Newspace parameters
Level: | \( N \) | \(=\) | \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1400.bh (of order \(6\), degree \(2\), not minimal) |
Newform invariants
Self dual: | no |
Analytic conductor: | \(11.1790562830\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
Defining polynomial: | \(x^{4} - x^{2} + 1\) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 849.2 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1400.849 |
Dual form | 1400.2.bh.f.249.2 |
$q$-expansion
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times\).
\(n\) | \(351\) | \(701\) | \(801\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.59808 | − | 1.50000i | 1.50000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
1.00000 | \(0\) | |||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.73205 | − | 2.00000i | 0.654654 | − | 0.755929i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.00000 | − | 5.19615i | 1.00000 | − | 1.73205i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.500000 | + | 0.866025i | 0.150756 | + | 0.261116i | 0.931505 | − | 0.363727i | \(-0.118496\pi\) |
−0.780750 | + | 0.624844i | \(0.785163\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000i | 0.554700i | 0.960769 | + | 0.277350i | \(0.0894562\pi\) | ||||
−0.960769 | + | 0.277350i | \(0.910544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.59808 | + | 1.50000i | −0.630126 | + | 0.363803i | −0.780801 | − | 0.624780i | \(-0.785189\pi\) |
0.150675 | + | 0.988583i | \(0.451855\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.50000 | − | 4.33013i | 0.573539 | − | 0.993399i | −0.422659 | − | 0.906289i | \(-0.638903\pi\) |
0.996199 | − | 0.0871106i | \(-0.0277634\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.50000 | − | 7.79423i | 0.327327 | − | 1.70084i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.59808 | + | 1.50000i | 0.541736 | + | 0.312772i | 0.745782 | − | 0.666190i | \(-0.232076\pi\) |
−0.204046 | + | 0.978961i | \(0.565409\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 9.00000i | − | 1.73205i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.00000 | 1.11417 | 0.557086 | − | 0.830455i | \(-0.311919\pi\) | ||||
0.557086 | + | 0.830455i | \(0.311919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.500000 | + | 0.866025i | 0.0898027 | + | 0.155543i | 0.907428 | − | 0.420208i | \(-0.138043\pi\) |
−0.817625 | + | 0.575751i | \(0.804710\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.59808 | + | 1.50000i | 0.452267 | + | 0.261116i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.33013 | − | 2.50000i | −0.711868 | − | 0.410997i | 0.0998840 | − | 0.994999i | \(-0.468153\pi\) |
−0.811752 | + | 0.584002i | \(0.801486\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.00000 | + | 5.19615i | 0.480384 | + | 0.832050i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.0000 | −1.56174 | −0.780869 | − | 0.624695i | \(-0.785223\pi\) | ||||
−0.780869 | + | 0.624695i | \(0.785223\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 4.00000i | − | 0.609994i | −0.952353 | − | 0.304997i | \(-0.901344\pi\) | ||
0.952353 | − | 0.304997i | \(-0.0986555\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.866025 | + | 0.500000i | 0.126323 | + | 0.0729325i | 0.561830 | − | 0.827253i | \(-0.310098\pi\) |
−0.435507 | + | 0.900185i | \(0.643431\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | − | 6.92820i | −0.142857 | − | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.50000 | + | 7.79423i | −0.630126 | + | 1.09141i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.79423 | + | 4.50000i | −1.07062 | + | 0.618123i | −0.928351 | − | 0.371706i | \(-0.878773\pi\) |
−0.142269 | + | 0.989828i | \(0.545440\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 15.0000i | − | 1.98680i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.50000 | + | 2.59808i | 0.195283 | + | 0.338241i | 0.946993 | − | 0.321253i | \(-0.104104\pi\) |
−0.751710 | + | 0.659494i | \(0.770771\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.50000 | + | 2.59808i | −0.192055 | + | 0.332650i | −0.945931 | − | 0.324367i | \(-0.894849\pi\) |
0.753876 | + | 0.657017i | \(0.228182\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.19615 | − | 15.0000i | −0.654654 | − | 1.88982i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.52628 | + | 5.50000i | −1.16382 | + | 0.671932i | −0.952217 | − | 0.305424i | \(-0.901202\pi\) |
−0.211604 | + | 0.977356i | \(0.567869\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9.00000 | 1.08347 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.0000 | 1.89885 | 0.949425 | − | 0.313993i | \(-0.101667\pi\) | ||||
0.949425 | + | 0.313993i | \(0.101667\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.06218 | − | 3.50000i | 0.709524 | − | 0.409644i | −0.101361 | − | 0.994850i | \(-0.532320\pi\) |
0.810885 | + | 0.585206i | \(0.198986\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.59808 | + | 0.500000i | 0.296078 | + | 0.0569803i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.50000 | + | 9.52628i | −0.618798 | + | 1.07179i | 0.370907 | + | 0.928670i | \(0.379047\pi\) |
−0.989705 | + | 0.143120i | \(0.954286\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 4.00000i | − | 0.439057i | −0.975606 | − | 0.219529i | \(-0.929548\pi\) | ||
0.975606 | − | 0.219529i | \(-0.0704519\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 15.5885 | − | 9.00000i | 1.67126 | − | 0.964901i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.50000 | + | 7.79423i | −0.476999 | + | 0.826187i | −0.999653 | − | 0.0263586i | \(-0.991609\pi\) |
0.522654 | + | 0.852545i | \(0.324942\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.00000 | + | 3.46410i | 0.419314 | + | 0.363137i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.59808 | + | 1.50000i | 0.269408 | + | 0.155543i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 6.00000i | − | 0.609208i | −0.952479 | − | 0.304604i | \(-0.901476\pi\) | ||
0.952479 | − | 0.304604i | \(-0.0985241\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.00000 | 0.603023 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.50000 | + | 11.2583i | 0.646774 | + | 1.12025i | 0.983889 | + | 0.178782i | \(0.0572157\pi\) |
−0.337115 | + | 0.941464i | \(0.609451\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.33013 | − | 2.50000i | −0.426660 | − | 0.246332i | 0.271263 | − | 0.962505i | \(-0.412559\pi\) |
−0.697923 | + | 0.716173i | \(0.745892\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.59808 | − | 1.50000i | −0.251166 | − | 0.145010i | 0.369132 | − | 0.929377i | \(-0.379655\pi\) |
−0.620298 | + | 0.784366i | \(0.712988\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.50000 | + | 9.52628i | 0.526804 | + | 0.912452i | 0.999512 | + | 0.0312328i | \(0.00994332\pi\) |
−0.472708 | + | 0.881219i | \(0.656723\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −15.0000 | −1.42374 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 10.0000i | − | 0.940721i | −0.882474 | − | 0.470360i | \(-0.844124\pi\) | ||
0.882474 | − | 0.470360i | \(-0.155876\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 10.3923 | + | 6.00000i | 0.960769 | + | 0.554700i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.50000 | + | 7.79423i | −0.137505 | + | 0.714496i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | − | 8.66025i | 0.454545 | − | 0.787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −25.9808 | + | 15.0000i | −2.34261 | + | 1.35250i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.00000i | 0.709885i | 0.934888 | + | 0.354943i | \(0.115500\pi\) | ||||
−0.934888 | + | 0.354943i | \(0.884500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.00000 | − | 10.3923i | −0.528271 | − | 0.914991i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.50000 | + | 14.7224i | −0.742648 | + | 1.28630i | 0.208637 | + | 0.977993i | \(0.433097\pi\) |
−0.951285 | + | 0.308312i | \(0.900236\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.33013 | − | 12.5000i | −0.375470 | − | 1.08389i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.59808 | + | 1.50000i | −0.221969 | + | 0.128154i | −0.606861 | − | 0.794808i | \(-0.707572\pi\) |
0.384893 | + | 0.922961i | \(0.374238\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.00000 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.00000 | 0.252646 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.73205 | + | 1.00000i | −0.144841 | + | 0.0836242i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −12.9904 | − | 16.5000i | −1.07143 | − | 1.36090i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.50000 | − | 12.9904i | 0.614424 | − | 1.06421i | −0.376061 | − | 0.926595i | \(-0.622722\pi\) |
0.990485 | − | 0.137619i | \(-0.0439449\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.50000 | − | 12.9904i | −0.610341 | − | 1.05714i | −0.991183 | − | 0.132502i | \(-0.957699\pi\) |
0.380841 | − | 0.924640i | \(-0.375634\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 18.0000i | 1.45521i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.9904 | + | 7.50000i | −1.03675 | + | 0.598565i | −0.918910 | − | 0.394468i | \(-0.870929\pi\) |
−0.117836 | + | 0.993033i | \(0.537596\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −13.5000 | + | 23.3827i | −1.07062 | + | 1.85437i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.50000 | − | 2.59808i | 0.591083 | − | 0.204757i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.79423 | − | 4.50000i | −0.610491 | − | 0.352467i | 0.162667 | − | 0.986681i | \(-0.447991\pi\) |
−0.773158 | + | 0.634214i | \(0.781324\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 20.0000i | 1.54765i | 0.633402 | + | 0.773823i | \(0.281658\pi\) | ||||
−0.633402 | + | 0.773823i | \(0.718342\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.00000 | 0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −15.0000 | − | 25.9808i | −1.14708 | − | 1.98680i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.1865 | + | 10.5000i | 1.38270 | + | 0.798300i | 0.992478 | − | 0.122422i | \(-0.0390662\pi\) |
0.390218 | + | 0.920722i | \(0.372399\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.79423 | + | 4.50000i | 0.585850 | + | 0.338241i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.500000 | − | 0.866025i | −0.0373718 | − | 0.0647298i | 0.846735 | − | 0.532016i | \(-0.178565\pi\) |
−0.884106 | + | 0.467286i | \(0.845232\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.0000 | 1.63525 | 0.817624 | − | 0.575753i | \(-0.195291\pi\) | ||||
0.817624 | + | 0.575753i | \(0.195291\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.00000i | 0.665299i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.59808 | − | 1.50000i | −0.189990 | − | 0.109691i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −18.0000 | − | 15.5885i | −1.30931 | − | 1.13389i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.50000 | + | 14.7224i | −0.615038 | + | 1.06528i | 0.375339 | + | 0.926887i | \(0.377526\pi\) |
−0.990378 | + | 0.138390i | \(0.955807\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.33013 | + | 2.50000i | −0.311689 | + | 0.179954i | −0.647682 | − | 0.761911i | \(-0.724262\pi\) |
0.335993 | + | 0.941865i | \(0.390928\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 18.0000i | − | 1.28245i | −0.767354 | − | 0.641223i | \(-0.778427\pi\) | ||
0.767354 | − | 0.641223i | \(-0.221573\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.50000 | − | 7.79423i | −0.318997 | − | 0.552518i | 0.661282 | − | 0.750137i | \(-0.270013\pi\) |
−0.980279 | + | 0.197619i | \(0.936679\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −16.5000 | + | 28.5788i | −1.16382 | + | 2.01580i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.3923 | − | 12.0000i | 0.729397 | − | 0.842235i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 15.5885 | − | 9.00000i | 1.08347 | − | 0.625543i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.00000 | 0.345857 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.0000 | 0.826114 | 0.413057 | − | 0.910705i | \(-0.364461\pi\) | ||||
0.413057 | + | 0.910705i | \(0.364461\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 41.5692 | − | 24.0000i | 2.84828 | − | 1.64445i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.59808 | + | 0.500000i | 0.176369 | + | 0.0339422i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.5000 | − | 18.1865i | 0.709524 | − | 1.22893i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.00000 | − | 5.19615i | −0.201802 | − | 0.349531i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.0000i | 1.60716i | 0.595198 | + | 0.803579i | \(0.297074\pi\) | ||||
−0.595198 | + | 0.803579i | \(0.702926\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.06218 | + | 3.50000i | −0.402361 | + | 0.232303i | −0.687502 | − | 0.726182i | \(-0.741293\pi\) |
0.285141 | + | 0.958485i | \(0.407959\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.50000 | − | 6.06218i | 0.231287 | − | 0.400600i | −0.726900 | − | 0.686743i | \(-0.759040\pi\) |
0.958187 | + | 0.286143i | \(0.0923732\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.50000 | − | 2.59808i | 0.493464 | − | 0.170941i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.2583 | + | 6.50000i | 0.737558 | + | 0.425829i | 0.821181 | − | 0.570668i | \(-0.193316\pi\) |
−0.0836229 | + | 0.996497i | \(0.526649\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 33.0000i | 2.14358i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.00000 | 0.258738 | 0.129369 | − | 0.991596i | \(-0.458705\pi\) | ||||
0.129369 | + | 0.991596i | \(0.458705\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.50000 | + | 14.7224i | 0.547533 | + | 0.948355i | 0.998443 | + | 0.0557856i | \(0.0177663\pi\) |
−0.450910 | + | 0.892570i | \(0.648900\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.66025 | + | 5.00000i | 0.551039 | + | 0.318142i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.00000 | − | 10.3923i | −0.380235 | − | 0.658586i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.0000 | 1.51487 | 0.757433 | − | 0.652913i | \(-0.226453\pi\) | ||||
0.757433 | + | 0.652913i | \(0.226453\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.00000i | 0.188608i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.2583 | − | 6.50000i | −0.702275 | − | 0.405459i | 0.105919 | − | 0.994375i | \(-0.466222\pi\) |
−0.808194 | + | 0.588916i | \(0.799555\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.5000 | + | 4.33013i | −0.776712 | + | 0.269061i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 18.0000 | − | 31.1769i | 1.11417 | − | 1.92980i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.59808 | − | 1.50000i | 0.160204 | − | 0.0924940i | −0.417755 | − | 0.908560i | \(-0.637183\pi\) |
0.577959 | + | 0.816066i | \(0.303849\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 27.0000i | 1.65237i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.50000 | − | 14.7224i | −0.518254 | − | 0.897643i | −0.999775 | − | 0.0212079i | \(-0.993249\pi\) |
0.481521 | − | 0.876435i | \(-0.340085\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.50000 | − | 2.59808i | 0.0911185 | − | 0.157822i | −0.816864 | − | 0.576831i | \(-0.804289\pi\) |
0.907982 | + | 0.419009i | \(0.137622\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 15.5885 | + | 3.00000i | 0.943456 | + | 0.181568i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.06218 | + | 3.50000i | −0.364241 | + | 0.210295i | −0.670940 | − | 0.741512i | \(-0.734109\pi\) |
0.306699 | + | 0.951807i | \(0.400776\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.00000 | 0.359211 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.0000 | −1.07379 | −0.536895 | − | 0.843649i | \(-0.680403\pi\) | ||||
−0.536895 | + | 0.843649i | \(0.680403\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.7224 | + | 8.50000i | −0.875158 | + | 0.505273i | −0.869059 | − | 0.494709i | \(-0.835275\pi\) |
−0.00609896 | + | 0.999981i | \(0.501941\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −17.3205 | + | 20.0000i | −1.02240 | + | 1.18056i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.00000 | + | 6.92820i | −0.235294 | + | 0.407541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.00000 | − | 15.5885i | −0.527589 | − | 0.913812i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.00000i | 0.350524i | 0.984522 | + | 0.175262i | \(0.0560772\pi\) | ||||
−0.984522 | + | 0.175262i | \(0.943923\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7.79423 | − | 4.50000i | 0.452267 | − | 0.261116i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.00000 | + | 5.19615i | −0.173494 | + | 0.300501i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.00000 | − | 6.92820i | −0.461112 | − | 0.399335i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 33.7750 | + | 19.5000i | 1.94032 | + | 1.12025i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 4.00000i | − | 0.228292i | −0.993464 | − | 0.114146i | \(-0.963587\pi\) | ||
0.993464 | − | 0.114146i | \(-0.0364132\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15.0000 | −0.853320 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.50000 | − | 9.52628i | −0.311876 | − | 0.540186i | 0.666892 | − | 0.745154i | \(-0.267624\pi\) |
−0.978769 | + | 0.204968i | \(0.934291\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −26.8468 | − | 15.5000i | −1.51747 | − | 0.876112i | −0.999789 | − | 0.0205381i | \(-0.993462\pi\) |
−0.517681 | − | 0.855574i | \(-0.673205\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 23.3827 | + | 13.5000i | 1.31330 | + | 0.758236i | 0.982642 | − | 0.185514i | \(-0.0593950\pi\) |
0.330661 | + | 0.943750i | \(0.392728\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.00000 | + | 5.19615i | 0.167968 | + | 0.290929i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.00000 | −0.502331 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 15.0000i | 0.834622i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 28.5788 | + | 16.5000i | 1.58041 | + | 0.912452i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.50000 | − | 0.866025i | 0.137829 | − | 0.0477455i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.50000 | − | 6.06218i | 0.192377 | − | 0.333207i | −0.753660 | − | 0.657264i | \(-0.771714\pi\) |
0.946038 | + | 0.324057i | \(0.105047\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −25.9808 | + | 15.0000i | −1.42374 | + | 0.821995i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 14.0000i | − | 0.762629i | −0.924445 | − | 0.381314i | \(-0.875472\pi\) | ||
0.924445 | − | 0.381314i | \(-0.124528\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −15.0000 | − | 25.9808i | −0.814688 | − | 1.41108i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.500000 | + | 0.866025i | −0.0270765 | + | 0.0468979i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.5885 | − | 10.0000i | −0.841698 | − | 0.539949i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.59808 | + | 1.50000i | −0.139472 | + | 0.0805242i | −0.568112 | − | 0.822951i | \(-0.692326\pi\) |
0.428640 | + | 0.903475i | \(0.358993\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.00000 | 0.321173 | 0.160586 | − | 0.987022i | \(-0.448662\pi\) | ||||
0.160586 | + | 0.987022i | \(0.448662\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.0000 | 0.960769 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.33013 | + | 2.50000i | −0.230469 | + | 0.133062i | −0.610789 | − | 0.791794i | \(-0.709147\pi\) |
0.380319 | + | 0.924855i | \(0.375814\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7.79423 | + | 22.5000i | 0.412514 | + | 1.19083i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7.50000 | + | 12.9904i | −0.395835 | + | 0.685606i | −0.993207 | − | 0.116358i | \(-0.962878\pi\) |
0.597372 | + | 0.801964i | \(0.296211\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | − | 5.19615i | −0.157895 | − | 0.273482i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 30.0000i | − | 1.57459i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.4545 | + | 9.50000i | −0.858917 | + | 0.495896i | −0.863649 | − | 0.504093i | \(-0.831827\pi\) |
0.00473247 | + | 0.999989i | \(0.498494\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −30.0000 | + | 51.9615i | −1.56174 | + | 2.70501i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.50000 | + | 23.3827i | −0.233628 | + | 1.21397i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.4545 | − | 9.50000i | −0.851981 | − | 0.491891i | 0.00933789 | − | 0.999956i | \(-0.497028\pi\) |
−0.861319 | + | 0.508065i | \(0.830361\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.0000i | 0.618031i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.0000 | 0.821865 | 0.410932 | − | 0.911666i | \(-0.365203\pi\) | ||||
0.410932 | + | 0.911666i | \(0.365203\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.0000 | + | 20.7846i | 0.614779 | + | 1.06483i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.79423 | − | 4.50000i | −0.398266 | − | 0.229939i | 0.287469 | − | 0.957790i | \(-0.407186\pi\) |
−0.685736 | + | 0.727851i | \(0.740519\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −20.7846 | − | 12.0000i | −1.05654 | − | 0.609994i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.50000 | + | 16.4545i | 0.481669 | + | 0.834275i | 0.999779 | − | 0.0210389i | \(-0.00669738\pi\) |
−0.518110 | + | 0.855314i | \(0.673364\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.00000 | −0.455150 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 51.0000i | 2.57261i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.7224 | − | 8.50000i | −0.738898 | − | 0.426603i | 0.0827707 | − | 0.996569i | \(-0.473623\pi\) |
−0.821668 | + | 0.569966i | \(0.806956\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −30.0000 | − | 25.9808i | −1.50188 | − | 1.30066i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.50000 | + | 2.59808i | −0.0749064 | + | 0.129742i | −0.901046 | − | 0.433724i | \(-0.857199\pi\) |
0.826139 | + | 0.563466i | \(0.190532\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.73205 | + | 1.00000i | −0.0862796 | + | 0.0498135i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 5.00000i | − | 0.247841i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.50000 | + | 16.4545i | 0.469745 | + | 0.813622i | 0.999402 | − | 0.0345902i | \(-0.0110126\pi\) |
−0.529657 | + | 0.848212i | \(0.677679\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.50000 | + | 7.79423i | −0.221969 | + | 0.384461i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.79423 | + | 1.50000i | 0.383529 | + | 0.0738102i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10.3923 | + | 6.00000i | −0.508913 | + | 0.293821i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −20.0000 | −0.977064 | −0.488532 | − | 0.872546i | \(-0.662467\pi\) | ||||
−0.488532 | + | 0.872546i | \(0.662467\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.0000 | 0.487370 | 0.243685 | − | 0.969854i | \(-0.421644\pi\) | ||||
0.243685 | + | 0.969854i | \(0.421644\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.19615 | − | 3.00000i | 0.252646 | − | 0.145865i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.59808 | + | 7.50000i | 0.125730 | + | 0.362950i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.00000 | + | 5.19615i | −0.144841 | + | 0.250873i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.5000 | + | 35.5070i | 0.987450 | + | 1.71031i | 0.630497 | + | 0.776192i | \(0.282851\pi\) |
0.356953 | + | 0.934122i | \(0.383815\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 26.0000i | − | 1.24948i | −0.780833 | − | 0.624740i | \(-0.785205\pi\) | ||
0.780833 | − | 0.624740i | \(-0.214795\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 12.9904 | − | 7.50000i | 0.621414 | − | 0.358774i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.50000 | + | 12.9904i | −0.357955 | + | 0.619997i | −0.987619 | − | 0.156871i | \(-0.949859\pi\) |
0.629664 | + | 0.776868i | \(0.283193\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −39.0000 | − | 15.5885i | −1.85714 | − | 0.742307i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 23.3827 | + | 13.5000i | 1.11094 | + | 0.641404i | 0.939074 | − | 0.343715i | \(-0.111685\pi\) |
0.171871 | + | 0.985119i | \(0.445019\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 45.0000i | − | 2.12843i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.00000 | 0.0943858 | 0.0471929 | − | 0.998886i | \(-0.484972\pi\) | ||||
0.0471929 | + | 0.998886i | \(0.484972\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.00000 | − | 8.66025i | −0.235441 | − | 0.407795i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −38.9711 | − | 22.5000i | −1.83102 | − | 1.05714i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.7224 | − | 8.50000i | −0.688686 | − | 0.397613i | 0.114433 | − | 0.993431i | \(-0.463495\pi\) |
−0.803120 | + | 0.595818i | \(0.796828\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 13.5000 | + | 23.3827i | 0.630126 | + | 1.09141i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.00000 | −0.279448 | −0.139724 | − | 0.990190i | \(-0.544622\pi\) | ||||
−0.139724 | + | 0.990190i | \(0.544622\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 16.0000i | − | 0.743583i | −0.928316 | − | 0.371792i | \(-0.878744\pi\) | ||
0.928316 | − | 0.371792i | \(-0.121256\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 21.6506 | + | 12.5000i | 1.00187 | + | 0.578431i | 0.908802 | − | 0.417229i | \(-0.136999\pi\) |
0.0930703 | + | 0.995660i | \(0.470332\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.50000 | + | 28.5788i | −0.253966 | + | 1.31965i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −22.5000 | + | 38.9711i | −1.03675 | + | 1.79570i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.46410 | − | 2.00000i | 0.159280 | − | 0.0919601i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 54.0000i | 2.47249i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.5000 | − | 18.1865i | −0.479757 | − | 0.830964i | 0.519973 | − | 0.854183i | \(-0.325942\pi\) |
−0.999730 | + | 0.0232187i | \(0.992609\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.00000 | − | 8.66025i | 0.227980 | − | 0.394874i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 15.5885 | − | 18.0000i | 0.709299 | − | 0.819028i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.2583 | − | 6.50000i | 0.510164 | − | 0.294543i | −0.222737 | − | 0.974879i | \(-0.571499\pi\) |
0.732901 | + | 0.680335i | \(0.238166\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −27.0000 | −1.22098 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15.5885 | + | 9.00000i | −0.702069 | + | 0.405340i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 27.7128 | − | 32.0000i | 1.24309 | − | 1.43540i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.50000 | + | 6.06218i | −0.156682 | + | 0.271380i | −0.933670 | − | 0.358134i | \(-0.883413\pi\) |
0.776989 | + | 0.629515i | \(0.216746\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 30.0000 | + | 51.9615i | 1.34030 | + | 2.32147i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.0000i | 0.713405i | 0.934218 | + | 0.356702i | \(0.116099\pi\) | ||||
−0.934218 | + | 0.356702i | \(0.883901\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 23.3827 | − | 13.5000i | 1.03846 | − | 0.599556i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.50000 | − | 6.06218i | 0.155135 | − | 0.268701i | −0.777973 | − | 0.628297i | \(-0.783752\pi\) |
0.933108 | + | 0.359596i | \(0.117085\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.50000 | − | 18.1865i | 0.154831 | − | 0.804525i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −38.9711 | − | 22.5000i | −1.72062 | − | 0.993399i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.00000i | 0.0439799i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 63.0000 | 2.76539 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.50000 | − | 12.9904i | −0.328581 | − | 0.569119i | 0.653650 | − | 0.756797i | \(-0.273237\pi\) |
−0.982231 | + | 0.187678i | \(0.939904\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.2583 | − | 6.50000i | −0.492292 | − | 0.284225i | 0.233233 | − | 0.972421i | \(-0.425070\pi\) |
−0.725525 | + | 0.688196i | \(0.758403\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.59808 | − | 1.50000i | −0.113174 | − | 0.0653410i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | − | 12.1244i | −0.304348 | − | 0.527146i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 18.0000 | 0.781133 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 20.0000i | − | 0.866296i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.59808 | − | 1.50000i | −0.112115 | − | 0.0647298i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.50000 | − | 4.33013i | 0.236902 | − | 0.186512i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.5000 | − | 21.6506i | 0.537417 | − | 0.930834i | −0.461625 | − | 0.887075i | \(-0.652733\pi\) |
0.999042 | − | 0.0437584i | \(-0.0139332\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 57.1577 | − | 33.0000i | 2.45287 | − | 1.41617i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.00000 | + | 15.5885i | 0.384111 | + | 0.665299i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.0000 | − | 25.9808i | 0.639021 | − | 1.10682i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.52628 | + | 27.5000i | 0.405099 | + | 1.16942i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.52628 | + | 5.50000i | −0.403641 | + | 0.233042i | −0.688054 | − | 0.725660i | \(-0.741535\pi\) |
0.284413 | + | 0.958702i | \(0.408201\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.00000 | 0.338364 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.00000 | −0.379980 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.52628 | − | 5.50000i | 0.401485 | − | 0.231797i | −0.285640 | − | 0.958337i | \(-0.592206\pi\) |
0.687124 | + | 0.726540i | \(0.258873\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −23.3827 | − | 4.50000i | −0.981981 | − | 0.188982i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.500000 | + | 0.866025i | −0.0209611 | + | 0.0363057i | −0.876316 | − | 0.481737i | \(-0.840006\pi\) |
0.855355 | + | 0.518043i | \(0.173339\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.50000 | + | 14.7224i | 0.355714 | + | 0.616115i | 0.987240 | − | 0.159240i | \(-0.0509044\pi\) |
−0.631526 | + | 0.775355i | \(0.717571\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 51.0000i | 2.13056i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26.8468 | + | 15.5000i | −1.11765 | + | 0.645273i | −0.940799 | − | 0.338965i | \(-0.889923\pi\) |
−0.176847 | + | 0.984238i | \(0.556590\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.50000 | + | 12.9904i | −0.311689 | + | 0.539862i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.00000 | − | 6.92820i | −0.331896 | − | 0.287430i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.79423 | − | 4.50000i | −0.322804 | − | 0.186371i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 12.0000i | − | 0.495293i | −0.968850 | − | 0.247647i | \(-0.920343\pi\) | ||
0.968850 | − | 0.247647i | \(-0.0796572\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.00000 | 0.206021 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −27.0000 | − | 46.7654i | −1.11063 | − | 1.92367i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −37.2391 | − | 21.5000i | −1.52923 | − | 0.882899i | −0.999394 | − | 0.0347964i | \(-0.988922\pi\) |
−0.529832 | − | 0.848103i | \(-0.677745\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −23.3827 | − | 13.5000i | −0.956990 | − | 0.552518i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.5000 | − | 18.1865i | −0.429018 | − | 0.743082i | 0.567768 | − | 0.823189i | \(-0.307807\pi\) |
−0.996786 | + | 0.0801071i | \(0.974474\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −34.0000 | −1.38689 | −0.693444 | − | 0.720510i | \(-0.743908\pi\) | ||||
−0.693444 | + | 0.720510i | \(0.743908\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 66.0000i | 2.68773i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.06218 | − | 3.50000i | −0.246056 | − | 0.142061i | 0.371901 | − | 0.928272i | \(-0.378706\pi\) |
−0.617957 | + | 0.786212i | \(0.712039\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.00000 | − | 46.7654i | 0.364698 | − | 1.89503i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.00000 | + | 1.73205i | −0.0404557 | + | 0.0700713i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18.1865 | + | 10.5000i | −0.734547 | + | 0.424091i | −0.820083 | − | 0.572244i | \(-0.806073\pi\) |
0.0855362 | + | 0.996335i | \(0.472740\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 22.0000i | − | 0.885687i | −0.896599 | − | 0.442843i | \(-0.853970\pi\) | ||
0.896599 | − | 0.442843i | \(-0.146030\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.50000 | − | 4.33013i | −0.100483 | − | 0.174042i | 0.811400 | − | 0.584491i | \(-0.198706\pi\) |
−0.911884 | + | 0.410448i | \(0.865372\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 13.5000 | − | 23.3827i | 0.541736 | − | 0.938315i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.79423 | + | 22.5000i | 0.312269 | + | 0.901443i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 12.9904 | − | 7.50000i | 0.518786 | − | 0.299521i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 15.0000 | 0.598089 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 31.1769 | − | 18.0000i | 1.23917 | − | 0.715436i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13.8564 | − | 2.00000i | 0.549011 | − | 0.0792429i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 48.0000 | − | 83.1384i | 1.89885 | − | 3.28891i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.50000 | − | 12.9904i | −0.296232 | − | 0.513089i | 0.679039 | − | 0.734103i | \(-0.262397\pi\) |
−0.975271 | + | 0.221013i | \(0.929064\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 44.0000i | − | 1.73519i | −0.497271 | − | 0.867595i | \(-0.665665\pi\) | ||
0.497271 | − | 0.867595i | \(-0.334335\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −37.2391 | + | 21.5000i | −1.46402 | + | 0.845252i | −0.999194 | − | 0.0401498i | \(-0.987216\pi\) |
−0.464826 | + | 0.885402i | \(0.653883\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.50000 | + | 2.59808i | −0.0588802 | + | 0.101983i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.50000 | − | 2.59808i | 0.293948 | − | 0.101827i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.33013 | + | 2.50000i | 0.169451 | + | 0.0978326i | 0.582327 | − | 0.812955i | \(-0.302142\pi\) |
−0.412876 | + | 0.910787i | \(0.635476\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 42.0000i | − | 1.63858i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 36.0000 | 1.40236 | 0.701180 | − | 0.712984i | \(-0.252657\pi\) | ||||
0.701180 | + | 0.712984i | \(0.252657\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.500000 | + | 0.866025i | 0.0194477 | + | 0.0336845i | 0.875585 | − | 0.483063i | \(-0.160476\pi\) |
−0.856138 | + | 0.516748i | \(0.827143\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −15.5885 | − | 9.00000i | −0.605406 | − | 0.349531i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15.5885 | + | 9.00000i | 0.603587 | + | 0.348481i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 36.0000 | + | 62.3538i | 1.39184 | + | 2.41074i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.00000 | −0.115814 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 2.00000i | − | 0.0770943i | −0.999257 | − | 0.0385472i | \(-0.987727\pi\) | ||
0.999257 | − | 0.0385472i | \(-0.0122730\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.79423 | − | 4.50000i | −0.299557 | − | 0.172949i | 0.342687 | − | 0.939450i | \(-0.388663\pi\) |
−0.642244 | + | 0.766501i | \(0.721996\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.0000 | − | 10.3923i | −0.460518 | − | 0.398820i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.5000 | + | 18.1865i | −0.402361 | + | 0.696909i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 33.7750 | − | 19.5000i | 1.29236 | − | 0.746147i | 0.313291 | − | 0.949657i | \(-0.398568\pi\) |
0.979073 | + | 0.203510i | \(0.0652350\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 21.0000i | − | 0.801200i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.00000 | − | 15.5885i | −0.342873 | − | 0.593873i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.5000 | − | 40.7032i | 0.893982 | − | 1.54842i | 0.0589228 | − | 0.998263i | \(-0.481233\pi\) |
0.835059 | − | 0.550160i | \(-0.185433\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10.3923 | − | 12.0000i | 0.394771 | − | 0.455842i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 25.9808 | − | 15.0000i | 0.984092 | − | 0.568166i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 39.0000 | 1.47512 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.0000 | −0.679851 | −0.339925 | − | 0.940452i | \(-0.610402\pi\) | ||||
−0.339925 | + | 0.940452i | \(0.610402\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −21.6506 | + | 12.5000i | −0.816569 | + | 0.471446i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 33.7750 | + | 6.50000i | 1.27024 | + | 0.244458i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.5000 | − | 23.3827i | 0.507003 | − | 0.878155i | −0.492964 | − | 0.870050i | \(-0.664087\pi\) |
0.999967 | − | 0.00810550i | \(-0.00258009\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 33.0000 | + | 57.1577i | 1.23760 | + | 2.14358i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.00000i | 0.112351i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10.3923 | − | 6.00000i | 0.388108 | − | 0.224074i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 14.5000 | − | 25.1147i | 0.540759 | − | 0.936622i | −0.458102 | − | 0.888900i | \(-0.651471\pi\) |
0.998861 | − | 0.0477220i | \(-0.0151961\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.5000 | + | 4.33013i | −0.465524 | + | 0.161262i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 44.1673 | + | 25.5000i | 1.64260 | + | 0.948355i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 16.0000i | − | 0.593407i | −0.954970 | − | 0.296704i | \(-0.904113\pi\) | ||
0.954970 | − | 0.296704i | \(-0.0958873\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.00000 | + | 10.3923i | 0.221918 | + | 0.384373i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.52628 | − | 5.50000i | −0.351861 | − | 0.203147i | 0.313644 | − | 0.949541i | \(-0.398450\pi\) |
−0.665505 | + | 0.746394i | \(0.731784\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.52628 | − | 5.50000i | −0.350905 | − | 0.202595i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.5000 | − | 35.5070i | −0.754105 | − | 1.30615i | −0.945818 | − | 0.324697i | \(-0.894738\pi\) |
0.191714 | − | 0.981451i | \(-0.438596\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 30.0000 | 1.10208 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32.0000i | 1.17397i | 0.809599 | + | 0.586983i | \(0.199684\pi\) | ||||
−0.809599 | + | 0.586983i | \(0.800316\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −20.7846 | − | 12.0000i | −0.760469 | − | 0.439057i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.50000 | + | 2.59808i | −0.274044 | + | 0.0949316i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.5000 | − | 40.7032i | 0.857527 | − | 1.48528i | −0.0167534 | − | 0.999860i | \(-0.505333\pi\) |
0.874281 | − | 0.485421i | \(-0.161334\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 62.3538 | − | 36.0000i | 2.27230 | − | 1.31191i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 34.0000i | − | 1.23575i | −0.786276 | − | 0.617876i | \(-0.787994\pi\) | ||
0.786276 | − | 0.617876i | \(-0.212006\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.50000 | + | 7.79423i | 0.163340 | + | 0.282913i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13.5000 | + | 23.3827i | −0.489375 | + | 0.847622i | −0.999925 | − | 0.0122260i | \(-0.996108\pi\) |
0.510551 | + | 0.859848i | \(0.329442\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 28.5788 | + | 5.50000i | 1.03462 | + | 0.199113i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.19615 | + | 3.00000i | −0.187622 | + | 0.108324i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.0000 | −0.504853 | −0.252426 | − | 0.967616i | \(-0.581229\pi\) | ||||
−0.252426 | + | 0.967616i | \(0.581229\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −39.0000 | −1.40455 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 30.3109 | − | 17.5000i | 1.09021 | − | 0.629431i | 0.156575 | − | 0.987666i | \(-0.449955\pi\) |
0.933632 | + | 0.358235i | \(0.116621\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −25.9808 | + | 30.0000i | −0.932055 | + | 1.07624i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −25.0000 | + | 43.3013i | −0.895718 | + | 1.55143i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.00000 | + | 13.8564i | 0.286263 | + | 0.495821i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 54.0000i | − | 1.92980i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.2583 | − | 6.50000i | 0.401316 | − | 0.231700i | −0.285736 | − | 0.958308i | \(-0.592238\pi\) |
0.687052 | + | 0.726609i | \(0.258905\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.50000 | − | 7.79423i | 0.160204 | − | 0.277482i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −20.0000 | − | 17.3205i | −0.711118 | − | 0.615846i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.19615 | − | 3.00000i | −0.184521 | − | 0.106533i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 42.0000i | − | 1.48772i | −0.668338 | − | 0.743858i | \(-0.732994\pi\) | ||
0.668338 | − | 0.743858i | \(-0.267006\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.00000 | −0.106132 |