Properties

Label 1152.2.p.a.959.1
Level $1152$
Weight $2$
Character 1152.959
Analytic conductor $9.199$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1152.p (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.19876631285\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 959.1
Root \(-0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 1152.959
Dual form 1152.2.p.a.191.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.50000 + 0.866025i) q^{3} +(-1.41421 + 2.44949i) q^{5} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(-1.50000 + 0.866025i) q^{3} +(-1.41421 + 2.44949i) q^{5} +(1.50000 - 2.59808i) q^{9} +(4.50000 - 2.59808i) q^{11} +(4.24264 + 2.44949i) q^{13} -4.89898i q^{15} -1.73205i q^{17} -3.00000 q^{19} +(4.24264 - 7.34847i) q^{23} +(-1.50000 - 2.59808i) q^{25} +5.19615i q^{27} +(2.82843 + 4.89898i) q^{29} +(-4.50000 + 7.79423i) q^{33} +4.89898i q^{37} -8.48528 q^{39} +(4.50000 + 2.59808i) q^{41} +(-4.50000 - 7.79423i) q^{43} +(4.24264 + 7.34847i) q^{45} +(4.24264 + 7.34847i) q^{47} +(-3.50000 + 6.06218i) q^{49} +(1.50000 + 2.59808i) q^{51} +5.65685 q^{53} +14.6969i q^{55} +(4.50000 - 2.59808i) q^{57} +(4.50000 + 2.59808i) q^{59} +(-8.48528 + 4.89898i) q^{61} +(-12.0000 + 6.92820i) q^{65} +(1.50000 - 2.59808i) q^{67} +14.6969i q^{69} +8.48528 q^{71} +5.00000 q^{73} +(4.50000 + 2.59808i) q^{75} +(-12.7279 + 7.34847i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-9.00000 + 5.19615i) q^{83} +(4.24264 + 2.44949i) q^{85} +(-8.48528 - 4.89898i) q^{87} -13.8564i q^{89} +(4.24264 - 7.34847i) q^{95} +(0.500000 + 0.866025i) q^{97} -15.5885i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 6q^{3} + 6q^{9} + O(q^{10}) \) \( 4q - 6q^{3} + 6q^{9} + 18q^{11} - 12q^{19} - 6q^{25} - 18q^{33} + 18q^{41} - 18q^{43} - 14q^{49} + 6q^{51} + 18q^{57} + 18q^{59} - 48q^{65} + 6q^{67} + 20q^{73} + 18q^{75} - 18q^{81} - 36q^{83} + 2q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(641\) \(901\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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
\(3\) −1.50000 + 0.866025i −0.866025 + 0.500000i
\(4\) 0 0
\(5\) −1.41421 + 2.44949i −0.632456 + 1.09545i 0.354593 + 0.935021i \(0.384620\pi\)
−0.987048 + 0.160424i \(0.948714\pi\)
\(6\) 0 0
\(7\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(8\) 0 0
\(9\) 1.50000 2.59808i 0.500000 0.866025i
\(10\) 0 0
\(11\) 4.50000 2.59808i 1.35680 0.783349i 0.367610 0.929980i \(-0.380176\pi\)
0.989191 + 0.146631i \(0.0468429\pi\)
\(12\) 0 0
\(13\) 4.24264 + 2.44949i 1.17670 + 0.679366i 0.955248 0.295806i \(-0.0955881\pi\)
0.221449 + 0.975172i \(0.428921\pi\)
\(14\) 0 0
\(15\) 4.89898i 1.26491i
\(16\) 0 0
\(17\) 1.73205i 0.420084i −0.977692 0.210042i \(-0.932640\pi\)
0.977692 0.210042i \(-0.0673601\pi\)
\(18\) 0 0
\(19\) −3.00000 −0.688247 −0.344124 0.938924i \(-0.611824\pi\)
−0.344124 + 0.938924i \(0.611824\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 4.24264 7.34847i 0.884652 1.53226i 0.0385394 0.999257i \(-0.487729\pi\)
0.846112 0.533005i \(-0.178937\pi\)
\(24\) 0 0
\(25\) −1.50000 2.59808i −0.300000 0.519615i
\(26\) 0 0
\(27\) 5.19615i 1.00000i
\(28\) 0 0
\(29\) 2.82843 + 4.89898i 0.525226 + 0.909718i 0.999568 + 0.0293774i \(0.00935245\pi\)
−0.474343 + 0.880340i \(0.657314\pi\)
\(30\) 0 0
\(31\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(32\) 0 0
\(33\) −4.50000 + 7.79423i −0.783349 + 1.35680i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 4.89898i 0.805387i 0.915335 + 0.402694i \(0.131926\pi\)
−0.915335 + 0.402694i \(0.868074\pi\)
\(38\) 0 0
\(39\) −8.48528 −1.35873
\(40\) 0 0
\(41\) 4.50000 + 2.59808i 0.702782 + 0.405751i 0.808383 0.588657i \(-0.200343\pi\)
−0.105601 + 0.994409i \(0.533677\pi\)
\(42\) 0 0
\(43\) −4.50000 7.79423i −0.686244 1.18861i −0.973044 0.230618i \(-0.925925\pi\)
0.286801 0.957990i \(-0.407408\pi\)
\(44\) 0 0
\(45\) 4.24264 + 7.34847i 0.632456 + 1.09545i
\(46\) 0 0
\(47\) 4.24264 + 7.34847i 0.618853 + 1.07188i 0.989695 + 0.143189i \(0.0457356\pi\)
−0.370843 + 0.928696i \(0.620931\pi\)
\(48\) 0 0
\(49\) −3.50000 + 6.06218i −0.500000 + 0.866025i
\(50\) 0 0
\(51\) 1.50000 + 2.59808i 0.210042 + 0.363803i
\(52\) 0 0
\(53\) 5.65685 0.777029 0.388514 0.921443i \(-0.372988\pi\)
0.388514 + 0.921443i \(0.372988\pi\)
\(54\) 0 0
\(55\) 14.6969i 1.98173i
\(56\) 0 0
\(57\) 4.50000 2.59808i 0.596040 0.344124i
\(58\) 0 0
\(59\) 4.50000 + 2.59808i 0.585850 + 0.338241i 0.763455 0.645861i \(-0.223502\pi\)
−0.177605 + 0.984102i \(0.556835\pi\)
\(60\) 0 0
\(61\) −8.48528 + 4.89898i −1.08643 + 0.627250i −0.932623 0.360851i \(-0.882486\pi\)
−0.153806 + 0.988101i \(0.549153\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −12.0000 + 6.92820i −1.48842 + 0.859338i
\(66\) 0 0
\(67\) 1.50000 2.59808i 0.183254 0.317406i −0.759733 0.650236i \(-0.774670\pi\)
0.942987 + 0.332830i \(0.108004\pi\)
\(68\) 0 0
\(69\) 14.6969i 1.76930i
\(70\) 0 0
\(71\) 8.48528 1.00702 0.503509 0.863990i \(-0.332042\pi\)
0.503509 + 0.863990i \(0.332042\pi\)
\(72\) 0 0
\(73\) 5.00000 0.585206 0.292603 0.956234i \(-0.405479\pi\)
0.292603 + 0.956234i \(0.405479\pi\)
\(74\) 0 0
\(75\) 4.50000 + 2.59808i 0.519615 + 0.300000i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −12.7279 + 7.34847i −1.43200 + 0.826767i −0.997274 0.0737937i \(-0.976489\pi\)
−0.434730 + 0.900561i \(0.643156\pi\)
\(80\) 0 0
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) 0 0
\(83\) −9.00000 + 5.19615i −0.987878 + 0.570352i −0.904639 0.426178i \(-0.859860\pi\)
−0.0832389 + 0.996530i \(0.526526\pi\)
\(84\) 0 0
\(85\) 4.24264 + 2.44949i 0.460179 + 0.265684i
\(86\) 0 0
\(87\) −8.48528 4.89898i −0.909718 0.525226i
\(88\) 0 0
\(89\) 13.8564i 1.46878i −0.678730 0.734388i \(-0.737469\pi\)
0.678730 0.734388i \(-0.262531\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 4.24264 7.34847i 0.435286 0.753937i
\(96\) 0 0
\(97\) 0.500000 + 0.866025i 0.0507673 + 0.0879316i 0.890292 0.455389i \(-0.150500\pi\)
−0.839525 + 0.543321i \(0.817167\pi\)
\(98\) 0 0
\(99\) 15.5885i 1.56670i
\(100\) 0 0
\(101\) 1.41421 + 2.44949i 0.140720 + 0.243733i 0.927768 0.373158i \(-0.121725\pi\)
−0.787048 + 0.616891i \(0.788392\pi\)
\(102\) 0 0
\(103\) 12.7279 + 7.34847i 1.25412 + 0.724066i 0.971925 0.235291i \(-0.0756043\pi\)
0.282194 + 0.959357i \(0.408938\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 5.19615i 0.502331i −0.967944 0.251166i \(-0.919186\pi\)
0.967944 0.251166i \(-0.0808138\pi\)
\(108\) 0 0
\(109\) 9.79796i 0.938474i −0.883072 0.469237i \(-0.844529\pi\)
0.883072 0.469237i \(-0.155471\pi\)
\(110\) 0 0
\(111\) −4.24264 7.34847i −0.402694 0.697486i
\(112\) 0 0
\(113\) 12.0000 + 6.92820i 1.12887 + 0.651751i 0.943649 0.330947i \(-0.107368\pi\)
0.185216 + 0.982698i \(0.440702\pi\)
\(114\) 0 0
\(115\) 12.0000 + 20.7846i 1.11901 + 1.93817i
\(116\) 0 0
\(117\) 12.7279 7.34847i 1.17670 0.679366i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 8.00000 13.8564i 0.727273 1.25967i
\(122\) 0 0
\(123\) −9.00000 −0.811503
\(124\) 0 0
\(125\) −5.65685 −0.505964
\(126\) 0 0
\(127\) 14.6969i 1.30414i 0.758158 + 0.652071i \(0.226100\pi\)
−0.758158 + 0.652071i \(0.773900\pi\)
\(128\) 0 0
\(129\) 13.5000 + 7.79423i 1.18861 + 0.686244i
\(130\) 0 0
\(131\) −9.00000 5.19615i −0.786334 0.453990i 0.0523366 0.998630i \(-0.483333\pi\)
−0.838670 + 0.544640i \(0.816666\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −12.7279 7.34847i −1.09545 0.632456i
\(136\) 0 0
\(137\) 7.50000 4.33013i 0.640768 0.369948i −0.144142 0.989557i \(-0.546042\pi\)
0.784910 + 0.619609i \(0.212709\pi\)
\(138\) 0 0
\(139\) −4.50000 + 7.79423i −0.381685 + 0.661098i −0.991303 0.131597i \(-0.957989\pi\)
0.609618 + 0.792695i \(0.291323\pi\)
\(140\) 0 0
\(141\) −12.7279 7.34847i −1.07188 0.618853i
\(142\) 0 0
\(143\) 25.4558 2.12872
\(144\) 0 0
\(145\) −16.0000 −1.32873
\(146\) 0 0
\(147\) 12.1244i 1.00000i
\(148\) 0 0
\(149\) −1.41421 + 2.44949i −0.115857 + 0.200670i −0.918122 0.396298i \(-0.870295\pi\)
0.802265 + 0.596968i \(0.203628\pi\)
\(150\) 0 0
\(151\) −12.7279 + 7.34847i −1.03578 + 0.598010i −0.918636 0.395105i \(-0.870708\pi\)
−0.117147 + 0.993115i \(0.537375\pi\)
\(152\) 0 0
\(153\) −4.50000 2.59808i −0.363803 0.210042i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 16.9706 + 9.79796i 1.35440 + 0.781962i 0.988862 0.148835i \(-0.0475523\pi\)
0.365536 + 0.930797i \(0.380886\pi\)
\(158\) 0 0
\(159\) −8.48528 + 4.89898i −0.672927 + 0.388514i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 24.0000 1.87983 0.939913 0.341415i \(-0.110906\pi\)
0.939913 + 0.341415i \(0.110906\pi\)
\(164\) 0 0
\(165\) −12.7279 22.0454i −0.990867 1.71623i
\(166\) 0 0
\(167\) 4.24264 7.34847i 0.328305 0.568642i −0.653870 0.756607i \(-0.726856\pi\)
0.982176 + 0.187965i \(0.0601892\pi\)
\(168\) 0 0
\(169\) 5.50000 + 9.52628i 0.423077 + 0.732791i
\(170\) 0 0
\(171\) −4.50000 + 7.79423i −0.344124 + 0.596040i
\(172\) 0 0
\(173\) −2.82843 4.89898i −0.215041 0.372463i 0.738244 0.674534i \(-0.235655\pi\)
−0.953285 + 0.302071i \(0.902322\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −9.00000 −0.676481
\(178\) 0 0
\(179\) 10.3923i 0.776757i 0.921500 + 0.388379i \(0.126965\pi\)
−0.921500 + 0.388379i \(0.873035\pi\)
\(180\) 0 0
\(181\) 14.6969i 1.09241i −0.837650 0.546207i \(-0.816071\pi\)
0.837650 0.546207i \(-0.183929\pi\)
\(182\) 0 0
\(183\) 8.48528 14.6969i 0.627250 1.08643i
\(184\) 0 0
\(185\) −12.0000 6.92820i −0.882258 0.509372i
\(186\) 0 0
\(187\) −4.50000 7.79423i −0.329073 0.569970i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −8.48528 14.6969i −0.613973 1.06343i −0.990564 0.137053i \(-0.956237\pi\)
0.376590 0.926380i \(-0.377096\pi\)
\(192\) 0 0
\(193\) −0.500000 + 0.866025i −0.0359908 + 0.0623379i −0.883460 0.468507i \(-0.844792\pi\)
0.847469 + 0.530845i \(0.178125\pi\)
\(194\) 0 0
\(195\) 12.0000 20.7846i 0.859338 1.48842i
\(196\) 0 0
\(197\) −11.3137 −0.806068 −0.403034 0.915185i \(-0.632044\pi\)
−0.403034 + 0.915185i \(0.632044\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 0 0
\(201\) 5.19615i 0.366508i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −12.7279 + 7.34847i −0.888957 + 0.513239i
\(206\) 0 0
\(207\) −12.7279 22.0454i −0.884652 1.53226i
\(208\) 0 0
\(209\) −13.5000 + 7.79423i −0.933815 + 0.539138i
\(210\) 0 0
\(211\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(212\) 0 0
\(213\) −12.7279 + 7.34847i −0.872103 + 0.503509i
\(214\) 0 0
\(215\) 25.4558 1.73607
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −7.50000 + 4.33013i −0.506803 + 0.292603i
\(220\) 0 0
\(221\) 4.24264 7.34847i 0.285391 0.494312i
\(222\) 0 0
\(223\) 12.7279 7.34847i 0.852325 0.492090i −0.00910984 0.999959i \(-0.502900\pi\)
0.861435 + 0.507869i \(0.169566\pi\)
\(224\) 0 0
\(225\) −9.00000 −0.600000
\(226\) 0 0
\(227\) −13.5000 + 7.79423i −0.896026 + 0.517321i −0.875909 0.482476i \(-0.839737\pi\)
−0.0201176 + 0.999798i \(0.506404\pi\)
\(228\) 0 0
\(229\) −8.48528 4.89898i −0.560723 0.323734i 0.192713 0.981255i \(-0.438272\pi\)
−0.753436 + 0.657522i \(0.771605\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 22.5167i 1.47512i 0.675284 + 0.737558i \(0.264021\pi\)
−0.675284 + 0.737558i \(0.735979\pi\)
\(234\) 0 0
\(235\) −24.0000 −1.56559
\(236\) 0 0
\(237\) 12.7279 22.0454i 0.826767 1.43200i
\(238\) 0 0
\(239\) 4.24264 7.34847i 0.274434 0.475333i −0.695558 0.718470i \(-0.744843\pi\)
0.969992 + 0.243137i \(0.0781763\pi\)
\(240\) 0 0
\(241\) 3.50000 + 6.06218i 0.225455 + 0.390499i 0.956456 0.291877i \(-0.0942799\pi\)
−0.731001 + 0.682376i \(0.760947\pi\)
\(242\) 0 0
\(243\) 13.5000 + 7.79423i 0.866025 + 0.500000i
\(244\) 0 0
\(245\) −9.89949 17.1464i −0.632456 1.09545i
\(246\) 0 0
\(247\) −12.7279 7.34847i −0.809858 0.467572i
\(248\) 0 0
\(249\) 9.00000 15.5885i 0.570352 0.987878i
\(250\) 0 0
\(251\) 5.19615i 0.327978i 0.986462 + 0.163989i \(0.0524362\pi\)
−0.986462 + 0.163989i \(0.947564\pi\)
\(252\) 0 0
\(253\) 44.0908i 2.77197i
\(254\) 0 0
\(255\) −8.48528 −0.531369
\(256\) 0 0
\(257\) 1.50000 + 0.866025i 0.0935674 + 0.0540212i 0.546054 0.837750i \(-0.316129\pi\)
−0.452486 + 0.891771i \(0.649463\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 16.9706 1.05045
\(262\) 0 0
\(263\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(264\) 0 0
\(265\) −8.00000 + 13.8564i −0.491436 + 0.851192i
\(266\) 0 0
\(267\) 12.0000 + 20.7846i 0.734388 + 1.27200i
\(268\) 0 0
\(269\) 11.3137 0.689809 0.344904 0.938638i \(-0.387911\pi\)
0.344904 + 0.938638i \(0.387911\pi\)
\(270\) 0 0
\(271\) 29.3939i 1.78555i 0.450502 + 0.892775i \(0.351245\pi\)
−0.450502 + 0.892775i \(0.648755\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −13.5000 7.79423i −0.814081 0.470010i
\(276\) 0 0
\(277\) −12.7279 + 7.34847i −0.764747 + 0.441527i −0.830997 0.556276i \(-0.812230\pi\)
0.0662507 + 0.997803i \(0.478896\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 12.0000 6.92820i 0.715860 0.413302i −0.0973670 0.995249i \(-0.531042\pi\)
0.813227 + 0.581947i \(0.197709\pi\)
\(282\) 0 0
\(283\) 12.0000 20.7846i 0.713326 1.23552i −0.250276 0.968175i \(-0.580521\pi\)
0.963602 0.267342i \(-0.0861454\pi\)
\(284\) 0 0
\(285\) 14.6969i 0.870572i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 14.0000 0.823529
\(290\) 0 0
\(291\) −1.50000 0.866025i −0.0879316 0.0507673i
\(292\) 0 0
\(293\) 14.1421 24.4949i 0.826192 1.43101i −0.0748122 0.997198i \(-0.523836\pi\)
0.901005 0.433810i \(-0.142831\pi\)
\(294\) 0 0
\(295\) −12.7279 + 7.34847i −0.741048 + 0.427844i
\(296\) 0 0
\(297\) 13.5000 + 23.3827i 0.783349 + 1.35680i
\(298\) 0 0
\(299\) 36.0000 20.7846i 2.08193 1.20201i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −4.24264 2.44949i −0.243733 0.140720i
\(304\) 0 0
\(305\) 27.7128i 1.58683i
\(306\) 0 0
\(307\) −3.00000 −0.171219 −0.0856095 0.996329i \(-0.527284\pi\)
−0.0856095 + 0.996329i \(0.527284\pi\)
\(308\) 0 0
\(309\) −25.4558 −1.44813
\(310\) 0 0
\(311\) −8.48528 + 14.6969i −0.481156 + 0.833387i −0.999766 0.0216240i \(-0.993116\pi\)
0.518610 + 0.855011i \(0.326450\pi\)
\(312\) 0 0
\(313\) −14.5000 25.1147i −0.819588 1.41957i −0.905986 0.423308i \(-0.860869\pi\)
0.0863973 0.996261i \(-0.472465\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −9.89949 17.1464i −0.556011 0.963039i −0.997824 0.0659322i \(-0.978998\pi\)
0.441813 0.897107i \(-0.354335\pi\)
\(318\) 0 0
\(319\) 25.4558 + 14.6969i 1.42525 + 0.822871i
\(320\) 0 0
\(321\) 4.50000 + 7.79423i 0.251166 + 0.435031i
\(322\) 0 0
\(323\) 5.19615i 0.289122i
\(324\) 0 0
\(325\) 14.6969i 0.815239i
\(326\) 0 0
\(327\) 8.48528 + 14.6969i 0.469237 + 0.812743i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −12.0000 20.7846i −0.659580 1.14243i −0.980725 0.195395i \(-0.937401\pi\)
0.321145 0.947030i \(-0.395932\pi\)
\(332\) 0 0
\(333\) 12.7279 + 7.34847i 0.697486 + 0.402694i
\(334\) 0 0
\(335\) 4.24264 + 7.34847i 0.231800 + 0.401490i
\(336\) 0 0
\(337\) 11.5000 19.9186i 0.626445 1.08503i −0.361815 0.932250i \(-0.617843\pi\)
0.988260 0.152784i \(-0.0488240\pi\)
\(338\) 0 0
\(339\) −24.0000 −1.30350
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −36.0000 20.7846i −1.93817 1.11901i
\(346\) 0 0
\(347\) 31.5000 + 18.1865i 1.69101 + 0.976304i 0.953705 + 0.300742i \(0.0972344\pi\)
0.737303 + 0.675562i \(0.236099\pi\)
\(348\) 0 0
\(349\) −25.4558 + 14.6969i −1.36262 + 0.786709i −0.989972 0.141264i \(-0.954883\pi\)
−0.372648 + 0.927973i \(0.621550\pi\)
\(350\) 0 0
\(351\) −12.7279 + 22.0454i −0.679366 + 1.17670i
\(352\) 0 0
\(353\) 22.5000 12.9904i 1.19755 0.691408i 0.237545 0.971377i \(-0.423657\pi\)
0.960009 + 0.279968i \(0.0903240\pi\)
\(354\) 0 0
\(355\) −12.0000 + 20.7846i −0.636894 + 1.10313i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −16.9706 −0.895672 −0.447836 0.894116i \(-0.647805\pi\)
−0.447836 + 0.894116i \(0.647805\pi\)
\(360\) 0 0
\(361\) −10.0000 −0.526316
\(362\) 0 0
\(363\) 27.7128i 1.45455i
\(364\) 0 0
\(365\) −7.07107 + 12.2474i −0.370117 + 0.641061i
\(366\) 0 0
\(367\) −12.7279 + 7.34847i −0.664392 + 0.383587i −0.793948 0.607985i \(-0.791978\pi\)
0.129556 + 0.991572i \(0.458645\pi\)
\(368\) 0 0
\(369\) 13.5000 7.79423i 0.702782 0.405751i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 12.7279 + 7.34847i 0.659027 + 0.380489i 0.791906 0.610643i \(-0.209089\pi\)
−0.132879 + 0.991132i \(0.542422\pi\)
\(374\) 0 0
\(375\) 8.48528 4.89898i 0.438178 0.252982i
\(376\) 0 0
\(377\) 27.7128i 1.42728i
\(378\) 0 0
\(379\) −15.0000 −0.770498 −0.385249 0.922813i \(-0.625884\pi\)
−0.385249 + 0.922813i \(0.625884\pi\)
\(380\) 0 0
\(381\) −12.7279 22.0454i −0.652071 1.12942i
\(382\) 0 0
\(383\) 4.24264 7.34847i 0.216789 0.375489i −0.737036 0.675854i \(-0.763775\pi\)
0.953824 + 0.300365i \(0.0971084\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −27.0000 −1.37249
\(388\) 0 0
\(389\) 11.3137 + 19.5959i 0.573628 + 0.993552i 0.996189 + 0.0872182i \(0.0277977\pi\)
−0.422561 + 0.906334i \(0.638869\pi\)
\(390\) 0 0
\(391\) −12.7279 7.34847i −0.643679 0.371628i
\(392\) 0 0
\(393\) 18.0000 0.907980
\(394\) 0 0
\(395\) 41.5692i 2.09157i
\(396\) 0 0
\(397\) 4.89898i 0.245873i 0.992415 + 0.122936i \(0.0392311\pi\)
−0.992415 + 0.122936i \(0.960769\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −10.5000 6.06218i −0.524345 0.302731i 0.214366 0.976753i \(-0.431232\pi\)
−0.738711 + 0.674023i \(0.764565\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 25.4558 1.26491
\(406\) 0 0
\(407\) 12.7279 + 22.0454i 0.630900 + 1.09275i
\(408\) 0 0
\(409\) −9.50000 + 16.4545i −0.469745 + 0.813622i −0.999402 0.0345902i \(-0.988987\pi\)
0.529657 + 0.848212i \(0.322321\pi\)
\(410\) 0 0
\(411\) −7.50000 + 12.9904i −0.369948 + 0.640768i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 29.3939i 1.44289i
\(416\) 0 0
\(417\) 15.5885i 0.763370i
\(418\) 0 0
\(419\) 9.00000 + 5.19615i 0.439679 + 0.253849i 0.703461 0.710734i \(-0.251637\pi\)
−0.263783 + 0.964582i \(0.584970\pi\)
\(420\) 0 0
\(421\) 4.24264 2.44949i 0.206774 0.119381i −0.393037 0.919522i \(-0.628576\pi\)
0.599811 + 0.800142i \(0.295242\pi\)
\(422\) 0 0
\(423\) 25.4558 1.23771
\(424\) 0 0
\(425\) −4.50000 + 2.59808i −0.218282 + 0.126025i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −38.1838 + 22.0454i −1.84353 + 1.06436i
\(430\) 0 0
\(431\) −16.9706 −0.817443 −0.408722 0.912659i \(-0.634025\pi\)
−0.408722 + 0.912659i \(0.634025\pi\)
\(432\) 0 0
\(433\) 31.0000 1.48976 0.744882 0.667196i \(-0.232506\pi\)
0.744882 + 0.667196i \(0.232506\pi\)
\(434\) 0 0
\(435\) 24.0000 13.8564i 1.15071 0.664364i
\(436\) 0 0
\(437\) −12.7279 + 22.0454i −0.608859 + 1.05457i
\(438\) 0 0
\(439\) 25.4558 14.6969i 1.21494 0.701447i 0.251110 0.967959i \(-0.419205\pi\)
0.963832 + 0.266512i \(0.0858712\pi\)
\(440\) 0 0
\(441\) 10.5000 + 18.1865i 0.500000 + 0.866025i
\(442\) 0 0
\(443\) 4.50000 2.59808i 0.213801 0.123438i −0.389275 0.921121i \(-0.627275\pi\)
0.603077 + 0.797683i \(0.293941\pi\)
\(444\) 0 0
\(445\) 33.9411 + 19.5959i 1.60896 + 0.928936i
\(446\) 0 0
\(447\) 4.89898i 0.231714i
\(448\) 0 0
\(449\) 15.5885i 0.735665i 0.929892 + 0.367832i \(0.119900\pi\)
−0.929892 + 0.367832i \(0.880100\pi\)
\(450\) 0 0
\(451\) 27.0000 1.27138
\(452\) 0 0
\(453\) 12.7279 22.0454i 0.598010 1.03578i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 14.5000 + 25.1147i 0.678281 + 1.17482i 0.975498 + 0.220008i \(0.0706083\pi\)
−0.297217 + 0.954810i \(0.596058\pi\)
\(458\) 0 0
\(459\) 9.00000 0.420084
\(460\) 0 0
\(461\) 1.41421 + 2.44949i 0.0658665 + 0.114084i 0.897078 0.441872i \(-0.145686\pi\)
−0.831212 + 0.555956i \(0.812352\pi\)
\(462\) 0 0
\(463\) −12.7279 7.34847i −0.591517 0.341512i 0.174180 0.984714i \(-0.444272\pi\)
−0.765697 + 0.643201i \(0.777606\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 15.5885i 0.721348i −0.932692 0.360674i \(-0.882547\pi\)
0.932692 0.360674i \(-0.117453\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −33.9411 −1.56392
\(472\) 0 0
\(473\) −40.5000 23.3827i −1.86219 1.07514i
\(474\) 0 0
\(475\) 4.50000 + 7.79423i 0.206474 + 0.357624i
\(476\) 0 0
\(477\) 8.48528 14.6969i 0.388514 0.672927i
\(478\) 0 0
\(479\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(480\) 0 0
\(481\) −12.0000 + 20.7846i −0.547153 + 0.947697i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −2.82843 −0.128432
\(486\) 0 0
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) 0 0
\(489\) −36.0000 + 20.7846i −1.62798 + 0.939913i
\(490\) 0 0
\(491\) 4.50000 + 2.59808i 0.203082 + 0.117250i 0.598092 0.801427i \(-0.295926\pi\)
−0.395010 + 0.918677i \(0.629259\pi\)
\(492\) 0 0
\(493\) 8.48528 4.89898i 0.382158 0.220639i
\(494\) 0 0
\(495\) 38.1838 + 22.0454i 1.71623 + 0.990867i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −1.50000 + 2.59808i −0.0671492 + 0.116306i −0.897645 0.440719i \(-0.854724\pi\)
0.830496 + 0.557024i \(0.188057\pi\)
\(500\) 0 0
\(501\) 14.6969i 0.656611i
\(502\) 0 0
\(503\) −33.9411 −1.51336 −0.756680 0.653785i \(-0.773180\pi\)
−0.756680 + 0.653785i \(0.773180\pi\)
\(504\) 0 0
\(505\) −8.00000 −0.355995
\(506\) 0 0
\(507\) −16.5000 9.52628i −0.732791 0.423077i
\(508\) 0 0
\(509\) −5.65685 + 9.79796i −0.250736 + 0.434287i −0.963729 0.266884i \(-0.914006\pi\)
0.712993 + 0.701171i \(0.247339\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 15.5885i 0.688247i
\(514\) 0 0
\(515\) −36.0000 + 20.7846i −1.58635 + 0.915879i
\(516\) 0 0
\(517\) 38.1838 + 22.0454i 1.67932 + 0.969556i
\(518\) 0 0
\(519\) 8.48528 + 4.89898i 0.372463 + 0.215041i
\(520\) 0 0
\(521\) 36.3731i 1.59353i 0.604287 + 0.796766i \(0.293458\pi\)
−0.604287 + 0.796766i \(0.706542\pi\)
\(522\) 0 0
\(523\) −24.0000 −1.04945 −0.524723 0.851273i \(-0.675831\pi\)
−0.524723 + 0.851273i \(0.675831\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −24.5000 42.4352i −1.06522 1.84501i
\(530\) 0 0
\(531\) 13.5000 7.79423i 0.585850 0.338241i
\(532\) 0 0
\(533\) 12.7279 + 22.0454i 0.551308 + 0.954893i
\(534\) 0 0
\(535\) 12.7279 + 7.34847i 0.550276 + 0.317702i
\(536\) 0 0
\(537\) −9.00000 15.5885i −0.388379 0.672692i
\(538\) 0 0
\(539\) 36.3731i 1.56670i
\(540\) 0 0
\(541\) 4.89898i 0.210624i −0.994439 0.105312i \(-0.966416\pi\)
0.994439 0.105312i \(-0.0335841\pi\)
\(542\) 0 0
\(543\) 12.7279 + 22.0454i 0.546207 + 0.946059i
\(544\) 0 0
\(545\) 24.0000 + 13.8564i 1.02805 + 0.593543i
\(546\) 0 0
\(547\) 1.50000 + 2.59808i 0.0641354 + 0.111086i 0.896310 0.443428i \(-0.146238\pi\)
−0.832175 + 0.554513i \(0.812904\pi\)
\(548\) 0 0
\(549\) 29.3939i 1.25450i
\(550\) 0 0
\(551\) −8.48528 14.6969i −0.361485 0.626111i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 24.0000 1.01874
\(556\) 0 0
\(557\) −11.3137 −0.479377 −0.239689 0.970850i \(-0.577045\pi\)
−0.239689 + 0.970850i \(0.577045\pi\)
\(558\) 0 0
\(559\) 44.0908i 1.86484i
\(560\) 0 0
\(561\) 13.5000 + 7.79423i 0.569970 + 0.329073i
\(562\) 0 0
\(563\) −22.5000 12.9904i −0.948262 0.547479i −0.0557214 0.998446i \(-0.517746\pi\)
−0.892541 + 0.450967i \(0.851079\pi\)
\(564\) 0 0
\(565\) −33.9411 + 19.5959i −1.42791 + 0.824406i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 28.5000 16.4545i 1.19478 0.689808i 0.235395 0.971900i \(-0.424362\pi\)
0.959387 + 0.282092i \(0.0910284\pi\)
\(570\) 0 0
\(571\) 16.5000 28.5788i 0.690504 1.19599i −0.281170 0.959658i \(-0.590722\pi\)
0.971673 0.236329i \(-0.0759443\pi\)
\(572\) 0 0
\(573\) 25.4558 + 14.6969i 1.06343 + 0.613973i
\(574\) 0 0
\(575\) −25.4558 −1.06158
\(576\) 0 0
\(577\) −31.0000 −1.29055 −0.645273 0.763952i \(-0.723257\pi\)
−0.645273 + 0.763952i \(0.723257\pi\)
\(578\) 0 0
\(579\) 1.73205i 0.0719816i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 25.4558 14.6969i 1.05427 0.608685i
\(584\) 0 0
\(585\) 41.5692i 1.71868i
\(586\) 0 0
\(587\) −4.50000 + 2.59808i −0.185735 + 0.107234i −0.589984 0.807415i \(-0.700866\pi\)
0.404249 + 0.914649i \(0.367533\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 16.9706 9.79796i 0.698076 0.403034i
\(592\) 0 0
\(593\) 27.7128i 1.13803i −0.822328 0.569014i \(-0.807325\pi\)
0.822328 0.569014i \(-0.192675\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 4.24264 7.34847i 0.173350 0.300250i −0.766239 0.642555i \(-0.777874\pi\)
0.939589 + 0.342305i \(0.111208\pi\)
\(600\) 0 0
\(601\) 5.50000 + 9.52628i 0.224350 + 0.388585i 0.956124 0.292962i \(-0.0946409\pi\)
−0.731774 + 0.681547i \(0.761308\pi\)
\(602\) 0 0
\(603\) −4.50000 7.79423i −0.183254 0.317406i
\(604\) 0 0
\(605\) 22.6274 + 39.1918i 0.919935 + 1.59337i
\(606\) 0 0
\(607\) −25.4558 14.6969i −1.03322 0.596530i −0.115315 0.993329i \(-0.536788\pi\)
−0.917906 + 0.396799i \(0.870121\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 41.5692i 1.68171i
\(612\) 0 0
\(613\) 14.6969i 0.593604i −0.954939 0.296802i \(-0.904080\pi\)
0.954939 0.296802i \(-0.0959201\pi\)
\(614\) 0 0
\(615\) 12.7279 22.0454i 0.513239 0.888957i
\(616\) 0 0
\(617\) −19.5000 11.2583i −0.785040 0.453243i 0.0531732 0.998585i \(-0.483066\pi\)
−0.838214 + 0.545342i \(0.816400\pi\)
\(618\) 0 0
\(619\) 4.50000 + 7.79423i 0.180870 + 0.313276i 0.942177 0.335115i \(-0.108775\pi\)
−0.761307 + 0.648392i \(0.775442\pi\)
\(620\) 0 0
\(621\) 38.1838 + 22.0454i 1.53226 + 0.884652i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 15.5000 26.8468i 0.620000 1.07387i
\(626\) 0 0
\(627\) 13.5000 23.3827i 0.539138 0.933815i
\(628\) 0 0
\(629\) 8.48528 0.338330
\(630\) 0 0
\(631\) 44.0908i 1.75523i −0.479368 0.877614i \(-0.659134\pi\)
0.479368 0.877614i \(-0.340866\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −36.0000 20.7846i −1.42862 0.824812i
\(636\) 0 0
\(637\) −29.6985 + 17.1464i −1.17670 + 0.679366i
\(638\) 0 0
\(639\) 12.7279 22.0454i 0.503509 0.872103i
\(640\) 0 0
\(641\) 1.50000 0.866025i 0.0592464 0.0342059i −0.470084 0.882622i \(-0.655776\pi\)
0.529331 + 0.848416i \(0.322443\pi\)
\(642\) 0 0
\(643\) 1.50000 2.59808i 0.0591542 0.102458i −0.834932 0.550353i \(-0.814493\pi\)
0.894086 + 0.447895i \(0.147826\pi\)
\(644\) 0 0
\(645\) −38.1838 + 22.0454i −1.50348 + 0.868037i
\(646\) 0 0
\(647\) −16.9706 −0.667182 −0.333591 0.942718i \(-0.608260\pi\)
−0.333591 + 0.942718i \(0.608260\pi\)
\(648\) 0 0
\(649\) 27.0000 1.05984
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 5.65685 9.79796i 0.221370 0.383424i −0.733854 0.679307i \(-0.762281\pi\)
0.955224 + 0.295883i \(0.0956139\pi\)
\(654\) 0 0
\(655\) 25.4558 14.6969i 0.994642 0.574257i
\(656\) 0 0
\(657\) 7.50000 12.9904i 0.292603 0.506803i
\(658\) 0 0
\(659\) 9.00000 5.19615i 0.350590 0.202413i −0.314355 0.949306i \(-0.601788\pi\)
0.664945 + 0.746892i \(0.268455\pi\)
\(660\) 0 0
\(661\) 21.2132 + 12.2474i 0.825098 + 0.476371i 0.852171 0.523263i \(-0.175285\pi\)
−0.0270733 + 0.999633i \(0.508619\pi\)
\(662\) 0 0
\(663\) 14.6969i 0.570782i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 48.0000 1.85857
\(668\) 0 0
\(669\) −12.7279 + 22.0454i −0.492090 + 0.852325i
\(670\) 0 0
\(671\) −25.4558 + 44.0908i −0.982712 + 1.70211i
\(672\) 0 0
\(673\) 19.0000 + 32.9090i 0.732396 + 1.26855i 0.955856 + 0.293834i \(0.0949314\pi\)
−0.223460 + 0.974713i \(0.571735\pi\)
\(674\) 0 0
\(675\) 13.5000 7.79423i 0.519615 0.300000i
\(676\) 0 0
\(677\) −14.1421 24.4949i −0.543526 0.941415i −0.998698 0.0510117i \(-0.983755\pi\)
0.455172 0.890404i \(-0.349578\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 13.5000 23.3827i 0.517321 0.896026i
\(682\) 0 0
\(683\) 5.19615i 0.198825i 0.995046 + 0.0994126i \(0.0316964\pi\)
−0.995046 + 0.0994126i \(0.968304\pi\)
\(684\) 0 0
\(685\) 24.4949i 0.935902i
\(686\) 0 0
\(687\) 16.9706 0.647467
\(688\) 0 0
\(689\) 24.0000 + 13.8564i 0.914327 + 0.527887i
\(690\) 0 0
\(691\) 12.0000 + 20.7846i 0.456502 + 0.790684i 0.998773 0.0495194i \(-0.0157690\pi\)
−0.542272 + 0.840203i \(0.682436\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −12.7279 22.0454i −0.482798 0.836230i
\(696\) 0 0
\(697\) 4.50000 7.79423i 0.170450 0.295227i
\(698\) 0 0
\(699\) −19.5000 33.7750i −0.737558 1.27749i
\(700\) 0 0
\(701\) 36.7696 1.38877 0.694383 0.719605i \(-0.255677\pi\)
0.694383 + 0.719605i \(0.255677\pi\)
\(702\) 0 0
\(703\) 14.6969i 0.554306i
\(704\) 0 0
\(705\) 36.0000 20.7846i 1.35584 0.782794i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −42.4264 + 24.4949i −1.59336 + 0.919925i −0.600632 + 0.799526i \(0.705084\pi\)
−0.992726 + 0.120399i \(0.961583\pi\)
\(710\) 0 0
\(711\) 44.0908i 1.65353i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) −36.0000 + 62.3538i −1.34632 + 2.33190i
\(716\) 0 0
\(717\) 14.6969i 0.548867i
\(718\) 0 0
\(719\) −25.4558 −0.949343 −0.474671 0.880163i \(-0.657433\pi\)
−0.474671 + 0.880163i \(0.657433\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −10.5000 6.06218i −0.390499 0.225455i
\(724\) 0 0
\(725\) 8.48528 14.6969i 0.315135 0.545831i
\(726\) 0 0
\(727\) −12.7279 + 7.34847i −0.472052 + 0.272540i −0.717099 0.696972i \(-0.754530\pi\)
0.245046 + 0.969511i \(0.421197\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) −13.5000 + 7.79423i −0.499316 + 0.288280i
\(732\) 0 0
\(733\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(734\) 0 0
\(735\) 29.6985 + 17.1464i 1.09545 + 0.632456i
\(736\) 0 0
\(737\) 15.5885i 0.574208i
\(738\) 0 0
\(739\) 27.0000 0.993211 0.496606 0.867976i \(-0.334580\pi\)
0.496606 + 0.867976i \(0.334580\pi\)
\(740\) 0 0
\(741\) 25.4558 0.935144
\(742\) 0 0
\(743\) −8.48528 + 14.6969i −0.311295 + 0.539178i −0.978643 0.205568i \(-0.934096\pi\)
0.667348 + 0.744746i \(0.267429\pi\)
\(744\) 0 0
\(745\) −4.00000 6.92820i −0.146549 0.253830i
\(746\) 0 0
\(747\) 31.1769i 1.14070i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −12.7279 7.34847i −0.464448 0.268149i 0.249464 0.968384i \(-0.419745\pi\)
−0.713913 + 0.700235i \(0.753079\pi\)
\(752\) 0 0
\(753\) −4.50000 7.79423i −0.163989 0.284037i
\(754\) 0 0
\(755\) 41.5692i 1.51286i
\(756\) 0 0
\(757\) 29.3939i 1.06834i −0.845378 0.534169i \(-0.820624\pi\)
0.845378 0.534169i \(-0.179376\pi\)
\(758\) 0 0
\(759\) 38.1838 + 66.1362i 1.38598 + 2.40059i
\(760\) 0 0
\(761\) −12.0000 6.92820i −0.435000 0.251147i 0.266475 0.963842i \(-0.414141\pi\)
−0.701474 + 0.712695i \(0.747474\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 12.7279 7.34847i 0.460179 0.265684i
\(766\) 0 0
\(767\) 12.7279 + 22.0454i 0.459579 + 0.796014i
\(768\) 0 0
\(769\) 13.0000 22.5167i 0.468792 0.811972i −0.530572 0.847640i \(-0.678023\pi\)
0.999364 + 0.0356685i \(0.0113561\pi\)
\(770\) 0 0
\(771\) −3.00000 −0.108042
\(772\) 0 0
\(773\) 14.1421 0.508657 0.254329 0.967118i \(-0.418146\pi\)
0.254329 + 0.967118i \(0.418146\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −13.5000 7.79423i −0.483688 0.279257i
\(780\) 0 0
\(781\) 38.1838 22.0454i 1.36632 0.788847i
\(782\) 0 0
\(783\) −25.4558 + 14.6969i −0.909718 + 0.525226i
\(784\) 0 0
\(785\) −48.0000 + 27.7128i −1.71319 + 0.989113i
\(786\) 0 0
\(787\) 12.0000 20.7846i 0.427754 0.740891i −0.568919 0.822393i \(-0.692638\pi\)
0.996673 + 0.0815020i \(0.0259717\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −48.0000 −1.70453
\(794\) 0 0
\(795\) 27.7128i 0.982872i
\(796\) 0 0
\(797\) 1.41421 2.44949i 0.0500940 0.0867654i −0.839891 0.542755i \(-0.817381\pi\)
0.889985 + 0.455990i \(0.150715\pi\)
\(798\)