Properties

Label 384.3.e.d.257.4
Level $384$
Weight $3$
Character 384.257
Analytic conductor $10.463$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 384.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.4632421514\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} + \cdots)\)
Defining polynomial: \(x^{8} + 18 x^{6} + 99 x^{4} + 170 x^{2} + 81\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{10}\cdot 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 257.4
Root \(2.98985i\) of defining polynomial
Character \(\chi\) \(=\) 384.257
Dual form 384.3.e.d.257.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.246559 + 2.98985i) q^{3} -6.63641i q^{5} +0.578158 q^{7} +(-8.87842 + 1.47435i) q^{9} +O(q^{10})\) \(q+(0.246559 + 2.98985i) q^{3} -6.63641i q^{5} +0.578158 q^{7} +(-8.87842 + 1.47435i) q^{9} +8.68786i q^{11} +17.9269 q^{13} +(19.8419 - 1.63626i) q^{15} -19.0110i q^{17} +32.1769 q^{19} +(0.142550 + 1.72861i) q^{21} -20.4836i q^{23} -19.0419 q^{25} +(-6.59713 - 26.1816i) q^{27} +22.0310i q^{29} +26.2344 q^{31} +(-25.9754 + 2.14207i) q^{33} -3.83689i q^{35} +53.3855 q^{37} +(4.42003 + 53.5988i) q^{39} +35.6935i q^{41} +50.4895 q^{43} +(9.78437 + 58.9208i) q^{45} +30.6265i q^{47} -48.6657 q^{49} +(56.8401 - 4.68732i) q^{51} -88.8962i q^{53} +57.6562 q^{55} +(7.93348 + 96.2040i) q^{57} +63.1939i q^{59} -33.5317 q^{61} +(-5.13313 + 0.852405i) q^{63} -118.970i q^{65} -108.562 q^{67} +(61.2430 - 5.05041i) q^{69} -59.3600i q^{71} -5.60477 q^{73} +(-4.69495 - 56.9325i) q^{75} +5.02296i q^{77} -78.9955 q^{79} +(76.6526 - 26.1797i) q^{81} +48.5283i q^{83} -126.165 q^{85} +(-65.8694 + 5.43193i) q^{87} -58.7109i q^{89} +10.3646 q^{91} +(6.46831 + 78.4369i) q^{93} -213.539i q^{95} +93.3544 q^{97} +(-12.8089 - 77.1345i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{3} + 8q^{7} + O(q^{10}) \) \( 8q + 4q^{3} + 8q^{7} + 16q^{15} - 24q^{19} + 16q^{21} - 40q^{25} - 44q^{27} - 56q^{31} + 8q^{33} + 32q^{37} - 104q^{39} + 136q^{43} - 80q^{45} + 72q^{49} + 176q^{51} + 192q^{55} - 40q^{57} - 160q^{61} + 264q^{63} - 280q^{67} + 80q^{69} - 80q^{73} - 348q^{75} - 408q^{79} + 72q^{81} + 192q^{85} - 368q^{87} + 336q^{91} + 160q^{93} + 96q^{97} + 432q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(133\) \(257\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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
\(3\) 0.246559 + 2.98985i 0.0821862 + 0.996617i
\(4\) 0 0
\(5\) 6.63641i 1.32728i −0.748051 0.663641i \(-0.769010\pi\)
0.748051 0.663641i \(-0.230990\pi\)
\(6\) 0 0
\(7\) 0.578158 0.0825940 0.0412970 0.999147i \(-0.486851\pi\)
0.0412970 + 0.999147i \(0.486851\pi\)
\(8\) 0 0
\(9\) −8.87842 + 1.47435i −0.986491 + 0.163816i
\(10\) 0 0
\(11\) 8.68786i 0.789806i 0.918723 + 0.394903i \(0.129222\pi\)
−0.918723 + 0.394903i \(0.870778\pi\)
\(12\) 0 0
\(13\) 17.9269 1.37899 0.689497 0.724289i \(-0.257832\pi\)
0.689497 + 0.724289i \(0.257832\pi\)
\(14\) 0 0
\(15\) 19.8419 1.63626i 1.32279 0.109084i
\(16\) 0 0
\(17\) 19.0110i 1.11829i −0.829068 0.559147i \(-0.811129\pi\)
0.829068 0.559147i \(-0.188871\pi\)
\(18\) 0 0
\(19\) 32.1769 1.69352 0.846760 0.531976i \(-0.178550\pi\)
0.846760 + 0.531976i \(0.178550\pi\)
\(20\) 0 0
\(21\) 0.142550 + 1.72861i 0.00678808 + 0.0823146i
\(22\) 0 0
\(23\) 20.4836i 0.890592i −0.895383 0.445296i \(-0.853098\pi\)
0.895383 0.445296i \(-0.146902\pi\)
\(24\) 0 0
\(25\) −19.0419 −0.761677
\(26\) 0 0
\(27\) −6.59713 26.1816i −0.244338 0.969690i
\(28\) 0 0
\(29\) 22.0310i 0.759690i 0.925050 + 0.379845i \(0.124023\pi\)
−0.925050 + 0.379845i \(0.875977\pi\)
\(30\) 0 0
\(31\) 26.2344 0.846270 0.423135 0.906067i \(-0.360930\pi\)
0.423135 + 0.906067i \(0.360930\pi\)
\(32\) 0 0
\(33\) −25.9754 + 2.14207i −0.787134 + 0.0649111i
\(34\) 0 0
\(35\) 3.83689i 0.109625i
\(36\) 0 0
\(37\) 53.3855 1.44285 0.721426 0.692492i \(-0.243487\pi\)
0.721426 + 0.692492i \(0.243487\pi\)
\(38\) 0 0
\(39\) 4.42003 + 53.5988i 0.113334 + 1.37433i
\(40\) 0 0
\(41\) 35.6935i 0.870574i 0.900292 + 0.435287i \(0.143353\pi\)
−0.900292 + 0.435287i \(0.856647\pi\)
\(42\) 0 0
\(43\) 50.4895 1.17417 0.587087 0.809524i \(-0.300275\pi\)
0.587087 + 0.809524i \(0.300275\pi\)
\(44\) 0 0
\(45\) 9.78437 + 58.9208i 0.217430 + 1.30935i
\(46\) 0 0
\(47\) 30.6265i 0.651628i 0.945434 + 0.325814i \(0.105638\pi\)
−0.945434 + 0.325814i \(0.894362\pi\)
\(48\) 0 0
\(49\) −48.6657 −0.993178
\(50\) 0 0
\(51\) 56.8401 4.68732i 1.11451 0.0919083i
\(52\) 0 0
\(53\) 88.8962i 1.67729i −0.544681 0.838644i \(-0.683349\pi\)
0.544681 0.838644i \(-0.316651\pi\)
\(54\) 0 0
\(55\) 57.6562 1.04829
\(56\) 0 0
\(57\) 7.93348 + 96.2040i 0.139184 + 1.68779i
\(58\) 0 0
\(59\) 63.1939i 1.07108i 0.844509 + 0.535542i \(0.179893\pi\)
−0.844509 + 0.535542i \(0.820107\pi\)
\(60\) 0 0
\(61\) −33.5317 −0.549700 −0.274850 0.961487i \(-0.588628\pi\)
−0.274850 + 0.961487i \(0.588628\pi\)
\(62\) 0 0
\(63\) −5.13313 + 0.852405i −0.0814782 + 0.0135302i
\(64\) 0 0
\(65\) 118.970i 1.83031i
\(66\) 0 0
\(67\) −108.562 −1.62032 −0.810162 0.586206i \(-0.800621\pi\)
−0.810162 + 0.586206i \(0.800621\pi\)
\(68\) 0 0
\(69\) 61.2430 5.05041i 0.887579 0.0731944i
\(70\) 0 0
\(71\) 59.3600i 0.836056i −0.908434 0.418028i \(-0.862721\pi\)
0.908434 0.418028i \(-0.137279\pi\)
\(72\) 0 0
\(73\) −5.60477 −0.0767777 −0.0383889 0.999263i \(-0.512223\pi\)
−0.0383889 + 0.999263i \(0.512223\pi\)
\(74\) 0 0
\(75\) −4.69495 56.9325i −0.0625994 0.759101i
\(76\) 0 0
\(77\) 5.02296i 0.0652332i
\(78\) 0 0
\(79\) −78.9955 −0.999943 −0.499971 0.866042i \(-0.666656\pi\)
−0.499971 + 0.866042i \(0.666656\pi\)
\(80\) 0 0
\(81\) 76.6526 26.1797i 0.946328 0.323207i
\(82\) 0 0
\(83\) 48.5283i 0.584679i 0.956315 + 0.292339i \(0.0944337\pi\)
−0.956315 + 0.292339i \(0.905566\pi\)
\(84\) 0 0
\(85\) −126.165 −1.48429
\(86\) 0 0
\(87\) −65.8694 + 5.43193i −0.757120 + 0.0624360i
\(88\) 0 0
\(89\) 58.7109i 0.659672i −0.944038 0.329836i \(-0.893006\pi\)
0.944038 0.329836i \(-0.106994\pi\)
\(90\) 0 0
\(91\) 10.3646 0.113897
\(92\) 0 0
\(93\) 6.46831 + 78.4369i 0.0695517 + 0.843407i
\(94\) 0 0
\(95\) 213.539i 2.24778i
\(96\) 0 0
\(97\) 93.3544 0.962416 0.481208 0.876606i \(-0.340198\pi\)
0.481208 + 0.876606i \(0.340198\pi\)
\(98\) 0 0
\(99\) −12.8089 77.1345i −0.129383 0.779136i
\(100\) 0 0
\(101\) 114.161i 1.13031i −0.824985 0.565155i \(-0.808816\pi\)
0.824985 0.565155i \(-0.191184\pi\)
\(102\) 0 0
\(103\) 70.0355 0.679956 0.339978 0.940433i \(-0.389580\pi\)
0.339978 + 0.940433i \(0.389580\pi\)
\(104\) 0 0
\(105\) 11.4717 0.946018i 0.109255 0.00900970i
\(106\) 0 0
\(107\) 50.9072i 0.475769i 0.971293 + 0.237884i \(0.0764539\pi\)
−0.971293 + 0.237884i \(0.923546\pi\)
\(108\) 0 0
\(109\) 13.2178 0.121264 0.0606320 0.998160i \(-0.480688\pi\)
0.0606320 + 0.998160i \(0.480688\pi\)
\(110\) 0 0
\(111\) 13.1627 + 159.615i 0.118582 + 1.43797i
\(112\) 0 0
\(113\) 62.9470i 0.557053i −0.960429 0.278527i \(-0.910154\pi\)
0.960429 0.278527i \(-0.0898460\pi\)
\(114\) 0 0
\(115\) −135.938 −1.18207
\(116\) 0 0
\(117\) −159.163 + 26.4305i −1.36036 + 0.225902i
\(118\) 0 0
\(119\) 10.9914i 0.0923644i
\(120\) 0 0
\(121\) 45.5210 0.376207
\(122\) 0 0
\(123\) −106.718 + 8.80054i −0.867629 + 0.0715491i
\(124\) 0 0
\(125\) 39.5402i 0.316321i
\(126\) 0 0
\(127\) −236.659 −1.86345 −0.931727 0.363160i \(-0.881698\pi\)
−0.931727 + 0.363160i \(0.881698\pi\)
\(128\) 0 0
\(129\) 12.4486 + 150.956i 0.0965009 + 1.17020i
\(130\) 0 0
\(131\) 121.212i 0.925279i 0.886546 + 0.462640i \(0.153098\pi\)
−0.886546 + 0.462640i \(0.846902\pi\)
\(132\) 0 0
\(133\) 18.6033 0.139875
\(134\) 0 0
\(135\) −173.752 + 43.7812i −1.28705 + 0.324305i
\(136\) 0 0
\(137\) 136.677i 0.997645i 0.866704 + 0.498822i \(0.166234\pi\)
−0.866704 + 0.498822i \(0.833766\pi\)
\(138\) 0 0
\(139\) −29.5616 −0.212673 −0.106337 0.994330i \(-0.533912\pi\)
−0.106337 + 0.994330i \(0.533912\pi\)
\(140\) 0 0
\(141\) −91.5687 + 7.55123i −0.649424 + 0.0535548i
\(142\) 0 0
\(143\) 155.747i 1.08914i
\(144\) 0 0
\(145\) 146.207 1.00832
\(146\) 0 0
\(147\) −11.9990 145.503i −0.0816255 0.989818i
\(148\) 0 0
\(149\) 17.5092i 0.117511i −0.998272 0.0587556i \(-0.981287\pi\)
0.998272 0.0587556i \(-0.0187133\pi\)
\(150\) 0 0
\(151\) −119.607 −0.792099 −0.396050 0.918229i \(-0.629619\pi\)
−0.396050 + 0.918229i \(0.629619\pi\)
\(152\) 0 0
\(153\) 28.0288 + 168.788i 0.183195 + 1.10319i
\(154\) 0 0
\(155\) 174.102i 1.12324i
\(156\) 0 0
\(157\) −189.488 −1.20693 −0.603466 0.797388i \(-0.706214\pi\)
−0.603466 + 0.797388i \(0.706214\pi\)
\(158\) 0 0
\(159\) 265.786 21.9181i 1.67161 0.137850i
\(160\) 0 0
\(161\) 11.8428i 0.0735576i
\(162\) 0 0
\(163\) 104.654 0.642051 0.321026 0.947071i \(-0.395972\pi\)
0.321026 + 0.947071i \(0.395972\pi\)
\(164\) 0 0
\(165\) 14.2156 + 172.384i 0.0861553 + 1.04475i
\(166\) 0 0
\(167\) 142.664i 0.854278i 0.904186 + 0.427139i \(0.140478\pi\)
−0.904186 + 0.427139i \(0.859522\pi\)
\(168\) 0 0
\(169\) 152.374 0.901623
\(170\) 0 0
\(171\) −285.680 + 47.4399i −1.67064 + 0.277426i
\(172\) 0 0
\(173\) 11.6594i 0.0673952i −0.999432 0.0336976i \(-0.989272\pi\)
0.999432 0.0336976i \(-0.0107283\pi\)
\(174\) 0 0
\(175\) −11.0092 −0.0629100
\(176\) 0 0
\(177\) −188.940 + 15.5810i −1.06746 + 0.0880283i
\(178\) 0 0
\(179\) 40.3979i 0.225687i 0.993613 + 0.112843i \(0.0359958\pi\)
−0.993613 + 0.112843i \(0.964004\pi\)
\(180\) 0 0
\(181\) 121.175 0.669472 0.334736 0.942312i \(-0.391353\pi\)
0.334736 + 0.942312i \(0.391353\pi\)
\(182\) 0 0
\(183\) −8.26752 100.255i −0.0451777 0.547840i
\(184\) 0 0
\(185\) 354.288i 1.91507i
\(186\) 0 0
\(187\) 165.165 0.883235
\(188\) 0 0
\(189\) −3.81418 15.1371i −0.0201808 0.0800906i
\(190\) 0 0
\(191\) 337.287i 1.76590i −0.469465 0.882951i \(-0.655553\pi\)
0.469465 0.882951i \(-0.344447\pi\)
\(192\) 0 0
\(193\) −227.937 −1.18102 −0.590511 0.807029i \(-0.701074\pi\)
−0.590511 + 0.807029i \(0.701074\pi\)
\(194\) 0 0
\(195\) 355.704 29.3332i 1.82412 0.150426i
\(196\) 0 0
\(197\) 172.276i 0.874495i 0.899341 + 0.437248i \(0.144047\pi\)
−0.899341 + 0.437248i \(0.855953\pi\)
\(198\) 0 0
\(199\) 0.598837 0.00300923 0.00150461 0.999999i \(-0.499521\pi\)
0.00150461 + 0.999999i \(0.499521\pi\)
\(200\) 0 0
\(201\) −26.7668 324.583i −0.133168 1.61484i
\(202\) 0 0
\(203\) 12.7374i 0.0627458i
\(204\) 0 0
\(205\) 236.877 1.15550
\(206\) 0 0
\(207\) 30.2000 + 181.862i 0.145894 + 0.878561i
\(208\) 0 0
\(209\) 279.548i 1.33755i
\(210\) 0 0
\(211\) −243.040 −1.15185 −0.575923 0.817504i \(-0.695357\pi\)
−0.575923 + 0.817504i \(0.695357\pi\)
\(212\) 0 0
\(213\) 177.478 14.6357i 0.833228 0.0687123i
\(214\) 0 0
\(215\) 335.069i 1.55846i
\(216\) 0 0
\(217\) 15.1676 0.0698968
\(218\) 0 0
\(219\) −1.38190 16.7574i −0.00631007 0.0765180i
\(220\) 0 0
\(221\) 340.809i 1.54212i
\(222\) 0 0
\(223\) 191.174 0.857284 0.428642 0.903474i \(-0.358992\pi\)
0.428642 + 0.903474i \(0.358992\pi\)
\(224\) 0 0
\(225\) 169.062 28.0744i 0.751388 0.124775i
\(226\) 0 0
\(227\) 8.76834i 0.0386271i 0.999813 + 0.0193135i \(0.00614807\pi\)
−0.999813 + 0.0193135i \(0.993852\pi\)
\(228\) 0 0
\(229\) −131.740 −0.575283 −0.287641 0.957738i \(-0.592871\pi\)
−0.287641 + 0.957738i \(0.592871\pi\)
\(230\) 0 0
\(231\) −15.0179 + 1.23845i −0.0650125 + 0.00536127i
\(232\) 0 0
\(233\) 96.0149i 0.412081i −0.978543 0.206040i \(-0.933942\pi\)
0.978543 0.206040i \(-0.0660579\pi\)
\(234\) 0 0
\(235\) 203.250 0.864894
\(236\) 0 0
\(237\) −19.4770 236.185i −0.0821815 0.996560i
\(238\) 0 0
\(239\) 317.978i 1.33045i 0.746643 + 0.665225i \(0.231664\pi\)
−0.746643 + 0.665225i \(0.768336\pi\)
\(240\) 0 0
\(241\) −114.189 −0.473812 −0.236906 0.971533i \(-0.576133\pi\)
−0.236906 + 0.971533i \(0.576133\pi\)
\(242\) 0 0
\(243\) 97.1728 + 222.725i 0.399888 + 0.916564i
\(244\) 0 0
\(245\) 322.966i 1.31823i
\(246\) 0 0
\(247\) 576.832 2.33535
\(248\) 0 0
\(249\) −145.093 + 11.9651i −0.582701 + 0.0480525i
\(250\) 0 0
\(251\) 376.853i 1.50140i 0.660641 + 0.750702i \(0.270285\pi\)
−0.660641 + 0.750702i \(0.729715\pi\)
\(252\) 0 0
\(253\) 177.959 0.703395
\(254\) 0 0
\(255\) −31.1070 377.214i −0.121988 1.47927i
\(256\) 0 0
\(257\) 152.041i 0.591599i 0.955250 + 0.295800i \(0.0955861\pi\)
−0.955250 + 0.295800i \(0.904414\pi\)
\(258\) 0 0
\(259\) 30.8653 0.119171
\(260\) 0 0
\(261\) −32.4813 195.600i −0.124450 0.749427i
\(262\) 0 0
\(263\) 495.013i 1.88218i 0.338158 + 0.941089i \(0.390196\pi\)
−0.338158 + 0.941089i \(0.609804\pi\)
\(264\) 0 0
\(265\) −589.952 −2.22623
\(266\) 0 0
\(267\) 175.537 14.4757i 0.657441 0.0542160i
\(268\) 0 0
\(269\) 173.556i 0.645190i −0.946537 0.322595i \(-0.895445\pi\)
0.946537 0.322595i \(-0.104555\pi\)
\(270\) 0 0
\(271\) −125.415 −0.462784 −0.231392 0.972861i \(-0.574328\pi\)
−0.231392 + 0.972861i \(0.574328\pi\)
\(272\) 0 0
\(273\) 2.55548 + 30.9886i 0.00936072 + 0.113511i
\(274\) 0 0
\(275\) 165.434i 0.601577i
\(276\) 0 0
\(277\) 226.300 0.816967 0.408483 0.912766i \(-0.366058\pi\)
0.408483 + 0.912766i \(0.366058\pi\)
\(278\) 0 0
\(279\) −232.920 + 38.6786i −0.834838 + 0.138633i
\(280\) 0 0
\(281\) 13.8834i 0.0494073i −0.999695 0.0247036i \(-0.992136\pi\)
0.999695 0.0247036i \(-0.00786421\pi\)
\(282\) 0 0
\(283\) 306.461 1.08290 0.541450 0.840733i \(-0.317875\pi\)
0.541450 + 0.840733i \(0.317875\pi\)
\(284\) 0 0
\(285\) 638.449 52.6498i 2.24017 0.184736i
\(286\) 0 0
\(287\) 20.6365i 0.0719042i
\(288\) 0 0
\(289\) −72.4183 −0.250582
\(290\) 0 0
\(291\) 23.0173 + 279.116i 0.0790973 + 0.959160i
\(292\) 0 0
\(293\) 121.869i 0.415935i 0.978136 + 0.207968i \(0.0666848\pi\)
−0.978136 + 0.207968i \(0.933315\pi\)
\(294\) 0 0
\(295\) 419.381 1.42163
\(296\) 0 0
\(297\) 227.462 57.3149i 0.765867 0.192980i
\(298\) 0 0
\(299\) 367.208i 1.22812i
\(300\) 0 0
\(301\) 29.1909 0.0969797
\(302\) 0 0
\(303\) 341.325 28.1474i 1.12649 0.0928959i
\(304\) 0 0
\(305\) 222.530i 0.729607i
\(306\) 0 0
\(307\) −19.0431 −0.0620298 −0.0310149 0.999519i \(-0.509874\pi\)
−0.0310149 + 0.999519i \(0.509874\pi\)
\(308\) 0 0
\(309\) 17.2678 + 209.396i 0.0558830 + 0.677656i
\(310\) 0 0
\(311\) 223.159i 0.717552i −0.933424 0.358776i \(-0.883194\pi\)
0.933424 0.358776i \(-0.116806\pi\)
\(312\) 0 0
\(313\) −194.708 −0.622070 −0.311035 0.950399i \(-0.600676\pi\)
−0.311035 + 0.950399i \(0.600676\pi\)
\(314\) 0 0
\(315\) 5.65691 + 34.0655i 0.0179584 + 0.108145i
\(316\) 0 0
\(317\) 532.192i 1.67884i 0.543483 + 0.839420i \(0.317105\pi\)
−0.543483 + 0.839420i \(0.682895\pi\)
\(318\) 0 0
\(319\) −191.402 −0.600007
\(320\) 0 0
\(321\) −152.205 + 12.5516i −0.474159 + 0.0391016i
\(322\) 0 0
\(323\) 611.715i 1.89385i
\(324\) 0 0
\(325\) −341.363 −1.05035
\(326\) 0 0
\(327\) 3.25896 + 39.5192i 0.00996623 + 0.120854i
\(328\) 0 0
\(329\) 17.7070i 0.0538206i
\(330\) 0 0
\(331\) 91.7273 0.277122 0.138561 0.990354i \(-0.455752\pi\)
0.138561 + 0.990354i \(0.455752\pi\)
\(332\) 0 0
\(333\) −473.979 + 78.7088i −1.42336 + 0.236363i
\(334\) 0 0
\(335\) 720.460i 2.15063i
\(336\) 0 0
\(337\) 82.1658 0.243815 0.121908 0.992541i \(-0.461099\pi\)
0.121908 + 0.992541i \(0.461099\pi\)
\(338\) 0 0
\(339\) 188.202 15.5201i 0.555169 0.0457821i
\(340\) 0 0
\(341\) 227.921i 0.668389i
\(342\) 0 0
\(343\) −56.4662 −0.164625
\(344\) 0 0
\(345\) −33.5166 406.433i −0.0971496 1.17807i
\(346\) 0 0
\(347\) 323.122i 0.931189i −0.884998 0.465594i \(-0.845841\pi\)
0.884998 0.465594i \(-0.154159\pi\)
\(348\) 0 0
\(349\) −255.324 −0.731586 −0.365793 0.930696i \(-0.619202\pi\)
−0.365793 + 0.930696i \(0.619202\pi\)
\(350\) 0 0
\(351\) −118.266 469.356i −0.336941 1.33720i
\(352\) 0 0
\(353\) 344.332i 0.975444i 0.872999 + 0.487722i \(0.162172\pi\)
−0.872999 + 0.487722i \(0.837828\pi\)
\(354\) 0 0
\(355\) −393.937 −1.10968
\(356\) 0 0
\(357\) 32.8625 2.71001i 0.0920519 0.00759107i
\(358\) 0 0
\(359\) 119.962i 0.334157i −0.985944 0.167079i \(-0.946567\pi\)
0.985944 0.167079i \(-0.0534334\pi\)
\(360\) 0 0
\(361\) 674.351 1.86801
\(362\) 0 0
\(363\) 11.2236 + 136.101i 0.0309190 + 0.374934i
\(364\) 0 0
\(365\) 37.1956i 0.101906i
\(366\) 0 0
\(367\) −398.726 −1.08645 −0.543223 0.839589i \(-0.682796\pi\)
−0.543223 + 0.839589i \(0.682796\pi\)
\(368\) 0 0
\(369\) −52.6246 316.902i −0.142614 0.858813i
\(370\) 0 0
\(371\) 51.3960i 0.138534i
\(372\) 0 0
\(373\) 606.592 1.62625 0.813126 0.582088i \(-0.197764\pi\)
0.813126 + 0.582088i \(0.197764\pi\)
\(374\) 0 0
\(375\) 118.219 9.74896i 0.315251 0.0259972i
\(376\) 0 0
\(377\) 394.948i 1.04761i
\(378\) 0 0
\(379\) −266.492 −0.703146 −0.351573 0.936161i \(-0.614353\pi\)
−0.351573 + 0.936161i \(0.614353\pi\)
\(380\) 0 0
\(381\) −58.3502 707.574i −0.153150 1.85715i
\(382\) 0 0
\(383\) 406.790i 1.06212i −0.847336 0.531058i \(-0.821795\pi\)
0.847336 0.531058i \(-0.178205\pi\)
\(384\) 0 0
\(385\) 33.3344 0.0865828
\(386\) 0 0
\(387\) −448.267 + 74.4390i −1.15831 + 0.192349i
\(388\) 0 0
\(389\) 217.748i 0.559763i 0.960035 + 0.279881i \(0.0902951\pi\)
−0.960035 + 0.279881i \(0.909705\pi\)
\(390\) 0 0
\(391\) −389.414 −0.995944
\(392\) 0 0
\(393\) −362.405 + 29.8858i −0.922149 + 0.0760452i
\(394\) 0 0
\(395\) 524.246i 1.32721i
\(396\) 0 0
\(397\) 53.9651 0.135932 0.0679661 0.997688i \(-0.478349\pi\)
0.0679661 + 0.997688i \(0.478349\pi\)
\(398\) 0 0
\(399\) 4.58680 + 55.6211i 0.0114958 + 0.139401i
\(400\) 0 0
\(401\) 294.291i 0.733893i −0.930242 0.366946i \(-0.880403\pi\)
0.930242 0.366946i \(-0.119597\pi\)
\(402\) 0 0
\(403\) 470.302 1.16700
\(404\) 0 0
\(405\) −173.739 508.698i −0.428986 1.25604i
\(406\) 0 0
\(407\) 463.806i 1.13957i
\(408\) 0 0
\(409\) 569.204 1.39170 0.695849 0.718188i \(-0.255028\pi\)
0.695849 + 0.718188i \(0.255028\pi\)
\(410\) 0 0
\(411\) −408.645 + 33.6990i −0.994270 + 0.0819926i
\(412\) 0 0
\(413\) 36.5361i 0.0884651i
\(414\) 0 0
\(415\) 322.054 0.776034
\(416\) 0 0
\(417\) −7.28866 88.3847i −0.0174788 0.211954i
\(418\) 0 0
\(419\) 590.728i 1.40985i 0.709281 + 0.704926i \(0.249020\pi\)
−0.709281 + 0.704926i \(0.750980\pi\)
\(420\) 0 0
\(421\) −475.989 −1.13061 −0.565307 0.824880i \(-0.691242\pi\)
−0.565307 + 0.824880i \(0.691242\pi\)
\(422\) 0 0
\(423\) −45.1541 271.915i −0.106747 0.642825i
\(424\) 0 0
\(425\) 362.006i 0.851780i
\(426\) 0 0
\(427\) −19.3866 −0.0454019
\(428\) 0 0
\(429\) −465.659 + 38.4007i −1.08545 + 0.0895120i
\(430\) 0 0
\(431\) 341.539i 0.792435i 0.918157 + 0.396217i \(0.129677\pi\)
−0.918157 + 0.396217i \(0.870323\pi\)
\(432\) 0 0
\(433\) −88.2258 −0.203755 −0.101877 0.994797i \(-0.532485\pi\)
−0.101877 + 0.994797i \(0.532485\pi\)
\(434\) 0 0
\(435\) 36.0485 + 437.136i 0.0828702 + 1.00491i
\(436\) 0 0
\(437\) 659.099i 1.50824i
\(438\) 0 0
\(439\) −735.647 −1.67573 −0.837867 0.545875i \(-0.816197\pi\)
−0.837867 + 0.545875i \(0.816197\pi\)
\(440\) 0 0
\(441\) 432.075 71.7502i 0.979761 0.162699i
\(442\) 0 0
\(443\) 333.798i 0.753494i −0.926316 0.376747i \(-0.877043\pi\)
0.926316 0.376747i \(-0.122957\pi\)
\(444\) 0 0
\(445\) −389.629 −0.875571
\(446\) 0 0
\(447\) 52.3498 4.31703i 0.117114 0.00965779i
\(448\) 0 0
\(449\) 396.485i 0.883039i −0.897252 0.441520i \(-0.854440\pi\)
0.897252 0.441520i \(-0.145560\pi\)
\(450\) 0 0
\(451\) −310.100 −0.687584
\(452\) 0 0
\(453\) −29.4901 357.607i −0.0650996 0.789419i
\(454\) 0 0
\(455\) 68.7836i 0.151173i
\(456\) 0 0
\(457\) 34.5362 0.0755715 0.0377857 0.999286i \(-0.487970\pi\)
0.0377857 + 0.999286i \(0.487970\pi\)
\(458\) 0 0
\(459\) −497.739 + 125.418i −1.08440 + 0.273242i
\(460\) 0 0
\(461\) 324.050i 0.702929i 0.936201 + 0.351464i \(0.114316\pi\)
−0.936201 + 0.351464i \(0.885684\pi\)
\(462\) 0 0
\(463\) 6.33727 0.0136874 0.00684371 0.999977i \(-0.497822\pi\)
0.00684371 + 0.999977i \(0.497822\pi\)
\(464\) 0 0
\(465\) 520.539 42.9264i 1.11944 0.0923147i
\(466\) 0 0
\(467\) 450.706i 0.965109i −0.875866 0.482554i \(-0.839709\pi\)
0.875866 0.482554i \(-0.160291\pi\)
\(468\) 0 0
\(469\) −62.7658 −0.133829
\(470\) 0 0
\(471\) −46.7200 566.542i −0.0991932 1.20285i
\(472\) 0 0
\(473\) 438.646i 0.927370i
\(474\) 0 0
\(475\) −612.710 −1.28992
\(476\) 0 0
\(477\) 131.064 + 789.258i 0.274767 + 1.65463i
\(478\) 0 0
\(479\) 259.094i 0.540906i −0.962733 0.270453i \(-0.912827\pi\)
0.962733 0.270453i \(-0.0871735\pi\)
\(480\) 0 0
\(481\) 957.038 1.98968
\(482\) 0 0
\(483\) 35.4081 2.91993i 0.0733087 0.00604541i
\(484\) 0 0
\(485\) 619.538i 1.27740i
\(486\) 0 0
\(487\) −628.526 −1.29061 −0.645304 0.763926i \(-0.723269\pi\)
−0.645304 + 0.763926i \(0.723269\pi\)
\(488\) 0 0
\(489\) 25.8034 + 312.901i 0.0527677 + 0.639879i
\(490\) 0 0
\(491\) 352.334i 0.717585i −0.933417 0.358792i \(-0.883189\pi\)
0.933417 0.358792i \(-0.116811\pi\)
\(492\) 0 0
\(493\) 418.831 0.849557
\(494\) 0 0
\(495\) −511.896 + 85.0052i −1.03413 + 0.171728i
\(496\) 0 0
\(497\) 34.3195i 0.0690532i
\(498\) 0 0
\(499\) 240.576 0.482116 0.241058 0.970511i \(-0.422506\pi\)
0.241058 + 0.970511i \(0.422506\pi\)
\(500\) 0 0
\(501\) −426.545 + 35.1751i −0.851388 + 0.0702098i
\(502\) 0 0
\(503\) 13.1648i 0.0261725i 0.999914 + 0.0130862i \(0.00416560\pi\)
−0.999914 + 0.0130862i \(0.995834\pi\)
\(504\) 0 0
\(505\) −757.621 −1.50024
\(506\) 0 0
\(507\) 37.5692 + 455.577i 0.0741010 + 0.898573i
\(508\) 0 0
\(509\) 468.752i 0.920927i 0.887679 + 0.460464i \(0.152317\pi\)
−0.887679 + 0.460464i \(0.847683\pi\)
\(510\) 0 0
\(511\) −3.24044 −0.00634138
\(512\) 0 0
\(513\) −212.275 842.443i −0.413791 1.64219i
\(514\) 0 0
\(515\) 464.784i 0.902494i
\(516\) 0 0
\(517\) −266.079 −0.514660
\(518\) 0 0
\(519\) 34.8598 2.87472i 0.0671672 0.00553895i
\(520\) 0 0
\(521\) 456.517i 0.876232i −0.898918 0.438116i \(-0.855646\pi\)
0.898918 0.438116i \(-0.144354\pi\)
\(522\) 0 0
\(523\) −287.095 −0.548939 −0.274469 0.961596i \(-0.588502\pi\)
−0.274469 + 0.961596i \(0.588502\pi\)
\(524\) 0 0
\(525\) −2.71442 32.9160i −0.00517033 0.0626971i
\(526\) 0 0
\(527\) 498.742i 0.946379i
\(528\) 0 0
\(529\) 109.421 0.206845
\(530\) 0 0
\(531\) −93.1698 561.062i −0.175461 1.05661i
\(532\) 0 0
\(533\) 639.875i 1.20052i
\(534\) 0 0
\(535\) 337.841 0.631479
\(536\) 0 0
\(537\) −120.784 + 9.96046i −0.224923 + 0.0185483i
\(538\) 0 0
\(539\) 422.801i 0.784418i
\(540\) 0 0
\(541\) −804.779 −1.48758 −0.743788 0.668416i \(-0.766973\pi\)
−0.743788 + 0.668416i \(0.766973\pi\)
\(542\) 0 0
\(543\) 29.8766 + 362.294i 0.0550214 + 0.667208i
\(544\) 0 0
\(545\) 87.7186i 0.160952i
\(546\) 0 0
\(547\) −76.3034 −0.139494 −0.0697471 0.997565i \(-0.522219\pi\)
−0.0697471 + 0.997565i \(0.522219\pi\)
\(548\) 0 0
\(549\) 297.708 49.4373i 0.542274 0.0900498i
\(550\) 0 0
\(551\) 708.889i 1.28655i
\(552\) 0 0
\(553\) −45.6718 −0.0825892
\(554\) 0 0
\(555\) 1059.27 87.3528i 1.90859 0.157392i
\(556\) 0 0
\(557\) 540.544i 0.970455i 0.874388 + 0.485228i \(0.161263\pi\)
−0.874388 + 0.485228i \(0.838737\pi\)
\(558\) 0 0
\(559\) 905.121 1.61918
\(560\) 0 0
\(561\) 40.7228 + 493.819i 0.0725897 + 0.880247i
\(562\) 0 0
\(563\) 1047.65i 1.86084i 0.366491 + 0.930422i \(0.380559\pi\)
−0.366491 + 0.930422i \(0.619441\pi\)
\(564\) 0 0
\(565\) −417.742 −0.739366
\(566\) 0 0
\(567\) 44.3173 15.1360i 0.0781610 0.0266949i
\(568\) 0 0
\(569\) 958.593i 1.68470i 0.538933 + 0.842348i \(0.318827\pi\)
−0.538933 + 0.842348i \(0.681173\pi\)
\(570\) 0 0
\(571\) 118.951 0.208321 0.104161 0.994560i \(-0.466784\pi\)
0.104161 + 0.994560i \(0.466784\pi\)
\(572\) 0 0
\(573\) 1008.44 83.1611i 1.75993 0.145133i
\(574\) 0 0
\(575\) 390.048i 0.678344i
\(576\) 0 0
\(577\) −355.825 −0.616681 −0.308340 0.951276i \(-0.599774\pi\)
−0.308340 + 0.951276i \(0.599774\pi\)
\(578\) 0 0
\(579\) −56.1999 681.499i −0.0970637 1.17703i
\(580\) 0 0
\(581\) 28.0570i 0.0482910i
\(582\) 0 0
\(583\) 772.318 1.32473
\(584\) 0 0
\(585\) 175.404 + 1056.27i 0.299835 + 1.80559i
\(586\) 0 0
\(587\) 571.017i 0.972771i −0.873744 0.486386i \(-0.838315\pi\)
0.873744 0.486386i \(-0.161685\pi\)
\(588\) 0 0
\(589\) 844.140 1.43318
\(590\) 0 0
\(591\) −515.078 + 42.4760i −0.871537 + 0.0718714i
\(592\) 0 0
\(593\) 370.411i 0.624640i −0.949977 0.312320i \(-0.898894\pi\)
0.949977 0.312320i \(-0.101106\pi\)
\(594\) 0 0
\(595\) −72.9432 −0.122594
\(596\) 0 0
\(597\) 0.147648 + 1.79043i 0.000247317 + 0.00299905i
\(598\) 0 0
\(599\) 68.6579i 0.114621i −0.998356 0.0573104i \(-0.981748\pi\)
0.998356 0.0573104i \(-0.0182525\pi\)
\(600\) 0 0
\(601\) 9.39898 0.0156389 0.00781945 0.999969i \(-0.497511\pi\)
0.00781945 + 0.999969i \(0.497511\pi\)
\(602\) 0 0
\(603\) 963.857 160.058i 1.59844 0.265436i
\(604\) 0 0
\(605\) 302.096i 0.499333i
\(606\) 0 0
\(607\) −1064.78 −1.75417 −0.877085 0.480336i \(-0.840515\pi\)
−0.877085 + 0.480336i \(0.840515\pi\)
\(608\) 0 0
\(609\) −38.0829 + 3.14051i −0.0625335 + 0.00515684i
\(610\) 0 0
\(611\) 549.039i 0.898591i
\(612\) 0 0
\(613\) 651.884 1.06343 0.531716 0.846922i \(-0.321547\pi\)
0.531716 + 0.846922i \(0.321547\pi\)
\(614\) 0 0
\(615\) 58.4040 + 708.227i 0.0949659 + 1.15159i
\(616\) 0 0
\(617\) 146.821i 0.237959i −0.992897 0.118980i \(-0.962038\pi\)
0.992897 0.118980i \(-0.0379623\pi\)
\(618\) 0 0
\(619\) −596.307 −0.963340 −0.481670 0.876353i \(-0.659970\pi\)
−0.481670 + 0.876353i \(0.659970\pi\)
\(620\) 0 0
\(621\) −536.295 + 135.133i −0.863598 + 0.217606i
\(622\) 0 0
\(623\) 33.9441i 0.0544850i
\(624\) 0 0
\(625\) −738.453 −1.18152
\(626\) 0 0
\(627\) −835.808 + 68.9250i −1.33303 + 0.109928i
\(628\) 0 0
\(629\) 1014.91i 1.61353i
\(630\) 0 0
\(631\) −77.6556 −0.123067 −0.0615337 0.998105i \(-0.519599\pi\)
−0.0615337 + 0.998105i \(0.519599\pi\)
\(632\) 0 0
\(633\) −59.9235 726.652i −0.0946658 1.14795i
\(634\) 0 0
\(635\) 1570.56i 2.47333i
\(636\) 0 0
\(637\) −872.427 −1.36959
\(638\) 0 0
\(639\) 87.5172 + 527.023i 0.136960 + 0.824762i
\(640\) 0 0
\(641\) 574.386i 0.896078i 0.894014 + 0.448039i \(0.147877\pi\)
−0.894014 + 0.448039i \(0.852123\pi\)
\(642\) 0 0
\(643\) 1217.20 1.89299 0.946497 0.322712i \(-0.104594\pi\)
0.946497 + 0.322712i \(0.104594\pi\)
\(644\) 0 0
\(645\) 1001.81 82.6141i 1.55319 0.128084i
\(646\) 0 0
\(647\) 802.675i 1.24061i −0.784360 0.620305i \(-0.787009\pi\)
0.784360 0.620305i \(-0.212991\pi\)
\(648\) 0 0
\(649\) −549.020 −0.845948
\(650\) 0 0
\(651\) 3.73970 + 45.3489i 0.00574455 + 0.0696604i
\(652\) 0 0
\(653\) 216.282i 0.331212i −0.986192 0.165606i \(-0.947042\pi\)
0.986192 0.165606i \(-0.0529581\pi\)
\(654\) 0 0
\(655\) 804.410 1.22811
\(656\) 0 0
\(657\) 49.7615 8.26338i 0.0757405 0.0125774i
\(658\) 0 0
\(659\) 611.696i 0.928218i −0.885778 0.464109i \(-0.846375\pi\)
0.885778 0.464109i \(-0.153625\pi\)
\(660\) 0 0
\(661\) 214.961 0.325206 0.162603 0.986692i \(-0.448011\pi\)
0.162603 + 0.986692i \(0.448011\pi\)
\(662\) 0 0
\(663\) 1018.97 84.0293i 1.53690 0.126741i
\(664\) 0 0
\(665\) 123.459i 0.185653i
\(666\) 0 0
\(667\) 451.275 0.676574
\(668\) 0 0
\(669\) 47.1357 + 571.583i 0.0704569 + 0.854384i
\(670\) 0 0
\(671\) 291.319i 0.434156i
\(672\) 0 0
\(673\) −900.809 −1.33850 −0.669249 0.743038i \(-0.733384\pi\)
−0.669249 + 0.743038i \(0.733384\pi\)
\(674\) 0 0
\(675\) 125.622 + 498.549i 0.186107 + 0.738591i
\(676\) 0 0
\(677\) 322.312i 0.476088i −0.971254 0.238044i \(-0.923494\pi\)
0.971254 0.238044i \(-0.0765063\pi\)
\(678\) 0 0
\(679\) 53.9736 0.0794898
\(680\) 0 0
\(681\) −26.2160 + 2.16191i −0.0384964 + 0.00317461i
\(682\) 0 0
\(683\) 451.564i 0.661148i 0.943780 + 0.330574i \(0.107242\pi\)
−0.943780 + 0.330574i \(0.892758\pi\)
\(684\) 0 0
\(685\) 907.047 1.32416
\(686\) 0 0
\(687\) −32.4816 393.882i −0.0472803 0.573337i
\(688\) 0 0
\(689\) 1593.64i 2.31297i
\(690\) 0 0
\(691\) −259.954 −0.376199 −0.188100 0.982150i \(-0.560233\pi\)
−0.188100 + 0.982150i \(0.560233\pi\)
\(692\) 0 0
\(693\) −7.40558 44.5959i −0.0106863 0.0643520i
\(694\) 0 0
\(695\) 196.183i 0.282277i
\(696\) 0 0
\(697\) 678.570 0.973558
\(698\) 0 0
\(699\) 287.070 23.6733i 0.410687 0.0338674i
\(700\) 0 0
\(701\) 434.792i 0.620246i −0.950696 0.310123i \(-0.899630\pi\)
0.950696 0.310123i \(-0.100370\pi\)
\(702\) 0 0
\(703\) 1717.78 2.44350
\(704\) 0 0
\(705\) 50.1131 + 607.688i 0.0710823 + 0.861968i
\(706\) 0 0
\(707\) 66.0033i 0.0933568i
\(708\) 0 0
\(709\) 1136.05 1.60232 0.801162 0.598448i \(-0.204216\pi\)
0.801162 + 0.598448i \(0.204216\pi\)
\(710\) 0 0
\(711\) 701.355 116.467i 0.986434 0.163807i
\(712\) 0 0
\(713\) 537.375i 0.753682i
\(714\) 0 0
\(715\) 1033.60 1.44559
\(716\) 0 0
\(717\) −950.705 + 78.4001i −1.32595 + 0.109345i
\(718\) 0 0
\(719\) 1284.33i 1.78627i −0.449792 0.893133i \(-0.648502\pi\)
0.449792 0.893133i \(-0.351498\pi\)
\(720\) 0 0
\(721\) 40.4916 0.0561603
\(722\) 0 0
\(723\) −28.1542 341.407i −0.0389408 0.472209i
\(724\) 0 0
\(725\) 419.513i 0.578638i
\(726\) 0 0
\(727\) 31.6562 0.0435437 0.0217718 0.999763i \(-0.493069\pi\)
0.0217718 + 0.999763i \(0.493069\pi\)
\(728\) 0 0
\(729\) −641.956 + 345.447i −0.880598 + 0.473864i
\(730\) 0 0
\(731\) 959.856i 1.31307i
\(732\) 0 0
\(733\) 596.421 0.813671 0.406836 0.913501i \(-0.366632\pi\)
0.406836 + 0.913501i \(0.366632\pi\)
\(734\) 0 0
\(735\) −965.619 + 79.6300i −1.31377 + 0.108340i
\(736\) 0 0
\(737\) 943.170i 1.27974i
\(738\) 0 0
\(739\) 1146.14 1.55093 0.775464 0.631391i \(-0.217516\pi\)
0.775464 + 0.631391i \(0.217516\pi\)
\(740\) 0 0
\(741\) 142.223 + 1724.64i 0.191934 + 2.32745i
\(742\) 0 0
\(743\) 842.850i 1.13439i −0.823584 0.567194i \(-0.808029\pi\)
0.823584 0.567194i \(-0.191971\pi\)
\(744\) 0 0
\(745\) −116.198 −0.155970
\(746\) 0 0
\(747\) −71.5476 430.855i −0.0957799 0.576780i
\(748\) 0 0
\(749\) 29.4324i 0.0392956i
\(750\) 0 0
\(751\) −797.793 −1.06231 −0.531154 0.847275i \(-0.678241\pi\)
−0.531154 + 0.847275i \(0.678241\pi\)
\(752\) 0 0
\(753\) −1126.73 + 92.9162i −1.49633 + 0.123395i
\(754\) 0 0
\(755\) 793.761i 1.05134i
\(756\) 0 0
\(757\) −278.402 −0.367770 −0.183885 0.982948i \(-0.558867\pi\)
−0.183885 + 0.982948i \(0.558867\pi\)
\(758\) 0 0
\(759\) 43.8773 + 532.071i 0.0578093 + 0.701015i
\(760\) 0 0
\(761\) 986.126i 1.29583i −0.761713 0.647914i \(-0.775641\pi\)
0.761713 0.647914i \(-0.224359\pi\)
\(762\) 0 0
\(763\) 7.64197 0.0100157
\(764\) 0 0
\(765\) 1120.14 186.011i 1.46424 0.243151i
\(766\) 0 0
\(767\) 1132.87i 1.47702i
\(768\) 0 0
\(769\) 242.053 0.314764 0.157382 0.987538i \(-0.449695\pi\)
0.157382 + 0.987538i \(0.449695\pi\)
\(770\) 0 0
\(771\) −454.580 + 37.4870i −0.589598 + 0.0486213i
\(772\) 0 0
\(773\) 590.233i 0.763561i 0.924253 + 0.381780i \(0.124689\pi\)
−0.924253 + 0.381780i \(0.875311\pi\)
\(774\) 0 0
\(775\) −499.553 −0.644585
\(776\) 0 0
\(777\) 7.61009 + 92.2825i 0.00979420 + 0.118768i
\(778\) 0 0
\(779\) 1148.51i 1.47433i
\(780\) 0 0
\(781\) 515.712 0.660322
\(782\) 0 0
\(783\) 576.808 145.341i 0.736664 0.185621i
\(784\) 0 0
\(785\) 1257.52i 1.60194i
\(786\) 0 0
\(787\) −565.777 −0.718903 −0.359451 0.933164i \(-0.617036\pi\)
−0.359451 + 0.933164i \(0.617036\pi\)
\(788\) 0 0
\(789\) −1480.02 + 122.050i −1.87581 + 0.154689i
\(790\) 0 0
\(791\) 36.3933i 0.0460092i
\(792\) 0 0
\(793\) −601.120 −0.758033
\(794\) 0 0
\(795\) −145.458 1763.87i −0.182966 2.21870i
\(796\) 0 0
\(797\) 1128.02i 1.41533i −0.706549 0.707664i \(-0.749749\pi\)
0.706549 0.707664i \(-0.250251\pi\)
\(798\) 0 0
\(799\) 582.241 0.728712
\(800\) 0 0
\(801\) 86.5601 +