Newspace parameters
Level: | \( N \) | \(=\) | \( 3360 = 2^{5} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3360.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
Self dual: | no |
Analytic conductor: | \(26.8297350792\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
|
|
Defining polynomial: |
\( x^{16} + 24x^{14} + 238x^{12} + 1262x^{10} + 3861x^{8} + 6834x^{6} + 6589x^{4} + 2916x^{2} + 324 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2911.4 | ||
Root | \(-0.400519i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3360.2911 |
Dual form | 3360.2.d.a.2911.12 |
$q$-expansion
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3360\mathbb{Z}\right)^\times\).
\(n\) | \(421\) | \(1121\) | \(1471\) | \(1921\) | \(2017\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.400519 | + | 2.61526i | −0.151382 | + | 0.988475i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.87335i | 1.16786i | 0.811804 | + | 0.583930i | \(0.198486\pi\) | ||||
−0.811804 | + | 0.583930i | \(0.801514\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.15545i | 0.597814i | 0.954282 | + | 0.298907i | \(0.0966220\pi\) | ||||
−0.954282 | + | 0.298907i | \(0.903378\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000i | 0.258199i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 4.79356i | − | 1.16261i | −0.813686 | − | 0.581304i | \(-0.802543\pi\) | ||
0.813686 | − | 0.581304i | \(-0.197457\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.31954 | 1.22039 | 0.610193 | − | 0.792253i | \(-0.291092\pi\) | ||||
0.610193 | + | 0.792253i | \(0.291092\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.400519 | − | 2.61526i | 0.0874004 | − | 0.570697i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.67917i | 1.18419i | 0.805869 | + | 0.592094i | \(0.201699\pi\) | ||||
−0.805869 | + | 0.592094i | \(0.798301\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.79858 | 0.333987 | 0.166994 | − | 0.985958i | \(-0.446594\pi\) | ||||
0.166994 | + | 0.985958i | \(0.446594\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.221571 | −0.0397954 | −0.0198977 | − | 0.999802i | \(-0.506334\pi\) | ||||
−0.0198977 | + | 0.999802i | \(0.506334\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 3.87335i | − | 0.674264i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.61526 | + | 0.400519i | 0.442060 | + | 0.0677001i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.50006 | −1.23300 | −0.616501 | − | 0.787354i | \(-0.711450\pi\) | ||||
−0.616501 | + | 0.787354i | \(0.711450\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 2.15545i | − | 0.345148i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.1072i | 1.73465i | 0.497738 | + | 0.867327i | \(0.334164\pi\) | ||||
−0.497738 | + | 0.867327i | \(0.665836\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 11.2593i | − | 1.71703i | −0.512788 | − | 0.858515i | \(-0.671387\pi\) | ||
0.512788 | − | 0.858515i | \(-0.328613\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 1.00000i | − | 0.149071i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.11469 | 1.03778 | 0.518892 | − | 0.854840i | \(-0.326345\pi\) | ||||
0.518892 | + | 0.854840i | \(0.326345\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.67917 | − | 2.09492i | −0.954167 | − | 0.299275i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.79356i | 0.671232i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.97985 | −0.271954 | −0.135977 | − | 0.990712i | \(-0.543417\pi\) | ||||
−0.135977 | + | 0.990712i | \(0.543417\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.87335 | 0.522283 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.31954 | −0.704590 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.27574 | −0.686843 | −0.343421 | − | 0.939181i | \(-0.611586\pi\) | ||||
−0.343421 | + | 0.939181i | \(0.611586\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 7.99669i | − | 1.02387i | −0.859024 | − | 0.511935i | \(-0.828929\pi\) | ||
0.859024 | − | 0.511935i | \(-0.171071\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.400519 | + | 2.61526i | −0.0504607 | + | 0.329492i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.15545 | 0.267350 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.00246i | 0.366809i | 0.983038 | + | 0.183405i | \(0.0587118\pi\) | ||||
−0.983038 | + | 0.183405i | \(0.941288\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 5.67917i | − | 0.683692i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.50426i | 0.771913i | 0.922517 | + | 0.385957i | \(0.126129\pi\) | ||||
−0.922517 | + | 0.385957i | \(0.873871\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 3.16961i | − | 0.370974i | −0.982647 | − | 0.185487i | \(-0.940614\pi\) | ||
0.982647 | − | 0.185487i | \(-0.0593863\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −10.1298 | − | 1.55135i | −1.15440 | − | 0.176793i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.99118i | 0.899078i | 0.893261 | + | 0.449539i | \(0.148412\pi\) | ||||
−0.893261 | + | 0.449539i | \(0.851588\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.4453 | −1.14652 | −0.573262 | − | 0.819372i | \(-0.694322\pi\) | ||||
−0.573262 | + | 0.819372i | \(0.694322\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.79356 | −0.519934 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.79858 | −0.192828 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.4560i | 1.21434i | 0.794574 | + | 0.607168i | \(0.207694\pi\) | ||||
−0.794574 | + | 0.607168i | \(0.792306\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.63706 | − | 0.863298i | −0.590924 | − | 0.0904982i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.221571 | 0.0229759 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 5.31954i | − | 0.545773i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.716023i | 0.0727012i | 0.999339 | + | 0.0363506i | \(0.0115733\pi\) | ||||
−0.999339 | + | 0.0363506i | \(0.988427\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.87335i | 0.389286i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.18641i | 0.516067i | 0.966136 | + | 0.258033i | \(0.0830744\pi\) | ||||
−0.966136 | + | 0.258033i | \(0.916926\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.19896 | −0.315203 | −0.157602 | − | 0.987503i | \(-0.550376\pi\) | ||||
−0.157602 | + | 0.987503i | \(0.550376\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.61526 | − | 0.400519i | −0.255223 | − | 0.0390867i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 8.49311i | − | 0.821060i | −0.911847 | − | 0.410530i | \(-0.865344\pi\) | ||
0.911847 | − | 0.410530i | \(-0.134656\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.39403 | −0.804002 | −0.402001 | − | 0.915639i | \(-0.631685\pi\) | ||||
−0.402001 | + | 0.915639i | \(0.631685\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.50006 | 0.711874 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.0556 | −0.945952 | −0.472976 | − | 0.881075i | \(-0.656820\pi\) | ||||
−0.472976 | + | 0.881075i | \(0.656820\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.67917 | 0.529585 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.15545i | 0.199271i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 12.5364 | + | 1.91991i | 1.14921 | + | 0.175998i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.00285 | −0.363895 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 11.1072i | − | 1.00150i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.4226i | 1.72347i | 0.507356 | + | 0.861737i | \(0.330623\pi\) | ||||
−0.507356 | + | 0.861737i | \(0.669377\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 11.2593i | 0.991328i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.52170 | −0.395063 | −0.197531 | − | 0.980297i | \(-0.563292\pi\) | ||||
−0.197531 | + | 0.980297i | \(0.563292\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.13058 | + | 13.9120i | −0.184744 | + | 1.20632i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000i | 0.0860663i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.7163 | 1.08643 | 0.543215 | − | 0.839594i | \(-0.317207\pi\) | ||||
0.543215 | + | 0.839594i | \(0.317207\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.52657 | 0.214301 | 0.107150 | − | 0.994243i | \(-0.465827\pi\) | ||||
0.107150 | + | 0.994243i | \(0.465827\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.11469 | −0.599165 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.34881 | −0.698162 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 1.79858i | − | 0.149364i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.67917 | + | 2.09492i | 0.550889 | + | 0.172786i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.27960 | −0.268675 | −0.134338 | − | 0.990936i | \(-0.542891\pi\) | ||||
−0.134338 | + | 0.990936i | \(0.542891\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.74673i | 0.386284i | 0.981171 | + | 0.193142i | \(0.0618677\pi\) | ||||
−0.981171 | + | 0.193142i | \(0.938132\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 4.79356i | − | 0.387536i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.221571i | 0.0177970i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 15.5590i | − | 1.24174i | −0.783912 | − | 0.620872i | \(-0.786779\pi\) | ||
0.783912 | − | 0.620872i | \(-0.213221\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.97985 | 0.157012 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −14.8525 | − | 2.27462i | −1.17054 | − | 0.179265i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 21.4106i | 1.67701i | 0.544894 | + | 0.838505i | \(0.316570\pi\) | ||||
−0.544894 | + | 0.838505i | \(0.683430\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.87335 | −0.301540 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.86529 | 0.531252 | 0.265626 | − | 0.964076i | \(-0.414421\pi\) | ||||
0.265626 | + | 0.964076i | \(0.414421\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.35404 | 0.642619 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.31954 | 0.406795 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.9225i | 1.05851i | 0.848463 | + | 0.529255i | \(0.177529\pi\) | ||||
−0.848463 | + | 0.529255i | \(0.822471\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.400519 | − | 2.61526i | 0.0302764 | − | 0.197695i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.27574 | 0.396549 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.99942i | 0.523162i | 0.965182 | + | 0.261581i | \(0.0842438\pi\) | ||||
−0.965182 | + | 0.261581i | \(0.915756\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 1.97879i | − | 0.147082i | −0.997292 | − | 0.0735412i | \(-0.976570\pi\) | ||
0.997292 | − | 0.0735412i | \(-0.0234300\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.99669i | 0.591132i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.50006i | 0.551415i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 18.5671 | 1.35776 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.400519 | − | 2.61526i | 0.0291335 | − | 0.190232i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.5288i | 1.48541i | 0.669616 | + | 0.742707i | \(0.266459\pi\) | ||||
−0.669616 | + | 0.742707i | \(0.733541\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.1050 | −0.943321 | −0.471661 | − | 0.881780i | \(-0.656345\pi\) | ||||
−0.471661 | + | 0.881780i | \(0.656345\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.15545 | −0.154355 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.78520 | 0.483426 | 0.241713 | − | 0.970348i | \(-0.422291\pi\) | ||||
0.241713 | + | 0.970348i | \(0.422291\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.62783 | 0.469835 | 0.234917 | − | 0.972015i | \(-0.424518\pi\) | ||||
0.234917 | + | 0.972015i | \(0.424518\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 3.00246i | − | 0.211777i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.720364 | + | 4.70375i | −0.0505597 | + | 0.330138i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.1072 | 0.775761 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.67917i | 0.394730i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 20.6044i | 1.42524i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 10.7000i | − | 0.736618i | −0.929703 | − | 0.368309i | \(-0.879937\pi\) | ||
0.929703 | − | 0.368309i | \(-0.120063\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 6.50426i | − | 0.445664i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.2593 | −0.767879 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.0887435 | − | 0.579467i | 0.00602430 | − | 0.0393368i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.16961i | 0.214182i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.3323 | 0.695023 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −26.0191 | −1.74236 | −0.871182 | − | 0.490960i | \(-0.836646\pi\) | ||||
−0.871182 | + | 0.490960i | \(0.836646\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.0050 | −0.863173 | −0.431586 | − | 0.902072i | \(-0.642046\pi\) | ||||
−0.431586 | + | 0.902072i | \(0.642046\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.0268i | 1.38949i | 0.719255 | + | 0.694746i | \(0.244483\pi\) | ||||
−0.719255 | + | 0.694746i | \(0.755517\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 10.1298 | + | 1.55135i | 0.666493 | + | 0.102071i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −22.2270 | −1.45614 | −0.728070 | − | 0.685503i | \(-0.759583\pi\) | ||||
−0.728070 | + | 0.685503i | \(0.759583\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 7.11469i | − | 0.464111i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 7.99118i | − | 0.519083i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.6516i | 0.883048i | 0.897249 | + | 0.441524i | \(0.145562\pi\) | ||||
−0.897249 | + | 0.441524i | \(0.854438\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 18.7440i | − | 1.20741i | −0.797209 | − | 0.603704i | \(-0.793691\pi\) | ||
0.797209 | − | 0.603704i | \(-0.206309\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.09492 | + | 6.67917i | −0.133840 | + | 0.426716i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.4660i | 0.729564i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10.4453 | 0.661946 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.1144 | −0.827773 | −0.413887 | − | 0.910328i | \(-0.635829\pi\) | ||||
−0.413887 | + | 0.910328i | \(0.635829\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −21.9974 | −1.38297 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.79356 | 0.300184 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.4950i | 0.654663i | 0.944910 | + | 0.327331i | \(0.106149\pi\) | ||||
−0.944910 | + | 0.327331i | \(0.893851\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.00392 | − | 19.6146i | 0.186654 | − | 1.21879i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.79858 | 0.111329 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 27.9160i | 1.72138i | 0.509134 | + | 0.860688i | \(0.329966\pi\) | ||||
−0.509134 | + | 0.860688i | \(0.670034\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.97985i | 0.121621i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 11.4560i | − | 0.701097i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 1.37287i | − | 0.0837051i | −0.999124 | − | 0.0418525i | \(-0.986674\pi\) | ||
0.999124 | − | 0.0418525i | \(-0.0133260\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.00052 | −0.121523 | −0.0607616 | − | 0.998152i | \(-0.519353\pi\) | ||||
−0.0607616 | + | 0.998152i | \(0.519353\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.63706 | + | 0.863298i | 0.341170 | + | 0.0522492i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 3.87335i | − | 0.233572i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.87788 | −0.232999 | −0.116500 | − | 0.993191i | \(-0.537167\pi\) | ||||
−0.116500 | + | 0.993191i | \(0.537167\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.221571 | −0.0132651 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.4583 | −0.922167 | −0.461083 | − | 0.887357i | \(-0.652539\pi\) | ||||
−0.461083 | + | 0.887357i | \(0.652539\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.1130 | 1.31448 | 0.657240 | − | 0.753681i | \(-0.271724\pi\) | ||||
0.657240 | + | 0.753681i | \(0.271724\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.31954i | 0.315102i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −29.0482 | − | 4.44865i | −1.71466 | − | 0.262595i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.97818 | −0.351658 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 0.716023i | − | 0.0419740i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 24.2993i | − | 1.41958i | −0.704412 | − | 0.709792i | \(-0.748789\pi\) | ||
0.704412 | − | 0.709792i | \(-0.251211\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.27574i | 0.307165i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 3.87335i | − | 0.224755i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12.2412 | −0.707924 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 29.4460 | + | 4.50957i | 1.69724 | + | 0.259927i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 5.18641i | − | 0.297951i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.99669 | −0.457889 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −29.4220 | −1.67920 | −0.839602 | − | 0.543202i | \(-0.817212\pi\) | ||||
−0.839602 | + | 0.543202i | \(0.817212\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.19896 | 0.181983 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −26.2914 | −1.49085 | −0.745424 | − | 0.666590i | \(-0.767753\pi\) | ||||
−0.745424 | + | 0.666590i | \(0.767753\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 31.6179i | − | 1.78715i | −0.448914 | − | 0.893575i | \(-0.648189\pi\) | ||
0.448914 | − | 0.893575i | \(-0.351811\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.61526 | + | 0.400519i | 0.147353 | + | 0.0225667i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 26.4489 | 1.48552 | 0.742760 | − | 0.669558i | \(-0.233516\pi\) | ||||
0.742760 | + | 0.669558i | \(0.233516\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.96652i | 0.390050i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.49311i | 0.474039i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 25.4995i | − | 1.41883i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 2.15545i | − | 0.119563i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.39403 | 0.464191 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.84957 | + | 18.6068i | −0.157102 | + | 1.02582i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.39519i | 0.461441i | 0.973020 | + | 0.230721i | \(0.0741084\pi\) | ||||
−0.973020 | + | 0.230721i | \(0.925892\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.50006 | −0.411001 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.00246 | 0.164042 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.9891 | −1.30677 | −0.653384 | − | 0.757027i | \(-0.726651\pi\) | ||||
−0.653384 | + | 0.757027i | \(0.726651\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10.0556 | 0.546146 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 0.858224i | − | 0.0464754i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.15390 | − | 16.6287i | 0.440269 | − | 0.897866i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.67917 | −0.305756 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.0986i | 0.595803i | 0.954597 | + | 0.297901i | \(0.0962867\pi\) | ||||
−0.954597 | + | 0.297901i | \(0.903713\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.0912i | 0.540168i | 0.962837 | + | 0.270084i | \(0.0870515\pi\) | ||||
−0.962837 | + | 0.270084i | \(0.912949\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 2.15545i | − | 0.115049i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 11.3661i | − | 0.604959i | −0.953156 | − | 0.302479i | \(-0.902186\pi\) | ||
0.953156 | − | 0.302479i | \(-0.0978143\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.50426 | 0.345210 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −12.5364 | − | 1.91991i | −0.663496 | − | 0.101612i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 32.1591i | 1.69729i | 0.528960 | + | 0.848647i | \(0.322582\pi\) | ||||
−0.528960 | + | 0.848647i | \(0.677418\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.29750 | 0.489342 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.00285 | 0.210095 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.16961 | −0.165905 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.4005 | 0.856101 | 0.428050 | − | 0.903755i | \(-0.359201\pi\) | ||||
0.428050 | + | 0.903755i | \(0.359201\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 11.1072i | 0.578218i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.792968 | − | 5.17783i | 0.0411689 | − | 0.268819i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.52954 | 0.493421 | 0.246710 | − | 0.969089i | \(-0.420650\pi\) | ||||
0.246710 | + | 0.969089i | \(0.420650\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 1.00000i | − | 0.0516398i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.87674i | 0.199662i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 15.1323i | − | 0.777296i | −0.921386 | − | 0.388648i | \(-0.872942\pi\) | ||
0.921386 | − | 0.388648i | \(-0.127058\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 19.4226i | − | 0.995048i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −17.1555 | −0.876607 | −0.438304 | − | 0.898827i | \(-0.644420\pi\) | ||||
−0.438304 | + | 0.898827i | \(0.644420\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.55135 | + | 10.1298i | −0.0790642 | + | 0.516263i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 11.2593i | − | 0.572343i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −23.7357 | −1.20345 | −0.601724 | − | 0.798704i | \(-0.705519\pi\) | ||||
−0.601724 | + | 0.798704i | \(0.705519\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 27.2234 | 1.37675 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.52170 | 0.228090 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.99118 | 0.402080 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.2336i | 0.764554i | 0.924048 | + | 0.382277i | \(0.124860\pi\) | ||||
−0.924048 | + | 0.382277i | \(0.875140\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.13058 | − | 13.9120i | 0.106662 | − | 0.696470i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 30.1291 | 1.50458 | 0.752288 | − | 0.658834i | \(-0.228950\pi\) | ||||
0.752288 | + | 0.658834i | \(0.228950\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 0.477586i | − | 0.0237902i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 1.00000i | − | 0.0496904i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 29.0504i | − | 1.43997i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.56863i | 0.473138i | 0.971615 | + | 0.236569i | \(0.0760230\pi\) | ||||
−0.971615 | + | 0.236569i | \(0.923977\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.7163 | −0.627250 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.11303 | − | 13.7974i | 0.103976 | − | 0.678927i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.4453i | 0.512741i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.52657 | −0.123727 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 22.4745 | 1.09795 | 0.548975 | − | 0.835839i | \(-0.315018\pi\) | ||||
0.548975 | + | 0.835839i | \(0.315018\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.5415 | −0.708710 | −0.354355 | − | 0.935111i | \(-0.615299\pi\) | ||||
−0.354355 | + | 0.935111i | \(0.615299\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.11469 | 0.345928 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.79356i | 0.232522i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 20.9134 | + | 3.20283i | 1.01207 | + | 0.154996i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.34881 | 0.403084 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 0.493919i | − | 0.0237912i | −0.999929 | − | 0.0118956i | \(-0.996213\pi\) | ||
0.999929 | − | 0.0118956i | \(-0.00378658\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 38.4919i | − | 1.84980i | −0.380204 | − | 0.924902i | \(-0.624146\pi\) | ||
0.380204 | − | 0.924902i | \(-0.375854\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.79858i | 0.0862352i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 30.2106i | 1.44517i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 38.0565 | 1.81634 | 0.908170 | − | 0.418602i | \(-0.137480\pi\) | ||||
0.908170 | + | 0.418602i | \(0.137480\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.67917 | − | 2.09492i | −0.318056 | − | 0.0997582i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 29.2504i | − | 1.38973i | −0.719141 | − | 0.694864i | \(-0.755465\pi\) | ||
0.719141 | − | 0.694864i | \(-0.244535\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.4560 | 0.543067 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.27960 | 0.155120 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.6966 | 1.11831 | 0.559155 | − | 0.829063i | \(-0.311126\pi\) | ||||
0.559155 | + | 0.829063i | \(0.311126\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −43.0221 | −2.02583 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 4.74673i | − | 0.223021i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.863298 | + | 5.63706i | −0.0404720 | + | 0.264269i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 38.9971 | 1.82421 | 0.912103 | − | 0.409961i | \(-0.134458\pi\) | ||||
0.912103 | + | 0.409961i | \(0.134458\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.79356i | 0.223744i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.4289i | 0.718595i | 0.933223 | + | 0.359298i | \(0.116984\pi\) | ||||
−0.933223 | + | 0.359298i | \(0.883016\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 15.5650i | − | 0.723365i | −0.932301 | − | 0.361682i | \(-0.882202\pi\) | ||
0.932301 | − | 0.361682i | \(-0.117798\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 0.221571i | − | 0.0102751i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −34.9489 | −1.61724 | −0.808621 | − | 0.588330i | \(-0.799786\pi\) | ||||
−0.808621 | + | 0.588330i | \(0.799786\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.85222 | − | 1.20254i | −0.362582 | − | 0.0555283i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 15.5590i | 0.716921i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 43.6113 | 2.00525 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.31954 | −0.244077 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.97985 | −0.0906512 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.0326 | −0.549782 | −0.274891 | − | 0.961475i | \(-0.588642\pi\) | ||||
−0.274891 | + | 0.961475i | \(0.588642\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 16.1660i | − | 0.737106i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 14.8525 | + | 2.27462i | 0.675812 | + | 0.103499i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.716023 | 0.0325130 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 33.1682i | 1.50299i | 0.659736 | + | 0.751497i | \(0.270668\pi\) | ||||
−0.659736 | + | 0.751497i | \(0.729332\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 21.4106i | − | 0.968222i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.74110i | 0.168834i | 0.996431 | + | 0.0844169i | \(0.0269027\pi\) | ||||
−0.996431 | + | 0.0844169i | \(0.973097\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 8.62158i | − | 0.388296i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.87335 | 0.174094 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −17.0103 | − | 2.60508i | −0.763017 | − | 0.116854i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 28.7989i | − | 1.28921i | −0.764514 | − | 0.644607i | \(-0.777021\pi\) | ||
0.764514 | − | 0.644607i | \(-0.222979\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.86529 | −0.306719 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −30.5630 | −1.36274 | −0.681369 | − | 0.731940i | \(-0.738615\pi\) | ||||
−0.681369 | + | 0.731940i | \(0.738615\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.18641 | 0.230792 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8.35404 | −0.371016 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 24.5626i | 1.08872i | 0.838852 | + | 0.544359i | \(0.183227\pi\) | ||||
−0.838852 | + | 0.544359i | \(0.816773\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.28934 | + | 1.26949i | 0.366699 | + | 0.0561588i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.31954 | −0.234863 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.19896i | 0.140963i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 27.5577i | 1.21199i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 13.9225i | − | 0.611131i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 32.4634i | − | 1.42225i | −0.703066 | − | 0.711125i | \(-0.748186\pi\) | ||
0.703066 | − | 0.711125i | \(-0.251814\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −33.8522 | −1.48026 | −0.740128 | − | 0.672466i | \(-0.765235\pi\) | ||||
−0.740128 | + | 0.672466i | \(0.765235\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.400519 | + | 2.61526i | −0.0174801 | + | 0.114139i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.06211i | 0.0462664i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.25296 | −0.402303 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.27574 | −0.228948 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −23.9410 | −1.03700 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.49311 | −0.367189 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 6.99942i | − | 0.302047i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8.11437 | − | 25.8708i | 0.349511 | − | 1.11433i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 32.2557 | 1.38678 | 0.693390 | − | 0.720563i | \(-0.256116\pi\) | ||||
0.693390 | + | 0.720563i | \(0.256116\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.97879i | 0.0849180i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.39403i | 0.359561i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.1007i | 0.431877i | 0.976407 | + | 0.215938i | \(0.0692810\pi\) | ||||
−0.976407 | + | 0.215938i | \(0.930719\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 7.99669i | − | 0.341290i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.56760 | 0.407593 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −20.8990 | − | 3.20062i | −0.888716 | − | 0.136104i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 7.50006i | − | 0.318360i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −30.5437 | −1.29418 | −0.647089 | − | 0.762414i | \(-0.724014\pi\) | ||||
−0.647089 | + | 0.762414i | \(0.724014\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 24.2689 | 1.02646 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −18.5671 | −0.783905 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.16461 | −0.0490825 | −0.0245413 | − | 0.999699i | \(-0.507813\pi\) | ||||
−0.0245413 | + | 0.999699i | \(0.507813\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.0556i | 0.423043i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.400519 | + | 2.61526i | −0.0168202 | + | 0.109831i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 33.8001 | 1.41697 | 0.708487 | − | 0.705724i | \(-0.249378\pi\) | ||||
0.708487 | + | 0.705724i | \(0.249378\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 20.7283i | − | 0.867452i | −0.901045 | − | 0.433726i | \(-0.857199\pi\) | ||
0.901045 | − | 0.433726i | \(-0.142801\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 20.5288i | − | 0.857604i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 5.67917i | − | 0.236838i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 14.3167i | − | 0.596011i | −0.954564 | − | 0.298005i | \(-0.903679\pi\) | ||
0.954564 | − | 0.298005i | \(-0.0963213\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 13.1050 | 0.544627 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.18356 | − | 27.3173i | 0.173563 | − | 1.13331i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 7.66866i | − | 0.317604i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.15545 | 0.0891168 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.4316 | 0.430558 | 0.215279 | − | 0.976553i | \(-0.430934\pi\) | ||||
0.215279 | + | 0.976553i | \(0.430934\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.17866 | −0.0485657 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.78520 | −0.279106 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 42.2732i | 1.73595i | 0.496606 | + | 0.867976i | \(0.334579\pi\) | ||||
−0.496606 | + | 0.867976i | \(0.665421\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.91991 | − | 12.5364i | 0.0787087 | − | 0.513942i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.62783 | −0.271259 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 39.9371i | − | 1.63179i | −0.578202 | − | 0.815894i | \(-0.696245\pi\) | ||
0.578202 | − | 0.815894i | \(-0.303755\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 27.0538i | − | 1.10355i | −0.833994 | − | 0.551773i | \(-0.813951\pi\) | ||
0.833994 | − | 0.551773i | \(-0.186049\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.00246i | 0.122270i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.00285i | 0.162739i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.6004 | 0.754968 | 0.377484 | − | 0.926016i | \(-0.376789\pi\) | ||||
0.377484 | + | 0.926016i | \(0.376789\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.720364 | − | 4.70375i | 0.0291906 | − | 0.190605i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.3354i | 0.620402i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.72099 | −0.109900 | −0.0549499 | − | 0.998489i | \(-0.517500\pi\) | ||||
−0.0549499 | + | 0.998489i | \(0.517500\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −11.1072 | −0.447886 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.75305 | 0.392643 | 0.196321 | − | 0.980540i | \(-0.437100\pi\) | ||||
0.196321 | + | 0.980540i | \(0.437100\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 46.0457 | 1.85073 | 0.925367 | − | 0.379073i | \(-0.123757\pi\) | ||||
0.925367 | + | 0.379073i | \(0.123757\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 5.67917i | − | 0.227897i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −29.9605 | − | 4.58835i | −1.20034 | − | 0.183828i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 20.6044i | − | 0.822862i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 35.9520i | 1.43350i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 13.4133i | − | 0.533973i | −0.963700 | − | 0.266987i | \(-0.913972\pi\) | ||
0.963700 | − | 0.266987i | \(-0.0860280\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10.7000i | 0.425287i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 19.4226 | 0.770761 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.51550 | − | 14.3966i | 0.178911 | − | 0.570414i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.50426i | 0.257304i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.6816 | −0.816876 | −0.408438 | − | 0.912786i | \(-0.633926\pi\) | ||||
−0.408438 | + | 0.912786i | \(0.633926\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.99396 | 0.394123 | 0.197062 | − | 0.980391i | \(-0.436860\pi\) | ||||
0.197062 | + | 0.980391i | \(0.436860\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 11.2593 | 0.443335 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −14.4620 | −0.568558 | −0.284279 | − | 0.958742i | \(-0.591754\pi\) | ||||
−0.284279 | + | 0.958742i | \(0.591754\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 20.4348i | − | 0.802136i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.0887435 | + | 0.579467i | −0.00347813 | + | 0.0227111i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 43.4639 | 1.70087 | 0.850437 | − | 0.526076i | \(-0.176337\pi\) | ||||
0.850437 | + | 0.526076i | \(0.176337\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.52170i | 0.176677i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 3.16961i | − | 0.123658i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 43.7090i | − | 1.70266i | −0.524631 | − | 0.851330i | \(-0.675797\pi\) | ||
0.524631 | − | 0.851330i | \(-0.324203\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 32.8390i | 1.27729i | 0.769503 | + | 0.638644i | \(0.220504\pi\) | ||||
−0.769503 | + | 0.638644i | \(0.779496\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −10.3323 | −0.401272 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 13.9120 | + | 2.13058i | 0.539483 | + | 0.0826202i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.2144i | 0.395504i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 26.0191 | 1.00595 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 30.9740 | 1.19574 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.6011 | 0.755568 | 0.377784 | − | 0.925894i | \(-0.376686\pi\) | ||||
0.377784 | + | 0.925894i | \(0.376686\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 30.8816i | − | 1.18688i | −0.804880 | − | 0.593438i | \(-0.797770\pi\) | ||
0.804880 | − | 0.593438i | \(-0.202230\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.87259 | − | 0.286781i | −0.0718633 | − | 0.0110056i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.0050 | 0.498353 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13.7409i | 0.525781i | 0.964826 | + | 0.262891i | \(0.0846758\pi\) | ||||
−0.964826 | + | 0.262891i | \(0.915324\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 12.7163i | − | 0.485866i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 21.0268i | − | 0.802224i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 4.26747i | − | 0.162578i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 47.6561 | 1.81292 | 0.906462 | − | 0.422288i | \(-0.138773\pi\) | ||||
0.906462 | + | 0.422288i | \(0.138773\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −10.1298 | − | 1.55135i | −0.384800 | − | 0.0589309i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 2.52657i | − | 0.0958383i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 53.2430 | 2.01672 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 22.2270 | 0.840703 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.7523 | 0.406109 | 0.203055 | − | 0.979167i | \(-0.434913\pi\) | ||||
0.203055 | + | 0.979167i | \(0.434913\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −39.8969 | −1.50474 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.11469i | 0.267955i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −13.5638 | − | 2.07725i | −0.510119 | − | 0.0781232i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.9409 | 0.711340 | 0.355670 | − | 0.934612i | \(-0.384253\pi\) | ||||
0.355670 | + | 0.934612i | \(0.384253\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.99118i | 0.299693i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1.25834i | − | 0.0471252i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.34881i | 0.312228i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 13.6516i | − | 0.509828i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 38.4552 | 1.43414 | 0.717068 | − | 0.697003i | \(-0.245484\pi\) | ||||
0.717068 | + | 0.697003i | \(0.245484\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.28125 | − | 8.36612i | 0.0477161 | − | 0.311570i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 18.7440i | 0.697097i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.79858 | −0.0667975 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.37304 | 0.199275 | 0.0996375 | − | 0.995024i | \(-0.468232\pi\) | ||||
0.0996375 | + | 0.995024i | \(0.468232\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −53.9722 | −1.99623 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 19.9952i | − | 0.738540i | −0.929322 | − | 0.369270i | \(-0.879608\pi\) | ||
0.929322 | − | 0.369270i | \(-0.120392\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.09492 | − | 6.67917i | 0.0772724 | − | 0.246365i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −11.6296 | −0.428381 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 21.4299i | 0.788312i | 0.919044 | + | 0.394156i | \(0.128963\pi\) | ||||
−0.919044 | + | 0.394156i | \(0.871037\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 11.4660i | − | 0.421214i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 1.35726i | − | 0.0497930i | −0.999690 | − | 0.0248965i | \(-0.992074\pi\) | ||
0.999690 | − | 0.0248965i | \(-0.00792563\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.27960i | 0.120155i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −10.4453 | −0.382175 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 22.2117 | + | 3.40165i | 0.811598 | + | 0.124294i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 23.5955i | − | 0.861012i | −0.902588 | − | 0.430506i | \(-0.858335\pi\) | ||
0.902588 | − | 0.430506i | \(-0.141665\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 13.1144 | 0.477915 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.74673 | 0.172751 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.2907 | 0.810170 | 0.405085 | − | 0.914279i | \(-0.367242\pi\) | ||||
0.405085 | + | 0.914279i | \(0.367242\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 21.9974 | 0.798456 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 27.8234i | 1.00860i | 0.863530 | + | 0.504298i | \(0.168249\pi\) | ||||
−0.863530 | + | 0.504298i | \(0.831751\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.36197 | − | 21.9526i | 0.121711 | − | 0.794736i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.79356 | −0.173311 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 11.3716i | − | 0.410604i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.5470i | 0.632760i | 0.948633 | + | 0.316380i | \(0.102467\pi\) | ||||
−0.948633 | + | 0.316380i | \(0.897533\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 10.4950i | − | 0.377970i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 27.3646i | − | 0.984235i | −0.870529 | − | 0.492118i | \(-0.836223\pi\) | ||
0.870529 | − | 0.492118i | \(-0.163777\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.221571 | 0.00795908 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.00392 | + | 19.6146i | −0.107765 | + | 0.703670i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 59.0852i | 2.11695i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −25.1933 | −0.901486 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.79858 | −0.0642759 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15.5590 | −0.555325 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −37.1840 | −1.32547 | −0.662733 | − | 0.748855i | \(-0.730604\pi\) | ||||
−0.662733 | + | 0.748855i | \(0.730604\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 27.9160i | − | 0.993836i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.02746 | − | 26.2980i | 0.143200 | − | 0.935050i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17.2364 | 0.612084 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 1.97985i | − | 0.0702181i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 39.4892i | 1.39878i | 0.714741 | + | 0.699389i | \(0.246544\pi\) | ||||
−0.714741 | + | 0.699389i | \(0.753456\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 34.1047i | − | 1.20654i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11.4560i | 0.404779i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 12.2770 | 0.433246 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.27462 | + | 14.8525i | −0.0801697 | + | 0.523482i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.37287i | 0.0483272i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 44.5833 | 1.56746 | 0.783732 | − | 0.621099i | \(-0.213314\pi\) | ||||
0.783732 | + | 0.621099i | \(0.213314\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −42.6704 | −1.49836 | −0.749181 | − | 0.662365i | \(-0.769553\pi\) | ||||
−0.749181 | + | 0.662365i | \(0.769553\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.00052 | 0.0701614 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 21.4106 | 0.749982 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 59.8944i | − | 2.09544i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.63706 | − | 0.863298i | −0.196975 | − | 0.0301661i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.16342 | 0.0755039 | 0.0377519 | − | 0.999287i | \(-0.487980\pi\) | ||||
0.0377519 | + | 0.999287i | \(0.487980\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.8339i | 0.865655i | 0.901477 | + | 0.432828i | \(0.142484\pi\) | ||||
−0.901477 | + | 0.432828i | \(0.857516\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.87335i | 0.134853i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 15.1462i | − | 0.526685i | −0.964702 | − | 0.263343i | \(-0.915175\pi\) | ||
0.964702 | − | 0.263343i | \(-0.0848250\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 38.5463i | 1.33877i | 0.742917 | + | 0.669383i | \(0.233442\pi\) | ||||
−0.742917 | + | 0.669383i | \(0.766558\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.87788 | 0.134522 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −10.0421 | + | 32.0170i | −0.347939 | + | 1.10932i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 6.86529i | − | 0.237583i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.221571 | 0.00765863 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 26.9316 | 0.929783 | 0.464892 | − | 0.885368i | \(-0.346093\pi\) | ||||
0.464892 | + | 0.885368i | \(0.346093\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.7651 | −0.888452 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 15.4583 | 0.532413 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 8.35404i | − | 0.287388i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.60322 | − | 10.4685i | 0.0550872 | − | 0.359702i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −22.1130 | −0.758915 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 42.5941i | − | 1.46011i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 28.2964i | − | 0.968852i | −0.874832 | − | 0.484426i | \(-0.839029\pi\) | ||
0.874832 | − | 0.484426i | \(-0.160971\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 5.31954i | − | 0.181924i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 44.2477i | 1.51147i | 0.654875 | + | 0.755737i | \(0.272721\pi\) | ||||
−0.654875 | + | 0.755737i | \(0.727279\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.70764 | −0.194742 | −0.0973710 | − | 0.995248i | \(-0.531043\pi\) | ||||
−0.0973710 | + | 0.995248i | \(0.531043\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 29.0482 | + | 4.44865i | 0.989962 | + | 0.151610i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 22.5353i | 0.767110i | 0.923518 | + | 0.383555i | \(0.125300\pi\) | ||||
−0.923518 | + | 0.383555i | \(0.874700\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.9225 | 0.473380 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.97818 | 0.203030 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −30.9526 | −1.05000 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.47165 | −0.219283 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.716023i | 0.0242337i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.61526 | − | 0.400519i | −0.0884119 | − | 0.0135400i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 42.9633 | 1.45077 | 0.725384 | − | 0.688344i | \(-0.241662\pi\) | ||||
0.725384 | + | 0.688344i | \(0.241662\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 24.2993i | 0.819597i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 37.3812i | 1.25940i | 0.776837 | + | 0.629702i | \(0.216823\pi\) | ||||
−0.776837 | + | 0.629702i | \(0.783177\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 22.2753i | − | 0.749624i | −0.927101 | − | 0.374812i | \(-0.877707\pi\) | ||
0.927101 | − | 0.374812i | \(-0.122293\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 5.27574i | − | 0.177342i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 10.0896 | 0.338774 | 0.169387 | − | 0.985550i | \(-0.445821\pi\) | ||||
0.169387 | + | 0.985550i | \(0.445821\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −50.7950 | − | 7.77910i | −1.70361 | − | 0.260903i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.87335i | 0.129762i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 37.8469 | 1.26650 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.99942 | 0.233965 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12.2412 | 0.408720 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.398513 | −0.0132912 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.49053i | 0.316175i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −29.4460 | − | 4.50957i | −0.979903 | − | 0.150069i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.97879 | −0.0657772 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.27869i | 0.308094i | 0.988064 | + | 0.154047i | \(0.0492307\pi\) | ||||
−0.988064 | + | 0.154047i | \(0.950769\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.18641i | 0.172022i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.0695i | 0.399880i | 0.979808 | + | 0.199940i | \(0.0640748\pi\) | ||||
−0.979808 | + | 0.199940i | \(0.935925\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 40.4585i | − | 1.33898i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7.99669 | 0.264362 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.81103 | − | 11.8254i | 0.0598054 | − | 0.390510i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 41.5233i | − | 1.36973i | −0.728672 | − | 0.684863i | \(-0.759862\pi\) | ||
0.728672 | − | 0.684863i | \(-0.240138\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 29.4220 | 0.969489 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −14.0196 | −0.461460 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.50006 | 0.246600 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.19896 | −0.105068 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 1.38568i | − | 0.0454625i | −0.999742 | − | 0.0227313i | \(-0.992764\pi\) | ||
0.999742 | − | 0.0227313i | \(-0.00723621\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −35.5301 | − | 11.1440i | −1.16445 | − | 0.365231i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 26.2914 | 0.860742 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 18.5671i | − | 0.607210i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 20.3283i | − | 0.664096i | −0.943263 | − | 0.332048i | \(-0.892260\pi\) | ||
0.943263 | − | 0.332048i | \(-0.107740\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 31.6179i | 1.03181i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 17.6899i | − | 0.576675i | −0.957529 | − | 0.288338i | \(-0.906897\pi\) | ||
0.957529 | − | 0.288338i | \(-0.0931026\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −63.0797 | −2.05416 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.61526 | − | 0.400519i | −0.0850744 | − | 0.0130289i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 39.4890i | 1.28322i | 0.767031 | + | 0.641610i | \(0.221733\pi\) | ||||
−0.767031 | + | 0.641610i | \(0.778267\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.83192 | 0.221774 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −26.4489 | −0.857666 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.25093 | 0.267274 | 0.133637 | − | 0.991030i | \(-0.457334\pi\) | ||||
0.133637 | + | 0.991030i | \(0.457334\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 20.5288 | 0.664297 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 6.96652i | − | 0.225196i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.09313 | + | 33.2565i | −0.164466 | + | 1.07391i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9509 | −0.998416 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 8.49311i | − | 0.273687i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 13.1050i | 0.421866i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 49.0779i | − | 1.57824i | −0.614241 | − | 0.789119i | \(-0.710538\pi\) | ||
0.614241 | − | 0.789119i | \(-0.289462\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 25.4995i | 0.819162i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.07094 | −0.291100 | −0.145550 | − | 0.989351i | \(-0.546495\pi\) | ||||
−0.145550 | + | 0.989351i | \(0.546495\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.01194 | + | 6.60764i | −0.0324413 | + | 0.211831i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.15545i | 0.0690296i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 19.3704 | 0.619713 | 0.309857 | − | 0.950783i | \(-0.399719\pi\) | ||||
0.309857 | + | 0.950783i | \(0.399719\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −44.3732 | −1.41817 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.39403 | −0.268001 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −31.0078 | −0.988995 | −0.494497 | − | 0.869179i | \(-0.664648\pi\) | ||||
−0.494497 | + | 0.869179i | \(0.664648\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 6.78520i | − | 0.216194i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.84957 | − | 18.6068i | 0.0907028 | − | 0.592260i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 63.9436 | 2.03329 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 27.8278i | − | 0.883981i | −0.897020 | − | 0.441990i | \(-0.854273\pi\) | ||
0.897020 | − | 0.441990i | \(-0.145727\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 8.39519i | − | 0.266413i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 6.62783i | − | 0.210116i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.73019i | 0.213147i | 0.994305 | + | 0.106574i | \(0.0339880\pi\) | ||||
−0.994305 | + | 0.106574i | \(0.966012\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.50006 | 0.237291 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3360.2.d.a.2911.4 | ✓ | 16 | |
4.3 | odd | 2 | 3360.2.d.d.2911.5 | yes | 16 | ||
7.6 | odd | 2 | 3360.2.d.d.2911.13 | yes | 16 | ||
28.27 | even | 2 | inner | 3360.2.d.a.2911.12 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3360.2.d.a.2911.4 | ✓ | 16 | 1.1 | even | 1 | trivial | |
3360.2.d.a.2911.12 | yes | 16 | 28.27 | even | 2 | inner | |
3360.2.d.d.2911.5 | yes | 16 | 4.3 | odd | 2 | ||
3360.2.d.d.2911.13 | yes | 16 | 7.6 | odd | 2 |