Properties

Label 882.3.s.a.557.1
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 557.1
Root \(1.22474 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 882.557
Dual form 882.3.s.a.863.1

$q$-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 −0.0853458 0.996351i \(-0.527199\pi\)
0.820193 + 0.572087i \(0.193866\pi\)
\(6\) 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 −0.0932057 0.995647i \(-0.529711\pi\)
−0.908858 + 0.417105i \(0.863045\pi\)
\(12\) 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 0.865525 0.500865i \(-0.166985\pi\)
−0.000999453 1.00000i \(0.500318\pi\)
\(18\) 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 −0.145231 0.989398i \(-0.546392\pi\)
0.784228 + 0.620473i \(0.213059\pi\)
\(24\) 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 \(-0.801019\pi\)
0.810895 0.585192i \(-0.198981\pi\)
\(30\) 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 \(-0.807278\pi\)
0.822244 0.569135i \(-0.192722\pi\)
\(42\) 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 −0.538578 0.842576i \(-0.681038\pi\)
0.460403 + 0.887710i \(0.347705\pi\)
\(48\) 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 0.0226013 0.999745i \(-0.492805\pi\)
−0.854504 + 0.519446i \(0.826138\pi\)
\(54\) 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 −0.275294 0.961360i \(-0.588775\pi\)
−0.970209 + 0.242268i \(0.922109\pi\)
\(60\) 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 \(-0.758845\pi\)
0.726479 0.687188i \(-0.241155\pi\)
\(72\) 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 \(-0.942744\pi\)
0.983866 0.178907i \(-0.0572560\pi\)
\(84\) 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 0.337173 0.941443i \(-0.390529\pi\)
0.983900 + 0.178721i \(0.0571958\pi\)
\(90\) 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 0.975598 0.219564i \(-0.0704633\pi\)
0.297651 + 0.954675i \(0.403797\pi\)
\(102\) 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 0.0648531 0.997895i \(-0.479342\pi\)
0.896629 + 0.442783i \(0.146009\pi\)
\(108\) 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 \(0.142112\pi\)
−0.901982 + 0.431773i \(0.857888\pi\)
\(114\) 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 −0.428239 0.903665i \(-0.640866\pi\)
0.568477 + 0.822699i \(0.307533\pi\)
\(132\) 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 0.698966 0.715154i \(-0.253644\pi\)
−0.269859 + 0.962900i \(0.586977\pi\)
\(138\) 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 0.0821839 0.996617i \(-0.473811\pi\)
0.904188 + 0.427135i \(0.140477\pi\)
\(150\) 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 \(-0.995957\pi\)
0.999919 0.0127025i \(-0.00404345\pi\)
\(168\) 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 −0.830938 0.556365i \(-0.812196\pi\)
0.0663573 + 0.997796i \(0.478862\pi\)
\(174\) 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 0.510228 0.860039i \(-0.329561\pi\)
−0.489702 + 0.871890i \(0.662894\pi\)
\(180\) 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 −0.348736 0.937221i \(-0.613389\pi\)
0.637289 + 0.770625i \(0.280056\pi\)
\(192\) 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 \(-0.986285\pi\)
0.999072 0.0430725i \(-0.0137146\pi\)
\(198\) 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 0.863295 0.504699i \(-0.168397\pi\)
−0.00543445 + 0.999985i \(0.501730\pi\)
\(228\) 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 −0.976353 0.216183i \(-0.930639\pi\)
−0.300956 + 0.953638i \(0.597306\pi\)
\(234\) 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 \(0.00847678\pi\)
−0.999645 + 0.0266275i \(0.991523\pi\)
\(240\) 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 \(-0.967662\pi\)
0.994844 0.101418i \(-0.0323379\pi\)
\(252\) 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 \(0.702103\pi\)
−0.993810 + 0.111096i \(0.964564\pi\)
\(258\) 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 0.322897 0.946434i \(-0.395343\pi\)
−0.658188 + 0.752854i \(0.728677\pi\)
\(264\) 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 −0.0330613 0.999453i \(-0.510526\pi\)
−0.882083 + 0.471095i \(0.843859\pi\)
\(270\) 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 \(0.303434\pi\)
−0.579022 + 0.815312i \(0.696566\pi\)
\(282\) 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 \(-0.963044\pi\)
0.993268 0.115840i \(-0.0369560\pi\)
\(294\) 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 0.806244 0.591582i \(-0.201497\pi\)
−0.109203 + 0.994019i \(0.534830\pi\)
\(312\) 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 0.173174 0.984891i \(-0.444598\pi\)
0.939528 + 0.342472i \(0.111264\pi\)
\(318\) 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 −0.133741 0.991016i \(-0.542699\pi\)
−0.925116 + 0.379685i \(0.876032\pi\)
\(348\) 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 0.829234 0.558902i \(-0.188777\pi\)
−0.0694063 + 0.997588i \(0.522110\pi\)
\(354\) 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 −0.966644 0.256124i \(-0.917555\pi\)
−0.261512 + 0.965200i \(0.584221\pi\)
\(360\) 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 0.0110743 0.999939i \(-0.496475\pi\)
0.871509 + 0.490379i \(0.163142\pi\)
\(384\) 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 0.851018 0.525137i \(-0.175986\pi\)
−0.0292735 + 0.999571i \(0.509319\pi\)
\(390\) 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 −0.832755 0.553641i \(-0.813238\pi\)
0.0630900 + 0.998008i \(0.479904\pi\)
\(402\) 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 \(0.368895\pi\)
−0.400333 + 0.916370i \(0.631105\pi\)
\(420\) 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 −0.0661229 0.997811i \(-0.521063\pi\)
−0.897192 + 0.441642i \(0.854396\pi\)
\(432\) 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 −0.580642 0.814159i \(-0.697198\pi\)
0.414762 + 0.909930i \(0.363865\pi\)
\(444\) 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 \(0.240224\pi\)
−0.728488 + 0.685059i \(0.759776\pi\)
\(450\) 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 \(0.0951531\pi\)
−0.955651 + 0.294500i \(0.904847\pi\)
\(462\) 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 0.385075 0.922885i \(-0.374176\pi\)
0.991780 + 0.127958i \(0.0408423\pi\)
\(468\) 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 0.0647625 0.997901i \(-0.479371\pi\)
−0.831826 + 0.555036i \(0.812704\pi\)
\(480\) 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 \(-0.933506\pi\)
0.978261 0.207380i \(-0.0664935\pi\)
\(492\) 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 \(0.199381\pi\)
−0.810159 + 0.586210i \(0.800619\pi\)
\(504\) 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 −0.691415 0.722457i \(-0.743013\pi\)
0.279959 + 0.960012i \(0.409679\pi\)
\(510\) 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 −0.415024 0.909811i \(-0.636227\pi\)
−0.995431 + 0.0954841i \(0.969560\pi\)
\(522\) 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 0.463280 0.886212i \(-0.346672\pi\)
−0.535842 + 0.844319i \(0.680006\pi\)
\(558\) 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 −0.373820 0.927501i \(-0.621952\pi\)
−0.990150 + 0.140013i \(0.955286\pi\)
\(564\) 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 −0.237906 0.971288i \(-0.576461\pi\)
0.722207 + 0.691677i \(0.243128\pi\)
\(570\) 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 \(0.163544\pi\)
−0.870888 + 0.491481i \(0.836456\pi\)
\(588\) 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 −0.0358606 0.999357i \(-0.511417\pi\)
0.847538 + 0.530735i \(0.178084\pi\)
\(594\) 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 0.639938 0.768427i \(-0.278960\pi\)
−0.345508 + 0.938416i \(0.612293\pi\)
\(600\) 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 \(0.0762396\pi\)
−0.971453 + 0.237230i \(0.923760\pi\)
\(618\) 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 0.185224 0.982696i \(-0.440699\pi\)
−0.758428 + 0.651757i \(0.774032\pi\)
\(642\) 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 −0.310611 0.950537i \(-0.600534\pi\)
−0.978495 + 0.206272i \(0.933867\pi\)
\(648\) 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 −0.957677 0.287846i \(-0.907061\pi\)
−0.229557 + 0.973295i \(0.573728\pi\)
\(654\) 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 \(-0.995901\pi\)
0.999917 0.0128760i \(-0.00409867\pi\)
\(660\) 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 −0.410644 0.911796i \(-0.634696\pi\)
0.584316 + 0.811526i \(0.301363\pi\)
\(678\) 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 \(-0.951601\pi\)
−0.625403 0.780302i \(-0.715065\pi\)
\(684\) 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 \(0.0738681\pi\)
−0.973194 + 0.229986i \(0.926132\pi\)
\(702\) 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 −0.643117 0.765768i \(-0.722359\pi\)
0.341616 + 0.939840i \(0.389026\pi\)
\(720\) 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 \(-0.782656\pi\)
0.775806 0.630971i \(-0.217344\pi\)
\(744\) 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 −0.655093 0.755548i \(-0.727371\pi\)
0.326778 + 0.945101i \(0.394037\pi\)
\(762\) 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 0.616286 0.787523i \(-0.288637\pi\)
−0.373872 + 0.927480i \(0.621970\pi\)
\(774\) 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