Properties

Label 768.3.h.g.641.2
Level $768$
Weight $3$
Character 768.641
Analytic conductor $20.926$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 768 = 2^{8} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 768.h (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(20.9264843029\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 4 x^{15} + 14 x^{14} - 28 x^{13} + 50 x^{12} - 104 x^{11} - 66 x^{10} + 640 x^{9} + 555 x^{8} - 7060 x^{7} + 17714 x^{6} - 25496 x^{5} + 24840 x^{4} - 17932 x^{3} + 11724 x^{2} - 7056 x + 2401\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{34}\cdot 3^{2} \)
Twist minimal: no (minimal twist has level 384)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 641.2
Root \(1.38361 - 0.573111i\) of defining polynomial
Character \(\chi\) \(=\) 768.641
Dual form 768.3.h.g.641.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.98985 + 0.246559i) q^{3} -6.63641 q^{5} -0.578158 q^{7} +(8.87842 - 1.47435i) q^{9} +O(q^{10})\) \(q+(-2.98985 + 0.246559i) q^{3} -6.63641 q^{5} -0.578158 q^{7} +(8.87842 - 1.47435i) q^{9} +8.68786 q^{11} +17.9269i q^{13} +(19.8419 - 1.63626i) q^{15} -19.0110i q^{17} +32.1769i q^{19} +(1.72861 - 0.142550i) q^{21} +20.4836i q^{23} +19.0419 q^{25} +(-26.1816 + 6.59713i) q^{27} -22.0310 q^{29} +26.2344 q^{31} +(-25.9754 + 2.14207i) q^{33} +3.83689 q^{35} -53.3855i q^{37} +(-4.42003 - 53.5988i) q^{39} -35.6935i q^{41} -50.4895i q^{43} +(-58.9208 + 9.78437i) q^{45} +30.6265i q^{47} -48.6657 q^{49} +(4.68732 + 56.8401i) q^{51} -88.8962 q^{53} -57.6562 q^{55} +(-7.93348 - 96.2040i) q^{57} +63.1939 q^{59} -33.5317i q^{61} +(-5.13313 + 0.852405i) q^{63} -118.970i q^{65} -108.562i q^{67} +(-5.05041 - 61.2430i) q^{69} +59.3600i q^{71} +5.60477 q^{73} +(-56.9325 + 4.69495i) q^{75} -5.02296 q^{77} -78.9955 q^{79} +(76.6526 - 26.1797i) q^{81} -48.5283 q^{83} +126.165i q^{85} +(65.8694 - 5.43193i) q^{87} +58.7109i q^{89} -10.3646i q^{91} +(-78.4369 + 6.46831i) q^{93} -213.539i q^{95} +93.3544 q^{97} +(77.1345 - 12.8089i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 16q^{7} + O(q^{10}) \) \( 16q - 16q^{7} + 32q^{15} + 80q^{25} - 112q^{31} + 16q^{33} + 208q^{39} + 144q^{49} - 384q^{55} + 80q^{57} + 528q^{63} + 160q^{73} - 816q^{79} + 144q^{81} + 736q^{87} + 192q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).

\(n\) \(257\) \(511\) \(517\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

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
\(3\) −2.98985 + 0.246559i −0.996617 + 0.0821862i
\(4\) 0 0
\(5\) −6.63641 −1.32728 −0.663641 0.748051i \(-0.730990\pi\)
−0.663641 + 0.748051i \(0.730990\pi\)
\(6\) 0 0
\(7\) −0.578158 −0.0825940 −0.0412970 0.999147i \(-0.513149\pi\)
−0.0412970 + 0.999147i \(0.513149\pi\)
\(8\) 0 0
\(9\) 8.87842 1.47435i 0.986491 0.163816i
\(10\) 0 0
\(11\) 8.68786 0.789806 0.394903 0.918723i \(-0.370778\pi\)
0.394903 + 0.918723i \(0.370778\pi\)
\(12\) 0 0
\(13\) 17.9269i 1.37899i 0.724289 + 0.689497i \(0.242168\pi\)
−0.724289 + 0.689497i \(0.757832\pi\)
\(14\) 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
\(19\) 32.1769i 1.69352i 0.531976 + 0.846760i \(0.321450\pi\)
−0.531976 + 0.846760i \(0.678550\pi\)
\(20\) 0 0
\(21\) 1.72861 0.142550i 0.0823146 0.00678808i
\(22\) 0 0
\(23\) 20.4836i 0.890592i 0.895383 + 0.445296i \(0.146902\pi\)
−0.895383 + 0.445296i \(0.853098\pi\)
\(24\) 0 0
\(25\) 19.0419 0.761677
\(26\) 0 0
\(27\) −26.1816 + 6.59713i −0.969690 + 0.244338i
\(28\) 0 0
\(29\) −22.0310 −0.759690 −0.379845 0.925050i \(-0.624023\pi\)
−0.379845 + 0.925050i \(0.624023\pi\)
\(30\) 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
\(35\) 3.83689 0.109625
\(36\) 0 0
\(37\) 53.3855i 1.44285i −0.692492 0.721426i \(-0.743487\pi\)
0.692492 0.721426i \(-0.256513\pi\)
\(38\) 0 0
\(39\) −4.42003 53.5988i −0.113334 1.37433i
\(40\) 0 0
\(41\) 35.6935i 0.870574i −0.900292 0.435287i \(-0.856647\pi\)
0.900292 0.435287i \(-0.143353\pi\)
\(42\) 0 0
\(43\) 50.4895i 1.17417i −0.809524 0.587087i \(-0.800275\pi\)
0.809524 0.587087i \(-0.199725\pi\)
\(44\) 0 0
\(45\) −58.9208 + 9.78437i −1.30935 + 0.217430i
\(46\) 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
\(51\) 4.68732 + 56.8401i 0.0919083 + 1.11451i
\(52\) 0 0
\(53\) −88.8962 −1.67729 −0.838644 0.544681i \(-0.816651\pi\)
−0.838644 + 0.544681i \(0.816651\pi\)
\(54\) 0 0
\(55\) −57.6562 −1.04829
\(56\) 0 0
\(57\) −7.93348 96.2040i −0.139184 1.68779i
\(58\) 0 0
\(59\) 63.1939 1.07108 0.535542 0.844509i \(-0.320107\pi\)
0.535542 + 0.844509i \(0.320107\pi\)
\(60\) 0 0
\(61\) 33.5317i 0.549700i −0.961487 0.274850i \(-0.911372\pi\)
0.961487 0.274850i \(-0.0886282\pi\)
\(62\) 0 0
\(63\) −5.13313 + 0.852405i −0.0814782 + 0.0135302i
\(64\) 0 0
\(65\) 118.970i 1.83031i
\(66\) 0 0
\(67\) 108.562i 1.62032i −0.586206 0.810162i \(-0.699379\pi\)
0.586206 0.810162i \(-0.300621\pi\)
\(68\) 0 0
\(69\) −5.05041 61.2430i −0.0731944 0.887579i
\(70\) 0 0
\(71\) 59.3600i 0.836056i 0.908434 + 0.418028i \(0.137279\pi\)
−0.908434 + 0.418028i \(0.862721\pi\)
\(72\) 0 0
\(73\) 5.60477 0.0767777 0.0383889 0.999263i \(-0.487777\pi\)
0.0383889 + 0.999263i \(0.487777\pi\)
\(74\) 0 0
\(75\) −56.9325 + 4.69495i −0.759101 + 0.0625994i
\(76\) 0 0
\(77\) −5.02296 −0.0652332
\(78\) 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
\(83\) −48.5283 −0.584679 −0.292339 0.956315i \(-0.594434\pi\)
−0.292339 + 0.956315i \(0.594434\pi\)
\(84\) 0 0
\(85\) 126.165i 1.48429i
\(86\) 0 0
\(87\) 65.8694 5.43193i 0.757120 0.0624360i
\(88\) 0 0
\(89\) 58.7109i 0.659672i 0.944038 + 0.329836i \(0.106994\pi\)
−0.944038 + 0.329836i \(0.893006\pi\)
\(90\) 0 0
\(91\) 10.3646i 0.113897i
\(92\) 0 0
\(93\) −78.4369 + 6.46831i −0.843407 + 0.0695517i
\(94\) 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
\(99\) 77.1345 12.8089i 0.779136 0.129383i
\(100\) 0 0
\(101\) −114.161 −1.13031 −0.565155 0.824985i \(-0.691184\pi\)
−0.565155 + 0.824985i \(0.691184\pi\)
\(102\) 0 0
\(103\) −70.0355 −0.679956 −0.339978 0.940433i \(-0.610420\pi\)
−0.339978 + 0.940433i \(0.610420\pi\)
\(104\) 0 0
\(105\) −11.4717 + 0.946018i −0.109255 + 0.00900970i
\(106\) 0 0
\(107\) 50.9072 0.475769 0.237884 0.971293i \(-0.423546\pi\)
0.237884 + 0.971293i \(0.423546\pi\)
\(108\) 0 0
\(109\) 13.2178i 0.121264i 0.998160 + 0.0606320i \(0.0193116\pi\)
−0.998160 + 0.0606320i \(0.980688\pi\)
\(110\) 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
\(115\) 135.938i 1.18207i
\(116\) 0 0
\(117\) 26.4305 + 159.163i 0.225902 + 1.36036i
\(118\) 0 0
\(119\) 10.9914i 0.0923644i
\(120\) 0 0
\(121\) −45.5210 −0.376207
\(122\) 0 0
\(123\) 8.80054 + 106.718i 0.0715491 + 0.867629i
\(124\) 0 0
\(125\) 39.5402 0.316321
\(126\) 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
\(131\) −121.212 −0.925279 −0.462640 0.886546i \(-0.653098\pi\)
−0.462640 + 0.886546i \(0.653098\pi\)
\(132\) 0 0
\(133\) 18.6033i 0.139875i
\(134\) 0 0
\(135\) 173.752 43.7812i 1.28705 0.324305i
\(136\) 0 0
\(137\) 136.677i 0.997645i −0.866704 0.498822i \(-0.833766\pi\)
0.866704 0.498822i \(-0.166234\pi\)
\(138\) 0 0
\(139\) 29.5616i 0.212673i 0.994330 + 0.106337i \(0.0339121\pi\)
−0.994330 + 0.106337i \(0.966088\pi\)
\(140\) 0 0
\(141\) −7.55123 91.5687i −0.0535548 0.649424i
\(142\) 0 0
\(143\) 155.747i 1.08914i
\(144\) 0 0
\(145\) 146.207 1.00832
\(146\) 0 0
\(147\) 145.503 11.9990i 0.989818 0.0816255i
\(148\) 0 0
\(149\) −17.5092 −0.117511 −0.0587556 0.998272i \(-0.518713\pi\)
−0.0587556 + 0.998272i \(0.518713\pi\)
\(150\) 0 0
\(151\) 119.607 0.792099 0.396050 0.918229i \(-0.370381\pi\)
0.396050 + 0.918229i \(0.370381\pi\)
\(152\) 0 0
\(153\) −28.0288 168.788i −0.183195 1.10319i
\(154\) 0 0
\(155\) −174.102 −1.12324
\(156\) 0 0
\(157\) 189.488i 1.20693i −0.797388 0.603466i \(-0.793786\pi\)
0.797388 0.603466i \(-0.206214\pi\)
\(158\) 0 0
\(159\) 265.786 21.9181i 1.67161 0.137850i
\(160\) 0 0
\(161\) 11.8428i 0.0735576i
\(162\) 0 0
\(163\) 104.654i 0.642051i 0.947071 + 0.321026i \(0.104028\pi\)
−0.947071 + 0.321026i \(0.895972\pi\)
\(164\) 0 0
\(165\) 172.384 14.2156i 1.04475 0.0861553i
\(166\) 0 0
\(167\) 142.664i 0.854278i −0.904186 0.427139i \(-0.859522\pi\)
0.904186 0.427139i \(-0.140478\pi\)
\(168\) 0 0
\(169\) −152.374 −0.901623
\(170\) 0 0
\(171\) 47.4399 + 285.680i 0.277426 + 1.67064i
\(172\) 0 0
\(173\) 11.6594 0.0673952 0.0336976 0.999432i \(-0.489272\pi\)
0.0336976 + 0.999432i \(0.489272\pi\)
\(174\) 0 0
\(175\) −11.0092 −0.0629100
\(176\) 0 0
\(177\) −188.940 + 15.5810i −1.06746 + 0.0880283i
\(178\) 0 0
\(179\) −40.3979 −0.225687 −0.112843 0.993613i \(-0.535996\pi\)
−0.112843 + 0.993613i \(0.535996\pi\)
\(180\) 0 0
\(181\) 121.175i 0.669472i −0.942312 0.334736i \(-0.891353\pi\)
0.942312 0.334736i \(-0.108647\pi\)
\(182\) 0 0
\(183\) 8.26752 + 100.255i 0.0451777 + 0.547840i
\(184\) 0 0
\(185\) 354.288i 1.91507i
\(186\) 0 0
\(187\) 165.165i 0.883235i
\(188\) 0 0
\(189\) 15.1371 3.81418i 0.0800906 0.0201808i
\(190\) 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
\(195\) 29.3332 + 355.704i 0.150426 + 1.82412i
\(196\) 0 0
\(197\) 172.276 0.874495 0.437248 0.899341i \(-0.355953\pi\)
0.437248 + 0.899341i \(0.355953\pi\)
\(198\) 0 0
\(199\) −0.598837 −0.00300923 −0.00150461 0.999999i \(-0.500479\pi\)
−0.00150461 + 0.999999i \(0.500479\pi\)
\(200\) 0 0
\(201\) 26.7668 + 324.583i 0.133168 + 1.61484i
\(202\) 0 0
\(203\) 12.7374 0.0627458
\(204\) 0 0
\(205\) 236.877i 1.15550i
\(206\) 0 0
\(207\) 30.2000 + 181.862i 0.145894 + 0.878561i
\(208\) 0 0
\(209\) 279.548i 1.33755i
\(210\) 0 0
\(211\) 243.040i 1.15185i −0.817504 0.575923i \(-0.804643\pi\)
0.817504 0.575923i \(-0.195357\pi\)
\(212\) 0 0
\(213\) −14.6357 177.478i −0.0687123 0.833228i
\(214\) 0 0
\(215\) 335.069i 1.55846i
\(216\) 0 0
\(217\) −15.1676 −0.0698968
\(218\) 0 0
\(219\) −16.7574 + 1.38190i −0.0765180 + 0.00631007i
\(220\) 0 0
\(221\) 340.809 1.54212
\(222\) 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
\(227\) −8.76834 −0.0386271 −0.0193135 0.999813i \(-0.506148\pi\)
−0.0193135 + 0.999813i \(0.506148\pi\)
\(228\) 0 0
\(229\) 131.740i 0.575283i 0.957738 + 0.287641i \(0.0928711\pi\)
−0.957738 + 0.287641i \(0.907129\pi\)
\(230\) 0 0
\(231\) 15.0179 1.23845i 0.0650125 0.00536127i
\(232\) 0 0
\(233\) 96.0149i 0.412081i 0.978543 + 0.206040i \(0.0660579\pi\)
−0.978543 + 0.206040i \(0.933942\pi\)
\(234\) 0 0
\(235\) 203.250i 0.864894i
\(236\) 0 0
\(237\) 236.185 19.4770i 0.996560 0.0821815i
\(238\) 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
\(243\) −222.725 + 97.1728i −0.916564 + 0.399888i
\(244\) 0 0
\(245\) 322.966 1.31823
\(246\) 0 0
\(247\) −576.832 −2.33535
\(248\) 0 0
\(249\) 145.093 11.9651i 0.582701 0.0480525i
\(250\) 0 0
\(251\) 376.853 1.50140 0.750702 0.660641i \(-0.229715\pi\)
0.750702 + 0.660641i \(0.229715\pi\)
\(252\) 0 0
\(253\) 177.959i 0.703395i
\(254\) 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
\(259\) 30.8653i 0.119171i
\(260\) 0 0
\(261\) −195.600 + 32.4813i −0.749427 + 0.124450i
\(262\) 0 0
\(263\) 495.013i 1.88218i −0.338158 0.941089i \(-0.609804\pi\)
0.338158 0.941089i \(-0.390196\pi\)
\(264\) 0 0
\(265\) 589.952 2.22623
\(266\) 0 0
\(267\) −14.4757 175.537i −0.0542160 0.657441i
\(268\) 0 0
\(269\) 173.556 0.645190 0.322595 0.946537i \(-0.395445\pi\)
0.322595 + 0.946537i \(0.395445\pi\)
\(270\) 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
\(275\) 165.434 0.601577
\(276\) 0 0
\(277\) 226.300i 0.816967i −0.912766 0.408483i \(-0.866058\pi\)
0.912766 0.408483i \(-0.133942\pi\)
\(278\) 0 0
\(279\) 232.920 38.6786i 0.834838 0.138633i
\(280\) 0 0
\(281\) 13.8834i 0.0494073i 0.999695 + 0.0247036i \(0.00786421\pi\)
−0.999695 + 0.0247036i \(0.992136\pi\)
\(282\) 0 0
\(283\) 306.461i 1.08290i −0.840733 0.541450i \(-0.817875\pi\)
0.840733 0.541450i \(-0.182125\pi\)
\(284\) 0 0
\(285\) 52.6498 + 638.449i 0.184736 + 2.24017i
\(286\) 0 0
\(287\) 20.6365i 0.0719042i
\(288\) 0 0
\(289\) −72.4183 −0.250582
\(290\) 0 0
\(291\) −279.116 + 23.0173i −0.959160 + 0.0790973i
\(292\) 0 0
\(293\) 121.869 0.415935 0.207968 0.978136i \(-0.433315\pi\)
0.207968 + 0.978136i \(0.433315\pi\)
\(294\) 0 0
\(295\) −419.381 −1.42163
\(296\) 0 0
\(297\) −227.462 + 57.3149i −0.765867 + 0.192980i
\(298\) 0 0
\(299\) −367.208 −1.22812
\(300\) 0 0
\(301\) 29.1909i 0.0969797i
\(302\) 0 0
\(303\) 341.325 28.1474i 1.12649 0.0928959i
\(304\) 0 0
\(305\) 222.530i 0.729607i
\(306\) 0 0
\(307\) 19.0431i 0.0620298i −0.999519 0.0310149i \(-0.990126\pi\)
0.999519 0.0310149i \(-0.00987393\pi\)
\(308\) 0 0
\(309\) 209.396 17.2678i 0.677656 0.0558830i
\(310\) 0 0
\(311\) 223.159i 0.717552i 0.933424 + 0.358776i \(0.116806\pi\)
−0.933424 + 0.358776i \(0.883194\pi\)
\(312\) 0 0
\(313\) 194.708 0.622070 0.311035 0.950399i \(-0.399324\pi\)
0.311035 + 0.950399i \(0.399324\pi\)
\(314\) 0 0
\(315\) 34.0655 5.65691i 0.108145 0.0179584i
\(316\) 0 0
\(317\) −532.192 −1.67884 −0.839420 0.543483i \(-0.817105\pi\)
−0.839420 + 0.543483i \(0.817105\pi\)
\(318\) 0 0
\(319\) −191.402 −0.600007
\(320\) 0 0
\(321\) −152.205 + 12.5516i −0.474159 + 0.0391016i
\(322\) 0 0
\(323\) 611.715 1.89385
\(324\) 0 0
\(325\) 341.363i 1.05035i
\(326\) 0 0
\(327\) −3.25896 39.5192i −0.00996623 0.120854i
\(328\) 0 0
\(329\) 17.7070i 0.0538206i
\(330\) 0 0
\(331\) 91.7273i 0.277122i −0.990354 0.138561i \(-0.955752\pi\)
0.990354 0.138561i \(-0.0442476\pi\)
\(332\) 0 0
\(333\) −78.7088 473.979i −0.236363 1.42336i
\(334\) 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
\(339\) 15.5201 + 188.202i 0.0457821 + 0.555169i
\(340\) 0 0
\(341\) 227.921 0.668389
\(342\) 0 0
\(343\) 56.4662 0.164625
\(344\) 0 0
\(345\) 33.5166 + 406.433i 0.0971496 + 1.17807i
\(346\) 0 0
\(347\) −323.122 −0.931189 −0.465594 0.884998i \(-0.654159\pi\)
−0.465594 + 0.884998i \(0.654159\pi\)
\(348\) 0 0
\(349\) 255.324i 0.731586i −0.930696 0.365793i \(-0.880798\pi\)
0.930696 0.365793i \(-0.119202\pi\)
\(350\) 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
\(355\) 393.937i 1.10968i
\(356\) 0 0
\(357\) −2.71001 32.8625i −0.00759107 0.0920519i
\(358\) 0 0
\(359\) 119.962i 0.334157i 0.985944 + 0.167079i \(0.0534334\pi\)
−0.985944 + 0.167079i \(0.946567\pi\)
\(360\) 0 0
\(361\) −674.351 −1.86801
\(362\) 0 0
\(363\) 136.101 11.2236i 0.374934 0.0309190i
\(364\) 0 0
\(365\) −37.1956 −0.101906
\(366\) 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
\(371\) 51.3960 0.138534
\(372\) 0 0
\(373\) 606.592i 1.62625i −0.582088 0.813126i \(-0.697764\pi\)
0.582088 0.813126i \(-0.302236\pi\)
\(374\) 0 0
\(375\) −118.219 + 9.74896i −0.315251 + 0.0259972i
\(376\) 0 0
\(377\) 394.948i 1.04761i
\(378\) 0 0
\(379\) 266.492i 0.703146i 0.936161 + 0.351573i \(0.114353\pi\)
−0.936161 + 0.351573i \(0.885647\pi\)
\(380\) 0 0
\(381\) 707.574 58.3502i 1.85715 0.153150i
\(382\) 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
\(387\) −74.4390 448.267i −0.192349 1.15831i
\(388\) 0 0
\(389\) 217.748 0.559763 0.279881 0.960035i \(-0.409705\pi\)
0.279881 + 0.960035i \(0.409705\pi\)
\(390\) 0 0
\(391\) 389.414 0.995944
\(392\) 0 0
\(393\) 362.405 29.8858i 0.922149 0.0760452i
\(394\) 0 0
\(395\) 524.246 1.32721
\(396\) 0 0
\(397\) 53.9651i 0.135932i 0.997688 + 0.0679661i \(0.0216510\pi\)
−0.997688 + 0.0679661i \(0.978349\pi\)
\(398\) 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
\(403\) 470.302i 1.16700i
\(404\) 0 0
\(405\) −508.698 + 173.739i −1.25604 + 0.428986i
\(406\) 0 0
\(407\) 463.806i 1.13957i
\(408\) 0 0
\(409\) −569.204 −1.39170 −0.695849 0.718188i \(-0.744972\pi\)
−0.695849 + 0.718188i \(0.744972\pi\)
\(410\) 0 0
\(411\) 33.6990 + 408.645i 0.0819926 + 0.994270i
\(412\) 0 0
\(413\) −36.5361 −0.0884651
\(414\) 0 0
\(415\) 322.054 0.776034
\(416\) 0 0
\(417\) −7.28866 88.3847i −0.0174788 0.211954i
\(418\) 0 0
\(419\) −590.728 −1.40985 −0.704926 0.709281i \(-0.749020\pi\)
−0.704926 + 0.709281i \(0.749020\pi\)
\(420\) 0 0
\(421\) 475.989i 1.13061i 0.824880 + 0.565307i \(0.191242\pi\)
−0.824880 + 0.565307i \(0.808758\pi\)
\(422\) 0 0
\(423\) 45.1541 + 271.915i 0.106747 + 0.642825i
\(424\) 0 0
\(425\) 362.006i 0.851780i
\(426\) 0 0
\(427\) 19.3866i 0.0454019i
\(428\) 0 0
\(429\) −38.4007 465.659i −0.0895120 1.08545i
\(430\) 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
\(435\) −437.136 + 36.0485i −1.00491 + 0.0828702i
\(436\) 0 0
\(437\) −659.099 −1.50824
\(438\) 0 0
\(439\) 735.647 1.67573 0.837867 0.545875i \(-0.183803\pi\)
0.837867 + 0.545875i \(0.183803\pi\)
\(440\) 0 0
\(441\) −432.075 + 71.7502i −0.979761 + 0.162699i
\(442\) 0 0
\(443\) −333.798 −0.753494 −0.376747 0.926316i \(-0.622957\pi\)
−0.376747 + 0.926316i \(0.622957\pi\)
\(444\) 0 0
\(445\) 389.629i 0.875571i
\(446\) 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
\(451\) 310.100i 0.687584i
\(452\) 0 0
\(453\) −357.607 + 29.4901i −0.789419 + 0.0650996i
\(454\) 0 0
\(455\) 68.7836i 0.151173i
\(456\) 0 0
\(457\) −34.5362 −0.0755715 −0.0377857 0.999286i \(-0.512030\pi\)
−0.0377857 + 0.999286i \(0.512030\pi\)
\(458\) 0 0
\(459\) 125.418 + 497.739i 0.273242 + 1.08440i
\(460\) 0 0
\(461\) −324.050 −0.702929 −0.351464 0.936201i \(-0.614316\pi\)
−0.351464 + 0.936201i \(0.614316\pi\)
\(462\) 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
\(467\) 450.706 0.965109 0.482554 0.875866i \(-0.339709\pi\)
0.482554 + 0.875866i \(0.339709\pi\)
\(468\) 0 0
\(469\) 62.7658i 0.133829i
\(470\) 0 0
\(471\) 46.7200 + 566.542i 0.0991932 + 1.20285i
\(472\) 0 0
\(473\) 438.646i 0.927370i
\(474\) 0 0
\(475\) 612.710i 1.28992i
\(476\) 0 0
\(477\) −789.258 + 131.064i −1.65463 + 0.274767i
\(478\) 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
\(483\) 2.91993 + 35.4081i 0.00604541 + 0.0733087i
\(484\) 0 0
\(485\) −619.538 −1.27740
\(486\) 0 0
\(487\) 628.526 1.29061 0.645304 0.763926i \(-0.276731\pi\)
0.645304 + 0.763926i \(0.276731\pi\)
\(488\) 0 0
\(489\) −25.8034 312.901i −0.0527677 0.639879i
\(490\) 0 0
\(491\) −352.334 −0.717585 −0.358792 0.933417i \(-0.616811\pi\)
−0.358792 + 0.933417i \(0.616811\pi\)
\(492\) 0 0
\(493\) 418.831i 0.849557i
\(494\) 0 0
\(495\) −511.896 + 85.0052i −1.03413 + 0.171728i
\(496\) 0 0
\(497\) 34.3195i 0.0690532i
\(498\) 0 0
\(499\) 240.576i 0.482116i 0.970511 + 0.241058i \(0.0774943\pi\)
−0.970511 + 0.241058i \(0.922506\pi\)
\(500\) 0 0
\(501\) 35.1751 + 426.545i 0.0702098 + 0.851388i
\(502\) 0 0
\(503\) 13.1648i 0.0261725i −0.999914 0.0130862i \(-0.995834\pi\)
0.999914 0.0130862i \(-0.00416560\pi\)
\(504\) 0 0
\(505\) 757.621 1.50024
\(506\) 0 0
\(507\) 455.577 37.5692i 0.898573 0.0741010i
\(508\) 0 0
\(509\) −468.752 −0.920927 −0.460464 0.887679i \(-0.652317\pi\)
−0.460464 + 0.887679i \(0.652317\pi\)
\(510\) 0 0
\(511\) −3.24044 −0.00634138
\(512\) 0 0
\(513\) −212.275 842.443i −0.413791 1.64219i
\(514\) 0 0
\(515\) 464.784 0.902494
\(516\) 0 0
\(517\) 266.079i 0.514660i
\(518\) 0 0
\(519\) −34.8598 + 2.87472i −0.0671672 + 0.00553895i
\(520\) 0 0
\(521\) 456.517i 0.876232i 0.898918 + 0.438116i \(0.144354\pi\)
−0.898918 + 0.438116i \(0.855646\pi\)
\(522\) 0 0
\(523\) 287.095i 0.548939i 0.961596 + 0.274469i \(0.0885022\pi\)
−0.961596 + 0.274469i \(0.911498\pi\)
\(524\) 0 0
\(525\) 32.9160 2.71442i 0.0626971 0.00517033i
\(526\) 0 0
\(527\) 498.742i 0.946379i
\(528\) 0 0
\(529\) 109.421 0.206845
\(530\) 0 0
\(531\) 561.062 93.1698i 1.05661 0.175461i
\(532\) 0 0
\(533\) 639.875 1.20052
\(534\) 0 0
\(535\) −337.841 −0.631479
\(536\) 0 0
\(537\) 120.784 9.96046i 0.224923 0.0185483i
\(538\) 0 0
\(539\) −422.801 −0.784418
\(540\) 0 0
\(541\) 804.779i 1.48758i −0.668416 0.743788i \(-0.733027\pi\)
0.668416 0.743788i \(-0.266973\pi\)
\(542\) 0 0
\(543\) 29.8766 + 362.294i 0.0550214 + 0.667208i
\(544\) 0 0
\(545\) 87.7186i 0.160952i
\(546\) 0 0
\(547\) 76.3034i 0.139494i −0.997565 0.0697471i \(-0.977781\pi\)
0.997565 0.0697471i \(-0.0222192\pi\)
\(548\) 0 0
\(549\) −49.4373 297.708i −0.0900498 0.542274i
\(550\) 0 0
\(551\) 708.889i 1.28655i
\(552\) 0 0
\(553\) 45.6718 0.0825892
\(554\) 0 0
\(555\) −87.3528 1059.27i −0.157392 1.90859i
\(556\) 0 0
\(557\) −540.544 −0.970455 −0.485228 0.874388i \(-0.661263\pi\)
−0.485228 + 0.874388i \(0.661263\pi\)
\(558\) 0 0
\(559\) 905.121 1.61918
\(560\) 0 0
\(561\) 40.7228 + 493.819i 0.0725897 + 0.880247i
\(562\) 0 0
\(563\) −1047.65 −1.86084 −0.930422 0.366491i \(-0.880559\pi\)
−0.930422 + 0.366491i \(0.880559\pi\)
\(564\) 0 0
\(565\) 417.742i 0.739366i
\(566\) 0 0
\(567\) −44.3173 + 15.1360i −0.0781610 + 0.0266949i
\(568\) 0 0
\(569\) 958.593i 1.68470i −0.538933 0.842348i \(-0.681173\pi\)
0.538933 0.842348i \(-0.318827\pi\)
\(570\) 0 0
\(571\) 118.951i 0.208321i −0.994560 0.104161i \(-0.966784\pi\)
0.994560 0.104161i \(-0.0332156\pi\)
\(572\) 0 0
\(573\) 83.1611 + 1008.44i 0.145133 + 1.75993i
\(574\) 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
\(579\) 681.499 56.1999i 1.17703 0.0970637i
\(580\) 0 0
\(581\) 28.0570 0.0482910
\(582\) 0 0
\(583\) −772.318 −1.32473
\(584\) 0 0
\(585\) −175.404 1056.27i −0.299835 1.80559i
\(586\) 0 0
\(587\) −571.017 −0.972771 −0.486386 0.873744i \(-0.661685\pi\)
−0.486386 + 0.873744i \(0.661685\pi\)
\(588\) 0 0
\(589\) 844.140i 1.43318i
\(590\) 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
\(595\) 72.9432i 0.122594i
\(596\) 0 0
\(597\) 1.79043 0.147648i 0.00299905 0.000247317i
\(598\) 0 0
\(599\) 68.6579i 0.114621i 0.998356 + 0.0573104i \(0.0182525\pi\)
−0.998356 + 0.0573104i \(0.981748\pi\)
\(600\) 0 0
\(601\) −9.39898 −0.0156389 −0.00781945 0.999969i \(-0.502489\pi\)
−0.00781945 + 0.999969i \(0.502489\pi\)
\(602\) 0 0
\(603\) −160.058 963.857i −0.265436 1.59844i
\(604\) 0 0
\(605\) 302.096 0.499333
\(606\) 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
\(611\) −549.039 −0.898591
\(612\) 0 0
\(613\) 651.884i 1.06343i −0.846922 0.531716i \(-0.821547\pi\)
0.846922 0.531716i \(-0.178453\pi\)
\(614\) 0 0
\(615\) −58.4040 708.227i −0.0949659 1.15159i
\(616\) 0 0
\(617\) 146.821i 0.237959i 0.992897 + 0.118980i \(0.0379623\pi\)
−0.992897 + 0.118980i \(0.962038\pi\)
\(618\) 0 0
\(619\) 596.307i 0.963340i 0.876353 + 0.481670i \(0.159970\pi\)
−0.876353 + 0.481670i \(0.840030\pi\)
\(620\) 0 0
\(621\) −135.133 536.295i −0.217606 0.863598i
\(622\) 0 0
\(623\) 33.9441i 0.0544850i
\(624\) 0 0
\(625\) −738.453 −1.18152
\(626\) 0 0
\(627\) −68.9250 835.808i −0.109928 1.33303i
\(628\) 0 0
\(629\) −1014.91 −1.61353
\(630\) 0 0
\(631\) 77.6556 0.123067 0.0615337 0.998105i \(-0.480401\pi\)
0.0615337 + 0.998105i \(0.480401\pi\)
\(632\) 0 0
\(633\) 59.9235 + 726.652i 0.0946658 + 1.14795i
\(634\) 0 0
\(635\) 1570.56 2.47333
\(636\) 0 0
\(637\) 872.427i 1.36959i
\(638\) 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
\(643\) 1217.20i 1.89299i 0.322712 + 0.946497i \(0.395406\pi\)
−0.322712 + 0.946497i \(0.604594\pi\)
\(644\) 0 0
\(645\) −82.6141 1001.81i −0.128084 1.55319i
\(646\) 0 0
\(647\) 802.675i 1.24061i 0.784360 + 0.620305i \(0.212991\pi\)
−0.784360 + 0.620305i \(0.787009\pi\)
\(648\) 0 0
\(649\) 549.020 0.845948
\(650\) 0 0
\(651\) 45.3489 3.73970i 0.0696604 0.00574455i
\(652\) 0 0
\(653\) 216.282 0.331212 0.165606 0.986192i \(-0.447042\pi\)
0.165606 + 0.986192i \(0.447042\pi\)
\(654\) 0 0
\(655\) 804.410 1.22811
\(656\) 0 0
\(657\) 49.7615 8.26338i 0.0757405 0.0125774i
\(658\) 0 0
\(659\) 611.696 0.928218 0.464109 0.885778i \(-0.346375\pi\)
0.464109 + 0.885778i \(0.346375\pi\)
\(660\) 0 0
\(661\) 214.961i 0.325206i −0.986692 0.162603i \(-0.948011\pi\)
0.986692 0.162603i \(-0.0519890\pi\)
\(662\) 0 0
\(663\) −1018.97 + 84.0293i −1.53690 + 0.126741i
\(664\) 0 0
\(665\) 123.459i 0.185653i
\(666\) 0 0
\(667\) 451.275i 0.676574i
\(668\) 0 0
\(669\) −571.583 + 47.1357i −0.854384 + 0.0704569i
\(670\) 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
\(675\) −498.549 + 125.622i −0.738591 + 0.186107i
\(676\) 0 0
\(677\) −322.312 −0.476088 −0.238044 0.971254i \(-0.576506\pi\)
−0.238044 + 0.971254i \(0.576506\pi\)
\(678\) 0 0
\(679\) −53.9736 −0.0794898
\(680\) 0 0
\(681\) 26.2160 2.16191i 0.0384964 0.00317461i
\(682\) 0 0
\(683\) 451.564 0.661148 0.330574 0.943780i \(-0.392758\pi\)
0.330574 + 0.943780i \(0.392758\pi\)
\(684\) 0 0
\(685\) 907.047i 1.32416i
\(686\) 0 0
\(687\) −32.4816 393.882i −0.0472803 0.573337i
\(688\) 0 0
\(689\) 1593.64i 2.31297i
\(690\) 0 0
\(691\) 259.954i 0.376199i −0.982150 0.188100i \(-0.939767\pi\)
0.982150 0.188100i \(-0.0602328\pi\)
\(692\) 0 0
\(693\) −44.5959 + 7.40558i −0.0643520 + 0.0106863i
\(694\) 0 0
\(695\) 196.183i 0.282277i
\(696\) 0 0
\(697\) −678.570 −0.973558
\(698\) 0 0
\(699\) −23.6733 287.070i −0.0338674 0.410687i
\(700\) 0 0
\(701\) 434.792 0.620246 0.310123 0.950696i \(-0.399630\pi\)
0.310123 + 0.950696i \(0.399630\pi\)
\(702\) 0 0
\(703\) 1717.78 2.44350
\(704\) 0 0
\(705\) 50.1131 + 607.688i 0.0710823 + 0.861968i
\(706\) 0 0
\(707\) 66.0033 0.0933568
\(708\) 0 0
\(709\) 1136.05i 1.60232i −0.598448 0.801162i \(-0.704216\pi\)
0.598448 0.801162i \(-0.295784\pi\)
\(710\) 0 0
\(711\) −701.355 + 116.467i −0.986434 + 0.163807i
\(712\) 0 0
\(713\) 537.375i 0.753682i
\(714\) 0 0
\(715\) 1033.60i 1.44559i
\(716\) 0 0
\(717\) −78.4001 950.705i −0.109345 1.32595i
\(718\) 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
\(723\) 341.407 28.1542i 0.472209 0.0389408i
\(724\) 0 0
\(725\) −419.513 −0.578638
\(726\) 0 0
\(727\) −31.6562 −0.0435437 −0.0217718 0.999763i \(-0.506931\pi\)
−0.0217718 + 0.999763i \(0.506931\pi\)
\(728\) 0 0
\(729\) 641.956 345.447i 0.880598 0.473864i
\(730\) 0 0
\(731\) −959.856 −1.31307
\(732\) 0 0
\(733\) 596.421i 0.813671i 0.913501 + 0.406836i \(0.133368\pi\)
−0.913501 + 0.406836i \(0.866632\pi\)
\(734\) 0 0
\(735\) −965.619 + 79.6300i −1.31377 + 0.108340i
\(736\) 0 0
\(737\) 943.170i 1.27974i
\(738\) 0 0
\(739\) 1146.14i 1.55093i 0.631391 + 0.775464i \(0.282484\pi\)
−0.631391 + 0.775464i \(0.717516\pi\)
\(740\) 0 0
\(741\) 1724.64 142.223i 2.32745 0.191934i
\(742\) 0 0
\(743\) 842.850i 1.13439i 0.823584 + 0.567194i \(0.191971\pi\)
−0.823584 + 0.567194i \(0.808029\pi\)
\(744\) 0 0
\(745\) 116.198 0.155970
\(746\) 0 0
\(747\) −430.855 + 71.5476i −0.576780 + 0.0957799i
\(748\) 0 0
\(749\) −29.4324 −0.0392956
\(750\) 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
\(755\) −793.761 −1.05134
\(756\) 0 0
\(757\) 278.402i 0.367770i 0.982948 + 0.183885i \(0.0588674\pi\)
−0.982948 + 0.183885i \(0.941133\pi\)
\(758\) 0 0
\(759\) −43.8773 532.071i −0.0578093 0.701015i
\(760\) 0 0
\(761\) 986.126i 1.29583i 0.761713 + 0.647914i \(0.224359\pi\)
−0.761713 + 0.647914i \(0.775641\pi\)
\(762\) 0 0
\(763\) 7.64197i 0.0100157i
\(764\) 0 0
\(765\) 186.011 + 1120.14i 0.243151 + 1.46424i
\(766\) 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
\(771\) −37.4870 454.580i −0.0486213 0.589598i
\(772\) 0 0
\(773\) 590.233 0.763561 0.381780 0.924253i \(-0.375311\pi\)
0.381780 + 0.924253i \(0.375311\pi\)
\(774\) 0 0
\(775\) 499.553 0.644585
\(776\) 0 0
\(777\) −7.61009 92.2825i −0.00979420 0.118768i
\(778\) 0 0
\(779\) 1148.51 1.47433
\(780\) 0 0
\(781\) 515.712i 0.660322i
\(782\) 0 0
\(783\) 576.808 145.341i 0.736664 0.185621i
\(784\) 0 0
\(785\) 1257.52i 1.60194i
\(786\) 0 0
\(787\) 565.777i 0.718903i −0.933164 0.359451i \(-0.882964\pi\)
0.933164 0.359451i \(-0.117036\pi\)
\(788\) 0 0
\(789\) 122.050 + 1480.02i 0.154689 + 1.87581i
\(790\) 0 0
\(791\) 36.3933i 0.0460092i
\(792\) 0 0
\(793\) 601.120 0.758033
\(794\) 0 0
\(795\) −1763.87 + 145.458i −2.21870 + 0.182966i
\(796\) 0 0
\(797\) 1128.02 1.41533 0.707664 0.706549i \(-0.249749\pi\)
0.707664 + 0.706549i \(0.249749\pi\)
\(798\) 0 0
\(799\) 582.241 0.728712
\(800\) 0 0