Properties

Label 882.3.s.a.557.2
Level $882$
Weight $3$
Character 882.557
Analytic conductor $24.033$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 882.s (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(24.0327593166\)
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: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 557.2
Root \(-1.22474 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 882.557
Dual form 882.3.s.a.863.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(-3.67423 + 2.12132i) q^{5} -2.82843i q^{8} +O(q^{10})\) \(q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(-3.67423 + 2.12132i) q^{5} -2.82843i q^{8} +(-3.00000 + 5.19615i) q^{10} +(11.0227 + 6.36396i) q^{11} +1.00000 q^{13} +(-2.00000 - 3.46410i) q^{16} +(-14.6969 - 8.48528i) q^{17} +(11.5000 + 19.9186i) q^{19} +8.48528i q^{20} +18.0000 q^{22} +(-14.6969 + 8.48528i) q^{23} +(-3.50000 + 6.06218i) q^{25} +(1.22474 - 0.707107i) q^{26} +33.9411i q^{29} +(23.5000 - 40.7032i) q^{31} +(-4.89898 - 2.82843i) q^{32} -24.0000 q^{34} +(27.5000 + 47.6314i) q^{37} +(28.1691 + 16.2635i) q^{38} +(6.00000 + 10.3923i) q^{40} +46.6690i q^{41} +23.0000 q^{43} +(22.0454 - 12.7279i) q^{44} +(-12.0000 + 20.7846i) q^{46} +(3.67423 - 2.12132i) q^{47} +9.89949i q^{50} +(1.00000 - 1.73205i) q^{52} +(44.0908 + 25.4558i) q^{53} -54.0000 q^{55} +(24.0000 + 41.5692i) q^{58} +(73.4847 + 42.4264i) q^{59} +(52.0000 + 90.0666i) q^{61} -66.4680i q^{62} -8.00000 q^{64} +(-3.67423 + 2.12132i) q^{65} +(48.5000 - 84.0045i) q^{67} +(-29.3939 + 16.9706i) q^{68} +97.5807i q^{71} +(32.5000 - 56.2917i) q^{73} +(67.3610 + 38.8909i) q^{74} +46.0000 q^{76} +(-56.5000 - 97.8609i) q^{79} +(14.6969 + 8.48528i) q^{80} +(33.0000 + 57.1577i) q^{82} +29.6985i q^{83} +72.0000 q^{85} +(28.1691 - 16.2635i) q^{86} +(18.0000 - 31.1769i) q^{88} +(-117.576 + 67.8823i) q^{89} +33.9411i q^{92} +(3.00000 - 5.19615i) q^{94} +(-84.5074 - 48.7904i) q^{95} -104.000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{4} + O(q^{10}) \) \( 4q + 4q^{4} - 12q^{10} + 4q^{13} - 8q^{16} + 46q^{19} + 72q^{22} - 14q^{25} + 94q^{31} - 96q^{34} + 110q^{37} + 24q^{40} + 92q^{43} - 48q^{46} + 4q^{52} - 216q^{55} + 96q^{58} + 208q^{61} - 32q^{64} + 194q^{67} + 130q^{73} + 184q^{76} - 226q^{79} + 132q^{82} + 288q^{85} + 72q^{88} + 12q^{94} - 416q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.22474 0.707107i 0.612372 0.353553i
\(3\) 0 0
\(4\) 1.00000 1.73205i 0.250000 0.433013i
\(5\) −3.67423 + 2.12132i −0.734847 + 0.424264i −0.820193 0.572087i \(-0.806134\pi\)
0.0853458 + 0.996351i \(0.472801\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 2.82843i 0.353553i
\(9\) 0 0
\(10\) −3.00000 + 5.19615i −0.300000 + 0.519615i
\(11\) 11.0227 + 6.36396i 1.00206 + 0.578542i 0.908858 0.417105i \(-0.136955\pi\)
0.0932057 + 0.995647i \(0.470289\pi\)
\(12\) 0 0
\(13\) 1.00000 0.0769231 0.0384615 0.999260i \(-0.487754\pi\)
0.0384615 + 0.999260i \(0.487754\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −2.00000 3.46410i −0.125000 0.216506i
\(17\) −14.6969 8.48528i −0.864526 0.499134i 0.000999453 1.00000i \(-0.499682\pi\)
−0.865525 + 0.500865i \(0.833015\pi\)
\(18\) 0 0
\(19\) 11.5000 + 19.9186i 0.605263 + 1.04835i 0.992010 + 0.126161i \(0.0402654\pi\)
−0.386747 + 0.922186i \(0.626401\pi\)
\(20\) 8.48528i 0.424264i
\(21\) 0 0
\(22\) 18.0000 0.818182
\(23\) −14.6969 + 8.48528i −0.638997 + 0.368925i −0.784228 0.620473i \(-0.786941\pi\)
0.145231 + 0.989398i \(0.453608\pi\)
\(24\) 0 0
\(25\) −3.50000 + 6.06218i −0.140000 + 0.242487i
\(26\) 1.22474 0.707107i 0.0471056 0.0271964i
\(27\) 0 0
\(28\) 0 0
\(29\) 33.9411i 1.17038i 0.810895 + 0.585192i \(0.198981\pi\)
−0.810895 + 0.585192i \(0.801019\pi\)
\(30\) 0 0
\(31\) 23.5000 40.7032i 0.758065 1.31301i −0.185772 0.982593i \(-0.559479\pi\)
0.943836 0.330413i \(-0.107188\pi\)
\(32\) −4.89898 2.82843i −0.153093 0.0883883i
\(33\) 0 0
\(34\) −24.0000 −0.705882
\(35\) 0 0
\(36\) 0 0
\(37\) 27.5000 + 47.6314i 0.743243 + 1.28734i 0.951011 + 0.309157i \(0.100047\pi\)
−0.207768 + 0.978178i \(0.566620\pi\)
\(38\) 28.1691 + 16.2635i 0.741293 + 0.427986i
\(39\) 0 0
\(40\) 6.00000 + 10.3923i 0.150000 + 0.259808i
\(41\) 46.6690i 1.13827i 0.822244 + 0.569135i \(0.192722\pi\)
−0.822244 + 0.569135i \(0.807278\pi\)
\(42\) 0 0
\(43\) 23.0000 0.534884 0.267442 0.963574i \(-0.413822\pi\)
0.267442 + 0.963574i \(0.413822\pi\)
\(44\) 22.0454 12.7279i 0.501032 0.289271i
\(45\) 0 0
\(46\) −12.0000 + 20.7846i −0.260870 + 0.451839i
\(47\) 3.67423 2.12132i 0.0781752 0.0451345i −0.460403 0.887710i \(-0.652295\pi\)
0.538578 + 0.842576i \(0.318962\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 9.89949i 0.197990i
\(51\) 0 0
\(52\) 1.00000 1.73205i 0.0192308 0.0333087i
\(53\) 44.0908 + 25.4558i 0.831902 + 0.480299i 0.854504 0.519446i \(-0.173862\pi\)
−0.0226013 + 0.999745i \(0.507195\pi\)
\(54\) 0 0
\(55\) −54.0000 −0.981818
\(56\) 0 0
\(57\) 0 0
\(58\) 24.0000 + 41.5692i 0.413793 + 0.716711i
\(59\) 73.4847 + 42.4264i 1.24550 + 0.719092i 0.970209 0.242268i \(-0.0778915\pi\)
0.275294 + 0.961360i \(0.411225\pi\)
\(60\) 0 0
\(61\) 52.0000 + 90.0666i 0.852459 + 1.47650i 0.878982 + 0.476854i \(0.158223\pi\)
−0.0265234 + 0.999648i \(0.508444\pi\)
\(62\) 66.4680i 1.07207i
\(63\) 0 0
\(64\) −8.00000 −0.125000
\(65\) −3.67423 + 2.12132i −0.0565267 + 0.0326357i
\(66\) 0 0
\(67\) 48.5000 84.0045i 0.723881 1.25380i −0.235553 0.971862i \(-0.575690\pi\)
0.959433 0.281936i \(-0.0909767\pi\)
\(68\) −29.3939 + 16.9706i −0.432263 + 0.249567i
\(69\) 0 0
\(70\) 0 0
\(71\) 97.5807i 1.37438i 0.726479 + 0.687188i \(0.241155\pi\)
−0.726479 + 0.687188i \(0.758845\pi\)
\(72\) 0 0
\(73\) 32.5000 56.2917i 0.445205 0.771119i −0.552861 0.833273i \(-0.686464\pi\)
0.998067 + 0.0621550i \(0.0197973\pi\)
\(74\) 67.3610 + 38.8909i 0.910283 + 0.525552i
\(75\) 0 0
\(76\) 46.0000 0.605263
\(77\) 0 0
\(78\) 0 0
\(79\) −56.5000 97.8609i −0.715190 1.23875i −0.962886 0.269907i \(-0.913007\pi\)
0.247696 0.968838i \(-0.420326\pi\)
\(80\) 14.6969 + 8.48528i 0.183712 + 0.106066i
\(81\) 0 0
\(82\) 33.0000 + 57.1577i 0.402439 + 0.697045i
\(83\) 29.6985i 0.357813i 0.983866 + 0.178907i \(0.0572560\pi\)
−0.983866 + 0.178907i \(0.942744\pi\)
\(84\) 0 0
\(85\) 72.0000 0.847059
\(86\) 28.1691 16.2635i 0.327548 0.189110i
\(87\) 0 0
\(88\) 18.0000 31.1769i 0.204545 0.354283i
\(89\) −117.576 + 67.8823i −1.32107 + 0.762722i −0.983900 0.178721i \(-0.942804\pi\)
−0.337173 + 0.941443i \(0.609471\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 33.9411i 0.368925i
\(93\) 0 0
\(94\) 3.00000 5.19615i 0.0319149 0.0552782i
\(95\) −84.5074 48.7904i −0.889552 0.513583i
\(96\) 0 0
\(97\) −104.000 −1.07216 −0.536082 0.844166i \(-0.680096\pi\)
−0.536082 + 0.844166i \(0.680096\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 7.00000 + 12.1244i 0.0700000 + 0.121244i
\(101\) −128.598 74.2462i −1.27325 0.735111i −0.297651 0.954675i \(-0.596203\pi\)
−0.975598 + 0.219564i \(0.929537\pi\)
\(102\) 0 0
\(103\) 59.5000 + 103.057i 0.577670 + 1.00055i 0.995746 + 0.0921416i \(0.0293712\pi\)
−0.418076 + 0.908412i \(0.637295\pi\)
\(104\) 2.82843i 0.0271964i
\(105\) 0 0
\(106\) 72.0000 0.679245
\(107\) −102.879 + 59.3970i −0.961482 + 0.555112i −0.896629 0.442783i \(-0.853991\pi\)
−0.0648531 + 0.997895i \(0.520658\pi\)
\(108\) 0 0
\(109\) 24.5000 42.4352i 0.224771 0.389314i −0.731480 0.681863i \(-0.761170\pi\)
0.956251 + 0.292549i \(0.0945034\pi\)
\(110\) −66.1362 + 38.1838i −0.601238 + 0.347125i
\(111\) 0 0
\(112\) 0 0
\(113\) 97.5807i 0.863546i −0.901982 0.431773i \(-0.857888\pi\)
0.901982 0.431773i \(-0.142112\pi\)
\(114\) 0 0
\(115\) 36.0000 62.3538i 0.313043 0.542207i
\(116\) 58.7878 + 33.9411i 0.506791 + 0.292596i
\(117\) 0 0
\(118\) 120.000 1.01695
\(119\) 0 0
\(120\) 0 0
\(121\) 20.5000 + 35.5070i 0.169421 + 0.293447i
\(122\) 127.373 + 73.5391i 1.04404 + 0.602780i
\(123\) 0 0
\(124\) −47.0000 81.4064i −0.379032 0.656503i
\(125\) 135.765i 1.08612i
\(126\) 0 0
\(127\) 113.000 0.889764 0.444882 0.895589i \(-0.353246\pi\)
0.444882 + 0.895589i \(0.353246\pi\)
\(128\) −9.79796 + 5.65685i −0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) −3.00000 + 5.19615i −0.0230769 + 0.0399704i
\(131\) −18.3712 + 10.6066i −0.140238 + 0.0809664i −0.568477 0.822699i \(-0.692467\pi\)
0.428239 + 0.903665i \(0.359134\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 137.179i 1.02372i
\(135\) 0 0
\(136\) −24.0000 + 41.5692i −0.176471 + 0.305656i
\(137\) −58.7878 33.9411i −0.429108 0.247745i 0.269859 0.962900i \(-0.413023\pi\)
−0.698966 + 0.715154i \(0.746356\pi\)
\(138\) 0 0
\(139\) 103.000 0.741007 0.370504 0.928831i \(-0.379185\pi\)
0.370504 + 0.928831i \(0.379185\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 69.0000 + 119.512i 0.485915 + 0.841630i
\(143\) 11.0227 + 6.36396i 0.0770818 + 0.0445032i
\(144\) 0 0
\(145\) −72.0000 124.708i −0.496552 0.860053i
\(146\) 91.9239i 0.629616i
\(147\) 0 0
\(148\) 110.000 0.743243
\(149\) −146.969 + 84.8528i −0.986372 + 0.569482i −0.904188 0.427135i \(-0.859523\pi\)
−0.0821839 + 0.996617i \(0.526189\pi\)
\(150\) 0 0
\(151\) −52.0000 + 90.0666i −0.344371 + 0.596468i −0.985239 0.171183i \(-0.945241\pi\)
0.640868 + 0.767651i \(0.278574\pi\)
\(152\) 56.3383 32.5269i 0.370646 0.213993i
\(153\) 0 0
\(154\) 0 0
\(155\) 199.404i 1.28648i
\(156\) 0 0
\(157\) 76.0000 131.636i 0.484076 0.838445i −0.515756 0.856735i \(-0.672489\pi\)
0.999833 + 0.0182904i \(0.00582233\pi\)
\(158\) −138.396 79.9031i −0.875925 0.505716i
\(159\) 0 0
\(160\) 24.0000 0.150000
\(161\) 0 0
\(162\) 0 0
\(163\) −28.0000 48.4974i −0.171779 0.297530i 0.767263 0.641333i \(-0.221618\pi\)
−0.939042 + 0.343803i \(0.888285\pi\)
\(164\) 80.8332 + 46.6690i 0.492885 + 0.284567i
\(165\) 0 0
\(166\) 21.0000 + 36.3731i 0.126506 + 0.219115i
\(167\) 4.24264i 0.0254050i 0.999919 + 0.0127025i \(0.00404345\pi\)
−0.999919 + 0.0127025i \(0.995957\pi\)
\(168\) 0 0
\(169\) −168.000 −0.994083
\(170\) 88.1816 50.9117i 0.518715 0.299481i
\(171\) 0 0
\(172\) 23.0000 39.8372i 0.133721 0.231611i
\(173\) 132.272 76.3675i 0.764581 0.441431i −0.0663573 0.997796i \(-0.521138\pi\)
0.830938 + 0.556365i \(0.187804\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 50.9117i 0.289271i
\(177\) 0 0
\(178\) −96.0000 + 166.277i −0.539326 + 0.934140i
\(179\) −3.67423 2.12132i −0.0205265 0.0118510i 0.489702 0.871890i \(-0.337106\pi\)
−0.510228 + 0.860039i \(0.670439\pi\)
\(180\) 0 0
\(181\) 55.0000 0.303867 0.151934 0.988391i \(-0.451450\pi\)
0.151934 + 0.988391i \(0.451450\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 24.0000 + 41.5692i 0.130435 + 0.225920i
\(185\) −202.083 116.673i −1.09234 0.630663i
\(186\) 0 0
\(187\) −108.000 187.061i −0.577540 1.00033i
\(188\) 8.48528i 0.0451345i
\(189\) 0 0
\(190\) −138.000 −0.726316
\(191\) −55.1135 + 31.8198i −0.288552 + 0.166596i −0.637289 0.770625i \(-0.719944\pi\)
0.348736 + 0.937221i \(0.386611\pi\)
\(192\) 0 0
\(193\) 75.5000 130.770i 0.391192 0.677564i −0.601415 0.798937i \(-0.705396\pi\)
0.992607 + 0.121373i \(0.0387296\pi\)
\(194\) −127.373 + 73.5391i −0.656564 + 0.379068i
\(195\) 0 0
\(196\) 0 0
\(197\) 16.9706i 0.0861450i 0.999072 + 0.0430725i \(0.0137146\pi\)
−0.999072 + 0.0430725i \(0.986285\pi\)
\(198\) 0 0
\(199\) −80.0000 + 138.564i −0.402010 + 0.696302i −0.993968 0.109667i \(-0.965022\pi\)
0.591958 + 0.805969i \(0.298355\pi\)
\(200\) 17.1464 + 9.89949i 0.0857321 + 0.0494975i
\(201\) 0 0
\(202\) −210.000 −1.03960
\(203\) 0 0
\(204\) 0 0
\(205\) −99.0000 171.473i −0.482927 0.836454i
\(206\) 145.745 + 84.1457i 0.707498 + 0.408474i
\(207\) 0 0
\(208\) −2.00000 3.46410i −0.00961538 0.0166543i
\(209\) 292.742i 1.40068i
\(210\) 0 0
\(211\) −208.000 −0.985782 −0.492891 0.870091i \(-0.664060\pi\)
−0.492891 + 0.870091i \(0.664060\pi\)
\(212\) 88.1816 50.9117i 0.415951 0.240149i
\(213\) 0 0
\(214\) −84.0000 + 145.492i −0.392523 + 0.679870i
\(215\) −84.5074 + 48.7904i −0.393058 + 0.226932i
\(216\) 0 0
\(217\) 0 0
\(218\) 69.2965i 0.317874i
\(219\) 0 0
\(220\) −54.0000 + 93.5307i −0.245455 + 0.425140i
\(221\) −14.6969 8.48528i −0.0665020 0.0383949i
\(222\) 0 0
\(223\) 40.0000 0.179372 0.0896861 0.995970i \(-0.471414\pi\)
0.0896861 + 0.995970i \(0.471414\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −69.0000 119.512i −0.305310 0.528812i
\(227\) −194.734 112.430i −0.857861 0.495286i 0.00543445 0.999985i \(-0.498270\pi\)
−0.863295 + 0.504699i \(0.831603\pi\)
\(228\) 0 0
\(229\) 188.500 + 326.492i 0.823144 + 1.42573i 0.903329 + 0.428947i \(0.141115\pi\)
−0.0801853 + 0.996780i \(0.525551\pi\)
\(230\) 101.823i 0.442710i
\(231\) 0 0
\(232\) 96.0000 0.413793
\(233\) 297.613 171.827i 1.27731 0.737455i 0.300956 0.953638i \(-0.402694\pi\)
0.976353 + 0.216183i \(0.0693609\pi\)
\(234\) 0 0
\(235\) −9.00000 + 15.5885i −0.0382979 + 0.0663339i
\(236\) 146.969 84.8528i 0.622752 0.359546i
\(237\) 0 0
\(238\) 0 0
\(239\) 12.7279i 0.0532549i −0.999645 0.0266275i \(-0.991523\pi\)
0.999645 0.0266275i \(-0.00847678\pi\)
\(240\) 0 0
\(241\) −65.0000 + 112.583i −0.269710 + 0.467151i −0.968787 0.247896i \(-0.920261\pi\)
0.699077 + 0.715046i \(0.253594\pi\)
\(242\) 50.2145 + 28.9914i 0.207498 + 0.119799i
\(243\) 0 0
\(244\) 208.000 0.852459
\(245\) 0 0
\(246\) 0 0
\(247\) 11.5000 + 19.9186i 0.0465587 + 0.0806420i
\(248\) −115.126 66.4680i −0.464218 0.268016i
\(249\) 0 0
\(250\) −96.0000 166.277i −0.384000 0.665108i
\(251\) 50.9117i 0.202835i 0.994844 + 0.101418i \(0.0323379\pi\)
−0.994844 + 0.101418i \(0.967662\pi\)
\(252\) 0 0
\(253\) −216.000 −0.853755
\(254\) 138.396 79.9031i 0.544867 0.314579i
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.0312500 + 0.0541266i
\(257\) 407.840 235.467i 1.58693 0.916212i 0.593117 0.805117i \(-0.297897\pi\)
0.993810 0.111096i \(-0.0354360\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 8.48528i 0.0326357i
\(261\) 0 0
\(262\) −15.0000 + 25.9808i −0.0572519 + 0.0991632i
\(263\) 88.1816 + 50.9117i 0.335291 + 0.193581i 0.658188 0.752854i \(-0.271323\pi\)
−0.322897 + 0.946434i \(0.604657\pi\)
\(264\) 0 0
\(265\) −216.000 −0.815094
\(266\) 0 0
\(267\) 0 0
\(268\) −97.0000 168.009i −0.361940 0.626899i
\(269\) 246.174 + 142.128i 0.915144 + 0.528359i 0.882083 0.471095i \(-0.156141\pi\)
0.0330613 + 0.999453i \(0.489474\pi\)
\(270\) 0 0
\(271\) −260.000 450.333i −0.959410 1.66175i −0.723938 0.689865i \(-0.757670\pi\)
−0.235471 0.971881i \(-0.575663\pi\)
\(272\) 67.8823i 0.249567i
\(273\) 0 0
\(274\) −96.0000 −0.350365
\(275\) −77.1589 + 44.5477i −0.280578 + 0.161992i
\(276\) 0 0
\(277\) −56.5000 + 97.8609i −0.203971 + 0.353288i −0.949804 0.312844i \(-0.898718\pi\)
0.745833 + 0.666133i \(0.232052\pi\)
\(278\) 126.149 72.8320i 0.453772 0.261986i
\(279\) 0 0
\(280\) 0 0
\(281\) 458.205i 1.63062i −0.579022 0.815312i \(-0.696566\pi\)
0.579022 0.815312i \(-0.303434\pi\)
\(282\) 0 0
\(283\) 44.5000 77.0763i 0.157244 0.272354i −0.776630 0.629957i \(-0.783072\pi\)
0.933874 + 0.357603i \(0.116406\pi\)
\(284\) 169.015 + 97.5807i 0.595123 + 0.343594i
\(285\) 0 0
\(286\) 18.0000 0.0629371
\(287\) 0 0
\(288\) 0 0
\(289\) −0.500000 0.866025i −0.00173010 0.00299663i
\(290\) −176.363 101.823i −0.608149 0.351115i
\(291\) 0 0
\(292\) −65.0000 112.583i −0.222603 0.385559i
\(293\) 67.8823i 0.231680i 0.993268 + 0.115840i \(0.0369560\pi\)
−0.993268 + 0.115840i \(0.963044\pi\)
\(294\) 0 0
\(295\) −360.000 −1.22034
\(296\) 134.722 77.7817i 0.455142 0.262776i
\(297\) 0 0
\(298\) −120.000 + 207.846i −0.402685 + 0.697470i
\(299\) −14.6969 + 8.48528i −0.0491536 + 0.0283789i
\(300\) 0 0
\(301\) 0 0
\(302\) 147.078i 0.487014i
\(303\) 0 0
\(304\) 46.0000 79.6743i 0.151316 0.262087i
\(305\) −382.120 220.617i −1.25285 0.723335i
\(306\) 0 0
\(307\) −233.000 −0.758958 −0.379479 0.925200i \(-0.623897\pi\)
−0.379479 + 0.925200i \(0.623897\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 141.000 + 244.219i 0.454839 + 0.787804i
\(311\) −216.780 125.158i −0.697041 0.402437i 0.109203 0.994019i \(-0.465170\pi\)
−0.806244 + 0.591582i \(0.798503\pi\)
\(312\) 0 0
\(313\) −75.5000 130.770i −0.241214 0.417795i 0.719846 0.694133i \(-0.244212\pi\)
−0.961060 + 0.276338i \(0.910879\pi\)
\(314\) 214.960i 0.684587i
\(315\) 0 0
\(316\) −226.000 −0.715190
\(317\) −352.727 + 203.647i −1.11270 + 0.642419i −0.939528 0.342472i \(-0.888736\pi\)
−0.173174 + 0.984891i \(0.555402\pi\)
\(318\) 0 0
\(319\) −216.000 + 374.123i −0.677116 + 1.17280i
\(320\) 29.3939 16.9706i 0.0918559 0.0530330i
\(321\) 0 0
\(322\) 0 0
\(323\) 390.323i 1.20843i
\(324\) 0 0
\(325\) −3.50000 + 6.06218i −0.0107692 + 0.0186529i
\(326\) −68.5857 39.5980i −0.210386 0.121466i
\(327\) 0 0
\(328\) 132.000 0.402439
\(329\) 0 0
\(330\) 0 0
\(331\) 36.5000 + 63.2199i 0.110272 + 0.190997i 0.915880 0.401452i \(-0.131495\pi\)
−0.805608 + 0.592449i \(0.798161\pi\)
\(332\) 51.4393 + 29.6985i 0.154938 + 0.0894533i
\(333\) 0 0
\(334\) 3.00000 + 5.19615i 0.00898204 + 0.0155573i
\(335\) 411.536i 1.22847i
\(336\) 0 0
\(337\) 527.000 1.56380 0.781899 0.623405i \(-0.214251\pi\)
0.781899 + 0.623405i \(0.214251\pi\)
\(338\) −205.757 + 118.794i −0.608749 + 0.351461i
\(339\) 0 0
\(340\) 72.0000 124.708i 0.211765 0.366787i
\(341\) 518.067 299.106i 1.51926 0.877144i
\(342\) 0 0
\(343\) 0 0
\(344\) 65.0538i 0.189110i
\(345\) 0 0
\(346\) 108.000 187.061i 0.312139 0.540640i
\(347\) 367.423 + 212.132i 1.05886 + 0.611332i 0.925116 0.379685i \(-0.123968\pi\)
0.133741 + 0.991016i \(0.457301\pi\)
\(348\) 0 0
\(349\) 112.000 0.320917 0.160458 0.987043i \(-0.448703\pi\)
0.160458 + 0.987043i \(0.448703\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −36.0000 62.3538i −0.102273 0.177142i
\(353\) −268.219 154.856i −0.759828 0.438687i 0.0694063 0.997588i \(-0.477890\pi\)
−0.829234 + 0.558902i \(0.811223\pi\)
\(354\) 0 0
\(355\) −207.000 358.535i −0.583099 1.00996i
\(356\) 271.529i 0.762722i
\(357\) 0 0
\(358\) −6.00000 −0.0167598
\(359\) 440.908 254.558i 1.22816 0.709076i 0.261512 0.965200i \(-0.415779\pi\)
0.966644 + 0.256124i \(0.0824454\pi\)
\(360\) 0 0
\(361\) −84.0000 + 145.492i −0.232687 + 0.403026i
\(362\) 67.3610 38.8909i 0.186080 0.107433i
\(363\) 0 0
\(364\) 0 0
\(365\) 275.772i 0.755539i
\(366\) 0 0
\(367\) −159.500 + 276.262i −0.434605 + 0.752758i −0.997263 0.0739317i \(-0.976445\pi\)
0.562658 + 0.826689i \(0.309779\pi\)
\(368\) 58.7878 + 33.9411i 0.159749 + 0.0922313i
\(369\) 0 0
\(370\) −330.000 −0.891892
\(371\) 0 0
\(372\) 0 0
\(373\) −104.500 180.999i −0.280161 0.485253i 0.691263 0.722603i \(-0.257054\pi\)
−0.971424 + 0.237350i \(0.923721\pi\)
\(374\) −264.545 152.735i −0.707339 0.408383i
\(375\) 0 0
\(376\) −6.00000 10.3923i −0.0159574 0.0276391i
\(377\) 33.9411i 0.0900295i
\(378\) 0 0
\(379\) −433.000 −1.14248 −0.571240 0.820783i \(-0.693537\pi\)
−0.571240 + 0.820783i \(0.693537\pi\)
\(380\) −169.015 + 97.5807i −0.444776 + 0.256791i
\(381\) 0 0
\(382\) −45.0000 + 77.9423i −0.117801 + 0.204037i
\(383\) −338.030 + 195.161i −0.882584 + 0.509560i −0.871509 0.490379i \(-0.836858\pi\)
−0.0110743 + 0.999939i \(0.503525\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 213.546i 0.553229i
\(387\) 0 0
\(388\) −104.000 + 180.133i −0.268041 + 0.464261i
\(389\) −319.658 184.555i −0.821744 0.474434i 0.0292735 0.999571i \(-0.490681\pi\)
−0.851018 + 0.525137i \(0.824014\pi\)
\(390\) 0 0
\(391\) 288.000 0.736573
\(392\) 0 0
\(393\) 0 0
\(394\) 12.0000 + 20.7846i 0.0304569 + 0.0527528i
\(395\) 415.189 + 239.709i 1.05111 + 0.606859i
\(396\) 0 0
\(397\) 56.5000 + 97.8609i 0.142317 + 0.246501i 0.928369 0.371660i \(-0.121211\pi\)
−0.786052 + 0.618161i \(0.787878\pi\)
\(398\) 226.274i 0.568528i
\(399\) 0 0
\(400\) 28.0000 0.0700000
\(401\) 308.636 178.191i 0.769665 0.444366i −0.0630900 0.998008i \(-0.520096\pi\)
0.832755 + 0.553641i \(0.186762\pi\)
\(402\) 0 0
\(403\) 23.5000 40.7032i 0.0583127 0.101000i
\(404\) −257.196 + 148.492i −0.636625 + 0.367556i
\(405\) 0 0
\(406\) 0 0
\(407\) 700.036i 1.71999i
\(408\) 0 0
\(409\) −159.500 + 276.262i −0.389976 + 0.675457i −0.992446 0.122684i \(-0.960850\pi\)
0.602470 + 0.798141i \(0.294183\pi\)
\(410\) −242.499 140.007i −0.591462 0.341481i
\(411\) 0 0
\(412\) 238.000 0.577670
\(413\) 0 0
\(414\) 0 0
\(415\) −63.0000 109.119i −0.151807 0.262938i
\(416\) −4.89898 2.82843i −0.0117764 0.00679910i
\(417\) 0 0
\(418\) 207.000 + 358.535i 0.495215 + 0.857738i
\(419\) 767.918i 1.83274i −0.400333 0.916370i \(-0.631105\pi\)
0.400333 0.916370i \(-0.368895\pi\)
\(420\) 0 0
\(421\) 65.0000 0.154394 0.0771971 0.997016i \(-0.475403\pi\)
0.0771971 + 0.997016i \(0.475403\pi\)
\(422\) −254.747 + 147.078i −0.603666 + 0.348527i
\(423\) 0 0
\(424\) 72.0000 124.708i 0.169811 0.294122i
\(425\) 102.879 59.3970i 0.242067 0.139758i
\(426\) 0 0
\(427\) 0 0
\(428\) 237.588i 0.555112i
\(429\) 0 0
\(430\) −69.0000 + 119.512i −0.160465 + 0.277934i
\(431\) 415.189 + 239.709i 0.963314 + 0.556170i 0.897192 0.441642i \(-0.145604\pi\)
0.0661229 + 0.997811i \(0.478937\pi\)
\(432\) 0 0
\(433\) 367.000 0.847575 0.423788 0.905762i \(-0.360700\pi\)
0.423788 + 0.905762i \(0.360700\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −49.0000 84.8705i −0.112385 0.194657i
\(437\) −338.030 195.161i −0.773523 0.446594i
\(438\) 0 0
\(439\) 268.000 + 464.190i 0.610478 + 1.05738i 0.991160 + 0.132673i \(0.0423561\pi\)
−0.380681 + 0.924706i \(0.624311\pi\)
\(440\) 152.735i 0.347125i
\(441\) 0 0
\(442\) −24.0000 −0.0542986
\(443\) 73.4847 42.4264i 0.165880 0.0957707i −0.414762 0.909930i \(-0.636135\pi\)
0.580642 + 0.814159i \(0.302802\pi\)
\(444\) 0 0
\(445\) 288.000 498.831i 0.647191 1.12097i
\(446\) 48.9898 28.2843i 0.109843 0.0634176i
\(447\) 0 0
\(448\) 0 0
\(449\) 615.183i 1.37012i −0.728488 0.685059i \(-0.759776\pi\)
0.728488 0.685059i \(-0.240224\pi\)
\(450\) 0 0
\(451\) −297.000 + 514.419i −0.658537 + 1.14062i
\(452\) −169.015 97.5807i −0.373927 0.215887i
\(453\) 0 0
\(454\) −318.000 −0.700441
\(455\) 0 0
\(456\) 0 0
\(457\) 231.500 + 400.970i 0.506565 + 0.877396i 0.999971 + 0.00759675i \(0.00241814\pi\)
−0.493407 + 0.869799i \(0.664249\pi\)
\(458\) 461.729 + 266.579i 1.00814 + 0.582051i
\(459\) 0 0
\(460\) −72.0000 124.708i −0.156522 0.271104i
\(461\) 271.529i 0.589000i −0.955651 0.294500i \(-0.904847\pi\)
0.955651 0.294500i \(-0.0951531\pi\)
\(462\) 0 0
\(463\) 47.0000 0.101512 0.0507559 0.998711i \(-0.483837\pi\)
0.0507559 + 0.998711i \(0.483837\pi\)
\(464\) 117.576 67.8823i 0.253395 0.146298i
\(465\) 0 0
\(466\) 243.000 420.888i 0.521459 0.903194i
\(467\) −642.991 + 371.231i −1.37685 + 0.794927i −0.991780 0.127958i \(-0.959158\pi\)
−0.385075 + 0.922885i \(0.625824\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 25.4558i 0.0541614i
\(471\) 0 0
\(472\) 120.000 207.846i 0.254237 0.440352i
\(473\) 253.522 + 146.371i 0.535988 + 0.309453i
\(474\) 0 0
\(475\) −161.000 −0.338947
\(476\) 0 0
\(477\) 0 0
\(478\) −9.00000 15.5885i −0.0188285 0.0326118i
\(479\) 367.423 + 212.132i 0.767064 + 0.442864i 0.831826 0.555036i \(-0.187296\pi\)
−0.0647625 + 0.997901i \(0.520629\pi\)
\(480\) 0 0
\(481\) 27.5000 + 47.6314i 0.0571726 + 0.0990258i
\(482\) 183.848i 0.381427i
\(483\) 0 0
\(484\) 82.0000 0.169421
\(485\) 382.120 220.617i 0.787877 0.454881i
\(486\) 0 0
\(487\) −119.500 + 206.980i −0.245380 + 0.425010i −0.962238 0.272208i \(-0.912246\pi\)
0.716858 + 0.697219i \(0.245579\pi\)
\(488\) 254.747 147.078i 0.522022 0.301390i
\(489\) 0 0
\(490\) 0 0
\(491\) 203.647i 0.414759i 0.978261 + 0.207380i \(0.0664935\pi\)
−0.978261 + 0.207380i \(0.933506\pi\)
\(492\) 0 0
\(493\) 288.000 498.831i 0.584178 1.01183i
\(494\) 28.1691 + 16.2635i 0.0570225 + 0.0329220i
\(495\) 0 0
\(496\) −188.000 −0.379032
\(497\) 0 0
\(498\) 0 0
\(499\) 24.5000 + 42.4352i 0.0490982 + 0.0850406i 0.889530 0.456877i \(-0.151032\pi\)
−0.840432 + 0.541917i \(0.817699\pi\)
\(500\) −235.151 135.765i −0.470302 0.271529i
\(501\) 0 0
\(502\) 36.0000 + 62.3538i 0.0717131 + 0.124211i
\(503\) 589.727i 1.17242i −0.810159 0.586210i \(-0.800619\pi\)
0.810159 0.586210i \(-0.199381\pi\)
\(504\) 0 0
\(505\) 630.000 1.24752
\(506\) −264.545 + 152.735i −0.522816 + 0.301848i
\(507\) 0 0
\(508\) 113.000 195.722i 0.222441 0.385279i
\(509\) 209.431 120.915i 0.411457 0.237555i −0.279959 0.960012i \(-0.590321\pi\)
0.691415 + 0.722457i \(0.256987\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 22.6274i 0.0441942i
\(513\) 0 0
\(514\) 333.000 576.773i 0.647860 1.12213i
\(515\) −437.234 252.437i −0.848998 0.490169i
\(516\) 0 0
\(517\) 54.0000 0.104449
\(518\) 0 0
\(519\) 0 0
\(520\) 6.00000 + 10.3923i 0.0115385 + 0.0199852i
\(521\) 734.847 + 424.264i 1.41045 + 0.814326i 0.995431 0.0954841i \(-0.0304399\pi\)
0.415024 + 0.909811i \(0.363773\pi\)
\(522\) 0 0
\(523\) −195.500 338.616i −0.373805 0.647449i 0.616342 0.787478i \(-0.288614\pi\)
−0.990147 + 0.140029i \(0.955280\pi\)
\(524\) 42.4264i 0.0809664i
\(525\) 0 0
\(526\) 144.000 0.273764
\(527\) −690.756 + 398.808i −1.31073 + 0.756752i
\(528\) 0 0
\(529\) −120.500 + 208.712i −0.227788 + 0.394541i
\(530\) −264.545 + 152.735i −0.499141 + 0.288179i
\(531\) 0 0
\(532\) 0 0
\(533\) 46.6690i 0.0875592i
\(534\) 0 0
\(535\) 252.000 436.477i 0.471028 0.815844i
\(536\) −237.601 137.179i −0.443285 0.255930i
\(537\) 0 0
\(538\) 402.000 0.747212
\(539\) 0 0
\(540\) 0 0
\(541\) 36.5000 + 63.2199i 0.0674677 + 0.116857i 0.897786 0.440432i \(-0.145175\pi\)
−0.830318 + 0.557289i \(0.811841\pi\)
\(542\) −636.867 367.696i −1.17503 0.678405i
\(543\) 0 0
\(544\) 48.0000 + 83.1384i 0.0882353 + 0.152828i
\(545\) 207.889i 0.381448i
\(546\) 0 0
\(547\) 32.0000 0.0585009 0.0292505 0.999572i \(-0.490688\pi\)
0.0292505 + 0.999572i \(0.490688\pi\)
\(548\) −117.576 + 67.8823i −0.214554 + 0.123873i
\(549\) 0 0
\(550\) −63.0000 + 109.119i −0.114545 + 0.198399i
\(551\) −676.059 + 390.323i −1.22697 + 0.708390i
\(552\) 0 0
\(553\) 0 0
\(554\) 159.806i 0.288459i
\(555\) 0 0
\(556\) 103.000 178.401i 0.185252 0.320866i
\(557\) 40.4166 + 23.3345i 0.0725612 + 0.0418932i 0.535842 0.844319i \(-0.319994\pi\)
−0.463280 + 0.886212i \(0.653328\pi\)
\(558\) 0 0
\(559\) 23.0000 0.0411449
\(560\) 0 0
\(561\) 0 0
\(562\) −324.000 561.184i −0.576512 0.998549i
\(563\) 767.915 + 443.356i 1.36397 + 0.787488i 0.990150 0.140013i \(-0.0447144\pi\)
0.373820 + 0.927501i \(0.378048\pi\)
\(564\) 0 0
\(565\) 207.000 + 358.535i 0.366372 + 0.634574i
\(566\) 125.865i 0.222376i
\(567\) 0 0
\(568\) 276.000 0.485915
\(569\) −275.568 + 159.099i −0.484302 + 0.279612i −0.722207 0.691677i \(-0.756872\pi\)
0.237906 + 0.971288i \(0.423539\pi\)
\(570\) 0 0
\(571\) 267.500 463.324i 0.468476 0.811425i −0.530875 0.847450i \(-0.678136\pi\)
0.999351 + 0.0360256i \(0.0114698\pi\)
\(572\) 22.0454 12.7279i 0.0385409 0.0222516i
\(573\) 0 0
\(574\) 0 0
\(575\) 118.794i 0.206598i
\(576\) 0 0
\(577\) 452.500 783.753i 0.784229 1.35832i −0.145230 0.989398i \(-0.546392\pi\)
0.929459 0.368926i \(-0.120274\pi\)
\(578\) −1.22474 0.707107i −0.00211894 0.00122337i
\(579\) 0 0
\(580\) −288.000 −0.496552
\(581\) 0 0
\(582\) 0 0
\(583\) 324.000 + 561.184i 0.555746 + 0.962581i
\(584\) −159.217 91.9239i −0.272632 0.157404i
\(585\) 0 0
\(586\) 48.0000 + 83.1384i 0.0819113 + 0.141874i
\(587\) 576.999i 0.982963i −0.870888 0.491481i \(-0.836456\pi\)
0.870888 0.491481i \(-0.163544\pi\)
\(588\) 0 0
\(589\) 1081.00 1.83531
\(590\) −440.908 + 254.558i −0.747302 + 0.431455i
\(591\) 0 0
\(592\) 110.000 190.526i 0.185811 0.321834i
\(593\) −481.325 + 277.893i −0.811677 + 0.468622i −0.847538 0.530735i \(-0.821916\pi\)
0.0358606 + 0.999357i \(0.488583\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 339.411i 0.569482i
\(597\) 0 0
\(598\) −12.0000 + 20.7846i −0.0200669 + 0.0347569i
\(599\) −176.363 101.823i −0.294429 0.169989i 0.345508 0.938416i \(-0.387707\pi\)
−0.639938 + 0.768427i \(0.721040\pi\)
\(600\) 0 0
\(601\) −143.000 −0.237937 −0.118968 0.992898i \(-0.537959\pi\)
−0.118968 + 0.992898i \(0.537959\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 104.000 + 180.133i 0.172185 + 0.298234i
\(605\) −150.644 86.9741i −0.248998 0.143759i
\(606\) 0 0
\(607\) 299.500 + 518.749i 0.493410 + 0.854612i 0.999971 0.00759259i \(-0.00241682\pi\)
−0.506561 + 0.862204i \(0.669083\pi\)
\(608\) 130.108i 0.213993i
\(609\) 0 0
\(610\) −624.000 −1.02295
\(611\) 3.67423 2.12132i 0.00601348 0.00347188i
\(612\) 0 0
\(613\) 152.000 263.272i 0.247961 0.429481i −0.714999 0.699125i \(-0.753573\pi\)
0.962960 + 0.269645i \(0.0869062\pi\)
\(614\) −285.366 + 164.756i −0.464765 + 0.268332i
\(615\) 0 0
\(616\) 0 0
\(617\) 292.742i 0.474461i −0.971453 0.237230i \(-0.923760\pi\)
0.971453 0.237230i \(-0.0762396\pi\)
\(618\) 0 0
\(619\) −171.500 + 297.047i −0.277060 + 0.479882i −0.970653 0.240486i \(-0.922693\pi\)
0.693593 + 0.720367i \(0.256027\pi\)
\(620\) 345.378 + 199.404i 0.557061 + 0.321620i
\(621\) 0 0
\(622\) −354.000 −0.569132
\(623\) 0 0
\(624\) 0 0
\(625\) 200.500 + 347.276i 0.320800 + 0.555642i
\(626\) −184.936 106.773i −0.295426 0.170564i
\(627\) 0 0
\(628\) −152.000 263.272i −0.242038 0.419222i
\(629\) 933.381i 1.48391i
\(630\) 0 0
\(631\) 272.000 0.431062 0.215531 0.976497i \(-0.430852\pi\)
0.215531 + 0.976497i \(0.430852\pi\)
\(632\) −276.792 + 159.806i −0.437963 + 0.252858i
\(633\) 0 0
\(634\) −288.000 + 498.831i −0.454259 + 0.786799i
\(635\) −415.189 + 239.709i −0.653840 + 0.377495i
\(636\) 0 0
\(637\) 0 0
\(638\) 610.940i 0.957587i
\(639\) 0 0
\(640\) 24.0000 41.5692i 0.0375000 0.0649519i
\(641\) 367.423 + 212.132i 0.573204 + 0.330939i 0.758428 0.651757i \(-0.225968\pi\)
−0.185224 + 0.982696i \(0.559301\pi\)
\(642\) 0 0
\(643\) 679.000 1.05599 0.527994 0.849248i \(-0.322944\pi\)
0.527994 + 0.849248i \(0.322944\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −276.000 478.046i −0.427245 0.740009i
\(647\) 834.051 + 481.540i 1.28911 + 0.744265i 0.978495 0.206272i \(-0.0661331\pi\)
0.310611 + 0.950537i \(0.399466\pi\)
\(648\) 0 0
\(649\) 540.000 + 935.307i 0.832049 + 1.44115i
\(650\) 9.89949i 0.0152300i
\(651\) 0 0
\(652\) −112.000 −0.171779
\(653\) 775.264 447.599i 1.18723 0.685450i 0.229557 0.973295i \(-0.426272\pi\)
0.957677 + 0.287846i \(0.0929390\pi\)
\(654\) 0 0
\(655\) 45.0000 77.9423i 0.0687023 0.118996i
\(656\) 161.666 93.3381i 0.246443 0.142284i
\(657\) 0 0
\(658\) 0 0
\(659\) 16.9706i 0.0257520i 0.999917 + 0.0128760i \(0.00409867\pi\)
−0.999917 + 0.0128760i \(0.995901\pi\)
\(660\) 0 0
\(661\) −216.500 + 374.989i −0.327534 + 0.567306i −0.982022 0.188767i \(-0.939551\pi\)
0.654488 + 0.756072i \(0.272884\pi\)
\(662\) 89.4064 + 51.6188i 0.135055 + 0.0779740i
\(663\) 0 0
\(664\) 84.0000 0.126506
\(665\) 0 0
\(666\) 0 0
\(667\) −288.000 498.831i −0.431784 0.747872i
\(668\) 7.34847 + 4.24264i 0.0110007 + 0.00635126i
\(669\) 0 0
\(670\) 291.000 + 504.027i 0.434328 + 0.752279i
\(671\) 1323.70i 1.97273i
\(672\) 0 0
\(673\) 737.000 1.09510 0.547548 0.836774i \(-0.315561\pi\)
0.547548 + 0.836774i \(0.315561\pi\)
\(674\) 645.441 372.645i 0.957627 0.552886i
\(675\) 0 0
\(676\) −168.000 + 290.985i −0.248521 + 0.430450i
\(677\) −117.576 + 67.8823i −0.173671 + 0.100269i −0.584316 0.811526i \(-0.698637\pi\)
0.410644 + 0.911796i \(0.365304\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 203.647i 0.299481i
\(681\) 0 0
\(682\) 423.000 732.657i 0.620235 1.07428i
\(683\) 1102.27 + 636.396i 1.61387 + 0.931766i 0.988463 + 0.151464i \(0.0483988\pi\)
0.625403 + 0.780302i \(0.284935\pi\)
\(684\) 0 0
\(685\) 288.000 0.420438
\(686\) 0 0
\(687\) 0 0
\(688\) −46.0000 79.6743i −0.0668605 0.115806i
\(689\) 44.0908 + 25.4558i 0.0639925 + 0.0369461i
\(690\) 0 0
\(691\) −123.500 213.908i −0.178726 0.309563i 0.762718 0.646731i \(-0.223864\pi\)
−0.941445 + 0.337168i \(0.890531\pi\)
\(692\) 305.470i 0.441431i
\(693\) 0 0
\(694\) 600.000 0.864553
\(695\) −378.446 + 218.496i −0.544527 + 0.314383i
\(696\) 0 0
\(697\) 396.000 685.892i 0.568149 0.984063i
\(698\) 137.171 79.1960i 0.196521 0.113461i
\(699\) 0 0
\(700\) 0 0
\(701\) 322.441i 0.459972i −0.973194 0.229986i \(-0.926132\pi\)
0.973194 0.229986i \(-0.0738681\pi\)
\(702\) 0 0
\(703\) −632.500 + 1095.52i −0.899716 + 1.55835i
\(704\) −88.1816 50.9117i −0.125258 0.0723177i
\(705\) 0 0
\(706\) −438.000 −0.620397
\(707\) 0 0
\(708\) 0 0
\(709\) 524.000 + 907.595i 0.739069 + 1.28011i 0.952915 + 0.303238i \(0.0980677\pi\)
−0.213846 + 0.976867i \(0.568599\pi\)
\(710\) −507.044 292.742i −0.714147 0.412313i
\(711\) 0 0
\(712\) 192.000 + 332.554i 0.269663 + 0.467070i
\(713\) 797.616i 1.11868i
\(714\) 0 0
\(715\) −54.0000 −0.0755245
\(716\) −7.34847 + 4.24264i −0.0102632 + 0.00592548i
\(717\) 0 0
\(718\) 360.000 623.538i 0.501393 0.868438i
\(719\) 216.780 125.158i 0.301502 0.174072i −0.341616 0.939840i \(-0.610974\pi\)
0.643117 + 0.765768i \(0.277641\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 237.588i 0.329069i
\(723\) 0 0
\(724\) 55.0000 95.2628i 0.0759669 0.131578i
\(725\) −205.757 118.794i −0.283803 0.163854i
\(726\) 0 0
\(727\) −641.000 −0.881706 −0.440853 0.897579i \(-0.645324\pi\)
−0.440853 + 0.897579i \(0.645324\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 195.000 + 337.750i 0.267123 + 0.462671i
\(731\) −338.030 195.161i −0.462421 0.266979i
\(732\) 0 0
\(733\) −12.5000 21.6506i −0.0170532 0.0295370i 0.857373 0.514696i \(-0.172095\pi\)
−0.874426 + 0.485159i \(0.838762\pi\)
\(734\) 451.134i 0.614624i
\(735\) 0 0
\(736\) 96.0000 0.130435
\(737\) 1069.20 617.304i 1.45075 0.837591i
\(738\) 0 0
\(739\) 267.500 463.324i 0.361976 0.626960i −0.626310 0.779574i \(-0.715436\pi\)
0.988286 + 0.152614i \(0.0487690\pi\)
\(740\) −404.166 + 233.345i −0.546170 + 0.315331i
\(741\) 0 0
\(742\) 0 0
\(743\) 937.624i 1.26194i 0.775806 + 0.630971i \(0.217344\pi\)
−0.775806 + 0.630971i \(0.782656\pi\)
\(744\) 0 0
\(745\) 360.000 623.538i 0.483221 0.836964i
\(746\) −255.972 147.785i −0.343126 0.198104i
\(747\) 0 0
\(748\) −432.000 −0.577540
\(749\) 0 0
\(750\) 0 0
\(751\) −20.5000 35.5070i −0.0272969 0.0472797i 0.852054 0.523454i \(-0.175357\pi\)
−0.879351 + 0.476174i \(0.842023\pi\)
\(752\) −14.6969 8.48528i −0.0195438 0.0112836i
\(753\) 0 0
\(754\) 24.0000 + 41.5692i 0.0318302 + 0.0551316i
\(755\) 441.235i 0.584417i
\(756\) 0 0
\(757\) −1114.00 −1.47160 −0.735799 0.677200i \(-0.763193\pi\)
−0.735799 + 0.677200i \(0.763193\pi\)
\(758\) −530.315 + 306.177i −0.699623 + 0.403928i
\(759\) 0 0
\(760\) −138.000 + 239.023i −0.181579 + 0.314504i
\(761\) 249.848 144.250i 0.328315 0.189553i −0.326778 0.945101i \(-0.605963\pi\)
0.655093 + 0.755548i \(0.272629\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 127.279i 0.166596i
\(765\) 0 0
\(766\) −276.000 + 478.046i −0.360313 + 0.624081i
\(767\) 73.4847 + 42.4264i 0.0958079 + 0.0553147i
\(768\) 0 0
\(769\) −1127.00 −1.46554 −0.732770 0.680477i \(-0.761773\pi\)
−0.732770 + 0.680477i \(0.761773\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −151.000 261.540i −0.195596 0.338782i
\(773\) −187.386 108.187i −0.242414 0.139958i 0.373872 0.927480i \(-0.378030\pi\)
−0.616286 + 0.787523i \(0.711363\pi\)
\(774\) 0 0
\(775\) 164.500 + 284.922i 0.212258 + 0.367642i
\(776\) 294.156i 0.379068i
\(777\) 0 0
\(778\) −522.000 −0.670951
\(779\) −929.581 + 536.694i −1.19330 + 0.688953i
\(780\) 0 0
\(781\) −621.000 + 1075.60i −0.795134 + 1.37721i
\(782\) 352.727 203.647i 0.451057 0.260418i
\(783\) 0 0
\(784\) 0 0
\(785\) 644.881i 0.821505i
\(786\) 0 0
\(787\) 85.0000 147.224i 0.108005 0.187070i −0.806957 0.590610i \(-0.798887\pi\)
0.914962 + 0.403540i \(0.132220\pi\)
\(788\) 29.3939 + 16.9706i 0.0373019 + 0.0215362i
\(789\) 0 0
\(790\) 678.000 0.858228
\(791\) 0 0
\(792\) 0 0