Newspace parameters
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
Self dual: | no |
Analytic conductor: | \(4.82290067918\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
Defining polynomial: | \(x^{20} + 60 x^{18} + 1522 x^{16} + 21286 x^{14} + 179593 x^{12} + 941588 x^{10} + 3057025 x^{8} + 5962230 x^{6} + 6517782 x^{4} + 3428244 x^{2} + 570861\) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{7}\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 58.18 | ||
Root | \(3.07256i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.58 |
Dual form | 177.3.c.a.58.3 |
$q$-expansion
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.07256i | 1.53628i | 0.640282 | + | 0.768140i | \(0.278817\pi\) | ||||
−0.640282 | + | 0.768140i | \(0.721183\pi\) | |||||||
\(3\) | 1.73205 | 0.577350 | ||||||||
\(4\) | −5.44061 | −1.36015 | ||||||||
\(5\) | −6.03179 | −1.20636 | −0.603179 | − | 0.797606i | \(-0.706099\pi\) | ||||
−0.603179 | + | 0.797606i | \(0.706099\pi\) | |||||||
\(6\) | 5.32183i | 0.886971i | ||||||||
\(7\) | −9.30133 | −1.32876 | −0.664381 | − | 0.747394i | \(-0.731305\pi\) | ||||
−0.664381 | + | 0.747394i | \(0.731305\pi\) | |||||||
\(8\) | − | 4.42637i | − | 0.553296i | ||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | − | 18.5330i | − | 1.85330i | ||||||
\(11\) | − | 12.6629i | − | 1.15117i | −0.817742 | − | 0.575584i | \(-0.804775\pi\) | ||
0.817742 | − | 0.575584i | \(-0.195225\pi\) | |||||||
\(12\) | −9.42342 | −0.785285 | ||||||||
\(13\) | 16.7819i | 1.29092i | 0.763795 | + | 0.645459i | \(0.223334\pi\) | ||||
−0.763795 | + | 0.645459i | \(0.776666\pi\) | |||||||
\(14\) | − | 28.5789i | − | 2.04135i | ||||||
\(15\) | −10.4474 | −0.696491 | ||||||||
\(16\) | −8.16217 | −0.510136 | ||||||||
\(17\) | 14.0828 | 0.828402 | 0.414201 | − | 0.910185i | \(-0.364061\pi\) | ||||
0.414201 | + | 0.910185i | \(0.364061\pi\) | |||||||
\(18\) | 9.21767i | 0.512093i | ||||||||
\(19\) | −37.4075 | −1.96882 | −0.984408 | − | 0.175902i | \(-0.943716\pi\) | ||||
−0.984408 | + | 0.175902i | \(0.943716\pi\) | |||||||
\(20\) | 32.8166 | 1.64083 | ||||||||
\(21\) | −16.1104 | −0.767161 | ||||||||
\(22\) | 38.9074 | 1.76852 | ||||||||
\(23\) | 27.8025i | 1.20881i | 0.796679 | + | 0.604403i | \(0.206588\pi\) | ||||
−0.796679 | + | 0.604403i | \(0.793412\pi\) | |||||||
\(24\) | − | 7.66670i | − | 0.319446i | ||||||
\(25\) | 11.3824 | 0.455298 | ||||||||
\(26\) | −51.5635 | −1.98321 | ||||||||
\(27\) | 5.19615 | 0.192450 | ||||||||
\(28\) | 50.6050 | 1.80732 | ||||||||
\(29\) | 39.1159 | 1.34882 | 0.674412 | − | 0.738355i | \(-0.264397\pi\) | ||||
0.674412 | + | 0.738355i | \(0.264397\pi\) | |||||||
\(30\) | − | 32.1001i | − | 1.07000i | ||||||
\(31\) | 0.257147i | 0.00829506i | 0.999991 | + | 0.00414753i | \(0.00132020\pi\) | ||||
−0.999991 | + | 0.00414753i | \(0.998680\pi\) | |||||||
\(32\) | − | 42.7842i | − | 1.33701i | ||||||
\(33\) | − | 21.9327i | − | 0.664627i | ||||||
\(34\) | 43.2703i | 1.27266i | ||||||||
\(35\) | 56.1036 | 1.60296 | ||||||||
\(36\) | −16.3218 | −0.453385 | ||||||||
\(37\) | 54.7014i | 1.47842i | 0.673477 | + | 0.739208i | \(0.264800\pi\) | ||||
−0.673477 | + | 0.739208i | \(0.735200\pi\) | |||||||
\(38\) | − | 114.937i | − | 3.02465i | ||||||
\(39\) | 29.0672i | 0.745312i | ||||||||
\(40\) | 26.6989i | 0.667473i | ||||||||
\(41\) | −11.3202 | −0.276102 | −0.138051 | − | 0.990425i | \(-0.544084\pi\) | ||||
−0.138051 | + | 0.990425i | \(0.544084\pi\) | |||||||
\(42\) | − | 49.5001i | − | 1.17857i | ||||||
\(43\) | 7.36421i | 0.171261i | 0.996327 | + | 0.0856303i | \(0.0272904\pi\) | ||||
−0.996327 | + | 0.0856303i | \(0.972710\pi\) | |||||||
\(44\) | 68.8937i | 1.56577i | ||||||||
\(45\) | −18.0954 | −0.402119 | ||||||||
\(46\) | −85.4249 | −1.85706 | ||||||||
\(47\) | 28.7287i | 0.611248i | 0.952152 | + | 0.305624i | \(0.0988651\pi\) | ||||
−0.952152 | + | 0.305624i | \(0.901135\pi\) | |||||||
\(48\) | −14.1373 | −0.294527 | ||||||||
\(49\) | 37.5148 | 0.765608 | ||||||||
\(50\) | 34.9732i | 0.699464i | ||||||||
\(51\) | 24.3922 | 0.478278 | ||||||||
\(52\) | − | 91.3041i | − | 1.75585i | ||||||
\(53\) | −47.3053 | −0.892552 | −0.446276 | − | 0.894895i | \(-0.647250\pi\) | ||||
−0.446276 | + | 0.894895i | \(0.647250\pi\) | |||||||
\(54\) | 15.9655i | 0.295657i | ||||||||
\(55\) | 76.3796i | 1.38872i | ||||||||
\(56\) | 41.1711i | 0.735199i | ||||||||
\(57\) | −64.7917 | −1.13670 | ||||||||
\(58\) | 120.186i | 2.07217i | ||||||||
\(59\) | −28.6844 | + | 51.5578i | −0.486176 | + | 0.873861i | ||||
\(60\) | 56.8401 | 0.947334 | ||||||||
\(61\) | − | 84.0505i | − | 1.37788i | −0.724820 | − | 0.688938i | \(-0.758077\pi\) | ||
0.724820 | − | 0.688938i | \(-0.241923\pi\) | |||||||
\(62\) | −0.790099 | −0.0127435 | ||||||||
\(63\) | −27.9040 | −0.442921 | ||||||||
\(64\) | 98.8084 | 1.54388 | ||||||||
\(65\) | − | 101.225i | − | 1.55731i | ||||||
\(66\) | 67.3895 | 1.02105 | ||||||||
\(67\) | − | 81.5123i | − | 1.21660i | −0.793707 | − | 0.608300i | \(-0.791852\pi\) | ||
0.793707 | − | 0.608300i | \(-0.208148\pi\) | |||||||
\(68\) | −76.6193 | −1.12675 | ||||||||
\(69\) | 48.1554i | 0.697905i | ||||||||
\(70\) | 172.382i | 2.46260i | ||||||||
\(71\) | −6.96917 | −0.0981573 | −0.0490787 | − | 0.998795i | \(-0.515628\pi\) | ||||
−0.0490787 | + | 0.998795i | \(0.515628\pi\) | |||||||
\(72\) | − | 13.2791i | − | 0.184432i | ||||||
\(73\) | 131.681i | 1.80385i | 0.431896 | + | 0.901923i | \(0.357845\pi\) | ||||
−0.431896 | + | 0.901923i | \(0.642155\pi\) | |||||||
\(74\) | −168.073 | −2.27126 | ||||||||
\(75\) | 19.7150 | 0.262866 | ||||||||
\(76\) | 203.520 | 2.67789 | ||||||||
\(77\) | 117.781i | 1.52963i | ||||||||
\(78\) | −89.3106 | −1.14501 | ||||||||
\(79\) | 51.9880 | 0.658076 | 0.329038 | − | 0.944317i | \(-0.393276\pi\) | ||||
0.329038 | + | 0.944317i | \(0.393276\pi\) | |||||||
\(80\) | 49.2325 | 0.615406 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | − | 34.7820i | − | 0.424170i | ||||||
\(83\) | 16.5553i | 0.199461i | 0.995014 | + | 0.0997305i | \(0.0317981\pi\) | ||||
−0.995014 | + | 0.0997305i | \(0.968202\pi\) | |||||||
\(84\) | 87.6504 | 1.04346 | ||||||||
\(85\) | −84.9447 | −0.999349 | ||||||||
\(86\) | −22.6270 | −0.263104 | ||||||||
\(87\) | 67.7508 | 0.778744 | ||||||||
\(88\) | −56.0505 | −0.636937 | ||||||||
\(89\) | 69.2544i | 0.778139i | 0.921208 | + | 0.389070i | \(0.127203\pi\) | ||||
−0.921208 | + | 0.389070i | \(0.872797\pi\) | |||||||
\(90\) | − | 55.5990i | − | 0.617767i | ||||||
\(91\) | − | 156.094i | − | 1.71532i | ||||||
\(92\) | − | 151.263i | − | 1.64416i | ||||||
\(93\) | 0.445392i | 0.00478916i | ||||||||
\(94\) | −88.2705 | −0.939048 | ||||||||
\(95\) | 225.634 | 2.37509 | ||||||||
\(96\) | − | 74.1045i | − | 0.771922i | ||||||
\(97\) | − | 110.495i | − | 1.13912i | −0.821949 | − | 0.569560i | \(-0.807113\pi\) | ||
0.821949 | − | 0.569560i | \(-0.192887\pi\) | |||||||
\(98\) | 115.266i | 1.17619i | ||||||||
\(99\) | − | 37.9886i | − | 0.383723i | ||||||
\(100\) | −61.9275 | −0.619275 | ||||||||
\(101\) | − | 159.617i | − | 1.58037i | −0.612868 | − | 0.790186i | \(-0.709984\pi\) | ||
0.612868 | − | 0.790186i | \(-0.290016\pi\) | |||||||
\(102\) | 74.9464i | 0.734769i | ||||||||
\(103\) | − | 26.7475i | − | 0.259684i | −0.991535 | − | 0.129842i | \(-0.958553\pi\) | ||
0.991535 | − | 0.129842i | \(-0.0414470\pi\) | |||||||
\(104\) | 74.2831 | 0.714260 | ||||||||
\(105\) | 97.1744 | 0.925470 | ||||||||
\(106\) | − | 145.348i | − | 1.37121i | ||||||
\(107\) | −35.3863 | −0.330713 | −0.165356 | − | 0.986234i | \(-0.552877\pi\) | ||||
−0.165356 | + | 0.986234i | \(0.552877\pi\) | |||||||
\(108\) | −28.2703 | −0.261762 | ||||||||
\(109\) | 68.2150i | 0.625826i | 0.949782 | + | 0.312913i | \(0.101305\pi\) | ||||
−0.949782 | + | 0.312913i | \(0.898695\pi\) | |||||||
\(110\) | −234.681 | −2.13346 | ||||||||
\(111\) | 94.7456i | 0.853564i | ||||||||
\(112\) | 75.9191 | 0.677849 | ||||||||
\(113\) | − | 120.908i | − | 1.06998i | −0.844858 | − | 0.534990i | \(-0.820315\pi\) | ||
0.844858 | − | 0.534990i | \(-0.179685\pi\) | |||||||
\(114\) | − | 199.076i | − | 1.74628i | ||||||
\(115\) | − | 167.699i | − | 1.45825i | ||||||
\(116\) | −212.815 | −1.83461 | ||||||||
\(117\) | 50.3458i | 0.430306i | ||||||||
\(118\) | −158.414 | − | 88.1345i | −1.34249 | − | 0.746902i | ||||
\(119\) | −130.989 | −1.10075 | ||||||||
\(120\) | 46.2439i | 0.385366i | ||||||||
\(121\) | −39.3479 | −0.325189 | ||||||||
\(122\) | 258.250 | 2.11680 | ||||||||
\(123\) | −19.6072 | −0.159408 | ||||||||
\(124\) | − | 1.39904i | − | 0.0112826i | ||||||
\(125\) | 82.1382 | 0.657105 | ||||||||
\(126\) | − | 85.7367i | − | 0.680450i | ||||||
\(127\) | −158.088 | −1.24479 | −0.622393 | − | 0.782705i | \(-0.713839\pi\) | ||||
−0.622393 | + | 0.782705i | \(0.713839\pi\) | |||||||
\(128\) | 132.458i | 1.03482i | ||||||||
\(129\) | 12.7552i | 0.0988774i | ||||||||
\(130\) | 311.020 | 2.39246 | ||||||||
\(131\) | 130.513i | 0.996282i | 0.867096 | + | 0.498141i | \(0.165984\pi\) | ||||
−0.867096 | + | 0.498141i | \(0.834016\pi\) | |||||||
\(132\) | 119.327i | 0.903995i | ||||||||
\(133\) | 347.939 | 2.61609 | ||||||||
\(134\) | 250.451 | 1.86904 | ||||||||
\(135\) | −31.3421 | −0.232164 | ||||||||
\(136\) | − | 62.3359i | − | 0.458352i | ||||||
\(137\) | 208.921 | 1.52497 | 0.762487 | − | 0.647004i | \(-0.223978\pi\) | ||||
0.762487 | + | 0.647004i | \(0.223978\pi\) | |||||||
\(138\) | −147.960 | −1.07218 | ||||||||
\(139\) | −73.8315 | −0.531162 | −0.265581 | − | 0.964089i | \(-0.585564\pi\) | ||||
−0.265581 | + | 0.964089i | \(0.585564\pi\) | |||||||
\(140\) | −305.238 | −2.18027 | ||||||||
\(141\) | 49.7595i | 0.352904i | ||||||||
\(142\) | − | 21.4132i | − | 0.150797i | ||||||
\(143\) | 212.507 | 1.48606 | ||||||||
\(144\) | −24.4865 | −0.170045 | ||||||||
\(145\) | −235.939 | −1.62716 | ||||||||
\(146\) | −404.597 | −2.77121 | ||||||||
\(147\) | 64.9775 | 0.442024 | ||||||||
\(148\) | − | 297.609i | − | 2.01087i | ||||||
\(149\) | 66.3172i | 0.445082i | 0.974923 | + | 0.222541i | \(0.0714351\pi\) | ||||
−0.974923 | + | 0.222541i | \(0.928565\pi\) | |||||||
\(150\) | 60.5754i | 0.403836i | ||||||||
\(151\) | 103.185i | 0.683347i | 0.939819 | + | 0.341673i | \(0.110994\pi\) | ||||
−0.939819 | + | 0.341673i | \(0.889006\pi\) | |||||||
\(152\) | 165.579i | 1.08934i | ||||||||
\(153\) | 42.2485 | 0.276134 | ||||||||
\(154\) | −361.890 | −2.34994 | ||||||||
\(155\) | − | 1.55106i | − | 0.0100068i | ||||||
\(156\) | − | 158.143i | − | 1.01374i | ||||||
\(157\) | 251.051i | 1.59905i | 0.600630 | + | 0.799527i | \(0.294916\pi\) | ||||
−0.600630 | + | 0.799527i | \(0.705084\pi\) | |||||||
\(158\) | 159.736i | 1.01099i | ||||||||
\(159\) | −81.9351 | −0.515315 | ||||||||
\(160\) | 258.065i | 1.61291i | ||||||||
\(161\) | − | 258.601i | − | 1.60622i | ||||||
\(162\) | 27.6530i | 0.170698i | ||||||||
\(163\) | −96.4209 | −0.591539 | −0.295770 | − | 0.955259i | \(-0.595576\pi\) | ||||
−0.295770 | + | 0.955259i | \(0.595576\pi\) | |||||||
\(164\) | 61.5888 | 0.375542 | ||||||||
\(165\) | 132.293i | 0.801778i | ||||||||
\(166\) | −50.8670 | −0.306428 | ||||||||
\(167\) | 78.3907 | 0.469405 | 0.234703 | − | 0.972067i | \(-0.424588\pi\) | ||||
0.234703 | + | 0.972067i | \(0.424588\pi\) | |||||||
\(168\) | 71.3105i | 0.424467i | ||||||||
\(169\) | −112.633 | −0.666470 | ||||||||
\(170\) | − | 260.997i | − | 1.53528i | ||||||
\(171\) | −112.222 | −0.656272 | ||||||||
\(172\) | − | 40.0658i | − | 0.232941i | ||||||
\(173\) | 52.2561i | 0.302058i | 0.988529 | + | 0.151029i | \(0.0482587\pi\) | ||||
−0.988529 | + | 0.151029i | \(0.951741\pi\) | |||||||
\(174\) | 208.168i | 1.19637i | ||||||||
\(175\) | −105.872 | −0.604982 | ||||||||
\(176\) | 103.356i | 0.587252i | ||||||||
\(177\) | −49.6828 | + | 89.3007i | −0.280694 | + | 0.504524i | ||||
\(178\) | −212.788 | −1.19544 | ||||||||
\(179\) | − | 117.505i | − | 0.656453i | −0.944599 | − | 0.328226i | \(-0.893549\pi\) | ||
0.944599 | − | 0.328226i | \(-0.106451\pi\) | |||||||
\(180\) | 98.4499 | 0.546944 | ||||||||
\(181\) | 160.180 | 0.884972 | 0.442486 | − | 0.896776i | \(-0.354097\pi\) | ||||
0.442486 | + | 0.896776i | \(0.354097\pi\) | |||||||
\(182\) | 479.609 | 2.63521 | ||||||||
\(183\) | − | 145.580i | − | 0.795517i | ||||||
\(184\) | 123.064 | 0.668828 | ||||||||
\(185\) | − | 329.947i | − | 1.78350i | ||||||
\(186\) | −1.36849 | −0.00735748 | ||||||||
\(187\) | − | 178.329i | − | 0.953630i | ||||||
\(188\) | − | 156.302i | − | 0.831391i | ||||||
\(189\) | −48.3311 | −0.255720 | ||||||||
\(190\) | 693.274i | 3.64881i | ||||||||
\(191\) | − | 14.2938i | − | 0.0748369i | −0.999300 | − | 0.0374184i | \(-0.988087\pi\) | ||
0.999300 | − | 0.0374184i | \(-0.0119134\pi\) | |||||||
\(192\) | 171.141 | 0.891360 | ||||||||
\(193\) | 71.9463 | 0.372779 | 0.186389 | − | 0.982476i | \(-0.440321\pi\) | ||||
0.186389 | + | 0.982476i | \(0.440321\pi\) | |||||||
\(194\) | 339.501 | 1.75001 | ||||||||
\(195\) | − | 175.327i | − | 0.899113i | ||||||
\(196\) | −204.103 | −1.04134 | ||||||||
\(197\) | −44.5489 | −0.226137 | −0.113068 | − | 0.993587i | \(-0.536068\pi\) | ||||
−0.113068 | + | 0.993587i | \(0.536068\pi\) | |||||||
\(198\) | 116.722 | 0.589505 | ||||||||
\(199\) | −125.217 | −0.629233 | −0.314617 | − | 0.949219i | \(-0.601876\pi\) | ||||
−0.314617 | + | 0.949219i | \(0.601876\pi\) | |||||||
\(200\) | − | 50.3829i | − | 0.251915i | ||||||
\(201\) | − | 141.183i | − | 0.702405i | ||||||
\(202\) | 490.434 | 2.42789 | ||||||||
\(203\) | −363.830 | −1.79227 | ||||||||
\(204\) | −132.708 | −0.650532 | ||||||||
\(205\) | 68.2810 | 0.333078 | ||||||||
\(206\) | 82.1831 | 0.398947 | ||||||||
\(207\) | 83.4076i | 0.402935i | ||||||||
\(208\) | − | 136.977i | − | 0.658544i | ||||||
\(209\) | 473.686i | 2.26644i | ||||||||
\(210\) | 298.574i | 1.42178i | ||||||||
\(211\) | − | 106.781i | − | 0.506071i | −0.967457 | − | 0.253035i | \(-0.918571\pi\) | ||
0.967457 | − | 0.253035i | \(-0.0814289\pi\) | |||||||
\(212\) | 257.370 | 1.21401 | ||||||||
\(213\) | −12.0710 | −0.0566711 | ||||||||
\(214\) | − | 108.726i | − | 0.508067i | ||||||
\(215\) | − | 44.4193i | − | 0.206602i | ||||||
\(216\) | − | 23.0001i | − | 0.106482i | ||||||
\(217\) | − | 2.39181i | − | 0.0110222i | ||||||
\(218\) | −209.595 | −0.961443 | ||||||||
\(219\) | 228.078i | 1.04145i | ||||||||
\(220\) | − | 415.552i | − | 1.88887i | ||||||
\(221\) | 236.337i | 1.06940i | ||||||||
\(222\) | −291.111 | −1.31131 | ||||||||
\(223\) | −37.6647 | −0.168900 | −0.0844501 | − | 0.996428i | \(-0.526913\pi\) | ||||
−0.0844501 | + | 0.996428i | \(0.526913\pi\) | |||||||
\(224\) | 397.950i | 1.77656i | ||||||||
\(225\) | 34.1473 | 0.151766 | ||||||||
\(226\) | 371.496 | 1.64379 | ||||||||
\(227\) | − | 189.636i | − | 0.835399i | −0.908585 | − | 0.417699i | \(-0.862837\pi\) | ||
0.908585 | − | 0.417699i | \(-0.137163\pi\) | |||||||
\(228\) | 352.507 | 1.54608 | ||||||||
\(229\) | 206.938i | 0.903658i | 0.892104 | + | 0.451829i | \(0.149228\pi\) | ||||
−0.892104 | + | 0.451829i | \(0.850772\pi\) | |||||||
\(230\) | 515.265 | 2.24028 | ||||||||
\(231\) | 204.003i | 0.883131i | ||||||||
\(232\) | − | 173.142i | − | 0.746300i | ||||||
\(233\) | 213.272i | 0.915330i | 0.889125 | + | 0.457665i | \(0.151314\pi\) | ||||
−0.889125 | + | 0.457665i | \(0.848686\pi\) | |||||||
\(234\) | −154.690 | −0.661070 | ||||||||
\(235\) | − | 173.285i | − | 0.737384i | ||||||
\(236\) | 156.061 | − | 280.506i | 0.661274 | − | 1.18858i | ||||
\(237\) | 90.0458 | 0.379940 | ||||||||
\(238\) | − | 402.472i | − | 1.69106i | ||||||
\(239\) | −142.148 | −0.594760 | −0.297380 | − | 0.954759i | \(-0.596113\pi\) | ||||
−0.297380 | + | 0.954759i | \(0.596113\pi\) | |||||||
\(240\) | 85.2732 | 0.355305 | ||||||||
\(241\) | −391.267 | −1.62351 | −0.811756 | − | 0.583996i | \(-0.801488\pi\) | ||||
−0.811756 | + | 0.583996i | \(0.801488\pi\) | |||||||
\(242\) | − | 120.899i | − | 0.499581i | ||||||
\(243\) | 15.5885 | 0.0641500 | ||||||||
\(244\) | 457.286i | 1.87412i | ||||||||
\(245\) | −226.281 | −0.923596 | ||||||||
\(246\) | − | 60.2441i | − | 0.244895i | ||||||
\(247\) | − | 627.770i | − | 2.54158i | ||||||
\(248\) | 1.13823 | 0.00458963 | ||||||||
\(249\) | 28.6745i | 0.115159i | ||||||||
\(250\) | 252.374i | 1.00950i | ||||||||
\(251\) | 135.007 | 0.537877 | 0.268938 | − | 0.963157i | \(-0.413327\pi\) | ||||
0.268938 | + | 0.963157i | \(0.413327\pi\) | |||||||
\(252\) | 151.815 | 0.602440 | ||||||||
\(253\) | 352.060 | 1.39154 | ||||||||
\(254\) | − | 485.734i | − | 1.91234i | ||||||
\(255\) | −147.128 | −0.576974 | ||||||||
\(256\) | −11.7500 | −0.0458983 | ||||||||
\(257\) | −133.333 | −0.518807 | −0.259403 | − | 0.965769i | \(-0.583526\pi\) | ||||
−0.259403 | + | 0.965769i | \(0.583526\pi\) | |||||||
\(258\) | −39.1910 | −0.151903 | ||||||||
\(259\) | − | 508.796i | − | 1.96446i | ||||||
\(260\) | 550.727i | 2.11818i | ||||||||
\(261\) | 117.348 | 0.449608 | ||||||||
\(262\) | −401.009 | −1.53057 | ||||||||
\(263\) | 272.345 | 1.03553 | 0.517765 | − | 0.855523i | \(-0.326764\pi\) | ||||
0.517765 | + | 0.855523i | \(0.326764\pi\) | |||||||
\(264\) | −97.0823 | −0.367736 | ||||||||
\(265\) | 285.335 | 1.07674 | ||||||||
\(266\) | 1069.06i | 4.01904i | ||||||||
\(267\) | 119.952i | 0.449259i | ||||||||
\(268\) | 443.477i | 1.65476i | ||||||||
\(269\) | 275.151i | 1.02287i | 0.859323 | + | 0.511434i | \(0.170886\pi\) | ||||
−0.859323 | + | 0.511434i | \(0.829114\pi\) | |||||||
\(270\) | − | 96.3004i | − | 0.356668i | ||||||
\(271\) | −142.359 | −0.525308 | −0.262654 | − | 0.964890i | \(-0.584598\pi\) | ||||
−0.262654 | + | 0.964890i | \(0.584598\pi\) | |||||||
\(272\) | −114.947 | −0.422598 | ||||||||
\(273\) | − | 270.363i | − | 0.990342i | ||||||
\(274\) | 641.923i | 2.34278i | ||||||||
\(275\) | − | 144.134i | − | 0.524124i | ||||||
\(276\) | − | 261.995i | − | 0.949257i | ||||||
\(277\) | −282.049 | −1.01823 | −0.509114 | − | 0.860699i | \(-0.670027\pi\) | ||||
−0.509114 | + | 0.860699i | \(0.670027\pi\) | |||||||
\(278\) | − | 226.852i | − | 0.816013i | ||||||
\(279\) | 0.771441i | 0.00276502i | ||||||||
\(280\) | − | 248.336i | − | 0.886913i | ||||||
\(281\) | −273.179 | −0.972168 | −0.486084 | − | 0.873912i | \(-0.661575\pi\) | ||||
−0.486084 | + | 0.873912i | \(0.661575\pi\) | |||||||
\(282\) | −152.889 | −0.542159 | ||||||||
\(283\) | 240.930i | 0.851343i | 0.904878 | + | 0.425671i | \(0.139962\pi\) | ||||
−0.904878 | + | 0.425671i | \(0.860038\pi\) | |||||||
\(284\) | 37.9166 | 0.133509 | ||||||||
\(285\) | 390.810 | 1.37126 | ||||||||
\(286\) | 652.941i | 2.28301i | ||||||||
\(287\) | 105.293 | 0.366874 | ||||||||
\(288\) | − | 128.353i | − | 0.445669i | ||||||
\(289\) | −90.6737 | −0.313750 | ||||||||
\(290\) | − | 724.936i | − | 2.49978i | ||||||
\(291\) | − | 191.382i | − | 0.657672i | ||||||
\(292\) | − | 716.424i | − | 2.45351i | ||||||
\(293\) | −321.271 | −1.09649 | −0.548245 | − | 0.836318i | \(-0.684704\pi\) | ||||
−0.548245 | + | 0.836318i | \(0.684704\pi\) | |||||||
\(294\) | 199.647i | 0.679072i | ||||||||
\(295\) | 173.018 | − | 310.986i | 0.586502 | − | 1.05419i | ||||
\(296\) | 242.129 | 0.818002 | ||||||||
\(297\) | − | 65.7981i | − | 0.221542i | ||||||
\(298\) | −203.763 | −0.683770 | ||||||||
\(299\) | −466.581 | −1.56047 | ||||||||
\(300\) | −107.262 | −0.357539 | ||||||||
\(301\) | − | 68.4969i | − | 0.227565i | ||||||
\(302\) | −317.043 | −1.04981 | ||||||||
\(303\) | − | 276.466i | − | 0.912428i | ||||||
\(304\) | 305.326 | 1.00436 | ||||||||
\(305\) | 506.974i | 1.66221i | ||||||||
\(306\) | 129.811i | 0.424219i | ||||||||
\(307\) | −569.638 | −1.85550 | −0.927750 | − | 0.373203i | \(-0.878259\pi\) | ||||
−0.927750 | + | 0.373203i | \(0.878259\pi\) | |||||||
\(308\) | − | 640.803i | − | 2.08053i | ||||||
\(309\) | − | 46.3280i | − | 0.149929i | ||||||
\(310\) | 4.76571 | 0.0153733 | ||||||||
\(311\) | −357.447 | −1.14935 | −0.574673 | − | 0.818383i | \(-0.694871\pi\) | ||||
−0.574673 | + | 0.818383i | \(0.694871\pi\) | |||||||
\(312\) | 128.662 | 0.412378 | ||||||||
\(313\) | 540.979i | 1.72837i | 0.503176 | + | 0.864184i | \(0.332165\pi\) | ||||
−0.503176 | + | 0.864184i | \(0.667835\pi\) | |||||||
\(314\) | −771.370 | −2.45659 | ||||||||
\(315\) | 168.311 | 0.534320 | ||||||||
\(316\) | −282.847 | −0.895084 | ||||||||
\(317\) | 431.328 | 1.36066 | 0.680328 | − | 0.732908i | \(-0.261837\pi\) | ||||
0.680328 | + | 0.732908i | \(0.261837\pi\) | |||||||
\(318\) | − | 251.750i | − | 0.791668i | ||||||
\(319\) | − | 495.319i | − | 1.55272i | ||||||
\(320\) | −595.991 | −1.86247 | ||||||||
\(321\) | −61.2908 | −0.190937 | ||||||||
\(322\) | 794.566 | 2.46760 | ||||||||
\(323\) | −526.804 | −1.63097 | ||||||||
\(324\) | −48.9655 | −0.151128 | ||||||||
\(325\) | 191.019i | 0.587752i | ||||||||
\(326\) | − | 296.259i | − | 0.908770i | ||||||
\(327\) | 118.152i | 0.361321i | ||||||||
\(328\) | 50.1074i | 0.152766i | ||||||||
\(329\) | − | 267.215i | − | 0.812203i | ||||||
\(330\) | −406.479 | −1.23176 | ||||||||
\(331\) | 241.399 | 0.729301 | 0.364650 | − | 0.931145i | \(-0.381189\pi\) | ||||
0.364650 | + | 0.931145i | \(0.381189\pi\) | |||||||
\(332\) | − | 90.0708i | − | 0.271297i | ||||||
\(333\) | 164.104i | 0.492805i | ||||||||
\(334\) | 240.860i | 0.721138i | ||||||||
\(335\) | 491.664i | 1.46766i | ||||||||
\(336\) | 131.496 | 0.391356 | ||||||||
\(337\) | − | 122.088i | − | 0.362278i | −0.983457 | − | 0.181139i | \(-0.942022\pi\) | ||
0.983457 | − | 0.181139i | \(-0.0579784\pi\) | |||||||
\(338\) | − | 346.073i | − | 1.02388i | ||||||
\(339\) | − | 209.419i | − | 0.617754i | ||||||
\(340\) | 462.151 | 1.35927 | ||||||||
\(341\) | 3.25621 | 0.00954901 | ||||||||
\(342\) | − | 344.810i | − | 1.00822i | ||||||
\(343\) | 106.828 | 0.311452 | ||||||||
\(344\) | 32.5967 | 0.0947579 | ||||||||
\(345\) | − | 290.463i | − | 0.841922i | ||||||
\(346\) | −160.560 | −0.464046 | ||||||||
\(347\) | − | 403.930i | − | 1.16406i | −0.813166 | − | 0.582032i | \(-0.802258\pi\) | ||
0.813166 | − | 0.582032i | \(-0.197742\pi\) | |||||||
\(348\) | −368.606 | −1.05921 | ||||||||
\(349\) | 449.445i | 1.28781i | 0.765106 | + | 0.643904i | \(0.222686\pi\) | ||||
−0.765106 | + | 0.643904i | \(0.777314\pi\) | |||||||
\(350\) | − | 325.298i | − | 0.929422i | ||||||
\(351\) | 87.2015i | 0.248437i | ||||||||
\(352\) | −541.771 | −1.53912 | ||||||||
\(353\) | 213.176i | 0.603899i | 0.953324 | + | 0.301950i | \(0.0976374\pi\) | ||||
−0.953324 | + | 0.301950i | \(0.902363\pi\) | |||||||
\(354\) | −274.382 | − | 152.653i | −0.775089 | − | 0.431224i | ||||
\(355\) | 42.0365 | 0.118413 | ||||||||
\(356\) | − | 376.786i | − | 1.05839i | ||||||
\(357\) | −226.880 | −0.635518 | ||||||||
\(358\) | 361.041 | 1.00849 | ||||||||
\(359\) | 405.372 | 1.12917 | 0.564585 | − | 0.825375i | \(-0.309036\pi\) | ||||
0.564585 | + | 0.825375i | \(0.309036\pi\) | |||||||
\(360\) | 80.0968i | 0.222491i | ||||||||
\(361\) | 1038.32 | 2.87623 | ||||||||
\(362\) | 492.162i | 1.35956i | ||||||||
\(363\) | −68.1525 | −0.187748 | ||||||||
\(364\) | 849.249i | 2.33310i | ||||||||
\(365\) | − | 794.270i | − | 2.17608i | ||||||
\(366\) | 447.302 | 1.22214 | ||||||||
\(367\) | 541.192i | 1.47464i | 0.675546 | + | 0.737318i | \(0.263908\pi\) | ||||
−0.675546 | + | 0.737318i | \(0.736092\pi\) | |||||||
\(368\) | − | 226.929i | − | 0.616655i | ||||||
\(369\) | −33.9606 | −0.0920341 | ||||||||
\(370\) | 1013.78 | 2.73995 | ||||||||
\(371\) | 440.002 | 1.18599 | ||||||||
\(372\) | − | 2.42320i | − | 0.00651399i | ||||||
\(373\) | −107.068 | −0.287046 | −0.143523 | − | 0.989647i | \(-0.545843\pi\) | ||||
−0.143523 | + | 0.989647i | \(0.545843\pi\) | |||||||
\(374\) | 547.926 | 1.46504 | ||||||||
\(375\) | 142.268 | 0.379380 | ||||||||
\(376\) | 127.164 | 0.338201 | ||||||||
\(377\) | 656.441i | 1.74122i | ||||||||
\(378\) | − | 148.500i | − | 0.392858i | ||||||
\(379\) | −204.702 | −0.540112 | −0.270056 | − | 0.962845i | \(-0.587042\pi\) | ||||
−0.270056 | + | 0.962845i | \(0.587042\pi\) | |||||||
\(380\) | −1227.59 | −3.23049 | ||||||||
\(381\) | −273.816 | −0.718678 | ||||||||
\(382\) | 43.9187 | 0.114970 | ||||||||
\(383\) | −4.98048 | −0.0130039 | −0.00650193 | − | 0.999979i | \(-0.502070\pi\) | ||||
−0.00650193 | + | 0.999979i | \(0.502070\pi\) | |||||||
\(384\) | 229.423i | 0.597456i | ||||||||
\(385\) | − | 710.432i | − | 1.84528i | ||||||
\(386\) | 221.059i | 0.572692i | ||||||||
\(387\) | 22.0926i | 0.0570869i | ||||||||
\(388\) | 601.159i | 1.54938i | ||||||||
\(389\) | 138.904 | 0.357079 | 0.178539 | − | 0.983933i | \(-0.442863\pi\) | ||||
0.178539 | + | 0.983933i | \(0.442863\pi\) | |||||||
\(390\) | 538.702 | 1.38129 | ||||||||
\(391\) | 391.539i | 1.00138i | ||||||||
\(392\) | − | 166.054i | − | 0.423608i | ||||||
\(393\) | 226.055i | 0.575204i | ||||||||
\(394\) | − | 136.879i | − | 0.347409i | ||||||
\(395\) | −313.580 | −0.793874 | ||||||||
\(396\) | 206.681i | 0.521922i | ||||||||
\(397\) | − | 266.530i | − | 0.671359i | −0.941976 | − | 0.335679i | \(-0.891034\pi\) | ||
0.941976 | − | 0.335679i | \(-0.108966\pi\) | |||||||
\(398\) | − | 384.738i | − | 0.966678i | ||||||
\(399\) | 602.649 | 1.51040 | ||||||||
\(400\) | −92.9055 | −0.232264 | ||||||||
\(401\) | 515.725i | 1.28610i | 0.765825 | + | 0.643049i | \(0.222331\pi\) | ||||
−0.765825 | + | 0.643049i | \(0.777669\pi\) | |||||||
\(402\) | 433.794 | 1.07909 | ||||||||
\(403\) | −4.31542 | −0.0107082 | ||||||||
\(404\) | 868.417i | 2.14955i | ||||||||
\(405\) | −54.2861 | −0.134040 | ||||||||
\(406\) | − | 1117.89i | − | 2.75342i | ||||||
\(407\) | 692.676 | 1.70191 | ||||||||
\(408\) | − | 107.969i | − | 0.264630i | ||||||
\(409\) | 53.2453i | 0.130184i | 0.997879 | + | 0.0650920i | \(0.0207341\pi\) | ||||
−0.997879 | + | 0.0650920i | \(0.979266\pi\) | |||||||
\(410\) | 209.797i | 0.511701i | ||||||||
\(411\) | 361.862 | 0.880444 | ||||||||
\(412\) | 145.523i | 0.353210i | ||||||||
\(413\) | 266.803 | − | 479.556i | 0.646012 | − | 1.16115i | ||||
\(414\) | −256.275 | −0.619021 | ||||||||
\(415\) | − | 99.8578i | − | 0.240621i | ||||||
\(416\) | 718.002 | 1.72597 | ||||||||
\(417\) | −127.880 | −0.306667 | ||||||||
\(418\) | −1455.43 | −3.48188 | ||||||||
\(419\) | − | 275.166i | − | 0.656721i | −0.944553 | − | 0.328360i | \(-0.893504\pi\) | ||
0.944553 | − | 0.328360i | \(-0.106496\pi\) | |||||||
\(420\) | −528.688 | −1.25878 | ||||||||
\(421\) | − | 508.314i | − | 1.20740i | −0.797213 | − | 0.603699i | \(-0.793693\pi\) | ||
0.797213 | − | 0.603699i | \(-0.206307\pi\) | |||||||
\(422\) | 328.091 | 0.777466 | ||||||||
\(423\) | 86.1860i | 0.203749i | ||||||||
\(424\) | 209.391i | 0.493846i | ||||||||
\(425\) | 160.297 | 0.377170 | ||||||||
\(426\) | − | 37.0887i | − | 0.0870627i | ||||||
\(427\) | 781.781i | 1.83087i | ||||||||
\(428\) | 192.523 | 0.449820 | ||||||||
\(429\) | 368.073 | 0.857980 | ||||||||
\(430\) | 136.481 | 0.317398 | ||||||||
\(431\) | 331.069i | 0.768141i | 0.923304 | + | 0.384070i | \(0.125478\pi\) | ||||
−0.923304 | + | 0.384070i | \(0.874522\pi\) | |||||||
\(432\) | −42.4119 | −0.0981757 | ||||||||
\(433\) | 216.406 | 0.499783 | 0.249891 | − | 0.968274i | \(-0.419605\pi\) | ||||
0.249891 | + | 0.968274i | \(0.419605\pi\) | |||||||
\(434\) | 7.34897 | 0.0169331 | ||||||||
\(435\) | −408.658 | −0.939444 | ||||||||
\(436\) | − | 371.132i | − | 0.851219i | ||||||
\(437\) | − | 1040.02i | − | 2.37992i | ||||||
\(438\) | −700.782 | −1.59996 | ||||||||
\(439\) | 594.843 | 1.35500 | 0.677498 | − | 0.735525i | \(-0.263064\pi\) | ||||
0.677498 | + | 0.735525i | \(0.263064\pi\) | |||||||
\(440\) | 338.085 | 0.768374 | ||||||||
\(441\) | 112.544 | 0.255203 | ||||||||
\(442\) | −726.160 | −1.64290 | ||||||||
\(443\) | − | 101.223i | − | 0.228495i | −0.993452 | − | 0.114247i | \(-0.963554\pi\) | ||
0.993452 | − | 0.114247i | \(-0.0364456\pi\) | |||||||
\(444\) | − | 515.474i | − | 1.16098i | ||||||
\(445\) | − | 417.728i | − | 0.938714i | ||||||
\(446\) | − | 115.727i | − | 0.259478i | ||||||
\(447\) | 114.865i | 0.256968i | ||||||||
\(448\) | −919.049 | −2.05145 | ||||||||
\(449\) | 612.041 | 1.36312 | 0.681561 | − | 0.731762i | \(-0.261302\pi\) | ||||
0.681561 | + | 0.731762i | \(0.261302\pi\) | |||||||
\(450\) | 104.920i | 0.233155i | ||||||||
\(451\) | 143.346i | 0.317840i | ||||||||
\(452\) | 657.813i | 1.45534i | ||||||||
\(453\) | 178.722i | 0.394530i | ||||||||
\(454\) | 582.666 | 1.28341 | ||||||||
\(455\) | 941.528i | 2.06929i | ||||||||
\(456\) | 286.792i | 0.628930i | ||||||||
\(457\) | − | 406.851i | − | 0.890264i | −0.895465 | − | 0.445132i | \(-0.853157\pi\) | ||
0.895465 | − | 0.445132i | \(-0.146843\pi\) | |||||||
\(458\) | −635.828 | −1.38827 | ||||||||
\(459\) | 73.1766 | 0.159426 | ||||||||
\(460\) | 912.385i | 1.98345i | ||||||||
\(461\) | −852.748 | −1.84978 | −0.924889 | − | 0.380236i | \(-0.875843\pi\) | ||||
−0.924889 | + | 0.380236i | \(0.875843\pi\) | |||||||
\(462\) | −626.812 | −1.35674 | ||||||||
\(463\) | 727.640i | 1.57158i | 0.618495 | + | 0.785788i | \(0.287743\pi\) | ||||
−0.618495 | + | 0.785788i | \(0.712257\pi\) | |||||||
\(464\) | −319.271 | −0.688084 | ||||||||
\(465\) | − | 2.68651i | − | 0.00577743i | ||||||
\(466\) | −655.290 | −1.40620 | ||||||||
\(467\) | − | 24.1720i | − | 0.0517602i | −0.999665 | − | 0.0258801i | \(-0.991761\pi\) | ||
0.999665 | − | 0.0258801i | \(-0.00823880\pi\) | |||||||
\(468\) | − | 273.912i | − | 0.585282i | ||||||
\(469\) | 758.173i | 1.61657i | ||||||||
\(470\) | 532.429 | 1.13283 | ||||||||
\(471\) | 434.834i | 0.923214i | ||||||||
\(472\) | 228.214 | + | 126.968i | 0.483504 | + | 0.268999i | ||||
\(473\) | 93.2519 | 0.197150 | ||||||||
\(474\) | 276.671i | 0.583694i | ||||||||
\(475\) | −425.789 | −0.896397 | ||||||||
\(476\) | 712.661 | 1.49719 | ||||||||
\(477\) | −141.916 | −0.297517 | ||||||||
\(478\) | − | 436.757i | − | 0.913717i | ||||||
\(479\) | −540.528 | −1.12845 | −0.564225 | − | 0.825621i | \(-0.690825\pi\) | ||||
−0.564225 | + | 0.825621i | \(0.690825\pi\) | |||||||
\(480\) | 446.982i | 0.931213i | ||||||||
\(481\) | −917.996 | −1.90851 | ||||||||
\(482\) | − | 1202.19i | − | 2.49417i | ||||||
\(483\) | − | 447.909i | − | 0.927349i | ||||||
\(484\) | 214.077 | 0.442307 | ||||||||
\(485\) | 666.481i | 1.37419i | ||||||||
\(486\) | 47.8964i | 0.0985524i | ||||||||
\(487\) | −564.800 | −1.15975 | −0.579877 | − | 0.814704i | \(-0.696899\pi\) | ||||
−0.579877 | + | 0.814704i | \(0.696899\pi\) | |||||||
\(488\) | −372.038 | −0.762374 | ||||||||
\(489\) | −167.006 | −0.341525 | ||||||||
\(490\) | − | 695.262i | − | 1.41890i | ||||||
\(491\) | 8.09712 | 0.0164911 | 0.00824554 | − | 0.999966i | \(-0.497375\pi\) | ||||
0.00824554 | + | 0.999966i | \(0.497375\pi\) | |||||||
\(492\) | 106.675 | 0.216819 | ||||||||
\(493\) | 550.863 | 1.11737 | ||||||||
\(494\) | 1928.86 | 3.90458 | ||||||||
\(495\) | 229.139i | 0.462907i | ||||||||
\(496\) | − | 2.09888i | − | 0.00423161i | ||||||
\(497\) | 64.8226 | 0.130428 | ||||||||
\(498\) | −88.1042 | −0.176916 | ||||||||
\(499\) | 719.073 | 1.44103 | 0.720514 | − | 0.693440i | \(-0.243906\pi\) | ||||
0.720514 | + | 0.693440i | \(0.243906\pi\) | |||||||
\(500\) | −446.882 | −0.893764 | ||||||||
\(501\) | 135.777 | 0.271011 | ||||||||
\(502\) | 414.817i | 0.826329i | ||||||||
\(503\) | − | 524.427i | − | 1.04260i | −0.853374 | − | 0.521299i | \(-0.825448\pi\) | ||
0.853374 | − | 0.521299i | \(-0.174552\pi\) | |||||||
\(504\) | 123.513i | 0.245066i | ||||||||
\(505\) | 962.778i | 1.90649i | ||||||||
\(506\) | 1081.72i | 2.13779i | ||||||||
\(507\) | −195.087 | −0.384787 | ||||||||
\(508\) | 860.095 | 1.69310 | ||||||||
\(509\) | 749.520i | 1.47253i | 0.676691 | + | 0.736267i | \(0.263413\pi\) | ||||
−0.676691 | + | 0.736267i | \(0.736587\pi\) | |||||||
\(510\) | − | 452.061i | − | 0.886394i | ||||||
\(511\) | − | 1224.81i | − | 2.39688i | ||||||
\(512\) | 493.728i | 0.964312i | ||||||||
\(513\) | −194.375 | −0.378899 | ||||||||
\(514\) | − | 409.674i | − | 0.797032i | ||||||
\(515\) | 161.335i | 0.313272i | ||||||||
\(516\) | − | 69.3960i | − | 0.134488i | ||||||
\(517\) | 363.787 | 0.703650 | ||||||||
\(518\) | 1563.31 | 3.01796 | ||||||||
\(519\) | 90.5102i | 0.174393i | ||||||||
\(520\) | −448.060 | −0.861653 | ||||||||
\(521\) | −191.543 | −0.367646 | −0.183823 | − | 0.982959i | \(-0.558847\pi\) | ||||
−0.183823 | + | 0.982959i | \(0.558847\pi\) | |||||||
\(522\) | 360.558i | 0.690724i | ||||||||
\(523\) | 985.876 | 1.88504 | 0.942520 | − | 0.334149i | \(-0.108449\pi\) | ||||
0.942520 | + | 0.334149i | \(0.108449\pi\) | |||||||
\(524\) | − | 710.071i | − | 1.35510i | ||||||
\(525\) | −183.375 | −0.349287 | ||||||||
\(526\) | 836.795i | 1.59086i | ||||||||
\(527\) | 3.62136i | 0.00687165i | ||||||||
\(528\) | 179.019i | 0.339050i | ||||||||
\(529\) | −243.981 | −0.461212 | ||||||||
\(530\) | 876.709i | 1.65417i | ||||||||
\(531\) | −86.0532 | + | 154.673i | −0.162059 | + | 0.291287i | ||||
\(532\) | −1893.00 | −3.55828 | ||||||||
\(533\) | − | 189.975i | − | 0.356426i | ||||||
\(534\) | −368.560 | −0.690187 | ||||||||
\(535\) | 213.443 | 0.398958 | ||||||||
\(536\) | −360.804 | −0.673141 | ||||||||
\(537\) | − | 203.525i | − | 0.379003i | ||||||
\(538\) | −845.419 | −1.57141 | ||||||||
\(539\) | − | 475.044i | − | 0.881343i | ||||||
\(540\) | 170.520 | 0.315778 | ||||||||
\(541\) | − | 239.083i | − | 0.441928i | −0.975282 | − | 0.220964i | \(-0.929080\pi\) | ||
0.975282 | − | 0.220964i | \(-0.0709204\pi\) | |||||||
\(542\) | − | 437.405i | − | 0.807020i | ||||||
\(543\) | 277.440 | 0.510939 | ||||||||
\(544\) | − | 602.523i | − | 1.10758i | ||||||
\(545\) | − | 411.458i | − | 0.754969i | ||||||
\(546\) | 830.707 | 1.52144 | ||||||||
\(547\) | 106.125 | 0.194013 | 0.0970065 | − | 0.995284i | \(-0.469073\pi\) | ||||
0.0970065 | + | 0.995284i | \(0.469073\pi\) | |||||||
\(548\) | −1136.66 | −2.07420 | ||||||||
\(549\) | − | 252.151i | − | 0.459292i | ||||||
\(550\) | 442.861 | 0.805201 | ||||||||
\(551\) | −1463.23 | −2.65559 | ||||||||
\(552\) | 213.154 | 0.386148 | ||||||||
\(553\) | −483.557 | −0.874426 | ||||||||
\(554\) | − | 866.613i | − | 1.56428i | ||||||
\(555\) | − | 571.485i | − | 1.02970i | ||||||
\(556\) | 401.689 | 0.722462 | ||||||||
\(557\) | 8.64276 | 0.0155166 | 0.00775831 | − | 0.999970i | \(-0.497530\pi\) | ||||
0.00775831 | + | 0.999970i | \(0.497530\pi\) | |||||||
\(558\) | −2.37030 | −0.00424784 | ||||||||
\(559\) | −123.586 | −0.221084 | ||||||||
\(560\) | −457.928 | −0.817728 | ||||||||
\(561\) | − | 308.875i | − | 0.550579i | ||||||
\(562\) | − | 839.359i | − | 1.49352i | ||||||
\(563\) | − | 327.402i | − | 0.581530i | −0.956794 | − | 0.290765i | \(-0.906090\pi\) | ||
0.956794 | − | 0.290765i | \(-0.0939099\pi\) | |||||||
\(564\) | − | 270.722i | − | 0.480004i | ||||||
\(565\) | 729.290i | 1.29078i | ||||||||
\(566\) | −740.272 | −1.30790 | ||||||||
\(567\) | −83.7120 | −0.147640 | ||||||||
\(568\) | 30.8481i | 0.0543101i | ||||||||
\(569\) | − | 616.454i | − | 1.08340i | −0.840572 | − | 0.541700i | \(-0.817781\pi\) | ||
0.840572 | − | 0.541700i | \(-0.182219\pi\) | |||||||
\(570\) | 1200.79i | 2.10664i | ||||||||
\(571\) | 518.165i | 0.907470i | 0.891137 | + | 0.453735i | \(0.149909\pi\) | ||||
−0.891137 | + | 0.453735i | \(0.850091\pi\) | |||||||
\(572\) | −1156.17 | −2.02128 | ||||||||
\(573\) | − | 24.7577i | − | 0.0432071i | ||||||
\(574\) | 323.519i | 0.563621i | ||||||||
\(575\) | 316.461i | 0.550367i | ||||||||
\(576\) | 296.425 | 0.514627 | ||||||||
\(577\) | 787.940 | 1.36558 | 0.682790 | − | 0.730614i | \(-0.260766\pi\) | ||||
0.682790 | + | 0.730614i | \(0.260766\pi\) | |||||||
\(578\) | − | 278.600i | − | 0.482007i | ||||||
\(579\) | 124.615 | 0.215224 | ||||||||
\(580\) | 1283.65 | 2.21319 | ||||||||
\(581\) | − | 153.986i | − | 0.265036i | ||||||
\(582\) | 588.034 | 1.01037 | ||||||||
\(583\) | 599.020i | 1.02748i | ||||||||
\(584\) | 582.868 | 0.998062 | ||||||||
\(585\) | − | 303.675i | − | 0.519103i | ||||||
\(586\) | − | 987.125i | − | 1.68451i | ||||||
\(587\) | − | 782.879i | − | 1.33370i | −0.745194 | − | 0.666848i | \(-0.767643\pi\) | ||
0.745194 | − | 0.666848i | \(-0.232357\pi\) | |||||||
\(588\) | −353.517 | −0.601220 | ||||||||
\(589\) | − | 9.61922i | − | 0.0163314i | ||||||
\(590\) | 955.521 | + | 531.608i | 1.61953 | + | 0.901031i | ||||
\(591\) | −77.1610 | −0.130560 | ||||||||
\(592\) | − | 446.482i | − | 0.754193i | ||||||
\(593\) | 1037.25 | 1.74916 | 0.874580 | − | 0.484881i | \(-0.161137\pi\) | ||||
0.874580 | + | 0.484881i | \(0.161137\pi\) | |||||||
\(594\) | 202.169 | 0.340351 | ||||||||
\(595\) | 790.098 | 1.32790 | ||||||||
\(596\) | − | 360.806i | − | 0.605380i | ||||||
\(597\) | −216.883 | −0.363288 | ||||||||
\(598\) | − | 1433.60i | − | 2.39732i | ||||||
\(599\) | 673.671 | 1.12466 | 0.562330 | − | 0.826913i | \(-0.309905\pi\) | ||||
0.562330 | + | 0.826913i | \(0.309905\pi\) | |||||||
\(600\) | − | 87.2658i | − | 0.145443i | ||||||
\(601\) | 962.944i | 1.60224i | 0.598506 | + | 0.801118i | \(0.295761\pi\) | ||||
−0.598506 | + | 0.801118i | \(0.704239\pi\) | |||||||
\(602\) | 210.461 | 0.349603 | ||||||||
\(603\) | − | 244.537i | − | 0.405534i | ||||||
\(604\) | − | 561.392i | − | 0.929457i | ||||||
\(605\) | 237.338 | 0.392294 | ||||||||
\(606\) | 849.457 | 1.40174 | ||||||||
\(607\) | −790.355 | −1.30207 | −0.651034 | − | 0.759049i | \(-0.725664\pi\) | ||||
−0.651034 | + | 0.759049i | \(0.725664\pi\) | |||||||
\(608\) | 1600.45i | 2.63232i | ||||||||
\(609\) | −630.172 | −1.03477 | ||||||||
\(610\) | −1557.71 | −2.55362 | ||||||||
\(611\) | −482.123 | −0.789071 | ||||||||
\(612\) | −229.858 | −0.375585 | ||||||||
\(613\) | − | 953.011i | − | 1.55467i | −0.629088 | − | 0.777334i | \(-0.716572\pi\) | ||
0.629088 | − | 0.777334i | \(-0.283428\pi\) | |||||||
\(614\) | − | 1750.25i | − | 2.85056i | ||||||
\(615\) | 118.266 | 0.192303 | ||||||||
\(616\) | 521.344 | 0.846338 | ||||||||
\(617\) | 419.167 | 0.679364 | 0.339682 | − | 0.940540i | \(-0.389681\pi\) | ||||
0.339682 | + | 0.940540i | \(0.389681\pi\) | |||||||
\(618\) | 142.345 | 0.230332 | ||||||||
\(619\) | −209.634 | −0.338666 | −0.169333 | − | 0.985559i | \(-0.554161\pi\) | ||||
−0.169333 | + | 0.985559i | \(0.554161\pi\) | |||||||
\(620\) | 8.43869i | 0.0136108i | ||||||||
\(621\) | 144.466i | 0.232635i | ||||||||
\(622\) | − | 1098.28i | − | 1.76572i | ||||||
\(623\) | − | 644.158i | − | 1.03396i | ||||||
\(624\) | − | 237.251i | − | 0.380210i | ||||||
\(625\) | −780.001 | −1.24800 | ||||||||
\(626\) | −1662.19 | −2.65526 | ||||||||
\(627\) | 820.448i | 1.30853i | ||||||||
\(628\) | − | 1365.87i | − | 2.17496i | ||||||
\(629\) | 770.351i | 1.22472i | ||||||||
\(630\) | 517.145i | 0.820865i | ||||||||
\(631\) | −612.575 | −0.970800 | −0.485400 | − | 0.874292i | \(-0.661326\pi\) | ||||
−0.485400 | + | 0.874292i | \(0.661326\pi\) | |||||||
\(632\) | − | 230.118i | − | 0.364111i | ||||||
\(633\) | − | 184.950i | − | 0.292180i | ||||||
\(634\) | 1325.28i | 2.09035i | ||||||||
\(635\) | 953.552 | 1.50166 | ||||||||
\(636\) | 445.777 | 0.700908 | ||||||||
\(637\) | 629.571i | 0.988337i | ||||||||
\(638\) | 1521.90 | 2.38542 | ||||||||
\(639\) | −20.9075 | −0.0327191 | ||||||||
\(640\) | − | 798.955i | − | 1.24837i | ||||||
\(641\) | 198.748 | 0.310060 | 0.155030 | − | 0.987910i | \(-0.450453\pi\) | ||||
0.155030 | + | 0.987910i | \(0.450453\pi\) | |||||||
\(642\) | − | 188.320i | − | 0.293333i | ||||||
\(643\) | −157.384 | −0.244766 | −0.122383 | − | 0.992483i | \(-0.539054\pi\) | ||||
−0.122383 | + | 0.992483i | \(0.539054\pi\) | |||||||
\(644\) | 1406.95i | 2.18470i | ||||||||
\(645\) | − | 76.9365i | − | 0.119281i | ||||||
\(646\) | − | 1618.63i | − | 2.50563i | ||||||
\(647\) | 1214.33 | 1.87686 | 0.938430 | − | 0.345470i | \(-0.112280\pi\) | ||||
0.938430 | + | 0.345470i | \(0.112280\pi\) | |||||||
\(648\) | − | 39.8373i | − | 0.0614774i | ||||||
\(649\) | 652.869 | + | 363.226i | 1.00596 | + | 0.559671i | ||||
\(650\) | −586.918 | −0.902951 | ||||||||
\(651\) | − | 4.14273i | − | 0.00636365i | ||||||
\(652\) | 524.589 | 0.804584 | ||||||||
\(653\) | −404.646 | −0.619673 | −0.309836 | − | 0.950790i | \(-0.600274\pi\) | ||||
−0.309836 | + | 0.950790i | \(0.600274\pi\) | |||||||
\(654\) | −363.028 | −0.555089 | ||||||||
\(655\) | − | 787.226i | − | 1.20187i | ||||||
\(656\) | 92.3974 | 0.140850 | ||||||||
\(657\) | 395.042i | 0.601282i | ||||||||
\(658\) | 821.033 | 1.24777 | ||||||||
\(659\) | 1245.68i | 1.89025i | 0.326703 | + | 0.945127i | \(0.394062\pi\) | ||||
−0.326703 | + | 0.945127i | \(0.605938\pi\) | |||||||
\(660\) | − | 719.757i | − | 1.09054i | ||||||
\(661\) | 96.3638 | 0.145785 | 0.0728924 | − | 0.997340i | \(-0.476777\pi\) | ||||
0.0728924 | + | 0.997340i | \(0.476777\pi\) | |||||||
\(662\) | 741.711i | 1.12041i | ||||||||
\(663\) | 409.348i | 0.617418i | ||||||||
\(664\) | 73.2797 | 0.110361 | ||||||||
\(665\) | −2098.70 | −3.15593 | ||||||||
\(666\) | −504.220 | −0.757087 | ||||||||
\(667\) | 1087.52i | 1.63047i | ||||||||
\(668\) | −426.493 | −0.638463 | ||||||||
\(669\) | −65.2372 | −0.0975146 | ||||||||
\(670\) | −1510.67 | −2.25473 | ||||||||
\(671\) | −1064.32 | −1.58617 | ||||||||
\(672\) | 689.270i | 1.02570i | ||||||||
\(673\) | 786.566i | 1.16875i | 0.811485 | + | 0.584373i | \(0.198660\pi\) | ||||
−0.811485 | + | 0.584373i | \(0.801340\pi\) | |||||||
\(674\) | 375.122 | 0.556561 | ||||||||
\(675\) | 59.1449 | 0.0876221 | ||||||||
\(676\) | 612.795 | 0.906502 | ||||||||
\(677\) | −797.643 | −1.17820 | −0.589101 | − | 0.808059i | \(-0.700518\pi\) | ||||
−0.589101 | + | 0.808059i | \(0.700518\pi\) | |||||||
\(678\) | 643.451 | 0.949042 | ||||||||
\(679\) | 1027.75i | 1.51362i | ||||||||
\(680\) | 375.997i | 0.552936i | ||||||||
\(681\) | − | 328.458i | − | 0.482318i | ||||||
\(682\) | 10.0049i | 0.0146700i | ||||||||
\(683\) | − | 743.492i | − | 1.08857i | −0.838901 | − | 0.544284i | \(-0.816801\pi\) | ||
0.838901 | − | 0.544284i | \(-0.183199\pi\) | |||||||
\(684\) | 610.559 | 0.892630 | ||||||||
\(685\) | −1260.17 | −1.83966 | ||||||||
\(686\) | 328.235i | 0.478477i | ||||||||
\(687\) | 358.427i | 0.521727i | ||||||||
\(688\) | − | 60.1079i | − | 0.0873662i | ||||||
\(689\) | − | 793.874i | − | 1.15221i | ||||||
\(690\) | 892.465 | 1.29343 | ||||||||
\(691\) | − | 652.050i | − | 0.943632i | −0.881697 | − | 0.471816i | \(-0.843599\pi\) | ||
0.881697 | − | 0.471816i | \(-0.156401\pi\) | |||||||
\(692\) | − | 284.305i | − | 0.410845i | ||||||
\(693\) | 353.344i | 0.509876i | ||||||||
\(694\) | 1241.10 | 1.78833 | ||||||||
\(695\) | 445.336 | 0.640771 | ||||||||
\(696\) | − | 299.890i | − | 0.430877i | ||||||
\(697\) | −159.420 | −0.228724 | ||||||||
\(698\) | −1380.95 | −1.97843 | ||||||||
\(699\) | 369.398i | 0.528466i | ||||||||
\(700\) | 576.008 | 0.822869 | ||||||||
\(701\) | 24.8059i | 0.0353864i | 0.999843 | + | 0.0176932i | \(0.00563221\pi\) | ||||
−0.999843 | + | 0.0176932i | \(0.994368\pi\) | |||||||
\(702\) | −267.932 | −0.381669 | ||||||||
\(703\) | − | 2046.24i | − | 2.91073i | ||||||
\(704\) | − | 1251.20i | − | 1.77727i | ||||||
\(705\) | − | 300.139i | − | 0.425729i | ||||||
\(706\) | −654.997 | −0.927758 | ||||||||
\(707\) | 1484.66i | 2.09994i | ||||||||
\(708\) | 270.305 | − | 485.851i | 0.381787 | − | 0.686230i | ||||
\(709\) | 521.844 | 0.736028 | 0.368014 | − | 0.929820i | \(-0.380038\pi\) | ||||
0.368014 | + | 0.929820i | \(0.380038\pi\) | |||||||
\(710\) | 129.160i | 0.181915i | ||||||||
\(711\) | 155.964 | 0.219359 | ||||||||
\(712\) | 306.546 | 0.430542 | ||||||||
\(713\) | −7.14934 | −0.0100271 | ||||||||
\(714\) | − | 697.102i | − | 0.976333i | ||||||
\(715\) | −1281.80 | −1.79272 | ||||||||
\(716\) | 639.299i | 0.892876i | ||||||||
\(717\) | −246.207 | −0.343385 | ||||||||
\(718\) | 1245.53i | 1.73472i | ||||||||
\(719\) | 997.450i | 1.38727i | 0.720325 | + | 0.693637i | \(0.243993\pi\) | ||||
−0.720325 | + | 0.693637i | \(0.756007\pi\) | |||||||
\(720\) | 147.697 | 0.205135 | ||||||||
\(721\) | 248.787i | 0.345058i | ||||||||
\(722\) | 3190.30i | 4.41870i | ||||||||
\(723\) | −677.693 | −0.937335 | ||||||||
\(724\) | −871.477 | −1.20370 | ||||||||
\(725\) | 445.235 | 0.614117 | ||||||||
\(726\) | − | 209.403i | − | 0.288433i | ||||||
\(727\) | −570.949 | −0.785349 | −0.392675 | − | 0.919677i | \(-0.628450\pi\) | ||||
−0.392675 | + | 0.919677i | \(0.628450\pi\) | |||||||
\(728\) | −690.932 | −0.949082 | ||||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 2440.44 | 3.34307 | ||||||||
\(731\) | 103.709i | 0.141873i | ||||||||
\(732\) | 792.043i | 1.08203i | ||||||||
\(733\) | −337.572 | −0.460535 | −0.230268 | − | 0.973127i | \(-0.573960\pi\) | ||||
−0.230268 | + | 0.973127i | \(0.573960\pi\) | |||||||
\(734\) | −1662.84 | −2.26545 | ||||||||
\(735\) | −391.930 | −0.533239 | ||||||||
\(736\) | 1189.51 | 1.61618 | ||||||||
\(737\) | −1032.18 | −1.40051 | ||||||||
\(738\) | − | 104.346i | − | 0.141390i | ||||||
\(739\) | − | 1041.04i | − | 1.40872i | −0.709843 | − | 0.704360i | \(-0.751234\pi\) | ||
0.709843 | − | 0.704360i | \(-0.248766\pi\) | |||||||
\(740\) | 1795.12i | 2.42583i | ||||||||
\(741\) | − | 1087.33i | − | 1.46738i | ||||||
\(742\) | 1351.93i | 1.82201i | ||||||||
\(743\) | 955.497 | 1.28600 | 0.643000 | − | 0.765867i | \(-0.277690\pi\) | ||||
0.643000 | + | 0.765867i | \(0.277690\pi\) | |||||||
\(744\) | 1.97147 | 0.00264982 | ||||||||
\(745\) | − | 400.011i | − | 0.536928i | ||||||
\(746\) | − | 328.974i | − | 0.440983i | ||||||
\(747\) | 49.6658i | 0.0664870i | ||||||||
\(748\) | 970.219i | 1.29708i | ||||||||
\(749\) | 329.140 | 0.439439 | ||||||||
\(750\) | 437.125i | 0.582834i | ||||||||
\(751\) | − | 450.913i | − | 0.600416i | −0.953874 | − | 0.300208i | \(-0.902944\pi\) | ||
0.953874 | − | 0.300208i | \(-0.0970561\pi\) | |||||||
\(752\) | − | 234.488i | − | 0.311820i | ||||||
\(753\) | 233.839 | 0.310543 | ||||||||
\(754\) | −2016.95 | −2.67500 | ||||||||
\(755\) | − | 622.392i | − | 0.824360i | ||||||
\(756\) | 262.951 | 0.347819 | ||||||||
\(757\) | 410.015 | 0.541632 | 0.270816 | − | 0.962631i | \(-0.412707\pi\) | ||||
0.270816 | + | 0.962631i | \(0.412707\pi\) | |||||||
\(758\) | − | 628.960i | − | 0.829763i | ||||||
\(759\) | 609.785 | 0.803406 | ||||||||
\(760\) | − | 998.740i | − | 1.31413i | ||||||
\(761\) | 1469.25 | 1.93068 | 0.965339 | − | 0.260998i | \(-0.0840517\pi\) | ||||
0.965339 | + | 0.260998i | \(0.0840517\pi\) | |||||||
\(762\) | − | 841.316i | − | 1.10409i | ||||||
\(763\) | − | 634.490i | − | 0.831573i | ||||||
\(764\) | 77.7673i | 0.101790i | ||||||||
\(765\) | −254.834 | −0.333116 | ||||||||
\(766\) | − | 15.3028i | − | 0.0199776i | ||||||
\(767\) | −865.240 | − | 481.380i | −1.12808 | − | 0.627614i | ||||
\(768\) | −20.3515 | −0.0264994 | ||||||||
\(769\) | − | 469.742i | − | 0.610848i | −0.952216 | − | 0.305424i | \(-0.901202\pi\) | ||
0.952216 | − | 0.305424i | \(-0.0987982\pi\) | |||||||
\(770\) | 2182.84 | 2.83486 | ||||||||
\(771\) | −230.940 | −0.299533 | ||||||||
\(772\) | −391.432 | −0.507037 | ||||||||
\(773\) | − | 373.454i | − | 0.483122i | −0.970386 | − | 0.241561i | \(-0.922341\pi\) | ||
0.970386 | − | 0.241561i | \(-0.0776595\pi\) | |||||||
\(774\) | −67.8809 | −0.0877014 | ||||||||
\(775\) | 2.92696i | 0.00377672i | ||||||||
\(776\) | −489.091 | −0.630271 | ||||||||
\(777\) | − | 881.260i | − | 1.13418i | ||||||
\(778\) | 426.789i | 0.548572i | ||||||||
\(779\) | 423.460 | 0.543594 | ||||||||
\(780\) | 953.886i | 1.22293i | ||||||||
\(781\) | 88.2496i | 0.112996i | ||||||||
\(782\) | −1203.03 | −1.53840 | ||||||||
\(783\) | 203.252 | 0.259581 | ||||||||
\(784\) | −306.202 | −0.390564 | ||||||||
\(785\) | − | 1514.29i | − | 1.92903i | ||||||
\(786\) | −694.567 | −0.883674 | ||||||||
\(787\) | −97.7362 | −0.124188 | −0.0620942 | − | 0.998070i | \(-0.519778\pi\) | ||||
−0.0620942 | + | 0.998070i | \(0.519778\pi\) | |||||||
\(788\) | 242.374 | 0.307581 | ||||||||
\(789\) | 471.715 | 0.597864 | ||||||||
\(790\) | − | 963.494i | − | 1.21961i | ||||||
\(791\) | 1124.60i | 1.42175i |