Properties

Label 1232.2.q.e.177.1
Level $1232$
Weight $2$
Character 1232.177
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 177.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1232.177
Dual form 1232.2.q.e.529.1

$q$-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 \(\left(\mathbb{Z}/1232\mathbb{Z}\right)^\times\).

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

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 0.866025 + 0.500000i \(0.166667\pi\)
1.00000i \(0.5\pi\)
\(4\) 0 0
\(5\) −1.00000 + 1.73205i −0.447214 + 0.774597i −0.998203 0.0599153i \(-0.980917\pi\)
0.550990 + 0.834512i \(0.314250\pi\)
\(6\) 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 0.718900 0.695113i \(-0.244646\pi\)
−0.961436 + 0.275029i \(0.911312\pi\)
\(18\) 0 0
\(19\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(20\) 0 0
\(21\) 6.00000 + 5.19615i 1.30931 + 1.13389i
\(22\) 0 0
\(23\) −4.00000 + 6.92820i −0.834058 + 1.44463i 0.0607377 + 0.998154i \(0.480655\pi\)
−0.894795 + 0.446476i \(0.852679\pi\)
\(24\) 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 0.987829 0.155543i \(-0.0497126\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) 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 −0.982274 0.187453i \(-0.939977\pi\)
0.653476 + 0.756948i \(0.273310\pi\)
\(38\) 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 −0.783830 0.620975i \(-0.786737\pi\)
0.929695 + 0.368329i \(0.120070\pi\)
\(48\) 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 0.995117 0.0987002i \(-0.0314685\pi\)
−0.583036 + 0.812447i \(0.698135\pi\)
\(54\) 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 0.946993 0.321253i \(-0.104104\pi\)
−0.751710 + 0.659494i \(0.770771\pi\)
\(60\) 0 0
\(61\) −0.500000 + 0.866025i −0.0640184 + 0.110883i −0.896258 0.443533i \(-0.853725\pi\)
0.832240 + 0.554416i \(0.187058\pi\)
\(62\) 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 0.998290 + 0.0584478i \(0.0186151\pi\)
−0.448528 + 0.893769i \(0.648052\pi\)
\(68\) 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 0.724923 0.688830i \(-0.241875\pi\)
−0.959006 + 0.283387i \(0.908542\pi\)
\(74\) 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 −0.493684 0.869641i \(-0.664350\pi\)
0.999974 0.00727784i \(-0.00231663\pi\)
\(80\) 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 −0.980071 0.198650i \(-0.936344\pi\)
0.662071 + 0.749441i \(0.269678\pi\)
\(90\) 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 0.998240 0.0592978i \(-0.0188862\pi\)
−0.550474 + 0.834853i \(0.685553\pi\)
\(102\) 0 0
\(103\) 9.00000 15.5885i 0.886796 1.53598i 0.0431555 0.999068i \(-0.486259\pi\)
0.843641 0.536908i \(-0.180408\pi\)
\(104\) 0 0
\(105\) −15.0000 + 5.19615i −1.46385 + 0.507093i
\(106\) 0 0
\(107\) 1.00000 1.73205i 0.0966736 0.167444i −0.813632 0.581380i \(-0.802513\pi\)
0.910306 + 0.413936i \(0.135846\pi\)
\(108\) 0 0
\(109\) 1.00000 + 1.73205i 0.0957826 + 0.165900i 0.909935 0.414751i \(-0.136131\pi\)
−0.814152 + 0.580651i \(0.802798\pi\)
\(110\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(132\) 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 0.794808 0.606861i \(-0.207572\pi\)
−0.922961 + 0.384893i \(0.874238\pi\)
\(138\) 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 −0.585231 0.810867i \(-0.698996\pi\)
0.994847 + 0.101391i \(0.0323294\pi\)
\(150\) 0 0
\(151\) −1.50000 2.59808i −0.122068 0.211428i 0.798515 0.601975i \(-0.205619\pi\)
−0.920583 + 0.390547i \(0.872286\pi\)
\(152\) 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 −0.985769 0.168107i \(-0.946235\pi\)
0.347299 0.937754i \(-0.387099\pi\)
\(158\) 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 0.313304 + 0.949653i \(0.398564\pi\)
−0.979076 + 0.203497i \(0.934769\pi\)
\(164\) 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 −0.205706 + 0.978614i \(0.565949\pi\)
−0.744652 + 0.667453i \(0.767384\pi\)
\(174\) 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 0.964833 + 0.262864i \(0.0846670\pi\)
−0.254770 + 0.967002i \(0.582000\pi\)
\(180\) 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 −0.827577 0.561353i \(-0.810281\pi\)
0.899934 + 0.436026i \(0.143614\pi\)
\(192\) 0 0
\(193\) −4.00000 6.92820i −0.287926 0.498703i 0.685388 0.728178i \(-0.259632\pi\)
−0.973315 + 0.229475i \(0.926299\pi\)
\(194\) 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 0.928166 0.372168i \(-0.121385\pi\)
−0.786389 + 0.617731i \(0.788052\pi\)
\(200\) 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 0.830930 0.556378i \(-0.187809\pi\)
−0.897302 + 0.441417i \(0.854476\pi\)
\(228\) 0 0
\(229\) 14.0000 24.2487i 0.925146 1.60240i 0.133820 0.991006i \(-0.457276\pi\)
0.791326 0.611394i \(-0.209391\pi\)
\(230\) 0 0
\(231\) 1.50000 7.79423i 0.0986928 0.512823i
\(232\) 0 0
\(233\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(234\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(242\) 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 −0.909010 0.416775i \(-0.863160\pi\)
0.815442 + 0.578838i \(0.196494\pi\)
\(258\) 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 0.896093 + 0.443866i \(0.146393\pi\)
−0.0636476 + 0.997972i \(0.520273\pi\)
\(264\) 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 0.956176 + 0.292791i \(0.0945841\pi\)
−0.224523 + 0.974469i \(0.572083\pi\)
\(270\) 0 0
\(271\) −5.50000 + 9.52628i −0.334101 + 0.578680i −0.983312 0.181928i \(-0.941766\pi\)
0.649211 + 0.760609i \(0.275099\pi\)
\(272\) 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 0.968959 0.247222i \(-0.0795177\pi\)
−0.698580 + 0.715532i \(0.746184\pi\)
\(278\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(284\) 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 0.688726 0.725022i \(-0.258170\pi\)
−0.972250 + 0.233944i \(0.924837\pi\)
\(312\) 0 0
\(313\) −0.500000 + 0.866025i −0.0282617 + 0.0489506i −0.879810 0.475325i \(-0.842331\pi\)
0.851549 + 0.524276i \(0.175664\pi\)
\(314\) 0 0
\(315\) −24.0000 20.7846i −1.35225 1.17108i
\(316\) 0 0
\(317\) 6.00000 10.3923i 0.336994 0.583690i −0.646872 0.762598i \(-0.723923\pi\)
0.983866 + 0.178908i \(0.0572566\pi\)
\(318\) 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 −0.630232 0.776407i \(-0.717040\pi\)
0.987504 + 0.157593i \(0.0503735\pi\)
\(332\) 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 −0.994164 0.107883i \(-0.965593\pi\)
0.403653 0.914912i \(-0.367740\pi\)
\(348\) 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 0.999711 0.0240566i \(-0.00765819\pi\)
−0.520689 + 0.853746i \(0.674325\pi\)
\(354\) 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 0.498608 + 0.866828i \(0.333845\pi\)
−0.999999 + 0.00160673i \(0.999489\pi\)
\(360\) 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 0.913493 0.406855i \(-0.133375\pi\)
−0.809093 + 0.587680i \(0.800041\pi\)
\(368\) 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 −0.972556 0.232671i \(-0.925254\pi\)
0.687776 + 0.725923i \(0.258587\pi\)
\(374\) 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 −0.315214 0.949021i \(-0.602076\pi\)
0.979483 0.201527i \(-0.0645904\pi\)
\(384\) 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 0.542445 0.840091i \(-0.317499\pi\)
−0.998763 + 0.0497253i \(0.984165\pi\)
\(390\) 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 −0.931436 0.363906i \(-0.881443\pi\)
0.780870 + 0.624694i \(0.214776\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 4.50000 7.79423i 0.224719 0.389225i −0.731516 0.681824i \(-0.761187\pi\)
0.956235 + 0.292599i \(0.0945202\pi\)
\(402\) 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 −0.998674 0.0514740i \(-0.983608\pi\)
0.454759 0.890614i \(-0.349725\pi\)
\(410\) 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 0.992502 + 0.122228i \(0.0390040\pi\)
−0.390398 + 0.920646i \(0.627663\pi\)
\(432\) 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 −0.919498 0.393095i \(-0.871404\pi\)
0.800179 + 0.599761i \(0.204738\pi\)
\(440\) 0 0
\(441\) 6.00000 + 41.5692i 0.285714 + 1.97949i
\(442\) 0 0
\(443\) 18.0000 31.1769i 0.855206 1.48126i −0.0212481 0.999774i \(-0.506764\pi\)
0.876454 0.481486i \(-0.159903\pi\)
\(444\) 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 −0.982004 0.188858i \(-0.939521\pi\)
0.654558 + 0.756012i \(0.272855\pi\)
\(458\) 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 −0.693153 0.720791i \(-0.743779\pi\)
0.970799 + 0.239892i \(0.0771121\pi\)
\(468\) 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 0.854377 0.519654i \(-0.173939\pi\)
−0.877222 + 0.480085i \(0.840606\pi\)
\(480\) 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 −0.819181 0.573535i \(-0.805572\pi\)
−0.0871056 0.996199i \(-0.527762\pi\)
\(488\) 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 −0.550572 0.834788i \(-0.685590\pi\)
0.998233 + 0.0594153i \(0.0189236\pi\)
\(500\) 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 −0.512331 0.858788i \(-0.671218\pi\)
0.999898 + 0.0142980i \(0.00455136\pi\)
\(510\) 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 0.735465 0.677563i \(-0.236964\pi\)
−0.954519 + 0.298150i \(0.903630\pi\)
\(522\) 0 0
\(523\) −5.00000 + 8.66025i −0.218635 + 0.378686i −0.954391 0.298560i \(-0.903494\pi\)
0.735756 + 0.677247i \(0.236827\pi\)
\(524\) 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 −0.914750 0.404020i \(-0.867613\pi\)
0.807267 + 0.590187i \(0.200946\pi\)
\(542\) 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 −0.998215 0.0597213i \(-0.980979\pi\)
0.447387 0.894340i \(-0.352355\pi\)
\(558\) 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 0.996082 0.0884397i \(-0.0281881\pi\)
−0.574632 + 0.818412i \(0.694855\pi\)
\(564\) 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 −0.712415 0.701758i \(-0.752399\pi\)
0.963948 + 0.266090i \(0.0857319\pi\)
\(570\) 0 0
\(571\) 11.0000 + 19.0526i 0.460336 + 0.797325i 0.998978 0.0452101i \(-0.0143957\pi\)
−0.538642 + 0.842535i \(0.681062\pi\)
\(572\) 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 0.833734 + 0.552166i \(0.186198\pi\)
0.0613223 + 0.998118i \(0.480468\pi\)
\(578\) 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 −0.921026 0.389501i \(-0.872647\pi\)
0.797831 + 0.602881i \(0.205981\pi\)
\(594\) 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 0.954521 + 0.298143i \(0.0963673\pi\)
−0.219061 + 0.975711i \(0.570299\pi\)
\(600\) 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 −0.773358 0.633970i \(-0.781424\pi\)
0.935713 + 0.352763i \(0.114758\pi\)
\(608\) 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 0.938967 + 0.344008i \(0.111785\pi\)
−0.171564 + 0.985173i \(0.554882\pi\)
\(614\) 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 −0.997259 0.0739910i \(-0.976426\pi\)
0.434551 0.900647i \(-0.356907\pi\)
\(620\) 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 0.999247 + 0.0387913i \(0.0123508\pi\)
−0.466029 + 0.884769i \(0.654316\pi\)
\(642\) 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 0.994270 + 0.106897i \(0.0340916\pi\)
−0.404559 + 0.914512i \(0.632575\pi\)
\(648\) 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 0.147726 + 0.989028i \(0.452805\pi\)
−0.930387 + 0.366579i \(0.880529\pi\)
\(654\) 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 0.996682 0.0813955i \(-0.0259377\pi\)
−0.568831 + 0.822454i \(0.692604\pi\)
\(662\) 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 −0.968612 0.248577i \(-0.920037\pi\)
0.699580 + 0.714554i \(0.253370\pi\)
\(678\) 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 0.993940 0.109926i \(-0.0350613\pi\)
−0.592168 + 0.805814i \(0.701728\pi\)
\(684\) 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 −0.360325 0.932827i \(-0.617334\pi\)
0.988014 0.154363i \(-0.0493326\pi\)
\(692\) 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 0.0755813 0.997140i \(-0.475919\pi\)
0.825758 0.564025i \(-0.190748\pi\)
\(710\) 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 0.256803 + 0.966464i \(0.417331\pi\)
−0.965384 + 0.260834i \(0.916003\pi\)
\(720\) 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 −0.635515 0.772088i \(-0.719212\pi\)
0.986406 + 0.164328i \(0.0525456\pi\)
\(734\) 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 0.936190 + 0.351494i \(0.114326\pi\)
−0.163693 + 0.986511i \(0.552341\pi\)
\(740\) 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 −0.489053 0.872254i \(-0.662658\pi\)
0.999921 0.0125942i \(-0.00400897\pi\)
\(752\) 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 −0.806514 0.591215i \(-0.798649\pi\)
0.915264 + 0.402854i \(0.131982\pi\)
\(762\) 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 0.565402 0.824815i \(-0.308721\pi\)
−0.997012 + 0.0772449i \(0.975388\pi\)
\(774\) 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 −0.963755 0.266788i \(-0.914038\pi\)
0.250832 0.968031i \(-0.419296\pi\)
\(788\) 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 1.10573i