.885253i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) −9.00000 + 15.5885i −0.570352 + 0.987878i
\(250\) 0 0
\(251\) 24.0000 1.51487 0.757433 0.652913i \(-0.226453\pi\)
0.757433 + 0.652913i \(0.226453\pi\)
\(252\) 0 0
\(253\) 8.00000 0.502956
\(254\) 0 0
\(255\) 6.00000 10.3923i 0.375735 0.650791i
\(256\) 0 0
\(257\) −1.50000 2.59808i −0.0935674 0.162064i 0.815442 0.578838i \(-0.196494\pi\)
−0.909010 + 0.416775i \(0.863160\pi\)
\(258\) 0 0
\(259\) −2.00000 10.3923i −0.124274 0.645746i
\(260\) 0 0
\(261\) 15.0000 + 25.9808i 0.928477 + 1.60817i
\(262\) 0 0
\(263\) 13.5000 23.3827i 0.832446 1.44184i −0.0636476 0.997972i \(-0.520273\pi\)
0.896093 0.443866i \(-0.146393\pi\)
\(264\) 0 0
\(265\) −12.0000 −0.737154
\(266\) 0 0
\(267\) −18.0000 −1.10158
\(268\) 0 0
\(269\) 12.0000 20.7846i 0.731653 1.26726i −0.224523 0.974469i \(-0.572083\pi\)
0.956176 0.292791i \(-0.0945841\pi\)
\(270\) 0 0
\(271\) −5.50000 9.52628i −0.334101 0.578680i 0.649211 0.760609i \(-0.275099\pi\)
−0.983312 + 0.181928i \(0.941766\pi\)
\(272\) 0 0
\(273\) −42.0000 + 36.3731i −2.54196 + 2.20140i
\(274\) 0 0
\(275\) 0.500000 + 0.866025i 0.0301511 + 0.0522233i
\(276\) 0 0
\(277\) 4.50000 7.79423i 0.270379 0.468310i −0.698580 0.715532i \(-0.746184\pi\)
0.968959 + 0.247222i \(0.0795177\pi\)
\(278\) 0 0
\(279\) −24.0000 −1.43684
\(280\) 0 0
\(281\) −28.0000 −1.67034 −0.835170 0.549992i \(-0.814631\pi\)
−0.835170 + 0.549992i \(0.814631\pi\)
\(282\) 0 0
\(283\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 10.0000 + 3.46410i 0.590281 + 0.204479i
\(288\) 0 0
\(289\) 6.50000 + 11.2583i 0.382353 + 0.662255i
\(290\) 0 0
\(291\) 10.5000 18.1865i 0.615521 1.06611i
\(292\) 0 0
\(293\) −18.0000 −1.05157 −0.525786 0.850617i \(-0.676229\pi\)
−0.525786 + 0.850617i \(0.676229\pi\)
\(294\) 0 0
\(295\) −6.00000 −0.349334
\(296\) 0 0
\(297\) 4.50000 7.79423i 0.261116 0.452267i
\(298\) 0 0
\(299\) 28.0000 + 48.4974i 1.61928 + 2.80468i
\(300\) 0 0
\(301\) 20.0000 + 6.92820i 1.15278 + 0.399335i
\(302\) 0 0
\(303\) −13.5000 23.3827i −0.775555 1.34330i
\(304\) 0 0
\(305\) −1.00000 + 1.73205i −0.0572598 + 0.0991769i
\(306\) 0 0
\(307\) −2.00000 −0.114146 −0.0570730 0.998370i \(-0.518177\pi\)
−0.0570730 + 0.998370i \(0.518177\pi\)
\(308\) 0 0
\(309\) 54.0000 3.07195
\(310\) 0 0
\(311\) −5.00000 + 8.66025i −0.283524 + 0.491078i −0.972250 0.233944i \(-0.924837\pi\)
0.688726 + 0.725022i \(0.258170\pi\)
\(312\) 0 0
\(313\) −0.500000 0.866025i −0.0282617 0.0489506i 0.851549 0.524276i \(-0.175664\pi\)
−0.879810 + 0.475325i \(0.842331\pi\)
\(314\) 0 0
\(315\) −24.0000 + 20.7846i −1.35225 + 1.17108i
\(316\) 0 0
\(317\) 6.00000 + 10.3923i 0.336994 + 0.583690i 0.983866 0.178908i \(-0.0572566\pi\)
−0.646872 + 0.762598i \(0.723923\pi\)
\(318\) 0 0
\(319\) 2.50000 4.33013i 0.139973 0.242441i
\(320\) 0 0
\(321\) 6.00000 0.334887
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) −3.50000 + 6.06218i −0.194145 + 0.336269i
\(326\) 0 0
\(327\) −3.00000 5.19615i −0.165900 0.287348i
\(328\) 0 0
\(329\) 1.00000 + 5.19615i 0.0551318 + 0.286473i
\(330\) 0 0
\(331\) 6.50000 + 11.2583i 0.357272 + 0.618814i 0.987504 0.157593i \(-0.0503735\pi\)
−0.630232 + 0.776407i \(0.717040\pi\)
\(332\) 0 0
\(333\) −12.0000 + 20.7846i −0.657596 + 1.13899i
\(334\) 0 0
\(335\) −18.0000 −0.983445
\(336\) 0 0
\(337\) −12.0000 −0.653682 −0.326841 0.945079i \(-0.605984\pi\)
−0.326841 + 0.945079i \(0.605984\pi\)
\(338\) 0 0
\(339\) 7.50000 12.9904i 0.407344 0.705541i
\(340\) 0 0
\(341\) 2.00000 + 3.46410i 0.108306 + 0.187592i
\(342\) 0 0
\(343\) 10.0000 + 15.5885i 0.539949 + 0.841698i
\(344\) 0 0
\(345\) 24.0000 + 41.5692i 1.29212 + 2.23801i
\(346\) 0 0
\(347\) −11.0000 + 19.0526i −0.590511 + 1.02279i 0.403653 + 0.914912i \(0.367740\pi\)
−0.994164 + 0.107883i \(0.965593\pi\)
\(348\) 0 0
\(349\) 2.00000 0.107058 0.0535288 0.998566i \(-0.482953\pi\)
0.0535288 + 0.998566i \(0.482953\pi\)
\(350\) 0 0
\(351\) 63.0000 3.36269
\(352\) 0 0
\(353\) 9.00000 15.5885i 0.479022 0.829690i −0.520689 0.853746i \(-0.674325\pi\)
0.999711 + 0.0240566i \(0.00765819\pi\)
\(354\) 0 0
\(355\) −2.00000 3.46410i −0.106149 0.183855i
\(356\) 0 0
\(357\) 3.00000 + 15.5885i 0.158777 + 0.825029i
\(358\) 0 0
\(359\) −9.50000 16.4545i −0.501391 0.868434i −0.999999 0.00160673i \(-0.999489\pi\)
0.498608 0.866828i \(-0.333845\pi\)
\(360\) 0 0
\(361\) 9.50000 16.4545i 0.500000 0.866025i
\(362\) 0 0
\(363\) −3.00000 −0.157459
\(364\) 0 0
\(365\) 8.00000 0.418739
\(366\) 0 0
\(367\) 2.00000 3.46410i 0.104399 0.180825i −0.809093 0.587680i \(-0.800041\pi\)
0.913493 + 0.406855i \(0.133375\pi\)
\(368\) 0 0
\(369\) −12.0000 20.7846i −0.624695 1.08200i
\(370\) 0 0
\(371\) 12.0000 10.3923i 0.623009 0.539542i
\(372\) 0 0
\(373\) −5.50000 9.52628i −0.284779 0.493252i 0.687776 0.725923i \(-0.258587\pi\)
−0.972556 + 0.232671i \(0.925254\pi\)
\(374\) 0 0
\(375\) −18.0000 + 31.1769i −0.929516 + 1.60997i
\(376\) 0 0
\(377\) 35.0000 1.80259
\(378\) 0 0
\(379\) −1.00000 −0.0513665 −0.0256833 0.999670i \(-0.508176\pi\)
−0.0256833 + 0.999670i \(0.508176\pi\)
\(380\) 0 0
\(381\) 28.5000 49.3634i 1.46010 2.52897i
\(382\) 0 0
\(383\) 13.0000 + 22.5167i 0.664269 + 1.15055i 0.979483 + 0.201527i \(0.0645904\pi\)
−0.315214 + 0.949021i \(0.602076\pi\)
\(384\) 0 0
\(385\) 5.00000 + 1.73205i 0.254824 + 0.0882735i
\(386\) 0 0
\(387\) −24.0000 41.5692i −1.21999 2.11308i
\(388\) 0 0
\(389\) −9.00000 + 15.5885i −0.456318 + 0.790366i −0.998763 0.0497253i \(-0.984165\pi\)
0.542445 + 0.840091i \(0.317499\pi\)
\(390\) 0 0
\(391\) 16.0000 0.809155
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 9.00000 15.5885i 0.452839 0.784340i
\(396\) 0 0
\(397\) −3.00000 5.19615i −0.150566 0.260787i 0.780870 0.624694i \(-0.214776\pi\)
−0.931436 + 0.363906i \(0.881443\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 4.50000 + 7.79423i 0.224719 + 0.389225i 0.956235 0.292599i \(-0.0945202\pi\)
−0.731516 + 0.681824i \(0.761187\pi\)
\(402\) 0 0
\(403\) −14.0000 + 24.2487i −0.697390 + 1.20791i
\(404\) 0 0
\(405\) 18.0000 0.894427
\(406\) 0 0
\(407\) 4.00000 0.198273
\(408\) 0 0
\(409\) −11.0000 + 19.0526i −0.543915 + 0.942088i 0.454759 + 0.890614i \(0.349725\pi\)
−0.998674 + 0.0514740i \(0.983608\pi\)
\(410\) 0 0
\(411\) 4.50000 + 7.79423i 0.221969 + 0.384461i
\(412\) 0 0
\(413\) 6.00000 5.19615i 0.295241 0.255686i
\(414\) 0 0
\(415\) 6.00000 + 10.3923i 0.294528 + 0.510138i
\(416\) 0 0
\(417\) 6.00000 10.3923i 0.293821 0.508913i
\(418\) 0 0
\(419\) −16.0000 −0.781651 −0.390826 0.920465i \(-0.627810\pi\)
−0.390826 + 0.920465i \(0.627810\pi\)
\(420\) 0 0
\(421\) −20.0000 −0.974740 −0.487370 0.873195i \(-0.662044\pi\)
−0.487370 + 0.873195i \(0.662044\pi\)
\(422\) 0 0
\(423\) 6.00000 10.3923i 0.291730 0.505291i
\(424\) 0 0
\(425\) 1.00000 + 1.73205i 0.0485071 + 0.0840168i
\(426\) 0 0
\(427\) −0.500000 2.59808i −0.0241967 0.125730i
\(428\) 0 0
\(429\) −10.5000 18.1865i −0.506945 0.878054i
\(430\) 0 0
\(431\) 12.5000 21.6506i 0.602104 1.04287i −0.390398 0.920646i \(-0.627663\pi\)
0.992502 0.122228i \(-0.0390040\pi\)
\(432\) 0 0
\(433\) −34.0000 −1.63394 −0.816968 0.576683i \(-0.804347\pi\)
−0.816968 + 0.576683i \(0.804347\pi\)
\(434\) 0 0
\(435\) 30.0000 1.43839
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −2.50000 4.33013i −0.119318 0.206666i 0.800179 0.599761i \(-0.204738\pi\)
−0.919498 + 0.393095i \(0.871404\pi\)
\(440\) 0 0
\(441\) 6.00000 41.5692i 0.285714 1.97949i
\(442\) 0 0
\(443\) 18.0000 + 31.1769i 0.855206 + 1.48126i 0.876454 + 0.481486i \(0.159903\pi\)
−0.0212481 + 0.999774i \(0.506764\pi\)
\(444\) 0 0
\(445\) −6.00000 + 10.3923i −0.284427 + 0.492642i
\(446\) 0 0
\(447\) 30.0000 1.41895
\(448\) 0 0
\(449\) −6.00000 −0.283158 −0.141579 0.989927i \(-0.545218\pi\)
−0.141579 + 0.989927i \(0.545218\pi\)
\(450\) 0 0
\(451\) −2.00000 + 3.46410i −0.0941763 + 0.163118i
\(452\) 0 0
\(453\) 4.50000 + 7.79423i 0.211428 + 0.366205i
\(454\) 0 0
\(455\) 7.00000 + 36.3731i 0.328165 + 1.70520i
\(456\) 0 0
\(457\) −7.00000 12.1244i −0.327446 0.567153i 0.654558 0.756012i \(-0.272855\pi\)
−0.982004 + 0.188858i \(0.939521\pi\)
\(458\) 0 0
\(459\) 9.00000 15.5885i 0.420084 0.727607i
\(460\) 0 0
\(461\) 27.0000 1.25752 0.628758 0.777601i \(-0.283564\pi\)
0.628758 + 0.777601i \(0.283564\pi\)
\(462\) 0 0
\(463\) 2.00000 0.0929479 0.0464739 0.998920i \(-0.485202\pi\)
0.0464739 + 0.998920i \(0.485202\pi\)
\(464\) 0 0
\(465\) −12.0000 + 20.7846i −0.556487 + 0.963863i
\(466\) 0 0
\(467\) 6.00000 + 10.3923i 0.277647 + 0.480899i 0.970799 0.239892i \(-0.0771121\pi\)
−0.693153 + 0.720791i \(0.743779\pi\)
\(468\) 0 0
\(469\) 18.0000 15.5885i 0.831163 0.719808i
\(470\) 0 0
\(471\) 24.0000 + 41.5692i 1.10586 + 1.91541i
\(472\) 0 0
\(473\) −4.00000 + 6.92820i −0.183920 + 0.318559i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −36.0000 −1.64833
\(478\) 0 0
\(479\) −0.500000 + 0.866025i −0.0228456 + 0.0395697i −0.877222 0.480085i \(-0.840606\pi\)
0.854377 + 0.519654i \(0.173939\pi\)
\(480\) 0 0
\(481\) 14.0000 + 24.2487i 0.638345 + 1.10565i
\(482\) 0 0
\(483\) −60.0000 20.7846i −2.73009 0.945732i
\(484\) 0 0
\(485\) −7.00000 12.1244i −0.317854 0.550539i
\(486\) 0 0
\(487\) −20.0000 + 34.6410i −0.906287 + 1.56973i −0.0871056 + 0.996199i \(0.527762\pi\)
−0.819181 + 0.573535i \(0.805572\pi\)
\(488\) 0 0
\(489\) −51.0000 −2.30630
\(490\) 0 0
\(491\) −30.0000 −1.35388 −0.676941 0.736038i \(-0.736695\pi\)
−0.676941 + 0.736038i \(0.736695\pi\)
\(492\) 0 0
\(493\) 5.00000 8.66025i 0.225189 0.390038i
\(494\) 0 0
\(495\) −6.00000 10.3923i −0.269680 0.467099i
\(496\) 0 0
\(497\) 5.00000 + 1.73205i 0.224281 + 0.0776931i
\(498\) 0 0
\(499\) 10.0000 + 17.3205i 0.447661 + 0.775372i 0.998233 0.0594153i \(-0.0189236\pi\)
−0.550572 + 0.834788i \(0.685590\pi\)
\(500\) 0 0
\(501\) −28.5000 + 49.3634i −1.27329 + 2.20540i
\(502\) 0 0
\(503\) −3.00000 −0.133763 −0.0668817 0.997761i \(-0.521305\pi\)
−0.0668817 + 0.997761i \(0.521305\pi\)
\(504\) 0 0
\(505\) −18.0000 −0.800989
\(506\) 0 0
\(507\) 54.0000 93.5307i 2.39822 4.15385i
\(508\) 0 0
\(509\) 11.0000 + 19.0526i 0.487566 + 0.844490i 0.999898 0.0142980i \(-0.00455136\pi\)
−0.512331 + 0.858788i \(0.671218\pi\)
\(510\) 0 0
\(511\) −8.00000 + 6.92820i −0.353899 + 0.306486i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 18.0000 31.1769i 0.793175 1.37382i
\(516\) 0 0
\(517\) −2.00000 −0.0879599
\(518\) 0 0
\(519\) −75.0000 −3.29213
\(520\) 0 0
\(521\) −5.00000 + 8.66025i −0.219054 + 0.379413i −0.954519 0.298150i \(-0.903630\pi\)
0.735465 + 0.677563i \(0.236964\pi\)
\(522\) 0 0
\(523\) −5.00000 8.66025i −0.218635 0.378686i 0.735756 0.677247i \(-0.236827\pi\)
−0.954391 + 0.298560i \(0.903494\pi\)
\(524\) 0 0
\(525\) −1.50000 7.79423i −0.0654654 0.340168i
\(526\) 0 0
\(527\) 4.00000 + 6.92820i 0.174243 + 0.301797i
\(528\) 0 0
\(529\) −20.5000 + 35.5070i −0.891304 + 1.54378i
\(530\) 0 0
\(531\) −18.0000 −0.781133
\(532\) 0 0
\(533\) −28.0000 −1.21281
\(534\) 0 0
\(535\) 2.00000 3.46410i 0.0864675 0.149766i
\(536\) 0 0
\(537\) −28.5000 49.3634i −1.22987 2.13019i
\(538\) 0 0
\(539\) −6.50000 + 2.59808i −0.279975 + 0.111907i
\(540\) 0 0
\(541\) −2.50000 4.33013i −0.107483 0.186167i 0.807267 0.590187i \(-0.200946\pi\)
−0.914750 + 0.404020i \(0.867613\pi\)
\(542\) 0 0
\(543\) −33.0000 + 57.1577i −1.41617 + 2.45287i
\(544\) 0 0
\(545\) −4.00000 −0.171341
\(546\) 0 0
\(547\) −30.0000 −1.28271 −0.641354 0.767245i \(-0.721627\pi\)
−0.641354 + 0.767245i \(0.721627\pi\)
\(548\) 0 0
\(549\) −3.00000 + 5.19615i −0.128037 + 0.221766i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 4.50000 + 23.3827i 0.191359 + 0.994333i
\(554\) 0 0
\(555\) 12.0000 + 20.7846i 0.509372 + 0.882258i
\(556\) 0 0
\(557\) −13.0000 + 22.5167i −0.550828 + 0.954062i 0.447387 + 0.894340i \(0.352355\pi\)
−0.998215 + 0.0597213i \(0.980979\pi\)
\(558\) 0 0
\(559\) −56.0000 −2.36855
\(560\) 0 0
\(561\) −6.00000 −0.253320
\(562\) 0 0
\(563\) 10.0000 17.3205i 0.421450 0.729972i −0.574632 0.818412i \(-0.694855\pi\)
0.996082 + 0.0884397i \(0.0281881\pi\)
\(564\) 0 0
\(565\) −5.00000 8.66025i −0.210352 0.364340i
\(566\) 0 0
\(567\) −18.0000 + 15.5885i −0.755929 + 0.654654i
\(568\) 0 0
\(569\) 6.00000 + 10.3923i 0.251533 + 0.435668i 0.963948 0.266090i \(-0.0857319\pi\)
−0.712415 + 0.701758i \(0.752399\pi\)
\(570\) 0 0
\(571\) 11.0000 19.0526i 0.460336 0.797325i −0.538642 0.842535i \(-0.681062\pi\)
0.998978 + 0.0452101i \(0.0143957\pi\)
\(572\) 0 0
\(573\) 6.00000 0.250654
\(574\) 0 0
\(575\) −8.00000 −0.333623
\(576\) 0 0
\(577\) 21.5000 37.2391i 0.895057 1.55028i 0.0613223 0.998118i \(-0.480468\pi\)
0.833734 0.552166i \(-0.186198\pi\)
\(578\) 0 0
\(579\) 12.0000 + 20.7846i 0.498703 + 0.863779i
\(580\) 0 0
\(581\) −15.0000 5.19615i −0.622305 0.215573i
\(582\) 0 0
\(583\) 3.00000 + 5.19615i 0.124247 + 0.215203i
\(584\) 0 0
\(585\) 42.0000 72.7461i 1.73649 3.00768i
\(586\) 0 0
\(587\) −27.0000 −1.11441 −0.557205 0.830375i \(-0.688126\pi\)
−0.557205 + 0.830375i \(0.688126\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 22.5000 38.9711i 0.925526 1.60306i
\(592\) 0 0
\(593\) −3.00000 5.19615i −0.123195 0.213380i 0.797831 0.602881i \(-0.205981\pi\)
−0.921026 + 0.389501i \(0.872647\pi\)
\(594\) 0 0
\(595\) 10.0000 + 3.46410i 0.409960 + 0.142014i
\(596\) 0 0
\(597\) −6.00000 10.3923i −0.245564 0.425329i
\(598\) 0 0
\(599\) 18.0000 31.1769i 0.735460 1.27385i −0.219061 0.975711i \(-0.570299\pi\)
0.954521 0.298143i \(-0.0963673\pi\)
\(600\) 0 0
\(601\) 26.0000 1.06056 0.530281 0.847822i \(-0.322086\pi\)
0.530281 + 0.847822i \(0.322086\pi\)
\(602\) 0 0
\(603\) −54.0000 −2.19905
\(604\) 0 0
\(605\) −1.00000 + 1.73205i −0.0406558 + 0.0704179i
\(606\) 0 0
\(607\) 4.00000 + 6.92820i 0.162355 + 0.281207i 0.935713 0.352763i \(-0.114758\pi\)
−0.773358 + 0.633970i \(0.781424\pi\)
\(608\) 0 0
\(609\) −30.0000 + 25.9808i −1.21566 + 1.05279i
\(610\) 0 0
\(611\) −7.00000 12.1244i −0.283190 0.490499i
\(612\) 0 0
\(613\) 19.0000 32.9090i 0.767403 1.32918i −0.171564 0.985173i \(-0.554882\pi\)
0.938967 0.344008i \(-0.111785\pi\)
\(614\) 0 0
\(615\) −24.0000 −0.967773
\(616\) 0 0
\(617\) −15.0000 −0.603877 −0.301939 0.953327i \(-0.597634\pi\)
−0.301939 + 0.953327i \(0.597634\pi\)
\(618\) 0 0
\(619\) −14.0000 + 24.2487i −0.562708 + 0.974638i 0.434551 + 0.900647i \(0.356907\pi\)
−0.997259 + 0.0739910i \(0.976426\pi\)
\(620\) 0 0
\(621\) 36.0000 + 62.3538i 1.44463 + 2.50217i
\(622\) 0 0
\(623\) −3.00000 15.5885i −0.120192 0.624538i
\(624\) 0 0
\(625\) 9.50000 + 16.4545i 0.380000 + 0.658179i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 8.00000 0.318981
\(630\) 0 0
\(631\) 18.0000 0.716569 0.358284 0.933613i \(-0.383362\pi\)
0.358284 + 0.933613i \(0.383362\pi\)
\(632\) 0 0
\(633\) 30.0000 51.9615i 1.19239 2.06529i
\(634\) 0 0
\(635\) −19.0000 32.9090i −0.753992 1.30595i
\(636\) 0 0
\(637\) −38.5000 30.3109i −1.52543 1.20096i
\(638\) 0 0
\(639\) −6.00000 10.3923i −0.237356 0.411113i
\(640\) 0 0
\(641\) 13.5000 23.3827i 0.533218 0.923561i −0.466029 0.884769i \(-0.654316\pi\)
0.999247 0.0387913i \(-0.0123508\pi\)
\(642\) 0 0
\(643\) −31.0000 −1.22252 −0.611260 0.791430i \(-0.709337\pi\)
−0.611260 + 0.791430i \(0.709337\pi\)
\(644\) 0 0
\(645\) −48.0000 −1.89000
\(646\) 0 0
\(647\) 15.0000 25.9808i 0.589711 1.02141i −0.404559 0.914512i \(-0.632575\pi\)
0.994270 0.106897i \(-0.0340916\pi\)
\(648\) 0 0
\(649\) 1.50000 + 2.59808i 0.0588802 + 0.101983i
\(650\) 0 0
\(651\) −6.00000 31.1769i −0.235159 1.22192i
\(652\) 0 0
\(653\) −20.0000 34.6410i −0.782660 1.35561i −0.930387 0.366579i \(-0.880529\pi\)
0.147726 0.989028i \(-0.452805\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 24.0000 0.936329
\(658\) 0 0
\(659\) −28.0000 −1.09073 −0.545363 0.838200i \(-0.683608\pi\)
−0.545363 + 0.838200i \(0.683608\pi\)
\(660\) 0 0
\(661\) 11.0000 19.0526i 0.427850 0.741059i −0.568831 0.822454i \(-0.692604\pi\)
0.996682 + 0.0813955i \(0.0259377\pi\)
\(662\) 0 0
\(663\) −21.0000 36.3731i −0.815572 1.41261i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 20.0000 + 34.6410i 0.774403 + 1.34131i
\(668\) 0 0
\(669\) −6.00000 + 10.3923i −0.231973 + 0.401790i
\(670\) 0 0
\(671\) 1.00000 0.0386046
\(672\) 0 0
\(673\) 34.0000 1.31060 0.655302 0.755367i \(-0.272541\pi\)
0.655302 + 0.755367i \(0.272541\pi\)
\(674\) 0 0
\(675\) −4.50000 + 7.79423i −0.173205 + 0.300000i
\(676\) 0 0
\(677\) −7.00000 12.1244i −0.269032 0.465977i 0.699580 0.714554i \(-0.253370\pi\)
−0.968612 + 0.248577i \(0.920037\pi\)
\(678\) 0 0
\(679\) 17.5000 + 6.06218i 0.671588 + 0.232645i
\(680\) 0 0
\(681\) 3.00000 + 5.19615i 0.114960 + 0.199117i
\(682\) 0 0
\(683\) 10.5000 18.1865i 0.401771 0.695888i −0.592168 0.805814i \(-0.701728\pi\)
0.993940 + 0.109926i \(0.0350613\pi\)
\(684\) 0 0
\(685\) 6.00000 0.229248
\(686\) 0 0
\(687\) 84.0000 3.20480
\(688\) 0 0
\(689\) −21.0000 + 36.3731i −0.800036 + 1.38570i
\(690\) 0 0
\(691\) 16.5000 + 28.5788i 0.627690 + 1.08719i 0.988014 + 0.154363i \(0.0493326\pi\)
−0.360325 + 0.932827i \(0.617334\pi\)
\(692\) 0 0
\(693\) 15.0000 + 5.19615i 0.569803 + 0.197386i
\(694\) 0 0
\(695\) −4.00000 6.92820i −0.151729 0.262802i
\(696\) 0 0
\(697\) −4.00000 + 6.92820i −0.151511 + 0.262424i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −27.0000 −1.01978 −0.509888 0.860241i \(-0.670313\pi\)
−0.509888 + 0.860241i \(0.670313\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) −6.00000 10.3923i −0.225973 0.391397i
\(706\) 0 0
\(707\) 18.0000 15.5885i 0.676960 0.586264i
\(708\) 0 0
\(709\) 24.0000 + 41.5692i 0.901339 + 1.56116i 0.825758 + 0.564025i \(0.190748\pi\)
0.0755813 + 0.997140i \(0.475919\pi\)
\(710\) 0 0
\(711\) 27.0000 46.7654i 1.01258 1.75384i
\(712\) 0 0
\(713\) −32.0000 −1.19841
\(714\) 0 0
\(715\) −14.0000 −0.523570
\(716\) 0 0
\(717\) 7.50000 12.9904i 0.280093 0.485135i
\(718\) 0 0
\(719\) −19.0000 32.9090i −0.708580 1.22730i −0.965384 0.260834i \(-0.916003\pi\)
0.256803 0.966464i \(-0.417331\pi\)
\(720\) 0 0
\(721\) 9.00000 + 46.7654i 0.335178 + 1.74163i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −2.50000 + 4.33013i −0.0928477 + 0.160817i
\(726\) 0 0
\(727\) 22.0000 0.815935 0.407967 0.912996i \(-0.366238\pi\)
0.407967 + 0.912996i \(0.366238\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) −8.00000 + 13.8564i −0.295891 + 0.512498i
\(732\) 0 0
\(733\) 9.50000 + 16.4545i 0.350891 + 0.607760i 0.986406 0.164328i \(-0.0525456\pi\)
−0.635515 + 0.772088i \(0.719212\pi\)
\(734\) 0 0
\(735\) −33.0000 25.9808i −1.21722 0.958315i
\(736\) 0 0
\(737\) 4.50000 + 7.79423i 0.165760 + 0.287104i
\(738\) 0 0
\(739\) 21.0000 36.3731i 0.772497 1.33800i −0.163693 0.986511i \(-0.552341\pi\)
0.936190 0.351494i \(-0.114326\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −12.0000 −0.440237 −0.220119 0.975473i \(-0.570644\pi\)
−0.220119 + 0.975473i \(0.570644\pi\)
\(744\) 0 0
\(745\) 10.0000 17.3205i 0.366372 0.634574i
\(746\) 0 0
\(747\) 18.0000 + 31.1769i 0.658586 + 1.14070i
\(748\) 0 0
\(749\) 1.00000 + 5.19615i 0.0365392 + 0.189863i
\(750\) 0 0
\(751\) 14.0000 + 24.2487i 0.510867 + 0.884848i 0.999921 + 0.0125942i \(0.00400897\pi\)
−0.489053 + 0.872254i \(0.662658\pi\)
\(752\) 0 0
\(753\) 36.0000 62.3538i 1.31191 2.27230i
\(754\) 0 0
\(755\) 6.00000 0.218362
\(756\) 0 0
\(757\) −22.0000 −0.799604 −0.399802 0.916602i \(-0.630921\pi\)
−0.399802 + 0.916602i \(0.630921\pi\)
\(758\) 0 0
\(759\) 12.0000 20.7846i 0.435572 0.754434i
\(760\) 0 0
\(761\) 3.00000 + 5.19615i 0.108750 + 0.188360i 0.915264 0.402854i \(-0.131982\pi\)
−0.806514 + 0.591215i \(0.798649\pi\)
\(762\) 0 0
\(763\) 4.00000 3.46410i 0.144810 0.125409i
\(764\) 0 0
\(765\) −12.0000 20.7846i −0.433861 0.751469i
\(766\) 0 0
\(767\) −10.5000 + 18.1865i −0.379133 + 0.656678i
\(768\) 0 0
\(769\) −14.0000 −0.504853 −0.252426 0.967616i \(-0.581229\pi\)
−0.252426 + 0.967616i \(0.581229\pi\)
\(770\) 0 0
\(771\) −9.00000 −0.324127
\(772\) 0 0
\(773\) −12.0000 + 20.7846i −0.431610 + 0.747570i −0.997012 0.0772449i \(-0.975388\pi\)
0.565402 + 0.824815i \(0.308721\pi\)
\(774\) 0 0
\(775\) −2.00000 3.46410i −0.0718421 0.124434i
\(776\) 0 0
\(777\) −30.0000 10.3923i −1.07624 0.372822i
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) −1.00000 + 1.73205i −0.0357828 + 0.0619777i
\(782\) 0 0
\(783\) 45.0000 1.60817
\(784\) 0 0
\(785\) 32.0000 1.14213
\(786\) 0 0
\(787\) −20.0000 + 34.6410i −0.712923 + 1.23482i 0.250832 + 0.968031i \(0.419296\pi\)
−0.963755 + 0.266788i \(0.914038\pi\)
\(788\) 0 0
\(789\) −40.5000 70.1481i −1.44184 2.49734i
\(790\) 0 0
\(791\) 12.5000 + 4.33013i 0.444449 + 0.153962i
\(792\) 0 0
\(793\) 3.50000 + 6.06218i 0.124289 + 0.215274i
\(794\) 0 0
\(795\) −18.0000 + 31.1769i −0.638394 +